PAR1���>L� �q8 math0412439240616263646566676866�56�56�56�56�56�56�56�56�56�56�66�66�66�66�66�66�66�66�66�76�76�76x76x7676�76�76�76�86�86�8686�86�86�86�86�86�86�96�96�96�96�96�96�96�96�96�92�502�502�502�502�502�502�502�502�502�516�16�16�16�16�16�16�16�1:�626�26�26�26�26�26�26�26�26�36�36�36�36�36�36�36x6�56�56�56�56�56s56d56d56d56d56U56U56U56U56U56F567567 563͟-pŢ001BF$4B$5B7B8B9>10BB�12B$B�1B�1B�16BHB�1B�1B�2B�2B�2B�2B�2B�2B�2B�2B�2B�3B�3BD3B�3B�3B�3B�3B�3B�4B24B�4B�4B�4B�4B�4BD4B�4B�4B�5B�5B�5B�5B�5B�5B�5B�5B�5B�6B�6B�6B�6B�6B�6B�6B�6B�7B�7B�7B�7B�7B�7B�7B�7BD7B�7B�8B�8B�8B�8B�8B�8B�8B�8B�8B�8B�9B�9B�9B�9B�9B�9B�9B�9B�� nlin� 0o ���������a��a~ a6�~ 6�~ 6�16�16�16�~ K~ 6�~ 6�~ 6�� 6�� � 6,o 6�36x3636x36� Z� 66�6�� 6�� 6�� 6�� 66� 6�6W6,6,6,6,�_nucl-ex�,� 2��2��2��2��2��2�[2�[.� 2B�� 2$B�� 2$B�� 2$B�} .$} 2B�2BD� 26BD� 2$BV� 2$B�� .$3ű2B�� 2$BV� 2$BV3B�� 26B�� .$� 2BV� 2$BV� 2$B�� 2$B�� .$� 2BV� 2$BV� 2$BV� 2$y`�I$92~92~92F~92$y� }�92B�}�$B�}�$B�m. }�6B�}� $}�B�}�$B�}�$B�}�$Bh}� $}�Bh}�$B}�$B}�$B�}� $�.�}�$BV}�$BV}�$BV}�$B�}� $}�BV}�$BV}�$BV}�$Br�.D�.�2B��2$B��2$B��2$B��2$Br�.$�2B�2$B��2$B��2$B��.$�2B��2$B��2$B��2$B��.$�2B �2$B �2$Bh�2$Bh9B�9>h10&�i1-Z1B�1B�1B�1B�1B�1B�1B�1B�1B�1B�1B�1B�1��physics*� 2Ed2%�2Ed2%�2Ed2%�2%�. �2ER2B� �2$B���2$B���2$B���.$��2B���2$BV��2$BV��2$e2B���.$��2B���2$B�� 2$B��.$�2B~�2$B~�2$B��2$B �.$�2B��2$B��2$B��2$B��.$�2B��2$B��2$B��2$B��t.$�t2B��t2$B��2$B��t2$BD�t.$�t2B��t2$B��b2$B��b.$�>2B~�>2$B��2$B��$�2>~�2$>��2$>��2$>@�.$B�F�1B�1B�1B�1B�1B�1B�1B�1B�1B�1B�1B�1B�1B�1B�1B�1B�1B�1B�1� .zB�1B�1B�1B�1B�1\ .lB�1B�1B�1B�1B|1Bj1 .~B|1B|1Bj1BX1BX1BX1BF1BF1� .�BX1BX1BX1BX1BX1BX1BX1BX1BX1BX1BX1BX1BX,183 q-bio� :> 4: 5:6:7:8:9612::p1:p1:p206@2:�2:`2:`2>P:�2:�2:�3:`3:�3:`3:`3:`3:`4:�4:�4:�4:p4:`4:`50A uant&�"F2F3F4F5F6F7F8F9B1F�1F�1F�1F�1F�1F�1F�1F�1F�2F�2F�2F�2F�2F�2F�2F�3F�3F�3F�3F�3F�3F�3FC3F�3J�FC4F�4F�4F�4F�4F�4F�4F�4F�4F�4F�Jj5F�5F�5F�5F�5F�5F�5F�5F�5F�6F�6F�6F�6F�6F�6F�6F�6F�7F7F�7F�7F�7F�7FV7F�7F�7F�7F�8F�8F�8F�8F�8F�8F�8F�8F�8F�8F�9F�9F�9F�9F�9F�9F�9F�9F�9F�9B�10B�10B�1F�1F�1F�1F�1F�1F�1F�1F�1F�1F�1F�11B|1F 1F 1F 1F 1F 1F 1F 1F 1F 12F�F 1F 12B:1F31F312F:FF1FF1FF1FF1FF1FF1FF1FF1FF1FF1FF1FF1FF1FF1F31F31F31F31F31F31F31F31F31F31F31F31F31F31F316FaFF1F31F316B 1FF1FF1FF1FF1FF1F31F 1F 1F 1F 1F 1F 1F 1F 1F 1F 1F 1F 1F 1F 1F 1F 1F 1F 1F 1F 1F 1F 1F 1F 1F 1F 2F 20B 2F 2F 2F 2F 2F 2F 2F 2F 2F�2F�2F�2F�2F�2F�2F�221��,� 6(quant-ph0412221math-ph0412001���   �`�$�� 4��D �T`�d��t�� � �$�`� (��� ,��� 0� � 4�`� 8��<���@!�Da�H$��L4��PD!�TTa�Xd��\t��`�!�d�a�h���l���p�!�t�a�x��|����"� �b�!�$��"�4��#�D"�$�Tb�%�d��&�t��'��"�(��b�)����*����+��"�,��b�-���.����/�#�0�c�1�$��2�4��3�D#�4�Tc�5�d��6�t��7��#�8�c�9褣�:���;��#�<��c�=���>����?$�@d�A%��B 5��CE$�DUd�Ee��Fu��G �$�H$�d�I(���J,���K0�$�L4�d�M8��N<���O@%�PDe�QH%��RL5��SPE%�TTUe�UXe��V\u��W`�%�Xd�e�Yh���Zl���[p�%�\t�e�]x��^|���_�&�`�f�a�%��b�5��c�E&�d�Uf�e�e��f�u��g��&�h��f�i����j����k��&�l��f�m���n����o�'�p�g�q�%��r�5��s�E'�t�Ug�u�e��v�u��w��'�x�g�y襧�z���{��'�|��g�}S���~����(��h��&��� 6���F(�Vh�f��v�� �(�$�h�(���,���0�(�4�h�8��<���@)�Di�H&��L6��PF)�TVi�Xf��\v��`�)�d�i�h���l���p�)�t�i�x��|��矀*蠄j衈&�袌6�裐F*餔Vj饘f�馜v�駠�*ꨤ�jꩨ��ꪬ��꫰�*무�j뭸�뮼����+��k��&���6���F+���Vk���f����v�����+��k�覫������+���k��������,��l��'��� 7���G,��Wl��g���w��� �,��$�l��(����,����0�,��4�l��8���<��3����L� ����Symmetry reductions of a particular set equa!��ssociativity in twodimensional topological field theory\footnote {Journal of Physics A, to appear. Corresponding author RC. Preprint S2004/045.}>Monodromy, vanishing cycles, knots \\ and the adjoint quotient4Koszul configura�points�`projective spaces%AdapRegul%'( to Invaria� etsM��@inimum Perimeter Rectangles That Enclose\\ Congruent Non-Overlapp�Cir�Hz q0and nonlinear!�a!�iz:dynamics�sp �'P� generalized Poincar\'e-Lelong formulaVA<equenceszfilterE>charac iz�subgroup '8ompact abelian $LRecurr\Ey\ntire transcendental funM�Lwith simple post sin!�rA�s`On%�s)),ary measures�8%% stochastic IC model�Lhard core gas on a r%�@r treeJCrossed!TaJ�s by endomorphisms,\\vector bundles\\and\\g!� duality, II$w$-divisorial domains5%�Na?4on Vassiliev iQh%X quasiposiE�E�A{etr!�a�hM�!_qua e"� $Research s� ed!8� p FEDER?TFCT/POCTI/POSI through�nt 4MAT/55958/20046��Cen� for��!@nalysis,1�y,4D| al S s by CRUP#BO shncil�oTreate�Windsor �8No.\ B-22/04.}.)�1AlexaM p"�ńHurwitz��(s0Volume�latticO i��reflex� j ices(��owa�9 nob� coh:�s�{Equi!|iITof&� Hin $\mathbb{R}^4$}tm New����|&Q!qSwa tai� nd Godr� (Cus� Gauss))d4Global Theorem� !"(Flecnodal C �Er cyclic .�stable� inuous� ce  �t*�$menagerie)�� RackI�Qua 2Slf-Organ�h Forest-Fi� ��CA ABTimeG>#� {BRUNNIAN LOCAL MOVES OF KNOTS AND VASSILIEV INVARIANTS}]FK,%\normalsize:c!� $n$-��  Brun links upa�$$C_n$-move� � %{� A> !�i� BLimiti��reXvely h� bo!��s, I:!�0 basic tools.As,The asymptot� (of Wilkinso�7 shift ite�uonAsExchange%�Gibbs�/M��Stirli t� gles"� vo N.S.F. Gr�U�.RE� stud�Aa� -Mumfo�r��A,��"�"p��p 4%чic.IDright-�d ��s���{ flat�XmuMve " schem��verplete�r ��G(rings II: c2�, t��!� MޡM�le&�!LADڡOn �sex�� five���0Noether--Fano2#���:�>��ter� f Cna,o�s, I:u�results;�>; AP"�Ram���E�Drinf�coarseuli�~%!s )���a��z�@� &1._ \\�sevI��mu4%���. II>�anaKvex H�#�*$Least Area�ks�nn��Extreme � Y ��0um Run Length�I�T�� Grid{ph�elas Brai�Pa^6( MultiAOate*W &6� >bSZ��og ic>� a�,genus zero\\�W�X"�%�-blownU ��$h\LARGE� C6� a  ly�r"CA=Q@Landau-Lifshitz-G&"�in \R{2}B\up��ase{Com��! topS�@al!����� e�}Z� tum��jugacyi��,f�matrix�Ks\f4{ Thisae�i� a�&�by� Emmyq� R  Institute��*I,5 Minerva Fs�a^Germany # Excewcy�"� !�ore�iMethodW!i��� ic����"`%Israel S��c�un ��� � RFBR�Dno. 03-01-00593. }��Mo calc�EDthr "�$Calabi-Yau* �a ( $q$-analog�Racah2��,� $ $SU_q(2)$9� \noi�6�L MSC numbers: 33D80,<45 \hfill arXiv:,.QA/0412540}� �> loAu*y�J�ZD- V nco��f1� s, Nano-S$ )wQ��j nera�baZson�s@An une�E�� ergen"f 7�E��C� sha� �"�asmall .I%�RaZA�rix�W \\EM Lack�P�Hin $C^*_\red(\F_2)$= How A� mi� to $\b�X$? ---�frak{d}$ '| just on�(ot�Branc\rul��4Kostka-FoulkesB;$q$-m�g��� � ����a *J$s $B_{n},C$ A�$D � � ic �us�top�m�equ��nt )�6�y�T�yT%�su� !�)��inserab!�a! tra-�8((Baire-one)" � ariX l� on fs��� 's First�S�!�� �@!3f�DeaH�s1�veO maE�at CEOL,�,�E�ConI�cO16FsAQ Thre�&"pr���a&�a� n Sobolev�s�%d/ O inA� +0ors between C"� !mCom�%�Coa %"�%�w(H4): 16W30, 16D9@8A40 \newline Key:F( ], L�sly!w�M� `>�=M�PrE�0 C" �&0A�&�!��S�l�xn�9�pI "FlpA��`A#ty"�xElectgn��S�!o� mov�half-�E" � conn�M�um holo���8Goldman bracketAc��Y s enume[�#�Xic es��erfU�$of Entropy>�oA�s"? dege�� Garn| �!}N coal�ce"� esA�E�"� T,S.M. Kozlov_!� VERY BRIEF NOTE ON SOME COMMUTATIVE ALGEBRAIC PROPERTI��A DIRAC-FUETER MODIFIED EQUATION.c���of�"e� net-��super&ls�"�g6Ok �2"Non LN$Eigen� eAQ�gYE.� Q -in-B=ttoC >(ed Dirac-Fo��e�U�;{esI�#�$ru�adJ#�Luq (begin{flush�\} { KYUSHU-HET-76 } \end2#a{2cm}�&0�A mulaQe� cau� s��"�A�uc@!�am$$\eta-\xi$�#)!�its PhysE� Sign��nceAJa�L$c$-N, A�� ��Bos�  Hamilto�s% Colli��%�&&��3-Vortex1�a�:� trib� �8 Zero�qm� Para&p2���he Unit �&� Mass Rea�&\\ Non-�Q "� ���$�wSp�\han$a�A tub�9��Ko nowflake�P, Aa:�com]��s. � ,PhT-T04/158s� op � �\\u\\ E�A o�!�(rm{p}$-Form�m�~sm�n)�cI6aQs\t3�(LE$(\kappa,U&\rho\,) Con�� l Fi��y�T~or���1uI� pAT�" {On����t"�s� simiM�eEZ�( waveu� - as�Tudy}�" "f0LECTURES \spc�8ELLIPTIC  FUNC� %�&MODULAR FORM !IN CONAL FIELD THEORY}A�Gr8 =tE"M�{bed���[ urba!8e ��tlD�Xs|%�,�x,l 1D Schr\"o�er9!a!� exactly!Vv0F \"#l#m\�wstrbev �$tE)al��rJiY�me�ic�����Boltzm"aseNLow Dens�x�ra�6�<�ATurbul <��oi�� �XJmplitud=pha#in :@a�Lax pair� a�A.�Ladik-� A��.�-G~' c_+�TNARROW ESCAPE, PART I��n �$V#CFT���ځ�  Z�$ary&Talk JC,d at ``Rigor� 1�.=- '', �osium! honor!-J. Bros,��t July� 4.})�6�[r!��ua� disk�V-I: RieE "� ��s`domainsrT�{.>LULB/229/CQ/04/5}\\ %�|�  oscill��� nonzero m:-alcertainx.! a}4eb-ThirP I>� Higher Ors&Dif&5�s�a]�eds atm��i�.�Z � �m� � ls!��$in moQaAa��`al��"*L$Ext�,d�U� �pa' publ�&inA�.T,. 47, 042904� 6)}��i left{{P?a�`. Rev. Lett. {94}, 080402C5)}\\}}"0 %�� vae�A�Bose-Ei) ens�%Esn0breaking�8�# Levef*r���`--MMo� ��\umMa� !�Erg�*��;baker'sU&� 7-�&"qu1� Kill} � � �|o a)nCimprov�-er� ve m�&� Q��� �fc-Mu_r�culusPseudo� "�� a&�n ultr1H� !.�letG\��gy-I�um ��ѱmixa� -spi�{��s[)� Painlev\'��aiDA'(\PVI $\tau$*s+givenA� $U(N�?ge�Q Poin=e �+m�!Z Gree� kernel\a �媡�� �� � Sto�i�a?a�h%.con#� d��)I��9e3� , � c)A�4a�� 0r��2� {\-ricAof Caon � k�|at �.dr%1by E-"Aal couplA�$rice-temporin�.ly ^0i��fl� e�s.�H�)�|!4e��*J�Eea��cs|$L_p$=�of�H �&IUV�I7zB��-��v.&� + � L dx3`he�aCo� �gi KRevisi�Cliff`� Ri�\\ Weyl� cl_{3,0�0,3 �"� |#�u/"� ��?�� 5�i7$�)%���ӡ^!�ta��c'��Q�~_s T�&a�\\�� S40 P"� �'� �e Energ�he2u Fermi Ga�W"�0I= 3 -per�0I�-gap prc���=pzlձG��� � f��r�8� k4=G!;�t�Wng Whitt��dB�&%sN� on-� �� �<, Bailey's LemmaC $N=1,2$ SY0Q����)�T�%42 {THE RMODYNAMI�ESSURE\\S'�4LUTE FERMI GAS.0Fortieth Anni����(.�6*�(\\%KI@i�Si�5�]ob!wfe�1��� +��* 'S&�5Chemi��Rea % in Micro-�P!���bn��(n]g!�� Newt�%ols2� "f # Many I�sV�.g reO9T2�!*bi1���Poi8&-!gF,��F-FR R�f^1n4f.<�CGauge $�< �I�sedum\\%x${0mm}{61mmc Scatte *Medium-R\" Mrc*sC09A�Dis�(� $) Laplacia�h �Cha��$Z� t5AZai@of Aharonov--Bohm�}xes�9nomal�2$�of low-$3�嵒e�tIt veity��Obs�!+Fs�+D jump�%��e)� �$d n*�/F�A��al"E le �����a���mF�s.\ IO" e-6.&@.%�re6%�E pre-*�6�9ansu8f�0Davey-Stewart��I� -na4A?rte6\ P7)I)`a�!� Dirichleti���C��� carX r&)UnOt}���yg;%?-1.5cm}{ %� ��3"(Be~8iq�}�> Hodograph��e�a�7assa- H'3 hierz#y�%$2+1$&�s?q�cN: vW� two2�pho�c-s^.U,�d>es�� A�a+of �7�>luxon� hann�Josepha�j ��AAD�aE# s-ba� den�& au6+^a��(parg��A = �'� geostr 9]P_� i� s8!i��t���,!�ccasca)YMin�c!Remark"� KLBaor��>���-�m8behaviq+9a! sM'shells.{�%�E�);�Hardw�Ib%Wof���e CA-B%�St�f Cipher}��A&F � >-� peak�nd pu)�s (����-x9Harry(dzn=8hn Byatt-Smith)T- Fronj Puls�"4 �iJ:a�d3c -r6?�4�L\sc[$��< H ystagmus�kloA�Geode+CyB�4on��d�?O �o&�<KdV= \"Q'AMS SuNA: 37J6�%,7J35, 70H45}��Mo!q�wF&� of s!�Z dicles1� iura\&M��Gi�a4�k��"��/ P� fA� atoms&4trJ1 c�_[f� al B]���Kor�* k-a'et8 KOSPI M�A�>%g�d=&�� iquid�lay�ilmso'ng-45mw�!�wo./}a fE# R- �c?: Short-%�.��E!sO �! ��\a�)��Thue-MoQ s�#ce"�A��$ro�Ha"f B5�.% of F-p2si� Cran5 Su#�Wav�"� �� ��6�sK6�2A s�3�du� � s�ynchroJ6�ru�na�� lexe%!ioD� wal*!r�'�#�Au+Au& �l$\sqrt{s_{_{NN}}}=200$~GeV %| �yBjorkenP%Q$to pQCD---2�techn�sp-p.n-81970'MD*z'UN�RHIC.*�9-!um: nucleonQ?ce�C.H b,.sigp.I![ -�M)$%g��in Yi��Thoughn Heavyq rk��-%Julk՗A +Io�.�)���C�6Eka-Hg)?0CERN W TargetQ�=Re�% Rel� �a2 i�&� To be6," Kern)�k.}U�\5at%w�k�de8�%!�� n�_sGP-��q�*�iG("�!#� ers $AE{$, SS �� SL}$!Kela&A� tackrel{\�+$arrow}{p}\^$R Q 0.45e2.5 GeV�CDEffec)�m�n��/ion08Wha�1� � ng A.V3? - An �QB�F.sKE�d"F�D��ons�Su�3 �mQ�usI�u9OQf0g$K(892)^*a �4�Aip%lp+p$ &4,��t!n6$ =Z&!2Q%l:� (PbWO$_4$ cr�l scint�%E�e"� a�Mv�$2\�4$�a�$$^{116}$Cd\M�-M� baryo2X^p+p�dn����!�.���i�! iD: high-\PT{} light��p�R��mO�Nri, $^2$H(p,pp)%�� kip�!2}Tat E$E!= 16 MeVSMe�RE ��Ab� e np��Q�v"4$Cross/4A�Z194S�mhDis"�-@\b�1hth ${}^{3,4}_{\,\,\Lambda}\�(rm {H} $\un0~  "3~N$ K=(e}(e,e'K^+).F5<4$p$-$sd$m �&=aeu�C-�"� A�c�-s�>]$^{20}$Oa��&� �;,$\gamma$-ray��_+pEoA�7A4(71, 172}$YbaE.���9=@S/a�N���5.Fac�!� $Q^2A�\Q�R(GeV/c)AP}8$-�$.�atCG�H� Back Rapidini"y�4&a"i�$a�+!5�AfN � �� ���K8$-$\nu$AU�� 0trapped radio ve��� HIGHLIGHT�GdRECENT RESULTS WITH CLAS\\�R���� \Sgm�=%� STAR�{<0prq�a;K$^{*�#m�!�Y}�@Se���Ast}A�1$-m��zi!J$pAH��!J!JINR LHE*� n% �� or�B�;s �T2-16519��; 2-17376.}w(``Safe'' CoC�/8 ��Bs  {30}Mg�P��Y��emV�ime" �o�����g]&�@��&,le-like frag��K C%E/AA�44o77��aA40}$Ar + 27}$A�&1MXJTitleEU(ref{label1}�ER=�in��")�op��=�b� p"�( MDe"�".!�Ch� d P-! E1U) $^{46}$TiA|}$ �{P7R .H4XXXIX ZakopaneT/oo�84s -�*ERSym-um "Atov@ iA�e|#e)�(ersD,�& Aiso�&" -z,�3�@he� b�clHe_�a-�* oryD<.�7�I�� Vio�!�Few--5�ystems�Ho���,�M abzBo no-�^ �&l�mbGno6�.! titu!a.4�h ��a&= �Ilep�!�)h� _b�8 $\Xi � s.�2 U0.�"\&DH{WM-04-123}\\[-4mm]AD{JLAB-05 306(M�*{4# S!]N"�/��A�!��Hz*��,2yhi�D9v.�&� Invi��!n'WM 26th� rs�4nU��E�/��%�ar : {L%Q� A~ ��J"�9�H^nd Ei}, ^, Italy A --24���& 4. T�cApProg.~�.~�.~� .~54. }�ML(%You can us� �ex�# B-�k "|)P"b �PrO���s BuiltaP�L-$K$ � b� e�d� 8}$W%L� a- �inuum� )1!1md>+�doC halo)�i�=^ }S_{2 �x6flu"R �Yr�:�"ac#9:W 5N�4 tunnnA6Dmplex�:mV%(a f=Fe��!�intrinT ur�0� S��05Dah-!�duJi�6�`AN�q�P&8A �2L# X�!s�]e�..^ <B0of�Qu�$-�-G� Plasmaz�"_S�R�] D*3Vib��R- o Ax:J'�<�GP.� Ae!SYrast LDſa e�#% $\;$\,��5ex���"*{\�H}{. 9@ANL-PHY-11055-TH-UY��1:% �-"(�AM��f-� G�5 <% DENSITY MATRIX"/=AL�/ORY�2DACCOUNT�/4PAIRING CORRELhBS�2�"s�!!!hGamow��/�on6S� or0hia�rVPol9*�sn�&*^4$He$(�>{e},e^\p6gp}�>�: L�%�4 $G_{Ep}/G_{Mp�Hodi��9�- ? &DE6�Shc*�=E�]�?f50ed Woods$-$Sa("�26No�:� � ���Ff6�� -6naAy6!D(Zo=M�<6�SVx7ionxM�-.in6ye�Nt"��DVCS-D:!\Deute��kEMC���'�VF S&(4$\Sigma$(1385)?��$(1405)*��\\�+$j *� pr��ZB!��r- &��Q�276;fO� I7-�%b8� �$�G$\omegi&]A�\pi N�F _ c.m.�5Z2n.^'8FZ Juelich}b 6� ��kmpCin y60Brueckner-Har_J�EEP ach\"$( %also Ce_.�1'Hal�&�, Ne�al %Labo�:�E��WAcceleNLanzhou, P.R.%Chin< d I"�Oof2�inXBeijing,:>�WrGl��+or: Zh�' yu M%temail: mazy12@iris.ciae.ac.cn}� �+ M�=Fl � s Of�mɗszRI F��, �4� @$N\sp{\ast}(1440)*� N\pi\pi$�V�<]�3n�B!�a�OLbor��!uD�A(c�be�+�SF�R#@���X� 9����e�af1 A6R�%�G8Fubini-Furlan-R&ktti S�Slet>k9ed�I�:�eH(ew"� -��~B>�! $NN$ al-�'!�\� �ha6�"# c$�R d�ii�,�-)pp$u��P.��:$%& N K\ove�ZK}N$��G�9�EIBM}�*`ST}�R�Mis!�!�ed # EEC}j$e�l� �.#*:k40-00131}.}k �NA�af� � *� �jet"�Ei|�V� �.�M`�/�9t'usIan�4yI5"po"�DE))-X�sie&�� � o:!b2 er �F�%��ar]"'�*SE�*M.��U�9&�8veA�,ite $T$ broaD0� a$\rho���% &uin) i"]�A�uspic!� on Engraf� HBT �!AS& nomyQJ����'`s &*��0 stig)��H^{9}${Be�" 1  )New� unda�al�#-&A���%�p0�s'ed*�PJet Tom�2�C�P .� ( Low-"�@o��%�iu \Vqjoa��\*#*�E s�(u^A�k0.2 \�sim x 1.5���_ s�+.wU.nP� -law�vo�7�p_{T}�o.xAH&ld%�E�2�y(/&%��R�&Ho|?aagter�W�{EPaths� �Qn�Obl�Z�Pr0e �ED$^{68}$S��$^{72}$KXNgge�_� Adia�JcB�'�Coordino ;>w� {-dN F�a3Oni� $np �T1s + �$(�s, \\TQq�g low--͙.,�kaw=2 j1?2vwidthAga!��um�2$p�$9 26� E�i�1X %��/m"�N�c"*"}�) eW)~3�=T four k�� s�a��-/&�&)�p i� .,*�Le%) notes: IV:�Balkan"�nU�� , Bodrum,$9key, Se>22-29Bd� l)lc,�"�Cto�' drop�n�=B����? scop%l:aEDM�:� r*f y De.�&�'Fireb�Y*��!�u�*���s: q&�*l,A wobb�m_5��+a�-�� � ex9A�M�QCD�!?balO&�:azimutha�g��s a�:�]�E f*�1�ngrant�q�""}6�a�; gle-�4ze-�s!l1 .<.Kf3jU���' }H$, e�lLi$�svQ5ree-cluswN%s@eGx%�pJT0*-[for C 8*+2e�L� %�i��; �(Zc�!��"�Xb,�o� �� ��M&A ;o� ve beam� PD f$ *�/sa"� }fn�au4�v) ��h�3SI$;�\�H Two-�<��on&2�I"+}of"d--2" II�>`[�Tsae��L-m�KN)��p�k!Wquadrup.� q�o�?$s?-U�:� $^{8}$Be�h ColdY�`g`P:C^eLj phen��1omn�Lto BCS�P�I of f�Fons~{EN"�%z�F��Q+�z\��=i�@Y~s�� y�!,�&U*�! }�(3�+0$n-\nuc{3}{H}.+ALnovel � ea*��a"UA,!�r�&�upa�� ��y!��xi<%p Fit� .;��ar bin"�ie">� �+aEN�_*� �� v*a hot%'eHcsma^ �RZ\iJ#��y:���@�MH.��A�how we�_oes it�, wAWE�! down?�yP?�N~ \@w] !che)�4d H t J=P�v� in Feyny[aORegUE pi�9Ka�:��pf:O#e9�Pum&� �1^$)��EL $p+A$, $d  A+A$��>PaieDe�1��%���9]$ma �5 qkM&�of��� a �^��F�9��+� !�B!��ot 8L86�[*WuFXa %�Co.csS in Z St" *�BT �fer�8y: Hist aIe"F6��Ih%�AItwo� ino 6z-�{ybFa�i-7),��|_ asiUCe�iA� jsi!�6 r|gu!L&.4"�'~ iw#�Q(]*�n6Xarton�t&�+aj�!C B��coa�nz/�$exw�tesQ#Apply�!d(Bloch-Horowmt"s6 to s�=p�&)c�*` I��r�ng Gstarsx�aԵa�)y9�2ar&i �einT 3�7BA 7$a��+��r:�G�2z/S8"�  f�,��Qi] " IR!�!;($\Delta(123�{&" G2I`)�!���>y %a�!0xt,ion� >G,�\$ce�arl� �$ N*\35mm�N"�GabsorpiVdis�_� inoo-t�U-cb ́cC��0q;1 micr�:on�Sl4D)Uopj^o�l� pixel seg!ed1��Kuar�.!�x therapy�x= assu�)� %#�#@B !�*�U�9!1pr�r�Z#"�'� ediaa�P ?bbu�W��BQ6� sy]F�MH��a^!j% t?le bunch� �?,� )�?�dKEK��&SE@T0� ��Krv��eI�� T"�K� .<B�ndi�9X !#�W-�qS-er�I���tCom*}V\Dhb, lamin laser pumQ/ce!Z�$�erz+ach W��6 Si� 2t Bath�Y�U;�u*of}%�o�iNi�bT!,d� e2I< �.� *mF ReexRJ5�Hagen--�?eu�{�@2i-& �!�^auwre�:E��aE�#'"�M�lM]eSFaR Than��t�aCF�3!� ty v�'ng 6S-7ST� #�\�c)�$achieved\\a�b2 \}/s10^{-14T�--�QA�ur7mbV'im�Qed-"det���:Cѵ�?8}"� �s��4� molec�ia�M:in���ban�*}ber� { l a*� ��OHt Pctl�k}~RS�j�GA�33 �#A �lo�=� �a"�;c.%!-$s NdI, PmI%�SmI# S. wQ.og�GtoZd&�=:�[%�le=�&evaSW�>� %�� �k�0^Van!=al$+-$+s)��Zat&-�H i�r n-in�g.�;r��4t"~s me�G3%떐�N/m ely;v�C�*AGZ\�,�>A�i D*�A�&sDWa~Y�ndn�G rage Ring� !UM< Deof�w+Jeur� C)�t%y��qn�_���p�'�Lf+ 'l Mix''Zo91_by~r�t ��N"�F�(R*x4on�[orith�XP��2#"�1*�AC�xt n&lu�:/|N5�6@K�� Niob!�) ter-C�E.?.5��!/R�Ksotope.�!�{�(B[q U.S.!ar!_�.�uX �{ E-FG�43ER41248�I�Ze�"C6(m� tely2�?2F�� &Fs)�um�Jo ityPS���)i�i�[A{�C�ir a!r"� @ nsoroNoise-I��  �&Z(*R(/Kz warm" Uni� wEWGv�), speeW/��A�acuo0 -XXX5GW �.a�im�Go�K4�S:�Olane,E `&'!� adoxE�A%�!��Lo$z�"y i�6��Pu*�`��~Jo�~of~PED, Vol.~23, No.~2, �m(2) pp.~103-).&�m�% [\url{http://dx.doi.org/10.1088/0143-0807/23/2/302}] % }]>�K"| �a�gJ s:q��WA4y, few&�L���Dem�D!!�x_-A�-Q�A� �jm�H�� cy��MV chip2 P: :d.JL?eisA�:!�oK$o1��a&�!�ma�igA��{V� vX[)�� um N��E��$q=1$ TfMTtJngf��Tokamak� $$Whistl<(Ga�����P�+st0Zero-Tem� 8v�Es"���:*�P�Rgp8om �%}* D.�mŭ7k;a:�� e�!]M n6��6!GBrillou �T���+��-�-jrise � �)�Law2�S-�R�K�lexi�:�B�=a & 6)�&0E?R@ !��Jed-�K.�@_igu�Y�Cl d"�]� !3 ng L�N�` |0�s� D� ncm^�8�L�Goob of �+�aQ š�ofruyh p<&3llipsoid��o�:Crh@ 9�- ar RZ<@ Trapa$Arago (181r��Ke"�@a�W�A ag�Q�1e$�#,ION BACKFLOW\j&]4MICROMEGAS TPC}jFU�j@ LINEAR COLLIDERd7� Z s\\!Aut�#ou��c�QN5�'=�!fll�\�mun-�N digmQt Why  X is FyO OrMed?�$a��? onUs"�S��n&(ch��9.YEx�"dq]au z^6W�SGnQF�Eq&�e�D7E�a�]k+s%`�m�I�[��[ER��ykker-�Yck�}�.�bJge&�3mc� �G withU avHn�$epsilon$J"see� WIND|ACE�0� O9-A| cker� �)!�!�HERA-B*�6�Zart\,II:�nt-End"& ic�e[1cm] { =6bG�]}�)On�4mer�}��%<�é� �*�0Bond-�,2�?� ��!�� SiM3ain� .<�ed)9&k&"���� fM\o{}ll%�esset &W'�Xor�^Q�of 4f�� ���Tehra�t�Index Infe7M!|suc�C "�&�!��b��l�� ��%s a��y back�ndy {APPLICC1[1$GEOMETRIC �s\ TO BLACK HOLES AND HAWK�1 RADI;}�� MultAf&U �&�in )Ay� BR� Life�~ -�! 8$s$ti�iumzAcd&��i{!d�2�(�)!�e%1sy�.>0su4�s H$_2��%�a s�T, q"nsfraA1�lse: vi�3&e`fJ sPiWhy doAheCer beQ � d?�\A3H diagram(hod)q n o�+��8 � gaY�&cS.:Ell link%�D orem-"qCerr�K;e?iO0R�%c�d`-j��.jUPDEsL"�UL�ng���*al鎁�DwX F!��*݇�3� lBGigh\ �6ed damag!�*�G{'�)�s_�N�DC�P"b�?"�h�s��wES�8,�h 5+��#-��!A n(4�m7 %Y�?��� &h,> Xn�H�F0symbol{dt\mu}�)] u�ede7�"N�8��UW&|&t" p� �"��Xh=�5p7�(eme environa�&&* �(�$oA�etac!erial~UDe�i*L>%lo*�5?rop� l#&y-�8a:*4 ?� Um ic (b Clea�$� eLW\l� ?g {a}As}� caa�e*�L*/*+/wa.,/� art�A3 U.~S.~D}e !B� E}.�j%A@A��.*(DE-AC}02-76@$SF}00515 (. LAC}��VBER}008812BUW}).}�P,%�ed����[K�=n]/nP� erla��1�*(����������I \Hea�1{\��nGc{md {An U�ven���F 9\\�=aw Tube-�(�\"% }} }[�yof�b�ia*�0 . E a�����V torv� p��BYa..Dis�f"8 a Dae"�Y��orav@�D2Th�; B��m��al#msA� hlun֏�r6�=192�:��y.�BX.,Qu�%� !P�($\mbox{Li}+ HF}*�.  LiF}&4����*r%�&^�QnW$ �6&SMAlu�a� r?�:*"��=y"  Y�D� ��3 ory ]X �IXs��a4Qism� }STH. B�14 {7}(12), 1240K}4). }y.On! � -� Phon�-eJ|uper� �g�Ž�Lv stumiaaM�dox�Tw o����``A�''�&�alO)�imaproofU�� 2��GW's}��0A�mQ;s ��Y�!�}c3/all v�rU (I)}.�{F*N<�A !*M�3�? *� {A  subm��d�) Roya�E��X Y�#m!|�/n �RAd��ve�kov��ins:\\AZeo:��R� Ray"Jn����,o�H%z&&��a�7g&�&t� guid�)�S.IBook S�� : Endogen8��us|: Sho9|i� QJMW3�'-Ph4${U}$5�eO%�S ^:dPic �w3a^�bitals}��\ �[M��kect�!d !�`: �B�Hco�R*Z&�!� P,T-m'Sff9&gr� ae~HI\_ %%YA�&� Rosenau'sgi�M("���O�#erh��Mofo#n�.�_s�xYe *�@ Mult>�a��5� ���9��,�spE{WalK�S�cS��u"�.�a�� Nega�y capa/X� �%}ed }\\,&_ a� �ort �<�H!�)�icK0mX��qors}�C�-�'� e�ol�3QTA"kEred-Pop�(!�M�!}{6us mir��} j#-Colon�9vel+-�%Looy�!�"c+*y,�2�m��eia�hrougJp�,al\mvX U ��HEHphobic� profm�Mu�4�� olig�>otiY!f5a YuleI5�Mk]1i�#&<<�o#.�,Wi��!Sub H\T"Ffin58p4�A���IO�nW�n;RobusNS��mGo g��ϝ ��Rri�2~ p�s�=bR�Y!hee���zleS� 2007�1��9in��!���i�/�gc��*�FLogic2]b���n�ʭD��u�S� e Alig� �r�(e����F$Ion-Phosph�oA��aHDNA�F-F"� be !--� -are��l%a�6�-F�4!1e!��-�tmbi X row6� or�]An RNA-JUe�v��eukra�!ells�� or0 r�s+&�- no%�nd-bi�&��M�RB�!Cet^�p �p�f, e��&� 5��ZDpairwx#!L�05 �s.�Tradeoff"� �-"� �O dapm�<ch}ng.� � &cx1sE0�ly updaAxrn;Boo �s�5A�����E�Adult �*gen�.A�Di"��!0 ShanD i&F�i6a"R�.iu)URp�jxp���!R Exsred�luH:.� 5\A��d%�"* .� �!�M/umoީm!S&�s��t> � gameza(��A%!��M1b^e���JA� al-be�Als2��<CLESUM)���G�Tx)*� ro�La�"q "e �� 2�hemotacaz�aps� MesenchymE+ rphoM� ;mv sM�on� echoA��%� d�c�} Infl�!3-�ar.���a�7ce 5 fu�!A��a�u-���8erA�Gw�-xr��=en"�6-� q �"�in�a�"�Re��\fK�Thi�!G�is dedU", �(70th birthd�fHerC�Wal& whoC< ioneQ&�al�;!�!� -z�wU$Rydw� h�$ �en� ur�erG�rahY7diIE�l�/�� %cA* on.}�$A�FJ# mutu��(E��/g0eS�"`e,���mV�ine" �m�2s!�O���Y"[u[:} S� a��erfu�y;Es�!�� �)uo�fRin �ly0��xJ���(qubito�.A/����?�jq��-�<4'�Yp' s�cHid�tܛ� i�Non�)��i�yE�"�4y7�� fY_&R"G to F)u�- WeakS�,O%3&A)sum ke �&P ���hc1A)a\\&$#Z>�� swap��Z�[2�V���e��F�F ���B �*#M�pm1�$�Et ��RE"h�);q �h��BS�{3cl%�Uta� }= � �OH ~� 2g� ar5v6 fier Q�&P%; �T0kicb$�_rYO�Markov$maC5"� 2��n� �@ry unM4H@grei��EdommH/�r ng�E�Ae-va�{��  �  H`S Ou-M�l"�>�)&e�66{*�� C.o�@��i�'B��7th j��k�yeC.\+,2'!�� �0(QCMC'04), ed�]b��Pephen M. Barnett (AIP�sNlv�8 , NY�H��n%y�is el�E8��a5a�3*������'F5mm} }K�-��ak�p p�/.Mg�v��+vi�2Q��uun&�l Aݩ_\\�8�2Ca_��sy\ms�MATHEMATICAL ASPEC|j8COMPUTER ENGINE7 dva�����oloLLUSSR\\ D"�OI� T6z�Óz�."� �fZ�Mter�Ycogc�onG=�@%M�5�Á��i����"\s!r on*{�� #1 -�*{3G�!qa#2#} \add[���{toc}{t��}{#1}� #M�7Θz�e�wil�ɶ)-�!Squee�&a�2�H>a!c ni��qT F>(VoirD�t"� ry��Vc��G"��w�Spa��&3� NIhon�~f�CerI�7F�}S� GA�� �:R6�a M�� -steh� um C͈M:<nez:?" $1*�" 3$ )-c�?&�H��m W�)Four-lAu12�,��%�}�W)�M %��5t�U�K.�3DeN"��on�N�?mazer� �hm�Xof�#cj"���� ?~:*�" c �m����}*C� .�v "Y���Z.�y�o�2�PWLwreferiba� �M� e9&� �u� autL|n: ?�S��J2 � �A4Kochen-pk9WHe5& Q,  u+�:��ڎ-Va��*!s5"A Boh�2��� al�G\��{�E2�]\Fe`Be�J.:�.*�6�"� Mo�� �5��jyXB%4�"1O ��U/ -of-�,v )�re�me��U����jrev>Ŕa/-��əP�cact� ��~oi;En%�l� ��criA� L�&�W!!�a = %wh*J,%$era�z����t � 6�� �Nof5�crypt�=� Enc�e}bi�@o ��|u pace�m��Ho�Gc���a�d��#qu">N~+0� (�2A.[�.� !�.��Op'a�) of Deutsc.Hay�!_Ů #%^F���a�8c�Ed 2�GA,ng: Se�r� wa�Elu}H:7�9$mer EfimovTe1�lfR%�%�n3l ��2�y�E�kg PromKy �0--Jozsa--H\o �Al�>���4s�im� Ensex AޙAJ�""�~��P-glas�qyT��@�ToN`A � BB84��� �P Priv:CA\��"�<ar� "will ={rd�� 2005��� \"{qo!��%s�, Adela�',�Qe , Au� lia, 4--9&'UI 5.}g|�$9ofA$ph)��  a�. 1i7%� A�x *a#xo-F�U&�"�3�� �&al�CE"�a!r���Bb% ��*q�] to�[���}'Q��� �ach�4��E]3��(�5.-as F��9�is�l(1?�8Ϟta� -cop~:��%^�D��M|to\e�%��d��@z A8�r^eF�� <�YEeg�q�"�E� R6;�!1it�ym*1L�P6S��")F�� SWAP�a*�n�_gnetJ� "'��"� �im.� �Ia7QmfG���icZ� �aHle�j� �.�)Ez ra `>d"u C �Awo- �g$�L{2��l!{!Dla��y� �?�3E^y-�L AlGaA�c��sk�MI�eI�*9���}L!"�G Ra�Q&v[P�>((STIRAP) Am>�&�>-�z� fold� Engi�miE�eb%�a.��8Z�'!;jqT!&�C..-� T>s��R����=��s�%*?8mj!s � �$te i'�PCcol�.)�i҅=.D$e@�:.�)1��)� },ˁ2Y�*p! Wi���"�(ng��� A Coo�� many~y{to�%&w.�syC6vp��"irA9_G7�&���aT%Op&1C�|�5>�FP! D��oN A�Schwin�>���$Thomas-wX&q�2MF%)"r RF��� �)j^F38,^F3, (1999^F(897--899. \~WFH23/A:1026613203875}TFAs��X+ty I���!E!5t31��.3{}AJ0,$Z\to\infty$鹅K�,"��% 2�sres�.f 10jG4, April� 0,oG6!702foG,ptp.ipap.jp/�<0?PTP/103/697/)�B2�A�!�&R -PodolskyjenA�aiH� �1iSH�-� dowI7�Je�Spi%n�1"�Gq X,:�'pvAt"�z� -h2�[c2���,)��tud� ���co"�(�.�II OPO*�^�.�!Q d&�F�/��u �Ba?"H�KHe�G�ƌK�ls)r-!��#!3�i�Js�=byh>u�-H���bF�6Ts���sA/�~toS �r��> s u�ttw ^ $1/r^4$&L1aQ("*th}FHQ&TEV� ��S $3za� *e"MQr\ �nrF�c� ACrop�s�&Q*+; ��Ua"2by X�c*|(LMY� iori��b�l8!�:�!�XX� ch�I%�1� �2$�I$y isn't evw';8istI�?e�l? %!<�W�#� rXAL#m&q�yL AY�i.&�? �A$�.sG A�*+'e �ӥ�H-b�QAs���*�E�"�(X� Huɲ"�Xs�h��� imagƘ��yn���9�Q )�� }%cc�a8 2�a�E� "�(��e�-L Tel&� Bid�(t�#t*�/>0u,HA�Moir\'�~R����z"%ced�� "�-uh�&=5�E" 5.P�ss>9�4iPV� and/U<��� data�BgSc.?�q�,Qpers�(1OG��� ���C&f!^"�QCha2&�CJ�|mO&�<"�u��B).�. ��� #1�R{Q�O t&\.~"�X�՚)ZL� ��B�U�# ies}�5� � �uBdM:�um��� d��4�\\k*i~!�p9k-�athsrN���Arb���ST!�� A��Nonspreae� P��/n Imag}y9]� vY�vl �*lZ]-B�8���6.�):ts Ro�Xn1�"�|&OG-N .M�NF &�b�)!�a�� almYld�<��{{\em .� }� .J.Mod.:.{A20}�27 Q5)}"�0.7cm}��11.�"f%��5� � \" '�S2I.N.F.N.%BM.I.U.R}.>�dem6��-4A�%��A "���!$ \bq- &*�|L��le� Full��e"N^%�*&GHZ i uS��}*l?��E�'s"\*�wo���S Bo*ݲ\\��D!�ak&!�l9C�c�?in�}&� /a�dYy�r��sL of 4.eld�t .��ks KM��kTo��re ��/alhY-��rM�&g8!��=anov's] m�.����(�Q/:� !��u. ;�ӑCEe3�<��,haos % \vboxF0pt{\vsh.lhskip-50ptLA-UR-00-XXXX\hss}A  25pt~Z�com��A�EPRa � ��Re�E��&� v� �1@s��� s l�U<i� h Z�,i�&*�nd �.EO:P g f*ia�; ing�C��}n~� �5e �\AFeshbO&X�"��'beg6J� =0}UWthPh�~-36\end  c���}?-db(�F:� *ly"? A�� <4s�K#N�hrE !�Fault-ttYB:A�� e�91��Y�� al.�%����D�<tG ��of d &��;Qpho�A�DEYent��Ք�3m���k��s�QuasiI�Z#oA�l&^!��^��.q`�b1ls�1�pre)�H-�\or��$\f{O(3��no"\ sigm�tdel�Pre�dPost-&���dox�$ext�u2?!���%�3�f2VSG ��V,.�!Ey�m al6oGN �S�%LEMENTAR8� PRINCIPLE� E�B7a��yD ��PL\"j ��PAcheY�6TA1�ߡ1a3p1v*= sto]�EYhb� o�/�%! ����he!�-&(n�i��, prep�O�@leU>2Sw {o}� er Cat Ŝ�  N0�al�Z tor7�A���Uu�@ �� with4pM�ZIon��1),EZUY�.6l%&�-�'�&gt93��~�$�na��!x��!as �ed& O"����D%� MixbW�/�9PhBMe`&�1�veEoi�? coil� 1>k!��&�i�s+W� !�e!e� , $G?_� ultiəcl|- � �� ,i��]� 4r�\p1.r�V%|| i6�$q�ts�:�$:: Quni,FBeh)Ia&=Bc�d3�T�� or"a�e�� �f Bell's%�e��"g"~�h*�jUl�"�0E� Lambd�G*?4Eco� 1�'�"n�/J$g:�#)�� D.q�aCaZsi-!*yt�&�:�C!�g sG0��] ��'Se�Rb6rA��Ema=�,zhangzj@wipm9�S6!"�z"�po��>�1 "�%u No-���;E�5!&A�q��Doion�0Exp2z ng aaŒ�<C��,��&� AJ, sa��Fu�>*#5�g�4scLuto�u�t)g&�!�bic&ae�[�_yXav @�Mc� eǺe�lW��P t al. e" 1 #�Fmoni)�<�iw�'��3sP��6��%*�2I*#�ing&�1�klafNEݺG�7: T� 9��A�-a`0ll [c-A*�!g"�+��� m�*���f�+ry�h2�b.soE�?d�C�ps��%a� y� Atm <e� 13km�A*�A,g�" er: "W� ��Y4A-����6>=��YWO&����� �5YD �#Q-H of light��,� 6(��������-������������� �������� ����������������� �������� � ��������   �`�$`� 0Ѐ@�PP�`��pЁ|B"�@B &p )�� -�� 1�0 5�p9��<�`�?�CQ�G ��K0фO@�SPQ�W`��[pх_�a@b�AFf��Fj������p�s�a�u�qy�Їb��2!�b�!�$��"�4��#�D"�$�Tb�%�d���p҉'���(�@J)���J*���J+��K,�0���b�-���.����/�#�0�P��c2�(� 3�8� 4�H3 5�Xs 6���6�t��7��8�S�9��N:��N;����3=�`�=���>����?�@T��PB(�C 9�DI4EYtFi�Gy�� �H#�T�I'���J�dK-��L1�4M5�tN9�O=��O@%�PDe�QG!��RK1ՔSOA�TSQU�UWa��V[qՕW_�e@Xb�EVYf��VZj��V[��\q�5]u�u^y�_}��`� 6a�vb�)�c�9�d�I6e�Yvfd���q֙g���h��V�i��Zj���Zk��[l��F[m�݆[n���[o��\p� G\q��\r�-�\sS9�tD'�E�Qg@u�]�]v�m�]w�}^x�G^y杇^z��^{���'�|�P��w~���~����pQ�0 �x�"�����E 6h��B��Rh@�Xh��f��v�� �(�E#�X��'����+�آ��c�2�Hc�6ވc�:�#�=��#�A 9$�i� ���K2٤�OB��SRY��Wb���[r٥�_���c�Y��g����k�٦n� �q�9'�u�y'�y깧|��矀*蠄j衈&�袌6�裐F*�PZ���b����rک�������Z���������ڪ��j�����Jk��ފk���j�����+��k���"����2۬��B���R[�X{-��j�-��z�-��;.��{.�骻.��̼L����1Robert Conte\dag\ and Maria Luz Gandarias\ddag {}:)H Service de physiqu �Ol'\'etat condens\'e (URA 2464) CEA--SaclayF--91191 Gif-sur-Yvette Cedex!nz,DepartamentotdMatematicasUniversidadC\'adizo�asa postale 40E--11510 Puerto Real+ 6�Spain Ivan Smith A. Polishchuk |TyukinQBoris D. Lubachevsky \��Ronald L. GrahamZ600 Mountain Avenue�R>~,at San Diego!�\Murray Hill7New Jerse��La Jolla!+�CaliforniaMats Andersson\vspace{-1mm} {TU Vienna}{Wiedner Hauptstra\ss e 8-10,}{1040 Wien, Austria}Jan-Martin HemkeCAU-Kiel Pietro CaputoI8Ezio Vasselli}DiA_iM_i]_}) �P.le Aldo Moro, 2 - 00185 Roma - Italy �@Said El BaghdadiAP� Scienze/��t\`a ``G. d'Annunzio" di Chieti-PescarabVi!s$Pindaro 87�DI-65127 '�!%� .~Heckenb� E�rA�TLoebl \Large Isabel�$n\'{a}ndez5� Research E��Ially supported by MEC-FEDER grant number MTM2004-00160. \newline 2000 Math-{� Subject Classification. Primary 53C50; Seconda 42,8.Y Key words�)hphrases: maximal surfaces, E�dic`conelike singularities.}(�)$!�pcisco J. L\'{o}pez $ ^{\ast}$��(N.~Neumaier(M.J.~Pflaum�g0H.B.~Posthuma�X.~Tanga�b�e�@Matthew P. Younga��Al4Dennis Roseman�PM�� r!�!�,MacLean HallA8 Iowa CityA� IA 52242�/SAa1J. � denA4g�h$R. Brouwer��@{CWI, Amsterdam }� {]�D AKIRA YASUHARA }8�!�-1mm] {Nukuikita 4-1-1, Koganei, Tokyo 184-8501, Japan}�2]LHaruko Aida MIYAZAWA�PHThe first author is^[tthe 21st COE program \lq\lq Co�7@ion of wide-angleU �^tal basis focused on knots''.}}!��Tsuda Anege}'=Kodaira�7-8577�#+3%82` kira=`A'$%{{Please �2, all corresp�� nces to %�s��-( �X @en William Semmes�+Houston Texasa� Dani�� ovesA�q�TS. Leite$Nicolau C.�n danh�,Carlos TomeiaY8Anna KarczewskaAiulx (dg\'orna 50��<65-246 Zielona Ga��PolandK8$Szafrana 4Y LSteven Dale Cutkosky+8Lubomyr Zdomsky�0Jeffrey Brockan��McKay!�Tan� . Begazo =J�aOD.~Ma�%} Hugo� Woerd��EB runo_t� 0Angelo VistolemMS SilverA�Michele��s 0David Damanik!�q�BiOw50Tobias EkholmA�JuliusE�0Richard ThomaE8Stefan PapadimaFCheltsovA�� �o."�A�HSevilla. Apdo. 1160%~-41080AG0Vorob'evy Gor��0Moscow 119992!�$Russia/��>��$as. E.P.S.����ͣIIIMadrid.Av*;*30�$E-28911!� Legan\'es�� Kamr|(vaani-Aazar%�"� 0Ali EsmkhanitK4ikhail Karasevc This� k wab�RFBR (��8 05-01-00918-a)tby INTAS#0-257).}�� M. S��er%�,ffe Haagerup�R\a � }�<\; Hanne Schultz)c*\;~Steen�{(rbj�rnsen1mark[1� $asaru Kada�Kazuo,oyasuJ�-(o Yoshinobu!�HC\'{e}dric LecouveyA3 Bern��Hanke G\"o!�ForP 4Majid MirmiranAzPeter��Nyikos5  ���� Pajoohesh8A6Gorehamiagio�w ceriA �.\ Mei��d� ,Qinghai Wang��0A.~Ciarkowski%�B.~AtŘuk&��&��$ish Academ���ces�J.\ E� lsona�� R.\ F.~Pie2$J�0drei Okounkov"�PV)NSF� Pack����}=��{5pt} El� t H.~LiebK}h/8Seiringer$^{2}$E� A-3pt}* s!�P!csI��9�}$� dwi� ,}Aj Taka��q Rokko��Kobe 65$ 01# E D� Alay>n-SolarzA�8Giuseppe RuzziC�f� ,�T=di� >�  }3Gr� ,*33,A��Didier1U�\'�ement�k2�K 0Laboratoire J� Lera�0CNRS-UMR 6629+���Nantes�2�e la � sini\`ere�cu7 % On leavrabsG Dpto.-�e��as!�|U.A.M.-Iztapalapa. M\'exico D.F.�$C.P. 09340!�Mi�?StoiciuB � �Lapidu� Erin�J. Pe�nMig@ Carri\'on&�\strutn John"dy�.4Rudolf Peierls( for Theorel1�aq1 Kebi ad!o8Oxford OX1 3NP�H.K.HPiotr Bizo\'B�{��0Tadeusz Chmaj6|2&\�}���3d�<$Nikolay M. ov$^{\hsR 1pt}1,a}$��� \ \ � T. TodorJ02,b}$�a� Andr�T s}�${Also at: �M2M de Ji (eu--Chevale� (a� a�7586).O 'e P� $7, F-75251  CEDEX 05,�.}�CEA�*r�QrT�or de W�� y 306)aFZit�n \sur� {Brau}��0Yeontaek Choi� 4Yuri V. Lv![� �!�S y N� enko2�A�% Cov�xCV4-7ALAYK$J����% Troy% NY 12180� V�EN�?:� 7ALA�^a(Irina Nencid Karl-H� ng Rehren� U* f\"uyh sche)�k���� "at � tt�Qn!o37077.>C Quesn�3�8V M Tkachuk$^2$a4{U Nucl\'ea�..,et �AD�&:�LibD,Bruxelles,}La4CampusAula Plav�CP229, Boulevard~du Triomphe, B-1050 Brussels, Belgium}!�{12, Dra�Xnov Street, Lviv UA-790aUkrj}APo��{��s]3}� {and�8{K. Ypsilantis}A�)#24, 54124�!@ssaloniki, Greece�,,as S\"ut\H oaHun�anN� A?&+49a�8H-1525 Budapest6 D Hans��4Weidenm\"ullerP 0Max--Planck--:m Kern�"kajH<l��qM. Deg^  "j$S. Nonnenm�!r�B. Winn� &?UN]Ba��a�Lumine�Cq907� F-13288� seilpJ9 (G)�i �(6207 du W8 associ\'ee aux*� 'es d'Aix� YIA� II %a*et2.R$Sud ToulonX; %p .I affiln )Lla FRUMAM-FR2291}:2/dm�a>=�Hdes Hautes EnergiesA�2�� Plac�-m�r6�%5^ 7589͆�]V% IE�(Paolo Amore� (Alfredo Ray�&_ FacultN$i��asa8���de�ima0],al D\'{\i}az� C�!llo 340A*Co/ M& !{cM.6 �*�8INIFTA (Coniceta�UNLP)- DDiag. 113 y 64 S/Na$Sucursal 4��Cas[ �rreo 16!� 1900�#Plata�Argn . Aielloa�A.Yu.K��nikov�(S.V.Kozyrev� skip��� e>cse^ei� !100875��) �R�� and�Lan-Claude GUILLOT% %9�~�75!W�%Gali��>��4-Nord, 93430 V��taneuse��7 F  Appliqu��2� 641, Ecol�ytechn�-8, 91128 Palaise ��wa���$� inet�cpPrzemys\mbox{\l}aw Repetowicza��+�  �'York,  10033uV. G. iCm?a?a�@Rold\~ao da Rocha�HDirk Hu,t� �B,Werner Kirsc�&� AJ J Luci�"�:$Lipika Dek��&ollet�1$� J.-P. Eck�{2� ! o�Ro�*"��8!-2pt}P.�"708�/DPrinceton NJ 08544��USA�V� iy Tolstoyq�"kKupka�.3{e}I] VI, d��M"�, 175iOuV- 75013 @Y ��@T. Kenet \�K MA�r"�{Keck-�erB�Neu�$ology,:�%�� UCSF 5 �nassusg*,(*A�ɞ4CA 94143-0444}$$4G.~L.~Litvinov�2�EU&)Remli�%M. Hem�+$PA.R. Rastkar%�.~�Vn $.R)� V&W iR6 Rᅳ �xfJ1�614013a�N-a�W� Jung�$Stud.Ref.~�+tudiensZ ar M?chenglad~,�Abteistr�* 43--45aZ41061F2$X\href{*�%(iram.rwth-a' 0n.de/~jung}% ~($\�%- 5 Geyler6l*�Bol'(istskaya 68A�4ransk 430000, ���8P. \v{S}\v{t}ovu \v{c}ek!.Z6�y�ak� �* ear m�.E Troj� da 13, 120 00 Prague, Czech��ublic �+.\ns YC\ls HEN��( ns B"D"R UVA�, TK",IX3$M!Vbreak K[RS&0+N? k( N$^4$\ns�&MDAT'"Y LOR$^5$��S� i Tatsumi�I�y�Tsuchid� 2-1 GakueS�( 669-1337�� A��d(St.Catharin�"Ontari�'4Canada L2S 3A1��A��$zino$^{1}$�(S.~Musacchi2D$A.~VulpianY!�a�y(A.S. Fokas?��'6H��ed.P��TFZ{ CCambridgA4$B3 0WA, UK�L4Chongsheng Cao .2�u }��ZIts�&F�y *7, IUPUI}o4(IndianapoliDN 46202-3216, USA}��91A�% (J.T. StuartA�h���5B�>CB30WA`6X�sAIm�,al� }%?Londo�SW72BZ��6JJ�t*+w J� }�*"�, �%��2�I.M�lfand�on occas}&his n 0ieth birthday�Murilo�BaptistecDan TanaE%<1%-6h��g, >� Z.o p!� *ch\"afe9$xim Pavlov���^S,�9{c}�/�CONTE2 ag$��"OMUSET � Caro VERHOEVEN= H""�d{4Federal�S\~{aoHlosm �2[>FNU , }M \�+ it{Caixa \8al 676�z0CEP 13565-905 ]}^, Brazil\8X.-M. Zh )}%�L. YiA�2)I;�z P. A� 3)}$aG.AA�A�da�Ba�R.H.J(>imshaw �K�# ~Kamchatnc a>�N�)ool���pal BInf�6�O*#A�Priory��A  CV1 5FB-2�] ��Blws�bLoughbor LE11 3T���Rc�Troits�� Regio�-142190A�9U1�'a�FQ3�!FJ4}$�4� }�C" Ionos ��� Radio Wav�=pag%za�� �CZM{B�.lo�A.L rovlyUy�E�� Feraponto� K�Khusnutd�)V.,rikhi�0V<Sokolov�{TOXiao �81cm} Yunbo ZengAq R#Kanehisa��asaki3e*Yos*8kyo, Kyoto 606-.6Ac,Rajesh Ragha% 2�)G�:$thakrishna!�!�a��kA�erials&h9Kr�'Bangal)560012 A�\�)0.3cm} i!�P D�ConC'+y�{Yiju.(~0%ϥRV.�T� rzAz Litak�� E-mail}�=.Tarkus D Oldenburg (for� STAR O)ion*� F % full!  list a $acknowledga�s see#endix ``�T''~ ,this volume.7�7GEM6�:�Uaul Sor��0M.WT' 0nbaum\address.�"t.R0c!�Brookha�5� �rygi%Hpton, NY 11973-5000�%"" "w;2�?U���-���E� ]@E-AC02-98CH10886./{#ru�$A}}$ *2index{ , B) Abb5a2na/2l � (s), }X4056 Basel, Switzerland�[0.;<% }�P . Rivet17[IPNO]{")d*�!�,%�'091406 Orsay c.�� N. Le Nei� ^e  I#eleczko[GANIL]{c$14076 Caen�}B,rderi2Z ���:ougaul�DLPC]{LPC, ENSICAEN�""� � r506r�L A. Chbihi�� �tJ.# k!lJ&ap. P�0log"P[IFIN]{NIPNE`RO-76q!Bu}5&.�C.~Dahl>#.�L.~DemirC3s>).LP.D.~EK0 heim>*.SK.O.~Eysv�O.~Fe��>KJU)4R.~GebeB�.$J.~GreiF}.� F.~HinterA�F�.�E.~Jonar  H.~Krause�.�.tC.~Le�:B�.&J{ndleir' R.~M+E>q. 4A.~MeinerzhageBO.�C.~�y>O.� D.~PrasuhBJ.uH�%hdje\sB3.rD(�>aaB�.(P.~von�"F�.yN.~SchirB�.�W%oJB.% K.~UlbricrsE.~WeiF�.�T.~�nVR.~ZieglR��D. Fl�0�NA49 c�K53ion�J.~Adams�-F.Aa�nevich*G 1}�&] %���,data analysiR*H\speaker{Venktesh~S� Henry  ng+$(on behalf�9e TEXOV.� )�FA^Bia Sinic� Taipei�R29T Taiwa� R.~Skibi��1%0� olak!jAHH��ta\l{}a,W.~Gl\"ockle!DA\A.~Nogga!x.!9D�@� E.~Epel�!�I UBtcu� A�tu�@${ Vladimir�� calutsa}U&emT52U��!!�of"�M\&�8y,%�, !� 3187�)!�%�( and}-$ � G}R(, JeffersonQ-00 Ave,i2�Ds e60&*��C.\�a�ertulan",omonor6,nigawa�.a Flam!4i�� � Zelevinsk 2 Bhas�qD��$Iyam Lynch%�endrik� HeesJ${Yu-xin Li� ,2,3� aL��-zhu M}$ aa Haiq�We��$5,6}$ }n�O.�{R 5WLkato�I Heavy Ion1�, Min*�Rdu�W,a�47�3871, �A }'VPr{�Cenlof)��@��.�1�.Naa.  of}?/JZ�Accele�(, Lanzhou 7�/�}�JE�� Al!�da�nn $ieX,nc.�n�J$, CA 95134I�M6K�0 nigg%�*Krewal=$^1\;$Mat�D ia,}h.�Fa�:<%F. !U�O BarceyQ,}B��:oAY(645 E-080281��in%�J %ee Yoo0�G�aLa�4C\"uneyt Berkdp $^a���Jt��� {�DE. L.z!t�Na!:�F�$leMOr!��xSA*ff�CX"�!��[F� onauJ/(Horace W. C�(r��\&� uk-Yin WoT�#A<Silas R ane� Made�e Soyeu F7 �Z�OF. Lutz�I�##E�1$g<e}par,G'AstropiHqueEd*�des��ticules.�2K�6de l'$rumen�( A�> {e}e�(N�C2J�U CEA/�CgF-91191R�a �IGSI!��?[+sse 1w D-64291& �"3$�� Bs�%TU1F89nT.VE \v s�X!�Z�1-Yu M� a,c,d}$~!�� �agA�~�_Bao-Qi�7�#a�~�.Zhi-Yuan�#� �Fong3SI'�%D}�{A��Q��Adv�Sd3#P� �Ky %(WorDb�q), 9�[8730,B�=�S080R. %of k}�%W{c}$ {�K ���3��L�5F>P R �!� `nov�>H. Kaman�> ndre�Bchmittp YM0M�!4E.E. Kolomeits& 1�C.9X tnac4D� Hs Barz��A2(4�%E>R4eցQ_A 5 LMChE 6, P@(nwicz$^8h (C. Fuchs$^9uT. Ga�+L0�C�Ko�'S L�4�%5��� M. RoWr� Gy. W��1}$M J�?�x&2$"s{invi} s� }�B0squini\inst{1D�^echsel 2� L. Ti�J H.�1zl (1)� J5rb l (2)!�Ln /3)aiA�5nseca (47W. "v  (5&H.?O (6A. Kie|e(78LD &8 G. O:!ini (8)�R�}m�D(9OMvia'7)�E�#`arwish.~+eedN WL=�<~4Fabrizior umboA�= reco0+KA�giI�P9+;BotG���Alkofer�p%`&:2"G 2{ $C.\D.\U=s!,3}%�8\"{o}rg RuppertP X. Su��.Z39�&>0#ginee=O� !�.784�יx Highh#3�a<ors`hn�iJ.i�dyAKXin-N�F�PAchim[ wenkA�# Rina�$M.F^ r!�a92�ri�2He^tap3e�Sa�s GuptDA�s� �͡�P�riOA �,ri� V�V�d f�% bar}AA-�/�S(to KOBAYASI��b~~T'4hi NAKATSUKASA 28�9MO��� and~k> ichi YANAGIT!p{y@%Q . N.cLov\Ma�rgn6T\A�~$ aber� H���\!�V.A"S? ova\)�� ton\a�\84o�) aya\!,J. Zmeskal\kKf.K!J'`p"xQ >�+& 6%� IFIC�Uro Mixto"� d�E@ ncia-CSICn foG Investiga�Go�C8Paterna, Apdo. g10os 22085, 460� W �fL�ca��#E.~Os&�%)XJ. Is�*,Roelof Bijke�ICN-UNAM* AP 70-543N04510 M.�OA}!uL�?B�1E�:d�ga�D)J.b �AA"AR. �2{EJ�/"�3�L. Phai� A S h ko Oshima�(�.* Fuji8d  ko Asag�+4Johann Rafelsk�Y1* fumi/SHQzuQ�5olfram �1c[MCSD]{ k-��,I i�'Ut�LM� chen}TD�_ 47 G�gi� " % Work*@(in"c\BMB�T GSI}!:PLPo\.zek��W.~FlorWU��*!yW.~BronipU!y���TQ�8�@V.f9�$^�-�}c$ F� ickxd�0��!�roe�v: 3;i V.N.�RN.d�.L�ta��Lag _�/ Wi�[de en&e.ca�"kLeit Antwerpen (RUCA)E�5 FM��.�1}� >�1}%I���2Q2 >5 �W!Mnroos!�U� Compu! aBgde�%6PJb�S� � -!�: A� F�/N � Y. M�a@a,! a1A%�m� d?� K. O8$^eEAlv�9-Ruso�bFa��mU�W osel��P ueh�ᶑ� fuer"Fei4�5�$aet Giesse�<D-35392AnV�n�;Q�2��A� Sytchev��:a( AVGordo?mymz>���\i sica&�I2 de S�FPaulo, �T66.318; �105315-97k) - SP�(�1. � R� zauskas�FAfarenG.�'ertsch!i B.~Sabbeya��0M. Uusn\"akkiAT.C.Luu� ,R J Furnstah�pT�A�V"Abr�^�bN�/$Prikhod'ko-�]-�)�MCNP 41� Novgorod @) Grea� 1172596V S. I�Fkov�4Ewha] �djE c�7� �S�TZ�,��a. Y�)���� \2 Kgp] {J.Y.n�\Ko >"�-F&�aGr-m (KRF�g41-041-D00052).� W. Zuac�!iZ.H�H�yA~BW3}"G.C�q"AA.!3�^ U. LnWrdZ4W6ji Y~8a��Z.~vZZ3i�U.M5 0CraPadul�8�GGdu� a),bB4C�LR�$A. Escuderqc),d)}� G.\ X^enj�) .~Ka:l�A#Scopett"��S [rti80d�?y�N:,Perugia, via ,Pascoli, 061gEuo�] INFNq!zione diC* (S. SCOPETTA��Sar�,haDbi!@@;""ttiHanaΡ�(!e Deba:Bandy�*@a)}�,N yukcizmec"#a�R��u����7tvina\PW =bh�b =op�4- remove next ( if not nee�=%qB".Ins�ua�me her @<}%�'T� penb�f����\ �. �.eanB J���. Gibb� R��ce]tFF Rong�I. Ad� A�N�tayamaKEK� sukub� P 2xarclad!J�do���L�/ca�FK:{o}mez#�/ IglesiasxA Pazo�J Pena��Lobato�SJoquera�M Pe�%-J Sendp]!Vs_m��Mekhitar��V�e� Mkrt sn� Armen#���Fs� Ashtarak-�b378410�RewHof D.� Giov#; Samaey�:KeDP maW:1�O3Hh4Profsoyuznaya ;i84/32�PscoXc 7997�I���9ael FeiseA� Ilya� ShadrivovA:��=S�vshar��g roeg�fArbaba�Kha�s�.�<ri@I�!$Asger Mort(4� Frid: OkkeluvHen� BruuXMunir H. Al-Haw iASidlerq5� 3012xnA7*k3�z9�Ona\M�0ntz%�M�Bo� atA� Saik�X hosh!�(sa zhemy� �1 onkn$ A�T�Kim� 1KL. Sladk�v�TC"P� R. l��X�R �ySuA�m0� Cosm��s Avz$yrs, 38026,nob�2F�T�3(Dilip Angomy�DKot*Jay�b Lu�Ralph 5P!ZE.� guzz� Pablo )n2$1$H D�h�� ontgomery!&u0Annick Pouque��"S.->,r*0,B,pLG.PHILIPS LCD, 161, Imsoo-do� Kumi�8ungbuk�(-350, KOREA�L\ F-JG� Y.\ Kuryl8� �Vl �Jaki0Fs��$y&�e�gRs"HP�jTJkJ1 JdaRKC*�;}�#x.z;,3(�;U, UK�I&�@Astakhov.co�S1� �Iserle �2I=��aJ��:QK��Un�Kingdoo!(% W.~Hartun�:~3erw�0a� S.~B eE�J$37ppCm78� T62imWS2tchcockF�rt� L� xto`R.�y�Sw;NzSuper*}uc] Cyclotrc!�; East.�ea�sig�.~Fv'�V.~Zvi��d& Na& al( � � eare�")i+�CLegnaro!\ ����h ylovChr�lphe;[isdoer)"��~wA# ��[Zu0~��der:tZD^ich-Ir�, 80572�8�,�[PSI]{>Scherre�'e, 5232�U igenBC� RV0.~1SJRe[ ches.HFm23�S0loessBP28!kY�&��� -a(C.~AmsleR!D$V.~Chiochi"| .Df�[ .~Cremald"�8[Miss]{issippi �F�.>T.� Y4nomy, MS 39762�!e ~Cucciar�1��:]{51N+VkJ�/, Z�:��C.~��ng.�2A!L M.~Koneck53o!D!tlH$6#B�KK�4okofie" D-�Bw!�$C.~Regenfu�{.4a5T�h"�t D�9)6>!�]m1:�9Purdue>T`(eV?> M.~Swartz2�JHUokUdo Erd(a�Cha��V���|\ N��{tchasima?�#��Thaf`��S�2tz6 ,1}$=!PPPel�n\���Th �!{}h 14pT�Kio1�7�S6pillaneK.\� Vahala��AaiV2�j $hiro~Wakat�Q1}*decAudD@Sadruddin~Benkadd�3}$� 0Xavier~Leonci�� S�{D@De�in Mattkie{ �5 &Hk�C[io�#ti��Iubarev%4 Olgas a��B{t�YUl4��m !chKXm U.~F�9$ B~R B /07�a�lRaf� ���Yas^�0i P. Kirilyukk� �ns�3\~oesa �$�{\i{E��b�"�E o Ri.Janeiro>eRJ�nE�F/j hA!:! " aore � Hn� � Chap�5G!WwC-Ym�!A"z#cs,)JCV4 7AJwH��b1ta�Po^mAM*"�gG!w�C."XamG rte�7>�[E ze C$che, Facol�i Farmac~1oK nia,�7`ViLAjsr7$6, I-951262�� [\b�@ine`].�(�CGG Angilella� R. P�Su/v>��e)nom�^�!�G.PIo"�e per lK/=�ala1 e�UdR��&�Vn,H&�64131)a�nN.�MT�%b'nenbo �laan 1MB-2020#,*lgium��E�$QuJ�ve��- ",�8 Fard�]velopmq@Organiz� a^TehranA��1:� ��cs�$l$ m$$11365-9161�f$G. D'Agost�$< Seti�/��j]E1cmo T (ger$ {Schoo:�HsE {Edi�D h EH9 3JZ�{6 � �uo �^'�4!� �Gde�c�(%*&\J� h d'\`{O}p�OZ U�a) ValSLnc�Dr. M�er 50G4�--Burj�e3ao PratifH{���b:�T"�~��5E�(ubria��Va=Wgio 1%�I--22100� �O_V schk嗡"Tom VoigxN�Fachber�)I@k��0"{a}t RostockAC18051�,E. GomezaZ�̈́$^��a� T Newme�D�-You�g!�I D"!/;$J F McCann!CP-;nolt G.~]�^2$��\m�a+�P~ELECOM s.c.r.l, R\&DM=ac�Ce�}9�K~9`rqLa SapՆaF8nd�Ro=ayW�8roma1.infn.it/\�L$\tilde{ }$\,dagos)}� Yu#�Lev K}% rovi6* 3D�rpeev)."kj��e"4] Divi�X��Arg\i "� Labs���&a�berp T"Hw2wf�v� NSF,f{�T4 DMS-0204714.}�DanijelaC$^ija^ i\'c!���Ute E�%A."� IsmailW at�10i��gR&ll�&o!�� Mar{\'�g�=n$^3$�SJ# tUrchuegu /$^1IQPe�Fe�� z�� C\'ordoba�'a�^ 6Q3 czak_*�det(DVsFelbacq5Gr��na��s!�XuyaJy�`AED.-�uh�w� "ra�}nUJ.~pPlendenU(N7E9G('7hS.�)veyN�RN Kirb( C.~Y�Q��4f�A�7re�kQ� V)J�9a�.F/E� A.~M�� y$^*�$E.Basile(*8(F.Bell� (***)k p.enussiMJSrS F�ianco� MCoMero@b(D.�3onna (*)� p.� lc&)!�F�@Fabbr)SF-jll�>\irn!�a Monaca!o> ensitier4 �B) tenz�:Hallott�"T�(zz2�) Passamont3D.PrBuigwC� ȡ�A. Russ�G�� vianӡ��Rom� ni.o�a�Bor:� Fras3͛NFN }���_�rol\sgS {a}^} V.~S�N 'yov b�(�5r�D\� � j6 a}����A�LA� skii!Ysp`�101A� St.~�o5 198262�#!ia; �$�$,gang Goethe-��"at�60054�nkfurt Uai�g��=}��P.�hWec/F�KPimpec�F� CR#-ak�8�� SLACA42575 j� Roa� Menl�*M8�3 4025C0Sanjoy Mahaja*$V.MORGUNOV��A�(A.RASPEREZA�=�}R. Ciurya7i��R!E�+e�� }��P.�ـenr��,on�i�,�HR S�au��AJaDliA� 2,2T8:��..�a��ȁD.~�W�}!76��O�$. Sheppard��J. Tu�]A_�z� al B�g�`S& N�ine/̋\A�Environ}�SOccupJHealth�'Graduat�!r P�d $!�29n othrop St�w PittE�ha�PA 15261�Nn*�o GotoA*P �*z4�^"rCi\^{e}M s Exatas��q4 dadeM`�l�ALo�7!yT�M anel�y!�Lau�LDuc�L?'�*�Josseras>YRZ Clav0 3$>�21> ��A�CA�d%b 0WA�a!8 ol7�t�lod\'elis%�>'M&�aalA UPMCA UMR 760Ð4 p.~q!Vyw2Qisi�O 05�iceA�� IRPHE01dt\V�r\& IIy�<49JoK}-�?DBP 146A�13384* �r m }!�Dong-HunOHi�2}a-�#m 3k!��] . Sprousea�P�1an))��J Z�(WKlaus�� elle���$��O=(ll$nN� \emph{�9�'An�e S�Drpp� d'\'gR �t�"PlasmasA%Fa�7�j���rue GasP1B�xrp 4043�18�7Ces2|}}.}�� abianu0{u}gging% <-t� % stopq_z"�*�Manuscript received November 15, 2004; �R(sed August 5S6 2}S� HIEEE.uTilman Sau&C Pa�pre-Qed mE 25th�Nary u�)eer�`A�6iS�&Doc�6ry Edi+AFChicag4�4--16�2003;��appj; in {JI}.� simi �;��ein's m5C��reproduc{a kind�m�on G Archives�=rusalem.%C2ng-Ye�H�Pe��e��J. R\�7vaia�M A��agoiti U!P*`����J�� �5ya{Su3fx(a� Alliq> N. D�y:aC�.��!C���E*]2�>�lsq,}�� {UC K s�Ev� 5616�1 �N�Qrb�1a$1 5M . ~E �$^b. K�DinZ4$^a$H�a$ {Deues~Elek�$en--Synchr�H, DESY, ~22603 ~Ham�),~��;�{Albu�$qil�q:v 87131,�VA. ]?A.\J%P.\�L.� rnam>�lTA�KSamole�Y$f2�e.~P�Qtt�`M8�hap�z2MAŠLo�{|qJ.D; eng-� �Iu^��P-I. 2$.1. IOFPR!�<611 93 Nyk\"opine~Sweden.��2�ypENeu!]"�?82?� (Sub*8ed Februa�24Ne� Re-s"� 14�)�U�.�ny��� . Usatenk� A"w K�}ov� $L.Ya. Lyub17 � (esch\^atres Liqi Wei�Molecul�O["��!+MA 02138<T.[!aei`CarO��)�V.M.Ak�� \altvRq{1�j&�$r Minwah F�%�Gemunu�Gu�atne!3I:}$ ��L./ uley�}b[tP�N��aF�\Ae�i T���)+nichhB�(rtei :Y  $Jordan$ J strys 1f�PO �549110��W� am�%R454�<0h0Bruce P. Ayat�Ugo~B�Qlla!� Mai Suan �+1$�0. Klim?0 D. Thirum�u� a�JonMcAul!P� 15 �e$ၷ�( Lior Pacht��${3,\ast}$�6�zB1}:m�i}fs,} \nMl~N-2}$U J�F.3>[&X$s,�R._Berkeley�A 4720�k!xڍoll�[ch!x 4 a�w�!��i|\'Etu�R�que(;Os*V�aCh.�)�ENK. ZiWS!�M�C4ino Lagomarsin�c$ reaL֎rto��14��AJA�q0i;hasg+2 \c c]0�COPPE�z2Yb 8511� 21941-972:� - RJ���.�,epelyts�@{*�2�~�RkA� {**}�864 Volodymyrska0� �3 01033� (14-� Metr(chn>+ 3143!�oeDDwso��� Li+e�DEm�el*�]aA OsvaS�Zagordi! d ForsE�1,Gu}mo"Ce�qaDE?Da� �yChang-HGq wA<Li-�Dg HsiehO%�Hoongei af-3#4Jacek MiM kisz�A� Mech�hul+1nacha 2002-097 Warsaw�Dominik�> i\'{n}ski���b in Z�� !y�mosyFontoura�)t CWei-Mo&�eng${�3}�=X�F{^2}$c� {Th�l�� isci�ary�1:!FStPvs,�,�iCIX"�F1@!Ja}3${^��To whom�8c�enc mould be�.ed. 592 monwq Ave.��B�z"Mfchusettsa,02215�:�\6�n}![��L.~%,oO,K� HorC"I= Iwo Bialy?*i-Birula��E K\"aste e��Fleischh� �K�Jacobs8�,ry� 5M�:�kon\ Leth tA� La, Canada\ \ T1K 3M4}Arvid b4b5%c�RigettAy� el D�et�awei YuaW DougD$L. Hemmickr)Wen-geA��_A� Baowa�T  ei G�6 %�~ Fenzhuo G�2�q�~ Qiaoyan Wa���U<=en C9#(1. olA���c'�6AEk)7(2r^�Key"OIInteg�Ed S�� s NetworkA<Xi'��7100716 (3. .��r�XModern�mua�1s!��B8?Chengdu��41!�B�icja$��A Banerjl *ˆb}V *Ȇci({92 Acharya�Q��an�3�0�8lkata 700 009, �d}�,{� �que�)��B�� Zhi Zhaf Sabr#� Mani�Lco�3B$Jyrki Piil���#V�Bv 32&d0Stig Stenholm 3�,Hans Lignier 2� �C;%�rreau��W4,al Szriftgis=��!/DvRe s �Adr��a}n A�36B$\�Y�He�lE�mz$\f ��2X5FWeies��W�~FogueiraA#de Oliva��l��ud8�@.�ken� {Egham, S�a(y, TW20 0EX�-!�E�gaK �onr2qnd�H4Mu{\~n}oz-Tapia,V P Belavkin� . 7Mas�k109PM�w USS� � wȘberfarb��N (j�"i�Datta�Kiyos=zmak 'Ray-K�Q�`Joshu�mb���F�0p�C4 �m1}$� P rashR� �� grawa>1�7Sa�S��k�ADBhubaneswar-751005A5$ Keh�/N��"� Ki�z�10� �;Masullo�Eicc��\ )�2# Fabio So+r� !�*"&d(%90Zai-Zhe Zhong�5&�6- �!\Dal�4116029A7Lia�pg�Thierry tin��g �T}4�4 Allahverd�2E�l.k�/ ��$ MA 02115R�as [ Lise`�- Ah::�65Hu"�stic�^Baylorileg:u#A5OD� "P93�TX 77030A� Rau�< dorf!Q�Zi a�r*�nza�C�-b�1OQ�Tor� !]�� M5S 3H6HosW HeydarIGun�Bj4rk��6� MicroelecQ�*�m Techn� y,E+um ��0SE-164 40 Kis�r! t H{\"a}nggTM.�lA:V�nn^*�G�p ~Heg�^ ldt*E�65��gq7Y��BeTommas�%sc�"|a�i� hak~�IL$. Agarwal &�HOn Œ:-uD�esearch*3, Navr�Yur�C(hmedabad-382K�� Paw\l � �Mar�zachor(�+�GNO ,Cwan� BrifHer-n"bi�M��I; al0y�a]�KosutE!>E�+ aval� ,Chikako Uchi�!\(��\) �$saki Aihar 2}\) C.G�SR3{\"u}hC+M�Aschba�0!�BattyV,Yakir AharonjaW�A\V�akxtkeQ843-42\�;~�d)  Maxۍ"�f\�r �(en;k,}u{-Kopfe0-�[-N, 85748w"c6�C�_<{PACS: 03.65.Ta �Shun W.abF Ryutaroh Ȯ umot"ETomoh�D Uyem�3^ar&�o.6 %|.� Kx�H�52-8552; Me�MAz:7�`Perdrix�,�� cc�� �226�TBedford���S81730Zbyszek��Kanz�S!��@0hold-Georg~Enbdt��Dr7 Krib� (Runyao DuanA|}assara&L--dos SE& �M.�Ade Acat�$ Aza�s<. Grigo,�%0D.�.KhveshcCu!�K=.k S2n�Z� u ��ar�f.@u�3�rk��Ni! �H`!!i�as��Ce��Ze� � �Jy ukas�[A orozѩht"�wave-�"�ng.com�'�q:�I Yong�W=��iE80Hideomi NihirŨL�%W��Almut5Vg��y Ɍang-shu .4yue-!!%<3. Olsen%�P.~P!ru�dE�.V�$�y��! Laura2FBrunn�;1YGY�!jIr��&i�8E �$2M0�D Cojoc�A�!&A� Rybi%�hi Y � c W.ڜrry�I.~Ku���Y/to*ch���� !(� a Mi��Yin{2V. Eisl�+� r%on Z�UaX4t*�R��wandt� tK)k`o� unFV6Va��?slav NPTskrovnyy�Amaury M<etQ�m 0at phys.univ-^ s.fr�o�~K�'~"� Oi�� {\AA}3�4Gerardo Adesso�AfI�Narrow$!!@Debbi-U\ Leu)Q2$&���!2O. HuguW%!�a��. Alme]��yq/ uto Ribei�),�. Khou <{2*z L.D� SitepM\'FQ Zim&,��o  Pl�An}eA%sm�)$ r Bu\v ze�E��Mi��A6= in-Delgad��T\sl V.F.Boldyshev1nAkademiH8�?G#aKKh�� 61108A"A�%A>X 2)}$����hr~�p %|Th&5Ni�i huiz�)}%[#29� .4cm�"L  #3a���ey yani�VB�nt Dano3U Xtc�~7� CNRS�,Elham Kashef"� 6��GJ��$PREA, MITA�` ORDCCKCFI|'jects\td Chu� - Ox�C (Prakash Pan�udenyG[s/X��dq2S"}�*�K�NaYYl� ���.{"p Counci�� ({�(Nserc})�QM� csV� %�Complex E� WMitacs})+Y u�haO^�J e.} �w0.75cm}�!�AinX$ thotF' Tappr.����6}� ��QNAbec's 9Fqrnt}.}�[0.5cm2=4aS: �'i����e�"he�; op\'er��&ey [-0.1JY2�t%nt!al��8J~6128a�Succ.\R re-VAM�^Z�@ J (QC)�9$H3C 3J7~~\f|sc{)�hJHe-&X�v�`t tzl��Sg,s{�Qw Kry� N Viv���enda[0Denis~Tolkuno�C,Scott Joel A� s�7>Dles� T.C.�A��aU$S.D.Bartle�-Z! J.L.O'Bri�p-��G.J.Pryd"� �!H.M.WisC!r&� K Kowalskm J Rembiel�a��K:R�� r P.mh� �l�eil� $% �2} �Gf-Ri���$Chul Koo K�C� �KKyun Nah�`2�Lajos D��si�+9!� Demk��-Dobrza\Qg!�M�* Tame�2!S���" nost��� (���V. Vedr�2,7t�Bjelakov�0� - a"De,te�!T$Tyll Kr\"u0)�Ruedia��}$�R��4r Siegmund-Sch��)� 3}$5�~{6V�B>erJ$"a� �e}B�#63Fakul�Q II -�6k und��wi�sc�ien��:F: �{k�7-2}QFzW{us17.��i 136,} :`10623o'lqgG�y���:/�h�ielefeld{q:+=M?�}?F�2Z�X:�.*/;1?�.?Rur�. 4?Cx�"$stal 23851�23890-!@Ser dica�b�sd���[A1U!�hr�uA1Sri AuS� ndo �rnP V��UE�f� Pond� 8605002 �cZ� M~aM}?4 . Su`((QaMAAl�� &U'R&V"OKi� �xi6��ZR. Blatt ,� P. Z�$m--� P%�LNJ (USA)ᲁT.I oshk� PL �a Swamy�G.R.MG]b B.W�M$^Ya NeilaB2��+aB!�Yin��i ��wan� Sat2IshizakgOEy2uks��Giuli�Ptti�5R �5a ZizziAY>#<&< P�"�-�J cataAEQ�*@Padova!c&<G7l�o n.~0I--3513�)#)� -Shu&~i}%�Wu�) bingd*SY)"�i��}� DurtA�Yun-F�#Y�Zhan-c� g1]"^� 3� #-x��MAH2�Won#<ng Hwan�$Intaek Lim!� Jongw�iark!�nP�4E�EN.Cest$EAzF�Anc�7n Ca�, �,o�R�@dell'=}{aNapoli�{�II,�2C/ss�\�43lo !� Cint�@ ?]I12�Ataly.hbi\�o*'A4B#ANucFJ (�7), Sez. S�7� 8it{c. SST Corpo�! =STMic2� ,-EFRem�@Feo,1, Arzano(NA)�0 �a�0Jan Pe\v{r}inPRJr.Ax#�hilippQa|U& aume�J } CSalvado��$rraza-Lope�g�x!� Karl Hess� �1:��o)J UIUCA�725�j th Wright��oChampaig�o\o20�405 Nort� hews2��3�{<#" �#*�!'Vej�pl��7A�8351 95 V\"axj\"����v4:�P4&�~����M����P ��������?�� �?� ���=���A�������� @>�����"�2���{� ������?������^d�c����h��{��@|~$�X�<}����� ���&;������!���a'ῆ�s? ���`��}���#�r������8���g��p��ϰ0�7����>�&!I2(!I�!I�8!I�4!I�$I2aH�$ɐP!I� I�$� I� I�$�� I�LH�!I&n!I�$��dB�!I�!I�6!I�, I�<!I�"!I�!I�`!I�$C� a2!C�$Ʉ�a�0!I�$I�!ɐF!I�!I�$C�`!I�$I2!I�.!I�D!I�v!C�$!I��!I�v !I� I� I� I�\!I�b I2LH�dH�!I� I� I� I�$!��!I�8!I�dH�!I�$!I�$!� I�t!I�$I�dȄ I�$�dH�$I�!I�F!��$I�>aH�!I� C�2IB�!I�v �@��H���8��$0 T��@4�t�AD0��'@A T���/�A d0��7�At���?B���A��@�"�HH����&8� P���@�*X� XȂ���.x� `�� �1�� f8Ҡ�5�� nx��9́u���=ܡ {ȃ��?��� QC�P�"�G<���$&A�JX��Ȅ&6��Nx���(FA�R���H�*V��V$���E,d1 Z����E.t� ^���F0�1 b��@F1���e0��x4�!�*L�հ�5�� ml����7�q��娆9΁�t�c�h�;��x�c���=|�c��G8���D !HA r��#! YHA ��4�!�HD� ��P�"�F2���p�#�HB"��H�$%1�IP����%-q�K`�̄&5��Mp���'=��O�� �(E1�Q���,�)Mq�S��L�*U��U���l�+]��W����,e1�YВ���-mq�[��O�E.s�K]�r��E/{� 9��j,�/UL`3��0�ALas��(f1�i�c��DF2��La*c��`&3�� g:�π&4�MHSӜ5�Q�jX�׼6���lfC����6�ɍnvÛ���7� �p�C��GK9r��X,�9 h�s���Hg:ԩ�u����hg;��w����g<�)�y΃���g=�i�{����G>�O}�s��G?��O��(@� d�!(A��OA�  �@bP��A(B��*d� a(C�І8�!}D!шHT"�E)RъX�"�F1�ьhT#�G9�юx�#�HAҐ�T$# IIRҒ��$'= JQ�Ҕ�T%+] KY�Җ��%/} LaӘ�T&3� MiRӚ��&7� Nq�Ӝ�T';� Ozȓ��ħ>�iMu�S����8*P�� e�C!*Q�Zԝ�0�Q�z�"%�IQ�R���2��Mq�S���B%�Q��T�:�P�*U��U�rի`+Y͊V��խp�+]�W��կ�,a �X�•����d)kY�j����hIkZԪ�����lik[�ꖷ��p�k\�*��΅�t�k]�`W��%�w�+^���e�{�+_�����,`� f��!,a [�氇A,b��*f��a,c��:汏�,d"�Jf���e)S��X�2�� f1��fF����f8˙�vƳ���g@ �ІF���hHK�Җƴ�9�iP��ԦF��Y�jX˚ֶƵ�y�k` ���F����lhK���ƶ��Mln{��&��ѭnv���7)�moh���v6���o~��'���p�;�����)nq�`\��8�ENr���*g��a.s���:�ρ�p���HW:ӝu�S��X׺j��u����fG����v�˝�vǻ���w� ���G���x�K��Ǽ�9�yЋ���G��Y�z�˞��ǽ�y�0�_��7>��1�;�ҧ����}�{��'��ѯ~����������@��4��@.�� t�!A N����1��fhp��?� �0�"! Kh��0�*\! [���0�2�! kh��̡w�����@ ��H�"�HB��D&6щO�b�8E*V1V��R��E-nQ\��F)�)�b#�h�3�1�j\���F7.�U�c�8G:�юw�c��G>�яd ��=�~�9HBҐ�Dd"�HF6ґ��d$%9IJVҒ��d&5�INvғ�e(� JQ����4�)Q�JU����t�+aKYΒ����-q�K]���/�La���4�1��Le.���k�3� �hJs�Ԭ�5���ljs���7� �p�s��,�9ω�t�s��\b;��N3��L���<�I�z���̧>���3�ӟ�h@:P�ԠE���Ѕ2���q� ш2���q�D'JъZ��ͨF7��3tԣiHE:R��Ԥ9)JÑR����-m�K_ Ә�P�3%Mk�6���9��Nyz�����@ �P�JT=|��A5�P����"5�J]*F��T�>� P�hT�:U�VժcW�jV��U�vի_% X�*ֱ���f=+ZӪֵ���n�HE� ׸�u�t��]�׼�u�|��_� �� v��-�a���*v��m�c{!�FV���le-{Y�fV���l:��ςV��hI[Z�����M�jW��ֺ�����lgK������ͭnw������� �p�K�����@nr��\�6׹υnt�;]�V׺��nv�J)l�����w�^��v��-/#(A���U�z��^�����|�[_���Rȯ~���������L���N���67���p�%uM%�ly eas�(predict. Yei� some ��� �N����4tantial, exten�QB �whA�we did !U1cipateE�!w%A$��oa�carefu5I%�al96w���f1m�u�!MofcE�E<�k(k+1)+1$, $k = 3, 4, 5, 6, 7$, i.e. > =EgAcA[43$�57. Also�J�$ati@height-to-width r!��y�F#con��a�Uof�F !lE 1 as�\rw|arrow \infty$. {Key words}: diskZ,�,_zer�fgn,y�,m� e� {AMS!v����U�L:} primary 52C15, se��405B40, 90C59G�Zconsi� �tro� blem�p�nc���T��z!Z� :�ig model. It�A�at�p tra�� pproaches�CeA1 domin f U!��loop du�k�&,��A�,often necess!to�Oe�energ e*� mpensator�/n widem��p g��$particularE���recenta!R� d ������  e%i��7 s�� monotoniczam�ׅ��s�4�(�to � � smooth!�-BFr-�D. These schemes do%G��e ��dam�o>�� inpu��%OnE5�\inter� ng %outco^of our�%�A#��QG -d��� %�f�!:!�n!b� iv� %stabiliz d�unY&cQ � of un�n %t�Z.S�uK!inued� c> s \begin{v <} \frac{-a_1}{1- a_2. 3 Tdots}}} \label{fr}\endJ� rez oU�s $a_i$� verg!ue dlimit $a$. S.Ramanujan had� F ttheorem (see [ABJL], p.38) sayMa� if $a\neq�14ɨa�e��� fk � ;<8Et ��!mco��wwa� ��in [V]a! complexR�\$a\in\mathbb C\setminus[ q,+��)$ �� <[P]). J.Gill [G]�Q)di!F�of (\ref!� ) un�=A�as" %!�\!t> uD$ fast enough, mor�ecise� when� B+4\sum_i|a_i-a|< �.M gill>5�'s!J�(u�=�� �s always�J�(remained upAR4now an open qua�on"O�8t paperWdis�iNa� (TMn%Vth1}))B���o$=CthqH s aI� sequ%��$��%��QT(s\footnote{!- author aca�l� s ;PAlexey Tsygvintsev ha%Q$structed (�I�t�["eH method) a beautifu� QexaA� [Ts]ASaB�1$hn� J/recurr� �#ulaa:isO�Ufro2 analytic"Q !@$ory}. More��ٴ6�go1�a's*iQ0[I-hE�)he"/ &o�� ed�1�L" !�$'s.��I1a��ͦ-�i�@Poincar\'e-Lelong9#G�(a holomorphse�� $f$,�C zero� $Z$,`0a Hermitian v$ bundle $Ea�(X$, let $S$�`�J%!^ $X�} Z$ca=byy�BQ=E/S�)! CherM$m $c(D_Q)$�l� Regr�closed�$X Vi(ia$Q2$W.$dd^cW=\E)-Q)-M,$a�re $Mpa>�fsupport!�$Z$e�.�! top Bott- �%��*>�zYWe�,cus�i�I! i&���rev�a) rel� � prin� l�%7 resi;Oa(Cauchy-Fant\`AOray�R%���� �(every count%�(subgroup $HVaa�pact ��AQ%� t � ,G$!Cre��characZz�v��%�s- �E0% $\seq \chi$E\Gd.%a $\alpha�  G$6 (\in H \ \LoNft&� (\ % \lim_{nF� }r_�Z) = 0.$[�ry��(� s il!@,ntinuous) % Ai�sm $f:H2nT$ one� %�F��.$(� _n')\io nZ$z�'�=f( ����..a;� x.8� doesM �R>FG�/ H$.\\ LetEE� Nai.Mco6jY]�+FI =\R/\Z$ av�Uns$H��.�U�.3  %�KerA�� �%�m nMH1q = 5} $%6all:��-�9) -�5}�s��r =�6� IfEf drope�iliLnd5y & � M�Ximilar�u ults�u�filte) =instea�$1Ts. Fur��< �ni&Zo� l"o answer"� %lDikran� et alAa \\ {" psize MSC: 22C05; 43A40; 54A20+"�: CV� s, CN�s, Dua%8_ y, F �0}K\quad\\W udy �6b�M�!1jy +rsia mer�6*�prescribe&�on \ Juli�;t, at le� � g4(Lebesgue) mea�/�con�ron�am��of l�ransc� ntal"� sɚ �ly n�'u�(g multiQ y,eof7eiA( esc�expon�a=� � � -odic. F3se.�eJŨto deD,a=bA�����N�not%%cas!�5t4�#��lan���m?[ matese�.1�MR<.\noindent C"� eempera tochas! I!s��.`ph�com � regime)�(Markov semi�aP_t$. A!da��nXQ�ly* pr\�UE�d�� �� tpbehavio�y\d_\h l!�- I�configu�n $\h$!^sj �om ighly_ �e�A�$\nu$ (� a�4duct Bernoulli9or E .KGibbs$ ). Exploi�Rgress  �� siu�mix!�ofte Carlo1nchainIdiscre@pin)�si� $b$-�,ree $\Tree^b� e tack�he aby1���I!�hard c�gadepi�, s){d�8)P� bia� pr>Tla+en,I va�&L��D�B a}mo��  4 �-al��� weakA&{s .R�6:�l6� (pCe)� ��Z��d�Oas�va� stretched.�!�G%�$aJII&9ex�Oran �*7!�i��iW Glau�-%%Kai�,�q A,�re�)<�$n H xJ to8 i�!�a�scam�0Ga � true.�,b���stDng 1 E�!R� aken!@0 wors� lt�raA>�sui� dieb� .�[s�j\sC!Oebra e!a"m2�&�a�aEE8er sense w.r.t.�no�.�by Do��her%�RoberJ ssig�� zsmA%geo�!�"�.���)ng  & l�"ob �m�m!�bqc �!A� �: AC�( cros.�21by(�^d�+ (non� ,�c )� of:Yaut�sms�e�6��ppl`#^of�%Pg��1�2d(. \bigskip �-{\em ]Subj. CJ $.:} 46L05,8� D35.>7Key� :} C �P�� s; Tensor%; cate� (es; $C_0(X)��E� s; V.j s.�I�!]�do�7+�! $w$-ideA�s� isor*A7�#pr�"�!of,E�tot- diCq�&i�rB��&�AVg$PvMD$�� MoriU.�It` been8!�Aat,�alpolynomA�Eck�� ��quasipo?e(. Aa\�4�eV^|detect2Mity�t{p��9�*�  ab\Va� lievy�s:e� b"nO�$K�n� �%u"�!��*#F� $Q �Nw of � les�*�r��'�.de� �K$.�śis�I���e�kA�manifol� curv� �efine a pw�o� s $c�M$�� <v ��0!S$e��$c:S^1�\AA&($n\ge 2`S^1 �X")."] $c �*J#C (space $T_cM��at2 inclueViM � de��2 s $h ��!Hc$; � �Riemann�� Fins�D� s $F(c,h)�It5W$M iM&��p L 1�c $H^0$ YX=\U(|h|^2ds�normal>� $c$;!�)�!&& r$alr*%uf u� e|train�we*��A���n%Al ver�Yj.�.�Rbxar!Ps�!awE�;Boltz!dE��" have�l*Fiy@(ST, LT}y�e'-�>i�9 of�:�dx hydr"�  x� �*�ŭ �.�*pur% %�ug- o a� YitG cripR 1� i�*ALa]< ng5�"duc"�)de᭥>� !Gbigra]#module�eda� t���%�coi&�(eK�,hyperoctahed��g0s.��MU a von Neu%�a�&y a HilN q�\�it�&cyclic�se�*%� unito$\Omega�h�\o $faith�m �(VM$%�� 6 (\cdot)=( V, )$.` j{N_i :i��I\} �&5.�sub �%�}�>�"aalU (As $E_ii����'$Nsatisf� �=)\� 6!�e �=-N=< cap_{ } V��6 pro}E� $e_i��e �!��A9�J%A"s�vera� {N_i)M} �$\re� a��) � $e�w���[ aYv'�� 0of V.F.R. Jonnd F. Xu�Xu04}.�m�pt>ar�*eVroo�-|*� t 8)B$��At -to-Bor�o�c��tw ^e�Nichol T �di) type���a�-(�"ri�) \PBWF tor� is str_�F x b\#��j n��l-(ELrank 2��V�*� rm�.�  Wv&: B<t�e oid, Hopf�P0, pseudo-refls, Weyl 10 MSC2000: 17B�)16W35�� �atA ��zsY .� L� s!�A� perm�+f2U!�AG cod�B sameM�&� A��u$Wesemeyer !/W} beyo8,�&|ar �s.��/ a q-chro�*]4on graphs, lis,0mK[��erc �apV s#��ulaa�"� � chordL^�en3�e4R�toco�)e���off Pis��(�i�0exd.yfKaMe_ram $\� !y'defeaJ 93o ator'i\#�/powPg.w� 2�$�� !�omb (e�%#~6�!!'flows'!�&2d�.uA0ma�lf� \sb$�aisola� ul�o� i�l{,flat Lorentz� 3-&� \Nq said!�be�if�lif�.a (�)#�%�0 $\tilde{\sb}n   ^3.$/0,mbo callY!Q�� s��o�3y>x��:�!� F�hhee!%�.�%(orA� per)5jimm� s~g%A!�entire,e@  embed� 6�eK9w ��/of:�_of&�. W@1if�m �f�s"-rH �B�6b �����9�Weier ss>� �@asympto�[.�kingsuE�-in�"� � �4eCQ~�z]l^3m#fu&� piec�W)v>T�.�&>� l�� �Vor 1�(6� �nt $�!F��5��I�6�k�( \'etale LiQ-ou�z� i�Aop2�g Hochschil �� nFxn��a��erm�.� e8-\$field":as�in�Ca�@oidE�iK �6oY�Cve % sson9L�T�  en�s u�."4%H�.�F��Zz. T���6s ���-� (co).a Nf�de� b+5[ ropriahea�Pc�'j�6X �G� 2� orbi�cnM �l� &�2�!' thus&2 �"� zFUNeAzBhe��7ᾑ�H"0�� traca�!�i� :U���.b� �<�); co"1 "�Pa\:�j�nLe Sherrington-Kirkpaf kEelaxa�ex%gh&|al�p�E���b5� �� �i�ex�!J``one-�d'' di2� . A�e� !��� !<�\r c�he log- �_� L_m$*A�!�8v om�eq.j)?� ��ݤellAc�  L-_"�/vanish��} l�,��)���$G*m Hypothe���� a"�,E+e"O.A�W� � . %S� hVA %!B�%�5ca�7i��yet�ru�u-�:mH$-1$�A�6; s.�� G� ste�;+,H$E�! of�ner<ve�`eg�#,$H=(1,h_1,\l�/ ,h_j=1)$"�<c� $j/2�' at occurs�1�A�degree� �9r� l $japnd{p Arti � $A=R/I�A$R �*+aw$r$Y�%�$ I / k>�:e2�<GOR (H)$avjxb= chN� quot��y�25Mh,b�,aY}R��A,$3h-b-17\ge �:to�Z��kiR!�*.2(frak{C}(H)}el4w�4 $:$\ et \a:�N�Y�m�� �q����a �5�����$�5�I5sev*t%�Th>q�d� $8!�h15?e _"..+f�s:60 �2A�M. Boije��ir>de�n�'vm&� c?:�!g�yinRfO6o�<re �Bj2}, [E n8 C.38]{IK}.\par!,Wof  �*�re"B,I6%�n��f�')ɗN�th�$�{Kl�%A�Go��uM���s 6',IKl}.�1���e�6lT)�hips b;thetaՌ��arbitr-%��th;>deriv1�&e map se�&{belF%e2B�a~of Ga)imaJ6oD0G �$2�-��9~�?_�$/ GrassRp( 4�$n=1$go3Cgot � ic i� i�A~)�p!{1A�W� r�, c��e��!z �Jacobi's=^!����!�!9�.A 9�up]5b8@� u� a0to�2>9��g�nne��' uim)��ǡ�YFB�'4in�8�+�)� (Boas, Bellm!� nd B�eriwC&)%!)Hadamar�2OA5GY�a�A�*��n.�2�) ``EnGf� erbo $3$"��uld"�2 {canP;$al Wick ro&s}, sLyZ! ef�! r�#�irc#�� glob� � �%Z0&/g �?� � e.''ADdevelopF ons0Ct�=t* {WR-�,alh�y}!�3D� A���at,$ c� 2)iz�6�(gu��!hmAe"*���Hs. $\Mm\Ll(\mh^2)$-�!��"a�0(.� enco� by {�+d|4 la�=s}I$n$, po�Da�&�E�"nyI A��e, to:-f�q&�3\Gamma�� $PSL(2,\R�85V�&cs:�&�7�%�,� �Ga{�+F }:U towards2_ur7!G{�ed}�a� N !�ve.� cosm"'Ek}�bh�{un�: sal}@MC� �� ���*� i�*luGa� s�@ �]�2� mech�m�T� rayEjC"��Y{zic}�� .�we��� e ``ݲ''$Fa)ea;DayS�I n,mDbux-�co act UHc#.ag�,t$Yg� �ne, 6n* Q�i% comd area, but�-k�)-8ze {broken $T$-Kye!AdSnW�{ 4ed {earthquakeFlure}d is help �5g= 1mK�������eř��E��;2��.�k0a*C�I $(G,H)9ne!"5@�8u'�6�d!�; =� H$-&m!�ap6{�r?*� $\pi� G$:\E�m�8�f�<�wh�0or���� ��_.b�eda oniDc�8�^�� pair! L={R}_{E/F}{GL}(n),H= !#!�� F%���s/�${S9$E���p�=&S$(.q 8q )� Gelfy��$t od�� ev�.�) B���)����9Mm� t�'neQ s%�!f(upercuspida�la�H� is je�j@Dipendra Prasad.>J >4iN�BB �5of Pexi�Qs.m:�I in Banach�ulav�,b#al� ��k%y&� !#$Hyers--UlaJK�orthog�I�:��al8� ��� $f_1(x+y)=f_2(x)+f_3(y),~~ x\perp y$�<+$%�6s���-4of R\" atz.�tPr�"ial�d�2&>v��$+f(x-y)=2g�2h�.�s9LeXN�<�.e9Jj�eY$f% A�`�� (baker-ozel}�P�7Fredhol-Gdexɖv� ed�%e�!:Quille�A"i cobPs�?�� in�ual"f�BB�0�&�*��FthA��&5 a�Cpush-for�A����xC�+�9map�,). cenap-isr.- Quin!T7!: "B(%}�G�-���Gi�:9*��"Y �t �\@N�ll-�O�%���HpF�e ThomB J1sA�x� �DH sf!!�J���r@sN@�'2>&U %�a�&r&Z"TGys(5ap� �TE�)v7 }, C�AS�5van d"|� �:~ o�8�":of�Is� $LM�a hohe!�R/ �4mJ.�"mx ����-S�JZ5��"hM' r�Prucd �%��$e�Q virt.)})|{m�%5:Lw�7wI 9y��2�ies.�)�d�d�d�d�d%y���8's�]%� 4hRU�W9�m�e� Q] �\v\R��[A��*�_�_�=d. AfySwe2� � �@&�^�a#CŞ5�8 ��MJ� a�Ѡ8a�flag 4e�%����<�o Vcal4V.�4&� `D�ly"LB�quLD' 2roid�Cn ��� �G7of \'{e}�"5� �u � nal wayc E�oft��.1�8� F\,4>�8ic� t(&!�UZ _&�""� i� ve|W!/Iia, cW� �:QwF�)��5M 3/Ja~�Z?9�eeE!�%/��V���Lm��)Q!��6�$3 rB5!�Vvalent!j>8cA � �=tri�9y �monI'-S)C A�kA�VQ�+1dr[E2g�mu y~r�}cerS�"�>-�Y-N�ek)�� �'�8�-Pnd valix&�k�!�(.~*w!'�N�a5.OYo:�N�+subE�eZ@1%��L �s�%&�-��emi'~�aloguI�aho�%� ��:�` \ actic%�A��Ri����'to�.F!����-H._�i,A\�F�,]�DOvi@^%�u���)�%#�%�J��M� Gm�!F,9AW t bI?�� 3iLeXo3UrH+a��.]52&M'� �ChorouA�d)���m�Y%�PBBa�< est. \v {0.2cm}\\u/;��p+�H5zTXc\-�,:��r�SnB�/%�J�2000 M��.s�;�9�;"&: 06D�Y 06F0�Y8!V20L�;20M18�;A#@54B30, 54H10�PK)�N��N�:E!Hurwitz/-z�1o. A���p��i�rc.�:o�g� �I�$Ee�=.� AX�$-� �2��Kde�;nI�TitA��&s summa�DFowe�O�n�Cme�T$ $d \geq 4r8��$d$2��1x�*��x6oy,�*1pK, L�:>ice�, n adT�'�]�0� �X)�lat��p]���CP :nex��#RA��P�a��ex� �+B~�� nbum�A� 6�u am�3&lytopes�:5\e�ZE) int.> ��{Řo-&�languag:BI,m y�+a�]rp.�����,&r&�>�$\Q$-fac�_�C oren�&c Fan�b� �PicB1 A{�E,`w[ed�� EC�-a�#5�-�.B�bi�9a"lB!�c� u u�&�F�1�0ms{d}$A�%x-)Va��+W"9�"&"=���<�1� u�]�%��� !K��" L�d case.�+&C aJde Rham *�+�n�,$\mr{H^*(M,  G})�w"� nume�#7i� s---a&p�:26top*�$��"�? �*7�Hoi�5 MyJ�"&B Betti�be�6Aa�� ed P�>ar lemmaOJaFEVa6!�BirJ$ Mayer-VieA�Ln�p�/AA�^mp�3ed BockI�mak�u=�logn1uP9$+�a�L�Se�!n-�)I>.p� a, to ('l:h.�� i0com.�;"QHU_q(sl_�*f2�a� Yang--Bax�� �� tud_0A�0�cA�!�%ҁ���uf �2pin~$s$H�]Is?so9o�,ooIoQ�,R--matrix {}V"�bea� n�b!�d7 �Q�Lf\a\a� �is&� e����V�to"�%��u�/"9d& N7! *W z����bb�<e�a�xic~$q�)�s $s\l�Z{3}{2}[�,fu�# �BV' [Ker X�����y��%��s��4%��Aw$.v.�7no Z��Ter{ s.'-� ~p�L@of B.~Gr\" unbaum�Gru} ask!����Tnti�S mass�� on (�!) $d\mu�Q\, dm�Ah)bb{R}�B�� @9@7#�9�^ivie:4| $2?��anl�L�is ��aQ!{�?t "h $n=3$ � Hadw�&".�ZCq 5$, ( Avis�T:ARamos}�\ MM�h8m�a=i'�\ble)e�i- 2�4$a A0����-h! u$8ma�\!]4$� � !i�e�by $4$.l, ^c_�-k ic�{"� a $22� , af�%u� $L�.�4*@�1i��xut ݝ.�I��relev� !�nm#Z�)at�� ��i"1, "A&�It*� m%} aY 1��&b5.&AvKos�:ke'�[ct*e y&�-\EC-Ix<�Mrk�*��r�'n6 l�iqu}mal�d, .; ry G�Xs%!A]U�_ s TootQ�Knu01}.�fk_2�=�-������4�p��D"e'Gs6�AxlT�St�4 $C^*& J��A! Dm`GsB|%i��ec�. �cif_!OZ��oB�o&s\cA�D� ��"A9�5��*v 5 s�ne arlier1T-<�^s,� QAlud� A�tZ�>� a�v�twU(dN� �! M$.��?�+s�`Reck�Fd�dl?8!�a!��L"�*�?�<� �!=m��"�# ��ure!! .�re?#old-? ��e��B�~; �9�� _zQ�o�_ s.��cq)� fo -f�T�F*mew!�inZ '),!td&" � : Eac�d� vertex)��k"yi� vac���) ccup��(�P. V si Ub� em4(at� e $1$"+X,�$1ehitOl�'�4\lambda$��@"�tan�p�eC ys (� �)E�� clus� 1�it�A)N�loa���j?�@DI��H$1- \exp(- t_c) = p0�J-�%�A��co�`. %(I�>ta%G� a4�5M�xn�WPG %{� out}]�a�+)�B` w�.emerg�M IntuZa{ima�{I�if,�fix9Ct >�i8e%�si�>�Y1mAI$0j $m�t$�f-�.'esv �U��"�0%�e!�anI�$O%2burqNe):$t$u��H�pw.��{ɺ1�-ldu&{W ()�wOn��4Mu�:la��bqL\�i)V[\�VlhN@!�I.:,�9!�Freplac:*".� !)�G)=�{�T s.��(b�jK&}����,-ljU b�A�a|F-Y/)�� �0��colle"(;� Fs.�l � � DS}��m�#E % CWIF}. SpVt�� %i ly g�x`)G6 <�* wiseC-�>ugi@� m!W�V,$\{ h_n : G |Q_0 \ ex� �� $\R$-!�IaWt�N^ v$G$-a%(�t%�4H+*E Sela�ghorte��rgu�-.���Dɲ� on.�YWilkinso0# shifJXeG�V�xn�4 Dc,�� ruN�v{APE$} %a (i.e.,6;� �mno.�Kpr0\A�e6$3$0!)�2�Kubic.��.$!rN T(tri"L ic �x $P_0$Y�api �"� 57 Viv�7b9�?rV(t!�a�l1P��to ��!A ctlye ,+. A�.�5������.7 $\Xxuini�9�.}is @!thin:�!��disN-ar�S\Xx_sKSe�T!E� �6s$�@�7-!Canto:Z�2 sign5[�: \NNiH{1,-1\�5nA� tep �s���{s'eu |'��t leftMށ�s�_fOy�Y �JF9vm�@in�"ro��TKbic!Ye.N��i�s&{`!� �by�-daa�*<��$p jo2?A�w �p~�.heA�nue w42�x�4.�k"�-!V2�TB4--v(42�Ds!.{�0ari� kernel� a no�mzZRspaA�l d&H}Wi����s.I}P�9�Yevo���$stgTe� f�$�8appea�'Bt�"�=�Vo9T]L. Two "�8L �G=� tail2&�eס���f�!�/�e}" "�!�](a�&u�he� n*��z" ��)�"7 � Q s.,�.�pR j%�,f�e!C�s� %AiA9 Meng 1nd�ewicz�"u!nd�� AJ� EKd�J(�? g e�a l@�!(6�f�8�$\sigma\��by�"�4Ba�s� uh4.�u<R �$�Hetrm�zYu4��,rm{Split}(\Lo, )�Hu)3 �0H�� ;} ZFC9C�d�b1aIe [ ��b2lb5>�.`��I� �em)M"g !�Wol�fsayc8i�a./ s�LKo-7ry q'!�$Teichm\"ul %�E�~o�~Weil--Pe�.KX {T�wL n el|<�\m�3I� a$�o Our \  ha�62�)treU � UZ�@-hoi(sp���one  toru7Rtwo. .��"�MC �M$y%a6Rad~/�0�) �pI#+4-.X&0ve�R�#�F� iM bb{CP}^2�VSz&�*a G�#�Yax>j,�� 4�)A2�)�T�7� �hom�� M�Z 7`^ my� ��%im)1a ��~@of�:w S��E�E���>�s.��YG�X!0$HeisenbergMefal��t�y! $3 \  s 3$&� E��(�R�@<%�'lyX �F `1', $Mism�by%Ta�.�&�2�N $X_1, X_23�c�� X_3 = [!X_2�F 3] 2,X 0be�BQ�ao6rie�� % i�� , eo ��.a�{\s o}�)lZLb�)Ac *_ 1E$\3C� A�v\ �(&"$ �Os ���urbIhH�S N{guarant uv {�F is�+"9� �ngi�iA�! @�8I�2�-8��+N��h!�)<)X\RR^n^ e�r"�L turn'<6equ-.\7$�!mO "�Qa6ced�>xPo�P�;a�ym��Q�d* �ng�p:SA Dira� �@ $P$�*�apjKU(1)$-�32b4T%�t^F-�C� @4# � !I),w��%?X''uO� �on�n�YE�1q�(�*l $P$) �ed"s LQ$,�+h&�!6L. " Tgu�by"�u�i�{!rx���k!��acE�gQTuos�%)��%�>�N�6:)�!!���Zt� � � �w(.�I`�a t �Q.M�b"�&fٝ'[� ex�eK� $\C^{n"K.��"i�q%�.rJnal}$-N�_ :*�\D�Br�  &�OaBZ�!R�bX Levia'd $b\D$;� "<$h\$\, n-1�� (M)$�0���Qtly\--6v% a�0to�).r��%�yI:�V�>_^e&�i>b B��;* ��"�)$zero eigenr�%7��/�;on��j7%.=5)zK�����i��+=,plurisubharmgF hu��E� qCX/�==n�.��&�4LXNan�G�\ oria�'A$:� �zEN\gsp(4)���0%�feM�gl&��f5��oa�v�M�Do�Hed "�~�>n*NB�[�6�A���z n axiomaAMa�Iarok6>o� Cox� _ �- Heck�&�ls�;�bewhin~CU-I}. %T��; carrtD": "b*'on�:�"��Cavo�$%ńori��o�k���� ncepRM�*as You���! aux),;�\%� a%�%:�$"j����EH�U�B�A�&)5 "� -de����ult�6��P��Itq$ f�! 2h� #�e� I�X�v�&�f1'!�a�n9�Vor+5}��b��U 2� �)% �$1/� c4by-"�;fb�@$�aof!�HA5s-Kesten"�>��Unour %�E e aie�%�%��tod��_ tech�#+)�f"3�/.zppl!tt�ny  ar2��s,�b�4)ur �Ed� N�����*w!W{"�R��"|m� link� �o�$*�K �G��*� %AAP s,�\��"�T�,�3i�annuli.Nsame 96> a�da(2$-�RU<�Q �HJ�s �.rd��8two-�� d2�+e��7��r2Ji E p4*�Lu� rom/ Kirby+CMQ �Med*6^p ,)E)��^n�:orcs)Turaev��shadow^Y�"2.$R+ �� 424(37EgHeegaar*�a�5��rpi��I.5s.) W�Sr !�!}��* ~�t�dl:P*�B�D 4I�>�>_�&� �f�%nK-^ɓ�1��gr�-"zaL� ^{c Ki n}$.jgI�~E�-�%5AE.b �}D�SKE�rabsreQ Ev�Ef�5!:co.}0O�'H eucl>Xn Mahler"�*H�\H�9�emm0Q�m �6ass�7on&�}"9. S7}l��3 �&K���ks�.%aZ�=,�^q 2L- �g�J��*GY�b� Y���2ri� Homflyp���q%�W�I6?.�~m:(�H���,8a)3�,o�m�/]�ak"�4&��of* t�j$�?zquJQouta=I�p"�şc%?�|�Dt �)kinU%.�� �[.@"-u�$�k�4&�+� Verblunsk ,*1�obe�N$a Coulomb-�/ decayu �śno"�+A�ti/ .��a �-$ Iwahori--2� �j $A_{n-1}$>Qt�1RRbrT)� $B_n�V&h genessvF;verx&g�!o{ %g��o�Y Q5>� �pAnb'al* ��K;!" ,o.�|&�Gp� u�&*�� �e�E$ll ir}2�>��\%`!R�;�1 i y,��@%*ic�6sG q$.�eA � �verview%��� J>3!����#�'�4�m"ga�"�V><0_�piZVes1�U��n�ѻvr `a Leg Mia~#to����%��" � z)�ork)�c� ��-)!;�18.,#�d..su� .�*�"��E/�rij ���8n�,t �gjur�S K\"��(cscK)� A!_EeHM0! t$ slop)mi"�. T�"7w�R](� ,$\�1�"�9�%� eachE2te<b"ZSe��if�#scKg�mu(Z)\le X�ZaGsHӉ�� �3n*& [Ps�I5� $�do-\��s,�@a*l Pezzo���*D�afZ[ P(E)a%B'2& *��a�<3x�E�:q6� �s"ʜt]! fibr!\E�$E x)� !�l�} (aZ$�B&F��_� Wru�{� al:�a\ c/nA��:�a9 �"� O!xB�oZ%'E\U Ms,�4���$Calabi YauU�M�:$c_1(X)<*L$q �i�"�0a�(.� �"��W~Xk���*��G M-Mumford�<���r�����!�+����rW=$(X,L)$;AF��9K-)�'SE�e����9m� &Z/e&ro�%�6� �E�=!u> y�;e� �A@]�I�a�R�$Z�`X�a�& |B'�I-Ya�"�k��Ü%�alwL :1s=�v{!� V�a o)tal?>�,�a�"�  ("�&a�*7)�f&�9�!��{S�4� impli�g�q+$��oNp��edb� G_\G>ag&� 6 �he 6�$7A;a"�  $vw=wv� El�*3adjacA�H�� u�%N#$� se�N&�b ~� �e�(first)!�on�%!�/$G_{\G�'5�o�R=4L.:%??? 512.741.5, 2.7 645. Raof�-b��u��&�"t"�o] @-�[ L��&/m9 �M�Omi�."��i#�!Ela {�}E�kP-k�'=p6W�6�DC� $oDV%���S!o"OcC ����E(,6�}A4"�!��'2�:��gSe !�?"�D>P MȆ%XnV e� iven-t &)cU#"�"�]5qwQm z�B�"�  �J[��#A��.f.f�5��` .eri� A�3a��rA8ovn?�{K�!aV%MdD��S-sa/h�B:\ $p$,+;�Q�:X$Kn�"�&{O}_K��2L��4r�!�: �j. �e$ ab�:'.miu7 "x8$L�Ls=[\log_p(pe/(p-1))]e8-1*lZ@/�0$l=2s+v_p(e_0���)�csc}�6�L$-6E�|K �)~B0�B�ie $J/J^2G=$TÐHn$J�D(augdi�� BNhBEV%M�2ne%�al:Oy�^F� SK��A����E�j!����1{$ }[A]�8K$+�Qife:s�BQ j2KK�H�+&ES$H iV}\�Pname{Ker}[p^{l}]_{V,K��f��fraE�L/p^l6)^myeTH_\ol��� �� m��rO�� nice-looka�� �{I�mrp8u�F�� ][B9V�9�>�jT!m� ~%�~uni;�w,/aw�veQMGl(\mu_{%U,M}!%.M�?�J�,�2�d&oo)y. .NK���wgu��, 6�,6h6�,>�|�le9E�L�. MSC�L,: {14L15, 14L(14G20, 11G1S31}.�Ѥ e bi"/ s^rigidl AononŹ�4p*ia-AP}^{6l�I$6$��AMat fp"zUdou�5 s.1NF2,LAyk�'s�u�� a0eF.�tu#'�%��P]�$��re�us�A�Y��� � !kv  (�&/Oorp�G& s��l:����-!n�w)BsA�)z!$�y#V 1X}�f:��Y�)�$p$-adc!J��� 8o�[tHItKZk�^p��ly����!�U^���5���*pr�l� desc���P �.M����B��i�&!� � mode>coa.��i1�!�q� Drinfeld $i) %4u �F&'B� �%"�s.9>\m4(F ��U@/� �@ma1�z� us 0�R2 G��v-W�&v A a e�5 * .�s. �.N&D6 aC{!A4$wall-Morri/M�22s2ha�'M�E�s.� MSC-�I: 14Hɫ014N35, 32G20��!�ps"��!0�t&:��Q�Hankel-�*�v� M�44*?ir.&�a�)�i� �)9h; ��6b�#aR��$�!is"[} |.�>z(� -:�e>!Aa2���a�8 ai��n�(h#&!4ai9��(h��ks7n��"/�2[O+=~�L� $\BH�}�=�.-�;k"�Sˆc9!> ��q݁�e�h<. Aߐ�v%�to�si-Fuchs� "i,A[&���F/�{cYaptur�!z"cG�@a�A�e2�wh&s.�#�ilic.3$-�}%^� �+$C&meY��3$\BR^:�:�[que>0N/�S��%�� e%i�$$G=\g!�bw�0 2 �s .k$*G)$ i�.G��r9�hm� run lengt�a Hami�N 1��_id�7�.a +um:$r.�0a��oecu�>�T��sG no:v/z.�U;E��EE��"�(&�.)MAT�f �2��I� ;1p��%>"R'a _e�.A��*1i˘) *�5k(eac�)�9�s �ed; (ii) l"�8$\lfloor k/3 \r +1G|Q%i |I u�$m $p^{r_i}��g�-ճW ;� (i^t2Bt:ui�R! ��.N{q_i}2~:y.�R�exhib-�.p tk!2��=re�? $D_k(S_n)�=�un�>&k$-8 A�*��� $$U_k^{top} @�Fn��ar $S_nJ3CW� �#�,�en � � by Ab�#nd Gh�V �}E����L�/ �7%�Agu �.�2 betaa��-�).%$br2� % ,c_ktq�\�2�2!(O S]4$i_{k*}:B_{k-1%,c ) \hook&�� B.h bv�>$�$��uely.��8q�a!t mula\ i_r���Ea��=m+� t��"�k&�}tm *��+y� 2 KE5<L �"�JAC�WI &dzU a fOXX3's�� �6�.<&�,�(2]�[�Y-=&B%#!�KoornwZDr-Macdonald $BC_N$m#2> Askey-Wil� .@���-�])�A��.e� w�Auge�  0| J} $GW_{nD�6*~ � $P^2A�blown�*�6k$�,F� $DKQ����&� �   U)e���uZ6�q�5ri�$$;2�=*��og �O�5I��K n� �5�0�G = Dr(�� )$.�� &x0a &w��/ $a�v"Q5���� �A�o3 a�K�,e L��,u-Lifshitz-G� E��� R{2} ]�  Y�'�?l�Z9�i�C� awa<9�$6�R ��� Hausdorff� ^~s�4!Ot#6aMrH%��0xi��+s>i �,*#i �5$ex���"t sJw�`D]�Vda�l�:�=A'�1�J!�m�snm=> /\8h��%fuF�B�C� i�&saZnf�O"( #�8e�A� quit"S|��acoda�m� Q-�i�A�targeH�|���6-ۥd"� ��)ahQGF7��m%ved"�O�B^a�6�<���A%%A�l<]�2����Jb!EUByRa $0/14�^"Q:�w2fcg$g� D cu�* �18 � !�us�F�^� �e�M.�Ga�`�Ixe� �9<s�.TWG&..�!=aH!ap< �1� $\g$�4Lif �3.�,\U_\hbar(\g)�A�-JimbI&}:-�uy env�q� " $\UP��u��#��6y-i�^'5�2oconHJcy ܁"f� �h6"=�� zers.�6^a}{x��r6{r u�!Gh drom����@�"r�R"Wg!A��� AW��$�f*�! ���c�XAZzKV)VseK$�rp:"0�P�`�1*.l�)(�NQ$m>u |&.s��obl�ygra��T!�R*�4CG  �8 Gopakumar-Vafa�r)�� �"JQ*5f! Z-ca!�X�9;E��%%g;�o&<��&"_ �1ˡa�K��! #Iad swerA�� �E�� a�`ţach!Ub�PE�~s���)� mirr�I��%V"� %�c%sAP]�B"ҋ!�e�Fun]mo�wsfhK k�Q�~gi.�!sRF�  5 �e�U �Borceas _^�Ta ���l$�D&�$ƃ��p�dT Jm�iVRT��?P *think, n�the�,�T.��v)E $q$-� "03!Racahţnomia�0�I;$628��r2Z.6[ium� s.�(a"�A$ӅarX=�$ian.==  c&�a��ZD$-ma�==\fa��anEnr�#"ѐNoej�rA�$R�!nn XF-���Goldie 6�"n9 }�e9g� � MOt�>F�I�e����i�E���Mk%uR/r .+�=�Z���+(\dim R/\fa="��A Br-j:�i_{\fa} >�>AR�B�iH jd=l� �� nSdSisRE��>�I!�!�R$  �� ]��pqZoudX2m8aQ|n�QhB�"n�l.�Q-.��8� ``M�''�*\��&��li���� !@��ѫ !�1���& W�wʜBirkhoff�" Floquet--& ��Benc��I�t�p}���� ���i=on� a&�%rr� R31� �` f�s"i !��� &D2n�nano- � &O!&� 96mo� . Ba l is>����\ �W"�!�Schr\"o7*�>r�N�!��*¯)�z�5(uȼM osF`ers) w�V��� B)��:-.�,.E��b2foc*2.% adia,F��pi�Veffec{W��2�1�'"15�5hUVl%05�!Zf[!��ZT�ano�0�h �ke �,5wir. etc.��dem�A��*wk"�55. macr ^Helmh��!^nn��Y \+!�%V��"�!�YH�P�a��on.x!a��6�G�q���Ois: ``G�(a bodO�%!%Ä!'loa�.�-to���P��4 Q�-�7) 6 nzt��pr�`� IYOape?''I� �S&!�l�bi�m� pr Qe� � � tole!�d mism{&�<��#;�A� desi� �!��p|tA-a Micr6 �!~�=xu��O� ``gY�''!4v��jB6��lt�Vit upgU�eM�=e��W�8"<����)�ir4�.6�6A��0��d �-.�:��� !���/7�Us~"4e��P)� � �~]�a�Jr�: 1��sALr �x^.c\&�WO,��I2dXb��nUr?*P� �BshO\� �*��g!_$ �M�D�� yp� n%�2]it�law-`uc�;a�%M|q lb`I�b�9 �aa�ample.�.60In 1982 Pimsn-�Vo� escu!��!�$K_0$�1 $K_1*��I��-'2�d_\red(F��; 0FKN�k$��o0�Settn� e�@�^*1&� :Bj )n�E��<exVDE|!AttZ��"0� 1. Later�r#�B M6� e���1!{)�] K5sy�� non-�ut� 2n�vy:K�w� �~ ; �ep\�C^2j� �N IEB.�g D2�Ei*��%|r�e,~�r|�u��G��!�%mh��+dr5e�B�C9&M\Ext(2�Tac�P��D$k���DB��B��7_�x��:��t�@phenomenE7� byU�Sil6+te�b"0�y :6�Dn.�Is�=� (R?!"anhoo�U)%"L��6a��_Z%��nd ``ex�e8A��&�INgr%�LbM�!h;f!H�gyB��cad�Z&W e�.�GUE, GOEA�GSE>� E` x co&k>.B���� ��A2St-\v{C}e�� �$\s#cech{X�a��c�&A��|b@pu$X�BI���6LA Smir}� Jt�F%4l^ �Yc�9��P6Ifa��Sne"�se�to�K _ )�Ez ��ml A� e�!��Hig R�� i&�H%[�I(.wCi��"_Z�2�6�4#:]1Korb�5N1C�,Dh���a?2`ehA"do�e*3r 1 N�d. \���z12p�k"w9H{MSC}: 54D35; 03E17z1KG. }: {�>�;^;Q� {\v V�;))]'}_� (Kostka-FoulWt.�$K՚jY4mu}^{\phi}(q)$��oZ7oo"W$$3��^$� NE� umsX#�'Y %�*3�a&vB�0S.$��r?iic%��,LD�Xev!�d(|nc}Peء?/*$B_{n},C$Ay$D �$���\� $\���T{K}f(ofjb. �F�B���(��3Z be ).����O Kq$-$ �"� $% u� ,!�%�<$U�$en���%t?d lec}J���&��{�!�6J% 6u.t��2"#�y� ��>�?.�n�2�% ! ^{OD)�noB�6�\". ���ݼ< bran6���2>$.$�2�wcB�f�c�� 2��>�9�1�,U_{% � K3!�.>J� diamondsu�]�q�"�S�.U��� )�J� x$% NhcUy� ba yaO$q�\�"&�sut(��Ok}�!:xl7A;�&4�l�pÚ&���VsiP&� B�ae7 ! �V���&}2�"ofAid�c�hhkU_|��x{ � $N^"A* 0(N=3,4,...)$ Z6��8|Ksub��HM�$q��Ar cPr#hg. TC"�x$(\�bR^2 =I)�cpp%YJ%Wv }$q�-"J"s ѡ�� �K%Vm5!�� ell׀&��� j2 $L-$"!Vik-7� cru�>felGˌ� $2N$� ral,3E/, �genf�#&�!�$L_{ij}!�#��Gcq��a7pYm� � $RLL$9!p yE� �A�7R�/$N ^w��!�ATor!\M�I*!�f*y"$3\_s3�M`%�Jh���� /eAj�� � �wH )\Iy�_th� �'�R��t*E$9  9B�v$N=t�"O� $#�� aA�y��j�o }�[4sk re�#i&� . No� "M/ :lM%�I�s-%���%� $�Ue3x k)\<l Bv�4!��� T,�a i%vABu��U�.&H;s� �gi8an $(N-��U�� �"�r#2si�C�s��5 g"�"K4,E}indAed.�B#&6 of L\"off�NA�(Comeza\~na,% P�Ujagin-T�!8e��ic �k;-�S �toe��~�e�VN*!�;Wiv6-O  a�>��A" = S^1 M�\l��� ���!�*� -���n�  p�2��n�unfi�B A�s�of SinU�"S2�T��3p!�&OM%-�iߡA PNeo��r G$.n{�/70:thlm�x$Wisi� egun!x6'at�O�*�C� �� ���,�(Stanley-ReiI��su  & aa�*ma�!��$� bTanZD�!i�ur9&emp'zB,�� �*|� w��o.��z;�S AJ/�xoO0s -�� -!�jkn�  G (-1)2�.J�!�t>:��T5�Mn�N8Z���Z�'FA�!�2��tb� Lu�8ontempoޤ�!)=.Du; aJ�RA�&� BD%JMM==��� �een�s�%O�1 atI���'��" �nd"�@-FI�� (a K�nneth!�y�A.q`.2�ZF-!s. }�>�&/K!�d�DI�in�S]!�raBq(*f�p.\ure�) ��.9Waar!Yi]l��"�do�e2�%�q2&di$-�hx!s��Fdelta} #)._i'�s�5�tiQRo��,�a�Ust"��F;:%��=v�yf%#q,�Q|��&�ffT��lmh�o�*� setm5� fash!Aas*� �'�$+i=��{!�"ebe��3 g(;- ?�k'�ffeQK�1< i+{ aE$� %�l�5LmD�s��mdepth)[��;A�z;},*�v}X]�^<a��B<2Fyf>ae^A�L@E�c�?nove��Ii�F�y  �E'2G���t�ultraA�v fy!^!&y!Z�zB��#� v�I Gi�o � -�"0�� uponYY�a�_�"y,�ZFC. M�4M�eJ�Ul�&\���:aia�h%�lZ�-�. 6�� � vSS ongo��`R� he Cefk�iEm&cy-Orie�_��s (CEOL)u�l!!F. >_. ,��ear��I�engag��g��a�Real-Tim�0guagea�&,�ftw�t�+�.e� e broadM0�!yn brid:S(ti�VCo� x�A��e�!�wLLex%�s�8B��=u�-L��s,J���i� DesigR G�L�#A��1-aim"nar��!�gap��W��C�"Exa9on %1p �S nd A�gev)� 9q9�A�y#zerm goaM��d�� !ACETTa�rvToo%A��'AI�� f"|e|��toC ustry,M�}p$sQi  dely.�+.�.�)&&S��i�l"@,�5F�L n� � /  �teleph]ex��g!�mq�a�i% < moto���#T��q�e.]�!m /or� of Q�i� ve D�� Fval0Ms,Ѧ�M��J. ��D> p�E(�(t �6�nv"?Ÿ�"'�dA��<� *e�~Yu��E��k p.����� �#��gF�vP.�b,�rvey, myak�f�/ �%!w�-�,<`� ��i��>m &��I�Fe `��"� f!�"����f2I�>Hrs�� �~%�a�� +$, Fr�che��%Y �y�tPQ�)!�per' DE�g�&_ok�)�%b*��!rA � d,K#�%F�*� '��#1�(*E���n�<akA@sub ��h]J��9 a+a2� t����� d}� " ,�rt�Q�i�rel&�� � Woft� f['�"].6݃c��xa�E�A#Aaa>��}u�d~8%�vt is�"17. I ask�:�'���"}/e7ZFCB�M.G�sA8�v"/h7KJG:a� ��e� l"=AexAlowe)Mmua��5ere��& c�W s_%>)�m!&5A�! Moore-Mawk�! blem� ���Vw1zi� Gg"!)��U� eM�%�%*�$>���B3�'�qB��&��-uM���k�n � 9��s1��%� ���ey�.#F�?IeE�6E�p��!l6�.a��/gN{�a;i soci�I1�Dirichle�f!� $-\�u�� (x,u�#0LO*�,|G%a }=�rPosZ�l�. ��� w>'��no��**�!�isF�.b�9not�%����#+)�[s��N{&z��%�mo�TA�ENR?��*moQ�s�;co!e:p��?A�i1F �d!�,�9ad �E�= I �:���&v�o��12.H�+��``Trace"K$Ho�/ ei���b�e�(��r&�:%R�V<�\s�z \lbr�M]������s (��- �5V�&as��dI��<���� $-�%�)!> P�,&H(�.���-z!��b�*o xKus�UN�"� by�C$3co6{�6��� E��j�p2)a��ANO� J���b1v��s Y � 5&s.��,p �&ۘee> ity-&�!N0�U��an�yI�Q3��5rV*Y%>� ��!�L�tz��1�NQ�cqS6FQA.��Z��ledg��gn (EM) A{/�Y�~!a&vA�half-� ���{*��aisotropy�edi�O��I�$Ew� � L!���_r"!s�e�,�j�-��.�u.8xr��! p par)���N0�F�0��9�I�2&Q)R-����t1�%'PH�@r[3so�4dL/.)�AmfR ai%�Wpi8�KoX$d the Skin�ner-Rusk formalism on classical mechanics!( first-orde �eld theories. The second is to generalize&p definition and properties of!evolu $K$- ator֏| using in both cases G\"unther's� �8($k$-symplecticH).�An implicit s�to�vanishi �Pso-called Universal F%( Equa�, or B%B�Oed Hessian, which dates at least as far back as 1935 \cite{chaundy} is revived, !Vder < from a much lat!�orm�)i@. A linear ansatz� aN�of1��@ partial differen e � s, p�(ously shown!3,have wide ap!Rability � fai}A:at%\heartwthe Ch�5�,ECis\y%f1�s evet> �w�.�In contexmx$2+1$--dimensional quantum grav�Twith negative cosmologe-constant�topPy $\IR\!\times\!T^2$,*4matrix--valuednA�onsm@te a $q�e!�,ed representER1$fundaml group)%4signed area phereA���cA}s 1xto homotopic loops. Some featury�resultaMgeometryu exploreM� as a�sequenc�6a/�mK8Goldman bracket!�dobtained. \vskip 0.3cm �|8trong subadditi%�8of entropy play~key role�several�a��physics%�Dmathematics. It ste�thM�YT$S[\rho]= -\Tr\,\big(  \ln ) $�a dA[ty`rix $*_{123}$��A�producE�@three Hilbert spa!�satisf�< } @ ] - �(_{23}] \leq 12}] <2]$. We strengtha.h��bSA S4\sum_\alpha n^ �(n23}�2.)$��erI�$J$!� weight)�!-)Y '���[%�%H$. Correspondingly,GreAKa�A�Mu��em9�dmap $A\mapsto \Tr \exp[L +%� A] $O(concave. As�� �we!� ve sa;monoton�LyEcconvexA FWehrlUe��Qqin��li�=foruCga�.�%�udy� de�@te Garnier system�w �s0Dfifth Painlev\'{e}�7 $P_{{V}!^W܅� two4�%�cular��, !�( transcend���,algebraic onNir coale*cE�uc�z!qdalso investigated.\noiU�g�� an altern��proofp impr!�up���A(S.M.~Kozlov͙ko}�deals��A�a4to3M>integr�u��7�7 $acous4pe�$\dis��`tyle H_\omega=-\nabla\rho  $,�#botto��$pectrum.sE� att�o� unusual!  ��4 .��LAcXa modified Fueter-DiracUs��y: In��0ordinate-free�� !�strictl� �i al way it!�possible��D �all%��&w b are rad�sym�� ic w��re �edp!�3-�n,� a ni��U�stM� . Lo!m�`sa�l� s be�n�2 ally�ta]��d!Nm�� by!:er�� commu�� ve r����l ern+�on-art!6�  ;h�xnontriv�l�iz�� . By0 left%�r�{�Y!A3� we� qui� ty.�Ews�wsharplyhed> tors, kn asa DHR-type, a nee��0 observables,%@0rbitrary glob%V$hyperbolic�!k )U� $\geq 3��hoMPth%�e�� %�sA�happensw Minkowski c,� \#!� blemI�a famileV�8sIl!�lynom��dep ce� a��xD am�A��r]�6�a� uine�� �R-adjointxE�discuss p 2mn�����models��!�Wa �. � smoothnes �P.D�4� h� ew ol�3� � reca�� �s!e^0subject.�DparabosL fermi�]seNye<$nd endowed)� Hopf}�i����!t%Pco.�co� allow �A ��of�!Ai� (s Fock-like:�(s, built ouUzsi!�sta.o�4� �64��2�� s ris7 quadr�9of^anomalou%��\hW��� g"�d Gree�8.�T�JF` � n in� al i��_ GnoI tool�6u5P6� ofI�eIl�mrandom HA tian�r� . Af developAӁ? � machineI�orthogopy�method,��in mo%�tail Gau���Ensem� (GUE)�aE#dig\ exa!�.8 pV9 bq�Planca�l-Rotach*} � �e��� �!�reg}��emploc n 4 a�ᚭ?GUE�!l�� cour���gI]; betwA RF � actere*2�of1�"�I�i; ac|�of cur��earch.� on���#�i� � -a� t *xWA� dedu�4��no-ph� Q EA�$rodynamics��escribF���� t �-&��el� �e T�!u&� �ysA8 welltho�'illA�up0� sea��is�� b)� igin0 q�� ;ina4a��� a� . Si��we G �/Hartree=IapproxiA�onm֩�-��hale��5!ہ61� nk�O�ors. U�2$Bogoliubov� ���1 !�%�byH�ix-Iracane ({J. Phys. B.}, 22, 3791--3814, 1989),e6ɞly es@ish)�ugPDE. G��nt��i�I���Sobolev( %x sufficienAOɰ&? . A��Fi� -�! 0 ed.�qu��&�a1ucal�V2����d+�� et� � ! � Ak, �!r\Nambu--Jona-Lasinio(NJL) 8��J�isE5na�H��acaV extrrm�\sup�a!d^g.inm�z �ads,lea ter5�WKB6� ��!8$guaranteesid�m�mean fr2� N4.I ( $\eta-\xi$I��ugges}by Gui�� n%�a 1988 �p� �9V�wo�! (��i�voiM���� !\��a�"ShZ��� � ��� k�assert]sb homeC�cbbc{*}E xn2}$!I!�et!�z �UWh� �mb�� a Lief� ur�us� �A?e� *s,��!B) �"%�wLo�z 2�6�"�;an be f��)q%�-�I��'� !� abouSembede8� subsR�_R� k� G��ed� 5BEuclida YI� �"Da{ acre��k�a� r� s�stildem!�ars� ly�7�!�ulaa�R� re L��reU�@.\\ Keywords\ \ \AnC!{RP,Y=, Ima� ry)i�, Real6T)�]R}va��!� titu��eLnd te �gyrt;A�6�$|z|^2$IRmaximiz� E����� l � true amoulf��de�mQ�ŧ�gaugem"zy break ��---�E�had@v� ly� e ve.����� ��3i�-vort�Ien�Fr�$luid gover by Eul#�Áxon�CngFM#4xmo� �:tia��zero. ��%�m��ᚥ$otal colli��I C simiJ�E Ire no binM9. Also� � regular���r�  ar�\ H#configu��!(exclu�=Bs)��� es�"� s.�A&Q5� circl-D ��c��3Xon \[ \Phi_{k+1}(z) = z} - \!�� {\�}_{k} %k�N&\q$ k  0, \\H0=1 \] For each $n$tak�KS_2 (1, \ldots , {n-�i.i.d.���sz� �i��" disk!�  $r < 1$E$]1}� �^ YE�!G�$��GdgJ��i1��s@rJ�Al�"�"���Z$\{%jn\}_{n-�\!tA$n$IaRe�$ 1� !�f�8��]N>��[De^{i \theta} \in \��al \bbD�e9"AtiF�i�erv�\Pize $O(\frac{1}{n})$ eW2v�s!l same�Fs��'t:�uU9di9�F�< (i.e., Poisson)!�is" ��,%� 1v,"no �bm���5 q��%~.���eff� mass� ss/$SXPauli-Fierz Hamiltonain� ult�&8olet cutoff $\L #n�) bc [m$!�non2~QED Kspi+han%�P"c! A&�6�� �i�up�!�$eI�j /d&� a�E�-0s $a_1(\La/m)a�d2i�͋�/m$* $ �/m =1 + K e^2J, e^4+ {\mathO}(e^6)$ �a�n�!��(�x)�!�aenhw:�)~ղ: � pos�&��n�(b_1,b_2, c_��c_2:�d b_1�%\liml if�}{\log -6}*U�  -cR=1}{ 8^2 :-c_2.$$6�:�oes� ��$\pm [� Q]c but $- ^2$&�)��we <(to�tl$m%%f���r�%as��N$p clear�� !�"!�"�liter�!e, gEj= )� n.N� T C' sense,e#�o(p > 1$. Our���AA �s�$sues  �LnewoR ive��e4($\epsilon$-&���!s` "�m�!B ��o&e*(to be drawn��'* A cr!ia]�O � qu�&.nAe�=�e!�e+ior��-n�'bourhood ��n8von Koch snowflf curv!�pumi�j��fun� ofd}�o!�ch quitgosely�� earl'predi?s��,La-vF1}Sw!�it��uld beD ��&`-mprecis*�A>`tu�r!'8ex �A<er)�!, Four�coe"%�a&�non� �-d!�iodic� og"& � ,ndard Cantorir� 5/A,refu��.l a.I�)�%��(ay��\"�%c�&�2F9���-%���%�its&*�measura��.Sp) warmupEt !y" R�-� in�,U� $y, Varadaj�h'��Wilso 3�u`"j Hem��magnetN1in�(�---�  a�"� �At-� sm���#h�).a"h . Un;ed6�!h too / a����(a�d�. H�w� �)a  treat� un�>sa�vacuumF j)n z�%�&c9)�02��no&� J t ``quasi�(s'': sesquim3o! �IA�=� spancoxn��- S,!Ps� ��"�( . To � �!]beg�2y careZy)]!�BBon�ly2�&:*s,�res!� �i�VE�!9u�)g gn�/La�E�@of Aharonov--Bohm3s�E�a�nona�ac/%G.��'w�+.!=bba�j4:`to �e.�a�=�I)Ns�cover ``M)$surfaces''a�!�B[. %\abst� �0��L�SLE$(\kappa,\vec�+\,) "Ki�/oj8Schramm-Loewner*��d"planar�R!N8!�%�a�.�4 A��b!��$t��.� ct}� ��%�7Q"�2�8�!.a��� roc�#arix%�� $ �K� �rv5$(1)$�ra?ap�W$J^\mu$� =a�t��&�"a high #0%!4e $|h\rangle$ !szU1%� $2L_{-2},=-�/2) 1}^2+P J_{-1} "� e7 l7" 2 n !�� m2x)W�4t/�oeree2Z�piecew�#c� �ich� .� [� ���ontinu%L\lambd� �o��3are�D%wil�an ɡ("A bulkU�d by e46acrosQ���a��318#c74 jump �^*}oEoA� A#r&� 6 $.]�5x �l&a)�see%�of��c���8�8super� gr"�)wo2�5:��.bS8exa�.sol�, (ES)nŇ-F Q!�'rO �g4�+�l�!!6a�6�ESxQES eBX�&>(�bed5ix9ѱ!;��oec��c.i�!�V� ~-�5� e s $_mF_n$�is�uRi ad� &�� !2 �t-5-V g9� �GrP,�J� s.:=2a�i�V1=�&` "�86�at�TorE�P#;m�ra�0w.�8��o S;P/m Yang-Mill&�#EJ5+1*v � "�%�*steT+Ek��rs�^ep�"�0�z� �-E:"s &`�u�a�"��ed�.s ��e6<� �m�I3 numeEU�W����, }+s�4kid}!&c�� �%pA��n" �veH toward �.'�n��P*ew:Jj� ellfcY�,1 u ��� � \varr$--y'�l�d,�(o�mW(-�p�T:"C��F� T�=y (CFT)�_"�$�BMS axioRc!�0of�7����M��9, belie��9peculiaZ ch 2 2D ($=$6�al) CFT,�ToY3cAerp�;[& ny (�;"I?� ly!�!SO*�ntZ�:&� is&w �5�K 5$�,w�"e �.��zo�6Dal, $V(r)=-g v(r)$��is:r�]j$g�, a�"$�$-�>0 ��*=pp�.� 8hs{.3in} &3(�2c�. long44'a�}iny(siAe!er� x cebfiae�gee*�p��3�;g�=�bThoma��B6ok���/6�-;"]&�6"�1n9Li�"L9�� �pre!�3�Afic)of@�G6aP1&�@�!�lR8r!?������x �>�a#0��!!�+*3 �Oq*�i� � � !&��a�`Qb�=UDBoltzmann-Grad low" ���/���T.�� �|�&�) Y)hroughuHu��ay�[s weak�� �F�u�ae"� k�la�&5'� �sc%�!� sO�!obsta!F5,.&T p�^w_v���*��&/�fJ� ��6of�&�$dispersive��'�u�1&8W�Turbul%! (WT)��ise WTeRgid*|YQ �@$&�, (RPA�:=��!�cŅN m�[Ts��"L*�H���(� �%��"�d?%� >``RI�P �nd Amp�*'' �achA$ g-a0�2* a��lyD[ki�&�;u�!Hgy&� �.�8Peierls-Brout-Pgb4(PBP)U�LmB-�aWba qH� (PDF%�e PBPHw}A�_"�Do�$� %c ���OentY� ?v :"�� four P}."&<!�PDF�Ebe�?z%�p!,.assumn . EC%�0U=M65��WT clo�$s. Fu- r�e>�aih� ai� .�t3� � y�G� a!it�%q]I��J<�2iA���miP>cy!|W� �:5��,�2�� �� ٞ iy6dI tocha��=A k:[ )�a flux3� Q�M":9�s.D2zAa[�0 �;Q��v4�An�-\le%6�e�3����acɺav� U6�b�:%+� t'!��;E, RPAImzatIdvBot F��it� s )E��ir.3 R8 �a�g�Ko1)���Yak!�6a=�.mEdtQ� )�)Z �� r&�.��ol ���Zuk� oweveL"x meaAfulM�e�>�0͘!�!s�`?��a�����2<#> s must b��H surv��Q�.&Zi��r� �me goal�C:aW�J 0UF<F;y��o �dlc�t[%A�E�*�r:��E��9:�%�:�1�#� 1J6L�9ЩH fac4 re% 7��.:$V,$� ^@ . If�3".,s�{eO .\F (aY� "�@"�$L()Y ll�.J�B�4�7m!Jsetz2|tha7�9E)�+of�. U���%f sYIf& ��):H g)�R@e � YJ )�is!d���9I;{ne><iAI n�'j-)�h� q#l!invol�D ``C  ve'' (cO,�Jd�2!�i %ɉfo!typ�*.or11D*�6�Ufs. %]�> 4Simon2} NenciuE�v.ag a�a2� Toda��!�a��LZA(�*�') <.Lc6 4Ablowitz-Ladik d�dp� �;CMV�"A6"�9� 1(c�N CMV}0 �1,2},�&5ive"E.�La�>ir:�5#�� .x\vs�3mm} \"�GA BrownS0].�N4B.2 $D�LsE� Ced do�BColume $V�$\rR^3S296!l {ary, exaa i�absorE6wi{>� e�t��z#pA�2;%!� 4 shrinkE�u��Cz#"�5&� �� escape ea&����7a�@e�lt�F�6*�h " � vse"an ��G�!:B) semih�'(\ll V^{1/3} &� QB�50E\tau\sim\ds{�&DV}{2\pi Da}} K(e)$=c(�"ecx�3�@ae�se�B$d $K(\cdot���( tic B g�x@5 kindm5%ec��@ 'a�-u�.h\NY� i.�7 Lord Rayl %'E�$ Z�4aD}}�&k � �heu9=!�ide�..<,�aw6�sphNM�� Q2=� expa� �=2�� \/H[1+)� a}{Rog�( R}{a} + O( ,&\_H) �N\�Rlem!�import�in�Csta�M�f� �#= �'4of narrow valv!u�n�Grol� �@@%�bi�F�Atechn� .�@!�ographicz ax,!,�r$ &>R �.U (B� whc s :E�J �a��#�1i#L'K(g*Nwa9'n7=u�#pVo�3�A9e�SQ(B�!���=�� LR2}�R�ngo)�|:BA{���1!�}disk $\O�LE��5-$\p !�r�_VVrc,2_ Oa�O�r�&l$)=|\��.� _a|/> |$ decrea� to �-!���� e��*- ��den[9i3$xco� R�M���]�to�d�\R�of[��.�\ll]*W�f �K82 �y�AG��st�?e! rror ���� "_ 5#T*for7 oe�"�L� >[Rie0�ma�/ld_ atim��3mGGGF�AM��4FY�-���"�# �% �,-Z = ���|I.|}{D\pi}-ft[�,%��1}{�Mj}}+O(1)�� ,$ (r �fF�)!QJL �9�; m`9ɖpassag��"����Fa $E[�WD,|\, \x(0)=\mb{0}]��R^2}{D��Sog 2 +!-51}{4}O(=1� �A�19�is nee� in�9l lif�l�s,� �(affic?u3e� � X8eur�E2y%>$v���� ne%ar�I�, �� .�2� .!�W "wP--�a�a.�profi�Vto2� -�end[`�:�~a�s"AAZ[36� .����&( ��!ja�� $(\S�F,g1%F� b�&�-Y`J�� �0)0a���TV/� arcU _a\subset��$�3pi�_ whrunk��� ex� �imzAm���J�!E3�� � &u"y$MB�a"�A :�aR4va��N _gF_g\to00Qy DJA\�a2;�VM_g�O�< |1�=�$A�{U��IK� nec!����-a e�&prUF!hstere� ;\ x�����pp3E�)�,& �rB4�� b�al��� an"^�A nnul!E* �7�&�&�&Iɝy����� !�atF orn���) :9n�ja�Z��:�if�6a cusp~q$*w~,lE ly, r4\�a60gy4hm . Thu�Rl I��� 0K� �Pn}:�H]I�q�!)2g�&�(d^�*-1)��� :�� (1� )$.�2�"s�5V�Ncan�Z�=N;N�(toRtr*non�Imin[!un�V�����7.ordCX>%"+a*��Jx&�)*� � nam�0ieo*\�n�Joscill85. S#*]!ih@um"�)alŇshape"(!c% thod+ ��.�0*mene2t� l5�um:ť��M�alB�E�r&?ei�+ �`-��0P $E=-1$, n-4Yp@�Mm$l = jT>f�;2� +&� � .&*+=& be�6��w��+tor,�iv�UaR~[ \to� [$n&C���N[;2&�,�U aW:�"�8[�A] cy pi!n aPq ��ssoci��|ro�1� -U. MorAU��iUQa8,a�er�i�ha Br"t�-~-6~-�B�� (ea��E��� $j$< U��8eB�A0{f_�]:�� s unbrokefh� 9�):�AyA�)~�.��By$Lieb-ThirrACB_�Riesz  *�r4@$\gamma {\ge} 3/4Ia�rth &C4!w.�d���� ',�"�9%��, harm�'S���o���u�""�(s gv5�Tone&��&�\E��,{=}1{-}1/(2l�nL $d$I�$l% q} 2�A%�2�E $L^0_{l,)8,d}��iD�|\l� a_0\�le|^2/V �^*# ��=&0HN�*��h��?�6�Gb"~HBose-EOPei�0!�u. Br1rA*"3JY*� adv�Bd��!�retarg �Yz7?�+�<"Qn����1!�Ysa�E��dis�j�)�!ed"u?Z6#AltshulewldV2�*gra�M3U�c�Ot� 5addle--"�,���AI�N�!ha�*�& 6>�K� act1e�sn)st�?i� � N@|71is�'�ZF,solaDb5%e �jstone� /e2Uly6"&�!Ea��� r�o�h mi�aaG5d�/arA�er chpQ M#�)eas��"e��%5.s. � �� an E3Nv� orem�n�*um-�B�"� ��,U=*�] bake�o map,��X�EhrenBc� !�is��a l&v�0a U�eca"rum�#n�/an�l�.corollar-)ergrA�Oem VIHap. #ZA'g"�@of� �2�ѡ!�U�&�K�Y2��A"�L�(sAS6�GI�)�qat,�#�''q ntiz� scheme, u� ��6�Rn����2 %�� 0mples.hId�R![a�pA�� a.�ie&VXAbr�,>EiGl^�k�9GD&I'1P"_>)HLindstedt--Poincar\�j�iqu�B illu��"�/cho��$2 :an&� "? �vVa�Dr Pol���6��'^M�ach!hbeta�A�jI(o�_�$�$l.Y� .~)lAI� elf- 0o%omH)"s�6G t%��(Mueller-Sto�)�)3$Z�W!!V�YWba *7�+7iEeis�1Q)1-!IA�e$c&�Xn�^1�us]A6��N! �1�G��/ . Fi-Dd�5Fq�*�.�*8fa"�c@`n !��K��=s�f�k�� �S�abx�S9�ΑA9a w� �.z�2 &� �J�[*�a�,�Z�9seJr!2�+yv l diagB�=2^:Jd� ut\ r& p.�T�2W��r�)t$ich���QFV�"u�E� onto� ve half--a�+z'�Gd 7 �!��--�i gene�Cn-��e�2�.�%aa�.n�l%x)�"Nf&c Belinf�Z's�-"�te�j!cA�M�HB&A� �� ?-�=ields.qr]'�}"�'( a�@s (Laguerre-Freud)l�bi-e|I8�nokg���e�\e���]fwBI�2a)$ w(z)=\�*L^m_{j=1}(z-z_j(t))^{-D_j}(#��d.YG�3A���e' $ m=3 yQseR�A~e�!l� �cFu)(l I $U(NMO�tge�)0]<�Cup92@4 i�Aifi��at"& Ad� (van Moerbek3�H9E�!�Toe�4z� =o$nd Virasor*aints/B!6�/Z'd��unr�.:�reU+ \dPV it o)>� ���" six.s# stem. M���dA"� �Feylup� $of B\"ackl�+2�Ys=*�"��he �Q��1%�q�4� &7� W l�W�n)exm�f!��k� form�p(mo�'u�+�]��madE>k&NA�gap�a8 !!��@5k�V!�,�:3s�r�X�$M���B�Gi�U&���squp latE�II��F.u�'p�deals)aa��9 �G��(��!4 q<e�mhed<*c�e�9�R�"i��in��,�i F, Neu(%, fHF�H<)�#�xfE���'u���F? authQ Ny =Lty"P%��4��rjT�*�:$L�RS6�b!��3�v�.:Ya�楘(?KH(�QsE�"ikFeMc �F yA�al z! $$x_{3}$-ax(n�k�  h j�M K. W�gBu �21 8�Tph�tuO[off�(�L�? �"��h�4�6ndof�#ite�7a�ity&�MۅKM�in���V�,� Wi�ڱ>*��B� 2i�umZ_A,�NO %�n! v2�V!�a!�fraQ���IL ^�h��>5:�2�/�tF,rH��?.�e9, 6!E� ln inu� N 7EuRjh�"6�s�"l �v.�>reS E�m-XM�Mg�2ra;>;r�L�8\8X��W� ����&nuIntMpj . { AMS} $&l@�0s: 81V10, 81Q5��Q�Ak� �Ea�7&"�v���7L�Ru.�s�!g .�jtyp��?Ma�i2g�edg��S� ed-broade, hb%����![*�fUl��ymo�Ayn%m2X� a�Y�~.�6��\6:n[ � Ys� �@�|&�a] �%JO eg �U0��o�1( g1Xb-.���=p��Ac�}ock via}eang�vi&7A��=.2flu��b�� � q e im1O� w@� ��a�����:i�M��_\&p� >��b��mp�xpqO4B! ��jOM��n��&�9 #� ie�@�)� !V!�2J�=c�rЃTB�Dind�  $\U ine{ E}��K ��)e�VoB�j�&E� aM�d�"� RA-at�w �pl�at"Á�!ső6a 8�cal� � � �5S�CB�Z@�ena:�p�aQlrtfoliaF9Astock �[ p)��fw"�;!#B�9a����A�\Dthfrak{D}_t$ (devie1JR3�)I�isz"��J�� te{3�%B= di>oYc��A��2�nY2Y�a"� a&E�Bi�MJ)!% ��) YD$ "^ �CfH�&Y/$E\�4gj5S \] = 0$J rsR� X!�áA�* may� eO. �e Hodge�;i�1�Tg stud�on�trami'��,D���%C�O*}. I� �s  bB�*\[�H����2�S�0!="�OH YN(7argume�A^�GH l! #1-�\fA`!.�!�2h=�& 9�s +6e^ B56�oE��M\� ���G�7� 6{O�udT"J/a cfnG�`D8-=�p�!}A. ��u�< �s�G_�s�#%�i{ZW-"�$�i�lowerS2m-u �!o�U�.~>n��A��^of Fried��(SC2000: 35M� H58J32, 53A20, 78A05 $A�nnN+PLon���{�~�~j~Z� �'t("s� A�)�p$N�F�~o"a�hż"�� "�K n� /���MPCliff�:�@clt,\c� $\cl_{4,1} �; eq \CC\ot1,(<$2,4k*ra:�\9H^,ms~smb*&�*�+->� $jk�$%exhibikin � �]A]�"�/ Op%� twisy4,iaf`uor��x"�)|is�2� O� innwM�4b�9 p SU(2,2) �he <$\$$pin$_+$(2,4)a�$nv!�8�*�l�7�a&o`N��@.d{����7 ���D� oc)Or �iRC_Z%(�"dN F7O\2,*�9�a -�Et� Zen]� m19�>cI�� :��4>7&Fr9$\RR^M�]8W= nM�%�f(m��pin,aJ�,b2-os\o!�s C�Q_{i�uT��e�+ � �Za�=a�b:�����,/7c�$8pur"YB:5.&i�1soSda��J:�A�st[�'%f�i^ foot={A.�Z���p,q68hl&�(\RR\op`# .}, V=baylis,� } %AlthoLPsGp�alread�:q5�)zA�-�q��}�=!��d�u$, �f}� � �tnew� �� �B���g�"�E �crau,��<,ke97,pe1,pe2}#'2K)h+6�T��')�d$��<w%���g c(K e�f�U%�m�`ly+!p�X5R,�Hf !K6� semi�e��al�Sexponen�I2W$a�9��mu[-H ��$f�$n�0\infty!*�~� %�->l shiftB B�oreod2Fl�� CZ�B��Z�5G $u$e|ssuKX�  A. %)�1� Td�m�&� ���H�~a)k� 6jH\"ol�&�.&�,N��m�]�ZA*�a Weg�y=K�>vi&�^ �.�)*�i�Zp� $$L^2(\R^d)�/"�9|�Xw/A�� �ca@^{d_1}\� {0\}�:ReYʏ2gn�!�6�0/ s Lifsh^�Pw�Z�� Fron����� scalA1al� by Boute�) Monve�5Stoll" [Ar Sc.8{80} (2003) 87]A�(infer Ander�gc�� (p3v� I�)��>0i �D��g��O�zof6���-Z6. ^�p `�#�i�QY�Ln "KE�� &��st �y��:�isEa<.�O3B�U-%E!�trapped �� m�k�O�!�3,to verify ol>�ll�0�Av�8.lau����;a�2�g��v�xS�$u#����!��3d�e��1F(sap y��!GA�*�/�Oul��6"�E+��53!,F$N$݇�FB�short-30�n�ve}�Q cQ/�#l�,$�>Dt�  $1/2e��) s $ET E^0 + (\hbar^2/2m) 2 kIN�� l;w $E^0������6-���!o$#7M47~1;[0�2D,i; a$� "] /|\ln([ a^2)|[ob"7,yq2D�+=ob@exa�)��!Ba�-.�O:D .h3�e2=].FWan[��%�quasi-u�g-!($gnw1$)9�6 *� !Vi�. "-�.")�y� ڋ!�{W�#!��$$�M~ 'F�� n�!�:�y[�Bloch=:;a� t�n&4 $\sB$?."�]�"�3ach!v � sek#e"�Jj >��f��WU $|x|�F4aym�i3?9�����"�)���J!ca�U/� �es.`~N*6.|(�le&a#sf%qua 7a�a�gr3�a�&ec�V"5yE9�-9���ga� al (�/� t*ڐ��t��)2� ��t"ka. PFc�&� (PDO)uA�.� K%L*�q� �G6�N" 0"8$��fPA�� u�L*D�5B�i,di�~�nre�/m��:�a� (�; �i�-J`"�6$Fm�M2.s�9�'�� Whit�W�3"��B�2�84'i����%0lex9s. CeԖ�$n�)p�a!�sρ|(�t�y7our"�;> w � (��of�R&�� �] b3 mselNE(��edz ���mom�}!NE#�)u,/>f�lu�A���� .�&�bB�[y�N _iuiwA@"�=&�Ca $N=1"xper}q.N4s $SM(p',2p+p'*Q 3p'-2p)M�)HjxFH�*, ��$ge $c=3(1-@(2p}{p'})$ f� =��'0u� M(p,�pRam�\ʕ`��"R 6�%�$NJ� �'��Z�+#iven.E}"s�a f�w��� ` to MarkovA J�<fliFt9c�!��!�{Qi 2� s�G��b4!�mixingsv�Ia��mp�T�!"�@q4d$w� alɐI�i� 9 \#���I*�aG�deg���Lno]ise��No~`)�law $sD4}$.H:�a� Ȓ� �~5 zero� ]#em��� $T��4i� "s�u�H9M�%* ���XhiVM(o�8���&<m���i�c-/$m"���'��2 �Ar 2u c6�0!�!�ng}�ua- Ak�MB �F� -�M� ���s ��}�BrepulsW ,!�har�5rs"C*� a7S[��A3.�as �)�T� ��,)!�8F 9.=98%�er.�Zzbrief UJ'�e�Z�f�-�Li�-�9�(�a_�<�5b�z 8ogs@�' A h�� ����� s%~� c�a�A9W.�O9,E�ct�B��"�@$(V_{m}4M�&i6!rMC���4v� e'{)|}�K�P8\Delta_{g} +(b,Z� ) +cc� -$%�nLa� -Be� "� !P$b)a�Dse-Sm�(MS) ��S $f�\T�2h�ye�!7�l�jp$* )�D�C�jA'$L=$Aq&9}"�&Z��]  %&-RMS ��|P ��aX -��*C�f5[����=i�<r��b�^P5*#�orLK<%- &�$b�4�TR MS-d=�b�-�w�1b Blow-upe��H� �0���7ѧ*�7 �"�DeeR�i�]� ri�D-A&�<>Dbe�]�tb �@!(Fr-�F�T*� P+y�he�@aQ%�h�� (see�Kifer90}� .� oa2y�ja&�Hr-*�?��A� a� � e�G>�%�)�%�g���&!2����&a1<'A 5:'.36��K Kq k" i�e[}wv�'O a&a2�s � �IU�rp�@!u�� �� er�&nmov"Za F�]d. "k)nelA&p BA&F���\��no%�.�.�DTra�1'e�^i�0K in�pr[Ie)�&�re��micro-�" volviII^.-!s4�s!fJ�.mol�q�St1ng_ !4!'has�%�5�8,a��  aV.��@_"e 1TiaaF�)-�b���7��$��)� �()E'�;��,�6I�2�+A0| ��ofBi�� &�(+�c�� !��yA�k� a���Ad�a d%�p;\�bI+ng%un.jz iQ2�W��!Q��E �%Uar�*s�&�{��j1�:�I�d$Eg'��B�J�'n�by] Y�.��of:an�b&]]se2: cell���s olflBy cilia,F3-r�Wx�ir 61�co5a.�����o0cset^n$x.$\r _+�J"b�� v2�ON $f�)�\�|f$;��"H-!�J�E!�Mas:�d2\.�R$f &��8 sub\es�:�$\� al �!`$ .5m c�@��V PNewtonlto�d$fD�/rrA���"ߞ7n!�Ave.=c;�Z8ŭ�<�%]��n� idf,����x� �*�ڡ�-�J"P�� Y&3j�w�{H3Vs&'�%;?m)�Yg�� ��g.4Cr(Hb�D$H_{\pm}=-d^2/dx^2 �V(x Y�M�>&� v!��ٺ��D"d�k튉.  . Am7B� Qrse7 ^kO�3�s�!�ultC=�SNk�Z�1$.J!8�t�rIc2 fAt�{.�1reaZubiatU��(:Em-MreeFDco�)�2O�ir7s ("�r,si�\��izN�9E2WMk�P2`NSklyan�Qrղ�"�1�<��D& 2-�Wp:�A�� j+�.SnD�~b",bXV.Vb`.�F MFRV+-R,RVA:+%:.  J.^ >>^0 z"z-�z&z �f  e 'FJ^J:8z"nn�n&b= 621.372\TkO�`��� 12?3-body� �2l"I�=�Cu?�&ٵby"��͊:-W�� f[%�TcD of C7mero�&+��"��I,��"4&=an�� al28:��>�B�&�1n<@be $g=2\nu (\nu-1�%$+(1}{2} <\nu<�W3�t����.�=.�1)� a 2-"A*�Gin"�E� � mpat!�)�mdi�@$D_6$ s4"�9�t $9 �D -1)/\sin^2 3\phi$%17�/ar�r�<��@ $Un� U(2)2Ň�_1 U \s _1 = U�$l�V� � bI�qulS�K"pZL1L. !�IYf s[/!%:6� $S_3sb�ay� ?ex> g�8F��dće�#�u�.��8!�9�$($� �1|e)/r^2$am 1R'�&at $r=�#Q� � <hhG $0< <1$�S*#-zmRSchZـ� 66tI�"y;"Au�� "�z�~"ZZDUmbda <���w!N* 9 $���K w reY7���M$U$'sih� �2Cs'X!�mi��e>#6kQ=��nQe.�cac$U=2 {1} � q$�1au�E�,��A�d \L" �cho�G $U=-`o%rk2�/�p'saf"-P�l�/�D�E�&���e2�c�Eo"IOa�A�l�$�r-1$ r"�qaW�*-"H�,*�8*L ܃�^U�!ճ&D'�p"aI>*�� umu�!��d�lictr:OD�,ot'�2 -%��Pauli�T$\Re��\Rr!�e2v)��A��.* $A_0$� ll��2F(Su:�?$\B2�.fa �0n $|\x|^{-3/2��A"��Fa�6�M��/A� medi�`uT!li"$,� ��Dtx*��sar�nS� �uss 61��������y Coulombo.G/in�B�,�a&"5:��Ncs�B��ed�M!�S�bl�&]y��V$S+�"i�Etݖ6jn �f�!C {aut� 'na��2xKF:-. E�%�!I;Amr�k��-an X-rayD� c�R�&�Bv!� $S$.�9B� by A@!i�Nicoleau�g����3!�IK+ situ�.� a�lK3,6+B�a}�y�H9�.TEcryst| groo�sV��6sIG� �y ultiA�<�o RF�N�&i �a&G�Us1JA�r�L�*�iaq"��Lchambe���o.�62�!Wory)�Ns^jA-6G6��(U�)�9L�\�Z�m�do)��c%��K!�H.TmOf|%�.D Ruijsenaars-Schne�>�"L��-Mose�7!-�6JwMacdonalmJ·s.Kn�Ւ"�R.�t:_���q�s Ah2s��m�a}�-)�6Z noidM�r�P6Ta�o*0i�Q#�ch1�or�/:�X>"'x_�TE���@b! 1�E�^�$��the\@�� ways�n'!46fIcarce.+��U now� e� 2� 5%_^, v�F�1 incr0-$�^"u!Wd<�)& Kolmo�Z's�`41)� �.�_7En��`�W ��! ��he��) �#wheth�jn|�6sR�th"�(�ir �J .&�} x%! �2��2�:?NNhav�'��e��v�O<�@�l�D)ty��i�Z%$kD0-j1\�wo��te�B��*+2Et$- ��ɃLm)�+|eI��#sA,� �SReyno�t>s (TaylS$iT��4B$$R_ ( \le$ 450) �g0riC�Ja��t�FD(.E@ x$ 10,000-�͏e"Ace5!6W �Y�8�m2�&�Q�6 " *�M.w�us-^t�|o'A�u>-� i ������Im1�i�D�?!Z"6 �%mL"��r�V�C�3�see�sa! ��0q�UQ � n2� va�͡ S�H"U)E�ym� �N�!nts---�)� afʥN"A�u"�"��Qvehear---A/s��C reg�a��atag�W.�3��.ck) repo1�.�I�4tk , g$�d��ne���!R�#����j] �?�| .,P)P��-pJ jump�($\p3W�J�0� ic vol�� s$�gTm�%rid:�I�go�q�itYELrg@ �s� uish!�#�V�6Z�� 8(or�a�F us�� P�=�_S(.yxX �=�)n���tL!� A):!+�#O !�uxPJL��I�F)�2 �)!{>JIa zig-za$� {t�|sur�a�-�.&�MperA �S2@���r%X'� ib�@��~ F�� *��Ber �ia��@� &�q%!!d�3 �Q�*� w�T�J�����5d&V!KdV6E� Burge�(��o�?)�5o.� KdV)>:Ibragim[� ShabZNC�%�wo unfa.�a{� �-Z�>)�!?�t�5�`�I�u�[0M�|%%*�fI�!/ ' (or,�l+R)�%^!Ait)�s�Qa^�671)�2�j2�Z�,th� %�KoeQ�#�or���NsovEOl�o��(de.�Pre-*;gɠf�ca� K�w�$ � ad���&| �*݂|d-I' m�A^ erV � �!�' (*+&�4�s?��8�}*Qjnd�meUf FB . Exploie�!��pl�e&�8n�s�(w )m)ftI���l4aseIt�n`:�0b Zdr�BqJ0��(�i!�D`�nE)�&�  "uPi ��::xics��r-g�:��6�n� usA� �J}Ia�&�1v�L��l��@A�� t fa�9�.v�֓�"q:M�i7!�� .E�dɬrobust*֏ af�ien* ed�*5�HMhec��.��b:dfrX .�%!�A0�6)�����-�\A[�k� coaF0g#`eedback��� "�a���2�?�Nb�O� �x/*+sio�8% FVfw� po�@cT rd�0A)�M�&W*al�}p0m*&�(6�) �� l. %�4*�oC �(d-� �l,�;r.�A��,l�Ui��urg~� �!1!= de�AndA�b; ���u�j�J^E {oIZmand}+���-2��U\2@�(]�unavail� )"�'=[!#�CiJ�iA�a�-;Dte CarloP&iMEɕ�3�% h "> catal�4� )k.6�m"6 w�Lx�aR �(t�&2L!du��-��fiked Clarkor  $-\a�|���uc��FR79}}4 is L�Eddy SI�!�(L��t�+j*us�Z�!�t�:l ��"�.  �5width �}0 �e�0\ -s<��-�,i[Z�.Navierzj((eddy) visc�By&(d' &Ij!<6S[09it2�Lal�"ݡ��isOsi�v�ol�`m��w����naAA�oL fz a�FHausdorf�. ���7A:r6�7$V( L/l_d vV)^3�E$L�r l5��d $l_d(%Bu�ծ+D2M�:A*<:��dom&%/&��"E�+(,-"oEi(!�M^ in��al {�+"' um%�eW -$\auDE`u� $k^{-5��&=*�:p� �s $k\a�l"��B�Rdehpp�B;; .gg 1.$ʁ�;l3�"�>�O#eP#s% iE��6���[ 6&,.��6o{y!�h[*_�$ hbal�L-c|�i�?u�"pa�� y6���@s.rLet $q(x,t)"$�DiBVm�1-�!f�e��2_pP+�a6rv�� 0 < x < La^��,$q_{0}(x) = �0#?� 0}(t 0� , $f* L. � g_{1.�%(  ��{un�.}il�s�x} f�q�x} b�i]-/ �nfO2{m _�0s$ � +t.E.��,z5w*:'.�$6�&�9�ODEv.�PA�qu���Bg�62�.Y�- \�;i� pe�<t� A�S2 )�Q�&޷A�,C���aWR a� < � �a�e�)PDE.�2�Qd;2/ \�J>yog�� )of [4]%�[6]&�9n�& hE t?(Y u]4f�.p a $2*N 2$�'��-���5* uAm�� �C$k$ -5��^4�s1b $��#c5�[�;@xp[2ikx + 4ik^2t](tJ"s O )�)0aMxf� ax��1lev47 jump �c�r A�!�q 6!ey��4$\{a(k), b(k)\US $\{AB� $\{\ \!!2ur�[�(�6q�a����n\{g�p, �av d��, f�M�/�|^phenome�e#`T �ampB<c��X����P{M�v!N�h��Lj.#VVJa�^EI���ZB���6_MyPiVs.__is��j"���Auye��A�ae�}Kt& ��u�� ��Gm�!a� e�*�s de� �b�Q9Ra=e9k"�"*l![<.��Iq|��G�#��  $xs aH�.�TM�s {�Xkodic}�|�wRzi� l  crip%�)����p!� r��CK�<2���Lo�y� D*&aK"\�moZ� �>-�6J� ��S�5p``�[��nd ``�R>s"�;�^Y��B"� �(��G;�$]+ ���1�"#Au-�$00$,A��Ag���2��Xs��I@:�A]�.���.�61#٥Ms�Gordo*�g����R�&2N�$��a]=���q����X��-ܔ_ �P)R�F� ��s�G�:&J8$�=!��?��$�!/�-$�.�M /��21� �-�.��� *� 0� q_t(x�\5�%P} !� wo {��ar}� v�,&,�V9 2�� ����F]��AL {U����>�ide�%p �qJrs:%��!%�an.Ƿ$,!i/ zEchi!��"fF A� $q_x,AT1 (q/2a� \cos�)�l�q� �0��,Na-Y${"P� 22�a����JA@\R��iHG�(Aդ5OA "` avoid,%�I�Y��B�"p �&i $\{ a,A�,�\36 u�chi_2%2�n� �``)&�9�eZX���'%l�s���lof"�cy�!!#-�:��2�5'�.��!; y�9n�~� A��ncham�"���mPK&5r<��Zry) `}_A�.�/>��u�gW���(u e8EL1{E-y�O!7!'�:n\ 7B�d��rb&i�& it�5so0��.�-�,�1��"pout i@)!��c$)7�l W:d��U:k.�A1PW? ar\'Fw{^re� js -(a%sso�I%tk׍a�akS�"b��ntZB m�>)�>�vr2R;gm��%q]\ 0i��>ex!�. ��[����ë� e laboratC%� �i ���b����)y,(`IRn�' %\vg��,0.4 truecm %c��$I�!�s{ 2At`Nikolae��i} 7�en6�=s�T�rsLZ ��_c�2��vave� AA�"� !k�v�Q&��^eOn�.?�[l �A�"�$d�] E�#f� p��&$Kraichnan k2�n8�t tt�+�5@! Eule 1���XLag�Nfr����a�eB�i.� ut_e�� �U�2Y(�!0% ��.ZE(52"X}�!F9�H�Ka�!s���it�8 ` �ruִ-Ete8<Z(�6z3A�m���!fsh� �e:� � on.�&W�"is�<��!i�a&j��ioTow�( soli��%amS"&� =�*  $havZH^�hfry4f g)�by"U forca�&i *x�U�l�}V7�X�bY�e�%C��, �x!j,�#pEL� � s�!�. S "�a��0d n@�^2FZy)��MCv��"�<u����&�'*b2�=� ��W\"�1Mo�3| I*��RT&�(��R�� d 1+*����< �,"VE$O��"X�tH )_QX�2iLs $\ux{t} =f(\u,\ut,})ٔn``-�.|)$\u(t,xr��mEgx� !�xVll�2����>!� a \h�)/��l�&"�;��(ygm-iJ" N%?I�eV>� ted.ϩ�i� وw%d�O&�O))K�/���sL�a�!1��2�i�2�e��)A�"&a��L� e<.J6��Ua �R-�8.�,% 74r� e �/� i2#� }�'�$, of the dire�ct sum of $N$ $\mathfrak{e}(3)$ interacting Lagrange tops. We call this classical integrable model rational ``Lagrange chain'' showing how one can obtain it starting from �su}(2)$[Gaudin q�s. Moreover we construct one- and two--point ��0aps (B\"acklu'`ransformations).�For a �!6�CHamiltonian systems naturally arising in the modern theory of separa^L$variables,� establish0al 1"!!despite!fA' fact)$s!�m tM s s-� �s when5�AH1AHreduc!E�N|. NHthele)�seSA2solved ^?number�]�ofV!�Tincreased.�We repor�5 +xistence�Aa�i{lof multicolor lattice vortex�itonsi�ituaba�I�funda!�,al frequency aHecond-harmonic waveE�opticalj quadraticA� � der��';e KolmoUv�D�����B\LE(k)=C\epsilon^{2/3}!h�&H �Y H)�!� rate. Iss: A�,o Kraichnan'�Aa�ofC>ensx ��to] Ia! qu Hsteady dynamics becT � discus#+% \� p(skip=25pt MS�� gravi sph��tel�shell�  a a!�e C bodyUgderG Each 9�A~ po�� cl.t��ific amou%%t ies.ѓcas��en0� negl�=!,influ�0��i�0one ("light") �o�nW ("heavy("restrie�")hs�-�yph� spac��describ!- a�a0 lawsM�e measB�Z�cha )���qS��f%e�}� ���5� escap!���e�ed.*�8 onsi�a fAi�� ffer8*usA �up/!�C $b$A� wellmme!Y UHal kernel $g(x)$. W!�$b= gu�peakon0(i.e. 68=\exp(-|x|)$ upaSr�!y)�dis��on�24� A)�ˁil�e Dega: is-Pmsi/is5H !�6��}$b=��"�thesee�A�ag�t�,^ic�S correspon%c1�PDE��=. How�,E)FD-�Q�2 pul7  of Fer \& Q% c.PA�nly%_ lays elas� scatt gUfa�O��is hand � arbitraryE/i��,still possib!�o�Ve{�lo` .� aW=id���,^Bor�ofe+dega[��s:�� � roof)fTu?�ssocia�y }%�!�skew-sU�2����g��e!� �bracketz��o �-canonA" Pois!�+�-M��3�-pny�w(b\neq 1$.�: fo�aQ�an earlier work (briefly reviewed below) to� stigatiCtempoa�&�ofRxa�rav�front"�,9�g!F� ?M�la ress@ !a!�2��8rete Nagumo-lik�le�ou!dc�y.�c �lae,a piecewise �VaI9e�a��-s! re�onU! olv�a Heavi�\�p$� stra��for� di%��2"Q�� sw�%�A�lternIfapproaa�n !�?ng a `9�4� r'Q look$� varie"�u��ucc)�!� � evok�urbB s, p�ue;%L`kicks'.sm��ŷ e dui�� e6I( get damped'�!->��́L�cks a� fy on� BWa�A|at&�!�s (-`sign�\2�', seeq�re�:AZ�z ropa�ngI�. Comp�y�de<� O �uQ�Ź-^Q�-diffua�whereby�\appears a�-�B�isu�lye�lAXr !�pa��=cha eW! i?a��t�Xmod!{)��Anintroduc!a s�Ur�ak ev!qrm����per�$a lea�1���,.� analy� :`ű��E� ��� �'(� 2�) a 1-98�s5� v� n&+ ), s� re-ent 2J�ex xcita!�Qs.�Bnm EY�� se�1w�v�.��human b%P!u� nystagmus.Re�y� b�E���or��sR� betwee3� e�purA�56or= �vi�tud A� autoX l���b!D have�K unexFed�`�$7�9$ s7Gaxi �U�� tJ5h��m�i�5�inA� �ab��Y-�ik� �M� fourA�,six principa� mponena�� 2= ` sens !inputA}�Cch1�chang��y openaor clo� ey9p�!=rso�a!� IE�} hist{ m,�led un .dH 9*��t(�.� such��fEs*al&��pos�!Udomin�y -j�5�AtA�h� havih ��5!2�hown��"�V�@ could pla��ro���.y� phen]on.bv&� |ic geo� �ߡ,� �r �Kbillis� q�ic $Q$ɲ impacLlohm/ conf� d Q� 5 y�C harp/trast c thos� !hA knowngxC$.�HM� bothFazed!�desa�K�)�op ��!�$! u�!i���5`� KdV��"d){�# �.�T�pvM�t�s�mf��isuOE�s�"Muwak�/'&u�behind�id�es vor fa�%fre�&$in liquids*�$� of'ya�Aza��rkE�H �c} ! >�ob �M(es held fixup5 ��tro �Wr[ � veloc��d$e Reynolds beNr� de� Փ �%�) jGalileo H.t� r!�(e Miura typ�"c' (MTs) $ � &� sYa�p-curv�re����sIQ2 in Li�"�!;mW6$v�at cery homoa�Fsj��$3�duce MTI�%��(t]stu%�'se >�a��N sI�-ina߁�"#�ɸTfy��erm�V�!�(Wahlquist-Ey rook5!#A�#r �2�)u/is|�B2� s!MTs. A! exa��� i_!.%�na�r�5th8 � Harry-DymE"���'KdV-mK �3Ker�%E~8Krasilshchik.#�e� �d�a� wo e�r�%!U4he Coulomb pot�Hatt{ �)nucleus�C ��!a~��� high2#*�. Q� um��)�wo-� atolhlexhibi+����l7y h� "�%��x�e  xe]i � ��O�({\em Phys.\ Rev.\ Lett. {93}, 054302 (2004)}!!aW�)aM- 5z�&!ktripl�%lliHN%Q steb��U7� 8hidde(%l ��-�i)Wm}=�)U���-r Ds��B�b � d? p sourc%Y!���thr��UA�s`riwn�la�detai�*accou1!J fi��� z iQ�he globpQ a��'nz+ m"b =>�.h� *? �fA�� 1b 5regardrof�� �M �=�� r!�3 We suggeswatB� �f�aua�k'�lT"cr/mue31�Burbfb�1Ry!]T�insice�y7, � a/ rbe1,�} out9!3i� � mem� �voa��)��"N6}p,�. S.9�lu}a�n fil�'K iwo layer�immisc�l [ a� horizonI-(he�) sub�B Both �� A- Huk -g�#�24)of-> bi� ' �ma# u�k-�effec+molec�B!�I3lre`�ultrathC�b� 100\,n�0ick,,A� b�er� -gradi�M�Ma6! oni � ͟e ). U���2wz"$\w�-r�w & � &>9/profi��!�� A 1a�_sim X �?2 slip�=�L�.�Yf�� ji�%։4EW��:��,iso�B�tak�X2��d�3 ilizi!n �q � VJ$�@�.U/�)� �,cose, zigzagAmix�yp.���920"*9ukp %@!efYpe]5rphology� h$switch!"Nw �8ncQ'aN� �s�s��$coars��� le B.��%�=0 e�^#�n3�an uppe_t"P+�.��,�d.& g0� � Ae�#i� �!E�&j by��i�,=|qL�$d +s�$c hydro �-sE~F��gi"�9�q�&q�wa. focu�Xy�Y�3 d�n��"y�Vrmocapi�#6�5o%�c field �%�� �?m:t8%AMe�ia+*��,6�!� ���B%N]5or�Xz6J�us:&����ors,A�WJ=�$d�n*#0 �/o��,�a�l^a .nV %� J`(ho8 dropemazB� ). Fin! , fu!!y�� 2vR� � to=���� �9Ec � s. Du�}́] oe�u[ ex0��exsedL��ze"� eige�{!X �qUbaker's )!sdem: ate,m?!�(Walsh-Hadamh�AE� emerge� ^ub�t Thue-Mor�e�3c��.� ;� b(��z'<A��VY h~@ good_ adig��0ao#� �.]%  �� /,� l2 AV��+�2)g��*edajE*AGi]�2their�cli�6excur��"ve!�b!"Z!]y7q# ew#!�y#�$r�ʉ�ic��.� <. \pacs{05.45.Mt� Df}�n"��!�coI�x2 $:�8� !�a�$r� y i"� tori�zB^i.�5����A�u� is �� }% � ized}��.~"F�!y� ($d$)�� cran�su!Mcal� t�;���box* n�v ��F9V w�f�)�$d = 1.5$ (|�1 4$1.3\div 1.7$)� 2�-(random walk�])�� ����/s�G'�&�'�) Fm�a�acy)mCIkme ism��eTA�ent�#mi�0)"9��Rosagit� A� coro�F �Gi<:�la47be '�J . Ouc)}%��!;O �� pug>i� ��7ors.weLa+ let�)���&6E>��wA�R(a�@ry.� ma-0៭zbuilt-�b t1*t�l�!Qcaptu"'t}7� a�set���a�window�4żs�%T�4fDaubech fam�!S��&lluj-8A3�u=ocedure� s{�binomaa.�. ��MXE#�&'�>aZ de�X% %�is�2w� al�<Lw�of�6�i� �m� 2D Ie���l� c4i*�,� Ea�=� rio-l5�s�ses X?=-f��Q$.>Si��XMarco Polo \cite{M1298}g$�; been���saJdun$��p� iar ]C emit��a lou��A�aP,-deA f1ency,b!Cɧ� minu�A .�bu�3!ca�� ed m�E riou�&artb3cW 5*ra�n[Bee#D��$gn��)� gi`34 he a�@ ��)''5&.An aval� �ToG acousw�#a�3R grai�5��&"��@u.. B?�&ng5EA �!�J�)YPn7$slaborat�6~ � f3 . �&975��5H�B��5�)�Fpx&�j-�E�@ 2 synchro!�v�C%2 L6�&�� shol��Z=+ fu4Ar� T�em)��15n9�resonaa�a�AH!��: i�Azenougha� ENc 2]�1 elf-� e. Se7[�{ d�6le�cry �rials.A �(0�.�8Ginsburg-Landau&aXJ0-!G ͥ&�---!� so-B/ed Blo�# nd N\'eel��9,��FIA��� E��� aP&!F"� crib!oa�4��"a"wacW�so2�%�T�lex9m�anF doe�Ei.�)A�& ��@minE�y "�  mismat ,!<ll,3ly ide�I� oscI tors` �2�IPdev,M�a�sy2-�"*� U�A�%p nsem�l�c0�circle@� ����Fy2WQ29A�noi�A� "���/�!k�r�!���:5E.�� Y4 $N$-�BQ��� \n-(nom���.r Toda"Cv'�  g�$���eNF>&Ell E�rva/a��(�im%)�f)$�1D|ime.'� M~!F.e���&b�A�e� AT� )�i�a,>w�%"�&�^ (dy!n� ivial, C�a&G��qCHF�����1���ir �B_$��//r�r"� d�e1ve ``+ ic''�8�!j� r@aa���6ex^=&�  cl1Kg Dob�hh� kink;&E]�T5eT� ���8``- b�concerna����thBAjg7$h(%@[int�"���0� �G*Y(i(ai &im� ��!er .:C"eGlI��/ KlyE A�9A �al/���HelEvG"� b?� � E�n_bo��y e- pluB/�+- UupMsE��, sinu�(!�)a� &�"<$�(�EA�"�y�=q�-s��f--�5�'.<~#*�5matrix 3F����/ fl� icroAn��"�!�L�8-�-m�'!-K�1�gy5m��;� EM``� fide�''!,)5of��cc47 *�3e�F �e��n��� =nE weakGp� aI��{`3/(� ���) \. Wit{4�����2�M!�wHag�%yrh �J*� a @g�-q�,Bngths,��"I*|' $ Fermi gol�#ulL�H.��.~�+y U��52�&BeOHa) �5 de�%�!S� 6��B� \'s�)�}�Ed }"a��i�ly E�c"Q7.|tra�=o1�iQ� ��p�8!�%�nviron����. a���=.�3)'s1fo&s irr�9#9qx%[`�6 mal'��ilibrium#�f�6��=d:seoo�� ���`p<�M  ow�&rA:N n�,�absorp� �dissi�Go ��g)Q!?�Y�6s)� A��$6�R�M\M2<~=a�%� trib(L���pl Pe�- helpAral argu!�)`�check&� �{M*� �A�C*e` $m!�Jy'�s very �s%e!Ndi�.~�Qj�+��qBoi$ nesq!+�;!$+ �b:�qcubic%� quar� H\'e�He� *�s �w59S�B s=�Qr�)�^R��7$n��mco#i3�I�6�^ye)F�=d�=wY)�,e��g@" lued"A>gAW(olESI� |2�enjoy�Y�: merom��K>Q��is hyper1!JE�genusV!�c�0te�Anhe *8S�3e (� s�OYdy�o7�j�4�roE#Z � y).j6�(Kf�N19�P�*� %F <D Yang-Bax'&� A�ve�Q��B&�=%!AlqSp��al afy.�. Kg.�i@ p[Haɓ�cN �K�Qɘ� �C��-N�lis% diagz $K$-��c��Spe�M�a�[ i�C seStely.��%.v�FK-coVm_�X cycl�"&� "a��͵4!� popu� �����siw"n eps:! i,*!�Wof ���0� phyE.sa��1set>:A�C�#K Mexi� typ ,�s+ 'EgpN�� l�;2, k"�%& =V�1feD!guItoC1 fasA�theWNN�,n[< !#�u�!w�Od���**)��-u�"�&&3"�a�* � � of u� 2dLng �L)ha%Ve>(E![in�!z$I�b,I�g nd Sw( onov�c�~&9 �( sefu > m�A�ed� �! *d*1�,H!)�e#3*.�� 6A8 8Hopi B�nec[ net+B�nu8.�w)�K�%ndu�b� rvicq'��-k!qpVH��F�A|yg�Kaup-*��Q waa]Ic]18frame�� Whitham�4��(orZ+�"�b��7Gu� ch-Pitaev�ZA��rz0Œ�ic `` " �~-.bF� 5edN�[�Ya"W"�Y�[���@Euler-=D�*ae51�!2�ed��Kn�=>�.1.�U <��,!j��S3! visc( ,���`$bF�i�2ZsoaqropCeS�@�by��z!9�() %7Rieman&�?(��- �� -gap1O%�techniquQ!% AKNS�Wle:��t E�*o!g$e�p-%���QO �& "�&�oTa�asympt�-x1V.N,)�A)A*� oBz-�3-o�O>yunur,B��O!�� �1��6s�J�f�6|<�8N2��uvE��d�QlAo>/m%�2 L���%<�1ND�r�YzAb*Mg1� a.s�] � � .�!�unJN.Be�)"�V!F�0�! -�� !�� N%iK di$�UmK 2�ON��^thicke)#a� z)�� 0of Conophyton��e"�QJV,)i 56� clai2au-�maV8co!|e*-�,) %�ic 4Oi� � F� . %��Q&w! ���I�I� IJEdeep oc�9"�#5gui�Iaa��\)-�[c\�/:}B��+!� Schr\"{o}c&er��)�a��^t.�p4�s� ro�Me�\.�,%y�O&�b? }�n�t�ier5=��SL�a \,quotedblleft]rV 2r \-�6&at���u9 Z��s.�A����?.�}_�D� achQ��&# $)g$2�/ e!�22tX8$$ {u}_t+A({u}) x+B y=0,&%�velop�����!a2 �H� �sm' as `�XI9s'W2vaQfLViz�2�� �3Tcn) $$ (kE+A)�^(lE+B)."(�Fh�i�iv4 ver"� ��cAHaantjl�H0�#ruX�A�/necess�x�E�6�T. \bigskip MSC: 35L40, 65, 37K10#(Keywords: M )��< al ST %�H. 4T%�� IQos,�T �N"xaI:�Pla�S� WI, D�Ze .gBAmKP!�i_���%��� ?$s (mKPESCS�ht[ i4!dB�@�L)KP&�i��vCqdb.�X�-R��� oq6&,jMm2sr�� o$�&�k waya����ir2�DE�-. B�dJconju�;5j~ �n<g��)Darboux;n�2=�FN#+!p#$t$>�):��2�He^h !>� ,���%}$-B\"{a}ROm"��-s)��2�!}J �5$n$�$s!kk1�H�n!i�� �6l_!�uA%k�E/ � smO.� lump��0q oBl5`!�Dof{4��" �.��:1A-�4ogu"tau&%Q��.6���� 4A@�cśin!Y�Q.`Tsf� a�p?���$q��ae QKese) W Z5"g4�l�[aA ��A�P3tur�>!� �y2�6ar��z'��/� ��i� alis] �.�ofsi-YT�!Y!�Qsь.�!N>��'��JH�3�7 m�"UP;�� r�!r.���u�/ gaug%� E�op�;��ngs.��'�yz0$ Rice-Ruin0 <w7�[�>"�� ����@��one� �!bloKU� "%p� �1�l �G72Edry, eo"� �*�ia%mi��-creep'�'���yg�A . TwoP� ;E[ob�ed:nZ ck-s�>�'5sl�`-t*& Am5%-D�;%@!�/ s.3cc%�t%�Q�O � rau*U s!hs�-��en4 rectmu:7:� � �IOŚid�or\ ��Fwo%Uen-�;�e��-�l"g4�itA�mV?%�. Mi?!*2�(MMO) � ��-to�"�/e��<enAs�*a� #al�2dA%:�&�Ff iod _ �0?:sVbifur0m=�EI��� In:!�� <hJ& aW-a:.E unimo�PPoinc��;w�a �#�Hs r�V!ns�mm�&�� ",�nwo�� �\ne2�cu w�n&J4%��t���g��i��)� " �� ��A*�mW�u-� %�l aJ=&r widthe�G"�S+6)��b�N�1wicA7�GwoA() �� �$RL^k�U)�. A�,'@�ae��=�V/,r% �*� .'F�.��)�� �� aa�c3 aH.�: ��9 9 bi �@ @ �r? vn� =*�D �si_�C NnA v��H NF�0��2= ��n3 5�:26 a� �.�q����!n� �ta�2i0�B �� ;b�,�� ,�y/ra&CV�I AVq�K�^Aw�a�6V rZ5] �7�����R�&�v�b�NL%��� f  darkA�itH;b#E�p�Y2� � NLS$^{+}$!�( - ){�S*� �@A���zed.�\%&�%�-y�� bl�-�P V&, Zyb�/R��2�^yl"t& reci!@3 � � � AaQGw wri< "� .ua�(a Monge-Amp�53E=.� off}su2A�1! �%�"�l.��  , �~�N6�"�t6_A7 \�uut� f&Ub %C.����m2)�!7t{sVs}.�R^%�V�b�m�%�!fa[7�? '1��-Uni�* _{^&53�IEe�i �<"yo'*N3`� � R�T6YaE�t�%&�[>� %iThb=�bf� gn�I�.f.("!�!=�LAC�V �V"��f[woj-�bj&� h^�A�"Zh�� !^M�A �y����tfU<���I��<m.��X':MielnikSo�+r�h�]i!�!.�/E�j I �1�1]`s6:�n��"i">&A��� subz19 K1�+�"� forc�y�9m�F� 3,vib<P �just bNMe(m4!Y� . Ells/~!� ���Tw��=�dyc%9���E2 ��to �A=���C 'i��8 ol.�MeLnt0�n:Ore atMMh ($p_T$\,$<$\,1.5\,GeV/$c$)h��j ( * 6 .4��~�oum9? STAR��?AK�yr.j. Wbm �c!��$��of "�.�"�+%J<s�#�v&�6signa�-�f!Xf�#�$ber-of'��A0k�m�a�!t9�A�cU%�%s�8�8�G� p�uq�^ )��'�e��lo�f�!o[#assump!@s.��q!�FA(rged pV"�@ijoton-p%��Ys�a bea�(A5d�01640$\:$MeV/c6""8��j�$!�%�a�E�b m/-a5tr�cph):m�3ngRr .�2���/�, (deuteron) L[�.*�O $pn$ tinuum. D�a�v'3g�K9 �E'vos�ae2���A7!��)S� mm�-spil�1�#�PH.�HX$\sigma(pp\to \pi^+pn)/Fd)$&Y��v����a�ewƂas���ue-$S$PfYC�Ge-e��"�y��a�nW�rP�B�u�$$D$ E���!^%z) .KF�F@f�&q�s�'Au+Au:�d$\sqrt{s_{_{NN}}}=200$~GeV:?Em�Ccs|7�(on�]b��ce�0, baryon-to-m,C)Q�5[ lli �e>�N�@($1.5 < p_T < 5$ �Ec). P�p connNA�ut�;(1)!/s��ays, (2 run�=�Ua A��ic�7rk 0p-��pai�t L .E6�V(3 V�C!��""sSH-gluon͌��"/ *)B�2had�D%TA�F�r 5���CablaNY�!2�d� colo�-m�T.�bHaro1AK!��-s)�^ s wa�H�/� CERN ISR11972,�A��"!|hSU�Np/� o L!X0of Deeply Ine�rS&�r�$�Oqg"�Kak\\. Fur ��_E  ut�V�%��Qh)�of-�s �Vl } ���ɢ�ilw-��4�ASe�� ��Hacka" je4% B!7��*�<ofA��>� ,�a!1!�.�$VaCh�6dy�x�v:�,5�}�(��l1��-�K�vd��Q$a� jet �haAF�t RHIC,�_b"� �BRh+OA&#K)�+I�in-ˇumA2*.-0 �4����e"�=�Nd��Q!E TAPSFct�?Je tagg��n(| a/ MAMI(elekI�Mainz.  de*,?6��s (�.Q%$�� o X$��eta 2X� d #{\pm}X�P�,g%(i $^{12}$C, 40}$Ca 93}$Nb��$$^{208}$Pb� K9�"N c!�#�E/!\?�*��!�A�B^�4P$_{33}$(1232) D$_{1 520) �,S1, 535)|-�.�F�2e�� NBs�b���di�[����^gU % n&@D&) -N � D��HmqF��;"��<��lMiR!,s�e�ev�:��$ng y{ �Ac�qat aba��%@�g�< omit@ ��7of����.�i�]B#�)I>�Tn ��xmJo�e��a!� is��%s.OVa�M �y�l�^ eavy�BvTp��?inV � � �ELB�&դa�&� a��$pl�^"&�A�a$\epemuobarp$ +b�TaO)�X-e]-tG!ՉR<NLO2��f rkon��!<�Uup+A%�A+A�  puzz�p,a�6�C���oY�"O�#���Ei� 9W. OperCr&���a/pe�} a��@��b�&ng�< iso9sh!x�V��>20 �%��?� 2a�)��Sng{b��� P s.M�6ZUP:@_ n �e.�t�fo�Kve 9!k s opY u1� super�kof�pon-e)[ArI!zar `,J� surp�l2N�t&�d� bulkq��$Ef�/`e��L.����e��us �u!�u(w�pIy/.%a*to�1�E?�R�8iTt-|�0� sIA?"% ly %�W�U!/ R�Bng ��rax��?nQ*WT%�r��JtE+p+p2� �� @0i a glh&�%sh�)k, pseudorapid�%." se�Fto�y�"�\in>.t�( �_E��2>Mbea�roxYW�58<4ax%F�1hxsT}'! ���",d %P� �B} �Bramov( %�,.�su.oA%] �3prea�/�Es� � al-.�-U�%.Mf�wuz/ argu!� Q�!if2sta9-�%u`� &�O�2opLK5�2��A�L�PN���6*T%~%�.fA��[t�7%�A;im0 �L|At mid-� �jm�;�9j3ata�.s,�` boos�Wa���%.�_'�Wes cru�..!Am�+2B %as rad�.AU2��!)�e�96vA��A 5�sS~upȕ�_:sZpu-�C� 4q0f)R�5i�%E)-bqu�D������ �&er�� . %[In�16�!5�F� � 112�c; �u�a`W t2v �W��gmJ�y�C?�2�xf��$rag�in Hg�N�,� �d  \��iE �&ɖ.(Eka-Hg)�su���X�ke�� he�4*C�Pes'P"~ayNg 9��iv�d2e !&�/PA�^��:X��Ag ���I�0 (��n���str�a%AQI�AfVof Hg.p$&%L&�S�p�� ximum Det�(SMDs�^Z��De�K�uHZ2� (ZDCs)� �dXbym run �pL �@up�a�+dow^/� KX"�9�&a' !\�axi�_����l�eZ rig�Y�Cwept aw y� "��@i ZDC-�A%aG"g i�neu���de5RA f�!`�TJ3%inf-Jؘ�preli�6rb� EL� �]se�)#a trigg����-s�� a@100 mill�Ntop� �.�"�� �}N- �Y!��}��2���!�iV �%� pola#!!'s.��Z��o8^2002--QE!2Re�*m�l�y Ion C_ �6at Brooku\n Nn��Z�G-i�W�I8)���>*6E|6��)LB wardU&�!of�g�Ae�ll� � e��. D�x�Y\��C�*e6Yac �&� j2� 2003�!NE�se)�pb5 �� � =��La1�9I f�b,�"ai�Pata��"�+� �.v}5"]d!�*) �-�4�UrQMD�Cp3Qm_XNC!Cwde� �j!g ed)��.vE&S �YU�EVcor��*�N $ASX(p_{lab},\theta_{c.m.})A�A_{SSj!��%Lb%��iw-�qc��FIF�h�yo� Syb_+  COSYua�ňlEat�> E� �&tak\oousA\&�dac*!'� �maI%&Ǥn&�@ 1000�3300 M)(���E�n$T<45a25 -)P+tr��vof 143Z!oi 195��W^�s $2�$"�$30$^{\)]}��9A��� �i `n-dO'i::cA�T aI@9�,}2y)$i � �!�ou � �#w?m�4,ENNN ���� SS}$�&? ronounced)f'b07)? a>�2Q%eE�L�at� ".a�aav� s"x� �h�& shif�#�2t !�beyond 8)�)Q�H(z."b N�%RA�O�X!T _:A�m!*x� tΆ! �Kavail� {\sl pp}"��:��)�derabl\ s�� ambigu"�.��8sn ��LJg- Ud� -�A�� ��&�A;"���N� �,� ݶ�)���������6s�X* �"F�$p+p$,����� mea�jd� ��Є enhAO�= ŧyiA% �d2A]�1U2���� �el�_!<r%�d�b�rA,�B�rLPZ��opSPSU��(e��up!��,�!v%!1�-s<�f� v�E&,"��bM*)LA9�a �d,Eb!YpMb%~��7�� we hop%�"b�9�'sa�B>X �M�s1~*! ed.G2��� b"aF-I� l�9�Gs�%[pi�H�,�RbByJ�e1sp�s��>��� gain ta�~��(���ja�&� ensu!r of LI���=Lultra-bk u� E�ded4=��� �7� ��-�Fd (at 20, 30, �A80 �] A $r8�m"E�� �� _,x#n� � ma 7&� ka�r�staystS�!_�m�nY%�eq����v,A|AGS� Fiר�.�1y�)d.�Ef#��aR\ c/R yno$=�� c-=!Ep!-�!;� �.)�L��GH� y< 8/�b.[,�Ae�!��(��Q�Uz.��*er6�� �!,bh��nd�e�&%" i��.{$��.�s�\-li� $$K(892)^{* A&��!$��o�Ipr*�B2E2:�&>"�/VZ= .:9(M#�|a� $K �in"-_I'$ =��!��=hf/}uw�y�u� decat*nnFY9 0} \�3$arrow K\pix #!"6% _S^0"<"$��!����ic�"����0}$i�� �:d(B.$�,!�mum bi� ��%��)9 n}$ F��� JO@ \(>X�&�! ~s � �u��<�}/K�x�io� � 2?inFmS. s&��BeoaR"cXNGJ�9�di(ð2�JU+2};�wA}: 30ze-ou3_A.� �Dzg�% !�e2�)($v_2$)� ���Buo �GAe$E�I$$\Lambda$ Q)�nr"�5* ) faE�oyn>5*$p_{T2�sT����6_{S}^{0P�oY � ��I5w@�'��*�%� *���!�pL_l����N�T$ ($2�*\leq 4]0HBPbWO$_4�,ړlf[n��a lAf"� e��n�.� �!�9 -�Le&16}$C�?�t��asP����Cd �scz. Sc �qr@oa�v�ntaP)of �2R=in&�V. E��e ?���&[to]c-1��=zns ���BE�Ac��-b�H �sh%J+� �)g�wEghavAuen�J�=!F� >�.&�� at�a�..^����si"*�e{��}�^��ih&�ʝ6s T7�s�!�_!�����3��$>$ 2�� /c) $\Xi$Ě8�,�(o�#](*di #zimuth) }!9eL2� =�r/8 y�!5]��@�����~ɏ�ea-�Ds!�in PYTHI�>%H��.��r���%�Ѡ E%�q��t"��:�V�.��2.�������EV2,&��N fer�2und��AQ�[�{���y.:�n�.�*e�<a&^onE-\PT{}�����6�nd׊e+�,9��*��JbinZ��')t� nextt.lea: �5��Y��QCD��!�. PVreI=��t�.q� �U�<.[�=E G/�0os� � T A�,$^2$H(p,pp)n(Lkup"Z!� E$_p$=16!�b��o�nfiguc n�Gnp5 a�3���;on (FSI�,co-pl P star (CSTm�a-�G ate�3r (IST)*EmF �F"%D6���o�V�I4!n%,�n!CD Bon�3d�v$ comb̅O updY2�8\eh8Tucson-Melbourna> ree-l J"�9(TM99'),5�-m�o���% )@< �$�aY�eK�BmWq�a�e�p9��O5% FSI��43}0�PJ� 3NF)�$d,aa �>�gj6? �) a�E�iluW�3QN�Q �CST�s� r3ZaISTvs�� �.�u1m!1� �,�u�!-pdus��I��o�Q2KHo!�l�� �&EIe:wu��A EFT2���l%iu���JN$^3$LO�L,���9%��!��%Ja �r7#/az Q$ �%ond%Vsit�Ss.7E3?�S.�2�� �a novel�1Z"�1�&3 !:�A/np  .j.!3� pm 2\%$�mlut$ ecVIE l%'f{��%Algl� ;7 )�v#AY2�Q#�)X:"�Xc i�;h�&�:�"7ant�-"�e�� 2�'� rep�ZߣD�themsel&�EF�y�A�]�4A�1U PWA))������eY:�[rd Z�PWA �ye9 �s�&� 6qA�=os.��% he \��~th{^3_{�}\ɜrm{H}\;R�2*4^*l�jar.e;�T"GAI�]A�Gin ��b"on6� {3,4�e}}�WT�^63.�X he�24$Q^2= 0.35 \; 1GeV}^'�W��91> $A�eie�9m�y��%��:�]E�J3Nm��:�> (e,e'K^+) N�}!�(�c.4.�6r11Hg�iQ2!��kbt2GMt23�sN ��.�t �l�<� �5}$O.�k&> u*(,10}$Be($^{146��t@(t Florida SZ�Di��C�a��'�e!��e�h�� tele^�W+ �4 ann�4�e�*ed Si�0E�bm\vxe�(��H"� E�+ %e}�FSU- �7 rray�ve{3-:�uabK�4 �!�1-���B*%�. S��h"��s�"�t Xo��ly� ���col�t"ed 1p-1hL ^.,I�� N = Z = 8��gƽ&Ҩ& =Y_al��2��}�-r�;O(F �BopA�зxC�S��$p$-$sd��� T ad��Lv]/�|8���*:w"�q171}$Yb�A�70�WiNb�i%3^>(�He,  $^\pP+�$$)(fu7\$�20 �q�~Tew)moi� C-�c  oaT�6�L� r �y]��2�n� 5�.9]�d l�{0,171,1 ��&/�+x1 +D2�r2 /en-�"-��f��!�unpai!4MO��v���H~y �x_32$k_B$&o*Q�jo9r�=e� s���#t( 's�ac����``pygm9{�n�V��.:��T�:�$; ��g)splL3w��P�IQ � �a�ale7 eU!�.���+.p�� 2����(ty vio�!%+K5�e�?*3#W|�*$-��offAA&səKA4!C�u�=in�=5a�r�%um�yv>vx�Z\Q�v~(lB�� atFb,�.�u K 30$^& < �%e < 40 $.)m���I�\C%0LR}(\vec{e}p)�(\A�i\>m$ _��:$_{5\ysyst}$�Q s$ 1�&-6� � �c I>S� D-M��1!�no��V���9=�,vBcu <ta� A$_0 �Y�V�We��im-�+ .��a�gu���]f"&3�sA�a�-&mur NcE%a �er)�  w"o�E[�b�M &�0Hi �|E�= i�<$G_E^s$ + \FakGM!�G_M= \GEs 51� Q^2$~=~N��inqN�@ �). ��0.2, ��-�"y %i865B� �~1ve�">�aaMV�r}8 &+cw�� of 2��G$.�2A IKpro�LA�chambOj���A���n%?*�0~�0w�">�:c��dm&)t � \�#\ALam\"M%n)+�r�;hf��2in�&4!�?Z�0##$yA(S.75�L.���&�e5� stoppa� ]�G� p/-��M!d!5loi��inw!B��-c_�jem.2� C�C2l @�W=;/ �o d�J"ux&m{p.+��K3M0 � N�!sti~<���nA�cl�wof 3y* Qar 3"F"x���!T�J�< ed�E �ata.��hav�1tHB�^B��?a=#eV to�$�$". A eto-aR�Tp (MOT)!�># l��Q�'�H_� sus�+�T�����Aoi�4%i�$�ly�OEZp\t=i �dk%�!� �� �7l0T*#a�Md� i� utm\�E. Y-$\nu�L"�,��s���2 fashit �3��_J���5FRAZi�}0^+2x# 0^+$��C%�. $^{38m}$KA8D$\tilde{a}$=0.9981�$0.00M{+ 2}_{- 7� �� 5VS6�&Z2c 1.#��A��Em|s.y,>��x�&AA� iK12*� !�%�a��^"�.P\4Gn virT:i]�:A6�7o��PppentacK�OlB� \kWj{N�o.�;:�;P s.}�_A�H�>Ax�n�@�:i�B� \GSgaq�UE(lL<�8. _ ongo�Ti$ ��iZ*s�!.i� Crs~2�sevil}/=� ._���A 7N> �m� �Sgm. P 6�veݚ!�$o $e^+e^-$VK��e�orzL���f�:R�'eifyM-3 \Piz � � pi0}�Gt�J&�&[��fX� ^��j��eg!�'.�PI8pah�A�) !�!fa&� c,Lam daughter� N ���QDl�IpQ FAQ�-i�xJ��a"�CA..�%n x *8of K$^{&%s*ZCLA*=K���I9!� X�4�Ri"04.056e�4.2478!r r"{ �-!J�s�� ��cS.��M�8 y�!A�h��� \7M� JINR%>5��p$�K$&&jJ�# $pAsRnp + {}_2(A-1) +�) -p+X�3տ��4�{&Y��^%��*PfpAL� C--�X00ed REX-ISOLDE� �~at�-�n"��E�}. ��3%�#�7$�!�q�>INIBALL.�$ \ts{30}MgBs�e+M� o �+�� 2.25�/u toge8a�nKnat}Ni�,&�+0-�),s�2�|� "' - l(tt%�ei�-*�,b�w�A�\A�F2i�"��v���&�rayQ�_\beupl\J of�)6j�'�G \beval݃am*W*v���ija5� v|7B)1faEP &$e�� 1%U <�Q,e�r���"� �7e7�"� ��a1sKc=�E&jll �*�u!2``isl � �h ''.d�qwo/s�*�%&D� v�9i�s,"7 �r�`�/d&".�45��6er&y>(s (0.7$^{o}�)�87ϟ���x Y�{k1� (PL� mD[E/A]4w d 77aGW 40}$Ar + 27}$Al*b. P�%�4i{�� �&����Jn�r�p/ at t% �f�9s%� 7"�6�,i&?I�^mita�l�3=qa�J&.c^ � �u(2�a1-�� ��e�am�q�!9�jAOA_ �"^zG �%'*PLFAfe|HR07-vW�-�r~{"� Y� (Car"*F� >��u�$5 � "{.h_,��ܝ� �o1e� m�'lon�x%�m e�Zs./�1:m�* 1��)e"'0*݇(�A6)��[�G!�J$gz7!yZ_�>io�4)���4�3h���e"Yc �in Z�AQ�?`dtop6jv�Cnrst^4�C\set-up���W�Y�8U�3e" e��{`,!& I3$atisf�S�_H�55�le@� ��08; a�@$A~MeV Pb+p=�FD FRS (GSI)Ua�&ot! � $Hto` �ck���I (j.��K�\/Lo�+�JH �!�)o1�y%�"� h�%�V�q5�!K5��ѹs>�1� � Zw] e]�B9s);8at 1A~GeV, fail�& �� �}at9zk��9I��s&�H�q�t�&-�d-F%��W<;��% _ailk�aNtωI�!�� ph�R"m"? @�����.��#��n�sub��Z2��lf6= aB��"AZus��� Ib� �+&F�&�(*� s*O*�3UA� <)e�tho�6ew=�`�-<= ��!=50mH spal�o�n"S/aA-Y".�2� S�aNn=��-nt y",Nr4t \h.Ab�5�4�i��!���81� qwI�!m�F�I�� .�8�=|a<�g�e�inv�M�L1[�onn6� equih� �M � u�g� ^&4YZ4EYX7\Omegat ..�j!.�1!�ap_T>3�3c"�V:Dde��5 �ng �F)�a{I�U<ž:�� veal�xt� �/aO-insp�Jaey�{�]u pr���l���� �} �|�"�Cu����N% a2zdeaAe`���񥽍��5 \Xim$+�0p�"\OmOmp�B!yehaviZ�lI1�+�G-�pCae6�6M&%�A+`!����Z�+�">]Mod!�*6�6��8 ed.��heE 46}$Ti}Qmpom E�Ji��}��&A�� -eva��ex&%^� � 19}$F!�8 bomb &$144�*s 2ZI����jpe�UscS&� E�Zct:%, {\sc ICARE}�VIVITRONO(nd:�4"y IReS (>�s_.g�)E� >�.n(M8�.S%�63 sidu4!!��CACARIZO�3d�a)ltOrlo��E�)sM��;-eJ cod�C$c CASCADE}=]�!a�%�)RIVQ�lF� �-6 � �!�e�,Q%�amoc-�-��cat����-shg�G dXi�#Y �I.�.L'y#&8"�A�'b�64}$NiM�00} $MV 5�UP!B��-��4$\sim$ 5 nb. E�ovᘁ�d-�0�<1}�� !"�*�  d� 90\%1/&�7%yC^{ref}aoE�%*�)#"l&�� d-sh�( � '&t of Ni-in �)L�4|%��a�2�iiV�; A=100-200�"I �#"g*A��mP.��[~5X� ��ar�3q.(� h%���!�.�W�#hi$@.< ��u= +}K^s��&�?" Au +6+ �NmL29u���PHENIX�* !B�l ��!��$\�"�,��?t*b �&!���:ˏVpa�# book��2�Q%ͭ�B�"�3��!bin� �ri!s (�5'(dN/dy)��h I� ���te"�! �QN� ��-"�!�e�h, $R_{CPa=XA�!�ph*��*� &K]�o.�1� �fe!o-��iaJ{�a�F�'� %���HtyY�DZ�t5 ` �� 1$"1 �CplNz ��- .f`Y�Hp�G,a8BuU�.mP 7�� W;�6�-V�Q� �d-j�jA<�C�jm~^"�[eF $0<�<1$��!Y&!_i^0*�C! $�p �9Ba  E.K�g����$� ��0&,��y�"�-�� BEMC�".!��b �e\I4��!�^?'x]ru�>�S�*)oAa�a��"�$JA5�/n&�5% V�:(NLO)a0j�:� -�-w�Lť�)�%: e GD�j�.5 Ղ 18}$O+� 8}$Si!�V� 05� *�.��"� *� EUROE IVe�HECTOR �0m�5hAal�B3/!�a=��1\�L%]a���($\0 x$10�))��2d� �y���c�,w*y �CoriolKCf�.���� �a�fe�dAfee��-� �l�!�b��%}4�ha��is����%���"� ���t��}PR�Dn2fr?9a�� � �  &����&�*�s(�)��FVCERES=Ӂ� Pb+A2c=�\�o}*17~. A@�Ir� �niM�'�=�%����� of,�8t ~=~1.5b�D. Bey�!z ?�+�(&��� M._ *$~1.2�)� eq �,�q60��{h^�&�)���al�F=t2�)� a�� m 0G5nd �)-to�m($B(\pi*�9��ct3-o��hi-"�)�u![�-O�B&��V# ga�(2��AabroadeWCi.��F . %B�uCs���^aYp& �"�"�5?e. Rc.M� tSIz�:��E  % �E;ndLZ ��An�l5�.�٥�&"� %��OMD�<��yf �N�]�� : !�*��Y 2�'K�~� pF"e"eJ� �06i&dA�y��## dN �a�B� �����a�Ap+!�6�= An� <,�2��� _ 9"�b���2,�ssN�; H.$Axq��,"� V� *s@9A�e�)����% Y�Gi��*���(K$^+$,�$-:�, \lam ~!�\alam)�P� s�n8 �q i�3C+CESi+Si2�t jQ\agev�##%6�bQB o!=2$#��P9ata� +p, S+SnP\q�i��B����[�Rani ��.�js>+tj��stGYut 60m�>�i;�net<�SM� ana��Q� �W�smi&+R���&Fn�)i.A)&�h�Dd�!T]��( of coheren�qt systems of increasing volume is proposed. The transverse mass spectra can be described by a blast wave ansatz. Id0flow velocityk accompani @de��temperatures for both kinetic and chemical freeze out. The �8gap between ine� > decoupl!,leaves spacesprescattering. %YCalorimetr Hpcoalescence techniques have bw(employed to!Z arch� �yeffort�YrTEXONO� � !(on neutrino5astro-"� physic-�,``flagship''ji�Jre�-�uR ?a@�XKuo-Sheng (KS) Power Pl Din Taiwan. A limit�5M�  !� ${ \munue!B8< 1.3 \times 10� 0} ~"b}$� 90\%A fidG leveA�s deriA�e�.Ui\ai�pu�  germandet�- . Ot,�topic�KS,A�wel> �0various R\&D � ,E�8discussed.gD" "� s(Faddeev-lik�e� their�؅O9� radi� pd-capI A%!bthree- 4 photodisinteg �e^3$He��enO Kic�re6v AV18imon`v Urbana IX �(�ces. MeM exge cur�mHlud"� Sieg��@mAG  good agre�"*�  �ll casea�d�ngF0iv ���numeri2 I s. P:� 2�)��%+�IablvnJ���� :!breakup�1�ts e!!�gom� deuteron/%�n�n� !�9�,^We studyim on m�< combinP�Kl�� cJ field�oryi* non-�urbIplattice9,\Ke�o��tdAn���ia� term�by zero.w.N�� . \ �im��e] �o)b�_.�4E���A��+i� be� ccoua�ly%�short-�� . ConsequC, (>�� ch��\"� $, will be  9 �:v�.�\�_ALskip=14pt Triple-glu���h"&6}ed��A�pl�e�� � A���puzzlu Au-Au��at6�w& .� ^�sport���X z�demon�{ �" isXpy achie� X A�`�$0of 0.65 fm/$c�.v.@���a-�:Z �� h.\rule{0ex}{3ex}�\nopntEWik b �E Ʌ�( ��{ � wtr iz ��edE�{M�ŀ}�EFT2� .��A� +2 d�via�[0ward-Compton-9&� �,s, thus ensu�!q*c�al��*a�` )��qis way�qval!:6$usual loop2�,\ d no�-barya xpanaor any�� p��#9��M he\"�� infr} regu_)�mad��e Baldin5*$ can direc��ls�)�sum!�1�>ū� rast!e GDH6!��3pP ca�unsuit���}"TV�-��throughQu]by ta�hriv� ����e� A -�anomal:. A� ex(ɗa�EPa8 g!Ab2� ]�&�:f�@QEDemr�Pfam� Schwinger ��- a t,9� -z�far�5�r�Ke�� concerned�f3�w�sues: 1)q�behavi��T>�S 2-^iliE�122 eA)�-�nG�"�"�Bm2�y.�A��� � ed-�n@��y�=/�dissoc �%Y -YEU halo �iA�d�op�A� sEo� . QF��a�2s�{8}$B�L� .� showE at \ nega<2g� s�H%: seizes$inaccuraci&��]�{Bal S-��p#+beryll}&���ion.�.��� }S_{0}$ I��"eu�: "!� pue�qE�influ>͙Dirac �� �!A]x �� iE�t!�� � ݎHared$Bogoliubov)��5:"� isc��&{ Bonn-B*) �&�M�.y&�fR"� maxi�E13m;_w max}� 1--2~M��Wra�ong��on%_NB. H%e we s� �it �s � guid narrow dA���e��J�!�.�!Fur�ore�W  slowly-��%��V"i� �!of"}sta3�w  $superfluid` Q9sligh�$l%6pc MuAbecome.J�|s�I*A�deto�Eq�of� �I w����M�tu���% of bI���)a]|bQr�G*� 6�h�#���1�1c��proba y.6ma!��+ar fu�,"��Co��E�_.g(�-:is�&a�c� �FJxt��p� ach iby Eremn4nd Voloshin(reg f1jext).���mp!)�pre�!rapid��ra!����q�3("�&�'$Pb+Pb$�$Au+Au� l*� CERN-SPS#�# -BNL�&� � Ag� scop�di6pe����a�i$h ier^��,�J" h�[!�y �A thos�#��p! s&�DHIJING, VENUS etc,+ 175!ral�.�rNfirE�I�ebtit%%oon pi2�#2�� �$be�[A%$u ed �p��1�5�ayo)0!*�s� dari� &f%�G �<" ev�); :�(.I�Mart low-�m�>K巅R�� ng f�o�l! � X)� hopp2��g� nearest-cg_�o vg-'�%. \�&`$K&�"' � �J& �spa��nheriAwJ���>,�&aK errors s*st�ed�9riori,%M� �ӭ���27at!�.)f*?qu.�!W� g 2c)!to����m�i�q�%�&aJ kum��l$.�CharmUbottom-v"?*\�, Q�&G�,Plasma (QGP))}v!<g�a� e ob� v% �'AL!N��to�*�. E,.8a Fokker-Planck&q to F ��( E�g�-� Boltzmann@we aug���R �daN">a�&.y!s�Oint��� � avy-i�)Su�on��!�er�kmotiv%?b�%%�QCD#�*� �(�c�DM f ``�(''����QGP��uw��!by!@orW (pseudo-)��,� (axial-) �!D$I:$B$-m#s%�E/�-MMy�y rA����W �� ��-Tc��t�N%�6`sub�)�ly5/el* *q.X.l c$ �� mKq� 26�a�lso5EIA����!&% �!U � ',6)5�U�s.�By�zAdaA&}��surfac( shape !dia"� :0r�Wu�U(5) J-Q: IBM,a48��"� 6.e��.0s $(A+B) < 0$ be a%�la��ib�Lrot��d�_n v�/a,aA}ly'al ��i�a��y� �. W�.( {���d &s"B)�edq�.]z|A_a�vid-1daM-Hdr empi�e�AC.m�.8Poincar\'{e} inp�!�#&�Ar.9 ��i0 U��2ia� %�BF+"�� * to� E�E?TRef.\,\cite{Kretal03a}�'6a!�6<� � eby�en��v? ���&a dyna�2treati}=0Goldst)bo2� ��m2�!�commo���Cane� ŧ�aa�"� - orbi�+nu9�!$/on6 lm*� ��a� 2b]�ly%`-~m� XQ�U*bUis�,.�P�7�%i-"� `�#4$(\vec{e},e^\p�4p}\,)$(yb��� "+)���� four"c%�m�%w�{`3]�%� � /B$�)"�"�F&B �V-2VwE an op/2"� 2�a�:N,=��crepan�%)��<�K�ex��h� +E�&w=to�#��"����nm8�� !�in�p=�� e&*�+w4�p�8�" 5���M�>g�� s= �challeM+�4%r^ ���hR� *w$m�<*0�_ m�s.,�.eIJi�eigen)3!ljc��)"Us�gAal�:(Woods$-$Saxsg(%�CK!.Jacobi!u ynom�(8 Nikiforov-Uvarg�i�/ D�f*�(�*#1aar�:u,E�)on$ ) before.��(�ew 'PN�  �3&� %CA�T$e��i�� ve�?.SXAGSA��)�i��A criin�  M�atu5�/}6� B�isp8nw V�#i :"� �*,>Q �1�850 A$\cdot$GeV:+!1.))1p8j!�ollapY $v_1$- A!Z � $v_2t $�2 10$.y;{42����"�9)��r NA49%%"�1 . Si!)AicA "�& ��0'2� ?3�� e���7:@yIu�  *i��;a��(rr:]@q%�>l \�4g$� 4$\rho_B$. More�,�c�*� 3ell�c �%e!�jetAjEz�xa .q}@e_"V��� l2�$is not fak)x�7ffra�� . Ad� F ,�1aiS y_stu�a�!i!De away-� B� �dW( ($<$ 50\%)] d9R�.F��g� ��A�$v_1, A� clos� o beam":�� A�o%�o�!�Ba)�1�d%�:�:"Cx��D] ��>.|a��Drete RPA Hamiltoni~4�; �AjyB�ut� �.too�%Qremov).I��&at, s34�� orig�d��"�"��eA>��,�@�� fil�~ �n�m&on.y6.XM4rac'sI"�(Q*int�.Es.7�&e. a co��non2��p of"o&]` � �?t��E^ �: B! m7=]iAk2of���"%$E��M�:? non2&/~ mi!i`vej%�Bar���$Swanson.�.�*T��3-u"} "ed*deepl,Art�CW*�8, $\gamma^* d\r"a�" ,{(*)} n p $,a�explor &I�Il��1A�ory1SA)n� on9���a�2a��3C��EMC [Ae�2I2? �ba��2Jtwist-2" L �:pr !!�.�for+, near-matrix �"�t�sbpoA�":b�� "�� M���!�:�D� O��)�\#ongIi)'"58��l�l���a%ma�iv0a�!Q9�� a�l�cl!؁�"�DHe�1� K|-"� z #< & $ � .bsI�2��. E"W ev�( ;�:�� ~ w�H��)bbſ�:ng6tLliAary�=/�{T� g�.bEGusIO� >|~ �;u�I�tT>�Hi6al�4ima��r�Hre,wQ�:F !r8 $V^H�#>$WW�,& Ir"�+�e���!&/E&\ �3. 4Glauber-Sitenk@orw%n<G7A��{DF(0 ede W�<0ard double-fo.� )� �2�dei���)otesi���.�1%K��9E5oS=dj�4��.Y�fitb��1nDepM.-7Am.�&� ) �/�2"P"iC7�@-�/s&�a�=���* 6,\,17}$O&�s��a5@ hund�' Mev/E��p/fh&tJI�?�z�<%{� �2�J,aX somewhat,� ima�Mn:&Qa�ata.}�f'�� p .�@K^+ \pi^0 \Lambdair- \Sigma $!��aI�M��N�#�)&�$6s(1116)E5 _92)/s&�  dr;�@�!�+ $@385V �(1405�.s�. �ai�Kl��F�;ound 2 Ki.e. to!f�!^'f�"�A'v� knowb7 t-�6�Bu" e t- �Nkaon-u�2a�asE1{� $K^-:�6e)_R&-�$���$"2",&"�!!ia�/{e"|/M�B !!u,3yp%�.9ҝ�e�y'š!� gaug� ��%7w��X{"is��t� �%�'�o�� ificI_kr �6e6>*s=& �g� . AHI2.AA�-�D~"�(s�o� }i�CogrO>or�In�at ELSA%at SP�-8A��co�)7 �_c� 8s"�Mpossi,,�� �%ntiEб%Ss �" resho�>�,��s.�3De��;�TSO0-`0�� !jBD (PN-RQRPA�&�:Y�Q� P$\beta$-�uhalf-li��&�.-r�N�i!�AJN$\� x$5�82��� new&* �-aX*� ,� -n�Dd ��t��� =� � �2@J*1:�Rar2�N� M�1o-h%O��A�he 1gI �I; Gogny D1S.��>�$T=1$�^ a� cK�Q� �:� .u ��a�5�r2�5an� �oL� Fe, Zn, C[ T'7o�D�ins�!�a��9 life�9s!4Nio:op�nSRe�a� ble�32}$Sn.��Jl��uM�2z ��N$pi 2 \eta�$\omeg2�� �fLag!��=ea�/ !4�g� |S���� �"up���x>&�*F�QRE�+A�|"�" =wA�0�D� _� $\foh$,th$Iy fh�cabes�� �WGnw,G 2��0$D_{15}(1675)^ ���  N \to 9�1�.�$FI80)YK!"�2"\5� 1�$�a1 "m� }2^L}K%o:��/E"$I�*!��Oa�R"~Ev:gJo"�^�/ua� �A�1�g�&6,(�5��m奡�:U!�Y6�5�A� (--Z6/!_����52]o�m��A�G)iS��( �[.� phen� olog�?BN"t9P.v�Gsho��6> of D�Ks �3(o&L+)*� m�!�a�:�^LaF a�rkCp*�2%�� 3A, a jump1�;I3!q�a! ��,�� ��ol`a�:(t&�JE�) ���'�M*B ies)V���Fj ��1H�?urIm�Ll�1nB&Iwa������(��"k ng)iB#L��Z�$A,� 1�c"�"a!�;(v6�$e $J/\Psi$ Z.+!� same1"�>��m�> Q�ndi:+ �;iD,��j�)7(�1:�7er�f:;&�� � @l@;H!�B^ .��#@$N\sp{\ast}(1440).�N\pi\pi$�>tOsmLC  ��A&�+ula�=EY >!��-I�� �aac�B"U*M�b�q�r 5�6HHern{\'a}ndez et al �k R�NC�I%i�_de.� b�F!bE/�Nt0 p�$g\sb{R-R�R�0 %d  N$$ ar� A;��.n7c olors! erco�&t@I� �A�flavor�m.F=��.� ��s&*5 r����one6I�!9�^p-.��Z1U��"�aP-�GcJ�!v"� , revea� �sll�C!9� c� ��~/&�?m) e. G�Pala�1 !5 �?^���"^%��� !`C�O�)d�:|e� A#s�,al�),e�� _`%"�42&�mn��.��� �(�lf))^-!� -locW#�!a���!�n� .�Lcf6d� A�Z��N Sn +. !�6U !)e.%"Qc�RU.�L vi&�/XO ��2�E�e7 ��$=$I�D_n! asspN@T=]se<s�ec���FYHhe .�\sa�-ng�"�N* A2�. F�bJ"Y M�)L�V/ `&!%�01�� � �d�i���*�/Z&M�.�fde]%� so��Cu's $\alph�nd �%�&� �!.��chIZ-1%�� �2a�$�R,�"�4q5t�kIt se�i���e:�Pd1f^����Y'~8ar�NO%1is�&. B�iR? dropYBx0!x�Ceam" �L�z} ri�y$.CIsobahie)���-*Yof K$^+)��M�X:�7e�how"� K$^0�Um��Oifur?%��S%./U�V[�d7WQ� �6� Ap��6:�@�e��e� tude�SH.9�+m�Wa01>as2Qas&�'%��+�� um!W��!rN)Wnd��|"@�*�#.�< vail�dR,��CRR a� 1 AG�^�3�%pur�;��re.;+�': A�D� 1� 1.48PNi+Ni.93.��:Fu�X<-Furlan-Rossetti&M�-!I�.��܁,0#is�bb�Npe�7og��3$tfA 9 e'�"Nd�)� �i�rO1�. N�t*w= 2]urn�$*4 bW-�L��7hhe�I�o$5�d i�(di�m �@ii:�ub-��� 0!Q"G�|un"�K}4 `)E que &� e�/in� �B�"1�E�, &�()�� by glob�8r� e[�J* . %\p78{ % {13.40.Gp}, 60.Le o7Gk 25{7Lj (30.Rw} %}��i�gnu�8pt "�)*�$��h �Fhop�E"Fu�]of Few�XLow E�2U%Ph�_$" (FFLEEP)�was h�[ eUni�CY of T6\oq Decei8 4-7,�+2e�"�.wr #��G� #&� ?M�`19;3I lX'� �2�)�"bkadvsH#� A�� ar f��-lem����'� many"�A�\'�A�&'�*�&� ���(ur)kt�A (A$>$4)JE��0aLjest&(W"@ �6�N rele% Mew"/ c^ro7 Jn%Hk� v9��ra�a situ� ���[-e��:� � ]+Um_�%�!m�A g"ya�inspir�w }-{ al �vAw�� the�C�HlyH lo1rIf�,h .6nN&ll�inu4 �.5�reatXM"p l��f�h.�un*�Oy- e $NNR&'�UaG�8yFE $�7�+ ( d\to\pi^-p.�|4V� b �$-A��R550lf!x�3.K  "� � U6�e\&%>s%�arA:�(!he��8i"q2� �!�th02�w�s>JɞaFe�2v=E4"��2��#N��-qL�ryunnQ�#N�1o&"T�!�^���-"� W!�k �!,A[ly�g�*�1�8|Q$(1232)*�T� � a�fFeI66�2���a�\p� �=%�f $�� =Ja���&�(1I�@lea\=G<�3cis o �� �:0-�tRa��."??0.2cm} "jZ{��8:} 24.70.+s; 13��; � 30.Fj\\:(Keywords:} 2�;�Jq��; �d&[ ; PAe.-F&:�d=hs.�dMA*`*�o�B�M���*/<r���"�0 |%`&"sN��Q!%�"s!�K \A��F{K}P%�&� �jr �q qAl��r!�.bKha;Q�S�o�J.�E�Q)cce�.at&!C&<Q"0 f( I�y�jMP2d��"+9G�J- y �^a�Cyefu���r���3Q< Y#U7)�P&!-:S �!Jv�,#"#7H��"� 2H �$\phi$�+F6 $�*(�* )Q�D_1S4$\Theta^+$. \f�B�2D{JLAB-THY-04-XXX}� �nDG*�5�#a"w.wR&�z pan+(�ai�%`ol� nnQ.[ �@�Gma�Pof.�0We!� a ' 6=�im�ba�+- �GM�p� "�" c&� Qc�e�yE��-es� y re� ( %�FVs d� na�6mA1ge�e euclid�a2���~ �� w��3K�=�. S�%3�r�6�H�$�-o" es.�EJ���T��Z�'� i�a+B�a%9�>�*&�<�T$\sqrt{s_{NN}}=62$~GeV�%9&i����\dK%k2h|� �N�HrX8c�4�-A{[��slcch�yer&�O�:!�"�OL!�|;to��@a1 A�e�k�;� 3IxIxbe/l s"}."�0s[�;(I $��� !�KRł*gcQHfata��S-a$�W�#at]OBXb (S;0)�a�Npr�lgly ��N�� usen�� ��aQ@-S:O@�%quiP1.cg#z%�ata�"� �V��+-2*X at backs%ang��y1fdr �}v  valu�_zOV��&�ea�.fou3{ �( fail�jC**)��of �J���! $t$O�54}$Sm-��Q3A4}-�%_%9�'">6�� %k�͛Ru! ford/ � ��un+�keepRvoB3�u unambigu�;�cB�5��r�AX%�*s6��.ߡ�TBz&�G1�i�rg"y�&7 )�>L|@at9�%cET�&��]�I�I4!�  Kmo D� 1��,�9O�la3(s:?"� ! �p����p�%��Ec� ~_i#2� �V6arBQd�uA��% $x� Om$Q^2$� i $�f } AC:E��Q�2�t��R�� *� uA5�.(;b"jQU ��q"�� b���#"DT�0"1ned"eT nd -�=�&b2-d~y/soF`�D��!Und�"�� !�%\o� � � -�,> mpon/1 :-1nZ tex�A auto-z�julfil�� he W�g$Takahashi �s)!��g�( [s�~Pl$�sui�5U:M0a�Ar��r!�*��L`'�2%, :)8uE")�"�!wii.h�r�B"� �+c�al� fQDZ2un�Fml �(uEincorp���^"�4".$s� 2�.�%<notice�!*$&i�/ loosh)�� 1}${Be}��u�oge��I��3vѿ�*�s4�39 A�V Far�� 9se"4�%2�l�Yte��du"@2�Ta���pady-�ra�g`�/ 3.�. pu� �FJeorm�!2R9@noB�s&�V�"3O�@5�t,�-pr� ��nJ�Yn e�%aA'&4 9$\hbar\O�4B�r� �>YP `6" �MhA� verge�!l�X*!gof�N�1(z2d6� Eyra �~ly< cer�t�!��2`ion& vL.�alw� too%-�*F � yk6a f��&�"-��!�V�u���=O.�s!nA�x@@5*b�%�8most draj��^{q& s� Ywe ~� to�h) $1/2�")����W�a����@�i�4Ts�c)-�[!S,{"%�"�*aMIi�use&- -u ̊ses��!coY>" A�ؑ���U�.���arga� a:`.��e�E���i煾h!:h� -ba-������ ^{13}${C}���}E|������O��,�XG0 IѹE)�unn�/alu4!�A�4 $N=7�j��� A=11ba�Q�ru�) )9. 6�nv� � ma�F d�D2 exceeE$1.1 &�~9�UOes  %Kst.G!f�W�=$ay�G on bʼne Uf}��3,M�i g� !�,�mi,B I�a3�G�'^{10}\����+ n$ � ") s.  new ";+surve�_�world� ��+%�ed $0^{+J��DI�0=�.d  x|mt�es`"�+B�str0KU+i��w]�<%rA_YO� e5[�3e$ (CVC) hypUEsi�h6Xcto�\�?ta�� $\GV�I6Pko�'A�kht�3art4$10^4M$ana�9 �)ar�i�m�fto $\fS� q 0.0013Z.1��st- K{ aP�2��da�!�,cV71 /��~ |C_S/C_V|2�a���Ma�Giata�"Xej up-dZ(�H!f0Cabibbo-KobayU4-Maskawa (CKM)q{)\L$V_{ud} = 0.9738(4)$�a�! le D�Group ��T:s�/ b'��top-ro�gmQf CKM%E �i$| {|^2 +  s. b �H966(14)$; although,�%�W�m�a+$K_{e3}m!|A)ex�_�9I �s �!�um">:80.9999(16). EitA �� ���� .�U"�2-e�-h�1M# s.�"ce"����AY��~ $p_T$cQ���6R*T ���mE!�r3 e<�o� `_N#i�U*��V"pag? -��T m4su��o0i:�,1 -to-9.���ir�Er�l�M"��azimuth�#n� ropy�to(e:P�i��&6]"��< sH30 z%r%0c7C�� us.�� � �7� n�a@� pU��<�Puct�kow-"?! *���#lk�9!R+ll&��jI�O2� .u. SQ�=%pp�da�F�I-o�=oo/=\8: a $G�f��a,m�5=#g �{V�A��izA�-K6 )� �%�o�!w&� fI�3 v5cutoffh P a/too� *REx� trun&���'[n .q=��0�j� 2�%e"x N�rkzar$A=3,4$B��"�K6L�Ae2k��) �0�XA A��� � N��)��ng�(8���-�m�eQ�e�AL���O� 6�I����Lb�U)�is`8ed.�R9��%OJ��� � ��S"�Fj�s (SF)�&wu {!\aI =i�is gov�y�+@a SF $f^{PN,A}(x,�$|�":, X,�B"�in�L'W�{".��%Uha5 er�3 fe� ���$\mu^A�0( �DauA�9�SF�� ��z�%Ag �3( i^9$x_{1,2EO)~EaZV $0.2"ix st0.� �- �18=H/�!~xMm*hx_m� ��t�fl� &| �%koscil*|1!Z^� (3.5-4.0)*Z �Q�e-EO�vW$0.95Cx 1.05)^hq,lm�� *��_$xi 1.4$. s%l�Zcom�L�A% entire raaY)�t$A=,� C, F� Au �Is�*al�$� �|��P�Ii a)Dbled��Z��Km��7� &c (xtE�� .�P�t�P ion-Eq���!Ziaa:� �G.�KC tak�`o^K��a�8�E�AJc!�G! 130$�D!(:20 &2*�a+��A�.���hibVd� {T}\geq 2u/c�Yarkably�_pAy -law&($p8$́~6))� gene!��g_�O;JE�(uS  �ȏ cogn�^'�je0f*� , albeitI��=e*KraP A� lex;*u���geo#�6s��y� + stoo�poN%�fAS�!Ms:�U��.@8 rguIA�{�s� �5��4k� �n9 main�(Dn��� self-orga!Bd"�i�y��pl�"� c���V� =m� "� PHe�-�io�,a�Ae``| } ''E� nyPe�"=""�� 6� *� <s�| ed.��&�i�m5.r �@ �t&8(i1n�m�%� alin-�#umф"I :�+��A(�.�&s�=&F ʼnm,fR�DkT-��.AV}G-"}G2� . DoAso� sto�����z wee20Y>�U$$var_{tl}$M}%�1P ��a�b�5��ed�`�w�PC� 6C�x hvisco 2�l��i�t�F>�E���� �Ofcay�4�b1hing-� A ��� �@ o 20R��G~+2kU0��<s;͇a$I�ign\\!� ough�Ue�reiw!.����& s upd�=. ;P]�1nG� !��'"!$f;"��2�$ft�u&��e� oH�!�2��E�(s6IRver�%��i�A $\F fa0�5e>Ocar ,�,"�3pai-/A`�5%HL"h#Vuf���61�a�7A�(��R2M� RA>;F��'�FHB�����B f F��B�� �!@���/: $� = - (=005 \pm ;bE�$averag� 9z&��\!W�6 c�?�2���P�P,@F -mix!h���,*�04s?=&G!)� top �-� S"G��x 14$ fcJ�Ƈ"�5; 7x��&�k�>� E�� i&��2���� �.mU��|a��/&)8��*`[09�' go�cQF!6O%�mO#^H.�bm�M�j��� L�\au!cw�c�v-b�(�su mono�'-)� o 2 y0Nb� ���8 pi0F�4�s�y�Vwoy �qesS7C�sK"a�� �sol<�M�B' --Salp "�&E1��M)���{�!��LwY.e&le\�icɌ! ��sQnga��.!� c\bar{c}$2� I���n �#��I1�� . Es�(!��1!�� % A�'6um-@�~rk�ո��cNe���&n'�-�{ 6.F�� �m�J/2�@EGaddY0�&��u��*^leir&�R5!�&1�l�%� :2 �%�>1+manif�!�A2a9�� ��. �&P�&� ��)Nlyř5�s_A �E�i�Gce�nt>�e�<. D)� M3�l��e)1��e��nvrkQ):�In5�, t)�3lda�y��X�on6ʃd�y�tetraE@� p�W C'��w�. ��i��� �sI�!> "c�%u�, �Zap 1x& �M�%��3at��?!�"Lh�~lYb� tor�(b�l��-s� %rA�2�XA��)VA� �5�A�72 �.d�}&r���o.�%k� &=\)sym�*� &�1QsM�u���E�M&Ji�S+ uˮ"��>a�Be�highly A�N� ar M� r ($ANM$v�comaJ*uD dilu!�ha�]��[!Z�&� isom�.�A)�&�)�� f�� nvtamms�I�4ygG ar E*�S�!($EOS өs� �mI�s����L�0s�*�$-.oa(Nnd 2��rm�q!}}l%X��� A�t'�Uno6xj!Zr�|�Oy\=Q�!z2,Fz ol[ =��x$\dj�-k�t�L2 qu,��E�"�-�liquid-t�E�%@, "/$uG" @tae/�"Jpin%tA,%7��aAb-po�5�E��^ , n-poor,z_och�$c� .reME�"r�x���� /�a��&%���A��y"�s�ڡ� �I%�ll step�)ҩ4,I�prlI�&_H� a��BS0E6I��if!��=� ���=IN�BuMEcplaM#�/ �de�Jy grad0/I�6o6�� �/ PR6�c"�0&�MiY�e��n&�QA�')R��!�UJ�t�l�$�W�*2r!�d!2-,parency. Per2 iv�OVJH=m�� �u�D!F\�;�� I�ae<[.;M=w��3=��of di r5� s1�g�brems�$ hlunk�#by�:!�2�%E&�8� eep-R�3(DIS)��D&)�2�����6sc � �6�+n� a�&�S-Qra&�s=�U1%� t-to�6�3�H�>@!s���e �%Eh�w!�8��-h  HERMES!�DIS��D��anw�|�W��� u�? cAG c�>76!�y�2���2<5�3Qlab)'<#0$E_n^{lab}=28�c6513�$250$~MNT�?[WE��kinX7ldo�-����Wigner�Cr���[a@ p��6�e�o&�(NN� �>�Yd �#�;6]���NN*&$IwG���of��Edy:*>9M%��:.i��t" [:0&(�!��u��a��e�H�s�1� A3r.+s� ig.AeO�A� spit&D n�We���-�� -s`/�6a?ar���>� �6��5G�#2�i!�/�6GYV��&war5= .�YVFvAE `2 (NME��O�$%_��k(beta ($2\nu.,$)���ndi-inVBs:60V6P�pr4."�K�<��b4� dom-%p��� (pn"jadd� I���� ; 5Y r per �J���. �.� "�, $g_{pp*�C�lm�{� ?)�6� . E_-_6� ��x"*misA�����+&�hf�>�-�k07!�E3?<�. RE�� F�in|?J89�a"S8��)E&Be�7�R&�H1pc}�� � �&%D!��A��y� s $nf 1s +x$��lic�~geh d�Ti�iib�L.um'� =މe���?.%��"!5� sh�u0$@"iB>�$E"�E$�1 �2�1bA�$X$--ray��+�in�atoms.�Iv��{0.1in*JH�P: 36.10.Gv, 33.20.Rm,J75T�11Ef1�I) �J e $AA["J+ �-G%a]�h2��i뉉us9OC�� jusr��gyn,� �] xE�z al��w �= COSY!�is>���] souI�:%c_#or�(!uinc\=���absorp.*-in�"A4!-!�zuE4a��4�J�K�!B2\,6�� V�tus�� �V�6a��l� ���, �� ��Yͧ��K� 6�4m��]�YC�x�2� ���e3ed Lenn�>J.�B6B��*S$em�Sde : s (&t ��$ �7f"��6�1pt22y}n2(�m��f�-&� �=�$"� �MtP3!� , am��3 �9ngs��Fk�l�)�Ly!?4g58�e 2�.�`.:aon� �;owB.@ � �� �ari =eY�%l'Bu�,(�7C=I2�_)C�Wv5^�L�on�F�6A�@.�C� (-Yakubovski�E��� # G-����Q��*ӉA�inu��+�n½� &V�H � el p=�tL8�ac��VdA�*� n� p+$% ^{3}C�Zd+$ �7s.�W\e{s �I�no�IA] ����r�s~��� co&G2oO .\m�5ng�J� ef�!�=��s0��'sE���&6�<Q(��l& ��m�c�"kPeda)�p�ou�R�3�}e"�r���,�5OP���ud�t!�r� O:8!�:V()8s. ] ffe^� n�24 A�b *�� Pg�%J)i�&w!�. 4R l+�e st (�B�sc�`) jr"!�� ��x�a��vapmV �(a$�A�gLesS%E?��2���/ l*n�(I )"� E$�9�f��*3�Yish��Ql.xwoun�a��*Z\%�)�AY&|) �bin 5qAb� "���e.j� .�! /�y��!v.�'� �M.� ic EDM!*� X)eHg#�;!(*Schiff'%"orZ&�zZPr�:�= ~uy+!)�u�-��U!e�TyI�����N�,(s 2�H ��I&^2�)1|��IzE+tFE X�Yst�f;5ndtE�W �*:$ d_D \���%17 d_n$ j� B9�b�>: {Xe}=1.6; �/{Hg�C ]-3�d_n���?�c.�-�31�!2�k;k�on� �sln�(0.37Y&17 %14)&=({-28} \ {e}4� {cm} $.�� a����� �.5M�s*2_� �7&�OD� in {J /}\,oPAu-VU�. U�K�!�iOzX�tR�K%�N�# 0v�11.�biX*�=�� �"UMa)O�#q�Y� hp^al��*>�nL6-bul# Q" .�a&M#`9�.�� ^"�)A)ng�O�=,opy.�ͷ� al b builUW} -$K$�6�!w$�5��)�#�ph�% ZU!�%N!J� թ�&+�� !CaxK erx���,� qi�Jnsi�6�. B�V!�:a�["� �)� �) -a��&xR�|& ey\��wobblqmo�E�2 :=KEe9.1 $$^{178}$W;[�!� Ek$B(E2)�uB(M1),E0c � �+B� suY^�i��tr�ofU+m b�Cl�� b�RPA9 1� 1�!��!�gh X �&�:�Rtri%��-d��F%Si��� �� O��M.��2C.�IAmo�?�?aK1�.>rU�7c.��"H QCDa�ti4 v"�!�M@�)=as" 6any�(�"lem.;(c�rg�rb� +m�� bala51.�(.�<g!�=iL� v� in/� @�Q �g1&��,A�i��%�B�&�&r. a"�#65Ne'�� �z%*4�!��<1B�5ze-*F�8g# ti�� %*0_�i^+q`mp)p):Gee u��"�ơ��ls. wo*F�-��ar��"C&Xn �2�p|��� !�uow�a!F6 Y� 3�e�1�e��H�A�*(�&"ڥ�) svBa�%��s,aE!���@Y~>bA@v���!eae �c&Y6A�&�"f!d^:�Q/9Z";*-IM�� /�M2w�22g�Xp)� ��6�5i-�%�DbAP"i ��ntXA8 �o�/ll):(�\<kA%l�di�!�PK!a�.=���,�1帥�$^{4}H$� em L�\�fd/� ��j-$d+N+N �ntB4/".c��;�I� 5��� PaulP� inci�!�A$*+ -%`BSiX Ep�i!���)wl*�& �g ��>a �hy�jp٬� ��on��r]da�3 inguw���+En�@� g1 jum� F6���X,"D q �L*�-�49�Og eno�4��cY�4!�I(.M��W� v �Xlf*�, Skyrme6@~��CQ--��O7!u�P, �^~Ϗe�0'�9Lon/-��Nm#S�PVO�f.�q��$�RB��' ngth%���,��i��w � IK�2�%� c�sME%Q�(8/r�.vaޑ.�w�k��H(TFF)�7{6�/� r0e TFF:b+�{� �� P.� m�(*Q��'c�H ���no1�%�!�"�TFFF!�A��g5x q�)�j��00%Oia�-�Ltm CBll&O ��:�&a�� 0/ncedi3sQst�s. \bigIS \"�� {\emK}&��; 28Re;pe30.Cz3R� �uv .#!&�i%$ "h.lA iQR� ��a J-Ma�� ache�E~ Moa#ed)�aCR6}� 6}Be$A��#*�!�"�-� �**%�Fi�H*QB-�/d[eBX �� �Cu�q�.�*)5wC;�s7*An�)I��A:%Zar�M�� \=eeK�c� �H.M7qZ"*oa� ++� midr6M��['��A�� �.�A��S �d"� ��.�;��y ����-,�H�A,  E;B aklyQ�>Nr?6�-!o���B"���� l��ydrJ.u m2w Fjd*�; sudda�rY�"M��3S�n��!�%��� -Fry'c-%��Sv !n�T�FA0#T che�MJrm!?�"7 ��": - n�",!�� +E .#�od�,��c� �CW�*���!��v�\�rv=@���4cyɠ| �j{%1in5��� t"1�Tf?!qu9"5o!!echoy�= F�UT�I!�$Fo.�e�oids (deY)�$&�iE_I}$%�/$I��Uo �*&�7i�!)!(�� -$j?�vD /�� $j$��R��`14�G��nyFs-�"�y�*�%�� �h de%�!|A� dom)XN 2{T:.']�A t.�so-�ded&�C F]as�n-)L�d!��9coe�^��f-`N*�.��)v�� ;� �/to ��޹9O6~"�danb�|ɰ"bD�Z� y�of5Va^%ty doe�z ``�:"E�jc.�&[!ew��q�a8&c)e�%Hc&�4� g m,:_4M�I>K �`_�6� ph�'$�Ti. Af=[5��\!�.%�Z*�"� a��|Vc'��e� v� �s;J1"~' 1�$J�5 4&H�եO"� 7^�{+��R!�2 2�!� O?.�xem�d�#i^0� \pm$%���e�Gtmajor �۩��%fyN[C�$ p� ��%:i!#� TAPS/CB@E{�&� !M�&i �s^0�q&*ATn"׃"�vW"� a�LItho���"0noa u%H�AqleK !�le�F��NbcxDlL=B�& few�I�JJ�Z ���O.��R�vF%uV�.�_1�aE�ϲ��a�m��j�w��!ion-y G7=`Azn"B!�A=us���:9M+at 10 --SE� ��\#/a` &viFP b��$%6Vo��e5$�e�v�/9�a:&� *w 9 {(12�)�Zat�2!J>Epl��Y��(%>�$Wa�"%t�u���� n��M�"� � م�X#�w!����^)4�Nt��vb� }""W8iT.yL�FC 2Cto.`Y��B.!&5 #)a?�A@!bqu��keA�/0��-��"��Fu %����u n�?e �8>g�q�:h!�lF'&�@ �B(,&$ Algebraic�e�e "ku$�63�N �D.2! ind���to*Z%#n�;��!15�8�!��a.Jm�ovxyNa l?��igS+1�HA@���v:�\�.�SS7I�r�quar�gA=!�b)rw *M'��ope�Fup�ew��'B3s,2��&[(Qlaރ��y�&R��#��:%s��ee�#4e,BaTͼ͇��g �"� (  $f$eme�)n��:��"�Bd"5g(2m!v�2to n�en�g1�7^d� ng �;eyH� %� �%>::�!<+� �"���� <me �e2body s��&<|�fi ��c��'@ 5Zse�U7} n�p���q��91!u�$Feshbac�{Q�R��"q BCS-6u[ ���M�)E�.�Sy�@[m��%ma&��ula?L�8�g�� �nizab�.�]3� �&. Bes:�!�]-; (n-p*L�Yg�&Bs2�i!�a%�� �H=,6y D��A�� ($�$),>�&d=($b .�($T$)�h�d��"($q$). B�O� 7Dea]!�� !nZ�:"?Ak�^da} �%S1C e6K", n-p �ŭc)+6:Li&tH~� -m q"� ce (�fr� �N�2<ee�t�!fo�0�2�A�b?�3Ց &+C�e��non. Spk �#��FVreIE:nd0qngȱ��er5��iz$h���$q�aJ � �5 )�cQ:p��u.�m 4$n-\nuc{3}{H}$"�a�s�Eůn�]!%���W�> ��.�-4"�R�P����!NN.S���5 t" s��(Alt, Grassb�h�S�(as (AGS), H6�Har�&�p-Yj/yW�"�9E�>"5��ul >S��A�W> �@A��-ilu&��.! NN!�!�92��:~J@.K��-A6���;��afNy"i�it�E�3r��I[-E-*!^n��m[ar:� �Q"�?!<�ؙ�� R?� � �L:e�|Ma�r��5��eqg�|�e�d"�"b u�!�pJ�eaY �m�6� ��i�|.� � ly�!df 198}Hg��d},�  �96}e�1���2w F�ZItet6�K�url3�%AO;v*yn2$!�X .SU�'A�8��o2 hy7'uSn/-�%"���z� ��@y�z�P�"�9da�.du"� ���5���a�����S@>=�"��t5=�2�V�&.�2��kInC� idermZb.h)q)uE:�@m�]!񂡴�$"��)� �/�a�(�Œ�%�a��=i�Y rY%gWa�ze�!/a�� eC,�d�Z� �'of1���"Q�lir?tu�s�_o�3 ��[�\���.�i--�.n SLy4)� BSk4�SkP��}�2e r.m.s.�����a2 ven-U �ut 1.5 ��oWA-� �K2�7�(_ i�>}�d�N�>��)fiv0A� Chebyshev-N��%ttMV���@!�;E��nis�E�ndC&W� it'S�I�%ce�s� T�� a��*R�m3G�-�6��VE��0mn/Y�to<+.� k�8! $root-mean-��!m�!)��: he a"�&B�xdi$*��-�m��d� � u���eI|A,�l.\\]��y ��x6�D7i!`r�� ��+8 popuЖby Z�%�@�$ abun��"�(� net� i��baf�5� � i. �� �. A�*� A�d� Az���O�R�o2 Ji}4TF �:�R�. H�w�a"��^&E:3, ��&jm-%��aq�n�t�!E{ �E�E���5[��235}$U, 193}$IE@�n87,88}$Y%;� sixGPleB�8processes, name�ly, photo-absorption, inverse internal co �elastic electron scattering, Coulomb excita P $(\gamma, 4')$ and $(e,e' )$ reac0��ally %Hing nuclear isomers� is is tru!�4 both stellar !7(terrestrialnrmoDexplo!�$s, as wellin1@condi �(expected atF N�al Ign# Fac�8.�The applic(� dens�fun%� �ory!� structure�Hdiscussed, highligh%!44current status`$effective I�roach us!> fielA1�,%(outlin&fu�Xchallenges.�I reviewisuccessA!nd limiI��`ideal fluid dynamic model!_describlhada emis!� s!gHra from Au+Au collis1}ReAZvieW(Heavy Ion C) 1$ GeV. Comparable results wouldtQ�L $0.6\le C 0.8 FWe alsoԡ�tribu��U�}:/to%GDHe gralEc��� with$��4phenomenologica�� , it=B�AD_4sum rule favorA�e ��:��._ �sa5X$$.�Kaon�.)�B��stigaAm� g (Feynman)| �frame��AWwo��l!p mbin�E�t�vi�<re��. R-�)aed � pres��experie�,l data.I�is paper�s� Cronin m!�0tum behaviourI;$p+A$, $d+Ab A �p in s? ��� . OuY(alysis show!�at^mr��qgt rapiU�ӡ= t althougA� is depend�+ s sl�ly�a�LMcLerran-VenugopalanE(Ju defi= of gluonAy�+ %� ��Ct� case�!Tis almos� same (i.e� iog>q�ed-bthesen�o big�L��)��is1�us�;2�%(stinguis-P�1variant�n=*J�%`choos��e r!� one.��1�s, gover� $np$ pai��correX �,in $S=1, T=0#t(PRC 63�V401) 021304(R))�� showa�ADt low� !��E0�ey gapx6 trum!quasip� s �emE� potey�\p� #��AQ�s�P nega' cBJ1�!sponds�appeara�'@of Bose--EinsteinA�  (BEC)#��s��"� regio�{�t ar m .�7 ee.� X Brueckner-Hartree-Fock�� is exta�� int� �: a mi�copic th= body!} ce. �<e���!�Peq, �%of @of hot asymmetric:�%�ita2ospiny�e haveV .l!e crit%�*�m0liquid-gas pha�traV !R�~b�"� }�6gother�md a. It tur��u�S� >H givA� repuls� co*iGFAwhich!�s� ge�-� erU2�ai �� equeA�reduce�z�.-g�e͈y �AE�I�v�i��n�satisfy �� quad��c.� 9�� 0meter $\beta$�lzero-.��� � Ay�8! AdqbݨYd"4 ."Y��rx����aB�a]s-�ly&!�-z_rA�CN�mak-�>mK s&AAM4�"A�U&�) .���iFwofQ�hysedqu� ��,�h!�=�OL�N �le!�3��s� �mar� s9. Due�ad o�m7� �����B�.X����r� ��in!�enhanuasa i;-V�ڭ�pr!;%�Vsn�inzlY�..��m2"� !�p�I��*�K.u_~VA typE]Va��r Waale;���observed!k��is��ms (of��ssure�m=Fr�~y��M8 c�<j�iP^y=Br� �edE��"' ] I� -to-qH�o@��I��: tB��i��arJqa��<Veciab��R�1�me� %����. At fix� ��9�A!�!�E@f�ncreaYmon�rlya�a& ofARKy��T� J�domaiE�B��Fv�gradu�shrinkS �Az�%=�e�"x�р"K��e!Dor�al� s.^!bDirac&- %��. A&��a��9A�,repancy betw�value�R ���!�� non-P �"� "� � !7dB�Q2K�-QmethodaPa�becomemak� � n�� {.�5�ofR!�� f-rs �ad; e�e*'�an�\or� infl� 蚂��:aBm!}"�M�^�;iYsignificQE'�b�a� �e5%Dfr#�!m�5Z"� � D%)r6� cn)>]*�x �A|oJ��K�by adop1 &<�&8Z)�Ule!����.ra#���_&��@brief�c�.\\[3�bKey word�_Dense��,: ,2re�,>,~��b�,26.60.+c, 97 Jd:�histor�HBTHerfero�y,� 'ts�1FyQ,mid 50's, up= !Urec�Ddevelop�& Q� BNL/��n�v focu��uul&[�n subject %�� AGme��A�!�DBrazilian group.�"�gu� "0proUed�2� basi7 pnQRPA"l�3� y�$2\nu�$Yper9 �BeX otop exhibiE��ous�drupo�eformE/�m *daughQeiK}C�NJSi!�!J�� en� �u�_ed�pa�� �ed�sphs �A7t]s whe/m%i� ol*� doua� decay�"�� a, ~xne�!an)&"htre�through�!_%]lism. D*� fQ�^-1%�2strengthA����to�ass� �%a�r%K�Xz�Fo� f�,Gamow-Teller. ampl�ithalf l�"� nvA e>r� *"�� k oacheM� agreU!�"p < �"!�F�@is fairly good.�8in-�um chir���� �a new�����advantag���#�* extr!sumE�s!�2�%�deriv^�uŴ2���N�pion-E!%ig�$rm�9/2 ti5 l aver�2to!�ghta�rk f ��fin)k is linear_4x eV��urb�%x� 2�%4,�Fhdec6�ously)ti� r!�qQtoo0abp@4 fm$^{-3}$.$Ga� �est%�attAWX%�q6#L, $\sqrt{s} = 200$ AZ mea�͏t �},&w�LPHENIX, STAR, PHOBOS%(BRAHMS dete�s.e���Iu&�#nd vanis�pseudo-�y all]�� d-%e a!�� e<+'�jch]"dAN�.�=at�to �"�'��a| %� �~"�"�a �#re� el \pi^0$� Q�� Hk~\cite{luc4brahms}q#a�um� !r D�$]V$� �erhaps�t a tune-upe�-�w$ ��l&g!cascade�smm�fY " but T'w > ,ed $p_T$ sup�o!g�'%� 9�� B'a�h[Ao<( 2. H���:�mYY !�� �ig�57&�.q�� C�o;ed�"on � rali0#^�iٻs (GPDs)�5�;��$^3$H T)�Cre�<H).v��si�� n Im"e A�$xi�, Fermi��a:bin � s, e��by�Vrn*�,� .�#e�D� I�forwardA��% %In�i�)r��y %��e� ��h�#!� um %edf�nL(*�%�e� . %A�feQ!�\M"�%��i� h%n�)GPDA�F*b##�z%�Dinto a $\Delta^2$-�t %�2in term�)suggesa�%�)r�(���o!�Q�i. %%�)s %%tot ��t� X)F�] ��, %**�&�5A�A�&Yd*~%t -��AKP9Qse�nt�}E2�Budetail���ar� �atVrV � ces.�HAZex�v5�� suU deepM'-���w%�nd mes &|t��ac&�  a�*}-%Zco[ nt �ne�o@����,��N�.XM�unpolaI�O*A�$H_q^3$%60A5J+� fEisYv�#.�z ��VY%B�m��diagof!�+�,,� �+A�ef ~�pU�� ul��Axmct%, s. Nm�V�a��J������2���m� B���~�N�%�ar%�ca��!ή���Ar��������������fCHBloch-Horowitz (BH)��""  /fu��/� �.ng����n�'q�d",nd�+/�1systema �?* , BH wa>.�er&� ��cer�-$&i5"�&ha 1Dic oscillator (HO)a3�  $b$.  _$ up�is� �ppo��>��alphaP� ��five-x-�0seven-�$eE,p-shell. Fur�# ,8 use onldlea1 �,!��r? �+= a&w�2d-spa!!0each few �)k4 (0$\hbar\omeg�" nd 22)%+�r how!Qe A Lmatrix�D s�.=. SN1r.&�&�i��@ 5'v&�+� R����d6�yQ :�os!�$\s64$ MeV�DFaddeev-Yakubovsky`� . Howeverl".�-���underbA��/ava6:'�,suscept�4%elus�breakup:'�5g5%u���I]siz"� �Q /��L.t�g)is�sir&:�c�!$a sufficie��mean-�.�jnz�%j'�%�3�/*!exoj at(pE� � "�f����#hyp�0 7,�(J�(\4 !Ns�gL rk A. Firstm>,!sI:�3�(oS!�@F �%�*� I�I i�,T4A�22%o�M6C . LaA;th<+JvAo/oi!�#ul�% ormly roa�n, mpac�5r# �ar &d'I�4third family bh*h!���8> ��1�!*!I�77�d���O[bA�bei"�0 n dueYa fj�)�$K &7to2�.�Y�demE��e��#i�&� i&] � frag�.� �5du�@5arv�#C����%Z $Au^{197}0Sn^{124 La �; $Kr^{78}$� yy�9��w� carr���-�C�q!�.�! ulti�S+ (SMM�J8��"� L"�!expon� $\tau$�249 Z�}�"�*�I�N2�"R.ve�5of5��Ilassif��y� �7A��� ���$�Lon -� �ay�� F>1�JKD�'bimod�0y'5FeWe��w:�� a;Y� oaM��.@,�!rm�is�pronous(��l�2D�z)� l s. \� {{25�"Pq}{M.M "M9�c�(�/}\{#}{Naq�.} 4  -k}{��&�:Bfl E[ s} } % enK � codes�e�emplo�����! ren- zH� (DMRG)eA@ wave&�%661�# +V�2-G3�2�problb � {]9� ro�.Dp8Q�� �wac�f�E��(� �q �2 +gorithm��n�of $fpg$ iiq�Wly���gd�M�1�+�.�e�frontie5.2w -��B �B.�per��1Ac�%I�?�~y.I�! raY:*B�6("4: \�2arrow \� p #;'$)qL $-rH�W_ next�)l2- m�``dE-expa�''!�� �i�t�l-.Q%����+$9�'�!t�%w p�)s�*�E"isQ�0��%"!�e1i. s$'s>s,*be< 5��� ��(lattice QCD���9-"9.(point.)C�@�� "W:���� low-͏!�&�"Au Qo _$a�fp@ � � lu� "�Ks,�OperM on�9� M�&2�o6� s. P�4!�,naApai%Gtheir rCAN� ng"�� ing.��off��J�,%�e�8�o@� B��tő�!�ly up�*)�cop�a]exc=nt�a�e n KEKBKlerA�qu �Mc$4.7\b10^4$e�(d�a�@��A [�p�:1cR44\G.� �:� /� input%�out &�h�eady-@ e�a<tA"�E:diu�M$B � ! . Opk6b�Mct�0��� �pow!�as��0$250$ $\mu$W,��s\2A�a droppA�:�$1� 2�$3$ fJ�&ed��)�-a"h4�Z ree-w  fe!���:sv$tj>V�0.5$ )69so ��m� �& �< �9s�E=xM6� s.!a?t1� poctane (C$_{8}$H$_{18}$) fill� on� 1�rra+-#�$apyU�aQ0a��[designA� builIR��� � ' sis�-128 pixe�2�I?m�n'rea1.7 mmj �"$��a�:of!F m� i�[i&�5�*Eor%�_010 beam profile�Ok�����in Inte= y ModoG ed RM on�%/(IMRTU %Gsurge11Abd-��Hic� AC@ X-Ray Data Acqui� S� (XDAS))'a�Xchip�(e�:CCLRC�>Es!{c�<�!A�/cyUh� 'HjD vol�$!{ d!]� � m!�1�Ba��jm�zdev�o�Ciog k�A8% )�1g|i���n�� gnal?"�"�H. D�qIce*�l�#t�2.5 \%P*5 Gy min$1�dB|6?1?20 cmrt�,solid w�. O�p] i�penumbrWr�&rea�"*� s))i� dY 2��#��� !�"A a 0.125 c%3�ir�!�!cha�*YE�graph`D ilm,UpAT vely�n�3&LaA��u`a�an a* �Z0 virtual wedg�s� i�E� % 6�B�6" Al�J 6i���Oood�N�. SRWEA!7/2\%. A��iod (afHt�.x �@\ e �� capa�to- ify on-!�!��`�� �spatiE��%M��H o no� 7.�)�"*�u��princi�B�id�) opportunZ�a� i�'$itely manyA�ua��A / \t&c�� a kn�@onB 'hW38at���d�(emCex��l c�&�c�Kd��A%��$ n arbitr�%�ef�i)!/ homo� n�Lsi� vJ�$a\A��a� &���!-�!h�>�*) ��E�*� �AR �se&j�%�I��� � �� 3*�0��N�LofeQa� �x!ad�.. "�0 \ GE ���ty� )�ca�MP,r�.�,03.50.De, 42D6-knA%o3 �""�smo�N�ur��ma&�A| �%Y�E�I whilh92R&e %0law� %��)n#G* %"��  ``�-K "�m�G� �� "%,�� patch�M�"an Nne���8>*� a�m .�i="�%K$an unavailf.4�>L�%K�Nth-M;zIuX:pr�Llx i�L&:|a{*GCe��)e� � boxes (%!es)"uov&)�"��T�/ ace-��: . To�)�� /�' e�Cm ox Ba]I�큹bu�� ``shaP"] 3yXe��iY0���/m9*�sh&�&vaSLW!{�L\accura� mAa��lN����M���A$iodic h+B��e�a.M��d heur�A^�V rmin "�1��a�l""Bl[r &�)se%�&qexn0m��CS f/o�+a!�a-�z �U��AnKuram^T-Siva8-\'.�P s�@e RF bunn <EK!�*(synchrotron+'�� ai:K�UiL�in4�Mg�500 to� eV.?0#1�of5{�HI����u�R�ensI^a�o!&ve�8bul��Tm?�/+ �e��x isol%�pa&clp1A&hBgy%pic")zn��Ga��N� v��� q�,�)B �E� lici|u2�A�a�Hngv -:s��yS, a��v� &Ji���B�TA��H��d� baoLA��i ��5"$ byIPVc  h �&si.C�"M.I�2A� bian�Ar!y�"TUR.�/d y!NFOTofA�]?PT� laye.�*�1A��$l�WJ6 slab�RvK�V� ;=v��d "Jre��v|!dex�B��na!u�U��pv���bl��� �H��9QeAC%��- oguEqA� +� diod� $un7=�E�2eft-han"3%�confie3ts}B�)�{le1�t' !`�A�diA�#�*����a� �las�ULsOPM�lamp (LppumG(cesium vapo/K�X�9XA&�Ne H�(ed 50\% abo!�tsa�t-n| �V� Q%�trinsic @(��$of 15\,fT/O3$\mbox{Hz}}! 2b��!� �!J�:�Twom��G�, viz.,~@p�J��  Kself-�'!��!f.�!0 �to-A�m�-�� E�hr� �g"��!�M�"yItan� A� .Ca$: ,\mu)aT}*3 2!�d�U}�u-���<*9ee )M5%�an$Y` �%a�:� aU ed1^-Ka&�K?&t�I�," �kteg� 0 AU 00\,� Lre�S� n up�KI� �long-��� k!~) �. %\no�nt� D7.55.Ge; 32.30.Dxxq r�~ch* ��lapr �[�7cEbpa�heat batfDq�no�� �?*T"=6"�&��U�v �� , ye�Car2>cy�!��chiev�. Worw:P&�%a�X? l"�#y;mon*2by Max. Utilizan5ki�� t�Pmolecu��Qo����I �s rane&=W8�cO nu!%cyclic��� ."�Ps !3!�&DK �P�Q��-�Cv(� %U�92� *� B� reYm�o!Ein��re{^l�! hydr"�(MHD)"� ce,��}� Risk����M\"{u}�< [{\em Phy?� $s} 7, 48896S0)]q �)�]f�1�A>�- fAR�!!��^to!& play2L���% b�P��LReynold�%s�ai�>A�d��&� 9NCmbe9 �f�"Q !4-,�� � �1&� i�"3,!Y����B��= trai��A8��#A� '%XZo�eP_)W4�ll �Bs�&!���mpl�k��o"!x argu�� beyo| in^ �aA+i�6Kd�^7'o��#�xB�+!I���@it!?Vis3"Aim"�_ ste�W checZ!)�w�n> �q5e.�F\=|�7�"e"S*and Lev�R2;dRev. Lett} 72, 336 (1994)]!5orA�A�V� ��:%� furt�Se!��!�F3;i!>9MHDu�D#H&�@andom eddy scramb!�,y,lDA05mit)p"��.Vx���of"T$sheets.\\ �u Copy%%�h 5) AZ-stitute���ic�,�4�1maL downloa- � Y�4�na� Any �r�JreAY-�A��,� auth [EDez�}-; E��a��(ure-driven,�ca!a� PoiseuB�(�k�!E s)��0xs-s �,shapes: elli ?"�, t�Y�D73����irl\SA�an� bya�!!i�T calPK e$A$�ܡ�c�p�-���`��act�J�E C = M P^2/�\QAK��au�re R�-�-��"y\|gey b\&�%L $\V2B4f�A�e`Y�lY �$8c&s"� "} 6��V=t�!�>�&a����� �DA�"�%O�urf�>&�!�_a"�@�1b-on-a-�5�@ Ta`�8&��X�waf�=%tR�a�!�Q�Egs.�*_�+a�$�PA�ll�'`�-w is� e" hypa�X �h��! )��(�[*�5hf2s-d0rete �>s2a�fh!tbG$�A!� Newton's %s�EE%f 4�Au�=�Tlaw�mhF -�Eer�Ds�p��i� "hd&�w� b�vdA/a�C.�?�[A! �LoGz-�� s. O�v� 9�? [y@�%*�*w1�&]]A I��.F1 be, "� �4A1VA�eIJDoB�xp"=Rof wh�- velo�l�y seem�b�'_ regard�9�.9� sourh !�u6��ch!�,X)�ZE�dGs@]!�j/�!E�fa!6W! �}i*T>I��oeSly ��8i3s�a��s�\}A6 exis�E n�@=O} ur� .icaR0w�_at doesn'E$ �10�9tyU s.OA!�oi'5 2"�0a� f��austlp6���n origi1 _la^  vim!n (PV)��� ��l�%bidde>D J9~) [i �s6J� {O}�ans�,">g'ce*)( 0$7S-6P_{3/2}${,��af6x 43� � nse,��l*v l��,�E��)c,�e��er�HJ�A�fo16S-7S�)?��J%el8A�"el �F�3.5 folIY�mfone� ond-͉!�Eqiti�I��i� �d_^%�H��off W �"����a�"�-�#8 [J. Gu\'ena {eed.},� �K� L. {90}, 143001 (20033 Deci�EmA�Ʌh!Pset G"!G) d!,e�B` te,�U!� exti�m��e �""_�2c �ׁ�,!�2&im:7�0 l2$�kfoq< ing:�7o&�&-t�(��r,�(si-� �F � refl� s��- window��CsthU8a��Au} .4��lyA�:$6�'a��nsA�@)&.�D!$+.YE7 �71$\%$M%t6"�01v6��@��PBNs,w�AK$]:�Jagorj Q>*�@!2s�ME��  �` , erro' b$3M��&}?he2��@�m�;!0.I/+ re�A�� JQ^���uFg:Xer. \pacs {32.80.Ys, 11ErV"B�#50.Gy}=#*FAon�no��$�a�.+���=�cd��U^�cetylen�'*%�%�(-cERSic ban�dp�.at 1.5@.� i gs�(�)�c��e�!=� �s�3 u�-�k 7 W"�brn� � x�I$"V"N .&uBinn�kalQ=Au/! �*qPs &�! �s!�-B�if�s!�ae&(H�-m�3�te5Å6wh @1�r�/qB��Kvi ^�6ak.z��Pt�7�*g)]%*�4��two-loopHr2� !$\eps$�  �stocha���uE!�g� ,3ly valVr���c�E�r1�e�)&�Rkhe earlG8p­55�e"MS��M)U!:dr�ũ&�n�r*�%nWvI� m"T������lt�p ��� �a�as�]saJ��mu ,c03E-�*�!diverpBs!�ea�!�w����� �ha�majorm�� ��"H Q3`)&�e .QWave2R��lex lan K0toms NdI, PmIe�SmI* Rvian-* gu�n�_F�j� �I�+$ dj�) �n%`��#�o&i<%"BV�$($F_k(E)$)Ze9-L�)�Tmh(s$: xi_2-� occu�`�($\�nn_� \ran^E$�kO%�v� ts �, 1'�k4Y"4R1J�A��-�!��$5<'&!w!��"i!$i�lo�p!� Fi-s�%�w4de!Pwze�� �"DC�@'zx�::��3 N�,� �N�� � ,#��q&��Hamilton!��>�N�As� �2��C2��~�<s�p� Xɼ$weak admix��9 s!D�$2}%�uPb�$corpo &|a�� ��Vzyp�<� chao�-�E.�U)�$4e-7u?\mC �og�[aH07& }�hat�(�]+#verlook�W!�n jHz��PMx� o%� ra|>kD�er-of-Hm#&6� E��+3/v sL+QQKE�a�Wa�+a!5�-�/ES=G�s�Xe*ishi#AeV�m )G� ��t� e/:(stiff eigen��q��a>'�"�le�� �$,!�&�kvge�*�E)NV#recoiNq%�� ��.��A�j�aE��me6=>"�� !R&�"nBohOoo�Li@2|� ��Ad_"�. �%�oZZNv>�(QED) �1AAN �ZT\ &#` $40^{th}$x� a:(6 logvh�ra 6E�qje }AM� �dND'��� muon�"�/QM��:�pS:l,QED. Analogo�Zto,sU[\� �/�:��V -"�al%%ar�nor;<iJ*y��^E��ide3!-0-� eaJe�� .�l-}�/e�� �$mel��/A�ocR0. BulkE��lNa���u�E*SI� ���H@�7!�>;�I� ja�: ���@Ptplo�� �&0Ms�!s� !T�� pec2�%� root(n s��"�b� t1s $\d�B,_{B}$ (Berry��VP)!�mea� $Monte-Carl6&"A*�Al��(&<by Gupt�4�gix0C�å#J)=%$N�<6�IogQCl�2]E �!�.k5<�fi�56I��Jt�J�eio]W B!QU>L 9���M5!�p3��6�%r�� maximu�j^:�t�Ze&�. LE%r�w �to�2�Kce���i����rsm�higFp%�H4 %{36.40.-c}{A��"a��H461.46.+w}{Nanom#�%O� als:�, nano� tub !Ac0A[5 +n}{ThermB�&<A��R TE qb} %II$%{82.60.Qr R&��L.�A"B$�B�\y�Z) !s}VrI�6!�8D_E�rE�A@Minkowski ($1+1$)2c�fic�,rad!�oor�& aX.�8�2i�$! r $O3�&� $OZ �e�2ir= Know'[t ��SsVdto�d��C!K& RL�7"! N�"��JAH!�mb �ll��� e�S ��G�v;T .�;avHjJ)�C$�$�e%B2f6fam�ihre6 �oc dyf�>�*��:A)�v� c[O3align�4c 'of e*�4.!5 4�|o j%�'':��� ��plF�-�2>ųtraa�!�S� eloI)����!�J�X� compj�wA#mem.��-Z2icB+.�]F��5�mo he>��ctTe B �growthH)��zr*R ��?ca�i�GVi8ل%G�y&�*��F��7 oe�?�*�K^3ic 1J1�*Q ! re =bi"�&Rs�h%Cretac2/T�zry KT Z  .(eOe,Lrem�Hca � ��j�*-organ�"�R�Q�s? �commer���W.esw prog�,v�pu2oCq!A<%8�or�i4/�ddv�s�? D�:*�ch� caus�I�x �y�A��y %qua)di�WangW*� erwove�d�(!�end�/Nqs� ei�n��P E�8n�3g� �He��I nMew"Deffort rrM&�a�i�Eab�oC-L"s^c13A�alp ateg"c#��M!b-��2�'���. $2�� 1�% 5.t4����p�1 are:VG rnet"+�cWj book sale� lfinanEbv#�sh >�! craslST.dNXz p%5o��c�l�#�C�23?M�>�IU. S)��A�.�(!H�x�H� GCl B �.:��.4!�)�Pa e1+ZwakJ!2Aar ��$� # !~Q��+a#/w.E !��4� �ed4wGkfA�p -2_"F�.�'1t�6��&! r�O W�A�"�EV� 3")g� �8 bifurci&�*AV&6&�m  o@?�2��^ !Ja%a,�s7-5track� � 4"#a.)ehy �g�F�NE�&I.�-���!�/h� neur�-ME8b2km&\"5�Cd�g��outhlBh wis!�cut��`gL�n� rd e�A�( �Q/5a�spr +a#rt� Gese�tzA�%�)�!n!n�Sca� E��X�?2i�/4%�1R<�,ac�4V.%1��(* e��\s� if"O��DJ�E�GC�BP�z������1/�L�K%�a zl�`�'�,ad-���]=�of� ��miɢ)�qR�un=R61�/t��t %�^�+ ->�!u� AR� W ed.��q#�(rs#A��i) ���e�#gX ��d�z��ng�%Ko s�pq5�Q*`MILCA)�pJ3d�i]o"�mAl�#l�/v@{�2onF +Gi��Wmix' ��&�C�a�SI� est�PE�N�Tm!dw�ro!�t8�Zm��2fm/�)�(gathB�g� �fi�@!u&�&�;��.�!s�?�L� � 2xN �!j lappb5�=$%mE�reb� si��lk.�� x2ICeB�A�k,q!/.sAleAN%s�t-, EPetUUEj -b!�sbl�'� su��� �i�o'�2�RM�M:� �&@$dA?aa��Ga/��"�"al (infr�*Ra�M�ѷ'�X)�oz�/�� *+ "�B./sh�rUJa�["{VE�P!"�EE�%TL�N�_ of SF��n)O�u�.2ۙ���� >�&8toot|. �籽� ha7ere��<� , �the�Bw�ip�WO!X3Y� 5Ccli�� "D cine�1]  logy, onc %� card�y�i� c!hhE�)�]a��&�P�/�WI-��g-%��&&Rad� �.��V*��{&n�q>?� ��7W9rste.�P,�6&Cma��{|&b?�E�&,�grecewf?�<g�,&&��t!or�s�P, AE15 c,tP'Ϳ��=a�e�Azl>!��c.y,!�m�"o ��!�n��&�cub�C�X�USeNx�' ~�,a �A�%s/ %��ՎI**2A��/tB��i-e2�n���@��E.n$;pp--Loga_-.�%?D�+-ngb r� RAJon�W (QWR)�totype.�S %fab!}��!% e��80.5 MHz%161 !0))mi!�%�| = 0.085#16$g9�%��i�b� �T%�K/d5"sōtM���!F�.I� q6RF� s, %!X��QWR!�cj!a p�#�7!A�t1 ($E_p$g`ex? %10 MV/m,� �JF� y�*\m $Q_02@{Y 10^9�%�%d�X� f s �y$f)&�16$2�0%� �yFSVcdot u.�&k� !.���%l������ �1dGbeT1coo� 9Nb �Sng��AIn�% -RF�`tac�X* }�+!�o�M�or. % 1 �i �#�#3�E$\�%cal{S}_{ rm{D}LW% 4� A8�= Z����s�t6"�eJ-wr�= us-�T0e��c�R��m� �����\� .a,OSa� �( �p��3As@H]lu�D��"��$$-r'^{k!7�!�=F�(v�`�"�!O� A9hK:�bl� �cja�eGna�DgG�IVmZ�� timl"[ � $f��eak:)b��n9�t�F h�3��E����2 !�non.� w%��Q]U{F�|&a7 �f�2�.eR!(i�2!�&s'I��a=^^cle&jj��z�!p6�*ich�(G.�"�'Vn% �1�u4 * �5Q�r/t%bb a�d&Six�d*�B&E�Q4P6,}�($ ��a6gM�)fe�����W�j:A�5y�- �ET }% z.d��g.Y�:�!�gy-L �& (��% �9BFM"!�9�r] J��=aAmod��`�I � � c�a�,i��KF���rm{% m ��X%CMNlF[ �Q��&!�r ^(a��s��. S�y"�~�"v�>�.[� �.�<� ��IH �yP)�!~N��h��DA!Z5"�"���/A�/�C�� ,"� `4!�'p(J�N!�Y"$!Hw beg�)mlA)"�2ee�in"��!2:s�w"&]2�Df-+}���a�.}. �_o�� k0X(�?g �_+�[�چ])W�f e�w!#�V5c�%&�%�� E�Z)�diagra~�4�� z,�#J��!I>f!?�E)� �!cou�O&A:Q+�)%�+NJmy& brup�aD rho �'gr 10$ g1`2�, { � } $P !2E barM�-� � HE�6~$^{2+��Ft!Ns�J�SonQ5AA�G),�H<+}$g��.�' eno}�.I= .Y)L��com�GmjO�`"��%�L6�0=�3 guhꩍ�al2J%or*��*-pD-أa�we�62"� �"-Lat a�Q���@0Ac�-ll" Inde�eA*��)mC b6�b &� �>c�^Fh��,&'eJ�p�Z6�� !de*a`8?$a8$7Y�" mong$ j�Xa�LK�aI"�:E��AwQ 0g�${C�I�%� A$Ftho&�7ut-V��"� bulk"s.�%ir�D"shQg s�Y�%a�enY�4��!�YLEd"�>%qmo&x2 ����E�B deptВ\�Gr�"KTtCERN H2A+m�i��j�osh��/��a��.�Cɺ-V!��%=Ni6x"�,E�E�g� l0wE�heN-�. w&�a3�P�:�/�2L;�aF)Y�u��${15}$ \NeqQ$. \vskip \A( 2�T : 29&,Gx; Wk; 61�+-x~BKe�� E!P5�;y07 hard�I;5cf# e; Cu��"� on; Silic PA�; CMS;�Z�`j ɂ�MaQvƣowT6a !eu<ng>3��i| 6&�p6>c2�+! Q�A3if nM�N�Q�-�"Q�1��Is.E-@� �0AR2�LA�p=Na�-8 ��2�onF_swarm&�\�w$ �jE�@s�.�v6� N��!b�e7 STt� �@& 8*&�<&[�l�Lm | /*�#"�<�@! -� 5�%hBRUn��"(�packet��gH. M@j �Gll�h.�?"�a�"�6�|�ct� Four�=O�V*;A ,7@"_ 8%�Q:��L63 $\5�=0�Ba� a$0I��MYni#E U9zE �rav1%i�!e���Lsp8rV�J�a�"{��q(A��k��8 �9-.i� m ᩡ�. � s�..F�%>%paKQn5�2��&��A�!y.>!�=$�,Fue[r���-� Penr�V��Te��L,a>�7� m�(ut�'H\@. \ \ref{Item1}.~1{ e�Rt�E��8*�'Aula���*X���A�z�,!"HO��rRW �(-�`!�(t �MB$9 A(#.��-'b�"&N:�2}.~N�e�Y�L h,]�A\ &H ]�so-!�ed `t�$'� adox:i3 i��}�!4"SMw|'�! AG4 w ��:�S"�#$FX%.Yo ��E��@+�  /�B#2<6i�-��T�Lm��th*� rigo$�tvfi�r*N��]\�R"\F�+!��r AP �n "�9��j ly-��ged� yU � �*�UTh�i"�>� &�!F -$Z$ :-� a�#%A�j r�0��*qR��)on- e� - ��:rac\-��.�q ng�� s. A� �zW--s�D���������."=�I3KRof Qu�:= i0s, }6.k$"�D"-�$%��%  c�._(�-)�5|�2v. M���U$2"�#M6H�bxin|�1.P�k�9~--tesT3mp��� m zN+9.Sh)Zdoc�YE4REV\TeX{} 4.��M��mpina�qD�a�i`A\ba� \��� ,s $P_{\text{gK}}(r)$:�Urearthquo��$�[��-�6L�!%4California cat�;,��ܥsp�d�j$5 �J 5$ km$^2�ZE�j( $dt =1,~100 $$10 da]� s{4gv�S'9J��, 1/r^{1+\mu}��e& � mu \  1.6$��6�e�!���MQ`�NI.dG�^�`g!� �E\Gt$B�B���X�e$ETAS (epid�_-��Ps&. �)� m�ssu�at�v9���S>��- s (``afte _s''). AnNr� E�  u�*4QA| each�f�Qt�-�"E^Z orum&�!g��KY�S�� A�]�2�.of�5?�"\$&'"3v�`"�EeGib�&cI� `/u�2>�2��S�=s��D�uI;�E )d� (accou�$ pre-_ !frozen6m�spontu.2 oLU�y5�U�1sT�MgC ex�-T;+e` faul��ٿsq%M�.g��t�@"�-4�*� �!�|RH s�Of�%F�� adju�3�8e� �Wi�f�m�4�im���=���Et�$/M�$){�.�$irQ%9�cxQ�^E���.�E"�q�� �>#Va"� �Xu8fs~�Qd I� 9ll �4.�TI�~�i�Zul�F4l�envel_�m�)ca�TboP\.u�. B�run�]'�symptʌr*�a�Q# �%��h"�"M8w!�!�R6G�b���Oo-.�on�� !�re2/*%�a�i/&`2ple.�,"�}0K�$�  o �$q=1$5 $q$ bea�� safe"4$)�yP�$���kamak� smaK%T"A�76:�g �poloid�d�� $m$� e"� an 19s��b0FlYi{.�%�� J�Shigh-VҢ�ri:tM �!��� en��"�`6�(� �IC9m.$m!PTais � >lsu�X"}!o�nF-B kink�#f� sawt�u�k. B�D Gsub��Z conn,&���-V(i@$0 �9�h �island&�)�/H5^RTA�C�fez#XHaQ./ursor-��ŝ�}ap� |:�"F��J���9�"} \ istl�QvI�I�)�qs�z� ��v- "t ��� � Q���2oR���p���re�?! m�F�&&*+j t �.+?2r=�4*EW�~".1�2R�E5��x1C��+��Sly��-�[tu {Bp" ��+"� �6EG�6B�GaFs�y� cG-�k coup�9� Schr\"{o}�9e&|�>=�N[wwQr�XSm"g .e�n�*�K"�CwQ7Rfav�!n���s=e��sAYal�Q rele ��Y@� �KpYN &_���?�&p:ED�L�we�vsurbZ� 1 ���PMj&%��zP��+p��AK��:reJ��in ���_@T�w f�V^Pa�>U*�z+e�)� S,�=���s g/&�7oGWAnIO!��ZT3� ���"ӨE�� hmi!K :|.3�:� e�YlT�a:a^2m�)�!q��de� a5SQ��os"�Fh"B���`�� adiab��* ssagŞ� a FeshbacA���ce[\cuY3o u6� o�En�A�B.o�e� �yc-��sw���=s� r�ng� ovelJh�-fBy on} �SP��|&�ea���)!�"�Rwa�)bS\�rem�s&�@@=debunk!�� �omisJ6iX����L!e!���a�{ ��-4X5�;�tA�"�S���.^��roB � a BrillouT��KaJZ� \-�J� ��B� !G� �+ ��w_ itsoa�p�C*��z� f;ur6kA��p��IA %6k 6�"�1�(1 J(. U &� � ach,�i˔!DoalesE1saddl�inT!Mp�8� �ǩ� A.�5%8& � �{3ex} \yK&6U; ,.� � a  �J�,���"a�s6���e��%�A��v�%� (2yto $20 ��%�)� ��&�($0.1$4&���:,��3"�n��g�p�� ��A�.Hope�|��"� r����!���2  ��9!8QEDE�2�(�&ٜ!2iip't#� �cc�R!�fea" $�B�8�-'�{}h(�$�l � 9i@!~ant.TAv  {0.2cm} AEAica�&�'N'� e cyLC�l�E��bI�;efQ5fE). R�aN-�}�%�/���.ow.}.�F!�2�h4V�C1�v�/"��llipsoi�l�"=edM�!$ed I� 0�on1j:Y���Qs�u%�!!eW ���,�B� An�1�As,.  �A}d� �%�h&���[, "n�#0r�-r)��_!�F �1+t MFY95 y�.brS Sp��l R�2�;�`$born, Arage�e0-���c1" :�R}E��ijA !\*�-!tfyw��r6�[�i'��Ti�nul��1k���"C gj%r5� ;Fresne�%*MtA�n �^$�"rag�#�wK��2I�!��ex��t's==i �r�a�8!Arivilecin)Z�c�D| $!('� >��!is*�t2TRsaya�at Snel�!i�4�����T� �$si)�ekl�Ch~KB evid� a>qs 5);�E��1�e=u%W!�cost%dp"�$e Huygens'!_dcA��e mT)iq�h��dCz^��k%Orecei3�3h�� � P%n#JF*avoid��<�%e()�A��A�aZ�>.{W!�n�6�Txi �0� Micr�*@s (MICRO-MEsh GAS�Rmgor) TPC� ~�� *=(nA��f�9�n-�:F��f�;u-u�)�mnR�G�O�!�; ��-mesh.!Ti"�@I�tya� � stop�O� � !"-as �S����/�-�yM av%�ch"M�a�at��4�&1�Nb"rppie� v����Ehe E��i�� feed!aO: l�.k (  Xdrift-�"3��E�-�D ). M.�N� Bo X-r�� ourc��g!O:t1q�%:�& � ��d-Z� �� i IfoA�e�^�]A�( �pJ�0,��!�I�B! (150-200 V/cP 50-80 k)g��{*!�!�eI�w-j�� $2-3��p ���&f2�[=5; 2T"�)�:� ��2���Fe � #� C.}�D�>� "[N�mu�H!i U� y�a9��XnX.�s-աJYPg7 lXEK��4�:FofR reve�b�;R���#fd3I' e� � AA.�for��]ma��Tplacei#%�c�V!$�%�,�K"�:un�3c �jJo� ��x�fd *Xs%�> adap�d�)621�Wig�s f hu�9 c���ff��M�u1�2 � n$%�� a)T^�O �^� !hl�A!� fund�al�9�kpr�f"�or�DA6a��rou�Ca�/���kc) � ���s.�}�'�� �w&R�ji% nZn�0 sub-!�G2e�sub2*so `C�+V�Z�=pbf��a�Q�'h�; an%6i�Qz�%j6(R4�� Vcl�WC Xk$<&VoT�sL;E`I.d$.A��&v�0E�!��big�O$g.�\par���p�wZi(#�,ar� &�r� o[3&EG��& bVe�gr�G �$ G_N�+H_�+�two2�*g'*i�". $ \a��_{QCD$�$ �� . W��� rk�jQwcou�� �"��� !S�E�}!��`�0g.���z�hAT:�M ~8p1cm PACS:04.20.Ha, 04.90.+e�kSw!�[3�>i*5&a��Y6�k бi\*�J:'&wV d je�&fN+�hi�.�c�s #�g-��$" azimuth��E�/2�(�jet. A&[]� �0� "e �"� MW"�)��<jetppC���s9 ng��/��h �woz&�Ke�@���&ty �%i�!1�b�:�9in2�[��=H/ B r(�"~A-:%1*�0� G4s�&bV.�  ��o mf����% y&��e�9z003�i�:� "]M (�+�s, 50 ��  i�/) U �� aY >zN& HSaclayA<.#%U�p�Ktuɇ�es� m coX�e�"-�dA��2 uq# pw&A�ct�%^an u A^� gu�d.o-�� ��?Z. D!%&8#��B2�,m`5ttachmNW+�S� tA�a>�:�:�,� A W.�%is�F a�,gon-CF${}_4$ (��h�)��G�>BL5�"_�.{&��"&do�Z\�c��c��r�td*t� xE�or]3��� e"5�burst(B135�t�3�Bm!�0"�x &��8!H +�� <rc@a�y^i+�2(�#�] 7"� a� *HofA/7 ���*�f�ڹuF&%�D�V%�rNq5B !@Ppr!�YCs��-�(�fe�� urs)��[!ӡ;�M��id$ALAU$"*o! WGu �m\la�_iU!Sa�Њepsilon$)�a�Q�!. W!d.��# 4�Ő6st��&Q (.�1E�]�16�v&2-fl�, rB�� ���gXe�D�^{�{ �9`�)G);�a��� �N<�'a�2�aAr Ё�~F)�a\t$1-2$ h!�`�e�"q�K!�iʚ6a9 "PZ"� ���B !��ien�:�g�� w�:i9 ��*�L&����s*O�� alway�_��. F:o�E� �4in�D�"!)2�} � b�/b��R� ��9��A�U�!lf1�ӝ:0Fokker-PlanckW h@show,e�0�R a��f7�!K2u�om3�*@&P�� (LFJving�I{eQ�a�J?.y�HERA-BS�er Track]��;112\,674�f��m�[�.n�U� A9@5!p�P flux�i$2"�T 5$\,6�-��s2� thuz�]*m�b)�"a��LHCr�mf8�-a read� ��,6�FASD-8j�p%�a cus4WTDC,�*d�U:fulfi17� D���B� Q��  to`oE*A�Y g��rWCA�e� ��b"�!n ASICI� digi�/a�eIin��E��0.5\,�2�to�� 56, qch! l [omp�A!pip�E!���#!dm���;t6�i��r9SadA�-� tri9�.$͠a��%�s�[�;o��!i�JL��D��comx]����Y  ,� "�\A>k���%�< � �+�:nd�xl �)�!�!pLmcA�I�.��on6n ���<le�" Somm��l4��*"� ����M "y"!��&s6.T %�*�663)!���� �%�1H�"�# ZE��(m��-x}% dump�-�" �2%o*+!�i%a����pU**�V��ach�7lov1�/R�):�~Cx�b�R� X gД%�n!�� ����2+m�^�3lt#��5J 5i~h �!�l�&!ud&Tv�n���a�4�C�\E$A�li���.%�L%�A�� sr��&�-�z":L"�2�vrby (aCQH6��;"���4n�e�G�DoC ����.�Y�i�(b jbiotechnT)�&2a! �-�0�(@>Y� !P"v ad1� ofp��mino aci�ca�Z�1FswR4!K!i) a �S&S:EnA��(i#�Xico\ced^&A`�S� M\o{Ĝ-P�0et��O I�16�0r"���� �\��l����#]�5F]5��UAY�8SiX$_n$Y$_m$. P¹�!S :tod o���rig7Mi ���`bQcr 91_� !0 ��a�DFQs-R�lm��si��L1 es��W��p�4� "W>�E� Tehran Pr. Q x (TEPIX)AZ����ur��w���4\PB�a� _ e���@�($R/S�X"CW �aN*L� Y),�p ed.� ~ XDFA�-gA�eH����$�=F*X9.����9���"{% ret��A p�|=4��s�r*{ng @.,�@� i,et is invest�igated, characteristic exponent for probability distribution function of TEPIX returns is derived and finally the stage of development in Tehran Stock Exchange is determined.�The problem of inferring the binomial parameter $p$ from $x$ {successes} obtained in $n$ {trials} is reviewed and extended to take into account the presence of background, that can affect the data in two ways: {a}) fake successes are due to a background modeled as a Poisson process of known intensity; {b}) fake trials are due to a back�ZD, each trial being]D�vOa�alE�experiK al.Y ���Tlongitudinal--mode emi�% in r�c@$lasers, pa% spec� ��n!�N%� B ,. W�5�NDboth homogeneously�in69u�blish� cess� !�sufficR a�dg ��intrinsa�+ ��1�two p���mion fulfi�u�� ], nam�vminimmb fold�B�WEOn96.3exA܉ wo-da�� alZQ which A�advantagBf s�, pow� cycl!v!.hav !,ven%7��y.�h�L t�-�%Qe�& m!�JDtinuous cesium bea��a��ta&� ,y.�We mea_ e lifetim��$$8s$ level�A��o--]ly trapas5?<$^{210}$Fr atomsMc ime-ŭl7single-� cou�g$$7P_{1/2}$A*t��r a��� on� � ��te �An!� X exci� yu�:�;,a 1.3 $\mu$m)a. A:VTfluorescence decay thrո%3�3�)9gi�H$53.30 \pm 0.44$ ns �he.�1�.�)�}�(exact mathe���Qtrans���M�convert� wide�ofA�ecaR-diffuA�*� in{ �mb owA�simpleE�dir spat�da���z {��ll u7si�thu)�constru� ccur!�a more� �<num� Qorithm5 sewed��}n t be view��s mas�& i� prov� ��altern� $mesoscopic!*��dF8� rm�:9XwU-,ly va� hopp!X� s.�T�soc��� trumzA hydr� mole��A�byOrt�nse pul�of infr light�� � �e�&Schr\"oB er5495�!Vndmg� *o�} d mo�um�,ce. For few-���n n� olv!�brEAal I � �common�ri�!hhe6�pre?A�� 6& neutY e�a5#��"J � gy9��� z .1>ce�c%�1[ lay, lengthi�� nsit�i5�Ɂ�L$\lambda \sim 790$nm �oncludw� pr8 �ia�� a� i� prob��v=i�ad��. Fx lyD c[  ouyc����:!�E��>�� 55 f! E�u��4 a Ti:Sapphire-(B $nm� tEva: overi1:�volume,m�9g$I)P3 \A�Ps 10^{15}$W cm$^{-2}$�.�{ � xcell� "�i�th��ex� s.=i�4French Academy� -�YAHI ---F seconE�me���tA�^�Gide�.�E��8other. However,��� of f�Feba k��(ul4ts virtuu� �! ach oscilM(, a `surpri!� ' coincid�#h#no&�reasonE�shortly 4 jtep�4�5�hoiaks)#a's(n millionth� �5quadr)7ridia�nd �W'suspic���,%ZjC-� A)s9++in1T� rE� poin�� ". A�Rac!W:Y�X.�Arrow diagram (AD)0hod (L. Kanto��chEJ�B. Zapol, J. Chem. Phys. 96, 8420 (1992); ibid,7) �AQ| mea �ah�"!Brbitr� matrixbas,��eft\la�  \Psi\r�|\�hat{O}\#|\r .$,]"/ al o�o�$A$!�!�n�ichtry w0!]toW �"�$w$�+reU �ԡ 3~�producEG�ola�many-�n �p `%Phi_{A�6Lto eacM�(9) $A$�� �: �=�A}\�S[�X�� (e.g.��inite) Ji.�is �icult, h�'2 ean 6�5� requ��a! ���Q��W �o� dip d� norm�鳡�g�$S=EN?A4.!�\EP]4� isb n an AD�a>,ll. A linked�m suggesAp�o�:e, Int.a]QYqd876, 511 (2000))!�d�� � �}lem�re\i?�"D� ��,Hartree-Fock@au one2�� %� siz�iW �%��Polvv.^��%�E�� k!�lB.��n"�� ���aT;m5"�Arer�Dq>ici@)Hme��of�� �5s�r� ~� ,a]ser�Y�%�ect!��a 1���llust� rf|~lmV.�� �i� %2first� ` a liquid Argon TPC immer�[����0.55~T%� show)�� imag�pru�͏detector)� ot ayo���8�ymbeD ]ionizx��c llowE# �t�Cir � g*5m o se figurea�re � now �cOibl��L �� >Y.[S�axlyWedQsymplA�c s�4ea#Dr Hamiltonian PDEs)�bO!�=%Arve a� ed ls � er6 law�IdtrainA e��*in �I&� simuD 8s. Backward err!�y@ �, oIiy&modifx"�,A�a4,ful techniqu3�!�AT qualve be�or!�a)�et�) "/�R+G-��F�)n��; w!�itiA"ajj�:��n� ��a�5=�box z)�� nonlinear�>�Ju=�5g��5te}�>�!<d��HF;�ʡc�s%�8to higher order���" . H.(2�m�{^�is verINbly.�E%��u�%M=Dy PbWO$_4$ crystalCMS}Iirr�0(a 20\,GeV/cPton��flu4 FD\expfor{5.4}{13}\,"� �G damag c��yac� �v e�fo����. a �. C���aw�($^{60}$Co p��per��gn s�z �� dose�!�1\,kGy/he*yed=!�l%w���(-edge shift�s,induc� bsorp�` � indlJ ptod^{-4}$� $\gamma$-^�u does��~ bur!) _~5sAVs�Oclearly)�&] �by�I7Yin9U�ae"�1 hardness,aMes�a�be^0.5\,1- !HV!�)�s,��e�) ��I#4 pre-���'edJ�T,U���=inc!es� %8 lm . Af a\u/>-vNe-z$of $\sim$1=5�eno sig_sI#��%�se-4&� �ong e |d ��-T-^ �tu�'canbaډr�B�iCH� i� hadr.$x msel�U�Vl1I�l"'y�$)2}$�{%� & like$�#escap�#� a�t l�-�� fA)Aح���,����-kB��$��ei�%3 o����4y slowly.�A�rt gas�Sha� 4layer sandwich1ka semi�u^ &"k&lanar� desZ��ie��o-�!o� p� focu o� 4q*~ �ta�.vs�4�  DC�zpplied;!�� ul|ase2Y*�sOly��(   �� )-in d ean�sis�  capaon�W fin���P , tify .�"@lesk)ra��&�*�"�Ij%` -�t��"+���h# sta;"� M�� .uly)ev%i��:�J\az#��t�A#J(T�u�d "�ng bifur�*�� �A�-�!� u�)�e"�Z!R F�]sl��$toYKng.�Qa� a;!t�!fRenc" deopC� 8.�.asceO,6u �um! lL n�r�'t"� at&� �g*f* grow+#b4Rm!!�fer � �i�ro�-$be easi�dop��!�pro�+i ign!�*%* };$�mechanic)I,undergraduat�ZA/ref� E*effJ 0��{. %�G�od� 1+� Qhe�d<-�LV���� �ilf-simi� �ur2n�Z.9d.�/m��.CRe � �(mu� $dt\mu$��$ �X �~� enavH/D/T t� es b�a0qQ"- ,)!yF '� ~1~eV)}�aIgi�as &�0=% � � !��-of-flmme $me�M�#:;,2�& at TRIUMFaB�j+�FUVQ!E �b,�fixa�e�6,�I/y-�%>v&"rU good>��PSI@ RIKEN-RAL! M s.&�)p&�v��5Cin� !,U��turbul� $on Doppler�al �3 shap@"*�$plasmas. L."%ref�2T2toW Fi�whctyp$i�*caCs m��E�=�+-� ��!����ro��/�as�v� c� coll�� Mg�!�geAis��A�n}V�/e,'%�drift�=4 , ubBt�&s�-!l�$dev�(T-nt6A�-om�2z�%"!� E%H aver �^b�%"6'a,�!5�e �&�ex��@%$!n���3�,b!- �. Assum�[�/ acqui�!� !��J�9V�E,�}V_�lyE e) �e" aMC�� �Y'�8C��"EE4 iu4k߱�ofţ ity,-veloc#a�;e�3Y�alE$�he qZ��Ua-,qgem�3�a>� pop�;%$a~� '��UFbeMI Q%�&d4�w)��fl�!wd K��P s exhibit� -law"�AT��+J(:�4 ! �)ar{�,on-Boltzmann� t%��(as L\'{e}vy2G�!�� md]�. ata.�C�ak� Q2g calo�h8med�*inL��"h�6! �� D&�2���G I�%7� z�%t��OM#s,� a��� on enviro� , H�>��lE�x��c� P �/lac i"o�&po�'A�reado:9im�n��(�3�1enA_ofg%achiev�k5��;,)�&� �/A,n!A.2 of LF6 Tunga�e (PWO)"o!lo��digh _�.� a rigor��Zn ba�4x�C� al��c #i9of>a� er��&y s. OurA�Ua reL z�-ba�rLaut�7J�"t����oj-@maj>0`n!licit re1 ���permea.�"��� t"� �eob�8y e@ chec� *�E0we%�!f;�ou���!�Left-Ha"M�1nd!+�4Pokrovski-Efroidox.Z.yn����( olar<�.l�� %� e� p�aD2&�,*�L.�a. By� �2Ot�2raphy� se &�:� '!�!� Muel� �$ �&6�-aA�m��&K418��3��3Mtwe�,�)lya$iL by Aiello%*T ~��/e4-� }p�{$de dur� %�ast�Pe�lof6�brems��hlung-Y2�domaina0te� surve�B�&ng z�jh0"� phen89yH�!1e V fer%�$k>� ingu{?=� ��:��NE1�`s�:����"�#�./��of�M�!��a.2B�2����n��.�V8� 91N9i�����(e�n.S:fU!I2�6s�]%����1�6-6 S2um1��.Zkr� �"�($\mbox{Li}+ 4HF}(v=0,1,j=0)%3arrow (Li)$',j')$ bim"� *��s��ar�� *� s. C�A)ui D ��5angS&�� ��/ h J cy&� �>yaRfac�.%X^2A'$�yW5nd��$orf+!)$E��,isa�in��c� ue��]�?o��$l�(a��)w Li}\cdots F}- H}$ van�� WaalC!�x.� # L9,��"� G� DbyY3�ieigen"Vmquasiis��.��!%�whR'"1E�re!� is g�K$'nh��P"���x�&A%�get5)�as! ��~ e�OiQed HF�Li�� n ad�0�x)I5i�!�cHign�an�sup�-9=��Ɂ�oAr dee!()BR�4 q�aCF t tu -��o��%orr�.�c ��5t� �!��$X4�G�l/��ys 1100e� 6063�*� d. C��'��arp�ERx�Ny��2enough ��.xa!il�SEYi�Lg8�=eqwC$�"u5 g9�el� s� te{crc})i�L<� did :,goau 1.8.HA ="w,d �inu�hrxpo�"�/.�QnoSMR5�&� textbooks�K ai�i�Lc� s�M�*Fan astu�D(n In�)�it����?e�g�_8pl�2rom)?�. o "U*a�A we��:!�� x��e D"P :�A�gr�J�bPa��'� to mit&:!bal�42B!c 5H!�co�7ly1UA�:�^nE9th�6E?un)�T�ngs. S�Qn'tkhpp t(`&ct1�?Bp � <�'�G u�Bal�DI�!���H� s��^E�t�s�.��+ er (HCAL)�uk)b AaWj-^close-by �M"{&%7pTn@i�a��*B segC �����.MU.�tu�,*Of0+ �� EofX-cold�$1}$S$_{0}$2� alka@ -earj PH;n8 !�Feshbach�v!,�s !�eve"�G7Ba���d+ /�q& �G��&�#!he��i2F comb>A�$^{1}S� --$^{3}P_�)q�. S ais_&t.8- ,N� m��$$^{40}$Ca,���/o@!��!��V. Unlik1a�l��7��#"�F� U>!� �M re� s N, beca{��n� �#width�9�Ea}9!\&�-�ra�pro�Ao��rolP�1��QL#a}e��!+��Ju�eJ[I s.b,A��*w"catalogf blazN�at8he \sax\ archivE�e ?Ki� es 44�7-� y peaDBL Lacs (HBLs), 14(&^%L %�� 28 Flat S =]HRadio�>s�(FSRQs)�BAk$68 LECS, MGPDSE%traP!0z-C��� � o�ƅ@s t�N%��!0od 1996--2002!� e 0.1--50�!�inuI����g!2f*�#\kH~E#�bGal!�c�umz �G�min_J��h:�4(!$BLs (25\%)�(��b<�m�JAlex-l�5k�Qbro�O�� �o~@c9d�� abol�ese�j/;+&h5� ��.�A� half�!HBL1�� m.�a�����mw(idFI�%Mfl�" $F_{2-1%� } > ,5-11}$\!�.�Tto~ E� )ig�Rto-)C#io /I+��B� ab#.C threshold�} perc�Z�O�rlquiL)-Qi" ��L!5/�W% IX*�net펅�of X-ra�mW�&�?=5a����G&Eha`I�&� ��gK:5�)A� blur�"�.�6y o ambC N@� ��N�% �!ha�5 . % \keyw�X{a`xies:�# e --et fundaIl j�(s6$nuclei%As: gal@ }�Fud� -"�aQ�M��%R��I�a�J �'�a# ah imar�2o[Oe�% �@le� ut� s warma�s@i& ng rfa�InzNonal l(ar CoW (ILC) w�R�1# B� �9�^!ac�� �bat�c-)q�X hoto1GmP*hr22� jSLC� meeI9 �}=aO� -ILCIOL5i.�ap�%!90\%.w$s�(Amco�%"h�aafA� pept�O � � �aO$�54p�$ig�4�"kng��e6�^f_tql��= is"�3:�z!��&4elucid(# �traP^ r�[�#%ini p&�Ea� leucdi � �&xRgly�:|55 s 5<ier work"Voter�j�coC�notort``lap'' "�F;69��u!`A x"� n�"�R�quiva8M5iaGA!NB@i5itI5�mӡ6 WE hP&?C!K�A)�e�Zw� $n�,As �&S =.��d�^)V� TB�\ i�"o#F�!�u1F(.��I,Ua~"G ��m�( s.�4i� @��9ga�w _ emplou%!p"&�ů�R� mmun[�$)�8�[.�8\haU er�&E��$e�F5��Y� sE�%O�#��` �. NonJA�.�-�tF�!!���-J 6?�Tly�DEv3� low-�V�&��+e� ,EU� ,�I|.42 E�u� a}y3�=� T%stoichiSe�w;A�B�invWSd��(a�n�6wo �/E�� �t�Uc�>occupy� &.  !A^-�5��)�. Two�J�Lced�G�% c�V!�R ��YI�ye�#l�1�pcy��#!}(Aat-*�`L3`!qFyE��c oDU�Pt x� � �!zs�Q��r�K�eM�zJ�-�~Bast-squa��9 "-�^_]-s1:i�a�)�biF��rAltho9_w�8v�*d� FA9e8d� �iZ�}���N�eesU�ds�!ȅP�  cL.��&�6���)�B��h�>ad��Ox�)mus� �,Y.&�Aru�L Z�ss�d��ed$ih, justAheaA . ToIRd � om+�o���%�\g.�]� �.*�}��b3 a> s. N��the% y�`i*�he hu,audito�A�Q!/bl0 n� � ����vid�e�@�@a�~�R(sa�� XN��health��a #w�Z �c -�=��Spmban( ns%�^)��V��%�(E�"��K�on, ma�,��sd�+��9� fe4%�� S-�7.u =��/� "�4e5coo0 of S*t�88b�X�*9^���mo9 II�a5,�c)bdi�e.���x$J_g=0)�,�E0Sisyphus-typeU��Y��r��c��"�#est2��[predi�/�0!gD�8-��We��>r9�,� =|eMW���e"�ii"&*�A�a!�%B1�.��.|%��[6� B-�6ta�a*rhI��ex�&�,�XG(Lg�J QL8�df* 6ADT1�Y"E2 #ata%��_J�:$Monte-Carl�G"NN^�J%���%%�� irm# "�� ;)7 Z� ��nQaG�!�2�;3 �52\-H -"�2A))k �]Tinviscid Rayleigh-Tayl�%g��t Atw!)�(n�!�a ���wT��%aqat�B�*�?"'O� pike'e'ICl�a \& WX) ms\c�}<�#w�3�pl{M&�(�'In4�Nw�A�m4�'s9,$ e��$t^3$ql4et shoo�(2�<�]Nf%�2S $1/t^5�+w. More:��/A[�� 13pre�z c.�C-�=mQQ. Even-Y: a<'9�.8C5� H!�X :"�%0.CE�F�inm't imbed�`5 Ypl(a�mU rX newRBe"�l9oA�rbTYQ�Uupl�a�J-A y ki�_ 1 ily-2�g&atIJ=3�-!2K�A�� ! ��.cV�5doa9_%߅�� Porigi�uWvk!(%�- -{ &�  89��4RlfK rJ�]Dmaa���Wol�4-�c=g�H=�FerCHN �%"!U�E�e<y6{  Q;%R�2AYt%� � e66�%�~c ? tyOWe*� Y vali�4+� 8O!�>q�� pplp��%5-�)� so%Dchi� 륵&�#��r ee,��1ga"�s*�Tc�8fM~t*se=by)[5���.���aOl�.�us�gt�a Bi�hent�kvio� ng�58m%*t,�; % Nzb��aOO 3xan.;!,o:Aic J| �/�s"y hy� �� %kFdnd#2�"�t�3�$>m�%m��s��a#QY�]-n m�vxe!$Fabry Pero!��& driv!I <�-mQ�2-:E1i��a'xplH9n"�Z�KE�iv�� ,�R�1�2�u,Wp�Ce t�W�4)�,ey&� � <$IB��.s�?-�!+�f�?iuf"heavi� a*!.!KD mI�q�-pq!"!P�z ns��home-m#-}M�)�Xe� yste �de(H�a �:�? i}� #has� 6*n(wslE �g{ s)a~��18Eips_~ b3,6,9})-> �Fpu�!S/,:{P�a`Ek�Oo!DA#�"*Sl�e(=830$~nm dooomaq+ sp�[n�Ic�� `.7j ��& O78O)"�31 rubi-AEc\P�@�l���!�L/=�A.4-�K�(�k�8software-@ i+},05ariG eAs&i,iii}��i�\ASA�t*+)�[/ystyrene!`��a "*p�< c11,10}��Q�.�I�� �&g��be draw5Ka�M�7N%*.r�� crib) ��&<biref)���`-h[? meta�\�@!�( G�ep�) {\emw .K�6_&!� �&� Aa�(� harpN4��c�k*;.�.XA�$\epsJr=\mu=-1$ ��UTdi���t��:X%Չ6�@@2�.��%�f�S�TTE�TM*�ag1He�A.���$a>a"M�&�AsheO�TME�ySiscuss�6�"r2 9r���|�6 s�9qR -�C)Rnov%{�subeD�=uG.iZo3 fH_. r&ct�=lay��ru�+���-~��plasm���@�g� Oi, d��V!I�Af���s*�e�es`.��"N;*z����&*Tha@Reyno�|st[C,Gv!�geoa�)Dou!_� (GAM)�_nRI DJ-Alfv\'�D ��U.MB& 2�wHB [$g�%n ato�s o#a i�9sep eci~Th&S)!3� �ing7iMin} oL �ʀ( "�yc*KE` �h'OK�--K�S�%K!�reveaWAT�C 8��ar�!IR:�A�h&�EAg�$��>�M&x-�KD 1� �ak�I_)�.� �Hmbet"�>~��7U&"�a�Q�b F��cance� �p �a���3?a�~g�-x!b? � pied� iy&:+,Z�C i7 prp�!�#t�e�& D�(��[� e��M"��4�~�#�>)�;\r� ea��D7e"�. cD�� !i�Lnc5�pe��ex�#g&?vh u�al]u�@ ly�$FCV)!��o5�o�al�E�e�= x$. ^~ ( G (2 �)R_�|xsa�QG a*e��x LJE��vt���5�-�[Mm` ��I�a�F��o!GwS am�w>aA� �5�s�%q � g_E� �j2� �apAM�z8dḯ"su�m�?pD�_u!�I��!%W�N5{ isun� �J�Á�:�Y0�tc!�radiu�m"�2zaFCAt͝ is n+*24C` d� � Gi1��J-5@I-5�bB@;o��>�lyN� u���H��$>�1 &�c�� bodiM �pedago����<�*^J �d�U��� �riefly.�0<��%�eele �4tY?86��.\ Burg�Ae`��!�e�=icaj�aGP $-\kappa^{2} x+f(t)$�p \in\� bb{Rd�"��%Q(�osG se $ 9��da�\!g�`�Zed-��{���U�6�YlE�sp�:an%�,emerg�18a Fokker-Planck9�: ��,$2�n�#Z-ic��=>bI\�Ornst0�Uhlenbe�n�.��^4ATLAS Pixel De#p innI�stZbm� 3track!p�%4 +$%r�L��g*�9� ?5{es��+TA�"�#is�&f�ac:*o�Fs, ar u ) barr�/�McYx&�&.e ��P �0o8ytA iska�$�Qp forwl� ��M�1;:h�e Fu"�er:g�! �BBrobust%-�-ed�k�UA�c5��a�; budge�5� layoF�?."!�A� $|a������.m�Ia��[ed.�_v�*eKoco�� jm4� �J<' ?s�v *�, add�Q,e Cond"�,�mAe*:� �'��&�&�*!�KrF!�im2qKE���!aX�aKLA#ist�:*n echofdr�S�G. D�zew!bf!�of�'A�arx �Q���^h2-��!�+�6ul�P%�!�������+�>I�� c�AQ i�Ifgas�URq)o�^Q es.��l��' s manu�}pt�2P "� .=W�T����  <�T. A%�5e�Ey�MfN hV��a�W0bp�� docu��e�!\{�/�^Pap��(of Albert E �} (CPAE)���-Iz:�C�q�BFr>W��*e \^8�#�b �pkE�It{J�� s�s:#0 Scratch Note��A m�Vcha�|gWfj3f�e��'s Berl� nd P�e�o�.��  ;�w.�? �-�%2�p�r�_iW &d�P �M!A� W�%.yA�H3"�� ���le�&)b % ��.b-Poiso0 �b �(V%zm"tau6�hy�m�.#.�� "� %����(��5��0%�%�%�vN�o�e!��vR T � (DR)![ $^3$He$^4+$^!� "�f��!11"y-A=TsSto�d R�H(TSR)!�$Heidelberga"��!!c!�!�s pnVco"f ��1am��{ ���$v}9�p�F�-zC�( Q# �Gnergy� 10 miup��40 eV!u�qa�|=�,35 �n �DR�>�Z">'�� }"3\A�s�>9}$O�30tsX�1}$�k��v?�al�+2�:W�Iafra�E�!��3�>�&�d��*LK �DeHA}!� o =�"�51iw�f�L#v0�A1\%!�+E Z)~}K(east $v=4$,@ ���"�-l �IZed!y}a|eW�E mp-�e�0te�|u�3B�switc^<d��&�!U"� 2/�I���� .RG�*t�snE�!S]�%Ip���3ga�so u�0u�-2DR1��-��&r1/��&����2�85�.�'�e�%G�;F�e�Ra|b<> �u1NB�I��C��d} ��E�5Z'he!!�9c}�%�^�!�l�7d;�x�q5[,wat ���($(3.3͏9) � � 1�H�|2 �co.Cb�'E���O$vW�C��k-%�� �X%be�7�1.2)$\%��<$1s2s\,{^3}S$, %'7.4(4.0F(1( 58.6(5:Pp PPXzdT2.9+3:S+ 1}P$. % AR��dA$2)H%G7VS��C[nQ�eo'.��� $v=3�yar$ �u:sA/u���i����Bkdi^XyN"�A ar�7 0.2Ɇ�RQ����;iW�smo��; :7.3 eV aX �5>�u�*�iat 15--��� E'�uM� ��N7}�u!%ujp&� inel�@c8>��Og s`�de �K�(h��k�Ws� DR.6�z�o q��bKUKpar��^s�0ds"�Yto�2n +ti�{ic �u�,om �* �.!!- four-body� x��] wave"�O. m��vi���* @�[->�:ZI(sma�, adia� c(&C��@��sw=Fur� ,  -n`Qn-YW�)0ge (SEC, NEC)R[i6Qm����%�� 2�նN!� 0r s�� �.u8 9+.6�Vw���,!]�Hd�� Z����3 >q�46v�.�2 i="�7¡��(a�@m�m��Fx1er�>�a�)� &tail.D�]"P �9�)r\ �2eg���A"�al 6^ a di !�.��%"� ng v>� $1/r$&�W �)/��loo+SB�m(e����lread�!gP1h�V�Ev/��� �v��\!X����24MRpt ^^N5�by���H�$ la&|^B��!q�d}���Nask���& D9�Coulom��5�oX2�eCRro!��>�:1oA(�Ba:E�2O6 ���$nr&���e_ Ad�:1]&(Zi!��#��QXm._�u0�W �lb"��Lsum�Z�NeB_[� �_ -logE6o.nA!(hyp�6,A�n iss�VprCJy"�A �s��7-{�r$���!��jYrr?>v�K�ch�4�aa�i3�|&�Ri&p�u!I��4 f<� *�g och�� 6c�Q�`�/s��Eg� Poincar\'�:!LO {``es�!��� �_ &7&}ethod''}2R�H�JlN{``@-La&AA �''}, w�` k!�!�H29�� at mw2��CbA�6K w'c�+ r�<ie ��,a�A]A��(nowad9 o�@Bayes��8)� C�ard;��qu 0p)�5B%��+es!�, l�� hods����3ac�#)mD�mplB1Lide��f fals"0Ng�a�%it�;!X�r�A@K?eTIY�pro E� dx@&`�1VJ8. SXuritic�@9�I� pQ<�qj&q�*�$na\"\i � :���.�,6�Bta�e�}alN;-A!E�!�Ua�out�d�b�=u42�im �&2zTBloch>{e!�in�A��h��*�d.Aa �V��avegu/ "#y!NG*,Jde"�gI A �Z P�^.} aBtnd �9 '"% 1�J;M ��% �mT"�q� gineeA de�/ 3_acA� �\oa-pass-e�%1� s.�]vorZ$fil�P&� (VFEA1+1E) 2+1 " I O i E��B0�& (, gr�N�a(VFEXpo� -u!'lak-_�!�I$r��hx䛱-��4x�er�!�F}(d�Pj��.FL**Area Ava�& he PAOdio�V(LAAPDs)� j %bC���yW8��M��scintx�H7iT, K�NXe�. Abso� 8 �ce�fhd. VaΩ��X�%KR��)K%`5Ts]$�* anufҙr_ub� ^2�6�a�6�(128 nm)Q���'�8B��$ve 40$\%$.�W�]50 `��`ho�8�kO��nt"��#-UV�*����e"E+o �hq !&�LvE�;� ��� e ��Tg���w 3787��As" RA�Ő�lipid bi��s)��%chݤalcohol�q��&�%d��&/.�51F(9d, ���s�� Ran �.F�Man��~Jmphiphpo�r�:WNg�N�)a2L+arse--grR-{ aNs�� t�IC���s!���-!A��(y"c-� : r= g| &�&1\EN� �cw�E�=F�3a�)�AY|&y��eQ�yq bC!s� as ?B"%�a�n��-�b @ahaQoA��mB0 �Rm IPaE�T3��E:pa ���_!bt�3�< e glycero��ckboneޱano._��e1>%`M�As�t��!rnbehavƕe�M ��t+r}V�):c lG )9 terdig%�8X�Ly�ga���1 mo!h���a�V�. um�f\�[l�|�1v� =%q���-I .��Floqu�V orem����! �wi~�eH "N7I�j��-EYane׹�&�f�M�+.:�I��N�"�aBRZon��syn"--�5�%(E�oi�f&C(F �VhKi�Ulj."!��M>Qs- ��f�a�=e�#!�jca�tooa�� �%ppe(� q--l�]�Z`�vAogy)偨z9�Mt.k�� Em� cԓ ead hD�7m��iE�-%�=��60%7�b�5 �xr'h�>H"l2�p"DY���u�% H�Jg y�6A`s��ez--E?��+�(bd�{ HD�6q )��l �e|!~6R�,Z+iy�,B\�"=)��so_�rh4b��.�Fa DiophN��1")�&}+�p*+*JJGd 4�$IB>x E,����D�gg�Z�! �W.�gto ``R ''��p�u� .�Jc��onb�.�� p�,1��peܙ!��Zu�F"�GmEPw/^go�pHo""ymbe//RaS*�d�!쉧�no8� A6� �s90�) te%I'&B ��by!��9J�am�*0 0�ir muod6z���%&L, oATa5MA}^s2\:J�Pct��wD-p)X�a;�y�%debanOI y.��$2001 Astum�JEast01}�*�ma>�6g�8�%���m/b)�a Markov� �# r�1�!$*��i Aug�U2004 Pi�I wski, Slad  �pio04}�1�!��'a�w� flaw��/�Z�F%�by9 ]!4�DI �0� 7!&�7comE&�aof2�$:�!Ea���rH"re�.-&� �)W��in&�%.�i�r�aa� re� al*�u �ko��2�A��6a�Ve"�S%�� g�9�2�Ji##!(^��� XH�lZ�� !5@!5bio� SM!Tߌo"�pP f� i���Y (fǹo"��j-=Z�HCgu�(s��e"���%W���xu z�SmoluchI�ds� �Qs&^"���v.�e��0H(�J (GR)�U$ ��kX�brivilegA�A�sz�rK�\ om�ie=�I y!��*61al��s (GW'sgpY" 9/ le.1Ȫ�a��(LAr)�o�S0�aVV�F�^�to��g�im�n����_ pb (O$_2$!Oi�` ). SE�n�A2@�`�  a LAr�5ft��mb�4p�0ipV�aCeae !5�Z�of A��� LANi�,� �*'Dt��V��5�a>�F�8��� )7�-@�fӥ�$\alpha$"O�s���VheTl210}Po$�7 augh?�/�>@�� Pb$ �g&�)%�-���- ud�yb"�����ene.�$path, toge�� �<Fo�FŶr�� i�Jh�!���7"�$b50~I !\��%u)�dE��v��,N&.ly",<$750\div 1500\ M�m$,Z�C�� =�1&bn � �.[�NH$-~iz��925)15)�e�pug-�� 3�&el%�$4�$~kV/c��1a�R(wob�Cog8�V o>�o��f�UA`'!# �vol؝�� �a"%@4�0.5~m��&P�l�5de�� ]E� 5��u@' o!us,A�s"xax�4-1-O� icM� �xi@Ls\ d�[!$.O%{vac�lɷ ure,s<e-iC]@;� i��A} de Brogli!������/� !/&J8�*6%s.}�)a New� <s R� � ��Xa�8�n; rac�S� �"�n ;piv��& S*�i�c�d a {��DWY!z�~r7c�!r<12 may� � l�kB�m�E�a tinyk%���!T�13a�,H\F--:�O %A j�K'U--�!3y�"JPeE� !�A .x;!a {�;Xmx�� 1��1s�=�AN���dM-�A }f2�,4is���9a {IU-]�} (NdB)6�^ ��Ld� a�e]�2�!uNdB6G�*�hkatT�2��'sJ T��Bvqc2��Ҫ�b�#��{�i�Iu���m�-U@s}&�t.�ddy!�Nl�r�!Ka �i�&3B 3%|2�* v��ia.1Jle"��,!unr�T�&� � �phe�a J<� {R�E�eB{�E�VR{TU }, {�c  52x�UV{in 0a��s> A�Z& S:d �{HeisCrg's uq�K$t��2o�!n.@4 tane<2�-!��F ron}��l�H{q��%�i!ti&� },.�9{massO(u%ce}�, etcaeF�fac[��~�e a {TRK of R� ve M��}+w"���Apa�Z, II;Q5f��� N�QB�� ��ned.o�Hnew;<�k �A�cor1�.�V)&s��eC �9- memory�P�A * ad�! *s (��\Rev. E 68, 061107 (2003)T " .��]�E�AV ~��.�Q��' �"V1���e,�ise�N @p� �^�3��9F�� { . Ef|!ive"=D*LD ,�d)�*e"H"� ��;�|. M6���!�rWH�Bl��ry�{: M1!FC|&��-�g"`�4�"�8��iyB�5 ed.zAsa� alog(!�g���pt�p�:I���1mod.* q ��' i.�k> 1W- �KAU empi�V-`r�`ha�ltcB:�)+5�l��n-=v�q,$on�0g�+�(�J�[�mn��" &�8&N�T% spU1 ing)%�G,Ld#%we�#!j�Aj<K.�+�a.${.��}\Ez�1 �&A�*L1n>�AM�F�2�Q(Lz$(EA's)�<*`*�- $(IP#)%K�$H_{2}O$�o9#._\(exC��l��&aB;on�k�O.,%1 � t�.y@ 1e�Q)�$S �r$e�"N=���-�eQ��!sۂ.��|a�Q �vӗ2j�����IbB�or"��aE� $(DFT)$�*%�6��=�� Z��Y}I} est��eW| fu�~�3E ���=5UIy�]����h�m-!OIt)��%a�be#-�a�'a� d�'a�:$�${DFTa0���1�{)�}$5��.�=� prom݇�p6i��6� �R�l�_6����1�x�6�s�O�ɄE�� ="ir�crtcom�*!M_[J= �N`�S¹i���A2a���an2�!�-$DFT$.�./p�f4c��a ��-Boarl/hoF&M�L-A&�1-7�p6or[� �[-3-� l(7F o)%go�n� |���9�redW��> A sP�  ��S ed.�q3:g�akgb]$o�E�QT �� �h.z;��&� � $E_{eff�ɭ)2� PHI$�I�7is�u��*i !h#&h�@� � \+!A*%:9�� 8? iQ02n%�eY�N 6Y f�!#0*4, Fock- 62�Z~luZӥ+m�!�double \ tu�)* '�* J% 4q$���,2�nonU!�Mne-�0�0e.1L�Ac�#�7 ��1��6�'o� ��+=0.345\F$24}$Hz/$e �$/C�"$.���z.S36rS (p*X'v�42V2�"�b�*�G���Zb�H v$!*M�is�r�S6k � nMbv�!2���IZ�g=i#R�ne \e�\(\ Lett.\ {9�'013�(5�. 3 . %�K^),exK�q_ydr���;� BP~3(p Rosenau [{z A Q�, 71938� 89)]�Z* ��`:�.4Chapman-Enskog�a�:��A� kdr�5��uA����2!�i7 "�in�'�X �Bu�^'",%�we� �"�%L"* ���G*!�{-Y� &�%CD6Y='#� 5d��Glob(�m�olEe�-mE��Y!fju`�a�g"B�+��"MZ $B\gets X.`��m�$I &�M).�g����c"\!� ��pO�I��(A)Kir&Vm!t,��.jf-�,A���^ �2!��"!�FT atU�e"u*e8�E�r+�2+�t��"~A�e�<33on�>neEu� d�)7u&�/�qVfnb+� � � � �MZ8�+�l,��V�/��x ����I-�| I%.g ��e�LPe�Mimpa�m%'w��hif�QX7v ein�!�Gtow ��R)y ($AFM$k�.��f�1�&����� i�Aen�!�.O*���*!=�-a )ces <��&�. O�  e{�E�R�Q6� ���a&��Y� I�� ��Sta(drom ${9>� I,��$ps����erarch��Ir1�r�!ed"u�#;F.�8canAdaߙd�+��e�0����"9aw,orEto �fu��%/y�����%�� ng*M�E�Bys�s.�%� �9D��a�� -a��6�b �,"��%4�I1yY�v^�8 �gg@�1J=,*�${m }$5��ar< *�� � ndE%6��"��q�.u�th�%�pla!9f�12[. Lmo�(w� � ��^�0�"�+G���N� or��cq�U �esM�w s!RE�.�&�\AkE�o*�0)$"��EF�G�be� �f!�>p�e5��"�_6\i���-�A o����U��)�a w� ario �- z 8�_�0 walk� anomal^st$F�br- �p!:�M��ale C�f��mitA��t�M�=R�%�Hl5^"lVGa��a n2k 8)nm��lEu��'x~$\zeta�~$\{1}{2} ���GE� �S "� 1 4j� a ["7 $W(x;t)$ �_ �eZ�i. PF a�Y'�1�s.�T% e������ov,t)� TlM�� @ me-��1<!t!�i7�*�s��3�5E�L\'evy%s.NVA�us�s.�.:"�1*� , $C=Tre`�ef�Ev��+���a�j -;��@�=�oZAm�m �T5�*��;B.�11��P�Xg�o�)� fi�w��# n�(��!yU��� �t#2M�-Qi�lsw $.\ \SDi�7ce,�F�\�ge� n2c%� x��i�A-J�A$C<0$\���ka�� �> H�Mth� iz��(I�eFn�re�,\A�ev�*�p*-$q$ (� �oV: $\F -I{)C}$)���*� lyER�:sr���ia� ($q$1�)�6$ Y$E<$C$"�Lz=�H�=a�f�K%�!�Yh$Q!2V,�0�m"l�] �)e��EH��M��,>2���a:�a��/phaخ`6n&=��a "memU aX�or"I-A�}�� �t�V�� **�{A���}�6��%7 �I�� .�, hel^�o2�J_!s onse�dnC&!f�� `=K��+A=� furt�P*������.*HP�!���"�!�0vd-!�4`v%F0del��� /�"��4v."s!TC t�d � � RMSD�:# aJ� !.v. "�h��� �55l )�iac�esP�M�aD%%[� + a�� acid\ mu os�uaMhv�& A�a�gW� e Go�A��8r)E=�7�!s8>m2z�ԤA,&�� l%��tv��\� ˩M!h���3�#a wN5A��Ԇi��͚J�2-�lrI��gbe^ly-��W2 !�c"G�*5 �a�5 YU��ybe subAm�: h� *�:��Tvi%� .���a term {"s �:� ��l��� "���9U�)" QA��"��a�5Eoa(M�Eka�/��An���)*'potenti�Lals.<In this paper we present continuous age- and space-structured models �inumerical computations of {\em Proteus mirabilis} swarm-colony development. We base the mathematical repre�^]Tthe cell-cycle dynamic xJto� ose p0ed by Esipov �DShapiro, which arecTbest understood aspectg�system,Bw�@ke minimum assump)(about less-M4mechanisms, suvs!� cise formgXpatial diffusion. The m)�i�5�0have explicit%�5��� en solved9�U�dependA�loa= physAtmkeuse�m]Hal methods designedA/IC {,, with knowna�vergenca� operties,�btaE@eY  resultE�ated!�.4.bWe reviewEfur%m^ an analyi�E� that�$cribes how!�rmo-�straina`A�e sta�5tyq�nativte influ�$tein evoluas�a A!-a�8ific manner. To �enaȑ�E�p��in seq]s�1�8s as vectors: SrS�h�+8principal eigen : (PE)�c��Hact matrix, a quant!%D��(mbles closem+effec% conn 2of each% ; S�:�througi�``interaOity''Flamino acid type, using novelauametera�ai'correla!wA�@hydropathy scalese�s!�r.K�mor!�rongly.TthaI)i�B^!t��ex�e�: (1)~�A� ge upon mm^�uunfold�$free energE�-�sM$ two-statem]�4s; (2)~Genomic5mxA8Age-siz��.wide GC!�tent; (3 �ma�]@�substitI�E9c-\y(ary average!��2�M�9`A� ry s1yw!�7PEAa�ewu. UE�-�G,!dera���5res�͉�it}�distrib��!�Iys acros�� }familiesa���:�Boltza�:NwA�verse�dHerature'' is a func�FofSPE��on���I\our�di1sE�in agree�)56��:�����rom z � Data Bank"ldajmin�Q�� ��fitE� obser����. Ia� estiaw,�optimealmost�izi �� avI del� ious�)&elimin�by��uksel��0on.�A spina�in,�=a�0a nucleotides��,!�identifi�{AlabelIKQ�e�!�0an irreducibl��.!�$\mathcal{U}_{q \to 0}(sl_2)$. A master"bA�vQ�ionYU$is written "a�ns���onain flip5Q �>U' vari�= �]�٥<� ed�ilibrium�E�is nic�Vf�( a Yue }��) i:\.$!;�rankeda5rt oligo.�frɕya8$DNA�Fin� ��� M calom tri3�Va�m���-��tra!Y!������I�$considered��� Go lattic"l �0  � 5I�s� �for��):- a d3 �  measurE�V��@ $\kappa _2$ defi�-m !o1$van't Hoff� 2Qn et9m , ba�� aximiztpɄo �%& s� vud� verteb� �� ��N� �J ott�U-2 "�arily di�d :. OurA"� sugg�%Gmarsupia}r�imU �candid�.W���� %�!�grade�rphogen��filI a] lay�y nonE&rN p� U, i)t!�pattern� u7�} focu� A�: ter� � cytosi!m�m�_�>bin��iga��$to recepto'�r2�w,�� orpoi Av�<%�q%� t ex��%@ . StcA�� a mi�copi� E(d���e�"�%UQ�A� tras]N�by�ra��&, b-? leads% obust )9�� AJ inse& �)E�5Q5du��.�Ae� oord� s (codon � ion-&&� "� (ies) bacterHsADm�X aigh�nI�9-"6 ��pace:* ��9 euBQ��!A�archa�� o. A��348a/tinctJ�availa"$in Genbank 4April 2007, be��!rth a5s-  high�cy��0�l�e now�5to�la�"�JAnewu�oe֡��L�symmetry����| �qrof�si s��E!� usag" AZ�ent��W�mo�tb at�(mean--field� xi��f also�ase"ext--�, o�mpk in� m�or Segre) ety,�) ��Na �on%�F �!�!�rA1)A�)fira�0 "�!�)%3&XA��wRE�ic G+C �nt�x�� grow�em�!�� ivelMO2.zaI�h!sird�!��m� curv� �3%�J�. F �h� .~PCAU�059.1\%, 7.8\%�4.7\%AS�)\.���>�2ci ear�L;ed�w���order�q�R|�par�(.@An ensv�direcam�� �� �"UA�o!Q�ng"� se,c�n1domlyI $N$��e�$ colors. M� �WsamAdlor!ner� @a hard-core (excl@)���MWA��H�+nesZ:�E�reE~A6break�!�S K��aV�@a $1/N$����p"��"���` of:�� cular� :��� � against��at�� x� but� gil� medi��&.�AD great��!!effJ % 1�of coa�g � d��criW net a n3�E�theirlal fee�)�le� �A�ia 6� 9�,�)ح�backbone� ly "����Lan��� $problem. I$ v�g� �)�= A.level��d $M$�7 1n I�L -0H ��E!!�SBoolean~I�ɭi��]vg!�>"�!�olH � �8diagrams. Notab�3Ť exhib�e,&��i�"���g� of��%%9roz �linputE& O(1)17!6o2T��lex>Psome ``�K)NZ$(N)$ \s.�� .� � heur� �%Zalign6c see)"��@is&� .c�=W4residue alphab LP �%so�P� ifO Dgndnt� blocevmprisA�"* ca�5g�$���seE��"��Z�aid�a%1d�Ui�ll�� suffix-!' tree�d- I�uŤ� U)��n guid% �-9-59b)[��A5#�well-j ��MpE� prov�per��"Z � (ed BAliBASE�-uMq��m��#yI �E�pro)W �"<.\\ \bigskip \no6 Ndou� helix � alka� p"al �`$�de��b!i2$ qual�� E)q� �!� �m�`i+zE�.$Li^{+�$Na K Rb d$Cs Ynor�.-fm��n%bw�bm$�n��e�  plac� �*�q��has1�F!�A&���1�.�<es�ish�}� q��masd ��P�-i�ore2cal !�=�m _b�� g�&6�m.U��of Raman�tro�y. Key i6!,ion,�,�� Jcy ;a.aM�� E�� e Spe-Area�  usua� �ist� � 3-�r ncer? aiP&Eee� �% time�"Wba�%�Lvidual-C�%�-"� "�%� 1� Tang��N Ginw ��em�%t�� �!���!�,"Le�'erKA�"&(, �� a8 via��o�#�ce,��s -law6�Re�as"�=M��s&  um"�#We fin�"at�-lahg c=R�hab�EsY)llow �($ �5�ly homo� us'.���motil!�er�&� -neg��a��V�a�Bby rei!u<%8IV piliI fila��A�es��uin�%ity. %�Y���Ky�r#�3a�y$, PilT1�a7v�#%"for�,�0exceed 150 pNz�arai!a�mg"�*�s larg un��� t�(_ �c&�!&�*bring-sha�+ �Y�%ahe� ��surk !�I ��-�<)Civ�?�� l in� �H�,C �^in=,%� i  �!� volv!�a small26A+ �A��ng .~'de��� a cir��rA�s ��ff6iff�1-���� B|n���/ng�icn a?ic,�.-Yt"ppo�&A�(flashGratchet),"0(spo���ATP�'lS��W���")�-veloca��1h.l%!T� -�"���" explv* um X (st!�ET)a��]%�"s1b,�str ,9��"�dkE�1By� my�q2/ !��;�of �"on�!]�Z1""���|I�JK�" xC= |s&ly�&�6`!�C� d!��� itu&.E�#ݛ�=�Knd��er "r"N *` 91%�J�~ icap�',&)l!`�0=���"� S,&�.� pilu�� u�/�5U���w`l� 9%�&}A�"U�!DY]�a4c�*��.�EGA'ec Z s>����$n��txic"� �b�IM��r!�ukaryo�*("``junk''� )�� a vaRNAA ,M� Af�"ory�: lie�(ż��a�x M� �P1etIS !?�er�UlifF/conje�2cX0.�np,��eA��.p!��mm�� y'',|ojfG�!\�Jly un�}dK chem�web�RNA!��s. Vie2o-cm�hyp�ve�-+eFJ�ofJ�re-wirea�elf��employ%VA �� v�"o uhg�in1�E�e%��&� ui� argu-zma+\*� I�!{�to!&�,�-"� �]s#gSuc~#ful��at ��m.wayg t�2rec d (! d} � I�. r�0�"KasIQ�4ulN�� t��I�AG poin1!m,4 �0pr&C, Gc�!uA[� e u&� ~,"! . If&w �)r���a�UJ�Aq�L)ell%9"!#nc� � d �U%[gene duk4����Yactual �0�19� . Fu@ an��6�agent�h��techniqu��%A� .R6 econ�/ s, g9theoryi neu�AD ll likely0a?4Aiin�stu!� e"�"��35`�)M� �&�4� s�.log;���'�#�7+ rguj�  �& t amhO*�4� ledge&p}5h(��nit� M�6a�pro- N�a6�z;1��ǡ�origi�l~ULB�ZBeca�4��~$�%pai9  ru� �'�m |s ���� a &"= of0 duD��y!�msA ��<,!�we�4�6"m �oup�&� ���-��abs�� a bi+t�'y� �x�\nd�Iˉ?at�6wF�I stea112��A��+��a�B ship"F Alog��|�1dI�mm��tor. O^ ��r h�t�)L� ^/� &6 u{,�F)Z�H97�F��b� de.��h�_0(!��5��! val�$�.�MN" �!E��-�y-lyaep�f8�)�Pa�6iz�&da fH#n �E�n/4rand-Ec �(RNSB~ �Y?7 ipB����f� is9�4pj5��-'ompet �.�A��$b� or vi�!A�aӅsl�� n enviro�switc�-�od��BM�w�#�& OneE6�0dap��� -X.j,�pa���rt #co� wh��=!�r!:Ush3.�!� UJ�F���m� � tL'm/QHX al6&�!%8�in+ ns!>&@=*�-ɈM��gT9-�%ga%>v outcaI&::-�|6F�4�D��� � L.#�# hang���(Uw";� arbovirus��1e5+&� hM4 �B�)� �0sis.�% Tex��abA- ct MG=�&�1� al doŔc�4dulE�d A�nA�$� u�a Go-�� �nual�izma�:d Lennf!Jo�&.�� ��/a!�a�)�)?"�!.ir�51/c9B/aPQ�+it �r""�3o�9A�e,R%=�>%a weak s D%��2fn-~' ?$Az�i4:� ' ��E!�$\p$ s� d��"��b%nuMu� �� � e�rA��6' unwheqtaneousl4 eachM05�QC��%[unravR!c�(f�"s�A��!nE0ev�� D!�1c� )#%ixQK� r, i.e.se�a�<�w0m�#*�3&&"���=1Tat�&e&c&i�ua) o af�!�etc�aEAt_4 way.�Despi�[ir� a�$E��@y,�$"r!�s��@a E�ofј al behavi%G#&� fV,ed����#A� abun"�at��JWe 2!�!��x�}R��M&�;!���� �nY{!^Cno�A|x�(ng� ɗnon-chaoj 5 �/��QlasGppl� � � g thQ#FD17X s�w":A�tri�%ly>c �e;�of%�" �*ths� r&� �ŝ!<�6�2� reE�� =�7 seemAja�!c��1�-���Cs � s*\1t U�$�te!�"!"���v%t3isf7�$s.�E"�,A �% year ��adultZ gene;+k<s*_"p_1o�.!�, mammalian b�. Litt�s� n,���,cDA�f�<� ole aT ~�.ade�e) �� ��P�o+#� �H!�w�0o�ł��� �#prou^[��inz/� (�at!IO K,�1K�remov�Z�)A,al too��*pos� ��chieva�67*{E�in pur�2(c, synapse-"�d% &�'.��,.�1��i-auZF*@%�I%k�!�E0w0%�!K as.��4hanI8"= (SI)%+�.�, Ig�,Eti+��"���v �aa� � f &�4#,�(��}!�)]Cos�%let�j!��+W#z�cH.o '%\P$: SI (�)w3�T �r-C�orAHE � m �� omWiQ1:-.�00s;qbZ�a�l~�)er�,3{ er���@nd�)e.6)!3 hundre�1thous� sQtO;SI!�aB��@ �h=J+Bc���m1�; �i�s�Ie�3o�!�- R&un%��;�+f�da�'.�E footk ��a;� %6)i%wth.[z%�)N DNA-I*| 8c\� !u!� H s] � � t�val�.�$!Fmon�� salt�<&�%�j!�aF�����|%-s�Jn�&E�Durb%0IorLH�Koex! Kha,a!y l�'�#�$��A-ens Sp sJ+]�4����mesocry�)�a�8���-������e.Z"E%E�.<�B��$�5q)tumor G?rtz��1�!��)�� ach�"� n=ge� bal amoK? t�6�G%n*{'y  J�m's�%�!cI5�iv!��nu,or �orm��|�s"Wp�� �+5a/- spheroid.&.� Uρ���--!Ae�q,� �^n�.(Hr@ � Volk�E) r�.9#to noZ,��e �.marrow%?�zC?:1?�Jre�m��)r� �i !Zm k P Q)M�2 e�4�A�e��g��aO*39p&ng�re��ed: (i)%�!����(!n� a;�\&J�jAlawgG!�e����>cG hub�Hi sa��qal� � k�c�  tende�'�J�?�no�!s 2%64;(i{Ee" ͑�9nt�"fe�p�( hier4�2�%Z&� �@lXN!Ndyp< (vM_��5&�E�e$9�&4��8� draw( ed.�By� 5:x��mp���1f2�- tE<pseudobo�b(�v2$C_IatoI�f(�ecu�'�-�  l�NI��G I��N*(+as 17H"d alJ2%2J$~/���2-�2!�p�;d�Dconn=AT3D�Y a 1D` "� %�B�Jx" �l�2%���M��>!n �"0� FSSP��3.� 6��6-��.`"^-a&6L�~x�� (VERn�!,��;. VERYa�>�-�Scytochr�c��l"�F�6&�+�s� a�he2�3&�.i��-um�n��or�I� V� �lM��n8�AM� *V72�-"+ � U#)�.a�9vng &8@B�.� �!5�3m��mB!`�(sub ps)exa CEt��?2� t ro�K&"A�"r-��7�%cp )ZP.�E]�R berg's�upA��+p!�ve�fu�.~8b�3�)A@�7�i@cO�bsm�,%�_L>�CohE�: Phys�#SV4,BGFicIbb R,s:[*�-N�; LTZ, Landau-Teller-Zwanzig; Mb, myoglobin; cyt c,2�; QCF,f�.�) a1/� r?��%�l pop�$��ZaN�6!(aL )�lemQ�� >!{�=V�#� refugA,at@%{ct�5|��"O#����sos!�"�Hpt) n �%$`PRc� ".�p�@�)A��$ 8��(�r bos � Ϳexa�n�'Eq}2!,eFL-Dirac� t� K�@�-exz?!FA�an}-%5!F,LBose-E\#tM(.s(,vijF�%�N.�CI ?!��o�'ig�ng� me�hyJ� �%�J)P fI�UHDgBA��M.�@ coll]!�� BE!��b�2a*�.d":B>r�  (u�fx#"� typX�C!<me�\"f in~�Y loni�eWe��1c�)�$Y#� al2 � ( {in vitro}�6;E6r6p7cho�el�Fm� �(ESEEM)& "0AK!9�?�efv �!h�3o-aj"!_�6wa�!u�  liquid�K ". P��o@,.�IS3X �"9 S":L5iBe�����!�a�,�in NMR�a&re�@�D.J� EPR.!�-,:�3%R (26%52~kHz)�'�8�U!�� %na�2m)�$S>1/2,M�s �Yw�>#�)m ��;� X� ��6^($S=3/2$�. ($I=1$o Aendohed� fu�v,ene N@C$_{60�Jm]V�ho�o �eI;��.�cisotrF:��I� n�A\$^{14}$N � us.�.�� 70}$�m]G wa;^( Talbot-Lau6 fe$ ��~th�2�W"%!idYfriW visi�y!M"d�$deb)�& �� ab3F5� adi��!� �.cA�, st i;;"7%�he�1� � %n �3 Ʌ�{H�asses��e� "� �m�G-canoni��.�$"qAin�7e�Sgh� wa���2& ��ofZ���8*, .O of"��U(%k�5�l#W��!e�7s Cc5�9��!K��0<dec4%��+%��Ja�@�em"&T!ho�&�MI|mGe� an}*arm!y�p �ro��Q�-#C!��� �graI/lb~ �b@�l�(au2M�"� B��2p� rap!3DAh"� a�u"O15 ;"*&���O@-on� �oscil��Ptud�a �"�� ,�� ��rQ:�g many_�3� (�&, BEC),n ws Y sD�'��0ri�A(| �F!�! �lcm@�Aw9o�_M!Ee)�!�ax �l�aa@S e�&���u�q(A�Ts)! m) d>�T%.� � ��] Ia�q^��% 2"� o an�0r&�1of�.� m R���v@�U�����magO1�G�I�cE/��0�"�8�x�ef q . Sp�"#a�� AEnC embedQ?a>Lja -us��C�(`m�5�!E�"�9a�ViA6�H��%-�bJ!�sTi #�.� �2 0���h�j|sup!8s-z�6tj ��o��@� mirroru ���a��!�E5 -is"2�.�R*���g. TwoDs W"-�f��/ea!/0 JO!.a�0Bl slar2��:1&�����L�subf uper�n�UR7 �M�.{�gmi!�eqx?p`�;�6iN/c&A��s�M s�����qime. LU^%E^C��� � ���dabsorp��,�A�$�1y�xt %��&e^=�O6.yzed.M� Holevo bo:%� �.mu1i&F��. iveni�u�*co�7 $1996 Schum�Br, WestaPl��nd Woo�Gs [�',�`. Rev. Lett. {76}, 3452 (p)]%� ����-032��`u\<2�'�+ A��gh��0�!mi�.2�S�Ag'al5"9s m�f�th.I!in". �"Aܙ� ��%�4SWW� �����7���yZY@J t2�}B�A�Uadn�� b�?fEE�AzQH� Hallo:�6agBdu~ mOvon NeuH�opy�(jdum9b!�mave�a\$2i5 ate,%�'Ŧ.;%���Yaba�mJ [� F.�J#9��U�&�9g �E�a�E�FR��#�<s�M�reehr��A��7a�Uco�(O.��!�)�y�]M�.�E-i�C��1Uu�B�@ty.�*e�B�*>)qNK�># mov��iI�"c [M��e�qA@V>&�=wEdGF($�Z-squ!9 HI��i^,bt*y.^a�gy��^�,x��n aut�5�(��*" ��5!8W|Ir2 >o 3 es m#Ubi"��by�%ABs � $\*$-�ga_(``stA}2ue'')&iA<<$Hamiltonia6Qo� �p7��  ? �-" \*"�is �N�3;M� l%:i,$t_ad ho/0"�!%�5��t�NiQ!�!tl�g?a%�!ex�R�RB�6��ak5c�,k ��:P� 2>�5a[a0 8-by imagi%�7>�i~bx ng ��( �Rt,&h)!^/ll-�a%��deJ�T:�� �Gi?X�� dard�r\"��&av&U8s�*j�a�j)18�S�.<�3\)F 1�4* 3ŏU�6�,}-A u��BB./���qu�D�a� a�(alg�\hmsEO�!:$ ��*"�Ou?'�vf� @.k&�WZaq�r��]acle $Q$A�} b^jf e��Es $Q^pp_$Q$8O*̡�pl�Shor's����@0\cite{sho-94}����set�w� l%~bpa $\Omega( \log 1/\epsilon )$2����-e�p"�; $$Q^{p_1},  (2}, \ldots$d |?��a���D�/up�.'E�-�w.t?3A�t�;&�$f�#&"4 �3cI3IrtWc�\na-( ocol�q o�Cg�Lal �Q��g%� ;uc%`qub +�9by fix�%-c9�Wc� �e7he�1,Du.+L�r�"x �rem�hu:!)entire�&_ , :c Air�c�$AC� M�.��fluj=a*%0ola�" :p!cito T2.X-%��-g & �#� %S�<s��]�A�J �>'p�he a�d�!;e�<^^�!VuL� .��\ul @�O%\�!!��O=19pt U Brow��D3 g�u?��i�,c�<( ��>� vacuWF.�.�!Zect�?nQ�p����Pa ! �}Y_ dB�!vG2 �6�� �~uA�8N�("�>, &��!�re�  "=�QiDc*# d�Ile-9����e�� *��oc�>"Za�O>�"6At)% �8�C�r�H�c!?"$&\Vy ��2A��97#��pre aE$�lb�yanP & �a' Q� , ac4d)�v�r�A~�%O�� �%�� A t�7e�P:\%w:BPand{\thepage}{\roman{ } \setl, {2} A�� zt%�%st cist tinD o ho^ skep��,�tow �/ 0!a `hidde*�W'9X�'q�:�K �6@$avid Bohm'�+"JD�4&�*a CeqJohn S~fl<3g �A� �� favoŐ�|. M"!n�&ina.ei�i�_`(&�2U):�Iq�*aye� �� teE_)wo�C�C�=�+�ve�@"�Nj6wGca"behin�d%9ub] �B[�er� `O2pC%xems (*�'s, Gl^ KG�Rker��Be!`)u�a;0p�*�!\h: issu�Y�E'm��oft]h$azŕ�Ve{�[6R%�< ed `9�'EH}=cW ��y��2rep�3e "(rN�Mwho"� raw )��(.!gl�] n�5the�;ac�@Ih>��i ��n��pZ��c�+ed�; �0)aFbA�disregar+m)� sophR���9 �mB�%� y---E�2�--- �s�y�f ity}";,aBA$ happ�zi V)"!�a���+4$��.�� �����"��6"�Jh&!0:��~ any} �M(�!@>d6�$� >�9B����dd�^�khr�-6c �URP�bi� > �>e}52iBorea@�Q�$ew>�!'Y6@���proof'�recA�W"}Z on������UQof��F. AD+;oYA��l#M�I��?>":���6te�e� bSGA��a� %����s ex�.�thQ�6]"i�m&%: �Y$ 6�%�� 3d�!x !ap@uIE.��wA`�&&y:�%/��5 of i��#A<kF�'!*lu��Yi;~�E/``�,�atq$'IW�#"�ins�inM e!x��!�vx3E�%���b& v�Ie� ";J�&}nwasq�&�\y 5 Alber�mSA�EE@@in--Podolsky--Rosdmaradox,E�99I��A�eru7I� �]�>�� &�xy�Ce��3��T� i�B omew!�Q=#�%�Bn+v�|,1� �A/�� �MUpBa � !51%, 1%)))!vgetErwin \ i s�Kpa��D  f� s `cneq'aeg%Q\�#�I�фA(%.��>��% �� � ��U"�u� ���9�---g P�h%Mr Da��"@*�e�`WY?$s'��)>(s+A�cM�EPR�TC�>��a�gSof%'Qy.}� ( s� oof�! a� �t��s�^aPGreen�0� Horn�Zei7)er�r�I�UW8 �WW �0 -`.���{V2liV'�Se2�we*� �oR�Q7w!�pq�J�"ver�|�.C a��% ne n] !�'�^�..O ;�s; no�= ���irTa,�@_ G 2��y.�R)�%>A0/� =X)!|b�U,D.ofM�deG� t �A� �A�*N��an"1�L@Cs, nam�AD�A�!�)t�V`�'�?M y�vio��;,e `Schr{\"o}�er.�Q7!�@<&{ GHZ)9!�%�I��Eoa�Sp0n| ��'/lI-�".a i/!;cXeI+�\� h ,vEK� �! �L rF -\�iH��0�>� �.^�h1 fide ��!y �?� sWs4] E�ach"\�A&x>^)m�)�I}&�>v� "i �2golden-r-y (FGR<< $B A�Lyapunov _O,6�*Hi*Q��+iJGauss>�packetmBwidth,w�H $\sqrt{\hbar }$ ($ $ beɌ.P,>kad�).c-bof9t��* ls�O�Sd�Tth���e9^8<1S6i%6bu :*1�& e1�=���*6��i/5W e!,FGR �b&c5ideA\s!g in. �o xpla�JTG�Lw5aa�-RSI`�ch}=i �a�N�3��oaB �Y�,� u Lev�w*�.� �I�.'�����"��'I v:�,-c�!�"$�logыh�C5sZ%8}9 he`)k�M���:ELvatGh7Xd~/A��*�w"-E�e^ 1�:T.6Wo�ke>S�\]T&� "Ne!�A1� <|Z=���pping� % �.o��s!� twos��\�_����v� _�7�{S\c�\E � ct e�16��,C߄y each��*��=re%|:!z�okFq��El�� /�=g�6~ ��<utpFy"e�a*�R I!P��r"-Q%� >RL�2E�4 i�� 5�t��m�p� )$ simi� (ones.�Kn�3s�d-in� �%"� &�)�-0.&�!;e���"a�u*��Om ��ion* 2-`(PD�6on�� "-#6�<3>(u~!�=NP%�Itd!a�� ��AA�!�\7A�Ee ��lo� ;  :l0%(.�as6�aAB8k�l�@� AS%��f[�A��F � �B���r�i�!�^IS� /�p.tT endl��ˁ�F%M��kua�T!bj-j[ trum���#fo�*)^I3i Fa��D6�*Me� �uE�ru�.��s,A>Ѯ�9-_�?�f f �-(,��2�A�I2O  v�&� :��m6l  �&E�*)ed��orthog�polynom�~.M)E%�"C9�4�U�!LE�o���dy]�:� nd t� �3ۊe phot�3MG:Sof� 'Lel�E5�an i)9%}!���%.� �(I��?�eac�6nq6��%.A f�,c�Xn*L xA�wo�8put�zb�~�7����� lAH, li"�p!"-Y�'a��Y��%�i "�<} velڍ�O!C�� Oe�"���p\'�6A�n��F�X�Ut2L�i�K"�5X 6lin�:a�" fier"-� <Oi�damᛡv 08A F �@ �=/ma6�@@ X��3~B!��rD�$" Ki�`%�� !A��4<3ou!� S)��KE\�a &n :t7%�roBn6$Bs�l �- al31%�A��!@9Qof���o}$a�D�"|a1�T�p%� �d-Wt  )�t%LJ�xL. \PACS{ {42.50.Ar}{ڊndDv>Lc} %�Mof B�Fs&��A� e��C2%,*A E��ff��siaVN] kicV�r�m��&����&� U7 X�?����4ic X'�!�-*�8!�?� ach ("@ 8Floque�>)�ր�� N �Ns, P|�58``sub-Fourier''\ ��'!*�7 I�vicO/yA� %5iXFYCa 6a7 nguiMLwo� ghbor��S�(� � sQ^E�a��xRd!|er��`L.|I*d $�e�?'XMarkovTa6�6lyS vG2Y��i�1��Bobi�  1"�_Ūs) a }�rvo�Y� �2��sT/un5��K�reeXS� ���/��dx8v���G��.� zSucjHemf< ɶ�5s�@rbitrD\�%%�G�Z!ze�I�6q"��<�Zq�h @m�-r�mB8t. BI, sideE5/ extr 1hu%�1 ��hK!�ni#�!. gy �r,"A ��<���6?� g!�, N!��n�ada�|G�s.gE2an%&�+&��"to mani�"w6al Hi0�=�&E�sRM�2��7����s] neH ��.D*� ��),p�9bof2- @���e&"5���� step�*s�/l*���#&g-�;er Pnd Soklakov, e-print:)�,-ph/0405080,��4��Sc <p:l.�;\�;,\ A {326}, 3��(2004)]QH��� xO.� . \\.�s�� 5.Ca��T ,Yz, 05.70.Ln8K2R]�[H�ps ��A%u/!i� Baye5up1Fng��*�pie8#����s� c  � h u�W��~ 5to�` Gr�&'�K�4�A:�� a&� �4aH 7 ��co��X � ^'�2��"�}�?�UL5A�"�cwe��Fo=�s.HMB&z��"&a�bit.�:�ea4l;)6Xonr��N Վ> ��I3z;"1%n &�E)�^"!l��?l�(up�!):�5llx � *� �w�C situ%�f7a�oK "e�Axbr @to li�&"�&�-Blo<��XLU �yy)i\to�2=z<�{:�r�n�Y�h�;|�߃n�b�O+7p>�dir!��.aced!�?0aYmaGFuP�llB9L2N 0 Oes��9�C� M����Q! 4?��WO!���U8��2�?O�6���E� 5d�ptAej!�N��!y"kc.�.v)!graphi_�!Aj! a),.1-!�- a1g; . A[8Cram% \'{e}r-Ra�tAn � em:arj2c7͠a�4 e}D�zed�Lum+�u�� pr�c��Zh%��?�0E� �W&��*S*�@�V&�>a�ncipl�*&\P��U�&e"o Hel@1�1�291}���"� Asf�Ol�&�?3bA�K"�K!��-� "VZA!!���Fd���[��q�n%=A=�Jr�ocular� �6=a Lie�IVI>IK) �) globeatB@�Q$�d �5UYM<u�6�B orAPsi2��� �%�.a�p"�Yaq t� P�uI+ %�>o 4�{f!D��A�vb2 w�;r�)d&�r��!�2� �i*zE�Zx%9map1Noc* �dc!R�"�f�JYptZx����-M&eA��r�j��� ha�%%r�i*W �%�S,f 5A)dig�~5ft���y9\aTF "�g6S�|GI 1g�� � a"d" �aP9 �.]aE��,��a.u�!S�_Tev  [?3b&� d�wl�4pe"Hdo1�w�T+ Qy feed�lQ$.��a�2wD�WNh"!op�M!wf�APR�h depo �ch�_2N by Fs� ��f}M{y W>�&-"�PXln�v�p�*�$ dhs}i. A�w-���a�Zk��� �� v�&�I�X�+ left�<�� z �W�" U��g � +��exh�who�&�e.:���+%��`un~ �e�*!M�2V��2J�{t}eem�Q<ar"�"jIŒ-QKD�t�|$ho�u�it� �u6��ind *gF#=nn��AliceO.wob�``Q crypt�yph�o`?s> � �� spli�@�]��AL�$laser j= ���%s'$)a07=,V. Scarani {���a\6�J92}g 7901� �A;� d SARG04��#ȡ�IV.�`��<in BB84�����>� & post-�� �]".�A��~~�!�Mjb�"h >L� B�$m�0q2��^g�I�iF�W���'"V QA�:�\tourQEQ�6� )x� �u six-d�-eoe�T(* �� [thres�;��=.%�s�G�.��Y|rix| ��:r"um!�nm�!Fnel.C���(squee'��.s�gappi& i51Bo�\ns�a�]de�h1W��2a�2�# l�<By y��ax�Ty 2Xqno�z�of2�,A��d*�ir�i,aN enha�<-�"g?Җ�lx�� �-� �g>*a- -y�BI��c�>l����PBragga*�N!m�~odD�"jFJ��.�e�ac :S��t�D M¥�p��= 12.�KRamse_4�oTy�A��&��B $\varphiXF"�Vi�e���� �L��s� 1[�a�oN,`�����9ise-to-s�^a�io!q�k�5 pin-YQg �  $\xi6�, <1$��Rq� �t6)d"I .;1^@n umH$:'� o�"M��-sPXe"�� a�k�y)OE�I�|lN�, $\zeta��KM� �D4figure-of-meriLgA�g�o(un%y!�%�!B�JL iz!� xi$))|Z!�Esbe.� 8 ����M�e��t_\����M��2-afW�A-tw�ng 2�L�H�!�>���H& Ys26XcmP�eA:��aA��O!ց�``NOON" T $|\psi\� $le = (|N,0 +|0,N )/\/ 2}$) s�>aWCf��_.m&A�$=�!co�t� lM"�W"I�s (�����dim_x-H�:�K $W(6Cta,\phi0�F�#��"�he6)!7�&a �!�E� i�Q �do .6 ,��.f��{ lit-���F��ic�%�}<�� �wic ge����aw tG}-�s�A�/a����6+�subja���b-��sp; I F�"c>,X5��"^E�1F��AQ &�Kb�T shift��rbe!oA��"�& �#�X�ou.I(by Hasegawa[*� ,A {53}, 2486"vUto�#i�M-h1L:p� V2�C�G��&5o a � :�o��� �m�59, 1meti���it�EI% WaghB�9}, 1715�9)] �&dW�.Sn�fe&F!�<c2��%�@GR �a�"9!�m���x� I� %8�'n^�� erUmIr�)-).%�r�Z �+n. n�s �"" 2� �a�$ %�Re'Q�@ ջ!�����y6,�gN�%E���,�)yN0/� ���%YM�n#� !�0f.���. %w�Nb!v isy.��!�+\I.bs@ofcG1J�\��b��@"ua.2a 1�!}�i�b� �ro�e)A�n-�5�-��� l�]A� high`*ir��&f�Y" e $2P_2 d$>�21$d$2R"+ ��%/�pV� �t�sIi� 2$r\: A=@9�a�N<of��Ad'!,!�*.� }� �qFQ��i�VD"cS%x� ��5UU1�$2 bW-,s�<dA�o��QE6�a�o � $( D \"($s D, D > d �%WimA�U G{?a�� �!�BoQ=F�E�" answ������� o wh�H3 $�eE��f�foe�4�Qiq� �5M� O-3!$N\]"(mapsto M$ \YXeJ1�&Qz .����,>z��.ax2"\ $(1\rka 3)$'$(2>s]�. S�K%F |� hoG'lo�!b.m ic n���UN��t"@�. L��ifPobe�ejEG%s.6da_S��] �(�9iveo �.1!�R�)pa/%�n3,-�|QsË�"oa�v�a4u�Y� oder�H�.��ws9��.$6w$��? c"`[-��Ma�l�5 �7�o#(g�!T�$�Gla&Z���x� ;� �l�<@${\cal F}_{cov}^{6�D}=0.833$, l$\arg $�(a&�9$% 63$J�fA�Rg 778$��� �eF=Z5��T"�5 �4�mod&9M�"Y�ersal}5�m�]"Ӂ <5��s �%�Q:c� s� <e�,E�"�U1Ac*� U� �E� eZ#Q�9�D� >Pl?��yc�d�:��Qj��,�+5�2porx nsw%:1�h2��iveCD��O'�K�K&5}-`&�-ququad�C s2�5���v2P!.nIaUU��>M@a�7+ab�X!�!s��h_I� d�0]b��8!<#�/22E,� (_&�S$2�O$1�$3 3f*X"��A�]+��tk1}S2�-'I�� PACC!s3'7:�+�+Hk$�w%�: Q>�, B! , �0Mi2a, SM^, C� ~�5 �.���Q|7MCmaz�� ee(?1�� se (+tuS.[DcIk��5�%2%?^ *�0A��|w���F  q��!�6�_!aEC�@n..�� �/2�ts�~�k�ed��:�_t!i>l��ay slow-AKsp�u�ls�� ��Q�d1Ian]K�iG0d &I(!s"�]��S_����8a� i��^�c�%!� l�d"*47a�-;T -��5-�t2.� ��/v��B b^:r*Ccoo�Gf,sm%�!d��N!0a�ta5{od&�^4��!7x��.�Mref$&a)� rans�2�hav�ien"+$2��^@�[N�" A^fi��M :ho÷&���co�Vto<g�D. �iY] =-�m��1�.�8�"}� ultrag��@e~c�W���C�m�)�))� J � k!�$=&�&�6  (zer�R���{!2mes+�"�cEl��n�v7[s<w=@pa�.��&rm%J� v�`eas� ^!�"Q�!a6q�/i�!ĉy��so�2�.�xP�Z98q��u���p#on�AzzX+/ ��7i Uo ��� uraca�rk yY'�s (A�\=cks).w�=�T�r���.@h�!e�Rl�N:����"J:6o� ��..�>r���-a�""N�!<0 7I��"7!�:�tu ^2��� �$1c6&3>(Z/�'��W] 8v� rn's�0%C6gU&�j �A,e&, "�Q.��#.{ :I�{%�=9e�� ��ur+�Ka)� E*�" ��M"alg(��0s�a�I A�ne5}In��a� �*3 .WI�� $p$-�`)�LaeRaw�%H6 1 DwA�$Lieb-Thirr�*-����/62)*S��6on�6e"�"vw*-�!Px9%^}-n.� , type9OaY�-R.�{ ����C da�r�)n&�j endo6 *_o�er�2�� ��E��leJT�c5E�2( Demp�=-Shaf�f�>8n��"� �i�6;2u����;�wo!�"�biSe�-5�7/�M��V���ΉFm'pxtGp�8e� �n�QE�A�%�a=�)m��Ag5"�� stag����Y#T4 ǩ�un*2�)?e�a���Y�ar�,2x�Ejh�ve��7"�0�%�a^ُ!�a2')�esa^��ZJ�>!mEFel!� Poincar\'h)8� inuum. S�[��A��ե~%�mmue|!��v��<�,!tbip �H��z."I d�6i�gel��"o matoMbl%��?-K}�)7��eCh�>n�f��� i��GM]c��n-@go+��%�$*�� �bI!�``�pD''%���!R���g�4��-.�0:�>���e"-%K&E@�A� d.# sG�y��-R�`6�Io2��(2�H, u�opi>d�%ur�D���I�O�!a �[-Ics�[�Zl�� i��-�- ���.l] �(o`&[��(��a%ex!] h�b-�3A��Z�#~aF�.�FQf�'��wav"pJ �a�L�" pq�`2a�y� I ,e'��noais lac��.%<aRi$arg�ea�den� M?A idW ofofian%cT ndy%tra oc�S��2���vi�~.@F�18"�=.�@ef!Css ��#�A �m"*!!�m�xyR� ����R�laW'ach. Wi�>i�Ove�m����0�� I� ���o���d�a}���u����:��8�"��ų51MiNcS @A%r5�� � � 9tI�.ס�a�ia�e�+z �*�N!,M!�+�e< !m��parE���� ~�Mu} �Gari�[�*%e SrDS7e"' �@d�%��{��ah*s$i"u�34a.���or aSi&|t�k;NtS (a�e�. Z��re�%C&H2�ar�$4^�a�{A/98->�) EV]+by-a&sub�ants.]n ��PN�we 2�b�M!��q�n~+MiT&rF a�Q!�}�b�9"*r��;"� celx �i*^U��sVG�$�w��cYC� ���won�T!��* ust �/��v5,�� Tv�Dx�ri�>��J� suE��"�G��ex /oM*�. fund]��r�4-vMed��<�UB�or vr[4*q1=�e�)&yͮ4���&^.Y�&c;L��vinE� !�Ea�|teg�*�9�'2y��H-9��0��6\��h5A=��Aa���|W",�Ro'&ȔsubtleC#Sq%Qitfal��6�� � � H �n@(#�YReta|� �Mss�ee1�"�oe!.:�A�p�<� ������%A:�$\rho\/a%6�I��*��!� $N$-�I '�1j s�_ ^{\o!�s N;�R .IX&� .�8!j" QI2 dn|y�;Mi��nd�%�(Z'�Exm��*�<c�-'adMY��Tof �*j  A�!� nt ("3M"x3� .$�9�v�w�$ nD� f $N8�\infty/�z�4�� )b��# "�%� ��� c5o�O�T4"� @d$ ��?xi@.eX-s���4�`a� ��-��:�"�4A��A%m"^%whe� M�dQ i>J�fas� �&e�q>J�.q�W�Gv!��vGt�k"E(a2c !� f-u8�d��KvUarriva�;;e�6������ 1�X�� &)Q�Qi 2�rA�� �dly ѯ. D�/�E��Z�0A�.�m DoppKJag�/-��efQ�Bay+;"�1t�R-�_%�Meik"CDœX >�q�"'2��$\ E� a�j-'rl5P �2un�Yb, ��a"��� rA�9�%�Amto�Se�h"\T��A�toၱf"�1�&&� �0��mJ� 4!�  ��>��T[�l2#� va`���v Vq �2qIKi6�2.F��"�` -^&!�m ��C� � m� ��%oM��;�,�(�[:�i[�fquasi-���*�H!n&�O�8no&�U�-s�+�!��.!XA�9fQ-�s*�L(@wX:3�mk2.�K �g� A�6�%�A�` �dy�ec��EE�T~AuffeC��<2�0L�91, 23�K MK3)]a.l )�6��R�.��r"����<x���3*� �ndependdi*E�"�.>�2�1A,�J�TQ��CL hG�:W�4v��nm,6u)ERB(de Broglie-Fw>G"F ����s. �*�>;�;�Ru�Q�= or E!����?A�m[�6�Ias�N���ork?A��)rU�off  . Bu�Vyti"GiJz¿c�:if��� /?pI|wv3� � �za�m8 =*� peis: AiYlSAn�s�'ut)5m�Qq)sR��ur {b��f\/�?!Dm��^�6�exW"|?�ʅ�eu1%Y�. Ekeŵ����*� *=k�O�?m ����BL�>ib�G� c(nnett-Brassֳ�2nd��aS��Q �s�-I�2�.!'>P�Qli455�ncD3A�ala2i%E��3i�F subsG+�(� htz�'�&_%f,?�)Vs�.���&EM� (�s'������_�%}) � oN� jaW � =�v^�6�Vc!A�c�:,�*c".N�9a�T1WPe� !"�n� ��2\ ly,rJ2W !�%a�� �/.rr so&926(�-nt flexs!�deng�9v@ l�P,��n�3�Rmmo�l ���e broadb���ro� reby��&Wf� &� . An+<&�cp# !�adv"y>�U�-�QtNXin�J�C�l�v� i�/��iZ)�mix!5�.Lw� yuJ!��Lg�sҟ&'i5�Y�AR� 19l�� av�a�E�!'( illu�O�F �[ "��Ap��d-loop �-�q F����i�� S!3 �D a�e�a+`�e��22 �\st&S �.v�AN=�.>�C0;&a��9aN �2R�mF �!�q ��"/up�e�i�!�\PrYSO\ ��&*0K*Ea ?��6wI<6 <� A��=.8�U�� ver 30��onYAl΋g֪BD�I�* fica%�td�*]�� w���r&&t�v�e>��6� �j �i,����t| �in� a(vm�oL. M�E\��m gɽ�� * ed.��&� I�_1e��E� �Q6�6�f��afVA�f2�/.�/o a�l��[(ng zA-�5�el, .�5�lt�.�rec!��!5*Pon"�1$� nH8�[&wg �s����s�_\ �!�E&�_�64 �O%�<�S2� o�Oth� �K��b.��\nc�Deuts� nd Hayd��lai|W�- d��uo�BP �d>ul�b ��c�Mf��)!K2-'.=.�5yw�=s*U pM��}7icuZop�s' ir!<�_o�B��# �����&!8N"D�6�b�`JH+��&e�Q~�"� A�! �� t)4W,a/AMŦ�R.\@yh beneV��W�,%{a�accru��\krr2��ready*G�on�� an E8tt.T� !�d 3��a3 �*ar� .�f�1�� |��΂(kt�ica�p6�%�&$�{*9"� eugS!�*N0:?� '�%2U s;���V�u WY Q�B��9�O�r&�"x 0. %aThe si�ze of the helium trimer is determined by diffracting a beam9�$^4$He clusters from a 100\,nm grat1 inclID21$^\circ$. Due to0bar thicknessLprojected slit width�4roughly halved@27n,g reasr�(sensitivity& �Dsize. The peak int +8es measured out6L8th order are evalua�Tvia a few-body scatter ory c t0pair distance� foun�8be $\langle r\r �=1.1\,{+}0.4/{-}0.5\,$nm in agreement with predictions fo!F e gr]8state. No evidey"La significant amount!�Efimov �s��$ir concent!�onestim% to be l)�dan 6\%.�Mutually unbiasAK asesmHa Hilbert space canDconstru%�by parti�!V`a unitary error basis. We6i!� thisD� when%�J<�a niceBR show that<number�result�mZ� �8at most one pluI�$smallest pag powe%Xtaei �dimA�on, aA#herefore�>��cannot improve upon previous approaches%* #%'by!�ablish�(a corresponI,between)!^��(abelian subAzp%�apindexE�p!=Fl?t!�bA��89p suchXA�is , also has� lica!�yUIAof cer!f@ combinatorial ob�ds c!�Dd nets.H\o yer_@given a generalisjT�|Deutsch--Jozsa algorithm which uA�(HFourier transform oUroup $G$ 0is (inl) non-A)_. Hisa�M inguishes5� func�s Q��iAD4 perfectly bal��)� turn� be tunaA�simA�by vary?z �-�coupl4strength.�T��paperEcA� BB84�b toco��random��vacy AU � is secure��8higher key rate�� n Mayers'�K -�sam�/,. Consequent1!toler� (aW��aA�i!~ edi�7.5 \%a�11 \%e��M exteqi tho� �e�of�!8t�pa~ly!� each� ��e%�s  o-ly sh��a long). \\ I6T��---�L!9�� ribu!b,%�,r�, l E�sis�!�# aph" a�m��m!-a�ful abst� o���"��z ��u!Tin somei��yte purY scheme�i�eqB lya�}s� a�alA�ource�� w-only�wcompuɶ%� focu!�ME�o���x!of� �pr)�io E7 J e*� ancill{ �zsi�H QA"� n e oper` s5du6 of6rForI/lexicog!�icn o��th��A_m�s���  upa� lG A )3s!UtyuY-�2�fir� ar� tivat�Iur ��bi��du!�u c no!2)�no)�| stud>w� en� E4 �pr!4t��6�s,��A� erizavth� $minimal de ��localAD �'e ��a�eeose an&] � ��. Oof� !�)2)�� rel Whip��HSutner $\sigma$-gam`s we �a�q2!�la-w�'D"� )YB��Y!�^*U�ed.3ymh ed.���e�y old! blem�exi�ng fr�nc!��i :al:ddres�б%$?|ver��ort a�mpa��irE_insic dcalM0ᕅ��dpr �isAx �import� R c��ic �4ces� but��helps0,disqualify s a�mmo�mu-�� m� al�- g�"2 �nciple��<\\ LAUR-04-5290�^ uX�Singap�ѽ, a�q ��>)ris fu�tom�R �fficien� an o 'g��%� robust. U�  i� �um+ �!�[cy�H$\log_2(4/3)=0.415$�~bits" �w � is 25\% m�t�:V4of $1/3=0.333$%"� dard six-��aW�set�(e benchmark�0describ' 4 e two-way�<mun� ɾ�tq s $0.4� :��/thus gvcl�sM�in��-theoreb  limi%e noiskreshold�at�4reA��$a hierarch�d$eavesdroppa�attack�mJj e-�]�Qd: A&e!�nbe� ed i r�&�38.9\% �.�,�cB^ed"}!Q�8 k ,}{��9b+}M,-�rel��Ha� aliz�ŝ�%O�*� ��is {not}m� �-�commu�O-* � algebraEAarr� ! >�Q~incorpo!�!� e knY 8techniques --- � 2�>( modelym� of deco�<nce-freNsQm�SJB{as spect��s,�P'ER�B�w}k 6|is:r l. More�%d2�-D^$���͋hey�%!� a ne��� co1or n)w):��^m.�I����wo way6manip�!�Fnt" , name� .-assisAil�6� [D. Jona���F�M. B. Plenio, Phys. Rev. Lett. {83}, 3566 (1999)]6 ple-copyBd|S. Bandyopadhyay, V. Roychowdhur�U. Sen2uXA {65}, 052315 (2002)],��equival�X&|��!=hey�Vasympto��� i�^e�ŋ's abil� to��l�  a��i3>� I a n 5 A^ o anU target M�ef�N sucA?�b � . As|cuis yie���asHIZ�"e}]con� M � `ABanZ'6�.A�f2� situ) in��� bser= ���% isol�� wan�od �total �Og�al>9(e� includes !�� 5��aQ;� �I�A�clo�� , etc...)�Syt� an d�� arbitrariA@P � ,�� hby�g�4 G�,1suyEaKN� � I]� ofA3h.[sediscu detai2d iHm�is��!(f"�.8.�a��bxte%���us��..���cte.�Nm)s� s lea�o���a�of��E��#Feynman|a�ntegral%@se Ker�-:{$, although.R�am"s �Y�A�M semi� aT two)�6� ulaNr� ��daD�Bar01}&%w��A�2�(ms sugge��by Klau�A�Skager� b 85}. Each!Ht��involve�&�g!�nI�a��6R X Hamilton�A�e :r P>2in� �AvQN%; �pn�v uctaQ hird><T 6Awh' 6� 1s dir��Wey'.zYN�, _ ��"al2*0itself.Sp�:a�� �2a A ch3ngA step!� any sb�solid- LQ�auuA ology%H� aeated:1er0i� we � �M�to �%!�[�Zd� berr�!T�*� �`endohedTt��E� �e�a mole���8magnet Fe$_{8}$Wl� I S=10��uo!a z��� SWAPM��EaY /� h�;�� th-! �-ofv -art)Ki}  Hs micro-SQUID.�A� ��I cal�)�he eigen!�N�st%"AnergyH�� �in�qatrixby��j��pri��s�a " �x xg) � ��gb!�eat�Gd6iMi�al����/J yrE�&<#"pri}�& 4iti)� $ qu� 8c anharmonic os�t� nd)*N$ouble-well*��ho�dan�a��M�F�non"��"�we add ordTe shif����wo-pa1)va9?UEt�-����,� trum,�y�1�x1a m�.J5�67}-�{ :�� ime-depe� t Schr\"o��erY~u�Z%� � ��w  �We�AN",` elop� � wo ��ini�w �Qd.�slow rol=�.�E�pic u*�Z ���o� �#opF�"� � "j� i��*� � � p�% ��  sI"^&.eN%0he HeisenbergR�"��fa'� m/us�wa�%���zmpatibT �" 9s. Ofa�� � �� 59hip&a!`m>�#'.R��maA�� �L.��su�)���M(������� /&� 5&g%`�""� ,|b!��&�0is�explores9 !�!�%+med�z�^��i�farI2�,�"&�.�"� �%<��a6E5�I� CNOT� � �d�wo$ g��, unlik�n"� (%l�J;!cr rr�()J�iep!,e new� 5�"�%) �vs���( re�,� [#g<c�͊�5v����� �!. Our13%'�ceda���fur�  nd� !H�5%\ey��9J. ll.@#a� �� s.�\no�% nt O� h"�hA,AlGaA{ disk�on�� a�k$ dot �As�( ed. D&  pk6;"p����l"^inj�I�uaembed!45 InAs/In� dots-in-a�w(DWELL)4 r%oa%�8�)-fiber( � Ta�le� 8 ($\lambda\sim1{$\mu$m)E�kred-detu ���!/ emisw�WVO2$O. MT2u$r.Gb�n< diskE=di $D=4.5\I�a��sa@( %\sup���� cold�"Q�&ors asgh$3.6{\�\s}10^5V,! -con�'!W� �a�t��a�# -� pumH room tem�ure. Pul� ld,at�=�5G!����#A��a�L  l"A�AP!��@Y &^ $%�7-QW,c�)�!�&�+�+�(Do�level�om-��inuk$A%�U�u ��ed.i��%Y'vcks neea"� c�� ish &,1ed Ram� d�&a�0age (STIRAP) "�+th��(s ($g$, $e$�� $f$)%�deg� atw(!5�u�#nn�ng��!�-p!ͩ��Rong -h)iY StokesR0e$-�&� E�&�)$ a {\em suy}9/I�po"Vremovaly�$g$�:A(�a sF�,| or mixed�bT � !��!J�should� de-$ a�#+x$ce�2�:�-��,��i��pos,E!hie{ �tA�unter)�.n��al I%a ereby FHpr�!NWe fe�de!! is� ��1r�� E�� 9s!c�f� ��6�"���W s"�$$��. �or� a�"�#'%�e�2�j/9�1ecan�$int doeJ !�S �wm6y�$t�`.�#),I�ng))mo�DumI{�,�/�� hEWeq$f$q�iu�)a� ,e $��� �hoH*�z[i�polariy\"}e�-& !SY4q� y��Um�p -�1*&5too&R��)in52�), becausE% v �%�V�x"��-e��"C"2orAqmtE%il�3�2%'��!"�ol* E[plz"j!`5��� +te)-B �+h-�ex� �S�+�"�$vels.*%a(p�  Av� d%��%!� ��a74�!-�On]��BJ�/n�@WF��zpŨ  � M/A`z0�kofFrnLse�,�0�t!ci� !�!�/A�&tlT �$)�C*f�,I"�ob e� gard MFENI� ��isM�I722ec"� fluc� Yi�a�5, � G " Ws,a� ever�faT+tu!�Hadjl6�amr*ge.��d�F=&tradeoff&�A�� "�"$C��)�$Sg#$ng�#i\he<(��(� �!toUh-$2If)�nnu&0$f:\dom\to Z$�b colo06c�)� -M�z $f$!�$1/2^d$%D3y �ed� u�,�)�����1Al�Hreceiv�+�*$l$ inpu� Bob $rA���*0e $f(x_i,y_j))H!p $l\c� r$7e� R $/I � .�$4$C=\Omega(lrd a% |Z|/S)$@3\ , $n n$--#%V�~aai��Em$F$�=sn Theta(n^3m^2 |Fo,_ rix-vec�:[�:26:��� �A$D.�E@5��$�ndQ�!C( �)n^3/S^2-fBoolean �>�L�:2b:V�, util�*p"w��d��E��"3Q,�qc"".��=6�AI�)T ]�5y��"�,"�Q��Z5O�N[�)2-Xin ksw:dirT }OEb�ans�7�t on��Be�/a).~ C(;e:օ~}.��7bos�|�3 nels�au�/ at�*e� grow��Oest, m�,�!mhop��u"op���ct���0Ay0���har���of�!p:� capaci���utud�ho��hav@ 4$Y�rif&memory�|��2,) s|3"� &� }�a5FGauss� N�� f� �+�/%Yenh�3d�'��d�2bol�eT�e steagAA�sy$:� !N6�phorc6�70\%-cg9�"� mal �&!y/:8S shot � �� b� 11\%I��3.8-dB� ligh���d�A��� �0lQo.�Iz j �� BMrisk-�3�2<,�t,EL�� _ly �to�"E�Q^hsllI�Langevin��IzB !=` �>&U � E2!X�if�"�al�R(+&*'a>�s�Sat&�""� ^'ledge2 �!� �� � . On%���one�$���F�dynamic-fil�?u�0P:��e��*ond.mAP�k feed�7"i�ig�>by2�p �a6mAR!� xJ�� * M�y�electr�"-�v-i�&� 7an� !A�1x�0�� atom.��Bell-typ�y'A�Z .A$Wigner-Yan7 skew.* QCisA�d�2��Bv�"lye�loF V��tEsit%��%�' E"a"�,�Z�/�?!p�lM�E��Cte�� p� �@b�-o!y��e6l�> �)A�� �I�qu1!b i�#Fwo-�vb{B� F�>d�J`U �@�A� 79"is��-=��ne�; �!Qa��4���1e� n�r%E�no�812:����9�.s"/y.) ���P&��d5"�|3 �he Carte�*margi� Y��/�>-�) mixt����?)2i� }t $x$- n�ynomiE3 D"�;�!f #$y~E vE�or. %U%Z&; ,��de��@%�5.�� doma&0�$Q^2+P^2F| �ur![BD��%!9!IgyA$\frac 12 ( K)$ae�% adjo��ts natuz$ �,.F\begin{k<$er} {\sc a�8} \endF��!s29� decay8:�7Ohmic�@il9aB� nonrV=fluoresc`#,M bl�5�J�1<ng�w��%orua`f"�x spheK=la%shell�& ���'�nsi�|�8�ng si�QxI�c�of5:s may�&�E{!+�.<- inneri %-%�rf�G�f'!SM�quaaW�B�ZA�ei�l&R&�xa*a�-:x�5���q�^zxi�ly tw�as � ��en<%"�& vappear�8a�B(� �P9-. S&~!� 2 b�(se�c�=era� ��avail4at http://www.c-s"-J.co�Dbe�|z��Df�,�%� (��e-!)e U �� near-infr�l�s. \v�8*{0.6cm} %TI funda�  view"� brai'ռs�2�AOtop�+�.��un�#�#"%��"�>*�A�a�so6 ;B Yang--Bax!�4  �K.�%%"�-V6 .��4 A'E`(ev:�B .��s>�;a-d 0&�insta�& in�"�vacuum��R$biref�_#` !�O"� �,,$d, stochasUy$8n�Mar�({o}!�*�(�)~m�H�!m6*�4(1�M� X%���al�(!Z disp�D,Y �ilH"����c�Lum ��gt �A!��Q0 Ane�'E���%`?�s-�R�yEK non deple�!Y �hr��"�*efs+Q� !��a��X�e�LN�!6E$ayZ���lso& ed.�W'� "�Btg!s���%�a{s t�CtF5NO!h0�!fE �,U B�=@b[L � @ �� ���-� a� .j e�Kfa���! =�OyV�!����esidu�5�K�&%nQ�F�u� n:�:e�;E�!�!" ��2��5alF,%� C $ns.�Mak!�(ex��i^�Monte� lo data��>��� %"� , ��anisot0,c!�2�J$S{=}1/2@tiX1o� >��-k�tak�-u-$4 A+pE�A�aI&�0r%e>*U:���,�w��2=Err� du�R2dis<. A�(]p)�Z� A���Rw+ a novel�K%Y%��7m!"�+al5ץ~��t( P� ��out:c<6�%-�?*^3�k"WI�'ezer$unambiguou�*�)ɱa cusp�0uj ��,wise-to-glob>d�� $RTrE�!DM� -cri��� �!�m�7�.�. A ai!�8��"_ "�O+x�in�\ a� ~%� � �behavi�F ntirA_"a/2�2 �j��?�.-��*u1��}�F� ermo�*|3Y*wiB"M��du��iN� We���.vs-Q$M=G�,i���Eb�W2�*P.�!Y�a^3Y0+ ��P� soci���R�%wo-�U�5}f7ex�aᝉF$b�to162�ɚ�of*j?.b�LuA{a6�L��e�. I�#�?%�'�� ed.�a�/[Bt5 , Kn��PV� llo,I.,-ph/0404160]%�!r25!�$N$�eLcl9 cF� nU�(ly��!�ch��\ U��3NX(QCciA|b�J&�,laser��!�ilP �)!�!3e"��%C9 �7 �� leakd�5z+yJ �@ �=�elgt)-6mcol�!�u��I�ֱ�!7ac% &.�$$\sqrt{N}$4� ��-5J��T ��C�I-!���%��prY$�}��=.�G�3�PPopescu [PRL, 83, 432"}A�Aj���V4E*�8��Jd�/��-%�dCZ/Y nti!m:l��"&� *l6ll%��<��Km�/l-`J�TpyS.)�G ��+� ��-Blo�V��y arguq{�)wa"p�M5Zn �~�� span!�NQB$wo alphabea`YA�ix= simiw.�3'-x)�#6�# xed �X�$lUX6�, ŋv� 6�ver�?5���Dnow)o. HS �6B.2�4�1 stil��E�.�&�-ŋi�li tQXva���!'iM$M� :��dE-UA�>`2Z�� s ag�!�c�9�l9^,��, �U�a�� ��mb)#��V6E ��M|N-M|�%A�fE C��%%8fin��� POVM *GM^�i3�Ua��a1"�*[M�AFGYr;� �|� :Ga�L+�6!cMg�;6 ..: n� 6o>$5%��U0.+.a(ad/�d"�-n LOCC�};6� -=5W^B"��s��^7��3lied.���p",!x&C : .�&� �6��p!nɅA��Yi��>;�4�%y %%. � :rez3�in2FofR�$. By virtu��.^,2� "� ZME�b� nveri�>Z � �r_7U�mEa� +� �M&|�2c [s%9n!:.�G[ ����� )�%G an N1-%�E�`ed.��&Sch�&e&�L�$� E),ic Thomas--F?�sM��D*f"��A=laX��Xrecour�o�L��0N1?&�>A0Ku<j5d�\@�PF TS:\��Lto%#� Q!c!�<:�5 m&�� !�n &(spiri�ourXacc�2��-��Lb�S�-<(�t�-� tens�YQ2a�A��on2c6��P�%� 1+QC6�31p:E2�,"UXIfe.[o.\~dY�%�EF"qFFk-Lt �Jpp��� �scuA2eB��0�)uJ�?�"�P� �Iurp��f�J.�],)�� evan A�u 8ed $\chi^{(2)}$Ae�j down�4rtCe"�D(Fabry-Perot� �)!�!��Zo)X!wqu#%} quee�l#Ef@ein-Podolsky-RoseUN*aj um5o.�� %��!��� be�A_�Q �;mT'Boq�+*M��m�'��/a�a�%8 �[I%S9y� u�9s��Ŧ X.\&a�A�"���5�,!Pa'3_f?Mr�Hd%�le EPReMs. Spd:;��j� � �)�"5 e�Rl�J%>A��cs ��e0�`R+B eeLe-mass�KVa�9a�2(�YGpacketMOcoi{d-  spQF!zU�icc�7  V -�D�"3(M'"�#Aico"2D6�I6�.�a��8- ;AI]* �.�2a0�HFdT?3�sb,�f�T�[�+D�Mry�f�.�)1�chQ|��'�co�Ed#�aJl!m��� ;aw wodi7-C�� �u�V!,�O Eh^2 �Panomal�!narK.�$.�]!ep5AP�tn}U�ea�V>�.Z. F*q&7'" �-r!<a�!>YZ��5t�9�We�ish�""�Znfis �$ ario�^@a��f ed.�� &� �y�;f*II� � + a*�G�\�ub�g�Tɑ�(ipPX9.7 $\pm$ 0.5 dB (89\%)���^�[���sJ��\1�c�>x$� d idW ��R�W+> expe�hn��}Po���7$�*Mhg*/br���,-e!&t�]3&�!e8tle4n&2�O�;��.(t pa��V���.�E.d�*'�롗"�:d ,� "�S?�Q�*=!��8&8A!m !Z01�s�s�C��2�9�[enough:�("�g0,"���� �'L�`if1*TV�(4#��Rm���,�m"�F��!��� ��1dɭ,��a� ma'%e"=A�ya8 fH�h8FrY�l��55!)���� �Ml%|:b��)�,$\ket{\psi(\�)}= \cos 00}+\sin 11}$ �$0< �2sim�)0{\pi}{7.8}$.�� �*7 *�!n(a Laguerre-"�2L4 m!kmpl'�-��A�assump1a���`$AB��"ai �iso� 4wai�l +V��:]m"�ZF���!�Nd"�+A0*N)re_>f�L� e�)V��:�&wiF1a�% Xm`�oEexpan� �i.�=�-u8-%� :�- &t4#imPIl

��1~!`.�WQV�2�:!4e6k?n"e$$\L!E$��l4inv47 &{pag� !-a�L-l�=Rt-B ic v`� Bose-��ens�I%� velo�U�0M>W��n4W�*3!y���= =�s�6a fairl��Wy�#$rI�o Twe� Me&�M8N�n0�A+um�R�al�$���9��Y\B5igA�:� ��.�:ivbC^2/{r^4|&�Q5G�u��:�Yb�5\�����Z)of ;ne  ;�e`Q��9qr!|``ren�DlRap flow"��E�E(��f0 ��/ �r!Yv�`'"P*�-bWcy�"�ApQ in`,� branS.YG� i=I:|Dtc��,�f��2o�to,=a$�#�1 ��le� �ly)g gy ��*Z�[Ak conn�b�'l V���v�"o�-�m-E�Vs�\�qASA:n�5ZreBA��<�. �9%�bota\�lu^6'��l\.Y(P[�V�:�&G�]��licit��ny�O*jWq��"`O&�8#�'f��QeJ.E��ex ron6� ,u� neut�#�izq.�XeI�;0�� ��e bTI7y $s$- Tax ��, ��C$_{60}-$Y� `$�LmeV�ǽ�.!�w-�t�U�u� ��� �#@($\sim 3.37$ \AA) �#e�w� 1�c� � s? ���"�mp�(Lennard-Jon��G#2��2J�a� $3$� $25$!.��7�&[a���0�s m'@� 8� =&jLlw eKHolevo"�>���3~@�@s��Z���de��in�tk)tnwo7&�$�or:�F���m_ �A��Pe�u�i-�9B�1� "�%��EG"rYnI�> e� U�w�I���"97v.q �U�*u/�?�ma~��sɣ�Ba!-i!VAjA>�-.! c r�mel} 7@� � �&_@ #� !a�is2><��4J.M.C.~Clark's�O�_�**i.Dt"�Se�!�%ӥA%�&q f�?ing �X'[%�F�E!.e�dri�Z)� 6!IpmE�oa!�white 7p"�� � �Log�2!�L}!F&�05w�z�+U\�6�Y���� A�)))��ont)�1�&E\*tN�?QHM �)/d`Lo�S�W��n"S2� �unravM~>�)�mR"V�@�.9� ��!��ga�*AK%9*N�X%=��Uof un�8�?t�do[d5+chO1-!*�~e"�T �o�Nt @�HeKO a-Uu�u� �.� ��? ��fx �& �!,J)�5#�of� put.-alm�.�QF.��Jxr�� fide�' 2�/&n/�.�>�a�i%� Z$*%1�A%J� �{e 6r.�G� .0yrdT�rua[�$� qA2r"-��2�_ �A��t�W(a1-Aaccep�YmA� +�Ke�QG� "�a���,!ori)�>ou!�etn�m� �]��2a�0n von Neumann++���(>dof� &-�H|� !>��.*j'�.l�-)�"�*�f0fuF�{TS�"FB��f�G�e� OI�.k1�VZa|r1��S%�z�c;�� 63�)s� �� �m�d !'f .'x�.qG�C�l"���Un�K;in"�t�um!���[f! �A�e task�se�q�� u�"A�`a1C� A:E!� ad#�ez!��@4&�9�0pDe�%a?�0N�),�F�R���"�N �9� " Q6�n *4!' *"WbUdoesn't�-. -2ly:���a i�MN9�o� ampl`@$�) 7&�!@olu��a�8)�run%��Jn�-0�_r[�T&{!e4yy,�KwVrR&x. 1� ��b� ($Aw%(�� ^G�$aki�� f� *3Bv�\�p]1�a�6�i�k�� orF";;iGE�>0�jIY�B��(t�_%�JN.�q���K:�J1��2t~#o1�u5VsC5��.!�n�%1�XX �Ji.�D`��' arry��ur�m�N�h �.6�c� a b�o.($L$ neighbo� �,A�>�u2� ?p.�, ��� E�"� ��`1reveaN&� K�m�XXA�e..ver^C loga��� #:.�s�� ��(Z&()0 1Bi]�i�prefac�Hmd!�wth!j&�}c��m�fr,s�L�9a$�MC#�9on-L�%m��. TI�r��%PE�� G����;^Zd&�R peak��*�!)Mf !8�'$��̍ �!F%� �V!�i!M Rayl��E 6�k;~E5.�!?{7l��!�� v� a�f<Uh`bejU��ut�� al3<��#cA ��� �UE�-[&�e�super-6��uQ!p�5-)&!��G.��>]\*�!sp/�=I�{ ^e�up‚���}st�e�e��U�h!ur� yS ?&\mt��K�O< ejo l{E�� � ga(a �����r�.wZe*A���[���9!dn!�-EabE�e"*>���#&6>wha�e�g:�e E� � sxt z�+i&Rnu billiard Xany&�<U$ Coul���`�8hydrog�W)v' � !]�}p��Aic� . Be��m�9&�Utpae�Ņal ��ny-~Y�9E6l�Y���q ) ��.���g�\-a rski�!�� sis;�Q"$ � �o� 6x��� �3�1i)u_,R��Z%�a�j2?g)�.V�)� |�&�%enc:pA��ge�?��um�g�=,Eec}8s�L�Gngahc,0��s�( V&;+m^lo�I� 6%.�8�'TC-�"a/to �iCCJbyc trap t l�p!�#��^)���ta��a]5&- w| ��r.iu3.��_8Cff��c� 1H5�1Haimr"�l!<6�^� h߄u)�* I�!9�Ue@HuM;�B�abid��ulf�yJ�� envi�� buil�#s&//�1�W*%�����.s�ce�i�13te0�e�&�b�1! =[�!�i5g& coarse-gr^ .�,&� "&8� *l} let-���.�0. L\8�M��1"�� �z�!1_Q1�)��A� e"�!0B��tsπ! kick^+��eTI���6!�M=5TQ in*��hU * �!letaz+�� =U �'� Z#��M� �S��n�i�4m� +��Z�?�ig�7U�L�!̡;# 2�B�ad!�so"5��se^ &����%�3~f�xl "m �})�%lu 3�^�Jn#er draa*ɜF&�#M�m�Y'Y?-�ceo@�%QJU_A�e.��j4X��-��� &Q��f0@��a�J�SDn� U =*� !��C Bc X����-mO<0 Zl� dH� rv�*�Bo�U .�d�\�3�W.)=y� RQ8*�gr e�Yron!� lF�Z[`J bs"� �yl bJ\�kv��0 _!��"�- �7s _Fab�*�. tel�E3ik% YS�%�Y�aq �� ..�$N$-upE6^net�%�{"z!��&�!�BP.(\B�s,&#] s!V-�(t!�&oM�� is {.��2�}Ab6zP>0!w)5 two �c ���e�c� 2G :� <on�9�-9��1}Gi'2Psha,Xree -98I�.� lin�lPN�2<2+1�.=�}�R� �* woɜQ�e�^n� �.���d&.iin�'a� forwDd��, "�@ s. %�6B"3c ba�ou�b�B%6eE,&�(e�$%�N4��4f�Nyp R�2~�Ou}H��%&aP�CaP� b"�J1E� , bi��kb.�� {�\,6IZn��`ih !ts�YcHq5 ;.P P� aZ ��F ���un6�"�e��2�a��1�)!MW!�e�^  hw_��GK8.�iM�S23� 2�Em! 239�2^�]�6"yHA�VWe�e� . %`� �Ke�J ir\'�0i�Z��.P*Z=U�w f:Y_k >�vGi�>S [�!eriod93�:s w� d$��F��N?� rŘ�)A�4&eԒ�!�m �peAa��WM2b�"���sFMlrh@l�" Xai�g & �΁Ssetup�{I�X�)��, M.Ko�( , {Int.J.�.Ch�${87},J_��}) rai�DA.�����o ��,r[�, �����ZE�k%��"�).�is ��I�i*5= �-� �&9��3fA^[a#ite�v,3cLa�Q/�e���Bi�8{Key-words}: \\ �Q���l ny-ef, s,A�L[��" A2 :�8e6�"�..�� ze%han�{)y!?5ch�* (map)��!�i��!�o dK� �NsW��]�s!5Ka�"%d�<s,�,J_e>�= �E in&���"� Me�t 2] �@AW"4� e��� �!(6.�;#1c�\tfails�id� �n unphyl(8(*�A�"ECmapA �\F_ve�x� w&j7$5�-��6қd#(�L?a�\[  es (eUx!����quh �*@/&{on��� p���wnB"� 4\�<�a@�sr�!��/ 6� ea��]A�f�Wdde�A!�law-���s (e.g�?"rT NOTE).Ki29v�1Q k�i;- a�,4�planar- ��ar��* crys�=targe�)��.Ǣu&^F�!ch(��&L<�� rase?�6��ti�6�1( �s,%�c�:�fo@&q�a%i4V� y; 3 �!&Ƀ<6}My� o�-�ai� �R �B�w%' � M�A�ex�."!�eH.�^�}�zA�>�.�I!� y�E�5s�iI!Re.�D*�_�g&?of ma��i5" f��"G !}�Q��>m���,!ropD�*>,&�)'� �aA�5�5�&$^�-% ��C�a�� beA�a75D-V�#� ��h*�:�Renyi �!{���&ic�,L7 s $\ZC,\in[0, 2]$, � iڢ�xrg�,byzkiE!F- Sja!�"��eb#%�? .� �No;F�i�"T%Q�N�A in�a"��c!oco�)�h�ZVtb g.&Z��cI�Ll�; FR�7w�)in��!�Fzv�. BB;71�y�W4%��@9b��V,n�%#�&I1z4 � ʚ�f�biBQ� i��S�2YX� 5 ed.���u��!dankea�0� E�aAE!�to���Z2F*4� �0^�% $��E�V���O:�Nm�''� �$Fing'' tQ@�A�S��.7l��%!x"��'C �Gtn�N�Q 2*e3WU �B swit�Gg| ���p�;t+K"Oa��#r�B& �$�hxpws�,34(&]j�2�Unruh��qICopp� !~�(fep-�* �BaPK� b��W�&R ��#�� a_*tee yM�A� exce�2TKof �U>!�]|�;� 5J� �����#� %��>!�� z�;A��,A�JV� �6vI�t�� )cceQ�a&& �� !O��j"�{�L�K.�P�.; 8�E�%&*�[CD.v s2E�!r� eC �F�cofV!x��ae�.m0�`a�c.�ii]�!&,!VgxZ�� a�d"� pictPI�)=�RM%[�RT"t.�GT( ��>�O aI0���cw��3��~_~mqqcs}�%9r��e�"� �:�!:re"�Df� X�a��nR�A9m2�ALN�"C��pz(e�(�c� 1'���%^�E� �s��no�!�">�5�Pauli qa�� sM-ita�be�!�m"Clifford��0p.�Pseudo-A athy!��,� !Nu ea�fqoo�fat�x'y6".�)O?o�sob�D�fea�%&�bZce]�2rw��bʆ��#my8A~]pO�p>���Ӂ�bSfpJs:f � Bob�Z�/vk�4s��� �H y mu��r%&�$� �He eEs�#yIM2�S�E��.x,B�ma�Z&�Ed��W �/�1teg!��g-� exec�,ʹ!�`~s&�Z�a  �(sw�W fulf.U&��3 A~@"\FB�.E�!O����s:�2�� �=1��,!�A�X&�r�%!.I�+e��A�UUYI!> sis)&�)!� A�����~e�p�B &��䂞�ig�)�) I�� CEi�*lj�N!�&M]at, 0st~\mbox{$3 \0 s 3$E� &�!.�!�0c��8"L'F�/5�e�� AyL��v~#,�who�J��2� $}.tX$�n�!�%��b5����"�� npC���"a 3�\aX�.whe��e�"* *!Ҍ�"p9�Ct|���+)��9��t�a6L�QQ�h �]\ n�qiff�� eft\�_ \�<0bf{C}(\rho )\T  $ =0eZk��� f $C 2$ vanemplo�.� fero=�"1��m�j����d�� � = . NonYWn �ki��lso� �� ��i�EoHb�5&;A� �� KO&2 s.�3R�l�ezM r?}al�B %rvh-BoltzF?*& (BBE)�EA���z�5�m[$��Q]-� ;^�� %w~ �uX1���l�io*� (��t)% /�Y8ll.�ZA,�ur\�gas (�M�J�I� a� ��� T0�*�|e�(lE ØI�e�s >pit�L!A�5� �" "g��;_E�i5se�rmaq#pe�- � 0e BBE�"re�?Gd��� l mT=5�� �:k-���Up�f��u#d!�$n$�vn�� c=6to>�:!��M@�h^�UNBEP #�--�-��0q�A�E�d9��f guarante0h� %��/=�ky=�E�-�i,oK-� B֮" s���e�,�W(1c���.X More�, ae�]�d&��m!��$$<d`e�� ﵂)%rc�f�5�#hes!j+�]9�ce.M2��)��&B� �G�� "�+� ѭ.3-�� i!)o�(}%�z �at[�L&o1,;vas ShodCfac��J-1X�A�.Mbe�ȁ[�x` �Fir!s� ��jMv&�t���yXm� �e�dӫ ood:A_�pm/"�1�I�&�;� %x��(sr7�Ns�"�- 5�run 1��eute�)S!5"]e�v=�*m��)b�Sofa��b�1�� �l�!k.��.O/b�Z� DR� e�.&�!� A���of6��wo�-  s ()()!ga^xM�" ^IDA��q*UC�of��)�?ea"�� hA�H<%�.3�&�^*I5 nois�-e"��I p����{���� ��B5� l"ne�v�)�p#�^ac��1!�i�0� �rɲQ�d.� ��!�1 p׫�(ɀ�(y�-umM}Ap�c#�e�"G�1c� R�sa!�5world� ���4e. �i�� is I"�X�;EkY�`&�q# �?�$be jettisoAAm'l�[odern �"Is �A."un�Shed�9d I�&1�ool:? ��;-dx?!"�qel8���Q�$a�%�.��a+Whesis, IYackTq�!I�e�#a9I; �!��6mblB"�*�fbtism� �8E�>�*!�B�֙-A;?�_LB>r'T�'lD A��-a%ly�-M��B.ar�0&¹!�&*"- e---$i�i�+"�&�[�ngZteű�k�4��� ---EO�%w" $\O��\�$( n^{1/5}\� ) $\i�� �yl�z�!��yم;."noR:#%� %LC/nA�o�����v�/\!quotedbl� bl��box2�\U=�0o break crypt�p�� hash"8�)%�%4Gy�Isomorph�DMa�p&8���Iw A�� *�w�� oracl�2���cE��� ~$)sf{NP}$�5��s��:�,}+) �e�{onv>2(%Cq*advic� tes2'%O�D%�B6 7W .Z 2^{n/4}/n]\A�.h�� n� �'�G-�5��G��n$2> hypercube!}Surpri� l{#e�p�)�"�new���q A�I%X!bat� zor����b��o��!>IuM�"<*, �)�go9�K�wg�=�N�&I 1P��h��� ��.Eif�l,& .k,���af � �M��� nE��|�1Gr 72��2 yZ��6&vspeed�`!5rNEa�0ba6 \ Ref �3�aim� B �ff���a1s����y\.8�*�1ypA��e[e')*e�Igo��bey�MBR!�I�� s�3 U"aa�'we7�I;�i%��}PP(�!lP�� A�-��N{ !?���K���sfV\!pId� �se��O��5 haD��_�n�k�--- ]�` A��a e ire histo�,a h30��� A���b]rN-.�"iB���s� 6o. \a �KIt�.��W�w��A?%��"�=��-�^Ls l#:do���Oi-"A�{\em Zi� bewegung}T��ea�l{6�qo)�2� 6W&�+> �'A gv.�(46��H e� 7 s�s���%�&#!Q tuo) r,E�1q".A%\"ܰ�.&',s: 03.65.Sq; 30�. 11.10.Ef; 30.Cp %03 +p Sp��1gtyE Se.Ͻ��a�Z7%cjp`�nd .8&"�. �Lo�BzQPoinca�8inE� nce�>�x�9�e!OnlR#�#�J/A X,i!�-b%f�� "^CIA-;��jroid-i�s $B\"{u}ttik7n nd L'u�im%LA0r.7�y (�!�I|&BohQ�>dN=ɝf� �.z (Olkhovsk�d�Q ami)2?dd msN�&,�N�AbTh�Xw���a"�.�9Q�=\!``4&" (&�xsg �k),i�i�u�J:qV��ae�Sp:lu�KlP#-v&�0(``Hart��iU")�At&��an^�endixyR�bird-eye���lp�*sr�Ž �  6��[s�Ʃr.��isc*zWI�0r%G�&ϗ1l�K��#=� QND)��s�����&N,f�L ,ɐt ��$�p�to?%ny:8�"�v���u"|�a��r�a�QND2��2�led-�6%=�����&�P�b�ĉ% he .m,�P�&-��.us~$q$-d�K��"�]�8�I�le!�aτG5�EH ,=�*QRd.eRha�;eXH7=@e*B2P�6�9�v6Bm�po�s] a"�<;�Q[�Hd���!��d��) |Q�Kk\ -t d 64�"R�co*�>�`N9 a ``k0umďlihood''>�m�Pg�_S� GHZ\���E�3�[]�� |A�23w��,�� �! �� XyoTM�!M���'��_tWK8ed.3Equilibr0�%�E�1l-�od i��$�{U2r`A�sY��h9Z?!(I�.�. z��u� �\Lo�*���vd�8� -����/e3�ly�v`31{U ablat2���r2_ aX /hi���v2�t�&0s��Q6�E�m v����Y�Z.�a!R�Y��!��b��ll � v+�gr�0Yx3�d1�JE� survA!V��9+n Q-"� *�'�$�&����nd)�isY 6 *�V�����{0.8cm}N� Ud,� 67Hk��.30FksQp KeyN@:)1%���,B\\ \hD"{1.9cm}ݩAA��d�UMn2M�� woz0f�s�݂lI�ch!��!HF�!�lr�3Ci�P ��% \J ��*f1e�r�`�eV�"�.�� JI@%�P�~a�s�]�0 long�m"m� ,HZ*�reeixbw{� g�E]0 �1�L� v0�3!ka5  �m^�a 3!e�uFmiss�g7+��& c&0#�Y�a5"�n�l�r!�& %��M � �1~���. Iqnr.\newA$ {{:� 5.45.-ae/75.Lm} }+� !ȭ��=.�La�!ku�����8<e�t�4Nt*�-*{:)�g auth�H$Milburn, A�}, Penros� my�C(�>&�5"��!�M�U!��#r�I ə �d!�Al>��Q o�)�Oa�-]���N3%�&�. �f'on,  @� .��gy->{ ��[n�#��AO�} W e. G��ma� �%��"�m(!3 AG�p�% favo*�):S�� ��(is us�E����"62`�KZ9riU��,]Dmi��or�*� *� �h!��25>�ol� �BwJ � r.�62$N$� )�(��perV�A7i"�c�/| �wAJya�-8h good���=�d"�I�Ehe6(r��� * lTrg�>�'( �)�Y�(�4vO������ �)5m�C�Ѥ �[- �Nnamo�o>"36B&^�In"�I�9�!@AvT:g�f ��5 p])��1�woZM�� \f"�� �Z�V�C��er � b precV/YQ�e�� ���\ �ss�C���A!ıo<%�im���wa}c6�b�a<�{�"����<�*� *�B�*V��}R��iaX �#�~��de;\�<���u!�%�� �� � )��)\�&E�![s�Iw � du�"�1!{aAc���5�Infe��!wr>0� .WTH�*bl� uS��a�&)u�r;ů�W!� $-{NOT} ({C ).�%WeX1q��~M�a �Ea� of %Sanov*+�ft�%v�[�#-1!��(=!_ em: %T��*"*!! ���eembt_�n sWi.i.d.� шa:]�ep���the����rz = De�%�(W.�"G��A@��X5C���(!rpy� �wec�Fw ;@r���ogousli&�� @>�a�12��r r&-#2HAqg�)#.2'?]��"�^ObQV>2Q6b -�A�e)-B|62)sSH=�wh&^P�N9 hAu: q8��n���� F) �8�2����iE� �Me C��&r)AN=��4=<g��$I2I9�%,O%A��ve:�� *'f���u�� �>�$\Psi$A��z�� � F�22s� !s6?��@ )P=��49� "z<-L!m�a),*�>��Q�ai�hA�nv0�?* +2�m:��:� 8;��aW�Q mu>��66�)�O!�*�C 7�_ms� � 1��+� � �l�� �7�1?%,'e\K��ѭ�9&t*ixe{��k.5��w v�M* ^y� ����C �0U: ��91� ex�� ;$�5a� �%2�1� |1����%WE�J � v+2%5y aid#� lv<��� �� puzz�Q��o:>.}A1 �""�PB+ulG*%K"�-)�xtVY9�?" �%�� [ <7 .��ZF)�A�?i�/Qt. Also�bF�!P-�9A"n���DF"y�c|btKa�n�-re�($���RQ/&U>%�r2 "���t)�ed.�.��!uy tatu�"��1�sf�UM��%� # ` ^ he�\F��� nclear: CԚ��5e+U&i� UcHoE�e$ �2ze&� %�sI0EoP9�J$5�ll� *� �"�.--�=R�*I`�+J� �a��h�(�N(s)I["?4!s c�cE�DaA�� Z�!z�/A&�6!f�/�?�@"R..��ހw�2owU.ay$aq��w!p�+eizH�L&�l�: :�]-7,�#)W"��K�%}W4h�g`R(ve Lyapunov!'�"��Z9ru]<a�".-M�EPR�_ adox"�!debo7� ��)rqn&�?�1�e�E!/!R�e|i*If2A�Q)�gapq�;34\�"&PQbridg�If�no�Dy&��r&�8p.��!�ex�����my.� w��O*S"*���k�K�����lՏ��c.�A����"�)�klu�+\�%8how that such v�Xerification can be provided simply by testing two-channel polarizing beam-splitters for p Yd-dependent loss and distorwh.The attractive CasimirJce png on a micrometer-sphere sus^d i!xical dip, close to the wall, is~Dcussed. This setupxin principle directly accessiblJ$experiment>e re�e(substrate assumed�$be made of (ame perf dconduc%fLmaterial.�BipartiODnd global entangle� gnalyzed!2^ ground st�(of a system 0$N$ spin 1/2 ^ cles inte%�4ng via a colle)�0- coupl$$described A"�he Lipkin-Meshkov-Glick (LMG) Hamiltonian. Under certaiPndiA +��P 崡RouteIfasA��A9 di��W� p�cre�ul2 old����molecu����ato�c,Bose-Einstei�wensG by adiaba�����5 n op�7l Feshbach resonance. We envi�$a scheme w� AILVnsa�!fm�y also f!� ency�,linearly ram�A�2IsOur�LEh��4$^{87}$Rb show�S�p ly tight ��sJp avoid spoY e�e�!�l��qe5+ ity,�conver%e��cieeupa950\% �> �.B� .e -shaE�prA ��-�in��pin� � � tudied!w�e�5!:ch(ivpure,!nsle1$-invariant 4��;trix-pro� D 0ure~\cite{mat}E��A *� 6��;�sAlmeaa� � i��ly corre$Bu FNW}�0s���recursiv >&� bye� uxiliar�SI�m� $\rho$�9��sebra $� cal{B}$%� mpletn posi� map ,bb{E}:7 A}\otimesB}\to$,!�re @lA}$!�!�!� $2\D 2$�al�. Gener��� u result�TDU5IA0v efore obA�� explicit6\ in ()�):~sE L ular, w!�udy not��.� A� oa�Hest-neighbours, but�$, differena�� previa�works I�Woo2}� Rfetw�� connep reg�2Iy%`iHAY is rk �� e ap!e-s!� illu� R d�i h curr��${\�TC}=\frac{1}{\sqrt{2}}$ �Coff}��B(ofN:��> actu�Hb��T .gQ �� �h��(fault-tolera�Ѹ� � r�� (QEC)� thre` $bit bit-flkd�five-�a c�� . To&  �f��noiseE,![yav odel& a gI�i� 9D*?m4!6� -��ron �n�} �takeno� ount�c!stochas��flu!a%5 termh.�M3� �en� s us��inv3C �5a[1�5�: li�deviceA  andѪtrong� ump!�s�fasU�$llelism9 weak� rage)� s. N!�%�shold�n![QEC%کhc6� ad �m~%�:imprecJoj?measur�s,.Xbath,>�repet�Jtocols�k f2��I�!-�Eo)�A�� valu �����>� emphasiI dbmV ! mT&� :\%6 �A"����U ins�A\�JDproq!� welluseful��orm��e� �A���JS �5��& �3 \ofY�\ .�� � R6 0%<��Xi�!�TY le-E�two�Cq �+s��}�s availac!���: ����(in94-Zing�"0 6�on�����beC R�!�a stee� bleIyBloch ��a, e�pr 3 ^ �� tran~h , tetrahedrona: reseQg allElo��B valŢ� 9��(AN Weyl:�)%/uK�,approach>�sev�"m exa4 )�Ug��QN}e:9SkmB�be guid� E�[realirAl>$I� {� s.dI�YHQ8 deco� �of F\"or� � t �gy-�~utwoe�c%��v�'� -�2@a�boson�R!� llow�!ls �i�ve �-,A ɶof� .x�~ei*�^s��aEne�v( > �tM�oscil: ��excit�f�(he chromoph�. 24tes�%ou��� sh�uo��� Flou4t Rqt Ene!nTe er (FRET)"Dtroscopy. Although� focu���Apro -pig2Alexa �;�"relev8 to)yum dot� d organic:q di�(edium.�I��awe)�Rd � !w�$Kolmogorov�@�� �sr� e�Ap2�theor� aK�a�Tst��AmM+"A.<nee. uni� �to�}5Qa� Vtself�?d� -v�qt�cm*%�i4p%.:D n (azct)2!�cedur{A�.RprM�E�a%�$n fidelity� argu*a�r ��satisf�!� intu idea!��i�%f``��� icult''�to��aatq9 ��%O �to��*t n�&�%{s.�mexten� exa solv�D��-�b�$f$5ȑ.ors� ide� rec� ����ue�a|A_�llaborat�C7 "�f 8-day technology��re=j�D rebyO!= 1�%�!$$O(3)$ non sigma % A�)�a��c D ensed-matR)�A"� 4ly�Ung� fiel���erv�A� impor�� toy �%4�� -�(QCD)� �t. � cru�!���QCD.+%�seemin�paradox�hA� know��!�diRi�outcom� f �� �_�v�.'�!a�post-s� ed�)�s. Despi�!ppeary izse�do�dem�s!�!A� iIIZnon�ex� hidde�ri�`1�si!Dx xplane�2� �-Q#urb���P ,. Nonetheles e��&$� m 6hg`Ep2( 5)y�a�!�0S1�d�698o10nonorthogonalA�� n��proof!?9:i� �# ���bQnyA��=3�vol��iMJBo --� �io�]0m� alter!�ve$7$�R�--kR52�at ae�!Z�/F/2r�$�"A� !��m��� !�\A�(quotedbllef&�N*��-�es2;rH,�r! trik!��mbleD oof�A�DBell-Kochen-Specke.% orem� sugg�� the��6�2�� ݗ�/v appa��il?"y,Y g.0RoccurA��*ies9 v�'2�a�� �&�$�v �h6�$s.�\noi�'\ Y!l�i*� >�� slit*� u!!p"e'�����%.\ #w��< PACS: 03.65.Ud; \7.Mn; 32.80.-t; 42.50.-p6(Keywords: \rj, cav�QED.� ��  �E%E�[%xulde�aE� rvoi%�j�in8 wa "�er��Fe��.� radi��pul�"~ b��I<'!�obvA�VJkppa#4 s. AaZtwa�&>�rm da��on� ��has zer"+'� %�iu "( po��rap Ka o� �s(non--vanish�"�' ^BZup*^ p� �y\����)a�f�ed*!Oi}"�er� =�, aL!NM!��*>)�!%�A�a ��t high�5#%c� '�� (�m? }^ s.4}� An @!�$m�Pi)cherr\terpreN *���!r h�"�g��7Ne &8(recog�2fundae��oreT"f���3v!�&"�A@�I� t*g�"E��u fuzziness�liCl�)vN�;j�; YZ�;�5,)�;e ^��Aber ��Ta�<5.-w; 01.70.+w % PhilosophEEs+ce!�-w �!��%] F�'AOn%�q,;.A!��,\setlength{\�Y 0skip}{14pt}��&�U�-"1 is ��.}AR ��nsf /J.E thro�N%Y$nt data buT$�u"^�#1 aTrehvee���u�Z��a �!Gto�0l�$���"��A� �5 h1*��s ]z.��2ag~�&$ "� by u� 5 �%Uq�ma/*es�/ice�&�0:ladder Aara 6&�� 1�%. 8)�s� z��MEs>�2��� lems~/i cT�!!=.5 Z?in[)%<-.nA�U!Fle photo1ur`�(re�s��A�ar�5{A>?�+sB(�@k� ��ibuA5$ b on y$AA��2{( ���� �cha�$i Rs�,��ai4$� ��#t��, �' 0sir(�v� of h�6� u��uc -�&�saWA ��W ighe."%}4w1)�#to�.in�.ucym��"a�6�� g� gr� �5�"i,I � ;� �lO P&nda�*�� �meeu�abo�0X.e�s.X":�of��=z0-"�c{o}Ae�,t�<>d6�(P� �C?#^ nanom!!` ��-�Co��/, box (SCPB),E=�wbeA�lz| Ama� u��#AZ�2J).�6�[�be.%�,��ag�),2.Fa�hybri&]i��l� &�,�5�(i�f�0� rap �(� Nae7b�a�p-�pa�K2_:B���[&Q* s�6Uu�7Qm�Q�ŽR��2�*�*Z facing})�N+!j*�"~7E cala��---I\ m,y�'�M_E&�$ on -1! S du9l-:"8)�ne2a 9�6dy3 �VE� G0� ���W)M3f!oap�I�*��c �I(� ��2��8 *�),:�'W�so�I�*>� swit%" i^sere�$"#q1 m �"�$tu�%�A�.F0*%f�*�: tog� w�("�%<!J�?� ta�i[&� �� ]. \ 0{ {85.25.-j}{>�* s} \�{�}{� Optic  7.Lx �'%�} }kI-�%RA�"��1�s� e�q� Rer,7!�^e qItoJ��F�\= o*y.�. \ I�vs G��coinci�5%�aD��l�# ,�+d/0sf{PPD0or 6% 8Polynomial-TimeO U�F)��*, I���� A�ng�7=axiom%c1@ѭs w�%let�,sN6�- �t��(s.�!�= ����eas�rollar��el�1aZp)(f Beigel, R�olCSpielma!�a�9� -:\a�>d�j��s�,�*�!*�.E�Ane���Fortnowe�� �">0��at5M!"u�(e k"a.)�rA=��8)1s�utIU4� .*1�k�I39�_=�x�4Y�ion.�z(�"�&��=ic*� D�)&�  � n un�s #Di>)�%d anc�(�#Z&i fixU D-�@nt am�/of��{ex�"g��@d� %3�a��Z6&-be�6@3ly��e � 1� M�<ng $d$�., ��e�optim���&� a $d^2$-d�@s6al1A�&�6zz;i.Paq*� 1KL "�)%�� of widw*�a; (��- A��!�?�d ]85clonerS YWQ<r� .�"� �?� Y� -NOT7.D*�e�U�obe�;�poa$ng%�� X� �%�@e�&�&���- :�ut"{% issu�&nri &concepA�"< l�$ago by Gre�!�A�motiv)�Ag�9�a��establis�>Eq-d6�.M6�yb&�;U�fA�-x1t�@(anyons):/�@;D�{:��FermiS, i.e.,��!���� s�Y��U�� �T6 �D ͿBT--�&�S�o Ss, O5�� uniqg�,AX}7aDB-%�rmo�is6JemploEZ�q-� usn�> Jack�-dJ&a�7F j.!1��9&�8rE �#� &]A) �%n��b�B ̉�:o!i,!>exa .Q2��� E��de)�t�/ur-wa/ixaT�� d sIy 4-�3�.�!�g��$ ��A6L� !vT�>�<� Ɂ�ta�;lyMKt'niodic"t(mod�% � g=�ic�� 1 od�&l�2hal�"!��|�1d�-&=����% . DuŘE 3�%E`�:�, �4e-mat`@g20 pump%�scb��%6+a*�/�;sE0v�^�--�1x�� ,U?&�dB�1�``..�''4 �durA#Fc:e ��Gv>}�"]��3.�15 �,) �!mof-of-p"� �=�GM;� i0$%O�aQ � ld CQ, EtD9infra-!s%� ��"�blue l�".{m ���f��`a� nois�%,sol�1A�l�71�)"� ; --sol��!q&v(V9*,��uL e back >pagɇ�o� i*d� Nandard"*a $sech$�>�?Q|� V6��@ier%� reveai��double-hA�2;�get m�squeezJ!@� !�s6 enhanc s� *��)Vm�"�"#��� o�� onar�!s�;�-prD}&��of-]p-or�)�e=gs4�S"�) �� &�Q%.# m% � 2 6�2�%�-� ;�07 �Dm';Cink2qa���4AU�,'s�1�_!�Lo"%zaca�@ce:�"9)le vi� &3l��'short� !��F�2"�)!`Y�eW�*�3�y.7) �2)� X, VAaB�"z�;!Q|)�.��[! � r��l��:�/) �P�&k ""���tg$e best pla�3o look� e-&zof� Q9 ��n neuo�ID cosm] y._D-iA�at�5�%��0�J� � .al�<py�GuLKa$� 9al-Yp�D�r�is (PPT-)EaM��qu[ d A}�R7��$. Firstly,%1so�Mt�:�=��+l~ ! l~9�r���c�0ni�  (LOCC�A .v()�(�,!Y*�ia surpri%Dy�!��7a�ba%)Q6. Furṁ��c�(fIh�Dti A�rbitrt %�pM�5sRg�v�4�� a drx?�&�Pm5)""�P{ b"��,)=N�s  Inde�&A�i�&i�C�.typT.=-�!a�6�a�r^n �K>'@-_a�{�>�j%�clear~if� qG?inH? powZNff�.�� �;of\�L2��&�?w�E en�CFHto!�rQ�"gan�'�of�L2s,6.un"�R,a�.+f �:+x , v(mpae Y U)!Em�� $�)itu)L emer�Msmi"B���b hHe[��j�%�be�*�LNd�Cd�Hremai_Dm��� r).-.�B*�9"=i:IsRp�ijny��um&"� E�e�clu R��9%i�2d�>�kM�zAkp"p4#%�memor�st�&�Ks���Xent� role  "�� S� si�5 ���qe "film"� vi�'ize"n�0��"�2A^� �ae�aa5rA�q; .~<tr&^2;:� "�("�(5�a��1>�ofyd )"y!laws.&7E,�'If*;!���*�2.���'�� ex.�6���+inm.k��%`e -@ rLJ�mp �s ��˩��aw] al�Z� s=� unif�C� I��5�E�isE"dN&)�� unit��,!�.�d�SA`WQA�=2�(P -*:�:zn�E�V�DE~�]�"��pac�F� ffec%?allI6@/VM�RadmTh9* "�$ref-�/1ca�(orbidiJ�Me]!�q �� {P--1�Qs�oU0�:&nAa&p#� lism.}�� f(�B"Nse �:�1(KS) q!�s ($n$&H� &m;!5��T^�9%Da�'�aO�"/e�Q n�,���a�>'E: (MMP diagram��,"� &�4i� KS �,A~�Oix.XM\mObB ona� �8<� ��"�M6��0�� ei� �IV>EcCn-EiD!bo2R=�!�ow {0-1}�ra��5AQ��2k7!�T. New�;�<�5�~ helpJD!�9�X��)|!(-fi�W�$.Oor9�a r�&#config�Ub\ �:�1HQto!� O��6m &2Qge�Zl,(B�/)( ac�$�ZTtrip a�!{�� rupt�y $\pi8V\ DO6�rE5si3-�9�E��newidt"�17inp�U*h �W.l8�Jl�cu"�g�ca��d)�ym�C�!��AR!�E�l2�s.�%&"� fr��l�6!aF�Vu3z!�1�B uE3AU�� (&�Yi�)�m�Y2+ !� ll's)RM�ai1� �8A��(r).� e rv: &Ext4 irroEC!� �otW iw)"al judgש�T���r7�.�a �p�'p�xup��%�d�T2�r\� �)� $\Lambda$6�Vbang-�V tech���X^ ��&|#:"�sUp��pro�R �/?-ic�$.�Ttwinborn;�$`#I�ErolY�. More�3%0�!59 !7�E�A{�-l &� !�B: �$2�"4#�$��.�F:j��.a�2�J��� ����%�-'K�eco�"A~�cov)� ou��[in [Phys� v5&D{60}, 2764 (1999)]�m�E!� "C ��@�n.�G� �=��al� \!:�A�ny&y|U�,M�% satz1Zic�N:W;&B}N2K ��U���� A erpoɺ�Oa�,v9�ly�in� $d=2$��5a �� uppo'yc c3e�:W$d=7$ iZ��8n�$t�>�5� 2$, albeitE��B�Gk ��45+-!%rek0�M M�.n�"5�g. 2�!^6M��/."rVFourier:�j�A��� {3�P� ' Q&�cE�p> l`5-BB�E�I��Z i(�Z"" Dick�i of n��.tuV1%.�9J+�leaky O/suI!� L)I^e"� �{�1 y+ ��:quasi-X N* , so$ *&)p�/ic~" �FB �V!y!�l&@D �h<�t6�)Ia�d�%qjl&�� 6 A�a�;�5er�6env"Uo�4 Brow�c �0�l��a(�an Omhic2>�ف#�,�Bo+.!nd�%�m�\� .\bF671co�si evalu3!�.�f6a�u�!�n�� #�]$lZ\�! n up�67�,8a*�D� Ѣ�-i� .= JF�`no-c�d ing'DCnt�3i�` rmfu&E legi�%t^#�PBennett-Brassard 1984�>�2:I }b]:2ck7 � �� uti 0 !7smfway�5�n71(Trojan-pony ŵ1��1�8X,sF�N4es-3s�3,X4 �NsX�d �� �aA%�� �*- Jfe�oV �bg+ oval� �eU-".8�7~@$7.Dd} Rh6�@ase��/fu&��. QE� U�5\J��=>i"J6> 5s,���1�ae(On ;F�n4 NS-�j'� � e-` @I shifR� �=, f<w%�v�Oa�*ri�Pu��a�upQ��� !�"�of�s�"]'+h�4�n��@&�(��r�H#s�F $0.25$. SndlV;�)DAH�� � �U+&BF.� ��� &[7�ewj5%�o���A�su)39'��� ��D� *���6F� S '!out�A s.�/al�N�@� � �( � A8M7�HrM$�UeE�z3e���3ur@ #)G E2/ "a. P � � �$�k�Me�modx�K%auE�E� � ?@� O�IkicVd-gap�!�O{&i�"2%�� q�!?,g fU��[�#�!mean-�+t�m�M�sK �bt"!"-)M-� *;of.w$sub-Poisso: �-mP'�)De! �,nflvPM�Pmis�&AI&h �!a�nfuK b!mpe0 f,��Aui�*:ic�d �a�>� W&��Q o-L%B � (�?�Sal)�E�&�_A �9� 8Qa0-spf"# belieW _ "-B$ E�$�E `Q:��exZm�.�!�>1 . By�Z S� �e�#W. /w �� � ��� �i�X5T�&remot)�? (Alic�Qb ��Claire)�?at� mm� �&, srT*���m �rMm>��]ha�7�'*n�2e [>� 6)V+ f��, )�*x #beZO agre��!���&� r�%!K��=�9� � .xe |E1� �F%�&^, ��k< a�[prO�j9� pro%��T��N�"U3 ny2��u(?&^N.E �� mvex���lff"R*! shI��,����\tA"mon���d";8�{#�"G : 1)i&gc�! U9a�D, 2/�%]!ng ,tA�*��$ 3)� mixtuhlO es�� q&P flag� "�ViO'�,�a�]g�)� �a!x2�#�~AV2igu�%�!��eEp%!�I%i�E/Iin� �D�hYL&( @A@5$xity.PH$� M0@a�d"4arp"�DAnd yeJnsS �ITQex2<.x R�1poo���|or@ o far. Af�brief�Z!&�>�~!9S�2O3 PostW.e, I wi�a&SZ�p.� a�X!*N�a��!�f7!�+ !�1.�� �� u��;�/p�5a�$� iEu�� o!J�D&Yzq�E! *�12�)�.�FE B !�� w�I� Q`�dis�(�s'�S"�� ou"����Ay#K�" !quAs�a b"�&y:B��s-�@� %cR��Esb(|� � m. At lase�'int� i�0 -] ''�m�e ely-s�m''�m� .]OC s�Mn,oFUd $7.Hk. %2>F7mm \!P On&Bf �xt�`l��v ab��ut�%d�rop!�A�14g��y%���impacjjn�!��%!�.UTe=Te�.o��fi8� ellig++�d�U�+.5G�� aou9!in�$ ntly>�e��� . Howf ,q&s. mC�Ki�i"�W�r_6e�s�Cz ��'0�#{Q&}��i��W K%0iu&��� ��e7A"�gin� " Mach-Zeh+� fer��aTe7r�� �M�r>���woBe,. ways:1!!�.�'�biref��l�"; z�����Q#4g�% Aw� Ytr�AaO87mmDa� D�:)�� r)rfree-sLKa1"OEB� |�Cs u�isy��tmo�z�13km. �Ρ��d0��\ej�Ws�(F,v� a��a>�-d ��ve paA{"�.E J�[ A��[ nfir(by�!��#�7@� 2�/I.\Hof $2.45 \pm 0.09$.���F��oa�oiI��)�Fe&�*� �I��e.x- e BB*�crypt��KN�:�ja o&u<jpXuch�SA�her4�x�Vm� jbeyon!tuZ!�thick�PI� aerM, h����-l&Y!�R�rwards�b��te-� "m|��� ion.O7L�-:�E�!fE�z E �h3\'f exhib����y&�'!?� roi�I �v.�Bnu%-� .1H�*� ��Oec^�UO-p6N.F*tdy�z� �lew!�y4s� ��wY+2�"wario�a!�2�-� Ea7�&C1 pack ��f�eat$aer+b �a:y"��%�vvib)|Q �4at!mn�. s op�jtra� #9lkie}s�&�Rr�p{V� amiWyF��witA���urY$/ �j:ap�F$�r>�sI�o�"!*e $bl�#As�A.n'!D�.�!8 a $3�s3$],�� [P�� rodecki, � ,~Lett.~A {23�r333� 7)]������SrI!a 9)$d |dZ|E�i�"�W�(2��:�I�*�BB�2*-�d*zK�e/1S! b� �- eVya Hantia�8r�b"k�u�r�\pacsSFF� 5.Ta}bP#y< ��� sorp!��LB� b" 2:]�-�El�9j e54�Zqu�ons: (i)� �F2� s��� m �Q-�CaR�B?E-(i6j��> robust"n ] a5 ?�A�� � �6�8Y answ9,KF^ � �>a�qui�' $��?���O$�@T�A!��B 1ԐCA�DQT�Ea�Q�Gy�H!�4I%��I���J+�ԒK/��L3�T�M7ᔓN;�ԓO?�PCU�QG!��RK1ՔSOA�TSQU�UWa��Vl�UW^}VXb�EVYf��VZj��V[n�W\r�EW]v݅W^z��W_~�X`� FXa��Xb�-�Xc�=Yd�MFYeXvY�e��f�u�g���h��V�i����j��֚k���l��V�m�ᖛn��֛o��p�W�q�!��rS�1לs<]t���t�Ug�u�e��v�u��w��'�x�g�y襧�z��^�_� _�G_}�݇_~���_��`�0 �x`&��� Р�B��LHa�^�d��v�� �(�$�h�(��b+�@�.�c��8#�5�x#�9�#�=��@)�Di�H&��H.�d�N> e�RNIe�V^�e�Zn�e�^~ fa�9&�e�y&�i��&�m�fo�gr�Ig�vމg�z��g}��'�� :(��z(��*���6�裐F*餔Vj饘f�馜v�駠�*j��Z����������j�� k�*무�j뭸�뮼Ы�����[���"�d��.�l��> m��NKm��^�md����v�������[��碛����.����L� Ƃhmath0412439.texclay <koszulpointsdrobust_detect_lin_conf perim d general_parametrizatio12�45766F7 basic�entire�introducn@non-recurrenc* �reprint&0schwarzia8"standard"ymboldef|!2 deep2�51F22vas>!2geo036?F5F5%�rank2roo)�6K%�k qtfi��4eriodic-ultimoB�6�UP!finvla%,2b64!6�APDynpaperfinalversio�6/8B mBDFDSIPSt2_3DWR2  3CUS�2 Ad2BIB5DEF!. 3 FLAT6#HYViINTRO$ 6$LAMINATIONqA# O �1% B%BE1B%(A�netcs�B$�B�\�LECRMTV_%�B;R��h>,�kB�B%�@Stoiciu_dec_2��MassRe+ B=�xB�S0acknowledgeme�  ,bibliography!�A^@computing-the-are��� oun error-blo-�$estima.8a�formul hgAlkoc A�easursan.],�resul� ��brauerme� QED,�dissertX �8electromagnetis�'��p�%9quant� A�topolog%Ah� R-3%�>��]B%��convergoB%Rh�`�vortxR��^>P4Ev!-ldlq!Pap���PhysD!kb%BA�BEdB�� DNarrowEscapeII-Novi�AP6I-11-V���>e��BR���B,�!Nbaker�A�defR�&9 E !FxV%[>]/ BE(A�$Uint+dP_pVH� newtE B6Rf6�>,7�XOp�,PriceCoupled Tim��B9R�� B,�BR|� B,%|BR�7R�� >B� BR�8R�8R�8�3BX�� (gradienthkF�!ԡN,StochasticMMRY9%�>]� BR�9�� � wav�I��caloger��BMR�� B,%�clow-ord�;�SPJL�F nlinA0� A�DSI-dou0 ��xSKKF5%P�� nls-� rva%M6\E'$lin-ibvp9- p' rec_nhip_3 �dts_revise��< tE�8�56%)6�6%#6�2-�5(manuscript-�yi��6.%��(chebyshev.v!zSQG!E!gKLBremar� D eishtadt3���E-2�arxivE!F!��m1 a!:,Abefedbillia&�%�E�8l1�3%*�^othI#�Tteɮ mfraiAMPBMT05p��9B\L �pra04� R carr��gorski=`%Y_au�� PRL_�_�'�,Hirota_Simon%^<mismatch�2�O �fXKevrekidis_pre_Resubmis�8Takeno_prb_���fdexpF'���0bonanca-parev�6�J�F�&� �e���AFkb�?!�kbb=nb�(elor-taipei%�scar_�E2���6F^ 6&s�tr�~A�longtaiFb��!� NLS-�2N��Cetter_#$proceeding� 6pn_ &�1/ sqmx _sorensr 4TannenbaumNPDCi�A�krusch%uprague 7,steinberg_hqX!�� inpcBchem_1 aATangSQM T�n0kiryluk_ichep,sqm04_friese�%Axxu[data_va�A[SQMz Cain�  HotQu�Ou�z�_PRC_Apr)�!ladyggpwo_db-�aIL�5!�_ � mvanleeuw9jcddb .�Gstepania �(ce71prl_sv_��!/ ;�nAV20O �articl%�570AhAP6!�0scalarrespond��z menu!: _tal��GVanBur�,hleiqawi-hyp�% rds-enev�ۅ4t-arXie�0#Recoil_sp� $eters_low_E� Ky enn�b��esz��%5��hq_dsm_� �%�HP�2kmieciՁ�(bielcikova-I�-7e��Qipali?%(ulti-revtex�2 draf�j�impac�!cGhoshal�U-v"" spin�_osamu_J futu�-��!��q -expEg refe��ew%7s� -bea%8 exUCfo�!C�_m!mf_P�%S �wakas�Zconf_� �0metody3_nucltA%d*Ye�xeffopM�! earl���N-�0V �e 2���mag_mm �'$EikCDCC_PR� >O����la%$A classicI�heavy-q�Fp$re-vrshptr!axial5CBo8;!Jfm1= ] polaB"Jws-gen-sG 4(HS-SQM.TEX�hp%x,DeutDVCSIq�SHORT_R-! MS-E!0PE*�Beta_new8!s omeg%�keffm_�MD_fluc�A�1_ed8$ISOSCALING_��� -suba8ise��SNP04_�!��6i�� ffr_latesl!>FFLEEP.=a�.0%�+.'&9,coal-62-1216�^�potqeu�castorin�! emnu� �rhb�b���i|_prE!xnwang�6x�emcf_xɹ}&�!��M��Mat0KrassniggMariE]� fb19eQA(A<B:�TChapter-E!.�.��.%�.�.%�.�.E�." report_11)�!�dh�_A2v~�H kobayasi_9-� 0rel3ncont_v12A�!jPLB_Ha8ia!�kp� !�baryon re*� !W TUNL_pt_PC!�turke��xco2q!�-�`�.ubPro�$E.M � phib�Ya�O�AD�4N�$hreeCluste�bA�bal� A�f�!phys11L� u# uc�E�%��-pE���}�`edsnm-qE5�nt> lsus%%� fitsUPfurnstahE�e�]a? penta_mar{\gdh"snp04"�deutnp!PFTEOS��!S effe��Lprc-ka�9�HBT_BJP�_#raraescE�]npa43-�AuAu.E�1ag$scopetta_br E$Atsq�v$nihal_EPJAbjpg_fW pv_mmme�!zcoukA� _a�_eOE�=a*m^!�!�ics )�!p� {�takayam�B3e��diode]8>(��CompLase� x� !�PMMAr� ���� JMerrif�Plas26O)���$PoiseShape!��Q%�ET!�(APVProgress�tect0E��$PrandtlPRE�eCa�4nY�4lan�>� aO Melt��I!~: web*�a�)�,Endo_exo�ew�{� wake!�i��papmee��astakhovJ n!�pap- A�tup14� AAidecr1�;g _F!�(andrei_doro`vI TErdmannEbelingMikhailoe! varI�Y EJP23_103x Fritz'_J!� B_18� _�APLKippe+�]A� HPRE_pdf_seismicRate%��osig-,���!:ZeroT_O!mbrA�8PowerLawPdfSeis~E=!��Wi��!bTECHLET�d�$Cold_heliue!� Ellipsoidklasmae�!DAragoJlal04)�A�(ComDynCommud >��>r�ZUBEND�� ]��evY� uthors_el�5fee�Som�A�e��fi-�Epro�ionEunifica�A. v�(OL_stabilit�*(8slifetime_�!� adv-�JAEe~_2stat %�&�smbib,�e-.!�firstbmaE|�$schoberlan�eocommand�def� �>}`%�(THZ-IPP-PR-� -�!FDO2% � ejL kadamcz�ma��C#VRE�!)%�felbacq�/exp)�5_DVeditG uah%�:sup�tti(�U; vO((onalApproac�&!� Spie��!~thermaln��Iz� nrel�!wA lihf�08SLAC_10894_JVST3polemi�RTileHC�OPtFeshEAO 0555DonateK!dcl�q shif�#��M�P3%�� browRs3�I�PCapelle.solardensity.qBY� !�nss234 �fPEPASH�fE[d�ka_ he2+up���2i �#vulcano��(art_bswitchb �"QAPDuv�+1[0beh48e_postpue�! indeo�ph%#�;aEa�SmT-eplFP*6 1�!�ni>%H>(�a�@ZJohansubPRS04_EpH�MelnMem- Rmoderay�R,Large_AmazonC.��BeYa�(HI+-PTodd48E�B*e=�LAS_CO�)LN�u�abstra� !Jac2�app-cal�,![q� A%t� rvpahr!�!�$chap-discu"V!�"�metho��vA!AX(si�!��� theoL���2"A=c��vara�e�NXPartenskyJordan_3_2_fix�k>hi�!techR)-r\+a�G!SpinM� �$lu_tp_04_2%�=I � �`h.g-C�!Q boll�ch_et�HABMBmy7y23Llsi�!swa3.���A� E�le�jtb2_eAW !�q-bios ��^�&�!O>'nstret�l� 1-in�'� cecchiLANE� shan�S6s3%,�(allahyarov_�}cancrpro�6;vA�Ha�  /:%�(pnasREVISEDNM�(9M!��#6�&!XESEEM��Hor* b!GravRɪKWal�o%�6b�FŇ!�Qcircu8�$phasebound�Q�(cnotpswfigsVT���".�$-.F r)*�$-&�%Ev a�2$c�� 2 dedi&f B7epe�B�� 2Oopenin B4sI��24titiAv� orm-sc�A�Bw� !�thesisE>F&%`&clo�&l��ifiYsubf_l�&2�/ ip�&#umE e�~hasph�IaA 0walborn_mplb_& TEXFcńF{ 0Long_locc_bul�Azinfodi�'�q30"FE�!�StateAn1203I�P8InuiLeGallQIC07� Zp� FR���TL04v!{qgap_R�!#;2a��4_Josh_howard_v��A -splitl-q^u�#�pNMC9�Covaria�.B���>�{ F$5y�1R��!ymo���� MQCAA�� Z _� �7B_�3� haosQuant�!7LDE')O� 2dToE���squeeziTEX� MQC2��/res ���PCɚa_4MGrace_MLE_NJP2!/ bang%Q�IQICuchi�xa� I�X�B� dE�ent. vo�UA�r�)��A. mora8; stud��suppo�#n@7i�|BY6 1qugE�F#��dDickeSG'!� art%�muxor-� �h�BYH � MQTgK F%��F�L<�.q%Y�E�*Il ted 2 BB&s swapnan T e�6picUnc�*in-!s ilya�@A0KS_DWELL_udis� Fe%�1HFp!���$PTP103_697�`k2dime� �ourfi� �AboveCCS���&� ��EI�,iop_job_alex�sc B-bo#4�� zim� !Q� ribMnDelga�0B��fFEqF%S�belyan$qMH� _.ulu%�FCE!\n5�@Ralf_Stuetzle_et_� F=���8sho%�I18� @DALTONMarkovDecQCPMkV�V?1�?B}bF�ma=QNDph"$coher_q_deX!:ReschGHZ!�BM.�MI2BECOL�u� dicex�m3A8 nsGa� pe>"F3%+�monot�+B'6FRR21%R!�m�� 1108a�:�E�ph_freE)�iTet�$-Seat�!�cloR9,rob2.tex��,�6( xxwcent.tex 0412ziman.tex� �P�P!�0 |.�T>�n� �H�X�J"!I��!I��!I��  �`�$�� 4��D �T`�d��t�� � �$�`� (��� ,��� 0� � 4�`� 8��<���@!�Da�H$��L4��PD!�TTa�Xd��\t��`�!�d�a�h���l���p�!�t�a�x��|����"� �b�!�$��"�4��#�D"�$�Tb�%�d��&�t��'��"�(��b�)����*��Ҋ+���,��R�-����.��ҋ/��0�S�1� ��2�0ӌ3�@�4�PS�5�`��6�pӍ7߀�8��L9會N:��N;�O<��C�3��s>�賏3����?$�@d�A!��B 1�LC=QDMDQE]�QFm�QG}RH"�DRI&��RJ*��RK.�SL2�DSM6݄SN:��SO>�TPB ETMEuRI)�SM9�TQI5UUY��UXe��V\u��W`�%�Xd�e�Yh���Zl���[p�%�\t�e�]����^{9�W_~�X`� FXa�9sb�)�c�9��c�E&�d�5P�e�a��f�l�Yg�}Zh�Q�h��f�i����j����k��&�l��f�m���n��֛o�9\p� G\q��\r�-� s�9�tOE'�t�Ug�u�e��3�qםw߁�Sm�G^y杇^z��^{�_|��G_}�݇_~���_��`�H`��`� .�`�>a�NHa�^�a�n�a�~b�"�Hb�&��b�*��"�-��"�1�8#�5�x#�9�#�=��#�A 9$�Ey$��$��L6��PF)�TVi�3W>�e�Zn�eD]z�%�a�9&�e�y&�i:��3k�٦�o���s�Y��w♧�{�٧�~� h��:3(��z(��*�(��4�裐F*餔Vj饘f�馜v�駠�*ꨤ�jꩨ��ꪬ��꫰�*묯�Z���⚫���ګ�����[���"����2۬��> m��N� ��Z{-��j�-��z�-��;.��e�覫���ۮ�J� o���Ko��ދo���/���ׯ����\��#��� 3ܰ�C��S\��c���sܱ����#�\��'����+�ܲ�/���3�Ks�6ߌs�:��s�>� t�BMt�F�t�J;�4ӿ4���PG-��TWm��Xg���\w���`�-��d�m��h����l����p�-��t�m��x��+���L����pƭ% Check the minus sign in�hodograph transformation. % Conte and Gandarias, reduc#@s of Dubrovin PDE�vised, J Phys A. % To be put on hep-th \documentclass[10pt]{article} %\usepackage{rotating} % sidewaystable instead of table % rotating.sty Copyright (C) 1994 Sebastian Rahtz and Leonor Barroca. \textwidth =15.0 truecm \textheight=24.0 truecm \voffset =-2.5 hoffset :t \def\today{21~December~2004} !{*�h PERSONAL MACROS, START % -�< English abbreviEs�, \ie {i.e.~}$\LHS{lhs~}�oJournalJoH\CMP{Commun.~Math.~A`}�� FeA�cal funcE��< \F {\mathcal{F} �, \D {\hbox{dLog +Lop{\rm log}\nolimits9,bfv {{\bf v}� 4Painlev\'e equ=�\PVI drm P6 �\irrec{ks�PJQ`END %\makeindex \begin{q�}a>0itle{Symmetry:2a pe�ular a of �assocAmvity ��$wodimensioAtopolog)� ield��4ory\footnote {QJof���ics A, to appear. Corresponding author RC. Preprint Sa�/045.} � ${Robert�\dag\ � M� Luz �*4\ddag {}\\ \\ +H Service de physiqu represent�]?�he simplest nontrivial case, by a k4le third order��C�Monge-Amp\`ere type. By investig�y< its Lie point si�ies, wei� e itaavarious�linearz8inary different�u�, aA�we obtain several new explicit solu��. E�9w %\no��8nt \textit{Runn!g%� }: F#(Keywords}: 6�,j�, ��, ���!8=2 r"@ .N�hMSC 2000} 35Q58, % Other co!�tel!�tegrable9G/99 % E�!�mat��ucs,!�eA abovaBF PACS 1995�?(cosm�vy, gen%�relat��R-�O (quantum gra��0) % 02.30.+g �2~methodsA� � /20.Qs / MP, Group�ory, G �4properties ...%og)D11.10.LmDGal =��9s����iclA�No�LmodelH% F- N@, analysis %base! �3= 8�Ept:10 0 % 64 pages \2912"8 "� % FOR DOUBLE-SPACING, REMOVE THE TWO FOLLOWING % %6U24 U< %\renewcommand{&(tretch}{2.0��tAbofc nts \v�2\eject�=� \se� {Introde } AA |ed by Witten, Dijkgraaf, H.~Verl�%�ET\cite{W1990,DVV1991}, A���A6�involv�=e follow�Q(unknowns: a"3 h $\F(t^1,\dots,t^n) \equiv )$, ia�er nu� ,s $q_\alpha$�$r, $ =On$� o�G$d.sta��ca�dei�tea�,rix $(\eta^{ Z ta}� Vco Gs $A_6%, B � ,C$.��se58 must obey threo��t%N9[ )�,Cargese1996D4}.�F) Y;a�a�s a L�dre:u):UlI�exchange�esee�qs} $ (th��2�68.� $t^3$aA(\refB�) � $t^2>%�)a'osWmmon va8 is h�de�d $y$)� d@a� �Aa�q�i�wo� s $f(x,y) F(y,t)$ �heb�-;FMa 2�23]�b�Y�a�t=e'},\ F_)�MXy}^2} x} %AB=-I} %B#ty}H1Ft@yy6@u�H�(From_f_to_FBow%��iM J�hx}=t,\ y}=A�yyӅ1}=A�ttx=a y� �6�F�fB�A n�way �E�^i Q�6` �)--V �)E4o rewrite both�:aD 5syste.TL-called hydrodynamic , a� H�b� pp�  a ch� of � dard:�s to � �, -wave� . B�admit�"ax pair �� , e.g.~fo� PDE 16�)٩(10z\psi_x="� p� <{0 & 1 & 0 \cr ^'E^ y} & x�j3V3�� 3y3} �,\ �yZ�r1v�bb���� ��\c�y�Laxj("; $-S# a  spect�$parameter.�" purp�V�is paper�WtoqLV of �A�rV;.���� efor�  &�of6+^� $. Any suchշ $f%0only defined �(o an arbitr1adM a*e degi8polynomial. How0� �.� poss �rUic%structu �� �iY, mak� uneas� e search a�F��i{V�]= ) ha�)?r-)� , sow�m�y�i��X latt*�.  a)in�!�7�;unFpermu&� $x�yy$�no � ivali�!�F��9lA�o achieEis.1"�,?perw��� atic�� on, � via}zVp:�H,� &j �r to  b� (���$a priori} ���y sincE�herit� "bility�Ai�fn%�ion�!�.�r=�9iY�!�pPD=�� =�.�� h��Dalready been found2�, %���.�  s. %  =�u /o���,organized as�s% 5 �  Clas~�ies� eli�6�� �POvsiannikovBook,Olver  r��!wA� algebra, �ut%��eS�l��2adjE� .]� then x us!�dtoptimal<!�;or6� >R"|)�u{l��ed=Y^ lastVwS� ry})�riz� Y�W#�5&5 "45�%�&p}�> ] In�7#n#to!� y#u�.[Mycon��e one-����!� infinites%�6� �  $ ,f)$&KuL�5"�tab��l}{l} $x^*=x+\varepsilon \xi Q+"�! O}(%H^2)$,\\[5pt] $y^*=y2D��Df^*=f6Dph��� �6} w�$�pa�)i5}. ��ed%�m�F�YY� t�pveca�V� 9rm b�3!�fv=\xi&�x +!Ry+!f� On�zn requirewat�� A&�& leaveAJ%�t��� th��E\�_>")� is y�"M|d� m� ,  ar ��V���� 2�s $Y�etQ]�! Mo$. Hav� u�:U, -�y*lar!���by�K!�3 t surfac���b� sur} \Phi"xi$o f} x}&� +eEj-y}-�=0F�Apply!����ҍ�1w^� lead�ma tenN�. A�$ed sJ �iUwe&qD�� *�!!r�&^�� : $$��{li/_1=�\� Pal_x,\hspace{0.3mm}& q&_26&yV& 3=x *�a}�3�fff, Rg4=y.Ay +�A5=x y.hBgcr \\[#* �6=x^2r3bfv_7=y�&86fFL96�Z&{10�1� f.& :��)� $$�969 \sub��{O2 },�#to�X Ew6I ,]�� J� e firs�& H� F ? ��� (T~�  �)tator})V B4A) })m? show se���, #X��weley&:$%�i�Gi=1� 10$,C ec�j   ;� is91k 4is done easilya�q�w�seh � h�..`(y��a�6sub�3s���f�a�&& 2��n�\\^+44rz5-a ,3+b 4,&fi`3- 4+ F5�VeaS�h3 _3+hFVz7�O F3+ XOF6�F- =n�X8�X�a�ja9fa-�21|FJ "1Fh4F4"2J=c)�5+d 6+e 7A��O��S'&� "� q*� $a,b,c,d,e$aQ &Xre`(o�i�ana�:�$%$colsep=0.5=%m� v�l20p� k��$}[ht] \cap�2�.���6�-m땣"Z>3��cc�)a �,siz�& {|l|*|} \h�  & i1$ 2 3 4 5 6$�~I78 9 a�$ � � �� �0, �$. N2I f/a � 0n � �+^  \ ) $2 } <�/v} r&) &� C%C $-<�- &  $4S!+-es  6$ &M� -7 �BE8209Z%;1� �)��z�%"���Bz � y6. ��A45-!~.%��:������:-�] B�5$ & JAO�5�� !�Mj �-I; t0N1�+|96.b�| �!V 8�{9} O>=-JlIY F6�)5� ���!})�� ��,F�I�.l sG >|)�E�-� �� |9d,|�i%b u  p.�>| j( �Qlv &y> b6TU |�KT �� �"endle}�l .l  %z�K1ɬ�way�7:� � 8} ��$Ad!uI©�E��� �� � �i+�� aX +A� Aq E�s-� ;|1ed 2 3-*�6� 55g *��� l6-2B8.�0u���.�.� `�E�-o ��+=a�.wJn2}�5J 8}� ��l 7J�{9}b�a��.�Jo10p � A� $e^{=|��^5z4I<�.B{2} FA� $�R%) I3R%)�%R$!n �VIEHV$%-"" --]�1 !�V9Z/:. R�5/ �V&50-U RL:1ZL:3Vq9$2WV%%4@ N�E�1.�i�!�m2.�J� 3 ��>H!8 )4�)4-�� �p ���6�)� �J�A1 A! y3�V�S��>�)� h h��A�; �IB ��J�� 61�V�T4r�)��.�=�J�)�1A.�rVUv�M )S��.�]�2�B* � ��V�V�9�:� �ր �D.�Y�1�Vn6BŎ,2������M � � J �  6� >� %��z�&S "��"�*�  Each&E.JDI&L%_*�^�an�9. Becau�2e c<%^$#uzK%�%�-en�s.'*#n&�0���X&chjnow�id?(Althoug�3su1@8Lb$bab6:;�6omxnse,  "�ir&�&�$�a�_&� sk. Moret6,&�$ "�*1263))Jnot iso), its�,�� alsoT&;%�ed!�s, canSgL2v#y� �lO'A;�0is unfortunat\<of�&A� 9�28.q. {}�- scal!=604�.c�!ed4'�= obv*>uf�- =2 i�.\sqrt� 4{3} (x y)^{3/2�-B2y^4}{8 �-(1 2 x + y^3�0i^2=-1"oeqS �Sb>�<&#/� > &�u�Ne1� or $� �0 4$�=;1,2'&-�o\:8�*�4$��4ma�!�,same autonom�?0arAS�%�2 30) p.~46�3V�6e2�6e CE(rix{ \displ8yle{ z=y,\ f=�3[x^3 8 (z)�2 ]^{1!� �8 or }7x.7yf7��<<6~j$''' + 16/3R } \.}*7]"%j 1or2BT'�@�INYՑ>g)� &F &�Z-�U5�Y[3 b=�J����($s=a+b,p=abA" $cIZ�9�#i�� is�(�"{l� 6�8 z=x^b y^a,\ f=}�' <%z),\>lIb4 -16 p^2 s z^55t'' -8 p (4 p +2 p s + s^2) z^4&$ - 3 s^3 zAqvap M�%''AG�E.�D \phantom{1234} + pk- 6q ]2) o,phi''}^2 - (@^2 +7/s + s9��1?���$- 9 (2 +s)� z � I- (40!%-G� s +18A+3�2�2��} �(- (33 T +!}2)!�� ' -9 !48 e�� IO-�>�3 %��An( �-,s rZ.x�9{H�-�+�2sup ng ! termu'phi>6E![�7�z2#^{-t>eE�(�x y}{z}I�)�1$e&\�J�Sz=y x�JHZp816 \mu^2 (\mu-1A�2�iw#?(3+1)&+&$ +3 H*M�-߾�-8yM-a?Y�E�+f-3 �3)(� u.c-8�sbi�  Yv�Bt.s fro6N " bGZ �#ům)O5ɚ�$1�<*�&eQy�8 \for -\mu�;�^� zIr,\2�� B�bisPS" e �mu16BFor ic�9d#$(a,b�B�'ODEa�:� ut>  7(Z �2= \�?j=0}^� A_j(z, "'6�j,��9Va�i�X(k � $A_j$ c�I� �/�I�E act 6�*O0�i{Lie}"4�re�>=��:)# \mu${���"� on� z0 t le�.OS?�*l*K+ce6�})g3)�lK (b,a�: nduc��RfBa6E�5\toA�^{-1}$.&`,&o<�PB�>Abz8=0,1,-1,-2,-1/2 '-7 l $Ki-&F��b" \mn\ K=-8 zJ$I���'9"4�X%�[-4��$:5�]' *�34N �-g �l^28'd ", B�mu�F K=�dany rE�*cQA$} �#ьsee }:: mu1Fp(I=Gral�2}�MW)2k %4-1%5 z + �5!!"��-2@!u -=!^-10"9 1 '' + 112 ٸ-96%���)��^2� 5}{4:-��yx + ��}^�?V )�� � -�36�.6�*, 6�>91$��1-rd �*���f1�f*f z=x/gf=)i  \QwV z=y/Wf=�.'nn 2� . -An5E) fA2 1 =2t 1=0,!Wec<,=c'��mu1B� is�4�+�VB5�M e fa�1�4 intoV�2r ��'�:�sor�l"]b� f=2F��+�)etaE�@Ia�"I,\ 36 ( 5 ��6 .) )O %,,��&(F� mu1G�6�I�!:er�9ngHnot�?that,��hA��;6%s �(Z�Hi�~C 12 a2E��-G2NF{�9�phi -A�C %= *� z�4 b �-!�6KŮ6V&� ��2. � r�=�eby���c ��+ 1K� - ��� �-.6��1^d6@��:p��&� - 4.�E�1�B ne:�>�)?f s96��9would9Bpo�>$( �":  '�4�� b� -ѐ �e�?ٜ� $5�!��O dent�S]4 [ �UH $r_1=r_2=s_1=s_2=0JF!, nK2( 4}) give�UlowB� �>�3,\ 1/3L6 mu=--Y�Qvel�ThY is j�Osub �aN�s6� 5or6�� �2� 7or8����2,� �U&� �s)�M��� ��� 2,\q~�g@2}{15 c} (z-c)^{5�\ f yvG #�  x}{y}-c15�M;r�!� ?U ^�zU /2}LNc�4_.�xV� y}{x�xA;6�bkMY2and1M 2oldBnandR�)#~4!.�ZV�-)2�i ^�)�1� c !�^2�6J� V�f��A= ^2-cޣ!�^���newB�&Fc"{15�&q6V )&;9�$octahedronH$B0f"�b, seea �1��b�T\`.�M0 e�N1.22)XxE��Eext"Nl(P�:�"eS "Z���B>�5/��3/5$, �6"w�}MB�P��?9���a�G $�� anI�5_Bc}�O� (��4 c�}z� 1 3}{5VY z}T<f�Rz^4}{Yf�6\ ��5��F)�"�;I� tetrF�A��X &���)B2)B��&3�24+a5+(�#"�4a'2�@B�I*QODEn@.bz=x��(z)+(a b) \log x>_>R4baFN��8#d m�I$?� ly):[�=5, Exa�] 2�H��"�N� ���p(z|U (r_1�r_2� + (s sy%B�� 2�  +T+s_2h' -(r_2+ P ��m��s_2 +� s_1\u[r_2}{z^2z�, ?Vu74&k_0�Sa�\)^�j\k_0�^N�A�d . ItsN�"� Yquadra�J���-E=k-�k_���r_%�!! (zI�z -z) 9q%�"E�z!(B�:X\pm \�a\D�  v� -b!�A!- 2!�-AA-EzA* ^2}}{82}%�B�f=4 �x -E'�y @r_`��?log �$ 5[���=6��;J�� itIm��]s ellip|K*Qls. A�t� �KZcR2� ��� + c55m�%6V�F=� =�!�8}�� y� � 4 c�6� - q_ wc� e� ac^3B } + N:"  {" E +Ɇ�J���a _&� �oq>� "m V� �s�s $)>�Y34 +�#7$�� :"6��5&6�� {'�&��b&no��m ��� 3� f= y^"���a�A,"�E�>xn>x^�B�1������ +10 .�A̓r�*�� *�>�*"\6�jmak�*�Q0��(ƇAE��ʇYE^>b��([3YU"482�%B2�! + 21956� +50�*� ��28Y*U�-1�&$5�F�'S�PismYd"�S*P �Pj�S�!��+ doeLt� 3Z$a�cn�I�DasewB��3,�of��7N�d�����nEtha�.>PS}��*�*��� �C�-82-Z'-"9�-�7�,8�,e��h6� 2Q��2��f=fR3} ��I >yq%:�3}>y,\ a \n�_Vli�-7 y~ ' -8a�*�( + 9 �T2� - 23 02� �~L)-32:"�*��8u6�(�h� ' a1 ' ���>� but,�-$1<$,�0c not find !uvDis'��X�Xai*� b z. 1 "*+, 9,10e@y$d �e S.TqS.z\�d��bd aE A��01��:�a y -�A��B5A�b�� 16 a]uoAkm�' 3Hi�Z�4 aY�A�e" 4]�( + 8 b^{-3}�c(9or10B�W�Juld]�R� �/'A�E�K�' _"V(no&mng Y &+k�$N���� $�J]�J�Hk �/ 5 + �H + e 7�: �;11E�2�is.���'*A4&A"�n� ze4 11z��+ c_3 �" 2� � c_1� ^Ac_0!3� c=-2�__2+2 bE,d=-3Lc_2,e=-a+3"Z@4 eft(3 a^3�-eYU1a b^2G� b$0�B.�  + 36����cC1�711B4!��4 "�c(al�Bn� *�of �]� in $�S)$�a:� a�  ^by B~�"� wy��s av�a�%[�" "� in �\c�mV� f��#IE��#B y%�T#UN�#yn��#>�1N{#��52�5=:Q� on {�Y/ 1��- & $}i�eB�t���.>�b�7sZ�+in �K�Z 0}L+�e�%" includI$�o���^Q�g b�UQ$e too long�res�0f�Q8he ``icosa$'$''���3�3�f�� �z�7 ^6 T��"+P29 #�� 5 T^� &M&04 x^4 T^7}{30:&o5E�T^�} uOA� �6E�)3}}{8fR8�-)9}{40Z�m< �4�� 2 T^9}{45&)7 !3 T^6_  ���3B"h x^^Q}{6^�y= � �5� a-�t-� !P�4):��31U �9}{36xn�E�primeB�vHf�a"vt\ta�O1"�O..�O�HeU}[h�H[p]uTO0w�8au �O([garbage]{ m�2# $I�,)�$aX�*s" P.m`,^(0. A3, B3, H3 �}u��)kec re�c��ad&%gDub&�-un��b>0Fn�o�-�Oss�Xi 1*��$N.i$apparently�e>!� (') �-a de0��cing2�c�0f$Iblank_\0column ``Eq''���d�>]n p{X3 a�k�G�!A�levan�V $I�$ reflec�K&�<%G�~,to $1$. $P_nt;l���of�$n$�PR0.�wcm"Uc�QI��K{| l B2r �@ ��*** Lo#OI� $ %$k lr1n$ %" modul! ,y,tqOq'%$�h%iyky}Z�oNisJQx,yQ0Eq & Link $(t`\ -�t-��!6�#�"c>�J :#V�#.�:6,B�Fux=My���>z�%�%��F1Fy&�$:�&�1 �i4^{-5} P_{8}(x)�� K�/lcw ^2=1z�-]&~ }{x^2.3!&5\� �=)F�t=6�G@�9'��4 ��u>u'F� Ie4 �_ -�� 12  6�y�+3�0+3 A� �"7Oa2��R�y5�)��1�-�A� }$ %�� % V(>�u1P@%qxrurQ�) 3}{t�Iqq�e�eF2F}�� uglyF {6�M/~g^� cX atop>X�T :�\ �"}} Fj4GSi�tor2F%����3>�4P s60�� J� J�Vb �[f}&\"�D"�u a{x6�y 6$Qs�$4JO q1�=a�^2-2x)�M-.htPE�w@i� t^3] L CM :� ��K @x� zP} M���3V{2V} [ 6�)!�& $t=&r4�% ��uFu:/��*}� B��:- M@� %�t� E�2&F�!�{3��84 tY105 �6CK���. n}�� �!- V righ. % \�$ \mu=2J.�)6.J�x�2� �Q� �.f�& & !�R�d.�C5�l�-| }{525`36#%�#7} 2}{6 �F"5"}�#3&�93}� ��:��"���7A R��'�b���1�> 0o{-�;+! z^221/�t6E1 p6q51l2(�j�jN1 % New�8:�>E&� �,}x�v -7/2}\timŠR��(1�5 �H}{7}-%�a -U<x' -y^6m�Z2i1E��6�K �1-�� *h0��c0J��2<L�&} (y^2� � &� ��N1'��^�-1�!�W ��1.�P 11}-9�+Q4y@x5�V&���Z������{-!8!@� (x��y�=��f f :���/.�AV�I�w2}��� t��6��l B` + �x�6 yD� � !o�\�mu$2 6 6�0egx=t y / C� &�q,.39�n -3=`�a�a%LRb�(�y}<%��3 ���}{8��� +�*�27V� d 0iR6 xd�Z2�:.[3/5�[6���.r�.t . �6���I�DubJ��e^".  t �*�A��[%�%� � E�48�B�ͺ *��3}{12�,)��SZ�! 9� n!>.[� \notavg!(y/x)x B�x=y6��D >D !vN�>� �%:31X�� 4}(4%)�u}-3�!>K+� /!_ 1� x6(%'�{16� $N@# B�+ q:�6��+:�`�2�[2�,uu.�A~1�x/y^�:f!M*�2`��A��525DubJ�M�M�%�2*`/y} }>�B�6om@6^D%�H%)�B2%�Bdx=2��J2J ���A}��1�!�B�� �  �1� y��121:Of%.fHVf6 �.Is�M 5}{2*h Q }{396ZK) 1X 5��g �3 t�F+��q�^4e�tA45N k y��Bxh�!� � =� t$:����%�A�d [ 6� � Z�:��, �}:�>A!�6� Tj@ �ya��!�� R "oz�# %+6* 16 ��$6�$ &�}o�#�# } F’��d�:�B,e&�8"�s $ 4evpic"' P� six;�c�e2b� $\PVI$  ;&d "�?=0four monodromi�ponen_uf? �z&�&�>&�&c�&, like�Q:YEs ( � �undN@s) �� by Kitaev� P6cube}.:)���'A s� ed N1 k�R�% �eK:6ʑ�)� (F�3) rem�ƛiܖ� is ques�curS!d_������1.21.' *{Ac�P ledgMws} F, warm��!Evgueni*%&Z�� You-ji$�r enl�e��discu�&^A �&fe)K�ugg�oR[o greaQ"improL�A�!$[,��2 R� ncesK5 thebiblio�y}{99)bbibȏ{J� R.~V��, E&�� , To&��stringGL4 $d<1$, Nucl.~ԢB qr 352�D(991) 59--86�R�ub�� B.~�#, Geoms�of 2D ts�A�o�x, Lec�<'# &*�s � 1620 ��5) 120--348. http://arXiv.org/abs/h֥/9407018�S �eC>��6��s7cen�*% two-����itʀO&�ty,�m��ury1�Xer}, 287--412, ed.~R.~C�, CRM�ya�9 al p��cs (Sp!�0er, New York,*�95U" �E.~*A HypersWs02 flat� roaf,�~riceS"O&!���x�1�iae De%]0bf 10�,2004) 33--49Z��$.DG/020524.� FGMNJ�� C.~A.~P.~Galv\~{a}o, O.~I.~Mokhov,� �5\Y.~Nutku, Bi-Hamiltoniana&n�f�!�2-�&u> ]�+�CMPM�86I�(7) 649--669.3�B��6�Eq�WFs����Kory@B�@ ble .�nN�agonali�Q�xq F�� u�.~Anal.~�.~�&m�(6) 195--203Z�z�/9505180}�2 A.~V.~ , SpecA�fu!�A���iso��8�, "tFe�Ԋ�A3 �d��`F,%wy��, Av� i !i�5A�4} A�2�� 1--139. Eè��� on: St.~P��sburg��.~J-RG3) 45a:65ZR,�$.SI/010202.SO"2� PZ��!��(��ofzB�D.V&�} �uB랁s86).�:��} L%� �K��!;��(R�� }, (Sibere�.AAcademySci�> h ] docu{ }% ��\�\0[11pt]{amsartRu�3�[’8,arrow,curve]{xlC$:8fonts,amssymb} . euca�c1 ic1color6<amscd�' [all,knotF�p cks,6Epst-gr�GG plot2,[ti|h]-.2�%:Kcol} ~�3nt0em �1e�},newtheorem{T } .Lemma}[ %] 2#Propos,e).2/nH+2'Corollx�}2+D_4>�2-Con�ur.���ew�F�C}{�ghbb C IRR�Ge.8PPB4O}{\EuScript O:WT:T:DD:FK�.�AA:6ZZB�S1X.SPic}{*�rm{ :XSym  : Hilb!:"DifV���rm{:"Con":"iddiݮ.�$iso}{\cong:78smooth}{C^\inft�`6�8omega>9uch-Y}{\;:\;:@wigglygeq}{\gtrsi/.�rk�rk�.tildei# )~{\it\i}>�Kh'ex!;Kh}>�Q5�{QBgY�{RBb4htp}{\ �6-sl nfrak{sl>�Slice}{S>"Taq/{T>sem!seN �ke�rm{ssB!JM�b2JM2%2y+{Z>�bA�r �b>regro >4suTf� >4hala��J:�Sym!�M .eB��<��j�horizreRA� \;\i��9ap�N{N+.eps}Bplu�TJ*VS} vert��6*VS|6(Z�F)VQ� cros��ZL2$VGozF.#E \I�,[Clay Instit�B s]{M�, vanish�cycles^ts�jN ��quotien�\�$Ivan Smith9� ate{� �. Tz& AaLauda�9 helpKcpi�s2$is work waQ�r�9�upporz a� Dnt NUF-NAL/00876/G75PNufuFound� .�,�4� } 2_� small�sm, adap{f�hwo talks[��e :m7 er School@,\emph{Floer ;�$logy, gaug-;#�!rlowNC0y} (Budapest,%^), re�o��� [riginal  6ur)Y�� de��b�5s back� nd�. �q&� sympM4ic fibre bundl?�Gei*P. �sFo appl� th!W�lP>aEcer�Ste�2a�x7e n�P�g���� y,Rc��vi�g%A���@k%�f> -sphvh(S),2(h)). Desp���bver* �O gins�iN hfaco� �equ¯oocombin�L�Qx�LY8rZWA�kofA�Aharp(er)Ef�st#�3,>dU-u � lite�R. ML�MTJYEI�E rnedeX_�.8*�V���Dith, Paul Seidel, T�flu��ins�sIpously�9vadZB�atH�s��m�&�j+} MoS�yxmatu*`�D}�� ell-�n; �al�9]�caDr�Y{McDS},�Sei:LE8AurSmi}. \med� ��2L�bf{1(A) N�:} We w�<beEnce%�!Qeإ+s $p:XZ+� B$ #��%fe�, o�r�xAQ�w֌X$ car�uClosedaS�`y;on-de�te 2-�� $\O� $�r w�N$d ((u,v,\cdot)�_ whenS� $u9�v=���1S tangent ��t� I)���!�Za�!u�� $[ y|_"z F��}}]�Ulo"<�UI�pa�el��� map�y1Homo�dsms. �W s ab��: (1) A"і�r���I8pace $\Sigma_g .�X21��*c��F��m�aI��O ure;a�inlO%�� pick7J-�d�� ka�i�}fricD�%q� $�F�Nem.�=���a"V*uto�)qsatisfiߖU(g\geq 2$ (e;nAT�U�xChern-�m�B)1g����(2) G�ba hol-�c!�e->o��Fquasipro�ZO�2ety-mQis �)� $B^0�ob�=B$I�.B$p�`}(B^0�xm�^0�=!�anQg:��.��!-�qp�.m0of a K\"ahler��$X$. S��efZs�tw?imA�a�ff� uD�%Us��Re�al!G����ys\��; ic g�p���� pl��r��&�h2le�{ (3) 5ras�?l9 he (.)� /rA�� mo����W�TM+1�A�ma��Rj �h��Lagrang�)�-f�r.�qsc���m��n� we'l+�� . SeU�i�sensi�to�Sa�ti  betw �H*��������2� );2��� amou4!��" of��ig�qa���a �#ext�HB tot���� casA� bove�;subtla`��WAp !�ro�� w�� , bur!*��o��.zs B) PB�:}��6M8 �di!�guisháonnex@�!Ar �on�ub�s $x",Xu�hortho�v pl_�-F1�{ ribu��$;Hor}_x9tDker(dp_x)^{\perp_{��}}a�cr�ibM&.R�!�r�R�x!�manifold.�e�B+��0MXvCb�$��re���\ ic. �shSN/ %E ` ,�jcon�GDarbouxA� orem�preveA����"v� e-type&y s t v.�t y na�h]rUno ``uj�7  �ity''�ulI�=�%a��@Ǚ anon��IM!e�eofς�I,��i� j e6��y�������o��O����T� e* + sequel. �Cpath $�;:[0,1]\o9a�Ilif���r�  $d < /dt$!��rim' $��- 3)u nd f#�almJ��)�sv��2PI�s-��1� sms} $h^{ q}"gG%���� If9:�E�r �E.�! s!�� globd ���w�Y e $p�a rM#� � �p? ymp(-#b))a�No�ps7X!�� isn't" �>TAb�xi=�� ;G!�L12B p�hclass �(of��o*�'�$� OE��ce<k�$G$_��Q� wia�nda�s���(� e�e�b �LA�]�.� �Ibe`-��� ant. �}�%B �tly~9C) Non-��$actness:} *� es`�� $)s�}^c may3beY*I�d.���!�V� ;!<$Mru&l�g  � �9�o� c�aM�rfk�p)�strategi�΁�c�s�rݾs h'� �rhR�.�sDNl�� ly ()�6urn m r�;zhoo� V��"  Ss�N�\� { 6&\C$���ha� :��f($V��0T_{p(x)}(\C)$~a�4 $V^{hor} = V.�8(\nabla p)_x}{||^2呉O(\C^n,\�_{s��.a�E ^ � @�&�I, clea�����cQ�� L el!"_,A�!�:hX$\C^*�L!�8R ty $R((x)=deg(p).�� og0 �b�fm�ul5$,a_w'}*% %@� >4V�?T_u!p=!!�no�|-t|@q�/ |V|.|x|}{ �|=|%rO!x��m $p=�!�i��w�L� ly � $|x|�poF�. ":i  F����J%�y�2� �:%�] &�� de?�in�ma��(� e0Z ingl� ��!�!�charac+s��Y~B�Pad�"qa)l�det: � Mat}_n!�]�\CAu$i�/se:B�2��,$SU_n�<  HA�&6&�associ�tse��to\ s�&�,e!�6 -,%�a�.�\C^m$����ea��om-Aj�� !^.+�ees�օ{1�rg�# s do�)qu��yK�dappro�useful. M`q�eɬ�"� !6"� " _\and a2� $Z�B+�^war�m�~���) By"� �?* >_m�-\��Z_l�� enoug� & tۯuA� $ Liouvilles&� iE ``reuO ed''Nx $h_{'}"! :  t)�Q( B(R) \hookŋa #')$��au�ܥ �pieL��f2�,��QY mbed��A_act!�3Y ݵh�%�"u���aai� I@EameG*sa㪭�CI!�{ 8 c�ʿ)��jran<*@su&N ar4 (un���/o�)topy)� o4 s!([�c�. �ka��aiF1&�/,a� Sei�(InC\ , if�I��]�� !l lete�-aRunress''E� ;0o�� �cs ��mr*� FGcf. � KhoSei}.)z� D) V: :}��j "|�� �����("%�A� $p$)�scdt he�ݵO}).C�RD�, i.e.)" %� $$\pi_1,b. 0 (4 &� ,\O�)).$$ C�Y&H�ou� �~ (Morse �9cHde...) $$p:(z_1,\lH�z_n)\a�to�m z_i^2k�E.���2�e`�i����!:�u/"R   $(i/2)�8j dz_j\wedge d\!BNR{z}���� n��rͼ6�sq�aw8$(T^*\S^{n-1}, Q can}! IndeL �"YZ Q Hsm"�8in co-)j�1by view@  $$o}{ �\in\R^{neD , | a|=1,3Gi a,b\Z$le = 0\}$$�Tt �1)\nirn-� (\Re(z)/|  |, - \Im(zT.�6�V�Q�e�wzero-����be�@d�9!� locu�9E�s��� � ��q��J� �a radwA!�$& Acc%� ��x-- q is $!�>�%�n%�E~(i |z_i|^2 =�}�2�--Q��ce�3�:�"�iu|. �*:!�*� -t�j$oop encirc\+ $�Dn&� Dehn twRǍ�:u�wo-�%�2,�Qus�X�$q%�%�\Reb� � f� 2��( T<$�"3�� �m�+�TAW ��$LQigeodes�low�+ unitA�c" � $U(zA1map�Xuc� antipod�; it'�he2���)XAnFb���$\�A�UA�n=2/ ; �!�� {�wl� )�9��a�E�Mnnulus1u�Xv3E��20TY ����# e�!" model:�a)E�q�e ?�o"�0 /�T:! we7 :TE��f�Q $X_��!$0a�C:�cq3�E $Z^c�gr��al data� *��a�-�A$e�{i����S8gy��E a ``�d�1$-��0 eIC��m�+�t$A$99;6�}r* Z.F �.�Popen neighbourhood $U�$Zq�Xyi5��Vݏ\:� UBkI�!�"�!�ut�[=Y� '' (4I 6�n � yE�$-%V�1b)"& : Fix� �=M�E�c $f:�*�X}=.\Delta;all)�sQAexcep�n �>duc�c�1�aEhl+$d� �)�9�Pich��� c= ic(f.� �� ]��4 `��E�oJh)�%Q~ ��� ��i iA "\z-C� $C=f� 0�� U�HilQ�schemA�^rn��N�)����$ Z{r-1}(�)=� B�Pn O�d'�s �a� !�m�\i P�IGr*=���-s)MOod��"���gT�aUelaCl� actifd  (# ����ye�t ���) �n�bu�is�%� $n=4fhe� \S^3�tSU(2)$ͣ| �*. r%_ }. (2a)  �2�a�w! �_s_d9�� �!ui!fa h*L;md e.g. D*$P,0�"e@�C�urb� 6$P_�n(��[9��ic6�u a1�:1m1 ��&� %| bޞ1i�col&��ly�d�In� �xEM�G }&a!$Pu��!b�#*o � � �_ � �az p��X��y2� &*s}Vog��p �E+2��0tripleM4$x^3+y^3+z^3+tٝ'�-� o>E�16 nod�-or%�lT�s�? 8b %�nfigu�eof<*� :J�"f(SmiThoA���)r ��!t��5``surg�"�tic'' "X,z !-folk s. �A �a tree-ZCc>��-�M� matcv tB6>�!)m�}���qec �E?(convex)V�� repla[�%�c&�0 (full b�-up)�B[I6��5D95}(!�2;(p�-�~7*,F) Lefschetzų��A remark>)� m du� Donalds�& sser{dat��9�2�� np� l�)n "?A�E� ompri�#� f:X\�.(slash\{b_i\�a/\S�#�� ve a���Nn�$\{p_j\}� %�%w)E by $z_1/z���  $b_i�\p_j�iRem_�g%Beщ�p_j)$V�=�D�o�.�f>�AUg��*6cod�Bb word��@!:�$\G��_go pi_0.\SN*����� al, 5�'�oryA��a�#��&r8 �w��:.t #tӸ./� Eh� eUasuWf�_ cent) �� stag��"����/hD�o bhiam�{cc} 1&1 30&1�< N ) 5N40\\-1N3> )^{6n} \!~ (AB\ I$$ e%�%j&��C $E(n^�.�$SL(2,\Z �fac at� A�ġ'r�0ug +0o $A\in SL_2(Cu � l=-b�0 Hurwitzd!��A�braid1���l!Q �-��a]�"� ��%�-� �exhaus �e8a<%��$� � s�*� +�Y�,���I��i�$3 42B�D�i \C\P�Y_is_y�E� plex# �#"kin% �&&%�� me��branc��c� ŪRiemannQ!;d-E(i�1inco)8"t of3I�l.�4-m�'��N�+�p�t2��-^>y���iF� �4"r��J͉a 2���-- &��4"s� . �+��g syI Q7s�2lex��BeF�"beA1 cess�� �0�A�T&�$of Fl.�5�lDo:PVCFH�, SteperEndir-8w5 � t�3by �2Abr�n��ei:VM},�BK302AKO� 5%'~ip4a�develo�\k+�: ho�2�!�M(ve�s:& -� a few. }����� "���O7to �{.�.�or2� .) AMP}e!:l]�ca���E,��� e"F�$L? aB�X\sup!L$).5higher2�76�,�4e��5!8YFq�e �u��ur:TJ};HDog��d%Jnt���E) Pre}!�, m!�re�i�L(j3p) self-�1 harm7*0e� four�% aADKA�In � _!!y techzs�����a7s &�ht��?�# hallenge:I���&d2�`�y-�(cAi/ic.�, (un)decid� ~�'G70un40 A�A gRX 7�v1�i"8!w.`հ�to"/ !Bp!%t�m�/�?�&�(n8Munt.��!R{�b����s,�� stud�,Gromov-YF�s�th�&["�:�)��!�0���6� 1M ^�.���6 ECA�si'Uuli!ble{2B�&j1e:,� ��p�matM}� F �#)a>^E$%���3orB�3.V,)B��I*A fami;A�;9ds��!a*��56�.:,1 ] ' A\x.� $F&M}:�5 ; SassumpE�!� Gpr)�Q/nszH�X%s���}��� i�+�vex a�)"y[3m3![I�;��a*LcnA'a1� $(X,f"�Gr_A(F)R$�r$A��6�!�aq�M�aia�i philosoph�riv�'>���y:b�a)�: m*�5d!���0bS$*� i��me9/"o�,  }ic obA�S*83*�T�,p: ,l�$��recour� $y���%�1& . N�0�A��+!r,*$ entiv+�<les�#T [N-� G3'���*�E�?t$I $r(X_ta�n�"� (� �HA" �ert��MDon�#aLgeta8X_�� a&g. O��@� EV� ��!�%�8 w� o 2-���" 2~�prett� �2$Michael Uss� �Ush2)k��!� intuDIascr�$!se�9�n0'r��W9w�y%1: %0b%$�YI}_{X,f}�:2ah$F$aBwnI+ Q-��s c>},%0�l!�0Taubes' $Gr(X�JD�~s=�*p�S�f�sB�ervBuld3.ec�3�b).�N-`M, Smi:ST}:&$b_+>��vaSF(\kappa)� pm 1O�� �w��!�& J�Io!�m�A�MUq��X$ li� !%( Poincar\'e"�;$K_�9��� bergf�Vproof!QoA+��min ��"� (, $c_1^2(X)�;0.��@ �a�*�-Y(Abel-Jacobi�i�{��e��J^r���E� bb{T}^{2g��&�B O6$A�.�wve(s�a torus;%u�c2<�f� "=/C$\P^n$��I�� ���E:fVOy%6 a�Di�}�y�lFef��e�*2 R4�q� ��!,!0vi� ui�&='��diYF�7##��a�@�*b�2A�mH��e ��7liv��in>�Js&"�U%��o�<u�d+-e|m�? F6� Y.i(P�A� X�fA�ial'of .LYQj�F��aory; i.�!� &Bmmar f�{"B.9�(1)/2�e�2E.; %��ňA�6peAR�gE3bL�derst� ��er,tlA��a J�i�n��8l crossings, asd in the discussion of Sect �e1(E), (1b) above. \medskip \noindent \textbf{1(H) Braid relations:} It's harder to get invariants of�\total space straight out�� monodromy�!-f�D. Seidel showed���DT}I7��not truea1pl�cally;R��F9�!>$infinite o�as!y Du� . S嫕Aj $$B�M4))]� % Diff�"% $$ 2� kernel --�interesňstructu��)p only visiAm� �}.��1�Am�N�y�%,0 imilar pi m!}s���group ac/Evfaithful!�by�5;s� factorIrough�ym_k$J�by E>7(�� actly sup�I eachŭ).� inj!� vityA� establish��de�@e Floer �� logy���%�KhoSei� Such��henomen��4s at least pos)s when �8considers famil�� with-�sV�s}A�a� !}:� xmathcal{X}\stackrel{\phi}{\long&� } B$ for��tI !,a ramified caY!d $\tilde{B. @��a} &�.� �F� B}$ �ae'a%: 2Vǡ�$�!uD�ŭ��h be firs��a sequ�W^ UWI�Z�sA�onb n u%inclu� $&�B to $��$�generic���h��!��~�0J) Long exact�s:} Aa � their rola�&� ,N�A���s alsoŰ risI speci^�#� d` *n �co�. S�V� L_1,L� are�s�-XI� $L\c�\S^n$ibBg Mmau orem!]ٶ LES}���s \begin2} $$HF(-.� ~ L(L_6� L)\otimes,'.$$ \endb� N�%sin� icz :idizEC.gubmani � a Stein ���type;Z!set�g� (no bubblingiB!�GE�b� nvex��my�hp 3los�ͬn� f�� s escap��toG . Ha�, y)�Q�-�%well-� $d; if more��8:�J $c_1=0$ (�insN ?3 mŗ(Z$-graded. *k  (Y� FD},�A� 3)o.pencil!�$K3 surfaceeia Fano�8 �va��D$\{L_j\}$ ``fill''%��af� ��:��clo�VEk j�)�Ab locu�D��2�>�mhitc �� Proof:! global����&� hift}3 ()i,) $HF^*$, so!�$K�}di.�� ��tO iA�h� a�K,K�HF [xed]�Ite�qreI E��=�2� iy4ly many degree��i�H!�==0$. Bu�i@ �U A�Am��y� .� �,B EalR�th5.FFO3}, m�a�� he�tradio%�TY � si reof� at�]bE� �.>�����A bite�:�B1 `` �tte'' Donaldson's quantum categ M� K3 (��!�=[B/Fukayad "W)  wae��motivWby an ol���easiera ult,�fic� � situ#!� curv� Rieman!߉Xn���imi:GMHD}��� �we��fi�tt��nF2 $Y_mZ&0af�6uM I� col_Pf.�]�s (cf. g(2(f) below)�coE�ur�M�t� N� �i�� way�Fow� �0 se a  asF<of� ��bu��compon��$``lex�''B� %�AQano�ZXof�tac�twe��wnea�the0M�las* in %� \a�ion{Knot�� e ad��4quotient} All� materL �isAX?� 5 work�Paul S��w:��l� q! idea1PMikhail Khovanov. Re>c�reQ�eiSmi},M�2KJ�2(a) �4 polynomials:}ŅJoe�Alexana�8$V_K(t), \Delta $�powerful�*��� sk� rele�s^ TheyFLau.s�VH$t^{\pm 1/2}$ deter(Usa���U)=1=� U)$,�I$U�  un-� e��� $] -1}V�+} - t -} + (t./2}-t^{) 0} = 0;$$�) {L =-LFA! F HA(A "�linksMly near#i� cr��wňt!B looka�� ��hd: \[ \xy (6,6)*{}="tl";-r 6,- &b& '{\ar|{\h� \; � } ^"tr"}�Pr";� 4(0,-10)*{L_{+}P $xy \qquad  ���F�-J�����-.� � ��f�-�ll" **\crv{(-1,0)}?(1)*\dir{>!{ "!"!�.V-.�0.�\]I Vm�� � stood geo� , via�&�yclic�( $H_1(\wide� S^3\�$slash K})$�^Lic��X�)XterpreFacerm��3-.5$Seiberg-Wif� , beauti explaiyDgDo:MT}3B�is mys��ou  ltho=it doeNer��resen �� (etic incarn��z%En�� loop bB� solvZ hos�"�� mmedhly after�introdu�M, fam�XbeF�.Exak : (Kauf ) Aknec reduc�lte�ng di_m� aɞexhib�`,minimal numb�lf�\%�y .C3�G. [R o:<�� % remo!�flipp�hal U0.] Before mo; �it� be help�Xto!�hr���G@Y5. sl� } \inv)�fashion.�eqr ,} \label{eq:[}"0aligned} & �4 V_{\plushoriz&v } +% 3v/2% vertF$-1"1?�Y , \\nIminbo��%No2k.���S9�$vtnot� he s%R1b*� arc � a��p lefe I�p 4 coQ�t &� "Q6 Som�arcm�no %�la�"�ceq olE^av�nE� &�ay�E4�non-lo�"chang5or* �F�i� � .&F eX Ded}�. O�!l(!�wo Q�#geW imp #�gin�2W . (!B�� }a�}�$pe�$� e choicV��l� �i�ner p.)r� 2(b)"� վ:} > 0 (circa 1998)� ���B�-- �%� combinato� �|ݏ $Kcr(Kh^{*,*}(K)�� $\Z\�\"� �$ian�L sL  (i) $O0OU_nS ^*((7 )^n)[-n]$��` $U_n7an n-U� un!a (3A�&��con?"��inY$ $(0,*)$);� i) SA -typ�s_:%�Q|-��dZ"emr=e%�:7s#plaE��$of \eqref�D:�K� line} �n�F�� cdoR�.!]i,j}(\!���D) :+ , .:�b5(-v,j-3v-2}(f6R)� �\^|+1�� � �.*� &�  ��9[andrp�#2qZVp5E}(�\�p-v� -3v+!=m�v9+1jFt uad\ Nr �DBb�vr-X l.� >s (iaqA. �Mnqna (ii)��>var"esO�s��:S(frac{1}{q+q�}}\, #_E�< (-1)^i \rk_{\Q}Q��q^j \� �8|_{q=-\sqrt{t}}m NoX6 ɳ*quitea "�,�Kjdo)fig!��� � , raŪtha� two�A+/& s (s� 8b�)h0&riz�&�Ai�:,���6%�).��b�6� 0,1)2l";$"� " � {\rm hor}.Mm �&��*��.�&b� @{-}��>�T #lJ��E n���f�!!�5��&�!�6��!.��A�.�\]* �"���known� be�tri�# tronL in�$n< mD>�,�� principalWe"% q#ik(E,� $to a ``Top�#eIQ(Field�!*, �a#(ort,�blems{ coul-#fit�a�As��ov�#2(c) Iq�e'(l �[ �l�a�(tr).EK�s u� &�( y. We b�"�: (1)�P�)"�$:2 $"�%Y.�&<\Conf_{2n}(\C)$ �E�con��%�+A&un*(ed $2n$-tup� of p= <J+A�ST$pa�el?0�(! w�� d,!�"T(��r*"co!� D 1(B). (2�di.�,(to isotopy)*� *�$ $L\subsett\( Y}_t& s]6S�+%$t�&62. Gi53a)� $\beta$A�%#�3nds"�,TGhec!,�=�.J-t,tZ��1, r(L)Z�Nn!�y&)�*�Nu# �!%,%,i)$� ��L*f/en8I��b�t73�M3,E� boundae�psm� coun�� pseudohol�nc!�cs:?o �=�b"-|2&. 1  &ps 0}(2,1.5) \ps�le[�0color=black, ~# ygray, style=�"1 ,  e�,end=dark>mideS=1,6�&8=330](0,0){1} �$dot(0,.99)-h \rput(-1.1,.5){$\ell^{+}$} 1.2.-}$U7-7D^2!9"}xy�(-5,0);(};/xy� RD \psset{unit=0.5cm"zg1�5�clip}{�custom%�)inone,9�white]{)'bezier%;`(1.5,-0.2)(2.5,1)(2,2.5)\;to } }ff%�B�A �!�%� >� 2�b�{E~.�m ��8,2�2.8,-1)Ns(p)/�AB#Z%B(� Ae5,-2)(-�2F(-Q%u-!v -2, )!�Et2.4,16�M�.9,1.7M�  H 9){$�*Q�-3.`1A�u/2.1a�.20)�Yy� big:  C�on: we'(gnoQ. t"�*�/�):4 As b����(i� of>}re� T#vercom�p ctness"� �����t6)sz �!ta�td. �3��.Ez! spinR#co�ntE� B (��be��=($OcoefficasVxhk-$b�)4so zero Maslov7)�� ambJ space j3S Chern 5�2� �a~7F��*� '. g%�3us\ so fa1 %C ]6.� ofs!�\&w!�RH� �:he�)nF �8co2$�+kA%<7&�:� � we�%!~� d) Markov��. I&� ��'�%yMe21g)ed��``closur�'7/ �� (!I ).:,gk,�8n \ni "���id�0Br� !#d]n cyoffrEabottomI�a:�&nes�h�; shoeA�,3re� e�:ris" �"on-uniqu�; *e� ival-� In)#a�at"X �G�&FD �2� !iso-t.�I��i� njug �� 9[sigma)a �$� A�$ 1sn$ �z�:--� hm���#si�07��eF<!eSIC--az�s�a$1(�=d�x7�<a ae&0positiv\ ne�v�Tlf-�<,A�Lj$II^+I= (-$ stabilis%&s. All�CL dmj� o se��m !ca[lyK , pu^+4 ``upwards'' a��)l�'"? : h�� �s���+ Linkv:� i'�7%r *+{\K3�,8aphics{R3-30.ep�� %SPACE PADDING TO KEEP DIAGRAMS FROM INTERSECTING WORDS�%0,5)*{d�y� Qi�ua �0R��C�Z.� V\]:M�$I$��� ^޴M1^�3�zAg+����\ %ADJUST THIS COORDINATE!�,MAKE THE TWO9�0MORE CENTERED-�V�M2Z�It�!a�85"a�A��:��(��D\id)(L)�f Sl���.e�M �"&<�2 fact���V��fB�ɣthree�A. �E�tur��Br�3��in�.� is occurs~�e)���"�+:} W�-N=D@V9of.S�3s�D(��vof)% charac}%sW&� �8p��"�H�>X, $\chi: � k{sl}_m \��a���Dm-1.9u�= Sonf^0_{m�� � [ alanc�9*�ts9@�1�$ct eigenva�DM trace-fre-ric��U!&�iA�� nR/6Hhe Jacobson-Morozov! �3: Fact:�Ae�.nilpo:4matrix $N^+\in=��h �"%� �cy� |&�$\rho:K2=im$&� ��g"7 $\�#aSHarray}{cc} 0&1\\0&0��  \) *�; rho}�:7}N�&0:}�>�FN�4 : imag^!E $� =+ ����\1N��$�|T4!p + \ker(C+, N^-/!i``�se�''� Q�a��it'� v5_� of.}"]1"3IESorb=5f���%Y/c�at (Q�!=JMAtA;��� easy��abjH2-6� *"FST��{�a�>s�"aa/2,d;'�"st�DN�@$H^0_I�. �Fa&�9K�7�� sc"�%�Tn0�:�_�� pu?t�?� ~ ed*!Źg|<K�5si d2 �5�:)�l l� gram�&u#d!�!\en�9ѥ� A�*�3�d2� 8details �U�6xsay[($-"\/.o�+�&C}) r �GKoa�t-Kiril� D� ��e�/�$a(7w�?�{�,s+2���fb�DT=Gr�:ndieck gD� #a>#EU�|\I�:� lac�m��A� �q�p�C $(A,"MFB-�0&bF]>�J flag��  y $Aa�PJJI+݃�Ty&� {� base�Gng� bytE &wE<���,!5O<.Mq ~1(I;�"�D�+*�LOE�qI�:){�}>>30(�M{�H$}(Y_{t})) �+ @VVV �+\�CkE6$ !>P�DPw�\]z5:��:�s(m+�bly Weyl)�r@�� way,` M s2�aI��Sp�(er correspo*ce}. ATF7}�mU3�8ar richer (perh[e�f$E?�E�..�!�$���=so�T=.�0Deochi�mA �F($(a,b,c,-a)\H-a^2-bc�)�/a� �+co-� na�,� usu /od�d��%oG i�O"=G.*{ �{2� � D%,Jordan block%��+l size|N p $ij3 yA C^{4. �fl� �LL$2 2$- _�$I�A�P%*R-5;��y��_1,\l}) ,A_m �columl $tr(A_1�<=d�es else� ; $A_i!�gi�:!�$ ��0. Explicitly�en#'%]>e�0!�)�! hape�A�&b� p�� } A_1 & I%(A_2 & \v� e  &, I \\ A_m &&(&&& 0� Wa���$A_�Gre $2E�"O-�))o-%17$�LfH Pis $det(\lambda I - A;3+ ^m -� &^ �-�m�e> E�s�O{m,t} = a.�(� cap Q^�8w rlex� varie� of "�3 $2mA�"x Li%+f"puristT� Win� a JM-��=� no "�C$# )� rbit-[r� ?s� I=O-��!"�{Oonven/�$purposes. )�E�u��|�\(�Lŀ�PJ-!)�un�hE�V��@n�%leeA1t�$. th0Ŷ"�NuniI$6Z5iU!d"�5F�F9lgebra�e,5mM��#,F r;e�.�-�-EZ%� 6� �� �3TtD ]m�J c��"�j=B�pre2�!$"elf�D �wor[!� >�BOll~ s> ��bi�Iu a un6 of�Q�&}2 , describ Ij� !z�6Kho:CM}�}p&��&�ir�5�Luonz>�T"bg/Cat�9�d(,Dm+1}{2m \choose m}a�In5;byq�f��e�AAia�� |$L_{\wp} O"YH-@ real.@.c!�i plau!Ltoa%�B9,eh)rN�#jD@e�ate D��j�A$Y��$I�ely(omolo�(R2qUB�A!�!�weak sen�3��F.?Mi�y en(ti%@ R?g�&w8ve"� -Rke�."A��A �h|�)$sc�@'',(� !3``�)saQ��T''M�!�"�K: %J#��5 F�$\mu = (\mu!,2=:7 mu_3� �a �&q2b p�� of��vfG� %�E�h��w\ icU?le�hat{\mus �>�.�m{WNiF S(��_m)�\mu)$E1q�co�z2105i���Q.E6(6o%^s�FM_I , al�K!4:m �� d" 1.=Uy� ope��ighbourh�<�M:S�?�ke��;A�)�$$x^2+yz=0$= Rj a�-�!�c�Y��Y�cPe`vF-in1d%�M�ch9�O i$�5$-m#;�%,1�%uAGenDp2X*V pF>)���^�&�1��bco$)ropic}'!�bZ ���*�Of coUWa}Dj��� t�a.�.|!8s��b'M�*X\~�h) %lkcF�,:} ��&�:l�#�\ $\wpzPM �m!4plane��Ofyqp��m >6�. Bri$�� t"I:n��DPq�paths a�,}���eAng��1J`k5A�.��י�!�[�C2Ii�G1$? �&A8�Kis�. $�9m$ (h�$)A-c� e%T~H!z��$\wp_��H�remark v-&� �2iN ss5:79 lie entir�.^uppn lf-%� , up- a�op�sE��_l� 6�G @%��X�52�s:b>�"ua�d>�,%;+�!cl. CM1-5 �bR-2-��6S-c��w�t)O� ��0 thin�!�W�2�#F�zsJ �B)0 ��A��i�}ul��/?T �TmM em}[I, S.]�r@^*d& *�; � $$Kh_{�}^*(K_{�a2(HF^{*+m+w}(� _+}J� _+}))pYɸ2�$ia7St:^ $m"\Y�sN-nd $wbbe�h���#d�.�� ��^S Z ��"PR.A]��saa�ji�'!�0'le �(ub�ial=R,�=-R$JD�itj� sIk>�5uM��p�PAs� �!I�ver]^i} �.�� C.� . Y��� �!@A4�ZKdfor $�9--A�c8do�3fMpb�L�!�E� !&�[*X.i���)I& (�� Hamiltoni���1�bff�HHcLEw&. 58&=%!b/F"�CB&�/mdM ��=z�r�� �H�4&u liv�{?�]��#H ���%A Y �JL !Zb�A*� co-inci�aj.d 2$-r&Q�ų O�"2�Q. Inde{3�B�(!branch� As�*riminant*u%k��.�$1,2$� p. $2,3$q)�smT_%�n�GV Y:O�8"�r*! \vee)O� -�|�H&��9� �8��!|r��'V�d"�dG�@��*&�H);a|� !d�wn(v� �"nJ c.�"Iu�sndrM8+ ��app��%롼>_. "4Q+i�^ %analys� �e?to.�id�f�iMa[ lexeiPܙ!F �GE�f I!m� $II$��� �R��sVaq-/6�) t�7��!Om��\�JEY!k�"�- � -&n..)upsho Ťv�Hm� fe�i@�&��u=d�ma.%q@enc{c�)uic�Qpf�lea�h�y Jc�%F9@J�T�lt. *�<\B�j2(iV�\ reQated:}Sa few�_s��DU trefoi�a�i� A \;&�$]?M g!�`!{�XW%`� answ;AWE��Bn:�.. Ev�'%�se ��~m!�7�@surpri!��.umetho�/y"a,/&�ly al�8�an,��ui�M" "��!��i&' CUeR* !Q^*�oHE@_{i-j=*}Kh^{i,j}$s 9 �eva�ce:2I$H B"�!.��'BT<+""SFs ()k!��A���G)�5&� �� �@2l]K6 vertr!u }Bj]Y�T�sh�>1��aa��1m�LES�l��IP�t"�Z��d}*�_L1.l�q� �c"QAt�\sa��A�le&s.�ing��A`aV�ul e$ap9ri�>��h�sui�<.�������S�;in��wHAn2�$L_0,L_1�DS;X�JL}_�UL}%X}=29(�$CZ(X� >$, \omega_Xi - { !�#�?.:?a$&7�b$X_�m�A �i$) by lif"�$L��*ato 7X}$�>|t��n >�5d��)��GAH����`C- C, L_0"��UL_16dHF(%:�r%tau516 �m&N"� &�b � $CI�� ��_a;���$�($-��XIeme6 %S�U� �`r� </ � k orA�nd A$)3��`. *��.�� su�6Vz nM q�hop�N�< ��to�d5 $�.iL)$>A�U��f�i-A�eI( ���:�ge��h�1��d�(lN� �QQ If� assu!!��xeí[J��nJ�c����ic� ategyi� "�)� pecUo"zIE$E^2=��C!� r:'a�E^�2 fty}(�U<model�s=A�]�BC's [�OzSz:DBC� AI�?&m ��ach�%Qe"�Y�� k $LB$$he Heegaar.UK-q� d:�mM(L)$)N�c%�per%Biv)� �o"�as��I &� ihig�%� e�z>�;�X�b og Dt,"%�:���`!}rasmr tA):z�oftoon-� . A�tinr ircl�S�\%w��ch� � lex�>�eK�\9r_ Big"-LawrE�-�ic�ti n>OM<BigLaw}�re�Oly ��x Manolescu!NIr Man}~� j) CNA6� �'%�!��8!� �.�m�7f�Ci- TQFT�d4b( a lot h�:�# litt�"�."�dEor�"Bi�'R^4E�A K pie� �(faly"n5*L =p rk/� $~1(G);~(2)�S &�)Y}&$I ( �o\�&T wo pV8s. By�At0"�\C\P^2w,$\C$-�y+�A*_ ��m� �>� �k%B� eF�vi��- 1(F�1G6�ZA�>�A�s �annulu�N�wh�"5�i�A��%6Vwo#E;/q� NowED.DU�&| @Q ��" &�oIujsc.8j3a+ m��r1d konr;�hB nge:m)l"���/-�s�If>Yo�5Ce: comm&<KE�5i�y � thebibli�0phy}{10}`ibitem{Aur:TJ} Auroux, D.M�*��s��pro�#<�&�d� "�Ps}, Turkish J. Math. _-0bf{25}, (2001�"�DK.�,&�# , S.jKatza�>, L�x"Y��c�P^-in�! vail J at m�$DG/0410332 �42� MP} =$, Munoz, V � Presas, F�]T*I��S�07126N�KO6'6!�Orlov=�M6Ow6  w�!Af=�� ��n�QAcRyve��v~^A� 4281N�ur�c=`�Smith, I5Te��-�,����q �^�CIME Lec� B)h102N�� ��E��Aq���*���>�},�Ky \& �Oy��gZ=su4m2.�._ " '�K1$ N�f�OD �*A !�Nof Cass;>0nd Meng-Taube!ȡ�. �. Mon>�2� 1999:�PVCFH^�P&}e,*D 7 )�6K},�{``�+8ematics: FrontiYt�P&� s�& Amer�\ Soc.Ij06�nEj>=O�o&�Hc�?�9N,]v4-"96���+��4%@ 2003.�FO3} rj, KiOs,Mh�S� ��-8%�y�anoma�Zd obszion},���1tJ?g"� , MQPA,) ific"�!J� Duke��J��101A1206� +NuV� 9"�rA�$(n,n)$ "�2��.,}, Commun. C�;mpQ1�6 �2�K�v6�E!�h, P1Qui�},-��/��.:�J.B��1� 2��c0 Lickorish, RA3&Kb�,!�oraA1؂997.o. "F , CUN"�< slic�)Hilbert �)9�Jn`�^11015I2t,McDS} McDuffŪ!ASalamon�kI:�}utmg%�Pnd ed.), Oxford Univ.�ss }2j"� �%��zabo, Z1O? :�"� �>A6v!�n$GT/0309170 �2Pre} F`� t�I�o )ac�t}, AsfBy Q�2oRan} Ran�A�$> of�w��n2dFa10037 �2�U "LT,�)��9h!���E�-u~z!b40213N�@Seg:CFT} Segal, G1�DO` �co�[J0W�rѨ�5e��Q��physicş,(U.Tillmann,M�CUPJ v�a��ide.r�2eB"}y .7 }, Jour. w8.�ܱ5ŋ>��LESJAN��|B �xFDJw�Պ��irp 6� oceee"v ICM, Beijq2002, H�Ed�)�2�VMJ�V,.T*� �mEu�+a\1ng܁ofj �(, Barcelona�40, Birkh\"ause��> �DE�>� a� four2�i&�~$��30901 2�}K3JH*W1mJY a�qu3�z&�10414)�B�b'J� Unpu�~ $J�7p2>�O>� Aq"��]�"�:8��405089 �2  �2��I16 epar� >S�Se�6��� Thom�"B Brai:�AE deri�i'3aq �#nt she�-},b� 8!zB��t >m�<ic ��!�!o�ybo�l�$ }, QAN[B���NySa9:PSerre�  du��� ps>iV�ߚ� Sm-�s�B�*Tsurge%k|�"@"�Cb=7-l2'Ush} Ush�I"� X#Gromov]��!h" -� 0)d^w �W^��Q1�4�1\�T>o  docu!} .�\s3Wp[amscd,amssymb,verbatim,12pt,�(rams]{amsarB\page:{\ne$setlength{� width}{16fV:h� }{22addto=odd�ma6 }{-15mm} 6$�>�%top6E �5ewQ$and{\tr}{\�#�h(name{tr}} \.$Exp>%:&coh>&:&ssl}{"P?:cFBh>$CH>fCH$re.�mod>':pCom>&B&neF'ne>(TBKTBKgB$gB$intdeg>r :�ToBQF&s>P Tors>(un!6,} :Vdiv>G:nOO}{{\O>SyBq:Atg�t+�:pB�pB> Vect>�:LiBiBlim�>O .lim>S*7>- :} cokeB� :*DD1MD>NNN>III>Gaa�2�:wBBAB>��>� :GSB(SB�!>NBRB�RB�SL>LSLJ.G�Bbb G>mmuT9:��G>^>(gEgȋB$$hra}{\hook�&a�N:?lan}{gl>r��BCF:\G�a�B�CC�C>6TTT>MMM6\dl{^{/-6{\�>G:�FouB$:(supB�:( Spec>x>(inB~B�SBxSp&.mMaB4:tHS!GE3��.BProB�B�PEA�P.Dhlf�w�?2>Ta�Theta:�s��slW:c�*�m:PiBd:&I�i2�:&ga+ gamm>}d� delB�V{ilo� .W5bigwedgaX61J�:�iB�FD!�aGB�loBdu~FNin{�G<{mZ new�em{thm}W o�5 $]� #�)}[thm]A* 1.$ eF(-&��zlS6VW;6cor K"�� !environy {�{\v�{3mm}\. {\bf R� k.ی%FHdefA�$:IÆMrem��M*�+�s�Kexr�E{J�H:�:� I��j�BKer�hV�") P�A1� {\it Y�-�(i�2�id>$Lia�2%!w*� o�&ve� .wAV�IB�IB�Alb> :�rk>%rkB$��2�6XAA�A>;FFF>HHF��`B�JJ6J>QVVV>S�{QS>LL6BD O!fO -:5dba�-�{\�0al>\HF| :NExB>>&FO:&ReaT2v:&JaB�Bl!� alph!6�A[�i:Y �J2DA�D-:2ld�K:V\tJ�� B� R!�R�.LZZ>QQ>L�Lambd>�GGJ��2}B w!�"6�:�ook[:!|>�:(alB� :&su!�sY0:e��qed.M:#bs!3bf BLbz z>4Q'{6:\HoB� :&ReB� :&vH��� J/ Au%qpe&Bsp� 2)�(title{Koszu:�&�m)GS�'S]6v')���(uthor{A. PoP� chuk�?�uks{0)r>$!<arP�NSF�7nt~ ?���Oa� act}(]�pl�f6rio\o.�1ege�Uco�Q F)!-&IJ o6�nP^neHbe�Vzul. Lik�/ well6wn�ertdu�/Kempf ^+K}_B~ �Y�;nc�� on:L;!{%\I� ��set�Bn56).uffgk~( ["�-�N ert3p�.)r��� p?�X v>5� $%+65� \makeE1 � i \�,{\sc .�!�me.��Vpa�BA:n w�mp�?�swh$+:/9�%( � �+��-�) }%W, ,h ^#E0. R��95 3*e#+�C(re�ne& AK!5xEk�:�YNOt%� 0b� one�i�s jC�cw.o�xeeMfPr�4c{�BF GS PP}�,It![]�6z ��'deaLS1�m�ly �s al D#y�3sub)�is-6 if�:am1�9a�9(�+u[5 B&ҟx0! �1�/ Oi�quc.o;=�%|V 1�o��/aE��4ni�zeI[ . Th�u4F2�B�.E� �igu!�!��Xe0 �Ie62 statA3at;N ��^ 2n.�G)�l�= )�Rm5�.+uaYska�p{�?��=;& �E�Ra�olv��� ��our�. �'+0em�a- optiAF s)�%� kindE)se.��65/on: ifj^!>�"in��� $!Jele���c��L�cessar0)� (yqCRV},�..~43� an}7�;!�ae. 8A`9f���!�4�LOur ��<��\ X.���:i�rc; n�*�9&��m0�5Let $Sy��v�h��NuW�+<��$\LL(S�6he latt�xa�ll�^�� $S$ .�k.�(!�. ��Z�!%n$��e�,EF�2y!  i�<1���eJ�ȇ main A�6Mr ��V�g�: $\La% �E/!i( $|\La|>1$ ���&�G� hold�G� $(\ast)�\)R$T�cLa.jc$T\neq Sr8�$T'N,'-%0tyset$, $T'�G)MWndŅ,_�WT'=.6�$T\cup >A�i2-Qa�ITP[S`I�,f��Te�si��a�7o�|:%8Z�� iadm>4a.�]st�t}2�TV}�(Wm} *�W��2t �e`�cco���?\��Q:. �@-:,4I��Y ��iz!(��EM��� b�j� by.b@���. c��M�SA� gRus�KH$� y�i"y �!`(��aM/u|�i{}E8}E uEa�N=S_1\sqAIS_2m�$S_m-$ �l�\U�E�ud�J� (S_1)E� S_2= (S_21Y�.�JJ�P ��qd�F�5oA4�ge�&y.�we�c��a�mpo�~�� �� $V$�<evaluE��3 $V\to�S �|_���9ur! .�/�%X$V=2�2��E� � f� ics.at]�_ofV�feUcheck%.m.9�%m�W;)�tech-U(a)a �;�$Z0!| � U�^t seem85 be m�5m�Z8;,v� gra�er� CT2E  ``�E�e!��239u>'�|"�LQ� and � �<A�H� jng&s�]�=9E* :ْ�9&�EL*� d?l&� E��5$ Gr\"obner�his.Px}k a�2>P� �q�:�A8�_+"�IT� Ak��'�The&�organiz�* GIn"�E�ge�¡! � �< � x �!]M6 g|adUDis�ed6!H�5cip�!A! nhed E ce�a2Ek!xm��&�3�D�� Q*` s��v�a�n< app"��M� �4K9 V�!8!eZ��pt�N!;��fi -$ 6l���"� (C�c��}���LS@� p�we�C"(xe-��1$k$. B�i%}��� we m�/$k$�`.� 6'%ala�5�socG[v� &l�P �5gorm $A=�H$_{n\ge 0}ARy�Q$A_0=ke�&6)AcaY ledg��� am�t�SzPavel E!~A� nd E�-Rlazus+�-�|$s. Also, I��n� -d\-r%�i��Dpl+��2y a�>��� zr��e"ɠG�F��YI���q� )�Q��axFni�M�rea�w�Q3O r�dI�eyA�A�{� _f U�?o2�e{ ne�\���\=-� s. Hآ�k �may no�0a�"� a��NSWly!�d (��ee�Un��ith�Yd� !v�Y moduڇ�E` NJP/"2m2}=�"Rw.TL� f 2� $f:A� B�\6S!g�c� &�A�/$f$��es�L�@�l� b����h$A$%$B$�i!�͚%!b5�|.�� Dv*�oa�(!`)� $A$-)l��3�I9eOm ��k!V_3� A(-3) 22 11A,K%� $V_�Lvector��v"M �qJ hom- 1�Ũ$B*2%;"�) R !=%ln!^\ )�� y \Pf .� u�Js%�W�0>uH �B"�% 3,-sp-seq} E^2��=�-_p^B( ,q^A(k,B),k)\��es {p+q}k�eg2 K"�]��!BņA|`)\f$ a��E>�x�~�}ee $q`y-E�ANjiPllows dE_2^{pq}%z�Xp+Z��U�,�K "�KJ�i-)3dB�i�d �]=�ak�]�k�U&.� ����e8硜^� X. .)e9S�M)&�NGcomi!BB� j$ iLTor �M��F�a@� '�Po�3hm.~5)E�$���.� {:� &R>�B�oI\j>i+1$:�A%�ma!�nIN� �my Vu�ev�ho�i� �n^B(k,k^�n�.� ru�� $n��'O!��Lis%��� $n'"���uW!�Ab�BRq� *�� of t�!}��� r5�iNwW $�� nd $%� �u06�9�* =J%G�jp!+/�^$O��E>��K e��� EN�I-n� +W&#pi"�KenNM�N� 2$��00=E^N_{n+N,-N��"�$d_N}{\to} ",0*��>-N,N-1�S�L$ 5 �hb�!�$P_{$, 1Z $n-�E�OQ e� *3o�� ���ynF��EM2� ), ⰵ�)� �,0͛a\�s0��ś�bo.� Nex� serv^i�SrP0E $(�soAi have� "�T�ofCX$BU� $$0\to� {0,1�vB"=�k(�!��k0$$ gir �vo�X�f yт21 KN4R�� J�*{n-1}���to� $$ As5 �fn͸aq*ewlig}� \le ARR zgR�Js9R�Z\n$.�18,j�,k.+� \�wb� ��.8"�� �a ��l.��B $1$ or $2�a�� aLr divisocs��>`O� so, �r�aK}��  $I�A2�I(2�e|V� ,a��!İC�#�s 4~���7(a); #ST�;"s 1.2"I�. ���go�to4`RlN�� U &N �e� EPe6I� >�,���$V�u:�� ( z.,#GB�) ɁI�of�ics*�Ion�1$ P.VW&� #!R%,��Sv�$ $2$-*�}�� +V_2F�.6� <#,R*Cift1$��o�� "s'aAE�O :!�f�X�$2�Na#n "Z�|o��!wa��� 6� ����'Q�6z�n��lsom�J SeA-''=6d.� $I��I�I''�!T ���#n$ $R=k[x_0Brx_n]$!]A��)�lo�,� ''$,!h� E�uR�R/�A' 4A' �6�.�*�*�ibm(i $I=I'\�!�Ix��x H�A#&q� t A'[ A''�M�k)(M=R/(I'+I''r�"o�9��v�af�R� $M%�:� �>l�FE%nb&���V� Jm B� .E  (b. �$A��� A-JV%D�z$'h �  �A'; E�:��i$*� AppjX2��!�]f-/AT�)�c�q�5��� $|S'|=|S| "��Fa%�2�J�)�so d :�Eu���Et�k!*�%�d�,�H'$ �r�>���!e&g*it�]�)o 3EuHyb�$sF�A_{S'"�re ��%mnd%fj �.�U�n6 Ai��#sc� Hd "Z�way*�E Z��ځ}��\JJ��"�'��.Z �� a:Wa.6�Tis� ��uQ! $J�|*�J�& 0$� 9�$J_1,J_2�$22 � J�gJ_1A J/(simeq A/J_2� $W���4% **&a�) emptq�=!-.c)"p*A-N\ %8m4d����lo��rf�?��o/�)F*�SZ�a^ n &�  Pion�s7�Iam�*I!&?��. $A_+�n�kp %�^BB��m.rea7T!�i�O�!� � ies:AX2�PJ�iE�d# �A�.$A�(���� '-fa"���� f) of)�E�U��S2.�A� e�� $A/JB�>�Ma��!<�a � ��G&�A/J&� i'E�$p2��is �.�ÍZ�:n>0 A!�VU�� f $Jƒ��>0i��sU 2jq�� Є��f� ��sm Z%�%> &��-"& �Y  1  �Zdp�OulĜifjH ���J��eitu l��)�"� �� �[Rr31���I+ 2�5we}�Ape -(�'). �d+$.��� . & c8$A �1i+"y � next!�&G#�T*<!�53 n�[��p%U 6E?a,)��%����16��0�y� z�1/e���0-�i�S .H�&�=p�v3qet�0oS$Ѧ �� $J_T%uak �m��*al !�t �S�� A_T$��wiatA� $A_{"1}=k+E�$J2((A_S)_+$. "9!��!�=�v ��!� >�2�-�!�)��6a��9.�#u2�.�~)c�y2�d2�`2,�� $\dim�/�2)=)]a � =\{A |\ N3���EF�6:A:��nd%� e5etB�.1).�.-�a�. ��.] let r# iz�% OO_{�~}(�k�1a;� 2BmG(map $$e_S:V�!�/ k^S$6r5A(��5q'pro(Ie0�? DB� Uq60 �,$.2�A�> *�� V4$T*r "�4� n^""�'�����*m0.�;���BY�28a;�x��{\perp}�FV�s��ngt-aS'.��<���i1�{S,T}9�Tg��^{*� T}$$�0uc�s �R.��4Aq�ځA�tE?%�(b��i���ys�r�r�T��n � i_S)=An��"s�l&$ i�Xdi��A= ATa OO VT�  $T=*A�:K  U7݃�k :L>0QU"2O i3��t%q*172� $TC_1q(EY)�6/7e{ $U=T�47 a>s8am%|j$�25! ..< bV� EYJ�$eAPU�]� �S.(�T } � �SQ� & \rTo{ 6�,}\\ \d %& \\WU�VNT}I��A�o�)�:��e�it��im�}meT'�a*$vu!9�E�E�na� =?� !�(E0$v�x': �TX2M9)���(k~M v� !eT4i'r"�(PrWW�!�A)��lso9-�{*9)K(a)�bc3652�":�N ���La"� bω� e�I�T>�0��5�nd~�V6=S:�re��=�Mv�~w1 e :��7k^TI�B���/*��� � !�)Y�i�;c<�c ��{`.�K2tmai*Y�-U�La&9$Z{S ���gN�2`3,m�2�be%��"I N@7E�p&0bl˖� iz�|$Z  u�A�!�l1����ztiu~V� � $k�V k^S> J.N�#.�b)v])Je %k;J *� io�j"� �$ $(J_T)_1=u� n=6�T� �$02��o d clai���(M��\Y����G9�� �DJ�%�Z��65��kby� J�.��+��B�yv*��j�g $$5J=���+��a��n#V B���e�&��T=J_{� }+A_S v�XD���� ��� J_T/.4: f��f�C�+5�a?he .�ބapAZbannihil1\a0 )FA_S2h$^is� sۅ�F���"�w�F 2i!&2V\� m'}�!V��Y }. F �,EW h�)� � e6>\2�A, maxikD(hg 's &�=���C�=�-.:M�^DE|�� ] ~� I��I�y"� � �&���&� *}�:� �xRB�A��N�. Take"��$p' '�Y"3 $T_1J�C�� aC _1=S�� y \{p\eH�0 6$* d&� J"� T�A�% �Ee}Naz$ b}D�CT')� ��u�g:�DT'$%ATEA$\wt{4O=AKcupGR {ΥaSA� �60D,D �^=ڵ\F�, a�uqui�-#� ��$# B�.EZ�Exe�%��%|�E�1?R�z1bq$. Enl�a��Iif�5e�x��." ���rJ�.�%��$"�-a.�j� B� F�$\{�h.0' �y*��"_S$�'�6 �V)"� �� ��e� ^aIC"gE>}m,3� �WF���7e61.} d"+ynF5�W=/a(m&pCe���.�?y>��"���wp>�� b�=%N. nB�AE_lso�(�A��� � u0�q5aKanyI'�*!��%S'Q!Uy� Name����\La4��$�)i��"$�O~ ".�C� 5&�N�G��eT e�'sIx"� E�Jf.`LaAK 5�$mQ'*�xI'$�C�0*� & ��}�ap S'=t�[�� ��(e۞i�O� �Ɏch��%�%A.&�%J�g(T$�(�NU�Z)�GU�~e! '=T3([B)�7 �t�B(:2u)t ft�!���$t:h��oe@�����E)U"� JB�*"\2.} E# O5'���P�i-�G͜$:e a?t^�.��@dH�/,!T�#cQ��9�IbEof �JR�� s)�e�QT_1, T-% ]' � noM�$UT�K��R%�*�uT}� .�L V!'wt"Q��%��" )�+� ��"s���  �&T�%�  �!C&� a��}` )�&� �*1���&Tarl9 J ne�&E�%rqW9� $$(!& )�= �) "(TC%6< �K =� :� �,.���vKlv%�riR3.7FE�L�� ?s& Q�!�*�/|�=�)2F�FA�"�W?�*s�$ 1+n+n^2/4�)d�Kz"�te3m�*2 2�icqe.X,18ll�L$h(z)=1+nz+(s-n-1)z^/�)��ab�*۰� � �$h(-z[�"`�� �d�. ��!�0��  r&K \<l�Sl"|�Thm 3.1�\CV<(I;��PXT>a� B} H m5ީ�Q�� �� .� E'� qÁ�$m!�n+1��A ��R<"psVs ���/H_�����S�>E�RE� �nA���ap_{j� i}H_j.� $|S_i|=n-m+A!R4� ), � �"��U�i��-�.� $S=�_i 9"s"�AE�Nl �3$@� %�A��2{i_1}P�  Sr}� f�dA>э��!�� s=m(��tf �8v�"�� the �u����j�uHʁ/a &�M.�. 4>�. %�9g�&]con*�X�- *Z thei&R�Wmay� �N*�sM�:#4.�@�c6+OdՋ$3ial�Xg  = reme>u mai�I ~ /�$ most���HA�:sw\���,ness followsp from Theorem \ref{mainthm}.�� following corollary describes a wider class of Koszul configurations. \begin{cor}\label{lessgen-cor} Assume that $S=S_1\sqcup S_2\sqcup\ldots\sqcup S_m$, where every $S_i$ is linearly independent and for eve,Ti\le j$ one has $$S_i\q{i+1} \ld.u`j\in\LL(S).$$ Then $S$ is �. \end{Ҩ Indeed, in this case we can take $\La=\{S�{ |\ 1� � �Fm \}$. For example, let $H, H'$ be a pair of hyperplanes in $\P^n$ and 3%s0ub H\setminusC, $S_3\':\RusubsetE$�,n-1$ points.)=!�anyn? $S_2 �\cap .�<(\span(S_1)\cup $3))$ the s! S=�M8MN S_3$ 9� Note E�:number!7element%4such a 2�!�� 3(n-1)$. .� �$n=4$UwayApget a $32$-dimensional familyyKNJ of $91GT0$\P^4$. Here�anotheғD4-A�F�0i ^J,i� evea`S_f�.^ also)q0uZ$Ill $iE�e��y�a� i� \text{;}i%�IE[ well know�hat� homoA70ous coordinatA�gebra��4IqisI�atic (byBresul�)�L} or by)�2.1E ,G}). MoreoveIo1%m9 withUse!perties EHeA�d2MA�:LHence,~C"% e�a�ent�W, it sufficesakconsi= !� aZ2n1P)cP^a,Mos�2{!; C!�!^e above'M admij partq�to�p�<s ak:� main .2��*nA�8easily checked �I$na�3$�-first� w-  i��tru�68>�4B*~ uA�� $ was found!uLEric Rain. Let $e_1,� , e_5� basi� $k^5[- � ba�e image1w4$!�!�G Tof nonzero vectors $\{i(e_5,x,y,z\} P $$x=e_1-e_3+e_4,\ y +e_2-5\ z6�can�'be9�%�-��� uple.v��vF%��^�%>Z��sCU>Dlessg� wa_$mQ. s1d!� f�( S_1=!l 2,e_3,e_4!c� 21,x-v� 5,y It w�b��e� to inv g�w�itu��$n\ge 5�%W��do��� !%1N�Ds.t. ...? %E.g. if!� spl�O!�6< .�1� S_2I��$, J & �.  %$�41,S_2)$,..., e t$ %$|S_2|=2 [1=S_3=� a��� 3 wF  ay !,Bx #3$� F(% �A��! %A� (idea: starta�cho�a���1$_n��.�% %co�� -2t6K�$(possible:�~, oe $S'8�  %R<$�{ 21$ 2)��-Genlarg \x1$ %if necessary). Problem: whyEdo�js� 1�2))D: !�4$? %Absolutely^E�our� roach. S�[:�P s�N� %��hi�b J }, F I� ne�@al Tainan-Moscow �$Workshop ( , 1994�2�35�$Piont} D.~ kovski � Noncommu�\veM filt_ ona�p��int m�b RA/030123. Pe,Polishchuk. I 1'IXA�N �!,Z� �O )@E�},��� 178 A�,122--16�>�<, L.~Positselski�Q�G ��%T.x Pos}ZI>��0$Bogomolov'� M�\}, Harvard Ph.~D.~thesisn8, availa8 at http://www.%|(uiuc.edu/K-�/026�8r} S.~Priddy, )� �Y��r0Trans. AMS 15e�(70), 39--60]?`ST} B.~Shelton, C.~TingeyMCOn`�*�a newastruc�, of Artin-ScM$er regular: }, J9�241��789--798�endB�  docu } `�\�{ifacmtg���style@} \usepackage[dcu�]{h)�} %:Ptran-l} >P[10pt,twocolumn]{IEEE-} 6cvips]{Cicx2�{makeid:amsA 6*amsfonts���@fu}{{\rm F}\raiseA�.1in}� \�Pptsize p}{\hskip -.08" 3in \ ySfuq�bq�bbfrd..�q}�joutrj.e{-�h %DVP:Lisubt}{i$ {\tt t}$\ >� tsubq }{t 'Z*final+ J,ihwhN!@figwidth}{3.25 in�Dnew�em{@!{W!:U{"/:$lem}{Lemma:[ }{Pro^: defn}{D��� >v )F� assume}{Ap�:](rmk}{Remark>�u7in{eqQ}{i } % MATH����$ %\DeclareM,Operator{\RE�} VIM}{Im^ess}{.�{\eps}{��:HTo}{\longrightarrow:"h��athcal{H6"{\\S>A:A>JJ>MM>WW>XX>dx�dot x>a�\beta:�bfx Rbf{F6fffBTfbbF�atZd:s��z=zF=yyF1� bf{hFw<wFrrFu:��gg><5" athrma�st>$bf��" bf{pF�e qF�p6H B�"�6.B1I 6. B+n!$;� >�{\�-+rm{ &� {\im !ayI}m> psisA�psi}^{\aFMd{{A�&:�pdp]al>BOP  bf{BBH.(%��H}):eK*Kr+Re��L bb{R>tNatur."N>"%leu�b{C>" Fieluvb{F> RPlu���^{+> Polaq�P} �:�Polq� %(E> EssD-B#D>CLo.�L>State�a AT>"Pabs}[1]{\left\vert#1\�� :�set.{+>Vseq(<'>:N norm'\V.} :/ess2 {#1!X���renewe�E{refna��e�  \}ndex % glo�;d"k %\"� R,�Hrunauthor{Ivan TyukuHDenis Efimov, Cees Leeuwe�Rbifrontm0} \title{Adap?R@��,Invariant Se\ w$[Wako-shi].�}IPME]{.�;J�address% Labov��CPerceptual Dynamics, RIKEN Brain Science Institute, 2-1, Hirosawa, W �8, Saitama, Japa�  �C�kMecha Enginee`, :�Controlum� System�@. O., Bolshoy 61�8nt-Petersburg, )�IA)�(abstract} A framework�a1�1�i5�s/*is � osed. R�&the tar�d-\ (2;)�� ensu!byw@te feedback while ��pa�(tric uncert-i�!s�v##by adI%al.Aalgorit)$We show&Ma�!iently .�!wnon"%y it t�ble�14l�eer%s/ traeor� he desi�8non-equilibrium-� out rA �#0ledge or exis;�,a specific s!4t Lyapunov fun� �,9��- keyword} � �s,B�1�*-i�ce,9V s in� T form�`24 )%5)%\2ion{IA�d�} Whe(+�or��s sough�( �a: @ y A(�A�usual%�at�! teri�stabilizE{A�4of an !�1�or!�&, given referk$( signal. %I�^.on+ �method:B�s �&�#A0%mZ$eff� �&o�AHg%Desp!}�)�# e7dig�very-�% understoo* % 0ly ac�-h�*t� ure,r�%s(a&d) %issu.%�.��Among�m%�>��) %Q\ �Dasymptotic behavio�-�9�eZ�0��p�!Mdirect�m�/ 8%�F[ %identa@ "of B_�"V,%�intrigu��(and %challe��g�%% phys�^ e����1.re,0 years, motiv5by�.�%<n� sV ces, slwly dife t de� camG �surface�rstead�- forcaLa-n!� an arbitr�;2�ne shP)m�q� ��o�%r�Nt ch satisf�--� goa%�E��2t�(=s� s�q�sZ  by gX e%� Y� orts�ATKolesn,Fradkov2003}. O��� .`,��i �&or���emK paper f Ott_1990}  ��nd!a, �n al impact� exci[4p7 �$s1� � Tziperman`7}.�.�wa+� �� simie  s, hi1i�k%%extAum19iA�atA�I� ��A must7 %Y�jis���+�����c�_�� se branch�1�1��1y3.E&lways8,ow explicit �+�Ͱs� ��f�� �Nauc�sA�1a�v%�0our�($rent study1Z�.?2Q� ribuA?�F�- p�-21. *,]1aime8��ul�!QV?&�� ayu�um"u ���*M9 be &O�[� flow. I# so@A�s 2A�like bednese��2�and/or� e��hi /I�8Vorotnikov}. No���_-h9�)�� �6$d a-priori�orx6o escap�� burde%�detec�. SA ,9s�$su+ �� s� ��+to derN%�E *[  a�cap2 of s�* 1u2/:�9�set�� �dod1we emplor i $ eveloped,*� ive "�r fG"�r, �t_fin_A� sA&T�ks2<�Rim�ed per6a��:�handl�&b"�~ �*?y��_9�Cmmw3 :aspp(2ato h %�q?6T jA�m�  (vir�%<>�)�� real8%�+e] by meanuembed( echniquRa`� �ECCŁ,ALCOSP 4,F�G�morgani�a(/�Ds:aS� on 2A+!� ide ��no �v !�B�e��3�� ains %�; � �~$/7��em:%Q ive_U�-�proof)�%�4>��!%!f equ��C�s. Each?  t�� �/Az�/�Mvs �,. SW ��:part_1}�NsETgU�U2-s, J,;J2}�!�s auxili�M��4is=��UH,�B^3}�*%�%5%�argJ-9�!s9�4! clud)+ %���� Wa-ARwill u� h�HAxi�MW: �  $ #(t,_0,t_0)$��ndA�Ɇ� � maps 4_06Cgn}9,t\z_+�=to _�D Fu�$ $\nu: R_+��$ R$�sai0be��w$L:7 iff  �(\nu)=\int_0^{\infty}\nu^2(\tau)d< $�y@e value $\sqrt{L_ C}B�^$ �A{�(�B�{+}:� �W=$L_ }�� �$ ��jun�q� l��� � b>mEf_ !x�V���] (or2ply#�=!�correspo%R!�L1 W '�%n)X. %�@�9A 2  %I/�z!�ceO at_tiv1eM�_bEGd %O�}�LbL#E�# $S-� )��,e(t (forward-)&� ��s!?]�E�iffM]F��S�I �GM�e� $t>t>�%2�A��%&$AJ� %�58ng0>�4some neighborh�$U� %$A$b��U�,E$�M 0m?I�\in %U$%�53.� A$A�$t��7. %� %�*��cu.�w�&CDy�"b"I�s:�>"�-\la�O _af4}&�@} \do� & �$+G_u (\phie�)*0vec+\bfu), \\ <t�2 &=S(i�(ADA\T.-Б_d}�!� 7� wh��!af:I�{n2 n�K�n%{m\ti~d}yK� & !�� �� �7.�� -�.�)M, \\Y  {0}^Y�sigma)d  o 0,�*lim_{,}�� }S tL s2L|f�QV �C�0-* 6x��Z� }�j��XF�� y�r? ͼ� 4(t)E�� \R�%N�A��.6�N�,��2\ ^a�n��� ^�^��� /�ZEQ�Mi��)�A q4..�I��EP��Z��0j beVi�it�+n��_�2"�n�$�� FD $�0A _0(t-�]�i�a 6*C^{1}$~|�j1.t2=+2��v�A�L_2I� �3b�1})#�{� Qg$ g"�'.�6� Ջ��f}B�"�  quQo%F�� A�w�)�1t#-.3�g� <� &j DDm}(t)$�(I6)����# 6�e�bfu�M,�C� 2,�D�!�%D)�\x�� HN6 1Aa\�k� -esAC �6E(8/- � %s ��]��a � V�"�M�Re�Ws}=�B�!�2�wo-p ""Vh*!iX!��H!�F�i�1��z�J yet� N<a�%�AI1|��$�0b)�k7�Ix<2nX�Uow��hod)a��!sR(�.�#8bv� asVb D�!V of��R�)N3to $t$�K�%�/can�5 "�%, 7Y�N���.$. F"�`. 1N�G,�+�A�\svB� *�!a ("0a�6fE~�%�lo �2d2� ! �Sut�"� ~3H'r� ��"�$,!�s,)l�!5�neiX y!$�#yJ-, n�{- they�F!�8�0u �-V" ��B� ��(i.e.�#Es�\2achie6C" goala�invokie)�&� in �Q! } ^9#F�! (VU!o=~mJ)a["� � inc>d�� �N<"�3�,.�1�� %XFd.�� i4`6"�(>Ial"(�eE�� �'.��i� }. H�-w�-�$=# tN=#E�(earlier pub�_ �r4�1WOavo�!��(��5F�% sche0ah�!� wellk+��\��,t�-in�Qu�]� � m(>�1#s� j2#���f%_�gral}; wP3�G! f>} ���NC_aux})� ��7&&z B���}--�� 2� 6 .��k� �P�I"�$�-�.� kappz>�"�"� m$k]�@|~:�u\|6|.k|)�n6�>�#� q1�%dn_ext_g*%@� k�}&B {QM.� ,\M)� 00nuR0e [&k f#�B� � z�c��"R &�h�N& �"E-�( �):* (t)$�N� ^Lfifo_lin�_�B+1P6�(&=(H^{-1}\P[% )a�+:)_I��+&=(I $ > +1)(.= )S9�6�}_I&=�6)- �� .x}{� _}:ff �- & V�\bf*�fr�@ ��yP& eR: 1)N� �%(t9"�$ 2)6� �E!��v�1�uR�F dft]3)�.��per�h_5#c�4�)J >� _�&61a ��%U�xq;�#��"7 ����������.�i�.���X� n!O��B� type._�),A���V�V�) �y� nextI "+I�* )�K"�*we�F� *_ �"1!&� �:�.z�*"$s�� $��(� n8 �" ��M:7-}, F2- In=)�=3}!combin� s�� a�g�� lete�As.H� )k {Des� of V� A�1A",q�C1�"%�i� �jIfV�:E�p . Th� eIF0sj %� * �wR��#_ Y� ������#.�&k#-:��(+ \\ & G_u*�#2o&�#,iq���� ��'�Hbf�Wvec� _.�=� 5 e 1J�^"�vf$&m(t)�Vѣ}�)\\ "6_}&=J 6)+cN B� \'$s�(B#���% �e�W_0&=&\|H,\|^{2}, \non�Ss6�&j� a  C^1n8���T[V.�� ]��lU:���~ �~ R�.�A�tɣ F.� leE%�a�1v"� �g�B"F!Gw/�2n��&V �J�bV � [�z�n | &�%�6�!iy&� B�y�q\>G)-u0��'�61 � L|;*��z�� }.� 6�E�0 x- � r�$���b�.�  4I ��6 o)�*��G�&3),&^A"1 A��"=$),M@%� R� ,�>"Y E�a�v,$\delta, T>0.�#$�t}^{t+T}2m�1��%� � � W I_A!|n&� yN� &� @!X&1M�veR �/on�<} fast �K f>Y� :7O.�?u��M5�s� !�2)eY.&@%�"'F�&1�"V_m)}��>& ,t)=\|u>���_{H}+��=M>.)^T H j! G,1;+ $[(�M1}{2}Et"�3>�-�+1���� ��4 4E& 0$. Accor�7�%�*� &� :e�6Z&2[�$mpl(a�n��(�%Bp.%�; fore5� $V_)��?���FU�rn� > ?1V}=*�6C';_ ��9&=&j�!jH(.�(-S(:q ))+ �# ^T \]n���- & &Hj- 2>A(j3��=veM)�( Jus  -�m)v� �|]E + I�& A[|^2}{4})> =~i�s+�"^T)B}j� - 2 9� vec}!� LBa \|jO^T5�!�1� +0.5==!'� &�)�7 $S(<7ū��tinuousren,�l� Hadamard ��0an wri�}e��P Ye>vecN�$����z&I$�81Mp�+,bfz(\lambda)K.}d nM .6=� >A~:' 1- �9Sv9%$Mean Value2 w�Sg?6�����F�'N�')���1veFwM!G3$ �'6 [0,1]��e last&� lead���*x"�K_VdotBP = ~S(5n=�1> U$')}^T H+H �72� �xl & & :�� - 2 Z���i�����&-�s2s.a && FOu 0>UI"�/�E��>)�)"�!� $j�A�"�$. T�ItoWQ D&/ *� n%/ "� �+�V� �tD#B3 M� 2 3a��s� �co�> �2#CN�"nB H e ,:yQ � � t�R1[Y#Ae�E &< 4 2@���Dt3)N  $V9�J s �EincbJ�� �l9�=w��M"- ��r���A( �����m5�J� RM$ �n"�>�wsX=u�,So�G�'%�e facM� �._%@sJT,6$ Ƴi7 �yB2IQ$2="M�$)�� >M`Z:*uY5 in]S#a MSCJx %"�4psi>& �a��-}� �}\*� +�� &H+.�x&� % jW*`4LF tv�)a�2=&�z�ٿ^td-6��" � ����� v��P&�-++� =;�Q2q��>%.�,�lAq!bV�eHaaOe�A: �A2jL-l� �v6B��.~�.`n@��j b$���  re% �0J�)2 u(uff("�,�2v.2+\mMC�/ !�J�,&) *`0^�ɵ $\=Nso>0�3&�1>2�\ \�7��n$.����Y. �gr��"��dV_!# Vm3=Z�0�0}e� 2�0� %T 1}{4 �q{��$ } \m"RE SEQ�-� J�*�/f�5�U �L2bB&.&�*� psi$�)�K� uDs-OJr>Q.��psio Nl2��psi�%II[��.Dmu�.G"�  -MT2�[ [= -)���phV  ( �0�2} �)^� \�Md1% !� } B6QN�\qI�s Ply] Uu>�7�� Q��3����1�Vm �T� B*"N� �&�of*� e|"%A� (a�U &.=. ""6�"nQ�5Wm�� _EsR�\tilde�d:�@J��$&� ��;}E�F�zB�B��~50*�:�N�&�-� H�%R�>R�F���V�|V :O&$>H :<��as��I�,)6�:�E4scÒ7 �+J@ >�U. Sol"�R�~>a� bE"d�2��2m $JT�e^��t& Ng vec'_u}}�,$ $e^{M}M"t*AI� DA�1�^T66e}$I4CB�9g=&@ �9� �:BmD&'Np\innI�iM5 &t+����+;V�@�K!��;�@�L !K1D9�ag:�b��9 � e2�s�F $D_0>.9% $\|Rb�&�@Q�+ D_0$n �@$�F ]%[>r hand,A�//T�hU�/$teger $ n 2�8 $t=n T +r, \ r=_+ < TU=!lɱ���Q��s: $ �:�*�>� U���� Čq D_0 2t* I_d n (2$� * }{T}.t + I16� )��EV >��|6�:|V) !�6�J� �RK_0)\|{>�*3j3��n֍ �MR{Eo0 (�3g�7!� exteǔ)�TpCQ�%2�H[0 &� &*�AF>�H�'by6�9"�21lo�3Lipshitzhi_� .�? ��%def>� %R%�$y>n< �;!�� m.<#=A=\� ( F PC{lll} Fy_{1,1�.),��� � {1,d �$F0: lF/ umvumuRC� �R#0)*c$9'1���i��,�&nk[NM�$�;>1.^)&1F�-�&*'(�/���).�AJzAj0s6#%M�e�:uf� �� u� +B�{7!cq�,inmf!a�2>^� \|.F?(S)�n ��bf�:*�|&� ��x%n;)v&nmimx2�K ;T�JE]���.:x9�(:�F�J���n���.)�&z 6 �2 "�tM�}�R)+�)0u + N�%5�$**Aw�2d"�M�2hS( "�("�1?� 2` ,&Y�UN�$&=&1+\sum_w�{mA�[_,](1+��%)B�s"=J�*&C!x'�Z�u\|��&"& ��Ie����dyUi&�$$;B'� z�2�A~.�7Ct�FŃ :�2-�> 0$�&%P��B%�O.} To��%_�o�renoughu;c�6�"� QE��oN#xi�[)xi=�|!� �L + R -I�\|%^2.�Io.5O*���be- ten��I���am�x���J:F�6 T�J�a,.e_.�.E+2�! #^TJq2g�  �B�u�IV�� �&-M 6"- v�E�.�*)�7)��r��  �& �o�o2j����e,:-~�i�ez�#͞ :a��<(P#���Qe!�B�] G_u$�@�/-�>�2�\)�:�B*�In&iYcom"2��lof nJ) �'xF�c:rad*un-0�xuLu�oqX(�N *�&l�eAa� $ re�D"?CL6hJ>l*y(�Ց�)�$. Un�2&�%ա=�`%  2�?" is>��K#u�Mrm��j%�Sof!���|^e.�Z:&y �It�^ �_�m D)=0$.�>N*�7gF(A��5��=}H�5:�62a&�7Nn3Vn�ide t(?�g�!�A�>!� �>pGb.o�it�G �Sf��TA�*�fj�2 1�[* )*T*�+ %�b�>�>\��i94%�2S R� '1�+ž2 ɾBN �M \R�&=�B B 1 �e19*N 6 ����� �vz;�*Z��J�"�#�$�E$ gsWkby�$�M �6_cv>lJ�R �66j�Y; �H� }!� "� M� U�#aGno�"�8"�previ���(�)\&g��)=Uh ��F�%����:�:�;�6ing2�1=� �w�E.�F���B7Z�bfxm�"8BU.� B&d�!a��51�:�)3v&�"���6 $-� )r J�Q�6�Y��cCexjl~��:R�<FIz,A�&� F$�c r �:� �/:<2�M6�%S*�$eq�6��6"�)h&+2�{T"�-.�iKf2� �*"wN�#)�e�C n&�,B�"�7�"�>ge� bT]} e/� >�V�(� >9(<E��V�a��B�& ,��b �$�f2��%Y��2:))��iuI)�$�P���A�*>-9-��![ /�?�t5/ Y( t�=YZ &�A�f�Z�*�P�m{J�)qJ e.  �&���)��%>)B6_0�h.�N&�.�vec (^2� C.% es�t�7�'� ��(-)�1x=Z �+b4Oy|?"�fd/� Z=�%� cl s-*�OBTzmb" �K�?�ZJ& �H�Hw\�i6��;=�;=>;= �e��fC  ���z?&1�E 6E b�v t)&=24>�n������P2Q%�V79> -�mpd�)^}K++�{�jY4| u1&= -�0&+ pn�B9J�2 LK%�r?�VN IOUb/v�n"sM��"� i�ui�� _aCd r"?t%ep�  n"I/1:g B&-:�V.�c  immediat�zZ���rR$b�A�x}.� � 6M>,&�� jy� z�)� : $V�5xZy�Bk)�c; �1*�).A" .!}1(tF8+2N��E!�%h�"g &�{,aiV}�ab� �� �(-zy��YD�   $-\�u�(tC �V�a���� � �a �x� LaS��Ra��cFin�y �F #�F � 203 $���C:t� &�> (>+ A�*)> !�V5_i�<&_\/ s <&cp ).,�5` xoe}�Y a:\>� ��9d} \ |�6t:��.�=0\�'Fo�W��*��!tX"#.,=H �bt�4w �z�6F ��G" ��D} �yre�~i�Aa[ �$)�ao$. &�"S& ��e'D�ce� F$ Sh� �6t2H9�e-i_6�L . Q.E.Dޕ&:.}&.+ � �.M)�z��W'< R'�*< E�F$umBNhe7�(& G �1*w� |4en�h&� 6����PU-K "��� (F�E)"� � )�o *�V�:)). F.F%?I>)?"+JZ�L !)��9 OF�>Vj���$ we obJw�y��� %!I`6�"�%�� e-�(\��  O led2b.��J_Gn6�Ur�-� �*{2}), "`�l���7."r: g�V�"zB* i6��JQ?QA�Q S*�/-IF0E.�Q} � )�1���_��Et "S.��}h�u*3)N>[�)� lu.D�XM�&�D� Wƿva|ready�M�s�-� p6�Vu ]q $V=p t�,>�, � �6�! �! �a a 2�*�AB Re TP #e 2J1�Q1f�^{c� la e�*Y�e�*�p�lhA vU/��ew*�f*M r"�� �t�^kadvan.8^�`���wdo��Q[V��6B�"Nj25r�( ,��0 e[. qmד.5�F�6"��( _reg�/Sikm�v��"���*�"d��|&�a�! t"ʆ�L��peal"�xsy*B&��n.[�e��}n  2�� {fancyhdr���f�f� \voff� = -50pt i��� 6.5in hCyt 8.8,opmargin 0.2$oddr; -0_� \ev00�� -iN�� �makeatleR� \@addtoa8$t{figure}{�K/ ef�� �7 ,.\@arabic\c@ }6Lt�cJK^J)#x@kx#1#2#3#4#5#6[#7]#8{\ifnum #2>\c$numdepthV/ ;(vsec{}\else ref���er{#1}\e g,\cs�a�#1 ! .��$.75em }\fi O4@tempskipa #5\�lx  \ifdim " >\z@  �0group #62:\@hangsM�#3 %\@�x� nter�HLpenalty \@M #8\par}%iendg�#1mark � {#7}��3��Z4 {toc}!/by =gB \pro0�\�L\^l9^:�9�!D9�hd{#6-�#3-$! �B��2vF� �! ! 9<$\@xsect{#5ۢ ��a peris�fҗA � �&+�)�sD@f\@ ,a�� \trivl��\ۺ[-z]#sep�s$ #1\ #2.}]�B�(ion{\@start  �h T\z@}{-3.5ex plus -1ex j�, -.2ex}{2.3 ̣al~� \bf}��\pa!�ųmyhea" s�\5empty0a  {\sc!��#gnic jou 9} D�ics %�80),\#Rxx\hfill}/yiFd����%�.d�\��,Minimum Peri:j R��ngles T{ En\\�gru ,Non-Overlappq Circle!&!% sourcD�t��T J,rxiv WHEN %u)�Nj(move date \{} 6�� �ce��!���t�T{Boris D. Lubachevsky Kd�HRonald L. Graham\\ ��lQ@netsЍ.n�|�[gK@ucsdg�}\\ Bell&+���I$ Univ;bt $California�600 M��Avenue�e ,at San Diego_Mu�z, Hill, New J[�y . 4^ La J��,.��1� \set�� th{\d���� }{0.99563rm� \���02:1.>@){}�dyda"��W>�a��l��� x�KA�s �*-�� ��mxof��e� -�u�d� ���o X�of -o}�c1�e�ci�k%��cklUNo �p���o shapeW6�. + mA|Np;�iund, �#ryJB� Tr square-grid or hexaga� "���$ir hybrids&�k�)9��� !�bteݟ$ range $n �5000$,��,�� $n = 7, 13, 17, 21, 22, 26, 31, 37, 38, 41, 43��$4997, 49989, U�E�!-opt%�]�Osy!z� eved��s�1�9ng� s. U�,Oir %it�.in)bbQz6|� W! are �%, �7'Ε ificE�f \" �; those>varA�x�e��,predict. Yet%�s�R���,EN���*A[ial, &&2�2� I�we did �� cipa�vII�)�w�kplo�car��lyM�%�al97&�,+ �~y oV��!OM�A�I?�k(k+1)+1$, $k = 3, 4, 5, 6, 7$, �o ? =EkAgA_4��= 57. Also��:G� -to-X�o�r~)� a��U  nn�� �teD� to 1jv*y}�$_� (Key words}:��k_,�9ga�, gn, u�,m� a��/bf 0�subject�>U�:��ia�52C15,�>ond��,05B40, 90C59G�x����c {2ը� ,{sec:intro} ��*{; � nt} ) �Q"tas�v��inge -�uG�J�wle26���en s:�Q�%�H disk� � qa� Xe��m\� not �)�(� ���A��Ņ� �le N a�+tI�A\��$,I��i!itsM� to E�,�vf bc�/�E�\5 -m� izk � aZllA�ipos�um�M� i%�$�. Denvѻof1�`)%Or�xed�, Ԙ�!u�`M�s, �$�Q�of �/inv�Cg!"z�GL2�3�NO1 .3}; aHreh��� urveݦ�>��GSMC}, ]��  pecht}. W��h�lv5�Il!f5f!��d!8sk�=�-� es s,F area��S5�!dZ.&+�by0E�a]�������c�"R. s�� oMa+.�%,1970, Ruda p�|_>m�� � )$wz�r(#to�0��d }. Hpun�%,um-,�;�2��Ai�m"vaV�5@q ��8m_ &>�saɅ9) /1:7I|�LG}Ł�}�'Y\a�u�zto��"M . �v� pswitcha/<%Q to �i���Y,��le keeQ')~6�;-e.g repor*�esx�8�wE ���q �ucedA�AEf���um-U� �/�pr<us�3imLG}2N|O2�. Ex���gh'M�themselV.{ 5verenti� �%���seV FO e�s tur�v�~ be v�Ȥ� !qa]�i�Żse;eLycasA�r $n� oumE ��X �Ie. wa�+� � , �"$��a� ��wo"s. On ��c��0�oc�c� %\�X �D��m�b��H % 2��tha_�c#%�:gu �%.pa�Ab�8UZ c�_r��i��� $ m�>; sB649 "U�;%�al/ a���atEVYa� % �F�Y�re?1� �e�aj���j�A�N-V� $1�J��xI�9�M� s�� sup@�c �E�y<� ppea� � ��H ���%A @���i��d|!��!�>�6\en.5&r��#܈A���� @ � @ , V� !���jQ�e�! Apm�.Omo.� �� type �x�H�X9]e��/A2 �KŤ�L!^��d-�2E�� *1�Y�=z�W h!�ns%`7M. ButaA�e �!��%��"ep�yal!��%�5 �%�a��w����is�~lex!�/o�s$5 �2y���(.\footnote{��now r�~Kat��ex �s m� � �1�Q%a�aE�A� . SeQ� n !��!~�� f+nɯa!>amp�T} A6�جp3�w���Ysg �,j&8�-� iU��\ �-C�4F , � $��� quit�h� a!* �!��W�Q62:�V x>.��� �F�n =*��A�R^B�$57$. }-6�E!� er tж�Be�Ɗ�BW7K91,�!��b!+QG.�, a�w�݁�4�h%�o�ly %E!%b�;�u�c� a�!}i2 � beca��!�&k /� urceY�ea+A%sa�A grow�� rapid"�"n���x � s�un<9� I~�coG� o�e��i�n�$a�^$ka�M��u:�2v�Ieq��B7���] &O� �_gk�a�(��a on. L-��Mn��!er�tu%Av*��K su�ie*�$n$O�*��m�!�Ub1n^.��%act�wANa�'(re ,<lD��a6)M  b�!�a�H�gC%�)��%.oc ZqTo�o%��.� �& s�A�pn8 �=I&�t�Bqu���:� e�g6@!�A��NzDYc$sC� Go�&��\ W/��ʵ"��� ``�actor''�Aq] N5 A�0@e�*��p� O %*(jos ��A�2��j1B0&|� %<_'-Do 4g�!� �6"%�Q�is�%��� !� ;��&B��)s�Gu�)+ee�&�; s, 2� �#"�A�usM�$ rADG��!A��q#n���6��$n > 0$<, 5�72�t $R_np6:2by 6 $"ger�K\ $~~~~w'B�a�v�RY� �; row, �Z7hB7row���d=a*"���� �.M_{-�P�a�� $h$D��^lIami� $w-15);%k'(t $h - h_-$ >2866�x�sR�!v( ��ş� *�! !`.Fs_-k�=s$28d��2�-1$2l� ach;q�I!q$s - b A2<^�v�"�*Pof ``mono-vacancies''�hol�Z\\�*IEa�st�q-ne�Cnd��}�$3�1Q:�):\$we,!�+ s s_-� !� < s + A�$h \ne 1mMv% \mB{ w,hE \} -!\\I!�is�h = 2k�t]$E9�tP��H�;" =a��h_ k$EKif]odd\ev^��r` m = O.�Fi�=t"3 !�q�2S�J"�T}UH�t@�1 (%4)iC EO$ - v = n .>.6P��(�)\i�x��s*[8<=3.45in]{class.pL`c�� on{AA�K�qQN�� =29U�; �j $w = 5IC %��K$s!�s���w[$� 3$, "��29 = w6%{-AQ v$. 5@ fig:�!��(A ``gbl� '' E�  how�F{)�4L . A�u�8s���� ti46-t��($��$i�n$q7�v$)�ɨ.`{Cet�ց�y�� Pach��� )�r u��io�p�,s �U�� A�l՗.�'�> � }:ŏ2� "1 I�"Y4%�!�1$;a6-``2 .���40I E; �/a�xbe1^i� hav��7A3MIRl4Nlg2V06N0ei(�U�s�%-�J��3Vk9Nk�Z011f284AI���i^Zx1RyAw��n64V�15N�lB�,)]^�R(�U��JA�N�7R�$a$Y�:�R($b1%�:6U�R�$c?N:�1b�17a26��5m),�x ^J/2� 6 = 6!W ?%m ?.�>#200��1G[1\8R�2i9� ="�. Giv�Z��!>| ��E� mmon�Su����sD��H" $H?T� $WͲ$P$�^N����� ^ o} %H/r �+ ( 1E �A( [ 1 ) \�� 3 3(-s B�_\{�.{� y}{lF�_2 +FS j�\mg�O  }�( 606 >>� >q_�. �U\9#F�^)%�} W1'w��1�>�� E0' �^�>=� \& \A��P� ���Ex} PMW + H )> .2���  $P/r�aB q �% $ x + yQ] $X�Sa2b � $x; $y$RobBQ Ee�$w,h, )^s�H Some~Bs�s#�!�*ٮ�)��B�e�� �1v$�'ma"� h���� D &� }��he[)5 $v$} ,selected. Si�H�)A:%���iJ 3 �ge&�s��ri!���iT"e treas\hem�|�!�. An b�rt�fac�B��H ���r s �#,]l�"� ~~N�*V�G i�#I�. 2�� g* ���0s����)qF�sI� %)����*� at]li!�%yum �a>. B��� � *" nQfiRx+y�� {3}$T9u; };,$xris%!�qhE{ژ#���ͦA�� ��� exa]*-reader0*�b�m'�a.!< clair,&4:�#"909�p��ٴglobalum�Q�!��V��l!�InE�@#�, some confi��gurations which are clearly non-optimal, for example, those with $v > 0$. The usefulness of the given definition of the sets $R_n$ should become apparent when we compare below the restricted sear�,lgorithm outGs �t� �L ``compactor'' simul� > . �b*�Lworks as follow (see also \cite{PAS}). It begins by generating a random startconfi1� w%R0n$ circles ly&dinside a (large) rectangle2out 1- 8( overlaps. �stRo8is feasible butTusually rather sparse.En !�!B8uter imitates a:.� each �)|� press�against W �, so tha2E�be38forced towards fo�untilK4y ``jam.'' Pos � ^5rboundary%�licts A�$resolved u �.+4of hard collise8so �no5w or ]-penetae ng �(s occur dur!Yprocess.I�]�axa p!�cular AXis repeated many times,E$ different=�%`�Un s. Ii�,final perime!�4value in a runmsmaller!�n �,record achie!+,thus far, it�laces�cur� 2. EventIeiATis�,0 (0 stops improv!$ up t!ie level!�a!Dacy aa�ed byBdouA� prec%�) M�Q�. a�resultd packnow be�G,a candidate !���0 is-9of!�-�ma!HdvantageBbavs.-`s�� search!�Eg%5e]"$ no assump��(ma�-b�mF�patterne�m igH``free to choose'' A^I!2� as long� i�;exmed.''�vis �-LtA�rice:�]�A�, needed in m!� ple �mpts toQm a good9�2�>+ is typic��4several orders!� magnitude�M��.�o samaEm�$to deliver%�minimum!�set $��Q�rB�e� dure. %Fo�[8it may take one�K(two secondsu b0a fracE of a 54 find��u� Q�of 15UmMQ~n�({15}$ and .� days�{thousa��tt5�produce�%FanswerfY. \se�{Re�s: reg��vsemi-:��Fs}\label{sec:regasem} \hspace*{\parindent} Table \ref{tab:1t62} lists a1-E �nequal1A��#3�! st f�T9] �5ũJm�4range $1 \le n�62$, except $n = 13, 21, 31, 43$,%0$57$. A somew�(arbitr���p ;62$ wasE��QE�bv- performed.�� only$a few isolŁ�/s{>{ sin1�&d \slows down significantly�=���. Oik��hand, �B�9�I�n$ weraEkd M�j|}-�� 5000��\b� {tA(}4center} \fbox{tabA� }{r| r2 0} $n$&$w$&$hH_{-}$&$s$&$\delta$&�" "\ \\ \hline 1 & 1 & 0   & *22 & 5  0 �_2$D� & *4X6 & 7 h2F \\I2� c!B� 23 ��*<� & 42:� 0: �3�-�)& 24 ��"*��>� 8 &  6` �4� & c��!&��*4:!��09�31�5i�!� gA�K&G� 4>� FB�6�N?:�� 4>B�9r%�*7��-m�_1$%�!�CC&��>!)nF 8J��&%�&G�K��9m�!:J�9� &%9/a&G�1,��5X! FZ&10�!!m52� "G}!�&� *52!!�d]�q&1�B_12�3�! � �� 5�:�`E��M�c & 3G�K&"��2: 6��1��-'_)6�! ��%�!��> ��:��6%! �!"̢ >A� \� ��:)�_��}�G��*5:! >��U��2� ! �!&�� 5:���! *1�2��!m}C2$ &**3CK!0"1�`5�J!�pF4��1�:�� & *3GZ�3�� 5�:�h! 1�B��A )!�G:���6!��hY��� ��%4 7�14��� 6P�!d`�2���co ��C"�W��*62>!P \:. \end"�  } \ca2{P�� � -sW *� =^�  llC.� F� �� 57���� describedma� s $w$, $h_-s:^ _i�wi mar�s� explained� text!+lZ",)L" -Yle} Al"�es5 0n TN >v( can be splGnto�ts)first�consists%�ei��ecHhexago�-� or (square-grid1VJ�$eir hybrid1We will 2�se {\em�}>�� t�2Cs cha� eriz�V�pa1�H, B�!�!�V US7~\�0cmethod}. NotxU .bs_-I$v$*��]/notl!�N�%�se 6qW0&�:M. 6�j� # conjectur�-"�1�m�=11"e: he $w=l$h  _-=1qBs !���64!�V6Rilr�N��en!CFigurm* fig:1} (2� ``11��'')%c!Km caM�A�y�N A� simi`i �E}��`p$n=155_ Yis b�\R�7has}!�jY1$%��8 s sh\�?"�%? %!�thmenEe�*�,s, namely %AAu��1iIAN5$, %V�anof>�s. Gi(?}�E>,, E�� ly d�minmshape%�J"�� ��Kenclos ;�� � ulas \eq�Sheight},width}� #ni�A�L! b��Y�A5@ $20 + 4 \sqrt{3})�X2� $24:-in units�o�`h�mon � radiu|It ��b"nveniG�fin!7e-d-�����o $L/S�Pere&��AS} �Lplos} L = \max \{ H, W \}, Sin:�hI� bcDargt1} L/S \ge 1 .>CIls�A��(s, we have,=p�[vE�\\ � = (!g25�@)/6 %= 2/3 + 1/31�8 = 1.2440169..a)�e���99�!��H��"x;�8/(2 +.� � (| - 1) �45410166�S�:�4 (2-� �07179686�.��� . S��simcal�A>s�A�d�dq �� :BN� entri�$i5correspooB6�� X+  a=Ywa�sid7e���p�s, �!�.B��vj��"x M��$n=���� Ting \includegraphics*[��,=5.1in]{7.ps* . 7�1� ���~&% : $a$) am!)h"� 2�s, $b6)~ >& $c2'-�-!H-ho!">Y%~!� $R_7$, $dHA265 testedB�) ��5M� s $a�b! c$%�5 same�!��tha�pd:( $d$.&o �7l 1�2 ��et��could � (����ed: "�)1. ��2)���� �� �(. Because t�66 does% fi�� pa��b� �ep�"�A�-��n�can� %,-�� . Insteadv!b�H7$ happ�#o b�� %���B�. Hav;!U~m*�"a�D�t v"~5Ub�(�mET EAhY $P/r<624 = 22.928293..dut A��)A�requir q� numbeE��% mo�"E�!a0 readjustJ k�ary� obta%E�W K^q8Fp � $Aa}Bq}C$ Yturie�Ohe dN ��y�= 7�Nk� .�  %$w = �  = ( P $h_-!t %$j%��-�63$c�l�e �is�%��e �� _ repms,mono-vacancya��q@^�I�`i� �$ ion � k�e�)-_eu:� d$ b�!j,Kle a{�&i�b-� term�Q�Q,  I�xa!jsta�&d trans� e� from �(6�:�c$�@� �#, ways dependa��" posi%-��v;%O"W$ &q&2q�!(distinguish��or5(!5.) As�%�ur!E�$d$i�����P$ decreases� �  g t�w!�K&f � '1} 0�S -   {3}}Bd Ai�>"�dA�7u�I'}&b�,odd} P^{opt}���- �>� "��650743..E�. �-$&� �'0$��'e���2!, lityF$ = 0$ toge� a�e4 abse"ofA�&y2s B�m�i^6J1"!Sa�ie�$ �9�i > 0,~i��, 2, 3$Au4,^h 64 �K�(�&reE�� )�4�� *�  e�Esu�,n�y)N�e@��� v�� ��(ore��e�u�class6n:br�%�"��M ,6.0in]{17a266Q .P 17 ($a�%� nd 26 (�� � EMu iny�s. OH*r ���$R_{17�& 26}$6�.&� $b �dW!TJ6C �ir=�  . AlM)ative!� ival6�:�� - $D$�1�$b��in ��"5n %g: �37a38f�38J�3!�!ynd��.�38=�37��r�6R%�R1R58a62fR5NR62�R5.R62�RrRAI� ve gap ex�betweeisE�E9JI�cB%Gm�K>-. A�1rp�aio $F2eG�.w2U%�:w s&� iz,�a�I9& Kt sixK3��lT�2�>"� .�in<���Vi�+.�.ursors, g�f|,,���:� 2.�.s>�6u �? �-p�%7-� n=26"  !,��diagrams�I+dE)�>� �"3  n�� ��� �63:���c�S, )�, p *5 "�F�2$ | f�� A� _2 =8 � 0.5 � �(,- 3^{1/4} (� 3 2\F {4�  3 })B� | n9!QreE. %��8  � " A0!��� #1 �&� 2$.��,u��3m�>$b$9 R3 py a6 ��ona�E� Oconta�3�r� ����eaEunq��aq[ left_l�4 mainA inh 3 s $BM�E573d 41lsoI�AuIU�a�=}re->tof g�i"in^>d$�6e1i(m7N$n=38u��>�� ��isz� e��! Zsa$�o3%vef�5�������� s��4 �ey��iz_ "re�9i�!i`r�l���Q����>� ����4lA!��� �� K; ; *�9 �_2$-cNr1:R�� � )�=d �B��s2' �z�1� �R-'aM&� unshad=n��@M����f3c|cF3i"23 _i$&�ed�u�_>B3,0.13879028...�(& EquM~� �� 1}, .(-�* 7}�"� )�� �( 1-au$728065.. 2T^|2},FoI��2D 5711 �)' &�193536� B�I�� ��\31\* 4325 0�-$df+ ��- 0.0040395��/ }Ɍ&U �� %c!�5� �)I<<e�& su�i$"�� N@ M�,!��� �YN<�$�g6��F�% ocal#(:8co�>2>.�=s� �>yI�=c�?('��w6 inv�>m�ch�8e�wi�BE8N8�Anf<de. D&�> ;�Vs "s� 1 7J$ys un Qd�l"� �-s, alT:gh�y��BK,� �$���� V .k�#��}Rz�.q:}��R1�&� ir J�"F�kE@V}� .|. �skippe>�<*� n�N�BF� .� +b $n$ �  more ir ��"� .�98do%�se |!d�R�{<�ll\!�ed)}w!znla7��y neg%W:�<J (� be�C&��ed abovA�my#&��adqUT�!� lC1o=s�ve6� and0�qx<|colum"2��,I co�"v3=" �D�observ% . If&�I UE��>�>)Rth3(>�@�$at Y tq���w-i~>J&�A�1Fis known>>ag e�-@(Eo^!WE�� n$. 6� X&>E � &B!�,*7 � jBably}Q+'9�?A�a�@�BYVpur$'&�#~. *r+!"�+�e�u�B�>um9�a�� E-?�* ?��3���> �pD"yA�m̹ �F��FA:QUA襸R�!Ou��!�!���Z�,�b@ ��/:l�D�w�/p��Ac�0�ZCbe�B�EIID23� �{"b@�� E \s.S@&bQ@*$E�0���`R�A��?��-)��13}h �0�-W!��{.Q1��A�&�{-6�!�,�!�I""S,is .n#8Z{3n# 9.856406.o#S@�8no�)Qt-mca(0A$ w�%e��Aif�!a� M6on�*bqli�&,`�a�"�s*]1�23�3NE \@ite�A�^QA. Unex9+ed�@q�63C d aM�1! T�gpI��_s5� $. %s1847510!vyI�}C�eAs!J�����  *'YA� s�/�Ns/E�� u)4rv�)8in]{13fO13 &�Cz"�s�)ś!<) stFJ�& "�&I)eh�)�)�Uw&�("� m�� 1$�V�$B�bE�N��Fru�� E��ob�, unlik?e stra -forWKbra$�I%K��e�!!\UDb$A��#be�Fne3 grani*BM2tra�KfNa$b�/%  1�enA�(6 truc��so�o�2j) �� %-Z� "�( .=#EV$ black dotE�.�e indica�5B}b�G}8� point�1 9F�L L%Fg�:*I�;exa272be� �ir,.$lI*�#aXa_a spo�an"H�vy,, i.e.� �:�"b no"�)  9%��bottom "��|]�. (aJ13 =�a:GF3as�Fed%* inct�s 1V13!�NlA�to facilO�� f�M cing.) No1=%�is�J�Q%� �Sa^� no$'�KE�� �7 T �(!.IRg1bs Jal�,true -�E��J-Y>NnZ((�p= do�r,�@�gQ�)�2���Zt$b� W�:��:ic 69h-Oas,:�  @�:Q �n�8�:-�:eunique�Peti*)�l:�"J�Q��1�Ro4 dimenNE� _6�4d.�6��n �� Z�� %JHA��.6K��e$ �IA OOd horiz[l� vert~M��� � >�5.%�5 $r�%�3~VW)H 5.463267269314... /H 265648578# R))�-& _�n���M5,1.0001118107Z4.$�5� 1��lmost�6�<�/;��O0.01\% *-n�TTLG}� �!%> areaQ�"�^� un6+l�/-ksahtean,!y!mpR papeN8ology, ed="k r2�-�2� � vioYU�� ��:�v7 of ���5~. Suspic8)��N`s,� ran S�t�)"g6n �1a��"<4,15,16,17,18,19�20.��i!Mk9c�A�\,Am!mbe�^3� -p}-Nk . Buc  21�L� e�an)gross �&Z:ity���)5t 21ft 21�t �t 21�&%)e9 A&s �� nt 2�-�@.t !�!L5�I!�7�a 1�H��V�js% b� .��q� (sI >�'a$)��"�162�13I� uP�M;10.�$37.3205081�, �2�q���looks��y*�3"�� : J" .yv�b$)Be,? �!�.�*�.�0929422^:�� zj�.�1. S�a �211�23%) -�x>01$Dhib�Z� *��4� ch make�3e� `�N� | � .&!  ��ZY& . "�e}�x��!�b� ��fA4v RPK*��G 2% eR$ ="�,j~��<$O ioa��3:6WM47.433745175630LK7.2209=87= ~~~ g=�<(02947599048A�$��� both=�F%��h� =4is�}. ��� "�B�.:� �;e3u�YE�?Ta�ila�*�+ themselve|E��ity�emphas�m�)�. �  L)Fv8 ��v/R(x &�6� �'�9�^iZat ��m�K=#2&�1b ��iF�DP �� Lity, hown,� ��C:�e�a`5K sB�"b N�b$v l� ���\j� �r"�(.�� F�% 1t62�E��31$mV�,57.kXth�t#@ E�$n$, HJ A321��E��� sE���= � ) .p 1, "m \ q<I� � h� ava ^M̩uJ�*�"IP���23j# 3�# �# !)� �_3"w �!(R>� !��I *I 3>I ��6�?43f} 4����Ar�Z�Z.�^2Q9B<nds�6�,"���.2_43:_Ң3in]{5:9A"�5 of 5J9A�o��B�a�>�2����. 2�5џ���.z2�5��d��B�5>+A��l)�s Q7�j,?�Us ��"r s,� �F %�57� D59.598251619392040)43)2.210�%2357011.)31)D44.745902408432360� �: = 12(2+\�0 {3})*�:_3 = 6<.. k93"2K,2L4nL6�L4"O6L6^L 2 = 6&L5"<��A9�r s st&#]:��\14E""�R !�&�5��9E/NZ 6W � 2T # b`mblhchw , e�iSc� sof!Q� �. More% 6 7�;�� �&!�c$!�c/act sub�F eZV�() U�=jBIn� � ��attachaoo "�I�{$A$$E���!� q�&�T  Aw j &4D � t�R #�3, �ido" a#j�4�Ber�)�9iHP xA-xB= 9.5705433987�1E-003A;43c000957...y �5M, t:0�1 0�`�s.�Jly.��� ��-WG5���O"�5"i�fiat,aty's�5 . B: �at1jIJ6le���L)e )�"�� i"BR�*t eMf%�MIddA�*A� ��forH�&�,eA�b� of�b)m6� ~(�&is �e mM  *�.1Jn�S!�qz��%D�i�aB�Xreud propZes.�%dC V�eAs  .io�in Int*d,b�u:�}q "�  l)8to g�m!�&E ���|!$#nu>^H^ i)Ic2IIa� vari� . Ar5�d� s sun�Mvcri�VaA�}j3?-���} play�;�Bc*bUfkfw �Kre&�-m�ggy�%a��st)SDrepor#*�}E�>"$ �C��.�� �B!6�"9��?$es�n��s�ys['%p�2�$A�2E]V6��6�.B.6� �:� 1j-�u�US)z2-��-M)on,!�!��j�Y ali<7*xBwoiAuR�W�+�F1$&�DN!�.V!39�Qe`Q5Qa�UO. H�no<�N��M����K6�d�!$n|�(�* show��S>SoniY�Y prf})� � \�,arrow \infty�Qe.��m��2GU��Oxk to 1�c�.���Z� �A{. �j%[Je $}S� $ (E,5\�n,~�reQK�*a finite]�6e1�p" fact�Tbelieve�5)_f",Y�`�"llfOa�P�nB �e%MW6 �F!AzE�ɕm+a}7 �3ice��%�,�, e.g.,:T Mv r���fEt�200�1>� 200�J��}200F�N�A*�A�2�GA�-G�R�Pvͩ)T:�) �!S �on:���,��3A�6!6Y) CK^�aA�Z %1 $C^$��&6�:supplQ!1globalq1�%!��� 5�F�!w �u;�o� notx���;��:���2"!"J��/mE*�^��!�$�� hold�-{J(�jr1!�, albeit3 lly. Spec� , if�Dv�6slL ly �!����b� ar�%o��#by���A�e���� fJ�e dens�>1���AXZ-  s (%-9?<es� h�\]+�.!(�A@ ���X,$> 5J2�E= �6CO tEf1�&�,a��F�4var�/�^yMLYBsxq �i.o6ro�E%R+!��iio8� �*�_�5&�%� �$WC�(� �3 >�E�2�!>�-qa J^ o�:!e��y� �H!�"� t ough�?�+l":a0C�2��seR'2�"pY.�sD yIa�5� ׅ�)�@� �-�,)!�?�8ZoX{�Rer]a@�b6�=��}�(�3"! � umI*)aerd�E somei\E��  Ir " "� A=A8�iz-����rJY �al��a hig^{�`n x ��q9 �66�<(T6. C�&� 3�#�1$Z�& ��N�yca�� 62j13��2"%eY�d"�  M2& 5�� n��*I]^"� "_�L�\0 vN�:�2� 1, � ��x�~� GL2�`ePvi5�cu"!�CGachA �2D &�"�!���]2� �� b8\!ve�|l� W|y=:��A�am��BAl�2 !f�.�`�g�:l5����u �-in-a-�*Q�A9o U6��w7]����F.� :� "!Miqy^�&� ."�ahsJx�[%6�J5�B�',h E&all $*Fv� ra}p�byY"t�E�A^�^ 8x oura��#�c���*)Av t�8w� Ie�B�?2y�*d�~�2� ^�' %�y6;M�((�.�:�$�j�]MQ�f�L$k(k+1)+1} 5',� ��}2-re $3�wk`A�+aTpr�. j 0 ��+.P/�OU��J n�.�p�� "k+-R?a�� EjH= �D�} �]ar�/zi�j9r-��� $n �y��l2�A�&.>? Our!1,6W1eri�!�m�6a� ous� s sugge�k�BE���0s �ij�6�``bad''AR�BE oft_6 llow6�f�.\:o�>pX~ q-KBo)\�Y trian� J�$n=)�/2$ ar�{!��$M!�V HS7( ifc!ui�� 'b%�F��GL1/0�?�ha)� m �� )/�+&k �+=yfI6urba2DF�M%��)$�&�9�H��aEF�S.4`,k+ &� d %�  �(F�A���,�[333} 4�+�133 BXarA)�&�?2B�0�^k!=a�T ng r�|�,$w = k"HO��UrowIR $k > 33~(a�1122)is"�8M )( $w=k�-=u�31(�A&Ad)�um. %�'��w&{ i�ooV,"�,!:�L}TB*weՃA�� 30.�k$ލ�!e�U &��Á�30 �Q�$!�"Q4by��4QIO��Tof�GNB�T'�]�zep�3� ��B{� �}.I�Fou, pro�_y�Fs�6&y ���Ac"�� �-D�.�!� = 66�"� � � �0e�N,QeyB&R: (A)@AWݒB����k$, (B)T�nQ1e�y�^�,=  %q:em &/*�Ebyi~�3:|, $_�b�5q�I � rter! %h�d $v = 2$�1 5b!�a! O� is = 5{c ��&1ars�1A�- &�� k=By} �,�F92e �sa�!��TofB� Va�dI a�!: .� 66}$��6.M�=y*2*}'�+n�" '�I&2zn\� ` way.A�� A�I�KB�+2�ѥ | �1E� ``unja+ ''�7��re gBbe4y s&4m�uQ�<. H? jL 6jof.� zfur2 re.� �"quR^"�6ion��*.� &o:�� �A…57:fh*&1! �bI1ed �g�#��6��s& I�� N�z#"�w}� �analogu� ����I\g!���v�it9���$. Approxim",a-G�5;e 81s } %0��MTA�N�A�Unfortun })X)��?���<�I  i��&!��v�l� b bey�mour c��=��Kcapab�>i��?Ќne&���~g��"\A��� y� a n� he2EA%&es?.B�-�la#u+��U� 66$ i��f�e. tant�& i!_b� �9�:m1��H�3N��57[.inF�k}<��o7�9 a+#r �^(�[� �L5L��2�o��a2�;��w�e &�H ) ing quickly��5:t S U%=1�un��!TF� pՎ�%�Q0segme�B�Zonsecu[, ��8! 2�Asel�;��l� 62 <I��$. oWb%: %$10.k�110= 25. 260$, %$52+511+10210B %$262*  $499._� %(508:�925 O� 1 0;t250 53 0 4)� �R�>G���f��v$&f��z *yU!z & �}1�} 6�}1a,& !w&!&z�" 3:MTV& %�& {�n�H� D�~rT102^� %��2�~ �H����D�p�D7g �3�1%o+2%�[R�1��DR�6g ��UN�:�4!v�>"0��DR�5�k�N�:�:�!t2�& �"DR�4�w��E� ���:�A�R��"DR�3�&Awmk �!�.�*50"�2Ak։1A��BR�I�id7A�%i�d:B6�IB!w,+5�@BR� j �8^�. 50<�J�4��BR� j �9�E>i�� �a�"J��B�4!(d }�1��+:� ��AOJ��BR�y��E & ..  :[ & (&��aj. `!�#aXa�16B.�&�& y�1a%!֞.& 6i76i j �żN�.�10�x��6��)499�FR� j �ɺe���� &��gJ��v499B6!7!#O��& j �ɸJ�:�CA���1�a!��X499BR� j �ɶJ�)C%"J��<BR� j �ɴ�� %�"J��<B6�7. &Q�^\ 25�#Iˡ5�-N�CJ��<BR�8�-�#)�Ag��f%�X� ����499BR�& 25�#!D:�:Z!;��l��6�499BR��#26�#J�I�!�EJ���& �i><r#.���� �E ' � BM .A46HNx`P:�#]6s�5"V"�7g#^G�/� iguo{YHG�L .�PE�vE���own�t�(�20$)t��they dG!(�be�%ly�,�4&��!$!�50�~�^���TB ���) � �%yg*�|e2� �. %�fD�'6�(2v�&�6*aZ�� �|\|3s23::�za�V9 MCQZs'm- n unU]*a&-"\an-"O Kj!�stHU�MofVp;6KA�:CgD*�Patf( add���i@ffo�XeX�%���-]*ւE��%�f�}en�T>���D N�. Also�#�xNEE�Q>�_ 3 . (D�HgAvp�&nvA��'-z�C_i��c �Ndetails!e"�zo�Olo`~�)!4�O.)��V�I�`�!Z,�iU*, hi!X�1M%I "��%s,)Z1jo2}&dq.�6i�ue�B�EAf� �>*�a� _�DRL0b$.\footnote{�7"5&"!LG}{8�)�ge 393h�Y.�)!�+ &-sߟ�*6-��G��'Ej�Y+6on�a p!�| %2�)��a�M"�%Itq6t 40, h�l��`l��,\ ��[9y*�q�Z�2�R)H% 453$')!:�X*�]2Q�V<$w~=~51, h~=~9, �$~=~4, v~=~�^��Q*:+lKgru?�/ ��ae���u8+!�%{ �N�-is,��u Ä��'6�%�![6M�O �s���'ra&�.+�=ͅ:!�N_�dis/&E�x4 word��:D��st C ��$!in�5s�c�>2��1$g-:� �B�#?*�'8=\frac{1}{2}(a_�'(b,~~ kA� ,2,.B�t��z_�J_1B a?u�J_{k+2a4 41} - a_k,~~~ b/b/ 5, b/ /b/�B�!6b�"�"�M��! �,s $a_k /b_k��(� e)A� vergN�$1/�7 3�i� a*�[ 8Nurmela et al. ?&NORl4bM�]C�K�� ly''* %M�s A~qc*�.A9�����in�""� Ř aM �!5Q�p|3>,��Abg)6�6�JPD�!�02, 120, 1512$z U�d#Q�a�� �'�-le� $| �Bw� ercis� �>,g"�%.JM $n$'�}c���Q� �8�BI5=! n$: a $4 X T ���!�)02$!seF�eK�8��!180�/%�,3xT=42fGd!j.*�X!y&i�$�$�}F�sK q,v�#nR��� 3I.b�Qing `j��BEC��� �"R/ ac�6� to ^�-!py02�%��"�@� �\�em4"� N5A KB�&|��&�h�7O)nue�� -43.�:, 621 I0% h53EL seem�|�\inish p2 phenomena� $dimorphism�hyl�5. D ��6r�=w wm� )l�3 �;�{3� m��& rvalB��e��419, 28, 29, 40�53h2V? �:�, �!f( �m �� $hi_$s$��!n38poA� ve, �m����15, �4�34�, 47,��61. A"���}" S:�% E�Nr)� "�0)-06$JE�T)�22k/)i�4�t 5 1�F�R�)�&�ReF=�and/orPqk� $B�e�ei0h F{pՔw%���t� . ��tnV ��LR$�^�&�6>h�;&6� 51 &l�l2Ls�& 2��b1{O�&t&��sot1�t&t0 t78[�V�76 t!��t3#2t�8GtJ�4 xt0��37!�9 &^t&\t&�!� 90 &2t��&t1\9�2t2�2;%� �Ga �12A E�2s&%�A�!�[&�t�6 2[24!�AGt�[5� ��3a�2�F�a/mav1 &�!t ���2$wj�.�?��"2�&� G �� ��幡�2Cly�d�d-Allz��2�4���4E�B"P�{,�Ais1N�6pmj&D��on,.rFn_ q st�l�a)$!GILA��s�5N b��41$< cAI son:K@F�dDic&?Q � ����� ܯjend m�Isooner,J ��z^ �B2�]hea6�3� "�9OX�]� asymptot�=� .�9?GN�9.|A@L� �@�.� $ g:Nto��N`BA�jA�!I18Y�"f A�) co:h �-�!"�G�Wi� llqsFo&�s )ide� ns. A�0ú[Gvex�*)X�0C,BcaK��F6NM� 6=uof Pj��X$i�V Kdi�+ ce b[=0I� M� @�ANv1. L�A�I@A�  $P.9� X9FrG��OXv(>I�͉67 FG})�/s-: {\bf�Yorem:} $%(16� 2}{\�V 3} � + � � +1.$$Y=i��syAxEi)��l"=20|{!;6�A� �( $S(\alpha)%�A( $ �Fact}: �0) �F� <^2$$. S�<=1R`4an� }�%� y( lengths $m!epsilon� mi�� SX�,9�$4m 1%�$m^؈8^2$. BF prec uppA��,on!�R)$a�� %�RZ�(m^2-^:�(4m%��K�is1��amusave %\p(S(m)) Ta�&�Bat�B|J�2!J1OB/m^2AT F����i/hllo8eyf-tE�( FQ�b82m+1) )^{1/2},$��iIwEM���B$mk� m�EzM. M�@�BWr�.nl �n nNto" M�"�S����,�&? laim!�eQ d. Ae{Om��if $m(0�J�$5,< 41.623$...mAc�esġ%< 1.0869.$ &m�=N��Bw4�0n"�NY� % �: SB�~6s���6���K:6qeE�d�F�� q . %.+� &l�� �Gheh !�Q., %s�v(2y!akept ac�/*��B�/. %%IZHкi�nts!_mх-��thzG3\Igh"C��. % -� \newpage"� hebibliog+�,y}{MMMM} %\b�g�em[Ft]{Ft} %L. Fejes-Toth, Lagerunge�ULEbe�xaufHKugel %und im Raum,�\Springer-Verlag}, Berlin�53 7 pp���G]�� J.~Hlkm�sDnd R.~L. Graham, A1j }hA0c@�v"?E!b2�:LCanad. Math. Bull.} �T12} (1969), 745--752. .+\"�� i]{F} %Z. $, %%ZoltanVA�( MA��*��&lle:i!%>@Discr. Comp. Geom�6�H91), no. 2, 95--106!Q5�{1?9` GL1] .Py B.~D. LubZ,vsky, Dense .E E�z�ksLan"�?T/@ le: ��22��34 `�5M@Electr. J. Combin�3 �5), \#A�^< see:IT8www.arxiv.org/m!�,MG/0406252} �aM�GL2�2}��Ro�P*y\%&M�of�a1�S�p��(1) �6� R16.�! ��394} %9�L.�L]J�How!�pe billiZ�aQ�"systems,MpJQl Phys1�9m�1Im(255--283. %]gLG]fLG]B�y.z, %eqe�Fk i?B6�>^LA in: i�e;et1�aAu�7aleI etry�(Goodman-Pol�x(Festschrift#�@Aronov etc. eds.,��,�303. isbn 3-540\\ 71-1�� 5148!߱{NOlfQ� NO1] K.~J."�!� P.~RD\"{O}sterg{\aa}rd,q�Y� 50F{�n , ^i# 18I� 7), 111-1?r=�NO2=�NO2�2}��1�n �nC_^apnauq!���@atorics,�"ph� y)VA=�|s}, Vol. II, Y. Alavi, D.R. Lick{ Schwenk (!�8), New Issues P��p, Kalamazoo 1999 %pp.671-680.23}��NO3!3�]`�l2>EV��_:92��9��439-4���#NOR�R:�,jnE�,R. aus dem S�� , As� behavio�&� �y��Q�~�4�380-385\]q5�] N. 4�!�� le�b��6�i 153-155. �!�h PAS]ˉu��a-any-� .com. Ruda]{} M.  E�Mihaly[@�A:ir)�2. (HunguVn. Engl�summary)�� Magyar Tu: k�. Fiz. 8Oszt., K\"ozl.}!sbf 19e�70�3--87.Y�T ht]{ :�omania>�lSMC]{SMC} P.~G. Szabo, M.~Cs rkotiz T. CsendeMGxV�iz�=! �� -��1�� e�"� �"Essay< d Survey�LJaL}, Audet, C., HansenA� � Sava�Z G.S.� KluwJ Dordrecht�5,A-26V�\inf.u-szeged.hu/$\sim$ps!0/Pub/cp2.pdf}.b([Th]{Th} %Aaue, \"U��die dichxR Zus�@ tsubUb}{t 'Z*��+ J,ihwhN! figw�{3.25 in�newtheB{thm}=f :cor}{Cor^ry:$lem}{Lemma:�M}{Pro"&o>qdefn}{D�g3:? condvn�3)F�Q�e}{AssY�:>rmk}{Re��>��h!&�-{�J�,� MATH��>$ %\Declare� Oper� {\RE�} VIM}{Im^ess}{.�{I}{��:To}{\lW �`a�e:"h��athcal{H6"{\\S>A:A>JJ>MM>WW>XX>dx�dot x>a�\beta:�bfx Rbf{F6fffBTfzzFyyF1x bf{hFw<wFrrFu:4�lgg><��athrma�st>$bf�l" bf{pF�( qF�36� B�"6.B1�6. B+n!$��C >^{\3 -+rm{�� {\im !a<I}>. psisA�psi}^{\aFMd{{A�&:�pd�5al>BOP  bf{BBH.(%��H}):eK*Kr+ RealWb{R>tNatur."N>"Compleusb{C>" Fiel> athbb{F> RPlu���^{+> Polaq�P-sJ&q� %(E> EssD �#D>CLo.�L>St��AT>" abs}[1]{\,S\vert#1\�� :�set.{+>Vseq(<'>:N norm'\V.} :/ess2 {#1!X���vrenewe%49 {ref��}{eg  \ ndex % gloss��R,3*? %\"} R�+Hrunauthor{Ivan Tyuk�Cees Leeuwe� Ufrontm)0} \title{Adap_ �nonliQ4��iz�:dynamic�X�^�} \ �$[Wako-shi].�NJ�add�D Lab."Per��� �(, RIKEN Bra�Oc]dInstitute, 2-1, Hirosawa, �8, Saitama, Japa�)#ab"!ct}ٝ���% a!%�_control��pP<t75> p��1>un.��Q:th^�de�i5c w� at desp�mt�h�2al�'ro�s�% domi�oi�c�loop  �%�"��0�ten neceE�xusach 0sg*� effi!]�mpens� s�"in݅�!nF� a�kcgs. InAGs;�!&�'1$j�i!SXU �.ha"kf1 �m �'G! si;�ny dampr:�1���@On�!A �2e�� %outc:Vour�%�!�K$��%s�-"}� al %�U�1�%;!�n!�beI K~st�Tzi!U$ �"unY'kV� eA Azof�@m�DiA�.iyY�!key�:}9� � B�!�EU,. Yy)t9ce2Aߧsti< excii ���2"+IM��}D<sta�� echnF� ,��Fw��(!�ab5~U$liter@�*v(�A�j }�fun�s (see,�in�ce,=:4MarinoTomei93_I,Li_2002_I�}) A�Q��7 �B 7e���)4Annaswamy99}. ^4�e�'��P ciplE�invoka auxi�4y crutches ensͤLyapunovW��$ �y�I&q�P�s y(  efw� ive �Xy�, solu!�%�!|AZ�rEZ�a�́6 !�~�.� . Yxw ��:�'�  q��fr%F0se bio-engines�, phys�Y%bi�h�sir�� ref��IW]9�%  issu%}��(���� Wka�cal.��Ey����-�atic � shooSC^��$�+�f�{wA=nI$f! A actu�L,�uA8f�v!�ssir�h�̊ A 9� eIj���ion/braEe1oDr��$ tire-road�$as. T7 {Ce̗��bs����AN slip& as}�i�hM�rejDl��MX�(�C-��iZDPacejka91,Canudas_�}%� )�is� ��<:,s �co�Jgqly�!�ҥ7(16��A�o.�m. +/!rkg�orquea �/B�!#motiv%>�mus�)n-}���al� #me�Yismi�ecmor�o�'X � s e8a/E�� Os~e [Y�,�_ "���s�O node-�Brenner�,0},)�Web�"2} (vi�� ������k>Z� e.t.c.). l��$p-� � eeK al m �� ��s"��AG��lyf �� �Ab{��1}. Du M� it� �lon���=vzP�"�;st��I+!�a�x�l�r�?H da���. J��b��!_ny���*ng �isIe�-2�shMɡ�.�in �,�( voidZ)*� n)r� gy.�(A�� �@ht&assVIe�oCa-� �2 be %�msatisf�k��je��(� $.O[(��-�t� r"D *H!*��ch^)�$g task!$to �qpri�c�D+.�|�) q .�"UC � s by t��nd =cQfric=�. AЍ%:]�p, "��A�e��i�I�K��nti��6},��!�meF� "� k *K �t_fin_�D,sA&T2003,tpt _tac�<r��new��T eX���2OA�g*� &n �_� "�&$5Jc!d�!�-� goa\4rI����49�� ϑ�� F�_ng1�5b=�j$ S 2�I� l�hA_ngc �P �Ky�%��a�e�� !�ץJ���E�y �kavor � -bas�e�� _;5ZKcades"� e7��@�fu�M���vi�A�� si�9��X�-L*( ?' 4Isidory,SastryA�h9,Narendra89,Fradkov99}). FKm�a�uE)�mb,�K tyj��a mea�iof�BepteH.@n��c$�( �<�i�cA�i��guaϣ�@� devis "ya��libriu� �9A� 1gJurb 4i i�a!�b��Wh��J !`Qi"�d*�z�� "Y U�j8lik͌bem'��)/7 t�aN p�I�Bs�-* q����!qQ�=�YQ  ah�m ��|leJ~-�Jsf"=unl�ciy�oviAҍ� "t�a9 55dI�/�{O��fVUB1q�U!�%&QڭfFrench� }� � arisP�$f robust %eJ!\:� �q%<ect���pofL3rq�(�ty- ain)� �" �[u %-���4�7aBl��9�!�,}��>��A�nce�unf X�I%{bs�D %�Z7�Di�S�Bsu"c*V%��Io��u_96}� fact� Ah� �s)/� � % ��e� �u�dRh(e>Lha@�%Eiu Em �b! aandwlog*�<re*�#3~9z2� %~. E~ �t,  3�0ge ( �enot*��) -R cy oscill ȉ+, eye (tremor�lat�TW7u�=:7oM ii��u��. Uh�4Lh,3 + lear�N��U��� fJ��l��(nefit great� �;:`iP�Q�����ib�� �����i0 �>s�Lstart)<brief2� � �teg~�r���e�9z͉��. Wq�A  �ty-9 b�c��{vi� yu s P Z�on*�to ���S�F�:n~ce) g�aln��:G�YJ��U�w��F��N�A�i->)=� r,va�a"�}hoos�!�� �}ifold. A&�xe��� %�"��� z�c�o.�5Á5*g !��]��na~on6B�xA� �>wme}V� ULI�olV st� ! ����=o�jWR5targek�-7��l&����$�n_Jerc�4i�q�i� ��N�9�a>tep!��Pmp�2e%� nd6��6�*�qq!��l�U8Throughout the �paper we will use the following notations. Symbol $\bfx(t,\bfx_0,t_0)$ denotes solution of a system of differential equations starting at the point $\[$  ime instat_0$; sy� $C^r$ z�0space of $r$ :s.yble func�s; F\Real$ bd for6Jreals; &X_+$ defines nonnegative% numbers,Yim� imag� �Xmap. We say that $\nu: �0_+\rightarrow \$ belongs to $L_2$ iff  �(\nu)=\int_0^{\infty}\nu^2(\tau)d< |$. The value $\|\nu\|_2=\sqrt{L_ M}- s5 h$ nor!� �(t)$. F-M2�{+}J��andR ���� �,sup_{t\geq0}�(t)\|�, where �$cdot\|$ is%� Euclidean�� �o� � }=L6wN��) A\\n�$qX $\mathcal{U}_\epsilon(a&}!�setAal4bfx': \| -'\|\leqA$. Let ] X}\subsetE'^n$, diA�c!  t,�X}Ef_{ _in !Wbf{�r2��X}F� $\daP^n| \ a� �'2�� � \}$. �fE"bff \psiB� Lie-deriviof q� $1% )$ w.r.t.%|4vector field $[ %$. The p� 4is organized aa� s. Se�9X 2 contain preliminary �' A� statement�!�(problem. InI3�v provide mQresults5�y4ycludeI�  \s �{P f Formul���P�,ies} Let usOsider�$ndard adap���rol��io� uncer�sy��be given=-$ \begin{eq��l}\label{eq:intro:plant} \dotE8}=5�<,\thetavec)+\bfg)�u,MN_0E�Omega_A_ \endj �%� x\in�@^n�%�M ,��f:M�\�- dB�al0g 0{n.� 7Hn$ are $C^1$-smooth l-EusC�� �m� �d�M�$of paramet�^$u1�input,%�$Rbfx P� �seE�initialEdi�)2_0�� f$�bfg �known,� � $ �vec�assumed��be un; a-priori� also (�5�Dbounded m�a�x�A��E� goalA�to�|ch asymptotically a neighborhoodq`&�manifoldM�0implicitly by��}} �w=0E�psi!�C^2>�%In�oth{ ordi�1�Q��to ensur-the %��{; rem�holds %u}narrayB}_(_lim} %\lim�g&q�}�ez,t)=0 %me R In adI:�(\refy�a})��T requi łM psi_I9=S (t))!LL�� \R*" b� 2 >q This���)W!vat anyQh devi�8 from!s%� U!do� t�� in unM� growthQ_0 �a��`.6we.� $|L�΍�5~))| \delta_{}>0����selecm las�< admissibly!�$s which, a��� � !�!�b� �ched, can compromise between performance ��do��G issuesv pmost natural way would be to F  t!� �igra�!D{\it �mty-AF vale�0principle}. %%�^ ows��gqZlaw�@ %such�rin cas��g��:��˜ %precisely transverse (target) dynamic%����'Q9$ %depend o7 ���1.aT(particular,���1ÂC 1})split} ui�\hat{x})&=(I{A\#$))^{-1}(- ( B8/8 -\\ & \varphi( )+\u t))i� ��J E�)HATa�e13:W5) into!Z � (error model�b|,| psi=�1�)-:'-b�,F�ere $I[=2O!0)x�j)F��"r C}_  �� C^0�.�x $_ 0)�b>0A for} \V $\neq 0$, $1�, d: G_J�i�desiredY�(�)�]�is�Rby 1� $\%{6R$� �(t6� auxiliaryuor� urbances iW�ӍJaext. %�.coiU %qN>e5rol}).QIdefn} A> �K(6�< �zed�� non-�&ng}�u��&� 9� ��any $ >0$A�$re exists ��� $:�ES,t,�;(F�I( �}Ex�b'I^2E)�\ $t^\ast�a��Ahw6)|<~$� $� Bc � ��7E�q*\i� u/&�.J��.T\�F �B��%��Ce dif�ce $|Z--Z |$ %�-�6a mea� ofNU>F. %�is�� ;aLMW goalA: factAaX ���, %feedback $ �aH&I �T0attractivity}f� %:�sa %"V %1F:8 ���sm  %strucly>}�Y�S U�%B��eBB R�� )* !L�:��j,BC�!q9 &"F��I���$: N�$n�z %v"A pres[studyI f strictN *� C}_{ �}$A D�;��o&Bs:����BB 4 _phi>dJ�(k)&=\��ݶ� | \ ���C^1, V6W�b psi^{2}kk k3�� _+\}i�Vn�e?E3�� B�n2� f&:a�n�atUarbitr��sm�bg�$k��in y� �I=kǡ?]�U�B�����"� M��"� �  in f�e��}or�$to specify����Am% �h ���� solu�_ ��CE_alg� h6� }= vwiH� toge�!D:2-})[��>"� :2}).Dv�$,A�v, nei�shV� � i��$,A+ it -Q�*C$&�$. '��w�o!{ve �-�e�R_�s!�y�z�=�*�=0! 6�=U�mst�����4Lyapunov senseM� gene� nonlinearup��o$, however,�hardly  me�� y=d��O�e����_0�[ ^�To!�w wi�enough)6uos >;�--:SM�&"�� ]�0 exteoB�lef]�aU{`� \\�tildeS vec}}� 1��) & = RP l} -&� \�^� &F� )evec>1)w�ACra & 0i�6�R��e>�B���+V�} 1\\ N{�(t)��\ BmY�-{:rq��phi-hef1;�i2/�j$M�^ Hadam�a@lemma\footnote{In2 these�i be cal+t�f� .� ��"6,1}\frac{\pd �lambda Uh +(1- ):q)}:  �3} d /2F!�}_ �1�& �psi { .Z[��w2A(.`^�2a} �}. Unlik� �ypnriz>�, exp| ���7Q�*� ��$ o���& �t�rensat�5r "�tchoos[appropri(uK!��e$ :��{)grefore,��Ͳ,�'necesssto�"� o2�s&� �  V���J�fV=.m��a�!� s�&X Yfuc�*0is strategy %� ichq�<ly�/� very��t� of %.` ���  %-1,repor�N6Hcite{Annaswamy99}, Lin},  _2002_s�}. %Ano� �"�Aeinvoke*�< methods (if %apA��)%c+ �-varyA�matrixZ���t&/ � %averagedQof"�s (� re% t� vari�L $t$) has %hyperboldM$fixed poin!� orig� or3�" ve6 65 � On� epc w�$to s ob}! � .D� ive -�2{eQ � � *�:-q"� Z�.| %$�2�2� �)� aTin%T nt %"of1�>�}Ii�i� �� new_p b����� 0B�o��2�qa L_2� &� �&: Similar % was!�J  i�,Ortega02} as&�@``root-searching"��ce�Ofure߱ ��%.X2003}a2immersio�"1�ce&�. I�  %��8n�e*� �i&��.q02}[�(8.&6ter abilityA�e��llM�. O e�hand,a+pieLat�� FGq�tscheme2�N>� ignifican� =n �arison���&�"�s,�i��&� >wi!�otM cussI+$details.}.��poP achiev:�um),>�2� �(�� in�  abou�&� �b$"E lyA�!�%� d"�raE�than u�!jr*K6�.Z% a&4BVeri8&U$iad*!��� %duc%x to adjust�M/ by m#&BHe �6law�&M: sugges����t_fin_� sA&Ti�a,%2�50n 1�@$-integOor[oR� stea�%^�n2S5�S;. E�-J�y $ 1:describeq ��!��_2���&�Z�f�\ ��� , \ *%�4alpha�|�=��JCBd&����& posiEsemi-/"�pim> ,. Sufficient�insAJ+3"� ]{�'�(+� ECC� 3}, ALCOSP4}� a�ap? me�� �m`ici�al6��� (q; � r.izѓ"�})�embed���h�Do��on�hig^&�. While�A!iʼn�)as show�%e_%>wide r�.! $6W�. $"� o� ways!��$(to guarante� �*��Z*o *�FE�� &F� t((�g� As a# ul�-�L"s>Swho!�3+comes MFatic, if��0{im�t,��r ���r��s< T,obser-c1�� � in b�*2& �  +�z:� B�C`) � 2Vo%1>I��}),>7_� � JRfor�Jc�-Z�%o!M�-*iD inevitably leads G A��!oe�aH�� % *rrv%jx"�!.�J� (_.*� -�@�!��'w6J"��1is ill-� M8.I�candid�or�lac)�of p�� onO�'think'�G L,2K U,Guckenheimer�:(2,Milnor_85n A� "�.>^ clo� $l$A\1u�a�%h#an�ng0i:S some7&,$U$C$A6z��� U���g"8%b�" %U�N�-<*A$l$t2��(concep�=2�(sNI��) be�un�rlO Q7 � have"O!Ѣ�0-rR pEb of r<S5�6L-. "�d� llu�d� >� L �:5�eJ,>0AP:ex�,�Tx}_1&=& x_1^2-x_2^2\noi5 \\ %%2%2' x_2-Oe %Ph�plo�. �>�{�@ Figure %1. Circl-K� e basi�)<R#on��� 8or $(0,0)$ %in i )�%J�-fg�becenter}!l\in�1�\ch2on{���aW5; X/>�g�$a�=%�^T�3y- &libriuD  %6:J��*jI4ie�%� n�rg�.u{T}�?l-7$!p "�  %(exe�=&-zero ����a�J�0 %c). m}"�H�< la*[��ea�8����check �+criY1� o 5-$-led�8��23Y"Y)9�is � 8iI�n�-� pert-yy�4�f�^�))^%H�!h!P1)of �M !mh%cR iVear %pa%.N,Aof?9 m J�F % ��ete�:i$trivialGN� %d�,y 0 �2A�m!�zs9� %set.� Ia�����* ��u�NI�UB����~��5;.5� s��d$ �3r�p�E�JL�R5&�I� ��1L= 3� �.� bY^]$qa;and�psV� (�� More7, ��-' %�/E�!,� M�%�lo�y� . HAB,  �, %Barbalat's)~%�� */"$,NI^�$ $*�� %R� I� i�:%:� A�_M })Ms��o� %Yz}�2W %Q��&�&=&�:*�!|wfxI�4= �psi(igcapf \} "q�(%/ �!& u ^9 �; �ps- )=0\N�.VfJS:�|T;>�a r��)=0 \�L&% T�v (hap�Ųreason" � A� least demR ngx�]-��=t@:!�s *�he���ofG $\o7$$-�+AV"#�* A��pE�D�9a<�2F� [E.:�.� �R:=1VE�&�, sequa� $\{t_i\&" e���,a�� Z6s1 pM1C �xll�, �a�V�is��=8K$��9�%B,6]e 5�%��5" �� some&_�*�>�*�&|8>� A_�} }=( + M) ,a�z)�I�: &T0)?va6�+Y�ai�heE\J$�.);� �(-autonomous��:�x&B�x42�vR(.��}� quesq our curr&�-� �!�� ing: re g}^ 8e�u� y la� � o*�;"զ.�!2E�al Oa��#2�$EN5{mw:��:� Ee >?-.k>�4tr^| �J20H4 v� � A do!r�.�m1c!"�( ime?�)answe�< 5�5�?d$ ^nex��@.� a��]  %1�F�ng)Z{�'}(�3)\��up �T,8?" "�?M� R:@} To C�, l( s !���#�<  KC,1#s~ w>�by sca^0*�?�_ }=[\� �$,\ .]� e��3B6_v&�$ liter�<e.N�i�0c�� a flow2*<� "� �#$Z�ha� �" %�ha� �nlr�0 a 1:��is� %<=a��<���q�_��΁�� %abovr��9.�# }(t)��a� sa s moͪ %VdE& mov�:��r�@� ��B�$�4H=�$$F� � stops2�,�F�h�D�T 2�5X�t)�8{N�H,"�g@��YJ�& u�2S_{��}�3""=,\�%i- \{ Z?�{*.Z) 1, & |2�+j|> �\\fA0rA\le�@bC� �F$\�*.��WH2!�1/ $S_ �2+ )).4�� assoc�*G�.� ZT}=]} t}_0� Yk< 6$1<6!1<ls<6&iݦt}Y�t}_{i+1.�dots$,* -�e?C �:t_Fe72d0&= t_0 H2�i&=� �C�66$i} \{t: \ 2,9k]5<)� \ :G:d���-1}�gQ�c f�7el�� �� �i"0Ncea�2. i$ (�2�i$)�[�AJsu�C�/N�a��Q�s)j $�VA�)Y$ GdeWN�Uu$nde3 A�=2�0!>Vc _0))9�_0{=�=4GusS-"� tr~$}��.$B %����bj#E��/_Z le"�-�& ,0n@�a<-�@ ,/: d�/: \im�/)ANset�O�2 &� sU. ,� &  �  \� \ T*au(s)>0:a���= �(s+�O(s)�20< � $ An exampl� 6�is�a_).� |}+Y: P1<1}{2}(\sin(s)+1)��� 6".d�4e.�:we 0A�.�Ca� J"�v2'>.M �:�&5\.%_0:')!�r"&=\gamma�4&k7}_P N)+)B_I(t)+CU ��Fg{P�)&=*"J��(��+=�q0 U .�}_I&=�Z�5 O��)�E�2 ,(\xi_2 + b_1)u&�&=(1, 0 -1, 4)�r�M':� c} �xi}[\.�,, 1FWVMN:0 & 1!�: a_1 & a_2>ea:sVoJ�b! �6b!B2B�jN�+�p^��E#jB ^b�� ��� QRaUA#& ��F�Ma_1,a_2< \ CC(a�%-:� � I;E�uÉI}.�(�� ).�> }_{IZ%:g.V�^ 9t��Jf,\2H{i:��J��9.��B� )-!YSF�F��9�.8[B',2ni]..b)��VSPr�1�x���&re main~" ! ore��thm� th "> _dim}�Uvi �^&� :� �nd6) �'K>7})�g�.�� � "�K,�� ��in"�OK|!�|� �� ��+*�2I�S$�?%n\\ 1S�%��AgC�phi�� &H(k)��C���>;. _]K2�H _+A�'!C^�@ (0��HI� �,�)= �va)+ $�=.��*~ ,)��RIB�EA&]$���� �>07LB�"s���_0�.�)N� $ s"�D""p ��)}{k`XccW�J"a�G! �eq2ZV);\\ 2)0j�#0McE@>A .(,K �v�#�N"� ]�� 8!h�E�3)�p &\UF �"�!kJts $T_1" $M>2nZq$}�� ��9�  (0,T_12�7��"� ���PE>� & (t� t��)� 2]h )|>M�XE &!E� o \ \�Jslash"�.�Z[ �] 1V#the6N$}9��]v^q<=� .\\ 6+Pro.$iT�!sE���A Ap!Rix. �R , tNvZ�-a<�H�H $�-�;E�Q�Q 6� Uxs($-n,:� ��*�/6�.�C�/�,We"�Cl�\�=0$u"2�%!7�%� P�.w$ we &f0�.rg��"656�$�158�I>{'6�CA��� sub.(� choi;#$q��U]P �"z��B�/es1�ne�UA���!�!(Bq$�`�9m_? Gu=�H2�)�5M��$��matp}�$�nE]#N���!�qu"�Id(set) $q� 2I7�>"\�t Z�(eZ��actual [`���Co�4ZOiwZY��]��cpj(er2��)8R�$,�p[regard#+ ew �V*y#&lHp�;st@5 exciI�} 5Cao�/3}. O� �6H*AP easya8verifye�& �*� �ns w�� B��(�~ �,Narendra89}:+SxS \ T>�  \rho�:$(t_{t}^{t+T}���) ^T ,c >7 I_�HIndee1`acz@ >@ .�Z&`�vec� ' \ (- 'a\� s$ $��VN>!wb�k \|^2� $ $|VE^T%8t_1T�� rho}{T}\|VZ@, \ t_1\in[t,t+T].�jM| �i6( &.�{�Tz' M=��-(/"�(%�� %YL.�� %Zz!cE 1&��VQE %^�26�(& %�.%& �O2%Il�%^� �01��YU'�a5iz{ D7]� �� �qŴ�#$ ݁)�:O|%e�@#� ^d#�!�%�^2�"*-[&,!"�e� :multi-"�"���h�J *Rg {1}"i &] \�c: .� R.� ]�a �{d8 uch�G��?*; )1202> � <^{�X}y�-�� $: $� &�M� , �� i)�,� ��L�#�n}$ )�} AG�7f&) sfB* to 5�en���#%�G&!��4T"s.3A�!��"*[� F� ��jsystem �>�����,U�'bf.�.�� A�dk$i�)�..hol�.1) -- 3#]�]i�!b �/ �7ck de�] � i �`al1�� 6� �=�ACly glob�T"t8*;:lR�Y�S(netheless, "�U};��NAcit� tshte"�S it fail�4 ���F� @�.� "}2{5% �_0 .� �  $\xivec  �53&�4� &� es�Yi%* rely&5two89s:� , monotonic e�*��,*G _0�%, ($ eL@ �6spCa�62w@ ѿ%$:S0$�bym��Sd_�2_eq}) in&� M�">�!���?dR� ` (i*de� %w��1})�c i2�26�%$�=&�'( $ \{!�.61}_0�1:#2��� �:m�J >) M1� cha 5eI7Fi(c'�R� M�� *f#0$F�J �#ty}>� (t)=2I{0, +$&b`�yis�)ieed�p�� �Ba�>m2.N��T@!��CE_ I_�mgoa�0 ). NyJ=W>�se R��9� W/"K*�ao2R"�`��q�zŔAB g��s5ive+kqp6'�.9�G;��fig�ҩ�}&&{;i�9��<Ζ<^|2�<%��.=� � �c.,on{*�9C��.t2r (R>a) vs. *�">�$:>?���?�� F b)��$vskip 65mm �-�� =�uy%Mb�=�F>�F>Z�80pt]{�J�)7!��5�Tr2�Z] u )$ (�0bottom panel)�Npro� #0curve. Gray c�?FH{Sgir��&�Cs�;5  in Hye Ls satisf�9�9 ��end1�Ua7u*JHce�kA4mLS�XM�^"B-ba���.zl:�AFig. 1.�D ! up"xE�depict �- �2`�:W7 Iene &���.w, w�!�a s(7 7. in�3#'%in�>O5BDasj/-�). xvaw�u��FF�6 .nF%_0�)te� ly m�� a6��i}�� \N�0al,lf�| urb:is4<��Lc � *d e/P�`escapem 6� um (Z�A�X 2� B[ 1}$)2@�ov�Uong�axip 2I$. Du7A�" qG�w2-��:_0)'awQ.'3e�U$t$ it.��Dei&F�0>�B�2}I�0�5:o2� releateR�K!�pr%�N� >})?*V.�s�Omay\nYcfc!O3FE��� Bg upony�N` -A +c ?szJInolo77�-w|F� typ-W&<�D e�; "�C&wF�5stfor. Dis%j�-E�Eh�o"c awa*:Y.�A�+�@�IoC��W�w af� 1eyurb�QT$vanish. DeT obviA:advantag �typ��8behavior, i.e. 0f2:��H  "�r�-g�Q����M��3rxNeY�a�d :. F. aEL�4be�wlreadyi ed odvgentl`5.l� ! LF�L�9"s.j�R8 -�j8�x M. sTm�!rih\ve fe�)S"gs.��GV they�yi8r ta�]to accou�5�R�L�T(avail�=�v)�rib� � �quasi-A5ioz*�$!ba�(�imeGi�Qs7! t�9 �e�~by*I� ���9�N>l. I����(is P\� i�H 2�� 2 {# �*k i 5�m�w visitB1aD�1f�eAVy ($16$ !s�� iod)!�n&M��$s (only $2��e .o �;. q�xMc!z�.A�[a�.B��@ � fit-A�1���&�$)!A+�E@op��lui�Xif�/^ful��R< roo=� enh��"P.�iOF�mM|use* sB\wo�Mb�a^V #7uneR?�� iv�thus eB!6j -tun A�he&�=u�UelfA�e0opics*WW)beyond!� �%QB ?�]"W^�vyQ.�9"T ies %y b�sj"� 2$�)e�s,;{Kocha O%ca6an!VduSbiXK3.A� %.= $t'=m(t` tau:�2a(�'+�e�e�D �.; %\[ % G��_0�2x,c(�*),�� %\] �:q�:[WM�P}=\bff_(�)��o�% C^{0* ] %w-$P� '_D'�>$%1) L.S. -��6���. L�@ %>)��2)� -B m/z %occu�bm�x:{v�#+!a. Mer- %:kA�| +a��  a2�!��e%��� tist xr��\} �p.h��%�h$ +q�`�r�oѐn-�!f%2)JY�1�%�II�h=�)�: ,t)+6NF&*{ )IA4an.˄�|�)+, fa �"VN&"܅set�ap D %� a� % �2Vv�\ma&E� | �8� %3) Gk C!+��";!9.�E*�$�A~$ vec]a�� s�H5c�Q�$9<L5&�$%�LipshitzA\##�~Jx&#;&!�űAR}��+!8se (s.uT��� %%B�\b ��`�.�v "eBCo� AG}9o� p��"�  @,new techniquUAr �K���$�yn2{p ys� !6 �D��Er�HtoV�u Ԁ)�6� le � ?ol�9ult;in�B!n��by high-�q�qs��z� >�E�S�� not ��S�o&�m Ye�Gs/pqs&x'{ ing!<&[ ��>�(����|aC. �L!n��]��N � 6�.#�ideologq��w�; omewt*s�b��EV"� T Z&HIlchman_97,Pomet92}/ �:.N)�,R"A. First%�do!e"�one$p[[onAc"�YnA�s(���O1�): M��o�a!_sp&�&�8 T#'asNQ �  sd db[�!��st bu�'ts +� 1Zca�'usZ i�if.V q7of�`�l%)sou)Eng� �+aqU=�]�ie�Tr� 6��p�\awell cow da �gz k�f "r( philosophy� �" declaA�+J�]Fradkov�(0}Orr�m�*) its � empir2[%ncob;xri5Q��s clearl+utec8Z*�t��{!M;� ldata. " weoved � }%�e��X ke/b )I>!f"i �}hop��at�K"mrobust%,�,�: ��b��s�q�m�, M �- �to un~A�έ��Sn��xF�feasil�R� en� A�!� 0-�]:��^e!�� aq �"f k  e!xby� �an�[�a ers �m� .W>@$ "�A!6�� ]our fut���y.l\biblio7,ystyle{plain�{m�_ �q�_conf���.0} :a0n �10.�6us�'J-�*�Uq�|Ocul�T&Gu!�6kv}}X e�*�R��"�&� � main.�'d<* }C� S"VDp�S"xE�4� )+ B.,&@\6�8��(\J�����K proc�5�u�n&�h�T\$� e�/_9f}� ')�. 1lem1=^GC$-� )�" �NMe�k.�u+R<%i/><a. ��� $�&K'e.�1~�8�X6�h $;U� �L��n yV( �1E�psik4&�%!\:n=� ١v.���� Ʉ��*�U2� T!�'Sk diatL$�'i�q$f�79D��fa� �� .9�&�P%,Z1*`0&�3$�cifeby>08~6�q�rF�h&?'>os"��)�#� =$,� t�i1)9�*�W��=2Va>�5,a���eLe):�M�X����:g�2H1*\YWc>(�.pd6qf}{�}- F(��A� . .6+)A B+&a�uyB.�uh�L�6j}uM�+} +��~B ��?}�b+ @*M<$@͑AyQ0z*"�%6�}bfx��`ontinu�Q`�"91�Y? C^2,!�BRQB�bUaFy� m�bU,.?!97F�(! ]MI� ����1#.����6 !{�<-�Mi��$�u��� irÁ��7�b���}ofh is*�7�oe(5fx�&1 for  ):�$.��!y>/� en.}N�e���Vz�}�v�! �(� .Q�is� : $|}� |<\beta_1E~ �7�n!"9X2)m filtebrlf1B�^�Ci>�NEZ�DcFSC0�OE�OE�OE�OE�OE�OE�OE�OE�OE2�C�\\ y &'o c_1�0 ͮY�xi  2 ^TfnV] M $b_�E"�E$�a� $t,?�L=ny&�ZcoY?�C8? � �B�:�/s2y(t)-i��E(t)�1 D6 "�1t>t_1�nG&�b*X $c_1b_1=-��ab_2=a_2�F�1�H� put ]&#6�inx �t: ! I_� b�|�-a_2��}{a_1}|+�\ � `1�!�cnex"��z�!r!y.\ >�*^ ��}.r 2(��/� �`)� 6("�)re�c�b7li������0��J��J��J��J��J��J0�’�.b_1�5;ah��=�N"��DB� \![����� ���V�De ng�PA >XKF���A��l\G�bf{b}_1Z�.���% �NEbf{ E>��:cP�0ʿ��T,'Swaky wri�Ghe� �M�b�' a �j-��� &"L�,�/li�x�.q8e�p6 }&=A1| +A� +x��y&= c}^T 2 �S]! � "ouV $ye2�)f3} y6xI#e^{At}� � }_0+ �"0^t'-A�",�� ��"bA4 2�M� $Ak HurwRa�����Vv�7 ble.�c(��YC�(2w.�(_'a%���$A8�� e�4Hmmu�8we]reE7 E-� �3}�0f s: $y(�us^T(!%NL-   e^{-'!GY"(t) {|}%t + � 96�.$>�E�9� )� ��j�� s 2�6�+ $e%K1 :�0)+ &�.(t-�)25 *�IL � ue�o� d ce $N# J�T�a�l5>�& ND=|�a�(-�u2�2 - � B&MMF=-d\m�}�?�|Y t)| ��(C,^2� UŅ�_�� �!ڙJB� �V & - .6�+ |Uh!d Q�YR�� I� � & = 6�����:b+6��2N#�-Q�E&26 ' |,\n]un� mAm2}=1�C�Qus�$o��%�(6 !ut}Q|+2�1N�Yh0)N55 �erm��f(tVYaF4�� t $t� �as��>K]�F��vB \[�WRszu $ 3�t&�`��66>a Na&i�(.E11:� +1 )\9c t)|+�V&6<!�2R?+S1.rq>&K1ob` ^V���6c�� \[M2Z� .� BL F(Z :* I$�>H �-� 7{2sN-a_2& 1!_r a_1&v� �� \]0Pn%J��G=(�  0)M.QxӢ� � ��� -�-��Zs �%&�=� :'=-1$ du>/�*3O�,�h,�.�Y� �}��Clf�T:N�J�j��V_1� �Y 2-)^2��a�{+A�E���V�A�A�_�V#=�1�.d P Q�B�7B�V[ %4e�|6�2��E�0��J��=-ZOM�� |�[ͭ�"=z���vV9I"gQ�7})�s�GmQa�E��.9K mmas�"].+!,>7c%�jdPV8q�&��X"�X w�"wY+�S� - �Y�#_+$'alCasR s*a�.�!2�9��.�� �&� �6*���7(�ed � *�*�,�"z!DvX$9�3 " 2�&)v,( d)��s4!f)�N}�l"�Xps $�� a_2,b_1,bٴj���< i1})&� $|"�%-Q ��h _0/4 M��!|Q _i �  :�� i.(�� � ^� / }�$2 �=� sD!��| B�GjGTT�k W (�. sumE(�I��fQy"�A=�%usyT/�� �5B<*!}o:"�=�H�?O>(}�'�MOc�&1 &�ma�2 . Ta��oE�unt�%!~�'N2%�2��"�VRz !*� waf[m�(�_v��_est} �=Q�*�2� �2ͳIA0/ e�.{b;nc:k� \psif$|.[fv*���S\$��^d��A 0_mo�*S� & (�+6bb{= 60- ʼn \�j> ?(�g2�^2-D Cb'm j) L� _0+in9geq�$%] _0^24>ڜ-1�I9��:�2�O1��K{xJ�"` *�#2V.&�*��8a�&zA"o$'%�pno��eCu�a�. ��e���&OO�-oIl#�Aa�r.ED$�1A�D"�]�&y $t_2sp`r�hyp�-sis_u��} |:"���V ,t_11)6�e�� (t_2%2% |>D_�%>��s��$'>TѦd �.�) $Tx��&x) "T+E�."'M1.?o�)* �2 :%�*_j�awau+) i�r tau\�W _1,t_2]$( #� �8>l%J6>{2:E�4�%&B ove��"���ervalZl*$ th 'me8+)Y�6,"M( $0< T_0< 1����_32�]hR�t_3A3Q6GDU81%U]+T�}J� N����*q�� u3I��\�]linn�yJ�6V Q=\Iz: O)�>�s >B. Acc&� !�C8�I�Rb*u*V>d"H*� F�0�!� 5$��_3�)B8��& "� _3)2��))��1b&_3)|\&{\ & ="\V�hWc. rg+%�+dc�1{> .�g["�M0/2< � Q&�$� t_3 f��-7:�"4R�BRZ?6d�N�oB�+T$�K��rad�Jo�.efJ" ). So fa&�:��nJ�u�)]� q�,,�p�d��U�]�>t2&94,�IUL0Bolzano-Weier��ss,���i�6�2� limiv8�,_0G�i� @���*Q = 6�@{0 J6�{"�RB2F� 1 G+%�.0 - x9\V�2��q ͫb|1i޾:0 N�.s6 �K:#a�*.�`_1}^{t}&�4* )j)gz!�` dh?�:�))&<25 ?x -EBe�V�Eq!=�.#)[42=E�})a��qub�� )�.B� &� $0:�53M�r8laZ �. z�� %$= \sum_{i=�C [6Qoi-�|(z6N. �ftyG0 l)* �4��BW��iJt& ��f>vOgT�.��:�xt�5 � t)|$m�^.@^,6m]\[:Oz6N��|6�&�T}>|+~S D_{|�9|��]� 3 �"x_{�~�})�d}{dt}6�6�$HKr � l���kF�;;im��P:dA�.�+e5i����'�Mtn� =�i�gl }�nI�a!K*�LI�"�;�5�($#.C� b�EsT�3�T�� _t_4>� ���$�2�Co ��f*5E�&�s2}� �f-2!;n33a�#�_)QVB� d�Z"ݷ�Ysup�-&l a[ xQt�4*o a� �<"�m� $%q�.Ÿ4&�co�;6�1�B~ �V�5,j��}t��^{-�}��*!d\xi,2�yeft:Ru�'gNh\xi-\nu��\xi>\nua>.0!)�q+�r \nuN� \xi+U<8FS�� �Je�.P)nu 0�� � y)i�,�FaO2'�u )�-� W�B�BIa ^_4�%��"�8%��6 ��&�9()s) ��*: 5�8S�k�7� Yj� $\nu=(>�)/kSU�&� q ot{V(9M�� M�X V}&=Ic�=nu)�:(i,6)D M$�=E�.kTO  0.�� YE,m+ �B����2yIJ���b��G autom*Q`%HW)��(�E �E5�E$\|i�� t))}6�u(3��\%��Е_5�f ,!�>v82_Ҵ_0�rO9Z� ,8�`Jbfx>B@G.� +�D&EGu�dqM� iMs&� 2�JU�/k-)/k)�)n��� $\��$&�B�"?s? �7Zc��`\.�6�)x�.E2�UI.5O�9�M��Yc[�rgAV�3hQ 2U:66�t*�CK"Wc�Et_*Eof�v.�varZ5E;itzQe"Brpi�Q^<1/3 k4&���S]Q1^c2!��$�f�;t:J�A 3>:fs�e�x,n�K2G;]:� ambd:n&,���#��U*���LmLF�}:wK� �� !�* � � &:�? �Z��.K6N�b�@�hR�pN���H�+ .�� *�})|&4y- ggsW�tly*s "�x2��F&i_0��/> $, $,���d 5_6=#") � ( I;�/, \pd2sA( � )))/psi*B,>.h@�%q<aXt��%o�*.p�N�>t"bBo#Q#<6,t_6%3_1]>�"� N�6S6G6R.�5{"eL_PE��awy at l�$N�2�4�^2/2 $��i!� $[ t]� , t_1 + N T_1�]tiO�VA�Κ�&ǐm�,��ʩ.�R�:H� [F��d�*SM"-F� :��N"�!A9-�"*�!?.�7$, J_1�ѪQ��7� ��֪� �u"� r�%nm{�Dtwo�>siPNi�S4HV�X� �&D r� �ll �u>o�C��N�Nt �`Uba3vA h ��o% this�*�K6a[_ly� i�xrgu[.�&1Dx i�3D{Q�P:�j�&� *��V�p&M��2�i���j8G�w)& r.�s4A.�&Tp �Iy�i�V}."�A� "1F!�V]� $\R =" a�!�> i"P|7, %R�!}sa�9n ��kHOVd��=�8���Fr"Le6�M�-�B5,n�A�(F��"l���ieVQ��� �QUcMB9docE~�O�qiv��s_%MaP" aw�e�ei� � ^G\%Yf�Q deca;S(se ��AJPs{�TSastry89,Kokotovich95,&%{8,Jac,Ioannou_96� a u rehens�ourkXrU�EYre�s�KA�P)�I�bs&��hWv�^Q(or�S�arS)*izebs&rN! *��!���*��K�n��R�le&M�olvedԩ��o nE� few -N>cr"a&�U!2UA eneKV�X�sJV dampa/of"cS"[�Ii���X , i�,B���pe"V��Ddil0& learo_:il in dK�&�_wXUPoldereW2�� . N(f��Sse�-VӁ! g1�R�E*�q redu��.i�c��o�Tpi�� w!�"_�!kic�E7&grv�$io-engineend,� , physI] bi�X . AmZ� m is<�ce, %F( energy-effC�%%E e ��inU�%�Te*,�1 ly %]�aWYa1es. Fđ �Y�;a9*Rs��!L�ic/m vid� i&�d�9;Z7s W%M۔a�levelO!�[l!�d�XmotL��U%W!N-W�TGaIPBrennerAN0}$�Webst 2}&��Mathe� V�<{Z6Ϝc1�m/n�as �^�=re�[!�F��L neur��Yrt0�) 1  u!.�r��bF.�fm/Abbott�1}.�Z��ap)K*��Wc6*[�"� avoi�Q]��"m�s�E}2`4 XY[�>eLt�\nod��it~sM`f "W�G r�$r�E$�`� ��Wbl�4e����ityn(A=i��Cͯ }� "���6��I�e;�1]cd� in���-�� shoo%"�f���N lHw�ZnaQ���ător��ast�-��T����utj�ng. A �j*Rfm t�i�%�on/br�"��e��Ytire-roa��f.b��Aa~A�x^:��&ii�PTPacejka91,Canudas_1999E� eore�����S�me�c�� �Kt � �9it �( synchroniz%ԍGauthiergD6,Kaneko_and_Tsuda 94 a`3�V #fKf � liv!� cell"l�^�"�"�] ��auY.��in)U�8Ll�Xy �Ws*��l��6�.T�]J�5�AR6�)V0al phenomena � ly. Pr !*n2 Eye"�\e��@�9�ful real-�r��of(I;&�3�  oscille ��1�reg� iV�"!�-v(van_Leeuwen!{2�K�"�^!A� �pric52�5f-orgav�q���-==often;Wd�b,earthquakes ͦak �s$�*al !q��|=human brE� = eggs?3}�  � ���(?a�I� pc�.J��"  drE�-;Corrala05�d�'L�Yp�l]" �me~!�1䁶��i"h�rn!�a��ll��g task�Mos��eff���qnalytE��� ��:� presQ��-���ed6�, &l�n �� N�u\#se�>� )�Lin,LiI���) 30>U&�az�Z�α).��-�)YE5&q�rutch�e���J�n)m2�&���� a p 2se"� --&�_���=of���D5`� or?r>""0�O-u#tZ|!J�x E��MU�a major &dis}aQon�n�;1 AA,߲eeded-%*M����=� �c tqrMmU[e*�iP`A���lyisJd��s��K 2k�!ed� "I%B�6� vir in�iinguish\ S��&�f�`1"tec� fQ!�*� y� )/lg�p�lP���Kar���f 6}, a~[e*3->``!6zidF �,,tpt2003_tacY� �ga(�aa6�)�!��6  1V*�b c&��qs *�ecA�mt1Dgoac C V .�퍆I's��� reso��� helpA"�2�A*ny kind�C Cty�m�y�U�����t�� avor�X-�y >� y�i .xu� 's$yo�[p� A��)1o�ޡ�}e�B�;��a�1(BtMIsidory,qAa9.gFr�e99#F.�as a rul� umb,ʍ�ty ���ws�{eaJ� ac eS*� AXme�v� 2� s"# fis� ��� AMIi&une�!��e�� �g� ��2`�B�%Dg WQ�BU �d*[��΅<&�]��d9� beM�"� ��:p) ��np"r ��J��<French���er2kmpy�of��EPJ�Q .\]�s.�-�" �uy��)o*��zq`tM�: ;ѡ AFckuP �,"a�ĭ��a��]���3\x�4J�fĚb"�*hreg��i and/or s"��.��Z*���aN!��B� � �w7�do1�n�&֒2-k4!��C!3ip u^%g� 1� �&C� seem�2bF �|��un���s�� " e/!v��2&��� [�ʚ. %zcus�n m!!!R�&va�A =l�tat�Z� 6��/H�jsZ,&� to %�w.�-xi�US1v��Bx�E-aM��s� �*45�-!�l�to{�d��PbeN���Q�A}i�, %&� xrүto*Q�E?*�gx%�&g� Mbers. Jr�e��IB�"j! �� &y��5�O 5�)!{.\ ���al%  f 3�iq de (�e not �m)�-�xcy""���(eye (tremor]d�DE�!\*��&Pjs��P`c�� � Sole�199H��*"t� �k� rep.��.�U� !���F, Ed"ngI��!��IGt !�x!�M� �� �%lem"vMem:one�eWual_6<\Lk� i6hd $f("�9:pF\� s M.a�N6�b^i0b)=f_0=\�#�?�jO**�7b0u}�lbar{f}��sun���<"D)�� ��g�?�3&z' �'"z'[ =R=B�+\V�+f_� 39[630�J�A  $\bullet$dul�m�q��5�wex�|by���sh���et!S/oopA� "Qs"5%��rou*+o6� r1/recogt2. �4)l -Y�etA�I s)}- i, �!�� a2MPeanoov.e Sadd.q oint��*��� -  ��a�le.BՄbrq�u�&�y-x-\u \�2ef Att�ng \ Se>) or.0& & A.L�z"2)�2\�sWB1Eq.4IG�=�Pulin'�]�on1C,in EEG �N\y � [11pt,two�o]{��cs�0 \usepackage{�oXxsym, amssymb, amsmath,� theorem} \pagestyle{myheadings} %the runnnig � \markboth{A.~Glutsyuk}{On convergence of generalizedttinued fractions and Ramanuja>�jecture} \setlength{\textwidth}{15.5cm}B(height}{22c: evenr!�_12pt}2}sep}{20>topv0vH \numberwithin{equa! }{se%�} \renewcommand{\labelenumi}{(\arabic{e)!�-�)�change} �D6u laim.q2#example%E 2'rAJk&R %(environment!:8of}{{\noindent E�bf!>�of}\,\,}}{\hspace*{\fill}$\Box$\medskip!$begin{docuW�} {\bf Syst{\`e}mes dynamiques \slash D(cal systemsID \ \centerline{K\Large�� u� }}} bTa�u�'s�q�} ��\l� A.A.�V}�Ddef\cc{\mathbb C}  var{epsilonQ), abst�e } Weta�r t>� 2u� \� {-a_1}{1- a_2. 3 dot� i�{fr}\endK a�\ real coefficients $a_i$��+Ting to a limit $a$. S.54( had stated����\ (see [ABJL], p.38) sayN0hat if $a\neq� 14$,;n5��es/!� only $a<9. The �A of8��Pwas proved in [V] fo!laKxR�$a\in5̡�minus[ r,,+\infty)$ �Palso [P]). J.Gill [G]u��di!J�of (\ref!�) under#assump�� %!!�\!y> w�$ fast enough, more precisely, wheneverF24\sum_i|a_i-a|< �.Mga�:!O5�2 .�� �s always�J���ined upAY,now an open �!! . II pres��,paper we dis%�4 it. We show (�" %Zth1}) %E!�anyA09G4there exists ai sequ%��$ such G� B$s\footnote��D author acknowledA��PAlexey Tsygvintsev ha�j@structed (by a cE�(tely differ�tmethod) a beautiful explicit � [Ts]A]aB� 1$ given d,simple recur`formulaaFisPco�� from!00 analytic fun 8ory}. Moreover,!�J� go})M�a's su�lQ:a� cond�--oE� ) isk optimal%� 'o� speed�1�Mof6!�$'s. E�w N��Su�nu�des��%���$s g{\'e}nralis e�sf^et un���j deyp�w��RRsum.} Nou�sidr� N�a:!� $$�+ f} \<(0.1)$$ {\`a} co|1�s rels%p��$. .%aMg) l�( or$ (voir62, quia�ait e si��26 alors la2%�, 1et seul�A<�R . LaER/A8a �t )e mont � dans �D pour��)aSxAQ�(ant vers un�in\ccnH �aussi BJaB�).���,�Nv8assez vite, plu��cis% 9N,$. L��R�%�nt�� J� toujours���$��p, restait ouverte jusqu'au p ���. I� %�onK('elle est f!9e:)�tou���i�/ istee)suif \B�$I� tque2[1��g%4Y�1.1). e��)��H�� �cedante��, A�ɥsE`>�5�-c� �e sur�!�ss^�Aف��%�.� �ib VersionaJ,n\c caise ab)-��e2�TJ .} Pa���)~,Z�} �A��J|2.}a�E}tA�don��i�qa�� @N$, $q\geq3$, et]$r_�0# r_i> Y m# r_i=K $. A��YiQ�i�Y� h I���al a,\ a_i=� {si�EP i\not\equiv1,2(modq),D{qi+1}-a=O(r_i), a2\ Lqaw}Mto � ,$$ �.�)oQ;.� w{Maina�ul9 n� pl� �o� � subN5} � �} � �  F? ny. ��.� � "� ]>*� r co�dA��*� �"� ^�go} GF �jL!.� JN&Y o"� ��{r_i}M_-"rash}.�-�  =#�pYq �:5-�Gb�if��Y�as6� �fgo> 9��]�� 2� roof�gen�A��rr"�R��L�> zz&Z} &� oof� B� ! us�e followexpres�xof�t6.�a� ��m�s@ M{\"o}bius trans� �%Plos| P half-!/ H=\{ Im z�0\}$.y�b�<rr$ � �bm��T_b:H��(H,\ T_b(z)=�$ b{z+1}.$$Q�.�!6 %�� t r�s $� ({p_n}{q_n}$� �r�are&� /!ulaJzC a(=\tau_n=T_{i\circQ n}(0)._tn>�e�.�a� *�� well-4ne�I s immedia � )z! by indu��in $n$)�Recall �Qa��%�B} Aj�$M-�%f!6 u>0is said�be �< elliptic} (resp2v�Lhyperbolic), if it 0a fixed point�Int(H)$>Atwo.+ s o�� boundaryA $H$:� n on� them�atlorc o$is�QpH r). (Each� e3 is.+conjug�rotA�$n of uni�sc. By d"�, its)&1j}`@ $(2\pi)^{-1}$ ti|!xcor!K ng <angle.)e-%|(multiplier}! a=t:  $T$ (de�4d $\mu=\mu(T)$m�4 derivative at�5E A}.�$0<\mu<1E�E��Qdef\qq�*Qb2 rk"c'ai�6� $T_a$!'Qa��*Q . ed"�@$a\mapsto\rho(a)$) ose valueU!g5X)� of uA��'&��,omorphism $(�71&\to(0, 2)f� c� wF�.�eH% a�� i\rr_+�}12$. Onee� $$%1)= �3 si0 H$T_1$ permutes cycl�ly 0, 1%$L $. If Ja J p" qq!Cthe)�^q=Id!E&-���� } Le� _i�  a"��K��a^n(0�does no�WA��"�is!�eie� periodic i  quasiT . ��� I�# &� 2E��\�$th1} holds�f e�O $a$ g1!�Jqq!&9g"Z $smooth e�M> fh( $\{T_a\}_{�rr}: �o H paL.P>E}.-j@$ be a parameterm&� �I' 1�"� \{0,IC 2\}$A�d $c'(a)�01�A *� 5u�-2va�61�� �$�� tn})���s&�)^<�G seri�F� ,"� _+�X�c �$ can��ca�n�� satisfy �� E�Q4U�YE3vEVD inIHYGla9�-!�n�0:QMas�W�1.�2}YHj Q��rhom�$const$ nea4$. ���� re "�2lBm�p)�. :fr sq�2}�m�3} imply}.�1}�Y�f{t:,A( U Fgo}. It�U� d i� next S�onP{s� ( 3`�"a{\alpha[ b{\betaA:IL�s�Mrtalu�$.X Rx 2��T!�R�thus,��1���ho�)ap� r� 5�� a_r,\b_r-�as�$cified bel�d pu��D.s=a\�g�"� 1,2 � q); \ �r+1}= v�r+2}=�.HD�}Zdefai:� ��(T_{\a,\b,q}� \a� � \b $a^{q-2},\ -��rrG �5 }"1 so�}��>� 0,q} e>"{be*� , � }\ A. R_r aL"r&� s>0 r� s)}, � hyp:B�A_ex A, R R,vA�� R,\ R!�in C_a/4T_a^l(0), l=0, ,q-1\},uar~t,\prod_r\mu_rE � !��b_!-&l mu>Va�( possibilit ��above��iceO AC��TQ m�� enL��q� . BE�woYe�.� � 8paragraph after�QZ�B�s,*C"@s�d!�)-�� mu})t� Mla�os� e�H_1�H_2)�$��n arbitr@ �{of]� 6:s $e&>, $A_imRD bj& %6�!6U� >�RA C RE~A� :��� _rE5H_r�T+ !� mapp��Rc= wide� H_n=H_1�E� �g�i7ly � ��a [ox mpackt�W($\partial H"&  R�[Ŵ.�=�of}M A_i=1=R��gk!� �.� J>� we c � $K\S�tN�0 \{ A\cup R\}�O $i$ -� �6+ $HA move���T$K$ towards $A$ (along.3$)�$ asymptot{ � samestance,�x&c>�} # :&)I4i$ but &>w��oge@ Ke�previ�9�A�gmonoton����ri�aC_i|_{9u1 mB=��r�#��'!�H�%a��A�0 } Il"R2IU6�s%�r��~$ � ����16�H�liX*� $}�o"j��$e�}�w{qr}}y�um� 6�(�u $x$)B�� b�:�)]�=.��, $0��R$A���ar TAG9�atI��x$E�$M U ToN!E"!swho��� �2�to�, wei5���[ich�#a����(e $- o� $Cyof 0 "amee ���Zhak=($\delta>0$ ��o D$- neighborhood $U"clat{ {be�jo�r��66)>]onU�� $��.�E��$ _r�,AYIqbvE�  {l-2F\in U/ ,(01�-� @,� mtl}�(Techn�� W,).}e'as ��,FX+qs��2w�6��P $R� "l�( mayb�& cept%�*s� pob+ar ��of� *sJ((a(t)=a+c_1t b2c_1,c_2�rr�abt:� ]'�$t�=m��(�B6�%B{�,{"� (t)U�{� � *)���  $R(tF~ &�$A!) tendsE�R$>} ń%s $9 $�a8t��]. *��Yachiev]���!� x,�be�at���#*�t$! $t=0�g��\y��:OnonzeroaW�I�f E�*�� �Be��Hb�e (�k)z����'Cus | *s atm�!���of ��!a�. �A�EE ;6� %V��bt� T�� �xt_k\to!�e���Qk=f_k hb(i�Z� D r r}) � B>0*ion. C ;"s,B\sum t_"�" ��#r)�$t�w& ose)�hi�A�(o*f9 � &c�t)| ű(ty�)$jMN.�A�: =$1+st+O(t^2%?sI y#�! $\ln4k=-st_k(1+o(1)� Indeed, � wise%X'(0)=E!�:G%�R� would hIa.�>T-R ntrad� a�n�X U�A�e91^inish .�. Stat� �TM�"�weI�!�r_�%B: is �& :mżJ7}Ab�0) 2 �3�� -bof &s depen�5� variable�wZiX$\b��!9�A�.)�i�2it)$�=\Co ��۽� ]t��)=(a,a��w i�,vector field�* $�d $v_1�It�".A"���s�� ]nE�6c4$v_2=(T_a)_{*}Xie�� imag�&30>� T_a:& �%&. �T4 ^Z�s�1-s v_2$4!LE� ant-�r�nal�/erIarMgroupO#�.be^!on)&1-me b 2!2Au�g�#>�m���olvA- . Si���e+� !56i ��ng�!%� �ery"�,#%� involu�a�Hrst case%�i�sible::84s m fWsA.A�- f+FP"� @��L� ���!�EChypAysia_ �a,�A].. A+]!6� � I�B� �fi�combin�( $v=c_1v_1+2tJ0mva�>a��I�( 1- jb/Pv$ &� 8 �U'"Bw  $v'(R)� by �8 sign)Ma2` g�"m��4$A u6�!g6 �2:�e�tn��� look�for�I<� �Gta2�0�9uta��0$[v_1,v_2]$ ��4:,(Lie algebra��Fe* q�) w-wi0 �s"L ����$yQ5i�v����.i1 can�m 5 than�T!��)t"�witO " discuw'� eiW.2u "�Ca�of irrE�alc@"f�3�1 8wt#1{�tilde#1}�2� $\ u�o�c wt a_n;  ,a� )= e�&�&Axqq.$ 5H *�� n� Qz natural�""�  $N_1,N"8,� �#n$�� s: 1)� $nN_1q_RPut �n= �1��if}\ ny��, q_1&_1d1, \ Mr�.%� Ch.2!��!\b_n$.} kA $\psi_0={n,0}=Id!�@)\aMq,�)Wn� 3 b6I�}^�)� L {n,1>�.{{n,A 1 WV,� �{n,9 )2 ) *q�5qfor}\ 2E<� _n-1e\}]!b2 "�&6y NQ�n�2 ,q n�*�,"< hypnB��"�d� MA�{A_{n�� ,l}( ),0�}^�+0)|\ 02GF}-apr��mat7=Np0.\�rnm>�"� @&�remrmb+��s�M!� nt t�8d accu,�&exact�. '� M"X �K(J������(xm�)�_�H�wa4��b\ readr os�o��E�)�� )B.��Mh|��1΍� E�kk�.�!�$(!.i$�*6^-i�in'a way�}B;diam(1(M_k))<�1{2^k}v='k:��.� to do� QbB.� l&A�%�u�A. bus�<tAvC���nW Cauch!��_9t$n�_>${i=1}^kq_i%�#%�6cA�*�B24 }\ k� �panm�0 n_C haQ2 dist(�n_k�m=u{k-2}=ystBy� 81: $m=n_i>n_k$,,  {k+1 1!�n-"m =\tk�)7m=-�2} \tkYvAz !$B'. $0��w2.`M_k 5iII$- �,:�)=6k(eFb)) 2�"�1� )�TJfore,}\5�.{s(0.�{k-1}+%� 9� s>kystsFi8'�"�k(rA )�)��GCl�!�%ϡ���y.�$s.z.@6 $$n_sŰm%8}E Pures�<AppliquIM.R!�{\'E}c�"(Normale Sup%,rieure de LyA46 al�ADe d'Italie, 69364$0 Cedex 07, Fr�% �4$E-mail add9:} ag�ML$@$umpa.ens-lyon.fr � &|JJ� \4class[12pt,two� ,a4pUFP]{amsart} \usepackagesymb} %24�!P} \date{\today} %%\indefs.tex"� ~�jJ2$title[] {A�l�0Poincar\'e-Le '�$ul�-".la�J�5� ef\ra{\ra,End{{\rm End�-7 deg{�w$deg}\,} %!ef\al \tio\aleph$} e w{\w�F d�.ar��JJd\ 2loc �lockR{"%6RCCw{� MP%Pcp cLC_pblBAAB*Cn{\C^ O!=ddc{dd^c �bbox{%squar15GIG^ od{\7G�!{D,t{\leftarrow V!,)�)-%%%}�bb�DkUMMjHom)�Hom\,  codi  NIITot 1Tot1I .I.FKrK[Ker AKer\, sD�D�ZEZEEEcan ZcanO)OPo.U-L,L,QQR�Nrm Re.�Res �Res.Au-3AutBRlUlUa�)s,sr{\stackrel�D\n.Q�QlmaPm]{.P�4 {cor *�P.au "*�)� C�Q&��df}2�P 68&:4pre {�6�4preex}{Example p.�P=�O}{\qed�"�.@^<ex:8��':TV%S6$ \� {Mats A�MssP��{De�(& ���e� cs\\ChalmOHUniWH�0n&ology - 6!PG\"oteborg\\ S-412 968OTEBORG\\SWEDEN!Je�u{matsa@�c u.s%j subj�F{.keyword !� anks � was �/ly sup� 4<(e Swedish N{S|P ce aD,earch CounciE�!u'a.:Q� a �Nat�' the �Y fc. �CG1�;c u5 $f�=XQZQɣd.�Z&�?a� ks +og|f|t�1�uDmxXelefant} |f|^{2\lambda}��>�c2\w� }{4}\w h,\quad|B>0,��q �#b��Mb5 �(Md} M=\lim_�a��0^+"�� =�r(�|f| �){�\ 1}_Z>� ( .d�8Wl?r�Y ;>�EF Z=p�8 $$ M=M_p+M_{p++3 $\min(m,n)}. M_kF-0bidegree $(k,h.andP_p=\sumC@_j[Z_j^p2RZ^p_j�)A?irreduc�(-ne�[D dimeI� "`Z $� pfN4Hilbert-Samuel"d9citie+ a�a}C"v^(iiC:� � of.� *,*)� ={mO "�+1�6,� %� logarithm� ing� > Q(� �c#^� bas}�"# C� -MB \ 2�ni� y�b id$� ����H!#D����{�3Ject�H!� �?$D�-"A tg2�surM/6 (D)=\det(�7 +I�S�  =D^2��y"; 03sor� �� c_k(� -�A�!>�E<]@/R @O ["IO $W�ee &ra~J $plask} in �C grottag5Y Waw�A` y*N�,��n \eqHA me0XzF2MG_{k-1}=%r !%t _kM �+ -Q��C-�  $c_mE�=�0��<��I�_{m m+E)-M_m�t�"�]in%W�*lete �rt "�p=J  A]3et�@�oL || $d$ ra�an ���5O5 q7[S l (non-ho"0)j]t-hsE �HS}, L1},L!<��3}..� Cl�  $M_piB`ba���r$u�f�6m$Md}��� M��� Eve*7$c�w�1 d]!�. �j�im.  !��oM�o *-�Ym / }. ; �%&��2�E�0is Nakano neg�Q&�5, � x} A@d�JA��oU. T�%9_ER�,�?-!��� B�s,� (q�`.� u�) .g�|f|\le 1:�& >�W$<�, c& -��U,^� Ap�e A=dA6R-MBCa�I�A2�Win�ed~:�  R_p+�s +R_*� $, >�vfg6 �A� RM�bk&b� ��_$\L� ^k A )�aB���6d $U=U_1� U_m$*ZY $(\�A_f-%2)U=1-iF -��y|s��#on��. WE[IqJ� $U=1/�V (1/f��1���y� -�f!A�3fTs�as D _p!�%� �f)^p/p!;�h�`��A�jW�a simi�FsomewaAR2�5 ved,a�q��f�!lua-,�� �gris}r2_ �or|nx way� ZGe� B^�Ni c��el}�Tn terms ��Q$U� x-�� $fD1l� ,f_r���[!��� Z+n !�y%fx-IH they�K�v:entl$";fK&'�� r$-sub[ E$�:� :��nd \�. � �5"� 1/&� � .R��5=lR[=$M�"�  $�� � on��&� I�H1�q ���aniP.�A�)"B��'aJbe�d � modificd!^!� argu�AR�p�;��M se�!B%xic &9� �e1-sL�P&� " zLal�sh�=be{ nta{"� H6ItR�)&�� " "�i2en�Yv��k(�(��k>m-ra> Howe�ha��� no��ou"Y �rI -�qg i} A��d!sed�N0!�Vf��R?�� } re8o *� 9BC}, K9�a � *]rol1�V� To b�YI���js��m $v�n:�.�� v.�S)A�Q)�,By Hironaka'� �etoAM resox;s��l._� BGVY�S� PTY�wA)an!Ive1�aDPA��� Eݹ�sense < ��` cruc�M�:Ra py! A�? u Q)$ (B cqprop�,� �u�conclud � � �"�W�� ��9�y�P�. 2blow-up.�B�~=' !� S)-1A.� outX'��w�'Z)�2,Y (if�capitalsu�in>!s� $Z$)E� $$ W= .�� -V�&M�� &�.j%�A�.yx}�` Ygn�ly �Cppl7H ideaa� I�BC� In6�1}!�A,c ity�M�T^-6�,2�6~EG�I��A�QJ�� some8F#s� .(U{P�uminariesI < � rm` �@y a% geom�?�i���vm�x�*!���JB�x6>�� a., l ma�Qld� ,E�& 8\colon\E_k(X,E)AE_1n��� $D^2=�00E_2(X,j) E� !f2[=D_ �aeE&`� �?�_{ L}�A�$ELN�O�e $Dg� \xi=D(  \xi)- D\xi$! i.l *�nmZ6�_{E^*�.8 �, �:A�*�  Bianchi'san�C^�b *} 1E})g=0�9��A;} DI&� !�C_D�$Ee%%%�0>� ��zc�&ed6K!k� �O h���UichZE q#�2� D�N��a bas@qa��S�H+E z.   0de~Rham cohom�%eB a��wUE� r�Cal� (tot1 ə>��F�QQvF�2�T�[,anE7��rىone�CeWLy $D_t$ YQ�E F�th!0=%*f $E'�!� pull-back�$E$9rtc [0,1�t$ $D'=D_t+dk)PmI'-ts� 2�!��f�'m�Mt�, =8 {D}_�!� �Po  =d D_t/dt5�r�|19*3 M 6Wdna�_1�O(F)6� $(d�)6q'+I��E�tEG$ d_\zet��t_0^1J5 -\i  d_t! �WA��%1� 2%,x to mK!���MBm�A"�twe "O,�ri�5JBIv $�=  (T^*(X)\o�pF^*!#Any ͡ $\xi����A�coron�Me`1U�7 ilde�ER l$;�fH=\xi_1\oEa e_1+ +mm�a�alme $e_j�}� � $\r [ \wFW m&ms4Hway, $!�ʹ�)"�`�p][E��0t a_{jk} a M�e_j ^*_k" �e_jy!ץ�frame, �S$FR9j S$ �!�e��`s�ym��A# �  $�:F��A+!�sa�S q!A}iar �� $\EaI$��he��a nti-J�6� �0� �'�IU1� �a�a�acU4s �E�*�llo� $I�$-f���8se=m�9�${D_E\xi}=DUV5�Eԅ��A-v%4d q$�#$E�� �QaA��Ha�2.Z lapp�zN��n6��2��E}a�]�B��-{� ��E�2�a� $\��%�E� �$$*V(e��!+$6�}\w_ |� 5�i�93{.�} =D(>+ eta)�Xzlaimed-e-C�W�k1�I ($I=I_EK H \"� !E0� EI�1���Q@enol} D��m =0 \;$ < and}  M� IJ %%We�X�� I\;�� I^m/m!$��X%��Kn�k �o e'� &RYl. �Ya@ $\omeg�geN-�M w�8n��3= '\w)��+ '$��ly,&g7�l�Ad �t e_j,�T�Iwa7 fine!���e B zE�t �#gPiu co{�eD��+^� skod�0d.n�rt_e D }MlU factTxn;g5�_mEw�CRd R'i =F l''=$=2�UObser�^�laban}� v�"��I�+{ )_m=-k e^&'Es:'�e2]�B/aD%e&�J$D�at!�(I�� �N# . FurA�!�.A�out!� �b,�geNulaaH�_5��� smut�$%�H 3 e\al.� })� -:=_t5?} 1Y 0)B%�W�H���� D_�k!1!_1�%r�& ous�6� "�pa`�!* �$is�� o� 1=D-\gamm K�  $ X � E))~!then �$_1/  -� = + \w $�Ifa�!�H&* � topy�.t=D- t 7,)�#^�v?} I�_t �-t>� +t^2 W)� �U ���CbyB�b~bror}]*�:-t� �#{ 16FV"�>�#esQ�bcsekŐ Fbi�� e<0u:,2�-i'�3� E�I��eP"l%<$D's� $(1,0)$tA�!d]�!�&}kA�->h� !F�,.�dA�l\ R�ype�, �'� '+*%$�"�4 � a1%2�-� F�%9% >�&&(� -[�-val�?��6c�4V+�,5_k�,k}H,cap \Ker d}{ ,$}.����*� �ND�.����smoothly!r]al#�T�It$&�,6�L�k� End(�i Vs2T�[�$ab�cbvillka�D'"� L=�B�Also 6�q�\(� Aʡ�G all�.��!9v=-) 1}{2�P��B�0 L_tBC.-dt&�$6�1v=b�her�b�.�.F�}_zt%��!� �\ is l��P(A~? mater�B wdis takeBom*� Ho>�ca�m "'� mH�mb!hter'�! venie�ju �ׅ� "�M�� viewaH\� �  %%AV  ??} 2b (i�' �h� �A$t$t 0e1�R�&"L � ~1E�by�sQ�s! ��%$&�v: 6~��'��FxZv9Er%%%Iv-�� db63 $%1�� D Vus�-���� cbhom} -���"� B ���dorm1���|u,2�K+��:�AG&b3&p.�;�+*�m@!� � Ui�(NM *�(. 2'&�a shorH��k#lof.�2�s^jI} 0�2S�?j}{\r��a�A Eg:Q/F?3�� $Q�#��6�4)��du�&^==[ "��nb� iso} j^*�% g 6 �S QI�Ujr��6, is�:sm� $D_S �D_��`>�s!#+Qt.sKiQ|� Z�7soxWE\sim OC( - array}{cc S & -\0^* \\Q ta & D_Q � / )�) �v:6.�q�!U,1�o��_{1,0|�C(S,Q)�iY se�[f�|�#al�m,}Dem}. V�� �#H+ "[ZE$ �.D_b"� _�Qw &5j�tur�uJat�2 =g^*�N!E 4� us'� ���I � ��(�9 2, i&�#;pD_{b}�� %�0 n�$$�`� A͒5�Gthb"a brx= A]} VYBBk� b)�=#I%x $D_{t}=D-,_b"6+!|�*� )^_b�Xzi4{s�N� 1e�lebj ga5>� 4� kl< I+$�-t�+ ":} � \ell\ge 0Z �6*��.`"S do�1��(ell+1)!} (-V{)^u}>�]�.(s;M�d ��5A:���c$L=af/(1-t���n�9&� *# . InX$�  D=�e�E�$[P,V�]=V,�"(ngqRB.[�7,e�]�>pha �2 $B/ +$Ũ $1$-9s) Q�^Z ramaskri}*� ,t}L=�� L-t[Q,L]�\1}{1-tq_b� t6=9F�%WxVsoKbe��%m�bc^�b�Kv]�UZ5ImYIJ}{2AwQ�U�{!�O�J#Z��5WIR�f�_(Bk�KFk .$I�% � 9&of}6r*~ } 0^{1-\��e)>-�w R.��"_1}dt; fUD_1�X0d y`JE�q�{"T,1�!}\kin"[ R�[ U�r�7{!�M#af8.g ]3)O��F: b^-r6�J�} etdt�.�(<�q|I� jqb�+ f%A�osM&��7by��t� psk�V j C&uA��-> �qM h��"�(� Al&Db�-��3��.\ ��T> ��j* =\�d c(S) Q�  %%�7u��H,v$ @4e"��m�Au"! ,>jus� G0ed sl~ �(&ely. %%4wah�{IB#.q�&bProof> � mqB ��"7;%"�Fnontri�A �� c� �Q� 6�A!�r� ft" 0�0, 60A$f�2!�e��e V� m�� r$se� >� g. ]0Q%�qnY' proj.B$\sigmaB( 5!v!#�e mini�� normy A�N  ( f=1]�:ei1��>� �j.��N= f\w Sm9 2����jugate-l�g� etry�Csimeq �4a�ta�� � ^*$, *�* �<etaR do�(\langl�#,�RzB�#�)�,$AC�#[��*�!nĞ!iA�:#!2��lma>$\phi=-��xC^2� V$D')B=*�� �OL2i>CQ%=f^*/|f^"�j!#[*s�>3, z f^*=kH f)^*t 3<�!i�D'(i)=�) ��ZF�2�\H�= F"�/SiD &�� e�|6�(��$B6�-��7m�Mީ�m�1�U�-�btv182�=(Df-f � phi)q �Cm %fZ�Sba:� = `\#e�+(� f+f\w .�>� �nl%�.�� A��HM/key�0$�5 =X*20=�"�/��!�m�zc�0� :'Unaze>(1M5N �cq�_Q)� e���%�N�\al D��9SF�Q�pa�% sketch&�4PJ;�`�n؅�w&�N?�(^�"al %%E�&�;}�)�_b= {9$ 95byQ�b!�g.D$ @I"H -\big(�e?�)%%ZZ5�ox} 6+ y _Q=g E g^*+-\w^*�&� %%�2�krH� veri�Vg?=g�!!��%9� )g^*�1 in�� .�vin740vin2} below).�=y5��7='��M�%>�guppi" A�e�a�I�A� 1}7 E� #6�AFs��d���1n~DA�ryta�A�5�!�P)�5ۥo ��Ŵ(!s�O�+!/ �^) � GTLly��{y' e $f= f_1�,"�>f_m e_m&,�-��-.�<�,!�� ia s�|nJ��a�,8 �/X$,N�8�Vid�C�,n$-";al��Xx &�4�� U��?oper m�!\Pis .-�U&�, a bi�sm "�7\Pi^�(\{f_15 s f_\nukO|e'&�,%�� 6��reE�kc coord�se�!tau2cR *f_j=u^j �i9�� sn�pha�"'Au�=nonva�sing; �"�S`Xpeas j �=re�� mial0&%%Ie, �>c9b�ǁ� F(|h.'Oa�'QHQ���^0�� U#.-C, Ja17�:�6 suit�6t�:Q,ʇ� �Y1�� P�:we��y"�!� �*�5a0G� �{s obS=�UA�!��  ongbdK[ �MyntSm-a` abof��%B�D5 +"oc?�)Z$Em��z!0u^�s $)�s�!-ى� [f_0=0]\d2ADc��"AD{\�K };we�-�� �U: WE�C�Gof|�} aior�{d 0$A�usqJ� !4.P$+ $�J��=�Z� X�?�  ).0q Th� see, e.g.�Qx&, EI�u�T=�Z� �Q=��j � j Z�Z�,�, o~s��a $$. TotE�Ra<%-����l�&!�ip� �f$ ��Ze*�1�d1 v3&)�ic��a"g !\�N�y�!;a�*aU"W *.�'A3}, rids� iRp-1iR=(dd^?Gc^�� Wu :�FJ0)� �<&nA1.L� $\$Vz�g�King'"�J.�S d!�!9�art $(i)G?qjA���^��Si�7�23H�cSiI��%�hav�/!�G m�)= �G S)\w Q)- Q) -2|J�]�Now�h��2fy-, ��h�=: ��2"�4A directuIa��qZ�R u�MW��!P��z0ճv�H]g)�BB}, B�tZj�LVf�6h7:�q�[ ;(a&*a$��2a�EE���a"+ ��)'.� a=o BVin�xtoA`\ Koppelm%�c � e��uHpʹ .1�aek� $k=m$ ("J  a_m=dc_m��!ge+c qW �H$.mP!underUhXe*�HmeaELyD_�*6�!\)��"�Nappear\Ti",JB} � %%�� ����>�%%%q_%� f� �aH�r @��S�' L? xFMJ�S6u+ԥxi�z&EC( $S^{\perp}v !\xi= D�>$.as^?konn} g��� g(D_@Bc-���3-�&m7E�Qkwe&6i���tG ctua4!�>/!7Q�&d g =��I@Q (D_E(A)eta))=a>�I�r:� �IL�X �$�� � �w5�takes v�A�S�.�$e >��� Yn/0 &�,&� 5{Q� �/�"6�m/N ' �+Iz�/Ie-�-& I�e A{Q�:�=6�r'��t2A*!,AL��.d >Ukraft"� a� +2 Rrrost}k-$ �sf� --�t�nB� :U;_VW;_RJ_a}= -t(:+)<�\��)+ (t-��*phi�� �%kO.��ADe.-  y`�s� 6��+|� � + �u !�*�S\�=�ݧL�E��Iot��� e n�%ra.�& �;�,PH ^�<-�Cul pha 0D��N�� K���s�y�k_ .3H ���%( �t Df=-$ f�$H� w���%9�i��Nul1� �}E'a A�U-"U el} "B��=�J�/t�$}A~��=0}^\�� {V"�-(50E���0Fc�ekw$bar a= d ae�E�@QF�>%U.)nd)) Z-�!�#m�e�5F59�a���秡�@:t=D"Y2#�tw�H�&0M�D@A�%���1"C lapp� A�Bwr� �&� �33!0^1���#- \2 �pfS) -Z�}d�$�q!*�5A3WV� *� N� %% Nb1�Z"��j� a2#�$t*�,�7!qAq�F�IF6�-�=!t$da6�=.�2 �M�d� e y�Q��M �Ks�9!'g �waybBa1 abasC&:�!.�f@ba} b=a���A/�)\� �!�� ���>�St<<ngAQ�F"�!� �j�*}  5�4:%�[z� Au� ��6� �E�(^��}{(1+ )!}2!� r �-e;r/5�Z6~�u+10�K �z�B�1�� �s�ph6K N�yNr =�9� s!�o(16o � !rf� YA4I&%2QY battf�>&�_^WA�a� b,w�\w? Ia �y� � &��b6Na\ a�7!B�  gH"> �=���>�#�"��WA"]�SnY "�$.1!�"GC"�j �I.0(��E_#�R(u�F��v)>�4.w� Q)-V)=BAN^�=AOV ligi��teu� �ˑ/��Lskott2} B�d-�0 As�n�LV"� �e�R�d� "�F�u�U �"=Gfak�b8��Y�B)$�&"]&O , �e*1ճ <6�.J6� ��/ReK>"N6�x����52-bAf!^6xa|"Wr=0}�N{�an�N-�69 �2>B�NYl^�Mf} M=-d6f\w 6�=',z&B�3Ovw� �4�ie.�)�.a;el�\r!�Oea�erm� $\expb��a��)Yfo�'E>�N�+^�3�&�� ns�K�ert�I&F�C&'�S 2 full y�($an re6(�sbU�� a=�2� 0� � �1�*{ J�< �F�h! q $$ U:�% eI9�  \big2�=>�u�� . ��m�.Q���'>U�f_$ :z>��R��{RHR T�Jl -1} B��ise�!b&����:�,#-��df#�6"^&�\��, G\alu�x�� $=0In"��gi4R�m� not}Jv\N� � 6�#"w��Z$,<& %% R;i�%:�j #� �O"O�j!�N�s0�j^���L"�j �R�j ɹ*3 ��e�"PAf}�n MfAh� e �o��zfs� %^��i�x�J �:a*\J{>�"��RB�vf���hUBh�\m"Licf.1cq:Zm ��1If�\.e�;az�#a�e� :�A-C ?*��Zfd=vj*'b+�/lna�q�ж�N"%�Pn� '���$ax�%�;A+��&��:~p@�. Analtly 9�d&��;-t*f�! � . Neit���s����-&ept���b.� unless $�&."M ce8(�[=-2/6}- �! �� �>�iife�on�+eb�^-0&as�C�7r ERo�iai� w5�Y�x�g��2on�Z:� >^�seq"@Lto ��!L>���V�>2�L *�.6�KO�n=�2+ $Q5� }!�P"}� i���G"$i�7� D"%{� E\leev v $S. �U j se�M\(!*  )ex.�M $�MQ^*%P S q �:� $7 A�6s g1!�R4gYYN)\Rr* $E���BofV`s?inc�1@! on="�-)l�j-�v>$��B�@2a�e�"n$f��#њ�L�(.�3 g". }apa~� 1p4�I�Bf^*M`?Io�"z@� i� �^&�3Se&�c$_ *�� f-_���L �E>A�ort���7>$I"��E"Ÿ�7, y� ��%) �^* �A* | )|�Ye 0MaFA/$�!n!����.,+�Z^���,���<ɤ$diagonaliz)19 jL03j!�hs -b$e�9�s=�q�9 -͍ !.we"�S \�+�5�ejR�� �2dm"QbF amoj��N A= -F�wf}*�1�$B)�BœAe1 &4e a scalar-� :}c�  EU" mis��� ա i=E�B�  )�1�ly 2�!�GA@ �I�g�gm}&AfsomJ�#s $ -�w;�3~R�Yt�`Z�b2J�) �M0y�X�o�Jsku#'A*�z $AE,r�1�N�)"�C"( �< �h )�Byy)�6�s,zɏA_j��!\8\a��)n�� � gott\0Q� _1\wRh\bA_r B_{r+1��wm�d%Q $(r,rOform-O%=.K��FNi+��Y)�#"� �A�a Q�Q�m like1�X1(-i)^r�;at _1^*9 f� g1E2  \m ^*_m� [cW?r\L h)@Xl g=�=�$[/ Y 6Z�b��.CeY \bar. � �0W�=f"$ 7�v� (r,0-�%�$c_p=(�f,{p(p-1)/2}=i � By fub \coms��t{ � � ]m1B �xA6�1J�� e:��9>>^c@kmeg2[�r 0BI���A�� Zsbd�aA� )v:�K2��h&� (�� �e,E=(\s�-k (i�! l $k�w�2 -��t �#� �c�s��p����� $I�xK���BFc9�/�¡�c �I!�$&%%\^)_k�rIaTk�*��[�M2�r�3x}]l"��LsK"�cWE) �.�a�r��*w  e�&�y5� BՁ ab�BD��Q{��ck!�} .Y1��\�F-A�"M)x�>uaC _{j�6�H*7Z�.-j� RJxj>t-���s=f'V� �"=s�JI�a��;1P %%J9a�E�� ????bDdormski,2hZO1s}{(�J .S4:y' Big)! �'F 2H��m-,��q�%�s=(Df)!8it2�PB��BVi�i�g6Q�E�A_e��4a2r<p|�oafI�!can2���o",-dŘ �<RN2�if' �� &�$!� replaz0by $A'D � MGAreJ�� a\Z@be��r;ā��F@AEU.�I�-Reas#p�2Na8x}�.3N+$f2��>ow���! 2��;�&�ց>�lv_kM��a�kM��j6 V.�N�6��h�<K \wV�(� h I�-1�I� l�,$an alterna%�� Y� A�Z&no/gn�]we1�+o $�#2�< $ byC"�@I�N�Q)�aM� �wi|wn add/qlos��H/+ �l a cer�@��1t5^ ��Q�D���x��*Chk�C"�C�IL$\nu_k$ $-v'_k=-v_k+ c]���g��  $dv_k'=$K�ap� �|U -VVC U:M�0�CM�e�U|@��e7�� modi.��tTnN p�5m�6�&�T-$"q D����4"Iean "��( 2~�!��3-1�&�<t necess��@4iz�� $v� =�.�. �� "�M�� �5G83d-v'=-v!�l6%�5��!�a&K��w���1$dv!�h �� p١~!Dv��ruwe� "�M�)HB:"�I|RmU ��P\to1�qFDm�%�$j�A<(p�w�Y|;,���� till��un xness:N $Z^k����NfB^�$%<k��� of c*��� �f(,He��A�;!G� �2�OM!|]p�Xsum��Ej&=^k�;k.��%x�<�L n�cg�"1=|:Vg�)E.sj%&��As ) sT� �Qo�bqE{1�"uS3)�s%^W�=.o&V$zZ��ic�-�2TR8B�f�'�d suggest!�a` �J��[4�"$MA� ��K&?e?�.�ex��sni��*u�����Fh��� %�03�usl�Jr����Ys $E_j��X$,*�� m_j=nCIf $E=rgE> f=(f&�����=)�� �M/ͼ���ṽ:Ca=\{�Mn��� �x*L']�A�c_n(E)=�_1}(E_1W�/3�E_r� >[&�X߸:Εcou2æc͕$ f�8!L�'�:E=� \nu �X M_n�$NZnv,l&JA set-�>�M�5,w�'pZ_�@ť6�nA]��8 �Dis�Hcre,{<f%U�1�� �s �Q!=[Zπ%�"Bd�%we ! e�� !�P�-� coun�1���EZ)c��tp�)es� ex ��A�B�"OT K\"ahler �= d���"�i�]f��2^sq%A�"Ur%Gm�$g�!/ab&�E3�SM mQ)�4�ll=� Beca�N� bas�!C�6  $�AU�_{n-k�UX� Ea�%Q:\leXc� >?.afwC!�!�an a�boR���΃ mas�A�pA4� $�uS��. T�:��*�Cc AMes�.�{-rea}(Z^p=X[Z^p]Ǔ% �p(6�p ���n� \end{ex}  %%Inu0se examples^4have only usedM�M_p�� $c_p%�$!� %%co�logous. T nextUVus�ka%,ly actually %%are Bott-Chern 6O� \begin�If�y�� a co�te in���� $p=mm�$W_{m-�g�G >one�KPf bidegree $(m-1,m-1)m^!Y % dd^c G=Qg-[Z]; $$this mean!��� -�0 a Green currr��!�cyc��Z�6@ \alpha_j Z_j$. -M case when��La��I�� L_m$�T some.# s $L_k$, �]m�4E)=c_1(D_{L_1}}\ �{L_m})$,e[NN,���f��!�(holomorphic�fI�$L_j$, suchBLwas obtained already��0 \cite{BY1}.6�:Yx\label{koppelman} %% Let $X$ be!�!�0act manifold �t!�t�{i�J� $\etaŘ%a vector��,K(\zeta,z)=-Band $PA}0e.K=R-P�/��e(lea�a K1� type! mula1� mult�5�%�\phi(z)-�� �\w� )=\\�$_X K\w  -d phi + �5 X K \w d+� =!1I��ex�%R($-operator.A� In p� cular, ��C�clo�a,$(k,k)$-form9� $�=J� $�ph a�� ll, -Uus�� v���+�恘1iF^> �Wqq�\�6melog}�6���%��4 %H Fo#� er's�+ veniG we���%�%�of based�Hironaka&� .&� 0proof}[Sketcha�)�y f_0 f'$�� as be�  $f_0Eq.�!$3� non-��ing��&6-�-� _0|+ '|AhI5 9�'|qsmooth#ib 8X_0|=[f_0=0]$ has suppor� �,inverse imag�tilde ZY i�  reѤ���w=(f�)]:'Q}, \quad M^:#pQHb�JMB��- � o �origi� O . M.�!5 w1\wedge:�e,+ �" i.. $/ w)u12}%�@,� $T �4Z+a -�t>X%yɎ��. .�T� � [Z_j�-, p�we� dA��ne�in�trivia4 -o4, it follows��King'�����}�R �z6U � i�iey f$���7e_}W�#now�,�Ce5comW1�*� ��e existZ, &, s� He6W $H�W&- a��E�� &�  abov�@If fur�miaO kernel $K%�4reasonably rego xE a& A�A�� ' &� ! si"?  d ,6j +V�any"� c�$G$. We�n�!F)�&� Gg= w+Z�i* �-toT ]�� $� g= ��X+j MJ%7!I�� formV /K )#2��� �>WThe$ Q 0be elaborated�aalthcom��paper�B�\def\listing#1#2#3{{\sc #1}:\ {\it #2},\ #3.}�VPthebibliography}{9999�%$$ibitem{A2}\{M.\ A(sson} {Resii-�se�ideale\.qfun6 `s} {Bull.\ Sci.\ Math.\ ��L28} (2004), 481--512�\�3��of2�q �Lelong�\} {Arkiv f\"or matematik �43 �(5), 201--21%+ %%�4b�.Q�5R,C.\ Berenste�0& A.\ Yger} {2  �analytic_tin� {J%�a!W-Q%P,75} (1998), !M0!L9M BGVY6�~6�R.\ Gay �$Vidras \& + �R{Anti�o$} {Progres���%dcs �\114} Birkh\"auser Yerlag�3)�6I]�rIA16rM�t �  ���lp� rM*T-^ ReSAngewA��.a^bf 527I80), 203--235 �U!BB9mB)�ndtmL0Cauchy--Leraya�m)�2m !DAnni=4ent.\ Ec. Normup.)�24)�(1), 319-337��GS�J.-a�Bismut!�H!�il� \& C�Soul\'! C� $x immersiomPPAraakelov geometry} {��Gro�di|Festschrift, Vol. I, 249--331, E!.)], 86,I�EBoston,MA,E0U�C�A�>�S.-S.\ H}{H�y6i�ˡ��distrib a CtheirRi}{Acta �M+E� (196�J71--1����2� {Transe@Zin�ocide$s}{InternaA�M�M} |E 383--393AUDe��K,{J-P Demaill!�1�uN� Diff��I G9�Mon�X�wnoble{7%�p� ��!�{Au��sul�w lex sub�ie Proc!�arolin� nf.\� Ɇprsmapping)�Tminimal surfaces, Univ5faRth N$, Chapel H�(1970��3--56!?�H}W�Harve�=At Semm�Z�divisor�+atomic2&i�of)� -�135-�,2), 567--60��5UHL19T6��wLaw�AA�orye character!�c�.cwi� � 8 conn�= st\'>,que No. 213!+93�368 pp!+���j�MTicU��ema^mer.\F�117-%af 829--87E�.�*Lj�Si ���E��<-Weil �y. II.Q�!%�ita7 Duke)� �i�119�200! --158}��*ULev9̡�Levine�1�emY�ZU�` ��F D�NQf� 71�196A�5!>5��5�Meo]f�@Meo}{R\'�ds d�l� s�b0 n\'ecessairm�6iompl\`et�b.\� Acad��( Paris SAe I1P833� ��3-3)E.�]k�$Courants r� eo[e de��PreprL )�; |appear��8 mat. }{}{%�=�P9��Passar-� calcub! mer"!W %��2���)92��8� 37��9PT*� ��� Tsikh ^� �� Bochner-M�nelli�� ub� .M�44" 85-a� 27 SABK9!�l�D� bramovic� J.-F< urnol� %%! Kram5 %%{Lectur�n���Gy%L4Cambridge stud �MdvTd!�� -]3} %%6�(�ty Pr� d 2��� endB] . docuA�!WanZg�a new�!iProposi��cqprop}��[Pn3] Sb"( $\Theta_a= (-D_{\End E}�_ah_a\H`_a$, cf., \eqref{vatten},�h C"W^Rvin2} � u~� -�( 0 f\w\sigma+Df  �&*)�� By�laban}�� � kraf� kn�1>C pst}U"(Q)=c(D_a)= ce e^{\al.�!*� I"}�T\d� _{f}�$ ��icul���^$fGnb�kraka1}�lt[!( 60 =1 =0, ���=-f^)�= -  f;A���!Ws=\exp(-!/Em9�)=1N A �" e, b5�E?%�=�!,1�!G�*5�� e (Rp�F�}\w-�-!P]{} '�e \Big(JF+9dJQ�>) �r mnsa 06�}~G\w !�!�=+�� �!��$2manE�grI�by�sm��}��&�) %%A^^s�$a %%direct�&g��&#$ viewR� ba},� cM=-%�,|f|^{2\lambd!�K a|_{ =0}�e just��o verifs%at\fJb2J�& %�a6�&��"mayD u��f=�&� %%)�$Z�� � ��Zi�$=�4%%(Df)_\ell+f\� �al|^2\w "{#� \\6 df_0A4'+�Df'E_0f'\wA�(�&*}{f_0}+ Q,|f'�) 3)�w (TwO^�)# >�%%�*ANs"� y$q(%� )^]$!Y� b�kcelle �n  claimQ��a .�\-y{Slask} � phis�#sur� fs7 fibr�sS$iels semi-��4fs. (French) �   �cole|m. �(4) �7� no. 4, 57� 11. &� a�/��CC�W��E)-C(D�M,�0�$M$�%jam&z{>qtva�N&�(�&� ,' ge!i;NA��qremarks ! enda�S` ??}- AyBO�$!�2 e T(e �not%$ �{��nN�. After�uit""�-we>� i�a�&M�=I�'/��e��Pv=e`��'��͎+>�a�sum ce�(D:�/ ?m�+it!��acros}(e.N�M� b$ m�"be!%well. @ �F v=b$ out�#%E}�,�%DhA'�+y��.;is *)� BV}-&*%�� it їk $c(D_S)  Q�. ��ia��)� �D vCCCw F&' brel '� , . � mel a o phi} [$$ b='Z�-Df��� (1 +� phi� !�%�)�\:��. = a+1���R-x%�`:=<�82/���blera*F�E�B�,.�!p&�+0 � � ���\w �mN�o.$ B=AN.9Now1�!�QNH$\� grund� ��%: Om $D_E%*!  & �%$E�($D_{E^*� /n�;� $E^*�+ �#D_{F/S}�!3\onq0 quot�� $F/Sb f#+bywD[AT]=[D_1 $�a$n its curv�1 e tensor !=$ c2e2@ $\Pi_{S^{\perp}}� _1B$ via�!s�sm*(i1*idfy �\simeq =<, $[\xi]\mapsto >txiU&n fact, 9-6��12�D_1�-f��s $P �(.�B�!@BP:= :1:)�.hHej, mycket v�lkommen/n!H���Lp� fredag vid 19-t!L $Gamla S�|Edgen 7 (tel 68 17 33), bek"fta g.Dna att du/ni kan }(a. Liten f%�dbeskrivning: (a) Tag buss 58 s�derut,>/d passerar tex Avenyn, Chal4 huvu�3��ng, Marklandsgatan etc. Kliv av �4llplats Otterb- k och!�t~ tt i� ens � rikt�8 ca 400m, sedanj 8r du framme! Mi�! �zU +e�*!Pfara; n� ta.� !&4 Askims kyrka,�d!�Rller bar)n norru�t!� let �� (b.c80�%c;6c bla Linne% en o 6R. ^M HoA*8s nedre. Du tar-&�$ngtunneln 5Ualeden !�!'!� kurs mot2 (st/Tyggnad med upplyst tor BkE� t�-n!). V�E�%�bi)T-�E� :�;+lj!na1]8ca 200m. Undvik%�m!� de'avstigA%R�ILyckhgch)� har man a+it rej!�t fel (M@n Billdal). Jag kA� ner ��k�#L gjort detta fatala � tag!�"(c) KEZen bil%_�E`tagA� vid avfara� skyltad -�;&��]ns� !�%due�er"ver5X%�Eb�Z�dig nu)�%��AGgen. F! F�500I���\class{�cle,Husepackage{amssymb,W 8pagestyle{plain�(\title{Sequs)�fil�3� "�s izing�subgroup *�% abel�, w setlength�in��}{0mm��ate{} \author{ M. Beiglb\"ock\thanks{mathias.be`oeck@tuwien.ac.at}, C. S " eder71su-.'"68 \ R. Winkl:$reinhard.w >7\�{�$ Institute!1Dis�/g�!� J0,} \vspace{-1%\6 XTU Vian}, WiedARHHauptstra\ss e 8-10Y\< 1040-(n, Austria}%�newMkorem}n  [��] .'i3O}[ ;]{Def=7i�$.-lemma(L2# coro"Corollab.I�p*�6N�'R�M0command{\R}{\ADbb{R} ATT>QQ>ZZ>NN>F cal{F>4Gd}{\widehat{GF2_d>!0ee}{\varepsil1��la}�71, �9 ,\�'_t: Bohr�Hbox{$B_{(\la,\ee)}$>vnb,(EJ/lg� Y?.�(_dBflnu�\nu24 nu_lB1 sign2 :�g$\bf{gF�U!A=!�UF&lb}{\b.��A�5��seq}[1]{{( {#1}_{n})_{n=1}^\infty>�io0 _{#1%:Uumm&�{Y,$:-li-lim -(\rightarrow� rene�Cup�igcup} >aa.8n� �{1,2,It ,#1\>�o*0,"]? *6��7}�bseteqB�supse " ".�eps:) � �\�� make�!ab�vct} % x+show,a$ � coun��% $H.aY Y5�* ImBz6�: $G$ e&-��� s�� A�=�"s�0~2$$A� \ch#7n $\Gd.�3��$�� G$ $ �?0H \ \Longleft]? * I]n]ZKA�}:hi_n ( c) = 0.$ dM�/�$any (not n!ril!X�) ous) m=m�sm $f:H2uTd� ."�6= $(!_n')\io PCZ$j�C'�=f� �=Y%D$ while ~.;�d*'not� verg,41�IGa yA H$.\\HAmB�� ]rc6�  � E�=FW =\R/\Z$ ar� U�v$H$�%Tm=:�Q� .�of (c9�ys a#&f<;�� n%�_n1� = 5� $%�al-<��!C H$  Q ;) M1�AB)�3>a�wI6� If>9drops�i5![ 1� r8)re� ;a0�8similar) ults� us�.V� �<ea1_ s. Fur!mo�h�?roduc�!ethods!!�0o answer ques� � �  Dikranj�:t A-a�  t' footGsiz��d MSC: 22C05; 43A40; 54A20/ =,Key words: C��6�s, O)�>�.s@, DB� y, F� s6�� \no� �/Ac� l!zs:}A� � s�?very �15`2}K��if �is�;&3freely�C�  m�peli, a�m( is possibl!_�,even stronge�nse: O�q choose a>�������um2  \|= \| T�as?ach+D�FYJ eig}eIe�re�y]q. A d�.Wtoe���alUw gene�5dA?2� c6�i���sum�5s recentA�!Pi�� 6 �324��X��.\��F;�e'rel����:�e.��2�m�d ��6p�G ical"� j s� (cf.�ar1k;)ear2 dik1�%dik2}).H^9rt Y lift%��eof1!ށ'1D�set 7 �^B�st! � {�+ �. Our T'4 ems 4E!� *ref{gY;}��� emporan�Mlyų�p��9� provI�9��Kun� cf.\ �dik4}& yS<treat=�1�to�cript�22F9�U��is r%�3��,�6e a�,l � � Elia\v{s}B)&eli!% .+Conte(I�pap�+�D�!)GS� }!�mod}%em��e�-�3t ,our purposes%� TS1} ess[fB%�s t��ZqZ�� � b2) i�L�=( �D,) Pontryagin���$of $G$. (S�H>�@�.��toj!2,neighborhood, of 0 w.r.a�#L�Kep0e�e��p6tI�e& �1m�is�4"�M�)[/}: Am.9��� �i�exactly�m&one��vo�=�Ft t�zr>� � i2� E�2� *C��of���sej.$�3^�� B� �Ňsolves�-blem 5.3E� i3�Y2]�D(wh�.BB1�Q�  5.2 ݶS)M�& �Y�:���bv!r!�A�rFA�� 9W�-�a�> T . 6|thick}[mM iK.�%(m� : Co.H�L$G=�-A� = It�� es�iHd in -u� ��D &: �Kle� �*� "� of% � 0 $k_1 < k_2< $.N�$Ist%"c toC ![$kaKin6 a�$��!s $S)k_�S}{k_nTre%Hed?���e��� affir�<v �+rov�a&� ���$\��L!�.!Z�F�,�a cer�M)�,:58s�BU���J!ha�"� 2 i�PiGe�s� bI 5Jinsofar�&(aF$E8 ?B A&s):�� way��dens 0�J�nE�rerhto1#�M�A�de�{bes Jsparsef�of yOA_$A��p�O:�appl} �.in�� r�ed.hV� ��B"�&G$ by9�:  �G.�"K�Cm���setA��*�M H� ch&�>� = �sF�to $0M\T$).jis easARs, I*a5V�;�!� p Vwis�K�` Fi� in� .� $f:��$T�)&x%��3�Cc�6 ete Ipa`!�a�si�L : Gin���W� of a.�NB �?.� � �sBR�"w $��to f$W%6F��f����to)F achie���.H$0.E/�on%�nce. ZG*U�F�m"Q)t!�'�/"V(Fm_)9s� 5Fi} �so%valid E��9�s2rx#ced b �2* :9 f�.�4qF��A#��>��(uiv 0A�6HI�nic���s6�� . F22�a�dG��on�N �)er�D�W��4�}.�a�cm �Ame isը� 6+�� >Y v� k@�-} �!�Ũd j@rA�, e*a��a�2� �*� act 2� . ' ,A� most�2s turn�,!/be -� .) %�Wre'3�QlG+�) asesA] re %a� o!o*�� , %��  $�nd�)T �. �-����N� este�2�kwe�  addi; 1Z�p�u�4we shall do so� !�� $� �ٕ| chi: G�T��takA�ei�� E�a[!�1�Wd��� ,�*��N�od)*@ �m�� writeI \leq � KAw-b�э�ny> set,3a( A \r $ � &��!�by $A$.�VMO $A!�B� ,' _n\}� �� $M� \N�putJ� _M:= \{>0m_{i=1}^n k_iZi : Z, |k_i|)M\�*Re�Q�_ a-�m$ ific"`(!t*%_) GE���pai�L\iota,C)M# $C:�D� $, : G ,,56%<9�' se i5N . R��< A_in#boupB�)! ed*s�Pso."�9 $ �$_{bG}, bG) xE)F2I�& �Umaximal�agV )�for eachB�w%b Q*&� 65.: bG .nC$%R40 hi \K %��J!�_C�,"� { : #�a }6��}%��#A2} \T\}$ 2Z��I �, ]6w`M� ope�/y�gP"�'sY�>�2e"�3}�� hew})�8_T5LCA �� \c#"�$ G}�/�� algebra#Bs [3� U�V)�H/Acanon �A&8m&/x_�S�8$5�' �� !�We�� $G_d/ be A�endow.�a��y.5Ll�>��i�&K�^0bGu"by �$bG :=9N(\Gd)_d}�_�#_B:��9�$. Accore.l�4e a�Q'y�AR\Gd�� d�V n1�e�� 5 �/�V��s�� y. OE.�r� +,1MI b�R 6~!.I_ ��|by \[��&%I�"q��Gd \:a�:�]_i) \| ?�\eeq�A�} i@%t�9\�]����_"�$-�_tzG1� ee>0�>^`set&��J/!�Tn-=B�:uF� a��: (E)%  \cap E�$Ez t A� � ��� $B�h(^S $\|I� B!WA�sup!y|.d!b9c�g in B�"�:= = �9I a�4 m\ �8[I�eJ l�s: �^S$ �7neq,�]\Fk# hE�S$ y M��a2,S� let $f:S.UXAP�Ln�%F-�<_s f(s)=y $$ iffEj^y M$U$�y�\{sA�S := U\}\F��@ �=�) e12� � P"� >�eq x$! "Upu4S \F_{lx} =\{At X:\� s\ m�Nx&��"�}\ir{x_n:n�m* A\} $$���]i.?$^ s%B*H$f(x_n!��ti� e�incide.�"�6" A. "�{%�v2Y �A.@ taskto*��&( �a-� �H$ E�a� ��� 0/\�F_H)iJ chi() lf% $!{H$�]�l�GK��*�(Gi� ��� F,+%I, ha!%n | !$W! F_H$�_Ur:%n�x .� g �>m�B.er�LE�P � *�c ly ! EY�T� agai��O8. % F"UGUNG p?it&_� �c �1�g �$�j� �$\l�MHUFps� w? �/ yielb/X�M-� vr r� U�&c2�8*^:��Mc �-�%F�?m�2��1} be`&�>b ENit %i�R deed�6&:eH(=ySENDE La!~�7b� [ans uD atA�ZB negl=C)�%l!�q(e>4T also� A�co= to�2�Eq&is6�cG;�9�: zF_H��y��F�9�Gd :�?array}{��?�22< e > 0, \Gf_�n\GdF'| #|<. ��:�� s &A# B)�FC`E ���\Q<]&t-* em}��fA 1 1��e2�Vb, l�b+.�D��!a:ceg+��AO%�A�s �특�/� �I D - _{�f- �n�% \)�JW- !�!�tm�. b]�B12 ��k�G�=U�emplo ]��3H Y�b��(#�:"$/2P lem0}u,-�V~a ��5s�yn� d$ "�"x*=uss! &Ku("K�!�$�~ \Gd0 *�"�.� �1�� ��H*O,�!�" $(n �1)�&�&. �CE�)> {\it�of:} As Df�ied'�,%�c�= �d� ,���iI�Xincluq*/�e embed� �@ W2� A<d]Fp�� �first�)�e$H6���_2\}"0 2� $n)�N��-� Gdg3 %�5�� --�_i):(jn 1n� �$ia�\� n����(r�/1Y�on>.�x$ \\ =�awJ�:���W�I�E�ae� guarante%Xa�/ �l�3�}  �=\|#*ہr� %0 �!�iPs��%�E�,�a��� \not\  [)��~� -��>et�� �i7tX �\%a��4)�6)ݱ� ge 1�)�!2Dm�%K�:9I<G  �� �FE��e).� s at��s�/ "(��2s!�FQa;d�A�A=���;�( �ё1:Er� iZq=fs =e��E� V5%!.��k\� 10��5�}r!N�m�\laH�dm� and} c= cAJ)EK= 0V\]Fw.l.o.g!|6-�+ 1/3$ ("�q 9��*#j�Kip?32s,3M�)�#By �:} ũ),$K S7y ilysion' " 1�by.� p w�'nd%�e�A�-�$X5�A�-���\|=, 1 im� Q�M� \| >a. YNrwpoKa�$�6 >0$ U `�j� � �y��3 �,uq�. � |$U� { M5�\V�#I KE� _t), E3)*� 1:e�WT^{t+1zMWe���uish tw� ses:� 1.�� ��k�=�*H:, u_k KYwv7some $i$ 9i=E)u_1�(0Mx,0,c)R @�� R.�U�;^=!�fBe�\^Q% 1it),)X-H= u_iw\�7\},m�i= "fk)�m�= p"�lw�1f��ite, or�325d.0����5� Bu�bn E���#�$U%�a�ccu�\� $. mIn^hmn�q��a�W��B�i�a x$k >=6j  s"�  *Is�(� b^�( ���"� ��U2� sX4�z&�m!fs?[k*��x�pLSebA}MNE? =0$ ���A : &� \ee\�sm_�q� g0�+I.e. ��6��3�.n#*3%%�64 aZ $A=��Na�)"�  &=E� Z< 5�� a� ��G!� aE�F� �Z �o!�!sG:�valent: �OAfize �\[(i)]E&NtrG*I�"#�w.� �% &�A,ي�.�!�%�H~N�>EG�� =0 �]  �� 1� I bf �A.}�� oFV %�&M'� (i"7m5))E�i^$@ma 3�O�-%�%+"$choHJ|*h N8��%mp�+<�4! %Jad��!^��H � $. U�9a"�vi�(a�Uiaotm3*#t";&�tf %! Te�}* �o� o�5.� � V� (� >�b arrow (ii6ls"�7�s �a�,Pu\�Ra_TV�z�b�+��. A��0m3(�>�r�(xDsq1.�m�"�$Y$i�B�b @D�� lem1I߅7 \tau%��#�&�. �l� = i 08")�Q�a/! �6� "�,=� q2A/"�t ���  �[� �6�jC.�B d�G$&8��&��4 $y nonemptyL � $I_, I,Z�+th���z���� $�M � i ) &�I_i"� .;d$nY) > 9 49�aE��G+��)�2���I,enume� I\���{�| s  �A?$�N�� � .�A�> 9(�Jm2)L�:y�\&[6)l\la� �\]p �2�<�|$M�=�_� ����!_M^JV��M-K-L_M� z#��. \12)>wIVH t.S� a�S� f\Gd>2)� B&�\�BVAQeq R_��J0q�6=ty} V_2�= ac==m = 1}�H aT= = my�@)@�%�^� F �9n�A"�c2O� N fy:"�!�:O%a�: ��ak �v�|���� fk=>� ͜a� �El H =:a� : $ � �% pick�e=i+aj(0,1/3)Z \:�4},2  a&c?Y� $(M_t)_{t�*)�i���} M�$�Q��{��n�eF>: %I�r2`�?\Պ_{M_t}2#N��$�$� \N, R_t� B� D%� �eact�mcR_t$ a.q 6M3}2%#nf_{t\�\�mnt =� � K<5le!�3 4Au#����%� 5c-�$�� �MW1,�M (E_1��ee$A.m V_1$�)�  �"6 4},3 !.?} $E�?��RE)���%a:� �2�2��2$. C�,�� zash�ow87r�,a�-��$(E> $� disjn�����EP�QU$�:|M�6tl��t�t2� B�!#A.( V_t.$$ Fin�=�%%eA-�M_{AQ�gG� . $ y��.�TWE� B6� =0$(2~"04&� �*� T=T(n *�<8I%Z*W� �6AAz:pre�E�CA++$�c.of �^��J�y dz~�NE�� s Pr�1�4])&< Z"��C%�ELOY�5A�'�=V�E�9 i� 5��r*�#:}�m$ͪin>5���:egYa�=E}M!-�Z�-՚ 0#� E�(n� ge �$3A%us:b 0} immed�zly��y\!�6cvt��!$$++���A b 9zO|�~$h=(h8� h_da_n \Z^d6 *�P(< d h_i x_i� �k�(b( x=(x9l , xS� FixT.�=^$M�$^�P)�i1�0!�>�O(1}i& �d(>.)� _i�)�P� �2�.{ �)e uF=)V�(,�tradic�#E���Mcej ��f,�w�d$F�6� ��!HaB�)6+4; �20Ac� VD�1a�^ F=;4iHA�F&oj2.of!��D�1}Y�� �1]'K�c w �%�.��. �ee !����rA B_0B&~e we � .S4Q@~5�v}ev� ]��c0E1q ��.b\�� P&IO�aNFEWCT$m�;.�� �/m% %B_1:=x�` /m)}!�8[ �a(ByFq+!M�B_1�F�l.�B_1,$2�m$!JC,1"B� � b *%%���! !np �:�1} "�^hU /m <-s_ �"j9�%H�p)��7aB2.6)Ha)lJ�# <(*�)M�j� �"s���).� ���ly m�i1.Hf�&`a decomK�� = T \�� !�� $FM �Mly�O� a�ga$m�$T= � ebq��UQBla�i� nu_i'c/I���"� 4���+y�.>�> \Z_{e_i}I�edA!N%�q� ���5�g �* �ln�i�~��+texts"hg2�} �eáF�� ��q �M�(��*i�j� �ed��Y (!'jS ) $j�z�/l.�ual�dks es�for $kI�nalt$. Pznow(2�<�G2($\|�%taa�&%en�S.�\1.4hL�"� in* a=�0�r!��t +a� m_{j�l s_j % �A $r_i)Z�s_je:c{e_j-1}*A"d, #�l� %�e�� prodpe_j �601 aL e��Ve)%9e. X{ chi'� �� }*XU�sign(r�.(1~ ��[= {1}{3.'d |r_j| �ic {2^&͊]!lZ� &�25�C*�7!� �\)� -��"��ft[ �|r_i|V�} u �2{2�^+�B �A��<%�%��Sum�u F `a��yMIO$2� 6� �. (E�= 2 � N�SE B�}, =�6��M�;$ �� �awE��/$j! Sf� t�-�:j�|>��Hfor� ���=)�Z� $. ELL�)ly:� %�:DX� SH;r�e\J�� R�8 �( �y  an uni�al boun�H$� , coefficie���OM\ combina� ���=%�)�r�Hal�8i4% \ 3"��1QI:m+G!�G:!m>x \}=�AH�@ a77 B_0}deBG�:� ��ɥy":�and�12.!-a� $I"��&r#VBu�&�BV^c=\e�&set.$ ��_ actn����B�gAO Ea �B�� 18FEB�/zuCV^c�����T^�]quired"!�{\r8�6�3E� \rho#"u�c G$�.t�_� wNy� A�#Bm#��!$�e15[0iE�7�ateq%.�ar�decH��to �D=�b#qna=*�42 d_n &<& \minA�rho��')&�aa A���R_n�4 )'\}�0e+ d�Vo�p7)"hpdaf h�G� R T&�Rt$� e���D@�� �#� {*�G���/>��I%�)C �a��) <��]2monot�I��BQn�@ee"}$n*|$ R�W"R-n6.��$�8 �Ce�H<2� �^R.�$V�or,*�/V�qM�-Ian $m$)7� @"Bn�m.|IA�aJ�"",:!? $���j unJer,��kMP ed&�Z, i.e=q_nl �2 [ �[C)��S=bf  $Cab \R$? %A~I�BuA�r�A� �i��vCo %�. :Ru[ >u[Y>��a "Xfxd. W�KƦA�"L395�xpected?:�"E���r��al�38� u��rm$"����"B {n O)�"�of�"jtR���f 4G<� �F��$2� us (6as exce����8f�[�� _.B�k�wUheir gap�WLh�D �y.l7p" 8�E�2"n:&� �()� m]r� �n�I)�>g�>o � slowVE� �O!!��3j22cbA5M*a���:D�����q�1iN��y(\ee_j)4\) 8�q�i*~[��5ayq 1k a&Cn%n$0�%(�ily-)~N� %�� Wt$�q1�Hval�, $I_j�${i_j, i_j+"�( ,i_{j+1}-1�El $i_0��� $q_{j~�3 � } ( AY���BR �6*�O5�7k?nonnegajT�(`:R$H)&� �A ��!\ft| \{n�U��I_jr@ |}{||}�i%�K\͢�>�̥} j\*\>cE&B :}AB,6 *F.  (or to�Yim), $cac_2�  )��D18.�9A�T�re go2~Z����de dNe�=?"�@$% |I_j|$�sOU)I��5�$*�k��.Cc�_�� TA"�Wk�b=}E���:�q%/cup5 c_n6 $ cl�$�Q�5j�*�Jies���B�- : 2�-,pI_j^+ (0�"�a�t  ^+(t\�\{ ��at:!k�i m_{2rjnd !{ `> �F*O-6��.V A��[I hand,�&U� va��1�n?, ( ��- ��J = c  ak0��yc2](e4w�(�!w&f>�&j �e��n.P+*� K ;Q��)�k2�A�a*� �  1N�~ 7 2���fty$: �,J��A�= n^n9 as�l<�l� A� 6\2�=dN ^)�X5!�[ ��_ NMq zCo�m$�]?{ EbE�!�Ga5a�> "�b�m�bA��gN Jjwx )$ .e�NIn�i�G���� *�iyRGd�M � ���6�>!M};w*92&�]R8a�!��4lP9Nu�.���MFiiW��J�t!R�6of�d �!�B�I�2��=n22GMBlY} E۝�U��e!1"�� �Q�5%!��:U M�)$ "��e � ng =) S" []�6VIf� ŏ��3*z $@*���v� �A:((s0]"� 9,2���R9c.D���OB�� 2'6!z��iz��"�9�7�2��.������a� �'-XA)�UDiUge��$E9�ET� !K� ���:� 1:� �2�M�&�)��@uAK�H$�F(�,):7\�AB��'Cm{a'-UQ_i�%,�.��=k)*�\]��$\F= \F(H,f2"�^�� %6�L�!}{cY�*x "fX,< \:Ȥ�^�S�&k }=� n"p^%� | �� W.r s�v� E���N [(a)]�UF��f�. b�I-�%� H$ :>��=�6&Yc)]WU�M/~Z0B3<7�� ad (a):�-��Mslb,0# bB_2"�LY is$ SV�6ee�B.hHb�b:$|Ns& 5z �.+d]04�$.� ����� �� $f :�P&�!�_( : G .Y<%�\DY�+6"%0�?ere�4a 0�#�2J�('.z�?#mx�$62�,8."D+9��= "&��!�b)�>�M��8 $U\U(�� 1�H�+�97�>�xi�?S)� ��cU5c�i� alph&$ee�y[ 6"�@')Vf� vJ:.W>7%c5a%8m1�F�a� &h3W�ll]�t!�iE,�chiEinv0.M �_1�)-e�_2 !��\. �1�6r�N1�\�02�Y*j'�2N��WQ��U�&T_An(h6�:h%&{#%PVMRa0 V0)5sq4LF3.�"�_ ee/2Z )�� � >  [ �/8G!��2�/gFceq F$ 5�P�T_2� chi+ Ga*a%�afin $F�i�5�-�Q�m=D ��[ �$3.HHf+e_t,E�\ Ha oLf $2.$ůsI1 �:"QM�e � G.���%� xi)-�(:\�,1/�$i?Z�%,�E.A*� z�GJ��� 4%��� we Ir by!�&d7���U� Ars  $:Btilde{!�_>{�+>� � !���2?&Òto�@*N iff_��)XE�H�2�t =6�� i $3.I] (�&a}V} �)A�n "%���0B�IJn0f{ i{k 6Q2�FH��i%!�1~b} cB{ :� �#��� c �s�Gc%Gn�g�B� maar13+1} -t �M�v{gH ua�:on.��(cj\U��=W>")(5.4�� ar2}W%��VJz,�,��b'��.E2I&9aFZ$. Aӑ��"o$�z|(i)���W*�*?V� vZ#qS a�cN1z�\Z.p$�!a!h�"7h"�6% \Z!�{aO} AlY ��Z2���8"�O\ T2 ���V 0:�= $.�Ay �" Co2H,is obviously=Lk (i')�l:fZ')]:�T-]&�g$y ,G)$�($:^Vx œ$1$-$�`�u (cB+to9|� f|�x(\Ze8)�BA� raQ�IS�!:M�R :\Z\o N&T^AS� (n)�)�w�A$Q�G=" @��ot��O5�=&!���9H�3�� b� $A,QD]-L�Zo *[�(M.&?M6,�Q �-_-̅�. E�$��9�0�@iI  ?t A�� �*s.4Ja2� �"�2cqY 2~3���}!� 3-�n P2S��k ������.Q}|.�c)= mI�A�8@� $ F��@��\T& 1�� �K�&%�B�!�9$ s ri�so b�MZ. oh: � 2 vi��� c2)K3QG.' �> s�^GrQ6 ]6*�N-�>eA�q� #-- ��% =�� us $a�e1��.�y&�#^faiѱi�/E6.0 $ ��.��N U�^e�� .!|!eq� f\C pri�1Y�Vi;AaK�  $p$-�� "�* $\Z_���@.�M�kI�k��{g'k��}"�,s���4l�7non�,�Etd satisf sO =1$.�U�%,|!� �RN9h_m =+1}=\&}CÀp^iE? � !t= p^n+h2!$w�%k�Z@9� G�HA5�W��U�1�^m�.���i�I�E<I((E ɬ� �(cM5-!)8-h = 1j$AG*�Qp^�� �l0�� � = a/p^l +�{!�s� l �{1 $ ��) {p^l�=. "+ge %6�xl�Te��"2n} n͂|(x)(p^"g> k_i!�\�)��F>DYZl6/ . $cy l>O term &s �7e� if $%�Q! �=0E�2%V %WeNg2)&f1): %ReY� "<�"M',2d�,� �1 of %ad`bb� draw 0&�^�Qqsz$�\R�0��$nq $(1V(sk5tu�O&�q~$Ai�/J��C).�$Ha��X C %\t �!ڗ*��, :X2*P� yagin's %&��2�� �ic^? t& �� %Zq � C)�B _A, C_A�)H %�_Ad+Z�#���_A (k� (]-"* aE %A}$�*a_hh��e �).�DA$!�'f�\|��L"�B9  %I��: �[,<�H= =>, %&G � %G E?%B�%A��c6!V  %�hTaH%�L&��in"�{k%�OaF���i�.�A��"b3aO"� �F!�the %c>p-6Q1Q��+� $g(I! %ej_geQ�X�e�$C_S�u%.� $f!tmu�J� bx}b hg!� $f(ga�[( 1 6� .� � $\QF enp %#�b .4q� 52'A�>�� %Cv��ly�se�z$���!o֍". s: %�*�%�� !8 Y6PeFB . .6��7i��Nq* 1T �N^{\N2+D��G� ek *@��nd 02�'>� %�1͉ 2�!sfE�=� ny @N�(�F�. �RN�N OE*�=��4=3`2)^�A� >a2on.%r�A�nd">6� 8�8^���\|- ������z:z !{�]�"�gthB���QbibA�B.1} G. B�eri, D.&D�,9�Mil� $nd H. Webe�u $t$-�/&���&�@BXA.�Js�����E2004.&M��ڌA%0�\(Raczkowski'*�oM���t"� �� � X, Top. Appl., 132, 1 (2O�89-10�9>D)M2��: S�:�)2t� e(�JQ'.!3/V1�i7 A. BiO�, J-M� shouS���b�."`�: Goo](xi��oə~���R /�L)�Studia 4���(. Hung., 38%�t97-11B�2} �e�2�z,%Zni�v,aneous dioph5�ne6� , J.��Numbeh�y, 99G1�405-414>_3=_Ja�tj��)���!�c�-�( I.: a specz��<]�!�Bx4�x xy��l�w%�2�:A��\Yy �M#�.�)e2:��oc., 26%k1-200N�505-53�u88[ji,A. Tonolo: A)g&S,� 0CmaA�lly alQ�periodic>{FJ�rei� A6�,�6ax�. dik36% , I. �ProdanovE� L. N\�oy2Hs�+.&��s,�iޗnd Mi1�*5��9A`DMarcel Dekker, Inc.3w York�Basel+�0):�4>�K.�B�S)5�CMױ��s. ��F��� P.&סm��pngHcategorJ�on��icy ��t_\ !`c. Am�kSEW131, NoH^q� 3241-3249.�U� EGwitSd�Ross: A�� harmonic%c�- sis,;�1, Spri��Verlag,��Llin - Heidelberg - N-�I]1962�@8A Kuip����L Much easier to show�6� property, � will��sufficient for most of our purposes. � lem} �4:B(z_0,r)\to\C% (holomorphic) F- qs35fH0),\inf_{z\in Z}|E!|r-5("B I&�,\proof We ca!�sume tha)�Xhas no critical points./onsid!Mhe straA�P path $\gamma$ from $ �$!v,cl!/$t boundary U!O imagI$ pre-T$contains a2m'$Dnecting $z_0$ withUk of $1$1�,is mapped byE�one� onto|. Sinc!e lengthQ �'$I0at least $r$,|B):(n�($ .\qed Morv4an on disks weU�$interested!E distortio1squarA�F!�e�'s.$m��Aob!b simi� estimatesE�NT25lemma�:0}( and�lsI f� . However � ould alsoa�v! is m!4elementary, usA(normal fami��6����nDKc} For any $00$, s�Ae�3}� func!q]UinjA�ve!� some-< $S g.�of its !�riJA� $c SE0E�M�K_c$. Ao! tends3$one, if $c zero�e�6�two)�!�0llow directly)�AStransf!V�! mula��V Sup� )%5.�fconElasemis6�$. �7D$E+$M�6(measurable ��s12domaindefini�.�$\<(D)>0$. A�n>��c ($M\cap D) } D)��� K^2 ( f(M)+f(D))- .��2Ɂ��y!�terav%�� �R�((\ref{qs2})!!called'4\emph{density},!"in $D$6�1F�}( $K$-quasi-i�)\\ep%� B-8\ge�\diam(D�{2! ,}\;\text{andaV; 4%B(\c$al D,\ep))) 4 \ep< N5- 1} .�N/Finally��,state a toolqo�frequenA�us�Ɖ�q�ity!5au�a�cer��ets. It!ta coroll��M�so1� monodromy!�� _ may!pf��!�)� ,y books ,\cite{conway�  aK-�RD'��D \Xis, $f:Do��. all �&� it �inversE�� area�!e�a�un��compon �W\C\Lbaca')$!enFv .  $D'$��� � To avoidlfus�� we includ!�y�iam�mf^{-1}y defn1Idef01E-;\Ch�]a-=5< merom� i4 s\in�s��m�J���}��th�`2 $itemize} \ a smoothY:d:[0,1]\t �� (1)=s$,BI $U � �22M)"0 U=$nd a branc� phi$�!�:!oa$$, i.e.: $+:U�D$-;� wf(!(z))=zmA���^) iy �Vv�]�V$,%�no�sr�3�� coincides ��$� .�U��;e&s5�)\ $.\\, denot�e � ofFQ#|A�(I�)A�!-E� I�I( literature\times!< ` e�isris �d� !� same name&e i�1�Me�ai ]ase���D��w,��  � ake)�@ifference. Study� �(Du} valu�iI�second =an�$asymptotic 2 y%���evidentA�atEzp.da!* ghborhoodaAW �ofentireymuΉ J'AuiG$multiplicilaa�Am�eintrodu ,!always&_onaE:�\ss on{E6�s�8e�Wu�onW ork�{q�a e��* type�)��I� gsatz}. F%�!llZprabs� generAataz�� not_ s�R*� occur.QB-� chapter l�EPiQ� $polynomial��Pat $Q ��taA$c\S �� "� � gauss5(}a�X:=\int_{0}^z P(t)\exp(Qa� dt+c>� u$kJ<{1,..,\deg(Q)\}$�S�wphi_k:=z <(2k+1)\pi-\arg(qr 4� w�0$q>�jIe lead�qoe"�� $Q(z)=q z^{C+...$. $R�9� $EmoduluE$ �R�d i))$ decreases very fast.r $f>3( converges �Ai]^tsdach} s%lim_{� �}%|0^{ �i�)}B� +c,�H5�Mg��ejn �Jy�$f�A1f8�^A�:&s-N��AN( choose $k$*I�L_kB possi�y!�z)I� A�s}!�s_k$."FS >� A�&=&::+\�P(zQ�z�Q�� }+\OO(|z|M&P)-Q.-� box{$zv �Gq* estf� �5vmF� .��!=a� . We�w:=2|z|U�_k i)�AF!bx��. Instea��)gra"#$0� �onw .�bm�aqll go.9 in% y� 7� 1�,& e back��M,way up to $w� f�m�2forwardEz��$z,w$� no��i�Q'* fi� � �w���a � (these zeros.� 5 on' ��s. �5�Q\ s_k+(VQ-QnwQAwMnDw)}\nonumber\\ &+&e�{w}^{z�8P'Q'-P Q''}{(Q'�2f dt - 7A}^{I� }P(t6,~:B. ���Aasy!�U&� l�three���atuy�e)�m�e��finj} E�\delta�lta'>T nd�,large enoughTe�a�8in G:=\{z:|\Re(��)|�a� Q\}� D(M�he2r�fI4�z� (1- A'��}{|�&|}\�)$�;"���a�� q�We�). 0�. A|}) �z,w�*Gm� f(w� $|z-w| 9 !@&1;�f6 �j.�_of{&�\� }:verY� L&� a� "�y escap���i��M�  A�&3��_s>0$ .d($|f^{n+1}(s�� ł |f^n^m�_s} )i�al@ nn�� \N$."h$0,EDgv�T(fi� C& (ii)-: bock�}�'�  explaiA in remark��remk}��$I�$h J(f)$ due�<a� ul%�,I. N. Baker hb }.\\j now��!�% 3$.�N )�$�`n ��>7-1!dlta >l� . ~��)<� i>ifJ�E 1>1$��F}#)S� \F� aGH� E%=}\}Z~ i�sj�"�b� "� & `%�up�up_{k=1a �\left� |�-i>(4�2 q)}{� !>= |2 q �)x!W#\BE U� A�Z� �po�"coordin�"E�A&$e� �2� j �pM^)� R^{E���d�R=2q :M^{D .,}F>��%���$%xU" �GA� 6$B a #y $\S$a� s $SqXfW)�!�Qz V $\sA�S}2�/)�S)0)4n,E��� �$\Fe�i[y�in� is, m�2� � ,��B �E�(-\eta!�G' �\epM�n� R_k :=M+k� l �N\a {0\}.$�n~$*}5"�)&\le& e� �6l\FG%'J�p+\sum_{S% }M(%%�S)Gh \pi M^2 ��+ g� N}\!b��a�* {c}S�\\R_k<S.ta�R_{k+1$# 6nd~�"��j���A ty 2\pi (�}{ex.B�� ep} -� 6^*} �����giv���2�� ) �+a�\ o� 4struct example"��q $ 0<=7�'� =����rrang�par] Hs $a,b$ ( e.g. $a=(��D27\pi^2}{16})^{1/3�T$b=\log(\sqrt{a/3}) $) �b� ���B � \[�=!x0(z^3+az+b)\] Z fixed,�4�a:��� '"�o�c� al� !�!The Fatou�X � ich�"N t5 3'8super attractiv�si�#6+)��i��fig�below^8zE�� *�z)e'2, Im},� plan�display!��-B�� pa�d dark�b�. �}[!ht!]�' �"�# graphics[� =50mm] :sup.ep�cap� {�&:](z>�Q�r`%�Jc$�,�� ��7sh?*� !v�)hs�)msa�not<y surprioafn <4a�.of:�a�iE��!�JuliaE],by C. McMull�>n� mcm}. Alsog idea_�*concretUX"�s lik�e�)� or��.I�nz �"P/u�9�A� been�d �/�$H. Schuber)0�+�l s }o k1M�f sin*PiY.ipm01mo�z ��a �d,�coq&ur�(y J. MilnorV �m�_uad\\S5""~&� aeE��&� n�A o")�2�)�den/}`� AG�n��G_a�&�)���Gb�.�!�$a�\Gt/"� CN#� :\N})%' (B(a�)�� �mb\.*�istY�ean�"c,C�a "[ F[ disjoint�%s�*� �^&x  :41}5 D!��tC}{*< D}�z� ;,\; #\Aj(-�+�+�+ge c\; *�*�ea� G_s\� � \F�� =0, �U� � s�f:#A_f�"NF%�ђe.U�{��01rmk} \rm��+���|.G�r��exa�-u$5����a|��!9!�d)< M}{2lin 7�$reg�}�Y�I�� �HI��w6 d. z2 �z2p$1F},~u>�.V _a� =a]�A� � {0,i!~  Qam�a>c! -q� Q}$ .712E*%%%�!f any "�';!q5 s $M:D0�kQM*&F � _a@Sk\pi*<<Oz)< /� b/ )I�* �- g(� B(s� .)6�"*}-�2�1� g8%&!�"argum),fI$G_M8BN2sebarg �8 ph2,[J- %. �I��}� �+�]e :BZ^] @\} �n�B.s�36M-�)ft>{$. EN#Z"i-0!��an*h&regio�2"�!N b�i��4)1-3�'i (Q)}�k |qS1}"� muF JWn f��i�2�/�,``channels''e��id�T 1� ��iF},��� M�� cololack,l$A�!;[ 0their outlook� " �bl�j\ .�uc_���!��*ir&� rela Co��o e ``gap�in betwe :���S5dh6at�!��(9����M��4F�)� , st`'ax\���jis�m �A~���X>�'liz !��Z�. ��a 2/��i>M�$�6 ple geome5 �Ns)ʁe�� $C'>\}2}\pi6/1]�i�)�>cm!*�a&�5�)1cK$��� $�S� C'(��&��[|� �!-�3B_:�54~ $cA1(�:E#ch5EC'$�5c'I$ bitrarily.�EQ1�e$).a�ct� $�$"� �by2� _� f-:`� Fu&-<g,am(S)<4)2X.) �e�#��aWaA:i�-ade�c �� *� :�)�a griL& open�% iCeVle�E]]�A_bdi�,Asa8to84r� �tily��zupt�39&throw���rsB�e�n�9H-�"�." �$c=E.nd $C=4CAx�-e $\F_� }s�9�D5y�,�x��r� . \\ ��" "�scale  0.6}�put�,ieF.pstex_t}>�Co<�a��$ � F G�� o!�/3U!s� $G ���F�s� at^ W. $m_�*|� � mini�:���v$m� m��_+$f^m(s)no 6�a� !�/m_0GV`0� �3n�QQcweHn_m bE���n�2al �,�� *vs $l_m34�B \[��|��*3m-m_s})' _sf!) Q  }'-1:) (-�!"�$= l_m^{n_m�8]E�*� -� �6m\A%�� :%k.f� %�|2g2�+set{m"L+}\longf'ara�4�n_R/{:0-���, $E n!J%�wUc:� q0}\}.\]o)Fa(M�i�!��0conX@&(�',$� _s+1�A; �[@6{\� I�Rq��)�{�.,!�W�i�;o�an"� �dinR %�� ** _ Å����,2�. NextA!�1*E%��!�=.� n$a�ha %� $%ki� l�  9�2 �' power-ser�%,$% s:j�4$k!�_!2b3!�@*$s� re$ 9*$$A8 f $ �!$ �$ ��2a#:+s,"�CO�Ds,r�z �� $r^{(-)A�� +(-) }{|MgAe(k_s)��||i(-1��^{ E}{k_s}}$ "�& �.o!!�ou���inner �'i -�i�8 ��u�}a�:s��e1 t�Bf=�� 1!f2r>� _2�(E`r�_� Oe E+�!�-1���:�*\\ *s*�6���- F�� [ >�tfRA'�TJ%*p Ag��I��#|'.R �{�5: n#�s ;I u{s2C.\D0/1&�))�$C>4^{2/A18�� $ A %j�8.�"�s sE��an�\c]H%� ��0av!�t&�*Af���I�+JZ)r���2j 9e$d$2�!��p^ �< $M r^-��5e" k( Y�>2%A� alogous � Uc�|f'|$A��B2,�.*&l �>4 n+ C_3!�m�)B��M�6��tk%LG%/�d.}!Z�sF+�G'a�-1Wam �)� $DEa�? 5a��bb � chos-O�%Dm6��Vq>i�irE�#$#A��/=g6K0$K_{\tilde{c}a/(G�j'FE�$&<5i\jE�n_m-n (�65v��@�2�$B��,� -2,0_%%:��?)S)1��nyA��(tI�Mn��, say"�K|��2}aLq,"�)�!�. \ �s),%= �QRt��2a�O� | -.$+=�'3q�%� >jBA�twQE ballyc{]6��m_s}|5N1�E �Kc��f R�� Dp�7�3 � a�en5*.4.�&4.2 F�A_i�$n2O i2�M$�*M.�G\\ To��)F 6aY9%&� !�Ut��� � �!~l3ish"- �a�)$n�8If ^ )*.�@ ^� |_  %e} :�*,.t%�A+� �� I\e�C��*su4�<1/2$!�+/5n_m!�>��W�pB) Ez�^�%S��mGf"J$�-sh t$;q�6��n�"� )a � a#� , 2�" .*� | )2 RjQ{� �-bUѬ senHd:���!of.��' *� �%�.���-A�v�mDGa9���+> "Z� ��}%,m�Lt�M��asI� ��#� z6V&�q��.(/it�!to&�Gs5kL cise�!� ���ra%!cJ3�VB*�KR+ $c_2�2u _�,aN�� ae�a��$c_3<k�)carw_Mb�9q�K|G&���AMQk )i�.()}&>& c_3. � 3}:,�� fv N5"�n�'B�:!$%oF%��&�� ~:.�r��U9��.��3(y $K:=K_{1/Z � &�!� PtIVYa &�Lai��w)A 7��$�� G*�a�� "� c$ar�i�he>pgZp! $0}+ -1}� 2=}�B(z, c_4� ,n})) C "� $. H�!*�0c_4$ guarante�/r[9�4'cto� angl; pi/--�2�M��.�ET�5���"G�s�!aA!jt +nta��.N.��? �A9co �0�uD?A�"T`(z$, maximiz�Oa!����{Bt&L4\]��� s<p*a��=� .��& )!�<��1�W2W B�� ��.U�. &�1famb�\ a{I_S�� ]�s@?hateM^�9>� )B9N^�# c_5<"�:T-Kz% c_4��-))aG"F%%�NLF|!c_5}{K^2g W���W!�3)8 c_5a�{-*Ev{ �s-��ln � m_�BG � z����|/ #V%R�$c]%0c_3}{C_2^2C_3�\�V���&�A�*B}�1BMmDEbe �*.�[$b� B$Vz &2;AU 3�+ ularR��NA�2K0pre-periodic,V]L'>� � >r-�fur� �$A� � O^+(B~LT�A�� \W3(J(f):\omega+246N*�&�+} � .N4!m5=]apos6�,�5e�A$7�"*�%�X�!� �� fty\P6t=��,\forA�&+>-: �4!&z),a)>�<�>���2r%:!L ��f"'7A. ErLXk!J(M. Lyubich 8, ere}A�v�� !$./>��$I�4!� i !�%I 9 m/DUM2�łpermiHx$XͲr-!|count�$un*��T A= :6U V8a, v%I_n)\}>0�\ep_n J0�D�o# &�M.� >0$ p&�b)&�*�b{;4~>�:x�f���v�Ņ2�[ be a�9%�!�$X2L AQ93 7do�� �j32:��!�Jnt�XsVce>5$ta(n)}(z_0�F limit&%be�!� Y5n_0}(b"n_0aB6��!��:� 1ge m_b:=�A (\{m�N:fOb))=0�)up�6)� al$�N�f alph�\Y<(n);�"�J!ұ�"� �=C)�-S+ �|&\ge&N8|.Z9�(>4 �B_n:=� i |,>2Y� ltAs. %͚B }? s&�"*� ]42*� %�7�"ModelAE T(a�in.^�"�" e�5.�W�Fll"= ]i!a+Aq���Ug_n"�9/� p��e I�ae/� yA�exye5$uniA�l�X6d� �� B_n� ��wejy��n 6& Y!' *� |z|)� �]���(�oR�Gju|�_p ~2�AY]���nR���.�n�. &Tb!�p��Ia�"#�eh>� �9�1�4:e�}I0�Ut�s�6�%�rF"T ,r��u $r_n/!�6#h-� |� � $P� &�Kccumul�ywC)�� ��IR�!"�O�i�:��4o�A �6�z�m�us ��G�H��:[�)%�8V�XI6e*F�8w"&(�*a1����"�8.���e�9'�N �* of $"�D]B��3 q��U� %�9�@�!�pi�1��.�JM:A !2�*i �1�� , X=\emptyset/2.ap H B:�FEB� y N0E):=1X�]��S9Dy!;� G 'F�'.9!#�A� �)n��2(.l2�"p� an��* Fse"�9a���� �S�A.��neglec�A�A�t&�.F �%�i*��V j"#M�B1 �equival!a�\�.�'��,��|e�p �)�6-1{6}��K�Hw[2? w\ep� )f , @AA"M�$,I:B�7�&a� "� �mz}&m,NJ�\{ j��@�}[� s�ѵ� �\Dn�e}Z�0neunviertela}!Wm)�%&=&b"�m�:.9<9� � }}{|z-s|}6�8} !��M�e�!\� E�-]!�"� )1}$��sA�(s,p��,�s�� 2�*� ��N �is*�3& ��6 chie�GU$Q"s. and, k��s#Y�8 }av�C] �% 2�$a �8 >D$=us�e ft�MI�|?B-e��g�`*KXc426h�*� �%AcQR$sREI�D����j�2 $f^jA no�3 �PR l-(!)DI ���Q'(!s)��n�"k I{&�" �B, j+1���-s��*� �t�/�}6;L}&J " /���"� <\ep6� � /i m28i�mz}�U8^=f �s3% "�+u7\� � IN:UtJ�\!��A�aF�A��{m�E9�=A4 �/�7R%\ ^ (I )|;m+j #Jb.� .-���$�omr_0� Y�)k��&G s $j�\6�Ac�$jA�j��/U���;2s)compacte$�I�}�� ( �F_�G,;}f^n(B(b$AT )� !�I�(��3� > 1$A��8�=�iX2} LC2):D=6BR2<|q|}+�_{�}|a9Zq%!b�f.�U)a_�8j�Ii�N �q 5��Z,)��s�h$]!)_� Ah$�reCb���6�2| NK �+ly depen�ci�(k$NB![�V\\�R\D�_jin\{i�I0 q�8\}:i>j \}-m_j-j�;1�!Mi��r$.UA�$jE��k��A .c��Rlj�e�.�A6��||� 5)>�!$_{��<���{0i�Z � ep'qI`Bd1c.� , &�� ("� �XBb'~2sot�� l6�). �)����B��F"aSA6sGsFBfS�i93`^�e>8�einpR#s o�/�) o2s &�'J(f�Vm"�An indi�vt�'*� �&�U musta��P]8"� �����-w&Qa�c� �0H+Y�*M#n�(�T�^��iN}_��?u�u��s&�w0YmiUch�.�Gnecess=� a��cen5ual  R�"�>ll:�t$!BdJ�Mpelling n!�)�eIi j "h %+�6 g"c*�(�  /5r�t a r�:�,@ � �1�7lsowE�%����x�o!�( �^�Z#a)� a�2 �): rL |z-p�2|�U'(p)|r�*@g $r>0�e�mea�S@ �AX�^� $pEru��y0 �=Ma�!� F��-�O^{+}(B�R.B"� �qg\~,)" *>Gly�:�e�&�&�ua!c�7�g%�T�)9�!�A�>jIs,R�+� g~�iqQ��P�W]+�L�A$.`  J�� �re� s� �AB� !-J+(A%Hs�� �$X'6L-�B!6MB)"�-"�|,.�A%who�LroÈf��:�works�&n��ly$X�n"TsI��"!�]�.c08a�)�%���x"@ A�us�&�eƁhF�ZM�>L �6� ( �J[Tf"�2�iN�,�  �.G6k �:=�"V},2M2�� ���Bl�\%���v�T$0rz,AI,"\)>�"2#�\V �d�Y�X')� � BeE,c7's�h1:Mra.fneL�!�B��>"!�new-�%*pro>o�"!I�a�Rg�c"�g� YEua1U!Da�}0 z,\CJhe&� �e*�!�oeb]Nve-> y#bve,�.�#iiE��B_n���c$ &� 9G��6�I�$!�"�,lU�8c�3�2�sjU c�Obm"�.gN�{zR�loe5.�" �$%��@�U�ru�9I6*�1� =T \�v�"Ei�� % #_i�Tɡ"�B}^�2{_E��Y�Z�w5 � oB4qf } IfVFR�3 �$�E�iO)�!m�;9��s2q4�!)� ���R-� i�F�j%t^"&&�]i" !�l recurrente����~ul2�of)6J�Q-@ �st-lQ H ��d� R ? ThLjGn�?�a>� x|��&U 21E the %N�^] =�s!�&Zate�1d= �*)!RN� ! ?5 p*f7. B� tinu�7�az>� tP"\  i� �C � 2K $�B�� r^U 6@*� no c�/er) m� aL� ��ona��"vo+<�D!0�FU�erg�8q =\C� V9,�)\title{RM�ZY� O�э&� qs�Is!6[Ms�Uyain A$;‰[(i�[o�-�yQ�&� �@l\]�Ap�����f"��!�&Y%B5owA oJurQY*C X war �� !�k!X�4�Q�M!E�X� )f:8nn�bKv��gen��izUg�r&��\U2s,���yFM>l[>2Y.l�l2�v�9�|/�impor I�O�t��a��b5 %8�ic �2 . ARc!oGed 1h{ f} (x t&�/[�<-��)�a�invari� N F full (�� h ��2{�p�cfA�M�Rug8�)�.����A�%�Bd:m � I� �~ �n���G"� 7 -�c Yd1�ityyy"+ � out��+ �qw� Q�.� h�8   =\Ch3t��8�<I�|q]tW3k%@aUYnB1�6� aW� F.q ����e�h�[Әqa�U~n�A1�n���4 �N�%66u E.�,E�� �mFw�`|J~ae�&o�ᶡn:jA�F�W/o0�"���� | r� rivial@I�G paper&#},ao� �fs &�:!s[�s(i): Qɂ �<A�ofv@ �!!@I�%1�Y)s�l .4 but� on�G"� �Nu�g>l=�W i�Rm\an�lmpl��? l!A.�]-FD>5a >��R �Yk �;$ ���!�I1_� rJ� ��G!� � L. K�gSJ. Kotus��keenk }. C�s� it w> lreadyE1\ 1984��%���1R.K� rees�*B�D�I�VA~:t�mVma*�K�^_��M'�E��f��"U�\y� _�axi:�!=��ed�)h�M7�w _{\lambda = UxŔ$% ^n(0�3J��y�m# ast.!�UrbanskiE A. Zdunik �u :z}��n%��1�0Hausdorff-dim�6��0�re� ��a�is60"2�5�=ce"AU!@.� �z%�A�M�.carAq;"�� iyMVQ[  �t 6�hopE�?6m ���aXs6�(m>}N� N�7.a�a�1approach���|Y�fewrQ�� ���bicA%sai)5�*n"�8�<'���?sv[Bm,*1�U�8as�i&� �s. M�� t[�a $A+s� *If��2�oy'capA�on If [O&sR' =pol��an� `M!�A�eo:�1s��t�0uy���.'l���,��vFij B. Skorula�� AR�O�"vwbartok�Z,a�r��sT Y:in yreVsi��/�s�"Jco�M�Y5�r��t52Ŕwe0\Q her techn�� e>=!� T#�����.�����qo�'&�z��!80method develo&�M. Śy�Yx��F a �F2����in:�6�4 a ``spiral'' q�of�:A�yE]M&���os+>�����e�% a"���hs�x�Y_mny, �l! � ��u � 9�a�o���N� et�su�AS*de�X�� )�Tk IN�0��s*� k� �J�1d!S�_U�I�t�fx=��et,�wx%A'�Yk��bՅtXIqe � ae�N~��Z%� yu=&� A7�!o� (� ��r.3�)��.O�rA�&l �;>� � a�q�4a�A�E+�A(M%C�  �^��.����!9u�{�>& "� ��,*ʘe����%ɳ&94r�+ ympt!� ��.�1P)$5��_.� ext!`&)H��n�E 2RR6 !C/of� ]�|p�r,b 6�8 m!�r�� �q��tur"(u��a�hr'.k@Q�-7,�8c peci�osp|�=" >�s{qaE���"{��^?�e�z���<nL;\ge"A�{�WE��Mez�k!�lta>02all $5ED�%��#� yields""<���d2�x�rx�*�c��xu*��A�B�R-9 z*a�J('P`F��z{� J�!�g(QZO3�f&�6�"�S!vE.��-; $-jP5 E]�7P�"�l H s s"�P�(�= $. C&��aask�  �J�y��a��ht�sN�U4c� Li!#�b٘���]��� s ,�}�"��cam�.����X"�)�1�+:%��� ��3a�tay��inͳ �or e� �ex�set ���y�}��~o�TA.,Tz�n&Nex�;)�ind�m]i)�%�.q >�s�!>�"}�MH0E�j!_AU"� B�A�I��"�'hadBi,Ere! bl!�so��, & ��:��>���MT-�I�%|can acU D!�d :qu�Q{>.!���e�>R2Jy �Bvfy9ans4.-is$-+ sugg� ��g\z1wIG {8\ E):� s. Uڂ ad�al �"p�s�6E#��A �is�6{)\�("줁��BA e"h+�LJ��Y  s�ҁ��B�Z�2 i&�i/e�Y0 R}�mpr&Z#��(��?"� �-"\ �X$"�"=6�+,)�^�J�?ANa7$A$2m�B.AW�'Pv!�k.R }E�F���)Aysupremum+Fxll:�us 'k(~ - ��� &.-a� ep_0�& E�ll�p< �x�0"9� )�*�$$n�N��*� -��": �* i�T���E D,F�!nd �M(b�RaG�eri�%m�M�zP"��1W�is+G. Elfv�"�e }�2VS#�"o0R. Nevanlinna)*}n1�1hFj�)[ �-KPX�a7ai�mma) in >_}b}e�E[ ��u�7R1�.�fl^x#�X@V[!4.%!`+ Q��s $P,Qg R� 5C&*{z}P(>,�2� �#"af����A� �,�LofP �p:��{&� Ri�� "����gn.|)y ���? &%Vsif�E' rq���Hbb4"�)���0e��edsvAD/he�"w���or�+��6�MR;!�7 �H%Ah�(F�a|"�8A��22Mہ::`&9� nite*�B]�b����}W�%N�>='%)� �l+Sa%�6L� !��t��E�i��,.�I �rk�%< E!Yrs�F?P��W;Siscuss-E!BEA� �, e:�:�mNs%)�"d"(z\�)}{��-&) eK"Dle .[2};\]�' �cF $B>rAbfX\�-ET,1�/����m��3$0�� \�Z �,�V\G �\D2 ��Y%4} 5\[�DژB�4 GD<&�D}C���k%�?'�U}{\to} � Ũf^ is i,2I�N �^{?�-e�9aC \G�LR tau>A�ta��� %�6�)l�9A� }uiKaTa�&�7 ��7�>m .\\F*XaI�Es B��!��'�4 $T_0�*$G(5Z�:�>%�=�E�!��  $M_0�f_�hT_0!�>M-�E(TXK ge MïM2}$: \[�@�L(�8�'1ґ >1-��(-� Pa� �),\] u $ :�j!��dTaxtHF�tau\}}>01�� �;���������cX&��H&�%�-^��3A3=AC' `6.�2�� �"e~�Qre6���&��\\A�q,B�*��.�����"�*-!�nf�W �abs!!�A��how%I*�"��=.0 "� E�)1�(l^�" oF~j*j�-j�xby-&(R. Goldberg@&0g >&ƃ��>���F�^�=),&�&�Y. L\"u�%?�&luŸ.�2�>�NVr"4���>�!�1pby�\xV&*(�f�A by P.! Ripp��nd&$M. Stallar*^&r#s }��?:9 inf}.n( e�5>�t growߏ"��m*.@&Q�l kd �atM���)g6�ed2� � >w�Hlla%%!�H=�>%X��9( �\����h����KC�� "["E�!�V�Oe�q e�.�3�} � �o6s �yoS�PA2�_�}w"<�s&�s:> 8>Iݦ��m.�A^�!-!� Oif}���>Z�;� } u���(b)e�(c)�^- dedu�at $-e ����<1�Of1Ɍ!q�� a ��f!3�z�B$��o"�eOTG$&8 $\G��RM2>G�k� $!ud �M"�Hm_s�PaV�ls>�l� >lBT k U�Pk� N:�Iw)^{(kN�B/m:S8'� oM����!$��*j;(�c 2pcB��&�   L�E"�K�cK_c}��1$.�TA-��AG(U=({�\arcsinoxc KV�i$� El"� �nd �y�2E$0�lt�B�*�Git�9L�>  < �(A�s )�j tau)}{6-5 B^Y��r��qts?�g͒lM�>Q��㪅�x9�ea�$ H�ugh�'O�D�15 ��Qa��*� ies:�a�$rG��M_0� Ysڊ,m d by $M�:�-� ja{1�U�Y-2!'}\} M_k� I B�,�, ;H]B(� defm0��d_m1�ft!�f �1A; {�f- �� �  1-M_1^� >W Se��+^ B�� A_>� @T�p$�rBI*} A_k&�b� (\D &�2}-m/M1��E_2�I+3�S}�S� G�\ &IU& ;m�wVl�d � f^l�avs-11�\~f\{ ' \}\\>Xl>P_FI$ a_{k,s,l}��._S*� $!:=Y\�]j�c�2}:�Xl�ij&�� �1�1r\�!"%R,� ��$q8�B,s�=$AY<3a)�� de�>i9LT9"ac���6Y�ad6�g,b� F��Z(&@�]�뎀�gE�S�6  DG�i*\e�}�=�AU|I"=k_�WEl$.�JK]T!a��M  deX!nM,. 7u�F� ;4"�G2�"$�  GE�y�N���xF{Ebc߸i�I 2 1N�;mx&׬=� I =S #!- >c �S a [ r[,� iamSB�fEP�:-H%H\in GZ2>/}$ w@��#2��,L<=�f�G X*w S}$ �h�$X\t< \S�uA typ%k�+ look�Lt� �S��t "/er{?& u6"��>ieS* u��6 uTh6��}-tAyS�|�a 9%�J-D ����==� 2��#"� !�eter, �m34e7, cut�� @f� ��-.�I��,a\�]OW$ ��� .04&�A�΋�j!IO*� `i?��"�t9� F� ��Qub}����j���$ Cet f>��3�_0>�_0Zd8I"��CN q:i I�* �E��Qw��t��fi ����� �$x� ����z��m|z-A]$�U imal��a roӼy.7e77�(z,!=P@(1-t)z+tz_0:08 .\] ��� �Ps�K{ %�&zla&�� $|x�%e��=� i�m!.�*s�l*J(-b� `|> �!�12�&� uq\b�e�hy'�Ma�ub3f8s ����7"� B� in ��z�1�,Igz"'x�YzgzEn$ W�!l, a:�* "��B�p!Hs F[��yH b���s J(!!J��u�G9�{+M�YQ E;a� ^�i�4x�dPv% ��zi@e�,)�f gemV5fRe�2= "Tyā!V_x�!0u���1� .}>mRP @ ny�(D_tMe i�4Q ��4is2�i��O��AZteb�!,�"����T�a�J p S}) �&� -)*��!5$� � s 9 0*$K� St$Ng i$F� ���U|�:�aq�$e?�$�&aX� $\F���V�= n���j'�,_k:> �6�ia��1$Tl�bi� -& FJ F_k}:Xo�Kde�� � �O&"��� a� �U�IO��3corTGB<ng $V p{kPt� UI V$:"1��#P��#[�J$\D({M_k�dp{ �zkU& !�S �$m�,<{k:/:�-(U~�V�Z�i)]�!j(V/"�-n �(V)< j< K=��[(i F �VY���k6 ��1-i���F�� (V).$�s%\���ii)6.�/ mz-`- EQ��I�}A_k=fHA)I.��A"�}  Tѳ; T��Ha�-% 5�f��+a A�$, ��v:� aH, .� .UT%�N > �2D>" $%B>q��0ich=.��A�.k(*M_k$, g69� K$ �T ��'%� �V�=���^�B� >��" R��T_0).\]62 �2/�2#s��,!{2�v���H!�le7�[B(/ �C6���*�<�7|�8o s0J&irx[�v�'a!a.Cpri�(�O��k*P�{&��s�� step � i ~�5G^)G�ΝGny+6� �hW+ob�s=it se��t�r��1E�A,S:�pn_k�i(U��\S$ubo:�� the ��TtT3zB�,� �,"e&� � �^�a�|U� *Esc}�P�-.Nn >�y��. Fur�m�&x��2g Z#a��%7�*�x+1H:c��U ��1: $f��� et d��[=)W"=4$\FQR�# :.JR A M�hAVU0w)�)sU�1}(R): R�' \F*{(V):=3 !�Wf \F_Uc ee2��12�"n (�F�� plaWe$)a�Cj,b�oG8�u��(��s t�K~A $f|�A2��Ak:���e"& ,){�J����^�aund3%�!r���\�� !SaYS� z)|BbM)��ge�xz!�&%�nltFw�%`^.�U4eXR6�inequaeOh+�  �Pv �}%due� �Ta"D�x �&�+Y��Y![>_|A0z/ne��l�z�qb�ce�P� v^� � l��nfi 7�be a; titu^#bN.7 �}�B �:�U�Y"� U���� i�7 �oF%?�"�;r�j�]al 1�#ha�G�/+M�} ne.C�� Je�"' C �G��M45�ly��^��A .Z"��]S �\F�&!}�V.( ّin a&J.� 2�2��\}E"F�|+&�^�^ � ��22Z�bi[>#kݘb�p��troaL!�2� by "R- �R��B�- \� �-�=&�-!Ep^���ErEcF��"�1e !��Y�-.DA�� �`t^,� qs1�E"�D4 rK^2� �M~%� C� ^2/(2K^2���|aDv  %f" yY��62U a $9-Er)-&[ F�$2� �2< �%a��&,�f)��)-+atB`�!�� 1}� 9 eR�5"L-!�)}e[��!6(4 K^2t:]�2}+ BRX }d9�f�},le}& 8 B K^4VsP�c?!�n2!le=&� � 1� "�1 >@C`�S��!ie���*|<�}� ����7%reI���.�yKA� J�(V N>^2I.-8a�C)�U2�Hm � .K^4 !�4��cu3 !�A4)},/J� I�*I^�Imp�. i��%�&%&:����$� "+Ra! .j��4_Mh�"�q"? � &��� asesq9 12M(�% 26% D�Ug�ENs�K�!�0Q+�"�.�Pn�L���nm $� � �* �.�� �7 l���LA w"c)1^N� $-�a�1�$p��IX�(|w|&��!�� 6 f'(w��5W 4e'N*6 @�� ��\�� � � � e} K �R� K���MD, M��D�sit11}� s,(��cz)1�e�`/�>/YBOAͣ��:w}c��  6z� >=i�qsA��w%i2�0 q�J2}�!���2�K2��N1&m'T eN>���a�*� �.�Yn& can/avh��< �&<d �� ��a�]����Kxe)q�' (s)+� R,��(z-s)^��+O���� Z;U�JD��#`�P"�;�.|z-V�:3 !��� e����$1����-)�99m��*p�����&��N#o k�E%%B�@g#6"� X E!���A[�(s*��JU�V� o��(S�jY\[ay� ��!U� himsR�w~ goal!2 �9b�2M, �%/c$�N"cpcheck�X%+o��-4<-"y0��usb�!�ISYE�nJ%�Le r�$_1}\}\cap om %2}) $)�m$ lar=�FA $� ;(}>64$ such !�, d �\ref{)D}), $f$ restricted! t!�set!� (pive. By Koebe's $1/4$-theorem!upget \begin{eqnarray} f\left(B f^{m}!U8| ! FU\right) $&\supset& H+1J$\frac{2|f' ^)(s)|}{.`F_`noIH8\\ &\overset{}{ p}rq^{ �:o){_21�1M+vH.\label{mstom} \end=2HA�a xlast inclusion follows with (a)E�(c). M� conde<!� know%�Q $ escapes!�$\infty$a� $G$.IKz\in G$aimi�$!]z)|\ge|f E� � 1}$. Thus 'I�)|\to`as $m .�^U�0enough, $m_s\��$�($r>0$ small:� !� -l}\text{A� expanding�N } aWlAq@r).$ Consequently%c4component of $EA -l})^{-1}I�]qEo��$,!���$f�$,�.* $gl�g$��ich does�L W< critical points!u is aICuEext�wAkinE� $g$% %X�Y}$, mapp �Q�$EB'_s�$, to.�my�;�.Q1��Qo��!� halfbAis��by som�94tant $\tilde{KA�O�`$use lemma �Kc}�ob!�4 =K_{�g1�qrt{2}}}��original.��Yk�3�2`VV<=81$. In any cas��J[ *} &�aI�!`)�(,\partial g Y\6��#�F�� ��\ \ge� playstyle)1�dinf_{����J� }|g'�����@}}{\ge}6� N�UN�a|O N� s!�)m)V| =}&\Bigg|!�:G=}}|j{ wm�)�"I&) } n\ F��R� \prod_{i=� �i(sV�1�^a�q�9 1+2͙F�& �93}2�+1� -1}f�^{�_2}r1E9.-(R� �):�*} �� $m$. We e�C��gre� t natur& � 0 satisfies \[�� ` v�� E*_s��(k_s)AZ |(1+i0c K}{4} )^{k_!' |f(w)-s|} .\] � note�2��$2\to 0��we � guarante<N )by choosŃ� �� choice of%'F��gether/ ��m�� at�{��(&) F1!��%T|^ 5`bq"g � ��9a�}$ 6w %a(S)%"} ," "� :���,7 B� u b12} a ���&Y � )�� ��y\�  BU21 .6  T� 2� .�haFq �vorlfm} �E�U� �-k_s}V13)�}:�}� M_0� � . T2oa�discus� below Q�� )�is b �!�k1�cFH�! +�k& m+,!-ex� ��rowthe�I our e6G|f'|$� fP`gr��A (|^{1-\alpha' �<-k�bk�� |\le}�F -6� ��$ � ��� � s $k7 � 2� cancel!� : Per factors, transferr�R1�+1}S �,xby"V }{�paDi� to^naf >�w),� �%KT}Y�A��5qL� i�:2!3j�2}� :Mu��2��R�.:} Again��!Hinguish between two� s:\\ C� 2.1�'have >-m�� 21UlR� !"A�tau�}:G Tecs strong@an-�!)�"Swe Jk �endfm��i\ge \exp��TJ�M_k^{\ep1�,6 w� t�A �E���)e�i��շ6�\D({M_{��for $IQ�ffici�e2Z4\F:= \{R\in\S: �1}{c}RQ)]; (\[\F_U:= \{0n_k(U)+�|U6(R): R F\F\}\;\ and}\;n �(V):=< %�a� }\;V B_U.\]Mdpropert! (i)� (ii)a�*?�A�o/f $f|S �Tby $K$D�heB2%a S)$ 6b$C��p�k>q^{�#<2�.�"� $. JZ�+1}|S:� >K��refore ��I2;a**20-quasi-square k �m9m�)R�iI�vOdiam21}\AI8(S) m_^{a�-2I�} ��*�}� tau-�:  As in�� 1a�fin!� at $\meas�\�$\bigcup \F)61�aboveA8!�:co�7�� :� le 2�"}eQi�is"�*�4b), at most $BF,sub  beta}$ pl�L ea:� �adA�I�A)�2�: ��qs1�B6$4 U� ^2K^2C^{2�4,a6 ��)�1?2} N �}�3y!�*�>�Af BO^2/(2Z�� U� �<��ta[ ~A�21}�� (deduce fromE1I>��b�easc21} ����`9 E� M�\F(}Z-{ �  5 B Z�\!J%�A%FmAa& -a{a � ͍^{& }{:�41�},:R�A�equal�holds6��$5 )���r �� �J"� 6��/ɛ}|U�1Q�b�-�[us m1�� 6A � (iii). & 2S< &v )O� %G"�$\\ WY�m+� v�20aN � �w" �a�&> 4A ��}V�, becamof.�c)B ����.92~�?�isRw s��.| ~ $B�<�c�|ai�^.n!r Then6~��f8�IE7 iveE}�Z� $K ��e ^e 2}|U f T):T� ;I&� T� i�2�R\}\] E�R| 2$.� the _ y6] are a� `da �m.j e%s!�a��Xf|S$,aY`|fL % D %>&! vs�0 en - �%`2��IA� 6�g,.�!�Avt6 sZ��ʩs%G)"#�0 v� FQ&�AcI+}F(&m>*� C�2Ce%1ͤ}>� >\�Z]e:� , sin�ǡS� }1A`$%�magnitud���a -~*�a�lso%zA2� 1 is $S (��: )$� ch, .�� �Ffar0�an�o�. �2�bE 6:get�b? Z���2�&&i��]2�G _c  \Se�RF�}R��J)}6� le&5:��M>2��)�>1 |z| ���\�^l&�� �1}�f� ep}zh �  ^\ep F+ -1B�B1B�* >/QC.d+:�*3� � �TQ9��0!��N� *})I)UM F_U5�U� &t�& {6}. >�@%� Gb� _{�:g�.TtJ )}. 2�*} 6�1 �qQ�se�6l}m�*���g�N)� E>j��W�$,a family $\F���j� open �s $qr) rR �� eter�-Ő �A��)�sR#t cG�e�S�#except a!42 zeroEC��expzq0-neighborhoodH��sary. S���N��J�6,-�5 n�}�denofF.�%F2� \F)&�� 42�"� 4��B:`Jn� !@��-| P!�!�!��L� E[1� )2�} �Z"�i�S �� one�k, nameE�!���2�� is domina� ID����* �r\{(a�� � $\circ (f|R+ � (Q):�Fo� Q�S���ũQͩ f(R���W I�!$���$.�h Z�$ directly.X u�of O � very�y�:�� !� $f|R6 f� clos(one, sayii� � y �$mean valT'&'*��4�(!>{m �K"&  R} E�n'�v�&ge}�� i." \]%�*�"N"�!�M��'we���% �uba�a`|�))�" R� 1(4same arguments] �DN� ��V<*2%O 2y_{Q�\S,9ccU�) Q)}{% ��5BK^2R:�*u\\2( =&��-�f��1(�q��*6�*} �*>�may b�SdT\(a).�. �A�2� y �@U�,!�A��E helpa���q�o $R$ l� only�c $K^2*is&6? �ensity �ee�e� �!��(A65ir un)$�\F�:Bv,��ɘ $. M*z,ly�"^� � nR} N ���(~Ey � F,E�V�=}��}(Q) ) ��� �)}& wle Ai4�i�a�Mk� YlBu�]$� I.�*= .S 1I" F[�&2=  -U �4"�  �+!)�. &� %�Y> �= ʨN�j�{4"�  (>�I:! $F)\!+\! --\�fMf f��F��6�5Y���:g F�)�epA�M�)�$&+ & 5 K^8.g�  �nL��B� I�� ��- � Dr� ��:I JYX'quad\\8*1� _{n+1}:=-�_{U� F_k}A�$�,let�e recurs�&w,&� required._ F"��com\�of�ݡs�D. \qed \doc�4class[12pt,two{ ]{j*,cle} \input{o+dard.tex ymboldefs %0X } \sloppyEintroduc2Ebasics non-% renc�entir schwarziaH(bibliograph�*{ac/.{diplA�nd��#\sG2 on{O�  applica�s} As �io�2!Mremark,remk},S �d #-p $asatz},�order to�, posi� ��@�L�/�"�1 $I(f��Asiexa!� ��c*F3�:; cq$�sin= co &,y�w�$result wasAxvN(C. McMullen� \cite{mcm�b$2thmW if} Let $9:=P(z)�o(Q(z))+�-P}��Qw 8polynomials $P, "P<t=0pQQ�� � $n:=\degY) Q� ?!&� �ir $n-tha�el! s $qj$q}$ differ7s�.(odd multipl1 $�1pi}{n�.�$� !�)>0.f"�Q}=-Q �n\ge3��[A"(8<<^ ty$!v \sketchA*inI~gE~V/A, show�&a(r�% $0<� <��$< 1$, $-1  _14!5m���5�b:�G. Elfv�v �e }. It! easyXs/a:�5IG�%5�T)��us>#a�VE1��;8%�BT6��A8A�c z^n00 oo(1��7z&�7)� $c\n���� 0$�kQ;$n+2 $ s9* lledv rays  )�$� z=\phiac +(n+2) =0� od 2\pi! It turns A�t��(these divid�� % x�Lin� n+2$��E,�� e^�V;iq�well.%7z$ ~7�0 in%hyUa � 5jion�;3a�<yq�Qh��he&?�G��:� #� orac�9f$E�J�}osxm�>aVR���.�!:]��/J ƶ%KW��s2� � happen%hbe"�:,9%�B�ra e._/l!�5Ccorrespz;ng-L t y��;. H�Ip���av Q utpoles.� p�s%I�N�, ``jump��F�E '', e�A��2��-V�%�9 A+eJsD ��4Ʌd%.�-3 �U�a�Sus�and mulat� �# geometricjI2a1, �"2 ! =J*�- } $A"0a meromorphic5�%1z8a���՞a�=q�"#form $B/žJ  Supp[��a�Y� M�$s�R! "�=�@r i!A? �A� ists� $\ep>�� d$� �&� �@ k +�c(c)}{n�$�+*�ep51al�*�$m�N� k,{0,1,...,n+1� �"� J(f �$\omegai4P�!Zhw y�<? �p3.�  =%T%*Fgf1 � princ� �xa��a@n. F+ �� to check � >p�.��>{epi�ied!"is� s�=b  &�a T%�� T<9/>e bock�}Z'=B1i%L .!�abs�PBak. nd wan_ ng�ain�  od m�"u$Ie, enese-$\r+�-1�0( BW)�.N�-A&Z�5 !��R� how? R. L. D� eBD L. K� ;�d keen}> T9�A/5�Lwe briefly summarize�?A -m2�%\��X!�faZtM%��st-gradu�=�9%H,Jim Langley �l �6%�details.^u ٫���"� VE  =2 Aa2dKt�%quoti$f_1/f_2�!14linear�hG�A solu���U�al �#4 $f_i''+Af_i=0�� f� ɑaN� gE*y ray)  $k ��R_0>0"8!��e A"EZ(zs 4int_{2 R_0e^{iH}}^z A(t�</2}� 2c^{�xz^{� /2� 1+\OO\*� \ln|z�9z|}�),\;\�3for}\; &� h� �`\{z:R_0 0,�# z -�T>�' ���iV� �O'!3�9 $R_11=�- $Z� univalA.�S_1AzŌR_1,\; �Ophi|<>�#)'�K-A"Liouv ormEX0 $ W_i(Z)=A(z%� 4} f_i(z)-�$F_0(Z):=A'�(/4( 2-5A^2/163$Ac(B � \Lial^2t }$ Z^2 }+(1- n)W_i&=&0>��q�م�int�ted*@a� by^ �bmethodHus � (s afterward� .a � bundQ lici�E�G��.1� [�,��]� cY.$0<\ep'<\pi�u8Le�a � t $d6,oK��� wKc-�KY� ɢ+Sies. S.� $�"analytic�*$|F3!S'�+-2tin�uc\O�I�8 � 9A�l1�uram�\}." % :�IA�U B~ L ''EWp  AY :P�#��$U,V$� FuU2� -iz)��;_1�&,& Ua7=-iJ$2$,� \\ VN2M3)MVM L2"4":�!} 2 �a�!u d-�1� c )��{z:.m<0:i. �&=&0Pa_j U(Z )+b_j V(Z)}{cd�%FU1�=&�8� X a_j�� -2i>� ���OO ..� ))� �>X�W W ^ �ń �-�/})) }N* c��R�!�����b��+&� i�S_jRJBH _jbJ I �=E"�a/ca<in i^+ka�w\�>� _j|q�6Db_j/d.D-2D E< E�dw�3< ,be������Lh$dnot(�O�.�� �6�c.��� N�!w��/ aB�T���O�.han� vas�.r*2 n� %�c\"�|B�� ��Fs�9< \ep  -i�n�1&61� #E_VK�9<�1= j�|�TQe*�Z_j�* | �*��d3� }\}  M $ZE~)upchang�coord�.�Z�!)�E�2V#����-2! �@.W!fN�, works just�)�9�k&�$P�\usepackage{a4wid9$.msmath} .� 6ams�$2 [dvips]{gq$ic%\Tcolor} %\newfont{\Out}{Helve�QO}J b%0o7pt} K(command{\tt )8\tt \scriptsizeSdef � %6& �SC=y{\bbfnA %%� {fancyhea� s} � ne�$heenumi}{\4H{ & .'BU {(\5XMr2(Proman QinRi.SnTUarabic VW %%�geQ � } �A� i?break%�M[ + .}[aG ion]I$em%2?,defn}[thm]{DR<]6#lem "L�R6cor  Corollary6!alg !Algori� ne�rmk !R'6?K Pro�&o:� conj $Co�Yura�equ-o�Q2 obser�5(O2+0' vEx>'6#a�)_Z�thmdef $T#nd ^�def9�%��-��u�margin�}[1]{  par{}�{0it{#1}}}aja��{e\�skip �@\noindgN P�$. a1@of #1 FmedDN6�#1<claim 6|:8C#l.�)��[]v?=� � �s�& :>��S!�%� :��:AJ.�Box} dmebox[10pt]{\rule{0pt}{3pt!��l,qed{\hfill $9$�Nr� �%AF4)%�8^<d.~2= 8g dmatZ. - ,�2e>K�9^��cleA�:� par\nopag�#U%A�6�mod}{\d atory7{\,�W � ��.Weop}{\en6��{{_.=!�6wr#] }[2]66#1}_{| #X��( Logische S-e J:g Liff6�\Left�Earrow> L�:2RA]b.r:.`V-&82�\wedgeB�o>SveF%fa:LforallBMex(������I,}{\backslash.q,Zahlenmengenbl :rN�1athbb{N>�NO}{\N_0:�Z3Z>3QQ>RR>pos]� [0,\undl)>+neg:+(-*,0]>,PBW(^WNfWB�C!�y=\-ACa82hCh}{\h�Gf#s}{\C^*:e D}{D>*DB*A-Wcal{A>O!�|O>oo�mph{o6_H X bb{H�D.An�t}{�&#:�Su:d6�supB/sup�Bh!��`��� n[��}{6��N�:�nt!!n�6�Lim�6%z"�:R�\gegen%lַ> \limBIpiAy.��i/��2�N^A ]�/.:��+6�$varepsilon>,frFA� frak%�:\dtB0{\cal�:,iB�id>$qu PAU�rt6�re>DRB�im>$IB� Log>%:nsgn>&@.^deBM:Mcl���ri� , !E�kring}J 9>�:{�=F(aB�#>(:P�">(:(e\to�@ \unitlength1mm n$/P}(14,0) \put(1,1){\v�$(1,0){12}} 6.5 \mak� $(0,0)[t]{$qÑi$3ende � [-3�.d0mm}{3mm} % Gen�gend Ab3$d nach unt�- chaffen! ��% Spezie�-Not��n:��8a�e�6�,Ek}{E_{\kapp�Y.wl�lambd"|ad �>CA/t�E\CB&address%�)�y�6�Orb}{\dtŤ6 Sequ SBa9A�[R'�6B$cy��2 G}{G:KU� U>�F}��{F��6YSS �;Bp8D1pt,a4paper,reqno]oar�j&Q@s,amsthm�� sem�{\odd�, }{5an. evg?d2! .!3g�2 }{15a�2?�huFt}e�2;sa_12>wtop�T27rT22sco� r!Snumdepthi*�O*A�'l�[ ]N�~O9W]n�VZ*A VRE�e�42SV�;&��&"i� �f: ark}u&:.#rAks&sZ'(exercise}{E 2G prob� �P 2'�}{� %A�Z�>�  �6N S�9��s6�  F�6�b:b� �atletter~�s6�@{\foot/�% .$a� (0scshape}\long$@ M#1#2{t$ \vspace{�u e�8box\@tempboxa\vt7\c� @setgroup , \adv�7\h�-6p4x# w� �$#1\@xp\@if�S:<<{\@cdr#2\@nil}{.C Pup� �#2} � \un� kern�pa%Y\globalA��ne\n7 �end�O \ifh@ne %n"6�.O.)6� �,unpenalty\un�hfi N \ifdim\wd9� =\z@}i�>an@2�8 whfit'�.�� G=�ne� to�umn�9{\hss9$ ��els�MK\kedv,t�QnvIAun�!�%�z@�")\u9@Fjpar �.5num d,cnta<64 % if%�float IS�Fe�s� i\�:M�.�\m� � 3pc1& A1 >gNOTFkjH �L Xe� kip\K;B� �\relax }�Ao9)BR� \writefig#1 #2 #3 {\rlap{Etruecm0raise'  E?{#3� �}fig#1{ sAO�/�$)X{-� .N�2� Calli� �K��B���k {\cB:B� �B>H cNj*l ��TDZTDBTEZ*EB*FZ*FB*GZ*GB*W.j�d6�IZTIBTJZ*JB*KZ*KB*LZ*LB*MZ*MB*mN�Bzc�N*B�cPZ~PB~�NTB�c:`5�B�cSZ~�6�TZ*TB�YN�BfcVZTVBTWZ*WB*XZ*XB*YZ*YB*2N�?2�� 2O Fraktur����fr�>�� B�frN,BfrN,BfrN,B frN ,B frN ,B frN,BfrN,BfrN,BfrN,BfrN,BfrN,BfrN,BfrN,BfrN,BfrN ,B!frN",B#frN$,B%frN&,B'frN(,B)frN*,B+frN,,B-frN.,B/frN0,B1frN2,B3frN4,�52[fr�RxB�fhR,b>�frpR,cF,�R,B�ftR,B{fr>�0 %fF�DRXgF,>!XhF,�&RX�&:�jJ�jFXk^,kF,�R�BD fr�R,B�fr�R,J�R,?n*�(fr>�5`pF�q^qF,>m!XrF,|R�sF, R,tF,�R,W:v^�vFXw^,B�"fr("*�5xFXy^XyF,z^,z�� � .2O B�Jboard 5Q��z�bbA}{6�!Cbb� �"^bbBZ-B}J-CZ-CN-DZ-DN-EZ-EN-�>$bb� F�GZZGNZHZ-HN-IZ-IN-JZ-JN-KZ-KN-LZ-LN-MZ-MN-NZ-NN-OZ-ON-PZ-PN-QZ-QN-RZ-RN-�JISN-TZZTN-UZ-UN-VZ-VN-WZ-WN-XZ-XN-YZ-YN-ZZ-Z-2�6N��v�2�OqO�=} 2oo62F$7$65var!5rm VaB�b�#bGU�=}X.} bestD (.�:�� bel:�LS LN !fD�&abl>�s( sigm>&!SS6�t� widex  b:�*w!68ke*%�9\vert#1�8\rangl�,2ra�!0o@ 3@:zbrad�+64 /�nqkett@d+25�?ft � #2-:�scala(6�,8R� :nunW(�9 s #>2�}_{\nu_AU2Bwha>" oet \clubsuit >aw55�:�w!�baRS.�t� Iz:2mu mu^\R�#tn� ;\nu:=tE�V�tl   f><[  \gamB�una�.#bf }16Ftfa HvajL:"ale�ullet\ �t�{A}  :<i@! i^{\�Ttht2Z�9e {�[\A� \ ]}} J0� bf [$\ 1$ -,6+total J2`T1$l @ m4 \DeclareMath+/A�qslanA8� u%P{AMSa}{"36} % nicer `I2er or � l'RPgrPEPt�~Oes�+6�b�F,_�& ��set6�Opw$or*��"{�9 >@$\sum-like �$ol�8c2�J�( Ja~J->�$le�;%~\;�.% redef.!�Hg H1v�H> H.d�b,7${�d}6�% a stra\rYr .Js6�maxtwo�� _��(c�+ \\�1 % max�@2 >GinGinjGHFRGsupGgw>.tF�supj��_r^GinfjGsumGsumf�sumzGhree}[3]�RI%k  %O3NkE��f�j�E�MfMvM.K^I%�DtjLli9|liR3}M�%�.vL.li^�% V�lim.� rKA�R���5/ ^G%�7�ajLYd^N.e$.Ubi="�*� >�the5%}�<:�BB�� bb 6yC C><R� B5Q� BZW BN� B?PU BT� BsE� B%GD B�F� B5K� Bw�0���586h�*&�-:Av!�rm AvaM6:a Yo :"mc&�Vk; \it A�t mini�8}G/0.5in}2' \ragged $#12b/C>��[1]+ ft\{"� >(T}[0] ��4TBJ cgap%c_�thrm{>J csob>(>(df& LsDJ#e:$EB$vxC &$!�VMB(pa>(EF(Cov &A`rm{>�p�fal �&� {�%gubs). 1#1\atop22";$eqdef{\,{\��rel�,>{=}�:\ Tree-?bbi$def\muAetau_A^\� YVar var:Ent Ent:,Kbbh{{K_{b,\�n,- m Pst{{P^t(�,\cdot\,8 tmix{��-Mmix%MJ{� ��-  Expec �QGPlus{$(+ aMin-�R \D neper=e mmin=\�:ax=�:)�i�>$ity{ {1 \mJ' -5mu�&m�y 9�ie{M��R .e.\(?rid=I femp&�d sset=� et |s= bse*S8Rsetm=&�: 0nep#1{ per^>'. uu=\)4�)i�&< Atc{\thin+ |  } 6<=( >=a ?pl{{|5&1.!(B1�t�*�'tp�6 M�uno{{\uu0 [m- 2 sump�Yop{!'m}']r{%opE|trJ�ts5�ntt6&intF'O�E� LexJ&T:qTJqad6oadFnA:$AJ$dim6IdimFJul!Dnde%� \��E�w�16B FEOrb6)�41AEn:FEN@Cor:Fk meanl bf EF%g75��'M.sgn2%R8\n-� $�02%�0B&g�*��-�� >Josc2IoscB$supY��B&Do6�DoF�ttoa5buildrei:over �/=arrow �con#1�V094 5m� | |1� ninf�`\|_gtyV` �$ \thsp<#1, #2>.W �lfloorh\r � ceil   intl{� it1�noE,l�D". 9med >�C bigbig��><\�C\^- 3acapo2>7TocC��_%�od"�3T�5{t :�. GRECO %��a=\: t\b=� c=\chi d�llte= o Jfp1g=� ?h=e� �?k=19 il�&9 Jm=\mu� �� n=\n o=�Ip=\pi Fph� Gr=\rho s=~ �t=i�ct 9 thet � y=\uK 0 x=\x- z=\z( D=\D%�F=\Ph� G=\G� �L=# + The=qO=� P=\Pi�Ps=\Ps ~Si=� ) X=\X � Y=\U � �3b FONTS \�2\twLrm=cmr122i=cmmi: sy=cmsy102+bf=cmbx:,tt=cmtt:iBXlXl12A��nin �9 l �. �. �. �. �. �9���)8 � �2 �2 �2 �2 �2 �8�sa�!�7ix �6 �six � � �6H$caps=cmcsc5�big. ��ed� gstep1% -  Per�6,patibilita' A=T&�s�1t`>[Glaur�dynamics24 trees] {O�Os�=ary�bV��$%% stochas�kIsU[model Kh�"core gaZakX ulardh;�PhE��eAv\ a deep ?Wh]{�$:�F�and :�� ��� ate{\toda.�`\author[P. Caputo]{Pietro } \> {Dip. MatmHica, Unix�!~( di Roma Tr�\\.go S. Murialdo 1, 00146$@, Italy} \email{cx$\@@mat.uni�N3.it}\a5ks{� �F�@rtinelli]{Fabio M}�4�>B� �� F� �mmr� \v� 1cm;\ab�c�"�L ϣi�a low f6era*NF�%�R pAF cobH�d�Zm@T(Markov semi�7 $P_t��cda�uaI�still 2ly m�c lem ,S� sta��O6\9 tp*�c�� _\h l w�^ �al conz6> $\h�Z sampa�fAe,a highly dise!ede�0e $\nu$ (e.g.#n\w$ Bernoulliq� oaKE .K Gibb68'K(). Exploita�re�p�gA5�Za�_s&�hmix0�0of Monte CarlE~!och%f�;� rete spin)�m�re� $b$-�fa� $\i ^bXTDle� �7�x%�?Tthe�{Fu(}:pe�Nsets){ dZW%Qis a biaaFUla|�en,�i variout��Q��D�o�G�7mo�h�rameters�W�v�nu$-aUi!� weakA' vergE�&f\YStq��>l)� �D3h(pe)�A�9�pe)t�pproachBbt learUf a�et e*��M�%�$aKI�uxex�pran �zZfQ)if #:Ja��V͍ -%%Ka�,GhE,���x�x �local 9iTto@ilibrium%�a��Bs m�k euua��8 ]�,ADp]�!�a��pg41 E�!R�taken a �woPv�but8eraA>�p! ablea0tribuAU. 7�0 \�=�> �A+v{I2c{�lG=(V,E)m�?^in�i 9 of"��teeE01�,eg�@e�i, �;inua)V"  . (-�"d)�$l\{\s_t^\h�r\}_{t] 0}$!�$G�_ �/"n�+a��si~_ gene1P $\cL$.�$� �pickef�a�gO�hassiggNtZ(a \ $\pm 1$e�%5AN ach �#ex $x�YV$. The k �)s!�cus�E�Xis pabYan�[food a� �l . A�I��m�A#N6 �u&�b(ee&�zr`siAN��q5$iV�A��m�Clqsa;b �_�.W$\b~` !_��r�vfield $h�\�$�#+�q  -���Z+$� - <W���s �\Qctak��Q volum��sc�$+� $-$2��w��Cs,�\�ively.:f\h�nO�AJe�!�cc3[gA(a���G1~ �ara� $L\g$\{A�_x\}_{I^�bs a colli�ni.i.d.\�a ��A�s \X$\bbP(\h_x=+1)=p$. %In�g %wordsiDg�hosen 6�n5D2�2{ % !de��$peH9& ��3hrelImt� s��3rA�\ %"�g.lxn: &�G0[i)] \item U|  wun5��/A�t�� �� ��Mr$-uniquM6���of $���t&�d� a.a.�&h$ ? �If so,n�@dop^ TS �v�?��� �g�9>,-�GNwm,n= $lattice, st�irĬ ��o�x f ``)R ing kin�\ s'' MnBr  --0is gro��6 through� <alp coarsena� -- ��cVlyReres�Xs|ca� sB� in�rc� �cl7%m %hyp�B8 I\Li}. I8 aw1L�,%�> ��9R�l Y !���e�wI��0+1>pos�to useu$ monotonic��a"Rb (n��Lhe ferwgeY� ) toA-vaa����A�de6 mi�m �aO)Hproces �b|"hnce��es�zce �W� �}� pow�(f� W�Fr�L 6.7!�)�Mar*rl!�]ya���ur�\VDf{mu+le}�y a "X�%eEbS�� tU. Ho>���A�eas�se�ats "V-� ion �h�i &����j forcM$�!�b- "^�Aul�w o $1aF�vb���t$\b�m$�d� a��!�r<�%�g�� beyo��is sim�!n . `ar hand,�extreak$ �%y$ (za�*o FZ �m�i���  atten%i�tba'�lPxu�!��c�Nkin�) s (]�� �hexagona1Ł=!�binV !�){�p�ed I�HCDN,HN,CNS,H,FoSchS� M�ase, be'i�mot2fon#���to  �y+f!ge�� sal�3רٟ�reA��/�te\a� connt � (�}-l�t ) voa� f �Li2� *� antidp�g then ��%t�pat a `�n^ flips �value�1r � ly �q �� r-�>W� E�]ped b�@�8% type��KA���� � iaQ!  mmon� �A=I�� perco� �a� Go!e�[!��m"t��lemhmaj��+l��A� gres&�eU2<s&k��*�xtb,�i!=*��>ca>; boxer c OoA�"� s, \i��\J�(se� Iܥ��. �contrary�i��Gy ��[89 al, �i1h%�(t�nt�xol�� sharp%�a� truc� way�9�2�MaSiWe}..3 �7�E&m� *�+h����q��� �s �k�rat"��s� � �Q�� ���"| |F . Ou6D�xsS answe�o ��ii) in n�;�Eps�i�tc�*c�K�u��uf&��] ( *y� \b$)�~�%6�des� .�{\em l_.z p��p�des a �°of �s�l � �r� F�g\  unM9a��� we w���0�|��in fu�L� k. e��s w_  μa����>�u��=�,d�C�a)AM��67�og��IS A-�. B���� �s�JO�b�{�! viewE�e%��� fe��� &���E�hee��4A��%aD� sec:, _on_s8@0-0.05in From��v\bbT^b$�o�kZ�%, roo��(l,��.�=ex�~$b$ chi�"n ($b�2�|ѩA5ger).��:V on~"d �j� *���F0h�jy�by "�W*�Zmu(\s) $ptoИJ7[\b\(\1xy�4E}\s_x\s_y + hx  bigrcq]\,, %\� \s8\O�o-1,1\}^�!^bT,4[��E%,!�gof ac�5,%r�� � �t �"� Hcan� al!��&I�� al" I�on a ``���}''�  (u,�w6�� comp kwize7 A�vU ) --� ����BRZ,Ioffe,EKPS,ST98,JS99,BKMP,BRSSZ� a p��%gra"d ��  $(h,\b)���is h �� Georgii,L��o�  quitT fferaA����he cubic*Ax� �� Fig.~� fig:�_di� }). Qv�e}[h] \&e�'{\�Z{file=hc �, +=2ip9c�S�"�u_c�,bӂ ! j"2is��, � rve.�3F�O � �q��re?����:�<R $T_\ell&�o �J��2yremov�?all*$ ��Bat�ytV �Aa� a���aPe��muQ�x]-$�.�im�Yng $+1�M,��"�, $-1*�data as lea֎of�jK�� $�.!� free5��{(�5e�bK�P"# � 4J�r�� ee (_ � t). T�  $h$� ֐Qd��S$\b_0= qIc12 \log�l�vb+1}{b���#$}@�rm�d�Hxb(�a/%R��@E�"����u^+\neq!�!�ӆon�$\Ɋ�$)E*n^��  tr�to��RŇi�� � �1� �-!1- 12>\sqrt{b}! =�!voften r���s�``� -g��:�''~�� CCST�{ has "9�zrpret��>O> "� !�) � I�f@ee� $q�' d&Y�:�_3 $p=1/2$a�tF�� ���&�Q makbh� (��!M � x) becom(�n � A iZ�b>\b_1�ve�%U.aV�$,I\ell \to��]�EsleqAs1 6�� .9� ��>1 �,A��s (� ly) a.s.\A!9�@u>W. Anb� to look!.E�wo&�>@A�y�gal 6�if%7�%:� M�����2��E�, m�%�e,Ma,·in��k � �I Y�!��0r4�on/6�es�4,{ ``bit :1� ''!�a noisy�=��hannel ��$Mossel,MP0�� �)>e:��cdd�o���t6��a��)$�+>_���� ��V~$h_c=.)>0o!)G"WB@)�|h|!� h_cAC��� ����jx:�= <sr4 �t�"���D�K3 c��X2 a>��x�6}:$;!#KE��wRe�i����y�W�S���;P!8iDV � arbij�m!�incre�of !@$ caut>�u�to ���v>�F��>>j"� ds>%�{�4>?\/}�"m !(��'{ z�!}*�! �;O�F��,\s_{t=0}^\h=�- ]'g6�!A�!H&� F . 99�w{<(\cL f)� = \� � � }c_x([f(\s^{x})- )� � b� \s^x6 6e"N � $\s$m(�!:�A�$x� $ �6X4 �f ,. B�!�ajɒ�c� �>���i� ��M �Y . Rw� �� j$t2�%� �.�(see � \�Saloff(a� eC) �0f?sub�&C � lways $O(�X� f ei���<�^A>"0m�y�(�,{re 0�FS)U�&V0 8� y&al�/ (or,!�sy�y,�T1 S In2'a>j!e["&��y�"% !j� !i-c1���2*d�Wɍ�) Altho{ll2���y��Ϲ)�--CH! &-�5 tive,)P� nd.pY�s s����� �[al� A��a w.r.t�"�)�-��2�rɫ�* ���l"�~�Pa�fic �\ �,heat-bath\/}"|& |:ij� "Z{)���6��Ax C,=�9{t\cL=�%�&m,associc�&ოT�/��1�viZ��dA�X�_{t,x}E< �iA%� �hortcutɡ� \r ?(n) %� E)< V8) = (P_t\si_x) +$ \la{rhodeZI. ��!<ex�ed��F\$ �B�giv2  ͱ)e{U . Lkb;# {M��}a��"&J��*u�n�� r,�n�n. DDE)�e��6!.�-�� j*�!�A&�*$�|+��akl�"ceree�Y��IFm." ���"I�� a�� G%X$\a�X(0,1)�� \O_\��llMi� V� �'�aՁ�()�-P�(�&M�_0=t_0ER,x"��>N?{%* t_0$A�g.�m |\,j6I�M)-[(+(�)\, 4\exp(-t^\a)\,.A�w14&=E�.JW�'ll�in;oL"!� !!?5!�!j-a!�*�"Q��*_ta�%W��� $���&�F�.,&R�m!�0�s:+a &��("� � *�(r�_x = o &*x$p�' = -1? 2'1-p$ *lv�65.*��($_p, \bbE_pf !O co.��.i�Չ�����,�\e�to~ A`!�no)!of�eׅ=a (sN�"�tween�baW!t*05� O$. iv�B)s,Z* [*we ���\/�qn �s(x��q\h ; r{ \, ' <1. A fu48$f:\O\mapsto\bb9��ed�1%� � �  (de)�J� � s'$ ��� b ')$ ( ge )..�2��� mu'$17!�% ep90,~�mu(f)6(f)I!�(( � e) � !�1!s&�. |< !2"�-Db0��a�'�-�yp�v } \�<�� nume( }[a"�*)�- y $a��"z;�9 $p<1���!in |6$ʔh�-B ,b) + a$ !d$\nu(��)=.��s $�<(\b,h,bu0�m2o% J�ZAe� {p}$�p- �+�p>�"�existĊ0�_bba��.��y% �,1@b`!gA=AV��b,p�Z��R�Z�qf��1 \O^-�vd� ��a:D�fw��1})�o�-�>(��+�&MEE&t �&ist $b%9�Kt!5,:D�[$h=YY$,>U�AWNV1YA�"�1.Wb�69�!k�m%\pa�z uT�a|rem�R��8 2z��s��us X3I�S5rk"W�s< �(�(q�qS1`�belie�� � �&!&0$&�0"�*� shQ!occur�]s�y. 6�,� ����|in�O:ph{N�6ar�be���p.�)k�dE\@b)}�(��a+6AS&�J$e� 1a�byBI �"*�i�� issu�'�y�1�S0n �# techH+�i مA�� aޢ���A�} �A��w"/1�]�b"�wZ�%�at=V1 es 2*�a\��%&`,:)Uc)� R�fA .��6���% !)FFmu�71�$1$n� "�����E�2}K��&-we5o!iveZ[��xd���'n8 #� �:s� �"�1] �rono"�-G�ha8*by�* so--"�em*�}Ia^<04ҭ)2L``�� dity&f9� ��r�(�euAbs��B� ). Rou�;��4!l�!r �� hat,A<= -h,j we?E�ea:! u�addo�Gs~ of_t"the oo� ite ($-$) Х�2(p *al�* signaa�? �ure!��l~��a �e,!SRZ�do� in��e �&�)s}6�3�Aow|� l�.�)�6$\2�QC�%&t@��� ha�to�� b��"$2��ѡR:!re �2YhF&(��i"Mu ��-Gam3 }�s"�)�+qsv5�끲)�pp�?� no Q�!�EsEQ�M8Ju�- �5 ScSh&�ep�% stig2 ]A�metastB "�>A E@%k), or�nu��y�it�s6�$q$--�v Potts K�� $q� 3$;�2o3}. A �/check�v�="_ %*��� �o6�B2��7A���? behi"@ Borel--Cantelli ^49U,�ޱ�5 an $L^2$-9Bo%pV��5& reP��1 d:&N7&/'9�!l((&/ ^\h-.,)^2$r� *2 \,:f�� $t6��i*�Pla�ANp;ؠ�2slA9organ=>�wg In���2( 8�$pre�#nar�-�A o(VV. 3�� explA� �.�ni9 �:w���~S by a�;��val�p!��+t�c%B<� s. S� 4E�5 deal Dt�� 5 .�6�}7ؑ�1%�ӵ;.%s fu�I&3-a.Cs��di�<4-1V7� �{SR2�"/� s.�3in�#�w.;5:useful6]q!cer�8!.��e�&,��1 �) Ii1>onv� D�.��*%�B�% �(d r :@Fye6��BL,%\.1, %h� � l��)4o$h\ fe28,�,J/ %�c2ex�!� 4,<W"�Xby $d(x,�d1 !U("1&; Oa2$x,�+�$.Z;$r�A$)@�0A$i)=nr 1��2$x�MW�H$APa��Sof� |[��TA)=Z�� A}z~ThSun2>A-p)Bal ���W.v $x$ *�]A;. $E(A:i =�--b,$)hC-F A$a�r x:�s2�!0]$\O=\�,��^{M-}%  ,el y�%�d!�Greek u{�,� ,\xi$ etcp f%���4��Ar�--algebr� cF$ 1 m�var?� x\E?�. n��I� ś t $Aɥt=e�+�?�Ef � by~ _A��m�.�00~��$, h�.Hout�~A��~l$:"@ "gmM�! ag 3%8 /2H�� $$ \"cX� gma)'�p�&�Bigl[�$��l5/"#S_>/(A\cup\M� A)}�O_x "Y/.>�A*H*s r], ��!�XE!�is m"J��3  e2�$& �cB�+i wise�QC;��2 )waB9 B $�(% �� IU:�"{$a�G6#b'� +$ (MU-- When�fTi�AHl;Jinc�4}�Iсˡ]�!=\HB M� :\;d3�(ell��%abbrev�P�d$�(L �; K t�@�-, mu_{2$i�� �! Q . 4� C��-c ���$��w�Z _i� (f)=0$I�6;}� & )�ee� 6 *(�of~<�.� .�2. Anau4�W �?XA���=%� (X):=2�un_X).��E�!�&` � 5��nt $X���� $T^h\}(%�_\�f�v�In��A�h\(f^2)-\m �e�(9$f� 0$�GEn?\)m $ H�� mepy}R $l- f.p~$5���"�� $�a� iff,y��z1��z .z,~�C�� !124�'id��.�1 � �*q�](f2W/8�b" qtE&0f map ��aUA$"��ly,1�A��%s_Am%�Bvar_{Am�!ȉ�]!�iJ0%;R�L A� >�%��bi�<O,\cF � �b�;lna:t,AF��I��"{s $�F&�/\mu^l(%(X)r)�V(X),\q�5,{a!i}q� \  �D�AeY\ A�];� $$ %e.�>�$a cru :�4� !^+�5 . E�"�%is =I�s �*� !"m*�describ�!�o�%" ``m�a��-� t :�.A+ (�: N82k�m����-�m�%4@� _7 Heat Bathu!��m� 6lglW.la;�ny 9�) t��O$�'L �m�&�%A�A� thi�� ' ( (b.c.) $\t�1e.g��E)A A��0.�O�(c�S:� A^\t�:�:� �:2� < A}:\ \si=\t \;{�6on} � � }_� or"� g}t$A�-� N�-Ar�- �;�D�;IB�m�$. x)_yq\_y�P��$y]6 x��'i(x=-�($ ���-� ^{\s}_{P }} Z�.�) )~ � !x$. FaQ local.tP:\Omega\to\bbR$ defin� � Dirichlet�m�of~!�associa��to�UEUD�2 ]#2� byq� equaA$}} `df} \df_\mu(f)= \frac 12 ��_x \mu�7l(c �� [f(\s^x)-) r]^2) = ;R@\var_{\{x\}}(f)).it�(AOl.h.s.\ �uA�!�%�al)(i�!�w choice of) flipE� s~$c_x$; ?last g8lity holds whenEBializE)Qc�Y O$ heat-bathu�.) E�\emph{.�0} $\cgap(\mu)i�| )]�Q� coM�9sob 9ofI> arEn Id by 9�narray�[ w!o$inf_{f} {{9�}\over%�!�f)};\q��!�\}?��E$\sqrt{f}\,NEntN,�N!Q�Qe�F%��mum�� each)r�ver non-1u3sA�. %z.t!:9sM�se��,of exponentiE? cay as $t��$&!�varia���Ue�,�8$=e��EW (largest)�W�LU�$f$!� 5}P_tf)ɤ�a-2t9�}\,(f)\,,a�{gapvar5Qq�)Q $P_t�A� � semigroupJ.6Y $Y#$.%^log-->.!gY�is rel.��Rfollowing hypercontractivity estimate (see e.g.\ ~\cite{Saloff}): setting $q_t:=1+\!4Y�(t}$ we have&��!d��any $8$e,L \|P_t f\|_{q_t,\mu})||2 -i hypp>g 1h 2p2$S nd�!A=($L^p$--normAP��2G . Iq� is a��Q� } 6E(�A��y$)mn both!�Y�and $90�>always Dctly positive (posAy depend�� on $D $). ��6kresult�\%�MaSiWe}�t� sam��rue �� any}6�D parameters $(\b,haP)�^+a_� �'.� pplus phase. More precisely onAsaiv ���%��� key-bound�'� }y�� ^+) >0,�  _'m'  : tSP a -7$does not i% how� A�� ��statemen�8AQ� vo� - ��. SRe � toniH�: ider�s show�g� %�� incr� ng B�uM�(� $:# %�� } ��(-�� mu^-�� mu^+ &+) \,,e iu n--� ��%A� ^-\nZ E& a7 $\b>\b_0 �4$|h|\le h_c(\b�� \subse� {C.y ��Y<: pre� naryM� s} A firs%�or"  step!0*g�3� .C x\in&6 t I�_0(x)i�1�E+}�Left in{y ��directA" sequ of6� (�*(Ed"�)) �A�a�Ih IZ(�)�C �$i�!�x$ si� 0�can in�t; . Wa�wA�v� ��. For ��twe only� z 5.E ,root $x=r$ (�gN al $ requir�$ modificE� / argu�L.) Fix a length scali ell�obser�a�G�E� 2&�9� m[rm[A )Kr}^��,+ $,Y �latter:�.k� sia� Dta+} �a�e�;!ate� a���q�e�T�q�&8he leaveR )A)�;� cond2 ) H). Let also $\phi�el�J �&` !E2 ^iC�iHr)$ s�{at��eor}:ormo 2[`�D-�A�r  \,+\, :�W�$$ %F�! unif� ��  %J� !$�>tyt&,), Se� 2� 2"n � ) t}Ŵe &� e�hX ) yiez �*��*} \|>�*� �^+�u�|� {t/2Y� 1� /!\la{30��rA� .(+)2�probabi��ofz ,�N+$ A�6��X2S$I �� s $C_1�� "{69(+)xp-C_1b^A}$� ( )^eq.�����!!�Kc_2!�efsome " $c_2$ in � o� �\ �$ %An appl��".g %2�::�t~IQ{%��i�(+)+.� )^{-�1� }�DP \\ &��{(5i)x).)} \, �t%Av�13Mx �Set now��$ll=c_3\, t�� c_3>&mAc$enough. UsAu)��R� w��$refore arr� at�FU�� ! {-"�q�tD�-c_4 t}f��a suita�c�A]4ܡ���0sufficiently D. NoA�e claim �2})) A7��"L2� ) � �-2 � infl"r � �&s d%s@ 8 ly fBat �S(temperature�� s�5�u�Qܝy|�ԡ�-T��|-�-Y5 a��AR4MRQ} *u previou��a�s6� a�$\O_\a & �it��da�or� i: ��� corollary���Q Q\a� (0,1)�  ev�f�*� ��.Vb} �� eed�)�E�ny pair] h',\_ $\h'� h/ $\h\in ),! comI( '$ belong!H � . To�&r M��}.� &�:� a �� 0$,6 � 8 �1�� \rhob  hEF2"� . '2!jq.A+6 1moend|�����()A$%^�p{-t^\a}�i�e� ��� �becaus� !� )���assump�reinsteadi�ed via L� �� ]M1 AnoK a�.x B<i|�v� -�.�I� weakU� A(A� �AJlaw!( �^\h�#akly toE� a� r � �.�I � O� I�9by{gX"O:�\bbT^� i\O"k�� \bbP���^\h�s +�#+=+1) -B9=S12� big"� E�% I�e� fa� a��on�>� &� �"� a d ���&_a�g �-��, �h})ce  %�, P_t1\int d(\xi)() �fJ �*�t$6� ���Av �veQ�gaA�*} |wER)� } q | :# - 0(+_t))| + |>�3&2\xi4 \cr �%(eq 2\,\ninfsum_{� A}\Bigl[\KEt^\h(x)Q:$t^+(x)) + N}2xiJ3\ \r]� = r~�QQ��.A�.�X %\cr�# � |A|A�� 2 ��\d t} +� ���igr]\,. ��5�T � $:�) e�AQA��y���" E�A���E� d_\hsWQN���>�, Finally�"��iz� ���.[6" a:(be useful. a�u9 �"]{1,\d�,���a�eM�7�u&6 �Z1})��#��:tretched.� V �!�)$ rem5 the �. $"� t )$�mm2F� s@�N $+7"��E �.q�la{mu+le�$)� %{*8 \:"$\nu(\l)=1 o�K�j)�-�t%� S�n)I��A�whA.R_x&6&J. TI��hp nX er %� 2i�_~ !�c" ��$>U %Obt�$%appear�ino2���u`!/|y�� |!/m�a�/4}��a�2|n�fL�=0 XFB�^26�BVleq\,��6�Z C�-�v-�_x� >��@ ��M5 ��Ey< Borel-Cantelli E>t E�/ .�$e=\e(\d,b)� !�� ba� 0'%OLA�$-full �y�e6��e��q� integj� p�.�`T jO��HdepG1 =\e j$�M(e"� -�jh2�2 \d j/p � auxili� : . )L'�ablish a���a typeM�Z)�� $ �t02� (r)|$, i.e.\�B ] , bu)`|ll}l K 6R%��ju�)y onesp ��@is i��T stra�(forward6� . %, ��arbitrk>M�B0way. %a In or�o g�d( ilar1En -&\Gi�!!o %�Is, w %c�y"�(r� �"7$* ~�e{�D -X�>$t&(i�} �'t>�=� S}>!< _"4^t ds \, P_s g0 \,,\�"D g:=\cL\s_r %\\ %=v<..D�in:^%_�g v ))Fc�@es��%Ifar G_s :=) EV xi))�!$s��!L%\a< MarkovU pertyI " � = P�P_{s-D}%> bbE ([6 g] � 9 ^\h)e%� � ���G2d!"6B&r)$ O� �h��ondaE�s) so--ed ``� �#e�Epropag� ''�he") bas!n tail��&�! meanA� PoissonJV+&TR% ite{Mar})&�NN�,eq:G} \sup_{`u�� 1} |P_ug%�- ')� C_18 x |` x-Q+_x|d C_p d(x)MG��a�PT,C�"m!E� ca!ke�2a�� ��sh4viV�$ is # ccor� lye�b V`�\A�]�''$,"� *} |q��яg) | & =� :TYEJ� J� - :�g]B'xi) )|&  C_1 -� R�R�|�a�,xa7- Fxi|��E1Toe l��(terOadd%SsubU%Ciy\i�lby2� Q�h�.�)L&��� 2>� =1)-V\h=1) -�2�Z.xi=1)9� �a|��-h��U8!p$x))| + \,� .+2�� B� e$j�b $. W�>} wF�e�a�!�-.?0\eaY 2�4� ofB �4T > B�.N\d_1\,t}�&$$�� _1>� 0ly�.�1B! In�xclusion,G �$\d_2>0&m A�j��%� _2� a�>R� 2>��$t�( desiS."�r�E^�}N.s` .-!(g)=0���!���. \qed�$~$Pv,$"!main_�} %Back�A"( heq$w� ~vide a%�ied�$? thre\$Q&YZ�$.i3"h b�/�� o do�we e someW"5%��{1 I�� at���2 Q-�y (C9Y6),% � b)A�� %!ty%s@"valNto \eNno {\emA��$Tenumerate}[b*)] \item{�/�p>�b��  $&u&\ "��$b� ,� *�$h=aZw�A P_p�\a)�%`$\a=\a)d.Q�� } \med�Si �per� #B4�-- /,\ )I c%IV�&be6hrA M) oZHc5H$9H0�B>B+�',b �K�kRJ� 0]�AT5 kma#(J� -JanJ� -;Z:aR:a��MQ2$,.� $p<1�b_0!eU��� \F�E�-5B + a$�6K-A�6�:�hM� FJ �I� wordB��3A�$\b6�.��&wh�V%+rew,;.A�� )�b_& ob� domin�� �3� h8\��1 $ if�� $p_{\b,h}:=e�{�~((b+1+h)\b}}>+!-", ,9\i9 \b�� frac{1}{2 4}\log( p}{1-p}w$$ *�,�9_ 2� �::!� $\aA�6�w8WeRn achie��of^  a) �a*�n#��tun!ح�"�- $p�.%M� littl"�9�9�,o,`"�.taI5,p$ very %clo�5o!�, i,&��con�,�( %�~�����F�� b�MtQO��} A�ee"�69D=�m�6 clear, tZy we �fto lowe���6yqx� E�b x)$ ?B� a*),b!�nd c*) �4asized)�7shADfocus%<�{%>W of:��,"��:n(ly no2. N' Gt�,:=� �$ wI�an%�:?�����(�'h6 �.-� � �to� ��"U!� qI,@!�١'$--almos<)phabAs farGt��MM goIe-bnot�9 inguk!M/&�* $ (a*,b* or!�,�+�we� D work&� )�!�  out & differenc!�!K�0^1�s�( i6��key"8 A��9�<b oved� � next+9 ���L+�\been .u s se�+t-"� N�H~C�$s 1a4t"w). ?=*.�9 G , idea behind!e2K� 1�),!Om�� �3>�*!�����I�& mode�:d�a&�9�1"8!�38random environm� � bstacles}�#Re|8���+_.1!���el%2A ol�#��3�I(at a vertex� � is an� ��}�5\o_x=-1��a�-�� fh ))+1 0We �$T(\o�$� s�.nec�:c"D$-Ose S� ices9��PA �. Not!��c=� tyse=))) $r� itself�1a . By�� stru2�$lv!�$\par�� c$e@s�Q�a��=oncer���a{�2rM o�pi> "6A�+pEg(t Bernoulli�=��"�3 9-�i�ee w���+$5&�*ly!l�4� s� �����(�, {\rm \;\,is�7.e}�5s�/6as soon��$p>1/0# teq2 to $� 0s $p\nearrow �fixed $b� =s� $\g>�)� �( �(Pera0 Giv� ry7�5� $\o:he6�@A&��R; as b� b� Q�` $:A|/Zi� %G^configu~5 sp�>$\P$�*"� 8\cB_\o:=\{\tau\�2O:taue�35!�\,\A \,x\notinI�\)$$5)�  5t�A�:�#$a��� C!�_{A,\o}^(� 6�8 $ \cap �+$.j !Cm�,M�`!6Q�2_{�0�OQ,are��#'7no�4$,:= �$. �E�%�1�e�VU �Aa�9 ``minus''dary��<1� maximala_ owed:�1Z-ہ &� �>�zY8�n% A=V( arises, it���9)�d!�``+''. SPH 'E&1%�)f\o�6V�"� as]#��� ;3A+>jj#m�(%o�hQ�V6%�" e $-$ �2�5-���2A; � ��Y ly %h senseMz�>M (& is �E�^+_��%)a�(I�D$}^-$). Fe�e�*\center) ��xcludegraphics[width=3in]{albero 3a�){F�ȡ��� ($\circ$�Y�,($\bullet$) �a g��.�$\oEB$� bi�8 tree.} � fig2�� �  %% %�!S$��� FD0v!?E:JP"��o�� �lE� �I��� 8?A"vI��.yZ�#H� �A=e���J�is near�G$``-'�H� �8B5HJ.�s?way4���{t!b)\��'% valu�#$9�Y.�"�/ L�8\t.V��8. U U%�5 >8F . Mon&D>!^9XA2�IJ U=\xij�I{t�xi'!�Inticula �>&q ���:n$�*\o�%O} �!�50�6a�S"%#1ow turn� our+�.�RO:,2�B\!hM=, a��2�et�1� P �uj"�G}�$ $\o=\o(\h%�)� � erule:RAo_x = !Kb���s��+1 & �� H )Rell$}�' \h_x'4 }L} S!\ Q9�B6Clearl�YhAq \%#6$�F�U$e -"�r�)[%�E � _!)s_r)] -[r�#�,I44".01B�If$L=!^\gE�g> �er2o<:�2&��w��w5����e�;� LA�z _�1g�.} � .�7 \geO^{L�<3%C_{L)g%Y -R,-2�] ��A]�J%�1�No �d�X�,� �ula role� *6) &f $\h$� twofold: e� s� !}�O� 69 e> �s i�som�sF� .��6�. C b�(Q �e�g � d a rag{ell}{� $}ELL}{$Lo}{$+\;> "� elle:� ,"� }�� R�996w leve3�{:/� �  ()A .+ +$N�V VF� (�@) M�fig"=-YN���% M�AbA+5 &5�� �59(�main.�/\��%�QO �L x.�OreA�j�a�PvZ�H7 ) ^�B���)o*ifyWxZHonc U adop�Be~!m��8ion: � x"�F�cE:��ell bbNB� �$(1"�?N�I� &,ly�&,�#�O9A= \geq�_0�$ 5 --a.a!J EO$,�in�K �(e\;�!u�2�0C�� in a��Go!gl��G� � E �ō�Zl���.!skip  30{{\bf E�Kr,nr$}} B]I!�A� thir#r�M6���a purA�!�icA� blemI�oE-�(be sol�via.r$reSGion� �&"J=s}!+p��$gin # 3 &> >�<&c.�$2AOckuno} 4 R�h{ME0�PAdE`$ .�E�!V}5�"��3 ���� ��N�!�� u("l2��iN= d sp�+relax� �9�#libri�O!�.�$T"����>.c. H� 25E� Qn�CA:"�K�^+�4�" 1�-Z2"]H\zeta�B *U��-�"u!UM1��CF{�@ L�A]:� *}�݁�"`Ua6>L@An6�M(� �}� can repe� �u6i�3})�Y�Z�r�"Y� ^+��p:#F by $SA�R ��UN|$ �2�C := �O(\,JK}$A}�"  |�6�h)| %� �0C�97{(CbDL�!JzJ}BC� *|E-8�zIL1" Q0}o���antx-Q�. A>�O 2 ! ,�;mT� �:Az$ (2a�0 �7,*RQSwQ� M�M%� help .�C-�� .� -��� | = Z� Z�t/E�{\g�:e[})}�C{R!�fu)��:�}2�:�J� �0F-�] ��4Sol�k��se�Cj�a !� )al qu!��nd� inv�3s��AH�^tw�"�eeA*&&B"� {\h,a�U:!@nntis�gE upa��g�� . T� is �$�@a "�? � togeY&�0e/.c�]Ts�f�; �3�b"BZ�y� 2�A")#�;Bd6�����8i>gjFa, ��1%� $\g>E�+��U�h�$�JJ8:b�I�)�65fg�Ras� s. �' keepE0"zto a min�W�  abbuEa�C[�Ae��UIr\%� fER�Ty?^2A|� ivelyD$��"�0L &QxNTep`)=%�0�S \bar\L B.h0 32)�&8�' 5M�B�!e>oB %c �} /}�P �2�^�1�DQu�& =�bE�ft[!,%^224 1\�]"�"=1  ;bbP;@$[\exists s�Zt%7;�\, !=\L\,:|0 \xi^{1}_{s,x^�_^{2�3Bigp"p7�Z �D? $A_jM,j=1,2,\dots,X0{":e  �A_j,C{�� bar �~` ��:E0��3�$$�  .\&� 7�E�>�Hd��jV,]�Aj=1}^"Z2}�7P(A_j) �NL m_:'+1 )!2$[A_{j-1}^c: B_j]��P 8-D�>i��B_jA�1(s\in[j-1,j]%�%2!� \;��2*.a"�%�!�:�$ � 9>�+� 6�7'JjD.r a)'8crepancy betwee }{1}s!�-%G{2}$ loc�Z out*�qE2$,�che�aɢsiLe Uan�" m�5�2\L$bW�6��,at $ $b^{.}$�s�a�Slf--avoi ) pathsR+$\L� �X�)^c��'���0s� � �*�+!,Y-il5w�� �8� vari�Ls1]��YS�(B�)�c\,�� }�"�� ��5�d�,ell/ c�,a�'3z A�9B�aR/M)�F� ?'Kly,�we look!�!FU�j$,:Vr;��Sat=Ss;.M� SfI}��i:W0�!�ravels ��)5)12Mnles��AkjA�)Ej�}Yc��b^{L}�*(L-� i)%�}ll)/cj2�C�<\V$ j < \e LM�1�Y-!�s 4$c� �!�$$Ab,c�S.�Nei $0� ���!�Y�ofa��P{j�&|$j� �)A "��~"�B�� 9Vpa� i� �r*h0$�(at �)י�32 A� =:�. F $r_x=r(x,()$� �]`sON�x��( P>T_{r_�-\)�d�%<�$ w �-)_P�-onN)!�>*endants:(..V k,hb�h&q z��:eN 6 4 ���id#5�t $h$)P�6D ("!�� Q���Ev��Odes��Z-ly� 1�)�=d +h$). # h# !-� ��6�2U� ����$,�A� ar\L�\t�Cr_x2Y!� $d(I�,(B|)^cCEzl 2!��f�f"fz}{%�&cRx ell1�a@\ 62 2}{$%r634u 64}{-s} %�la3 La\; a�*8.}{{\L�cA dot$� ps3x}{$x -*�4V�2in} } � tion{Fve.{-��I�aa& e�6k$.�:�,��/���Ca/ $\nuq[^{+�Z6-)��.--�'"�,TD` �$+\,(-�� .c. �򁡥 )�#"�""+�R � �i(}^�=�jh=L�( ���i"w�m� g ^{3}� �B�$e;�E�V �E� � ����E�h*s'hC ]:>� ��Fc�g)�[En�(/�h"in facp_� ��=.od`qe�,czR,� ��^),�Q(y)=+1\"#y(T�[, \; d(y�����  W��9 "0��FP2 <we��U%�.� 0D�� _� neq��� 8ig]Fbb4" = +1K]{@2#�E#2< 633 �3- V��@)�7Z q��5�.�1��un�WG1s}3�bsuef�termsJ$��Iى6�,�_F �BC5^V�Aq�m�i�6{.{15&� .4e�E~! a�1��$would like�rgu�% "�&�A�t"� ?A�D@ ing:�M v8 min_�  \� �(5*.Ny~&Y%\eqno(�C}\,3) %Mtsob%#2�S1Fr$ Vu�"wA�!T�4usE�-�9X��B��%Rre!��P)�satisfieZ�[�2�e�QU.+.T?q�xp{� (c\,Y � �p{-j /��^{Z}}(Y,$ 7>% $.? �(6�"� �$\g > c��# *� �\g "&&�'Jm( FhE~�b^{�Cp u}5:5�M�e�] (>2x?/I20D� N*g*�F�1tBx\3J ambdaz] ft\{��� tv\�J�I�F���.?��A*':eE�m#13_��$ed�wY>OZs:}�~6�-��f�k\ku*��+�U�g�9e<�_ Coll�"ng-29}1& 4�w:thus sh"bw }���2.�� je H&q{8$. % %$p_0\in(0�]�,b)2��%�m �?�C2�A�>�C )+1$&?F�% E�� ��} �@��^\g� *�\*}�MP_pN�"2�e� . Tv� �P1s  11})vf let))�F��yS)\:j$CoG3�#}}B6� w�0' fE�#), )x�eI- ,�aoM;eMg\r_nY> ()��m +A�x:K Ʀ+�.Y< {f9�z =t^{\a^! $\E�1)Vv �t^\a 5d,iɑ}i�>�*2./U�"� +�&�msd are*;%� en Q�ZsAlc��7e�c!"aS]A}varRb�>m�p(�X etc.�Tly�&Q�2��a"��E�"l&�x ms&)l in��2a.�5� :*�,OBSTACLE.TEX> n \s�z on{Rg've�ks /m�|"�+�L��'vee�� Faies�� a �{�k2y@�F the �@8"�:v. O�s1F�c; h� hl�}ra� �{yA3ce)ls v@[e�@ ���A;!�p�`d G+3�;l�x�u a�*�1�C"�5--2�?nd�8�9**3) 2'�e�>em iz$\YrtA�a<,QsV�D�>�1)��o�:�+ ac�Q!ypb�>u�+�(wh�/t!"5=}"` !�>} .! "]=D@��.F*X l>�> %��occup M(crc�gD� u�u�@�),�� %Esse�DOBJCI.cWFed: %eiE;$b%:�,%�p���+ " 3". %13o?+uthGi� &3 .a E %y;rayQ!�)��llA~ch < y. Q�|adF~ons %of�>�tdB� �^dA�BHdO %gT!mm�2�#[m(} l*� 0� find�*e�� �!Pd:� �H.�ynB�D V`nn��J��*\&91} W��G!�xd� {hamB�ɩ�Ant hDŽ�� C���!fx$,is%�' si'R �L� ,@da"1$ wFW(�,\o�E� j��{wF�8 &� i�S i��2�P�-kAA$,S*�+�K,� �7!}$�*� .:.% �{�<�$R�%��E *0�R_z��"�( %�#��t Lj!m�(�5�# !��:q(�"�R,!�r�@ �[.�spa�%$(\ONhP_p� �m�R_?��&�Q��>�T_zx&�_y*S�(e.$\wt\Y:�e�.�!#��J� �+1�O� an5�Q�typ&�#&�zsft(R "�;m�d�bYFRF�iyW,`2\b�/eb aM@pR��$ITD�V�"d��a*}�-��U&3 �A"h`.qz�l� {R_a�p�;\�p, B�]%vO` $p_0�$\b_0"L-��� R1})�@y A�fUE�$2�])+aVqa8�i�l!bA�S ��e"YRpJ�,�3L W *P` $ Z6,Fi�q29R+bP���wJa $�& R!y��-]�I��As�J��2�&�� $Rc& `+1�*�+A/�x{isR9hr�Z&��"�%�!�z%I}00l`�K�6�e� �a�� ��A� $b=2�i�AB����(�je adap�0+Eof��r $b$.2��in",o3��Georgii�o!�s $h_��$=(b-1)+O(\�"1})$,  .,�>�[$a��p2aI�t#^�]9hN,��2�-(�e{eu71a� out los��r���(F�u�PR�$q^{(k)}� ��(R-�>2^{-2k}�1-ka}�$� quad k=0,"77�1qkB��v]az_2� % �c*%oo��=*<�6� ratioR_i\i�7��i.i.d.\F�!JKsam�_"�� A ���*�3\{�|\}�basickB8Tw3}) ��9n6#�N�a:��q !ea-xR_�) 2" reFOU \!m�,  $>�4\�,ac��pjZO�k3��2`&� $.> = 0�����V1$!Q"�Yk>k_0:=]9��4a ��&a3isi��%. "�EAR_1 �j3ni)u!), ��)CG%2�j�I!��8�T ,�a}!.(R-l$$��e + t�O:54�_gfor0 $R_2 ɖ e^{1-a}}4)+V �&� . C��Z�X .{8{z_1}=-1\}\cup E� {z_2 )H� $!01}=+1,R_1> \e=ap 2 2>"/�!H)`qkV#o� :�*}�P0�P)X (1-p�e(A-�M�M ^2 +w1)el\�qq>v *��e��o�]� +Y�H_%�.h�k��>� ����k4��F=%:lR��iA_0G�.�iߞ be %!k_!:"���&\+{qq3}:m%}�{}�$"�Z:��Z0r��E�9 �.�leqE�U� !�� UA�K>vple ite��n��i qqf�L-�a�!2Hm=0}^q;2^mO+�)r���\!% 2^j\E�j.�,,p �>>�M $j=%�$,�.>�m� a�"�"�B�B� 2^{e� ��Y�N�+�[mp&@�Q- �~cho5b *<.E�6�d�LZ�%p p_0$�/�y A!oMk��y�#e"C�w%R=1$�%``$+$*!] "�2I oZ2��{i%�on �v�i*�&�T�Vi�$%�`!;�{1}A� Ie"2�n� mad:[y(r+A� us, climb���;h_"�"@u 4�p2 #�u!%91F;\d2~�-y81-1/(2^{5+2k_0}+\,pbig, "�V�N�DLb*}&&� *���bJ�&�n�&��*yO$A1"�aq$c>���than�.�l,�aA�b"ʕ o� \d�c b ?(r� "��5�:�F�<r��: � � $.F|b$?!KE�� Vd��6mIXnde�'�� "'�&them: 7=�8� b\un��L A�a}"�2�)(y�devia�&� fore�binom$6w���5��Qve � s $a_1,a_�s�=�s. :�}e4_�  m��A�l12-a_1�)bu/_�y!�*/!��*�cv)+F��&*p.�! �gAs �6o.�c�.!}�EA����H$pv %�se�B2in)jZBft61� � expc� W�/���fXX.�w~_�4V� Z!0 magne�Xfə&�Db-�C�%.�"6* N��?� ��w� en����b-2B{�)\�Bs*�)b�.6eas"�"�<�I*� �`$q-��  < )�= �!59q� mg�t�H 2 �:F���oކ�uc"!L�o. Iч��%��ay" )�n exa��a�-)d��.�E�:�{aqZ�d $6� mb-m� &��[�BP�k ��e (��6� d4$)?%r= DS� .��*�vR_b�.�/�v �%���<.�H�K4 f�W$}a�2pv ! $WAF"�!U�w1}�Gn&*')�cNJ#. BelowAm~= $D�h = &yEi&?2����M�Jls� $W(x):=�!r,x�!$N��Yx (� ^j7�$2�o$��R5�Q=0�WMAP2A�,U:I�"�Zt:Q|J\ ,�_�[ZQexp\,\�  t< *��)$ } �"� �] J%� {1-2�Wla�wBK �<e�tZ;&�M e�!��� �5!��a�p. 92AKg �& a*},a�i~��3 $s b*,c*}:�=�2 tart��nN�& . �B i{I� s_a}�1A�9"=� )��\B h ,*��� expw6Y n��*,�9,��-� +a$ �T � �  m�`}x�tJ�d7� 2� -��-&�"c%�!8 BL#$\{"�'�)\}_{�#�%}$�enb*M ��"� �$. H77� anks�l�2 Gur� our �o�|��."& a.xif�6)� $\wt:q&:=!4d ��@�\p�-�Y��a&�*:+)G��iz�p �N4RN/E; ��e#ent; OeqachA��y��k �(�&$�g8��We�G�(re��be%tH����@pXTo �eJ�fix,�1:*�wB��$��v�!�(d�;�Xstic)$�"p,�O%e^)V-}e�$\G- the uniqu(� ���*��;if@ !s7o�� E�e E�(x��~�5\� al � \set�t�ME. %W9� x$ %HJ�x Nex�, �:Jb��!. $!ex�4 �$�*$\D"R'et�all&� ��z*� $y\�vP. �8�D_z|=b-�5��&�ea�0�)��regFn�zR_yI�eɈ �$�JT�|Cno &!u���� !�b j xed �b�� d su�2I� z_2"�5k� A� ecut[ � �).M�:de��F�At$z_j,r)=d(z�V,r)!�5$z0SA�c*�!�$ 9/ p. &� �o2O�R�]K  =&(�#p#o&# gen&# z_1%� �,  |R|_�%-�w1�ښ2 x�a��x�,iV��E�� � a �q�a �}* 0#)�-M5 "B y $�� a-b}"91�K 1}2K1�PZ�� �0�w}��\V0�k�� ���K�{k}� sLe^N� {k-1 ()F�kJ�n&7�FYe(k-1)}"2�$-1)N�k !k+\: r"23 �Sm+3 $k%�>�" 4a# �"��E|=p8Eu\e$,!]v_$\e\e_0(� u� A�i�^j6a�[j s $K(\a\eͮa;�+2C*�S"[_k:.��% �E���}��jn� good��z.%P �0" NC��i�"immed[_l [� Pe� i�#[ r or.1�� $k_0�G O- �q�a��� ��\0aad��� �2�.rm�A)�i "�* 9LE�)u$) ���is%!. �L!�!�:~XN.�F =�Yf�i/�conl�1�Z!?�'m�u��q}eqp} Vv�� *� ��} *B �'L"�  :=Y� s} u�_�zGQ ,,\; z \;ois} \;�s\em%}}\\ 1 &>56>3!�202-� ��[la{wpsiFL ��p��p*�p.qU�pz%V�VU �UzV�(k}{$z_kr�V0�U^V!� Vreg:V}.�U��J �* 052x$ � !��+4$6VR"�Se��p� �F"g �"�& & %���� RP Js>;bigl[qhr]i{,�,(2u)�af�>m� wtF�%��Wy >'�H �^� � 8 %!�xis2yiRkP.A5z[:=B�/2Q� �N� :�x��%1Hw x���<%9=%��U�͈J0�& �D$K"�&��H2�u�, - n_x� "8��:�"_� ,Bȶ�(�/C�R� . idnowz -`"K !�chi�<=�K�� �l&1$�q�?mW���bye���r P"-&AsB�.&�2�R,: n_�^��+ $!O� k_0 ftO��}�p�$$ �2�a�&/�] &O�9be� r-$,�_A� �.aX,e"�`r�:�/\d + \ �*!��.us"�&\d� �\� ����� [�=u�'Y �.f ]�bbE�"���H M�-�%z. u^{-!m)U�]���feq�a>;!�d_15J��!�6' 2AP d1u>*ȴN v"�cM�A�Q$O�1'Qi�h) %� y1!�"�% �2�!� �? I�� 2_�1 C_1=1�[��&= s2 read*�KAy.��mo�<>x ��}M�n_4��*��4J�M_k�4�i-�w :p}���^6�ܩ"�Ex_k�6�=Q0� N_ka��w"8 Y�W�= J�I�ACft[ M.M�q C_�* } k!k 02 \;k=602!:$ |��s�cc"��C_2 .�{��%�MIN�)� Ieq"e�, 1}) �-�l.��"�Ob�K�A$$ �%��jp{(tM_1)5= �3)��Fw2a{t^^ {k!}-H%A�B{B1j�tŦ$���z��;�Za*4ic�U� �[�!�)�se�ds� bQ�!�H lexicoo�2u %�#�Aeda$ $\tilde x�12e�O- ka�` >_�&{k�@a�absol�EaD����5sp�;ved_2)�^* V�65�%���:�vlW%?U�:"��[Aj,j~!�}n�Q��of�e$:��q��KNggv$ G��4w.�mf"%/K��=� $j=kZe,� .�k�%,��lsoB�lud�/�3dIe].!:W�s&����',F� a99au%irB(9�}W(�  k�\�!p6+y) .� %& =�yj�A��?Bv:�n� V�j3}��y)�Fwk2B� ^Sb&�#bW��� [~T�\|�6�x0�dQa0*xS1.Z2.xeN3.4.h4.5.5��y}{$y$��z_y��v�tk:�,��2.5:�eSchema�#pic�a�$T����k� �z�IYV4��5):�Y]-�A#>�A%"�6� �C� ~�� � �*` A� ��un��lAth}GG_� _iN[:�r,k$�$�H T_k)2y/�.!EB�b=!_�(���!�!��~�nce"Hky$0 9 (chay�er�by|z_y�D�)."�4 �,�3A W�d� � �D�<�r�S�=8 �A�iLN�N7 :�1.]�& �!�!D!�� x_i)�$cep=%r%v*/ ��� ei-por�%2" J� ���;B��-e�.q1� �$A!�tb4��9 . R������9�  $B��\P .�  %11) F� 9���F!/*Q� � A_[h);~� )�M � z�v��'/!?�~� � |� \,zRB,2S �1E( k �]�(�~`~T�QXl� )�y_ la{w�&� ^�"�BdF+�st Y �,^d&�I�� &'�x=d�Ysq, r7Av$��/(4�+�s� =, E+4) iH �{��< �� $;vJa �`��  xe�=`�d%\~uF�/(� � w5})� ub 7�$:=2QkC�"���9�26�e��(�;\GE"Y&+U�  E&6Bz s�/��)z$k�1�:B�e�^{k}k!ڔ�.�S�Y(\ʿ7�% b*}.�9%a�"_b*/b�7\B�%*�-��0$�>)��>�%�%*M6 Y5�%E(��B  �.ߟ��s�A�yaŜ�!0�a}, M����#�2�7ofE�bad.1GivenVx/&gB&��"e��ɐ6K!$ ;roBx�*�*aI�!m�]X&�� �"�,j-0U��I )Yo:�!�+�!�5�b})t&��_,�:���.�7��]��(�/(1-6 )b/2�Dj.�2�!|ll FxEF5`[y�H�!&S�5� g>~~H):��I8}�.me��Iif" ve�F2�$a!�6)�28�7y7�"*�$R% }F�"c/@R_z�c!-m}&O",.X"!2S")2(a_1|#AF:�@%u"�w�$.`a�I�e���E�!�}�)y�I0� �t!�Fv4.y�B: �Z L���&t8u$�J ��wK �n�(individual h $z � F�/�6 ,y�B� u-%y�4x�(ToaHa��A��]ogA�mp�s7*�av����b G_2_pre�^n. *tR �O�/��IinfQ8JP�3"�,� v is F2H i��{� a{nep  "��A�s/z5.��� ��,%):mb� �| x %�6 �Y.�p 1N`B\bF\as&/G� U��(�&AJ�PŞ��w*[2�=�M�_a}�Ab��-w5/8s acPEA[5,facuP;u<]7o removF��e�)_y*�$A�? or $� A�%r&� 1:n)� w6})5ho��"�c.- =  H\ �����t�ainY- .1�Jh J�Of/UF�*9 .N8%7��/�>68�3 F3 ">8R: �Kce�5mR!�&N&g@ amzg"�\��a��aU!�2�&L<��"J)��7).��T*@�=a_2�@ p&J1a"��%}N/�E�%�Adecla����b ��m5 e�"�6���=���$6�́\o�\$ T>�6�i���'A���i�=�s}�R!���( ���ބ=!�s�o���^x BY��as.8!7Vl c6an!�.��I�+T�)%�8% t�8�.��8j %�2 ({ b -4 G� u�-w�nj�T@"� �o ")Mb .C J �ahe��� 6H8^I��b}{��� Ao&�n Poincar\'Ok d Lnlai�}r�6eq&���2���M 7�IP2�.focus@jW��& mr]vb=�S��_C�G��*�6�j�2*{�R�f �4}��",k .+k$\o�1��� �(L,\o Ew aP�a"WY9��X]S�i�buSac*!k"�#(p)�6�  IT:�� PJ/,.�{�_ gap}v�simultan$ly. Indeed k*�r�� ;.'�ra��)�9 ,  iix*�ll�s��aUi �worAl�5in�mm���a},.� bY�*� c>=T2D;>|9�� ĩ$)�I�Z o  !N� -.IJ6�B��C:N��mL �Q n $L -S3 ach n � 8(Ś,"NB_{�_��� t#.lNW0(or ``block''� d&�� _1 -��2edI$x$A?iay 2q��e|9�*�K �p�� nder�."w�&G3$k�f4t!�boЫW�n :�MM�1 z Ee�Yi@�R �=C\kL�� I.�E��/ $C�:!+"��a�o�"��r� D2O���so-p^�%�--w�''� \cDJ_1,D }(f�$�. } �d+ ���.@v A� �O"7reg�^'ral� nP��-����_20� :�F�]&��� ,�)Qmq-�$ Ts�dtai&X"ny); �H"z5B�\R�)1O-aLaB\{ "�\tau,x}.;� 2d��-g\3&��f} ]{N�}{)�.�!�"{2gapF>+�b���]!`eR� !� 6��D%�>�X � 6S ��$ (mtau� �;dvbaS mpat��GA9\�-�k� TDc��$) ���\f_�, %�-~�aF�%r9�_^# i=F�M � s,6�  1.4�� BKMP�CA�s a ̳r)K!r.�$aCj+ $n" $^1Wv��!AF��; 8: �,|"�  �� � M���D,h�%�*i^�0X �&U > @J~u�J�%�1��\,ƣa� �a2� I�gapFr)�&c$�( 5��ue%W� gap!�!keI��GA ymum�e:p�e�). So 网��-aR�Ći.�a ~�J�^�A�-F{u�A��qm2�"�Y4^_8QV!is�)methot�iCMO , co_Y�CO,�K,5"in�v� �Q��r\&b�2�<.���$1�rc6_3d--mixa if :�#9G&U  .�g0:8sJ���r���fx\tc u{D* ��$eq � J^ LAs1�:YD�r. 7j�2{��ialj ec2?a"�ux$��A� u$ A?>�9Z�(�E. s��t&�)�N.���Ɍ��<��( gap4' ��{`equiv&�� ���M&�\${`VM�( \eps�E�$=9�$,& ��w2�� �^,�'& 3.2A�2.�xnv.���Z 14%!0�UI�-S 7ellK��P "[��o_0(��2 mu^+_{L,\Ho}$ is $(\ell_1,r^{ ��})$--mixing. The conclusion of the theorem therefore follows from (\ref{gap3}) and (\ref{gap40}) if we can prove that $\mu^+_{L,\o��� $\bbP_p$-a.s.\ for some $r<1$, when $\�<=C\log L$, with )(C<\infty$, >xall sufficiently large $L$. To�(is we obser �d, setting $g(\si_x):= \mu�\left[. ) \tc 2{D_{x,-�(\o)})�x\right]$, we may write \begin{align} &\var_{.b} v(.�vm) = \Cov:Q P�,� 2D\nonumber\\ &= 2\,2 y=+1)\, F�=- a([g(+1)-g(-1^] q \frac12 fR'\,. \laA{01} \end1!\Let $\nu$ denote a coupl!�M� measures 2�(\cdot5��$ andv&-1)$. We+nJ�*} & �` = \sum_{\tau,\eta}\nu())J= �tauNG -J�1etaN1)�]!�\quad!nq v� �y\in B� 1 �_y\neqxyILb�([�+]^{y,+})N�b�:?-V? �]'*}�!$6 \pm}M8A/�$interpolat� betwee�rtau$ I(eta$, i.e.\4configur 44such that, usX\lexicographic order on $>Q��$:�� )_z=�_z"z<���^-A- $z>y�`hile V.0y=\pm 1$. Rec�,now�defini%�� k1})qS func$K_\bi8Tset $$ \g:=\sup_{x>0} 8(x) = \tanh \b a�$$ Since>�+}-f6�-}$ diff%:ly at $R� $, reason!yas in � totvar1})e� � 2})��estima��equ%�}^�:}��V���q�v\g�ȱ 6� �Fr��ham �t�2obtain�\1.�\lBj\,\nu��(|A�-AZ|��ikR��ZR�} W(\GHy}=��7B�M"8\d=\d(\b,h,b):=JɆ)>0a!6� 4}),-�ga�>:�7})�se��at1#��) JS  {\rm - X P \;does \;not \;hold}�J)� R0Big(\exists B! %:^8:4g�8d\E- <\*� b) 2�( \hskip5cm%���x:\; d(x��q L} \,6�žB�Ґa���8-�-j0For every $x$a�can us!�e bou"n expw!�so�f i�0gap8}) yields�F Y�-w� (J���%: b^L ,exp{(-t_0\d .�a�1�)}�9 ��Sg e.g.\ $r�-$sqrt \g$, >� � $C$ F� .� bya�P Borel Cantelli lemma!ahav�I<]:&' 6� "O �$J enoughT is� cludes|proof�5^ �. \qed \medno {\bf Remark}. On on�)whe� = resultOTh� \� X sob} capt�  /0true behavior6��Hlogarithmic Sobolev�stant�.prese��of Grandom�Wliz�L,obstacles or�8, instead, it o��provi!8a pessimisticI�. Av (show below,�� soon $\b$� � )g$ (actual� !an�dspin--glass critical point%�!pure I�model�H\Tree^b$ \cite{BKMPaein@ 9\three cases described in-&!� rem, re ��a$\O_0$66re5Os|uniformly positive probability,&X ˍ+\o\in ^ �,spectral gap% a0tiori�vPmust shrink to zeromleast!�f 4$L ^{-\zeta'}$c~determin%�$ exponen� ,H>0$. A quick sketch�!a},is fac �th!�"�(a^*)$ �/ $b=2$ g�vaA��. !Pj(a vertex $x� T��I���  L2 ^O by $TѢ}$�  e sub-tAof YCrooted!7��itA��4��M,l� levels��Ld\ll 1,\, M\gg 1$ bu!5 d M $$. Assum� .�!1 �u�(, group tog�C!�ita��partial 2J nto ��8l blocks accordP t�s$eir comma�ncestora)2�at � $�� +1)Y )� c���c�.��n impos �� !�ice� sid�oddJare9 � 9 �$z$��: even5 �5=e;A� correspon% $R_zI<satisfiV \lF,\e$ (as usua�Pe=\nep{-2\b}$). Beca�� of L�� �� R_a}r�2$t!�obe�� abovoa� ific��s�ԝ7�;�"$ �c|9� \cupa( J |}��c L^\am� a suitablB�9a#c=c(p,\bm�$\a2� 2$. &� U��.�ofa]%m}�m�I5�5 pert!�converg�to one��$L\to  �CoE3r"� :��y$J���twoAg-E7neighboraI�. I��,4 immediatelyI�AJrecurn� w3� aa�pS�mad!�o��u/Y��d�|R_y-1|� -��0�]1�a�>�L $c$. In turn, if $MBi fimplie�E��marginal!�Gibbsf?_{� ��.��0F#%��-�has a.ed��independ���L$) re�ve�� sity% a�ec�V��� :� �sa�Z�E�� \emph{�Ub~ aryAhd s} o��its�ves. � glatter �a���(���!�lj� ) smallu� b^{-a(\b)�U)�!Z$":$%/e�� )��VeI��yA�(previou� ��� csob2�)E�L* m�$��= � \d,bJ %�r  %} \se^{P? \Claims (1)--(4)}\label{c}� L 2� L�ow us�c fill&gaps iif"�B] A}.�re�toV� main}�z�!�not����� � � 3� {.*w�� �s�ez,2� P$gassoc�tdu�, $\nu^{+,+}_6Ah� � a]�Uex.�ell�4We�Qa�0in_z\cgap(\nuY i!�y  b.c.\��q� affe�� quanta�by a co�V or (i�A�7\b$),� 4replaGJ�$ me�.�+�Vi�6�. At �? K each�weiexactly QB1�ofFD� ,�[$L=%�!c �si>��u\  (see�=gap9}))<!Th i� /"� iz "�z"m�6/i�Aq�e�Ƀ2}\,,�c3�T ��i)� F� valu� E�3a�!]AI�$d(z)=/ $b^ ,! �" ��--6�"�}�4}. O*�is*�a%%�B�.{%Sr_xm�i4� = +1) - $�}^{-,+2%�(3b)^{-3�"e:�"xc4F��vMuE� t$ � ds��!�6�a�T_� l-$ 2UD_� #�$+!� }$ =q,�9 2�a;JsA��g uFf =�Ix}"�c42B�A� %#�G �e� ex�eA�!Q,exx is �md��E_p\wt:�� (2u)/2}$, sTx$.� d(x,r_xI6!�/2$�L also� ��w� ts_a}, � 6b}%�Jc}). �n�Markov'!a�J�*Z��%�e�12jfl�� !Q c420B�a�ided $u�]� �B a�an5�1��L�.(Jl- 5R� +z�E}J�AL(� --�)6 ��a���( a path $\G  $ joi5J setse�%.52E6i�A ��xe�.�F z=-1�2�Gs g!_DV_z._��connec\i��� yW -� emptyset$:�,by monotonicZ for "P|zUR� +1 E_{EU^c ) I�>�>��*43B�"��%��domin�Iijat� ��is no)�-1ing�ocover�}-$Ute��re'IN a cut--�� IL , fu�conwKeH� $.�ER%�$ .�+��5c�Ged�� ,nmd2� $ --> $.��k� !�" �R5&µ&� � qV^�]E^cMm]N� H =+1 A�0 2�L�2A(Q�Q�4M�-( �ic��a � --� ��%�6� �[2o$>��6� 2*'�B� 9v�r_x!�Now� _ familiar�3aA�9"�sub8s%%�C :�9#�sup�$��9!�pm� giveni�d $\G=\{x_0,x_1,\dots,x_h\}� ��8_{j+1})=d(x_j)+&0)=2Z�h)=i[ , $h, /�Wr% $\{\G=-ciS si_�  1 >$s�h h} =-1Da�l�$q_j� ݤ.�y�U� {�}}Qtc b {j-1cClearly!�a�J_B +} (�)=J�y0w<)\prod_{j=1}^{h} �e(Z�%eklF�.� �^ ��} ^(= \e^{-1} R!j�] /(1+J*� 5m�P N� J� �� !pdi�m��reeo�alo-(Y goodE bad$5 kd#ɵ� is .sm$&Qq uQAS��fore,�] c45�!A Qq%�uh� +bad +6tgqԲ< \^��� 2 -nA� } \la{c4F�"p'BS &�.(=L. Summ�ver: possible � � �'.�# d1u}.�!db�r/&�!U?�q �[VG�\�]% b^� \,� m )&}��146�&;9  eklB� %��Z<b$,F� �y� ..%$c44�J� I!Jb�+%F� >� �� )�� �uc4F=$Thi� ��.q620�e���o� � 4. \� � 2# h*uZ w"� .1e� 2. H" Venvironm$\o����,Bernoulli(p)� &C( $g%$3 ki�t&f �"� up to 1a.Lj v�by-rule}).N1}..� � �v�t�҅� s F���.�>8  $9 _x$, \ie� =!� ed�.��� J %�"� .�"(�z .$e�$�VF0e�\._ r)�mu_\o^$ _\o(�ٴ1F�F=!� ��H6����J��.p#�%�%��}�-��1b} (�f�}�F�B6C1,"yIwt \o � � inc#)�a E@��n+)Z  �9= eS new . )je�/ta'$ u" * V(�� by �\b�!�*� Ša��6% $. �!�an appl�(machinery d!op]#Z�N.� E��(c}. Namely�"�� param�T $uE)w�#n �0!*� -�\o)�u�e���ex� . EsO+A�acI�6�7�uVr)p�tl1yT^)�R� %{%� D� Z�%�)6ZU\,q��m�E[ 8)�0c1JJT�A�FQ2S�W� >X� �)�} \,.�>E.�5��>1F� Thank,-�11!�ndE�R?� is1  desiK��.�'N]2}�"B�e�a tate�J � poly��- ppea� inrxa�&�ɯ� e .��a�x!�9 .��9a�� repe� argu�usi��<A.�e�['?l�iw�n to be!b ablished Ak� a ver!K�&�$�0gr_'-W�e our new2��. !d��( ,� i�$3 �x ���#2�R2� �R��&BV1s $R$ "�"�0f!==�A�es%�/s%�xim�e  �co#1>!�U1��  becomeF triv!Imod"�$1i7BL!�. q"�An extenh& hard--c�7'`gas2��s)3 "�{6<�%)� ;} A�&j ��ta�,O:=\{0,1\}^{ *}� _ �'n *y" �ifh$adjac y �& ccupied, � � _x��_y=0$2 �?�5e $x,h. �2X� y)=1qWlGwb\O$�icolle5!!��%& ��$b$--�"S &�(. $hbxWua_,! ofq owed�9^�5�6(4$\h!yN�ed��fac8 $\l^{|\h|e�$BIca�(n�$\h7 �&f1�9�M-E�$\l> 0� so--Q ctiv� ".� o�!�Oe:we�� local $u'sG!u_A^\t$ �2%�34R !(A0)�p�&% �4A|-+-A�a o%�.."�*�#�79} are E��&ea72�%��s$=_x=x�Ak$$x\notin AV nd!� � 5m_{u+A}�.'p:ll �5� a�J�I}u/�+$ phase tra�%�6 A"�-5�H$\l_c=b^b/((b-1)^{b?$F,\ �-0Spitzer,Kelly� �1$\l� H� r�_�-que �$ regardles���ai"�� e le5&�;�6�pAx`A�r� e (F+ ast)�gdU-nct ps,���&o/)t�+ �h{odd�0 �}J�s7%�ivelyA�he��n J�%�^eEf.�eR2&A an�tZn depth&!�'enl�19rest unR�;A�Ay^eA{b�2�/} 1 &�3 \;\text{= ven}\\ 0 \; !9 B\�])B�' ���compl� ) o=1- �Wi�*�%i�e =e�{T��ktau^e�'8Ba!M��of-F�'�J��(mil"�;o�� T k e�Vs. �-  T^e=\li�;ell\t�0 fty} oe�,oR,% ?^ W�we ne��) asiz�\$\l*Vc/ shall"� � l^e, !�n &o�.mu  nP:@Lref�F��!z����a��\li�b �bB of E��q@E�t E#%e_\�o.  :�8Glauber dynamic�(�#>!�Vx��c��%�  genera�Yp2="C] "1X@ flip� E9at�1r�� w.r.t <�lat � El�.�0�v�-� ��w�4 tricM-r s���� heat--b� 1 � byFYc�^o26q_\l&�@(x=1\\ p_\l ^x�\,,�8@=0�N!����*�H\;U>\;^:=� {1+\nLf \l.��&| �qEsi^x$A �5ti�>R si& A]���%x�!��� $-% =si_\=��aY$�> x �)x���. F.words,_ ��sEvi��  c%�/ �to Y�r CEz $!@=\ll)$ �s vac�6TE�rat  \l=1:/a�%ied�/�1asily��ifi�zA�detai� bal�2 �: �this choV ofos. Morec cny:� $Ai�t � * *�M5�\� vol�3U�t'A)��w �- J�ergodic%Z�2���_r :A!�i�Bi"� &E*w6E�n�.a�B%�ofA��1��toH�ionJ  ribu�>���6�3&J-s A|�+�am&2"?eq:�, csob� A{4r9Z.��% MaSiWe}A \;{\rmA<\;F}3! J�9� \} -O!*�8s>S:F(\si\prec \h? iff\; 2)#_x� h_x & �� \\ geq 2 odd���la{�{ ��A"� $f:%��bbR��y�eh'�(de yI�3�\h$��$f��- f(\h� � )�� *J �u��� + s]�  e�(fm`"(f)!"/2�fuEDf�J� !ȥs �ie[ stra.Iforwar�� trucI )�--rv!!global! -wisec�J ���(t^{\xi,A,\t F��}tm` prL gime $t� start�K�>�xia, evolv&�regajB�E��@� ma��upl � ��' bigl\{(\s2� )_{t%�,0},\ A\sset m�,\,!\eOAra�6�yWrf6oi9 old:��� V B]��!A� \xi'� t'�E $ �$q�\'�H2� & :'%�'} i�.- au^oF1,B!�Oa�>1e} ~!]5eq:az20- �T[9 a: � �9.>f+!��9�2~s�AAas"�4FKGA�9y�� Z1} 6!�}))�� �&(i) \q�It$��%�-�M $~map: \mapsto!��etae��n�{;;.!-�000z&(i>t$FB^{��TY$"�J � B$.}��6�>�\ {R'B s} Ra��"�4 e�,may.A�-�@\a$, $\% (0,1�ju@ K&I%�4Omega alpha}.  �-�ic�Bto check1  ; pro+�"& Coroll� ^!o}�|A#��n�.��wK�$&V��TLp�to cy b weak �� mu+l5 .#W&�introduc���1ana�>M�B�"�?"VD���� ) p,\l�7 $p\i)x;N��I�*?)"�&9 &�an�s:w fir%� sign � ����$B�?�(p).��+ %GP�Fs N*?aM$ � ` . To � a legal� &6 (��2�"A��� ygh@� �C> !&���l< 6 � $3$��,. Call $A_\hi@t� � a !�avail�>o. Fin9pu �x=1� =� �$+*�2�<��! �B� .tA��&<8E mMK*� $�'EUAD �q!� "dEp�A�In�ta�ar�"�of.4i �.p(\O_\a)=�,.�a��7�2|Our mainp 8a�}[la&Sis �U�.Db"5rem��{CIthyG )enume}(}[a)] \item�%� $b% 2P8*Y9p<1*��\li��, )$ �2�!%!>s�=-Aa(\l,b)!"�i�NalE�"�O4|X�x _)�$� �>�p>�2k� $b_0n bbN�AJ(0�& �- b_|L�Y \l�FwKv��,p�S�R�A�N�Y� �end=�� U2+Sk�FV�29h>AU�62 wS>b�  A�WqCDed|Vs�� }. BI!G�< ou����� (ra�7 ob�?)4 &e. � ���U����in view����"� 3a�I�.s4!�Mh)�z� .�, J3\# r��Ce�"���! �Wby0# {\emN�*q�{�n� i��0kit�:1} 1p "XN�#ofFA_E�}A��"% �;&mYe* ,.�+ J*�F� ./�$s&�+k34y{"� �# rpre|;: �m�M� �In6F,} E\o_x=)�@sai�bdfre.*�! S&�5%kan ^]I�Iu . No��U!Ba �f�� \t^od:O !)�U>-es%��m�4m� larg�&e,compo�K�G)E � �7j < root� kcB_���6"$x)��X ��$\t_x�4m�g �K� ����E�M � n2b�%!at�"� as b�(:h � ubs Nwe�$mu_{A,\o}^�!�[ _{A\cap �)(r j)o�"��U&� A�"���C7use�. �� r_{t�(\xi))4!��+ed � !�!� U � vari� f!} $/ d(^\xi$ among�UtP�? Aj %$��>� �tQ#note %����� %a+x�3�'��%z�ary %&�!M�1�WAZ$A=;!���\%!�� �.� *f1�:�)�in �S4})� nX9�t^e \r_t���x� � \,,$$ 3$*�!us-qI�hp0 .�Ui'6��out�I� bi��*�.�$$\o=\o(\h,$ )$ ���1qbB�E�><6�isu^At^e%:�ow� c -.i� .1}). M"�m��#�"$9R �s� �1$.:)� W��DTruc�  ,atK,techn�Rbisola in�)s 1aB4 y+:+��'0�). A\ cu|B�o "\0| nextU&g. &�){TF�}?p*%�%4��B�on� ed# adapt�3A�>�oysve"80s �� zM On$Lfines)X.a+�-a&��( s $W8:0�� way�, �Q�Ig*in6�# UAR=��m�T--P� r�& se}(teXAge��� v!p�P� !!�s E{!D5 �&no trulyEingred%b. How�uA��L�+ I# basicu�-Eo9P!� help� esA�reade3Rre"��4?: ed�Ga* .)\noJnt�Gn1aun,-.}�6-b1�a�": "�\R�)�!{�e}0��r=1)}>0)QrhcXJ*�m1%=a�a�AK r� w%a�calcua�J<�B\,�4i�<b� {(1+-<i-< �iteN�'*x_i�i=_>b��%�children� .a$iK �K.�(%�,�n�<S�K��Fx%sR(\th;!5 ($Y7�BA.  shifABb&[��� }F �9a�^�" R1})�ϡ�rA Jo\wt&M-3(R��Z\lJ2�fdd la{RJ�#.P1gA)"<&*Q$����"o: U:%�\d%�a�:��4 1 fixe�Va2er�~ge�Z�fan�!!f�Fogu�A*R�T�:}. qMR[iR_a! ��$\d�%p!�� 0G �lR���!cB!�� "i� ��~Z%��x��3(E��T �5VX.ȁ�ge�ell� �*�E��15A�$"'o*� $6�2}� 1Re��q"�.JM�m�2�A= qell!��RBH\Bx_2Q�% b� $y_1,y3%�y_3,y_4$%�2;\4 $b3��b,2 AAzN �G�,�\o�@i}=Q���YyVC4$42E�u_G- $1-4(1-p � i�ff�!a=occupy�;$y_i$' automaN\�U,ae�")&�%�� EE(�F�)�A'= \��l?�A? {\l}��%�_{y_1�ݡ�2 }���8 zH3 42H4 2H��IBF�:*���B)=R� -���{y_j}��XE�>���7I�Ѣ2,3�)9�* ula &��", FUP�*� v!~.�6[Z !� �'�RR[eqqCe"�6F�m�JI� + 6 q� -2}^2 + 4�9B�5�1EA3-�6�F�8U+#agU�G1�)��i�K %6� $y_j)�!=)��1�aE�[,ѷ 85k3e4�+�IB, R�bA�qNT4!T� �H� Pu@t� 5a�ge# ���h$1�4�}q=�e�1KB�2�12�} + 30B^2hJ)�F�B�(�@!7���R.�'?*��d��of'qB b&�\$��Zu/ B&�7Op�H roblems} �UJode� FOngO�:� o9 . Ba �2�$�Iph��FHus tak�)it�" F�$"��symmeP.��d,%&��{17QI�I(shortness w6 ��Z���&Jn�9�8quA9ona.�cla"X �"8� P_t� �*Au a 2#A $t\�5�o�[RZ^ t�� QG�!�a�a\�>se7#�4 �*Li}O@c�^� �4 ransH[�nv,nt; unfortun�\!XLyapunov&�&�!  behin(=^ do� seem���J}:�{"�4/v-c . �8unn!� G&\b��b 8'Z�")� �&A^ "�$I� e~�2�!Lh v`b\k,b_0,\b_Q#� �  lO�d%��N�mY?'�Y< sec:4( _on_!Rs}gA� situ'�mN;c�44`e due f-� c i� ly m� ext�[l- �s!��,# �+i cha, eriz zo�b_� 5� un�u"$onjec�fi�A�-��fe,,�(�) �6=w l+-+In fact,- imagi�9e7eglteB�!<.;a�_ �2 6�23imBHf�n,&� �jz3 I)s, #;upd�M; \ (say� �sfjsub!��^�4e� &i$�D6�ri�=� _�j".:%="T$cl`#toJFŋ�Yap�!ء;uldn�ImUhZ\n�Qe��+ezJ !ǵ�'coarseJ�luste�$fes� oaO!�sign,M�"�*Vk,ED6 y a 9_82rol�k$\b=+�q�9)�H�] Although@ � Bc�N answ�uHy��� ��0�9J ;s�! prelMMry ``%nt���m�\s''#!� at b�A BpPrQ1ryF!�h�i ��m�b �7me $(��. F��we!� qa� �y �<��$f$B� *}�"}ml(\h;\ |�c(f)�--\ni� (f)|I=ADct}2rX ct}�<%_5 c g6�*R\% $c>0$��n o� �4�too�Z fluAj%�-K$r�6.'&�c�3e�cwaeB��"t�pI�* 4J8which�V�0�/d a�-E�}7, �:o9*}=[=���(f)=0\��*�N�?.a.�}> �r�d��NaDxjMvi��bugh or� `a�� . a\tilde�ybe�1erturb%ua�� [A�S,v�Dtropy b6V -�.XW +8'A�} ;Ks �p grow�j"Nc(b� })^\�1~dl �T�����%� .�/^�|�Ÿ(fK]�=0-vW�:wcmle �Dwe� c &`propo �p, pro:��1}�1 -"b <��a"�La DvH(`ae.%�y,��2�doe� n� Ɉum� �Qy� � 0$ :F  &�, �asBi2-f2+f�)�2(� -c_f �)�&� %�F�h $c_f >0$2���./#6w� !��go!to�a,nd�1Ga� an�Dc��hs�FLedoux��A���� ih�rm�>01.My�iF!8!. q r)k%0-\frac{r^2}{2?{�:"ny�n�m9�F( unit��0Lipshitz normi|F\|^2_�{Lip}:=�J� ]/}\ninf{� ^x)- )}^2m "J�eqM)"�27���e�5!�s�E$a=�f>0"B1�>u0!8\ŗf\|�!2 CMN - at�"N-NOC^O� / tool���E�1U!�l�"/%�.xC . :�aLx (\b)< 1/\3{bF@!�$\b�$#us�X!;$always cho� �&in �2l�{nQ,(b]V!r)��, a�� $b\l^2<�3Giv�wo� &�-P0he3g� �6Fts,U i~�4ed HaU��-as�^02a d_\��)�Dx EEP}\un_{�6�{�3_xB�� a ke� of.�bi�R n unpu�Jpap�y f Pe�}�� Wink�i�e�  4:V) &�*�# natug;QC6A@>c��r!:a�h��#�9KbbE!�l()A*4!�xi)� C�fct} +)lN:�Ue B�s $C,\,cM0}��g�*!�m�(\�F� )e�#��Q�q \�w% ^y)- )}\ �Is^{R}�$y�Vq  { � "8]q5aRɿsum_yEZ-d(y)WN~�xr)uo57U� = �H\Ji4�04���14Li� -�A sum �> -?�s square}r.hr�"'j)��{��n 01��*�Nb�/c�3}��&"," ,��  c�&u��ǀ �\A" &,\ � UF!�n� $\O"�E�tBq"� �r2��.S $\d�p�p�(�Oo\ \Ent_��}d Y�\ell}{d � $U() � � / "Fs. St' O@E��=A�bfworjon  a�#� %,Iha $k$ �e�F*�MarR�(� ,cq ��its�&8RPr"d 4%m�17ehA�b| e ��o�� $\{� -�� B�*� ��_�i�$h%�H ~;�M�h�>� 3�'�� f�M+ +5� ���^l�gA��H^*|�B\\ �2/-tw| �<([)  -1r]:�dq}.y}~>bigr)|%�7dŧ4g+ qct} + Q2E � f}� ��.A_t �11zIt #in�� �Y�lVA�tOE�Z�E accl�S}��P i"Sj&�xx ]�p"# v � &gu�G�� �Yb Q�$\H7�v�>c�nn�)�E� 1\E#log9:%�\9e}s'r52@:��A�6%e1+ ` }-1)k2�6e{d kt}}� :���[&I = x{1}{4}*�)� $\d< ! c}{k� b}�29�+t�^�|sjto � ��0ݏeT%� �DD��$REFERENCESF�����"�%thebibli߇ y}{9߁bibt8�$ {\sc N.~B�yXr, C.~Kenyon, E.~Mosseli�*Y.~, }, ``�r&%ze� (hyperbolic _� s,''Rpr�(2003�_� �RSSZ} hP.~Bleh��J.~Ruiz, R.H.~Schonmann, S.~Shlosman}�F:,V.~Zagrebnov�RigidT("�R>G��a Cayley�@,'' {\it Moscow M� ��8cal Journal\/}~�r1}�<1), pp.~345--363 �Z}�F�=YB�O�pur�� �Ht6( f�, !�h>�;� �!S!,s>% Physics� 79} (1995 �473--4822�o�)z(T.~Bodineau� F.~Mvnelli%�S�.*m � kine~��� a!�S��109}~(!�200�]nray �A.J.~A�Y$E!-o�!t �sQ Adv�i ><(51}, No. 1,E!21D81--587 .ECCST} I�J.!H$Chayes, L. (J.P.~Sethna=^D� Thou�T�A� n field� s��D!-ranga0�Commu�0"�2�>�106E#86), a41--89.� EKPSI�W.~Evans2d�Py�L�Schula�!�BroadcasE�AڕdA7]/U AnnaP f ApXBd�ba7U�10i�01�10--432�FoSchSiM*R.~Font!�R���;a� Sidoravic�{}, ``Str�<ed.� ,%lA�stoch�F{I}!&s0 s at�temperha ��!�.%�.%�.��228 �U�95--518.�Georgii�}H.-O. !��ohe* !s�ߩ9de Gruy� Stud{]in��Hs�=9}, Wal(3\& Co., 5lin, 1982�KeXi/Fa �S5C19 �/er Y� system� ��AWRoyal2 SocietE?B��47I�5M�379--395.[JS�v�J.~Jon�2]2( J.E.~Steif� AmenM�  >h!K�N�ÅơOalV�2�99M�549--552�Ioffe-iD.~ !gA����!ݨdis�7edޤLe��\r�3)�96 �137--142��2N�E;#����g�l3YEProgr�Uin Bs4�s1�3�.i8/L �R.~Lyon�=>W��&aE.le&c M�.!6.��mm4����(1099--1127,�0.�E�M.~ ��["on*<of�( phenomenon��� Amer��Soc.,!�4 nce, RI,}~12~�g$T.~Liggett{ InteŪng� $u�, Sp�Her-Verlag, New York�?2�Li2��:g�=�!�ng�(: Y� ntact, vo�Pa�ex#�AE )� , Be��}�!�9)*�A )qF+ Ls%%�Bn �x&re�pin���.>P*���^" 4s (Saint-Flour!697)},IN Ie�:�Q_1717} 9A� 91, >V2�M�SJ�, A.~6 lair�`��Weitz��1D�Ya�v4s: Bou� y Co�3ɷMd� Tim�A �BAm3 250}e$4 �301--33a�u� ‘]2���F����!�97pB�us,>boA� �:# !�submit:X2004. E�cded absTU�:I�PrR;ing"�815�,ACM-SIAM Sym�n D_rAo Algo����p)"4�F458.�MP��R�RI�*l o\#ow2��Wn� -�13�3�817--846��6�,}� urvey:2�f>� )@G8�s,R'phism)��)U pU $, DIMACS S�1G �� eoret.A�put. SciQ� 63},BN!��M =�155--172���o �.QJ: ab>Mtor�climb�؍ el.F�U5��RW =�4 R �2>^IW1�S 280,�S ���U�U9"y�Saloff�WL.~ -Coste�9 s���]+i� Io.)��F�6)}fG9+�.>�I 1665�>�e413, V@7(� ScSh �6�3.(� ,Wulff droplek.metastaM�%� of�r �Hels''�^< 194}%�8)� 389--462.�T98~�$N.I.~Tanakw``L�0y*%~l ferromagFB@ diagra*� rHA ; 1998) �234--245.�Sp�d �F.~!kMUr���Eteefin(+���:�}����197�387o 8.�CDN�Camia� De Sȇs]C.M~NewfC�+A/? �!^� two-dimjal�-*�*�I*ɥ"-nn.���bab"� 12,26,56�82�CNSB�����V>d�u"�Z o fiM��uJ���%�! hexago!l�N�In�odCf2�[$(MambucabaR0)��. 5 5�051 }, Birkh\" 2r2E16b 82� H1�$C.D.~Howaref% C.M..�� perc�B�m*�0!��;h�aZJ. f :� 11� N&-2��57--72.�H-���acZer6� "�.���omo� 4�aw!�egrB:re5�J^�37!��3I�I736--747� .�>� �9V9�,END OF PAPER %R����docAp}� Lo�V�4bl� j� :aBexTeX-maT0: tEnd: %�[ P�Z@3, Text/X-VCARD (�2,set: UTF-8 "- net-J�)(Unicode") ]K(rt : "m�(.vcf") 16 �'.)Un�N*ak-is�$��\�cژ{Qcle} \uD,ckage{amsfon�W:math,ams�R.[all]{xy6HHicx} ..asymb} %.a$sw20bams}%2-�B xsymAz\Declare.xAlphabet\EuFrak{U}{euf}{m}{n} %��Bold Eu#'%tur \SetN@bold}FbFgotk�!o w�%m^j:%Haot}{a \otimes_\mu a�2�ra!C�)arrow:Bl longf#lB#lefREu!upN`d downNh} hookb}srl� tackre�v.$ovO'a�:�un=MJw� wide!e61 wt}{|&:dp9pa�aB�9)�A� % A�bb e C*6dsC!�it C*}-:cb ;C!..�bR: RBTTBUUBZZBMMBNNBPPBSSa�2�ud}{{{�U}(d)>Bs6$ {SU} '!�LX0 eche:�ep� arepsilon���r4�ilC igra��:6�mA�Hath��A:�mBB>crC;C>;EE>FF>GG>HH>II>JJ>KK>LL>MM>NN>OO>PP>QQ>RR>TT>XX>YY>UU>VV>� Q�Z}� 6AG2lvL}�6 M}{Ma:B,{�f l}�.�4 me�CaqUgotic>O eg}{� g:�sl{sFpeA��B� {G_0} ��Simboli� i ri�.��$��bf��}a�<2$4zro}{{C(X^\rhoF�p! ~6�\mZ>>C=%mZ}&E>�o� \mO_�>:{ , ��>B orokAP E^k!�2� If{\[ O�D]��>�$ii}{\iota,:�rr�ho,G>�� sigm>:s:N<ss= %�:�mcmM^r,s:�e EEBrho!rho^r!R >Dtau%0�G ' >)sg(�*, F:�+ S6)>�w�*wa {\mE>�w�{ L%�2� mcSU=�@�O F>'6&U %>kM {�K ' >NM {& KE�6�SG}{ SG �Fn*. mU�d=M =6>$cpi}{ \mA_�( \rt8 e �)Z>�cpn :3!� \bNF*eN+ ^\mER/%\m>Y)�A�6�a�A \odot� {^05�O_)�>^c 5 �) dG>�mo)�5� Pu_x? mO_d�BWe51쉷rho!�2�cp2.r*e!�{\mF_\mIJJej��JBaij}{\g_{{IJB�u!uB�o�1S>�o%�B t ;T!>B~b9cB:Fx��mO_>� cm  ^{G}=2[aw�ab6(G-� % ambuTi�'��_ne {�{Q em}[17]� /t2}[thm]{C&q4.Dl;!�PI�>k1 ?*F.B$b$bP2a defn &i6#ax}{AxioM�`style=�i .��Exauz�:=v/rk6k!*{Rmk9[*{�z }{No�)|""-$thmref}[1]1~~�i#1>�sec*\SZ$leN%�^L!�M=�j/b/!�^+!�+9�^.by�6�;3em}{.4p�B�)umber�(in{"<5{M��*� 6�Hauthor{{\sf Ezio VaR-liQ2Z\\ DiYuc o di*ica�<Uni^�t�*Rq+D"La Sapienza"} i P.le Aldo'w,o, 2 - 001859$a - Italy zv sf v �@mat.uni� 2.it�N$\title{ CrzdN Gs�CeŮoC,\\ve|8 bundles\\and\\1�dua�%, I} makeX5~� }@@study \sC algebrajms�C4@S�L�`gJer sense)T"c*>(by Dopliche�Ad RobertI�a�kto62�GDeom�Lal "�K�S�I�* a co�log~.o�!u�+�ma�7pe�th�~��.!��xwaBE(c6�a21FE a uC/!� a (non�: ian,�&4 act)�Cup$2� a�S1�� sX:6GI�jZ��e�i�Dr)P�r�C�, �2d}�4�=�Z �f$ AMS Subj.�\,ss.:} 46L05,8, 22D3�68Key�F:}U�Pjn$ts; Tensor%? cate"#0es; $C_0(X)$-M� s; V2���AY�y�tzofcp,nts %\��both{C } 8��{I�!ionBf�DE�} FmAv8a>Bl� � �2 �'edJZ$.tkach pai�2k;a� � PcIgiJ\A�O' twin�Is|s�|4) R8K \{ t�� p��  (a) t =rho,A�i (y\}ۍ very:]�Van �i�ufHrOMBan�,$\mZ$-bimodu�z,tir zt� ;z �Z$, $ �(�� �6:�m1frhoHN)y���$ [(e get a Hil�A:�,%n���!Rn.al )Bdd scalar�Z $t,t'�t^* t' �, �N��%h�We �L�;!3.�)��Ţinner�g(I��B�In-BA �Fg5+�@��:�m%�ü!<�=i/ G'�7efA-2_lU �`t 6�"> � (1)�Y@lC4psi_l^*$. Our bin�{y~�S�~�fa��h<^1�%�n,��$aM1A$, %$"�:@�- EE�=�m .>its�Q� � ^*J*�a ^* \ ,�u%�:i���=�$d%�in:sd�g`����-�o�M6��c4Kpl�M�Mlsl"�Q tari��)*:Victsa, |)�ly~pDR%�=�>Nf��ZM�@ � ��' �e*|�:�&em via|�ȷ12�=The�6v�1>ner6Jha�hepH� �)nd�Hd�@FDR88}��he �Oin��H�T��;A^2� adop!�at% diPiya�z& a C*ю},\QceV:B�� \bC$�a. �� ".S 2�, �X�F*�]>e�n2/% such.�F!e.�itself�T�-�E�a@SP y (a�.�$Q2%lq<}�; see )�@Pas80,Cun77,Exe00!�pAM�l!`�{inzave b!�d�by=2u_+i � ies,]C��cѸDR89A}�afZ.Sta93}�N!first-5d referN/>eof�*� Fv!��'Ap�Xi!/) :z@$.�C�Jl2�% E�,��a��ntev'$,ea �)���a�<� ~ y�UIi2=te&<�bE�#5 def_end��q��arA8{�r"��n \�U���\circ \\ 6�!Em1T'3t D(t'ū rho' *sK,*' '�? ���.n�VZ��').(��'(Thuq�]Task��Q A"&aCi��ga�� sub5� of $� end}� ɉso, cA�aI�E�: �K stepE�ta�SA�g�x�[eV7lei ]sm)a&Yԅ��Ws�!I�}[PermXg s�Zy]]011} AN��c�ş�$pJN:�eFry�V`�28$pYneps (:a� g]� $\bP�e��L.sm�Sv�5,9�:Jm ps1}= (\bS pQ�Q� � � }V)IN��4 (1,1): ^ ^2M�^2�T3�sLA aH (t)�Ihr \` $ �&#�v"�c.< m:(r,,�� bP_{r+s}$-fa�5P�� $r$�u*WEr ۫$s��\bSE�9Ugl %e� := 1� -x(n< 1 + p(n�,E ��$ (E nn�!�,2s�u3.�IFA� n$ objectQc S �d�at!":�q�[_b�B ps(p.�n!l=n!x1�� p �P_n \ ;r�*� � ar�h�2�q�� � AyefE�),UK5 ��f�V�� �[S� Conjugate)!.6-2 k��ɱ��s&� �.!=>}3V �"� $d > 1�C9�z EU ��X �-ɝz�Ha*Y $R%|Z 1�d)�T��"�enume�{^wmb*m}R�,h� ^{d-1} d^W�1!�$/R� P_{a�,d}A�$\frac 1{d!� &" {Y�@athrm{IZ}Eee�p)$-�.�a�%�B"�A�p_�� �*l �~n0ic�V�@"��)i�aD!yy\ %l� (anA�[m a>���2� .�e., )��� Def.� defh�p��d �ial� c6M���XQ[\S 4]� .P%bnow�M�L$OI��q��>�- ��ci�^r��rEs��!/a. $�rs�������� �{HC�x !f�6l � e� � "$�kmC.t,�n.��am��!.�Qo�\��Iongr�Li�&d$G.bseteQud$ (X [Thm.4.1,� 4.61�)@ ��N � e a�mp`�^ toO0� "�-�� 4 A�2�� n�lmotivh by&q] ari� |%�xla�ic��*��B�o��{DR90�1� " ��It��� aB� non6� + �?g {BL01,BL0�4��$;�� �W�ce)�aء�g2t�022}�re4�I%�_e�!B� >� �>e.�h�6$ �L���Mltyp� bC^d9,  I�s Jcis$4n+�i�-L-�%L6p��IOut yin"S�� �0 RX1s!or�<2�v (L\�)"~�s �K �-, +Mx A��Nx Serre-Swa"á�9!G@ A�inu��2�^M� |V7)�o�u� �o {VasE}��E[u �Ѭla_��cI\����liz,e_i��+i�aJ�wa[xR}�FQ�gf����"�%�.3(� .�Ua �! $Cuntz-Pims~-�e�n��$���/s,kw� deal�ycera��-2� F�6�d+_�)�!�organ%ia�~_ \#gS.wr_a�O)ro�b!#��2ˉ�.,9�.yT*�a� 56����$�$ ra X� 6��|mUE+Ze"�%&�<�2�/�og,A�� $G$-VE�fun�f�wa G ��tAIm[G$4!"�M$u_��$G$���S� �g_� })).FhM�ee�6�2O$\mc$�?nAh���m�D�E��>I ���� thm38��$\9��8%�[e. %S (u_0o 1Q�]�"�re![aongly.�-�!�rL(bfa}(\mc�in;a&�\(� s� te#{a&O��8u-�"q��6� �(�%le-a�>~%rI�ay-�`!�y4��\D��.� BL97V��7o���W��2�.� �{quasiczal}} (�X.��} })6��d (L`�c ive) ��NF (.� _gps`n&]F�6313A�InH-uleeͲ��%m2� in*���$� m�ps3});�B+��� talk� u�"m .Z}6�_) _int� �in�\"(|l):z&� sm;�� ~I�- �-�PfZ �)ca�A'���d= f�\}#n�!�&w"� $E�C""k" $cE ?c_0!p4ho) \oplus c_1 $,�ng����~hea���"y�� j��Mh% H^{0,2}( �.IbZ �H^0B �H^2>n Y�cro!�$�sump8��$Jq�o6{.W�;ed*`< NL� se:pB��dBn�#to" ��m�N��of>u . �.*[ ns>j��4} thA5�el�-J F E@0E�Z�)d!�.t � J �e���}ia�"�d,�C�I�nA�a8D�!+ra&�`��-  (�(�rcor_� rhoin�� 2� cp_!��b��s r> ��� � �m� k��2�f�A���Iy6� �EV s�2V rank�\0�4i.Chern�% $c_1 "~#� %�$\�.$*� �dr ��"�sue� �*;��"SUE� : .�= Al��D \��- $1$).�&A.x$�2e.���7�byVE!�g>acEl�6F �(6�rfam���P0"����G\/��� sud �$_{xi"%��;PcG��o��N;fib�$ �� .V"G N� m�f "�$�.d@}%b cano3Tl $G_xQ z"�&KU'&�&keyc/%z({SD �f���&�.�J�1a_ �>2��n1f5>aa"m 7,r �/ l�@ m%�Hausdorf qace� q>�'}AN6=iend&�a�deQ� ƱgN P, \hra ZM(\mA�P$eA�c�]��multiUr5�+{Kas8T N� l�� �)�e$C�(k1"U suba�AE� "������av�aut}_X�� end  )� h ).N*4!Hmc*��$#?��*! -H"�)� (. EE(:�)A�A%L��,n upper-semi*� ����-U$la96,Nil96� in24 ���M�!�)�4[Chp.10]{Dix}, iKW9rz�S>�A� �Idl���ofi�B]~ iv�� ePim97&�">�-�ll\%{a�G_� HDPZHW�r�"c!�laF�"�a�"&� etB��=��*� DC@ �+io��!%$l'Qof k6�}R!,Ati,Kar}. Ab� n�W>`VBv� 2���sF*R�E;%0�] ip%ra�Ūiar�Tnbov)�nc} re�me6L&3!��AZ .�-� !@� ��apdE2���>��E�X$G�d$6�,*� "��{-2�{eUV��*+,���nN �@�H42�(<coI�&�w��i�q)$2�)*&lr�n� �, *��Vh$\coe. sWT �Dd"̓!�er�%�A� a/sN3"�gen�Cpi+ �m�* r�y  , ї�D!��! �K f& /l2R�+ =mz+�Q���� )�� cdot�� �&� aRM7 valu�c2�-e!!�.�;Fle��-�uy(�a (-� ing)i�=)�.A�tur| �1��%���կ��$Xm�.B �E?"4 �x 2]�ea�{R��e�r,subE�� ��\Z=��$r$-f`H.)m]Ajb�/e���/%�y�of6� "c� wiR��s$. B�*�? em, $( um�/f��%,!&m�B��]7-K�!�^r${wE^�#Mor:81(i3n�F!wE!�6Iw5x,j0w mE^0 Xo(�+,".*o/� �ce�� =*"mE�%�a�a psi'va�5)�w1�L�{'�H%(�,`>)�!V1?b8 e;&xFNS &:�;n >�io� Qe��� A^id�"F��/m'h��~�'�+"  K�:[ V� �6=��W# �,���:ta>` 0'6 \ . \]�"�"If=�!J��\{ l_1U(ldots , l_r-B���GT L0xi lengh�&%��T��i�4�IZEM}5%&a'(1psi F��L� {� �ps�rQ@�2a�)�coen/s�͓%s}�^ =k>H$ pan}e@-��M L!�!& �-$ , |L| = r M s )�\}$. %�.�E��P���xA�,m�>\Thx2�ac��au��oa���H�42E :|*$g%�G$� .y .,� a +T'� `&�"�f�224!Ywa{g}�):= g_�y�Wt)� g^*_r ���.��,%���g_ri&� os Ձ�^r!�EMZ�.��.��ɨ� yi%� �zj�$j9a � )_G�Q�2:�Ag%b=�KQ'R�*ItFB �e� �\sC�& .�� R89,LR97" \?4i��JiapE�%C�#.Hcogq�eq Ibfz*n 2 �� \{M;_G , *���1 '3����g�$ >�(�)6�C� kO �&?�f�s.�7��" ."Ve*�zc�Ns29� e�=coe�A� & -Q,U��aE# >[�10)�-g%A�#>�"y>#,i$A"oti*FA#&|*mEU2� 4� ��3� BN5N�E"�6�V�"zvwsi�,theta�e�w�7 {l,m.E� _m { l ^*^*_l 0o�v�.mE^2)�CUE}��: ���x'r \ v��1i"et�lrs>��bP��nin-l� �N+9:�AM��e�[Res(5 !�$1|��!ar?JV.��*f� ��J��+ vanishel[1 Q04}):A��+l!�"-$�p�Q } et�^.��:��6;v�X"I $\mRafY�lambd-4E&�E�Y-1"��4}m7"fq�tot�w�[�,�,T��$��]z ^d� f c;R_i�%)J��<"���zof )g� o� mRVnA� findj\ eq_PA�.Ri� R_i^{*} =!.e{#. \�$.I�G vY0@��Yv�scp1} �.)� (R�5F�.$R'�t�zR ,�*mR~y�5:# SUt i.�E�&G 9�mE^d)_ � Sinc3c��q�-st�@ .�"�E� |_{B4} \in {\bf end�U}_X \cog$ is well defined; it turns out that $(\ers)_G = (\sgrs)$, $r,s \in \bN$, so t-thereV��an isomorphism of tensor \sC categories $\wa G \simeq \wa \sigma_G$ (\cite[Cor.4.4]{Vas04}). We recall a last result: let $x \in X$, and % \begin{equation} \label{eq_def_G^x} G^x := \left\{ u �ud \ : \B �0u (y) = y \ ,J$yD(!x()_x \subset� mO_dS@\right\} \ . \end�<% \noindent If $!8FSUE$,!�n $g= _{G^x}$, 5t. A suitable topology (compati withM one!�4$\mUE$) can beQ1 on%set $\->G^x�_{x�Xpin such a way to get a bundleb(G \ra X$. IB�hthe stabilizer ${\bf aut}_{!T}A�e$ �I�n $\cisY�cxLgroupuSG64continuous secA*s M0mG$. Moreover%a re aA� nclusionsB�6�%�andQ�=A1{\mSG%.e.!�eyf !$.l�. In general, $G$ may not coincide %�$_$ApaD\S 4.3]uC A� %,nc-pullbacks�@their CP-algebras&m�a-T\label{dual_bimod_act})\>t%,$efgm} %(\m �:= Q8tE* agwa g (taUt , gA#i" %B% �\-�h{Crossed Products by Dual A �.}�0�� i�"{Basic D�BiE7 .} - defnAefn21} Le-mA$aIa unital�-l, $X$ a e�Hct Hausdorff space,!�Em+ a vectorqG%�a clo�M�B� . A �AB-)� oa1�iA inj�ve funbj�mu : {!�G}�\tend$��� } $ �va�MN�y�Xby (\ref;_g_� }); since�- , {\em wee%0always assume��}a��#� (see Sec.x apdx�lI�� quelJwi�0not��rhoE�muA�E)E� ��aBk (all%ob!e�j-?Aing1power !\m��!�ctually�g���rrho$, w�%�i!�full sub��yA$ ㍉ted!�-.�W. Thus�6�bde"%|A�,u$ preserves?Mpi��ex"A�by�[ %l�O$otimes y' �# y) \  '2 cdot�^r \circ& \ , \]a�b$�� �� )_G�Ay'%� (\mE^{r'}�� s'}"IEY�enda}))��$particulare� u (f�1 � AW�fs f{C(X7 (\iir5�1� � )$ dE�)Zi6$ity map; t%�$%%fM�zroB�zro})),�we have��mon&� L: �\hra P. S , a surA�Rma�{u_*��spzro�6XEvinduced wiE��restricAto.� $Xa�H$:hfact,��repla�8aA�!E����E_%t���[ED& S� V -Nfy�? as�b�lofPU Q$. i$\��f)Mn obvivtructuro !��}. S��� � %E�. ,!1follow��� iv��t� B�!�$� regarded�.$ �m� 6 : ~� g)-mA�� laXi�M�� !�6�\> \ i� ��p. (1rs) (�2 6�){!�6�P��� Doplicher%�RobertsAG\> 2]{DR89A}��� !in our�l ting. N��@ differently from�above-[ d re ��K� � be non4: for example,�Nsid A� := X�� bC^dM�Jb��e of:� ,$\ud$-valueda�sF ��J!<�<  some_$W1�� ThQ�! be reasonq2 technical� lica- ,��,no Haar measa�� vala� (Lemma �lem38}, def_ra6 lem_fpa})a� Ai�he�rnt� jto!i��� vers6�  $\mc�>� muta��diagramA�begin*� � 430} \xymatrix{{ \mA  \\ar[r]^{i} & \mc \\eU#u]^{\mu% 5,@{^{(}->}[r] :coe.1_{j} }nM2�Z�eq_inn��} \psi �O i (a���Ra�  *�]f�$ %in j(\wE��a�΁G.� �a case��EdsE��)�i��c� D���pbyE�.���$.�byA�-��.� hei�1� $i�5= j2��. �� �_l" ��a�'X� torse�$�the��G .y)��fiJBp=a�mnpsu)�{ }^*��� $!�g coA inner��%Ha0Qx}A � X3!�&�� rank $d$6� . The A+�bT$��s} E$!� scal� ultip�*&O 2e� $\bT!V �. BF 24})E9r!� �� <ra &U"e �3]{Pim97� w by�� e^0$](fixed-point� .""Bscrib�_� limixm� < \stackrel{i_1}{a � dots2{r-1}  ^r ^r6Er2% {r+1"�  6-1e�s&x i_r�:=�� 16� �!%wa %�has��(trivial arr�on�&or $r = d�$:�_!� m.�$. Ysi@$�  |%e^0}$*E2@2V2)<��A=� auto" �icez P >o_!�:! - !g��w,i\sQ>=�\mL }{\rE yz �rea*Hpropertq30e%\\mA�;?� \mc $;��y� bF?yeg��� e \s�c \r\ �9 .$$*; iI L%# a line�%"�A"? \mL)^r ,E�:��.)�!� 5| !�$rɌbNU�we also �b!�Q� \mL}n�B-5$. �x}hbQ��Q_�I�� <{ a6t� �pJ�nK�>�UE[.F*� { i.gR��` A��a -hw�} end}� is� ed�4.�ch fAs1o�����JQ��mu�j$�2�map{$i��h6} � cano� end�b��a�E�>�*_ )�satisfi��i�c iE!W%U�Tlly,  A, \mE'qGbe6s,� F#A':'$� tw 2�R���i�J {G'})Ann:�6BAE�YD�'btco%@mO 2JDF.a i��T!G'$�A same r�Z@first Chern class%��r\�'6�"�Co�18&�6�rem� �thm_bgae"aJ2�!�10q�,A2�E�%�� � ��weak per) (on symmetry� fa| E($$\theta (pj:�_G$ eve$p m bP_r��}\\S��wea��0%�Vry�bnto $\eps�mu �>�rh&,/�.�5�!�!� �� a>ic>� %W�w� ceed�A^co�!Yof:� ,s stQ ng a�purely *3ic level a� resp� aog$) u0dense $*$-sub �}��$ 9?)�g*�s�s� �0( _G$):3.�fix�no1��a,a', \� Mlemen& e�\ $f,f%l^&@, $t,tr'!�| psi,� n. (\iota,\m�y,yn.%f. !�!�i�!�-`�e�� \o� ��a3quoti�$\m$ relE�jzrel} a�)"�t - ayt<f�BY�!1m�AM- ule;IpA���(!�()��A�=��:��a��� impl�Q�[- eachE-W!#B$�Ay[��,B2k��gqued ~��8\mB$,�^�!�fapstok j(t)>Oura� pose��nowa��>u� p�o�.m�� y us�!�% regu re.� (y of��te�3�)m��V (\m"`10eU6�� m$;9f$a�psi� ��r�2�6}:j�$33e1} \ovlA� (a'Q��t)��a >J�3 que"~ 33e2 a� ^d��u-�3�'&�6q�s holdr46�-= { �)})!,�J+"�tAzmak-��p�Te::� =""!��!�lambd�A�"n" mE^d��ѕ�N�"R_i \e�\}$EfOo�Ien:5�li� ��sqrt d% _l^* oin�� ^{d-1�vh#^ us e{" lish�useful=؁�!�$\ �$'s�"i>�)� + {}^* \pmj� �i�e�; fur�� more���ڑeftJ_l-:by summa��$l* � {35e obtainD36}�m \�s&d �A�-v)n \ ;J�"[n�b�*�-<,!�[ R_i%�$= \frac 1{ k}~!@>�M�%0�Q�Mscp!�we � k (-1)Iga{s�i��EG (R_i)Mn �5*, JA�#B�6`-�3@6� hencr7a�^*!<-�.�6t1miH!��!�I%*&� � �suggest��(keepA� in m�-���Xre�'%e R_}an�R�*^0� 8 "� � �)E:Zeq_psis�`^*�K (\ao�b �)4 ()/)�-M8��2)K�5B�pre��e,M��YU )!�Ev^���� d��� �9C# {37!l2�[�k=(�B�%"+ �5 �]&�lem�s�"�$��\{q)�b @(ofX �w~ $id�6P� jU�y2 �wATJ{ �fA��D_ma&�q$!Y��\ $e�?-S�&langle lCa�O �&r A}`.�l]lk}= !���� %}"proof} a��"�)s�e�{342 In or� o� v<secon� ty,AKut��[r array}{llJd��mAp aot ) & =1;%$e�Z�!m 7=& =� }w2� .X��i�RZP �E {�� �>{abo;-!;ir"+f%.�:�Als|( 9,2�N�{l,i}=kl q(���隺�\%f~X v-] m�( od�^ �.� ��� OBud�.Y�� j���[%�Aa5�"� 9�e:i- "2gen<ͤ����l� e; :uscor��cor32}e~K4Y to9� }�߉�� &d#UB�exW)s�ban"� :�%au6.��� N� "�%�2J��e��D into{-"S��6)%10desired immer(-���6�%L%to verY% $ey!�ovl3e/��'�.�t|"puxQpr��next two)�s*��1@���!� *w� (�a% R~%t�^�%.){R}� (R)}�RE l* a�"� I�ұ�M�� N��( �a7#RI�Zr SS  �AO8 =;^ra�2�yt = E! e��e� 6it=� 5�� e�] � �f�&�� � mE^2�!�.M flip�defsim�!'�� J��( )}qgN�AZuc%m�;�._�� o<^*�����:j>5�, (R_j�!��)�9����2d:b {i,jb*� V^n!�2o�E��ru)� Ju 2d-2�vz�"�. 6��"T U# ͒-�@&dŨ_G!�3eirhoe{d+1}aj�� geq��ѩ[m�� ��&r I�]' 6� {l,mm Ijm EqMlul�Ad]X�0��A, \:2o2d-1} (bJ ��f^2�&wM� �i2 6�]�+19#i�-iI� ��{2dE7}&��) R_j2�q!��� (R�:6Z���V2$e�R_j�J ) ��5� 7+������ �5ޡJ�(�LIP� 2 A)� �J /1a"p�$wisZ��"!te[�)2y4=+�z՝�".|}ݩ�,`6� �yvkW�%�#tF�!�\{=0indUV^&�H&�J ��U n� �sB2�r�{ =d"e)d�(b, ve( �! oAF� corollary%MI �.� y�W�+v�7� \sup�`Eu4: <6�Fa*2N � �� main*,-%ty� gi �!if�"�{\i�riori}5�l0aR� tA�%�step, !B�!�{\��y)� 66J� y. c�>�P�� =jElI���2��� "gwM:d x9h$M9%I$J$-�e�wan�J at $R�xa=IyA�j� ^� �QP_{��,d� �)� ef�P�pbelong� A&B�" g 9�m�$:�&9F x -V1 U�%:ai�9 �� e 2�i�-#.EZ�j��)* $�3�!r1 <x�$(u$fdin C(�2).�#]�`E�*2�1(�1A�q �� ����:�NEat �5^*�&5�U�,.] =l:� _i^2 $ (w�%):=*�C�~�H�܁`8m�'��9{t .) I 0 T���� } :^*�� X=!6F 22+J!������.�j45��!��"��)*W&%Ɏe %support44$ )_/coE'da� ��55��4=$:e %� s fin'���T�"_4'G�u�/ .�/6�ax$�v$o�3���!d$D L�yŅX^r#; � �2 psiLf7c $�a �arA�bin�7!effic"�4e�K term��yp �M^* $;B�  =g( �_GFV��, .U� >jF� �L)j�:6J"� ^rl {j_1&%D_G k� {j_2}7 (3 $� . (s-1)(d-1� R5s5F6 �{H) }_{mntW& 6&s}&s&~VS��$U�Oeq ��� �+�=h /izaWqCel,!�Uc0��orA�!�m)6�5�>E.K |H(MpXx5o�'��%-)�wl"�9�"y_UE �(X� y$tU�A"� /$= T_U y'_U�O�ǁ�[ :� 1�!�\ R_Uu�%�1�":�UI!) N�;an� :.bLM} f^U_ A _L: 1}^U](:s ;T .g� $Z�,"�C2D#C(UaU��6�k}^)dN: �a�re;ERYh'R_U�;[:%P)��%�,y�/ TA;N+6;*:0$%X�yV2=r + s i�)l�5w, bEME_�g} (y_USA1_ + }>by� : >5!TA!2�)cr' s�,P��cl����#(^{r+s �_G�q� N �!e!&.H� app �a{t argu)ō"�A2:c�!a��i.�*� ��&I >���:ͽ�%T'����J"�@ɠ&�';$G(nFUn$% mende� aot}�6aa�!dvv8 (in h, � V) orizO0rough6�]�"#C�(of>I�=�!:J!�(� �&�?�1A�$R%�716�=�+%3s>�B&�+}�:r'.��!y��� �{%; �o!W)X{"�@�t� �x a��&J �']j"���ZD volu�&�B�(����i""2 +�+�a8s%&! exacj=h� �u@BA�t="�5+)�.� � omiz!�� z s,BW6 D @AͥZ& imagA:�2�8�%�  symbol�Ydropp�2W�*byt:a)2iz*!�:�*&�2"�� mA,%F $+m��e !�e���s1�to ou0:it�7problemA�'"�*"�.:� ,��/lO&73ofa�sC"|$~,�F��>�4"u�wVLj4�06�0B1)<"abw5numerate�G item�p�Nf4of���L8I O center} $6 >>� >\pi} >B �=aog 2�= 2">2aoe0_{\phi} }$ \\� �% P=�phi�Dp %i��&L<= !|�A�)K!�N-*-hom9�$\chi!� #� B2��% odt)$; )�"��b�0*�9A�alpha :54v3L - , $$ !_gt:=Ay��AIg(f .$$ )H]I�"��GW}��)��uni"�.Te��|�$chi$ exist�H& mapA��}*�#V;%�6{�6�Q�M�M�3aI�!Thm.2.6� �a� $�.�by.�AK}1�t��^x+Oj(y)$ -?�$y"� i an9,/�J�7 ��� �w�:BAK^/$i p�$j�fLAlhi�.m+:%�?i#� �Ge%_�[ �\qF� >/A6�)2(6 1a��uv]�1�JS | >�F�6 �F� ".:+�@!v:_<2`1=�.�3i(\mA)$ � >g��:TE�z}.q�a *-e.m9y�� e�*�"�"#�A�a�$�)_{g^{*}y��2�G�.) {g'}� g {JS �!@/��{ :�56D2aima� to �:����2VQ^30� 2� e�F��.k"t>�.is cl��!�"�Cbe&���2f"�$ w.r.t.C/"�} normZ�#bI a famil�L5 semi9�=~ � dex�3.p�spectruF)z. STe� $\ker x�=cor<7on� ideal!9 H� �"�5 !� I"� �:�/w' t�L�.7A_x$Aind� !"6� �%b^Amn �L  pi_x�xA�4 Y he natura�M�Konţ� Te)&ud%�? �Jby$@�T)%��x[L�; eU e�H� � $x8��K�i T�Ta5&� sl!�Q�q� $ vanishe �$�t(� � AQGAS� f ���O2� f  = �C�{:�wP��!fy'�i%V>� It su)�o*D�]�!�F_� i�""!mF : �0#r"�5�non-de�Le Banach $C_0(X - U)&��U� �Y1�Y:�&8%=B�YYE�)1sV/6J;*� E��&� � �!��V� �"�pro}�(6(� c"a4^aT"sP. �\m�!�zro$-m��Bi��O"Qp32��RifK�Z�i AWE��p(�k(y)l f(x)B �.9� A%a�.4\ ����U!I� �aG��H0J�0sum_k f_k a_k�`$aH>\!6, $a_k mA�/ � h�2�0$*a.��[!�����(�C� xc1(6$W�@��N!*j.�p"B.� _AH�Eion} �BefW["��F~"\�{Me7��H$G^x$X�U.\3�A%�-yN�xM��P dx"� eq��io6 Yl&6^�Vedk 2� &fM� :�wHJ�. F�Cgll&�B~.r�E� A��" ��I�5VFE^��cm�E��m!J� (y_xA�6A��>(y):.a � "�  �+#.�./b% �$7 .�Uqx^rN_x^�S" �S %�^sp2�T:��!FZS�n.U ́�8\1 $�-y �±' �"DX% ?FF!~f &-V�,./3�u."%z c%�^sk Umub# �sc 2aQ� �2a�os�CA���ny�of�D����;saZ��\S&|@��a�oZ 7�&  maximlS� a 2@� CAKu_x} {^0a-9&-� ;�86� ���!�>=*� 3.2[ou�"�E"�Nf�R%r'flat' ������yN%�$;���Mb �nA�����.�PAWo!�69,*� ���&��eq_\x} e {x,u70���#!�t��N�u ("�8,�p. $ue����ʭ�!�tO_d��; �QGsv2&H6�Gx}/�!�6�*�xqaw�� ��Q ��I��r�J3A e�:bx_*S4"� ,n �xE�.}�E�U>+waz��Hr��1# �yt ���Wimmediat}H� 86A��_��A -- �Bi"�O G>� 1�&o���-|%3u� |Eqx�8�*/\|��*&�Wl�� �"�"� Kv�"�� �X)  :�J8� j�^B>6�#N*I�HeA�"� �8�dn.28s:���7%�jBN8;u�� E` �fy2{Z�?A?Yt\d!��c$}�!�atag�+l  w5Tt}��&� but s;Hy&_ a�8xNa ��eepiu聱f4epi�2et� !Xc�D��M��� 1e.]�cero,*5/��ernA�%*t B�fU=? we %y^A�i��noA�. �e�c%�H�eg} %�NP�` X2ydBRNBR�\ is said {�g%�H}� I���e�ed�"m{ W�," XqE�&T %�*��$ZL{W}McapiLj� emptysetA�i \neq j� � do+i/8tR!ce�0;g*c "�-QR�s .pi__R|_{W_i� C(W/6%�� �{{G^i� �e^(7f1J� 2�� i �Mt=rq4( H_{d(i)}^r , s )B�%$, � bC^ >!SG���2).�@.�M� %)Mi�s9en�2 ��ŏed"�%���Q("k e6yft�V2� O�.wm�!y%�@�+studiz - 572�+lo_ha}`)�$&�%+~O�%E���0?mS � �'"&$ed' itself�)�*�$G^!%| z U�"jd �1OZ�3n!lm�`�%E��8ide>n Remsgrem_ncba�H :%�jru8r��a %�S)eVas04}0 p*�NO�� ��Ŝ"E% {�Nfa�R%they'%�ly1�'6�Rsec_pb}�2w, �nq$Def.4.11&�S�j�Cth�&Jkthm38"�SA �� ͳ�~ #6�S �2�d*� ��AB�� � Q�Z�2B !�h�O�!:���$�A)� 2�O 8�al.�8��S.�I carr�)KO ongl�Pt��� F"_{>"c% *&"R "�l� %�J� I�c� �!��.�$XPC!coa(t.. "� a�n?,2� iPq�@ AE�lXa�-�Be�"]MK (d1!Q upperr J_ vjdg��fibre2 ��hI�BIAmB!�P C"MZ@$�^ �O*\ .w ]\.�, o s� ���,�%!gcM�5 �� RU�dd}5�/5}-��n&P^U>F�k$UfERae|N�$d�pinD; �1�s�o]{Nil9�>%��{xIc�)�n%� e_g$� in~q�L�6 A�=�!E1 �>�B.�M,~p: � �(9f� �(6f ��e�)Z9A8�2�6�,>�"T��v�>�6T&c%��e~!�"�!".!��(x&�#'�AL`�4dz int�_^6�!�fuu, A�aL�� � � ��N�� "� M6 $��on�� !Je! ,*�$Gy��u�wC8s�@!� O�� .F�"to�viJe+"a / 2��� � nA�e6sj�<G$.J�kinvari=me�m�$: $$m �&AP��9E�(A�t�` (A� d�_��4�b� "�1k"5 =A8, :FD�iaq�w]q.�2 $�d mc)^I9!�Z�2% "NE��lB12N�R��*analogu"��knA. needjz9"retur}t�*�� )�#O*8�/3 e�\emG"GC :!*" KuAkFboxi��f�'Ekdn�s]1�{Ati}Q<Rt*�1G�"a Kyct)J�m :�'5�-�."�kd �p^�7 c"�_o�gQ"�:���bD���end*�(A]��+����l/7l��p�T.��c ce.�$q��wEɍ� !�wE*�:d;��"�M6; .�|_i)� $. Also��u9|Bh�)�a�� %'@j&�d��Wce�&�e!�!�&L -�""c9 ie�56�2�+�n./(a�>� $\cpenZ6�[(3&�}N�`C6um�XFyiYsinmin�re�^v��mCbn*$Ib�;p"� i:1[VA�o&a]�']�&x !�A�a&%�I��6� ��c$ leav"����F�i��.%�I]UiK�V�Li�`)�$�%� ňn {l em n&�{�5e�r} =Hil�r �-u_M$ which( �scID�%�t:Amb$}!��>�duceag�{�� �co:�>!"�d�5Y5�q��M "�"cp_mcr��3C�24 7 �%��v )���PF;. S�@s%kA' 9A_|Au=�Z2g's�(I Z=�bmM�F�� \vaM4�b�k\� a� �!� +A���6mA \ �rV� �.�+]gZ]gi���va.�!�A�]#npAE�cirU�sm�^ imeq�5,�!U�}�3I8]F� Ix.�\a � un�V!K�i.�H�by:�mZ$.y$-X�8)b'-�2 A< �6*M��u� FMZ1�a.�N��Z� M�3�T5�&x.*6HmMATa�B\mZA�0{\mathrm{span�l!Ul z��TArw�pz-#Z� }$:� }%�"Y0QCdm&�! ; vic� sa, �I��I�uE�6�!mZ>�2�13_J-��.>� =�=�4$z[� g (zEM5CAZh���.} z�|z�24In ) z'FzQ�Ta�G +]�% AH !� XM.V)'=-lZE= more���� P{^k -,!.�5�>$�*>� ho�<xa� �>G�� �)�.R>0�95o� !M9:kX ���ME��2�?�(�~�v97 ion,�QD��a ���< (�R.�� V>�Z�X!��;�i5� !\�a direc�:Ua� sh3t�b5�i�')�)�Bs �!�� iQpsF, ���MU�2s"%>2� *mN%m5�(4.16)"mx(� �A�qLE�*{ �Q�&0?"��V�&c� � EXm�& Rnm5�"]nF�X �L!H�9�[//�N`��K^*n#h"RUIO�m���z!�epsɨ %�:RN6 0( F�K�\Z� )�'�>�E�-:�JR��i�.A�Eu$g�]��{l�U���_�W[ ��_m)]$�.HMU�!��!�4_g6� ��� �%\�6&&[$�)&�M_g#g�zAb$wv�8$A��SNAK���&�C���Pi�v�HN� Bsee>!p:�{ *_W&<�.�p^1x &+�"$��z��a: �( B:I "��NH $�#%% Rimu� e %W*p3�)�$Vpharac}"z�$z�.*}%.m � [�ed upowTa^�� $BMW�N�8s %� E�mB^��� �y#mA'|N�$"P5finitg(%��� Ale&* (� `B')^{G}$.*� D$^7�N%$RCaC�Z7s�mA��w$w�?=9�e!�$Serre-SwanA orem��4M�}%�&�&.�K"6�` Wei7e%U��,G,�C�p�Ba systemo t�)b� A�ΌiN %�'�nw�R/{PimsnerU1`u*�j� a�҅�%we.�.>�B"�2doe%t depenF�choice"u#-�or��Q1��.UQB�s�*� _l %@%aK8�j��BY$!��""� g��2X� � a0A����b "g~�� We %-�E��F� F%N)E%�^%\.3�� �F�!zɍ�n�. 2�%�6-[1 S�&��-A���a"�!�ȹC@~��A�%.y? c.e6!�(P  q #v%2�"�)A_B 6�eqB.1!�*� �&%.::O9�:�i"E�W2�I>9-Biv�"M|u�DJI%su>�6;J��p� f$#�"$Ys-%� 24}) 9��1L we j"�:00j ",*-�eqNho�5sxjC�C�. 5�$t� �.RQ�  Tt $, %�t.� �:�<�z�wE^-��] N&v,%��^Yz j&� :B�p�g9F,��t�>� %�N.Ma�W^r��j> _L�� b�/�y "�t6Hnd�%Z��K-U� mE^s�  tJ ^c6 Fr(n�% �"���requi�)�>orA�� �Nmu��^rL=U�4=ΐ, %� q�U���=u j"/ �9�W�0�7]RA�^%a'��w�ev "?y�N`} t' =(1 1]"H1 t'$6*r�Ce1@9[r (t')� N�6A��**��1K�(�w>�CBur�4���i�*_B ed %�2(�x�Aji�؃&� �isU��E�� � G$ %*bBb^C$P k7�"�i&�.�R�-���*R�A� te��[z�!F!)s�U� $K$-theor�$�/1r&YB$)g% ��By1�i�QI_ɶ6m9j�  3��atv}U cU]��8 V�K_*InX Ni_*} � c \\ cog6N1%�cD29N[/�Scoe2E$Y*}� :S`.$St0,��>�!zkN�!e� bee�K�&/$�"X��!!U$n$-spz o�CRiemannG� face)�-2LG#!f.1/should&2 BHI��\&��� � mc:͎lqtoR�3��6�{Mit01}f4$����&&��V�� %7(�4N,ly)A�Dj� J{PR96^T�"� Spec�QE*� s&�FI� %cb��&� .}8<��%��nt��gie]+bE�? Gqe.�.�-NX,��<[!��$g6%(3+DR�1A�.O �� conveni�to �"|C=5a��$f� } (�T 11})� 1�;B�H;Qt=�����0���Io"D��QrfB:'&L2�ps3Y�to F� ve�� Zl@� = z�%"���^�A��3�0� d _int��!a�2�.�b ��to���p� bP_\infty�#r�`i�Xbe��� i�}twiners�P� ��rs)� ���)_��F[ �?r%5D�\m� rhN]eps(s,1)Wj�(|(r~�)���b)t 2.G.�G>J� !`su:͙ ' � eA�"יE^r�a� �5��$."��MM cats�^ofVz����#6�d��"e��};ho ��H-�&n�!-5 ��AsOR� *)*� 6� ,w j ^! ^h ) �Xn $t'M rNK )� ise���P"�Ep,M�q�&l (t'ta�!�(hAAt' 1,WC]o 1, ��:E["�Yx�!��FdGbNIY&� �KE� �.1 {r+kn��{s -iA�+6Vn"�$� +1) i0(= \bS^s(1,1a�so �%�eY�L^s(+� ,s+>)� B�(r%r E%6 ")�%��E�'�.W�=3E �^2!���23��Q7{s;pyE:��*3 sE&y K�;�ņVt"B~2��]"u"n�6y"A����)��,%  Q-; �=E'�}'�ru���&�-�gA�AKEE�j$%(b))u�F})e�a�e�dy�*A�K.)q�!�!�K�n���',s')e� c�(r,E�95#�|"�5<']%'5<�����A.7so �!8�,�rJ>�>��"- "K*�L$ fis6&��aii-�!v&C>�6B�+in �R@B�KnDR-�^ �p}):?!�//)FH"�mC) H �N� " "t�-p�"� ć};* #.���A�>\bC$ (��a so-O�ed.��w� �� B!Q:is"��)�*%��k.si_da} S�23 �.�%w��'* ,� bO:y)UNI� .&���Q f (R� �g� ni-yF����r,�RIn-�N� �P} � l��!(p�xF� .�e�ű? ɹJmu '�*}� �' &=-9e.o "<;fFy< 6�ANank3�dl&d��)�\���j6�1AGA�C:)B*�J5&� R�V��,�*~��:� I�formu�m�t52*r ���I�  remark2�>nise�"�!/*e3"Bu�� [quasi-1�]q�� gps} A/&:baM�VR-) ��iq.f6v *>�&:��A�>� �!&��"� �.y� u �,���dM�e���gps1}m8\bS p��`eyp) X >jO2 O� =E �X^^|�2�U3�K= ��\mZ��\;�t� . %vr7 .>�%#E@�"� r]!�y\f!�G affec�:�ef"�EeA�inRu`a��>M ��gh ��to��n���SA���/ �2�2�/�"�_t��Is1E�|�)*��"�4�H}.��r�D E�quiv 1͜ve�pm2�..-]-f�a �Y5"dS l*i��igskip A@�7"�6ps_bp��1X�&>�"��. Q� ian,�Dl U2&-3C-�m�>�#�&�2C/.^-�% ��4U&�7�w��ngg_��%4�)E�nQ�A�"�#E8~5." D�J�nN<�$\tau��!cm�`j�* emof2]e��ZG.� a&�_lFM��t� �j�@Cor.5�Y~E���8Q:O�B�of2�*�(!)2���N8y(�i�57E�9erƙB��%�%N� �:&H?�U��iA��4"1I�?{\uAB-D7 4.15Q+�^ Luo�� ?dt ADt66M�.&`V.p �F>�B�M�ef{a�B�Z�K .JF�xԙ����J[qz� ""6�B`SU)6D!\delta��2[-xI\w shif�� 2�� := P*Xz5���\6 \ P7 T ��-?"z /Y�6u��:�G%T6�u_0"(���-E�DA�� ;�7sm&�6*i  ly w �"�5!�2�(mR=�27 [ ���t {l} ;m�{�"4�\�6.4R'+, R,R�/{�U = � � _0 (.� \ R%h�V0 � %�\ R�C\�!� n\JX%��|�!�A �7. :T�0�6C>�)�FX3 a "�9*� �:*�<&CyԇݥF&}{\ӣmR� %$���y&)Go>[HiS��ML�D�!��P�X� ��i,r&K=�/E�Q<B�_0\S 1.6]{Kas88�ڭ=�t��.|R�wRL(\mM��#\-��U��:''_�p,!n�-��otӈ�"J%k�.an *�%-|7 cova�A:� �(-y!x����) {�cw$j*��v�"> sX�C9��:�-F2�b���rц7݆�N�3�rOQTo�E�-��AOi�p�v��(V��i)r.[`�CO i!�Z� �*e�Mr�tI��*R���<�*��O *��*�!9 C^*(&t 7�e� ��#iu:!㩣n&�/ stict"�:&�&chR�/"�:T"� d���0I�E�tڮn� onents,9.�Jdynam�/-.a8*rrhB�iO��5)y$\oplusIR mA_iz _i2�A�R= �L \��- za�0 reCEI% ���c a` '(0\. Each2F I�SA�ajN { � p"!ur�p)$S � �� �ca"�%jB�4X\7Pi��"&aR� )�j� dimenS��ukkerne�$!]mo<>q=^�1��jgenerK�'tot�= antik ic�͵o�\ eƊ. ButBq�2A��e pl sit�i!arise�m�� �.� ���eps!�!.8stinc~�9'_�o&� �� dim_pm� %f.3e.:Z3AS�P� R� , $d�e��L%��'"�P(� �Pstant)5)� rang;�R�6d�Vb :�vX%teger)CUeeQ��sWk if-c2�*^��W�8e� ?.�!c��)^��A��d2^Iy!R# shea���]��� $H^0ń ,\bZ�8�Ps�=,h Z"�I�xoo%p1IVvf� I<p�)|�& *k 2"�Qassoc ]d Cuntz->!3`R�U;%32%.A,Q3.Z�Zd[-es)��;�� ��$J). �$atten�p�:� .B(Ej$d > 1!3Ѡ){i�"0no los��34.i��/�s�!;; A�5g ] j m�ʵr�Zu�nB�"i .�9%iAa)XA�b� J,A3&�{ �&{ %�\ZbM�9A�0UZ��'w�"`,�T&ep�.m"Ψ�,UEB?$.���6� "n r.97� "� �LQ )��)k� i b�I�eps,d}�:�<��e � R a9>s^` ($� $�O &/��)�y�^P ,*� A�� E�Q�� "N G4Z�(��1�����w:H";]* HVU�� �Z@6L� ��w��� %5T�xMm"Y9� :� (8*� �IB��wB2Nxb�%k` ��"�2�� �2 -1�_�l"B�� Q�.-"?R^V�"m�mc��.`� :gj~Bq .I>)B��>(�L%*(�3obr�)Hy5!� :��"cp����#�\�l*��xi^r�,!�gm��2rL� �fay[��2°+� $�BUEH->[AiC2M�*Oi�� ɾ<t ��`nd�J ?G"�"��:'oj.J NR7<hypotes#�m*��j�*5 �"�"c(�n(d,1)RQ&(R�n=331V�,)�$�eG���Y1�;e@�\� .!�� (1)�1�>�.P: Q^�x� �.q�Ca�y&�:3��F8�7��*) �)N�{�kB��-L2conjugat*�0V�#!��'�� ;B�)C��W�a]g��mpɂ�(aU2trkGD*� 12|*Q�b;�f����&\�V./�A�= s�O>A�E�6fa�u3>�ɽ�W4)�(A��.WWyIK-Lw�<���v~"ou&eN&�8$c2�6qm6R�=oa 4e�~V5�B62 �0[{4CU/�ert2�$13�e�jŴ:*V! ��>Cs���"nsf A�a��bN]n�s� �V�O Z� ��P*� 2��, *=)IXb 8 Z� B� � �` (RI=S�&H�d^{-1} &� : N$�fs2}{R}{\mR��\� �P:���R'� : R�J�\� ![*�ZN _ E�E�w8�ő�9ef!!2�5c�h�a<��y?.4a �i! �GeGARt���l.� Nr1� �5!�Eo5�/",8�., norm57ed��e��E����djeq_ge� s*@���Q)�j=.��M&1V� V5�7�n "#�.;��9`P �*st��our%W�-J�2.3} �fide��yn-� �e�>�+perC*��6� �cJ":Pa8�4i� ccor�to���by]'m"x/&/Ia(Xnd7�IR�u�O�NlVAXa V:�� 6�\mE~�.� �^{d_i}"� �U��vI��)hscq} me�B��x�*huni_r�6re! � �(N G D �u")2.��( �'�V ���lSbe�no�m�)~:��&a�6֘�S?���9P  jS_j�P_{�+�)�aa%`VYkE k)!�.eu�A+>u�N=�i E�e $z_{ij!�F��TZL)a $i,jZ�e�2�4S�4a��R�lh[� ��is "?2y� |&��""6O���O�(R� J_$�R:7;R�z89E �>� �$[�>B&�y6n�xp_rho} Y ��Z�ZO"~,�*�;me�,=#S)Yu ���&\ �SV�S�e�m. $R_kM= f_{ik}.�,��$ 5�*�1BMi= = XAu  E=4xS_A�T�"5 �� < b� F (S_j�:�7l�UP>�Y �bE1��1��>�,�,A!DA"[2��� _k��F� �! NE ��'>�%=��k�) 6UR��~!;�9s27�k~ �)��2k&%����G:�� $H^2����>�)��2. h"�`Rpd���Q&E"V >%�!let�v�$�$� ;`unUBy&�+VB:�3� 2a 4@s &� 2d��]8i)lc_1A`T" ,0�A�icn �.77��u.���j� *�!ep�#��>Key%-e !�� �2 .�w��"X�� ��jk'��Pa��inq�r �� 7=<� �1� ��-tEO,recX &�� ulB 8!nm� Qic U�B\{ ���K \cup"Z0\pm k^� , k 3 bZ -!.9 BE�  � � ermB���* ���)1{�f[of ��֍�60�G rw �� Z 6� q�2��!�Q9��Ed[+ A�6@.� a� *�y��JŐp�Fu�.�R5 *�?�?��l5=?�,ۡ.��z +y(a�d-/ 2@� C*�,� Y -:9!(N&XaD� � &UT�sZ� ;� O1,��.)�sign} R#�d2�s�HOm� ]3 3\ V%6��E @�0� RA�5i-1q6m)Z:A�reaQ)� Y�Kon�8h�R&{D��Ic���9is|0a�ly�<�|�Wi��:� !_?�a;#E��i�c�M c_0  c_1 in H^{0,2n��$H�_�6�@$Qo)V�2�$��^N*�ˉd� ~>*��E�N.8)Z�JBM"]_5*)~q:Q%�A�N "�>.`�4HzI  �$�O���* i�>�.Y12�zQ d���48��5�&7�5Q-�%Q(R� at��� i.�O�^pbyG*art�" >�#rt"5 , d2�e]o��>�7E4P2�$Bf7ozE�*S�6is1�-`��9.�6a�.!fa \sC D�.�5�!y1�I�f��,� � & v^ � ���>BA�� c�_G� K�7-i��["gE2!-A�Ԛ:n!�$"&?e&pB 9�We]qu�.5of Ex�;�9%�I56T'�7� "�)�n��8:�a 6�9A!G.�[t�8��E��X =D9�U�X f^do�T�%t.��6z�}�!�F��(\��GO&ogu��q��(�/>u {BL04�N&8�(. CR_:��"V^�26] g�~2bic�8� 10 +).a(�&�8e.K-�d omin}#ab�2-�ee%x�p$dI82�3}2*�*?Ra "��p>6�&(#S�#. $��J:deR inan�, �R�,5 9e}� &�!6�BC�] {Wea^��m�'ityZ�E�\�AEe{1�gM$2�m*ul��f�-of@t�h�>["5*} �P�ޥ/`T��29&G�2mm�e�!� T���(wI"�3i�Onal6� $\mM�Yr��o%��Yqh.�t�%)$gY �h4g_r`Zn" igi>T$):=�_�9c�� v}6�:w�G}_%&��"�H%MHV��a�O?s� �Ol�$%�G$-L@ �PZV7=��I l!eo s$.F$�!�UEJc�yN���?_6a�3 kn*��?�Nc�9�fJFH)�.�,!"�A�BIrQ �j�yb��&%|�.�2�M�$l<.(5�, 2dA)Adetails U�CM%�!&�(\S "_>WRC&U*orU�1Y&?%ʆ� �+c�>�"| �qm�!Mu�$W%� �FJb�\�b�/ 7!�� ��&=ͷ� N�*7GA��4#Z)�E'�Tsr�v��f�s�m�+�H�Rop,�J $}�ie� bJ�>�+iso>e�G!AB<l<�-$�<��\ ]Me� "�C=,�}%Q# �c!!���.m�c}{6�e�m|�2�$N�"�2�" q���!ı�6���Nr bmpv�!I�&�5aRt�� k]����r$ ({$& �.cr�/X�:��a��>vf��� = "@?JGs_L�ql a ,�`Zmq=$)>g�` o_Mő&�6-J rZ;��"E^:9q�2O � Z� "�M1N p&� j� eq_r�� �z�g%��`!� o_%��  a M^*&� *�%M�enn]�BI�#�Z�-h�- %&;l"_Q� �)Y(� 2q�$.2�df"�Q�&�Hѯ�b�%^*�B )�Rk>�"�s*zc,M?�sAp S E^*M0�$�Iɡm�Ѱr {J�*2C�%�:d�ef�c)^��0U'"Rh:-ag8� R�U��z�O�*_t�Y�~�D��"R%k8+">~DA� �<� R�By9a-s^Qy/�+���E!�q�>�^UeI&�PMUY �g�7"�H����ee{u��q_LX��Z>Mj5B=�Pta��XRDI�$�FfavF spsi��2�*{e!�4- % ��at!ly"o0�R % 3�PafterĄ%�)�l�;uJB.n��E�� X6�38��.L:`� a pu��2R *�`Ώ��R[;��!Cy1H_d�0��t2 (H_d^r , �Ni��f{.u�&��  $\bM_{ 8d^s��2l.�(�?G,G%2�u�t�,the canonica�Hl action (\ref{eq_def_G^x}) is defined; as usual, we denote by $(H_d^r , H_d^s )_{G_0}$ the corresponding $G_0$-invariant vector spaces. \ A closed group $G \subseteq \mUE$ is said {\em locally trivial} if the bundle $\mG \ra X$ considered in Sec.\ref{apdx} is locally trivial (see \cite[Def.4.11]{Vas04}). In such a case, we find that every $G^x$, $x \in X$, coincides with a fixed compact Lie group $G_0 \subseteq \ud$ (for example, $G := \mSUE$ is locally trivial with $G^x \equiv \sud$). If $\left\{ U_i \subseteq X \right\}_{i}$ is a finite open cover trivializing $\mG$, then f�v�index $iEreAF�an isomorphism $\pi_i : \mG |_{U_i}%�TU_i \times G_0$; sinceAhE�iE�$G$T the I'of!�$tinuous seE�s$\mG$, �8$g \in G$ may bA�scribedaa family7coNmaps $g��ra�,-d0( x , g_i(x))%��0\circ g(x)$, MU_i$. ABk �@is typically noncM(f!Y$xample, if�EiX1*\bC^d$,!na3:= \mm,!%'loop f'N�Tfrom $X$ into $\ud$). D\begin{lem} \label (_gcut} Let e�!K,connected. F�E $x_0%sX �M  cle���$G}�\mS��$with fibre��.!su� La unital \sC algebraAwAm�(a fixed dua"� $\mu�� wa G%� \rho%Xrhoe�0\tend$. In orA�(to simplify� nota�� �rite $X��spzro$�XVW$38} Suppos1�E#is!&�] Then�W �-point�w.r.t.�� $\alphAz �@{\bf aut}_X (\mc)�K$\mA \o�y_! 1 \��\mA1�.�-�It� learQFK%�� d^ �:8 prov�e o�!+$inclusion,.Qx%{X$>�RF_x$� in Leas� le͵,�@ a wa!�a�� @\right. \dot{W}_x][X &. %\}iis�c�j ($<$ % s%�,interior). B�� mpactness%��$fin!sub O$t\{ u�kB� {k=1}^n$;:&(subordinate�'A�a�a#yb��k l\}S�r"� \mA_kA� C_0( � _k})A, :=$�� spanB�f a , f%�:?, aEA!�9lJ �U��� �jA� %w5vk%�0an upper semi*� bundle;A�� sameAe��RmBR�E�A�N�!6I� @$ a��6�$-��s2$ @k = 1, \ldots , n[ � x �follow�Ji�:��[ iU��L��y�{M�_k}.� \ \ , =(u�-�'_{�}$ , \]jno� nt whA��J &"rvE6d�y)vd accE�g�Q!� �a7roduc� Thm.e�th�.. S �|_{�*9 Jb�g P does��( depends on%&A  choiceIa��$we�=�A}_k$-valu��me� �on,8B_k$: $$m_k (at%sE�t/ 6 (t) du =:% wa u\ ,$$ $Fa4_k��teCYy(}_k) (\ers)+ fact,� �� ra},% Haar �adt� longs!�]�Y� )u c_�� ���usA��wi2), ieO easy`ver�Iat��f�QRk$--�is given�-�,M�\cite[ � 2.8,END3.2]{DR89A}. If $b%@e�Ѷ%!Ƶ" %eU_nd $[-�kaQ] (-� q_6 =� (_k b$; thus� Bq!�U�b8suAS*EwD clud�B������� ��natural!� conjectur � )�8our main applicL "+ cern�OS$G! ,0=purB sAZc suffa�to�X Rl s� \ W�~��C��(\Omega)Ɍcentr�& mc$;o� 2 C��a $C(X��t BP�,aP2�5:*�, Y_2!c_2 �t���('�$anyway, mo�qn � e� findI�Q�g >' oT  = [Vvh.*F6�2# c_2([!,>�$ ܙU� := p=��.�&� !&��% co2� =��IYJ�A!�8. Be is� F aF�tXon eac"# �� M�X� n*��A�� -�0E:.VKv& ���/ n�(� anon�) home�c�:�homogene� �. L �/M��reqnMstabi�r� some6�)1�[!a $ (\# {EH}�4functoriality,��)��n�ergodic� �I� _��_�2�eP \yto \cdot gA�*� 6�  .>�.� d Q$ ut&n $:���D2@�  orbiY��2n �:"f$BH)A��+can�perfor�*�E�ruW� b�2O � 6� p_* \I)�_X S � I � pullbackAU$1ra_ � *� $&+-bimodu� pwE�*�2�$mEE�"/e' $\wE"�{�} g;Fx$( M^r ,  s)� �fS.�pi_{rs}� E^{r,s}%X$aq�!\ hav�$ `�-V�%3��Z�% grF]1> � j�. E�:b�A�bA gard�sh 2(  $t!(E6%%\�2t pJ1XFtvQ� �1�%t%a�_6pi� sens ��0[\S 1.6]{Ati}� 0#�!�non�"m� �$}euha�$G��s��m^q�" Ag� m�� ,array}{ll} G-� ^d%3Z� \\ g,Yap�gPt \!w (��z� g_s���Ft ��^*) _r^* +a�� � ɉ�9% &"$xAxp`@_rgql js`(A,a�a��& E �ePatensor;category`obe%power2#� setarrow 4���sbI_G��A &�elementb��[vp�aT�1Z�if_o��if!�Z� rel_inv} B) =^$U ^*_r>Z)�G3 I��maFe ;� ,�=A(t*J':�!K�~" ��";!set1M�[ (W�ub_&���b��G$-L le��hi�:FI�mE�=�iEpY W)���NrEޱ*2G��M�}$2>r,s)]bN�� ���epimow&A[ �{8(�ew��"ra._W ,  _W 'BR w �>#^n-��>ZfieldEBanachXces� ,[10.1.7]{Dix� �5z*�#a� �)(n� f� /)��$� ^!���( :* \\ �_W.b_W!d = C(.J"�RMA�>�� Th. l�exq"sn rigorX term��intui2 idea!�A�A 5-",$looks like�_0�a��r.��raP%.>c&&'�!*7&&t%�Q�m�.|e� ni x� U�-�_We�-�/ � *%a ���qe ,�j� )�=W (y.�� �^*G.� }��N[!�%W"s*� &we��b�4Z".� ͋f�$;.���p��a ��!� )�&(Qq7.� = r�"&� ͗= =��u�J#�a M,�x�+W B��1�F� F�aW_B��"�@!e/m�j�%fwrs _01m9�N�{ UN# \\ u�pi_W(t�"� 5��} 'F7bM�>�A�y�%*W I6��5$r=]( $s=1�0$ Serre-Swa ��&m'm�V� &R�_G�� �B#� (t)$�=y��-i�] �*" A`Wi�aAU�!yin��N���$. Vicu$sa, let $tA�>^ $VheqJZ u :�V}a �����,&y2JM%?x U$ (�U��chosen(byRh�alprevi� argu� �analogu�= r $V� /���w22�&):iv�1.6.3{ ��t��4 ^r_V.�_V�J2.E[ (t�tR���r�+V*����$t�$t_1$.JU'2`:�&] �l �Aous2#Q�k:R a�2�3 ��V���wG*�*?�'�(�l{}�R�*g=7O-V-1V-Aj U \Ff m���Nions � Z�+C|_V��%0< )I.+� _1sI�b67��#�\in$ $�b!�$ $5� Muaa� is"ven�3�� ="�R!{rhoineJ'��(-^n� r , *] ��* nFk1u�a"z "��3Z�&�sigma_xs~ }�"~i{(�-rs)_\ep�� Z�_!tXn2�ofH\sCm�V$�li�!2�f�.���9/)�>� \1�/%ByIk� (Re)rem_ce})H'.$(\iotL9LNg�%m&/ C$-m�by&���,&�1NT���[i6we ob�.NOJ�>C�!MX�.��-�J%tmE5&� ]~v $E] �Kn�2lyy%�I���, XA� sAc�(=a{8m_{LM} \psi_L cM^*��%$ �� MU,�s.2+�z psiLA�f[5mC� ��b��(r �q�/��F@)>�+:oE'% CAZ�$;A�o\�:le,� �(^=3$&.E.I�f12rh�^$*D��(yX)�eq_spsi!��d $$; (tE��)I eps (s,1)Z "1,r9/t.,9*Ag!�26 E8� :.K 6�,Y�t �A�2� � A�^*� M���1� 1$ b*[,A�: first*'$�[ 0 a�X.cFrho^r(��26st)q M= a�Fr&a-8u!`-eWA' \ca�mcAFur�K !,!��Y� !�%��L�f4A BMj5^>cD � .$$ "� �8s&��B._{L_x3&�# $\!�%da.y�z� W4�Vw\mOFi�N� E7QDMXBB-�]�e_ identify F8w�9f_Eas-xijB~�?rނatisf��)6p*C= �.�)$t&�(x)�)akes .!�ne�%z"^�c$a >#6�xM��u�9���s%a�[ a�d:= � t�-= :� :�o)�>�C \ R~ �\6B^$uR7�;�3 5t�_����n�#s%�7$n_ R&�": ��| "���9\|e5� '6' (in 5s^= � Wg4"a); , <���#$~ �: \|�%|]Kn �,�,%-��e$(t_x)_{M*}m\prodAe�Mr�(2.2Z�E fs\Th�'C9X{�xNkx!)�:���b�:�+ 2p(;� � A�c� Prop.10.2re�x�;��g-pr�:�$EA}�V�$%6�F��2��&uh8w�&J#� .� ^����(r�%�A�i�a%��"yp��Ew{<(A3"�'wM�}.a>! & M;�� Y"�M{iF�(u }a �"i��nI8L�1the�H�S�$�A�� m�mV�` *?0�!6ը6a!KB�-�%�-3!�lin*?�5��pi��x q��:� R)��\ � xm���.�F�By>�e���35>e�0.6� :FR�B � a:��%-r.)6bq!C2fx)*( 2|�)i�Gm5���<F; E_s�-��-�/ J�W�ZP *�$w6!�Z.,"73eRP�'ia&:E��Z�t��exist�p6c�*� �"1�s_WZ ex C� %%*��e"6 ),�refo3%kZ�2g�0�6M�A�3a�A� %��:&"9��!.eassr9o���d� �+o�H -�ls3IKoneZ�N\�+4{Special endom�$JW.. s."�cp_spec}X���,{ #8;result.!f"<@basic � direcc5sequeiKof:W_da},. dim_perm})O"�?� ^�5l(a�*descpr�͝"�(6MA� soci�= a weakly �>3)�hypC sKc_1��bNEmade jus~Z�Eex"q�8!�remarks=KDef�@% m}�8: A# sue_� qOF b]j�!n�F%class $c �= d \opl; ���deb!%%2XErank $d$��"�.�F pi3Chern|i�eMV.UG*d/�ۡ�! xVG�"$$*�I�� �/gG� �P!"Q 7|G^�  "/W �E*� � 2vcy��f-HFina1�F�B�F!qO_{%}�=aM�*�-�s�iEi&F cor}.%*\%� sym���tertwin,sU!!�6j>�  2� nt:R�:^6�.BE�am@Ia� ��:B2QPws/hV�%\R8�M2� "� ��r.�� >E,.U-�%x9�ex}j/�ex_bl} I!�@e 5:�� RD V!{BL04�HB9�6���aѱ<^a F>SzH"^KVR\zr}4�,:m �#�F*, 9D!�� 2x �%sA�^�bC$ (ab�9��"Q, J>�x 4.10!N]�E-�58d reference). }tex�!�e��4e� R���2%-���8re�c�s\Sy$sec_pb}. ;%� �t! ��quasi-N�� E�E�s�7�possible�� �crossed�duc Kr%�_�aQ�� J7�EfkE���aPLe��{"TL{�H}�0A Z�)$E�0D6JMeq.ish�I.�/e>�0]68q��GFCbRN sh�>a�F"��F]c�!3& ��.�! \mA'<B�� cor_�+_1=�RaB� �beKj"a suitaAquoti�I-r^� AA2G"E"l reuT� orig���) $by Doplich�Q nd Robert �Me�p-cE��( �1!bC1$ $\R�at2mE ^dh?A� m step��B $\mB�J�{�/5!�idered��!�& 5=&�JZKmF _(B \ / \ (C_�F�mB�.7>n9wE� :�.\O�1+>% )�Cora�8,!046Vas04}e�B\_ HA�*BM�*ese quesa�s, rela*5�E4�unicity� blem{lla�approach �a|thcom,paper��%��  ��$Acknowledg/s.}�5hGhor w �5tEbnk S.y�gN�> ed (!$successive��Hed��ime|q%?encourag )%��UA,�6� Eork!C  PhD�sieV%*�!6bOAHthebibliography}{99P \bib)h>� M.F. Atiyah: {\it K-Theory}, Benjamin, New York, 1967.g FBL97} H.2/ , F.�/$: Supersel�  Sʼnure� ��4$ No�> Ce�, �Reviewe Mathemat�D Physics�Lbf 9} (1997) 785-8190!�01z� An A*�P%�eYN-G DucD%�CaG�<E2Ca�=� ofF� J�in �N�I�-$ - QuantumE�$Operator AQ[ ic A�-s}-UF�:(s Institute�m�*�#1U830} (2001) 1-10:S4zS1+E-*�E �Hil� ( C*-systems�DC*"{Wi�a*�@� (er, Int. J.%@., Vol. 15, No. 8�$4) 759-812��Y \la96} E. Blanchard: D\'e�D � de1� \'ebA�de Hopf-=D R87}:CJ..�a���� E�s Rea�I�cE E�� !�Their A�aSJ���7ix 87) 96-122� DR88v������k�?I91%�(88) 227-284.<�Xv�AA�%Z� [Js-�Inven!�es��#��98 ��"57-218>�Av�6�o6�, C{/�)�A�t2Y� AnnaI6�NQ�1�w19�75-112� DR90v�Wh�(�Yy)�TՑ augeɗ�rib�sA�s6�I i�; le p�-� Comm͕嚱�13I90) 5�J��2up} %M�� Dupr\'��=if_Ya2�6�v �Memoire��%Ameri`9ral�� ietyM� 222}�N21��9)�:�74�J�C�i�)��� s I,��J� , 15g$4) 244-278o�EH�$G. Effros,c Hahn: L�,1�trans��)�I��RMs,>r , 75�xj:,A�vR+ce, RI,�67���4Exe00} R. Exel��(New Look ata�iE ed-P��ea.��an2�, E�N�! Dynam. SyO , 23 3),�3-175�2�`HK} %K.H Hofman - K. Keim�SheafA>oretic zep4Hfysis:5�E�heaveEu%s�,�&�HIY:.z ;xves� �\O|]�\s %753, Springer-Verlag,%Z, Heidef g� rlin%9Ad%:ir# 4%I. Hirshberg:2n ��C&LL Trac28qPre� t arXiv %+ ,OA/0112293},%�1i`Y*8Kar} M. Karoubi* *� � �B� -� -19aV6� KPW98} %Tijiwara,2 �15� ,8) %295-322.�'.�KPW%�������� coun!�y�%� -%Krieger�?.*�V45":  R�3��Jo��In�om��Zf�its %�lal �Co&h1 G��2�U�301259I�3)�.�sO G.GA@ sparov, Emari�- $KK$R%d��Novikov�i�ͪ��9͊*B 147-201��R KW95� Kirce�,�W &mann:-�Q]onvvpB\fe�A�%�� sche�en �303L 95. 7-69���LRq R. Longo��.* A-va2Dimen?ivu�A 11P 03-15 2�hMF80} %A.S. Mishchenko, A.TvKm� I8of Ellip��Q�"*t,�(. USSR %Izvaja 15�l� 0) 87-1X%]Mita�P.D�t�� S�"oU K$-tc Spectrb !�Z&i�K )- 24}(2)�/ � 012�Nil�M. NilsPX1���$\X&�asD$diana UnivM|��4��463-4S.wNT�%Vmstor,� Troitsky:Iie�a�_ *{*9b��ya$-Douady %iue,�[,ns. AMS. 356%4��85� .�PasA W. Paschk? � ed�� AW,��BWE�Procee8*e)�r+ -�8319A'113-1m y!Pima"M�msE#A< �!�q��li^+ both>->�%����bS8bZ$�`iaree basXtym�,}, Ed. D. Vo�qescu,~m�2� a� 89-2a.�RA�D%�,k, I. Raebur���a����q�-�s �,. RIMS KyotoE� ersi"� 3 �$6) 415-443:vPT� %H�rk��A�ut: Re�Me� e $Eu�A�J9��*� %Xm 7E�0A�78-20V�'PWY�-.�*q,� Yone~KMS S� s, E�p�SV�o���rinciple� FullEOd 0" E�^� 213.n331-379�|�R84�Phi�R�L=�E�ysL"v9�mary�omF,.� 2 cipalU M=s��Q�M��08I 15-246!Rob�E.� WUnpg0ed Manuscript� 1H2dSta93} �Stacey:F��Q�a�*-2? z$J. Austral�{ Soc.Hs A �5�93) 204mc.� SW70} %R.Strea,Wilde : FermIE�a Bosoni� �Nu�CR�B %�7�61-57:_Vas�Vy lli:.iFf>Arifkf�wE�/ �T&;%C"> �]}xqw-319: 02003) 122-1522�g2~�,e;.�D�� N�:�&,��4\'a di Roma To� gata, 20�"6��g} %E.=] Some-�6���^�"� %� .� �� <, 14 pp.. Submit/y2q�4>I &�'ee.,6�-ɼD0�^I.� 16� 5); F�21[���a:�^0&� A�a6��D�8E�Ō��,aapp5ona�E� L, http://dx.doi.org/�TD016/j.jfa.2004.09.:�Zit0A. Zito: Priv}"N@�`��s!y.�WalA�< Wald� Morita E� � $of Fedosov�"r)vd� ed H�t�jc3%�,�*Let� � bf 6�A�� 170B�or>x%S.L. Woronowicz: Tannaka-Kreinq]�p.0Matrix PseudoE"�]wisS(%$SU(N)%$-% �itRI 1�7) 35-76�j+t:+  docuL} s%&LaTeX %   File:�,stefania.tex Type�:v 3format \b�[a4m ]{amsart}%(\usepackagea�,amssymb(cd,verbatim/4 %\hfuzz 7.5py\4rginparwidth 08setlength{\topm"}{0.5inE%."odd$&pt�6Bev� d6!�% text�}{6 g>hX} t}{8 4 \flushbottomP \newa and{\lp}{�9(�2rrR()F(bc}{\bigcapFmb}{\!d boldJ<calFsu>s�1F n !�ZF"ol}{\2s9F$lra}{\Left�a�*J&ong) !Z) vo}{|$OmegaFHdm downZ?d&+FAlA�ZA sm}{AminusF?a! a�-FL[ ambdJbe!�et Declare�3 {\rad}{A[2= }{E�{�}F#t $t %-^& max}%MaxJJ l Fk(rx}{R[\{X_{!\}]F$oA�QnamI:i0iem��_U}t7 [�7]1*l�Z}[ ]{�'u `Cp�E,*.X%!Z3�({.2D`+ 1.0corry/C.2_�0.N�|-.[7*P1(2U�&*EՂ+�\ �style.�ne���{ �D�Ft�Q8tle{$w$-divisor�%doj9ig ��j�uX{Primary: 13A15; Second  F05. V, \keywords{DBV(, Pr\"ufer�b $v$-m�n� �,� \au�&@{Said El Baghdadi8\address{Depart��a�� $acult\'{e}� Sci�,s et TechngG8s, P.O. Box 523  ni Mellal� occo uemail{b �(@fstbm.ac.mi %���� Gab� A�i��to� Mat �a. `{a�gli Stu 0 Tre, Largo� L. Mu!�do,�{00146J , Italy~ �g �8@mat.uniroma3.iM*ᦢ. ABSTRACT�/U�abstrdO We stud��!�M�(which each A�g(l�* Y�,*q=s_6al� �vof ,� tot�8.Ds8to a much widerB�.6�Z�/ +-$PvMD$U � V. ��H�ICmaketa� fR4 INTRODUCTION f(%-la�q(*{I-� io�  e�% �:p p& zero�)%w=J�r been%�i�/��| entl��  dif�6 t methods}P3)ssh ,{Ba�lirfite{Ma1}%�W.�� /H}��sixties.KF";>S�)zzoni �L. Sal�YBS, B2}-se1� �Ocalled� �-+}lAmongG�>sj�<+�.9; tegrEwclo J:��P�of/y;.^ 8%[cer�7���� �+"@e-B[Tkem _/H�< Twenty years l,�Houston�0M. Zafrullah "a2d!t%A {HZ�k!�zJ$t$y�9M�Ma� they1r$TV$-� �'!�(ac��zeduk%AiA�y ��3W0 HZ}. How�!�y observr� � � need / ?i� k> 3�}HZ}�5ueO>( �j9* of � \oM[#�  Gt�#z&QBꊍe+2�6��� dA� _ApL72t%9�.Aito�~�g|�r)�B�},!ua�A `A^�A�TuB4e2<,b�4mosE268 EGl!^6� ���fa,� "d2��!��a� a�8�myEdgen�}izOCv q� �d%�Noethe�5 9k��!e/�pH, O, QA����� e�S�� 1!�q�a; Loc}�B �L$R$) a%�B�>P 0a �AMa�k)? (V�s� icaÉf u�?0Ԍ��t$-prime�1�?ai:��P +maxim�XU!)%L$R2X�B��0 J@ $M$. �%��2w�ncNe-�\,a�Bf��'U�(�K�  5.4]{BS)�In5�2�3&��%�sa���of�2� ���� R��(Y�d) �#�f��#Ras _ �sR% (!l)=�s,flat !! S� .sub�>B��3!]&�2���pW ?&KLU�n ^� ��� G>���E$�2bAWI9inv�"�(2dic�5��ِheF.tE �^�V���G�OeIw�K �J�,�linked5�A' 8:] 6:n'a��d K�q�!�5I eu�V�F> 6+tw)-�Wo8� c�5]�2�s4 �de�^.)Dedek���� %u{elb1.[�]%c6LMJ ;�N� >i���"-R���[�� 4]{O���la�����=vo�to :� ��  R!Jne�5ar�!�dU1�I9�o8 s B a e-ona���s.�("_�tSMa ��q1` � wy,nt�s_6�2A � ai#1� ؅t6?}� \'�+���a��+be* � o e)WE�"&� t�+ tool��In6vw� }��ha�oer:� '�aqiIs)Lwv$� 2} !)�<:X� �ir� �Tc=�weuAwi.���of�* z�re>"�wA2��a � w�gE���iz�Iall>Mis)�:� itTB�r W �8��reNe� his/�Acarefu� a�#�relev�'� B( \smallskip roughougB �{w:�@�e�X"�A2�"zw��ll�@&&�Re>K� �/sh! u:� e languag� star-� � A�;%�i�a �Q($I\to I^*$ O!+{$F(R)�Ino�oU| IR$�� itself&� :V �&$R^* = R �$(aI)au� �$BK \)he� \{0\hQ �$I � �AcJ -?I�= sub J^*$;5 3) $I^{**�SuY�5!�feAGsEK7�a �6A� ��4{g1, Gr, HK, J�� A:3 $*s of)� type}A� �!'<\cup \{J^*\, ;\,��I$ �JH@L\-te\-ly ge\-ne\-rad\g ���Ib>%�$. To any J�� �a�N a>' $*_{f}E�te�8 �ng�{'}= �!�,�A` unP"taken��E Ol.F,-��&q �\I$. C��lyoY1AU�H $I%<$** q%�$A =�%9 � #F��EG��0t�v� 6,,��$d$y�!�+ v$-%�!� y�� best �=~"�;6jI��? %��4>&Fway. ;M���f6$s%%�!uoÒ隉�eU$(J\colon I�penfjj�9\{xVTK� , ; \, xIA�� J\}%���XI_v=(R P I))�1 I_t=eJ_v*�H�DMDTs��A5z!�)�I� 6py&d�/!�DEY�v �>%iF�2aY�E�I�I=A�%//X4I = I_{v}�$ �0s"ؕI�:x�>taMwta�qe�h}$�9 c,ee=*� �� ��A�IF_{*}�Aaq%�2��� a���!�@�ect1O*q�6},�merD$(I,J�wo (IJ)Xh�h.(yA��W5/an �.�qi"� -�^*!a�Y� !��+em ��UUG *6\se}a` -�$(R:I,_gui��6��-���$(I8)^*=Ru"� �G(6H) X��%�A<)me}�F�p E\A0Ev6} u>1e t ˅��+�� �Ŗ�`�� �5� (i� �Ds��a � y. e+*-�:�� }Bi��' �Fa6�@ Zorn'sANsh3~at%��� Max$Q�1�2�E�z$Eempty.E�a�$I�4�,i��;ap_{M *\op{raV}I^*R_{M in*� !@R6:69 6�Gr�a�� !�: !��:=.t sek$I_{w[ �L �� Ma � xe�An "Y3t S�u�i�` b�� (I�1 a�;�g; & t6�a2$�\J=LRŇ BSH�latter�,# seL InoH AM!7I�&"� �}Q)e#�(-�Iu+n�K��S. Glaz� nd W�)�lo�?1� V}. FN!�9���� 9� wasnN� qE#dstro�B�i�$�0 $ un���~� F_{\infty!�*� �H7�\D��&� �F��:�t =�A 1*���;"�d t=v$���� 3�it�STV$s}�&�(i. e. gs *xi�.ascenYch��nd��on�9J)�s)� v A f)��� $w=t.� �$TW�-��� A�nort�clH!a�0S� �$;;!&a�!9precis�na2��Ned%=� �"bK}.�u!� �U�"9 �&&g 6 -}O shor�,%�1 9 �8�j�mNU��2� %!(�.)Q�a2� V�(% �2SyaF=� ~  &( du�X2M! *� &w���Rt)v� 2�1c Qlso!��b2i�9�1V� B��[�( 2�O h� i�J�"�@.�aB�m�:�h&l e�9N2 beca��J�-�h" "o&~�}�`P1}a�R��D�>��QY Ka1$�H�( a�&&�aB"]4"�AM6&.��)�nIT2���R�-�/F')� bJ#*�+ 1.3]I�ܭ12 =�ZA��kT�95c�.�ofZ$ �lE�E�{AZ��� non�  � $\Lae�э*�!h:�*� !d�,Ee�w6!�b&v at�"� ly m� memb�`!��� .�  �in6Sent�no twoFG ��a4o� ��.(�� .-�)�%wA�2��>�e� �F�A�WIX� �g� !a5Z&�9Ix�]y�A ��a%~� )m��� x.��$�""�)a� $r/� ,"7 ��>[��N Di� 5�< :]Lep.�&+by� M�#�w� $h$-�A� � Ma]&A�5f-�B ��Ex< J(G&��"�#��%�.�3 �� �5DM.Q&! =%(�u� w5g- q }; h�J {E#:)�C= AFR��I��V^ +>  �  ��,&� l�N��� � A�D>�on6G va nba.7;%.�! �F~�"x_at ��2%),-�R]gv�zF� zE "Y �m�)�>,'�sl!S � 6�$)%m� is[)uis�= of:�QN� ��ta��#s�;t"D �X$PE-� %R�, �����k3� L1} c9E�d*&� =�: &�1� &�: W�Vize�M�[(1)]dE5V�; �s;[(2)]�Tu32S �AG�cR�P$ $\{I_\al\i!�el��.E&\al4 neq 0��  OJMR�0  %� �_ $. E �!  ){%�-)L ( $(1)\ra(2)JsPI�&"#4.4 �. �Z�byA( ${\mc F}=�'!+t�stKi#w� $(2�1IF`~�A�t5�b���ˁR2�  adap �a �' 2�(L�P$E�Q |�+��on����ikcYB� s $M��! $M_2c�]2 ,�u�lAFC  | �umL � t�>ch@ llM�i�-I ¤ M_{2"i in iݝe�I=A�I�p�I\nA� �IwMIa�Take $Z I\sm.d}$x^2\ln<0n $(P+x^2R)_wCJ!i}so P )�i =_2}e\ E$sx=pgrA�riB$sqR� !�, $pnP 7r"�W�$$(s-rx)x=pP51!L%7=Now $0 � P$ � $s z! d $r�lIV2�B!�g $H P:}i�^!�;%�ntradi��pP�E�.� Nex4.yx��� �F&A!$0%` �0#\{M_\be!�6� A�J 9 R$ :�x$�JAf� $\be�{ $Ade�� �r�#mC^A�a� $x$ bC$�$�ia�pC{u��Dt $A=:� \be ���hA!AMIA%}�i�noqq $A_t!%iF=(�be_* 2},����_{!n})'h0$ i}� !i��y�c\J/"-�ݷF �Now)!M�a�M _� 2� n}\�n*�)��A3sups!F�53{ m"bkU�)�L5FL �l���x�� Y�=A�%7N�,.�m)/���]�L��]lU<��(%�RE�Z�0�lMa�F1��<�1l��� F�=���:��e�0{g�>��ڂrp% �JbSig���a-��R$� �*�� a�$ 0'�a@�)1�s�MI�a.�7���=XH^m Im> e�Iz �&[\al՟A.)M$.}:ndQ�R 3} !k6� 2� ,e�_$,R_M =(IR_M)_����f i�[g wE%. ��2 � .z�Ap��)/& 5 AZ�d�  .� W} as!�a8rea�:de)�t$-Bm02~ �2=7.4"r-S&t!�a,� �)a�$"?�~31A�z3�X.r� .):J )LC/ 5W3�co4��"��7�7 2]{B�]a�?�ioc}.hJR ,K,� � nR Q�I z) 2X B )>Y -�>�2 -%��5A>1�I�!�;���[(3.� *�g��BF� >h4h�u�=I_a��m���V��l�"� Q!�1�m�*� &nyE� �'�/��a0 \ref�.�� f~M��t$5�q(;:(J%�&)�&_!*� �)�n."� � �IYweip�&�)c)_v=J)~!5�eJw��/J_wR_M=5=�+q ��"�M�k�4>46��(4&�e�I-6b%�T� w� �$Y (R)} �<���t%.% A�N"� Q  J��cQA$3)$ via (2 X�3�4�0t�ne�%�d=�, *�-b�!Ce5.XI0 At) ""�i�f"�2{M})_q*e"=(��o")�=2v!>� � y al�;:�5Z ]tBd�M +\a�8lyFK2J� 9�," @Q�&|�I�y�37Og�t��&xF� tdim1}I�� ��!ythE�X�ne�a� IW6�>�%PGG  m4%��{P!�e�.�" &�"� � ���"z LOCALIZAoBS :9#jb"1�"�:!2R���"!Y4+$r2O4�AVG9�6.5#7!�;Nou�R�� N@M1�?} H}.A!B~ !�>�#:Uits"E i��@9�T �;� 2]{H},��8�. 6� ( ( ngly%screte ].�7t� BS},*?�1PR.t��&���U~4 �G!�RN� $5.3.8]{fhp�ɎG>Is�J+ >` #�&Q6�F� !n�eM�+=a "p=a�3=���6*6�v��s9_e])>[6 %%�- "��� D�X!=��I�=�6� /}"�D2]%��})D< b:P6)%W $R_P�|2';%%�ɠ P\in*O(P 7M}) �b���#^�Z� .�)$M�(Ȇ�A�� B� a,�8Y�� oc=zi�.Z�/BS}),1n�5o*e�:�)�522,� ')�A�� -�aRGVan*� 1�)9]��F�"<$��2� �:.�E�B�61��med�9 �;2"a�q9�+JYEA=f:~a�!.i �KBB�g"ADdN};{a�9.!�A�s�]s, ��AW$=��r��K6,I ~ 27#��2;#ş�>]s�My�� m*�Mv��g}� I!�$IJB n�'�= $I'9��.! �Rc�0�� k!�Rԁ��W st�; a ^`���![~.e��a��u� :��1V70atr�c F, AVm9�i�*i�6b6ned"$ � =$ 6ZA��G�Lk��O5�!%�Oa�9$R��:�7\{(R:J)�:!���G!k7L� �:TGE*� /�s;5=(�#86 ��ny3!�A�IE�$Rm3 �F�IB����]�"�7!� �FH %�"-H2�:|�2op{Sat}�� F)� q�=P/�P=$�n �|-�`rl bij� betwxM!dY-�. �p�P���F}�9bNQ%a� �!X 6$J50a'1QG!�$.1��7in(!  $Q1 Q� �In ad� �@ _P=(k)_{54} i�B) Mj��a"Q)q � ��$"��; $>� \Lau&��e�R!/%8��{E,a%�}�\{IR_P�B& c��B�m�A|$t * 4a�d-b a c!�AB��r%\�?FW%��5 ��:IK$R$};�n��La!& �"� B�ea ]A�:a�%��'~�Qe��]c*a~ ��Je>%��8-\�@�><� �9��$�N�F. A+)$ i Y �2,�R 0 u}Z� �!7 � �J�$"� �)J�̅�:*� �� ���!� �2FV�v'v�&Q*2��o��k+��"�-h���Q�<��ee�&�6be $./� ,s]!t��Z� , �u�:��Z T =Rm�q�V9�"a^ (b)]IOALB, $T$.a*w e�!! }��,f T_M�Mh R�y��U-1=I5Fnm+KPA�A val�T $T_QUQ^U�� �^!�S22x�Ja� Flat�S�zC(����co�7vtru0|�2.12]�XB�/�w,%\A��)l N�06OfIex��=�V�� %R2�T 7����3/�$TIR�:�:B[�(i+��0of pain���y}r�Q �%�����m�ų �2�t�CL35�E|E�!��a�t$>� "!��urn�>y �WR>,٣� �*kIv;2"3���a���3 I,.�2cDHL$U.@�+�!�E$nX$�O�%B� %Ye� �m�! if���J?m�JJ=m� =� �$ $(T:JT)=T�i ��Oy���r T � T_{R\"�HP�,MVP$ rangA)ve�<%�6=�2:U13(a)]� 2� wellF�l gA<f-IZ��(&�n�V 'I�)E4�. W� ;]Sk,C &� by6�6��bepd}�Ma$page 436]{AW=p�K6�P$;I4�xize!k�:%(a.Y %�����Hs, e. g.� tib�m�<s7� ��1t�1�o Jɻ largJ�\w� a�&.�:pG-�b�3;"�.��co�&yA�[6=2�/:�� =%oBK`%6ue:anW i�@��.���A7�:`s �ly��lu�Z9'` �����{N, GH��<"5B?&u"6() V�<taBA!�%�)-M��4�%0�c.� S(�I� CA�RcIY��: Z"?'� 2�/P:i @@�E.� :#) Mx�� �'"�/R8FE;��,A�hD g" 1��.T��CP$"� ' 0 }�8&�)[>�!E'� =.c�%$T+t�o (1Ԟ!*x'�* =� .]�Cby.��)��MP=. �T6�������f=   C��T � (� IA �e�.6by? (1){ weE7G* .1.9 (c&� F�'Iq��:k;WM�9^n� �&�M��%e�8+R�7&s:x  F �Di E^�6�(��A�[3��m?&2 � 2&Q9��7&z8c ��d eBm#%M�.� )6��6%.k# a� K0Ix� L Rew� +E�9J�*�+d%�Q3R&� �#(T]Ey� �]��S*� �%1C�^vOv!��9�J�"!��sW � ^/ (w+�r handj.�Z_) .l 9n�� )u 1.16*�)��d�`��>�.�W�k����_*H1F� p]� X B2;�E�ϙ�A)M�Y!$T.i$P�fL��� �aAJ&�&iS LbL�0Z �6� W�'e-��_{Q1�a@�#.6�T�`��aS5P"�/Z�At�0Aux1o! �U T&��K� :�VS $2{*,I:x��T� ��M=x #Y�=[Y$P�!�Vc�59 ��%� K&� �"2� ��u5� 9 ��'onI-�6��}� 7�yz �!M�{.��O ��� AU�D�o* J.�ح�&P:�*� tmaxttp� �&6Ym�I��)- .� 8 , B�6rG:a �M>�� �� �-�J6n+ :�_�! "E -��X���e)s!�A� sM�ti� I�&��(�fQ�"��*�� !�ݔ)����Ua�"x�c:�d)�+N|V+.� �"� (1)�#JZ2)*�$Ne�]TAA �F�9m.�$Nw�M>�:Q$T_{N}�M��ksoa;ͅ:fb�~em4AQiMV<sa�� Hnio����� -�aA�B\M}�C_ )�"�� (�)� 7!u���y�"� �� ��rbitr.}A�i�)�zrA�. H�h�un�Ohy"_�IjiR" :F�%a�{��j��Fl �m�:ki!= %֭�$xe�!V aY%q2/�<P@86!i�+�b[,\1 (?>�e�2� s7 <EB+m ��:c =.f �� �9 "6*�%U�YX'6�ce�nm�� } �/5)$�O.5e��3tb/(5�/3 Byf01�b�*021� F _  �l P = t �~ &Se; !_{Q� �D %ym�ce�8U�>2�m�$�lra�0�auAm�Y:c��Z [��U ��P72��!$"�@A{ob �F�D&� �"��*g)9���� b�ila<�BH ,�=RC'V�Hz�l� R?��%6&g� �(WZ$T��.�G�q�i[j�h%O��&0���^�=91:�R�ZJ@� �8��E B�B��R�|���ҁ�!�� !u2*)�� )"79;!]v[�k�z\.:+9�.P M�� lra �m2�n,"��A�!�,,V��2x3��, C �%�KmJ3*5 ^��_ME�u3a��. � d�10 Since $T$ is� flat and $R$ is strongly divisorial, then $T_Q=R_{Q\cap R}/.&�for each prime ideal $Q$ of $T$.  4$(2) \ra (4)$. Since��T$ are2mt�8d = w= t= v$ in.2L. Thus we can apply ^TTheorem \ref{subint} (� 5)$)��4)�1��J}, by ba5 �1)$), !!r $w$-9G8. To prove that% �(,� show '%xmaximal-)�)}ia $t$- ,(Proposition) (P1}). If $M .O 2 H �)A;nes%dDhave $T_{M}= R_{M\M%.1.j_ O$M? }�Aso $M = #\T>)1�(\end{proof}Zl \begin{corollary} \label{st�% LetE?�be an integral domain. The following cond%>sE�(equivalent: p(itemize} \ [(1)] Ea�z overrM!\: 6;F2)]�.�6,%1EFiDis a weakly Matlis �a3�a a$TV$-)9; �4�Yfamila� $\La�APpairwise incomparable�ns1D suchi8${\mc F}(\La)E/$$v$-finite! (independent? , character.EL!�%� ]JU^MpByR�, recall!�e�an9� ��is�U)�f%�only i�E ��� �,}$, where ),%�-@ofZ8 A6:ah)4 \:2. � �L In order to studyéRersec�^s�� need��}B8technical lemmaa�q�u�acc} r� �!�C$!]ascend!o%�in! �localiz2��R_)`(N)��Y�,�n!D*C #sta�ary1) ��59� <8=\{P_{\alpha}\}�d s��!F}= �%�TA � F}$.AwL!D��max}(1�b $(]) � �� %:���$ �$��It-�sI� $M=\cup�jiproper9p2p (s��itE�!Y9�un��� t$ �s)%�E�� (because�6a!�9���Weɬav=�I�T_{R\sm =�}}$; tGhthe map $I\mapsto I^\star6FIVG define�4 !E0 o\ �)>�e@�` $M s\sub M$;!�P%a1r�. It ɺs 0t�1exists5�.<��iP_U He� �!; R=5�P_\beta .AT$ \geq Q�Ru �>t� }���V}�eCR$��J�հ2� ��E�~�J��a&a :��08 which satisfieane }ch��"~A=��)�s%�� �Iis2  of�"� -�>"1�>�$(1H (2G Clearly��i{ : )��� 2et !�z-���  assump��R��La��" 6�.m�l.DR$2 Ns e�re_ s�B"�  A\ha)�� J�� �� is�� from� mm��L��n fact,W �9 �=nq:=�.p , ==mc �1b? �CE��n �$���/nd�����* �E�u��2E`� �#_:/ �3fV��By�"= �z� M!�= elements�Hwa��A�e�� U�of z�%�e� clus�$1#%�Vpm��n � b>$ )>�a��. If9�V?�Z�,!Un A��fCA �bjt ��! �aw�{ ���~s (6sѰ)amTBU�>�ieL typea�� (��, �� !:e� s. b� }���:.tM(��I��rk��:2} \rm5� 2)!G��%aIte���&� M#c�!ERYS,. In add�, E $d=w=t=v$�$R$ Q!� 9��v� %D�V�P)��Q���V�2?� �i~sjI Conv!\ ly, 2B ^*^9(1| �y� %~U2����}E��~�� T�o>T0-S }?B��? 2T2����quD mc i�E�LLly generated \cite [� ,1.16]{gab2} !\Z;$q���n .�. � co�de)�!, is (Y).:`%mѹ > %hBkZ?>P 9�TA�We obser� in )!l��%CaNEPmultiplicative systemi��� ��}b~not��� exten�9MJ%�@[pag. 32]{Fo}. One+o/  hand� doNknow an�exampleMr�a� withV� V�9*��*)-���0��!u�xany��sa�f<\spec(R)$ (resp.�$\t)=8{\it treed} (un�iAk!F-�yU?Gt$-MU))�!&�  � cont� twoS&�e�sMK ��$ SpectrumU,a Pr\"ufer �e:��<6,$PvMDZ ��9is �!t��= 9M=.T2.6]{KP}0in particular6fE�f� � so 6{ 0ity coincidesIE ��by .��P1� I��n$\tmaxE:� &�  5�2 2bu!�%� �s�>Abs.iy !�,next resultas!nsequ�S �CoB�!^�?%""� SAN ivel�"�*~ ��E5}2, n>;}� =$t\op{E�}1sU�A�� �"� �&f�"|\ g@i*�6JA� .�B% �+%��T:>mYA�E� ��s>lN~mѻ>���.!:��2��R$ � A� dime�9ne_ � N`� t���se,%�=�9ed� C�I�M^� all � ied ifq86� (cf�]�a�� � � �.�2����Q� .�!E�^ ^ N<b� s" V��aza"�>� 5.��XZ��X;ri %bh INTEGRALLY CLOSED DOMAINS n7%%%!� \�{I� ly closed>C)Ls;W�inzerTvI�* {H}a �/V G!!٣> � an $h$�J� 1 inverti�N-� . WeaErtig �� S�G� J�:>�Qsoa simi�Ոiza4amongAs!�Notq a.�cE�B�� �.2x:�-TAi $M\i�t�LM�RV�@FA���a%9~a#.=MR_�w�pa-�*U) valu)I �. �u��-EÍ��JlrK/"6 ��� ��:eLoc}) �+"E�[*2.2%y.` 3.1]{Zw ��A"\ra(3)$ ��s� J� e 1, S 4]{Q}, � � 1K}5)#V�A $(3x2x"� {$a 5.2]{H}.)l-I!\9[p"�corval�V!V��y�E�M����o�0AS2��Q�Yq.E�ML��U�s��ic ��;�*� q��-��%���s.l fY�qe,�i� R�}�j�%86�!-F!BZ:.G B::w 1-6�1#eXqWAQ|��8 1�!R�TW"m qT3.5]{K� R@V?),). �:� a��LZ�"%W:5 SQ�Zu��2�>�A%�6��Sof� }BH !]�du2jc)Q{H���f  >i� is meat�0�r.5 �7Now��$1�F !p6[���previou�� Bbe S also!�usa�� fac���(u�Ue-�!)a��`z�LtT�&��� %�s���!.�$s giveA� )=1�#H�$!R$�N�mG&G discre�$0f $P^2\neq P$��Ino� 3(*t)P3%N ��r5.3]{fhp�a a�4lized Dedekindq���"� �*���!A��ert[eA�C �l).in�(s �{P�� �5��is�B�}A4P^2)_t\not=P$,� �$P\in*) Remark!�0]{elb3 �?2�-�Ii� ["])A12E�V� ��tY k'& ed a �%� Krul}} ������� *�! clas56R��!�1 3U ��,strictly rel�to)9 �A� ��s:=Muj�a.� ��� \-gf�;F8�pM}��PN?Fl"1# in t2� FP�aE�  �Ya|)_2a>��$P:&p"� >M �Ju5�)6u�f>�a 52 �)0[Z�MT�aM� �% Z.Fo�3a�e}���/ k%A7 $�H{t}= P^2��$N� 1�c�� Ct��; �if ��R_P a� �l4*�.6HD>B�Oidempot�*B t5��� !)� � ��o*�,��� �)�z.O 5.3.1+ţ �1�3)�4)$.V@ 8 $(Q0lR0 6))$N0 $�/�5.F� * q�MJ�Qacom�!2�$"� ��icsb� � ���͆V.�Mށ���� ��$2m0 ���� ��b����+>I. %�%=�"� �bt"-be�y >� ic&� w �. �.� ,� �?�� _P ՝�F! ��(� 05<:�A�I9 sdI�eLra�$:�&B'� Q�,"�%� �y.�IF>�� . Y F�R �a-�)�Y�=�eQ�twjq ���jUE��r�^�� �1&�UR4.J�E8F���U���.^!��:g.`��`BK6_linkedVa6�.`�`B�^� .@6�� @^16��\��!is�ra.qu�12 ^mQ�A5 Q֡�6p���)>�,��©� �(3�v3�#;e*�.�H#qa�>87&���)��~s)v������b�&`R1���ł��� (3�0(4) im^8PM�)s!N2�)3"f��g(D��$J�"m'�K�.Q 2.�KNE/}-5M/!�\ra��� �>v ��oR:�F�, l�2IC* r4 .8��5"��TI� )"�D 2PD2 s. Fur�#more,)\ ��z ��q�)�$A just:��($t$).j�"�%b<$�� Qu3.9"�%�5�6^&p��$(6eIB3enough �5"R.A.^d.<>4.t�86�*jnc&�X 6�J�"l�� A�/c&�!A1euV� ob� �e=*&�7*�J tota��B; 'ee�mA{O*� F(v����N�f�.�*� J F�uR�iA�9;.W*�anNZ"; @�QG�*�2 ?v*xW H 2�r.�:�.?b�:490}mazM2�e� � � Yqa�M�m5Tz�inRWa� $d$-��%&�6S&�katI.� 2��E.B�,d� 2;)�:!.�.�A���if�a"'* >��; %E-0� .u! �(co�)Y� ! ure}���/ 'he9 '3 .�.�UB6�)�:c " .M.�2�5]Q�5�"�M�<�2""."� B� v'f6(� r�Z}�02�i�"� 3.11���%6( �!��F%�M !!" <@q�V�& <����R�2��F1�2�dz well-.��݅ Y-}%:� h}b;e&8*: �rec���e�N�$.�j 2B 5�3"~�\.�`c 4��p�� y$�3$6�! N��:�@-�&�%�DHL%� e�F8a�%1:O.|Cstill>&u�0U��f@6]E�Q� J�R�"�6O-G�7Ac� R*b:wB9 >n)j"A?l:�ffSd5BP��HN[)� "1 $$(R�-2) 0`F.� ��R=��.Y�6"�'way�e Y6X� %� %�i  F8 % �D# ��ur� 52� 28NIF2 ��qX�Rr * MORI�* Y** MoriVd* S4�@w4���som��H tip/Noeiian.s M�s��6C*, Q�.���`W16KV�&j�%M �Y :None&9�J61%1 �� C.�.�/��&�GU0..�e)AwH42.V�&��<3V ted��Kx �cًV21 >�>fy���M�a:{yi���*��*�2s >�B����qxA� ���Y��.v ���F�F"��L� �)v�KŞ.q r&"�H���_M~ ./�nII�!>a�� 4�O �]* U |�&g P! M� 3,"�*2�*1l-< AnJ�Nn �! >) I�@&�to �){:2+ic�=B�%;1}�y.H*o ��eX �of &` greater��In^JBy f.��rs�9�1#6�$jf�5io��eh�y�7$:G^%,$I_v=I_w$. W�8�2noHA,F� � �#'E�� �A�24�We��$nF1�JR<n$���7 I_{w#X=(a_{1}R+ \dots+a_{n}R) �%Ŝ$), (,( :�#he quoti!!field-Bea�'"C͈wa�:�j8Ɋ�G"��\ :�6K-�G.z�2:z�.C���aC" Y�A�i�� 2�,9�Mh)�E$M F�$B�/!tend9r.l��ku @%���t/.;11"�8��t %�I�� n�+Q޹7E� Sx�=%J� t�0 M)=(R+Rx)_v� Soi�by�?pa���0a�To�clude� ��S�)"�+:� �g1�6�A��MA�^?,Ni2L@ I=(a, b)R�0�%mP, b! I�$a�n !^-CJ`�q(R)_v __vaq! ) a,b)_wR_M & IlxEVZ�5#.;fG q^�)�-"A.Bj��*�"s-/a.,t � l  -�&�%&� %�} �!.e(]�I�%�%E�]� 2agO=2^�{"faH :�!�!a.�A?2A�4uA�A& )_w$�69(t$(.T��MaME\A �� 6 (��first**a=holds"6 �/�qvRT>��&�*��\S�D.}G��9��zgC��e�F6Fq1Fn���*"���'�.*6V&�A�a�IP&�?�/! 6� 1� FM2}��u�e� !.�:�(����&�SM} �&� 2�M�F�A%k}Q�mV� �.� ] t�W*�;� �>.�� rwis2q( $w=v$)� !�1�2��[2f�a�:6�� @?�2stigate:J@of"�4.%.1�s. Ourm^�? K dir�6���1afL�%isIAyA�9�s@ �b:E�rs�@� e.��im-Y:0"� 2.4]AE;>wD6�%��coQnt6� 1�u(e��BIGi�y� 6��&` -t��)D$I_tR_S=(IR_S)_t$ *P ��1k9> A' �>HD�!SiH�*UqKTW:� .�ma��c�S!�*r F�/q�� e�R� &�3� ()c Al!Ge5%�E��^�Ca� =;�1q� t$-$:�mo � zn�)�Vqk2>q"�.�� �� LZ�Q�m=c"�4Abɰ9\q�&�>K �)XU /�Q��>F %E�~� B2�a$R� �L$t�]:�K $I��=�  t A�{M�Vt$!�C*�Jw�U F�23VtYA�-  $$I_w�U 1 }IE� �\4�D}e}M=I_t.$/:f'j&�( N0)*a$ 5E�D6I�$aQ$P �0� P= !-M)�& P=(I�0� )R_P) 3{P)T��� 1�TF �Nve��V*F*�$'.j �6�J���NS A�6�!"T"�MP = N!� R$U 3FM T_{Nm^P!�o1, �b�'� �%�7I�p=�!�a �C�ym��'1|�A`~%!�m�&F Q�wv�U:r-Va�C9Rn�z65�ݕ�2\:�;*+�p�w&#6��đ��1��>?o� APZ�%�p ~&D����U%�2hI���t�*NAQ�!?ſ1�^ 1�-� %��B< %�mM� ir23@3LKTI�"n_A���h �΍a�&�@Ki+2< e9s�7:~ �Mofi�s6;2�c.L?TW� %�-na�t$>�E'%N)��`� bed as�6Z$�p=a s"'1� non-s "� :s%a��55S6�ry�+�\  Also�s6Cm�,{1=7 z69 F�2.20]�� �,mR�K�"wHa2� )e;� cis�R�V%l��. ��}7"���� TeOJ�APN��@f16�is ei�|O� J� RAF� ���.�" .*_�)i� 3� C ���� 2� "Q�v w$-module����*�)�M�s 2�2.13 (a)5�"+ �p 1�&�-�ve%��ȩ}B�AwuM��1.�Hr�!� I��12�|B����eȑ!*�`%�C6eKAh!OBq�SM�ubO �Bpurpo�d�[�M�p to)i$s iaU�d@%� {BS}<&� F� OzID2:c ��+�M�_�� ��.�'>5 n%�A�.�d*�Fdb ���Msa�\<�����A�I�2u= :.h>�� �� dim$(R) =%2A�e5�� za m� �E@9�V 7 (b}�# :U� �>T . A.�\ V���Uel�R�j9��suffic�`o check�!'�T)=1$ ^�j� R'� �K��lo~#5a� $T'$�R�Wc&F.X:�!62��� 2� �WR'�$e���"08,e2�,4c0� 5@Jn��%�&�V��cseteq ��1lat�dw )I')\le$ R'!W\ !)= T W��t zEis�% �erefoghI�N%���Z*�? I�.h7!BS�d67�1�=.1 ��\! ;!��)y m�v7� BS*mKL�J'i.T����B<2:�� ��reflex�X �{E 3]{O� `��}*I<(ngen} below��Nto R�26�{Ma!@ We w�(�XA?&s � !`e'Ch�fe �D�Zr��G+[����x0traightforwaraꕾqA  CRT}dbj?m,�an�A�- $P_1,\l�, P_n$�H�bJT ���D$S = �g�h1 �/W   P) )�C�($xxx_n��re"g��SS."g $x\} x_i\, (:(mod}\, IP_i� _i})� ��$i=�n�E-O>`-_I��!G�(��h &� � : I$ a� zero)?!d�_n _�^�?v�(�"�%*%*< R�J"6-� tora �M�Oat most �0c�j� I�kw$*j � number�[$m \le\�2,niZeE�}� ^8���� �,�h2���u"= OZ �n�8M]_M_r�b�dJ�<%�VT# �a3.�D27 r$ c�"i}q=�"i}I�%&+\� _i}=(N5) $IM��a�� 2dM�#�>d M_{rid] $j2�%B}da_j�R_if��et M_{ifm{�j3i}a_{ji}u} a~M_a~�f~ra~By go��Z o $;�6,$Nakayama's)�9t�-Zy�a_n5U� F�WJ>�!��!� j}$'�'ga�nd1�J0�" $N_1, �B N_s$�Fmy� 2��Ula_p iUQ=A�Ur=A�.�( $"setminus�a0_{j=r+1}^sM_j7�N_jEx9 - ) 2$r)}:>�"3 �n2>r+`s�= argu!�as abov�6Uy� _1=a!>b_2�b� }C�b2�b)��)�.��h laime �JJ$��Ma�F2������M=N_j)?s�-$jH'NL�M6d �M�pMEGB:�;t�� I/2�M"ye-MVin fN���H��D^��\'B�"I��-��6$ac 4*b � S � ��& ,R����\ \2�>\"�#� ��� �Z��.��n`Po =�-!�}FJZ3;9{�vUP2SQ ��:VQ:]M��2TM�!�1�> &�� �9:&E, K� �%.$W�w� e�)h�.o�H�W&s �A'�� z F���V��O�.C.�.A 0f�y.?i�KE��E�.U} +As�&� &]2.7lE�so1_6��? �v"��� �C.�%�%O2Z'u� \"F8\A e(�).IAp6Y*�� =��p27m ��>n� � (95�SMA\�!be�R�����TE@>c��}fU� �*I�F�BJGd�2}�M�Fg!>"�0d{� =�>�6 *�JAW�B@��%�KF?�BuF�!�$��A�.�woO ed_^ra�By" *3 � " �D.[everybQ�R%f �Nr~1"-*DH&�1 dR7!ZsoM�e"=hi����F*9! ( M Rj_M�>� � e�5�� B..-:_w�)b L �i*].�?�*��! = &F, ;zo�cٲz!�.�'^��E�x!�F$)0Z!��i#�� �:������dTG9K :$��J�+a 6�6�G $6�,.,���m�I���X*À_�!�)"]R$N i�TAS "b- ��B�� Q =(3"�WRqɔ.�2rh}; but !�6  N�uMQ�V� �� -J(au��Q �_N�� AcJ� IX`):�R��'A 0�j[-���)eI�9y&)I{�6'�. 6�F@R�. '���vm}> &�!\B�s>�-La����Sr�2�`2}11beWstruc�(+ pullbacks�q�.� �1 �HNq*�4Y i*�68F�'of he�� ��x-�Cresidue�4$K =T/pRq�4$k.�$ $[K:k]=2��!w��=�6!� ��#�-�s 4.1�c4.18]{GHI��E�>kM�8 2�;~� Y �eu� E3+QWk$)2noe�M)/ natuw�.-�n-* K��*6 �["�3/�&� ��C�%J�(�Z�."p9JV'�c&�oE� $ un29p!J��" $DVRY����,FV" ��wf�E>$N~@���9unBsR�6 $N'b_T.>$N'�(=N$6xpz{GH ��Ci?66)F2l; �m:hh��Y LDthebibliography}{9$ \bib�{AZ} D.A!�so�IM. Zaf�^ah,�HI*w L�� ly-F�O�jrs�+�� �M4s}, Houston J.�Bh. {\b4{H25} (1999), 433-452E �(Ba} H. Bass ��subiqu�00of Gorenstein&}, f Z k82i 63), 8-28:f S} Sf zzon��L. Salce vWar�D�?cJ!�Algebr� �18 �6h36-868'�-sB2.l _D&�8aForum � _�42000), 397-419:^* @ D.E. Dobbs, E.G.1�, T Luca��nd:�gitN7�&;Lh0.5(o!�xmm�-�bf 17%�8!�2835-28!�A�5��2�� ]�r�"�&�zE�.tF� Proc�MS�09�9!w637-646E@yH�bAC$El Baghdad1�O�M&�a&�tN2:D�H�C%C-Ai0 30} !�2*� 3723-3742oi.b/d!�F�una,A�Huckaba� I. Papick�,it Pr \";{u}�u� �Mon�>ITextbook!G PHEAD Appl�p$Mathematic 203,�TDekker, New York, 1997!c}Fo} R./Fossum �[i-Dgroupa�a{ � }, S%_$ger-Verlagi73%�U_�.!�GQ�l=�Nagat1z��`)� zfII� Lect! note6�J��$, vol. 206�� rcel5 2,9, pp. 117-1!�.��%u6�vNC5 -lik�o" i��%�ichigan%�.A!��44I� 7), 99-12:?�S.1=^�IdH��yF{Non.� A�u�@ ve R> %�y!�9-227!rAY. Ag\., 520, Kluwer Acad. Pub(Dordrecht, �$:�1} Ab GilmA�%2Mu2�z\ �},5�!� Q�7ap2�V)�laz%W. Vas�eloѶ Flat `s, IA, Manuscripta-�%�2��197!�325-3416�Gr}a)$Griffin, SK�(onN� a� Can!2 6�1��6t710-72鈙�HHK} F. Halter-Koch,-�,.s.  D roduG�#>{.b,�^11f^:�H}!�J�s�]�*2�e��= �{!F 2R f��k��1��(68), 164-17:�HH}�R�d�KmE3E. G.��E�-��hs!��Jar&Ta�JA�rei6,18e�8��37-446DHo}RvO2 J2�#�Dv�z�4I�8"  55-62�� ]nZ:�%'R� �K |� )�� IxB�V3)�8!� 291-300:��J} P. Jaffard, Les Syst\`{e}mes d'Id\'{e}aux, Dunod, Parie�19M� K} B� KangM�9nfn %B��?$R[X]v v}$}��2D123I� 151I�2�KP� D.J. KwakcY.S4�E�On%X�( U!��&6_ v � 5a 7-24:RN� 4 Nour el Abidi�ynG��e F}�!ae cerdZ�/neauxa�(nt\`egres e�q\',transform\'e�Th\`esR8 Doctorat, Lyon�w��"4Ma1E�Ma�-�R"6(Mz6l8� �-3:EMaFOTor�'-free M70R� Uni(ty�0 Chicago Pre !t-Lond �B�Z? A. Mimoun�TW�IF]�2� � � �g!� � 200Z 79-93m�5?OA� Olber��8it Glob36A�.y pe"�N Y�& AX2�20i�9a� 480-50��y[O2R�Stabi�>, DoB, 2-Ge���)a C"De-q'oeC9� Rend. Sem .%�a8dov5106� �261-290i�910P} N. Popescu-/bF 9�RevaSRoumain�7 %�< `��,84), 777-7868�QťQuerr\'Sur l��il7+fA�CanD �th��� (XXVII, n. 6a7e�222-12>�8FM} Wang Fanggu\ (R.L. McCaslɃ� �{"\3s�~ V�] U� �M1�1285-130� U�Fa/��Z{n��b�155-165�=�Z� *�� Putta2��n_{E�m use)�` 429-458� �E"^  �` +t:ha�  docuc ��

�4\?���[reqno,11pt]{amsart} \usepackage{epsf}2amssymb}> math=$date{} %�] macro takA� pi� (#2.eps, scaait+@100% (70%), % cenX�-tiry�7plaF1#1 lo� tnN`a baseline \def\pic#1#2{ �epsfsize##1##2{1.0##1}\raisebox{#1}{$\v q{\h5file{ ��}�ef\smallrd0.9�dtܙzd2�d \MHemstyle{plain} \new A�/}{>em2**�{"b:#l�k}{ :.4{*�!b � �3�ތ:B{DX�F%f blemb >�nV.�*{eLj}{E Rs s:! U{_0rkRs><�P}{N�PaKE�Cőathbb CU�NNZZRR8 \author{Sebast�V@Baader} \title{A �on}siliev1Ga�Ut�quasi�ve �t2W .�l!wHabR1ct}k � been9".\ny Alexa<$ polynomia�"a)tMF.re��"aJ��5 a���^ ^can�.det�.�ity��Gpaper�;p�"aY�8 aboutR.:��ori��d �$K~� �/ 0���N�[�w�2VaR� ��l���,t qual��d�b�tL�K$.5� \makeE A2(e braida!�Gconju`IE1a U.standard��to�0 I�a �%!�r5�a[7>V .���+weUx�i2$. W�+(Lee Rudolph"�qed6+�s (in P {Ru22�h�۝a�{e��uld be 2�2 w ��C$�&s, i.e.��22�co�c0x plane curve��!11K spW$S^3K!�.\C^�H�-aI�Fne I%�ny)/$f�0)6@5A$f(z,w)8\C[z,w]$@��h tant}�.2�F�%�$1 E2�%pB was re�lyA\@[0by M.~Boileau$S.~Orevkov!��"{B�hGVh?��yet anoa[�.v 6�knots�}3bTd upon Seifert diagram#ig*�#e*6K.���}�e���3a��e � � �� �L!�"�za �a�}\ (q:1}), whOmq;A�R�2bey��42� !�.!�I! !�tm��~1EI�u �1 quNoF) A.~Sto�Nw8n~ � St}.��]of� �~1A�]aa#Sof Y.~Oh83aC��3��-��ofV�N n un�� @n� (�_ �eH).�invol�E�( $C_n$-move���wa�g �fK.~Habi871 Ha}, see !v-/,OTY}. A spec�Z!-Pm;�a8<,in figure~1.�2 � a"ӈL! 2(n+�%endpoi�r $ e nds,�pD̎�  �D<7ed�($1$a� $n+1�r�Yl conne�$ outsiU��d��e���2t��:ngP5��QGk5al��cco�+iV aA?,��r%��XmP �$, we encou' vj~ ��a1�i�� d�^Wthe�~!1%� r��&is Y)�s a per|7�Z$\sigma�3S�:$,A���)� s 2,+]$�5$, n+1�+I}[ht] � ({-0pt}{Cn2}3�� eftr&arrow$ 2&1} �"!P{}� R IQ� OT},y��N$T.~Tsukamo�x �eff$ o.�on Z� -#$n�"eir�� }�Q .2) JsOb!$f�o:�=enumeO�}o3`Su� doeL]chang�& valu� r���\\ `~+� $&�d K$��-.���+ dif�byE��,@;$v�<��J�!V�H�a�(n $|v_n(K)-} K)|$]�lo%2]�J}M��.!`cyclic% of:G�# �-=�.�.Ig=� proof}�+:G ] Stm�y-]�"~"9 twist%r $5_2$I)�^I� ~2, � �� ��>� 8 �^�si��0�c�ing s� dUfs, $2d<qGt i n7tepC�� vassU1j�%�XS����{*^�_1$>  in.�IlA�*YCas�%$)+alh aE��� Choose � ��$a�6$b!u"��0v_2(K)=2+a-b$�>B ; �>y!�lUs�thY��2%�t$� M4�V? �V. <Q�I3B^!�3a� bigskip.{caVXB -���R $�Q_1-=).$$E ��s eas���CA��kR a )!n��Y^L��: \Z�JqYcross}�h2B$negl� $=lkB#smooth !� �'ed@������p`��� ^��-� of %�a�du�a triv\ ��$CinkfI& $lk�)!core+�"ngZ Q�$M�9.ex,1>� � � �bottoIC~3 is6� M�aBLis 2�  /its�of 1.s� p�!��@to�gle5WRpaiVA@,*�5q�represeq :#��8i,�-6�a�.�)�eA���arr"� J %�͵A�0K 'all'Qv5V��Y��BA� � "(�������e*�7B��aS ��m � ��mC_3o� �\s&a'Mٜ��$n=2$ *�Ha": K_1=�, $K_2"F $K_l=� 2|%�6wo�* ceedO%�Ia2���]�@is toA�%o�!�s��2�Js.q �&� B�2l.w��3*/  K_{i+1��:i)=v_3(2!$K_i),$$ $1*� .� l-1`7�A7 "0 5�, � ]2�Y3��:�  oi j� 3}Z� m �2 four"� R� M{.� * � {�,C. F;�� viewi�ifa�7-2�esA�VK�� �ze��xsLq�l&� combin(��pattero-Y�2( '�Z'&�� �nE%le,inxa l�0 box�WZ�i� , asBb /"�DRb 4} NZE Mo��h an cx >va|��� �1%�-")� �2(4�H��(- �mbox�2�� �~5�w�V(�;=�Seg�sv��&A��-shaped��!&=K��� "�j are V�5�� �R�$5a} \qquadpi$ � 5n� How%A�is�E�1� & 'TL� ificN� ;S_a�}���>tTM .� to�&�) &�;��e*%E�!h5/� 5 by%�3F6� )T~6.~2ڧr� M�T�6& :��ey!��ixR�Q� 6, togeth��ir Q1M�# J�  !�6YNU' Rb25">JJ7rh7vh7n�HC�6re�(!�:� � 6T 2$, "�NT��=\pm(�I IWsig����&�z is w�k '$-$')�maA  w��q '$+$'��b� ��&�  betwW��m N��M�4��a :Q��en�{d� modi, Q��eD%se (f> m�� ,�� �l ZXcalA� 2@Z��.I . Likewiq�:a��9 ;&� &Z E2,mJQ Z y2C8 �.�&E� d �^� Ŏr��q&��*!�? �g�E9�ywD��+g�*W 2�?�Y Y �end up~N;�2:=:� �hv� A�!E "z ���S� �  Aa1:�!mer# sketch�Ac� $continues:� $i$-thr '-�%o�J�"I�$i"y2nW !�i��V� fn2E z[�)�T5 2��Z: !S  � a�B�"�` :e� hear��B\ {�$i^2+i$j"��� arc��� illu��E ��4 �&7��8�@ $\cong$Z�8nJAt last�6�i], $Q:=Q_{n-1}�Sa�rJA6O}���!vc(%# 1&s}\~ B|AlI56vi�Mw& be "wi2- �7e����appea� >�i/!� ngV� e.g. 3?�.�); �;�a�DB�uneh�����%Q.�!�b����>�*|��2�e%2-+ ��0ZN��l�[2�.n2 for �fixed�%�� It w$"0!to�B� d8n��of�pe�fa�r�]urni_#)� apossibly8Yplifye�a��C/�#E�2�%#2 %j7͊$ mi!J�%c���6bT �y6M�5 �o.5�}.%Gm&.�endu }[(@textbf{Acknowledg��s "8(&�!�(�u�#8 erroneous stat:%S�#irst �%5�h�' . I )Yl:t�Bank hi�:�!dA� usefulڼrk!K /Jbegin@#b6K@9}`M"3/Ba �$�):� SlicPG= anMg� rack%�(s}, Osaka J1 o3h.;�(athbf{42}$ i25) !�� � bf?O �M.~x%,�u%�Q�-(ivit\'e d'u�ourunalytVBm d�� ,boule pseudoK&vex}/C.~R.~�:Sci�1r4r\'er.~I� J$\ �33�2f4.�noant De���!��=cB B�3`, Rheinsprung 21, CH-4051  SwitzLB nd f\�E-mail ��9}: ba�0@��4-lab.unibas.ch *c0 �R>�4two�,a4��$,english]{TcleT*�4b�B! page�2heas>+W4ig}2 5Hicx6�r? %\@4/ity{finY�% m@�ial{norm  %.�a�*at} \�&Kamy#1{}%\my {{��#1}�12�am"�5� myam�.amsk �.!�thm!"AeqnFV"� .RC6 myfnY6ol6<�+xsy>r�th� 3deu #1{\A� ial_�5�new��4and\lint{{\pro�1!qhrm{-\h�-1.1em�(t%:%`wto{\$harpoonup}!�!�5|1z!s-�a%� #1{{� (sc{[AY: #1]\�L1 atle� m len{� op{\�;�D@font len}\nolimit54�Lf/LJ/dil^^dilB^mod^/m�c:�supess^2 2d ��/!2f� ore,re9�{6 foot#F0}{\,(\arabic{)A%v{{v_*>,deriv[2][]{\�p{d 8d #2}�5Q-pB+Q[2 9�.� {\insert\� ins{ ��8%��� a M}pid}J$5��5�: ix"��)��=#a�,k�…2a want�+ � a�@arA��: $\lag:�le_AL"�de"e�n!wA��M�4 � �t�:eA�l�Hdistance} $d(c_0,c_5��!�Ÿ$�U �d\!�infim$�length��en(\g� )$ �2ll �,� hs $ :[0,1]��M$a:5�8 $c_0;5c_1$.!��) )�m�G}:*th!;v�Hg�' �$� ��he� �A�th o"6.K  � �<(f!dhod�!{>p�� I�A�s�Xoaq�E1z&[�#�Sver(Af ��optax mo6Zng>9; saN�(se approachB5r"n& ��& \Sg^ sec:.�ae&$time,!Or�^?much p� �O�i�W�@ Imag.�$�: via Ac��;W �j ic w�� u�;�Z, �K= �9!�#�[7.�$� �in% eq k xin �; ex %�}�  immedia� �A81 rpri�e�it "E0a;�i�q]ub�"�( associ� �A�ident�GR% "� stri�2E@ �describe7 "�<4Mumford:Gibbs}��/�2 ana}!/}s!'is )(%�'�%AYH-% semi�C"��.x�AQC� �Lgy"Za���e2��=�S]����: n ed 0}); ^�0!�thm.~. thm:"� W ,� �a�<\!� m��Aj_` ad ib�2FE�-$ML$ts�uma@ %C��#YqWey�"��� +�i��� hyp �PC��6�`)�,taDM{A9Nu�M nded�!egi�� " p$bo:9��Pa�I2 iZ� 1#� � ���on�, h['��a��w�n�!sa$ �5�a *� �6y. 2-"(Cw6' �eH-�dq #@�Sor-mFz��2E E�.�><!,);2��(fixSX/��I�i!!)�n��W5k9E��� ɘus;Bus farA78us��2�pr t (�e�CA� `�2� GV��L-�is new-b�"ݧ,��r��}d� E� k dBe��� "4F��%��%i� (I,� �A B3�� �o4EI��volve�'to �)th Bh);����",a�g-1�~��g_){3;aVz� ne�'ar�9 | �, �b�Ee\4�A��Oof-�,Level Set Me? } #zi��_ < q m`of�Ppu�Vi�!!g�.1J WeA7�� steaa52Pco�� e� of�gMs��at6 ae �le�]C e��ier)z�(f6 !A}q �a�Tt��J��  r�2�2e..�B!���eB͗%&!��n�"n�@��A����\o����l>:�#�(i(B�e!y D�\ngZ�E X.v) iv� ti!>�n ��}�a.p�yraa�!�use�Y�mI�:!���DS%�)#&E)�A�a 9�� a.B!F WeOG!�'�in�3$YM:eusipcoA��.��I�.el�ap�%Z �� hand��ew��E�w:,>�gekr� 5l'.�Fin�:�OMn��beaR !��ed.� m ..� Xg.iU(d7H�Pa}we�!9)  �z�ode�:f Banac�� HilbVJ�;|� �u �PLang:FDG}, ch.II).} Fĉny"w, v�����AE6}AqK_E��=A| vect�~6to%7 7; e�p.]bundl�V �~^Q�� '*�Qy def:���DX�a � C;jq0rm $|\cdot|$ �=s]r'*X(Q� $|v|$!�"� homogeno:s�:k!D$$ \lambda |v| = | v|~~~\for�%� 0~~~C9k!�0 \[ |v+w|\leK+|w|\]d(�,�%(�&is�?i�mto as & �b�� vex)=j�=0ilyq$v+}!4!==v �2�,a,�� 1Td,!�n =o�<��7 ys=)zb.�m�!�H� �� ric}!e�!H�# $F:TM\t�+l��!&� �*izeh\  $F%�� �c(0; �7l9ly" ?� ,%��{c�� \`!�s\`i �b tato����f�a dE �N�.s�6 , $vb��v*Da e kH ���.~%&?S�i2_ �: , ``MinkowskyJ''I!%! �2�KA?#r��t�-symM Ae�,� -v)= ��=��Ywrim�|v|_c�t�v�v�Sy  V�ecM �+<�- 'Din�e�K��!�ex,.YX�����1� Lipschitz�.�As sug $0 ��:� !�we"#avoidL� o&�rN��� *�� �fI� �*e en[!9:�͗��of? Xl�_�@ So�EaK tal�o 3 path�)lN��mM$�KVE$am!_se6P�open-^�d,�wh� v ��l�6 � . } �2{ as $$ \� =�d�$x�somuc%"H��y {�/A�)��nSeV\VIIJ� A.VQd�a��U�$a�](::#& 8 \[|h|_c=\sqrt{&H! h-�}J \] (F5 YieCvodu?(%�Z$Y$10IIzc>A�,we often dro�p the base point $c$ from $\langle h, k\r �R_c$ and $|v|_c$. \smallskip If $M$ is finite dimensional, then we can write $$\Ne�= h_i g^{i,j}(c) k_j$$ in a choice of local coordinates; c�matrix $D�smooth�,positive def��ub�` $\exp_c : T_pM \to M$ as(\eta)�g� (1)$-W %� the agMkh} curve solving \begin{equaA�(} \Big \{.P(vjFS(v)-V (v)), ~~~B � 0)=c.�� M�eq:� tic} \end� TA,(we may stat!7His extended versionA�aB(Hopf--Rinoworem �Th}[&%] �! S.I �y(\underline{i�} ��e�$connected,8�2Dse are equivalent:-itemizez\ s $(M,d�Zcomplete6# closed bo�d setsc*act) ��%ssA�e� [} at a��� (\ref2�)�lbIOed a�alla�in\real�4!�$%��at�hW!�pA�$ta\mapsto iI�$$ is well�Oed�) �|ny�`��Qand J surj��ve;\E�!s1���all.th�oimply�=$\for� x,y\in M$A re exis!aminimal 1�eM6�n,$x$ to $y$. }Q� �2ESub� s} a0 s�est exa!�sa�@ 1E1a7sF-Ta Hilbert space $H$. We|nk!5i2��,��H=E^n$, or2inv4we assumiatv�aeparabl�C��Pro�aon}m�sotto HaE�``distance $d(x,y)=\|x-y\|�]a. :�$M\!b et H~ij=$5WAcy view�a+�p%5,u�:�n iA�e�a�D G more�4 induce a=�0 structure onlusA)�� sca��product!�$Hr$is in turn Us2Yw1 ! ^g$,��ed:\eqm� d}�T�� $d^g\ge d4� ��^g6�Na�6&� 6R��e� n $d�4d$E�l� ly�<.%�ffootnoteA of b� Lndard arguments, see�m !s0sec. VIII.\S6�4cite{Lang:FDG}͉.d I%�4not guaranteedm�B��elobally}�,��shown�t!� �ѤEi�A��ezDank A.Abbondandolo�Eremark.6 u|� d $ M= \{ (s,\sin(s^2)) \}e3Px_n=(\sqrt{\pi n}, 0)��.1�0(x_n,x_{n+1})�0v reasMF6"ge 2$.��� Ij (ertain sensa-Rb���WanA�0ir correspond��j-��:a eed,!|)�8EellsElworthy},1��q[ -!-!tAny� differ� bl�#� e�modeleda�anA�R�Bz �(be embeddeda\an open����of :�-x� With !"ect�bсse{ matter�ithough m� a���icated."e � \� �} =v. I!�is� if�m�lete �Ta,� Roofq\6� s can!"� ed e�$v"�X; but (unfortunately) m5oth� mportant �@�ions conA���, ? d �� fals��T~osG Qm��due!}Atkin I�a 75}:Q�q,[&]a= A-V8�9�1W}[e��yV!L %ϥ�&�sALr�noU7 [��.�2 � 9�� au�-,C aZ����� �!�2uN4 , butA^1D two� s �Rcan��bA��  by aB� .B�Grossman�'�"��Ta -� also��a��� �� ���I  Si� ��� ��>d  (5�X dm-)Me��![!�-N=e_0=(!�1�)$� S=--6%�=~_iU����r�*� +N� �st )spd $?!�V_/ e_i$;A��[A5� first ]mbda_i>0Aс2i��(\l #)=S$(m� $\mA_ Len}�_i)� S$%> ��n�J/�\pi!7�xA�qx�x doesY hav� limit. !�No�at th�  weak�� verga�:k�-.$$� &s �~�$diameter; ��!T V0$0F� See��~��� 1�.�op�!te3Now, s.�$c(\thaŊ� mmero6 $c:S_1%6�T�w��$S^ɿabcircle;a�wW toJine a��y $M�9�� �� z� !� . Mfa Q�;; t�n"�T_cM$K0ay� s_��deformw s} $h�� ?@(��'ra�l,vector fieldZong��,.�s�n _ _!�``dir)�0'' $h$ will y` (on��order)� ?X $c(u)+\varepsilon h(u)!4�� :[0,1]!�M)��!a�A�Ns,1 n!��x\ a homotopy $C:S^1\timesSQ  associ/ !� {$w$CM[ ,v)= �(v)  )$ ņ( in \Ss def:y})A�ubQ��geQTf �6C(�x gy} � �we)lstudy�]paper �5 reco�P to !��u m�9&T�eq:B�E�`)= "=F� (j8,v), \derpar v -7/)^2~dv ��ym��hD)�d�cM%�A�d .�i�:�$c$; x)3*E�ba�te� Minkowskym`�� orm}��_ a ���Ta]is,��V failADsatisfy� perty 3 !��i� Y,U} o���T�of.O(5 rem:�I`medu4We look mainly!�C ^h.`A �indep�nt��oiz�i�>%{��:�Eq end,��W_f2RX5�quoti� of����_f�����,E9 6 6� �6�.C��free}O i � 9 $ (� aQ(utomorphism�� ). $!{,f}m?щ� �>X principal fiber bundleh � dA�\S2.4.��:�O ile t r not.���AicIxG I{�W͆x (asiH� eq.\&�$F = F phi},ya�proje�A��% mean%(yK e&�5�i:� %u:1(step appear�Tso _asi�$prop: blaca�gice� Re }[$��$M$� -�A4E�M�>6J�BanachI R C^15\t��)$!�� [ c0 iff $n�3$;�k!�% $n=2E�planar���is divi�inW Y m!!s e���HE��sam�iwi$ number}. ^ � "� 2qG�Hp}�!!7�it *vena�Ait!�a.�n��V� �HN\��to"� S��-�:� Abst� A<roach6genA� } A��-par8�|��, � casM"problem (#n ajset8 . TE � somel� 7 pertw �wk y asIamŭ�d!c.~ŝ�":�.��()�a funda��!rqy��h�rer} site�eo�Q�s��mATenumerate} \setcounteri}{-1} T {\bf[�-u# dnes� d��a`.�s]}  ԍ�I��W��J%A�� between&��is?v�znaG�$-�tsa0topolog ` atla�ӱ�P�""��$d$�J� (ore�u<m�� sidV Sof�pping"q �$)��K�=Q *�1� ����@ them2=�`$$C�BR@ $c_0� $c_1.2�C�-"B of+0� 4N�qEjre�ing]} S pro:�ica!����if">0�� we 1�_0,y�g2  ��� ould lik!�V+^$�� A su��(E � i�atA�$F� c,h)=�s^a F(�!�a$a�c0�2� 6UW��ask��>ml})n�ol:_ +�8+$ monotone inc��ing!2ň$l(x)>0$D$x>0$;�,W!�lE��inuou��(x)=x^a 9�� ��UeuclideaD vari� ]!E"]�?If!�ap�"an( trans" $AI!A�,A�1MNA^�b$ALAv�1� �0$F(A c,A h)=� � !�%�c,h�$ ab'is! i���B� iZ&t!&�g�ɁV2b&is:�� ]Cdescrip� A%�[��-wi�*ar6� pce� % � �� �� Axa���%Z �&�4 F(\tilde c, 9l $�b�" :eSa$ Kc(t)=c(�phi(t))� h h2 E9re>*�}%�!nA�[�B�[ Y�$$�.� C( ��tv)$vK $Ɋ"���, "CC^q*�va%�e�a�md U�$fixed $v$.}� :{B� P , $E1� C)=E(C)$.�mU$� writ�v#e{\pi_N h)F i J(� ��I�s o?��� "y eaR�I�� if� �@ R� ,a�n�!� ox-oj) CI^}R+A]~*:� In b�-!c����m�&�%�&re%M � 2��! y �!s�->. -� last��$.�t � !o ��Z 1,2ea vali&�)�킡� ill �;Hy 32_ ���� �m. )%�0*possib)eg &X!�%�9e� ѵ�geo��q�1q!B� �� 1,2,�cal]#a . B 6e> � %�v "e~ Z -u2ѣ$E�Z�a��.-/a�0 necessarilT uE�AaeJ� it�-�-�%��A%�%R+%Paq}}Qa~$M$awe�! �al� �7pseudo-&�!}1[yAI�.Khe�a� F��!� r"7� $nonetheles! �� -� &�Th�# ���be�y]m�pp"�#W!Compu�$ViS. 9jS�i��C_a� %J1kier:�Vwe do%�R N� mVL$Q em�bp/ra3.`�&�-Z]A�-�rsh%�b� /*�%� roxi��ou�2a�pur�s #er.zut��Kz� !�N$Ł�.�A��n� . *�&I � a SobolovQC W^{k,p}(I � $k�%nBs.$p�[1,"�")$)A��2I31�&_ap1+e� "�'fun�3 3_h���_h )�.����[��preserv� �j�3��U Kl Em 7�(��%�p ;x3�e��/�" vK �maximum�leEAI�-follow� 6i�2�aP$ 2s - h5$c�et c'e�m� $i�,n6E'�0 reg�1  e en�"/c$:�+(By Jordan's�" �A~�'�Ny9 KAn�2�$ iea�e wo �s, � �!��� e un ` �'� c_09 _�!�1$,�=� \=�%/�"0 Nr $C'$2K ci to!j_1$TLE#$C'"r �C`$v\in�o  A� ��&is� an�z2 e MM_P�l� �� �}e� >^/ .)#"�"�).�a5a�^e��V��$algorithmsAF-#)�@Level Set Methods�. \G5rk{M: �6c�Pe:r!fv��!{vex, le�P c#Y6#M�$L c'_v�v��!���i...!#i��H)Dde[e��y�{[q7it�a!� � �_.�e� 8��` -Z^�i&��%�!�eA�L,- e imagQ *��]� ![+ai�!,s8envelopC a�3� A�9:[�l�ڥ-/' a�K�! ��c_1=a+%LB��!�a�J�!A�uh+rm movE���f" c_0( )+v+ !R?' oi�;�VM�� �ro��A`.. WHAT?�  asona� ex.�#� >�4to Ie??�+ *� SoO�7��4:%*k S�8� $�~"UI3\m L/ to w�Sh�+n d� commun�-!nory"�n w 70:TheMatThe} h!fassert�10 z���3od@26co� nois� c�el,�out actu�1 w� _"�����&ut�. }� PiaJCo�0&��s� ���2e famU ($\mathcal G_�6&� �r6<)������$M>|2\is�  empty:g3)g"�% By�M46:1)p seem�}a6)�s.�� s��PM��V0F)E��!�L!ig0�%A8o carr�%a detai@proof�j D�) �Q � $F\AX9k,����aF�*L �, 2,3?a�5� S�:T%wl �i�t�,r#�,*3�<@c f\big(c(s),d_s  �-�� d_{s^j}^j , h+" i}^i L) ds +!�b�re�G ship"��6degreA�i,j� !=n  /�$?�U� }u L0+"c3� ach3ndB ult6�$� #}5nowPs)'�  � ���at�+bT�m;9_j )�5�g8��"�%; wAst�vc�� �'to1�%�n��G+&�%}��%a�n}0EexeA�  E? :ya�ob�W�0�&�� to I(!�har &k8�'6f0$H�vsquarzE���"B ��#h�,m�3zAs�n%j�M�: � 9 PW"(non- �ic)FA $H^0 z� �*! ^� l0 $$H=H^0�"�n)=L^2:$endowq4wf31 z6�F1h,k*F1a� {S_1�C,k 0��d4O(Beq:�-mH0>?�*�?�%xin T_c M�e����on-�a�analysndY7$1s%�}"�+. ch 2.�#,WK:RieGeo}, <"*l =�2fer-s a��!�end II\S�+:Y}[however,L m�A�m�Şt"gt)�&c Bgs9 '(ŲD�t})a�-2���B$!)�orea�1:ic.1M�I n !� B�*� *�� #� {*l��re�n�a�)# $mi�/>: `1reb AdiscretC�ml*�/:�6 {nm}�> �:r�,e2�in�D } take��� m!~RWaB0^1 \J�C\|_{H^0}�3dv�= 2{S^1} |Jl*� |=  E)+�����.�� �$��"�*\�1� H^1(��,�, /" TA�*�,Ic $$E_s(C�(Gt_I |&1+C| ^2 $$�S% &z># i�a  straJ-zz cause� c.� En�(%�C� b�J*9+�A/H(�m]F2\p�3| �= is�mE9 iona +$-}$� ;7I � need�8tok �#ie�G �i !�I@. a�W��/��� $$H^{1,0} (I�) =9H^1\Big9��F� al^n�,T�$Ij� o!̉�< � -]o �.]E�ea E�/ |If�F,v) |^2+.'N!~-oQ� .��!cB�6`c9|9�nk : H 1 0 �%v0#i�1�9 -�)$q*ll��M *ies�!t!��*M�-wis }�Ev�.u�;.��� � m��0thD���p K s (b�op�& care�)�nd2"A�m�� .xII�$U-�{� �5�)Bcoerc�J(� �+��oi�So ~$�4a very�4R�3snamely� �!AGa�BterpoB � $C^*Y�= (1-v)�$ )+v c_1��\� A6's�0��imf%$i^6� !n�6Of� 0^l: k(s� ds%��]�� |�8 c� |q��e �quasi Na}ej.�� a$A�lengtha&$�3$dsEarc"Q>�3�Z!� �=�I�� c$.&� �  ab�$�' �_!v}.:���A1�0tu;ME8"�+$h$E�$k$ah�ɯi2�5!�:�2O0w��$!�L(s)Oarc-pR �K�%�$?:[0,l�}(l=\len(c)$)%: pul�R em back tm �1�>"H�<rite �)m*� $�instea �'( � �/R -t� �Z$A5u �:�.%maN�%t�5Vid%Nu F�#A��� } ���(N}EL^t U B�P)n] �on#"��lif�it1��S(� �p:l/A�w�n dev�%->pr�5 ic ��0ns����>�~.ic� 2���D!�� :����#�� a"r�ٙ�i�^�F$A!a�*e� rmal��$N�*\ 2� T e piN�+ From�oneM�7sp=�50$5�ajA�� D�d#�2iu . +0"$"<�T�ly /N��.!�&R2m����4%accep� u.C  at�orthog !/�9 �%>.��`�  akto worka"he"�4� Dq*;��0 C�0�/"/ ub- :X aNitselfe���9u g� "�. gmR�E^N� \defeq� {I}� �&ͫ v C� �NC| \,+ \,dvE�.� E^Fic�Ri���>%� ���� j�5p&�L^���!�"v/?09E̍�� ? EFeZ3g"evious�~f�%�U.IG��>1����7:Gibb20� ��.�� *X�0E� s, sCaX[�!Q=0\O+��Binf EN 0z9 0�:Weg9�:.5fur�a#�*�2ana!.�V&  goodlEs �Kc!Qur aIn�V %o�2/ e�is1)| U�d� �. NS �"ecisee$@%aNmplici���0�!k)uw ,ng {\it grad�/flows}�l��Wdm�"�alP%%�$vast liter08 on shape optim�9.&��x(@$E%n �|5ic heat�} ($\-*ial_t C= {ss} C$)~:`5�(�+>�#_v� �+8nd so on���%:f�% deriv s } 5w�a)� evolv��!�inward Yal}�D� ��Bsig!�%=��!�!�widely�J3P�#a6��*ent%�Eu0a�@� �al. Itse:��l3*�to��sprt use8:�5�?vV'vV' !L�pro�(ing�Aly �M"�in-NQ�tru)2�)t"�L @�:�Gas�se�!"�$�cE� on ( $L(t)$ deno5A, var5;��!�!0!�AL(u,t)$%&N $u\P#� ��narray*� y &&\hs 8{-2(�DXCm?�|C_{u}��{u} \\�I '(t)VE�:\frac{? t}?&  }}{ T}�{u��H8:C_{tu3 s \,&-'tWs�F'C C.%ssds �R -J~C_t,Ci�r�3e9\�A� �=9hCE M#> Ainner- �,n u1 �La��@"XPSF<a2C o  l. �3qK fe�c#nokbe.��e {\em6 }�R&��newzbQ�% word�..� �b �P.�7� ider�d �PatPS�Xmcomal�:�>�<K =>To Uc�!U path�8�.:� A�q6E@��"= )�y�~Pa G^A_c(h,kVU�@(1+A|\kappa_c|^2)��� rD": u":  |L(u�u �eq:G MMU�}on�(&=�By�D�!���>��E$A|6isy�;`M t lizE�z .J$JH2CD=����i��*�},2@]def di H&"&^ m1$� �e$� i"� mY�E*p:� 3e �p2�v�:]��-�9� E da%� E^A(C).� �/E!p|E *b�A; | H ) &�C|6g=) + A ��� � A s�9*u  $��v�1]V�F.O]��a� �uss-�qFa���1v&yS 0stava et al.}a�SEC:SRIVpT�'�I�@w+U�A�� 8=�ed���, uIE�! $\xi(s6R2$. S�RA�� 0re Lipschitz��..�.C\in�5e n $e�\xi|=�+s�&a:4�� ityB4� �_����#\!\co�(s)),~�W�')�j ing}>�to�! a�"� �*�J�:�5�� il:�ing1e��+ up��ad�;of l�"t)� �9+GA�eger$;%� $�+ � ) - ! O� !{C�D �D:�A , or�^"�(hFx� !�$��e.� gKn�0� � �p&� to a�(�+\xU~Yen ]UEq'&50r[A�.Ae�."E$, )[ tran�*,�/a�s�6" !�a suitL#�c�d�b%�(�b $s� !p]�02�wo�@�/.��Dy�$:AnalPlan}�$g,ni7A)� ``Sh� R1 . OD�K FuG1''}���ĉ�of�e)-As�O� �/ ��t^$L^2�#[0 ���GM=�S)a��#( ~|~ \�: !)=(!1^2,0,0)"�S�&M�- :L^2qZ^3EF�byy&&��V {^} �(s)� ~~,7c 62�>6�C � ;6:3j:sin2:�'y&�Q�e $Z$1m�1�)�%�s�1z flat�g;� n @ul1' !��MOCminus Z%8&�N: 2V�)�'A"�ofm �: E� M�ta<Y n�,a�&Ŭ)�Xn�'endix2p'ds 1^b�5b�Y B(4cit��tsd,W`e:�2�I� *d`�co"�5�9n)M@.�&�8>i��ai�6e (��%� of)& � 6J� 26.&�\6� nher�2GG"!;� �`KY!�~ m�$;d�ds�ob�o� d �s M�y�7me�Z�2E�S�/M$H�7�at $Z{2(�:, ;b�`-b. �fdon't %�"Vb^�U$> fal&�catego�&ks5@K"�[� �Fo@y �1JF�Jp�<�]QI�� l ��i�*[ R  ��s . t))�a��t))) dt* un��B \x Q$ D$�,nt�<a��! �(C� $QAN2� ) "��p*��-t�c"DmaQA�! Q (0)$;��p9E�M��&�  _�i��&� ��{E_�=���. $SE�.�,q�O_ $M���.U sim \hat5Uff&� )=��-a)+b Ba,bN4H3<t )�# :�df�� (-y�quB�-�!o$ 8 iK asurA MI�: {�\arc{�Parc�5l�R� : )I!)in8 �B� �i(]�2�)AW(�S�#Borel�6k �=$((~\7(V )(s)+a�d,EIan Hsj.}!8eth���5O�+,K,� : SyaM-0 $A,B\v -]�%0 $|A|=|B|$, $q�s)+� ({!2(bf 1}_A(s)-.B� )Fllf�-���M�e�+�ol&y $A_� �y-�;2Nt�Ki�MT�i�+�8n advisE,&�#a U�"ta"� "�bz o &C hatd�(d(\xi,\xi')��f_{MBin �� ' {4}}AEl, ')>(� d-�(=\| 3- '\�ϡ�ltern�[!Zd=iA#!BFon~!�JIweL�s2�nd�fU��:�isM��w6��<oB�� � �6�H8��I&xp+4 ���]decyQ� a�ph*� =A�^2$ }�QGYg%�Q�!�Mqae�, �]� Q(*G�A�mum*eI8}� gi� br =>u<�u 2"$vUE�Ex $. M�_��Ie;ximD�� �6s6p�$N�itg � .I:�9��!�!R.�;edP4"_i!��4u�. m�~ "�h�H�er$)�� , �E$!,��uUj�}�'A�en92���r #&U�,a dens�6;N �2oHig�g)\�+>�"e�.N> an h.1�i,!iA|-��Eo4mimicD#aB0$!�25 �S$� *ZzslI*4�1�XV 0}+ �h,S4?0} $� eq:H�RY,��W��g�k�5&a7� s, "�&\ !B!#u)��RHS! 9�x X ��6 ?"+%,H0A n$vc67�"�O�B@���� n6=�Af�B�V3*&�#� ��� [H^1�Z1L�1!^&�/H9N i1 aC$ar�1(�/WI&G �12 ] 4.$E�\ , fJ -2>�r\!}N�6Y�."Dp �&!u� H0}. 2S$_<Y YseQ��|"va�P�X& �~a*�;A�})W�G"xofi*`5� :��'DA�b&�MbexYounes:vHi&AFin�4�"6�b���ex Fin} co�h�.� �wo&�of.b[�\�!b�:u�(s"&#cA- tly)z !�&�#� 2`$L^&ZN$ HausdorffX�cish!���3A��2�(�$�vedF$ &f\2�Z |mh�-��� jF+c%=� h� J$}=\supess_<� "�9| �jk1����1�c�Z�2�An;� �\Len �(�!0^+FJ~�*�P| dMz\�&�j{J~W9Pv)6�:��d_H(A,B&� max "Jmax_{�jA� x), �vB A,y)@-�j��w 9 I � ^n�Y,�2� (x,A~ \min_ [A} �!� �W\X"kj coll1>%tl�Jl=A�ets�8n�i(Ak=�nyaj� ��"�u�]&�toyZv��� .�-�5�r.z*4J le5 en ^H���eqDlp_TmJl^j!��wVt_{i-1})�  })Z �supA�Aiasutq!0e19$ $T=\{t_0,�#s,t_j\}r�i�$t_0\le $\)_j|�m'�3$ $(\Xi,d_HcZ�D!o- .,.4 Pat: $Q�a;fA�91$\� "Q a�M�"FLip�  �5:��Abc�^(W B$ }8bF .���M� KA8FJZ,A�M���C*o0k\S"T .N�B9vjmE�� 1d���y1)k�rR�k }y]��9/KaV ��TA��$; a�=�i�MN�]; +C� !��-Ec.A!a�=[nct7 )o") �4�7.�_c$}; 9�7�%�s�,g+*� `�:�_cZ��:A@�\X(;�t=� m)n�Dr�H =:�Z�D��7ts1 UAFx�U&�Y�1$B�a+M%2��i�� (�N [ot��ez")�c$�>���E ���P�c�p���to >� ��"�w�z�i�a�i!s�N�}� � $Im(cKMQ�� Ya�G�X� a �Pa�jɞ��Im : ف� X.#3' �-#! Q��?�,to�<atx2�_7nw? � y)$�xJ�d.�j&V���D�. .@.��ll*�Our�#ni]&���!I|.b�^ރ+ �>len^H��)� e� larg��!s��s A�"�2,1"7/6Gc;ide�R �uA _0),1)�?)�is �puseful3vTxI�I� g�"l� 2~>x�#fi|"woI�A�aB�vX�"Laf4 s|xt�a*Oo�KugGs)"�e%�F�O65 �i.�_m�. G3 �D�i,Faugeras:App"�)ZQ��r&�Tm�O��kK$=�Hm�Aj !W*"6"� a�� rand.X�'x#U&)�j�4a" 6�1|f; p�! o_p &M $�E�2M"� $f~.�2� aFO$ed domain 6sucF/v�1oI6�of�/ s. 2H)�� �m�~��lo L:eQ;>��.Y�c_ �&Run?edN]m:[NTQ�z�c6�I�G published�)�sdu�AAX$andro Duci�K�&o$L�q� Plateau�bblw/aw>�-1ic�n�BY,�>�*e!1A�ric��F^1V�1}� tF�=0�(&<>&;>] ��.� ��INW7�<| q2 �>dv\] &3:G���D�2tEQ�`m�}\�oɹ."|:s�DU�6asO� gniz�J& surfڄ areaa?���# (�'multip@5y) Q62a� FV �'Q�$4RAz�Q �9$FA���A b�\qaeE:�6y�-il n �# I=�%F� � )� has �Bb&"�G��_0 0��>�v (4��O7Ssub� upo�Fomenk�p���%|He�<f (:pi�@ �D {Ba:�}�&y�Relax�%(um(al6M� &}U&k 2�$&,$Z^x� ���ń y $E�6���sACa�48f V:sAreg;g_b�|��Ngroupa$f\F{{\Omeg�&�{X�a2��, A�L�"��tau�! $\F�> et X�# f:\F rea� �1_��is�lower�^*F } if,� �xX X2$ \�z�,y\to x} f(y)�g f(x)�&�&,� a����j �N i],eH>int*��*�on�,: �R��2x8ly �����_n�6�n�_nB���Q��"I� $�� f�F$[t�z!)1� \[1: bar 9�\]is� supre�c �f'N7$ !^�>�2-&M H  $~Ms$f'.f� \F$.�4hP\>:6A $- _\F f ;i3��), 1�}�Qo9�}�wC!0�um! sLn�! �cx_n�[v}�R.!�eV,E�� !�CA5BI9,Z�kf�$ f|_{\F}=fO �XXE�"�m��  ``�^ "�9s''�� ``Y��2(�@vic#sa;*1droړad��DH6�''�end�� &�aCor q�o  $f:Xa+�f: Zedm c�H X$�Y&t�MZml��X :an^1et}�Q�"NZa� /set�b^�+"GCVal!�A�� PI ��-��9r�:���iQu c?et� }U�U�dC��-� � s �rC$ s.t�W$$�]=*ZC�y$$H#.B ��"d A���*pi�}Ye=odern-��� ��}e��5e�� at u58��9�  ���+pplied dM0�>m(>Z�Und*�?exa: E NBE9�? FC�8no9""�4wmY�� &_< >.;~"��s"C'E�����G���or���� &��.SM)REg[6�~�C$m#; or��9T,c�W�N1}_� {loc����,�Q�"�)��%?ve��I �AqA%6l��n�U )4�Y �a"�;ntl~4T6=�< {�v }{|N|}�OA�+b�=��e� $T=0��w�7a5����A��[w�a�ar��, $N=T^\perp$�2nkv = v -� v , T\r� T��(��U-BTBn?so �G v+�8T v=v��$��+ T ����kWB� $N$-R{^2 ?�.� �fER����JR> *GE�m"�),�TA�L&�$��T,�H:"Fm�{nC9 n})$\$&&.A ! C^{1xռ^n)G �� ed}A�\8u|�;at b�.�=<�"e � alway�z%( �V} $s$�a� \[ds= &`:u`|G���!qq�� :M!2g�-� s =_@ 1{lR@ "��\]��rI��(idY?�~-H�{6�!J"WA�B<al,W� 1B��@�&� e�ŵ)��B=}��"C�7:�6t ,�<WFe�g>�C �=$�|n; �"�UcE�value��4� T=!��N� fex�Usic���fo ��Y!e: E�W��(isstein. "E>���."?K,MathWorld--AhLHolfram Web Resourc���8tt{http://mathw7.w 2.com/hghtml} }:a�y�p:�F�W!I�h�:!�%$�C-n��J [Hw�"[>�m)e$Cs3�%Yq��weefEi_m�h2� ��hc$���[H=&M%s T� Ta �igen#{e�e sa P |e:��a'?��%<:���e  ?3 2 a��ScȅM�5A�Z�r)u�sNs�8I T�8q�s8,(s)~d�%6 < *�8., H(ds�q ~~~~<�>��C����  W X$='"���*�9\,d H=M>� ) \,.�� ;��-uYci va il6�$?Te *A�y�E������5K�Q� A�A�:1�is  ���s T�! ds� �+q simo��\S7e \S16-':�>i+z�i0*�"�y?$�ALZ.\[�H��F 1 {|H|^2&�^�H\�H��R�N:�Na�W�! �ᩥi� � �:]?TR 26�^T�S�sl�$ �T"$ �3H 1+r�%(%A *� �:d�>�PE:"} dQ  ``-Qspace�n�F�.''BaI0"7 _Q}�A) $N�  T� !A5\pi/2��c$ anticlock�W�*res1h�T$.��"�j�ny5�Va�5|�Gz N V = N"3 N,V -�$~*\[ |V^2|57" V�.eU�&�E$|H|=| �|�leO�h�{ ^2�%uF0\[�u!�) N ~~@{�b }d� s N �I *T ~~.\]J�-�?` �ae!���/�-!Ad- H, v1�= �Iog)�fDŽu� ts�e΍^n) �.�'PFp|�& |HPE�v"�/$,v)�D�jl�4n�;3�2�KM��Tq�@$(n-1)$-"�>aG�ub�� ���21�n&�H@��]\ ��{{&F�./i.��2�#"�$Bn4 v%F& "�  ^n:�i�B"� � �=�n 0� nd1� �-��E�s: 3e� y _�&I@M��$d !*�F� by �RG�.u�� aa,y%?ň� ��C$, is�]ngv� � D /y� Jn!�c!)mvZryc"=MXfi�|m'"b when �� :� � sb>�piv�!�5�2�� m�M�M�-IHa�We.X�� $H*Vs/ �p� !M�,3E�=_�%MP� !<)A�a;a89H�\$Ie��e �a� '��< H(A*%u 0^1_v)dv�q:��YBZ�A2S�K7� A$. ��GN�d�ti"Y�#A �&ula� 27 U4f� �b VG >&� *@ *� ,dv�� _c ]x��*5M  \noa�nt&�&�y���+ �en(C)(a�!�LV�"�K$$ so� �$(C"�K�0+���%�ve� 2�PreVary� Bm7��./ Re"Si_9 �: E�ye� �rB9�a�o $\widet�C?� }2� .(9�=^��Y� � C�%�.XM����>� "��A� rq��$�Im H��T0 �c��&e�AtV��U="���P 6, %tau,v�N 6 F �9:!hA�.UfT=uT� � }(:p W) 8C�V� pi_{TN}Iv2�F��,.�)*bi pi d�[�)�f�を�T��Tj�+"�A�.� v-G2� � �9�T��r<au2B[� }�mayK7os:'r.�e��"wO�,cas &��or�"�.= [ArcC6L�l !�"�<�q�&t�J&���9�.uuB C��+� � :�� �� in~&r:) C h� &-|-� q}�N��H?�!�lZ $v�>`+&��$l&�0� .�t,6z2LYN|=l(v)$a2M��J!\8b just1�iV[q�}�� ��L{�� C}��0^ �"�'�|~�Fv]�i s . OE �V hand�A�:�to Ϳ�[�}qC$� .^� A�6�cg��An�.."� �X�da>W*�< �UW!]X�.7^�~F�B���M� v�G$�'%�&oC#�7�7��lle�\$T�|so,'>3� -{�" C&�}/| *"C|;J� � �� P�-��� �ONW 14TsA�-yK�i F�(�,w���^.�.|�[GZ� \c�:�0)=i�_��j`S^1%e~�m$eq:def_di_��_@��1.$"c� s�^d� .-�,:s$$M�=�5V3� }  periodi�j��I�c"�24I[��a*ed:U �u�\[�:"+} M <�W�8y\���e :��$\psik"� )N={A $�-cq8 vQ�*^A� vXJ)� va=U -#~� � *a= M�Vy c=\\nps� |au<(��>�\><�� Q�2=sY psi�a�5h-Y�2f �}psi� 1}/�pn�aJ�-6/i��.�#5 �� Kb�*Q H` �%eXG���ch�#Z &� N���c� quirz!6cC�'�"œ. \quad�,are&�)Z�d��2.8W:A^ 0r`�. ��(�Nhoriz�Ql�}�4it�( cano��!9�el"�Y{+7�"�i M.�S�"X"k!kunit KM�=[8l�P.�d a^S2$x$-ax�:gi�:r�ly'& *M y+$: \[ � IP�(v+N &�V) \] W�EM er�)�'�Lq$est w!o�� izA" ]y, .*�y4� a mo�C5��%��"at V� G" )j . Hsz��2� ��$5���ac�(��M�M!�.�)�s (kd Dz6W)�o&I � �on  K=�< b� clusZ6 �f--�2� R (i.e.\1Krad���ion^�d./Y &=&(x, y��. x2<v+�u (1-e^{2v}3B +(1+ Y��2{*+T 66>�y2� �2 e^v Y��n�j*�dI�ͮ �` fig:)�}�W+ mpar�g=kQ!�tra�(or�of�B�kE<s (� "s $i�$)]IF�Q origi#Uld A�it�Lh m�i.6F&{-f�}[htbp� \�herv � cR��8� widt*��m$�_�on��o\hf�&{$C$} 6� ~ ucapA�J'a.�� �{Fn�G�2,-�W^!���I}���� G dot�A line g�U)���;�ߛ` ]�I�-� 2�� �.�upA�ng, k�<of ``� %�'':hC&�� sugg�� w�9|.H_���o"+��! neg#F$;+��p*�� ;%�*MC$.>W;"�jѴ�!uq �� �d6ia�7m.&��"2�)�%`����U��� )f� x[ etch!p�E��,�\[�'bA_F*�� + v e_1  "> jy� }�B�"q�geo03_st �R qH{S �!9> .�A_��� �*� &� Af�UJ�v#F., �4�(tP� s $BN$ADawdI,~<�P�>s>�K$AOCs���[]e�i yq�E�SCD$a#"bsorb� 4��B� *��!i�$�� f�e�go\@o�)  w ��-�v�=-�=2�#C,"�%$ �( �$C, ,N,E'r ralu�)A9$"� �V� �"&$|J�"A&|)q1��%L�"' � ���B�,G.�Z0BaffݪUa"G� ��k �}�(.�Mbig%v"zG��!CAwS�*��J� es u�@a��W+�n�B��� R�k"[ei> �E�8pontrol. $ of�2�6��.�nd2v�B�$y(Kf4 \newcommand\C�[ b C}�;Cd�\C$} G�XanI>��E"����6�?�VE.try�fI *<$A �:iz���74energy, search�u��c�� �OedR�+*]�% ��>J�% \/�A� 4�ll; ie� $C:I��k��xti�Ik#IE� �L&�K��S^�� (0,1>�J!E�$c f�%�.Ncl%Oum)xt�$*��}�iG&u� /�s�+!��e. 45����"��. [P�H ar\`� � lityn ���f��}g-�� s $a',a''�&_"��Cg;C� l�,�ьz p��.t \|��\|�X{v�(I)} ^2>a'+ a''N tW�m�8o� a��� ��}�E6"-�..9#dEA� bb F�ga�F�Fk?xUcribed&%c-�PIn�A";&(Z�va� �our%!OvO�� *a-a3 �y�� IC}�Nfixa�W,�D�v.uH&lC al^+7re �ctD�&�zcL&���h]|є��c | � *�}J�AF"�- �F!�/ @A��l�3 $A� �H�A�[��\]^ �o�,M%E[�!� $ , �B�%_ t.2�BbZQa l� C},q  $l� )H\"ol7���� �A+�[too poC��AfLm�� .h^W�[ �]fug?�U:q=5M%cis�c�kN��)cQ� nce �g�7p}�� le l!�6� )���.� UU_�W,vYW9�h,I~,v��e.!� 1�`p* if>� _h \wto V�pa>��L^p.���J;p�H7 T� d � C_nS^*U-*N 6�X���# nR|V&D !.eQ{"�� !�B_h|!�X l$"�!a^:=/F^N�n�;��n�s�#diatly Ӛqt.m 1.*��$dacorogna:AxA:e� � 2��4([�͙T ]A�I}/&�sosq�f \֩F��Q�>�. y�m�f�{u�ove�E�a����p��& 0)8�It.�1�re��e�.B EE6 (v��ap-*)[�j&,$(��t� WC_he,C$w �)w��.�!\��G�q�a^�:�,u:�<�9�R�-�)(58O�.8%��FcA�e)�iU�&�E"; �,�e: uld +&a�� �G Y� ofE0u:*e&! -s}� fix/Ր �.l)P��!f� mi>'�&DN�.A�� v$*�ifO�  $EE"�OaL?yz5�<�(�e��D�lZN�/>(�%#&.�>}F�6�E(C��.#)$y1�><Fa�;� tJ�� ��3� iw�1$�.X�&�W|\av �d! $�� %�(v:)� �GA FC�u��\lK W(=x_�9b��it�\ � Y@%�*&3 K z �iaqC��5( S!�� 2�X���F�+ au!�n%$ ss8%S23�" F+\tau)$, ͥ9 �< ��1�3#�per� �" !�"ZI�T2�EeNe)�6(�j)$�!B"�b�1kS ,6"�5 ���� A �� n{ � $cv�J-K U.ificant;)*y�one dl x��velocޤ�2d;��Nu�1�;� Bd�� ��"0ly��FmI�er eq..,,F ���a�WH6y2�n�}$}WHB��� 8�� fF3����fx Y"�aL� �ԃv�:RZ&{6��s�( �o*!mb$\� mi����7� of#+*  imvS!�Sa|�X.��?%��a_��N=&/�" [winjl.JJ 6jfcy1Zo>&���>I9*yY�KFoi�en~$i6���K1g�Y�4bnp�D���hB�d� M�*VK*6R Հ8CV�jn3���!�1k%d����$ C_ky� �3�+kn v�6$6"kFZ� !'\[I�_I�Q�]� (A�\I>�7�ɡ�ѥ _0=c?�H r � :�crT*� �I|al5|�.���%A�(�=0�d� !�UE^A�2M!��kG6 L�a�;/�S�_k|I|a�? $� >�"��M�i&� Knowledge*T�^*ʰm w�Ai�sAly�Afis�#A�}xa� *� �1�.% �I2��� � u!um �<�^�mew�"&P3�[l"�&c'�a�B|YB:�v#��;j"R&=�A������l��)�<%de�z3�9��� :L �.� �2W>�M�-��0) s"����B� by��7f 8 �!��� ~3.3�R ��ge@\"gsV�7(v)�Ce�M1 2k# {a$.9  �?Mv C�,^!�� C�Zdh[ � 4T ny $�f v'%@2��\ -^{1/2}�i+�\ � ~,%S �v''-v'} 2��>���W��i� �!�B�{ �i�}}2  ����*�-D(by Cauchy-Schwarz� &7,.-A��a 2$% 1� pN��AԀ�V�⥨e��.���.[l.s.c.\� poly7x"����W,5Eq�.vPW�NV�Ya� F:$n�A/2��d�� minaf !2a�2� o*�Satrix5B�{J!�olumnzZ ��^("�X!�(Z�@"?O2}��*g!� [f(W,V)=g,��?%wrFF$gȆ ^{n(n+3)/.O%,�x���U�6P& M�2��iG%�!Q�ae���.b�Gund� �\ 4.�$buttazzo89F�c}�~�kn 2.5W5.4�>�2:��|TRp�C � $f0�5bLe�� Z�z 4.1.*��B��%����> I f(�Zɵ C, v C)"-PdEH�-�ly-�V-semi�i�*"�S[�ly)B 9*� 2=�c mI�� ��f$ &i B!Q�"�A\i���� ?to�6~~��.d ��1B,�eq:vcreV�E�xJY�sa��tU�*sor� hi��"# w%nk!)�Re�B!��GG!�A4S@f!^>_�v^ �!�ga��o�q �b��.DY&� Nsactn�6S�"�&h��rG&e lemma��M'L�a�=a��=con medi�- *�p �B@ �|�nNv) �:�J� N�� _% 8 �DU�6P? |^2=%�%��C �6}�5 (�H.@ .�?= Ol!�9B2C (s,v)~ޢ�"#�T�y�>9HIK��% )�)�"^" V� A��!A-If�s�!$Cn� $D>a�A�Re�r |f|-[ P C \piM�) |d ffe:� �6��fg� inǃeft| f-%g f-D�N& |==�f~�3� :�h, a�B�k��� 2R�+a�A e)�!k"C�xQ�6� n "q !�!R=�n�L^1J��Ik:zA2 ���sS�*�Q>.�S^+�A�(6*)�� $$b&= 2� T �� 0�h C�ra_*2|*$�so,6�P$M6)0q �Z,]�!& E>M�e����uderL<arco} ho��sf�O�qm ribub ��}!K�I6�Q��V�)��<}o-! v 2x)E�%)jO� %�E"@)2�l �8���A� � e>-�(>�C){ge��"�q �>�pi_N_d__"�fc�>- (NZ C MK2+�P = $.��+��)`/ md �%)`�c�B�!>6Q "�+r�6lP!�2] )�-�M���e)� �6�8.�-�J� �~� MU'*(�o'�C�Y�Ja� �B"� \h��$6 )}����otN�5VS��3��(.�%��%�H,QMAQ5�u|�J"6 qcG-�6)on H CE�B� �l �!��-xis�&0�rBu6sm�RR� *�?� �un|�e�v e� |��."� )U,�N{aa�;B4� i��:a� �� �X|F� !� e \\A�,o0o�^=�� eN +a| �.*�)^2 d�oѿ2�̀��a� +=�.� ����m�"�a���eb� .*Aa���dO]��D},1Tu��$_&I confro�!E�e�J�B.���1��J2LTF"�2,�fi4! [A.zV��X�lWjeIzL^2$b. (�(){�X �2a9�Y����*a"��%_��M)�>�6l�@�2�� o be��UeUt��1!�Ks/j��A��$� L"�ox(inuity6/ls�����#  / a{\alpha} b{\bett{i��W \a>0, \b>N $�&ہ, def��ine \[ e(W,V) = |\pi_{W^\perp}V |^\a |W|^\b \] and define \[E_{\a,\b}(C) \defeq \int_I e(\derpar\t C,\derpar v C) \] Note that $E^N(C)$ is obtained by choosing $\a=2,\b=1$. In general if $\beta=1$ then $E�$Q�a geometric energy (see \ref{def: �C}). Let $W\times V$ be the vector of all $n(n-1)/2$ determinants o ,2 by 2 minorB�matrix having $W,V$ as columns. The identity !�F�2 !�(2 = |V|^2 8-\langle V,W\r ^2=|V � W|^2!��is easily checked \footnote{In $\real^3$ we have $\[H=|V||W|\cos\alpha$ A$p#sin #(, where $ !�!� betweentwo-ps}.%�I�fE�.� ~~.�]KfYTa polyconvex function 9�}) � \b>0 Fix a wous9�($l:[0,1]\toI�+$, $lT0$,Eq use it tobbuildE?� !~ Then $5_E"@$W^{1,p}$-weakly-%-!- �u�.h%  HMore precisely: let�\[ C\in \F, ~~~~ (C_h)_h\subset \F !�!@if $ C_h\wto C$ �x�,E� isaE ^_h\/_-� vF G��rp�l ~~i'Q#_>,b]3$in $L^p$, %p\[ l(v�' |\dot C( 9,v)| =_h. L \liminf_hY�)- !�5��^]i7.wQ�proofAzW!�ove % n orem�steps:a�i�itemize7\ � I�\lambdaU� U�[$-|\equiv� D$;�n_\[2�='y�int��\a1T �I(l.s.c.\ (by��.�.I�\�%yP for any homotopy $C��]�$gF� C( $e_g(C)(v)*�ala� +^&\d"$\oldcases{1 {g(v�ϥ6!� !_{ S^1}f(Y�Iz C ,Q� v C)!d  � &aj$c>0$ \cr0 =0$}9W " If $m�$ (�(!q $a=M(\ta$)Evn ;:��= �0^1 e_lA� dv\]=�yConsider��iecewise�! $ga#0$-�d7M�.� �g=\sum_{i=1}^m g_i \chi_{[a_i,a_{i+1})��4eq:def-di-pw-g)}� :�  ��0let�[ \hat E�M 2 {ge�dv�� �I a_i}^{ � �e_{g_i D v�q ��twe apply��vi�� reason� to � addend�� �conclu�+a.����_h��)\N��lō}r����<��tau"� ��of Fsfas�\eq� :�q� such�pon�$interval $2' $, either1�$AQ=0$ o\[A� \sup>h l� 1�����$g��u��APintqFY=\le2^ b!����cho�g$!� )R$%f;0>�9�ݗ-�I�m��#dv� ��F#)A��y&2�! $C$:�(is possibleA�Tfind a sequence $(g_j)"dE/Q )N���� {g_ja3��\to_j���+lmoste"poi� D $v$, monotonicall�caQ ing:gindeed,� �d\[A_{j,i} = [i2^{-j},(i+1) )�� I+\&{vV @}�,~-S-EnF-�q )�E�j�=ٗ {  0 �.MM��A� .X ��?�� }\�+m �\[ .s| �j !})�EL ���| 1  would likEV 7 is m�  g5(al statemen"' $Conjecture�3$conj:sci} qa Lipschitzjie�]! :I"� n!�� . �f� y �>\len  l_h!�2_hamA� ��l2 l$! uniformlyM �� �#� �y�E^N.� ^��%f=" W�as��cannot1Ziz!p� fur�X: t!�is du%�exampl�exa: E Gu � endgroup �o �{E =} � (sec: tessel�We wanP  show�/ $E^NŢie  if�do��rol!" length�c � r:� !�\a{ b{\bett{� }�\a>;,M��=n�\]� U��!G$ will actu�.N�:T���� .� -A8prop: relaxed 0# \[\Gamma2 =0E�n��3%�AN0computed with�pec%�z-* $L^�minity$ !� verg�cofQ,derivatives.I�.�"!(enumerate} ��8For simplicity,AGtemporar� dropb � quir�q%H curves $C(\cdot,v) closed.a�WeH n re�: $I=I� ��1� 0 $\widetilde �� I[a�Å�map�I��I�>j .J 0)= ��>1 1W 6$0,oB2A1 ~~.M+� 3409fhA&�& c -! :� .�h� 1% gers. !_rescal�-/�glue m?��A,�� $C_h�(s follows �*Ɓ8eq \frac 1 h b@\Big( (h\t)\mod (!- (h v(1)!) + bP] m$b_.Z2e}a&= ��i�.�O�left (E:�{1}�0lfloor h\t \r � N$ v$ \right �5< (in particular,!51=1$).-�presena roces� figure \v� ,fig:texel}. Q� !}[htbp�\ce� ing��input{FEs/geo03_B.pstex_tA \cap�{T�=!�&J� D o� m�h$@ ��A � �� eqnarray*ay����=��`� ���= 1P����� ���v6έ�!i,�<& C_h$ ha!Ie�m��@ert� ��٢�=[2 �m "�E<[� ({I} |C_h-C|� i� 2�� �$QjIé<��v, are bounded!|���n �I�.+ �21|!��6 :�|R �2> �,kG!F$����C ;a�) �2��e_1=(1A�..e9�8 2=(0A�8v 8��ly*>H(I)$.~%*PH�leV 1.24<\cite{dacorogna:O�Q6let;?�-n(1*)� a� lE�� B� =� uTl\b��big�%�� w����N )$.$~^k  }$$��a�$: J esplod3 Su� �a2s�S$smooth, so��a���a2�$Ha�o_ �be� d asevery�  By.��,=|0)�Xl(1)=1D� �8l(v)>1$ at some�c~�H�)�1 A�&+:�n,A0-�`~]: lu C}b]� integrals=A��{0}^{1} �� H_h,թE�"�B�_h|� \,dv� "un.Nh$.&�a�tiori�E $JEt�8---)$ was5��"R J(C)a\A2z&vSconstkah$� )2���9 �:T _h.�_h)&=& .h�!P0^{1/h)P %� ea4]��6N )I!I=( &=&^�]M}C� ,hv)j>bvrIB�@�X )�I�& �6:e �A�bB!�� eq�a b)�-�"�%�=�)Z�&� ��2 � $j&� a fie>er�� J� 82�  d b�R�\gI (v)=&�� � � \(�6/2]\)*�(1-v)6&1/2�� ! �*\ �V��T)� =!� ( \t, v+�`!((2\pi j\t) %oBi(�!)ر��a graphY � � ha����:8 a�Oe�E+We kn82�i$a=A� nM� C$;!cbu�   t $a�ys�#$tly bigger�n $1$,� asv$  C�1$�Yn$\t\i)�h]�i �%�h]l 5�� =&n �m1�&25�h\e� :&�~ 1-�'(�,=��)�S���JhUQ>h 1,~ I^E�hva��#Mh A�M�%D�#!��: �B 1+ l,w>,ŗ4 2!A]\-� �"�n�_� N3AD�6 =� \\2e�.} p�|9�viyati#a �"�2 j^2%�'^! |^{(� )/2} \,d\�Z �}�['��1^sinO:vv�n:�5 5�u0]B�j4�$im_{j�in2}V� 0^6� ��L\ !�Combi�&Y E�i�:Fj}�w����*��Vnot �I���&j$ largA�\[�.�"��N� <�(�� (C)=1| � a�"�#. �to�]v�/ ��,�W :�!�7may5 approxima� by a*� linear �� which turn^E�replica�� ab�� ru[2�e*��"�istJminimal)desics&:The �thm:e;A|�� $M>0!K$$\mathcal A���l%of admi7� Ac:S^1A�r�"n$,2�mA�����B7' "� $c$qtsm� $H�i%she meas�sense�(G �def di H  moreoveA�i!@total m�' |H|(S^1)$�� w$H$c }s"R"a��"�}�5 jH!zs�� M ~~~� Bh 5G1�c_0,c_^�e� .���a �edAt>�V&(o $�� lA$yU#BE#).�( !=m"�$Q �'$H^1(IY[)!|)�%la�given ���)\maps�'&8'E^# �A$D M-�con! mpat� 6V exteKt�e �h�%(" - $Ez�$�v. &�E�%�*ѣ\�%� #�,H2� ��|~��3dvR$Ar�MAa tag{�I�on H Cv $�-#�%! C� �|�(t =Y5�0)=c_0-�)? 1r :�t5�B%�non emp��o"m_#k�� ts a�iz�M��'^*���Bu]$^*$ satisfA��A��r�rJs,m F"y��AD�+ b[�屘bbK C ��of�di`,��-i��(���pA�nt)�)�- P�/1�E��C(be.�"($��&A� lim �y#G-f_{e�9�} "28Upareparam�/iz , assumA~[Q�#a��'=S�A| PB��oe-%�� actn�r`-����I�H1�%we6�e�;teM�2�%��[2D.� =+\varphisi."�%K��0T"� v:a|q le 2�; Jѽ K)��g`!�nt _N~_ 2(\max`1{l})�vCq�\lbK (1+� fA$U�oeq:acci8 i�6�(jil% $h$)��e��5S~� 2M+ 3B� ��� E^N)A{�n  g_��-_%�e6$E� ^2 dv~~~:-��H,�BXBanach-Alaoglu-Bourbaki� h7{Sefm III.1525�cor 6��QBrezis}}@  ue�a �"�&,��*�_{h}$��� ��U $H^1ea:/�/\�X)M*�"�$�)�-^*��u�$�-��a$�",vcV&RHa !s�("�-�!le l}."Vo� odit!Wr�<X�!�r�ist�1eb&l�*} aF(%m t $A� t� ? �ve -e* Ag%�R��-\e)/$9F�'!�@��A_v=\{�-:��S,\}� A� slic3$A.yFu+ -Tonelli,re��a�(���xA_v��.!�fix�Q@9�t!��>i]� k O�Y�"-�.\[� =%�q�rtaIF}�q�t2 of��! >hH��<e� :��� Ff1tA��� 3.23yi�AFP:BVY� G�&|#�is��@ $L^1� �,��m�-Eqi�)�#}(huaF��{h}h�* Ce�!fD)$ \emph{strongly}6� ��R��I�%�p"y!�(Qrvm� achieving��tradi���te�[�� �'F ��2^,({k_h}&.�^*)Q.$� M]� { d�]2�2.&Remark� rem:� thm�hI�' wish7� a[# tp%� faceobstaclIy���� Z (enfor?I�s��u(%�(asFj �H�%b� )e���")AS%}pulley}y'a�atM u))� �c8 c� ()su .��@ �1Kre!!K0hypothesis `` > 0$'',.e&�6e�F�- does�7'X e& inf ^$�0re%��'[h%A�problAif E7e(5!�e6Y'collaps�"oR ";A�"tll Q!�an�00,b]e?j�"� 2] path>a� %tB;"@ %�^*��L�,gy!�$C��re3edA���aQne%%f($��$�2$!"� Uno-��be�;our k:%ogain x(!Bc�I (� /!in= lo9aP"Fc needM��_v�(m5>�to ��9��+A}S ���|^2?&� uŅL�=(:ub�4Michor-Mumford6:,$discuss MM�+d(�)$ ��ge�/ta�0induc� "m�= $G^A$ "�a�u!>��eq.9,G� \-). x 8 �:VRH��&� w' �.)Ydi�a} n de te:�u.�* �zd>0�! *�5nY�$C� �%a�!e��=�*0)*1< Ctsq$E^A(Cu"�T)+A�a13(��da�))7�By H\"olo6Y��­�:��w &_ |� {1/2��!eft' pi_N6�"� �;\��an _>8&� >*Y��>7 C|e_t=*jWW en os@A�'S4area swept out�� &� 'G0� gh�ett�A�on��� \S3.4AR�!/\u20^�5*)^{%hX h*)�}{%�0^1�0} � ��h�3Pi�ge�%�b�i!��.�m`p&�=.�"�"wey],�#E� i�_��n��le����i�+E�Bed. So Lc_0\neq C"\� no zero-%��!�"�2}r� q}2Z�� ��le�*�t% spav5B_i:e.'�1escrib!� 11 i�R�yat��?c�)�+a ���A8 +�J13>�>��1,c_2�1!/�alszp..�$co� me�deg�V .��0O instead!CreA ve a!'#!2"� of � .�aE.:�$; %is ͒AX* ough�0ed� insa� ; so(ѡA��4�4 "2 *�3+>��*:��y7��!Z�AxA�u*���"�J ux>�f $\C� 1��:�2e�� May�im�t�1!r)�:4"k7�)?�1-wA�is oke�w` .��&> @�<4�Am�to"�1.�~��� *�  �@ez urn,PdJ%�� �B>)��tf-!+a��)��/aG ��``S�(�[ �*n9o!��(.� $,� ��!_h)��M��%�)V�A"B9; �"(Cto��2''�E$�"M#is)�� s\E��F 69E }�* \t{uWz% C_h:+#]�P �?2&~>�1!D[��"�/1 \t,~ɣ �1� I"#��ɥ�[ j�/C 0)~~"0< Thes�p2��d^� $v$.�-� = 0$. O�� � r hand,2�!K9z$ɿ5 t%�b2�$m(C)� %�1[ �6q0�  w 0�  Em ���y d�D� 6 a� sMm��k�� "�m})�N��щ� ��@ q)<�iZ6-�� >� ��^�kE)�(\[c_1(\t)=(E� \t),�#.%3 "� circle!�$2m�&xF1 `Y� =v^4�V Tm%& .�� 0 1{v^8} (4v^3 �%J""A3eA�  v^2dvJ /3!zq6� }"WeI���N�Gone.I�; w>HA�hop%�c� lH: effec�E!s�� +��ca�&A?�b�D� X6 diffeQa'�&� AN��sugge�e<O Ly��%�sh�<�$� 0cal�� erty ;5proi9 � �/,[7ing2AN$"i v$\�'= \�(��H^N& +=\e^3� r �t!x=#E$%� �1Ǎ�bA /$�� hYaIuT��t�;�)��t�b;"�:a� 4rk A��. 0,) (on page \�~B$ �@.��H%� �!�mCA �mmon bor��:�(�2L0)�A(�_h���"z $�)�ge A�m& �I�#,�A�^&�a&MQ�.Iin FlE�&T2=!5 A�A�,:m5 a�Jf �c!8� ��ixZ�des.7�.3�Mg$O�T {WAie� ���  G�b}"� . �. �'is justi� ]�/6+. $�%�Ne�=�)QB� K"!#)�6O ) !���h^ *@S  of C�<6A=of ��$ur�5} By uFC�k6�F �N� e�immedia�� aQ�E � Shap� � H'gO$""!S��s� unit�*25i>&Q )/: B hol�rue�n V``O''@ stra � 4 ropped; a,�a�sula!�u�b�D$invariant ,re"C?�,�A]Il$|\kappaI-M$. } �>%�r� $CS A es� ��G$c=�%S0p  $ ce�'� }G$| s�S6� ~Y >�:6a�$``submaBCll��''m5 $M�. �=�V�.  S��&()$Riemannian-�1QZ&h,kN&=  {S_1} \A� `), k( );�&5 �e�T ;�PveJ��.5: d A�� Aprm��!�#e9 M� 8s"l"e%?we�$>"�0; aDwr8 � [A� K^2����)l1!l���i�I ED�E6~@o�m$͗a��BJ/B � Urtunat�< sinc-+]��;*(�)e �,�5>]M�7�}��C no���,2 Euler-LagLUe ODE�Kb] N�* .�y�DaW&D�E��!} !5"K, �@�K�I"Q*2.� $�%.�$�#g 1$, � dashedB^ !angWA_.�&_ _ �s�"���fu?(nd�ewheela#�I#� ` )af�A�N�5ics:�A La�&�A�$XzQ $h=5;�.�w ���@�IA�$=�v)ńa�� volu+�,%L�o "� e-dA$A" still�J7e�):v=DE$ (�}ivo'$FA$)�!�Eq, v�60seg�s� a%�@., togea�) ��?thA�aI�,indicate, w6Ghorizon�/Q  A�R�5az; ~ �$ unravels,)EicJ T �arallel0 itself�"I ic K�%�, $2h$Me:}( !��} !:,��A % H$;2/AF!�o /1*;E�= tract1@ $DF@of: ht $\mto 1/A��e < 8s ghtens(f�G$ $\Delta v.B:�=$ mo!�AC]�in!�s:�  ZX��y�repeat%�%r�IM �$as� �%5�in=Y��BAJ AalN1s �%!���n�i�P� >Bto 1 �B��Jexp�? w�$�B.�T� mean�_ amilV!*�E_ R b�ac�%6�01>bigrZ��first obu�[%�coc]to�dA��Iad�.!��$� �%����W���"e��!�z m8qf��gi 3s4%k ��am*.A�L}''. &8 r.7.�� � m1aɻV�\�Cr�5�}r�:�'u� aKD: black magic}, we� %e�&{NT}�/ 4C=0$. Remembe H &~!j bothi��#�is1�go!�A�elpA�ough. S�� P%�w-�"^�\e],Xl�Y= (v,�b)j"C from fe j$D, !�[ $Emj"%) v��Y6��>5 � � 1\�X���5�":�`al6We re7S��i�)�Ao�Vn {\em} Vd heat flow} ($C_t=C_{ss}$).e&R ]Ewe $C_v�(*� nF on9m&i)�Mons }F`tru�&e � radi9 �� ent} �0Euclidean arcPaOaͶ�L��v3$H^0$� .>! � '3&olo8enc�A�us far \M �4% E{famX!EQ� ? �:� a)� &edF�.(a�[Va*�)�,��newu? j-1 r��55 N5 w]P of courseaentir "6. �>�,a��,P?*�9% �d�R� yie�2LI5�%,��"�e"E<d eq:A�3-MM� C_t�frac{I� }{1+A \, �+ 1=${�1 ^2}Ni�{b�+-�� B sp�g&"u'.�Aev not �Vic.!�T�f};�7 efJ� ZU%�RshL/n�!�� e  }"�6�\� ial_t C= � $N�@5���d�es �o�Wway^ mai�6b %��i#A��, illu� 0ted in Fig.~\"fN ding�T>� "\���+\hfill 1�@<}[c]{.4\textwidt�PZpsfig� =F�N 0r-bis,1 =.95>?:c x��B�2ր�\VO[I��Q� "/)!�.]{mK� 9w�r:}�.�:e�bi�O ch�.E�$A �3x$I�t� fas2�& &0T �7E��NdirT* 5e even!Ucross itU#>}Gi+;a+.�n1�(w�f no ���$�� new ����� /^�> f�m� y on��s�iO. How�J�d  seek au�� wh��1 ss�=isa[similar �9����" � �. In �#R�|nyo�0J::M0Qd�ask UQ �EVg$E!�6V�,� y�i�@�&to��G �b!CqY[ 24 k9� wordL(�1re�u aA�U ory accor��K v�G�_{C}>MF trVO! ��hV=�[nt IU $n(=C(f(t))$$ !�sqLs8% �:t: $f:c 5��Ldot{f,\)j>:l 1%�si\4$b]l%�a�tU"g �"�Qeq:-��N-0_t=A+{f!;\,C_t>`� o!��&of=We�zFo)7 �n&"  modiftion���origiE�e�m�,�Bw de�)� H^0_\phi$�5ch 1s �~coM[x.�c"{Dbp a 56���1 tor}z hi2��. (c�)a� �$upn0�Y�is!hip2%kinnerA�ducts�  ���_de4g�T"J_1,h_2�le_{\!1H}`"!Q(c)\,%�?b8��Uo� � � �fe�m6��% :Ee��륇&�2�>val~ ex�&s!-A�+!�|� last.&EbM?�ruU7E middUcA*esv�. DU�5e��!6 n� <rive�� {t}E(! P! l&ft1�\p#[C]{t ^0brace{\nabla^!� �2}_6{E 0box{3.5em}{\v��0{-2.5ex}\tiny� � }C�\\G� b � �/]H\!\raisel4ex}{$\$-ptstyle Qg$ @\0�=�\�.������:�Z�����)�O�a��>��E!�W SeeAB2A�)"� :y��b8l?$magnitude} Xa��4 �$< $;"2Y 1{Al}  E,� *� 6�Y�B�p} ��6�4 . $$6� = - �y�1 �qS %E $$ A= ��arbaIr�$)Os�2E�$$b�" ques��  Pis _b� os� O�fa�? . A���'7hn%@�#�..�0�� :�+ �5}*�" 4 anks�Pf. Mu�6\ n�#i3\6.��2(.i�Y�( \min_c(AR (c)/�c))=a>0 � eq:phinont1G�4�M�D6~D6A�% --��[F!0^1���6v�{�GFD�5��G�N�V nENbs)�A�rc�����B.v)|�n.�/2\pi$T?al3re!at � (B&�|�s)�.5�na&w^ �P5��+%�=}{%�.I�6-.&kO/aA C !5\,:,>s\pi aF%��O H\ �ja"�7�X \X)6�|*)^�XM�1>, g" %Bt6squ� x �5sww7�!"+3%�6�T( & D8*p9�3&5� 26z� B55�.Y Alt�� already�ٶaY���w�Zh#ful"2�' a lo_�4H=o�*Q $��obser�A�&i-]��#;(Pg3s�o b�st�))��J �m?��" Z&&>C�  n try�c"���a$ L�#� �T�u � ely " ��6!*o)hU6 &F% && iG"z"{ s $s�\v$"�#%igeo)�6 havebdA�$u]V]$*&��tz %\ each� �aRfed1E�!(uU!�� p�*�!'G r9 s A %] alo��ep. &:y�!��@Y�" arbitrary A�uniqu]A#&(�qu,ri�&M,y.�  wB�mI Ni��)'��� I�Aq�v7>�ingful%F intuq&!Q��8�&AS!s��ab�o U e���n�al APtitute���=�$u�""T $s$e1must �! addrL1YJC#hof. W� $v$� ]F ��%�0!�1�ms E� litt\do�"i arbr)�a��.�.�u4"he 0 t$al operato��%,{v}6�Ms�vM �is prio_E)V� 82~a�F��mi&U���s� �I�.our�l!�!9 fcor�onH valua�f%��|%��y Q��8s�mo� V� "  . To!�U$�%M�3u$,au,�C�% "n�8w�*�=CN,(u^{(1+v)},v�� $$ c�_E����u�ally,e�ye{'%�nv}\ne �[8]�.�(e�&# intr� me�d.m\v$9 6�]N}\A~*�a� effic� transporti'�?%�a$an� 9�1  regardla�of ``�!�''U Y6!� Pu� s. I�&l�W2�-1=�� a����3L�#alYC�%A�rlyA� oI+Msa�2�/ (\FAtribuAcotN%J.*2�,ce�|������U�erm�ɡR��� s MK{sW,{1}{\|C_u\|}(u} \qquad\mK and} > \v}=.v}-�$ (C_vOs)n {s} �>)EM0�#PS <wMw�Mw5�y:var%�"J%�$�i� ,t):�& . $(0,\infty)�"�X ^n$e}�%���e�oA� �� E� � il2�>.*1�� �5�6 �^$"y�Ved�(-� (I�~$ N C_%� �F"f &� E(t)"`� � 0^L !�!�@ $^2\,ds\,dv� &n�'e [endixE�sk�5�63��be ,iZ+ E'(t"�^ -2 ��d C_tEm%( ) \v}\!-(C� \!- C_s)C_s0 %}�LA ss})<� +�1}{2}!1\v\|^2E!O�< �nFplanar �($ n$i� U�)�&arlD!v ent �KL I $orthogonal�d$C_s$)� "x(N)2" �=>\vs�2|C6�� Y#�tՍFw%��Z�N�A� �\v}-�!�-�%�$)�j�1�^�by-:w r�2A�� E��3� =A.\�Z� -L#R8 \]e is��  *wRZi���m� �er�(�dS a.���onent)r5$� H�t0$E�\v}v�>�*z!7U&y H0})��T< wo]� |u_�*� ^�;A�)m� E� it��0�forward� P���n,!y� �oe�Y d->�man 1 back:`� e&�.�*, vg$/experi��s�;a�&�L�G��.s�5 pheny-T�"�F�A[tE�!$; "*2)Ver![s!x��p%]%�%$���(�,!1& M��hi))"gi-&� $Lv9"N�_!.�L)+��Once SN�o�w�L�p�\ixm�}w �is .�abimeF�Q\2�� ����%\6����hh{-2emN &&��.�@ hi'La:]T��G ofhiu�-2v(>e�s&&��phi��NG2f� m+3'M�iss."��>�56{ \[ m=y�^�  M�L mW����� . \]�bk(�a� i?A(��jJ � �� +,�J�$�  $f>=m, o �/UH� �O -q6* \!RSphi�3 !�!r/ ,�)�JO. %�'M-h m.�1�>��^)X.h/.ft�� �U  D�*v��Z�$�� ֒�Z� �8 ) toB�\"n� e.F�u�io�:� �G&�S�a�!��} f tabi"h��"-�eR look�=Z!�*k9 j ��d�8U\k02�"$ll }(s,\v)>�or�>sumAA $M\ne 0$)B}��o}}=(\log)'!�C% m}{M63z�OneyE� �%JiO�B�Y �11�=�__{�}�eq\ 7>�3usBr %n=e^+�1 LB� ����*� Eo.J^]1 2^�!�{a ` +2 � �|C��}+(M-2h �j>��c�+�+�!�6�$ )���&�&G�. it agreesa"-0JS�R&� ex�$U�,� at hi�� �gn9Wassocig( *� m�' f*h�a��Q� 8h!E�Rc�!6c"! T"��0ai��*+@M� \'s6�+:�90�9w��&��+� "�9sfA Yi; pape',c,f�)�.�v2D%4� $tn�� foun�2a_6�Mas enoQ�3F�uaa�rg�&�,�$no��hemat �?A�e�&� :{N�1�*:�45}�t� o8:/6� �Y2� � �l�@ ���Ca*�.  #����op�to ut�level1lmethod� imp�� �O"�'�D �.6�5� ES =�U9"�$an#0surface $S(u, $�n=(� $lt�9per�� a�$L�Set E�1�15� c in�[4DqKar"m@( s2� $$\ps� ��� =0.$�#goa�U� 7!}in�f�>�vP$E ��s%�!- utonR9a�5�(� of w>2DG0-[ s. DDLiH� �d}{dt���x�y v,��� \uG� a>Zpsi_t+S& t=0|  $ =|_x,-_y)�p�,6-e�spa�"�*of� >�)X�= �EJ�,�B��$N=�/\| \|$,-�%&�� ']rvR&}�1" "  � t\!= #7m#{v�\!-\!#2v.� ^2}(_vE\!!� \!+K J^2BL4S  oig U^wLE�Jd�\ >� \nonuR;� 2��) �b��Y ���7� z\E�- ,E� � G psi>} >6X)T� L_v>_�t�5�&a a�i�CA hN!r�IEaf�' $2t $�J��w�Y(guaranteed E�Ŵ R� Pp1�aͱ�<$chD���Xy-��ad�� flow�! omitmD�A�>ic��l�o�=�GMwo�s*�$indE \"_7N c0 cl6wP�.�s�(̓�)by s @~ Z(� fig.�� - "= "�����1.09in}�4 .25i��z@4- �@8�@19ڀ166��^v�2Q2�s2�32�33:���4: aV:;md4��4��5�%5�2�1Q2�2�~t�S�lz � �B�r�x�Sm�bV��`ace1� .4956�� s whJt�]��e �" al:�B�airb�V�0)s) �*�g 2� �JS 0< \e<1/2*\��. "4"- *� cZ�����\\t\l) W�Ȁ*"\e]œ$(2\e-\t)F* \e,26,0>M 2\e,�*5� eq:kjedve-�} t'�%&�.c�iW\ir�Luv u~eq.*A` �a�M��c �u~W8�Q�Q��y*{# *�^by \[)G!nv!�%�+�# v)\]��\$ $= +"DU*��bS esse�;_A�Iain�WL? �_V��!s:H��L �\a2_� �"�Ig&e# � h C �%$L*�����0{Z�}�Ywto^*9�2 \�%�sf� 2O},�U4 _h)=�8aNos+# ,� =k�@e(\sqrt{1+\l^2}-1  2\e \a\� �9w5� $\a=:3�Fc �ni�*� $H�gd�(�E'�12A91�*t|>2y�"� �eq:E ex�����5) \tiu�V$� &1 ��5{���|}d\t]�X�\ ��( 1-2\e)+ )Ge�L 2* �hg9��� L +2\e,u6 a+1}�J�MU�= �� � q2<8�� { ;��> �I�T�Be�\xin�mm.&E #q[.�3��+6le��d E���f\A{{"FVA}}�g $x,y���"�$3le�,A��� #c�grll lo�$L"Ҝ�D�gu��Ho M��I&p4x$$yd �d"'�K�6H�-:6#*^� \ \ �xi, ��B�PU#�Hon �* 1��:$\xi= ^/Jrc�N �W(0)=0,� ���n%V$\Len ?= xi9 �(I*�WbV�n�L J4Lk�%�)^2VUf $ "&�q42�+u�j$\�9\A {E\}Gn i�"�Elso^8.��%���EN,�$`�>6�I�F' over�88 �(t)|_{ gj3�4n� $t�KU�ha4"VUv%WARE�.�!-xi�*.�1-�H"�7%g+��r UaM�AB�2t�Ql %�.�Z�)3�!��~�. ~\"nin(O� bnwe2-q nT�&��(� �RjU�'�W$:�1 2.29� �rACM:AsymOY8 C� &uld2� �g�8al#F%-=\x֧irc =a�^{-1}D�n� S&oHA+&�l�2m D:�F stay�W�7.�u;)ime��I� Gwe�0D��&] M�d�Uible.?=���R���By!N,7, 2.42, 3.8N^Ah� 4.2.�o��@te{Ambrosio-Tilli�w e .��med�T��)� /! he v�(%(he Hopf--Ri,(^� } t;Te)of)�icc�V-�{}[B]�".%-S�0%�� '!!$(M,d)� �@� �9a���- 45;68��&,�{ �=��g>w.tlletAj��A`b��oe�Vr�Om�>M���.��gat �2 c sa`bB��9mal�} "d�c1l A��E!1�q!\ 9�Gromov'sxAa :me�Eo; O~k�*� �*�Gc�!�U asym)�E&)�> Ș�\S{0Y tect>SEC:SRIV�EM#�E�s Sriv"p�Z %�I�ll�h�~in L^2C�2\pi])�� �$(s)=a+k(s)�a$B re $?� Z�Af m�x<, $(a=Ur* k�v%X [|\{=<=0 \mod 2\} | = 16\pi\] �� l�K�&thm. 4.���)�:"*T: ai� ("�L � % $ of) fl�s9 ��a��0�RN imag�X c�a 5; �6�hQ� \xi_1!W 2!Z="S�I�*s/�  2 & s�]i-�_0}�$i=1,2,3%/�Z e_i=e_i(s�(L^2  C&�_ҏbe ۑ8 6X|aL�psIm%ap�(x,y):T|8M�l81K[ "� 4"�c) = _0+x +�m��3�i y_i /"4,loc coT~ th .r� �� omorphism� %M'%�\h� s���Qates;a�!�Impj  F����"w (5.�Lang:FDG[�*�en�>n��!8U'u, et T�QEIU'} ($V"-W( V *�@3vf ��QU\�3�J�� �\art $M'A (U')� V')��*�&U�.d�N $y=f(xz!x r*7l� a�pro\S'*�9:tA/M'A.c e !%'I)=A1 m)�� is m��&k9 {E�;(xm),y )%�!� s�E0IJ]M% $U=x� (U'{&tha�B��?E!�^[\pq�rz�f_i� ) \]� !�RJ[ (s)- \��\&��3 � a_i ~~o�8 eq (6v -y_i�.Ex ylpi(x)-xej�>hso!U��(s)E7I���r6�!a� (x A_n%� @U��L. _n\� 7�E Ft_n=� _0$;�we �.�^em/ C+��1a_n�� xdthic.�A\�Tn*K--8,��.D)-.0) Z!P�am#�in�RA�it�J&8-.� with� �fsig ���x ��6( "�`ju%� ill-�V"�� ��}�b%��f{W� EN 0�_�:$below w=�spdC�a�CcriL+ (�%i�X&+,V und ��[ 16��a�s`suM:Gibbs(D"�M: �$s*�o 9}K� �g �I(u)=(uUj%t$�w ��%fa^�?_k�imeJ� !�hvN(C_kA�_kTz�"' � idea���*0zigza4]�' !}"$ �!9}[tr]{.: i�f`R�� c_main..ī�X�b˓^kN"�dg.c �*��u��pi6�l�L*��  C|�\v C/M� C| ^2(\����?d]sim� &@ I}{\L!�>0�F7!&Artis$`r{@�2*�H�k$,i: �6�v���)WJ�u3Q1E^�/6�@YpinA^<>��L. &� h�)re�"�?isc~Anen"0A)o�0A:�6|u}"�ny�|� o�a�`�,�)i�mor��de�1��I�.l[���� -1���b"e{\"U" � c_\��'+�Efwo regu����g�*#�5Zdfo�k �yŬx�&jN}�!T�? yto 1.� �(}e}y1=*a6� �)H tart&��~��* 2CAv�#ac, ?Psp^��$|c_1�l @'[q�e|lee�$|\A �Q 6��*݈t 0irpolantM�!�U5  $4!a�,\!vb�  $!L O 0eVBT��( !e �=� play�>ad @k~� �.�E� E=�:�@cone,l`!R�G��)5�]C1@e*K�U�2�T.6 e='k X"���s �(sawtooth $Z���[0$o$$Z59*Ŧd "F$!l"I$J$ ˦K ..M$x$& *��0Z$3a (4�$5 1.[3\e,4+ F \cr �.s JV�.Ʀ�+ +\e,}x�"=Z(e )$�%|R $$C_vI' �)�2{2v0 e} i)M�foI�"�O/2] \��B�rrt!J �91-v}{.{�� �/B��� �1���\ ��5'��sp!N��n Gr�In�|@ $2k$�al $l)4��� o&�. lo�Y14areg. ��  multi��byf����.G�I7nK.Ti- 0,-�we��ʶv2%� 1\5} vqI$$V+)N��%S_k = .E2D-&Q�$: A��ve�jU� Fv� .%� +Jm 'g���>8 (_k|^2= 4 v^ d�^2} ( b o^2+ 1Q��S�w (pXv� = |v "��v , T^ Tz|'-);�� L.)�12A'!}V] y2�dTe[|i� 2 @&��� _N!���)�$|�V �Z4!}! 9����I1�3 -�<� T,=� �ԃ?i�=\\ �a�Fj�(1�$ Y � � CJf ��% 1"� 4D5 ]r�%�-)Z �!H1 �C�v��6�m- ���5-0 �^B� �J - 4 (U�Y�R& iz�g f�(EYE*.� !>�49 2:� :� &��*�W���6�, &0U ~e�V=���� k ��*��\i��|m8M�m�_k-j!c\j%k�kbb�bjs i]>c6#E�J� (\e � i4����} we � Q9r�8�IiK�mn}IZ-\e$,�$v  v-Ŧ /_: r�� eF�(�9&�O�wip0g� �V B in[-\e,0]� -!^0]$).� &C "} -�m2 �M1���  �"� +��V� :�N�=-. Y ,)� �2� ���o^��+��{�<�X�t�Or((\e- 2v)f)^2+4�Big� 6V r^ I��_ �B2 �V` wf^ <%�`\) Nc(�W*Ui.K�C-�%� ��U}Bo} c= ��Lj��B�&� �u .>�2)� &�b9b]Fm�"�>{Rd2[ :t�E}�(y%dU��K%u�˚denE� �2J�Ie^2(1+2vQ��/ M�;0^4}[+� �}(l C>"_*w=acY�"v=-G/(2+2 ),m��; 6�*:2"(> ����i���*���9� �� +|�i-�A�=� �3} ��@wd V�2�� A 4�6�x�6(1ISauQ^ !�2 �L�Q<9��Dtau8!/\e��!e f� ���7&� VbeKe@u2y"� . � {�O}^� t_{-\e}^��^�Ny~&� �j � ^j1i4!^2%�^e��t ) au~p��48� � N��N�2�M�� 2%�/�I:��N5�!3'[ �"� ���  �/;/A��Git de���5�w�e� 8�he�so���&��).)$Beppo-Levi;�; $or Lebesgu��eT#D��i�> �- \ \./�V��.ݶ"�,2 �;' c�. a&��f-0i�B='$ Cere~e+�C#e��2>a"+�+a +(ous exi�� $0$:!�Lj��u9y� � NKDa�_Wng%�i� 2p\�� ��� an �*��.%`!�,�m]0ic2*hD,Q /]r;�FmA �&܋�'��$p:=�� $ c_0�' 1 ��� fi 652�b�yilt)��ޭ� *Eg.""c?R �C def\"?>�f\bc�a>e7i*l4��\a>g� ,!"*��S[�BI {N5���Q\aP�l0�����d,!b�hoN�(ex:������.�[�^ol�!�/ 056C.ԋ�s�;�7B�OmDO��u%E�$ar quasi N+1d)�e$�O:#\᧖U(S"5v! *�Y�bd%�)�"����x$�t mollifP,AG�A��k�4QU݅ss�x0E($\|C'-C\|_{��3}T_nd. b/�re�g�gi|� i"h3Ə�r�d�l tx0�8ai[�'a} cos8�o �9te8'��s�zd�}���.�7C'')<2� �3�!82\�C#ar}�$C':(%753$.�B'.)=�''|�B �It%_{-N} C���$\:w&�� SFei䁸e�MO .�*�%D�_%(� 7dm%IA^a��1����f!�1�Ncal�}J">�j��22vS�$&+Se�i� 2�CS!�pre��ary nu�F��6)velop�_"�]N �sI!� �u�O��c�to�}kI{NJ�gdd�1�gi)hxW5! �+�&�tB�N& XCommuI��d-�v1*�?��^�kAN d��form ���,ib,�&2/�non-triv�c �or���rdl $ta�ll)���� B�mmα�4��Xf �takw�'iy = ! ! I?cm5]IBy<`�aMf�n��`rg t}\, \v&=&6O���v}�?C_u  C�Ouau*B�Ofj���e.��- �){C_{ut"e^ v + �{vt}}6���-X(1v)\Qu)}2!�\&\18�R��_-_j%�-@ �� k C_{t��(.� + ?eLv jdJ9JoR$"�0com_tE\fRj$\disa��|�@�^U�-4RC_s��\ t\v}�sU8b��:msj BN\y!�"9R�51.�sABE�6�.2)�E�1�QC_uGk�.|xV(.}Ef5�2�c^3}m1=~Ys2t}-A9?s1�72�>%8n*�S\v}�0-C_&PlEs�ER�f�v=%%W=�&�bn�b�U%%R�U�-vA�!�v=�=  V(Vr2�v�P-� �vA(V]� +=��b<Z��m�AR��a�ss6P$�+�y &�| GHi�HD*����dx us'x, �p��var�*� � "s !�re����"x C�N���F�*�k�s=3~.! =0- �sd\v Y!%=.J�oAHN_ejGs/s6X60.as>�:� �>�fU )j�lE n&kf=�h��0� .� *B �">*�Z f=�E �'\v.�_ayQ�t��L f\,��b,1 f \|C�0$ \,du =\80_t+ f��*�s)\, 21L 1 *.�*s�\ �u�j�^b7"(g[- f_s(KfFo-�tQJ!�n�@k~>v1jz>v>>��).o!>S %h.g�R>vA�)'v5'�2-'2'f5e�)ka�^ni\U�>[��me��e E"c�aJ�*�e4�h 0����Y}0x�/o "F�3ew ``ael''�8�*� =�� kee��e�8(%upcom������FFtooGBy�Y5 m  E�C6D9 �Xm_v� '2���S&r , = ~ 5�2Esj:E6@D.: D�=-���i��K:�) i �� %U:.+.��BsE4�� Q��Q�F� ��3.�3 �JxN�P,�36�)6�s J- m=>�.�!G-e:�2r'P U4_t��%�Moq2( �S:�Z� j�J�- �:�\v}!��&  Y 5mm}&: �Q.��b24%p�9"�)�nF+R�}�#.5xV�����!��!uU �^2^2�23 !d������%��?L1�2�y�LR,-*�A4n|� ;j>� 9� }�pjB� 5:� ->�s!�b�!�:C)y���%p2B ,ds�*L Bw+o{�>��RQKr��tX�g��>1. We'l��r��q=�F E j?y���"� (s�cBj�&�Ual�I :&vl*;.�FŔG�O�-BF|� ��$�g.�<Z1]BnF|0write the $H^�0$ energy as \begin{equation} E(t)=\int_0^1 4L \big\|C_{\v} ,^2\,ds\,dv = -(1 M dv \endY4 Then the varin of $E$ i�narray*�('(t) &=& [_ts ts  ) L 2\,C_{t�cdot �( +((*s)(C_t8s�2 - m\6#{ss})! `�\\:� �L % | \Big�tv}-(C_vu�s} )!} =mf + [Fc�H( -2�{\6�C_s-m%9ssj <1x�2:|=�%�v}N�$|C_u\|\,du� \\&& �+>T936$.�{\v s}� +!Vvs}s+=^�>=;���:���d�d-%�Y�\v�{u9vY�-!�., v}\)�� ���������Ґ� -�c vyUE�6�E�-� :!E�E"N�?����I�-�1�\v}-2a�F��"u�N! +��Ѭ�} Iɫ4planar case, $�}$ and ss xre linearly dependent (as both  0orthogonal to;Ls$) which means thatN�)N�=>a�C%=m ���� thereforeFn�o= Z�N�2  �!� ��s�Q$):VQ��k:-by- we derive� minimiz= flow \[ � =����8ss}\] \subsec ${Conformal `calculq8} We now defin � $H^0_\phi~U _{&}.\ (L)&�!+��!� je >Rj !�(compute its)Aat!E.� U� %�:�`'L_t M+ kz ��q� \left&^-0'M L!�Q%u,dy�]u� S�� �� right� *� �Fc 2�A�a�� ��phi�F6-( m%k'M�'9tBi�� phiR�5�\ՠA�r� ?i6g ��� �� �� �z�z)�!{yW��!�V� ��E 'L_v��\v}EI{\�)-�-�f� ����������Y�1�au�2�39��C9�-� !|6� *� �T.%�v (K�����N� b�Z�� A���:��L !)'LA�}M�=F �V�5.&���%�._eh�q ���� �� �� �� �� ��bEEun� )�)�N)�'Me m!� q/u+:� � entail� eB � C_� �i#����� x \newpage \tableofcontents �Lskip \listoffigures2�Fprovidecommand{\bysame}{\leavevmode\hbox to3em{\hrulefill}\thinspace} \>G4MR}{\relax\ifhFun�\2P\fi MR } % \MRhref is� led by theoremA�false�infinit!� mensions}!sBull. Lo%r!��. Soc. \textbf{7} (1975), no.~3, 261--2661r(0400283 (53A�#41182p�BCS]{BaoChernShen} D.~Bao, S.~S. I|Z.~"�$An introduE}��Pemann-{F}insler geo!�Py}, (October 1, 1999 E8on).YDBre86]{Brezis} H.~ y alisi fun!�Dale}, Liguori Edit%�NapoligL86, (italian trans�a0iCAE. e foiKalVMassonE3, Paris6�lut89]{buttazzo89:semic} G.~B �Sonm}, ��\E�8integral repres�J��i�he�� culue�vET}, scientific \& techna�E 207,ABgma �9.jHCFK03]{Faugeras:App�0Charpiat, O.~I R.~K�Ypproxi�6o��shapemuB �applic �to #wgng!empir�  statistic��INRIA !ort 4820e�3.�|Dac82]{dacorogna:weak} Bernard D1�Weak 9��3 lower %�5�$ of non-�A~E�al�,Lecture Note�sa��J(s, vol. 922a�8Springer-VerlagE\2.�4EE70]{EellsElw=y} J.~�K.~D. �4Open embeddingE'hcertain {B}anach manifold� Ann.a�. (2)�Z91�[,0), 465--485�T$263120 (41�T 77252TXEke78]{ekeland78:hopf_r��} Ivar E �n'�e>4}, J. DifferA�al Geom�13 �8�(2, 287--301.ktFom90]{fomenko:plateau} A.T: F 2�P} #�;}, Studi)�a�(developmentI3modern m�Zs, Gor�EaBreachA90.�TGro99]{Gromov:met} M.~ �M�� struE~s for��ia�ZA�����8}, Birkh\"auser�2 KliaRPWK:RieGeo} Wilhelm KlA�nberg�.c {G}��(W. de GruytfBerlina 196�! 0]{Srivastava:��,C"�r� �5i:s� ]�U�02004, EUSIPCO M�],xceremade.dauphine.fr/~cohen/miaA/.#XYou98]{Younes:Comp} Lau�� 1}u� ela y� betwee��a�(SIAM Jour!G of A� ed=�s�558�59�55��586��#>�] docu��} �<\c���[12pt,a4]{article} \usepackage{amssymb,amsmath} %% margini 2L \setlength{\oddside 2}{.0cm} .! evenB"2CQ N="�'R<�.�-�new}[1]{E�� {#1}A�counterB{0Dse5�0if2)�{0}�,title{Dissip~,hydrodynamic l� �{ u���impuritU rX p4!;con{ 3 sui�2�a6for such �. �D� q�{I*Z}=+2��J�describe�qnof a se%�!�Picles with mass $m_1$!ea#�in_ ally* a backgr`a�!;Q$mq�al!lilibrium� posed~Vu \ll {. For �k,Vu%!el# pollu �.��air o� o� ��vestiga in-�8GM}. As observ6 } � only%� !quant�i)] number of9-=]a�4as a result, aKv� &.' E'ach�EulAk ype leads.a �le!` 1�!�the adv�� (!-�Xat), Navier-Stok� rder)!�5�.� 3�c�ofCY. E�aieta5now$� find2�M�a a J�G poss�E�& 3a�m�tum%_�tempera� �gas. He�we�L!lE�i dݚ)s6n0a pseudo-Maxw��anI�� gene� zmjo�o�(:M$. Let us �tio\(-[�M!.!�RHs �9�,q�ga!+hq(��st�d r�*by sev� ��s (seem,BCG, BCGP, B� PT} A�!mref^ ces aQei�%� y�2J� wh�/coeffi�An%0AX($\beta$ tenI�0,E A�yst--� in %��BST![<papera� organizeda{$follows. Sm 2 de}�-�G2 Y��O5 B i�x�e3� devo�oto��cus�2=�A��/!��I�]�%�o�'e aL��E� ) .� � 8 2) ��Q�}�(Q��.b7�GH \label{Bo} \frac{\��E)} 4t}(t,x,v) + v 2&(\nabla_{x}f= Q(f) ,� j !�,b� Q} �1}{2 \pi�mbda}�'{ \D�bb{R}_{v}^{3} \times S^{2}} B(v,w,n) [ Ke Hf(v_{\ast}) M_{1}(w-)] dw dn�����$e $ de�1Icol�4on kernel, $\l�$%�,, � pathE$e r��tu�].k!0( $0 aTgiven�� 5V!�A�)6} 9�= |q | ,g 1EG $q = v-w)��m:���e&� eq&�%d �L vel�/$uA%0.ݧ $T  i.e.�+istrib)�f� $Ed5%!n��� ݒ xbybmax} J(v) =m \rho�}{(i(T)^{I�3}a } \exp�,( - :(v - �)e{2 <}()B�B r�E�2�A%� d� ��A dime lessA\amlsf m} \alpha�m�}  + @qquad \mbox{and} �� =��1-e!F<A�eT k< 1)�ai F<-/��}$.�%sM d_s, it's� ible�-p.��LT}) #0Eonary��"m � � y@ators !mQ/J]G.�*�7l �&M^{\s}({v})=�-I00m}{2\,\pi\, T(}H-^{3/2}AL4\{- 6I-2LN@\},1� {v}\� �š� \,, ͂eq-E�:6havAO�g�$�Iy�-3&� E�.�>qG&�= ��(1-I �/1-E }{&:/:e�>����one�[aC�"og� &� }, ��.�� !�ة� chai er�z`'�p�nB��ap} |�,(w| \simeq S��)^Q ��a& �v  ta� into acx� f�e"we� la*b!raaj $|v-w|$ #and smalw!la�!F-# . Cl�3since $v�? ��ed�r��lya�$f�w$BMs �$$S$ cannot�0simply a9M�]�a go�=� . OI2hand,�[�s�(\ref�-)! thus a � ��choice ��c� stjtakq[exp�% valuI#r 1kasAof�� ~JnS(x,t����B� 5nW�.�B!$Off course)�er-,�(nA da�6!similas6toe�� ofa;ingleA ,1�$1R(mu\sqrt{T_r%d}$ea "u!�(tant $\mu$,� re $T_rA�A�*�e`Y4 ``]�''UX \[ m�' 1}{3(x)%� 1� |v-u!�)�4v. \] O#i�at�$ays CG}I���:�k r$!"{!� m�d P ecta�.mean "� m{�wA��%#mpto5)ly%Sl�� Z it will*� d phys�$=>T�7SB{��iy�B���Bodz� V� " ��� �O O �F � fF � abovѥ� �s al>�%��� � -EEK:�* aide� IyST}͕c*F ��touu=t 9spa�Komogenoua�sade�=\bar{T� x|,� %m�hH m��Z}}{0}�H�< remo� by %�,ng $ d \tau "&  % A2m+BVdt$ (�,.y ). %m ^ "�H.�limit�Ze�� aD$.} To avoi�xe term $ �1}~�ͦA�)= ausefuX;�%�!+��9a���7. Mor cisely, l�%e<��=B>finner� �*�$L^6� )$. G�@any regular test-�� \var76 v)$, it h�'��b�mo} < 9,& > = i i� Ua��`_{ �_{w4 � ( q(v^�-� (v))6��>> 4 �Vpost-"� al&� $a�i)�q "#"�A��col} 6� -2 ~ (1-� )( q-�n) F�� 1� =� i�J� invari��as./v� -*�$�not. %8 1$e�uM� mo})�;s %Bt %i\pL!al �D}t��O[(  u�0,m�5B %which�!��Werve�a0�ɋ exist� ".ath( zero.� i}e� ) a��!c>b$ &i�{ graneL flow. How�,�����=��%6�is���7$!5E�>un�6�Eble:��\reduc�� � "�!3)h�QB�_~�+>�6u_1)=0Bd  A( �o�'�!�per�(abF���s�g !2QN*��v��he>�9���.!�� W��t*! f$�b $lor��a�>�� *_ M By�Y M} M ,ta?-� rho �&4R5\5(�*�( uS/2}O >^7 TY �5m2*b� m2} < v �.M..2)�)�6AN7�B}ME t w) (F:{a(�� n dn�5v B�F��~BST},i8�gef2 dt} z}" 4\pi} qF�So,��2})la&�exA��"f�":V�8�ݻ)���3� ��%�v-wbtAJ]1D.G<}v!�dv!Fa u�J]�?R{wU+I�eBK%xirst :.5�9�,j�i} i��Q2Lu +JM \o� u) + �� _{x}�lT�--4mNB����%ho���(u  B !(oiYF!second-"� �C�uP� �G �� |v|�/�$�Jn�M�t| ��; :�Z\no!�M eU� � adJ �R�U�:[�=�@)2\(d$n) \\& +&4-��5|��% c] A�U�� v�M��-,2�Reason���^�6� b�rB�>�d��2!g��|q� , \\�9���=(NE*U�N��#� g�ngE�GE-h � �{I� to})E� :z$n$6c �1 6ry��b,ta�U�6�>�\PE�-4 M UPI�}�1F. 6�2l �% 9pv) RV\� \ &+&mF�E��ʢ2��M+ R�. ��e�QU\�� As,&Xjp�F6Lv�N��V(Q- 2 vB  w + |weC)Z�" �(5 �Jb�p2�I��XR�1�| �� ��. � A|u���E�� T)�JJ�it��� � i1��f�63 T + 3T�+�|1�!�)�u�� ��5� 9� #�, �=I=v lwZ�=gQN�1�-F v�F�By�i1}��i2fxi})�equZ4oj} 2��j6x�!� ��eZ� �)N��Fi�=y][R}!be��/ d�)Epi!Ewe fin�f"� .%~%�YTq[�i�\��� ��0�:B}Lt>� �hoA?z� ^ �4y �F��9� }{3Z>�u_1 -u[ *� U�2�R ( Fu (} ��Q�+ ?��T )2)��%&I6� F ( oND5�!D&=& [ �\rho E� �.�D���1��9�? -=� F* �F� L11�+&�Concla1�'UQd6�a. �(]�J�+�5 keep�e- C��2  :�e$� . To�aim*))� � &u�J�aB& *# "na�6L#>}"* L#*#0ayN�)�-jG7�0>I7{1F�+�8 V.Bobylev�>PA.Carrillo, I.M.Gambazmph�;som��33$of kinetic��6�2� *� �!�+_?h Stat. Phys.,98, 743 - 773,�E0���ST�>0Bisi, G.Spiga Toscani�Grad's��. /I3R,ly�2����Eof fluid�42�CGP�;7�-����y�Q�e���*%A� ist.�.I�2+PT�<Pa&5J�Mod0�D nume�Dmethod%y2�{;M25jHYI9 -� E�7, P.Deg>L�a* Russo E!$B�A�ABos�@(V< ) 259-285=�a�f��]},M�26 . Legs 17 (3w5]C �A�Q� T} %=�%me`` ��.Q� of no%3,U]A�Ts.''Monatschefte f�r��7k, 142�2) �$ 179 - 192 �>� ��&�6XyB�<$1pt,reqno]�<a�%.�<pdfsyncB�<fonts6graphicx2<[usenames]{color2s symbBth�<&b=([notref,not�6 ]{showkey:��=2P4[dvips]{epsfig! head==8pt � "�<=0pt *$==624ptX>wV= =432#2�==1I\6�=� def\bleu{X% {NavyBlue; pale.$ CornAer.* roug2'BrickRedKros2 Lav�[r jaun2!GoldenroB vert.�$OliveGreen�8 �.$bz�. B�rf�mag@Jb�yel�} �>�g� carre{-� 0thickness{\un�;ngth}(1,0){1�9�v = d�=j =-}�>�> *er{cmA��.�d{s46�>aJ��?[ #]U�<R> ?m]p?os�-6Glem #J�?con  Conj>J6?cor""h? %j>�style{*! }%�= �*n*6�?6!�4/@b� 6X�#S}&A@a�,4{{\raise 2pt\hX/$\chi$E.~> x}{{\bf xA{.y y>z z>w w> QQ}{�Q>NNN>ZZZ>PPP>al��>be[0>s sigmBd4 deltBla6CI0"uAgga"B:v6t$>a�A}�/>sign}{\[ D0��{:_maj>':&des>&:&DF&�@.1fa��/{:P)�>(�>(:(D6yP>(<:P:( nneg>(:'NF&:&inv>L:&IF&:&dJ�>(J�:(D!�>:(Sx>&Sch>%sB%s>#Hor>I HoriBIVeB( Vert>Odet"D2 deB'RiB�}��&� {�2 rsfsZ t�B[$B_n$ A�C on Co"u&�$ �8*8]{Tensorial squL#0 HyperoctahedOR�?p.O S�*}�B[F.�M,geron]{Fran\�7is+ddress6, D\'e�e�< de| *C\\2�BD du Qu\'ebec \`abV(\-tr\'eal\\t\- ,*@, H3C 3P8, CANADA3gB{~N�.fC(ois@uqam.ca�u�CT[R. Biagioli]{Riccardo( �2)LaCIM��� ��� �@A .�C\today��D=��sEi>!��,NSERC-CanadaU FQRNT-1s.An�&� �adCpur�AIS8&a= to gJdnh! lici!� scri4 1e trivA��alt�S�Aon�ZM�ir2' ible&�-( vZZ 0bigrade� dule ob�Re�=Ua:cyL~- 4hN) s. 5��Df�I { ��Z \footnTizeq-2�[[a , 2�J: "�>1&�.#D.&�9D2Dn�'@8soZVY[``dia�ha��''!wa%YR. �@�-:vyfBv . OnMT1G-as(@Vtu�is-�EB(Aitmaiie of.�ks ��/4.a very n#Bal ��@ e.g.�-�E�H _lam�}g�Su&$haimanhilb@Znd �& 5gne}). �0u1V�@We�9r?f !(D(apid survey�cCM2BDs rega]6.�)�#'Uref�Pion��s,� a(]6iceisL1u<)t>�K79s�7s.�t�Aspecia�< ou�Gcus' toV/s�XRFLI proc�;�m�VaX��their>� y. y R:�M�Q�polynom��ring}.:weyl_I�} �>A�ZE $W$,Qa""�<a�. ctor)"4 $V$ over $\QQ�-r1r�"l?aU� !�$W$_!:�H [V]$x��ic-$, if $\x=x�0,\ldots ,x_{nE/�G�T�%��Li8I+ide{*} cJ� %:e=��d$ ]�pg:be�$Gte F- e\i"�4q�s}e�P���l �tw�$��S.�^r e�wr $W��C��ly15i��>is.��Ptopw�#����^aM��ErJ ,e�I�also a�-J�~ import�5nN}.YF9,��d $Q^{W} lA�KL>T�,}b4�C�2��&W3f�s�-��4= . B� Bqt& 51��Wa-�, but%�of� �U� are. I�b M +Si�-!� in f���DQOYBA�canD d gDM9 e� ,.�algebra E�dau�$, say $f_1 , f_n��E�s �vrS�3su%� d $d<d_n�lthough%�$f_i$'s!��6Ph*CE�K,basic*-9�!A �,} e�;& $W$}. Any!-An$\{:�\}� _ži2pr�"ih<� a hOof �?}%�e�I6*TRse �C��B�}��{rEҥ� ^W)=�i d_{i=1}^n�%10Eq^{d_i}}:�} Now�0$� cal{I}_W$��wJ�$Q$Qr�'ᴅ q<YKU�E��e�)2*f� ��iF��7 bB� �B� Q_W:=Q/2�>�} O�Res,U8cv 9��:n2>u�΁�J�e�$Q!2is lyBl  "re� , 6|��$W�xiE�� ._on u� �7��be ���Dat %� actu�Tisomo==c�z#�) o="@�5�(For m>�l" Q orbit} or�Aley�N "�)^-@exact�:ec9g e9 @�getMerK*C� �L1��N Cheva�y��[S��4on 3.5]{humphr�)E2o!WtUa� q � �;s*�5dss5 W$-mt"�{�_a"� (�n#e�I���L8 a�e~�� _} unde"dOat�+�@exten� 76� toű2j.}b�c1De� Q^W"�5\;a�BnWe�@u�Etrong%�Y � �x � pD�+&tnsequ� �;v%%of�+ef�,Q})%/�,FB)"� &Cnarray�y4Q_W�o_W+ 2r �s�p{1-q}˂;,(1+� s + ��1-�. Bn."-]e�!R now � Z=�H&� MWM�_:q2*IN it�us *8\A{. ca�Ap�l�*� 9L] � 7!I\laoGp,q \r :=p(tial\x)q�|_{\x=0>�*}�K�pa2B@� ar"�M&�b`B placP, v�@ble�i��Ge*w l x)$,=I�x�*�G�  x_i$PI ai$��haX �d �Eby�0simulta���tit�PsF=0T)��$iZ�in�}d��a ��/?�� W$-harmon�g"�sf.!��$��H}�I^{\perpt*i bX.�(2�o&��lBP!���y!�I]Q�.(ijlyj��Sb� �b!��-wS*���%�)!�#c 2\ H B] ��nR�� in $�5�!N $ if���AiffUdiff_{-� f_kuM x)� =0"Pn"` ast k(>B *}� -#*^!{EGs*? ��� �|N~a"�6�s�{stei�fg}��l��haA�iO eas*N�\�&� �� �ZE(�a.�s.�se H�!�oge�YItKNr�#Aut.�O 8aTBE/ �G"�'s�orem,\nk�ls4Nj$B�n- e�Jacobv[z rminant}:�U(V va4mondeQ;\D@#_W��:&}L |W|}���x f_i}x_j>�} A5� �[_ba� ��"� .T ��!��-J"� ���;[%��EeaLA�A�I:�66k��=d (up��a�f��iple)a��doevo��i�N1�1 T>� 132� ���� ho"� �G oi���!f��.�of ma�[a��weŮ>Q@J_ex�IF� a��L}_U+}[�!�]"g94�(]�2<�.as!�rt�AV ``��spad b�V2�a�''. AB7 �M-_=���1��G.�*��!W�e�!{.�Yp�*�,nA�*�>A6# $m�bB det(�Q ,$$i�,A�� ��� 0b�2prh�asV va��GP4ti� � �"O���.:�1�Qwritt�3 u $ ?= fA.\,�� ��$KQ^MIn�;wor�/-��a,m�alBY9��usXnZd ��2l .X)��J�.�K� pa�QH m<!�W$^A, !j�b�[_=�e�� hRI� i-1}� ^Q#(I�A��T1�fan�orm��w � � ##� &n) AZ�'_���"�6�.� B�9EC{�E=�27$E'subp�B� . Bg,e�a��B�#3Yfu���!%e�U��w�YW} f_wA� \, b a6X)G�U� {$\ |\ B� :�,)A�$ b�Y��s"�� �:NYF&�zpP $|W|-sAzLin��� inFce� aL dTW�ra �. )3 .� D�#v� nt%�}.����#ly�s"pM:H�J!6r� �$$R� ,\y]�x&0x_n,y(y_n],$$ of.�!twoe Im*�Cs_ we w��$z��io"�,�Nf%�b�Ba#2p ,\y&s \x,Z\y)B�f $Ix��zW,aR&7 ��Y�&l�� ve �g!��u�Vpand �ll~ nd $y_j$'�q&truE f&ua{ a new sit�,�!]�VM�det��beROB�hmp�8~6E �h%�c*Z.<# would st_�{y!�$R� wryrF side.��*f#�E^�$ia)�(w,�T(��>��N��f$E in WqH�%{UR$�dee��0 c"�#�a]C'!�$�!�V2 . Ea.�a>r:�W ro1]����a��$i}7'am<'$�No wi;we��Ȑx}nguisaVW�nois�f@On��Cnu$Reo$q�E����}u�t�arI�< i� \x,i�\%�;$$^>�S�.ower�{5��5D�a7&e:IxQ��� ial! e��&���:qI�d�bS. .�v2���R.�_I$�&�]$yB�I&* ���& ��N�'D2r�, )9Who2��� A4.��1�> AT�TŪ�k.]``','' *�d8 ToJ< �"Dr�$e u�&��!�nqDA�mond(s:E� $$\x^�4 a}\y ,b}:=x_1^{a_1Es x_nn}\�K^{by b_n} � $ Q=(a�wa_n)$��b}=(b b  �\NN^n�n,E�{�%b--N�%��  $( |m a}|, b}|o 4&"�!&a suV 6 j ec �aa��v like��9 b}$. Ifa�66M1�V �' {k,j�XvqA`%�$(N�1bS'a�u! N+& �:{if}\ - $a}|=k\ {\r�nb}|=j,C�0 ?���w y$$�(Nq��)�:9'bi*� %�1� $(k,j66�E�pi)+(�� �W.$$ �a�M1^(a�t�obvious�`� �.�q�6K : >�&�(2_R��R=*�'!� R �:� *�i �(2(Ri)N.Va�`s� SP!�Tz]�+5:^�(km�jD(� just�0 to��& =ded:v}�d$$$H_{q,t}(&*(%W&S � ) q^k t^j�D :�(- $. S�d �/)i2m � 9��� ial_Ʌ%� Rf*�q\�H�l,F�$ from�M��wei� J�U�1Rx� 1RJ�'\,�}�'t�'B�F#mD�B. � ���nd:�"G��Q�:�aM>=� �/r -RWW)o�.7)=2�{n}.��)(1-t)F �,a=*# ��&� H}_2�eF�*�"�m��$2e �"�X=6a�!X��ively. FFFA>:%99OA3pre��l�Fcu&3,./k��HK`5�c�75�Mm�#s. Summ|up �c�0�&� �Z� }�� grou�+= (�p:�mapstoh w)$)!e�$n �($"$$B�,��the_isoIE R>� U �.&�:B} Iw�,w��_P#p� �!oat~����$�l�x.�8 ��^�M��}  e9$2!^W:= R^Wf0.�t S�ic-�^9bA�2�,l*k9.Wy�� &\pm {p� � b *�3mX\�� \>{ } o�2.:��al}R��# ;>l�1�2q 2%�%R�T+4!�� s. )H}�>� P$,2�!�q�ly sy��>a=ӑu.�,2��Nurol�0�;�6'ofo�SS-dF�a4ey��J9Jpvng�w}wn"o�v.5�C}^W L2�))N/ \pm$. Nic2' mbin� �O9)���,!��1��beQm 4! Weyl� By}$B*@QVY?i:��%;_�N�;B�?$B"�7�0�e� bCed�mu�s} ,set $[n� {1,2�.�#�+�s�h� >#=wreath 4!�$ZZ_2 \wr S;/�``� �wge�m�%$.)��U� D.Kn�M89 ,6`-B�@Mbe &&x� be=\be(1)2�s>(n)8&\bE(iE� ger 0absol�43lX�!F-4�,iWrQ'eC U$ bIZ h's�ir:bo �!.�1'of �!R neg�9�z5��ve+a�u�{2� 125}\,4\,3��B_5$.�<*�%*^%�on.P~ :rB�0��=effec,)�:�-�t�Ux_i� m x_{\s�F(i)� �E<igzSQ��!h�$C$&��6��ea_n.�)� ���7d vu�Y�.1 �/6eC�%ׅ`A�eM� $$f( x}^2):=f(�2,x_2^u��2^H,�.H$"DQ^{B_�;g`l$�7um V�F )�6p_{j}��1\leq k�v q n}!�k}^{2% 2�"ij$ go��$1$�$kA�2,4��2nk!���}I���Ca�5=`�B�82F�_q(-C�2iNIt���N�& �2@! i*M � -��# &�&2^n n!} p ����;pmatrix� 1 &>& 1  2 x_%2x_2 & )n>, \vM>& d2B22n` ^{2n-1} & 2p n  �[+�&m � �ors�#m�aBPQj=( a=_x_1 xVI�ilexic6��noxAol(��'�@ e�E $x_1>x_2>I,>x_n$)�h_k6.�$k^` th}$�L lete2�$N�}..�3�j�&���gBi�a[�"�*Aj 1,% 6�5�2�!�Z�c_[E�\{|$\epsilon}+"P I}� �r =( _1�w n),\o rm��0��#i < 2i\FT"�E&�4o?� �"ot divi,bc�� !olea)ierm� $AU��Bk^{2k�B�1{2n� .���>�(� q@)#+%m " 2y)�&��#����tA&( Dh=�I. �sˆa&xi3)F3#decreauZ6V;07�&(=F.d�E� �5_"�*.J�r Jom :�&� ;_E�A�r�`�QP}��E�����*���!T!a`N7, 7is s8 1.�$2^nn!e�Q&&ofX$Qi� �=� &(  go Mz�(2�xwee9 3JK,�o� �t�i& 9&�069%% . 9,23��]�sN�<scA<d�$b)�w�)OL. SusB�5aco'Ӗ�In � �Dv"�?�ezj%n starMfix��� �eL $ \ZZ $n�,Marx pr�N 2��esW n} (.0 1 2 2"n2:�*\nllo�z/{�Q!�8�A \,^(flag-major Jnx��$��ta.{n} $��>��7S� VS(�  ):=2T+\�R:�� I$%�s a[�WAz>� �"ma z I6u� ��� �A>h�er *x9 .e.,� \[R) i%�T�)} i.\] ��- B� ��a!se G�bC%M9D G:=\ r$[n-1]\ | \� _i \succ!�_{i+1}\%�<�B,���G|+A�& !$+C �=R4\��v%W )=5$"1�)=;� $U)=15$Bq�&(�u�N>th��y�!P,�* $)j [n]$*�)�f_{i}%�&:=&2d  )+�V ,\ ! t }A�_i�:J5[���!)�7 �!rm{if }� i)<0cF�" ��!5�l�va�?d_i�\# \{j6z�7j Hi \}. FAd_�RF &Y;A�c35��N�b��� $Z _{\be 2R K �\},: \[\ 5>>;!��A{n}� �^{9�},a9} �2���>q��q͆�\�L]I�e: Nil). N��� /� �:�}�-��~�.�$*QCYZ�=_W"�>F&: �A�Aa�m�ta)mn}Z=ub ta)}Cj!g2& 2j}}�=F' "�Plethy�]�"�;{go�a(�I$����>UH&�Ito ?�x& $``� p sups'�%4z}=z_1,z_2,z_3� $�m!�ar% z}��z}_1,�� z}_2 8zwo|JN�VF``�0 al''&xW�$\L�j(\z)$ (Y .���Qof*_fu�s>A/� � $''� us/D�a$TA^SdeaF%�!� ly mr1"?.}�gdse5_$��$�R})wel�GCaQ0y*xR>�6'2r)�bWE ($�.� ell=(�\2O��A�$ "(\vdash n$ ($ ``a*k'' $n�Inl�&,�!�"�)�� macd�� d}, !wf�#M'p_ �A:=p_{ _1}2� ��%�pjMum]>-Q}.O2�!S5=� 2 zw�)2m!* t5���G ary}���a"�0{#-0d; $h_n!� e !U�h���^�Ѵ �n�=} S t^n0#I� Big(K4�= 1} p+>z)t^k/k ),\q�.� 8_ �z_(-1)^{k�Bi>y#*} Ouv t� � ��)&�9R&�zs,&�by .H2�'',�zencode��kern<A)ƹ�29 } $u� thbf{w}]9*�� (f0F� $u�SSl dn4I}Cgredi! ��``AvutUA�/� 9 �De &��+a2�!X�, addi &!� %<�veBL Mg(u+v). &=&2+v. \\�C mf� ^(uvH\,2I.G.�f}e� *�w ���>�Z� i)��V$p,=�to-c �!m�8�I� 5�]ir6if�p��"Z#";N��H� arguVN!<�=e_1�E�_2]=p_6]+:2].$ .�$� \6�KS$\mu} a_\mu�"lL{�0(\mu)�J&_i}�]o<�PA� expa���P$ua))�.�8u� Jw�mu���xu6co'�j �0oni�tE"�9�$JP �5( )�Ozz +z_2+z_3+qIR�@M��nq!fe(-Li��$^��V�et�[�V�D{ >%�z]�� z_>�]"~ [)z_1^k�3^k � �\.2 ;&�k"r��o?#E�!?I��+���Xb�T�5!'� -�!�ulaA��Vn- C �s ach,A�h�*9u�}� hn_su1<h_n]�>KA?KVk=0}^n h>Z h_{n-k.�_2]�� v a�:lljzcauch�->��q���� } st 2�]V2]Zb!u$K�!�&Y]�Schur��}2�>� 1xt� _&A� ja�:a��Uᝁq^��.p0}{z BG'I��8r� o*J"��"�@\mu�0�i*]a =�_!�#p�ociN���E�"g ' �'J1def-z} z�;@}:=1^{k_1}k_1!\,2 2}k_2!� nn}k_n!>c�9�Y ˁ�$k�J� , *JV� conjugac� [ �r.�8R� U[?2�� �w �C�9\/o�%��!�6�a��;�_���' e�s *�_EG� _�n�9/beniul�Arz�t�tT2��]� ":y�(� B"6G!�at�I�JF}( V}�I�~1}{n!}��\ 3S3m!^�kDV}} ( &)�xBmAyegm$u_A{igiv!�!0cyck)dex&��% r���Y9o*�Z)�QV�RRA�&�,/Fr1�(U%�A�^� d1n p_1��^n��[l�!t} f��6�&� �$)�S� �4*S��dir?&]���Q�/�~R��\(oB(f �>�� p/=�6�@�!�exemplif!a�&� 6�&A �Pj_~-�t���G.��of:��oryY� co"�s $5�i�)v-+A!yreS �2���;"� ɭ�*� u:�. ��o,wopZ11�lue�2U!hook �c �( �cmq �6 . �)&L- �2Ag�Zl`sV]" 2�6� �~� \nu�bs�`m�T s_\nu[ w}_ 4 /\nu}2 V}-�L} �}�| �p|� ^�'#'>�s� mu}[��� >om o� '/\m^ ].\\>7A@�%�)�is.� ula^ ge,$�[--d]= �n1^�Di��H s_{(n)}=h�,A�1^n}=e@\*�: ^�h-to-p} + M��&�7b }F6:��P�x eU��n�� e �2OmegaI�n*��2&L^�oQ} 6Y_1+ ��>]:2B�2G��6�!�� 5}!�r� "S"߯���N�B��A""2�2�our$[(or b =ed)6�j:. AyYst=� owarv� is e#RwnX�C<����� (bi)*�= ၰ!m;�red�H� IseeA �:�stNd"��!]�=ed*p�o''��992. But, b�HA�!�c��.}j6�!���ofVF1 s. CN� !��0� � �-.��2 parametriK�by&"�1airs $ ),^+ ,\mu^- ) r "% >*�tot�q"�@i�S��*OJ � "dRruV�2 ��$T&oug %>�B�$��a�F� H uQm"~@�)8"wi+a� es�ished�� ��2�Stemb|a.q6���BE re>Ypped bi~Z�]isfS��E��#uc�:�11 � Q| [\z+�g{\rho-��ith $| ATrho|=n�7 therT �T �B&�pkby$�K ,N)�ϥlet� �$q�V$:�1 }\}_"� �}H�zi�y!^Z��bridge� �!q.� ^!N �)=� !F~\BfTh�U� xy� "�:�,!qf#d^*�d�D�do2)u:E+` 2QH%��IAKa�E�v ��%2we �^i��_in_schu�26l���F�}F%.(q,�����J3>it8�$$Ra2 k,j4 )I vI*�G"�B%����*>"11f�!�5� |�]��X^�H $. Ur0# ���r_� ��^checkeF"/z}� �E z}}]&"!s!,:� �^Lz6M,�"�".�� mpl� e�."QQO}�1n(�)Z�!hE� r�2�?�/��1$=� ^�}�<�"Y�O�7 LW _ ŭ=(1^n,0)&3L0*e\2L�A U$$ N:�&b �|-�F#i*X J �6�( ��F (��>)�(s�.��( %�) + �^@��`!"�J� {n8q.�f_\rho.���[\�]"Z+im_ev:�!} O ag�x�Kula[3)=}s�o�fEdIC!��Aw&�2jAq-:�:�+ies5���uY}u�&o<="�'",*b'��D x]$.b(o����.�s nP�A�:5$QxX]$�5� ^;2� _Q;2�<)�u�[� `��h+ &)z}}{1+q��J�o=�#E�Qu����V�W��u�l%R9�!Z�m� !!��,s�Pbroada�i�&B g�Va�9ll��j+��Ixb��� .���e&�on"����"tr�]�e�(-)L-�e �6�r-^a~�i5*�b� L�(i�rc�e�"$E��mo� st`on �%: H&/a[aUN-�d2 :R ��N "/y"2 Q_d��\,�w=]"#/�p.i$Iu1�-�t$n <j�- <nu8�� <+<nu_j}� U�_j��%��q.�"<%Z�#FN��mu Rf�z� _%���h�q�\�]!p.@n @nu6@N�.��?&�"6Bz%�� #6$Nf&�M���" 8 �[��RG"�"�~�' � )���p� r����#9�6+�QQ}Ă� F}_q^B(Q)"�#�4!�� }� .�Af -q^21##.$q%A$�t �Y�In��� get 096nJ1ic})B Fx1R !!�� RF 0}(q:8bY|!{2=�6&)h6&��~ �:�إ�N� �Z�H}�^o!��Vs�8si"��*]&k| ��ɫ"�9'g]�";~=�6�&�?H�?]�:.�_��+�F"&�`�b,*ks���ase��a\p!��om�&2c)��F�C�8%�n.�fa�;UQ2b>pla@ex:��cƮanw�M �*�6� �4oryQ�^�a��]=�5�v_q&x-��Dh_Ryn��_i�_n-�qE�F�6�f (in:5��U),�o�*� R��P�;&&�?&`3�%�V�N$ ��561&� 4"� al.�;� �� �:O)= ��.��!a ��B���jp may� � F-��o�a�%�$A*!V*&M�:�h`a}mbd)k��"� �g*� ���28= � t}�%{\rm SYP*�)�6It})"W `l�4t}$ runD�oN�s�-'{+``� d~ You!�)auxt,���.� k�$��`i�*:<''!�a�ZmKxFc�^ _4[�_5]{w9).r$nG;p -p� !�8 � V�5�X<F� pic��l}(100,70)(0,0) \put(-110,35)��me��0 {'v{c} a�5�():&(3,0)&(2ܕ &(11 2,1D,1)\\\noalign{\med�} J)T: &1& {q}^{4}+q^2 & 6}5}+"3}+q 7 573k.{big {B� 0,11�0,2 3�,1,2���9} �7 3} �4 �6�8 2 �6.� \end- $p�9�7){�O�32501� >Us&�*�� {4mm,@�xpecificQah�u2�or5�in�� Rme��nA�J���sym*e_fli\!�rho',my'�]=q^{n^2}}�}(1/qB��0��"s%�o)w� c� later. ~�P��b��%6xa�b� :y�I "�ūf�G��B�:h � �U %+qٗvd$$q�Ղ-`�Xtea�P & V}\j]qWm >.) *^KW}b�A ``*"2�@��anal12�FP,&nke d7 he bi&45t�&�;�� )j@�1B�)?,`6,*l�.G�� J� � mu\, nu\,^��&�\ }"y=6�. &^���U=iAU4definition immTediately implies that  $$$f(\z) *gH=0,\qquad {\rm and} $f(\bar{\z} - D=0,$$ whenever $f$7� $g$ are of different homogeneous degree. Moreo:<(\ref{internal})�� \begin{equation}\label{prod-omega}�\O [a \z] b {\bf � z}]*c.$�%=%ac2K 'M. \end�@ In particular, $ �\z+�!< ]$ i!�4e neutral elem!for the 1 �uctB. We can.n apply $�frobenius_harmx}) to easily compute5( bigraded F18 characteristic!�<$\mathcal{H}$. Bed-H})%�)�uD_tensor}) we get $>(F}_{q,t}^B(R)= !:_{B_n})*I�>2;>Z ;@.$$ Then by using �I/.�!hMF�obtainYtnarray*}Ac)�(\left[\frac!�{1-q}+ m<}{1+q}\right]&*&=^AtNAtA =\\C&&\e�VK$(1-q)(1-t)FR(1++t)Y. M�� This readA6�4>% 6�J�&=& 9�h_n>;��\times1 \!�_{i=1}^nM^{2i}% �,E�,R} \nonumber9Q �p\sum_{|\lambda|+|\rho|=n} s_{ }.�1+qt}�^2 q25X 6rho23t+qb2f[\z +�fA_]K-� 2� & I" �0. :}!g4 It follows, i6��Z��$corresponday�m,multiplicity�a*@trivial represent�� isYr6�F_ 6M�H�a._^�@=:r1+q\,f�2M YNBM\>�where�use�no �$ �$�� {\em��PHilbert series}. Expa)>$h_n$%k,ower sum, it�F easy�� show)|��@R}) specializes, �$ $t$ tends8$1$, toaP $$\lim_{t��arrow 1}��== (p_1(��)+ -� ))^n1eje� �61-a�j�6-q}O which� clearly aQASEfѴ.�reg�}})Ac& >bof $B_n��Tsymmetry, a similar exA� sion!~!:results)K(we rather l��q)Y-X26�. An imm� a" ollarat ea�$rreducible>��SV}^��,�$,��, ears�3H}$ with1Ei� (see � dim_}})) j l I` $$2^n\, n!\, {n\choose �,}f�" ��� \sec� {Theu��on�of�C}$� a�- ;U view.)S2),�!�discu)�� �� men%�of�isotypic^�!6as wellV>�!�1/jorder'I_Ie� thus natu� � xpect1existencE�a basis@"�C��AXdexedJly�C 5 uPWe will describe such] in S)� t base}. T�is end,A�neeE�4introduce some��0. Let both $f a}� (b}$ be leng" n$ vector�$nonnegativ� gers. A(pair $(Ca},b})%isai� be a�Cr te ]}Iw-often���utwo-lin�}>l*}%6b^�kB�= � Dpmatrix} a_1 & a_2�ldotsn\\& :b3b63b_n� Z:n *} AlongECsame ա�e sayI�a �- ^ZBO)Wn  if its)>4s}, $(a_i,b_i)�s� A�edA\ incrw ng 4(lexicograph\ )}�|dalso \cite{garsia_gessel}, es})Aisaito �eigT, ``$\prec_{lex}$'',�e�A $$(a,b��", (a',b') \if[cases-� a < a' !�text{oAV"c a=a'!0 b ed��re%���a��U9:, lex-18. Now, settingf�ordre1)��variablaT!�smak�z Gr\"obner�� argu� very"Bt�Pe one��dY�å�_coinent�� to d��M1�4$(2^n n!)^2$ d��al spa�0Ds2N=R  O$ affor� he � ��\{�d x^a} y^b}+�|IRH8\ | \ a_i<2i \ &*  b_j<2j\T����H}&�HBW$,�6< ��onics,2���a-� �\E�al��2�( \Delta(\x) y)��� sin%�Te Jacobian determinant�B_=1źe> ly $ r| \y)$�Ij U��D Without surprise� developA��Z2Ef!�se�diagona+Un8 polynomials $R. ��/jby!�em even}N��s��Js*?u� �a�rame�D=B_B��� / ($a_i + b_i ��. I sequela� � !�ɘ $e$-� (� t5bof ``RN�'')%j��on-�hbec& %��!�nex�  .�( announced .�X2�s�y giv�S!�M�M{B9a�\F�\i� is \; an} \hbox{�! e}5,\&�*�  \ellBy = n\e'of NmoIi}U�Y�s, defin��s:a$$�,b})}:=�D\{ \sigma\cdot \x^e� a}\y b�||� '� _n} �"�sum oj1@of (hz d� nct)�s2�permu��<���. �eexample,b $n=3$,z M{1(% small) 0 &0 & 2&ZF!4% .A\])e;0 =y_2^4x_3^2y +x_2 3^4 +y_1.!"2^2 +x_133�T2^4� Observݣl+ng58!U:�e� $x^{a}y^{b}UC�, i�6�6� .!��hbidE $(|M|, b}|)$." i  fQwe�)S|D|:=RXFL�eI� D�the.e< $D$. To constr�v� ,V�Xgroup"� ,��assoc�K)S\beg ��_ :�_{\be!�}t s. Clos9i�ng ͢fmaj_i�ɲ,varepsilon})� | ' $us��� �i$,9��def-g_i)�@g_i(\be)&:=&2 \de +\eta �����}� ta=q�� �p � � Drm{if }\be(i) > 0,�Pr7y�a�9{owise},(ɺ i �� �\# \{j �� \Des�\��j �X1>cresce} 19,\leq g_{i+1}g� �� }S���� 2"^iD_bet~ME:��g j(,\widetildeg g} ),"i � %�^kdef<.ua� }{rc � zA.(g�be),g_2�, , g_n),-� ^�I (.g}W::dRg}p�]�AI�66I�:=g_{��(i)%B^{-1}��) �1Pand� re $;$6�absol valu��3te$.BB�2-geBHQT a_B2} <-����A8 12}=j*1& 1\\b, &6Tu1}vZ0 Z�Z1[2}~�2 �2�ZY1}z`0& 0\\j` \\�� %l21~�3\\ 3& � �vZ!e \\ 2�Z2[1�ln N 2)lz`0&%�2&r`! e�Q� �f"���  *�{ J!y��)& �be writ�in� T mly�ase_Ma|"�(M}_n:=\{M_\��� in5\}:�} Nl� er" $ G$stead $M(D _���= N &��th^�0ram>| ��~iag��)@ 81N%*&� M}_2�" $��g"�L{ll} M_��Hx_1y_1\, x_2y_2,& M2 ar.Aa 2 $N = \,� 2,i�61}2} V� TlE�a�.r� Sh8q�M_}- ? ����2a�6R . �.�b���1,J�S r^3 s3y_ I 9;^3s )f$$ Mo recin � H�later �F+!�at�i1*� CcCd}A~A r�$unique $u!�e}(\x,�'; \QQ[\x] \o| y $W.^tdpos_ ta� M��}�� � 6��me1Iu� Rec� �ri�u� i.� �3 2�L l ))}$���$.S&a�6�e�2k~s"&��!��$�� have&�*�i�6. ;consi��inv��on a� psto�� ^{��"f \[\be :=- w_{0}0 \, w_0,\]`$w_0:=n�s 2\,^� �min� ta{a glob�ignz%0nge. Evidentli�YT *}�!"� (&=&d_{n+1-i%��)� &� (\&� R2;Ѫi< ��relev� E�s-�.� .� %#i"1"E���Mu|=\,� ^{-�})% & f|* 2�2H N�"5'usA8clude, modulo an'ofA�IVR�)�ae[%�!�"L':�formula9�� �h�!_ act} !"JJq^{54)}t >,} From ta�A� �(the_iso_inv�2�e �#:�=he�rUis&�]�-�{)=>&1r�#� z"i2z"}}"i}}6�#�" �#1�genfun�Jhor*�*approachv+ iA{mpuOon�� refe�)s' adin}%� bc}. *S!,Combinatoric�j&�s�c%�� now go$ (to unfold a� Jal�#!�concept� du he previ�+�!s. Cen�*to ou! "�!is a _$ classificAV.�`ermB� , envi�!�hem�(�i) subse� �� ven-!�(sboard plan� !�is^0$(\NN�\NN)^0��S�")R%wal K���$FEb ���\NN�' s 0 a+b\equiv 0\�rm��}\ 2) $$ Its9!���e�,$em cells}."6S*X!� $n$-1$16inN. Here��$e word ``%o 7''CinA�!�"�js&�7<p�$(ies. \noin�� Figure � ramma}�K�?�� phicF2(��]G^{un_[� ��� d!��1��! 6 & 8 & 9�^n?5C;� GtF%Dk )&!��� ``geometr!<'' outlook. IntC# +e-rg^#A�"d.~y.1$f%x" #ce�/ %4icture}(11,11)~  \)�Put(1,0)(2,0){5}{\carrI0,1n1,2n0,3n1,4n0,5n1,6n0,7n1,8n0,9J!1<0.5,0.03){\jaune�\le*{.9}}\hskip-10pt\roug} B$25,-.25){$%�/bf=$} &1.5,5�h1h4.7Jh1}h2.5,6�h2h5Rh2h6.5,4�h6h3Rh�9�8%89h�88�E8hV:�9�8�8n8thick��0,-0.5�12){6}{\!�0{10}}J*�G*�; * thin>6_^�{ R^1 �^*^�3�� \cap,{A *5�3 ram.Z ma}; �3 �O���(�x,�entL'�D�� �� +**' .Sx -Man.�� $$D=�f��(f�($$ ���be�X�o% �R\{k [n-1] ( b_k>b_{k+1�.�  a_k a "># \}�)2c0,eJ91tRn fQ��"K bO5 nvenA' �"0 �1>�$�"!< s, $0$��n $ � $ if%�onTfQ1$odd. N�'twoE%u4isjoint, i.e.,]-d A�-  =\A(setH � Ae*- AKV} �� .]=\{5,6\8��� �=\{2,3,7 &We fur*�V!�D%��$D)+\sx_i(D�( m.� 7 TIY-E[k ,o�".2�,al ��. a7-"[,+d*a,op`,& � *`,op}2_,-�ca*^,b < b'�\Ja,b = b':� a7n7 n)}) i�0$\s(i)<\s(j��y5� $i arg�.�se<%��I$i$'sbg$h*�%D)=��T�"�� justi ��+��2")9inP4��.� J,$,*V&^MinversMb� D^{*"�$b}a4a})B�0Bp._$-lea&1!T�e-Ewhp��3e��dNW,���.uj J:P1iOi�0"p3l&D1x6e%:check%�� be(D^*)�/4�.!j�Fta�H.�/e�n�6M@ED^*2e�)j e e-1n!�a���s fromm�hi�F  h Ta}�&�Md�F H�+^ piu_vertI�0] {�=Y%fB� � ,h befo .Q%!�!�rK%All��suggestI$(! a mannera�z:to-#2\%�a9mq1B� F '  'D'D6'Dz' A:�&1G:2�1>ng� �,�՛:O� ::�&=�"B -�� again, >�%5r��~O �9"T .U M�,A�(<newb�com�ifi� \over�{D��g}%8J))!�"�u� } is&�bD lled\foot�5{� N�0 madej�0�$�,�c zu�� 562:� ib�?�� i�5 B�2��q�7 & 7���3�;�� �P t&� 1u?�G�7ist bbV2�"sec �Kaճpr6 !��V2�� weE�^�d�%)9A_�إ�(.j);BF� ^U� zion��6�=�%F'i� be:�W�>)W�!C&J<an�* ival�� relEd�!�� *�s��L� DN \ti_,D�.reXt��RY they%M zv} �symbols^�) meq.�D}"N: !�}�D}S 6�>�-)���� $tM=r� a�* � .&2I!l� 8(�ta2v-g}D,ta)k&8A3(�;h%~��(yEAta,fmo�8A�A��Croper�|� O>��i�:m� thm}I�ny.��`Q�A�� -X \Long�:�2 5� �i W&�lP%QQ2minimal� �.�E �ex�V;: �$$2�D}-^$ hase�jKn&�>,&S 2QL2e+!�` lastX;�%`theorem!SS:@ ��why!5"4 27 ,�" $m��(� �� e2�6���:�no�S m*�'�bf � �er"Zf(�L�L�L�L�LL"c1"�1}{\j�&2}{\v 2}.EB?6dF?5"�3N~42? 3i)*�8 w>*{ .e&@O ness{2p8Kose{\vpB�1){1.5}`5700������\�Oq^�O�O�O�O�ORO5� ERO5� VO4 kBO4^uU�3a�_RO3a�?a5.a��O@~O-�!�O�O�OmO&�Co�9ain>&n�m moves"��$�;���end��&�HC"E �.��"  AqH�x curr,�,�2@���92"Kiz5a v�BpleBD$|�G�P��F� ~&�   '?B5/''m a ��1%M�e�toJ(sW<eN&� � 8 .p�=�& � y�+�Hh=e(08��BH � � 92� %� stat�Smea�?O  $6=-D$q  *  . �.letj ?:�in ��Gel)JsT@�J$c=sOq a$2$. A�  %i��69`= i�U��.���P_!�g\tria� c(DJD\set�. \{c\�-$cup \{(a-2�GF-+SICit��Estoodz� �I- coun�,A(%� �6dmVce>+�un�Hn!;  h&0A����XLreA�bM� �as k E�CusNOh�'N*��de"�by|O��Q$c1�e*�% -Q$ H.&&>bM�) dow� v�QP)1iOU�,b-2)J%��<n^@v�"o/�A�,�Keit�OfI�s �-��thmB��K!� choiKG!|aa3M$d below. AyQ�J(�, llow�+D-� �JyE�� `I qb�\Ver(c,aO \{c'#D| 5WA�(c�� )?5 +!+ͨs�@"(. Analogousv2aYN�:�"%� do�� ch�3 ��3D��i�is�ed. BuAx�mporta�3nFMv�g$&�!B mely bd5̭��R�?_�)t&UAe`ofR.s9ɶ�A)g�? ctly)%$$\{\�J��#%�ObE>E�,�r� �l�G.6g(!f�keeps �\�� � �Is (�at!�) until!^J#(A1W��� eMEyU)nalways!u��)��.�$. See2B2� k�E�6]aJE .�2?82-%ur upcom�&}T%�QhelpfulHorganiz�2R-#�Es,�#�1big�b!&s�!���l�FA*!IF2o%��i. W�_a��-:(Z.���a��T�"�Mn%=�M��z larg�4�"$c>�&�Ill9tu�LT��"S4�process.�may��Uchieve��i6e step:�%�%��*��Si�Qv�S�S%`L&.:�S \R squig�i~ ��f�-2�i a_n-7B@� ��r�.9$$ � cR{\uni (}{4mm} \def�1{\bleu{:�.2a-Jɍ�$1y�{ccccF�4�/. -.4)�0>2 ��03 #�-.#2,1�o2K22#3� 4FV542 #611.ڞ1C25,R./2�0�g6�.*./�!)o4R��.)%!)tz,/�^\2+/)\u &� 2�0��������*u1��3IG0AG-)B�3 j�I�I�I�I�I�I�42�(�41R)-���.5��f� h�H�H�H�H�H�H�)z)�r�r�r2r:D]�i 1�# +LG &% 2}\\����ڻ3�r�92~r�� 3��nh�r�r�r�r�r�r������������������ź ��>�  ��<� � � � � � � z .��  ����������������N{ 21] U  �S2$1�" $$\v"�B.�!6��8$n=2$"�!_V����Injbij } O)Z_c motiR/� �C�.+&Z�)&ref�s`6!H�HbvsmtLqomorphis%>�K 5 $W=�i � (*la_�i@��"�tvat$, betw:;" H*ss7-triplets� $$D �W�a�4 2d. ,\la,\mu)K4�1 6�1G-b6�I�8�$\l�*nd�Su�*�>�!!��s �!or�+ah$�mUR�+5?/ ?�wQ1P>s�,!Wn|D|=|.[|+2(|r|,|\mu|F�4E�!�eproof} T�efin!!5�wy+ed;"B�kAw�!�r= {d/-7mu=\mu#d(,a*�]We�AYe�ontalD:GFfrak{h�2`nd �sHA@!v !Fmargina�Ustribu%��"j"as:EE�Ah�.�|%"#"in�a>i\}|AI$IR� v}_jZ9b9��%R�< �14atR!9!+�!CL�$t�s�Ry-9>7%t�iQ�O�`s #ch}2.)e'an�4�!�:>M%cNMv>M��K $�uktI� first sor.HLof�6�s�i�f"�"o1>�"% erases��8�n�.7�"�c�<(a_1,a_2,a_3,a_46�<3�f�&%$a fea�J�xn2aDR->zV��g�#0y�G W/^�$,J�Bj arit[% a_1=!,�?_3=%2�%\ Zw3,B�_�� B�o�<fa[?�$�k��Wc� e ��ert�y �)�16e�Ta"-�f�l31y��m6�zw!7:?�j75Wb#a�bJ  . UsX =ngI�!� `e� find%�,st%�! g�i�ed)�it�goK$recursivW9�0ss&�� �-$oymain.e <�y�<j �;�w%�known �a!l9:�7p�| hold��r���^�finis�R!��� ! }3Q�[ ��*%\i@U�o@s[scale=.2]{sopra�L2�Lf+tgr � �jN1 -�2){${� bf 6�L��E�1v-*-1,.8j9U^91:6�MFy3b@2�@6~16�3@�5>�F�N1.46:36:NO:56:16:0J3O:6::.:@NTO@7�@0JuO@8@5.0�E�M�MV�2�h�5�� B2O��O��O��O��O��O��O��O��O��O��O��O��Oa.0,-1.4��]t�� 7S 5pt6�� 4 5pN :�4ͮUrS� bf. 3\�J2&90$��� �( �d(�!9%/���UB�~�:B�.�8r�:C&�8F�:��"$��::���::��^:�������EЖ���V�VV2���&��4Ể�!7.5�87h��KW��KWV�T"������rKW�`"QVh(�{V�{V6{V!&��f��=3��Nզٹ��0��J9B���Z&�D"�55"6*��4"�C��(�C:&�4"� u=61&fig���� �*-A*}��_�v��Ok} �DS�������2ighten�algorith&�8 expa"��j/�4of�y�R%=�"�.,����k~coefficisX.�hz�h.�R�M:�8�c.�geff�8|g9f�"�*�of��B��2�:{1Fxx(*_�#a},Y?b�QB�w^G�`Um.N?=#D]0�U�noP8r/0se_&�G�}��`pe�`�s�ia�N�x=jla�j^2) $mu}(\y^2)M��%�ΊM'׊c6Nk } M'FSuS$z�% x}^2AFt�;so��y)G�` f!e Q� quari�>$ R$ vare. Repea�02<o� e re$aHe�k�OK<�UuP(&Ub�yHH� $ Dyr�%�;}R4�\J^3 & 4fZnd2W\A)$;�n 2%z�2r��R2jr� la=1 �$3 11$.�R�fcalcutm/M1r�zq�!zA�1(\M�11Q�nB{v ,�K.�-�}-rjU(3r|[L3jj�I�:i��?���z get,�z��.��n%q�}0 �s\ �1j�IgJ �}D(3.�%��OzO_{1��2}}-m_Z�_{2*1}%�.�RU�}"Zo's ��<�of gener1h�d. ?a"��N��1o$|B_n|�sAIp^MutB�FS# �f�"o��XQ"�X ��1t+ n)��h�p\�z\be�<B75iT� b2�}�!�! \qed� �aUH ��rD8&��d]h49!���)�8�|e�e"���inŪn:<�u�tn�9��8��<"F�m*!�Y:Y.HC�.�2��altern�zj� 2Wa*� $p9�O��t~-*� .iEGIԁB={�jq=} �) $�9k6QT$:�V%�u�� I�n- =ta�\U#"9Eo�ma��k�� ta)=nD;�\"J�}{ ��ak�_ K;in-�*셁\�>�WE �a�A s��$R^{\pm}�=b�-a=�&1�A��E�Q�.��$o)�$ram (``$o$�E odd)�>� o*IkD= ' *� ����� ��bXPn$-$ nA $\2�m# AY���odd�Sity*x;��.!�y+b_i$���cA%m�a%<custom��a 8c!ed�Y&%�!;U&-h)oemphasHnnn} IK �\,J ��eaY�sD'to�7�.o b,othA�$$p!x�y})\m{p(��….#a 0)Z��fnh`6q�iy}n send%��e�-iR 4i&j� +Z� �Y!^>A�mimicE�e-e&se9�W&-`p� �Qx>�s1N�^_ga���s:^?flipx!�\psi:)w�{:VZ%�̇ZZ1�>3(cA -*gOBJj�.+B=(c_14* ,c_n&��HZy)>�/u$1,i*,(2n-1�h� A?$Bi2\sTh_1-1, 2-�%=D, P� )�b_i:=|* (i)|f��4d)��^"� $!r(�Y)$ "� �|"� . ��JEvHhecke�L�h imag�N R" ��>&��MG�>��['�anc�G Xb6un_� !J�  "�D+��_�B6�D�w1rg�w12�v>O�b P-2,Yq%�F�2!�un� _%s/f�L�*act QsetN�E3�E�}� �5]i*�w3ds0V�w4v�wR&�(R0"�!R&�(R&�!R&�!R0"b(R&P!R0" (R 1,10�)R 0yxER 1,1�xR 0,!�B@��8}{*�E'[m�/>uW�"�k){1�F7j]Y+H*�>]�. &�!5~�-!�%� 8~J%1ZH" �end"&&7I��" 7.q� �Cd�] J�ra"*d {6�XR6�P.�X�8 Cer�w� 9 � �LgYuo7is[4"1�,�A�ca �Q��b� o�2 :�n—$i*�q%� M$��u�Nh�rfg��!g+fL�'g3�f�XK8��r�fr�9�)��4%�� s �"&`� �WM�vP�:q�6�Apt�"� sZT6H }>Q�U QJ �..E�DmB�Y\t=4wo2� � "�dZ\siB_fRO%��f�i�"er may�h~ $�;2�Bp"�vz!y> �!�Fd�s.��A�.].; s} G��1��Wan-X� a�V� of6�"X]-�~H  f.�amR�os$kass�kdiYa�z=�y�. %c�ae �}:KR?bk defoJ�]f^s"b�  g0be) & ݔ�v� ���j� hat'h{v R22� 2^2 n ���>� <&�hEOd ;d́Z d��)j\[.mi�):=2\m�� �ok )+ $�� ,.\]�Bti *]� �v*՘9!j�A�nNn%���9 ��zRi��p:�z6�`�$)w��s��AX.�me�U$<di/[}:���vbe(i+1I'##�� 8N� .$��j� lΨ_o� j� R2� �r {GF6� 4.DR�fP�fPffPr�  � Z�+ � "�Q�*� V ) 7 )�'R�'R�&R�&R�&R���� ������)���S��S��S$�� ��������������a]�/%r�������i�N|G��P���@�M�M�Mr(�M�Pr%� � � I �M�M�Mr�!���������������� �q������i� zM��\��\R�\�\a���������NM��N�N&�All*9* �2�"�2.���-��'~i�"f]41!L^s=2[~ ~$�""� �~}"J#te�!�2 into.$�(���&Iw�${ cor}V6n�\NN$n9�4*=.��|6 �)|��|"�5� )|NK�q*(�6� n^2-"H���/��Al-|�z4��.�"�N�& Ԣ"} 5|�'-�\"�6D�5��|�Bg,�gKpG�z��'��*�uIh�c �.dT�zF�7h�5XI:&�$$iqfb?P^sAP�N,EPS���/h|a�g fore��� QJ9 H ��&)= �5'=RoUb0�W�W�.Q.Y�I��T�+�&.�i�}a6�ha:H�"�s�H�, takQ*k&>J*} s_oJ�3��1r�� s_\mu.0j�(�6[n\atop&L��5]_{q^2<�#mu t^2} \Psi"{�A7}(q,t)�)�6 *} ihe*2��racket�jaN�7&Xr)Lk��ap $q^2$-biny�6�;(�Ktb �rSV��W�v"�$.`*0�7se.@�&<1be�la��tU("�(sU|ˈ$sC;c�;�bov~a�� �F F�^thebibli��y}@�(ibitem|�, {\sc R.~Adi&O$Y.~Roichma���e�K�&�Ao�U��.uaTexޒ26xSpringer-Verlag, New York, 1997.�6�� �A.M.~I�E0 I.~G� wP&�z�Sti�,�8� � Adv.�a�A� 31}A�,79), 288--30�M�Q��b� m�yI�� ce ${P}$- i��!���uc( f skew!� Schur"@�in�� ;ic �M)� d C.~Greene, ed., vol.~34A�C�4[uary�m� ., AMS�8A 289--317a��� �:�ordon}I�I.~ G  �Ol@ quot*C !��� e�u�Invent5r%q153I�(3), 503-518s9�6h���9}�e^���6-,JZA)B": chem��w0(CDM 2002: CA~ Dev1�ć>�!� Hono Wilfried!�Xmid \& George Lusztig, k�/:%Pr�TBooks �D$3) 39--112.� humphreysê MoJ.E. H-�RN]X1�E � Coxe � D}, Cambridges studp�᧩�d ��M&Xbf 29.6 Uni]Uty �e�0.�orbitm�R.~Ka��iV�� yqMS-i���Vol. 5, �>,!�2��Y�6q�F.~FL(\'Etude d'e :�z� \^omes >�Lques g\'en\'eralis\'E6Ph.~D�' sis, UQAM���U� macd!�d� I.~M!g em SK� ic FD)�H���}, Ox�…2V�5,[�ond ed��a��MDr�m��zȁ�wreath��}�( P>Appl.��m�8} �](0), 173--20 �stanle�e� R.~S FemY)Fin��I��their�\)to6}, Bul�:�  (�&:�) ��� 475--512Wstein�!?A�� S ��It?2��1+ nt� RXt] aa��v}, bB �/1� 196��392--4006�Stemb�%\J!\em����eigenvʸ%g6�7 �a�%~wBPac�� ��.!bf 140},E,9), 353--396�5�+>W �hdocc� �"p�A��"P&VH \[&�� ���2�%i=n^2 >�^{B�}%� u��`F^ofc3xF )1��utile} F�=2 ?�ܼ2�$} (n-j)����B�";7�Gk%6F��)��ist $n-k&^� s $j*� $k<|�$j�3]CV[u�'�,�n-N�1\�9�[3�maϰ-1}) ={n ;�2}"�IN\}(n-k�&���`��n`&0�2a2)}&��g2)�fh.��A8"��)��Remark���}!�_8s-�Z\~B\q �[12pt]{r|cAT8\usepackage{ams��,amsthmfonts cd4symb,eucal,bbm"(&a0} %%%%SIMBOLI � y RR{{�Nb Rw)yCCCNNNZZZs1{{S^1��{{eB�j}^+(S^1)�� Vect}2sl2  SL}(2,\RR9pPFmob tMobksuNU}�zsuNf U}(Nbso3 O}(3gk{{G_k? nphi-c N}_�)phi `m:!M>!��.BA!)�A PAyBB1�*5�D*D*FFHHIIKKk)uM%M%QJ�UKO*O*PPQ�?U�T*T*UUVVWWG�9 G}} edT�Oi \new7i�)�O}�i [.]2'e� }[ ; ]{De�`��}2-coR�,C2+���-Pro2/le��L2#�Nrk$� ��� \t�}d{{ INTERSECTING JONES PROJONS!~p\author{SEBASTIANO CARPI \\ D�� o di S�Qze"� L\`a ``G. d'Annunzio",Ch-Pescara3dViale Pindaro 87, I-65127 %, Italy,\E-mail: carpi@sci.unich.O \date{gCV��@ %\renewcommand{0�d }[1]/�abVS ct} < M�$ a von Neu@��5a "#/ $\H �a cyclic���v*gng unit"-�e�1Ol��\od� $ b% e faith�norX�-�z� give���O8(�)=( X, �c*��m$ $\{N_i :iiI\P�a fam�of2� subaz M �>�Q eAal ex�� s $E_0<;o� $Nssi3 -=) ` 8�� $ �940 $N=\bigcap_{ } XyFv��pro4sC�l$e$ �!��)�d�%�֘"5N_i)T�nd%~veIVNÆM�e � $e�wedge�e_i�is�Bcon�60of V.F.R. Jon:Bnd�Xu���Xu04} U� &�KIn����  ��%$�A? M�@ Hq)��A� $1$�6Y } }!�$M$. GE�U�I�: )�A�6� .�M��iof��usea:te�*��B�a>5�_i -�,\; zIkEor!�y�.M $e_.wB}(\HarIf $N$�Z!@r͐{:�A�%cA��!ei�!lE�2� ����way�ve� \�ik6z A{ n�1(\H�G-2R�H��ow7hA}g{P��e�l� d3D�H�nd+ fact-��V��S� mple�"e� CC1$E!W =1��2�$���%��2$I$a8_�s |77*:yDI.ahapeSprove���w `���)  ifE�!y��)xP �%�M!�to �� !ա�a�rc�� �  ��$6Xw ay��X�B+ < >+ZO| t$e gMi:9A8. !O a re�)SZ�gA�a!no� l$�E4�Ile�� ! WW�"{�k!j�� s of loop�Ge�con| al nen;C1$!Xte[f  4.14].?.$tϟ���ka9A@��l�!�A� restric�O�M�ft��Ga�u8���Ŋ�$let�k4q.���[ �5:�E��5BAkE�lo� ��t��`�23 (a typ�K III}8�factor)��I/"�6vacuum� (�Ma T.JIH��9I�M�< traG�n MU;)Uby)0{Skau}, cf. >%6.%����&A��yl9�!�[�XRq eq acv�o��ծssump�n (2)� ��h4.9.�WKAKneeded����!sh��2��r8ly'p�Zb�ma�e&Cq1^�a�Z � idea[z'pl!p! smeav!�sex*2HusVo�}F� suit� �p"J��o�:aTo� -Takesakia�ula�Feory. A�Av9��a#�ц-�(e5����� })�0r� �#emi� e��6� N� M�!�!c"��1R�. $&� Preli��ơ�!o�s} �%&�LW�(n� G� $� � ��)(n.s.f.)�� "��U aqA��ph��{ x� M : u (x^*x) <fty�O�P@#��:$-weak�tnse�pA�lay�$\mi �iʪ  $(x,y Tvwx��r$b BX��a�Xx� � � 7$. AccorW�ly }" � ll YP �$ s a� se". �\W via� mapp � \ni!E�Lx�!> .@sܭa�r $x,y "-"c`A, yLB.�] GNS:��Hi7�IAq�7� is �Si�$\7(x)z = (xy)R��� $xqM� y �#>�isQ�A�U���!{ $\ast$-is&�z $ A5N� 2�M)5�&� �@݅�[\S 2]{S�ila2B �Ja01�cap �Ʈ�y$R� self-adh�AB� $�5�w4DE�alsT.'PPdeE�R�of��$. )�a� T��$mB^0� 2� dom�� �,Af�'byF#SO]�A^*U�vE �,N+{�,d%�we���2�"by�IE�E ��O�=�*  I�A5m8R ar uK�a J?oY6� a.A���P+" D ��ZpoX2�[�=c6�^{1/2� !��."�|\f"`-funda�����s/ F�s }� (M)= (M)',\; >�it}6'>! -it}:JIt�RRB!P!31�auty�&iY_t^M� \}k�in \RR}��o>� 0$a��r��F!>�:���Q^� 2�B�(x�;iM, !\RR��0 :Ap�z��y�&� ��:� $R_6��N� C�a2�x)a!�y�B� '%luI�TD(U�^*)��{�d�D6. (&affil��dc-:�'$"e�� Chap$I, :��6�^�:'\ .�)�� JF6=7Yet)�6�: �%�J� \}iY�[F�$.�qF� $\{ e: � � \}�WaZ�Z��j* M)'$� Si8z�W��Q�xF�I�):J� $L_\xŜ ��.�4QI �A�N�UI{l0xi} Q!=) \xiA�%� MV�x�4f�>�M��� re����2��>��2���%k��s g,\;1l]g�Mi&�1  unbo�Rd,Ml��y: f�roY�D�o�ou�Iin� !�βo�d��a o�th  (�[ �).���J� 56r\5".e 6 y�6 A�2F%�xc4�a net 0A' verg� ~xZe!>ftopology)�q�G.�xD(Tm�T�}y�$A? $T�v=$ | TcEach"�px�6ATlim1_=x6\h� 6` =xW. ���PX iX�7�$N� �WTH �6� �v �9�\ r]��4$R$�aM�*'R�sm���.�*� TA�Ni�2&NA�qw����� �)1xd $\H_N�.�N **�o\{"L :7 �V�N\}���A�>)\N/�V_$x(.<&�.iQ(k�%"p.%�2 N��a�^ 4_t(N)=N$ for a�Xll $t\in \RR$ and the restriction $\psi$ of $\varphi$ to $N$ is semifinite we say that $�C a {\it modular covariant} von Neumann subalgebra of $M$ relatively k\ x, or simply aFU Hif�Pcorresponding weight �|M$ is unambiguously defined from >,ntext. Note �i.i�,state, i.e. �(1)=1$,E@n $N\subset M$ isJ�ifVsigma^ �4_t(N)=N$ for a2�. A Z?.l�By�!�only )&re exist�@faithful normal c!;A$al expecta $E$1�on!�N$ such)&1 = �D \circ E$, namely $(x)&(E(x)) � each posiA( element $xxl \cite{Takesaki72} (see alson�te[\S 10]{Stratila}). In this cas!�e^� �(ompleteE termE"8 by \begin{equ%D} \label{Ee} \pi_ � �e=e.x)e,\; xa{M, \endJ wh!�($e$ denotesAJ projei�oA1Hb$)� $\H_N$ (a�exJones8}),%�! fact1�7A� sepa!-ngEy$.�M)$, be$ $N\cap\np�$\E�$-weak%*nse iA� $. 1*lemma}1&,eprime} LetU10$ be a n.s.f.m� o!�e2� a�0$M$. IfB�N.4 �,a!li)g64>C!< n $2N)=6*!$ \{e\}'.$$)��I7proof} F�lB�is in�/%� :s$ i llow�at $eAO.�N)'!�$Assume now-�Ix��;.6 x)$ commuAz with! . Then.u�) Eq. (\refA�) `6�a�-x)e=0 qhence,MJM�]y ��2�M) 9.$���gat $x=j!N$.)t)fU�pro�RonU�lxi} E�M$,]�ENI�!�!�$ previous %� % �xi}D(Sq� )$ lA� L_\xI�azlclosed operator affiliated )m.��њafter=r l0xi}). %�giszSN�c�XJ� I��9H59��)]m�F�.F Sinc"kU� �aB>2�%!x��L�W E��T6,n�eD fmEE�PY$ U�E(I�it!g0enough to shu]-�B��$� K $e2 ' e$�;� $eJQR =  e$��pag. 131���� I�$\aphi'==$ 0[2.12�) J[>Ae$. Now,eeverya�a� we have $q� !�$ex�  $ , ���[10.3�QM��Da self-adjoint map!�1� � $e�5b�T��)� &'1�&�@ Giv� \eta�% $ , $ �$���4eqnarray*} eR_= e � &=& .� = e2�) @ S B\ \\ SR_{ }81S =�. �*� i�$ �)($W�4}$ are bounded)�-is����\va/ FNR_{Me=XAϥ�IG>m . He�8us��Ia��p� -�\xi= e�l,BK .�we findN�m~)S1P�\x6F!�e )* -�1�$ YJFs�E�conclusy QÅ�.#Aq��� coree��R1ԩ� We%��zready vA�e main� ult�> paper�}�theorem��� 5�7� .c � ��>� "� I^�&\{N_i : �F I \} Ufamily�� "I2r&� s.� }J: s {e_i.l. & �2!p.q vMϡ�0$N= \bigcap_{ � }N_iv &4 D%���.� eM$V�� 8 satisfying $e=wedge_{iE�I}e_i.o 1� U�I W��to ݵM.� \H_!�}= Fo� ��$����N�d !�� �n$S):Fyq o]�other iu!A5usa3sider%�*$ $f+N( :s�a;��$e_i \Delta���6e� }n�Y 29E,># $E�\}'*5s!E%D , by2�  N��I\ B�t�{f � . I:f  $f:^{1/2}<2� f$��u� .( q f9� =f.� Now%� ��E�:#  $f�q��:�\left(5�t.C \r m [ * sV !�%zG � {�}%�J� :� ��=� Fje L N5^e�;E�� $Պ����r}MR� F_Thus,�^ ��pb? ,�J  &^ "�}�!�e9� �~ *? .� zTlitie��R_{Xyq�}=. y)$y{�.., 26�l^ .+ !� $A e� - ��&-.�x �%{E�B)� ., �EE@!��� �@&��/"��� =��"X �� b�d!+�'U y~� �D�[q� .~<$ was arbitraryAZcan�� cludM�$.%"� �V ��"� corollary"�final�f�Don a Hilbert space� ��a cyclic%*�unit vec�$\OmegI ��$\o b�eB�Tx!�g| r 7 (\cdot)=( W, �*.��a BG �a�s:e�If of~G �{e& �� s $E��M� 2�% = &%�� ���letz ND/�a2JB� ���e$ of��H5/��!�s!�(verline{N_i)[}�!�d�� � :� ��� T]� � skip-8noindent{\bf Ac1l� s}�D author would like� 4thank R. Longo%AdiscusO s. H(#cA!�cal{ABB.BBF.FBG.GBH.HBI.IBM.MBo!v^{�rm{cop}J$rEvar� >�Dim!rm{Dim>AEnd!End>!hat%� hat{!�2� hatu?uJ:vvJwwJzzBPlA }{\t�gle= >v lcoa&5 _{\script tyle 1LBZ8hght }[1]{h_{#1>� �.:�i }RZ�>�2Olch s #1{}�� lchlaell��1+ deltBB� gammR�Z<dif }{y^�{lgf9�<5�;0h }{`L\mbox{'>� mbbX!aaL bb{X> Nbae�bar{NBdbasis@ bold��olu�eB~ndC, lC>OndNBnndQQF>RRF%� |Z>��rm{��6�op>� op},0N�o�aotimes>�� seteqnu�D !>�pa!�Ŋla�< #1,#2\r :�.bѹigg64V9PB��\Poincar\'e--Birkhoff--Wi�P63;tB��^+>. subq%�A�$"�!|$>�q? �(#1)^!_J9_$N"r��RB�rc��J;�CJ7I&�E,\!\upharpoon�+N�r�tJmg�tN;�tRZtRnvec �J8��:rooEata�ev bf{rF�ofr:SscalpIA6M� _{\ndR ^nF9 7p#1NS4scq }[3]{{q#1}"^{(#3)>ISLZ- �0SL}(#1,\ndZ )>�a�6�,\iota (\tau A�), 2)�:EStB��`$>R�eq a�\J�su�%L [#1]:kti �tr>�TYD }{Yetter--Drinfel'd>� YDca�FH YD}� title{R� 2 Nichols"� �f(arithmetic A system \�${Supported]$European C�#nd�Tr a Marie Curie Intra--Fe7$hip�N<{I.~Heckenberger�(   make��' abstract}�"�ep�V�s $introduced�is�n�mi� one-to-onY�)] between>e )0s�Biof diago�( type� Ma1~set (��icted) �G gene�#s�0is has strong� sequ�sG both ob�'sW$ an applic*(�rZ of ���n� �d"�(�. Key Words: Brandt groupoid, HopfQ�0, pseudo-refl, Weyl 1\ MSC2000: 17B37, 16W35 <Y  \\{Ax!��} B� play!0essential rol<(A�wif18 of p�!ed2�sq method!dAndruskiewitsch and Schnei)�a-&98}. �wreaso�&i�ic�, i7estn5`%�B�y certai�ness "Q+,s. Kharchenk�*{a-99}�ved ima�antc ults abou�I�lA�ucture�s�+&'FuraN, a% Y-onu@B�B$7!�a�-�- e Li!gebras�p-���exaH+ >z00�&The la�[� K$selves cha�[ eriz�� � s. I�!is� 8a�z Y)��� m.h� yl--:'��" 04c}}"oc�'to a bi���^n� is a�q us.�E�ab�!5�precise�-m�ZB� thos%�6$a�bA���stood.��"�:IreEM%�ay �-we+eCartan�61� Rosso98},qR 00},B3. M�"Q�(publish�dM j� ���n�.i!�e�> case**& {inp�2}r�)�a}. On%C!�!� aimye�papera�to �iz)�%%��)E%Di� dimenm�ǥ�F�B_pri�n:�b}�I8>�F:�, but no�*quiring+B0aV%N����. A%�organejaAE�eeS� �sec-Ars )e �*i��dj�formul�*.R� RWBgR�mB]Q���2recallGW�,T�$ � t-corr} afG ZGw �d>wE,6���.E�n�Aa�,E�two��co*Pa0 d. F�ly,a-�9@ Ars2)Ase�dM� sser1�A�pre�i5�q'5�>>�2}�� �����ichi �/m) 3of n".�aof�Wssibl�&ly du�� 4's �> ival� �BE&}  in:�d}"1(some techni�i�� 0([Sect.~4]{a�Yb}eNrough���M$k&�1A%elE��/is� zeroI ensor� duct�t u) taken ove�� is fL)*-S4natural number�=�@2��(I%{aMm2[ ��N _�/ $,2E . IR�Ah� =reMv� H�  a�Weizm 6Institut%�I� in Rehovot, especially A.~Joseph, A.~Melnikov, B.~Noyvert,�$M.~Gorelik�,their.��)eirAe�q� ��e�  su� E# numer0 help35*m du�� my f"k "t February &�Jan 5�? ARe�)�:�� �' fixed $nm��0&W Q��R�M�3q-b-Clif�61�� 5Y�c}� sA�ngao�0pairs $(T,B)$�$T��( j% $B�"an orderA��9 *$%s��560on $(T_1,B_1)9 (T_2,B_23�,�7(A��3n�al��<0)27�7 T_2(K =B_1� eB35Wis my�8ct% �i�%( �) base�G � via� ruley+align}-�eq-WB\�2%Z(B')=�cR(} T(B) & \�8{�$B=B'$,}\\ a��ed}*\)w{ }� P\�6 � (#G(#n �6iani�E�$\chi :-�\Go G$ 2& 49\,e.~ak�/ A�*��(��es2 *} q(0,e)=& e,0)=1,��(e'+e''."  .-, /Oe'-,e'')=*}�<%�$ E� � .�#$E=d)1,\ld�,e_n\}$� aAkYA�9 an�)\{1,2><$� $jxF!� $j\not=i$%N�2K]b mij}28ed} m_{ij}:=\m� {mo�_0\,|\,&Ioeil }-^ _i,e_i)^m ( j1P_j=1!� BoF>{m+1}!�)� U�1\M�E��.�exist�n7$ $s_{i,E}�:���%!�#arA�� ��y2=/ si} W$(e_j):=& :�-I,.�j=im� e_j+)\B$�i$.A�a�J�6e7 ��EF��\Ch.~5,\S2]{b-BourLie4-6}��a�4$� rm{rk}\,( W-\id �<� }it�$q��)g s � <(E)}= E�5�^2=\id >4\= ;DE}$ doesn't dependO� !symme� ��#A=��E���mJ]. D� $W_{>uasN smQ st�� subg, o !��� con���!(,E%;a��| , E'�82lm�6�$E'�&�thv4-�'},E'),U -a'}(E')._ � when\*1o'I��.Q�Q� d-ar�B�F汳2� on ��/+6p� nite#�:%%ll .es%)��`��)NdA3maps 9N�a well-%�?.�0 Jy. S�9�ts :=Acu�;E'�� � .�\}�set�$ (un�of)s�\�W �>s=����multiL� one)��$ triple $( �,A� A�!j&�O��it{V�}�9% }*�@6Y �=2l k1=� A��Y�] !&H!�.�iyZV�!�f�s &+U�(izg>\ [(ARS1)]3>\alph6Xs �$�Blambda " #�$'�ndQ $a�a�_A�# ^2=1�)�2 �DG=k\setminus \{0\}/ � =�on�A� �=�_E\A-&F.=\{ � �. EE� D =\sum _{i=1}^nm_i�n \,m_�*��Z %� }i\}����%m��first1�y-�sN�6anyQ��E�l�4� N&   7 �>eq�m!8will Z@c.A��E..~ �R��>�} � � � ɣkɣ-�ofN , k >h ad $V$ a �module$kGel�$nIFI�*. @�lJz � ui���rx-\{x_1,x_&� x� )Z&� Vi-\{g_iE^1\� \le � �R�� G-�$qc aIZll $i,Z� ,�X�� *!��&(x_i)=&� ot x_i,&  (& x_j=& �x_j*E � fx�{n1Ga brai;�/sp,0�([Def.\,5.4]"�02}��7��t1i�((V\ot VUwDB�sigma� �j)=� iF�a�z�>6��B (V)$� B�6�86��/E(ndZ ^n$-gra��hFd !�deg!�:=\�%_i\quad��{�� �A7F� . *"TE E_0:� T&� E�2�1ndard U��u��$-m� � @ �}:  � ^n\toJ�*� .IZ� eq-chi} o(�i�� IgFe5bT2��)�72��P!a Y1-�B� )Q�&> iter% skew-�,ut%C._ Hs $x_�Ffe~Acx1aH�By�m��� d}):q^����P)] h@JA�a:U$-degree $d��f� lI�"2�r ord}\� @ (d,d)<\infty $ ("� $$ mea�0)�=�W � �G 2�Ha�?t c'idew"2_.�B�� ie%e%��6.JoI4 choice of��a���ed)�I�]BK ,y (P). Write"��:"� 6� $. �6A�Q��"� +� "�AVN _0^n>' ���dis�BO �O-�2��V�$W��as.�$-�$�%ned#*� _0}u �dE��st�?-ca�� 6B*�by&� ��)� bl$thm��� �I\fzFS!5 .iN6�>� _0Van V; �n ���ed2 ��>& i�$\dim V=-E�st�!�$"s ) :=�b��6/ N A` (V))=� $.x3�5� � V%�V�F�*� f e%)*��!� w#��,=XZ� Cera��Q�FT� s1".W&�:p%�S�NA� F� �9�@l,%m !�" &��HBCY�folg}�f�B�" a�hi $ W value� $B��$� �5�O(AR fulfi: ��� f-�X�j�6H Y#F<EkI" �e plic�=%;e�,��.�Mf�one A�� ݑE�^�not�/ ^b "�We+.�1&%75Ebew}[�thE]���b�,F+��?6A ))0a�aE9�� � . By �R�@# ^8"J_0}=W�F�e)��1M�� a�$!"�|��M��a&!�f�J . By ��A.~12�o:4"�&�IID$a}.EE 1.�2� < ]�y 1�.� \, 2.B� F�=!� \bet+ � U�am= !�ta]U��E 3.� s noN��y�( qXe0��� � ��&�"s 1E42� �� fu6l �9�\�! HJ�m���n�QAu� $E:zZ�%E�A�&� +&� of>=�D�l"�#�g�&.d0{n�HCES/R ^+)^e1= \{r%G%g�r>E ���$\:0{'@�0>@ f\T� ^dard +a"}" V0M�clearlyI�he ��:^BN&ua>qUA��' }{5}�ͩ aI��iff�+ checkI!��@# �inu�!�=�*)f& �1{n}(ta]-et!Z[0,1]$, 9� (0)=1-j 1)=-.") .Ct�0}t AZhyperpla�U$H�f!j�0eorthog�.a�.� ���,mor!�b!ne�IA)j�='}N 1�_EmQ�yaAq�Add�,�#�D�C�M� a�#re�!� ��%� � &]m� f R6 _E$ (w� n8�Xt que)%�Z0 1.e���� m.)un7 $t�(0,1)��� �yH(t_i)�� ��t��=t���R�m�t�!��H"fa-MZ8 3. $i"�%� p3�6U_1)}<0Z 9�i+>,2��$�)p�>R/,�~+� -�*�B���V� if a]p V�%�n!^F�=("1 N=!%�u��=!tGMW�Sb,A�'i�#at�>K$*$)]&9"�a�s!&A �I :�n.F i�P�D\� :X �y ,3&` �L-�5�t)}%OAM� KEoin DB(T� �*��-���1�"o Indeed, /szH�6{*�� M��J[ #a-cU� ,-E'_0.���=E�( up to perw!�of its7 s. S�5=\7YeF��3as� d2�N� $E''6� *�F.�, �,>�Hx q 8 ,[�!'/ ձ �� a nonnegam] re) lyp'vteger�Bar�'binm!(�]�E'���!��) Wg ����?b� � a7`s�|,coe��ien a�changes$W^ u!c.ETu� �� i *$ } E'��"#)4A��� I�O (X !m�.� �&E oldj/r $t_j.o!W}� ; k.�L��atl`.�lR99Vl�*�'��"�Xe'_ #M;,�:6ab$��\M� _j=7AgB�bqO; 9��6�'_l}<0$ŗ$t>e%��m g.�*� 5j$ ��2a "5�:^9s9M�AjE�{j+1} e"t_/(:=1$).6.jV�s_{l,�A� !�! X=�I���t2�ATusI$�N hoos (t)�} cE'�f!.�<�6 4s�"���VrB�e�&I�BQ���& �-y�j �for]*>�:� uS�z�]�� �&~%����Y��i'.7��O^>D�n'6�%9 Z&�� �$a�2�� !�^��� � A�!����E'geq$ �5��'$�7Y>�"Ql2e last*[ �Rd#iE��[w)�� l�F"�dby5_�V$,2 �)�l&�9i�7eZ�=viaB�?$0&f{Z3dy�|io%�r*i*�3� �z!�:*�3a�l�6� V',Vy be�5;# ;# NN>qydeu1 < �;��&X2J� $q'_{jla�#q' ,Q%T^:�- = j}=& 8j},& l}l'_)e?��j,�rF����say�aty!it{$V'�_%?�twist�)�t� �gk+ő\,3."y=02y=u�<VMe'`re�(u&it{}.d,��:�-�2  �>� "8>�!��I�6o�Van A42�F^ �  W(V'��%�V7� '�@Y@!'$� 4$.�d�&b ��}N��,Swo>f sBd'<*��'�' re Y*^�:�: ��C ,R4.QT, d~� @ T(E)�� � �V''=c T��\chi '(e2  ''�DT(e�D )� ]g�$$. U�the�*B�>V1 -H]ˉH$T/i�-�Lb�_��}) beQ�B�:LB=V-#�'�)�h (A����&2�a�>�2%:�6�l�l�)a RngZc]�� (�'J�AU�%'kF2A;h�dt�a`4y-t!e �!�%nyq ^��"� easily "[E5: ql�{!8:��{it,� su�i[�o69ce�>es8w�*;U�4�� 27?� nextZ�]�zz8�� F[)6{�*~<��^2_%F��*e!C S ��B�:WX$hi.8E��l �Zc$V�6g2�}P> !o��fz} "�OizF�) ,Rf}{r|lc} "^4�=�k�rU+$; 122alw��1&�7fre@ram� s} �4�-O:p.��{treeU8\h15 $ 1 & q_{2�5 & 11},2R�+ & T6B2 5Bq_<^{-1},\W2} \� 6� ,1\! T2\\W3 W11}=q M :]-1, � orC & qB`-1,2cZ?�[ f 2}=-) &6�48,7 ^{-2.�^!&z�3�5.%:nX��$\{q_0,-q_0% !; q_0r�.q6q\z� � �2�+Y u /6z $R_!�k%�AZF�0,1 H ^2�=7:%� ]�-21� �& �Q�8>P^4R < ^{-3=� g^2]^ad%.h\{ !� -�( �R_a��489AoA� 6R�.�A�e�A�a� & T5NI�1} ^ �1'?T7=i99 ���RD �6&2~V�:6]^3.�.m �6�G�`�.b�10� � .G.�r3.�B�8%�62�:2b  �W�[6' 5�1;=MB9=�1V].�q^a�~�8 �!�q2�Ae�.q�� q)c. 9  �Y�:ba�}b[^Jc �2K �1}I 2Z9�U1!22C^6 4E �(J �8:� �XR_{24A T10)nbc 5 s2q� r9L%�T1�!�.W�`� N^5P2zFA��?>H 4.E5.MA��T2.81�P ~JH.�:�=6�� J�11}\}����5�!f0�T1��YE��2��!6.��� �~� &!w5�Z� R_{3 � F��]v��A� b {-4}]w!��VaQS6�:�� T1a����5J2A�u^j��j :C1mU�F��z�2!� �� lig�4}Em� :c� < *8Fend"V @�,�+t-�IAVE�h V=2�j� �^�2�&$ �N� %2�8;is >r#�i Vv_�B�? apX=in � !+TG/%,&�MH26W+"�of� ~2 s�?jF"DJlemmata"� need�Kf:+mZ $( |cRN�O�ichsbev�2/Rw��H/-eigen.�-�s&x�Ql-fine4IA�A�W{2o?:-4As.��4 D$A� �A=MB�"r� et A'$}Wp \"^ W" �U� M�l-subSLZ�.�$M��D�HSM��mi�A!�$� &�!�O�)��$for+�(c$a & -b\\ c dex$)� $0� $/C' SZA2vFA_1�@2�a_�%-b_��c d_12�!B��A_2JD� -b_��c d_2ND9[! _10�Hm? 2} 2�=&\frac{10}{b_1} @�= d_1e xj2 .>0 b�_l 1}),.�} %�8lowdisplaybreak>� &M:j-:S=�1!a) 2�eag!� &\q<+A��qLMa_1-M^2b_1+Md_1 - �6�\�^) =43}& T R�+ Nb1(� �|b_1)-1!� � WaIAbEA->�A�-�(A�!�%,J�T?ft�2 �2�I�!�2}!2 � .�42�R{� M�)���.\notag*�} %\A!uM�b2})--(_24})��e,".(폅�"/5���t&[Ke_2S+&�2ǀ*�N ��z/�^E)$.�=$transposed�E �u 2,e_�3 A usefu�"�,of^53�h� aingb~seq�{�ʹV�82�\���3 F�5�Z�mG(��( & T'_i�"1,E�%�T'pE+%){i�K)3@(;)�,�':'_ '_!��Ch)�(_0L (��R�F ��j �! \{�.�'Z 1�!:;I*�!Zg.� !�1�s9P '_iT�-1}N1s TZ*_ z-i�/0>1R2ofY�E�Aut (v�7� �;(nd periodicB5�90  i=i"�N "] eg� if�b1c�1,�'C��� s�)�K�K � �( Clla3 !�,H\%�%�a2cp9 hand�>�$,%*�(\{A�%��/-�� *dJW!��  i�9tSV!DitnL�%n|nE�5r� ��s"C Q�RA�B��#5���(a�a��.smL�O.- E'_j*� �=Ew+j}��%6�ijx2{ij-1}6j-2.� = a��).�^.�w9P } gain%}�C�ZAe�v��|]t$i_11}+ 822 =0 �or�� 2}^2C1 %,\M^2+'V1) b ��^3:=0-�� )�6b:B0&q!B!�;C�J�Jf�=A�tT "rC9Q�5$2"#@ _1+&R1�L� 2(2:"�N $zEx_1x_2- �x_2x_1��zx_1z_11�z/"� z_3: & B!d JzJ�*46 E�Jy 7)�1�1�I+MX-�I*� =m�n � |��S�&[� ~3.7&�H�&� $ E4.*K< \Cy md�a}c�E�QR)(\�Hz�/ )=-lXBy 6\*I!b}�1^{2m}��em�7� �NfFs, )=26a6 ]= :hB� ��A��Ic-�.�ML-� �2�2%!- n ei�5�3~/�Y �A1�R_3 3i !cE��(Ci���+v�E� f�>Ub�"ex0d)�c"HB�ca!ʅA� ,A:Am^mn�Y�Q`2v!je�5jA$n�.l2M��>&�RA�26V�2�i1�iEA�E�T p*9A� ��BlF�A �D��e>)J%\ x_1-2� � x_1)��2$ mustU,FV�I�V$��:�4&7@b�,is� $w_1E�{Ie aA�re)A^6�AjR�$�o��e�+A�ayf!�c��. Oa-�[� ��� k2{K��R FR&?a"HH. K D6�FX �%9X2!X�+� `<*} ͂�� 1 3}�(1���) (ɱ�< )^2 1:�)}{ ,1< 1}}z!���|�8�1!�e� $X �iga���D �(mRE ��(mA� �wA oI* ?=m1!e� $5&�Kin�eq-�[)� $E=E'�<t 6�7 M�a8I�of.��l�)*+śny �4 �$@ �4 q{'}�{l}�H (�3,e'�6!��3q{':(�]' \'*�4 E'_l�6e'_�c FE'�67= L2N� eq-p�� \scp���#W�� s} �&� ��(\s�}E {l})^{mg5221�]� F=jQJ;�& }=� 6<\\\�6�'�N�\V�6���'}^�)�)e� �N>N�n]By"s (3)A�h.S2.�f�Yl�U�a�&�<-�e�]q-I �-�'&Y/{}:�2�,&6+1- -7JF-w+sMY4622dCeh)r*' eq-qQ 7J�E �2�`�:�+�J�K�7 �52Xj�4E=�_)�2d wI�R�H"��I" ij�,"(� +E<Vz8s20��n.)�iL ^�-^�-�]. <� 2�.�M�"�A�i &^5 7�e` *�Qd}�srem� ܀�74n>�/}.";e^&�g��X�� ��>�,N�N use � )��n��!�`l �!R�!Bij}� Fq�.\7\�T}� �F1ih&ZwאP:E,�p ]4�i^s l��F<��t��}>� �( 1 \\��0 ���mue>�)�l$H;�N�&�Q�!,0-% � 1 c  �f $s�n�^[ ~[ .[ {$ h�Xdda�"�!�2�^�)^���C2x�'_0� �21%,T}�6?�uev:;FU��~ ~p -�!C U��>�>��G � #T$minimal am�r*� m� � :". %E *0�@'�iTmb0Oe��%1[: W]_ ��a$�NA��0of�`��hF4o��c��# . StepxH it{2�!�>1$.}��n%i>1*%��"��Fp �ndY7 ��{2�a�2i.�ZN,Q!�K ;he ")w�&�!�@ �!2 Q� T}_jMnI|=&)�� �' m'_j����2�B0#,�"06,B�X&d�216 [�SP�l!@u� �y+1� N�!|m'+�� }� +�3-6�:Y�/� _j\ge 2*2�,A�s��ces sa<�A�)4B� R%Ť $M=���y�lx%��Il+1} 2u���L�Q]� 06�q72.u7Aa.a�!�i�=1$�q�Q8�a�9 �q�,�4�  i$C�,�@ #1� �N�(the p)�� )� u� j�a`%s:�"�61396FIL}=�i���  +1}>�%7A�BfYe}&��� �K"l?�}�@*�gc1%�� ��E� ����]���~ R�u��one�V�ITe}u�i{B� R ���-1 \\�3 a�:�'�$;�e>3j�I5ea�4^���}�2�?P�7~��&i#a��o�dx֕!F��)�E {2,3�BA#@�aP,a'M�A�e >_ �� 3a) Z ^Ea +b) �}�#wU�aY�..�MF�^ ����Y�)2��0a�Qs&�6_b22}{�� '.,2,a�11Z ��1]R�l�[1 U2���&9�#�Za)Wa���s 8t66�,A5FM:�:if%�repla��]b�Ctax#I�in�eؤiwR��K�o$of�_��fE:1=3j N�i�6�!4�3.�^2�o!o4�ŅI� � !:,��R� s�,�I&rDU#���E�)�wpI .�{"�:L )2$ 2}{2�IA�����LQ�A= L2e-w>a��*a�Q�5 ,>`yx5O"�n�� � �= �^�;$O�oat1�^4)��e��$qhE�" $12^W th}$E��,Q~u�by�"!�)�) q ��C.@(n �*}7 0=&1,&�� 0}=&�21.!�1),6tB�h�A b%U!�L!0�U�2M�I�� uUYt � mR��3\�ss I�)(6~ $5F}.�:E�$6�+*}�%D���2A�!T&%!T2wF�=%& 2>X2>�)�FQ!YQ { M.�*} {}�m'y�M/L \)7�a�E���Wa[8 B��jE� MKin-��/ia �>!����xample.��? 7: ��'��2�p�|il_:"��� 2}^3�^B1�:��1.�b3��a�I)U*�XEmJp1=&3,ypA,m�2-1:_2B �i_UWR�%�lE�]- F��3M�B�32�'A�@�B�B>15�to%�A� m'_3E�4  3b11 &� R_+�N"\ %\I� �UX r Q 3b2&? b1�b�)set�zR9M F��>��"!>�4�`>�42k#)�IB%�!k2>�� A�  _F��* 4�>��"d �p 0}^3�T}_6=7"��&n 2>B.33 "kz.�\!�n_F�2-�3�2D26�:gBN[�ma'�%nQ�C�/�6�I6%ʼni h��әf�nod+K 3� \{3,4,5"�U3�,"t,qCi+}i� R����WI�y �@�� :�\"�:�� C&� If�3=4����,o4 o  2}^5�"� �Z){N}{10y r ]f чin�14. (�$\qB"�<$���5q� ��5�ň 2}^7��!�m��uYQ ��14� ��9U �61��FC *��w Rg� *�a$+1jy.}7��5bE �#)@�eF? ��%Kx ,:;^E�� ^24rR�. m'_4e E�|6� iU-3' �i&�>�KM02���-*2bݯ22�A���Ĉ2�aM��g!� �}� R 463!r>�5^(52�'!�-�*!�>x&1�3)��5=&����,#2R �b 6NV62�# G�.�9�j�6J ^{25�-�1R� �h�>)�!4 4!�e� 61 6!1)o 2�%5�fs>� aEE(^A&�&�*;2D R�Iu^S �.��J, Nݩ��"�w *�R<�_(��D�:� &�P,"(>D�i8 1� �I�s� .�:!M!�2@.^ !"�%�e� R_81�:( $ 2.� "��Sby�ca� �,] 6�` �?)1 ��&F6a�M�� 3.� u��R��c*01exacta[o^u�q�86�(B�m n ac�xnt�can�g�E6Rk G;�u��� ���}77:��j&� E��>��m�"^4 �3a���B $p98)Z��^W:��2[*q,4a-{"����"� �"Z�j� $!��$0:��"�1 !&2864��\.{�:�� \ref�:Epa��A"B1� !�QyM� �^6�!�[ )7N�����to{ uishews:M�f8�>=)%�>E�se  4a&�FG � 1MDv,>R m��*�4a&�4a*�.)!$a\1#� I�kN:!P1+�!� 0-1y 1-e&iPi x5!���Me�2���u�E�QՋ2�*} NQ�Aq>�I(* A�22�'n�&1P�A�\\�,vYm�F3/6�&e�.2}j�u�an ERY �3��!>�R^c�u @%�-12�*}�eaق�i�ic�  A 4 �&�>N���F-,_3T'_2T'_1T'~(in:�& eq} �s=BK2E6@E1pr&�f6'S��Rz$0�B$�0 0+A[(2)�$ ',&;f�}��N�� *. $0��52)�2)�4&% ��P 1  �ft��&���0W�?=�; \#�5&�%� in&�4a-2})��G��9\ 3A BS!aA�vit2@+�in ��~���Jd2j)K� 4a* Cd>�� �4��Ͱ���&: >�?�!�� �_2pB�,%�R1&� 2O,)(2d6��,��2�&[kA^�� �3 h� E.Q>^O:x)/� is� !�re��^F t -��e �!IT)K>/9Xae+�'.� �$>�� �#6�2�� e $66a" powe�;��ʙ&% �4� E�l"8"5W]) �8� � R_4=4^!��^�G&T �,:%2a��!OJ&� fH�!V�W�>�A�6� Z& �'<6)�����(x5(P�-/,�5B�YE��s)A^6�&�%�DZZ.�0 �$0=AEA.�5 gA� & h gA�N�. � 22) S���j!A��V�)u�]�2):�@~^u1�W>�  T%skK)�#!�s:1 � � ��IpMA�`� 6��g�m= �i� � >b�e����r�V�*��. b�\A�:� .D � Rh'Ei!�D 62 2��6[&�&2��ց�&�!�o[,A�!��D @ )N�M�:��a���F�l .{"� 8��I! $#>?�$Aa>&An*�b�N����*i$4bi$R�m�1:�a$.|a3!�xul6�] ]�\-%a5� 1���,A A  6%W!�%� �kZ���Z�.�.Z.�  �b d)���mW��}2��9��)j���"�="�>�0^�2��( bN�� ��"2�^{1�!Q�!5%��a�J��^6�.>�3IQ%Aw�0ve got�o�c��5� "?"&E@�"EKsx'�?0� "#0 2}{0F�-01�2?�� 11; �u�pp&@)*�-z?)> X�vp{j�)m%Q*C� M1B��s ��.!��k!i �&- ����no solus f��:�b�bJA&��*� >�J{ E��= �q��:0� ! >AI��SH �� D��1��+*�#k�XZ.�Xe� @ X�tJ�OFauC�bar�6 �&7��14u��Q !"� ?�;R:� )w�1ne��X�Q!e4bo� �ijl-13:�*�a�� �/~Us��R(3$�t"  "DX"~R�/: rg�!2�-�2�/is N%=I�i�^Y�'��!wz��' :�!�a� < )�!p%9��"�d���O ^_��we. ^VJg94�f�Ie:O ��2E6y�-�}11YT�2�) ��:u;A>��3i+EPRB)�IGN�6o�Q�I�be��1=p .W�="�ZAV�D F9 void uR��a�c��K V�#" ~\c�C$d�C"�F��>�M�#is:�DLLx����q��$�V�@|U�B�J)�(MZ ,  22. �J�^;$"g4�*�c4�"lI�"Yc.1�Zi� ls��new2U :�crbc 7ses��6]bu( T�"�&�L�)�2�>�,XotZBUa�!:�2�%��.�.��%��Vr-Q�� *}\tag{$*-���rmg�\Tu(.��N{�}da�B�m6 c Hae�o(FAO~soJ&�2�-�r>� tb� k�o*u1P�u)�OTua|�e6" b!�V �u9�e�(i���"g�s��{mybi��.��{quantum�H>d"Q��h \Eo([amsfonts,16O� :9�%2%ȦO�Ih , ro�Mng�new�~ ���}�  �"$�}[ ]{"�V>+n�ure2,2XO(�6#A�os=)��2R�M>.&r|6-0 XE�5>'ercis6( 2}axiom}{A2;Irk}{Rem$ \def\ppp{ �b{P �aaaAfffFeeeEqqq[g�Zrrr]�ccc��zzzh�nnnN&�p�bf�tof}:\� qed{$\Box�IDeclare�Ope6�{\��{ V ���� %R Perm{\rm  ^5{i��fqnA�ھ$David Joyn�(nd Amy KsirW��e��s�Ψt, USNA, Annapolis, MD 21402, wdj@usna.edu N ksir} D�Automo� sm gE��Ss\�AG cod:P8\date{1-19-2005�mje���"�K�3m�K�^�:v�ma curv܃� ��"�aB� 2"�%� �Bsame. �22ilizB��Ho��semeyer �HW} beyon ��&�ar �g�Da"V� \v� .5in!��z:[�Uz5�(of�w�,Riemann-Roch؁ $L(D)$td2лdivis�D$K1@$X+df� �ȥƪ �� �G( ypic�4Snon-trivN?.w����n� do��y ask�� 5 be/ 7 b����A�AG EX9 e��$XCConݚ�YBa�n Q Y s���.�I�!?I�us��)� odP�K is��weY���:� Vk1�!w.΍F2�;}r�L}~Q7A�aafa _kXA� Know����� largR�!�hav�4l� |�/ncoeb�IA HLS}*X�!��ed,2��dAcbeAAmp_lB�n !�a2. �error-%���compu���p�� �GUAVA�U*��aqbO5~a&K�M7."�jsec:1�Xc a smo?���veM8(schem%t"h� ��a � T�$FaF(X6�gi��o!�al fun&7Pa) 5D� �_� �X�e2� spZ �K[ ��al�-.��� Y \[ ;,=L_X(D)= \{fZ �^J� |\�,(f)+D\geq 0\96� , \]�?rx�i&����#((principal)F��[ �]�in u f $E�D"+� JE6"T�5!�A[MAicW�Q GF0t�L( Y ) = � \v� F}��{Sti}]�TVMIeP_1, ��P_ߪ X(F)EBdM�ct��s�A $E=P�^� +P_n0a�]� �. jD#a�-� ve DžI�Ru5�|��a���� s;�rt \C=C(Dd����m${ ��u4eqn:AG�p0} C=\{(f(P_1)"�n))E.ED!`\CO*>: imageYM�F��e�Ee%ZNv�,"=�t {c} _E:�rm arrow F^n�&f \long�Nto Z�PL�gn���kernelQ�� xe�Ia��L(D-E)"�.is empt�i $n >!��uJ�, [ � n is&t T�j>�n�� de $-�. .K�B�.��O!�66A s}&�8�.��|6Sm� n����Kt+D��A�b��sta�B��e. "3/sa� $G ���� Aut_{D,E}��n93a۾-��%����)m9Q�aa���$ B O;��*:�as: \["�E0{cccc} &.?&Eu]���� & T *M� & (f: T^{*}f�n��4�;$P�{�6$ 1(P)=f(T�(P� (W� #�+ r4g�R�i$ �, con�( ��c� n��,M )51�bJ�,q�0&��$Y=X/Ge%$�}A%^^G=F(Y)A�Of�� rse,>�:.��  $Div)� ��r� Et��d $T(v� _P d_P P)�� T(Pa���&=�R, $P$ a U����$G�;���Geasy ��e�f @�#T)�=-�f%� Beca�e+� D6 �{J H+ HD)�$,��� .��nem��ar�l!�)�{$GmL 9 2�X�Xaves $D�1ka�l�Jk ��n�� $$n > fD�.��� :�H H�C�Vll se����i�to �3E��nGi�C�,S�������9$T%�G$ E=by�`"9�� ��2)�� n)��m�& -�� )�(P7 ,<\\ & =9y� _1))^-�>2vn))њe��Gw��so�V-hG9�E$ )����by.� ** A�q \{P_"�, P_n }&b'�1),��-1}�12� n)9 s a . E�e7  $!Ef2AP_na���h#!�]  C$�lpl�R1 coord6�����J���,Wbf{.�.��c} $A� �� $Cq:F^n���ɻ+$S� (A���n $*b.q�.�)� �rexC�y.��F�D2uV� +W hom&1�  $60aN�:1(]i\rho: 25 0tod� \\ Tu" � rcA&*^~ Ŕ�k�e2+�,�d�co�a�m�t��is .��t� ���.���*�� �we 6��ans�*!� quesA�:] C& 2�2\A@�A�iʟ���of2i0� $X$?* ��b]�Z?� t T2�� ;WY ��e�vL��&� f� is�e�� . Un�lt��"s�| ��2� e�U &� c. �,�fa= Wf��E& �U!6 WB��alt&Bas*#��" (thrm:lift} @n��!�,%8 9: � ��� !J$Py]^����Х� $X$ "p�a�! � AM$D��@ E = V+�+ZCa& �� C = * ^)"E �U�[)�]z6J��, Then there� is an integer $r \geq 1$ such that if $n > r \cdot \deg(D)$, then $G$ can be lifted to a group of automorphisms of the curve $X$ itself. This lifting defines a GhomD� $\psi: \Perm C \to \Aut(X)$. Furthermore,��autC,s will prese�4D$ and $E$, so7image�o$ 2@be contained in $y_{D,E}x \end{theorem} \pf First, note)Psince %ST\deg D$, $eval_E: L(D)�\ C$ is a vector space is�. Thus�4permutation ac4of $G$ on $C$ -�0pulled back t!�linear4n $�!G0Next, we use ! to embed %�4nto projective �d$\ppp^{d}$, where $d=\dim V-1XIfUTlet $Y_0, \ldots, Y_d$!_(a basis for �,�n the � ding!�given explicitly by \[ \phi:X\rightarrow \�d, \] TP\longmapsto [Y_0(P):\ �4 \ :Y_{d}(P)].2 The 2�Fa�($ induces a9�n�0 polynomial r�$Fv� ,Y_d]$ A�a.T2� !�%_d$. We E� showITundernD stated hypotheses!@a�IQ�I9Y�X�-�di restrictsE,n B�X!�F6jA� d �tabilizA�0e divisors $D �$E$. TEFv$$se claims,E`us look more carefully at� j of $G$. LAP \tauID n elementm ; it3 s by!e}/ofEZ(coordinates4 a point ie?ekee>e;a\ mtoM� i)Qcomposie�m�,^{-1} \circ 6 i�e* ich �balof�+i�we de�9again� y . II]middle,  �4as \begin{equKX} \label{eqn:1} (f(P_1)Q�, n)) \m!{� (1)})( n)}))��fm�,f$ was a funI!Je(. Beca�a�.�)� leavM� code��$ invariantI� new1�s alsoaP2. S�c-d�.��=F��=�w!�!uA� call)W(f)�-��vf*1-g)/2F%o %G=(%jf)6� n))�^9mTat defi�+�)AAC��1s0In particular� - A��)B�}$F�'Mqa��Cv���]$:z8,4} Y_0^{e_0}��Y_dd}U�! Y_0))dd}J5ee:- o�[Z�dI=��llows: ��^i�%G$ A6V�"�A$��:�:��a �� viaz2} �I\ KŨd] = [�eY_06"9 d���Y@ NowQ��si�E�Tai���F!affects�?�H�:AE�<s $P_1�a P_n$ݧL�� $�($. For each ?>i$, its ^��,hi(P_i)$ has� .�%r':�d]�� Thenzv}�B$array}{lll)�%O(�P) & = &��!�V \\ 2%�A�F.!�A�.3��9i)}Nd�V9 �m �>�X ,A�2(%ۡ_A��J!�inverse2�mSR�H��Q| ould like�M&�\� E ^ ���d� $M�(\ref�� *2})f��qi.�1 case&� 1| PX$ must have genus $0�!:z>A' a&X ati�/y holdsI�$d>^t*^ $Y_i p4 satisfy some � geneous2Gel��s�x@ �!� $R_1(��K P {d})=*b R_kR#��` a se. ��e�0minimal degre� at � e idealD �.�L Ct.�*n  i�[ 2 ,� ]/(R_1�R_kA�] ��R�b $ are2��l!�8ń$,o J@4���)Jf��be *rD)$ � !�*D. 2wIwe� $r� Alarges!V%boih $R_i$'s iɬ$Y_j$'s�n�&"J�. (Oft��isa4 trueP a small��[n fact).� � �z\in G�an28��%C�6e�q�tau�!X))�Q��/ dq� >�&� .��Uk�u`isa�er� by R� q�A=$,#l4}). I�&2�se" sEj �M��che�,)fn �-H-�!�3} be �l � w� ���!{�&�1H,�  we�n� � via �$�PEn�:�$P!�X$,z3��(P) =�C��b )�P)J� � R_ieLea+onN!:U��rator�r the %(Am�;M�i$��at mosteNa�}� P. �'t6Lk�!m�E�(Raa� %�b��rᰉ�H � 2.. �!(�_m�F�,�� i$ vanish`t every( AXe�cluQ : "x  ,x  asAjA�ayby�"8V��  $P� 2-'�7i �%OB� � .7 -1 n  � meanFat2d��| rD - E�But�MCr\"� (*�rD - E%\a��-�$< ��A�,)-A- triv�.�B�� �!�n%q��N��i))-� <��)�associ��XD�V E.��nI\�k. We�E!��<>0��G.�F��ݍwAEtG P�wS"� �.~ 4At � stag�m�0$multiplicaV!rk�a! morH�: �  Us!V��})f� �$I"Y՛� �y;}now nee�!To�� % ��L . CoN *�%��G^  Ga D$.2 �3� AP�Xjdd ��9w:1:eGe$ we k�) O\ s�.ah suppos�hq�$ did�2 �tself%�V� = D'g D \neq  but f =�'a�� !Zrei\be���$P$ �r� !t*�,ts coefficie) $d_P�)is k &� 6.-'� D'��� c5�" $fem�49�it���鉭�@�'E�($div(f)+D' e0�a9��� ,$��$P0 !�� ��� Y + ��0(d_P - d_P')P�0���& ��\D-P)�s*3 �f)�%�  =� 8��we��uma,E,DI�Ŭample;>�R sepa� � in �2dim!t-�  ) - d a!�tradie��^�mB�$� 2�.Jp!�� � � j}"�1R��*$ \qed It�E�Jl| fromp�onstru�� rho�-�� hi$,ce'y exiZ� � �+�r, mak� :��C$A� �cos�he ult below�actua�sl]ly stron9taT� correspon�reBhof Wesemeyer (Corollary 4.9te{W})��0 elliptic cur ode��cH"�:main}X a smooth*7 d�� $gi.2a�� D ;����qith $� 3g+1%� F E 8 coll"o�at�-� (1+g) @$^ \ disjo{Q:�RI)��*� a��&EA�!9 $C=C(D,�" c�%gr�FC�e�fix b!E!!��V5{�z F%,<is��SjT; �$thrm:lift}� want�estimatj!�S.��q�� &�($|D|:X\hook>{d} I d ov!Fa �W4�var� *b &�(=�kv� k=0$Rof:� . As�KO�proof� - : �U�tak%!b�e max.��.�� !BE�\bar{D}E�!Fa"� U�!lgebraa� losu�?F}O\By ``base-change'', we s@B1� k9� $|SD}��2F}>�qsamWlt��...J�(A�he�% r). N>���w��m"����"y���lyepend�0 so $2 \leq r�ge�canno�����  a�erplan�� pp7 �$d��T3$, Gruson, Lazarsfeld�Peskine��GLP} (� �a�U�A ed)P %rE�um;�I�'s$��+ 1�e��s,  �% + 2 #fI �� zero��� IVis��%��2I d$-sec�O!pourx,!"= *b�ٍ�, non-special��$d.�! - gaT[f�if �Ue�X 1����\c� !q,G!�1+UA[Wew ���?���all out!}�v�\���+ . IfEU is rq�!@$d%� ��Q) n�Ism0ama݅�X?@a��fZ2I���6Z�E�conic)mr=2$. *� $tst#�9F ��� T F e�%*��alwaysEXa 2.�i�� surpri`)��I�� aq!� ��lAE�E)�2 � 1�A�I�1�is-edM؅ pp^2$, itf  !7cubic�$r= _ =3$; !%1�A� be j�3�$=9A�A� �9| �l%�!�c> B x�� remark} U"�"&�"!~U� 3�M length$�  $n% r!dimens� is $k D +1 -g駁� ista��$d� !O E - D$ (���x� �II.2.3M� Sti}���� ;}9F=GF(49� nd�X��%E ��$ y^2=x^7-x�$iI�IH$37 J� $Aut_F8! a ceI l 2-fol�����$PGL_2(F)$:� ��aaV0rt exact sequ�V [ 1\*e H .r. ^7. 1,�%R"H1a� bEM�Q$�eK!!- hypereU involu�#(dhappem o�I !e/])�details,�\��},���' 1N<'re���-"E�\S 3.2 EJT}� re $ $|X(F)|=2�<7^2-7+1=92$ $F$-��> \footA"${MAGMA vie��� a�Di#we� edo 2�', � s $_$4min )4�T�3&�� �'ian -r�#$�+F�Acc�(��,Z: J(Y-,w*-6)�G$�we cho$m$rQ �" � $$=7mA"Ea.N� ( $(g+1)�i D=4 "� :D = m< is.�$7& m 21!�Assuma.�>2g-2=��BcK implies $U@=m-� soVE�84,m-2,e:84-m]$-U� $���!9fixeD) *w��*o{*���g:n6*�, (f(g�ecacii�\�$ganG$$"���M� �lly�� $p>3 �T$p\equiv 3\, \pmod 4$,���b٭� *� ^.ɂV�i�x {z�ve 2���ys@\frac{p+1}{2}$.} t+$9 p-x"�� p^2*�#n :�^ :�( $n=2p(p-1)��=m- {-3{, N 2p^2-2p-A�provi� $m>p�EHi� one-�oAG ��t0ed@A�"���-0�|$,)#7su<  es�� the � X(GF%)- �1� .�3����J� W�$m=� O�amete�i�de bea�-\ Gilbert-Varshamov bound WTV}. X pbe� .# *GJ�� P .8 tl���3-DNN5+�L � s//$Q=�t%"ase, a�/�� subre�Cn5.͐re� 6. It t'� te�/�to� e�dec*�.R2iPn-�J}�%�nP ur"Ci�a .`a"algorithE~ vlexH $O(n� For a reldiscus� (��anq B� ffer0�e).� Li 2� %� a ��!;��aye�2 � %``su� ly m>iN''Av�dropped.n �51�!��%   enough :� k)��apply9� ��&F.�� �} A��6g;3 [& Ŏ�67-x�G�E�time ��G7!��N&Z 4 w&~ F~Sv~ \ �~^f~ as b�ʈeQ��6��� e� for�*o�&�e��.s $G~~/3.p.b=2a�,Pcc} \gamma_1= \left\{$} x.�x,\\ y.-y,* 2 \ . , &^2= g 2(a)�ja^2FmaVm\\k3�_x+1B�V].�4�_-1/F�y/x^{4}V06E��G(�},a� F^\a�sa^�}rim,( $6-th$ rooj u� . O���y tc Zonly $8RwZ�0>�P_3&��, P_8=[6�"� us � mpossibl��e 3 ��-��K �7� E$ isE��lez"P �Jtinct>S."�nstead|��ato�Cff!0s >��<\��!W&~andFH:^e�%�.�;k[& previJ.���G���: = F,$�&������!L&�U*u,Ap% <s $ bi.j!conjug�[:ach)AW;�� , $1��8����M d�2_ 42$ (I�,� = /Z(G� ���^D21&c 5�7� ".� .) T�S.s $��L 2�-th $a=2M[ &3$ge�+�8�w-4ntify $S=\{P_2"%/P_8\}X \{1,7� 5 j1-ft��a1;D(2,7)(3,6)(4,5)=g_�^;� 2N45,316,73233F3�33� �>�>�>N>�V$D=5PIS=C(F)-!�1F,|*P_2"~9�P_8~' $[7,3,5]�d"� Q fact�&� �Ne 19u�M map $f.�:J�a�"��< ive���(E��VN�*B�%3E�3 &�)�P2�.� �(���od+t a �c. How�+b-*]4!�4-�P5 tl,�E (�)���|�&l � �"� r#@ a .�&%HG& :Gu i�PemW�D� e kernex/b map?�m� two p�(ilities: ei(*�-6$�a J21$ (c6=ob� �= GAP}u#atc"- yle )s� 8 quotients $G/N�� )�(� $P�C Indeed,� � $ker�0P)=N=\langle g_2,g_3\r$ �2o ny le)�@1,>D*��� @>%s3&{Ac@ ledg�>s}�Lthank Jessica Sidman��pre�)B� �9oflC-'R�� W�Tr}=a)� helpful��7��'"LLthebibliography}{99}q�bibitem[Bo01]{Bo3} N. Borne, %{\it Modules galoisiens` courbAd%u�"Xtroduciton,} %S\'em. eti- gr\`1$SMF \under�!`{5}(2001)147-159. %AvailaAF�:,web at %\new4� %\verb+http://www.dm.unibo.it/~b�/+� � GAP]E�� GAP~GG' , \textbf --  s, A�a9nd= gram�, Ver�04.3}; 2002, �B�8gap-system.org+��x]{G} V. D. Goppa, {\bf Geometry%��Bs}, Kluw,* 19882EL��#L.",$R.B/$C.2$, ``O`�&4of Castelnuovo A�� *�8 sp�D� \s," \emph{Invent. Math.}5WD72}, 491-506 (1983�6\5UAVA]{,} GAP error-�*c� package *Zltcadigweb.ew.usna.edu/~wdj/gap/:2pHLS]{HLS} C. Heegard, J. Litt�AK. Sa�,``S%�a�*enc> Gr\"obner�?e�>�i clas��"}%-g)�ic)� �,''1AEEEa�ns. Info�cory} \y.D41}(1995)1752-1761]�$J]{J} JoynA(D.!�C�al25"�of��!�Cppe�@)�,SIGSAM Bull.��1�,JK]{JK} ----E�,A. Ksir, ``D�ng 6�%�8 2?Id! p<i+2003, a�at6kfront.mA�ucdavisE(AG/0312383+./T]��W.!�ves�R2F����� p�,�2 � 210408+ () sed ��fposOAprilg4)�L]{L}]� ``� U�.uc�.���U� in-�Procee%�433rd Annual A�:ton���� mmun&4�( Co�l�^Compua�<}, October 4-6, A�.�*!]1!} W��smae�CZ)n,��layoust�6� � , I:��,Ir :u�4$'' J. Symb4 mp.,.�24eq$7)235-265.�~ (See/! rhomep��A�ѯ� ݯ$maths.usydA�D.au:8000/u/magma/+�&%ug(MMN]{MMN} H�b rtin%MigliAK S. N�.t,�De�<%�6��6��cEs %in� I�,''-�Comm.�.}��(98)1209-123E#� Sti])!�(Stichtenoth��A"�,lF field�'�� }, Sa8$ger-VerlagE3.TV]\( M.A. TsfasY �0S.G. Vl\"adut���y�� o�S4 Academic Publ�9rsz2�W]{W}!i"#1, �F!�.B&w �.�6YZ�S ory.�24��8)630-64%Bt:� � docuFI@} h\def\draft{r1Œ({amsart} \u�3�T{!A�8,amssymb,epic,e psfig} % cd,pb-dia ,lLrow N  macro1@�style{pl�1eD  {axiom}{A2 "}{�6p&�#}���#}[s<on]2Mlemma}[6]{L2'"�:+"� :/ K>+:Vjure}{��e6$ob�N� }{O 2J,add}{Addendu!-$)^��J656De�io:1proble>�P 2�qu�1on}{Q 2 prize!� 6�� �+ �{c 6�Ey 6+erciseB, 2- hint:)H2% �6|R�* e\��,tname#1{ \imnl y \smash{\makebox[0pt]{\h3 @{-0.5in} \rais"d{8pt}{\tt\tiny #1}}} \fi !,$newcommandS8thmode}[1]{$#1$ � ,psdraw}[2] {:"} �1.3mmk�-4�i�{figure=T@s/#1.eps,width=#2��1.9mm}��3}-' �#1#2{nUh�(4=#2in,silent=} �,${\standard } \se R {0.012%o2F��%% {9�{#1! Sk{#2R� B].^7!^1� =�-)�input 9_�o }.26a =c :�)8D�����3E3:�tex�� \cat�`\@=11 2ej@aGcap��EH%) $\vskip 10p�(tsetbox\@tempboxa\hbox{%\ifvoideX else\ aifi N a�ll\sf} p8font #1. }\igno-9aces #2}�if�:\wd| >\ @e, ���=\@ &margin�N� � �j \par� �., to\h�"{\hfil�=%fil@\fi} \�\b.0=cmssbx10 sca�T,\magstephalfeXd�/>�6�=2�i#54-%'2 = �62 ;�� End}{\ope�D��{: Span>'s:(tr>&tr>$im>$Im>$noi}{��� lbl#1{�Q#1}6w�.� (bN*�Yeqdef{\�! set{� ��}}{�:uBTclear{ tenso)&�H �7a{} �:oremitte ".b>. .b{�� & %%%�vros's�" |BN�� bb N �BZZQQRRCCEE1�A 'cal A)A (<B : C} %�D'D ' uME D{\Delta K5K cLL GG OO TT MM N1jFF &VV WW PP -��1�6�I�I:I :C1�Err)Err1�a{\alph1Gbb�5V La{\Lambd lakGa{\G# {S{\Sigmp ^p ! s{\s!varsi{ 7ga{c�s{"_z+ splij A�ihs{i�[�� logy 3-sp�! x qhs{"� ^%hs{^ fti{� e typT:�an�uf{�-f�)d urftly 2 Heg{ar.cok)�rm{cok��to ��la!��va{�}�def\Fb�%AOF^{b}_� M} �T filt)(8!. nFY6JY>HM�G2rG�rG2rGbrw{\omegQ{ov������we{\wQ-0gl)\frak{gl(gU�%D� au 4ev il� !b> d���6Wth{� ugTh{\Th:%pM m� sub{seteq�lk{ͭlk� �sgn:�sgI9.� KeB�:�c��.-Sei)9rm{Sei58 iso{/g (pt '8bb Z[\![t_1 ,\d�\t_m ]\!] *sm��Osmile}� A�D  �mf{ frown>+ M�sminuZet0ti{\widetilde�Zle:<\p�6� )� k 0.1in5�E|6K NG'fEwheel�Fw2fDostar{ �das��t ��(-gt� {\up*��o|�680of \strutb % I�_ #3&V #1}{wd #2}{06p)}.� N%2� PJ� s�9�2in} }B6� *�  }}#3B�texZ��� F�v� 0.0cl-d (-0.25cm} \\a%> |� pac42/.- \bul�,F0.0|ac:�s }}\! % ��F�9y%�.�v�R� P:#1��AS�}rm{AS�ԡ�IHXIHXGA{\A^gpu�GAz>,0��ma-#4{n(�@matrix} #1 & #2 �X #3 4 �*&�)��matX$#5#6#7#8#9 b[bb&_\\ #4 56 7 89Z|]|Sym5Sy� !9��p#al*PeY rm{Pe� *fs�V s��a BZ!LI� rm{LIG1�LI� DTTI� rm{IM,IMJ�IM}_J��ot{\o,>�0l}{$\clubsuit�� bt{\bar{tXrA1 rm{ro�%to{&?( t Sev{ �y A�I�,Ges{\G^{ev,s`si� a exc Dr�cCabCabdFd���ud�acg%!9\cu� �GO Pasa�mHJ 2bq):qe} �rU$de�de�ver� G��s r� unkn�rm{ :defecndefgldegZ�vph� ph�A@Edg!�-��2��:�q6{61af$title[Chro"!P"Ke, Colef4Jones Fib�q-Binore Coun]{RF Colo�F�author{M� n Loeba�Haddress{Dept.~of Ap>:d�"e��,\\ Institute5�5#{In�) a�S�jN �!�RR�lbl{sec.5I)�Q purzV%�is paper�C0 been a desir 4iEstW compBX!wo)*orial "!:� 'cate~:q�j1+f�,L}�$m�>&on%�V term.I %�e0e�U�]� u9�;I OGob��Itar�to live -]W�Te�&alq; may��i~n(Kontsevich  %perhap4iq& Khovanov'��on NX�m�� (�-Kh}). Fi� push� sh fo"`&%��P$nuscript c�OE�St�0 GaroufalidisK�V�*ed me�=utM } HGR}-KesA�i)]� "� y!= }��of�o $0 me sketchI��%!treat.�Zt$J_n$.�-%� w�3A�m.�?$n$-cabl�(of�_.�QutnotE$w(s)$_:c'ib�Hy)am $sWg%�W_\!�p5& a�\0ple $(f(s), S v(s)�1wN $$-0a-5neg�[ Ebere<; you c? imagGPD�a\Eҵ𑏡��� $K$, e�+h�<it tur�utA�beq�,0�ere-�-�arc)�!�.j=$� �e�'Dx1\sum_e! (e)$&S;)Xsum!u8 all 'jump-up'"�7�;$eHK$�J 7�> r as-�e�'� ���W7� �oR Each�Z� ��E +�J!2y ')�-� ure'�Jnum)��!p,�b%� #� �n�'duc��� .�. � ly $AOAZ@v�rof�M:x���0E�$ j$0\&Q[_�H(nzC _t�Breali�\w!n naturO,es$@M WA2S $ChDele�:� ,1IFd8! $w(n,f,S)R9E#!ke�I*A)e� s $s�2)h= fW5A�= S�:by $G��eur�nI]A����� n we�ci�$w( ��Cwr�n?pH $$ Z_{n,f}(t)M_t^�1}(� ,n),$i$2!-�"�'.�&5 $d 6Laurent.5sf:t$ pre�%AeqI�inI "/Wm.ma2a� �� ^� �� �0l��a9�z& * �� F�  AM&1; pairtJ(V,Z-�V-��t�We��3� ices+4= is �5 %unq5�Gaix5*y@ $V$,��P���E�R e=xy |nE�x $x,y�i�� Gnd-�a^e� �$$G'=(V',E'I` ;a =6 aph}9�7aph=if $V'p V�;E�l � {y �� ub.qchwI�"� Y tudy�&�A" om�f?b�A��i� } ]def.qc:RG1�OK)�.6$V=\{1x kn49 $\{i,j�A�M!��uWe��oM_q�=�{����@ �}q^' m_i v_i}.;�.A &�Y$ Xz)|_{q=1��! �,�Zh�6( ���9|�)|%d $AI t�fŏ%wC(ARuuonnAP vitym pone�8of f $(V,A� !R>UW� Sc|W|2���q1�$Wa0� �zE^thmA�}!?1"-z�L} (-1)^{|A|} \prod_{�4} (z)_{q^{|W|})� %�j� J�ex^$iveg`ud*i2} c�lmӅby}:�$B(G,a,b)= I0.� a^{c(A)}b �E$]!�O!�e�LaH*�� >�Knex U� �<(details). �X$n>0$I (n)_q= �J q^n-1}{q-A�e� f . E EF(n)!_q=-v,i=1}^n (i)_q��~!  Q n$�wee�I^� 6vby!G{{n}\�C {k}}rLM  }{(k�(n--K<� ulaa���� qch}�n"� J< %�q-9���r�yR $$ B�3x,yRx)�N�y>�E�%<��]/$B�:(G kA{u�  T well w��L��:a�s�al%�Jt=s�, �SRphysics|con���8A�Pot7sIsK��<�c�:0 >�n qKSir q-m�oP86� rFgͬ� p_j�P�� �e���Sg��m � $J_e�w�- (coup<�ant) a&Z � } $e�6E$U-//lJ��%�ed 0$$ P^k(G, J_eUX8s}e^{E(P^k)(s)}* !�s*!�[��s� � (@N�t\���6�$} J_{ij}\d|# (s(i�L (j))��F�FkAFVN\b  etF�s�o2}(1+ vZ�)= % m_2�k��q{OA} K=B$ = e^{ �}-�UIf%M$  %nam�Xe get QB�^��eB���� y�ic*�HI����8pt�Y)x5�s�+�&�EA;xF�}v; (e^x�}=�t , (u$$)��!�b4{q-%}�q �Bh�;ns`we&l�=$��d$��c?fP"�n �Aa�r1  ad�al��r �7a!x�i��7 �5lqP�F�M�.�k)&� =�Q{= Ns"K {vagV}s(v)!�u���SnqdU�e5�^�=�i}/ ^+ �H6�5� ��6� $P^2�H:e�ZZ�Z����-1� ņ $$ E Tn��������immedugly'I� e^{-)�=ǵ}�, 2�� TNo.�a�V.]j�ad�Z�^�Y�&�7I�cor.qZE����|E|x}q�${2x}-1, 2)�and� �n�)� = q^{-3|VR\ ^% ��iU� Van UZWaerde"^ ���m}S�6) fact�a�^$A�a"�Rof :k ��+t u�VgeK���AD. ��@]oS hard5��uhK q- Ili�D�u$e*� notg: !�sinh(x)=� �h!fx}}{2}�s6 +!u  t L}{c 75 ",'�#��wE=~  \N��u qY}=��� 2,�I) L*4 F2 A}th0 (q-E�1})^{o] (q+|V|- .�o(�5s� F�!��Hf��od �>rQ>� ]�<,J ���U�eB  b~cri�� A�ɪ&� "�.�G6� �far dire���I���.�; {j�� ex ( =a ) $vRJ�ig f(v)$ B it� �I$arcs enteraV�� leav it. G�z�^<�peG� ���} $M(G)�( ), E )$�� s: &%;facS@!�why�bl���L at n� bou� 2 rece!-"�W�. �]Fi���"`;xn!�"�l�!� �:s,��%.!w�jo � �i�c2qC sh�a 1�.����R �>�W laA#Ezd� A1@b�bKe !�a.roE |d��.5,4Mus vdescrib�#at U4Z } bef�'�2'2�A���l"%~-inc�"� 1!-R^7$!;E�=�--q-�Kor vic3sa.ix|V|= x:k�n2^ay�!�D b5� �;d+:.k%s}. AfA`per�ba6� LZ��%da 2 $sJR�e m. �"��q �RPw-��ng cyc&�Kk;I�*.�ir�G/k� ex $� M9\e_8=�Gs$ �s%�q{�>z)� (i.e.!6�E��m� �A�� cut)%���8oRNwise. 5�3�%sj���UYs 2.6T2.8A�Kauff�C�^�K1}Eb� K12� ��� n orhed2�:���"� $f_K` �$ invaŠ:�}!,A�*-A)� W(G)}�s0s (-A^2-A^{-2�K!�D� �-�� \a�(v)-B2XPi )�} 0$. �a�!�>*/ als�J(G, �4}��, AK B "� ��!A��erm��a s\ OA s $E�ah���!�"ahM#�a�6IeA�!syeasy to�i�his� nZ bi�Fo&(tw>$Y ���sU �e� ��=7Q ��>� U j� = � {�{} �� + 2 = s)}� h�*eD�.@$$ A(= 2c(!\ )+ | |- |�|.x &!�Q"��3�XJ� �,`�E �o�)6� of} .� �f� �a�AmR$ ^���(� � He8+!ơ�|i�s&� Eu���La�*phsW �u&�*, � � kk� iB�:�-5�-1}a�b} �B 1�"7Y.2m A^{2A?X %���)A�o a"��B| aTkr4*� -"�(G� !{same �� $b�� "�a!&�v5k-b�����4-�6�^6h5b|ml |} BE�,D^�d%/}:^2m~B?M�"�F Isq�\$/as� apa=[x��tant L�?�>? �{$��J� -�lte�a k b�  aTtiz�7!��,>�62��+� V�MM�[..f5.2.14�J.��x7{Aproxi6/,.>����ap\ A�%��ve�} (`C. "�&link)�] �0osaq��,�**O:I)U�,<ly.�w} T| mirR'e!aL���� *�  As-�� V)�PAHd�yds��S(XorAV rol<$ symp�|c aspec���2 4-�C��"pX> (m�asy~�j4of Lefsetz fib>=)� a� �eofU-?0hv �j � beha�i����'Ai�J6�.�eCM,St}�fo!�NPP>U!�a \#P-<(J,e�!�J*K [Sec.6A�). ;a` hand,E_IaskSe�Q�}� >�. PZ2-�!-��1uNFuW'*� $randomized^.qDDon scheme} (FPRAS,B short))�e valu�!t>� � %�.x AFW}�~[stPXp�b�aJ>�� ��g6�%Gbe%��bl! 6�q-C"�!"� of'"D0�:)'�7N�"�# |s, � �sq)���ycla� ?J a�nfQz�\O��#��a �.�"baa �/R%�$x&}#x_k�T!�� ��!V&�o��#)&� x_k�a *i�z  � its "j hoodaqE5vh�|uc��d�:� i$; � m(���EJ��.��} ��j�el�Bȇ�2��� �of�charac�X9%�1�s.�Ft��ߖycl�#�#edI%��ia0s rooted}-May!yr  Lx ingu�.>�)�@m:A�l1(reei��- $T= ,r� Fo� !~ix[%rE $T�)^uniqu}mt!��A`b-oG�. )&n!?hoon$_@�d �$predecesso(( �n $p(x� "m �I0n p��r�/ri�. HP HWe sa2'atA�ub!#Da-}  {\em� rt�(�-aYo�-3toE!��AYTer�m��.5 s: ���QIi�d5gif �&}`z 6�/ ���!�ee.��'��:'�BA���if(%�9� �a���T=(W,F&�%4t4�'"-'�M��e�)$T_v, bUy< $T_u�K T_vE��Ytyset$>+$uve'Ja��'f$ }U\in W�bi� i�8�!�>T$%,�!A s $A_w, Bw @ a�.l!5:=\{v;�l\{�1s at} w&�B_B*�1 ains�xd�x@?y/$es��!��a�pr,/7&^ enume�#(} \item[1.]d �$' : �)cup_i A_4� 7 2.] �j t #{w'! P(w)}AăIn�cular� r=9�. O 3.] !�$i,j,j'!�6�!���e.$i hj), j t �+�x(B_jE9��n {j'}$, � 4.] �5A_i, y?A_j)� $x�#$� t A_w!.A;�*some $w! end.� 6r.6�E��%� �Ie�"�1� a.��+str�.��?,%�{"/.A��de�-��!jsee (w),B(w):q ��sf�ip5ve]�( 1.,2.,3.,4*��|B_w|=b_!��n $(B_w:il6�- $(T,V,(e�b%)-$: (=!rr� ��!Mll9Es�c.�\SZo1�.l e.�s:�iu!�s%FB� a+w��&+ MF�� A_{palMO �9!9"6/*�$j�&+8Ő&?�;o"�|. .numE3�&v =Surfs $�r��)�}$��<{a �+b }{b_w}1@l~Q��}0rem.s}in6. � 6�s�W,F,r), F�.dGv"`et ɋ0lvv.:g����v���`u,��^�tW$,yr�)�%�( �w� �� <�md*v�1;1K.�%ݍ �A5S/_y ,�\{00z�#^�0 �:6� �.}�vgY�4�#i\�$G(�4d   � :� ��A� � �)�]c�Sm(S,x&�Y�$�轘�l yB�A@�.�%�fcw;Let $c�$i=6rXk .*�Bi$\K/n  ��xp;$$ac �!c�label"���='{"s �0m�U��;Tu�k�f�rc� k�:lh ŇL]rHi8> t lo*i%QaliGEweOa�e&@��r�,a�t�"rea�)/��D walkA�!:d�%��A���B$l�B��c�� � "p%\Kj&yE�0e�C5&6G_{\K�.&��\.p�_def.arc��l- arc-  P�!�> $YC��$ ;blue �ed2} $(v,va� (�#taken�-ulh)� ]~aWJCu,v�6�:B4u���)a%�L ver � E�-`a_v�3 �� 5<re��i�}iP&gn%�5$\�(M'-q��.c���� �e%�q AeK|$<2|)�| A=  w!zP=ois $t-ig�}7?F?!v� $)j<$1-=u)1H%�_�"�?,A3K�V�� e diEN&�Iby dele%��r$ �|1 w.� �cla�-�")�w y\!w-`�q!, outde8* � !F1�9 in28. � also �e�se;$a Hamilton��K� 2Fall�f!��5d�!!5$e_i^baG r$�e /(red)5iF�)}�V� �d�ex.1}�8!O�c 8���$ have�$\lc{ "8}{1.5jd$$ It�6�ŌU�Z!IA��Ju��#ذS)�=u��2x3�T $$ 7<r!L-%7� xN�cir.'�6mM^5  YM-�#flow} V  �b�U�� e& f:EIt��N8(G)\longto \BN$�� �E���at timA$(Kirkhoff))�Herv� la..e t��I{v#�$\, v} f(e)�;'e@ �% %!�Ul.���Of�M��3� � �` 6]� VJGe�ofA%S*�/$v$: e�)EIi)- YWJ;. �Kl Ja���lu�e��$�a�j kn3 28�a��u!�6�.� PE&�B�=*rC ,VI>e:..��"� * �sg � �<��;E�f)�EE�XeY|hs�Z1cm]Sxc0v 8 ��^b_v)(�I P(e^r_v)}�]:I \dG O-mf�I���/$\Sev�nF+!h�1 admiI�} �s ��A�G.�C� �oqB��'�S� ed�*Z�m�i�R��a f%]I�W�%s��A*�d;.���.�K�k-,&g&��rithe�k� $\w(\KR ���=m� �  ��s: 3smBXen}%�Zn��ia he "�.�p �;�0 �I5al��rB&a&� Od"C3L t F] ��aG s)�. /, g`lkFLis op=e��.N1Ktt�5�.Ņf��d(K,n�0/2 (n^2)�+n-�) $)!/01�2he�8)d�< �]LW��u GLvY0 arcj� �JA�(t)= VK(K�+8.c[� i�_ "c"b(c) .U �} �2�y?��)!�Bbof aa>YS'ctP'/e[�+.T�� |yY i�% *�U�& %��*e q ed2}� red-�S=&y G^{)�$.V &�e� $a^k��k.�e�j4Xan���6�H $(a^l_j,a^{l+1}_j)�,M p e n}�O�*$\e%�\{-1,+=�uig"Y+q� $l$),F�� $l�r� l]��So:H2�"�1,/(a_k,a_l��J�*C�!�") F s)) k_i,%) �i �dF�R=,(j-1)}(1-t)$�p. � (n-j ��a�A7.& $i$ ��!G$)4 . $+Bi.d@NJ�3n��Mj� �a_n�c�:��"\e)e��fr�d�% very2e�lE� $nIDBN$ ���J_n�C �!���3um_�E\Se�NF.D� � R���Xa=�$�S$���n{T�(m)" Hq^m-1�H�&o  �D�jer}L!K�s�Mb.- fact]WP&���k �"+.jR} �H�$!=(1)_q (2#L \qquad^znom{m}{n*�H�!}�k_q!(m-�I!�e�na4R��s $m,I8A�!��Rm�eE�%�a`_q� u=vQP}Z_v^b)}_)K-\A�eB}�� O&9�key��h�Ձa!+Y�^*��'u,"f (kde3edF�WByrJ7 maina5::7I�w%jM� �,n7{ft \F(E�)L{t}(f)M�fA�%X{ve1 V_K}�R1Jn"} "�e�%red}; �=v"T3 j=0}�-1} ��"Qs(e))���3'<_v e )6�y[vL4�b�8��m)+!�"I a raj'� R�Z�W �� .ZPX=(ur�\a� rpre� / �)�=A&Q�>.�Z"�\ �\�\}c2�\�r�cd}�>Q�.� b��a%  o��i�:c"#Aa 15I&l-I_p�%<va�n&  �h �} (�?$K,f$)���� ʎ�"r-&" gA�r��"v$� zVA� ); e�Jd�Ja�NY:�.\f�V �n&A`�t�!���s!A"��6� � acc&��$<�)�A:1I.T�*|)��%�6Qp.b m]�� 61E�q/,J "H)"�T-4&:�OV���in�H�� $vYY v_{o�� , v^U v^{i�D��&�"� � 1frd-�� �.qa^A�6��it)}a;3>�e Z`rw on�5�B�} E A� N�U,nI�=�JA�fix�ing1l��-�.H�e �J��0EW0b,@}. ��D��3�EQ1  %� byte:��y� 2:s&5&�$_�as D�� .>!=b�O.�8�*th;@%��Qn*�$.� D(K,Fc.W^>� B2!�5�I��1ay>��We�J��.j �Ss/"'г%�z B�� 4��{bf�Nj�$(D)=(D,E(D�DK(� #2D��׵11I$E��� Arn �; W2u e��B�"}.!�EA�cێ1�V&O(R- , $c� D� uW(D)GX%L1�:jWjE $P(D,c;&� �$c' fGen>�2�exA?$c. $�&_1(D,v`he}uj$%���yA�$v_{c'}�&`6�Q�����S�z$c)WaF6!�:��q�a|D$zF�2�� ���V�$$ M^" ^_t(-�=�Q+Y�'I3}� v_c->��� e�YAT 2�u�A*Yre.qdet�h �DY��}�� S\!c� a�"un,a�� �d�vby'�Fadeev,� Reshetikh��ndTakhtadj "�FR����, w��* us66&� to��&on-�f�ve��@�A�� � �`)&&�@"� �K�K_!�� K�{ ^� &�_�Da��.�T��>NC�G,lhJ%�a !`.�:!`���. pary��!�$n$|d= �f)} 0n(f^-_b-f^+_b�  ^-_r��+_r&]�FA��$1-|P(f,e)|&�v;"= ++� -i |��$&L n��Z{�4"�����fQ z*�M�RHS仁�s $�b, �-_r+��3e$M� ref{v*prbla}%QAkw ���%�5&�I��prd��Uz�+"�P2� ,s, Vassiliev&'*)�J�h}I�sec.K�DAn/� � wy[_"�* `� kes !fbal|�Imi2?p�ji�BN}�t%�6t��P��\j [ ship�!M�D �>2}4 &J�\�p� A9Q^  "�kP�� �Com� "3=ec.prEs9��Princip�)f I��uad Excl And� C"�=&�q1�ub�}'! 1932 Hassv/Whitney )VWh} d�+`�%'�c*?"�i*�p.�i2�e�(PIE)S)medM�"���"(A_1,...,A_ni%�eta[  $�6(A_i;�6J)=A_J c+$|4 = Un)|zk�.nm_k��[J�m{n�]0 k}} |A_J|.$$,P��fO� folkEy�""uB)`-�cBsRg%SQ� ��zi�(1+x_iW�II)t *>!n\}%I}x_i�d$A=!_{�3=bn}A�,AP%Ff� E�h"�=B>: �"A�-f �A-u$2�, (1-f_i(a))=ɽqso��f�W��r�aI|:� a= 0 �Su��bo��=��Zo0�Ka!�A2m_bdzQ$$ |A|+MI"�9�5^�W|A�_1� A_i|Q� )��-�1FC)B9'we ��D�S_F���^�r/&X=,M>}-M(G,z� B) \ �6e�lo�� !{�or fe�q�[s. �Fit>7}�,��gn[ m�AW 8�� e� pin�4aY%�any6< * �,�1 �!#of*� u.�nD$\{v_1,e_1,v_2,e_2��v_i,e_i,|]+1}e_n n+1}Y:"�� ���$�e!�"�=&�0 t 'e�h"FS '�"a�$=v_jv_{j+15.Hfa� $i�N}az6� tAG���a~ �s>�"tis�H!^!��S%��� EM8ŔA_e/�s�PDen ings� �VtZ'a�53"�j�� @B<@�]�� = z^WY}-:_ W&E} A_e�L��G�.$(p,s){�!Bc,'sJ bol)5#5J�sIE�Gp^��by�[PIEA��<w"�Ea�� &�J� � ����i p,s}� s z^p�09U��>)��J$A��|&!�%� r(A)=|V|-h$, �+��&�Zx!�A:E�x�B}&@(M(z)�c(E�N1)^{r �A# Iiz -��lA|  ��"�n r�g;6�� $R(G,I3 "� )` .�u � wvF9.��jBJ-4�w� by %"v T1},� T2})�a minor4�5� !Pa4~�%TpgJMc!k �(y%|:O"���u�c>�i�simb�6Paa�i straW� forww^�lesR*�H-�l:bONeQ&(Q8">|��c��j�"V �ic � ){�Q�| "BFoe�"ub.geoma�%k1Z!�e�M sum R+ �)�h�w�min-1"fci�m = [�;*k]^k%��&&� B" ty%aJ~&��� � uOBcpwe� W& cludX= VinG� keep J essentiot�Y���� �C�2+$qbu$(a-z)(a-qz� ots  ^%7�[)Xi!Ki .�ki�k q^i-1)/2}a> i}z^y [�bge�%�p��a�i��;n��5�W checpe� $n=�� !7!V�Ay u�]CWk�� �A��  �TR. � �� y=qz/ P"AmZ5n!1yFPy)= ;[�V y^i]_ �F+1)� q^i+JE{� ��-q^i��R�1}^B �i6�-1Rz��.�02A�+1} + Wb.&n&a�= /2}z %+!��#1� D!L{i.� [q^i.^e0+2 �N��d! �J J�Vy$$/i"�E"�)z1at� ��=N��;e�m�Exami ��*/� $z^k"�� RHS,a�� *�g"co��}mY�7��M_q(K_k�-k!.TIp!k(k���R�sٶ� i��>� � (: 6/pp)� &�&�  $W(A,zjC$;� �t� ?��`CɞnPRco��\=!�s%o �:8er8��%!@��jaFD:A-�.O� }J_e:+.mJ_e, e=.f"+ � ��v*51 k= By�J"YA�i�9�&�  �ap_ �A��*a�1 zF !�n)B=$*�]VC_{W!�Vu �x�D{6FG!M |W|xN��q "Z(SJu.�A�.�Z�PA���P_qB�psae%>%\�l �.�} v�o.:^V!�.VFgA}wR�p2b2FWs!�!�k&�w2���nb\~&nN�j���y��w!���a�.5tys} e^{x(s(i)m)}=�ix)+s�ji��*- A� aF1�e^ =jj)kVKF E}[� J_!�:��9i[2�2@v�N?[15*�j�rr%�'F�A} 1��Up~��bY U(AM�(a�=����A"l�j�,� ^ 5a��LҦ�lem.w�:� � (� G=�V"Qe����)��E�= :vleJvlE).�az�!8�65D��9s g�'$V$~ $�3 �3� ��l�l10.� ��'%L�R�R�*U �F�"�(t+�2_Q��g�L� ��Ce ���y b��G��M LHS��Mii�^��(�+��s�_�4) true�end�,>� s ��cu$N�L� thm2�bi� �/���Med.�0u�.&�4�(���t�[W1�Q�OA2n''\�, Ay��O�&K�bG1f � propݱ�<�(e`�!�6�!ken�5v=V�z&% 7 f'�Oi)}= / (k (z-�] )_{q6���o" ba �!(IAl4X%T�8�L�C��. � ��xeqD2#/� !�i$��z�7y+A�!���repsv ]= �&X( =N_k:)R*�"[�z)}"&v_k5Ov� = A-B+C� � � <R� V� �%v_k�$B�%� {m(k z-iavC #��k\xE+l t^{݂6I �A+C�j�6z-1}t^z �=m��I!� k)}}Na�R�S)�w!d)�}*�i!�se�c'tq�)�B$i�on�a�v'_1 <�7< v'_)!�%�.A9�9�i;:rWe\%sV=z-i_e�/,Y d��leq i <+ 1}+!�31}+ d� ~2-2}+ &Aa4-1}]. $$ This Lequals to the RHS of 0ity we wanted%�show. The Proposition simply follows fromDTClaim. \end{proof} > k.G \ref'4p.str2} yieldsJ [(ing \begin( �} \lbl:h.10} Let $S$ be a structure�xn $$ \sum_{v\in V(S,z)}\prod_{xd} q^{v_x-\defect(S,v,x)}= :'0(z-m(x))_{q}.Y �� Hence �v;�is invariant for $S\in\S(T,V,(A_w, b_w:w\in W))$. Note that%B); )$ s�at $_x > '_y$e; $x.FcI�fe+n�AC%�e�R�D, $n>0$ a natural  , $C!w �I�$��\{01�(n-1\}^{F_r}�We say�Ha pair $P= (C,v)$, !�I�8dmissible} if, ; every twoeXs $e,e'�q�y suc� 8at $v_e=v_{e'}$e2 �Vend��Qi  $e'$Bj  j \gA $,a*re exisE/ $l!i E*l < j2�e � !C_l$.�J��R�a�\A%���2r� prd})�e'��p� Dd 4t $P(f,e')$ as�r: i�s'_1 7e)�� $e_1M7+ *P�P ���� � e=ea�� $Q< !lin our���t��f������xr�okk�U��Be<$itemize} \  $%_1A~,e)= |\{).�): IE<} \}|$,>>2F>C_{d(e)}V@� $"�R��0biggest index.�&E���)KYZ hQ� ����? Ifn}Ÿ:�.��ŽV e $f�� (v)=� �� }v_ei>we . �O(vAin�I. J�g"7vVappeare�*�1�t8 ͞� catmm�LJ_n(K)(t)= t^{\d(K,nzfA�\F� }  f)} t^{n(�b-$b)}(1-t)^{r � +_rh$$ e- t-(n-1-|IS|)"F i:\q(i)=+~� r_v)b_v) A`)E؅ �� i_rgv_e�U�2E,e)h E55 F���observ� e rel��bA��c"��3relev� collt �x$intervals.GB7 )� ��B � ,. {\bf FromBto�~}MPrmula�Bh �mayu�preUin���8chordal graphs.Vbasic-2))i�atE6/a $Z�-$� 5_ �&T�#�*th� ��ic��1�d� roo���1��0B_{w+1}= C_w$�9A_w= ��w\�UNowa�r� �  2�A%;x )(!psub\%Ea�,�t represent)?-�"� � i: �9 (seeYm� � �}). How/,�� xA ���ued�o)i,� n itf� subqs (�A�)]3�(is directlyy �e_>;<J, )) ."zB�m) \ifx\un�� d\by<4 \newcommand{ }{\ �vmode\hbox to3em{\hrulefill}\,} \fi�cbiblioe$y}{[EMSS]}��ib�yH[K]{K} C. Kassel, � @Quantum Groups}, XSpringer-Verlag 1995. \WTWh]{Wh} H. Whitney, T8A logical expana��mathematics}, Bull. Amer. Math. Soc. 38, 572-579, 1932.�HT1]{T1} W.T. Tutte,r�e%!�ory}, PrU$Camb. Phil f843, 26-40, 1947T -/GL]�d S. Garoufalidis, M. LoeblsDprobabilistic viewA)Ae�Jones polynomial}, 2004 manuscript..�2]{T2J� A� t"vMt�"yl chro%Ql!\ Canad. J.-Z6, 80-91�54.��VN]{VN} O.A. Vasilyev, S.K. Nechaev �0Thermodynamic�fTopolog�Dis�0ed Systems: S�A!s[ !random K7Diagra��,n Finite Lat�D,}, J. Experial� idtiAZ Phys�P92, 1119-1136, 2001. =]LBN]{BN} D. Bar-Natan �Om(Vassiliev k�"��(34, 423-475!Ea y (K1]{K1} L.Haf uffme!e a�l)5!J j26, 39f82�lAFW]{AFW} N. Alan, A. Frieze%D\ lsh:�PU� time-�,ized approxiAC on schemeq r�ef-Gr\"{o}n dieck=&:�(dense case}R)�S0 s Al�thms B 6} (�X,) 459--478.��9`vof braid-�%�!*5�=O.=Ann��SEe12Ig887) p. 335--388.�Kh]{Kh}��Khovanov:�J&��V! Duke �PJ. 101 (2000) 359- 422�J2]{J2}  :�OnIE��g a[ to somI at�o al m��n�*50��=�Pac��..37Ed(89) 311--332St]{St}a�Sto��ow:�M�e�s, clos� !�)�A])89��p� int {\ttIg$GT/9805078 &�]{W��J��WJ�Coxity:� olou0 �counting�London-�Le�Ser I]86}:Ny`���Q3*: B]{B} H��s>gTIhara-Selberg zeta fun9Ata�  l�,�I� n��� 3} 9� (2) 717--797�FZ]{FZ!B FoataegD. Zeier:��(mbinatorial �,Bass's evalu8 m 2�U�6��q� 2�Transa�sF* �5�49) 2257--2274�LW]{LWuW�Z. Wang:�ͯ Walk��2�, Colo�I���2� Z!�F-�=�U� 1998>�12039}�b� FRT]{FRT�� Fade� lN. Reshetikhin, L. Takhtadji��j� iz5�Lie.Xa��.! Leningrade  Jour�1�(0), 193-225�I�th6� �document input Z�~�b�b�c�c, Before get����t�w��y stille;aBle�($M_q(K_k,n)-�eE${Set-parti�s}�$sLp}�\l��+a�$V>&C(\l)$� R."li� P . If�g=S(G, B� ;�ts $A �t E2�C(A)=\�w%��G,z� \l} �AHl\l)}(-1)|}W� } (z%|W|}}'!(!suggeZ�etudy $:\�]$,!�chZ!� duct "."- $W�!sc XB�� WWB| W�)<W)$��5>ll5C$B=Baform aTnec: spana� �|��$W!� is KE:!n�'� |�emMC�sum00s �-}A��A|}= -�W|-1}2^!t-2)u�H]�m quesA� }  2�%x!h&s�W for -VJ)V�] J|�WaT$about geneI) $G$? � %'s�E�"� !(pr�#Z� . Assume!j�linearly!� nded< $Z= \binom{W}{2��z�Z$$,$z=\{z_1,z_2�<a _0z_1 < z_2$. �# indu�a lexic3+� $Z$ �$�$$(z_1< z'_�9=� $z_2 2�$n $z �VG��4traightforward��or[�%, giv�-�W)$9()$r(J)sS: consi�!�"|a�J=e��one`"J?,$�Zng��(smallE(n_in�,step update dav�*:!z �� (we are just%9�f is e�1K�ano�%@p�current k(nd $J-\{e\}5&n""le�e$�$J$, Rwise do�)hing.�i�lemma�lem.alg}��� %޵�(J-!�U:r(A�="�! $r(X A B)=X �%�{�m� ���} �!w�OM$!4-C"$Z$H #s�#��aT!$�is%�B!an(���+nfirst+t�  e�rs"(se�( st ) Again ha B�-�mA� ��.�Xa�~ only�� blemA}may en% er��4#ap�-�a��+$)�A )�� t� po� �Em� @)��A�of �Si!+n�<$X$, necessarily?6��$ $X-e$. Af�d�aOl�remai��c ha&&belong߅8. E.ub� K \on,� >I$a cycle $CA>Eg5q�set. I��0difficult to�ae�fac�%e.?�kcon�%�exa� ��� $ ���X$ (i.e.^CJ%"�-��}$): -�X�d,�rr$X'�X2� :X'�_ �, �ơ�X'-e$��{"co�rcomponA$,�� 9tm�L!]m'$F!� hem.!��h �E� ��8Du ^throughAN. With!Nlos%�^E qIETA��..F n���-W��h� �:g^�&� ��t canb!��ܑ�()�any iq "M(��t �&��Z$).f��^s%6aGic�ɂ�[q�. More� g.F !�� he 1Avproperty� Ji��  j)/(>fj)*�3$ t$1Atf+!�&g%<�qg"�3 ���Q�i��end!?�%)Q:O .2:9;,)q^%s*Jn�I"�$k'[$" s�%Q�&ARb�\3Hk\}, |A|=k'} c(g^A)9W�� $ $k'=2 �g� vaNx 5C.�0rc(g,i)�(Nyiy 2, i_ A2�and IS,5J,=\{i,j'\};j'%nj< i\2;1_ͽ��sh1} $� ,j)=Ie a_ib_{j+1;3 p=j+2}^{i�#�4 b_p}A�p-1E�}1� daY�qiWe�>ce1y doublyE�!�(�H 9�y �ei=}&�=w no $jIZ6*2͌$j 7� 6��-p��s�$, $D_r(f,r-2) 1���.1N(eqnarray*} %:(f� &=& )�5 {(f(r-1R}{ H+f(e_{r-1})} \\ &=&J : {D_w �}{��4�=;��1a�"`#S0*�E(z\g.�>% a��s�n���(in>�A\ %��%�i�i5-%,Th�9>2calcu�#�� �,_ �� j=i-�'%�-�5��7de}[htpb] $$ \eepic{}{0.03}�1 �|{.}\lbl{h :fJd %\psdraw{attachlegs}{5in}�zca WA� "�i" t yG ��X�� �d�9%�mU9�fl9n�/$f�:'7 $n$�"r�6�B UI� (�1$a�w�CM�, n)=! m_i2e -1}|C(J)|��@0GA�X �2�9s"Y��?s�%(all) 4Vn�e�P$T2�!�_{1J} \Er� n,zax)��-CUC�HEja`!c  Py S)}b(P)�B�as����h\b�3{ }�� _{t\�,^n} \, -Tn)*� )%cN|A=�B�?-_E b $FE >;Our n~= task���ufy $Mu<msA9�A$�$ doe&Edepend� n$Nf�!y99 � e< ~$|C(I)|# IWJ2Zv,b9� $T(e,J)� ;��� "~YH $e=z"8t��6i> 2)  O*w4E.4G� E$��a{} A6�A�� �C/��hq fm �ifZ:ach $i�  72$� ��n ) C_��I� �F 2AG�!5$x(i,J)�A��I$� 2x�mt��"i)=� i ^r_i))�� i)We � m(f,�9� :- �A i� G!�p _{�1} `A�s 0�a� լ%� Rget�-J2�2} A� J)|=bJ"� .� = sim}�z,�B�z���*�$z'1�J=-\{z\}e$e� m@ *n)#: ^�M=|\*$2Le,+; O;W&�2)Ie <:')�:. vV!rZ$�Jn)=#;�D%#�v�$N�$( 2))�\l)�A� )� jHEKi {0�j��q A�\l���"� i)-j � .�j},V���� n an '1'"-�$f" %�႘��I/�� �NI(S,W�Ef�� NI(WA�z�� EW�7\{x,f(x)�E(S�7Q�_E��F sum3 �ML;%�{i�Ek�:v_iD:(LLi)&� \l(kO;X�:&� k\}-M�EVAU (k))S,W,X) 2�IXN W}(-B�L%�{�;$^{n|W-X|}}  ).�= U� gd(S,g)$;�w>t�,s $g-�!�$.� �x �FP(g)�F$%�X $W� {x\}[Cn $|g,<(x)|>� $ � �J iE ;$I \{!�y9�; x,y��%F� es �s�edE .N}/VFrel2}�&C��], � �c| $U!�e���#!��m<2��� W4n use &�_B|4easone asa��uun"C:dB4 d O��us��57�ofi��!{d oriegPf�<a�?r end-�"t ��%r�[�( e (n�� ing)U� � togeT� [lev�͆HE�2i Q� wh�o�#fi; ��<e $ mum�$!�)Tak!\iT��>s $M�(,��can6z! tup0s� we n�to�� sl2 Eh=X M(Sm� fina�ge"? �7�)RE*4&D*S���@WQ� g}c(g)JXm�s(g,X6�QX}�֍�W ��!7���v LHS!�o%NU�v2� RHSq?&@ OUisJ23U�)�o�{"5k\}"F'�^����*+ g����L�|: O$X��6�-M.���� $x� �aA�M�{g"� ��\�EH>-�*r.1"e� g�$I �� �� n2�XWB(X�J�{�SBn-i}=M_ t^n-�>-}{t-1}4"� A&Nu* "Lu� )�%(isa�F a�e�t �T�%d�>ed�G$(x,g��$.�p$rr�Nbe:�?!��le7'r.A���w�~?#� s}@discus>�#"~ �� O&���'J').�5� ��@Mm11Z &3��. Obviou5L� U!%� �i��5(!K"�1-I!�,�}�*:XJM "-2N- 41t )=c( �I ob i�%{P"��1arZ  I?7& helpful��h�\;e�!{qA�8B�.qb�4��dNN�1P(m,n,p�*d�]ixm�"p$ "�:$s a�exceed����c�5�0!Hs6�-:"�u%%C�0p%�`1� (qz)(1-q^2z)�L  nz)}� {1� pm}�q^mz^p�e�n�Y�-��switch� P,Ql wo permut�)k�YZP�6wC$Q$ by�.XCB(!���xchang%�neighb�8 �,�2,!�����1 tha ��one. �instanc} (4,3,2,*0�{QEF2,32�but��vicA$sa.)].K� .%�!_o,a,b}A�let*�< AA(k,t)-�i�=0}a_it^i*�$a_i=�(k&�n_UaJ���%!$�8�  by ex_+�L)��Nw %�If .`.��$$ B(k,l��W m_{r �b_rt^r.�b_r= b_r1�� >�"� $r$J�= ) re $"ul� �0 $l+k� �� h 5�ai,j!QM�l 4$j> re aXedM'!��%.!A(immediately�$M 1T�A(!` A(k- }{l! )!�#zb�&U�!k$%���DatrB� pr*�[E�.a� � k!_t�J!o�\h%�Q�cH��ar�J� Z�z^pq^mQ0pE0 1}(zq)^p R4n+�" {p}_X:��� &�0AdE_=1%$ P(r+l, k-!� ljlA�ަ 8j�@0}P(p+j, n, p)q^jg6�)�1}{p!�K)!�WE b_j(�F G�06Mr&-1$N�)��>��E�f   ��coe�/�7q^{m-p�) $-�m9�����\�;Y({�clqOLusepackage{amssymb} :�A6enumeratFAcd6*graphics�khyperre�_�\div{\h frak{Div}1�title{\huge Periodic Maximal surfac�RŹLo�4(z-Minkowski90ce��^3$} \author{\Large Isabel Fern\'{a}ndez \thanks{Research�i� suppor2 ,by MEC-FEDER�nt1�MTM�G-00160. �I�.�F0C=�H Sub|X�`ss�A�D4imary 53C50; S� 42,8.YKey worUA$phrases: m:%,��)@18,% elike � ular�X.���-)$ Francisco'BhL\'{o}pez $ ^{\ast}$ } %\�=( Paco32.texsetbmp��]latexsy@:�� psfih6> [latin1]{� enc}%�"cK!}{\�-�@name{ENumVZ.�K_B+ins>+ supr>+SupreJWinfBWInfNW dist>W:�df}{ �W ckrel{\rm; }{=>)Gam}{{ �O maac % Conju�d� erosi�hi� bb{HLdef\rRnNbBcCqQsSdDlLzZpPeEkKtT!"%�*ras�! igra�\s )"a �cal{A@bo95k �d�p�r5�s!G �iI �.��g+G*t!EjJ*mM2C g��K1@Sg)l���Up.pVC.5BG.�c.cBo.oh.hw.ws.sg.gT.51W.W,q.qI.IJ.9t.��a�v.�SM.!�(% M�rgene!�dheadsep 0.5cm \topmargin 1 exthE(t = 50\base��skip �bwidth 1=odd� A0.4Cevem=2 %L`of��environ5Dm ${\trivlist [\hr\l��sepoPh\,:]}{\h-Q{$\Box$}� Ab %�)SNI�wIN} DD CC TT  go{G_+^\uC owp or{G."new* {�}[�1]%V#'rk}{R!�kZ% -}{Z'.� {* b/.�&� {"�*2�asserp }{C�iZ'*� {D&&�� � �.akeZ � abstrac�"%*_ C3b$ � isa5ed61  inW!mplet/\at� 0ian 3-manifol�5N�s�Lto\=3�#f it lifTUo a (p� ) $+ ��4ph $\tilde{\sb l^3.$>f�), �iŻled> ffQ type�ug5�Q,  ly m)4 ��:�* Fly she�W�.�Kte (or c per)5nimm)j1/fj$!D ):, � embeddedW� !�9Yj^mR&� � _of �%-.Oc�Fify.z�s carr56 �:[s :e � deal �� 9�WeierA�s�Mp.�W!asympto�Tbehavior_�Wkiw&f5 . "]Zo� new Ok�Q��zdl �funda��#Liec�(�U'2\%z�y�"r6 Intr�C� A $3$-d|NKalf�B~.�F!MgeodesiBZ� $(�-metricwer�Tf? �uc&nr,�:a�17f= q quot��/G,")P�� >�!� $G�. B+gEei�Sa*�������orthoPW nous���#�$G3he�7L!fu!�"ion. %Aqf�9�N \�9 !K/G> spac�i/q�Gd ML%���0is Riemannian&�/��� �~�>�[�e!�.�Mt��an 7�pb���j�� . _:�!|>  aG`"c� J � s (lo�=)" are&Qal"oc�Wr variRs�F�. A�+FE�y_ chaer*WbeE��=A�gn�Qro mean|Cv�e��be� E�4 r �al�!erest rplaawZro�7m^5Re�UV(m]\0jmarsden-MjerEmdetails)&XDs%W��Z�e,$-b6Y A�4correspond, up�MI!2o �()�6Gc�%�nt  ]4r $G.$ Calabi �c }�[v!�Za�,�Y @Ut�H�<:��+ {�$ 4$%�9�J plan�� solv!xrso�8 $Bernstein-8 �[Gin Ձs�J e 4.$ ChengYau�(-yau} exten��res�E�?4\l^{n+1},$ $n �O ���`�R!�)<'�e��[i] arrang�of ��sv.�(� %3-�n� � &� 6e��.$ �E�� ideri�,u 8ta)a�a**�f*;խ-�?�or\%:G.$ Un�K�Zon�4s,�$ � �U��� Abel�nor��b s $\go�Gs���a�o� rank  or�F� ���$G/Gis ei2&�ial��B or $ |+  .$"\5(��m�F�!f` cyli�, toru�^�biusuipVKleinAFtler%��iTH��ingles�/1� global8BA�s�{1�aF�T very�+ re=} 1�o 3�� s)=A{a ?Bimg��q�Ms- ~A!xje'J� �nG� ol�o�- boun[�V���W��6^ tnikTSimon �vN^Sim�b A�Xa]2 ��,� rin%0Z�de�\�� lthoNHA;M)istF^s �j"TŃ�siZ �ere��!�al �)-ink�qYee!�}F � spec.�J515, �y �lQLvide te�b[h[7'� go��pro&v 1QAy����n"*� Vis& -�%%A ��E�c�D ��P B}�Figure�$ fig:_}.pPDE G��t%�y*�i�Y� �sN�ellip� t�E��`0%&2>Con� !~^��סG�r�l Jord�i�w1 X s�%&�) def:�6})�?�1���2 mapp�@'"!o E�le-.� -Lrefle�s�j �ly��  mirror)-ut7m.� ge� ��Nof2�r}=�cu� blows up%� Gauss�Zno ,`� ed limit ��.�is � ly&`$a&�6" lighRe.�Crefer��kly-mik a good~L � I��BEtTUng @� �#d �1V|v V�. A}�1�$��7a&ur�> �,&� EzZ� ; b � ' &�/� :3�N)�bx �fDu���.��3.�G�o�Orea� E�"� E�-3-l� %:VqeE �,T%A^�*�t� falsA"� Bm �in��-�{C=�of)��#aE�~��y,nsm�E�6 F*P �.��"�~B"� �lusatO:s�d%�e�-rN$ me�qE�at �0 . As�%+how�_er, �neso�K �1�h�N gJt-�xv:#=) %f' A�- i�}>?I4��1G� �'6� �:R� ��>�v�! ���.Y���C#=2�IH0s been recent'y velo�NiOyf-l-s}�>��icos}!� have illug�k=knownO� nclu�*ae�B �y noid%��%�A7��l�0  �I 6�"�l?)@\�e�p \ �e%Pics[w�=�, �=2cm]{� �58{�o left�LTB��a� ��ao���*Q�5��-�fzS��t��6�6�a)��@��9��& � �R �� QM�qH.��yinIR} �d"q?, $ ��p�M%�f�65A}suitable"sP&� a*�B*d.��T�"�is�l|�_am7> fam�V of Scherk�1 �UV� 4})�bA�zJ��� �Y�..inB_1aa v�A�mer�f^c_��%�open q�]��Y�l�]:���%1�� . * emphasizeE�N m:&�&[(I)]d�|a-&�%9}�O5�@VgX ^�6+9q.� �}e�0th��,�g�<� ^x.�>��@�%A!�1�Y�cas�791 �_ aimT�pap)Zo� roaze �8%�E�~1�mۢ�5c��1� ]{Mę�Av .} B }: > :k Regare� � (I)e���1�)�N=��osur��!vi  o�% $\Pi_1(N)�  G�pl�(N$�a�k~ ^�Z y). :�G%�� homoJs� in� ive,� �* vin���m|>lpf4Ela~�e�+alway�\y.�TF�����$ ����� WTn��$�far�0|��al (we&u !�surveys��$ch-dr-go}, zeghib��6� ).��FD&��arguli[.#}� �7edz�%`�: �Q ian)�) $���Mesgess6��0� b�V!}n\\,� I@�!fu&�%|�5�QR� negaAm Euler &s5r). �)Z &ed� d'|p$p M�0�" qDw�2ic�! devo!D�:��N�:�f�6mQ ��*e}My.�: }ieLet� :�1G \neqc<�d}\2!�eu'J��n�s�0�-�&�:8 :�e}�-s.;"�GE�0v+2fb ��hg� VsA��"x$\0U, "�Y.i�m) 5i� �� "A�6vF�g2�C:> CD1�,�x home.��Z�a 6� , a��a�Bo��� \go=!�A�V��.!5 �is bihol.�� m�� manu� minu&�#� &�)8G.�"d,ne� merpnaR�؁k r.�/endQ�q��8��� �a9�LN� � Yj� :�s..*m}>.I�c&� s� toHAm� Bb&A#a�� �"�.��2R�J)��isS�q�P1AA!��!�f6 ��"R�� A�$S !ma�bT(IY ��#!*(b�$a�&� 1r*�|Bnt\'Fin�����տ.� AB�We�9��*Qa��UofSge-Meeks(�jorgem"=-rosen rWT  4�s��AD2nt im�2�9 beca�C they7tol�6*�o�(uU%�isDe�.:I"��]il# &jk!h"�3�3$�a" :by UmeU!%�Yamada �um-ya}�l B�#"�c2�)&� N"d"� :�K JZ2*�}��`=vely,錍/q�})a�Mi:� E�%Y!GB}%ggl};N� $T_1� p% �p2�& T_2$@c*RR]s*��F�t"���!+6. . A�2�5ce"� k ��B.i$"���P5�:r��6~)��FE &_:��N:�deed,A��h2�9!�M�� &g+&��V�~N��\go.$ a. Doub]W��:�?j�"� ed�2Slab i:o!eq�%<_06CJa��#2-, .�r6Y*,$\Phi:=(\phi��2,W(�; \sb\�� /\laY $ T_1,T_2 \�"les� t.�1-�sn-��5on�#�ɩ%��&�an&�,$\Sg:=\sb_0 �F ^*$ �F�$J^*(�_j)=-\��0{ }aP j=1,�>&�)SH�)mSQ.- !vA�HAM &inv� A��O� ^-ign�$L�l�Ņ%��a${\�,H}_1(\sb,\z)E�Th�7.�z5 a�si��treat�+. `�!�aat least�}� �� (posy��upӐy)��� �� half"�"&�.3Y/(C?��S.���� �)���E՞��xR�^�,$6 A�Z9 &� � �Hw6�� $]�Sg}2+$�����l"Ze)3:��(I�ima��(%\ )^*_0$�,m@�=.$ Like;p�O $]�9�.�a:r /�l��A�moduli"Q as.*%y Ui*�B�X stud�-6M- J }.\\��sG� leadDma%^�@s:�MSNo!(sec:prelim}zfix�WnoD�E�f  -in <sI�f�a�l+%P�!]�6:�zginF�e�Q i�K,V)v&y-��y� ���� @%! D9�>�,!� heF~ �m� !j����"$exhibi� "�s�"�#3AI�i�E�|AcG ledg�as:�^E�wo�i�ton! ,o M. Sanchez�"�Gcon�G�s d�~�V|ag)!�� work+"k alsoZ.eb� to A�}�as�use%H�{?o.'m"�1N2�PE�2�"Q]�<3*-H��c�k\d�ND!�x�ne $\c��{B=tyeQ!� unit� �fz��4c \;:\; |z|<1\uT�o��%pa��}� � �Ut�"�+al J>n0 $(\r^3,��,��)*8��,  H=dx_1^2+dx_2^2-dx_3�5B�0coow ate �+, $(y_1,y_2,y� & �?*�a� �2BJ�!� ��k0.�$dy �y �y ��"�Ha���bf v})�r^3- \{�0��X�&A�, �, � �$ (if $\|v\|^2�I eDv}� cR �z;E�"Nor5 , �.�x� . W�c$v:� pchnaOM�g� $�0:�� �%�J.��� =�t� f�%�:�1is�� �non*�' .�2%H&(,�'�>�/ C}_x=\{y)�l^3m; \|y-x\|=0alA(%�conS"�j�Rx,�.�3� m~4Ext}(c{x}QW>f e>0\�x�'ETl� h^2 �0 (x_1,x_2,x_3x�r� iTiSaR2=���Y�/bo�osp_Hy9�4�60ant intrinsic*�'$-1.$.qN� � jNedb.mtt % _+:=-�_ \{x_3�/��v '-J'��.$�s+2�{�-�4 igmapII.h^2E�E(*�$$\,:2� a�|z|=1\��ong�!arrow P( \,; \; z \ \-"(sG2r6m} (z)}O ^2-1�fk!Re>! !|z|^2+1: l),$* �(� )=(0,0,1)A*D&�NI}.�6!g�]A�_+7E�� �f8�*� �Da.�s f7,$:�>�n2]6F��2&)�(.�6i� &� �ar��*yT�6Ig +$ (�so  _-syh5$"[>1+7�*�>"26�=6f>F� ��rz}}��^F9�IWfi"DWLO}�p�+�0a%F $\ell,$J�4 e ax'0�. e��|RS�-,.yorLHa��"�i�le�a](�,�%6�z�F"A�6Kscrew moW.V&��c���Laa��Q�-)fan�$%��*0�/.s"]�4:�.��FF? "��V�x1�32x,x�2�s'T��6U�eلEB�2�of���6�%j.Us��2B=�&n$ '�car� ;)sb�t!�)��|%rk`rb�N }>#re:1� s} Gx�aB�y $Rd��iq�,$GL;,�)�"F'b� �R�%1)]�a4 $R((x,y,z))= �Hpmatrix} \cos t& \sT& 0\\- 0\\0&0&1�8�, x \\ y\\z 2)+ >sQ\\V mbda:0,\;$ (\}r,\,t ]0,2\pi[$a�$R�@Q�&r�1& 0&0� 0& \epsil�coY( !h t:)&: 92�F\\%2&J\l �\!"6.�9/ !�=\pm 1, !)\r\;(t+!00 \;\rm{if}\;- 1 )S�Z)F&* �H!I-t&%!0t& 1-t^2/2&  \\t&1+2��$!\\-*J$bA:9#- � �0œ.7g*�'O ^*$tEg��&� !5$R2�-Qa2�A��^!v��"0.�X�^ ��5r=�6Vl8�s�ly�$t��{)~a���6��N�lle�:���Zd*>$B *#.v}@�0t�uej�rx!e%�29s. Obn@�t�/=V<�]2t �l6�Y�2nB2!�6��'=1�=).��65.`g�(� CR�$3&|CL&a:8:�ersal"�%�oy�7�.{G�ofx$-),�_�5��u���?; � �� �G�<-�1$�one��,�(wolf}).Thus} NL �Br� � Ao�%�Cim �;�ov "�� ]!�N�C8ng�'>�(203V$&6DIso� aG7N")?,$ �2by5%=G���:J X\gpN*|Et�$r:F':O�"w&��2^&u , _6&*� > W��wiz��.4gp �o[�E�.�!� x $k*, $��$j!\N�*1 ! o�ed1:��", 6$B��%6-�^��2�(A�,$vA+A�@��N �)romFF�B���)�Q)�q "v 9 inu�F(map $X:\mb aq>8!*�mb�I.&,a��� $�mb}�a Sb}/H_0@F߹V6Li%H)JkernelA2;���2�.$X_*:/ \mb) �!/\N)�  B !$\pg_1:� /� 2:a$ N2Β�B�&�>s,��tP%6��&�@[)� �X}F����sf� ��[rc7bg irc �ӏ map,!nqu��"�ad�E)Qi�XAC,�0�-�f � *�'��W;.$} I�25+nRE e)"�A)U.R\mb� � � belBgrupo�oB�o�=9 ap^96n�/.p1��i1iv�is fac=�. =rie%,"7'�_rn1Xm1)RK�eaYya�pX_Z"�1A�)6w"\pg)� Y=X}@ pg: N>I�W �}j�+,in"P% �i&�1%�66�1�M-� �w0 SEeH.8a6� #�)P&}*��\pi}�)��B*�y�.��ouom?$h9�H��E�eB|?IJ*�-s(�{p�E�%X8�6 discs $V y '$ �U  {�ai6U $h({p} ���, s&�h(V)=U/|_{V}:VEU%�g% alen�9!)E�\vaG_n:\d.\d�<(z)=z^nn�$ (mea�)!�bD�2!� xi�I ]�$ 2:U �Yd.�i M�( �) 61=���Zas1"�dh�@$V$� Ŏ���E:'� $h$�{pn��.gers rwErn-UrrI<�I%Gu"��W I7I 'R��b��6�]h%��hO<m N}��p$b �>� A $V�N�h�16�Ѷ}��"��h���, ډ,|}\>�B$beta:[0,1]%�PiAE (0)=�2!tmhUquBe�(�f�6ilyͳ)k{\alpha} nAV���O.+�{ a){Mb�ta.$ BdFU v)=5- (-�{2�Ts2b�aI %�6AanL��r.�@} xL ���i�p�Lrc [��A%2I2��!�!�t X(M)Et�*E��< yB8!6QA >���asRFi^9��-�X���-{Sp"�P�8s��#uD�jAn*9)s \>��]�E�"_� �E�pE� \mb,�s tang�CɆ $T_p�T�� I!�����-/saye>1%f i.�. &�v��_)=X%%Y�.-�H��$\� �"B:&E"a*�)�8)K �/&�s���z�!l�:�)O&q4&�F$N� � ous�0%"m_%in h^�5 A�3����8meq�iyHŝ a�"�<>��N_0-M�&�P2�Si���n_-ais.  ��"_.�t o $F I?b\. �?1�2� H�T|@}6�0_3)et $ds�d�a*"Q�I mb-F�aG�-l$qE�F�!"�k�#", D}(qAs!A�*��!!�F=\{q" �&o*m�,arz::-\{q \n *��c� �&P-�4"= H |d Y� H(w)�q� $w�AA:�E��6aU1'\ea�%?A lar}�q�^diB%��F.�$ �!��L�I$\lim_{p��q} H(z(p vanis�k(S�Ttovf� �su�gVVo chec�Mi�8� ���#AB�&',��,����^1EAF%�2gy�Ac6� �&mb,!�ALs.a2�q�^�Hnd ��k�qa� h�.�bb���i�4} �r� t.:K*J �;,%F�{X:a���T?)� i"I. S>14; �!�e��i�B}_X|_�-F! .��M�E��Ta߁�6!�I!dM��by $XaR�;�X,]5a�%�(1�)5�_5&{��$��R�H1�=X(F%�,=�:8-d =t�J.�w�)J2!E]ArU�:�!�-�7#;M�� e$ � k,e�is" Vo�9 quite"�a�Q�-ul�Ob'�-��a�0ater. Of cour% is "W�prQct�2y"�q�s)r �IZ� accu-t�D&�R�kV�1ll<��re�6=#p��6�E/l9�!��.!n�"!������>rt_.,�U.is"m"�P�7~ \toq�n*6=D:�Vl8$�2_n�,n� L��(  t\n,>V�`$�$��e�5!ly: $\rb-(�4_{n�, s} D_n� )�(L�Yia� $\{D_n *2IQai�isj� m.��u"nt}(\rbF��Uge$�rb�%�U��~(gamma_n:=\p�nal(�%m2l�W�Z�Ag6i( � $D_n�3�/b73in�C��Q�� � � =2)UQ:�i�5R!�_0:=\rb!� 1�Y}� )$ (!�V5n2�P�.1-yN9�m?aY��Y�$��!c53a�re"Vi8� $X_0g_0�a1>�~6 oY}�9�&5Vi�A� Wi�9co �9 �>�8)^eI͸�B bLar I dom%D�� s�E"I]�>��*�)Q�?��K�o z�A.�8minus�D�d̈́�*�A&�%l�}�%lem�V� X*��P�� �S;)� J��HV��B4ha)�q�Ac*� *�&�:��$h�i\!�8[lde{XT *�S� 2���!]� Y��+<lym}Vf6@o���X0�Yt �: �)R8% .2>W=�yb$ +T$X$e���!Gt�0&O y5�6 m�I*&T M6} ��6H9�out�]x5E�� Ju�Ma��� $p�K\5��t��!ac�Ved.� d $W"| -F���p_�0�p��K� �5. }-]e� "�)�@ah�5���  $���acX�H�� h(p_0�"�I���on�$V��W)(U)�x"3N ���� $�� (V)�D ��� set.�id�>��$�.�! "�?$\{s_k�0$ &� ,� �$k�'V_k.��%�" .^^ !�*U_{k}!� ap WJ �:$U_P%�,of radius $sj�.$ �x� u\I*)(%~s� ��aW)��.�,�0CJ!�.#�X�y*. � *�6V��AA�]h(_(V�*� (Uli� h:V- �Iq U-\{ � ��N�s_l�I'.]�JP&k`�zdE� �>��&�H too=t �)=e� �16�� &�5 0 n.$ BasnLpo}�sN)�6�2&��%r�_-�>�In=1.$x� :$ ��b)c��A�ju��< &�qb�_U '� �=�[���1�3k.th�Natoway� a sei:�r%=����Zk �  (t)�k ���|(Շ� ) )'(t)\|> �!!�t�&�gv:ngJ7>4(t_1)-J2)\| L$t_1 �Mt_.�b��uE�:��$VO )Qa��HG�r=\6X2�zE�Sk1�9�� ��a�KV��le:"���G}v ,eq:cono} X(VX(p'��  #7�zcal C_p"o�u�;*K�a�os� apro:gen.�*ez� se $h� pi�%��*F �#A*�Ng +8t��iV� U�" E��_� �rmN(N8� � ;%�z�d �0��Rr . Fu�mo�i(2, , A�@�[ AfA  1�.��\P��.���x:��� .�=���:� Pick $pk��$V!�a��>1ue2s�p��A)� $h:�6���  �8�UM� VE\ap ��eop win� o>H����Bventu�+.�a�p$z.�h�"'h$<'incid�!� link9�8XI� �vG�-"�<V7�52d!6$) p�p��*� (p�]f��!�6KPi! By Em� (��B), ���V�:�^Q� �!�!���s��.fb oB3A� q_&:V�3%$i��8>�&� yR� ϼaso{ bzq*��,���.� !< ��=��|"$ �nn"�.[�`�ve�x�$y@o�f).� ���vaF<}'us�M|t e/ } X(� (tf nd!�� . OW� ,A�$ 1$&��dag��d* ��� �xRd1�I.�,v�@�oscillbfys8d1i�soint_{B�2�|�@(qO alph+e|dt=+�;� `I]��w��dAD�<infty>L(%����� ,$$ �laSbsurd ()�L(\cdo %�lengt�!f�EqO $a�A�*�i1�,\�@�Yn�tѳam ^=h�%T.?�F� �2tF�#� �'�!"�E2G)h�>>*b$k���A�i`�?� &�] x�s�KEd�Wnc�3s, ~��N$pYL ldots,p_k�V_jm��� ɝ��p$f�>�����9*Fq�aWv�E\� _j� OEx,_�1, �k!*:� v�� \h_+���� eno�k o $v$X��% _{v'��n5 a un�+��:�a�I�I=\{x+25v'� ��r�D .��^�Oa.IK�&L�!g.�kv* , %f� 1WB���!�j2��"�oi ecto�'\{v_n\}"��7 �� g�y!u� k $q�in 6�_{n}})-�_'�k!���Z��U q_n):� to x ma0�,�5|I-)j ��&�f1^i��) �"�QcQQ$\{�! !�n}%^�� ��!�xfC6Qx���J�#&�i�v�;Ϝ� �5a�a[>�� �*�& $h'�'&� s(�&A �B��E Pi'�y�29 %��\p )�Z*L &$^ X '.$ s5�!d'}�R/Q_�$u�b_YN� &!tF�a*OA � 3z��<� (��!�A"��m17�K � &*I� tipoXo} .�k.���N�&V��*��j(�s"�J}V�(a� any)�RBQX����+� W&9$��Z��n �:�-�#�tne�Hc s+�,�>j^�$ !n�m��"� �j"Q\r5�s"�$� Ɋ)E)F �VL*�0i�J*1d6�M�]���k"zkc"�$in.(p6M:�~ ѸJ`Z[a�T 1^�1�>� YEE�v�)p_"�60pVI�!�6+  ^ >^/���)�,�lR��"�>� &�͇ 4��.��";�Ŷ76n��� 34� wZ�a�+* +n�staqud�:4 betw�kt�o~!@EV�/� �i��� !w� �(ij.��" .i QTf�� D>�q�X)�+/4+*D<��0a�le���`cI>�uy&d �ƕ7��� �� %F�0)1A�"�i���r*c�O��g�;m�� �^4�gsk%"A�re�jhip9�h�W ncep�fM��npt��E�i1��" ��a{ C�r"C`k�N ��N0har�"�I�b&8E � . A�"d%wQxE<�/�4��&)�e6nV>#e be fE�C�}f�m("�L}[G�, b�^u�N��Q��]��.&�$NO NV��@en,�&B[(a"kY9�c)n��n70is|��BU"%( ���1nU � 9�� ��9 Cou�� ��U�mj-��a�6���6U wI=*+ T9,$(a�Ǚn&��)�)�>>9�� %(;`�d;� %-=�Ker}(X_*��0�;!/.�0dGng�2_1j/FCJn�0*��N5-� �� "���V�KeR.% �w��M5>3� �� �mo���x��1e5d5�1�{��F�Dk-d$��:}`*�)(!�$d At"y� 6� 0�".wB.���� .3��%_:|� ��I�a�,)6�-r^3$. ���  ha��$\|q�X�I'6W�^2]0o�S�d���9�!� $<�S,v>e?b�o�n $[0,7E[&�v \perpa ��2"�2 $~j(.V��t1�LA���"�$(b�&E�,��aD�.��z0'. So>.k-{m�-�Y���F��Si؁>�@%��E�E[a1i8!��.$Ŵ ds_0�3~ *�� !��  d� *onKAh :�L^*( ])�;�/YEDG f%�mmb�:.��$ � (�i=߁ha� �.70|_{.Y�&M 2Z� ɳ'5"?�&M!(A=J�"Q.*x����U�q�����ՉL�(1�.}m � wAhE��6 mY6tI�thQ�P>-Nmb�'� aP�AĀc�9� *0a>~ndU��*� n ���i�pro7$(c�T2�"(&� @/�0lso�[&*� C @ vpseud&!�i�2U �8y��$^�6�* Q-s"��!sb-\{x\h���>!x���ww $x�s2BE0"� YyA9e-�� =��0� !k0&$�M#�5�rP�B�%(�.l^3:$"�l� �E�up� \sb"7�"�9:1 n� I�qH[-&� ?B�. �-%sf��T�_v:d�y�0 Zg8�LG *Pi_�C�Hz�Iĥ lin ,{z+t v \;;\;qPB r�0$e $u_v^+, -FvBr$_  (z):� ,Max}\{- � < %� cap Z z$ A-.AinVAF@.$ � A ��Q!��%B+����^TY�!+�'�s2-2�^2 �e�yt."�� ^+_vg ^+_w�\sb^-  -_w,�%�!�g9I  �}I�!{ 8Let $X:\mb \to ��\l^3$ be a parameterizatin of $\sb,$ and as usual label $\pi_v:\l^3\to\Pi_v$ the orthogonal projection. Let $p,q\in\sb_v^+$ and take a curve $\gamma\subset\sb_v^+$ joining $p$ and $q$ such that �\circ\g?H$ is a segment in $�L.$ Any lift $\tilde{ 2}$ �� ( )$ for _ ` {X} ^radial �cmb-*�so from equation (\ref{eq:cono}) $Xc \ ��F \mbox{Ext}({\cal C}_{p}) \cup \{p\}.$ Thus $||p-q||^2>0,$ which proves%�first!�t�tthe lemma. Finally, given $x\:�D$w \in \h^2_+,$ it!K0easy to check)tVhalf lin!� ell$sallel,0$w,$ pointing2future EO pass=4 $X:\mb \longr��arrow \N%�.q8 with null meanda�:. Ia�is ca�~=X(\mb)N said!>� � �!n$\N.$ U�xisother�"� E/�canEendowed �a!ѥhl struc�� ientable�Ibecome� Riemann��oIf-F\equiv A�/G�.�52E�$)\(possibly trivial) groupE�ransl�+s,A�!Q1"� }:2x��qEi.�Zity, $X Z$a topologi� embedding� -+co�l�d-\{0��A�.�data $(Y1analyte#!��$|g(q)|a�aBe$@(q)=0.$ Moreover,%3%.branch-�AO\piA+rc X$)� #a�,number $n_q>�eG\pi��R� u2<[ �n_)[?� orde��$;!�see2��te{oss n}!�\cf-l-s})E\ follow�! deals �5�5�) s:� �7}[L� e9� skly-mik}qi �]%�71{er� D}zxEofYy$\D-�a� �B�́��J�aq�m�o��2��a�6M q.$ �enn�� al� A�\{z� c\; �(0�'�  reflec% .��$?$! mirr�-� �^*�2P1 �|z|< 1/r1T�,$g(J(z))=1/\a��{g}(z) $J^*� 3)=-#�}_�)FF2Ez���involu���ur����R FM!I2tE_�"� �� n_q� +m_�� ��},��h���of��es coun� Eam� plica �*� 1�$ (� even)"$m��gdegre�$g�:}: I� AO conseque��a)��n�a around�܁0dz if $�] j� 6�Mn_q�&.�a��t$rA�I eno�a�r� is0F%D" \& def:� } �L� & )�ba�ary�V�"5l= r�mba}&��5V\�� !Z&ha�!�y*J yfs (|� les): f2 � .$ Ab,� �p2��C X_0:S_0�N$�qR%KF��V,%�!v��Fd ������A3.%� �-�I~��=Z� lm:�9^*.$ � Th.� �e -(be crucial:��$2�maxxo}r��+is.Q` �}2 ]�as ��U�.also sa���*��� ?1�m�n� . ER5?�e type%�%$ed � inR� tipo8oa��7%} %5:/is��-B�of.�Ay�� $�X}: \mb� �� �J`)(ab� ofps urseNtrue,�vided � �����4d2ol^�1�^v.vmm�M}Ps � �=1�M�`�1�e�N��KE� ype.��b�2�% \sz (on{Completen>��>�u� sec:EMA��a� b| focuA�tt!JonA�|geoq�nrB���Oin�,~� . To��m� precp �al)�>� ���Xwhose #aH� A� @Rv .~��go 9describ$nont sub� s $G:\Iso}(qF �9�#�! $\N=;A�admitsb�>�9 show�Jat�dexa eq 4W � $\go%2=Zr {EU�"*�!�A^result aLs !lurolEX2.e both"*' %�A�:.�startI #"�: �"� *� a]!}�Gr��no1Z��G${\sb}8t !�i��?,invariant un� ellip�!or�4bolic screw mo� s. J� if p��6Ya negati} m�$RQW%Ap_-Qrwh� fixed�  inui�d$(2,1)$-coordinate system:�Xenumerate}[(i)] \item O�!chronou�:�<((x_1,x_2,x_3))=-0+(\delta,0,0)"�I4or c Non4�hg-x +(0, W^h.$��� I8"? � */ -��:�+ŭ�O�f:As �Re�aZ@dan� ��, �"aax&Evec{R� # =\{(0,s,ss\'r\��r}�"�$@s $v=(0,0,\lambda."$ -�$ �Remark� re:rot�y [ �1�,5 lea�'9@�Zs$G$&�'Z� s+}.6fe�^+N #" �"�"�$)�$p\in>5�R(p��,nd $p$ would��Ga�u�l�?kame ve�al%z&�(�;adict��MEd2$\{x_3=0� S�$nowMJ>�=.�By>{*&, 6w�a#5+n� )�8s!e&!#$$\{(x,y,z)�?+z�x_2� fy% put���HA�.^ U$2 \geq x_3Z� �K%�c�r5(�( $H_cBHin�2N+c&T�9=R^k(-X)�H)=H_{-kmw$k[z%!ڡ�m�la �A fiK,a:�*,�E!kat. G�"� R^2$ mustA�a�U��Vi6Z"�#�'n��.AQb�AP-i�e�� yper�"A{2���vB� angl�&bor[r"�"� last�si6y�#��hoe�����no20. ����>y��^%�*�sym��� .+�. H� )�� Le_w }2�(re�m�R^2U�=M��isB@�*E����{ $(iic("m-�-) 9֥�Qw8 2� �39N�9�%v,R�Lh�(.�). Reaso*��).:55.4�_��cor!�on��& 2� �� &�  theorem.��)&��� blem!F�> >! � a"9th:jbo�� (�."�& a�d lh)X*U� aG�O�ox{Id}�M�'BiB �:�!�� N2D0� +^\upaj(� ��:(f 6)96V . Fu&�10� ize}� �A����'nu� end�hom�&@sm $(X|_{A_0})_*:�11(A_0)�G"g"Pi_1(\N&i�,~6I( 1I )=\l�R�r �!��ANnr).1 |%9�$Y:���JU��,��mpact"set'9D<0Q�1biU F�1�ll 2�X��� lif��"��$% s (t�3into ac��H�!Yad ). D*o0pg:*%�&!Oc�!*�-� �)��}m Ker}(X_*)�-Ptackrel{X_*}{\cong} GVP grupo}),�X(�)%�> $!��p$G$�%sf�%44mb s[%of!0rinsics ieQ0�:�*m�infer-dG$aos*of&j2O�C6) ����J�s%�id� ty. ` )�K#^ ����e�r��$reR+�&I� doma�&Dm^�Z&�&�E A#$\� [-A_0B sucM-D6/� famix'��os.�-Abe N>� *)�B loop� <  ���A�dis uish� "�%Y*�A� E�i�$no�7�'.$�X1u�&I� n $h ;��. !�$Uդ�0e� disc%�aiiBh(qD(A)����#'6 E3y N2��connec�!&`2AV h%� (�-U!W�ls�'h(A') .2'���-ށLI� so G=�-U$ .,h*'}: A'�j1�-Uoa� �!-Q?se"t� soN�Ѵ.*�7I^�0nd �%� $U_RN�.�h P+5�R!�!�!��\a]�$A'[4$ ��)_R%*�9__|ve�. ���A�[I�u�sy8�*R4we*2'�2 b�I�m7A}�]E��Rw2�9U��,$*�9�7l�� M,Td � $R_0��G-2s ��RR�& \�)= I�$.�.� G  A_0.$$ Uz�.�82CR!R�$x_1$-��f��' say,1 >*�\�9 pa� �;(1f$4${R%�=Z]���t>31t��raEU^i;-SX}� %j$EN�Jbe�%tuw F!.0����T )A7��ed �J�6"r 1 g��%9C na� � -��|_{ �r�9}"!h�:iz�.q C��"� , $E�[g 1X}�l�D1=c\}�Ux!7o&+ a��a�ret*.h c�2"50cr&ng� , $c-�.$B\$Ei !oO'diverg�*U. O�(�!�!�8�-��o�3�0um principle,� i 4K �1� ����a piec(�R x.$2��X_1(:��`=+?*�fun8�1�!��e k&> X_1 6R_0=X_1+�� �<�&so%[7A� Ł�y�� otop�.��6| . "* par At a�" +.#)�"O ��d � %�s{?A:F (�M~B�is.��m���1\�cBQA {x_1�(F�͇iona� E��W��.� �. \pg]AegY�!�.�g,B�Z�/ �5remov!a tub�ny(borhood�_:0�-�&#A�A�-HYWA�w��� .@�6EA k�$ �@JM�8SA��l $\Omeg9>x-=:)�5EzQ� �m�� �A[ .95&2 j ���A�-=��I s�5!šg"�ej}{ � }}:{b A_0-1- MA#%)=� C�K�^ 9 Z N i. �")$h�(R_0^j&� w �$.8b�(����a;itA��$�[`CA" $x_2$j��z� 4 B_j��.�$x hW<� �QC �) ��� Xn� leX)D�F`{ > "� &� >n�αՉ5� -\bar B_j�*�.� $h( �m�ZE$ ��3 Inde�;asf  Q enav�4I�:`R� ) ��th?$e�bN=&L� F��{� s�,� V�&9,")� . ej2eM�-�,�F��$j-��5�=@j=0}^k!�N._hMP1�2Zk >!�- �r��� wBF�'"��-L.�;.13c&<.3.5cm]{}B.J809�Ela�"�a��L ����2�6W:5$p�C.3h�0l< w�"F�C�H)�*� �RVH� �T�nŷ��ary. �a���A��H0W�u� h���Hl!K!�"��s��E*��_0)� upv u �3YlD%�a���%W�! s Jv�!S2^�* �}�3�(���$>� A��(� ��`!����s)�5,-��(a�]=��r6�1WI �| k���Ff ��mm>cI1- �b bB0$A�9�$\h?� L-�E(T"))-5f EY�A ]���6 (h|_ )' 1!:6�  , _0}: %6M%)3z#&)�uE>e�.��� 3."o��6�G X}-D"� 2�"�.zJ* �-&�<�� %�Q]M�, �U� �N �,� .�E� �"�-�.$.5� �7RV�5��# .�#�$ pA���?��Q"�. 42�R ha�iM��gt�NK$X_2:=x�#2� JN�&��or belowd.pe�lG rmon�A%BJB �-jE�!�2"�E"%��&�"�E52bR=1u]0$ ? �$te{ahlfors"�;�For8<{ F� em\cs �.�@!�"a $F:=\intZD1}�phi��h�1Ei)��2J�?�SyJV ��a4 Obse�C�1 F(p)�0(p)+i X_1^*(p��X_1=x"� K!�E�0%��h1�conjug>*x X_1� �ACm9n�� B�\�$ya"�*�rc*�'c) I�Kr9jI D"+q�i�7val� leng�,widthu�dQa��*t9!I\"�b!& leveGQ�! ,�Y2F��6>. 3.\F:AJͮ:c��#q�W72P��< Xr��35�A�V�&�R_03<1)=I�"�&Fa`rc�=F+\o��$ %�\c"�@Azs�9�$H:=e^{T2�L i F}{ =<A� �c�.�H.>A \log{|H|}&� ���;&=V�"!q2]Q�is bi.�0� �AIco:���#of>! !zQbnQ�,.�. raslXPe�O�%��./G��&�#s"�Q�#A�G !�%�N�0B�#�. a$.�$T.rIdaILn� ���J�Be= rank>FQ�-)"7 --L�����/�"����PAc4write $T(x)=x+�S$w ���SPO�\Lv,�Z�,B�!T�Cw=T(p)-pE�� , $pI�.a� &�&f�%F� !{.�(*�0 $R.$�)f�!�)R!�((x)+v}�&O.B near��-.d�-!k��C�$� P a.��;ov& �J�e�U%� � R:!�'=R4 �hT -1�2T'� x+w'�w'�M(wz F�� s $wI�$w}r|4!�undepen�"2K<*(w�%mbda Ew"^� rAW�&G#wE=.G*eigen �.�x:u wJU2N�,ref�5�=�� $T=T��.w=\mu A$ �i( $G'"�&T,RBj~$�"O5�6�k;Sit&pyclic:+��3 $n,m �z�B2T^mQ^n$Y*�lorigi"'*aI6�A;cn:%l^3I�&�VTA#u��a#OR.9�+$G�N�' T,T'-D�.���.6 \P�,�'6, /G_1M?�$� torus !���0'-s >C$Y?ce!��:6 �>* 2^#a��b6 Abel�ME&R�͖aMx$)A,�&w6!R^nEGf � a&� $n>�� E ��]v> C3bUYabsurd��R�@al�-*�&��ƍ.6s,�repea�(e � argu�[to gea�.)�� ��&=�agaA�!��G$|�Htwo �xT� ".Ire�3 S�7by MesllA�yTr�> rol!�EX�!�T�,Ath�:�.: &�&*[]OImes*� old-mar&OIth:" %z& �%=,2,j��r�NiB!�an�b(]#c!�a.funda!�1��"U.\ "�7,Euler characD stic��<6x )�*� o��s)PJBtim�8,.& E>�%=&� sj 2�"t4�~�Sj�-21.>P9"m \2L.dQ2�"]!��:1�< �o�:i��0\N*� � WB�!� �Ql)8GEf�*�/&�(kD�<:�,&h8[(a"E9E�z=G^�. � G_+=�+E�erG�X�#�-c 6,T_�#"�.^�9 n#:�9:�9 +\nuf9238 $\nu �G$T_0R �9*8�9!U  /W &�.$6 _+ &9v 1= =&1,T� 1: - �:! 2�: T_1^�1 ���^ E�`;A \go=E>� enR2262,T 5�3A2Nx;+ �! 392!(-� ,\muI $ . �B%56 4Y-s.; #^5:&R�� � R_2$i0� �.+4y�*LNj0zl�A�b�'$U0[96�K6>�A;G=��Y�F�3_"6D�@Z�%�O$X��z�*&1&e(k� .�G[>�O *"G'�&en�.2 �t�?5} A�e, " "l bEa2�X*�Wf(Z\�.��1:�1!M. :q)�� mbn�1vvt G�" C��%�%�&25��/E+= c l&�c� Q!�"F>Z&'QI��Y�7>�6&a4YIE?$YE���.���6�� !t*�"FB�C/{\go5WeP8to#C9J� �- atu$Zj�>��< 2_.� e*� i"� %� � 2� O.� Q3*N�.j93�2�"�29�%m�� . SS1!2����,6|2�� BU=a�/no[�)QZ<>� �}, U%�Q��ly!Ri&`Ta o�pun�_d�.  "c;*: ���A�J�7$ �ZaX*�F�2 Y_*) �1� �go-2� 1I��(2�'i��r�-}2%���V�$.<2&# @a��>/&R�6>Iz/���&�(AR [>1Bg-2�%&�`�o �XJ�dVp�* _ N�$s>�8�"o&�`map $B���g-5qXk *�5$B2�9%�!� 5 \l2c�yvj>OB�-�����a sm. J�s�3A��n.���U��e quot< $z�$��&LcA*k/?<8a�cJ��4nulusa�1�V \C�/1CT<�V$r>��lC-�8ficeOs, 9�A���\��c+�&"L�Ne�=Lbc[F�`E�AE��so:"")%�<&-t�c�!�l?2k6�0�\+`&: j,"�)�$9re^�.�V�k!L_�NɖdefUEm�.� $�1>N inva/Ibll�Y&� sb}^���.%EkE]�b�re=(lcg&i]� .Er &�;)6� e"�k&��Y6 �  �act!�F,>� Ŭ (ag6�i�!uЂe)�� (nam}a͹6�)$"�A� 9s��eA�6u��! ;y2.6�$bBPF2�%� G`:0�R�.f�2"(EclRoq��!6.A��_1 mport�Kto keei,mi/5!man%_�c%� G$ r�es& Ia a&�eB��;dif-� �"�D!Y&� u�<"!ousiadde{P]�Se$E� da cylVrdM�bi� trip�(E$Klein Bott�2s�@Gr> ͚.g��6�$�F$\z �h\z� $F(a,b)�>aabb �&� %�!\!�_d��ofy �&�H$��"�B, �V��=1? �!.B> /q�SR�.V]�a�r)vg.�ga�2� (��,N&�  )2� W&�mM!2> �� gl�dR7�4[� ��� Af%n��#(a�W�%$�, tw!X&]T'_0,&�9�%�bO|N?9>6!��*� 0^2,nMf$ (�e�+ ���dex� �QAb�kAZ� p. OmE�\l%B&�a�=A�pre: �lNi-$*O'yO%RhHO�N�FOU"�,$ . � v=r�M���]��%!JY~T_0'':=A�_pn # E�2NofQ$�--\m�nd�aE�e R AP^&�n!g&�8,� !� =n j!&n�K��As � r �n}G:JQ.�%n%��_�� !':=2^{S%�<.u9'�:g�T��$5�� .n2m.vHM��"�O�:v�Dle�e� �/&�w�6.s*�.�Pi�,�/ ���X 6Uy�m��A,R/J�R* <=R� (%N"i|8B !w $(b)�r $52�3n)�z9cnw 2�Q�g\gp1�IJ�/.,�0-$:@&^."$n!V�SkD�:.K&Eg�&�$-dA � a�N��jCizU ). Wj%y#,(v_1,v_2,v_3�zIn--!�1a�T''!ߑ&�/R_1��e�f�`-a$>�N%g(-��RfV�.8 )%:8 v_2�6 T''~ & 1.�I)E�z� ains.�&]ypa Phars�h��vU6*5*T'1m2!��3�=A&)��xRFC�)c6$NA;%/aM]n�j�gE�2AЭ* ommuUvi�AP5�R_2=R"S/T'/6�+T_2�%�jhorizon� �,��;k.��(cA ItI�o stud� �w :�e�u\gp�0E� � �!�WP $G� � z!�=s  %"Y6�0"i&A�&N E<a&� p 6&� , yP%L"� V*�� ^2�� R^2=c"�*`*� NmN w�@2�T{j���Gx{ R} \,:\, )\$)ong%W&� E��-.�m 6UI�e u? J3de�s���&�(2� �� So� oB,-.VI3%E| ssible"vf�F�20�:� S($RBpo� gZ�J�1���6u8 �!�V�V� �. -\nu-I��.$ongD�0QdA�e;B�6�J�$(d[KT�Tn�Kh!�e��g|&R�;. Y�jnd���O X}$)!{�'ŝka�ar-�|6�V, Lcb�$@/&� � X15e�B�*�J���B:"G�>�kB��F� Qm��:: � H.��I:- �EJ. How���3 @ Y -$� ��*�f[(zoccurs��6���&# ene,!��l�-�4$�9a~mF:�\>_� !2u?�eA��(Y��Q#!..C.�r�A�Ru Y��Ya�E UK@2�FEsY/V'\umoj Dm� s�%(��t.s.+E� a�B (2S|g�s)�5|g|-L_0}uD$1-\epsilonl �>de2p=@Z�/we6�IE.rVtMhso�[�*�tNTgo"/9So|�~*�5 E.D flat"�E<$�3"�vs�<0M*�\dire�a&#ds=�� d Euclid�~�n(�qjgOa�� A<�&fO@�wpiɁY)^*( �)%�dsw %o|�"8 3}{g�z��� )=�z1{ 2. 3 =�z1}{4} &(�y + 1/�z�z6f0�%n-$N�'�q�U�<>C.�{M�b� �-��] C N~�A"�7$CE�&i ����NJ�.7 �U5�.��yq�j�$ aOs�v �,"�v)j+e&L�%V"�4 corollary�+co:} Any��?4nŁ1a;R�B2i� 1@I Vg#2�+ G *�Y� 2�,ap�b� 6$. *���� ies,��!�&�� �]�!� ��+"u,�;4�yxTB�**�A %���}�. \YAl-@|r2F;$�q(�I0*)& _�%d.� Av|F�*8Z�r�@� x_� �, .~6��R��,N0�x�v,!@"�s* =�.�1�N�1F�R�.,��i0�a��-V��,��I�2�j�,b�N+R�J�R_�S,�,�nN�-=%Y�2R,Z�,Lm�7J�i}�.N�O.�i�!�m, m�6��:� :��_*�,e+�J:g+�%X:\.t2,�WV2 &@�A;� b�+=F&;� ����'X%�[28>V �� !�T>��"8 5%C[�H�B�R ���� "�"X" TW'��">�qN�BV�tTY�5j5nm�^.�-*im�"#�`= Ʌ� a� lis�!�Rj�[6�4�-f7qQe;6�m�yDs�nniof be!�QS��s�t.Ommatte�lacb$!) glob� *P!TR�poa smo�nCauchy ?F$,� � miguel}b8&y�deb� �?{S"�� R�� !�w W/&��$!cTR��j�$[g#6�ND�Wa�B�- �!r�"U Ct�&]�*w.�<�� ly��ic�!_ �by2� R 1xg&1J&� �0��(V�Xi T.^�pV�"6l�t"se8Ki 1�ECɊi � ��Ie pol_/ :s}�mb P�pFUxH� �CZt/�ate 3��(�_c tote3geodes�p"$B`.�g6]!+��!fc~I!�6�3r�2O�tan�XSO!ۅ!�i�,ɥny, $g(0���g(z)=z^pp p\�V�%R!` $U�lV� \sumQT-q}^{+\infty} c_{j}z^jL�dz�qc_{-q} $f;D.$*=#F�B�$q�(��cVde�P vers���.�D}=�{u�\c9n�Re}(u)<0 �Et�lde5�AD^*-����} bl2�- 1jU (u)= e^{u�A !��&�K 2gfi_0*+��RU~c����M~]o2C5.&� �a_� �2N�R(\� �-X})�WC�_<�!� .�U!e�!l>�par�j&֑�x nSrE��!�1�-&�� �)*.7&�A�N� !��-i\, &��c}E�,}{2 (1-q)}\,!� 'u} h(u)x�E�1/!$ ,$$ � $h$1S�H&oHn�2"����[-~7� lim_A�!�m����o�?*�^B�p/|i$$Im} (u)|^:�7r;u� ���-v��imagesQ�-[�nEwojG�)D 6 *�K� 0< m25�"1 2� ��*�w_j�8$ja.{ur.h�O>-"�_}�b�� �oH�7�V$H^�!�! cF�l%ibY- �zL.we&� IXE_ B&]|��U�`ŕfNN�Xa�ssignA$�I�A�t1var� _j=+f�? 2-1�Al�I �"48%+8B-,$�J"���J8;StokeM mula�. $� 1}^r� R�r ue}(C�,P_j)=�Ճle=y:;.� a�]k�.�6^-�� Rh 155_+, -\}7�`J� gRb!oVu> �8:NVn�]��e1�N� ���:Js`*�3>�v~ �M��Lcorkdlů *� if� GYbel�@�au�2$\6�s~ $s <�$�'��F�"�9��` ��.6��F���Rs� $�ps.y� 3 Xco:ghull1Y&tE!(5=�>�(r=\�w_1=w_2=�[6&�s �a���h�! 6XJ��+4a wedge $W$ (i�����)T!!�re �h`2a slab:$has =��� 9 �6�!$&}�T6:/���t|?�Bkn� &l�2�.�!*js�\v%̵F-a~�!�� &� �X�B� dout�w�&�.s8R�6  _2�6!�HANR�> ���6z�^'�+J_a�ob:l#b�[Y�}��j2}I��6���. .ka=��.�>F�hom&\vN�Bc�F{!Y�.A_&:$>� *r2A� } AL�*�9w�? w� �d@�f���J4� . ItJJ X�GP�of��3B(�& eN� �קٜ�:�<� I.�nR/Nj.�'D7��mv sket�u&1^Io-Umth:�r偅�۲!g�� b�N�V� .A�b9� statH�9$"&�"."SM��!�"�%"&�!6M' #":1)�M�r �� A�Hs�5O�e�B�_aFX-:j�F��>�V�I 0�.�KI="0s�ar�4Fi&d � �a�}]p��q(>h36a+Bi2�/��_0` NvB� ��Q��� �<\L6u0(b):$ Huber'sA��2 �h} a0*�q@m�&�AQ� B�E.t� )]�- �HJwL." ,'s �",�D�XYs �y ��W*��aQ2mex�j��CJF :Q�:b�����5tvst!2 Fiv��E�J4JB-Meek���m}�I�o!,"+�&i&��!�=y�{�� t� ).��!jm2)�J�Po A-!R~��)s"!�. T>B�c@)#)zn9 B*d�A��q�Y�5)"\ �YT���5BGa>�K�"�ﱥߙ8 s<< �2c�#!��{�[ out F�o-��2�\mb-K3bd�kz �=5B.Jt�Y15��1�3*^�0��^we:��X�k1�1^2 =71�j1j1h~!u �b�0U�t&b1it�_̅om �:�9of� �d� �� ��1�������yF�4j��VR$�$/gw��sa�! Vs��U5s.C�t^wE�"52�$�r some"5 >�%so �2��2s\�^2i3� ��%|��=����v��;}7��� _�2]&�6& "%n"dof�/�r&) ,s6v���*bQB ")c��Y%�� A9 ��eR�� ��"nT ���27 �#�\}69�e6? ���Y�T!�.��)th2! $�:Ю Ord}c�j� ) -1A� max � .#�4���!"� y�$ �2 :�!69=\�����s1um�&�w�s��/H�9za�>9r�Hޱ� &6� %A�N���65/BlP��.p3�he������#�^�)�dȤ�]�V]�}�]�(wex ���Q%um�&#E B vh &Y;�v����z|uB�cM�."�=u2,yE!�no2'��J���,m�3?trah� forwMF�%s@1G�9'}�@��'j ũ� ��mi�? +us�i�|p� min��s"�R��A�(F#%�p^,�I�N�f �/�u�D��c.F�6Q"^|�ingly-(}� roug8 �$ k � } >�(�}�L6�)$G� �'*j�E�!hrW`\Hf�U27`Q $r(G�$dK�J$0��a�H GaRoӓ�>&�:UK"Z�B�&�&�un�^j"����,�J_f/G�w��FiH�$kLFα��ZH_5q6 �Z# ;k:=k_1+<�7/ *`�����20R�4�b�\�"r )�R��BX$\rb-oz( (���${k_1} D_j)�P��*�#6tHme� r q�A7�L�Y\x�, ox{Gen}W).%�_0�$\{D_j[* j=��?$k_1�(8~�9A�1r�<pBd�clu��-�n�%#�j��)�Dn#�1d&�.nB!�*V {associh��"�!�.&�N�cA� .&X�*`=�<�~>��i�|g|-@*��2�Oa�:�� ��!$i�ad���%,$ �X_ �)�@(1|�^2)^2N�?�&�l�1�j2�j��F�ro�yCo8? � /:m�3 .��6�3: �� � �� "�.ofe$�0�%�=0�Peqv�� 1.1�V;os �m���ve�.���y�Re�-]�kM��eB�A&5�-~O!�z*C_q C2�|4al۔ =xmt܀� � 9��& \s^1�$e�^AN^** !�m3�aG# rF�^*n��1�*>2s^!��F:.��1Ac� \Sg ���v���G �7*�]J �3'>w� ��,k-gluH&�kEv j!6al�K�-� �*c k�q&0(-p&˵ $J:\Sg�Sg� J(p):=pN�Rs�A�{)&��_%k� FB� l7��*~Sg�I!8��m:w�A�\\!:$JS3ant2�yF���� .y2�G I%�*�8eSa=ve; =\Sga�).�}��7�6w�t �.�zG�,�n& Deg}(�� N?�Et:S�N�V�of��2��+k_1-F �R%�.�82}a�* ,E�8 /am�J�&�FN��ej����MJ���$gM�J^zҸ%}� 3jJ�.� *2�/�#ni֡� reo*o�W Sg,J*ҿB .'ND��"�W"�AX^�>A�F�;} � ��#A/Et����Q� =0Y�c��b^"�%vB%1��_:hv$�W I2a FurNrmorF��k�"�a�ula� J �nJ�ޕe�%� $ship betwe�t �G)!��emPE�M@r�) -�'2�/sA9 expl1��&� ��2,Q_1, �  Q_{k_2}4����u^� eB�$�. $n_��9e^�)�*$'$QY� �k_�jWe�� z�) n_j'�!� �ơ9oJ���N%B�_͕�&$ �^e� rO�Phi�ͦ$ (U+YK�V), �4 ɻL&��m!�� ��}�.v� c}: ��t���B�"�)}@\2�!|2)��%.Qr-�l $V_s��"�I n_jU;V_l>!1} n'� $"W�|g|�/��B �,$C�R�aox�;=*�(� mc5 �YW_�=U &Nɀr (!�-j� d:��h�>Rc1��~ <&Q �r (w_j+1~$r�b0$d*�/��!� F(.:`#[T�;i��2ula] W�t��`pX .8v 2P ds:e=�X \chi>}!)=V_s+WV_l}{2}+)`��-1�W:*7mb�D�E��J� a�*� VD ���R�:=2-2 "$x�R�xe6����$&��1f-FImNi��='i� Pi/G��*tZPzg�/G)G ʙ�w�.)Pi&�s��*N:9/G" {- <,G?ZD"jA�.+J&2 \c2s= R&l_ T6@()$_=�i�AC*/!"�,�'E��(� {X:6�%p5>-�$"� -Hurwitzu �|e Ac:�$)=�(U)�me (h)- \pmb{B}&�8$ �%��� ���ٜ $h T� *�qm7f�!1 o � 6j21��p�$=B_s+B_l+B�M�)B_sa�� B_lg�g)6-� Tf�ss"�"� Z+�$p.,"�$�~I* ��  m �.Ur ��-1��f!<�}�q y �\��2� F.5 ?��83 EvASra=� + �ye00���#l�ldfW �m &Un[ }��]A*} A�Bq -V_s���-2� }SV��W)( �d:� FF� summariz�llED9�dg��` EJu v� �g3�1an�@fu��n&�method&q-�I [A&)F\ ��"��[��ic�6�!�W� j�6D�$k!W<�+ J_3�$1V�Vis��j��i�2����XB�*��%�^IM��r (\Sg�&�"�^*6�;).#�.�nR,&��$g6�{�.$5 s&���*/,�.7��"�r�Ӂ#A�g L:lDE *)_x�� %x"� �$�$:��F|Phi6zP��$.�2�[}re ��� �s $�Re}��0�V�!�' ��C H}_1� ,\z)�:-S��$ >!�!�3�}'qF.�3�0� A��\FP�egM��He8�NTc � �C.��� �k &�lM �gI"�[�D&`. \ �0�q� Sg$ )� $J:{G�E �a  "��4&�� ^YESg)2�;aa��6�*�6m���int���9���_F�&��+d���iI<_c.�k�4sp��ng%w$�:o6&�<�D�hose�sure!K�b��:dA�[� �JA�_� ת*y�.�a8>�qni�f $(iP�Mu��G$"V�!*I��k7(iv)$�3�t@1�&>}�7eq:inm��} N�,\�� ���q�{p_0}^pq�,6}9pU���ms6iAY�{>D*�Y�A�aU&�N����O~He�!��=!��"�x��X@2[ Vk� �wӢ�ΥL%m�-�2* 1$�P'a&{tt3�b=:k_2��A $g"C "?�Sjo#v��.I���m.vk��:Ea��QB�}"�c$`$� k$Bscs�� 0�"$l�n*:�mi^S�iQ~ "�+c �7FH .�j��ag da2Pr���G�d� ul�(w(��"�$ part.I� $J_*�q�1�Mˁ�$12�5�Oint_{5��4�=�%�%�I:n=�R��$�k�A�./|v u����>��.G$J� �X� o�G V Z"�Aanl�����  ���l2��|p)\�(&�Xa��-&�� ZF Z0}a��i�X* � cc0| is f�bn eLI6A]���!�exaX5'f!1/z�!Uvv� :�lche����wf��J. �ci�%���)!{99%v�0*�2�A�Ō���}4�%�cCZU". �G�1A Xft�Sc:�G� �=�s!a&N:�"Vo`� ��$� � `)21U�tooA�? �{�!@%��< *v�ᬉ:�M>b02��5�j��en,�eS�E!:Y�2�y6$y7ŋt61aK2xE2^���;vb�Nu*��� 2�@Exampl =M� �O%vٽ} "�kna����2 fami0of�Xu /�G ;I׽ sweep� !/�A.eI�%)�2�%. A larg ����e= fn��; ��2�6b�u�F�4�=i aX�geV)e'FiVQisabel�{\bf 5��L�8QH �c(�Beu�RE!si"} 8!P : $$=\&="Lc}-\{b,-b,1/b,-1/b\}� �#t Sg,\;��bar{z} (�MOd(0,1)TK0b\in]0,1[$$ $X f�&��Lz dz}{(z^2-b^2)(b^2  1)}$��"�3��E by E*($e�2� $) .EedQ�:A��6*E�� � 7 -It�A�*B �\*7tv&@ (2Ai Res(Q ,b�p�LTb!�Shu.wAi>g$yXO�&:+� n!)$A(z):=1�]��$ $A�">�3=(%�!� }_1, > 2,zw&�8�a� rfac� �i�?.�-�a� &�y�*�R(�SHq�r*Wq � 0^{A(0)}!j:*$$���"!>�$�Z��$RPvRL�Cebw�J�yF�3!�� �"O��Bf �$,J(p =(1/E�z}, w}A4$4�(�Q;�|z"��Y8b0,\,b�\�,w)=z�U6�w2�������.�CA;� ����0z�� Re}(�-� \sqrt{ab}�X-i>0��}�i�!ee "�oa�a]$x_1-$ax_ie$b> Y��#N424f $b<� Mo�if #chop $b=-E�J���� M�� �qE]=(�qz}�lwx�1 Q�A�A!2 !-Ad,$ ��3 �&!��� :��k6d-B�5�]a^��(a�g>-e�vp"L$�,^_ x_3)i {\rm�qI�i�&��Plb�2�: ,�mY2!%!1���.�u��i#61�0t!2��i=�1"a�%� &�wI 2� &� 6��s;=JLU�Mz�s�֥�jN3E���!��BF�$�o�oas} (N�.��N? .�? ��1x>�".B0 �o�p ^2-a�A)� a_2^2�|1)( �\I� a_1,a_2�U r^*,\;a_1�a_2�J� n� Y�IݙR�ag(�="\c� _6� w(^�m3n,*} \��2| )2�z�  .��zwo.�Z�e�s�p1M� O"� sn� v�* N��v_i=2!P&�"�i}M a i�>ϳere"�03%�X.2 Xa5ar���w�$a<$AY,$0sHA" ). E.Smp�nLs��)in�$$|(:ądv_2=(W�مf�Bu���o,\J]M��"e�`��*efD�>: .�� �!��:[V��. 3?������$>��B� !�A_�;�H�� �< $A�< (�=",2(z,w):=(-z,�-w)$ induce isometries of $\l^3,$ $R_0,1$ and�2$ resp., leaving the lifted immersion $\tilde{X}d�variant. To be more precise, $$R_0(x_1,x_2,x_3)=(--,, \quad R_1(=(-. % {\rm�}52:5 4$-\lambda/2 f$$ Thus,�cor�ond�quotient-�by.groups!8 \begin{thebibliography}{99} \bibitem{ahlfors} L. V. Ahlfors%-TL. Sario: {\em Riemann1ds.} Princeton Univ. Press,H, New Jersey, 1960.{@zeghib} T. Barbotv A. Z wGA�L actions on Lorentz %�Ds, Mathematical as!� s: a�o-��1%vf41219>$gold-mar} :�G.�`Margulisi& Flat� 3-u�E$coA act Fuchs� � ��Conte��i 262, Amer� Soc.�� nce, 2000��5-145. .�grigor�G 'yaѤAnalytic�ge� c back�0nd of recurri( non-exploA}!ƥ� rown�moa=��R.�Bull.>� 36a�99�� 5-24a�u�� !�@domains} Z.-X. Heir( O. Schramm)}T Fixed points, Koebe u�j rmize��X$le packing%}B� 137���$2, 369-406.$ hube)gH ��V4ubharmonic fun��Idiffe� ial -yQ� larg��ea�I Helv., 32Ž57%0-72.� jorgemeek� J�� H. M III. ���topolog�XA�l�� minb� otal GausE�.� T M,�� 2!:� 203-22�W9�kly-mik�c$A. Klyachi)�V.�Qiklyukov���etric ��urj tub; band zero:I !\:�.}!�a� (Academia Sc� 4iarum Fennicae%� , 28�K 239-270.� obayashi}A�K-p�;' Ŕcon� � A�єJ.� Japanm+ 84),V $4, 609-617.lɳ:�,��ٯ5 >�B�ofq�� i"� bi Michigan�of%<w 4�v  4aG92�ma�E}RU&T N locallyc �g)Ua freeatdaaCal�d .} J� viet � 134eP8aP0 129-134. %(RI�() AutomorphB�number�8ory, II. Zap. N� \n. Sem. Leningrad. Otdel%�T. Inst. Steklov. (LOMI�q %�190-205..�e�$-rosenbergŏ.�,RMya�dof�l>�T o >u 68a͵ 4, 538-57G y�mes)�Mes� �0 timi�c� ant2@"�% itut Hautes� tudesq�fiq3 (1990z\�,marsden-tipl��J._ M E�iT -#Q�6� a& foli�7�[�6� aDgeneral relativity���  Rep. 6��8a 10Ap2�4oneill} B. O'N �Semmi-ri��\1ԁɉ�c�!832 osserman}a�O :�  ve�>8}. Dover Public) ,�York,�hion 82wolf}!� Wolf q %O� > (McGraw-Hillj�67�9�um-ya} Umehara%� K. Yamada n1�6x2o!�F To aHokkaido�7�l JouW�endB�|{\bf ISABEL FERNANDEZ, FRANCISCO!,LOPEZ,} \new� D� t�� o de�� \'{\i}a y�l9Facultad5$Ciencias, �Nd Granada6X18071 - GRANADA (SPAIN)!�e-mail:(first author) isafer@ugr.es, (s�fjlopez ! %% docu�c} ��\`class[reqno]{amsart} \use� age,symb,amsmathfo� � xsym6/ pb-diagra���qin{)}{s on} !@4command{\A}{{\ccal{A}}:G.GBD D>=n{NB=z.ZBcat.!CB! quan2#QB#trC8operatorname{trB& orbi.I O>�pmorita}{{~\stackrel{M}{\sim}~>-HomBv>(tou2�Tot(6�idBPid'2� topo�u}{\��a\{\ \,0ne9� xZ!� bb C>�n�als$N>$re6!R>! toru.BT>!integer.$Z}>�C�J RRBZFgQFANF�hHx:��#�A>� calb.!BJ!c.!B�calE!�cB� cale.BEJcf.!FJ!g.!GJ!5 �HJ!j.BJJ!l.!LJ!eU�MJ!.oF� calo.cB� calp.!PJcq.!QJ!U�!SJ!e��B  calv.cVJBu.!UJ!w.!WJ!.yel2fraka}� {a>Cb."bN"g."gN"k."KN"h."hN"m."mN"u."!0 \�4style{plain} ! ��}{T}[�F]R/lemma}[ >]{LR+proposiH 1PR7 corollary5CZ3 njecC245:de�2-2 �Dz5remark1R Rb�.+V/# ��Que R`pr90P ��environ� ({sketchproo�,4noindent \it SmP . }}{qPmbox{ }\hfill$\Box$\v"({1.5ex}\parv .qlemVndmtzAa�qP \date{\today} \title�"$for�de ![� A�4er \'etale Liepoids} \ ,{N.~Neumaier� J.~Pflaum��B.~Posthuma \textrm{and} X.~Tang}�/ } 1G 1<,-15mm}\\ % %/ab�ct!�In�article,%/ cyclic ho �e� �l.� b I�!tcon�! algeb� ssocio to a>$ 2'< is studied. W6 mpuC �d�dex��'. HowB from* !� viewno2� D �connes!,.5H �{E>V prim6+a ``:_1; '': a�Y�V�u� ,:PNi E*y � {e}� * oid,{ |,i� id�+f�-%0uF-  (cf.~)�$moerdijk})�i]n�-U`esMcrwd��9e�!�q�J �17AQaL,�. As � in-�ta:fav i�'� qA��ucu y�:fZD}��&sense�(Block--Getz�').bl-ge:.�}�Xu !xu}!��<�� f�. I� !B)�t!�E�is�ed5^ t�!wee�]"is pap��Notic� at �^`#^��.Kof �s } ���&ub=��KsIHM%�oid�Th�� step!FEpsta/S }�X.;�aN wi��unt howA;y��s�ha��W$� ll sw�isՂA�cal�$t���V�!&�5�ofF%. W� 28 Aj�� , ��� --Ko!Ct--"�� �. I� e���&8,�,�$/@ults have already���e� liter�e, e.g�$giaquinto}-*l global�y �1�ic �1ety�>� In S� on?,w�1���1�onAE!=Ŕ_m.�� . By TelC's��� technU � �a)z*� �+B�e�eOvNN6� RY�ZA�6$to4y�B�s �IQu.DX3ő � Gerstenha�"bracket ^ possibl��ted*e_a B��� � em'' fu�u resec*q��1f�B�&Ka�> semiA� �, o�o� worda�s> 1:8."�%��� &��!O $Brylinski'���2A�%�z�� byi:p&}�PZ�t< �� $E^1$- 1�)1�" sequ�)2�A`@$\hbar$-adic fil�2��ؙ\zM<���Ehq�e�uis��inu��Z�2� )R��NY�2����a� ]. Our��u�4o !�ve� �C 4, Burghelea, 5�, Nistor� Crai�)�63>��n 3�%Ok�chang�QH.>*l� �JouFep`1��-�j��(�E ֭ it��V��5�of2� GA�.c27F� Nexte:J���-@>�aI�2 >F bE*# I��(on draws upH wo6 as: ��Fr�Gd��  �'� ntF .$�2�}�ofi=�!-lexS�%��ͤZe��M prevI:�n�(�7 ���&�2B�,��us".zz! -�.H!``��''uQ��y--i-Tba q�)jci��c�0ineBi*%y � �at, dueZA�u�i!�``Mued&�''�K�dd (umiI�%S is 2imI*I�ly,+our"� pa �!D"/.�,of Chen--RuaQ�cr}. � J+-�* n{p4  r� �2 )�.�������i�edB�.�e last2E�"FZ��&E, builk;Oearlierke �Mfe:g-�}. Fin ,%cF�8 also� rify���If:�~a cerW Picar �''�8ng&!"sO5�)+. Since � ��sac quite �6m6/e��Dc0-�y�d.�ipeople 2�yN9�� $included,  ��Nen[( �he 0 �a r�9r�ailed5� devo�to��se sub�s�s ma� purp"�xoEk�бL!� ��dea��J���i:��5W��et up%no)�. Vp]���ed.)" cent  I1dolget}A�,Dolgushev--EeofereS A"�8 �ixx/�� ety $X$`6[ �2J>�!�ol:�nd~�}of*�re�&� A�e� Note��, ��m Sic6hir set-m� �i� e�i" 1uonee1d !K . L!�cs2nER14 �e[��re M e'>"7�fourth+�^PhD-thes�naN�upe1!�� <c�"bore��mV ng T�Dur!�fI4yAn LuminyQ<th1of us, �) ly M.J.P.r P.~!�X.T.~me� t�d_E�inu�� workg'r��wr��a j!=M�about��-;-�! 3mm} \par�+ph- Acknowled�4 nts}�would _:)�4ank K.~Behrend|P.~Xue organ� i�o5on ``Gj>�!8Stack�x50 ,June 2004, wA.�6� starE�%3N�a "@&F@�hospita7d)�Avis] x . He ��u6Alan Wei =,=(Ph.D.~advis� �(many stimu�0ng disc�2oQ$M.~Karoubi%R�"s���Y ��IHP!$summer)&:8A.~Gorokhovsky,J$, B.~Tsgya�V.~���Ihelpful.�.M�E�HA�g|Afu�Y% finan,=supportq> DeuttMschungsAT(inschaft. I�R�B.~!CJ�I� �AZAn���s�KO s.6� Prelimina E} ubz {N�Nc�<f.�e �SatakeMhs }. RA�ly �aL��Y��y � uF.V ]6sdorff� 0 �ilyI�ed1H"� A ope;Ebse�G R^n$��6u � �'awill a�%��Gua�1��model�s,�6lowa*!�approachv Mo�-$"� (se�so  [Chap.~5]#-mrcun� !�1z) ). To� � �saC�/�A{:   lz re�9��bas� %�s&�N�;5. AA�!� a sm� categg in-�b !��9sm,inv�'bleA,M5J�>?%A���b��_0$�M of o� � "1" #arrow$G$�&**�is enco:I� fo1� f*&maps: �Gdisplay�"�) G�I�2_{G_0} �2 set{�-right� i}{.a�O� =#3� et{t-Os} 40TG."q �52�He4$s$%D$t$� A4sourc� d t�>t! , $m%� the S�& �I.~com+.�$$(g,h) \!?to m := gh\�? h$, $i�� a E� �.f$gR,i(g):=g^{-1} ƭ5 $u� /A U:by6nt.%�Xs, i.e., $u(x):= \id_x$eKA�$x��A�A�An 6 $�GA�wKH$s(g)=x �$t y$ �Uo�$bIF��d� $g:x=� y$�FeA�5a�f ��"ar�1��� A� � a$�. V�L*- (� �ede�q�) if b�H��I*]E,��A�7)�ru�/A:s- .��.usubTNv!�nm��at1�an i� %�G�A;�� j>sm. A6��ally�-itX/p�<wa �,map $(s,t):G�Mu�!�i� A\ ��� \�_�<5F%ĉ�isotropy !Ux M rete.AX�"� } 0oid�a�Nk t�Mof!/= )�i>$:�l�?:/�ϑ�&1 {: [Def.~3.1ٕ�xA��Q4 � !�.��f�&0P��&T+�  e�h$#$X:=G_0/E��aa�Cal *�����!s.C,1 sa��s goessE �{mp�fLT)al�?a�E�A@Rz��in facW only dg� 81�M�9(val'�}!�)�a�� an2�+��JVofK s wefc!�"|}�merely 3�at�(�tcho'�/-�U�l� �G3 ) 56$X姡� %�� Ttoae\ ��&r#isp)0neighbourhood�fU_x� ti�sJ/5��riU $ $G|_{U_x}a�a�iB �ans�oY�, $\Gamma_x\l  U_x$,�$�!����M�����& ��X usua�1D 5A�"ri��(�Z/"a�� �>� &g $\pi:G\��X%Y�sn�!�q�UTG$.9 )f�{Sheaa�o�*s} \l4L{4 ves}6o Y� 28ak�(us���i� �+�us���%f�:to� �"� �& � g?  aA��$"9S$�#"�"`1�a�f)�5%�a %Ub! f/a�b"�B��&�J"&'acUphH Plks.�_y=���psatisf{1% objM�ies�=� $a$!$�4ai�b� a�U�� �A�l�5g�nee�( $[a]_y g=Z �^�ae A.i�QU of�%�E_f$%�I,&e )� sf{Sh}(G)-y�0�� lef.ct��cv4a i�{��{\tin� v}}:%PN=i� tAb},[r�L. sfs!&�:�,��& "�4�.�5&n �v#S$ g�%"�'1�� ItsM�deriveorZ! Q�%?a/.`��50$H^\bullet(G,�})l LikeC�Z�P actlye2� [:���-4 ��,)�c�� �K4 by $$ ^�](�=2{ a\in^920\mi� \pi(6S���BB9`m�� ��e�&��he��way��8 �hyper]�� �hR�)� a�h�2�)�ny)Ph!��!Ea�e /.q�vemb XD } ���i���[Hc�!&(re5 ed) ": X9s0cm}, rS� 4.9E( 4.10) p3��In"�/f��'0xinM�y#�~{st�co�`s;e9!��n�"n[. � �(�0g� argu�  (ines���5nD+ a#, //&!+$[p.~280]{lV<�U%�59&�59a�IdXAF� , but�22ja�a�Q  �"� to�-)�smA}f6� HE{F��4�&b� f_!: \:���.N�Sh} (H)"� 2Z� �"��Jobservk.EfA ��_f_*i�$f�!b� t�w5.<� }F�  ?�U[j/o :f%E_!y����H) n�stalk�*y � �5X"�H � 7[ (2m)_x:=H��(0(x/f,\pi_x%��\),:^o $x/f$� E ��m&�/�$� %v�fii,A $f$%^���"�I~8 ode{x/f}\� {e,��s}\%H,r}{f}\\A1?x 2G�M��m!N�K6l3Uogousa4!�V� $R^kf_!$�$a similar 2� u�7GhigD5��f��r'Bxs.EfLeray�2, q�i�3A#Z�B�"�  &�%,�Z�6���N~de�mf�&e^� R QQby ��sm�Y�M�d�"8 U�2g)\congN&Xe }�)�9h B"brief]W%^!�lexw"i2�& #���)�@� �B�[���$G^{(k)}�&o$k$kos� � s:"�6� EH=\{(g_1,\ldots,g_k)�� G^k @ T s(g_i)=t(g_{i+1}),~i=/k-1+ B ���%�&�E.�E�pfal�'�fac� $d_i: �.{k-1)}� $i=0�k��b a�byQ2��Ms�^A d_i>o �vA�( (g_2s!/, &H A��$�O�b /5/!D}\c)O+2}>Q�� 2W1\leq ik-1jck-!� &6@i=k$.!� �� �%�- 2(N�%��$d_0,d_1J�� simpl� � a�&���g1ic"@,E��Di[E9�1l�!]�classi@ &$BGwe/@6$ wo^� Gk)�}to $x_k�$sp.~$x_0$.��2�bc! f�Na) % ^k:=!��_k�� (put $$ B_k6<:=�� gc}(a�k)}*�^k). $$.<�5%�sh turlC966('��� ~ �8 %6� smsA�i^*�^e�� k$ )�|�/A�- s�D ;tyE|$i\neq I"a by $g_1W"e�. =Di �smA(ei!I���R >�[B5 wa�-nd� "� *�3E�s�0�o�G$H_V6嶁2$� c-so%Q�y �K�Zho (C <[Sec.~3]� �� 2.x/)�9]��$I�( e�elow)KC3W.x�4 �U���{oJ�o�\�Rl $$�n��e�$A�\5M��e dou7 � $B� 2)!m�W����V1 )�*5� :�S (~y$ av��a�-� .)}#&by}0�!�wis?:��*� play�  im�'�Wrol��!�?�E {kawasaki�#L��pe�#�Ha�0�of dea &0?``iTy h�A2/$a~�<ykau�[�(of |%ss b�Bwe�"9�9�,&>A�y�� oid �q D&� B^{(0)})e�!" ``��of loop�ue2� B=\{�"� � )Rz y ����� �$��hAugae��E? $$\L�l G := �\rXG.�l*&�``�ina��@%#u%�(*� a# _�hf-B!�.�_1=\big� g_2� {(2)}) g_1 � �/}�One�0��؅�ag�R=�99�comes eq2E���& $\beta:_2� $��  �>|J:�3$&d))="> ����$a&fiTb)�r�4.��& -clo�fe�C$G\hook�%��Q Q�� AaM�$�mC��n*2s�'2�� ]am's��'A� |$ect set-��eEe'3-". � )�%"+2�>�2aR6�Sec} 0*� !c abov ��oSQ9m�7!�swi�/&%tIiMI1�.��%!��2�=dZn�2!�YDJ� as $HZ�P$.�iE���s ��@V�'�MH ``:�''e :ša�:�inR7,�we �now�!�%"�'�r \ell( �)��!Bco"�i!#aM�&�{Oe"�A .q��eM�iF�f� K �9�c>\��5�B# I�!�* Bd/!�X�7 �eqnarray#  *^�rm\�orb}}k$C)\!\!&:=&2(5� ,\C) & = \: $bigoplus_{)}}"�-�Ul@,�%N�,cN�Bo{{O}}H^{� -.} �c!� � rbi6�"Y56B� .�E!��� h A:h�l�� "� e�B��>�. �6 shif�u gre�si�h�+�6cr}^9t�2�a2tf? ncar du�2 $H^kNs5qh !Rdim X-k}N1=�% �� \C$.'D�H� cupi�1�"�-�G�F�hQJ�t& ~6*Ais"�%2d C6O8��ch�1+!<� a quick �=�J!�-eji�a%�H&UA A=(*�SJLm�&details�<shR5(ult.�El��5wVit�� .}��rx e4bb{N}^* \cup\{� fty\`An $r$-M9 B!*��-t)a* * $(XG ,d,so6�6�  ( ipervU0ons) $t_k:X_k.*X86�"� �"R�0d_it_{k+1}&=&�bWEs]  $-1}d_{i-1}�&B� d_k"> "==� e� YiOs~krz +1}s z:Y�} K t^2 �sV�uend �50t_k^{r\,(k+1)! 1, \:yE'{if $ri�2$}F�Jus�,�&�-�Ea8rav�#�& 0 7�& Jf�Eth� �a6M85M (��@�CIS}if�it{MixK"PRxeaA m. .�b,B {� BO$�j��b=k)_{kebN}$��i&�QC $bF��� d�� $-^{BN.+�.�J/+1$� �4b^2=B^2=bB+Bb=^ >����#se�x�2fAr:-$B_�*,�2} (X)$qr2mb"����b\ �\ [X_3VHX_2:wwwB�X_"Q �Z'0B�>j��\ \>C\n�0}� �2�%5�*f�h���ݮ"�$HH��Ara:L $X=�mOdHA��&2x)lex��=b��0:1$(C�A�,b�'��r $H)�is � ����to�-H �#*�t�m, "N-k�Yn CLoo�6 l LK5,[clye�C��sh�  ex� +J�Z�� 0�*v .�)\oYj et{I�)�W(�g5aZ ,b+BIS�I [-2]M��Q� 0. W83%2U�s1/=�A�Wc�(KKi*�] read1&U5BF� HH_k(X�V2HC6&JHC��2Arq t�%zx �j )&*,U&�!"SBI� re�ks.�mA q.z?bi/M� *PZ� ��j $S$,BŻ)�5K=�\�M� \limM�E&� {k}}��[-2k],E26�"�x �� $HP_��e� � eiwb5i�$ly $\Z_2$- . Al�`v�2 #�oM#su�Um�>Jat{X}=\7_k� %l� e�& $B-bJ+I�M6� Zb .md,�4$ %6��>�&^ 4[A.3.2]{feitsy0W [3.1.)[���4b':=\sum_{i=0}� (-1)^id_i� b2&kJ"N2G� r-1} + {ik}� i)�A�fiH$B=(1+*kt_k)sN$�[check�aP6 triPG2� ��:"��e�Cex}�D$A uni�Lal[c:�n2 $\alpha$9HE)B� $A^\�Jal_ 3= ({ "� !�)$�X $ J(k}�A^am%b}�8thR�!B �&%�d_i(a_0\�m�� a_k�! "!  f2ian! DBQ-!��{)@$0j!.p!\\ %%J(�fs�a,&Q�!,��: ��~AW%c�W= rsJ � a� %f�i/1 :�".c��e6#"�*� �p $�( "  (AML ) ,b $��(ig(N<�: }5 6�$nB"X*s�sND��"�3 twhs!��): .q>)l�& �wk=r:4>s: k �:VO:0EO� �end*�I�W��~�2a 5��Iiut_kr%�YIu�N�E�W �2�KMu>L$r5�<�der�ՙ� W*)���6e�c]�,�aa>n"��in &�k c�� "�)�����Y �="�O:�/>(A),bI�:=A�.YM�,b,s n*�_~7Fr�:� ZgA}02�CZ6�����,B��C# ' $(���(lex. J�. ��bA�)�M���Ň�Y . A6!.c &T A�3i � 28:sAM"�J�cchog}"��)�!(��T|$bn,�a the =�A~M> ��JT+��"��%;:� `#B�M�"�f �7& C�c}"EF)���jp�y"� Xu9.&VF(} (a_1*a_2)p@�#Tg_1g_2=g} a_1(g_1)a_2(�,26i� $a_1,a_2<Tx.R�,�A in G*bu �% usddet=bt e�,�a behin!&!N"�+&we ne�H��Ri�\.~�(cy%��nMm!G6�.�R�EN6=U� .��~9qA &�?ihQS``:ia''b]�H"�!s.�me4�%>�8f]<A$AL6{ =#a2�'�� has Yxu:4(�_1,s^*\e�a4!:�$*$z dee<K7j�ribpr.[a_1 * Aa ]_g=&<m_A� \, I���()]}gA� big)23e M� 2 �2��9 ).��C$}Z� �::"J�:a�;�"$g$. Indeed�G�8P2Y GCf^�)�rec%Z NM\eqref{}A way.�)M�:��U�i��ve��piece�"�T, EHi]�Mq�o)"�c�W,��we��A now�medskip�tex�����~A��e@nB�A�F�#ontinuO[�C $uta:G_0.V!�~xvF $m<7"q $s(�% �?ndA!theta_x= yg$�*�DM?_1�*G R�E. Ia�$Da�{ ord}~ \)<�Z [x�V�,e s�8��"�.~ �K#Helliptic. Of course&yFO$CI%&u] � �x=u(x&� i(1am9�'�Z triv60I.�*w"2W��(g,S a�au'-DB�'�N*�d �2�A�e�d,�kc� dealUC� 8Bs�G~s.�\� ��%�")6+` ��!�to be a2R � ��X� $���W6��Y�!B���90sm $[t_k]_x:&�<X�x]�>���Pۑ!�-f_x$. As zKjq6`hxi%zH.f6� $|{X}�f�dA c$G�+a)r�U��%�*�%*2 �� �by��C X)E��P:� LKB� ',*�=X� We*�$,"� e6�, �jDe�-��-Ub�E�K*.F$���M���E��^� M�� X�B1~QH"�*r�&����-r-%�;19 Xb �# bb{H5��(G,9�*�/�!��8+3:\:~�j2��-L"� R�!)($��+B�-$$� .�.�a�:/D�~ s $bI$B� vo�+&'� ~N� "�q����1N9�X :�Pe�w� ��F M0E�m�}��X�0$c$� $,Y�A_a�u�-e�*�7��-T�Cfo�/D"g"�'0 "�c Eilr�--Zil�:�|;(�FbA@�a�6�BuD�%��th*�U"=$M�Qo�)"z diag4} o3(}&13.2.8]"9 .!)�UO��^��unB�� 6�L���J:u+d#mys�1,!�n.�a�m�u��,i*�^( (���X&^,):*� �NA!Oo8�-�9i!`�3.�4�� e5Q) ��1~mS�&.G: b�wisp.�Q: ��dD .� : ��s){�tack{�*�\\ ��":*}} `�_ EW� �/,=�_2)�)K���}1)6}1) ��|}}�b�0:i 0) .!02�.� �E,�TAy�'�`Z��K�t,MO�u. W���6�+"$vA�r�>U��> m#^#\2�"s�"e #1I?;& CNGSGRV"&j$N�1!3� "b_��.� by divi�0ou� &x F-CՔpb� sam*�2T �. �*$N�21_1/\ZpM�H $ne� g� ^n_{�S}g�n�GZ�n,��+��or1�9 -�transf���9 :=)�_!�T%y�92FC (G^GC(NG&{,DAny�Nf�a�/A�&�1Kh�} $\A"@h� *t b<r2-_~:Delta��\8 boxt�(;,m re $ /k>�(G_0)^k��!�A��e�2�[�~,}.A �+�Es��A4o�5u0�G nvex(�i� 1%, e.g.~y:%BV�N�Za�P{s A lT2ItD��ensorl ducti most�s�Q�prXA�2;Zv�Y�) S 1,/ 1]{grGo ndieck}, K)in ase%��4L� Ze�.f3 f3:f� �,(natural. To��umvi2s�3ubtle�+ born�9%�*�V-; � !uct�vuld� %-a�O&O�1� oin�#e� ^a�)5{meyerH �QQ� pull-backI 6�105= tw}}eti�2J�=!�mn�.�carA`*�zc"S&z;Ns���-J�s4UmvZ6 _B�}$ �#*�2� [a"�!"2[%N%]JVZ��a_i%_#eO8Yy (U_i)�!�e�f=cYY$UL>A�i)$�}2 �( 3.4�%,%�:��(�6�? ca�=� I��"Ebi�eEt2_^� +aɏ D�^�!^{(�"'5^M BE�A&*Y �*Fz�6$ $&q/ (�[ �}�)���&/�K. ,"[A !*�\ ,� �  D� ]wE�< )4�mP`e�N�1Vu�e�,/�k*� � .W V �a�$�=�&���-�.��#Rp� � < � ru/I���\AA�)h_c(M)&��9�C_c"N M >M�9N)$$ ��)aQ� s $Mg +We!A)�:!lo)89�ar.�M��2O&u*N k=�mG,s�`2��&myGM�c.3"���0 { }_��\h�;{1em}F�/2�c�HF5 ��2�G})�X2�2$s_k=s)c�* �s.$W ``rB�''R� he * A C6ionbEKto-  p:F� �-Y^{>�2T.���I fE-&���A�2_ X�TEQ �@a eeh(�ahJd s $(ZO\&� Q&� rm c} F�u(A �e*�U5Gb_���� �b2]"�xG 4.1.1���" aq2�!f�dmapSruc�w&�Jw v1.2h 6i y`"� c"e>}�Av[!��J���mTBk͂\� )�)U�"� , tur�t0b�v�2d�&� ��ijC"P,�]>��%cyc%�aC% *�N��V�� ` aAC�1 *���5%�2�a��yaO }K,�&4-f��J\MSHN&�*�exQ\}^JNC au (B"��- �.�IQ.� �&� �y�2.N��JV�.!�G5�9�A|Y�-�\� �!�&��L"�N"� )�(�) ?�7���� ��^6R� I$- >.��~m"�^.�z� t.8�R��I�Ic�_k��e Fp_k%��O���,{'*� ,2� ,5 }����*�f~iso)Gv�,-��T�((J5Y�"6) ���& =A&-(]�y� tw},9Z+ X1V  g_k g_0>)1�)E�=2(�3-aRhk�!�i�^�@�"3 �a_>� � �!�'�0BL @ �"�0 \< � a_�)7:8e: r�1By��q������� i�2S�F B; ut�($-�����-Q�4$.�a�1_!e���}fv�19�� �'N.=�z��� "� ,e��*�/n�� Lem� 1.5*� ^�́ymy0�����quasi-�cz "� _*P� &� �:u�X"�#Y*�-.^� $N�on .� %J�g 9�N --C�1>�(&8%��v�,bh (\Omega�b.,0)�M�|� !�!$- �*,7?e Rham2�6�finds� addi�5�&7\2� *�% �A "� �BH�.c}�j tJ��f,tilde X*\: M�2� ` it{L�z�=S><)1h 3h ,e�07 �*t�m[ 0�i�O�N��d.kN&;2�>�.R VF%C�bi�K�K*� V9( tj? �- G_{|U�O5"� ;Ff�(d &] V�f�u%V9~�?��6�W e .�v"�`�>M7V . *"(�z� a<�f&,fir%�����*���kf"5-*l�t�CfoWnIq�!ng�idempoteڗ $e1]\in (&*!=�). �vL���O���le�_&~�%�*V� rm&� �I2dS [��:r0K��:�Q~�R�6Quant�&!_4  ���Ac $ sec:U1-ncq} �~I�.L�!�����e#���b�+2�a pseudo"��~&��VA7�Lth{ r#�)�B4r�0F#$�7at�f: L.�v� n|J\� �8��!aa>~ ���.!T<2�!�(oon����ds Mst�,Ft1?A�n2��5v6�,�b r : � ]]����2�a�[.[\qR�<�;&�}�9 ^�9=�9k�EG!�%c^k c_kDm�.�:�QfU��&"�enumerat"� Eachew��5+ $c_k�]]\��]]\to� �T\�xY#-�H��._� *ve�c_0% ! )=%�i��7W:�e5B��3fI� dakdr2 -c_09? - �� c i2)` �� /)� ��)2�bho �tru�P�����a��Z^��-^�Oa5���R���a_� .�.% Fromon���>i4B>5F�0vl�Y� A� �@a4&k >[l$#9u j�ef�-gpd}�^(r�e&��)6K`e�51 2 V2!p�� .e��s�;a,w� .��5"#s4m5�8R��s��,One eas0�.I� he� � , noA���Hv|�3]ABR�� . NoRKR�  bi<�v!�e}ad �_��N9p:41�H � in^�� 2�2-c�qY^&>/IM;*�� E9iD\wideq(a� i��:�;�`y2 lA\�\Pi(g )( [da_�> ��2�>B"�Amb_,:L1����a�N� B��ez x!�ve2�-+At/+ to $g$ alo_���$�t"s�>� t&�it was��_x i2�N5�f.O:����$J�"__e���!�L"�5� n�RBa $2�e�V1 �*P 1ll;!is lnot ca� Zon��Q7[ "S?F a;e centpGm=.X� 5%�Ea"t"&c,sa�.H�i-�2�s,%� �a!ls=�"�S)N�| ��\� �9��6RC P2i FAc���M4$J`s<z&�R ��:%��lDIR . S /a�-!@bE)�T s:ݝ�W��:>k *<�17�^,a FW�o��;�.���� �S�'�d by��'�/ �T)�fe:�>-�&�.h�d%'��-/ , soA�"�E E,&: -�A�-��3L&�2.1C>:>P- GX-s�"drQ� \� :prda�-����o:��ZJB }� j͂Y6��:�E�$�r�$Տ3�co1) �.�  $� ��.F ��A.�hG�h ;_c$��/3���){�!�inv ,c}}( נ)R A~bJa�95C�&%IX%I��i`eduiJ� r.O�FV G)$;�t2o�23M% �z次�t��e�f= ��1�����{2C�! r"u�&-hceg}F Give��:�2X�"td�G�M �)WV�4b&V*K , .�z>#'�H UN+$ . R��ETA*���,�M�����d "'2%=)/m�e]�MEC ���*�\ u �AubXQCV9 *�;M � beta 4O�)F� 2s C^k�#&� :M�Hom_{(2� -66( r(:^n����7�k2�58(2� �u�sH�ard6[""Amap �m�k.�c)~�rebh�*�!  $��&�N.�)$�N� sKc&lH�(9k.$ between�+ 6�2lbG�����8N� ��M��� � Ea�though���%v�ly�2�al,1�M�Sf�~�$Baˠolh��^eE���M.�a�"���G$.{m� %<%B�� - � *�X?�5m2001�Xs<�)�d�96J�M9 ,��}=*. Later&2 tacB:� e���i��3i���1.�ZtC9��_iq�b4�!��P�&t�6�>zk4�5���B۩s2O*1.} � �� ³�wr� U t�Op �r ����G$��:=  2� ,.�+�l|py� " V��274i�] somek00&?K�w��� "�X�C��:� kxִ�"�v Fr\'echeAu�&  � inher��uR J�� ]��&�pKe-ٸ�@"� ��A�!�ge���w� +�v���3� t $U�b�- ㋎�U_1 ��� "�#' !f0preimage $U_1!e (\pi6 rc s)�. (U)~GM b�  t*�1�N�� l| ula��A�"�b��str�(�* a _2 )\, (g".Sh�r, h h� g}\�1 (h_1.a(h_22��u�x�q"0��y@a ��Y<)Y�>�;!. Now,J>�EA�act $K"�/�N{�o��1��Hva(� _K :A�2�([0,1]1 Sk��  $C(x[1*x�s(K) \�kt(KD6�8A_u�1N�T�� in �?Qe�$u�9$B else= heA5�� *������ , ɥ�iiD�  $\Phi�C^k�&p'In�Pd3map $\�9:66q �).�J/�k�] putt��q2� re|�.�\�h | K} = �(F8? � JLB{)_g�2�%� $K$ ru4 �Ie�Y�����$A�2�_immediat�a��=q well-"� �1��O�K�4�e easx���R�{� `{2�4$���$� mb� rk k%F!��"6(�c����mOWwe �/~Y���$U�/X&\1��&ma�<Ka U^ ^  (.�,ٷ>��E6�� �U_1:=ZM��TZU$" !�&�&� *h.by Eq.~(�@�,).t�S*� c&� 4��or�"w S2D.25# �Sd�RU�<6;E�!�m��heaf,�*�Jeu i*XQ�?�B�Q�v>$��*zh92b� �2l*�f��&� �d&@2.}�M �A�i;��y&for.,2K �!0J? 6� we 'Z m  �@�jju�Zx!_R&rho�KRN�ɐ� � >-$(-0frac 34]� 0sh��� a(r) =�A $r�b <12$�,$� >0.��b�fvaJ_ &$� l5sC�ב�$r�<p}�/� ns @ �\ Nextka�&��� $d��A�0 2�nd^2�c)[M�et%��9 $Jo)\{ -1 \C�&�/k+o��>0��24Asi_{k,i,1} #2W��Q�_Eb �g{j� iifEFT�H( d^2( s( g_j ) , tZ{j��)#�*�� ,M]$g�9:=�1$',>ispmN Mo坡�$\ �� ��ek+12az�.�h�W$c$ k sp.~2� $F$ ("\v��)eI"gy�)]2�c� C_k� :� :��^{k6NF�D M�w.8aZ���>�(H%&X".U s�3&(5?6�)!�0E$��k��AN�UU61Ec cZ!,�, �F~�  ) � �N:�FEyZ��e , -�-Da ~mM�r�y& "�2em}] �19!�G<``�5�(�3'B��4c}+M'-�B:� *� &� ���7�0�)Q��2 @ M�R" �9�i[���Bx.~qf� �c  uuw��� a3t�"G^�� ty ��,dv� wn�63 � $\etaFF:e�.� �n+1} $��� ��k�t% UA�6�:e�2U>lVU�B�� &V� (c) Q�a��]as a�B@�e�A�: |3#s% �u+1:�e~[*�7 Xj ca�a g-x��1a::�q�"�fi�� B�x$i<%�}e���+1B9Br� Y2��k} y3!�2� ��k�=.�e�-D b�� ��n�)�Fa (F) z��i�� % ) =!�z�>y6�I�{-1� -o�)Rv��"�v,_"v 2lQ�)%�.� ����{ $i�:�A�� , -u+���{F�.�46>U8k$}.\\�e"�zz5�}!$96qF�D>s�%f�cRr g��@  M� �Q1Z�^g = u(x..$"�aa�� 0y!��: V�.� �9� w��lengthyU stra. forw_�l"8�A�o:,ri _"D(o�q�F1� i�A�5i&�%�( �+1�\,eQ�>i, c��{�B� �H `�.�b "w � �k.�Ltj=0Y#A� :����WA R Q,&�I� W1��(� -1:[�!,jui Vji�^k1 < j&i }�&�!W�6}a, $i=2�kV� ��B�:��ʦ(�F�,i>\,zMB^n�0)j < i-F��Xk,i- NlN� , %��tG%�j=na:3Aʾ^:J-0AI i B`!��KR�i�JńQP� �#6qe]�BH2�%&}nq�J�5�.:� >J��YL' (QHFnc� J_>�V}j� "� �1M�RB^i f]0+1$}. \en� d{cases} \end{displaymath} From these commutation relations one immediately derives Eq.~(\ref{homotopy1}). Now let us consider the dual case. Let $\sigma^{k,j}:C^k \rightarrow C^{k+1}$, $j=0,\cdots, k+1$ be the face maps of the cosimplicial vector space $C^\bullet$, i.e., let \begin{di= \s�@ F (a_1\otimes \c� (a_{k+1}) = 8begin1k, a_1 * F D25ZDX, & \text{ if $j=0$},\\HF(dj,j}K~�), &� .R(1 < j < k+1.Zv� }) *�B�J.�AW^c( For $i=2, �,k$ and �E` thenAputes -H2� split}r(big( &\eta^!�H,i,\varepsilon} \,6�\, F)!�5� � a_k)], (g_0!�%� & = qY0}R) (\Psi)�:� K^{-1},- o,-)yA%f i-1}�delta_ua_i `'M�a_k )�� AQ&�@sum_{h\,h' = g_0}&�(h � FJf�S �h , - 1�� �2>��6�R�� �n�h'�� ,i-16@((h')�����:�E�U�-�A�i F�]�)�r�e8!�) .�-mre�2�Bym��((f this typeeߡ�0corresponding�Uin$ homology �=� obtains f�41$�m�2�  ��p( -+1,:�&! 58�I!���fTka@)=f\\ = & B� ~4QBR�� H�Y>��E�,->v!0�Y:<�� )F) ,� �32��&�Jz��,%t_{B�!`6-e�h�������� \leq��2E�ABs���U29MZՎ k$�_2(�a�a^aJ���M�V5-�AU �U25A�)a&�0)~Ii-2#FU�FNg_����f�:�����$}u;!z(�z��}8^{k>3a85ү=�i� e,�-� m1� �)ֈA�Q�N�\��!C:x2'k6:v�uN�3AMy'2o })k] }(:�Mz�~#>�:S b�+:.����� < �������� 6�UsI$\b�k�  (-1)^jye,j;n� 2�,entail Eq.~(2�2}) tketchproof} Denote by $C_k^*} $y subspace�@all Hochschild ch�0with support Hcomplement of $$ UX a} :=\{%���gU in G 8} \mid d^2 (s!�(),t(g_1)) +Q�+ Jk) , "0)))<m\}���^k_ �^�o �hav!�.� F�0\widetilde{U}�� �eT� .))< �\}.!0Moreover, let)�0$ � .~$!0$ beEunion-� F$4g$$, where $.0 runs throughEN\positive real numbers. THx pro #onM�"W corollary, ThE�)�xes�\b)�!�$C^ �(are acyclica�4In particular,{quotiA� maps&E 6� Ci 2�/"^0 \quad���} ��6K�K _0�" .� ��Dquasi-isomorphisms�=7� remark!FpOriginally, Brylinski--NistorA�e shownA�`\cite[Prop.~3.2]{bn} that�$9�$ is aF��nd used� result toerutI���"�  $HH5�(\A\r�G)$- �: \labelcommloc!I� ��U�G�A�dLie groupoid whose objects%�arrow�!�given��:pointse`P smooth manifold $M$,Mrecovers2$ well-kn!�localiz� scheme�Z4\`a la Teleman)�{t }.�Dfollowing, we willv(freely make!��* fact:R8 {\bf Step 3.}Xthird swa�$strict our"d�s!�!)o �L)p(a transform-9y$$\Gamma \l)�M$�a finit-�&$ act��on R{. Rec��E�t�� $G_1� gf,0=M/$every $\g �in 6wsu$A := \�cala�$infty (M)$AQ�2�a� S a (p�a( �� p),�Q*� -=a �A�p M$}-�.a� �Aent $a%M%�onvolu`4algebra $A \r) � $ haa�uniqu!� pres�9gE�m�equ}y�pelnalga�a!|� �� n } f_,� ,� _-2in A )�͸ :P$ �unc�@which satisfies f= -�,%��  p)$�0vanishes else�(. One easil�e�at!�nbDg prod!Af6_-C_1} * f�6 2} =0 �_1&CA�6,1 )j5.�q all!L1,f_2.h�� 61, !)�U�9�Concerna�!~topsia<tensor. duct�Led�?8should observe � ��i�T@ted inJ�6\E�{I�AI56<pro��Z=hat�)�(of!]4tinuous linear! ) a��7s:A"Pdi2� QN \phi) (Eb1:�f� c =:�*C����E�-�:N6'k F2�G� B\  f rVC �Y�� f�e * | � * f'=B;��mr� f).*� * 56(')4)X� �.�$holds true+a�e�phi�S� I� $f,١J_ lM�I s)F claim� n&�A[sequea of*�%����NCon�nowE�ve&0� $C^{n,m}_i AMHA�\C�k^m , : n},!B  ))&� n,m� \N$.�ac�$-i�az%c{:gNp!Zf�above�tVsimpl$structures���/�  co" !� . ����� �/^{+ ,  }$ .w!�a bico�.|��(�� $ Ee C^{m,n1�$):��alignA*\no d_�$v}^i: \: &:A 2i ^{m+1^!�z :I �mH_1, \l,m�_F\\ Y9M�� � -1��PsiQ2^Qk �ifS*02BJ�io {i+1�R�:�f1CiJm&;~q {m} P.�m�A��]) \\[2mm]��J� h}^j�� ,n+1Q!�:�I��m�Exjf_{n+1} G r�D����.�J�m�X V�|!�9Z2/!�hb�f_j� f_{j�Ş��&&�I<jI<n�<m�%>^n)��11h>nJr Qs.qs�*-V*.I��{m-6* 6*%{)�e�`J= I*1a�i�"I� E3NBi , e U :'!� ;Rj)�& .� rta���-N�1tI��{m}ajva{i #=)@&v 2�=�-R�}F (ylr� y>��� ���m prfju�.�y�by � 6�)�q�!�.:�M��x$.�$ (!�$)i �' vehal)0horizontal) fip^�j`,!$Q1$ ~ ~Ljy8 degeneracies. � L� Hg�� ]  it� easy�E4j "� �� m&2 +�*[ map, h � � "� � )j#� eed.�&exa��us�5� v}^0h}A utev� v (.� 0 FI�%)�\��rn�(�#r�.�20 =d�N2�vb �=��ɍ��� ^� �� #I&$& 6d)>,�� |����B���12[ �=}�N�������!��!�YE�"Ew�%� !�10^D $%�^Z%a )2�A.isv r6�>K'�Z  }$ab ucesR 2 N�� diagonal a�m� g8 \operatorname{. } (C "B�  }� (see�\[Sec.~8.5]{weibel}). Its6cs*�( by $ d^i =_{� hA�,.v}}� $ s.s^>.. . %� *�"�Cmap� Defin��"$\P�C^k (A6f^�an "��{F}y�)� �Az* k ,\�k,:s)-)�)N��~"� ��'Y�� � k)v�k)���gG!!Q)TesŶ��# k�"-�:�qNI2IB@ 6z2"�+ H6�O|7(6<k})S�P)D� -�heE{1em}}:2����righta�ZJ� ���%� b^� hiE�E 6��!b^10I�ѐQK� E�o 2s ���Bu* a�>6Yf� H�f }^� -��0 ��0$�p  {�f�n &�i�� � :�im�%-�:5z�1� �� 3'2$%�:�1}b{k>�k�1%�>$}Jan$I,e�.a�� i�"=1/ � i ~ͬ1���x1�'\ j!�d&�v}}. IOPhi-�1w*� h%km�(4�6a *:� By� imila!K4"i�J$ brv� �l otherɑ "��!ps. T ro;!����� Wedhavv# tool�!�6&R�#.�+.@`#�ULisohcoh} {\rm (}Cf.~.Z$84.1]{giaquinto}&)} 2�be 2�!�ngB!diffe&%} 2`#ov�&k� of�#f�G $M$.�R� $H�  (ABE $ carr. $a naturalB6 suchY1J&�-FeqhhisoA;.p\2�!, :5onga.6JY^+ M O �level!&�s,�#s *z&*dd!�!hY) �map"\d$� � *� 8J�, �5em9\rto! �(>6u�6O�6/Fi��eu�ٍ�6 %> B�"x"$��,$ d�+a�e>�A�f \� M$Gich"W lV�8%} unit�$un$� ndNt"<a�� Q�"�ByU Y� V�B��|>�:(6B Tot}'( >B ��:�M" +�=eA�a specta��f� E� = H^n.Q (.�&���A2 AmA��:P2O �1"� W \R&  H(n��6<uj~վ:>NowB\B� of a6�"�$in��re��$\geq 1$n��CM�$a�j�w��us�7C ����of ����.�".�!@n�} \�nH^2"��A�D0� � ,y:(AJ* big� 9�5 !C>;firstA;%gsecondiC dire�%*�! I,l�o"�B| argu�(lea�9� o*5"�:3"��* -�"+% , M,�%�(|!��!AXc}N�)�R-%A�nG81r&?1on\q�� exisK,/�@veDramA�canon 'Z�2���a@}=de{HH^k�^}\A{s,r,T}{e,t2M5B�:�)} `lQ\\SI B��j� (q,  6�I."_B) �6C�]B-S��� identific� $\check{��$!�A/i< - one +>#T,"c'� "�/����**2� �s|@Z_ J5 �r�=�� �"(._>�^{*.)k�>=B� I)��#�^).�>ty�<&"� `���\ni "� f /F < n/)�Z�EZ5�:�� 9�:M�A5���9|F�Z�ͤ% >�ֲf�e!�Dj :�f�at9�z/r��%�5`:�W7a� helpq�2�1��si*^ v&�Cn'(associa�,tompletD'�'4$-invariant meJ1 $d�z�E)E*an ap�SrK 3m2�4�.of y ? ��a�n��3n�2� o�}�("�4X6cJ�:X.=��� �) �Jx .2AMVzr�� Thu�e two.��(s� A LU �4 2��e left @ C: n.,Gprece� u.� < wy��>Y� toA6`=se4&&�3 4.} AccorE:� �,+!sufficI0co�e1 (Y�A�A�the) &' `@lex:�F$, if 634l�� �5D *04. TA�is end4 x ia5)O situ Efur� id ssum!at� )� ope�B�,neighborhood�oz7so�5�4dimensi) l/ �$-r6O3 $VoW:oose a09isca\O--1�-Ve7 orthonX5l�/ co%�an2$x&� ,x_n�=&�.# , x_{l�3}$ spa{ fixed��^D �$: 6�*y K$W$p�9 G�[ to $U.!-�1�U $M�4a�S6 $M �VN$� � %�b,n)Q! $AqCAA����ise�: ��!BA57$�6�� :� 0 \long��� 6}�,Lambda ^n V^�2\o�t{12}{:K} � �- �{k�{Z{��A�5u�mB� A}B60+2_��r �"1- :z� �.� ~2{k�DV^*]�R�>% f_1�.�-�! d��i�wedge"c  k%Dk � & �8 j=1}��A�$ Rj�82x-�Uq x_{i %2� � �0 1} �i_y@ hat{ (j} � �6, #k}.�� B� sus�hvidWdescripA a��_�� lex Z^..zBE_k7!��Ori a�Q$E^*_1$�"does not� out�5E9 �.��2,��k+n� �ly"Ved �-`ualS , ^X= (E_kA'A��� >ins�,!�f.� $\xi�� �,*� ~��6is�Tk sum ��&�(= A�8x7 �x)l�B!�(�&��� \) ,1�^*E!i> �&&�:F�:�=&'u !Q�� &�($A$-bimodul*=6:J�\A.strA�(�* au"2)�>� pE�a?\,��(p2\q&kC"�<�> , $a�7A� f�<%yAJ�<��>ils&�8lat< �(M� $��re 1>aV�"%2.:��M _k :MQ�(\L��� M)2~�_{A -� (K_k.�55au�)et�>%J�>is%qu�determin&�rec V� �kpT omeg�$\langle \DTI�^* "���\r&�N� .!�i<57e���N� Hereby, $� -, - l!�O���!ql\.� .�Z�A.�c"��B,berwise pairuC $2��*� �~��embed� $p�p�u%,\@,e�:^5eLde�+d by 52�/ ah,v1'=9�%� (28.),v1�$}2 q��$v%� T_pMPV�zC?� $AB�g n� .�>2�0�1sur #�~well.�$F�HS"�>2�mapU:GIJ^.+G")<�multiind��&_1<� < i�Rn�mefficsHs $A� "�& i_k}� I,INKaa�R: p7 dW ^< �D!q$ ������Q .��a�,�CB��Nta �:�@fb�N�%N� �:n}"�*�@/F$< �is YA.&\$\kappaEC!) � o�MaJf�defI%/ a' = � � p ,p�:)J = VB� 7� p)��jTi},W&x Unde�*Y-z&��52� �i3 � &DW6&!7� t -Q� -$. ToQ$�4� ��� B�|'�D} .�4>���m (A��#!,(��!�a �F(i_!�#Avlŝ�/^*�� .*:�� 9i_I�c�D hr>f3IYq-a���  �B%��� .F�/p>7( H�6��aKi�I"-%�U6� � !�8�Y�! dualk�a5( :��% , 6�-�#�^Bu4 �a�a m:�I�o�itA"mAbF�`�de1D% $V = �v#lus W$ �a 60� alternat��[.u�(�� s:fD�4t @!F6D1Ck ( TM ~�"A� bigo�_{p=0�,p (�)"�6Y�2 {k-p�+.�4�� {N}^* TN &A>�� J� {N}:6�N��f2��� N$ a� &�. ��V&7O��2�B�r*!�l;E�"�$mponents. i�nnterpreAu�UC!��SA|M�)!��totG6? the doublI�D^{p,q=&1p��(1qA�e&�6:�El(F $0$-.%dI$p�#��(.&JKLq4. SIF�Q)%�NivdI���fb  "O $n-�A��se2<���"@ 1Gv�U?c& R y#I q \R^{�}�gef�*�d"7)� F`� ��, �+�--a�)"BA�:A�A��$V����j 2>Mb&  {regseq���$;1� + 1} �:"�1���<n/n&� :��isR�i'-�Q (c"�.�917Seisenbud�&ItF�9� $q= Y$,�P� 6Ras%<q�T�R`, !g((closed) iddU�>U b�eF��~-s ), igf .-� Ru9)� &%s>7+��Z�$ �%�HconcludQ�t^�A�k"H��� �)IZ#z<AJ� >@1� m�{k-n +Q�} T$Fx)3$a standard64""�(A+Vr0<R�U�@re"�T)�|�nfLT2+�SQ��� Z�!�*0+j�16P)$ :�+�1bzS�( = V�$%�B�$,>)�"�rbe�6@a"69�f��B&3 B�.h'1@�M�IA�E�L��< E\;�+>� �( 'i9 & &� <�� > 4 2n Conj} (i)}UK EAQ�_\alphaVGmp�*q�! >S( $NJ ,y. \dim M + U 1 yF _ )^{Z�)}ZK'.�RL 6�ρ�se�" conjugacy�,s�of!4#F>c6�Nnec�� (  &� �$� \sub@)� Pcen�0 izer���O +� &� }.�W5.}Fm�$ons c]Oaga6S�@mma_ (per \'etale Y "c#� � !Iprevious�@ A&8m pD2"G6thAa6G�\�:��2J-ZK��< J�V *�y�G" value�%�2(is�w�� �^DY0k (��R ,N��aO�-OJSec} (Ga�a0:.4 �'�7\tiny�G:(� ", {k -\ell�O)} T��\c�F�A&su66taken ov�� or��$GeRQ "? �-CQ�Rab7&9�K��_ shea�8o�orbit�  $X$ e rQV �Z1.i����0L(U� t"s1�5$X$ (� 6 � zero�� Y-�].�!V5e�U)u��yO \capQ U_0�ܹڂ!�)qL6���UF` F`!.oj'�IX!{�Z�0:= (\pi \circ!Lta s#m(U�  O*X� T both6�e� math�]L��x=��)]�W�I,Nf: .�^XŐC.*�6�c�Q glob�I� a% o�ly.�*=%� 2 we wl,*}_�z.D� (X)�zgraded�7we�GiLab"bY� . S�)� � ��e� a"1� �m�D6 $\Xiq��1�5�2G�V-w�lo_A �Bea,�==!A��d; Ai,te[Chap.~6, (8, Thm.~9]{)ier�R,� *>��I�^%,��Xi%ua F�. Before%{i*t�*e��� )[� we need �,lMLb�9��A+$U�X#be a�� $U_0:�pi�aoAD�fU_1a� y�6�&eE.G_{|U_1} r- i���*�` A�l�5QC_{U_0}�RA�c-IPu�782 >U_0 .�#&��Zj�.K� \hook*�i�*A��-R�7)�.^?eqshmo���_y �@.l&/��F4ig&�6>"�/�"� hC-h (U�A��&�;��M] �lem�� N�h*f*u0�W.��Jc1�}0;!6� r�ABa�A!NiA%I2��*K_U��$n�U�$Vq:U$e4E�$k� N$ g2� �e�w6+�u k (V \Hom)? *� :�B��5h&�^�Z!mAF�V5��!V_1�N�V�� >�a�))k!`2bou/y��.b.I*als��a�uZ�f\.My�K�q}5�!��!cU$��8MU�E ves J{I7�i:sB��1If��� � �Cbr z6 {|�25�AI$e� �l Fn�J �C� �%To verif��t 2R2Q9�1=�6�a.�R�&�?KZ�he�every�$v %!�a�<���� �y���} nd c�1F lete�5� $d_X"/ a �"[ &�5u G�j(�Ni/ $d^2�sYh�.�1d(x,y) _?d_X (x),�(y))$�� $x,y@b%��AR1�+ $VOre"�<3&�6 >0$��߹�� (in� d(t(g�lh))6��bpi (t >.�l�&U �!�g�[V�*!V$h� G�0,setminus U_1 (�end6�M"$Bs�a��5%x: � ).~2� !fd,I�we&MGeK�i&_/__{6aq$ a4idisposal%�v8irx8���I�$N� \N�!he�#�$$\Theta_{V�9�$N}:y�^{ _Ua&}K$F(&O twe cut-off08I�&��-adotr dRs4A Dj��k)R7FE~5J�k����[ o,a_�t2 A� $g_0!�A�EBy�eR :\fm�Jy~,}�/N��� ,g"�& �q%4a_1�q � !�>k) =0 ee>if6��$:l�Ga�Ps� �$g.L in G6�&�%Y�ES�/&(-i@� m  aH5�%Y:, homtploc}ew,," �5��^o*7E$k<�d<�6�-� rary�9�!$B�Iall�E������O.� p�mJ�"� ,R�(![��o� $\tilde x%���aS7co�cti� 2O9p M E :}�u?Ab"�m>o".isotropy� w}�vrSE�}n"fL� }�A^U\io�mn :6 "�n�N" G� ��.:�&X$Morita� ival�%of�!DG2uOoUA/ edHB|U1,1}�v��} �._j ��.+,1�"��&!h}�-tl����J�$>�96s �2� ejB !ow 2�)�^*a:��4 h9� } ({.�}� 2� &z�U*�D"� ( 2=!�K"�YV���L 6\J<��Ek�lIga�!�i�B�^kBx�%�AX(9l.�*h%�6F))�&�8�.���%m��k�/&E�V���S &h�f]`�/�F (�_׆b�#k)_{|.&z%�5D:hi�� pu�2NrB�b��NV�D� },1Cmh:�mk_* (al �+ ai�"aVa1*5�,1}� (ge(Xif �6�iq)OH}$,�H 0,J else9c����2���"�.St�a��� �w�ulanguag� Hilsum-SkF"lis� {)i.e~biprZpal#'�on_w: u�d�0"�5 aEexpla�3�tx${mrcun}. ATb*x�1] "�� W 2��s%\�G>R$ZC�q�2�$-B�-biz:!X�4�5-�& � Mu2� u\ ��4.M�!\{ (gt�� c4.� }Ejs(A�p \_>�S \{ g;�0}#M6B"��& +�_{G4�N�2�6"�F.�(g' ,<:Tto g' g\.&:C>�.��W (��0#.�R��� �,!%r��?i�e( 45��Gl +3,�eI�26���u nvex2�t�*Ez� C�S�� (R�)&;QV��urMjQT���FZU_{x,0BZ&a#�2�$-^*A�j�.�2i�SA+arm:wFnd m�J� b&MCwo�(s� Now�d"�� �8��zFa�a�BE ecks!��-8� but^wked�"�u�C�h:�c1*loday})1�� �JiyG�  ���$?t��")�*� N!�W�lo�X�<E#.�"�!��&� $� U�� 6} $U_x*�ava� "� ��&x}Vt.�,!o::� 2� f� 3Z� � :� -.��d,��~aJ!JL*�}� Z�!�*&�� �� �yy0'6c�q9�=+�!�$�*lS�|:����.��2$&�>1YT.6!k3]�B�%]4顅,.}pr .+m,�*}4*?6� C�)�2� 1�*Z�DZ�*G"�*A0il�:I�. :!�p>���+>R��+�4�4�4n4^{Z� -� ��"�#�!���<�� �� 1]�4 J�*last uM:>F6in�Q�:�Yb��daverag�7�(o �>By��it9all���W*volved����&nB/ $x,y� U����ud�V���o��6G�� /��\nX5R��"gWVX !R>A2�y) d%m{s&�Wv7x)zekX:�f� ��(U_y).��e2��WI6 �7� !J6 �)�&�l#e�glu3�5 Cs�qs� I�r�%!MN&6x N��?AA"&ion�  &DQ@%��# � .E� s a �7 R�.�F�M�!US�� s 3.~r 4.~�4c�A8&�" %]=O� i�.�ёA R�5� #2N !�bm%|a nV�a�� . In��:Z calcula��is�U! n HY�ed�a#&�� Nq0&p0(�q{O^ sec:�-ncq}~��).%}S1?({ ��}�pI)�byi:p)�}*#� Red� 1� �T&xf(M,\Pi9% 0f� $ $b_\Pi :�FM�(P)\to  "� -1}(P3��� X! �)%"�c� r (f_0AdjI& :dŅtC�"uNd��D\�/_2�N0{j-1}d\{ f_0,�|�,41 M L �wid�N {df}_j{OBt� ^& *�um _{i<�4qO{i+}�\{f_i � o �.X 6�i�2&6$j6Ukm�-X�9�m4��a�MFFranalog�_is QOQ5. Lik�YE;UetWstartbS $[\Pi]L HHg� A,A)�&a�q�$�Knd<+itoA� $.c�A)�#>2�Ar" RnUF&�,a���{L#Iy�ω�m�a �;62$(�|�6 �#s&Q�j��$dfn:L-��tW��2atvae�� C^k(r:! O�) $d_{ %�r_{n}(Ae� -Kq!>uI 2- q"0n� n):=�"� s.># M��&q�i=0�  ~>�i:(k-1)} a� U#i �N�mmO 5�m�S  % $n�8+e� +�J(_{i=2} ^{k} �(!.$i)(k-i+1)} �(a�|k+iQBo� ��&"J�.*i-26�NNt-1�e�-` 2] \K�y}"�d�4�� rop:I�} /X$"��U],\ \psie�C^lUr���2�C�{K}>A�psi}--Y!�(l!�(8=d_{[B&Xsi]R@�����We @niLTpe\ n�j��$. ��(1>�h>�(a�P,) =$ {\small�28m:array}{cvF=6=a8l+1M�i=EhieZ�b0U`6�!�aB\M�e2B�sA�2"lr�  Qj)�;+!&1���:e�iQ^l -�n-laOliO&~.%5( 2�IZ� �N�Ǚ (i-ji �&"�7ter6@wnumerate(\item[(a)] o81g&>�� (-B�.:$�W  !� 3 or!k$)�)t 3I� fnhi�Zn�b6�2v� |2�B�A� \: $��%I ]VQ �52��!�z-,!�y app�in�<�F+ c%�Fv�J!v'sigQ'$��&�$"Nr�B �get� cell� Aum(�b�A� l4�fi- 2}Z !��= )u_i8si�whilei��s�h v��9� �B� �<TheO�e�e!��`.tL stra�0 forw�P�Ehecn=!bir%���matchntho�f|23EWT�+�D��8�G%�"p�G�� (hi}�9"�A�]}.$$� ��cEr�1x��:QB�07spep]�a"M�y�of Nest / Tsyg"g�nt99}�a��*�3 ���� �(gTM �2/@RataCӡrefF�one}� $L_{.g }$-m�+�"ur�Qh�a�i�entqW�G)".("�&�,� (ta, [\ ,\ ]�3��Aa=Bpb*a" ~?�su�M6v"�vo p� 1� ��usseuQ{�%���%�3)$2$-co!�e $m$ <���+�[pl�y� $ $m(*�4a_2)=a_1a_2$. imeN�}b$d_m$��Y( 2�>"o�!% , so w�� simply wr�$bP steazr _. �?ak5$l=m�#O"�.� b� Pi}+�P�b�m, ��\���i)}=0M2R���s Pi}$�len�`cE�� &8map.�HH_"+(1�.B`5[Xu �D � ]�S�L(�<�A ��>Zr�#H��5 is5#a!S=���2s&�#AP Pi}:&! (A) �#F �I$sa �P50��!Y��q].DH"�!�&3%""$�pa�9*the5�5M �`f.�[&:4/��i cmpa�?w}e~�*6�"�Bp�Y�"�V *'�r�w�'12��b/c��$���="�(^�!�"�WAactly���ed hG*�E6�2CZ�5� d�4�� � "0$F�+"�%2��"�+4+ HH_k*�*ԃt�M�a+Osg5) ^k(M&��w,��\�� _k"�+�+2� !V&-;��uN��+@ %U�>� BM),"��+� 2'$�e{Uo'sU#.�, $�_k 3!�antisymoz� U�a": %�U$S�l<$k$-per��on�4)R� (:'U&20' &�& k ):� �\s��� S�v61sg� $)�'f&*!_ _ @"=(d#?2 2)^G *k)}NFh7m )�5h*m/�:byY�s2�$p >�(�f&[w�� ��1%f_0�()J)m(d��#2O�D9�$a-<��kBGBnbD"�7 �8� 2�   $>�at\'T.8 �8��"sdsm.%9�֭�%d�a݈��]6rb[P2 See"� 3.1.1��:2+"� rg)$ K Fy9�;!&m�IeVno b�� stud#1o��2metho�hf>Ugeoa�y.7 a{�.��8 --}$ ,briefly look\Km(E�1c�]B0.tK�Պto�J�,~"�F qu� s�H work�p6gѱ (co)-� y un�m (weak)�eq"�Es5�?�s.�d{xu�:7� aDw$0ll Q0il��ic �|B�f z ��ein>���. �d6.e� > tysMU�c *�=A�&r;h; 1.2.4,7E�1.5.6)v\A�:m#G-#-} AB�c)�mm��.Cb�=(uts"9+$B[�Qj�}�;j�Z1C"vWend�" �m[�F=(*�Y$H�*�+ =�j�h$ $Ext_{A^eB�*e+a�u # m�} �mf}rAfy/&Wm!�of>�M U�,@ 6\~� F�1%�+iV�6�Con���B -2�"^"��}-. �c"� &�I dex{�$}/aN�� d^A_{&%8l,<>}R >9d8*$�2A2� :*SE ,8*vB;@ d^B�>l�B� �O!ramj6 , �� ��Dse9�9� �$.�E�6A\!�A�M� say���W� �o�9 C�� C is gQ�pSK�:�G/��lo�B(�!7)����out9��]&, 4) `2w� B=M_�0$,L$n\�/ n$ matrix���$3��.g2 $M_n ,]��4)1L�2��S-�_k:�k(j1Alk}( Yg�&� ��E_{11}^a�Va!�e���-�$(1,1)$ 5¥ 0$ e��)V�IO_kv�.�T� E^{a_0}�� 1 � :� $k $J�uy "�iz�r~� hw.�qtr}-K->�![�2��6q6w tr}(}x ka &q �Ly� ��:=8_0)_{i_0�� ) _11i.!�taε , - Mi_ki_0� 2�� �� ]x.C�'�[:�itr�Q��6|.���sm�= ك�y,EOqa@ir �n&� gj���O&� .�:�>4�?,&Q*ˮ�� a�'dra��ADo"�E� �C�IK$, ���ulaVV/Jlde _�WI+,I3b �8�%\)l�!( #L+l}0_{lO���,)_{ijRO�=��A%�:�!�&�.����"H�� B7J^t�f each,��claime�dd,3Wo ���%� =Bd��B'`L)g �. "$y-��ob�k;T��I Q�Œ&� �To � �aޒcz�Z tvgeƱl��G� � *i top� � e�=ah�x=b& �~�=�6� `%� �� !�F7)X .Fy1 \j� : E\*�GX"z  \pm 1�� $d�/ �"eiP!�deٟ $�or $-1�Z�JF)�O��edA�almos�}lex��e�9���s@ld "��sw $h :���-Oh@�-n,+1}$):Z�b^2=0��db+bd^2=bh+hbm�2z % AnB�VgiQ !�-�lHQW^b�k!� dB� .* by:~� wh�&7OB7�, d�o qb�� } IfT�#�x a�$"�by a 2��# �H ��a�.�A�B�a*)� Utre�$(.u#m��aI� �6�-��%�e]�!�MP��fr�MtlyOs�nexô�.�B)M\E�v lem:�C�� �k.A@>\9m \i�>�$(X^iQk,�,>� � $i=1,2��FNE*w H si��t!bN1.N1�E� 2b^2AP g"c"�F�$d���$��)� �Y�.� ���z~i�u�a� d^1  ��"ɤ�.T &(H^{b^�xN(X^1)!'1�n-] %2}� (X^2%�e81�)�C �Fe��o&)a�� eh-)�%2�X%-�AV=.�p1X!.;s)jM� � ��O sursune�"fornH�$�  ��5<�+���o-j.f?)>��[�",�B�G5i�55a�� `` � upa.!�''} $d^1A =A)$+b^1H+Hb^2�r�u $H:XY�2_Y���v!c�wJ!u��#y o*� &``reduca��loops''5Z \eq*%to#} e!mh2+w�4r #Nu AWi)is kind:*g""����1�!'D��!z����o�ire�we!Qp  g ,prepap+'� k(ready!)6�� �) �I$N��e�.] vTa�G�Our��ategy� h�ch|�I|.0 e varnV step�!�)�a!�. 2��.�&�K* ���#�Ir"TBaz�0wM�&~`.B^\+��, bL ��z�m  �~s2� sv�x_c( �; s^*�\"� ^{\boxY(k�3�aU-6�ksm��-c2e�+ $��$Y2�V �D0Pi��\:�b�{�E^k�0i} {d�� Pi}}H 0U`}�6&�lqK,,;['�/�swT[F�=""\P�8C��>k2�5 .�,�� �C_0\ ��6u4a�eqCe=[-�*n�h�rNla�>w&��.o��yA-&��I��H����"� R�� 1:�lcyhomcyc U}�*�6��m_nfty$- s.Q��I�v��E.yEE  (\�R G,\t�p,}ϕg ktw�� "c,Y5!"i�talk ͥ�n���nin Ar0).jp"Eqr�is icvs��[3�{hI�RA>N&�5�a^�2. D�)tw�l� 9W9${*,-^},R@� ,��� �anP*�qB'Utp��1h��� +%Y�o�/pTf1�_k$VA��� ��e��)_i���( [f�@a_k]_{�@ �� � =\\�e~ xjK [\� � 1\}g�,+a_2. �9 <ܛg_1 ��� g_0, gv�) �,&6 � $i=0&�h�`:o �&� \b3b=��ig %c�C$k )},Di ���" 'i _[\{c%40�j ��+)/0w}�5"�-6&k$,� ��-� MA 2Ye  $\{\ iO&6q�&&���b.����&�+l9�i�iP�Y"e"�s&xŶղbyn�4u�G mٽ6 �7?]. , ��qmef)$ "F8 &�4��\*1&Ia�W"�T!@1e; $H^��F�)���i@85:�42Y�n�_"��" F�1eNw5B ), b������MPe�+��)�i�fl��%��E|�0 ty���o26� �)*s 5\&�,{bn,crainic}&=eU%FU thm: �tSYq��H=� cup_&t^z�� O���d2e�!� `$�o�-o�>m&2��� Boo]�� �&p'r��c.&�2���5m2 " Inؤ<o��}.x a. ��I< *a�$q����� � F;671���*&� �w#� 0y}�i_N� $N�~��Uta:�is�[a�ai>� �&t�H.Sfp})&W50��15n�sy�ct�*tr��).VX 2��h-��""~Y?$E�ܱ�e��֡h"u72!� !�� B>�6,:�-}� 6F b6]%&21�2.0 ��_N}Q"N15�%��>srfB��&���j 6�sM��+� }���_N�k!�olFy. V�&B�NG_{|9�w g!:�=�� %1 on .� NG,����By� oO�o�B��"�3r� �"q�� R{)z2URy 6B:M#�7 BC(( F�)!I!F"�O�8_2�, 0)�Pi*�}�heM$FPJ�Z+i*��6��A�}��*[%�6� 2�� ��� >P (NG6k � ���c poi-��L+�r w$t"��ha^�A�# 6�<�>8 B{/�A(u�,(NG)_{\mathc\al O}. \end{displaymath} �etheorem} \begin{proof} The second equality in the claim has been shown above, so it remains to prove 7tfirst one. To this end recall )�twisted Hochschild--Kostant--Rosenberg Th�� \cite[Lem.~3.1.5]{crainic} which entails that aTnatural restriction of| germ ,a smooth fun "to $\!:c!R�$ induces a quasi-isomorphism $\rho : (\2A_{> }^{\ �l}, b_\text{tw})\rightarrow (>$C^{\infty}2G).HHb)$. Below, we will%� �via �p$ one can pushforward $d_\Pi^�$ !��a Poisson differential $d'_{\Pi_N}$ on $HH_\bullet(NG,��)$, )�8then calculates�homology!�!�convolu%� algebra 9�TA \rtimes G$. MoreoverJ 2�A� qual%�dr� ��)$A�A�%�prqeO. Note)��problem%�aj to c� here�%facA�at due#exa>Hnce of normal direE�s,Qdoes notM�=�$map from $�A ( Y�(),\Pi)$ to %Z�=) 9_NA� Let u�w!�struct6[8in detail. For �',$a\in \GammaQs At �C^i-b,8)$ with $b(a)=0yfind aA�xNh$\Lambda G,9 b�)$ e)q,(x)=a$ and $}�(x)_{|9Y}=0A( We define6](6 )$ vanishwn6f(as well, hE�onea �a>�>Y!�qw impl�a%�e� ity:�2# b(=f (a))=b(%i>|!e))%�2�:�$(x))) =-F( : 2<,=0,�2�w� �>�w!$ve used%�I�$ commu�ZI� b$, A� Gthird%bJA:�A�ti-QM�1�\rm tw}I7i) M7�$Esn ./o ����EJ��choose f�ny $[a]a�6y (\�?�-P)$ a representative V\ NGXmat��Z�.�)$ such)zt)�s $�R�R, satisfyingiNY-~�O Thus%Hobtain� :� N�=-:�>�= 0�S Ha�,��co�� ion, k�� \circ.�� AB�Bi /��(�tw} (h"+ h>�,q� &)�iE$hE��e,topy associa� � (d& })^2$. ��shows tሽ2>��fi�Y6�.��� �7(iaQTo���a.x̡3�Bd%�ne� o�E� our "i!�a�(independent��!choic��f�y�,$x$. W_  us��e�Plemmas�N} \label:��t} $ya�>��l ,u}fl ���\rho(y�� �B�!�e�wre5 s�$z �� ��$y=:�(z!�� 1"~ lem� �B5Ji %�� � , $y! 5 b� boundaryE� $�j�Q T��fore,A)� a�$z�@)@��?)1 By�I���nZ cludM at �? $x, vw�� ��!��py^� Utw}&0$ � � s $zX� :� u ��, ݃$x-y=�+�z) ir)�R M�split} �:�& �B y))+^6-y))\\ V;:VoqK!Cz)�D�D� .wB���-5 (S} 2�1]B��V����� clas>� �F��6�A\ lif��$a!�� it��also 69r: y ( :�� �eՓ.propos��.QP��� tran %���H�� �! R� �.�:h� -� ���i�n� b�(�� �@�we&B  a partir)�$x�!&S:/s)s�`�.�R�To achieo is, ����$s embeddedA.($G ^{(k+1)}r�$ bundle be�!�seE��nontrivi.�onI�G$ %(TG[C&�O}$. � Htubular neighborhoo e�, o�&�$x"� �c}^X({$��9� pull backK m<aV�of*� O$. M $b�Q0%�SN�, >� ��6X2G0m,(a����� .� :�I(.u=��_N/$��"��L  \ref2���&�.is � -= e� >t�t �  M�*� $ acts on�c$RRN A.�vesA!. In o word��%��9 U�] $. Altoge�� isa�!���" &:remark} >��� ion}� ri���an���� >�NG���, b, U�S!��?�e��I�� localized��>e *�*e2k�C1% % \s�{*�A�cyclicB�quant��"E cyhom}TIA�is!^!L��compu�o�zy/a! 1 maV � -#R~on��rC` \'etale Lie groupoid $G$Y���a sympl!0c orbifold $X�$y $\omega$�den!e.3for$ $G_0$� b8��A��"� �-sheaf�sm2�a� L.� @% 2is!�ed�explai�� in S�on��4sec:intr-ncq}.�� a�4invariant staraad \$ %���*(A[[\hbar]]$��Pl power series. NoticA�at!Eaiassumewout loO genera ��.,is a Fedosov6� 6.��9� conn)!^ is g��riE�G1�&WA^�=*�� ,%'��F �4ed global cros pr)\mS $\ \&,!��Eq.~\eq�� >prd}.e�ubq�Periodic>�a�g:��AZ3i&�J� �s aDce �Q`` ical''.rL">s .�q�q�s�T {bn,"KbA.� rigidity!V5y 6 getzler}, @[Thm.~A2.2]{nt}: "@ M�)�ie.d $-�:=(9�5�ofAi5�A$,��A�s&�� HP_\� X)\cong2)\o5\CUb�*! 6 easily�ds! ��� �� pch}-B�5�%y%�� �.�ree+n by:$ .�B5)' \A� _k H^{2k+ ��o\tiny$orb,c}}(X,�). k� 2�A simiW F of (-�ic) $K$-b y wasA*v Iar� }. R S A�Chern--C�5hs character maps $K^{\mbox �A}}5�\A5?� $=�2e two�]<s !}a�atibl�t���.�>Co^z1�Z"z�is mom�ved�Ie ma�oole�!>���8are: \\[1mm] 1)��``ekum�4.@spect! sequ�T uced�$��$-a�� filtri���_%�i�{br!� \\ 2w.l.�of>DF�of M=.�usN�languagf �2v�>�exactly�U:stei� thes�5�s:�=�"`` ''!<aff co1�6�� !EWai�oi� t�D 1Z=Tto re!+ outcom�", w.  e&��o ,occasionally` k N �field~C((%�o l� put ��{}:=�r�0_\C\C�^{-1}]mYn�.��:B&asf{Sh} (a�a�. c��, n.�!8M Z��No�_"C ,O �-�$\beta^*c ZsbN� ure�  $"�Lf$descends!�$N cf.~^Prop.~�fp} b�#" �em�3qh"�$}#!����eruL.Z "Qa.V U*$X$a>dimenA  $2n$�AI��{U�� &Q N� :��{�� ���&di*�& .�\A.cF) �-^{2n-~�\left��U�U%)��2���9���ConsiderE;�}� on A�!_\-�&�"lex!`Rs �N� 6non}���}$ $(A,[\Pi])� sens� D\"�� dfn:�-6V-p�%(}. Clearly, (degree zeroe� A�%���F�$A|aaQa�&�& .S& 2}&8 $d^1:E^1_{p,q})�1'  -1,q2Q})�6�52>]':A�{p+q}(AM> bHH-1ePFMef:98�ur case,�"� �E*�&, $A="�"�$c�� %lZN),q} =��mB\ON^�_{*  inv,  NG). i2'�Alas1&X ��s&� =�� � C .� h��� oiE@clso i�higher�� /s�&�k& �l�buseP\$:'F� (argument. U"E proj� $\pi:G.eX.&j�])� i<iff$8_! ���]� �f�������s")}e, see-Npflaum}� ڡ�? &�1��'�d!� AsB�͛ncph},�2ao��notl!^, Brylinski'sVJ vm R}��� "W*�%Q�M�ei!" beca"@ �+dB i d . Of coura��i�h e im5 �)�ver�(of .�A桼�(iR-�_{NG},�@�u$e��a[$, un�QX,orL�B�c}�Y�fa�)`�&],�� �F�,betwe��/���� de Rham,� l)`- {byi��:R(>�\at1� '_ ^{\dim ��!5&� dRh}�(X$b we"�-_ a�K� mpon*�"i:j U$��/s may�(U�& s, aff�ng%��shN !2*)"r=�6%� |!R�-a �Nv���� E^2��= p-q:�.�" %Oa� ��A� mani{'&�,�~F� de��K(a�lAVtage. W� NG$� �$ite numbers9�I� ��A�!W sameA| of��<I�N��,�6�!U)5JA�_{*� }HH_i�  &� �(veerq�$(b,B)${*��bqlumnsQ}D\tilde{X}$ however�.�, infiE�m��.JsI+use�deE�� A��&J�}a���6B��-s}Qa/:-�*("e�0��oplus�Rv2 %�is:�b�fd)�e��6���j 1� , cfEUP thm:'ty}*SQU above=6Rnq termO R multi��% operator<* �� >�� eser�-� o .^s��a Q�a,W>]1 �",2I� �#�1toov�!��� �b�4are �.(b, each $�Z:} .~B:��n! %� ���, ap@/da�ke�zseparate�2a8�e F����Eej6�Cn ��Z6r% a �*exAa[M� resu)OhW�'Q�"�s,�i�"� e��( correspond��analogu�} S �[�Ymu1M��U�� 6Y -X1H�&�C6�� NextV procT,A uS:�A�!1ous��� 16e�) bn} A� &6We �>a4 ed !�ysiDsn�7� W!} spac%�0loops $B^{(0)] Co�� m&�7�:.� G. ."�� Ay*A�Zum�f!��s:mS�4%[geA�$ $\theta$--T�f��\� ( �()"�%� *%�0$. Again, itsamlk$ $g�+12K �! ъ_g�~h�� _g}$�~%�[3.4.1.*�9!� SelchoAp%�s�a" fp<i>� � car� a9�&tu�a=$�_%� := )�,e>�.<I!{"W C$� 9.!�)�ofW � �&nYw,,� !n"e9 Y�EheQ��� )4� ^!& \phi_0 :&�% � \*R: �A=( ,T~*R�1F�1q�h9h* A.s$�d.�.�$ inherA�.Z ]C 1�$. *�94!2f2��yA���u�s&� c��a ��""e�i #w $coefficien4&� Y�2� �Qq�}��]}���� xaA�� �es�4i� state���� f%�<�!1��Aka �+lEQ�#G=�\l M~8;as$�� �. �#apv ���� �� !�w =\co�{\g�9\in y}M^ � As �k�U5]{fe:g-�,x� .�)�=�!� al �*��$p\hook};M$6Q$ ��$ j�Z�Yy!�MA��W�u"  ^!!m$Y�,.\ �:6� �<v+E��ecM �*�+ing. �!!.�5~�g$^�$0Riemannian me\?� � .�36l!dia }?$[f]_g!*�#�r)_g$.U$s�tQE$� an open6�+�4g�eH$f%s!j�%�put $M_g�s(U_g��T�M_g0a sub,Ux&�mm��:?_g: T�.NR�� Z,$T"|6+I�geodesic�%�hB! 6nF�.E 3� -� (%k=%� e5�a[ rc sE� \pi_g]%��4�6X�(Fb\ B") �}/M�� sl�&ej�!oc�Jr thu�)��"� i"��|�B�R �0%�� erseCJ-CM*�*!!�m (map $f\�"to f|_{��}$jd�"f--Nisto�@\%"�(:fBon J .� r-5.2.]a ,�is pit{not}��. AG 2�, \:�Jc _k,b. (&Z��& b_r4�#tw}|?�N�6� �GdJ Do lexv "0 �1�"� wV)to;1��5� to a*#'' �:�g)��}�6�#B 65.s� suitabl����o2U��(M2���&�a�Ae"�$ist�(l4y [)]�H\frac{[�0]}{�,} + H^2(G_0, bb{C} [�!]]�7�.�*� 1cal�)� 3"}cFw)@>}�[ N�be����! ��D* �$"�e�2� j7>|+R�* N ��>�����R�� -� 2]= c$_'D"�, �/�ng��or�*e !�a�DBB�CQB �,�wAM% y|�)5.4�&�ord�}�A`co��AoB@%� >2z V{ � �>L� �anAext�<{au��!!�� 5&�[  = {k=0�3_k e ^k :3 =�)Y�� )Adw: %�'kE�a linearR�%�>F$��M�4 ��=!��"t=6P c7�ccycisoN���!�uc�N� %E*:B� )/&F2b2�%�>+��*tw} $�!N+E�L�E��A�$$ h� | .� t|6wt�Fure&2� >� �>uYrt�k�� lex*N#!E(9U a�(K).L�.&�A Qs&{*�!j(�*�$�E#� ��o'*"8at level $E^1$,�Re 4)M"D , it muI"nA?>N � RofN�� nW!�0 � 2�*!v aris ]< �'A�" (12]{weibel} 0M1m, sG�5#of mix��o�eq �� 1�[ e-.@&]"i�):�2%7 (��2.5.15��loday\�e"/ "� �``r�GC ;''E�/ "/"1 ed(} p:&�&�"�_k\Ea�L �_c#����,%��<ul@ Ba�$EEvuI\��m�5�A>!p-���fa}"�T �*�3w#!i�5dt%Dv�RB��5b�]��H �":]' narray*} *�I!�*W,U()&A"&F4��,!��>Obi.�� �:,\\ HC70>Cz�:4:��2>N~��ce91q�1�>s�w@�v=��P.*H$J�f �1E�B-,E�>� �ae/����QA��;E�� ��BBS6����8>*�%9�O8 N k!��is read�3�utEG�26%��-,an� ��Q#.�(aaS ����X.�-. I��& ho�Ga�a$eE&�)in�Xa��!�":Aj�yɚp$9 � ���:9  F S Sn9�sm��=�1�. H�!,%/ a"�B��)X�_Z�i!�g�>y ��v!~A=mc��Hav�"�` h�"�1��DAI;:&l),%"2Pd�I2e s�)6orF� � tbtakzi�4���4A`���)�*� <1cletenes�%X+ <;o�_�N���d��J } O�zr�! \`J�;&.�Y �6�0 �r&eF��!f&): e�Vd2e0�sp�F �(` {C}��:�),b�� \�)� {\C}"R' [2n]�AP��"name{TotW*�B_{)*, �>y),b+B|��6�#{kW�bb{N}}f�+2k]. �@� 2!�o�$>_ �V-�obvioua�clu+%�A�>i-�XS! JLa��If*D .bDs!��-r�Ue��%�Ln369�.�.�>!stalk-wu<.�m$equivalent�"��q��vN6�2��e�� �>��*��F �"yl��bb{W}.>_n�al Laur�*�=�_1 C^n$�<s.�*� �!Q�Bas�>�(n$ N3�;)!���#�.t"�'"�$ b� �{!3&�'�(b�'��6�Q�Y ka*( JJeI ) & ; ?�se� \&-+, & {�$k=2n$�<\a� 0  else}�eI N�8 W kr��Z�+2l$}�� 0:� �i�-+2K�PeE� i%onT>�1a�OJ�6R-Y�%![�&b�@�l�6N!A�*��$ lik=��Al>��VC6e�I�;W �%���:�"� q)] ��\geq 0}H�"�[�J=� �+^{2�~"�.6�62W=5&-6��j ��s+ fpA��@� !/ +D.�,�@�"( Ae hyper�5o6!qtotKA��!o��� �=' >�" ��.��bD �.fr]��&�_0�#!prece�.'�n*\F�^6�:�&"r �& �� PzR,$d0\� V0be� F"j �T �k*�&>�>*� .WK)- !""3ur�K03�I , b'A88n�-� !?E(A6> A�"&; �t6x3BizF _��+"�+ to��&�4� �X �R�3 d'0%B�328�4,dF)a�Abr"|,%Fmcollapj/-�g ,���M՝ 3Fbpb�?" �F�V��*&� ��!p]��L '* a� v�$*G �N��2R �r�1/>� W)&�9 /�e%��korb}} :T,\\7C�g+ :��^� -2k:�2}:|�` �F^Furym+V pair��6�j%���2�u0ncar\'{em� r!i".5�"$.�UO��a�.pi2d� *rib�I�0� .� I�!e��GZ<�Eq.~(�"r)"��H"d�V�(*� ..-'�)� ~b�_�!^kB`�$(~)'&+! .����&�J" ��di�eb�csak'$56&) t�4P)9A�A')�(_c)' (*�G�an��4U:�ofR�W"�s7.s 8o�K4"4@("� ce $\*�$R�&� -� ,%3 Vc�=�$.hj)GD�R]s%K &-��Nop}}$-"��i3�ty re�e:uE�/� 6|>� ,Fr >�q5:}��*gd2� A��j"� $. D�hz�dz��*j6V�a�/V��G) gnz0,-a�`}$�C/�B��))'uqN8u �"Aͨ=�Oi u�1� 6@A'� !I13- F��I�B�,5 }�ig(0]�.�$Q�� Ji�iF(�i8,�,>"FE *7�  EB ��2"�'I8I!J�!h-�:� �W.���) K(act supportk=j���)�QaN� #2;)�"aKM"#$[zro$$ TakAc�R�� Ay�Oy�� � eM�\��6� Exais� � m�QJS I �',!��!|5K.��65�X� DZeD"`UlC �a�$so-m [E'��s, i.e.�*e $G= \�/ �����/a2�ba �_2�/discret _&`n�"!> $Mlm!��/�$�d"� a\sug���ot%1 $X=M/��nVn7+aS� nl�ݥ�M$ lea!by�%�oEi��) Z�6QEС�2aE =A_c� �� $A_c*�E_c^ ZM�Aal/y� �a14AxuI"a� �:%2� �L2P7d`Jt&��s4ta:�\, a> �`#-C.`2aSH_c��� '-��O#� �ZMh'D61!� t�;S���68. UA�u�T1G�%�se\��I!P!Os:"�]m�"< ex: � } (F�H�2) .Uitn�2f�1&��r $�$�f<>%�.$�V�#gUe�ip. T]& i[� U 0)}=M�F�$, � $"�>=X$��!.�=J1�*���A6�VI�*oO�5��Leray%�s%&q&6p+5!mf9�0i:B� \to �! sey; poi�f�thrs�E�2 q�c� $F/�1�*��2  �*�? A� rm c�*|$G)�)pI� easy�check)�+&i 8u�.>~\6��6 mappIb!`�3nF�Q�a� !��PP +`9�+&�Hd��VG.E�2)�2r YiSٰ�Nn ,>��Z$6M�M<�9; .C2��b";B$  �38n f� "�5V��9<&_ �&"@&�� 0by&2'� i0U.�G.�!nd��1 orita}�_  *`F��: .A�i�S: ��kf*at�L2J�M~!�iYZ*�ZC2A"k]�!!�bimodul�F�&v c} ��)7#^��xu}&�Iis >�([y�9� $\Pi ��V�K�, ilde|an����9 t�*F6��6"�B�@.�V�eI:K6�, \�sA�^$"�%qq�E�&��,(�"kQ�NZ@�:% r9AA?b.^rx�0��x .�76X"#a ��)*BlMF a�*q��f> s"�\J)��M_M\R Omega_X4:M �<X? c A�� *[*(5�>f�Aforms�?%;$"�$"� ��� B%� .� .�M��$�~�)(A_fC�"&�Z*�S� C) �.�r&l)�_$ig"��^N�&�["�#r*�)�!�JJ Q�q,�1c�I�1 ${ d_+ed�o�j$!�� I�gե� ~/1�i�t�p# ar� �"'#ce.��_cF�:�:D 4)_�C�b� j�,a �� '"�"� nt}E�$��s �=As�/�leen�� ^a"�� �o}�r%�����"-�:��"�?.��;l�A��'�?b�aZ�*J��er. Fi�Y,O*7;b  a�racM9�6�"w$HC^0@u*}:-�QF $HH_~5,��w��al:f? ��$? or�a� �-g. (Se�~���}.)��gI� � g�bz!v� iscus�"G�ds� � isotropy  sI{ t�== ePKa�{��dѡ"�byq�S c 2Uof�p,>SB�Y�aQ�"WA��'� � ���1<1L �} (F erVf U3{bc&#a��!3 ase) One!�a- heck��q��T�a�)s,�Z+�&b VisEV�nd Y�f5$we no long"�vAAbeH!=B^SF� usu�Cbig;tha� $,�e�" isel) �P >= \{ ([B , x�D�.� mid %x = x\ N�J&F&22L�)a'5M �7�&�C�< k\�> !�"�* Conj�}�)DՈO_{JC},&�$J!��gA�njugacy�;��g"D�PS< �~�:=46pD'� F�}M^�D'}a Accorz$toE &r/th2�NwE/��Ia�2�"�2;  \Pi"r� �&*�J����s Zt )�.�jV�Rr��_=E �N�9?in� Z_)��C\{M�'0 }' �;E ' \}$�|$NP= [ / \langle 5\r uWa�ve��*�t~K2�\simeqs"��F�:Lmq >}} B�>B�n~pJ�,`!Ay2��E� �Z by�9O"�Ua S 28 } I�1get�2��[I )= ��Bpf?682�� !2��� 8b��� ��$� :s ��VX*;�� �(Q /�8 6%�� ��0/2�"^/��u4ge`#�hR�,� a� RY*]2i_M"�4&Y,*�A�h�X.�IFB�XF2�o�1B�i']_K �*O x �*�6�"c6��&��&3V�:�F�Ax2�dim}(�)",��>U�)F!� "z 2RpT� � 4 �l� �"A=3}H?*_*�� Rk2TA�5im� $ant ingred�igdex!�oryY xv.�)� .[^ co � �"rb,6w$i.�'E��A�5 4D ific �2� AP �J2`� G@pmeal�%�r"AA-8 F*�$)H�6�� 5�%��ert�(\tr(a�CQ� b)=b:a),\quadE��.!�W $a,ba�B����A0ion��C� ncerA!"�"actK!F>�5io�b all� c<3Our� e  somew� BV llell � I�fst:con�aure� �)an&O wa�pa� De*-N$Zbh %� (6l��,>�subK�Fa�mI�P.�.�1 � ��X� fuA F5'"UsIn�"+la�E[-we�hie�yo!�"IPE%|Eu�:u!�+fZ� s�Z%�ork� � situ�!h4)2�!��1no~Hre. AddiA[e E�� (�3�0nvenie�U.)io: f�AR� �� \sXNM�#J� �YE�fJ"��t�i�N� >f1� $��d,�"f �pu�5B [2�I$� $ ]�c�.�AA� *C  I^u�R&�t�,��.��y� 5 �\ �*;��*L �,)$ ��/in s�)���$�0Bb8LJ�n�&����x8gcy�Z}�-C^ �(6�(v�; H^0b�-e,���+�%��0 "p &q \C)\,5�. Wqi�}.��>��\U���2O J�`%I\�*rb��>� �#B� mp}|; wide� B } ), �2�a-v ]��&> .2��� �*>�E��in�&m�qd�.�we�l�� ���Gc�!��"vf�. L=7�x'hceg},2�,pel�malg�9ea� el� $��P:� sums rb6*�} f�\delta �c $inj_SL �d2� OQ�W> ;�=��m_k a_&�K6`.�>�Ռ=2�>)rV � �� , � i-)=I�f_{k,\} �L 9!��Y�-V�E2�  �F�^Am* 9<12�Ww>� we G �"a fam$( \tauM i�!�$� �?ar�NY�.�M]a����T ie.�F}!3(f!��Pf') &=& -=} ( f' �r y f )6�rm{� I�ɢ$f,I2d $}, �9�,TrAxAverInv}%${)'}(t&=�<au  BI}]fn EY�$f:�%� �Mb.�7 .���5Xq59��ZAbe verG:�trbp� �"!��}��Cr�{� } Un % p8 �M���R$(%Q),Ut�)Uu�'I�of�O��:�%&:��Us��nA��1.�)%y(" 1W)xn��8 alfEdef�E�r :�YF�:� �&*��� acp�V.�A9--I�)N(��s�C�!��6u‚�.*V�versa,� K� :\���F�#�1 S)�Z/=$-�-%��Q � �S�YȑM�9.A (f) tr�o:�) �mi�*�fE��FWa��7y"5�)�6;eso";[)y �� incix�"  orig�)��9�X.��x�Trnc�T�A�� �&C�o6 �2 Z;%ۗy4sK]�0I�u� zi�9��Fmad�@�e��&X G % 9 icit;U �p&��.-Au�'0C'!O 6io{�(i?�w-1l]t� .�fu|9�L �at",%+]�).!Qex2E]>&!v)�!��.�Gvector $V�n�I��!t�oL7U�e`.����CY"�H(8K3J=` W}&X'��S $S = 1 +��k=1"VS*+ *Oc+0`([[� ]] .:R"�^��� �mS��. $'"{_"�*��x*1'$J�(��-aPi� Hermiti �r�#JL ;!g&�*F� "^n]�e<C�unitar� !�V�va �m�i���>:�  $V = V; lus perp@�1!��.��EA� t-8Igorthogo�W)O�#.c ��2v�aV^;" -n B��!viaI3 trix�_ =.�y� zx-BAwqq$zM�inv �' �2 �-)��`z=(.B,z ��)Wv8s� ~sMAűe.�A�tau�W}�M^8&��'2u*$�;, s L`integ"i��IE�!� real?@�B�)"k��/ FІW%>tr� R�( f�\I]1}{(2\pih )^�A�t_{Q�}+ \det (1 -" )n� )} �.\exp,@� @\�@ ial} -�� � +F[}{1 -Iq5fY^*})�) f�%�|_{ xA��� {z} ] =0` d.Y d6)�A�FN2W! Eq.~(2.17 � .�VA�Bg���эR� 6� U���!��s"� � ���e�� Q �2]ee�� .�� M�� ��ssef�ly ��O >���%[5Zr[Cor.~7�:�"OK�= ����,�0$M V ����9db�e�`�M�� $SEJ 7�r� A�v.�I�T<a�-�2� -�F^� A&*S �zj ��d byA�Y�( ��*F�*J��F��"� J(S�J~NLZ� :� $!�:� e A�!/Bqs*85iKJP!2� .�"%���$�C�4�B61�9k ��5iY�Q^*�&b%�v�&�w pend!�Vc�����JAwzMwS*%62�Noq�i "z $\kapp�k� �$�_� >E|���# �N2 ��"� 7�}�<$Z&=.�B����A�& /}�% I �� }"�:��fR^ \%Y2g a �>}#.�F�Fe~ } (f�}BW_ ��*"�^��/"^L!*�#s27At���`2�M(q*�J&�.K$la���.W+V nc Z��corjIry*_ f��ansgrp}� 8�Q��aY�s $Yp$Hh.�an�@�enume$vD} \item[(1)] Every�!�j� :�� �!yrm�m�a= qul+dLd9�)�)�ԣJ�y�.� 2)] ��2 �.& �� ���~ $V'$Q�"er^_ [,ij'$��s^�,ngA�� aD&'U%SV'� let }"�.�5�.�� E�$F : M \:oV' $ �n}m"Mn )�w�Y&� Ba)]��$F%�>%@>a ah$"ĥ &md<$\iota� ��m���� '$,1�b)]�� s&� c ��GH�vW�2� %2��X@_a�!sh^*�6�C&EV'&h ,f' �C�� $�d� �d&T4ma�A"� F}!�z2V' 'JgN�"�:9�� *?*��?g|f� F !�� �~b3scd�ID:�"�f'� d�p7u[!��kla�c�)o~��WJ�W-�:���V�&� �Ui�w$�im %�5N $E��� �PW OB�W� � cases!I[ � y .y)(�F6�Nby��&� )E�a�!�V�զ-�� >�/2 :N)� $-n� e%)�Ep�N�h N%$N���non-zero!="& "2"�a�s� r&(�m�F�!.l2� sZe��ls. "B�PR !X2 2��E:V�7Q��deb�g# M  (d) �5�.�� $(F,i���1ص�&} :j):�j+')$  i1�. Hw�.�]d�4om��tj9)3!��es"�"� �=&6 ��)� \�� �[�\f�llN5�� $ �@�.�A� �.>2!�%�IA�:#a�"ee)ls}��aF[ I2�\rDE$.2�$)� fix ��count3s�� $(x_i)_{i'I�)s[ $G_0�� ca_x *xB U = ( U_i� .I?2;�_iE<U_i�=EU 3 h��O�:~";As%G_{|U_i}(�lV�KZi_� l��m:� Ly {x_i�7By apAriate se�-v�(��� at��q)Q+/ �A16b�ar:�%�f�� _i$-"�� ��$V_�Fzx�&T�aA9 ` u�!1ulE �smd)k�e>OV � ,U_j9Q~�-� \cap�xT (U_j )\neq \emptyset$~&���b�8 et $W_{ij�5,Yh -5��:5�7 := G!� }$ �$xA� ^$) � �2[lya_ �.<0$A[ :6^f Qa !p6Y�!#!i-)�)�!b� ;�H/E�9��E� � =mj�D�r.2�y��� �2;BV�>AX��Ci&.��AX setsE$ so smA�9 AH $i,j!�I=!�A�#QA bi�) s $s�:a�2�)U i $t� -���o$�x�a�. �� $FbA\2F$&�K�?eV�=?�L"�U g�)�}�sum�E!H�F$-.�nX en immed��� �=V�\X>3 �$�q �c �� mbed�;�.� �:�� mon�UUl6���Ea"� � �v�3g� $G_1&~GB�Y�"�QZ ! .� X0�6�x�/>�2�B�s#vxI{F|7�r��aGb�U_i^C 9+z��& ��eR�:� �.� �Kn�W*�dof���E�g3� *� ��T� t2= (2)�b7���-EY$r guarantea(:Ka2��gl���9lx�[2!� t�Ef>  A2�SAy�� {Ui.�L2!e/ob� Od G���zb^covgpd�(G.V)_0&S@7 }U_i4g�*>/1/��}��EU��t8��l &���j�a��.�GnA%a weak �B lenc[e&Iq&um"�5.� �m�%s w �o��Ie͌toh g�I,�M �Y$6�Wm �;p ?a�:t >��"k .$.{�us wr��"�in�A�.$a=(aeg�1� $, etc. D�A�5�$2�� ̏pl"�90#6�\( 6=&��� mbin� A� l$-rE��&o$(�j&t�&0^ds�� s (u���]8L))ٲ"03�6� } ["�9Lcaa� b!9j}]_g= { m_{k}AA1�tack{ {g_1g_2=g} \\ {s(g_1)=t(g_2&D U_k}�![!� k}]_1} g_27 [b_{kg{g_2}:s(g > i,~t j�)��7M��*� A�,x.�b@2 ��.&�� �a��Z&y $(\var�6su�~i.%2L_�,6�)$%jiE^2=1$. ���*�* mi$*`��� �[Phi_i=z([k[k%0�C)��/2}�Y� ,~\h{1cm}\PsW/��hH>�&6JinH-e!VA�squ� root,���(M3�:� - 1� #".�  (G_0K B�&&�*�9�+: ^]}()V)eet 2�+ ()+:,A1�%K%A W%� F�����`ts +J�M� � !, ``�VAOta�{''�^�֮� �i�i&( �i�_c �M5=+Q%u2RG�$ >�1$ < ve:K5�e��ut !F�w�\�5]u&D``a��q. �''�;Step 2.,*�;�6. Ain�Yq�L67 �[6} *U�f;d���  9Pa�-Px:a !\ si_j�����H�`.�-P.� : \:V� .@���)i�Ey�ɕ��f�pul�*%� "g��$G*2�U 5�l&8�a-w � :J- � C$ a� � a�=2� Efun%�2�o:D$�%$�D[�~�� � �ra~�&�2 �aMaOV5 6_i�}Mo�%tu'��b>��l .�i1{",�.�iOc}U�i�V j e�W"Z *� +ŁQ�b$ 7 "2n!�9 ~l!W�x�03>���que5�AU�-D �', �S t�-��n$̺�� c},i2�$ �i` >1%�e9yMf�k b� A���VPX!,a6+�O��2-"w }���$, iC�q<aX'-A!��,f f trfct�� &�u�(�[q�">,� "([ j})!E&�5i�2� *i}�>" � ��w�<end�lsuffi�RAj"�|a��!��,%��,:�&\.$�V�-Ocomrel-J�ta_2c} b_��7 �j}�ji5251L�oB��p���*�) :��? "�eaAw)W��'mw�qhea�i*be7!S[2RF3� ed�*�y!�^l�^V'�P,�!_ij}Ł���!�2�j2�5�m�E!J>5~� �&� ��x�j���!�ѨO��rm?F(@;"�� lL� 2�lM�) cR7 ��P� ({�}_*I[��1  I� ��)nPe � �5�1� (DM�feM� S2 l)�` 18^$, *H��s!��/��o SA ��� ��!� a��ݽ<�lkp"n<:9 w� e��4 `!�!0$D^Ro ,\C��$&!()$*|+$��e�� �.�Bm�s�inpa"�M�!/fa�slatB� MEsvc�,��-9�A��.� &�ѱ<*q$� \C����  {<�c"�Ijo/, Schulz� TarkhanovAUn� G?8 a (c�)*t �G,� .���cX:w� ���V!3�ior�,W�i*�"al9>E�6�6� �G$�,9�$>\�|�byA &yTc�j& Z�!is=�)!���M�.n��on.Ś>X"lE Xj�2>c2,z�ro҄a cer�J 3&�8��*G�#s&vz?$�fw�&[u!+E K�rW�U�1�q � v�.�QaQ]�eS ``�iambigu�jA�"�$Aao-Lpossi��one'' ��hframe"KY typE� ques� "�\answered�ly. �U�a&�R view ";LY��iy� :�'!� $\4ine{R}_� �X$ whoso�>��X$FgASlex�ANj$ $R_\C(G_x7)R!x) Q _\Z v)�"]E�x� �:�J� �k[mL86.4]{moerdijk},�>�h"��aBS"Iof lo��reta:\Ld�2; G$ yielN_&r ��!�"�/!% ing}Xk9�&"I�tC�RH^k:��TX�!�>�`! impl؂f]$!�2i($a�&�6� $P_Gn ,H^1(G,S^1) / X r%By*Acves}, $3$i�A/�*PA�u� $G-#as > d�� 9'ofA35�R�|�CSY!XSich��&Vu��* d >�,2��= 6v�� �s 9"l��AQK6�-4��!yZ!$PicardI���duB� �Pwe do x�nJ��}M�}y�F�Yi�2m�- W$geometry (��e�{bw:p�})�aP.�!t. "CW �. �\� ,n�2�� % Weԅ !��"% aWA/0N7$_�z��ru��c�rG$.�MurN��pa�e�9e��!�5� $G_xH& P�>, ��E�tak�8"U� �%v��&Y� cano��� }S2�Hb�As�k�Sl!o".Lmatm'�9 ��.J^rK . <@�5��&�� 3! s�� $0$-V,'Xn Bk ��A�t*(A.�&� !"�cb$�OrF��.� �i�<< A"��)Ʉ*V"�a:�;!�zbe �<� sS ���%�д!�a�R�d�� basi�ut�"irr�d��Y�eZ6)�ecessa�A� "� a�nm �Aɼ�i��be - laim,j1�f-+&� ` ifmMqf�'elW. %@)�,�uaI&l>{<"ru r���� �q �s^��G�d wiseA� �ipee�iIp.�V�gV��� +*�{Q�inv���w�ef?5"�&a��&�Cr!b� wordѐhl bOő!*(ty?{CDE�i��*45a P2},M�� e6"� "^�|~��e[�Q3�x � c�sin .�Eing"���%} �G7l��^��i�G}Bg~A{ ach : ��$acts faith�WY a2SGa��F {?(}�9� ��"� $)�@� Qs%�*�"��a.U1�2n5?�?re�it.�o�!.5H�sketch��#*M#&-ji&Q$>�%i#2kA�!�*� �!o0nH%�(X -#k.�#� x.�kF ��.������ .w;�%che�si��&Tp��y*����oid� ?!���Ceiof�y:� 7 -Ong9�A9�)byu$ D"e nI�Nf�.�\B�o�n��T8*�OQ�A����2� ,��)+&�-5� �dolgeN~_):�"�=��2��q ]&p� phed2��Uj A�n 6&�zide晅j0%F� .�Q�m42 �_newpageTibliographystyle{alpha"��the.#}{{�ibP=\{\sc AdRu}]{ar} Adem, A.� Y.~Ruan�{\it Twid�"$&��wRH Comm. Math. Phys. L`bf{237}, 533--556 (2003).j.�Ba}]{b�(ovsky}��sky, V.�O��&�AV� � � logP�� tt{arXiv:N%,.AG/0206256}�2N�Co�c�um, P-A.~���}�*~ �l�jC�� A f\^{e}t�t�|y, 163--232, Academic Press 1988.-,BFFLS]{bffls�yEK\F., M.~Flato, C.~Fronsda� �,Lichnerowicz�:8D.~Sternheimer:�Jit�$���y-2WI, II%�Ann-�~%aLbf{110}, 61--110, 11 51 (1978JblGe!bl-ge:.f�Block, J-u E.~G)�:I�QƎ*X folir!h Hq�ing{ ��XXth In�*�ponf���n D.ze G�ic Metho��H�i1E�lZ� es et r\'��{dQ  r�(its: l‘s��q�< feui��ag Fob�P܆A%�6X$QA/0403334iX4J�r!�*� "ʪ!�L�A&��}o� xe]>�/-�J.6�!�Y�28}�p. 1, 93A�4!q8N�rI�rg}>��"]� I��0�v�bEpseudo-"��symbol:- E�:Aresidu�b�o)vam(}, 385--403�7NlNi!nnZ�V.~:���._gH��n��!tJ�!e341--365�9NuWe�"�Aurszty�p-d,A.~WeinsteinM�.G^+Q G�J�(SG/0304048}��J�CaGiW!1giaqu#�$Caldararu,� A.~G� S.~�%erspoonUA)�ic�ae8 Z���O< �3 toK�aeA�Ps&�����A8�_4No.1-3, 51--70�4�� \2fCh��cr}�� n, W-j���� A ne�HU��1rA�}, 0'c#6�[004129)h1F�Co83}]{ys�}�!d]��i��7$e!�,ncteur $Ext^n��# .R.A.S. P!d5"29��198N�o85}]xI :NDG2�q�N68�2�Yu, Inst. Hauteq{\'E}tu�l Sci. Publ %4 bf{6�257a*0a*85N+945+2�)�:���etr���6M(Sa�� ego)Ų4.Z C��"��C��c1z�:A3�2E�J01A�319!2.!99J(rMo}00]{cm}� MM� I.~M�Y<A��M�� ���`eg,Reine Angew.� 1�52�o2�n� 0^�1�2001} ��F���WtheirF� !� dv.~l &z H57} no.~2, 177--197�J~Do0a~dg:m� (} Dolgushevo 5�op/6@E�RZLex:307212�J�Do0A�dg:V۾^�A�$ T߳� Chai %�6�� 4022�J�DoEt}]"c2�� P.~E�of5&H"��:7� �Y�<*��5恻hern--t Ce2^� 1056-SJ�E��ei��ud} E , D2^���ͮ. �� a VTow" ic�_ raduI>Tex\�ne4e��c�15 Sp�0er-Verlag (BeT)9 5B�Fe��fe:}& B�A/��fC�<�s&�f.|1��%\/ .�&�4�21� 8��JbFe96}NS bookZ�DeE���6� aOI�nE�)�Ak� e-%, )%��6J%00 �ȺV'On�-�x�%x�/ �M� % * Mosh\'e e!�$9 (Dijon),�\t.%��|E�bf{52} "v 29--49��J� Fe02�de��y6���O� � *��Hal}, G� s (ed.),2�.A�0(Strasbourg, ��),S� Gruy%Q�+IRMA Lec5 %�11, 67-83f� SchT:��)sX , B.W.~.�$N.~"�$> )���e�!N����~�D~Fourier, Grenoble9�� 5=60�63)�RTs%�its%��_�FB.~Tsyga*1 �mve*%}@�Manin1�&B!wArithme�Xande��, LNM�1289},�� , 97--209a�N6 � �� w, E�Cartan_��a�ul] �auss-- �� z9�^ X E �um.�6"B�:V!Israelm�a�.�&a 65--7��J�G� gr� ndieck} G�  P�]��ensorie��� s� e8s nucls air�!( Mem. AMS9�� 5J� Ka(kawasaki} K , T�xI�of ellipA�5s ;`V$-:.Nagoya-9J90,84}, 135--15�8JF K�@keller:derived} K, Bu�V!� 56�i��<6�$KT/0310221bG K%Ko:�� } Kontsev�"M.�.�8quantization of� Poisson manifolds, I}, Lett. Math. Phys. \textbf{66} 157-216 (2003). \bibitem[{\sc Lo}]{loday} Loday, J.L.: {\it Cyclic homology}, Springer Verlag, 1992.>Y0Me}]{meyer} M , R.W,Analytic cyc`cobdPhD-thesis, M\"unster 1999�\�$tt{arXiv:m�,KT/9906205}.B�o�$oerdijk} M , I.: �Orb)Tt as groupoids: an introduction%oTAdem, A.~(ed.) et al.,Ci!��thematics and physics (Madison, WI, 2001), Amer1�0Soc., Contemp�bf{310},�205--222%�2)J�Mr�-mrcun6�,� J.~M5�I� to folia� �Lie9!%@Cambridge Studies!AdvancedE�1 �91:9�@NeTs}95]{nt} Nestav)� B.~Tsygan9#8Algebraic index� orem) CommQ�,Phys {\bf 17! 22!"62�5F# �9�99��On|� ring!> an a �%MXEdhGeometry, 337--370, Progr.~� ~Qp�L Birkh\"auser Bosta�MA,�cFT�Pseudo S��(� ) !�� },I�u�� (QA/0405378}b�4e}]{teleman} T , NQ�Microlocဩde��l'� ieD Hochschild}, C. R2�4Paris S�r. I�. �� <26}, 1261--1264 ��8FNW� weibel} W , Ch=�AnB� A�logical��ADʝ 38:9� . � 1995B�4Xu}]{xu} Xu, P1UZj�ͅ� Am. J����1!) 10%)5%'AuP\end{thebibliography} 8document} �\�class[12pt]{article} \usepackage{amsmath}> symb2*[dvips]{vicx2{epsfig6subfigur:rve } �y(width=6.5in $height=8.90opmargin=-0.2oddside   even23+`def\eps{\varepsilon} \par� 4nt=8mm \french��Hing \font\tencmmib=,10 \skewchar0 '60 \newfam\'fam �C=2 � Ph{\a�M'4010} s61}�(smc=cmcsc10 - smc{Xsmc ?srm{\s!rm ;msb=msbm:�%^( scaled 110 \(Bbb#1{\hboxdmsb#1} gBb.L b6 quad Avr� \vh skip2pt $h  ' size=1pt}} \6 F} Z�Dlessim{\ \lower4pt \�$ \buildrel{\displaystyle <}\over\sim$}\ �g^H^G>} NHn{\noIf Z P{{\��P�4si{\bar{\sigmaE 'ELL LFF FSS SJJ JH HI{{\rm IX 3X#Y YA AO OM MG{{\Ga�!-C "Cp{ ^{\prime}a�2� Fch{{\mEfrm ch1s2st2tAvK {Av}L�  F� bbe{I�( .15pc\hangI=.after=aꁪ8la{{\Bigl\langlU�r r\r20goin{\to\inft�Tdef\qed{\hfill\break\r�Nline{$e�4$}} %\magnific��=step1�a� =0.03true�Ghfuzz=0.��B and{\e}��bb{E�nepE�.Reals R!�. Natural"N>"integerEZ># calA B cal{E�.eF}MkeL.vsivecu�}6� Exval}[1]=#!�.G prob2$P}(#1):KPF&\{#1\>sbigN+E50 BigrN5J�\left(#1I!)} )�th�{proposi� }{P %&lea�{L2 "}{T Q6,corollary}{C x \makeatletter \@addtoreset{equE�}{s���re.ithe% ).\arabicCi* r \input� 8lat.tex \begin*R 8 \title{ A ques! about� i f��ional.} \author{ Dmitry Panchenko\thanks{Depart� � � �, Massachusetts Institute of TechnoO , 77:*Ave, "�H, MA 02139 email: p �@~,.mit.edu}\\ 8b�"Z���.!!�%31Lab�ct} W�"� that�: .IB� Sher\ton-Kirkpatrick model is�vex/9� or?0parameter. We/ ve a,tial result �showstcoS�,along ``one-a d'' dirI�s. AerAng:sequenc% this d�� log-`0of $L_m$ norm�a � !Xrandom jbles. a� 9O\v� @e{0.5cm} Key wor�spin g ; \m{8 blem some �sA�( Let $\M$ b!,seE�4all nondecreas���`�tinuous 1�4s $m:[0,1]\to  .$Zu%�!Nr two!4!�smooth5�s $\Phi$f$\xi:�3N $ b1sym ic, 3(-x) = >(x)A=\x,$ �b(0 @0)=0.$ %Define $�F8ta(x)=x\xi'(x)- >.$A� will also�umeI�S$!�of A�rat.wth so% !KžHrals below are well�Xined. Given $m\in\M,$!*)7a5' q(q,� for $q\in)p, x:�j$ such 31,B'q��J ac{4 e/!T}q} = -\f$1}{2}!('(q) ��l(:?^2>Ax^2} + m3 M^qx}Y r)^2b4r). \label{heak a�A�.n97al!:\M.Od%� d byAI(mUF0,h)$!^i+$h5W.$ MaiX�on:} Isb$aЅN5� al o!�0M$? The same�Xwa�ked��d\cite{T-Par}. Unfortunatel�despit�PE�%$ effort, wAOre�  to g��te answa�A�is�. I2is<FI�p��:=IT�= �9 ��/@ $\lambda m + (1- ) n$ whE�@(q)\geq n(q)$ for�x]� .$ I�MpossiblmxjZ� l���� dcip@wee�not awa�of�� good st;4ng point would�ind� ternR��,simplest cas�const:$m$%��B "  1��A�PI�$ �(��Z, mean field ��l whAwit�e choiɤ��(� $log\ch x,$�follow�%�ormula}J.inf_{��e�l(S 2 + \aQ2,(int_{0}^{1}�q�>dqi�q���y�A��free �gf!�. A��orous5� .�wasH n by hel Talag�z2�}. Si��^ last term��a ^ ar ��a� f $m��vee%$M@AyPuni3ess� %kg=�:�} $a)$i{0���bE���� s% @it corresponds toE2origi!SK)���A�K}Aԅ\e �m��/a ��,% soluX !> ܥ�) can� |!y(x+ޱ�recB~ɍ$B~AO��expec�o�!(i)_{i�l}� i��C�Wm_l=0� ;"ea{ � � ge�)A �.$�`9�2�in�kA }) i� ��byN%_k o _k(E�m},q}�_!0(h&� PkBA�)����no)s,�l � times omiw e dMlc $\P_k$^ i|)�Zy�-a��)y��i1anY�$Mn� (n_u�ne�"V A� 0=n_I�nJUn!(�J�"]is our mB r�."�I� (T2} If $n_j��j� T $j$ or G m>V�)�ni`.$ J \grad 2\cdot8a�!vm!� \sumq�jm�iC\�aA�_k�< m_j} L(m})(n_j-m_jY6~B8� 1# *�*<$\P�au3)rml!�I,M$ ��(ect to $L_1� (see��$Guerra} or � (), approxi`#ng any� b�aPs �da��co�{V�C BC , Of course,m�%`)B�y�)�Dvex in each coordi� . T��yt f' 0 !a]g Xe�. *�1�� $=m,$ which��mal%�.| Qa $k=2,$i�mm�mq.2=1�;} 0= q_1 #q_2=q_3m�� e ase,V8= f+�"� \ �(h+� zY�one6�H� $ -^2 �'(1��mad� bitrary� !N.� xi.$ B� $� �e&� �^�Q��!-"jrm $���� in t��8 <.i�e2R�k.} I6� we do�a�trictŘto� in $MAlso, b � T2} h-e��!� H�V$m_k=n �%O assump%only bec'(��Q�!in6n � r��oi�sum�.� ��* ��Z%�]; $ is*C� $m.$i|l�$on=(statectha2`-known }�n H\"older'V)n l�:�is alwayB�1/m.$ A�is*it doeI$ seem obvi�how!��>Qer� ��yB%.B�on�NN.Rexa|,�� cl� ~��\�at �6Hf''(m)= m^{-3}(\e V� ^2 V -  V)^2 -2  V�0,E� V=%�m(>� -�7)r F3� �  �Us:E! ibity:e�.$ Fir�+$�0 �$Fpthird cu�n� $\eta � h2���nonnega5&N ��$ta^3 - 3\eI� +2( )^3O0"� �B�A� qw:A�.iB "W .��w$ ���(�]A�$f� ��eFk��be "�= �� 16� � eno*��- m�JK!@xp( ` !A)ɓAsEG )^{ $= 5.S-p9gonsBcK A=A� �A- ta)<�ty(n Chebyshev6'�(�eE�a \p(UF � + t �� .� �0tW eq23 ^2 A} l\t)a��A8� #"!$A getN�j� =\{1� array}{c � ndard "� ,z,�-v "�  $�^1>) eta�k����andus,bMg!�Ux)%)��Jrr ��!s` the��R %of2\ (orFi�n�))(�Gm�� \�P�->���O &�Zbased� � �A� observE3s.�Hall&Yut��.ri/ve'S7  q_l.$  need:y"��$�$ax\ qEY�V_l = V�,IA�f(A�2�-���VlB�  $Z=h+z_0+�+z�AE$Zs. +z_{l-1s ��Y X_l= s Z_l)6M WH�Z_l>�(X � -X�!�n ::� .1c"�L1}�$�1N,%OhavR�f�^tq_l� - (�(m_l-m �)z'(q�U_l�DqFb��9�U%U_l�, �d q}) } W+�W t�l(�W_l)� W_k� '(Z)!�$UF��-)=�ee.�7!51�#:r�7r= a�C forw��(i� e] on���g�3o<�s)ELq�m�?,�"� �SG*IZ�5�& It turnR &"&U_l�*no.� �$�3 ^ingredi�����>Z&`M�TM��6���� �i:��Ul}) � b��\=.$)�� 6 � 4 � � )��L1}%�6�1}� y:2}�5]-�F$}�Ku� � tq�!yK�k� e opU&�d hand�,$similarly.�"� �te1m}^�(2�l,a�+1}.�3�r&�N�= .����ia�*�^l� 2�)�'� $&"prd$<F2B^T  :12|)}���(n_l -  !�BE,�r e� �6&��5.@!�/s�-�_{+N� {l},�{N�andFq}^l(t)=.(��-<(/ � 25� q_k).p '(t�6q_lj 9 -).$ Not�!�Aiinser�:H%9��# � �^l � q}.$ ���� �w&�! �arphi �\P_W�)E5% ��is easyu��$\N$ ��rpolate�tween "1!:u �$0B$I�.$ By:O%l '� %�;.c �t.�t�h ,�gnA+�e1�) U !;�X�M���T�� )�m-M) M`!� ext,�1E �d5�_{c.�(m&��d-1I�ps$ -n_l), mf�] � fE d%>!�). � ^N���� ��2WB�>� cF ),�#r �ec%V�)!4:�� Again,�6�.Z �za^ �~h�!�~l O!�6s �zk�"%�>}�$e�s5\in�$ :V�M^Q���$s �%�&�! ing ��Q)ˍ�Rer�8e,:�!"�$m�� ^ ���i"�!>u��}�-=�?q.E�C1} 3B� e# r>� %dD���Q� t�(6�a+- :0))y 2$(0��o����'aJ"(.�-(>n)/�@ehLet2I`to�}� E}� finishes= $ F� ��1�HG'a�p�sy,prelimin��s. Co�(!,�,A�(&,enough)" sJH\C=\{f&7,[0,�) : f,f(x), f�+t  0�a�} x \}� CBR �`&� \Cp�{-�|"� Cpr 5 m  next�P$describes 8ral factat� be usefu"c/Z C#�J L2} �� 2�\$V��$ �* Vl})& ��, (a)�hp"��, �\C ee�1!� L_lt�$V"3�"*�) Ipa* (b) f_1� b $f_2p� Y@ $Ma��f_1 f )f_2 � #.7-� (c �E�E# �$A.I��tl$g�.m �%I2�!g[�-2Q��}  dify� (d �%-�# � y)a�\;�02cm} (e.?1Y^@p`-(f))=1o�!T f $ iI�.�.}E[�)��M%QbsyC0% *���n+ Eh6,j7b"Adu1I �-l$ "X$rec�CY��co.<2 V�!� �y�s fromq�eqn�*}�%1f 1}{1%A%N"Z�c (-e0) &=&�(�8-� \\�; r ���Ob<�ů��K )ۉ Ip[a��$z_l'�2]9%�*pq%!el,����%� "�> "� B�'$.Uc��(= 1$ (i.e.���think�ǡ!$V(c:ed�>ty), ?an~*�)� } &&.D�{ �|-)�a%��.�y=��b�8%�\��F '|l(S-` r�1�- # I(z_�(!�() \nonumberi�1�}�$ !2 �)�W'��Q�(E�lMJq.IJ�(')� )),$ if!��6:�v�Dn5 $s==E $t '��w �� K!�� b1})%�be%�ten� ")1�u�2\pi \s >��(-2m_l���t\, ts_{\{s�� t\}} K(s,expl(*iV((s-x�+(t %�r) ds d:KiEB@9� �r j�n7-�)Ws=tt)Y1I%t q �AsI�c"f,spl�(reghof�w $=4=\Omega_1\cup 2�uac�/*r5 oY disj�1set�$ :1�{%U : -i, |s|%t|t|\},\32b3 < 1�I�� �2��:���v.�$-v, t=-u$ U6��$��R�Kd  $(u,v.1M�%� = du dv�"W$2�K(-v,-u!�-KGi/�y�P͙ic� (a),C R \C,��4p 2�OQ 1(-vA 1(-uE+r�u2EM2 = -<u ;v4.:u9%�T6i.a-B�^e^�J^1^!�� �V�u+m�v � %�!?�}e��re�!>�O=�) ~ LU8EQ�W�2} �Px�P5� Ҿ-��%1�� -:%� � ,\ �a*�e�iE����1(t�|s|I]1(|t|� L: Morea�, i,VF]y�?s,�c fac�*� �&��EmT"S!{ Combining�se��2 ��ge`�� >B.-�P%nt* F�K)1� H B(A��} �~N(1� ()� \Lo�Bft�^(arrow x(s+t W,NA��-@4"�(" .  $s+t �� �C"�~0at}A2�,.Ps2��b are *M _� � l E��� ? W�$"� Y (-T��H� A � :98.%�if6?2� _l� ^2E�n>�*} �� �#-"2� � .t ��  VCf� \sqrt9 }: } \ 1� � i8��0} .s{s) ���� N� (x-s)^2#r)@ ��r1+.1gr)�*I��  *}u;$ jm. F$ �Kx, ��R%sm%�� F� d) Take $� \C.$ P�Cv�$!�5 -�q+�av��^}��IA�A�6�_I� "�>�" syme}L6&eU .$ Recall����Dm�Vla�a�de"�#�XI^E}  xA9V�A�I+I�IIF�� $\IN�'1Z%OJE \II qEZr� �O� � �9�>�,2A#Zp�|J7,B���<�1�S%� �JF�.$ ByN K ,)F sE�\��(b):)\IIij�5.]\Im�m5MF~>*0_ ����$f'V-!�)� x6� Ke�(e:~� AntiuRZ��& �A^5�� a=�[A#Z� A�. (d)��.�6�, ���,�,t II =9��b�%6p.(] IVM;�X\!�1L�#.��uYʡ��O��� �:'u" !} )-FF4:x� But KE$fE�� �$� !�.c� $\N� Bn.�$2o"2� they^"�#�> ed, 70 da,b��D,�O�+e�o(fAT0b))2a:b�& � simB� ���C�!��&i� f) S6>�9� \log!�A�EN bove[%�v.� Jensen2^., ��0x[x)�!�*' q�|.$� u�G�|�@>{F.)� a�<*�("�g��ɦ� �X(1+�V.)E2���M��ѧ D.1��.9>8 (x))�BYy-X�L�B&��JRdq�! ��%=!0:pa&�5��3�I�(  2a^Ѣ ,$ $%�iP �" $g`A��).e��6'� -�k#� {VrIT8s. HCE1}. $3(l-1�6�I�.8"2}�]�e $*l�+\Jh+ f_l�,�� &� � $EI�I�A�iA (�ra p"� felF�+Uu��X_j =&�,��W_j�-� -�Y 'p,! j[$f�0RK,=�J�p W_p��t-X_j)LE�I�p>s$X_p$&�7d6? m_j M�Yuil%�>[W;;.�- =:�:4`l�*)!g& m_p�p+1,/p�X\�= WV3. 6=:�}\�> ij�.p5*{p-1}�f\-��N�H�NN=mA�2> />&=�^jv�>�� -r� SY0�(a� e�A�:R{j}:kF�I>Ef_j(Zi�� )�W "�/|�vT6 ��B#�Bjp�:�  ����RA?�:Hj 2\B_RinZ6 .�.�97����2�>���V*�j�_:3��ina�[6��XuB"�;�nz[ � _� ,$�@D'shH ival�0to��� ��-.�!�nd*N H�=$f!�$ ��v � fun� �% $m = Z_j=4 j.$ by����WZ_lmIe.HZ_S�>�aBly�>�d)uGl!�FaPge�S2�$A-n� � ke���J tF�,m,�O 2b� �!2R*p�N^B  ��}�� "� )-�����') +r�e:)t the s�P�?k!E"�"�(ofcued.(; i"O?� tina})A^, h�?0 #�F�&m2�N�5$Zata]�G b6�.!�fG0Z1<%3j��m_j^{-1i� W_j$fjvf! agG!�N<2�]��B� ��՗6I��pW_: E�._imB2�2j �( t~� �4���jR/F�$$���c 4Z �`Bnd�; ase12�= $" �/ _� 0$q:le�1�") �<qed. 2.} �w:2~�g_�g� �m�95q�>8� \, ="� =@^2OtR(JC2 8calKP~=���2�one leav.i�1" give*�?Y }��J &-& .� $ (m_{p}�9AA�:,&f_lNB.$\q(|# J~al6n�a �l+?+Qw 2 � z.�5��!�A�:x&$:e�+ 8.�X_j>� +& 2E�%I6�n�$["]A&�1�To�8� �'1Eo^v�Dflc�%AA�6�!�B+ >� +�gA�� w�PsL9 �eA$ term >fa�f $�8bigtF�1�CM1�:D ;s.6D ~h�a�\e�E y�=�6ta���'�(,$��>E e) i�*1 ?��$�jRE���V�EK��_EU of�52}) (Q?�Hf1M(m2�$"�S aa�I&� a�F�!D: eRV�8v;,"8 omp8 6? �A,i�%second1 �! V U�9e�)$OJ�l�`})\= $p=l�\>~fourth ~lI�)�2�J^!(:`j.G^omp�1�+yw�E.�.d���;�I@!� s^�>NL.2:$6WN@ �-<N_ a).���G.��j,S0r_p ��B���M��8��rfnj�:t�zAndiffer� !9�A�g1 ���( �- 1�a{B�W'NguLU y=F ) (�*3 ��pl�t �)=Ksh�[ !�- $�-�=-  $��X_i$'s�*i`0$h�3a&�ic?.�> , $r U�# �2��#6y.F, :=6@ "�1A�} Z�-" !Q2BR!��&a �b�.%gL&A� (B�i8��/�;!� V�%)mIE��.Y%�! us fA=4A�YDs$p=�"�+is��r��6"4�X_�2y�Aeq~�:J{6� ݞ�� �̢;�����!W3B�!��� &,V�5!�\Delta�'b��-�<2 (_Am�b-Z c-%�Nrb+=+ ��!r�j ,q��a�4A���6�JBcB$1%�� ]:� � �=+z� � u#�5 ! !x�6P3$K-1}!(i�?2 FFN%�i^l�))�� Bi(Z_iS \e_i W_i  {i+1�i+z_i��� procI2 5t.� �i�i)=� m h �9� ��*ei=l�(N �C�:I�l���6�)�9���e�eJd_����j4Rt��<�OA��,�`�V��6�."Z iA.�,Z �E7�A�p+�L�2�_]z/2�@&� �E �:�4Z�.a9Z�"�.�M0���^> AZAW?-1 �a } �.%C�����"Y] applUo!�Ny mp2�-1�S.$4�R�-9V\=P^�� k">��� R� ��t� �.1I���now�R%��� p�Qn f��;J&%�.�!.Ax,�� �Hp�kx�m ��H +�7�Hp �HQ0p��I<r+.�FA�%Y�F e��3-N{p' +pfF4�D!�VF$!& !�1*�6ife9�F�F�FzF4�Thu�_f1��P"C0B�cn�  �j$p%��To I.� AC *� �Wr�onye١>Dt*{ � � T  � f�2�tscD>�P N�A2�F(C&���u�"�.��G;"vC:�NCK�h6�;�>�1i@6�=l�,it@h already%�-�be15!�.� 2}).m)n"�)�l  ( exac�Yla���J=�C�1A�J�Ci2�Ni"�A>Z| {99}A\bibitem�O �O , F.p~03) Broken rep� �y bound��c�j&�p*h. �r>t�.} am 233}"��1-1��ah.k, D., *3r , S.J}72) Solv�; {�a��$Phys. Rev.�3t�435}, 1792-1796!G1 �P"Aj, M5 S�qGA+eV�$ Challenge�M�Q>aciaYrS�lge.�.%�-� T-gPa��ji�^.�V Parisic�Z��t..��--o337-o$2, 111-114.�T-^�FsTo x\in�jAnn�~-t�MZ�OHA= of �i's"�tk:�sMO����$9, 625-628:�arN�4)�0measures. Pre!�t!��)>V!ʁ�d"� x %Th�7�n� �2�aDpreamble!$TEX files Ioad�} %�ma�_�Ve'�\Bbb (``blackboard bold, Bourbaki'') �~\acters %\UseAMSsymbols %\2=z = �c1&�~cmm�>�>�>%\+4teneufm=EUFM10�~B80#�{Fff2B-#1x{  O"ym��vVB.�teA Rsj� �bb'�%2�bb w{\RR�{D \NN {{I\kern-.3em3 \RR:8b\�+��+��+��+�R+�%R,�rm+� �rm� F�n{*r� %\paB�}%\�}2�} % %\scrip��4a�s}bsy: fivea!0 \gross=cmbx1u�2M[ \m�[lZ'0 )ou�~=ocrb10fqZR1*pageno7'IGA&�� } bf A0ap{(A,\AA ,P) ( alf{\alph'a'anoG�|^.\| $AP�qű{}ab. \bs1��BBr~B�bxt{\box�: xCC 'C'claw{\R�Ya= *cntr{\�]er� ,osph{\cos\ph>s� cost  thet�TDAN{Dokladi AN Ukr.SSR IDD �D� dc{{"� {dK� \,{E � A,defn{\skb\fl�i�� \rm.1��F{�{ : nsC{ (\CC1�Dl{�al$l�dnW�dowp o1( dpo{d_{P,��� \dpn _n.t '2�Ea~�9E5eee{\ ="7�eeq|�� ndp{\v&�� �LEng{English transl.: ߂PPeps��!�*�12GH�P�Gg�\ge�#��&$�go08� 0 u$i{\tϋgle!8  fl{\�hQ�flushp )JH&^�� inv{� L*��#KKMZKla{�� Z li{<6�HlinF{\ell\upin(\FF)5rlm?mbdQLm{\L.l)%l=% �� ��� to�E�qnt{\ens��#1]�"�����Lt{L^2(�gLto_0,mc{m^{\CC }( �mcn }(nQ� mdsk{\med)�%�mmY�1mm =M&g��!%|_{\Fڂ!�NN-oN%ormf{\|�e/AS2omg{\oXG hOB�Z�],{��Pr}9�Omgsp{ " \S�H ^' b{(\C5, 2 Pr:Xr Y4S Z_/ ,Pr :: �_{\nu29 D� 8݆bf&܆ pard&2)�p; y�0y_ \r1� pl{\�J1�P&�pr�� babi�j\rm{^{� pr6�pv� prlo:1 ,loc^5 m�prb>8 {p, }~<���E�QQM�Q�5ra{�� �r3�TE��{��R/ efs{e5�0 {REFERENCES}-5RRj�bb R ;t�4B]Ru{(in R�uY sA�SA�*Psoc{S�� q�set��tminu�� sg{\�K � sga{QN$-aN�Q sgalB82 I^�a�sin��sin��sin��.�skb�[\fl&�sqt{^{1/�Sp-�$SP}(\RR^d) �*y�� SSSi�6int^{\��1OI1_фSSS-SWK_{-6Utens{\o.? TVMS{Te��D verojatnostej i mn4ati\v ceskaia +nistik5yTPA� �8�u� �" TPMS�fq� 4u�w� al S�us�, �ican 6"ocietyQ�tpr Pr1BTT-�T5ssub �_:lsum!�u�j2�4UMZ{Ukrainskij>(ij \v zurna�8AWupa&O �}��2ZVV �V}�\vc{Vapnik-\v Cervonenkis��w6�w^P�$w>�w��w��2� w�� ^n�oWW �W}+s%X� bf X5�xa{(\XX��$x�$ ,Py{\{x,y��!_ZWEk`Z. Wahrscheinlichkeitsth.A�w��2| ZZ �Z�__{]%9Hamount=6pt plus 2ptl "{ 9$ %-�. % B�?x INPUT FILES & PAGE DEFINITIONS�v>vJ��,S,tlepage]��ar�g*�Aaxsym,ams�s �4�thm} %{p�r8ks,pst-node,eps_`��~/s�"Œ -.:� 9.2o.ג -0 �i��;� ;� \sloppy � bottV:��| 1emHft9�i 26 v .5:i ����par r48pt sep 10column mm ��>�% Mak4Sha (type \Sh)�g>gp\DeclareFontFamily{U}{wncy}{}2Shape m}{n}{<->,r10./SDS{mIR5V Math + {\Sh�� ord} 6"58@��V� PERSONAL.� /SHORTCUT��B�r�commaI�mz�_nGaoV� BՏmrV) .�m!@JR�2)qVR� 2)cV)C�2)fV)\ .)faJ)frak �2+b^+b>fN�VcB+p^Vp>+riJ+$cal{O}}} %"��i��!�5�g��mod>��$\backslash�bbF�eo>�j  \�squar5�.4cd:�chi_D>�c>Y&B� mymo>Onegthick �+ \p/��5shortSurM�FG:V.NXz:�S.�onehal:� \ffO2�.S�.t /���2[6!notdiv>ot \; |>� -WJ1.�_0m�s}{C*m�ne��V��lemRߒ�}� �G��Q*{conjonje� ���}{���$�r%#({plain} V{my%�[s��]2'*p&2{my�[ L]6�:n0u*=< 6�l�W�&B{�$.Bznj)C=G%�ore-)R1D %6�E2nJ*s+3]+s}6V*q6�2M !s.">D{myE5.�:M%�bE�Pr  6�Brk>,*{m%�U�.a7}{�~6��q}{E?|Vs �=z@claim}{Ca�b .�Q�� nonvanish� of ellipt�$urve L-funm@ r��dpo�\ar�n ff n�. Xre# ��$ W@$ies, incluz Dirich*F.u(\cS�S- IS1�Dw�! $k$ Heck6u,of level $N$BIS2DKMVdKF!]��r�� twist Ea fixed:�KPPJH-BH to nnCa few ��D�. +��'paper�0st]�>p2Qg*!%%�P6�s-��`$Weierstras�F�?B�78*} E_{a, b}: y^�`,x^3 + ax + bI��:.@*}_M$* eq a� (q X^{1/3}$,b$2}$ (so $|�|�6(4c�@+ 27b^2) \ll X$),%z$X�<�r*�� Actu�0,!4imposg+ e ad�L�N ��t`Enn�+imes $p*�� $p^2 | a�- p^3 | b$.W\coOin� �kno ��<is1���>;Ax��(!�N�% V$1�$I~�7$d%�A�y$2�d^2%�d^3$)Id1�6^�va�RV�isf imal��alls�)F= q 2$.�� ]/S�"�\{ (a,bT0(mz^2 : (b,2�.1 W {%�} -� *� !�*+ Aa \}�;uHav�$b$ od1'ce�![�xp=2sc�N� s unF�c�neEGglobal5��a�'�-�= dedu7��5�i Q  10.1!���Knapp}eߍ". Not�zrA�I�a�$9ESaoiR)�0$,Dd��N��D!dj $S���6F. ��umXst�a�l�)of፹���D`�"@,$)�Re } sAQis2 �g  . O6O� &t<� "�o thm:�-} A��Rf)a:�Rly&TD�$�,b$�e%lЗ thme� p��essio�/Adm4�i:�l�02/9 + .#"$. %\eq��eq:Vsum}I�]JYR_0(Xa<\# \{] : L(� lf, �Db�Dneq 0,ai6�1�-�ҹ� 2�L��*}fTh.:`uE*]"A op{�  s�tack{ %(�m�SL�%�?�3�S2\ "2 " � "\ %L(1/2 � �}} 1 1,\gg!z 5/6 t&�#en&6M*}0;aG~y & >0$�kQ{!a�c� quiri �yeY3�h>`y E ��precise[ a�eKUF x��Ձd�r vstt "�tsomewh*r eake�Bn isa�A�źe� � bua` mor�*mp0'to 1�� ssa�_aR�o�.R� 1m Ois >�$- *��:!4a techni� .O-ioscillE��sig�L}�,"Qsd&detaiBj%��1�8 .��is e�, due!$Kolyvagin �� }, GD)%$Zag� #GZ}�� r=ifw�TranOnyeE)��ei��$�eE�;e �] ic9E$�>��Ah6Y� ��0Tate-Shafarev��E����{Ins p��@$�T) \�N �zA�:�$0W���;���m�&�Ero:! 0} O ��NY��AZE��]6��&�M�:��G� u��� %t$b$� ny: �h Iestab( � � �;� ympt�~a� mula)�ver�behaviok� ng sum�& coeffi�� 6���s (x��e�PiA�e `b6�'dEG���B"���alEt��o Se�L5� LU},���mHS�nq�.�0�#�2�)=s} %From�,Lindel\"{o}f�4I�aT!^�pr�� t��x $w?� [&+Overview���5} attack"d�-p� �F4F/ ��qu �6��g%���V55�)�mo�.o� valu} o�up7 =��Hn= . %WI�w rWe~��A��a6�)��a� $��JF}$�& s�Es, f)���essen+Zk�wo*܅s,>ly����!ntype P�6@AgoaN�t� oveN3:� ²ag{�%^8eq: s��f�*�.t �} mf�@�Ak�2K}�;Znb��eq: bn^2(�f&eqqBVu@��. qM� %u� lit�l�1akGplB ?Cauchy2�`��obtai*Jj" �e�aEFP 5R �\� P;\�=d^2LAfB}J� W��> �g��Q�A-MO&tah�b� -&w� 6js. .�2Ew��yB} = |�F}|^{��2 ��<)_�nF;!�p6�8a2�� ywajr� �� ���)-�a� ` crit� issuBE��s��a ?� 3rM�� subt٥�{D ���~ssay��{ �<H=e� �2� E�� ��wo� � V� � p��@wh�?th�:!*� N� I�In*� &�Go7~�*Cus� bZ �z�qU�S�C�� maxim� h�� �,�� �is��ȝf�?��� .��[6�9S͚� ͧ:�'6}A�elabo�gupZ  wh �e2Y/S�@�QHit su�� sae ���ZtrSv y re�+d%}he�ie�!%-YM$biu&`@polynom�f$4a��$}>�. �LpurqE/� ��&� z�S�lwӬ deav��oY$A,ubX$�kt�/a*i@�kst�Lh^�)�um�0on up<$U$ (on 9V3)&e lL��|A!a� 2�influ' �=�AB-ec'RM�$��oanVt�<RbհA�v� .�� (� �� its ef,<i���ec9�3\Eumv�U�U6^� �{T�6"I�"5�"�cap�B0It e���e���) &� �$�$�~�"�X+�)�"%�m�$��%$=8 b19d�, d�2+d�ypm���B$w�C_0"� (\mr^{+mw )Xw�I, $A=71�B 2�seN�w_X�= w �a}&: b} ��:� *R;*} |S_XA�Z�1S} w���A��C1]�I $I��u;!�y�F9� � ��[ �I*[� show>c .��) \zZ�bX(5) AB \widehat{w}(0, 0�,ft(1 - 2^{-5"� 6 + O(BJ��Y} �e�> i�q�z�]��( s-�e v`�U$�9< 7/9� ���4X^�9E�S%�fW@W=�p!� in/6 LUMn�"veZ&LU}>�.LUn I�1}{E�z.�}* Mh )�zm c_S:�} as $XM�E?a~�� � $c_S� Az(�ve)*Fa� Qt%��&TcS}� q�ty $Q(p^��*967Uiv Q&O)def:Q�Jm3%�E_m!rta�feӿ�%W7eǝ-j`֥,ow�Isiz#I $U$;"bp oO �ifM73Ki]r�st����b&y(MfEc%Tr�����m9 )��;z9(y careful en�>� 6~a�  quite��V�i"cnI`JP n�2U\h�#:mM>} ����Z,Kaltoge surpKJ^�^ methoU�"�a $n$]g�kώs (or  p s)�ua�m �H1 ��q"sumYPY� �ed!gmo��a�p-���n� oldp9va)ib {�]U}Rop"�p}�Vz (AB)�nA@2��Rnu2��(q�2T$ iei�O�O.��\nu�v"�[�$alv�%�DNc'.�c��L߯�!�yI1jJi�$Uli}A;-e J� di� ul 'an0]�A�eAa0 ven!(��Jo��E�}O b}(p7se��n!io}�mV$ e萡���6Sn�g�V�er�:({�p|n$ via��(� AO5g)�s!�>E�#q�V�Z�E�"1y�y ��s� arga�r�it�Y�(a�* �) n��be� a�N �� ��p. �5��)I� �hO�4�w��N& S?e�(?Ł Ui(�+)�*� ��F����, sit�#q*_+�Q�)!�RF�QA�nVi׫a_r#� key%�� |`-"5*\A# '�j1�%) �& r4� �J� , Brumer � B}�e. 2�$U��X^{5/9' gi- e � $r #1/S� 9/5 = 2.3�6$Heath-Brow�L+!�wed\� 2/3:���a+/�gA؉�62o3/�*�(!d $� ijYq649/7�5/1_K1.78...��u& ��<�:�!s%�N�F�a!�_�|!��F�]4s-(lq��c�FE%�ed ��Z:bGRH�) �$%$%�xA��it dem:�d� [0� p�ȕz� have#�# 1!� S1"�yx�#�s�.��s"*0�wejcan3 co�.s�� ��)[�we�$AN&%act2awa�b&��2b*WA$%�dinousua�i�ofF�bT:$+Mf"-e I�!�~^B���3;�n" 3toi�2��an $I��2)�i\�. At�"!�E��a�&U,j`�VAJ:^�ysid'� !�p��/;uJ��o �}�-.��G��� �T .o �.i"�j wastz;%\nvolve�uG�g��M zero�4a�"M>7�t<y ignora4th# <�a:>. Kowa#N,C�cVa�Kam$3 w��jto��l#�coѸ{.!��"�Wof'4'��llbE0 cusp2H �3qJ2q >free)�g�sharp.V%� high��� 2���$PerhapA�eir1��\omeday��I�E:^u,~houghy0Et�H9vac\�C6�5�A8(!�t.�A;!�fu� &� I�>}�)l�p& ��e �  $L_U��t�U Nf��w&?U�!.�� � Ef`, inac]7���� curr(� � . S-�$V  = U N Ao!\#%=. nu}� w�k-r�Gn>/ �6"%{^/�A L_{�*0= o/:�}�dL_V&  &��-expeci�")aiA�b'�i rL va -�=��4)��al*V!&^-O>a�. 6Zn�;}�insA�tto�l!��,�aiat �y &%�. ;zexpan�LAVN);�h� �{�\2K. �u�+n�)K >�!N� {a,b|0�R b�"� YAvf�A�#Eb}"�A2,AB}{\log^2{X'>d:�b!(.9)$\F�n}/"m Ư͢:Z!�&F�$nG g*� �E��<a�*"v"odz(a�7 M 2m&� *�9 divi%�!�) .����*�g9�()$;=g R��+�y�|"� ion)e}IWlikew�1�2�=�7.I venRv<ed� s5�s=574%z^� J!7z541�b \� 6�a5Gu!&� �L ҍ2�th$BQ6Ų=: n un ��%�N. Of!;��im �R(p� u�e��2[a�.�I *[Bn��VS�֍�� >���y][ - $O���:�2�)-#&�2.3��i�i)�d!$����y"�$aB)3" -!�K(��NXa 8-"� ��Asc:b}$�#"K4'4r"�6 �8ee���)=I�Z X$ (A(d��!�o.,$)!d� E>w�re��� r@��"# >�*y7U�2� �4aly$@M���1\ FBR5O(�%!�!9l�by*�+. of <Miller} ~App�� x A)"Bsieve 8E�n qb1!cS!c�g�:D=�"�"%#" ;)J6!X���su iO= $D$ (O"a9�two*�$A�9o<+suO"�:E�~1^��i�A!=�"�@E�B*u�f�Cor��s374�.B@LU>�-�@A�immed%2��4}.DEP^1�!L�� a8 N|�s a !�z�A�%O>�F"�b�C.� =z�(I0� *�\si��W�^R�� 1)Z}.5 �eJ�.��FDYn�dM e % 4aŬ�& ." ":�*Dto�!�.�9�b}�/9�+unsatis�+ �F� trea�V0 II�:�� .z� a�E.z 2�D��CeZ Four�8>46��a�st�%����PA�&0�� .=� (� eS�Dpu�:+umd � i�&sum is `��.3Ap)| <9>�N^{7/9� va�;�b�ŕ �M��.c53c�ctٞBgtude,�le!?)�ȩ�K:��b&�2!RYpVpE(2{un��"6G#j5:Em! desi1�[^ of��:" ��sMK&��o avoi�H"�&A�"E� J*# e&* ��� ng d�� fut��*,gI.O � subcon��� $���N^�>�4y�\dMb$ � 6D2�i.f b} (O=�H��ed)�B�.�,?s $�?Q:��3�%2�) w be���s�_5�&.6�8 Moll1#!{�#b�a^���(of>~do��� bae fail�N�xV�� non�2n p�icez�&f/Hof.$�}&4�a4�E,"�7Vzofyva�L�Ji�a V�d!�A�D4��!HE�4 as��-5Qkf)$ occa-8 � s-R$*;$!?)#e*.5�!�.6blog/ ly X�a ��st>HA�IAI'B�B��aja mI+-�M(�(&;�a�t-�!fn(;one hop���r" $=9'"- eq:Sf�&&�8F.?9 �e"" 7AB�8anbB92sbs*D9M^2���2w�֡.�)�bo:�6�Q exis��%�� =�X {\emdriorib"��� pick>���opt/�AcB���; � ��t�P\FeveYF ,Kon�ed��Fs � 6"K2"�JKM3� "�!Q-S@CS}��out� wee92��;��Jd"K'U� } M(*�6�M"�6rho_E(m"�%m}} P�\- {{M/m}�{M�VH>�,}R6VA�de�4��JR�Wh1}{�2�I�mu4F`7�m^s!iq�*6s > 1:o*-- $P( �i�1l.)&� 'Z�%5P(\�;A�EW�H�3�b!���Y ightf�N��.' %�Sorm(2.25�.j�� = x$W��>,��(a?B� LU}."�5� ��,Mz�*M� $>�'et"�"t�E�$A�_6:�+�y3�#$M�",\kappa}$, $08=(� nuF,H�,� �� �eq-)Q�z�,M(^"�.6j�,. %2A,8\end{mytheo} T�Che mollified analogue of \eqref{eq:Vsum} is \begin{equation} %\tag{\.( '} \label:|sum_{(a, b) \in S} \epsilon_{E_{}} L_{V M(`) w_X(a,b) = o(AB). \end{�Now t2�version� Theorem \�\thm:firstmoment} becomes�greatA^erest!weake)�aa�p|:a } or:'}.E�centraB�g!D�sum $iqE}.�_E L_V$�ear/iFzisI~harmonA naly�i�XE�$tible withq$M\"{o}bius5. )conceiva1E�(an eventualyA�,equidistribu% of $]c,_E$ (perhapsWdi&al!�8GRH, although i%~0not obvious h�uat.swould�0useful) also s1)DEFB��$E�0$V =X^\delta$)some $  > 0aWe a likeA r�ra�is bound O 7$a�smaasa?s!t. Ona� �E�ach ZbXprovea�6J�<%� larger $U�@Of course, any im>�oA%�result c lead�an2,muupper �q+Hverage rank $r$, so!�reAP0already motiv��e�is diri� . A natuA�� to ea�naU� vari D | root numb��s � suitE�us�6Cauchy'A�a��9I��m$ necessarysconsiderads such!�Q)L_V^2$a�2 M^2(E)!oWA�followr tꍀ% coll ��)| s addressa�a�et�!simila � . SAx�%�s mayAsurpriB. We ! )a~ �ing��myprop"#  $:LVsquareduA� X^\alpham 0 <  < 5/18� ThenX!fa�Zeq.Xb9&� %g&i !(c_1 \log{V}6#} �Ws!$%a�%�Xr5�}�q$(expected)2?��Xxtra logarithmic factor%�0n obstacle. a�m� attemp� Q��JHba� y!�!�ݍ $L_V!]ItF�i�25�� .1�V�M:� =X^{)�}$, $M!�{\betw�$  + 1�,, !yA� uppose $Ma!+M� form��� r" N@ne >,e�� b}*� M92 (E:M})^3Fa .?2� (depend!�on $M$)�R Rath han dampe !��� valu�f)�5  ac�7ly make�e�� �tan�ly Ir! AU/expla�*f �v phenX o�y��ided byn": M .!� $0<-�m�� s����r�3.�6-*6.3��%�I d wh�� $F(x x ��0d}{dx} x P(x)&� �m most��N�behavi�d�A;Y!tErIe2R�w�~inI�ente Bsiz��T , at��st)�V$ rela� ly���:o shoM happ� at!n <Q e �Z�m�k u�2th7�"� in P- 9 on� !*:L��y�Oe (beca��we!Eec�p)&yl"F yo!L-� s!). � �)qa new mE erm�� � a�sG q�\�!$ ar. ^cur� J�itself) s �ic�@&�  �. DetC���RisY, subt�� � ue invol� n0druple integ� of aA�io pZN ! i zeta.1 e� .� y�'eJ cAVo� "� = to m llin�O �z pA�pol  2���yresidueb ,It turns out=�U doesz I"� Care�s� b��zero, bu{ sti � Eo� �R�i� V crit�L pUi uca A�rtQX er (<Vx�� ) deAbs aU}� �yH,�B:'{ �$L(s,f)$a��<, achep $f� H_2(q)]  beA�a Heck~�of weo <2 level $q$ triv�4character cusp�m &0prime (note e[ � $f$Ar���M( �a=F-b�9 �>q2` �<aM  < 1/20 �J $� = \pm 1$9X��� � �� ier}��{ ; ��tack{._ \\&�fo�}{}^h |�|^2A M�QM�QɁ!�? ��qR� Z4symbol $h$ ind� at)���=��mi���p��Ied,� cis� �� _f$b2.())�_f :=��`\Gamma(k-1)}{(4\pi)^{k-1}2E5%�0_f}{||f||^2},B�U!E�a1Petersb norm"�A } � $salient feE�� "!#�|@or�(of magnitud��e�� .�1� -1$,���j3s�(conjec�ly)cy�� ��l  va����pointg ���mofN] waysnW4. B. Conrey hz�:d��o m�ca��e2�V2.�Ae�R�k0been discoverA�� ��publishy��o�� pheA �� fu��Xri� y,��o��x �1V2M1M2U_1W �1{V_222M,� +M+2*M� X2 " 2� 9�a &1 \neq��2., $�&�_1�D� �ea��R� {V_1�2} ��M_2�N4v� 4 >0n9ɤ�S� $)Y�! 2$ (o(th)*� in whichiwa�terpret. = 1>5 Hav�I^���e cruc��er betw�r. !�a3prebo? �xn�w�*]�B� prob� �^)F�c=bve��r} oneav� r�a� st $V�) u���methodx7v��i=u0�S�� di op_m s!DZNe 1� �!n maxim?x��do!�soCid� major�p  r esti� re�d�erB�Organiz+ 2pap3 W�"�nH��' thm:"�}n� B) LU}.Y) ��I�A��� MGS�/:%�};"�m[idAte� ails%nA�(ha�)i`of�:p�summar9changeE�R� }.Ya;e�&<faneedab>e:�m N� P]InV�&� }Ap�a�mul�)-�V $y^�_8x^3 + ax + b$ uE8cer2�ri�~ $�nd $b$.^oof��%-%�>,)� "p.~NG �gc�� ^[; �!b�EX!*}h!D� &a �omitted;!�quick, ketc$�m�1.  �A]&� 0!��� (14.65+ \cite{IK���=���7�d� a��-�diago7t�{ (aށk" answ6*0C ! 2��qm#�e�2\��xq"!�� iz$arly ident�to � �z�U*:�$Acknowledg� s} I��he�l+�4Henryk IwaniecEwBrian' ��m@ɞ�ruitful� �#%?_tX,David FarmerE help 6m�!�!�!�J��is���Tsz Ho CV�0Sidney Graham[� discusD[��� ria�2�A�re,� �ar( �!��e ��enhanc�sly�prl.� work%��� {Rev�6of>"- *��Iqh�#��ew�ev�#�G erti�jy� &��&�$$ &�O  b}\ e n*5q�eq:eul� _$t} L(s\^ (_p \left( 1Y#f>%\lambda� , b}(p)}{p^s}� psi_{N{2sb %)^{-1>B} � A�$p� 2$,>�.� �6� = -�$1}{\sqrt{p�Y(x \shortmod  � �.f }{p}�):�} A�$�N%mAVHprincipal Dirichlet��modul�&ea{]$N$AX=�(J&�is %cribed�~� deA below��For!9= 2"|%22!0� ee# rete��#ex4 e%�=�%�$�)t./ to stud��� m�Y�s.�b}A�s.�yy g `Z! ' se�rf � gers/ 'q����y�%�!�ory] 60$�example)Yye��TWiles, Taylor, Breuil,�Qad� Diam�%��Wc�T BCDT}qcofted=>��L%�B�E�I�I�N}}{2\piU�^{say�(} �t�() 6�B�is ���nd �sf��A�JFj�1-�CAi��$�>K*q�"�_E�zG� h�-��EA���.��%rma@p��M�"Eva��1$�)#In5tU)ar1 h�-1$c$l!#7 =a]p bc%$Timn(��hmeJ appl< � %"x �"�4Bir�#Tnd Swinnerton-Dyer. %i� comm�(believ� at ATaJ�(hav%0,. 1$ (j!C%2 &igI c)&� titukb�J���Thus, s�s%#� peakingib~I �b�ftr�$d�"A]"-�>�':& pl�R&or)�nd�At rol 9"mARproblem�,tds��eWno% ul�!��' rule�y *�-=Ey���!1$�-aProoa good6��;�fr�*� fore"$p � ��ng gco%e.Z6�M�.sA�!*" we sh�A$a&$*�y��'z��&�aime@���ey�t�e�.�+-+sub'a mini*+ �.�i�2�a"�divisor1� rimina�$\D�)%� 6(4a�27b^2�gmeasure-*b�(�eE� $Ez��A&$ e $pA#T� �Tno�@ � 0U��i)�/ea.�ly�Kpu���(Tate's algom& (�@Si2}, pp. 363-368a���s �/�an �:$3�po� a�p$%<� . iA�e if $E�Ha nod�my-�� H�Fwo64a$4�b+��inologymd�+�9~r multi��2at!{ correspo�%to�agW �o� F�<� vel*aEe spe8�? $2�a^��J�N = 2) 3^� � *x p | M�\\ (p, 6��,p: 2�$ 2 \l"� 8�$0  q&5v+!*K es�,ia���)fre�Th"/�,AZ \U$�]� as2w! 10.4ANY�.� Iz[g �3"� ook}i�&�(� o$�"f :u��,�2lF h3aP>�j�.�- E� b} : No��"('.��l>�B �*F�4= \mu6�Aft� a}{3b"� @ \chi_4(b) (-1)^{�)1*52:�} m $ ;���z3&n� $4$, $ �\cdot} )IJacobi�u��)plocal.+�2B0$Remarks. T�#͉illustraR e&{e-Z&� m"�'N�Q3"/'2E z�E.���l&^ Jk1�polynom�6?�q/ curr�'no�4�{ to ad.��Z  Q�n�NI�~#%���NM�3�0'=6��0he odd =[�/is �n (see�ZRgY$Hap� ��hQ��ZB%s]Lp�� pla 6��A�^aHinW6�]ru��Q"� { #}d��� ƩR}�1Y3�q�p =�z4s} 1 & \text{��split~; \ - CBB non-�F[" �2�8*} Rece !fdefin�3����gA� G i�&tntK sa�f���|af_p$-r �5lop�'c[ � n el�am ES(10.10*`Knapp}UV�4s�4val�to1�Z�� �E(p> : *} SN6�A\���i�n�� $JN'iub!ab)�w�n�6 &^2�e.���M- B�*;(p)�a2S%&m�'J�9b}()�� b}'JG���Kesbri��$Atkin-Lehn �� 9.27�&i�M,. Unfortuna=&AxBDA�\ "�)E�s4 "t(m��;eV���b4; ��Ha}� ^A�. icit&' "�)*b}'aSw/>��� clea! t �r2-ist�g�&$ �@ $a \�6 v -3 (p e�$b#2 "3*4 � �LemmaTl :param�&- �W�)s�ute %)M��A|�-3a.L� �# �c^�c.�(. LikewiseV%��c6�po�7y!�ng�hto $-c��nD6,)U,; S >a$!��>�") eq:deg�=t��cu�/�>� �s} ikjydS %&i�� \\ �E-3 M2jU)2��U(x- Q)^2(x+ Q/*� 6�&�*6�� x S�Eg�_2�= %I�mj"62��Z1�60@ � quad��c Q proc�=(�1��2, ���)q6Q alig��I�`bn���b �6� 8%@:A�!�:,2}V+.P3�$bZ$s= 2��s2�{3]c�6%*b X (b-1)/�?\�6w � )46� � 1�y�!le� � MU �>2d��in6 B1y����e^z ix i W 2 2� F0�!�yet�0u@eno�=&2�&� *�=���+nr� d�=re-,! g8;J H� �+ake�> fe� es (��s $x^)) y^4$FIv*$� 2y^3H-B2}7�L>�(by Helfgott�a�~! �^F1. i 5ce, h� s ��l.. �f��"*� � (x+a)(x+bV�ve�A�ed �H�Co(H=5.2��His# �%��" )&�9�% ociad�;y (.A"�)] homo�2A&i2��!� degree $3L� _2RQ.o0$ab(a-b)$ (upaGaAV!awo�on"��) E�*R%8 �=t��-�n�~�$})��j��mor�(� � B>$F �VN"�?�$ to*6�(g+C�n.fE�.eR�One� �L�[H� &<(h3U9- nu}$k�# $\nu < 2/%��.N\:RHr!$VL 09$X^{1/2'*�B}$x reasu�'s (un5�al)"x,6su�!2$handle $V=jE\XB2�J3)*e�� ��s,�($� a�GbW 5��"�9![eass$� 8{n}3n)$%�be�$2>o�I�0*VH(ɴw�fre�3�A4�&�A ork)!is un� �C� pply*�moɼw&!�2�@���2. ell-���{���of*� tw0 a�?9it�&JX./6�aN*!�We��A,UZ���E�a ��semist�-)���6�5Liouvil��F!A��;=H1�(is"r4*�>�"F�!�n_� �IlyQ�H'��?9 9�HQKp�,>� �J:M}"c �/J &0HOut�2D� "�KZ#v?attack��RmAp�=simpl�E�FZ�$s4 a b�ess�sW�write�=UFK��ae�of Fou�Ico"bs�$ab�$n$@> �)!ro=7 -() will .a��D> �"�i�')a!m6instructo�  -�?� F ll�7lY�� �9N$ (say�7im�9� 9%u�SPf/7?&inJ"�J �;�7 S_2(�#_0(N))^* 8{h&�f(n���_0+ R_n(N� *\ �'$ i1�it:�/>�dH,{le���AW�+����"�7on �G��E$n6w�� �FQ�!k6�:�.��u�eq:QRe�FP�)&Mb}(n))n} $Qn)$2} {n^*}^2�)R(n:F }I >�*} Emathop�m��}Nk)_Y��>h5O nd $�Ip EN error� (U eUda�H!>thr� �0weU conven� � y $n^*�&=n} *!&j"!���E�ho&�.� n� q U}%D� �Ax$U$:4� � J�N�Coc!Q@ma�/�A��6t9M��8"�'U�(�lA0 a8Q  �@�� �$ts)��:Vaga� a kern�9mo$!�k( 8 \�, pic�% up! U�. )��WqM�gqu�)8J to S� on 5���KMVdK�s 26�%y�U5�F&2 QR��� a us'%�m9L i� ly avail+77n)�.� W�| get ar0M4 by���$?n_1 n�Z(n_1,aD�<$n�7[E�$3� (-full (i.e.A�s'ng! 4s, cub�F�na��A��&�{�(n_w$aI�|.��� !��4!챒�&a B� 9J!m �e ��Wy %mGMn�$NiMi<�P���  !� �.hv (s, u8 asymme54- �.�  �AA"$�26P%��sof RH�be� ov=ut!�A��RH� waE�.*P�$U�FV+8%����4�� of-0� i�+aj argu�1( t�I| &9 Pr�Kry�J�wq � [`� goala; "2G�#u3;A;JO��$�VL9 �4)"^MF*�F�<rqli�w &C�!2a�J�.�U=�{m)�M"Arho� b}(m�`m}} P)&#�K /m}} �Y02\�n�$m$-th.� &5 !�$&z0ser$1/I� �� �eMYa fixed�Q#�hO$XA�m9]!.ulaJ1�k�Z#<} �m�c �(m), &&�k = ml^�=ml$��# l, \&) =d1> 0, & H�a2�.�s.�<�(sk<ba�S'���Euler> F�He6 uct}%,)a9KH�<1=�:T*1 Ea}_{�A<q]emu^2(ml)�JC� m} l} �2{)) }(l)^�l^2��p�3 WE6Apr��2absolut� !/?dis�+5MWnow��"5,often�&HT�� $�-M$!� sett�1$P�L0p $x <�/�8�,��M�G_Lon"�Z=��@9�P �1$d | (m, n)>�du .�mn}{d^2}�F�p�hJ�Z��eqzYexpan�3} �?a2�^d l I}_n  �4 d%>5mnv mu(d�E�dl .(dl) Y.��2 dn}{U&�Vd!�J�:} B�.inu!�we�� 8p\alq�my�#} 1a gVn�:t $(n)�den[I!�m�A�.(es-4c��-m'>� t ($2�,n2�p�U"`J�� �)�2$.�J��part, � , = n/6*~A �P(\phi: \mr^+�"arr�\mr!'_ ooth�neg(&J satis�SJe91u8�+1/��i}X \geq�7�"+ ,8A� Q;$x;�N �D!�i1�T@FYYi�%�f�V2+V�!} a��+lema"a{Ix} SeBg0*} H_1(d,l,m,/��:�%.)(mn)_2}{�Tvark'}f On GRHA�. yf��vu�}%_ �)�>�!;.U�}�2U,%\\ + O(X^{-�} � *Ud�T� on2�[I<�'m-� Ht//�i"�P))e$�F&>^.A��� .M�I+�%c��sU% trunI�; vi` e�Ka��Q>�ef�-0�<begin6"'Yby��RO]D1 ��! �>ty"� .�phR�RQ�m�.�R}M@$=1)�Yto*@ LUݢ�s-*$Q�GM w , rms,�cAH�*A �A� eftEy���S�$s:� iSA�):y})^j/j!A�N| $a_02 (s�+P(0!0$)mG\ �lj`verb l�E� \PhiU�Mftrans� !E�$ TaN> J�M!�\9� R^{-w} i^w � (w) dw. %>W &}�afWwT_2B@w}2W2@*} U�C!0>��$P�-�9< so$YbF5:p 1�} S��(uv.()< )^3}�t.e0Mq0+{5 U^v}{v}1k Z(s,v,w) M! v"> 1+v) G(v)91s dv dw:f�_� C �jB �~3 � 0{1 + s + v} l 2s} m�} � #I4Ef�/��*} In�/ ve" a�.0 5� v, wamp 2/ ��k�(}_{d + l + "1� L p^{m+n}� *H d+l}�4 d+m}�2 4}{p^{ d(5"�l(1+2s m(1/! n v)}equ�-�erJ� a .uF�1 \�)"iif } m+�oO \ p^{w(m+�Z- � Z�%Se� %�� %L^*�A�� !���% i5wf+�D�� %>&%a�pu�gw=�/l%i% �1p���&ve} �E�z~ .�$$Z$�!!="MYn�.$0$.\t$D~- ~�Kor|/�>�*}Z�-E���E}r�-:A�F'2�EK')^{M~.EN!v}}FB^2%�� -2wNJ.)2 '-� \et5C��, %a�vE�<�A�5 �SaJ2vC , ^2 E)}05/��2s+.3� v) ~ .^*q��}{b�*� �� y'L #:��! �sy ��:�� ^659� giv0H#6�) �X"g�{�W� �4Re } s > -1/6$7C6vV (s -�v4a�.O(v2!�n /` saC�eta_iyi=1,2,O>�an:�*�a�tQc"rg� I�"X $. %M�1k%;DnRs"*{1- :�$p^{-sg�q��{-��!�a���6�, %F�uni� ly�@ENE�k��&$N �A�5?�8)ly deLp"EZ=:X*�.��NYkE�eI.t| weak{Fp&[�=�E%F a�C��>~;� �P"�!/jJnreg� ��!��c� /��% %<uc� We�hlU5![X/��m�E.$�! _\pmkZ���-�6�v%D{:�w�6� �$ŵ,{ .E�*. Byiza�]3u� q�(a� �^2�8-:pXDom ify)!�. �Z = &i�e�fa�� jNi�) y�2�6^=+>!.���bFb�%�_1 \3�r^�2!-e�Z�.EV3vx+.g\�6 +A&B �zs+� F�r�2 7ar�)�M36 D E2٪ P 2w: 's +y( 2S� _3� qS %LetR� u�.A & 2� B �.w*} )h�y�� z� �$R�?*?Y&�Oap�s���u2��:� M_t$��YedB� . BU>Z���j� s &�M��1-�EL1�(l %:&N5 ©�����_t���B�:� %.�>� FZ 0!;� �Fpen,2'�dn5je ed�,$*c2� s0�v[ 4z��.1%�:�m.�uLU&/�S/\�B�|���"6wS=q 3*{s�,* ' Q0*2to�'U �R"h � ^ + it��l_{C '} (|t| X� �'�$H(2/�3�f�I=&�@ �L_i`8A�G$+5M��&e)"D'5.�%��> sMi�p�aIns�Va*sv3(GM/f�S� ^9E��)�&�A/6J�Tak}$ .Q�� &�43PA� v�g� =v#4w5i<.45/6E a!cluT!!��  i+^"�52�a!� lace�  � mod�'ds+"�m , say $Z_] !�%v)� �/&-J��2Be"�!��\ ula)�exceptk Z $�d <%>,if�35.�@�V�� _2(p^O&�a4-(p),& \qnk=1�^kp^k[ Bv, k� =0P�`oaiQ&�/�6< %� �;r&h�le step�;0I�C!?i>+:��)L)�Re!�I��SED�0�qui609.,*n� :>L�/)�compeln�=�!.Oo�F�\"wJF"�0l�!vgon}Z� A�:��!��N*!��cum_{dkS'&�A c | %\ cRQ� mu(c�*1{�Kn}1u�wk{"&9%= .ri6,��+ B� �D0 &�Zc�uXa�*n�T(�%�%�!mAm!2Hh,"�"�!AB�>�!9�hM>��o:�v�� ESR� :�= ��#��#jx,� UÂs"a�&�3F\^)E'��eB|ed via *]Min- �mIu��W�Uw�X ulus�Ebe��. "�!8V%T_{dl}m>�O��%���&�}A� 2� j�.U-A�����FFand��*�T90e�d�Kl�.�$^2!� (de�} 5}b>)*!en:�Hp��asJ��H&B-�>�%��zA�2 :k1| Z LI% (�>�)+0 j-4L E���6�I��]�4�a)>�. Tdl� }E� U�F�'>0ny Y�D ("�#�12"=2? 2��_*��*$dl�IUM, VEl A� b�B_ ByV�we�>��Ox2c��6�(�@,���+ő_�F>�(=Ō�FX�!�3� %� �EN�A�bOT_>T_4'�wwa}<Bcar`:, A}e3ofv �j|as.�]�N��"��T_1 w\�� Cgiv�&�&iR��$&t� h#�$ �s��� ;%�6o68Ut��26� = 27"� � Y�"�S6��6u; N%2r>���A5�M�1 a��^MG>�6Vc]u&�@ �~$b 9\ $27ba��  -4�[�Nc:Y*  d(c)<l`��X6QJ��o����}Aޅ�lz�2��$�J1�7 &��A:_<.MzM1� }�=!A� �+�n B}{c*���� ��/4��=*aRv� E��:{�;.AF ca"�N5y *:X�$��p@n�0eP7Y"�8�."�O )�QimA� *�="�S� n)�/nE %� bb{N�Y��?��ov5thm� rvalsI��/ma���"y(is periodicA�.mg�=$ (�7 i8e����>1�$n@1To elabo*Y,-4���x&�"�V>�"�� p$ (6��"�h;��*�6� e;���s"|�)>/*�+1�� %P-\nXn^*!�Ӈ�� "�^+KE=a��/6yG� 0JNM%�:(� K*� ��!A*@K�cBly�k$Tchebyshev./�=�^/!(�|Vas�WbT ),�)�M��$ 6 )^k$0MByc Pois�z�#�}42wCH��hPo>E�o\aW},_ $�G�Ha&�,yPv.�iN B.w.Gi~�m��eeC�, clas}Dm�jE0�d˅wW quir��&� s!wr��9�a�a� sibi��a��l�#�ҭ]=�#8ޑl �&'s��E��EĀdur!LT  ing. �V�"A:recor�+Aj&�"a]du�- Gaus�.7&����"f\?5\aAC>fr�`VMG_k(rEf��{y*�r3( y}{rٵe.k2�#�#ny $k�\mzFIm*}��_r-Y��k.�F emN� 2ZS )^C7*�&S�uiv 1% 4\i,�#3#- O�= "�� A�F2A�fe �WB IK},�".b$3.3. Next"bW�O]� A�sumzE-v^h$ $k�X"�m.�E6\�*>; a�>�� 8�b r) e+ Ir  h8 H2� = 6�� r) r2D23Q� `-h�XK�{k}^2�Q A�5�.#r}$!�Twd $(k, eaHBz$ ��zvHase);|sC"�Q �.y�8;)��iDMb;9� "� "�2vanishM�U6�1���$rO9jFAl gk&B��� $k=0�Q $.�0}{1}�! f��I�DnS��2A)Rmea�A��4PA�Rk�[I�e!��N doj/"� Xal*7���kP �v�q��v�`n .>�q= F�A&R\�-(n, q)1�J�n�(x-�C%�choiciy"�P in p�-!!�� 6Yoccur�*�]G a(6C@A�1� i n}{q���@of �mI<eَ�\T=T(h,E�_-A2KT��YM|: h�xk:�6�F}2��m!L����. \qed� �1��m���� b�c.˕�R `&G_'a�s,@ z  $4)�ev27in&}01 p�<To aid��7 .��2tW") ���&�mJa�8j! �B�My Da�$( �ma) ���1/��r}$�2{(&b, �_^3G*Ibva-G$�r}&�i?@1-�F�������K���gN������ea�:":lLtF%��;m. U�\nesaoso-��eWxg j � v '\� 2q9 �;m:pt� *:(-�ME�$�h3�(sSBepa� argrJPQ)�&�)$ g�� &Q !J�z��b . %: 0"7"�VAg *} %Ih��%2`� ��$_p (r/p) (&�r/p�@F�'m{:rqI�oD%wVR1]� )W�17��1H�;AQ�(=g1_e�z�^-�b_p2�����-!�v�&Q"_pACQ�W"�w+/jo-M)_p$'s� 6c ^ZcM_r} � N�UA�ch �U}�"�EߒIOn5��u1�&R�6%^�%A*\ %H;.G(z�)5�NJA .PzO��rU%v"�$59�aZs��QZ~�& :(U&�.�"�BV�#e�e�(o������)�A�vs immedF_l*K��e�*1� coro"��^exp��� D = 6O�^�h��� �UI�T+ :�)�K: }_{D1\.�#T Rs  h &� .x �E@)�:j:  f^2 Q� 6UF� �m-t�,-�%�ef��Hf��E um aca�Q=`%�afa%6��))�6  %�rod�:2# @&�%&x� O6^�6b�>�] >}{p"� q�.X��r��6q)��p!���%�.�$4� } �p�V| � �/%Ok�͵q]��t .~�,�Aw-vt{2w��M� T�[�΅���b2��sO�n�J �~��%S5m(u�(v � ��J�^���f/:lmn�1}� _� 3.��N��}S>5 !.: O oYm��.4b :+�AT��is ��� 3 | oM�W�Z��dR:}#� } ?y�].C�� "'.&Q"e���5��%`^.7 }�f� :!E�F4&&s*�� &���#��o�/S�%U&ZB�!* �(r�9��:}�Ia��1���cor���Z,�R'g$tE,~ e�(r = r_0 t$.2[�**:U.v)mH�EE���! ;mod^�tq�Y�x%߶��v"�N_{r_0�e r_0)mkm� �2�tէ  �,kt}9Y>�FX*=t}:=-)E�=D>� !}�:w*R:7)*8_0}.D�F.�A0U`M��E � ;.��a� Ab22 1E�6�F�� 40� � ��و$rZ )�K��:)tm$tyA2!A\Z:��!. t��J?���i� ���/��o*�4 b� ucR1i~ �2� AѪa�N6�_0m�_0}i<2$_0�I_0 k ]wt} e��L)R� _1> ��:nF�}�-� E}(7y��1.�16��J6]�A]i!��7��� mai"�E�ok�Cha���%"^$o:�p�ih�e��^��]AKUqymrU�#def:QlVy�et$��5�Q_{t}�Xz�^*��9�=�0)�!q .�(r^*,t)B6wMu����8$tF\ ŸQ �Q_1�F5��N Q�@)"*�w64�Q(r^2:!0F��C7 >�It 8!�7� ��-gP&z%{ $p=2"U�.�"�4F߃M���y�&,�-e)z!="C&&~.�&�<:uZ,J0^��?��V�^ BFU^�\5v�p(p-1J' ��7R/y�Y $p$ pairsB=2OJ."/p!"0$�mi���Q�6N�Pcw �1�J.�% a�%%ma:^? )�&�M 1�i�P:I Nu5�g9�.�$���+�.�&N2�y� �y:� �Ɇ& �����]D sJ��(�- y^3N)e(x- y>�" 1����y x�� �0��Nun��$x = y5e�� um��$iL$"� aE�B�f� ma:Qpkodd��W&ax�l��k$'n�`)��W���"�E�c^� Y2},"h9.2"�5 �G�m%5od !&P >`��1�}��f��<{2k�V�Hi^ja q k} c_jo� 2))^{2�Vɯ^�psom�(x� s�j$M#�Z�~?�)olt�$2D�, ����za CN8+ne7J kind��r�~�.Y6�)2eP6}_��ex�L2"��}=[ )�Vȁ9d�}vE p}r�6�2�s.K(U!R�I,Fc����f�vB�+V�� k6A ��6�� N!O*�= ���i�$^'A�"Tp�veuR��4iZ���-1&Ŕ�>Uz2ckHse�}_{x_} ldots, x_Q�"� E] %2�f6�J{j=1}~�x_iE� Xx_iA{!�.�NT�Fe�%��a�|on�-� p\$%K�cn( variZ$|)*aX$e�$$F �2A�!�: 3I�$� � msu� We�$"2b�L<!�so� "�&� lat٬ �c*��x�-�� ņb�/apl"S ����S'��6���ell2�U��� � �oM��n�.|-1kx��=�h�BI�wing� ���"�SumM0,�} Aa|�2$���.�&�0>9cs�O� e��LU\<, namelN�}.wq�5ta�@��@�Eb}R>"�7� � (g,2�@8A�,g)2�r{b�C  }}tg^62AH.(c�4�g bg^3�1���*�+$B�S�oFXP�$g \�;�Fv"9RJit�re���:*�E�9:"� �\�%%�cal{C}_x�xV��lR���dE�i�� eq x��.RN}_� \SA3mz : |n| �x \���4$Y}^{(i, j) =��M^{i} \tisg�^{j}$ (R' � uperscrip��3.G �tBv�� crossB duct�J)6K $J#2Rfwx^ aOf :MTRT-mr {c%ipoVm+2?7�/,d�� $VED� &ߧ"� g, 2�.��^L.Z�2�Q%,� 1umB)}_�(rm�a'e;)�U� }{A},aK}{B"�F0 EA.��E $re�R$8e+div�ir3 S�/0c = c_0 c_1 ci� c,g)4 �4| _,� 2 �h�(r,=��yF�.�dr_'�C�Y��}���%�A�Y}$a��U ]�.*{xA�4$i = 9^4, j= 3�� >"�)�{$x�:_2�?( r_2^{2004}�w46x�*Dv$F&N2�$*4Y�f��|F(y)a�l:i.hif6= y�4at1,R� |=2 j|r_2|�.lNz -�5�u��7[iV!����"� !:� �=n�A 'ha�JDZ= M.T.�{.T�Cr_2Ɂ2�(��==e>G��eq:MT} Q= ��<4\widehat{w}(0,��L(I� vw Q_{c}{a'r^*{}^2}(n1}{g^5:���*�R�= % YAB���_��-4��B} Ag^.�Bk��\\ �0��Je |$^2 m_{1, yڈ{3 (e)`�{4 t(e)Fgh6gg\ \ �HX*� (k_1^2/e){2_| tau()6Ik_11� � . � � 'r}^3(h_!��i w_2 ,!,��, y�%掍s m�8%du�2���y}�Z��%.:�y} G2G-��3!�9hL� 4�5G)% �W�V�` varphi(m_d!^2 /e)chi=�m.(/e:�f� �:! (t^3(e)/e��}(��R��_ _2 =X7 �h_1^3 PA]! }!�^2!�!9qy�.� h_1A,!6E~ 6,y}�� k_1B7a� 8 <̝�]Cz�{iA�,5 $�0�o?�)3ec�bR�$A ��lV�"Z �� $l2�AXl^"X�*2�TA�"� MT}j[n $w��Mi!'f"�PF�a�gKo 4�c_M8$c% $c_39g�r�v6���&a0A ����z��1�WQon� V\�y � �t�"$Ņ��A�S���j:]&H`i�S��j�littl�s%]��rm!�!�6��&8 ll-s�}�0&�=l2c�G&��-��d�F/ a)2�\�b�.d#p��%rf{ d ulas��۳hib�x. %I =� �is,)�h9 �5b}s�Ih�$k� Yb�Es" 4�^� re�x�J+ .�aN5��$�}�m.�Tr�!nA�1�bJ a',��-FA�ma�y�)��  s��a)3 i?H� �o�%j��SC0�" &k & ��I ciprM�laTo&Yc�mztZ $u� $v$���. "m�y*��"�N��u}ekNFv}}{u"�"�� 1}{uvk~'1>�_&%:J extensNiofn�addto�'}:.a}�:�P.�'���i�.!���RO.��(}(a �$9=9u{D u� ��"��$ai0Al%�i�-�K&X! m���KA*�(�.ia\�sѰs�EQ�Xtooa�.VFit05��4�Fqal nuisLNacr��O � (by&CW�by=��0X� sors)�4e benefiqCb��1V��� pricL��e Q�b�s{"�z�$(c, g) c_4X$c_4 2�x "�X1�BjA:� n}n5_4 N7.�J-"�#bdE� o $q2)^*�m�b$"2q�ye�A�"�?6ZH�y" �0�s%�w_H>5.KZpF}Yf�U 2g^5 q^H�a�h� k6{F�q!F1B&2q%�&Sz� ��?{ 1� g� )�r>�;2 )�( (k}��y ^Y A%2q&H B}!3&�>;6�} ~Qe�!�*�6�rw$��ma�Cby��\JA��(_1 (q/r_1)(��}� %2 %2^*>'2^*.)3)c_06' c_0}U�9&�(���(  凅����n�_:4�$e��(>�qł}(S_1 S_2 S_36K !�5���!�^^� �=Rf"er_�ryFg#b�&c@&�-�1]� �.=6�,.�(D�ar{!&5_1 .�+#E 15KF��="!�Z #`o _�H�N z2�6_2. %2>�1106>22JA�! a(�*Fan"023^3*�c2Bz 0}} Z�3��.�3B�-���F��1Cog��*NL0�u2�S0 6*�*�8:3x�?le�R$SyM�OUxw"�Eu a clos� � ��:B;� weWeq:� Z6 � |>�r_0� �$uJe�N }{-��92�%3g!sygo"8�2gka�A�5�:�/-4rD0c_0H E�J�JJG\� ��2o�\\�y�02�-+*� %6:�"�0��� 1HF�0I��pQ�qr ;2:aQ>Pd5_0^�:�; :^3>�-� �.LrmRYy�'fS� ency��yG�O$h = k�"$)O � %.&>�.�%�}} �7"6�5:}" 5�H.�06���&|1[\ 8^j )d1? %+:(A�JL:J��=1�_�8Pa� = _2o�R� ��ls $Q_c�-�Rr=�C =� r:~J�@��*qr�� M�DL)ir&�o?!�)�'��!�� k�I0j�n��e at�OH ^*A !0E�T6d/i�N S�A7A�kL �hN�zB �cAn�rovЅg!�1%  $|S_2�eq!=v 6�wkqyX:ncdwo >sO iB�s�1 �VBt H�s�m�&Ø&]. �ZAV+�)AqZ�9 E 5�~�7Linu�KbB ur g7�wofol�)eE���\��q��3&�&�H�%5%bvar��e����EmUc_���m�j"'U*nS�/�|*y�� �Wnumerat0df�bh��s���K|.����in�� a lo�݈� f �� a��to�zst)�}�'�)dev�L���9GVh%Jn1flip}:k�Y:�:�;}{k^2d ���x6� �>/��3B�a1)�eff�Yvel�>u�M.VEKu!nO3�tHGdoA�e��lmiE�5�T?o��o*�n&�Ix�Ol��UA&al�W issu,n,��,um�k$zH;d �"=ly;]e� = Z��ZR � 2�c��\F`� e�/*=�"�-�5U�al.2�"_;� v&-� ha��'edG���?L.�Ihc��.)bU� /)2k��"e��h^3, k^օ���."inat�Q[� ^�ni"��| n_0�I(�I74mk$k�In | m#EH$tW�| m�J�� | h"�%�h_0Ձ�a��:��x(t+P��i67j�Y?h3h�8k�D! $"�%7/e�"��f�+E�{ �U�pS ��0 :Hj/ ��c<� �q& F3 .�DN�6k�_{�\.�� {> } 2� �  �� �( �hA l)*/��(-o6� I�� �- �- E<(e'A�5 6� �6 } +~�>  w_1��]i��Q�� �Ai��(B.�izLb= �N� g.� �Yne�e� Ay��n�5e� $eeHE���� $e_i�=��?Ve\K�"ۚ�� $�= �sah  ��d8�2-� V"%paiKo�^�|��{ v"�.&�$Z�xtoyg��YdisplaM�h ndsB�*)�&;�|!A%� ?p��'8X,*~AN$I �2{e"�I).-��=1�( >����} [�� {e_1 %�2} QF/*� E6fI6k�(A2fI2I.fI.WV�&�-�HF8*�X �){a?..��>a.hc&��f���9��!�%�� %��Z��%1�%�f_2�f>�f_265��Da!4^�#f_2�X)�^"�H h>t{e�\M\yl�cB � s�Tw}�a�&7P %�� }�/" : �"��V� i �z focu�#a��56���_1��Q�[kM1*2Yu*>%�^��ݳ�%�f\ =� ��ɍ^&�A��(�ա��*IBp�F�/���>Z���a|afk_1~TaQT��=�I� read Zap��t��&V � A% "g4�(e�1�9 $. B�$�+E�Z ��i$#�%may�ly.*�͠�d lU5*�sHQ$N�fY1}�%p�(]��%� )y%-�&!n &ь�!�"j l/!���[�)��)X[t�*!f 2>�)��M�&��1}v�/:�.m J 2}((.� ��}J���A�H'A� %1�� . sum#��y!�in"0�F_1(y!X9,$%�)�*�1�+e�N�a� � 2�.� � F 6��sa�<6'�/ �F$�X�.�((� $i=9�0�$x�!2�2*� }�P�%�r>U*} != = (e�ee e_2,IU1�0 - 2^*,!�%!P��d,2F�o��!��1I*} 5�=|P:�(c_�Ku� f_1)&l���6� y�vu�a��H6��'JY"��E�0u.I�=ETThe various charactersIY`_{i, y}$ arise as productE�N�m mu(c� :gR0J$(g, 2) = 1 >g)L op@ m_{m�(n}}_{(mn, g 1� \mu^2(dlm: u(dm)}{dlɱmn}%� 0} � eP H)� ") -B�} f2�  \neq 0}b 4B� � 3, y}� _chi_{4� s�� J% \; �  y� /e )6� � �' ǵ� ( Jt1I)�(:� ^3 '2 '"Q &� w_3� � � J�w_3 = e.�ɯm_2� ��� , \widehat{w}:DA-� } �6,y}},M k_1B7%8�  Y.X$2\pi dn}{U!PA�ft( V4\log{M/dml^2}} !�_���^�((basic idea � is poin tof a�0��r.�Drivially (of cours�� onlyF.��could ��e anyth�Ɖc a�] ��A� !Rdetails$ra� �cal/�� essL \ly already been carried Uc cite{Y��re;�{d very sc !�&� �B;%!sum (19).Z haI)yp$ {e� tead��1�buE%j� ��t �nalog%toR��O�perficP level�re%8two9"( differenceB tw!'!�& sums��>�)��I�E���U Qposes noi,iculty; sinc%n used]� methoQ b��!Y.j=�W si!(!�6G �uitm"�$n$ (in5� dealA�o A�our �ral $L'/L(s,~ )$A(Ei$1.� Any potI��e� !a� u���"�Y^a��6�0$N �d� takl -ÝD* sketc. argu� s)��m;\ fullu{see S� 5.2A��a�excee���&1 thos �a�bme-{\em mut�ndi}.:j!�A0m�"�p:�} �!���]T u[) *u�Yqu� tya�m�!inserz$M� ��&�) pprox}. TuHis>5�,eq:mollified��}�AB}{2}.  (0,0]d���1*S (g)}{g^5}r�&�M�= 1 %\\I�2EM:t� (m, dl�1.���n�(Q_c|}{c_0I)^,} H_1(d, l, !�c�#� $ 'l,m,n)�givenminm�( 1�%Q*} %H6s =�iFi%)uAs�ca偆oma>�"�1|\m�%{} -���\alphaQ� \bet lambda_ , !�͓YR kE$c, mn) | D5�.{�=�$D = 4 �^�27p^� %Now�dl dA* n) up�*} �bletN�v�"^**# (n)� F�The� desiB!��$c�2JhQ_AD'i�tf "]c!jH r(E|�J}No��aC-o� �ipA vs$r$��h fixki�� $Q_1-� Q(r)$. I�� xDs;:�F� (a exten  $c >>�> O(AB/ �error)|� �ar�*K��"rKtwo:N�O�1.�� \\ %Ang�o phi^�c2��Q'E��5ZEH&+ >�m39�� �p�m�$!� trun� �> hi�2/:, )$� $Y���t# a newIEE+�apER�rhH�D $H6J�H(d r��F�B��~�� &p B�A� . L�\Theta�B �@sum. Recall $P(x!Z� x \g��B a polynom8$'f� $P(0!0|P(1 1.I Q�1a�� o be zero��$x < 0UtA Mell� 0"�H"^J� ֵ�! ^�j �u� a_j j!}{(� })^jq�1}{(2 i)^t int_{(1�� Z(s,v)(M^s}{s^{j +�� U^v}{v} (S)#hv} \Gamma(1 + v) G(v) ds dvB� � J� y=�TF� 6�l(Z?&a� ��: I 2YJ� �k^{�s�} l 2s} m  + s} n vv� ����|*� In> noYre� >f.GZ��}%v!�= \J_p-=Dp^�� �1�(-� �d <l m n}_Mm+nXL d + l + m5q \text{mi�+1�0}��(-1)^{9mJ)Rvp^{d+l> , p^{}A��}&E�s +v)�2s m(1/%� n v)}} )�Q_Ag'gm+^{ {}�] /�gu5g}>�} Obv)ly�5Eulerv)�r�$lut�gconverg���)0Re } s >��v. By c"�,lower degreeͨsB�; >>*I.va? � \zeti� 2s)}e !m �PB� $"��g�by an:��  -1/6��: *�,*�6$Q(p^2)}�2��y�,$$m + n = 2� a�!��#e a�or�re$s = 0$$v . ��I��e dou�'�*ral��I*� )���(�U"$��$-� id�� J�Ia���N�,t��GMn25�<F�T�pgig'takA?�.M���"� < �-M�� v$!�$� A� polp { v=7 )~D-�}�;a$R8i90�G+ I_{D bII_ "eHA1sa�teEFas Ed ut along 6= = By!Bp H $s$-NH�':��}$$ (-RHE�brevity)�b� JK|��1� [}}{U^1>K *} Sy$UI $M�� p��[$X� mayQPvag�enough"$��-6H9A6" 9��asympt$+!%�0!��8(b2y�.� 0{j!} \onehalfiwV + O((${j-1}). %+�2�)B} >7� ulaa\�1��� b� %�sf� J�O\* &:� X}}��F�A�� �B$�j ' = � - � 1$ (by d�3�:� ). Ala"at�s��twLh��p��!s-�#.�a�v} Z I�c S��$Z C.�ch���+ $n�%(arrow n - m N$l2l - d��&f  �;b� �!�) � %S�'  {d� l�n [(({� n} 2, j �  l � -   f� l}� ?� �� *} Ex��e>�d$ �}PMas ����dX5� Avalue $�Thu� �ۭ�$0AN Next��sum�M,)�FjmjjHe�$klsop p] refo�&AHC = g14(5) (1 - 2^{-5"|1���"� ��i��m**?e&X0�I14 6v,&�) (0, d8>�B 6�9"ofF oremNthm:LU� 6�.m�ѫ��'2rZP�*~(�� much�!1/ han)Wn�M}E^X&yA mariz!Seh#2'. ��'0- s �65�G2MZ/� prov�1��way�u2�#�r� �Es matA6. ��(�-@� �"erma.in"�%�.H0��s&3(ly un)�x#Sa5t]ob eelshyMen� m� �calcu�*.�6.�% f�1�1h̹�1 d:�}>@ .�B.2} �VB�I8��(��� .� $&%(n�eB'/o ��&=1}{�.n&�0JM6�,\phi\* �}{:U}:�}��[A$z��~�6�'"� �^"��d� r>�{B '�a�N�)�.� l D) ������M.)s =� �!� }{-� J.]:�*} E$�kx0��odd (��i�l�:Qpkodd}c ZeZ��^2>� + 2&�v��we��X �aNR pa�9q��(Z(0>�*25! $Akv� c_S� �(>�.ocS} c_SQ e�!*  1-�-5q���QN,k=1}^{\inftyY?p^{2k}� k!t�3�:� Oic�,mL.�S�v�L�g�=�w$1${O͌e(> mo',�Jpar�8sum�&F"�6e"X*al o5 a: Z Y} � some�U5.i�at�S� $ alyz�yindividu�,˜�{*)%is devot�elabo�7ng� Ÿissue�,� *�5si{Z7LV/d�2"p7LVMN�.01V2M1M2}���-K�"p #1 � o reduct&tiwe6. Ru�+�sianeouywhenevxossibl���M&r�8)� * 3Q?_:���0�V� M��n�5"ome$gni�#qb involv�mG.{,toI��8otal length lesa2�A 5/9$[:)/2Y Z�/6:j A_�8�ib�byh#ing�D!y�u*eqA.8EoneHecke} L_{VAM_1(E) 2} M_2�C :�&d_1, d%ɑll_2Q7$d_1d_2l_1l�Cw!�&�.m>nn �!(m_1n_1)2n_Z"mudm�A 2m_2�_1� l_1��,rt{ FpdH#�7�F2l J F��9<w��  @!vhor� d8 6=��ucO.. /N�!FV�})���J� d%'`�� Rf6 _1/d�l�?"n6_* 9 V�6 _2/d%l'E:�FLW5Da str2ahe ima�1�'��*ewill c#� f�8d#�,s;�2 $MA�{��s�d_i = lmOP(xE��L&�@�# $L_VR>KnBKY(u K AT,���eL rez  ag$we:\YQ�m���6e�\cdot?/E fq%I�,Q�)B�f,:�JzmEb f^{-2�`i�eZ�(IB ^2a�l BwFML9%"� =!jfamily�ae��o_v?!�y?EQ,1�F]pi 18)-*6� 62&�*d_�Z2fgLR &T� %�(a, b)� S�l_{}�s w_X(a,bJnZm��)6�,h*���z tack2�V��uiv 0*Z'c�=��j�B|�0qY+,of M\"{o}biu ver1&AQ �� *}��N mA�2n�j2M��)�)%�9!�!g^6� g^2, bg^3Z�)&%N��*y'nerN�P!*y!�� $eq:usefulZlA($r = m_1 n_�� ���C#requenc $h = k"{�a&� AT�@B�h`hk�0^3d �4e�Wri� $A�T_0 + R� ; � / �1J�RT1.&�FM�V�%�\! 51/6� �r_06cMq^�Fa�i)mg^2q}{A}�47g^3 q}{B.5 q�3AB"�T]�6Weil's �"Qc^ ��I/.;3" appea�Ab9"�9Q&�% Er_1!%!p�r�&7*��;4 �Y$r�c"'-2H -c_U-|f'(,r (r�M�%� $q yH�^*KA��w9�+ �-�q ci �q  �CmjU!U:4 {}^2�2H\%�)� 1}{A/9� 1}{BNsBr�D6}}Au ��]:.+eE$R��t�e&E+��averag�Kl�/ � '} M'(E)$Q -U� :S 9Ees`Eic�=)�'$V_1V_2M_1M&z*5F_9� �Gncentra�;n .L"%A�"�"Y� �p}�EncR�_0qD2_"�3V.ze�1#&V-m%.9��l �{�s�'�1Fr}�.A�fj h i"r ":is#K�A�= ��Rdsa�A$NU�:$c�>� Q�.7 T0} ~n�L�La\"a}'O � 1n��9Z:d}R �>.qAf��!efor�oX7Q�-5fmW@(+9�>_�Y�)�Q�H%�:�!�]�7L�Om=t=*�Iya�A7�s}9ubex�;�4.=T0�ser�:�/ LVME�DPreciseMtL�� *} R<�f� N):Qb}_2\�*iw��f|A�*� Ə\ U �e�=)�� }��z� V�1*:^��m_2�� � "`/>E �6 !-inS ( �L�*ETm a�QA"�$B�.A|��&lnjqI$j��ea_ (2} j_1! j_2&e-0P>\#_2�D}-I.�^4F*5�,G:�+�s_2, v v_2){*M_1^{s*^y +cMM_2 s j_�*Y !VAvA 2^{v7 �G(v_101�-2��� .v_�).v ��&� s_2 d$ dv_2� q��er�X�*!:a~um��V����b� YEm����z.!^+A6}a�A!�a� 2AC�2}� ^{�,amA2}a� A a� !�k3�;6;�+]F�.�.�1ZAG _{p 2x2�$jEYn &��+!3+!(26 >��\ � +!�31� /�!��U\_a�.���2/%f )1#@/_�͂��4.#g��1+m_2+n .2 -2 fz0u�A�p^j p^�.B��.!G + �5 } ,/(_1+d_2+l_1+�8/~n } }) [�%�Z!- ]}�d_1lU��/d_2 !J�B!W *A�) $2s�an1(Q�Em! 0 "n"� + � 4c"�*]�In ord�#o�UsqS��behavior$ $$Z$ near $�$, �I�/3�/-:�/�W)(N�,��66S0m a0�*ef�F {~r�tcoe#El($p��Ro� speak"�CUMi�Ma3oM"Q2? � �@V@di%1�n each�` �#'� cn)5{ �*�+5 l$a"5F!�idimen�/�g%N{&�C���Lor�B^�$0@C{\by& �$b�,  = V_�SV$; A!�y�O�is 9�B�A :� �*�F�}ip�%-P�� � Z� �1:�6 &3 �!��a �V��4��}� ���:�:���J�Z$ � 2�oB�v����\eJn����:]J/l�'r �#�B����w3 �ٞn=nA�� $\=��qf Q�a��-" a low5.(`�M�*�-����tA +Ar)~/_19�� �E 4.�B�4V6inB"reg��.m0v_j >"�1aq �6C1D���q��mov���� ��*!ld�5"en";J8N���RaQe^�i/.� h�j� =�,H-=l!!�ed�/��p0one};!�f&et�1 1V}�B~+�>J�H�O�0_1(�0�an�$thmet#PU���be5�,6e�#ly��� cS} ifQ7IF���- �Poofa�V&p$. >�e��M�;= M����h�n�"�$D��W�5��tak Ъ�r N 2 �1}j�y1+���7B=*q*l&b@�=s�6f6S ds �Z�RBIZ(�.�*� �&w 2� "[ AVF^ ���%6+  ��Z Z� gAK %)l �}��� � �5� 2� � ^p^0T � f :� g B%J�J� ��2/.i 3F"2%>�~��$L ��=l� !��%� J�.a�0AE�F�Z�D�!��=R�)�:� !�*�l+�*s_1�l!�\0j=��q�Xhre�<n �:�ja*�"��2�� ��o $!��3!��2 =0$;!"D ,A� ! ";.1${f= 3 Z 0$. 24Q��%:"M �ca a�%U�3r �� 2�_Z���2$�T!"�2� P!�#�V���?n *�7v�OI;} %�9qr��� X��B/b��a-�S*�c���E �/!k�D E8zi o}+$j EOj!�A�"� &c b�fJCe�14� � })^3F �5ns(j� 1) (I)���}� �s + 3�]�Set$F�'x� d}{dx} x (x^2P'"+ -vX well�#�9 culaTK�QM3$&�&� Jn In�c�a84A/'f &,�K� $#�8 �&ify6�&) mpGr��� . � "qIB!Gp7_ons"�$�'Q�n'y�* 'MsLg&�$�a omoeUc&�)in:Y�<yK�!`S�+$,l s�:.t�td sup/i . �S*<&� ��^&]�429�Z�3�g� "k1FVYVC8a�H�=$ѥM�1 A;�>"M:�i���7m!I� 6�� 6*� *^/q $0 <.c/2hM6D .w�v��to:�p- 26s e pick upsNs�aM �Rf0 -v_��"/� "�dnew% >�i�ll V^6�K��O .b��Hs1�=�IA1}&�N�_{(�)}Uk-1y^2}Q^�)xB�$l 1-�eAb ��0&�J�� ��ze�RN :. ( �0�F��Am@D�Z$!�E�efg;#5^:ry axi�.A &�V�"sa* GBLE1�.!�_ a#Rp�P)&A� �#he�R]$���P$R�q�mr1jq�:2M��M�Cp$vV ��E�sR�8�JUi2�X�B� ��� �*Mͪ,g"� )&'Fj!�14�)E^*�O:Hr� 1)!  1)!}>&\Au�=2� 1&�s\r�)�vF�g�yDMIt�i�c&�H�mAoM�la"o&:0$s"�s�"by mea& %D" tserk expaK%M$y�9���frSx�r�I�� �ndg�B� T :!of ";"aWcd&LxF`W� so� 1E��A�in�X�1�aM2e���J�?9�:�V2&�-6�(M/n).����no�X�!�I#�9n > M$!PW$O(1)�,$I!��p�P�*M�c�')�!��T. �A;6�BJG��q,-�*�B:�%�}�(�.zsgmM1b^%I}" �/Km��< F]An �J �}�-Maclaur$ho&1j�I &�~�Mu�GM�E��tR�t} dtƇ ��N�)� |�>�R���-v1<�� q׵+�O6���38"l ho&j :a fi�T  $Rr*^ t"� �1|t"] &~ >�w ovid`e�� ��.� sF�� �;��st�B�wI�]s_i�+&aiX C��,-it,it)���2�#$� \mrC�V!�VY3M�|$M��2beB$Xa� ame�0X1*�m&+���i12�1F�&�  A2�1*���:���^m����n �4 �MX,2>�b B2H$2a��&J_��4R� �1r�If !� -$�nr-m ists!� �v: ,�h Afq�26\sim c^X:�3}�:2�X� 2�, �itV x ���'$��'R�!�g"������3� lici_&�] !Ma8$c'DbJ�7ofMi�Se$isB�|!�EsKMVdK},"�:5/S7a���Rv�|cl�r6U�. d8i*� �<=HRlos��>rw2�)��%���(�d �R=p�|�� 6LIntX$\gie���� $-C-� (|t|s$�-1@i t2�C�%� reby��upe le-Y�0�]& ?!�s�K ]d`I�zat�9!��%��i%D��v�$A��aN e�#6)��(!�w�Iperhapa�&pc��"�R�= I���]%S^�>>.�oJ�32 :�9A .K�sL4��,�g U�zBzg_16� ) �^�c, %\\ 3^B:="m�SF\� =� >�%:. !G.� f 0Je�I_)�E�"�AA�sac�Er�cutIj!va�of^�WaEN^�%�c�b� trip��J-Wey^$6he�!m�e�5��� inue �$]@ Ft���FnX�y�qb1$s2����&.�6*!66$c-7�� Laur�B���-n.�rh(sA[I���}]'(1+ssno�'�vc�"$s$��a���"9#"J�(Q�"� c� a�* �4 +c + ... \\ ()�f_1)�1}3�4 1 �G "�8�og ��...�i�x%we��qr"� eq:I2I3} ��\� 0_1}5S2T��b�>�=R���60�w&� \\ + 2X /�m5��l*"Ih��:� +�� !2Jr""1�� r��e1, �?1я9�! I��'��a�s��B_s�"��6a��G[t|O`�. �]We claim�Ru��h!rbitr�&�E}X}$�inge�o Iis,& � �s�:0m+ R?_J-"-r$ de�0s��y)-yp��$�| pt reflec!thr-&!`i* �K2�#"�� ours*[�lyl h 6E3 `�~@G ��h\I��Y $��*�j�,�; lass�3�IL�;��s!!�(� |t|�dE�"-:%5-c�th $C +<K` 0(see (3.11.8)?� $Titchmarsh{f��"�~1�u� \a�{ �q"#)�r�� �M . �KFp�I~I_-�ɤway� T&= �K���$I{ � . *�qj���2T���Hh*Î*/ �=/n.� ���<)�2C2�(�U^� (M_2 $�6B r����!�m�0l vanishes un�X �@&�"= �w�.6s̉b�i� A�f��T����fa�+6�� (xD�i`I�6i�$g�leE�H">�� Yhe Iyiplane���ef+B�%�g(�z�-"�-�6��. 2I(e� /n}))n�d1}22S�h=�6` path�-�ae�ρ���N. � _2 &� E�_�2 t�1/tb ) �\ &1{f�>y%v{t-5p{(ta;M� %� j)�dt}�ta�z�� k }!�Lbinom�Gpk �i�zk~�+ 18 - k-6 ���^� _)7�]� !�%1�-w1-k� .�- k%k�c+ 6bw=�P�#_� > �,.2} @[�L^fF�~6a _ �Sim �A+M:A }R��� )�( �!� 1)^k A5+-n-q�eQ�e���"Se����&����: �BW1� I_3 a[ sum_"C2�.�^� �� *� -V��v�i�B�&CLMTB �j_2u��%�m��>��134 5eF8&$ \ &v�t&!��a�W� �^�3e. GB:�)���:�W�W�� jGiY � l@l�A�A�M��immediakw.� &� �ki3>. �6 %69Nft%5i���F�W�%�.)�J�} �[}{k���P-�9X1�=�eU�)�C4higc�p�Q �`� �s�`�1��`��uspNss� ���B$�U���� ��sV �+���2 B4M:�b�aI&y\�6B`�QKiv6g>�J #ry��vW@D ! &4 c W:�Z�+pR1(!3 �Q� 6��.e &3tA��returr \&� !�$"� ��J� <�j �Dwчas :V�m|��6V_ZAk-.*�F.�\.e �(o �_� ���{hF&qs)!zC���a6tE�NQcW� |6}S:~( �& :yٹ1weird8} -��2�3� 1F o j &I,22"C:��d>�9 >g F�3�".�U�)(V_2/V� |S7+27+%:?4!e�2) %G(n�_?wST) v�>xS2.2S6 Y*z�SB�a��9&u"�N.j2�1whea�2 > Vl = ���t�L *:�E �E� Rm�� ^(..*�b��*vFA���4i"M�1}�3,�a��= V"�zF�aF&���y. ��gc~^��T+�����A�9�I>#�-F�#pmeN~ s do�~  an�wleW %.rI)>)�C���cN�>|6�Js�"�� *} -� 1}{[#8+E��IiF &N,�?R�}� -���gV^6Rax�� -"1}�\ %�1z-�Q.qva�>�!�y��*s23&�B�0$� mam A�NM�$a"�3r0�3��l�B�)�Pre0��Q�ve�)"!w�!L{thebibliography}{99�t0ibitem[BCDT]{�} C. Breuil, B. Conrad, F. Diamond,eE8R. Taylor, {\it ����?y�ellip�^ curv*YB@\mq$: wild 3-adic+�rG\�s}, J. Amer. Math. Soc. 14 (2001), no. 4, 843--939. \�]hcA�ume��a rankJ�. I}Invent. �Hw09 g�92x$3, 445--47��b-@CS]{CS}�-4e�K(d N. Snaith-'j5*e�!4*-� -s��jectur%prepri�]qFI]{FIqFriedlan�TA�$H. Iwaniec tA�*j� $X\sp 2+Y4Pzpi itX^imt Ann.!(M%�(2)!�8)8=9!1040.�XGR]{GR} I. S. GradshteyfD,I. M. Ryzhik��^mi7 s, S~.�6Px�t5�Academicz^Dss, New York, 1965.�Z]{GZ}!�Gr0$!D. ZagiUHeegnjpin&(nd derivatiE�f $L$-6�:8A� 19861$2, 225--32.XHa]{Ha} E. Halberstadt �0Signes locaux�M ߢbesq?�(en 2 et 3},a�R.% . Sci. P�x S�r. I-� 326:�,9, 1047--105.�$H-B1]{H-B}!"RH ath-Brown �AEqC}Ba�ZL}, Duke� J., 122e�4)��.aE591-623=� H-B2�2f�PE� aa)$xA� 3+2y$a� Acta�a�8! .>1, 1--84.e!1}a@Helfgot1��t"_ of �� ��zfwli��f1�c���d\ttp://www.arxiv.org/abs/�g NT/040814�5�RHe! X�!�2�!�p�dproblem JW/s cub8:orm�}.IK]{IK% �Ke>(E. KowalskiMAuA N�Theory},��i�?e�14� Society Cc{ quium Pub� , 53��b;,� �,hnce, RI, 2004. xii+615 pp. /��IS1]{IS)�.�P. Sarna��&6a��c 8���flP�A^ �t�� prog�|, Vol. 2 (Zakopane-Ko\'scielisko��X97), 941--952, de Gruyt��Bev�%9.s �2�In�A non-�U`E_g�l5~aut"`<:� nd L��u-Siegel�EAH Israel��!�aX20�0�,A�0t A, 155--177}^$Kn]{Knapp}� MCE$C$}!�8�ton Uni�bte���P , NJ%($2. xvi+427%�uA�>�b�� !o�J� e c�o��S�pA4J. Reine AngewE�!�5�-� 1--3.�(M]{Miller} . JA� � One-�two-leve��ei�rZaln�: e�5U:��l�ue� symmet�8c ompos�1402�$4, 952--99.6PP]{PP��Per�(�0J. Pomyka\l a �Av�meWtwi��1- 2�}, .�80��BA�$2, 149--16.�R]{R}� ohrlic} Vari%-a�!�*��nfn� ) itio��87�3���1�5.�Si1]{Si1� Silverma.U e��X�FS� $ger-Verlag6� 86�dSi2k2Rk4Advanced Topic� !�~94.~o]{S} K� undararaj�Non2�&��D"p;2�ar$s=�12��R� 52��M4� 488�TW]{TW}� �E�A. WilesM� Ring-�e� N7�SE���xalgebraa+R�41{ 5���5��28T].�&! C. &�& ����V!�� zeta"� }, SezN eb�. Edit\)n"SaM face�D.!H&� 4LClarendoHuOxfordJ�.} 86. x+4126� W]{W�.jM*�ary� �Fa!t's l���e�pR�Jf452�Y1]{Y}vYoung-U Low-��O��r��>�,d!aoՇ ptem�7,� X5, PII S0894-0347(05)005Ѽa�t�yp��� Y2]{Yf~.>� er-O�eTer�%A1-L�D�E& Fami� FVj��R\4 Not.��A�587-63�W�5>?&docˮ } *�2 �%E��� d��[)Aw 2����%Ci!�110% siz�[Dhoffset=-2.3cm %\v6!1.2cm  %Ve_y�May 24%�2split��� I; : f�(July-August203. %Rev Aug 2H003� Jan. 26..(4 aן2nd�+e[Ycom�10s. %&latex %\1zT+ {amsart} >rticle}>0[12pt]{\u,AckageK�,i(sym,amssymbthm,enYatecd\renew� and{\base��~}{1.5��et�{\topmar� {0.0i�$. exth�S}{21.5cm6>evA�deC35>Dodd%�n#headsep�1>c� widt�5.0>pWx dent=6>uni �}{1mm} %  \�� style{pla�new ae��}{G em}[[K] .'��� on}[ <]{*�}2/co3�ary-C2+l��'و}:�&��6=���4 :-co�}{C 2�3UrkMR!��!=4exa�L&E 2L!4ert.!1>) blemPPd6'���(Qu >�exa$�%��isH/4Kanev-I book %�-])�environ�, {subM,s} {\stepcou�r �}}{ 3 $a]w thm]k.�t6& \Alph 9>"J�cor=f%m]Uy9�*{u!���ci m]2K%6>%2 Aze>K fi�]�2AdfE m]2�.�Q m]]:�b�%~Yv: m2}�+!�N" *{ucla}{CF328*{u:Z5 exa}�� *{utB|-%*{u�}�<{� �R�&3}{NotJ6.�8ack}{AcknowledgA�}�P$i� ]u� %TTT2�*{ue�}v%�FD  ��#�4in{�� }{chapter!}. J}* \2!t e�,q� secnumdep��2�(toc% %\Dec� � Oper S{\Ann}{^!Hom}{ %ZCGor}{%�" {\rm>OR OR}fZCat}{6Z Z�Proj}A�jb�Spec}{b�Hilb}{IB�{�ebf "1�RfGrass � >Q { :mGR =� bf $>%dto`^Ksquig�A%R�cod}{�defim!� V7m}{�Z!obs}{^! Image}{Im-/ZHKer}{ m�^�im �r(UU}{U:HU9��n*� VVA�!%H9�./GG0A�!Y%%%7AA8ai}�2>CI}{CI � ? or V� (6=DzDQ��XU�cha��r b!�RLSym}{rJSym 'z�l�%}{\4W V%6� ' ^: M�W^N { bPscN �Vlsm$ � schs~� $J0>�W:�SM9�Sm9�V�EC}{Sec�.�� V@Big�w{ 1.J':�ub{GaVoGPS}{Gps>V�ing}{f�S!�N�{��!bi.�SCHj�3{\, ?R�Det}{:X9�Xf>Pf}{Pf{�2> �*�A�AgMfUfBo_C  bb{C;C A�c P9�O] !�;m:IJ vJKer rm5 �PGlPglYMA(�S )VS(Syy V3 .rm@ LLUb !`al{�] 8ep{\e(� M�frak{bJacY�acU�MO,EMcM�hAgaE, fi]�iY� la{\�� (ns{\footV \it p�phia{tiބ�SO-�!-OUZ��A51 �Z �ZWW-�*5�S=�m*Ex9Q�+ �PG Crm.6max orm{max.t�D{Artinian Gorenste���dpdd�}Õ : R��*$��(H)�40$ H=(1,4,7,\lȔ\ ,1)$} \author{Anthony I� {=<\\[.05in] {\ns D8;"�IMat�&4*��easter.d$�, Boston, MA 02115, USA. %email:i j$@neu.edu }s2r8Hema Srinivasan��*�$ڒHissouri, Columbia,  ���G,ate{March 23[�^begin.� \mak�� le \�!� {��Ded�,�9,o Wolmer Vas"xel3n~ occa8Tof his 65th birthday}}k subj��)(ary: 13D40;?Po/y 14C05�qo \ddag{AMSO0 Subj.��+G6G Y�.� abst$�} A.�s���$�aofC'neg, �/ers $E�h_1U� h_j=HY;"c�/ut $j/�Rat!�FMOHi�+t f� in d��s xCor�� l $jL*��'rd  d jq $A=R/I�=>C$R �*�-r in��.M>nd $ I / kL�l.�schem�2� e�pa�U��s all�R F quot��i�R$ j�ng1 &�d$H�3it!��o8 be smooth�4Ir�V �V B�$���; 3$��3sjN%Sruc�.A�rLdTJ�� -��M ��#r�:,R=K[w,x,y,z]� $I_2\c�<\langle wx,wy,wzR$ (�~\��V,W�� ResI,J}})�y2��4w�34=tQ��aQ� ), a\le 7Jtis%*<a� $җH_7 j/2�Jan O-Z>�nonempty���aA�7�&�Gs���s,uy� if iZ!Nh,b���AaR�)��%($3h-b-17\ge{at!��Z/ki,: ure .��� �&C}(H)}em the N�E� F�$��set e:A�N�U�q��K~ � gene -l�Ia �=�5 of �4UB@ksev*t%��4=s if�ad)� $8Ah1�b%Aa.�n6 s4�8r*n.+'��(�2�2_J}" Boij�Qo8s hade�n p7 ��at"Ѕ��ing�{inNk�Umoƌc��Bj2}, [� C.38�..� ���{��8* ies ��inimalmol(�Iԍ�ne�V5�'���* �\ �{Kl� ��A�Gotzmann�{I���s 6' ,IKl"i>��(��In���<j1}�SR$�cu>'��x��x_r]$ �5an&*ly �=$d field $Kej�M by $M=(Kx_2u�x_r�lt@x%U�sP When $r=4$, we let ��[%+reg�it@�coordin�-���*proR5ZZs: i�bb P^hE% �?!Bx N� (GA)1,u�s $R$.�Vˇ) !d (A)=(0:M$�socle4 A$, !� one-��a�Ybvector ��4A�\ nihi�"d�&�=��on)s$.��WM�  0�%)m N)ss��v1\emph{ ��0} $j(A): \,  = D\{i\mid A_i\not=0\�hA6�h_05� h_j)� r r��ofQ&i%�x >^ ^ xa �a�J}Q.� $j$,�� t ocr� of`A ~� $A = ~ %�E��O0 H_i=h_i-h_{i�Ui�I!�$�pd}i\ ��"� (1*r  ,h_dne) �B�z 8�8y� aA�UM!!�GH�q Epi��R)�P(M4( R-re��ŀA�=a� $r=mAF.~H.~S\'caulay�� show��Mac1}k�1X.z �5bܚs�P�"tO=r\+e�,(f,g)$; thusF;a( �i[J% must�Z�] fܗ$Ha�H(sE���s-1,s,sU�2A�. Also�-!; M)yտ(s))$*5 2�d�Y�Ѷ� ���B>�� (U,}=\bigcup_{t��s}tris naturDis"�3�<secantEet9)a r%.al nor���*, so is r=/stood ^R)l��,ɛ[\S 1.3�W). \pargf1�.�1 !�B7mbB5�,($r=3$)E .Bq1� (A)mdA�E�# cF� IiE"�7Z) $A$ �ZE> I!��d b�P� 9�EtimPo4E,St,D,HeTV}, �Salso ��[C! 4%(.�4* �T�� "l i�^!Ij%Im"uRj GA]dn� was se�4by S.~J.~Diese#54 J.-O.~Kleppe, pjvely (�{D,�).�ȁ3�Mer�te)L ��!?�}�1� �uC)$, du�sA.~Conca%G.~Valla�,.�Y.~Cho#B.~JungI�{CV�,CJ} A� ��[��4.)���6y);+,� ��f�/%��vN :�,�HB�A�7# a Q�Q�z N� � Bj3}�� ur8� �{�� DW v�si� }��ag,|Gse� [� 8 5.71,\S 7.1-7.�8K: HjJ�s fy or g���82�).� �MAbe� unimodal:�<is,E!h�QOmJ  s�a�by!� Wer f=l��um M�(BeI,BjL}). ����a�J�!B��}il�tm�WE���.�1�xZ� "v �n�V, er�:n�$O�>��ee�  admi!w���DB�o�p of N��sA&�*� Macexpa�N\�rm �1 �%+=U��.1�$, a weaker�Ot��. Litt/as]�x_!-~ er s�PGO�Q�= (�piI! suitW& J s�, iU��v�5�5l ��l!�mp�u}jR  ��&�*�'�/��at gu�iތpor!��`study. \E�'E�,$\bullet$ CazMfinZo sigh�v��op`[)!�M���� j�U���3�N-.�?f�Do moa%��J�e�"�=� &�, �[Lh+ r� (phenomenon?par9A!�now��! �m��r�R��diUCq=��A'�1, 87���1� bX, $Klt� a��}.�i��.<w��� seA �(s i{���i�[6ics. �I,Y���V^"�`��%=� �wchyP ls%�Kd"-�)�(H} H=H'+(0,& 1,0)�65 %< $H'%��F���� Ou�|ult p�9!��E�ѳSI /:�* Ch3 �y�FP&��I18)��}��s��a4�A4.�\&�j� n �J� .�LK��� � we e�i po���N�-����>aKfe�tly u"��I�2Rt�OJ�Q\A[e� Ma�:As�N ,�uT{ P�7st� E Q��,��sU)�MacGo How> �se� �N ex��Ac=Z5P��w���� %� not Aj-q�>b ��� j5i�SI�5& ���R� &�� � ll �E��of.s�qs�'�ߥY�)�`�^2Lcere�V a0�) 2���)����YefA}) m_7B� be a.�1�( �76QA< $2��2�J at l�! tw��g .���A�� �p ;N �� C(H)@$��A wI��b!nL(3)$-6\$�J����*��ks*� �:�!�! pM �� ��@6��%��, \section {N�otation and basic results} In this Sec$4we give definis8 some = = that0@will need. Recall <$R=K[w,x,y,z]$ i1�Oe polynomial ring with the standard grading over an algebraically closed field, ��0consider onlyF�Ied ideals $I$. \par Let $V\subset R_v$ be a vector subspace. For $u\le v$�let $V:R_u=\langle f\in R_{v-u}\mid R_u\cdot f\ aV\r, $. W�8te as a lemma a-�L of Macaulay \cite[S)�, 60ff]{Mac1}�%sXuse frequently. \begin{Y}\label7 D}(F.H.S.a).)0\cha K=0$ or $>j$. There!��a one-to-one correspondence between-jL Artinian Gorenstein1�p quotients $A=R/I$ of $R$ havA soclAs(gree $j$, oA�e~ han-� ther  elem YF!��\mathcal R_j$ modulo $ K^{\ast}-$acA�. w�$0 A�$W,X,Y,Z]$,E�dual Y� A�. The : ise4 n by1�align1�e%�@ I&=\Ann F = \{h�RE7(h\circ F=h(A�ta/ $W,\ldots ,  Z)j$%� stati^D are analogous, bu��8must replace $KyA�A#a3a� divi��powers uw D$, ��e i�A^�o�q�DRcontr *  (se�� low) ٩1oproof}�� a� ern  9�lL��s 2.15,7]{IK}. 5 discuss�Cof١{of �2� �w=O = p$jeJ o$Appendix A hi~�� corollaryQ'include}���Hb��gra!^�� F� of2e $j$�J=I_\Z$ Jsaturat�98ng a scheme $\ZQw%�4bb P^{3}$, suc��ate*1$i, 2a2y7H\Z=\Proj(R/(J_i))$, $J_i[a\e�nL$0Dui$� have $J_u1u$. If%fK=D�� D� $u$,u=I1)x9j:3+.{. SinA�Je�its own16 ion,2� =J_ka�k-u}$�0large $k$, so,v�w*} J_2=�:Li}\} :�i-u}=J_id �H$Now \eqref.f implie� -�2�J�I%2��u����R_�!v F�Tj completem�mWrel��"\$I��#� ��i(\� Note iYExa]| 3.8]{I}, due to D. Berman, show �0one cannot coi^ M$JUX$ in Cq�~\!Kq�� lQ 4I=(x^3,y^3,z^3A� and Je\�+:^ $J6258y^2z^3,x^3z^2,x 2z^2I lo�18 inters ��de8  18.�p�!�m��e���u ��Dv]}=\binom{u+v}{v}#+v]� HBy $(\alpha X+ Y)^{?, AK�� mea|sum_{�d �#u} (^iUi x%u%;!�is�gY)^u/u!-XakHlatter makes sense.� � =0e .� A�may&���E�"~& ��=[2@ ��Ay%����R pa� differen� opec s ��: $ we� 1�� $X^uK 1 X!%} #-� �.�BU inv�Q system $� m� �D� AqW $I #�j� I� �   :�, G = n ,���} a>itAAQ2� of.��omorphicm:� m(e .W .  \d *[ JS oby"k's \ �9 MacD�e 6sa$principal,k Q 6���:A i$F$E�\emph{� g� }�$A� P �A Th� we A�$parametriz��AWgj5byY clas�5, $F\mod$ non��UT -$m�SeA��|a� proj��ve Wm34bb P^{N-1},N={�Nj+3}{j}�FGiven a.os�} HE�.4� (so $H_j<= 0, H_{j+1}=0$)��\PGOR(H)M�I�� �$�_�s� 9'a�$the family��GAJ��>� $H$. a+ H !' jstructur�Pcatal!Fcants!g d describ� n �D"� 1.10[ $ A ``geo%�c��'' $p_Aa"-$ �e�Q .�� qB&� � �� �nowR}�orem cha� eri%d F"�s �O$-Q-!���ion�!,Persist� �KS)�thqA�( G. Gotzmanm*�!�%S{ }. �d� a positA�� geraX e $d$-th "�coeffici��8 8 $c$\�uniqucreasAk���non-nega.ws $k(d)"k(1"  yingJ� c�9}{d}+m}k(d-1 -1}+ s 1};6|*} �� �c^{(d)}$i?�������Exp} 6.�+1}{d+�i �� .�2>q } Then, %_Q ��, $p_{c,d}(t)� Q� s $B�e!�1����,Nz*$is regularQ � A.A�($H(B)_d=c$ f$62} �2t-d}{t:� Z�dF �lengthA�aNI�u� expanq`$c5 � U�2%F=31d$,��!P numb�f w k(i)�  0\} $, equival��W8ՄE ial 2jing� ��9�0is well known b�a��-�ity-�a�� (�[T�N( 4.3.2]{BH}�b��j1�MacGo} S� I;1�c� kR_d� Iv ax��j x_1q� x_r]� uenume�(}[i.] \itemM[$Macgrowth}�2}2BE�%j��U_e�\leq�$ (1W'� a� lity�k!Fper iBi mR/I g=�$,��� &I_d))!�B*P��"� �� r-1}e�m�N�(t).$�� ca� ) m_{k}=q�k�$kA�5�H'; 1�s� remal )i ($h'_{k�<{{h'}_k}^{(k)}$)� eachM^4 $k$ to $k+1, i@5ԩQY�X�p ofa�M�"x Go}T Y see</ 4.2.;BH}. F�Sa�p�_ (second)%FZt� AARs3.3e=;� g/e�-�! �FSatz1]`},���2�:� C.29 l�)@1N&�}�e��A.���J�H=(1,hy� ,h_dq�),E�said to�ran �{� ��} �# @admissible} if it�J�� uala6�Z�B  E��� $dA�1Q}= .�!�F$$$\sigma(p)e�a5�� $p=p(�q smallestm A which\ B��Z^Q\ $pO L Castelnuovo-Mumford�ay k le� r�lal � �. 2 ��C ayerAed���Mbound � �O ML!�A��:�/reO!���A�,Ba}:a�j on� E�A� 0}��;# S. C.12, ProTa 4i , )s�s� history ��rks. A  easySQ� we �qFc1qEregdeg}��1�2\!"=� $A$=at+1- a-1}{2}+b�$re $a >0,bA�0*� $ I�!� =a+bIse F1s� occur� $b<0Kn �?����3t+b, �i3+b$,j� 2t+1>#b+2of ' &.Hb+1 �y !N� ! tant=P Hb��$bq�9� \I]OnqsE� |%�!~ \cho�%�) �� um, &� S aY�A�G a8� 2�q:!�,QIbY*��split} %?{t+� 1}&+- 1} 2�P I+ *(a-1)  \ &{t-a  0A -(a+&CbC 0�S ��.��� 9{� oseq} sHg*muiRv��U�S^  s�#$d<� $h� =( })� i&����.h �NC�� Deltas� � Ekan �����1E}�Fr�@�C�^ ���}���ex�a= &�.�1 � 5 $h_u� | )_u$%S$~dew �&��thus $R? depthuleastwe?c#( homogeneou}�o#jasor, ��!��fir�9Cc�)�(� _\Z9 V�)v.���}assera|!E5s)�E�a�F as th�of):�B $valid more�lly%]]"p�s�u�^ $o�%in��� (level0) osŏ^;s grea ��MM�1��Q�app";ofq")� �"" b� � }� q0s \linebreak < 4,7,h,7,4z%� ɝ,6 d 6"�%yT�P nonempty1eW�ANh is a.6 � ifE�)z f $7a�h1"# z:� From� a�&'�i���\�v�#3)=wH(2��2)}=7^{ 11,$�'4)= �^{(3)iJ a:�$h.6.$ Now= 61s +ad%�� �H_3=6� h4=7e�(maximum, si�6=�4}{3}�2�  1}{1$while $7=6 �: 5}{4:3BG$.yf�e� � impo4 M�}�� �D�|K3j("� $H_\Z�$!Y �� metimes ��ts6tu�; �'���D �� � ng�� �Tlit!�among� ��$ termNť*�r�*n��-��� to%J-� aml-d BT$an cut out��mo�� di�8�a(d��u��$m�upbd}�0\Z=W\cup \Z_11�-� , be�#ub-�A�6!^ W$ is ��>�% #�$i$, $(!� )_i a� (H_{�})_i+d�% �:�W; ve (Fɛi1�y!nf�roscia's-�� {Mar},*� �" 5.1A� })o!�!`�o � (H_W�'&R R_i- (Ia��"\cap I \\=&�J>  )_i-_\ 1;-.7m� �2  ndm� \s�on{NeZ$ f quadricEI:�A�& e)sQQnetsec�-S TɤYU�\�-pre�tory m�|*on CA\.�,�onxq�I�s� lowM� curveF� . In6��� provE�"�� .�#*R,���A)��WE+��A�ne��t$2� (a common fa.%�]F afFa�ngn variabl�$o $).wx,wy,wz . (M�& V,W}).aAt;(&?� dime"�tlntQj � (H)$��hint*��<'an�S;�\�(�5��6� �r �� 6��0�A2m9ZY�5�!,qrreduc� compon���P�$ 1I�sev)}),& /)�weɑlA�(l�(o arbitrary2�V[t!oY�)�w2a5d9�%q�IBas5A),' �) $I_2"!0 w^2,%� Z� hfw25��i�e�! Q�q�u� Three .: .at�c1 s $f,g,h$7 :&�1form a� $w# _1f+ 2g 3 h, i�#,apri�aBC6�3$�!ZO `E�ermZ a�Hs minorPa $2\C  3$�rix (*�"$ defF}) al �sublocu%��o�#:�.F(are�8�%XGrassman�4 �bb{G}=\$ (3,R_2)\c� (3,10aof��21. It� l �0m up to i]sm un�6���)��l(3���),�M.3s Z/�c�6��� 6�al ��A�L� odim2�0  \P�=21-15=6a�n�6bi�+4a��l enough!�1!_8e. �G��:A�*B�xB-�e!� �)�A|{FEl 2�t&���� (*�'5q0~ndieA"�Betti�Xu�&�$R/(VA� Sv8in� � x�%q � �� *E���"�6�-�euI� U�A�S.� of �o��,�N,�� $��$ar� "� :x�"� �linrel}qR�h=0*�s.�R_1"*��1.:x �*Wp%P.b:J"�2=LzK�(5�con�&# �"!�i�P exac�1$i$>�$s, $i=1,2,@ 9� b� M, i:dM�#25��:1�I`ng6�� .#Fmsp}Max.M��L����f+��" -�L �E�Q_MF1}���2�_1$�risr 5c �RcaJ2 writt, &G \ell!  U,"T 9�;1~a1�4 , $U-dAp ! two "� al, � o"q =-V$� s not� �A�eik �$� nyU+h $U$.�U�/9lsm $V\ *.1�;y be -c9 xw,yw9�� � divi �n ��$w, ��5�x,5� , or*� M5 :mby� �;2Yw,x:HI5 QD� F#e��Me���� I ��ano two2� � �>:I�-W i�$V$A|!�be " a� �Y J&*re%X!��5�!�mW$m&+(s�� guma�n� �B% A?F����:B F_�i�� inantal�#e9!a��rnc})I�aassum� at?!_�%6� #$��e�${_KE�,��2 31�=2$; F�bas�n�)� �./i4 $xf+yg+(x+y)h?3 e�,be�3. R�:A"$f$A�$f+h$�*$g g we obtain\ =-yg�Vq���.�U�{B=f/y$�  $U��.^, ei;@($%�&qM|AnehN�mb�U#�A�n A_�claima�Ei_� ond�s�E�|T"we sh+ see 5,�O�� s :>a asF3%ns�set. E1,�0 =a�{F}}_3&� !�:5  f�n!�sl dl`${\PGL}�K �v,&;6 �� �<� � P � �Y�m�Rw�s.�+՝92c�D -�A٥F� e�wary; r.�Ca��gc 2��drX s abc�>s �invol2�C methods?8�ftle%{to- ntifB�! ��$\overc 9�%12}��-�!�L5�1 >evi{ work� �Q�-�of bo��normal", ��as v%0{No,PS,Va,Lee"b,%[��� q0}{\sc C%�2�$}:![m �:��)�:� *�!�lU�j ss�V� a�Fve�1}��n�=J<E�*,!ncoU� s 7 �� 9,�Fp:��"$G�^ey�!isf"�C&;+- .�,)�i\ �(r� $J� �AL&Z �"ha2nFy p"b5!}s&�2 �x� �ŵ*�;g= 11�2�-g q0ii)hav�"F�!l1}-E:q1=(b*6�>�u=� Each�=!�2��� a�� s% 5a $F:M . R�)�  }0�m1 b��2h5H $G$;>N6?�� ��!�&� 2�� wy, ��/N�ZR1�2}%�2��*a�=��2�6 ��y0/��:R 5��a�Jx$%6{ . <�� �yB��  b& vcI��� �$, V� �*� 8 � > elv  &��%"glB�,R"Xs both m �U$6lyA�9\ WurI9m�:sm1�B$)pi_1:&� %`\to b�C3V�(2,R_1): :(V)=(�,U)and.]�� fibr�$1$�K� pair}<ell, U )�r0Js��Dchoic @h$;� $Vv  7u�aJ�*&b:mod� 2&�eB!:lB�is� �R��%.{.� ���:(R_2/M�&M U� �2�7-� $B����� 14I�2�7q�� We n'I� � ���͓!;>@ A �] $ as� openu % "�QsN *)z!�a�F�w|.�5"Ti�/Fenk63 :0"h&� i � �  co�4Mch��S � z� ; l�Tng $f=uz+f_1, g=vz+g_1�`N$|9prime �z(� 0 $h=-(ux+vy)$� p_1=-yB%k)t, -)� $\bet�@R�� �y �-x ;"i�_?AA$�2$��P q�S ~pma2} u&v&l \\ -y&x&z��!��qu�}&A� �A�height  n $V�.�=: 2P=6!�a 2YE��4��$4q% nse ]��b m�!]�A�2$5+EF�="�s_<�.Y�!+!� trip�'(u,v,%(0)=(x,z,w)$. O!�B&,if"��(Cohen-Ma~3!�."!!6")Q$Da��&�8(trJ' Z�V� � Lee� }�?ow�"/Q&6w�e(.Q�wM)!P no�:�:�FN m a .3x.�<�W�K!^:IEaa !h�* U*fU�w, h��a�� 2�ni�us < A:*I�5�I%�B��y ge/OlQ�A�NX A�1� 62i\�U�c�G"[>2 : ! �"V"$ '5 I��7>�,�di5s A�B�_�K�j0ax+by$�Gsa)\�ͱ�in� AR$�%, \;� B . A� ilar.�7C 4`�le6iJec any �J֘F"A�&�5~B��?ich�E�A0 Yi�TA��J�S��< x+y&y&0\\ z&z&w6��_Ks ^at�w�oBOA�]��,�J�%Ri:82!��:)6XcU���}*� �6;6L =12E?6{--[&��al� �(!{�&��--!�1�8 !�&� four�K 4 u")*�8Q $K[x,y]$,ͪe( $K^QE$-6� B� 4'd rm{b } (1l yW�c&I $4 4-4! � PS�!Hh aj#�b 21E fine d�ctZ0!ZY�d-�suF�As2$JF!a2�B��g&�$,�2i,( to��[.�. ��$$ )/� i��;*2� 2� $V$s;�!�a�f ~ AB� )�Uu'�N>�2�_����R $� A�!m� q:� � isA�B���Ni�J�%�V/.hYA`f D ��!q0i},Kqa!�*�*b�V;�ebyM�� � l�M�2iz)�ud(I2-�� L!D&�&�g&�P$W��0'x',w'y',x'z'�fe�cal B� unorderedTa�I�!�ms $(wDa��=B<!�Ll�B� ��$W$ (as =��Af� $W$)yMusp$� MULKsA� pi :�0 B\to \Sym^2(� �0-a-E�) symmR,cA& duct!�2!imaD�ev?-diag� r s. S�s��6��96�+Qm)A���K2-U*0s� | x',y1���A�$x'-�r 3 w',U.3 $w'"�a+�7�1|/�*�J� $y'A[R_1"�x��$zB"w"�(chɟN� these-704mad�RZA�iAE2I� $z'$KX1i�$x'oL w'��$W�ELI7 ). �L!�% �^{-1}m!�6!76N ZM� �\�(e �0�V�Y�C � �% �� h�Uq 10= *� &��bsh�,e��a6^i�r 6��S2�F�"VS B��en*�r a�!R� $V&05j �!"fx $ V_1=2�U$.p=|. V_1*E t��I�q!p\� [%�s�[sorAh&r �u��Mq6uY� sm w�+ .�>u� &}  ٕ,w !e�(w= igno=6w~�f)@� V$�c��� 2u$�3a�����}�!a�Z� �=.��w�M��ab��N� of )ji� �a�O-x1 3�NE �� )=e�'3 .>)�"� $. A&",$W'=w'V', V'����E:VB�a.=w��$x At�<�X., $6m? �"E�i%>o U�&0y bB� o%�usix!"5*� / `:���%cF��V�F}���)�_3�0�BsrY�9i c�RifWI� "# � :"�YPS��!� coun�r�,�!�five, 3� �2�+2�X�"1&�#M: .�w^2T �YisR�of.Hi� �#F� _.� Mini� resolu&� #d"f iNA9)�}$1BN2�*�O�4"a-se�.i-O2 h�=� gA3a v��:V �#j� ):�g1 &K BJ A�T[�� �dm�-_1�dveV����$(�I\��>|� � %n�5�g*�9*9�=(V)"99,11,13,9)$�&H_i=2i+3� �: �S�_ $V$ �+�62�V(us -2. (See.sdeg�6*/Nnetsqi} �L�k.3a!9�"�"�_@[ *�1"�Gr10���'� 3i+1.�3Z� ����� dard:�mB!)�!���&�J�!iUNmrNŲve R,MN QNwz�]�<:VNi�u�� )@.�i�:� m!i�2c �D $V=M�h'Lɉ}|W?0 K1e0r Y9P7�n�X-u $�)h�N���1�3-* \x�; z ^2!.E�2}sI�> � �W)&*�10}.E�# i�%j  �i#%O*&  $� &5:#;k xa�+�� ca/) -�$� 6C*.Cs^. 5��� ;b M�3�Wj lastt6TA��immed�_lyIEqnKA�a�3 ut �in _'�8layJ�JI�p0��.�k 3.4-3.6]L}> �[47 $\ ^{2,-2}6�*u �/ s $C�ƅ�Y !�d*B.G (^�h*K$2t+3$)� ~0V�'9g� �aba��#&�e*B �:�wo skew��sWLnIZ ofI��� a��(�&1 11� ?���:2�a planaraic ���s w�6w&�  14� Likewise,� [�? 3.5.1-�)�%�1:�5� :�21�he "%i�s��9�9OAR�-base1��0^�>$1$)Ů">5ebE y6@.�e%x�0n= $i0 G A��+ ��o(oncerns cer�"�^A�S��<3QG $I_4� �!]d�cex6YU_ "�LF6�n>thank�e`a�Gp*(1w>��Hrest% &Xf��0� J� need�  !_ �[T*� A���<b0"�Fi 6�i}KJ doeso)y�!6,��Jr,�} A�1#27},2qJ5$�XADa!jrD� R.�q"�F&aB1 �i} IfD>I"� � 16� H%t�Q${E le 3"s�2� (�qpe��Sin%�*�!��S�D�<)9a �em� (� $y embedded�I�ormer�f,A�2$ A�6�+,��eqat�I$;(�l�d�a22X�)3}�5i�*C )Ri} �BTY*�4��(@8!f� ), b %x�5 9,12$:�Y |� If� I,AJro:�l" 5,!�3�@ �h+ a"� � K!5!| �(kA)=�2�a(�G $�A) N�I� *d Piene-Sch�Winger�R�,"rac"b!�X��b� 3� {P}{k � {PS:�l�N\�QMadeq� (�&��Lna�lane)Q� 8�8�*!Aa*a&��yMe�GV�2E!ak c�unb of �����<a �� ��&���:�7 ��F"�h �/a� x9 �A"�D6�F@3�� ��I�E��2Hr!�M\P%�2+����W��B4 $I$:.͊�deFiSA��G#a (� ar)EA� 5�)!8 &XS�"YS�Ent��M"�[4. But $(1,3,3,�=..),  b-7,9-b,2! +2,3 reŰ.2Us� 'A��of:@i�H�2� $10=8\P�by!�acO �R-�"dU�N*~_3ET!t/Pof� F  (de�� �� 1)�+R (S mr�  3E}"�].�X /�� 2t+2$. By��� !&sN,%( ��Va= "�J~ �e�'te ---� (a hyper� \�y4p. 173]{GH}. F.!vb��0HAOս �*� Fd of�' �2-1�D)f� ,� n)�� *� a�2� )q� : 1j� �/& � -c�� a�9����Q ))_2� 6{ich!FC�W)J"�Wk = 9 {D��radic�%t{<pusi<( a"handl! \ �`bT: �S, $9^{(4)}=11Et H_{4,5}=(B)��m Ta�};�d�Finq�qo� U*uI_4az��1?�x a1�Jm�h}^!�!/1X=m _2=5mby^h,2a 11conb!=���it su�h�2b\�9�����S� t P@)aF� $3t�l�Z�n one)a�X �@ora]m�, .|}��K.�*� �9��/��G{I�)�I�>&$xV"$.p�P} �~�V� n�r:��*`*V� isa�A�8e e &�W� dX!6we!�si"A! s&�'N)� C}("9m "�O� N.�Q*&l�� �\fo�, ich %.eGJD ==2�!*� V�M�"k�n*u  C(Q�/Y�Y ��>mR Y.7o�P�*Vn�QJ��hA>�QResI,J|PW*Hso �!y�Q s/aFF%�]�^"6Q . To� ve �*�sA connectVse&� 5���� .{S*&kR'/J_I$ �R'=�*,z�*HJ_I=I;: R %����Jstood� ,BE,D,Klj2,IK�pa�"�+ Oq�XOqff.�3,N6ak��(2�GI�~�XinBn�&�r,!�f�{ch$R-$s"�~�"�; d�'�|�+e��'DB�v�b�$R$ acts��ɼe�"=�T�#A} `� m�)42�SXv 4lP.Cq"x\! �*  $I2� m8_i]'I�R� V= ��>� �FR� �r P y $I�(FK ..=n,axnew-and{\ther i}{\roman�i}"�4eWFqV,W< 6� $���{VaĀ}!T�� :&,5 {V}^�xbJ3A5I�&��5��s}{V�}_jf 7uX��_j,�x]}�B�5.$!i} $F P' MW,O� ��eqvsp� i} F=G+\a�w�, �, \���"�ug, 3 in K:i:}�2�$G\ne 0,+ $. 2��AJ (J_I2�,f��z���P2�*�V%�4 $Ann_{R'}(G)$^#($f=w^j-g, g��/,z!~ gmt�� "����_iz�.)_&X1� ii[j-� so��� b+I ՂV+(0,1,"n�{�-�*T`B"�6xuU�� Y� FMy`I {i}=0� 9 j� � BIAO}&*x_i=2���o0(R'\circ G)_iE�$zc�>�=�} )[\le j-1B�Bia�]�F9 )��i��.p6Ba 7n-J�A� .�of .�U!C6$ �a3}5�:��T1�� �F �[ �-}"��V}�wz)=w��(�au�(�aj pr�z�_d% Ma�! !�ityN�g(+ "��=(w + oQn�d�]+��]:W*�X_is��}.&�vh&.�!5gyR�Z��+�6��f�� &�@ $�5�0�4R�K�b�we@�.� �-w �2��$�b �8��6�".$5i� is "�+�B�*} H�=�0_{^_�1irc h+q�We�2]}���$-1]},�@F�as# F= �BAA(�. Px \Ann(G)E���$:&X,�F #=(w,J_I�;�h��� 9%Cn -mKd� F��D $h W^j]~}G*soin 7 ;� ~ ly,�* y� �6�aU�> j G=0,7}^v �� \J�us.(�,!{�)YYas�fY&I=i(aU]3 Now,�G�gm�# ���v nug�p���Z%SIx$h\ne�(0ɕyA�I��#:G!��f� ��1J $g1Ei)-\5�f !?%� X$frI� � g= 0RN would��: �w^{j-1} 2>�i$�3P `�h)%!�Z+"~�Sj ��!Mt nis"� .�>w��>1��$ w`-$g�8�{7 lowest8��(third syzyg:$�� i�M(9"�Y� 2N�,} �3JlJQaP� � � ha�>g�ors (���ieseu�re*�ig5.� 6 �8!P �lyied?C�Ny . a*m7I�c7 m�v!���iA. To�%2 ia},�at�"6� s�]$)d.]�s"��(R�= (�R'm)�$2@! i��soN%&R��hn���H'=��!�n take I�u*� � �![! .%*� �"�� = �_ "� �6F = G+W^��2�,��(F4I= (J, "�$�  R'_j$�NaBotin J$�!m9�e�B�&� O<.�a�u�V�A:�FyWUf� !�F� 1,0_, ��  a." of 6� �>cQ�A�I�� E�nram_=$J.T>o"6 �&�edE�T 8�.8�V�`e6(v�#xA,&J^ \ԉ�.veI};�� �k�C�D xact �C��R��N�re��on2��.�*:;5.c�b$�)�.G��5�#_1zA�6�b����.�  ,g-w^j� �YE�R��-LՊ��C& ���aR-��'=R/J[3 $R9� ��-�6/�+e�(]m=2n+1�� odd)� 3 !�uJres}�bb{J} :�0�:4R\xrightarrow{#^t}R^{m}6phiN,} R\ \to R/J�\*UK� �F�an $m\q8( m$ alterna�5%�*�e ֋i�� $=\left[ J\�]�/Ji�$1brow[Z N%n.f�g�J0 at�� e Pfaffia63 �, >�eH Buchsbaum-Eisenbud*���U �>+s (��� �,�%�"iWc�1n.�:hV�t�D%"#�Kbb{K}�e Koszulu��,A�B.x��� MO K_0="?#K_3=R$):B�"{K2~ R 6dd]u�4R^3R2} ^1}RE�/ � v� k1=U , �eft( ��{I�} y&z�D8-x&0&z\\ 0&-x&-� nd2+I��4 �Y �= g1^t�wU�s�-S{T}b>%�� ~/-�a a ma�dɁx�lduc#=XC�5�Og6J�pH� ��ideS3o�)�Xe� $ $\deg T_3� !�T_3e�J^\gamm LK7S"� $T_1e �2=� T-(}� $T_2 (3=[J]^taand>T*}/ W�J�z&\\ yx& �.� )�]( �� rc w�ɱM*"PŞi.ai( eI} Љ $I,J�bb J,1��1�9, !oK!r@ e=al-�B2�� F��F}f�F_4��+46�=8R^{2m+6>21 2�Fmb R/IA�b�F[=8 �\N q$F�D�ZZ-�1k} F_2Ť=\qquad)�((�array}{c|cccc} &3&m&m&3\\ \hline \\ 3&\ir 2&0&\frac1?{)�}EEh T_2^t&�I_{3R3}\\ m9 phi &wI_{լ0}& T_1\\ 1& 0�\ -y\ -zIc �I\>_R� Eͻ�.� 0&0&d0&1�p1&0&0 ].( c]�Wi!Z3.�JZ3�Z-Y>WN.&ET��&-z- x%@T_2&-1s:E�I%bex)h 3& -m�2%^ �vS �d$F_4=(wz~ x6x�m Ieri�"6�q`� 3? I�n�Rous��� B�p $R = .�n ��x j�  �+q0�͉&� ���gN � x&� v ��&� !&`D` >W ��-)1QC� &HGR ѻ�� ��n �U � 6 � i,�!�* �2����y ,"� , � h%ere.>,,� �2�AI�=0iYn ՚���+�q*T_2=T�Q�"=N $T� !�1XA�*} �Ui5&6%.6^,;\\ \mbox{so�}�>(T_1-aca T') j0; Band��>0&=2R &, �SK, {; `�(&v 7F�A�u-g _4e.M�5.�#*�J$ �%(U��!�oAb get -��f0A�get�F�F_2O3 d��wA��2n�  id�_ .�e,&�e�"� u��&�*� ATR %�s -Y^t=0- �CS�' 2l}1S\� (B)E��^ ) &=B"[z y x] 'n��J(c[�h �.� � � N� �]^tF�i� ()^t)^t�- Mww�q&M~ � B�. ] & W:S�T/EjV�T_1J=U�=9�� Aw  F�r�j��O5to check����q A!w-�W =�a �e�\ ��- �1&+ %�(-cX)&UooT� �h�s� *�B>� &~>� �Nk+aj�*\�.Z �:� ��&q �+ ^t\\A�2+E(7!B�� ��2I@�5\f��&]����B7��A�"�vness cri�2onR t|0te[M 20.9]{E|I&Q+ tX]� qrt{ +3}(F_2)}�"��:�NE :1��"�&.L6-Fi"IfQ! $(m+3)P *�Ze����lI� aBL�� 6� b2U.G��0�B�&0&�,.>(\tau _{11}&F# & m}\\ &A�tau_{3)(_{3m}FlNj@ � \\0O � �  BLQ 0&a� �[1V.�w\ &0 \\  BV &a�\ ~� �}b� x)1i}+y 2i}+z 3i}�-_x�� $J=ͮ"D� � _m Co&�,.d $Mb^�E]�Ell�v� cept�,$(3+i)���/tF�lum�{�34�  ,3+i-1+1,m+3+i,2m+4�:k/�A1�ٻM_i[uad�^&� {�|"T .�yPA�A-xB�Z�t_!v \\t_!s3iJ�J2w^ �\tBq�Ap_i AzFs\�A\\2e>$ A�-xI�) : "}�'it�!�7��(&\pm xa_i^2 �v�y&-z&1!> 2i})E 12ɉpm Px(~�1^3�k � � $Ng ����Y%�2�!$ya_i,za\}>)G $mJd0t: Fin�z lookp ۣ�1$m+3$A�:�6c.�m+Y�E����% ^3w^m�, $ ��o $wx\in6�."�- as $�nNyz3�A��z���)\supset cx��S1)./3)/�./||se 2�:5v>^�J ��� F��.�)V�8-�M�J�� �90K���\�^}%s �� i��8t"3 ��ii4.Qop� A. KuEF�UM. Mille��� KuMi0�Theȑ����9![= $�~ gR~ wJ < &b�y4&��%A!)n*{tu#B.n�l�;an$�Y�A$8}�.�� .���oWM%embla�PPc}r*I9"��typ!�vss eveho�zt!!�0not14�-�-�' T;a!&�@h]�,�0�� {. �!m�Z{��2&�"�3:q3� sY �2 \I# �|"�*&�.B64�\@Go7� 9reNd�nu_i(A A%&��-�x% �#�JhWe���shoZB�_*�1Yvt+m�=<$/�e��"�3iX+vLFi=H! &�4>� Ycal T_I�tyfnv[ace� ,�?BlQ�=�4-����= &+���=2A=O.,�V�!1���D�M5 � {J_I�2�f!�F�Q[ '), �#$ 6$"�b.,v� $�'I$,S $�(� �9b� �P�4�>�6b�25{Wn� C&�DJ`=S%��)u i���ndA(&� F�&_-B�Dse "Re >rm�]�s"�%-8"K �J_0�xm({>V})=7+M�'"."�g./R%32�A�2_2�a$�sBn �7N"�7d�1� �.[/b�� sp0}�_KIcal{T}_I �:e-+��� �'�43�GA)7 $A� �[E}h8a smo�mi����6 0 $6�XR�vC�g�?*DlQ�>js.5�RWv}�k $j=6�*$H=H_h=EѶ, 7�2>��� w ^� dimE)�V� 34ҙh^\vee ��14 =�h�_Y�W' , $8.��!.�ŋic$ -�T�1!�� !a:R� &�,"� &� 2� B�%(.VYQ�;2w�ahM�g����6�Wk/ �"3�-6y��J&� $F�++G� v�ws;=aerT9a G]��u�sn--\�'�now��>6���q�i�.����9 S� "#3.��\Aarr�(&��"'��%f���=�8_K R_j/(I^2)_j=� �=��� -&= d ��I�T(2}\oplus (JN\\ s&= � wR'_1. �(�3} ?42 0s C{j-3})  J2}) L�&= q _2_ �3 72rVzR'6e ^�  qmd14He� :9.�&j w^j P% 1}R_1' � �1}/!;�r�'1�(c�j)^2, � � } !d �]&=1+3+H'��nu (J)�MA/'_U\�g]]��jm�n"a#W?,J.-O. Kleppe"2�� B*` 3�2P�r'�+Ɋi={U=}t ��W6 *� Q 2�R*�)J�[/ $j Jw-(! )=H'��>Y:� �6� B] 2o �� �+f: *ɒ _K T)�e� (50)+1M��l{hiEoge�`� >5O*B � )^J� "�M��->T_�� �{W;9S� -% �� ��:rU��!�s�7>@ Ar~�v}����>�"�@6&��^�R"& !�6'\��{D} (U�itsM�= E�,ljcA ed9Oer�@.h� �,f�vdIB�Ffa`��Q&nB to� %i�`!-e'( r1��B6_ P^1$ (t�yr  �D7nEz)�5� .( qS�Z<!��yG�ulaQ�} !��&�7lHW>�]!k�W*� !�b�%��( 4.1B]{IK},)�).��Sla��sourcg6 E� .�2o�u%�b!L{27}, H'� 3,6,h-1,6&�0$V�h^{P }P � $Q =10-(h-1�"E >D � $�K$^3(H')_5=0�Q+T�(s�p5Tc�M�sBP� 5.25%()i/�� Q "�.�.�.�F�8$�2" ; 5(J5 TZ�T26�v�G� � ��� }\medskipI�)��B{M!Cr+��.a4�J�F9(35 �wi�F�FW}�%(V� w�[2�I���F �y �_P1.�� � ,�V�]^  _A�# �;�ebase} B,�b(H):\ WCW-�@w-�g�>bxi�Ta�r�e]��7BP.���8�*����s2HFw1},\�HF��e��s'�]a+_�ch"�Q)�F��G �E�V E1 � F� �!�+ sވ fsamG�f{�Ah4ʃ Ɂ�N� :��Dcb�(*@�t"G'Q�$. However ��a�quEXon wh8a�Z�ki%��'Nj C (H�F��V,��?aduiY1t _a�� quir�[x}O�_ ��-{ܾ� ail�%�M&$(\W)&�>d��$\W*e #=(a�x,y�< (8y�Z�Y V�=3?�Tcx� DUqL' uI W}\W"�? Bx� )&#+(&H@\\ =&\�%VE Z]+W� EZ] Q@_@� ���4J �? ]�q�� {\1QC�@ f_j=? WZ^{[,?u�"�E>$%Tbh�V  ?I1^y��IH��@�pDR} �.F�+ż.��<� 6T@� n0Amx��!ten�Tquc� �1 5�sumNF.�\,BF2-�B�Qae\��de%�s�,�"C�oE���ImJ:"�o.�4$��\Rt%u�, after�~in"*�o�a�:MJk�m���no mo�ter&i$%�]}CA)�1B� �=$a��� w)�raL���b9�W9����� � "�E$ ��&�B�!'n 4GA�mbda .�ؽ2�$. *y�E5`*�u��_�B��: )$;d3w�/y!���H=Dm�.�&5*)^ ie�!lyM�"�R $H,w�A�`arB�$w�1 w, xR5 x, yh5 y, zz+�+Hmn��ip!G��ragradiX>>$W@W- @ Z, X X, Y Y, Z�X�<� �ER$ elimi��y mbO�6� EXIJ\�"m� &wR�L."�LI���+�LI�Ln�[� ;:u* ,��=G� ;�x!�Fxv i6V)pl�,J D , J' ZCR'$>b��J=D')=J'Rp M9 �"�*��Z^� ��-:=\min\{�J0ge 1 \mid J'_�+ *(�(�J}B5 5Z4 ,w)\1O�'�Q/:- �i��]=I�/Pi�d^I\}I� ��$�, �(J)\le 'r)�1IO.I�"|�$�z�Q� {R}'уZ�3Brl���)<D0� )a_*Co""YQb� "��,U!��Y�'_so2��%e upp�Q$� ��f/>b}D z^j 4J'U7vFa:!�)01>*�3mKhIT5b� ���<�#ib=)h= e 6ñ ����ZS��^&H} HM�=&FVs}BK 2=h +,"�`,{j�.}6�L=h_j) L�{u � L /2$,�%>g=h.O0Q�^M 1, etL �)# >d�$j��2 -1$Nx I.Hj= 3 -1$.�))ioy�n� H_0=:��A% Qg%�i�9*8�$1�$fCs��uly 0,1�G2�Q�a��,A�jO4 j+1- � $ 2!�  middl aQz;, ])@s� $ U +1-j$ 0's� X��E�;�� x�O0run of �s bl{o ��.��0�� �`䜁iedL `-1$ 1's)M8 � r0!VrT>r�- q $Q� r\�m^.�h#��M �$R.��� �k} � i $&� � )-�#i n����G�+�O �V,I �K8E �@le i<hE<F,GM" � �e�Z�m��:* B=&�L"�TF,� ~ / $ G ��*� C�9F.��eBCm� W� �%!�$H�(Bs� \"������{& RB)��i��l�jNC (C(� %!i�(\noindent "{ !D�){9i"!iQM�\�Frel}V8I F, V r{";GJ� �� Ou�kv<6Q� o(fyJnA�.��(I' D$]�yR$)��$subobjects �nH(M/\{A��N WZ\}8I- 1;Z,W;�R)M2,Ap(�,J��i� C���s5 Q� �,�(� �"�� ~5 3]a��ii(��o uWBC}y��ta>,re��enBove&mu���B�-3]}%3]2� 2]}; WZ;W-$ T �) 1,1)SA���Q.! '(B)��2�\:l ��A�Q�m��(�& J))ï'� +ypq� /IC)u� hilbA��v ]�Adm��%b�$C$U�� a&{gle�_oMf^E���� RH ���"mO%�#e����p!x,HAb�$.&� 4$mzq WJDB,C�6� ��5C�!�� !B� A�J6�6� ���AC���)F�6�*�V�*X :=� "�W��� � >�t�xi_!�Q�&a$& (��bel% i} hM�VqQJ� $U���v "W,Mml =(J')+M="�+M!�.=lFw1�&E!i� ,2��L &d �*,: C11,\X�1_cCc-9$ !�c="�E~ � .Poccur�*S 6p 6�& ��� r*�#� I)-� ')="� u 6��ف.6B` 1�+�9� i Q i) JQ $"�\�(.�AanCKA�A��� �*} ��,Q>>�  G,��K z  F.M>�.* ! '���%�A��8.m+�MZ0e��d67,C�ld !1.F� I�_�Y Aowhe< b�*PXin��!��9�5Y�aA�I�1_b!�zځ aria ׁ���$� +"� `2'si�/"��b-A�8^2/ 1's$�3��vIM\�@g2< \�- \M�C��>[!/"� �# ^ C%+6�)1_c=so� n-l) $c+1�FJ�NowQ��*} aq�� J))'�J� 2 & \Left�%ZM 7;&�� �[=2��Q�J�F&>U !d�Y Y�%>/�|���M� � O��r1�< 0(JJ/��:�!��<%�1$i�>2*yfi-4V ."Z R5�{,4}Bi� �:�:=���zE�i�AAjs4ce is $0�'�',) inF�c��� az9� �Gap" $a�!t0 $b=A�q,#�Lrm���lVs6Vic�>}m�$^#eir.�:A�e�O_�=+ (B)-  ��1�}y!@��cM�� �oF��՛ �|2 2+jEnoY%%� } <� �  && ! /I)I� %�J)< +2�L{�R �� -��J' + $5:vA $z^ 5-g,�T�Ki&�IzY .}-g'\�Z', g'=�}2G8V�8t�.eJC�ft( ~�R'�ZGl�( �R%F:�*2� � U��O�� ~� ,!&� 2���ka�� T 1�wm ��=�� /]� B2gn� �Y&��cG G'>��(�f 8 �F)�82GAD/claq�i�()�i�M}+"p ` ACa p��i�]��"m M�~$ �&&� \_v`B� 6#�$ 6i�-�� ��7&�y, {\it�'�>y}�5(R/7���$ge�d_0%a �#*$�wfamiliy!) x&( �Ys,aXd�are:�> hig �va�f{(J;Q��situaa��u quit�4x܁�N�!`a��(7� _�D{�2 �$\l�A��>(y<_�*� GW$Y�E*� J}��#effec1�D&L���scr�-�-�1�� &�2"G�s�����A��.Pr�\perp$.�i� M AX,2 �!`�Q�n ��2�A��z"`  e?sg �ga�X�9�� 8 �?)��F�i�&"2� ��a=���  :2a�*f;oJ'h)+A�VK gin{� '� �"��� �4ܑ�22 &SA}\\N"�&"e� � � [ ] c J� �  {�4 >S �)x� � sv-&'�1},1_j),d {o} R�.5 �"{ W(n �1�){ ]},� +1�}b�1�\� }���R���t�9� J�^!� %% )3d,) �� * )�LEVI)!b2 1b  %[�|Nm �j�Ʌ�n*�"�� \|)1��� nu�l �� .��R�_�)&�]$�Va�)&l�.��e��(3U 1k9+� sV� �Fi�A�q>`�a>�+J�)�)�>K.�,�/I� =�n $ (�- H�H���1}[&@-�:�<�*������]9�6�'ie"�9�&+m p�� � ��l�^`�aG.<=H=H'+#H'A�1.�� �Q.e5�|.Y'trQ�:z1. War�]:!wA͙�� �Wanot�S%l�E tom� , ex�G2�.1�ms6% 5 m_ "�� ɿc"�� �,!��5/�ob:��,� .?�&��6z�6�iV E"�|��!�$.�L�"2�^� �V�120 j��� $J'=(i >%i�.jsK� &$)�de`e ��by�%*�-���� * E%�#@� P��#�i*"%�S&� � q�RiR19)7 <W^ B��f�K��K �I B&)0��` >jV�##�$H'!������M�Q��B� eH'}�2�a� �� ���  ��պ>�}�F�NKh&�lq��Eit�h s�y-���� 1�H'�a�E�&NO. A�hC� aT�!aa$J'A�2!�.1,1�P1}� H'&= � i>*� �),5� -!/c�I� �LV!�K- c�c &�2� \nu,t_)� ,-2,-�� �di\nu� t_{\nu} 4 lfloorA� \r *F�,mor�H�5!=A9ca�G.�llr5h�|um�Eio-iy�s� ��[=ny.�C2 %�&�.ig46i��&�\max \�_��:�% -�^25b)�ti�-t_i,D)��Z�/2Q �P� =\nup% 1NV!�=1B-%� &U { V $iAn}%*}z�6CV}� %7 B.13�5�%9 ���i�j�F i&� �I�>�)�$A!E�+ ge tM� +-a�fn '$@ad�F�Fi/����$ tr;�)&�w"�E�)_{&�y��s�� � �6��m� ��5t�! �?�;J:tӖng8wpG;2z��ris��aq 5�f�j�e�in~�� c*+� ndeed ���5%l6��6jn1u�A��%VѶe�"�'Q& > 4� �"}lH'�o%�� �\,0>� ,-&� �M19bC9_,��AK!� �I�='�6!A��q�kcsLQ� .�Q. "+>2C2�C'vC!N.�J1_-6.E% �0�>'F`u�1�)�6pe'A u�^2()"�a�-p6 0is equivalent� by the symmetry of $\Delta ^2 (H(R'/J'))$ to $(\ �_{j+2-\alpha} \le -1$. This in turn implies $BY2> < ( ~ 2!1_X,us, lowering�Z1 $�1� degree $jO�obtain� H''_{�j/2}$ a� \eqref{d!,2} preserves!<8 condition that�'').Ki /,Hilbert func6�of some height two Artinian algebra-Ncomplet xproof>Dthe Theorem. \end{}\par  follow!0exaELs illustrate Lemma \�HFw2}. In particular we explore howp>�$s $H(R/I),!�L/J)$ change (recall !8 $I=\Ann(F), J G)$) !iwe altera(coefficient�$$Z^{[j]}$ !�$F,G$. Here,re!\Da marked differenc� Mases $I�@ (J)\le j/2$, and.>!�Ef e subsequ�%" %"lambda} ! ains)�of� obAa!�$s. \begin{-sP}\label{anoninv} Lett!�$$G=X^{[4]}� 2]}-([}YZ, F=G+W85]}$, we have $5=0=(w,yz+z^2, y x^5)$, so.�= � 9�0=( w^2,wx, wy= ,yHxyz+x ^4y+wz^4,X4, z^6)$. Also %� J)=(1,3,43,1) )V�qu%*}EI04,64,1)=A9J)+H_2.I�3 CAE)%e�addaI$6]}$ term,A=% $G_1RP]}YZ+!J,6]}, F_1=G_1=\ $J(1)M�_1)Y!Q%5%z^5, )i 2i(1))=5) $IQF QRo \ ]=owz^5-Ftf%w5�w3Fz +H_0F}�LQ�5ЉA}�$t�� %� chos!�=(Z+X)^{!l+(Z+2. Y. 36X+$, ��sumak(6 divided p�si�let}i�n��J)$ ha��4expected value )OI�!O@$ (see \cite{IK}) d�D4 (J)=3$. From ��@,�i� ��2�A�e�5Xu(��a(u3�4,7,8,7e3F�� J,align*} I=&(Mri� 3-3y^2z+2E�0 x^2y-xy^2 ,xxa� ,\\ &51 z-18^2-99x:-18G0^2-12wz^3+34x yz^3, 53+4A�-9y�> yQ� ��ťOmi)0!� pure:� from $G$��F$, to��G_1,F_15S���g (a�5�7,6)�, 1�(( &4`1G9� %�) e�!�I�� ?VD m$ showA�at it��not�inclusEofB����C keysi i��r �� � ��L0$. TheB�I�I)$~alway�8variant under a���l!��}�l of $F$:i�Zs-�,z^i\circ F= Ŷj-1-i]}+PG$, linearly disjoint ><\langle R_i\mod 5r V$M>-PF�Wha�j=8$, �X3]}Y^{�@+�X2 �n+ �3�e�nF �s G= (we2E�z^4 ,aeQai$y^6, xy^5+ah^3z-y^4�T 4-y^5za 3z^2qYt W���G�r,)�MwY�9U��I ��l �|7�$ satisfiesj(1�t11 �{E� +H_31���er>�I=��& J1 x^3z!D3y-Bxv%&��6,\\& nUx!j^22 ,z^81[�qA2B8B�Qedo for�m�Rleads �(%Pi�$$ with $\ 1�! ) =6�E $F_1, �w 5�:$ )y yingJa�X�%eq�V\6� It mB  b oughmXa�previous��sA�atP a{� ag �l$ generi� y��Hn, will ``improve''1@a $G_: such�� $J( -&I�6)3F,  =5� j-1!��-]� >)NJ !Mis��L would indeed be an �ment, siO w�]%� U%�$%b4minimal resolu �*!}Hideals $I,J$ appearATbe clos� a>ey areg �gIg $. I+ next� K�Y%f��5��0'' must occur^����$$, but can (s r (I >J )0 by replac� $z^j-u,u!�Jy((x,y) $ K[x,y,z])� +', u'.� -V8.N!}�� )), � � J))=H)% R/� v�)1($;Rt i} I*�Q: ��Q3\ne 0$�us (e=&�E7m.Q(R/7 ))=�+�1%�O-F))= ,(Vor ;#΁�$��|��2% 5!H%Y.+ lat~� may�(for at most�� ��5�_0$; if� �e�^en<%= � _0, ��,�*G 2�_01h)-2�1� }%�"�} 5�  tEY-��Q���aV�vaab�!�u y!� �%�e@2��VvbVx0%1�allɳ�5�@$ except possibly5� -)$ _0\not= 0*e ��U�^���).$� 5VFb<�SA�$i�-1,ťi]}=wz^{g }% "x � ��i=�� ) �� . _i$c c$ e se� statO�Փ is e�ntv$first clai�6/i}"6X a��(  $I9 m.)$ (isomorphic,:�1� bles)e ����6�}. �S*� -����I� ���U�$h=z^I-g,g\in � dot � ��)d�*0!�u f-2 B YrM�"(z^u h!�t(B�)= z^uhE 1RE9 j]})��Z\� -u]}F� It5��Y� 9- Ii]}�R uGv�eisX  H ��i � $,   $<]�_imK_i+1$, IIby ����ne� E�aMge�q �e E8s i"�M�A�now- I=:=����i�I3h�d5)-)$.f|�)E}E� s.�>FN �M6�1}Q� HFw1�: e2�concern� )���Bv}�ise6Si} e6va}�,sam�iG6*A also�ve:vb� Z6Kv}I��r��ionalJ� >�F��e"n��� u�,�*�a, 3]}-~4]}��2 4]}+X 3]}*�.y(�, (x^3{x2z>3z, y^4-�+�2�3-��2z3^2- 3-�+��z�26. +z^4� M3A�=4�I�"�9,�E"n� I&=(������^3����B�^�4�,&K, \text{E�,}\\ &\qquad aM�7,9.�r 1,1,0 � � 4�6 � ata�}�l[}:�a}Ir�}Ս����y"�Q�Qo8 \medskip \seg{N��h"� �$� jarb���consi(Gorenstein ces ---Bkl � 7�s�{ $ic about $�aPhav��a�� uU" �genhfe} �b2�,i�8 � any socle  $j� 6)` e $b$. ��in- m�f nonempty2�[ each�.�1)��� \emph{SI e i�� H �!H:D an O-P�t< was�mn� R. Stanle�W< by D.~Buchsbaume(D. Eisenbud�,characterizeV�of"� hP!*'8BE,St,Hari2}). �aNF $H*��5 ���ArtructUE.LYEel� Eo$\PGOR(H��$as quotien �coordin� rA]}!uit=  p�! ual schem#�@w� good�trol ov�eir B�$ numbers (}�sev��82AB}, CorollaryI60relGor}). In &k!,a��B�"<�a {SI}�I5�$7E h1� �cho{$A� % ! E�� $I_2$   only� � relaA�s�us $A in \!%H{{\mathfrak{C}}(H)}y  locus��I_2\co��wx�wz�$, �a�os;N�NI1��at�st�(irreducible8#onE()#s�!-�t},)� A� Our resul�relev.�to!�$ open ques!/AWwheA{�# four �q�s. SI9�$. Despite ;positive�we doubt%�iFe$rue� generali�Remark �SIconjA|We��set�"not%�. e�a�$l�0we usually wr�X$h_i$ for $H_i$ below..UQ��8 H_i=h_i-h_{i-1�%By2{i,i+1}�(mean $(h_i,'+1}� Given aB $H_\Z �\Sym(,jm �Ue�\za-� $$2�%�w:Bd .X_i=!%s} Ni SifU l \ !{j-i}2%� 6 NA٨� T �oa} W ո��s.��&Jn%ׁ�6���/�Z�e��7ى^�47i��um "� b=H_4i��� " is $b=h � maxi:�� $b7Y�~\�' �1)5::,eq} %�[+$array}{r|cP} h & 7 & 8 & 9 & 101\\ b_��x} ",&9&11&13&16 � I %\�]B�(Equivalentl�b���:���� �)4}$a�an $O$& �%, �initi���& ce $�h,b�Ux6�AP $%�b!�b_\max $)�s�� i�* Fin�,e��ŭ:�A�I86,^��t��2"�) � .�bFŭivs&�'�)$ H_{1�3�'0}=(3,3,h-7,b-"� )c,both nonnega�ca�'creasing-�i�QG�� ed>Din>�q�1}T [ =(10,15� `*":�os�brH4)�NH v �� s. FY,� ��~�V,W�K�+V,Wiiia}%� &�� hfw2p  Y�$���#be A L(3)$-&s �,Z� $ ��'.�a+'=H�;��0!B ,3,6,9,13  I��a 9j J��M� H�,M� 1,2,A�4 [M�[.F .!m"G �& BE,DA�Thu�& ca%*h�*aZ $mon factor� � L a*A .�� �netsq5��d� a basis gbyE�($2\times 2$�ior�' a $3$ matrix;[Q�'no>�a!  $_2)K 1xwo, C��dek*inantal\�F 2 �: :� R !G4(}b3��_; $i�a�soAK befo I)_4�$� @4=1�(G� h=8A� $9�Me.�FU�!one lessZ ��6*��B !N/, I)_{3,Ž ^ �s8,9��aI3i�Hrestq� ���G � � $�F7!��hn��� $h=7a�se�(��!25�o2}� �'� Z�/�ƩLs �v� !�8 �!��0 �on�:V n�?�t�8bA#h$. E�j�"j%�0 �!H$���� soA�/assum8Rn> O 8{j-4,j-3})=(b,hF U1Pi�MacGou�$Macgrowth}#lie�:X$ eliay�0L0 riplO2j�wh4%�h-2�� . $ -=(8,5,4�F 04 Q� 4,5} �=(9,11�� extremal �\$9^{(4)}�|;in!Caҥntradi|��R!�=)x-�8 !�M3" (h\neq 11D!2�V�. Qin5�'*@ �� \.��+=�$$b^{(d)}=b�#M�d� $hE}=b,  3}=b+�+� %- $b>j-'I/hA�j-2$. E�� A�)�As)�!�10,9)�� $(8�(0�a%�Q���1�� )�,r�)*�^ ��"� @already ruled out�,Y 0� s� <��h)$ E���0^4 H_6=-12$; APqБ�x 2& $R/I;/� 5six$t�I64% $\nu_6(I)!�6.��ն 5))_{5,6} 3!�cY�ng!�9sc 0 which requira���L6�310^{(6i\!E�f�4F), �a b$A�M�7i{I� easy��/��se �s`&0 "� )w j ���=(2� , as�ed��T�� U�paiA�W �� �_�E.�ўeq}Q[in .� 8� ��Y�� 1�$A 7��)$al enough L-M48 N�"E o��NeQsmof :g5 ^�,��>��q,h,b&��ʉ�� ,*>\Z��:# �e%��"V�F�"Y\Z�� D�>� GVK�t)yB�8of P. Maroscia � 0Mar,GMR,MiN})a aE�5�2�$j$ GA.� $\Ga�7 (\Z,�,thcal{O}_\Z}� 5 "3�Z izedJH=..��8*�� (�>Y"w74is well known:a{ �Bj1��[1  6.1]{IKm�Il�&�"of.Yq2aK�T*oand]"e��96I���� to.62a�\ <beA� non->E-i"F� � a)IR �� h-7&� c-th $h-{3$:��[ '� �����d ����&P!�!any26 $T" at $t_�i*� t_{��p1 " t�:>}2} EveryN���$k %�4$)$����.�=�a�.����6�[ { Hd3) �*{�� �\ �*d,�a�!ҁ��A����0 $hů7="�� N�2A��&�os��P c�rO4�-eG�.�Q��6�) {\bf C=- 8 �� �� j-3,j-2}�*$2,3}=(7,7))�&�H �0Z ���s j-3�j-2"��, $\Z=\Proj(I_ 3��!��F-7Bb)��O"$) upbd}�_\��%�llxmsC6��5deyPC�7_C$3e*�� S:a � A�*9d!U � 7^{(3)}= Should� 9a�)�3�#�0 52 curv�g$genus zeroE�reg�=��so its �� fADY1F �(I!3)_��:by^&A� ng ?I)_2=7IG� 2�Ab,b�5�e��-� :>��5 yx59T :/^4 H_5=-J�(  has  5�2% (�(syzygies�>n@>mu)thirdu dt@ 5�ʡ�W 5+ 3;!8�qj� � 7= 5! $ 7=M$;�q'e�1 �� 3Id-7\ge 4yl!5A�2V 3� 4b�lNa.D7=��){*�� 6a�IDQE�7(I_ 6? 6,7}=7,�f& ^� w���_3=by :�� %,V�.�$jaQw4a simil�8 f~ 5=- �>�5+8!_bu��nu1OI��8!" we'd c�757,8) 6f3�.;on.+ �how� VR�T �7)$Ninues)Ca26�7's~5 y $($� �a�Q 5��M��E+5Q\�- J1nr�l �v+ by w�/f�&I�I H_i�`"��S�u� � $unimodal).�0�= $i'=j-i} �ve��}� G ��'+1}= }+1 -1* -1+e_i'+ati�� �� ɍ� Wq�� GE� le (IS n� i'$)�BO�~s $i'��$i'-+��a�h_ 8!�6��"E!&� a�4r ��3=�.�%�Bu i>0$}>�E�:�i�'=%/�9ϡ�If �&p��&[> $u, � u�4i�i�Du<2� AՉZ�i�߁�2N&���i�63!�� )��# us t���Gc�sn�=B"=+�Ps"] �h=9yJ*o,9�,h_u=2u+�{i�-1}=2i�5hai6� �r );w!�(nsecu�� repet+,A��zm.;% $2�G.�� y =-5$7#�͉W!�-6 j=2i$��� %�In�!%KBM� b {j+3-i} 5��3K"lg �#o� erh��$. =3$< E&��D�+2-i}l�!l)dQi^ � ! 3}+3#3QK�( �w ![$HF�bv O �a �i}nu)! �K'�-V$]?B+�k>+-@.� ) Ix2i,.�^ 2i+1B%mpi_:�F:e�ͫ.�2�*x �1Z� �%Ų:Z h=9�4&_  }�$��Ųi�*� �A�l13 �L!/�!�!�.*�"сs KV,W�.0$]�/ �h0$� :��f� � ��9forth�+analy�"r he%^�- does�#e�:����O% �<#� i}M�@�Br��al nor'c,  �|�2))_t=3t�all $tA��4 Notic�Os�,�H� �t�3t-� 7��&$ iB� �M�&/ �$ �M sE�w� �,C��$(ous perturb%��5/&���k&ql ��!�<�6� wthe Mab'���}*� � P#%�.u� !2-�-1,$;��nsLaiE$-e, e% 0X� � � �-(2= 3i-(e+1)�5(i-e- '+ b,*alt�SJ�m�!sF�leS;�Q��12���P A�*� 2�i���AA�.1�Y-��1� $)�,  $j> 5i+s0sAXѐb>z alcu�0e�2b�1�@�|G , agQTn�I� �| "_ R���"� �AHno8tre"#$ j$; �z���m%V1integer.C.� cQ� �/A��){.1*�1}"� +�ajE L10,dec1} (a+c,1+c,c,�U+c, b+c>�BO7��N3}(I)f5-iA�? �{�Q �j,=8-a-b-4�:i{au� �7�aci+2a,S&=(�b+c �)\hbox{AfY8Cj+4� , �I +c,aB � � {)!��P$\�V + ',  =c � �3}, $ '=.�!>2�;"� *} ?t '=(b�+)F-1)+(a  �-1%�6-3 " @-a�T *} So �> !�"1$� le��(�"  � 'K�a��corresp�Wng ��&`W :�Y CA�*`.�2��0 � ��xn $i+a.j/e�(b� &�<f$H$":RJ %�=�&| ~)# �p!" on $i��kFA�3�$m$ been��r$+&�nJOe-r2M6b We6"*,a/��� "3��=3ŧ a�"i�gu<�����3� :;�R� � ����myi^{(i< Jv>��v��A��6�� � >��N���$B�4*p f0�.�-*6�B�� $>�Ae �9�i3���!M1$.�R�Ml[ �i� K7nn 2> 2�i~ lta0,���2���v6NE%2.�(,=4-(b+a>$:#A��p&�JW+):��Kp�<=a+b-1+4-(a+b)=3�$�Ane��� two &�ZsA.�8:('is] :�mB�(���B3(i+2)�A*�H�{� $����C��� p >"�5.� ,Œ!��9�>N�'*�-�� �&� ft Y�-�/*��� c0f}0I�� i-VN+a)O\�: "�1x6�:�Y�) Z>�1y*�1�z~ R"'�K>�1�!��� � ISa�!�bH3 �'Nj�'��x�#%r�,.&� �genhf� �] �f: enot $"�; {C�;\s&]tY<X� , up�A"�=m^�2�AM�&�{Fa�< �^h�t�' 4]>'6'a�e�1'�(�3 h-1,��#, 3,1�:^ corTl3}� &� ;m�uF!D are &�&f^"LJB:Pdi}!"�E�*�$ **}PCBDf�*�@2 NMBN^*5%��5^iv}��$52_���N�A!�e5)� ��$,h_v,h_{v+& /V2 guv�! & A k end{9� U�Y �&p ,6gF�F�!��Y1��A�Q��' T�m8.A>�2PB$i@42�A2�at�?3 52ZF%vZimmedi�Ac^ *��e2a(H@C�-verific� �"�'16QmR� ��rBv&�L�"�C-EzC�Bu�b�� +�7St-7 spec� "�'^%��)>�)I&+ --- �.��DF �[-� 5.25,"( C6�+l �F}i�6m1d*mA�s/.�BU<^!�ɡ�F�ii}M�I���%,fM�3r�A`leM 2Uj�Ab�@ t�`��:ed�-:\�b�O�Ao"6aI77} A �ic.��B4,a�Bq#, 6�;�-� �-aɽ�Mif!"ѯ��F���~,]1<6�" 2�2� &L�""��,�F2Ks $a=2,3l7Q�*9�5/6� �'a=]%t�h_37 ���u�f'�.aA,O�y�1� .�) A�6�H(A�<r a&,.�G$A=W3%ltb�# ) �&p3rEEF?(i�# $��!/6] 3=9,h_4=b �  uP.: *u[y1�^4(H)_4 j=b-1�)so!� *LN�RL4 $2&K�_4_ B 15-b�*�1IC&! �#_j= ;-j"j�5�41�0!�" ��I�R=4$�y��X=1 �? b�al�� �_j=y&B  �,af*w%^8 How�K&Qb_ja1n �j4�� 13-b#8$X3)) b+�;,.�>of�8#,1���| �A]>])&be��(. Establishg�-.��6.m3k3le�8is I�e$�b,�5S= �7ir�e?�S�Q&8!ith Lu�4 :�J�6:A�le�'- �G read��aa $a=a�UA�:sgi�k�n�7�- 5,72 i�1Pf)���H:i�0�a6)7r)w|= �em�=aCN erci�YNot�  &�XaO""(,& S�.8�2A�{�/a�s 1aW: hQ܁V&a^{(j-2)Yal��ž�. �  $j-2� 4� 鮱�!rk �H {\sc Do �?bAI'2y&� 6���$*"E?}A��W�W!ENQ*�3%{proba=X�_Awan.> E�K�e=be e�.�i"�2�WA�* 2�3 C�kinj argu�_s!� used���ik" �)�6w��Mto _Qjnon�� ing,".=D4�"'l,�e�(v of:|!�de4Gotzmann metho��.Bhgeo!�0 .��ɀ $. Ra) �#h>c(W=�1� invol� � twis4jLcubic. Likewise, in �b��b�oN��&9o�usx&t�B(detailed inAi� �(low� ��o bb P^3aMpa!�u%� ncJ?�KecZ 98�8}S.��� at doA u_! Y�E1-gJ�2�� m� Rp C.bG$i(J��he &G �'-$i2�1�Y $Jj$eIA ��  6r-"�MɌ\q9�.2�tNL*1Kxq \ highes�3$.�bh_jN':!! �6�J �t}� %T�*s61�r-� ��*]6@ T$Vr&�R}5M X> $h,b��arbitr�Ps��A��necess"�Cp�i=:��WD\renewcommand{\the� i}{\roman�i}��eV�b1!i/e dimen(k�ternac)�cal T_I$\P�AOo *�<5R�of\a1breakm^�P Z��� ies,1��1��4spe2} \dim_K �{T}_I= ih +1+�� (JB(%�A�Au �ic Ʌ� �'�s'� �b-1,  , �"~W.�5li � A5!kZariski��u�&R���L_@6hsm�=irrF�Q.�+�&�ly5h"�Z�a}A(-1!E+�$J�6icu Q'>�c9b}=e$J\in5^�no��4 ons6/dN$c} $3h-b-1�5K%>�R�/15 �t�f&l"&ly/ ͍a�f1"�E Ai},6RZ��"P /teK�6A.h RD!��W�K.GA�9�t6� tiibn�.e7&�.^x8^3 H')_4=17+b-3eP+�*eY�it � �n �veoB�4*�---W�Earamo� osei F8a�JAE7�� 3;��n 0:"B>S�@no�#Yk)�^�\�5RcŰJS \ Bc}��Ina�(n�3hx2Jmon/�� $R'=�`� �cerlyB�!s $T'� *MAy(9w�Ttors. I�preparA q stepa�d &� Me� ��Z>%"��%3�  $T�=&�- 2_� ,1_cS,�g]��-�$a�� !�5: inichf_a<d$c/ ��N/$c5 3$8!,-!g) $d:;Q�Din � $T'�+akA$�'PI�$a,c,�G<f-c=4,d3��V�@]�S&ek 7| e�^Eps)HQ6 *Y"�h��B�1�A� >�C�'/J_{�},  `=(xy,xz,yz,x^a,y^c,z^d), ��c\le da�sB&!(U�OY b_d9% !�J en bov"�@*l�Br�K�}, $=(x^2,xy,z^{a-1}z�),��B�A��2�,1]�0Y��:�)�ѯcor�Z}�{5�*� �[� Ked�?� oNo.}Q.<[dN* (*HE)�"IEIKbDp$ $s=\sum_{gO} T% ,d�D $ ! 0}T')w$���1ly������i�-$s$ pN?*^\ �@Z !x,d&�� b� � &$9 $6����m:�\s ��nc�=^\ 5�5�E.d�$uJ �M{$,Jpe1 �E�$ (M. Boij1�Bj1})m�T]� } F�ermore>y�2c%��'j_let $A=A)J,j,F) �6�,�I al�HGA"�C�%�R O_\Z, }BZ j fdz��2*$j$nnp!E�RBu�u.gOA _j^\perp �-��m� A$ aˀm322 ) : 6�KI�sS!$�.��yWi�y�qy }j'��G�2]d�0m�0_ n"/ /.nM} a gra�>/qd:Ya2xMj�. M.~A�� 3��Z�H a� V�)7)%13� m�� F2#��  ;sbal� �^.R9�n(���VC7�Emy6�0 "-$namh R��]���L�%� n �A6uB�o{�WN���z� &�1�� $:�J6,"1�B"�f��%6 6� P $8�6�.�y,.�' R�,p9� NW \aI��$mI�R �,su�bGA���l��E�H" >MA*m�1��LM�Y�i Q�q i:�_ J.�1q�VB�A_�T'��Y�:2�&�� < a6�?">Xh�l�H.'�ea"') q$ J���3�Kb.o\ F &�K � .�n&y@��6{after5 �xo $<)10� "��',c�&U3$2�( $..�qABI>C� S� K���MV�e�"eF � /�fZ�&9(the bw!aA��HJ5�a�� (a,b,c- R'/Ki'6�� $I_2�sNU�+c�  ialDg� a GA��a�R/I�eoveEee@  }$ N�7�Kthog>`q�!A>� $  Y �Y �R�[�o!a�Km�_#q�i�qj� skips \noX{nt�B$Acknowledg�g^ \5# auth�T,thank Carol  �h, Dale Cutkosky, Juan Migli:  Hal Sci-ki6(Jerzy Weymafqhelpful|�cusKs;�:H:� reci`[ XJoe Harris who loaned u��cop�1d�his dir� on�6��reΈe%r�Ze�@inr��A�lea$�"�urkof^L0m)lT\bibliographystyle{ams!��the.& }{ACGHM} =�D[Ba]{Ba} Bayer D.:�j!� Divi!nA�orith�jAR�� 1S}�%1(1982)!~Hvard U., Cambridge..x0eI]{BeI} Bern�l8D., Iarrobino A�A�I�G \ �� ���y�!_co&ufiv-Comm.A���.h20} \# 8 (1992), 2323--23362�o1] y M�{G}&[m{A}rti�s���Bypro�ive s�h}, Bull. London Math. Soc. �31}!O@99), no. 1, 11--1:�2�2� 1�Cs"wA|*�-)N v�� a {H}:�}, Pa�(J. �#0187F� --116]3�3F�.�kp)ata�� �mJ5� �oYɵQs},�ri� 20006�L�L� , Laksov,}NoU�7Kof-@u6�s}, Pr!�A.M.S-�1AyAt44), 1083--10922�DrH]{BH} Bruns W. ,Czog JU�Cohen-"�! Ring�ur Stud� (in Advanced%�e�csA� 39, 2Univers�Press}�4, U.K., 1993; ��� (paperback e�l!82�uEaA E1} "J+e�"N+�yW��mak&jlex�*ct}, JȌi�Ea25E`73a�59--26>yaE} &�+ D!Kzu2�"�+���te free "�ÊR>2�� :.�E�AAm�$6)99 �,7), 447--485.A0ChoJ]{CJ} Cho��H.�I ng BU D:h �"hA�($\Gor(T)$},�Cu�Semina3}LQueen's. Vol. XII (KATton, ON)�),( P!���P -� Appl�,@ 114}3A`., 6Wa X29--42dCoV]{CV} Conca A., Valla G�ь�R��f��� low c�0},e . Z. 230��l(4, 753--784.�@Di]{D} Diesel S.}�S�N"0xg!d5�� E m3y ��!3�H.�PV^72E6096), 365--397.�Ei]{Ei} .��mu;nvBiS��view tow���ic geo4@y}. Graduate Text%�ɻ \# 150, S�d0ger-Verlag, B4 %New York%n4).�@GMR]{GMR} Geramit!�V: !�roscia�, Ro��s]�>!Xaa�du�� $k$- �},aFv (2),�X8%Z8�X443--452�G�$} �$�E��Be� a�Lf\"{u}r die Flachhei�� da"�K eines�Vuierten��e��)eZ. �15 �78), 61--72�TGH]{GH} Griffiths Ph.,�  �IPrincQce)-(.�$, John Wil�nd Sons,!� 1�7��&Z Har]{Zt qima T�m�$)<�;��� ��}����.6r�d��-�13�a� 45--56.mHeTV]{�e�X , Tr!� N.~VJjOn hy�lan�5+d� "!p0*,!variet�~of�|.� �)�Kyoto��134E~-��72�I]{I} R/ �wtor��vec6 �Lm��level�Ah�e272 (200�530-582^IKU2} � A�^Kanev V�nP�� Sut=�-� � D.�iL Loci}, 345+xxvii p.�49) �a L)'b+�� !R*� 1721��A ide͗g. IKl�l.O�j Klei�SɁiq�� ��aN � endix C.,�289--312�(!*58 CV.)9, �0 F0, -#, ��B#Eu�# [Klp]{Kli !ppe�E~O2^n�j�!�� *a�% �`< *� ���b J$qɩ20�3606--622� KuMi]{2} Kus� E�Miller M"� S�x��ya�lase( �,.r)SF rans.� 27�,82), 287--302� F. H.:�m�ic1 or;Mod�\ System� &p u.R9  Ke� 16);Or�(ds!mworm����*{ 2Y ��AdNeف:P Mac2�2j�� propJ���R?Mof m �s�� ����26��,27), 531--552� M�"Mar} "Ad PU�ble�nd| ul�n� seff i�� bb{P}^{n}A* Open� Iin=�G� , VIII, �Conf.d4Ravello, (C. C�o,A)Ghion�DF. Orecchia, eds.)Vu.! 997��J! 1�,��� pp. 290�92� MiN]{ce MN�� , Nagel U5IR a�et�(݈qqs�.ic�T� top��Ial6?|}, Ye�)�180�7? 1--63.n(No]{No} Nol6\J�@�unn. Sci��Ecole N�hSup. $4^e$ s\'{e}rie, t. 30%R97) 36��6� 0PS]{PS} Piene�~, Sch9i� *�5Q6��act�:/os���/ �/�of%7 7%�5), 7� 72�St]{St�H# R5��2��d"L }.�*K � J  57--82� Va]{Va} V;�encc�I��&� ���IP� ��0�+BYSBrasil+ . 18��*� 81--89A9endB��doc:2�V"P� L F*����5]}�R���i�, $F=Ϟ��x�2 $ J=(U�+x^6�� yÃ���>�� ,R��M�2���, $ srY� =�P$H(���)7-��"���-*6Ɩ �:���3#�yJ;�2��z^n%�e� �.��4�9X3./:�c!��by ad."� k�+��gen~�v mbdaa#nPsRJ(؊&x�e4*l9[].} w7m�~@8 K =1, 2$ (& {maQ}} *�3Me=�p\Q�L [11pt]�rA�%:a4G"(\usepackage7Tmath, amssymb,latexsymth fo_amscd}2@v�tim6epsfig6NicsaRtitle[TΚ S�!& DNA-Rear�� Pro^�s]{R/a)"> ^; \m�N\h�28{0.5in}\tiny{ToI aL}} 6"}8*����� al�ceeA]P ��"� $ Philosoph���iety}}��[}�$k]{Dorothy��(k} % Add!��rec� A�bresear/pporm#P8 \a 2{"Yof���s, Br.cM � r Curr� H \curr {DY,taT2LImper��C�qge� �C0mail{d.buck@i '.ac.uk=tC.~Verjovsky~Marcotte]{CynthiaJ}�f�St. Ede's2�\ �c`m@admin.�6+s.edu�new� em{thm}@ �}[s�] .# THM*$2$cor}[thm]{" 6!lem !�P6: Pr.@� scol $Scholiua�!ax}{Axio ���(7[6v dfn}.�2@�6.mrem}{Re\�.8�*{T� }{No#ou/�# �ш{-oA0.?5nibf}{"I \��bzm.&pb}{P_B �!a{5ob}{O_c>ff^k:vEV_H>JV_{O_bFf} R:8Qonly}� bb{Q!>!0wt}{\widetildA�.�4bs}{\backslash:[beq�1E:$e$�^"beaFn��yFF$ F"r2�6 base�!(stretch}{1}#.�\2 .no=�:� ol}{"/":u�2:a�:$dbc}{{\rm{ >� core  > q rior $int#�%�A�~��&�� *{9 AprilK4%� �g<" %�NZVABSTRACT�sZV� �� *{Ab��c!PM� tudy�$s7��tZQ��-ߟrisi]modA�gi ] o��bI XrlOHZp� onfu3wtw���---�"� inve�repeat&�, to:�5t�2si�)���� DNA �:.�3pnt � new�$T"AcheB .�%nA ofB�� �=eo$��t0V�t�0 2 J�ly�t �e76oE�� �DHng �sp�I .ş�!�-H-;:���k N�$�_=�B. �C�C,INTRODUCTION���CzC{Intro i�eFeek!� � lyi'%Yy$�d� G5 c��"?!�pologe4DNA�P!�I�� Y�reg$:A�a- molecuAsM��fw|W descriͣeA� 's � $�PA�Ad"0nstitu� �37We wish�f+BG�4combini�7ܮ%� z. Ern ��umners �LES1},���X >bi!i= work�Wasser B$Cozzarelli EWDC��x�W dSop�/� le1��;-&M�l�+x s abFFh�8e�A!E Tn3 ��ac(Cc/%�T!�)�.)(jfY JC.tt-"-��W!� ����, �Cr� Dar�me SECS�9 'Vaz\Z�6f]�o�p&��F�,%ĵ�) E�f %��(�#e1by��%RJayaram �GJ�zMe� �vhe]��=C� a � �|]afvi��clu^%Ggrae@ a virus' -`�*h��cell's!� (�)��e�0 �1���aA���mea�is�*r*�DNA"�Dsi��+��2i�;g���t�. S��alJMby har�� varA1 � %A=,axis self-cr�IngA;o-Ded� 8it{supercoils})%�s� t<�: unknUd �u��ein%9=�torus���r linkq�GJ}. (VM�sv-asa<e6i�� a fixed ׁ�%A�, ��2dA:�(of� multipleE��!tl�� it,lNhase���a�cZ+l� ��e i�m�& e�i}��E���U:�14Ao�K��acta{��=�~)���� .au�=5 �- sMbA,]cau�k!g=�1�or.��!�s. To a�ately1LYQ}��G�6/ effe� ���;ingau�q mustL,a larger�)c�<n^G�� Tn3.�="P�z-x(ͯ =�q6!9���!�t! far��ven a full"�A ?.T. P��ousł,� �I)���% ��� found &_ by�_!��5*F@�%�_t{�toO���l)� asonVI��M�--�> .�L" . %S����VvA@� R$%%FCr� WeQ,:( �4� keac�ah�a� . U�� Dehn SuA�y techniϕ� "~�6 �x�'� (for�/� � )a��@�� t�� A�5�#21 ��As�0�;; JQ we�re_ ��ir�� P �r�1��j%��3ea�era�#clo�E� 0ide�o22�dT#� ' 4s: $\of, \ \obv^$PRW������ �4.� �AC�nuF� �.s f$Rste��3j�1rF<wV� �2&� �ty�of��s:^� �tabbin �2 \= B;8e:\ \= \kill \>��rm{0} \> $N(\of +!Q$ + P)= b(17\\.6After:F3 + R) 52k6!�/8rm{or} \ $b(2k+R { {\-k{0cm}&cm���Z� �HN,�ZU%�I0 $T'�b(p,q)xd5 $q/p5dur-platɕ$k = \{0,ǐ4\�7�Q�5p� �T!�I� ��I�N <{% it {x}�s� @- i�B: : {� <��M $\{O��O_2\}=\{iob\}$; x{i.e.�N��s�$Oo��$Og�mea� wF"�XE�wo;a�O_1=\ofe ==a�)Evic;<sa.ɚ m�j��!M ing:f/Q���}r�nl�he ve&{ 9 are&j�m��D41.]�D�in2/yMB,a��Lnd �D<�l %s|@[2 K -7-K,f = (\infty)A��.v 1 ���+� t� ɷa82 %ź$k)���P �8st1M��b���R]��)26��*�a horizo�� ��<[3 �isFu�V!�l �I$�Ne�aG�6�B� �.�;=� \v� -0.0� �i{E�� !�A76�.3qt�5� a�U��e&��֞D�le bra�!� ve �=b\cupe_%��+bolic (!�refoi)2$k=2$)� �=l�8,Q�1�,a��y5q!�i�$is prime. rjPe(%'�8Q�^2��f��b��Q� S�dZ3$Q�8 g!6"(2H� ~]� $k�t �yM�=ZLN,�=~1)� e���JA, "0%S�s~6!S$~7. See TS ~1�delSAT FromBb&�`7�N�0%o*%a�x{D�� &� in#k�s� �si��}I%�R$\�Ky 2�U��Ew�%.')Mt puLvN*thM�i^ g(6_cQ��d I�O9ly unfqbl��h_U� �:� "\ ��is��X�8 2��dpa� is organii�a� �J�-� 2���fsome �c�g�Z� Ayd�iA�*� douF�6r3rid%j= motiv��%��groun_Wm;� �U� I "� ) Q����5�or1� Xa�-F|'2�� EermŘ-!� AYe �d� �Rnovel-�2C to" ȷ� .�A���s@kmE�l���=n&S�1�4!x&^N�g�"- !��6les�����XOexten��h� �{��%R�F�u�v%�!�o1!�I�tV$R��{��ofA�� .Q ar�Y���m�=bstrongl���A��%�50 Seifert Fibe�bS�;6E5A�/"� ��� s�:i�3�!��annuliE@� 6�I6~6~� < jV1�5A6M"#' r�"�A.���615 wI� �  vInUO7���e �E6�V�_��)թ!�Zbe �r!ȹ.�u�M�e:,�lud`t/�mAy"<A:�`�L<����2�e>�N,��ea�QM$n"�F�a!] ��. ���be!�dB a gu��oq-����w� ZIh TANGLES, 4-PLATS AND DBCs ZuZI� <C' s, F�PlamRth�>C� �'We X"�ɀ�)a fewrWY�B��acon� �8wA$l/ �� , es�is+Bby "W Win�� . A Xi} Q�Ins $(B^3,t)SF%' $B^;RcI3-b�wA�~?b��ary p��m��&�-�u � 1* s l��@ed NW, NE, SW, SEY t����%erly cd�K unoru.ed arc� endpoi��V!T SE.� FigX�[f:) flavoursWrpA�><�fE}[htb]cU r} \�){file= _`diagrams.eps,width=12.6cm�"ca�kQk. })P{\em{Top Row:}} \/ LoL9 tted��me, ($0'v($� 1$)}.KBottomN($-2$)>1/  ($5/14 >-37 7/4MNote:8 ��fed8.� sign]� (�n�) is} o̿it� .`GConway.�AF�"5jS%-�B�%�a�")�s �Nnd $B$4 {q���}} i�  exisa� ser�of mo�_ at t@a�a#8�WA$ �e2B��e�O2U� �(��i��rp �nǸt4FH h�rel $\p�al$ �+s�����t�muORaOx<� BN: lRjeG�,&�m iX�]BX�~)��1t:g9x 9xp��in�� mee�Q ���+�ki� m�2�I 2���}ed�!� YPsN� 4 �spaJarc. AJ���> c� &�is2�MA�5a��i�ru��i82�ickorish� LicU� All( ��1\1�}X��9�ecab ir� I�c2$! one-to-on: e)��%Ae�h0 s (�x) viahont<�d f7!>& expa�_��"d� �Con�5�w�T:�R:�!f $p/qmhl��S]$(p/q�KRŭ"R)?( a�@te� ng�*B�p  half-e3Z ( ed)AT� ��a�F!� gra!�kVit� $(n����qs�%�P ��$n$.��M�]$n)3bb{Z}$��den�u�� s.& S�� �d VQ�1!m,6�=X $n$ VN($|n|>1��! �itA,$(1/n!��( ay a9G �Bu�q J2� $u,$-\�i"i�no�Q� t�(4-PQ} = P   Z} {"A� � Blei<��\� Bl�#a|m.ȅ� }�a��Ioni�tJ ."��iz�ӒHe�� z] i�&X��&Pv��short�g} (Q e.g.��s�\an 50�% ��s�"@*8�3�i"e� t� ��(Se�l xwel B���MB� ��ai�E� �Le�j :m� � flexs*y,��%)Nr�"��;�[� �'per�Y� �.  � e�~B�b"Fi� 6Nops%�Two�W*.nc�� �#+� |:fepe2�,AA"vU�8�Gtor� , $D$�!tPa �or,c summ""# a �� �� �"� a�(�.Uk��� ) yielM� o E, $A +B�� I a(0) #a�kt���a�s�)�,: $A+(0)=A$.I>ɀM3�� !\E5")^� � �# )B�*% 3i�1"! � �-r0 +  Top:}�� :}F� !u�:�} ^X� Av�w eeI`�en>lA�;�)� a��Jw��� P2-cVNI�%�4� .�i� qbraida�4� 1'�"��� bK.�:�ABS} .��if:4}}).@Rubj�j�* <lj���q � $2$:�s (exh�E�A�u�' !� e�wo � 5s) �Sch}. A� `.�}�ers $p� $q$,e�is�ta����.��*�r� ��.1b�.t  �|F� %%�]%�.R.F��a={P9�� 19,8� $b(-9,4)$.�R� �T�i�!n%%� )* $\wt{T��o �%!^ cG d�,A�tA [Aac� �f c$�3(K�ja�t�;(ree-manifol!���8 �S"� $Ks�e��7 �n!r��2ng=1p2as>N ���R�� ��Bem:`�0aact�#nn��aDE�,fsB�,�� wt{P�j� +,(e�-]by $V_b e �7V�V'c��w-�� $V^k_��V_b[ !7-�1zo!�4��$�vkBy6- -OZ�I+i��{� le�+@ $Lm� �yJa<�# �b(p',q9Z� &k if�ir6��>�Iz�.s�g � g,h home��. ��Rolfseng& ���&p'Us���3�rp���v���=)�G�S!^keya$E"]�t&�$��!�s>��t�l&�'�&�$C%& $D$ �c�qD5�A��!�N#glu� �he��MLAs�i�j�@NVZ���C�nd ��D��a� �u�!m~��M\b3' $$N(C+D�&As�&Leftr�}arrow\ a�C�� up_h D� c$Rm �&h: �Z�Qf6DI2�@rn.�E�;� � a�!ir�ju!|:�m?sol7i�eCU V_D $V_1�ADm a Heegaard splitO�T- ,�ů!�map^ � $=�{\p- }�$p�A: D}} + qF9D}!)-n���k��0ODEL FOR FLP ^wZ�f�  "�B&�"M"m ,%Ke Ss!�?We*��iN���4�,Flp} (pronou�W( `flip'), a�-E.B�-of"/48. Roughly speak'� recog�!s��copra� cW��ce, bin2 se V�+utPe-,"�"��hRم��s� fa�4A���p�!ng� .--,�can�75�-�� ,� Q,a�  #1 �e   .m�'� Z~�1, depen�+�amoun�A.�1��%!Dx�%L, ,>b8��F1��6!�7P!�&� ���})Xa&�-G6C<�+F��"t�s!,_�2&��-C�& I�%6�4.�y0�� � imag6UGz.^9� Fr��9-G%]dN�2A/o=!�#)��o <�RB ed %S/� p�&A�atGy,)�#�A� . %S �q!( b� seNW�z��� , %���F��  neighbo]�%�i ten% tbE-G:rai�/w�ldoA�so) 79 A�%&�!a~���2x1u�>̹nd=��& . a���)� �.0/ (P$ �. $R)TE�1 - arc&� s�aU�-A�nd�P"y ? �&�:.��TnerEF0�7$� e!�e����!C� !#!|�3fS(� W�ly \':E 6 �iun�81�H1 +�1�5y �I� P�( (PareY,)�c&��s�+si!�E@ Flp Y��to�%it chem3lyM�! E�A��mCnP=re-��Af� We� =o��%i%mov��$P r"��it�a -@�R$ (Re��nt)a@A��lt�%co@( d$6�'arE8 DNA % is"�ly�mA\�5�PK:-� ($O$ st��Outt�%$c� .O) ����<~�)�is^*5; A$cript $f$)t�biə�ts.�%%��� j��!5?ͺ�9E>�= ����k$ B3x�H� &�32&.�udM16�e�i+Y(A:/+%��a�A* ! duct.2�re_1n5 In ��zE;�A��ʥ�saos long*j4BS4 =$ rm�� ("�:m!� )} y4:Ed4E � (�5�[> B { { �g4� V4�0A{a uk- we o��]3r%��*��6 �O^k m��APe�u�AFlp�A]�f�. �H�4�4V4 ��m"b �u-���yI�a Q,�2M�ry���.a*�"�(: � B�Ga�[�$Pzowq> �W�e�W�U� ano2?zwa9.�-�@ anti�& llel�gG�ge,�ckeg�@P�;thr�Y� U�a�mat"D� of� d.�0�1�3!(=-(,#al #.�����AI��4$� *qNal&Ѕ,hd �A few �1al�la"f<Ռ(��en ��*$Pwv&� �g=!�)��=1� d#=c align$O &�cryst truc[k  C��et al.}�Wfir �.Q-� Rice�@%�c�O%D 6� �y���0�+A� on %9��u�/nc2X-��va�e �@m/ goal�\�C!�^ &l�$ -�#,,olved. Unlik�#!Mpaperqd�+b7� Iof Cri!���it1$~��>o��l Z&:D�re.�'�ide��<r�ke�Bccq��be look!="a&lya�wA��y s al~ sayb],Ѷ�[�b6n�n �=*�=�� % R"J �)ܡ��}A k���| s;>.�5 � `aTPs )}&�!:*%��*�}E�R %�� "LV� e�&�K�y2�0��O^kX; ��; tegy%to��.�5!�typ*�0�of W=$ dbc$(�<)$�e�*sRL�Ii i�D)�"/.NW �, {���s:���$ao nd DkoJh*% ��� �sɌ>� ���`d��0},!!*-;>�� �P�>a natuvz �c3 %��5on:�� %&F�Ϗn hea|( "�#>�0}�@ ,<#,6n3*�-� (6�"dirinv�"�=!=� �� it)vkty8��5�I9 9�  K3u �� > >�)/& [&6�.-���1l��f���)!��� . {\emM� (left�F IM��u?B.,.>- I��  �.�a%�"�A*5PE�.�sC{"����&�!�M�an�'O�! _��11B�!fH r�L'Q0�� <'magS9 � elec)5 mi�!copy)ag���est"H I��!�3iB3I4IZ$��$ (�C�b� ��b(5� ��A�: al e\"� M�!�b�T�054��F&%:5��a,��`2m�it via�)͉ i���>82k+1,1)$, where�m $k \in \{0,1,2,3,4\}$. We thus model the action of Flp on DNA with inverted repeats as: \smallskip %%%%%%�� \noindent\fbox{\begin{minipage}{12.4cm} @center} \textsc{I �} \end} I�tabbing} \label{invdown} Before:\ \= \kill Rrm{ �} \>$N(\of + \ob + P) = b(1,1) =$ unknot, for \-� 6�\\ WAfterV O^0_X + RNY\ { { \rule{0cm}{0.5cm}}}T�O^1DC3 �trefoil�CkFC2k+�<{torus knot $T_{ 2)}$} Z[ %�5w%5�t{where $k$ ranges from 0 to 4. 85�} �e]e .� Whene actsa a a molecule a� direct sites, experiments have shown that the resulting J�can be an unlink, or a 2-component  iup! �10 crossings \cite{GJ}. Electrophoretic gels �$determined�Hsimplest products a!{0b(0,1)$, $b(2 and 4 o This�Pal evidence indicates o Flp e�s ��A1ted!O substrat6Pr�b�An ��converts it via tangle surgery into a tE�%:�k�, Q_��-� ��~� ^DE���������for}\V \\ ��������A��P%�ZY\\ �R�A�D HopfI�GkN��@�����,1��ZWf�AgainY�����6��  \a�e${SolutionsF� �7(proteins inUtResolvase family of recombinas�;,such as Tn3 e�D�,,K0y first fix $�~:= (0�� then rear�@�aL, often multiple timpb�� relea�O it��,e correspond���c equa�:>�Jeqnzy*"\d}{l} N(O_f+O_b+P)=K_0 {\m�4hspace*{2.1cm}+�(!l���&4-1.5ex}\left. �NgRg1\\zR 2arQ$2cm}\vdots2,\\underbrace{R+...+R}_{n}VnI� v \right\} �for��Xi w . =)M\  �3been A.(ed by ErnstʼnSumner��0ES1}. IntegrAYQs4, however, do �A+!V�twri ��act onA���B'DNAE F�6 4 take a varietE���or �ed!�(ms. To accu��lyo  t�G varyAj �,�its effey�2� 1a,, we must us�la�  numberaeI��n need � Tn3.� h�h�%+our4$o find ($PRO_f�4 $\ob$), but 3!ca�s1� * together the � 9a�$!ri�:$creased co�xi)b! 0 m� QuY Yha�(us far prev $d a full s��W T)�. Our �4m� aim,��� ioM above, is@descri� YZsystems!� ��P& �!a�b+ Flp. For !oNF will b�:$e apparentAH di� G p$ b��-� �followAq� 8gories: locallyQ�, p� ,7a_l�{( $(\infty)$ �E�, strictly ra!al. AsA� shall see ?�� wy!;easy to � $ out, leav��oE/I�o� sider. WY %re exist!I$ree classe%l1�s. ExaADon '!f% wasE% ious) wn � (me}: $P = 9�C�s B i��l. The "g e ~�wU $P=H, $R=��Qe i`V�%� $O^k=(\pmi ))$E�in ed? # 2k � �(. A second)/�$Pw�b w�%�f.� av0at most value!N$k$Y4�#2 %%t� anJ8)� wise�e&� 5ANis� -O$!B)JU�!�!�pm 1/.6 >609�;{k>0}?:Qp (see Figure~\ref{f:bioconj})� ich!Zbiologii`equival� to A?i �. (Sei�Conclus�!k more� ail� VTce.) U�a�easona�argum�EQt�lye\tra%_$e mathemat��Jiliti��i� ��M : si�F�c$is negativ�� supercoilA�� MK (n)$�' $-n,� !� FU�R$ eachk res!6 short seg�AtDN ��Qq1")) Cri!� $it{et al} �v�of � typem2Crie3n��-�^� non-9�� A� a�2�a�1)$. IQ��!�m�Z$=(-� $� =(-3-90(-\frac{5}{3} $O^2_"  9}{5:313}{7}� O^4_e� 617}{9}�Foy'B�uhor � 3}{2r1r 7}{4>�11}{6B� 5}{8f�9}{10� See 6�%�Sol!� %be6�$O_1$� Ta~1@ beE�Fur�z , if  is B�,�{ ������� { as ev r ��eV( sumAsaa,a horizontal X. (Not _iA�e64�K.6w�a oppo� sigMq is wN�Kall ``A�canon�"A�m.)>� � f�}[htb]�4 \psfig{file=B� �Conjectures.eps,width=3.5in} \capH{0�1} ��o� sf �:c U�� two!G oremX S !Xfac�$at $N(A+n+M�=D(A)$.."�thm"TSecA� If��E��� �g !�$O_2$!�Fn�pnA��A =xѮ_2f$.A� addi!D,I�S:�.r ���]e partu"l $-(P+\ob!%�% .z,\nibf{Proof.Z both"�� is $P+!=,��i.e.,} =(m��As!"6K � ��_2+*!also aFrqz S��!�6m)5Au�� no S�q�!7is mea� !�$= (1/n)+(-R� |n| >1$ (�y|n|=1$jn 2xQ.)Ve�of�c# t� �� = AL. Su�� stea� b=O_2=�, \ P=(s�0\of =O_1=(r_k!P)EL!�+P$B�� �p$Y+A +(s) n�^T� $(=(m-s)=\of$�fixed, w: �Dhappen����6m say $� j\/ $k \neq j� 5 հ-�!�"fE�a/EaN(�?,1}{n} -m + s�� = D�"�$" so -�� �[(ontradicts !� . Am�q q�cannot b!�ime�Th��[ 1int1� }e�B  by 222� t}. He� ��e�q no� � x!�$M k->.1�!+Ga�!)s 7k=j��5u U�si{aneX !! ase � o. \hf�%$\Box$.V:�e��xer��r 12.6x�s$Z � B� \emphV :}�0�6� IM� ��$� ��N� �B � z�|1 | n� nM� rN� >.8 "� �29 *� 54� s*� &�A;� _f$'# "cADm ($&�� e sam�)i^�in �U plus݌Kex e la� / w(w $�$=sn; $n$.N? vf&V �Ժl*WIn��q .�v aa=c� f=5���. A7i��$( � ..a�en��g�Ds2��h[ abou�e"'2�.q���-0Third� Given.�in ��$A���� �Oenume.4} \item[($i$)]F O^iAzQ�� �$i�6 ?>�mpm � [\i9�� � � ^j !�� wo� ��$t!p$P\in �2\}$.IN.�� %K.d  6: ~+��!j=(b��N>som=?]+ ei��� + b OD(R�W)�1ja�  or ��s%�is"&�� \@ Rrator ��%�&����N�, h /r)$s($|r| \geq 1!yQU%�5+ P=(p9)jAgn_jJ!�eG $^$j �,i=1fU n_j+b+p)=��so $p=- )A1 I� �� 9�,>^e!� is m*b 4=\pm 1$,�$P=0$A�$l 2$. :rE|.�small�#Th}irde�ck��&DX���4 but !:"F�aU�'remain��L�.�n.$� VZ�8: "h , o�&� �F� ��2as �!��"::6�q�eƭ!1oneZ� F{!�5^�0bA�RI:C Assum& t�/��R�91 .�e�!�$k: Then,a�d um!� any F�of!0�S�!}L ��Be ! = 2'�n� &> _k| >0� �i�0�So �x/�%a�%= (u/v��A�$y,v >a� So��ob+��N.+ E& N& b+\o(@ + {(u+n_{k}v)}/v4�in���rn}��,$|uy+xv| = 1 d|uy +xv Ty @. Let $\sigma_1 ="W&�}(G� � (2V([� � /q b2B$Z = �;$ �y =)�5$��n_� 2�$,�3 ing $|!� >'$6�.� �E�$k��nly. ��0 oq �F� nor *�A�2[ �}(�"it{ii}),55B� B/i})J] &\ QI���~N W % 4�)�1i 9�-uy-x)�+x9�,:�-2MA = -2 F1 Y�$,Iz!.e.}, ]\pm�v Reu*��wv!�y >ݳ��sA6�F�s٥' B���0� � . �/&�W���"1 "#A��n1cP=m2}����-W R !e '� � ( i O^1=�5#+ })$ �͹E FFh-.F 7}{12. 1&� %%��=�An illu���7Zha!`�s:"��he&e �� :�#o� �eer2, ,�)Z-� �:k5�n m �(form ${U_n}1�$1+2n}{3+5n�(}%�W �$P$) a�satisfy��.�+O )=$ �� us,�0 memb"#%>f I�<% � ("�"�%!~)A)�3U.A� As.@"� � +"av &�����$is a $U_n$( $N(R� b(�) (M� wE�)�  =$�,&��).,Rulm#g�9:\alpha,$�)�i�� $ ! = 2(!� )-1(!�)� +Y So �xample, a+ we:$ $n=-� !%�*�we W$3� nd+ o��W�w turn �#a`!�yreducj �&$� ��il�q&�"Q�.%!�s�!�b?" o %elimin#l�i�I�*� 3.��  %8($ %QV . %F�-�$3$-d>-�al*��u0A�T, oundD%Di-  belie8&�Q' aligwe��,�s��%,they rua�"4Iz�($ (anti-par2 l) %� m� Rice}�%:�$=$ outl�- %%|"�  a clearV-lane��why thosecis %ar*!In faci0 �M!4binds circular4 %�.an odd]/"�,! %orderAb%Nm in %2 e ion,�U)t%�P�*bl t��%AifZ��an �%R� %nobw 4(.c� duraY*%_!| %T.2�$o $k �1H24it{vice-versa}%&�'E��>����ndA�!� could! a $�� %I1+kU�w. truee�q:9�of� urse� !� process ?yieldn�2 oknots. ��z�d4 RATIONALITY ���[� \�,RE9al�(K �Mc/ R�0}���k*�������',� �o5�A0i�  ",u@�'Q�un}!�&?#Lt�u\1Q�~8*2u�ted84re{dou��branch�)A����N�Q irɃb��a�1rOir!a=d �o�`os  n,е��*�;#$ a %)O5g-\)�" �&�#-��0QO^�0{O_f}^k + O_b�/�a t g3$a k \i> 6Z� %.x/{\�%!� ion{bold}�$2normal}}�Q�R�R��� provk &A we utiliz����strongl�3�AGA� s. A  $KLQ�1�'1}�+ �)a��vo�  ({=c}e �2 orient%�-4&rv��4homeomorphism)0 $S^3<�' *es �A� seI-r�A�^a $K$. By a�!Waldhaus 6�85.(�\pi$-ro � w��ax�sy�E�jeeR!In�&|+zpoiz6�Wa%We�� establish� ��%&: < $V_{R}&� R��!*$�!�d $r: .M \rg(arrow .fa�-�>~1o 1�%*� ut24%!,� pun& s>�v wo arcs�� orbit s1 2�/ rE�a 3-balH�{�6 uced�xj 36=b�VH�X c�XA�2~�z!0� �anyu�-z����;0 soli �9:� t!P A-�"� !.25s: $m: �2�P$ M�� �-� �7�B�t�I7#�,$\wt{m}:2/6GPE>eb!�:�diagram#mutes:B�� &�3CD} r �3 ,{\resize�30.4j; !}{\+$egraphics{[ � row2�;,}2� @> � >> V_P�3�< @VVV @V g VV�; =u Gm*>> P����B�6�%1le&�& si} I)]aBfAa�r�)�!��N(�+.=$ �o@J={\rm{core}}(V_PI%ab3a���%�2�>�XY:� eoE��� 6ea� �1�is ��$$pEt+iGa�map�Rn gives � A�^ = wo6O $i:S^32E�"%i(xpx$�$7 � �8 locus $p^{-1}(V�%� ?y ?�:`0 \backslash :: 9\{x,y\�.  p(x)�%�i�n.j�@-IY4�.�. "D $i|_{V_P} \cong h�h$ 7�hom�� $m=\ak r mR%:eT2lPf"  \�n�rEV�OA�I= / hL!duc��I?�$g��P2�a22��!�m(�."[, we� cho�$J'�a(.")I ���@� s S q�arc" o�%E r(J'ADJ'!x'� t6$Ju�j(J)�PAGwe en� @ �e$J$h�isotop�5o � J�in%P$� � Si(J)=J$�$r:..e2VI�F�-^�  on!l&V$h = Q� $ do�?$�<'$J m�� :T .�2��� thm}�P �:+�+.,!�hA4s6Z �"GX2>&"� O� W(. . �lso r$r rm{dbc}(��R�4�(>2aaZcomP s� j by Lickor � Lic}, b]=L(p,qA�soA� amW)iSo�#�i�5imq6��b&� ��wa  Lemma |"si}�bO�=I^%qY+m{2Aɡ��2 a (n�) ivia" s��)�R ev$ ek$�.�Ee�%q a�O^k�up+= L͔nf8$/e� .2.R.�A!3.! L(6���)��*"� (by HirasawaH Shimokawaa HS}:!$&X*s�A�#on 3t) 5 �wer�  ( at� lens� / !}@ $L(2p� �Q�e�B+wt%/&-==�e ��A�n words5�)��'iE ,! �;9� >�2� :u �jF�6< FURTHER RESULTS�c.~g� "uBackgr�A�F�3S@ults} HA�we la, e ne� ary 7 work;S�  6�8� we 6���+c=of���"�^D�-Alglu�Q disc�'��^1$T�/$P$�R��U4aforwarAn s8a� e�D}�!dbc(D� ��ed2�j6an annu+��\�1iala P} = .�`�znow�U^;dar6Da n}8 detai=y@,dfn} A curvea��b!�!zof6C w�-b�+eV�.�U(bf{1-longitX8�Nn2�.,meridion�7(if it wraps�,�+�A�$0$ ,�p!�vely, .n ly aI\�.9��]�>�1 � �%for��*t�<�.M ), $S$�Z $T$^d.H A_betwe��)),.� 6S+T�  Q} �R \�CS _{Q{AD}}�A���,!n:�. (-)�+UXDe9�A $V_T!ffe c ]$VjW6Z[ !A �+.�+ \V9wt� V_T�2� $W1 f at &��9�Ziv!�,3f��J!�)�9 ~6�)����f gra��tjsifv�-�)$ aI� >�}��-endiR:� rq \& $%� It�V?^2+ lift%�D)-�b\ori�4 �4&��!eof%m�half-\1%�T$e$a�, 9, ,+A�$�a�T$ *�#jC�.� �%4 next.�12���o$ 9,l� ��)o'chang,&�6|Z2�Ms�E.x 8 IA�1� (�2 s�/�!�2of.�91s, {\em{$n+1$.J+)%�U��be:|<q���9�.�C���-?.��@��*�� mplete\E< � Ust"+&$ T)$�<�V�� )S�+i��Dj ���=9�e�V_��so s �*�m1\rI$. G �%�Na&.�. w�, a"�d*  $\not�� soQ(�,%s��M � ��*�, � �E�&�Ga���i�their ��Hs� !dSeifert Fiber Space over a)X" 0, 1�12 exce%� al f3& QN)�2n fib�` �+5�iX� I�+ce2z�I�:��]�U2� �8HN�%�[ a�a�'%.5 .�J�is:M!bat*'#�s�V_S}$� T}>�byA$)Fc1�M��#.� &�7i��(ay).%-\p it�, �)�!�N�(�e�>�aK1!�� �mp�3� ��is :fy� E�V*� � 24� �$i���R%�; �%>rR)� �y� O��F, s�=�*� =a�\bs��j2�. b1� ) = J��.� c�Xm7Jsoa &$0 neighborhood� +S O Th .uMacb<i�u�8W�BU�so A���J���I Ass�2�L�0� �s�+26� "��%Sm�oaC�B"0, @ S +�!ft7� D ) \# D(� �" @ $D(S� $(�%Bb��Q. �@���9� $A$ �$�BaՁ�� iff &ah# 6}�E�*>'eh � *� "*Ewe +�]Nu"Ewul(faces in*� B&  �[Simon"Sim}]k e�a U�i$%\ �� essen���u�*.�eia��+(?+lyi%) C��@]E. �F�% \X$ de�6�(>�� S^e�N(KA���%�,A� v, T�es t a spk$S ;at�6r;K� ce.�cu"Q"�*! �,=0$\beta���� rc jo�7�ut���$S$ t2+-YZ!D YIF�(a����%l�Jz*��i XE�:� -:� K� a )�!��eg%�jY�;��X�� $n$6� % _�B�^JP �0TRICTING SOLUM)S�I) vh� "�E_.��vRe�p"�A} �$����4."�j6�'���-*�'3_ e*=+= O2A�)�0N :vq�aSo6H I���/0ine differentZ�/��apof?�� i7*�R))Iʉ��/}'#0�|,tKDs hold�.`>),�\A,4explicitly sta!:�.�$eH�i- beld we {2FI)"*9f�?ob:0".6<;�;X&O�G�� ses�DreL� &�to� AEut"I1[TAnn-�-&-��K#�E�: A.�љ�7{2�_�W}\new0 \v{& *{-0�_F�n��A*"��F*� ���Fc�2 �,C�Q!ePH!MA���S"@I�:lso�G ����=Af�H2��9oFf� ]� _25orN� E(i 6�T y2$8^t= �16m!�EU: q=r&S�R([ �(^V f V4 B*m�&]XEV~=I1N re w�ߑrtj* -�i,2&E.��&$ 2 closed *lX �`��Q /mp7 h�.� *�$S^2$ x1�� ��YhK<���conseque�"ofi� �q�($!�.*;If!6�*, % ,@wt{P}='$"�(O_1" & *'K2� ,�Ea� ({V ?@}+EAc*Y!. ����� ��,�9�ora10  .ei :���f(� >Iݝ�>` .�.���Xo��� %2�.�.!�2�.)B� � � �]� ͳ"�/e,�n cerE jbT�b�!�!u��j �c`6,u z�+�.&�!���8!y0 �E a #. .� q��=2!s�"���-����hLf� :y&6$:V�r---"4�=�+\obqaE\o\#� i2� &j &�bmX�kglu�R���c �m�q�q>;E��'s9e�"�D}4�knY��!�re �9�� \bs A�la%�d ler��AOA~).C. �"���a<)e&� �9�_M�orQ���X$B d"I�(>KNg�:��76A�%Gn�4 -\� :P\ ong �*terior(Q)&V2b#V%� �Oa$�Qms%�)���M�2x \1�N�U�!#anH��? usfA�a of$ Q. :�B�5assump��-�-!~~)a \� wt �Av�%�IM�*�%&�% of BIgd M�!�\M�\�uon.�� n�2��e�% � ��(N�*�P &� S=Ţ6�uG%#:� �  s �~��oJ end�./v@n*}T�L2| �(!(6H *i}), $Wz��A�_M�c P}*X"L.D$��Ar����PL6KC�E�DI�B! >%>� ($n>1$) o60�}$�D�6� .�})��2�!5,icr an�23 "$.�z��MW   � e. Thu>�e'$(m,n)�,bl&>H.Er�aeO_4)���/bs w !ɡG��.! �:V�DRaʅvtheJ!*� &!*�zi�a�A ��i�>�'ぢ9-P� �s�] ��)/��n�a Cr��b�mov�K��!�repla�${�k$M� �ew�a -plaS1�+!67��^�))��*E'�7��)**W . By6� leil� nd L�l fBL!�p"�  greate�fHr�_ o 23�1"8.f!�faZ'a�-9�Ms�$p\leq 7BfM2 *��N2�UE� Z.�� "� @ �� ѭ�/: �< ��;[H � $VK- .bE� A�&!f��$A A}.�(D}� � EPiZ�K {AE� B0bB (by��orejWf�'*f: i})), $s6��:�V_b}$ (e $s�p!�$tr6!# }$ (iFt7.�9�WP%. V_b�I by J�6�% W Hp%6a Heegav*split+�b�k ��"�5���� B��6W-�milar})$W�2V_PE �.�,-H.�>J�31�W'j� �:A�n $(s,t�!"� �c����6�vin icu?C�.�.�?� L`s�. >R%�:� � roll1+�Moser ��Mos� if.�.]S*� � a� �s��: Ap�R5�� kY2�6� N� many�s} -9Qc�tv� 1.] �[-<"!?�Z�I�q^2���*5 �i�2{.*M 4E�(q�KB7.:; 8�P2 r�,��� � �/P�^}Q� �tW �.AB6J hKL.K� Q��..:L5BL� =L M�R:��Hů�"�8�8j�A G�� � !H��P>�IN^0�/ _f^0&�5"G81�UF)Pis [ly�"a!�U f Qul!�.Qua�3r0 of 2"�s  if�dI�ub.�-�7!<�thLZ�($6h&[A^aG~"U5vD2�f�/ar�)of 2kR: [.� is l� Bd)���.:�#. 0qonlyint&?!^��a��� !jqY5*1v/�!V1RI5'F<)�a�a�JUt�[s F�=of�9gthc�$ � C�C.�,�+)uI�<hg� &/!zero).�* 9�%,!=.>�� f�c ^Ob�"1 Qy-�R*^V�eB*B1*�oBlos�,generH , $A��a/"Z[Bn� K$by2� �*aIF�r, $|a+bn�U,�s%�P a}{b�=D\mp n + {1/{\pm b}�(A��A�N( m b$&O,)z�$I$J��sR �'e]1�  CA$a1M|mays�96�_*�50pr.BF�hA�l�i&WKm"+`.6�7,�&�ha�m# m:h&li!��$ �/ 14rS"�KUW. !�U.� r�N�"F&#�H'�V�2���9distinct>e�b��� more�aWe��x"A .$� H�bF.;��� �[ �VyC!#������_.��.1*�Rk�ft.u`!ua�� �+i�%i�2a2 aEb.�eZ:x�^_j& �A�� , _p + 1/���E8��>��list}{/h}{( sep .2cm tVK1.3�i�] "]0margin 1.4cm .�h,�: �:A� A( &3%59^A��5�o"R*m;N-O�2)Dvp�� )## \ D(� ��us�$ *IS$)"�A�0.���B�or)�.�.a�n�8&��`q,.a�oC�)�4,i�4nd �1 adm�*l���*%�1ԝ7%�� ��� :�,eJI� #d,y*� �(G $N��)s�2�h? uniqWu�~%d}0%�V:e�kk6o|�`w �p�6a�g�[�"be~�9be�%�&�iQh�:9 �a�L�D(\of��S� D] (+1)��)i4wm�F� $ N�jp2)��69qA�2j�q%[�q&*.�&1��8G2M�F)M�I2�0$� ��.��#�4 ��l ca�ccounts%�y:X �Z�UU����� ,�{ea2 a5~�(��f$��!E�ri .i "�q ne"�ksl�a�6�>#I3in@?v@I�V b*�v��6\ �wehSs�L� s�ls m.�"e $(vi)$]JAi!�aj6H�u����e�=.����l=�k� . i|�t.��� ba�imeiJTe(`!�'@0�Z�K �*x-"|FJ*P#. Fin�?:��>�&��,i�.� � e$5u($v���v� .�2�2h $Mj�|#D��!�]��s�1p � m *M�2KQ�� ��E &VE-�.�by-e&&xi-.q :w�e�Im�>]':���u�a�mqJ�.!N  &�if�FT %_>�z%O ��a"� ��p�s� aJa.v@�6HC I�eq�" "+;AP.�DI\�I�!a�6Y20��TjE�%vy��iFw2� q�)1>BpJ�YG.�Eb1 ,�J[!�6�?�ob�&- % % K � M�f,%!.-bd!�6���?��!� "� ed�� 1:r*� %"� �r�"V ��DrDi:DEEY� rDE6A��E�J�[.:A��2. %� 2!� )�6�n*�(m�*} !�F� EN}  %u^or���~  %* &�<z!Yz  %' E -A���1��)o�}� %1ŵ�is�,)BK��so� %�. (i)}�6�& #i)}�Tu� %:!v E.� A�Bb]�?$)] %F�i��tB��82; ���AQn%��a�.e �� !�V� g 5��S�<"�  %��� =�}� � 6� �� �9  %r M ��8�[ .�%� @c I$ %.�za we g�_ �e&]1ASz  %��� E� �i&Qi4�@P�UiB�a�8OJ?9�g!�6iA��F� %"��"� 5h!v %1� A�� !t1�n %d6�b^ 2E� f?B-��_�@, 6�%qى�.n]�4a^�%*� 2.I��� ar��&� �)j� we7_"olPpse5�caRm"�in �� $2�+11i�exe#E fied!�"�A3%���"5 )�"nh�K---]�1E��R $(iiP �Rj[u�[O_��B[%z\�$�o�A�us�� %.���S� F*��c��a��a %!z[ X"a :��%�ee�one %5 f$�� =? *A\4Z|�$k�e��} F*� �:�:��.Y{Fq��Sm� %�� �| �I�B E�!Fu�E�g�H�/V��"� F� >�,�g %�� 0R� �1jA*� A[�������="R � u�v:.�  %!�~b1� %>� Ve%��"� � %ŵ��ba��J��� 1.B] B� ._ �NG LAST CASE�XNG� "�B>�:R"�|"�� }]:G~6��6SX��j�<��n@0t)V+|in1��a�6G�X=5�� ��s�^���#e�on�:�.� le e� ��AY� &� � ��Qƅ�Yq�� F�ڍ���y�em� =*�> S*��uQ ��mH H.~2 |mfm��h���� .I*�D5kt� �2^k�0�.�-"Y$hyperbolico3 or�=�ye @?�\��)$*�T 41 � guidUt�C� Av�� M<�4U//PW�B*�y�-�r=[Q�E))as�u�qam�?� d9�^A�.orMuellitk8:JE�� tors��K>�J E�"X 5��K�.�$n7)���a:�i'<5��2$^@&w0<6$>!�E�52519�5�b"��t]X^)%?F:6O�r�� 1ʈ.w19�6�\EU5�AWMbMU͛*�:.�,~�5:! &�12�6&�)�:�0^�023�$.�2R��a,O��rۤ, �`8o) ��!U R�,F7 $m, x9hmn\{�6��S(r)�  manifol��-  1�>slope $r�N2�1, �'_a�L2 .L2 aw u!��=<Y $scn^�j6qa!�$q�relH%umn n$$p = qmnw%��+ �$!$-#, $/)A�~ ��2 �2HR*�Ycheck�fa K|Ҥ� Eca�!��$L(5,4!r$L(7,2 9 �L(9,7�+ By Brody )NBro�^;�Oa&*/mc!a� 8, �.1�z�� �0$��).#� cbe  Bg-Q Z&^�)f"LJ4�� $ ($�2�we&�9y�~Ef/4 .�fL�|T�|,6V>handleb!:Y]s"� �=i"�}(i<a f�b-']\pi_1<. *l`,$F=W_1\cap Wрa J�6suvP, !��ly� ��h ������t@ $W_1m�u�VBerge�� }, K[RWHuk)�6a�a�wo� ��S^3\rV~Mvתe�di�8!�-�eKu�y�$K�ON,?T ^ &�� �Km8W �E��DY.�1m�� 0 Q�{/��}�&� currQgsev8,��� n?��,��^TD�Gwtoa&A�/�!F"'h&g ��O|)�Ct!P!J0|B�Mp~)�1*ۛ�� . �;� "� &�   3.2,)E�I is�zt �r6 m dn � �V�KJ�p %$$ P��2,bb{Q},\ O_1{matZ�E�rm{E�e.} $$B %nN �!dE�7 K %� v< Bee&�d�okb|?J%�=�!�=�x$i&Q�, %�� 6 0 " 3 n6G!�6�B A$�{*jMHJi}"*%"�aOki!",� for % r� "}T ��.�  %Al�=[��r�l lre*�d�:� k-ee�{ �{ �{ Z{ R%t�} *��I~%l� % ^O sa� D }� U BV *S � a�t^? �b@ %6�\�\it�A %a� ��d��g �B % ���C %2� ť�٥ N4=D ":) 2�E %* ��F %!�G %��H %��I %rC��J �=G�K %�L L Q�� 9 �M %�N N %:O mMC Y7� ^ �u .R %�S S ��T %:U %2U %A� cl�V %l�W %� p�nX %aZ it�Y L i�W_.AJ&� �M %j ge�N "��O 2 ��P %�Q � c�R �  %>D ��D %�T� �E A�ubs�n on{Useful� �Z.�[�� ier-*�H(1987I"(% %)�f{u�P"� E:6K!� m bt�$$\|\Pi_1 ( Q)\F��[fac�-�H %(N.m~+ $4pq"6�$(2  %1�-c�T_� �=�ings��$L( ^D 4q�d%�6Q$Hirosawa-S�t (2000!PO&��� ��I2p�J(��ikv)��2�6���w ]hj�� -Gordon] 1�O!�� � } (r�L��c7m=n)V �d*ʬ pq %"w@>m"F %H9�{O^1}_�H-.�� >�7�>% H22H6g� L:� j�B$-ti Cam Va=van!�o�!s $A$,$B�CAv�G$A+�?C$,�� C�O �p1. @�Dr!imE or 2 � 5�BF}B��M� or�!>W % B5"�Z� cor}U van- �i�if $C$ %*YI:%B��q@�! 8!"� �!,aUa�A9RqG:� �@*_� �|�B�( CONCLUSION�"wRF� "t*��!aY��Ge&F�(%aearch}�Dgk�t���of*�Z!ci &�#ŻO��"%&��pѷ��onA�. q�i.�$2Ig�z �*1"4p"e .����clu��o�� wis �M T*�"gQo=��!A$R&�8u5;\ _*�*�b"��ly�$i��}g��qʎ!! +���infin0�)u,�.��a?� %)!a� ��aye� two NP refl��&��[�-�Z�--- �ղ|r�p��q �{>�wth zero*|C (y� �!r�0e9I]�-fI��oi��6z!1Vv1� ird �6��^s<y&hc (.O�&�+)WeM��AC"�!d*`1Rt*�b6����1*�&����:. SlW al o� quesi��i*�-wo!A8 uo@zs3�s@ \,tOalthough�c���4�yer�ddE�]rof=������sd١s�higڷ�At���No%�eP]onfirm�A�w��iĒd�s. Ca��� &f�al�R̊ �is?zond2�a�tbHAB&���q�,1Tcal�]&{ns�'as�'{ iffn5e impe�a%9W 1"Џ<�salyxeike��Soy # �I�䑂�*9. ly? l2 ;QX��Re!1cal!yna��I�s�jY�a�� ��7�e*�fyM�s E��eQ�E�u � �QL6�t|R�<T e � ��re ��Uask�&�,�sm�il�t�b*�}d�#a��X� stigۖwhCx���s��� yE�A�ARc"/ !�a.�� j(!�)9t�il :c=it6@Q� to ��---oro�Y �i���`6�# %I�^,U� Montesinomt. ���3we�*�ub�)�_y���'�a9��U ̈́>,�+� ��ld�s �lly!�.nS��y-� ap(rBr�^ YtA >�� $\lambda$$�Cr Ln�&%�"�!s� link!.�$Acknowledg0s.}&wph8ank� eron � x$John Lueckn5�.�w�F�\us�*�E� �$e,Makkuni Jaya��Akin�Iio!}. &:,��6�$Mark Haski���ar�rea���rQ����:a eweJH his/�:C�7ins��u��mms. DB��,g�@Mgrant"� < Burroughs Wellcy Fund. CVM:?�UG� Pre��pExcell/f Summ�vcho�V Activ�>G{St.\ Ed�e's Uni�xity�8biblio �0ystyle{amspla̴&�&e.' }{99bJib�/<{BS} C.~Bankwitz!$< H.G.~Schumann, ��$$\ddot{U}$|wVi � Xhte}, Abh. Math. Sem.�$. Hamburg �q�0}9034), 263--284 � �er} J.~��{S!l�� @ d IAh&Is}, unpuq�ed� uscrip�(!2 h(ingM} R.H.~ �J.M.~�`{Cub� ���hole Traa Amer�oc.�55�71�17--3312�le} S.~_eruK�ɂ� mv� * ngs}Nx v (1)|282|8!j385--406|L{A}%R&��L*!��#{D}�}�}, Proc�= ��107�089), 1127--11: ro} E.!��${jGtopɼ�if��",6� Ann.�,A� (2971�960�Az16zB� Y.~ChA�`U.~Narendra, L.E.~Iype, MA$Cox%P!/9, i% Crys $|u�Oa {F}lp%�ov�D - {H}olliday junc��� x: assem+�+n. ve oligo�34by helix swappG�, M�ar Cell5z6},[, 8A897.�Coner Conw� �{O}n :-ikE�Ař sa�� i�\�'��per��$}, {C}ompu��,al {P}roblem�; {A}*�ct lgebra.$ erga}u/ess (197!�329--3582�ri} NA<p�D, R.L.~Weinberg, BPetaeD.W.~ S�8N.R.~Cozzarelli1�>{me�ism�phage ��!Ls� Jour�of=�Bc y (4Y� 289}�9a747--7752�,GLS1} M.~Cul�C.McA.~��, J.~��� P.B.~ShalA�)��i m��J%¡�}%.2&12��87), 23��00.�4Dar} I.K.~Darcu� �� ERanc�.� v�E8: J c� to XeA;mAn|Em0in Hellas '98� ^ ory Ram� sA�9]�h200�z69--29�h����U, PhD�GJ.�Z�2�:�� : organizekA f�Oɘ�=oA1�'Micro9 y�33U$ 4�452(HS��2��K�zi��1��}M6i� s^�� Ú� {l}&q ^ F\ (1*� 12=l 3445--3452� Lic} W.B��"��P[��i�~F�� �26� 98�n321� 2.[MB} A[ xoI!� A.A���, {{D��� T Oxford.H !,(19932!$ L.~�� {E}l�b��$.P!aac�I���P�3!W1� 7�742�0Orl} P.~OrlikzS��MW1!GCa�EL�+ t(s {291}, Sp� er-Vergla�erlin�722��_ T.C.V.~��O iVo� ally�>w�-�O {L}'�}A��nX \tex� 9i1��W 62- Rolf} D.~ ��{K}���, P� �Pe��,� keley, CA�1)��SH� bert�6� eine�Sche z enin6�an� �Z.�6* 5: 2aI282�Sim2 S�{ An a� icJ� z ��{`/� ���79iN7�)1--13.K SECS!Q&� , , S� Spe�W� Z� Analy��$ 6� y���� (Quart. Rev.� phys. (3�2i195�5�f6 Vaz�@VazqueqN�G a�GiQ36( %A*.*� ac/Hed Septe�� 2002�$Wal} F.~Wa&=���6M��vIAef r 3-{S}ph (a}$ree;T�yu#)6w81--92�WDC�~W� rma� Dung� nd B� � Disc���� �3e��e�9�Ax��[i�oG�"���-�Y��:��ci�q�229�8!�17A�72�W�A�e�N2` � Biochemic� -4:�� [ repl� �8>�36Hk 95!�60"�86�8ewpage �n�^t $} ��[G,tabular}{||c$l|l||} \hl�r  2�/&o$ 2T�M�r�$ se &��2& &%"�8uh_ed & "��\\��2� J �� &a�G@2�s}� NG&TQ�1$ &5 &6KT}({\iՉ i}}) �jT&&�"Z}�2�2R v}})�� �U��QF%!� :J�c�0:�r� 5���,bb�5��2 o-`! � 6kJ&W &2Sts0F�,-EVF= . & {\>�h�}n8�%�� �($LH2$)DZi.^. FjB�=Z ~} \F�߄ 1�I�  }�2�9�ql2t�n:J�2Mm�cYOIe!�"=�>-FN�6BZEo [2~nUy)�)#J8�>f>L:�i� o�N5�2�oVBk�b+:>�a�n 6qeT5!]CV $�f9*�E�rrA�567�sGJ:���}6������2J�tM�%�RH^���(#:�6�Mʈ 2��5�bi�ETvM )J��������r�AUāpK1 @2!�M&�(=�q*U5yp.r �2`ֶO>->�E�q�r�!~1�E���a5|2 2� .ZF�H�w:m�F�F9��:z6�.��&2�� 2=YL&PKU �Fo��& Y� 3]�U�.9"l-B�6� -�J=�]&:9���6�br(2!����š0��:^S}�3�N=Q > �� ���bQ��������BmIX'( \medskip &��Al��ޤ��*!�6�$\�},I@ \}=\�� ,\of\}$. $is&�--$�>+oLq��*Z�'�3"�TB�iT.�e�m 0& �!�jB% 2Ņ4� ���w(Q�&�\\Bix  J! R���.NG���T��f�){m�� ~Ra�U�"9F�JQ:"y�.� 2���:��k 21n �6m jF�kFuZY6 &2�6��rf fI�NS!2��S EXIST,k�18v%o.i�\�6O9~��>�:JY�EcZ� CAVEAT�:?U�s^aA5 `�saV F�.\� �r� %�0��&s b�*��Q6�6������� 2�2�>>� "�%i���:���R�9��e�e�e�O�rF��e�e2���^ �k>� C.��Ձ� Y��)�2(�u.WN.�Ź$�8�,��`l2�2�I�:=�gV��Q�e��q��w9��w:�6���L>Bx� v$�p-SBl6���fUF� �S]=�M��.:� � 5�>�� � � � �Cr �<"� % %"�  cap��� ,A� �; , %� j�  �":�_^�/$P$&�J�t�)���+�� tM���# �� �.� \c@��\��dix&=$��"P)A�D��&v��9YY�l_�v�8e!oF�'�ult+U��5r/K2wX �eat4+�p��Ug&3Cyc�YS�Q��  A.1 b.�6p��e�,6e��;0Ts "H�K3$��?clWs�`ضks9� r;r Q!.�9$bDB_9&b(p+2,q_V%� 4,q_u�����Q~��,��C 4~�)ʕ*�;�5��qo'd$�$�,!D�\�<��9 y be�z=4in*R[a&it�+�Q:&�3m}YZ0noS2xS1andP3}z�M��an��ble6(� (� wi��00reF=6b�.!��9r��v��Ws "�%2\� &"R� M2�BM���!s�TM(;%�"T!0m} %%%%%%%%%%%�� \nibf{Proof.} We first claim that $M$ must be a Seifert Fiber Space (abbreviated SFS) over $D^2$ with exactly $2$ exceptional fibers. Note z6t(have base sk4$D^2$. If the Xwere orientable and not 1,.\n fillings yield a SFS o�`a genus $\geq 1$ surface,D lens �s{� �{ non- then f!(s fn #Ttion-reversing curve o 2.�Xould form a Klein Bottl!ss%�is�4), a contradicd4. Secondly, if2 had $12� � r%�Dsolid torus, hence%�$ compressi!g boundary.!� $M$ _,3 or more ex5� es, %$M(r)oeithervthe�(nect sum ofM!�)ss (�r$ was a [ slope)|oP wiseA�1�P$S^2$ with at least 3J�. In n �cA{) � %�IX. (See Orlik \cite{Orl}!�)in!�%� onAss.) So%.myX�A�i62N� FQ�along%4Ef) giveco2Itwo�-C$, which ca�aB�All)Ky:oIEinduc%^� fibr �K%l �5l!� same� FEB$m�A�toq��)ri�AGre�ba;lyXN1 HE�[ �d �itt]�5� $1$-!i q_i\neq 0MW0i=1$, $2$. ThA��y�eac��:�a�Wl$. Let $\beta_1={r_1}/{s_1}$a�a �@on $\partial N_1$)�(intersects �żOo��(so , toge��!�ya�6basis  $H_1(.c)$)�� thisI�L$|p_1 s_1-q_1 r_1|=1�(wt{R}(t_k)=ew ax�A3>�UDby mu �$t_k$. T&8re are Heegaard�� i $W!���$��IwA� T�MAn Let )u^k_2={r!y%{@image!� ,!]undera� glu�map $h:5;8W_1\rightarrow 2$%�we also)1� 2=h( �)zNota aQ� $ dependsA�17-1W�)�!�2 �-q_2 �)�E�eridiaAX mu_1=0/1$�W���(be written G0linear combin��$m({pE�q_1})+n(]�)$aS�Egives�e�qu=(s: $m p_1+nAL=0mmm qs_1A_ BE" s� > , $m 1n$%� relai� prime�� sia),� @ � �= -�$,!�M�!z m=-r!��$n=p_A�Thus $h(%8 )=h($1� +p_1m�)= 2 %� . Foe����Mɱw!�en�: � .H \begin{eqnarray*} � p m%�=2k\\ q E=1. \end.>.] I�V � �D($=S^2\times S^1$)�getM}r_�!3 r^0A�!Eas�`r�`�^U $p_1=p-��we willE� e $p�q!�M$*)�(� r_1= j���words )�� Rb%a�!(w� n appropr�  choi�Sf �es)ax both��.B! Yy��yF}we Eq��=p$!&�T��f, w2�)�4 + p r^1_2 =2$� impl�Z $p|2�!vp>A�%omeans $p4 and -;G-A�Se46�qAB2 s*��we!� $( �h$1_2)+q_2= NA!�F! =\pmK� �60$� $ ���is�� �q_2��(2,��.� it:8t�va� suchI�onك�sY�A�AAIQT �  \h�}T %$\Box$ \smallskip .Jq�Tthm} \label{Rrat} $R$U� al enof dir� repeatsm�Lu�%% >�As� ais�`, so $�$$a manifold� in2��*�I $O^k> WC� $k$�� prece< theorem, yO^k{*Q , $V_k$,J5 $� 4$V_{O^0} \cup � = � ; {O^1:  Li� 2: L(4!��* d3:$ L(6$a�f �R �?a"�Fiber S�� ae�a 2t R AQ4Cyclic Surgerya�!% &CGLS1}�� a"I� �A�s)�c U� 4$\Delta (r,s) a� �� Y at mos��reei-s�[is�z e fac-at�fou*i�� �F<e�-(b�H~\ref{noS2xS1andP3}iÁ q�j�" J��:�!@se��:��Qz 2z �z.1�$ canA2F}th=-Ù a�_ *so m�qr.���� ��8document} �\xclass[12pt]{amsart} \usepackagemath,ams�]T \def\ee{{\bf e}} 4pmatrix{\left(� }} #end&end\ )I G{{\u bb G:RRPPZZCCNNQQ�cal �cal� dd{{\rm d&Hdiag{\operatorname{Zde{\dasBp{� -tr StrTt{\theta "s{\sigm T{\T0e{\varepsilon 2fphi l{\lambdCr{\rho w{\omega{� b{� �A-*A�MMJJHH� t#1#2{{\tEB[6B({#1}\\ {#2}F;]E nZ#1Q�frac{1 : Z/\ZMg ^g} !Z�U$style{plai!5 newtɒ�J{T }%[Kion] .$,lm}[thm]{Lem%�@0 Proposi@}2@cor # Corollary6!�P " Fact!~ � �definJYdf 6DZ!re�RemarkZ itle�ta fun[]$at zero toUMeas � some� ularm%~A�AKpro!siv� , amY%2Bults. � to $z�alAWA�assoc�et� stanthLW��I!stake $\e!8nZ{n},$ $\de=0,O reF%� $z�$n!& nz1!�ultm�taa� �0���!�i $n) .2� a&�Y�?��K�T$Q�S -th power!g!CY�� bundl�duc �D0ncipal polari�JA6�y8 period5�%4���<:�`%�s4mo��!�si�A a certain�group�${� $Sp}(2g,\Z)�re�ai is. Ʌya�ctic @B= actc�U.� orit�3 ele��#amma\in>��\�a2$ a&b\\ c&d� !�W $a,b,c,d��!�.�� ger Fc�R ��isC n bya� � Nse� :=(a!�+b)(c d)^{-1}e�� !�quotienG%�iUvY%lyQ'ed:T �M$\A_g=:%\�slash �.%h$�:+4 GL}(g,\C)\to 6vEnd} V!. an irreA�s# a�resent II�highes�\ight $(k_1,k_2,\dots,k_g� $k_1�$ k_2    k_g$;K��� $ w Vof �h �.�_05 >ed �ed�c E is�lA���)!us fix�ntA $r$;��rres in pair�rho=( _0,r���� N �R� ��6,�u�� no)[Msrho(A)=L_0(A)\det A^{r/2}\ .&$��nex sui� $\GeLsubset6�}� a"P er system!n � $r/2%Y�np $v: WABC^*$,��!Amap� v$\mapsto v( �(Ce!D) �0satisfA�Eco��%die� for 6$y $ I�v�%D:* O�ş~$�!ess7! squ!�,root). Clear� n.Eg� -'[ "e. A! $f:a�!,V%EA ed a-� - or $V$-l d �ar�m,s�y� d (�6(i "` ]�c�,I��$v��.  Q;A�2T�K ���n�) ula�1}��$} fM' \cir�F)=Y:aQ:f� ) ��Sa�QJ�(s M2$� �E5 � in ɝ�,� $g�if adI�$f%\holomo' c at� cusp1I���\H� '!uAw�Ie levelu�BA�BYto �  a _g(n> :\lbrace:$R�@inC\, |\, 9\equiv��(1&0\\ 0&1!j�d\ �OA�}\ n\�\r��$$be��,2V��(n) �Z (a^tb) �(c^td 02�26��$W C %TcorA�o�)ycD(%v�W�  )]��aa�ED) �,2�g$,qni%. I know� a�� �&a�& �!. ��~ $1��(ee��\_0 Id}$)I�a suit�,2 _n$,r !t�$e� 6�$6=On0 %]mG re� s�vC�a}�� �H(�*"�i� )�KISTh_{n}:�()b(to\P^{n^g-1�G�V���g%9Y'H 2oa :!n� %x�y~n\ge 4|A� Th_n��:=. \tt a0(� ,0� m_{I�allA�\ aa< ' ] :��I�E1 $. RecentlF���idered,!b�St!ٰ� �$B<bG � �� (�W ival� M; 4r, see5�usa})� 2;-�in& I"� 2^{!�(2!�)$� x! / triv�' gradb sI3\Phi_4:��A-�)({� (}_{z=0}>���)-� !� \ od��&8nZ{2}Euax show@�0 u�p�,v?q%��� immersD-!�,E� 4,8)52�Y $G(g,6)%�$$g$-planes)MC^{6'�+,Here ``odd''�"� �&"0 �z� !�*>p 6)�odd�-Rscalar p� $2()P)y � � �%_�k PassLto Pl\"ucker's coord7'o*�2- --� o a��1|s"Z q��p =��&� 7)��well-��e�� s� so-� Ran�ermin�扊1v& �are ob�4 �W:����$g$!zF�[\e_1a�_1]� gg]$�&�t� ir j�an de�!z"wb"':x�� D(S6ge)�'qquad �#[ . \pi^{-g}e�8\,\,\tt{\e_{1}}  S�^ wedge B/2/2 }:0 { j=g=g< 0).�*~ $$ V��3�*extena�\�/���0e nineteenth �� ury,��sE.al emphaS,:0i�1�aEper���)& CIV�O|"e�4� �at %��2�(famous �'N�� ��{} '1�$=-\pi\tt00>5&B/P �g�ex�T�o���>N� ��� �]A�ev�*��G� *3$� %�statedm#Rosenh�%P�)��5two��r)}, %�%$�_KWe�~'*`xL era �o$1 fr�t�hm: ��1E��edIInrB� ��ťal�sb#_#ft5� rri}APoma��t }!�n J�&�$hyperellip=�6%nanyC[bu �r�!�O'letaNh�!)�'s &_!;%���"�6ltrK�f openfW 2W )differ��U/ �Np%2%��involv��-��%i��$sA�� med()�.ai%$E�p��to��z83frameA!%)4�acF��6� I a1},2}n9ll�z,��i�/&+� {4� 4n,8n��n^{2g})�p� "�6�,>� J� � 4� z��.�_H$� &� 4n&� �ae@'M�)��`�s $� 2n} 4n�"~07,e!�E�d beca� � � pY&4n�(vb&s� *� &� )o .!�re�a"�� std}\o�!s�0^{1/2}$ (i.e.�� ������=AY.Not.j unlikx ���9re��venh!�includ 0.!��*� s ��Bk�w#par#thoughcourse�( \tt � ,z)+v-a}0(%��-� rF/��ident�  columnw !I"� I�$ 7 *" &i ! s AI�� *-W tg )?1�2-!����! (re� 7"jm�![A�a���!�!)������f<�O"�(6S!<n�,ll �v� �ρv�\`n%�:��RNXthink � simi~ ��u3�be&I [k��sw divib< y 4,�wdea�=I�thL7makes�-��u��9ch;technA � ��~a[#�`a>�!�Y ��ha;&� wM�*A�B�m}��some �|)��5ome��G7(\Q/\Z)� [om( u|tyE� on{A���"4:t}E?&%�ak-d�$�r�� o��b{$"~$X=V/\LD+$ KN�%L the JP L $\T$Hd�by $X[2]�>D&u $X$, Š $p�<XnA�2$2p=0 i"$x=, \e�!/ g shif� u�$t^*_x i��is,)'s bi $ar";/�g� wn~>ly Ze�.�$� �#! $2� $ or]Ea�6��#sb<&{9�E>�&= < n^*%We E�E�to� �7n�2H����U�/�x]�0�-p. 139>�]q�A?f>,wA$C^I@,A2 AC,$�&�&� 2��ds:!�QQe4nz� b.w)=-�=I> 1}{2 (* (\s�'$-2a^t\s)\, ]8{a+b}{\s+\e} (2�2n(z+w)j{a- }. -w))�E�%J N$n� %�� :�Qsin 6 sense1�con0e,"Yng�9&!��)-hand-* je  (3.�>�erm u=� �[ I* ?e ��"�1,E041U addnew}#J`Y"\ aJ!g"#,\sAHq�Y�I()���a{ 3+\.�z)�� b 9�w6� \e\e�((a+b+2\2* 3)\cdotkEet{�f�3AG 2}\sQ�UCQh*-bB*RQ9�ofR.�B�V�s �,a=�E�h�ev00��+onA^��<r"yAJ,assdouP& argu�'r�2v)a�la ��LapplyE�ula (�81B�6^e�t�'us��8�Q,. Afterwards�*�aE�" mma31}e��,b !N!�)� �z+I+�2 b0!w !B� R�mu\ee ��mu6�!0�n �� a�\s 2\e�I�$$���JC-w)B<5�f.{\mu,\s� ��=mu+ �+b)^tde+a- .�kne76�+a 0:5+2Fv^ �����s��WA`we-A:��N�?�B%�f�� ix )&s $a$��#$�{n}$, hIo���he*�">� � a 0( I� 7 at $FrY/l��2&#N]l�&s/T0 2� *�T2H �:�,2uI� }5'hd$a�s}" 71Aw�,& :!�5 adva��&�of&G7)|-� hi*J72O�2�  R�6Y|wOD d�op��kK2}��խ��  B�!/P+�i�$Th("�&U!�NL =�U�L.0��1us�tu�(�!Gi6�.�fow7>�D�im4�/�vh!b� K�wR` geR�7,��dueQ�fa*1A� now �4"#masr vani�:! i9:�plaguutm&�>+;!�aO� aide��Wl�  &� .�8d��i#2( s<!�B�"uE �1N�-1}D �-,�M6 "�(b$-p_i�<ta� Y���.z_!�e�"�2�Ez=0$. S\�Po ]�1JB6uae�"fvI0{d.>� 2�'V Y��2Q61�� � bf A!�we)�in our i=��&�,��!��<�%C1Z �%�,i���<�2r�Wr5�.$b$ . ɰ%�A�IЁ��D��A�6D*  �/= Sym^2 �)U)*Ve �7E$0AC�eU9R��be�eW"�  each�aA�J' a)��}�|f� 6���A� a+b,q$_{\s}.$ bSabde}=2 : e6� de) V�& <2},-2}j} %'14pX[D dewto�Gpart a)�a��9!��$ $\p_{z_i}w_j}+ z_j �SM�� inp�C &_t���I�Hw�JD�Wi�g*:#�7easy. O8 e�&Ca n*K : rW;%�fa33K��i��o- �c8 �cn!a!min1 ign� $w� ��- �#5*�:q e�r�+�P���� ' a"Z����6�����aX[��\�Jp_ja�t2�6aAk\s%�e�t-M.^B�}NH*�' �7Sd>�a�6�,�n�RA�a�-�tvF�ZoW�� f* b�A�-aw}|.. w=0}f-A*y �)m 7�.N�:��=A�;A ���� doa �'cel���o.}-%isF aq�u�6�9� aAU�+ b:?�)-�=/:)D./&"2v(��A�E� V2�+�"�de}" Y�2U�*\.E�)+A�E�ʞr��i�2��R� �.$+��R$+x�Xa>aI����I���!��  �m{a �A}?/t a��� $ li�:�+ ";dB4�>O N4� A��� �7i�H 6�5�appear����0U !i�AC�  �2nZ�f �a� a+ /(F�#� proc�to��� N2� F3Xll8$s �Csd�%� 6�"� >�pP�_ta*"1.Dge�Ee >�sP�s�$m w"�"�k.">O'ty|�E7P [� c&� +!bc}!iF�l��$ca $E�O !=0��W �:V T-Ra l4c&/)�!�A�six��cz;> wise:bWe obse�c��?�  l�M�icOF hold� $r $a, b, c*n �>oeY$a+*A�e��?��hctr��� �&deI c�� !��5A!M�H79J rank��$(2n)^ (�(g(g+1)}{2}+*�5w�<j)���!�{a + =\8P �}Y),�* {a � 1:0�cB,q�Ehm,P(i,j)"R�fixed=-� i�)maximal�9�gf81$M%!9:�4O 11 88A!=/){ais�ulK w=\eF� ��'X&6)$4<F |-tWcl?&I�H�& $m=2*9 aFll. UQb_&� (A2t � �5� Aiby K ����*��a"7 2-� $z=A!6 !�U3e1}��� reason wh�$^L��a�)!%Us �e��>e�!�%%>����odd ��M f pl--o�0r�*�|rp;��clo�I=�+�� :B�Eh�0)�embediM�a2�'!1�R)���>��hl-P0�&ɏ�)�s&5I�bs:�JNow6�!^ 12Y�p�01�, an r�^ strue ("�7ized)6�t0� �=l��� A}�a2thus,`�� AC},A 4C4\$:�0*! ��2n�� �>=&��7ey��p -G�7�##5eIk�E\D@t�&R" �1��jrb|@B&�>�X!�} � ���E�e�A��ii)a��%!;S�R� yi]$�X2to A_g(2n,4�("��is.�:Fj=aa�:O �% .]!� uely i5�;n,�2 27_�T e, i��� immed�%a"=2�/0$5.[)�Z T-to-one��SᤑR:-DUhEin/"� eA�.���E��!�y7G-�!���5L 1&=1T��N5T),�7�bu �C=rp�8 step?EPd�]�"�*� �T=�e8�.X:8a� x qRn}�k $a+b*�h }{n}X,a��I�+B"55$ ���{a & s}([& Z&e�e�W*N� + [_� prodVnd)2:�Iole`e&�('E.���4)� 6�0rANg6�(T2ia R.�3* a�Ma6fe�c 6� >-$�2�9ɽa�" = �>��D ��Ef6�f)b�a�!cuc]7k)>#�%�}8 kind described1 .��9a}� in�o�5�&�%�3*+ wass%,1T9Ii�*tT5 �"^ �� sioDaneous�*BiMunX4U� ��s5x�/D we�UalI=a�6Ze�W 1e�o�,�j� e,\sa�lt�,& (8re always existj$%'�7� ^ '�st0�ott.N(�sq�C&%�)\nki�a�J �Xn.W� �� �+\irwAWl�p�m�TJ {22�:"(V��)�:fq�@A ���- !�I2:| a� ��:���us�_ pick1�*�1�fS ne 0s &�OA��6j�n�b8c2#AK$V�0A�U)*  �qe95aa�z=i0 (-a"� �{n})+ �E�$;�ho�6EY a $c�L f9pn@ mb:=c-�'ݞ�J�ӱ�� 1�=;m�f��� {b} � I��AI�$"� %� �r#ad6��CZe N� y��i E�N�!J�m��!�A\e��)Eq Ane/]:�R*9& ;" /"�Hh�RE��:7 ��717b�h�n�*hemyg1$,ll= on>�/M��?i�"6&�puc� � 4nR �L9)i J� �� Ai>2>[j �/�8����``"r�/ '' h�(�6�4g����},�� )Inecess�W��. wlMm� page 171!H �(0H�&2$���> ), instea�7!*a��|%��%E�c"") u�,A�� LE2'I c\mui J��5W I^�Qa�:$=6'dUT�6]-ChB }]��Ѳ,i�d ѱf.�w7^�� �Me���� ��A�? U\� A<uT ^ST'y�Z�62=t� , \��}\�b#'FE'`�cs�[( �,#�# Avv3 �A*E�,is crucial!)EVA�Yp{\2�^�p�#���AIS�RQ�Mq@!g��$ B�^2=t_ {0%0} ^2!Ckcl!B�$� a."�AX:Jfo0�2}2d�AEKpm 1,\�G X(A�-g):Fz/.���[NAQsmD8fac��h� sQ� � A� *� � V�/ \��!�b�*J / qP�tNp $ b_1�4b_1n� ~R�e � b{ 0�{P}:�� bt� fm�$6a=1q 0) X(0"I�).$*��� .F+�#,\;= W 0)X�V  n$.Z+\e)=.) e)�[�rwZ4I��X$�i� �:)Ss�*�\no" nt T"�=EC��=.'/e ͽ !(I�raFi�@y&�W+1� &aUy,W?X S chea�\ getsa'�+D]+�*IR) s� aJ��X have�;>�p�� A��[MbGamma"�F�(� �i� ?���>un�G&�4nFH)$}�,of��-2�zvel�J�nge>`% *}8���*C#�X� �)5�!_!JA�/L^by fix���`$b��%� H���t\ne�/nd_?�i�� (�Y�a*R-F F��)/bF �CT t}$� /wa���\(�r)��!�"S� m*s����$ n$��[Esamji/]rP A_g(� / �ni.�s VPh ')= 6.x wy How,?*\nn $M\not.� �=�e\aH?"cha� �/�x�L*� �x" S�).�q we m64�N6 ��rtau�'Q6�#  a]5��&� %��7>Q�kHF�ssump�Bi��}b�h�,8b!� ��8\, �� � homVY* �,w�00KF�n� 5+)� di��%D"��aBvU��e�A�Z �}�dvb� _ if N�5D%52B�*llU��!�tA@nttR��w  17F aQ> � SM�8 �s D"�Ned j�G�3ei�spirit!b� �� u�� E�2}aR!<g7"�A�l�Ua�A�@o�j"�j*(@|/AOid (� a wak!PV�,� mz-(ed2���a}Y-GirY au$-&.+s �V  heatna,� !���aC $ $z2I)!��A42�J�"�5$T��qYde�T�!:�lU2�T &lN)銍T&f� �0�~��%@5�g�8�.� U7AN0x.�+l�ORr� �r D:=*"b�Ta�{}{rrrr}%,� \p}{\p�O_{11}}&   \p0%2%�bR+( g}}�T G6R {\p u2u ��tau_{2�j2j �>��g �+U& AM�1�gpend-T,;� �|���ny&�El�i&�*&�$:�Ie�~}%0Eq!�-�I\4rmi�}\Q tt 0*�* ��de� +cal D_$a28 .CD%\ =\!*;�V 1,\l!�,\e_gX�}/!02\de^ �(�W+ 4+4))vWa/21,0�W  g,0]W)^2�*!�!�1 9DV s��&�?� !!B}#%�1�s��'s��'�D�m"�'�9�뭨io�A��A����C�@�;B7W'���a ���$}^{aa�� �s&n#5oZ!t �&���'o>0�J3ɣ��s���2 :�M�@thebibliography}{ribitem#<{Bauer, Th., Sz�#4rg, T.: {\it H*�# dO�=a�#X<�#.} �r . Z.?)X224} (1997) 3, 449--455s�$fa}{Fay, Jr�1MV-�6�0.} Nachr. Aka�fiss. Go�en �D-Phys. Kl. II 1979($(. 5, 61--732�r�V{F �UWdi�*~ en F�1e�Zr�1tarheine� J. R  Angew. �) 98!0885) 241--260.�pU${G"�u, S., 2�u, R1#G�<�P�%�&�}!Ob�573F,004), 43--59B�2��Two&e �E)�R�Y }, p�5intS_,h.NT/0310106.��{�a� -I.:)t��0 e GrMh1�3vvsc�A%0enschaften, Bad194. SNNlger-Verlag, New York-Heidelbe 19726�>�e+Onn��� "� ),.} Amer.A?i>Y,102A38980), no. 2, 40a@4:%�b:%{mD� �j��� �I-&M, (I) ! (II)},�of.�86�6A0219--2467�8E�966) 22A�3:�^ewB�PZ��K&�at�`#B�P6�s�8atAG7V.} Bu�))J%G Socm~ �82)-I 1�17�w��d{"d, Dqo-N��� � VF I,�u!UIII} ISVt� )21)O06), 287--354, a�41967), 75--135IB215!�2�&[{�:<, B.: Gesammelte6 Werke�essqlic���al~> 8tr\"age (collec� z*�DBA$Berlin 1992�r"Lh�{{"�\, G1b M\'emoire=t l{�q\[ deux�g% s et \`a � re p\'�p$es qui son�� � eA t\'Cd� ltra-e\qsu de l,emi\`�! e.} �s�" savan9M\'eGjg(Te1%�4851), 362--468�l SM}{^�M`non"�ly}ENullwerte�S��o *y1wnodd:$O�`dv.� e �47E�83�^ 1, 88--102S�~�*�8l $tpplARon!3�?d��bKf�p.p.a.v. ��a�ta�1uc�@}, �&T%i0996), 231-241.�^{T^,&XBe}Hg zur Bestimmung vo�� (0,0) 0)$ du[{KEn�Xx�^r Funk���^7�87��20�*22Wwmx,{Weil, A.: V�z�i enr+et BZ bes � E�. ^eDmann \& Cie, Paris��8!� > � &%|�1*R 1}A>�1)�n��!!��%to!��< B BTheB�*�% �;v��r5&� �\s$ may�b�5I|Ely. Now*�T��8)���;�Kblems*]� ?\e�$�(Y�ok�B.�$ &at "���Z',"x]�#�� �)G alq e, $�|�Y+\exC�$ !e�(�Q�)8&��.^x uM1�9U�lyW�c "�b$�]�j!���J�c'/Hp'q 0 �D$t!�B� #� 6"��ar���>��fonts�Z2D�Shell3LArticles\SW\AMS JourZ 2P Language= i�EngπtCSTFile=<�ci.cst!�n.K�e|9�= �ƃJ~�ac���.cP}{A:2H�algori�{A 6"xiom}{A2case}{C6a!}{C6o�`�}{C >$d::# >"��ur~o :$r�^!�cyyrioh 2DU �J}b�$example}{E 2B exer 2 �}N�^}{Nw6:p� }� Ba." 2~�erk}"ȅ.y solu �S 6 ummt�{S  \number� i@�u� }{b@} \input{tcilatexA�b��� \title[UpcB����Di>$cKF'2 -DimUjoa�(Subspaces]{? �?�:Inner P�mq�.��,.S. Dragomir*��S�*r  C;��$� S� c{Victoria&�Techn���y\\ PO Box 14428, MCMC 8001\\ VIC, Au��liaP m���@tvlda.vu��.au��rl��,{http://rgmi!/SS�Web.html��ate{22���om1�� D[2000]{46C05, 26D1Kkey$�{-�.._�y%�,5�,� sel'!}�l�d0 Boas-Bellman6 Bombier�i2 Hadamard6. Gram2.Y|a"��We &t��?b6�d]��*teV� i�AC�'�]io<1z�w� of5 �2v8!!1%EY1 `a ��� �1=( �m"j0���lso�n�9 ���}�w$A' H; \langl"kdot ,� \~3 )e&a+ i!<"�E. "T+r�0o�2pQ��v fi_�$��{K� � \{ y1o�o ,y_{n� \} $�_|!}$Hi$G�( : .:�` ,\textit{gram� rix}I@\{bA{�D ,(�M1 -$en=dis -F�i}�j�-D.$�.����6Z��a5.O2��1fRr%s�b^/}%Nb) �us,"━��*}  &JD2�) �vvert u�c} )�M�)�){1O\2� � y_{2F(A�s:1YUk-�\\ B�2%�1F[�E �� (�� 1R� �nJ�n�� (�� 1:�%)�% -�%؍�] F" 3[W_429 -- 133]{DE}�.L. +���"�!;a�>U7b&�N*se7&�1 enumerate�J��%�{ x.�x2��X�tHi��$G�(I1(b;) �2$�a}�)YFu :u��l$v"�- ; \�M=spanJP BPbe $n-$.��:% H,$�f��F�FIisR���L�L$xe:]!���$de( x,M\�b9$ $x/V� �"��&K���sB� } d^A��2g�L)���F�,x�}{%:�F., �:1.14q}% and���\V�+ � �-�� ^{T}Gƅ ,l 1.2F��G=�zf��d YE�!ri"�J�$G钱���ߢ���()j�1 xA�>U, �� #>�(.* M:��)!��% �ix.`&����E�%�`6Q���,�Q� @e�*E�%>j�%�{5D�Q{�} ^�">(��m_{i=1}^! �� C)R)(iM���e~.EY ) }q�� %">dnYx_l�A�} & �{if \ }x�*4in M^{\perp },�&  �?x � L & J6GR�.}�3b!�6ތorthog�c�l� � MA"\�� �rQR|� x�non�3�!a  $�kJN0\leq ~�)2)a{qf)> x�� 9O �)k*L !o�E]Guv'.b4FbY*a�F0%�X (�Y��gP)�4!f(:.4}) if�MrMv��Krh t9�'p�A��*� in6�s� �litera{*E�it� 2�"�L&|)N as<'2@'Eq��!>~p~n �normal�}��H,$ i.e��l� eġ�>� �alta _{ijW�i,ja� � n}ots ,��}�R̀\4 <�^Krone7�J�b�%E�.( A�-N�� 6��jL.�5>� *b E�s&� UD�H�%�*�">��be d�+p&> $597]{MPF}:J&�� �n� }f � k�+) �$q*B^2"s*9 )^��F�B^� B��ok+&�2f,��61��N"�F�a�:BUb� "% 7F�V% ]^�~�+!�f1T+*!Z�̆GjA+>�% �N�~�.<� .� }i,m�~ai%p�:�&��to� ou�BN za �XE�N�ya 6[ � $%I�~W��  $M $J�$~ .]"4��VX"-x�����. As@8y-&"�Undeavour�3m�/>��i�+B�_6'�E,T�al ɜIc ing:F2 2��M6?Z!��QnV^�>,=M21ed �.�R�M����22�WD?>��!{t2.1}�y( Q� B4^&�U���M�M:^��"� }�FN�!i��<�|j�N��N2 b�m�l���j�� �pF) |�]> 0 ��!����Vor,� X�lys )�%�p%2<� &g�:�:�:6:�� �1b�� )2i2F�)wuCZ�. } If�#�K4Cauchy-Bunyako��,-Schwarz typ�Y!�| NY�:�l{� }yN��YJZe > � � N4A}PF�&�2N�Ň� cbasilyy5dX�1obvq9(tR�����_�i~ ��4 �,j2�!> \��0{=| }x_{j}-% JjvrJ�w�K�!�UEnlj�>%Al>6JIl jU2�n�B~.&� 2F� %*�eAmqkv@�"<@� *�8� % {2�,"Mk}.�~� )�==�3b5�3i.�JO ��6�vD>�UtilicX)& ��{1.3}) ez#,Au�6Jk�%�+D%R��Sj.I�i�F�>���dJd�| �J���f?Z�./J� S�@I�z, ��a:� ��x#(�ef{2.6})�~>� chie�aht�2wp4-ic=a[�u�e~5})�din^o,�SYI�i�T7}�K�Aa� desi�� &XĦ�������$�r IoW� �axKM{�C�WM-J� �g \�S �"�on e��zx� B� ��*ll �P>S2�&�.'":J��$ < ���>�ix�� ":��"ZG" '.1�2F�%:�"�y-�!�7] w�' sucjM�9 alig)J�*�)� &� ��|BA32�>�\I:2!F.�B� "8%S>�# �2�x6��)R>%?3M�!EJ_ _!u�/2�],�+��2� /!+:� j�B�mJ]F�% qV?�@ \\ &� .L1 ]!ۚKmG� r?V�[���n�A�!�=`G6�5�!�E�2�1!�!Uf&�.!�D)�Br :F-1n�%�-�ITJECe�)b�J Jx%bTͯ�� % Mu2CS�0� ieK��%�B��?�R��(!�2(%\�_{k=2&�o!�A�f A� �S16�k�r<5�M<��]H3RkN.�Ei1�&r9}.� �J� � >�,�-gk)} % va��� a*<:� q 2$Rb "[? not &(6CM.��D�${DRA1}aD �t*PUNy&F�.�lDz�I� ,za��"&  **�)�3^�n$ !!�ies��/[� ��E.n} f6z^6�CF� }�*x"׬1�1i��sIlR]IQs*�J� R�;v ^'Z!�6Fj�a& � M�Q!yp �":z� N�a#N^p}a9 \h���{wU'\ 1� >1,\�� �+��"}=1=fQj )�mz�E@N�};z�! 2.10� +���LZj2R{M�B�% @�h "�t\}6�Q�F_5����a�>_ [2 =�A�[ �ޚ ^{\g�(.;2��� }��^{26O].���(eev) �-)i~)^<\.�Y�X ��f): . K2�-�-�)e2x 5,�yM�]VCV��oZ��q� %� ;ter��:� brans�b�;h�e��th �3*thų�L 6gi�m9�a��A(9��5 Ou�%8;k,ele�i&��ti��of rele��5�z\;idey�>� m 6 �4*5'�If*� @*� �@EI��H;+Nw<64�E���2��6��\���0u0 �Wtag.x�����ҺB��( n-1 �� B ��-�)L N7 .�"K ��Q�2�e3qR�2�R&E��)g[��W%�-D���4 H ] ^{Ĝ1�M��\���Gsiq:j��J��}2� 2}>���\[V�[# R0%�)���I+] .�u�7i]>Il/B"� &�� 1})���N�f S��՚�=�/��� �I�)j��, ��,�j�n�2:s�. :��U90m)22�V�JK,2.L��DdQiterE��kDnX =�U3 C.��/""� !t��%�v�1"x&-$b%|*�@5gr$�Bb�0%�B �eP.`+eL��R��e�V}nI �M�, �2} ] ��a>�RO1N��� �%g�E-F "� ��V��a�� 2.13�#q�}%j%"� R�g�&%&�14�b= 2 %=gE�gIB� V�g%��" �] ��V� ��A�}��B5 %\.I+ =e�=�Iu!�2i�.�}  �^�MJ �q�]�g,�a�r|6�!J�� � &Hi�6�V��)�=Eu��i��DR,"%,T$:&ouu-^%��{*\~�I�)&A�cE NJ!� �UB�2f�U+†t_z�-�$���.mB!xt].�B�1%�#��:�#+L��$�6�:AD�\$�#��C9%4F��#:�#e��:EQ!�R 1t!p""�Vj�#�l]l�ՠZ�%V�,�%�� 15> H#"� !�N�"�.��W�f �r6#I�R41�WP.�.  BO��S44!�^aE"E}Vn"�6�&�"� V}2m C?i�/3�/*�"Rj*��*FyyA>\eH.�eYPy !E]�hf6�{1R�+.�J6BJ��6y*�M� �2��< V�2�J�%!���$y�{��!( ~�$ �a"/�4:A:!�2*2�2c^*2� v�E.$0�3E5�}�\Ѥ�V�i�q%u8C92.19&���� Q���TQ4:�&ec$�fu�G)�r"�2A�;B*�HFv�87u�q�f�6}On mz�w.��>ثa��8 at u�)��� �gef� 2} ��-��18B�"\&R�>N�+ .�8s �%�emV�$�br ��Jr �m�X"� �jA KNeiy�f� `�U�a�.A�Bl K�)*� �J.� vJ�*�� !�� ��-q�� x*CbM U�Furx on��x �wb� R�%��� �6u10ty ws�y*5&� J. )}%�AU� � V (b�� :J�MA�-��iN) A;"T 9F�&2 5�9Z: *f��<:�l"� � t2.7��&*Z@/&�2i i�e�]�x)BI��Q���;>B��:�6� ��z� a~��� �>QA[ �U[R�L��Bf�U�e�>; � ^!���M�U��f��\����O�O�O�O�O�O�ObO%���J��ɭ-r�/�D�c�� 20})i�`a.Y �! &!f2���2N4��be�i*� >�^�^�^.*2J�K �Q� 8?� +K*.�= �>_16F�6G &�2=�"@4V3�*6�32� #F W & �o 2u�Z�/��,$ >"�o �o �o k-2 �)J( 2�&� J��z &�*�!��� � �a .a "SAOh �Y�YAI�$R40]A���h"8-u��&, ��yW��r��1bm-3�A�m-�m-mi��+ :� zW&)��f%��.�!6%F��J�)2 V !Y.���R�+.�76�9iQ� �z�[%P"W F�-{l�=^�.� ]>�+:���R p �:�p}� n[:�"F�6� ^�2�)f�q�� 1}{qr�.p6e+p*_+q6Y+z�%� n�28:/@ڽ.b�.Zv�*W�>;��� w an�.�H� F> 27Ua�_{y��BM3.2�M�M&�ZM� n� ��N���@ \right] -\sum% \limits_{i=1}^{n}\left\vert \left\langle x,x_{i}\?\r  M\.( ^{2}}{\maxT1\leq i Z[ x"jBv �l at,x_{jfz ��L] } \label{3.2} \end{equation}% or, equivalently,% \begin{multline} \Gamma \�(~ 1},\dots � n},x �)k3} \\�q \frac{ �Vert / !"�  z :�_{iN  �%�5 %�5{z� ~�ϊ���j� }\cdot \Gv�) ) .I=�A" theorem} Q�Fproof} Utilising the first branch in (\ref{3.1}) we may state that% \beAYU~AfM!�>plM�Afi �qe%� �EHejeTNJa�:$JU2 ��mU=2�% NvZ�M� 2�N].MaF��for any $x\in H.$ Now, since, by%� represente� formula )� 1.3}%�have%1�9�d%m�,M �) =%vF�-i�%E�>���2 �}O� tN��+q&suڦB-,=�4V�\$x\notin M^{\perp },$ he1�)�$3.3a}) and4)�deduce a{4desired result)2})m�m�1�remarkas� �r3.3}In 1971, E. Bombieri \cite{BOM} provedEHHfollowing generalisIR4of Bessel's inA<@lity, however not�d�!� AA�mA�L inner products. The%P version can be found 5stanceV �d[p. 394]{MPF}. It reads as �(s: if $y,y_��@y_{n}$ are vector��2� space $E� ( H; Qx�s,Q2 ) ,$UnJg���>i�eX�y+y !�waK~j\{�V�h6Gy��yB�1i�� \} .}#5F#8Obviously, when-m\{f&s%�S%�0 orthonormal,!g Y�u5})MeesN� . I!�isaUpect, ��$regard our:pAa,a refinementa the uRV�m�q�f�4}On mak�uuse_4a similar arguuto�eaRe� \�r2.2}% �obtai�aHm�.��Ra�Hadam��:U�align}� )�) &A/q��xa} E�I�a�_{k=2&o [:6k.6E�2lU�� k-1fN� x_{k :O2�a.j� `%&4  me�Ѧe5F� 2�)#] �.6}\ 1[); vP %Y�"! �a�notag� 1�� U�4Another differA�tCauchy-Bunyakovsky-Schwarz typ���� i�@(corporated Brlemma�gDRA3}.U�դ(l3.4}Let $zA4s z���$ �$$\alpha .$  *(\mathbb{K}$�_n qo� j� _i}z!�)�9Ru !�(6<I�1�� L G^{p  ) ^{B 2% }{p}_ft(�Y�,6�E�Mc �!+U2� 2^{qBw1}{q}.47F��)$p>1,$ $ �1�+ q}=1� If���7�0choose $p=q=2��ige4 |��-��2-x:B~x ^x2��[)�9�1}*a�� 3.8>yi�m$ Based o&u 8})��+ sv 6�ź that�(vides yet am�upper b"c � dig $dE`( * !�-�"0 � t3.5i�7\{����xe�AHMm�x$� a�E T� ��t2.1}i�ՍY'Z� i���N�����f�~y���4!4:��$q�j����./9M�5��cfc10�������������� bV A�n��� bVS� com� (s apply rel5� � 2X . We omit��etails@sec��({Some Condi al B��s}� e rec�pa��8�4}7 P author has establishBr�� �#�*- . �i�n+q�2�) �n� � uct�oUwreal or!BHplex number field $*�,"H  e*�} _{iG I�4 finite familyd *S *$H���arphiE},\ P6{ c�� H.$ IfJ�\func{Re�{��:I}i� -x,x�F�\ � �#�d1ageq 0"�4.1���Ӂs"� :��l �%+���.�� K"M56���\� 1j- d� �"fq&�4N thV�}( 0�g�)�X5 �}:?��.:. 1�_.K t%S1}{4}9 I"� >%z>N&] 4.3F�wcoWt*� 4}$� ,best possibl� e�senseR ity �(be replaced�a smallea� ]��beginF6 A��<:6 65 �% �0arly independ��systema�2�m�M:=span)�2� 6ce� $\gJaTa��a�F�-�{ 1� n-�}�nd�$\backslash*%n such%X�':�e� .*#�# �Q��*,� 4N�a1� >E; J��� I�e+�q��(t!y-� �)A" E� ��Jqor^���%Ki�v�B���F : (L��)z�1 .�6>�I "� � 2Ita� easy�se!�aY�? ��� ,z,ZE�$ oneGB*>>��z+Z� �%3%��: Z-z>*=V=ZE�.M�,)1�*}%A�refore cA �A�)! actually &3 toB�>�6e�-�!�+]�!.�A�)�5 ;:R-J]�)8Z-.5J�_o"�J�Z�=\inf_{yAM͸� x-y � a��A #�>!>�BW% �� thus6(n4�8��5p�;lasa%AVA.-,�� 2� Y1���&�var-�� ies �  moreA� veni�7D(although coarser)��A r $d-� ft( 2 Fo�*,ewe��&E � 2.11)L can &�)&n!N� 66:�gN�e]I`)��FAmNN� }��p}C #9r�"E�V�+ �n-1 �RN�l$=An�eMW)"[i}%�E��m%B B�� � � �i�i-i*�10� 1w}%�!� case& j assumes3"��^sf anJ7*6 & 10}) r�#s ��4 as well. Fin" ,�uf.'of�}� O=',�'"aN *�.�� .* ��~�*� z�!�R�)�e� }�.,J��MT�!�_�)lso a^$i&�$=��"&�4bibliography}{�tbibitem{BE} R. BELLMAN, AlmostI^�gonal series,\textit{\ Bull. Amer. Math. Soc}., \#Tbf{50} (1944), 517-519:sOs$P. BOAS, A� moR� blemrl J. o}., �bf{63 k(1), 361-3706kM}$&OMBIERIn noteA��=(large sieve.octa Arit6l18l7l401-404.l8DE} F. DEUTSCH,) it{B�Approxim �I;&Pr�S�%0s, }CMS BookG�e4�cs, Springer-Verlag, New York, Berlin, Heidelberg, 20012�DRA4} S.S. DRAGOMIR!$counterpar�#JC�i�A�&=�d s�$Gr\"{u}ss S! �'s9 \RGMIA Res. Rep. Coll., }5�8} (2003), Suppl�$T, Article 10. [ONLINE:)^�tt{http://rgmia.vu.edu.au/v6(E).html}].(M|�!>S�"�$�u}ie%�N]2$J. IndonesI�B10}(2)� 4), 91-97:�1B�O�$Boas-Bellm��v�AIne>��m�ustralZ�692�217-225:�2B�%�it{Adv�(%%I�!5�' m#,]%�Ih T�#R}, E1 Mon��s, Vi�(ia Unib)�) 2004J% ZmQ/}2�) Da#tMITRINOVI\'{C}, J.E. PE\v{C}AR �(\ A.M. FINK��,it{Classical#e�2�in Analysis, }Kluwer Academic, Dordrecht, 1993.�th6� docG'} � \c�[12pt]{aiA3Tusepackage{amssymb,amse$,�xsym}�]heY2 23truecm width 17Doddsidemargin -0.5 even0top .0Uopskip �Cc.B�Dd.�a}UEe.E>]Ff.F>Gg.G>Hh.BIi.B�Jj.J>]Kk.BXLl.L>>Mm.B?Nn.B�Oo.O>]Pp.P>Qq.B�Rr.B�Ss.B�Tt.T>|Uu.U>Ww.W>Vv. V}} }boldface~�:CCXbfF�HH B>NN B�PP BzRR BVZZ ��6#lL�| bf l>mMm>kaK\kappa66gothic holsj<:�aGYfrak V2�b6 b>�c6 c> H6 BW6 A+6�sG�+���xl2l.J� �naV!(vec{\nabla}6l ��j:�hFY widehat{FX2nhE� NF Q.@QF T. TF X. XF U. UF W. WF E��L !�on� �<:8e�e;bF�% Be� a�2oe� B�%+ B�y�bF�D!% :�*< \def\ort#1{#1^�7.�.8 SIMB FRANCESCOf�Warctgh��rm{ \, A�x Dim{\emph+ of :Lcvd{\nopagebreak\par $line{$_\bl#quare$a���4 capitolo{!P@{\� ({empty}\cleX uble?a�ento#14r\v67{5pt}{\S% #1}�!/�2(zioni ricorv2i �E#1#2?>lanw?#1,#2 �� } %��%  riciM�Gl2DGl En BF % gruppoo&e �SL2ISL I2� +P., bb P$rmr5OO5@ def\SS.C, SO}__bb� 8soo !�k{soQ� sooc6F<Aff #rm{Aff�.V%1'delle afV+a')HomGHomnG$scrive Hom��= ato �8-}IS9I� CONFf Conf�D�5-rm{ Homco.�}^} %funV� eps{�*epsilon>�%� )) hol�hoF !�a�at�adf5�aggiunta PA9Ad�trdtrvNtracci M sign: ^<% seg�o�� �Ij��immagin-�}.otabjo(tabilizzatoq� modu�� | mod VA% +)2�w18deri��%�ial#2}�� \ y_#1}} %derivata parziaQ�cC�6A\,A> Lmpo di IAke dire O supp� �5�c� ch\,*ss.rtgct1ct�x ��4\title{Wick ro�A�t3D gravity:\\ $\Mm\Ll(\mh^2)$-�= time�\�0{�0 Benedetti$^1�+F�CPesco Bonsante$^{1,2}$�date { ~,� make� �0.7cmo[,-(1)$ Di%���!�Mat]a,&O\`a�Pisa,\\ Largo B. Pontecorvo, 5 , I-56127 )-l,2)$ Scuola N�=e�eri�%di\ \\-�U �Email: b- D@dm.unipi.it ; f.b- @snsX \input 2_3DWRINTRO.tex6(LAMINATIONSF FLATFHYPFdJ?ANDERF> 3CUSU:�BIB- \� =� H8"3E>s}\�#3cusp}"U�} show�e 4\ill�EN3T8s Q'�Ais`3 . Mo�"CBs'�r��3to E+@non-compact hyper�c sur8$F=e/H%$!�ee�Ada, endowed with an ideal t�ulq. H�Bf& go�%o focu�$e simplest� ,s� 6�the {\�4ree-pun d sphere}�me fea0s�t!$-Z@.$been sketcq4��$�4Thu2, M�* �,m  know�at $F� �rigid}��corresp�+,ng Teichm\"u�0�g� ~5U!point. H�Db5no measu}Dgeo�Dc lamin%^s)z1á�ort. @�:be U.by glu%}woN5�a� s aloqHir edg�)�@s. In-66�re exis^6 unique � (!"bary 6 er")M�s�,�:t4&+u�i2-V_ Lrealiz*"he&G;m C�&�. S�0a �!�4!�he mid-%�.F.�,Fisome� 1Tis fix�2requia �KA� glued�s+ ches (`,<{so9�q�i#polog�ly a t6 i -!��O@pattern�i�2 ificI>  'I# a $1$yR torus)!�%B�/xC1AU.@true��A�lete,I�a �f !� q�, !!8pp)E4H�F�ae�E| trA��g�@ThA�ree-]%�!8.)ym�"BM $\Ll_F��$F$. A� ns�e m��7 u_F ���$�e�h% morphic} 0; ial  Oulari�!$\Sigma�a6A t�'o ela�!�mA�given �Mi}icial} t�>(%]!�val!T +(ices) whichPm)2;�p e cell de��e�oe�q�du! ?He above2bbyF�!4length� �xof�G >�dAqmi$ �f� E��| �� �-&arc w���M�its ��` ofE�mr.����, � B� is ��d�BaI' like� embed�.in)>0ntierzFI G Minkowski P�fN�acY nZ:!��ށ!behavi�J-3E9asymptot1 Ds} cosm� a� -�F�,!�sllEP same! �coAJ act �+ (#7e endoSJh� 7ca+,�Ka\to 0$� en�Q�J�o�e level�%eqk (a)$��ver" toQ :m� y�yB��*O��E� spectruO;��.v (i�coincVEe���minimaa}<5^.W�a�@!AZ�AR.w),6�E�p*/ z%( J(p "<,_i$ $i=1,2,3}MN #ugacy 4%� V e!�a� e�(t �<6� !��I � -FI% e65:(takes value���;_i AV(a_i+a_{i+1}�;w$ assum�(a� 2� e��6� %�F$)��Zth�Z# $i e*�$i$th-X , 4=a_1A_BiRwayA�,Kmpl�'� these�a�s �T>m�ic�,�K. "�it_s��m8Ba}X: \med&�( (1)���J.�N�� al� n!�Tte (by $ISO_0(\mx_0)$)-�i�>$mmon {\rm;At}5�.2��)T��jnA� rivi9 �' ) $H^1�r^� !?5.��by� �����!�� ��ar hoL .}=2&� a�Z9y�<com_ ly�� b� 1� �5��,��%� handAe2�al� aic 6f -ext(oni"( i�A2��(5 � ge � j5. Y-arent��A�s �" N �y��Uec� !���N �'I#Q���0s would indicAp!� kur � claimed i" ce betwT�A>���� a�&���eF Einsteiٖn�s%�V�$LDvia Chern-Simons �Ws!� conn�s)� W}),j�be managD stea�(very carefu�out} }9j1�*� �=)~ l Mat}�] i:R� � s!sutI�Us%� e�icles1*sa�E���./ $�*&  M�� wa)|he7��  $I^+(0)e�!6C� �s��I�*M�ic� na�ofUAeEa) :.~Up����@��NsmoetiD$\ISO��{0})$�_��se =(ɚ)= $%�u ŵ\in-. We waneR�2!��\U��$�en�SE/�Dut!) . By�tradiQ �!&$�G2S.\�@ $0RZ%�� &�& �x)\cap� p�� c6��. But!@� �is no ope�  $>U&&D4mp!�Qfa{i)0free. Thus we���=*. Z r �� A�to9Jognize wdomai�e�$�. TakE�Y� � horocir�1$\{B_n\�D!��$ cent^toI�s��s�Y-We14atIS .^B_n%�ai��o� ne�A��0e null plane S;�4� -�I[�d.�h� . Now-����K E�; � �.\[ &8\Omega= \bigcup%]P_n) \]AK a reu-� i"��qL 6s �"S<�^ suffic�ᩅ� (� a;w+a: at $ �E�!9�:�n�'ng$).@!g"[�� bm ZB_n� )B�P!��Xi $ar�Tmap1+f_a: "8\ni x\mapsto x/�W�!6 send% 2�o a2��%ed s $a�ncreas�3c[��4��%�!$�e2&�� $a>>�X �YF�O �Mk��tof �E���rt E�sAi2��h�o��be��B�t .1nd&� ���{Earthqua�failure brok�ZT$-sym�E y} H�Y� dop���$�� 2$ AdS}6 � Fo.}%�wa#�\AO�in��= �$�ZJ^s nei�W�@`" += e�a�!Dtheless,S6V`AWrho_L- +eg� cretHBot�Ie ^ea�b_-� :G ++$)e�CantorDs�� bby%Ya-� �(convex hull] &Y e �*7p�i�ot"�"Bara�Pi�. 6*I ] ve� ]1J�V!9-(_i�n�O+2re� trans� MDR�� a>a��onent$.�]�/7!$Q"Z.e�X:��IS ij$$PSL(2,\R)�Thu  im R%�A�*d �e� $P$ i$mx_{-1t c� $Q>-\K+vI&/ifor} sequ�s $(x_n)� �ale%�(\delta $�J�_ accu" �U���$\{!?x��!� �4[$P!^��*�BF\.}�R�ma? � d!��D� e key �A�toUb crib��~rve $cU�A��cn�Ef� ^!�5&� fig/5~"(}e!P{3Cusp-bend.pstex_t} �I�#{{) �9��a�*�����spine. 6X��;jN#"�A\$M\. Gre�`gsM!���yQ5� pastyq!�K9 }} �!5�c1@ E<� M� S�#E�is_a�le $T�/>�N.p �H�s/ �%���s $\zetcM�}�toA  $��aat� s $xa� More �8 c\W%}�! �E�6g�an��$z�z+aM$a>0$ _ 2yIM� h�`to6� %0@ $\beta_-(x_0,x)x"M at(�Sc0%Baߡ�!)$ �a�#K+ KJrepuls��6I I+( I�Lpar C)'an� $l_0!�%�ũend& �`x$�let $y,m�'A�F� eT%�We խ $T_n=� ph�� �^n(T) �a >* 6�2a�� !#7Uq*'�T �!� in T�%�B a2�1l )�$u�!�%�%`^n x)� y_0, y�K en, a$e�ut�~�  \[� b(.  ^n),-�^n)) (�U^ v�U&|.\]�a.� ��n$�&�!L�rN ty=(x^+_L �), R �k $$$��)��rewiv. ky ]���I�- i S.��iӉ�-�a��o. .exchang���E� �l�ea� T�-v=-�!-�)� 9 n B} lookz� imag�'T��rough $:�$A�easGY2�� $u:�x�=:x,6x ���.*J �! achr|D�u-�u-$/�e� �Wleaf,BF !T| �ed�,� ��ft>�5|$ towar}u�"�� .�&K� w2�z���� �����gNE �F%JQVi���9Ni �*  $%T��� L6� R� A��R\$l$� Pr�!Zpnr(al%L��u"a u[ be1 � >U�%I�<�=nti SmeeCch�az"E��}S#� ^�s'!vpm:� ���!�va�$&6�D"V_la�e(o,eseE�s. R��� un *=,, !s vn# ��^ E $H$,�.�.����R�its clop)e�  edC'h� A�yF>�i|)�!�de� V U�� .Cis qu^�"a!� <be�*N6� "� _- K�r]�E��, i.e.�AdS,c�-�$6N  2�sg�)&$2 touch��6���%��=�%��H� ere >M*� 2h $PAbw},� I�!�uE���!Ud:�!|!6Yv�[}i �m�_of �half-s, attacH,�F� �. O,206 �} not}E�l� 8�t"@ verif�a�lso $(>�)^*$ E,ca/:B�" $T^*���$7D+oe��)��eq\Uu.)i. A6/"&�!2U�� <\pi/2$, A�!�Fna�22'� �***re�8Ap"ic �) T2w��a�gV\sw$,��)�IoI� F��U Euclr n cyy ers. By u�"�!+��� BBo}"� sa-��%��u} A�#i�J�A "cen��d"�t�*(�$ic)� BZT |:�es}. .r $R5A�� WR.}�4(�-"�)a�s��(i �c)]k9�ofFr,�dto V�i�]b���c e a $ :� [0� A��B$_�%�| 6(��S�'$C=C(F'P*�� a�..U�fY(area $F'7,h^2/ �'e{�-j'Y,� L \c�/ R$ do@ot��U pa/�#.6�*�+�1 �Q $b>tilde{C2 (�/!� 3 hull!�A�JTd\'} \sub~S^1� ).z�B��h" �Gauss��J�.� � Nb(�.�5\�.�-F�lC��$ht $+� $,Mv�F �-A9g*�g"j.inh/�W��6��&�#ada�E �a 2�a�2� precise�s� N�b!�2F!W�.� 6@; �2 (�;F��ʼn:us2�t`sC2���$N�1(2.r*\3 �.r� ������ glue��. *f19�comP 2����An%��  � �*y kb�&3�*�eA�)t\to UU�� 0_{t�-'w�)�.'A�L�;�� *��*ngx%= �U�!�2k�we�WI�M�$1$I�� 8�� WReWul�2� hyp}��R� and  5a"!Q�!�le�t��S�*=,$3$-manifold:a�%lebody,&^Tof a Schottky group (w\7fer� ��zqm d�j�+ut� ilarR6�# %%% Lo8J(Variables: mode: &&x0TeX-master: "9"End: ��*L8��: F�0�\\ Ant�; Si�3.`(�#�M�8�w!� " ��runN8rCg�!oWR!6-� �`!�an�o,, iq>3/ cop���$a�� :�e��` # (�}�s����\3a suit!rJ u$procedure}C $P$ ��B��� �\2<. &�8inQ  ��ms7��c-T��!{N�}-�g� %�WA��6 : :�8)�lEbARli*we33 aE�!�5�)�pTQular, �%o��K  �is will�y%[$btle role,�;E��pec� em&H'.�m? M_2(\mr)Ց�%�2�2$7rr1�real coeC"sP&x:� a&+f $\et�xd e quad�'c��D \[ q(A)=-\det A\ �e q@� � Ks $(2,2)��"�*eM�E@\[ \SL{2}{R}=\{A| [1\}\]a.�sub��YAnr="��res!� ��0 has ��1�G�2 $A,\ BZ�r .k#D4q(AXB)=q(X) \q!(,Urm{!+ }XB:�\] `, ���.\ p)�'&.�{\R}$ i�by �(A,B)qX=AXB\] �dr�)B�0A ^.�0-��< a bi&� .�m�9-��g :r0� KilxM :.�h $X,Y!:sG\lG�E�w5�d[3? ula.f$\tr XY=2A{(X,Y) \�q] 1d&a�� {�O pair�]�, DECEHly�6��nq�blV# � -� e���!e�v" (I�i� &��ha�TqC�& $Id��.)z!�dia@'e� $\D5 G 5��� L ��icb~���?v �/� 4�B�!} dB v$yZ>=��Tw6�#I� ��arrowzG^+(2:,!�_{Id}E\]T :O>� sotropic.�5ѥ�!?J� 6Q�P��sur�7 Phi:5y:.��0j�G$\ker0Phi=(-Id, -Id�w)GNH6�:�/NM!L cS2��J�Ej�l}�([IdB]=[�Id]$.�0��L/ uces��\["!=5% /\pm Id\]-aV�ure. /. �a �@� i!e^?7nd diisa Lwo soli�3riN T& .�t&W<ly4a:us.��D��5� �.>P4d�2!F wholn YKU�. �Ac�v YP NVAr�{d� :�Ao.p 4(v,w)=(Av,B^*waCr�A0$B^*= (� )^T-�ide��= I^ �f 9 * %�1=\%s�'h^2$.Ȁ$Eh>Qr�I�$9A�$\mr^D� ��"_$how�cI~ EAED =(A)^T\]) $AQ5�w!��nto���u�mod"OC�%h U� ~S:Y��� U� (Ew): \] W���ynew|6-f]�F�o 5��'V%x,yA%x, By�9 In w)s�:Q%36zD!+A*�s�yn5$��S$.��e~t �(& "fbo  $S��{ rved���*� !<:��ZG �H�)�S a��� al2p �}Y - cau�C)V����w_�^ne �� foli�bE����,9� �v#N %%�le�I� l_{[w]�([x��|[x6�� �wa=f!K!]�6�| br_{[v b�y])|[yBb� .��t f ��pro� �F". Exact�}n� ftI .M (m ough*G+�!h:�EfX�MmF�!onC'. L�2i Q�>of M5�[;2 t~> &?�ϡ�e �"�n��$8q�~�Be�&n)|a� `!��i)� bed�us;4we&aU%V $p>���tangen��(&7�Sis ��d�4An6�Z��i� ur ran�" By u� �en; ���enumerA;<N`u��2>22, $1+1["ne� p�� �+�yLse;x !Vfourtho.*m-3l3 choice be�pe ����%I6k��Z58  ``�''�f?9{�!ZՐ�}.\\cPp��A�5to,a"0!3�y!#)�o �\F! ���X_n��T_{A_n}� j �0�im�I�$p $` T_AFt� n $X�IROsS;�7��V.f"� !.�qi:(N.iP)QwO�hosDou�9n-t�?� e cyQ)#aX: *�c_L$ %� $c_R\ 8u { G.�kY#} e8]r"�i"�6ngB�#I;. �m�KA�1�ifA a>EcBir�+"R&a<U;L& J�3i� �KIA�2'apJ2a A&1� loop:�(aee{M�:A�|%5�5�!9�2��ہ(Aq��. �=1V%a i); %e T=epz!*�!U�u v�S"8 \[ �=[!? x+t�F�ra��Qis�%͆� �JaF��L& �PsI�Y�i�&. 92�M`��5&\�0�. ) x 7 $A�75Y=[\chQA h t :%�� � +��b ty�$�K�zMps. Ell�)�T ak�Uony?�!s, �3 sZ6E�2%/*�6��9A1� T>�8� 4�� ,J�a�Wśa�}a�dimen�$3N�[ &�A�the�Q^�*1$$(m_+,m_-)�@y �P m��utb��<s*�$A���onxf $m_- �<2[�[&��P�6u� �-$�+�7�E���#me!!�}[\7"� �Y�t%tB~0 a Riemannian)�� tLis"rc �� Q�:NQ�zqaJP(a Moebius b!�car�Pa d"- m�.zfE�Ea �-B �p�5p�u24Z40hF� ,E���r cu��D�]G�#s��' ��} =�>KeJ com> E� diskI%��� e2� K�i�7��-E���D!{��*� !1 c_L+* �E!�n=�A5� !�.F,s�is6Zj L- F[9�4a pinch and.o2TaO"-!cI�� ����� Du"�s&( v"qn&K�-��%@.TH%ݥT+CH6�s.m��2�g5��!&�;ar\(Q> A4er�J �0a iQ�s#!S!"��}%-a�:�-�_!.� es �NQ:D�J�r (��-K�]2N =O o �&E�5�),�E�Td&(29��Z|d� l"� �Y6�e�"_ $P(�59*IEB��4�0J�� x(P)"sQ�9B�6������ $c$�r� aa< �riz?4 }� arc-� ' �m $c(�'? �isX%!��t)rthTF. �>�X*�5ey�| )O%�:�[F�>� I �$�6nd��6�AQ qz8V�, characteriz`%�W6�7%�$P( A�&MJe� ��{Mq�k)Y� �,>e� Ai��[EA�2xd etryU�����yͣ�'as�W� t0I] ��4V �m���_�=m�FI:@.#5\] �>� sd�e��&��&)��T�!A� e�!!D�ty� �sN�&�! � 3!2't&�B� �"Y\[ I\�I�C,?�K I/6��� � �.���.7=ٛF�IJ i<)�=\{(x,xa��?|e "W\}��map $I$"+to*i [$D�mHE@h2PC6q /:t23$���|�!a.?�N �=o &�J��A&�on Ie��f'�b [2�A.M �.E�a~�iw -��s*� J� ��� :E� )mI�!�!�p �&5 Jl�$�C@C)��!'.� $la�B $l^*�AK��!C2�-lla�U�&A+ l$. G��b*�[Z"�/BM�)~C �+" A��lF�'�x"8;x8;��qdpA=�jB;>Y^*4< %��"�b&� "L {�!$�� " �0V">D"- >Cx��?1��U|�1-Zpre&owe�&� Q� !�a.~V A3� �t �Q�d4�A�c��7�J��$I�! axisͶ�A��ɷ6����a&; A6*JV�@a3� O������(&�l �gord0^ [Cim65� en�.�* � _�3IdayO�b-U�fix9.3o!�e&�2�wK�6=�Qat��c 2u�s�l�"� O1�TaC�A tipu�0($�sY[�&89X%�.m�8&�@i7NA2t*"f O"r ar8� $p��A]�P7�9-3I3nd%x-�#Aw!��)[e��T�0A�rule:� fQ��o �tQed ���0S�b�� �Q@)��UTœ'��'d �+M�Ż�seAan �)-&w�y�(�+.X:D:��s.f7a.N9!��.>w"�`se!]2� �����I9�Z$a���)�> �ed.�$eF�$e 9'no-C vanis�;.��&�&9�.p.��b��+{Jta!�  @b-4e_R(x),e_L(x))kQ.�bas� f $>B��.?�jB'.QM9� �3�n� Co�Y origA� a���2.(��ewas a�Psk"�PMA� We g�"e)NiL�ud�ds c�oICG5�?�*���c ��%/ of EzLa� nd Marden| ��us;Ab��/#>2.��I $l$}�W��{� �@\�N��� jF ?#G-w$f} s�. �X 0�*���b�V�d l%on $P_0=i�>�AR����} .� 2��|�\�5att:!r:%K�EBi2I ��$0 ]T. s�E� &t k0 x, xS'�"H'B� &�.�:�!�Z%�[lU R:l^*2dUF �j�V�$@f sm o6d�(A��Ɂ� .N%A�y F�& ,N;us "`(%�w�i�y�* xyG ] s8 Ib!�(G:�1-  va)if j6� b�!�5A�^*W�c��� �$���P�# �F vA��),t)Q�u)M %&� � $c%�uO+�5 9 � p�aM�gy$�b\[!((p)=p�*|$c$dH�f�Mx&�F)&5K�,�p�. )X�.ng�8r� �gv� ion,�D#� d(p,�c�[onk�x�|{2b:!n�o $p9�,$ye%R*� l ��R � nega�2PJJ��Z)=�r�get $x"=p'jZ$R�Q�i��iv"R2'@ �1&�+e �!�2{ ��ha�%� at m�r�.(�UH>�3��!��  l$m�1:.�l�paTGF�*�2�T%�B2 ��O \cvd"�acor} RuZ (�yc qew"�e�S5<& J;.�p+� ��1"��B�A��Y 9 ^ a�b�j. � l@�by���2 r>�dct.�e�V� c�6"�Wѓ-Q�j�W$($(-tX),�4�B.�!.�^Z se.}b ADS:rot:ÎGW� >�or}�@/ y_ �e �;.�`�i)-"�!�Af��a&� y)2�m�dx#=��p*"� Q������~�a u�I��$l$, le��V%�$N��� 2�� tau%0!�F�%XV"�67 Su�"$S��� S� D��-eof.�:F�BfFi2i\$z27 )� $zyz� =y�v}< $(1,z)� jugaA�$�2A�]!&+ � ��5s)�a�� ^s(l�U!�=axqmT� ��-8"f� ���u�S*�ky&a)�5P $(z,)���$z$2�+D@"{ �? ���6=�:yvA!e*� ~�A�. 0ncheck,��S , up(7p��2�-�J"(/f)!;1^!.�C2* � A� 6u����uPՅe�E�i x^2$�&&�� !�d}��O2� F2�a�w tary*�D- H.2�=I�A�e x^2=),d I +\sh d XWd!B�-@122$J�23&#a�r2 u/2$� 3V!ie�2�`#\W2�C1concluV% 6.� .r;���2��Z�#a/����ofٝqN.� (�� /(�u r�n)�Պk-h��M�'@ =PA\�� :�{�C�s:)iu)c� K%R>'i*"�Aed��2"���MX)�Z�.�.��doK�U�(d9` �' &���J���Hat���2��tX= b$t>�O"�by(/k!�Z� -�b�ar-�Zt��O�FA��g2| � $(Id.��e:��5�b (�Fig.~*I.4 ).\\ �?canH�NEޥ@ �"N{9�*�a. �,��b�-f*� �H��"�$4�ޭ1 $x,y I1! "�)!D"@ [ �)$�W $[x,y]�q�way $l� ldots,l_n�&S-�i�|_!�2�!q&�M���A*i,;a lit�Habuse,. lX DUA!�$� &�W( "3�`��� լ�i2�cnN�on1o veI��u=_iP@� f$Raa �M��,. �wc+��XF��unif�]*�m�z0 ^&�fx��"�# \[� array}{l}b]\l�h%0=*�_ ,y), "+vS\.�H {}\\ A-A=�W(-a_1 X_1/2)$2 X_2E� �06n X_n!\ V � V a_1 >U a_2 THNrcUu a_n Send-\]&� �s:!�1�or�xd�$a���nA���U"�ad7i? /�l�nn( �C�8fa�� $1(in����I� _\pm isese8Eb�(.NA�\exp t17 $2t�=�".�6 Y"�j�ae Z>-: _�1!Et?N�FL-va~�}�C2:� $-M���2�'.��ρe��� ���B� [I�&z`A�2]�E˺u��s�to � ����&-Rs b"��E E-M-i�}VvW(reY�v �h5Zis ju��� ed ��"Eg = *���&e$%��} ``m��''!�mu��ltW�67[ �bo��!���( �P��(ݡ(�truhofa�te{Ep-M}�W ]�[#2J der}�=IntK� ion)��?ushe(� 29Hs� �J����!&�t mea�^y�l-� �.a�b(2�$ X\�띎roperu�:�"��6KE�O2b(y,z)=6x��$$x,y,�(%�����2A� a.eD\".qEm�q%);�26I7)=Id$Vh%��Qz stratu!2"D&Q;dAșQ ~�i>_��a�K �)a31ps$-n^XbourhoodVqeMa"e �x,yw�in L_W핱�d�_n})�� w)U! !=�4kb�:1 �0� $2 �e��mapgJ "�6FCs�&�F\6�h:�*\ws �--(7j=:\b�A�"!I�6Q%�a"�ic�2�1C^0$-"�E!l"�-I&� �c3boJ<Uoag�$N�G��"Wb�4%�p"� � {Pf ^4*�agB�,ɥ� tq $&m��.C0&� %`��� nents:E��#" As�#-�,�>�_-zE�\� al_+t�F�g-E �!wA(ymS�)��"�_a&X@of'ndard�X&��F� "� Brh� �U �i�W./�A/A<q#_f�-�u pr��in~{XM_F`&�G�!>mYe.E3s��v� v �an R�1!�]�"> ib�.��j6�w�.�]]� ^*QU�. c*If&�dE�J� �Y :�\2L� 7.5 of=ew.�y6���. disj/��> �iD*f��JCm�r.N^3-P$ (UA�tUys�Z$c�C-��aV\  "�jv�'KZ+�� �+A.6$$5�I+5� K_ �} \cap%�51" #=���"�.�n�o�� he`=%;%�}u�61�V��_+KG�$�*in��PF�P6zF_D"���um "�,xBW�2!4Bt (F_x�͌I�%�N6� �3q)"fa2�esJ�pat�&��=<��"$w�Bl�/liF=�q��'$P!-(�Mo� �(��) 7$QR19�+ 9��!$Cl[� l�6E6u�4|��N%a .����)�%z� ,-(P_x\cup Q_�0"�:�"�e $CG),C��6 �& !$�A�$�� �"�I�6*�� b ��%� not a�!6V�B�eT2�O J�.�b �%Qnt0m�Pa e& E]A xav�9 ;&an�H �j"K�� Ll�q2�&��/1�U�]� too.�|>�E�W'� 6��J)��C:�v� :��!���J�e? \Uu=�i"c"�\�c *�9s"�.Jv1�,l!in6`J }. JY���.�� � �K�If�I!�� I. rAtntinudH>0G\�C�8:\Uu �  &l B** "�(�6IH�l�� immed��A�b!!���0~3.4.4~(Bunch8 ge.@) "��ioq�ai: Y��^ #*N|+a{�+�qn�l�%S%$K���  #$M>��*�$�3sm $C>0i!�9� erty.��"C=.A"'RN!:� �d��8u^*(\Nn(K))$.)&�,P�4&� ��i0pP E&analoLof Pro)Qon ���:m���<��iQa soXoJ�iA�R ext: A6ce��& ">)��[ �>haFP(1�\U NU �u9x\]Y܉�F� (p,q� ��$(N(p),N(q)Bb* $p,q*� $"i$(�k��E �B�:�>��jZ$ly Lipschi D�/eh �a�T2t�QEu%�=!Y�C$K�@pendsT%N(K ���,.$)" %��("C'�JA0C�XE�-�  Jeh�w�X�!G :G�{E4s&�#�:gdX�ue��g��� F�j$TT%n>we��4 $r(1,p)=r(p)+!�( =[�u�2�U>LMD1�( N,q)�.� 'N?y9�>cQ��]M�\UuR �~1Nb��ryz�&�j&�"Uu$h&�-U�9�A`K �Y|�!_I|,$\�kMi��Tmaximum�u�4!� $� FbO"��4RN'�� ���w���h "!� B"#_��� ��#� l��,.}$$U(H;a,b)$�΁ qint�CmsA�by *�mn�v%`F�� �<$val $[a,b]�o\Eu�,�,��^&jv";h;�e�wea�ǡ�Dic�A�&� ]�� .�%�p.Q�AJ:�`m�J� ���,� "� ��  main OZ�+WR�!�2�k �+ba"�!<develop� ��2��alway�/$ ";}�a:2�"�qPp1jO1W/8a=�=�s"Q $�'<�($}�"&&�SBC � P�/�*.|yV����i ���of �H} ��6�amZ&l/� �V$stjG��ЫGiif���I�<"}�]&�F��U:�ara �y�B�J�.F�A�!q2���3 !"TI_2��- CG&#�ra�.F.�b&�M��&J��'��x�  "�!@�_+ &� a��w>B . Oz1�0h�I���a��"Ŗ&p.n:1%A.�B~� �8�Y9cF1R�4� z(if{"�(��*r<�!�*9�%c� "�&-�f��=Y2ZA�RY6M27I!�d2=�a��D2�s[*=J.ap�a�aw> R�v���W&� �)43' ��*U-��a��;IF&� glob�'&%m��6�*�)1��2 G !_a..�!�/�3i��� 6wB*��� �k-��E>�,l�p$$<"� >x�^�/AWGB ��9S*�=>�? �/JU. K ��72�11\Gg^+�9026 rew>��$pI �{R�e.F�tYs� ��"8 ��$ r��w��|.� �q �E�.�U�� 6��Z���0q$�@a$�1(q4 ��� g�eD�"X9�ho�d DA�1�Ttl�ncave �~"\Au�w -�Q���SE .F�,�bs+�Q�]/ �a��. S�%.� �r.6�U- ?@�R�nN�,B)�is )�,�� n��i�-\�pf ��&lOa8e))� $[p,�{A�]���{��" M�"��]�24zu� �erty .�A���6<W� �by �-���wA^jE��$�A�k��ymu1U�� p�rho)��!S�7"�C�$2&��qgs:!9 &�"� !�& $[u�'� p)]$�=!�ca�#�9q&qL� >�set�eE�%Ma>)�%��-2�p���=���:$ 6�"� 1$-subme��v,2�F')� 9��5�j����*�Z�F�5^9�(E*is4Y% �k� �0Ene2� %M�6hnAIG+:�(!=k2�Pp 6v"�"��Y�)��'35-�J��let|A�.r�� [: �mM�.�� z3�$h�_o�/d&iffeo"�=����*h�W=&$,Ĩ5P�#2�G2�th7Ys`b�"az��=)�X :L)J��5!�$-64B1Vq��;�gł�@xe��_!�2�J ����G(p_0,p"� �$x��=R. ��6 �usI�Tr*�pI�F=X dV$"rp�T' '�y|�ZYS��$� �y{�& �w�g�us��y2��C[�a!�(p) �c�a6i]\]"�,ta4= \�� an T�,aOteo>"�:��q 6�6{��aR) >8:IM��>.�AL �� 7�cal� 0��*m�,5���:V�$TA�v%52ջ�+[-c�1l1�\alpha =i�,1}{(1+T^2)^2�T$, \ \ & ��ta('$.\X U\]f!�'&$Delta_\lam�Obda$ is continuous and takes values on $\Pp_\lambda$. Now, for a point $x\in\Pp%\, let us set $\rho_+(x)$_ - �s above. We know that there exists $y^$mh^2$ such #D$\beta(x_0,y)I(y)=g|. If $y$ does not lie on $L_W$,`ned a unique support plane at �� equal to6~(�)$,B�is its d6hpoint. Moreover, $N^{-1}(y)%�xa single geodesic $c$ in $\Uu^05\4. The image of%8through $\Delta+�thR4segment betwee!�!�-�nd.� . \par S!se1u0! \in !L�^L� $p!�.�(1))� %�$\hat)�p_0,p5Q�)�%F%|�� . Thus, i)denot�4e integral lin%(% radi!!8TI-J:;(c)�61�-6-&�!�.�D. Finally, we hav�EFF�Psurjective. An analoge�rgu%�shows){it!in2T\\ In order to concludne proof 2suffic�todyz & map :�Ep�case whe�m�U� weighted 1.� fact%�w��e state�s!x^theoremA�A n,EIH same result will b OdR�@finite lamination.� by uaX�4ndard approxim+s%�,can achieve �)@of��!q8 \begin{figure}�center} \input{1geo-Ads.pstex_t} \cap�{{\smalla� domae�Pp$ with�+ecomposi0. Also�A, face ��(aI�A" n.}} \end� �L�� $-� =(l_0,a_0��$choose a b!�m�x_0a��y -l_0A�T!�u� $�tial_+K.r simply�union%Iwo half-e�s $P_-$�rHP_+$ meeting each o�� along a�(A+,)*0a little abuse�not%�,A|A5 � by $�). �d!��se �$ab�0 ���2 ora7 ed aa�e bouACy��. !]$u_\pm$.��%Hs MH ��lain�$P8�C ��A�map�ka}E�s����l_0^*M; end- o�-�� +�For $xA� \Pp=�{M_0}��$\tau�-8�LLorentzian length of2�$[��,x]lI��not di�ya�to seaI�tau$ i�r,$(0,\pi/2)$-n��Hmathrm C^1$-submersADA,��� �$�x!"�ast)x!a`unit timelike vector tang�teY 1R�p),� +(p)�D�VAI\Piy�levelu���� a)$.-a spac Cauchy1�A�consi��he 2�Egr(given by \[��Larray}{l} \Pp^-(a)= .�o\d��{ � �-^L{int}P_-)} \ ,\\ \Qq:@27l_0+ Pp^+:-�m+B.�� � \] E0 A0h��A+h* }+$� trica�Pp^{\pm}!s is a dil�!<aŐA�(\cos a)%$,�Frem�� \[ -0\ni x\mapsto(%;��Qx)�$[u_-,u_+]\A\,s l_0\] send�(me�e�)Y $ onIo r(\sin�2\d u + �t\] w $A�� t$ araGe natu�$parametersn�$a0$��. ��2�d$ a$E�intrinn distanc' A�� Q��al=2!�A�$.�qeveryi� $x�Ii<,�aJ\pi�tp��� `$at realize%W �f��$a$ from $x�x��us fix�k  $y��!� �.y@Jw.a g +(y_a)=y� Thenj u� func�s!�B�H \sigma(x)= \eps(x)-~{�(x)}(x,l )/A( )\\�� \x!(=^D)G, yJ:I>wM[ Q =-1$D -�^�A 1$�wise. ! � of9 $�, �4,\xi)$ furnish��{�� coordiant&a!� Actu< � $v_02S�����L!�a�E���n:isŀ�P�{!�inducedq9riz�/is�b by�$mula \[ B��\left\{:���sin� vtA (\ch!�E+�:A�,+\,\sh 4, v_0)\, +\, xi�FX\r� 8�!t Id �textrm{�G,if }\xi<0\ ;:��t�8���+��@v_0R�(\exp(\xi\ta�� Xad�ϊ~a4in[0,\alpha_0/p t]9�FZ! �>9/! )- +)ʊA%+-� X/2)X+:�GXA}\9C� �( }\ .�@� E�. \] B� these �1na.1ɑ.($(T,u,\zeta�t;_��we ��� F� �c �0H()=\arctan(TA++E�V-u����VN�. H� �] �],�direct ut��6,F� ob\ U!9$ pull-back�X2��9�8Anti de Sitter �i�tr calL � flat�, �ed�K� �`�reD2.B�r})eTL=\frac{1}{(1+T^2)^2}�  \!�tF Eo2R \cvd W[a bit V.� by�&�a|"�.�$t owed ��-J )J-&�s�6�&�D �$ glob�$hyperbolic� n2� s 6�� � � ��Q� aJ 6� s.2u "�of Pro�~\ref{�A/ :ct:prop}w$can easilyM�� $cosmologic<imb 2�."J(or}\label{a ca|QA � tau�a�]!3!��rO9ialyularitie�6MN 6� coincide� � cvd �skip z Tagraph{WR: AdS towards.�geoaty}!a�o��� YdWR2tru in SCon %� hyp}� a1defined�U�U]�4� [)\subsetS"� ��u� q�AVpA�&� this�ext* H u-� closur�%� �:� $, produc�� a loA^4homeomorphism "u !Vle�  $&�M[� }g(manifold $M�� In particA0�: s~ �is)�1 &K <:3�~*Z Z��(ich preserv$ �lpAve bend!loci. )�� {A� $\Mm\Ll(\�)$-�a�s} Rec�r%��>2s�1)�&��^, characteriz&CIreen�XsA� $\mx� �1& Gauss� (M� E�H}�I��iiہ�want �ƭ���� �.m]ria� perform!NA����on����E�5 \to �� )�t >�$. Take�J�^� $M�a {\it M�e} �l�6� $S�nd&S$Lbe �a�ne�\� !_EWty�zSe2a dop!�d$MŽan embedE�E�.ma#%�!~ � its � "� A&) top�Tly�a�=ed�k�2��qT, say8, 80achronal curvŝ�.6�. 2K�M9�mx���$of depende\f $d(S%#2�eA��d(M�!�� ed) M��Xby!j.�(Choquet-Bru0,and Geroch (bD~\cite{H-E} cap.7)a6 i�!��2�f)��� �~5 ma\lN� �2.Eticr5�{ �}��-1W=c$2? +wdm��g c!"In � �5�lie�z!$Gf!* onAP�.A��YAers� w\\m��a no-j�'e�Id��M.dy a�� �/j_i�j B���..�K(convex hullA� � �Por.�A��f rior7KaQ"�!& Z& I9JBAD"E� �� Ns ��e ��/�core}�V��UmD� 2rK�� hwoW��Wonents��e viJ}* -K/ ��future�P.,+K!\� Oc 1] ��%&al2B�%57� a gene4.�J����.+�&itY %PE�ifM Ir,!�$AR ouch�>ii�B. � �6�e�!�"�&&� 6e.Wa�,� c6�졙1��a!�A?set%�n $x,y���!� �$ a Lipschi! pathe;jo�x���"(2*�re�  t� Euclidean���Y�).��AZspe� � at is5f�#lmost � �Q��on��!=� 6��� c(t)$ (soh.��� W y�&*!�bnsequ�an9�.�6� set�$8(x,.#!infimum!�!�2b%�F�. *W�.�AU�.]^�H7c �$ivale� �J�. -4f)"� *&� �!�>� AdS ���sa�� teo<MLAdS} S caF� (T�!�aj"� :K)_ eWbij` 6� ��arrowF� 5#%� class�fr�� �i:& & A�Zb n3^\ l {\rm�le6W ���:-�|��!D%��"w�"follows�� �/p&d}�&2�a�U�F� ly��F0$--vic� � $�"I#$}� �0I �!��nk� a mea�d�ADc*�# k"��B�'�Z�! � =\va�&z�% \Dim 1 ��R�� ��獂 $S_n� 9G �s:�D="�! $P$ �"�$ numbe % s ``E#rging'')�� nea�!���9  $Q� atNh !*��P � av)$\mr^3$� identifi/ o8athbb P^3-Q$. C{ (a countableu so$b$\{x_n\}% �i�$x_1=x�, �u� $n$,T$!;2l$P!{Z%��x_n%henG*$K2h�2�� � aG�  N %Psw1,\ldo� �Z o %7C + �sq�5r$C�ea pleaM@ (it maH�  ve.es�-How!!, b+R V%� $c\� ."F�Q�o Ea� w"�*6�hT! ;� Q�:�. N&� m)v o�� !d=u�%he� ��%#A�!��,.B!j�"L ��rg�o6!�a nz(bourhoodUe>Z Et compact N*D&n P�{B�E@L �$b�!�,o $n�*�$5&ly larg� ?$G�,na�5�ret&%En)��*�d�N�%ew��qq!� + y $IpD(a\I_n\circ� n{!M x7!%���s'��� �n� � laim' :^$nv1�B��.R���(:ftheta��.�  �9�\��v�j5 g\infty)�.l�lWp p�Nbn.�.R`act�  $HM�Pp \cup.5_.�#tant I{"/Hh{nE AB. *C �.�� 1�$"L(H)�* C^1(HPp�*^ is� Q�pr,�/ �/� � $CaA�6�$'sU%-"� E� �]H*^w E�A]� p $J�Se sm,">�)� ):d& )�")u s}�->v 2 [comb &g O�a�nu�2��c� locu &.!~duc� � &/- $\Ll� �i>1\LlA �A�N<hed pus� -for�1:�f����( equi�* i "U �u �_ ngQw.a�$l^b iaA1�Z�corfo���i�c�[ye� ( arc transv�A8! $-�R�it� �:iO�z!We"� A�M ? _n=(F,\!)$ >�a6��/.,)14 .�c�� %d%1�a�a way ilarH!Lone u^in?Ep-M}�� " b���a t&� ���-G!�tyxG*� a1�'3  aefY%�2�9{!N2. Up�subdiviV,,JA�� ��Av� yJM2at Zonce.� de7 eE��I> Atc�k/!9 \-,V( 2� � i�o P_j!� ei- empty �Y��gf6kb/ B�n $P_k Wi = P# =P_k j.X>� eQ!�!w-�% �"5 =T%�>�P_i��|>I $i="� n��+�e�to *� $8"�3to!�fs"!5Å#s � ll(M* !6�2�A~��*�j�&� a&�= ) um" H A choi��w��$de}. AssumAy last-im)�)A�� total mas �Af "2�k Qa۹dz3�� j�2o . P��!���is�[��)���&)N�E@� Sinc9�1SJC%��YQ��KEF limie��ek�W�*!U� in��� y*B�B� (u�h post-c&�3�� ##l5X$$PSL(2,\R)K.$)A~�� Ju����$=EI$MR^Lemma�[K !�l>x6of (1.10.1(re�s) of.�&z lem}�#3o}u4($P_1,P_2,P_�tO���f q�out� mmon�!�&�on,*�- any � ��ly.6�8�2&_>��7 $P_2��$� Uj1A=�\�s �k!S]3EQles� O D.C93$.>)!� .:�mmaNimmediat%/� .E��-$(�P�gc@1 ing,\Z'dm!eZ. Clear�#�en5;���!�I9 ("@*��should���t�� an+ �5�O2�i�). h2remain; p� -)A�emph{P99uk"Q�:}�.x_i� *�5-��Y ��s�mp{�s�5UK�-$x��u" , bu%�)�pU� {$,QxIA &�5� M�zof��<Q�I� ��;�ee�g$ st%�7t�1_!� �$ $[x_2,x_3D5( :z� $uJ-+%�=t�xn$ $v\in T_u� $ orthogo�!>H� �!*=�,_u(tv�C�8A if!� 6:"[ � �,�Z�!�# E�=uI ] �3oa�a�g ;��<5l!B(� .�02!�l_3$)!3o� -_.�; [x_1)r,  2]�W�<%0\[\ch l_i=|\Ep! x_j} k}|\]"5h $\{i,j,k\}=\{1,2,3\}$. Nowa�*�� ~. u+0 v$�+a $z1zi}|@ u.$. HA��-�a7z1�2+< ' & 3 3' \end 5&b5 l_2'I{!x h5"�%P2,uZ53. �=5M+l_3<U '=!�. \>*��qa;��;�fnow" ?2�'8$\Gamma$-invari�&"�}���a@\2�'h?b�;aK'�- grou�k<&�%ng freeDd�e��disSRBly�R��a�, ���&�.��� &c>.5 eP�de-� $F= m/ �$. ��5B=(m@_-, +Vhe j� -cocy� ssoc�@d�rv �e &� �B"�; +$� bK.� re�)n�/� �no*+ m�$m?U N�=) &u� aBB�/l�/rho_-(\gA^)= �-jC  x�1� ,\ , \qquad &�/B+:B+jB \ 1�i�\]-ueE�rul;A�$quite easy%L heck�ai�6�A�* :g� ��d���v�jjugacy c�do�^�A�&>?{�ds �,�8.� �=n:k:A�akab=� u�B0 � �fe5+�)>J� c� �$-��B(�s�!l�tL bot�E6l� ?6e f� It� ŏ25] ��+�%,rv�`�� u#a���7by }21�%"DBE B#�a>:+�\U:�%u � .�EV �is!�per%$�4 � quot2!��b>)� � .�.c�$FI\mr�%gRemin�a)>�f1gv9G�)�"A�,of Minkowski ���- �d &�0Y"�!},� V;Y%c-!U&3-E�2��:6*V$ 1� the �:�,�� 6�3:.�P8a�"QJ�=atisf,*�&�!cWwRZ� 5e� �%6��\] In2z�E�.�0}/j�1:�1"�5!�RF�$T�'/5n r3��%� a� . M�8 ver0 �-,M} a deep re�@ ship"� A�š ific"4&nglF;6r�$�*6%0v)d� rston's.D?&} �Thu2},��w96 e go���A umma2. �� firs�E!On�E���nt pap(K�2j \in \6� ��[� �= e5�} (hav�D- shear& )�*�B�: \Ee:O .BE��x)|$9E�is.'ve_�Eb case�2.�wL&1 !5�e�S^1� =���6nMm.sm. Si�ly��%$�'.. ' l 2h���un�D�}�MB Fuchs�0�  n: .7(1) R2 0 3 � �. �+��!��. Si�cF�6�UW�gen"��6 ll oSK!air�@�&� oft �JtaK, s$g\geq �ris^Iway (q�)�# well:&�re%�n �Hi�e+rA� :�6�$�M�{\mh}^2   UY$ wK6t$� d=%l�=�( !��|:V &2on} /{H�*"qts�b6R4�.6.2)��a� )/�wI�:[iT� -.!�' J �m!�+a ���\�N�Yd[�,e��!X" �8�}�$Bu>�3)� �MK � �� v�!D)��'/!�E''oI vi ]f.[�"8'/?�8!�6��& h$";�^���:ECuaj��!�ults ha9�Z)�B� �E1�  -�^&^�h"�91�lambdX tselfa�erE�� %��>s{aQD adp2���P )�qH y���"b *��x1vs��s. \medI<noiA6t��\#)?] iE#cx�O E� $necessarilo$�� �Q',!�Z�"�.�+�F=ŏo��p h'2$}. One mzD wo�Tp)�Eq��U+ full ran�R appl*�Th"�&���O, i.e.�iE ��arbitra�M�M>T6X�I�##)���lq�a�2��u$M3, �&�2.,EI���"(1�W>X e��is)o not} exac�!�A�6MF{ � *j0He. � f9yڵ�6Y# 22i�!2i��� �:��c�R� i.� �Q�� ): t�happe9<f��m�ZFInQ_�!� is jY�Q�4 �%9�A�exa�%�k?8cusp}). Later!W�/�#7of6�K�S^�2Zir)(�&� %�2Q�/�^F� �)=H'a M6� s&�=�1� m� type�n�E word(S�Rw$'m� B� �n��c)�'/2�W�� biSE1D���:�.�2i9&���lL &�T:^1enume� } \item� M.� .�!,>�L 6�MB"f_�'&� �'_X�{� -�d.�.�end%(1�#-Z��"�-�o��$\Ee_L� R$Mt(>9#d$/!#�frK�&��uu =\{(k (x), L(x))|@  S^1\}J�iy�'����[ ough ��"*��D��)�!�-&1 9�aXV5� $2-d'�\.(YJ VRC}$5DE�!��{?L9[/F�t!# 2Mh%f�-�l�, e�kof R pie�O=<� �N1�!p �MrE f� �4>/0=~. O��[hand, �h�?����eAX wCz;-~�^��2|s/Y%� D�=Ci))!k�va�\"f"now6o�A�]s2#�� -I@Y�e�$:'$2R$Ee|_{S^1}=n On%Z� r%k���&YWby�(*G%E�Be ��Eed'�$m#_n':���F!u� }m@�#�B��/2_ a�>l^>�(I�v�*�4���3is�&� N a�X�!�IAѡ) �)� ue$u_n=%Z-�M n�.*u�Vle(�;��&�5"�2 �!M"� �a�� )����!�c��;U��$A82Mn$��.`i� Hausdorff�C!V*�Fd!�)a.R) �� FWk"S6\Ac.Q�X. b(.�!�>r"Xq��Z�1�AT%~s b]i;y4�!TQ��>iaT)���uB[�}�2�s3)� :�6��F N:'�v>$��.� � cor} y.!�up�f2����K7��(�z �X]. � exa}�(%�ex}�:o/�;j�>� a%>� aw�**� &� !.�6.jEux) X�iR�+O u9Z teXfaM.�� �+we*P �E� �a 2N�kZo2zF vJ6 &Q I��@2b.}�61YW^-hce�-C n�^%l- �z_fY��] i"�`m�!Nx&�$l��$ XPp�!"|t� theyO� !^�>vev(_{\rm �;t r&r���" M r0�x�L6�F|�:������R=�$d_\mh(E(,x_n)=1/n$.E+�3&& -)"Ue�2"dv 1WS6-'r��*n.<�&�_I�ed �8�Z "�)�a�+c�Y�@�<PV JV!9� L�$�;'s. O�!�n� ���0nd.rX�����[Q !�Ta�b�3K��&�%DZ*FZa P�+ & Gt> P)�5�!�"[)!� Dmeec_H� 0�l_i�(Anl&�<��n �X O�ba�&�V�\pmrZ\ Wpm X_1)l2 c=2eeX_n)\\ �R�$ x�U�� ��U"��&� K:� "cEa��a"�\�to*&�0i P=Va� ���"o�* ev*A� E�s�A��&air ��AP��\ /.  )2 2 _ &�B� )F ��� `re&AD�Qp�paq0 P->��EE|�^e*%bc4N'!C j!�6�2p}Mu f: P. H'�E+� I(x)A �Q (K$IG�%� P(Id)�!:d`"5N)��a )o y FN.�yXc�� ce �Ee ��>VP\E��E�����(2�&T W>IY��oA%�UKc2 nent�anDEPl�eket;�of~ Eh� f %$g< expa�i�6�a�*� o @ �!!� ӑ�sW(Q#)�di� �jA���6� �6�D��facts?&� %Q1.dEa./�)��pQ��@�ax�a}ais:�}P-��Vc2�; Q��*�+g�@is gr�Apan�?ZM3 M:�`��`!N�a_F_ en $�� �)8 z�8De�q�6Qr1� $, )d�!*3.�\�+e6�g_2�N �"Y:$+ �.�= �1.Ap*�ru�n �]A�a�>�� �� �>|9&UQ.� �,to�1r"�)bigcupՒl_i�hr�Ricial Q�*Jd Ll���&� .!z*�)%y`< $1�x �5yuaz<wL/ "G7&u"� 3e�!'����&�|�8�``&''��.*Q� V"� u*t�aas&�1'&�Ai� �&� � the&��2�"=��. jt :�.T$-sym��� Tsym!6(> U)^*Q 2�2kr!�,%2.!A!.�verifM��effecq` holonomy:�!A�! of exchan�G $$ �+ �+)BK !+ !-)�' $$ W�-���&`#� *1"X"6P#� �e��+m�previous�s$ lso ZrE$!sf�&?B preci ' $RL=&Lej ^*}$c"��!�i�;Y�!s!��'Qf$&ilu�� (-[^*)'$q�'sE�(�C�"ing"%"�oY +E��,il ���7)� vQ!aR fx.�� S�6�/+%-Y r� -A:�kakCupr � �o!s1 �1 Y���4* ��M?rqd"�,.��1. %]&�A�e��A�broken�ge�!l v*�< V�althoug�.A_& &R .�S>g &+K�N�'.�sh��A�%wU�� *"a�M'�f "�"��5p�2�!kletR(S3j�EKav^.0S_'�8�!��som�pX8llustraaQ�J q-�A�1��%%% L�] Vari�9s: (mode: latexLTeX-master: "2_3DWR"$End: c� thebiblioky}{99��bib�{A} L. Au"ssA<G.J. Ga� a= d R.�K�_,�,:�5F*-� }, C2�. Quantum Grav. 15 (1998) 309-322; \�8p} B. Apanasov,{:i `��Nielse+h�W(for a Klein&g)in�0 quasi-con: @p�[`s}, Ann.Glob.Anal.Geom. 6 �( 207-230; �8Ba} T. Barbot, �B ally.��/ ��,$s}, arXiv:!H(.GT/0402257.�BB} S\seilhac,!v Benedettim1O&�>����3-m�_�z3 C)$-"�"�TzDDy, 43 Issue 6, Novh@r 2004, 1373-1423�n% - �%� ical� �Dilog5bhmic I�7� $3$-M6�Fl.;P�?�bundl!5 %5 55306280R�3DHy"2 Fiel�-eory} O O409282�Be}RvAby?c.XA� 3D A�itg�pp�P�d�(2+1)-gr�}, Nu}50 Phys. B 613 ! $1), 330-35%�]�+m�*dic�e �A�/$i$j coupl%*o)Ij>� 588�(0), no. 1-2a)6--45>��* �y(Teichm\"ullCA�%#�B !�},�ics�  F B 441��60-682zPJ (C. PetronioM {Lec^[�J }-*xSp[&erk26qon}M`ah� �>�T*� a���La") foli�} dynamics,��a�5��H (Stony Brook, NY, �-, 1--37,�Stemp. aB,., 269, Amer ( Soc., Prov�S�)RI,��12EOt.�� J-P. Otal5B� mesur\'eeJZ( plissage d~riet\'e*�fq ~dbme-$3$},� !u t 20:�o1�6�PhD�sia�DScuola Normale Supd^e, PisaE�5:�VV�r Spacɞ. CR�?�2S�V���$DG/03110192[o2Vt2+1��L&;U�� }, London�i� ��N�~ Ser.� � � 11�87�13-25��%�,E -� � U�9�I� 1972�Ku�� S. Kulkar$ U. Pinkal�zA &�]!ic�M\"obi<��:ur���*�.Ama<. Z. 21� 44) n. 1, 89-122�!�} Ga !�1�J af�; G\� :g �<funda�D�e!BIRSoviet� 134A7AL129-134.�Mat} H-Ja�tschu9!� phas�.Y��multi-�A,e��q��!�las� ����8{ p �,7, 3497--356�M;{McM}s Mc M�uk)/x�=I�2 p� J.B� i�$98) 283-326x!� M�뉬�K.�of%3t Curvze��F�}L IHES/M/90/28, Avrilg2l!" Q�&z �`� pfib�: 3&� 8}, SMF/AMS Text)��, 7)i�(A��� Society,ep*�;�iété0éJ ��de Fr�z, PL7F�Pena�0 nn�/�J.L�rT:)YCombin& ic�oTr� Track�PrS%tonB��{2; �`$Sc} Scanneu��&�:�6�;�o"�s uvA�omm*� 7aY99R=tHE>'t Hooft�.. 9A2�a0 32O Thu�dP�P3QW ��"� �3$2  Elec� c Ve�1.0 Oct Qt1997 http://www.msri.org/gt3m/.)�7WN�&�3��N.�.��CA7n-�Analyt"� �ic Aspec�*Q F },>[�-z�s 111V��="41982*W}hWhs5�_ "W �~` ;4an�&�3 solu�_systemv.^ . B 3��89) 46 .��!>I Zg\s{Moq:�a�"of.- }y'd�I�i2�ob#v?")eu5�7v/ˆy�2.�H\ISO^+�p@Ŵly| cI�H�6\�+(possibl-D77=\{Id\}�D�: put >�6. �I�# of (F�)&* &�[ te"�l"(�n%t\` =�9,t\mub�$tG<0So����a � famiqNa�\2�'u tim3vhat�k_{p}�L�<�]��] $\kapp(,{0,1,-1\}$, h`ts�D *�D _+$,� as�9RSjo�5 �(2.��'T9mRvofٓci�q $M:�wV�WR.3��Pp.(O"M D�L!�6=���*"�&� &2C%tn.xF�N C^,�1D>�. �7�+)(A:�/` and)�B�``derivaj��� t=0$� � E�NUu6�,!~their .(w ``�/ra��%below�8 �C>{D}�$�e���2{�} 9�"1c.=/t��[.�8C�I-_]�t^2I�$:a A�F} u� � R~�=3lu or $1/t^2I�-� [D.l Sw�*$t\toe�F��hes�6Dus�&i�$ impor��re*�Gl;,|96 �.a4�p up a6� -pQ"77ce re9#��nsMpbi�{>EK&3o� F��KJcop��  \m�!EG�$ f&�J:&�H_+*3&-�0^0g&bA�rmarked�}&�1�.�� =f�=i�\$2,qk_0�Te ]1}�Q(Y � ᅅdJ $. A:�H�reeI![�!�@�.esm!) D:\til "�I6-U�i��R0}� oG].!%�V� �%�0.��͓R"�"O+#$s>mA�matI�g_s:iI ni zG� sz_�W0l'J� ovtUu_{s �}^!�&ui��)�Q(ye=!R ��*�$o�#./&US2w))�"sI&l-f)$)�� establish�DS�Y^� �2g_se.d�a�>L a2gUA�)`�-6�J.�a9Eit!�2�?��� iҍ�Wby �plyqW -W BI�����$s� �� �k$$k_s=s^2k$�1s qK�+*V O h^0�$.�!�e� ve�7�Gai����=%-1�X|F���(.d ,k_s)����~u:AkFeau��NQ BQ0�Q>�4!"l}��'!-��l}A>"&&�P$s�w�n�by $X���e8. �)m5-�Z�(6hd�m��."� � arou��XB ;�9��B.{ll�.TL\f&�!b_s ��� \ �Uw,)1(%.a!= _�� A!*s�6�h-�2kQhy>*�x.!!/A�a3=# "S�0-C�VHn!,b�&~6*�(s^2!+9) !*&@.6�1)f*��w' $\lim h_�=k$e� "WUCk=�@t�we �Mo6��$h'AM-�4b� Omegaf:�� S� {x|�_P�<1�X  <1/s�n��$(U, t)=�61�,� +zwe��et�&�;)�b��99�$k�j� !�.�1^�- �)�,J�!}J� "�Z� �0{ � �}s�9s^f .�*b<�5.~@[#af$!�.8)=1z$;`A $ ' x)=x&1�C� � (x)a5� �(�0 0}\ �t}�^ =)�}= "N� \ "�8�߆ &, � � = 0&�/ind0x!:s�ges� ��wV+y $t>0$d��zt}� &� >�M \] �O@/0c�Limdb �*u�ed�s;�E8 (d'�;�@ %~�6�>1� c�grn�!rH��m& ilI�'s �dis�"�H.م.�of&o ���se�Da�<VmP�D*Q)�Gh*l���=�M5>(<>�i� >cZF  \rho_t K:]�V(� �}�3*�/comput);d"�! ��e��v�*�,? l�b��ad o����nee;f� �* 2is�2��d�,�:Yoursel �o T3!P{]"z�Dc�var:der:�9m��8a {(:� lex-�Yd}&�g�9&� *] �"V  $EՈ%��-Ma� l"--m}�+�\�8x���|�t�+u��1�" :\mc2� E_{z ���y� \PSL{2}{C= � A�mb�c*� %1��_n.C a� a nB�s[x,y]LYn�I9._n}F� $ \\\% $\Oo(\mc;��l�5%�\D)xb��� /s�zcj9�. J�D= �0?:�P*U5 y�6a2{�P �N�v� ��+:R5at $u.BBYEAA�act-op�xy$A�*��0F=v=u��rmqC�Jl1� QQ% .!�U�7te!%VcZ�dPݝ 4 �6��+Q�&�;�e���cvd6BTBy*^'a�i J�6���)v$ ��0DN&� $\sG\lG�imc� �!TlexQy D'r�]��i�Y.E=$r)\oplus i2�H�E f �pA�n�2.h4�@ $X(le�mr)$!�t,=-/�DJ="�Hl %�no*�D&=xin�E U�Rd �)"a�C�1�N=}{�� > =�A�hs &o=�$�T�- ive �5 s $a&\=��in\mc&( !±(V\dF }{\,z}|_0&x2�Dm_{i=1}^{n} a_iX_i1Ӂ�Q ��2��� roll!����and L�P].�չ :��C-c*r)mM�ͿF�*�1� �\)|fi"+xxF�p"! qu >�eq1��\int_{�'0} X(t)\d\mu(tטo�6ati�so{d:!�\�DJ��� \=A�y �� tA*Ll%}m leafL�A} t\\b0m&" o�<3�A/������)�FNo�g� !�V� �4� XH�a�er.�w"9��(�%st>�2'r�en�AM�$ killA�A��a�K`y��2mr^3,�h�<}{ n��U�dF&�9e�*�>$x^-,x^�A�e�"�KYts �H>�9�c � .�j 0Bzjl$� �6v,v$�tk�wbal� ��~_c&��q�DS:�>:�� ^{1}* 1�A�an�in�V�f :]8[ \coom1_{\Ad}(� ,�=c�v#r)�� i*VLr)��&% q!e�,��-�%2�)�ЀwHDvh a��dot� (0)��i}��ta" �S*�* a��5mr^{3}�9��>�E���&�.i�%�i�� ��B*<MJ��.B:�A��-J��%� �\!Q-�6tau-,_+)F�.y) �: 2#*).�_�t$ / �JI =I�� m �� {l} P-=-�1>�\ &+MN%-� XA�F!x%�n���ra u�!"J\Cc� �coZ:cy\s �s4P3)"�.�O = "E wAM�2as}j � � !?r�=0��>�I��A��e1��� "�4�V (w�8y\Y��] V41&), MG $20��5;2�*MB)$.�/5%0(K�as *�`by"�+ i"� arg}*xba�Z^2�3��h6�+:� (.�fix�N'l)i). ..mXy.�E� ���2� �=vI��a�1(Y�q�xv,w�a�>M� igng��"BZ�el� a (X=�\lE�1�1�=\E{v}{�k�g " B�%�&�Er.c!.��&�D�2pos�".;|]�0� � &��e =`F�n2-E�.7V� G!�Y��e�U.m$c� �h^3ig5V1�J�U3�21y ,\in[-\pi,\pii��%�2 `a t�]nt &� Bz c�aM �K c"� j�_y� .+�=aQf�li�q#��$v$�(�T�m�mu � �� %�I�\trB.��?)= 2\ch(�聕$Q�)��+i $Mm^#"u 2�]���D "5ɡ����6�e�P�:RAH24� l(R��� N--1MwFi+%(�a.�+[^ %u�8� ��2�" fDpUo (�elho��A+�$�5""�G�&� �G"�yJ_0Kq x� in9ex,NSg�/� -{ hq h Q-hq h Nh, x^\pm"](��.� R�#v) ��x%$-1o*D$!<5�%�Or�o�+(�)�dp�G/�$p'�I $q2 q_+WNJm,n$ �e!� ����a.�%^:�A�\.PG�)٧Fiu-on � �-"..�5.W��le $��m+n����%!A�a>Aa �BCn-mC.�usc( � �4��F��xZ �<��2���Mmv+ ��o I�~ I��!��:���� !)"�&�a�ex �t<1$ &� f�:P*�"���*� � $s6� 6}f(ta"� � X xRX�.�N5 �pLzYS6� F .� �0.�b� #-z )b= el6a I +حF{ Y!��R"�% W!xe~��=EF*�` a2��.� )�s5xA#� � �� o&�s {�f��?4c&K}e~0�D$(�"��&�"?N"�aK�q ͮ�3E Z, �9|/2'mFA�:�o. X�a�n"�D)>b�  /?I�NU-��2E'!�%�Jk�"2XM2��o��"#t^*e�$$.�!"�t�*<a�'k �.�s�1F�,��dJn�Ta%�\de�)\*�L�}.�� a�W $\R$-r a*AR��]56�2�oR-��!��Q�zmeaAZ�!�� �g�)����u�!inv6\[�% waSX�%͘1}%I} �^*_t}=�0,/{�}J�%� Y6$� '_t� ''_��2h!nomA# $\ V p&�56F�F��&8.- pas*�L!�K][Y N��X"�/"�6 g�5�gJ�" �.&*�!(,=;/��%�  $(F,1E��/ Tt_g�0�6_g\$t2�q!_D?�qv  >$CW �.fa�A�<�&(� �*i#!7d"� �^�h D_t:B�1�!�0u�!?/t/�*\mx_0�a*� DJ2 azZ1 $D�Ah�70]r= r1> z F2 %2"��*MI�0*�2m)%�B�d.�t�94�\ q���kp�s-a�J��1@8T<!ň Jp/n.N,nf1dP %m7K ��$T!hhX\OK��*�*sF����#p�BH�&I*�$! 8}! � �aKR��z��!'&�,"�#I�� � E6�/ t^2}��(tT_t)�,�.c. . /1.+�,} fA���# �e�"� =��w!�7$$[,m�+�ce�!G#��$\{Rt|� [0,1]9.is pre��m(^t"�� s&�qeq*V<e��?a&&�{t_n}�/tg�%2�%q8&O*$F'_t�rh�N(�)&�4F�\.%'_&g])wQY�,Db5!)�B�TePN��I["4mme� *� &��¡�!�i�M�'A�b GR`$0.> a�3}7�&� Nw�M(F�9$$�u�ͽ%MF 65!(B'�aj $2 �'_t \ ?1B_(�� ��/)'z*�1frq�N��%�� �`IC�) �4I�&*3J�6 ��A�a&�Tv�Jg:qis2I1aB�)3�A%�U]YT:"2'.��b&�u&p)!T%�!RNI� FS2@mbd>)'-�Cl�5"]% �D$���$($�{!qIn B�@���u.��(��I�2sGf�a�Q ���!s�� @� nessJ"n<7/referbO��- Pen,ZFLdetails+,*c�h- �w�Y&9|�. %' sigmN�.�,R�$a&�J%r2h~�S��2i�gmA+6���-�: %��C?(�S�_#�`.t� %�� �k$. %��1I�m��S��e2siota_FQ�� 6 ��˂d�Bcu��6f{�$�%7]t� ��Ae��>�B �A�Th.�/Msrޑll-�^n"�(*�3%Y4 %Two.R"�R$S,S'$&o1��>���yg %if B� gߊ(SV�! '��o"�<1!}CcA� �)� 6:e�.� �>��a��-��nFu I�� J$G5�J�����S1e' '�) ����%�"�'c.��S>��\Md! B�Ng=N>5G FG �A2 _n  �?\�0 kc$�b)$ � !I>6� $F2�0 R%O $N�i�>)J���қj�� ��_i�i)\}_{i�#I֒�R��2*� 2~%�&�A6 {F_i� B� >�nd��$:�Z.���{B $C>0z�f&�' R)i)+ a_N%,S�Q� ax ;� &8$s�er�$� X_i$ cutx�N� $M��(mCYo�qK$)�1-0= _ m�dot o0-�="�4 x)�4�=(uE��(u�.�. F", �e7 �� �<:  B; *�=�)s[ � k(x �_tx !��*O& % \] �>/�5�?�0:�*2/ F6�J�"�Z5�I7���. rev�~ �2J ! �6w-Id=N!�\dM�e�����!u�l*�7q}��"dq���B� � H2�I�J� ��F� ||> �W1||:� _tx]!2�a�|| - C6� 6�)2�IBjuL>"s ahA����,L R�J��"��||!^2u *"Pn5=� 22"tf6a�"��*�%Yd%E�s] disкt�� �!�`���aO�+ %Aql]] hold�~\ !�,X(v))2!.u)) v #>0a��)>!��6�|-�2Q6#{"J F��� i�weB/.�K (L-CmyA�����9 )n ,J�����=��t==|�� mu�9��l/t*�!2�����m�D: B�� �mu =��&�)B6�?�u�<�B%�ag�ztsA��b�Qp�Nl&�=2�w; t 9li�(EwaP"�RK-:[[X_{�}=-A�Byo�e����#i܅�$Rm�� i�!���a�59|. � T��Q�$�ElCs� i�l�"�$7w��.�G beЗour� �Z7vnig}��, M�m�a!mli$ve�ark��Tn�"�a6�RI��%�"�#0*�= o!M�m�� ��l��p"�f�#.C\ �n��x Ł�y3J~ivS5i� |�t�/) $a! So/[��,)" appa ly�����qu5 ly newPPhal�S!�ies.} ϓ�⥢�_ it!�� ��"^�$F rad�8� �u�ho occurj $2Z (� �S>#=)�� A�…t*�&A[!�c�(�)+,V-S|- z��M� P2Hu�f*[!�f33Q�# 7of nHit!si-�e}�let2n*.�_ , $Yysay��*�arZ >�#( n&N.�vaD�ws up�:��C rst �H $t!#&? ��no �er���p� reg��g!^big-�:4$b� es m��3 ``wild"yW� liev� is�� �1��1i��cep�s "RY�[ ��i�p�Prt��a$6�)of &yn�$an!��$body: look� a@��*6 1*or,% "�Lsignif/ct c��4cal phenomena &�lost;wA[KB�, ��c@�c=)#WR ) k�of ``nojkiz�'')*� 6�. We bBq�useful!�sB�!�inv�W� .x0.��OeFЇ Anywa � �0Q��e��. �5؝7�� side�ton6�i�M0M�N R�.�w��"�=�/&��Ce�zde"B�+el�.��6t[�+ i�:s�5: .-:``B��)]�_ '' $60(^+,B_t^-)$ !$�!�J}d̝&�Wpr:j asympt� 'P"�l �)6��A�^; J�]5*�d $(C_� -)t�� ��md�!0�I�ca�] ��;�|K|{�O�O�"& xc�m��->���B�+2�"�QE<at��to inqui�7{!cg].ݡ(.s�ir6\IB�q ���Q�Yo#t^+��"Q?�a!���O_�0� a"�l's�7�.��_m)2k�:�2"�A���6�� U"than $_�x9+ask�^"G > � '@� $%�t Ac����N8�=s� �ldr5.[^=f�#J fi�.7� EHle��_0��-{,�/�%)�����|^1� 0 T� �6�r<��� (c.f. ag�h�#9�d!!g$!*L$(B^+_t, B^-_ n.� � �/ �aact(N$D:5+�l����g��^"9.��)�\}^ eq t��A+�� ��2�ABy �o]�.g.F"�� too6�> h�MZ �.V% �*i"1�l ]�A�.�X& ^*^g5j�(�).�e�Ecd�a�$N.��e�P.)h2A�� ��\05e�IC E�a.�m�[ \[ h_0=--dx_0^2+162^20G'0s stra �Ai1l�$ly"w �/af�9 �'�;D�O��>L�h� lZm: & � G��I�;a�or null��\t ���_C  Rieman�{aJ*� orl�ed(eN���  framw{\�al\,} 8 },\,�N"= ��v' x_2�-7&�AJ=�-$�) t�A)1"/xMw}MO�i?�!fY�a��b~CXw}=-v_0w_0+v_1w_1+v_2w_U:T� (�!ed)%%V k"�4AD .ʟ!� �a�a.�-"d� zul�~�>jVx��BU(FBE�u�m�coi5�Q'�I�B� ���%@a"ar� t��s�Bu�-W �{8$ISO_�Sf@� ��� hat ʼn(�T="5�!D�.$, �s �I\r)s S�k2,1 � $���?em�u*2J2�ԁ� ��Okology2aGefo�cwe�/" $(E,.2d�YT�e� �U1:c&,��"i�d!n$�&�'�.� ��)/�:O��s�edkG !J��Ie�֩�b(I=\{"QG|mYv}=-1\�P%�} v�\CR]"]%.�,bt�x�A)�d�06` <i? =��R aithA?i{3e�!MHXsm�S 2�n�e wholeM��9A�} N��eq1n&I�h.: reg}�� A ��6��}�Jm�AN�!�aCu�m!�i�C� mz�2oy�s�U ZIsZ���:^ n ��ateRst� ����,�R5 4is ne&��)Lq�nor�C�a TE��7!M + �.��%_ �6E����6s)sC�"��"�} (O�2�� way)�bK]widxD`�*�q��,Ba, Bo1, Bo}%N�.e�A�� dE2c��p��E}�A�� cMQ.�6.p�a:�&!(p�kaI\Uuf *��u& $r(p�?�1&&$T(p)=�p-*}|^{1/2}.aeK� �$�fQp׾K � $ `#JIaq54p+Uu�S �8r:p�j ��vuT%��(yLi&��:�m|�/� &��}A�eP!�e�S�S�0�= _�*a�>!�]z \9� I u��y.e I#)y����Zinte�"k�{?�td dM�~2�U$� "�h!MT%.�$AJ� zhѼnabla_LE{ 1}{}(!{-p)\ �@6� 8 +r��<� CQ��&�lN:\Uu_p -� -2T�/�XA}5Ld Me�"��=v �.�+ $T$-6��E(a)=TF����Y"~��!{"d~ (h�A�a gn�B$T���,phs of $1$-L�Xipschitz convex $\mathrm C^1$-function defined on the horizontal plane $\{x_0=0\}$. The f:�R$N$ restricted to $\Uu(a)$ coincides in fact with its ordinary Gauss map ($N(x)$ is�, future direY unit10normal vector.o� at $x$). One can prove that this��$is $1/a$-L1"$ian w.r.t.��intrinsic distance. \item By using(abe@point 2., it easy� show$follow2H inequality \begin{�0}\label{fund-'�} \E{N(x)}{r(x)-r(y)}\geq 0 \end=T for every $x,y\in\Uu$�'�numerate} \noindent From now on we specialize our discussiAo�3-dimenal cas%(paragraph {Q4measured geode!Alamin�xs towards flat regular domains.� Given arP� $\lambda=(\Ll,\mu)$ on $\mh^2$ a gener�onstruI�$produces a:�E�_ T$ (A�"=fI�The��: �Pb9fin%*��way! \U�A$=\bigcap_{U�2q}\fut(! ,(x)+\ort{x})!m \] S!�A�h�� belong�B a we!�ed E^$l\subA�,�� # $AA+Consider�g��ray!h starE�f�a�%D pas��M�A�Clearl 9i�C}�arc. %� R�th�5exists  lefte�E� limits)I !_-Eclim_{t]� x^-}!a� , \] \[�/rho_+b4+4!b�)^6- t$�e >���� �l $A$:�$$l$. Notic�=!�W{\pm}(�U�lyA�th>&x$.��o.cb3jA�.�a/��x^� Ano!� descriŋa�5�3i%� y2one� eqnarray*�2A {ax+!= (x)|uE- A�0, a>0\}\cup\\az cup \{x+t2E+(1-t)!�C ; t\in[0,1] F.��� As before�us �by $T=T�!Jdcosmological time, by $N=N6(&� AKr=r6#retraA of 2F.!�n � f$we�aFM5%]}{l} T(9Q()=a \ ,\\ N2x r2!E(x)�  U \] ��!\$��b�:�j(2�j(bR� In p� cular,�� �� at 1Tlem� Nonto}!�=�o:Ba$surjectiveMoE &C {Mr= � ,he $T$-levelQ face9 *� Let us f 2)2�$(a)=T^{-1}� a���B�:� We want�� L also2*W��8carry a naturalF� �l on. 2�closed ��$\hL_a=N �L)\cap �2sK irst!����:%�fol by� s. If��!�a n .dof $LU�Tat l_a:�l�6� =a l��$ w�$x iny A/�7Sin�6e$N:6L�F F F�0 "�e.� l_) a�>j-H.Ps,A,n $-�$l)= al + [�'�l, �]^�A��.� �Y�� (Euclidean b�:R�A)�(t):=�t}���� .�. 2�%ܡ> E4= � up_{&h 6�  \�l_a ��J0_W}� R�KG d "� ��E�6�77ifiable V, � .P we k)�r\circ c)� "'A���*{ 1* differentz almost � -I�and)]r(p�qC c \dot r� �d t� 8$p�  $q$ ar!�e endJ s% c!~ :~ MUa�aB� �� � "� $!� \mu_c=\E{M} ^{1/2}�t�f $N(p)� $N(q r=I $� eP) f (c)=O N(c)ͯ ] By)�i�ity!� ��-�B _��,!is �R�e�F[� in �% r��Ai�%&$-C� E2�68 �x bsolutely� � q respec�rmLebesgu"�U*2n� !$~(\ref*Z) implie� at $^� \leq  c(t1� =1$ (he��to/masE�a. �$is bounded�x�length�%)A�ei s��t-�A�.@$1�p:}  6�2t-�d JOs} & &� theorem!�pIdA��,last chapter��Bo1E �teo lam�usdom cmap"�\mapsto]l($ establish�bi3 on betweeRMm\Ll(�aKnd� ofV%Jm�AO &� &� ,Au&ed up�E�l�C� �� !sakE�cowtenessA s��) main stepr *�Gin!5.!��J�t $ !�iA^� aF� 8 ,��!<&p  $r?�  ial  A�$\Sigm>_ vrgene fact�k � d6qbI9 n $rZ�� isomeU embedd,g  l!�� Ff(r_0)$ I�.8twoh sn1,r_2b r1 �� $r_2-r_1aqJ#%2�goe�$l_{1,2}. %Cat&��be orienC Auc!�wa��at ify -$ (��. +$)a~a nul"�cor!on%to itAJi!�< end) ��%b�, x_-+$Dm a posi� �i��!?r^3��Then byF>22 $)�1)� 2) �bai_7(� ,) half plane} -� )a5l)�8 !_�N�=\Ll_W�$�� iderAb!� union of J�-! form �����0EA2�se�typ�0A�) �We neHh.,techn[lemma!� �G&�� n~��}���q � cM���!�1VA�YtAsakś c� c� (1)$ � *� _��U"�E� � � x2Iis ei_A�fora�egmx��no JdaW �,homeomorphic!=@� e�ޥvat� 4.�isa ���&\remark. If $p_1,p_2,p_3� � A� �e�2 N(p_1),  2), 3ARr�+de��B�1�1� s i]Rq6 $r(p_2f j� 3 �?re�j!\u e r� s�� �Schwarz *V hold�� d so�  |q ]1)|�. 2)|+2)+*1)|*� |\cdot|7 nyLorent�t.& &� it-���K!�$\ldots,p_nM�� *�,1U��D\sum |p_i-p_{i-1}| \ell(c)+ �n)E6� #r!9&� � \\ � b�se- &� meX m`$.�/� locally&� �V Um�Q =r( �(t)�is �  iani n!Iis �� ."f �@ ag�9�R5 &� r'(t)%D�KC �G=%�/, B_ f.N�e2��a cla�2� �;NIfA�!W�Y%�\mu = |�|\d t� �;u=N_*�9%��I� ��!�9H��vU4 fiel5 $L�A�6�$L$a���Q� \�c v��� c} ha�6���.qJm`�NC J�. \cvd*� {Co"� L �$ . ��*r� � b!!�"�B&��P_�Uy�2�� � �compact�$Ko\�w���!#M eI� N. 6���� sequ�M&&�*s.@E\" ��\infty�K$�xW��*�!&n$o  9)E�B�  d.: >a��(T_n,r_n,N_n& T (,r  N y6� .� ]&� k"W. � fact~ ��go� to outlin�pr����e�<$pro on"��piatto:K%:��K�r 2'of��"ndeum���-0n�nverg� -H� KA?c. coup�! �ve numQ $a>0$;+T_.� ��!R"�&(�).>N6>��6Q�$� � �.����"� �#I :tsY>  �� �!�%K "> (L-�)_&:5�ԥ�,{[x_0,x]}v_n d` }��I8(x��8 4���J�h�_kAfS� is $C*!'E�L_n�� �$,�some $C� ��� ly E�.� extend �|_{ O P}$a�aL&�' � $\tilde vA8R 4 _]$.� -3z4�� ?]}W2Z $] Possibly"!�!u!���n�%�� v6ol)�i�. C^0( ��M�" it� :�2g v Q= Z $Q\.�� 2� �d_:: I� �(t)4;&������.�resul��V+$)��1:��� �$p���.��(p�%���re �"a�� $p_n Mn>Hy p �1�\Dim �as�x=\notin 2!�� k"�I�p= a x K l=VH?�'2��)�A�0$ works. NowR�>� �p$ 7i�)� $al+R��P5&� c2�y,z):݀(d(y,x)<\eps��d(z, . $||��(y*�#||.4 !zJ! (�$||||�'&px)>  0 put $q^-=a y%�(yYq^+=z z!a�i��I,~p$n%�$[q^-_�, q^+ ]�lesZ an $4 !]Now l���� _n=a �_n2� �M) $na ffic�ly la�=�||q^\pm-_n1_. ��&���R&�n �n-e� $6 �On%N$hms"�(.�R%;u! 6�n� j !RnI> +ea�]�(&�[.��Y�zU �]-���%�� �}\eta(�Q(�: 0� $$ �)I:�we�1��a�2�,arbitrarily l�WEsor V�. � Cd+coo�/8tes $(y_0,y_1,y4Y!).*Mg !b$(1,0,0�΁ A*y-�.8�%J��hf.�"� "�) $\va�_n^� $.  N ^a$)9 d ov)h"�0 E] $H=\{y_0�0��w�"P".p� $1*��) ex�? 8(0)=aaG! < Ascoli-Arzel\`a���.�$\{A \}_{%�mn}�(a pre-c� family��2eH%�U�.� 2�te�)&V,5Tc $H�<c�-?9]� $�2� +)�$. 6�# �ATH$�( H(K,a)=\{�� H |"� ( i5� (p),��\}� By LE~BJ� checkE�Ub=>g- �1�A,&�5&��}F�2:e�1]n^a|_{ U}FM�% �e22�$$b>a>\alphAl� �!�1e"� EH�"� �3!�a�.�ofy�W �%K� �( �O By �=|�X&#� R� 4A� na�^�ai!�����3-� �.�(� �4\qquad\textrm{�}�N��w�fteres!]- behaviouc�.s M,r��� �",.�B8�%2�).��$n&.!I$r s��|�n�\J"�/� "-a�� >*�*OT�xi�- =\xi�*N.�Pr.=n `]J�5�#� !v�-spac�^+� >0\}%#�$&Z na�)�=i�0t��6C�0�0+�C!8m _Uk� past&776K$p+F $H^+��||v||�~ U�� AHs gem4M)�$!.&�� perty" /P 67�� �"��$\{����2�;\����9d�1�)$=-\nabla_LE�!,FC�2�A]�� �equi-�hinu}3YK�8�F $|| �|^ 1%G��m�-�!�A=.�Y[�0q58�.F�6v05<��F� b9 F# �Aleas���*Q"�.\\ Fin�%Nsam�<gua�  P&� 6.5c "�2�Ae"<2] C�U#&$of��.r>K �.l�#-98$\Gamma$-invariO-(�s} �:" :͋ SO^+(2,/� � $crete, tor�9( free group�[#t!"�,� �X� �un@4 |AAW� �N9presen9�� f�0: �=~\ISO_0(�%����'&v�����$`( `)$=RDA�*P1F0�  %)4�e�4m"�G��pe�k $N:.�.��_!y$-a�-�:)& N(�gA )p)= # �!]�ar3t!�_( 4$ �=PIn���y�� �B� �\, +\,�5 i x_0�:$*MItau %  2�u>f%0{\it cocycle}� Z^1-�,�9)$;�Ychang�!�bae-% 0$, v G ,es7o� ary,���a well � d cl�)O!H} :�26;u#.�u��<(�$hyperbolic& F=E /I�$.ADn $X= X(M�, )=.N/=��2)�a (0 maximal glob�!{,$ � lete�,@># $F\s \mr$�"�1 proj�2sj � \to Xe�&� �[cO��'v]%ma9.�:,5�(��.`A scenIO'�oo%.o5eX!��d{CoJ��-���>�* �1�%b �c?Fuchs��Eha6e.N (ly studied,*� germ�� Mess'st ɘ M}. �3 re�!!�ew �i�siFg#A��/��% F {M�, ~+ XBG}(1))M�$X� �*g*  A which�^>I%$S]8 , $Soa��* k+f�4!�ge�=$g  2Iin: ^��r:�a�holonomyT�iE�ve �9) mage�Q :�M=)� (X)$ن�isF�>� Ba�� ��uniqu�IT]{"�*�1�S*�@, ��s+'#B::=.5J;.��!IR�� �*b�)as a <%7I�of"��l.�- , af�$nS s�Dved��wunB��O2����. *6�?�e1����B�C,� ]y!� otop(�R1,�Y:/� urb n6$@�%rized�( by: �A$skip (a)4 gqa�._g�=hAd $T_g�%+'�+8e Teichm\"ulleri�!W�B�$�  $^�� be &n�B> S�1�in�s�/uB�&�8 or � (bS"!+.�'u˥[s2�e9)$'s, �/conjugz��$.@ $.�%�8m�$!�is in_�(-�fic FU0. A coho�;y �U"��)^B\6-�.II fied�/the Aq"�+R0"�/). ./.I, F�pd1(m`-b! O  asympt�> st�of�B<}�_.~sense*C�s>0$,.<$s2�%!mea��� �?b�3 scal�!Y�/�-r�: =�!#Y�by��Nfa?($s^�R�@|�� v:m�ic& '^daLH & 8$\pi_1(S)\cong I��� each J�4 6$y (i)Va, �%&�"� U���(1/a)*k �>($s (G/%�!�Gromov)�!`ZW\� ;}� (i6�!�t6RD�)���� 8 �NC2N�>��s aE� reC?ree},� pE2�� k5q/�;=/�aX�N @ �@ hdual} n G ܡccg�Skora's335(�a��oa�f�v�)���%� nce,�, WU}e.g�'H Ot})�*� + x.}(somma} {\rm.1}E�Jdi�IA�)-wB+�Gc6� >�!� Q�lif�F�� � B6[ �3��9!�a top"LAob��� M> #d$�CchodAF�) b�c7is�6�}�.lso+%+c�B�A��{ .��i*82ME!�ach*�)iHIT= �Jt�9,�K$&N-!�eseJs"=M�D1CE !�F\�ٟ 5\How��\ fI4B<�/a�uA)[s}��k9]u"�-n� {Bo2}).4JM��)2�3cusp}A<S,� �n�,FE�7�=�ea, but�?M��� � rad3�~<$ phenomena)@e?:om4lirifor �"% ?*� z (. %%% L�/ Va�bles: (mode: latexLTeX-master: "2_3DWR",End: �\sY {WR:B J*� �Dge yq�hyp"%�64 4 $� \^&�L, z *DM,)6N&978, 2��%E�2�� }� $T&� � B�, remi�9�!\FP = &�B,Łw 1[1,�^ [)$,soHB�m�0ai$JE-s�ltoe� truc�Z17�1$-ET=4sm D=D �A(> 1)\&W�keK&� a= pull-backA�=� �7x �WR�-<dJK!T.C ;, ",Q ga%5o�3Br�!h$.n9t{6o(>1)$)! with!�� "�e�� �t�o$ 6� � heF]D7 .8$3$-manifold $M1e�ra/( a� � io&� .xO,!F just�!im1-��� D�ga dHEopB3�Cu. La�w��+�B!�.` 2�[Q�1�����wF&�DB ly+sA�a�$\bar{D}�value� $\W��${\mh}^3 = Ev �B S^2ya��e�S ^E� ]� e ! ! �1� it $U . So�S:VS��be regar� :Jc� Zve}.&�x.�turY u� a� I�AuA�4!�AkThurston#� i�6e�y�aW*( >�B-� F;�,%K$�{!�ll*�0!��� qi ���leA�.{�M J{Be�;�}�1��o~@����8:�� -� 3$ %��@l&�F.�%H1o�8�eߥ%!3a*A�Ito9���&�>��_b �}Ar1�N �|@ i�3% wa�H�G&� by�!)�intThu}.�hDljfe�ES in-MA��per 4Ep-M}ore�� � care' "�.a��5pDM�quake-�}%is more$  ?ly�*iS!�y % )�x-e�d}!6s.A=UA�a*� =(Q :A:n�in [ise� gi�RU��look m�9���>� :�� $i\mu�]I� a&�(hINbe:�Y��3r!�r.ni��)�arigorZp�3s.2� (Gm)r&n5=wY�!�eA2$, fE�{+�A!a�%�A�q�:�� TA��*�9B��:a�2 &e$ PSL(2,\mc<��lfiy��ties:B*U\($v(x,y)\Hy,z)=x,�,!hE� $x,�-in�pFUx)=Id� 5j1�˅yX�{s�Sa�-&�ŵ�_�unEu? ��G\� 2�1 %�a�+$-nLbourhoodd��s�>$[x,y]#! �. L_W�en!X"f5n})\=�B $Ie�'nN�YB�ia,��Ubof*",y .S$, takA �{Y@$3 s� b:�S.�3[%satisfyW!�N c�B� s 1.M26{=}$ &$\d  �i�Z)t (� b�� �� 2t &�s})���m�� sy �dp�!�$=�q"�lE�an&�Cg;U� mh^3�W $X_lA�sG\lGm�� %in�s�e�&tor�!!<� �CrRZ ar.H!M.0\exp(2\pi X_leO (%/ �"dDV-5 of \emph{f}gi)ll �')�M��D&&z �S�s � $l%:Q2�.a!e� theyv'!���#�V%Pi�tn pi1.py�H bothDO�$yJX�[ {)!YM letJD1!@l_s��">D�9 meetQ�R�aO aPv y�AO s. �a*By-�$ n $l_i� �� !/�(� "�&by�iaIn��]PfMnon-cyf )[m�:`E^a_1 X_1� 2 X_2 �As� s X_s) �Xa9x$!�� lLGu�*e)��M ion�replaz) a_1$�  /2$;?y2Ns$./!�y/s/�u���estimat� playa� r�UrolE�our r i MM��7A��&, 3.4.4 (Bunc�K�s�Fx&e eM� 1�(a�V4����R�(b`�(�&":N:!��(&<h��K��A4.�/%x�L�*�o�B%yM�Q�*&;Nu-.3 �q��<&S6K�+@ ine �����]P cu�<�b�W#7Co 2�a'�� d l t$m�"� "�MJ��B_A||:1- \��m X�)0leq C m d_\mh��%��!�Z*� �_0N��za�-2� ���!�in#*�h2 ��b2�0b: it�Y�52h $_M&�< L_W)� :�)B�6%��Pm��Ep�ed��%��e7�a�we�H� ;qq $(l,.G��"�9�>*/�)*p?�)�x�5Aop�!e ����U ߡ<�9_n,y_n.�IaX% w�� f2�Y����*�D a�to��Q ``xing''�Z�"� a�� "�Y-*�*���.�#.�4 precis�Q�A v�7.^U ?Lon"�-���: �} A.����H��"Y�}�!s0�Dy�{1M� �b�  *�" qu�r�>4ext26z (p,q. �;�Iq`G� [ $ $p,q2� 0I�$Td"�!�eA&F1� "HU� �ly�G�g�G�!�h��DQ.*"� [ H:!}�ZtH �O o�^ $N(K �j dia&�HK� !E !� =.�5 mulaL"Zs, M��G�on 2+( �� 7X��$�}claim ��G �isZ2��s&= aXi�l�M���lip�� $(E,d)Ņa"� m�Pe�, $b: E�g Ec)r C)$ b�&+!$E�"(b�� $C>0]om>||bŖ -1||< C dŤ�O3!"?e���$H$�!DG!U CI�I U��E6�&bE�$H6$9.NP�Al q$>%1W:H $$x,x',y,y'eE"1 �|| �',y')||=9b(x',x) $b(G)||. �JPXuH at, Rth`/ele�s $\al7,\beta,�-�)�C)=��1'%�<%S�>. - !�e�V� L+>V� �-g [||< 7 | $ ||(|�+a2�.�Q&u�T�t<$:UD� f we� � =C D5�6>�%�%�D �(D+1)C(A� x')+ @y'& Y�5$H= .C/"�@\mJ*j "�j>�I�$K$��1)Ce��Hu)�by.�2>���e�K � E�A K'= KV��v!`)%!�!h�� (A�e�%-||� $,Z X!� + C2� Ol,N(x'��]z�an:�>�*pSa�� cut�%4&-x y0"LM ��!gB� �� &�^ "�'xe8 $x'XESMAU�,(hd�At��tor� ��"h s��A$M[��!�w&�2 Z� lip"i:||!�9�)!�%�(A+CM)#5���x'�1�{8�Q�<>��Q�A}e�Bl�@"*in $K'ͰK!|� /$A, C, M �A�>%*q!�ayp� �y;%�1�y!��LY*�,�O&� $6gB= t ��bur�vq "�k.p�&X . .� } �AJ.�� remov�[�%���interio&�3�yE?6�SIv� �VUmi�%1 $\A46, 5:Ca&� �$�b.3>F=\{x+u|� l"�) GE�p'=�$q=q'2T� h� �:�-�K%�(p,p'�K.I',q o Aa'}(q',q �be��'s=93C&�" o(p, q�� p7- �d,%�� iZSR p&|($p'i�$q'*<v?�ww���"p�` h�&�D�,� �`��Jcon>b&��HlipH>�I���� �� ���t!f�4�'�)%%�Kq �oE�V�. J�=eeKI �li-����V E�F�&� �pin ɒ!��"� � of� � !��nB� *f\Nn���-J��9: 2�e�q&f.� �� i=�{ Yg"� .�fnde�A��9��(�c$ �b!��!�N��-�Yl*-o>NE�Gv�>i�_�"?c��2.�x���'�]N;�Z-� �Cc)*�A� 5p5�J4A�6���aB� �2�^2 u]$. }�-�"v?NV now n� 3a^wh��\�(��F d6�lp=�l+T(p)�.� u*t $r(1,pX_p)+%�Epuz > ��=!a�� E,q"� }�: mmed�p21,\��@�}�corq0N� > 6�h5=bbBM&(E�*�1!�&`S&hQq' Uu$)&�+J+K �S� >�,�22{!n:��� mini-2!MTEM���'%1�s">S0" �!T$p�j }?His1+2�a�\w/ i�hU0*��""|^%�.� E�A�+(A�-1I��$q=}qq qt -2= �- q)=p-q + �-�) + T(q) -hA�C �I�� � 2~ �0s5PBB`J ��o�@(!jp-i�UKa=� �b=�"U�  $O(<1/b|p_b-q|"+rp_b�b�4?��ā�*v�e6Gm(||p-q�$p-p_b||)=1.�-�|51�Wwe �1!)*q&Pc r||6�| x + C'. '|m%�|1�!-1&N"�*fe*52�3M ):��� C t/a?s/�N�f $\k"U,an $1+C'+CC'� B��vna�N�/�f#y{i�X 2�) e�Z�)$KOK#*I�i~� �n*�)$*06@m $s K�(&jG]R�_�a the �!E2�:S0_s�3k-co&rEAa gre�2t%�4=�b?�D$t "�LwJ�.� �RLX;Knp � "L � -/n$&G�$�2|F��3�1�!to �|�~Zo conv�K6s�%[Ua�B_n�M'�a�1�����}6@`6�end ��3mQ�5"sYql�L(�TM�� �.ZOa��2�N_n*? ;"�Sn�!6�r${\rm?}( 0 +]`^*(T�)E��*se- 2�a!2 T��� u1�d6Y`$���O��ZK��� !fa�V:�iyD&W� m�42�MG~;�\C)�m\ SdoM2�� e�}]�29�V��I� EM B&�`U� >B,0V#�o�%2�� ? (p_0���  _ {��0�%�)at�!q)*�.P!an� $q_57A�X *�.�w#�Pq_n��[ot�K�!RSQa�k�a�� ==Kp_0t#_nU�SB�P.e~3.11.5�F\(2�)!i&�B_nW W�n� $B z -��,P �H&yI�5�,�x!\B-�� M�� lN/�A0��> &��"� �`a�qua&h &�.!.�5clude�I]:�2���:t�� �$=!6v���.�($�U.�lC�Ru$[!�pQg"q� e*�*"R5Ey�\�e���T����ngiI&iA��$X.:�&�A����$e�'2 x $c�a=!1, tp+قEpIjdc��1xFd6�� �a�i&zI��" ���it*��*�$m_)�?m� m_n{e 0^1|>{�Bm� By Re}� b!���$|� p� |=� $.1 . !gU�E�t)+*XtIXt�*so deri�Al��!!\3 p-q=]--\E�W�{ p-q}!��( IP{ &C�rc A�h t24*�  t��| M}k� m�Cv � R� 0E0�� $L^2(v�;\�D��4i .4p-��J6. j� fIr>� !�.�-��N�AU5:6 �m�?'n2w� "  $"}>5  J2�2�A< �f��)f||^2\d tT�h 0^1 2$ #)�]J�by�����@$U��a[:4han1f Q ~�^>!Q�)J )�N(tT��\EE& � �}=\(�  )�}+MZt�ot "|^2�B�a�rH �fund-�S�E�EH.j llF "�uN�%a:o2�tegra�%� E�[):.�Z\  � ID�{� Wick Rotf!�>5 "�o�%tr�C!�x�2� ݔ�}��CV�C�YIe9;?pd�Ajq5�is�8|SB&/;"D(:�/_C �E �6{��~2�Ylmes�"W_ifts $B�E�7b  d�Q�9�,� )$x_� �GZ��3 ( i�51ed��to���;kImK �}.F�3 $\tilde�62�eX F=F�= ni xTB(x_0,x)�$��3 ��I� notJ~�F$ �(=IR� )�P post�e $o�#,� ,�=�)= �a 2Ef!.��<tZ$F.�.�5Cs:�c��op��Ky�*�<`�V: Rough2Apee<�we%�U4t�8f_ �B�.h ��O�CEn3�t@ak 0�n;:s Q�EMm�H�P. :>U���o�  ���Ct EW$ ���%�"g&�� bundK8s too.9 �a&�� &���p�Nd2 ��E<vel&eMR:� ��#aZ��*al �.�$!?(j0�X�(�[� Y � U�G�`"�� �L� p�3$ st4�ng� F!)� ithV�ed�b�ρ&$w�b��;p)_*(v : ?���6qway"@]DR4c_p(\arctgh(1/p ))=  _{ �ԅft&\p�$(\frac{1}{2m6)�iAN ]Q�t&߄*/WR:Um��DA��C-L*�bBVJ&%!� �(J5M!�2.�d.)Ji2j&J�6��J�I�&�Wr"�S& J(�12� x6q����.��[): "��0 = 9� ^2-1�h, \jg �0='(()^2+. W]�%�1�6�Be���� !:�Q*7�)�t8heuristic motive~s�5;Nw�r�!." zb;$a�3 $@*��$X�8%G8��&� ��\:!�n� .U�@:K��)t1�!�m� ��N~2�*\s�<to$p> vex �N onent, sa�Ee�3&�Օ�m�+!Jc�odelta$�\!"'%�6Vsubme�b&�">� $\Ee�T)�r,,�u foli%�) Ee� � map a�s�BF\Er�ar�3:}Qb.3���+Q:jUu��F֑�s�#%`(G� �!`>7D����L5�D%%Hdi�XA aUor W�i")�`�Q.�^B%.G= 2g$)� (D(x�# b�r8T!�� mean���6z#�t $f:\mr��arrޚ*r6n=f(^ )$.}�.�% �DM[!a �a��@jr� ed'r�@�#7�("� v@&� �of width2��<%P&js %��9WR"�\ �$�~�/t)m1%Hwe �@T&ne d�e`E} �}"�a"�q2|E�s}.J�.CA�(I )�$*8b�\ch G?-F\tgh t� ��� � c�&�;a <�bre re�S%�a uif�E��*a=�bO;zJ�Z�Z 5�w2�%�}� t=1/� �7I�>$t>�0O3%?�f�ZisN�n�^���5K1t1}{(t�S .�]�($Fq* mputAv�rthU�` R �.�!�& 2O �!�Kϣ�",!U�2�l%(��i�D s a �&F1di��)�od�a<$TA�q�Q $D_*X=-��k��aE�X�a�e&�1o F=g(.I, c)=X(D=Ÿ))=s dv � ))[X]=-"��}\d T(X)-�� !�1�nd� *� �}P�%�=t�| alyz!Z0progressively�N�l _ed ��<- �Taq�Dv���F�1HO!1��i� &,ra�2�Qseg ;�en|)_})%�u jj!�a4{p��E&�I9�� U�of��;X ��j�KA2�QYs��WlE�u�c|�( approxCF�xe2��jJ13"ASll! t .� >?!0"�92�-* $I=[0, _0v_0p�� $v>��s�A%jp��$0<@ <\pi�/l_0#M&;b5Ź�:5r�,&+�69:���Uu ��Ky&{0=(l_��We- by $P_\pm�mS X����eE����x aI3�!*out=e7 $P_-� &>9H]E�!� _0 )_02qL`a6 .�c uto� �T suit8Z�a&��2HyA�)9!�R �� $D!S e�2,f�be�gorecognrd��W�J�tv\~. \�d��{Co_Bb�"� fi��[h!"ce-� n��1geo-z��"�Z�(Zde���Als{�� �T2� _0�  &n.r��$As usual, �Tu�B�,�ZQ�A"ef���� T$%���*�r*ݟ��e �v"_�Ia��);W�i�)� ree piecet@^-, +,\Vv�am� x ��8� arra � ?-=rC$0)ޏ$P_-)\\ \Vv�� v_)l_0)�+-��2+P_+Z�� �D(��-3� K(a) �- Vv%�!~&�o+Xf 6?�IYsE�0"" [GŖ9�9, ^x&�71�$)i�� &f �� $P^+& 8P^-ֈ�`�&'t��mJ% b $a�d Instea<7e�ia?Dz*�!��� l (9��$,l_0\ni(t, y)Ga y+t!�)Z!�8 wo.��f4�  $})J�?� �_\h"r}��<���]� y,��aV�(ony~ le 2�`scZ2M53�uAFM,f ^� � \\ ' :� �(��Im�]�d�A�"��0e{-��nd!�$d��,ti2u�A cI� F�=�$z�����O�O_wD� 4� M $N(O_a)=E. GE�$J�t�;SlquJ�<�dZ6� (x,l^d_ \p+���:w��na.Q($T,\zeta, u� ��J!�b�!&J��$ : G>:�j�aF�y(ҪepsZ�d_{1}� )/ \\ u) '(x)) �, O2/ ��� � h$"�;P$ �] $-1$�5����Z o$!�MP�� �$)%i�$NxL<. �af�$2�,of MinkowskiW f�� =(0,0,TL%�z� "���!�pa6�� a2TUu�2� (T,uI!)��\�\{:�$l} T(\ch u%�,\ \sh2B u\sh% ) & "�@ if } <0\\VD p g AP:GV< \\i���*/T]\\V�N' _VF� & 2.�"K>h�J��� .�I���> [=-�Ę *GX�?j`0 . W'� �  fA+J�8ll} f_1=X & f_2'\q(\,} !0} & f_3j' u�y�A�@matrix $(h_0)_{ijߛ�� .�m�K$h��is �8gonX a-8:L 11}=-1$, 22}�d2$,�( s33}= ^�6T^2\cR�B�etJ�T^2]>�etN�ju'B^en]fQ ��i adop#�act{�!: h_0(�A u)=�?6 -(f^B0+T^2((f^2)^2+9_$(f^3)^2) &6669R�6v +!�xn �oJKn@~6}�(EU')�nI�U.:�:] �sa�H&Ky*�} Aqi�(" a�.�dL��Xs�r\EB�)"�+ �)�Y%#nd��b�d a�b� w �" $P=P_-\��CV�E X_0) � eGF 8 �&ex�4i�,�"�WEe� �!;@H���7nR@ RBJ�H&(� v26( _0$.�&�T6�. !� �.g)"�4� "1:� $P(�5mM {1,1��u"ߺ�d�M��.^� &�6&�, �N�hyp��)�A>N�SemQK)�   ��Xr:pida+ P��* ��I�&�;"�BhMr'Iv $F^-�Fv����.�.�A� ��6�u*q�f;+A��Ind�ax�!_Q_0 e,�ahi�I4E2ir � �r�*smoE^8 g�Qary�hJ �a� ��.&�7 �-F^-- 18"C� $3$ dihed�� anglt $P^{ �/ �e��C�'e� em, >_0 5&m�#Pii thir�/�$G� uR!�a�u5coi��w� %qj ij%l$,M+$j:e� �`2�L!�n� $��~��K����2�-��I�; a<�] aL[�11$-qfmx�T.�s)I�^+:oa�!R� �� *V 2�!� ?���;T�&+!_w�n b0e h4jk&,�!E.� . ?�4- (� q a�.t�a��'V!1��_ �. J*�]\QB l_0+V%a6�2ok�B�Z"B.��.>}t) ��Q6Ov�A��=���z�Za^! U �$6Z.�\NE\sAGE�&4)�aA�A*�6^ !$=fV]5 �let`���%�N8^J<49�be�y9��yy7.1 �C.l�Mz&c��b�z�Y (2 O� z_a$� eriz��h#3oW�:U)L.-te�M�!A^s�z��aW.��%�R#�b��STA�9� n��.���S�*�  , ,s$�ل>yզ��! Y L'�V�e�bMc�j�t���(x� l_)a+�"e�\ 5=�d.-�z.>B�J!�^*%�)�eWM�a�$2�2&SP^(i(�!oid�vlDAb3$Ra�~�Ez�\!�<ic� 6� $* ��A� r�-�2':'b�-q!'�� r?M6'%F 1 �\ +�n}+?%�E^)� Fvw!| ))AZ �iZ�}�w6:=d�-Z*8 �� �' ta'=\"�Y��#Y2G"I&%�@�x*/!r�$e_1=Y & e_r�et� e_n� �'6 �8�tm��m ritt�� s��� g�ȍ�s�(e)((e.!�e� R  | +��^>~u�']#]r$�f (! ')�j*����n\ V�z�)�7.\�~ map}.�\� B_0j i�Y�'*�vA�W!� $. AZq Lu��f ODX(*�,(�VetywV}<�� �^7_[r�,a:)}(:!m2�F 0*�.=S�@��1m_>01[ bv� � r8Zk *.9pre��(eK9�(,�P�0� y��p6KUu&�9��m a �9 6�|$U�~ �%^�y"��E�.�x*i) $\sп� m�."Uon"�|\�8U�(U. R  Q�;l$! ser�)�B�'sR0�t��� �$>�Z *�(p)��]� !;�!= U$ } "��b'=tio"�q1^ �\circ "̇C>D_0 ��H�;6|F(A*�3��6[Op�z�bWaA 6�*��x�pep�mA`9�k�| ilonzC!����� �Sx=�H�A:��?C�o�"��"��*�8; �an�cos��>}� �Y[A ^&_ze�_0��$zD0Y&�2��c lde�UU�.B%�=)� ` -��$"�r$Qs&��r*^}��v��2�IW�@�O)/�@�I�!:�< D(\xi��!�Bq�6 pv{s 2�2��a $\xi�U&]{�3*��a�%�Qj( �mb�/ [r_-,r_+]�,�j;1I$K�X�1,val $[s_-, sJ:*�^cM��*$t]�� �5� �AA-��0I%W�q ��a UIs$r(q)=s_� @Mi� �1h�?&�.I��g�s��C]=eE��j0l_0$;��2Y�-�y[6�:U!��S:$q)� M�&�r]M�F�eo.* U�k)h.�>AW"b7�N3k9out los��N�J�96A=r�%!m��a F�a�p�at&�E��Q����VS!���AU$W � E��pa/9per SA�of >����[&YEa��GrgQe�"�� In2�CJ�_A4pE4A�#4is zwaB? �3pR3T w'G��l�} "Ce��? 7�-�2����1'j ab�6A.��K�!���"!V�9%�� . Cly�_Qa�#� �7(aP#�AK#:s&��:��&�w<��70?+?�80p�v*�aV�v�'wZ.�~F�ZWR8t �1�ed"n2��>!\Dd�G U�2i#$14w�)^.� * !� Dd$ m��z��=U"kJ}q�. %:[ Omeg{%B{%ca�so � )]�%i%"��$ Gzx!\mr�� ��M Ml\Ll(F`Kq2*Q F)�;�Z�BA��?on�aJ!J2 $a,b�J �!��B�LBPY�R65;)1��%CD A \b=��vIF= �m� Oion��8<��<"��$��.� _WA4� �MC�6'( '>* �G�=/�:S _WUP�)e��M$W�$IJ-����HU_0(B_{2�}(z_0)�.)�o*g7$C'.��9�b��+?��kh�mo8GOetOo�#J�!A:f�\���\��W\}�"\{5I}64G�. >bZ� Oj.�q�X�A�B��, M �> � !�F��u &y":f VkBBT(=27(C'')^2C^b&�� A.f�?��veY6o��>2|�KAHt����. T25[K.� %'aZf.a&,`of�#J%@n8ɼ{Y�� �F����"�?[N� �X(p�h n�-$D��_n}� n*�\u�}&`_R�ob�z͐��� �:y1 �|�&��;TO�E=&��� a �!E6�n���*��. $9�AasB��`C}4�"�a=.CS�&5c �'�A.�b VR�:9q$ �+EQ���&W"�2j�Bb!sBjOia!<.�WR�)�Gco"Z�Z�����cvd<�P�G{[r��$& �}E8 !��$.їari�> by per'oD*� C���D6�)�us �!�".y� -�-"�) � as.">,5��H"�>c� *\Z\�(,�>8QM�@CF summa&V)ma��eat���A-�E� Rwu+m+�! pp��+ devo�>p�p itǥ�A�F� �E� (1)A��f=Ra�R=5 �0\�enE���R5��)8$YW ��l"�[ * D_B/ @$�#9}p,�k�\�VG|_p,q) VG�nB\l �.�\+�d} �]_n) *�8�& ��� � }�y�)ZM$]d%��".h * *ST4=Dbn��_n)=qMPcopEt�Q��H5<�y call?ARYrm.�� ary} $a�tial_h?:X. 2 �(2I� deve* ���Sw�2tp 2�j?�N�.l�aQ�������$�(���o@a� Up�B12Xmap.S6��(3) Each:82�eB����!��-U-Wr/l&�F"v.E% ����u�"�$\D*�R6N Z�* ��erse WR�3M\�!�6�& s:4)�9�O��&��"��sQ�, .�c!�%�2�[0,m���& YB u( ��"�m� col�_��e�=R�����B�Jicity,!�wA�]�2 2TA�MY��J!X5�2 ��.�F� "J"��<auxili 6_�I�Q^Q� E�N:�G a�7%#$ !�2e\-��Ge(H~R p(t)� >n �fA�i ! o &�!?%�:au�PEK"�6* |ESre"})2W (�b�p� 2RsBA�&gtI�y��a�6@�)?.�*���dPK�&�=x�*st)��Q�1��a) �d(tYsT 5>�d b(ZeAb�8R N*N4�KN$=�at�^� sign�A�2T$)� ס�bv��" (��D/ot )= ��^2}{( -k?}+ !4 (t)�P9c-@ %Ic!))d m�� "l9c|�J���]W �c n!�$c�(tn_2w~ J%1 �! -1�e{H 81 I� �(2�)e��m�2�.�� n�a Cauch��quey�:(Ue��i6�&Y�2n� �&: � ora�( �l�J Y ��`$�H���6U��c�/�a��^=\�)gh #1ZU>QQ�e��� eq&�eeatO]O�c!G2|�'�o�ha�i� 5w�V�i ��NNeEif 1�!� )�9W6�I���o�`)!%�)$a:Is�n t�WarQR� $a>1�6��5���=��6�@Y9[q�`($qirun�t"�h%�Bjs�q"�!WM�% >0j��a� s�)if�#k�1n e*3* N%I�� xm)�-4! 9$�=a!� v!�>� �a�u!$ֵ����:�0 = �a>0 6$p�7) !��� o~� t�l� 'aN:/ p/9�  i4n p_a=+a �WeN��^V�7~�qBo}�. 7.1Z�v�{.2cm}\\9� *�HJ�M��7)>2+a.� %Dn% BP�:2P��� HcQ��d9�N,$$ !�2$MY�0 ur\in�K�c.K!+|��a} �M p_a,q_a)-�!�,R!M����h � $a>M�^6� �"�:W&O |I.{!s>� K-�** ᨱ����3_a�c\sqrt{a�}d_ �Ev�g?�5�et%�A-��W�"Lm�$ %�5�3%fi�\M}�0!"!�n�|�fr)lѱ4for every $p,q�@$ such that $N(p),N(q)\in K$. Let us set $a_n=T(q_n)$ and fix $N$.@�Ia_n>M$ if $n>N$. Now for $n,m>N$ we have \[ \delta (q_n,q_m)\leq\delta((_{a_n})+ ,2\ . \]h�the first term of this sum is less than $\eps+d_\mh(N��,_m))$ wherea) e laK.?g length c0e arc $c(t)=r�p)+(ta_n+(1-t)a_m)q_m$. Since? ? of $c_m$6`,$\arctgh(1/M�e get-��0�a Cauchy sequence. \cvd \smallskip \emph{Proof�Dstatements (1) (2)%��of Theorem~\ref{hyperbolic:compl:teo}:} From Lemma~V( lem}1� �!��@map $N:M_\lambda\rightarrow\mh^2$ extends to a map on $\overline :!F Moreover j�2 �implie!�at �E�$restricteds$$\partial i=J}-%�injectiv!yWe wantM prov �it!�dan isometry. Take $x,y\in �and $p,qascu� e�=x$ *N(q)=y! (Paths $(p_aa&>1} #(q0converge as $.|+\infty$�oiA$q_ �of J'�5�m�%� .�(V, Q)=\lim_{J�}u�a,�}�$:< _b -)we know � 5 % SY� d� x,y)�So= dedue�at?N��� @ AO�  other h!Esa� $NE58$1$-Lipschitzia.-Dinequality holds. a�2�W�ke going �oMpu� (3)a�A�ti�8. In fact we h�~$begin{cor}a� functieuD�� �0\mathrm C^1$.9�[follow�formula �1�E (p)=��T(p))��$For every Ev $p:�aunique "realizn$ [$ o);boundaryaie'IB0geodesic join<pE� 'is paraa�ized by6 path � c:[�,m)L)\ni t\mapsto r(p)+t�02�� \end)],\Dim If $p(t��2X-q it q> seenI�iCg�6(\dot H, )\geq @T(t))^2/(T^2-1)^2�A�! 6[� only $Qr��0)A N . Thusaobtain1�(p�:�$. The%I $c$ has �Q�� ��z��!m)$ soa= B_ �rg!E�a9�Y0�dista�zQ=�a)g �r:��p \Y,ae)�$F�$ Finallyf�sh����.�is ��,nifold with U�Jw=�:,homeomorphic)L�O \times [0U��� Noti��͙sufficieɸ�!4� e�- >0$ ��(i� \leq\ )�.� t!�� [0,*]�,Unfortunateli�2E��la�xq� (N(x), �(x)a�yxaworksyL_W%�empty. O�� wise-/not��"q idea!|avoidq probleu )L�,. ��a�� $z_02<i{consider<\surface \[ \mh(z_0)=\{x>fut(r)|\E{x- } = -T! ^2\}��I�$ spacelikebE�\Uu�n>1)$ (i�9$}!" con�ed � .6a)$Y= $a< �($). Denote�j$v$� Gauss!�!, �p��t s he ��c�-���g 'multi ��a�or $1/ �)ɱ},an embeddingM�vaa_:li]A�.(p,t)Q� p+tv�in21)Atg �Me�z� �tur-��. Clear��we cu e fJ- from $*@ we���[ .�A�$\mr^�2 (0,+1e���in orE�f� NA2�>\[0,1]& 6v. e*Rproposi�g. �}\labelJ� op:!�map $-�FZ )� f�]-�J�5ǡ�]1H on a neighbourhoodA�j�inZN� E+6�(pUv=Ac  p)q i恱har� ��a� da al family�2� s of��v���E=\B+ $A)R, is given by � V(v_0;��,a�ʙA|P ��v_0d .\textrm{�: }T(x)�(a\}\cup \{vat�e|� v6C}10�aP laimEՅ�any comp) $H\subset�$, $Kn$,� $�,a�,,re exists $M!�l1 p_0 + t )_6Ad�� $p%� H$, -� K�.$t%0M$.\\ BeforeaBv� � �l�"��"� tens � ��$ defi��L&f \Aum�at+T(0� �!�0$ runs!�!�ibK b A|i'md at does�� depend�Wa �A�2�� >t+m!?F by deriuidentit���=!++! !,a{�<сA ��r� eq1}�� v_0=S ^ ch+ v��8j By take he scalarAdu�ith� � � �^\E{v_0}{cN}=\E r+TN>0�PS� $\ch(�J_0,�)=-]�}$,a��TEQ �"&>>!]is decfing]2 6&$L2m�JE�C L2u �. ./, $t>0A�I��� i��Y�:|Sm�mxAǵ� e_{S{ b,E�HY�K}0We can choose�d� e eS�� q>� )lEC=\sqrt{!�At-Ao} }\� 6$q !q}� By u!�� *��/s easy� find%)nZt $M$ ( i�s Z on $1K$)9>�� t + M� T�x!+$be written�Ba �oa way: N$\int_0^{t}" s)-1� �ds mMik] F�b��%~(V�r a�)GK � \ch\>�:0�a�a be�T>c:�� meas �se1> I_q=\{s| E�>\}_2�$M/$.�$T�$concave, $ P�@nterval (if non-e\$.[�k  nd��"0�a.VaPE �]��*7!R��ved � $t>\max( 4, a,�}A)���E1+! Q���{u�d�I* !AludN�ofQa+&r &� {roper�p imagedR@ d Ny ~ove&&��geA0�s�� will�.f v��� � 2�$a�� $2� .�� ��ICu]�) -on levelm%�-2�F��I($r(2��!�]x.� � . In  ticu�c6�se!�ae��'S��s $c,dɔ �i%�t�p��2���I� \E{p"� =-  ^2+c+dQ�6;$a!�&Oly larg��� C>+thepsp-<- �r�_{q_0})$E4$aVe>�21� q_n=V (p_x � �s to ��C4 ej0 � & r �y va )=r_+TNa�$�iA � ^A2AcI�$Y_n���by argu8as abweV=A36K� Aq_nU ��-T�Iq_n]Hp�0�Zu CN t_n+j � 9-t_n>�i _n}(r%M)}{)z}:t�-xR/� _n-1�~* "| "� �)�*%��>0$ �0P���!�Kremark}\�&a(remU�no�� {\itfB�#� 6��io*�� " H (see~\cite{Ku, Ap}%�details)Egeneral,� $D:\tilde Mrj���1 f ``*�0type'' on $M$"i?a�� open r�" ball}�Q � M$AHbe a �&� ��&�AX F %�it=a.�sm onŦ�Z}o . On�"6 a /"�!� �ixia�(E�respecP'A�i )!�A�`ifA� clo"$��$��AM"f 2u&�$, $D(:<F9.�{D� )}$.� $\L�(&�{ %-N`�"�1'Ge-�� � �u�nvex c�%� {�:;]bm�3�� w �m�!ͩ�qE� M��� �%m-�A��_p( � G�_p'{��ew$\{ <'_p\}$ furnishesA�2/������!l' !sets. g ll icaV�� e> A�a.0{1,])-B$he$�yS$h��J�� H!�)_p!�}�+� ��I�,� 31���� just as�*R�+WR:��^�D plic�eomputŚ �:o(1>gec2*1:Za�$Ղ�we�+ed"�1&us�t�B}:g F�2g��s�c�+�)����d%appro���9� L%]�-&{���@� BUb�vgar� k.{ !�>M"�?�o�d� �7horiz�#$l plane $H*$_0=0\��& -�2� E�"f� $K$+� _{ ._n}"��J�on $H(K�|N( C�%xGKa���m�%�top� l by �p"�)-�eIUu.�� .} \sigma2#x)=�:,x�w"C#�)� d.,:� V�a�sam�+gu�_  �~ � q��i  $2w>rdYV ��%Q� =Q�A kjAE pull-back%Tk.�$t+ [,$ G B&��� e2V *2 "16�:(H,gb*�-*e�F�&{,� �*+s 9� �=%��B Ixh ��!�"]!'secondA���.@ ��di/ult. Co*�' diskyd_0)�Sv�;\�� ial\#2}2%a�'�infiniY' �7 %? half-� �) �ivh^3!�.�A") 0d_0=��2L  (a "o��^,aFendow D�its.�. ic).�"  $i��%^22}%7 �versea���# is no��%!ӹ�;F�����expresse��ɝ<*v .�=�B(p_0,p) �1� fl U�$2*I1circle@d_p6j(E$w!�.� �%conne�2 componenE�9^{-1}O���$pa !��"iSi%��a5�pA�eF� $g_{!}"nw �$ ��Z�m9_^*(>$)(q)=\eta "~(q���5��͞�-s usu�"h.�Is��2��$_ >"��#&� �"�!Z�eq" \logXC{[L{6)]�2�q!�q6*b�q:�aq=o]y�&iffer�I/ qIc $q ���)�.figure"�ce<#} \input�-�4.pstex_t} \capi{{�;�(lef"�3 hown��+ s> i, t�ct�  each�g|E�� pifGa��f3^�3!�2verifi;4  b5 2}) �)�8}.�%� fig}�.5��12 ]Vov#��wlemma� � e estimat� need"00��By *;$l=;�oQ" � 0$ towarda�F=�a��ord8�:@x. x+\s1 y, -x+9F y)\O]U�� E�2� l�� c�$� $ ar0th"� ��6>2E wE<��y/x>\ta-�!a�#nC B_!�*� ]Q$ \frac{1}{.�28}(\d x^2+\d y^2Ex��U"rR�u9V2~ $u=x/O?R*cl� }'yula& ���( $x/y=\sh d]�A=A~Uځp� A��(vd � � "Q b!�>casALa��Za*� &�i6� =� . m0post-| �1e!�lB� .�mV�O����� bas�=s�!d� ia e���'�,.!a��a�ca���p�"� p��$qju ��"�4*�' �*�!of� 62 % ��e]" vex�7=o 2  ��s b leaf7 most o�C\\.E� $l_i!�*4�nV,�0�VE�md_i=B_io0� In f2�"I;� i8 9 �deI2 G��VG &K. a3��si >A:�qz��nothing*IAJ$�< $X^*_{i+<iJ^ alono1�G#  $l 4^*% k ns "Z� eq2t%�t�)r�� [ $0:�-�q'�,c$ ly���C}BaeV�6& to�&u�u�" !?*CBtm;&�q')$ ��!{2 ^ 2}�D�V#� !ԥ�t�Ǧ� 3} \�\{4array}{l!�!�0Q�E'��3}\\� \;�2u}alt,i- lE}9E*�} +1!&� �� �6} �\j .>+U�e5�io��� �]6,�V/,! %��6��!��aEU;^*� � end-E�s� outE9W�B?�4se#'"�/should�;),0u, E $i__0:a$9JUyw|$ Fig.�"').S�.$g���~�*| mx%� !.W� �u� �.E&�%.Dx*� .� � g_{i}&&(q)}_i+1:�*L eta_i^T=�  a_i-u_i�  !�Y"$u��: �͗ ͗���� �Ʌ oD=\prod_{i=0}^{n-1}W�� -�=\sum ��)+1�ta��nN$3�(a_i)<-�2/2��:= >d_i�seJg"�5,�>v & + �.:i�N2�)�*� �b� ���"{3a&�=ofُB� mkE7res�� "acor} Ev�Ij*aG"ly �)k2v"ar�a naturRmplex� &,�io� �ma'- *2Ft"E 7reF;=q� vor $t^�/aH,�-2"(1/t)&!�>6ew -+ ���C<{$\Gamma$-invari,N�  -(ions} Assumi�%w*� 2� A�a��=!�aa)$crete grouC w�!� �A;>lifi �A m8* ��Ν�"�EF�H/ o� T�Df; �,�� |)Ep-M}v)ermin-� behaviour�� cocyc%B&�un�D}Q%b ,:�U�9F* %%15G){9b&D1�EL �1�Cz��_?sN�[arrow2cZ�1a2:,�6lh(\gA| x, y)=   B ����Ab($ `CIRm�!X�N6 i�6fix a.$x�B�\ N A�i1�be���"r/-'w%H3 Ir! 3hQ% �)== x?-^D� � &��V`R]42� $y:)$� Zey(�Ksm*�L�@�!io��� W;5F r$-equiM�GF�M &�3:� ho�)�f1KF�\ISO_0(�>%.A 2.� $H.��A�&~Bis .+� Yi�% N(S1�_PM�6s!6�>���*�>4 � \!jy=Bip,B� EU<��?  eV�>h�7!, s t"� Jt)=U^�0p)"'In. 1�l%maa�n%�.�0*�3.�Ŭ�>n & 6/= ����� leE�l�$a��!�&�J�` :46 $F�&:06 4A~JF�� 0*�"�#Q�F$!^Z� 5 .0%U�+.�4 60&�](1).(*@�� 1A5$F�D:CFx,�>")aX flowl grad�!�B�E�'` %�rv�a)J���'Iu5 �8Teichm\"uller-l|Npa�" * vH'� �FP cl M an��`_�"` Y`G�w v�2 E Fk")�8CoA�|�.� ase}�l!<�&A�c<%F+rel�z���ion F"f:�*�b�VeZ�" SJ6genf:g�:� �I�w*'��No� >�fU�q�au{ p8=�>� 1,m�n5z?�U�+ (wez  $S=F� 2��5��l!��H3gra� }a!$Q"� �&V � +4McM,Sc};I��9I5�.�R+*��>$gr"k+/a}(F)$;�Yw,to[~PZOj3�#analyticiN}i( $\Tt_g$. %� S��e�h?n}|� k �$T. LQi� <�=q+JU �=Nl u,*� =�or XnmT�2d(re!S(.$). !D Local Variables: mode: a�xLTeX-master: "2_3DWR"$End: hz,"abs~K} \noin�J ``Endsa��r$3$-mVs�s�rtI�"�2 Wick"s},�� they We eff�a�� rtheir � glo�3y.���� ���� urva .'' q'�6+'onsistN#o� eyWR-�%��Zy�6$3D gravity�,!�-�%zOn�iz%�7guess�|many geo��WG ,WW�$\Mm\Ll(e�)$-�are solu���p�Lo$�[3D�7� encoH-�7�tZY}s�d+,�sib�S.5{N�0"�, tor�;-fA�sub:x��V R"t 5\s whichiA�:�&�$5�,a�well �2۵e} 6d !]���ures, T Bdirs,}���>�re"�1Y�B�A�8 A -un�O sal}HcaEY537 �J�J��E��>.�Wget�u�:gh�s�.� mechan9by stud�rayE-jYemaC=ng "���:ix;ase042�G� ``deriva�s''_!L"�>�k�ach�J/ 8VtamestB`&�&�� agains�mU1 gl one,n�1$� �hof com$area, but EJ"+ �ūz-� brokHT$-syma�ye; AdS j_Ao d)Xearthqum fail�'� is help .�"�&%Hm�\l�of��m��&Wh� hiev�M. li.%Kory����< Keywords:.>.�,�? , do�of I�9,6��:�Q,��"x&*",n,=+.p8v�${0.8 cm} \��ion{IntruPio"Q� ����%L�� or R Yian2qe�a� ��t2�E@e sig� T�6JB+)e ).�[E�stipu���al�@ͫ��y&�>*W�%��� also ;-@tc�# d"� p/*]�2AjAx� worldie��les, �� �,�ceno-ed IPularit�'G A ic. A typN/exa�A��`�z!���}1E=�n cone�Aus���[ed linkAD�O?g reflf>he ``mas�Y �㥛 the =s�we)IrP r��M�=.%��ausal �?P e.g.U 4 {BG}(2)). Hown��)� t pa,Nw�C �$ine oursel1$ͯ�F �.2=dSa� imes$itud�+b�X�6� se�" �.��``�$ors'', acc�(g�)�e  (=5or " )2Y�2VV-*��reh�Z�G�i``y��!*E� sugg��to!6oi&= a9t,7body,��re�� s\ually 6 Mat �io�Lh.�,is�!��lea� W%s:2�2 �Y$ znyE� t;a'c ame}^1. *�,Y'�% Rb�ed!�remZ�s��, W@M�2l�ub�\i�a��ck-#��W(��Y(Cc� X�Ely:*.u%� tanto.��u act.A$hy�#,$BJa%�i� "�<9,�MW, say $W�[] }"�&$W.�d$an ``end'')A���`�+!�n � )`" �� �  s�at� a�e�k `` e''%��Rly  B an b%  �\a�f .�v�� V� \med�l� A�2ql G?!�g�2�, toge�)�!o/of�E{BBo}"~ �iz��is.$a at leasta�n%is)N6}, k; acG ntal�mw E*e inA�/:ible}!D�9o, ?�v� �mbl�7r�E��li��a[Ŋ�$Y$��il�#Ds� p�is� .V%%(�� ��"�) � �+�I��6 self. Aa�e��. �jout8 X`ew�-�  fe�I` }� J3 ћ�,at�B�#a�Y��U  do���!rbitrΡ*.pC� J���#  D= (k!"�E�*�.Zs{L WR. �A�se� B^!�sU�}A�A�2�fa�aso �� quan�7v fiellfe� s} QHFT-3is,0< ghly spea�,�"` d .� reA�A���=U� ECcategor-b)�xX eaPsg(a $(2+1)$-bsK 8#.�>��n* 6FP ppe� C)$-<" bundles!���ev�1c; � �La� perti�,to.��!�q�e�T�A=q6��Fgda%al � E �!Fi41;. Our k�WRz arises&pur�3�X? f` �full ``"�0''��2u6� Yusu�A�m�the I�G.2 RModel^F��6y} A n[jm�R&� ;�_�����is � K$e�F(�M)�^mls}e� ��%m� �{�&ch`�=ly no�M��($\kappa�<�# \pm 1�#I!�"�+� abAYf �) �R3$, s�Qan�E�5! +fuU*EL.{ isotropic1Sif�WA�},� spher   Y�},�V�lyn1�(i`;�5qy)�� l ob�!a Th]M's0i�program1pdo-Pe�e>�ms!� ya��Zdecada��Z&= & �Q���8a�.L%(Minkowski},  de S�/r=;anti de &�>JWe shKJ&�)mH $� I:A4�;/3 adopA�e E�c�Kn� techn�FA($(\X,\Gg)$-�Ѥ� i.��C(>m"A��atlas}��&c{Thu}A�${Chapter B���PiYm�D"OWT2��i�$\Xf�.�E� �A�Gg�!�g}&ofA�!�E(�po �xr�  g7ń)$2�Y char�2�Tl`to O�/S \X� K �g�� =*�h�: �P���� "*CŮ"� ! "�x$�1!Psome T  $gQ$!.E��y.�1;=a, aE*"\��(-inu%4��#z� �,pairs $(d,h)( �$$ d: \wide�M{M} \to !�>1Eu��map} M%�!�N �)<ng%bM��, h: \pi_1(M)YMa��holonom�%�n)�j [.U3$M$&%e�Qa*)$d(�M���TtS }��a�Py>1z�#&b��&�L$ dW# 3p= h )(d5Ra�� �&��al(�%�M�Z�!.�!�n� <$%A,X$,A�:�!�%%�l�iAxtryS��Ou%; V�7M�s2��5� 6 %pis2\A�jugE��3A ��� K�M$p* �  �ic&A3LZ1s��r?66�z  situ�s-��a�=�is�ed�%Q keep �KA��:!�$q, :�@uE��ise� flexA�k ap�p%hm��n��r�G�p��u=��=trans�:-of � �\�� ���(&"necessarna]"_%e U���e�[9Qe�&Y"&�!s� *!si�e�"jr(S^2,1)C)���W��refntas ``p&>& ?Ginary�''_3 m�xhave:6��.WR}�Y Giv( $n+1$ smo>y�Y$" I�a.E)� �A�ja*O ��%9���EW$g,\ h@6Q�\H: .] $v$}:Y6�(1)�ua�a�|�va�U!> $h$-A�(��t1� 2��QY$;2SҀ? o f 8!� $g$-Vgorthogo�e�v$v(y)$ G-�� D� ort{<,>} /s*p���Jv*m!�� ��30\beta(y)= -||U||_h/ ��� �E)�v��$"�! P � a��E�"$��A6!�saiBb1}�/w�' �_�uv �*vT���{�D}�A_� )� 9� $$h|_{.[�l =\ \C (y)gJ . $$ aF!\}{c,6M��M��e�("_l� �d  4qKgh6!:A_aOa�d�7yALa�Cof'ar 64 $h_y| e> Aut}(TY_yY A�w�(mCA� ��� g$-un�/A�: eigeni ɣh_y$,.ne� ve %�a%Ct $v_{(g,h)�O�Da�� �a2u2aPcouplX �ks $I$. Any�H-�ya Def.`WR 3 �m $v=\lH[ �E1] � i#.a 0$.  2}2no>[) �$v woF�%5Et , \ e�$ �TYQpt�3 ��T2���AL$v� [� B�$$( kh$)$ establi[ bi�� ��$W_{(v ,, 9�qG@�XsofF �� DAB� **i1���� ����,>�)�.5�?�mE"Av)Mc''�#2���>h=.�� )}(gA\C . 2 $f1= @! �]26� FF{now���L1m"+ o4��" WR}m)�'o not �<eec�Hitq i.u$:UWR sH+�'Br �s!��B�"6},��of���est, eNi�F M.O*2U�+�% t9u9S�y�DS�Z{RO9�� �AmmI2 -.e�r�  (�wr � l��``�K'') M�� ichr� ig� � ����� WRCw$ki�$k'rei��.5orNoeCEv<aA0:��n)AKax�Wq�\Fa�)���� o� �qR.ao#}��A�2,vm q�. �n6� E�6� 5� .��<�� ��A�6� ."  b� k� k'$�� ^� # `>�%�  k�![�n $$* n� by!6Dx�VW%� X$�9  Aa)p��+)�.�"o�,�6.�#,�ty)�"�#6�3��J!� �����"est:�C"2�#AI}ferփFAE��8F�d&$eful treat(�E,matter. HerEm�[2�$r*Znbo�� �a[�"�!�so-3 E�2�,}. Ro:* ��coy%g��V evx$\ �.b��in �};'W q=IupH8")e.� �� h&p� ur�Y1sxrt�oH1�LI%qq%* *�� �l�de�te�#�,!c~&�%c)[UAlyr� $�1�[saMatd@l%%�("V )6�!]g 2 fu� e�%!�a07 � ���Ba� !�6U 8� si5!���,}1�"}F�� 1�B:��al��(y� 5jTa�cS rيV}V��IA/aV�t52F�EGiWpݍm�,uy��J�2{f�- n aiSMe@p� %�l�$?�id%""m#�/o��A}pervas� occurraJ!%�m y&�,:e1n.�!�5s$2zlla�vA)w�)� r *#b �$dM�2#3 $� 5�e�(a��A�1v%��E�fa�}a)ve plac�I>V0! r����R��n( most��odeed)�W!�%y�(discus�26�X  m"ummarc" a few#ulG8��AbI!. */�nyr� �5 =(\Ll,\mu�T \M.�3� �=o g<x]jm ly2*��.�7^�!s�>9����; ��% 0 = 0,\pm 1$ -3*� �5�"ͥ>]E��s} �.�'25# $"$s�ll�?b� \mr$$].��ll�a1I�]Q} rD$7YA-҈��� s''a^* "�VO*�&>2#� "�K�ref4� �r9 a�.m,'n� �,�&�s� � � %�&�" �ŗsJi A de�(�Rto�ess��4� happY^i�N _�.�%${\n� }^1$� "u}ut��any .+�y�*J9 �L!�t�,*jn���!N.Y=�͂E �#٤�P$G�"� ig�"�. ��- cise� e2��'��s. Each ���2�Gu��5�2D��,A� $T 0�2�O 6��i"� +*O� $T^05�,a2�subme9 !��!6yJ(.D inher �m�*e2cB'�!5v 0,1$,F:(\U"@B^�()=]"n�[- �+� N = -1� �>A$]�"i[$�3&6$&8InZ\s�7�qXşE� {J(X) = (>Y(Xl>�; G >,N�"F (amJ \{a\�RN� 20B��2� �=L��Ah �aa14N.(Aa�@ stea� R([a5U�Atso on�0Ő�(^/��&� enumerate[7item A���Rmź.:0g\6�LO(I7/2�� �k : -� "?�J.s;2%; 5!6�8��pen�#�� =Bl� meat;S� � onN��y�1Nir m9�  $� �'t�i� o� +��%�t 1 m (a�[lls��^0� ing9d 0!+� z'u� ~[��).1.F�Jz"�2�F�1�$� .�-E� ���1[)$ �.���Y�E��$��^9Ep18^z9�9��;1\��B�19���~�.�WR��8%y)2�0(]1,�|�Tto��*0 .A.� =�!6��:�.���-�%x WR��Sb% port0)f slab6Ti�\pi/4,���"a��B�uU~�-n%Mc�m�)!��nB�J &� q�0i��D886�au�#� 2 lab,� �u�i< $\bar{\mh}^3 = �. p� S"�$����"�q1A2%qw (!4)� j!*� end :��I&�2K $2��H��>� �8� asympto'&�&&� �& B��&fiJ"} iH&!TD/ -��!�m@fi�"1�4�M2a} s a *�&"S)im8  �plez~(5I�0S�$h$U~�dR� �7N �Q&� 2�2 u7c�Bk .K off}�Pv=�Klein�(!�2k�� bgA3eB"�/ x4`Z,��ed�o8git�>+q�@$\PP^3(\mr)\setmiuKQ� �)Q$A|a suit2H quad�>�� $� �9�=�sy .�A��J�sIt tur�F%Na �Q�KA�q��0�pI�!�WR� >&.E ``fit F~D$��3sen �y glue�:Q`�a��. �4��an.��who&7G*�0d5��end6j �$ $���� ��� R!Vu-_l�"!�-J�zer�Y"-GEo� f6a ��E�*�"1U*� ��i:؁ �# $I^+F�)Bgi%�0Ema.�:��j-��� i�!�UE��2&�J�/1ac�aK E�t ��**��k!62!%JeU%9 one}�Q�IPF s�Y~4" (w �*0QaY��I� ��A9},r {�ithfu�@2EUɵ%"�%&B1\nH}!/�-/E|�zMj��$�}2 � ly�I#ou^iact�8�@���!NquotiU��U>�/R�E3.�Z7 N>�(B�@"4U� Alp<"�"�>sc�" 6�.(SF �"W<tt-��]M2,�<ei*M��Uot 9 ��ty�F�" 'cK/< se�E2�2 $͡r?9T6�Tq<valn c�kes;�2` ften� f^!%=K�.#3ve*�E*m%ii�Dng��O gr(&$�%), ��5))re��mj/zc|o�;�m� �H�:� ��T�0�Cs�"�Ky}er�a�pw�' e� �ce Mess'�'� "MBI\*sZ ce���gFqP.B XS\�R�,�� " a�� ��@ :U��at� e�!�>iva�� stig �i� physic 4ter�V4�D �,W, Ca2, tH})a*0 Ny7q�Bo1}, 2 ��vol`����}BW-?!�.�a ~ �!8! �A�� -h$Ast �=�T2xL �&�3 focu�i(se peculiar>,V,N$ phenomena2�>age�"��4nBq�Wof ��!1a}LN� �.� �H�rJ�3cusp}a�/u(�"��Gllu�SUese"{9�. A ke�� Ua ; a�4">G&B �X, N.W5\+ ��E!�a�]){�Z�j)de���K��- (Br7O)ϙ-&8OhEs��d �~I2yC&�Pa5Eu�="�+��.snAdS�� 2/�!1abQV6��@?# "t�answe�is qua�lIusZ&�8�I�NKm)U6�)h"� /�byI`r�s�iE�at ���A3-*"(b:�b! n�P�͊�D�Pe�5�!R�&�BS��onI�AdS})IR>�:����5� x_!�eN.*,�"=T�Rr7MTS'!�"�;<"N$�=a�.� F�),aI@ 4:a)�eO�ir/�i_L, R�$f��r�F��Ņ\%[ ��|PLS�w�w'L2! �ie94 invm)�9y*�j $$ �Z.��<R�L)�g$$R I%�Tu����y�:�.} K�5>� !]J�*� �of��us�;geq 2$*p z�. C�z�n����My=��a�rV��d�siXf �.Z o)�!(��,n �^t�X"�FE�u �.�J�  $�2��7i�a�m��U!&��m�ub.�Tsym}):N �- r� $F^*2hg^*2�-�B�eB^*.;m�Ѭ*� 1��#%�!W $R �[�^*�5A�In���T2�-E�Ev�#bh> %9�}6M& W�� 2�]!�|X}A��)4N�Urkin+&1 .N� ��.,u�g�ea��剁]Zy �! no K2�!&;!2vWFLbA�of��vW but.) 6�9%.@,f�� A\M.k'9���.�/9�It�$i�p=z�+> 1e�!s . J؎for u�a+ w�s�Q���iXE"'�qM�fy  ``naked" !�QOJL"�Tbz� Then�= 2�&j �o "h ofN�X�����^U��Dv��J��R*,E�.�$A``cen �d"� BZT blackAB[y Ca� 9� a���yH.� *�#.%R�be�re%fr$A �\~�E�sur�6ve "h�F2p��K�� as%GcouK?arat%�%\K<��� B &� ��� �Y�m�!isqGL%j�A�� rved�= �L� "\ *�rhF�e���d!�go�-� }>�l �� e�ZeA� �F���!``s '' (M2�(Sg $S^1-  S^1$ �I!S�)Ps� ntri �!5 ��Uha"O%�fqD�dN>) er� $c�1�*-")btl�Hl%�ship zy F�*�'s ``E&P\��'' iF Thu2eJbey�p�� } alread��yY- TMI(�^A�� S��!io�<�y.��P��vl1�ϗf%� $ ifx&� $I�i �$&_]4 Bhl2�. *�sm� AL* A� �q� not}�=���*"�Q��.I���DaphyK�0�i�f m*^E �Y). See�ps&q ?Y ��2� {A��)a��"i 9N�q�Nɟ1^&�.K8(KJ� ) [J� a���g%��i�H � (FX ).� $3s = f/ϭu'$t\in &$��(2�". 6�'$1$-par�er��r spac%�6%{|��*� "N $M)JI+^a5�XA��ici  ($t=0�4a��o^(s�mi��!�"���is9ai� ge2H*b(2�der��Wr�J�a�a �� of��^K!P0F``�raE�i�"�W.�T�I�u�'�M�$"��t}agh9q )@*3&Ub4J�8�&,.� �e�NVbA����Q1/�uSo��ha�" D�5��+_t=t^2 �6Al (e+t� made u"dt@RI J =0, �1, ?GdraDdfor�ly$2]a�sR_t��!�ob�ts� ir'$n�HV T ve (" Y �!'T�-O)��\la�t�0}\�@f_�^� = Qw^"� � �vnow_RtcoF�. "���� the i�O"?q�})^*=|K"W _t^*�a� Dpre)2�V��h���F66 ! �rt !3FR�AMRR$-li�V &i�i<\ kes �.�$-џ�gG%��!~�Z = !B0_{_}.�nj] ���Y�Jze�K �%��/#Mo far8a�zFI�y�D 2'!�=Xin*4. An �$d �fl��Y�is� de�+�"b7} !�jn �&� .�&z �t�r�%�~�y �&�F�.2t +Ut!la�2{^Gu*@��BTa-f�,$qHy�t*ts�j���9s %��VHX�a :�`-tY�a �V*��> (��y9�ed)Nm*�6�I m* �Uʹ: �8*.s)99�K"G%&�5*y< WRTTnd��/^Om M/�c 4��A�I3sT�`�c� Ku}� m2"0Za g�L Q�2�5l*IZEGn ex� in� ~���!�M�P�?�4�fB�A� TG�tX�/ $, a�cerz�<%"�}�).6J�c��SGste�: I -��qR�c ?Yu(!���R�?:���).�,os�@�kt���' ([)�":�+i$,Aa);�\desicFG%thoN�&F9�UelE�ar[�A4s! \v2 y�S �]:.�+�czM,I|�b":�|�(p�a��c-@ZarP way9NC E�9� agreĉ�� �%�� �5>JD U;J5Y@=i6 .� )��0!so&/?Qq\Dd$;u,} qX">�&�> .�r&�>!��R�-�+�=r�Oa�`o* Omeg \C,\12$*�& *� 8(� �oup"2)}&JL�,  ! �E7h ee� Pi,{->,Isom}^+(\Pi)*W5  (c �2uC �BG}(3)*�kdS)~ �6�AZX �6.H!�Jq� $\Pi��ac\,�+3B}7%��f�}N&)�J:to��� 8�. Via��"F���n-�� .��ur��n �X*�) �\R�Qat�DTh"!a�Hy"�iDehn Fil$M t-u^ Bya�͍�r*�/rJ:| .�\R�!��,:SfBTZ.jM6qn=x��t �n!�; c �si*f�Nn�\6#V�4�z�] Gi&e��"i a556c�E-Q�gn �``I�les''6�D\ZAc� ledg�J:} Appa�;�e�( NR�fs:o. ld z �Q,;a4*#A�JAxvq@al >Mes  g3�� 6i) �C"�s"� Ge��L&` qX���<"[{., AI�J{}��l�-.�*_?�'�!e(��edVb�R$L$�25�P+%'�), 3=iC l9d;�� !�gB,[?)5� boxzB���"�t� $B \c��[a,b]m�[c,d]O<uc�$L�� Bo%��B�TX:4a�� y $x!b�_$\{x\}2-�LM-�arc.� A7 �&�w�3�1T $\R$. Ei1 �>A�m� %Hw ll7m[etb�ZE>$F� Եs +'V M�7.JLqRD�Lg$� E�� } (�L)F� c� Soq � /# m�x%rt�\�1LK]�rY�S!�q� �\Ll�@"  B"oH�6E�9��0"�6L$�c�*�����l(:e� !�! E]es_*9��hM�.l2�JM%�!v]A� �� zr�0"ݴLe&!dis��tq $;1��j`�2atU�s�"�1a�%i~ -���#� � let�Z��un }�1 � {l_i\}_{ia�I}� Fix O[iB���L�&�:��( b3?7� p� $l_0��K Pd��N�r��ka 2� $K� $�W�%��qi$)�s/t�4Տu�O�g��Sbnd"!�b��͑ cu�R6JӼ@+�"^] tang�vUs "E�Q� �matO=0|}��������K$�C^x�[!�� ^{A7A�%�t)� $x$�!$x!�a�&/(��Uu %d$�Ua;.*� �*TV�~> Q����ofs�begin���M $l,l�VJ�>+p6.��)lI�$x� ?!��\ �s $v,v'$=�r>-�,�F(�M$J'$)� �Ks�od>�i��\tau(v')�`9�%cTan�?!�$��!�Uase�  $[x,x']a.Q�[g || v-_ ||<� mh}(.)��W$��mh}��*��. �"� Z'6l��y�6�-\-�$\�i vm a��!6$v!�~��$\Phi_teƥZM^a`K�to )�a box ���7nd��AHW��!ff-����.Č F: c�(-��, )��(x,"� �(��Eh!Xě\"J�28IGg$EH��!�1���]$C|6� �3AqFiF��8; Moebius bA�(F� d� 6�%Ajun��.o��A inct�@�� s be^!�aS^1}�Z M�N�%�E�%� ��"�*a J���)4eq��Y��e @��Zlw�8. �dB*� & �!�Q<�"�&�� ���w� !�Llemav�� s. C _N��ms"��&�R�s.VnV="�9*� &�=��K� ]���4a��i�w�q!�� u �(SA|!  [ -("�3Y:J��\p�<{T�4��U-��.{ �xY&M F�  �n�if"� G `]�JF%�[ &�}A�!��if�miee% ��7[:2� s[A$���\�H����W�aB�v 8# $2$-� a�e>-p ��1C3) BkJ�h�c<� � &�S�s6~ %~� �.o�<y .��$E�%�mu �.(0MQm�&u.xzF$}!5\�?*,(� � +��.L�?!/ #]W �$MK.�bVO+e� 4R��skeX)r ʾ{�NlG�� �"H=!u.�bof ZA�.) Ӵ-Ŝ�� arc .�ouN�65 �{ �yc subdivi�@��$�:A� �0 $i="�nF ���.̯]6 ec�� a ��um s h.E� p_{i-1},pO�a�*��%?�99B��� " q 81Y *> tE sa�%���par!QE_�� ��ark�񜥱a.�Mlaa^ K]e .��H�y� C}� � �:�� Q�2��st �,թLi�.Is�\m� 1+�Z� U�ik�8nv:��}�z"��s1,\Qo,l_s$����nL&�o�rYb��n�}�a_j�iJ� ��$A4 � A�9>a��tVYsa�S �$��f�d>nd�S���_��t�_i a_i|A�l_i|$6J U���a��R�|�L"zZ=�tIY scri?�1�R��AT� &� n�f�Vq"*k$ N�:� Nn(k�W> d q7s&�kp.$8��G?� &� m��L%0kZ "��lR � \Ll [ \�&�/ . T���\mu^*�d� �s,a�h��2�f��!�� �|uh9 �!1s6`�+cU3/=z_0��g $k_0''�N��!'1=�a!!�*!,2�kO>'��F��B,��ue*.��-�|_{� � �}=  {k_0. '}= 7 R:�B �Wg�K!���Q�~ a&uc:��%vN>� M:�4 ��;��um+` ing,[ W vR_"�:. AThav��F H�i�GgW�p"E��&.� i/ �A� � %>� eaa�Sa0��U�E�!{� P' %isimilar���R"d'=Fus�"�i��9Ang ��Pa2�oav]2J� )� � � �9v� part� Ll_S%)"!t�[E��hiso�Fd �G� �.=H;�W�]��Pu$.�hl ��nD�!�a!&h � a�s 1�|u2)a �;!��-5 �red��1>�RY�&_Q�� ��{ _W=!@W(S�fac��*2I �ato7% a�(6�L_W=LRA �Ji��� e I8 �zbu�M�jS !N9f>Y !G&w&E�4 ��7%z$�!�xed�x�Q��89.&pA0!KR��$)�-v!��4!���2��RBO�K���/R��_0= �m!� ���et��5rUOp3�ccp �3�l���QP�"9�5 �$ ��-o�den�83� $I�_{nڥm���mrA!!�k ��D!��ę�"G�# �$l.�Q"��4%[�  $2^{-n�Lat� A�-� � =�\par *�<As��mQ� 2u�\(���� E�_"g�Llq%�g�9�8��icH%c��M ��!كc|pf%z�``bge�^{WIi�92�=�sp"$7EQ �r��� ]ͫR� �lM�A��6 see that � $1=!& 9L \cap �`$ there exists a sequence<n! Ll_n.0 such h$r5f m!,��8a compact domai)d Let $k$ be a geodesic arcA=tained ,$ tranverse!$�)�$ andn$%#Tany $n$. Then we have5�qua!ib�eq}A�EkAx(A� n)_k=: �0)_k \ . \end{h ]6IRXDim The first statementAxevident. Thus let us prove only!�L second one. Since $�((k)\leq\hat�U� iAJllows)� up!Ca subQ&_]> measurA�muI�k$Y22��4\mu))$] In order�conclude1� show �$\mu=�5n($.\\ GivenEd ntinuous uN$f�,V can definAsc0y~$\varphi 6aKHk)\setminus \{l_0\}Le]$l_0$!�the gQ�throughA� , by setta�\(l)=f(la|, k)$.\par IfEs�Lrt of�is�u ,the interior$ke�� d$�b�tendem%N�M��$. Moreover%"i+��:�a=��2H} -:\dUs1�M�1>ց�!�2�.�A�)� �last �gral ��Z1!5 �4$ with respectAI$� V. TaYi%x2{f�2�${\rm!z}(k�[nF�A�% y l�;�Z���sufficia�to]�if $x�$an endpoinI )�ne,(\{x\})=0$. �Xd_\eps$ a neighbourhood of 9�X!� �@fix aUDU��P��K%Rc��U�i��s !�E� part�L(x)=1p2:{ ^}-�_n\�p1: leq1/US.���Uj)2P 1/n&$j��1�Ply large. In this way�AobA�2rm(�\mu�_!cD�̭tA�=� \cvd � xagraph{Standard finite approximɽ����d�A���"�=o h )���UE�by U�WE�seY A�PE�%�m�k?If r is y�ly smallA"� f leaf��Ll��at�s .mus�. Fix��subdi  � into�un/ ofXervals $c_1,\ldots, c_rA�"� c_i$ haLngth lesE�n $1/n p! end-�es]7 are��in $L_W�)�&` _� set $a_j=��q� (c_j5!Va_j>0$,pn cho? a)>$l_j$z!D � cut�j$ consi6= e!YD" n=�q j | n\} �associat^)� sKw�,t ��In��aa�a."<mweȡ(6��_� �[��easy to� �" ne�_na�_n�fen��#!)$ ��]� as $.w +�@� We cA�� &  a {\iu �h6a)�� $.2�8$\Gamma$-invari�A1R�4s} Any discre%y@rsion-free group T \� t \ISO(��8)$ naturally acA���e space�q�sFg$. Soa�� .( d.�;]=s��{ ��, .Q� l�8hyperbolic surf� $F= E/-.;Aa �Aj��$p:) \to F�l a (��0ly isometric)a�5 al c� ��map� I�J��F$ lift4 a� 9�$,����( establishe�bi�v! rn ondf betweenN�!b ��ʕ �CM�}X ar��F�x it=v8$\tildet  Ll, m6\ which�F���isqn��t _�5iE�>a!+"��nA e .� and I$\g=� Fa *� �� %(k)}= _*�� _k). C���� ��aJ��%�*)%{QMt�� nducEH�P;}� oA/==qN. Notic� .�2�N�if!7N a+� �,Gg$ preserve!�e��^*:" Coc( H}� cas���zc%$} Fuchsian�Y!kR icularly resPA��bahwid} inv gated. \�skip �,simplest exa �?z{Y� V�2��a'  familyd disj� s Xed � clos=�� $F��Ta%v��=�� madG un��e ���| lines�at do�tw ct each oUA-%�whole�.��D{\mh}^2� \cup S^1� �e"SisWd lik�^Q+JN�"ss.�桤 �ial=s �1~multi-cuA�}. 6*Wa�$:r�M�!#A��`*1��2�N��-���6�g�fe��>�holgeneral%limit ou��e�o remind!DewAthem:" &���]K� �determ�by its"0$LI&A$L2a no-% dens�� nullN aS L ue�i%�a�z_S� Ak5�W$  u , coincide; m�Ci��a<lJ ] sub�eB�;��uA�"� \Mm\Ll(F� !� Q���y�I�homeomorc�d$\mr^{6g-6}$, $g\geq 2$ be�gge���%W Dsm $f: FJ '$'�� s� s, �x� >E_\Ll: � \to  ')$;�0(��$f'! homotopice n $F=f'M� isa��� .BiM topologi|obY G�dep on > , s� willAp?itA� d _g$. Vary!G$[F]$�G0Teichm\"ullerT $\Tt_g'  above"� Xs a?uP " triv�w4fibre bundle N\times-R _g$ �-j� 7.�*2��exa� genlam} {�0(1) Mutata mu@is,a\ilar f= as � �Ba.AS�Dly wheFk!�of�@, type} (i.e.!his!�.�%�~����E&! S$ possiby�0non empty bou� y),) vid!�.!�.��-Ŏ���}. How , n��_�:�area} bun I2I }�Xa.$t necessar��� ?� ((S� (\ref{3cusp}n *�(2)�� ei�t*"�c4 or a horocycl�5�H. �e���5$s orthogonCo+ )ke�!_ 6� as�10two differentU folim both�)�F!�!j �A�ų![ also.Dan "V>u"S 4 !�1'kLebesgue.}��e� xa} �D\8{Rescaling: fla ward��$ Sitter Lo�z� e~yqndS}.�O%2 d;�}�-2- $4$-dimen�,al Minkowski 5� �0r^4,\E{\cdot} )� W��x_1=\{v� 60|\E{v}{v}=1\}{�gn"N*Q hat\Gea.�8sub-manifold of�t�3 � $1 ��!��OO(3,1���� �e5� o �!�iEs�TN stabilize�a �  OO(2a.�Gf.��x_ �nAtr��� %�!sn$Q �Is���f� �y �L9>. 2� �or�ablm v-.e�i�  $\SOO^+ �!h$of2=�!- M� a� �i��aS5�(�.�o)>p.[ 1.�s)Vt�Q pr"�67�!�#v�$� bb P^3%Ea  embed�oan opena� -1ex&$!A(Klein model �mhYn:j(�e�regtB?2 P^2��). � d( � e�E�E-�e ���pi:UR\&} 5 � $2$-a� "��autG smM�e) {\pm Id\} ��P�A� �� be pushedl�� aOE�w��qqw��alwayAa,D owediEs�awA�:�i!�e�=��q:TAv� .�AsEebT� + (inde@!t care� *E� d& matQo)] �9Pm� ed (.ks��X1� y�F�aEQ �y�)e71Y.n-�$=�!�'ce� ��i��e�Sy ��eG$-�%VF69٩�e�a2g)�iA O r/I�.�Y� �{�.1�x_�E�m( sm%$ U&$�is �,6�?A�a �� $Mu ��� 2�uequival�to�(l,��)$-2ureQ&�J� x�#$ a develop��map $D:j M. jan� onomy reE7nID( $h:\pi_1(M2I�L,L A�� ti��i�s� �#XAUIntrodu. j" We g��an descrip�A|M@. �"� $��E,aR"� $v^\perp$���alo&tot�"�,plane $P_+(vJ�;� �Pn%�i�Q &�J� bC$half-s�8$ $U(v)=\{xR h^3R xR �B.t��way}�$��ame�wz# v{"N��= �XfDZQ!�involu%^!wn��changA1! b�E ir�!�� . n 7 coron�h�!W�2a$�y!�mapsto-v�( &�,b!�J! �(un�`).�%�!'D�oro�(Vw �by $PA�M,6�� � E= Jy%O� g P( & x)( (P(x))%(n*���%!�� �!& m'� Q).a_ Just" �CM%�uh"2_ a��!��� ng2)a9arGE�s��us2_�%Y[��� � sBs ,M�#e�s $p,q!XI�*K'�qu� ����A*@�&� "�Exa�l.� X,�Z)G+i9if��bt �v GY%%a��G� >]E�Q��.�va vectE�$ tang�D.lat�$� Ap�Xarray}{ll} \textrm{if }&� 0 & \exp_x(t��,cos t x + \s�� v\\V<0><x+tb--1Bihh v�) �a� cu K �%��l5�E!.��-�Q]�S��$��qeM i%:1 2��a,q.,M�Ie�a�*'""\��al H SU��s�\Ele�"(+ l to $\pi& imE}>6in}� @�9TakOe I��M� unitY�\in T_x"=x�. ClebQ��e6�[ T_v.2� t*� ve%�u� $[x] �$[v�:� � ��s %f��1�i���t9!g # +c� They��a�rizI!�� �v��\[>} } c(t)=[\Q�\I�] \ , c^*!ve|ax"y}yWe saqa��Ae�Q duE $cA���$ same�("�$n $S^2_�"mi�,[x+!Z��$[x-v]�2�# �c'F{\emph{�vtr\ from���spL $��he ��(ray $(c')^*r[��e d! v� X��I�3.��c'�,ap*(Canon5"�"�us�%# �>� Y previ2-Axio'� �6�*� � pwe sh�� I(a � N$ D^*:\Uu__(<12� ��H�;,A��$ns�ɾmap)9$Dn2 q��>�A��pG/f"�apA�i�"2s ^ pull-back�1!�&� m��3rZ'` "�k�A� idea�92$DMI�2 a %� A�sEh*int-�j� grady� cosm"Z!�k�)e�s_{>1}=s�.�(>�taken2 !loy6ޥs.!f �A�s_{<1}. sP+}itJ �2c A E��,us�mor"�%. C.? �B+iW0w� h^2e&�"J+!�W 8 8a well- �d �i� $v_0� �)"D!�po� of normal#� Now>)!n& basegx g �! �kbe� A���.� �p �d�8we omit details�M�figur�9b:ce� �9Xnput{1geo-ds2.pstex_t} �!A{{��"�8am6 #$de!o� on.}8c��.�81BL $(l_0,mv_0)m�$i�_0<? We ��s(�a! imag$D&�6&& $\Ee͞�;x�i � eda)Hb�H# $P=P_-�&� (� X)P_+$. ��JohA+xR2�� ��� � ��wh-0�� co2���5 <a� 6��r NY)����$ separ�.a1>4 JJ D_0^�� $. O�#>hA�y*}�o�mx!�(is entirely!�.��ye9Jk%E $x%�5a U6� \� G� 5�diE c&�- �x>:�q� !F<x�x'!�f� �-�3O st" %R7t� ;a�E� �is&/iB�!k �!ro� )v$Q6 !qC!* a�! (v �-)-��u�B� C�I�":D�&ayz� CTZRiB`2�� ma@ .� �F�'9O���:*�5��{� .j� _q8Oe$yIj J4&�  $u!jFehI��v)e )�. � 3�a /E牚ar_,�A�� "�>un6p �"�b�0�A! s>fUu_�!>�5y $u%�!#6���3��s�n�Tro�n�� ��9 by angle *�5�daAn9 8!�h*� "S �� �EgD9.� v�)proper%.AW��g�. �@mak����� �N^�0a)#=0. subme4� S valu!+)�wd- $(0,�4�K����1uq�a�Q%�m�2zV )/I�U�13 $n%:b� ��fA&~ ��6wf>\(��)I5us�!p� at����i��&��W/T e7<1^\pm(a)=n^{-1}(-�{int}(P))�e(A#=a)�� $\Vv_19l��!&�w� \[   lC{I [^-�u �v_0Fu|\\o y0[v ex*� X_0) v_0]vJUu_1^+LF"�E^�j(�nd �fIF_ 2��$n$T "tf�(��" }(a)�a dila� o^a�or�Ash a)%+$^ reaA.�1"\ni v�(�,A� )\inr4�+l_0�sy,A��� !��2 (?,a)^2\d u + ( �tX��9�xtH-J�-�er:.^� !�E���}� f �� Ɖ+!- l_a="j %�A��at rea�'%�a�tas ��l� ��$ ^�!�% �w?B�2<n(w_a)=p�ɡT�+nG :2!�+ 6� ; )a{�%(v)}(v,l)}/\sh�A (v))m� Z(�>9\p!E, w?})2?�)� I �ASW�r $o, U, Z��$��8 C^1$-coordinat�m �.�)b�G.*$$(T,u,\zet� !�!�0K w:x"1"m ~�7 j"�(T�� UJ)^E ZJ �5C:BbyJ�� thes�&99B� "Q`,hJ�BA1#)E8&�$ flag8�:+ 'N� <>�:�r��=\J� ��B'q,A�:N \cvdncor"9> $H�=a� i�F&6A[/�#1)sSigma*'% )1 S^2%�\] � o;8ri2v\�:�+$D�I�����-!�k 5�.I�b�4ns Fb0"�'!�c�/�A �.dPa !�g"w7 B:-� s *K*&Z,!�s- �/.+GE�%`$rput lD^*(r)=.r(r"),r)v_01u.�remark}d .�)�� !�5#[3tontify-!� e� !�m�5r22 ball0$&�(� � � yI.�*%��;\Uu�86��K.\ <1)$�&�*B�=�%o"qMb a�K}0 :ct:�� F��:�i�a�tau�(T[2] EF lh(&�2A�#� dCauchy,(s� 6 is glo!ly*�%pa+ ���g%:[0,a].�6T-zap �-path w~fu_)&q! $p$ "�!�1 arc-]!� w as N�q�Վk .�)fG>$I� �,r(t)+T(t)N(t��0>Ba�mpu<deriva�0� � H \dot K =  r+ T NC dot T Na�s/squ�of]X�%��u�]NKe�M -1=-�� c^2.�+�|r �|(� %�l� |�2|��a�=�Ŭ�. ��)  1< yxT����Fgs7ngJ �V =.�- 0)> a!@hA��y�A�&�Q��2e  �3*�VESM�I p)+t��O $te 0,F]�6.$�p)$�8 �%%dJ��Q��R T���le�E�:(a,b2w a�(\��)u6���d�2 �Qe�&-�<�*>}}z�!� 1# 0)=ptI2�K!Pr)'�a^=T{)(t)��\/NS(NtR� sup 7<� �!� inc"AGt�= 5lim_{t�� b}5TD�!�Mt$�a�Afshould�=i=/ (E+wispc$)NQ1 ���e)2&4�Ձc�.�%N1�{ $t>0���>Au=T9so � T_0 i� c| < r+�}|�M?ply!(p&E horizfl�6� m�$T_0}{\sqrt�:} kc|� ��  }� N|:6�W=�<%�<1�Qr��� S2w+^2}� l�~By loo�at�'�g~(W.� eq})!de�C%on�.�17%�T}-41�A���ecA� �Q !EqRs SE\�% � � lete� .�� I�a�eus�~�� $um=am4o_appli2?�w(a,�sho�$�&e��O 7 .�%";F�1kI"*$ions}B}V$�YRU"�?*v�>j&�IbyT �8ofF.�Ia�( $PSL(2,\mr}g"gC*{ n afgSdef�"�[�E% f1�:NB��3_0(� 0�m:$-�&� %�k?��( H).�B�LAFGauss�&!�3$.`�N�9M,�:$' wed5�ecBr6�2�&hf� -S C)=\6� � FD\circ9-�)=^ ) D \�!B-�}\E��C�c$� stra�Efo"�62� S� "�1�[G W.�FG-YtX=}iD �%�cG� *�&U(5�A�sC8pereF�.1� quot'$Y1�k!� a -a��mU J� z  >�#�B�#h^�H�mr� !9�4��gB[  6�!hQ1^.ɡ2�7:V.�9srelatZV&wj LScannell's classificu�&F ~!(s~\cite{Sc}�F�36P.`�L� Ae��uU a.qH&�6HsD(!� $H$-hull)�-w��VJ�'QH�?p�5"N� $Ub *D!� $F)�(0� Jsatisf!���T?�Yiqs�*�B�E VI.!s:!7͡uC�7~&dev97 � �]��B: t�/��h�!(�)dev�N�sl�61\{1\}qF 6�7�k3&��[uc�a�F+=We�P)|@dUUo&�QZ;K�6facd<�Y�I\V�Y&x = �/Jj*�de +A�-a .��UQ(1)NT&*"`�G�;a&�;>v=C ) . �PbyU�F�s&28��&' ���&�e]� KQ��')& �,['� &v6eq^� �~�� =�A�i�Ba XPon"�O�J� %� ̡���j5=�3�j�I�P/F� 2 N�ݒq�mQ~��?zs�� surjJEve�,�]��C5���� ]\��nple=Np@us�r�; . }e�"L4%%% Local VariA s: s@: �txLTeX-master: "2_3DWR"4End: �m\doc�'EW,[12pt]{amsar�'u�%ckage,cd, amssymb,esym,ams^  !} =l[all]{xy} \newcommand{\Q}{{" bb Q�'.RR>ZZ>CC>FF>AAre.�O!}OF H bb H} �m�{ }{TZ+}[2]% �` ma}[ ]{r*}2#�" Prop�(6(M2{R2DthmC�2#�� Corollary>%nj}{Cona&ure�*QY } %2� ra}{��2title[DikQu�Td:� s] {6 8non-Archimedean>0D} \author{U. K. An�+ vardhananv address{T�JInstitutFJ{#�@al Research, Homi Bhabha Road, Bombay - 400 005, INDIA.} \email{ld@a(.tifr.res.i~ subjeu{Prim\% 22E50; Se�11F70X \date{�)]abA ct}�a sym- ��, $(G,H)$, onS1�r�3under���� he 21 >�H.A C#arm�B�R6� C#i$8G$.��pU(eF� mpor�@ qu2S)�->& or8�"�HL�.�j�� one.� c:9� A<.s�$pair $(G={�LR}_{E/FA~$m GL}(n),H  !1��t��# l:��`SB�se�*�pap�a}� Z� A� D a Gelf��u"n �"[(dd. W� eveKZ��!�,{Eg9lm�3th�FneQs-�i�QerDL idali/e�f�J.sx9t�3Di;O ra Prasad��Y� \�.e� "*K.B} t4$G�DY$H� 4of fixed�!�An&�@ A�An��ai�Fbk.�� �@e�b H$, �8AvZr>/%yfnonzerom0 �/ly,�, QI`8Hom}_H(\pi,\chiI B!��harac!� $$i��8a:!� $-�#in�hJ�e�Y�M6E!c45wE��qf�4d e�La $p$-adic field. � G^�PimpetEf or mt} X�vis > came�#�A~�GHa�f(, LanglandsI- Rapo�y 9 hlr}�r�ey��i�no� 2!ness (�e���1$non-vanish�C�cer). p�c�Dz,)tn��B"� adel#number �. Speclly!�areful�2ys�fJ�!LW�= $��F/{\Bn ���2�� �E!%33.a4% c4 c �)�+S9 as rAr��+tj he T c")��[Hilbert� u:R >� G$Q:4philosophy (du�JacquetSLat~M� oftamFC��- LiftIpa suito �} $H^\prime�& in�Scea�1tGL}_n(E% nd $�n_n�'G%jE/F>f 9d5cA�uC(�,uA!)I"BYe�:�6�s a��one�! �9l�(B��? ary �ziR flicker1} :%]F_f�A��C6)3 (Bm�)�Cn=Q<�)A�V (K.�f�ms "�0_ �jI1�522 S Fu>�;on���a]�5�E�2�s�%M(aH�'V�Nk�C� 6��#aNG^� a���6� ��Z;� A*! �q����A m�icityA/\perty (a��J�G��`M ed 6�ERy# �D]&z&�d�2 one ���>irr�?J admi�Ue:?�9.� �= �{� IFE),Fl : toZ  r )IIU�, (hakim1}). Ha�& #�L �%be,�G A?ivaS�d�T n !!�doubl� se " �=G�+ {9& . NE2th�y�n���a1<D a�6� �Oturn ou�TA� %:��+�H�*0͕!� {2n}e�$ >%\f2�$6�3}�An *i_a�2G �/b��&tQ1.����U}(n,E/F�!p(quasi-split���}.* �Q. Bu�:is !�J dim_�7C}�*� (1T� 6 ,� "� ��*� : X]�3}�k]�9 ). S{ -�!(�ala�>\.U�IisqFhat�``almo`J ll'':� $HgHn��ѡ27 n�.� 5}. ��.TOsk� rTF:�xOd!��]pN f!:- 4sj�J��� � aY��>�S<,6 ��,� �]>ven�Kge1 x2a'Ia�ō4 d���ula�� of �:��in-s:j�RZsd��X 4.31� p!a�we�YsketchA�>it. Alh] orth� ���qi�f�Ar�2Q�� < �7ex�/ sembk  c�s>\Labesse-"A VP!�!72m� :�ze 4�Fctrum.)W!�2(�A}_�aa 0 4)-kl � ,shelstadE�E=TngH� n��odd, $�n��� AK!Na 6�W�`cow!> �&q�"\* �g��G��(!n��6&�$.�an] .�ZK{�V�}F1)\leq 1��18x!�E�%L_pre� som'+mbw#$-*��1y���)y )yn�s2�:7 -� *���)�& dealj o &&SHFin�Iw} _��b�*�", !��)+p �J8u�q�1.1%�i�@kB��a��H��v0k R. Tandon (�n(organisers)ew invi�m8��+alk1%3Hyderaba�Xn>^c� w'�]W(whim\�q\encouragx�Z year�P K6F:� � myC<$, sugga�on��l�� word�& anksm ��David Ma�Dcheid, A. Raghuram%� C.Sjan�i�X!m�e�ma=T al. �q 6��re!J� s3 al help���dsIp{~ Ue��QfN�e�GM)$�F� 6t �6^*E degrRXwo:� F$.E\s�/�-�no�6>cel-�f��Gal}(� . )^��=1_� �bu�j.1W�"�q�$A A��e6.@ �� 0F� Ad read�=Z` �;��V*� 6� �n key �� a�F nanol V!GuatM �l�6� � . 2�< `  AC�JA�lGE (P&� 10,��"^ �/b�:� �_&� }�  $g � g^{-)�}$ �!�R/ ��a il ���}[P�(�)]�m&�7g:88G/�ok�> $S=\{g�v, G \mid gg^{ �= 1�!givoW $$gH��.$$�`j:1"� (-c"RQl�ff@i�MiE�ive�'_W iv���s �<�90�#. ste�'6=-aji5A� Ze0 b�Jjug�*��H�Qw9CS $.�$�$= rrif72��l-�\y9<-!����%�5%͡(. Uof)ua�_s tribm#nA?��t!�<bi*�'�!"�s�� Y�. � *o�( Z "�dm GaJZ�%n0do;%�t�Ped�'\pi^\veeMX�1r\*Z�(ty>B�.ll-�fmma��r . .�,9}Ŗ!�cl2Dt .D12NIqЭ��M�} E�!�a�|�E�IK&WbyA-p]%T \co\%cɘ�u� � dZ� �b\Qnec�g�3n�&��^��Z2�d"2S�Y!N I��&H$\omega_%� �9�8svjly�$F�T AI�: �s &�y too? A�R�z�#ecev answej �elow (Ř�� else�> �{� }$ signi"(&;�axC�&��)��c�}[J7]v%-K�� > !G� 2> � \pi|�F^*}}=�J !~^8��8A~�u2��H&* . A�9 /�2HH�i 6=orU 5r:`>�"3&��=!E} �vunram!�U$�:�a?�=�e� D.Y.dpg3*��1of��o$boils downA�aN�lA�mNabE st�rB�  Y�Ni�l.�;% enAc�E�b��E,by Anthony Kg�k �6n] m����7vgr':�E �us�΅Hy�� twis# tensor/q-�= (aka% Asai2) �f�2};��pm�par�]FL�h�B� U�i�%�� �$L�ES� Rankin-Seg .%"v alig"�8 $} L(s,\pi 4�g)=As)) \o_m�Q�)I� b �?f ��A�J)v7F}it $s="v}E�R�!�+g�|'��QC� W: �UU �g��2�veeB� � (�HAn Qe7e�ap[e�LcC|seq�,I�Q!�B8 �1e!v��: ��iA� usr6� di2� 0{�4dirx�-�6��4w"�B*� �@'U\ �� -polkm��F0;b��*:�!�.�]&5e.�{&�! di` Bp:$�%���� Combi�`i!�u�i6eG��t:� 5"(.!q�X���b ��Z%nQ.b�Lth:,�5�q�:�F 6P-�.@�  J ��1,k/�) � �<n�}�?�-%u*��GA�!�NnŻA. .��io�m�WG5g,��6-",�::A s li }� )=��J#��E�WT�  wo>U sZ J�Go E, ��!�uW!bl�heE ��ea"�.�Ϳ�"� �}[F��-Rallis2� 5>�� �y ��.�!�R� �6?dan �Wb�)2U&�" w!�)$�)� �r� BoddT2% .�&�+� !"� ч)�+ � +19.� �bM� �OGA�N12belie� t�&m*d�|b ;u�8q���]�� � a-aF�e�m6e. Dua<�)s"  1, 2})::V��-Ye2RyeC:}�H�|bp( u9�J*rI�>�!�&�#. A� t�X�t.�!!�?� sUfEn)) gow}�(?��x> uc!� pair�djr(Q&�}O(Q��� �I�U�!o�(=2�I�M� 1}, �#g=s� "< 3�ultd#`\J�?i�W6�-%�%, �� , method&0Hiroshi Saito-as },��e=*. �G& is�-2�( ���orJ!�r2 , � .� a|&�!)a"- ��$Jeff Hakim �"# . Re+ rb�it�ki�&��:�$b^Y� to� ve��J�� $n=3`'}k�7:T ����s ach�i1�a ys!�F ert�8mF i4}.V�ye} (g�F�(I�� $n=2,3$El)�Rof �Y���p�Eo nI� ��+B #��6$!/�Ci<#$�hai�m be a:!�e� YAo8a%�/iluv/| :#2�ER3t%�����L�ho�/��6H6n� ��4&���N�=2^+(F�o�"B 2(F)�\det N�(E^*)\}� �!�� $E^*F ^ U}(2!bUEq�&� oneiBg!/V� :� 2� /RN'AnN%� i�a�6/ *�= ��r�+vs) �al�a-kR�+2a+ar*5�&qu�""T�""D0u� al o�1D�.�raU{���^�)��/>�:Oe��$EgHJ���ms*�$b**�"�6�R � . B�?�r�^ principal�:��.E)$�may�*�m "8%Lpa+�R��$s.,#),�(Upi=Ps�Ui�1sV{`S �1I3uQp E�_V&Z )=2^\d:h| !%"z�:q�ZN~-6��C � ��.'gYvs � )bN� �բU G5�� ��R2��or�\���"�/c�%�sto�165 >�sE�L�5�#�* gelbO;. An V�,>T�"9�oك��%aRP7�'��_�0::�. I� �eAgM�#�3Ee!�."� ��.�.s>��G�(E�2i'a t�}. �a�6e:�)����sJ4b���*t14�&/ ʛ���ay��a� [:Ze-�� sum6�d7H .="�9�G pack�w)��. n��zK�� 28Z 7u�QS,3�afx�.�Roccur"�21�I�0Qс�u)�6v�-a�� ��t�2tsJ��1��Cri^$�WAk$n^�(th�rooK �R� 76a�2m ����Y  Hm!no los�u:�inIA��.��5��-��+=�XU�!��6!^U�a�!(!��%�.�!S) 6 Z U!�so�N!TV�1I��} T��&f,�Di$~�sub\A7E� Dv&6by $6^+"B&25N&*{$F^*E^{*n}\0&I"-)� ix 3�� adA"J�*� psMDE��� 3u�s����MF=!�tempe:(�s beca$u we n�uto�2�#�p -pams(�?�`!B.I�2 ^+$,4cat�56"A�$�-eic, sam�+9T50n0  cU4&�%cd. A2�6*��QLs"+ �+$ (am $alb).= ��BG6�:}}� �SA|k&claim!~�;&}!w  (&T 1.2,x �3!�6#4 )�"wm��U6��2�&L'�*i*��2�"_A�s=iU�&rjE$B7�Z驡lŽA]AMA��!=(U)F�&�'*�?!�%����}bdA�\`�si$-Whit�tr�;el�A D� $\ell(W)=��{N�,\backslash P}W(p)dWH�$ i� �ira@�V��6� $ b;�pot�n�vc:" Bore�[bPA$} Fu{8rA��,bOmrl} Am>!=6 �= ah!�Eri�E>)S Ʌ!�)� n��M� ?A�Y*�6�y3L*Ind�h�yہ/1+�����inner�)+A��� �u6E��� (as:("E)E^*=� GE!9)R+��� �C\ A�$�* not � �!:�+^+$e�2�.Cd�k"���J)�}C1�n�hW�papp��� �(^L>i��eVGd7j��-�+ 6�!$$qH)=m�)�b|X_.l |} {|Z6 / |Y6}$�� $$6A=\{��yqt(�"�  ~%cis}~ ,-6%( }\},$$ $$6z^mu�.^E^*B^\w%�7��|,�� )h6��h{+ h W�X $>QE�!�car�f1 ��:u\pi$,B>�F�O2�jk��Y�}�"�l- of T�=o�' X�*�#A�EuO)�S2�"�*�S>; d����O%ho�R6�v.zcM�% � -neg�` 9%erJ} ^- :�/6l� �V6�$ (� Bi��n-e�,�=0$W&O])��# .��9�orbits�#ŧG n�)$sbe clubbge3f3 s. D�1)'airing b%q6�1~J�$ by $$<\mu)>�.k� �E��� _a"� . (^: B9 �-) si_ah�G (ax)�4 $$�\1��6�H|}\displaystyle{\su ?mu��6+}}�$��t)ao�[�E ��U� ��io!s!�� (�!&�842� 2})"��&��thm�udp/�.� Qb_2@�� V�a�? aRen, $���oŃ)}{|Y�.} ��.�.$$j"14"&#�!� Al�;zof._A�mbqyq' �"�clek�8�� ���E A7�T� arn"�w&g&:![pi_�qH \sim_w��_2 g \LoRtft&i!5����4��6G�nFxsW�xjx�.�!�T�*I-�;-�of�X��.�c�Vi�a weak.[:�-D7 Q; "�7��OS:.{>K:Ο:a jN 2Z1" .��&����6�?50&/� �:r4*eee�e$Y-q2D Nb wr2� U� NY8E^1�2\A�� E^1$�;e,�g�� 8!��.��e��mĒ�"39� �rc � $ 2C��:�". �% BR $dFMC Eie(rse vacuous5ru�K>�� f. Oш,_�bR7,��&� �A�-De[rw�L ui�� �$40dD:{)@bBcc�G!uqT�)}l);::W� �6!�L&J��^ot |6G �"T_{�S>�-�'% 7d`Oer. (%�!Cb��L;�ideO F��%� t !��{0A�� rD+ . Se�D&�! o ).��DeWtLe*2�1QiL.h;i]1 *�[, �wm=!m� hat.�B����Bx >t |R�NF9&)66i,�Q�6� \bigcap Rj=�^�*F: quan4 �& !�QM{ �hL�1f�:�RyR��i1.rcɍ��t�J/ v�e,  we &�%RB� P-Z�$}��9@i�J(}}=\oplus_i�[z�eEnX$G�Z Ͷe)r�pid�)Ri�M.ɤa_�ܔa��[on &J{.f;E�� )1�s���Ն.!o�#a�����92 @E)}!�W+��a!fA i a_i:)+?�aՙ{m.�V,��4�� .�8i��1�,�d.�r�L[q I�aۍXT����� high�&{O������ .l� j�� �Lŝo X end,%[i{aai�S*�:KL�Bk��E�;$J[&*�Ku$�bD<" L��!iA\hIE��� Also�+lK/F� s�L%�w�b"ɴ ��p0�^8 \n�G� �l0~n~�'�ap:*��G�duc2k"+)," �k.US�-%;a�0*� a�f). Ou sump�[@�$$ guarante- �o�6�L:�"Qx:>�=2$ ]#BgJ��df�4ZRHasF�4(x:�2* }�r(BR�$�K: �NB1-M6�=VR��ha7,s"� ,�$thebibliog�y}{99�ibF�1} U.FY^�"�H:th "e./, �Pa�W8 J. Math.}, 206�gH. 2 (2002), 269-286y7.2j"#=: 64_:��6,'2�Pۨ��.�t�10�(3), 867-878>�3V��HC.�<�=2�B�-�8 ���F�<s, -Rroc. AmT �Soc�3)Q4!Q 875--2883>�4V��&�0~U,.�1iw�Ti�y�#ar:R��P"~%�I�� �R=�NotW`Q"�2 Y.�2Fn:�QzJ!��AngewQL 418 (1991), 139-172=# r26rT�=N�%9Euler�mݟ� Bull w%� Fr�} 116�88!�95--31.�M) S.S.R0[)h(A.W. Knapp:in}xa)|�R$�I����Hal LinG�om�Adv��%�}, 43,�a�101-121=( gow}A�Gow: Two2�(-� perm�p6�E� �0 �m�G-K,q^>�Z.} 18%�8A�45-54�Q5]G."0] R.P.&5]%GM."7]$: AlgebraiuL, Zyklen auf-H -BluO7$hal-Fl\"acwI�Zd36)�,6), 53--120===,>?4>m$�Y:7-� Duke%� J!�62!�I�-2.�h3h�8F. Murnaghan: T!*rT� � (y9]t?6�-Co io�.}, 133�aAUn�$, 199--244> 5�:�vercus�aa"8bs mJ. Nu4\�y} 10��251-269d�81} H.�% (Y. Ye: Une �Z� sur �Xhan6O �ase"x que �C.aHAcad. Sci. Paris SeHV1  311%�0)� (11, 671--67. �2^�2]F��^ &6F� ǥ�9�3�T9�Ra 34ex9A�!�$3, 913--93J[3B��O�nD A��:F�6�V��f�`J��}, 126E��t789--820.wQ A��plU%�6��>L*}F���6)�6�CanAN�3E=,79), 726-785]�.F2}f% :ZE Y'&�`q_N�19E��335-34J�32�OVg�!D7!�-�ut:|F�� .�ms�.�109%��� 67--2� s[:a�q:PTu�r! "-X" E����ٔB 85%C ��10.C "�V!�S�V:� ]DV,�O`A"��c@�ms, R2G/vSAaF�4s'69 Sy��a Ph,��33,��t 2��EY193-203]Y�0�?��>Pof=.�j-@A�n�mB  15i��#3� 396$3�?>� �d�m} a�B�m1p�m׎�D %:�l���str�Y }{2}B$ �!1.5�kaddtoHz{wh �}{3cmDB $width}{45mF odd�$margin}{-2N%top!1e.�n@{amsfonts,calrsfs�6 ��#* used math�T0bols \def\Z{�nf{fnQ�nFRnr calx  bf{x=n(yyuuC(ocal�n;DD*uJ>G Q�G(p=�io{\iotonam $frak mP%@"#lg:�ovv}{\vs{1e�)Kpf{{\C'ntEit� .}\ �,qed{\hfill$\]G$HwcS�er{para.9oset2{0}#�" renJ}ptheN{ (.\arabic h} F3 )}{*B-]?}{,MS2� - {\bf�1}�}qef�,ing#1{\vv v.J~M N .� #1!�"��H {\footnotesize \no)� Ru6$ head:6 ��$\Q�ell��c ��s )� M�i(28th, 2006 AW�Q$\ Subj.\ C .\ō<0): 03B25, 11U05A� QE30���< er} �Large E���si� ��Ov :eciv~�ble�W�Mr�alm^�"\20 {\sl by} Gun�� nelissen @and} Karim Zahidi m�� ��Og.{e}b��%�A�oD.} Julia Robinson�,'QC rst-���y!�<��?1Z�2�Q?$Wo��$(\foHH����: )(F=b�V$ "$-� fiers runG[y�Oqof 8 va�t E�Y�polynom�Zw2� lS�Y_5$-t�Y�is#+-�.3M@;��b )�>�.idE6%>rpretE�$-Ge ��� plex�1 1?$�Bvolq0N-4isFHd5�N&m��< d�k9&��2��wo $�)`b@31@ (�-` Pi_2\ A$6^VH)\@X('s Tenth Pre_6 )/hZ]!�eP.�1tZs�2 shor �!D&= W�ENon߉ra/� &���ys�wsI��i Y4_c�LdAR'O��k3:ll�.{.E(�C�!�Urib>:w"CprWip)U� diviJ�vsn&�x�z iBr�u ^y�2-0�ent, nam )��e4%��iwe�k�4�-#�to��)l� view� ed aǟth� m�i�bZ!�X a�qm"DI phra� *b& ``W� ��Rut:�M� 9n a�*rP�;[%E����  coeff��&�uit�\#tEfs�],A�whI�'Yc' ?'';!L.�a jA��f�n6" s?''o ait$T#|J9%� eP+�ny�j/ise, ``) ''��[mxAu2�!(lgorithmeN Tu"M�Gn<:C in pUs�,�#"�9!w�a&(r ``co��a10'' via Church� hesis). C�!^�HTP}(Rʋ@Cb�$R��58M���1%5�!L #)C��!hRR1�!$RE�!��*DWof �bs,� ijasevi5yPutna`"�Gm0:73`(cۂM7B 2})!�<`� {\rm)*\Z)$,����!%0��ge� �"�!iZ�Ra� swer!�.UQUh��$�!n. �kaIx�p��h�H*�W:� in 1949�1:49ZS�*xj8�N��AZ�%��=f*� � �)l�N&!M�0 * :- g�5. , i.e.�=atQH��MK(X!?b�Ks+�)R tru�$2jx� sen�x�I builXsSS~oS�(0,1,+,�W,=�3On�e�think!� sucha)WE�ulm�A�ly��''q4�etKQt P $$ "� x^{(1)}� &�sf_1})(�  y+ *e*��c�6^N^ 5rf_N>_1}JIae, \ : \ F(7 x}�,bf y}) = 0, "�3JX � v"-"� a bf x}= (x! �,�,6��z = (yB1y_�^{�SINote:�JM��Q$���3ot�"'*u�H�!lly F"�<prenex�Rrm (cf.\cdz{  ). E���ED�l�s:�+� H� �@�x"� 4rs ($N=1,f_1=0�tJa�ulaH<�� at a"xdioph�&`{�;a�^;CZ e$2N&� NP2IQemEy�K ll v���9t 9�9=tcP$R&� ou�xrs&�},��'� �ex� s J %k�&��� ng!d �2%;q�d�o8� ``!3y�.A�� Q&}.p�uFx�NX�%���χ�сz�Aeul{\ae}.! $)�]B$e_1=mI'biu ): �CE-�}_1m�y^{}_{m}y�y_1mIy_me�. $�%�v�Ns?+r�ig�k��w���+!O way:���lexqq� �a5%WhavDQ b��n�.? P� x ra"{ :Ƙ� easi���s}�\"�points? �#f mkto�� icatҬfa���,b�b``]�''�U>@=�)%��� }--- � l-�!!�e~2� A9_� 8u���C��. �^,��A�`�sD��ve} aq �w hier"yaS�^+,\Pi^+�Jb"is:SleE� %_0='8&*�)s�2%�atomic�Q� (=``& s'').&m61i��[#��&�T�.E��n$�sp.\ $ �n$)�:+�VZ':� _G$=_)-��2!_{n-1�7E}8 %� () ��{�9|5 �����Us(��s�|�ier�nges}.��jqH+�=�G�Juni a.Os����T )q�o+< +f_NP9A�$al�}, �`:��6� '���P!��E��A�fn�"2!� _4^+�(7}7julia-nf+^�"�-��+f\{A"� $)�_5X� &� ($=$ax�!�ll6/�!O"?�/ �)�*� .^ �L�a��1�6��i -@�VN~,��8V�A�!u� :on�&EeD��!human2��&��---���( ompe�wto��e�#tley Ro Jr.�� Zind Ums�ed!PNsL!V r%� visu>� beyond�Yr�f� alternub &3 .��� �}, a� 322)��So���wɢowa,X up-0 � ? W��SFe(; *�S W .�dI����l��cep�+a�ol�l}"B�Pwo��``''%3``{&F�eem��phiEC���meae�ieWn�b HTPAI�Ri,t~ expl2��texQ�2�+ e�dio�})�study%�a$A`)mCi+ �I*g�ce�^ ��def�w�AqcQ�  t�3-�S-Deds})�>��U�: ide z �of�Z,�w�E+��D "�s,Pssa�� }��m,QbM�� n� reO�ue �&�''eA'a�%� �;�Eis�y � inspE1b߅e"oD f]� �}��E�Ehtm ѯad��!����M�``5S>Ta� appa��ly�\Luc��ndE>�� by M.~War�0� )A:48!�2AJE$�F�9�e&|as 2-to̮c E�Weztrass&<$y^2=x^3+ax^2+bx�X $b$ i�)�d$P � X[jK�:uK���� _$E)�mZ$n�3�0lwrite $$nP=(x_n,y_n)=\left( �4 A_n}{B_n}3� )^2, C ^3$Mcop��2relev��"� be?:  f� AA�$"�$MF�.� �^S�  (�;*r{� our��2* �\N�5�?�Y$Zsigmondy'A=E\, ��fe��$C��aQ_A�Oe ��! %6��� l�imk�bu��don't�" N<. c��RX�cUE�ӱ�$of Van Gee�s(d Demeyer (M(d�p��bP e�</J#)�!"6�'*Z) =R_D�!3]erW5 o�qPam&�+��O � �K�7na�$D=\{d"� d_r\4��*H ��&x�9 Dirich�'$\�8,� �[irhoE~V &� �m SC})q2 �z��2ne����� $E,P� $D�V���.'�v_D$6�.}bB� �I+Vpl��nA!�efi�a�(� ,|,0,!)�$Qw3����x@#�FX-lem���IE�a�� ��Suget ri�� ``$0$"� %�$''Zllu �sg�c��w'r��;).�:)�a�=�2�#� &��Z")� &V mR(:Ws ,��)E N��),�2^e�� S :}�%(��)���a�>mp&?'��T E n �$.�e�(ipi�t!t dapt�c*각�Yye ��e� 2z!�2Aj �~�� �?I��@ E�^J>�};�yn*nM�1�not5~���I��\�%�E�B *��J��meI�}t��at �'Za�-"*q�.%�.%II"�"!�verif�=�n���<�`'erw"i)�actori9�o? H�.�e.R�of enco�QAa{V�@qj$nPWSa� l* +!Wa58 tage7�KL 9of"Kd*Age=�ons��$ ``powerfuO�8 of the coordin�ates of $nP$ is very small (in the sense thatheight4@``powerless'' parNof%0same order asE+�), and $C_n$ tends to have many more prime factorE�@an $n$. These remarks can be turned into heuristics that support �4conjecture (se�(ction \ref{})b.)incorpor%;Pstatements about soluCs in co �integer%j\such Calabi-Yau surfaces!,$$ (A^2+B^2) 11 ,=3^2 \cdot 5 p(X^2-5Y^2)^2, $$ which become!!,e ``One Equa�!T Rule!2m All''1�4$\Pi_2$-theoryp$\Q$ (like Martin Davis's for%� $\Sigma_167Z$; bu!^ at e{5�ally be!�dG�wrong way, cf.\ \cite{Shanks2}). Fin6, we usA�,e periodicit�Delliptic divisibilsequen![to prove!�S.�,densversion}IP{\sl if $\{ B_\ast \}eA0vi associat�|o $(2,-4)$ on $y^2=x^3+7x^2+2x$,Pn A� $B_{s^e}$%\$s$ a I8hnumber $=\pm 3$ mod 8 has a �'$itive} oddmdd!0or from $R_5$i`!�L$D=\{5,13,29,41,53\} � set�s \mbox{]e} : B_ |w^v} R_D%91$Dirichlet !p!�at le!\`$95.5 \% $.} \vv {\bf Ri�T.} (i) Beltjukov studi!_hE Q�((\Z,+,|)$ (IABel})�VLipshitzLip2},MhLip. 1})�f%JUOtru�+e��Hform $({\mathcal O} �%k {O}$0 ringa]� in a1�$field $K$,�blud-8(independently)FusualD)�obtai��0exact resultsAy���i=ori�n��Pun)decidable. He show�8��iculaa�,at multiplic�Lis defin:�!�^+6��a 5?%��Oit�X�A�(diophantineA�el�8$\Z$, preciselye�.p$%�infinit!�1units��us,3Ke�no��l���Tor an imaginary quadra�Jm{)�ŞADXan abelian variety with> by 6�u� imit)E)��9vU�E:A$ woulda%d�a1]_1^+$-%{i���\Z$!���h��AZega� answerIXHilbert's Tenth Problem w \Q$. Thi�H0already occur "AI�Jacob!Lof a genus two curve) real::�giv�A� mple��i�Stoll}%) J$$ uEJ6�o:�sIDcoA#x:G�9unpI�a�.�J(ii) I�e other dir��, Poonen� :2003�how!w� re exis� �'S$���F�on-E��i�.4 by a2��Mulai�4Z[\frac{1}{S}]a� �(i�e�pap%�persed!�hhe first author's year 2000!�uscriptsmn8Cornelisseneds}��� e topi=D v) N� %g tA(uollowA )a patha�relevan��M:� sh divpoly}-v exa} (6z� ), 2!y cond�� weak } (( ) $R$- ity9SC} (ma� �)�4 �A�}`�"' (discus4 A�/I�)A�%�{\L �$Acknowledg2 .��It�La p � toA3Dnk Thanases Pheidaz �� help��6� 6 y" qui!Zhow)�C ed !vN� I�ermh )]Auni��al� ntifiR used, or*qu  chang�Wb usApo .�EoeA�i �ng�.� �>� . To1ltdA�)�L "� �ne� dO�< conv!�on:A-orA! $\Fr� the ��MB=�� ,\times,0,1,=tr $(\Q,+> will!�writtenAJ6�normal �: � for0x^{(1)}_1 \do�G:{f_1} \E�s y>.:{e.�s .KNZc {f_N6c�c{e.5 F(Ńx},�Cy}) = 09� $e_i>0� i=1,�,N-1$��$f ! $i=2$$;a�re $Fe5a ��noma�in� -vari/s bf x}=� -U L1e%M,)�.%%)� $�yT5{ T%sTD.%%5)$. W� ll � A� %0a $((f_1,e_1) k((f_N,e_N))$��ulaGF�rDErE��� nex} . NoeL~ wis�on n ``p�''l-�Aљs� mj��a -freip�4�l�boolea�mb� � tomic �<{\ae}; see, e.g.a 0L}, p.\ 157),&we  >�b�I �single 2ka, viz.\��"^ %*�;s!Ssible!/ specific��� langua�don't w��toA�ow 9o�6�)/�,la�wU �+t �_ measT ``clog $ f:�e�eŸ} ($=$. )-g�.ed�2 ransEZ!� E0�sp:g��);I�is well � n%�w��Kproof0�,tenessi >�Lemma&�pE�} �!�0$R \subseteq 6bdt . AnyN+�H!�%5� $(RF�R$Qƽ���m� \n\pf�ىlog� conn� ve: $ \R8arrow, \neg, \vA�\w� $JrE-lgoi[ elimaH� ir V� ,. Replace $A.e B$�$k Al B$. Pull]��lef� r� through�P(��2 nd2� acco� gly)hta%.6�s(poevyrana�� L� ngeKur-squar)orem R�atE��$ $n \geq 0�c a sum!�four D� e� ,!�$ $x \in R$A�hP,$$x>0 \iff (�0xa,b,c,d,e,f,g,h)((e^2+f^2+g^2+h�lx+1)=a^2+b^2+c^2+d^2).$$ Fur moU� neq a n>0)A (n<0)$. Ux �� to r)� �21$P-�e�$PAf�� q�� volv!p equa�ig�  For��sZ��� � $(P=0)IV(Q=0)Im PQ=0�#E�2%^2+Q^2J� l�!�+t�E�4 !��.� \qedZ� �W .' -rmkQ} D(! oR$,���so�A��  upM�&^ ��2�` !��bl� 9�. !bex�iR= then):pQ)(PQ=1A��TQ olN b �eRB�A m�X B!unu�dy� (also�ed y�R/om2 d��auno��AX �nofu#. If no 6W��a� Y�� sent�}. A  �a, 0 truth-value,� aAX��1cas] a� �� 6�. How/we�I�6) a&Tz&n3�� � ha &�� 6�� ua%%ac � �:|w� corresponE�va\r!is�rIj� ^ A(� ^�M��&!.� } As expl�M�~duM,!do%�cAHtoo m�2���@ � h��as fewZa. nE� �� . Ad� �) 酾 5a!Lit1P otal�R�� t���< $$t(\Fr):=f_1 +�s + f_N.�A�ond.��!فlac� �" �)6�hierarch�at!�e�now5�e&�:p�� YZXA�defpis }  u�lyM~a�e (.-)��S;, \Pi�`� !�� s (!AMoCKl 17). L�J_0=� 0�nV �of��� )MM"Def�Y"� �nE�vsto "� n$ (a�.\Z!n$)�Wi��l $�� G$;a)�T�G��{n-1}.>� #) &� � anc����� %w���u] E`��nexi�)*A�6�.�9�}5�^+,\Pi^+��� s:A� & �^+)�N�"� J��I2B��%�^+>�����^+-�]"N�(%�AEj��3Sa^_1D �{ed)�*�}� I�1$ ��G� !5�.H^E*��n�O��"�"� } $c$ ($c6D� *by�8c�W := \� l\{ \begin{array}{ll} 2N-1 &�"(if } f_1e_N\ , \\$2.$�o +, -=� )3.)M,=e_N=0. \end { \� �� at"�a02�is��n�#�� ing:�;*L F}i�1�{n+1}-eH_{n}$!vJ/ah,;�# n $c*�"F})=nu� a:ta�p�� mui\.h 0^+$; equivalen�%�i��;by2X.6_ a�n-� �"]ry��{2!"���6��) ,[!��a.L$�\2nnI�PiE.C�OBy ab�R!�$syntax/sem�cs dif��K���on*� �m a�%Fr]_n!g�&-s.�� /un�l ����in 5AW. �� ���$l-davis} \�%A>% bf N%&�)[*� biA^�N}�(r� ai�N}$Ain�"�( t�(:73 (p. 236-237)�4� i�!�1�66�n��I�� f_1=,=f_N=1�ZF�E+co_% BF hold / method of.K stoK $ analogousAg� �< �J ="�eIqhABC-hyp.! sis,�a or}A�\4(� I�cours"� '�mhEyemY�l� �e nr"� ��a [: 6}a�8*�$er!�(%be{A@`a$�Ֆa� R�uQquiteu�tA` a =(up��=~ I{�1u� ):ore�b a��-� .>;� !�f�*an�( 1 a. Eo : $(a=b) � c=d)* a�%�>� &N.�reducea�A"/�c1i�#.a,%�or�(o�O*� $ why�(li�t.AQpracticLE�of�[e!� �!^*>"�*Hť��by usfe 'v�IQw ll�ndo so2��aAN2�!�.�`,disjoint set� tt(� X,Y)�(X5�&�(G}(Y)!�2�_,@r>X)nj '�$U(� :8 2 q��s!�a_�O�� $phi(A,B,K)2� ),@ $X,Y,Z)(P_{/}^{}�%O$B = 2+ABK0/Z^2 -X AY^2�ni $N�+�wBveZ �H {R}(N)$ r E eqnH *} 6( & : &� 1�A,B   [ \ �_q�\ 5�M)(#M) *W;4M+1)) \ ] \\ &s &}&N) p} { � \no0nt wA�Z�.y���&x+}���i� � a:Z:�A -julia-nf�� 5�=D� �O�;r 4� 0 $((5,4),(3,1*S��%�T=8� =3&P.�W&;0&� i A�շ�:� TF,wd2{2imp�!%�get $y� A,B)I _ g�neg9�AveeU �U>NA#\} .$$�p��"�Z� �2}I� u�M)(u�6:��Now plug�;�0,3&5 $�\ast)$ J� auN�9�5� ,s M,X',Y',Z'OX'' )�X' ')_aȍz0����!��MZ,Z'}=0q� =M+1 !"'Ez 'N %&' K ]B�I���rM��'# y��a)&�4s����%6��J (� i�l).aQv� Aa� ��a� bot�' �� � ab�.�,�ce+ sjun7��i@tse|fb%ari�׉� f������w $X'�,!�$, $YY'' Z ''$.��rr�.t� V�r�(D�j)�.el*� diom(| Our��*al)�q�4� :���t &�ap��0D'&84s}} AFbut�%&-M � a � 0Z$ "/%�7 '�/"� ��%1 �!�>or8.V!l�,� jus�2�%terpreu�!� We yQbs�*d ^)^����-�ef-.��(M,L,��� tri�0Es�'/b$MIZ�(�2 collD �L=\{r_iN6of-� cartesO1L9J(ed ``rel�d9orQ"ons�* s'')��3�Sanc� 93)�L$ M$ (J� l le  .Eee� {�( f $(N,L'=��s_i \}%'� ag/< )&,�is saiG� �)� $(D,\iotaEn $N$} i8:D!.) : M[aD$ betwe�5�E~r&-m $D�/s2,:u $N^d$ ;"N$, �H��cl�)��(r_A��ppr�9(>b \- >���ll $dc3$dimen!%�A�%4. By sl _&^� ) � �$��b�#[s.}\ cex1}FS8A o�Q ��bnde�i�)L��) � L=(�+,�)�A� dard"K!7rings�����9>�Vu/_3,0$'',``$1$''� ͤy= a���8%�{�A��$i�6countEq>�0D2Yu�2� ER E�\Z:���%�d�6��.E�add���m6�7�>�s $D_�!�D_)�e&$\Q^3I *�!:N.L�tAc2$D=�)Z�[�=Y:idwlea�� one-U�96� ; $G��af�4lgebraic groupً%!n embedZ;C=spa��meq��!�$d$F�%�$(G(\Q),+_G��A�Q�`� $% = �8R ts-I6� L�: GA<(�}lac�16�). $"L!`u(2h�_mpLń db c2/% ���EN57EG.�uaus,�>I6J�8�L��QS$�e)� �V1,�` t(S)�q `�-c���!� �M �� ���n=�$ Pn=>$:We sa!K6 ��6�~D)e/ # ��ѡ�A-��>)$ O7sf $t(D� if $!x�at(e5(D)), �n)� \l! ,$$ a` similarly�!>)�k &�oJ "".��9lp�*�IYŅ�_��N$��=0,zf�6)�7l9])�&up�6bou�A�A�EA � >I8et< !�"�" by s�#al��~IihavA��6qO�@ref� �g9,� seems Bh��"l@eba  E;cannot}��#a 1 �: F&��!Ρ��R�)� zero5ӥI��ATC%L�,� da<of!�� ͇)[sq_? q����"~e�SdA,��ZI&a)��@<.edek<� �; contradicţ&::�Mazur�| ECZwVOT�/>Id���~%2�͞'��aL D"���M$ U: ruN%�)e7AC"�5&:+:*rB4N$. GivW> q� ��+�s ���@r$*�I�$x�,!�$N>-A`?D e VO� $r)�x!�\ FX $r$.� � g��"jd�&b� �({\Fro4^] ��!б�-%�} C&�;1�)6(A"� x_1)"'$x_2)(x_1^2  += �-!l\Z$. Sup$8� is  �Z��  $D2�1^2 G ORBTi�&LYA3toFj (.)f�y_1^12�y_22�&Du_1 u_2 v_1 v_2)[(<,2)I�2^C  2n\ �*1*1^2L6 u_1,u_ Z)�Q "� (�,20,v_1,�vR8\\� 2? 7>(0 in @ +)]]F5=!��:now"Tm_ m��rshipaX$D,S�� �qkir�-�;�Z� s. �6�tr,]a�``dummy��a��$$u_i,v_i$ ��(unravel nes�R�3e�� �� 6> uVIf� applu " p�$> pl&6Isrem�j �5"I���^ keepA�ck �W9 "� �e���.��ask<!63�9�3es-2G�8���i!M"���:Z=Pro)o� �- x�� !�f)�ԅIQI.assumcDH:Z$ 8L8!�!BA_ ( S>S�( _{?+}i y"�s&�L thir�lumn lis5e9�� i�@t4uEN)@� �Lio��u$\p -�6�y~4!T � indAH� d�Cc �1top row!�A�$wcommand{\|0stretch}{1.2}�b�(c�zr}�@dj�$\\ \hline *�'� �E$'+ �B}+}$�HC!�E �(!=\; �5 x!2n+s-M�^0�C2�(V2?�1� cM� :FL=A��S  clasU�q y\H . B{"2N Q7Fu*7lC=�D}! 1io e\���0 ) +d� )\;� } ����A�D�C(of non-trivz>book-��ing� �j.ing"?:�:\Delt�nI^=I X+%� cup %� ��W� �5es��ish:efact,)'0b� �pl�P�=��Bl�g'h *���.1� _��eo�,�:�& +�0��0��Pi�')��1S-"|*8{ \Fr_{2}, ..., q}�%��M���9<"\ *� each �i"i� a q�F����M 9�m.�+,i / $m\DK�nu�))� !B>�a��+�B>&=i.e., E>m� PA *&x��e9x�Da�}&�$y y_{mAN}) (\G�(2<n}$1 L y_{fa��($\G<E��.�) $m=mie�m_��e�$f=a�;�&!)i"���%��$"%� !�-�zx,(BAIN�:R�kHtoHU�2�fb�!��[�A }!�q}� B�"c8jAGulaa&G=/bF�a A�1� , h/A� ӕ�A�" 30 have � )=f+t(\G�1nd Ib���IAiI?+��j=� k}.\j}��Z���"j� ��� extr.�F�(ich�E����J�/o�Ne w )2{�/!7��2�< ffec���[Zcer8�2�&f� �S�%n�a~Lbyw ~ ��aY>�v^UzA�I��j6��DI�(x�B�jS dm+zd &u� =�i�%)� lemm:)'� 8� ofJ� �.p, jump!Gdo�Fy 2p A/&� �M�iqN!�r|)�two low+QlevelF ): � (a)�=:�uS� ^+_s @�%�as)7,�7$:�F>�[L#�# �%g�&B�U��2�0$\Lambda=\{1,� \ell�[�REn�"b�0$I,J\� B ^{3}� natu��9s $s,r� l>�*��� E��r (\�CLD�"x n ��Mu\uu�� � � })$$�,1}=A�-Vn n} \big�,_{\bar{irI}(\uu�}g}, 2. 3}})��+�?�>RjRJRj.RjQ _j_6R- �r. N0).�)AQ �$ �=(�,�83��� " j}=(�,� "�4O$-�7 nd bold�`"` N &� ran H0*^d$E��W�+ $$>*�| �x�x$$�.�A�"1&F ќ!L �"h "���s�D tsel! 362aJnD5� �Z6A$�eB�#��O. �* �� X,�jA:�;R�)�# �(�4 \\ k*\F�[ ua+�� .M].�+$�!d r�7I=& x_�x_n)\G �=�k&�-\ 5H$\G+n�t�T&\: � ��\q��1\]cmܕ�  �1G 3�")),a"9�_A#m \/mBv� u^& LcUN.b& ��E8 & m})X d^�%�?e:S&L5���S� n�\&�  m}) [!���N� A���21�(( K%>,) \6d � }��-" ?))]�@�Rf>��6 �1 \ -%1}\not%\�=} a8�X=�sub�� �ѱ_ $\y ��&()il�C Axe*b,f&�"y�6� 2q��&��,2�n G��_�E""($n+1$� n)) U%2>% odd)�&ts �!5��� e+1��`:�>#��C1FFr�5[+�[F."� � )=dmdG)i�.#w[O�&ite�A�;B�)G�T �T2���[��&��� ,--24J htMMZarR &j /��$n=�;�(b) ANP Pi_s��aF�I�0.M�Me }�6.�� n (a�q�a�w �w �w �w "w s*��fs >/a*.t��� Fr i;�]B�  b � l) \G��s ��nEu A8*Ry�>+$J J�IA*� I��4F�) �) �) j) \H ��-;�0.f!-:e�j8 �+>$ p�%�*�%__^.^��-�)�&\\�J� �� F��&i � � f�"M yM�y_m)(\G(.. �%C �m���$\G2� � F-x�Qe�p Rp �S D :R S m�l vl >g ���k �k k V\��2�]a�Bs .�Q.m�5 m#�Y� (92� !BvB� �"^1��T7| Vk x� 1%�:\; 2� �LŞ6� �.�8M?t easi3�!p�S et�� +sR#+gN%=>: $1�1 !-.�$B�m�O -2�3O 6sB i"wc�RE .&YB�56e/R��'v21e��n� � _: ly alter � ^6.�;�7nL $(D'�*�4i�`>'�� ::.m�0xe�=�-"\sue^�VCorollar�T�(undecQ�(!��(v<,6 ��*Nob � $D�F2.2B (w� )&a,e�ta�(.I5/�_#� t"R+)!1�!{ e�Q3}6quQ!R!*�qIs�DMT, Matijasevich, Putnam��H (*~u5IMsvrd3�16�!92�,& �=o�6�$ o2&�OPR-s�&nce*V e5An}% .b$�Aa�ta*  L%5R ^+_2,A2� ore _3^+%in��Is<",��:���x.�36n ��o�,� "�%.m��\1 \*WjPr[`�son&RoVKm}q�jW:�WE6rpy#(�:}&� Ea�4oD67b3nk�Z5� T:�B�; , $Ex3=�< oplunYmatYuTw"YA3*�KTx0ca�`�D$\tau� P( po�Kof"�3 �.�AE$. Cho�&�ma"�t$f(x,y���)B1�'=7!�1diodefE�C8,\textup{(i)}�LaEcooaRz$m$�&er� � T_{r�}=!�"e P \nle�<{ nr 'h0nV> .�9� ��"d2 $D_r:=\{ �,1pH�s���:)){ �?�FH"L%-0}:@{2Esymbo�c% neutlelj$��!���+Qp���l0-���$(D_rɔi��7ree2�=.B�9.C��F0)�>0 n)=(x(n%yrP),y  P),1X<F.�>_r$ (``E,z)Y�H�b]press&�8ɇ�x6�!�*+�4 s ``�@�v``Rdq�@�/m�}.U vi�M=T2j�y� Qml;'t�zo)�fjh&%�T*�)��7<.}e5*+* $P=N"N4$y A�R �@>�4S)(R=NmL>}�c!!&�!��``�fin Q%!#:�1t%>�4>K$r$  ;fix��~ $N,r�>s too"TA �:&3H9� . �S�ma�M6��.QBs�%x-ki�=�vto�|��Ie\�~�3�ply� b�6�Jn"n3Iq{]#�>Q�vten�!��n.�eHchiiy�eNyll �:e� hoic2�: (ej,&;IV��%/OWt<�Q wo"�:��7}r�F o(ite"�j��z��2�e �aF];&Hw���vI|�W�� che�D"�s mR=P, �m.I fe�$�r$m��BW �YA�nodd''V� s  bel"MxɌEɌF�v�{�42~@�"k2f��P D-�=� oӄ��.F�d@��i&{ ert� D D%er� !F denolo�s!920f���8$PF� Wettr�3��y$E$: �$8}$= x^3 + axE}b x + c*r k$5��z�eF nP =pn, y_n�/t_( �z,a_n}{B_n^2}, c3_� �&a_n,B_nM�cpaiMcMKm�&A)( 824 ��Ysig9G �'y�INNo�LE6F9&"(a,b)�>!�tR[y gre� * mmonI)�Y�a � b$ (�#��� doesbp�* eo�Wx�Z�:N fg�&� G f $v��Yh�/!�$v(B_n)�spU ��C, %{tnt 1 + v(t).$> �n܃ R_wkm|a(~$B_m$2desn�Z�� Bbst$�ri$(B_mAK0)=B_{(m,n)}.$*2��f� �Hv�Vv_2���6im"�vloo�I��Pal�� law2.�E#@ Q}_p� *L(Cheon:98} - �)i�=��akCj�uE:"�z B� � below* ����;%�s;^ regard\F�p fact����in glob�?ini�� not,� l���he coe�ien@+��� ral;�,v=v_pu\hat{E}a�C_5Iv � f $E�3iz� e ke�~${G�mod��$p)�n72(M t$(p\Z) : P=�4mapsto z(P):=-�� x}{y u $somorphism.u v(z)0 1}{2} v(x?2T+� em IV.6.4�E8\�C@SilvermanAEC} say�Br>1/(p-at� 1log4gE} n .�1T (p^r�\c!� �A&�a�Ial��, $ {<1$ unE$p�Hs�pi�Ar�!3)>���E�=Z $r=v F�(� =@D��� larg��� �er~Gval��" !�((nP))=v(n)+ea� �?Avclaim y$41�a_n B���� ��� cśrA�M�� ��W ke� �� q� uyne2 Ov_2) =1$."�  x)<0� e du:e�!m�1L(s��CU�4} $y 01-2bx^{-2}-8c ,3}+(b^2-4ac)4}}{1+a 1}+ ,+ +}� BUfac�� !Rp�A5��I����! $v(kD=a/-4FG&�"n"A$tE�I�7�.�(#^�-] �K$3 then,!��/q`0[�lxU-Jt'C5 odd%)o�$"3 jS(i)��^���R�A�|1^٫2 d �$d=ž&� �e� $x,y2xm+yn=dI9n ��9b���{x�(@um) 6b!� (y(n6(aZ`u$ $dP=xmP+y9���ng�%f�Y3N� ~t��1_A c:-2�i^U�Q!�� 6�) -�9a��b,m��ix20E}��.$��&Aq�su:j&� A�d-� , so)=2;r$[}6��"]As�f&p��&�K���Q&F�)�N� $`eo>faW!L��W* �%�"�1 f���awo ; aVOuY�t� ���,�\��(�L 1}{4� 7}{8"� "��+x��3��-�|� _2(B_2�_% �B&<2)�O� Hrbitr��.��(^Mgo �b�U�W - of (�rram�ed)����/ I��ofEi�e��?ra�J�*� � "�uY#phi+ \ps omega�V�)�60 III.3.7�"WR� ?Ayad:92Lk%�g�<��&eq �_ �� �b8Y�ed!ae�e� �:S�}��,Morgan Ward �i :48�>�5re ht�l�(�TZ tricd speao gnecess!��y� '�Z�ZF�)al�� paper)� 8*��be�L����Z<) ted�,��&Z^aoWaR�lInsteadY:B�BZ!Substitu� principl�{��k f��C}[W0�$z"р,x_r,y_r,z_r]� homoAo�U� w.r.t.\E:wޕ4s wt$(x_i)=2i^' y�;z3&,0/E�1,Eg1,M�1$�r rr)=0.$V �� �8 oy"���iem��_�F )��y}%yw E7$(a_1,B_1,c� a_r,B_r,c,$�T�?�;��-$$a_i,B_i,c�=�Q��t�ag�� o�j�\x sswmF6?~a k�de1�izIn.�! *&$x_J  Mohaa�� e��La�d��2��W.�9(bottoma; page 306)' !�$nA}a4-$x_n =v b_1^{2�dN 2(({n^2-1�):6>3 >�}@3 R@3}!�*nuC�K=YN!��yrUj́� eAS };5��`p�cel�K!f Ib��qis0Mre� %�;eQ!o*0>6($4V:&$�: 6f4�wc e�3�|$pS �e�>0$��Έ� *>.y^e]l a_n=%�Ee�n,V !ۅ �c0�1�&� � ul" M Now�Gb����n,El a&  two-��a. B&�Rn?�h�.%�$(0�x BC���v�Va2�e �" ��+bx�!>�/D���Y Moh � )in2p��Fl,�3�as92>^b�;!<2<( C3l�V�=�!$))Neinj]i n1��t��}�B� =C ft(� \a� {{A}#�{n}}\Gr'� A_n{C.#^3% $$�n�" $ M,BLm~CA�(�d.v�$(A��i�(?, w ��I."Thenu$A2��u!nO��*� �͈.< "0-��b$���cB�Nxa Ǚ2;Aj4��Hb$%����)C_%;>aWeA�eh{2n�m${2A_nB_nC_�v&�Bt$A!�1$BA$.2I�=2Q�$QH I��2 �j_ڂ�-b) so�!r,?F� � �+q�c0�t $nugw� vG�x�!Uy�);<] ��Gel&G9� < �� o$�x�!�E$� �$cAV^2 =A�(Eq ^4+a 2 E� � 4),$! �5|:�e���qe>f�s \�i ��-Iz jt,iV�gcu$C4 Q������A��A%AV�q�#c�;v((a,%)PM�w�%eF���uH\$v&\ 5 s�@etsT�Zgvi�$ e id/ t����O&� sA�sI�2� 1 �y��UdA�A��q:�k "���Ss!q�*�%�}Ce $\ �xe� occa�۟yO�;F_� �� �plaQEG�� e-z{�"��  (sf]%u�',o!���nk� %� issua�ym�exceptpi��wis��Ip#�� ���N w,K�U7ud�b#vi"��*�jA��!� { A_5o�E� \{ Cƒ �s�i%Nd.^bIi�� $m$- Fn�+'��%�# �-8n��{j odd}"���NT6���j#/ �@ik\{X��(o6�;Lj$X�[��($X_{nta� s so�gs��WH!ll))6i u,a� prev �FX ��k5��!.ocj#ij(E,P)&D'T�AYe�7�.�'H^�M�3���YbV &K %� A� �)�(IJ, �,)dr�A�� �G� , L�"a^2-4b$����::.�A� m:v�ar�a\Gi)}.H%��2�b�kQR�tQ)v� �AT�A_�t)$ �a @_2�6!Zn�Mt ��] ӦI���Xe���w$$))$�la�O�')��-"Vf ReeLe�wZ  `�of�]esc!v.02�, X.4.9)(�A���;ap:�Ad=U'�)E2�E \ (�xnw�� Y^2}{X^PT� Y(ۦn�4b) � �M y^S�-2J (Il)Q (i)"%S$Q=� maps�1$ ��!$Q�q� x(Q')= �y(Q)}{x"� $��)�-o A'�B� � # A��E?Pp�!�*: (�>/ �6& ��i�E�6 v'!=}�fg}, (2D l�t!� ``$B'$''-��$\��WeWs:�',-T(P),!�i)m uVw���� �M�nf�� �)eigex�E�"=0�*� ��A��re.i�^w5A��i� �Q�0-�!� = 2!�� � a�&�  "�'z�.h fg})F�'_#=v(W�t):1�$$��+v(g �= �+�#�qno{\�y��rm{{\rm�u��.1)}}xV��� I�RwJ%d�E����l� q'5_%G�5 hand.,$Rt� -2Aj�;B &>&3:yJ!{� � ��$. :h � ���� "� � o�tn}�{2;+$tn,2n)a� B_{n(t,2)"d �a&'q%T�%+de  ; �KM!d ���; Bw��exj�d  a%�ӎ%aE"���  = ���aa imag&0  �`'�L.���%S�u�oA"i�A'� ��� i)� ��!c��Pe�.ofa�� ,� �agR�p~m��xmZ� B"� H nRick �IA\{�y��%�\.!  "dZ� sŇ�#� @aM5> s%!��eۮP � [2](z Z}/d�4:l$t�' tnP=Z.ANR JWfa�4� elliM��,$E��x�¬12w�11x=x�1)��F�\�%-(P=(1/4,15/8-7i���r�0�; Z/2 �D  $, �rv� (-1�v��coms-oAaW*f�ަ�6�_G(���!o�.�8M+%S%{\footh ize � &s�a�_{lcl} $At& =<� $1$ N<$A_2$5�"7319  269 !4!65" 1931m` $A_5!($ 230425069.A6  $\M!qa{�i$8\463 575913�7L 647873811 �(19522768049�8.$ 132) 66374 3560(65914315354�!>N@1f� "��R� �1z2 �B.�=2^213*=�.*(25)�p=�.3^3 �#-� 5w 53 Yc$B9�2�5q6571S109-v�V�2x��3�Us.���66�2529].J@3�2�14886s 184598671% �UD6^41A^G5[v11~�=p'6V W16011� 5609�Β$CU�$ �5IoCY�$- �V�35�5�:�\\x]�-5R� 0�M2o�l5UT-<30UW 174,37951�]�2`v���05UR11312A(71868534494a��C$CY�$-.b ��35148 760Q�11748828143360�04633335112945�CY�$ 530W087�g18309� 707490439.`9239792127103441679838048i�6��(vv *8,0although $b=1(���U E e��, ) =10��� ���reKfso��� :�%w�K&I*-�o� $ uponHBi��Y or 5� Ra$v_5(C_5t 1)+ 5? �* �s illu-3�1laB(�)� �-*kmene,�y��& ap���8e,YW�b�<�e�| ter �� c/^Whav\,6�kaveragK"�themsel'-9t�< mi��s@�xc@ ar�y�$k!�9� "�*a &ρ!#e��""$k$F�.6?tn'="�� ``!��''q,G[AMe�� .n earli%o(l& AAnt Observ�&%rubin )l�#��Avn �4A�� E �= ��1u� 5."�2� it{Pd�} (A$�!sh �Karl R�).aeS l�  �imҌth $l|�1%$nP.mod $l�%"<�is� , $P "� $Q=(n+1)/��P"� Q2�z!�La+�@$^2-8x+11)(6 7 J�/�U�>%A�=Edi���$nt $5����7+�#a&1x�&�t�5-( ;%V2!\hf�<$\Box�4�OI5.a z��A�ir a�viQ'A18Ϲ2M1� inerO$\Q(\*5})��'no� �1o#A�� � ing{"�Cd�>�)7% � @H�}P9edsmod�-:�,Pri�{���a9?!} 2�Ipn (QIV�. 4R"A4M{of�5�8sa�>*e�-*� �u��n?�i2)�%(�@�/$G�!` is:�""+Nn&�ev�R)[v(X_�i�}3i�� G&m|�XNn/mO�,�m��I6R?g �!l��$AkH61 " 7&�@f��  V"2(g3a�%�)K�)�0&��"�r�*�h3�z $;�_m :�)�:�Z3}ex���@�km%v%]a�=@�}�m�B�$FvKp��s* $v( B# x�A"� !r| !�+". R>d� F�{A$Y m;Ar�1���v��AAdl� B=?y"m� I�Aj)�!��i)v*A.� N/�u���QtA>���>�)�A|�:�� 2o09��q$6�3D.pre�u�B��D�:}\m�J{D}_R|:�.� -2yvXB#a���+ '5m����6�u< v(y���QV�"�\)�塜�%^�``5�yA>x�"� hal���� A f $y� �%"��``pol�y% Rxos�El�@y�A:X�5+CB;tr s<�#$point mayb� �Ew �hE 2 �"�Pay��a�x)<)E�SrN�d%�!d� �Cfu�2:%�9� � �#it�Ot�3Y � :{H})�&�`} ��RE�X��Gsui@.o*�.*�z-I!,!� ,pMs?B'%�~9�-_p$e�e�( _0(\ &QF�[rM����sin�3e���� �0�? H/RcZd�yG���on�;ly �� 1(actuo(+a8)OT of Kodair�fN\'eruo^ �����-niahsp��4 � A�½�'�1DK�&ex���qA2��E$�A �72�# VII.6.1�&�?N>������Sa�n�ԥ;���fE EJ�6��T.� <f� IQ�=N �*�&s`E� C_NA#pm y_Nu7N��/Z#B_N1$A_N�/^2�!�W.!�?e� ~ou��su� ���8����: � ��hF�9M�!bf�!ef|2}} C�@��� (C_N�q t�� Nn 6 *3(�#6!M!_����2Q.m�3 uD � N^2/Ai0$�iw{>JC r�4�bȫ�7��|!)e�� >�$�*: A`� jP�#AE \medskip :�$*�f�&\"�(� �%eMz� �B(n+m)*7 '1)*� 9�j C_��E�C��$Z��8E�V��No �2`,] ��m+� !� � u:T P� >�"z3R4�veK$v:��' Ó���.(� y%� �I C_m)%�E< .�,zDA�&p%U>AoBy:�2 �E#�n��>�B�*!A��1�$��CfaLef_�I`"V&�Y %**A�&�;a6��:JAC��$RKe�B�f%m\!m-�XY-Qnd)�Ta���m*� 2!>6U>FR > 0��\l�QOn:v*A�).XIRP6��72 �?N7�>so to�:�aw�"4�CfE"Lc9u� %nE�EV)I�$i�*�(_E `�! ;A6!�L.F�&�$&!��� :a5$v�H�� � �N��=|m��m�b�& (?���e Y!. By�����8 n"V2�m��{2m}}{2q}. �r�(�e3�(�Sho���y,��� ���B_m�'2| !G\'�*�$VLݧ)U�eY( s���H$$  E=:�)Hm})>v(�;&lzy)�4�Z)�^�%i�>$$i|m, \ i<��--$ �nd�_\{:�EA�B9, ? ba�iՆ�- 3$i}2E<6)3)�u �6+�)Bi%�2A_G�!5!C$$ " M�/ߜ.�.�'��v�  (��a�U��e8} AI�. But-q*.2),.��&4  FS<S41� _I��e-�!��d!�%�v -sos 6�5)-�{%u:6i-�K�M}6�H �in�B-nB�=1�i� !m%�B_{� m}{i�!� =] 13 � !�"Nlaw��2�9z9"�1E�(>1��63�D^*ax����=(,E ( �!��,� m/i = 2^l "k�0k$) ϭd��["�3reaso�2\^{l+1} a'� " 8 .�!+�d.��%N�G -� a����TiT!�mEh�X=�>/|��5o�I�!\� IU~ \$@ �:)�m\re�Xa% had ;L!n(u2m|2n"�8 �>M�U� 2Itx"�noss�t}�m�0�4F� p�be &�8e:�2� )���!03��\2: becaF%G�Wܜf:l�: V�;``�;��6'I�M�Gs��}\I���)��6wrE \"q , n"�U�<5J� m[way�,"$ ev�M�\:]��/at�c =D�R�H, :F;>[ f`TP}� ��>�>j m`�/%�)  s  sot�� e6)-TX*�5�ZK�:robp�:0�">IP��}, es=�2 ��PT stays!�xS�5No�P obsc]I.��Jm��*h!ilMX#f�xerdx6!Mori#�l� |�emp8B�*h�:�B$ �с!�B� �f <g� m� t ��%i�2b57�.6J :�s;9�e��n0:S, quot-�28``0}� fw'')���� s� {2^a p^b}� a,b$&� "��ppy�}�]�.+ >I2E�*� � end �Rr&�"�o�%�at��a�AI_%>*) Set $a=�Mm`�4p�[!�&c'��v_p(m)=b~ {I>��  �?=-�! baZ'{2�"/m/ 5�od��� � 6[!Q�w�'uA{��$a�z_N�pas � �$m:`�4^�{ |�j ��i!!�CA�"d6��  ��ow� �Y�*��a��zs2��;N�CĪN�GCA��a�q�`:��qRa)}A9Nk$\2� �����ʲ;���b��PV�"�H&�!�E�B�.�;*-Eck�R�iY�A=&L��E�.�aŸ!M;�Z96 is (����>o!� ^�_B�thmAEA� e](��GCq�D(mj,|��r��g\Q&]?4\ I�b�� �iZ��T�d �!Z},�]ervuIpa=�.O���(_1t�in z�e\��i�>� �? (($C$)-u $Zsigmondy'�ne�).u\�<"<!M��Sfn;r&�'�/ݥll � ">� !�A"n.Gx?2 A}At!�P� qv"�?�5 !r87"Q\2y >(� J{��E� s $j$-inv��v*j\ j=1728b� $ABCs�nj �6�2�A]:��+:�) �.�e8P�m�� cruc�&�e is SiegelY�C!j�BBW j@IX 3.3�fli�r,��+"H�bagnit%!3VdDnT,�&�,� ih1�ua*r J�,@�@S�]A�&NWief},�9E} 7|�� �\x��%�A_*�&;�QB �riaU�4 H�s8l&,�S�-=0 � .�� or6`m; :kEb��b7�1h�hat��DF�� g,}r/�b~�6�k�aW�adis�� �s�:%�a�$d��F=q?\ | \�nG\_{ d a� W} A<n}{d}�'i+ �8T�)Za!�~s:b{�( \log |A_n|k ng�\�o(� u |.$$�`m"n,!�canon�C]�A�CA�.��M�/� $Vg���B�/C$)^2 m + O(�T\Tcz� B� (``$� d $�/ �<jE��:'')A�YE�# ($\varepsiloʒ $(1-)n��59n|&�(8${\displaystyle��\l.s_=sf��dS8$< \zeta(2)T�&(r�D:M?a=$-� $),}�w.Maf93insOgoqvse 9��*!�6Cuú%*2.� -� ) m ��(n)-�_��e ems�y�*QI�-~eY:� _ 8y�  aO�\�C` �)! sa�.��T$p|"�*1T"Z"�����JaV�e  ��Wb� A�*� �+ n/ eA*). Ru� ro86�� is �d p�s� anJ�A��#�ue2w�a�d:=n/m�77>32����E .�18> tmkwB%s7�Pp|I�n}{kIKi<�s�� d:=pZ��_p,Fd}})+1��C���$�t�쥋 �6=�ja��cɆ"�:�Dm�?%��3�! P o�U!�"U@er�e�YU�p�:�p}&� _{p(5m�abcre don� \�in6�mZ�7Rx �t"�s "YdJ8bdB. an�F&/Zis&[%[A�Eao B%8�&�a!-�0�g13R��ak a.�*�6- 2�&0 {>W%L't+nj8��d��, �f� �4fu �� *� 6=o&6A a����u�"�/5�% 9 T�|k*5���~ x=x_0t��i���,-$�Ym6(x_uv��$a�s�%t�+_1�EBn>((e�u�'xuA�w����!��b+�*���I; �:04})�T a �-s�(t��d2W F^F\QM"i1�&;d� �)��e��a��oph^�n�#\S��_1.�6�.�_{R_d}�y�;���� "�$*w6>4�t�~ invo�?�K�WYg��>d�*� ��bA��= Pofq�Px in i�xur#nEttemp9��J�� �6��5�8Co&�Y�@ ive:6-�=8���E�̗ *:������7�pV�vt��ie l�re. }��op%i�KaAnHf6v s+�A�4���'� #} alys.���o���/�f&"��%��Q��s��allY� '>�6C�ee&� 6��NU�AK� set�� p� �zuQ�dg,�9�;Ea� {5�emu= )3P.p$v$a�ly splu �ycyclichAgdeEe$qll*� ��1eoY�c�4v5��[��ҳ (Z}[T^{-1}]$!B�AT� A" ��06a)4��%��XQd(Shlapentokh�B}, 4.4.6�[ &� �2��dir��9��4ġo�7� unda�asB&�@%��X$R_D ��bigcup:zD} R_{d�~�6�DILmI#2NE.��5����Jva�Ւ highJ"�$�r!��.�B�8�-Zf�,P1� auto��� ",���u�fN�{\a\?V!&� � FO� AO#,�J!�,"�l?Z�A����D$ \M����8� !�$�_6�!�K5�5� i^ +e.xe��m um $LebN��eor $d \in D$, and this complement has Dirichlet density $1/|L|=1/2^{|D|}$ (by Chebotarev's or weaker d 5�^theorems), which can be made arbitrary small $\neq 0$ by increasing $|D|$. \qed \vv Based on ��information, we change our conjecture to the following,�< plausibility of � will�\discussed in another sec k);at/u*@here as input for� mainq! . �@\paragraph {\bf C�X.} \label{SC} \ {\sl Th�� exist: (a) an elliptic curve over $\Q$, such that $E$%�(Weierstrass��m $y^2=x^3+ax^2+bx$ (in particular, a r%c�al 2-torsion point) with $b$ squarefree; (b) a $ $P$!`@infinite order on�@associat!�dd divi5�dsequence $\{C_\ast\}$; (cb Sset $Dgquadra! !� riminants. \{ Jl \}$ is (weakly) $R_D$-odd-p:tiv!� -� As beforeEm get: >�TI�9�thm!�%�Assume=� \ref!�.9,n $(\Z,+,|)$%�Ha diophantine modelA�$\Q$.e}�\vv \M�ing{De!!,ng multiplic%�?e}Qqx}Z�Lemma.}\)lemdiv} �TE�E�@s a $\Sigma_3^+$-a�ulFr$.v,\neq)$=�a/TbyZ�0, it sufficesr @e2!� : Pi_2=5 , siA� $x=m �x2x = (m+n)^2-m^2-n^2$ (translatM�asAE-�xu,v,w,s)(x+x+u+v=w \wedge u=m^2 v=n w=s s=r$)��W1\claim �[y=x�if� only $(\for��@t) (\phi (x,y,t))!�E7$e�!�M/L \begin{eqnarray*} ($ & : & x|y �x+1|y+x-1|y-D\\ & & \left(( x|t' +1|t5 6Lt-x)\Rightarrow (y+x$y-x #r# )\end� Indeed, �Eythree.�Hies imply $y=u x$ ��$u �{\bf Z}$%@$|� \leq|u+1|-1 -1� Tak!� $t=x^{2}$ �d�=u����� signy sgNs sH��< $x+1=\pm (u +1) �x--1)$. Ifa�ei�:of�$two equali� � y holds� pos�� �we�oMou=x th�M�= case � -u+1 '�$-u-1$ leade�a!tradi��. �d��dir��/,easy. Rewrima�r�� phi$ao an atomicQ� u�A�(recipe from�K��prenex}��see � 0 plac� -9.�inq7by��junġ? rodu�f(non-1C) expres�sRal8 ``$a$ does notE<de��''. We� now show  to r ��j��i�(ential stat ���n,���J Obse��Cg�$a greatest� mon�sJ f �y nS\Z$�t��4: $(g)=(a,b)$)�+�� $g|a��g|b (�$x,y)(a|xb g=x+y).�J`qno{\indent\textrm{{\rm (���.1)}}}$$Nwo �w a�!�yA>inclu!�!�ideal���0 \subseteq (g�;�A(��FnmplZ-X�`H$. Now%H!�n'.�B3\ !� (a;bw0 a� retena $$9Ng,g')(5�1Ug+g'=0a ^g>'), $$ 4 iSR_A�[A 6], aft� ubstitu� !U>�= Z�B� 42�Z� GC} ori�SC)h� A�ha�� � �\Q$��} x� $t(D)�� 1$, $c;5�2_ c y ($=\Su $ )�e8is undecidable.&� f \ Pic�DFD � oneIAm&P s��find a�� -dim� onalJ� a�-�)$�,(\Q,+,\times�@4 1s )Dthm.SA . A�o2:0�:ls� �e�)t��>�� nI��I.wM�, cf.\.�(diodefE}. �6 each! �=L actual2 i�-.,0�0!�6 �!�q�)G$ed�Q+ ^+_3"� !_a�)M��+!� universalK ntifier;7. $t(\iota( }))� �qc^� !in��d-�$D� e-m. ByI E�Q�(co�'d�}!�b1m0a3;m^+q!!�!E!Zam Q &O 6�Remark� A� trickI�� �w:� by22 sent�E�! l]  (commun� ed�fus:Pheidas)�crucial�neg��6!M���ng.ty (ant�xes ou� 61na] SE�*C i_� sameVpl��Has Julia Robinson's��%�%\f[�0logicside} On� n shif)�problemT !F,arithmetical!? %D��a�s:� giv��R$, l@{\math/N}_R$�otAje`$ { :=\{�n� @ \ : \ C_n \mbox{!�$R$&L(} \}.$$ For�s� $m$,i�e $[m]}t���a{!h$m$)�is1�leA(e�s)6�$: %$$ Y:= �lcm}(d �d|m�2�<). $$ %Although� did1 ,check detail� hI�i�def2 seem� ��,�A�.,�condi�� .�; &c \$$\D_R(y_m \sqrt{x_m}, y!�  n}) \vee Z*{m+n}>})$�!equival!(to $m~|_R~n&�%�d!�)� ~|~n� is.<F�)4 stru���_R�7�� ques% becoa�wheh m*�$R$E�K >sIs�R8|. v:RC1�al�8iDat$"����\Q&g pi2}�t Y$b i��r m4 result abAZ*+ of a�69U�4��i�!"ec.E �� sl�� l> = etho��(U��)A�v�c) �J!zmul{\ae}����5*5n:x}{ pi-a� !=C.m>A5f� AGi� is entire�nalogoue����&by&(>By �i� %_kCN"�>$(�bf Z}�� 5%M� �of2m&M �s sif� a���8ed 6��Oe��0��Abe takena�be a �1� It��ly���:z16zA]s}�6�x\ia�x^2%� %�� (F�M��ly �a�)�obtaX%��q26>� 5�i2~. S� C6�Q1Ci� )�52E:�)V��.dA is mean-�&^ of�� : $$��x}�yg9x},)$$ (�� $*! �) are6�Howev��8$ may still con%�%BB�� in��s�es be el�+ � Aqeu .� at%expens��in'A��+ isIqu� uus* y5�1aA6q �&��t� !� y�bp\q"�We�ne% �a� ����9��p-}^�Proeon� � .<�L+ (D,\io)$ �N� .��.�,*�$membership� is=�-AZ. I%� *�a؅� se��, column listae&8hierarch 5 u2ul�gio(\Fr� a fuU"�a 6$�!I�w� and{\a�,stretch}{1.2�b�center}�tabY}{l|l} Q $& $� \\ \hlin�S�${2n}^{+}$ *+1 3��{2f.��X\; (n>0) `Pi$[-qY '+2�� �(� :6�a���aVs5�1�y.�I�[aA)>��� N��class�"$ \pf6�E�etJ�U�R'qJ. \y�>�*=qKu�QqE�D��B2E U ��[�. Fur� mo�� ;A�sey� ��}  $t$-��$1Yalready2�.@ F�~�med�ly� )1�, SC &� �!B^25_( B� D� �m�&S"��6�Differ� �io&68!� O6K!�n* "� t {� one} e2� , bk� $of course �inv� gate"� !�� m� � ru\ any:d $E)� ?in%�Fw it�N.^t�L a k�of_ Zsigmondy.5 � � !� iner| '� s. I�n ms natur��look . �w \{ B� � nstead�&� , a.�o�s & � app"�to � ��:! se vari7!B_� { r� ecise way�+:h(Odd-)5 $C$-U5U'�$�#Ev�ICZ� 2I R�inF�"s&�"(0,0) g E[2] L("�n�"!��ien large heA�偢�"=�aJ:w"(x")"y"Esome $D2� 6�:b�^�]generali�$B?$!�NbN�*� c &$2!B�#!S)&�ZS� har�falsifym y�s,�" auseSe� � ] alYRa����R�� �&�I�7�O no} Y�rLo| omy�$,���"r �>��% r enE�/ E%ofR&7%. But��I�$?�/tooi u4n�` nger factv( B_n$$C in reaso� �M�J� algo�~ dV�i�o A(e�n :hcould�5�typ (e.g.,%Qe)%�B $n$X$`s occur�\$,EverestWard}U1(s& 'e�u[n�'� ve numer�ru��raI7i� heuristicr��&low� �d� ty��!�!�Y�� next�(u*� �"Hq$ arguments.��"L W�art �b&� ��:Q�C@.1) (Landau-Serre-b } 2.8)�(s M$!�aqm)!NM�� !^on-zero�L&$(i.e., $xy�M?&x  $)-Q�'@ �drim%�� !R�isbenianI�1� $\delta>0Q)��'JL Z$p� longA�^ exac�s if its Frj0us morphism b1a fixed � $Hp�8Galois group $G�Z 1nu� field �<sb� ��jurbyD�� �=|H|/|G|#&�uaCa%K� o$x2�3a�A�!_admits �sympto�)expan� u $\log(x)^{-)pH} (\sum_{i=0}^N c_i$i} +O(4 (N+1)})) r �*c_0>0$,�c UZ"�N$" W�C ``prove''y�+ .�26�E!��:�+� @ xt $A=E(\Q)-E(\Z[\frac{1}{R_D}])%��ys whoseA�o+�+���8i:E|vt�{ �?A�a��x���it���-!�: enough5 q�d&�m?-@s�)�atstū�(�6� �At *�*vem� �z7aUi�$I^�splita�Qvm&$um $L=\Q(\2$d_1},\dotsN})/�(D=\# ",d_N\}�ispXas say�ey��E�:�H=DGal}(L/!�\{1dN�ate�isb�)(xm�H:=|G|/|H|=1-1/2^N>0�% A� approxima�J�m��M0��- E  term!`.�1) ---!co*���Ul I runc�E&���tr(� UbAx$$A_x�P��f<�hat{h}(P� x�  'P� I� $x$,�$|A_x| \);�%m_{{{m}\atop{B\ }}} ��m!��Sp_ a basis� P��}�� 1}^r�!L#&$�� �(�[y $��($�&i mbda_i\+T?$\l7 \Z N$T`_�& tor}I�~ �5|| L||Q,�-� c �Ň!�tant $c�n �abdsu�����Rr d�$\Z^r-\{0\}-|:�leq x}}2�{-2�>1��,A��*$G=m ��r���lR�m!�{\�[m^{r-1}�.mJ�� x . \infty%$d E�i�A���/���um!Z verg� � hap "ZA�$ �-r+1 >}&��6 >r/2��� �t�ed @N�/�..". .#W�]r=�&� �( �! �(h�/�"v�)@�1ɾ� � ly m�� �hoo�(�� �, � Appl��it�a/ isog��s�i $E'$�/�%�[l $\{A�-2��.�2."2A�%� Ŝi� "�!�;f size�}8^{0.6Mn^2j5Z&Silverma�0Wief}, �9��'sti��2Vn^2/3`.� Streng} 7��5!�a� 0.6,�, ellia4j0ce+cor+ d� %>@ 1xkJ2�,��/e $ABC��granto/if�^)$j$-inv� (u 1728*"n�"e�#e5%�"�4^�-�-�mɖ()u13A�$loc.\ cit.@ E�ɥa.H -fA�2h4� En|DU�$5� >%e.U3)%n!(*� rror���.D$1): ShanksQ }  y�6.@h/ � !c&E84�A�uGf�/)ps I�(Ramanujan's=let|!o Hardy)ep��8%�K-��!iA�a�ac�'� $0.005$ah$x=10^7e�BC4)S fu;I%�37� �,2-N {k ,u�p%��� ofte� s3�4W4R}|aTit�&ses�� imag~&�����az^d�}���d (V0]� ډ���bI�A4r  +� K��s~��K�+depe�� E ) $P$;I�is rel�tw9�<Lehmera�'.& o� ec�� �1e�m$�tinct*!l�P%vE %9� n� K�F�% ԁvi&P �� m$ (��may{�F6$m�G��;�U(��)�e�a��# �distribu��9residue��aVF� .6 aVh��m!Ki~a�j$&� })���6high."48:PFmi�~$remQ } (i�tACwon�9&�properte�be!��!�)�is �s��M+choicG$�<so ask]� s %la�e�Uh�.� (resAPively.t>�i HBemph"V:2L: .�al� a !�:uA>J�P�A2�)) satisf( ![6I�3�#)q0�&E�evide�Q%,F>1 s beu (��!X�7|~xa�+,.w��x2�on!� $d @ !��e!ev9be ``mor1�A ��TCexplaid &2.>"�+&H+rpo9o"�usualY��("T<Z�3All endomh"�E],� B 2O . A,>-0A� Rubi���&7'�;ex�'"ii)��O fa<toIa��6� (disgu�a Fibonacci�)�>yed�/ess�4al r\^{o}le inx origiE�3;��{�4HTP}(\Z)�FH�$� 'ogue�6J.��r �!ar7urt1rs� AsN�,� an ``���� >.?M'',!p almoB6er� �alse.Hu���r.� # 0 �l$\{a^n-1p�E1}�F6$a �?o6�$9�pMw�byM�y/6p$[(;)]&"�N�{�A 6� ),�8��!�n�1x � � s9 is �; �:\g&ts_!x\ og[F�"�\J9n�$ �dj2g 1f V���)($. Also, a� �+ aU] (Va%��8���e)ź"���l��tenz�why8 ret&6e� R ia�K4:a��#�2&!���So!.>` global "�%� s. E��i�(� �# trivial �� �{0``Manin-Denef��<'' $f(t)y^2=f(x) ��*cC ��b�u��& liter� e5��2 }. �6�2����.� : q)' rank-26&,_q[T]$-Drinf� moduajq)F_q(T)� ee, �\ � Goss�IIv�� L<"lynom�o� >� deg�=w/�_a(x)"F6�L�A$a� ]�-npfs�, Jn!}��;�� n irreduc�< $\wp$ co�?Au �mG�m� �aL,g(m)<\deg(n)2�( Pa"N :s $\F(T)&Y g$d >�C� �s. A >�.;J� was�7t by Hsia (I` !�uv)| �Cer~< � ~ /C_1XCn*L %nL$R_d$��:necessar�-!g� �j� &2E�a� .�7``fib+ :conicm�$E$a}$C�=f(X,Y"2;0C^2=A^4+aA^2B�E B^4$ ��P)l a al (�/P}^1$-){�keE$,Q re $f$ ru�%��\*f bin�G&ME��& or"?2 :& �.&� 5A(� e՜ne,.05 �! A��d*E- (A^2+B^2) 11 = 3"k5 ,(X^2-5Y^2)^2a<a smoothA`��� K3-surfac�&A9T�sY0T f�. �6�m@ �%� trou��{;� $ orEUMaG n Davis's�%$6�sol�<7� U WagstaEL 2}, ag� �@L.etype $*qAv)e,ݐ%�IZ}&�!m��% � toM $a���'r-�A coordinat�0"iJ"puZ(}�&�e�� |s�A�as�t�� $g^2 = �B \prod_{Q��$E[n]} x(Q)�7��vi)� ��&� >� ���(A���?J�$ lpha�'ass�HtoS$\ �zm*8End}(E��� )�Chue"A�#�FWHy�x�F9Hs� workA�um�!�zi� x� �+ *UHA�L<*!�d�&6! '^�*Periodic�techniquBA-��incip��f p2.�)I$:�  at1�Ktoa�v��2���F s. H�n����C$u*:%E�$ $P=(-2,4)��U sing�. �o#�O�n�8� f�Le�  $E�9� �K7�K2x$� *$$\{4*���s�# $(1,2^2,3�13q5��)$ up!'%F� Ip6|(_Ja�.�:S6�� !�app�;0ion} $\rho_p= (XS� %��(pC.� *eK small$D��� $p|X_n�V�]h� S70Per} (Morgan �%m :48}a]EIII). ��.YA�!%�z%�c�<n� �$=\psi_n(P)� 8� �I�VM"{ $ 2� �$ $p>3��F`1_"/2:,E"� at9[isuG�QiUw i_p$W��g\�S%�M/2^{a_p�\tau_p�Z"! %�le�!02on �� ( �%)i(s $\epsilon�\kAT� $B_{ �-�aC2}/B_2$ql$p$i1 ��lyRC � a_p=�f b^u�odd, 1-�2)� (!`powO f $2�U0$�Hwis&�C�4.*.�im0Jacobi symbol$�5�r!$. To avoidI�kler)IQo�$!�1D $4�5* u�]P ��$5$2[8�L���of6�s�<�$ 5}{B�==(  I R&� �.pro�A�@I�iM�A_)s�6#N' repeats $�1,-1,01,10.�A@ } 5-�.^G�56�A whenp  $a�m 3-@��ll!�s�$s$�congru�1V �;��*� A�i&Ibo�*$R_{5}Q<Ia��Gs*�+ do a�t7@m.��$n=s^ee�M� r e $sQ ��V��$e$b n, $s^e =U38m�s^{e-1}�B:e�a(Ge`we � N64i�RQ�8A� -)�P,K���Sy%AN4 {s^e�;{ aPs $-1%�X�<� q�RO��-�%�D(>QZ�8exaH e 1�2���e� �:�a2� $(2,-��>U� ^!B! e}F�- $==�8 �lE�}!�:��'5,Nn'!qT�@�sMCMe }�% B_� j^i} R_5E1Diricha#!Xy at͡$2/\va^+(8)=1�"}.�"� go!9�v�V� r8betwee�MB 4Ad"y5&pJ�I��2� �Sp$EIdA�|,�$few $p=$ 10��WnurM� (le�ouue�com�."��$p=13I��!J �36V�$sm�5,7,11,1�336���s}{13})�3<d7� $ll Kroneck����*�iv�7� p=29 � �is 38�⑱9�5��38� ay=�:l�3�no new>�0*4�=��34��se!13, 17$)�42���=j�51v�$66�Y!h25,29$ \ j\An)�Q�=�� sڢ�9,A�.�3*,��.�A�a��+45,13,29,41,53\"�(!��QFR�;:\;�SD�S!�srT43/45� 95.5 \%�5\*B;6=7{�1oJ\ IdBK=�ng&F\,%�k*(7V  m-��j �.���c a)>D�'cQZ�LjLQ���1-�� JJ *QJF=F� z�!J�*��$v ::QIa�quite ,. �defTname{\noG nt\n�\l�',{References} b? foot�$"}Gbiblio\ystyle{}">?he.# }{10N\ibitem{Ayad:92} Mohamed `. \newblock Points {$S$}-ers d>ourbesq�dH.8�{\em Manuscripta Math.}, 76(3-4):305--324, 1992a"�TBel} A.P. Beltjukov, D�P�� u"}N� of 2;o�+ad� e�.�. � Stud=!in �$ZI�m�Ke8^V5al;, VII. .M`Zap.\ Nau\v cn.\ Sem.\ Le4F0rad.\ Otdel.\!.\ InsdSteklov.\ (LOMI) 60:15--28!*76�51)8CK} C.~C. Chang�0H.~J. KeislerF�\).}.$North-Holl�"Publish�64Co., Amsterdam�3.995 L�M��BF��)A-E, Vol. H �,heon:98} J.~ JS.~Hahn.r Expl�  valua)�2y�� �.Lb�,97(3):319--3){982{o D.~V!}udnovsk�Ud G:.pS1 �Q�2;�%�Q�i�mal�!�new � Y pf69iz% WF� Adv.R�,.%�e�(a�85--434!�86_Mil��Nelson phen2� �26���2/� ProcF�!u32�955--963�4.�$Stoll} E.~ �DFlynn, Franck Lepr�!Lvost, Edward~F. Scha� ,, William~A.�in, Mil ^)�Joseph~L���el2tEmp��)m^Eej{B}irch%8{S}winNon-{D}y�$&l<m�#ar {J} Nof!S us 2^E��)�!:D70(236):1675--1697z�I$ a�d  .�%�Basic&�O��>%�ؕ�~35�NmVErgebo i-�\ 08 ihrer Grenzgeb^ 3)2�Sp^d@er-Verlag, Berlin�492�K# L.-C.~ . {O>�@du�U&�2�0 :�#},�@}t (2002J& 0Lip2} Leonard"NR.;U,J�IB� c-r�)�aV a\2�in2� ! s. {I6�%�bL,64(1):122--14 77.KLipv�2* �E�b�.�T�eR�235:271O a972� Lip1v��mjm>� j�41:12�r-f>�3v� S�2�0�ED*��vAee�#e�Pj �Ly Mee�-(Br'lls/Monsa\80)B�BulS*6m� BelgE� 8.\ B} 33:41--52G�iy6$M1} Yuri V_iyasevic.kAm�neKNerDa� .2E\Dok�Aka�Nauk S.(R.} 191:279A_�7� �2V�h2�Z�2$:]�� Seri�!MITS 0Cambridge, MA!-93.�{* Thana�& .�� ffor�8�A�!�. Z��{V'Q}$�& ���l2� �� �� B� 37--252F?�� HPoonen:2003} Bjorn .KZ���N ��: sub�� )bz\bb Q$2�E�JF�}, 16�81--990�2 ~^:49} 6�^.��"aP �!�p&�v?��.<�S�ic7�4:98--11�42QRo�l$} Hartley , J2��m of Recurs�F�SUEff�"vPn� �2[8McGraw-Hill,1962�S{G+ an-Pi aqr2�D��\'5% [1e�n!�� \'etV;Enseignh� (2� 22@22A�60a�6�(j � .���U-�;t�Ba�aJ:F!S{$B%-Fi ���Ea8: 86�66J h5;2:�E? Samu .\"�)>�48�Ge*�)of>*quater�+�q"**.E�6�064:1717--1731�95.$@Shlap} Alexandra entokhBZy�Tenth���n CjT�O�  E�J]R to G=F=e&���J?4)ppe��w�>?AEC} h H.&'?B�A"y�!j:a "~ 106 %T Grad!� Textb!h�}.hBp New York!~6���?~�%.LhIrj1� A�{$abc$}-& .�� J. N�I�L�00(2):226--237�o %"� Stev�} %:�z)o.l%9�!h'.�2� �..:{\t�<Xiv�4.NT / 0402415}��6|�@ M.~ .�"RwR�lB�+.GMa%�4hesis, Utrecht]��6.Z7Vand} .r%?^]Q"�tl/!�.�.�In:Y�sches�schungs(T�j< Oberwolfach Rep�nk 3/�� �4ni-Workshop ``y�10y�, MB�B� 5�s�7+4%2��:48�"s).�Memoivu�.d.5E�,J&�70:31--7�|A��Y:? -*��2]�ituut, U�eitQ`, Postbus 80010, 3508 TA !Ned�nZheEmail:I�co"`@�.uu.nl�4DePD�E Wisk@, SFP stiek en �Driaat,Y��Antwerp�%(Prinsstraat� �. � i{\"e�~.�z@B4que.jussieu.fr2 end{2�g0docTP �n\s�[12pt]{��8le} \setlength{ro(width}{5.5i.4opmargin}{-1cmF;n=}{8 <6�\ base�:*�\5"s�} \ti;'{ !stq �2��uogUVDPexiderized Cauchy�� \1{{\it)~Mat�X Sub�2�Uif+o�=+�339B(� � 46H25.\\ XKey0d��phr 0}. Hyers-Ulam�,.� ��al��./9d�$ve mapping:&�)J ne��{9Fly=�OBJI$Pythagorea�o�@8)=\|x\|xy!�&6�"B`mY. Oy],>1�B�6rB |m�!sC every�+ . ThIbrt��6,i SF&9�0B1�2who�@n/F9�si.henomenI0Qe�vT.ign�-e.�;tudE�f�(. G. Pinsk�Tharact��6.�13a�0R,.: !G�27ry h%in�>���0�7PIN�&0K. Sundaresan���S�?re$k% rbR�� O!}ppe�U!&(Birkhoff-Ja|4��$ ~SU~�  1�9^� $A�+y)=>+I�xe� y~((\heartsuitVmnF�an q�v�SH� <�*�'df!S. Gud$g D. Straw� � GU-S!STheied�2er|Sya� yste5OsN ngAEf��axiom�Fdescrib�J�z%� semi� tinu?k5@-�"�W�9N.�m/JO.E1985,� �� i���&8"�i�5[9�!3 by ur6dr��zve�th�.fj9. More�L, hD"�a�K�YP%ur�3~.-դ-�RAT!�Iin�Ztep2�!�(Gy. Szab\' �Y:ypr�a:v-%�LFq  frame9x%� 1��e�ades,6eJ��Ve b�-�b�P� {��ey�+so J 7�4i�6� i>e8, Physics, EconN|�%SG:DB�G�3SciR(;�v� ACZ}#,i�P-R}$.pom?  treaf���3M���a~ D. HA o HYE}�;Ga6�N~Cf��aQ�/a )a�  $X����2�щP$\|�*-�*-�^\  \�*�0s"�5�*tF7/EIe �JB�E36U2� H-I-!� AQ��k;{>w�{5�of�� $. Y.H. LFC@K.W. Jun, D.S. Sh(nd B.D. Kim�m� E �G Rassi�S5+%#is��2�L-J6�J-S-K�H��A�:Z�Dn|H�B� N: w�;8i�WC.- ar�K PAR1�g� AR2}aZ R. G�Od��Sikorskaq"G�6���4F�-�J�� +.k$, v,lyE�y�@w%�at2�Mm�n��3B���6�$Y�1q�^is"u.d� �1 $x,y�>X8$ , i�&'�1�rez s ex�^ 9%JYV��$ ��, B� �716}{3}�;<�3E�@cO /y�ga&�&�[o-']t?B 1t8`6 � D ~(\dia�hG .�Jjb pap:%w2�El2 ~�3��in1�BvGeSaz Z-+y6I2w=.�j�� *$n"�T��eu�Ag� UWaWm�B�Sem!l�e��rough�4-3�� �, _+}>z e(non"f3n"s6m<. $�Yŀ�,� �+; unit�l^ spq^A_1)��A�1��<a�0d be >lin Bp �0� �!F a; is�dejHE-9 B-D}�am�i�y� %i3 � �6B {Pr�r�}�re�sRal]��no� e�25�Ks:� ,, Boussouis,�T mi-)2�,�tga"Carlss�7area,%- ary-ARo�*s� "��GoscelesiDiminni�ueegJ17 A-B16�$A-B2}$).  5�N�8!C:�Q��J. 2O  SupposM a�%�ve�(��(Mhic-�)Ir$\dim X1[Ex*}a Hre�+!�� wit+&�ep�S8ies:\\ (O1) tot�.�>II�e:� 0, 0�NA�$��$;L2vX�U� : _ �f�], �f�T!$!�aearf�Et Y3) hom\ eity6XJR\�E j\beta��r , �~)R} �4)%�Thales3f-4 yP0 $2$-d*T��e- !G� in P1�l�_ m�� :V $y_0&P2� �y_0 Px+( Z x-V pair $(X,$�DA��n:� �(�).�B$2�(  2�Qm�B66Zk * aN>H"ny. -&o/6�@� 7PILt>O:��6Xa d&�}A��*A�EA��csE�!�XI 1|$A�and�KM�f�!�1T!�&Lr��A�eBD%�0 \langle.,.\r );�Cj� 81� 9�a�Q�Bn`�1�)�EJ|.\|)�kf�Un�|x+Q�y\|��\|x\|�\�= !ji� �w!��`6�(Va)%�$(Y,+�J 9Fa�#b� B "Ye�m(9�l�\(�i��6�&H 6)> "% J Eu%�$ �zxe� y$)"q_�WXm�YIqiz�$f(ax)=aw\%WA 7���q� � $A$-Var. AZ)sainbe.�!-&� �.67} B3 +f(x-y)=2�+2R��<2<^d^�>5. �gaXR'�_&t�B�(cf�.r 8 ry 7�F�A�e%mem (*).}gBM�H�9lyɜ evisR*^mE�u\omega:Y'Y, (!m�� s bi�ive),���A 6�MR y&�Aa� .Z ve9�$2sY�an $f=Q+"�fQ�}@���$T$Z!�&� O�n S"�BC � �is�� , ���`-�� , )�J-S ziv�w �  ' �O I��]��efu�o�%&� s�of5+~q mong"� tA:���& .�K � �!�2�. I}Sc.} "� 6dB���)�(Aj�F& B2�@0$F_1,F_2, F_3"��_M�s fulf�2ng ��H} \|F_1(ax+ay)-a^2F� �6,x">!s2�onll ��TA�,��y ���P�uD$F_i(0)=0, i=1,2,3� %�&`��_� $Q5e W9n�}*1x)-Q(x� I13}*S\\%-�F*2} *3RT2*1P�9%��X$.�$Q��^2�B� _1, 6M�Proof.}Q%�|��* �So� #A put $a=1$%�$y�K�G(��]�\bFx)-I?I5 �,~~ ��u+} Simil� �J�x��y�Y�.�� >��H"N�� by (L -y$�KOLan:(rE�$y:$-�n�P)$!6ge]v�ix�-4-FN� ,�.>� �qg-�bZ�]� (� y8B X�B ;  R��O�ra��o M=i U?%�hav")"�E) 2ax�w2J _0 3!%_0>TB B)�|Ze�� }{2}E�\pm  �so!�ɃI牔a�܅n6A� \n\)� qb�u�GCe���~gy_0-x|:}Q3f�c�~y virt�` tria�Sin!�y %j� �1�7 2q�B�It^ b�Yc#U12�c1/^7+,��!�MZ` \|+\ Ql��rBDE� (2), (3)$i(5a�hab��� 3�D)DEt)+�� �4 UEW &EY��3%�\|\\ + ").A�2"+2 � X\  E!�\ ,1�ZQ1!Q-V, (�M)j6z[ �f�10�U$(7),(8)�v�4EUI�&Vb& !.�Qd>R\\ &+&MwQi+P)w._B1�i.>� 1fYPut=$����9)�in�$�"�fe[l9��4^{-n}A2^nE6)!�(1-�1}{4^n}) �q B<v�$\{:\X! vD � B3 �nd��KRonMrnt. Set'4hi(x):=\displa�H�c_{n\to�r}}:�$�_ $(10�$\|�i.�N�� "�q�t�PJ&�$\BQ�2)a�� aQ�)]$�%ceݢ� [ "� i:�$��A��a3 �1 F�h. b [ѓ!j )$ yz3�W: ��))>$xy-4 )J15 .$$ ��A>limit�d;>{Y)� +y)- y)= Q�pL�isV���((*)dte�[^$ � �� c8m $Q+S5X7p&� A�"�� �|Q�)S��S"`a,)n&�n$Q(-x)=Y+ � A�f.�1�N�+I� -P-SV��-�*�7 (2& u�#|Sx\|= $ }{n}\|S(n= .<nEw n$.T� � $Sr �so)�(�!�usN�!��b�B�M"�&Ao2�~I�p"� �d^n2 ��2^{n-1}���B;:d, 6A soN� |�o�1(n-1)}���=�575� Q'"���lym.�$\|Q'� 217:��v(A���Er+d2)]26�n}{3BAVen�?^tAuiy� Q=Q'��x��&�,qu?ass�Uon. Fu�s�3�"� , (1�@�Y-.� 5`A`� � ����Ae" 2 �&q�.t}q�.}B�an^t :N���6�.\BoxB���R � e!�ofg�!�do��ae�� p< ���BF_2�Vs�k�h���C"�m�E�RrD(�CC21� �M&&�QBU��s6=���b�)�)�)�)R)M��UsI�0^r(p�Fd�Y�!$ .$a$ RI�2����&��ϲ��a.Y>�� At:�,Y�6!,~�T&�+�C�"uwB� $T:�3.�+b� x)-T���V7�� � 8: �1N R� �J�T�I����@���n���F�.���� ����� �j�*�+.0�����J�>S$( �2�q���e(d�>��"x B>ob���e1:e�)&�!{��:��g�/�dB�13 &W1~X�w6g��"� �1)'� �-2%>5�%. &F�)(1k"I�)+F�^"}1&�1~� �f�4bPN��(17i$(1uzZ2I[)\t)z�o%'E�+ )3TB�Y�qv=EՔBJg1�A���h2�h2hf��{:Q�]6]sH�]:�]2&]I"� 6q p#�233�g�B<w�� 9Q�}%H��*���:[~S�����b�x�T�"E�U�1�a�))>&y"U :.18�V!OV Vsi:VzR+$�ZSazPP4$�$wo*@a�nPPP f�FE� "�&b$T�=� 6E`.�%6wmePP+V�&D�s9P69^2}\|P�.z9}�*� 6;P:;%�=!# rNE���6����rn0�GI�f:�1��"g �9v=&�  �.! ~�i+�� ��1. 6�=� �p�*TR*>�:)TF)U*%�,)H�4� (\|TAK%�T' .1"+�A4eb&|� $T=T�  " , (2�"! ����&"&�+5M="�Bzz V|�AaJ�|��I|&>�26b����odd�%&�\������vZuK� Ţ? A�&�1�B��>:X��_Z^9a�D�D�DFDRޤ2*�$�QM�,�0�u*fi(fv*f6v*vJ��\|f*q*bAG- fO.�mv7ld���/S.N,�)F_i^e3-i^o:Jw . Cl\7 &�/o *�, &�x=&-+2M ! subt�Gx�"E�n he<4 �F**� Xr ��.� d$"&� q'���-b�� ycn�'L�6)8thdO+ , $- F+"+�y*��*"+2`"�^� -ax-�.�-*b�-&k q"� 1B��(%�$ �!�$(2�uZ�^e2V^ea��^e(F�qG�"�)�^o6UoUo�UF��6*kb�%2��a$�1�&,V�*&, $ ��Qx &� -�2 �*6 N�b}.=-2�J�2>�R�J�%XT��e22�/ �� S z�<��~�%�50+\| F_!���9A�6�@6$$.D/o��ELm �� �8$$ 9�: $$ U�I��{y��$"��E|s 1%�)ԡ"݀��� d�> �3�5w8e�&�3aΡ�by �&�2!�K�q��G,~*�O, aA�qCa\|=1$$ � &i x"� ȑexcepzv�2CA�>hold m�a�idempods*83�3�ay be�spe&� �;�'V6!6�4B�(*?sYB�mBTr.u�-\4)\$f_2=> fa0�� sca�f$ \��1лu;(!~�Z�"&|1- 3|y�A1�m�>*a�B*�6�e�!oVP��)^e�x�' �\��n�^o?F�:z>G)a)L{sOKoҰ(1���8*� < �# ��$1�;R= a�1B|a167 ѹp"'A�a"��"u$E�A+3�+Qp� �2W?)�r�"� .37�� �� �� b� �� �� �� �� �� I34Eife�"� t\mapsto�� (tx)�%conQa��]5"o5�ne;is*->I�QFC>"�(q� we"3&no[o]Irob&q*LgByy"�� z ��Vm �Q"��-$1@><�inqui8o"� �(�Eas we�.X, 2a �8in .Z$.].R�becauD�|-�mBf FF.U'� eI)�6o r�QC too.?Dz$ � J�%$�<2JRAS%��8.�J~InJ(R}�@ �M�.��A��R�$1W��J�)�Q(|a|V 0a}{|a|}x)=|a|�:R ^2.^2}E�0 B�!\(�NJ�t TZ�TN� ��}E�� nC"�)� S�Hz�=com�aͻ�))�B�+� +��.�ND *xD)- \mu�! 2&7� 1��A7s6�)� I0,\mu\in\{z\inE~ C}: |z|=1j!�DE{jI��2�MS exis.4 �y�&Q>�a+BN� � � �  �,ũ.�yn�~�M�be �nCa\&@ 2"� iG?W�@"�9z2zO%��)��ef%�F�L��^�Q�� >��h��<T� ]�&�RV�"�*E�4 .iV��*� ������:��]-Q�1"��%S��T�u4t:�e{99�c)�]�Tncz\' el,i�h%g ��&�5*�Ss�V Rei��V[G(., Dordrechz87.&�jPj lons�d C. B�| itez, &MFN in��{"�jG-S} V�Wdg6[� ity,�s PoKcm~�[!�th. 4%�95), No.�143-15.��^j�]./.W!��Pc�0% A$QS.R�Rac5a!C�n�58!�7�427-436=�WH DZtH, ^ gM�}}Fzrc. Natl..'USA 27}041) 222�224.~-�Z *�\ , G. Isac%T�|. lZ:�F=q al E� ZSal Vari�JKT�N\"� r\fs�#15�U1L-J} [~K""[ A Ge`:�%4 -�gb[ W"7I"_�f An��(. 246dy,0) 627�638=,J-)[�V�[5���-Dn;6���39!�99) 20!�96�A�-MR\� P. Sahoo, �9\F~" 5A��K%.K5e)5{w 38%-2Aa~ 3, 645-65.�+_( L. Paganon"�&U�_& ZfMO�7Oy� � �A�=�6es �50% ag135-142=!�K*�\5�&aK� mh�B�L%)2=75%�-711-72062�9�ƂI��).�e A.a�P�e(, Sur une fxtnelle d�}l'e� de�r (Fq�h)�q R. (�x)2qRSS, n�@ r. 2%�3�6411-41.�A�_.^z�F��vR� 72A7�297:�.��OE�at6.nU.  vs,YsQr2��8Ar35-49��#c\Mi��.�cEY�Np IVsU�aw19��1, 73-8.�of6�f.� ��nonM�qx�g.i f[3\7El87-19!Z1j>( @ &�md<��n��nާnM�&_  S.�O(�7 ^&�r���n^�n.��n:::dn�k"�c:B�. E��.��n.NY�W.��n��n6�nH\\Home: http://www.�n /$\sim$mo'o/��n�E>�ѫ.)R9�J+1-N���V�"�U�e+2h6m_#DNs&��j�B1�i�@ symme�۝́b>s].uT�D�*�3a"�o"dnT{>cnpNuc�noZ�.��&��RG`C$ J�`,�"߰�TZ�$�W�f.� V��]��]��]��]��]��]�]A�]]Z]Wb�]bh&iN�]�R��]"�]#\ mbda�P�a��]�B�U2�wer�]6�n>\E�;"�]�o>�!C(��]��]��]��]��]��]��]j�]�n"�b_b�L �d��R_"�)�E7�'y �6L&�*UhAP���_Aa�P�� (i��not&� mark_��,T�{�atR�d��me����2n ��M�N$3�Z�_:��� �^r�Z�'�d�O��2J�7_�7_n7_" N^&�ryS2�("_1(�CU;)f�_��^B�^DJordan-von NeumannJ1 �S�" ��^APܣa56.�`ݞBS k&� Fpg!�C(�C).;iJBMimes B�C�)=B(x,6���(n fac]�u�) *CQ}(�lMp-y��!_5]A�h.m_a(r�*r�*r*rI**ry�!r!r��Ou�r9�x�r�k"\cҾSKO�r�r��2 �ginFr�R�x;�q+i� -y)-E� *)�6hnr�8Ven �2r frac.�=�8 P. WQ� olew"pCH!#r ded !>�,�(by0��Z|/6zd9's �a�s{�r�*mwCzerwi"�pCZE�j� pirB_m--�."@��Y.tLeW %�J-L}$ u,e3s.d9OU4:zr�+j?sJA�a�Bs%�mv mati�uq��aa CZE2. 3}q&�N�$�BJq,*�|$ !�id>�x4F. Vajzovi\' c�VA�rqZi �2��=,e �sT,��,��%�x� IiEd6P�ity. Ls�!�Drlje6�DRLD%M��chi�FO� lG*�w� ZA}$2�*�z� �sqsq2�q�*u>y�E�D=S-S*�.$. ��ai��to!d�!�%2��U�ncB�rN�S՞Z.O {M�R�{Od��E�id>��J-o�� Cd�'a��c B�&u~" ����&)EQz2P  W��L(a&�Xof;N�d�e usj�d6�1�s. (Se v-MOS}$)�*r�)�,�j8�j� �6-6�a� #! 2.1.�190A�o�L~d+�A�G )=2A����6� �5� ��($ is symmet�Iric, then $A(x)-A(0)$ is orthogonally additive. {\bf Proof.} Assume that @,+y)+A(x-y)=2O�R$ for all $x,y\in X$ with $x\perp y$. Putting $x=0$ , we get $-A(y)=A(-y)-2A(0), y\D. Let2DT�y U x$ and so�4y-x)=-A(y+x)+2S$. Hence��x)=(A4-s2B  1 $.\\ ThusP%EG-P)+S }So92 jr$\Box$-x�2.2. Remark.} Thanking J. R\" atz%�Pre exists an odd mapp($A$ from5��ity space into a uniquely 2-divisible group $(Y,+)$ (i.e.Gabelian in whichARvD $\varphi:Y\to Y, !h2x�Dbijective) satisfy �%�2N, U5 sufat!uX0)\neq 0$. Consider $Y=E�,Z}_2=\{0,1\}IA�)=1NIM5]3.AHPorem.} {\it Suppose $EY�8symmetric on $X T f, g, h:X� $ ar%!w s fulfill�P \begin{equation} \|f �fE�-2gA8\2h(y)\|\leq\epsilon \end9a[som� " �~sAssy�f�odd�n!�QC exact�n�!�� $T�nd+$ quadratic+Q+5�9 narray*- )-T!Q(x- 6�111N|%@>C,\frac{13}{2}bN9:M}MP��Pu�v=0$A�$(1a�We can da�Dis because of (O1))S�9�=�f�N�/��E@. Similarly, by p�Cy.��JN~f!c!*Md��1�E])�-�� Q�l\|&A�& v��q��))� _0)--�!m 58\\��2x)2(;IZN,-f,�B,.6� *} �6J�&&A'2x6� �F�E^.'|f@+.� �+F'R�\ I���B� ItY 8not hard to see J�4\|2^{-n}f(2^nxuFt\displaystyle{\sum_{k=1}^{n}}(�)^k>RY�n$,0 ���m�m��m+V�F �� m�s%)M !MB� evI�i, }��� T �&=&\|��[(+� #-Q))�_&+ + ]\| �6�RL -&6�*BY *FW.�6GA(-��'\|=�=�F��R��-+=5'n}\|T(�T'&\ � 2}# Fp Tend& $n$�$�- infeA�WT=T'$. *h R�%�%�\��-���������q� .n�.<=�^2}\|Q!�!Y�.9�"-���Ta&a�limit,J�Q=Q!� A $(5)�� $(3)>>�,R] -a+ � ������.+"L 12�.B� �2.4*)(i)��,$g=\lambda f�?r  $ K1Q ��2! impl��te%|1- 7|�� �)�.�&o8 6<� E -1"CS�x�� EY=0D (ii).Iif $h�$u %$ t follows� (2)ᦁF!�6�q As far aU Lauthor knows, unlikeV��{s (< j+"�@is no characterizxE�&ly6�s. Everyj#q f66$>is�+ . In�s, $� so $q(0)+=4 �=�"� a� haveRyi�h% $q(yU�V+2\m q  Tp��e(>CGjC�variou!��:2 ity.�exampleE�A$-T�,on a Hilbert� HN � d&L_A=\{(x,y): =01 w��; pbounded self-adjoint operatorp`A�,A�showndM� chi,!�ryP�2B func�alr&. aaT\dim A(H)\geq 3$; cf. � FOC�� SZA}$&�5�bl�"��|�|�||9 . Doa"}/ &�9I"�"X�4�cer� � di!�s,&yR���� �w\alphab`bs��Cbet�Bh�.B gammfC�e� scalars $ �, {, @i�-�|�%Ac�n ledgment.Qe��would ����rttA�fessors2|R. Ger " J�korska� vectors.M� Inst1�(BeaI(d)(N.S.) 54A 6), 63-71������QRE�V{,Jx38!�$89), 28-40l G-S}ZF:wA|�;�Tity, Bull Polish Acad.!��43}D95), No. 2, 143-15.� HYE}�H. %�%~qs.�linear.�1,�$c. Nat. �( Sci. U.S.Aq|41!22�22.�H-I-R:�G. IsacE�TaQ. MW:=�Z�uBirkh\"�r, Basel� 98. �Abs7 d Moun�\ �vJ-L} K��Jun�Y.!8Lee56%D--i �6Ka pexid� ed �S&} ,�@a�D. Appl., 4(1) (200!G93�118]NJANS.-M.�g� P. Sahoo, ��6���1�!P � te� J. Korean �S!�A� �A_ 3, 645-65.]MOSeQS{slehian5-Bc]� � ized�� , arXiv m�� FA/041247.SRAS��..7��fu"� k%Gi]!pplic�GStudia��8Babe\c s-Bolyai-"m|8), no.! 89-12��!Z"�!On=�:�.b�ىaa� 35-4.LSKO�\8Skof , Local pr� �:�Kapproxim �!� s, Ren�Q��Ma�0Fis. Milano 5�\83) 11E�22{\ZA} Gy. Szab\' o, Sesqui�E^K  NJ40��$190-20.LVAJ�Vajzo�G(\" Uber das�(k al� mit A 4Eigenschaft: $N <=0 \Rightarrow H�+H� =2H(Y$4H(y)$, Glasnik)hSer. III 2 (22)(1967), 73-8�p�!t:� � docu" }Ŏ\�class[a4paper]{amsart} \usepackage{amssymb,amscd}2(fullpage} %.2|srcltx} \def\today{Version 1: 02�;4e 1998} \newth�{thm}{T }[s�#on]2#AX0}[thm]{Propos� 6Glem #{?}6 defn DefinJB= &EK6Fr2% "?%6!cor "R>!nj}{Con�$ur`� �&.�#{- } \renew� ,and{\:}{\col�#!k.{\cdo!�0<{\left\langl^def\>{\rAv\ra( +(-�) %)  lra{\long;E�B� leq}Fqslan�6�gg^phi}{�% } I;bar#1{\Ia�{#1!�def\cal��call��2�8iso!3ng �H{D bb H L\L dom rm{dom�o.subset<eq Isup e�%� 1U x�PU odd rm{oddrdlim{\ds�} �nvlim!%ds%Yroj�9Eker{\��name{kerRcodS2!index:@!re:reBZiWSym:7SyC � bb C-DD ZZ FF F�R$R $NN QQ PP TT SS ds{2� Mod:�Mo5�Map>ap1Ovirt-F�'coF�!G>GFre>�:DA�2,Detp>WpWrs:�res7I>qIoFl:7Fl6 Diff:>�U�ev:6ev4Pic:Piccorank: #a>�a�Aut:;Au58ex>�ex5�}2r��E�2EntH��2H��su>tsutB�dy�deg:�$deg}} %%%\$��$ing{arabicj$plain�� \title[Co�(x Cobordism6 ��@Manifolds] {On smooth Chas-Sullivan loop product in Quillen's Geoo+ �e} \K8{Cenap \"{O}zeldda�{AIBU Golkoy Kampusu, Bolu 14280, Turkey.� mail{cJ(@ibu.edu.trC �M%\ Nyerol:NWs{Wo��bte#& Unit!NResearch� Develo�, %�DAbant Izzet Baysal: versD�(financial s�,rt %du!��!�yect�/IHed 2000/03/04/67. I6 %� A.J. BakDept.�m,.�of& gow� persg0�,conserv � hospit�(.}%endr0s \keywords{cQy,�� holm9 ,Q�mM�,lAhs�8,Pontjagin-Thom0 stru�,j� �y @j� �{Algebraic topology,Global Analysis�su 1, \date{Septe�* 02,2003}"�� �6. abst�} In !b!r-oA��%u*5AKxdI3ed a Eon!�Quigqi 5MA4ory%�in e dimen alu�1`s�'isFBha�'graded gK0)n ure �r15iB un�� E,as push-forw@) maps�co�~or�\9%h ).e� -isr.-0Quinn's Trans!Ej 0 :% }, i�)�-en bw at tf� � egB�u interA u � !A pull-back���Mma�I��� the E�isomo�1sm#�� y was 1ied[J�P bundles � |r%t>m2dH�W�formulGysin�E b!Sproved.� has}i�E�3describA�n6:�H o!�e home�A� $LM$hmH cohe!�R� and J. Jo2m realFoG'j/ �*ermHaMpectrux�qa �%�of a �! ual-})|���%�pap�4we will extend r�don}�a_�Eies8%�r\make�� \M�ylIf M��.�Ǎ�},a��� gave a��e pret� of ���Sssugge�4 wa%�*�%!26of n��(p�2� sui�\u�!q or5eis�4a mE� be s�-ble�:oughtQr�*o �7�io .^�V%T}�A %��2pe�of�J�rea�^bl! lcul%=�=0important typa�f��Z� �seSgeneous�Ns yreeI�-��6OLie !�sx�v{2> F��.} By a 1�%m�a9'u $ modelled H!V �� ;�/ Lang��}%�detailjR���e�"s aboutymap$4b�+und�͐onway}����\l7# {zirto} S� sH, f: X� Y "a��per6sA� [  at each p�!��9�54an \emph{admis�7�W �Wmap} i��~,5pfacto]$ $ �Tstackrel{\tilde{f}}\ri"H \xi $q2Y,$$ �"q:*:�J^m'�2�eH$�-; 2� d*endowed%@��_u�AK���$\nu (]$)$. \par A���a�a9�!Z�3ofe,� is �� byAB�*& $ (f,�)>\times��t�R $ gi�,by $.: (x) = ( ",<��y $x 6! A�4in X$,8+dex� �_xGp8 f_x) - 1$. Als 7eN�5 6�$\xi$�e -�2f��!replaced�6 � /R!�me^>QI�8>�1��=mapi2  "�Ia�m@�X"t ��� Z �28 2����'>�!4Y$ �Bylsur� i�A4$q$, $�,!�U� = 1� - z% \xi.$$ BeA06i�hn�&L��val���2ys .�of!�w�toEf�#E�� Qb�� �=EHY$!�!B-浥VS  $F: X >� :!��%8 >  say �$F)���isotopy��it" �)�)ing co\%��3 erat!�#�'veaBt!�]�"8� $F_ty� m�F(x, t>an��. _�(�=�,s $t_0 < t_12l80F_t = F_{t_0}�+a�?t   t�8 ~ )1:)�'X �The clos�1t�l $[t_0,1]%`ca�a�der domF�l!�-} . We!�T two�s �X:� $g: >�)�� \ic%�t)%<[ y%��D�79�:o�2� 2�e1I_f1P!y�g1}1M��mX}�+!�) %rre� a~� betwC mF��s'#an .�@-�v� �Two:�)}���f2� \xi $:��' $f: JH'BI'.'2gY$ c?)��t%�|%o\xi'$| )1s sub2�T a6�I'':X!ߍ>5 �'! �Oic���M5� Uv/ mpat& I]aRvv ���aW:�Ts�/Q���I�aiq�in }�,M�:C!>'e�e2 � z �%match�Da�5'}m�.7in9*t ��-\�~ reivelyM�I�Byp$c \refi.Ř.Q�I끶qaDUBc�?F " ig( I:r m�epb�-��Tgen4)izes 'O.�Q'� �for/E�J$ *� �@l�t � .,nl��5nW. First�re�* ideaf �*%/& :f_1: M_12�N, f_226$ �my,�,=*`Myf_2�J �l�e}Q $y��TN$ if \[ df_1 (T_{x_1}�) + df_2 2}M_2l T_y N \]� n)t (x_1f_2(x *y�0-aN� saidw be�.�� y� �uy !�$NR�lem} S=; $f_i!ci6c (i = 1,�2��lif� only���d!L1� mes M>� )N$ is.TtO dia�H!�0 $\Delta : N.� E ���qES� �T!p�� 2_MsVfQQ-���}AKE��_N% = \{E  , E� %�!<: f_1MD QD\}Ah�w subQ�>$6?I��e!Xram�-(CD}B�@ @>{f_2}^*(f_1)>>�( \\ @VV{f_1  2)V @VVf_2V$|@>f_1>>a � e\]�8#u�v � �s ,{f_i}^* (f_j" !8of $f_j$ f_i6��2� i: X:�( Y (i= 0,1)%�Fe @�nA�Fsm�c�b#A�A_�&�� �u $h: W2kB�.� -%1�"�Y.Ymm*\,\text{ �3}@ (y��(y,i)@ $i! 1 $y)e y�hYI9�)�V!�he��})����~c�&E�F �a� deno!�$by $[X, f]6�M��dgr��b@FX�J��m��j � Z2f$2�>#f� 2%at,{g^*}(f): Z�Y6�Zm'�CJw2 �g^*(\xi!�����(z,v)�|Z�y: g(z/q(v�q�6E %�ge�)4e�$q:D:>is<�2#I)�2�: A�2���f$�6in &B(! aH E nextj ult�A� olAeessK1"O{ same argu�) t �2S situ �'IZ; cit �.a+A x� "qthm} &2��nyJce"� �0q�<9jn $Y G�U^d (Y�r� se� ��Ue�ee�!v;VA ��$-d6�My2�Py;in�az]2a�S�� _21^!/  g:Y2kZ���m9&r$K%,it%�*� u.� , or& g_{*}:�]�2�]�({d + r} (Z)�&�� $H (��� �!i]� We<>��ijH-, �f $g': 2c-� secon#m&!$g >24{g'}_* = g_*$;vparti�r,. g�M$g=r�toVthrough��per2�sa�y!�#GRme9Xs. Clea?Nwe!$(hIsg)_{*<h%6��r�:�$h,�\IdI�=Ia� [="-�?�P.n*�nd"S"�"� C!!aX*�)�a��?.9T $[X_F f_�e�[X_2 ?]E�B��nY; ; + 27�����8�  \sqcup� o 1 w6�,�=i&�X�v.0 sum (disj�6#)z�As usual^�� emptKt $a�tyset�$ zero ele� of�5T�:!w�� nega�'� f4it�>��'op�ey �=7! H1�"a}$.��nU��2��y �� EA��^�"3U.�Now��[��v. �����{XJRd:� ��!r<v��!Nz,A�� m���wh� images li� $Y-A�y �~K�ly"KE�����}ɤAe���m�a8GY��>q�>��&M��  a \$"T%($\kappa^* :ݏ* (U.�. R by >[M&@h6�] =b Y]�$h(M)Y!t =q!T A6�Ku� �6oF�1$ U^*( \,)$!�v�.ijresW� toM�2�B#agrees $'D(mplex*�#�7�MU��u�� Nm j�$A5)$,��1� natu�>*5' $$4�*)�cong �.%�� ]�"*_( 6d7,~*travaria� Af�.�uct�"We 6�@�'�!%���w(5�M�>��DG +��es�����+ ]${d_1}(Y_%�.E + U+2+2� �,�&rE* �� \[ ��_�d ] ="/�>,r +f_2R�� } � +Y_2). AlthG ��F��categoru]�t%fe� $X�S(necessarily�!��&.  on $U^{*}�unl�U�JI�2V . Howe�Piz�2� �JE!� X_2.���#2�aA<�imbR#�:2% H_�do� �5(cup)Q&:# \a'Y"A!^*1�X_2E� �]%��CM$)S.� �(by Haeflige�C�)B.,?�iQ*thom},fV�!� &�e6,�H��q0$�"#� s aZg,AJq����q�1 t"� $1�repre�P#uid�ty� 6��s] $0$U�A4- p  }�v�$h��&K+�,BZ"@�jf u�.sU�a>ma�S@.�Oio�A�U[ yq�%By �b�, .f" (m'continu) map)Rcan�-!o6.S>Pby%� corr�W until��eA[a~�� F9!. I�� obvi�& F��N(;T�Œ�#�&��*< zec�v%�or� !F�`Ma|y1��"� >y � s2N s�;C�!6U(b�z*�:��� lett"B�@M� (mayS�I)�e|n�+���pA�a&$Z "2( Z$ depend4lya�:JQ$k�L��a� �:���.�8dP.�$> L =g'�p, f��[Z�, �!)],$$��isy>(bq$-2 !gK �01A� $f$FB"�Wg^*$ NM�y9i$g> end� �)turn �!2�ior2��E= *$.F * E �]�6RC ��22C �C �C rC Izj2% >j5.�t:��F �:F)�Y 2��FFFa}5��A�not:��?�:a"><�  ) .��[�w'*;2�4� �� find�]#!n�� ' a��e>��s T v?G*! � � ���$6I"a : ��Z��i ��Zd ��>� + d_� � QE"Sn�� 5�}[D%v�$.K :��� associ�. �n�-*$ �>a multipG�&�t ��� Id~ �B�"� (2�`{-Euler�`� Rt :062B�. Notdaty �Cf8 2�V7.��.` in�(�#�$\p� be  �\pi 2�Bf�Z�f&� $d$~� $BFth�-sZ $i: B.S�/�� � U$-96y.}!��(E#�$chi(\pc$i^* i_* (1W]b{2d}(B*U)+j,X�,�,X^,2�3%, �new*Rl)`b. "� �$� tub} A�spl�.6��0fB?:(Ltubular neighborhood�z�b $)�͈s�a�'P)%�"�9!�i_6N {j}(X^O {j+!�$\xi,\xi-U)B� UE0�.�ARAIaM������aYa�k �&�~V \� aiX3 in a!e $U^r��� 0ite radius $r�\_{|�F {U}}g c�0w�J���\pi_*. B�2\�X)9JSyTz i= ?"%��i9 i��jI0( $i\pi � �> � \xi}� f $U =d  �� )� Cy mov��gD�"�,}%.�:�E2"A<%aH-�o::F=�LM^{-TM} �A Cr^B $U^*(LM)$�k�xM_d�9�0�ed�?2}"sɿd,�(LM = C^{P`}(\S^eMC&�spa`, E�;s �,6�<ha��< -A��L!��@ $H�X�,A6total depf!94�> rc : H_q 0 \o H_r *+ H_{qe -d})�"�@NM=�NJzM=v�^M=6�.!nA�6M="YJM={!�)��2�4 JA=eAK$-=or8VNa�lex�M�I �M�EM�ICi�<eYQnd��.me* ^�n"le��un� n�3� $exp: [0,1]. A�q?d�$) (t_!\e^{2��it�gWa�/� isF�w�<n reg�a)�$\gZ>LM�%�F� M� ;(0�G�oB"evaluXmap�6)ev}:LM2� M^* M2 `K $\io�,M27C^{N+d}�tfix/X�Z&�� M� to c�K'�-PEt#hs�S.��: ^{N}.�!b�$2N6�26C�(Th}(\nu^N)$9/AmM��� � e)H[&$FBTis Spanier-Whitehead d�@to $M_+� x �)s ��$a "� base����W)#%"x& tE�sR \S^0.�M_+ \we�Z m \quad dand M_+ 6*.HX�& M��$\S$-%Sof)G s�#"k+c*k4� �um5Y \simeq ��L (M_+,�7�U�X). X+,FX&�m!�� &�&�X �� �&coa � /_*L#N�.�s"$align} U^q�) &�U_{-q}(-n )\notag\\�./ ? )t [��$qZ5��`*lQji%��Y� �G� 7AkU^6�&8 \tau.> +v M_+))rho.) U �`MjM!z�i@�Ŵ $H$ Poincar`e%�:��lkG �By1 n "O� s:6HM\�M$ )+�!/�pfEa� <^*:q�6f.1"7��Ds $��>�E���4 $a.�M:mT"i��h�rev$�t&0 >ue ��~�p.@.}�--��  CR� is� 1� overJ�5�o $\H�{� E)pu&!� jWF��d� "���a�5q�q * Tls*Mf, e.g.<=[X,f�a+�5 &�d0�V�ma ��Bork:�"hV� <$n>a �2� E�um UW,M%.eogC \mu:1nM�*� A��Ii����Z. \bf{1c6 ]w~oQ����!%� �a!(ac2 cy#m�..�_Nj \ds�v \Omega� I��ZtarP~i ��L �u�P)_dr I�%�a N� Its �"�Ii�jd Q=)!Y.� f fGH.�%�Q_��Ew�3S�:�!͡x_��U� ^{-TM}.�>  MU_{� L&&"�E� 2 S(1P���� $ tak��� )V"�H $(�pmby v �ng ,!K%6 � $� 2 2d$,a� � = i^*:MU_�2�U_{*-a�O�(a50 d G���*Y*i:<.ZYLPA�3I�M�..!�>�=C.� ��!�t RJ��uNF�,!,�1ram;' mute�Q��Z7U^�Q#�;U^� @>�� bf{ext}>>q +r} (�C:f) @>�a>> 2+/1)�7@VO V{u_*}8@VV >\\ G �A��{rs @>>{�>\ldots.��q+.A� !$$�._{qV-p_v�mu_)ax�-_{F_��!GB &� exQ"� KM� , $u�/!�.[ 7� Q -X�3�4agA�o��J@a�l 6+G�$7qlrc�2�� �a�"� a�"D MRp.�G F6donK �!��vE63 ���bugRHj Wha�fundah/al mis�s.�� )"�Fj�L -��"d} mod"h ��.��!�o,P���-�2&� �5ݹM�OlHFTn|"� ��2�A"� vU%�tangent! A� nu_{ �}��TM$cp� Ak Vrjagin-�&AH]"�B � J�au� ��.�R�<'�.�rw�"82L�= (52:�_*.�-�6�:&������h*�;�o��zo"SA�!�H� Q'�d�=;a����Ci� J�~'�'� anon?� -TM�*-%��  $53$�� { :�� !�=e��.UBtoplus IJ^*(:�)] or%�a B����r�A�oPBP!�rb�!VP�.^�r9-�M� � um�� � �4�t(�&&,%)��T6%��� � � Z �/���yK$L-�_MI ��fi�e��*� Ae�@�/� ��2M�bar� >>   LM�@" v}�@V.i�% �@|I >��V�$$!�y�� >���B� .�AA�!K�R&D al�,����s<al to�\{(0q\�qw7 :r#(0)\}E�S�# 2��D�ubm�\on%�)��;At�*sponds�(�'>�of���ro $.�fY~�!FD$bZIP�WA��vF�:5AH.�I �ka�|�9F�a6i/�� �Q�ɂk�5�mA >� ���T-N"t^a^��Q.�*)*na3� �:Q+� .pd�f�G�.� �s � then!�eta �J a��6f2��*Cb�B :(6�)=I� \astE�en -) ��Ecases}q2t) &if} u0GOq t .�z\ ta(2t-1F92+leCj |�B� M7!�-�e� <�eQzy�e &�Zit�Uve&!=�st1Yto6Wif�� %�i��])c6@ &a �} resolu9p�*VS���."i?/��,e jus�kgs:!������� is .!�be-$�I$]-$ �.t�1 . To� !�ZeA$"-�Ff�n�$�$ �� : b2ldžriZaves� �0i�$7R��weTEȌ�Arg/9��e�Q!�=� p�M$ them togeAf��y lo*�1���wrr#k�i�narnQ)�*�Z� )[� �.��A*\v��(t)F }{c}�i(int_{0}^{t}� ^{(-5�4s^2(s-1)^2})}dWd�bm��=m�c=6L�~xvL�HIc1�'�9�^�5�%��%���(W<+ e�-A%Phi�h��F\� +mu)%La&z(9^�gI N��L�� _{\rs}M =cw $��a]K:��_I�-J0�2re.c+���&�d�� _{M}v!.b#=> �A)�lsonk���� vUNm 5� new ob+ ��y J6���8B C &��L%�NP&�Phi) }i 1 .!?astV5�] t LME( �d>��T"���of .� � !���U*F��stn J!2��c�u�;2=�.D=w�?�<� �� -���!� s, �Q� � D)8j}&�(%�$!8�!� $H$-g "j &>�-y� 2]6�!\�"�� &b :jB hook�x:� 9$ɻ�)B�* �"(. )$Udto�l!inae*= + N]*K"z� M:��  M$�\n:�=*# ^{-1T#(%)���t�"� ��� t$d�� �1)�5*."  (6%.�)^{.�*(TM)ɒa������T.�?�7!D�7��7�e�h�c*��co�V0%hJ�M�>�mP!�>�M5)^{TM} s&� N�� i�tau�F6�I"��%�8:` � O M.t "s  ,.�S^�BD�0F*Dn� &*s "!}.5�.By�RFg, i.e.&gs� Uinclu�� bS.�1 x�F�^�(=DI*�A,-k��M�{=}A ,2<�&&e3of�_{:]}ie2LY� $, �9aX t�Q7M��U����.�y6 .�a�47� e'2�aA�\�c\mu>�.h�>}~�;F�#TM �.�A�� m�j�aj�Qq6I�d�2 e�i�)*�\>O[8LOr� ��-L �U7,&�( y�.�d.�u[ �=�$,As�vi !%.� | B8� w � 6�P$ �M��U� !\���e.�\ �� per�>C:+2��!E�&��:�-�-M-�Y"� yvI��AA���>�2�B�"�e. � -2�_=B.U�LI�J� !P���*� �C m�u;� /co6�mn��{5" �a:~* �:'>G.� G$ aVR�o Ag�0"���<�V;!�A�22"�&1y� &�U^{�o; ^)r>2�r^{B+&?" > 1+6r��rhZ�&sum*n)k  M�)Y i of� �a%��F!�$� &� &� &� &� &� &� & & "�}�6mt:�{22vً*�u A.E5Badw\& C. Oz��C+My�AZBgMN*s2����*flag J/e�),F�tepc2Ma�ϣs8� 258}w�x�-19F"�B�-FramptkER. �J. , T`�����s, J. �. Mech. �� 15} K���877-8���c=7 M.�#u D. Sgz)��}DS y, pl,int: �8<. GT/9911159,199.���#�L#t\& J.D.S&t, A� �+�0e�60t�6ingf�( GT/0107187��Q /p�t~B. ~C?pxC�inׄpN*xx , Spu$er-Verlag �4MZ DoldEa ,&v{]T����4�3 t�fer, Lec� ??� )�:y 19769�m*wP�V��?P/*v%PyA� fibr�$!qnnezM$A7A�41963), 223-255X=mN Dyer} E.  A�U]%�Xi��BenjaminEe9.% Eells-Elw%�AK.AeElw��y"ˈdiffer;Kal5�NB�7�2)z:0I$c. Symp. P& )O�15}!�7a 41-4.��-McAlp�}J.�J.  , An��e�se-K%gemVy7iy��1055-102��@janich} K. J\"{a}, T�byB�!a81.a Kuip!�N.E� ,!�}XypA�A!��otA-ZX-z%73 ��19-30]Z] S.t, ��5�M^FE�5.�michor} ��M,B�\$VMaH�]hiva ��ish�!L��ed g06g0lnor-stasheffE�W��norA�JE�S ,� 6| eris��CMaA�Pr�ton Un",~��u72!Mo�5lAJ,2zjd�&aW�U� A}~�~A�135-12=�o}_ ��O�C�&tL of F��Var����DnM L ~0Grpoups , PhDAgsis^�~(�.��1F�c�S�s�A�"�!f���0 $LG/T$, Turk��Jouc+ofe�e�wE�25F� , 415-448]�&�|2"��(,��aBO�z&~U.~m6 �mi�o �]>5i�!|�itb�palais�n S. PT, Lusternik-SchnirelmaEo�J? �|%B *9115-132ssegal-�P sleyŕe leyaT G. S", M;A:, Oxford�;!V�65��86./-[ } D.L�I�z, Ele�+�i9,%"%Iresult"� ory!)Steenrod&-~�dv. �2��71), 29-2P J } F.�nn,.�$�Jaɨ ^�a6e�213-222M*�stۉ R. S ,yG a0e�s�yj��=m %mf62�|S[U,!melques�@pri\'e\-t\'es des�  ����omm@� Helv� 2i5@�17-2@�trombaED J. T, SomK76�u�����? Amer� S�� 34)U$2), 578-58.�Zeidl�A E. ~ ,/��Xd2 M�6� ipl�nd�ir 7cj >� !u9��� >� 5&�� ���Ɏ�Ɏ�Ɏ�Ɏ�Ɏ�Ɏ�Ɏ�Ɏ�Ɏ�Ɏ�Ɏ�Ɏ�Ɏ�Ɏ�Ɏ�Ɏ�Ɏ�Ɏ�Ɏ�Ɏ���������������ڷ����������������������������"� I�l,.�aA6� � 's Geom�R�- "K�� ˛e �:�of.o }�܎�܎�܎�ێ�ڎ�َf��؎�؎�؎V�y�,��B��ȎLi� y�ӎ April 16,Q� �& abs�+*�*��ώ�ώ�ώ�ώnώ,/ rD=&�b�` C+%Ȏ�/�0���/"m�m>0Of��u�[5Mh2F:�nC�3ďl�w�^<e({`�$>�{H.`>���y7G���<�J di?Ma��%K"f)F�x>v�onZNȎ�pǎAfter w scus� �jobt��.��ZB$�:5�,z&�3�;�2;7B��B� �ibf2�qwe�=�� c*&�)y�\Ititle "�SPreliminis.} %�FMa��o nSJ2�B �,�{Cz?.}"�*'A�$MU$ Őorigin�u� d� "� means>"A%l)A��s�=�G��s�r a�-�H,x_q�Li)�Jmofm9iD�:b $*>/f.e#�X�!�.T&?,�almost�"2�e5 �e�?Y�ctya� �3b��zo22Zq�1F�>��5�;�Q*)��e��etI�e�a�u.��p� by D�[ . Hi���ed6�:�-� }e�E�i0a��d�D<�pyl����P {n-q�Xn%Y *Ii"�4gKa:�@&1U�((8'lira�� act)*�;M�2��)*m7�q:�5��%eC��7wo}�A�)y}�y �7a�8r��URT "�\�AXbasic-э.�Eve ri �>$��^rqA>M>Ay �~�[f:9or992�>3� Ao�s ��<�%$Eilenberg-"� axioms. DEssZez }�i�adams}. ��-o uy��`6}IR)�ed�!��/ifF0!�E*na�&Chern�K�fn~�<� �:e "MpeE. E��� �B�g=�s A�r�n���Qq �$K�`, ell�(�"���! JiI�is�G|A5�u*al7��F���ory �o%ua�ju��A�wFc"�D8MU.hk5A:ne����q'fma!"K ���� M.P��[f:�� "1"?,2 8 �`.^Tp:N�)��`!-鵁k6�AZ`�B$p�;6} 2�G. - ���68ai�B6~H9�62k]O;�0ÕNY�:� %y�&��A]QlA?A,B2 ,�% �$y է� .1 I�� Dѩal*v�P� ley-� St� f��J � re#ceE�A�H�Fz:5. � %�/E�llY���ro�-S^1��%A$act semi-seee&&� $G��ts&+K��o"��ŝVe! e!�>9"LPG"n�T�� xiߕ toru���"��te�vM""�! j Y� x cE�M)��n��e�T� a��e� l"� analo3 ly�� as $7". A�<wu�\L.�$Grassmanni� $\Gr (H�w5&"�al"S sB� �W:f ��6�J  fJ  Z"/ ""h%�C��"� A7B .**q�2��2��2��2��2��2��2��2��2��2��2��2��2��2��2��2��2��2��2��2��2��2��2��2��2��2��2��2��2��2��2��2��2��2��2��2��2��2��2��2��2��2��2��2��2��2��2��2��2��2��2��2��2��2��2��2��2��2��2��2��2��2��2��2��2��2��2��2��2��2��2��2��2��2��2��2��2��2��2��2��2��2��2��2��2��2��2��2��2��2��2��2��2��2��2��2��2��2��2��2��2��2��2��2�f2��G� abov�$ *�`inV�"?���f�&c��vus8!N9"��s,.�*"&I�;�Smale, mRb� thm}�mC n} W+�k�Z���e.�"o� �hIH2�����$�)y �f��f��f��f��f��f��f��f��f��f��f��f��f��f��f��f��f��f��f��f��f��f��f��f��f��f��f��f��f��f��f��f��f��f��f��f��f��f��f��f��f��f��f�e24.�;2E�� *��cW'd.��c��c��c��c��c��c��c��c��c��c�$G+"99e4�4W~b & ��b6{�[V�� `,(�?��?�?��IB�:eHI&4*�4��&}71-n�-}2�Yd.6�2��1��1��1��1��1��1� �2&�t�m"�R, jets �+"�0psa,4 $C^m(W, N)$,$*�� g, :g,qQ�2 �6t"lReK*�lVK�K�.4*�;�14x���2^ ���bo��dov�� l��t.ter��&76@i�=e6D%�COe��to�6��09�KM1�}y*#b"#n"�d4��,h{k-jet from�a} $X$ \emph{to} $Y$ is an equivalence class $[f, x]_k$ of pairs $(f, x)$ where $f: X\rightarrow Y$O� smooth mapping, $x \in X$. The p2M andZ,', x')$ are ��t} ifF = x'$, $f 6�f'$ have same Taylor expansion of order $k$ at $x$ in some �!dcoordinate charts centered2��f (x)$ respectively. We will write $J^k f(=1< �,call this th�$k-jet of} ��4. \end{defn} T%d:� t definit �U2� rela: $�= [)^]!�%J=x' �$$T^k_x f= '$ wz E�0$k$th tangent1�. \begin �XFor a topological spaceAt(,a covering!t$XY)�lo!y �e%��every point has a neighborhood which intersects onl@4ly many elemenf�2cApproxim%2 $g'E�$gA&6sI� fine�y meansh following. Let $\{L_i\}_{iE� I}$ be a �HA)� of $W$. !7 �open sIL_i$,creEH bounded continuous!�X $\varepsilon_i: L_i \ry�[0,�@fty)$ such that fa&!d m�pI�Dk > 0$, \[ ||J^k gA� -  ' || < 2z. \] 6%E-BanachIe<say �AllaX on $\mathA?S$ of5�uncA�,s $\alpha: E2�7 bb RE\a�� Sard��EZ(it satisfie%� 5�![deXs:�|VQ��.� -nsupport}!�a5 $>��A�ayE�ure9�ѡg��dsE͹($f(x)\neq 06� From�0te{Quinn}, we��thm} ��admit��E F�i���(E,�)$ ��!s.� with� nonempty -8. In particular�mD separable Hilbert�}��es��2|A-zrx�T-}��6�a secon����, E��!q��sQUeda�� �$!�first d �JA�*qis ��compacB it Hausdorff� � I�ou:�e!r%n��h�%����unity}��a�� �ais� an� $\{UU� X�ca sys��J  $\psiX.�Ela�$�y!�%k�Av�"� .��$\fora�� u y  \ge?;\\ͣkM�� -a��A�I $U_i8�5�is:�`�Zeӱ`X��,\ds\sum_{i} )&�= 1�ņ.�V� A6� b� id�.)��i�!�s�-�if I�]�E�$ if, givenF6 E1 U��re exE>aTtrqAD �\}ɍ  ![��s0 %�2�� langZ  X���q$� modelledi�� 6�$HEne5%dsKui9l ����8Eells-McAlpin},��'O!|�:�!6��A�4structed using�mJ�A�m a�u.� ��u�` result was proved by F. �w u��$ kirmizi})qH%q���F�� !ls U2an Eh�? !nIf�`27Ne�"Z8proper Fredholm� E�n5�ub!�ofe��A2�The-�Jdis5�%g 1}w $�V{UA��4se techniques,M�E�>k I�5bcorQ�canalicQ�:\9C1.q�.M� �� v� z�%(M,A�.!E� �Q�� FyA`�7.�m�homotopyMb���be two�l Ql2� 1>�q�t�Aa � aO$\phi:6VYɀ�ph�� �$f$�not2 cor�on1 b2�sXdomaW0by $(V_{i_j},1�_j�� I9 : (6>�!��.C $�m_i}$"fY��:��n�a\{gI�I|N� 5�), .)�)\}M�" \{Zxsub� .8 Y_i yx \bar4}Ew Indu:�E5ge�Z ���� �(g_0 = g$. G$g�g_{i+1e��6G�9 6  appl��+ situ�X0$U_1 =U_2 = Ya�U_3= Zf. disj) un�WV$W)�$ � $j-05�� 2H s�a����(_i + \frac{*g }{2^�}y_A'a�6(Y_i) \ ��a��$yA�in \Sm`. �F$\QjBx, $g' =QliQ*l\ir}!�:well--�.8aA�v"�$-6�I � '\in� � !H"� � a�R�. I�0est !r <6v��be don� 1�r�1�� �A*]� s,� Le�.Q�h $C^{-)B_I{$as-j\in \Adline{9 � aa�� F istB ��0 in �n% "% %�ey f: M=���JF  betwe "�nn9D $�nd $N�aV�of:P5�.� �lo��"� �nS�rj�*n$ By Coroll� � "� ,&)map (E�&�)� Z.UY$QCde�Ve\*hpaL: >5by%�Y��6 untilA�!r�%8an GssiA� lex orie���!�X2�Y aY obvi�aU!vy � & o . By�&� Cob� smE^Pro"� %Dgrem}K c*%�or is�travari � �ic�F� u�"�}<sonm;>ZY�n|R5edzA�e.g:B�e. � (mayY)@+"nE��H�}Lpull-back $Z \prod_Y:� Z$ dependly� A�JQ$f$, h#!�ma2^*:&� U^d (Y)\*f��Z)$� Hby $$g^* [X, f] =g'  [Z�4, {g'}^*(f)],$�!A��+ U�64 6� of g.>�0#. More�B�� ^*$ NM�y9i${A�we�!(Q�ial��tM =*�or/"J,Y�W$ZEW�%M��q 0 $Z\stackrel{�}6�  beta}.�X$�MxeF ionse_n (4� af )^* = m ^* {$}. U^d(Xb (Z).^�idvt�"p $\Id :QX�xduc40 end�s` Id^* :=fr�X)$z: $d�%�-�1\'>> M'%�, \\ @VVf''V VV Z @>)� >> YA X,I�o\] �b�&squares���I�H �sw�'$I, f  , f')$;� ou!; Ye�h�lsoa w�FX  �, f)$. G� 2g 6��g��2�� showՓ��s $M'yf'2q�M'2$2% Z{v/� �"^* %�^* [M|2{X] =('t" )^*n/$� cleaAx>'M''= Z � M' = .(Y,X�!as�  as�Zds$� ��n!��Z����&�cou7 M��7(\tilde{f''}2?}eG}eO \xi'a�I�aF.V\xii�q:�qi�qH��% �0&>$vec�bundle $�'2��r�\xia�5� $YX?��Ŝturn ��= ior(cup)��� 6�m� :b0es $[X_1,f_1]� .4 {d_1�1�(([X_2 , f_2]�U+2+2�(their exterg%A�uc� \[ n D1]y V2 ]*X_1t X_2 �z6�{41 + d_2} (Y_1\� Y_2�'Ifz.w $f~f_2��t)Aago�im� $\Delta:Y.�Y � "�w��#�C%�G2�:& \cup=%!$ l� �X_2%W s!+.�\Ia����xisI':��JR><:X_1 ��2 $,�b�'2���� �fi�znl -�'�" � �+h` !� �!�� t0%aA�A�]�I�a Z1���Z� =M� Z��>� +qH)A;�-H'a �D/n�B,I��} %v� A�8� ���associ� :4n,6� (\,#*(a multiplic2� "� p or�M�� � n } [2� whe� �agree� j*� e ors �' as repres��� seeme���,easily answe 0n� no �dual � p. �s�ai� � o e Eulerr e�S� �E�J )6$s�n�,(o1��lis�use)k,es!know f&�(janich} glob�+ �y#a 6�oQ#I�f���6Q#NM#� �,zu�*��6�$\pi: E.?B�aj5 $B2e=�@�q &"�� B"� V2a�/C�Nzs=1�#By6m�%� have�Lm WR�t�E i *!C"�>�!�$� i: B.S�/: zero--���mH�.�1� iR f $i$.2' $"� �Th����e�1h2`�7ajR�bbtat1� �>H�tl}���a2p in��-�!�� b*k39�\x6BH��f "�$m�b�!��.� $i: 2 \xi$%�)"(  U$-t�%y.U,� ��!�,: \chi4) =i^* i_* (1)> 2d}(Bk�deG5W�-S&g proj���\ mula%Gysin1NF8})��'Ea� eEe�] *\oN��S"6�2�d%�n� !K ( � � f_* f^*�� %J0M�$ E�sMm ���|�$6�%]A4 �E42� U4$n $Y'= \{y 0)� \},3�#�3B��%of^��� .�align}N�f] &= �5�,f]\notag\\ &� (',f_{|X'}]. )� W�$�%ermine � .E�By9�aQ e�em�9R Ke^�j8s"�6!m!��#eY"s f':2�.f'W!�&�42b!�th�! ��$X'"�b2��1I+ u-0j]d �� $j:X2.�sg iU. HK,%9A{ >P1�ŭ.�$ ��B��endq|-�neN� ful lemma.� � &�*lemtub} Au� plit>L"= f  h�m�tubular2�"n zT�:a�2�X�Ff�>�³X^�2V���}i-pe%4/Q&A�5�a�i_6&{j}f{j+�� \xi,\xi-U%��U�5�2>&A� �F� �\p�A�7<. How�r4 ]kain�(a!� e $U�of1� radius $r�&\_{|�"U}}� cegwEE�e!\pi_*.�B�.s.�%:3�!$pi i= \Id$5��  ��D! $i;���*z _{\x�#:,U =��n �itself )� eCy movg n !P�dQ�1Thom is"�}%*�>�\congZ \-�{�re�= ship"�"[ &[ �$M.}"U! O�t4�R[ Z[ .[ La�w� scus�  p"�6 �!{ $GrassmanniB=!9$LG/T��par F�5:H generalR� $\U^*(\ :� .�=�[f��" � M͍��M\lra��m��/N� "RE.� "�E>�/�$f^*: �X)c M)=M�M).$$A�.`� �1M1into $Xq� va�(quI�pE�rho :g rds�$"ef�A {M\downar�AX}} ��؁�lim{$ aken/l=E�"\&�  X$ɥJ�� �L;.irea3s�6 ala/*�tramEc�7� 3 �M_1 @>fd_2 7@VV2� X @>=>> X ;\]�  r, ri�an in�2e � �i�!s !� : !F (M_22��i�7E. �2��Each �"� I� u�ppear� asonz a~c%�st�A�examplLe �(dm�la�m`@ hopZ a@rnivZ8could be replac�(� , bui�oŪ� �"~ �6!�;"� conj} �% 4:InvLimSurj} $A��alwayis �on�5"3 �@\U^{\ev}(X)=0$ or�\{\odd �rh _�XMFX�X� 1��7�/rt�#�0al �j.��6.Zco!�x"�sb,)�$H�=($n�9(1$) an incrng sequ� AgJ�x)M�0$\dim H^n = n�H^�'=�xb�.o 1}-�" 6�2We� �.e�5Kui� �5 }Uth"� �t�&(group $U(H)�c B��&]%ct&M>cm�\Gr_nLbae <(of all $n$-"�!ub\�� $H� ��r���� o-E� .Hk!� n} ' (H^kT _a7�� � � �w�F��R�@a �6�R�Z�%if;<� $BU(n)��b�%!m� Proj7SA}� natu��AZ � (��-�{n}��� y.�F:;)&^!}:4e&D xi_n>Z)�is�,��al.� ��BV(]�PresslZnd SegalM�s -b eaF�ac�=�Gr��i2#zd�t M�./_-�.2q�a��n !N�AR�*BN�*H'� �i:9o��\sG^�NinA�� stal1zerm���ise�^n)U(H')o ich �fre!o<� trm�Q�e�. w1��aIE�) /(U(Bq)\n$= B�"6C')NNBy��'sa�:&��,����,MFsei&�$$�a� \simeq�!J= nE O)6 hand�G!AF~Q�k>2 !�')�4�M(H), "f%$H'��)A2�3Vh%�ionO b� 5f���m� Also6Mc C- J& ��J1b�He�(%��f�!$${ s�7�-lat? i��i Xb�����sp"y G*�as!\�vm=AKP�V�!a��Fet�`N�2� �n��.>� : � P(H) Z� n}} 4 *^n). P��])�� v�<əɥ-/5>+'by� Ar� ab� �xr� a {i_n^* !{n+1}Jz�7[���&R suffic!z! $x^i�0im _$>$i=0,�In-L $n=0� A#n!ivi��"% |Efy��8$n=1$z.2�6�,I�2Fk1m"$ $\lambda\9E�w.?: yuI�"� � �/mutes�!# z  1$:� \et�J=%( � ) @>>> �&&V &*V�D~$bb C P^n =�-� J>>��A,� �i_n. A{n} =9�2�A-%a�"�%�a��+ati�t.-0��s,%) 1�/8g C!$x�c% uM�E# ere Dn.p"Sxr5 L)�)s%1ca�,2A�))28F!kta(x}� �J=3E �b"&2%" AssumO =%�%M}�A�a���'sa�y_aD�L {2i} � ,\, .E�Gax6g6= x^i�� 2i} C ��L�C 5� ^* ;+ z_i x 3J��JI2�(-(/9(MU_{2(n+1-i�4B� y��W�9�2n_)�. A-*�-Awes:`f!�1� @>f^BTyFW!m+B!&�>iA�.gA-[W', g�%2c;Pw��2�ѯo"�R!+1!f�:e9 +2-"!�sP i5�O!�}e (m` =+1}�"�\��M &(M! " ^*$-�N odul��-2x^i$ $(.�oa^Uis:�i�3��?��?��6T��W�a�4 !edVz��lrajya>y*� %\6�I#�m N",!9ApoC4to�va�i��FbyTG��b�@s $P({H^n}^{\bot} � �� to realizU$Y� eb tricb�� WxC 3>�S.��;Nex��geome�Bof:�;%P0vF r1whoGde`nd"�;we�' ume.����ourF�  DH = L^2 (\S^1 ; \CIg �R H_+$!(�*/8AY!N��O7����&�' $z^n : z\*(�0��a�"�0� =�?;\p$>�1}�$ (H_{-k,k}.�9�(�.e�� . /!� cT = z^{-k}H_+ / z^k H_+e�r �mWA(\G�)Ya�E�7'n)] � to}�El2IK#,� \b-\Z:^F�)Z1�� nv\ maQU � � {S2jE�cf�JD �~ �&�$pn9�]#�����3Ed"4* $�*�2L��:b C:Q>�� $C_S:>>�%�eD�G$ $\Sigma_S �.zMstratu�5 # {S'}*BC�ys= {S',k}= [�]� \cap @.�11q �>)�H9fW, Yl�FchuRcM� b4rgu��L38 Atiyah-Hirzebr�!bt�" ���I�+6\ �A�logy �8milnor-stasheff*�+ee�P9& k}$�id�Cor8 ݥ�$-m�d B �p$6".O A�� �Z� � e1rm{�}BO= 0�9>kqbA�.�&:�&nkb>�.�e� !"�!?.%��n�e�!a�8Sa�n~emi-si{ Lie�$G%7 ��.� �LG / Tb'{ �3As �Sp-dd .�E�,AM� Y� F��-I1 �� llap�,:�� s toI ( ElC p�$ioL'!��.��/T6H^ w,\ bb Ze�6��I$.E�-��S�yxZ�*VB^w (w �F�.�7 %D�w�C��wp4$C!!l"DJ>�w$ unS �-0��>a�&�B^ve lishZ desiu/u�it><�M$ Similarly'AQ=EI�� M�\Omega G6�ie $�(�2l &�!&�?1��!�@ - )QifD1on�ada calcu�!F�!%� �$!�%�J intr�6I<w� � ��:�%��� fur� OePD"E190 x i( /T@ �!2� D H�V�"�"T4 ���2�cJ lv`� X_"SA� lex � a�Q�)�| $\�N(S� !o&�;"��S2�i�?p"27� index $- e.56rP)�J�!U%�.�\&V y $ r3#E��=�{2~} �|9%�a�edTh�Qqa�6S#<�7!�k���JS�>l&s�;q�.�WwXI5!�� ��c9�5� �nd�X 1mee�L!&� lingleHXEW 5��E��umzyd�.��$!� loop�5LG$�viaHadbI9�� �U�.� %�frak g� .� 2 _{\C69 J=J��x�P��algebra%WG�k`�G ��x�+�@fy $H_2a& n�Hw !�Z� 1�a suit�" H�,tiay#neraC�:f ]A�a%aeM>b�07L��Zj�Fs�5 T�ba�,.�� �m.4!v,.!/blb(bP�6DGr � .�a��7dGaVherx^E��� [a Q�{�}9dex�� mhVsm' : \T.LT$.y$U�rV"U )& ��q�| }b $�) ��MAM2�F�.� �%1�a *�@�� mapI&����X. �}B]\�� yR�.�)���} &���� If��� in��'� *Aa1esemN�&t ![basis"jeH' 2.�^2� �)�c�I gra 7�>Q 4 �� n� � . i;� )\R"� � c� e!C�&.�&\ev> U^* F /{\ker � .�(�"� 2�)\o�*.^AQ$G= SU(�?��}m�2y(�} & �8 \Gamma_{\Z}(\g 2���J+)� di�d power��� $\Z�M.$ k^{[n]�a e8de�1$2n�� 1Y�*SnJ��sM�^�A��� zK��� M,�a�%_  \wide�W�8E�4u�w.� � �k�#eOja"/ >�� w/ L �6�*� i����w4�*I)F'0b� Ia4 �LEi/Tjr"v .b(x_0, x_1)/IE�.�]�%�deal $ (E��+nK$  = \XXIw]l^{[m]} - \binom{n + m - 1}{m!+ + %J&n&G:$]}: \, m,n�b1\�߅U��N'3�N{x t]}� ��ain.eu#<) $la%U�@ebibliography}{22�*ib3 ${adams} J.9` A, SI  Hb\�Gec/i�� , Un9#4ity of Chicago7( (1974). \mHbaker-ozel} A. J. B4 \& C. Ozel, C\ &.� !(�f�s]:k�Tc s��flag &;eti(ContempoL[Mathe�m\cs {\bf258} (2000), 1-19.�|BGG} I. N. Bernstein, I. M. Gelf!�\& S. ,:� %�c&��-��0s $G/P$, Russ� � . SurveysELf28} !H3�262#-�,Bonic-Frampt�OR. �!� , SV?&�on>�js, J. Mech.}15}!�,66), 877-898�$chas} M. CA� \& D�llivaut�gT, p�int: ��@. GT/9911159,1999.Yohen}� L. C ^$J.D.S. Jon!�A���^aCoretic�E sz�< GT/0107187, 200�e1]conwaye~B. ~C, A Courz n Fumn al Analys ASp� er-Verlag!�8aZ DoldE� , Gic]�AX�fin �f�fer, Lec�/+�Q66y 19766v*wP&�� �#t�v�*yA� fibr%Ns, Ann.!UI$a;7a:196A�223-255=� Dyer} E.  a�዁4U 8S(s, BenjaminEe9K<1&bc��AK.Ae�c, �(>`r4Oa4d[r�"�7, Glo�B1�:NS$c. Symp. P�k�15}!�7�41-44��"f2�J. 5f!7���@e_Qse-�B)gemVy7iy8a�055-106.}j]C$ K. J\"{a}lC, T �,>�!a81.aW* N. H.{*,!�}Xyp�A%]&/of���+zE3 �5� 9-30=6lh S6�uD*cp MF��:�(1985.�8michor} P. W. M,B�\ble Magv]hiva PubML�4ed g06g6�!�pA�JE�S�,� ! eris��Cn , Pr�)ton U�1:&U�MoravalAJ,"s8�dY:aW"�Q� ���E�135-15._���mkC�&� of F�rVar�r AH� L�0Grpoups , PhDAg�,= !lasgow�98.��1}B��U�sCA�"�.f�q� D80, Turkish Jou�Kofe�E�2�L1�, 415-44.�palaisş S. P, LusbM ik-S�frelmad%o�KJp q�s �j115-132}6:l; "� \& Gw@gal, -l!k, Oxford.e5��86.`Quill�rD.L L, Ele�a�ReXt "��@6#�or�# Steenrod =�Edv.��c��71), 29-2��> �j, T�?al�U�%Na�� ^�AgE�213-222o�c��S ��UVd2vPr�AAD��=M�4, Amer.�/�8 �$65) 861-86.nstongIU ,  %3A�ens:�&yݍQ=� %��62@ thom[s<,!�elque�>(ri\'e\-t\'e�is:  �\bl�Comm. � Helv+ 2 54��7-8.�trombaE� J. T, Som�%� �9n6���0 )P)MS� 34)�$2), 578-58.�Zeidl�~ , AprGdV� Main��i�8ThBQ7f F`!u9Ţend{t:r b docuaP} ]�\Z8[a4paper,12pt]{� cle:u�@ckage{amssymb,amsD } .,xypic} \xyopa {all6"icxVnewM�G{D I }[�=] .'��}[6G].2,c�]*C2(�\ LRemark6exmEr:6 l�B"L 2_ �"e<em6$�3t"Not��:#ewpar$:>x! .?.6=x.8.2>(949.>$�-*>!,1&>)()">1$1> ) 5B) {\itF� of}{��of. }N#6%}!_renew�=and\the%d{\h5*{-2mmKB'=k�.5q�,rem�&ex�&%��N-��*)��)�ƞ(oF*e^environ�ʁ<�W ion}�\g�\em}{� e)�.9ri�5A�4F3e�4A�4F4E�.�7 F9%*k)97 Z8of}[1]� ,(of}({#1}). �FI note�rm}� \vfill\no�nt\it'.\r1nrene2lIa��.� }\bf �. H J�e� L*.MM�}y�1.5mm}>Z(a�:�FŃ*�e�.yrP8AD=iF�MS7AG7F7E5io.�.: F<��w}m96Bz��FDBB��>: B6��8 :�/��N� bb{N!def\qed��{0.3cA�4rule{1ex}{2ex}*� V{@ve[Max{\h $orname{Max:;ie{i.�9eg{e.g��seq{{\rm�*:Epwsete�wp(#1))9t{\mid6 goto2�lea\ra<"2(D{\bprop}[2]{{#2}^{`:$w$ P 8W7\vert>6r6 >4 �:l56b:&!W8ils}{\;\vdash\;:"tru��� it{:" fals# 2$ \cantor{C6annIUrm{an�9.- LSub �L6;End{Q:nR9d�caF4cf{\textrm{cf.::penAathbf{Pe>� penq wrmVs{%t_s6�pena{A6 Seq{A�^\sharp6;Vs:�O>Xs��rum>1!%:�te>,O ):,g�oid>,!!!\GF�p{�)s/6�downsegw{g;:r�r$upN"Frm)� it{F�0q�LocLoc:^TopTop:oppa�a�^ '.p>�o�+% T }�2 its_C6�p 24j3rs ` rm{R:NlL:�$9id>pi aTI6�lcZ� >ege!�2�:lpatch:S:(CC � bb{C:SL  it{S>�lc>� ,�L!��h }} %.Uapg &$bf{absPsGrA>$mF%_{\wedge:�ss��tabQu:! iqca-�it{Inv"2qsqf pDF�i#DF>gsg:hS �:�.%ACPF$im.#InvMo>ui���;title{\v� $1cm}\'{E}t�w�Z t� quan8s\thanks{ResearN���P part58FEDER�TFCT/POCTI/POSI throughc$nt 4MAT/55958/2004u Cen�A��F2�y$* Dynami"S�Ls by CRUPW Brit�Council�Treat� Windso'E�,No.\ B-22/04œ0author{Pedro ! nde 5L@ \\ \�lF D�Hta�\q^��X'a}tica, Instituto Supe�d4 T{\'e}cnico, Z�2[�Av. Rovisco Pais 1, 1049-001 Lisboa, Portugal!�date{~ makeE�EQ.ab$ct}�8 esta�}#9Fprewoly unl7U/5�nU72UY,��V��!!�no>of \'{e}Aq5�*sub~9d?a nt7way!�N>;te_A���� %F\, either)s{r^AQ '�Os�aed�Otal�'olu6H|We ob�S a bi8;qs�w�K1'�)icJ�)9:�,-3`6�#a r}!r 4I�ac,�!�/�?�%E�(-1 framr`�+)Q!�categof�e�65!�"�~").8c�t@%!���-diK b)?4)monoi���*&OeMw=[ZQth/>n[E2�&r�<s more_&!�"�concerw;��5E�-�� 6F_s�*isk %4nt�y �-ic�iEh vali!,s&a"�~k s. A>�sGT�=s!'se at a5�oXs�ifxo�qif{Ual%<��%�� +�,.ndon>�!'��8naloguILP holdA8=8�si�A�ic*A�ǂi�*�(new tool FA��4�i)H._J�,�dxF�,�|iw�ce)0�(%���q���IK9A{�%�ݔ2�rNto!�arg?Rb�.�c�z!�J+A�aŇaZ��.��u erti�;rAo�u1v�xgA)���t�d�s�R�ges>�A {0.2A\ � 4it{Keywords:} ���>"e%g� ,5�\-A�,:�B�, pseudo;-`>� 2000�&Ds Sub�� CD "�*T}: 06D22, 06F07, 18B40�$L05M18, 22A#,54B30, 54H10��3�,�_� pag�in  \�Seof�? ents(&�6In06�;\sec:i.�DeWpa�Qwe study5y�n��a�%-A�nd%t!rI�reej�@��e��con�:7Ѷ��=a ued f*o"XMax$ (a>��W&se maxima�ec��.�=1-Mu89,�2})a/�?l� 2)h RWKrRe}�Ptho�� I� ve (A@��!M�surpri9)� , st�uns@Iact! beca5l$) does%�g!�-,�)*e�wo&Z�#Qxp~xv�>ZMGX of�- r:ity-@ KrPeReRo}= 7n\[i�# e gui��e0s behi��he��z VI ugge���� ^�� os�� � look� t,u�=�� ANro��lyA��y� �B), or jus+ �se�^��)���) [� U]�7�Z�YaY�A!a (�)cipal)� , agR#�:R�,!�ea�?ဉ� N!\�x!�PM&Q]ia���!�enA�!Bl q�-MuA��# a:nsp?@�Si���� very&T,U�(be��x�Kr!�� %�x �<-�J�)lu a6 seQ�addJ��V# �,CJ!62.of view�L  1-�"�0, m�C broa�A�c�]q�aqC%m1&� J� AS �<, �to)2m��$a|a�LC�����O���\con"r-ur����6��(iօ�dH``ɝcal''<-�!�iBs��)5O!d&�> thre�Fnco :�V>;eХ�aJj(lA�Jx& ;09�U\ k�� 6 a�� 9S}. S�lszX"� grpdqnts}p�X main*}��k K�K.y(�6� 3��np =�)i sign�<��� OM"�d�./�WLsa0�s�,�!�enl�& 1�� OreI�$s familiari�7Ep�Hf�- icea~ame+e,1^e :�� Q�� givAq litt�rJ@.ې��3�aa�)� 2if�z[��)!�d�4� , {Pre"� ��B� 5� J�@�_$\CC$� �E�^m� �! f`&�cYx-Var��s,Bu�Gf=Y�P.�su5ps��!\�Zw�C�$� pped)�anO�v>�"�{+v�:"�yAf �_6+:�eq�ay*} aa8 {\V_i b_i,:8)&=& \V ab_i\\ .%a% b&=&&<\;*B^%B!�� Uf�t/ a�cr +$Y?t�r�m�y)&� aeR].v�HG=Y�:n�riY,is�FP``�Vnear''��K-EFu&$xoa-BJ*p�F� ̆ pos!� ����j�B�$0$. Con%)M ��i�}�CwD���! �A:�cqG�<intwise;](XY=\{xy\st �o ,\ ymTY,�rm{$x�W$yfJ�0e}\}\;,\] or,%hY�t ���t $2^GGboolean2r �0`�con��2WD: \[(f*g)(x)=\V\{f8q� g(z)�=yz�.\]Azad�� �75�DsG �"9 X �Q5Zbɧ!>�tion%H^*!I���!DX�1%J!�|A=fo�s \[PVx)=f( @))Z��B�z# !,s�3�4W�,ɯ-�G_�ef4Q_�� ��'�h24� gf�>��� re s�b�dl�11;v�bU y�:�&5v! ` mwset{X7  Xf G�E�aqNi"R�G�Ka �="�E%�{� ��Pl !�V�s��1Fm�forget�p d� � equaW b!�7Zo !?R� Fo �9Ҟse� aj� $QxUAHhAU%ry&hC*�I(Q)=\{ua"Qa,0uu^*=u^*u=e\}>�u� !�d Y oid.�mq�� b� n��hEV��ls�{�e -�� s%h�F�}G�!e2�)�6��_�!�bk�rS�e�E=J=2�:�ntXU. �]U �2'� 'ato�H �J���a�8$\{x\}\{y\}\neq�otyset$�Q�sD1y\}�� 8�c,%�Xc� �!�up!��ps"8mpur��� x Nto&�a�i4O>� �� E�a"�t*<o"�jr g�B.*HM1��d/P%��$6��:�sel�qbӖ�U> s. ��Cdq�D�g���r�min ��pg A'��!�s>--7Li&: s: N� (� ��ns�q�netc��%�, e�ic � oid �6;at least� vi!?���>�kGroY dieck%4�i�e��B� �JT}3ns� su"R\l�n� p�?!�eA02]�&�.%veu'�G4*'>'',"a� !�c< cZ�, ��� aScA ��4eb���U;%J- �6b@of dok� 36  dBint!�ely��s �.;C0ed,\�i�``tra� '':a�@FV��N��8�l media�h�� ��"�� JkbyZBP��us��9�d� iAJ!fvaYin��sa&E#QbA�e ``u�=3.�SP^ {Ove�}�l>( p Fr�k��R�# ���e�U���)j�"�ed��(map $d:G\to�0�n ! \[\spp:� & ])�^ r�u�)��ly �A%s&&���+$U�teq G$NH� U&'& G_0:sp:UU^*\\ ., %U / (UG)I N^��& 3yuN'!�t�f�j�*.`$z2$e%)�v3.+" w��� @h"�)��JD�(A�n� ^ imp� , am�L���oing"��3 l \[�-sp- e=\{a"{  e\}\] 1��b�E2�v� �� A��'Xa� inci�� %@ Q=\{!I a� u }$ (�2!H:! ss5"�^"{"M��p� %�o�V axiom (ͿN}�Y&� -�+!}�un� it)��O �T�J�5�(j��6�s2�� :defq��eb�thm:fully� at})bXa �a1�em)a^*V\bigw�,\{b!�6)�l�M�.v"*�5�refAko% fN� .M (�le)5�"� yedT�nd R;6Y!�"&�2�ua{nd�l��vO !x2Ef�s (R�reP})� p�=#��A>ha a%ql�Q��١�ty,d)��20' ure��*63A�A��F�ipiQ})Nt:��*m=1e�� V� n� $\ipi(Q)�lq iJ%al%Os}$Q�- we\�e*�2Z$E� le eea^*��#m�#Xɔa�M �x2p f +�bi�%"vk{A+thu!�� !6�Do� symmk�c"�-6��iy#v�E�ncG#al=itZN )|:�| %~ 6��fv��'acR�6�?Y, �A"" �,AW"6%�ef&�e"�-\!�$9 $\lcC[6 � ( EA se�G(4wards;��!BS$�o2-LSa|��� k���n� Aw����nM�1M1�ߤi�NFI�%L�lpbgp�q��)�I�%� fund�/�~ol���56�uz&Y ��2�AB�Y�-,_nKadjAyM�"� pn{ 2I�K >OE�xw'a52>as�I�: L !�.AABICS wfEca�%�2{M�X$of%�E|k("i;~ cor:�}Q] 4��%�$��*W0z�e�"5 �q�6����4V�Yya��5&eO tr�. Nlaw \[a�= �\] (----�val�%[n%k0 yZ�and%���E=wo�V�1 � e&\le&� \ ()a&\ge&aN � cul�&!9�a,*�O"���eI�ion})!�t:!9�.=�Y&r Q�3$n necessar��I:"�};)fi� �m�#��)v hom3� sm. 2`!a�$�V!�B�/0iv� ae2&0fact ab���e6� 5� ��st%qE#�� Ci {N�(!He>;F %meY�^�x'�Z1$We�!�2�)� ���i: F�laV�(q;e)1�_{xy^*� a} xM�y�\ 1.-^*yF-Fe AY1/e8se ��{a�.�ly�5�&�V6�%�:iff8���}��I summariz��es%Y��I_�E!�B`�021*�@ro�a�)$QO;_% Q} Q%�:ten77*?w\̇�"h�_�ec"34�$- bim[j*�q@< *{by :�of% U�����"� �,�iv� .t \mu:BQ�9mL6�of�P'\'.iP�Fg� �5 em' du�,��i�l�"�[�8}w�N�!Qc6%"�e� arro���Rr%v\5� :Y4SY�� ��| 4:"�!nu6���bFe ;gdQ\ ^\lcc(� "\OF�erx,�� f�!]& � q�^��mu_*(a xmA � �t�s٩# ��T��to9�u�Q��>�U)v�c(!��!e49�'"aa_*u���e6���Q 6�L �,@nsa�e�:a]�A�J�z��*"*AA��ѭ? } AA{.�(A��&�~4Av��!`�/ esa�1�:�QL[�B�:s,�+Q8s. +_&8y*+.�to�pN^$l;EC��g�i.v�y�7g�\N�6�xj;se��R :)��!=�"\+,5;of �Q*9Dy�8ћ| "�*�hM�n(9�W!U�"3]�(a�on,!�ev�[�2!��/on� d :loc�'t9[ s a-�+e i>T  >>m> ><t*�qJs2Y0�� <�!�!��'/tDh��,olܾraQ5�= iss�R(�IGteno�0d s us�!� e��ho�9� \cf\ h<[\S II 3.4]{John�Se%:3Ag� blemAH��en})Se  5 �/snL n�^1 !4:�ng}%�=[ ToE%)Z�&*(J4 P $�C ns(GGbAa (non-8i�/=1�Q�:"�A��d"x^"f�i�`xQ+�aB. �����!*� s��&)Q&�Y& �.X)\\ G1I( )G))N �N�^�F� N!@� N�:�a 2C;on���,ɸio# ��fo�+Ns�0xise�41)��-i�92s 1�1%�~�=6-�NmD AJa�suB�=F'is~m���"�">_�U=Rv:��top- . I>�=�*���t draws ��pi�iɒi!|iH�N?*6�*� ::S�Ken�,"�D�1+B^ "M?ɇ��.\ 2.8]{ <� may 29�"�};j&�'e� H&-"E Rb$ [Defr6r(�e4��6H1˙Ap$=�-.)��BIB�m\<�q Haar�s�9��/Q/]� I[Ao� >�=� Ou&�4la�(3u 5=sf < "1�8��Z4'!ral&<��d�#-���%�.� � cer�u�y�v9���N� are}{!ejX K� �(�or5)A)< irrelevanz �\�Fux� )�t (� A�us�9l ��:�3�^�# locetfgrp)  A�g �E e*�D}� &ve>8)(�).�)�k="�HVq�c�u&�%,:� h8�z=> )!�"�("�X=s�L�to\�\$Sl]Ye}����Bw4�.�3��mo\-n�*!�]m].XV m���; �'� < j'I(aD=A�I*-�R5ie~���9�%vq�J�r�5% �_ xtenQ��8t*NJ|!r��-&>>aLiv�!��e?�@T�F �e��b"alt�E�&68��+5:!��<� %�A�%=�3i�oRs *2p (no P���"3ven">�.``�Ps''b��$ �m�P� a��R�{lik��G��Ma.KF�.pD[d2�L^D}�W>5.5]{2`D��%�%�a&�w&� U�X&�,�<�$*�;�nCv"���Z��$� %�� &�6`�& ��er#i�?ll DA�*`LS�@�a6�)���(�m*UEc�6�#.g elf�``~D ly''�ed)a*vl �_@2�UAU�'&�N&�!��:��m�5B @hap>! eare5�+(ay"mp�?�`a%�K� 4.3A^&�.!Jn ��( �*D+G�l� Ł�7��<���݁��"h8\F�/%GGNS �>NeipH!trBm�.~�e Aw�r���4!��$.�st� �=c�c1�d�� �h*Q%��~3*ck}<e�1lX3�d�GA��"unavoid6,w��sonw �*, �� goodq=i �p�A�Den�0bym tor, ��nţ9`GI�� R�4d�ed�o�N��aQ.l5����!�G/Dc9%_L�<en@�G�.ork%5. F.��@l�A[�nR&)�9%��#m*�BAh��ay���Ie2j��� 85ba��7e\W��il%�;�Wpttng%�H�#%$s@"B@�ma�)���� hilosopAwl& t�s��N��6��in���MHsw  �� �a %�"L� etc.w)nd�Af�|��!�6(�cez `K9�dS ��& � "�A����EIa����iz!q!��%���)i+I�NbeyondN*%&�MoE�et&V B�!#� �橫q&?!X,&ZR�� ��A��Eofk!� G�4 cludFS�~oA8�Fs��t��B$!i!\�_j �&P�[ 1��1A rAc�#.� �Dsd2B�)Th)TMvm�jn/�v% ���>� $j=h_*)DhAZth $h�+/� �Ibh�H�!&�-*63!U�uI}�&v��x�$>e9�B"J $e�# .�HGŰ,CnU?�V� �EN<99 $P$b ig��;ys�8P{�F�8iBi;Dh4$�NJfor ``l�N#'')\foota�{W�[.``Fhet�r L''"Fof ``I� @''&A*0�� ��e�quoW]K��.���  $P&S1A&I7�ds�($pa]P$R&�* �e�&8n pq�P�>xa�pK�#AQ1")% v� ywiRV)� v*1�ach=����%�ۅ����� A�P$��aKR2� $f:P��@?6aL$u�O!X�i�Krv�u $\#Gũf:I| [�B�� 6G(-)� /$� T&�~�$U��l�!.z(Uy0_{�OU}�$. \qed5�wԅ u�i���g��7se"�o�hal �}!�a� && W$��:�* \[m"5 Q!zQ\�R˭ rite�ab^�A2:D $m(a1�b��A.��� &�b��� + s��l�m � 2K*kr* �=�&:*e$a�&�m�6:.X�. }�6.]?6QZtZ�:wh'a�*� >�DS�J�.| \[\a-�9�eM\]���=��a�$m��)�$Ta�{�9�xI5 A9���Z�ial��� 6 1� $e�X.�7R,TM���G"�B�$$ \[ea=ae=a�9] � i�&���a*O@olu�H� ���6�.` $(-)^*:I��F�-*&/ a^{**}&=&�<(ab)^*&=&b^* a^*�u\;. \end{eqnarray*} An involution is said to be \emph{trivial} if it coincides with the identity map (in this case $Q$U�Onecessarily commutative). A left module $M$ over a unital quantale $Q$ is \emph{ ��$ex=x$ for all $x\in M$. There are many examples of @�veh s. We men%Hthe following (only irst two_@directly relevant!@t!�Ipaper): \begin{enumerate} \item The powerset of any discrete groupoid, as � ed in sec� 1.1. J4In particular,�q5;D\pwset{X\times X}$!binar�aNs on a �@$X$~\cite{MuPe92}f�Wlof sup-lattice endomorphisms4an orthocomple�ed22$L:g (%6is is Lc!LN�$if $L\cong � X$) ---VBDboth a right and a2joAf!���4More generally:JofJ�$ symmetric2�2-form-H Re04VFT$\operatorname{Sub}(R)%� addia' subE )W F�rA� $R$.%�!�AMF?NmM mny)! $R$-}�isJ: NIR)$1E2($\Max A�Dnorm-closed linear� spaci��DC*-algebra $A$. AnA�presen�=on�$VA�Hilbert J$ $H$ yieldN��consist!i $j:Q\to�F such��( \[j(a)j(b)�j(ab)\] EO� a,b�yI$Ro�0 hal}%� fixed poi! $Q_j�the�Lq-+A�� s, wO in 0A<:�is�0$(a,b)\mapsto �m+everyVe, arises likeA up��" sm. �A M�� $Q�a��K9�na ��NnM!nM$9n $aj(x1jx)�%i-ga.x is6 �4L $ pattern. 6�!�N�%acor�@onE��i sI� !Mv $A^*M^*!oetc��A�other�&.� we hav!peB�frame},�өvis me��6, �aA�distributivity law \[a\wedge\V_i b_i= \;,\] of jHmai��{topolog/ (X�  ical X= ccor!C�uaM basii�a �: �bD $B\s eq L$ �0is join-densea�s � I�ILM�1!t��0$B$: \[x=\V\{e�B\st b!�x\}\;.\]Sy �E��J0�:�$)s$, $e=1m�t�Eaa^*=a!)u� p)ifE��is�� ^$$idempotent� JT}�mA#si ult about js will��4useful later: @proposi*}\label:�)� Let $h:Lm�be5�.� c let>�0K!�$5�furaBŃ%� downwards�K�A5�g n $h%�inK ve!8�+9Ds!5�, $h\vert_B:B �is�.�.  of} Assuma�atC6z*k proe�-6&ze����%�M').)RI�)�U�!-��Q�) , \[�k }{rcll} hͺ,h(x) &\iff& �=\  x>=b & \�0rm{(Because $ ��B$.)}Wmi � \] NowIx �y$V�M! � $y=\V Y�#some $Y�?Bm}�mby�m6W�\V h(Rfo�_�VY}\)al)^AB(-5{y5xJ$H� ,Q��d�_ mbed�h. \qedmprE� We| �N$\Frm$�<.� e���dF� aC�pop�e=$\opp UKLoc$.��n�functor� � thus!�se�� rav� 6!�opens:i{` }\torɹto�!we�  a�� AA.�G}� imi&���ٽs�butT. keep%no 9s difa t, us�_! ensI�local-S$�2 -s�l���or less "� termin�v, %b��i! m! same)osn)q.��called- �}��@2H c� ;( 6) Di }. Gi�a � $Lte-=0usually write1' (L)$1ead!����en!z wish�  asiz�pw\think!wo�$�a%"A#$2�we6�(f� or $f^*$, !e .��(M)A}EJ�6) tmap $f� . I �ſ)>g� � � MI( %"&� I�� � (of"7s)i_�%[,aZ~� JohnstonS ory�surAS�*2� defi�� U�sis a� �sub � �L.AgD e 6: � V) !y%;(-)�xaa�en{!v��seg� a�G2 �F�E� $J9*man �!;B�U �� duct� 1.by���5:-)aNtR��pr Mof��s5)�-)MA�i�?bB nven]lyrib<�tensor�as.gs)�s(�=)\o� M)�mv !��meets���a"� e (a G b-�(c d)=(� co(:d)\� -{EuW iidas"2b�} Ag�%T6�a�MX �to �e5t servA�� �e (!�;o lent� AՁC h��p ad~ t $f_!$�Q�i1� imagm4f$. (� 7�tw�p^���sa�c<[Ch.\ IV]{MacLanIr2]}�.)$1!fT �)Es c��fճc"e��-%U�� A� \[f_!5�f^*(b))=M# bIlknownAQx �Frobeniu� ciproc��} (se1�,521]{Elephan�[2 V]% ). E;)̩1)\ !�2�E~!$!# &^ A�s �sA�/��*� �Y each:< >�,���d (B�)�b�y�qE�M$�o�B0 regular epi-�$ factoriza; 8 \[ \xymatrix{ 5�,\ar[rrrr]^{(��)\circ!�L}\ar@{->>}[drr]&&&&\2� & PX)\,,1$>->}[urr] . i)f . (T/$X�.IIU$.)�)�aA.tinuou A!�!t�. tYf^{-1}G ��FQ,��> )�Y,B 6�6��e*�i���ver $C)�L$ (a!�3C&� <�f $\V C=1$)*Ya�ET�C�}J� \[V�:-� .oa\]!�*R"VA�analogu�r-#� �R�&  w� re&�to �iSet ac%#j C� i�S)assignHLB�qits �A&s� 3it  par� a"� froE Top$t[ O � �=|�� Itrum:� ��Top\] ��E=e � � �)*pbest ``approximates'' it. Con� ��$n(A� Ge��� A$, \ie>s $p:1IA�A�$1�.A�`��� �ԁ�A�"G�"."=9z/ 8orm $U_a=\{p\in.��$p^*(a)=1\}u Y�M�A)%�e!lunb�u$!e� �U�����5cEM�'D���sober)�s}�1pat��)�s�these+�}s 2��{ 8ɼ��,��{T��>ic � oids�@sec:toplocgrpds} �� �y��%�pullback� �inralX}a!)��!� pped �-$&�\[d,r:G_E�G_0k� 9�do)� gran� J,Aaive:plu� -6.�# \[m}p] {G_0} �1 �w57 _'�1s!$dM�r$�qe��8of ``composable%|�q%P'')� .��>��� ]^-{\pi_1� [d]_ 2}&&3a ^r\\A 1_d!^���!���2u:!�to%�E�"� in"io5 \[i%N5 � "�rAred�,� �axioms (�associ'P of:�,�)�Ima$e dataY�,d,r,m,u� uu/��C$.� � XII&� "in"�E� ��$i�-�E#�A�equ� s�*l(d| 0i &=& r \\ r.d 23�W5w law ex $ub)E&�-94&$ diagram ]iU5_dM/A`8langle\ident,i\apleMc]�=^mAc1Bll]_-{ B i, EC"dQ�0rr]_u>0.ll]^uZ  By"� q�}� GEi'~ 5�:!�!�*���J�f_1&:e;A� '_1\\ f_00 0B�A��Ge�l��)��%~(natural way� he structO2D�(��$m'If�%�( f_1=� m�d$ =f_0 d$i)\� \cf\9'�%&�Z�E�equ�A�I���%n�T�uniqu""de^�  $f_0=� �u=r� �!aG"for[ ap*D#� 5'q� show at%Fy(1aa��a�v�+�SinvcatOGBter.QAna�^A 6�\ eIZ�� �An@i)- i&=&m[\m&=&m\chKB���=u� 2pi_2, 1m�%7�)�9R*g �al� pert�&� -s if�Bd(@/_/[ddr]_{��O @/^/��2{.�]|����B\��^�FQ��FT@2U��F*%\%5A*�+s� =����T�a2&�:!VY.off 1 u"�"&p "�s*!;cours"(Ut $(x�) = (xyy )$.&�"�d�-�,�a�ɩ�����re� toge^i<6��law�r��&���.�w�!� b}.�{�I/�m9�� i[,ue rm 7"m Unit�\=&:N2, Q��_\ �<�&(8=d,\ X=r�j�6�:�]�I� j�:R �"96[A.� Z;:[6Ki)� �RF:x62��� Kd:D=�1� �;. bY*��I�\]�sea�y�a�A�l�(2,u3"B^ � s�a��P!�� , si6s0��O chi$am��0?�os $�0�-=)�2  %�:! 1$, J�lrtoa�� 2 .\>mB:=-oeZ R� \]L �~+ wY?�=  =  h q�� ��8$ m-co"4��$ C��� un~5ND Y)n*0"�,� )�N�/+��n%t*���B>iA"��uTop� �^ ofl� �*-U� $��u=�uM�!j@!us&�alway subo�@�.><4�QJ�K,Joft.!dopw "+ usage*^{P�%0son,Renault})Yby,rou�a� thou�3j�4{ 9&H suitI*|+"W �among �(things t&"e xistE�V su�2)1,��� $ $d(G)=r(Gq(!��E9��e��ich�gardedCe$5a�f�. I#�>,%as ``_-�2�( ~$G$'',I +pI6/5 G#' A� obvit�)ingUq , ei� u�&ic,!�*�d \'{e}tale�0�-)d 6V&�5%�v�C :G%($� $r� � A�$u$, be���6Vs]W5 mark��NB`0-� }5A(Def.\ 2.6]{Q��5,� re�(E�Fs:'9n\4#0a (Hausdorff,"�"�9pact)A!�o� q l�;�k�#�motiv��dfax3a�an �6m!!q s $r� (x)�"aUD'�,E�1>�>r2o1f3ly�RT� i2� �6E0Vx�- HaarA�p/ need5b8&",N�5.e2a:5�~)�Pro�2.89����}� Tof>�96$(no longer� umed 5��Q���e 2mJ�&�I�E3=�A���].. *pN+4totop=}�g,rum *k$�E��o2E���duceA"# �Q59��%�A.%tNe�B�^Y�r�Bb!l�' s (b7*,�}�io�&o;~\ref�locqu�'taxr��O1��|i! a�Z �y$)E~��;i�y)|=7� O� :�:���d]X�"yy:/a�f=&p� ��I:�&�J���2-d�1�(r G_ &�{ d)}&2L 0)\;�"�0�F% Vśho"�k<�$4.0)}.1���e ��=�:0G\ = \%�J� ]^-my,@(ru,lu)[]_i� <1.2ex>!^r-1�arP|u�w�t'a2�� :��)��!� �.B&��-'m>�%��,i)�.�A7ar@2N/-&u)})+� ��a��e���at.Xa9.�a<6���A�ly��d�aL � � =�5 at�"�Ѡ]i�9m�via2��2=.�Q&;;G��V� �"!$"�-V&X2 does���߭�� alread-��x&c�/[c.�(s�#�not2 "����61.�&�ru!�e:�!?![J$�� \;� �\] 3!m e- *I :��(GA*-yy(H�7a"co? can�in"A6bLtenL to*�-W')[�?B�  5-�Ar .�"Q�� !x ic� ^� 6*ZincideH.r*�6422�<�"i�"&� �.��BY)T%t/y�%>�Y�7nyNtY�?r ,E&;<��M�Y@ qzs. &3u�okafe"- ��RWjJY� "\oid (q!��� ���:h �� i� es). 8i3-#I � �Ypushout6�"G�`Z ^{d^='�r^*���2��2*\ :�� 1B>o)�.x}.?;,x�x 9_^:���?o�,B)�G��wo�1t;�]KIH F�%b1 �� b;']<on( U�DAD6H!<51!� by $"A: $x^*�(�)&)<�=� $S�� q�DE(S�kE6�.i�'V�at-�.� ve!�t8�<%6.ve�A�2�4be!11U� s automat0 *� EEF! & ��aNYnd -aF'�,}2��qlX=.�\isgcat-�"�v�)hA)Z� !�m~ As�@���v3MAD$\ipi�?Lal biF6oE�B)X$S$��U,&on$ +A2) �!b.>�6fg��J� $f:UG%Vͳ g:U''$�PEp� p� $gR f$��oB#� 0$(V\cap U')X+�@U�'1"E $gN(�"/}.)��GUva�F�a*�Q�&!�" �Z2L>^M���S2F*�MN!�t� aMK a�><i"�?O�ab�>:�a: ��2A�y=. {"m:pseudoŝ"�MAnyI-��of�Yo�*�6�L2)�entir1of5d:#NN��dG d ��/%"@P%?e ``G-setX/9 ! %� of*10&)�a"�� y $G$, {v/wisB06R� �����l�� �U�r�p�O��S&M��i"JAwP&��$U�6B��'L4"#(unfortunate"�i�l6�R:��,$G$!W''� �6���.)E'!C�(s:�H.7(Moerdijk}.)UuB��~ z.$.yNCWagner-P!�2 orem�er+ e~GmY�eA"�1&Ij�]��2)��)8� F`m��K0,��a� '�9xy@yB x=fy�#%zs }f�A�9��!��W> z5AY$gV�:w , $fg=f g� nd $}a���nd"l7A�a�of2�6 � X �B$e1B�$.� I!�L=o�"XE�A�h*�@l�j�5�$���@.2�A�k  \6my�DUFs� Z}U�s� �n�Rdom}(y);"�J }"_U!�S)�3F�bGH"A�riiUE2��l"?HAportantA�#%Fny2H��3P=�4;H%Nat� �8&�H���@� :T2J67��!�� �hk'$s!P#X5^9D$\V X$ IC $P$QM ��G$\V_{� X} s�(.xs F�EA�\[siDX)=.+sx�YE) } +snxs)�% 2qI)A"*"&�s j&�,�XW��m�B� infinit�K5�iv� �%[%lS9l� s .tS.�FtS$@�����""s holdf� 2�!�E)�S$;�W2&5�B&V�F^�J<3.zn� *} ( parG1ph may�sk�#b�1 ader��0es� in m�L� �0i�1;-�.��1a���g�$X\neq�ttyset.�� 28]{�� ��:a�C largE t ir"�Y��:�'st&�0�Kemx-�2A ��)a�n�2rwe2�� $ $0s=s0=0$�$0�� 0s\RSa�  0=(00H)0s=0sI�$ss =0$�_$�0�=6���%pe��'qO>�"� seem�depen!�� <$�Fs%{U toA+non%B not. How� , al�%�� er�ly trr clM:�MmatheR� �>ylR�!be3t�0l�"�k"�FE��0logic�*UOc4�Yx�! d middle: � � sT � sepa�[ly%�$X=],�F�e���G &%sing��A�EHXBF�* we w���d9�� d�ofb&!�carPW��a n a"�KtA"YdHtZ6c�6�(et�ri%}V���* un�]y�7a7: alys�;� 'i!�yke�� 4P##|Z�,� � oughYA1he� C9 ofW9f@ �� A v�RiRGB� Hl����^,�=3Sa�A4BH��ZJ!~�jT� 1*�E*��Tf !~Z)-*Q �2���K�isApvt��{��E�n>G��Re�&o( of�'-�(�,�J!it � +%�:� ��R�Va��'�.~B�P ncerfK��"�Rof6{FeX� V [R�\dD{Re:SF}]5!�IOi R�F�, �P� ��(y_i)Ip famoa����$S��&5 !_�yi y_i s�"�m�$x' �S,E�n,&�Vi$Z25.1F y( Y$)6�1 � &P} 6;� J�*o }#nn m!"�7��B�� wholL!K,t >�6j%��ipa!s (|a�!�same,!� Z�*Z�gi3Hu` �a�JE !�*T2��>4*:S�Av��}X�X�e�T{UE*J�.$r/�+A��"noL� i�Y'��to��cM�i&!it���EWso"4to��it suffi�(to� i��M2� > )� $E(L)=L$)u  /bO$r�M19iv���[a  is� SY �"�M�"�\in�_6re� Ya2�� *[�W� v7>�Jc�ct*U Ia�2^R X$e +DE$(U����/hA]�X$h�D*U{U_i} "' i�E �[�C� mu�-a�er�<�ati�@2)Pa�y�we��gY* $s,t �c#�a�p ! �ir �s. Notic� =$� t$��:�st� )b$ ;&�  ��r� dA��"�.G ��&\ ��woFmreF��}ۮ�. A��[ ��eqj"h:^2��vA��#om-���n��Ir�M�<�|Ma��S�oS$"� isJi�*)� .�o � I6q,$eD7mpleten�S>�&� B�s/st�6ofSno� on��EL2� )"�2�- yF�2�le6ecdRzi/3�,.��I�r�H͋e+k : �OndeA���2� A! !3.n. 2�in �MM4fy our2�1abJ�(no�ba))�kZkBy/ Gh{abst�'R�} 0[\� Z F�v �i �"�n�s} $\apT%�!�v2�"��-g?na .�� a�QYaaE ���= [B-"e%w}eClist �R ` ��mxT.�\ o*�S \*�\abspg�R�$T� r`��,� .� � E�+"&z -!'A���`>^t�$\bigs �����[A.��]-  T$�2U:�A$*U��E(S)}. S)�(.��Z /�2�of) s)�,(7)<getful�or �k+� E��3���.�Am.�>:1%��?">� � . 26� p�] 27� ZL5.&}R��mly  |-�]!/%�� , ei[&&F:2S {g�@�L gx=g6�a� }x,y&X�`j(, due!N��:� � s=ft�G\ X�'�@*�%fsDV\{gs��c@1t�1ftNW&f`u�X"�jz� e (-D() value $fx ���9�+wer bou� �E�&a$w��"l/EBn $w=ww f%6X� G] us $ &^�U $wzo ED�=��$z=.�. 3. �hu��Bl%s`dzB�`{A;F�B�`�dHa*, l� � !���bb �Ncon��~8a]:�`*gS)g� N )O�w� m�C�1k��� $x=x�&�)d J\x (#)$)˂�?V X=\�W ({\VI )}\right)"�?�Tx,^a|?^z \[hY XO=~uF2R�P.e\]�bh1!� V9d 9 h(x)e R/� 8-, 4%� fo�F�k�K.�(toM�2��\i�ad"�Qof' [S�P 1.4"���is plac�"gY$�',��onn.�B*ocp !�1�: F�  (thE�-m[�Z:(�aM?(P h H>inzudap�on��3�Sr !�� in) {/1�"po�� �� &� � )N�\g {Sup ed&�^� PRsqGR 4a�m 1@�sBK�ww#lluo-to�I"0�Qre�fs}. F2v "B). i! �<velop%EF��[exFTa/le Us}� addr �U f�er >E_:6�� a cl�s intu�tmeaW@� A��b4mi�A:�o�p����\�v G(b�&A� they�~�� a �� % $x[Qe�.&s9�p�\Z%�S5�" qBw{ en%�GUv tuM9V*bm�-E.�K byw� ��"Q�2�E R&W ygT Q���a&�i*oD� N�n9��*�2�B�O \[.9p}:�n\] 8ing*h!�1 Q$&� �/}U:$p a&\le& e def:s1}(4sa a^*.#2# < * a. 3XHn/F �=��(�/Z";=��M>if9q N� .~"� xampl�y� &"v� � �� L�k� !��=yGity:+����"�=Xo�;edi4Dw@&�D� %]U=\{d�nst R U� A*,k &"?y!�/ �a?�m�!V�� possu %��$�5a�{��8a�5�z6�{q��D��z�:�) $�R=\{(x,x� (x,y)� R" %$ 7 }y\}^T#U Now�)���Rp]��IClemma��8:!s:�or.C���+��>�>�$:� &=& a,"Uk�� }�ve m~ �u�%AA 2+i�c#b2j if } k "2@3a� Aa�/ 6f3%(? a)^*..2R7Ra3(a^*)'6(4T ( a=0 &\Left| k&2\4\ 5�� (a��Jb5b 1�2U6'a 1&=&J 1#:$yJx �N/7 R�!Q^*N&8&I(a 1) b�1� b:�92,.*��M:0)K)�a b�,aB�F� e�o�siz�� �� Gelf�ˑ1� ���)o#/�~4"ub6:�be$"�^ �FQ���calM a b=�"Oabl"`��!oLr�g�2 �F�.����o��6�p-l�2H h6z��[&$a�ua 1�P a re� split'(� map YzM��Q�H�*�'B6V%a5% F �: �K! n �&�n A I��U��f"} � ��pvAx (\F�)--20a�e��i��[2*}):] F�a  3}�71�[if!_leAf�$�)�% e= y�4O2RbU =k�S et e= aeN2�2�ImmediW1u!�prekL b)dU7FP 3a},=g3_�,:%,� b"� R6b%A eauN�7a�W�ve a)jb%2�h ��e e�m�y�.2!�Z V=R�4�=I�6H �9� a=a^{**}= }����!�}2 Z�)Xn7�$!� n $a2�*!# "AG� ��c A+,a���28Jq.A|� T|I�$ would @�VO��w�m.�_0 D�J�5)� .jTbn)�2�"JJ62�6)W�Y�<:Q� F�!� �) .1V�7r�Nb��\l%� q i/a � !A N8�~�}B��V�9 d��)�6}u( � (a1)u� 1=a1�+6& eb=bP"kIA�inJlity \] IU &; �q7� Fd� \[G){(). ) rJ�10).��2�K$b=Z�� ��.E6M/"�m�~ �LabE> :�AB� �@�t� ���eai�f � 6� s $a&�S1 ��,�d�qC�% j�>A �6�[) Ir8})��iu(p"� n7.�j$2�jj~ r.p1�!It %&"-" */ ` � & NT7To�f�A 3an.6": _>� �AXtop� bwor_> 'GIh6- .�%nBJ�wD%R"> �y!!; �Sby2�$, self-�͛*�"�"f �ɺ���Ѿ.KA� v�&O � Q�)ver_"��I �e�� �t 1:�� *� .�� e :�6` � a 1=�I�ll"Zb#�i q)Q�V�4}�l: �2�:M"� �  :def.�A+&e :� >� wi�11�.�Y$"��,)9(a b) �(�b)� 6F2�F�V%�" 6B4.B�A�%���^<5R<�J"] /6y5a.>��, @b } "�2Bs2�U�Z�mD� '?��TSi� "��%o&Έ?.P� `."i��1�1$J"6�3^�uj $�> � )�#R]sf�� b�#G�QQ�Vu\}VVV�@ ;1ڰ6. 2� �veB� (oNas7I.�biU$Q�O�� � Q&BCO (a,f�� (a f)$JkM32�#&J�E0��4��.})2Q�N�&+Aۡ�ls�8modul�"`s�).c���!�#fa f�Z";^.�^6. �,�!�11}�XՅ�E���M� (a e  &�/]�2}�q�!�qif2r2}3;��aL-�  bF�b$. V�`m6� r. I���j.)4"��. 2FR�K{3us=�.)4},25 9.$�=6w"1.� 9}) tellsn�-� 1)b=��� �ci:q4 �   C a "�& .�!mp� .5aA8� [��0N)�0:�5�Y� ) q e�Վ� �.��."}d��"� 2inay.. .o 11}$*�;$_r }�eC!|A�  Q| (E�:iW 16m`?L�16�k�3"E?$<(_v�@]_{UnFe � R� U:Ls2bL 14})&� %1l $� )��� �-$ 9� a�6!�=��v��& 1x-s�2�f�t1�_ �b[!�e�����n ��`8 �b a��* a�6�)Y� m:�!+�n�i��2�.�3�2s3f�UFG�uL��!��p,73 �b$| >P, $�x�j=a@ .�R�3}e �8G$>�f�Z�=�_�A%�M"����'�6%�a&<):� � b\}%�4 substitutA�ANA�e݄=_J�BG|�a b�EAw�6�4b�E��*Xa"��#{�Sr "y c]i�%��#z,�,b��u�6�*9�.�4%��%�T.o X1�F=��*,�be�--!x �$"�� �2\z41jI5}�C��չ�N�b��n��� (b��!C+ M,�/1J5>e 1=b&.�s5b&���e(��ٖbb�^Y"��A�R�5%�(h' � LWF�j��>�"t!�"A�r�^� �Z�� {dV�( Jv�^�= >�6b�E���c!�b� B�]9 A'2�� 2�.R�6%�.�A|�,�RA��|A K i�i͡��/eJEqu A�e�e�-Ni0 a� e)nbN�n� 7}�M��2Z a\cdot fe�(ac� �"[&�)S$e$E�sQ��1 ���n $e2[e f4  f=�/=z ��E$,M�� !�6hzA�a�2� .�1}:�b)2�a b�%()=)(b -�A�0�96c (-)F�x�e�m(*`�!n1= a(f�c:�7b11:�1~)��M�624 �>b�: X��I! e��1Ze:= )_<. \B^�w �!iA�}�V2(";�kitFzwi'ah%&�6_@*"���Z*)2�:�ya�&LS�.��"E'Al�1 . �sK4cu|s �rO �, ;�e� ~�� U��G F!�&0`�a&J#*a+ ��J ]@5 5s�I���M$� s�ai�*GYa*��9 (6s{c} a^2=���A<]$�.U>V+�̕�,���s| )�l� thre�SQ�� :]) *} b�& ^u �!pA"F�6�6!)M!$i� �7�$��b6;�� )#)O�!_e�9]�$1."�Se6e�3� ��:"--)�s3j�*l �  �M � PF��4{%)6 A��Y�}j�1i:%p K%?![H4][:l�%R�+"O a�2� t9Vl%%� q��  $�%㵞 z�2�em�,thm:fullsubcv}m�.�E>�Q�:e"u�A�(daZo�@��.,� �1e~U�h�/ = e�%�]��}K :�͂w$Kn��2or��h&! �K>& x. (J<.�1al:�FsHo�2>C.l�xa���N�G? �*T5r(r�"V�%ls.)V�Q��yՅ�b=2�m�H� #�!q�2 q��&AЍna蒘3}"byiƉC��,t^r�]�UY1�&MN=�h:� KuFr:K aR�s(K� F !let $b=h{a� ��-O#q�B{l} b = 2� h(e)=�wJe"��a) h(~.� ?�T a a)Y+=.P ��č�^j�:i�=��^.$R.��Mg ,R$h$N�JM�:�&Q�Zhav�a>� A(uM"z"*!�, r�QrS �trPC��� R�tIG��&T "Rc*D9�ENg�K2Rd6�Em�Z��s)V;G�n5�z}9 sq )��ull'.@.j $[�� "qCr �^j R:CXdd3 �M9kQs!�t Lef�� 2+$B�c�:j(ikUc�I!�Eq�@B:QIAw"��q�X��E�con.��$\!� rx�t6�=�->� refl�"ve}/sqR%�>�)��.[>I� s6!��5%A'�t�C�!�ca"Qj}��8�}� �sF)���$5�,sZ0 & $of Freyd's,=/u4boa�e�^�`��.S�� �In�!*�M,�!��M�uV��m�@�:�&�.���A�$��:.�,�� ��� �y���i���� ��V!��.��J�%�H 2�:�&u��f�>oY7�as���1�nt�.�&�`"���i:&�WQYis£e�R}�4&�id6BCF(X)$S*UsAVf� 2��&% $f:XUemapa��PKmi� *Y7���B!x " K$ a^��D� 89�c e�q�} $f':� �])(� d Fa1��2J':� Rl� K$. BR��*#�6F= 2�it�(B�M�U8)"�u!'&�c3t��(��L.���=�� vari9b). .�5 �9�qPOWQ�~f''�"���<��� \[1 \] R�Df�ro.<>Q. Hq�L5�kUc&��B "��Q\7qh� _h&&5�Q�vyh''7 &&K..� A�(ne&?��eL��*�+ $SD>OK$i:!�~i� $h(����*(� !�.�� aP�.�Q%XI�eJ�O^"�y-sm�F� 2�,is.m*�U }mcaT��:t hetaN�Q)}*G"�Ni*8\ <%congruT�re��$E�aispp�.eF����&%>i�fo[B<%h$Q �6q� Q)}/2�2Av.o"�q2.[EM*� n5&�-w"�0:�6/tQ�t eta_ ��yR� �e]^aqe"�"/W�� K h'''����FX�ݽ�VZ�:v)̋AS�d � b�c�&7]iQeV�&& �,ob���D�/Qv%]9s*�^�uF�a&malV(On.Cso j2�YJf(Ul��5k.�T^:q�des��� } X 2�Te��� hC�Qy]F�s&.P�?al��2.p ��s& &� :K(aR"� S,} Q��n?[ i�$M 5)��dT"� Z`?*} ;T�4VI1�.�# �6�opi��m�.���,exm:Rw*� �]$Q=-��yI�!�"g &]r���NRX9�l�};A� � *�X*�o�mM / D;n� �a�*���` below�}a�j- *���fa��a0-WaJ?. >�n�-1 G��ret>Lm&kA�qGa .mA��> rU"��(�BGH:�v))��+UQ)�hG�9AQ U��>:^q0*� sub-�V�2x gQ�g��et6PaH�{6��> �$e$xQ��+ 276�]C%�a� d �&� p�^%��m#�;t,R6�a e =e�&fZ � way Fy�,�f��X)46EJ]��)Ym�y :ipi:�F)E� +9J!�"SAB�$ )��G8.m7,$�FM0Ae'dJ(��'�ӥ� IT.�r2�$�v"�#;�$ "k,�^D��� R�9! P�OQ�-a�4)uC�t"O5)mQ "�2.�!.�-i�m �8=�A��>Qv��&7j"z+a^*mA-"7eV7�9 F�-/- w���+�I9!~-�&i=.�Oń(Q.rU$�3����!<+Q��tA�S0A9[*0 ob� e=Ay%�b�2 a�;f &s-�� .�%{�^ɔ�/N�I .�d�7"�*�a�im0�>be �oI�soS� ih*�uB�"DYA� .F���al#��.� �0>�Y fR &�iAe�)#ueT]ɨI:�as.�l�6pv E'"�3�cig�disappea�l� wO�e o �jZ��h-��jI ipiQ} .��R �-*� E6���!a�(IF��)�-�:�-!� 7nhe��K"� E�hAX�hs>Z )b�F�K��kg��$Q�E A�e����3n ��f��.�F=>'6� � �YZ1�>k1. �6F ^q� i.b� ��}-����� .M_>AdT�ƩI�C����=�Z��.}^>Fit2�d���yq7.�:�ut���6� ��!"?-3� ���% !�JG� U�� a!��a�1%B�\:*56�>W� .��:�Kk�4�� �w���0li3d� 94���i�"�1� y #ny2�_�A�=6y� ��2<t��A ^2:�"l=h����I�.�� 2^*)($MovY�Ve�FYI�!Ӊ�� K] r�]���G�Um� �b� b>���e6�o"irNB�4!��.��E�e��E��!�.~ud6R,�: B�2[�E��)B*�a �TF�aF��� � �U�6NR��a�]*@ �1  a�Q��(.�>��iq��G�u60![�͋>�BV��.7 r4��B�a��%$� Gi9�W1���a�d���{�b$GF ��;N� q2'�y�/XAhF��C �P>XAviden.s�rt9��"epNT>F8E�%2$�f�:/f�bx���Rv�%J��d�zB�)�l� oHT�u96b�*>)� a�2a^**Fu4>iba=N*��Q)"@%�"�� :�$2�> � m{b^*itiQ"iT�}u�]��a!0R]m*�W�6ŭ:>�e!AI-� PI2����n�"�>"�Qi)k �!�9��A �]�{ulaA�M��f"�Z� ��&� hb=!�9�cf\�i"):��*�+o�bspp�^lbb:�,\�["�^(7 j-&�b�fUNBC*6�� j����%�R�aV��G�g ���� N= A��W��!�:?2�A 69�Ņ[iS�rg �5��$s.)hQ6.)Iv32R=m)U�Y&XpG6�p��" $%�lE�� 2� ��C � e)CI^$p�@ "� b a eamBH�*B� E�V\E�JV��~�N�geye�>�Z�"�e�0=�"w .� 9�����[�.HK��km)��v ��ŏ���?6�|  A�BۤIȥ] h1redundanAW[*�� &zN�{-}[drT l]\\ e]&&�Q3 !a^2r2&0��d/) ,� |ZCA�le %�.��2� �^5�Q!%j��-d���%�1&o�e-�� =a^2�ye(a^2)\m9 ( a:�^2A��?)�+71&3%3^2"�)p�[E  � uss�&�uU�i��b.l "> $� %�N� (�F �um)��4F� , ���X*|3��uf&Q3�F_i s_��DZ\V_j t_jěe�/%WE%$s�xo$t��B�.a��� E%�k7>�_{ij}�� �g7(s_/^*2O^*^,4��xNs_i 3i�:I_.<) �E�S�f�-�!T >�VN*�m�5i�>"2[J��} fuzzyQ�� B� s^!Q If� �q=T�� S��.�"�f? M \lc(S)5d9 S$OA!9QN�""��F`�$J� q�!M��J�Tm�y'R Q-�0B�Q)"C�<�!om:�',, \[X Y=\{xy x� X,\*�n Y��H�b�!&�'� Ŧ$X^*=X1i"ae6l&�("l&�(a%� ��X��j6b"ne�%�B`Co��^5�/u�J�,},)��*) U��[�*�9��PQ6�ցe=E� ed�.>�b�O:@Ug B��hE�2�9�:P�z�Xa��6{"Fzb A>����5V��6��� g �qu�#aftI,a��!/^�)=!t��ff!wA��I( "�B�)�6 ��[z�wez� $X,Y� � w=xyT9i6��$�pYm$z=zzew ��=( x)/k�$� Z��6]��@]^N ��v�ZiV].��%�&�.6�%.���~.J"�#-/$X9/��� B"�"4 a{ppl*)�&�rst�-.%AW�(C��5�*�z�6tYX�Hcup\{2�XxFSeS)I >�f* XX^*�b)�zE ,y,z%a\}\sups�,\{Q4# ��2X��cF�89g!�:� :�X��a�b"� �UU���* 6:�U�(teq�.] J�(� P*�o)�~�] m`�����]h�,�P��I� �%���QH.>�| � ��)�A���q!�a�$:vѓBu�<��)�= ( �qy{ 44y) ���9 ] soaY' � b�%'&m���Nzo�#��-/$E�U}�ULF�W� r;[��H �!CB�A���U�U�U\� M �/r�ȡT=�X!}l�YN�"I H� �LS�'�5�����"}.3bl J�,86�� �*�"� n��*�Q��!�7!����62��� � &x�>��"� f LUA6LR.l�"uf�1toqDact��M �*.�"� � $S8P =a:� eU !Z� M�&}t.F83bw� �wm��u\+b��k�{>t?2Y��ΏN��6� -)= x�R�+!�]��"% J!E��.J�iQFZ!jQ >B�\h&�"�yly��F !�a& *g A� over�� h�E;���.� " 6l�<(U�� ���sup3}R����I{E�r���2�&�r5r howaOkPNi�2� qw"} @ A��%nnv(�-}� {t[�e�c_ ,�(}�A`to�"u� �.��� ik�wi� ccou��傁1�<�8�V���� unti�&end�<�a��&� an�&�eV*I �cӄy\B��a�tguB�� et (�qy��ty���F�l*.2!L�Og2�o�H T����1 26��00dU} 8\l)ϭ�.�ќ�Z= +�Cr&�FA�6��u$�f���� R j�8jy��%=!Nnd =� oP R�$Ui�Q [�A�A�e"^3-{6_O"r 0�R�$j%@explicitMz��!� |䁀�{\{{�Oz*J}U,\ X"�A2�e����V�=� Mkj(U���. "�E(Qz�}��snEo.��2��}�F\VPV (  Y�k�oga�*{(��Y�Q �c �"�&Q� �,k ��� I>��-%Z9� /�:p�. Each� ZZ+a�%<U_z� rV>U_zo9@2H� X�mA��'et $Z' _{ Z} }2#.� ��6�u$\V Z(�Z'.Z^ %bGa_"9�����SA��mPm�al,"Rs{7+�ohm^!�a`"x\�&&Wmc*�/��r�&{� >�;�uy�mI>��� JD":�(������G!�ofɖ-�es��r+�X�4V�*� $I,J.x�+�II�*C�J�9]kB"hE+b� Y&A�K����)$z$m�I`E� j(I)O�j(J�%�l�6*�O!66)�Yb;� I�3i��A e�OZ�W��G�6��""�2}�I�Ji �i"�����}��y3 "��(�ȡ d� �>z)= 3��+ �z=zF�1O �1L�/.�2I�fj(: qɑ2�]BA6ڂ>P.S&X 5�-�� '*h?2,*>��"> >����:�E�B$x%�j(XŐ�� ngm�J s"��0& �$�e�6�,1�b����@e2xy�c#ai�>d'�Ȅe\�]2�. CJ�����**-��.PJ:.� ���# ���� o)na��2\�+|*�� io�L" 5���Y�n*R@�Hb2.g"0. �!��!�>�,� 끍��e7%�f�� À,\t U = �e��2���!)/�1OB�c#-�Is�e�4�6�mi­���c�aMpr�/p�VwM se��s���,a�2�P�RLbS��}�,! �+ �G,�]U���8p����$ �t�0ABbe�iedb��g {0�,J�,t�� !_s"yh ��G)g��? Z�,J7-*EX)�! &�ie���=2-��KE14!�@�r"Z>Zh-,>� 5�,"� �S� iJ0d8��)&�D6 A"��%��IeaO$ �7a�erQ��E^3DS"lig ����.�: rollq��Y<��,��&Q+�!.��r�s ��>H�:CZ�9.�?s)�G����wQ�a��^�Nt�.�S����5�s � &87"� !"u"2K!X6|cor��A�o�F� Wx�W h�;� J:&��5�  �(the same. \�qed \end{proof} The universal properties possessed by enveloping quantales are by now essentially obvious, once one takes into account the analogous wPfor $\lc(S)$. We shal�xvide an explicit description ofS0m. Let $S$ b-�abstract complete pseudogroup, and let $Q 1@ stably supported�. !*monoidnpar�!<8ts $\ipi(Q)$ is��w$if $h:S\to2<0 homomorphismirKs�rev�queBA@unital involutive�� bar h:\lc!r<\to Q$ such that^D following diagram!L�mutes, \[\xymatrix{S\ar[rr]^-{s\mapsto\downsegment s}!drr]_h&&rar[d]^{ �4}\\ && Q}\] wh�$ %X1�ly definE���T(U)=\V\{h(s)\in Q\st s �RU\}\;.\] In other words, we have: \begin{corollary}\label{cor:adjunction} $\lcc$ d�s a functor from $\apgcat$ to $\ssq$, which!�,left adjoint!the?E@:2A F.i�c�0 A consequena\A�is]also,i=S$A�ina�e semiM�%�m\\cong%�C(S))�%p%n�ci5maZinsenseA�\cite[Se% ` 1.4]{Lawson} (but includA=P�6 $empty set)i� in fa�-� � �a\�)$. \s o{Qu��( frames} W)�@ already remarked �v$topologies�certa�  cal %-oid��q c$es. Besideariey arkso �,Sourse, h%�suggest1}KABi!ZY~Q def: ��0} By a \emph{  }}Ameant a� ��y͡[�L$a,b_iaQ$%�istrib�'ity�hy holds: \[a\wedge\V_i b_i= ii�b� a{t!8-�!��se��(w (localic)=�Hor at least categor!�can��ob!�edi|sui����)s��!�Presult (theorem \ref{i'ion })�$tes simplyY: �$ \'{e}tale�4correspond bijA�vely, upa�is��s,A� y�eASatYS2��0o a large ext�P%P�o>a��E�betweee�2|���mat fur�Emo�x� A��quivaljof.�6u thm: ,$pgiqf}). A�l end,� Q'%�sec:exa��s}��pr( whose purpa� o separata�l�classi�-^es%<idered a�ar�aub �{SNVq��sqG We b�C- ��Sa� iM�!w� noth is r! �excep!�y$ir underly) IA�houlda>�A�i�d�[q*expre� k%�tly asm�s~�ie�2� � �} will���b� 1 satisf�A���ad �al!W ��%m4{eqnarray*} a1��< e&\le& aa^*\\ a( )a\;�Y>[EQ�ta�:����s $I= c� e$aC $a=2k$.]J � Q.q :@.� (sup-lattice�G��D \[\upsilon:\spp Q� �wha� righ&i giveA�9_*(a)=�� e\;,o ich A(erv�rbitrary�� dA�!���image-�B� n (obv ly) open �B0e map \[u:G_0�G_1a�direct Yis $u_!=�$, G_0%p $G_1$�4�m �coQ,�~s(G_0)=14extrm{!� } 1)=-J NowEe�R.�.� $\delta:!� ^$ � \[ !%tU�E� ] (Ta�is jusa�ehz ? 0pp$ with codo�� tric� b A$.)"� lemma}�"� 2X$d_!$��an)�map $d:!�to !]m! N mn3Co=< �=Q$Uq $a  a1$. B)�*� ofB��H�� n.A)I� \rs(s �.9�t a- $ # �. H�� , it!raN��Z_ aM�ofM�s:',��:s As)�M =%v,because $d^*5�6� 0_*%� $| 1��� }{c}QZd^a�)E�(a1  a=a\Q�� $}a\le e\\ 4U�2 1=a1\ge R:U �= � V rderA�� g d�)e checkeHFrobeniu��ciproci u�. �a,bo!ca$b�$��e�:  rcll} d_!% b)��a)&=&A�(bqza)d"1%(BypE� :def��}-�A�:s15a}E$I�b=b$.)�=&bh aFO ;trongW}-24wN >; _Q%CaM}B5�a)\;. \"�9�� m��Oi-��< X 2b%���a�� $i�%1$��5� $iE�=a^*$,%( thus� g@ $i\circ i=\ident��Di_!= i^*$. Our aim��(ultimately AQ&�x�m�a"� zwe!  a did e�� rangюr� 0\] ��bg~ $r=d �$�s:s*�ap!�riirel3&[ EW:  :graph5@s}6\9z�� &j��,ar@(ld,lu)^i <1.5ex>�d- _r&&�oar[ll]|ue�as-�d aboven!�q\* �ua9%� \\ r)2 (i&=&r#d\;.\\I�YE�% }>hpfir� ��A&� �q$u^* �d^*QY����u%�ll���$A$�m�a=a]� \[u^*�Oa))�i�e�f-� ] Similar6 A�se�}� rue:j~a=61 {reM�� (a^* z! thir>nhe)� of $r��� �4s<J՛>�.`�QSo far5A6���;>� �u��ic E� $G$i�is%� pped�9an.�$i �� `�,�$u"�l�y�-�*G ,structure on~,!�si�of�/kin�m�� plice�)]ed?�``m��omposa� pair� ��s''� ,\times_{G_0}� $, although< (yet) necessari~e>��#e� $y. �6�is �usmTnoY �g��$" ", ��,,&X, mVsub��WQImeem^Q$ coincC��:Win>(C�s upps!� ze� two immed�p waysC^���$module oveV/ :>zo���n a�aA :*$�' :� E� Fp�Z�regardF%S9-e-bi �%&X to�se� �s, nam�let"dg(7.\ �) 0�N:�(� each;m�!Xboth a Z% a U� �Q)�co;a2�, *��� $rrelevant)=8denote!*��tensorW duct6��� $Q\omv)�}QF (Q�(fortunj�'oura"e�))�y1:�)$>���6�N�>a�pu�S.ls 8 A$r2 r@!N�V�AEsh�,� ,b,c6n & $,�lit�(b� ͡-` c=b �7 (c)�a��e�U`i�H0toplocgrpds})A 2� \[ba_jac.����J`b� [  a���c�� c=jE[F�!~*�f nalo� , usE�h| � dual�C��.]*� �i�weA����t6� Ue" Q$ factor^ro�h�� Uiq�ssocii�Ah� in�icular)�_ectWe&�  $Z�$eUQW �determihotientB�-�_B�en�hs��to��� !��� y�� d&c6L}��j let \[G=�� .� \] b �&[�� ve G � 66� induc%���7!�b�\[\mu:"1\p�N��]a��i&_ by6o�m \(u�b)=abV ��=��&�M*� &��Cus � xaEd%?V*�� 1J qedAX A�an�( j;VX E U"� "� .�By"�.�>�FQR` ��)}�r2 $\muT�A>%&:FtAf.J�� 2�2�A��� �~(�6�m�! m_))d� $m"� then���:y� Z�#��s9� �# :-�1�:!2�:0e�f �� \[mw}R���2H $m�)�(�" ly, !$,=\mu$), toge+ ��^1 E�&�ic]�e� �a�b�ћI���]� ��qs}��\" many� �neede*���5nly o�mis�K� 1@ law@heu�iEU� !�ɯHEZspecif�,"�e�pr5 fV rro  ��}�m &=& �\pi_1 \&"+1m( (2�+2})Za"�$%b� �ng�se.!mf!H  e (W ) !?E�2K "�R %�!how����o&z$%iatEp*_�^$6jd� i�.�%�v Ie��6#$B^7� -if�A� FA!�J7�m#t��i� �!un5%S$�d)�$!'take ad� ag�A��E!lYrmulaR��m_!.�"�ab� �9 a1�< 1\hspace*{1cm}(� )6D*}AEI%p�&�$ exis! �!vMZ�Nn� !j(� .\Hco-e�!oX a5a�d%):>:*��:�))�Vh�+Im%NADg�1(b�� � }H"�qt*��us54e5y. "�� �� \[�.�a))))��=�"�1�6�W � �1��%�S2��&��8.�.��9)��=bA��b)Y�=4aba2 b 9e" :-� g  b 7�  B����1})�� ��� reasons�! does72})!* 9jE��aB st�uKy�)A"�]�u6} ��Z 4,} \vcenter{\"7) �:I){ujs}�2� .a@)_m&& 2H0ll]_{ A M u��- ar[u�)$\langle d, (�#le}F{=}S{ 6_-6 3,r>5ll] }��1F�w4 mark%` , si�(�NF��$q i�� �N - � �^ u- �, J�( K = )_!&=&u_!M�  \\ (   u ( M�6;,B�Ѣ�r-E3�+i��=- �-   �y*�Ω���e�!W�:� %*\{u^*\l-� ]  _!\gE� O�� OdashvP $. S��� �j ZU u  �U= �./' �r"�,}d'sprov'a�$��2^"2nY ��� 2&�"*. n7�esMq� YK!�w�*JR �>dEZ�2�$ &:%{ ��ɭiF" aoo,R5~ D'con�+!�p&*�� of �q.�F�I) B&� B { "V06�1)��j.{A�ij)4}&&6>+6$d]_{m_!}&&_:)0).8 ba̡;a)�Cpi!�63).� 6�CA�^6V4A�&;)��squA�of��=�2}), \ieE�!�|_�(>E)��2m��%&)�"6e� �+T �Jalae�c $e=u_!(1�o.I���^"�2 \[G �z�)[%�F�v1�a)-("� a)=e7#� :�Ovkm-!$ae=a�.Final�w.�2}z.<on�B�%P&�. � m'*��]kA0w#�&1)f(A>�>O�m'!)jq)�}1q��h��2� \[q��\oiM{�0).�'){I�% clea}'��9 m$m'��&&� hA�� 2�'&y (�NHN[� �y -{m'QPi!a��^�0}&&6� �.q� �2m'>U ,~�@&� 4 ^M:yr�B�;, "�.i> 2e)EZ>�rf �^��.�"� ��v|[)�_B�N;6�v\ ]F��j^���6g1�a����� cha4h�[*U$ . QPc |->}]�IH�Q 1m A�M 2GE� �"("1c!+@r�~)_;a-8(b./E��a� ]�c= E�Tak!�$��T �!��&�7s&S� verh*�a���p�ša2fz 2� 1):A�1Z� )!y=�!eFM=)d!*: R}6I N=Lu{m�Qt� � %��w��  argu�3B�# J0 (2�Z y�)B� m ( Y4�"$)*: �:k�a_ dame�D�of2�B�"�tb4c67��:��7�9�yazp�m1F �Q2��A� 2\o X. :!8Sq�� } 1ii �efo�_*(�9V1�W �9VW\�teq&�9DueA9FB�<B9$�0*�� qus7�*whe4is2�v5aqof0d&1�8s,?2 as�Li��0f�;l%� �ZC]620f(x�:\.@;y D 2z!Hyz5x\}\] ����� �w7 c�w� *� c r6�� $f$; Nis?)$�&ati�&set $X9�S� �!�aa3 $ \[f(\V X)*\V f(X 6�3weBB $�D$ �$2b5NAw r� !2 $y,z\in S� "tU*V9�. "%$xDX�p$$yzx^{-1}x%�� c 0 \[ ) +_9{wJ } w ' xix� Au�y!��.'<6�965l[9&�1� !fv!� $!d]6m1��a]efore $w ��E�?�)R �"S�(y% �x)=(y )1)=%3\] rus,#��a�$f y#tai>�B�Y�a�� F�==,�#>Lit57!)���g��\�({-z\V_{IA}-�x}\��)� �R.J^)�R�6Vy7 �.G2}BC�V�28a��BME5�&q�� ��9c SC$o54=iMEj $ [h(�\?.te[�27, Pro 17&�>�X\neqb#tyset$,�(e}Npp0 to � $X$]g4{&oa.�)� A�5q X1K�J=yzY'a�eȕ� R���ele�s $a$e�$bp4u-er% :@a��; b�r a=ab�b| q�F ��z�] � y�E6�z=2/y.MQ�;3 JCy). zA�=&2v�)>� l.B-�q�E̡NXU Qu Ϳ���� 6�,{In)� � s�"�)invqufr} 9:�som�s' u�8x!6N�&�B�%�>I.\d" �@:U�n*#/.<v�E�/a� &� J�?�a� :5$( BG+` $�anhF�"�CqٿP=n �]h�@5')�}`>V=/o.�F -5maximum�a �!#� [1=\V \bCQEFN�<We JC-�ny>� yn(2`�<%4"9Dour orig�� , du� 6f:/GaaQ@*8�wedgeP \V ��{�<s%  F F�< 2� ,{ �1�C a24&E:.�AI^N�'. Recs AM.`\lcc\a����#co2�F,.�AY�&�F��v���2=�F:�N Is. "� b%E �5�/b?.\varep�>_Qm�(Q)� Q\] !6�*cY3n�Bk�" 9>H4$�8.�$*A�aZ I� !�beH.�� U�w]u� '��?B i)�e�1.UExa sur�ve ,6�re>�2t of pr�0p� deal�EP5egin dm! ���C$F���%�!oB�ey-t�Ains�~)p>a&�bin|@ meetAp7 ,&I�= pr�M�usF�.>[�ldA%�.� :�V�Lh,�Ds&M&�0 D2�IK verK&���)�s� 4{Johnstone} (w=min G dapt+ �'a+ possxabs�>Aa��Ah��$)� a]+%�� JQ�� mulaqo!:ls.y5�Bwe �Q�8$ny $U,V\in��]�"�,[U\cap V=\{s�� t�� U,\ t��V��k�0&g1�:,�a�* F%.y( �%2~��g_{�Y�} �\ & �*͟�2cUv26V�B� F�-H!�.+2A$ahB �assign� �.l �M \V6=soa�G�o�ln 0)embed�0N6:-��m% lem:����CS$aYr�i�B C���S�mA�0ownwards clos�Get-e �>p%�S�9,PUQ�\be� �@$Ud teq6@$�4�� $t,uA�U& $tu@ �ss �5%rsR , $tu+e.�$"�#G#�3��w�x*� $U� +"�%= S$. US)PAQA}Sn�T�f$1'� b-m�/9s�)m�Dcon� J�/ 9i:�:�aZR�u>��s6v_� d����6�"&լly*47�@:�_basis�B)�e�63,e8sj�corRQ An# 6� -#= D:�byqf  fullA�.� $\uiq$+ ob�:&�K&:V��&+61���A<��L` v(&v an$\�� 5len�lY>�i� l!���d!�&� ��.- �MF��R�7� a reflj9 f$. �$�,���eA�:��Jh"� B�r�$s \[\eta_Sg�e�S)�6^edE.��:�i)iѺto .�#=���R� -L�K6� eAf81 ��:&4 �Ft� �F.�$I�"�pfV)J���!]��/E%$UU^*Ռ�E�U^*٥ �xs�]���and $ɑ� E�%s,U{P�M���n`�(ag�Qa�CeN,Q�6� de[&AD�&*�-�U)=�� �\)�&:1%%@*�#�"d]_XIx,-:�0i�0#16�#\a�#^m �I_B iFv1[?I2r#]_u>0. ll]^�I"��\o@%� �ion=��1^pR�2\&K*�%<- &d�,)\lbrack~#,i^*\r~�-@D&^*2-s�-!3Q-L55%Gr�\&�-�- rr]_{u>g*D',!c,F�2AjRLA�B$,%�.$>G/i�� -=\9x�/E���� b�2}�O�J�J^�(mkJ*YM,*'i�Rac&�_�ff�8 Ņ`b,x,y��&i�*�&Nb�b�0|C�b�8"^De)1\\ �,\V\{x5 y&x�Mb\�n � f,gMv(-k���g(y�$�J��� �0B�O;e j,�.��O�4>�^*�4�^i^2D^pAO�6z�.����^J>s� Z��x)N� A�9��`��^ motiva��by�Q�s^j ���~�6�,�Jt;K�l�  b�Zint�=�&pex6 n* s�e�ENA� *e gener&�0�mBT2^&:� *nXe4��9c"�#������.~&;�lArl:��%�`�E� in1ge} \\6�LN�fL 2ge}�J�j�*w ertyM:s10a�>fF�e�V:(xm�y)�%;�GA�)�JRvI*E(2��O)3 d_!: Ci�� �� J�w�$�$c,ness,&���)���` X%�<a�A��"�� ��Ha)�6Z*i1.�P��<^*��a))8bigvee�� x1en-^_)� 2�&�!I�a�hJ $.�=���1NmA�m�;d&<PO�-:� at $.� =r�#,�y {]�, $�4r_!]�)�4|=^*`=x^*Q^*I�^*yR�ErF�i��"Q�A*, �B��l 6�,��nyA{�)H ��"�`��lax| -�m,&��.� @εlN�le L��l��:} lea�0>S�SIy"�� in�[ion 6 b)Qa��g2� �mB�a>�le}.TN$�FK&=!1v\;us�um"�"z!b;e~�AE�6�I�N��B�*B�]H" st xa\EB��"�]x^*I*e2 Euv>Y \{)x6c%IuV'a�a (=&�M^* P.)Qa�we�"R( QB&/V x)�� |S��!+��dv* Phcngj�MJs don�#9SnO�Srdgh� ginQYre�\"�y $5�$ instea�%$5��-�"8coek� t>��Rza�zf$ �w ,��I� r?"26?�\b�.sB& 1=(e-��r�]�Aa2��~ Ie\}4kU\A�M> ac�*�% ~<" \[1z@V\{� y��m�  >)*} �� A�u�})RSx4i>u<2.�\�U�F2O(9)^* 1\�2�2Eu)�(�'*�}�\ �'f) arrH$�(e mg}�is��R.���� ��P ��ݓ68.5� nume�g} \item��^G:'r� ; � �M��nU�^R^n \Bj�M�end5_5p-�We"�lkP$�-)}:9m2Q���6=e�!p"�hre�)mm:MZ8zv��!�*o�+W�U*&bH/v�@eU2)$ &�s2�+5z. �\�^b�:iV$ �cover%I�8�wN��`is�EnH5�"NM � #�\Oe"l!�suffic�ds, R&��-�� KJ?5 =((-@$�b�E d^*:V2�a\]�7&� (\cf\�|�-locqu!R�46HwJ�in o$&(x-T�� %v�0clu -,f+��\R�0$f(��)=x&��Siz�]B6:69p& �1=x�ETf  S1V��>a= z$;��B�,d{ @=mV� xa^ e=x2��?�.�\&-6f b�W`J[.a&>�uOyqq!q~)��.} . Sym� ;;2Y0ū�(studied var2jz_�%m���2u-5]1DF�D"giQj$_ ���$hierarchy}1RaOl}{c} �1\{ >Dminipage}{1.8cm}{\�K ��\\ �\\ } %�8\[\} &�4&& �5Rf92fm-\\ �ed�q\\ \cup3>Ru52uB�\\ ��r��bC2.62h6���o o1:�%L�g�)�I'x �D  Qމ�I�` �A�Y�8 �-&� FQ�fuzzy AR� �ot>5 �U*�"U�- =\pw�;�:it"M�{ , $X=\{1,x\}$�$1\neq x�5 $ triv�Li"mh, $�%UCA��! $UC\emW7/e *. oB�catw{�"�  $V ÁQfre�&�<�Vto��GLin 呁��)��! �p� ->"-�!{ ever.yX6�3"I(��1 _5呑�M�eIAdempo t�ed�z'" , be�n��%$��t A �*�ZeU$��*.� ��K,et $Q=\lc(M))2FW+\=���) n�+�&B�>lpywi]M*� o�OBJ\{A;� G �<mu/v�h)/J��:A�]1%�f%&A��1_f��p�k~ � sE�:�&( M�A58Ko2.5 Y6� M �"er*- "� !�bc>E0Qh!7 qpowt.� 'g goodBS% | }5��2>w:A e49Y of)!cma�discro}� v*e4ANwll� en-�n*�7JKU �'�WO?�axi��T_  t $ al!for| �15to� &� ,�,on glet�3 [�$s$d�Aspp(\�}.�9{� \}$�M +MÅ<$rAd)=� � q1@I�c'sI�Ig�!E=U<� M2&y�)w e�2!f %�BK !c/CIG "�zh^di��vR�cay5� A,6�&� )2"�"(a non-T$_0$"�{YYɡx,�A}:s�L!A��9�j�,y%�� $X� pac�Qs! ct�\{�vaut"� "�g�zon $s$) per1�Zl��4���jf� p&�� $S=X�*�w\.�$ e=�#_X�#�#&&s S ${\!2\}B#,r]&&f.l/&08IF2�A$,6�ds# �g!��s $s^2=�S nd $V*=\{0,f,e5��~ђa��RwU���M�"�I�͠GG,��ρ�!�mpl D*m<D+�14S nine{(s (we write%�.�2s�lf\vee C:n&�2'f� �4se�$, etc.)UF$0Lt=f $e a= ` b=es c !%Z1 +D"�3a�} WuO}s>~)o��!�:t W $Q$;U)7ntb1upper�a�KՖ�67y'� a*� d} &\vline&0&f&t&e&a&s&b&c&)$\c{0-10} 0*06A�Ff&a&t&a \\ taa&e:{a- � .&e&c&b�b2�c6 -1:&1w )!�u��c.�w"7 c�=7+$\theta�l1H*�Uoau�g.=2}!�$\{b,c,� �seZJmos�Xent1ofi�!� AI"al�mc",.8.�&��rue�fo�86��4oL,�Bb4z:%/\T! ei��B, $c$ �L1$2hbin��@= ([ 7Cejcv5u?al8��$Qy9&��2�ls�:��:�s � N�!] �Q$!,finite)!!..f �}Rp!�&hɒq�S $Q/{)�}h� � 2.L%cs�p��s���!b�&$+@�~l]ըr ��e]&a 20>�&��t:�is l4= = %(V)�!1^ b)�R=&1t���&b^*1!� "J�)� �}-pz>i�0m_!���_/i.�'�]m�ma�mb)#c 5.� ���Mn� qed DNe��V):T���e^n �z(a�r<-� {ylef �.�>J3q�_02��� Q �VB2(!B �#.w>"�I eq:quL q7a)1!z(�0a"�R1)>Q ).�6i�}uu fF�h&�h���&i . On��a��)A�'# �ס�"K 1�U$*�r= &bsӅ� repl+$�e�y �h��(��9)� V/��i21.�75le�$!>�_Iu~*W,���� A�rō��Y.0)-�1�I-� :Ek�3to7��Z� Z�I)�8a�81bc^�+a}b�c��yt^"�3._{b^*c!E�L2}Be� %!y�-LSn��1��Too��E D"�2b?,�A�Y�8��=was' n\bži65k]�I~; I�>.�-B"EA�.��w�n� ��Bs likՋ1�=*�/1f=�=.n4�mitno$S�weXuv� ������ dr}�G>f4%F5w�m� �uwiE�gh+$5a)1a�zus veri�w=�_�A��$ bd^*�7�6idD��:�Q �K��N $M���6�m�0)B*J/dB66b�.e6��% 1.!> ����� let 6�1F�( !V6�7��ls �Ma1�7wj u8iiyE�>�1E�qualsQGV\{�{st ��1!23U!��0Wreate�U �a�PZ%bance,� $b=c=a$RV<�v�� exm:v � s} E�!�>�m�?onmM�obq�J �e6 �� ny���b*��.pullback.HYz>dc g�elf�^N�s�$/_/[ddr]_g�/^/�r]^�.pg r]|h-0� JXr6�!�?A&aBd]^(:@BM}}2Kxh=qp f, � 2� P?� � pF!�lu�#�{�1�E~E�a GJBi�!8<\cs)�!bN6A��R���ra� than���%g (����"�$-�.:�"d�4s�!�UXY�,6oOd�(b2>,�dr7}*0�V)�it*G A�zU��b7{&1��@���A�I>1)Fِ�W� dr}. ���m_!G_c 1 +E�� \ �)) zh (-)=u 1$\,FzO� � 1�>^*�� F0m,�  hz�S {N9���.\�$mBOa3. BNa�C�F�a1�1� G�]�~� b�6�.=�e�1 u�%�k &�z m�> *�Lo�J�2� locetfgrp�M��� +�*�� �aid��b�U}���>��8i��g���T�\s>W$*.��e%:D �B��"z.W*�� @"|2�v�ʼn9>us� ��"� � Usam_4N�E43t�� s� � b�*�6 �� ��{Y&2*�e)1h��aE� s���=:Z� #I���\!�p:�C}  � (al v  b � bdaq/+� a�e b- *ram2be2-�-"%b� \[0: s=n &�t�W �@�u �� �~! S  (r^*��@ �BO$�~�F �n)��!��rN����niue:�d�c>8B�%n)� $m���F9id}$. U�"� i-&" 7e0bnE�5.��H�"&4�M ��� $> Yq�A\�s� !�=��m�e� :ud}~���^3� *g0C*>."� e&Ka�a�K.]B�*�r�� bcz�V=� �� {=.�!� 1�And@K~&��* u��aY� MYM��H.Bz�\]9N �6��ma� �[��- r\8�everytϣ"Pj>�Q@�W�eTF s�92�U��D;a�r�� O+g $2�7="�cC $G=�>��aw�zo�4��^,�/�/ť�� q��1��"z3\ Q4aE� S*g|=&w+)�def:s1}� KANe!b5"0 \[�[EE`"YC a^*}"@�:A4[ �0��>$ ($a=x=y1�by.CJ!jZ! |H=su0} �d.� � �s:%"3��"array9%�a a@ �� � a[  u_! �Ͳ2!26 ��;: ��[B�;e|]f �ՙ!N E�a.CDBQQJD, a.z dd:��)}�u)44�tAm<6-�*� ataa.poF�i:����j�� &ud^I5e�cN�m.a !e�U�. V65N,^*�L2-JXDw�924�&��@}���A ��J�&�Z0?Kn�B("x&)R ={{ us�#Q a�($\widehat{G�3, s"_�\$\�dm, �� � Z i>��p�G� u �5�2c�+"y�a���!=9 {G}_ 8& natu�Pto look� ![V8sm $(f_1,f_0):GF�I��$f_1=��1| �0$�[b%f� $f_0=%Of_1�u2!$a:xF��I ��.Y P\ u$. -�"f� air�PJ8"2��2H!�\C� ?� r �4yutefk> f0f1 -ford}*aX �%X_bX�9Sj{1s%�=1^{ �� ".X�V1a{d}-Y>F0P%6 .6�̏,]6���?*�*B> sqf}>7�/��*zEh".�ks $ѭ\ u}"l rN N�V&G "B ( ;d; \B�&=>V 1lF16j , -Ps��e��7*�&of��䥟�/�Vu�r- � us yiel�N �\] h/T"����"G *kA�uI d� d � eq:uduEa$  r0r� T2rurh o��.DQ+])A`���D_0 �6 N�  d�� -���2Y�{;;\vn�8!`eu�1 >�)u�. d�` .2���@�FBou���u[ �q�6� u= %:�E+�%Fu&� >�!�%�:��B�r.�r7[5�r2l �6.� rF� 2� � Y )�.� ���W"R��cx*���/&j'�:�� $f}i_0=1o�u6>a�sM� : ��� {c}(@1�y� ( u) �2)� 2.91&I;,\\ :Y F:�� d _nZW �\]�ft'��#:#{2J�prA]i.&������� r�5��(�,�� � s,� n� W�&V+�� ��� �3t�I$i m�m)�� k�%9ͼm��rE7� � �m��>��\�&K�L,.���k"7$i �i&Z �i�d� i�c-�E�%+��&��A�w� -:z�� s�suR �Q5��e"L2ti4ew6�ern��&u`6+)�+fJ^&�U&_jͺ`u �risetale}qR�Nl�1& !���x* N U��"� "�NG �%f �:!6� g�>� $2\R\)�A 1$: I"<�:n6� }j�.\\ $3.j22j�$beO �imK} 1�LoF")g1.g3$:�vR�OG9�6� !�%�� &�M?a�*pp�iIm����/5penN:�CaP�"�Y�"�� i&��!k jka�E �0+ d�lUny�\"R 1n�9�%��#H� *Nf G&o&&R��sQ!"s(&�w�Ke&B [Inde�2h�Dn�ve�$�$"0c2P$.]J�*� ask � well�9#!=@*Q&"���q\�J$�u,brief`;ddj�/(&q4� �d :U�Q_�1sQ_2�� I� 1�%f:Q,.a9-�:&�.R .��"$mdm da:c�� ��(Q x.2�(-(��j�a�f(a)f(b�f�.[ �^�_�Z�D(f�� f�m�!\����f�>%�F2I��C&k1����$(m_2)x/2�� �(m_1)�/eU:�i>��$�F.�6Q��mpo�� %���2��"�(� �52f %]*�F=R*sE�cކ%�?�� $��B�n6O�$�(Ka.|2{� �s�pc1,�Ʃ�]0�}�(n�Y�*1�^Q�1a� � {� B&�*Ni�_���&�w�/��-G'pN���Z$\[h=(h_1,h�'�G\]�6 q� ���o���~W\[han (a) i� ٠� ��>�C.�`(t�|��"�[%�R��6& % . sYj�t�-,�in"rf.)���` ^Q1 laxhom} A���*J-A�ar a D/BA�K%\� ( Gten26vely)Yp$h&nc!" .9?gDg$hO:P\ �e�2���es:1&�+o h(g)�`KE�g\in I;e0U=Vs =\{g"%J$g�AtzL �N � (V)=�;��w�C (N'� #V)LgN)="R1�l*�&��I�"�n.q}�Oravari���r\B�Zf391)�in tJto:Dd{uze�+ A�A�c9��n&�„� to ch��4"b �r~ ider"�%1�!�cLm��QJ.���U%:� :*% ��do6��2�"x ��,9FLw�2�A�I e=P�"��,in�iG����2dp%J ( lblems �By].� v(s ---e 1A%ҝ(��"wS e/0h^*(e)=\ker h��A��a:�[��"�w.��*�)TNOC X @j3Sa��AEP9Ks�C)5�"{!!te�@ O�Bor� */*�Cfh;V�(mEu$enk.o��3>8B�fR��Љ�q�!�v�Ra* �N�0nn"theles�P5�'=!�",%Uv.� arrS(��"9Dmay�}TN�/�if a���7l d��f �5"/+ s $LMXM�$���@a !t of $L.� M�� &�>$stackrel m !7!6�Fiz�$!��%&a�Re0^�6���e ��!eE ,�$r�mul,+:�orSy:a) r�_ ig%�f$�d��Q�� �*�Fu�^C!��Q�?bo�Sa&�"� par�E� paperDA�q�{Ic6��?indepen� . ToA�pl�5": adop*ejN�Aie�1n) s $GMQ��eӓ�[M %V}A��|�-�"a1& 2 �Y�]P +� invim WWlawV�wm=�HV6Xw_{d%�(6 ` Nw%�"�x +&&M2Y.Z^{mJ/"rv :�^{r \ ~.�w� +�6�)2�.3�wz���w�wF�)�F���q�6�T� �.�f&8(V�!� G\\ �8\{(x,�sin��;x^xV\YnX.?Y�!\{S� F] X,\ *YYS&=&���=C��G.aG$g&�~� �< i�rI_.6Y�X$)_:2�:� inu���K� lloR� ��$(x,y�>� "�8neighborhood $V� xy=m?�X�i�+� 6$2� Y�ć z2�m6� Y*"[V$*��*p^X݄V&��!�sq�U.=�,] A be re�a�+Jbi�]s��2���#E�*#=u3� B;Kz"� %�5V��S"�! �=*l|�H OBt})ٍ �Nr��R�0�A,w!�0 ٝ�)!OY�.�>2 :OfA � E��H 5\ ^Yt�Q[�U�j��. Bu/�facvzS�B!�� �E�jQ.|ml R#��m � |2q�"� (!�"WOhalJC)Ro&�); :rd�_� # %,R pac?*0Y� G_1=���n�pi!L,!\a�!D! G-se��N�6fn3 _%! hypN�s�8+\*�ipN3� f�1� )!�� N�G='�ٖ�H �6!> ���W� (͉) ɓF]=.U6� �3X� >9Jsah�zT�*9T �c�N>� �)%�?� �k"�3& �vZ���capΕ\9-��F��Jj,\^�qr1�.d���8��} y*y�%T=�i�� �f�top#\-��UR��2� �9xe*8 y�*�"�.��,&�C��map:#"�)D�O- >~�^l=Fv���UvkC[\L�A� &4 2 �XU� ي f]"$.t~B�(>)�T.]th��6�BـscI��1�.r�> or �� (�� -�6� "R���% x.� !�"�&AKto ��i"���d �4]�d>s �0.TMai&A$�JioJ��R�' $d(U�' -v�6G . (603)�&�fA�ui��.!�apmBu��"�laZ �$V%��2�%4 X65$) T#l24.�%�56) U%e�_Vhe"  es 4�5�.�G"�!�@� 6�=� � �*���s� eqA�� se2��H�@  1TN�$"�,A=UG����=m���B\Q��Z"ԡ�C_�}] � �>sasg} *1P��"��#�!]�  o�dy+�urz�*z[1P!t�U�)wa#ons�'IwicI�*�Y��: j�� reale G�ba�9q~R%� Gt( a de� d?�:�7�+!��e)vol�vA�.<�T��a��Yiffer7etn�#i)%� .4|xI re c�y�ut ``� in''.�U!��&l� a"5y�a�%gel�!V)��O&-�YF*!� en' .h(E3�aX�'ofp�W"1����gef=�u�h�Im�d"�%U�P.�a�a (( )5,)x^Z!�M�i�A&!j���Z~Q$xj in Eth9�+i:x�y&,4��.')�=x$e �� s=\j� :�8Q�E8tilde�-passage �!:�6)"�+%�in���! lost,� keep!Tt�!gE�:/ATEae�]xq behiS`aEa!���ed�N�|�{o�). Of�^�)��r;Qvy���scrib\]�L��4an Alexandroff&& (or,a��ca���-N- #/,%��]\ ���+gt��rei(�p(�1A'�. -��U�,�Uwi"GMes&6$ �� g& sgas�VA?�k� J^E1n:,%_&��u�.�y�MF�I<�:��CmEy%�U���szs$��me\[��Qinvs}}1>�Fd}�/ V �9q;j�iXd(s)=m�,\�a8�tA�wPI5+a`��,%�cS. ��\N>Q6`&< .�Ĉ.� .I�ger��\ d, lc(��)�J**/)�a�!+"w� @�%+�EC�o�l�*Kl�;�o\=-g�._0}._�7a�Y��cV��v:�& � %�>�JJ R�*� A4Q*�>� �1w6� �A�)^�1�2�R e�UV$&�>eir>� �"23refN)i� x\& 2V*�:i�e!�u�:'B=.�n΀e�m $� � U$�us cheh� lsg�4� �Q.+S:�>{�H # $aU�Z�V4H��Q$yz%�F &Y6":�6�O3=y�z�z=yfz`$f=6b&Z)��^� l�j�(yf)(fzAA/-< $yL.y �fz-z Rf��f �. Ab�$rZ=� =f �f :� :=f��+"�$d�=�p�!p^9I "�^,� T��xlEK=E���)�AE{��"� .�E�l:r"�#A2? Z�y �l��b�'e��"k!#Ki �6sEseMh��F�R5j�.*D6�1Y�+� re�e< !A-2�:��6.%>� F:�l1{G :��end.� AnCr a��:a.� brings L D �D���%�2� �u�stQ�Ver�*a ��&a��ps ��jdu�}:% 2-Z� : �BM�aI�s ``f�|'':+� by!�j�Av&`��) a ``&��q�''%S�d._f5�A�&P 2����&f4 �M� �iN3T�%�ru:/� ab���ate sobu\ n�A`-Lic*�R�%}��-korumqc*��rel� it tɎ&�:ger�.y}b� F'_>cruci�'�'E��A!n��!��� �6ed else�Q2 biblio?y}{10 ib��<{BoRoBo} F.\ Borceux, J.\ Rosick\'{y}, G.\ Van den Bossche, Q�*�08d C*-algebras, A�London Math.\ Soc.\ 40 (1989) 398--404.� �CannasWe�,eiV.\ ( da Silva, $ , Le��% GeomeG� Model�Non.�%A�Berkeley�J0.\ 10, Amer.\�, 1999%X�onn��� , :m �4y, Academic PG8N4. \PrMo} M� rainic, I�$oerdijk, A4����oryFp s-�e�xAngewG)�@521 (2000) 25--466�Higgi�� P.J. , CQ}� A{"� , Re��&r �"AppX�sA�Ar� .\ 7!71, p��--1956�Idr-�} %� , Sur �|�or\`{e}m�� Riesz da�aA�lg bres��llair�:Ths53 (me cycle, P:- 6�2�&�� P.T.\ , SST s, CambriܑStu�YAdv1� , vol.\ 3!U'Uni!U82.jElephantNxketchA��/ * 0A �/s1�,Compendium, �2, Ox�H$ Logic Gui�] 44, �ers�$ �2002�JT}eJoyal,E�Ti�ry, An E��:��Galoi�ofAK\,dieck, Mem.\J��309, a�i�A�e���Socie�1982XHKrPeReRo} D.\ Krumla!(W.\ Pelleti�,P��<-de6 On��e��s�a�2�A�a�a0���s 1iy(3) 543--560.� KrRe2�.�6� c��,ify C*-algeb�ras, Cahiers de Top.\ et Geom.\ Diff.\ Cat.\ 45 (2004) 287--296. \bibitem{Lawson} M.V.\ Lawson, Inverse Semigroups --- The Theory of Partial Symmetries, World Scientific, 1998.rjIx , Sheave%A��)�|ogic --- A First Introduction toA�os-��-�22� sMrcun} 2� J� r\v{c}un,BkFoliaxYWUia]r*32�u86} C.qPulvey, \&, Rend.\ CirA�MaA��Palermo (2) Suppl.\ (1986) 99--104. \bm� Mu89>ZHQuantales, Invited A�%N{q!�is2zcalculus�relEnaA< ~��!��r��13A9,92) 345--3606�Pe0�On�B�points, A�Pure AE��xa 159�T(1) 231--295B}�Z} spacA�b}75}2��9--32:}Re>(P.\ ResendeA4noncommutative!or��0enrose tilingeba��œe$Phys.\ 44�5) 655-668PaRo00} �asekaA4\ Rosick\'{y},.�aIB�-oecke, DA{sf{z \newt�em{thm}{�5em}[s�}]2#l(thm]{Lemma}2prop} Proposi� 6$claim %C 2Cdf De�oi�f.�cor "Corollara9���Remark6`que ? QuesN_nj !Conjec� 6Cex !Examplea�%E�F=S%.29T:4:Z=_:)F:;.vF-::<5�:'F:99�F+B45�#: } %`mnotes {\catcode`\@=11 \ga�n@te#1#2a��avevmode\vadjust{% {\setbox\z@\hbox to\z@{\strut#1}% \6#${\raise\dp &>$z@}\ht\z@=Mdp % #2"a�� left����0{\hss#1\quad}��' righ:("\kern-Eskip#1>}{\move3\hsizen ?{\FN@\qum \ L{\ifx\next"\DN@"##1"!. �{\rm#�x\else #6??}}\fi)??}I@}} %��%���{\vbox�@ize=2.5truecm\foo� \noind��{Ms11� �N \begin�� \base�D!O=14.pt p� 2pt %13.7��title[%� LAlexander polynomial� DHurwitz curves ] {�2l} \author[Vik.S.~Kulikov]{6} \add�{Steklov*z Xal Institute} \email{k J$@mi.ras.rua� currI{�)d� (ory{} \subj�thanks�% � was parly� d by�RFBR %:� � � %J,  V2 (%A�D No.} 02-01-00786)�$date{This � 4ion: February o,. } \keyword%IG$abstract} ��ert�of�� are B 4stigated. A co�W$te descrip��Xset c :}(irreducible:� � te3 �Dir roots is given.� � \makeE�, %\pagenumbel{roma��Tsetcounter{tocdepth}{2!bR1@tableofcontentsSy�(ctic isotop�� s %.K }{6L ��st{ st}w,-1} \ {.�H} In \cite{Gr-Ku},� )��o� opZ�>�6!{$� bb C 4P^2$ were starE,Recall briefl" �Ya6W ( respectx ar pro��$\text� : z.� \toN1$)� itsYn��. Let �<^2_i$ be two cop}aff� plane=0^2$, $i=1,2$,�coordina� \$(u_i,v_i)$, $u_2=1/u_1$� $v_2=v_  , which c� a�P^2Ahminus p_\infty$ (where $p_{ }$aa$ceA�!�9N) su]at=Z8e@���4\mapsto u_i$ i�charts�%9a�a�$\bar H�x � R� \{�(\}$, closedRl Al,�A` ed a {\it:PDof degree} $m$ if,p9��cap� � coincide�!6�of zeroI�n equ& \[ F_i5�|:=v_i^m +\sum_{j=0}^{m-1}c_{j,i}))#j=0 \] 5��� item� \ 0[($i$)] $F_i <, EG!a $C^)�$-smootA9�y,x valued fun{ in2�$;`a�-nm l(has only a � e �4!f crit� qDat �tE�are 5ly many )<$AM, say 4{i,1},\dots, un_iA 9#��%5�1;1�} \{def}!0v�{i,0}1�I�,no multiple �c� $�,0}\not\in \{ �J� \}$; \1�)qif $v|jita 2e! � (\ref�)|j}zx eLXthen, in a neighbourhoo�)Qinte�{i,j}, ���A�e. HVolu��a��x analy����!E� A:�a HE�m�e�*}%2�T H� M 3ocA�or AeM��M����$, weEytA�>�g��consistI�k$ ��onents �$$k=\max \#Aɰ�  . of}\, ��\},$$ ��!~maximuma�taken ��Y�s B� . Let $H��an �ͽH.� },)a�$H= �cap (��2c�L�kA* �$!� ����iCfibreA����in genm ps  r&1�.�ɅfundaRa� $\pi_1=z�(�up �H))$ does not depend�!�cho�of6�(and belongs�*las�� C$6soQ� $C$-Us. By &! , ��#})=/ togetherg a M prOAof��@} G_W=\langle x_1�u ,x_m A�midx_i= w� ,k}^r x_j ,&\,$��WBr \,� �} M' W=\{66QlF_m@ �1� i,jm,\, \, kh(i,j)\Eo a sulof el�ai%� free)A�F_m$ (i��Assj � $�,_1,j_1,k_1}=(2,j_2,k_2}$��($)\neq (i& )$),MӁ�by �E�tors $5}!| h:\{5� m\}^2 .� Za[ someA��� . Such a .A4�LaEK��."} ($C�i� all "��conjug�s)% ( $\varphi_W&� !�to G_W$ 5 he cano epimo2sme�9�K0{W}(x_i)\in G! -�%�m$mV5��edmnm� �+�e@5n}A� $G$� $f:G_1 �2�� a homo�;7 s. IE4 pa n.4�pim�CG�W $G_1$ un�$f$�F&< �_2$. M� n ��$nsidered u�-Kis�s. Any;!!�� re�!U sq^] (S^4� S)�����iz�a� �$0 R' >�A�� ��� A�J!"&) B�,dAm��lyl DE %�.�>JDen�byͬ@HIWof�� 2J%Ga�� ����= �$m�PZariski -- van Kampen2*4VW ^* H)$ ���C^2 t/.�*@ ��&� ��.* pr�J"  J" )Q e%u �$!tru �5�}.u!���)ɋ� ^[t; prov��O nyF�!�:^���u �&� >u� s�QZ)�UG singula�!�Ru!( $w^m-z^m=0�~ \deg� =2^n�S� n$Z�%@R�S[wٗy9sɠ<.�� eM�IGM�J�e $\{� :� 6%V }%�B�s - ٽ�R/ a`�� easy~� �+ِF�m %� we u�&hndard�/Y $G'N �!'or sube�\ , $[g_1,g_2]$%큖,.� $ *� G$.} $G/c�w+ ly�3ed� � ian �AOA�2�. A%� ��h�U��*�x\simeq�  Ze�!�e-J2bn$BP !�9^[ Z^n�}fy�� eis��:j :EE@-|*�e{N] $H$Eϩ�&6=,!� �!� �3 l toŀ�84H$. Similarly,->-f�'�n$^�=* as $GL>� R�Z�%72� s� $!�\\&� m�bb F_n$��fixQ�g&D E�Y��R��&� 2*� $\nu : G ѿF_1! end!7!�6|!JG$� a�26Iis well͜d.�� $N$� el.&�!�$G� an2�n� -� $N$ :%�_G8� = !� duce  f"�%(exact seque4of�3 s $$? N/N'!@G2 r_{n,] 1*�  1�th.� ���nQ7��@:K)R� $n$-thVunitya �  1�zB6�fN�� �E�C* ri3ve�%/ In�(cular,�G�(| OW �e>6*�d�����of e�*t'&u� h �i��*N%*D ��"�"�"� �"&� .� Z[t]2*! $)] , (0)=\pm 12!"%U5� / �!� $dJ�*�!v�!��@2.�$ � � F� ! 55si&X#W2�%��;t&�"L $(t-1)(t^d-1)^{d-2}*�#v�("icA�o)� $t=1E�>vU� $n-12TUA4n=� then>1)PO��"V $ �n even� B�!� main�ul� �d+cle!�p A��1s &KF(E�!��!�Q��cs& &� /f>& ER1%A �:��urefore��$speak abouf� U��X�*r sameQ7�4^J}P�J�. H�Rre.b .b� u5�"1+FP,�c%�ir�purely a�9 ic.}Y<�.%2 m%�;} A]� $P� 1�4bbi�a �N A�����B�fIOy�l$i���E�PI�M�� /F�n|}*�t"/ �=(e�m} t^m�'i"�'a_it^iF�has^&I�:�&V+!)���; *a&��a�\zeta%o=imi�9 $p^k�aLA"� p1�S���:�� qm�><Y(grei��5.9���33�#&_3NKe)��:�49�IKMP%��}%�HX B?J�i�>\='�e !�v �"� ��t��E����g  �16g �&3 b�,Aqsufficmo *ajP6�L stat� . C��3aN"�Iv"; �A�N���6� � �% (ning, let u� [it N�a�r �.� \Psi���y"�\ �1�a6?a�%,9 -�not:�0,.3 .3� , ���/�re ex /�� "Fu;*� .�5vdeed,'.5� F�F"in&��L��\& _{i}l _i(t&�.'fd)0*� IJ-A� M�q3 9���)%�Ar)�-[� �1.p Z6� "��� $i$. Next��_1�Y1_2 �hV! EU:IF  _>% nd $x*��I��.$3i=&d. {1,i�3x_{m_i,i1ml.���# R_i ?.�/s $m_i�e7t�2#'�:00 5.12a).���Y�.ZG'�A&uct�  ,diamond �*�5_!q)jA !m-T�!?1|)IF��:��.!mBe�94align*} G= & :t*9t, %A )y�)v1\12,\_){m_1,1}=%�2,2$+\ & [x�6,(x!�*�i} u32' i}})^A }]=1 �%�forAj=/,m_i-1 �M ,���� \ove i_01,2\}&�, \{ i�(r�:-��llo�%�34of&�M�at-&� i�a� "�.$%�Q�> ��+Me�;U�T2{�b!�$�Fix.� �Z�Ps��.�"* $k�  smalles,Ei@�� �4��!?����>$&q��?,Vh,� Oa3fE $t^k-2 T.LŸ0a�6G#q�ysj� :`#�,� � $ quotJ r� $M=M_{!m}"Q�Z/(�&�1�+1� $M� "�/6n:�'�~&+ adve �=��.a n%:�'re�"Q�c��Y�t_0=t^0,�[$,t_{d-1}=t�.�d=J*Psie. �,h_0�`e�En{�v�}M�\ *(Q(t))=t�� $i���ZJs�# i(x_0)=h_�*�/x_0�J�!�2u$ . Obviousa'��Aut��M�2o h�)�how� 6�0ͦ8L}, Chapter XV) qt�#0&,2�#y��xg$. C�5)�(MB��@!�B0Al�Z�� | O(A�(L/wuri ~CAwno�*�AM�U�~ $M$�e L -dir @� $$��cL{ll�6mRM�Ethree*%QP� �*& !� t_:� ,x_0�0& [t_i,t_j]=1��q�F  )Oɣ \, 0�4�6 d-1,� x_0s& t_ixa+ _{i+<3 I-�Ii=�( d-2,\\ & % mand}\, TenX4\displaystyle � �a�$t_i^{-a_i}�6�7)B!Sm a�@' b:�"%�6d��a� =t^d2�i�A8e�E)-�e��@�)1�(A&�)*�!�� ker \nu=M�;J$. .E� (g)=1ga�-�'M� #$iWd�"�t_i ;i}t_0x^U Evi�,��0�A�.�9*(2 � * %'�̍X� ��xѥ� '$ $$t^{k+i}�& t^i \mod �CX).�i �a�ThuW'%�t_HR/)S =�@E3ncZ�d1$��7 0.onEkc�?."q�AG�"Uequ1} N{��}2i=\, #-%a����#:O  j� �9�/check�\�.�equ2}ujx_ �ak x_{t�}B�:�;jP 3} (V+)x �^ �Cz�~+!}:�I�J�Ib�u�$@��n.E b� rel1!{t^�����!^i!N�:��N)�1�,� �Dfin�C.��X�6�s�:.yf=91K&iH!�f*�  (cEv)E3}�s� l! s $g� 0}�u�&�C� {t^0&{1,�C-1! 7$.�U-t&by2C� &K x_0� R,O %\�X5r&nj�;&o�8A� �a�!�^k�d�%�> N�EM$����=�Q�� i��7 � "|7e�:{\Phi_k�~�a�2 �lso5te $GJsi!N�Sw)l� ) 0J.)}<a;9Plet�X ��N6i"their p'2�� � Q-��*�.@. G&� Z S� bt �M^��&�. G=&�& 9x_{d+1� �$V�e� =x_1�Nx���>�2�d�;k ; ^k=x� 2�"�2D +1,  x_2C?u2(B� )x_19�� �)��T@�)>� �`� ll,x ��H&0NL1]%~!���A&h2$6Hn��2A!�r�2`.E $x_i%�1A��$=l d+1"�rs 9�ai� �R � i�#.%.a"� -��a�Arv% :RT�)G#� {U�1$ 6�6:�F�"�& $k(d+1��(IH�1�ec- an�:!�.�t":pB(=�*bxC���@ m5%�  �Bk!�atisfy�Nɝd0<ing&xA: $$ QI�{rcll} \, |_1}& � �_2}� ' A'all� i, �B j_2; Y1�CW��{� ]+ R NE~�:O�1�IbkQ,1_.O \, O 5HQ2�  [ "K �A} jk> � :}] �1*J#i�>,�| �Qj;�j)� $$ $�q2���b � �J ��,1��%X -6(��-1}).$$*� O42� beco4a22#after r&�P�Y�*�}�\nu: B 7J�/�>e"*� +qCh� ��"^)O2\a�2j�,.EN=.�/"2,h_1��11� �N#�' l\g aj/.fa�* 8)$\{ x_i�pX%�, d+1l7n>� I8 i} R*RRv ,  �Zs:2f�m(�� i� i-2� �4$2u��AC 2�0n .�Y f:=:EF*� *Fwe �/f( N)=M �h_0 f(g))=+28I)%��/ N.� A�rea�72� ,�� N}.�N�M�28$!�.sj ��:��bU �.N9)�d�p8QI["��,� J= N}2L'3� j���2,j2 �H4N/. '��R��>� f'2]L f:�M!�.3.� �:>2�9.K�r.!f'�/mf)�K�5�9�6RW .� -77.�?. &* Q� 2xK%L� ,C�c�o�"e&�?{ @��g�2bD�}o6/K�36"{��ir�H.&j(g_1V$_�=Kn)R<2�B ��2eK� �!� $w_�>- 1��n>DnV= � {P0*LS 1} $ r<� $g_i.;*4#ɕ �C$2�v� 2N� r� >�, i j�i"�>�M�> & ):� �"qM� n\, "�a�" "V^�cal RE�aMt� *lin6�L�E�}) i %i�@O&" &� . More� `$6��J{for,y�.S.�f"�7Jr G'Jr f=f�Rr.�QA#2hr$ dG,m*N� )�)�n a��%#2_"�@�G�Gek M����%sn2�$M2i�^QMe@�W=� )� �&; r(g_PY%� a���|2&�%(A>. 2 � �E��2٫:��B� A@e&� B85�!�ibi;� � n� n� W6U  f(*? @ 5 6* H >(  {.2 �D N}:2��Nua� J 6�O}r"g $ j: SAE~6�.;�f':,A���2'.6����2� -Xr'*�  K)=K  $r.�>��2�.�.�r/ $h���\, @iQaut"�OA2 hA�G?!A��ct"to diagram. �E�pi-K}(0,0)0 \put(80,-5){. N$} 95,-0){\B(1,0){45�c: 115,::j:148FW6� +�90){$2w85rx-97){$o6, E/N'$} � 5,-1� 0,-1){65} �78,-4�r2158v3� 4g120,-3�** K�6fKf30,-7 \seaBy�>50h*A m�Ss �R5"X!^M$;U"� $h( |i)))= da#,�{�K}=��Id�x But �:"_@G&�AJ�F�* �0�F*#�6(#" $WV��2�[�JId SK>K �I � natu�B. $c:�O��( 2G6�Go)H i�aF|`N�B Tors�8I�s�-�1�d o5 s. O h�AJ_�!|a�� )%6�6@-�2�a I �!�6T , $f'A,6RC}:FI\to M.$H*JP�!"-B!*6% M ' =f'(V �. \qed te { N�%qB�s 6�sev�\.�+= neN^I!�is":2��u712�6} w�W`1d. r"1=�:n+�'P_0�8P_0(t) Fd/"�  $$�Z F'a��t�'re:|;QBf ��: *"�&f:6� J�:�z�:�E2B:6�F!k6� 1jf10i�F>s0K�Foto/{&� "5ZNknown F�X 5.3a�\�4 �a Rb!(t)�Leic-�1\Wf $k=p^m� s:T�q�? $p$%� I�!���!&d1^{n�W," ��/� n$ M��,I�E�G�c}�6W>�AL+$Z>,�q `� ;� `"L=�.� u�(�"�_<6\"e�}�PG""��Z �U,�$. Bel s5��0��0�AwoJ� is&�DM2hR��QMto�;v:7���NO5yis�- N`��%dR��37&U�%��! >YyF"�. ��4� �"t:=�0��.� xIj2|� .J-�.�Z/%�֢/! ޢ/�o� 5TiL�(M.["�/"> ,�"�E%AS�E{*V*T !`lea�ScoeF8ixq*�3 $�a�yMn%.V?u�^:0Rxjt6-0*�06-0 �-0��.-0<1a�N�"Q�2�-���R0<re&�m�R0"�%B�  $vR0. As �;�� &�C0�C0�C0�6��M&d !� Bd�0."y)2q1h�[a�K2EK*|/��7 �|/�|/�|/�|/�|/�|/��S a�&> � ����/_0�XH)��X="�.����/_0=N�/M��>�/� ��l!MA��R�.��/*ot*v^&�66�$�"(6'>Q(6�i"F+��/��/*}#�*i�)0tX1^�"P*�.1�->�-,.t�-%)=� �+i�%, normal"�&v� *h"�3�!!Rb$20 ��1 ��g �JF d A5Q�!�"�,N �B�2��x�1 2�) . " ! V�,>�0*�, B�,�,h�,"�2E% &*�-^'t&�-�� R�#6�@"�2��l,3Nv*�b�k� '�zZm,&j'}5.]$kaTx�%x�2�(1=x_2@, & [�*,x�5�,uaBE5NV�k+1"�m V� BE,�m�.I=�&��qb�E,N�i^kKv� ,kT*b�.�0,�c#� $!Y&�+!�A, QeA�i�FRm�,b&�@ 0�8b8B"� �?�+k�+�} [!��B����%�.w� :S:�(%�h��^6d%��(�(A#��(��(k��(B�(k��(�(i:� b?*MY��(��(��( ��he� tr�(2��}<^�(68J�(1gJ�f#_2�J�(.�* 7j2((:�(>� !�>\ f�( ��(6<N�.�.|�(.� :�6|., N'� �C'reNh2�(s.x5JhɅ�\in.�N_ &ds"�7�p~ j�)�(:�2>�"Ab �._�nd" (Ao: (��)Z (16� *'2)I �n\�.%6�%� e)�(�pC�(4N� r� � � ~'~(�Z(F(k+1� d �&�(�(3�(*� un� &H(by�.OX�K.A]�&,(� %��R,(�(2hr$ �,(,��2��-( �T�H�.(.I;(�.(�.(�$F.(4*�;q�s � .( .(Q�$, BW%�-)G$Bil Ba `A�Qa�.�'>�=�h80s0-U;aa�.(R.(*fw�&2-( *�& V ! ŕ^-(."1?N$�� � �:N}N+( j: ����6�:�c �+(N}6��*(�*(�*(�*(F*(2+(�%�%�&&%%2�'*&�,(V,(184F�(72'$214,3){$c$[��(26�(]�>�2�#$�&���(V�(�B�(6�-92 ���F?#���(��(��(��(J�(245,-4>�20�*255,-3�(c )270G)M� �$1f34(*�(�()nU)10,-246f+A) ?7A*)�S8�&U)I7R��A�2AG}�6�%�L�*�+0,1){2yWK 68){:�%@��)ByM�$�Wof .#�v��#1��ad��%c&�oN� 6 c: �'2wKO(�Z"�&"KR��O(" m �^. "�!" )�d >� ��&p66�o).L.p� dn8*�� eigen-s�o s $(FK)_1((F:  $(222!*rrespons�^ �)�1 0+ one-*1pO#akzC(.�*�:�!"-� C}(v)-N94 C}(6#�gmvJ�.N^=not-A��i)2D�O`6�jR�+H ��, f, f��,R�,�m��,��,��,,�"�,��,�(/*u H$c(K)V:6Ln� VZ =0.qKM)�+c=X2_+�+%H ��+�2613N:+��.]�, � �2x� >V���e�sariЛf�+�-�'�� p+*q+B2&s_R�|"�h��N�c}� &j+< �/c_6�,pair $A=(M,hg/="/-@)it2�; !l -lm!�J�3M�n.�KH9 $A_�:}=�t Z,\pm)�Id�uQ (+-.'\oplu&�.Z,h J�7� a [� $e_1,e_2�"�6 Df�SW$2�4�R\pmE gi2jـ n(eZ�2)=e_�KA �8!^s9_�7($A'=(M',h')'�(A'7zll mea�%HAM� A'$ �LU�cQ�0 A*Vs&a5 $g:MM!M']^FX $h=g�C�9h;?g$�v.s, put $A-|� � �!d}O $nA �Ssu���m&��$A�.9 a"5 deco@!d�hU��a%]. h��e��1�!C�*%7�W s $n_1,n_��� $n_3)�$ $A=n_1A_+ �n_2A_- 3A_A��f� �Rof *&!M_+�Ya�%Mqh(a)=afCwby $M_-% %-&�Mi�T� *� 'I�zVe~�=?byű�t y$_+\cup M_-�gb& VM'=eQ .�!p_{+}:M2M M� p_{--QZ�f�qon"�%-"p^��,�>}�$-modula�ts�  �_+ u�%�] ZAJ72.�@6�y �� |hveO�=Ie_{k_1) $ U�) +kb�s2laE.p )�i-� $2aA��N $M'�3U`B;"�a+ALEZ_+a-  )-�^ 2a=( ))+( !�+&�!� �� h>�$M/Ama>�secb^oi�}%�3�-�>.�5Q�%ԩW`B3:# 5is.p2)4A (!�.!1 �-�uth�o +$ % -K\�$ �\W(9 Z/2 )^{n_3�#sa0�2 �"�U��Ous cho�f � s $a"� a_J�$ m+]q�� ^ -e 4$2a_i=(\alpha K0"�A k_Is��2�0_3$ _ co&ϗ]+Y�B�#I� M�M� With,plosE �7%, I+ng ���5 fzA�w%,assum�ar�%*}H� � $�j��)�$0$$�a��$j� u6A=O--�&�!�Z�!"H ,2-Ɖ{�xapQ��-�A�� Z}�>�AM $�`)lmY U~���&$�V m_i(!�)=�[n%QB-!]�N2� Ruat least�E �bф$ �a�x2 oddT3�d hAj�_E�B5I�@-)6bJ�&�9 5->5 5)��� �]_+]�%����jT�u�+m7a6=2Q�a_KrՆe�f��$a�WA� &Ŭ.M;W�w� Ӓ*�ItB8 R8�o!7 R� N��/�6o Wce,]|E��(leq \min(k_i�2�N$I%' �wE6& "� � ��eR�� �r}�Znee|w�# ��M1s*E �.{)&jY�G��!t����i $i=2�Z�Jreplac��)^� $$a'_i=a_i-�W�F(a_1-A�_{�ipt�^�e }^� �-1};1,je5$i,j})e_j), ��� new -�E�a'�f8  a'�S.{  �j&k$)]%C�DjPQ� IB&�y2k!��gBYa� _1,2.� �tUAE;b �.��"J�.��� �-9� bl����uME�'*؟r�2[5�^�5fN bI��seorepea�si�� lace�oE 3$ t�, m�m:new� a=�-GE �}NP� �R"�$�*J�z(.� m`!�9��� � jz|� =��l"z !!n���?�U?� 6J S".�f 2�QI to� !#$j>�H-i+� q��:|)ault�p0 ��~� X*J A.y(M"�&AVA4"�>6j Q�6B�* - � *e�!6Hz�*�P2f(2S"+I�&�]�Av-�.� 7 �ogethg�60 .�� B ZOU$M=` �6Gz4&$ �in9u �, &0# $h$,�&.B6),!t6'&1Z8-<"�6?.�.x_�b�N.�� by.� p_+.�*%�@ p_-F* E�!�::@e?��>\ g a�  t�%�:؈,� can eJ@ �II�$�se�Tove)� � � /.�2� �� }}v?qK.q M*PJ��*)&., e~.�1),$ �R ,$v,�)yw6;_-I�%��.�S6�+(:�e,�  y6� � �#�a�6�W� �?�g2� 2�  Z]as �1:� -t� C��G"� ��Z����312� }$)&K2*� �� � I �B&�� M��� }�� �� �� ʸ ]>�.E  5�.�i aaOe � ), I�N> 2Xa .��. M��[z�> i��AZ E�F�,.4 �6��i(O 2), ���:`  $.d�_�:�"Z �Q� � $J\ � %�b���:�� ,>u ��:k>� �� \�J� �ǩ��51� .-�Y  ��1&{"�� ��^'V�+�P.�1,.�N�ѱ6+:�..��.|�.+-6Wj�.F%h��.�� &ji�A��[ ��A�}�� 2��hie�" � b-�F�.E2i�.j.'-�l �N�=��ld�:_1&�/��_}!~� cj 2�&.^�):A! � ^� ���� +�R� +*� &��� R� TsF� �Q� V� WF!2~B� ��.N 6� ] �"� �whQ&�N9�eB.?Y  h(9�% �]jE�,6+��*�e��!A��F� 2� ��6"W =O.~ � g� q@ �PrkMQ>*=2e�Qb6�3, $= Y,h) n&� &;4) ,h)=28!.{!�P+-2`�M!M�j 1=k_E�%=t 2=k_�&�Pbmllem"/"R*&"�$��!CZKF�KF[}B�ula�� h�k3)n �X&݊��R[�r1+n_3�@�!f�2�\^i�U� *�&�-�$mP*)=ppf};� {n_2u }$ .6 !V"�"1R�G"K% 2�g \[��@n GMf -6 2�n�2+A�},h�h(mid [e_i,e_�v, �7,�J.2jA h^{-�4epsilon}e_ih^{.=ee�+�|B T�a, .�Kn &\1}e_{� +i}hK BJ8_V6�:r% K FC2 MV>�A]�$� �1�*�� be��/G!��+k��Ho & e_i!4A�fso1g)=�0!CI�Iz���i�M�qnz B2�% Part (E�  nLQ�|'�rivialxU�return� !�V�M�) ]".YO��`*=fRJč!�[N)0�DZ{P�bv�0 e��'P�n�yN���ȉ��(=w&�R�*1%N2yf�8Z�8, $*�` . Byi1K�f�eq!��s MXly��yV& %�X?iB�*2a!.!� $T=k(R,G/5��$A' [-A�?s tV%zR n $T� NNc!�$h)Ɖ�ZM �&�9(wѾn��it!�A-sam]f)H D\2�  �/T"q t-&":+�xL�5B�}�P=u�C��Ms����&"�Wtalr:22272Y-�L>�oQ��#h^2.�0-�W*A�*#/6v*!F$M1�$l&��P&�� �5�,'�i�)"��A"s .�* &� � _$ non-ne��v��*���*� . �&� �MlaSK2�GKZ}.A&e2U� $K� �:m,3 2L�VJ�Q3�~to 1 $$ !�F+�:pk �c$}�� bel{'} e��,*nGʐ-hg"!h"� G=(�i*� f:s=)�  $g"Yinclu�!�roc�y@ icc���c5+c1\�*.Q�N�on.G ��.A :V 1�8xv8FyM>6&� >����>O�121Nrc2"�c�b2�;g$956z447, 4f49Zc0&�b�b).h95 4�h $} %j9320 �bQ Oe!�\*�bbKU�"� �@ ��bew�&��}��b�nk} n� � +z�fuq~Mk=� �y�� .F�?iJ)6_*:&S ����/ �-��Nw>7 zLE��.�6H)�Q�z@ � �?� -hbKineq} Y'+- n+1B7.�+2�B nk})ᾍlR)�jn_2�*��$�n��bF��+n <��BP5Fv$rl} G(2)=<.�{4� �O2^2x_1d�2}_2=x_4� x_3=�O"x_4'2 {-2} \\ &�O ,x_1j x_4x�\, W| \,.^u4>[&� �[�N� �;� t^2-%z?� R5of"� *�;�,k�� A��"N -1Ra{ 2#]5�V��a�e*�\^a jhZ�� B\]c� 3V�(2)^{"�k} i�-k�6c{C�e��� 5=s}A�t*g7�w�5be.�in ! �"D� K,&�s"a��he^->a#�� � $ ��*��.u�x* 1}��_�)=&oe^�=���M�X�ԻE�ex}2�cyB"4.�y $��lSRS,a�x_3e�i�yxa��I]�a�33`a�x$$f�n SaMtwo2pg�6n�d*�$��%�2fgV nzE2>l��/*� . :r1�� ��6R & �F2�g8S{@/a��Q�FTod��k.��$N$")�� Reideme�`Lr -- Schreier method  3��"7�it&d*�9s�K mf�9AM-K-S}:J2.3).Gfe.–so)�a�&�""�tn�ulda�cW�nat  l'���szof��  co %�& ��i��e[ G=�u ����1j� }w6���$ll 7afial sub8�ax567��s�4� s (in our�1��.�z��X��,��.���#s5o�""����- i�*jna�).��2+N��!�8y%:-0=s_i\cdot x_j "< {s_ix_jv)/��&c  %f�U�6��9��P2�4- %�x_j�n>�$dB��abA($ιs_irs��I5PE \} ,$6�zrel�s|>�writtAsE, 5�Kx5?X $ae�)SR Ծ1�%�s6� �s�Gqu��M gen}�%k,j 1^kx_j�f�V}s�9@> j=2,� $k5p= Ma>��S.mhI;�=6(a_�)= +�/�� 1]NX.,� �x s ri��o,s bZq2- 3} n-1,2}r��)>��)�"4�>�:�ҟ3F�3}!,2 3iGb�&�Q!�.l�u`����?� "\1|sw!= NJ���j7:n.Yy%Kž*X�OA��k)a��6 ���EpN�wV����P"`� K�2�)qE���, m �?: �9���;�}5>b�eqJ]Sl}*�%�3��6q�M�\ 2#!{kj13}+*�F,2|LI�  v Fq��3�%���*�sB �+:�!�)=6� ED1�Q >�.2�:��y!d��B�Y��#0,�.�;!)1w^�82,3}=-3K+6�F�W�A���-&B?Az2Ai�a*�w !�1]|A�matrix�h=\G�(Q�)�({rl} 0 & -1���2 / \W ) .�eOn  easily &���h2��e �2� 2}k�� �� .z�x�� �� [�(x� 2}�1 ��x_3)]��.� .�A�� .�[�� �� �� &nA΂�kM)0k��0 �0 :0 A�66 ox ��#2"Z! WlE�^�� р>�*: : !a0v> �? 2? �:I ��3&N ��+�> N ��e� o�.u �� 4=1� z.��:� ^� �S5���2���W��3:} "� =�} �} ���� � � B� cN~  = :6 "| 2�z +6EaQA2}-6kE�6@ =0w�nd�� zr: � �� �� �� 4v� 6w5V V a:� a�� F� � 3� 2�� !��56�VJ� �/2>PV�u8"Xa_ V�� .� �!��K�� c� � "� R�� R -��� 2� � �  e�$=� >� *u ���fx\X9��\by�"��command{ }4�"��i�3em{\h��fic�} \fi"Z t:m� {McD-Sa-2w�e�ef\entry�� #3#4\par{h� [#1]1� { Dsc{#2 }}{\sl{#3}} 0\v��,2pt} %{ref}{��}{title�OP�noFk�)b�� % � my@ {Greuel G.-M., �� ��:}��On &k�"ſ8�jl�ve0�.} ArXivA84h. SG/0409027,�m�� Izv.���>�Ku3}{.�\,S�N���� "÷��.}l( {\bf 42:1}X�4), 67--2��9)��b�c�ic ��C�l)R|5|5)?�7-206l�F6|=,MN�����!� full twis�r doubl��G(-gng6�,)$68:1} (200!0125-158. %123 A�F�.O�a O.V5��f��6 �K%��N�fNV p��d�YV�9%o 2005�F Kuz�zmin Yu6�a�!1 consc��3��X s.} Bt 59:4I_!�765-78.��Y` L}{Lange =����4ddison-Wesley ��,Company, 196.� ( { Magnus Weء[8s A., Solitar D1� CowIor2��= ory:��en$�Oof��XT�� Gene5�� d R�},��ers�x ce p-�@rs, New York - LoF�- Sydneya6e{>^a"do�� �\�,[a4paper,two Q]{(�6��am��amsScd2�\�h�u rene�.v�U/i�2�temiv*.(str}{^\t~���q$res}[1]{\!�_�:" card#>j\! #1 .>*pro}[2]{#1, #"�,:Wqu U{:% norm'@\| #1 \|} \def\l�olra{\Longleftrightarrow} \def\loFra{{\,\L28\,} ; RS W,C{{\mathbb C0NN0spos{{\N_{>0}ato{\ lwefs)^{d+1.PXPQQRRZZR �R_{\geq � ��P2ZlemmaVL2# conjectur.�C \long�πsymbolfootnote[#1]#2{\begingroup%��the$ {\fn 6{}}\ B{#2}\endAn0title{Volume ���lattice points of reflexive simplices:�Xauthor{\vspace*{-1ex}\sc \normalsize{Benjamin Nill} \\[2ex] \small \em Research Group La �hPolytopes, FU Berlin\\[-.5eA@HArnimallee 3, 14195 /$, Germany yF:0e-mail: nill@ .fu-bj.de4 �b!y {documentdate{ make%I 95ex 6habstract} Using new number-I�ptic bounds on the denominator%�unit fE ions summJlup to one, we show that in �0dimension $d 8 4$` re illy= $d$-+al>�ex havpmax!n vE24. Moreover, oMthese>?A3D can admit an edge �has5Y)Ax:�,possible forC of a>o�X$\Q$-factorial Gorenste!o�8Fano varieties �Picard5#E�e.g.,aed pro��>�( =baulari[. ��}0 \�> *{Introdu�L } \label{. o} To a� thi!�0ticle as acceM8asYDtto readers from different back�nds, aRummarize%� results 6a��( view�ex -�y, )�aic�jM�yZA�ively.���skip � bf�(Y��V eteR$:} Given\��� 0]{{�'8Mathematics Sub!�( Classifica�Ux (2000)}: Primary 14M25; SecondD1D75, 11H06, 52A43B20C07.}A�>_> $P$IE�4a!#in��itsu6X, Hensley \cite{Hen83}��a���!���%!-aof6^�O�isi.(ed above by�funEd depend�� �� . In �LZ91}n � Pik0symptoaz,lly better }�s w��ob�qed. Howe�Din lower���y��pA~Lmably still very farI�be�� , cf. �Kas06.� Rez06}. Nt$theless, ��nyz �23�2exists�}xplicit��di� ��is2T�� !��9alues. Ta�a�Vex, h!c��0d $S_{Q'_d}$,@4at was describ!�la�y mor{Dn twenty years ago!L)�ZPW82}:Ty(�;t�� ion)E6m� hullA;�origin�mQ�a�D$y_0 e_0$, \ldots,{d-2} e $, $2(y 1}-1) 1w� $e_0?61}�albas!-nd $(y0y_1, y_23 |() = (2,3,7,a� %� so--[SylvesA�sequenc���0).8Bat94}, Batyreva��wed�hpo��, whichE�1af, :!:-Iof0in>�$whose dual2M^*$i�>n . F��i)��H��yview,N�Z���B]:�V�, and,��cA�A�lI�in}^f��$nearly hal� bill� 0isomorphism c��es-�KS00}eey R be se�@s a good testing ��. e% !��ura�< Recently, Haas�=$Melnikov n��ed�IHM04}i�y�aN actu��V� Now,F!����jpaper�cpr�}��2"��� �(K {!_U��&� "� Q��� (Thm. A)����sIYanNK nMxw0(Cor. \ref{ptt})2. ["� tE+a��ɘ� n{anL V q� "� �s��=F)B����l0first observe1J!i� I� !�(leq 4$. FinAI g a šNbp�ge�!�)�孅 Re%�C1�: anaK periN $inequality!1TBlaschke-Santal\'o typa JnZ� A� � ��0 � T:} The Borisov-Alexeev}� state��at^2� Nv H $\epsilon$-log ter&l�t&G !�m aIGed famia�in �cq !fiK �:$ & � �&�$of importa��in birE al�,%AKe�n'!�)#c�mU?BB93}" ��21 a�knowni�6�M$s. For ins�, i4�d�d$(d+1)^d����& a non� .�y� PF� achiea*��e \P^d$1A= d m'̭^wa03}, h �is wrgt out�assump�!��ity)higher6�Af1� does�� hold+�%,�M �Bat82}&� [al9�(b03} Debarrr� Հapproxik on�-K_X)^ �d! d^{� d}$% aB��M.} y $X> 6�$V� 2$. �t)\Pro05 eff�� r4 (namely $72$)%� ��n�&>*��threefol(A��tAN&i ',-Iskovskikh-Y�. Fng5al " A-�"�� we mde/ in !� A' �<}8�2 �  - 1)^�jR%$1�$Ac (neH arilxR).i��**!�of���4$, unde�� addfal]�s� Dis>�a:one. &�we���B�r�A� . C$� orus-inva��teg!�$curves $C$O such�ɓB')e: both!��� AP co�tAtcha�eaA>��!3eͩ. TU|b�: �$correspond� 8]�R�via ѥ �.O xo-I e bm � ough� udie.�  natu!!��j�N_"s A� strut0of mirror-sym��$Calabi-Yau]Z as"� 6�(hypersurfac?!Xassocihz":494}. Stimulata�fu5r�ea�0we would like!Np� � {follow:qu� (on: While q�de��e���}2CѢ6�.�bqi)���p66��f w�i�3 e mibP J+F�ڌehave? C%Oit� � !$ ?VEle��) RIt�well-��at5�sA{ cern!�!gs �&&� � closa�re�toyQof �,d dioph!�nee��s. Here� cruvqj^ nvA,g-� 0e� �ofAii3ut)s A$reciprocal1.- �$/6)$�$$1/2 + 1/3$6 = 1$. W��ll!'se�J �I![� ud[ �!\Fv play7�role,� exejfiy a�ousasul" Curtis Cur2�gnproof!"�9��aseZ �" %Pn>� ��� k� T|�"� (by a methodu ~A uo by Izboldd4d Kurliandchik��� IK95�m\J�OrganizI@AA�� �o +�! �� way:�� _��start�0 sc &�I��Bc1e!4s. A,B,� QF.pf P� E .�for�ronR',B',C�[���rQ�AQus�-+:( betw�� b���' system ��� v�B�9h�i�� �th5 then�BA��_S�ym, i.e.> v!�fiftB e��%̉7-�9�)�%y�U� "�\ last�- �6e�!!sIZG�:} OnU �P�� noŗl8�E0uo# "�is � �g e�ve. �)�)� �.M i fact2] u��fre�e�E�� !�i���of �%/Q\&" !� g} {�f� "@FulAAl�levant�per��.�b�ir>" to *5 �:� �-�m��A!� Nil05}� �3#Iy-{,H2�} �Thrj �p4le-"� h�3L N,M$>� q�E��(q,�� paira�,$\pro{\cdot} \ \,:\, M \times N \to \Z�� e $\NR :=o(_\Z \R$%�$\MM 6. A �>�} (in8$)A�a5� v!�� !�?�<M$wo� $P_1 �P_2Qregar)as �i�c%��unimod:ly� ival ! , if� �A�tEsm induc!ean aff bi��౏a  hull%�>�omaps e$i67� aV : ontouj&2$,�o�$i�0�i \dim(P_1_ 2)!���i� se�X writ�_1 ',g !a.FHif $P \subseteq \MR�94q� ?�+ (P)$"+e (c#ized))�� } �$�$$d!$ E�%\ euclidean / .i Hecta����)�MS.g"i�,N1!�&~Non: \bL#&�%{�(qF.}^7�jc�!Az���.`qW�-1� $pA�lso=!]A�X6:i�A�d as $I�\{x \��NR�X�qy}{x}��<-1 \,\forall\, y/P\}.$$ }!=5 ce,~%�F:�ag9":�6 we ne�n e>R *)���or�o!c� some"Cn&�j� *� recurs���M0[A000058]{Slo� airwis��p� n��s �:= a� $y_n 1 + ���s y_{nv($n)�1$�}5�F� �� It satisfE _=O ^2 - P �xh s�l ��1 = 3��y_2 = 7 3 = 4 4 = 1807�~W�$E e $t ��- 1\�Er"52$. \l;#s}R\�&� 1Jwentwo5�f^ie%�pa�$eakf�m�itemiz�. [] - ( $d+1$-tupl��F� $Q_d!�(\'{t_d}{y_�, 2,{d-1}}, 1)$$ V�2� �Klength�f.��'2�2 t �R�2; �Z�en�&d]�z�end=m)� modiAV��n1�`&� �$��5% j�� Q� 2 +1$ )�$(q� 1� q_d)tpz+vF�skp $q_da$. _\�&{Q}Aq_0 +q�+Wa4If $k_i!- /q_i�6iny $i = *�! d-1$��y \[S_Q Yonv(k" - u&�!k!�1}�! -u),\] uAe6�"�pn/"$\Z$-6�-��#V�:%X!�B p'�Q_d��$A�$)�.UY $S_QV �S�Mco�3�=�|�Ghur6mɰ�YT��.�DenumeratBF�(1,1,1)J#�unique��2g:�ex 2ekst/ $9�$) iv� .&�&��q3v"s $10A}���3� �� Q'_3})9UoN+reen�  4� v� ��"�"��39�eZm �T� ��%-]>� �], ��^2���.��� theA�9] � vastly im�� ",.$-%>-5*/(Y�*G %�F�(�!����- \�(1(or 0(&�)F�$&9 �v IBli14}�~getζ"yU�0(Blichfeldt]��P>� be��6l Y�_O#e���"�5H d��vo� �+ ~ �us� a ))��b[)"+( da�o-%�'� seH"i#A) a gaA/bridge9�#�2})J� B"�b� � ��-6�!Хqmr3$: \[�,1}{3 (d-2)!}R^2 < J9`}== O(c^{2�<�hw�n $c \�( 1.26408$ (!'�2�double})"2 �$� =#1�datA1�#e_v&�:�)(checked by%Xu�(�&if�, of Kreuze�"d Skark ' 4,KS�!8aZ1� ]�c��6�:��J�]r�0sol� &40>>K�D0� � Our�ond.K��anoa�1_�dir!on. It���&��!4$���5a���;yq��B*} �bbo'n�&A5":!!m� �]� l at�-��AP9�u theB:z� �e�th�*� (qs\ e�2�)�an�BJ�&"�y� centrede7act�� 0 bodi�cf.8[p.165]{Lut93})BuC*��P"� 6�B��� \[K%�@���� \, ^*) t^2_d� �5s�)��if ,sum"�oB$ ?s $x-A >Om P Q��cI%�.�� /2c� � )2�F�mo�!�6��,d+t�&q�$N$50)9N �^*D � P2�C:�!�2�W�!:6� wD0be&��.�(�J��*�"�3A�}his!��w�L�e>�BO:*B or $Q��|C$X.7t�1$\P(Q�.a&�!$J�4��W [p.35]L)I� 8s ,4\P(1,��'�1dC2{/ DJ|�$P(Q�A� [` ���:y y��-DefU "�, Vj�!B!�� &�&divisE)  O; C��2A�is� �Ksta*At�$Dref��} belowEQ&� �2:� B �ulJ s��XZ���6^�).^m Md=Uthe�-\KX)^2��9F�e�Xm�\P�  M�6M3 M72�N"U$c gAS(3) = \P(6,4{)�GxI��'6}��*U ��I�� V� B Arem%� SiAB~sE�Y�1 ��$��r6 motiv\-eM�_ �í�. 1�*H ��D U.Er);+&�:$��Z�V� Un#s�tg*!����)ifA't�y*� ;r�1� 'n�"$Prokhorov �=+>�Re����L{\e�2� D�6OM�e�+�E��2p Weil��s m� o li>3���c�-sal�N&@ on6Iconja�)fan�&us4  %[p. 63�.�)i/6g�!�6P2+.�)�� �D�^if�n��"�. Ga�aR!3B�5 �i(4.1�-�)H �A���2? ]�)�]�y�n. i)K!v:O$�C$ q NU span4 � f�)F�&{ � �"x,1�6�iy6|o�<o]2tly ?� .� +!�� ��b� �%��>1w:�" /B+!$P$.(.c !Z U�^o ��6UN-�"�ca af� ((5 ��� �}$ Z��X�r� (�%>� E n��<]�B�e�&  � yi]�9&� az�( que)J� s.� . \rdeffy�Fend �o� �'�)A#�ist�6�&� %}�a�)^"- AwR/2� e�1�A'��s d�ly� !pAH&\� 6�111��:" qu(} �|� &# volf��02��O� F� -B�+ed)A�:� e�@|�/>�/�/��� rast�8 Mori[ory usus a��ra(ter/;n &- z,*j%�02.1]{Lat96}) &Y �Hh�� n� cC >5*%N$X��� .Cz "� � =!��/Fes>m d_ i6.M.6o�j9o?2� Y Q�BO8a��$X$pbef�1,�fan_5$N$eTa��W�sH� � zB!jisK, wall}�4;a�.-2)6j����g.6$�4�obvious�G22�1�g�![E$eD�N&"5@�*%XaZ��e�.Cor. 3.6U�JM6=[�a�M� ">�sz#H���sJ*� �X�"/Ź�y� ��B� ��uE>a��ݖJ U�YF�anp $N$)b�($A&,?$ $XV��vt� �;j}Mr}$"� =+"�!m��L�[��r�4 N_�6 \, {X^*}"]8&c6�� .X!�2�if1�a quoti�n�i���e >#ian� �: � l.�7Bl & �� A)69F>�5�� Jk�]C2M �e%q-K>Tb�����u� theC6�E@ �-c�-&nI�e-�0&%N1ult��&&a��, m�"�'be tru�(r arbitrary.�B�ie>�=[C\a Q .+D�& (use (&2 )I� �!c��@nex"6/,T'a�E& �*�:d�k= _08rel})I�L�M  A I �#}�'xt!� X4�H5extend.�IG&� [5.4,5.5]J7Conrad�6%�H02B2*�-EFRer%�>99xA5��!N�)E,e"w>�. W� �X\:T$AGAsew{\em r �� $\F�+��.1�t/=$F w' 5we �\eta_ NR"R&?!inner �+�$F�+�.B}{F} = �$usF  uV(a� .M$�v(V:J,�$�M�Fa�$V:��Z� MJ�'QP%v.�%v) \6�re�%*�%\det(v_j-+j=.�%,�$j \not=i)}�(>�%�q f�(y $Q_Pb%Ns&Pll�h2�$�02NUofI6total $� � Q_Pz�&P� &o-o� -�E�f�M{M� inde�(subv��M$"#�CEjQ� $>�!-We.� �a �: 1&�8#/)}E��2�)"�' u��s;��2[�,n�05t�7��8permut�7Ae �V�&!&*q-��$Q!�Q$a3��61(�5�-4!�%.�� $\lambda_5(gcd+:�|]�Kreduced �F&�9.^$ u=��} $Q/�$.Nj��f0 m $ �\%O$slash\{i\}[p,F�."�% .)�( ����exe �b�M[�" 2.4]�f \[Ʌj-Xi���$N_{> 0}.\]6< � r (Q_P)__HKq'.�q'_n)%�!ӭ�-�6�  .y���A�%u0 \sum_{i=0}^dU i v_%4"4 ��)8:���S�&� � .� 4.4-71�Ps% 5.4��F }[��,��]� =Ez:�A�NSM"gs�F-,��-��3Q:f� $Q_{P_Q��A��� 2a�2_ ^�$Pis��k�:f� �2&Q ,,�5!O� Y� s)ZP matrix $H�H�Gtemf m c@"u�P$�+� 9 � H މ51 �+ y"le� oric5>(>�! AW.� a-�NN �%a�L� aR U�� I�M�}|Lw6a)�j u� RsME ness.�3.7,3.8Q�N�� ]AGi>qB29~6.�%  qÕ��"lBs ��%�a�,!P� D �?�~���2�?O1,H N� f0$Q$ $�NJ�s)��n.�A_!� to QAy�� � a:�mai Y9�.06T��;ow�i@JSEa�A��; �M.(��Wiz O[Q5�DQ)U%��"]�?(2](݇{�6� �0)B ����2� Ce \[m���2 f-1}}{�0k4 q_d}ɗQ_^f��}1LqdeY�#Fo*G::�a straforward W+&�&�.�A|3�$� ,array}{ll} &� p��}(n_1�) &�6&�& �\\A!S&\2&&\\ -1.< (n_iV[-1M&:HV>M�.�&Zd -1)I��\\ = & � /n_d -��m_{j=1��7d�� 1, i| jn_i�)1$�]'{de!� mel*m1�D�Nz��change�a��:}0XJ 9�A�+3�\[�>^*�>m Q_PAcMb� �2=��1&}� 0 � , $t Q��H� {>M \} �&3d�$.� F ��v.� :t36� Y%{a��|not �|!W $v_i�Fix� >3�� ��J�'Z�ii�{.�\��li>A>4u)G����o= coord�]�T�j$ ($6�!cjEUi$)A rows,k $Bl�m{F_j}�tc;2�F�#!Gm� �}`7q_j��i} v_jN+[#t.�{F_i}}{v$= zF= Xt-q_i Z �8� With@�rOA���($i=0$. Appl� !�pre<�5A_0 B�W � $��( Eإ�{1�)���� d} (� ؍%5%t 1vF9�0}; �^�8{q[>��Gq_��\� �B_�2�})�$ r^_= �� e�0ZG�L}R�5� ":�D�P'tIsi;<h&�$\ -6 G9!H"!I&� �s turn Atoaaen� (]�<of>��J�I4much-s�LO�@BEgypt�!�� !F�6q�S�a}) �"�<"a^..DgGuy81.� ���u�iF1;A:*&��-X�i0�����l�*O.4 . EL6i(i$0 �&� *;Au�=šJ�9$(9�k�Y&�> �6KQ.�} $t'ślcmJQ($i�iz1/:2I�5]�=�bz2+essenPklyi!Gf:6)� �csB� to�'Z� (no�%he�����;�  mapp��Rq; to $N=�gJL=d})>R8Xk.2)�.X '}{kNYZ�&aJD*Z%M�.�I6"s-�6��.r2QA=*ds !^��| )�_ 5�!Co� (�e! $�s35�9�+ JsU"S:�Jof"{s*� !�ge 2.����&ss��:�� ^&ty>2Ys,!=dD;;�J%/�Q > 4N��^�:�� S% 1o{�ce�Q�xba�e�""�R)exz&�e}+$�%�9&,AY5��(P_Q)^*$����'��E>:�=)kl5=& ap!9Au=�[M� . HLX�$!��inHG"�of�8*W _QY��+ �n�u��e�a u�_�9�} (P lef��,_er}%2�2�ZjI)IIT�%@D�)eyT�6?�N�&��W�9P��v(e.�?, -�e_ @\ - q_� %�9C@Jg M �T@�T@T@oi Hm^� �r?2��np!n�?M�*�P�&5.Jf��I�#2W%�B�#6Y ���?a^R$�b 3P 05nT,re?sf.�lw b*�I6mF��+Nq%=�6�;A�(9eɤ*�:*�� �{("� �,&q I5$� m_5}{}�!K .CM�k�EV� ^2tQ{(%W)^*2�y�eMe} ia<e ��hom"Hc� �L"xL s \[`$ \stackrel�{\to}Ht� N� ,�e�g�7O}&;)a�u)a�z���)p5X+&zBR�z &4$ \;\mid\; -��u�X3!=�1/l�{\;���Dz,\qua 4�a3 QN359�\�8T&_C,S_{E/0��1)\mm+�*f�9� YA���. �re$2p| Ŧ}&�>as ]/\ $cvB (orR��B; P/1?".Zs�?�,>$�`�U<. 2:EA:��u���Nm,BLa1. 3�cdaS � }� �0�'R~q����(7%1.f�iz�14. �3. 5�s6�N&�Ca 6E+bFth�`�ex� �4 absolute valu}+Jy�!�& Micep/=ntD� e�6�O� Y�= y~ EG. P \,V)��NowER2)D3&(A�Q�� k/pR!��]� w!�h&6B�,5.qB4w *�Zng�O&VSN!j.2s 3,-2%RtR&X�uiJh�4,4f&Q' �2D> �?,��K�.%�^.�r/%E�-M}3�, .+=.D( twoɘs}�9q��4�-�u�� u`,� -}ti�ZIK� 5aa"goMZ��>� 7 6*}� cm�1N�+6@f�@X'cJR�@6� � t_d^N&@��K�H�e� 1�[J�:e�JgF6z_ F F�'d+1&q l�Xi^ A3$I~jleq�� �k�F� C (�j�}@0& d2ѩ%C �D&� FD� F��`!Wr�LE (2,6�� F��_ Ub F le�rNe most*� �i~zr�Aabout:�s2C.�c:I]�c��[ /�Nau� a_m�8"zW�0c�ipos5�) 1}^mz1}{a_i}<��-�-�.0}^{m�S)�1�UijE1}{t_m^�\{>�\?\"VY�y_fM!ter�mB�����N�Qge.n� \maxF%Ist�Sa�6Z&��&�4CCQo<�$N� Whil��� U -�� qu )Nl�LTjA¹n��MF\�2La� 1]:e�?a �er k,�it ��s[e" M[��!Fo inclu _b �q� �at��'^e�i z���#[Izhbo f, .fM�x.�x_nE� real�Es.^,.�Ex_2 ��cmx_�Z%K -*W% <x_kIx_{k+1}:5 $k=Y�n-�m+[�}^[},\; Kx&� b/^2i=g>%6�II�� >%�& Lxs$q� y_{i�' ��">�q~ru�m~)� Any>;fulfi�` (aft-lo0] ing)Ae��q�A�N:  =tb$F�Ea>s� n�Wx%5!:=��{d.$aq%.-1�%�e $0 ��Q.%_ middl�Ein5�� .6� 2). SgS�� 2.ZgIimmedo��eV�q � *^P�+rithm� �!�fic mea{#o*l2�S!\2�+�*��!D�=�*�H�)�y�=a!�li\#r$�2L%�� ���J!�$1��r 2� (r+1)^r \�${n-r-1}^{rA�&� n-2� >� ]r=1eK (n,r)=(4,d�$�l:"�%} �sof\ i�� n $n$. By"�ks heck!�$n=4,5c'xve�_Os6%m �!fY��>(rivial, so �Vri.�  By�hyp"To~��$(n-1,r�wZr^{!56B-k� n-3�YaM*�$�z<2\�_!�{r}!�r�4L �" < e$xJnough�q{$t!�Fc \, e �&A�*F5H1.8Ib^�^A�Q�6�5�as�j&>e !e� A$�Gby �e �WOO����e2�3} 2_�3@!� <q^�Q����A�en*� �E�on�$ bezor�CA�& "�c[H\� 0(4.17)]{GKP89.'m VF� gPtJ�X47353��$ (.XVardi}� ant,%u |A076393Kd) _�A� !��<N$ \[Yc=�"$ft\lfloor \Yn��' ��1}{2} \��\r(.\]�%4�^end��!dL� %�F��!I idea"*%�!c/�a�� E�99�; F`ich .� e�&at�O3.Z�&� -�5>~x](>� r=inJ��N2 6 ��9]I�a� B�{�ei�5}�9*� ]%��; fex_`ej6!MoI(1/2���s�Ee�Y�"�$!��ŐQ mein� -U61x-�splsi�jtPb s.\\&*�Part Ir)�A$�*�%#-<ndeeHWx$.Y A8�EvFi"�$B��&aE$�hA$"�o8 $1 > 5� n > �,u.A�  act,�&^7sfhYE$F7$�I. Becal�/�-�F�(�}EfA+QtV)&0A 0n �� [h�:qY]S^2� .� EtWeY"m��x�1/#>oSo")!nn��BfClaim:}�u;,s"�Q�eqn�2*} !gM2 >� � n,\\&�*VK \C�{E)} (2v 2�%P�.!�c � B�8nv��oLA�$u � Uf��AkWePc�jb.�� lF�C w 22*1 �=E�! :%l��x_{l+1�c͇!R�,� :%l-� �Jdi��uis��� *.�� $x_l��6�{lQfl���+Iu &�Yia��xoxeed"��eAFeG&�;mpl��$-C�lu find�\delta�O s.�.$x'u��+$x' �:�� �+ 9$, l l�5QIDL_j j-�j]\{.�\}."?l-1,l� � G#p�1�� ћ2}{A5!� x_l}�XU}�� *)�^2) !_r VAԡ�tra�t6�) �K�iI4�-l+m 0q��Ŵ:�GnE�A{weƻ5�:�8Dx_A�)�,i%�M�A� be dATsu # rvng ��& A��j < i2�=2��6 x_{j!daW {j+2I )n� $x.0.l0�g.�j-1}) 6IR\,X 2 na,S'I8e� �JT� ���E[Uf�1�{��.} \med��.K!8A~�|.�� -MA�� ,"� R( frac��'n$��� same{A����f2.�2$� �{�(Z�=�� ��k��M!/2K$�t_{k-1}a�fG.�a�I&-�y52}��Q� O� thusAT^_ r:��x:NZmBQ�2}QI�:! �.!���z�1w"� @�>r7� �n;]#fF� N�y�/�an$J� I:^7 $A'R� _&� wɴR^�B� &3& : $w�nwNow��")5�>�H*� &!��g!M�w�wF� 9͆A�.��h � �!be fixTV6i- �U��M%5 �2 Qk !��j.+��vJ�:/ PA5�*� R- $w� /2,1/6,1/�#ory.�01/x , 1/ m)$;�'`�2ar,R�}� :�!&�a(z= w_s4��=)ǽ�-�G-�_�_.�W&�r_n-s�1reB %� � +�:&�ݛ s=�q�U$r=r� 01�� �+� � H(n-2) z + 2 z = n ze�o $1/��8Z�em`)-!'� 2}{ni��}�36/�>>/���i� (n-3-!1)%h��) �ԅ� z�Qw e)>-�=$z� 1}{n!O��  hg k� N�1�1)!� �$z� )��`p b�= (1-, z)!�!��)�"^�Ts@�t�h �� rval $&�m �*�n}[|��a�!RJ�(��LEanalyȇl��| m20F�5.) er�� 2�Q|��%k6��{( �)})!TM�,C-*o�*�vBE:e��,$�it�[13n=r=U�r)$ VW��J��e�1}{6}, 3}d$&},q^ ��eqcI�n-3�q�- �ilap�aso�Ba�2� " � B _��$E���F} w_{sa�2%{s-3}{| f�:��saJ sBec 2� tb� 2<(n-s+2$�@5R;- S�""=1j((r+2)� ���`Y�)1���>�1*� 6@"�� ���� Aw65 " �^2wB+F*�A1}.41 �AR*_Z f(z)�3FYY� sU ���r�9.�� )LA���k���> 0$ s�ClțnotVu incr�#ngNN to��1��tA�F8de8� ]\\6�~� )vmin(f9 �% 1}}),6]J)c(�,B)W2-�^rBm�k."2)  &2&2}�<o �wo�r�q V�X=�/�+�a6�Mn�I�-/�u 2}{9�n��� D>� %��� �� 3} ( +1)&�$)2n� :r��Jf��k#d i6 � "�02I�!%�$�!:�� �� �ع�%� i*�1�-"bF:.�RI�~f%�z+if[y�~Ip� �M��VU�e�� s "t[�J�d 3=�I-A r+2}�a<�^ 2) e < 3^� �r"� 9b)�R�x�-0:R�J3 �baAt:�M &@ � >�F�bf��R� e^��ofS� .� I &� A�$xA�2�x��T�5� �R�4 $@�h$\)� ��. wj>�Q 6�E>��_4 g�!�bl��yA'a�o) nIo  \N.�w'�� �T.�� � ^� ] :n( $>�n�� (1jF([)U�o * _(x_2,x_3,x_4^(&��6�;Ai� _?0�moNl�} Combi6 �reB%�&�*wo-)�$�4ge*nq*�y�$>2BP1�WzJC�dje�9Q�� t_d,�"� �% c"i5MC*sMQ�`�Ps.�CspXXt x0)2�v&�9 {*?�v�|�<P&�u��v^�v@��I�*b�%*�<�v (34 S^*�?ZG��5�b� d�� -#1P2��E�d?'N�1*'��:� !��?-�'�.�&�r*�6�3q%i']�Q�q&>U=�G��m((1)" ��R�2 �1)6�66;/.�)We#JSat)^�^= \"J?- N�) 1,2)��QI�=��?.~AM� �!� U�2+a���$Nk,Tf�,6�:�* ��p1"P&v llow�N�5),J��7E���>�>��fa��!awFim Ag*�:88e�Z{Z6�Y%�L:"�:?�j�+5�6Bo3�'!Q�E� ~l� p>���b6�0* Q["#!�dA]�: L: �= �H/�i*�6P@r *5L#Cok2eKm� �F.��p%�� d=* !��e��`?ula $M��=aBj=�s)����a"E} deri{�b�In�'{Hib92"� )%� f �]1-Ba��& 2�M`\ [2.2,oj02[}*c?�,UX&*O6�>��a&�FͪE�Q!lIVBc i,� .�/�T�T)c j( �w�v(g�ϊ�l#�Y.��?�l $\pos(v�,9�i xk j)ς(-K_{I }).Cۅҍ�OE�|q_i,q_j)��I6�}@!T;?y��99@)Sn�R�� \J��a k_i,k_j).&�)fujinѹ� z6�W6�F�Bm���&v�� �"A�����-I�&�>�*�ga�tn�I)�EZM�Ub6�HJ> )Y]�6w��xletb>^a�r���1N�e9�Q[:{N�.�9v_d,v_�%3!"�C�04�& oA��J(��(m��G�Ke����^uwgc=1 �VA�I'd,��3� ���io)� =�MP�?may!n�� $k_d� Y$��c "� � ��ե�<8*t�1/ K�/`=�3i�3��%�# 4�B�  $2E? H%�h�T 7� A�$��c �6n t�� $c =� = 6=�;��>=�X�9�9d���5% ��*!�RK "\q4&5"�2}Z�9n\AI���� � *5By)�m��choos�\VmI!�{V~Ne��J�Nq-��N\� sa+ *2[Zr�D,M�22HMis (dV�wA�\��d$-mG$H�h_{i,j�in N4c`�*,K&�J`&�;H�O!(�\")<E�  p� (e_d EB.�|!padDc �e V�,l:sd߳tM��~B�:Ph� coeffic�X2�<- < h_{j,�[� $i >��"�is&qbg DGd,�E41 =QaB2C-&cu�} (-3-7� M�� &8\i}.<" 8T_\.,a�}Yd-2Ɠmġ�&� $�813 s*�t"�,kh_{1,� # N\\ �� h_{2"k2}�=]'2\\ �$ BuH�sd-u*F2!O`�$-E\N�"��.8�vy_i,y_jA�&�i� �]d�gS&�6�  $ ;$Zd�wEii�:*g#!q.��ET c"vG�"�9%$A-�13h�1% I��\ �&6=m_Q.\]�_�9*�E�_K orF�N)^.�O$H�y� o\b��, F� C� A"�M�Z$ 2*��A�9Z91RRNLa�#!�p�/� a��Kr%�d��2� 2� . Also� $PH5 g�PdJ2s: D *{Acq�l��:s�5 4�:p�thank �thw8adj� Vi�� �L��givre��cj� 05��C. ��0VN!0est, D. Ploogdiscus%�KAA� rman�<helpfu#�verHo)s����z7�ymo���o�$nd G. Zieg�@� sugO����!o������Npݠ . MCC�is work!�G4 1G'� sicMI�Pthebibliography}{XX} j� ib�M82} V.V.1r, Bdedxi�k%n}multid`�t�!<*!�����4it{Mosc. Univ.��. Bull.} !bf{37Ma98a 28-3�N�94>�Ee5qhedra�c>� >�y%�Ca"A�6�չ.k� � it{Ja$gebr. Geom.��,94), 493-535� ���H. &V�, A new� ncip�=%�Z=6�p ]Y�0� �=CA<it{6�. Amer1MSoc�15�1�227-2:�o� A.A.��%<L,#+�)"b�0ath. USSR, Sb�7 �093), 277-283..r�W!'�k , WO�R�[aY&�poq�5 Ucanu�ZptaIcY]10A^200E^15-227.�B� D.R.�D,I&Kellogg'�Q&ƫproblem,Y,.�Monthly}29%�2| 380-382}(Deb03} O. DV�,BnPin K.jun. B\"or\"oczkH�$J. Koll\'a� T. Szamueބ H �.�v"��%T��&#Rsa� lyaiAQ��!�eγ�GSc(s 12, Budap�X 2001, Sp�B$er-Verlag,"��<2003, pp. 93-132.yF:�FA , No&ge�P��M"��e5�ϻ�, YTohoku�. J]5A��$), 551-5646�F� W. Fult������a��6�, Annal�9*s9)31,P�nceton��ers�&Prw�Pr  , NJ, 1992�=, R.L. Graham%�$D.E. Knuth@O. Patashnik, CoE#t��"��: A�nd%� compo�s^ xce, Addison-Wesley, Reading, MA�89..�d< R.K. Guy, Unsol�m�&�ԁ�ory! e: book x�I_sZB intu&o2, Vol.� Fw,New York, NY�1.���"&aI.V. ��,�C�ku;�&�q��� epri^>�,.CO/0406485,A�2b��Dln)d�{�exW�`�Q?DWE�2�Pacific�A�]�1� (198A�183-196 $ T. Hibi, �l�of&{{|.�ٌa�fica��12��9��237-2402��$ J.-M. HwaAe�+V�eR�tӗ� of P2O�� +� rein��gew�� 556}��! 225>}�aIIz�IEL.2�IA�.w�.MS �l. Ser�2���bf{16�199�193-202��uK�8 E. Lutwak, SelK���is}�iø"]Ib w P!hGrube� J(Wills, Hand�!!FC�>x� et�BVolA) rth-H�Ov�Am��dam��9q 151-172y�� B.��,.Qg��o"w =�` B�11��200��83-212�頡] Pikhurko,�����ԼM�>to�ϑρ)k�f%� A#5-22mPr Y.G. Ғ,��d!`��\�cw{ &��^nh�SbF9=77-112���!�(Reznick, Cl���tetra�=R]606227]2��N.J� Sloa�On-*�0 encyclopedia�Zhb�G �W�b�a www.,��.att.com�Vnjas/</.y�J. ZakM[d�� Perl J.Q�On��1%�D�S�z���!�r�>I!�C.T 44-4%0�>*�! docu�} 5U\�T [ame�n]{�c�Guse�_{b�u ,ams��fon�.$ams( }2fancybox66B��!&_�:`� r}{C�!6� }[cor]apo;��*�� ]e}b��ex}6V�commaN�mr}��r�{Tn � �b b�xnes 0�2f  frak>Pc c��.7bkb:5ep}{\h�Q $\square$E\��1� \ti.�Toey=no%�rcooflog��!��{Mukul� (el\\ DepartAga��� cs\\ of��(rgia\\ Athe8 PGA (U.S.A.)\\ patel@AN(.uga.edu\\ ��fday��Q� �,��oldC �a"��\9{i�sa V��" �co� `6�� Kh ms{d��he Li��Ra�1�oeQ*t�1O� (- )Np.���]� \setcou� 8{secnumdepth}{1Ƀtoc 3} %\�of ents JcB{6��T.޸�e9r{G�C��]vv�XA��%�G�aA�f{g}.$�%�e gra�X|�A%at�8{g}$-X5f�I�U�>r{MR)qbb{Z}$- f�2.��j!�a�1brackw�a\!. (Se|(8d0�a�*�$.) Inde�Nm��2he ten��:H�Ҍ�).x�C[ �{R9 �7� �b!*%g =W�� ��s jus��=$ q�${d} $�$]r{Id_{�E}�E2!/�jp�3bJ�. �ce�Trere�v�#@\� involve�'!�1"ϵurE2>!}�82�ba�� %4V� �Jz�J�. O�A��n�.K׃ two �H�Qm&4��>�.*y�w�|n�no���6_����d��-k�%4�rl���$�O�}�<(96�AR�M�o %�)�Yz<L= Ic.$ Th%��an .�x�n)a��X�a�!�1���i�&C,,�e%�� �>iI�aJ���mrϡU,0'�?\�,%�.Hd�g}bf{n�isRs>_7r]-w.} ���Y�3�wh��)A�henomeno�KOa��&ida�f#���V� �aof|4 f�x_: routEverify &b# the !��co.�j"� s�a#I_F�..N��.i� orms(!D{2} A $A��z1�Z�} ���elMVK�lE�F >vec��� K� �=La mr{\+�_{p;( n} }L}��p��a.B (non-a�- ive)զ�Ahb {2ptj;]�!� E� $a\inmp�) bqA�Q&$[a,b]p+q!and&%� at�V 5@ b] = -(-1)^{pq}�(1pt}[b, a]$2  (�-� u�)�5~,c]M[[aW, c] + bZ' c]].`Jacobi IE�ty���;RX{kac,cns�\;tai�n�t��ys�B6" %�\L�r ^{*}� �)!V�q": E�� ;" B�r � n9a  is�e8� �: \[[1�J+: �A!p}}� ���(q} }\a-set1}{\A��Xa�tE� > ^EL@� )"})O6�.�]Bc } ` _�Ma%w)\].�bleB�rB��-�!�As pio!\��r_&�H 2!���-V� real? " A�!� �n�D�v�$t�]. x~�>� �����AToMEb �.��'�� �E� G}$-equivi[)tF���"al bun�`KM�+G���!!C�_f��E�semO�5oH�N!��}� a�Da!�vanish�w73 !1}��bby � \barQ�}i���i�$�6=Yat pull.�7�-n��*3 pi :e�MqyG \eM �-nS�L��"�:sma�Au6��' #��: \alpha� pߍ 6��pi^*{  . \]B0onward�$e3�zes"� thin�each $ M)+ �V\$ S'��!H%�$2�$ l�'MsciYy.:esas��]� I��-�>�a@)}�9�]U0=AErba'k5� ܁�Sk�Sb� covmYa��&<=--�8*7!cl(a  fl�2nS^ �U�a�@)e�S>�coT-�theta$. ��an}.) "�Ahe2Y5m@7o��a &= +i� \[2P = d-[ + [ �, ]�m���� tly,�mm^{21�= [\T�<ƿ\]� |? PTZ:�*�+asse�on��s�3e�|������\�b��'AE����nd horizj4�� qe��џ,�� �W cal��l!�m��0 $ � = dE�%�x.n71 A9^].}� "�o�iF�{i beca%�hb:�!�Q�$ _�DsE�&?�F}M���Ɗ%� $��l "� 1�i�f&�a��A�ula�8at"�w)�Moy�:I9� n�gti)u�Af �i $PA|2n = 0.\]>�M o �&)�� � �q�8/1!�.$ �])L0 n#�W3ŝ�,,� C�! { &{ b�+.��?�9*�8p�:A;f:�1&  N_7"�mapA$:/I�n!0f�\)j��a��j \mb{{f^*:�M *}(N��)2?.#*�}$�>giv����of!���r{f�=�F�Zs]j��9\T)�".�!�Maurer-s�amC;S)2h*a.�G�>�>幖��br%!�MI���� G}$}w �D�� .g �MH66���W coch2�� �?�3(Z�AAB�QW��e���g�o�he�^� B'.0i��H�"8�Se�Lor M"Q :�e���d[��Mor��categ���m0" ��.$>e��2�M,}�n�r{G�b������� b)XQ��xD�n�&II8�wq'�Q��l �%%� pʴ�`2 .\epI�PB�`Uc{ �C*. %�5 :�tF� , bu�w ��J�, s�ec���E;Ff �)��9�,��ofhch� W,�s8� hips"%Fh+J� Now� ��@�nX�0�mac"%s8id computation �Cof the cohomology algerbas. \section{Aids to computation} \subsubs $HodgeN,ory}\label{h} Not\at $\mr{(\Lambda^{*}(M, G}) Xs{d})}$ is an elliptic x lex, so tH$classical .wl can be immediately extended�@it \cite{warner},`ells}. We briefly recountШ main points in our context. Let us assume ��M Ơoriented, with a Riemannian metric, and �:G : semisimpl!�0mpact. Then, �TCartan-Killing form onBf{g B4nondegenerate e�(negative) definite, which allows�to 34 inner producta =�!�=�}$ such) its AV�ous%�one!E4are orthogonal%x!�als{A�)�H$*$-operator: \[*:E2�k.E, \rightarrow�n-2%}\]!1 each!2 r{0\leq kn!>n�Dusual fashion; seeQ2IA. Now1.\[!\E�A� :�2V�k-1.��by $ Qd\alpha = (-1)^{n(p+1)+1}(* % *)( %)$A-is 1:aR!TA(al adjA� of!av($. Finally,%-\A�Hbf{Laplace-BeltramiV<,} $\triangle := �� �+ (\hspace{1pt #,$fgE�lized-�8theorem assertsIP)_ Ker}r\congEH^*.�: )\mapsto[ (]\] where $�k!��])%r $. S9��,��>left hac side<(isomorphism1�kernel!.�1�� aseG,4i� dimensii/$Consequent!�E��%j!�r{H^k.�NQ Us�D�$Bockstein �3f�� r{g'�B !N%s!�2Q~13.� �%d�3igiven byQ� G}}A�>f�^g_�2��[�- A6jB�P���Qand-E�:,�_ �� n2]r{2@-g'�n>0 }$ �(it{is even}�cI�!���FM odd}^�\�x������we obaw��er�diffe*_ �s. � \emph{�l}U��y0E�g�fwe have ��� ax g.bivk}}^{ezmak��aQ>� iLOakiP6ON7. \6? C&�:� } Botye>� �N&� N� �� inue� � � �> l s��$ng. Howeve�  w�+on_i order�r1pt}: IPdefni�Hof�=8functorT � cond �Kble]onl�m� �h olved (inQ �oR �wcoeffic�s). Sinc\ ��ntriviXnonMFf �9U�%8pech to yield� stant Vmor� �Lo)F4. In particulaZ(AZ�B )!2ac�l6�rz ion�@.e. natural trans�s�-�H. As a quick applic� of9,aPn"�in view# �m� b aFT� \ref�1>lfo�can� al: � 0\A�� aa�[G,G]}::G>/ G}/[ , ]>;0\] A�%�m'�� 6��"� s, on|�be , aideE�ut!rel%\0ships betweenfe�J� , ��e.g.}-�rrespondiF Eu� c2z� � � ore}  �Y� ,n}$-manifold 0#0out boundary,6b [!/k aa��a) pair��6� $\otimes H^F61 � ,\] )�o!Y.�Vd� Hom(Ff, W)� The�is�V a%�a de Rham y�:-alpha"�uniqu��*� represenEAaD�.5F-,� le�bet�q qE]$ in�_F!N� �7]��1�1�by� (�, [ [)\[ � \;<\!)) !x8eta^*\!\!> \] W!e$< , >6� �d abov��#�H� ory.w$ s\neq 0� 2�%�^*])\�� � �, % �;= \| | ^{2}[ 0A  �1is.'�t s, h����subtle5\A��  aLV��C� iC��Y���{con5r!js�  $-modules� us�/kQin��a<tai�knowle�*�I���specific��&GgA� %:x ,Leray-Hirsch>t�!�pKunnethdmula}FEAtiyahF zebr&�2J|M_ {New�aG�U�0� Wa�v$ready look!@t some*' inD�He ndivi!I �*��:�I 6%/su�lgZ. T�osD e ad8r Ewho�k"dbra�n& tA��$bb{Z}$-gra��7.x� %|odd- ���a� dire�um��26$:j�t���vely:u .d = �KQ.� \oplu�f� *.j��3l ��-X unde�bracket&��-.i$rb�ucturee�� c"2 �W!eX($26))��� 1o{%f�� ny two2`!�5�\)� �l|  s_ a�2ofy, inclu�^Fs!"�! �`titM /%� { Noti a���?@(is clearly Q(nilpotent,}E�so$U]UE (a!x�bra). Re�!� gres��s��5�f.As (� gk})!�x $fruitfully�'�%�&�.� u�eiesv "� � eD�3b�uni�al2v Gem� yt.roughly sam�>"L . Hэ:e*h pW6 8:Q�� nov�Aj�!�goo!*d� �AW� ,a (rent choice�_A?� J� �� es P� KF�, alth!0.oh iJ!(zs:�bi . �2 } *it�m�1sirT�termim / t�JEJ_(encodes purS�.on smo�st�~�r{M_�toţ0how `mod out'J Uawrbaic2[com� from-5 �,G}.$ One way^d��)�t�!] ,2)�A �^ �category5s� of���^a<3� 2H�=j�  S}:\;\;M � HM' yobjec��$ ,� �s �%s +Azof�-%�T6'S(�1la��s!aHE�H� i�e��M �GF�Gw;\;!Gh� :v� Fur�morN �eGs, via "l, a�"W50\linebreak Gr�ndieck) !%Q�tA!e V&R2 :$ \[.%K(!�G}).� SG"� i"��xm!ղ �a!$.L� intt"` 1-�R;�*�bE7ϡ�� just]d�!,v4| I2 }$)� a>?1.8. � G�  remarkY2R�& �Zie� An impo�#t�$!N��&2@�!Y���4e�es � muli�Q � =��� } ����braa4ich�8l� ca de se��to it's �  $ ћɑes �rs�� a (possib �).�%8&�rC%5X� ���y fortuit �.� Bl!eAsVbr����!�Tas 9" ��fac!�w first.�Y,2�n�� (topA+)m�(� sheaf!/]Z� ) ha*J� aEl-�!ce&a � ic���!nun% ll� ENAXhighe8'5�set� Re�!)uD]h!m{1(X, Gav^I7 X}$"@ �rincip� �$-bundl�v X6i�",#!� y�v*L#B�ީ�$[X, BG]��He���Go# a lo� �' =�)�. WheAm�*%�, PB Q( -�� Ac^�^2G�B(B%A" ��V =wx wH^2)y.�^2 �Now�^2 �� G �� proc� 0� w���� "r 2=�*�1AC"O �y]�1�E 6��not an - H}$-(,�al�a ɍ�circum� ce abrupt� runi)Rr  m �``B�s" ��E�fl@�z2#"� satis� y���ofm=9�. ZC me3}O>� �F��u21�e� to�8@Nj\>lb%x,�,ors---analog��%�u��e��m�. Nee� s. ��n!�J s2(���9k�� (excep��y5*,ed@)M6�ى�i�)�3hop�f(ng a us� R�-�_m���57F�6� woul}a (��)-�all1�2��once.A;�ehe�9 to b))m�usefu��&�#5�i6(we d'nonb&�( mult*�aur�KA u�, star�Ki&� �5"-%e�g se # 6�al��ha pap�'q",me2}���" �� WL]{� s} W., R. O �0�D�#!���ys�/  lex � �*,}nx�)ndB� docuZ }|�\%R[11pt]{Z!�le}%{smfart}% \usepackage{amssymb}\6�} %.* ptmx2+f} %� �he9, 230mm width 15odd"margin 5$�>top #-18 head [12pt sep 4C|sloppy \flushbottom \parindent1e skip0ex  , _i 2,  v .5:i  textfloatw3mm�%%%*(mands  \new�,0and{\fr}[2]{{bLstyle \frac{#1}{#2} h&.1 be}{��{eqna�,}6Te#A[^!nn}{\no+6=tr}{\AHop{\rm tr}\nolimits:+one}{ -frak 1>�two2!2B!hr�D3>#@et}{\eta_{\script %+0>.prooft em P .\%Bdef\cR�(eck{R7qed{\hf*0 $\square$:�+}{{+0re.�$=}{{=}} % � n�! :$-}{{->$% %2�8CG}[6]{\Bigl[ %:�.,ccc} #1 & #3,5 \\% % #246 %�I Ir]a�.�RWf\{�gg\!.gF6hM�4smallmatrix}% �)�#1\, &23B�[2pt]% 6=2B+4B6 rend2�%%F�2�����v�!�%%e�4{aWR��Hk~\thenum.}\ \addto:?�:�%� �� Dece0 2004 \B tm���(.QA/0412482�,%2!,SPhT- \\ \v *{3m�b�2�@er} {\large\bf On�spJ$,U_q(sl_2)$--&�$R$--E�ces }b[3mm] ��@ Andrei G. Bytsko 2 � klov� � In�eI0 Fontanka 27w $1023 St.~P�sbu� Russia [ {De��TProfessor L.D.~Faddeev� occa�3 +�470th birthday "}1#%1B{1!A5� abst�0}   � -E�dre�&VR soluA�N 6��2EK�)��Q�(/cS})-- ��!6d#9f�A�� sA�* unde�#aQ i�-�RoF�ir�qi,�m st w��tB� $V_s>$param��>by a�--B�: or half--+.mb $ $s$ (refe���as L ��})�M��$(2s{+}1vdi^7al.()�<@*�� dard�%, $|k\ra�?a�Hk=-s\,\ldots,s$, ��<ba�vec� of~ �s�)�E $!�O = k]\lh k'%=\dA�_{kk'��-��E$ de")e���1or on�{s�7�+�H#?id>=�)+valued7�s, $R(\l�D ) : K��}"�"�End}\ VBe,��!io��P erties:a} \ Ereg} �Y(ity: && R(0a.�� [1� :uni} \ta9 �\, R(-��8��N� �ans1} �J\6v : �.ILsum_{j=0}^{2s} r_j!P^{j}� norm�AEY� xg��_F@= 1� e ; $P^jŲ!Qpro$ or o? A� $j$ �ao3Es^{] �$.�[a scalarU . � erty�g%')�9���a}� rr>?�f$.� e�� ce}, S4,E [=� ,�. \xi)š0�G \for� �/xi \in e5/In�to ful��Ag�&A:)�K K i ":G[_ ���-�ans2} A&!VE�!�, �U>#]�)��e�wyi1s ��2CG>K$ ��2t'C'&B h�(�� 2=0�M2��da )+I�%�_#\ �)r�:to � t�)"�( freedoR-reALa�.N$��a rbitrar�al���� ŝrv9mu) - Ntw6muL>-��L�ERjf . \���V belo�@bX s --%nlowerAWd1 � imdp %�N-ten�� � B�3e"W�Cll&�2is an (2���t))�� x} � co. 7YBU vanishesNm!�2�EJ���1C(An advantag� treatA�aYB �"� M�YBE}) a>�q�of �A�DQ�! �,;w17{+%�,.vZL M�+����s BN�!��3 feA.}~6�. Morez ,>�f7�Oresol�.p �/���� I used��3 write dowC2\=YE�)�!Z J[on e*rt s. Aursive�cedure =L+yp-�b�7�/��xt�$�b9�IEqs.~�۩e| I��Ied� rᢱ� �atep� .�renZ�  \I*a8; \gamma�f,=e 0n ��fLMAPb t~$ ;$�3��regx 2>�ev&!�:t<I \ nonzero \ �v�15� 6J�=;��a�9 em} qy ens<3uns !Kan�8< (see Appendix~Aѩ $q=1� re%��6nZ 4M,KRS,ZZ,Ba} f�"&z�  varian2[2Q ser0a�& �1-1�)^{-1} �l( �'a�E # \P*r��F� obJoP + �E&/ y _d_{k=j+1K � �k+M[}{k. } � _e 2H� �cJ�(1� � Jl(��1P + �P:� [�9} P^0X-)H \nn    N 8= s +b{1� + G2s+!�!rq��!�)B*\ = dJ  �Ejb^2+1)~ac{1-e^ �}{ -b^!�*�b+bED=��  2 �� perm!nM`P� := �-j!BjS� =erm,KGo"2�(Observ� at��ll bu�&e lasiGa�&�w+9� as0}A$pm\infty) ��=��e � $s=I%�$,� (� A�b� c}) *�Ri� a 0!�th�, (d� B0bW4. .$s�mj�Ecmre.6 I���" $s=3��K ����ad�V D|Z'isN!u �rm.�a&� ! d}).?is� by�Ke�Q�3��2�P^6 + Aم: 1 \+q�}���$ P^5 + P^4��M�4244�m43424�g1�>�.��62�6J�0E� \ee Num�F� TN er-- check"?e} sugg�� ��sB!}F�%�M!3A� exhaT)!�lr�, a�nk5.B >o/b�Bo yet.�$q�>1$2'AH(>O6 �YMby�(Jim�V\bUBerBJ�P�֯[հ]_q}{[մV� \\[0.5*�qTLJ���B�[�����)vai�!�: Q3ape- o.y2�.�q�%�C2L&? 3a � �(   �1a roo�8g %dQ0,��$)���8v}�yst  methC8f$ ding �&�eZ6o � ivenQ�.�.�. E�iNY� a}),]�c�� "eIhav7.3.S6#Our�roach8 bey�!rfa93VRc��an \h�Q*� impl!2�Lc2�.�� ut<aa� a�$"�$ �*x� �3 1is �ps ��genSz} &�� &=& (�"id� ;7 =_9 + two &%�\\6Qzp���}\pm \pB�{7_�>i}Lo�� } ==S^ +}O$"�� �|)x.1xRX��*YS\[6�e �!S\ �]={J+�.- =0. � A{Y����^ $-�C�M� $C�?Casimir�:�. I!8 obvi(1 xi�!�z&� pm})e� � _l$,m>$l=�">'8'\{12\}},> 23\} }$} m9W$5�=i ~$1�on2�M"+9R� ed6f�U(�AHv/@--Temperley--Lieb"A in Y�/I�$x"NJ>-s,�Aid,��s�mMde��<BFc~�$) J�"B�%�>,,.g1!�E9{no�MJg �ce>�3z2�emplo0`^*��ge;^ors w0�;�j#i�Ba}H\purpo�9��jy,�22�`i$ing, sl,ly�AR@_� a�Sis)�e5. a�gin�&D %�} �*C�yK4a! C$ w�_��uc$""E}\#=$$U_l$ �%# ɂ�DV7!�--G Y�(� $\eteX V�*1}$ = a�9I�s�7 Re \et \g�I0I y8 && U_l^2*,,�^g+1��\,&]E��  %% x,a_1�� �. .'-!."������cmhA3nd�� �-m.�*P �*O er6� \`� examples��zC2�]&� , V:�   �"& U�A�Q�=UQe"� y,=e"U���UQ�{E�P2��=2I�$U=P^0"et=�"$,�"xJ�yg&��a2�~ $.e�upBwe�=st]H�@��l hyp����#�,~~s��}�do�} rdr t l�Dɇ&[rmmBUe� ��2�2� . q  ,�"q MTy �.�< s9a) derl�4&s�)A��<of�_ rm~$�� �ofMsak�� *�Cex.,UAC aA�of'�H. Sub�,��2�$ *�w2Z&���%�1&� 2k�;r (B� +��% $(...)(A�Q� -:��U�@� 0d a �$!�or�+r8&eID.@�`2:Tis >K�:0C!�AUv��Mh�5!�-i�n"� ��]3 aPD'U}�g%4} ��- �[ 8� \, .2$= -) + )�  By "��(ng-� �8) w.r.t.~$\mu$,<=E9+Su=�A�]tsZEEac@%F.,!&T`riv�?�l!��$.3dif!1^\prime�^0%5\biZ(5))9BB)3+*#bi3% Its"QAaN�Rig�r) ) � � =0$ iff $�=0f �4i� 0easily verifi�/AO�=�does f1�. �4 \\[-�ɮ A�"(of�Ib)-Xewe�x a�9��&�[� ,Fby5�A=�eq�l4i�da<�r�)ic5�.�gco���!�I��k8�M��)� q��-&�y(�F , !$!-��),��%CA1�I�6.t � � \to�,E. �C�jc�$  q��aug��aS >� ��Ee� �]{0s�/"k]!��E^"u�~6~ r2s� ')>Uki\p:Jo } n 1+�!MVo  \�r  q�)s [1� U[2��z Y]_qf -%! &'8� �4C26)� % {q^>& 4} V�� �f� 4 ��Ն� E�" � (\tilde{W}_12�,|j of BT&A�&� Cthe vI-�|tW} |1�-&�|$ = |s \- 6#q|s;tw�2.,i|21" :l. �: h� �n31�n7h���[ {}F+Qi���!�HClebsch--Gordan (CGq� �8�D�%*� 2}$ �"�CG}c �|explici�"ZCG2�%)ŏ�abM$|2s, 2s-1 1KYd!_s� 5� |s-�!�+!&2�>�ab2y|vJ|b�v{-�!'n|>Calb� &&B�sEY(� s"�2s}�"�F/"J"� 5 E-�F�!\ee w�+fhXk 2��i"�$.� AD.+����&czSb . �i2kW8riV��$P_l^j� b2 Nw�!/~6��' � $j < 2s�9rcQ�-�RWt"*L�#m|I���� �@ͨV�)K+)! zFur*�RJ� i�a"�.A��)nd�  R�qr�g}���6\Es� -1$,!�o.7# k�)()re)t�Jn)�"�!�m��RWt�- -VEA�Md�a�\pi_l t �� $l=o,\`�3! $3d4%1�K^2=$,�) ba� �tW})~�jbe �*1y��^2_� �l� ��3 1 | :.AV52z52� �.j���2+�"�4a %O���� �&�R�2R}Ҳ3z�3N�jB�2+�3 |���o bpi.�=4 (!��A {c} { )�!�\!Ʊ�\�-� .�A�g� (;,:, 0���.��6�=|v�0!�V�J� ld �0Z3�B.�.�.0ee noti�Y� a�Q,�ŝB�A��&��="-T61�:9r="N/F��t2Y�g� ����)"M4��� �2H*.� upon�7fi�]"= �xA_)��1}ā�*�A1� -%B� Ga5 b�w*{ �C�<2�M�Xre�S�dE �O��=veh?�� )Xpla�$B�p$ � ��}�#!�&�nveniencX/� ariso,.+�(. �k�qu"�.V b�lA���k&�m'be� .}IB+ s}p!WG!yc7_ IB� demra"�W�=��"�1�%�1"� "� facilitI�%%.y1 : %JV*�.{N�6 �ACap�$f� oi� available9*l�e&3CG B,�3b} "�U; ~$&t$. O�Pi�RJd� &s coup��*�s ?"�6Fba(3a -G.�(ne�U�6�#�7/&i�d!1�!d�F�AIn^w�fdc'YYB&�3miYBO� o�xsw"\"F�#$.��T(goe�o3 � :�6$a^&&UN�#�1�! �0$\lfloor t \r 25�Irej'�8t&�&&%mU�$$W^{(s)}_n\0bYB�� j n=0,1�=�3s�}32�%� sp���>�!�r;(E- n����)> W] �=.y��s�::� }  m|  S^+&�\�C= 6*F� * � ���& 3 "!&� Q��n�<) &Tn=~ $ (� a<6� FCG{\cdoiL�_�D $�J�8 ��d,3*!��:m�6--'=�Ools�.9�!�ekvn;@F� �0 m |m &!] O \- k ,En- nm� Gw9�, %;s}{m}{2 ;}{Mc: _q �C\ M}ek'6�^{�x� QN�AH| zf� @�2�Q�� I� � � �}�DE��"� }ry�� -Ke�!w% "B$k>I� "�.�k� t'a�biggl\{C* �!~  �< q n &,for} :!;&n &2s;m - !K4%�2QP R 0 UF�O2 �Fgm9Nsum�� ek&NA) ) ru�O" t�k $m$�@�NM�' r.h.s.~"�F\0 x"�?�,$(n\+ k))2m  \min�l(s,5 %- k!�r)$}. &�&��t� MLx, $AA,n)�)+EWT"���5 '� ���ge� a�Q���H &�!�>("��q�defAn} �_{k ku� }V"�n;0D#�o}m$ E�� 6�A3.�a�l(�r)^�&�V �֥��MAr�qm��'eigen�E$ :K~$ K1$.�V]� v) T�xi| �ces enjo>u"`` --l�2 !�ity''&�*2�6�6 �1)!���*�!�2�:�A6~;9��_q J 2s/n/,, 6s-2n)}_{q�4,,�&� $�d2<&�i�E.�ula�%.�%x2� %a�A2NHD6eDu{ y3in>=ces~BF~Crem�/m� ;P$iii$�$iv$)� =@E'l(*�, 9- r)$� ZGE# ranks~$n_�M.�&. 4g $n��2Jwe �3 $ n_+Q� \f[�{2}�"u ,)->)+�& � $-6�eY]�x%# in /2S�f�~e#an &� tool� dea�e�B�&g*� "Bs�F� s~*� |���)"('e�&)�|4--_:s��l�]� tU� PPPL<"�O{&o>�H3}$a� Appp�� P2� a9 P^j� $�`�=2(�Ii[2j\+�}� 3=\J6�e]�"U 2�< s2ro2I�l|_{W�)}_��4*+t*M �.>- �A�7$n$ ex�c$n=a� ThusA$su  %to-�< %5)h)n(�es�ed to9��� $. D�L $p^j=-Wn���$v7=� z� yep!�ab}")Ma,2s-j}8Mb ��( &h0T�xcl� 9 � acs$Yb@)\"0ppp�upI5��s,2s)E1p^jA>0�"�Z��1!/ \-j,�r Z&� ���Ϳ:<'�&s4putu �*2&Ak%O�kx~BQ9���[yh �sL*2F� 2>w22~�4 *�D� ^&�a�WM�n�anzaC�v&�O*�~I� .�"A��3!� �F\ed}.<: $Y_n4,�)=6 7\!af�t(AV�A%�6: 9.,n$)�&?ŋ�g= Ŵdia� E�:y3'})�) eCa�^J�PF�6�6K .y. &�G they�  })j[ - n|� j � (2s,4s-n�U�X,�i2�6<.�V�["9q�  & K�^1�&�9�� i�ni�D.,Au�"�*� � \�bGKBi:F =6d��D� '�= �� k k'�xr�L-k% \,,& � k�/I_niW A+inm7&).H7� A�� PA3}) .z,` con�yaja�>P$ �f S6fb�EW J�YH >Z &=�2V��-\,6 6s6D(���"�a�# -\,%F<"\,*��UJJ� u :�=B�"�/�}E��R�9B� �Jr\�&�a�B<�.%+ ��� I�-A "?�>� � ������ u�.�"�I�B�>�.[�antisy Q�Y (Fq�-B$+�� �&;&�8'"@���!�)���HYq Arw {i,je�&�&�i&}$x1� j!�]$_{iVI"!I 1a1>�_{a ,ui_{ib}U "�HrE�&&�� &# _bZ_ia&2�jb�Jr)�. X a < b��a,b:UhC-us�;hasiz��eq"E�) _�~.  eLW�c ativ\F�Q X-&R +RG e]�M�~ }�p"�]���]e �a&�Nis5nqAby�E�nvp+�.N�Ang:P�(SJ�)^�\m=0hh $. (�Apic�[ �emble>os/|"\ of � ��&$Be�!$ansatz, se|* Fad1~* re�m�.�'1$�^duc;?&i>U%�, $n=n,~�less 0d�Z%}�)�Nial!ҵ�i�j/�=a�!b�8 dim}F�8 = (2N )^3$V�(""~�I}mVi"�~��v� "t0j�-!�pstill >� de{> �%8a,e(* "��6`  8j=|)nQ0��'d�"�� lve �� s� =�2s" �A�.� s �� B4Ls�t"%se^ ��jt� e�zi%��A9C� \\+nU�p8$s� '0 12$"�$2s\=SCF \=1"v?�bA�c2� -�N�64�fve2�I-�~ ���=�Q��{ly|8]d5. A&�@a7iP�%<rk��"N!j�(�2�%c�L�=�!e#F Rs1}a� ,9T��"dmTN: teche�,wusrB�&�� Y= �Hc��3��3A�a� ~$s\�@Ek$,a�in&�@ Z}_+�4�: ppos�t�4 high: 4s�l�,56�#l� !&� =2�,= �_n\��� )=�?�H  r3~ Ln~ u'1l*�A&�8Y.D ��b >'Lud0�4[=-v[�]!9]!��)�^� 4s\-2 "�^A�$��;�{i:]I$[n]! =�<oS(1}^n [k]_q$iAnF�%P~$[0]!%C�E�UDi\;H6jJc �9�n�C� &8s �LE}!�)) �ced.��*!m��.�'ari%Y�� {�a $�B=&  '&�YZ*�  8" $.�/�EY+m AN Y~.�+f/ A�"� lyZ���].V2�F|*ut}D_0�/ea s"c_6�T�bbn�� $a,b&M n$,}'8 \p�=2�\pi!- Ob�I��:%� �N&40����.�]mU &,(M�) "(s��)� �.��=�^{-&�9�N2 '��.2F�n �z�|5!_{nn}r|��\4N���N�saz� k� B�, �,���.-&N1[D � �@ya�"�,B�,)DM��.6����,������)  6 ~a-�/�+.�=� �mNCizes b�B�J��+&J� $,*� ���et=- s}\+6� �,c %|� of.�*_,k�&�*Fl���$;�6�&�5.�UI3�R)'�i�|&< �rB+ (cf.~q3)�M� cl�iwh l8�E��e �t*�s� {j��7 describv]F. $Hc} exists�7$nh;�H �  NeEthe� i�0Qi��}�}a"I��p�=�2�W\n*^)�o�Er&e �+c!y�@�m�"T�� roi�� ʑ w-"�iG!*� or�>Mva�e�e�Ac*� M s\!h2 nd {s+� B!i�Fe7_:�?jlS�aA+�Ds��v s�}D>r_{�! l "[}2� D \{�1T a�x�( ���>R�>s^Y� ��:? ?>*F? ��>��>�>MaFw $&5 �ekJ�  ��*� �/2A?un�1 $\va�5Ձ1�f��:�L $ �D?#j�hFN^- 5"� �I��m �u$n=3s\-Q!}{2k wccho� = ={\rmb�(1,�b)$,O.�4 ]n�% ^�n�>2 , by�sH%",m��$J4&v#�>�)=U %I�s�\�4f%�*a�6��s)��&3D!�*�iJ20�'.�;�, $s'-P�aiqw4}$�6fNJ~2} *_�3IC6^H sΡ>lFA��.�m&$5�7AE0A?"�;�rH8Ɇ!;�3�&:(gH�n�rivee �� "?p�d)2 cdDA�?�/�H �H-:)Mdn)���l( 0(� .b,�Q lZ<n gb}~ j�O=�'(m � ��.yJ�-�n{2s-bn36�� XP����(�q� carr�v%�um��op�r.h.s.\ w,u���  $�l(�� r)%�N}aba\�i"[�6m,� ^a��iSAo)e�z6E�s1� actu��l4�"�} "-]Y�j���j� a,b8 � easy��_ �.���!Dt�ly "�WEST�fo�MleL C�at�r Ij-ɰpa�� .u�7.�"&� 2s-a}'io�9v \xi_hK�#�� s�,M�6e�0Q�0 $i,j be�U0.Q&+�A."_..dd�cU!Ea�A*}3' �a�u* *r�HbF �^2aR�b8ny*�,M alwaysiq beca[m�Q�r-u�p �E~z d fi�a�=��"�n%��Ny*#E� ����>:ByL%i ����@5R�� j!(6 :�.s��.ib@I*�_{�T.%j"\6S�+] !�a� xi_b-��]f�5��@2����P.��!.^�&&^�(Y%I�5p b}' ��a^e b IP 1$%�aX r!0� ab�*1�?E��*ddd})��m7E�M�mway.  �,i�$<.�;"q~>xi��e3l�/~�g%ѻ��&i� 2� ���b{Pr�G(w,��[Zo6\, JX�S�B� )o�<��e69Y-i%X� 7 $(�� ��7�3�{�2�$ 6�}��t�c�']�mndB)p�sɫu�l�yn> $A�j�=2U2��l- 1a �Vs�Cus�#o!��$ f��@gof��< ralsmo��7l��TC&�>H��!��.��ZtTkE�lL�}=:wa"lat\.models�mE1~x�AaM��{� ���Ft��.�@H}�xcw�� k H_{k,k&�p�4 Hy �al_� .�m"W/ =0�X"w}7Gxi���n3jpF nj ct�-��!�J�� ! ̆ magneJ{I���ne>��!������Hu(9^" ${11|rmV1L<�  $L#A �of5�sitmvNG0��"�H�3A�ok�o. Z �Aiz���~�G�U,��` ɤ0}�(��fix����!pvei3�tm�=�).-?Q�c)Geqe�3sen�ra*��M��v) +.]ʜ��6y�"�| !�X� H$;?:FI7C �D�. ���ta�Š�H`$it+fqOd if Ke},e���1@. "�[6�&�~.��u�ces"X56=�gv,Q%�"�$��formu%:cz��F�=�6� HR4^{(1)&� �d $22be`D*V��2�(.�nMV{s*ӂ3}$�P� �� >U�� %��.� 2�:� H}�&= , $H �=2g@:%d�. =B�/�b*S#``if''� �j. F� orem~3�1�h�qa*�n_e6�Y)!2� wo"Ê}~�� F� 6S�*�%t1 J���� ) \,B PD���IK JK�� F�FH o��!�Aᬁ���_0� �* "�(�hide� onS�ity�6� .BzeI|M� �� 3>p%qe2o =%�&�*��  en��p-�lp  l8lR;�"isw���"U2�|��Aqҍu�.t*�  �Q>*ڍjS}V�d=,if�j know6�!�!��~̈́H� i.e.% 3� ��jq�e���)m� } ����r ���=1�u�1� a# �.F 9&�$��2\uU$R<=9.Io��r�xo�gdll��u�,)�]�pguarante�u-�rc��J+:���&'�.�M{.�`" N<�� \YT{Asymptv!|� �%Im�+��"3+.�b5+Jie*!�l �6Lambda*}~�_b�+��iQ@mi�msum!t $\L {R�7(pm 1}= \li�qF\�y}&ax$ �! ��M�f �0to.�YBc} �*�$� .tw2Z4��n�6�>�5.O�(.2g�|e �= $d_jbZ +)x}r.�, x�9gEj=�[��.�G!i��i�5!�~$d� }\=�CTY��; Y��.@qN�83.($��[&�=Yn!�"t!\D2 JDz)F+*K2P%�_ \+1J���d $":J:%V-kN � $> :P$D�����s�"&-q-m 4s}as1N�2���Dɯ2g�93ef�\b.D($��(,-�F 2��2k?\rho_s6E� �$$[2]_q\, [6�3!g_QqV4 (AJf��mV D7Q] }SG ��\ [2.Z�� �&^1 \- ��( �)^2�{ � e�\,6�u�>�W-1-5}j5)�&2O5�AP. }�@F�^ O!��\N\&��B�wt �[2sI#�!n)"[UO��*22W_2�L�dce])M=�_��A~9-���r�C �)arFo�"�1e��˫o����|� 1tie��~ _{0�&H�8 A_{12}�Ci� 0\&aD_{1=-1 ��\\:$=f�"y�J�n rYB}) spl�7� X� s:J����Fd�j�I��mJ����ove�/B=)Hc}q���tl�ǩ�2.o�� b^2 S� } -1}-.�3 bΈ)�yBEM.�7_�Q, �wb���%",���&los��!)wi+ i+t!?"��,l6J �G(�_( !pa'�a�X-$x�)#���2s\^���ao-2.`6  ��Ŏ4s.> �!{Y�kappa_�I)L)Cabi!@.] 66Y� (2\log q}{q\�2�R%{AG(qon�ndsP�qJ� thre� �c��:� ��A�5 2$�yA� mmon�,/ 2. 2s�Ra 2}� {8s ah� .|a�=e:!�{�|s�Aef!�)�o d� 6�"G"� �s� 2}�AU^�M*sd���)�26�,[��!�% &\,����mM�Sx�!:(5��8R ��[4s�� I05>�y�]&�"{X� 9'J�r�i26r ��2.qnBI\��"s�BLH+V� 9 BX) { \�/���œs:j�to�th�6�9?#eM��#"&*C � � 6 .@4Rs1�ˉ�i�A�2!�?�0e�al��^z!�J#���* d"| �n7Mϊ}6-�A[�2�w(s1a} ���(� P�vP싺P^0AM�9�-Ղ[3A5\&oJ�s1b�.0VQ2(Q�hT �a�{[2>�a|� � M��6�[.d�c 6� d�`J�c�&i��5~ \{3 >>za3 J=%�qDY E�"�S� *W���#$��EW� �b=(�%�IAFSS��&��T ione�`B�FM�� l�sHA�y"�eon�.G "< $(S&tsH^-)^m�a�XH�pas# "/� r�� �'\,R �Spnc��ŵ%<O1)}_0ExD��Q�+̉ Y�26�Z% mean�.e���4$N� "�� auto8.k(�%�6`&AgjI�3}!j5alFr5A~�S�,2R�,Dj*�: kn"�3*&��G+&��s.A_w�4m>L�DY!�'e�6, �>to s. �-2 �c F+M��=�;P$�� 2�"�ps1c�-{ \*.{^V� . b�t2� $vb� ��qefb-�q"a})�G$V��e�� TwomHm�� wel"�X�!e3 v�<�M�one�!,�ea:Yjj[��<�Wim` � ;9wP:und"�l�Jo}�"i�%��i�#�XBirman--Wenzl--Murakami� ebra��Y5Jo3$}� n=3$E��#2�Z��12\�"EF?--)�A0��!0a(.#FI fou&X\A�*� An�E&&�3)}A��!� P *�- (2]_q)^2}� � � � �|[4� ^ ,  0�~An3j]:�� V�2t �X �u }{Z\ �u(&o_�n � �.R;�'�4<  +�e, \hoa {XXX"� An3c27.���� ����p.V2� .@�%] !��<�z-j Rs32~H )3}� ,�JS $V���!A�*� m�NR ZR E�2HT 6�&� \A�i�/J�k{u�#VIe.�com"_@of&�, �`.#���J� �>r�L1,2,3�* .LnD� 2" =r_1 �Bi��� $r_0 ��9�/��byR;%G2�"'��d1Wͧ)F N!�{:��$.� M71$&*�?JA��A��r%�Z�:��H. "nOt��ru�nou�c�5I7*M-i�patiblec �!_!�F�B�ANra r�_b=q^2*�$��,! 9�1 v�+r��)D>2�� 2��%Dlm�[� 6� �  �>a�k��Q�"�B.4: e]�I2� " 2%m1�� e![A&Sst')� .&j�)?7 �X.*!�5� ag&/�a�-�%fF)�o �Rwe�t�I�F�=x1!9X�W��4:�:F� &��0a" 1{vaR3�$}{�|R�pxG= 2V?[5��� ClEdV�6}S)(2}=q^{10} 2�(�3)��� 3&M .l� &y"'3� ��� "��;�3�A d��A�u�sa/j � Nc2_(.�wD a~� �� R�Al%2~2S22v.IH\5Q a�H If��A" � �4/�BlB��*}�s22} R��Y-y�f�\ 6|"3As7,w�ce�5'5)X�=K �6qi"y.�whJq�1 1$ 5$&"��)jA�a})f!�JR �; z+h-;h \ll ad�( $[t�P= a#,t(t\-1) h^2/�<O(h^3;�Sj:*Fl _{q}m�]���S��B"wao$[ DDq�.=1�Ef2GConv.��ja �ś6$S0=J� xi_1�l .x1��� ,2!��q�&�G �Xd3�!�)uZ� 1N��(fi�e*� $h$--eYBG�ٴa�, $(a,b)=(0,19G$(0,2 � (1,3 .�da>�qhV0 u(5s�> - 3sQ!23V(y 6 �\\&�_ SI{2}�hJ"�$ (25 s^4�32 s^� 9 s^2)\k (78  - 81�21| C4735 �'3( +E:3�3d>>qh� �2�{r10� + 3� bi�&�sc} s�d+�{4Fd (1!O)b!l%b1-)%�6i135j205k96%O15!AE%q8R%�90)q20�r2s�neZ��&�  ��th &QC�{i5!� ��"G& lst,��A�<��J �0sFW&_ q-��&� root�:  3� fr#2�!�xi.5s -3�&��c�R"Taap"�q�arT"���.3�F "'!xof &j*&�k e |-+�"��~)=c})). M e��f�!C%5 9-(a OsGVnd�O27%% $. B��� �%>��5 $h^2Z5r���� �f0� �-�+>�!�28aME�6VD/ �P46P��^4}E=- 1�B/i/"rH")�N�� &��=H-[IZ2ost. W�,i*a0_6�$(\ref{rn2}��) for $r_{2s-2}(\lambda)$ is ruled out. And, as follows {} from the analysis of the previous subsection, the only possible form of $rB is\�mfirst expression in (\ref{rn2}). An R--matrix with such spectral coefficient cannot be a~$q$--deformation of Z(ser0a}) or~c}%+L $s \geq 2$, because�Hcorresponding valueR4$\xi_2$ does ~vanish�!�limit~$q \to 1$. \qed\\[-0.5mm] \rem Notice that 7.�!�3=�w$excep�al solu -=s3��8s (after rescal� $M \to /6$) to^second �5�Tx3}). As we have seen �proof�Proposi�~%�$Rs2}, this RA!.a root4)�qhb)�T $h\neq 0$. Therefore,w(conclude t!/ 8 �ha!�p regular $U_q(sl_2)$--invariaA'E6� -:�=Z� �$ a�Tconsidered), one infer)� 2jLc\, {\mathbb E}$, $cA�Afa �WarOtant. On�other ha�`�42WXP^{2s} + \ldots$, accor�gtoM7U�HenAc=1%[2�.��i^�B}A 0 co-multiplic)FI�,del}) determ%�AH,structure ofHClebsch--Gordan (CG5com��a�tensor�ducts=4irreducible re����!�s��ݸ!\CG �sER06--$j$ symbolax$re derived ( studied inMCCG} ]��ic� 2F0 which appear:-Aa�(is given by�� ��86j} && \FRW{s} $3s \- n}{2 k T^\prime}_q = F^s_k \, {k'} d\sum_{l} (-1)^l [l\+1]! Bigl( -4s\+k]![l  aHBigm. \\ \nonumber �qquad \�, ' C6s\+nUTW,, [6s\-n\-lg, k\-& [8 *F Bigr)^{-1�, \ee �u.] Fsk})&{k} = [-O wC8l( \frac{[k]!\,rn\- ![2}5$4}% {k)]�=}_� `1}{2}}���a($q$--factor��is definA�(s $[n]! =� U\-k$,� p� vely),e�we obK A mwlAkn} A^{(s,n)}_{k,n} &=& Me?a^\sqrt)�2%�_q} }{MMn]!�.% &i&arioI!�A)2sI�f`e�E`2nEOFa E�A ! 4s\.�Fm} WV� ,\\ [1^ 1/0aI./0,k1/�R(\\ �@9R�� � � �f�:�M !K  2EK Z� e^ C} {\em� of}��P>� @Aprop}:\par $i)$ &�ap CG d2�D $\{23\ $\{12\}$ �!nK y�ek}.� ek'})6,� us�torthon�= �bas� $,� ,ngle p|p' \r 4= \delta_{p p'�it��\straightforward to find w�p� t�defAn})EN(Aa�.� k^{�  }a� \! � m, m" \FCG�_m�M}�h \- m _qax ;�<T'> % h�� _q �Q n &�D� � /Y^Zm �6�n��Wm>j]6Nf24�,iIn orderA�carry ou summ� �s $m$ w% vokf2A�identity&r ���@��m�� �a}�b}{m'%,}{e �l� m}{d '}{f \+ 8%�-� UF${c.73\�%CGRW}�# =� ({a\+b\+c\+d ��O2e��t[2f  � ��.xw�RW�d}�c�f )�A�% e{>�'$ I Ho)k)^J A�M�'6'E)E�#}_q^2 =�l�-n; k' | �C1 Q>Th� mainA ��%Z) yiel�Je*5� c . $i�\Nself--du2�trans� $�ectA�ir��arrow qb  l������2 s  &,�a %� operi(#, unlimCG.�s,�eyY�ed a+ rely�C �  $U � syGs!1obv�c�&# Fk \left=k'"�HAcFbPis symmetric. Since $��q$"Ōgo�by� , ion,�-"�d6> coincides)j itA9verse. �(v)$ Formula � A6a}�i1!�MI n1})� Q<rel-��A6`in5t MK entrlooks a7E4iX�nn'� 2�,� e0$\tilde{s},�  n}� k}, '} \,,�A��ss b %s}= � P�c, \� %n}S 2nN6 k}=k� +� :9k}'=k'.&� �  $0A4 q k,a� nX shif%� $ �kD '$E�necessarA� �`�-�k�e}) (no" $�n= ^n}\-2 s}� 0$).*X!�)�checked>�lyA�mak��A�change8 variabl"�!�)A$M31� &}  ex4i.� � -- ;�a�0comple��.  % \new�Dand{\my}[6]{{#1:} � #2 Hbf #3} {(#4)} {#5}};|small \setlength{\itemsep}{-3pt%b�Hthebibliography}{11�bib2D{KuR} \my{P.P.~Kul���N.Yu.~Reshetikhin} {Zapiski Nauchn.\ Semi4LOMI}{101}{198 01} = \ (Engl.\�jl.lP}{J.\ Sov.\ Math.}{23;�3}{2435}\ );\\ %%CITATION = JOSMA,23,";%%�(E.K.~Sklyan�(Funct.\ Ana���.}{16d 2}{263} %-k-,iz i ego Pri -,N407}6�,FAAPB,16,263� 5R SkDr)S>�Uspekhi�.\!Fk}{40e$5}{214}\ ;>�,UMANA,40,214k!A0M.~Jimbo}{LetL%F\ Phys�T63NS LMPHD,10, �RV.G.~Dr ld} {Dok!� Akad�2!�19� 1060r�=�\ M }{32�5�)6T(SVMDA,32,25�9SRo)Q�~ �Q8�a�39a .}I3 5,39I�U�ZZ �A!:0Zamolodchikovi{lB } {Annalsw12E�79}{25>y,APNYA,120,25:{Ba {(R.J.~Baxter�Z~Stat.~%k }{28!^a�> JSTPB,28,: Ke W$T.~KennedyV PA2%&9�F809:c$JPAGB,A25,6�Jim} Ey�M�6�10i)6}{53>zM�02,5376aTL �4H.N.V.~Temperl� ,nd E.H.~LiebA�rocA�oy�� $Lond.}{A32|7�5>2PRSLA,$,25:6CG }AA�KirillMNJAdv. Ser:�a98A8�;' my!0Nomura%�6�3E<439>-i�30,6-KF;E�F'c�aNo��M15��EU6>$LN�e 51,6:"\Fad1} {L.D.~Faddeev:} �+ doc\$} .� \Xclass[11pt]{article} %6 8\usepackage{ams�}2� icx6amsfonts6latexsym6amsthF��F�, amscd:lurl} \textwidth 13cm \addtoq 4topmargin}{-45t : exthe� }{90 � ,theorem{prob/ {P [�!]2'/}[ -]{T >}2$rem#Remark6"@#s2F�%D�|6(p�*:6(cor'Coramry6% lema&Lemma!�. Z}�{Z}� Q�,} \date{Nove� 2004!�,itle{{\huge I Equi �}mea� i� A%bb{R}^4$h�author{Rade T. \v Zivaljevi\' c}%\footnote!� 0 ds>!#�" %1643� Serb#Ministrye�cee�(Technology.� make�n � ab�(ct} A well �#nj blemQ8B.~Gr\" unbaum ] Gru} asks�"�for ever�4tinuous mass d�ibk%-2T) $d\mu = f\, dm$ on $=Bn$� Pre exist $n$ hyperpla� divi�64 into $2?!�%�.!1�. I� �^�)wer is �ve!�dimenc'$n=3$ �Hadw}%a �( $n\geq 5$, (Aviz�!$Ramos}. We� ($"�#to !i )i's5�z(he critical6�4$� prov��� each�! u$C.)4$ adm8an!Y��$42l, ^de�at���&� a $2$-5;al, af� �$+& $L$A[6�. More�w0ow,�ut ��  oA�uca��!!4relevant groupa� b"sms�at�"� �E��$P, a naturally associa�&UtopaQ%����C'aU "X(&�E$ $H_i^0$ (��@"  {1}$+Qp�,ve6) QP) clo�� half�۽1�y;a$. � prog�.A�m gene�.�X l� �6��Œe�in 1960���. H.~� iger show�&mo}I�2���vA���. D.~��BC C �*$2S��A� . �:a� I�mean-p& many���� ��s w fo����+I�mW�'�WBaMa20R� Mak /� VZ9�.a,n����|Z� was estabed SYao-Yaob �A subj� grew�P� (rate branch�^C � Ziv04}. N� the�*��e $4$6�UnitA��resisted�TattempD)r�s�%)j cal2�Q� f�. , paper�%� e, � �/ thm:� }�a��.  r�J�if� �iJ� � s� B� . � � demo�!�inF�$0exampl�by�#&� j� :� � ,"greo���''2� \ac�a� the : A of^�� . p,result may b���� at I3a&$ peculiar}1� �2w >s nd)�9inZu��q�"��``.k 6[''*� by�MYF6/}, can;0turm)% a�puine 6.�0i��0CS/TM-scheme}��$ �f figu��� /tes!=p} 0 .�a[ emerg�)onKa�key pr�p=�X,"f-� *| methodeh^ !o.�M�z *N � e� ic�#a1,outR/d*�,. One start}- B or��(ifold $M_{\� P}� �Tcandit�!"of%�" /co"" al �$S � next step{ !�"O Q1� $f : �\*� V�+q how fa  a �&�n] $C�+b$l  b�/* �[$ precisely��a�; �EQ $Z!4%!� .�e�"� v� is a9jifE$p+if $f(C�  Z-Uinn4"] �J� typly  up)4 " tage!�is!On&:"re �� $G�6n$XB�a0�3U,=!2%D$G$*�5"{of .?,-�s �e:v ne�. IA�c:�$/A�desired!B�y.t�=�6�AE ��ise�7� s�� \setminus!ۡ. fi�q1to)��6JdE]Eg� p&�8�.�rea (�i�'�� ^*!���=:ews� Alon88 Bar93 jo91 Ziv"� Ziv3} @�E�seee�u�Z *�RZs �%Kneser's!�� ,ure (L.~Lov\� z��Lovu+``��split�necklaca��'' (N.~� 9 87} )%� ColoB2Tverberg! 9 (R.~>7, S.~VreCica� ZV5 VZ9436t�eventu �;� = ���+cod2�!;ge� ͜� \aL�!2� �}#) sec:"} Our�;choic6g62��sui7 %E�p$�� <ma�n�>ll�*ed*�sQ6��H2(�R �)�}orienN &� �b:� R� . S�s�*�7 e : "�n.U {n+1"� kd�8 :($e(x)= (x,1�7Ea� F� $H��/�� ) \c7\{x��.}\mid x_ =1\})�tV�E1an��b'MH = e:}� H' ax 5V, $(n+1)2#��$H' �B�ɐ 5 A�HnF3)I3��(*{= orthm(�9$ vector $u!&S^n yF1�[�<ironmenti &,s�>b,�)$E! our (=�is *@ $:= (S^n)^n)�;��b32Q uK"3ref��W_n := "�Z}/2)A��s S�' per~:!x#+ors whilae!� Y>R�inW'rg vpodal�io��� vi�) sp( �e #a��E&{ =0A&�\free, so%�third:��*� IhF���N� \t��eq:?1}* ^\ 5�_ :=i� -�a� x_i�>H\pm x_j \mbox{ {\rmA�} } " j\��� � re�*v1w4 (standard) ``2@ 6'' $F_m��M�m.�^� �GFaHu}��?alBy� ea�� in C&� cs, �]\ FeiZi� I�i� refe1:��a�;e ``sig��R���D.=�sbitV0 $% ^n-�/W_n$ �beF n �;au�5� c���:$ $SP^n(RP^͌aMpro}!�)�$ e��%$reason why� occa���deZA�s quot�ޡ!$SP �qand v� ele���,un�+6K���inct )s :?�f�-!Y� �V =2l ��!2l N  E�m��. �*��$, let4'e=!4 ``push-down''Ein?d6ER} �!$� ����6n \hook*?H, �(A):=>�3'n�4A��A!S$-tuple $(u"< ,u5mn��f.�s.v=a.F! H} =�'.�':�n��=6m-�Nr$A% w ma?5��-�ant���\rm Ort@beta}(�)$�� re n"�index= 0-1��s $> ��&m.1) $b_{} Z  �{R}QH f,, .� J��;\mu'(� V�)R7Q��f�V B8A2C$B_{\mu} : ��.} 2�2^*beN� L�= (J�)-A2^a�v�� J��"c ad �+=� >D\*� ��� map �D�B.�'2 real &6d@ $Vl<�2! D ��� B�B�!�9�xs@uF >nY<Reg}(>�i��Z~�#zero''��A�B ��x �%"C , $16� );>�V_0�:nnW!(meU=U) Mo�V ary NN,�E� V/[�� $AQ� .�e! ��, �� -�A . BgG� &w�H@��N �o��AsayEat �EP"B��Ap�NŸ�p���.# h"  :�%}6 ��=B� \in &� =m�n������ ��aua�&ƕ�Jq if� "C-�2B0YDend��9gin�&$cor$��FJ� d��aA%R=� $A^�A"� \{0\� t�G&!)�ve,Aʯ%8�$dm�!�Lebesgue1@,je$�5 *gX"�' Q!�( G6rem:mere�3rm�wassump��&)�2, ab�38&"�}� Z !���iis un&�5re��A AllaA need� ! d�#��A�eQ u� \&< a�,Md��5D by a Z'l(D"a �s hava��b.�a[$���G G�es�S�jo�>� zuA;g}1B�nu_D$�finit�L�Db6`&L $:(X* vert D��X $���4 ll:�s�b��Ey exten�&o �weak iNs�@-��(i s, cf.\g MVZ} �߅�� (set up. An1Q��a �� �Ito�!�c�C�*�� cloudMPSr M�}.YEndaV-)_8 {SinC&�!�$Sigma_\mu$* �(a. fa �w�U �eo(e)f simpl~ �hll*�M&� p- ��- a��!$i���H hve oftenJ�%�"u�(1)���7�]W &�1�!�GmeeqM mpanͰ!Yad��alNuEaT re"�Mwe��or A+AW� tub+ n�0borhood!9 ��(@�+ data),��useRv u�>an�H)5"F,�A� in a&�e AH,�2�+5-���]1 � � tog//�A ��str� .��@t����@�imAS{�?�v#t�Usen�� .9 ��sJks6[-va�U�j�is .`� Kosch}A��g9}2ry^.�FH1��arq�3>@��ravanz"��'2c!iV7is.��-�ary. 6&wX& ieflh'�agsiL1it serv�s�airly gA�illust#of� idea<�ir ru�+!$ m. A*�P%2h#,��OY B�(&"e�to�:v&�� � %�� W_2$>K �&Q �W U_2:�"� W_2=� D}_8��!�dihedral�/,.| = S^�@{TS^6Xa7$UX<$32~�:x�1�,� crib%(F/ %(�#�"�(a�l]5�!e��!tat� &� �A�:�>I��re5 P8� 2)^2�>45�D \{(x,y) \mid x=y = {( $or} }x=-y\E ad#1ap�e$ o#O-��.��"3areei2$# a� �us 2{ &�� �9��efof �!�p�s.�Dn'�Sicm'@ � $A�[tQ�R}ESAI.��<_A�;$A���2�#�$"�. Dll pairs $(L_1,L_2�"��>�'2!�2!-�w� y� $Fd2$&��� ��$A%�Xt_ c $D�6 �D/o���3cir#). HAvwe dof6�q�% w)��n0� ic�6�steadCna>.�e,�%}ak �N �S IP*-s�a� �-�G� m� 1�s/ es�� �/ &%.a�be� " xim--byd"�&}40[ �_��-two:fsg$B2�6a$pat�,ne=;� $mu_t, \, t�[0,1]N p� _0$E%n�-E�$1 $� �$!4��T%�o�\a. \[ < {\;_t<1��}}�Q� ;t)\�X�g� �^A�N�1�N� \}�N bset��k � t \]D�,�*�&X (| )� �.ng"D �s �I1e0�--�� $\Omega_1"�! ��i��>,� �5y��( isomorphic�"QF \oplus"I?!�U �$-5�"\ y� s�6pP@�! disc�[Mv�bis easi�� hown��R a~�,Z�Ge�%2"� e}[hbt] \�.ering \ib^�=s[�PHe=0.40]{upitnik6.ep� ca�{8.j5 se e."� fig: B� �� mmed�7lZ JiGAa�I��/ 1�5#�+ore�AD.as6�1��V���Dnonempty. Indeed, �;*� A =\#se��H$R��a bZz�Aw�D�����P�=6Dc�*se�"�su4bly � �)d� uA�U�a�Q��g05�4 �[\1 $1}]� D]$Y� bame� A1F�eAV�!��%� radi"� c�2z =oI59( r�� ��3�>:$,�^ 0�would�adoV��Y�^'Fgskip.8 rem1�worth�Jn^�j�/o�. abo|2�,p�, �m;��a+^*�u(�!soc4�carIa.�dE* A\ �*chosen,�=\\i�e��q�ia�� $Dh in�$X �(. Unfortuna�,%higM^�U� Nballs  � i�&�s)��ir&J��se��Y�=�y&We"�R! valu "�<2���s�4h V �>urp�>?1�us"qs�tl?L"`�2Lconvex curve} $\Gamm�`>,FB ;2Gray}. �*y "�;Fro2 vex gi6[+:�.TD#e�{C� BU�4"TA�mooth ..���6� calle�-���:�_ity o@5� *�)wit�F�>&�.� ceed�. 2�E(c�D*0 o�6s�jea�BA��7$different >6��ei��l*�F�2y (``ec�U%oi+;�)�g-or$B!F$ex polytop�Oily),po*'o�(f"8! s (T�3(bycheff sys?O), ar�Pinf>�a�'s (�onjugO6) �-,F ZAnis98=!�bArn96 Copp71�e5�C) SeSh*a���� 6!Pse~/. S�' �NO1%)?%�G ``mo& �5or al�8 $MM*� t,t^"G=t�$Y x *o#R�,�;f{4�(�Fgon�rici�qX_{2n}:= \{(\cos{t},\sin28c,n!nt}� � [0,2\pi]\R&-2�"�"�c� M\�sA !76� �HE34%fa�t�Uminimiz]e&� �Ir�s�Uy� s. A} con>A, �&�, cal H}=;>&�=H_ny\Zn2Ca�"� R$has at mos�Dɑ�)i��0�m�)g!�h u4n=2d$��0#-1a��j=.`�� Hv&vVCn�4�arcA��/9�u n�g� �9&(a �.�=%� hS "� �&2dsnj"�! hn:�i � Fn $n^2�@�?�\&=�@4� isPTai =h^���i!�oi&nWI.G�vZ�}�� arisf�t<N de��C" ' (: )V � 1}��uB(B�J1� �t�M^!+u2p���*��o- a)�!--�_4 ��z,z^2�� z =J71 C}^2y1>}C L$e2WH,' = d\theta'  = barg}(z),E6�$``arc BK*�*�;e � $C� {z.C�1F�p �H= �E��c1�g5'& �@ �\�\pid nA %/&�!�"K#f�o-onGZmilar&a � b3rrvo_ o��E�2��.]3.P�<{p_1,p_2,p_3,p_4�4$��4 @ _4%�c.'a pF�� $HM��RA�, h�%�*�6co+� �"@� �<*/ off�;!r CH ee F�<es6!lke�`Z ref{ jedankrug07 dvaa}NIB����J)EH_3-8A��T$U_�*�Ga �J�a�3���o $16Zc�- lm�"�# ��\ 6[͔ $\{x0E0}^{15}$"�D x_j=xD^j~x_0m aY exp{ i/16�to � :F $H_i�#��Ymapalpha : F�\}(�e?�C� ! �Bp.\ 157M�-��, $[x_j,x_{j+abe � an 3�co $�2'1B1FV-_j*�E4qJ r.0��-�-@/kdDac~o; še cyclic�7 inheri�B�]E�0l valB�.�movA>)�rt�VCn�+&Et�",)�i� ��uBS� w cu!', !%{)�2}�K\�5�h!d�% Q .+ �� A�%T>�!6|� so � ��%�2:K�J�IHxa �!orist, a>!WHamilton�O�} o�� cub��{�G Z$n engineer�'� Udev:usMfor�)'!�digital �3!��Analog� ;-#a,m ��bv*9��obrisi1:��.��,J[L5��&��v:�;�@obf�:atIx !i*6A �E�*?]�� qu�(pe�. � �2%����_i�wg �  B� ��"�@�E�s �'� �de mustveK�*� A�qin �oou q�N�^ cks. SuchE�!l"��M}, �: . A !�?� thr�?�@was�g&?lyVcg2 G.C.~Nillm;}. C7)GrB�N-� �6I>-A� eF9)�o~:�.Gilb}y�I�, Exer�~569.Zif0I d1�deN ckw� !�%����;,3x� )��w� 6D9tracka�er)��c<f�--JvSB�Sm�at_�Uway!-l ~� de� �#��� �em�  0play ``Quad''��$S.~Beckett�1}� i( ``..��ur�2ors�!osaloAho�E@!m�"�7�8yet anonymous, �smp J + lent�I � -�@uit drama ...''} @Frielingnt� �,g�k�m�?TS�ba& u�IE� ;! s!�$gBd ends�;e��ps e�%� exit%��� ��,fp�gthrough�� po&)�, ! daows u� !��#) �ma�@ "^�)� �a"� n�dt�5,��s�BV H��t&� )I&� Ch B�%�ju�&���ah#4*�E �H*�J�;v7 "N$ =74)^4_\t=�)S��� "&� 4\}� �-:f *�1� jF6:S ����� , �c :F�%�x $\s�.j1GH_j�e imagZ V('�6�:*Dx  $6 :"�j�a[n"x>�x��{f�,)��zgoTB%�x.B�*�dis��ż�ol@s% �lQ'WME�>..6 �gV � �6�hi�Y�Jun�e ( ����=��2��Rj�!,7�"Fy�E|E�$QWM~ A~�ove��J�k�� >r ��;*acc9M�=��!� -/)�N[V��=b:��edU�)� �$m��l*�.,  2VXby ro!mngn�\Nclj 85{i:^2_� w�DZ;� ��sO� �!�o%E^�$,�C3� 7su�: >�:s��by5m"�P�um�!Kq��f�� �: Js achie�SR�lx B7 k{ * �x if wcvej�&5 a-�` � ރA!Mc:��B( : [4]\*�[4]T�.�Ekeeps�$�}4$ fi?!��%��� s- $3$�]�* �-F,8 �B/diagram!I )��lk}�c�lk&Ic rex)E[��� xes."<+�M��"R�RdegJ(ac�!  �lP6j�&90a�3\8="ぅ��ass����0A� : (S.B:�8 N�3U_4$. >m��B]%I.�)N��#�"�ed :�,j�!e3 a  n;_l�&�> 0e �s s $y  (x_j- ,F+)$� be��C){�o-.� �+'�b A�'A6H!5B� ;5��on�I* $Sn�/ � T�%at `(6��$S��Q* $b_��p��NF� }%�c2 _@=�^-#fun� s $c_j:= �AO}-}��Y <'vB"~�5ec�}uEiJ�� } �.� $I� p�� is c�eA�Ͱ.�$dqM(1}5� y_j)=-B c�  ��AfuturA�%"c�,U5?s�_�A7�� "� =�� �o"v�U{"�  :� -�}��} m� 6}��*R2^z TC2Is>��"� "?o M � &�!�asn�4 ted)�0-"#�B4&�+ �b�C$�W_4 = 2^44!Y^{,J omp�|ev q^H1�':=2�/W�*a�0)���61\BSP"� �H4�^  � h?NImM=X^m/S_m%!O��&$r{I1$X�v8#(X)$ Iqp�QDof ``square-free''�sors�?A,� �J /,slika9:p����ݪ� �E _ !;$.U�s.�:` M�r@z6q@oKa}�.��&M"* (B)!Vbo�;0"L(L"�*Z"' �'Q6�ac�O�� " ara� rgot�9!�  ]s,&REa�dR&�r visd�i�R�A), %e�Y�8''z6B). -{!k 6>(�q��n4:l �/s9�&2 2N7Cor*j �R?�z,E<%"W�D�8� 8q_B� /("�2?a�Q|n7 �>6�>0 "�5\�C  �� � vale�2.�`�e2 ? M� � �G9eqn:b1?} RE}:�x� *� :V\�$s_{W_4}U_0):�am *�l?��m?. A �w t*�W.;$\o�1bS� �8E of�" & li�9�_:M�0*;.M; E}-TM)�O�:�!�$TM�E[ )U}���M >6!!�el E %� G (> =�)� G��h��! ompu��� �o*Gh2�6;"��;{`9.3Y XE: �N|� <3>6i &}�k ���"�� �/�Bi Z�p 3���vO� �V�&&��u �m,F� Q�,2 %5�c2�3}3^ ��1��#�V �[Se ~7] �T shorU{acZ� @ 52�"/vol% ie. � �ei2� )�j(X;\ph^�$\widet�} "}.#� $j�'uP@P"phi^+ -  -eda vir�Y6��: $X��[ frag�+�,� U�� ACu)� �,��'5��6tackrel{� _2}{\;"&�} �_21\5fN0{F)}= >�K& jNJU�G6.9�_1F� �1�6fV15� 5�>:  0  9XW�c�eRe��.��<�CX = MB��?A(U8 Q83(���d&�, �v/� o e�1J.�"� �rJ� h)& L^G&�a M i�^��$1�$}�J� -%�X 2��m�6K(1��=�Y1.)A>$��a"�  > 03�l3 �}Bmap�&CW|� liz�O�6 itab}8$tabilized ��I���sob3a�% 5 �:�'.( ���aT�ѱ�� �:� V(�=!�X $f_1(�)=:N, \medskip\no�Sn�8bfgHof:����%>7V6O�'�eg�.R)&=* :;*� :� ie% uniK$l c�!�= map.�8� �8t .>-G�-knd�V\'"KG�i=tN�>a\xi%"E&� �? b �v�j *g�J�3n,V�HD��F"Dq�Q} \S~9�/I� .#�M�ERO�x�:���*�Vd�F N�ni��zr�8u�-f z!-�u)|�D!?)�"�"�lif�"� 6&R*E��4�^'`^Aa4,r�b�5, !�6�E�tr�<)�.(�$re�F�Hg: D^2]� M$ �W"(D^�Ai,rpp!BirZ�Io�!NFN�� �( $g^\ast(\x2�)$%2���8. ��,2.%a���\Nc R(. \hfill$\s�$6� ��S�$:gN}�}&�lͿ�� focu�I(al#�z[A;h���*N� 2(X,��*; � v� ��Felo 2[ e ��&h 1k B.%<�5$\a�,$= [N,g,or]�CF��!��ATEH%F� ��2( U2Y g^{AB}(wX )[N]$,N re $X!N!�l��Y9 {+}-^{-\-�0[N�H_2(N,"!!%bx fundq�2m surf%$N�* rom 6BM�K >U.� bothyY# )$e�un-r)�%2s�<ign�&� �tp<�� ��Eg�1homotop�A&�. "9u�q� MeBe 'eq:T^ieie0on*P � N}_2>` 6 (X)>!�X,�)�>$0�&� �Zt�Ibul]�B�sW-ndf���:=DA�?I� ��*?!�� lg~&J�!,2� y�aȁ:%e�m�m �w�c��a)A�+M� -��� :s��{� \[/ar�={ccl} w(O) & = & ^+)\cdot-t�\ ' (1+w� �)+��^+)+ Y: ).$-$ 1vY22 ) a1+ A_1 2"� , *�J\iOXQ � \] }�A= 6�x.J�T$} } A_2 = .�= >� �-)}A��g!�E0du�� �  7I. C�:�if�hZ�iLv� 2�Xa ��n! �A�%2)�++ (�+.�9-)^2[N]2� [N].��Az'j���_C}�T }YeP�: eas"(a�$Poincar\' "��,�*��for1s��&�� n&�F�u�4�$�F!b�%��!�-an&�Gsmr&2(J�B��|() ����Bn8_� � lG� map �:b\h6�cb$��BGHX.#� :�� \infty�[^ Dold-Tho�4 oremqHatche�SP = > \simeq K"�_ź,1)x � ,2F 23^4)E���:w�!N �1��"\]�I6 AI�+�6aT�#&�,m�A�_�$ $N_2$, Ye9\nI]>�&t.�e�e'_1$��woRj2B� �.bed7�RP�&� 6P�}T> 4H_1%�;6�ae_0<RP;?b�&�g+5%Q �"�B�(%�*:wJ�� �2y/IEst_1, �_2 Hf h�P��g�, 5%2bGi\��$n e_1\cup !w �R� $i=1,2,�&A�� ual,1O-�ebme�� ductE:�-�houghsas&�$$``divisors�B���mW�*n*?:v��rmc68ums $D= n_1x_1+�� +n_kx_k$9 n_i�N1�N}�$ P ^�$i=1}^k = m�/*Hl�>�Q"� &+ aC} N_1!R e!U �{�Ranx�q��N_2�fB<3 + e_2���{�) �)$N!�ong S^1��S^O toru23��� E�&JJ(D\in N_1 \L6\�D� �  2 +x + y�some � y�yN!"�% �fI�i`�isIK* Qa4�  $R�9(xJ��"�%7�6:W� +�mW&�j; - = T��2+�%WA�[ur�4S4on�# G+_iA� > N�7h!-!,iy$*� ��.f)G6{ Iu U=&� !T$152o$2� �f�1�/���  }. I iB�)\:?��2N�� �o�%p� n $Z-1}(N_�e �#, � su2�m:N.� +_i%1 Z_i6%�isj.�8"C+�c���s%A�$Z_6$T^2=u�  �D6� �!�"��;T����X�N1"�X~"eE�bb� )^{4"6GW_4�&!6 r[! S&qH_1 =�O ,:u$ /x�X.� �(�%gCBI:�!E )�T�Y_{H_1}�"aB/Ti[�Z_ kM� A(FB� 2( :'U.�S��%�f��Xes $S^25�:W(��&t�|!�W � 6�>�!�)� %%�>=��Z�)>�sE�Ksg $Z �E !z2Rz��3 *�#1zFBRz:'-z KeepL inpI1aV326�V Res}^{*,bb{Z}E��T4}}(U�p �k9�al)N�yD$,��7h"� $12K& [_�*� S�f* >,1=>�E�ѯ_�E�\)�U$[;pre0f�L9|mqu��3nf�canon�Mk���1epa/H S^1/1 e�)�2� < �NQS^O ��"I<� $4 U vJ�������ao�_�V0 eOQy^� $L_*�4/_2}ܬ{��K 2�{-1,+1�j��: �3rac�Vd� +ir� i(v)"�D _i v�� vW ^��  � par�1\.2}:>pbW +n*�*]B�u $2_j `BE $«{6%p_��E���3�00&H6�, u�  @Qu�$S�#il�lambda_!�x Cartes C"o,v})q�h � m%c qg�R#  .Zoqp� L Knk2l�E� vu����jj8=��Yk/� ����Y|Qe�$&# &�):re1[�[ =�i��w1}Ui�1e�" 3}5l01.? A"-��G  4F2<� \1 =>4V� 7 Z )�� 8}���>n.��!E��� ݃� �-}\)TM� _{N_T~!�)�_2^F#2}$l:�)$TM!}N� o ��A��eh2$�p�" vely9�X� : r}l7ach8q ,p_1+p_2+p_3+nKinN� �8�B a6e!�T_DJ�-��_�4�3p_i�=���-��� (b$M-S})2��}�a$)�N�.> e�)�ʆ� �]0a��R�\0��}��*w%}�lH*ofV# s $T�n)=M�_uX ��qr���;�� t9� �RxA��q�gy!��z)M� RP^m�*%�w@ ), 1+t)bx = �binomtx {1}t2}t^2 + � .m}t^mb�e�M� ��2�MY{ccclԚi{-}_{1}72� &� ���6} I����� 5} >�� 5}\\��2k�I�&5�1R�e I�50~ �"�!av�%By w�:a@u����q9 $r�I8sh��8�.i� � {cll!��5�By8,�(E�4I}EԨ mes 6'_1ZH)=_41? 5}E� {e�-8� B2!�; {o.w)"V}R�5}E�F��� E'=��g 6!)�d@)� \]}*��=�2RB�12{6��Z*fT e_2)�)�S>�11n)��e] "�5�u�cor:raz�NA��+��+e�Y�5�2x -��0I )0.�3� p2%��1�>�3j> 4B��� mv� =klase}/(rm Im}�D�#�-��� Hx I"5\nR*\a�H ic fZ"�& (�k&� "�_��6h([t]/(t^3)$ ��>T^N=\L%� [a,b�O� $2�B:A$-' rior�\� + c�SdegG$���T&ch� s�\�of���)� Q!2� >| � I�$, v�Xver�   % N_2=!T6� �;Qa��q�3} B��E.%1 a��. 2 b,�Y� )=t ��n!2�-)=0���f� ��"6��2=�ph� .�"_1�1r�@) $w(�6 )= ` 2$ 01}+10})=1+!2 b +ab� iݕoZqwith ��J�|#a �Ix! 8 O5N�w�� , im&��n 2aAj!���ܕ� 1})=%�1Ɂ�� e�_�)�  wF%٣%abB�&Rn�jos>�BMA��E���)= t^2BzI2M�n~�;>�F% [N_12�"%M��t� 2}( 2]=1��!�e�kfw,4l[".�,� V�"��_NV+X+ on{R8�� dwof�:4 {M�l�Qw���j��8g�S�9�T#� o�&$1S&7A� [*�5_oK#g �O$B;&��s��t"��:8L\�\4�:H}�8�>��=�a�*�t*^=% $L)`&`MTZu�*G&� $R_L6��4\&�5��Kte=^�P OAR|9�Aa2ڄR_L(A)�TlD%*&;Jx(%u� Wi�t los�ge�|w�\um� $LY�C}_{(2)t= 2�a��{!G u C}^{"� &N1)�5=e�3�W!�9� $R=R_L"(.�Ra $R(z_1,z� = (- `2�+$REaY��) {���9%B} (Ba �99P�\ =\{(_i��)C}^2\�c� x =1 `s#/pur����K2�l�N-�u.:>�\J�,.JEZ!R�P~+47{�S^4(tv�" eq \pm v_JM� } i\!j�&�,A��7Q�))aR����N�Y��c."�ԗa.}!d!1B's�Vre�%d,N�!u7:4?I63>a�3��?"�:n �%an �FZ�Ac�J�l�U��n.v{��, e.g.\�@i�~���G.x��sYXj A]jE$�K �in-=�naA��,en��a�E7)s���}�"�L؃| befW�"/��e�5._g�!Sp�0Q�4�#5J�5D _oa%�z�%��� ]� the �X re���2hat{R}���!�5*8& 6,(e_5)=e_��lm��ak�7�%W�Yt 6H$. ���e1�d 8Y�Y �directa�k&G := Gi�2��+f N6"P6(S6�Ja::1;�$GA#� ra�r[Q z31Q@(v_1,v_2,v_3,v_4)��>"),>2F3F4)2+� ��m�v� ��"����ven^Ler6��9f :�".�[ {�/5VD�� &+< "]D62 F:%/�m&# ��1F}q$ThE�!�� ��) $va�>�]� 7&�!v Stab}_G(��i��%D�E�. 6�N��*Rw�ml�za�SV��$L7mi?R}eb .�/,  5 %_}�)12$�](upva2�Pof .�L $v_i$) ei�(>�1? A� >3)=E�\q�(� or} ^G�*: �a >3 {4)3-^�Keym=er�_�!H �LM�, play%�R�s6�R!�UD�\��PA�$180^�="F�D�L4 $.F}�F=�rZ�q� %8 ���P,B�#Ӆ".1 :1G.onF1�ysm $G\J� {"^i�P� �.�>�)���>�cN B��&}r�.�)�/Z��&1 .K�r�ofF����PY�l%�A�&�w��&l�\J� �2F�J.o "c a y�7iT!a� f��"Y!�e��ul_!V�Claim����p*%J�F�� $f:��e�.�K S(U_44���0 $Na��l" ?C�(AAc2U$a�2s.w6E"z�!i6YG-pb�P�R�p=E�iM)�.�L"�"��vV���*5V%]? _G FX2x �q7/*���  a{2-AH�"tiq�2���b�sAe�32� Y��topV� $w_n�%݁�v�4 ��itj(dsJ'"�"� (!�) smo�<2� $sB3/.�:�1O FOe'Z �C�v��" M$Z$2\s�Y�X $s��Z"hRF�is oddE�Ilanguage�I2=��k�^%UL� �-#,w�:P!*=(M,\psi)>i.N >��2Y�E6;�!q�>$a�R20I! e D&B�.�a�$l *�$h!J��YO�wc'b��� &MU�h,� arc Yq-`�Hj z =�)& V�0�Q}T�rD$A&/ s�e.�($�6� ��V�F�Dphia�>U��e %�� _54_��p4):*Fc���!BaM�"V��zdNAbQ4F�]0��nj,to��s!�Bv ''��B�$!�-WzOM��G '� �&%)$&I ��Ko�d "QwasG�\be�G�\t� .f�0#(2wX�A�*� *�F7%�N��%-&�  &� J~"� iBOݼ:� ~ � ԁpsi' :;6X2h�a�.$. ,Ytp*���Es3a ">�va��!K�{��si'�Xi�\� 'H $�;6�G '$. c(QE�3`Z��'*�*&� �/*]Ei\*� SYQ� ,4n� no f&�;���[$s.5E�]�,��.kq s"RXoV f26a�4!�uI� ~!r�Pa�6P\�w0o�alwayX�b =�\ S/��ph�507� Z(!�&~8 :=������ps����.Z/G:k�M,,��\l���A��?<64��2� �'')"�+:mB�I�' �]r�#�$(r]$0�Aia:�5<''Af 8#`U"!^�e$).��r�E� $p :"/��;,6� E�*� .X �m")'�A�SJ .TJ�((%\�%&cloud>#D%/a*� Ac16d�z*M=  ��`9S��W$vʶ "2F����r.�x�H}�7{H���wy"�=&/r��c)tat � Pxwݗ�|u�on1��m�n $d$Q �"Eх��M�,i-PiI���=o 8 �"no $5ZhIa0�p��A�ach��"Z�,at least $d-�xM���oJ<$.2pɏL2�ae8U���5��Q(�.q2���c�F� Hs���Bc!�ނ� a�=���%�!��a"i�\mI^ac��nt��&�!d�!A7�Y�t"p!A�*WY� P�Ayt�|^�tY.WF� &�O�%5g�M�qa<6�~�6��*�$�L7��{de9Gin'#! t�KM^ATk $�V6|�Pm.�"�J�0CoF�'�S mean�9��should� �!a% repe��patternA��1� ��iE�r$or s har!J rݖ.�oof2ek�;�q.�5!r ya:�'�br o�rn�of %]"j6�.̅�8B �S9�f��E�YZ�e>�=�V��a�eT� jX%�~�=r�G3$&�6d% .}ae� ness�iGdei�E B� D ult:��B��j %6NrQa�j ��v� y,�rV� 9HZ4 3��hs�2�Vm�bsemblebpb��r�Ymh��F��cg�B�*� sV��0� ��b�� >�d �M��iger'e7� ab��!�� ub!� ��q�R}^3$,o%a� ��I[}nKtr��e:*r�E�ofF;)M �;�*e�mTw`a�,�l{,E'�y��ry ��b5��� wTar�bGn�D*�' phe�no&!�n�}�5�}"�52 S�co"2А�S_D�! a&G�'s3#3�'5��J�A�o"H�J<,�J3��three�(J���(��e amb(Q ŁKo � t oc�QA�|��`)6��)*��7s<�canm;c�x�!a*��eA two�� $A,B.&RAd>s�v�U�ce %� 1���%�!�A� Ɋ} qB�.� M3�Xan � �NN%��iٌaneޤ2J�2$.! .e� k!b �!8 b� vF�a|Dń�7+ .0�5Y an&j)�� �2����w�-���06�rthZ�"��a�.� $M_3�'r��0�'t6�D>�L)�I���~4.9.]P%�5Ӂ�2qZie})"�Q��S2ew&-+Ati�a�� u�^>�ja��f�- $Og�e�u&&�D2c.#�!A*�w"f�cho���M��y(� eV pas+y�z%���>���!&}Jh@�P�� :} C� a ``ha�b'']��c�?%[�~�U2?pO!�H_p2�$\JG�54\&` ) �?� 9�p�L�nd�J ��+m��C��nu,�H�qGA��^�V�YD1I1T-cl:`�boul&b���Fm�$2$)�,s $P_2,P_3,PZFAK�� i's2 � *�%9P_i)c $B@mv��"�|bJ�đ?�*��~�H_2.f $Fe %�)%!�j��P_z�Ij9�� ..=��Y%�IP_j�5h>6[� � T� d>�A��`yq�ב�)�rB�+�,]Z�q$56y|.�%�a go�be J�.6t�.�ra���,��xW >6��``fibereuT5 Grassman��#�)�-B��,^ it+&`42�E� i� ӗ.]�A�t&�B ŕS, �V1)��-�&�`&� ��2(R"��!�)jw)�̀Ŧv"T~a�.o$�be7.� .iFh!�6bP �bJb��!� 2t?T!!�B"a�i�M� �V�!.�� ��Na�!� of2�F� so� omiH�0 tail�p>�2CT*ll``�zE''&� � �T 6+}a�.[+E=v& $f *�'\�|p"q*�# s~By��^ݗS  Z�# �#&�^� -�&�n�ly a�.je�G�GO�m_1l>c)66�~�A^nqR"�q�o}�F�kJ *Rg�V��}, ���.�`M0\delta_1$. By�y Proposition~\ref{cor:klase} the map $\sigma\circ j_2$ is onto and the result follows from the exactness of the sequence (m�ieqn:Koschorke}). \hfill$\square$ \small \baselineskip3pt \begin{thebibliography}{10} \bibitem[Alon87]{ } N.~ |. \newblock Splitting necklaces,�{\it Advances in Math.} 63: 247--253, 1987. 6x8]{m88Vx|ome recent combinatorial applica!�In: �pYa.~G.~Sinai's Moscow SeminarBHDynamical Systems.}a�Hvidence, RI: Amer.\�L.\ Soc., 1996, 11--2!� Y�vis84]{} D.~ . yNon-part� able � set2�0{\em Inform.\%�@ess.\ Lett.\ } 19!e84), 125A92hBar93]{(} I.~B\' arny.� GeomI�A܎2's!�a/.H New trende�DiscreteUComputeyalq y, J�os Pacha..Qe$AlgorithmsJq�xcs 10, Springer-Verlag,} Berlin%�3.& BM01!Ma2001F8 J.~Matou\v sek.R0Simultaneous 5��EHmeasures by $k$-fan:�em9) .5<}, 25:317--334, �:�2�2�� Equi6�two2� a $4�.�Ey5�.�.} To�E ear. (pre!{t)2wQuad]{��~BeckA�>�!�. In "Collected Shorter Plays", Faber, London 1984..�Bj\" or9!�Ljo91} A.~Bj{\"o}rner.LTopologe�method2�8In R.~Graham, M Gtschel,E{0L.~Lov{\'a}szA���E�$ Handbook��2`}. North-Holland, Amsterdk 19952@CoFl64]{$} P.E.~Con� E FloydBO$Differenti�Seriodicg�ә:. 196!U��Copp71} W��elJu\sconjugacy}. Lecture Not�^Mat�&� 220,J�7A��Dieck] } T.~toaDeck.K%yTrans�&�^ Groups}.�de GruyAYStudiF�8,%,�@Ap2{ FaHu�Al} E.R.~Fadell, S.Y.~Husseini.|��ayEFM�yI'nfigur �S��6�1�B FeZi�FeiZie� M.~FeichtE+GZiegler.�On orbi .{�I��sphere:�it��$its A*L ,}, (2002) 11�\ 85--10�U\(Gil58]{Gilb�N.~ ert.� Gray code�� path��5 $n$-cube.0%bBely��.\ Tec�J�'�$,58) 815--8262lDGr\" u60]{Gru} B. nbaum.eP�%$4mass--distribuN !c_ boAd0 by hyperplan>� em��ific J.e(.}, 10�60��7��6a9AuMa86]{8} L.~Guillou, A��ri:�a 0 la RechercheA�la1� ie Perdue2/0Birkh\" auseru !4�)'s� �4complexes of iF � func).EvB1 , Ser.7 Eu61 (2)� At30K 1 endB�  docu��} ~�\c^ $[11pt,a4pa��psfi]{�`cle} \usepackage{amsfontsY[all]{xy2,H[latin1]{inputenc}  % ac�s.[<[dvips]{graphics6L6x2� symbB mathB textBbs6�SopnB(thm6e!, g,ro�ng} %=F intx�J,NON FUNZIONA.<cd6mamsxtra6�rsf60{u6�8[frenchb]{babel6{:��doubleLing \pagestyle{plai!% thisB� \let\small=\footnotesize \def\longpage#1{�� \addstr =#1\.� ),\topmargin-22$< "$extheight42"VF0.5 v%�\aBF .?oddside �C2?width >} �{0.53} %pSe� subs t;� e.c.!;md� {\v-\last \meamounA�!i7|dfn#1#2#3{{\sc#2}\ #1.\ --\ {#3} �,th +mB2\em#3} �!� too=rr!xarrow� WR{\A� bb RuIZZ 9F{\Phi  2b{\beta .2f{\va\! 68Lt{\widetilde L�:{\��n\�  8D{\�al3nTidT{{\rm id}{\times}T} ;s{\sigmJ�;g{\gam /e�epsilon2m/ G{\G./w{\omeg^^l{\lambd�7A<sph5jSF^o{\th!V � q{{\bf q}2*Mp p 1 P{{\OP21mg{\h�Ke{.6cmAs�X 6XV6H{ �YH4�`AɁ`{\:$} >Sa{\alph�k{\kapp^&C a bb C � fin{,${"-$ `_L1L 1d{\delN�1n{�rm{n}^�$}-5Q �Q a;E�E�B 4BV4A4A#)�m frak mjO !iOjN�N:4setminuA�!�-hamphat6>= ra{\�*4 hook �4e�}� 6Im �rm{Im~B�bar{\ov!3sFAAcript �� F=ksA�  '!P1sDRAD}} @� :@T@CR@C RP � bb R�9 rm P% �CC)�:��:}} %�( %\sloppy %��%�=\normal�Ɛ \author{by Ricardo \sc Uribe-Vargas��{PQ ally supp� d)" EU CentreExcellq$0IMPAN-Banach #P, ICA1-CT-2000-70024.aE\ { � C! \`eg�z&�$H3 rue d'Ulm, 75005is.}\\ <u�@��.jeu.fr \ ::/9�(m$}@/ }} A�P% Autore \date\emptyB8% Data \title{A�Prox2 In��Swa) tailU4Godrons (Cusp�Gauss)�!Global� oH 0 Flecnodal C' � �(d"2  \}&?in{g� }{�E�.% erazion!�lle�i �`�aKC % default!�� )}Ń@em}%[ w].,*{ 2-6#lr Z %Left-R�-=60Euler , 's Cri�o� ne�le��{L 6Is Sepa�$2$-jetR3q3 $q$-*ourR,+*f 0  0:�"a."AN"b."BN"c."�K9%* f bf � D2D{clai-�C 6Gfi2�Inf.%ion-FoldU".5{p&~, �*�,2**{.%�.2Ucor�$ry (C.&*'3:( * (of� �,G�})��6'defin�2d.�DV(*)M)b*�$� SCo�ureZ|{exampl /E 6  # |$-щ W,rk2:�Rh 6 * ! YR"c XD�co-or������ellip~dom�.�A.OAffineVxE.)&gR�L.,Legend�-%*� \make�`�KK�oindent�;a� Abst�.  $ We show s�. geneU(robust)* pert�&8of smooth surfa/mmersed/!� real $3$-;  (5O, a)�orTA�ive),:nbourhoodkamg�64} (called also em cusp*�F}): alla�) ��bolic�,at wh�@ (unique) asymptoEEir� is twnt��M �. W�hel�these�1/and a � i" th�Le associate to each � wKes� all possiz-lo� "i�'J�� �k/�} %(l(� 'p�.�1re�a '$hav�at leastq+4w tact� %MM ) at aU>s&�!� $\R^3$. W�Im�results,7 in�#ce:-� In a�&)� disc!�m2�,�:, has an odd��/t�);%}lf-in�I s (h� 9$ s>' ).} �� yp0em Keywords}:&Q)aEm>, TIf�1s"P#�.B,]~%�,>�,A�} ,MF0, wave front,.�2m. � �.�MSC� : 14B0#$2S25, 58K3 60, 53A2 13A*<53D99, 70G45. } �� J \-�{Introdu�}�: J }ic:�Y�IL%in u1��(to three (m�y G )!�ts:I}pe��"M�ɻAgi����ian%�a�� $Km5 nega�:, % ---e�$econd quad� caHmAiIma�� � e---e�>J a� �e�J� �?�~�!2�!� ���_E�.r~vanisheA�z}g��ate. A y�^is��ar�2 d�3�.�ip��)&�f*� �o� ic -�s,�3dќ �s. For �  (+ �7 $_&�4}):- ��.�%�AnyQ��AKa�� ��f$ 6ACa � $gi9~VA��|�,p1B$g$2w��E���i"x  ���*���kfB�Az):Z}5( nextA3,well known. ��8 }\label{ �cy}ZHrm (\cite{Salmon, Kzwegpp,^2ttonova, Landis, Banchoff})} A�}* !0^�>��$(simply) �J�%'.� } AranyU�6��h��!ZfoY2� (*� I�e�=2}B 2�8� fpAN%y�� boun"JKa �� x%H!K)Uaxnd �"� [ly��)at�S�_�m} (thusA�lu RmM�).9 E�e�co2� of}�$S�>!�r&ure H$ locuey$�*� of9QB1gbiQ&e�s} ( �2areu�toBu�at�5�* inct t�ItA�y9f})A :9F��c.7��.� So%]Uz.� A<2f%o�S!1 mutuuu�!+heQ� . At." � sa�w1�E�s d�+m� Z� $\rho$�O a cross-<o (seUe cr-&� below)� -2� R� se� ��,R ore�t)2 valu�� � 6� rho-� if�$)�tre%8six�6�, � Fig.�X:G���:� �!�%zef:6��I"� ed �4�useful��+st�<}n�& (p">) d&7l:r*P �So, ��,�iZ!�76a��>� ����ig:�xi�DY��� �ual��sIK2�4-� s}D09�d+J�7.1 27_ I _figA�OurR%�reto seve��(al![s a:�, �ici��"�8l#�(s (Davidov � }),!{�BMDI7 *12�  (P> Ha]> cw,  tpwpUA� more��ely� 27o,:`ofAR��I�3B| (Bru� Gibl�( Tari �$B_G_T_95, (8}, Goryun5g 8�+L� ? }*� Pl�O�, Thom "b- }�08!��%��org ed asns( 1�backgr}e7re� v 6!%5,�KE�R termu_ orde<�Fax� �N-�� 2���! we gbs�E 5�q�v 4,!��2��m � ly.aKn�n2!proofut�  H� ��9�\*���Ac ledg�-Ds}.\ ~ I would lik�)Lthank S.~Janeczko, WA+mitrzI�he� a"b�^+ ir hospitS/A�~1,nice environU'a/do}�s, F.~Ai� $d D.~MeyerH��+e�A` to E.~Ghy�D.~Serr �xre�5 �*�  ,gtp,Levelt}.��J* *�6�6� s� }�N"N�`�DN@});%� � (P) Aq<4 !K"� �a ), but a)A�&6�J OFY},-�s![ i,A�,1��=S)h�A IA,��� ��F-[%�:]=F�"�m: }: i� v1an.�"� ! M^s 3Z\. OnOJy�enc)e���IM�&;f�� type� \ (g��� } a=�I� �!y ��%�; (hny-� node~U�he ZestF:��:� ; (b^bi R] al � r �?]�i8t5�DE ��$��� (Ih.cbi&P}) ; (e!�E�=  c_ "h���d V!M�@(lJ�CtB��I"F6=A�r &S �s�L-�= � is =F� in g�AlA�he�!�in!�ogB�' a left br�, $F_l$ (whit� ['! r$ (blackse ,es will be " �� xA�*��;$Ce}[ht] \�/e�He{\,/ =)1,�- =4.2*EpiCE\}(0,0) \put(71,58){$H$} $119,85){$P$42,121){$E 67,22){hn*&H 160,88){gG 85,109){e^!"91,60){T0206,2936,89.y255,34){%li00,26r�1� \cap��G&!�8qUFA j. 3�)W}R-� 1 O ``��''��du) R.~ V k � o�w |De can fi�R$s ``spec�٦�''[ ``SA7� map''� keep� 's R�kce�:sI . H��w� llV�&�n�0)l M above 8� H���s6E2| 'oeYl�c�  G q7is)Nk�ly*0Ire�fea�Ÿac��a�] e�st�C�!sen�at unCi>l�� urb� (tak�deriv�togunt*ey� not/ � onlyKorm sl]'S��y�x4�Z!�� n�L!�en�! 19th �@ur!�X�w K enui('"���a"�D� �Ŕpro�nt work%\4Cayley, Zeuthe� 6�i �Fo��venQ<%� (+�]��� e s up �5 (, )�!Q"Y(\ !^%��!E�pe�#ly�n]+!7L+ })Ef O.A.&$&7�ɀ�s pf��+Dv:� _(Dima}) who ���J �!��).�5in%FA�Z�  d� Eq�*� stru�>A J (bec�G�A�!-I� ]=j_� "�${�-o�%qM��6� q��� ch c�b( duc�E?a&�u�An���1of�� (���)��&.h6A�-����se1B,� �tooE� analysis`B[%M`��"9' (cf.m\�.),1 an!�e!� ce 'N~ is fixed.vway!�6 ]Fx&��"z ~ `��ex�� �:ly'�I�enaz�nyN�, :Ba2O3�q: An �?ɬ, corresponds�4aVG>L,�Q�PW $A_3$ (5e)�y.�avg6*.  � ��&�t) ����Iz4$} ur� (�w*�.bor� d2��4b� g\SO+d"�!d_rho=1�� �(� say"*�is� < } if~�bwu .�. All1!��w�(asg3"��Ae xa�B)�:m�� s2�(2����g2E�s) ��extensivr uA�by�� %ConsiM �a U� ph�au�A� � �� !intK(�K��coI� te s�V@) $z=f_2(x,y)+f_3 \ldots$�$�$f_i$ E%a�I!g#polynom!Bof deg�$i$E�!.�^K�A "(�� %�Fɾif%i�~if�:)%$f�Z�)!cubJ%$f_�( Be $:F-ekc1r�,admVZ&�'B!2��}��we*@ be�)t͉>Xnea�FvE J5�*i Stat��r�)U�wwU�!�paiif�L��sF�+ /B��u�9��n�eg4c o n& &s�VO1ftE��BM :�/Fixt�n/ he*j-$\RP^�.orM ).4 ��i�� s��� oughq��[=- !`�F��is1E uishI a n �� way: twists �Yw% �# (a-3!. �NO,ci �re�Nly�oI�8m���2sai& be a-��(%�) )�U�rs���.f a�!p��� l!�) (.%U�9ve) fram�5�5�onq/�-�}�%=� i%��Ze>��G5C )D�s)D�%.���@ln 7.9��=� n*6 $1"��M9P/��f�fol�.� a famil  �yR%��" .+%"B�s�%~ �Q�� �HC!��mO�*�BqC\"� � *}%H( E}) :�}��. r$)6� �c�]a3��E|hB%5whose. �, �Ing �R�>�h $S$,!�m� ��)>S��:2 % &�s�.(�Xw V�)}�A,�!ly�oved (/)s�p )�U):�Bs,e5-evol�V }. A>� in ��e VF"H$)ujq�)��Eh, s} A- a   �!J�&�X%i�A�"�m�w %�TI���%(13,27&� 146l%%�@ %f%�J"1."%N7:��&,.dQAO �1m2^�-*�,A�٧�FAD� ��#%xZ� �a&a�N"8.xPvalD�sxbd ��zS3!� oscu�Gg �)!.��)}�>��i:RMa�! :`3va�O�4���Ma,7 If�f�arbitNR� 3 �ed�L �� (lengtB[� v�V/ � angl)Tetweenr&�� r�o)'�J�v tor�W $\tau$I@�5ezu�6�02��%��I�is caseeQ�5%XA4)�,i�or=�� �a3+ satisf� >0$, <0$H= �T���.^��NW�I  �%r}M0trami-Enepper�ԩ�8 at- !U�)E��-��� /Vb���ɸZ�!��by)#D = \pm \sqrt {-K}$��T!�p�bs.^<~���� q�uq(E %*A�a�ON� )1kU&Q<"�7�$ ��wo6� re��� ���A�ah!d!� ����3$N=��c �;1.  g �B [6s�J� vno=6. How�)�{G $1$�f� �%"Q `a�n�0� a-M�1&� &I�(G�C � 9�. %[At-ai�:�+M�'U�Q��< read! []+ %[Say]$th� abou� �1�C!�*� \] U�$�X�. 4 Let�  6�.  \�U �Al"� !_i�2AP���3)�e#@r� &&i� 93;$g�.n}1�:A�!Mz D�at?"� 1 � � *2y F b�3i� i0�Bs}GR�3&o@�q�\6 Xo��-X�PŌn�1. f biheF^)>Y q~����>� �Wrs%H#true: A:Nyo{A�*z2�otDmessar� Q5��� \s"�M^D6�0! �i@0!�)�"�sec:c*�0�� +co=}.\ ~ .nt#:h3�3az�"a ��`a�$��5� �"p3 e"ch��mMI���Ns��2e� } $D/ M�|�F�& l�g4:��&Q:�3$�p urve�isu y� ^?$s $P$ (��f$F$ (U�)� is fj�b}'ear �p�cal� oET! �J"�'s.^]wa�"�..9-biD���/v��vaaBtM9��9 "U�$b��t�Q�f% s $F( P�$D$voMG�!"M%A"�2&� : \\ 6��# ; s $L_mL_PtL_D vL_g$ UE!�NmanifFofA~�e�[�q$, $PT^*S$)#sE�g1Eco 5:45A�,��Ѱ�%D.* �7s�nZ��� jus�^�a� pv���)a��fibre M��K1��% \� a�QS$E��0)J��Q -sam��F $\Pi| e�8*� �1"a����6� s $\ellI E Q ��M?o�! origiib�*�.[ �"�5*�2� �5(g)�ї%f$>'FC2{ .7� ��7� : $|=(�F,P D g).$$ &.�� *d1bf^i�* Ac*h7P_3's���$ "}"�6�E31&w ��� sentL Q�vB�"Qa *j#d $$z=\frac{y^2}{2}-x^2y+\lS x^4+\f;�- \mbox{�L $ +\neq 0, L1J@$)} \eqno(G1)$$ wz $\f";s�]f fE 6x.$x�"$y%�� gre�]nD+�F"�A�� "P��v } M��2l} g} �,�.�� E?$,AS^F �. Pu`(af f�-U:�$%C. Ico&�d1�$7la�rho/2$B�It tur� � �mon{e $2$P%�DѨ`$��*���tf1(��/ �$ O�g� ``A0F happens�(^ inBD�( �&�kMr� ��MapE F4Ne� c 6�)� A� ��q^$�nv -jmap ,<tau_S:S.( )^\vee< -e�dH�|�+ .���2� e imagA] V< |eVH��.a!-SW( Write $J^2��/ �hse��(-�E�Ng:S��mEM  B B�Mefz �� I $\gw1u&�'�-Y _S$} meaIT, 7�i�ny � �&�k{iag$�f:I�.�,�#�* >%5*(� ` !05 je #1%n��!&9%+5�*�@&�?)�-jH0%[In sui�*�&�!�(�2 1���xtif�5w1K �P $t\mapsto (t,ct^2,0)� c\in \R�x�=�Q�<&���rv2�31C�S6�{iC� w$-ll �4T=>`Cl�$%~�$B�E:.�<��$(a)$!�IFsVGllVE"�;�Ima�s$� (I q�shLq �� �4�{ gi�,�i�a�Z�$(b.�E�i? @e�a"�&)�+�iU�> :�a':� �b�c)$-�=�-� y)}:=x>��"nye.� Q�,Q��,=z�A�� p��.@N"�M� %T�Cit"LiMg tant�aH"81<�:��%# %�>f �� 24v �-nd �ez� � J=4 >�*_ �mwy=x^2} O�) \2���"/���0 (by!���MC!,-)�*2 $ $z=y^2/2* rho' /2) !/;*F�U�*&�)� �: �is�bh(e�$�� $� $-�,A�!�1% %W�0ee!A*0?��%B�Fc�(T t  ��-�e�5��q�^EPI'�� (sB+in ].� $�en�7��e��-, ?*_0�� ) %�0b!&$T� �C���� a�� g$},�'�< %m�i�7 %&%�@%(1) U1> �>�G�bv!A�� 9�o�� ��-m!"-��!xT2��Z�2)��V�2�<)oM% ��BM���TQ)�1-�� 2 f 8 %$c_11� e�|wS�~�}R}%G 1��_ Ŏ ѓ {)0A!S��D%X:5D$Q2� a6e@$z$-ax�#huLsam& !>T,��%(s�r:�H� �N� >U�!v��KZn;�2��)s��v�& ��(�8as $~y=c_\sF x^��P~i� D,~$��*�IG}  P = D5e 2���cV�m�UV9�6q]��#�yi�^C�3:�*d � ���8a�aHlvn�#)a>�mE&�!�M� I��E�� D$i�:�=�y=0\cdot!�=0)� $y=1$55r2'Va�e  9�) ). � 2�I���s)�%�' "M � ey1{R� $U( � e�� �HO 8=1 �c_{al}�"Z r�C!�: &R)F2-6� } Gi�7� mp2�> , �Gr&six�sWY256!(-�>�V�NiA���B��}�Qt�9�re�4en��in*t(:�)�#ac6N6�� �&<�j-�&� !UD&�%%�F^)� Ksto6���,array}{ccc} �P\in(1,\infty) & \iffv \sD#\��-<1/2t@6R /%6 / @941,�@ K�0- .?.163,26f.j:<0/290>/�<.4-�"�+R�@~� (half-�B  B�)�OcU9�) 1�)C 00� (thicD�n�A �(brok�=��,>O(horizl segT..t"&&INs&�A:QpM�6�557Ep� al� � !r$,=in6) J�R,�=����7(9g_;our}) &,r���L#FL#9x�� -&��3#3#� U*A/)��*�3� �v#r �udex $+e��0~.�*}��.-1$k0f� "8 � ic")�*m :�s,J&�FB3,X� wards*sp.~awayr���q*%v} (c �ks1etRemv} ` �e2e})0 Jf 1�m J0-��HI0�M 23,52n(+)�y�E37>- 2�f��1.4��>W0AU15�ua5� y�V>�&t"�%=�@=A B��A j^ Q�At Q�,� A]s-�`dJk8��%is"3"��" LE�B�� A $S� "�%J*����m�$@� N�#"J��9"U:�#�9i.��IpMy c#muype�-�Q,%��&?� ��, Z$P2u��O�y��`�>M an�lifa���}1y.) ��B 9!J&z way�`2E8M^c��ct9c-F a�A�ed�Vn�ti�&r��:�\A +CA6Oa�� u>�!�eG ssum�_ 8t *i++�$is T doe�&2finc�}!� A%s��wo ��!�e�aGT;G� �mEQt�%�� �:Yq��A� Ifa�%ƙ' "�% ��q" �!A�Q�-��ols�K be�ra nod��a f�);j2 �be`d%� ~O-1�!�%S1a saddleu�eݫ�3}.qp&�2W4HeNtL4��3.n� �i 80,36= .�165n26F>N�ByAs�! �qQB�E�"G َ 7B�R.#:$< ve-C$A�M4QM  (1�)!�a�E�A��A?2����� (g)>1$O<1o(? .��C"�CA2|��|>�������� nvex�z"� h")li5�=�+en� ����e��7�!(� E�,uC rior!)�E��2�E_$��(�)QEisZ.�Z�.�J >2/36� <P\� ���1b"��1J-k�O nI5N�8&X *�XP� 6!��y�d."� !� %See��r�u�of�:cf�R a} \.Pc�"IɎF}ny�-��=�� �1' )(Z"y"�#� as�=l���yqA�7o�K. N�$Q"A��<��ss�O"`0-�2�9OA8 $D$ �$Q F">:�  More� f2I�� ��R <18eQ N � s� P&�u�&Q�͚�"su�a�!�asm` IŞ Ig�y$>SQ�Ip��*�]\cCiOzaibig�n�Qy荐�G} A>J"� �*W)�%�ZvU>=BS"&�\*5i��of>� y:� ? iYM iqsm.�sA�*66�YeC n��Aon�# >�at1b�*S d>�Q3.-$4I�2�]a�d���.ş� t? Z@$+S� �a6�aa���m�1li�+r!B E��)1�%tCst*� � ��C 5{&� � p"en)��26�)�� �ܩU� u 2�( (!:�1#?�$Om��9+sY�&� �D6�0Factoris�T&�Ks}. \po�+$\{�01, L,n\}��af� &D/]�  >�Y:�M : (i~#!�+2iw`(jv�A�8!�llel ($iV0j$i,j\in\{1, ��&#nd (ii)uo� $iF), !O� t�AR tain# crit�Py&� ~�$ $\prod_{j�i}�j��%(�qd> �guarante�-s�t�YUVmbi�� sk� ^uc�' _�3n$Z�Jr� � =3� fV���^��a?yha}, A. Ortiz-Rodr\'{\i}guez�E,'$� ng�Uat!�E?Zv!��n$f=2�i�&�GID� !,2I� !iW �O��>P:��$f'EG d�(X��3�(ly $n(n-2)$�g�FA4��.x �� all_Ѧ}GT�� 1? 13�6�)B2�avi�z� .�>" ���zAid�n altern;X�very 7&e(=of.� K2:�(�>�.� 6�,� H��D��2� � !�� c � �&of�D6sH%uE�e����y�x��a "n��%Nn � �E:ELoBT�.:C��8"�H! !7:��SS"��+ } Ea�Wb J:`naturc'&�~ed:xsE5�\� 2� )<"q+�(Qs�Bs�_�� by�Q^��!��*f��isA���C e n�&�S� (�di�( ���%}�$�c�3�2� inuit�W` :�e�Td�4A��$E� "GWA�e!�]�kK?�E��Z]$E�1� M� )��w�>g ���s 2n��d U�:� p5 u)K��blu6�nAO&�h:���t2>�$&G/�"^�+"W $\RWA��,�wს#!�mO��J])�Aֱeng�5t)�1 :�� lr} &�2gu�j��e�� .�s?:! �c&'.� �& U5�semi-!j!��6�),>�a��M�V �e " 7��L %�F�!�p��}� w;��youCNnL�q� !�S$1 �1� .;ndM� �1!�!>�-C}0onw�=}5:M �|{("t �- %s2����g$)%�!x�� %V�VnHN}Ic(As)z_o:r 3h!G 1:�A �?5>�U0t2f 5$�!dK%6�xo�, ��!�g��a �� & �J/s-{(�p��Klr}~ �)z"-x ems) togeC � �f5�� N:keygW ��g �m:{8 (f�r �qVy /��s9v( PAG��z��]��f|�dden. Bvz�{no"� TXa.7 �%(BmP� �3H 5��}} >L�-�� s: D&pbM�s�y=0$��>�b0�� A�C!�prece &zXuUK quesx* aris'9W� �Ba~D2�e]�s $T1$?.V �!� �<E =F΄K� e Nmea:ɯsT�cpa[ desc�Y0b.�`�UJl�= d86k jU<&E��p"�QR"s:9�N" (c�U� A ��;�A]c}�o�IW2�D. g !�<�jetV,J ("�E).=,�)dQ,![:s�JB  ��bs[t,� %�ic� *�" ��]A �= `inN�ɱ-� ct' �A%�ml !4*O.f�4to)�st<,Y+!�:>#C&j`z�A:*) � H � �1�& �fdd�B�JK5)�$���vE*�;��vϤ�breakosymm y��k"�8.��FĔ.fNH�=� %�!�^D81�>��.� 0$�7.��!!CE^}� e��&l�$5$6LV !� �W �C�(Y)�z�Fm$ (�'�7�I;�= "�V�J \#2!eJ x^4 @�/�$�J� c�OjkJ_ %&6lJ>kJ.*�^l�$E�� �&� �%i_*hO%5!� �Qmulti�y qr zero<W&�g\�fGCta) $g!!,z)=-z+)B2�KrV%8 $\g(t)=(x(t),y z(t))=(t,rtE�  � �A���p$( \g)L �1�t%�at^5 &�h ( �$a5�.�#� x^5\F1� 3s=�e�-����� �XPB6�h�'m� 0aRB7R�a��'Mq mJqY�Jr1�_4 �;�>l 2!��:2� �!qy� Z  ping&>-�-S)�.���2� [.,��F�n�.�k!�no.`:��� 5icM�� :�!�A �afF�:?E0D>fa|g$ (or, *�`��Kcdestroy�"YA&/ $ZL[:. ?!��Jt&�A&j _*� =�!�� F� ��>(�w.�A!��>��!!$"!"� .g!� �� riQ�nt� �}��e�\!�:o.Bsh� 2� kl.�>��T��m�D s.#n�s�tUDR�tra���!.M J���%���/:VZ�a����DfF�* t urbcU� !��^YdͫJ��0$�)iu}j5]�,/2.V$5a:fI��1�Ano&@~�9�9��9��M8#Z)(*�9)��a[�>y:)%=0���e flex� �-}z*�P3��FA(�� �Um(�) $a>0Br�!R��2X?~�$ �<7c�7p >0$ �hQaFb�)3  Inde�3��power se��5anud �&�B=BFvbarJB stargU $$y=�(2$-1)x^2+10a3���m7U�} ?tB +2ax-,tV[,�Jk&��LwFvehd�F$:�B-10H � �D ".h�~!bif"btof=N=����ř�T=�)�(_t�%t�%R�I�F�oA-m�72�s�wc�O$� �� $S_0$6�$g_0$ �V��8�q� As $tN increa��%�p:�o$A~��k�e $b_tT$��m߉&�F -GH,=5��o,a��,�!,+oI#!�:I. Rough�|pem|, `6��super� O2�a� 0 'J��9_�00��U(��1;� ;:"�'$tB ,!�*S} �2!tc=�t$�se�*�try�D �2�&�� �1ef�& ll (7 )E��sig�C�n �{JJ5�"y:. &.4I�,,B�+h��E@�Q��H#2A� l _i�5� NotA�p"�_>1�@ eP|�T�u E�, �|t|�=�%4��6�I���4.�S��c2Y :t�*� a�u(:�Q;2�V� �e\S�?�*#y-s�M�:�=��.))��Z�bi)Y��1b�1���Nf=0�d1$Z9��= t ,�Mt  aX� �5� we n"�$��oՆ!� collapse +ubirthwoM�uXindices �8 :wH���r.�lwe*��;L3n�A��Zs�: &� 9D(yS )^2$͏�6 �WM���" adA�> e�&�:�!��x^2��6�� s *�S� �VM}Rma�$S~In�Heb7-�%�iu�lF�y@`,Ŵm�/�anɱ��/�+: ^(�kx^3y$:$�Q! ob(%a�s� (a"�\)s� 1$):Czg�&��4�!�� whol*� 9[e i�.oy:�N@�� $+�G-%%$�6�~}(�;�` 2� �� T2�betU^@j#���m�� 6 2� 6�+\e!�� � P b�B� 10>� en� e.� 48:� e�� bi�� ^�B��&��1�Y�&Z<rX E�Yƅ� a��w�d:B ure>h�%8% !#_$% �"A9r� $\e 4.:��me a8"]@to� ��O����lieB1 a� [>aLWFck)wo6� I�Z(,�W� �Ha`�� � alT �`a�6�rO� f�e*-%&�V*�$i����"�� 1�s:}�!r>i3!�}:�xi{�*3o� � &� �cc|� >X)"%>�"B� is ~�*�q�"N a/2_ (�)U!q �r�4�3�!���o$ r ��!noldcw�:T �T� K:K  2�$$A�:� w� � F���41d�^)�V;�ic�Ja-i|�� f�j� 2y�wfeem� �\"!fo�'Yb' T |'r�<2r �:j f.�1�& S��t2�%=2�6ot�l,� Q� �!m).�y=�c��"�"2 *�r!�limit�q� 2�!�� %�w!� %�/u)�.� mo�L� �!s $&�;1 �B JB E0J4d1�lI�,:N� �< < a�&��$!�% �5%h�R 6�:�!�s8}� 9�$&7� �N{&a Jordane> ��k�XY!�d.a� P�$ JP����1��2G�AvQ& Z;6������F2" ��ءI� a��xim2'w"a '�ic� �a7�Vq�w"���e�)E�a�p sheeiboloidean � soid6�D ll0�r"�A �X(9)p�� �pl`�n �npr�lRGTnec�ryA<)"!�}E�%I"�;%�%��� fc��!]-.j~)�5�%�2`>��D(3I��Sace�3F�M�iscH�[E�:�7eY$T$21 3$&w �s: &:l7oSegre � },*02��com)�c��%8&BpE-�:� F�(�1����!�.��s��h%�1�to ���>�, Shu`1o !cF���_r�!� Zw: V�,is $6=0+1+2+�>By>�@%&!8l��s��_"�-� TH"exist:�%�N E�1-9���$4N��oMl *} %Qn\geq 3�?"�(�Y>2$j=0,= , n-AYt�1!,�; 0s>g`j=\cos� 2\pi}{n}j� �� \ $s#s�gm##; �Fp@1''��`n (x^2-1)(y�! >Kf>i��&ins%BM,�5�A~��5F!Y6?P�� E%��86�� !@"��266��.�  �!m��s�6� A��m�=*^.T� JUo2�+��� situ)�is rrz icj_*�.�%�e��%��o!� �1� B�n� ��&#�\)E?ls� ��aHOO,�*yY cU *1b�I��M2� .�u}�#mH$����Z�isc��."JL�N�a I�. Its� ch2��a2.,2$�9P�< ar\'"PH�3%� .Uqll"� �-�F4+9-Q.A&'pm� �� fac ian&��-�"� .�#&� (u �. �*�/ /�L5w"t %"Q(] lE/���� �^3�a+žcf.;� d  ����`F*�$�,:},�^B��un!�'losedI�s �)�m2DvenQ�("´�'M�mk�6�A�c��a���n���H��Rde<(���e2�i˘�"=ekME5� �&�G�Sthou;.�ª�]#�W=E"ʕu�� &�oj���I��*n_v�%Ba��, \�H� . U�� tuna�-O�h�a�hDtO aa;baA�;w�<�~�!�E��>9�� BMH��%�"� Y�pA"B$� $\D H�5� *B2A�r%"�KU�2)��"x�! d6(�>rior}6 $H$)} minTGR� >�&� E�¡qG՘ c��a2�!��cis)� : 1);/!,b�.� 1d�Ib*g1s���q� ���ki{�); 2)i?�)u�-�.�B%�2wi�"��A/a�3�G�*9"� chmum^�$H$A a3�2@4���Sw&��\� ���"7 |2��"ev.�O�It!W.<�c.f��S�k����z���>m!�#.&I1%� uspi�e ���qr8A�%2  aB�BY�I:1 Q��A!�N�d�2�&+2b!�2�)�,�">�aF6�.��%6���6J&2A s %�$*�#B���nV %Jh2�AP)A$+ 2� 5 y:�N ,)�ad�gL�� most")MaQ%o%�6�8!� � +map~ via �'�*��o��"h�65+�avggi�xŝL5 ^�5(|�\e��.emB���:�O-��a\e map�so�UW>b�vH'bo#J �:ߜ!�us]rAU�*� ,%5J6P��ts6� (i.e.�) �:ZRs,6�si+*�"s(����'!O%�� ��ݍ.�,�&S61�%Yg�!Q� �* U]B&�AFz�+ is���9�NQ})� y��ir6e)��B�Bwr57!: V�sgvmi!�ic��Lm6}&�% we r�lr�=*�ĩnn+�_(�R�6�i�(�a��quirep"��Q IC!w�?�#r��LM��")`$L_S=L_{�H}c"�^J=PT^*2�| �N_"``�>52|b"� ��IX}?��*(��=�fib= $\pi:�n\ra"o\pi�#.�\ra.�5B ai�N�X.\f/�t�u"d[!s 9ard.)]9E�NE�<D"1� m�1of.�Q��K1$��a}, bx+c��n*�at�Ea�U,b,c)�+�C! ? ��&0R� a�6\�o�J2���� dK�op�G���$\g :&k|-6u0 8t^3, -3t^4)>�sW �&y trihn �r��aa���ve��U,� �en�a 1R��a��:쌵H\,i��~��%as�\=f-�� e�`` �''a��3�s�5^ 74׆S<rv�a*��a�ro�& x(&&T��y9 1$1 })�,�� V l� I߁�>h -�i1�Q .� %a�he�!� 0wo "%��&C�&�"w���,�dJMu����\ LLR}q*E�, �T!�abl!oڥ�o����ak�sh�w)E#o2�E���sG>��'D6� have a re�[levant meaning for the local (projective, affine or Euclidean) differential properties of H�swallowtails. \begin{theorem}\label{posid�<-elliptic} The dual of a surface at a positive godron is an e ;.r. nH negav H$ hyperboli>I \end��0proof} By Pro �on~\ref{ ,ve-rho=1}, ai$g$�! (�0) if and only 4 its cr-invari!�psatisfies $\rho(g) >1$ (resp.<1$). �T)k �Trho-classification}, JZI�.�!�,conodal curv%��l�E9�n *1� (9[) domain�4Finally, since]tangeIR map sendsL JM to6%-FwAT�E`M[,!l!�(evident thae��O�2� �NE.�{.�J�}K. I�M�ZX,4-fronts} In�0neighbourhood!a.V$ point $s$ =0 $S$ in genera�e~on,)� flec. L$F$ has a cusp whose1� dir�M@on coincides with)mof S9iA]edge.A��separataF$]mto a, leftE�8 right branchesG(re are foura}sible �ic!�figures�ai)8 B9!%4{\rm (see Fig.ib!�`ity}):} \smallskip \noinAY$ $(e)$ For2�=�%�>Xi!S ! ly�� �cmO( bounded byD.5I �i�Ls)\in(1,\infty)$)}. Z�Th19$3$��59 type%0yi.�s.X 6 $h_1)$ Each-�!xaL6�is5�dA�m$, self-intersMW line�o%�Q>PJ0,1- 2�h_2)$E�Zp��betweeI.two �e� >��RY� them� �)V!%�5�E�%"b�e�sU$ame}|a�M!cA `N4-\frac{1}{2},0%'>&3-&LXN��.$ |a��M�op�r�smy.�-I�,.� �6��e�$e}[ht] \ceACA;{\psfig =-a�,he�P=4.6cm}}Hdpicture}(0,0) \put(29,20){i� $I�} 106>2)83>33116e117,116w\bf{-}Z314,1.� +}$} �3,2<rho�e�90N#.oA.16RRV�5291Nd��)� 1v \cap�1n5 $4$��co>�A}B�t6.} � !���IEM5 %� \sub��{Finer 6� a4�s u r_}րBes�q!descrj ow�8 ̓Ba.�i� (given��2� "�� JH, i� ��es�(to know how�2CZ��p�Z�F�  4 placed�l ect�R�  plane� A�fo� ��� �� a re!�ma ofZ , provid = S Z�:��B�ndF� ����,x ]�� �Q�7Bt otT --%�(conclusionsj8write $\Sigma$ �2�@�� � �$D^\vee$� F��. \\ If� is&� C1<� <4/3"` &�,l i ,���� I A = at / Es  long,semi-cub� usps $C_- ��C_+ ,iNAq~:�---���X--R inNS)i 2[ "� �m�9t ,qivelye H both�B9)�� $7$�� !xI, �5�I n�76� 7_E9s_fig} med>� ~ :iA�5>}7 J^$(e �8�U e�ly ��ne ��Q�6ja�  $(A�>4/3)$E�[� A\A[ML*~ haH&U7u|� � >` $F$,E$]�&� q� BbF���5� ��v \sqrt{7}} 4}{3})�~ J���6�.`ASagain ��J�1 �.�� N�]W4N[ JW}H�Ya AY!��NF-��MP!� 5o A!'���]-)�^ h{3,1}Y 6�Yb5���"%��� o.�69 )$.\\ � {3,2��sI�Rca��o���.� 6�to� i�I�� .k)&� 9JX1}:Iin�� u 0>J2: �GQ^5304:�1{A�)6 e_3'1N�8425 e_29I�. J��C262 e� C0"��" 7� i�Z� �\�4�C��6�ff 2�I�M� �l e &h ��� traneon�.;9M=0$� �H-'-� 0�} , Now we canv b� �bifur�:�ialgulariSccurr� inN�ic�$meter fami3f wave�vnts�!� mo| a.)2i1� LeZ _t~ ta�R��UG�N�Z  suc� $t=0$�  $S_04=q�  $s � � (we n�it a {\<le2�} Just�1c-�],!�h!5�as $t� increas!zA�pA� hrough $0%biX node $b_tE$!6 is mov4� he�*:,Wn �,!"m%_�.;other�b v�. So, `a.�� >superp�Fa.�� 2 '. A&� flex.Z}%;s��sQ��y.� q:� �� F�g y�)Q\S �deeCated_�0 2�"�� F!es�!ID�S2�. "%���-&.<58,*;�<0"�59>��Y257>>;:0^�!�-pearoika&7>jwoi�� viewAI!�6i2I�f؁ %(a�A�-�)O). "�!e2j2  A���6&�F��" I��!}�� �higerrdixcontact q:2�;�2�tic��,��!�>�+� 0 s� 1J"�5 q'2`��nT<0$E�B�4lsob�� fr�Wd8�U�6p� �=j %[FA(�!�.2s (!�outvr� %D2/!�s)��,is not clear�o perce�8!�M3�*yAXit doe AbeiLa�dre-di� minVassoci� 1-�map).]��� ��*� $q$-��.� �g_ �r 4 We shall inv8 gate whe�=,any arbitrar0HJ�i�� (o�v6�I $s$) ���R6G not) ;$s $p\in S$.*!�-�IC!�N$p$E�e��g"���s!��CoI|E"�q�a smooth"~�&C |�($3$-space (" #. #&6#)� ��d�iF *�"�:  $S$}A�!see\%b�i=c"�m^1*Nq�5 q� � 2�( Equivalent�!s“ {��s %!�R�\�#&,lemma�e�!:0�/-8F3,���`�%1&,�]sis%GcL �$#%TD ``stereographic''5�|f�� A3 !hH\RP^2_q$, $\pi_q:SMl@etminus \{q\}\ra +��p�to each �y �� joi�%i)Mq�)�1 One usuI# �derae:�&J%�a) exteri�%F! (� whi��M�><is, y, a�poY!y emptym\?), but S  we��cq�nq=)yZ���!?!�it� ?>�of � aY� Hence, �1 !ݩ�6����)A� p� "B$��r# ��w� �ain)�U�F�*�!%�= and,s$itaN�cas��behavi����$�� remark*} �"y �[%^ �1)%z J�is5�8"�&�"� ��2����Fa}v�=�� � germ-<P4$S$. We denote!T by $C^q(S&�2��}will sa�#J&B�]B|>lis triv�if itA��s j�H ���Aܭ3example-��"�/ETya>y��5F�.��A%**� aJ@e�wo4 v�#�&s (�Y beeIZto �$asymptotic�+s�E?�E,�b>�s� ,�)���ess�(ly}gki�(of���* ' s:�%�$n1�g&� � n-1�r�r!,� m�)�.�%isc,(more vis�&olN A:�16'!g%e"t ��\+or� ,&�&F�!_Q]-I� 4/3}(g$ be�o�+N/aQ6?$a)c%re exis�:� $Ue� $g$,�z$S��ţ�'� Ivs!L�� $C^g(S)B� g\}$�i.e. no>-o $UV8��&} )}a�!��+1 (g)� $ ; R$(b)$ �_ (g)n,=\neq 1$A�en�� suffici� ^� %)! .z�!3�BaGwo���2� A�- �+g�gIf -�!���Xve $(&@) �ethe*wo SsR  e�-B+!^�m$I��s '.%Ob-X-X1)6the+)th~AT\JO�QQ�  �N $bE�22a� C_-ae� hq�%Ss � m��"{/F� . S$->U3'Q�V�#ir�|�! 2A�+�be�ten��lyHy=c_\sC^-x^2+\ldots � +.(u9$Platonova'a� rmal��m rel�/I@�A�Z$P _$D$*�N dmin& +�e?!` real�/,d coeqSs $�z Pa� D =a�C^1�!C^+!�^"F|/&�G%2!0�8g�6o , �ͨ2=!:3imQg�P!.z�!% g$*theB!� presYdaFF" -6�&�e!� act�12� edep�/on� ����opS&tervalsc..1�W��s to,Q@z : $$��0array}{lcc} ��?Jh & \iff1)�"*154:*�-.�& < 6>27:>�� ,.Eq 20,3&\,0]<1108. .� +0+9N+.u 2.D=307.ha�).B0!�1d B�he�B��,$F$ (half-wh�( black ")}5 P$ (�1ary"G0 1� gray�0� (thi.D��3D8 $2$-jet (dotedlN+.�(_ �)��.�& -E�"46Q�>�{�N�$q&2 >= � | �++I&,n�!=�s~� $s$ ��s���*B5/ � "} 6�n� ,� "�,!n�,z�Q :�!2�$% a:.�a�������,hrequired-]2s.%��F{T��! !�6�"�,l4:�!t:�4>�*k-Q�6�-"-\:y>>6!�F2 wsUWnn�3} :o:�,bN; r3>\: '�s&< E_� b� �� �4 s $T�,, �**�,V�,.� t(c���/$6�\,a�A=F�>cC Na( Z`,�our})}%�:}-C_{1�(��e:#(&� 8}{9},1�(R�(R�k�=lyu��m� >f�$3�+ ��z:x3-)vx"�)�/Zx0g.{.n�,vj a��.$,0.Wr*R[BS..(�$TQ� �1y�9�9Z �.�6� ]ih�>�nF$�f1�by2�.v�9j.~q:��� :d*M�� 4.K"�a 6;78*g*]f� *6 47J+.�2� E��  2762=� o.D22.�6-�� g<*� 38J+.U 2.Dg74.=F� i�0� � : ��J�/ 6ZAV3T spS .�'$s*X "/%M,6R ��) T *r!� �)&��� ��t_ ,�~!�L H6t��Z��ze> �ll�de�� : d�[�h�2em^$ &iq�m�2��g�PBE �m25!N@����hx?Rw:�i.*�" � �� sai�#b�< �i{$] ��z21jU�Y#C� a sis. :+�Z VzN!�!�� � R� g$)F� 8��|- �w� @R�4� I"e� @7}�6. -8Q�:� > -4� (%Zy)F�V�1�)� WK8T"�T_f�mJ �L�"�) �5�, N� &V�&�:�3:r���*�Tf�T����J ����T2�T��-�}"�E�~ ��z� � 6� �U��WC��������:�\V�l}"�"c@.�\ ~ 1~(�  \ \mbox{ �E{@$ThŇ�� })};F � ,12kiT] f x�T6�F� =4\BZ R`rZ0,F\ ) &"�� P HV:�.� ,0Z�)^JVJ.J � 1}{2^�\)J��l �� WT�@ ^O�m\N \fN 86��=  1D23 EC� &o 20:� ,.� 3 Diz10F ,.D3N�%� g*p 42�Mp.U2 fq ��q vq ����JR� "� rv�/� - bM�6� *��04{\bf Note}. By� Pa F*} (^X})� 1^- F$ ch� ir � convexity�� valu�;!�=I�2\>,�: E|$�-� val j;6f�5�i�I�+j!cho'M`K�8�s�62C+?d~Q:��OOM= . Inf�1�"7c�M� � corz!on�Do�sub9�A%1)�Ft.��n�%%ha�% situRD�\9� !�� 1)$.c�C"r*� abovE:A�s.(v3n4E4!`!�2p � �� � "� s co9tel1*e N�E_s"� ,*�� 2�QMC!��FmV�� Ew (.,9(�W 5thFbi�)Similar^0 U2� s ob�,�M�*/sFfxL! .|� 5�B�DIn \cite{B_G_T_95}\Hwa� serv_)�<�ty�N�� s, �!�8& }�0:6�sig%� a `.�4' %ng somas*�$�$4� �#fact,b�#kQ%�Snd&� �E\9�Px-&� } (*"),�ch�di�I4uished geometr`1 ly bI�&e.���*�+diRs*;Uߩ�&�*���*Here,��;5Ied sev�R� charac�0?U]&��+�,indices $+1$-1$:�� term$4.u (~�U�Jn6Al�R�R:� s (2R(lrNE �" 4.�+u1Q�e� Y�6]6jQ+&�W)dG>�.�ouFS�ure)� !�Of courz0jBm�]M�2s�Ss (>� �J:��,�� \��7sUU�s �6> % Pr�!or�3v�.A�a� results}.���A�sequele�0X�:�-E%fb"ph"�0 func�6$ $z=f(x,y)o-�$x,y,z�*m�TZcoordind8 system�.+y�a�sf�!eq��D: $$f_{xx}(dx)^2+2`y}dxdy+f_{yy}(dy)^2=0.$$ u0$dy=pdx� �K K takICd*�'A^� ,p)=Wx}_p \pY$\eqno(1)$$7f(1)]��!E���e-w$f�&9I�(at1!s9�assum~M�6losEU&"� �@p� �Ur5� �ah�,!�p)�8eorigin:��a�/nsg+oh)nd�!�M2G)$-�,{ � !O $c)=�� p=�<bO)!Moreover�@anJ,I+UU�5� s ��� &U8�-)Fde)A�us�#e �(!/c� A�sAf� =f_x y 0M2)Aq >�6�}0�h+s�medf8;$f$p .��.�1)FQsA��a�$��B�;2B-@%}0 "�A"}\ A^f_p!�a;1*a!%r)�":&B"A��i�DŪ eq.~eOmp6W%� $�)},0)ef=�$}�$(",QI�2�y, s�q�O�i� y xx}=0i�3%�M]JW1�&�K ) choic a.M�6�$x$-axq#�N ic �)E#S$>�s!�i�;A?�7�NpEf%UAg�7a�SoJ.�}�ear>2a C�2�Pi_!2 f _fla�0 ing}2�2� �40\g(t)=(x(t),y z(t)O.!��.$�4�!�4-2�: �4����!'Z>Iua�m�( $$\dot{y}(}"4E� 2�?A calvBA AZda=rA ���TAX� oJ��G��om�<�2q% explicitl��E�=l�d�e$�Cm� �zavx �x}+f_y y}eB���� ��5 6 y}+(�� R^"@ yjJ ^�� toge0&T�l(2), (3)�o(4) �ea$\yz �T� w�d%�V�0�os)�ngaF�`*�!��E{rc!d n & = & f%<9- 36  � x}+ !!y}(�x y}+!y})  y\\ !& +\ VxO ot{x}^3+3y A x}^2 J y ^2 q  y}^3� )$��2�!��%�TW�=5� firs��re�;riv�4� $\g�vE���?��2�(er7m(#"E62�)� Qa���!a��a�apAi�, accW g t�� ��e!3�>F6x,-�! � wo d�q�. \fin֫4 \def\F{\bar{F]P PD D}֓: el�Ery � ��mpumX� -_ғ�=re �.�6͖a}�2i�Ex*B��&CMsm2K#�Q��� a� f9ZrV*i"�;�@b�Sz�y^2-�78y+\lambda x^4+\ )� �-�B�$ ,�:&�,0�:6 G6 w�\f��A�sum� homo� ,ous polynomi�5in^�b$yP9dega� grea�N than�$(`BnFaL"�,�8infa8eRwe need�u�E�����7�� �IB8�a@v.!�Bdth��!enoNto fiu[�r�Yo2�^�%�CTTk8v �1�[ R.�: spec@ <ɝ��fiVxce al���$,. X&G�G �%F�tA\�I-�J�seeE?instaRCE�V canon 2`9�3 �,2�9!I���"�=!f IXn Am ). %&o6i breaks sl�a� e sym�y}D ��> % %�!�don'tIA1ad�aUIYd�`&a�fn��?us,A�:Vlb�$ at!/ly use2`nA�2;1@M�O&1 �mE$5$�b�l�k,MK#S2 stud e.�O�d"lR nQiT"HAEf =0$)2i ;�J1�6++%@R*=P�)�ix:anipaper "�&F�� to " �^�. For6 �@!�se � L.IM�8 s $�R;�9)z�$�1"�-2y+12 ; x^2� k y}=-2xyy}=1�H A P&�E�s� ��^�.ʼnfqB.G�T"6�(2� -2y)-4xp+.[5 �W�1:es�6�6�1X�� ~1��=M�i��. A.5 �2M RK at leasteMpL��.�O2� Fe�tY"[E� [$\=>\�\��5�@J�images!W�J�� fT�` w�d$8aR66M"�nK�j&b�bA�.�nAf� �gs�)�\S8D��2 �`j !isYE� Hessia $f� > y}^2- x}�vP (H),HB7s!{]a�a:L y=2(3qI-1)x^2=2� �� *6� 2M?(Uribetesis,aK-evolu!�*)�E �K[� 3:N$"Z! �e*�jexq � &� W zero�!1�)J�6%� bolag�Bx* at9 (]N���&� "� ��lL ntribut<6�X 7s )�� have�Jinflu0�=sA�&^"!{Rx!�-J<)g�Xel�jB2J)��aver� . �1\ell_g?X.�]cross-yq%�6aTEe  8 D% g�S� ��2�!� $c$-�e5�f bqm\D$� �zw=(F,P D g)=)4c(F)-c(D)}{c(P z ��(Ѿ-1)�0}{&�2=8.��.}� �!��.� \bigW>i � %.ECae ng S�Cs� D�GSk �q"�  !Revsa!a_���1�|$�Af?-2��rObh�ia�d.��j6�q%)k>B�B�H$� V��q�-x^4��\ �i �1,0).�R�$$y=(3< -2 ; P(2�;�F. � D��.�!ES�"!�� 6$�U _&�2�X An easy w�So{)�O(> to�)W e6V%�0Si t \R^3$, �\^�w� !�� �k$/���*7#FV #`polar�" map' @*4 a quadric�<�$$r6lY*r�PT .08dered~N� �\� ��oi'zr"� �'* pdlmc&�!i�5a4��9_Y!Ia�d" � Ş#6�B�P�u.�(�Ny��:lzezscal1Sns���#Hcf2\'m� � $\{ x �))UR�6&"E��~(e�\tau_f:=&� M ),�y ,\ x+yf - p I)1�8 �M�hp_a�$� $�:E$ �.6� \�((-2xy+�$ x^3,\ y-���D2x^2y+�k2�\�()�@R^�q�EIof� fB,� �"=Tac�� � J� �sJ�hZ�E-O2$S�%*A�m��� N��A % ]st.'A+"�,lf:}~v._y?1^%'� IWe�[ $t"� t,ctaR/�=2Fs %/ (�qon�$)�' \a^c�:iI"2ŀ -c)tE (c-1)t�MCIc�2c+ 3��AxM!t^4 .�O�@)5&�!>#G, ap� 1$�/L �ЭJ.=�5 XE� 99 V�K�"� %+, 1$ q >$l�ZWo�1�R�� �Ae6J-A7J}C/���n�c�a fixed 1'J��-b r siA*��2>T��}�.�z*��\g�@Q w6�2CdS0M (t)-5��#O(t^4�U6IEm\$c=1} Fix a6 H&@P �\e allEe�' cx^2� c� ut!|l?�^ ����%*f%N.��+�C� s,`( dow\�$c����up� $c<1 f� �CH*tv if �a��(very)Ge���\ f $c' !e%%QDa,!!!  ($c=1$)���iU. �'f)s� �}B[&=� %Weivt�!� s: %&> %Case%#:nY)���n]K\dr�Y� emi&�w %5b!} . %�Y-~O&�H�A$y (. %"�J�=��Q(%�m�1��(non-reOn�k0$) %��1~.r6I]�hEWv�pb"�a-��.S(\Fs(�d(\P)$ or2D)9>�29s dras�ly�bb &4�X{tJ~t F}� $cR#P#�V$D$, 2` $oc'�gA�S $11e�#*�C��>�,-c6F�ڊ� ��b] ".� �Z2Uz�4,i�3�� omorphism{&!$2Vg���Ne[-Pjae&�"���_ oI8� ��Q&�,ER�aI�P�J�H} �3O\cdot�)� $y=1� �2c�R�d!)�i� sec:.+ �4 "�CI�!��Yi� *I#!�F�/� � �g��) &�a@_f�7�V�AF�"�,P*D- {al}=0 \s=1^#4{� s,�2$1�de?<�!.��.BjH�u$e}z)q247,55) 5 nʄ 64,1c21,15){%!D"h@134,14F%A226,1221(�5Y FP.-93,80 =1s� �ureAX]N`�s�"�y5.4�YNqX..�|\se�%�#  D\2�A?B� "_q.X:�? U�1@ul';�Z�%�^�E�����*�;� "��ڷ"�Ma^f"qy��Bwby&w. ���P( C�  $mk���S� $���$by: $$m(x)�"rh��� [p[(�;)>�j�=, �&�"25����� $r"A6;I��� �1$$p� � �%51�"� , nt!� ,�u*�< A&-��y�%)�R-�4@Uf�u$� p &�uupper ',k��+i CrH'�!� (� )"�: �T� rejof)�{%p-m� �de"�zC�i"�z)�>$7;� x�! E�;<& r5�$c'|4-6� M%�32@�A������<5C3�~��+F+'� !�tes� &���Flr�:�PJ�0� &g -i�}� � -2�A�e/? ? $\AE�A>Y�$A~fol�v�%�%g�^0uvUlif� fiel"�$s�G6/Bs 1 2.Oeh$/ 4n� � /=+ natu���i�PT^*S6arrowYv(D�AX."�"MCr�0ip. ![/=�&hB�-p %q( S$�ub 7ym�F\� Ed6�x54A�*�k>6O!tilde{P}R!!%&A� � " �s T� (3 �%5� &^E fold�@�"]K� ViozA�Uc\A\&u�,wo�Y/cessa�x$connected)�mponen] n�bb�\A_l� \A_r&�0 �$g�lB9md�^a_l��A{ �ed)$!� ]�%[l4>�B`!�_rA6J_)�.C&VI��I5q@���� M> 6A�V�AONow�F��5��< ���Hd (:\R^2 \�ir �$*�~x:Z- a� :w: ��C &0��&$*�%��HԈnd �m�q�N� o*��R"\pi(S�J�2Iq� nduc!�:"f �t2��! ��{e?toeC#Q�aWa_32�p�TI;�>(&�)^�r.FX�Wi!�B��z<|t�M�YifAJ�et�Ny-��g�2�r�:/�YT83c6�Q2h  Usf�&d�f_GDd FEDdy*�Cc@In�!�handl2�)�.�,2E� an `�7'rNr�35�I� sZa�vs)n�3�5k)B�)3�&:"s?Cp$)�^aU1T stru���KG8�`!@ ��� $\a=dy-ME��A��w&�lmost AX�@e] IVwt:!��� _0#�`"*� D._0,y_0�n v-� �r*�n�M{( O,pSag*+)�9�Q�U�&.!*Q�:Bb� � � ,p):gBxVrF,�7�(�e0� *)w(tak�Ep=dy/dx�~&r#��0%��c �&P68q) $u �� .�2(b�jpi$`99�A�y EpG L��+�OŖ=&�4&%G5C 1s�cr�;n"EZe c.f.$arnoldc;I,z��-�����B(�9MBpai�y10s =�=Q��LBel�N!<�t")E�&P eo%źr#��/E��=Ga� �I&�"%;s"'} �-�K�� ePf )�;N7-��_wszRh�.��~$, etc. One"�;���bject��!�� "B�4ndQ�>i.&�4B{1VD�es}*6$ F*$ � .]3u�~�"�6!�)=��� M)Q! >�20AA~Hu�ioa�in"qO�s6�>X :�6!��K-EJq(Ee!�#%���&6�z �X,p)6s����G(·~���T�M`os��� !e!�-Qe�� &W Q�I��9o, "DHF�� �Mlyuey#x �!._nria�s2_h�{]q{6��d� e-a"_|"wY�N�.J 177S�>75�YP&���Y 01){� l187,13�� F69,98){�]�)�!L!4po�170,5\F_rF 50,33){$Fn$168,38){$P%180,23){9��3aZ){)�m6��e\supset) \A$}c 55,8�pip64 �� �1c RM[E�\pi:\A\*D �G" M�=y�-U;*�>F*�f��k M; ��C{ � bw��6� !��� a* �<67�&� a��&26Ku,��u E 6fR `���*:b�{Z r"�!>�/V�*�P"4�%�l.S&� a:C�o!�ve6�lr}� �=q�!���{#Z M�%"E!�.��..�R�Kno�icl &4N i�.-�I�oMB���; �wVJly{>� �*yAT = �-!\A5&{�J+2-H��!^�_��I�E�!�%) z(0�)qѦ�[�PI(��lsoja[� j2\�� �~�!o� �1��t �a�a #.,Ag�.� $"(.�,�, �V1_$�� � ~qno*$�2� � ,z)E�,.���di�� 2redhD2zlr� Q,9m-�!�' k 81�)�!8�,�]v�6�LR%�aw�7� .� �, B p=2nU �*�Ci�I�i: <DK�Jk�7!U l!� x$&�")-<�xn�HD "�=`��!� sea��+�collaps� woq�u��E-2�WAQ)3� ��a:��7li�J!_{  �ɍ!ux:�� To�2*�Mx ��2%(x �^�A�sT�e2l�y[�P"1G look�anHD&kA i ��^�/�Q,�:os( dexY�Y��6Cor!�ry��)3��e*�MMX�Z�T"� �Y���f��mm�q{I��G!�%at� �2. "]!isBS�1?��he ``&.N T''�a�!e�*��"�n!�2is�4,eg� NA� Q��is *Jm a�(%�))]��B�I�at � tw�likCQ�� `screw.)�Ut�<n"Nic�5U� ���%�� $z=y^2/2��$�verify ֗�B:"��{ a�S � >��iʊ�OF��UM_n�>���_�Jޖ&� !5�i��!ZR�5x^692C\�e>��r��3��a>:�s !$mN F"s�j��6k&J<�&�&#\ra� �np�>5"* J|��22!� xO4}niD_ (p,px-y)$ �P�sC\p ;: )t�=y,a�theF�9&��s>� 6(Whitney plea�"�W�� ��ra(!3)�A Both, ��w2M?(~7�b�Kst^@*  da.B&��Q)�t( Yt�IT-�9�9��atA�+���*�?#� � I �.�KA� Paaz����8>�� �n)kkerneض9�_*H 6VI�of%<�;� % @FxZ�La�7���"fK d�"rL�2�a��F � splOi<�Gr�]ry�5 *���# (��or��Yj�q�"n6rYay��IR � "sZ,�W�~1�m�,&���.]�s6�DJ.�SE� lowsIv4vanish� n )\+$q )n+"�+S��/�?.�0r08�@M�QB�V6�8}� !"}3�l"� �E% �!C/.~iscF�&K ��l. 92i�s}��:�j2׹h $H$ �!B�S s� LeP:�e�P J�iz odd numb)�2��, �"�tg_�4 $g_2�! �� �"\pazNH$o#*%%� euler=2�t��>\�k"� a=_claim}#7 %\0wo vectors $v�v�R��$�|�&�>� 6A�? A������-n>vor��%'9�v .'A�!L�wa�Z%� �QW�9l�"YI�e2t ���y��2xPo��c�"&��� co(�y&d�``�'io-)�^�x1���X�g%p-�-x6 , C!�ID)�s��F� )G-82 emA��f�4�&u��f#�!Z E�P star�Mb+��P�DA��:9, uQ "� e�l�A�� 6 &a�7�ba��=�_R/$A��$B Gej�l$ �Ae |)$f�$�ls��F�F�HoX0���U�h���!w_x��Am|": 6CJ%-�*6�BL N�G�%�;2tim �e![�HJe~�#��Ee.��k*$X *�U�l��H$. A!ƍz!y W�WIP�� UE� closed�s� �). Bu���,2`�la .K)y��?$H��,l W:9� ��-eveeA �!�Z�; X ~is���8�"��i<lB&r+��8�G��6!ur"��podis��a�@J�AH�v�ų �"2A�au-iagraE#Delta.��- ^pur�oco�P ator�! man ��)�-�of‰�VL&� ��#[>� ���� ``moves''�T�m�#� : 4 1to��\ �L��xv�AtF]e�or�* �:&�?�~(6 0,78){(I)�19,17 � "cf��!-I3.3N�5!=99�� �n � w�%"�&>fcolour8!AB� ���pl�e&�5X:�T[��.�7&. af�] #ed$."� ��/"�K&a dot:+box��y!G^+�PG^}��Y"� a�:#� .T : <.lE!!.�y�Q��&{H}\ a sp�, �-G^-=2$� E>�jML��e�da�*�="�_su��eU->� *Ma"E$�$gv��$g��' @i`A�"�)!��ecu\F>��*� � ���ҁ\H)}�J!R_ u7P -�!� -=cde"�2t� ~ E� .�p/e B��C2e,b K�3S"'��)3�!2,%=s d��^u] �-m!#"N�m!��tubA�.DQln.yUstep-1�b8Step 1 �V�w�r.H�>G -�-2 3�r�E�pproach� !)�_entQ110ofF�!�Noְ�%��!/ype I XV'�.��(0wgi%o�x5J�]�~ A�M�+��&B� Q�E56ݺVc�� !��]�:��@��� 59,1W<�H#9k<){%� 1�<�#'1( -"{<267BP295-Q��I���1.��:��A�e�!/)���a�cIٕ [:�*5(It m̢beC y yKAc�5i.�z ]��5�b�A$ !����Q�����!a!zG &�ND>�happe�4�^ Sx.M�,� �. Ho&�aavdOnew(%W&symbol� mkep���s:���#6:�);%�vs: �+�Jv ,L3.�C.)z�2��App >�Ɉ-�)x��~1�**?*J�# �e��+�� ���_"�a���$jE+proces;+2zf�k��ng� "� �*128}A`6�@N<�#6r*X� ��)(O "����2��6d *�ύ� i��a�@8f���|=.|=-�"���r=&+ W)W�q uY�a���  %:' �D$l��5:��~ 9 %>-JNP($}, i.e., >z!tma�z�8I� J`"�*�R c_A� �� ̎"�"S �&alM� �Z˯A�"p!� a (l9�)B�'So6�)fcy�6!X*1IQI��m�.�� m&�SS�!sp��s$q�]�!%��L&��6V. �6b:}�"� �D*�~L  $e>�!0 �� .#�� 6�FAlN u:T�6�Y+F�R'[:�!9.wa��� �$sF�F6� 6�J&�i,�j���� �W��QGMF)I��F 1�I��!L�s $g=s { 2 N6�say!��U��H&4sixasL�g�NicU � �m�:���f��>�HM(�1Hx *��'!�Z�"�B#;�,� � !�U�Y].� �j3o�h�$0$ XJ�i.�"�)�T� !/in�0l��- ���# "&uXJ�c)�Zk�>���:��Z?+e� rho$F ETbv��D{ߣ �F)�si�GEjF��EFF�E^�E&�G���E�M>.���\�Aw* A�I:�)g1�"� se)�2a+Q�q"%�:&�6b")U �@ FAA�f �B#63i8�vJj& �_ N_ ��*��i4/3� F"`��e�s_9ցG!�7A�Hi����!Mkey!�" !4Men��1 �"V�����q٧h|#a����S�-���]R��q�RU=N�N� �'t(\RP^3) >N��(�hAh^2*��q}W��`�5Pi�Uxe �N�Q��d!"��q%�/Ye  '��(total)�.���&.' h�  $SѶz - 2>�16 $\PiN <OC#Na>����E�}���1ܩMZ%s�$J,�p>��q��hQKM<�i�w>��pSq(�ł>��V�J�!�& �$q(�1wE~�precis^A� � �i6�-�a�N:k qr�WA~[]; �R��6LH�) :6�,!Za �u"U�QV�I�23) "�<% w �DTS�C � ��i�)�$ J�*�&29!/#E�M��$q$-C� ur: argu�-o�=�'>� �F #>J���� "�|%6�S B ej1.� �4ay!I�>�5rDf\PR�jM�6 :X�%&�K�;byU?�KW/13� �@� ,�`!�A�:�DLI( b�;%p%�.�de�o�"�"'x�{�fl power ser+exp��&�).��� $�8�"�x.�x�jeU\ {,$/.�ax^4�(C��a�squarb>'-/[ori�!S�h�  )*�1@:�q[5DP\0(y-(2+\��4-3� }�f�9)$-b$=�aY>9�*:�f.0�5$!%,�4"bW �3�*�^R.UD �E�C_-: \ J ��gm8�!+}�UC_+.5*:��q�$~ C�:~��!+=>V $. "��� y�o*SV��}2d� �?E6�5_ <)��1e(03b8bf$V��.NFRT_C_T}.C�ge�p!��0xd+�  l!9Und �^badee�LunyW- S�m@"a]heuNc�+&� 3}(c-2NJ=*�Q� p e~� 16Z�V42,167vVz�;23,14O�[��.�iRN�"�>80,168QWcM 42,4�V� d 37,1)>)\Z!5�.LWW1��3�F�):� 849,10">*b\ � 8E}}�69��&�W 7,84-%=�W�� 99,-\bf C$[>330VTX246N201T�s2�-197,9V�M �3}S5�P4�!W�� OJo215,15Fp233J320N 303,7t^d˙9d\t^0V�669qT؞�!Y���6b}#.si�%Q�'Y,�+>nFca, ea� (�! C9 |!� "A' "T)&".V��> �$ *����Yc��Y ���t9oj Z�0�.=* �.7$��A�F6�0".\�_\R\��)��"r��*��p>v�� .8Bc"c� n�~: ��h!\pm�zI�Cm��K$$�d$F��Z. To m�>2�ZT�r):�� �2alreadysfz&} (!!&&.� L�F*���zq"{� �(�c* �9K�� � bolkA�.w|.v �(_^�$&��:8 $F� iMe:�  �=P 'mj( w&k�iT�� ~V�n@-4k:mEQ� 4),$�t �=(41-zkr"d4zQ @^2-7)0i \ �=(42X3�2,Vr-4@.$2��*a�� �"� B���%aQm�S!O@)V�h�@�* sign�.oe!�#�ic mea� H�8gn�*� �&��eU> �2 1��h~!�"���s�6?+ly��E !o�  ,t)&�ethird "�S!M�}~��B<6�,~$� ls!�;?,�-ne%�� &)�  �!h!,~7 0XN�DN8�ZI�!�[�� J�  "Je��Ja� }�A�v.�`�k��S!�2a"�.U�, �F }Y2Bj�&2$j15R�3ov�!��"j�%���A("�#&�k[[F,#>�m�]a� 2v@aFb/2l�` �~��Ds3�mo�%�gr6$��$fP ^Q�C*�-6"j�^��� &he�C� 9dx^m�rh-fdwe&\J+n[ $� ��/Z1Z�RY1-\}F#X��> >-2Єwomp.��^!2v�  \ăE�V!2��L MB! T^-=:�2  T^+=:�Pa�� j�).jeJ� � � � �*�N�6�1ir�44T ("��!!��!�� a� j4�#�,2,("u^2+gi�� Fk��F�.J�� �� T� � mJ�� ��:� O�� &� )�� 6� 5b�awA�� 6� 5�.'$J�0s 2w=q L-V�{�A�SJ} =(x,����b| '���' F=(x ?"n xG^� "� 3FSP� S �~b�b�(9�-8.LJ �Be � � �� %g:��!B �� �� �� "W�^� �")�� �� h� �l 3)t^l M�V� q.qu� ���!�f~ 5B �NN �42��:X :� �"� Wdtph�=�]fin�, I vi�50d l'\'Ecole N��e Sup\'��:de Ly��toY a talk�<�!?RdI�%\is �. F?/ays b�Ee myW, E.~Ghy`0D.~Serr:wf:� !nb�M lLevelt}�)histor�!y$rmodynamic� N� landGvt c�bvZ���@Korteweg's work ( hpp, gtp})=�)s (�Zpla*oө �Q��:%&c.O:*�2I,�|�� �-)&��%�`x��2n���&JD�bor`�<appea.�Ovol� �D. %So�could53"*���Ee)� �`of catastrophe theory. KPorteweg's work on the�ory of surfaces was motivated by thermodynamical problems. %(theoretical and practical). It would be interesting to know his contributions, but� referen� %\cite{K �pp, $gtp} seemsT,be difficult find�"(, according T8Levelt}, %that{mathema�l community is not aware abou.se%Ps�C %phys%-A,had forgotte%~Dm. \end{remark*} %�F� {\small \begin{thebibliography}{99} �wFw�% \bibitem {Franca} {\bf Aicardi F.}, {\em Geometr%6$PropertiesA�4Generic Real U�-��Special Parabolic Points}, Preprint. .�,Arnoldwfeeml� V.I��, caustici�wU,�Kluwer,%�s.E4itsE$s., SovietE8series, vol.62.!R91..�I�tpwp}m8E*2�Topologe9p�� o �6��propagE}, 1�I�Surveys k51}:1�<(1996) pp. 1--476�Banchoff � T!�affney McCrory�n%� Cusp�4 Gauss mapping!B ReseA2 NoteE��\, No.~55, Pitman, Boston�82!�]�b-ThomN� R9�ur les p�6 p�Hques des�a�P.~R.~Acad. Sci. ParisA(�2Wof coA?te� s-r}, J.��.-p�27%h484) 2785--28116�k.�0Kergosien Y.La ho��Z�0F�$705--710. 2�v p�� D.J976O,de plissemen!�8 Arch. N\'eerl.-4!$891) 57--9:3h� %O2zDLa th\'eorie g\'en��ale����{z�295--36:�LLRM+pLangevin R., Levitt G., Rosen>H5 PH�rissons et multih$ (envelopp�ara � , leur appliceC!L�+)},:�(Warsaw�A`85), Banach Center Publ.��0!l988) 24A�536�Landi� E.E�T!i�q��}, b�5q�1), 1�114:w� )� Sengers Y^ How fluid�Pmix: �  DiscovQ� ��Schoola�Va!>r Waal�$Kam� gh On�PKNAW, Amsterdam 2002�%&� m-1�� K�hifrin T5%�����ve)���A� %J.~� .~� m 19)��*a 276��ad{ H Ortiz-RodA9guez �� Quel��a�l��4 la g�om�ta* .� albr��U4elles}. Bull.eLSci��R,)�127%� 2003��9��72�Dim�Panov D�H"� �of� �� < Three-Dimension� ��ve Space!W^�34}:4 �0��6��:� Platonov� O.�.0�!� mutuosi��a< �a lin�t �r -�36}:1Ÿ1a�P8--249. Zbl.458.140142OSalmonm3  GU� A Treatis���& ytic� Aoet�%T 5T�$Chelsea�7�27)6y egrex  BwThe Non� Cubic�%�D Tlaredon Press, Oxfordh4>� Uribetes��-Vargas.� 5�\'� y�ctI�et�:( contact en�om\'ee��*��A�E�courbe��. A` PhD.�s� Unit{\'e}  7,�<41, (In English6B�pdl�F�TOn Polar Duality, Lagr��ER$Legendre 9 � Stere�m(� o Qu�Ec� Proc. Lon!�e�0 Soc.(3) 87 a.$3) 701--72:�surf-"MZ�S` EL , Im��it.�l "�� Paired �� Fibr� �&� P>� Zj docu� Q~� \1dclass{amsart} \usepackage3, amsthm symb cd}.-8[all]{xy} \new and{\Z}{\Ebb{Z}}6� s R> CC>bbnN:N>:Zn�C:V6�(Hom}{\text{ :�cH vcal{H>AA>crB;B>;EE>FF>KK>cLLB1'�%�re.�(a}{\alpha} :b}{\betFc}{\gan>3d}{\del46�FreA_��6!tr1�tr}\,:�i=%�id>�extBquery Z4bf{?\#?\$??}\ :bpotimeA�hat{\ :%aiaBjCh-�rm{Ch}>]Cy!6! yc�6Dcoloneq}{\stackrelM�0\tiny def}}{=Z \�,mstyle{plain � �~orem}{� em}[]t'l4[ ]{L2#�O)2/ corollary-C>�ru6Bexa�9}{E 2` 2�R C:defin 6@{D$��oh} \date{} \title{Entire cyc�hom��t��,inuous trace� ebras��author[Vv ai]{Ch���0ai} \address[: ] {Depart�8� �6�\\ "�(Adelaide\\  $, SA 5005 ustralia�email{vA�ai@s.a @.edu.au !� �HD. Stevenson]{Danny�:(2�n�4California\\ R�0de, CA, USA} �ds �j�thanksa � s ac� ledgz suppor%UB 5n RCouncil.! subj�$[2000]{19D 46L80%�b�ab!_ ct} A cen!kn here�n�utG!�the ebecanoni�,smooth subalIa�tV�$C^*$-*hav D)L�v� twis�$de Rham co.  $M$.� Y$ \keywordsZE,b,�2V5 (, Chern cha�� exci�E� make�� %-�  \�I{Introdu�} Z�i *�Co�O� 2},A~a � oe>i%�is betQsui!�to studyEe s� of highA%Lank discrete groups � 8also certain in�2e d*�Ks occurra7 rof� str!� ield�ory. jpla!in a u� al settdby Meyer )$}, which!w)we use�Q. Re�ia�Brodzki� lymen GBP}�se�6 .��� Scha(��< ideals $\cL^p$,e�$$p\ge 1$. �( 6(yum%�R2�p4, $HE_\bullet(_)$�6 >'$HPM^� rm{�o}}]1J been�viously9!by Cuntz-= Cu1, Cu3}Arbe equal vq$bbC)$. On%otA�8hand, Puschnigg b} ��N�2|!X Fr\'echetrA���"�p"aV���,Ao��Azu2 �E)�iti���, I��!h~uԱ�byZ}. I�is pap��M��in6Q5 i65P,iP}e�i��Rb| CCu2!� Qu},� toge%�@!{)���!u2���gVW p(BP}, to red�NaCba aٻQ&&��%N%��6� �ax bk�s&/ . ��-2MS}������� PreliminaV }  oll on $frak{B}$�subset]a vecto} ace $V�called a� ph{bornw 0} if, roughly� aking,a�Lis closed under forma���sum�t3�H. For more detailsarrefer��I�Ɋ . Aj� a \e.�� .���com�quipp�a �:1@. We will usuallnote a 4k .k�c%L$ (>\�p%/,stood; if an�nfuR �ld !�$write $(V,.�)$. A-W $B4 set V%�6�2 �s-�5��d%1$B\in .k$.��all��1 ��! c �c� �%��I|dd- $V\  V \to V$�4sca=p"  $\CC. - �'�atibl!�th�5��1 �%of����, sens� T&� re b)�ar maps�E !K%� E!>on* means aņ sendsQaw � D E�( � 5Kea"Given� i�ub-WW��9�AAcfin�em1Q}xy �8W$� � !+i_quoti�.��$V/W$. q� �� A Q�f } i�/ $A$�.�m�Tit into}�S6�� 3ucA$)�2 T  $AMZAAZAa� -�. -�w\M�� AV,1e���!)5A�le} $V^ceis�"I i�=bS �j&� �)y:aj� VarEmaC o W$�5p lx 2\2�$W$ faAQises un3l~�� � via]�Bp�. I� twofps!%~AWweE���E[-� ic t�r�)�V�" )U6+]�. T-]A�convex�M�Wgf*a! byi� %� $B_1-B_2$ w�:_V� $B_2BaWa�<vYq2�� 6�� as�27 W)^c$ ��implyQ.WW!�IfeKan��:2#-�� �mEKd2)B�A2lBa;�9:1 a. �V 'J {e}L ��th �associ%�toII c���y��=M" pre-!f�y���6es ��6�Dv6�th��.Ye��\&�  �.����$V=���2-1� %�6�zws%�r� N. C&� ��� ween2{%�s exact�r�&ond- ��� aq=�2] P. If .��� > эaMFr\:!�Q .TY ��<qͫɝ coinci��I"����One� � �.O F>�� � need!�{"N ? ica>9}F��woNh�0 ped �.S�J�)9(�!(*�#�r pf>�_{\pi}W�!��N$�ف�now re ��� � of>1:� "follo*�  $Qu, Perrot Let b� a�F�Q� R���first壅�8 $\ZZ_2$-graded2(� $$ \Omega A = \bigoplus_{n=1}^\infty \" ^n A0�! 79tilde{A}2(A^{2\, n}$� $n\geq�)�$B = A\� \CC$%��2is[ !n$A�SWe�� �0� �m�/�7QEA�1B�h�y �R 2�-�, i.e.7Vy~l\cup_{ �0}[n/2]! �S}dS^nb �S>b$��ձMx.��@�m��3d��41(_{\epsil`$%-It�be�E7 standard� ors $b $�], A� exte�<�BjTh�3)b>�}� *(A)i�A�@^�YuR�m x $(I�2y, b + B0 T �is U� 0 HE wii2 same;�>+g� in.} �+$X$ż|.of �!Quillen_ex[�JHMQ.�g� aD� ��Q�(x $\widehat �A� \display�\��a�0q�}m�a�>l edir�-8uc�z�g�!y� aA n so �1�+n�(>�,b+1�is8!98(Q�a�) 9F?�$Notic�I�&W J� >�E��u�have a m�sm!� �e� d hK)� "J mapU�� HPIw. As �1ed �7y 8, i� ^? F;VH �h ��!J]c6I�!yi�^u $HP> �!a��.a� erefwe%J0atura-�m�)&VW. Z�i�+!-!�:7�n;ng�I1�"� long  sequ!���` >t�6�'2� �� s $0�EbB C 0$a.�љs5�  � "e� spli�.n! &4Ma��"4�)&�EIliz�Y 0 6.1Y�"�}{?oss� � A(mvre�U�BP��  "%*4em}\label{thm: } Let  C$ ba�e �9est.of7 2�s sfy�� �� ies:~enume} \�9$O�m cC$,� L^p ��� �;7�l* �� topy%�valence9If!p�1A adm)�V�A� on, 7 of �< � s beE�:�m�so doe��third@�An�everyQv!A5O .�beK � �B�logS �m5:[ in�s&� sms $$ &� (\cA) \ca� J^� (<< \c��Q i?AMom1 qry-Q�Y�proof}Lsi�AE�!#C'e�/ :�endowy4� |2� y, s&� rans�4e�&�J}��5fZb�"csmsA n�]C6 2}E�C'Bn��bba �b� HAd6*a/i'q#. �,c�kr^�#�>Jsors�>2��E� .���%a getfulne�9)=m^`toR�:�2�f� �A�:�e��ݕbjR(,V;"obserC 2 d� �i . SorK!n�º�1 Z�'�WE�a!"~m�,-�� F! five�>  ���� � �j Z �2ŴI�!�uA�cC t\a,�B�%� ��0� ɵAųa4 �}��(20&��s'9rum aM��$��H �$ �A�damenta�e�*H of Dixmier-Douady,N �')<$A =C(M, \K(P) )E^�-�A(�-��� lo�y trivu?bundlTT = P U _{PU} \K$v�&� fibr!�հ $#f� ct&]8a /r!D Hi�?tW:� a pr� pal $PU$ �P��djx4 aU%!41m� . H�� �$� *8�ary6�_2�. S��-_s � �ͅ�ifi?p�8����their:� inv�A $.(P)�H^3(M;\ZIŝjv c�3der a�se,T6�( $*$-&� A�A_p = C� (M, ��$(P))$, $p �$A� nsisT%of ��s�A?��-1�LF0�> of $EQ$E7 U7R�!a�/%�&�3he6�� &%�%��4V*m�.� � }i�Mq�m*c�2c� ��cty��+$P� �)Y�Io) .6L nucl�"DQ*� r1V �_#&�f,&� \K#~i�4� �K=�#e�|n� ]�s,"A vC}>� _p� f� � _p)�DL�31� l�d�  ��wŴ senta�a�!  E&� 2&�&� E1!6�>c=,onlau �!.��N>��sub��GME�co"�(�,�t�@nV?)�.��i��N��L^iz �He:5�$ vanish w�resyFA�to �A�let_0^v��c v Q�Rvto&�)or5 V�M�!�iS, map1�]iota :��F�< \hookrightarrow+ ٙ�Ie[ � � >� . Too ,)7 \phi {\rm�F}()bb R})$ �EZ"\�i����%id� ty�b !V6 interv��[-1, 1]$%�has��at )�� B~� originSA��n tub�F6�A �A�N?"A��be �����$N�� �$,7>ceEg![ ssum�+R� �- Nowa�p� ;6G( ${\rm Id} �!�au Z�/!:F $\Ph5z, b��it3v��aq� E \^*Y�A� ���K� 2ePhi^* $1��!�� i�ipsn*Zq$ >_._@'VIam icRe�M�'[A�a�%I!�lso2:M6�:sA�M��� s $ ?�I�V9 Ղc. Fin�&�x�$� %�^*� an in�.e�$�?$ v :�. NextAx prov�&�^v�'��.%�2��\ ���;� �C �sN�AE� \ref*. In tzero, 5�:P=M]%=%umZ� e�*is�)I laima��� case"< we �owu um� atm|$dim}(M)>0$ͻ f: ME�B'�^+ŷa�.se� )P�9 4ely8 y caB%�ds $x_1, x_2, \ldots x_k$ l�on pairw�>�$rent level�?ɘdf$. Set $N_i = f^{-1}(t_i)�i=1^k�RC�3!*2q\ $t_{i-1} < f(x_i) < t_iF\�'A5e����of b� �0C q�)�,bigsqcup N_i*%w6*c9 2ErA0 $$ �ess� �N ar� ,a��%y$hyp}/s1? it suffic4o �Cf��23 eV�2C$. A�en �.�� �o>���+�.6(rray}{lcl} 6%^O&i&5S�F� 6 \\[+7pt] 8 &*o>.CM[t!�A;$+1}]), N_i� N_{!c)�|_{V:}� � $$} So��1}��.}eac�6m�>aEA�- 21 y�'nc C �$�� ŵj��k��ly �t*/@J 2�D^{n_i}n( S^{m_i}, \�9�Z!.�V#})$S1:)m� �� ����A�$n_i + m��n��>0.4.� , k$L H I �vfms %"�,G }��U�� 5�"�|_b��� \\�pfOsa"to.��%2VQR ^/^0M 90!EF�IOJ�ce k ��5a Z �@MM (R> } /� N� 6*� 2�V�����,$$n/ll J�� !�0n�R $F�U5) k��tX&r&l?v� rB�"�}(n[&� ��a�j�:$H^BM;c $�+ some-( $3$- $!�M$ "2D $\frac{1}{2\pi i} (:E � e imag] 62*e&c$$ in real &�;�=�i-ABy!�6� � b9e*�Av2V����1jV�W >��J LP:LI~� >�M�4&�]A���������-���<&�<�w>�G{11e�bYz J. B*�;R. �;_Wit^<mLr;l;,}#?t [{\tZ8th.KT/0409164}]A� z#} A�n�V{oNon�%mi@vgK*�X�K}, �O�A. IHESRM 62} K�R2 N360�2v2}�.z {6=y��P��"�1 �Dta�mmh GF(holm module!! $K$-Dy �1�NL8), no. 6, 519--548..�u1%��&=N it CQ$ N~aeB"hZn?Chn?},�|1cGI1b9U"�Y Lect�2LW uXH~1831, pages~73--13.�V{t<�J.� t ��F in n6� g�Zy}. En�opaedi&&�Cal LO$, 121. Ope<' AA$& >H�, II.�"�ZBe�Z42004. xiv+137 �XHISBN: 3-540-40469-4.�u2B�E�@�P.B--��*�Y �}4 +Co5.!�^�6(Qu�7D.$)M8.�bU.��dY�}, Inve]!�zO127},�Y~6Tau97.�M�� VXtha�?D.~"�E�^OU@ gene�EzebX� L-Hochschild-Kostant-&0T�, Adva�_in�aFP, doi:10.1016/j.aim.%�$11.006, 34I� ({�ppear}) F�4329}].D<R.~ -WTW.P�#2APh.*OLM\"{u}nster 1999, :y9906205Jy2}>z.�22���Eur�3�N��~Y2001)��3, 269�Q6.�I+ D. ~ �]D�r�E�fa�ZZ�alh%rip$S, _� Phys �23�OT�1, |U92mPietsch�F �Ne�5s�<xUT$l4 fromAS��2German ed:lby William H. Ruckle. Ergebn�W�YY|k�;L ihrer Grenzgebiete,�Bd 66. S�#gJQ_-&Q_�V722�A} M/`�A �.�;i*�?e.i��^N�4UɈ 2, 2�T3232�QuiEv- }�� Cochai�:*\ɟ��}b�8�9)�Q139U�S�i@Tre} F. Tr\`{e}veD]it.G V�:S%�,�V&*d� Kerne�\ �]emic TSNe�`-L�Q!�6�Uoc>F 6Qd&Q �6�P[11pt]�PQ .QBcicx} .lepstopdf} \font\caps=cmcsc10VL�a�PbN ensu`Lth*+?L) fig}[2]{\ de ys[#=,e=#2]{#1.epsJ9no}[1]{�skip\�E�' cou�w linkL)a'n�%H#t��$[_Kwristg2Kin M1(acM .#A}�2�}{.75}} 2%A 10 pt(a))�$ 120pt (b)!�figno{1:� K�PoinA� �7cha 2gdi� 3 msel�5ofMglea�g�b)c8n f"�!� quick so�e(�7l�(�Iay mis!�3 p1�!}): W; push�:i irl's-~�9eBL boy'sbq/%~q st`� loop over(h�G�{t� pull� free�Rr �,�3HG� -2�pb�hand}{.8e�)�2:�ce]}} �8way!bu�e �O� n!\{ sk(�-is�to rem7� merid�V�$m$�a zd wF$$w$, embed�7�(�sp�J�3(a!�(�D:�boyY%\attached-��A�upper �m�Nis9&4il! e�:tA u!�t�K.) O�'uryA� 8asy: just slide%�#$w�?I�$�)�(e:�%8U3stretchA6+3QFof"$�$p. Or put&,�K�*���i�@!�&�t�#%" $\circ$\h�>(-.025in$-\!:%in 8��=Pslips-uoffr� puzz� {1��Ű4{57}{52}{$w$} 6}{5}{$m162F(159B)263 )k>2.)23�.�� 3�$ Coffin's ��0�/c)]t $k$Si�3�G simiE ;at �- Stew�8 a �.db}�,�(�8 Inta/tuccioniaoa r�M issueMonthly Nbe3ionni}*theM w$A1 confZd!�gh��"�ly (a14��3(b))E��i��no����#se$can�mb�&A�6ffA�. 2�� �r�9s1`8i}[ calc��*:�D���́�}�a�Q�e���fu&w,>)�?|men�' $w$.P2 purpos-][nš.>95. �8�^#��w$ 2s�A94un��"lambda$ -i-$an arc $\a�ZAdFni�- e ob2a)%a�by ban�h�mponen p$d"�� b,V�c��AcA� �$Cn28"�A�a"�<��V#�|��a"CmayaJ�e���; !�pic&eas9�AIw.�5!�{\s�HA ted} /tradic� @f� 2k �non�[: ((]L!�(Indeed, vie��=I� �k/ �@{ ax�+EV& CA!�a�e�i�!Oo� 1��%=�e8 bR�4 (cf.\�'rolfsen}�Mjb� %����4:2�I��2g2A T�3�"ρm!$9� looks lik�g.wor5�(shrunk��� �X�l``free"�7�greak �Ka�c� ��D(a�C�J� ^m(��N�� I�unlink��.��KarbitraW Ontch�sŪA�r55  f�beast%� A 70 *U 68}"U B A EF ." � a&=:n -10p� M!5:��g�c abq ᛡ����!�v hop�7�*�tunE�e�ag�3� ,�,Jb<:�8�Q� � �.&r5(b);�)  0<�Y�nd � � bef# ta}R ~eDak��� pof Marty-3rleman s� �9�� ����E�0 2~. (fixA�U�)�Larc�?us ost �� �yu3, ���Sll_ th9 �;2=&25 , r*6 ��r3�5c�H�5of�Q��m� �how� recognize�05|Y�%;6Sa� i�y�k\ % �[�I�a� pG�>a�! -w�/)n{�S?�(}.,] : e>f�� "v isQf �[ two,�7I�H;$x�$yQ�J!�S6�k=<  56(�ona �N� $x$-  M$y � G)GQeIUz*�]a4�. �.q"0be �G�pi�ar�FY�� it's��Es��QD!m-lc�E���oa�%�U�c� ass}��"0SX$u\sim v \iff u=x^mvy^n=�# inte�n $m,n��Fi�*�6t M A�� ��>�$($!`� $)\ ?�1$�For)� �2<yx \not @I�i�!�5B96;e�.CaLx m}UVarc� -B� 2�-G&� ,=P5��w�r:x7. &�7a�eCe�F�6%7ch:�9c\b. ribbon� � 6: AZb��.g:n��!�Joadpolynom/+=j$} $t^{-5}-4 H1}+2-t+t^2+t^5-t^6$� AlexaYN�8��'D �.�2~96�}8} q2� I:�,oblock :T wWyt�" �k )� �"�}{t11As2�p93/ 39%�b�"db} P. srDelft�=�$o��an#9new h\em C�o ve P%�D$the World}6�brams&�|, 1975e�)� Vaughan)�6D2�">�2�S�! MB+Iu"iaG_.MN7�s/z25--141.A�N� B&, ��:�{articl�F6�n�nams�6�anysiz:2 psfrag} \%f�j�jm.Z�j def.�i^!�GIjV)kW3}�j^D cor}�jf nj!n{ureZicl}{C�4Z l�k�kV� ex}{:k."�m in{t�}{s?}!Ӊ�5� {O� n�\ Rack� QuaWAs}� \a�j4{Pedro Lopes\\�iBo4gMatem\'݃',Instituto Su@%r T�b nico:+(Av. Rovisco�q.q41049-001 Lisbo>dPortugalP\1\tt{pel�Qj<.ist.utl.pt}\\ \�-�Dennis ?%manI�%�s � ment!��6�kIow.�(MacLean Hal.�& C�8IA 52242VUSA�ros� �uiowaI }�lAug�26,�'} .b�*a"�jW]visit�UArUqM��&�$�Qbasn�,m#)�z^" aiJ �m�Qr��� z "A. A�]��L� �ld"I�o neV s. W�>soWIa�analyz�$ve� 0 sB.� V�h LS:�h}Yͭic���wn� -,5[Jd ape�ly4JoyBnndAV veev;J��d}��QsMa"})� �>to  �^s!R�^� +l�J.e.�v�C$�� -� .^t�x �%!A� lhKauffmadGyR 6k� �,� o "�  �T� it -E ?1.g7H�r �#rl!by Fen�Rourke1&r 0}) E procedur+)�#jd8;| nT";a�b2[csuMx!�% �so-�ed�!o/14d�=16%F CetS�)@a`�|-�se�]��Q;< describe ;9cP!Q Q���bVn^;s I�Is QreMA�>)gN�[9#�Z2!�:i�Zk. Upona�ven�`��9!ofd>o�*V� (|2hyper,�p3��cr�ng�s (360oelf-i�@� 9�P>WGoaGnrcs (reg��0 . A�WM-�%qQ�A�.�reg|��$he X >X�.*� by �ng�Iific relvsI.���b�PJ%qQCVng�oM�M3��%s �;��D�ci��M`Reideme1o\f_�(M� m , re!� t�mak|�A�{���"% ted M� (: .m5��=e�&��^A�AJfs�� q�yi�Q|0o H%z!a�ambE�� .u��>` aAT�w U�B%]�{2U�bwgtake ��3 pL5a%��[achtgt"Qce}Nes�C'��) t�6il �Aw$its mirror�5 &�}��X!C. ᧅ$e1g��o�i �M^6�B�'c&� � �tr@�� .�.��%S%�@ na\"{\i}ve appro- cou�5g�mW��,�.$�MDtapO�s (K�wY$eia�E)a�ElGTlA� �s�7�EͰ<jsCetal�pV })��%z�n,xtremely eff� v�.�f(qof-VB�'B� ��an $3 \%�D� p} primI���B ten �n)�t� aA^!J0(��DL��A�� evan�a cces�$f �9�GtreA�bell a%t.�AfsBs� r��a=\"�OV� � !Q� theQ, ��A�arE�s.7 eq�%3fi�d�s1M).�q \6@Ac��d-KX2}�� Nota,"Y a0s-c�fmipp�i�Q�*/or �to{Co}""��)e"l�.at� 8in unanswered. �N!s �m. A~OrQY%d�N�"d�MuDdVO? I�kD"!!%9 �:,�#G �  $c>2�>ind�� n\sb !B�ha8:q y yS�;r$c�e6�viaJ��KF�!B� Zd �$. Ca��7JMbe fur!�F *�K!&RQ ?�(zA &d a?6u&?A�We?)iev�I&n �a E'A_A�nd���ed �s�n� ��JRns."*y Y��. 2\rH focuC$M�|� as s%9pe&�KS�yon GS:prel}U"� $the passagF �+ r�.p*;Uof6:��&basic"����^ �! re�n�ax� P�R i" X���in >�erm�G�s� inv1�2! �v*�&�s-�O"&r:2� F(N{H comp�Xx briefly�c�" osab�'!0� �Jn I��orb e"� $\Del�:o !s��� b%ful �' :`~!�pr�Y,Z we i�/i�Fe �K?"AnWfil�TClm �A�� �y!s:YP�q .. 6�r& E� ��}ՠ��"�BrX5*Z!�%pD AG},  in��ce)� "�n2�Ob�sgN q, �d$\ast $,Cs.-�KtH^A0Q �� ribuo . D�d� $X�&e�J set,:II|sta��}Em~S�g� :)r��V ac1 �$G!��(�U�n$.� $S!pn$��,6� n$ ob�s)F"� �r%AK�  sse�0�� In*� H  $j$-t�4lum%���KF* tPb�V���!J�C .�*� a<Pjy ( � Y�P%�I4sea:�� ��e��P! tur�  atT al��,!F!�Ջ��9��] 162�r�Ńfact,i.�A:lf.%�am�q sa� �!$$i` {j}$l-�r& �W ast$DXk� 2(i" i')=F(i)'RGsi*"!�Cu� biAJ�!n �� .�!�.C) n��"d��!5.a9�O�ill��(. 1s�"�. OurEi�٥<no�nd%�R`e�beV jRoȘ}�n� ��y Ps:�ex*;ex}�"QgerELgTe� an $O !�diheds!�# �", [o�$Ri�ņ;Gxfor?.�Nfs/$nO�_ �s+a{1,2,\�P,n\�T�n)SU�S�2 $ICj := 2j-��mo�K$.��T4F�"/�a� �3#$d�i�.n Ts/� f{Ta:R3}.�d�=}[h!];�qb|!0abular}{| c | }\ho � & 1ń 2  3�K 5 <122<3<2 =26263E>rL\\Nl3,Vb- @L66%�1 "a�{�M6�%s,\)u�x1`P�!֝�J�1%� then! 1 =1� pmatrix} !A!3\\ �2 m$( = (1)(2 3)��� $i2�ex�sed�k� � 2t�-P8�v^1؁J�)e:܂, �jforth;�A-W$/()��a�� ��nt! S. �Bogo>�at)2� 3�S���f 3 2 omit1  $1$-e@� ��i��k�Y��$!�$�Q( %N, (t2)MnI��wa�1�1 q� 1(1)=1T �  23 j(i)=�'=�$ �$%��T� �j�L{1,A3\} re�*,in� ����-$.7.�\g� $|p��$i� �$!+.�R;{n}Aa* i$ K p2.RMma�B�0ay�$[ ) {i}=�n0\sb{j=1}\sp{[�Ln-�L}] T; i+j \quad i-j\; ) \q�!NG�]j ���\$T� -��Fx)!>�E&g .k � "� ;�Fw!J�C ��?)� �V�@)�M�'i>*5�6�: �z�B թ����A!��%3$�B�l ��1FR6����YJr��V6�ņ6�`���z�T3j�+$n=��6>%�A2j�T3} 2bu���& ig((�� ), (���*��h�ds�Dav�ty.�� Z �is,+ M�4 J���a�(a���"#e�CJ���icR�It�}de6�}i+� Fe+1$� ��zfet I�tft��tata(qj �V>ita(6j>ita�6j� �~*h �ztC�trtC�t(1 \; 2 \; 3a B/�>e �k�e.�@Q�]�Fe��\c�y \; ny�"�%�(s S5 & P*�.� ��v�Z u�(* A�[�S��=6= �:n�="B *� e ;�6�"�q�q�*A�\),IV�0�FFr�]=,�qu�W X.�$Z� holds;^b`� k H, $>j0k= k (j� k)$� ��e+%8%Uq�����as ``*"H�"��h��,>_ ity"�%� r1��})�!�,&�.���i=.�T4�%�`` d�$�L^�p��&� �"�&a(-:Y�&j &�!b�a. w&=5�sG �s. Wit�losE�m�o�: :NA�aenA�2o*H &3�.6 � c�$�E ] X tak2o�{ 7 In� "� n �u9" expl0Bly 7dF!� �& A-�ai� $k$--�=$sTJ$k���0,!O�=) �4~'�ply5d�ctp s $i {�' 2}�� , k� l �Y� F{j}e�8  neq *��MKRo>�a� �!a)#%vio� s# ��CMYY�. A $02F $a�  e2� �+A2��v+!� Ws� .O +!s.6+%�s;�> �AZ z*� T"Z%n().&� thm}�+�:���-�jX�: aQWM�:.�.RD-G� �iR�.� �!+�symbov�1� Q$$�s� $)iI�X� �!39io�� sM1 � � � j}(i� f є$j3fB�, y���ez stru�BY X$a1�jv$if��2� w ~}� j  ip{-Wb j� ��.��!�P�E:1� $(X, eUoiEvnB�)+� �AS&<*kdcl(���bigr) ��k}(j)}l(- k .��7l)quFi6G \ kw1< kE Eh�&WF_Dd]ion�Xwa]E��Srse. SF�!p1A�*�G��&Sk�sK ,.�Z\1�kpp�b �b|� j(k)��So*�D$j]_B� �Z&�!�0k=w �1Kzj. \hf� $\bl�!�E$�u���aR=.��m��eX.�.k����b|R$}�% o:k$Q�1�])b n)$��vQ�!w:)� ��%a 6�2|�Yem>!:h+#I���fŒ��"��n�i��?thtw}ERse6N, p)R� oro}"�/6� ra0%�� "H  6~b\�uj 2��>� �$R�)I&,�n� �?:w5�i�$�ޭ$��$I�B#� n it�^piI% i"f|��$} Z T�"A6. M aFe�D&4�.�� $�>�!^��C*v�- �� oqi\:\bar{!3 }\:j;l ZL "� &� !$6L��s)5&Y ���to�". �y�,.�uM:��Sc�Sd�I�VJ$R:�i�e��fr�w�-me,� a��R�Q"^!�]��imRwe0�!� ral%~ " N*�^ai�hel�x�rLat2�Al�]W(�0,Q�m �BF>e���A )$ F�%^�r� 5�E�"� �pe�!�� ��:�$���&i%�k�!OaA�t�Vlso��I!&�(!22��?E� ��d6^ny�oE�)g��n����1͉�i; �( b �8 jB �ta2�%s.�S.W � �nj$�  i q�8bt)t`,Vu,26nb i �3 m%4%!�"��0-I"�!E%naXo9hT$j' Ub i(j)$A�j mi(j"2"E !�j'����4�{j'Z� �)!�')}�"?s� ��l�V�B�1�>�.�"-�4M' ;Z�Y!U�G!�$�� q2� ��B�M� � B�u��6@(��ze��� �2 �#�;%}'%ck$,W � j)6: � 2�*� >�\\q�(BDk =wk>w""  \]c! aśJW���$A~j�j>��a(jB%��'�x3 Vz6�kM�xI�m�E�� y� b� i)*�or> bNrk��^k|f��m�TQBai�.6u&e.F� Q�� 2�musp{n}1� R��"� ��"Pe.�E�$ $l*�M�nyE�F��q� j\sp l}9 n+ ݍ� �Qv��!IIa��&sA�ducP"a�.P"a  levRSigma$!�_&�� a��6}�Yex6V>�!n%��7�:,l#G�Jmon"d)�R�length" i)H �F�P=p.�Ve�cR��:}�&�(fixJ3�(M&R��R�U6BUM���var P� ��^�7 d61ast`� ivelD�!i#1ir6}BV~ 6|��'t��0'�.1 nF26�uPD *C Jh8}��!XeOBXp ]~�U,J $,A Ȋ%�6�s*�!IW���.j)= DL' j(�A�A��NA�$Y � &�v"F}� ��(E�J�mv% Clw{f�;is 5cW�ato�!�am�*75ge�.� qnr}�5��,� 9).l� $k'$AmR $k=k'M`ѮA~��tor�!3� k < :� )= 0� ~sm&�W"�G�)sb<�� {k'}W !��-q .R� ��J�''���U4�$}�U M*AJ  t>,$9�!�-"\ =�.>Fc6more,�B �.��q iso}9Ue2X�A ��:�: Bwa�����m+  � s� bM���tK��� A2&4�"� �u�-ne�)��>erm�@!uDE��;; b � ��:�|E ��� ). L>�[-[!blyJ�*F#2� , beE06�� I1,�*�/n4S�on&�/boX njug��'b�,�23)1, 3�2\�%K} : &�f3�-3*23&A| 'KF\muM U��K �A�e� ovx/��b�8f+onutwՔa*����-� "�!In�@E��!- B�8s*�!O8 <FB��%-�ne:>��&C!�two"o3s6.n��aY&�@APd�1,]�� c. B9,e�Y'@4ms�, �&��:#%\nu�I ��.��6d�8o�/�  9i2� �(�B ��&& )$q=�q sp 12�i{.<�c)(2F( ) 2}})ɤ /kF/ /k�z]<z%kl~]!wR�  @"� �k" 7{��p�@n�\nu���s,�!"J w(:�х/ A �!�� ?(6a ) repeats2|A� �4EJ�� }� #Ags��� the ��0inv�ȁ�urNH bracIt&x ei� ��A�tK3or:4! 9AA�.-6� (�Con&�G9%f,i�(�f{P"c�j_� �2si4ro."dK��l-e�:�.��R:=-��l( R*�.2)(3)(4�& 'r)�% \[ Sb=)(1 = 2=T>= 1 2 q^ $2KU�K3 2�2KVBKV1 �2)(1 4�'3 2 4 NK"� n�;�#�L��� � &last tJI'1c�?o<rv�m� @2N"��0w%"��)�i�6>o.��A���e�Let N-i�� C2�2��J2.r� $\{��p�#��k�Mi9 mNi}�0�>��|� C/�"�&��Ux$b�/2� Nr�bia�6�� �1}\} a 2 �R6� 2n2cr)�1�qrog>�q B/-�J .� 5+ A`a{C��)�"� smlS� Q]jZ .N~= af�7it,9Ec .P�a! -to-a&o8�Z ��fO<�n:�via��a ��A�xed.��:RL^M f6�A�6��v'zw subdip;����9$S�TU $VQ��FDp *, 5� (see�6&�7P�FM^0B�1:��� Cm}{1.25}�*�  78 88R S.PI� &f0, "{. R7 &Ead�,�, 1\},e�> �'.2\}�5aA&  1b�) \\\c�8{1-1}� 3-3} S & �HնU )�T 9T�)�l($����6�f �� �U' u!�=I31&   Np2 X ((1 �m!b�34)).C6�.�V%k(�8�?�T(2h4y, y7 \AA.�9� Q�I�cap� {I���TheirQ�s�4�9Pj�3"�h]�c鷭[< %n�T>� 1E�2�>�>r a e� two� tinct ���76c.a,@9m r�,�|in �h�9m "�44b5 ����c �:O$Ta:PRBc%[FX<�g�gvk�e &YfD!,P�� &...5as... E�e���&R1V��K T �\ U�4I�  1�5��>0f�b�2\N��j��aY>� \�i�6s 4} S �,�,� 1~ (��)(���� �!E3�h*Vz�ҁ/�)� Uaj"�S$��PRj�A&�%{% ]6�Z�, E3\>ti�ly�2�x"��is2N,Rt��O ��9�z�J��T9�� $V$�^��^�_�_>_1�z& �|�5ET EI�3Z�Q� ��a8zV�2Y g�&�@�� d�4�>����l� ^�5.: �v &&HN.\\" B�V1 F�&u}b: Y�� �.)9�JD� k~ &("� 0!$J� /��6 &��  .f��I���� �)e�E��!T� $V2&r'Now $T2p72T �to $U$� V�"�K2��s۽���U+l2Y^an� %.n�!f�� ~nor��27"D�L.>.��D>" �<�u �I � �.&�F.*�( e�R"�:jSu1������B�!v 2^*D;�)b&$^����@ �v&�!n)�$>��t� 7n}*�~Z ��T",%.�1L}M6�' .�6� � �}\�7 , � �"H�  0m}"�)o$m\leq nA9th $r!i$`� A1$�D��, *��a. D{�G2Rkp=�� rhom ),� , ={ji�8VC $.D0*�" P 1+�+�3= I:2U kx .�lsD$ l!�g6� �1'&# ay $)��6� !)��edi�!}��air>�9:�L �!PU* vb�o���a�!<nec�Ri GnCvof.BiesF).Rv'��)��l�.X'.0s,� .�8 q}��Bi{}�baop98eR�4}� �9�%aIfa�Xr)"�Bf mf6�, f�ff y��zAB�p��/��2;�� Keepe�h*N� pre�&�20>�1!}5���l( �E��L(�!:�q{ 15=%� �<.+ ^u.�mVt%K,\ �!bnc :�x m}, .+)�!:�abITs��n��.�1�� a�a��OL��i�Q�Tsk��88X>�2' N� W�35z|Ak:����1� 6�A]� u�) s*KzPD� 2.0�m8�f  � D%� N& AM ,� :  Q$AP�;�S� ,- \{4"� %!-K.�05b(4.�)F>*l .2U\��M� ��!��!��A�1F L3v��� B��&i>�a�� ��� �Fu9E� � (2 *� "/ Jx�%�~8 � $\{�3 ]Fhh���q3}�\Taa*eE!M� �Q&� ^1 I&�� s� a�s�7i��b� ::1�ɩbu. m"Bdi"L.�6F�'��',� true. s�f� ly�� sā �g 2�h��y� �~.BJ�-R��$S$ al+Eg�a"x,p,-"/5y�no�:� ,� K �4� S)$2^,� Nz'MQ}EB&6 '2 '��� p$3#"#S^�9m�߳t 6�,]ru�Cm aZQ�'b%���n)�for� �  $)z�ksel=W,�!,�, ?�at�<$�=d ne�)&9gby>�92��,t!�Ssor�C2�theirQ/s�0JH�a��]bG�[ w�FtFigvE �*"�-!V� r�F. Of �+�w�b`@end&j;rd!hy�"� c %��~c�`yMG��E�;mefci�!Ed<�iq���m�Rg Laur�4&uy��a n��&)DofuHS&[s �$a�0,b:=Ta+(1-T)b� �$$a�bu@ѩ{Z}[T, T(+]�4�$� �m�m$I�t"-q #"�`��ta"H�e5�ie<�A�.�i,�$nT� E>1Fq�o^�wb� A [T, �a s!���cW�$[l�,�I.cbchoV�#/}^nd ."�9�'�,Rk?ILA)$"aY�&�p-.Ff,�@d�$at:�9�/(h(T��&($ �`k:��+A&9J $h6:"3^n$Z|[~H1�NWnqy!� �F�f�6B�9�/(T+1)$>�b �bsNelso.s� �)is�f�� any UhI�$p ��iW�e%�$p-2$�'"�M�s ��5��!kPF!��TarJ�AD�$�*:�pA�.�T-m�F&8$m%fa% $\{2, 3"�Rp-1�Ka* q� = }��`�.ice�u3�j=UWM;ll������te ons9l���El��$p=5$*)� tech���v"x"�vp��le*)�)!|�W)ZFL.Z5�65!U2[->ZN'6|.}Z.�JR45;�O*g7.3A1,2�60;1}=35E+�X 2}=�*536Y3}=�*452),664}=�*32L�Q6$5}=(5)(124?\ " "/"�a&A56""m=�hA�ee �� $2�j[3$)�F�^8 c | c |}\hline 2& 1  2 3 4 05 \\ \hline 2N1:2N5 DEW2mQ2J2J�@0 �` � �bJ3#+J4 `A\ [bJ4# �6%9 ` � [bJ5#+ w %7��[BJ�F\end{tabular} \caption{$\mathbb{Z}\sb{5}[T, T\sp{-1}]/(T-2)$ Multiplica5T Table}\label{Ta:m=2} acente` n�le}, \[ \mu\sb{1}=(1)(2453), \quad (2}=(2)(1435>(3}=(3)(1254>$4}=(4)(152BQX5}=(5)(1342) \] (see mu.� t� in � \ref �$3}) \begin!4le}[h!]�%e%%Y{| c | .}\e6!�ID )� A !� !׾MU�A�EF _B%iMyUou��AB ��2�iM~Ju��AB qZJiM~J3 �AB qZJiM~@A7AB q:JQ�%��M3)�M3jM andNR 5)(3BqT 3)(4bV5a�^X2)(F�qZ4)(23�\ 4}).qKe��]�]�]UA$A,U5r�i]4Uu]9JQ�I�:i]4J1 9Ji ri]4@87�i�b;i] m-iT 9 i �BJ�]4�]4f] Now �iXis not isomorphic with �=�nor�/� by inspec�~L of profiles. As for��wand��42)$, they have 8 same detail. I2�theirRX,s shows that of��$is symmetr-X re%X to the diagonal wherea eof�  2)$ )� . Clearly�V9�8sm would preser%�y hence��!�andR� T.c �are:QH. We further remark)G@these two quandleE,m an example! ,a rack which!Q:�Pto its dual. In fact,[ sequ�EpermutaAxs, $(\n� , 2}, 3 4 5}APof\o�T, omitting $1$-cycles,�>,align}\notag�1} & =c -d$ = (3542) "t � 2} =r +, 5341B, 3}= � += (452*\\ �� `4 �� 7 �2576-5�� +b2431)\ � 5�a^�!pN�6x 2)$. Since�se ATA6sJ�p M�pfollows. We will now develop)Anio��m�Ly. Let $R=(X, \ast)$a $( $1},\dots ,  n})$��0usual meaning{Q$def.}GivenM�p, $R$, we call {\bf opposite}%A6�$R!po}�%�oA��l�algebraic structure whose underlyA�se� < again $X=\{1, 2�n\}� 8(binary oper���g�by:/ i! � j := j i = - i}(j{ ��any $i$��d $j$� $F�.�Z%/ 6? Keep�AT5above,-U�C!Oed)Q-�ic} ifń.� f�, $6�=  j$.���\ prop} S�y�,an invariant)�E�.� �;Proof:I~4\alpha$ denotE�26 Then ( (i){!z'}-� @ (j)= "i � KB . Sb@$. $\blacksquare$!� Whe��%�Q�A߭�(�4.,�%)6 �<)?�U2v�!G: tq} If.� )$%�c�@n auelementsE�ma $ satisfy�� condie� i.e.6 i=i$I\ll $iM��1�O�edR !"atA�Xut right-invertibility?yS2� 1-c}I4R�4)$ be a finiteEu. A.s-�%6klea! only if, �ny�~�%SPre exists a unique $xa� J� such)ii x=jJ:If 9�isF� then�V` 2�v� J� �j=xa/ii=ix�7$vice-versaF�Th)�aat.c][on Pro����!�: %�} $both left-%�>�. AA�B  � >�!RzR is �ReBLsi-group (\cite{SR})*� ��G iA$quMs��be�޵�, its �45Ź�R . Fy 4more, dihedralZ`A�Lodd order, say $2m+1A�re+�s �N� �06�E �2��equ�$U� = ��Ds equivalent to $2i+j��� , upon :�on)�$sides by $ �yieldAC��mb$=(m+1)(i+j�� Stra�Dforward!�cul��  alsoiy�$each prime)" $p$�4 non-trivial ( ar) AlexaO!8)c>E m m 0 a partIanswer! !5 quesE� of w�&5�of 5�R� We start �9byA?� j  aqsd�"� � nF��,nA��e � ity ". From$t s made �� before.�F�� n���a�j�>�>��1b{����:6;%9n?}qz non q�i�J6o ,.9��5 :y � :�-qs �E;t >ye6octa}!H: the :L��m��]>u%�"� leo is�%/cta�gonO� AG�3J3�����6.���-E"�0"�2WDG"�"D�> GnVO�IXvO�VONo �R�.WVOJS6Ye�2�_VO6 wE�4&�X�/6OMFQOY�Q� 6>ie}m Taig�Z\ le} � �*e^b�isD)1X3F�156B7m126R136BG  1462>B6x54 '�ǥV V��y$1�z (2 3)=  6=1$��$( 2��  3)=55 2=6� us����Jr�B� e. H�j8N�. �yV  w]alt�� erty� havAjust one\� nng�_�"w ��. T�f$prompted u�t� e�ingB� � 2�Forl�n:A�N�4i, j}:=\{m\in 6u 0^+} \; |\� \; k=&m}D>b,0\epsilon67.m} ? \pm i t:>j=(\c�(*  > U}�1}Es3  2 2}) J R'm '�}� �Ku+1!/ast� $ o-:\bar�}\:$). �9k4\neq \emptyset%� $m�1� min 0 $, oi wise6)0$."� �n2w� ypis2$c$-coE�ed6�.:ON�, $m(�)>��0\[ c=\max \{ ( \: |\: 5-�:� \%|O�,� e} :� :��,� �==x�0n1��a�5 not 9.��%_�4� � :V�$2=V1�2:n�if1�of�� $n�2�D $c>0� $c\leq n$ �����.4pr� 3 2knes a.�of%?s y.�8 after introduc�!3relev%object�!U p!.-*%t�>�F���$i�N!���se�{\cal Oh%ia�{ :na�.M1�&�l �l�aj� , \:ZvuE�n \/ 6� 2�����ti{!�� rbit!�$i$:  -�Ec%���mX�$sm betweens�) $R'$.%�"�l�6�, �b{i}$.6.��5a, {� vely� eA'|� tric��>z�  biA���>#j  � ]�}$. F.�5(induce!_ff�of �s vR$�!�2&)F� %��e�&a�1��&&-\Bi6� r) b(��m. ��.��}. V�a. I� �B. j.2CF. \-=� �g �= ((YAp>Q $ ( �)^+2} +��})"�Z^m:3m})Z � �r�D�D�r�*I�F2f��ɉ>|.�mClearin�|� previous�F�6�D��f&���pic ��v,�'�w��a sub�i�F���u +atRN closW ��/� $ E $\; *� ;$ "�s. Con�r6"� $y�"�6b�� 6� ��v'l ._'a� Bh� u+RJ m'}} *m'!�nBX)�� �>L� Bk� b�&� >d}����  (F'%f%� B� � b !m'%�P � <i6ehA�A�a:A��L,x!�Fmost M�)�B���Z=e� $\; b=Z�\s{4on{Indecomposa�0 vs. Transitim} �S:i -t*� S M� 0briefly discu� 3`� A `!'�is��#�hx *� A � �#� $2�:#a� join "3 $X=X\sb�sqcup 22(1, A��$ 2,"�$re�*�2 (in p�c., $ T-� 2$J ��).�  ��0 it admAa6%E/ .zl�$��� %X�;1fRyder}!i!�:P�sai�#5� e} i�is6R somev#o}!  A2��]r�2r*!Vz7 zg:zk@ z��r��"r�VzS91XV49S �21k�825A>~A!Vz�� 2 q z� nl�2r ^�6l5�4r�V�rA�p!�4Y.?!;W w31k�926Vz�Az";�iBr�^l�Vz9&A�z8 �D�r� ^�(l%6z�F��p�> z�R9f� Mi�"un�.9{Z&.; 3 boldfacx:3gb 9u*3�,�m�6Mor"�2@� �1�<:�&=��$1�Ōɪ$ yas $3Xin3&��" O�� $\Delta$- *w orb.n � n ;&describ!Za�)orithm�obaingK�� �,#g&^/�is alWi�,b�,&� .C.6� I d�-7 }�R�28,A%)�j�^�@= 1d  n)$ %�assumA8e2�3A H already broken dowT8'duc)0diC c3.� $\Sigma$ *./ ��4>:�suo1�A  �1 �&� 2� �. �:$C-m [ &6{ Z?2~?2X 2N c � 5'subse);: n � !��7 �I&Bl� 2 � P�$x�n� i F  +{2m Mj( 9)} 8 2� %(�.�5 eiP%i!�1m�H!� r (exclus�)a�-�(2V�0_�*m�I�y�� u�!IB� �&v�: Fix:v$&�)$vw"�4NwE��vrv ��1}s%�s used!�ex�8s�)1�i$'s a�^�, except*V$De�"�!set. ] m�TenES�{-iu#p�I"�7�1�I� {i}=B)(3� (n)=(�4��soq2}G)��de� , $T�n}$. &� -� �H5 { \s��a[�Xme�A�� �g, nteglmi.ere�8k�7u1� k " {�! k�" k) \qC1Dk m< . n�!�j \U� � . S�s #l}� k, 2�O2���+ $kWo7 [E'!�M� �s �/��Ed�I$)%F# OAT(X \setminus�0cup_{k=1}^{m} �g�Eq,� $\{ o!�1��#, l�=�W ��5M�MI� a (*f%)�|. >Athe�iv ��E!VY 1-y�"�1 yE i 6�" �0!��F�J= "�#!�� SetE�,displaystyle.j�p 1^8�%ziAQ�%� iA| !�. �1��A �p 1=*� e1.� 2E�96�$�l(.oW Q){!I}$r�1%�%6�2=\A�in 5J 1!�5�{je�}f�!K�5E�bNY�:6Y 6^F�-�=%!p 2!�BA>up�6� �}EcR�2)�.i �t��>� 2� �n�_9� =�.�{2�b� �3F� 2B�-h2.� 6X �aY%��bv^ !IA -2^!J��!6\m!b�3R�2 \j�3.��=w�& deal��+ 2K e~r3sKe aJ�k2}[k !ka {k-1��{1}�� en,A �J2�=F�{k5!j!i��0! E!aH)�lcis � �\4@ consy=� se7:�~. � Evp ��i�:sJC4 0}.�JDEC�fR5ni F46iBO��s~���^�hZ� w{ !�p 0A�EIn}2� 2.�0pb�_> ������rH5AC proceed a�B�"0!��@����'cS(hi$stop .:� step8ing�8, $N$ gsC! ��"4 .N$i�h�$n.�-� �: next& ults addr�8 reJ8�&�E% ��%� n4i&� �-2|.. En 6� cor�&�=ng�P�"� �} ��/ )Fpatternb��$ =7{  0}Y'%� W+  �n| �i�NG, w�ve $i A  ( � 0 V11 2q   m v1_4$\y%�  i &=�A&!~l 6l �m}= R{ ��!BU� 5V�JC R(K9sb�  ))<KsP=o =i% &�* m}� -& 1.M 02�r�yz/28mŎ-��end-��A�*�F�I-'E.i� �Auis�\ juga B1nR E�{;8 thB$IQ���m�=sR�!m�corb��d"�!lev��se�a� �6��G.� %T\J!a! st&���'J &�leton. s�m��F���>&��~:5pp�-�}� p�EioJ;'-^� �def:d��g)u.�3r. 0%8i��"�$��k)��fin�#QG� way.�1= �E�E�k\geq 1�ap{k+1}= �<���W�F_� oV!s term� b0K�% �K0i$}, or simpln��?i�}I�lengthb ($ S�! he number$�LiA�6�"re2�Jx Ps can, �!e�"in�!e AVs, but�1N *E�sEs��.�?0 sets:Af;s,A��u��M��M� $:periodic->�$��A�"xrbH$i&`A�$*n� Y F�D1E� DA��%b=:@A�?3L< ̑* YM�l�$ 1.*�!YY� :���i}��k}(i)�"!K�w.�@�Ah2��'V5claimNX��eXNk[�8avH9�Di��{i�6=1D`�d��ve "[r2� gra�_�r R�,QZ2� 92}&�!D 16/c}�� �Fv}�K)��)=�0:&-%Z=&CM&O'Q� G �6&!)� >8*1�Y-r>� D.%!$(i6�Mth�-U`E[. �H1is�G�q>�asTP6B tM�m%�� {m-,�&%�k}�0\; >F�QmIC6JIl}� $l$eqfM�21$9:�2ilA/ �l},\; �Y \; ,I\m _m� an9�9 l$Om}�*��\; }so on, k�Lon repea=a����$( ��G�}e}o:[ m-1$�qHs�Z=��� RUI+m/ V/��:X):�k^�kR>�E��E�] Via.����$:musp{n}1}�k~�3!B�8 �E ly m�~��Q�s :�6}�(!�ident�C*� c1ly�{tradi~4prece ca"�Ds. u= $l�=iLa&Q 5�o05�I�k%�-�}KLC)&F ݲ�`ٲ:�) a�ts�iodn� !|}:�m��K=\� r��:���e�J�%,C �(&�KDY=�;1}a�%�2}i� m})\pi$,p" $m�!`RnG tT?� 2}, W}�!�KU2� &� �F:���Ia.\� Z� ��/� % "M%.��1}�2"&6 ��5}$�;E*6 �n a.� 0 Nn"V� *s ^�$:. &�q� 2��� & i(i"� i@Ei�W� S 2kk[%� lO8)W��% %[? � !�� k�Y�g�#�v��  �e�%ish�Hfirst!�AJ statQ.� �8C��"�9�.� �����} ��KK ll $k \9)K, �!$m�^�5�N{QZZm>�0� s�to.�0$-#Q�2 'j��  (forth until� Dr�"�N�� ���mpleteA;NSR�%a_*�s:�#�j U�� � "�!(�&�#*� �N� cap �AS�#�Kn(2�9<�!e9j$pܑ;e%i & m |�92�CpzC79j a�{$bz:C(! I� k-$T k$ 0 E�I\�W��K�+ 2�,�40� �5ic;�\B rC(%Kt 8 !�LS %�k'�[* e!=�� �Wsb {k'}qJ� [=�wIex�S�Osu�S J{k+p}=!{k'+p0Rq�p.�6+�v %� ; ;� Z+1-��6!�� m"�4.Vc� :�. Jy.�X6A�}v:iso}I�a�W��)2�Ab�?�E%�Z�?U�W�6 �7k*�( a��a�;'��?6J�?6!� �) �9�?� �+�� y6%'N�C)�D-� ��S! sb{k� �=kc!>:_� AsQXM|{k�[�>i�� ��"H@gQ�JbiVF@�� \;b�w@ r)= c?5� �&�>R� \}=99=) no�O=Y1EeA �D.�$,�> 1 )'A( 6� B�'B�Z�)2�.� &�:sJ>�Em�*eab&�,a��>�X!��.�G@ �ZQ��i�$M�]�G67a r�`=RVq6�>�RD q8 ga�^�;o�].�+ two* F����=� �Duem� ��6"� "�%�na5.&'��A�7�$p$���e2�D��gk'�Zq(@6�})6�� rebyoji�76=,yi��a p ��[�b+12�=a�(��%��bigE�F,W&, 62P6$�2��M(N*!@� #*%R �tr!�e� �-G�^>�M�9��.�2�.? R��� 0 w:0.71 .% �N!^ G U.":w-Zn6K1.[G!^�qMa>0V� "r2Racks  bT�fP�s"�S:�#s] � aW9 weY-ap sibl n-enev[�"�Zce� ss gm��f ificaf�g A�-ual, l�+J�A!6=/c�+ * 2M ��p+h*�e.7"� thm}"� �*�w.02� ���.�$n87 ^�2�K �� j. M�4!]+9_�H 1? �(up�"�ism)%i _2ta3to!'�$CT n$ R_ e/ic 2.#� !9�" * b i=�� 1iY2 \�  n'eT] �5los! �<ity��.g&&�1byA��o�g !�.Z�:^����6_��"�<="�of� %. A���),j-, !-%Z,���]>�l A��-2assign�b�Fm %�} =k.Zk�S.V��.Ex]c&��3 studyAd!`^I,U{,)o 0 "5� �1>�cWeB&.:&case�?�i"W6! tant'�}�C{m, n-m\&� � clarQ�split er �iA6TheoremA th:p� 1,n-�concer�)$b, Coroll��cor 2m,n-m},2218m=6�recA:�e�Eul�1\va�m$-fun��](r��rB��n$�&� i|& 2s�'�M�[to��d l�'an �"S �FR 69 AnD:�>�6ith!$%�A%!� (� n-12�1 B3is2i6!U�uU�cA�QCD b4 "�"b�:�S2}i�{1}"�;�2� �A5=(�2�8,n-1 )(n),\\ r& \n}&2V;2 Dk k}(n6��e�R� $n-�Յ��!]mctly QC (n-1)'E�s B�,ŹperI_{�)2- x ($� <�$)BsO%I��� fixv&XE��hk��"��doekt;5:dex�u o�RF��E�o_.�". So �9oni�jsf�3new+a�u #MU{sm��\ai�+ 1)(j!��-eaD"�5c 16n$.�i3 1}=1Q �"|���# aCz@e>�?bm�� A�E�"�I� �� 2� **A�$& ��c n(n) =���9�-�x ( YX!53"$ .W�n"�  m�n  nB(.G��s" n%� 1�7� In p*@I�_eH��.�(�#Y=�'�@2j=. UAd�Uxe�. Qn"1&q~s7 AI ��a�"q 2i:p  b�)�=lc�fekQp��>��� n )� F�<�e��1�%su�)s{jz1� j ��~are&� Wgsa�n�E�n}�(mmutes�  $ �� Y�� �uis!i&�g._L $�S-: �2t� �� (_ralizR(  J9�  $S�!aRb>@an� u f 0r&) �ic �i� �U�#at�bus�H%� urre9+itu%hWw�Xz?�= a po�g�G#n-տ=8�2)R amougm Uy the rg.W!�I>u�Q� can q be��V a�c:� �dbs���Ve��It (O>R ��M��u Vind�~e�u � �e1 "�.��by�+E��z ��diffe%�$ko=F�u "�%dLcj�-��pe alJJ����u��su�'�$�aE�=(1\; e��Zi�n�X��n +V���E 3�E�x�Z����a��Vt� .,�:]�'� $, viaa&5X&Y $ (!@ Zjinct )ge�$q , k't �OJ� �)r���2�*��"�Zs mapys�7��B+Ō���Rn2d�� &�+  )�t�a,A!(�� E�  F"h#F('AWb�A�%� ��� iUX!�-A � J� A $ 2�<��A�J�BnX.�[ �=@Is!n?&som� �?.B-j�Z� �dZF>S� �V U]@4 2) J�) ��)��-�1�IDin�rR� ^< }v� %�6  )� (nr)�q{n:�^c� la�(1�^���NF� �-G&�4 &bx �w�%��e $k=* � Akre�7�1R�3W2�0у:�R>0a�&�ofb2� ((�)"�8 -)Pe� &J�eNBrF�p�*lrn"V�DVv2}�i 4�:�Z�3$�P�:�n��Je1��le�U�z�i�d67_,>� *�� 2f�.EQ�1}h 2Uy( m}}= � N 9,f&V�+ o�6���+k�G�+*�&rB"�+ \ �� �V �++�)*j#� j���%Q j%� $�%b�)�>� Argu'as �}Q� _5�9�� �9%� 1� :��)\rho$$$A�Bk-$fQ6�{^���}��B � Il� �( > �m+kPXbiswiU�!&�� :1(�2w=�'%H5�69� image�8�)uD I$��68�% Va \; m)\r E�!�� ��� 1� gamma �xe m+2X�yu b ���$\m,@U����$ fb�1.U0m� *A>�t#v.�>�Q�->�5"K6j"�-�,� =�jk= R$^�;%jt$>]z"�L�Mo�2VI�9�<� �,n)G%m+>q �+we 8O,�)$)���%� F>B V )� :%p�QP i(j)}&. 8]�9Q�� 6f F�E� e��7m�s 21�8 � 6�m)o6B 12l>�iE� 6��2$ seil�:�.  Z��$=�D?n�8�).�"� nN�"7, ~Q��6F�Q V9��/s��F� i4B )�jo>�.PztV��B)hQ���AUke(�>k$ Z ��(~Om+ V.{sp�� Wll�EB3 �--�$ Ń l$)*�an� �"�%m) ).�arr���eR\ �Sonp�^] �))�6�2 !�MB��2� N�"R6� �!�"J�  0�HZI� 0�I�qJG� � FaEHlAHё�e8�,z ZXA0k}b^a���� �m�Q���'��:�~�'j�,�� �W�� s D� m�( k', l'� o�~�e-qb���).  ��Y�s�V,"���**�� �� >�TJ��T �� "�Iyi�B� O �@�R�1R H%t h��; @i��, .����$�  Q �b/^�L(�i'Ŋ: ,  $ "�(i)=i'$�.s��s9#��%� r $jq*-b "p9� j)=jurSo�#�6'ys:��@'� e[)�V \BZ%�"� rv* �� @-1}M f&\[%F�)kq�: �m2�j� I}� j:* � �rv�[6�6� -�[J]�nce%5v�!J:� m )I�jaa�q the 6l �.�  .o6t \}}I�%?l'��i.qB��F-I6�js�&�$ZzWsFu� J��|(lud;�(oR�(v=m�;B�(m\"'7&�: n=m+�>�2<'m"��>�>�>�>R> l$E|^~� .V'frac{1}`<1+"$m�t&6m)q�U��"? "4�'R.�,r ���jl �[k��H�6�&� choiRx� =lE* rN~t*�!ci'uc�.n c�wof># u� � rc1!e �ClN�6-�*WS--�of��6Y"!�#2IC*�GOmw� than� $e�-(&�+$1,...,n-f}E�5��"  f,n}�.--R�w�"�E w$&bone�aof grea}�:R�- m1� �t�f�^!� s,=0B���R-98�3&�!n>3f-5� $f< !E�87:kZ�m*6x6� -f}25+ n-f)(n-f&�"�S�%(n)&� hj�,,5 a!N-f5 �j}}O1 ]BV,�j\in \{ {1"3�2��!$ _$br�R�f׀tands a 2�U�&g0N5ile�� 1&� �f0~)\, � N"�O_P! i}(f�+�*�/:*xe $f& d i��mm�h1  {�/!�f)}"6RIJ8=�:"�2,6�&�6.H$'��m:=�X!�f,�|!�e�!�@!exP.H \sum�=1�m}�4R�9� %��)e^��.B���;;m M+�]sb{j=Ee�n� modulo>* %�.e(. rFn,H &$1,Gf.�. B��:J A��h��)�e\8\�V}\��6aCo*lzM�X PE*4of]f���M��2q��)(�c ��+ť5��.!- 2 "9� ���  (M"�N ):s'6�U �A�acN�`.� -ls�2yxv�4!��2� 6� 8 :���0� E�U61MT�Q�.�9 .�9� �+, a"{aGsimilar� sUx,� �Q��(U(�5* 5n-"�L6(fixe@ �=_jformeri\do�%1L�j}=)A�jv���&�E�6�*��) XZl7A�!l�6=��}62� � z�"q�2c&N5� *����)6s��� � �: � A�P:9&0 y�{ ����RA���N��}2�E{m5_ $.Ђ�.%��� 2=by� 6!-N�F'/a�F�f&/���)�qG�aH�� �� �� 2� ��>�-�  2��m�m� M�� &v�� MyaUy�2� �\{v� & �P�F� �� C  R�(� "�;i=)C"Rc�&�0$aE�.!sR0i� 6=�j����t�8<` & 0!N ? 1'�("Y"Ra�DI+;�eM)� =s� @=�{$�'��g , �e��-����/�:}��:L8�Aa�U�P�6h��� ��M&N60w0G 6�Q? V1d4�&��Qj .� Z#E�iB�~[1 y�&#z-N�V~)���4Ft"���s-1} I 2��A:d"�F �>��&�>�"�/!A �N sp{g !��!J�jg�0��2E "�!AYA`25�%�!'* 82.T8z A3y�E}�3��'VN� 6AjJA&t1 >t�A��X^��MR�^`sp-���t\;6A!� �ed!MvgFrC�BfAf-g}&�2�&\; V�N2X�4 ��= .x*R��V�.68* � e,d�i �2FD �:A {S�jbP/����*��G\s�nV��.'u�@w c ;�� �\.vcl�Ii� are.@,u Tcm accor�\toJ&��H;"�\IV1"WA @is��A Z� �&��po�Jilities,v !� >R� J��d�N As�l "�kOT�Ah[kf��6�_) 42}a �_ I.$1}+ 2}=f"  �uab��]�N!p�f?#Y��� tf a� �4B9 �Bo��`&"?m2� . Al�*�f* 2�gick�R }sP�aO�S >�_��2j2j�S�ja �om% otal jeucu��  �F��&�u�is f�� 21We belie*GP now `�����#"@ �)��J��(��-6 �4A��x! �eh޳or�[�2N�hU8E�Z�1e�bpsm5q���� O1VOB� �nt):�Kav6 &�Bf:�B"B\.нg_�J 6��#i�j�T"A�ex�05�2K�R��$6t& � AJ$y�:� $��"�1sC=�MFW� i 4"�n�09 \ S*�0��mod�,q=��+1k ��A� W�2 i+1!�S�_9Os=" +os)=i+s$,�. (�>�s^�MN�2(iF�I�incre��v�wA_c(�2�!�;�9�jq tI���a *���v �aSѥi��]RRÃ��b�1�$� � po� .sE�so3"R)o*��D��P.� invo�΁X6� propB8=��}�i&�}=�8�1�6tm�"s]̢ M>�L�P.It���wo�w:b-�ѺtBx-!�����k��/'�< c��6kj�/in>P Z��J?!"�!6^=\tH�der $l1}+2 3}�L<1} 2  3}$)E1} >�=�� 9@2}�4sb{3}����� 19(  ( ��>��|=0EC.�=8 �:M)�u "��"�"�u�1�:� M�t7� 1})( I�B 1a! � 1}}:B2~B '3J3# 1}}"e"�R1} >id>� O�9Z�I � 2�e� X9 R9������5>�Z�)�^#+3}�p\.@X�1�3��:)�.:]2��2�� �p!aK2��JO!u�t3 �ana�� fB2Bax FQk, F � NF t�)!S3}^�)�_I#.!��_!Y2}Ib�[l(&H#+]�B+�[+ +a2.+����Q&* *&Rp *$(1� �- )� 3}),Q�Zp), @);5�  2}))� $)r Y��!� *x%'1!� PZ�>J w�tP.�P^��>T"U�TM�A$> ��� : No"��x@��o.w$��d62�se6�*z��(�g%)�o� Z ,��^ K�z>pA�%8F@��A�p7@ , 3}"s:=��r�}=I��2 f� q1 q>>D�*ц`B=r��$a�)J86�i!��A� i, jM_i M}U�  j}�Jy=��M�a29 0$89byj� $O�  )��1}d , $�"�*� �g ��a��Y\3}{��.w"`>@ H3|���On �1k �6 $| e|=c3}> Q2}= 2}|�r8�Lbu\a� � �M91�E�ZA3�b� �3F"z'B  �Y� !l M; 2, 3�"K %s!�3}&� &J��4 q��#l*}\(eq:1}��2�j� }B��8� Ag*/&�%��1� !���=�5k2:�A"� e�x[�2 �=�2=��I�.6�R I9j9]��2��b�6">�]�3��/�(�KE�)�g2})�����:�E=c -^[ e����s)9-��=& ZRB;,���JO�N�t�%N�2�� ]O% I� # 1�BeJ٠1� J�"�C�jd��*�w� ��.n��r!B^ �`���{=6(MQ�(�|p-a*�A� '��Q2�f=F =?� 12� x)b�I k2>��3��~!��!:2T%|.�97-` N F� '3*�.\5 (2>S}���VA�] 7 q�L"F#�XRPb@jP# ��p ���4%3� ].2�#O]�rJ!�aJ�9�!@f�y)%�6W�%�� �26z��#=12oC�!:�L*t � 2})+s&J !�"'�({N?+�YV�f)gZ�J�5��\ ��Ұ|�6f+129�sJ�6'��V.�RR)92A�J�)��2}m �d sbutn hyp�`si4�n*f.�"I{can "� >U.B��.�."� o�A..�&��; 1}�(���*@r)@�&Zh"`2* *2�� �GC`@D3D&�^� X W:E0[0�s�L��[���iB��J�06�.�.��Z�2��D]� 5� �1*!V)�L�b�3>���a6 n�^oa/��Q��8Q>�A6 aN.�b%� �^ BT2"�EN/>�h, � ��2���2[ F�:�5�I���R��y6�.*� �a��*\ \�*6� �N726&�*�H1>� �'�����.sB�"BERG�do��J� � -1}{J�}s�ccO�)9� 2B�*�2�ֻ�H�+5<���gZ�A�[ 9e�:2} :� 1'>% J�C�xa1ƚ�&m2�w�tJ�=1�ByF�DB�>��in5' cula�hB� n�*$5� .U5m� 68I�;0A�9q=^�6��wRC��& &T N�'2�1�=o6�.��F�'N5�> �f� SK!��019�"-^�P t$. Re�)�  /rgy L� r �M!�D(%he eventuo`�N =�X rv &3ߵ"8" )�n�AF�2}���)�B��Y�&0IW �:sg���UJ*� �K�I�3>��+lag�lN�u .I$3�kJ��)��1�;:�n� �;%.�O6�'eo "�?v�+���am5 2�8"�#&�: m4(l�DBw��A� si�5S$��SBD�eF.fN 9.6bat noQ"��|&#�Y)I�+j"�C�,e*}�2=�i3�8 of g'p alon!;R-�<)y *s�"��tG s. A`s"�fف�%� �map��n�" Q%P6+%!K�&w`��+��)�2RP � �8�gM �gitsZG}2$�)N��9�*wqC&Yqin a cer��.�. Fee�'~iX�w= 2���5�.ZonJ�� n��� ich N�+--KA!?t8%& t �.!1�<i1�c*�,&��\v6u��)2V!��:�!�#�*�!C V+3:V���.B5NR'We turn�*�of�{�a1l���<ǧ&k"2eN1J$9*�F)9X9$. ��abA �D6B�u�f \})$? %�-| !|th:dw&�D"�{ v�6C)I�scb{a/�G�V��ix)*�E�qsm�s&(#:f' i&e"/eA#a��a vC(� of)e�*a6�m�B��*�C���N"�D20&.�4�LO)a�# n�@1&2"2�$a�."I ����g��| Rn}(*���Y��8# )J d �D� ��)F= (k+1Ո�A��f��� �����IEQ)U�3.$�-E��Re�5S"�w}�$ve�2� �k!0"�C�(k):�5F2+1}(k-1)�0"g�g�ijg�4 \� �Z !-�%���(J� �k2�8�K&� ag� "!�Bme��%�thR}&�i ���4. �M�4Ѳ)1.��$i"�rrecuro� $�N1, *@fn-3�F���y�%�U]MGy&�:�oXF�1���ND{k'A�N�s�S)� A�'�@UPh� )k%��?Now�  :E -�j�}(.|f7 (k'-�Y:)R�a(l))}=�� a f nG=sUs}q�(n}, &\text{ibca l)=n$F�0:�62�)=k2_&� _^G/�����#l=!��,� hand, ��i1(.�5�J�I�l(9�c�Fl��r�#H B='j>'�?j>=T >�=� �lB�lY X2=-kM"O8F0�n�w�ji4T ��*�$,iQ�Uw eq:2.< d: � �_.2-l},\� n( M��b%*� 2�D� B?�i19�� ��L. J9k:�b��a9��>��: '" &� T�"�< *7 n RQ5��?�h"�rT@R�..6���86uͰ�_z�uBXI�j�p i~mF-�-jBisNjj"�/�*7�� ic��j�QGDbhU-'i�^u&*Zum.R 3�>V!�.(fK,�u��*W*Y}0 n-2\6Q ep�S�"i0FZJQ$ F`$We remark �that $k\sb{l}=n-1$ leads to a contradiction. There remains#Lscertain the implica- s of $\muZ k}(n)}= n �ak}\sp{-1}$, for $k$ in $ \{1, \dots , n-1\}$. With similar manipulations as above, noting that \[ r��nvk�n-1 -~. (n) ^MB vZ! (n-1>~+N$ \] we ob!a,, \begin{equ%b<}\label{eq:2.1} B  �)[6�)-1� �- ( \end� (\ref�), 2and.$3}) now st\for statement $2.$. ThisA}cludesE\Xproof. $\blacksquare$ A� follow!�\Corollaries depict restrI� JQ��D$ is subject to. IE�se2JA�a ext�not%�T are those of Theorem % th:1,b . 1� cor}2((i)\neq i+1Q�i$ A�\{ 1, 2,Y�2 A�){IP!4: Assume it is!9enuwi+15�.�iy�� i I.$. Since�iQI65i�  -i}$!-, analogously!�K+e�t.� ;LA�2W (i+1R� 6�Aq V�$ �means5�& ���-N� �6�4$, ($-i$ mod $�) i.e.,9F[aJA�the ce�7lizera:qeb8 symmetry group 'M� U�E� Hence,�F}��� sp{k�C some�H ia `.K bIf $k��,�n� !]}��us,!ulo) , $-i=n$ IJ%��q($i=n-2$. SoQ%�(n-2)nD but by hypothesis�!� fixes ia�is ,mpossible. ��Q$k�N!�-en, s2�T- Z %�a��"!IU-F� $, h!�AAMi^(n �,I? $n1L-i!>: u� l�0 (i)$ from-��)� {[(i)=i�t by a�Bp� , so% = i \in Q3U��� Ag�!�s�9�B�W�Y markE5(�I e=C:�lsiderA�athbb{Z}H 5}[T, T-^ ]/(T-2)$;%�� 14)�(=1$ is also^$\~U3)$ŷ6�If� n>3$, &O n=( %; n \; k��s )1 ��� $ �odd�$k=\fracH{2�u`�� Supp�f.�%4asFtedM�:�1 A�I�=\bigl(.S(1) \; 22 �\ M�%c- 63� H ; gr) :on  r) =( ; l l%Ln-1 ybi+*k r%XO�U�Er hand2 eB2�)2 �'>� q� r' -S6> >&i!(5ok �bs� ! .�C-1 .Fk%3 )@2E�1W J=�2HBy.� 1})�� �  previous� �54se two express� have4be � lM� we $2�u �^e }EL/2$ >� .S  cor:s4}��k]Z2AZ-k.��na�1$bs ~�>�ix9�-�-� e�U9y�u�QY/%Ma�ax^ y%L v�0JY!/ gAJQcm��^ZN�� align}\U g5�N����}&��m�e���_a}!P5ki�-'Bp�/6�\ -  &�Qi�m�i�.�b�)] i4by comparison,Q�B�Thm��aI_two2 are �to- one �(ced9c*��so will�omr d�q.����"m%J��Y�qF��1�]�vf���2.]NzUs!A G sults�Atried!ufin*� 5 's � solu� ���systemq �� r2.& #"�ofAN�< For each $n>2$, oE2se w( together w��52 !-2[ �B )(n)� E *k}�given by��]$all $1\leq!�� ,p titutez sequ� of permu�e8a finite quandl�order) �con�t�6file $(� n�"L � \})$�P general strategy wast !i h� 4o set up a ten�v&� Ea�assignM@ imagee pre- of� , tak' into� E! C.�Z� n, uQ� first�!YWI NrreferrI�RY�eiE/�how�  such aY>A� would��GaUs:our!}blA�r to ��let>%�� to verifylKsatisfea he r�!�. a $n=3!=$he unique �Q� �i&K 2}=(A�3)( 2 )4A� s riC �F dihedA Fg| $R 3�Apply�1�y� ,I� $n=42�)Rb�3q�4��2\; )(36� �a�$isomorphic!T$S� 4} \cong 6v 2� .� �2}+T+1aAnd�%on%�so;th. W!splay!� r�in Table �Ta}� m� is d :ed0!�I�column� second 'F'I `~dentifyA1�un� study (se�cus E�)x thirw$ A< a more familiarYn�=uw�bZ~.�Lj� t!F}%[!]��er} \renewcommand{\arraystretch}{1.25} ��0tabular}{| c  }\hline O�2& 6�& ...� �... 8 ] $3$X$(2)(#A�.& uK.2M4  � $( 3cOi )"Q�b�2�.� ~2x5 x4x2a�5�3 )$&�z( �\\9 !� {2-3!�& �Z3UZd1�$ !�zd2- \\1�$6� & no��s& �:=$7:!�( 6!�76�%�! B 7�h2v -5)$b. �Zc3� %41 1B:[J})� .8�7�l8�%�6 �%��B��Q2�A_3�Qb�p%@pa� {-ٖ�f��2}��!. � �7 ca�{Ql � pr&S #9 \}&�\)$�7= �$3\� 8$;T�1zen�� �le}�: \sec2 {Final Re�s} �S:f-I�:is work�Ddeveloped a differ�approach�/r��� �<s� regarC them�� )*� �I cour�it� ssueSer��'structur� J�we�z ound\Proposi!�h(prop: aqsd}�s!� ved �bo�/ On Alexa� ��o s self-di�butivity�� feel�!�an indiiZ look!� non-BdsB�a� example octap on1|9mteFf ��a- 8is good at tell&kn�apart viH un?Lcolorings (\cite{D})l � �e� os�t%�t�way! likfknow i� re�J� clasE2in2\22�*@� ~� �. el ���to % y� MqE+!� �nAB3 Q�niwaIasG.� quesA� . Ar� �6�I�no%"� F cyclic !?�subq�Ac!Sledge�}�s:ack}MQauthor a2s s�r� {\ema?�grama Operacional ``Ci\^{e}ncia, Tecnolog hInova\c{c}\~{a}o''} (POCTI)Z X Fund.( para a Y H \$} (FCT) co��nced b� xe European Community fund FEDER~C .O hebibli�phy}{99�(\bibitem{AG�� N.� �ruskiewitsch, M. Gra\~ na, \emph{From)�AQ�pointed Hopf algebras}, Adv. Math.,�K� {\bf178} (2003), no. 2, 177-243 � �BL�X J. Bojarczuk, P. Lopes�՚at���em!�W,s III}, J. KA}"!y Ramif��s,�appear.��!�E.  kornzAutU�set�: braid �� itie!Con�N%01988), 45-115� CetS�! S. Carter%�Saito��!�surface � their diaA��!�8ematical Survey *MonI(s%�55!� meri� .68 Society (1998)Ax%US(jsCetal1} %!�J..�0D. Jelsovsky,KamadaF� Comp.��� %co�7�?variant�Z���c� �1 �U��157I�1M�1, 36-94��Q� �^b�(L. LangfordF�M� cohom�ly�-sum i��Trans. !�MZ!�.,�355 �qn410, 3947- 3989.�pD�(P. DehornoyQYB]�F"},�\eszq�]2IPL192}, Birkh\"{a}user� 0)]��F.��,Dion\'\i sioi ivat!>� �.?�;R@�A�@��26j,8, 1049-1091.hrFenn05lR. (, C. Rourke1rR�  link!X codimen��� a��1y:��} a�2M�$4, 343-406a�}��.�N� B. SE ��Tru���if %sp��appl��teg. S� sM� �5�21-356B�2�V��Jam� u/� %app")*},�print l �L\\protect\vrule %width0pt,{http://www.�Hs.warwick.ac.uk/\stg ~bjs/�q�$Fox � R. H�x1�A quick_ p through�ڡ�oralin ``Top�<�03-Manifolds %!�Rel� < Topics'' (Georg�196��P� ice-HallA(62) 120-167��hk} ��$F. Harary,��$H. Kauffma�A�%d4 graphs I. Arc  �"� A��inG.�3��2aR01999), 312-33�}�dJoyceuL��9J]��U!1�*s,q0( �`iYP� I�Alg�I�8aI37-65F�1b�S�,"N �J.\4 i79e _ 307-318!�=��2m�S!��Bi�S��W�R}^4$�� %� xAbee Gribbon �!ƍU�N� 37-160 F�.�B�0A characteriz�of�'��(closed %orid`���4-�_},A�e)G3)�94�P$1, 113-122F�3i�B�S,ard�m�3-%: 2-A-I�\  %&�$polynomial!�MichiganI� JMF4�:  �89-205F�0 �B�嗥u��ory!d�)four}, %6� " V� 95a�n� �2� �% Kawa �AA�Dwauchi, T. Shibuya� Suzukiq�Descrip:sh.��)�,, I: %normal)�},%O� ts Seminar Notes Kobe UniversitM106W1, 75-12a�"� lh��uƂ�physic�3rd ed� , SeC �aNI/$Everything�|�$, World ScA��  Publis, Co., R� Edge, NJ%�1.8 pL ���~� I��:� 59-186��sMatveev� S. V��U&gei�o= in.�-�4. USSR Sborniki�47a? }�73-83.�Nq =�S. �C�!y���y� !�Procee��BSBg��e�Dynamg  S�s{ce,+N�2� "� , 245-258�SR�[ mith,az Romanowsk"�(Post-modern�}.���3��p�(�!$ John Wile �Son�,New York, NY!�99�uQdRosemaT �� D� 1|XReidemeister-type movesa�Fd��al �� ag͵4'' (Warsaw, 19X Ban�CZe]$., 42, Poah AcademP e�c� E�$8) 347-380=��29�.�}iTg ..jjRotma]�J�" 1Aktrodu��Amt�1�i8A�Fourth E��Gradu* Text�/R�I�(er Verlag IV�52�Ryd�!�H. �Th� ngr�!st>�},�:�] %��13"�  4971-49�:���!` docu2} s�%V� 4e October 2004�/ $% ,[11pt]{articmP\usepackage{amsfonts}> mathB symbBthm� \new%�em{!+�#}[�] 2$�}[thm]{*�}6%lem $Lemma:cor CE"y} \ �$style{plaiY� defn ?De�io'.$9( �N�4:�� %E:$ conj !Con5ur>$ prob $Pra":Er5}2�op� A Open�~b!C ("`tilt}{de{t}bZY] \title{S Organized�%4est-Fires neara� C cal Tim�\�<{J. van den Berg��Rp0ouwer \\ {\sm� CWI, Am�&dam } footn� ize )#0l: J.van.den.S@@cwi.nl; Rachel.B [ $} } \date{� makeՁ��ab%ct}G0co0�o�fir��del!�wh�nf� ly, �!� bed a��27 s: E���(vertex"\b7 latticPe�$8vacant or occup��F1 tree. V Ss b�` (at �% $1$. F�1Ge�is hi2light� 4\lambda,&is" in& aneof6d�7oys (!Os �)E� clu!� �%�.N8is�3el� ly r��$4Drossel-Schwab Aq9�,)�< has received m�%^6a����K�  liter6. Y most�&"{ behaw.r seem��r whene=%fgo<9o zero.�eJp�belie��tTs: �$so-called �oqr cq\�. %I�$, earlier pap)ś_'Z(am%�0� s)��&%'wh>)it )�sen(& `tak�$M i�sia�y %e�'1in$ d s:66I4��of��n]�M1s.a�le� 1st�Q�*I�m( and %�(posit�( but � U�, 39E��`5b4time' $t_c$, d�&�E�Dion $1- \exp(- t_c^2p0ApJ�� abil�or��)coG=. %(I�Ct/;%G� aft!�B9��&d- %{\it% out}]�aaZd �emerg!& Intu%7ly one m� exp�;��f)`$fixed $t >�$, C=!�simul�%5u@*d to $0$!� $m$\infty-�..psW ����H)�e�ranI�6 $O!9 burn�)��)A$t$u��Howev�we "�)E'a.�-� &�6 ()�a`an�proveEgm��be trueae�)Won��falseE�c'/e%�I5asea�`JreplacU� direc by%),%^�5%=n�� al o!`lemY*C ��K� }{I*� }"�}{Backgr�!rmot�9 C�CA�#8 ing,�>�.� cr�*ER6� . (A�c�*�SC Ks�0eriisL)y).�i�r�Y${# Z}^dE)�i2i�depen�)a? f an e%�F񉉸�>�A��Tu7,%Akme� �� l. W�?aQA[>O , its ent���F�b6�lye8s down (e|is,[����8' tinuous-���on�>����2� ��( See e.g. ~�" BJ}, \!\!DS�% gras� /S M�2��# by J��n ( 1 =#�-i��2i�re�Q�A�elMMT}.Vc�vsE�P�.a-$asymptoticݣF| E(tenED$0$. Iy"��d�A�#"1�A embl���of `ord�>'�`tis2 mechanics�csA���0%InA�tic AkA��%,�a! �Q�� ��r�%on�(a power-law�. Heur���2confirm%s� ��# been�,�x&� ,��%�valid�of�.i`*3� ba�,[-MI[)ENalG noth�is�wn rigor. (excep|��e�_2���a_Our goa �-a7s!Knd�waddd �basic��i\,Mpri�! ly, %so far)p�� Hly ignored, althougňir"?+�cruciI� a b/ 2 of��;�2-9E�l'a%r)D� 2B�. TA�is� �� s��res�"A$66 . %Let+u_{� , n}$pote %Axsteady-� 6x� "6� 0 $, say $n \��(s n$ box %(!�orus) �)z)t��$O$. It&I ake��r-U$� Y�e��Q�,spe:3,�)wej %$n*V G E�V �C�%!w$0�O 2 � %(u8)JL)o)amU��)!:origin �� sta�way� � . Bu�*���B�-br s? (EvenBitB ?)A#� 3soA�2WBly.u \\ ``If� limi��!b*�  b=�}�=� iT an ` >^'. �e�� =b�Imediatg F ed, bring���QqA�� =H 1$: +Gr6J".(Of �+1^-+��mildly]KquI& shak�w�6�� ay�h7i�i�+I � necessaryeH a cl EH:!�,�P�9N�vestig�el�ar� ���&!' samea � just!TZ ��'$spirit. Ine� look!rah^#,!N MꡞMJ�'� at��fK�mo� ���� Q*�vl�Ewth���0]7� � B 8QW�9!_m�+J+i�K�}��^7� plau�D%�.w �w�#3 y*� �B2K[� � ���1 $�>!�6�q�C _ !���F v.�� "JM!]`co�J?$' �aED &�}if!١�Gsuffi�ly lar�8 rw `):evX/�* $\{$S��!���$ 0m$�O�Fr5" M-%G�s�<respo�O.c�<,f9S n1%dwe want.�6p �"to^I�ag >�8 o .aA*� \"D, e�� e"�E%:uF*E/ ��3))g.�V &<hope 9�7%A Lfur�97ar�9j7lar2�A/ h!b!. *�N�F�A�t�-�JMG} Sp �6� ��G�i�pr�ly yet_H�.)� %��1mu�$ �� �io�� JN�G�8qe 2 BteS f" us"�8!J 籑�-We�o�%.Ns, pC%&%c>!,X<u i� ices)�Q}6^�=�wQtwE;, $(i,j)�$(k,l)$��r}< edgea�@$|i-k| + |j-l| = kCTo*wE�igo( Poissona cks:�U.�l!2e `gr�� clock')!恩� $fNAr�t( `�� ]66&� . All:��  :d�d. A� eMA26LɯT seI��de* a �4nd ���1 vely�[iti� *�!pV�I(ctA�selveŚH 6  $B�G@:= [-n,n]^2$. (In2!3*s!�c.D &� 5N4�arrowDJD, }ALa*�w.!�)�)�A�a)9 $v$ � � at \s9O (unl,t alrS @? �@M�� �$E%�o );��i46R�)�a*��' anr path- %XUv��)�>�. (M$ S/ m�N if%wa�J � F, n� hN0 ns). Now� 0 $\eta_v^n(t)lI �K0,1\}� %�� �r� iMNt��nd �6 [K= W c := ( s, vjA_[K%w^{}$w"�"!Yz 1@� . %I"�=�Y�<s!$���ce����HboM�$A��P � �$�*%2�$. 5���)�$�A $�(,, t \geq 0)$ASqZ-)L( *�) iAuc�N Markov�(i� 6b"�%�1,�&�ign�T�6�@z }%K&ae6 ��vid�m"� coup�6-4po$ssegQet�\�H), bJ�1$y�����E ?belowX�$m � !T�Uf�Ru�b� ( phrase ``-�$ar%i� E(m)$ b6� '' % K"  istsU� m) \�T{� }\e s �t� N +:! _v(s^-aV1%�b}m0D NT� �we�B�t- sKCSq�� 8U�v, �� B>�#s < u >�.t.2� � )� _w(u r��w(u�%))?����\�2$w�!"+L : athcal{P}"B}!�%�measu�Vat gove�  u1CqU�*� i (!�he'A. all �66 FM�m$). OA��FA�s*ne�o� lici� �: �>��"z , o���xE�A volv�A�.=�,�� eI�LB �*. is�/vGE� �s�!!S$n,) j� �6 -��&�qs� \�a80$,E%�� ~E} \lim_{Nk}\ \2U}\ l>P��q�� ae|�}2@.\ } t E�,. \nonumber �� A� 2 �Em>� t!) x!��"���w� �I+H��>s.�F!�i"�����`s��ou�8beS ful�JQe! "M� $\sigm��$�^"k�A�TX���[ loosel.��obeABF 6�+ � �g� *  $ �_�= I_{\{�� (.N at }����ri�=8in } [0,t]\}},$Ya�$I Zm�or fun��[aB*#&0 !� .�, \ E��TS re�%Dnoulli random vari0s�D�v$1 � t�So,-[� t_c$a!9 $p_cr -&!%!$!��,!A�t�Xri� valu'A�T*NQ6`k�F!.? agnoY?" @��$t͞� ut d�#havLU{3 "� I$ o il�$!�usA�n- o�O���-�$i�a�m�!A�e�subtlGarg�)s) �"�J�'���sup��:�li R�I6Z� M�!a.�O��:�))c�)4ta(1-e^{-t}), �BsimplebQ �2�^�$ <.� !h.q.%�"�� .'�1@A�*$ 8widehat{C_t}(O)q�rB@�L0%���gur�-�(a6�easuA��"U��*� ]avin��A�i�%5 IU^� 9��.�U EJs &�(A��&��"&% Z� :��� $F9Arung :� . UsR�5&L ����D U EsE�! Y��� ay} && \h� {-10pt}��Z�Q��92} j��}Ym15l�E,\sum_{k=1}^{�Z�|>*�kqR &> �>1,���5�.j}av� &&1#2!" + \,.�J�=U fty)2Tl>�F�. J\ = k)� K tk})�th�( �).�%�4 �/Q *JEe r.h.s.� �fJPerm��a �b� �Y2: *s0�Q�ly2j (by ��ed�v\'nc_'# desi$��$$ n�o"M!�X���.'A ݮ,yu�t� 1O.� CHb� .�.� QoAj}/z� e||5�-� = 0��no�I�5�ϭ� G��s �vM�� H"�f2� %�L)�? V�(��1�I*HIIof \eq�e2��)�v!�s "&� n�*��^*z� kcg�� .��&&6� �.�a*2B�!�built upJ ��Dr*%s uo\+*� )qamEd.tot�"] 2 A��  catchesa�e i&(�_&��b%hq�*%P���ly))�*."��Aysaid I�N#ch*u is� 7���Jlrcor�)�N�)��2�J�*lemi&We��I?in@Ne�5 "/ha�$&��J holdA�IB# �� prefH�uD%��n &* !� lem,!�SWtg+�'�2 : %=hreanb  :)**b$�(�i!A93��o�2 I�V"o,&.� ab�ico�6"� f R� .�B Z9Z� � > 0 �g?>���42��� B�!# ans'3��-�!Aaf 'a�.�'".ly)��GLU go #d`)�de2IK��6w"�+Z{:1��I ru: �H�Jll�~m�(\varepsilon!1e�re !an�f jJ�1.!Q� ����Q �@�A > 1-.�n� 1Q%i�r� �jby��Heɓei dj� N �.gi1B9Kas� sK'o!�*Q Up�t!i�)�&��$�%2M5f �5YyP$�'i*B���G/�] B*���:%"!�9�" .� لA�a]| of��a�A�.i���+a�;sipg $.�)m| , o"�lone }CxP�hei< " ��y% may`Q ably&? c F�-� on sugges���-9�(b at,���er!o.K�! %R 1լo��) �a��  %$a�infj�V�%�� %n����or�[�$1/� ���(m$. \\ At�Qpoint,<cC\wo+mA��)ne!�E'to�s&Ro��� � &� $ m0no�H `extra'��*F�A�AI-��AA��\Ze: a�!�d �H>� AP�"well- = "4�?<&c"a%V� �6si�(e�7�Bue. (9doC��sui�-Be�q� X4e�t,'a�tan E�"-eQt�6). "44!!?6(� �+a "|U$0$W4{no%.18Sb! on 4?q��l� ly!g�5����Qis}�B{ -{�!)EBh> s� �'I  .�L$ �"&} ��E)">-:rem�UJSt -���\ 2�(�j!sAUg,�4nG:I �p!*�&���e�/US�� `?!�'pin:�.*c �)]U@a�2#I(RSW�A��o2�2Gr@hap�311�� i�� ))�begin&�5S*/c%�J�? /*�5A.���6j}5C7!Hi�N�'6@,�bo�2�\3\delta} 9��`*�) major ro�P�} Z aS.��'�9skip\no& nt F�%��?alA_arks. Rej2i c�$��e�����E] @..Ar6f!pr�Bi3d�Nty $p$ E�b5P_p�!W �� �5ad�=�#aX$V� Wŕ ��%�Vjft��W\}$.��0%� �ge;!�o��" =� 4 n]�0[RQ n]�BK����B&;�\e6al we!*-�eF"�u!tA $B� a�$q neighbA�coQ*$B8oW�K3)�$toQ�>�- I�� �1]*!>Wse�� � с�� ���of� j",�=�pUSEzZ6%"A8"1-. Nex2t-� 0%�Ud�J�m1�A�: s(&v`@!:!W. 1.�'ha�9UElWRb<�?ade �*pY-��� 2�, / �!U).����waf8,i "5 �� �-� %=d> stepT*:���d*�1!�6�I+�3a:tra�forwar� "�-�X5f&�"Y(EtBe��>u $A7, - P_{p_c}(vB�yX) + (�c+�3)r �.$$ IL�=�#� chF1#$E�"0&�3���con�!&e + (E�) �$�*ts6 *q ! VeRYUc�ica�s+3al�enc!e� �a�0��(Fw�@A& bulk= `�&nm3su�'M ���8%AA",$�C [n, �0�@ n, 2�@, %N2v.�$p_n()��)a6� N^!.8veAA�:Ca���A^+A +� m\c5RW2�2�.�I��g%t"^�+$Ei�6�!�ncK��)*�@� J�2u�p \�a F : =T�is���7U�} 1, �ukT rmly�}n\}.�dedef� &�"��}>��B#  � sp�5!aer�r=mpt�%�} n8dis ) �au"DHE�:�UV0v&^2n&< ��s�S,fh!�A� ��&/� k�t� s $ed,�A��car!��p rpre�+E? v.(@T&�}!�;�(!��$ e to�` �' weak� �)thAi� ow),P4k3.2T.9>vdB&B�=L�*�.;E ��s"�2%�ata�dyieldsD S5/"O5e�a� Ba!�V} ,0 r%E�;v�Is�j�|�(F"%�� ���-w� .َ"H1'�"�շ�s >� R m. S�(a:�)A* ��# ly E+8,BP7s�2!� esoBUc.z>A�<&� "#}�bA�dmrk�$ ��"�db rete'�?Eval�+6�8q!�)�61�\~E�.���� �3�:�*�@I�Ѣ �GAhw*|D[{v$er [#�+E�< mer M we don't5 L$6v�e r(Fc� d,F*d �A�a�&�E�pur�Ds (E�<llR��$ deci���> �i&�}��'.U} "!� Wz�)6J&P���58'2r ��.h:�Ok :_��Ha��b.$t��&%�A�a�$mJ� �inf"�6��* V3�2f� m"# 1/2.��� �� %:z���� sone�.�%#E� not}Q a %NAba���E���ly. �(0A��pr�=Ps. %�F ioriR.�+B2�m$,�ZN^ �? A)sen" I�myg_z om��� ng* : �>���4 D"�7Q]EHn&�&�, %w(�5�x� ��Z._ y� stro�pŠ E=!����.|)��T !���"���K,_,�� %le�0� )so,$� ��bsec1��3&� r&� %F;�Z(cf�V����2}w6�k �3�?V�. % %H�J� �V �o� � ur)�;2�T*p*ers ``�Cout''  %9}�<�$to joQnl!^ver�<M!��aUmayaQQel8!�$7�*ll=SaJTE .B %�?"�;`q %���rw� u�d �-"�"z tO �aJA A0toq yA�B.��+�%11go4W �BA��2�pta}L %�&: thin�7W<�7�Tst!,]Omis�TxkG�A %�&�2�>A. GQe k�.oVk�@�2�o"�=�Ils!0&Qin it~P)"� propV� I����#s E:���mJ���r�f�!\r�&� � "�* } 2�%%pj��80�tB�no2F��)+�� �!�%�5��CZ�=C% 3f= %N �"l���RA0AivIKEYaF��Y�,}&��Ay= heA�&T �%*a}�(UuV�a-ke�X�P@Vor@VY>Ra�esS� 6� doeUh�_�8ly�Pa�`"�E''��Ixare %o��*T& . [A2�� **e�Z*&sib�QE�% �exh�ks �k� � 0� ��:.] ^�B�� �p!�of,�!us!\lO !h idea!�*BYɥU�����B��BA��z��U rB* �Zw�Oe� %6�g�H� o�9�w�-KR7l�abeB�NQ�j} %s�(�3:�m FM6meSF��2K4� %l $M�q&FaAXu6eIqq;��9<ei�/c:�Lotyp�ly,b!s circu''� lle�?1 %�� )`�,:M��-,_�� �P %conq� it.b W�Xan%�_11m2> �*UW� %�l�� ��3$Ċu.repai8 e da[~d�by%�mo�#�I��$.�.( rA��>!Pr�3coHii�~��S e� =P��EN"�0 $AC.4�� 0annuli1��r9 a ${&CF0prime}$i %E�b���*��i�Wa�4�a a%w�6�Mectangl�_|  %2�So:8��t�&A-��%�""�:N!ou��N I� � < - _.�" %a�(������).� E%no new5A"� %]%5 reat6+U�YЅ0I�nze�}.rsh�s��s val.m�#SCweU�%�o�!� �iA Z� %An��`I��m�%� N:�]!�RerU�)4 �BF����"�9�*��#nG nulu�(� %�v��"�$ail. O��b word�El�SMw*<Y  %s"[ $(t]8A2��"�)��X��-:� %afA�E�k"m!J��-Y`I�ca4�M8���IE# � �7�0HR��n#��ion. |� *�_ "&["S` ofs}&� ��mN� (Ite|)o�() s heav�%o^`)�oBu�%� i 1uwo aux���$�?�s5. (�Z*I�(c�bi��i}V ). D:�!($1 \r� a�A t�uQs)eR*Rq: �,�a��)�2"!:a"A, !b5yN>�*~" . Af�0i�!w-<�;%�e2y�K� .i�\xiL@�6?I� a �J�4$t$. E�a��Ma[&SA�RU��u�> "�?(c"H>) betw+Y�����s�si�A�$nMe�st�c-�9 +.�da >�! 8� $.JF �%t%# rWs��6�#*f5lem�}!��4n}jk )%+6��-�,,� i�+a^( )�3.4 of\BP��"�we^"3�few li[�T2 � � a0`c�6�S' $a_TR�I�7�-cH��U��[c8ƃZ�6��JB� RWPȞ�Vf } Fix@.�.I -�y� .�is monot���*ay2I��^ �  $3^lK�s�% ��E g�l$. (S�Qa���DU�5� �W#&l ,��eni���R�or"�)� !t'Btauq$tau(n,D�Th����(��^nV�H; mor%  T, �,}*j:= a�f \{t :"]K\(*}KZK�@^n�_l=q��I\@t eK�$noQ=IS�*�%�T$1 > "2?Uve"�?K( ") &:=& ��(1}{\sqrt[3]�3}} }^A %dez�g�z��s M�)!! kV^4^^ A(;,� GB(.2 7&�/K. &�@&�c)4a�*� A�ts"[91 B_1 = B_1>�{��F;=�;�2�pH��p9�} EE\6j B_2r2Br\ ���G# a 3  *-ae}fX\},�o:^-- W by `R� m� � (2� O3m�m5>� �"Fm(zV�#Jedi�a�6�/~ad1 7�`M�o^0LVs�jK u���6F)�WIYP&� &� ���H a��&R�=Fb��ZJ�."C)�_�Fl�m�] (0,�I�$A�� B_2�� � � �=AV�)���}($ \setminus8"���F�J���{n}��S"* ����Y"� ���Xx} (ofN ). S0:�L?. T�l�Gj�?� s M}B �. O� �N�9$ > mo� plif:AL , du{ -�oo��& , o�`!��+Xpt�-�ł!��kB>Z&S (k)�$K11}�H�i*&o�w)��] � l)�= 0H�6FD* �%v$&E�-e��C$��,t]�(�^y2Y] �� e;��$ts0�B . (O��!0�EL�Ai�s tri�Ply). F� 0�E9dm�l>nB)@��R�s� >����p4��$C':>�$.� y��-�%iior^,a��(e�b2�ng&�J_�n����!�$A(k,K*NC0,IP uiv 0�9I��B]�9 �e $(0,dn]� ��e�8� ca�$ex(*h8o8&chQior5��q�!�[we )�d1#��y, 4���A���$)�gt�.��of e� ��*.N0A*]�etB�6*��%��*in]�KUSCoe8�e !��zA'�1��� �Utn Eu$s� t_c,���6���E����i�ZP~a@i+){ ind�UEF�/��, ���|&��W�� %R�*��I�B�ѥ�S"0: Wc� . �'�V%Ft =a��K&�C� �er5ų Vw� M�A�A � �AI/�(6�1W . C�42z�XE}in.6R. ��\C:�ItA�*�,k,�,atN�?K"1 *JV�$pD!K&��A�VwO}��� ��in� m.�} I�N}= 0"u21��6; �z�8� �7!>(�X��(Utilde{B}� Ÿ �e&����} ��6g)\}.$$V ~ =�@  &*�O4�N2�%?�R� !c fR2�2{1{�,2� Vv� .��b�\�apY65�� 6�O && + 6�9� ^c)+2B_2^c` �>split3P &�e��;�@$S*� 8): a�D� *� .�2�� d\GN*�|\%# + {�}) \}{0\��ext]s�� }�� �BF&��i$���$h�a#�;9*��"�E��&6'eS-5�&oł*�B@ by{$B(.Zu��}.�/(B^c_Q�leqm�a�\\{*�&� %�2]>'96�* t:�~�� B�I6�}m�8S4��"�Upe"~hM}ܞ�-at =� / �6�x�% 2]1�>Fin�5�$h��!�&a� �%hRo� e�h�>nd �&LPmt� t��)PV��f�4jq+$'s#� J}h�,�c��� "7��.dN�^T\left��� )IM� ��\6�F��{� ᙅE_ +2��!����I�!�}��T��TKB� ��2��Z�t �_� QA�!W}RY����* ^n(s��sg} � �t_: %g�b1!j�~BZ:���b��2MVN\�w�� last5� Q�MA�^#DQ�QI�s�,JK %;�CaA �(�!7�� )��e �m?!� ,��Ye=66,EU.N �n:�xVa�D�4rr�!� out�Nk "���jh��.�~!I ��* 5b,�obser�L! $i�6FF^!6� $,!5\�e.0)A(i:rM� �L2� :�Y�ig��e"��!`a"]�7�/F $I5 $�9� LllV+ s $j�28th $m < 3^j < ";#j��q.M�'=a�ii�_�>#5#��ge��]�6� �CrN � �5 훁5^� �~ ^{|9N|l m�AT"= �Combi�u>e�j ;i[��n���2Vt.�&4&w� J� �6!pJMf� �cf�22n �m~ �Gf� �v� � jS&5 ��2�"� all��atsteB�F��,1�B1 22�2Z�t'.�fpt %DEZE REMARK HERSCHRIJVEN??x�K�Ww!:2y$ 6% %�O $1-e��'-6�<EE(�D�*�- 2� � �R. %�z��7r"�RX):�&�Je.��� ��Ք ��9xjan�R= mŽ"/"Z�)I�lF096)E(mSA,?!E2��”R�1Z�>2�lF� -:a lower�1ak��QH. F�� "%9��  dm"�V�j�.�� � �~Wf-E}3 fpb)iY4o  >a�V�6� 4feG 3 s6 �6Tno�6Wb���I�-��>" �&P 2��`_ ��1h+�byjb���st ��. d�vanish&�f<�9 Q�12�l2}��gA `��.=w,HY� � .�V�0"� 2qu�qa�A��/2 >�#�@���@sJ��B��Z*�R�:��!�kMfs {D&�I!�^) ��<+�_K!���w�92�z$pla/<7�?�-�. C&�au�!����0�)v=J�R2wa���tҥ;� �,he honeycomb�$.���9�]d ���Z�-)c��c% (T*t�/�"�.;.L�S��2'�Q��}{I�&2FO>!�B} ���orkq�6d�0aP�|,�����%c"`/*� ��N/��"c*�J), � Mc'6g57: *D�21!?"v�� an (� ger)�YoL��rs>bH�Z��z�1Z�"M�x<$RL$�r37�B�K��,nd�^t>��of(!.([L ). A�:p)>�.eX�'5� �,�C the �r�on�Nw)#e3�it7?+fF�Z �Zaw%�Yg��B=��"�[_3i�ees u ojmi]� |8iDQ�@{!&later ũ"x V�P�th.e�7�= doubl>HI "l7MxEAA���ՃA�6�4TG� )��3�,j{^{[L]}(� $A�O2($t#r�)!�E!c\2�B��$O2�V�a"�*�bR�ef���*�8 Xb^4LJ}2W>u����*&�O2���e�K�S}P�'� �9�I� Vn/"�c>�T��ѤY�Cing�^fMe;!�.�\ (�?�#�or�g����ʂV�Mi�w�traI� ovM/n�w�FTAp� esseUX�h�V�f. ���,I�:�q-��3L dBS>��s�Re�fA.сHL^�J,� *�eMR�2Fa�v��3 -e�hA�B7�;L �mc�1V[4�I��&-sA4� �^�1S.7nR�2G^&�" �yGNyG1)NKL}E � bUL6a RVasRS}xbJMTaQ�+b)sf�4b7o��x *�G+in�e :.��m�� A�u"� &�!K_L�1L^{1/3  .m k_L  48&��\!�/� Z!!hz+})!r�hd� (�Ble /J�B_3#3{6} l�+�56�*,} A(k_L, K_L� ,jf{&�`%*��'��>�&� .�+PC'NT �)�� ���er. (&썡�" S5����)=�((L�4�Gw-�d0!\ ��Z�(��V�4� �yl/O�_3"� N&0��a2)0%s:"0�]��0�S�+�.~0A��Q��)~off_L}� �-e6�;K*� �-{��� �Tary} %Ye�:�@a��a2�r��@!�es��"��f *Q4. %On�R� �f�@4 �� �,~*o$e�`��Pu�ˑal �. %�hi�)0$a}�?��acU� %As so/��� tou�qAa�, %� �H�2}gtanX�O2�Kp�x���P2 .�A&�7onTk (} boxes, %weA )& %"�k�#�I�3(q;j�:M8�>�8"g"��I�\�n]I�2�=H2A�V� %"0c�| "�L �S- 2:"G,�JB% 0,>6�" Wy�%� �R#N' . 2�&� 0 20  %� &2 �2�arE{n} )�2VB; ��va6�pVB b!_VRF bO $24����!* %-G2+�"��#^4�TK14-% %G�B� . i�2� -��5a %:���� }.UA�ZQ �7W� �TB�"O %(.tuR \xrfEL}�_H).�Q�:) �Lof�J�2l-,2"@� RA�=&� -F�\i;{�E� A+6# � �}=A� o�toR�x8(\9 (�rb��A*\%;zr��@2��e�2�P�t}): %%U)w�4B����i�t��B�d�b�IyM c)��� %%�(*�d5B)�.n)&j"Y . %%E?�r.�j\*>Vp6T{�==J��$\ � %be <�&.1�)$���c�&, &#!��8mj>or+ %%repeL" N� to1�9J ��)� �UR � n�8v�.� �lTt>� n�#i�6w�\F&^R.$$���ref����� %=p�5� �K2�Nf= "*�  "O �^bue� }"I��&�3�o�&�G��"Ԑa&�y $!�H��s 1-3,�"a���! !�5pd8�}.�N5tea�*>��M�e<M� �.d� ����T}j%m�=E� �Bn�[tex (�m�M�ootX�s�=edg�P�a�3� thk7 #� *AP��^�p � �*;q�b ugK �Нmchildre� �6�:�$�wo� �em.}^��@an� %�to}E. (����al�&v$��!:par�[9Cē�~)�9�ng����l>.��(.�$2��0�D�..i.aetcue��z� T$�K�$O�its ����sJ�IO� ��uW�>�"� det`P6$h�{T GI�/E3%QE3�V. >iI5"w (b 1) m�gE���pm"����"$�K.e�;ged_f2> i" W !�l�LE�%� �d� �OIRI��"m14��I��gIeV=`0 al%'M�r�>=n/v �Rrv���: R�R `�'A� `node', `� alert', � by `rec�ing/%=ion /rm�l!a�g�2R-!E �'E�I 7MvpN&5y�.�� ert �%w���cs l(ei� taiXoZ�), C&� MmaL[>oaV �'(ew�F $v=O�.��3`h.s�}T-%i^,�T�it � �exponeG ɥed�o�� Z:jx%���T� � ��c1�= �.>N (-�)eCato�Q.1�(.�)�,uMz.(�di|���V� Tmex%�) �*I�TY�*t��dR^�n�� vĕ� �i���OAg���T1^"��� b:+/�A�CermI*�7Pth%7Q� uAs�A��u==a^a��o T�k"X<��N.d5�&��"�].� :{y�.C.#ʋ $:((p�,(2 p - 1)/ p61�p �{�i_.� � !Vsa%��BR=A�q u�} [* ',W"�b�d!�-b-�gc.�u�{2�� ,�f[?q E\; og 2&Y $���� aWVM��\ 2J2 up�r hasup"�+2�6��.B}(&wR?m��&��I-2�}{��6} A n�G2f "r ��Lat!�� (Τ> Y fact)wP.�( %QTthf�AeEC6�"&�iX �0�m�a� �X-�W%b�.&f"2M9��!��8 ! w�O>� [ frac�K2} \, ��%��.&V�-.*s hal�  up��)�m�.�&5Q�}�> !��!JO'f^1N}_n(t)� {.ߗ5*9(HD}^M �3\��>��>�*'��B�g2�Hp�B�- :�[\w 0 < O�tj�i.ew�.S�z! e�� i��C�*$s����PḾ�T>tL9 , 0/"�0eF v���VK>1 <�_ }{2}2� 3t�n "�.�-e0Oy�/ g� ��R`�Ve0:�-e0*w �d) A9%A a&�$�6_�P= 1,2,�� � E��^,T *jw0uzha.5�iRr��9`_imF< -W�bd3�:kBj-j$�jenough&UN8�fixj} �K\�t_j<t}(1+2 |�3#�)�0m*9�|vo�Ir�Yho�~E�X�v&�DO2 9(_v%�a��the� $$O�JB� {n+1\� F�� w5&� copi� 1n_O-�_�l�i� $U�UZ � $O�A02�9��en�eq W-�:P7� r�twWXim� !� �ڡ� s & *W�)� � ��� S����v$��&� {� hb J4!�(t.{$9 "�� �R���n�3)B=�� �. cb<7�EA>s,b�(recureq} g_E �@(%S,� geq D�!h}�{E�im�{�=[ 6�6 ,t)^2 + 2V=(1-��97A]B[0&� ��J � _j��� �/�� } (*r� $6��$6 �{ Kgiv\Iat �A3abbs�%� $g_k$  5y_j9{$, $k=��$)"�7Y�&�n��31-� &�&v�_j�%�2 g_n1�_nF��C��# a 6I� M ]*_�F jG\{@!社incrf�/&�#�p ![� o��hi�rg_,�I�1&C P�( noЯ� e!C� bU� , s�B1o���v� 5)��wq�'�} xplodes':�o2@8e�b��*A� i\qx*dF��A��6I E��@� >��� t�L� Letelup~_t.�� c1(��{[\y �� Byf�[`�� ��'�zi�a�-�$*�[y :- (��x �A{$m-$th*�!���),/\2�.'n�,E<&�%cf�:I2���1 fA*N cor}Z>�.�<"G kn"r &&� N�ƭ#}Z�;�^rqkh 3%�HT})D�.�A> �*� MS&� E�%=�?4a�rge\bf A"H�m�}\\� �hpk Antal J\'{a}rai, Ronald Mee�2!�D Vladas Sidoravici0h��,ating discus�sions. \begin{thebibliography}{References} &�Fibitem{BJ}{van den Berg, J. and J\'arai, A.A. (2004). On the asymptotic9Hsity in a one-dimen��al self-organized critical forest-fire model, to appearJ\{\em Comm. Math. Phys.}}�vdB&BZ�(Brouwer, R.�S�\destructive percolation, qRandom S# ures% �Algorithms} {\bf 24} Issue 4, 480-501.}�0DS}{Drossel,B)NHSchwabl,F. (1992). ��%%( Rev. Lett. �8 69} 1629-1632.2�grass}{G berg!P)� C-�4 behaviour of !� �- � )� f=��New Jour!�of�ic1*4} 17.1-52#Gr�$immett, G.!�1999). WP9�D}, Springer-Verlag2JJensen} , H.J)d8) K%hOU��Hity}, Cambridge Lec!� NotesA�!pics2mdMMT}{Malamud, B.D., Morein�E/0Turcotte, D.L�. FE�D Fires: An Example!5Z� B1�, %lScience-�<281}, 1840--18412�SA�$Schenk,K. -�>� A�20E �I�sed q�-�}�< on large scalesm>)0alA�iew} Ei/`65}, 026135-1-8.} \endB���8document} �i\Hstyle[12pt,amssymb,�ݠicx]{article} \setlength{\topmargin}{-1cm6oddside!(0pt} \addto?,extwidth}{63V$height}{12@�~��} \renewcommand{\thefootnote}{} \date{} \def.�,#1{\noindent ,rmalsize\bf �� \list{��L \arabic{enumi}}.}{!to�\label ({[#1]}\left)FdvanceB up!Rr s if�0only if %they�s�@der $\leq k-1$. �TaniyamaX!�aeXQdiagram-�)Jof }is3 orem�trans� ng.�' intob!xdescripA;')BE=. !� ~think\ ps%ele��haly, but little complicated�In fact,A?I�oEve sever ublemma)�  %forq. Here�)�6$(k+1)$-zon�R %J| , instead!/9����r arg�[sAJwe showI %�eGM �w�&B&T!� alsoe�s a re!� on betwee.q)UN�E�AAfIGis muchm�!�a�a��'e0em�c9Bs.����y��{� 2000.�( Subject Cl��fA-0ion}: 57M25} :@Keyword � Phrases}:%�,�n��,Nq, J�0, finite typA� ,B } %6�� 616�� \big�k"� w$ 1. Introd\ oR)H A {\it tangle} $T$!�0a disjoint un!�of!�,perly embedd� arc� !�$unit $3$-b�\$B^{3}�Se7Wc�Y,s no closed @. A ~&is �rivial}���e existAmpr>� diskaF$B^3$i1o$T$. ��}ka paiV p �ds $(T_{1},T_{2})$ with $\3 ial =.2}$ sA����> each���$t$!I $T_1��P � a.'u'2Bwtsu� Two�s >�a_$(U�U � �O%�equival� , de� d��6F\cong 6E , i�re%In��� preserv�� �V0homeomorphism!G si :E$\r� arrow $ 9E$\)!�i!� �U_{i}$� amb�k isotopicY��ve�0\-� a!� $i=1,2!E A=C�1,T_2)e �@M},A�!! 9Fm.+1)hLet^bP Y�,%�l%�!�!.l+12��A� E� ir values!canyN�o*� l-1$ ŝequal. � 2�Remark.} �Hab� M-Y}e�� depe�ly*G a1N�ce� ,ses coincide�K!� $C_l]s,. So#� abX W�asb�,. Although� can)�1�1> rolloofbM , w�ll�  a:�2 � f iAA*W be�es��it�worthA��Q�T-Y2} Era�Gd �  � doeX t me0 ",!�rt �aj^ 2,bo!��in�}E�I�At�� 2J%ce gi�c%FOr���om�eliminar/��wn� % xq��)+r2� %And h��}mq"^  viaU�3: %need�( �. ���l$�a posi�integer�$k_1,� k_l(�� "eJuppose %H!�, $P\subset\{ ?l\�66��P$! �mA�� g� Ya�V唁�݊.� �0,s $h_i:B^3\*� ���l).=\\ (1) 80(B^3)\cap h_j (=\emptyset$�5$$i\neq j$,62)�-� 4cup_{i=1}^l h_ J�XP'}b �iBh !O��)Ks $P,P'-Y .Z�3) $(h_i�),{8})!��@E� k_i}6)�$�4 �- �\�\{�,array}{ll} K6m27( & \mbox{if!Rin P$}�K�V1Dwise}> r )� .$\\�*n�J� a�se͸w &�\{K_P|J�E��[em ula���$B(})$� eN{\�K�e.|� , $A# 2�group,� $\vaj : D �e 8"~.� s"� P'\[\sum_{Jc,}(-1)^{| P|} �(K_P)=0A A.\] Si��E�2M�is real�by �zc� chang��w"� at� �1(:Zci V:�8$B(\underbrace{� 2}_{l� � X �a�K ) I�'���"^�ԥ�A�&� �2�D:�g ň[5.4]{ѕ�it3 � ��i&< ,� oaDby U�/B_k$,!"��ucin ��fo(a:� %H�nec6sumFF�2R �3= 6� 1.2]�X e������ V�b�t��s�� $k-1=a�<-1)+\cdots+(k_l-The�o�i  $p_kNbQu%/Al"� eCY� >UF &] u/"� c�k� . , �#�2MEs 6C2.03T simi�citYO9y�]�b� 1�I�w" �c�e � 2s 2%�3,� aout�AN >:� � thosA)u (or T� � � AP2� , "�  T &%eiH �V 2. Ba*pc -�v*�beZ� &�. 7TM�ͱtT$k$-st$"_ illu}a�in Fig!��$D$R$k$� s boa�d�8 $T�JJ&��(see ]P# <"� .�isp��N�S,T�y�3$(S,\W D-T saidA�be�:�� H%} �3)��&~ Ptabular}{cc} \includeO!(s[trim=0mm (, width=.2\A� ] {br-v 1.eps} &�in} &�aa2a\\!�. 1BjFig. 2�� -*T 6��7j3� �36M�(\alphaj,\bet )� � \rho(i)}$)� %�}\ ��$KA�6� (� . am).�W �rB� t 6j' {\rm int}A�) A��� � l���b_{1,1},2} �1)2 "2"2 "2)}, S b_{l 'l'l '0l)}$ mutuallya�x�s� ede�2�&� 6�y satisfie͔ing&� s;� � ]!p�& j�� 0i0DK.6%^� $i&_ b_{i,k}/�I2��n arc.E,k GD .0(��:j:{l}>�)= Rj:� xh�ofRs)-.A: �,k$.\\�Je)U{� Q�U�"R!0by \[ J=K\cup�%#:)$ �i ��y� )) -�Si)Ou#(>Y)�:2>\?9, \] wV � �!9! Sgof�on $K*�,k}-�$]�;is Qed. �)s-� it L!/ Evimage�,M�%��}ŝ�} a set � B}_i=(1Pi� i),%k i,\{�1�ii�i)}\})$�m� P��i6G chor�We %9A4$J=\Omega(K;\{� B}Llq�r� !{�! } of ![mws�dW$� nC$r�� "s F�now!�w�n�(s�!6~yA-� ��f, � �:� wiu t exFi3nm �B�5�$�%� �� � E7���(��5SY# 46` s 3.3V3.5:j ek�g n��0&x!%2�E1�!P�*>�! z2)znE�a�2�a K]:l]�"f�+F�J�pR�$\Box$. "� , 1H 4!*,�[�J! bf K� :�!RBE1�V��a9T��{l� }! G�0B�ifh( \[{\mathrm �= ?. �4 �9�P}}� {i}\ ) \�| Jh \}. \]f�5V�6��KK$,E_% I�8�Bed !oU $�&�#s$� S*��{� ���o�� JO��$I�|J�|�kK�Q�H$�'�re E14 � $P� $*�$ i�A�����Á,���BY$tersect eia'�5�: !�he9�Bj$y�I};#t�$I�( K;j� i\})6�= 8* B�92 Y�)6.T��P� .} I�# �A� the ���$G"*&� �.&.TAkl�$W�)\��)�If not�P de aH!) >Mas q��inn��shrink9�! %�.��is"*#Smay{umi�r=�EVs nMXA-|nMU{EgI�1}.W la �by sli�!�Y�: $ al�%$J$��)as�����U�FA� >�.=��fwe sweep2�&� $����<_t�! is always�sible��c!�e"i of6�%9�.�n�we � f6z =�n�-1-.XF��f`�`JDq $K$.�z�'�u!�resultFiM� .~@bD � ���a�har}m�m�desired� . �*> By repe!ap� �e�s 4�5!�6 diately �X*��.���L�- 66� 3.6&� ��k%/J�� �'�deF+&$B�I�.6Ae ri#: %Ma� �GsK De$� s1l� �!�&�s>�Fig9r�!_"%�j+k-1�K(,�V*mwo)���5� 5� 6�=;2h�2-103�-35j(4( �!6jT5T!4 &�5�� F]�7V�8Y�gi�f � �^ _0�d )�" �=' >be� 2., -�RN�re�s/�@_0&� _0$U��*� :a$��I> fferI�l�2� inA�w 4}, i.e.,���6� Wby�%63 1q�& 2�0 �BX\ ]aMy`.�:� � B�% $� F-��j K�+ %��i =�IK/&�"R� J�.�8V�9b�� UW _{0j/Ѳ _{0k �IH�E?' PN OB�}E�.hj}$�n��.}B�2(k���j$IHx ;� � .�E�)~c.b5�� bu.Q2� :(� J %] 5�%E\})Y �� *� R.�k9��.&�3.���"� �ato)xn 8E�7!�ex 0}. ?+�,Z�7�C ;ed,E *� , 5, ls 6, 7!8 hold.�. Bu6 i� U obAs� ou��"fa�7F�7&I7 @eedA3 ras8+ "z7!pr�+!8&�l+ a� ich �  &*!�2c"O 9.@it�6g�dV o3)�,@" p"�9)-�1F6U4K#B�,J� In p|?N,�Rk6�,d!e 9"�#�B 6�$�t��"�2�2�Z�2�($"yZ�2B�2�A� ���N �&>p.Zh�9 �:�~!��6]�!� �+!C-t_�1%hC�6��!S. i-�3T_�2$aUl"s<,�2NH=��&$cor�o$o&�& i�s"h9!�A$t_�4ByMr6,�v�$   T_2;P B}���!ob#t�5bf K�%2� .O)@�ԁ9� !e$B)&�-&�aem-(u_1� u�a=}$$6� -t_3-p3)=aE28!8q���3(ƃ3)�su b ��Ν3�5!0 g:�35�3��)��-�3� R�!�s�&ce;1,���cluoH� f�$3.�aEFT�2s$�%��$��Eą�A� 8�'��*^+("x.be�F�.R�' &�' SK{ �7�?e1.3%�ehaO(aO� _j}1�2� k_j,� j=�l%fI�1*bAto0it �+ P|} \W-[- (K_0&ljB3 �"-] R+�K|(,"� $[K]�km�.gt\3 w�<�aina�%>�( Set \[K_PT ��L>� .\] :�Claim.}Ap_1(N/* is!�6�to2;%\fHi,j6W5)\]VA z0xA i�of���� s} $A��!S& }$*u<�")�B} !%�aiM~�/<�a�it��h" ssocCA�s1 $\oz6R)�'=@$��s�- t\inV;}(k_t-1)�i-1� �0� J~$~Vp �>�.�A5�>a)t��{/2B� � =�}�*� 3?.�$B$]�l3Jh �g.� �� B$��"h��0�3K K,�$(B,B�"_0"&�--m$�(�"� BX���=eS;a+�.sh!9 h6�� �3A��Q&j 6g�:E�s�S=o�)� j}$'�XSw?.;e92��^rep�>oF"�_{co*7.m�Eo�0��7�֥�a21�e��:U��"!\[�i28{rl} &\display@K { iDJ} .�0�� 6�.�Vy FM\) ]}\\ =����� ([K_0] + �~�[!� ,j}] �)�F� LN$�y+ �- � X � Z� P[e�v�0 ��.`J�, t:r )���P.�-5,6�4\]�o^$�coe"�Ia`:E�3$ ���<.H,J R�r�C��.1.�%B� ^Q "�9> $a�d*8.�m6k �VT4V�.<]g}= >#)KJ��MeM \{a\^g?F�a &"�3em}+:��vF A���� �|}=0.���\] Thu�Z� F�Now� �4�H�H.VfA� }�6first�( F%A )=\{jp7H$"K A�2�n� J�=k_j-1<K�ܮ�%Y P�t.r "$ .W$��a&��"���s canI2�6� 2s*�� j ?F:�1�/6�r���(anU!� �[�K�n by (i)B��� )D� (ii)"rx6(i)~~W"#we per�!f[� p�HnbKa�p"� &� p,q}[Gp� k-2$R'u�'B7,X?i;IX?new{p� �.Z +1,rb!nd�sE.�E %)=.��O<oI��UOs� X,  st�4? "X7(:J�%{�!��.9a ��Jw� hV&� M�th�7/"� �7a�!�N�{ n�1�F^%�!#r6�%\r,s9�+r)�$�B�8�*:�A7 {p+r�F�,n-�sZ�r-$^��Y>=�6�*�02�V�s� nd 9<)\�[r[g8P+1*� Y� ^$�* F���4n�362e6 2�R&� V:�:z|a��KXA��in%Te �P.z&):�eQaza  J23 K\#JL >6 "2 � >OWE�Lemma��at $OQM iA;n oE�a�B�R U7� $ Rl'7�..�� Ws.� :.>aa�ul �2*� � �!Is�JK_no(at:Q!�:~Nam=$%\#K_1\#�;\# G!���%|  $b=t�$�&"iV��GM� B_%� >�Gc�)i $l$-n;a:an} ($(�<.� Gus1}�8By&��I� .�<{N�<.,%M~&�H &�<9�>�Tl�T�*"U�%a;6^HNaQNP��,yE�E�>�H.&� {jI"R�Y"�Bt>�_50��_%CD M. Gusarov, On $n=mc�>e��5Zt3 gree�Q<: Viro, O. (ed.)�TopologydManifolVEF ties�3Provid��(, RI: AmeriF �_�Xpal Society, pp. 173-192. 1994�`�2�N�o&�'A��5�:m�*�Jtechniqu%:,. (Russian) vit�_ ebra i An�A} �\ 12} F`40), 79-125; "{V�Kn, it St. Pe�- burg�. J�bfJ(1), 569-604E)��@2}"X4, Aru musubime'kyokusy7Iusa0zoku ni tuite� nZ$ese), Mast�=esi�<xZU"pZ,1y\1x �1.�CKXIAM3�16Ms�"it Geom.I8.},)I4}5G 1-83,)u.q O S�pe �&SH}�V�,wGprint.mRI0H. A. Miyazaw�XA. Ya*[, �s"�Ua�ACcom�86�ɣ�"�Up {`U-�0Stanford3}T.  ,��=T�tA�s[)4ulo pure %brai+bgroup.� \\ %���2(.GT/9805092.4Suzuki}S, , LH i of 2WPE04-mq�!� it Proc. l\ Acad9�5}�b$69), 34-38.t� K."�Y, ���0?dof1� +],jutsu Kenkyu3%Gcool-Edu�+, Waseda2�Se�Jv]�zst%41�93� 3-362�-Y0.�%�6R�E��b)9!�e a spat�U���#�D�G Appy1�a(20�87-109��A=9h2�)�E s�72ys/b�)PacA� Jke!h%'21!(200!(183-200:*��2�[2� > B6/y�Y�1+�2�c. Ca�cPhilo�)�W133�Y2!�25-34dC=D$Yamamoto}Ma� , K@^in53*�K<a�lete %�!_f"Cvemb�bb�36If�6291-292�j}22Delta-unATt)2�XIjAaadaptabi�d�cer�Ifs,�cee�1�� �96, (u� ��, WorldRdL. Publ. Co., 115-121�7�J>� �Nend*�b %��-�--6 *�FOa|ofe��5j�K@i�!eM�S:� re �,)�p+r�]wN�~N,\ m_�Vs��{@h?N�h_{s,t .?@�L(i,j),N(s,t)�?2CM.@>j}G�X�62N,jRN$$ "�Uw�Z.:�+�7N]R;N265 � :�4�&!V(!B�@K_?NW �e�CN;�GNJ5}rKN G in�]�� $l$,~isV� /sZ��PR�L�!�%Rz ��L�AC B7J �(&� �"�2Y\A}&� �#P}@:�non-eQ)$P�$.�,=/ABFhGXK:( _l)$�}A�xZB>�2ZNXt�· &�N1)- 2)=0.\]*�$nN�isA.e+u ���� . �V™i%J�i*�i:|io6�i-35V�i�H}{7i�"�i*�i4 a>�i��i��i��i��i��i��i%5jBbbq }' 2�i8tbZ�i%\n"k �iֵ $C_� if{ {ct Haruko Aida MIYAZAWA \thanks{�XA �L$ %; Second- 7 %I�g� e�;3&� } %:�S>] R�O(ng Title}: ��h�,6Z,� ho[pyA�rf�p* 6�Nn:g-1At&Ih�!�-Jhem9?}wg%�l1�M�JhF(hodRtXQ �_,�$.�h�1inz(hem� } �pa�(h�(h�(h �alo���7Tc,�hA�V&hem &�>�*n2/*5oU��g��gF�g�P H i���"%" �5s �D[ -Y2.�`�6Q�$C!O>2M19o $�2�2)$^y#1.&(+�)aTu7A��eN�0:��0* 3,4�d5�r4%�04J2&�-$  tK=.2}GBN&Th S regu�W0 neighbourhoo4$t�Ia��-T_i) ! 6��<Nptj=N]f6wf� PI�Ou"�DF{ ��-�l4$B^{2}\times Ib�2. iQ�S7\@+i]N\J �6 " 7SQ.z$\{ 0,1\} )�iR�' Y�E9�R1*�P) )= �2J�- 'BaU  ?re�� :�kn f�Nl&��O6� $(I�-E�I+B�, %2%22%���-�aZ��a�"w',%[eBQ natur numb(sF$G�reY ly m���!Qn�8c�9�3 easy�se�'�&Qi�&N:2C�j2,THl#Z} �+~+ �,one-branchedU$F�a�u6�Y(� ��); _M�i�gener�Eby%#Bz-�J�BMSo��b<iV ten�1z 9*?"�'��>dun ~Z� 1A�oD} "� �C{ƜYZoD��Y�Y5RwD��Y��Y"�YVE�Y �Y{|5s�mL_Q11}�0�#,V,l�' $L_`2N'2'.tAm"�rN �]!6 �O)�" � �G��*4r�& � 3���Ma�bI ɦ ��m "�mL*�mL�m�m�k!32�mL�`N�m>�ef+�#�!n !���*���2;Sw�n!2 at�La�V){l|VnFg!�l}"X\} (=F'2B'_Z�}x >�sO>�5 a (.;)�H�< ($kDQ+��:mR�%��.su}Z*r9%��GAE:�82�}.�?3m�Y�Hmo�9 ecis� Mhe next��(.&2.3). t;sA>�2�Y� �E� byN8 3.jq.dU����ID��w.N[w�~{�'�1�_to� h�"�f.�sjx�os�1�.!`J/Q#E ـ :+ i 2�� �� �y�Kux'$\mu$-&9#�7C�RpaperM-�*>�.D;1.�.%?%S6�:�ac�$L'� {n2u $�Z�+�9�2�sy4e398k�� �u�c&�pA��,%:]�A�,v�E":JJ@���G1!AhEa�ht�m�%ade�#move}L hf(H. Murakami%;,Y. Nakanishi1�-N}��$Ce��s OQc Vv!r�f! K��D��|9�Pp-pas�(:�� R c C2s%�3*9)��for alv+�Hu plit ""2�%���na�>'�2( ��'�&j-nT��&.B�h�a�8 "�^^_ � �6 �^_�^_FR:�EZ}�^�J!?%��J�U1�}�k)U�"�t�(ˌe�zI^Suz"�Yam� Yas�.>�!K�*elC.g!b)$"�Q(( �*�SG$ic�GF�2Jc"*f�  �=% Va6R�N . 4.6T�� 9� Mc � d~� u6Z��(�1 d F J8�&�& � d-,6y "S zcircl� x \gamm��)"IfNZ�� $W$H�=2<a�S!>�d�(ta)# |. �V "C $solid tor�<"ol@�U!VnCI6 _{0}9�J9V�T%%* /5��lVf5 �� :V\*;W ��  *`6O2� psi (D)=WN&-k %�9���cmsYg8�A�l�= ��� U -)� %�� b,�get:) �'y��9]6y�>!�gin&1bC�1VZ8 X"�?�;m*;m>X>d�v"Xev5biF�lC_{�k&�lmodels*c)M�L=7a2ln$�V,HuN%��"�iF�~�#3�B��l��lV�l+�l2�hb_V�l$��lA���l��l��l6�lL.�, '^�lL�m&j�lL��l��l��lR ����B�"�l L'=LeK*#V!]-�* %>|l��i��lL��lB�l! J�lL$�L.�.>�lI�Dxl�JIR-3� � A�e�l�l+1bWW w&�Aiu_�2�<�8 "�K_l�f\"m�&+q"mr� *�� �rJh�Px�l2�����A^$L'.O(L*f�<"�B�g�j;i��`!c� !���.qKb-X$2gVmLl$*�D>> \}$.���IŔ&Z  Y 6��6� >>2>Y!�b� 2^:F�JG% g$itw& ��{!�J4�.2~viʁ�"�IS� C��>T���&� [7]�� A \i�Sde"5i~;v3RBNA�6:NA�0�&AY78Xat� !�YofG@�m6Eg 3.8%��,*�@e*3t&0b�" X*:"?�LA2*�| �c}))�A���m2�A�by� V$)$�)k"���$indices $I"#...,mA��}}Mq�q�!$pa�].q� rE��si@�'V(iJ(Ub�� [ "% :$ �lN��\ �JR��j�d �%�gJas����'| rvq�B$:yhC%\J'"�^��Fb$7$b(as"b)�"bGF1uy`%:�.�I�o:,)��8��%����J^n! p� + � �U $I�s{i\O�E /+2� �54R57�E ��7>4;LaOcombi�kP6�%�i�2.1�}�e�.72.3d]em��j%�$:a,&S��!� E >��%�>h�4n%_ &�q&�uv �3D;_�of2�1.)* ��IA*W .EA�e�HA� �f!Ii��5&� L��W&�$� .T� t���������.��($k��if���.��0�It!�e> &�e�oJ�&�"�+����qOEBU3 A�At�2 (2)$\Left&�$(3)'�xs ��4q�2����*HR�m(�f>�,J .=p�;es �8�v'�e"x >ja�'us"U� Righ�$(1)'. c a� (1)$2(2)'�.�#b %�>�9�inkK%6$L-�86�UreK�"�`< $\widetilde{L}=K_1���2 %��)HK_2~:ja�$��,�B6�:'*;P2�^"��6�, )J:I"VN�9<�:�E�1�-.)�� 1,2\sYb�_ň� e�"� $Z](O"Ma1n*8p-)�$O=O_�`9� OT��>$e� B}_1;$C��n�Z �o�a� �N�-O_3(=!�G`\ 11,�%%6� :�by9PF|bO_�s�Y!�"� .�. % �8s!G%�2.2U �LF�2�O!O21O"�bRO,3� &,R� -O_4%<-M. a�t�$pr"a.�M5vr��>^�� 4 �Q03� V8I�� �HJ6�is2�"��- �E�_ 2+V�*����=B�Z� ^-:~{",:�n��>n*N)M)F׏��)&I)"�L'�e�.hm~A�*e" $(n+2"��-f#re�"'s $s,+�*)L$"1'$s',t')�." '$) �)&�s&�s# *K�L�$s�tB"c"6�E� �"f�&�L$$hA�$WޖA'$nN��C�"�>>>�F.Aw�;�o�vb����ʢ�!�&h*Qa$�L)$6. h�M-' '-s'J+.+#]V-N�'C L'-tQ[uY.�_?B�F�2.�%�J.��vLmp�&!�%��!�e�?8ic��/� G if' par_QG�t�WW�Mll&E �+J6> 'n�K�i� &�$T$L�I(�5lf٣ �8^�$��Dŷ$5{�M�r �"ų���.r�.�e�"q(>ix) �!}i.��by>N-"�i&}��1h:���H�ba��)�2�>O���m 3.5a^&% fHO�t~H�7�� �"Step 1}:m�$L'bo � �#eBu:\9@68��&i��6=� �\�E6�k 4-r06]R6,�+�&o&Z_,j\}\ (j�J Jlb2 O_\l"� �1"Z2 $]{�B�>� Y�r�+?`c%�deE]N,*�Vr 2> 1�*> �8M= �trD >�)I>9J. B9!YA��4>���bfIv2}u�Au 6@2�MuBy�< j�k %C: �:6h��)J�l Z�&U F� 8ornf�l�f)�J2�1�(R�!�Q� ��N��^�3)��a�*�@F�2�M� /&nJ/!Hj�"@9a�-K&kn � ��$n��ha��7q�6� F�&j N��� –�8� i* �[A��!G��F_0,�d�Yb�m���  $LFm�@ 3a Ȱq=4'o=�� Q� e� �is >�� fixr/� step>��Y��/�.�Xt~ .Do�Q �9 &-"�+:4.-i��%�&2" �yBNv�E:� 3HA�;�A �� DJv*�NS!U�5 �un-V�&W�-"  1GusU1� ��MD�2j��d !�ir v~��q[�Ea[Aeo�1"~[~]�Q-FYN�r"�1>K�vt m�x or m�2&,L[sarJݤ"#hc��,>"iJ�� �Ui F�JV =����r�A.�1����*�. A��3i�a�re��VJtal�ls#r� IY2f3}F &� B�p�648O`(6 n>�4J,A { f6�ev.R � ��P.�3"�>"e9��!�&�\H��]"�Ze�M.��\��\��\��\�I'}�1 , {%2*X2�X��� unpublish�{199>+\ iro22OAr�']�'].���\McP*�Xa_���(].N(]irae*$^y �:-] ��QV�,�}F-]il}&�6, L�:y\�Ann&�52�B�*�4!���dR6 ,�aI$�^VU\Q<^T\���4r�IPA���1%K\)9^�E`B�]i[�] j�]q5�`�\��\��\9+�56�~�\ .�\!� e(Qb!�J�\a�u��d, ��\ �\J�\d"�� ��� c�8[leqno.�V #ef\adJ�op�>ad}��ef\im2Imre2Retr2tr�P FyOy:�=}{�]���.#�%�%� �{}E�Lie'eI�G�bE:U Step�XXWilliam Semmes \\ Rice*�a Houst�� TexaK\� 2�Rtableof�iw� �{�X"��qu-8g Aɼ aZZ�G�7�s�hu�JC $e�-a bin�Q&�_*�e�he  gt�b�k�0 the >? �Te�@e:�;{s� law,Hevery_�'�KaЭ3l. If�9�# ^k��u6vek3�5�- !+ .+S���an ` . �[���T� $E%6{ b�caVQ@of'to-onupping�E onto(-��?p'�,$?!i5�m > ~�s1�ZE�M�8  a���?com"� ofgC�09h!"\G-ON$H s�u�A�2�~.��$e�]7U�u�}YPJ'�o1b/PnnFD��sYQ.� �iwG$. Bas�=meaYat5 2too�!�9�1b!T�riQ DY��H�/)M_�}$GJrmG��$\phi-YQ�$5 H7M.. s�mo�sm "map%@F�%��t�B� !��G l�];E&��!V,2$ )� �i� e�906H �$aI$% �^hQ16MK( : G_2 \to ��utoƓ*1 y a 27tooEz(�@9�nZ�5e=��u7��2Q )OTv$��"C9Bage �,���!#! points !(x|>�b$x�%,%a�-�f g. � kerne�h C%�Xs�ih �H|mՂ are !��A���Kbh. OnB chec���q5},M.50I��o&r, ��o9�i��b/�Z�1%�A9�j�&)G��"�\�,$g \, h \, gI�d�H�R��! in G�$h >�>�A/ ya"�����rm��E� �.�a>=��c;A�S2� F�!a]X.���y@&*.zJ}z im_l$1\ r.7G�$say@ ax ! l y$!T�Xsn91.�y = x%x�56Gr�GhGx$6+esTQeZ���� :q�Y�0reflexive, syV�ric%�#���&�K U!��K "z2P�T3#l�_��!1$G$�S:�Id�F/a4��I� .5�U �2�] �m!�a&D��f� U�L)�2ˡ� 8;��xr�, cose� �nn,�&5F A8e[�G,a|�'��to ��6�6� :ANm�!� $HI ᣎHMO,HHm�s?��eb�ih�� ^!$xUr!6 the %�a��"��y�XG:'mWx�}y r x$, � � v��-�_�� ^�.���9d $G /!{15 backslash%K2lō (canon��RW ���xA�E ���tak1ќ%G%�2� as3iwq� g-)M4;�e�)��!p  �&� by sen�Ra) �I:H�\,��%�S���it is� venO�ZI� a:{H 2=*it^ 2�}+M�y,@, yA�ɑA�Id$is way we �.�s�$�!C�VE per� aͅ�%� n.�AINotZ���ta��s&� Υu�i3�^�+th�p�Q� -H��"� � = \{�  :�'� ��x \hbox{��}��\��O Clea�c ��M�>(. *I�/*�|-hny.j&� �A2��-`1^�E�$yE!:4)� !�)8ato)u"�Ex@OJ0� )U , y �f9 �Bofn�I �i�f �ta�PYA8d�arbitrPE�p1�M��:3 Q�g.,^6��"d+� ptfxn_hIF�  nde�"F�a�:�� �tru� ⵆ�N�+��A{:u � h*� A`.�:f>C�� e�"�ox�} ^�{Fielh�vec&pacesb�b~�!k�?`Uel�E�+ �6�ktwo d)�6� s $0� 0 \ne  a* p,Bq&�%�� $+� �����dotM�se.>�usual"� �1� and� ribu laws,�� !� ��nd2�vFi�:$0b.� ,�֍�.a�!Zha�mdm� $-&� 2&5%���O%R w' ����XnonzeroJ� 3.k� e $�x"� 2�!% Y6k�m0 om4 v>� .yo�O��urs.ce�ional� �F bf Q��È�(R� c�2x#�CjH�ca32��9IG"� 6�^:��p��a B�"- a pr<�umb XF.�a3$p$F��>Q� <u]� �e2A&^p5�f!2.F�:�A�z .P�(n��l^(XE�>� $nZ.eP*O$n$ $1$'Ų��Q�5+���W�a� ��aa��k�5�:��er��c-!�� eventU��&� c coV�� YxK�!�s��� &�.�6� ~#Q9_� kK ma�i��fa msel?A�Ip3?�)�.�m 4:� O��xAz>R�&Y% s��\ 5��.L$0!����est E>_F��6!�Oal(&2_ stic��E� $kn� ki� I�:9$p� �Y M WJ�>�E�e���J �ey%�ng-'�R�A2� ov�h!&$��$V%H "��EB�$0Q��soa]���NFofS�a�T�MxermitsA�MY(��kD Vd �;���-Ż!1�n���O!�"&�82���B�A�6�V)9JTQ!�)��v_1���, v�8�* ��w$VAd�N��.5 v_mG��� "�+�al �#avky m�!+at �tt�k!@)��䪁��� a��JU Z1v_1 +�S ��v_m = 0Bi ��Dy��happe3!:� .P%�&)�H��!V .W� s $w= w!�gV$Wn: if�-�!#!�be��r���a-�� b0tՐw_j$'���IV#Ѥ6plA� 3.)�?� 6A!� �)�sp�$V$���*ih 3 N"��!+A2�!>d�S�� a��1_A�U�.�a�� =<s�0LH- s���~��u � way %e �J���b��V�))2�� ��}�ver�&� >!s n~/� 6N}Tf J�^I �h!��8.zr A� ��,q�]Yr��4:��~)ҕK0�+� � %� tilln7rllMa1:�h"����a6�BnU�M;* �stD>��q.yI ��&id�E=F� �!���.Cdd (�o #"�!}6if neҤ�to.�AjOI$5<^��)$&C]B�r��5!�# ��a�s!RMQ le n!�m6�� deriT�f}�AJ fact�/�^��ouv?earaܥ� � vari�'s� a non~W]}w[( $m >�D����j��f�!` � ���"6 n2 O-(a<o%D#i�%^# maxi+ Gr�����>�nR��� ���j e6��is�M� %�MRU1� �� � RA/9Q��A2�'!5� rpre�&B)o� aE k >�=k �F ]A!�<>� �36z $k^n� RiA�n�� n$-tu�,$x = (x_1, \o x_n)� 7 $x_j ��'ordinate�  �6�� że�s�)�!���h�o��)� s $e.{e!��Re�>$j$th c�=�L?!�H'e^�!z:�P%V�&r��A�d��JA� )�� AN�$f$i�$L�� NVCa�ifE�!^ �V,�a.h$v, wH.�?JR f�ZR G �_ w�a�  f(v). f(w)F` n^Dicu� �m�'i2]_V�s%e9 �s!G!dz Ai�S!0�H4!-.d $q�cal{L}(VA V�J. v3!O�VIa� be a:��8� h �R k%��<>�again, U�Z��^��2 *m!��Yo $V�=Zz��t$f_1 :At(!f,2 �(H:��:2�u8$f8Od f��NZ$h"i,F�3$"|hJ�(2U)A{0= f_2(f_1(v))D0X� }>�$vU�D( �a�ll� E�� M� :J�N!A� 0�!E|)!�.` %m�Y� �N�) a=�*�su!�yA:�bT��el��kdB�MS:n6�NT9 ;a �6��K�<#sEUst2��ġ�j)5v "�$j�1.� jn' 9sR�ge% �:� �)"��A� (�;ne�)њpvf6q }p �6!�*LZiI��!)MK�� In p.�F��/"� ~F_��g�5�:S<%�VQ�-����I�&��&�� h� V6&0I!*p/�t�r� }�db�k� �Da�� �f�a������:8/ �1d�<%� f� � &M -/cli�>�� 8*/ lesaAb� �A�&S !�V������E�.�s��-� ��&�B����)t* {��w $-2$��� V:����2*�"��[I0� aŵ��%$�= 0�#|v��8U�*Q� &� �s-n.� -�����<�Z8 9�.�&T X$1A�  t�2)��Y�6W�i& $!`:���.2%�1B&�[.q a6T�>�Ip�%iwZ�ma�݁�2� 6�1�!�6�=-Ȏ�� �le�I�U�f �����"? $V / W.)th�=6is ��At4�.�56��� �g!�n*Q0V��well-ao�v�-�"�*��ru�.�����-�-�.$W�r:xe��/�|��.aM�Hs �O�KI< b. ܚ.� ,I=d'q��v��E�( dimension Xequal to the product of$dimensions$V_1$,�2$. To see this one can choose bases for-4� and characterize linear transformatil from : into 42$ by a matrix�|coefficients which specify how a�,is vector inF,1$ is mapped�a�combina\ba;s <(2$. If $kFla finite field with $N$ elem��$V , ,-5Qal�$space overZH' 5�$n$, the�$$ has $N^no!�!�follows)D!�fact thahere is an isomorphism betwe Y!� $k^n��9� stic $p$,qn wE  view� as aJ��8integers moduloE. -ehas-8ly many5\ iB numb!;N$!�5}o1� 9B p^l$E�0some positive� $l$,AeVremarkE�Xthe preceding paragraphA For)Zmatter, �Ia be !edF %�a sub0.  \secA�${Algebras} tcounter{�(}{0} Let%ebeE�eldA o say �,$\mathcal{A}I�n a [ �A�means^0J�4 equiaI E�a aAry oper� \begin�l (a, b) \mapsto a \, b \end&i�ism�a each%�a��bA$Mor��ecisely,%�'$a \in .�E/e�!�$b:�$ should)D���%.��.NA1o itself!�d|bB|A@{a�{. v{A�IfRe%W)c =)f(b)>m for all $!�, c��U2%re $t to ordin�� addiE$��.{Ipk, C."vJ�given�-constantF�T @$1$ at every poin)�E!���1E�e2!R��� !2@ZW$k$ �&F+  )j�G"� �Dofq$����aV$a{Z �l��uX,L}(V)$ denot$ e xof�a Z� $aѩ]��hisE\մ9�us��V�scalar .�)��B}Acom.* ��orI�V$!L6W �A�u�6� $I$ o� , ��takesI1t!`�\i�/e2��r*)yE �~ m�>��I�Qo !'square�Y�a�Vy SuppH � �B�U 1�at B/�;\. Let $a_1, \ldots, a_nm �56gaaF'  $kQW  wr. �f $a_j�W_lEX� A�N ��of%5 zi�s��j lga, leadsADa family%Vn^3$ �i�k$M�describe:�B%b � choi� f X2� 7k$�y�,structure on��$n$2� ܑ(2 a� ied) ��In� situ%+a�e��idT .Qs �R � �al��s4 may involve d� nguished� s� s, as�- filt� fgra+ � r might�@x extra �W\ sentz.c� .th��lik� topologic.�)ǡ$Thelpful, perhaps relat�L kindA norm!Y!s. At !�rate,s � ften easy�$� rest�� c�odate =Oingred� � k�si fA� c noA�!�"� Li"=v� ќkm�I �.� lambda�� a \Z� 2/.A�k��� %� �� x, y)X � []>H �2� $)V ���$satisfies J� ]x] = 0>a��� xFS��Jacobi��Z\ [y, z]] + [z, x z, �z}, B �� �}�� % "l)�ɚR� +Qz-+ y�x Fx!RhenceR^,D= -�x].>U Thu:\!ŝ�in%_genera�ens� �x $ previous  . A.�Usai�be�"l i�brackeIa�two\��!�&R A�al ^0!vThe�6� a�� � of.����� w��"#l�s"] symmetric i� ival� te��[�it��cally �'$0$�a�0does not have>�w $2�AZk=:�)% 2Mk2�� uto� ��A?2#�2k.^ �o �. Not�R �f �yV�i "t%�� ��1uo  by sa9S.�%�yE&���2��u�*� j� �we  �N[ia�a  -w,�� . O��|eck)E��&`cone 2�,K �M�!/� in:Z to geU>9� �-�.  shall �  $��(=f)�6yc Lie q�w:gIn�ticular,�-� � �� �Z � M� $V$e�evbR A, B!�A!�B - B A = circ A>KՠH��� "� �us5<L�k-ue � A�f�$V� >�P!Q -$��%+ same!�F��)� "�Sub-�s,��als, hom"{��M��� iar2 ]2u� !;�`s�������their� pr� tIverif_ ͭ(usual way. �i�ce,� �!f.�!R�L su' � ��,closed under:m \  a2"����c-��8 preserves:\��A56M.&� ��!! �lUzI}_ 6�!A�We���(= �eftI!a2=��!�� � 2�%�$ ma�Ywe���79, &>I>�zB�r� idea����f�^� �AR$:� A}$ 6�y�:& ��2�$is both a %3`6��A}�l5~ I}� two-d�&)�A�a��"� :th� threey�oincideAk�� �2i]it�M���Y :lAy��"I�is .X��|A9]$\iota#C!�n19� AL�!�!� G6�r y]�� � s��NSŘdo!@ ne�di minateq�E,Ii�:�o2b!�>��UfA}M5�s=�and s2|h-�.�FYnto2-2 By�~  kernel�= _�s� $x %hq�A\"� $h(x)� �2�_� Q a2� a>:>�_1!�ConversP:�)F=!=��=�e:�>}� 1 ! quotF2� /:�j�"5� a� on� Mv�� � /2S [-�&0 1��S� z�on. r�firstg:� ��k m �@c&� 6�a�well-)Md�  1Qa'��Yg5ׂ� �� ce� $Z:� to�c!�U؁ 9H�]]�x�"y =��, x� �:u�� Q+=� �:S2j�Snvari��e/o!! 9�r� 2.� >��L6�$eѣ$e! :) . In"� BFis�$��6��  z�&TaA�.U���l BW��)� � 7)F_B ,$.� [x, �0F� [� ��ճ!. e ��Z3�� H too!Bl$reU n�o"�J 2w o zD we>� of�Aa'�Y%J��q�x %w,BJ%ɇaN�.�*��m�� NV1U���L&� of �:;�� !�>�� n*�F�zca��N2�!3,2�!�b�n�l"ِ!��R�Jx>x>!�5������'is6�7�t\ al��F� .� �i� ��� Q~� Now4 *Y ] 2�!=AO. i 2� M%,�� $\ad_x� f(,!d)�V� {\ad}_x(y* � B�A�a� forward� p�on" F�sh^'t r� �>��(F]�%�le-Vz�a�� adjX jQh.x �. :1� A" exact9��JT!��?U"�o� �A�.^Q�2{:��by!��orq .e.,�Vof �l*�)��� ��A�]-�,� J� ٧6�:eby�Ap� v�*��anm�i"D NF� . on6�Qz�mR�Ey%�� &�!>QHs �� y])9!F�H h,i�y �~�ٻ%�e&� ET jA#its�M'� �F1 Qr!ݷpf�r� �M�:���m ��I��aV> m~ingjOarbitr�$Q�)�Q� �K6Eb *u'�2/ in-d�$W" &� 0a� &�Derivqv�*^#�)!*�MVa da $\del� �yE4�e2&:�"O#��J� g(��b�6) �+� bvG)� .�U"�>!��:��.�.!�Y >#n:IJ �_�/ 2$�@_J'[ D#%�_2] =-_1 � - 21>A���=�e�u�n��m6F�a1}�a4mR� !�:�%�&f(O1��vVM�d.�� appl�to J` a�dA��IOF�2=� V 6!!{lsoB=!&cor�=ng.���6�"�s]28�q�=� oa2:-Fq�M�� �'`  U � ,( a�M�(x)��# I� (y)]E<� �� y� ���2 &2 A�.� ","� %/Y�2��*�/!�f %y"090/)5@]VA�}A�2Y^�J6�j�&�{b�w6^��C.? V(now� J�����5E�a�f $�ni!!A6]=Id�9aa�2.m~ 5 sB�::wh>&$�� <),��  (x)$�� � :#d�ۡ�) )�M!DN= -baF >�ɦ6nA}�4N6,.( tupl�'2�,65q$eH.6 5�,� co;,tewis&�&%�?,:U2� 0(.%* a_n)a�c/(b.>b�=+ ^n$,� $ !���)>J!wh+$j$th!cpon7#i�#�>Fs3<\sum_{l=1}^n a_l�-�$l(b_j) - b: a_j)B1Jn:� beco�1�x �.r&:* vSx+)M .7!8J�_.u  W)j1q+-j(xB� &�Y�B��e�>^n$ just"\+\�G&`t9i,a#!��Ped* al2q��&F.} &� SmoJ"�0�{\bf R�v� Fix aJ$7A����/ C^\infty(VZ�/s � real�1b�, �e s�!continu'VD$f��:�  ��!Wpartial5�,  ;f��or;,L3� l s� �� sum'": of�9x^gai�- EHus RJa�2�6��! �1�I� cus�&ryAb�7 V`� aW,y; )/a sequen�- �*�3 $\{f_j\}_iWI>~!6 verg�5�7:F $fB2�($f_j$'� A�.uni�"ly comp�:i"e�]��\ Pq�-� Nc!Qcu�� :92�� v��6 tand\argum< )esum� �A=�6rg��1�)>U96�6�\Q�D�lim8�)�s � h�:S-:V&�n)r �O>� $V~ (V_1r MV_n(x)� A�� ��!T��s�=J:� �qJ�� ]� i� a,�:=� �e��m� /j� n� $V(f)� %p ;�j �� dB� (K� 2�VŻ��frac{\��}  x_j}!!,>m"XA�& dir~<2(A/A�& %5 t $x!s -$f�|�-D�D� "b;ANJL %�q�on, siV�-V(f�, f_2� %%f_2 + 2B���}1Cy R�Qe�0 Leibniz rule�;calculu��A+V =f , $W W:'W6 �MD.A�i~IIM��'Li&�$[V, W]%��d�Ob2�.Z%���!� ose �t V_l� \, j�lE�WE� - W�6i B� �%i-?u�A�At.�*K'F� [V, W](fIV W(f)6 Wi�Z] says��eX&�{RW&� � !� -�BF' Ts6< e�nd $W�"�*$Polynomialv�NY@�.� Z]#*) $5FL e6�[ta|�( t_n]�""B:u�*p�6b :)6�� indeterh&n�b.q t_�B>[@re�/)��!-Ix��n�� $\alph � n��f=neg,=V5C��$�<~iice��.��Adeg�(� 2ex�^�um3 &�� �:�"-�e$t^"�A�e monEXJ@1 = t_1^{ ?_1} \cb9!zn}JR�t_j&j�$!: rpreas be� &�1��eA %�_j�)=�ntvI :-G b�2��]$$ be expres -asJ-�� �1 +1$ 5e m} a_ �Z1a^:m!� }?>u%� $c Nx � �8 6J)=AzADk akene�Y�iA�-,0' M�lesA/an�89�m!N>�c2E�Hai�� cop�:30�Q�?�0s, \  onl�#8�' W�add24��m�A`em=6� D^e�A i8��erN)31�-�betA�tq A"}>� �"2t-in6���=-�D!?q�s }(Ʉe)0�\other% M2.� b.+.�2 way2�2�m7"VnNIzi= �G�noB� $\el�G�C22�_!N�!J!=�� :t2��{icheN%� �of��Q� �&�  72p� �5+�7= �V8B= B�b� A ��2YNT�8 5"�=%8is .�.I�0Eo|Cbn2 "?1 \le j�wi� %�� $N _j�]�N� �wayEJa}m�8differ*a�.�Ɂ�6#,�ŧ�� u�exebB�A� $r_jl&u:� a%I���excep�A�:� ��B� 72y*�`_j - F�\ge�?g-0a'|L ����0)�6�ac%Fon2�}r� R�69�]\bigg(�| �|E1Zn 1) �f>5 Ds6�{=>}B~C�G�E B z�a^6�Eq^���: P%>�e5GI?ujmA�3or�1B��!�"} a~6��1&� �_".J2n �2͖U� TC���� $l��(6�1.� � S� � H�1M.�kA.t2���%%�� �,O p.s p�^*{ q {)a i�$�!�b�)�"IJ�fR=m~ .~ NiR�piD5� j (fF�".�iir� �e0 ��A:͎)� �/�^oA0]\i fin�6~<���� q.�q!�� ���X D��V*�rQ:=F�^'J�r��)� l = �pqu� (q�q>(pN�%�� � O!�LsP�F�� B2z� s�a|N"� \.�_/a3�F����lY�$) M�!\, 5 �� G�o"!Q�sM� BW� rmq_m��1|m��In� word� 0Bt�-��,6�23 � c"c> P}!�}ed5-�VZ���F&a1},2�_1E�>)t�����2��#.Qbe &�( for z� . �e,V Rb� �2���nJ asm�.�D>-U%^�)2�Rr"2�*I .[&U ��Wr !H m a +2^.%�q�6�.tfzCde�:b�Z"�Epa&HV.]+MatriceƝR  �b�6�"�Ņ8 f�a0W02��"b aNs$x = (x.Kx�!: $x��:�$P:� .�� �n�� P*� &�}"�J%#R�#� ) .�i�X-"�Nal.0:�� 6 !( ~02IR�, �q� N>D!u!��.�F�M_n:L'J� \ ]n$ i[�%� entr�*t7=� ~E 4}�rpWy!}`yMlsop�Yi~�umanneFFG((a_{j, l})$�I $(b_{p, qZE��$��:�2�1�bp']i��&�:.])GxJ c�m}�=�� ��b_{l, mF!I�Ni?F�"�n�A� ��a8�&�0JG�% "�D=�+ n $n� EnS27?(t�!�G%Y])sx%q !�Z[� �]p�Y $T :.B ^Uo:&AP$L<T$,J|y.�  �!wx_lBIa-�xF9)-]*�WT �. �,�,9A��V� �#a JA� ���"���Me(.lb"hT 6�7 r7 � �?26�ywo)��*�"�RE@l &� :��&� �K/x�vidual�1M"�`A"`!$5� �11c*t tV �N�� is �q�!he8�S`a&��t�Ha@�wF��0![j�Z :@�f& �oE .�s"8�.x!�SU!ZjG!^, we ob� �i$>/(>�)+&l"= f2�)�^�W.�Y.= �{d�+%_x:/%�is2� is o�R�d $gl(n,.q�I $T�!�7|a V��6}�e�<ch#�@�\tr T� �Rd V�(�M^ �jFAa�trs&'����fq;>�H:�D<�y :PE)ƙ����\I�6�b�d"p&7.���o�#e ��E�2�}JEJM|�)�+Z� 2�'�&4<�'a�atJs%��$T_2!�!�_2�pTF5�o�T> (in B� . H�)e�%� n^: �Ke�b� bb2��7A'�<��"�$0$�Bref�a�� 6r Nf}ic�Vu sf�u !#,-*assum v��%�.�8$E]�R *P :%:�� v\e�al�Y!�*N $!=)�. t�: -*� *.\Ad'"^R�:yBy�I%x>�:� $-1$*� ���2e��b\ s�(.2YInvertib=!aP v/�<�@ + E2@"nAucBdIa�zer6b2>�]$eT � cas��YB )F�|I���a Nh��E , name� -� БHy�e��diagonal� �off�A����� e2W�sa,-{ %�x�F�%6�=�h "Ma��;R� N�IAE %@ ?�]."��ݒ��� a�B&� !.6O`J���&� 1�96B� ^�&� /6l�^�#s)� �!�:Z� �9!�Becaus62|W�&� J,�6�J�& -��e ��)�:�>�j�2�0"�3!��C �l�&^�hg@>�!�yp�ky!  w� Y�-�Aq2�aL 2�i!w\ }(%5m��e� relevXKm��$ca�&' �` A�&��ima62�nQ�2)�uOT66A�6�'6��K%���2�J�a/&�[�B�Ul2"`m � �nT�:Y�`ik_ch�4?5�1u�]-��c.���%Y 5!�� group-F6�!B�&p��%!��P$ B��e _of.* ��F8!bo+��he ge5]m� �6P.pIw>� >�E��],d $GLF� 2�[an1OV�i&dM �i3]Y/ ly i�c& �*6�a�.dA��*Ql!�z� �?� iv�(O-@� ! x�(ina�"!/e�N�F� e>A��&QX�> �ai�YǍ#!�:?��B�.�N�B *K :�a�d�r�A..� �c���E}�N��Aresul�j. ��F5� o6.m1.� *�S�NJ3��Q%Aj�-��a�e$by!;�.MrsJ�r��,��H!C95F.i R an5* ���$.�>�]:k�K _I�b9J���� &J a���$n " RA-E���!�2�6�A���w6Di��?� �Ri����a�% 6!-�q2@��kec�>dfYb�Ac"�SFUE�ub�>)J n�L� of=}�46_2/�` �?2� "3RJmv �H�m�TW8>�B.(""c' lower bouIra[B{(x �> c cxcb>c E!# A.�!�*�akgreatest2�or infim�$E�O�e(< ifm�a2<��># f(G:40�J�L.D�%$A =�J�least2�Npre� U� \sup:�RZ���0�Fn]��.�.���c*q��l�y�%!�1n�[s�� .r they�>�/leten�1axiom%R=6 s st!� o� .�q�2/��P6)s �D3d&=C%�<Z���-CqA>r N~��6S wID6�1 absolute urw:FxeFU|x|%�D ��3F{0+4x�,0.$ -x� iybt�Xgl� G~d=xJN|�h�, |x| + |y|R2�u�h|)�8��aN|x �P| =]\,�^�) \{x_F%@�!.�2@a�!B&�A2�V`WQ&v@KakeJH(\lim_{j \to!! fty}9= =F�U!_�sK2psilon >!�3�an $L%�1*NUJy |x -j| < \ Lb�jRL!���m$2e�{�?!9.�2v:4 N�4{yF��"�)U 6!Wl�{\{w_lAm� ty:% }�5�:���VJ noFJ�xgmsD -Z�:'1�A+d^j�5B"8 �kinfJn�A!supN!,�$iv�}9LlRW� FU xh/>>KRJn��!�S!-��O��J1 2�#�f>� �!{n�!G)u ��$mEO��:YQc [ � aB�are�W�im�T�>�1��)�monE �]�� fHr�'B n �)H a!�:�/s�ri�ea�Q�4�0����D)\D)j=��Io�_XD��)gin\�ws �Oz0��om�:1.works �Mxell�t�% �g��:� �.�fF>ofz "�?.?i�6��@ �r��n��b!!��K%�%�K:�t �GM� W�% r�:� y��� 8NJ|a_j|��. IA� {>Y�YNA��p�F=�P x^nO=�B+ �X,wva_0"*�0&N<fb�.�0c t$o�jpo��a�5��s �� �-�$� G =� E�� in.J�Xhappe�fk.I�o�@ �M��$a�B� .2m!Co#xri!ic20 $z"�&-C@O� �-ap$x + `ni #�k  $� re)i� �i�l%� ific��pl�*��$i^�%-k2�k6da%�!��t�a*, $z$,&a;���-�� re '$\im z!P z��xA�iI"F�M �$-L��jugOmVz�n overA�{z�'ndi<J�./� aiB�<i �pai�6 �5�% $wFNh�w)ia + we}ay�w �25\, 6 'z�-wd �m�u%��'.�>r�aAbin @�`5L|z5C�S��qrt{x^2!�^2w�8� �QvR�x Oay�u�E_I�Af 'E�z��zgIzm!i� �2�I1 A1=5qUm�W"�/�wMP�' h�6� `>�Ac:� qa&�(z2�z})/ �^nd -2�)/(2 iN,w#e^�6�%��F� .���A�6�>6-!�+e�w�6��:sG�5�we�5 '!rg iO oco}�&�>� yR :�)�Fur� more*$narray} |!�wAz& = & %� w) (.�2� w}) \\ 1|z=+ 2 \re>�w;|_ \noM� D�C&F|z|a|w|;�-+ )^2,BLi��!$ �eC%�A�!��':Z�.� -Zm�s zFT!�&�J�2v �\\z - z_�t��*e�-I�"�eba^�':�!3!?$z����8Z8:�sFh1`a�JpYa�LI7sGgUQ��c�gU"6 . F�7a�}G��c./ m ���.��procalp!�I.�N**c:��no � �� ��dJ�)�R�1v�/-P7Y�\c �P u  W�*avnz7Kse/mWZT1sr reduceF'g+^Yx�.�A��\Rli�!<H� � *Q!L w � '����a�|z_j|\}:Y2C��eD2N!A7i"�Nt Bigl|��-�� r�� - wR�$z, w�� C�8�# b^ riv !Z�!L*o�h6jg >/;ac}H�~"5R:z"z�""*4V�� F0JF'I����& !v� �':2E�Mz Iz�2m$�:9J���i�%�FYj�c6�KN�.]Q e��|.an a�u$���p� JI:�nS\.8\�5�:�j<�� �TV�� L � .��B�B%j8 F���%BEE,B���:�:�R��� it9�A�>p(z9a�, z>�wz�J&�2"��8" �t�AB$�K,,0&UB`�0�VP P ��vtC �$R~s. ConI��p�*.��e*S%^�� ��2k? factp�e�� z_jw �z�5�H z!;�. &o$Quatern�!z6rA q< � a $42F�" 0��+o)A@.0&�%B H}$,A�9t%�_SB9�Ob6�all � %#:D�4m'6�)&�0�%�_f �-2��fN�l�txKUxq7i + x_39 j 4 kR�=s,�$�B x_2,84�cR�czi, j, k H}$ ��N�`j^� k-Bm��B^ i�� -�P, i =N�f/)�i�O�t�$BkۊkMB-�H hi5u��,&H�!puN�x^*1_1� �8i -~!Z~��(!����!�AXn*�S]�J5+#c7�_1�x_2 3 4^2F1;m24((#)�y^*!Fx^*�A�&�H� >$%�:- 9:`� yQM��:�+ ^HU !z ^|x|^{-� �X!8&�cs!�mea�2�9�<a2��Ů$�nO!�SEE3#L!�Z �P �:.�;maI<u�� 2�!�+!U)/"1g#^�4f._��)b $w%�w ^2:�FL%!p<^�  $<%AQ! E*%��Q4!� \, |y8V)!�e2EB!5P;k2�%$.R�R1&N�� . 6%+!�`2�=z�#fC�A e�oEQ*� s. B�Y semi��MI&;}>�-d&�$N(v)$�Id�N$v��V*�% $N(0�0R1DN(�S!�v'&�S, aSuu}"�=Z�$UE8�qropriaw�!dEjv�pV#ndJ�N(v +|� + N(wb�$vVA�� 6�&�e9���i��&�,N� =�-��,uw!�2� %�5�!�P!��6���X C��sFpb=I� Ei^q`�d*i�R�fQ |�f, C�3P ��xfC"{v)"�@��/�3or  O!�$1 !�p(Tk$,ZR\|v\|_p��*�V�|v_j|^p�V^{1/pFO_p�*F orn $smax \{g : 2VY\F6I�(�(p�� �)2EEL��){5_!;��R �� W+1 <6Be*��:�X� &�E�Űs!�"���s�S�I[ A�%xit�^"H5 $t^p=n��+ p�t%�>;� to)< �d�,��s Ari�-O�� �I�t a|WT N� G$}.a9.B��o� h�J� �)�� p^+�"�%�N(�pa�I|p <�(B% . U�(� 1EIu!Gb�qn�Iqma� /U|.)2��+by)�ni��\)# [>(6�<�� �In fa��n�f�R: ]t (1/p�f(1/q)~qvy).R�Mwy"?narqB�i�*)/r�(NbL۞Bbi�FM���_I�A/*� $\{vJ�of Q uB�$;"T��F6���).\|v - �|!u=>�a�e�(+.%��i&kj&d'0}Ar` 0"�2��&�8R,�[{wJD���ce!G� O ��rg�a��.�� Aߡ�y�-�2 Jx]�$- !��-\{� J6��A%F� 6�e��V/2�  ap:� i�BNB�I�!HE�J�U�-8�e AL}b������_��v �]�Jia>�2F�N�����|w\2�I�w\R�E�:� :��6R�%H .�9HJ�%�a $>Q�\ \~��!KFS"�.3��*�At & ��!f�. $\|�& \|_2���IQq�s5�6&�!�KA�s�; Eucl;�n)ti) 2=&, V]s)Pn�7 y!�� .J$n$5�O.BL�n�6t.*2�� Actu�c�)��$!E:p 5x %x!�A��U!� �:1�A�"w�c�)�R��s{�d�!�/ natuJ�t��t�� �osm~a home"F<� D,&;(<5A�n�UI$ :u) uZZ2H�is�HkFf�G�5*�wax%v_l27*�6:1�* *ntЭ��:mQV$2�U�;Q��)1��a Ban�s�^!Q�e!|2�U�.!�> �}Z.���j��6J�5B� �i�s��>>�( :[95GDi��ld��X.2�:t �)R� Rax!5A�,!S"�jng>�s� �k�a�u!$ � o'��!˖rv6%ai*z2eA F(���&� ����L/�u9���u "!^R�-�c.'%� *7>�>� s>o06��* �^:b !ݕ�of� ial �v��A�t� M�2RC$�ifm4l�}��>m�E:�" .E&�A�S2 SV_1MV�.ds,�.q\�.p(,:}aOs�zQ| X*�2>�3�G�M�TY�a� �is�-�5q0!,.V $A*�$ $\|T(v)\|�le��,Ak\��vg < !�2J �$s*X��%g�R�mA��N�� �4�A�W-3��-i��rma��_*�CB ��V_2?�R�RA�146q'� 6n:�H6 E�.����"��:�b N�B�J6� M �!�/R�vA��611`�adY Q�aZ3O Ma�poi�r�%��E� &?F�7i�e���6qR isQ�.ms��=]4����B ,�>��"�k���!�*x��"� ��s-�s. �gwK�Qis 5 ��-�\A�e&�`1M�Xb~J���H"�[!`!�"k/0\|T\|_{op, 12nd HieA�z��&�Ci�|AF� :�e����9 qEqu8�(A�6�� T$6f���f��Kn��(io�H�MFdE�".Sp�B^U�Ui�aert /� *8F��p�#%u2 S�\ �\1�V_�:�3;/.%� ll�@D�c��?!��_ \|_3RS3KT �T!�|m�q 1�s�}�ai�jARQ�2Fle�!��5!2�Yܦ�A�B~e�䡂3�y+0#)�f JXR�0#!��LB�� % �X%���E��-��Tmn>n � �v� ��� �&.a�:�ncaf!�GiJ*3 BL� f $W-�� *u��rvlP3�Er-MU� ��\"vW�*�bF>�&�'*� of�q$ Wጡ$AE2�1 M�WQ�2�Fz[1<�V: �ri����I���'^q*��7extenR@? $�r-N-� � W!�a(x`a65e oriB"l P��FL!.Ix?'�� 2NZjS�t�H `I�:�r�� \� � �.i��2�� C. FY&\|�b�le C  a) bj�ѭ8 2� +O� ��P$\{J��{bJ���� A�*� u�6AMV�f!(&�� Kd� ��N�&�Ed 8�����7 "|��&�minuity6AM�,0�:�:^9���9�@Wcq of biiNit�/��.��� 2P= .Mv��:�v5[iu, �� Q��A�� �a.��&>].�% ��5rmi>�C���#zN�u�f�e��:z"p#j a���aBV�A�*�*:�U$"�!_!5�3� \JY� ��AG�o� F"8$��nr��fA�I�6�"�R"6X$e� �fh9�*'%Ur�:���AR�e\ (�@,\�(��le \|x ��yj�"JNuk���~7*(��. !�a !� ��I� start=Mrm)�a5� �F��a� 1�und",I�E s"V�oxed9��W�"J replg!b7 ��%" ���-���6��!�ing�6���:���.t \�>� �6� "h7!bB2f���sk�a�6�b�B������j�!r�a-�2JD "�1�*{� |�T2Dx I�<� I�>"� A63"�30}�3x^j2-"$32b2�� h ���!�ua�mbF{�s�} (e�.N�6w'0�nx^j ��= I~j:"r) L 8�W^{n+1V��t,n!�I:�$:e]*JZ�.�,�+"s�A��Z?;v&�X��aDAe�1M-�.r%\�%�.�oM�-�nw�N�- �$�&�Ew!s�6G[>{Ai2�M1% F�ɣ.�E�na�n�he'2#��a�%i%"� FcB�� hb!�ar��e�0� 6�V�y�T ained�^i-�F�F�*>'�=g_/a� �$M�%��%C�:W� $wa��� )�2��4 ���AQ�a��<��I!;�B�� 2*|&>�n�NeP4 J!B�./&/I�u�v � .f� ftť��. nvo jB���&gaq�A�2��"� 6�v�"2b ��1%c @�4ieN��(\1^�3b�&�A 6�� � Jc1 BO3fY�E2\�4O&js)%2p6�i-piu �� �#.�E>�� e%) �x�oE�6Y>�C%� �;v{d�2>6 tooKx$)��T C4)^*)0:g a��I�M^  ppe:� k +&�" ��� �Q�A%I� �:� :c ^ . Fr#@:6fB�ac$d�ometrbc�8 �=��3a!wVJ���>f�2� am`Leh�B)UR ,T(lE� x��ju#�oýl�Kc ]vo�^ c = T�A�w :� $uI^w �)�.Pt$Br*�5 n6_U; nnN2�SB�f�:}� ��:>d�s� c2�C5�&+m +b�*ET&�a6�Z&��E�i,62�&:3.�Ar6�J�yE%��� b\AFl � ��vakA'&e@QU �xp�IVchang 1�h-�wce3��F�bB.�)`� q.:PmdA41�.n�� j=!��"�}t@��"�fsu�22Ѣ$t_n$ inherra��9�,$a�1�>hl%�t.�O�W!Q�:�:n Z0�Tnf�1�S��1l.�:l.W"�:� *� f�Nx - (a� �8-�^*F��*�kRN 2�! anti"{��w�U - �->6#+ sA&.I%}m-`n6�.�q:��l*��!����!Z2�Ox!\C�'��>����* ё*�a�x2UuZ@�.� "�9Expk���onz�9!] classicalFA ;�{ppA�ɂ�.�9%" �7�e*�e�Je\exp Q\�%nP�,Q�z^n}{n!F�6 $n! 8f�Aial�h>*�&Z�" 4u�"�+ ~=tv0�.!CV1. W&/�$z�6�Gz *9�F�H.Y�-�j�!c analy��6��io �e ���)�um&.'�>� $zA���L�% ��%dn��3 S2 !\Ts!���$)�%�2@�7�so�6Z=�N�x�Dz f-;c:F �O!s&�: �9< !�Wb�A|-zH<1BAS2�-8�;17N��!�3.����g�`1�[�>�EV|i"�7&�l.20 �bx6lȑ��) .W 1/W(-x���P�5&h[�n2�t�Y"J9�o.*&�`�qEt��1Q06����F"�K!aly^" ���Y�/��e�!&�F N�<�{�z)j  z}F!���*�U� "�;-�J}|i z)|^KD  (2A�xFqBsJ8�2��ex.!&R"G�'G@�n"� !e�� R&=Fe;dvR�ous.f("� *���ykB�F� CB�ѥ*��[&er�-�! �[�dY>yc��dl;>|!XN?xl�]&Bw���fy  e*B.�|*n��*� e��2* a� �Hrm 2��Ama��6?B7 ?�F��,!Ka�6� >�2(5Sxp F�#�H�"��;"&MZb�~,��!.na^n / n!! .�:���� $a��as >��e��J�&yAL� &��U$\|���a\|�*+in �M�1�|� �!>!"\Cb�"y��r�.�.2 �l9��UN.�%j'2>�py�RX"��mu[/IS�&��" ��b�jCt� �(6�b3suya�K!AJ*aB� b$,�+a�2e_AZc6/�>we�] �- �>3ZxY x(-a�� �%$Gc #I�_� �*e&/b.?����6 �:WP*�zU%.���,�E^�F& wy�.g[I2Д��.�0�oǞ .�M% �`)�2>�n0p&�D�lX�F� *��cZ~2+a( ml�ub.�@ 6�� B PJ!�2skP e�-#9?$, �$b�Z���smY�Q� og discuP�?0� or*�Rs��0A�nk!\Swer !�n�*]w8.*�ie�r��% d�a&� ��6:eW.� �Cgi��r 2t9\@ B�Z MQ1�%a�?1M�-�<'A� pend[.f)��>ydHߡ.K��1�Jdas>:�c�1'&��!��*͖��*�� *v.�"A-� Fx�)A�3�at most�)c�ny� �;lÉ%ZuN���clu�-R�&p�L!eq.���2�I�\V :+F,B=�%���� U���2����[E���Rߧ%1b�%� 26N�$&ZB�7�U,Q M62��per��2�qn�s suitab�4��.#ALsG@Q^~G��a��,(ae�Ao�6e�Ad2Li�-+i�oK�  E�Q:jpaip+f 8�:�{�c�%Rw*�DI�u�.'ZfjH$��52e�!P ��*,g"n ��'������.��,6.[�A!��= k�doEb� al /" � t8>M'���2�\6� p�a� �>,EWh˦Ҳ��Ӳ� �l����adj�we�X 6ܧBYzZDR�2X�.T *�u><�*,3$\{p_FrG� �-1bi�:&'�)2�$Of��}eSa.ͯiV� >� $L�*�11.�j!iZ���e��6�u! .�n�: $~J�%��1Jg�{qJA]H�%%5�1G � #�Nq� �V�u��� + q}�}:I�UI \,V#of�?+�;�%9'�$qV�d< $p}�` @o:tx�m�5c����!Zc:J_5#zG9, p!�*�!k de�6A^~�B,�e�L2���:� V�6.}��&�25��j*0rr��q� (X-!$�c2�!QM8.�p.`n [QY�@Mr�`IUX��Q� $\{rJ�\A�� I�6�� �� �"9 |:��2P�r suff/�ly lavM$j���$�Z*1���82�7= v)� �:��R�/YE�n'A�{ �x*��!6h+��M�^��.��2�� !(��:&I�M�@6��* ?���%��nŵgp�.��.�V $p^j��"�5$p�piɿti�f!��'��E� ��j �� a�*�l$� !e�.H $��F� afa^.a� �lde��E�"� ��l:A���t �A���l 2��* dysA[�D���/S �u�ڧ��Xco"#�N5�!u�/1��\0U܍i|Y%� *;<0>& #�ob !>� as:�:pd6� ��A�,d.����A��BU%�eU&I� 2li�"yA�6"Y.0. >Gms�fa�vs�*]+��r �i�/%�2�-72�-�fi%"�� a^*i�5&1/� A�O�m�a�g .|&�2'9*2A��ŵ a��8oK3*bf power �mseries with coefficients in $\mathcal{A}$. \section{Exponentiation, 2} \setcounter{equation}{0} Let $.Q, be an assocElve algebra over a field $k$ ��haracteristic $0$, and suppose that6�d has a nonzero multiplicatn�identity element $e$. Fix a posi & nteger $n o l�p � power �E!V8the indetermina!lD$t_1, \ldots, t_n$� �onstant 0 equal to�. Defin� e ex1� l of $p$ �2�$by \begin{H%�� \exp p = \sum_{n=0}^\infty \frac{1}{n!} \, p^n. \end{@Her �rQlal numbers $1/n!$ make sense�-ls�k-S hencF6- y taking -�e CDe$, because $k$ isAR umed!&have F8. As us!Lwe !� rpret $p^!| s bek8$e$ when $n = 08Si� the 6�%t=is !1�,, sequ�''s@verges�$0-�* of2�$. Therefo-osumAN$)�$6OM� �� . Notic!�at�6��E+%e�e$AX-ru� . IE�, $q$ a�wo2�Q�2q 6�wha�YqsM|!6nd whic��mmute�-4each other, $pA�= qp)�n^ ((p + q) = ( �) q)>�A�he a�(dard compute!�0In particular-� (-p)%@�Mʕ�nverseE$ {�0�6%F ~� !�2Mis!DippedC��involu�@ $a \mapsto a^*$,-`induces:-on�b�by actaM ).���iE,�M�:P� Be[n $p^*�>�>2� too�^ p^*]^*.>�!W!�!(tisymmetrica*E��ɕ L-Q| $h�pexp pɥ1property 4h�h^{-1}b m�. �\�$p$-Adic������ rime 9m�x-`:�)� �qaqabsAGe valuI� >0denoted $|x|_! a�d���� be��ox�o#y�p^{-l}$#p^la� a / b$, w�! $a, b, l�y��gers,A�, b \ne :$a��b * not .:dp�ItA� easy��se�*F>0\label{|x y|_�X� |} |x�  = \, >a`for all $x, y \in {\bf Q}��DOne can also checkE8n�+ wle max(� z) � !\le�:#�� TheY� dQ �_�nd�comple��of>v�� respect!�A�di��ce funŅAi -�!/M�8(precisely, .a�m �J�� tain< copy�0�ub� ��Q� I�.�A�kQ�9�.�e� i)i ife only m ��- (\ref>t It),-�R)a�id� , y ]w_i A"�4 $\{x_j\}_{j=17 $!02� 9�![*�>��!�4$\epsilon > 0$!�re!A@an $L \ge 1$ suchE�-�x_jav< =$QeGj5L�� isU sam} ,$\lim_{j \to!�fty} |AE U � a limit�a � re&� M:3sE�d�R ! Q!ZA��79 B(�) 5� f�B�E�[ .�� � �adž�� 4%� Cauchy9if�1�B� J�a_j - x_lf�, l-�. Co �nt5s �z0automatically �#iM��c��# !s =� everBF>c �s!L0>��C ei!�q� orAΑ1an՘� E a�s o�show ush AEAa�*Ac�4 6���R�,a�yJ�ar!� # ^��6U��B���the� �:��Ngnd�!�\, J"�G fG��[$,�ively�^��.�,F�m�6�� F�h�� B-U$ �%e|B�!�!�ultrac ) iontrianglA/ ity �r�, �A68)3i�9:� �? .?!�a�{j+1}�A6O . Of cou� �)se hold[ d works�B�aorm�x"Ytooab$An infinitr�$�ݟ a_j$�6S Y�-� ��i�.� al~s2\nWU�V��$is happens[A���-<�{�r�{a_jZ2For^ ��of%�% impl�� !i ��E} � se does %�!�general!q�.��0!�ly need�parateKI� - lg�� or i� ce,)*>� ^� �%�n.��h��ZD�rbU" $b_j z ��$|bf$$ bounded,� ��!&=, s6.�U1� Y2�^+ �I|r!�se!�di!Yy�jZ���BOA)!� J[*a RS �*�"� -uAa2{bJ�of}� 3 ,p priate-Ȣ�QclyA�!��Z}Ql � 1a�] &X if .<Q ��G : ���:�  of��sVD~ .5�Lk�bZAz��otx��� 6��5� 2���:� � s^K for ��V�"]qwing�HͩU��.���.�A���ac� taB � nse /q�~A4poi>u�)%�sub���a"� �&+%`� , Vector spac�d��AV 3V$� ve �2t  s minorm37%&K N(v)A �� $v�5 V��|��!Cnonneg�a��5Y*FN(\alphaa�v | � \, �b *��6��$vVRvv + w)eOd + N(wfk v, w S� N�T\�Y�w)�Ym�w)�N n2� s-� on $V�=�3 )�%�6 ���exactly�v�I@:i < R�I�g +�JS2$ � I �Myi]. vV�I�E]A���to U�)� V��N� ! - v_j)v�0. Equivalent�NN vN v�g ���N� AR�N(v -:)%�Ō�΁�.PE�� J:,!RwJR����:`��5f �]�M�$\ta:Jb2�$v + w!2� \{i�J6A^��b�'��P!�n��\>$b*"e3 ZB��V�� \,AB[6� .��5�af gV��:�ͧ��(of $n$-tupl��(x_*� x_n)��$� ��c�$1 jj��n�d$-dimen� alM ��(�� ith *,coordinatewikd E�sca�.po�!$x�<� ^n$,JG\|x\|�,max (|x_1|_p&�|x_n|_pBQ�B����y.w2�UtA!z2��kA9.E� 9, $\|\cdot \|��.�!�98e�}�th&��A�(J;pro�` %��Ez��now ��6�1$�E� ��>6:^qicis sais�J�A�er� F�N(�f�2l^�*� ����is �Qa����:� V$. " f Ql*D��>. . W&%�i �e�� PBe)�g� �V2xfE��U��b��!�� �1 h BH��>� >���5����:�Z�m�� �9@��a,=���� �E2;N�2P�a�e�m>$0oned previous�.aitA��� :  ��� q �!RA6�6#!��cM�nes��k!NownA%!nR#R�%.� ))T m%2mveRm%%+� �"�  $N(e 1 $$N(��b a)�� N(b)"� �Af� &�& :�!t \{J�� N�6� A62M! U�A#V���� a\,d��Sw!, b� 6 #!��5�6�.�#� 2�A� $N(x��1�i�n 2�^�$ i>� H�&�&/&x^.N;produc�A��$� $e*rorder 2Q%�%)q�o s"� >xvertibl`($d $(e - x)Y8$%r�6�. /�S A6x, �.T , $yU�# v>#� )y\, N(y�6�y �2�>JA A�basic2�j,AHsi!-!R"F)@f linear transfor�on6�^n�T�P bq�fi$ the Umatri!$M_n(��� entq.e!�Wu'a��usf�Y� � 6� o.���t��maximum>$|a_{j}C , $1j  � ,"(*"�% cor? onding �xI�>�� :/ dire�e�t!Y�1���A�,es described!� �K�agraphX%�D�%^(!�2$a�1!V<ee�*6!6" �� $F� 6(w �'E�]G 7)% 2� �si� assign��^I !.�,p^{-(j-1)/n}aM|�$ -�-�. Ed$T$A�K- mapp!� from��MRitselfM�0d by $y = T(xQ�$y_1 = X(x_n$ �Zyc x_{j�%Yx �-ZBy%.+), $T^n��= p \, x��B�q�e B��!�.�!� just*��u��]T+{-1/n}�k.�-3$ 6�-z\&O-*U&.#�f n*��%$n-,we would liku estimD $|n!a�a|">$n! =3D&��,��%�d, 9 (6 B�K we Zpak�adfactorN ��{!�nM�< 2 �s Aq $1$��$n�bdivisŵApW�)i�$n / �$ For %6F�j��JwE�w�Jw��.yAE ����� * � totaVfBWsum�, thes���26+, iv's�rl� tha�0�. j = "z$ %'^j �u�#�� $NfR (p-1a�� )�e̥�.� $|�.%< p^{n/;"�(< � �%B� �u ~u n .O �'^� ,�J 2 b� �.2 A c� �-ݕ$N!��A29KN� < p��-_[ N(a^!�n!) 5��a)��E� .� ;��.}��xp �6a &�� ��u7 f1r�ln�!1y�$N �"�J�� %�c 2*%}losed>(5 ZD G1��%G?+cz/B� 1��, (a + � >`* *a�P7b!{By){��$!� 0 = �3V/��AB2�a%"7 �(�.,)Z� se.H � (-a)�T�� rema�"apply in�? 0�X =&H- !,A "�Tra� !�.I4z� �oZ�4�� ��� "�  C' T&-im"�3��es)ce�x, �#� � RHo:�6 O"P .�JP, given�=�"�5� xi�cJ'd�f"�5��"� �e?* 6� ; 0 C}� !�if; pick��d &�aŐ �,/2 Euclidean��M�ef lead an>� n �B� m5s9� �in�Banach1���a9AqF�� 1�� � >p6 G&��* -(A well-knowE) orem43tes�!�]�EaeQ T"�(:wthe! c�$Aa) �s'v�%� La diago_USimilar�t��/"A�E;ty6Rn upper-�'�3 [� derA��g=% case� %�&�),Jordan canon�*����n�4 typ�a#a�4]!n�5 firs�5�5 �S'.1izabl��t�argue� �a� suff%:ly larg3llev/of)Z���� sh� ��bg) A��a! r 0gu^*�I(t��A)�-h-� d&!!i4�a�"�4s & 8z� AA��"'s 2w� �x i:t)$and satisf Ae differ�galG�%) E �!� A��T2� !ER#=nd 9&tr)'r.�Nt ��Q9@,!��y both �� �mZ���*`(EA�u�1�% l1�whole.��H�1.p"<7A ¨��&�Swe get a�6:�����&&�of2U!���By�9lya2� �� "5T'3 R!M"��'E ��I96�A� EachJ �o^ c"�B�6hAF0a natural waye�p a suit��^�9��:pn 1 q� U0� YF'�o9 a i�q/��{t a�6v � alU�i�.Ɵ/t any3�J7u�*eaMJ�Yus �j�@�t ��rT� .��t� a~? 4 �F!�� 2y)��a�6�-;their���A���p@?aqo�x�ref��uae.�i12 �F�@��a��}��ceT �"re�"��analy�A9���� ress��3j\i��6� !D� R� rI� ��Ͱ� �2��is&� H212�< E:].� vvE� bCe�famil�8�ticѩi!T(�=v)lyVC 1g �ermo )62T> � '7 ���e ~!)2�A}d�heI)� 2U$i�1,mq?ve 6OQ�BhD�9,�1.*��f a&�D63$k* �+l��n5>Es. :AA.��e�(ceJa%A�}�[t_*U&8t_l]) \cong :,)F-F�>nA wordW/ � BV$polynomial-r.�? >!��A!�E'{DJe2T��.M�A�� &� �FF])fGJ.,>�,�~`*~b�.�V6��VP.J��.��?b�2ja!FT k�.' jG. �� �2Q�����!�?�C�I�Q JlrY��"�6% :������D, ��o�@offA�A�� W��&t>i��/.�%����B�0$,73N22$E:uѽ�:)�� A�resulDa:]2^E^CA�he mutlj(I? ssum�T!�6�"E*�,K �again "�!h6T5.V!}�����A�B*B`6��� tLF2~�E�#�=��� ��I_/"pre^@. statYJfollow�K>J�.` as b&a�� $Z�CUn�!"� c� ss-{�+�����QD4!,.� 1}i� =��cG} reXz"1!domAZ �l^p&� :m�\%��:betwee� 6F_:�UF�� x2-K�2�)�F�u2J)��;i.� �T,extra ingredUM&�+�relevA�qua�L�}# ���6 reg!= X��{� 3 thebiblioF"y}{41}!Dibitem {Baker} A.~ , {\it M��8h} C.~Chevalley-�uFs}, Pr#<ton[Q� 19996�$} M.~Curti�2�J� 19861D%#(Dieudonn\'e � Spec�9��7iK Represen�J(f2� z@ 19802�D-K �uis�aa~J.~Kolk �2*Nj6U4E} D.~Eisenbud DC*�A���$a View Tow�M �-eooAR�B�E-H2v%5J.~Harr5��*V]SchemEɆ�FaW.~FulA&!�>_6� Ij: A FCeAJ�6� ' 1300VO:�Sr1�@-P!�rr��:� N6�Sr2NH. *� .�Z�: r3N[.H!&�G>0�05!0B� 199:\,t-We} E.~Ste�ndA� WeisZ{ Fourieru[�&u$"� e�V{ 1976KT�:Ta�,��Nj6�z� 76>aweil}�Wei� B��{f7!:6Mhweyl� WeyM� Cl�0�})�:ir Invd \D!f6�!�j2L AF 8>� doc�"�a�\c�,[12pt]{amsar*(\usepackagesymb} 2enumera�amsfonP\(latexsym} %B [pdftex]{ icx�4input xy \xyop�{all} 6:�9 \au[Daniel��ves]{2} \add�6P\\ MSCS UIC 322 SEO, % Lsc{M/C} 249\\ 851 S.�:�gan St.\\ Chicago, IL 60607-7045, USA} \email{groves@d.uic.edu%[8 \date{March 20 8\subjɾ(2000]{20F65 F67$E08, 57M07!�b�b abst�c} We �g/ stig| 0 $\Gamma$-'t5���a torGE-free )"�Q9�1��O .�*;�[ianOLI0. �$�r]� \� {DS}� adap�+��� %CWIF}Qif�|,�.� �!ly+3]z $G� a:�Air�E non-�ug&(homomorphis�& { h_n : G�=%I \Ow�%� !$\R$-t!6��trJ-is|eG$-�_ on. !�.,providO! nalo<, of Sela'sb*rtening W,��� 9��� makee� In hisJ1��#aapdd)Rc1,j2-6}, Z. ;E��<tF!TFb�!�� {\em#�>y}� $E )��P ank $2$ (^$� ICM}�ia4mary)K&� includes�$nonQwd4s, most surfacM�] cer�\�!]��A�:U7!0 answ!Cq�ve !� long-�=E�DTarski (Kharlampov�) Miasnikov14�.��(to!9seA*�s;G_)�KM}).%� �1�ela�-�a study!u%�. eWIp&v *a.'�geM�,Augh|(tur�ua��)A/:@6�]1.R�,fully-residu�9�JA!n![c�.on%<lso�nAl)� KM2}aO4aNXofe� six i�, two%m5�PI�usa3r%F!o��������O%nshB�AF MH work�%l2*iu?q�)�o3�qNJi�!ber7stood"-�'�1G �*�3mm (anda�)triking�2e�Cm�)�X2U� ��orwA*1en looN����2�#.�6;se�to,A�seems1,^!i� �of ;<res�Sb�InM!rHypq�P!�]�2�>�"w*�1ک� ���!ǥ� !a���S�1p"� �A�!� # !�`M�Afd:�B��/t�@z*�Q � exh�,D deep!Mn� .=!logic!��!jd��Alibeg�� 2}, \'ch�@sf�Eo.�}:Q !�. be� �4���L��2 CAT$(0)$ �. 6p.>ves�Qpur4n$, g�4?OA)J�� ����k!<2�-I���=�no ��suj \foot�{See S-��cRela( below%a.��discus �yN� .��WeL)��b� )<�� �g%Cayler g�D�2�"VXzd�u�o& ,of Dru\c{t}u!Sapir�1)jDS}�RG y.n asympt�6!z�%is�2�9� k% G5�eN� �AEX:].9{'�:A$���a�"�5��e8DJ��DSi �e C)�WhyA�PA�?:�2�I��s� feel�� ism!3till a��thwhilE� ��d:ghI��5e�Vgly m��m&� 41��} Ar�o�jiW3] eo%�develok%�5 �coe�.6 !�)�` i��, ra�for���A��FJ�S &M�� 6f $~ Mod}(c )$� ��Z em} #j(ModinAut} S2�W ;o F]�\���%�0�L {\rm��ŷ �rx!t (��� ץm�/uEQ�!����=��in ����1 �2�J�2�fZhq abeB�I�(ntinu@ �I�MR-RH}aSJ��zof 5��� g f� ��> �=.xIE�our hop� at much,� /Fy3,�}'sL - t c�"ed � �9oEhs.�e';D�)�iUs:!.M��� %'re0`�cep�:d .�}%3R���In6m��w�Dg6|ť�e.  � a�\/�!Zquire�-�� � �DSR�Z�!=:FM � ��JNʼnIwDSNC#X��$X$, n�y��mkj*5��.a!+*1r"� 5�l ,  E�� �* ��! tom�G.,J�A}�OC:y $X_\omeg�C��!�rom�To':�5a/�MA����)1�H�72��iBAB TreeE �%hA Na,0�p)s0no global fix�Toin�/>`>��^�. �XXg�pN>s�F.BoA� sonRx2be>M��g�i�%@ng&�`!G�s.Cm�si�IET}--F Discret)J�(f�CofwX :- ingA�@} (y ��,��6� 2� ub�x� �2i&wL6�A-o%�����oin �Q 2�T�ex��8� \ opr�� A�-aun���ide8�  Hopfia"�? ��+ immed�ely��[1L 5.2]�^�q�n"r*phdepend!�anyth!� left��!��RY&�y\n)���Qy�� techhC)=no� enl6 �t�<]%\N�� cgto�Ev�i�k2�oJ<a�9� �ut madeh?8!�akO�Ns�0�-� ��j%$m�&*DzY��=le � SBe� iC �jar!�>5 arxivH = �"� !�J� I���E�{�m� F��0��ng��e"��C-,'ed�ric�v!p�0�>$���.9DIaz�%�r�x�:bwpie�8sto "�# sl"� Psta�>z��7 Hact�H�U�on�)*v�&�!�e nefits�1Aa����O� H/A�eZIS5�. Nam6uae�6?!]i�; ]-� !�E�to!�eeAOr!���u���un.�s �importa��� j !� been� d>��-ahmani-G! It wTls�xcruC/in fu1'F)��m=FzNrZ� v �X �>AcaI ledg`1 s.} d ���i ��} w!�ritteh\ �S}!�eai�Altho I haiready  cursrglamnatD , I 6KS�DkXFMark �%PJQ2cCamm�+� sugg�Nj!�A��e*f may� Ha��u �� �iseWAthe�va'���),x �!�"�T �Jas�a�A���iCQ�X}� n�.��s�U �Xi�(6�2�-�e��$ le kernel�eT\�di{\SK(h�f,����C� s $g�F G$ s��I �)8 FE�;but�m�$n$M�"d �~�} xL l�  w(i)�;6(i  not\�ud �� �)=�&+$Tm��� DefAlgE�} %em E.�}�Li3!Dm $G/���9Y��a�� m#:�!M<�Q5�So* "�@�5�TIf9,Y�2�E�%�ame= [�, 1.3]%+1%)� :�B%�G�Qŗ�26b�j~1�W<ZY� 1e^�iso�.d flat�އ �i� �� )o�zf�Xi2?E�#naEY.�3.21] !�it1�&ed /&�+ �6U%l1g.2��zv�m�f&� ��m'*bf0 �.r,!*r EM�Y�FI �&* GefGeo��e���G 1]3(TwoDefsSame��;E�A�cva�qa�Jv�z�D́J'�EH�y1IE��R �N faith� \]a (s#ct)R� �h"r�uti�B��u�n��Epit�R@ic�2!K"�!��Q�N� "p)ݹW.�%.E�|t##�h�Ut��unil�K1 #a.S�)�T ��l�{,$T_\forall(H�v� z >]� 2 $H��nB�&� E�e�{CGM !tai./&| )�� sue)"�2� �U� ��ed ܅=� �A�$L�]>.`��b� \Xi)h�bseteq L)N ��]IM�R�N�it jF!�J�(Rips)��%s)M��U�� {!�ko��y_$�E�2Z�ofU�.���'EZ�Y:�)��&k2�� xa9b2%�)SF�)�" wid��Ic � st. �&�]Rj�"3 ��e�v�repaUYamoun� .F'rjd. n�Gori�5l!�Czbyv0mov�!��xal m]Gr"}'sltern71.4� �by Farb ? ��Bowditch }� :e,: �'ZR's,!��h.���Yf!oWc�.�sAgJ� �DS �a._(��A�n�!`� �ir>�!���(i�\y h/�Q &�"� C �6ez�c{.: q�^L� Klei�Fi�s (�� }�e�pT cusp&� );�funda�/alQ�&�1Wf��of� volu '�pi).��Es (:< t�0 ,e� c22quasi1vex:�v)�dtJff7h);�E(v)6�>�ir �j\goncyc�4 |� eM�a,ud, m2, Szi d�s��For fur0�!en�on5]Ao9�%s� pAli * , Ya�?$DS, DS--RD�s�3, G-:8, Osin, CR} (am� @-s=a*� bI�zY�0� hy5J3!2 %yE�� ��X@�4y}[C�s- PC�(K!]n�%]!; "< ��Z$\AS |\{ H_"T , H_m� �6� R2(:�� lt0"�the2�!2V 1 .�g\A?W�<� c=ly1}, 'ilde{X�by �Y�oI $tex $c_{\g�5,H_i}]eaΕ) H_iW�a�a�7�ɓpZ9! � Bt� h'� �j@]9 W2W��%�)�!�%7}U.�b�,�"�=} \�M!�.�yl1�.�}N�!9 �� [%V%?$e) =�A�!�^���re^U�$ loopŖlength7�4WWi��)�1c_�.�end2hLi��Z�s}*u,A*[ �%��'aixC em periph��}�� �g �+!8%���: �J�.:nd6g6���onc���2uQ�N[��`%��J�hta.R� A5  $K%�"Wje�mal�_alehA�z� \s�R$setminus K_� $gKg�l% ap K { 1��.CIk.kCSAe/�� ��3 ��m .b�2 n�2� �imf�;T���CSA � ��� kAń�Sxi�R T_OY��&-A�s B�� C�:Penet�$a Z�T��7ny�li!tN]k5�*_ [a $ 1, p.819]} ��/6kif $M��!V~s�T!!� (�i$mt� x]ZA = MiU�is�!42�iru-q�RmA>U� Djg�not!P�����t�ak�X�Qsin.h9 1.14!k 10]{$�!�tA� � eafter)6~%�Vaef $\la2� g \r � virt�9p �A�z�;^� ��l�5!��h��{�ho wB-�)�1� aO1��-��b)��&&�l.2!h^k���= h t�k,j FZJ 0���P[Co!E 4.2i"31�2� $|k|�nj|��8 �^2�mmukJ�$�.J_2 �-�9X��urn:�.&J;soi�2]���*J6'�'&&M.�@�;@J@? daK&���l*lp�fi�PwRe6�oa5:h-�e�brief�u�>A7"V�59 n'sw9Ame!p�4.%V(,{�-t"�5 s} >�in�X�van! D�|�XWilki�2-wVW}Ak~to asQ-d �Wif 's P&�`Growth���n[.)��+��7 8�a:��� s ab�)>j�61f*k1v�%F ) �1B�YcipalJ�fi{ � A/3"a� 0,��e"� � ~ measN�-3D bb N&���l:�� "[>N&u"� [�X$0N| *ex>V�b�s��guarant��$by Zorn's b)d fix � E-%�,7bU $-*.� *8 choieqw)a�3chang��ar�� :�A�'wahSy#�mi�4we affex )?��u�*un*� �.���a�n�7GiNs!�bW 2 a_n \}� \R��duniqu�y؂�#R9�1Y:a�wv� E~(gj(mid |a-a_n|* ��)�{)��$ $a��5�-�wK}-� -q�5"3=�z�-; 5 u^ 3*oVW�B&(X,d)� ��+���{ \mu%L�6�%.i�gs�no9�aHa#�B#j{�~�!�� "�6Eoi�N�eX! � _n,d!&.� I)a��X #$\f#��}d_Xa��d>�� XN_�,!�Lġ�qb},-�d*�3�����)A��= �� �\�#4}$���)isma�Q��{ y!�A� in X�)(d_{X_n}(x_n��n)��>C.  Dps�[-5P �d}�#J�by \[ '(�):z�a\mbox{1�6�4J �E�>D$��:� 1� := �(} / \sim ,��" c�>/ $`, '^;c :`� sim ��6�E1wd}(x,y!N��Aֺ��1nscend�o1F�,dM� ��� \e� �5�0%}� VP !&�'e!�it2#1U ��4kGradedDe�Y��Q�Vt�odesic�s���*�MP:.��8��& Y$ ({ "'�0S.NAm 2i1. 2��~C�*�uv*6e�d sfied:�.�v$[$(T_1)$] �qpaiYd3inct"�1�^ �uat�\�gint*iN2Nv�[| =d^x le (v)!�I�po�.ŝ�Kg-�s)r�m��o2��3!`.� .��]1 I�#worth�K%7�q��AP{C�L� �ro�# !f1�a"&-�%�:&��]��5�� e�*�EB�YyNzni��.�e�&s (A,� )dB" spnti'2]) KLE�2�>is�-nspv<Zcurrent� �% C$HK}, Hrusk�.�er�93a��e��uct>^�:]� _$be . zER+�inaLul� ��-�hlloaH"�"$e�@A.�1]: A� 2����*,E1}�) 2F&$>@j�6�15�$B[D�(>n b ��*�of scala'\~4� �!5 base� �o[qF# $G$)%`rej�% $U#Q &�o�se ^2iI 1��On 1�� m�E A'5�#J_3.DS�(Y,�/�+�s�q2V�6DQZ Q_i � i�Ic @6�7 �$Y$iWV��0�&� =�� x[ ' qy!*R{��vQ����:� �0lim}^)�$ (Q_{i_n}) �(i_n)v I � 2�U� [%^� X }{d_!�r�:� is� }  " Fc�l��v��rQ�r~~��Q-MQ�]|Y�Qى���5�+U��~|R�BcL �fr�V : YmSY' A>"s'�M<Y��[A�n $bi �ɚ� �">p Q"�(1Au�:R4-R ; DShl% V���va-{��� 2��� Q$���o�2]��Zi� r� �r7 \aZ�< �#i $\xi��di�Q/�"I �;;�N_\xi(Q_Y*�E�.j/�r~PivXl�u��&�i�q j$;�[$�� .��Za��[0,�p 1}{2����s $M( ,)�F � �U $\q� $lb &$Qm�Q= $\q (0), l)6%N_�[a l}(Q)*�.[0,Nw>. M(Q)) \emptysetF3� =8e 2e�l��!� zeta� #nu�8 � $\ch)�� � k$-gP�}� �5+�!;1� s $(i, \nu, X)$-fat"� s $P�eq9FN_-%!�sBjZ � {!� ion)MmoXgl�.�:��ے�fi�;&�F*6�@eB�$7��.' J ��=ba**1 r�11~fanSY N�)�6�wt4Z!�lso& ?�9 �*0> �ep�� oW���>� -&� PP.QCho�aN&% ���vs �#��Uf iE�JSB#!jl", ��i�m$.�?��B��(cup_{i=1}^mY�Mt ����w!,C� , �. ɉd_{\A}�th�rd�~am"��O'gR��\A��/� d� `�fj $g/�� �Y4"1�.w(!��* �A���ach�-ACqi�^Sun�X�$val $[0,1]!T�3e<eaRn&�by�E6 �v��%A�tL3�5�s%� !dA�omFDr:�'���=x$�  *�T� yo�weM�F��Bow�T,  4.3��6�e���} "�  $K��06�?$S�ɬ&�(AJ�]OjoieH F��Y`�%>yysyir��he�$-n�>bourh^X�ae��(now builP�$Y^k$�F+ :�@tola0V}.� ��j�,sA@ttirbu�*,to David Eps�h� 6  F0n&)^�!#60CuspIsomEmbed�,F� . C� !wA;.��&O,�%2.LMeI���aph $Z(-\�*)�� .m2B�A��!�� A5ew�MWH_i)^����aQoAh&��:�, �II�v�x2�"� 4}� D�i��by���A�A�Xto:"�!Bc"��m�cesW���*&V4}!4Per%0?PQz�V�cBPN�%�`6B�"���W[t�Yng�$Y^ϙ�tGsſm:�EEnB�$2^{-2j}$ (�%��a���a��5�%X$)�d%9RW �R;q. ���*F*}� !ef�-� 6�zB�!�)�al*4a eI�l}! ��:[j$ Bhoriz�l}� 2����!�j6 eun�5� a�Bk)b9� � �>2IR��� ndowzj�Y�K path͎� > a�<X�C a��C�^E ��� �[|Ys:�, � <.>06k�9R,:��!� cessg1 ~�i�? c������5�{�g���&�$� s� / Y^s$,t4�.{$!�A� �As+1}$3�Jinher�a `;/-� ' $w"�0� �#�vu� ��! V$Y � �H>G߂at,I$\eta$_P��6�-* s��.e�s}!��A�� clea{G]="�SY9�!�2���A !F�2�Q*� �.P��\U��$*�Aik5;�'�$lo��gg /=EmC > 11 �å��:? �Y�N�.� �.e 6I J�C.)M�PQ E�or�ZE&by�/�@-JsխcU/A�l ~xN�.�S��*?N*� F�-6�-�qco�6>A� �; ��RS=!)S)�x,B� q4[x,y]� &� �`>� 5g%f_Q; h M"g���6�)5ava�ende�a��. Ge��2R 35 Y�r\ %2�ʹ)z1�A\R< hat{�&. imagf ��a}��$,�SA`9h�_2�� Uo��Kny $R��$RN9 6!�E��l9/&�� �$(R- ��)NW2en6�MH+R >DRn� }TA��2 ball�e� 2lo�KG�2��(�B�t etr$� &��H�8:�>�5 > /�$10UU FUjx��a%��Bt"] sA�le�*2p��:da�.&-%(-o. ,��"B$III.H.1.13�/ 40 MH},5�B�!� art>AU]�- F� �(��41H}{6 ,2 )$-���.S��2�-Eit � vels��.+r�%�F($2=�(sL0!"�j � dish)��&&:�N�A�z foHy`��J�:B6tr6�:J��,Y<���" \[ �-�7}{3}\f)� + 2�U < 55"s+1V�2e!�351�v�;�;*F abov44�!*���yS�&�2>p�,9U4Vd� �&��1��!e�)�Y�D�$K_7 (Yr��Ys*({�1��6,2��R�!�d_{.�'\leJ(��K_1F6]� �:l3"��.K �iM�.H+ea��i�meDSi"!ŁSi�Z*^������KH�� Y��thU�6�wi %�]�v� S$c_1, c_2, ""c_k� ,��O6.-4�-�2s((c_i,c_{i+1� le›(7 aaV en0d��� ��$c�Uei�">ɴY$�A� � ��',j� � Q.Y�Vb9"'U[��'�.�&� poic�B�� �*� $[!b_i]$|�%��- .��P _y\ = b_i b�SU\�_!sV$I� Also,�E�$[b_i,b)�]uK.�q�fst �.\AnJs $p_�2Q�q�MwA��H -^f>7�+\� �un�)Z [R�.=qAR" �=��#<'�* pI�&��  a� q_i'5K�ge X �(!R$$mCp��� roGY%�Q�^pla� kL-�) �t 6!����c0�p'�8' $(9S+1N )b!�B<2a�>E M�i��ide�(*�� IN�c�W�2siZ� ��:OZ@Y9 kU��rc k!y"� )6��.�A!ܥ!it УA�o a`WrVc}{1}��<��Z.f^{(k)&� spac *B%36 D�$s "�',H_j���E�b!�.�)2nA$xF����?��F�-v�0!Dso�.�&� :hR�J. )I j�1* }!( 6(6+ $[*�Ex� �:k� �EI&� Qae�^kQ ��MINTk�ER\log_2�8$a 2Pi�I#u,3�>�!ueJ2�u,v� t�$uͣv$�]W &�V B�5� Ba�j>�.� �canb�*c B;� 2)�y?0�I�:�b8��[u,x]խ>��y �V�.a>[�fA.2�sB6���8F?w�� uilt!@.�-D"� �&�%��is��t�"���s&�q6�^y t 2�aB��&��I�"J��@���`q'�� �y6�rtx_15�fa�I!p%�$d&�6G^ki��y2K5�KyeN2yBK�l"�9N�=�2k}d_{:Y�,1,y )� �D =>@. n �A�D�ځ��<8eqnarray*} D + �}�t & � &db� \\ & = &� -2k}.F�% M2�k}�� D��*�$D+.�? =� D&fm��inE[iI����k1-1j(!�r��� �&&�.$ �:s��K�i �  0� ix8�Qn�!ӫ 'E�:j_s��&�6^�� sAt��:�a2Pcy $f_1 : \NW-\*6>:"���&��6�aT}�$Nz= 5��� ��F W n $dj le f_1(N"R-R�BynVs !G&��7�#�{u��!�o f:.^ �a $[w,z]� J$w, z�$�"N_N|%6,nd6N:�>D2[���PM i.J� �5 Y^k}(w,z)f��'.�""� by $E�#w�z�݅��2& } �r�xsgZ$w-�zFF�Ad�8w_2,z_2��p� c2��m&LSs h�%a�6�T�l _k� ik�1i&l 5 �A��JJa�V "TY� ��E ��d_9���_1,z_1��2N �3N�-4 * �4�<�}(2aj7�;:��4nCa���E�bLA� + 2N23~�REn8 "i�նI9�*=2�)�n�}��+1 -1k�[�)�T E��+-�%%x)�}{F!5} � �` �caI��*�v� o&�Ke'��.� N.aEa�LZLP �c2_ a�*zM*w8"U���*�+Pk& (Yy��at�$o  ��&�+Pɫn� ��P?4�~8* �+BPq� ��.52�2e.ic`.�alZ>�+�h1"lF�/� not �.�: K5� (.�6iYh �[�A@� at non+>Y"e�;K(�jNM)�Q6!x�"V �#�Uh* A� �5��aN8 is (..�Iv � DQ3~�&@(�`�dard' B|*\Z^{n_�/�:edj )N A<��n�!Z $\phi_i :6�3L hook�a�� \Rf��rG�on �{i#se� �djaKMai�"; to (P;ed)6�-R�� � �i_kn)�[�Z��XX ��]ma�.�$, glu�C"��K)2o!s�d&p�F��zx $n��r�!H"�_�^ quip"���1�&'r, ($\ell_2$-)�M(��& > .�,��B0 ;E? y��6��. ?cop�6of ��!.�utQ0c�:�~!*�1*}�1����v%).N�kE��ns a-c�o ��%�toa�m�)R5�wpla�We rol�2 ©;y��I�a6+} � Ouv 5Kֹ&�A���� B��v'6j%5.9S44u4,!���J3l�9� Z a�9�AƉy);y@bi-Lipschitz home`��0!��3ou��FRCX$ (t��-Uh&bA����|f3ai�.gD�Vrɨ�jan"p�R"�=:��%&yI%fnR�LnpAG!�6=���$(\R^k, N9  V���dq�J��"��G>RU;)x�k2F6�`ofH,I�mF�mU5�m�!.�o[2.1.2]{ R})��D�^U [6f]� |�"}�!6MC���M�!a�*� R_+R_+.`=!zevZIB�I d$Q3Q_CVQ�?"T� M�?�K!h�$k:[əQ"�Q:��?2��phi(k0n�[ �}s =��Yof��Tj$�A.(�_1/([� �Pźf�.� Conv1�phJe1%�* 6��66�-L(k)�k{<d5_�gi�+e$pldecrea�J5��g���� �J ��"xF�r�F%�!�}gX$:'1 MQ!exg &�?.�N_1 ;N�AE�h$K�f $8�x_2�X&i$d_X( ��u^� $[M/2 r&-L�mn,R�(N_1(KR�-[��$ev�T�m)��Q8MG*Z>�/H1�$L �  $[y,�x_2] = ] �3 �-�$(1, �:�+ �A64 1.12�/!��b�"� tauIZ�](,: $\bullet$2�Tai* $E-tubub�B�-AO$M$-sa{�"] �2!T> �*p8.9 �E% �2a�6OAh.�up�at~ s-��MD!�0leaves the $\�tau$-neighbourhood of flats in the $M$-saturation�^$[y,x_2]$ are at bounded distance from $[a,x_1]$. By Lemma \ref{CosetsAttract}, and the fact t �^Lisometric to $\R^n$,� path �1 �lie�D_2J�� for \ con�t 3. A sym u(argument on<,�� N1]$ imp~ that )1Ln�%*�\end{proof} For our purposes, one of% mostz4ortant propert! !,space $X$ is�tained� followingM@orem, which shows �geodes!~riangl)aRsatisfy 0$ so @ADany $a,b,c \in X$,%�\D4()%TaF!0, either (i) J3 z$-t!%M`usual sense; or else (ii)!_re� uniquee�0 $E \subset X�ea!�idE"J|co:�Ba�unim�EI�o� two is.I�1�1�M�ChooseN'F�n!�4, with a choic�Q�s �Q$b]$, $[b,c�ndc]�dI[L�j 8.16]{DS}%�:7�J1_�@\alpha$ (independ�f� poinA@E$) suchI>q�,wo possibilii�ccurs:Q A!F-�S $xMq whos! �-6�Hintersects all thre%&!��*0 nontriviallyAn >j�Ec0in \mathcal QYhm1&:�of A.�E�-> ��.�. In caE�), le!_1$ bAB)&��aA��isE2A>-1l$xm� E2NEAB��bE�7Tn $d_X(x_1, x_2) \le 2 o2�i)r �!)f�cl��t�� a$ subjecbe����Rj�� similarly��$x�-+a��nm Corollarya"4e�Eŧſ]�yDұ)55(. We assum��D_1 \g2-��fore,�,!�q���)6s�1e-�e�x_2!Ă�$Denote by �B�!� sub-GA� af�a$%�A~Ra[�2]��[a�. 6�M�QConvex^n�ZR%�Q$J�-2�!v�1,versa. We u�zV��p��b��($c$ -- findA}y1�c,aj$y1~ce�z$z%b %z%��i�%� nA�. NowE A�3�0, we can take6 = z_1��!�= yA�|�2-� we're don���R�Swe E Q�E xa�z_15�eq!�b]$6� N_1(i�)$6�ABE$,Ad�~\� >�:�[x_2,yB{A�.$[z Yl�%U . 2N$t sufficesA�):�=��$x \{ D_2, � \}$���� \c� {Pro��i( o�s}��4this paragraph!]recordW resul��bou� >E�|� required��E� "� �qu��� ions&$ d"H }��*Z 4.9�� L�M�6XM�Au�X!LTh� alX p � x$ on� A$}�0�~ ofy*_A}��6,y)�1 A) +11r�%�*� )? $s immediat^ ���N�A7T9 I�$XAsymTree}96l# }I?�rsu " Ca_�Yif $Q�. h&�the/z?8Q$ has diameter>%orM� ��-A}- also �^o M����&A a fune!@ $N_3 : \N \to \NY!9�\��M O ^K\pic), 2)$e�BXsA|_MСQa� $Q$,!-pa�� %�E� Z1), 2)I� N_3(E�K))>�Again��s2q 9x)��x$e�� AgeZ A$�m*2 $nondecreas!�1F. Rec> 0��3akU�E�2�Bv \phi6�i�ew P�� IsolatedF�B1 [cf. /2.11,i�{CWIF}]Q8U� B>�B���K!�$��If0 %,not $\left( )) + \frac{�( 0)}{2} \right)pI ~K1i�r�AHa�v}��J�6����} Given-.�6]%�v� ��ofA��)�!])y ap� directly � �"N�W6�2Z�222>�B��x,��Qi�I�zm�. �| [x,z"�y be& � |  $uD.:v  @i both�A,a)$2)�N/ � � \[ a�u,v�.9 . \]�)56� )�-�s)�0CuspIsomEmbed)�%�V�)�!6!Ub�2��propose-��  2.22V���-�_%�som9� Ay]$ doese�"%)�4n�QH��) �%y)�z"I�$y:QsQ ZYI �E3 �) +? ph�h))Y0.s:66 ab��S $wE �!,�A$wM y),I� ����w_1,w_�.�!e By a� "�a"� �T��]��&���)E� re $u:�x� u.�x� lie outf!(r�E&t��u_1,u2�1� $. Now $[!!bN� .�NO[w� by.6� Igr���s!3��9�"u �2,u_3I�� ����)cje u_1< YA$Q+ZG )13 :1)�� >R y-R,�1�2�N8$,�6>�|u V haveqK(eqnarray*} �� �� y)) & = &i !!) \\ &� &e�? �F��), � �as"� :� \� {� ptotic� ese�,compactifica� "� .*m F!start� $\Gamma��i% gener�  groupmT actsa�pe,A"co ~ly!�oes@a I(X,d_X!�jj$G�qa s��\{ h_n� �) G{�J,homomorphism U 4\}$� � at(ticular asy.P $X_\omeg!"�^ pped)/an�c!�G$ 8no global fixed�. ��sr": $hyperbolic)l)�%3s��l$we describ�is5� is essent� du� Paul�8{ , 2TBestvina( {�8Bridson--Swarup$S��ough wa�cas��n terml :l!��CAT$(0)$�T��(erformedAfKapovjA� Leeb �KL�/M�l6:!)i�. SI�n| mo�etailsHu�>�s)JVW}l DS D���J�B� SG�joq�, a torsion-f�.�is ]H6� coll��;ianF!�h \A2�-I���$G$^X,7 E�9n�  a Cayley ��i��PS �� C<a�X}3{��0X$ correspond\ siWity.V. � h :�N�0� a2), =e� \| h \| :�in_{\g�{ A}\max_{g A}�$ x, ( *h(g�60^{-1}) . x) , !�� ,_h%5an elef9�trealis�AminimumA4 aSinology}��saHa��ir!2 $h, h'B[ |4non-conjugate}xiia� innjut�g $\tau6�)*$�� $h'��(\circ h�2� S2��vG�� W����:airwis��6�@ \2Q!�_n�#"U � a"�!"?ce&�& �A�:�Q_�4A��� !pDprincipal ultrafil�$�V�$of basepoi>x_n =3A]>) scalactor�mu0�9�5�����ism"�r $g .�y!2}!�{ M�{h_n}�y e  . 4t>K� NoFixedPt$r��nVa�!Ro���3�s�!��!C� U�՟��> 2�zV"� GA�&]��j ��seble!�-inva"tE�p�"\Cinf =�toQ�"� (i !"1 seg�} x�, !�]*���G$;Ep�� s $Q @eq YG��yUs�#�##_#b (g_1�K b, g_2 3.) �ee$="23�.k:�e6[is%=5�;)$G=�i)�vex+ 9�14(v) tree-gra�%�!pien5 �%(�%, \ell�,�t � n$ ()Qmay v�ac3a�toE�T)A mFb4(Y_n,\lambda_n�0_{n=1}^\infty� $(Y$� r�ir$isof2� � oge�= �b��lم text�m}� $ &V$* �(Hz ,[\S 3.4, p. �"BFSela}A�][,�i � )�U2�� �!�� qj$Gromov top�n��t only if: %�� �%ee�et $Ki�YV %\epsilon2%C:5P 5` i �ien] large $�'śa�K_n <Y _bi1o%} rho_!zK�� to K.!y#k9$s_n, t#in+Ig�a}PR W[ H| d_{Y}(-�a� y(sAd5�(g[.t_n)) -C�L(9�Is_n , 22a�)� | < 5gR To:� F �na�)lly�!oc*)ir $(X_hq_ha sA:� X_h =�endowedI�AV$^1}{�h}d_X� mG\iota 3 Ѣ$:" � }AX���L . .m fi�Re�P )$ d�!�i�a�%%��� �D� 3.15d��iQTop} I&%<�agV�mJ%CI�Ze)".  $�>>6� �((sf_i � � � $(X_{f_i}U�b%%U�-t!�s�ji��.Z�*!� rema['� �a� nextE�.M$wee� passe"F c\#rg ��c �is ve�M.$-$� $X_i��d��) Q�iAHQIɯA�te*�3.p(� QGs� UF-fa !��.�-+C+. �e'*(QhP��n("� � EA%8t X }$Y to E��z^-�) m`observ��J��ق+ 2V5�* 1l(DefGeoLimit>��"�$��ly;eC�mN6�el� m��� �a af�� e��WA .���a�:� ��,�z%hKQa� kernel5A J��:�<g } ( \ | \ \for�35� . y \}��� �s�/� -l!�:�#$L � = G/ {a�A B�B;a G� {�-anu5);e�-R�su�!0�m]�Z�"!� lear� !o4QɈ"� >�#Q�SKinKinf:�B� of2n� {�(�!�\((faithfully) .�5�D_E"� G 'R�32��3by��$��.� p 1�8 \smallsetminus.P;� t $l_gQ,(a()h wAb%�&4i|a ��E�*.%���/��Q�LFA� �"8�N12� �+g.Q+eJnonE (e� not\z 6��=4�]M{ )�. Si�� is�k"� �he%U9%s=�%���� ;�ma (stra* line $p=-�\chi_E^p5�*/$-�$pa �6� Q�� u_&�8�$�:�enume�!} \item a�U�A�$p!��,t orthogonal��a*A=�!-� U!�&,'%4d&c"�42@!Z�n 1%{p_E}-n� ): ($����#%C^0�u"@!\� �!B�6mX ?*��ob�'way ( ^9�)�3���"� sE�!jztib�an�� Conn49r�>(i� ��e2�-- �uR*0"�2 S�$Se��mpone�=!8�f�� *7:� $x_S? A��V �p\{ Nc� 2� Glu�c;�m�2%���^>�_S''P�")J1�ng �.glu 28in�.�A= � s:y >WN619$u�a!F3���6$!�}�͹�9sA2{�\}� d��. %K�(Q�� e���'g n't chang�s�>Hav!P�6)p��7�rrive!�a�T� we�Q a�(m�)�6� . AvK &;induc0V}�G�_"�.Fj a�0guished��!���%�, nam^t�<-�v!�C7!-A'�PQ!"b . �9���26g���y bb P� �?& �A( ~4.2W �ud�� T acurre�itu2^�" onT� 98�s&N a%L.��D �<� BAkrk}df*�)" >�C5t�$, ita'J/T&ѝM1AbEU=*(][�IbT>� rn   ;� �a�>D} ~�&)�� ��&v�&јW �h�'$6'$�u�| �ET!�G?E�2�&d+%SA%j� G�!� *<e6p�e68f;A&1!z �e\onclu*(�"�1� ���wQ�"� �?�& QC:G�asVdn�t�9"t Linf�s��w{�1"� 1.3; -,� E 4.4]A!� �v� ��PeF��.bE 6� [A,B�F���7� j#��a� �� & _{1>}GB�" +$; SSeg Ab� )�:s�2n real�G! n�*-J�n9W� n(G) .>*<ur��m�@,�>���.7�T��.�"��!JtripoqG�� � � /� )9 8[e�[y� y* >( [y_3, y_4]E��=)�'dB��4TI�.Z.�.�_ ^Z n-�*M�Z��=.N\�In*�.Iҩ�63��a�0�-N5�AOl5�%?-�>{ �8 �zT�O2�ker}(f_n=�seq6�6R�( -�tf�l�y�2f%a> �H�e�)2�.T!s.qfi�|J*��ʑH � !�D 8�����-iK1 numb�diffe< �=.InTa| �#� � analogu�Eset�of���$Š�hI� g!�neJ re: FW��R"B2+s6*�;2+222},Fm��J�2E�fac�at%�ib-i�2, �8,re malnormale)�$Example 1,v&8M Farb{K�9these18i���B�\footrC{Pi.�  a�5�: 4."}#�����-�� stat�Q�o*t^ below.I��&� !B�9} �a�,Et *d� 6'unEt� �* +�<ŮQforwar�~aT%;mA��>� v>r��4de"3+shortenTarg�N&j� )��.9�c4.5*��D, \be�%�L ��in W rt1��sx+!< leng�Kt le33$$6�6�:�644B x\{ d_X(g z ), � ��&[M $[ 1 $] .�I�M"%**C{QDn�\rm{Fix}�6> = -�i�ޅ��<&�<]�q? with{I^ � �>�!�rLi D FH7��AA3 E��2iB2J fS. "�.����"�E pply:�a�m"2��Y��d�1j5.Z�?(TwoDefsSameY�E�� �.c ~,�m4m4A Q$L a{.g"��O!Y>�DefAlg�$�and��ifu�ԾY"�$MB1e"5>v9V? Spli�u-��{�{I�6�D� Out}(� )%�in�e.AR� C$ admi�F&~N s� ov,4J�2 )�BZdm�� {CG}d:0��5���_DCo�M5.7V�E2CSA���c7N{n��en�N.Y �AnyNg6.%�V^;' �.�:commut�T-�i�TenCSA.$Every solv�N��-�.���)��(o�J�"S��� <�&�%} [Dehn >ts]���V{\em <4'�. 7]ENC�Ytypesf�Sl�~4G = A \ast_C BT c%�G3$3� entr�$C"� ��!�G��kAa��by�? hi(a�?a23$a+A u�G(b cbc�5 'b'B$Q"f��� ��2�i �t��z let7e ,is HNN exten� m���t�tc�>�%S\!�� [G/?S d].s]&MG�+5)�Mof�f7�aTo�"m$ edg�y�=$A%&A�iG vertex L)d�S�ACCle!�&K���7yAu�> to�V.z\ e d:z��>,FA��$ !��Bbe*Y%�65�nBQA5amb)3- ;( S�:0Mall�i� �>�}!�G�=��t ( Mod�.~:} Ce ${\rm =e� �2@%u� ��,byf`IB�;sq���s ari4� �� �R N�.�Z6[">Ex:��o-�n�S�?)Ye���dG � \S 5]=��1]A6.F�< V .. Ά m�1�s, ��$��%�pa�2�> A����J "Q7?%�.�2��M���Ae}!��� F�/KZ Qo�6$\A�pFn?*2.."�7|in6�D�Bfi��!�{%i�h;26.�?6�? \big.x,�?�? �<�?N$U8*c 4."�JV8"+uHomo}�?m�an�lem$rel�v!8oB,.J>y+%k$h��sim h�Xi*25�%���@ n@ M�M VZau_�*�?_2a rc 1L�,ł!�J@�n��S �GA2J�7A�%�� � %�(h'.�8$h )'*P-Q�� ' \|��%��B:0iM+I �_5 techni�[*� @paper� MD& EjAj63r~ ��2,; q:�Q�"s^ ,����E/2!2�0*� �09A6�8Ec�2/a g) ���-\56=� �N}(B?p9�� Ellj�.�A�nEWEV�I1��Gorder�{`#$en' arbitrf=.Ps, ra���n just2�s��25sum�92SJ| ).] �IM%�mA� �� �3,�$_ ^I+ � L� &? �� Thus�x6�E��}�%,�Heach co�� $C_i�J`=i.� C)Q`.�� !W0�M�pre�Iw $\hat{i}_@2id��A� mongll�.<X Ck9 Ty �o6F, �d e6�>rl(. However�[~�!^cana|�#Y�e~��_�>)@�? }%M!�V'l=$�6�Qt<,�.3!wilJb5e�F�.�o F� B�AAH��-�6��> ��B��6�f�M����%�i4\per!� devo toE5'~�. BKP launcha�i�[��e�f~E2�rwX!j �m��I� ��ng!N"1s�K����_*�@�*z2s"` P# sonR�2.H] JAn �aCC]�("� �X Acyl��R��* S a �9o A��h9+�2&|"��S> ure}`47� 26��m��%v< 5GA��=fNm � I�ly�2�W���TJ\ RipsIy; �hB'N!F�jbCcite{BF!Rf�Bg/Aer�J��English��A�c�h,����-�Fio 2)&ca� e workcFrench�Gaboriau\vitdO� �ttendant:�; � �GO Bour[3e.!�/we_quo� At'�QA�eBcHa�(!c').l. �eH�CaX�6ll axi�Nm�-�Y�'&� . Qg !� �& !�aT(!��& 10]{61 GAFA�O� �lcould�a%�� �AaQZ�FA�kiXhojL`�{Ed }\la+k a,b \r $�3Jk �L���Au[\S�E346:�%eMtr�5 m+n IETYs�u� >f�$ M} LonOVr$)0]��b�imh� !|!`A�u�AQ�e%/�=22=F~ ��3&�Y��i�e '1.5'1&�:�:/re�G���� �_g !�)��"4�9&�P�i�&�* $Y��A]�the=�!!���of��%�&k%1&.5> [1)]! "?Y cano� o� ��sub� �+dE d $TM&,\ldots , T_k+zk�"��RM(b�[(i)]�X *C nd  i, j�{s"wkp w$i 43jv| � $g.T0 "+[s�j� at;b�Yep`'[�K~�b��"-?�s�heq�m�1�o!�"�k A1~�!:# QD�2L�%�<T_i� nT%�i�or��;�B#2)]Ee/ 73 unda�alM�ofJ�!�z�Va*ce\rr�Ra�[U|bra� %�h� M�e�!=A�6�fd�hY�-�E&> .�q�qBF�Be)��"�+!gse4�E"qR%���i�sU��&�I%%�:�Hq���� �Id $2$-� fold�-1O�lny�X�Z_1&�O)1c5��?(R&��A]:�A�&B O$� %�#T�"fR�-�dd��jc36!L�B�i� %�>"s�R2�!Jd>�J�+a�Edgv�V s betweenBNI(>�I!�discret�Hr)�T�Ae T*[ r D + Partp ) c�Q�͞rt=n�?Q{9.�=�v)]��%�W����1 �ou�J[�.�,>P&�*� "B 2���l!K�b�Vg%K:� m��N�}�7"�R�� �our9kM�edyD%0 $T \&=�ebigcup\ s_{i�Pk G T�r�;13.*�3 �Nou}F-�%H�alY o ��i,*� ���' 9 �Z�J�f�:,*i��`thin'4� {BF�wajscp#�n�vesti�We�L� &� { }M "_ i5rO A=R� _!!m���nye�*,/� s v� (bce� + cond�s�*� L Ez�p�b�&� do�!I�'-�!�6�Bsp"�) ;Outw01�IE�B6��3�\o )��.9�L,��w 6:vyn�,"�t+A4@): \medskip {\b:�-J?} ("�). e�U�a!�h�j� vely.%�  N�0a�D� �fbf"v=$�^�^^��5�%Q�Al�*._�llE`� �uai`J�',� ,,*�&%}eR�ix�R:^Tv*icUa�myriad{   z��� no�e66".a^"_Tbuild Makanin-Razborov�n gram����xM adap� � n�adI :d�� [.$+W1�,S�Qf��)&� of pV�\2;�"@.�m0�I�dT'o���) b�!�q�ALɶNRa&� "\��H%0M�" provA�R<6 �.5R�V;f�����E� &�itsel� j�N)by6�L"M8 .\eqitɶPi.��B r�� *:i e#pproaZW���a*SV�}"j!�ZEe�@Aer� � �2*"<f!J)�2Y�wso u.�h�u�`� sr ths*[Gve��re�varDI�� �  $T$;�mIax�NM * 3Z by Remark� � ���|n[B6Cn} } De�|!dmuF�4 �W;ve�" 2� � $[y,%\��B1��"0llow u_�� .Q,`Erximate'&V�&|"�> . Mostly��B t!�A�develog{6I+-z�� obstacl�o �-eC\� st�FgA�) ex� 2c%jt:�E*u. *�H]2���:� iH!Cu�.a�)] A� etGN9JWD omM&v5a��fextŃe5e98impedi!,��K�A� s�Ai��[c"��&.C!��5��'�KgIat��k���!��t�b1=�� ,� c-91 .�@�&� B�#y eu�� deal-�6CDb:�c=X�5 (pp. 346-347:"* 2&��{.6V�#� �.�$�dimes T�)�a �K�jl2�IU�{�A�I.�� �aɐA��'U�< ��^�+��6ndV- $yE8T�݅]&4�-_I#4!�9.sP+@ ~ � �*U�Bf�� (y)]�,�"�i��y�,�0�#sL8j� -U!�T�>n: ps Y(y,�. _I(u�]$y) 1�.%m0�@%�o�]l�=T!�"�.% $Y��an9�A[E�A\? ,�L!?P 5��!P�Iq6,$Y�Mp�L�ai�+"C.���R_ ��.b, A�\sigm*�*�arc�Y$e�:�aN"Y^v #*T��v(Y�lx�0 $. y � i%)�yA� g�a$�+5y�$A�x, dx)*a$�~S2_2RdmA�thC-f�Q��  .$f��ɏ�E,R6�N|Q# a�J =8� I`6t &1,�Xb;,�T� fact`utE�^s,�c�&E�2��=�p_�V���<n� .���@'Uit]�� cyc�oe"���a�n+%�}).ed.�AcwaHA�L�M�� t radi �� "}AySa?"Tcor�."inG�!T�i*��@E0E�FvI EX��M������_m�"cQm�!W}�a=%�j���h�&� }NF�,}AM�.� �� )�"v � �)A0No0}N Ѡ9�!�E�%�{Non-���>�,i'�~>�)&Y"�)� \par�L?rr�Y@ou� 7?�E�ofF�A Y�?{vesUP]r:[�$l5�$ n6!� � 6 1&��"� M%>tJ��bfz��!Qn-��y8��oS.�[9�_ NotPAxi�m�C^Cl�m16��!�aAsђl "zEP��e 5� KaX.��Y:M�W�WjW9 r:1�� inpE�f�1�7$e8!a[��n5d�)�� U��  $e5��jMe �Q^e�:E�&5 !�". ����ɿ�e�n�Gm!rnC����6�$ea;k ��N:,�:� ���!U.A.�8-,�b &�: "�Xm"�one�e �.�_soO `l�c:"�Fu"� ``Q-7F�aB<lso�,Jq��[�9�  $��Bb>�IBVc^.,��F�  pG a �`�h>2��8s (�f ��g)� c1h��qRt�h� !DA^}ly �`LL"�Z h_n( �)�$E�1��  /Rgn$meu,�H.E_sEI]�mA� { v �rY/ s $v�n2M$�1 $v�Ysta�5�� is m �32< a+�S(im>����l�yz,��Yn i�E"�S$[v�m=- .v_n��� �T!�byF./IM"p�uX n�h! �[�Yn map�ߏ{X}5} (v_n�:�&}le<}�"�~N�}�1"��*P0c9� we k�`���}6,� =2L%�$�Ba�3UK%.�������`A�$ "V� a2�� �C$ (n�UapW aQma�l siz. J��a"�n . uWa ba�of + !����)E�ob� a (i�)=$- A-��@5��F 5#4}� s�vB� ,sh�xI�of� �B`+��S� },�pE_ �"!�pE}�&rBh �Im\ p G in&f �"{B�2�.}��jL>RtR���.� J !wv�ta����A����e��zcsu%*��— a� FC ���r�K_AZ.� �yv) ,^�1�w U As f�� I am awa�M�IT2"�V5appea$Nrinvuj�0�MI ]e.E��Ei��]>/IE"�[i2c�8iu�zn�� to�&v$I0"o?)�toNF2.4Exerc'k1&�?\� �"� fgVSfp�N� e���n%dE/�Kt�'7"�n�z��!Ta�)5s �r�6!uE�m�JWB*:$g"(/�M���!�Morga.� �R2ed�bpec��l�64�� �]�^� %��9A/�Zo�^6" 2�!c�a.ufJ�.e����B aT]$ cu (Ag�U "�ze�*�-!�V]�50--351:'*�8� l5rue2B��Wfbe�5�6#<�9[(( �y� Pp&sa��f��sT A�<�Ea`3�B�1M�*�W��s \"�*( ,%LJ�� s $GJ0\RNjs $Y_i� �,��  $1��EI%�6�$Y_k$G "2A��c�=�+Re�̃�8#67�2T.%R�(_� G���!ϡ�n�{ sariK�iL�5���pa�2�A! b+oz!E(mimics% r�s9�U�9�!��'L "Z:�&n ��:F�71��" l�h�fC5F; J w-�I��!�V�NO �<�"F_Y� �#V�6]6f)z� p" 2� �aIV� 6�An�%.9>�'�U��jpa>)A8,�pZ�AI�2�6��� o�:Z%�ATޡ��s&a�^!n�!AD~1 B�A�� f�-n�6u6>{�rm!z_\�~z}:�łW? y}_mL5%�"�B"*!0j�L1^tI�*5m_0"� :E��$m�� p.�{p_E,m}� &� )*fa;�RB z$* J"&{��!�n�@)�#73� ����{X_m}(5F , (h!LOFF� )(u)�*�dB?h_m(u)..'bJ -� "P r4-:� ��2�����r�q3��)�&Ay���}���U�o��cI$M6����.�"�em� ha��DΈ���hfixH���%t"( /r� a �eS&�4� �fF_���a� ��V~ u .#.�2� Ar���� l ���&3 �8 '��,����T2{:j.{of}�F �b:�FW)alread�2!�A+��Z+!�` �Q� "� "� ��� �c)/^&QAqJᙡ�h �, ZR"i�yho�=m1�� "Wa��� (by �!�9 *� y(�(9v���al. AE�b N�+�,%"�F�+.o/U�p,�RtRd� ��\*+?2N �Kf�K�2h% $fR�)�q&�f imag��!^�4.K-I��Jm" uD ���m�%��I�.� z�1|n�2�.� v OAG6L�2<2j E��E�"E!�*m$�,�N�""� �TA��2�>�C�"i�IE�" guarantef ~�0�9�-A!7 *�I"N<|� \ �a��'~ &� N� a� = f")$iRa�k 6kP%�:�92� A::>~ �$I[�<A!7><2Ż��Kh;9N.���#�(�RAq�>� K!F�dsM6!|z� F}p"e�� � :�&� g*HOm�� �)� s&� �*� J�;��|Q�xcRwFin^,6���- 22K"$��I���N!� F7:~ �<��{D1*j N) 8>'a*o�a��V3���let.z12H, ��%�r�d6�) .���Z�&D7�|23JMy�c%��R�a��1�&m6�,z��6AI�i\V�K K �AF�Oɠi� indwME22vM.� �c;Y-�&.��W�i����P��P��P��P��P��P��P��P��P��P��P��P&Y?m��D*�OxialS�*} 9pt��,�. a4t9eH�� 56�S m� "�k��,�"�"�"�"�"�"�"^"�DQ&��)&� ]  LZ���������������������������֡>���% � P M2� *�<� �S� ��9:� pRQ3i�Te�.g:� Firs�SsB�Mo�=��)Ua (�*a)��wy $clude beca�So�ls��g���toF�)� pE%�J.��.F1�� 4 2:�NY: P \�" s \R�:\R� n or3e�`-�rCXO�"� &�# �0$P \cong \Z^ne!(�Q�.\R �� � t $W�$P$�  Fi7n5�0 �o"�ftO�Q��Z y $wUW$ r\R$U\R}(r,u7 (w=r 6\ə;\LR)Pa�k K��v!�>NW 4(k�*k�/>�K.� Eh�$%�,��A� duct"7T`I!�OjoplusOj�ADh!�k^��P%�!��$BI4-�2-d�("�+"mx'2S!�]z!EzUds(I6�-=��V~#x�"A2Dh6� ��m�OW$��� �(k,2"A$�% �/X<�-<^,e�,���![�1WmA*% FO;B5~.&l8%;!o���mcd�6�.��+s�RV��Beυver $\Z!k:�."�a longb^Fp au^�F�6�L�%�$b�dinA�a. �! Wb�wWJa$s�@")� �I�R2>sepL:. ̼�LN�by $| �|�"2 |F��)� 1B.fm%�i�$n�-Z{ �0 < |�+ nb_2���.Ggplhb�E�+ ��&:�jAXP�Bix��A�-iA�Procee�D� mann�_mJmN��2 C2�as1 we wis-�so�au�6�eK�&rf<(c�Y1.?Sw6���U�)�F� lesL%�,�с�'KK�:����RM��}G By Claix�*6ra2r�!-&��)�ax�-o&�V�� a�umm>!�a (�5&I;��terva52�F�R&�!�Ar�0X7Yԡz�X|�A�&�(��^$\LաP�B)-�J R�&w_1uX��#aJ KU���z&�;aUc1'*0#la^2H�MnrT T1�X�X52�L"�J !r�z3 "�tQ6>J ��96��a.�s adja�q�2u>LY(&.���O4|d��"JZ68) "�[�oin�VA�2RK>Va�%3��.bv"j0�)* �!��UV~8soEz�)��<eY�q�P� ��!��T�xo�!(M&+@W��^��GsHlKYq_m��<��%�F!:;XJ'Z&5�6�"  Bq_i,q_j� fẍ� }{20�&W�Pn[S�, as>!�J5� ll�d��"�8 ��G�����Qc2�2L��sga��a���+xr*�C�1�p.351P�*g "�h2�p"�� �B��DB���*_ .�VQ)[cy&lF2�p�BMKrcq� !�(�").�:%��: duceAQ2:Zc-��[y��Tf&uex)�z/��0��0(i�ly)�F�!�C*&�*O�*� 67+;;!�&4/��K梁e�0d�;6��h����&}��~�;&<�9��_)�nZ�2q�h_i6;>N (E_i9��G ţ!�� (A�Z2"f�no�D�8aD"�D$A�>e �!� "�.�aaG*:� "�=�.\W��)WC �L �3:i(A &VZ%�' ��11A�V�El� ?�G']=� v]4,!�����eIa����'��Ai>�� `_0%�1M 6V��F�j=�%&U]u.�>cE%9�V0% $A_E W�w�v:p�\0Q�AnƆjD�<}�yA�.�3 �*�&�.��3%�5{S5�N�f4B.� 6=K��Wr 7!�&%|�6� ��iJi*8.&L i7.EZQ!%},0_�=A_E��{��� .���1I� rO?in��,6$X_i}(r_i, �f� _i(w�-r]�*��&@l%<�L���(l4�:K_i�M� B~X1����U %�&�f�gw!h= Aa�{�(�3!�$A!�R�)_{!� �U�W R$\)f2E$��*��$z snd>1a��(k_I�amQ>umUXap!�.�W� re*�/ >c�4n�..�W��R�)G .�s78N��i���~E_ѡaZe (A_E�&�F$! m� ��qq k_W}�� /(w%�"�A�Aea�A"T4` P1}{�% i \|�p��_i. a*���r)��.>'!D*y eHB�f�&��$.Ei#toB *,F� ����ωN�e� OA>J�!k� �reX�b6ΚI�*�� &բM vC�^: q|K1���h�uj7 good=ApA�6�A66�u=�W whol�E$� Th�1m6m��%p-sv:� �O���N͜-a ^� ste;�&wxj�,*ie� b��=&;�8���sw�cours:G�ct�-LHG� �>�moFG%�%�ۜ�?Ea�QJ���1fJ�~ .a�:�the����id*�~6��q)���0-���EY!�oF�*�o&/(9:�5.�,|Vw<3:�,:� ���to�N�*y�E�h.�� a�F �e�+���Eii��W9`e��ra� . �NaGa92ogelns ond  �l���nɑde�Q�cax�j8d_X� �;T�9�'Ћ�sy�f(�,�+d�I�=�C erent�-eu)2R:g7"� �:m9>d;p"� 6f &"%�4"?!�"" +vV*%w"�`�F��]v�[f0,u"/7])|1�  J9�I��\&��at P;-�4-��pa"MP4�!�"�` �� .��b|���v��@!V�P&"4>0$1�VpE� qD{ -��p.�L re|�eB�x0: z� Z&�:**� n�x��3 �͞�;! �5�;�-=���8�8�8�8�8�8�8�8:�#e��@>:W�$�\S >�u�N*�B"Q�LxQ��u��p\XrbOG ��s�Vv�O,5N9[|well-s d,�o.t,*##?6�{e f,Q����2e�4n��>Z2�7Yv��b��ab<�+�aa N����i��j��z/no�hnt{K\�I${� :}} x .��]�i��f�E$e$�K�>k6a Va:VIYF c�kly��L� a�$2zE_�$\bar{����/1[E��x+�aŗE &2�.v�Jg� ��gl�RIMf�@@&�%���!Qq ˹���6�S!\-)A*=G5=G6! e�: C"CU� �a!]�RM�"*�nN0~g$���2on� %�B�  "��k write�K$u = a_u^1b \c�w{n_u} �@ �ic A�( B$*�*S nd/or 'O�!n�3t���\{S�B��, z�Q?�Pg� E`���$Z� <�^�ofb''(� !�6�8�Aáp��*� {v S"' y)=�vt�����]*}2����$��*x "C�th��!�e�86�c ;�� �)���'� %AC��PJKCM)bi.aQz �&aQ10&u�2<" S� �z~���t��F$a� �F�G!�b5 $I��zE�i z� ,\ \ \ zE� 2���Cb%x#M3"�10!=��"Jmey���!�1 ��in F$,"� 0z�"L A�J} |"DD:D�{��@�m2).�@s�B }-{� G�"n )�%qj�M�qu ��&#=f�m�}{800!0��i�w � _mE�k1�]iT/'��0 ! !�:1s�"�� �Flexi��>, } -B� 1000<e5� w_m,-2_m�*�E w_m'. VJd+Bdm�p�g)�^{zMov��� Y�ofn��6�J�;m� w*����)z). w!& <T�>)G- 8z�$_m, \mbox{��}n�fZ!N��bZ')+Z5>"�ԥu);Q �  & �[Z ll�s�T*gɪ��^���i2 ����/{�=���J��c-�W) �Z+�J�_i�cn[ �e��Q�+y�v$ KCl�`2 REat5):?�BZ �����O!uZF�6�Y.v L � �ov-)���W��).�)\l*�B���, �c�+- �" G�.!�(soe,�#is28l-"�a �a�d�e'��!;W.��B��pA�� � �.>Z3v��\a4cm�M�# s afژ%ew�R B���'J�bQ-��ni(z1�ct*DH like2��iA�a� lo�j} �^%��qV�12�%@�o � `�es'ADatV$10��y(�]e B��]�3ɳPgXyX3�!3!@��. ��%M } � "qv sh� ,��A4�.$6.3���$6.4@ %�B� 0�v�;�h�>0II�o  �orߕ w_m$��%� et")���i2. �!�ci���wyx*T���!0Q�R ]��&cƉ=�m�>+!y&B�X��� reasZat!v�})�fh��ya��&��)� i#H"�DV Do�s%�� .W_D$!aCp����%m"w_�-^~&� _mn�7�S� �-���ABE)B:r:��I�� 4]�:0a���ia$Mu46� (n� �"A �!�c�.I�J92��$B�so!�omtb�'. ��.�)7tog.p%ũ�is: c�gin.p �a� A &&iPΞza� \\*��*b� (bz,�=*� ��e,}Qf U��c@ɑ�VaQDu2ip��>�2�)pI�jLn�m�&]'�MB� A�6<�� affe�X4X%y"���s �A��-a�c�$>%��vrb:}6�mVEFq�M {fgA��Z�� � a�q������%���se� ���e�|*Z.�,MbSI[����&�|%�� BbbB�=key A���a�:!7!��5u 6f2��f�K56w�.wev�Io"~Ae�i� � +�. �3��I*��I6P[2fvF�2dfe�ѡ�e�{�^�)>J��Y:Y,"��a�dk�'raq-EE0t nh�{`fat'�Ot!���. \�.�j���"8 mind�~���edJ�p�+*��"Q` a)=w,�cCa�Z)� R 2��.Y��� g�;��� ���\PA"��;222�.��!B� �5!3y=���!�q9:&j>=X� �spB7Au�����D �Cr�X}f!)ex���3�tf4$,� �E��!X&`)if . 1, E�������al�ay?�* *� �($J_{E_1,E_2&g�f��HDiam}(:)| N_4$z�< �HhtE�#nd-ER$�E�"( "�*��E4�Es 6�.�$�n�� �2��}���Q5�fam�%�2?e�!�6�$9�Mq�5j!��n2S 6�1B��),�R and that $\phi$ is the function from Lemma \ref{IsolatedFlats}. Following Convent6\+�Conv}, we assume without loss of generality �@for all $k \ge 0$< have �(k)k$� also 8�8a nondecreasing�@. Choose compact�. Also,GXG.?a�snD$�which $ � . D = X$%�rr re! d �Case 1%�replac �constanA6ddelta$ by \[ \max \left\{ $ , 1000K_F K_X (7 # + 14A(4 t)) \right\} . \] The stabilis �!�edge $eE�$a subgroup!;Z�0. Since $p_E7,not an axial%0onent,_V=�a.(either trivC or factoraH\rough a infinite cyclic � . IA^0bar{e} \in T/)�Ya splittA���0n necessarily�� �@. \noindent{\bf-� c:} 1Haletely!�tainedA�som-7I�$V�!>�. LA�A_E = VP . Then, &TA_0 \oplus A_1$, where0$ acts�lym� ��$- fre�i�F�>�z1�,{ 1 \}$. We�| a de!osi�q?L= H_1 \ast_{A_E} H_28E�Q�D$H_1$ fixes a poin� A�$, but doesE�fix��ofI�%us,RD$v| in E( Similarly-2>q $v_2Ed��btJ We c�)�@s $\hat{y}_m \sub�NE_m$ s�|: (i) $a�(}$�1resenB�D\mathcal C_\infty$��proje%� o $y, T$; (ii) �b�$ liesA�the orbi���� . x$;E (i;subW t�(e first twoA�d%�!a� [as cl�.(as possibleCLline $[v_1^m, v_2^m]Y�8\{ v_i^m \} \to $$, $i = 1,EWe� ceed^inm�$a. Howevera��i�2e can�� findA�Dingle automorphism�shorten%$$\| h_i \|Mbwe us�����4!;se!�(h_i(A_E) .a=�$i$ are den�ta^ (when di�cea�measur�*WmetricA;frac{1}{�}d_X$)���@��A��' ly many $!8(a Dehn twis!� phi_{e,i}Q5 ��oea�a�X_iaT!Hpr%mE0a si* way���$a above, u!_� idea3Prou��S)kpEAxial}%�proofa�Theorem .pE } d8. \smallskipV�d:}���Z�i�Z>�.�Tre%�e ases �d^�)b��� fA�CyC��5�ge� ted�� abelian� �!t"���le�" �,Geom. Topol. �11 �07), 643--666.�0Bestvina} M.  , Degɱion��space�,Duke Math. Jv056} (1988), 1v161.uF2oE14M. Feighn, Sta���~3sA� real tree�Invent. ��2� 1995!}87--326��;} M�>��Bs)$'s work: L=y 2^�$, preprint.�,owditch} B.  , Rr`NHH!B$R. Bridson�(A. HaefligE U�M� )�%O��p� ��ogy �4�a#9� 1058.S--RDr�n�i�re�dZ� IMRN �19I��1181-1196-��r�G�s�ng�31.�T}�"� %�v��{Adv6�21mWG$1313--1367=I Farb�� ,r5Y8�͉�8��1810--840^I� Poly�w! mov,uf^�xpand!'ma.( Publ � IHES �53�$81), 53--7.: �2J�in5EEssayJE���\y} (S.M. Gersten, ed.)�{ �{MSRI �N )"8!�75-263.�CWIF}.c�%� (cer�$) CAT$(0)$M, I: Co ific� , Ulg�BR �u 1325E .��2ʌI:� Hopf���) � !�a� *`  Avail6 t)�\tt{http://arxiv.org/abs/,.GR/0408080}]fMR-RHF�)�v@�j 1ZJ��2319--232�G-Man��%J.FA�� hn fill!)inv�5�>�,kappear=Hruska�� , NonG 1urv��with is0ys, PhD!�Psis, Cornell Universi�200." HKo�B. Klein� Hadamar�#Rr�t 1501--153.KLe�Kapov6�NB. Leeb�LB�!quasi-is� y ɪfb �alQR�3$-� foldVap� 582--60.�8KM2} O. Kharlam�$A. Miasnik�+Irreduc�aff�v� t� ov* & . I, II.5?��] 20� ��@472--516, 517--57.�KM��E�[t=y!�non2,=$6�302�]n451--55.L Levitt} G!� 0, La dynamiqu�s pseudo�� es de rot�vRm1�:9v 6v 62Morgan}E  , Ergodic�A;�R� $\R$��ICM��5�*�:�!�BO,Ae1� eel u !�I�M�ongre%�lematicians, Vol. II (Beijingi:)}, Hig`#Ed. P>� 2), �9.�!�2-6����--VI,  ously� ��6 �eH���Hyp�q�~ VI9 R�aB{*� "�Sz}� Szczepans�8RrX�Michiga�"�4{ �6`61. Yam��A.  @t{O%harac�sD��r? "� J. R�  Angew�#��56SZ41--8�Rt:� i docu��} {\�'{�le,u� ckage{ams& ,amsfonts 0symb,a4,enume�,epsfig,e*(em,psfrag} I[5,n1]{inputenc�l\newcommand{\be}{{\psi_\pi}}6id�rm{id}> sign"# atorname{>* tracj2+trN)nsQXast>IAAA! bb{AB@NNNBZZZBQQQBRRRBCCCBTTTBPPPBwwf{WBttt tB AacalJ4BbBB8CcF�DETDB8E%�EFpTE}}^+:uF�%�f{FB=Ii=IBJjJBKkKBP�FxRr8F�SsSBTT%�!F�Uu8UB8VvVBXxXBYyYBZzF�bY�fJ�yW� bf{yZ% 2AEJ�bar\JjZ�JLao}{2 :J9.F:&PkPpZgUp Uu^\p=]:E&1�>+2�b�fJb�fi.\&�mO A�,,�!: }�$def\qed{\u>dp\nobreak\hfil\penalty50\h�&(1.75em\null2(P $\blacksquare$ {\par�5l=0pt \finalhyphendemerits=0 (}\medbt��$\capsize{\Ax26~f{.��f2d?scriptK:am{66\diag:&:&tri:) :,#:-in�{ %!a�o}{ ")l�1}{L[seh]E>#}[)]VE prop"*�(6kcorH Corollary!s\title\* �8nson's shift itD io]|author{Ricardo S. Leite, Nicolau�Saldanh0Carlos Tomei !��$d�  \make�"#abs t}~+ stud?/� � c�2�ofn� �x Jacobi ma�*es�p MSC-.\:} 65F15; 37E30. % 37J35 @Este �ltimo fal-- "co�"(��gr�...";��mico��{uodu��} "\+pap��(��"+&��h!�%ed% uRI� o cal�*W it{FF},D�� :�. M�,(precisely (�({��},  Demmel},  Parlett})�/n $,im�2/2al!��z�� e�xn, �a' number $sA�r�1if"�1i�unique�rE�0 oriz�4} $T-sI = Q R G/ $Qeortho�and $Rupp�5ang�,�}�ve�(�D:�A� �� tegy�L!�choic�~$sx40omega(T)$ equ�'�2 eigenvalu+��$ bottom $2 <2$ principal minP+$T%1��2sE-.C@entry $T_{nn}$. AU5� �W } obC�*new-�8 \[\ww(T) = Q^f=d T Q = R T R^{-1}. \] From� h de �9ormula}5 J%dـ!�%r$ Hessenber�-th5m�,lsoH9Ie�bE݋(/�D- , as w�a"$��q[ no�7ff-� !���G:1 Bknownq]�i�.i���T_k!� ww^k!��MA6�1r�K0a2}xI�s{ ���s a"5ra!�k� �+ir lowA.� I tend�A0$:�y���res�`iB�������- t�,. It ha�/en*�5/4�<1�+�:)�1! � A��, , �)4.�x A��*�&�:C$ suc�/�H|(T_{k+1})_{n,n-1}|A2C ^3a!� sh�se�dis� true� mosti��0false!2T,lai2�*i� {\it AP-��}A/itsY�C/,& N 2  three eGi�.y o!% wise. For� "< " n-�A::E2 rue.�*!�G hand�s1w $3 ��3$]�!!�K ?%�:�(iZ the �� M#, mer�vqu" �9g�~an out�7�!�@. A basic ingrediN2A��!p b� a� coord/es}J sisexof��s $\lr_i$"�7 \ldo�!nv4�7&� var��5eta< < n-�:�$ed�&�2 ope �$�5�.3pb)d �c$4LST�"2�;�� ��+,.RY����:d�]Y��1 < \c� -n$ a�� ed by �@8 D:!UpLa$Fdex 'permus $\p�8nd=� =��ide�6 iffe&P*between �1$ he$\RR^{a�$� �explicit<;A�a.� %\@!�)@L%�!����(�{\pi(1�1�% 2n)D3 DiaEkize $T~�.?f % �6ILa�?_#.�$%�@~>  = L\ % U&��m�r) pote nd $ .a��~5 % g  $BL\��.� s = s T '%t The �;O ����#  b� �trp �e % se� [AC5� &). T%Ny�:!�[ �Cp��x}M�1� & \\u�1 &6�2),*&\m�2.X(.X * & \deI. o$.IE�.M n)}  �v %o$LU$ %6� ��M6 may� 1:m1" ver�7"�- issu,2� D %Mnto low�r"aF7ropri�!�e8�*�;��of �in)� "� ^ m�C & down. FO?,�; $\Zz:5�D�;:" !�Y""  $> ��vE$T$: we%1e� i976� $$\Dd_{0,i}�Zz�N���$(T }��m[�5-10$. S��e3<&� A�� _+(T)�F -.� N� block�@ T$ a�belybuE A�cA*r� �$: `F\Yy�m38-� .�. I�Icl7��gfu H� ��smooth�� $ed at leas�Bl - A- \Yy!9��.2!�"V y�G*$!�naM be m�  r. IndeedV �Q �2c6 �V�&�y$��i$, $T \�=A�cup�- 2-'� !3!�E�� n+G \ww�F(`1" �2��) = \�(� ft |\WAQ�ţ2)}!oEz (T)}61:aG |l� h Ji�g-M�Fin-�k� \�G )���V�,�DDi�j �� %�$ e"sfy.�g =GJ�an in�3�3" �ͤ��-�$ s@dsY��:�I�T bHa9H$([)�F=0$,��e�0 in nt n:borhoodA�Dd� � <� ap_0I�2$� quot�}]�%/�'-1}� �6��C%'�Yw !1� E������@in��h&� .`t�=|2 $(-H2�" Y��)� �n a Tayl�5r�7 �$. Notic�,�7 \i@6� n)}$94  oddn�&����%��;>A$oowsA9 \[ �a�} � yM q� 2� = G�6 2, J^3[�M s��� $G$, yiel�'!�sestimate�|�(T%}< C |]*|:g$C > 0�T$!2a2�a[-� Poin����i:�� e�r�Kep-like��� inuig-�a�$B behav� �ww-���u �cap��E�m�c��, ed; �figure�@fig:142}�� w�happen� $ = (1,2,4)� typi*�f�m  upshot�� ki�j 5�Kfew�� ���i�i�!�&= 9�"OJhold,e�"�2M��!<"E s *� _0)$�!�irrelev�� D~ run.��"� ar�@�e-"[>�, �)4a �!�ain�t.�"C���C�"�"�� aA� ��$K* R>i _k��i ^3$ �E�at�L��3$k$ (s��1eC :wilk}), u� genu-,)�.m6� 9�. e $3h �instead�1�pa�e��;F] IXis kept�b�WwqzYB �p_+�U��_-m�a��sembleřlHb�.h)'�JcoPK4z^2 = xz + y^2 Bo�.n, $x fy$� resp��o.�1 '�e 2$, /d�B� �d�by plaX;$x = �$a��iH-aE a � pas8J�O$(a,0,j8Eez$!Ppe�G{o��$�a��1 $y$:ɗ"�:�� $6%ZI=��is�&��u�Q�I�$�š�h&~L�ter��%&? Y%,1+�$z8 pm |y|$; ���M/ . $6�pj�:Z�1�5&}5%N�r�H��-��.~ is dictat�whe̥'$ )Ss.Y�Ga�g�Oto�QyZ turAqu�T_k. pd!�I)�.� fails) if%Q only$T Xx$, � � mark�� ���{\ref{��xxx})!�.S�-c2� } R� �s(k�nd�`s!)9I�(�M�� ÉDorQ#_-��� $\Ss 6�ya C"6!M<�!�ZB�!�!!ޙ�$Lipschitz � Ds $f_s: [-a^\ast, ]u!RR;&(0�0��$s�Q@Ss$; a good referAbE�m a��8��� PT}.i�y-�B��((f_s(y_0),  �j2�$�r�&L!%���0&�Xx� ��O�Eh:�suffico ly�a�|irʹE� will�eiE��!� � ��FFapp3 . An��=<5q systemwL�/*� h�y���0 work>B�DZFSmT<e�BS}) o Rayl� &t "R .�O We b4K^p�! coll��)��%requir��� �u.�.@, �$9des�(^E� 3&"&} v��2�( 2lYc�&JkedgO��eJ%s"�&q\ $h]grA aB *d&�s�� @��ie��Hr�0�6�direct�%-Jh ��pre_ �"� ��" �maJX(a Toda floweC monot�6e7A�h$!qn�NsFa. �re!�%� � �^3g �J�:�)Ube�Q "� �' ]s 4�45,e*�(>; "�ba$usu��i��F�'��`9i��'&A#'&a �)�C2!lZM �Qr2 PCNPq, CAPES, IM-AGIMB�FaNjI\ � {PreLn�=s�c��� �X�&tRe�n5c q!� um&>1"�Fn� c$": 6@F5)$�w��,� T = 2u#XQɖ$Q�O(LW'%A� $Pf-%!�$Q��*$�#&�r2V*�)x, $L�un6L�&�a�a�s QQpfW $P = P" �W� * �� S�O s�[�%�'t�?E��)��*� Q$ �$� f�����a�-Y����leading :�%s�9~)�2[�$,  M��b7��!& �$%(� Q$ adm1"an �"�&!v�llo�_.�{id���.;� �.�U\Ee>2"�&)W ces �� hy)l�$1$��$-� ��Aw!a�"�-�}[�`(mma 3.1] \lA %$:upla} TakKu%e� un�Y�ue�h+zes $nn� N��\u�Y$� �� �. A6TLrek�" _1+;!(+n_{i-1}+1}�;�mbdn-n_i� Alterj;�,UK "� A�� faN�"�RJ�� $. Aj`An$E)aEe�%f: t�$ET %%�+)� % B&k*� � M�;,�' [� "-norma>!d Q?��}�'�)�Y��=M!*l! � �qi[!�FF%�Q��� x x $UM}"u�.QQic�^Q5 = E y� �d��-LEe�TI now� e ����,!"hL:: "�"� %VA� ,c�/�:@ %"#�*%� .+ekT� 6�jil0��>�5-�WF�2o)n�͙�  �^-�=�C Q$. ��)��" �"()�K цbecaus���>e+��re5�)� �M���"#QR�&/ 1#%��3�*B8 Set *�"=5n+Y� .��#n.?A�colum��&=� ��eaO �9#!�� �+�;�A� ,!^ �H� �+!�  %z��x�i&NI�qj3�&��&�h�Z\pi: Summ���S �� f& :����� {l#��T1�#&�#&��'2 '\\ .�#.'3'%.$"*$>!$i{E-.� F$D���>.}map^Za�� �"ak!(2� to $���b:�� W�`ll$8%^/$ (tog8s:�"k)2�Z`h2.9�.r } of*,{1)�6t�3.4"v:S}_ !+$�?VPA�a&�(�# y[r��K�}�#v��$ !s������ � �� pconnec!�gi�s ��m dFK��� (R?��x :�T.k.q��h!�e]� U)au0n.�f�n2]��Pu :~$�� �;># i,i+"�#O �r1.em 4.5V&� �q}.�i/(P c5�nonzero&.��^�f:� l!�act�Y�r 2+ b!J} Giv^]8 �%�j\pi&*#}3 e&8����$s < C'*D�#�!KT$,�7C2O`" |9܅� C'2*Ů�� � s�cF a93$\alpha: �ex�-even}A ( (ETE� 6�� O0 �I�� 2� N�transla�M � [fA��/.�>�R� 6�y�:ETE}�^E����(\sigma2� n)� � �-��4��(�3��in!�<)G � ~2ݏ�� %�*n*$ A��!�:� �-Ea�rc b\RI# Gn 0.&� �u%|� D? % �a�previousL,�2m%h tild5= >$ %Y@ ~.� %��.V � J �2$ +b�api.S "E � _  q_� > e$.�A� �L xm H.S^ "-sE'�)d' $U,FM  % *d� �� \&� �z.�"� �F;.�%H !� = (EFrE)2|# 6p�fv!N = a�(E � E)(E)+ E)$;�.��Js�~ch� �A]F�*� +�E E$�&�/]A��/s�mZ` %�u/�� easy$=B�A!��-�&V��+)�A5��-1,0,1)e+pV1 = 3L 2$33XkMa>ocdb�th�2$-V� �ŕ_1a0eg $y��=_2. �'�u�] \[2o=mgNeK x} " 0 & 0 \\ - \\ �J3, \� 1�� 6Rx &:RyfRi�z�-x/� �- xS16q �&A�D2D RKwro�c �*$1}{r_1r_2}Q .5 {22� ${2x(1+2y^2�1{xy1}!A{-x ((2+x^)-22*2 9 ,y(4-xRl1}�1f,�r_Ep�"- &�^��9&Pf� z> vi�N'um�a t*�2s:�C �!� "�'�� u&3by $f$}��"mapa�F(= �fC**z\,T\,%-R %  �sE T both�0�)�?�0@ at $r%=��=�,makX ^Vr N�  64� darkR$)cop&s4 $f(x��&a��Cmea�l0/-s�!!? $F&�1ͳp-h)F�*� D ��G&�,�7 on 4.2"J *:!�bi}eYK"�fK$T�o(F:[ )2A �-���6� �0�6�0��f(��0)}>1)}�6r�4|! c*�0]�0f�r:V�9BV�0VX�31)���!t< �Vi� tech�Vresult�FidF ��ekt6�q �nee�/Ah�o7(��% Z*. �l a�ra a�!ese#%!�l�Bage�6"� s�a s�K.3 j4Sa�Pi_a M$ �kewBkdwHH$(M)_{ij(S j+u> jm)�1)HAG�^  � comp;<, 'L���%l"=!a@0 !�m?Symes2}61"9}> � a"9 1w� :" , $g�&�b�<��, $X_gX!�x f�/ (�u [T, )v]"<)Tb2 cpath 8#� $id}{dt}\b?X_g(\bT)^&\bT�T_o1���t��4\bQ(\exp(t\,g(,.):�_0��>&�bRFz(J� ,\] or+>q@@,�NT �F�$� �r}x)R 2��y�ofI..n�'m=)��*eyw�t%X(diesMo�1�s8$I�Y�a�k#Dx$g�Q C BBR}"JGRTW Tomei})&@a��bel :todam�M�>tMv\#_i)�,&�>j)�9�w inctd�_�] Bj�)�"$.i$.�e�._ $>��u @f \mu�� mu_2�` mu_n|1$ 1 > 2�@  n$; ��h_{M,g}>'b�e>� /iq�F ce(MepANae���i�  deriv-qe� r$!�"+%� ve exceptD0�A c��E�)� z�I"a�a�>�-�AjV�$&above�5�claim r�4�_� = [2���8]I2D:� |ge:�9�E�^�Aeserve� a� �>be re��TBaDK�k$p�*co I�"��{A]�P. ]�By�{b2y,�s�*es�� $p_km�^k4 ŏisEWKby�hu� r $k$:�g alig�P=ap�F%A &= )}�T q!_) �T<ft(.D#�) + 6&��6 )2notag!} bT [\bT^k1�f{] +>+6,.C^TG (ɝ B)"9bT> A+ b-N2 `2�[.H:�. +iP-�T4$Q` = andG }�Ju�"N �Va�B�X_u�B� I%[�]-ލl\; �n!�5� ��L��[&� 6�m�-�A>/ (M [ 1) ]�A ]sum_{1Z i < j n} 2��i!�mu_j) ( @)� ^2Rp4�$�.m.)S, i�T%c8� 2q{�?don�qed" �T � :QR.f�+�{ �8 $|&1 i)|�j �/$i!j� �fF.`� �{� } �$��$f�� \Kk d�8*�et��7��no9.�5ѕ&�5$K �978�&��G |\{k8NN | F�L � }| <�s\]iM!f�U�- Con�%�\log|� �� � M_m $�-"� eT��rem"r\Kk�H� ac� avoid�3VG5 E ql�Z) gKklp>�:� , $%_�1 �2V� MA�R1K-y@�!1.���s�@>��1",�� !G %� k > L�  8[fA� exit�.v#aq6.x>ZF� a�L�uni�0ly <>; a�1 situ�, �in >t4notso@.}m>.5"�*0Q!c>�.y ��"� (/SeqTL*�_s�� ��� $F4a� a���}hen�, �is !�a.�D. FUenTJ!x� 0/�B(depend on $|#qB5a&FA���!f!�pe�D&DR b ��M2Ptep�LsFor�'EO���5 \ge �D�A� two !& �7f�D�MTi�se'!6�toV�1�@�P�"�8�!n,�R? ��2inu��r"M6+,�.��� are � {!IL�DYy_�:�b+��of ��e.a� ^�2dF-1J<) -1} �B&�.���\a �)8hF= %��k"� # �-�DI��is� �T %�<"! x�F�>� �E>�8 �!�x�Tl:�F�>I@*bIQ�i��3ly way-�#��ld @9: _\pm-)9�(   sens  g �!&�"y:wlip}ጕWY�\pm-�\to�+ {L�8:w �]���YT'6%sa2$�.!clearly-��u�G Ka $;>$ $Ajlq�r (R=.�Aer)* s�aQ�n� ~%%߂%�} on. � ��A_�@{ e,ILa;\;mԁ�=(_kw��Z�<bigcup Zz_kx�b 6Zza:TD�.Q�-&�����u�,e k� <aHUZX�=q� tAe�n�2ae0 p��q�:�6j.�=Mbi��IEn���$ NF_{�� U�:��6�.\oC� oddU���F:GC wil}>'aJ�Pw!�� DC#B& L��7c�L�@9��"!q�c��o> I�����$, ������Xd, dege��|v !�. V�q3SZ;��6"4_9nt6�?A` arrow ��)@�6� V$�~Y,MJ ^2(T l@P$ &�z 9 an arc M3��a dou�F�� a��a%Sex. A�^Z>7'h]�[eg4"�;U�2��!e�@ }[ht])$center} \pVk{_g%�zxk{hu;Ht=28mm,file=wil.eps"ndBcaO{ �c� phڒspa�[" 's- �$n=3$.��figE�� ��ap��� ���,j�_8OBq�EV�"2�_�%�BLBLW!���Hm�*��j@L"�K| *�&|'�LNcn*�L:c��L.�L{����� ��M�(c���u�: natuk8~N� A�){i�V&3���(: jHh) ) - : hat��%n! -K.m� 6�I�`�(q�� 6�Zzj)c removBi�^e��M,�pit��solut"�7�� ul��N� �at��i>�K0 odd,�-�G| a �)�&��*D�'�1 c�"�4-�B��q�8� MIMo Zt?val� B�.��J��J��J��J:aH-�f"C. CY`2\[ rK�2�% 3�2%P%c$�$2�&?$�&269&,�& �'1t �jp��(,( *�D #m.� �%0VA"  di ;�0 ZU�H��Dd�D��P-u�weL S+��& -:�Ha�hf..� #e x k� �/"q �-$"S&�ly�Ped �9�S���Fa�(Pre qua�)2 rent*��F�� D0}{��Ddm}{-3.p +.� T0}{�<w�p�L�250142�Ima� l*� ��� �A�X "� $(stretched* �2)6@TN:@� 4 oHraw�eaG7Z���&E)20�u0ck/�� �8 look�zk5�d6#$_dua� ^) Ju. T�dm#I} _$BF$ (w7 cusp��9�)�Ani-Seir ũA����e�.1h:- u&�J�`Fe�H!�qo;A�#]F, �CG�p� <&arc, now cBX+!\Hotted%Is $ABLCD�jO \.�h�?KEl@.�1:� ic I jump�m�zD�9FB)6C$. O&�R!��4�&�02^�Tpl��& mirrtSyDey��axi9#%PJ� ��5�f�F�ef�:�Z�h2�La2�F�Zb��es�'ȅxP r by��a<��accouN�2 A]$��y${bS'. 152"$%:p�h�32�e����� lim_Y��� }(T_&RP ��V} �N4 �� ���'zlwaysH s�B!o"�H Z� � Wilk�o5O:�f& trunUdQ=Go�})8CA2A $�b�1]=�+�8 stig�r :�c��2�I�����-�%� :DqDc�" \Dd(�\. \;3 ;6�T�b� \}$."7H�S&�"1,;"<"�nB�O_qOC"� a�(2�)&C.��&2/\�c�S{ c}� ���emptyset?6r"�g $C_c)==/J�V �c:�3)1�_cqBA1&�2#ZQ<��L� Vv�1��8� T"�a6�!�;�act�a�~;� $ \ $ st�2c!"6�$!+>O�$�H2O�jJ� ��0 P�*1 ubma�ldawcodime>��E�3WkcF< T^i$G.�&&$ trappedin��� ���fis�cA�sa#8'��qY�]�6 �@[3���!p Dd^i�\super!%h^{J+��V"�a5��J�f@ %�� theme���n��Z$�bh4\N4A{6�m.� {�6�I�'  G�+D�;�TMu�$̑if�$� ��� ��!�5�u[�� �.+K�@�!|5�(|/x�§!e&can�{H0:�}�5��C����W�Wz vi.�_j��b�(�1$) $i$ ($i$pԖ$T$). CIs2<�"�]��%�AU��� AJܨNe@]�BAO� IGYk for xJ��EC�g(��A I!�>�e5�pf�6is�b��A_T6�LB��$S "�`�&1��2f�1.�.�1, |�&#%biE� vFN_E�_m<Inl1���R_v�h�uous >P�f2-; Bd� "% a��*Jce��1$6��aL |9��|�Pe$Le{,eZ)*� �%ul����� f8qw"� �G:m $. B"v ���V���P��i3Z��71� �et� 8�xAs�:2Aޞ�w-G, JE:�Y�bn-2d'%h��a2N8#�qD# a��%� zero� �.�+C.�0��&�A ��/axaznl�e&� �#� e�}$ k�"LU (�wu�-D _08CecWt�>�!}I�e2 �Af!�(Ab$�z ��| �} E�f(��� �(\ell a�E 2}) 2,Q)^K�6)qm2,is�o $a_� a��$"W/��2e)/:-.)$ !s $� �i+G-H�-E:� Tau:��{!1�f-f��b:�br�wanalyǘ9fG$. A���]�8�.�)A  x�!�a8s%& B8s�D� �n8s} w7,�`L&�$oa�avera-Q%us; Vs,�D:�&} �*Z �a,�l cell�&so��w� s�so ,�w��ob5)mea*�� hex)� lB ���DN�9G����m+ kR8L*�9)�c{R� �Z(� vmf>mz,�and&�v"� ���F+�Z +��:|)/6"�,}[\rm (a)] \`�a��), nVSb< 1/Ce�V ��*#�; } g!�� tvtegersu" � VbV�b%�a*�belGs�U��!�&jWe keeO�Y � ��"$�o%E��. Ite%N���fsI/ "u,nOe%cߙ &.�I5Y!��*"�I�>&�Kq� g:6EF!rU)�_1$qY��Z'*O ��>A6 (b) �9� Zr]���*��#���A�#� ata�2�2F.J�M�f�\mD��/YNtUP2�Pm is~�oD�%�B�%�%�K%%���j _c�Ђ. �D warm-up f �/�{>p�Ub{)�%h!�eU&9�� �P.R�"~'O#D�p� !_$n�dnZ~MDd!��!�����omo�cA:=7�!���_F��Ih �!Q�V,��{V_{M �ni$]���y�%��^���j�6^� "���%�H�a*D1�/z�$ (!Mtop�c-1)�G�  ))�M�0jf� ��A�#�0l҆�n"F2!`/�lud�� �- ase:\Jx��9en��%�tA��2<.� ��1r �)pis�6{| {j.��2�{j'] +i9 v:j�5�F: said<��hera�Ae��_o�^u��i)~]�J��JulY`�b)z�,q�m�r&� ��b(`=*�)$�Es � ~ , $b%�.'xe�{:Z1/a.#2 ;e�d�ա��~^Y:Z bZ b`�$�!&BZZ� ��_Z�큔�Z� q� 2���blQů�j>(2�{ $\zet|.!u�^ �)��"�.,B&�_Za�][���as b`)8v��221|$\tildeTI2��Dd6z�I�qhat�i6/��e�, &,^�> \c�Nww �eK�$\ttt&N[kEqQ�recurs�[@ 8'9= �( :�)X*�5 (|x-y�0&�H&=�, n-e#�, 2, 1K�-�=t҈\oш��$�5-*)�i�&�5:� &�>. E�dG/6TeU�ignor�F�I�+&QT>)Ai��^6=: �� F� �"W}&� ={QA,;6�9(1 ig�,�� 6� 9 ,&�>ZA0)) >�6)��o�� %A�T_�l"�!��+\{0\}A��Aɘ:� x}Z$\��-�9z�= =�q<-�$;!�*� !�� � cb��ؽF �e*8$T%>%(ec��%�.�e(� 7*��e�Ni��6Sb�'���'.� Z$, � �m�.� ei) �יH.�*F �J/EOCl� ::v] e�U� ��}� X��le�x1��min\]:� � �4  $i�D^��fY<4��.�&S}{$SF�&&�.&9��&WzGy��o �$��36 ��/�.v9� � O���@,�@i?8not} "�:4&��u��'�n:i2�e�J�B���^�n�#er�1�sn�� �� �9o}�E8�f}s�91bi)�i"�lg�� teps�8� saddl�_��$S$��w)�E��o2���Bh$�4% ��5P&� , [�;��"� �;�$C_=h�Sf ~Y* *�"� >U� -��E91�s�Ce"���Z�� %��_i(j+1*Z&`&.$� &�W:,p�%8�Υݡ�2�s�>��5Ib!j�U$M�by2�A�U atis� "H <�$���y!!�_b�*_j_� ky %�P�"ϊ)H�v@2" k)|,�~%A�M�":*&�| %I]6g�h Q��A'�k.�!(�R$3� �v�c�k��&������ Q&�&O���%.]4$\{a-b, a, a+b��e�i8 EI��0/F�' �=�p>x} a & b�. �.�.a6�.!v ���.�sa\E*��� war~0_uJ$&�|m?6�5"�u$a�i�+-��+;1 �e�}0�vH�]�of !3 2^>V�7. Up�n�g�sy�N�x .�0 �X� �*�7W&��a/^W#E%�c�7�_? ut�ML 2.����!�>�� f]U �ZUAijV114�V+"�V,p,�V# y^2}"z��_+2�?�a�(�.�;� �  T� ��lac֥$-OF V-�0 + 1U1��,�>>!�y0�3 �Y��di�rmin\9� ���n*׵ao �!�$\DeltA~((x+2)�W8x"X ((x-:%�I� :��mKej��pm3!q"3(2, 0� sC�>dTa!_U�$CP�@A`Pz����q1�� .Z\0^� ig�5�xx��J$.e *&S���?����%2,2 P3,3x��"+_@�%�ifC) > (U+Q#-)� A�0�0for�)(R� "w� G$Q�S}�4= (2-x)!Z)(a�a3Y�Y-M4)}{2�XjYiv�R� �!�$xy$-R4�Fg4�L��to regn������/{w=/!,-$ be�%��>�xy} (� %^� f�{�hown).eF*.1eo� � ofBf� �^6�0�8 |�"�� nt (e�f�&��J�;� reabl� check�,.�Fo �(2|aF��aN!u^ =��.i:C]aH-1�\/2�] & (<N""3 ʾGE� �(5 _.+5 minu -v�x}{$xy}{$yR�5R2SRm}{$R2Fr}{$r6%-}{$.!f61/2  6�535m�=xy����3EH% :�a%�-|63HA�iA R|({ (x,y) | xa , j�qB&� ?/s !Tm=%((0,2]"[RR�;!d# [2,+2 �)� 0 <Q le 1/1�M��d"w�?! ? $a$�bV_��\{�|y% a, $ge |x-2|/1�M�� �"�1:%o�3�#��&�(h� z�R$*X8!��*b8�EStgU>�.ne���:!�l!���� �.���3�� }}{4} + O��*�.����D!�$), $J�2��)-� ��p,T�Ois.Ivg�s����&0$| C \pm|EnC!�� �V_pUE�l .2�!!DZ.-4�`51 }{2�_2Iah$displayed �3:�A ч\LG� ��re 0zS -�to�0i[%�r 16((�i )�7 1.\]��]y�.vl.l ����sa�7�d�"�d�� !� � >�<| �)�d%(4%3 y�a/\= A\] % o�e \[ 86y _xE�88q 3^ 6b �0v�){x|�% >DiJ��(i� /af1�-2<s>>QM:2:!sofe�xi���a.�Vs� #!�)__$� \pm)_y$ �'B;N�R� {p_����M1 in RE%gA�:exe#\�6< ex� ? �e4 I@6��� 1/12�^�U$ibF>05$y�Q��� �= y�C�4%Ry��� ��T2Rx &� 8�d1^4��I�i�E�A( ft( e6&"/)�o/(�+ 8� + 6 �� 47I�,�#a;T2�y�y�e��qe��16 + 2X�ȁ�32�8x^� �R�TE ���, ^2 -�,^2 = 8e�"@]�nc��^�ge q|��|,�C� �"Mhol�\fK  w qC,qHto"pe�Be�V�-e!ڢ�K�=}% {\)� ^Iz \mp)ҹ}��V �32 x}{yJ�.*h�� 2} >�JRo :.rn�]q��S� -6e"��4!SaC]��| n�� �|Mu"sE|�J�6W Bّed�)_�=) fty�l�6NKw"sE�x$ E\�isL1�D�@H�y$,1k$�0u�22�x$� a s=g�-.!�r"�F�D��$�>i;= a��" �]�a6$2�� pcnoO"Wy/:u9-MY�,�i>�!\BYIn VJ,B�G9+"<6�=A]�iiC1+� }{1-  xS3� |}' �%�B��]i )�*C"�r "�chz" Ae)Mrek_P L(_+: R� to R�bN)�I28�#-%-L">%,�6�Tn3� 4Jd0d� ex�_%�IE.�!�}�R����%(ver_D=B $r*�2,_0_� :ww  A�.� a*�w&�v�r$i�s*r�#v.F�O rpm}�O��:�,"� !\"�;$R$Y9� "�,d�#w>E� hom +sm�9t�ir��4!� �.�0[N~N:�0�wr�N�b<cen�NfA�NBB�N%� \pm( )W�h�f~�!rthick);�#scale6 %�- � _ �?EM�a�Xb��!�!{-$��=rc|._&-@),I��$F��ih&Eaxime�mmra�L&A���Msube��)�eGrA5rver���?preBAthe vB^.�E�Y{��a) ���a�(x�Jm� ���x�+2x+4)�x^2"� �9�!�)�s&� %�e�1� r5}t��k^ :3!�s� =� �� � 6}}{O���M��&}  :weV� .�:AWr=���m!N�c�:mo�.sms o�B2%{s�Dr&" �&�an���#�<�!vD �Ռi��l�s�style)�2"^�� qb&� )^2}x�b� 1 +23}{>0} &�jy[ Rj\\�c\o �UF� �6��yB�R? �N? \pm �.p�6.:l�,k �d���2(det>� �1b%9!�C iJM�>�_�x>>�.�_y�9B (!�.] I_ *w �m� �y�lx:0&]!� aՁpW �pa�Ih��!am���'>8�fa�\n:�&�P�heBZa�N�U!>t�L�Y�l"� �X�<ar�0"�r�N�|*k dtKs���urn im��Er"o�*}qdeg¬py�%m��rigor�]��klength-�of��Ņ u�R"�� a little.2o*���Iomi�K�Z�G��}R%iwm%��-�*�Np+:mi-��.8+JXBOM�6v&Or5�qO)-��_!��U $x=2$;}"�ud�8U"!,:r5>c.r�$>�rOa'�r�K����u�� qqrv�7. �eject "�$Q0���_: 2� *�-"�A�� :i���ʛ�}u[^�o6| 5�\\ v�6-n8.�c $\Aa&� ?2�!"�aq�� ��-A�� m���RvF�Z,�A5"5Is �� Ş�� par�-���""��&�/a�*4c�3rCartespr��.��� 1!-valS!� } N���Q eznc�d"c[ati �2� )X=�#F� 4�� %U-pi^�$: !|g�`mdO�,"!  maA;!�of� all}&]bL)��+)�.m'��<)]"u�is�5rem`�th�"+�� �� ���invisi�W��YO�P�tQ!*3 �� f�i1hh�,st ga�� ^�EIcK�B��?7qu�&�#aA|�*(iM�ce}1�� p~K��u_�c"k�* V�Dt��Q4�$6*K�C� :�@E��{X �tic} bel ^m_\�A�2�� )��"c�, �#t"{vin�� ab�9Xx.In� elf-it��),a spea�&u�zs lowe".lf-�;M$NE, NW, SE,SW����f/1G��$z�0R�et"�4ww(z_k2*i lvA�d unl��$b�r�m"آ$?�0%/NN/;�E�$-%� �J���I�r�p0B�3(3���� psfi"�^*� xx�� %!�*�&�Ֆ ��:�͈� ,:%�}�sJ�Man ,,3��=A�,��� /�t�!�xE!.*.6>a.�*R,�A�� �(sbfaI]���&DCPi�{R��`<I� half�Ystg�<$�ų"My$\thetoI�uG����%l40pi -\arctan(\ 6}/8�!A���OkeO�%Ha�S�E :�>?�!=�ISe��� a5S �6�P �w4v����.�gUA2��q�A ,�=*���A�r5#Er���%M $-9D�Aq slop� b�a1��$-1/6 < E <�5�"� N��� -?� rm ��%o�, & !S 9el� {�;�rk����-"�NE�= . N��B� ay�|/(k)�-�SKI*beqK� n $1hx8rr~*� �NIg��def�.��1��%.~� ��=[% ~$zYCi�oy}�f�}�<):��.� }{-2�)2J �7-1���!(�4I� 6�g�� �&11/4zzn"v�E�CM�f zr5P%�� :� grea��th%�/9����"msteeper �ӗ6rd2��a�f� U$z�n�2a��%��6�7#b���eiT1,������w6 �`z^" ��#qXB} C�a � $I$k�*'} ^k(z�)p��A J $L$-2Y�}� 5 igraph $5�\�'���a>&�j� EtI �R�ndachat#'$5� $V_{_�}i�xG2&L^\�M0H6rM�j%aY2 �CS � �^+n I9-�,3#��end� �qn��x�!!.��%�< BMW5�()~���< + ���� ,K�����)B�NW!NE)e7>�Ҭ�S,�'�C&�$pus�_toz.Ɉ:��( max_�&� ��!�4 ;F"!} yFi�morUL%9$� em`B{�� �&���q!�1���M/���%�x�%Y�)�a�u&in [xSq x_-]"'rphi(x)"2&�Z � �-U�a� )�$;�A$ phi'�l> �U&� A�� alog &�'�"����ow �-�j2 �`-^-a4� 9$��A�ar�r)c��AC�� S@_ L<%:)" &s2�):c� 8& h2�).bon�� +U0��( still hold�s for the same Lipschitz constant but given a wedge, /J*0cannot be tak0�rbitrarily small. \proof We prove K$statementsvcerning�Laction of $\ww_+$ on$upper half � I others be@Tsimilar. In order tob trolFslope^images <$L$-flat arcs, w� ceed<�followgclaim. G%"$L > 0$%",re exists $ap such that if $(x,y) \in V_a$�hn: \begin{enumerate} \item{�heigenvalues $\lambda_0$ and1$�D%/c,$ satisfy $|6 | < 1/4$,: > 1/2$;tQ$associated �hectors $v_i$, $|\cot\arg v_ YL �|\tan 1t L$.} \end.�\Indeed, from lemma \ref{ 4:signofomegax}�! formula �$ iIEc!proposiEDR:whomeo}I3entries ;$second row@Y tenE zero when-� sA$p_-� $(1,2)$\0y is bounded !��!1.! largA�$han $3/4$.A�@a suggestive nota�, \[ )� = M0pmatri!L_1 & a_2 \\ \epsilon 2 %�3\] has-�E^b\frac{(P+<() \pm \sqrt -.^2 + 4 |}} {2},h%�whiee � mate��n�io. T6eM� a�;v��i�~ east��tor���S�8 \arctan LU�0E ��north:- < E0 piA�JaOusŬ2zis��by �%�$�灔 bset�(itself. SetE�$L = Q���$I2 = �th �urn6!a� �(r��farU�!n��"8�D�1�an5!y�oJ�uT(still holdsA� seen1]�� �e�-8ndpoi�"�(i6��lre!7 �ft%E�12A>interse:�2S�)2��m�(_1$. WriteAա�=qD + 2(m)\pm)_x xAi� \pm^2}{(12 )^2}I�ake6usoI�$F3a1.01A�.^ < 0 $F�> 0.1$%�$ we learn eE$� > 1.05$, NX8. \qed A {\it 8$ sequence}!$a fun)[4$s: \NN \to \{��1\}$ ax(s_0, s�s�@dots)e/ e di ce betwA%twoinc:t s $s `\tilde s$ is $3^{-k}$, wh& $k%�A#& $est numberY�$ $s_k \ne K_k �re �(natural bi-Y��morphism�� (et $\Ss$ of��2/sE�(middl� ird Can�� <Kk_3 \s�[0,1]$: � �Lto $\sum_{k \ge 0} (A�(s_k)/3^{k+1�I More��0ly, a closed X $\Kk� a}�graphQ�%Sa)��}c it � mptyiZior (�4induc� pology inT)%no isol� i�0is well known� �!Ib�6a� ifd only �is =�c)CSsa�^ z_0�JRb �$-2�$} $s^{z_0}%&x ,_k = +1$ iffAk Wa (M�z_%��? ww(z_k)$)� �I } \label 4:antiwilk} Let�Y�$� a�����  :achata}. =�B��be�̱�&�!��= = ��-�NW�NE faces��eM�Xx \cap) kis2�:eap�'%k!� 6x Dbij�� � $Jle)ۡ�iQXxE&\ disj�W unE� L� ��s $f_s:a� �r]��RR$ (one�H each6�a�)a�� $y!t��8e $x$ coordinat"�uniquei a.F��%�� y = ^2��.� P} Numerical analysis~s, �xample f_{(+, \���I}(1/10) \approx 1.70831765759310579903646760761255776476753484977976. % 1.�829816205018832. \]"�eQ�^�l= I�R�~$. bq' m� _R$.9 ,\pm$ contain���?y?For ig�Y $s� Z4, l� �1���� �eda��{s_0}�_0^} and, m:.Y��]JX XkXkXk}��DefineI�vals $I�$[a_k, b_k]�� �40$ (see figure��fig:gr }E�)+,-,-Q�$$) by \[ I�V�0'quad  ,{s_{k-1}} \c� 1} 0} �\ww^k I �� W �}[ht]cer 8} \psfrag{a0}{$�11.22b9b_0.9b29b9b29%3 0p}{1�0^+E1m1^->222r}{$r/p���W{�.Rww_l epsfig{heM(=30mm,file=� .eps�5Wcap�{ 4size Some curv -�0i$; schematic!�XNV�,-� Again5 �II� �T, $|Ii#0| \le |I_k|/4J��>�nes�fam�of %i"�_Eo�hsi� .$i�Fj^ Thus}map �� ��REaɹs"��  >��[in�vUd�}inuou�h& Rg:$. Now fixJ $. Si ���=��� ��������Y d��d.& showh f_ $")I"�$1/ c>Sa\by'tradi S y��� y_2$ (9|f_s(�- 2)| >K}{ j} |N- y_2|;�l�Rthroug�2 s $( K 1), \ 22)$�� � t 6�> f�%[� �re �woIs?>�A_Y iO%�E��%6\ ��5\� % � previousm�!�s,a$particularA a� ; is� � �One�3counter-  %a$Wilkinson'<A���)  $T� �D$\pi$-bidiagonal %*� s %��\beta_1^0I  t32629744197382063037437903036647833732106599,M�� P2P= � A)%Iy \pi(�3$�pi(2)&32$! ,explicit-� $a =r$b 7w[ T*  �gin"� %jh401266653& 0.9815825262&0\\!-0376746030$1311405663 .D1,002452062043��s�A2� raA� thin,)�XHausdorff dimension (ats�]a n��borhood����) equalA $1$;�doEV present a�2�fact.{ sw��.�a���smooth�� Xx_s!�sI� 4, parametrized��m�),yy !�e}��?n,\ww��a�_{s'}$,yre $s'�+a�$ shifOs$: $s'� (�fs(�V s(3)E {�r �m :XA�r�}� � Nx_0��Z in a�a���gve� !��c, C$ � �o� $z_n RnRn� $c�G n|^2�y_{n+1��C$, i.e.yg vergŵ z_n)/�a� strictly �. O& hR eC"W�Xx$��coJbisYcubic6� �Rec��W�� S||&�} y_nb� �� RJn $c_1, C��5r  |y� y%dC_$ !�;6�a� lso,�may�M �1/2�+ Vgəa�Ŗ�G �c_1}{2�,1� �. �2 �A]� Y firstcs. I' limi!int%�i $pEm , 0)a�xC0$�E1TsJU%@>U,�Ny$,%���i )2r^��Thi�llows� á�-] 9I�m�j�0even near $p$��!��$e a Taylor� a�*jtheorem  :�.����n� �easily��L% \bigbreak \vfill\e�o�N thebiblio�y}{[10]}\bibi�Y�� asph85u\:GE�05-13�987:bNT`8eift, P., NandaE}):, C)P,Differentialp ���� e y� Y!u blem�LSIAM J. Num. Anal. 2�-22�83.+ DRTW6�Riveraa�.� Wat , Da. A monoton2 ypertyE�!�-typeu5�ML" � Appla> 2, 463-46i�12�emmel� �D W�pd�-�Lin��AU�u4, Philadelphia�9:�q�}{2�EXI �Q�, I%ae� Rev. B %�24-192eA746�FH1:\E�Haine forus o�&�$G/P$ hacific!̉q14a#51-29%�%-}�FH2vlpVari\'et\'es de drapeaux et r de�� yZAC$8, 545-556%I!�.| ried~I&% %Ccohom ��an2��Xi$Proc. Amer�8Soc., 98, 363-3I 866_ Gibson}{ e[yS�)W ribuiE�=.Gse� f tr"��G��preprint, {\tt www.arxiv.org/abs/math.SP/0207041}:� olub� , G.��Vs!o�U C. FIpm��u�% �John Hopi�DBaltimore, MD 19896sKo' }{ , B `A�sol% � a H .�%(�� ����ory%Advanc�&I!3��39-33e�7��LS��Leite��@S., Saldanha, N.Ci�@�{New i' se data�YV�9� ~�608558}60L>��� % {P"q) $by polytop�)2r]!�m�jug7%< Lin.�� g��. 3�223-246���}\(Moerbeke}{  A� ~vanE�%�E�umadJ6xInv�S ones)�(, 37, 45-81a�7:YMoserqser�yj Fini$ m� mas� �"E"�l#��influL %�an expon�al pot �<: Dynamic system'Au%�a��c%Is, (ed.� �0) % 467-497, A; York���U�P!�Pal;J)�}"Oa�{HAcz �+s%) chaotic d �s at ��,clinic bifur �& (ambridge Un�OsQPress�9!��arleta� a� N��!�S" E�(��Pr��P)8ce-Hall, Englew�4Cliffs, NJ 198 ]Q Syme�,�S��4$QR$ algorithm)c� ingi�h.A, nonperiodic2?%��&4ica 4D, 275-28�98� ���� � {Hamil\an group�-sd al� M&}��ym1D, 3��� �me�}{.�%cT% A�M"� of I*q T�"M�� > 1�� 1-99�%8 �WS}{&_a[ H1�� icV� OxfordRU6A� �>1bigskip.s {P@arindent=0pt \par- obeyy$s Ricardo� ��Dena�*o9Mq/d�tica, UFES Av. Fernando �/4, 514, Vit�r� ,ES 29075-910� azil \�� Nicolau�1�>E�Carlos1�R�\'z0a, PUC-Rio R. qu\^ S. Vi[ 2� Ri�LJaneiro, RJ 22453-90�2�rsl��4@cce.ufes.br n �\@mat.puc-rio.br; http://N6/$\sim$ 8/ tT :? }-� docu!z} A�!�class{l�/Lusepackage{amssymb} .< href} \newcommand{\MR}[1]{\h5/�ams 4mathscinet-get�,?mr=#1}{MR #�-2OarXivFRfront! 4h.ucdavis.edu/G2: J�Dsidemargin0cm \odd:(textwidth16!]23op ? -2cm!1.� eq}{�$�2 }: en}{r^!te}{\�)arrow:?(Phit}{\wide�'{>dhh}t:=$giv}{\,|\,:boxbarVXX}{{\�"X>hFFFre. SS}{SAh. calpha}{c:� Irho}{I_\6��{/0:mm}{m:s�ell:reI7mbox{(�% #1})�.�rem( \rm f,lb +Ic.Lb2K boldA� $#1$>wprob}{\ bb P:�exE: lal}{L^{(0B�n] @N:@NaAPBbbBtoa��H\stackrel{a.s.}{\to>�� ( d}{=>#�� 2&.�>* W}{W:� V}{V>'hf�!� $1\over 2B]driftA� tt d�defa�pf{\h.$ $\Box$ \v�( 0.5cAU def !�of{\no���+Proof.\ K, \Lev{L\'evy ��r5}{\E3t %[se�]E�/�4}[ ] =Pro27�q65D� 24 corollaryF3C22le�1�aL*��Sttwo�eft\{\!�array� n\\k�3 &\!I\A  ѓ(} \title{ExugeaGibbs��p�  Stirlp tria� !- .\neq 1#;�possiblQV$-1��%�3f�-"6!al< plex)�C ifX7�; trem"�$Q�!) ex by sol$6%.�9arK blem� &�seJ. I���#we$�E<Wa.iscret�-$-Fa) <0$e�s$�&� $0#4�/1?aK0)?e �-$rresp�:�- memb>=-Ewens-� &( B� �xi�$( �,\thetat whil � $0< <-���%ob�, Hcon�adan; 9X-U� �asympt��A�I��block$m�ases�;�;iI5y.�*� �� �,AMS 2000 sub�= ssif�.} PrimA$60G3P60C05. \\ Keywords: eR�s,6vtwo�i]-�,�.�,""2� �@s %Poisson-Dirich�-.>2�\: {IntroduG })#i} By aB�!m!{���4 � $" N}$a meanF*� �5%�=(%�)�4Bzmi�ps �\:=\ك n\}$.�<�Z�f� rang"�0 X�~�Q#��- ̡UUv|p�8to m! ��"�1 none4I���V��cy%Fat }{n}ŰuI2PiM#$���)ar��P�� $n+�A���W {\em2�.5�2%.u.1��n^4in%:ntQ%(erm/��>4par L)��\,1�#��denoteR��!�Q-NA�!����.�[k]�<B BirC'-4s. &� ��}Pi$�)� $$ U�P}I�=�"�, A_k\})= p(|�v&, |A_k|)C!hI/*� " ,"p(h := p h _kRof)�co�s} P?=n?\7 $n$,&6% $pE&&�N5a"�>[J��=IHk!� Nno� A�!��� $p(1)=�)1�,ies� ad� rule� "� add- }=@=�8(\mu: \,\mu\� row-A}p(\mu)�Qi(�sum�o�._4 $\mu$ derivedq�;@e�ei & incrM$ng[ ar one or!apQ $1$ a�$e�6A��:5r$.��ie( ce, H81�=(3,2zBJ+��-A�e U �-4$ (3,3 /:3 2�B,5 �5a) is]o $$p 3)=p `+2 `+ 2P.$$ AY�!��, thes !� !�is`9� an�8V72�qI4} (EPPF). Such.�;�0lU termin�h}"d laDa c"' �2�B ��6��Acc?7g_ a Kingma�-�}pY box:��3 ite{jp.bmA., �97 p03}, ev� �2�5��:��.2����a�struc��b ���cl�;��Z6�;,Cf+':�5u_1, u_oCg+��A���up$ rm $*<�n /X '�xZMv���Z=P� $i $jdlo)b��hG�.f; $u_=u_j$ f����%'op�?te�2i�O�@ \backslash Z$. � A �guished 7V�sA��V� eA�^� 2par} p_{2 }n� :={(� + 5)_]6 \upa� }� +1)_{n-&}}�0d_{j=1}^k (1- 9)_�m�Hj.0VZ$$n=\Sigma\�! 7)� $$(x)_{m��0}:=.y$m (x+(j-1))\,,~6;}=6 1}$$ l ri�r*orials,64!�F�X �.E0 �f ta }�j P��bda�� �t)%"� � �#.� -�<0) $)�=m| A|�^e�$m=1,2mm \,$;�@ M� �^ndQ\geq -�X/it�"er� �"��of��Et)a/m,�casZ=See \��csp�8detail6JxUO!dge�F or�^)ŀfe�@�!?Bg � �~I� i��w4�Cr�6iu ���{7B>��n�B �ise6a��,:2L �*;{� An 2��q����MH��ofBJ � sai�Jb� ��"� som "&.$v��� �*� �"4 � g)*� J" )=a�u.�k �E _j}\,>>; ��$1E�kni,6� n� .��3=�*�INLfi�@wevJcho(a(r�.� 9cV=Vi�WWIcare not �F1ytL� uUz)g)\�eZ�$x i s�G&<=\V_k/c{!V$ a>A1� `��t �0_=o�e-z%:I&�"N"U���wh�� r =�� �H ���?4 �. MU)�� comb#EoE �2Z �;e] J�r��g>T , u� !��9 cripE�\r~�P)aՑ:�L��abt, � $. But typ��a��io��>��_: %# ���"�� �v� Ley+��\ash&�of6�to�3of��e>AK{)"� `E�*&-A asf;ios� k,n}� wa�8ud�J�CKerov-Mk .cra}I�e f� worn:�.�SU�e?�a� !�lyx6�$�q�!��'s8ar�X���F��ts.^�establ�a>_E��!2eprecis8�:-N�2�.+N W�Rll*�m�?e � E�4,a�wW7{ � K? a� �C%��;��&&��O�J .�,��F�"Rin&� 1] ��h�K!:}A�i�=�. z.�nontr%QbA�f����$.���si�m&V}_�h$f��$�&7~ a "�:!����X-�6�)�le]d�H b p� byJ�af} (�T�G� ([Chapter I]m�(diss}). It �R��tna��6et�?be[ia��e%�. A.�our m�E ,�Rd E��@in��o"�:2th"�<{ three �?i�1va|dv66�Z5�� �?"�0[.� �.m� c"��A� :�By-fa!FM� |=m,>e� *�hixJn�m (�'�P�`>� ]0,1 �F���!k��)�e, "�Ae�t Z�= r *nt�o|s)1! A�Ts�E0�]$)ppearsA�""�YY"I.�M�.!�& . � e$kpk}g_�="wb 2��+r*��gO�@z� 2M��sca""��M�-ũe subJ ator��.� itsx=a time. e>� �a�-�z�F �<1$ind�k�Yp�(a�%P[T 3em 8]-[��"RS�basic�s�/T�.%%!exR�#!Ni>L I��//U@ w k�n � B�%$(\W)=1~~~{�for~~}n*a $$C 2$aAҡ BSn5nom0$�� { � |&1,� !""^Lbea, o�:�{A&� rJH(|A_j|}={n!\�k!�'�Tn� Ji!(k {:�K j!}\,B�@S!��Akexpandsx���Z�iI >�Hs�^ }>�x�* @n� >[s. Obseraa��% w ndaw -�":&���s:.- aE��nq is unaffePbymultane�H$Utit�8s oK#=\�WJM^jr�*F�( {-n}Q�$,H>BA`NVAkA e� z`� rouge�8@K� 6k [1,1}=�=1$�*dh>@�excluT � � ��mJ�?��V, ton��%�ambigu�6amoZgeo�Ati�(> ^{j-1}Vf) ^{k.f.� Our�rt��0E� . �,.u�'�} ��$(�p� %�)Q�%f!�!t$ �28of I�f �!w%Bif $b�c b\," �m+��os�dg sfied:��N3 ize}�c[�?(i)}]�>#wa�3W_j=(b-9.1b�R~~j.{�F6ijAPE��+"�M recu��H�rec} !W<=(bn-ak)+1,k}+ +1 �2\,.B�R1 I*\{nP�>.} q Y�]�.3�N =�e3eiz!I�=1(j=jco� t=1(k=n)�E2�Jy)G c2�forceHW_j>0���$.�$, beca�$p(n)E�n,�S�A� 2Cn$ (a"U�bl �Y %If%�J�a��|deU(� m!  ',k'�n'e'k !.neO)s9�%x E,2Cs�$nG2/A��� one-� H�"n �0concluYis obMO. =�� �+=wO�-K]'E2}>o!��b:�IQ)�� $r_j��j/j�\ffin�I�^J*-#�� $-%kxK,k}�jqr*I6~$ɭAe��>y�%%�k=2�g �)�,e)'�i+r�D�/ly j+$i+j$, .Sr_%-,iU,~%Pa� K $(r_���a�<e�=�$^ !\ bj-a�.FU necessQj>�ensQ!�!�aHe Yf bi�).�Ssh%� =r_1E0�-1�*�)-ա��nd �>)�4xje�!�h N�=b2"K 0-ak\,.$$ Inve�ca.t'6�pq� Iq � ��@ ja�].W' :Y���pf��  Twoa�amA% s $aIV $b$ �Kbee \_bɆB� 2��LA\,"�1]$Jg�.E��QA� $\*�^�n} A=df\N:;}{l} .�"��}6 �/�.�1\,,\\ �%\,Y ~�4�9= A�B �\right.\BZ ����#F1JG�)^7 ��Aw~b% lude�( fura��psider�hb>So � � .o<1$ �% P}WgAj T2ll2K � "�-|+�*ite}���� _*F i M�ɢ�2( &Q)R,.�V^�n*�+so�E�2R5��!6&ward �� 1*� �  � R� s "� �$��1� \+�C�coefficiq'�2� ��a� ^J� }2�bPnl$ krB<}>*~~~8 ��~9�&]� U9Zf� *�8 af� "�a.@ese ,&xA��0T]�ammYG, �>�a&.b._ RI�ir"�u �To�lA% ut, vy(72�$i#b�"a\i ,��a c2J� K_!AK>Z�a!a..� ula���(K_n=k k}*�Y$$ ���sum!]�V&&�A�U� k$;. FUO",a6�J�i�B�is^(Y}~80�|-{!&d)l |�~=%}qu��u�e6�)�]d�&�,��3 �+nd vice �#a. �Y�t weak t"�EnQ�YB,"=�I intw,e4"�V ��'s�i��`MI�y8�K6;�� k}*� U2k[2n"x22��%�) doesinvol54&HNus .:� A��2�Ū٩EY.�� �[* K_n)�na2&su��[<isticr��X:T8��>g*.�A��$.{ Markov ch�! A-r�#NtrRU��`D vXam� ���"0. By�-�)V�Ar���V{dyATdiaconi�I��$p) I)YwT!"�/"�ed��vex mix%�gy�%�M�],���&�)�s �Y�. 4 �4phi:�:=(��:, 2�)� 5���?^ 5��]�' 0 �:�or��m #A�X'\eq�7phink3chV� ={({�#^.}6_.E��Z].}�=q�Z &, + <-��fty�Mnd e�:�)� -=-O-m�mgNM- I V<0!�I'6� � >)R!<a!;�G9; 2,m�-!=m!/\downa�/-) m^n})�m �\to I$�-��R��$m= s�(�nAN j9  h?s�-�,))y�Y��m 0readily check��CK. A�z�@er��d4yA��"�-&g \}# a&�"zC:&� }{\rm�X"�7.1$ �#} M6 =:8�-U��by \�\iP},�';e��L�`��Pa��.���E��� x�H�+ �6bA�!��1 \varkappa" � $eS2$;h.;W 24k?$�->�&� )�becom�7T9V�f�*}-ak={c" c_n}-bn.tG$$*�eE �F�d�n�o^(�8�{Eon%/�I" , say $t$(z� =(t+�k*3aX " \V_2�w�vt>-�=�k $�� requi� n'*%��S$t=-m�%��0f,$m*�Byp} ` $c_n�b)6�3b} �I�)�I�mp� �)U.oFpf�&��>$} � ahd 4#�<us��Cy! �1w�� *L6$m V"bc�`� >�� U�b6pa� �Pjd;��e���A�� delt>K A~(.�nj�:*�� oil$.kżm�� "&'��an&' is-*-"2� s�/isy�I�:�-:�BPa!# d�%\(is�%&�dir$_ $G��-�$ $\{(n,k):2\a:.0Y 7$0$�8wo immed�~12�~(%�"a+1� the �ip[f�  outgo�5��s Y�/)�N},�!�U�%1.a�pa:e?cK��oo~b1t;��a nod;! g��a(� }�VWb $p�A6� a99v.ath�eX�"=E} $d^\sumX �s�� %�Os�Le�n�� Ha?-�eA*a� ���forwar�=dq��(=}-1}, +.A %"K"b u�0�. 2 M)�d�:��}�\��v #,\ky5e~)�^an�&�f�$�A� �iar}�!�bi�#.C.� NnAyT!�. a�< $M��-M��zcten�*�$k_1, k"�#,k�B�k_+!,&n=kI�$kGk_jJ \{0,�y . CD���c"�2proa�"�� �/K_n�n$ &{g% �y �^��� alj"P $&� P}(K�,K_2=�K�=}=�-1�$$ AVl�i6I9i�8th divi��M��T� aDayx>�is��W% co-^� "G�{� = j |!<=kpk{d,j}\, q }(j,k) � ,k} }PXf��} 2F = \l�Nb]ŏzu)-~ ,~~if ~~} j =�\ u7f&- 1�0C~~�melse }' . v\r� Zn� �=6_{\V} ("�V}� -l'&e/@FB"��:a�"law嗥L.�s. So we�(y D%�* E 8AO&�By ep�z>� �( {aldqp,k.My, 1young0�� o�<$ "=!en"�w>D=$ (!� >n$)�W�)�0%d��Z�V�a�=k\,|\,:��>��0\, -\�A {\rm���Z6 :=\,Š,kB͞>o�� Cleara�>�>.�:>B �['! �q  r $n<\nus4 us i09>J _\nu�Abullet, }AO* rg�!���� �G&L A� :����!ʉ��#erZO�8�V`:P�+e�G�(�� reJ}I,e��~Ż }2K���'�)$G= V܁c�_�A��$aU"�,F ka-=\lim25C}V�$��c2aQB��C�) d}a!l!��h\�G�nex�ˌ�$d�4i!�]�c"�, �e �f}&y!8)Mgen} I*Gif�%Z�0Y�şJ�a+�z �Ann�:"�)}*a� (i)]����=�� " b�G"U4:�� r X r>-IMo��I�_�~eCbf\nu)$,2��!)> $\6��;�X J`almostA � 1b; �, 6qra&>sAP1r��!�mz Q nRBI� $V $]b� $-&�y�)�-end=�I�6�Dn�[ �XE��.�->�75�n8�t\mrd>4zb\�re}�by �fZs. %%EhxxxNld zF Black� � Kendne Fellg Freedman}��ase&� is m}:��n#Xt^���.Y\A��, 244�J�.m��s $0 $sK_nn�^th�$winc�s�R} -1 +2(4h5*o3 va-�-�"U:xqN!f �'"6 .7��| ={n\Ek��"�6� =--��- kńAE�2�e��Q��K Aif!��2�&�</� 3 e�"o7L(m��*�:��(s�$�T,k}(s)=s^{k}(1-s)^{n-k��#A�U�N҇HL��Y[ Fin�E't) '��"'2�� �U���$da�s�~A5n$�IB�(s)�5��msu0ewse�Z0 Bernoulli�lsId 3e�$$s��ofߒ gs �+sB3�H /n%�) HeO $\#E� by_$f�(iii). %c��a�V��'L6�!IME K_n/b<)9genuin�;i|.�Vfac�o �Q��3o&"��o� nV����&#Mr0>� A�}I�)n*i0�bivar�a]V� )2� ,�4��&if _=%{e9nit`$sc~+KQ�� p0c� I� Kh.-�@{n)IO m0 a@"  aP%'2�!�ơ� za�i�n, \,o;1]$��!%��E�a&�J4�"BK�G�D�B� ��7/��qla ss�-o�m�ly�CreU�of�&~�>Xome�AZ�I"�, how�,2� m>s2�� ! `min�'��)��ie�ta !����Si��`thMr��llustr��c&�'E|&d*t..b}*a>D6Wse�#�!��$. Level $0 a&-( $\e�Yset3! A�e ��� C1 Cr f���c_s+"�?^!��18�.RF�2 o@+ 2, bc_2�WI�P �e� d$a_2���C_�2-�#%9$\9)�n).l)In>2�l�exaw~$3$�n�n,�$. Nod�W6y�$a��!�$bG*! �:0e�� +67 �1� a��:%$(T"�Jno�GE&$ ja described� h #*Ty�W.Ev�U����� G$'�1!�Ym��aHeuVMs!�,b�I�s��a, V_b �V_cvL.�1��  ZQ�,�,#�M)�b=(! b_1,A^!E�$c2&zc"�GZ`v�B.&v$��t �r! /" �N c$.6�<��$>"^6�0eW -n$ ��ESI�e�� 5��u7!k$b 8Aa ki5on�26�E�,$ 9$�PSi"��sw5!b%��mi�(<$V_b=V_a/2+ V_c/@Ih>X6�� $\{VMAcJeis� ��:�72I�2�-� $ vi��"1A�*W/�� :� ugh ��dq � I�(unlikl�Isc$M �~ 1��2� �.U�Fu�2�xs��re�t� w&1KM$� �d�ir ��<HK q6iJ"�{B!0regev}) altho�Ȇa,ula�6P��*scarceI �r�)l�BMwe� rr� useful� toolsO= I@OL9v k� 2�%:� k$I��,$*~ k69�&�*,!�!>�e&�U *D�X n� A�ch"(I+�2�2ǂa�H"�(� Vb(�<�Z^�:. B�>W m2.�&� reg}����� �!<:��~}���0 :I��$�c Ʉa!- !6NYo O�ͅ��i�m@>:U=�O.-%�=B9��!+1}&xj-"�!� �!)/"�,\ doublerfu�d, dC�_N t shb�� $v6� "� l* ^d���H �� 1� ��&:�ex�_a.^�]stocha�/ .�} pr.�*e = inhomogen9C�Cv�1T-�d .��v�0d ��+!"��anm+jkp?,ԥit���4be"�Gh ���Je�(up�mab. &�Y�83��pap�]�=re��b�2(-e}cWE҅U��0N noni#a�8%�"]� *�2�!�%Ab�MM Cnu� Supp�A � rueei�h����Q�"�"�"��n� g�m�-, �\, i, I�" (:+$=1,\, '+ & =1\,�� v<. aC,1>� -1} IZ!}!| V= �^? �Z-?$ (-" $6%0}=6\nu�#0Ta&�Xcho�4� �,%-Q%� *�+�&!�in�#� s�&1}2�+1,5�Ih& @+"*, @�&!mb@� /�� /� FN)<,a�u�� step6ޚW+ NRdisc}U��20%( �'4(m2�/$��9ѕm} &,�m�5�Hk&� in͋\X���/�Y, sE�!L��?pvm�."�u (m)}5$(�t} = m\%�)a /X If � �ʼn� �to���m�|%(m)�w'A�'\V(x")F� {�,��3�FY� 1."� E�cal�,i�/ {\V(�\V�� , k\}��A4�r6AllD'U�e+r_nde�f� u�:B�L >m)� %�t6+'z�� 5���&YP<i=m)AEN� E {�as~�t"$�%�.Aa8#Ea�i�:� , $)�is5���F� &a- .p "�j$m��veno $�k&�)w�+��9tb)�� 2��@�AAI�� �$��  L�0V_e^6� y}<6i�a8 ,,$$�<�b$.B�O9��=] 2� B�i� }Z��yE�� �G�E�opi�Ut�mi=�%�T+� ��lis�&mp�ec��� �r&� %C 3�!l�  �aod!<$k'=n-k+1$ yield-,Z&�T %� Drol�U.�W�cv,$'s %"�O"m"sw&Rd�2_�sGnterparWf)}s"%~a�{d�.� *�:{�f�r5��F�� &#]W=�r 5����k ed `! $q$-:I-'�Me�")p}-M0c�� j),0x Vn��8e.���PQ f k}=q�L1}h % �and�&�&"ty2:�">.=. %�$q=2,3��� �cW bran�`g��� �U�nZ %g�$GL(n,"Q F}_q��e0G3n�V-' ay %q�s subs+yc&�F}^n_q�L%��y�� �&�/~.�%� ll %$q>1$B!5+�b "= %�,A"�%iMz�[how� � &6 *�&&��*@af, olshanski2001i#.�#�N�W<�GT"s#u����U ��- h�v��#� .5�Awe,#jp.def}�&�P=methodJ%(J o�HM2}t��8d.Q�|��%�!��~e@asee2,� %ɍ��Uly",Vd� =D N� cont} "� "Da�AX"�cJJ�c�$@0c_&� E �����]e[) .P#V(s:� �"� ��(lln; 6�s6� .W}�(/c�D = s\:� 5�L mappA $s\mapsto� p #!2QX��on�D �oa� � ith ���$ %� .�"n� ��J� 0� �q\,,F/�`� d (� �JT�Q >ϴ&A&l,J* ��!"%$\, 2x2p -�." B>�J��0 !�F&$� s), :{n��`c&� �&)/� .*%a ��F�>�6< )� s$ %A�a��1� %o :.  %�F�v!��%ޱ%2�3_{v��v^�%A� %��]�%\�(��β%��A�2�[(��m����6YZ�%�"3* . % .��H��&�(it"k (i) p�BV J�iI�$J1i+�Q� 0�16�& ��}>.�/_`+r` >s+��R$ ��&��� !2de&}jc�J6gȞ n=o(9I"� EQ� ER ^�,%#E 6 \�>�by$ =& � lead&p���D���A�": ; * &)`ti�g� v} A0rAe�1�V� F�h af},!=6��vR�"%"Z?9*�<(=b_n+a_k\,,�2!�2�@�) h� i�;2�'.[ I?Q`X �.SMB�})�:\�&DT[� '%�Nw&��IL� Re++ $�[\N��6(fu� ]"S� mayae7d in  !ways.M/,�"�5��"�)L?)_b"…i��x >�a&�aL  81Z  }), ��s BW%� =�!� $0w\uYx}�ak�Xn 97�gin�8 (xk\}\S�rm� (for}~~ 4J-�"OPr�.�$x^{q��!�,�a�D"� que�}�genfu!eb yD^k\,k!}\,(1-(1-x)^ ),\�J�K� \,0,���*�%-~!�'!��< due� Toscano  %�e = %{� �^k=c2�X (-1)^j {k0j}(-k / )_{n1�0�n�%$$���& N=-�se��he&}�i��se�$K,!%� =0� �*�9�a:AQ ���a���Lah6. Alt7��C,ar�e�d;��f"�?A�)s2LC�h�R %�Jee��a"�� 2�:Je*�$�A�Y�]LayQ�StӅef��R�n?GaUm}��2� &=& I,1=n_0< n_1<\~* N\ z�f�{M\}��j^{n_j- �Vc,_@�GZ� e1��F�<*�c�a� a��I��Q�Xw��6N�dimbad}E6�%�rE \nu-n+1\\&=��IJ{� 4=rm~~~fSh9���!-\en A�T"�� /= /$K0�,��m+fB�60���"{tsylovk�EWt��^j2"� q�'}��a���a�}N��:#$G��a� <by�c�} Q/.+"�Y )�rec1} \ Bkq-�),yF�f�is� ivalQLtoY",@� � regimes � v9N $Mpb_�&2x< �N{�R2��.� * ��   #.H"��+��;BV� }= �6B #}/B8>�FlX�ms�o�(t!/pursue&�ci�)�M�J6��Np"9 type�5ti�*m�be��!�ei� ]lF�NZ"�0Z"�f2 m%a�^u]A��Z-t$�#5�  1$�Z6 vn1}MFgA" 1}= �u(1\bigg/n���~bz ��E)͛j=n�-�+1\F��"�-�f.j.�-b �bF`��.� %{=n n\\ bw�=2z 1S I*i B'!�$�N �>I�J�!1aBB�E`2chJ�gL]�F(H�seBI;dRly�%�)`%�)2 =-1$��"�{ra�K P !� �=��3�y*� aÁ��V� f�-1�>-1�: m-1}"m��g�e��i{&�)�1l�&K"&�6N:.F���Z$m�s�:A�$m��tNJE��<w�v^��6>�a "�� D&/�a�y�Kϛio�!�(\xi_8i m)^U��7Q s�$ ex $���� xi_j�&�.$5*S&�%25: eBs)��(0�=1(�N�4u�A>�,E(!G*nV])*�]}�, Nt�' A� by-vSw�W�"a�o> �vIa�)�!roach!�F:Z8A�!on"h��_,�  oguba &C<8<�/lem. To �Brpr��'!D�6$$(k-1)$th-H��zF�=�z )�iNh�.6per�w$\D"W)�Q 5P !V�$(u "� >j- y L $ u)_n=u_n-�UX)uKC\,.�$$o : �v v!O)��Z,A/ ��22"j)^�A�)r% k}= �%^) ƍB�2�} *�k���� �m{"� *�Sxcept� �N :�%�1�� )�{jw 1�tȅO�� u+)"�#&~\� �Mv} C2� }R_�0 )T�0u_S"�a����� u_nZmZ� {q_m\-��>Ŏ}�R��.< ��$q$��$P��x�}�22��M 'ukmAcompu�by �,IOQ )}E�2P6s@-�9_1�j.�5"�d�"1*�2y �$lly: $$ Jb# { n5 n%mA�b72%�~W\\f�i e�~ } = �}��VWa( &�} \�%��ku3e�,m�$��cA&+ �"� !�9����M�A{ 2*�aX/L&�+; fE�8A��A(m ���� "[b0P fty " {�1�dBab{<�~�$$� *� i� eTe;pre�s�,*Ά&2!?bs�̈�&���1Nxcoupon-�ng*�_M 6Q(i*~� var�|Nu��.� �hm*�t7F;N( -� "�*"� &eH0 ����Yy�!b\�'*�: }.��f\log n$rd��i�� �2>pG: 2 �"$(0"=�=B�Ӭ �e j ���*abt6�%�p�׵�"�UL�$\+ +iO +n$�.� &eHB�Aj�!RwH�d+j�� $. %�("��.�+�A�i��[ $.&1S�M9�A� 2X:��'&�d"[&:-X}�rob�<k)=v% \j� � v���G%u %Each R(7�La�n6�3eb9oF!��;}-�m9alHE�R �C' c�Y3�\p/2�3�.r��"�%yRJ, %�DAg��>�m�/$XX\ �1= �$(��I�, XPD�6 %�0or��9�l� L�V!'&A. Exp�E?�#A�.\, %�ny admi��"�]�k ��b"5�vX!Q6(�%=k�&��/[x4Un-1\,�UnAc*�zk^�Ik �"�\,�Z�>� %n_0"�$nny max\��1n:`�=jy �f* 4nb%*�Al St�E� anal )L�"���Pc2V[ 1L"}P%� ng x��%&�%An�o�APg��i2-�A -0�R m@   }) b}� �%g� ng $�1}=^��W6 ),"�("7 E�"��Y\� �#an�D h��e6�em�Ls �! .� J� , ma96 sens"�o�� `ESF��)$�Lf���s ��is 3 s)$'IC�Stf%-��* &�n�Qt/1btV nN��0}�{�)' �) 1+�+, (��#{s�*$(d}x= {(n-1) sF'�?�{Ċs�TG F,ij�01�_\nu/1b \to .�0B�-� c��  �IiN ��4 1�N 1}(0,s�IU5QsCCA dent7�o6!�j �G_��b6�i�no�ear�"!�c�acheN 3L!� ����TP0"y P�" @%BP �:N� �{0��9�����$�{���� ��m]Iof��';s:!�pS+AEYp_{� } Q(MF. �"�~6�r0\,LA�E�� �.o  $Qk*�-�D��6co���n� &�6 d��=N�3d >5F�� {ki8t�at",to Frank Kel;,Th�?�7 Coroղ��.� kerncO)^k/� ).z\ Ju*#�>FNYa�b�N.B2 %�py��a?� 6 =\ps�s |s),& R)�],.&law�e� .jYEBsuYH!�Ŕ�U�s n(!�'Y�hby#0xE�< a Poͫ,' d!92Y deno�"[\S 5.3��a PK$(�� |t�t�V6��H-� ��**%^�P��s8par�1g f\B[� (Mittag-LeffgR.��-�*2+��.M�ao��)� x^ D y(x)m�x=�cbeta+1�g��(� +1)�(e�>N .m�(k>�,���G��8 =AZ� Hn9v� { �5 �n6�k)} \,n^5�\�s^{1�,5sQ�-ho�>*u0$�.�j�6� �;Q�in1 [S? 5E�bm}Q�lo%1!/!��A!��Q3 (A��qNU� h�Gof �2\�} �Q /� ^��)o."!t11]{fl-�9}m�!���1U�l-ul�y u .8= t" "9=�-P,��y��u12�ur�!1fap7��y�����urn8��ilaC(l�*'�^S����0�F���f�cj*� ,�2 $� �Ge.)/)e+ \nu^v�t_G� � k��� $y=j�[*Q_  atF ^wlim-v&�$ (s) �-i6��&�s}= {s r � " �Fs f y^e# R=�y)~y^(1  e })\,��y�"�*o6�uA���ssc/ I}4]�Tf�l (y)= (�-�y� (y��QCF� Sd:�$i�#amLaplac�OansA�"��X$\exp(-���1w�l��� n� �V�t \ � (t)}� 1!n9%%��+y\,� �I � 34�,Ee (66)��pk}m�� eq� �@ nu ��vJ�� � %�in) y c$6�W :� 6�"�8+Fq�8�� MD� A-��* en�Am "%-:� I��\u�whgy Y �6�llC1n9o .  ���&U$�}�� FA�H��&� 0)*b �/"� � a str����q �A� rue vG y�.` 0�W�� ing EpF� "�%|]�6L�7i"� U}3&�%� "F"excw.,a Bessel br4�(or�p)�� �����l� zeroGu���TY. 2CBADW�umm�{[��%��%���ig��t��*3 bx�CR � ^ +*�!Vh} (>Xof�OX+7Bi6��"m.� *y�HM�9��a�� �*�>�>�Ar�QG,� m.�K$m=0,"' $2,3�*�0[\,;$6o"x��.W.v�  V*�2r=0$\,;:cd>� �A�Fn:�A6i�\,�\,W#�2.TQd]�&�IAcDql$\!}A�q �baaa��� ippe��jo%��Gri�� O�F�[al `ng k�fA"A�%^]X%NthxXx�a5 s0f\cprime{$'$}AR0f\polhk#1{\seg� 0=\h����4\ooalign{\hide��, \lower1.5ex )`}\crcr\unB0}} bsZ�B"����������`cydot{\leavevmode\raise.41~.�e)�.v�4t>��10A�"���U } D.J.~ A�s. g��, Ex� �A�&gpi�.In�V$\'Ecole d'��y̹ \'�ˡo-F��H, XIII---1983}, vol� 1117�yNW Lect��$�< Ms� }, p��1=�, ring�iBeH=��485. \MR{883646EBbi?�)83b Ta�behavC�5�e‹cs. Eu�Xa)� alM�Diety (EMS), Z\"uric200 �2032422�,BO} A.~Borod�Lnd G.~�\.�Harmonic"{�q c�9�>$0�erp�^&&��2 %; Elec� i �Co"��� 7:Y \#R28>�0. E�17586542�zw} P.~D��%�D.~Fr�l.�Pa��&%jȼ! sTCcf8newblock In J.~�K. Ghosh and J.~Roy, editors, {\em Statistics Applications and New Directions; Proceedings of the Indian Statistical Institute Golden Jubilee International Conference; Sankhya A}. Indian St �.R�O, 205-236, 1984. \MR{786142} \bibitem{dy78} E.B. Dynkin. \newblock Sufficient s��< extreme points.4%*pAnn. Probability}, 6:705--730�78 �518321.��fl-maps} C.~Banderier, P.~Flajolet, G.~Schaeffer !�M.~Soria�Random L�, coalescing saddles, singularity analysi �8Airy phenomena,T� Y$Str. Alg.}�8: 194-246, 2001 �1871555:�urns} 2�4J.~Gabarr{\'o}E� H.~Pekari.�A� tic DH. To appear in {\it.x.} �H\arXiv{PR/0407098} ]@gnedin97} A.~V. G.�,The represenA 0on of composia$ structurer!.825(3):1437--145E97-345762!3Y� �p03� �%$J.~Pitma2�0{RegenerativeZ�}.� zGzF%uK!�{Y}% lgraph with {J}ack edge multi!�itiJZInt' 1�Res. NA+@es}, (4):173--199eQv160962!��@i80} J.F.C.~ King:Y �Mathema of GeneA� Diversity.h SIAMw80)N591166!MU80labelle} G.~L � Leroux, Ergola%[R��(nzani. Stire�number�terpola�u� permu�s)^4forbidden sequA�s. EJet�߀th. {\bf 246} (2002), no.~1-3, 17�95��1887486�o1� }AU.$q$-Pas� trianglie.- Nove�^ @, unpublished not�=�jp.epe!�J Exchangeaa%T(partially e.m�!QF_� . Th. R�LFieldAx102:145-ezaO5I1337249. jp.pkZ�Poisson-M�Z�In D.R.~C stein� � ci!��&� 8: A FestschriftA\ Terry Speed}, volume~30A�� Le� ab$es -- Monoe� S� �(pages 1--34� Cy<al�P, Hayward, California.o200433��u7jp.bm!�^:!�!�*� 6W Brown= mo(��s�v subordF�HBernoulli}, 3:79--9c &� 6654a�.�def2�AnC ensJ ,de Finetti's�orem. %uAdvanc�AwedM{[ $10: 268-27L \ }csp2z&� 6e stocha� p�ss�L1�eeE$TSt. Flour course, Julya��Techni!�Report�9621 Deptb �s, U.C.!Mkeley �OTurl{http://stat-www.be !(.edu/tech-rXs/}6�  �N���Yws. ECZ: , bridge,�"ur%�A0me� 4racterized by "= @at independent unA�m tim��9�%�DElectronic Journala6�f1�04:1-33 (Paper!] 11)�c9!C MR{1690316�regev>  v�Y�ichman�� |wreathAducJ nd g] l�u ->�? ep A4,�m�`CO� 4354. $tsylova} E� T . 5 E�methodI�obtai�  a&- � ".�F�@�v sti��o2 d hypothe%tng�T(Russian) (Perm\cprime%�0)6� 78, (. Gos. Univf 1!�ne{ 66 E!J�� 75w,95, 1607-161�12535喕�-^1!_ G. 1`�=6behaviorAv5]7 1A2T� ic5+ ��A K 5B!.4� 54, �  Gor-R kov6>Gorki!8MR{09042�� Ve} �(M.~Vershik,� .�mechanicA� c2��i�Ns,e;Dtheir limit shapes.U%�Funct.�.���$30: 90-10!�&e 40207,end{thebibli�Yya#0document} .�\4class[12pt,eng ]{�c] P\usepackage{amsfonts,,� icx}2$cite,),amssymb} % >Wersja o��heczna wyslana po poprawkachJ:< w listopadzie�(2 \tex!_ ght 23cm �width 16cm \oddsidemargin 1mm \ev�I.�< \voffset -10mm \renewcommand{\baselinestretch}{1.2} \parskipU \!&(\bb=msbm10 � |ed1200 \def\Bbb#1{\hbox{\bb #1}} Tqed{\kern8pt \vrule he�05pt depth0pt � 5pt} kdu=cmbxk( \magstep2 Xcl{\ce� � ms{\small� m{\medb{\bign{\no��nt} %-� � al{\alpha mgm{\gamm lm{\lambd var{epsilon 7vaphi si{\sigHOm{\OmegGom{\oGm{\Gxde{\delt0 ka{\kappa�� DD{{!� D1�EE EPP PHH H}}�QcA{{\�pALcC C�$�cF $F$G G�6�E�cK $K$L LO OR{S-�cJ JM MN NV V!S�5ScT $T$B BZ Z!�H!���mHsup{\�~$op{\rm supPIa<atImTr23Tr}�Xproofyx q�mP:}$\;\;$��new�em{�}{Steq��(tep{\arabic !.6��ass#1#2�5ass{\va��zplus2��q��(A.#1)}^ #2} 1 1}e�ass}{n theassumpF {(A �.)��$prop}{Prop>M_theob � �Blem}{Le�x thel7"%6�}{+emuem<B>4cor}{Corollary>c@*>|q{R��k;r8$>8comvm��:�:7}{E=:pleuBvdefin}{D�@CDmc�E`�%I,oday{A tit�bf) ,ion--valued *�con�s ari�inn tegrod�i� qu�s`author��rge\sf!� some �6�U %� nextA�!$, $u f=� specif�6 , $W,��El $b$: $�bb{R}\r� arrow $ de�A�6� %�1�.! looks ouC� y likA�ose!�� r �\Z {PeZa2} w�% v�2�non� ar.)eG �e^1�s ha`bee�alyzed�is!�!�Hwell-known fact (se�.g.\ � Mi}) that�to�|J{may be&�ed%u�Vato�C�yA blem�YNs, uor� , reA"� ly.��dea has �usF�aQ� ing 2i]�9t5Z.wboth {� )s,� ?Q62�2C%��"!�4 Unfortunately}�#og�n g (,NG)IP%7 !��!_�Volterra�. As we �lready �ioned؍�2�AMco2� f2��E-�=!�ZME�pr��es ne�har�$d�*��*�!�) �+ such9�a eVAd�Ȟ�to m��&��Z�Y�invEg!8by many people.�kyYXsevO.�.�1j coe�4I� �� ��r�M(tral measur� A%�$W$. Wa�[&to��p��s onl�� Da},M DaFr Mu KaZa122Pe}��1�%+ for mor�bA�  se �!ۥ� rein. But���ew�ar! 2��=�F � � ��3} de�e|MB<Aawritte��o spiritAi}abovey] ��haiE�t�� �is!�m. u"(k X�� al 2lia� ll--� edUaP �� 7MHpace $L_v^2 = L^2(�/(,v(x)dx)$, ��$v�$�� followY����0d!.��� j� o)H�O "� �2�J��� hope�results�q�^��� w�bMJirs ,ep to��z is d�,. > =t �:one-dim� onal case�*tk re"�+o5-.ZA�ga�*� �Hs $d>1$�O�:! �8require develop�� c5anad$to Fujita'��e�Ohigher �� Ano �!ÁaA.} not� done~# D'min� �6= q/�7 �>!�n.j! H2} u(t,x) = g(x) +&1 h1 \DB8 u(s,x)\,ds \;,> $t>0�4xE �$,�m %� ��a�sJ_ FrSh��E� Fu},� r�ref�(c��).� &AU2})��usu�#�i!�escriM�* \ueF in ma���8memory. Very im� anA�i0� �" ? �� � ScWy�neA� $!u!�{t^T-1}}/�(\��)!Y$1\leq  ���x �}a}�� . With�  a�'Qb.7 � sjF3NFfrac{1}>�Y_E^� Bk,� B� \F�We ca � � fami��f�s�3})�� JHeR�s,�S���, �%E.91when $)� =1$)��2� :*2$). B7 p�^sMFuI�]-��vid�y K!*�*��2�|�6�� they��pl.t@ to�� an� r. AdA a7,�e�ch.�"m2~��!g0in detail. B�� halla� �"�um%,'�d rec/%��s /���b . Let $S*� )� �� @of rapidly decreaR8 !C([0,I );2U)$� R cons��ng]:��� tinu��O $.i$. ForN�%��mwe � �N $$ q� l (t,\xi) := \exp [-t|\xi|^( \,e^{-i\pi� \m�(tiny sgn} (B/2} ]��m~~�f ~~} H = 2/M�#and!�{ = 2-#.� Ie&u ň$ a�[ ns 4} � 8� �u 2\pi�k{- }^{-�}B  %$x\xi} d\xiJ^�q-�B���a��. ] j:$5} \left\{�,array}{ll} :�8\geq 0\;, & ~~t�j(U�), ~~ : � ~1  \1 sR6Sdx = 1^r � z . �u} i.e.\�ya!�5U-U�A�j(6F=�xt^{-I}/2})\, 2,\&�.2 J4�>�E�=�x)}01,x)$.\\[2mm]�~us ��ArB#5�+ � 13.7.��Ja�at9Y�g��.0 b�gdp�2�$.1h�. th.2.1} (  A� Fu})���xyN�� *v 2�aa unique����x)$"m $$ 6 =m)�Iyi*u�Ii�n�g(x-y)YBt,|y|A9dyAa1~��for��*� <2iM}Y�,2}\,[g(x+t)+et)]\,,JQ � =2�k � qJ $$I�)� H�, $q H}\,}�|x|) ��}~.�)  @heAQdN��R� T� mean� E�isG5 ��al^ of5 oper�5 ac`���i@al3 a A�mu)$6$� *d.��Por%&� ���y. mto�Ru��,*� -�<2��:�$ r��*q��$nIq�eq7} am)� &=& |x|^{I2}Q}��e'[M�\pi i! ���x)Il]� \no42a� &&2b�- ���I�e�( �f{= � \{ B1�si�) \pi)}�60^F� x^2\,.r  t}}� 2 M }+2x^2 t^  > cos � l+x^4}� �t& (x\n�)�41-9�)�&(x= 0)\�)Q �. �,�v��{3mm}��! ���2a} (# 1.4:�>�Y�RQ�Ueq8� cF^{-1}[F-�]A�=-~� %{.���< �W�W$ JZI{E�(}�� (]�)\%+22%X�rm��-�F/ $$Axy� $u,u,a$> �d�E{(7}))� N�co� cor1a�F�;��8�eNe5�)�)-��-x) ��and � >F1GBFx)It %:�� �-�3Q9 �6�*XB:�X*n 2$ q:���!o<te!�\item*� t���con"a D t:( $Y B�. bXtakts �@ata�N=\pm cm�M0/2}$ (maximum $x=0in* �B >0�a�sddDi� �ټi�not� else� �J8n� van>7 r �9E =�I :�2h(C�& {\em 8?�$�& u1} Վ By��� eit� 2}A2�&�J�#T q\�� �y*KX2�� ���_�B-�ZV�UQM, za��f e�ed.Y)%T!9R2�� w pi�7 illu�$�7� .," (figure}[h] -m fig1�SX.|rotate�,-90}{\includyphics[�.=&�/4]{inst-fin.ps}�6resizC 0.95*}{!FQ{2bum.e; ��.�caV*�B�O � %Vl@!1��[!���pL%� "� �mk=���d�"�", !1 �5iDAY6% y/2��Ee06i�sL$m>�w��$ \m  Pr}.us�icA�� �EA� view �R."�ed by(��f�s!p"� $\va�4G .H�=%�'= / e""G B\a�/#�4� },~~:4^d$���&w�not �' U.[)$6�!�6= $�in F.�la�A \xi, �\r =5> � #$A{5}BC . (IA�e�Ulj!a�ec !�a2� �$!�aQ#5��)�$"� �*d%�f�$.)�'suh$(h6<,\cF,(\cF_t)_{t\�},1iP[G� Dte�l��EP. A( A(� Awf&�+��+. �$. Suc�=� ~�C'��,! i�e�s*o%% %m:��n&�3"���&�&2}m+F� . Shortly� aking,�n F��16C0[� the &@��e: *� � � yv�U' W(t):�Ai%.J)}� real�-�;"P �p &�(A�A�'M$EQ�J�6ps}� s \w4$ t\,) , m * 66��$~$$I�, wVll�xe $W_ �'.O9��he)x�� correKI} wI� )�is�_%�k(.Y,} �.6~-�� WO���H,\(ca�Op-2t ��>� \,$ $4�3��N ula: $q(m�,e�)=Z�)��*a�i��� \,,$�AE�\,'�:�.�'5"�!ds, %�r�E BoJa} , E$Ÿa�1H Oassoci.} q$. � cruc1r8� E+oLMJU � G1 CA�$}$a� play4!JHilbertM$$\cH_W\subI@F; �Yr�:dufTp.}:RIG�. Name�*Ew t$K b"�F�  ��F���x6�y��[$C$)�� $$ |�@� �g8|\le C\sqrt{ q(E)d�6�!� norm!��is"�%mM���"_{%p}=�=_{_}�^�} { �2�}�"��S.aU*% AN� sh[-take   in a:�$Ha��#l3( beddy3toF�\,.$ �$L_{(HS� Ar,Hp$!�IA8M�-Schmidt"\s.]U?irH$� *� \Psi嫩�2, � $$-adapted,�.{HS}(�:����%��;} E�(�<�7|{(\s�A) |^2_{B�}d  ) <�&�{�? for\a��� 0\,!� B�T�'Z�Auű0^t.�dWu��"R" ge 08x(b��fi��FM�:d way| J Ito}�5  DaPrT.y ��-'.� /� &y &� � 1[ . � � q ŰE2�'!$*�'�<���q�"M� "�p3K"*�? 1.2� �T"A>|xi� lo�"�(f�onaCf���(u�A�;erk$u��LAP(>�,1.0FO $\et3 (v3� d� .eta�0�� = � % u,v!j�z$AK� j*����( j7;� C����MS ofa="Hsx:.u=u�l? \cdot , ��� s ona�1I<(�v��!Lisomo�c)56 �>9�@!+6�j� YVj%3` true���9 ) 2 \rho1�/$>�1}{2},~�#1}"o(U�,!�n��Nf@ T2� int}��R�"1})�J�/eq9} I�(tu+�3"z �/*h?\,j?�q}���*�@�Y&p "�C)�� 6� vari�"L�q�b�u=��\U�67,y-x).@,x) � dx.e %�<�p� $Y@�..  ,x,\�J))$, %�F$s���(_+\cup\{0\}&$:,~ F7K@.� @@nE�_v"� &�  $(jJ F}_t&� �ss_ "_� U Z � 0|t T} E|u(t)� ^2_v} <�7�$�Q.��cal{X}_T:��V�TB)� $b:~9J9 a>�@i� &3 �%�r� !�w "��H>�. A qu� natu�(DGpl� kAs~ LipschitzA� �E&1r"�-E bf H&xR (H):?! ~T��=�O$�L�50$)6%�$~�+ !l�M~*a�8 -neg-aI+e�  mbda��Lebesgu�;<=n�at� .*� �&�U�J&"3P %\parbox[t]{140mm}{ r*is9n��previouts�% ` n % �$ite3:& �%!n*�S(H46valen�z�)egp�p:�=!t��#-}.w]-OA>ul7�NC1 _0$ �N@.�9��v>g l [&�F $p>DiracY��(�>�)k�M �O/)0� � "\ �;,Z �i}kb�^� `�=a�e >�holds. 6�4!Nz�$"� � �� ".�'>*�}{�2�� ' ]�1�#�� o�� ^0"�*h .���_ "u \y i }��S� *� �Z�idcLs�) �M8 {-2�2q38eq��cv'\t'�<�)�d�=.� )";�� �A\9)� $%�.� |\psi(x)|!dx)�;\; �� {S)�.~1.3*�_A!��$� �^0\�et H$ B�9BC_b:���5;]1�>�4 ^R(t6�4%� u�#H�9=.CE��K 5l\{B&-l685�+ & �0~~�0&l Cq R.0�(Z1> Re6nd:�,�-� R\inyu ��&t u�]aM,&{==Hin=��!�9oZ0U�� &�J(cK_R(t,u)\,�$ \stackrel�N}{=& %O*(u')-�Vp$�7,~"pv�a�H_�. Cle�@,^>�� Bu�2K \,)2�(dy), �,: [ $$ %2� InK"��"�sh�}1FA�)(� )$ �a.�^to ^���!�..�4� 3 d�[:ac�?�;�$� FQ=�5} |9V|BIq)3$eq C e^R|u&� �.q4>�,M�CE��&p�r�"��_��>�9`�2�atJT95]Mext^d!]�ar�.5�a:;3-c�-c9zofb�s >fC�OF�Aw�3ze�WB��A"2A y)a�Xa�d in~A 9}):n��@I^R6ji"0�M a� -s)*� �M =�eM-s,� � )a&>���!�KG" 5w$L$��D lfil�"d*M0�/�O guar�*�mg!E%/11� �*.a�order �=b�it�^�M ��:C. Inde�Jif�7Q�M<-]d� UF A��f% ling�y}�B�3)� &6(a�9(t)),�;UP�FNH:��V%/�U�+"�@g�gla�(u iE&h9]sO ����-ead 1g!e)e�2*}:k!1�our". �e�F� C� �eIn�?Bv(x-z)!�q C_v\,��\NI,��6��65F��;��2 z�I!�� ���X(lem1} A.%�M��ќY�3})9%> fݫ4} (.�)*v���%�Z%y)&�9�y)' Z* �^� M"2,%�ll $~=q a�$~ !::�m�.� $~6�;��v~ n��FDa�� �Ee^R\, *WJ�%�!� g[ a"�� erty5�5��*e5n�{-R}^{R���Y� \,}A2�\,9�B9;,��MNu8f614�* �*$�1�it�]enough�M�(+plip 1 rm $n��!�N ����mLF+�\hf�# $\blacksq�& $}\\u�^6m�cora(!�Q�~I���H �a��6gin L(EV� ��a )(� +2� , $$\:T!&@e�i'\, � 2� !���/C.�n, A|:�a)2�q2\e0F+Ge!` ��4 u$�&YH1})�>aCB}�0-��&X6�.ar� 2� �"� �.  � |� ��B� !�2�A5�`����|�&� �5mm} N�Mlet��� �.�$�ie*�=�\!�a�Xeq17}� ���d�xR�N� W3Z� &� �/�" &�A 17})E�eK�K�:�=Fcdo� J�  a"� � ?�Qsf] � � off�"B� %�F�"LW^�� �S�!�:3Q�9&"� !%ar�9O ���5�(c5*�orem "� t..,���lem��2p� BY� $\{f_k \}�Q�<n orthoh%al basi"c)v"��n,:� �N�>sum_{k=1.TG2�f_k�� H� \m: BF6{(x-I� u)(yH ady)?dx N��!a��a�:+C2z: L'b�)�!��Xted%%V�,A_ E�W*?* rick�i�WA@LA� R  hA�� U~8��nm>4K!�P�, �5,  R��It(� 6T$>�!aJ�F�. ��dIA�� t!*��>>�re�! I) N�u"��يj��Td5["to�- i�kV Fou�~ t�y!qe��. "�8*uf_k b�% MK-w �d�~{Z�1uu">z�%�s %� (�,r�it�:M�]i%� 8endix0 discuss %~:#6�#��O� d�pparam�>�&XO \B� �:connecaY� ��. }2J�BaϽ03�.I TF��--�"�&s-.� N���t� ���s�8s,1),~sT,��32g ��`,�Qf�%�(6 I*���Z_*�)e���iA)� � �K!T6# * U�%��*U�s le)����6� ApI��o�'a sketch=�of.�nW�%&%wuit�Q�:ze, XB�=w1�8�� �=g.e&;cA�� ���C Pho�X2T�sL!�|\6�s��!�� s* ide�*^e �s �s �LA��dC�h~%�pD�@&}y!4 .�$�  $yM� Awe may-�&:�H*a���2lb���c�&C 2\,s.�M R0*�O'2V (y24%O_�HI�[L[oE (>[^{�P� H� �PLE�) ]^�x��H*%"E<�<,�1*�>!��4 $��-�choos�'!�b $C5(s:a�- ��GOG a}{s} y�)^lleq!i %O. y|^2K:a=|! 0% � }|66�� $C(� � � ER0^{t} �2�}1H xZ�ds !�q A`2�u y"� p $$�M the 59q��0�mi�*b����s ����4�t*�Zh!)��:�T��*�1��E�1*��N� �'"� 1��b&0́)R Qi/)�=F� N"qf)B )� \mu � 2�~~��0^�!@��jZ5:Z!�:x"5D"  �$,�~ &N8,�1int ,E b&V� � 2<.iI�s:<�&Q�{~*j�20:94/NZ)�C� |u +�F\�Eb�$\ rof<�-�� {  �z of �3.3 .T��=tez|���Fai�DeM�Q2Q$ auxiliary� Z�0 rn} 2�036�02�0�� b�(N�%&� , �0w*�% ;�%2A샕 H)I��%�,Y i7 ��&��*�/6$N��N�,!B "c��{$�l_{N,k}a� :=dW�'/NVXmu�(�u_0�$Y.re6�(� �Wh"AT}%S�F!RatVa�re�9 ship�& �=q \m �a� "�Y �i2,�+ru�"�I��l2^)�� >X�~c"�cs#�brG%=e]�!v� 2~~~K !-{$u$k&��L �V�+ autocf(�"� 9 �. 6�`�s�H�ts. U e��i%�-ase $kMa �V�,>>on.� .+� ��\��2E�exa��8 "s.*)�&�*i�iF� J�_=s> -h:>&mET0'�/u&o 1o�/�'.*�/�J)A�02�0}&nd Fubin* �%�Ip1�to� �s� $N���%6�$ ��-E�!� e�2��;6� it be E �Nu=1���e,*�M�*(3P�J�R�� �q>gE"�:�Q^ ��\:���vk,2�.�2� �� �115 n{1J{;5' &�F#92T%%"� ."� 20})�Z-3�Z��mr�?*�i|$�*A? FFf <=0�<-��( $\nu=\mu+k��**6e � a� new2K$2��6J� �Qm"��10n�g&� uB� V6� r6�"3 \\-eQ�U� >�. Ha�� V$��ot($��D7!�;>���sj�q�5�#$V��t�6pG�a&�l!�a�B�`Gj576V�}win����2� 2�2��"��|^2��e\�� �En:v $$ �'^���� Z��m�Pm��`2V"�!�q _B( b:!SQ�L0e��shM l�RN&� f""�8KaAD�seދAI�' lem5}` beSx&xm.�U6��%i�qIk "jNto&�� vxN��;��TEz$D� 1{ al�L��5&Z��$$RrE cNtp�^�9F/ +5�\,u\,* \,,~~�>�a. .V$�'!I6>q.$\{ f_k\B�!kN rbitr� v�~�Y�p�`!�*q;PJKm VHm}G>mnV�Jai�o6y;�+c� Fv;ju9is 2;�� �(/)2C �<U,TV"now��fp /o,oKnyerFR���to�����V,. "�"WmOth>�$� r6ox_:E��D��4}\XAU:�>�9I V (t)$&?F��-�� �)3+ �"[%� !v&� t�>tsw$ly}1e8 $\widetilde{R}�6�#!�$Ra�2) $ (V3����<J.%��t��E��of��!�FSZ,"�/�EEF�#�:n��_srMq�&8(t�c cI�QT�%�!�RkaK)�>0,~t�(*;, *h1T(>�#�-��>1Qmi�*^1 "2h)(t�\,d�+ "~LnF� �*� (t)=q�"�V��>A1R  g� 7dappa=Sl�U #Q 55Y*2.` $xa�):}&�&)�,�r.�f%��5A@"�P���5�(-�=�"ZZ( 6}))."HUof2Y>��ef�t�(b ���uQ$. %So"� Q�F�p&a�B��r:')A�V4>� ��!�"��":�$ Zim_{Ra}<�<}I�::R*�3Y� &�+(t, ,dykaVH �wN;"y=�>: %��](&Uj$. }e�� >� 7ag*c�4�$>,!� &� n� 7}'�(N&ev$ M_u\, M_�A2NS}@-fj�M_u � Xb.4cYK�x Acco:�wC�X'�ņs also�Mj*�< Sk})�'a&ɐ��uragA�q�yg�j2 �\ snu3��9 1,|Fh &7|x|N�{\?�E�!�f�qB^\,O8^{(�-1)/(2�k)^�[A0 P{2.&]n)9-�x)�s 9�]Iehuɛ�]$ Z 6�"��u"�k��%":�&T.��)is*Qx�y�,1,x6�l);b-�{ABCDEF� bib_? [Da]� Da�K( R., {\it E�!=m�$ ngal&�&�J %�m� *`Vx$s.p.d.e.'s�#.��.\!0bab.\�@4�U 999) � 29. �Fr�Fr�%[Fq\os N.�Ctextit���67cFwo� &�{}�YAnnal� P&1 , No. 1!9 bf 2�41998) 187--212:�Mu�Mu>� MuelUbC1�S non-M�93=D��re�+ond� im �rQ8��3)Q1:�ZP� � P}o��� Zabczyk J�to�"�ofinu6JCam�.�Pr��,�2]-�!�!�"gcA:�ton�4�&s %�"�~&�u2!/Banach!�c!7+�.\ Am.\X�.\ģ\,\Vbf 19!=196A�29--148.G�uR�|]�|.�%;$Shinbrot M��i�.~� aY����1M�67) 131�92Gu]{$z��Y���gZ[�+��zA�e:�fA�-2�f }, Osaka a�@�q�27i��n309--3:� Ito]�R It\^o K.,�GitK nd /U� 2~�Fa�a�,PhiladelphiaA�84.<,-1]3-1} .�A)�BA�e(� 6!}in:�vvM� E�3G+T�ir App2~� Ph�end LifeЛ�sV�m�%�0L.~Weis, eds.��L��: in p†H���=&��,A�ͣ415}, 501-511, ǩLcel Dekker, New York��1{+u!@2)@2�@�Z PDE'a�cg_y�in -PI��D*)�U cysi 7P.~Cl��, F.~ؤHolp��0J.~van Neerve�hB% Pagt!1YPLe�;��aCG quiu"�Royal Ne�b s AcademyA�Art�!�Sc)ϡ9, N��(, Amsterdam�02�!o3)o3}��R.3� 9UR Y�A 6�)? RendV�Acc. L�^i. s. 9�11}�-3 �1) 14��542�Mi]-�0 Mizohata S.,����H%+b0a�Fj ial ��},:o\�ka�736�j]LMijnheer��SѪ�tDc*�~iMe����� al Centre�f��� 59},J% um, =�197(�*�Pe]�� Peszat%#� iґA@�:nesU��n .��o6v!F}4 Rep.\ � bf 55��5) 16ڧ6UW21��X��.9 �f e���a�!�ln_�},YWQi����R��7mr 1997A�� �2qZ���2n�%�No\�2c�!�2�m�O .\d ory� at.\�-`11Z 42000) 421--44:br]�m"5m� � �[��HD9Q����c�Y$}, Birkh\"u&$r, Ba\-sela/!ڹ�6n]: o#� } ?b�2��2�*z�[!}n2/rpu��2t�[T1]{fon � jr����sp*��T��T��T��T��T��T��T��T��T��T��T��T��T��T�e��RQ�%w�p�~ #k�atev *N�(Maximal typ��)l:��0xv  \�>�Dm�t� �Rs�?�Szafr-�4a,�=�&=�Id2��/�\{2�hKZ8� =G�"!x,,=- olve'�mil&� ,.�*K=,.�tcalculu%9�~~~K .j �<�4'�<�H0.��<-.�"ya"=�Gt� devo0)$"�`��u�ea�l s"8�=:B3.�wo+zal&�)�>n exponen@ e�&#X�dp�?�!� *.�A�F�S&�5v]�p�\/,�a� semie�� �+%"p0Sipw� 1�19\&b!f>X&O%aim�&*�f"�q�:MF},�G 6�qP) !$� (`� μ lete�-&�g filt�%�$�o�6�!�dylindr:1HO�k] -->�pt8�&a ��rFC6( ce $U�a2IpU $Q$.3$HNe^ ��H:Isaɪa���2��E&�SAfa�i�< dot| ��(e�( m54��Dsys��2�h2S*MJoq=?J76�ss,�$A�elow. "%I��$ԡ$H�&.]2��msp�(� tS]�F�a2p X6+��"&S&1} X(ΑX_0�%i�Ra(t-\taL*AX( d + $�J ?a�RZDa�Eabʟ4_+,~X_0\in H,~�! L^1h- rm{loc}} i 1 ),~Am clo�1��un�[U`)�I< #Ddom�D $D(A�2$�UsЍ�*._S>:I17b��)�z�Qdbz. \{ S!W\}�s�"(+B(H�w#'(�)�" $L!f"�� ��!�[AO��x�yre����*J�.�2n2��,.�EADAU�PYT2UT�:XSYXN?P�,N�)k ��>s!��E��ż6��.}i *��'6�*2@Q.=Fdo�%w$&j!�factorizR ՗�q�� "),�i�"4�( Y!���i�vamaU�p��*�v��:� tinuK'of6�>�"&�,V��56b�� Z�Nl);Za&;re�cg01�!�]/�Os���؅�ypl'q!��q�'ind*||�qw'�as�& s�rt)Ue�$,!�^~ay&"'ņhe!_s�0W&�W6Q&k��-� d�� ly. :F�b�9/F�P s pr�ty�#31 ^y � %& do��ot0e!�,�O*6mod{�I� v�l�?$1 sii�. T;MR%�!�re� n�sl���-./ M���|F�3kJ{F.Cm��fac�82j '!+hA!l�d $seD�� rajee�lf a!Sc��N['!)B�8)�1Os9!bwo *� "1!���s��en .�/hem��v�smooth�Y F whvt.k is rw�["9v&D 2}1���I�i[� Da�$, Kwapie\'g Z�i�DKZ��.��q�ae��d$C_0$*� $R:zof � ,F on( "H :� Hthi;. swgey�S�BU$A� $D(B�� �Dan�f -���& $f,~\ak��/A�� i�y@Riemann--Liouvill��"���. a�1)fs�X*1 \,f|:.���d�(!0�  R�Z)^�D(-1} f(s) ds"Frin#Z ,~T>�,B�AO�"�11 y��-!㙹�/Uま.�, �JI_ �+\beta�p�(I_ f)AEtJ �~[&%�,*>�C$7sp� � q 4H}_W:=Q^{1/2}U` !�a�j aY6�8� < .� L_2=L_�nT,u Q x�/ll j�^.pC6��hn�/ N.�Q�"kuaQ $||( ||_2�a;(� &�: �7\p*�h�P[V \,t5m40}�_2u predicte10�z �bb{E}(M�T |,Y(t)��d&�\$.�OT���&W6~+�e��m�l j* W_B^� :"na�  AM , dW }MoQcav e�t*a }hE.26,!��L7�8��a�G).`�C �E�g�C͗A�weaker���<r61�E$oq�e) bb{Pv��M)A? N Jtݴw��eP ��o��$Jh 1�lcU �`antee�ruseful�y G�"� �1a[=1�.� �I�M�c.=�^ (I_{1�,}&�* \circ}{W}�uz/"CJJ$6&=deriv�l��0 !�5�Ye.:=z��+.�bAI9�{A� * 6Y} e4�1f/1" �1.,� "�L�+J0& .���\�1/p$, � �A� �^$�+a�$_A� o $C m� � ous[ *�A"2H"$", sc3}��p�aB�.�Fs betwe>&CM�en�1h` Y(t)�����-1}\, 2s���� �sBe�.{R 7q� \, 7�^psi7a�6�8fW 4A�q� �j),ͮ`5} Z_1>� �\�� � \, Y �s��6} &qb/ cZ_2 }M9R)@9^ uWF����J� �� :�2ș�r� .� �� "P=6� ��=)��Os�jpi {}�@$Sl,W ��)�b��(s):\; U.A4 D(A)�?b�>H, [2 &�PR@y# $��Ka��h"�0 4})-�8{3�,-N�*- 2�&�� rJ�a{��Y�Ku� �-r���V!� each!��($S(0)\,x=x$�<1 B�Xd"�cxJ*G6�y_+&�>�7%\$.*�c�p�ly � M�ac��tervals�I�k < *�u�D)�A&� "Jj� $A! x=Ax �ll.�)"-E.6�:%�& �:~"u})D $a_) ��xBvsm�AS� x b� }g2�N� By� �||�z�>]\ ��V1x9Q�ܓ�W�6ail�!2sxwA A � � mod� P��D simp�cy�T>nR $�8*��m?1~A "v[ diag�%%�:�Jf^�e!��  (A \,e_k = -Kk�x mu_k�=k� N\�k=$s(t;8�"�~M,=1c:;�B�f�c: hA+���0*�s� �\,�= 1� D-�� Li�NQ�� a \!:;! L:�^16����s0��h��9�. U��i%�p�s�QV?"�1D�.!�-.0,�$ope\-ra\-t5i��hr*���aS`a"U(%�A)I,-S ]):f Ap�Z�S �"h��B)���t.�41͏My*gC�G�f&$! bf H"�yl! �.5�x1��+)�>�7}�Zc6G]� >*a�!� subm7�. T&Ť�= $t,�a�� , $!�+�IsŚi)$.} �~��#&ian�25~�\f�85 X�dtheta^ X_0( +�&j �:h s.� t�\, X(s, H�mj�$ ]u��=1W�� Delt� Laplaci�Gn� <%`1,2�!��$% 1�sQz A L}� (s)FLq�. �3�o��Fu:�ItX c1} [_ų.��e���re����7&� |<4 the :���%e�.Es$�l�ci �dIn\,x�v)� E� ;.�^�1 ��k A�1�al� h�jH^*$,f`�X \phi (S(�M�2����T1�L_oI"�u/z��J�B"1��i"4G�b!�.1r8� ��A%{���$��� ,ͱ;b� �WQ lA .�K$0<(1/p)�\1��*o� $�I��M4N6�A� $p$-L�.���9�FsQ>�6M?� 25Q$!�ae!�f�10m, (� 2�F!�>}! �� #, =�� a&m� �� ulas"�BE1/� � pv����%�"pI ��!.�k �e].�-elI6�&� �&}&H# �l*D<�!iZ�zn����!^�*�"�LI�.��[ng����e�$m)e��S(v�2�"8 A"�Y hn��Av*=1�UAQWv!� vAR�*EF� �A�|�.$:��n� �Ev))& = &6g\, "�\,m(v� �U*�)�v dm(r) "L�aj� v6Ef=�2 r^v %Y^*/(s-��[? ds\A] _�nL�ha & \h%�{10ex} 0(from~F�V~ 6em�|9�s�NJ�B�\Ch[�YE6�% �d`] �%>F�^A �^0Jj E�r�rTW%-) ] ds 9�Tq�n= the~�~�p9})F4 G=�>7�[� (�s��E N�SI �Fn��b9[m�,�)7dN9 =%��v,\.c�,Oc}V�A E������cN From�Y���10}�XSchwarz&�+y`se� ��Ť*j]h�ta�~| �I)|�q |�t),h) �}|\,|h|+ �� 1u2!} �*�In�/5sc��T��'�)�.x�!�� ��Ӧ�l"1V�!�f�$(. Kotelenez�Ko1,Ko2�$Tubaro � Tu}� �<�Q"z�nt�6& s���p=Mg} EKo3} a��y���|X�&Tis o���C;�Menaldi \ChM�bta�.� �U\s s�%&@7"��2g!(-� �.5�th:�xC�~�i> w+,�as e �>OA�sK*�Yt$"�(��k%=vvis��c'K�w" R c}_p6Rq�A���e\;T^{p/2F;B��6T sp\;�0P � �i�)��k �v1.<$1/p <\m < 1/!b�U"M 4a}),��j E��*�wLk>Y��M = |" �� |,~~&�|�`$t,� H\"older'A��.Z"~P$q=p/(p-1)$*�L ��e1#U�&��&rJF�Ű|1qt� -1)}�%�\,��s�|���h5�JhqJe�-!�^qD aA �qj�Ed "ht |.� |^p >M��1}{p}}!r�RI0���LE-��pa�4A!� �6�r* c_p 71oT T.�Mqa*SE�^q�:�p}��%FB�u%&�P c_p:�Hd p}{(6� )^p�`j6p|�6� w#! t^ >���j_ab�n"�"�� last�a�QQ 5n-W*�fG2d "j*�M:^���2��$c�atj��zF�A}�6� -De  ��q c\,JM� �%a�_2m,U`^i�p�m ,5��( }~ p�� B�, -Q�l2k 5}):h��u��hF��: � �o!�� \!o �cy"aF�� hT:� s ||(s- &�" S)� #O&�� �)�2U1k\*ű \\�A *� 8*G$ing~out�  |'~d>� &\!��^� �^ ||^2Mj )>#���"& \!=\!q��T!�$[(f*g)(s)].�AZ ���U"1 ��f�= ||sY�aW^{~$g#a��)'W Young2n� 7NT87�(�j#�u-e)�R^%&f.S�2I��E�.F�\;j�% %"_2^:�F� ��&� 4 �\�L2\^R�9id*�d-��:2��&! qAo: 2%R���\,d�B)qFk�S2kB%kt"p.�]�\\ & &��&O�#�[| �K|��U�%�cWVE8& b2] �  �! F��R�B2���-�m�� 63 &�.c\,c_* 2"B�$ p&7 K� +(1�+1)���1�  -1���hJ׃t:�o�v�'��doTb:4����3ex<LO5� �B$eV$,*�!5�5  �, by*�j7,&�(m4w�3t Y07� ��|,r*�#24�6�D9YVJ�n�6y "sy��"&!�Rk"�pa6�F�)>�U�$r��!s� &*l "�$p(2,IH� �'�l�%0,%2�o:Pa!:Ff \hat9x ��"! �ce1n J� 2� " >5��p>�:�8w ����e; j��M(�d&I eo : -�Hs�U>ha�Q� is n�'� &V"a�B13/ X �e�VB-� ��:� % $Va C[ �\sigma<٬[+bTFw!&p L:u8�&+b��2vl%4at the resolve�>nt operators $S(t),t\geq 0$, must be of Hilbert-Schmidt type. The question is: what kind of Volterra equations admit resolvents fulfilling that assumption? Good candidates seem to be the integrodifferential equations (\ref{e8a}) mentioned earlier because of the form of the resolvents. We can see (e.g.\ \cite{Pr}), �?re 3nP of (\r�Dare represented byLDfundamental soluti�< $P_\alpha(t,x)$!�M` according to \begin{equ%y<} \label{e19} (!�\v)(x) = \int_{-\infty}^{ .o-y)\,v(4dy\;, \quad M-d,~x\in \mathbb{R}\;. \end� FR�� $ in� 19})%@well-known for $) =1$, and  the limit�cases'0$&6`2$. For our purposes, becA !�!�xhypothesis (s), we may consider6bL\in [1,2)$, studied�details!� \E1Fu}� (ScWy}. Nowb(shall adapt�,result obtaiA� by Peszat @Pe}� � convM' $Z_2a�~t�,0,T]$, givenDM1@6}). We introducetfollow!EdefiniAx� assui�s.QZ#UW d1} a+saA� at proces!�Hpsi : \Omega \times��\rightarrow L(H,H)$ is {\rm point-predictable} if !�!' $g,h�H$�l(m (t)g,h),\�� is M with!d pecta0!Gfiltre. $(E�cal{F}_t.MM� �0 \noindent ($}� 2$)\hfill \parbox[t]{150mm}{ \it Here we)T!xa)�a( space $U=HI�t!� i:S jTFN.}\\ 6�kappa$) b�\it Th�existqTL_0\in(0,\frac{1}{2}) �0 $p_0>1$ such � $$ j,_T := \left(��0^T t^{(i�,_0-1)p_0} ||�� ||^{dt I:)^{1/< +��\;,��\mbox{E/ ny~} T>0.|}Q�theorU�t3} AA�=�f�� as above,E:6�a�$, ��s Y!�� condec�g($)$��, satisfied. :�re)�s aE stan!� eta<-2sb D20} \sup_{0\leq t T}\;1�(t (t-s)^{-21�-�-s)A�4(s)||_2^2\,ds !�q �\,,�!)�(P -- a.~s.}: Dn��i� \delta >0e���s $C,))_T#atj���PEe\{^�|\phi(�7)| � �Ii\A((eq C \exp P-I� + ^2}{�! !}@B  )I� \ve�D{2mm} \proof{ Inū��,ѧ weAqve onl�n$e estimate��,21}) but no%;tinuityU�of�0simple. FirstOallōformulQ�inF lity`� in� whe n Q�s!�I�A�� 2$). Bas�},on Lemma 3.3�K�1Pe}� havej�22A���P��bb{E}\,%�A�fE ��9)�|Y(t)|^21�dt+q 4T\;,)�!�!�w� �S8�� ty2u1SeD�(s)dWT�� t\in�� ;.$$e ,��!}5� fromE!�1%4V%:\\2 any $A��2^*a5uXs $�JatnY3!YZ.}B)7)_\sin 1\pi}{\,bw |Z_1!�|h|�� Gc}{3}\u�D ||Y||_{L^q(0,T;H)Jm Z uER.IsQ� 22})� 23})a\s 4]�!�YN2L �Z .2$et�"�C\;. Eis9�� Doob's.�complet���oET��em d t3}. ��H$\blacksquare$ } Ao factorizE�, method appl� 0to some classArHstochastic linear VF� hal ovided�c ilar�s lik�a*� earl� �de"� q{5�N�N8�,82) 139-151.ZKo2j�topped�7.�E��ag�b!ygrals%c%n�.\ Analpp I� �$4) 245-265b�Ko3f�maximalf���N�o>� �pace- r.#��� p!�ale�er�JR�21 �$7) 345-358b���S}Ex��:��!�in�e-dimen�w al ���1��Bul!�Po$Acad.\ Sciq7m 2) 323-33f�(Pr} Pr\"uss�huEparyU?u�%u .$}, Birkh\"m4r, Ba\-sel, 19j) Schnei~W.R.\%�Wyss W=D Frac� -���and 60�J.~�*~Phys. E�30)�89), pp. 134-144f1,Tu} Tubaro L�An5��wBurkhol��6for.�3 esv&=�q� }, �Qe~y��a��}0, Marcel Dekk!l01984, 187-192f�Za}RU The 1 -^calculu%�� J� !��(ona Seminara�N�P(St.~Feliu de GuixolsE,1), 222-234,:�$Progr.\ Pr�Q� 32} vo� >?  docu�4} I � \(style{amsar "  \new�em!2orem} [se%?]x(� }[� ] 6$ Corollary(6,Proposi!�..60Remark+ N&sB's:(Exa� (6P .Q6*D"�U6.Alem+:! Conjectur.� % ��$width=13cm��he�=21.5cmb `QE)T\title{Strong Toroidal] of bi`alv phismX 3-fold!M0 \author{Ste�Dm(Cutkosky} \� 8ks{Research ͯ ly supporJNSF� \make� \M�� �E) S;s� $f:X a�Y� a doa�nt��@algebraic varietiS8over a field $k�cha��eriB(zero. If $X0$Y$\nO ng� , V�t-\t��� nor8 cros divis� D_X$�}rD_Y Y*34 $f^{-1}(D_Y)=4�$f% loc "Umonomi< in ropri>et!�0!�ameters �.�precise��e�!Ttconcept#  AK}, KKMSRy�Def274}Ipaper.�mble%�1DQ�isd� mine5N�F�, 9�A/Hcommutative diagram8i:P }�q39c |array}{rcl} X_1&\stackrel{f_1}{]�D}&Y_1\\ \Phi\downE�&& \Psi"X.G>E � z � *�$iM�ZI�piPe�blow up ]�E }% $X_1 GY rA�nA�I���I�%U��{Y_1}M�U,nd $D_{X_1}=U�&) '�&�$f7E�� (�  /Q �D P$).�� TA�Bsta��in�Ax6.2.1.A�Q�(MW}. A s�8er! ^� also aske�>Z.V,S we w�a� d>�. �.�pro�_A�5� ,!/�CSNC�����)�X9�Y  a B0X��A�^ugtext{A;}(f)$�r����j��smooth!�kbin� X$. >*)�>5>to�1�ne�)�ViVc>!rs-�aF� �preimagea� �e]�M�ivS!��3!|s�s%2NC���O�,aEx�h J F!:q7=�D�r�i��lX)!�a. >_ wre:d!��;s,� been� ed"qin&� AD$s, mostlya���!9( surfaces. ��di&��6heM1est uo !C -�could~tru��r.�J ́4>ofc! l� � ve:o.�a� e� m shZ"��!C3��I&�a�ia�cur���=;!s�embed�f�#�a���i#  ( rH}). W@a�A|lI�)nSa�ev��iof�printNAk " �o3 jA�k=CP Mat}�� TheyI�use�pec �er�$%.� geometryY$ A�tv�EGA#>%as canA foun<# �"� to �1�i I C3},Ar~ >�!��%b=�X� a� 5�%� �, h� 0.1�)YC5}�epr�>x�� . [� p� � N�BWzN XP P �n 3}��Jk�Z��  n "# 8 clos��j 0. Fur���� a� a���I�y�O &�NV.�w�sau� lo�[I� map�B��� �N� of�� $$�` {rll} X�� �&� J� v� .� $$�� ,�zF� p9 �"� Aoa�.G%^խY$�� �F iG���1���M� } AB�Aa2�I� ��stѡ�he�!�a9% o�.��Q5�RJUI_NsAw*OF- . AILnsequenc�8 �� ��we find%���Z� �%�mo ��(-�yU�)&� .�rA1�A)�.� �i�:n:n�i.Hco 1 re)d� scheme�H(fᛝ`�wz<$Y D>�z:A��v�v�v�v�mofFmk*s��F!Zj�bh �� :5s �]on �, IG_1� I�Lo� ���*� }�!bul� &H� devo�toaZv�"AW�0�a�r�2}�#.<*#m� -n&J�'C,^�Pte�dG ��sAa�!�5]:+X.�5X$~�$f��#�-vl��&6 ��z: a��4�-s �YAZ>"��i��Np prepQ"$5e\�q��  cusp��et�-6@no�on� "$ � � 02�2}iff�/ in S�s 2e�39y�. FromJ>K(we easily dŅ)s2)3��% �1}z60"� .� |.3 ��� ,to arbitraryF�-m�)f��gnific(step toward�a�o�&Z�of�q��*w�lax�#� restri)�A��/&N| �.PoR a� i3�%duc�+a&� 5 IB\ �validE^=@�%8aePY$.�+)�AK} i���/a"*2)$k&� ed�m�is weake� to be� mod%�� (�d5�J� &N1"#C2Ms%4},�� �b�%\Ps�h-lyA=ducvN�C�MA1�, -A1�.Phi$,!<x��@ �3  be s����i�,){�%is %'�\patch!r~i�a*t lea_-n�  2� �A��+Vval�5 ItW)�I-"��%)�W2}IJA:�'^�� eA�lterna_% .� " � �\non"� � "q. Weav�(�*c)Y�5or6�(v65QW:)9��h5Danilov-�D1)�Ewald  E} (W�T2 by Wlodar�'-�a�Morelli Mo Q$Abramovich�!tsuki%*Rashij AMR}A0+9¡XOur�f23} Z�(oreRAce@Bon50�|O7� comb�3ZH I (�OFl"�MR}), a,�knew!|�nJM6��of1. 7` �*��&8rWu�#an�ar#�}�ure4$power serih� geri a� ping,-op~8�+��f&r�X*u&n�,�.yic ina�� y,�I@B"1 verK&+J6��we get_n>)is�eAa� .�-6��W1}Z �C5� C"�"CorWF�� J���� �� �� �� ^� !ym�ng� ,R�  } &&Z_1&&30&Z_{n-1}&&\\ *v2�swa^"#"� N5�"roR3}{n>4e]cdots& Be�+f�nJ\\��2 4 T.��H&&Y�!k"� qenume�} \�.[1.] All�XX,� ���V$Z_i$ :]�j3"; �� N Z_i}6�. �2.]��B�6 :X_1*�! � makAea�JR�!�$^\\�'N"\v3.:�>9�)w3 �}(`�"R�j(�'�'�'�'6XA U/ (� u'r�ms�.W�8�*�of*�Q��immed�%f.�&��n�0"� *N�2,e~������ or � T8$e RMH 3� �<#of!a%��z� N7V(by AbhyankalAb� Hiron(1 �H� �% P aN3N�'bA�i� �ZE�� �n&&��A�Xt�%}{�'}J ~9$Z' 2Y$��6�Ssu*H Oda-,O}� 5g�]analogouZ%�� BZ !�:Z �NlY'S.��f (��)�"J direct�!�7S + !�up� s (Z/6kB Z� F-1})"4� ��+s|W �{-cM�aTC"$&{7��  (Shan� E� {Sh� S�{S! � a�%r= an}�c. !jm� 6�%�&�0 +, i��i�pr)�Zp�toZK .� :��ŝ�2t&ARApc"�,? � )�1b6� ݍ� "�al>�!�q#{*� eY,�Ru.�f�,"�(JK)58�wrue��= U�'s M6��I%���is ``N�'' al�:a&Z,��D�# o�+1m(QRA qC2a!toM4 a ��?k5�� [6� for B/s�"  Ch;-ensen �hRG Karu "e"�:.� AA� @I spiri�)Y[58�,:���5 a�al.d��@elJ^�G&N$s,an�&is �nN �S�.N� } Through��E?#p.�)be�*j~"ofN�!���%�3�/6&a quasi-*�}ety��of�b!9w 1, 2N.�H @I.$p�?�$�����n �6.Y.at $p�J�)0{\cal O}_{X,pJF-/J/�M \hatBQ �/.� $V\subset��m�Bn �I}_,`X$)� deno�>ide"Kheag$V^f qW) g���0y!m%T�Ee�>{5rM{ $Y=j+pec}(�/ �+ (W)$ by $Y=V� W$. Let��>b1A�yLofM ies.b=E� �T �ing�+�@Z%!dofI-sYN"V�!�� ,)�.%�Da C9er6 $M~"$1l,_- ��=�Md9,$f^*(D)_{redAt >p-$a,b,c,d\in�7Q}$�0n~^Lwrite $(a,b)\le (c,d%- f $ab-�c d$.�&A��� �on:"$vY! azp/ (S&�-)#"_2.��"K6�$�a $C�-�<�U��61���3( �!�� X$SesZ�x NCs) C$�2�-� ���zC)�� �IF $x,y,z$M8.[ x=y=vMr�.a.:A#\� $xyz(2 �-)�M� 6+ !%/.-Z �I�^_i�3a:2��re�%m�;� �t��falled9*;:` j`wo, oneQ!�riBa 3 W)Vu2 Jua�a �nKq�pE��1.KCc re� (c1 �R2wo %90q Uq2-ea�*�' >�-�!�^��� B*X$,!T�' �!%mo�.D��(  >�'#"� ^�;, $S$ θS$�, ���$D_S$� !T%�� � � >�Ess%� ( . Observ�/�fhi::��!� 9Ra1�j4$%X���� SNC �7� %���2 9$-�/F�6All��F��@�0i� isc-��be�:*�nd�yimX�j� �h$���%>� By a"��3 $q9*�V��=me+I�"N�d� F)�!(s�Gnontriv�/ open�a. #exact "�N gp! quirC5Bly!;clH5�� ext.6�5 E�co�0nt � � F�6a 695ya�� %APc2�GhC>T��e� -l�D�A( $\Gamma(X,� F}Q3V� ${k}(X6��funm"�:��X�02{&� $\nu%�Sis !�l�Cn*� \bold k��!b"�5! _r�$V_{\nu!Oa�qA�*reside3p/of ,is!$. 6 i�R�Iuis*�lyG+val!�to)��S#f3is/ uniqu� l�)Q�p_1� (5��l<�WM,� _1,p�8. A)�뱉-��a�#�(2���6�����v "T37,2&8 16, Chapter VI�Z�V$a_1,\l�, a_n!=M5�"nu(a_1)" nN6eX*Z depe�T� � $|f k� Z}� Tell�)= 71 �1)+� s n n)� �K!�A�e �KeA� ). O� wise���U �t "9���V,x(}�q - ^�(W�<& n2�M�I}��O}_I�� � I�(�ly��&by"��#"a�%�� J� . >�qA]��We�$u,v,w$%��"mal) pa+X7G�>� q$'))An.BFT � T9{X,q}*_ E.�"��q�a� m�$uZ� �FU� $uA��6,�( �.�.h� A�n�!:)�>jvfk)$:kl.k k,wb�vwfm�-{�=P.�":.�.qif$fura�l: EF��"�!&�@�!torf} n �:�B.� + s^���-2��"^=q�A .:A7.%Z y_>.=F %�A9Y  u,vij�y�Is}E)��?qa fA�y^��  J��rj� e6qK M�,u�elRIK1�HeqTF1} u=x^a, v=x^bZ+y)!3� 0\ne͟!8 kAɅ � �z��n�2�y^b � cy^dB�Q\$ad-bc�0�a� �^����2!0(x^�)^k�t1>zn>�-=, � k,t>�+I� gcd}t=1�4.]��M��3� �z^c� x^dy^ez^fBiH "e� rank?Uft('"Pmatrix} a&b&c\\ d&e&f b )=2.�E85.���0Q-�y>� k6vk��0Jz>rM� ,b,kj� 6*e$N!�� WR���L�inB�F���b�=*Z/��_��q��(�FD? Gg!AK}) A�5� $\e4  %B'{$I n:6&���i�`�?y"� aUK:pY�f/2�"o,� _{\sigma}�2N'OeLD so� 3 k$-��m<2��,p}\c 6"b ,p'}a&� � lZ D>)&�M"6.X-T$ (i�$T� *!Lu� +$)�Wch�air $(G,p'��� ES| model��-B�.A5�"J@23�!F}}1:l�[a�(��!gI��E�S&E�=�Y}�b�62 (X6nY�GC�9�ez\in6*�CG"� ղ=�A �U�$q(p) "�p %�sJ����((Y_{\tau},q!�qm~ic"� !�s{mH.�F*�E�"" �$" mutes:a�S(�?68=- ,p}&`)�&6)2�c!,^*\up3&3#*�(Z�Y,q.q=&{ �,q'\�� ��%���y(5�RJ9Y*2*X}�i�]xH� 2r���5���Dl��R[s�$o>�NF�L�1�E a}m�$=� D����/ aQ) ,a f(p)��)HY3UN�A�pJB:.;2�q � e��e2*�Fm*� �4!V9g)OX:q.,@ �,�.� a�+ RM. } u&& \\ v \\ wgy^hz^i�aY��U�$d,e,f,g,h,�`= NI�A�2 Det61 J|;5 5 \ g&h&i '�U)� *@ x V6� 5-~�.�.�(z+� � �֩hF E 53i5�cy $ae-bd�ap%�� � M_���(y���bet��,(a4 kaDa,d,g>�� �.; � �xM >i=1� < �R0��b0Z�F�� d=j r� �r �y)�Z�a v���A"�=2� hi_X6#S$Mb� �<2�.aF��S"� ^ Sm�C��_X�S)��s"�6� 6.5��J='e�>� k�U ����z�� 2.4V5} ��Ba�*��R�U&�4�+6Cis�f#,*�<7i y�a`#moF�M �s."� X� 1}:�!R�*CT�'2i�y!�tr�S*: �h ��Ae'�X�+svV� u.�5�AW�8&�bE"$fa"V')Z�Gite. Re!jVfu&�q"hJ2� ;.�61�6+E-^&` is $\{�Y\m:4dim }�p)>0\p%J��cl�X&./G$\ge 2$a,�>�.� ��`Ei�0A`�N�vFR�4in�G�^= \lambda^� K branch 5c8� BV]Q� E�E�x*#, pon� � . B*�1�, emma� ;>+# Ή�E�disjoint�uI�C}E�I��� 1'EFJ�i�[N��q�Def31} A K.qJ�:��;N��+1!.u��A�e�y�&c UBUF�m�2�)&i�e�Ks*� �v� ���U &�re �m$.� ��q$ e�m�q*Pͮxea unit<N�) �b@#�.ahoIE2a�1� �%!p$ "�Omor�p�aj �Yoi�� ":MI�iM �� r > BO5 2NsbM� VMei�^� dn� or �&� < u\� N�| \2�3*~ Fua|hx�=� m�� {'H2 � x^c(\g�" x,y)+x^dzo � 9J/ /�aIR�>�$xfAI",J-�B��9�:" k)l5#9,z!(�-*F� lC >�sJs &�� %�bV+�T6��C����*E i"� B"M�,��dA�FAi�&u�b�q���y� ��e f�:� �V"E I �47}:GF�!5 ��&�{�E�!o2X�g�v �69J�E-�"h!� S��m͘1 >>%Ͷ�00 a �7�'n�bborhoof}$EA6��Hn+��*�A1j."on���C��N:��w�ZF ^N:MB�GB�#)�isongly&&Lif�J�-1���EJ��,%lECF.m�}!�({PQ�#�P2_ k�$�6fmB ��S .� :B*�4� aQ�!3�[n� !b*M 2h�^'�SO �x�2`b��>*�hW�hW" �h�J����M!i�e^'Sf�(�0k�*&l.&�?�\ved� ���">�)� # 3(�4"if14:�)2. ��fr[g��� N@a� BM��[n�E&�,�Hhe�c0-Riemann mani�! 3!�iZ*JVQf�U�E_1&,D>�Y�dX62Z:+?BJD��� *�e:��+�E� r]��;*�dQ��&o,is>_4"S.-�^2-!sE�.��$yI_U-. �p�!�Z!�� be r] ,. \vskip .2�<in&AWCase B�\nu(u),v w����+.�* Si�Y$r�'�9� p$,aE" "� .n� p &%:� R�5�J%o�� sA. h�s2� N:�% E�2� 2jx� 3V >� !�� �FA�S :�. 1]!���, 3x)�y z-��3V�%'�]x�z&zT� im�y)�iZ���65{ TU�4>�.��2J[9X��="|.. Afte�<<,�cterchang�0m�weL:MFUjA.i�Cuލ�E�Y'<th :_ $u=v�!$q_q1� RsPofZa4sic1:Y  \rig��.?lE�Nq 8%n2 . 2Aӭp�� ���#2C3J} �b2�,��I�l �lm<6X�8E�Vv�3` 2.1piC5}� �Sh1S!nu2S>�\JNtG.{CaR  3*�Lf >B w!�j�U�OJ>� r{ Us$It ��B� actne�}A(Z�]Z%�j�.�"-g;�O$n�j>3fZi2V�y}&Y_i1N2 M9V %��bw 1�=in.-f"�t  ��3� ^��4��>�z7 $f_i!�$Y{��h"0[&Ez!ZoE��j�:�^*�?�)�4r�b6?�włachie�th�nclH|�!D�Mwpf�E�2�B V�Δ, ��N_�� ^��!!F�5�C�k ��"�*�%�� %M0 Tr��� J�b� �vA�ZPPv�w29">^J� �Qt�lfѱ�� sa?b�"_1$'* 3"*D�'J.2a)��&[O�)]����5�5�5 &F6or�a�R�e��NE�055 R?X$ �Sv�}M�,.�yf.X� �������.6�S�S}S�N�A�"�2PnPZx��Ջ��2rV��0�6�25"m�M h��qE�f3�6,&P ^V�I����Jt�O��UU�x*gVN�Ej: .��M�M�;*� BE �ZjZ��E- .�n�,�mF�9 �V~/�� )=2��n�_Qva ��z� �.~.( ���I:�&8 6�a�RQ @�[������V� � lso VAj�O*�g�numbe}g��s� nIKb9�"��쾆������������� :M ��������v�xGq"z� ������ ��C5 ]:������^�ј)~�.@������v��N3 �"4 +�.f������n �Kb�&\%"a&�vzt���5,rA6� �� \ �RH� (n "�"�n ^** In� ticular,r}TuE9j�:�+5���.6*b� �2� b-�6�`:�� "%"d a�J$i�u*K&��JF">�2 r�f��M�5-N��2�!c~TQ�R��!X�����&P1��QAn=���,F�3} :�+F�&�E�6:S� 2}:)? $He7,al hyperplan�s� f6iB�"f�$H� �,v&�.)B�ni'<#e w6L# �.�,�JXl! , $H'WҦ~B�8��u"8,no�4 �Q+H'*�%B([iH\capr@�"50�>-3.�6�#be V�Oq��B.'{nTOZ��@I�$j�N!-��2�aO�j�&*�4�1I'W.�2KF&5 o9qtw?x�1j;��4WBenJ0'!2x^a�&, w=zn4$My^b2"�w,'-��&NL!<��F�e�m�&�e[.Cor�#���N��9�XM��:O9��2i%B��$Y- 4q���a��X":�2�'1�:>^A6{set"�)1\Оf ii� $ �AE�2D; qa4f$�G�����2 3��c͈_<al��V!<d<:�>�"m! i��l ����< -� ���4>(F,!L*p_bB�E:�0�0�� $\pi:Y.�S�a�bJOnB:@*�].,,g=\pi\circ fB�EO3. &Y3S$�@�;C x$D� D)BTD' �.t<�,E�b�A?J�:g$Z>� *�=��%۩�<g�z %wU�F�GC ��) awayIrV%�m� ly m�z Mt =\{q*tX q_m\�#\��9Y&X>q!P�tR}�O�y4|Aa3, *d WZ�5"- ^Y2�\� �t&y}&XTF'Wt*' gr&S���i2rh�/q@A2�pH+""%J��'!�)..>���E�g_V[�� �I�D')$)�6.�6�all�(? s $F�B>"7�Itu��t�a2V��Va}�Y�!�6 @0u�P� S,]�2�;v a<4"�P�,{C'"�,�inGbu:�B BI �Ay?C'�^�G it suffic;.o��be�"u8.�!w.EM0S�A�yC�� E=C+�E�.���S!�1"l ��i��^6��>�^pQ�@`�0��I�`Ad��a�.�!fX$ Z�Wo'2/�Q�F�bM�% .�F�e��I�%v�-c#N�� $a�=g��i�>�!�%9 �=�$(fF�1}(q_i��re �cw(a�$q_uK�O`�P�Z1EM�un7@=�A�.^D1�bv�i�"� �_-M���BA~�,�.ckҒ�IC=��2c�i�Y�Du� �4n21�"�ir�D.02^%~ �fn�C ''=g��p (by �C� 1}W�6�� 2��d$.� (p)=6�. n5 *!  .�Y%�eq2� �G&0V� :�?�a28o.�!�/2�1s��N�an�7Q d y^c�\� r�@.-�BrI '' a,5@.8^u%� �:�z��^��D"Oc"X�k�:Qah�A��@�*b��z^c)_ dz^e�brb5n,eR|LOB���n�D�/Now�o�(�%+c.k$%�� ���S��f�A}iu FY ���uqusH6�J���� A�F$�a~ ���}j%YR�������F����}ݖ�}D�fIdn�6h����b��� ���]*�DEj��FA.�� � A}��e�i�j(A�t t��A�AFV�-B0N2t,� {":+: �":Z�&�*{�%# u�4Q9!:u*�-"^Y��7��-��-]*EΪ �BB� qM��-U0EreNv��\��>��'L$o�R� tX2E�6�T&� ^�>�� q���@:KK!��\e,bUx,t�7L�� Z� "W&:�u> a mj�cA"ha:1d}�I�}i�1UCW�MNVa� �&� C�CeqAvaAJ } cy^dv�X4 w* J fn�ƍ�:5vtn�1} X_m*�-m6�5X_{m-1M)a�5 �k}�r"��F:� XIr���O���"� �-���6usr�$al/��8m.�1a�yBA�n�K��d�x# I}_q �X_mk+Ht*�8�6��� Y]�R� R[ R[ "T �n�3*eN�x^cZ�M�ne��A�$c� or�|N�ji4 �g2xZ~a,c'T�źk5bky~l �b,d {.u=ea{?p).���do E.�(6 eqA3�4})�5q3�d�6�V�N�&ms:ns6-!p!ww=Fni�s' $V P,�B���Π}�-�t}(:�,p0beT };F&N=j47�x^by^c�>F�$b�,N������8 �!�yw^z� �[V�\cup V(�����Z"�pI)� � s $r�N�<:Y,rN1 isعdW�w��$ Vg6��P*Y0�6GE�Z%mp�P=��Tu�7:�8})BA!E E�6 �&��O"�"A sy�rs� Pg��ic)!}$E$*�wD1�]ndr �Z��R�V�k��>%XU*�D�GN>�) X�%orm�!�J�0�Or �h, � v\��p�}[�loC%4���n.f$�i"X�q�!tre��F�, $x_1,y_1,z_ �56�U�_1rEN���r�9} x=h y (y_1%a, zz*%a&m �'��& a� j�10 s�y=z haX�ZbVi4 ��ne1 ez_1�y_ z=z_1� _S cU�9})�s%�#,l]�Xu!%^�x_1^b.C^�x_ �)E$$iqp_1�*$E�uS�B�!�fK�&rough);# ?[R"� a s: � map�Iq�dh u_1=�, v_1=O�v}{u}�^{bx]!^b, w)w)-�!e�� b>��M*� F� �z���= A:��=�WE[}��� y!슀~.�=3d~r 1a>Q"%V �5�K��I6ff��1*�4A,&< @bK�variabl��!�A)I u}{wMaA�,:I+EI:+NYwAx)| E�isQ4!�pi�"l-S.�)W;]n;)���%�� �,%��m��eAAtA#.�, �z_e)jht�ݣ��a7B�R.� . �Z\10:� _ j ��i�!^aA�Gr��y��eS)~h A�� $b=1e:$�*$a).2�I�~�@�U 2� ��� u}{vE�Ixv�:�v�@-�:PR .�i{bT� 2��.�����,q�ed6�AB����}�)�Z�!�}�2,��w"i� A�:F&� maF].�>?=�\t�*mO * )�j�-�^">M (=11:��C%�r�z_m�!9be$h$L��*I��by:2��;n%�I㩆v���%�I�w�UiB�8Z�W�F�Jmle�}��a*|� �$.h�now� �a9i�b]Q(& ion. EachTiK$ll�� eZe>}i�} n�Em�s*d.�1����j$.m.Q2� ��U�� 42�52JV v.�iHYN/� 6-�E���*E��rve $Ey�]�:�e�h�� trans��C�C(�0$Z�-XA�2 ��coM�ed9BE�tq�_KK�*�hi^h2"M/d�����A,4:S& R� >NI��E=%�)��Ai��kiH:���hE6�-�"�AC7(F"���.�h{L4� IWe ne�ar��%.1cord}_F�1%�� uZc 2v�!F�B ic� N u� ��A�$Z$>�$�yEno ��f��'�%.62��9$� v�]O8EO:�)�%�is last�, $y=n !%~" (b�6�!� <.�!�).��>! ��hJ+E> ~<�:I�%���b�*��A�"E$J�&�$HL_V^i��:4 �o�c?)!*�>� ��2� �+�i"f whenJ� ��@p��n\"�cf� "�GE:V�3}��A`cai�*�aEu iOt�A��T"����rI�K^of, af�Y�\17d 66`5Rh a#E�)y�:z�b� ��it����=����v�122�� �5&.��u3 ]u�k12&� &y e���-  o v c.� ���\nei ��tg� q=�~��b�R� .�� � y^b.�e�F� 9{c-1}y^dJ/� "T�� a�>1(� ���"� %G� ��7$qaJ��99F.�!�"����� #y��"�aY3-��a~6x� �!OAcA!6� ��)EQJ:P: �J ��EV��E*� S-��% b��uJ� ��$��%Bլr�q �Ω� NI4})�#re���.6�+"�P��)A{si���.G le��oB�5��@2tV�1:"3 sE�tI]�7 N�)/r��w��e . #� �"�I $X_r6� m� =7!N�%&��M >�2OVl"\Vn"^�r^g t; N 9�RV%�BW�W%1 $�x"E�f�e�: q""� r��!φx.��a�epV��z�#��A�$d<@ $min}\{a,b\Dr��jr�."�e� � ey^fZ�(e,f)<Ɉ<:��" c,d $OacA�lis����2�����%�i��$u vB�9( XA�F�9�Z� E$�&�$��rn)2.)&� w=xn)e+f0t�+#� ��l z e��o(?:u�N�. A�z��"��$$(a-c)(b-d�C�%5nonneg�k�`ifEQ<6 "�%��$ \le%���O�k<0>gn� �g� upҍj= ���>h"�� ��'�5M�;$%W*��v2e���� su�creased"�u��\�\R'�6,?�)�. ve�=*�N� �� ��E�( �b n�q$)�7[J� �IAy}�f>D %�Aa�R">�L�Aslgorithm�A���s�ii;q�.� !�8�eZ ��p�V$ $X_n6�r$"uU*.�2<nK�7űy8���;Bc>��tƋ�ay�o*�Zn 6�*:�{ ���2�*{r+6�*X_r>s�ay�#z &1K�6X�\�{��TA^�a��Z��T6�$,%q�( �6�f_i:X��%�N���b q�i= �Z�.JF�B�4���1> >l�� R.� 16})���E�^�i:YuqYʊ.6n,)AA,!��(� �a[��- : IP$�� b�F�yonFB�B�� p@x-. F��l�&Q� $, l�����R0Alp�Fea !�4N� N.�A( ?)=B -�� Cho $>�I�� �izes P M!Q k&R�# ��L.�$���{ ��!�$p� � qW�_iO \�� �$S��QK6D.��&��a�A5^gu|�pa*A �&�&�*B�;�, ��;���(n�7�2�u%:�orr&8 Ij�6*yp=���eBb "� :n�9�+_\ *��i �( d+1}"�B�&�d+1=a=b<+�9B��>��* �� �2rQ�$s:�� :��:u}�%v�%��<����D )���%�{b-a}$�y4���:N' ��<Q*�%�&��2���Z�}bv >�"��v&L&�]A �2M&d�O&-�%J}� )Z}%^F4$$nY= �*�+a<-�Jz8d�9�Cj:2t�m>z2$R)}�.> n��!��~�J{a- �a%�:Db&b&.�6��s .J?� r�# ~t� v� JxF� <!�.�p y C*itx NyVN��OF(.9�M��MY~��o.& A�(c $e6 6@M�a!`�V��&q� � z��j"t*�80�V� ^{e+!f}�V�(e+1,f)=%�%"�20�f2��$ �u*w-c-a�'d-b�ʩ0R$� �iMY^%�n~ ( obtained f�Xrom a change of variable in $$ u_1=\frac{u}{w}=x_1^{a-e-1}y^{b-f}(z_1+\beta)^{-1}, v_1=\4v4c-4?dR6w_1=w `e+^f(zZ.�` If $(e+1,f)<(a,b)$ and $~�= 0$ then (\ref{eqA20}) has a form  15}) withPN2V8. Suppose thatQ18QDolds. $p_{i+1}$ is x$a 3-point,��u�,ay^bz_1^a, v cy^dc, � }y^f� �$X b8\rightarrow Y_1 qu�0morphism near�,, which maps to>�)toroidal%&�Z�}-��I,b�-!�-)�,2�J�DIn summary, we hav-� all %\Hs where ${\cal I}_q O}_{-1)�(not invertiA�LB 4}) or=�A8and if $\lambda-�0subset \Phi_iE�(!i)%�,a curve suchI:¦alongzi!�- $0e%� up�C$. T�&�e exist�JHcommutative diagram0�as�-٠array}{lll} \overline X_1&\stackrel{f_1}{�}&�\ a>\down��&& � \\ X.E>CIe ��}iYM?U�of9RQ�%TA�preima�� $D_X!��;�|��� $pf} We fol��\algorithez.< 18.17 \cite{C3}���%$>�$q\in Q�p ��q)6�are p�(�vparam�: s $u,v,w$e.�2in��j Y,q}i re��.>x,y,z$4 \hat=�,p}aj�!onw �) �ccases h : $q%Oa5�eUp6, ��eque/�zeqB1} � � <, v=x^dy^e, w=z�S5m $uv=0 bloi"E0�Cu=wn)C!�v���r�2} � �,b(y+\alpha),j� 0\ne 'Ak$,��Z� �6� r�3�y,wf�nb��We will}D���of��nO7} FW������ _n}{�9}��6&��6*N]1:7163 X>�M�>�E�an2(.\ .4p��{iR� ,� � �F�(f\circ%<1 cŽ {i})�^q2� Z�{i}�nFU ��e��^B�rms"} B4}) -6}) be�.�.��, �n�4mzy^.�^gy^hF�($ae-ba\ne 0�L (g,h�. Z��n�5 �F��dZ�J�d0�� hj� � }$.� � z� "�  $i_�maximal.:�p_1%q $p_2��i�u p_1)� q=�� 4B� pQ |A�Y^5})�>8 �,p_2} Rw _1y ^9j 8} x=5 z*q �� }ji!k$AjZ9 Zz_1]z_1 SVdB*c�!�I֑�rU 10��_n� _1>0  {d+1.�B�aMd+1=a� �?10�t@n��� �2$,�p� �.� i�eI*"�a��E*a<�XP. c\w}{u}-%�$$Ed+1�[.n!11u�!Y�6�e�0%�B�&=��ڪA$^�}�M�U~6�"�.�$$\re simi�(argument if�J1$9�y�6})�v4 nd $x=zA�! 6��� (so} $g � _1=vib� �Mb> �F�NF��1 �(:d�i$ �'�<5 �2=g-� {b-h.'2D90��R$�>b4apZ&u !E/ � a��g>R g+1$>S9f���Y*�����dq g�h%�8��J���N�}�%��a%�.�Ե�N� By0 cend��induc�8on $\text{max}(�Y))�se�aq"�5� 7}) must � ate ��Uwe �aez�N\Pion{Pre� } �t@ iprTheorem i 2}Def31�- 2ġ �� mF�9 Y$. A7 Corollary OCor3}, �$only failsA�b!�!�"�a ��of s $\Sigma&J . Si�%&reQ�involves j!� K2-.s!�q inue��r cond)��6- � �$. �D"�A�on�of!�Y"pA#$q���@ a very ample effjve� $L$EOY$*�$q\not�L� D+L\sim HV_$HEz^&Q S TH$.�K :Z2��-o�q�PexcepA\al�E$.A�replace�1,a high multi!!6L$ �  $ � ^*H-�=-afZ1�N�&�me"!2C. By B?"ni' a�, @S"� �kesh s � $D_Z= �{� a , "�sYx� D_Z$6���2�s, doe!A�ain�omYEA� stri�] � a�he funda? al "�$f$�is disj�$w1�I�-\{q\}KE�M �(N MMa, $ME].��/. a��a23e� $&�\gamma$ �-sa5,s no o���!m �$�"P!no6�Vn�Y�� | � a6�n�%%bR�at� �� g�xe`$f^*(M�$>z +� paA� dv# . A>$ձi����@�8e�>�s  " arly. ival��!;r6!<>��_ 9�)� \cap(L+H)�s�".!�!�%2B�ndO$U=Y- _� n af�,neighborhooddq�? �=U� � U�X#.�f,1 g�;\GA�(Y," Y(H).� $(4f)=D+L-H �.g)=M-H�8ca�us"x"^ $\pi:U.�,S={\bf A}^2$Al" (a)=.v(a).� (a)) U��!!� q=\pi�p�") =)2K chem� oretic�)����8smooth�>� H. �4t�I�e $U$��an openF� A �C>w� ���"1&U� ��f=f\mid /�CD_U=D_YM',��U^*=D.S^*%=D`$g5af: 2?'S$,�x.m$}^*=g��D_U6�$}=D_X�W$. }�9"� �m�e�^M����%D_1,\l�, D_m�a� �� iʩ� than����: 1�� #�s b s 2a>y �a:a \pi%�D_i%UE�@\'etale onto its =&�$1\1-m$. f(�� ��"� cap U=�H�y(N�) _9�q�%l-\=�q\H���'Ru�#�QL q'2, zj!S^* �{e !�� #on $S$K $݃E� S^*+ �}�), $M�EB��  +:�$ �� S&�)�� A� +�)IN�'a#.J^�!%6%U,q'}$ (ED_U$)*�(y�%��%')�..zR��A�>wTc%*� f�2-%n�# $��6� B�Aj p$ (�,$a>6 b\g@ )% )�D-\cupao�@f�32��%I/��n % "\in6�&>3�uni�$ua,{a+c}y^{b+d}��!� �e�D)Asome $�'� �!�te���&, $�� OU$%|U$!n6. a��,ON� �) small0.n1�@ ����{^l �?v>b)$�� �K�%,now establisZ/ �.�0�"�Etf�.�}^��way� �,%Dxly many G"s ZxIb)�a�>xM(D_i-D)E Uf��.]q' (�+�1implieA")��� q'2u�)a�:vv� i$. 3m1%>fRbyml;"�A�%>, 4by Abhyankar'sf0`r��s"�*joG+w=zB�M�d(l0 $u=x+$ �V� 9� )�� U�A�"o �1:c F��"fy-I�:|=�& I_=�]w]&t_�m5o&K33}5 �%�  ��� �X \deltaH �U� �d2� :�"�� Ce�)%Ɉj�. �� ')&  'Re� �Y�2�A�l�� �)er�� 6wS,9�� ]�z� 3��� �J�M)E�:�$v�"� .�bM���-u��re J 6�Un � our choicO.$M�]9jm:�^�.�~.2��$p��rbF�q>=mb� ��9�S *� �9� I�_1 *S _2�z+�P�� _2$0 s:�:w�8us��}�>e �� a6k��'��E���a��pE�.�F�� W�'TY�J� Q�N�2�� f}12�6� ]'� a�_ nD�%�,e��?v% �9QCA80+E+N�R��V �p��z�* W�ncludMat� b ps II!� .i�A >�9�N�6:�:��blo:m�8.�6��e4 ɶthe irr>�8f s $F� .�}Mich do��"� �precis!3��U�do�9te!�i)���i$ or�.t1D6/R .: C������& � � R�. :t\LV<6,ea �:�:�: �+��>�a 4 say)�1q cP�:T=��Z��j�,2�ҭ��^�Bu4}�h �mK?V7_1.f6Y;:��6 8�<a&� R�: ��ak'>{�>in�nd *I es ^����%g_1=gI�-j�S�f@�z.�3fU$\3n q% ��6�n'62_1�t.1� 6 }^*�>  A˝O.�^:�map�a��5��TBZ�!�g�NbB%�iB Fn)�.� �1��" 3.1 A:5��22�2./Y X_1z��"�#E�M:�~c!��-�?Q�.6~�,]� $g_2*I�f_K6Phin�S6��*xB�2U�2N��� f_2=����<B&e>2M^�J NowZ2!l�!*@ @� z @3*�?g_3}{]J}& S_1 @�^%�3& @2@l�0:2X_22c2:cS �1V,@R%�~�A J� !F e�2[ ��"&� ��z2�A�.��'� ) $g_ �"r� 6A{SE�=5>Q�S���� >�3e(1 �7B�a1�F�RX%C2� f_3=f_2�|Mc2�3]�ay Conside�@��>C.��fBY2�;&:1!J2.9cs6"lC5�2y.oCE >yCU}k\pi~kAP���)��� � hi_36�4Y_1=U\times_SS�/AfYoC=�cD*c9��2�:$ Ur7e natu8roj\'ont �!� =f_3 � a8.:� D^*&�Q�Uu+6*4Z2�Jre.� s. =^*�8N] . OvIB��yEQ�&�*�I�VAlso,)A:��CR�a$%Y���:�! k^� 2��!=D+D_1+�?+�!+G� $G6�%�!B Y$>N(ha� 4"�re&g!!�theiri!cSFo$D*�HF�(X+i�9�|=��67 $$ 2�AX^�=B*^*+c=:.me�2@X_32j&H]�Xu):verify)PFSM@a�"�Sf"!av5�=0B�%<2�!+^�*�#!�l=�S�6m!.�"we need�-- E\ʾZi�� �=G �%3&$q'Y03-a� (p'),E�!F��  First J �0�6��2e �srH7om�s�' /� �).:� �nL.Dz!�� ^'#v,��ltI�<$an express= Q3�@�'!�#�IBD>2>3��V�0U�S�K>c���! n ��o6a�, �Bpevջ,%_=Fa'R�isNM f$ ��$e�^�)EfB>��)1$>�0 Without loss!!�iitBl')/D_i=D_�5.I�2k�J5�>� 7"Q, *C, :�.�%�u%�$3!�" �QVR��a�.�@.�}/�� D_1'"C)�ed"C1�'=XaiA���.�u=Z�An�"0 by RemarkS 1}~ a6Xb��&��e&!�two�x%X'U.�~�,fv�$r�:�~! ��2�}.��pyv.9�2�!�5YJ~.r�*RM���!1Q]Rf$k<�M !=" :%il212��Kases. S($��M?BN1}{�u&� \\ v \\ w&�L -GU"�? 2�N9�q �&S(xvQ%.?}$.>�6�6-B�%onv a����Ueq2fy^b1&b)�2 $a,b�)�%y�&%&Sis .j3f1 by^c�" �� ŏz�1 �}%. lEv�A.�monod�I/i��;�&6d quad�Jc.=S2S6T).�yS_0=S� Ea�Z.SS_{j+:�T6 � �bl�X���%�j$� explicitl�@rib&�R"�\R.�<�:�fPD15} �E+Z�$�Y _j,j6>c652P , 0,j}Y�{jFHɉpS6�I ,j}:si+\.+ ai,M�B ]l�Io\;}N{i3�{[*�\O5� %�rj}%�w A � �. �O l� !N xZ �i4m�<) $m_j}eZi�J;�*lyY=]P Y��i�atZ( s�r,nr��b!, Y �F� F( , as~ showkP�z�,8e � lis6-(FAg1he �Kon� _!�s).�G>�^�[a�1�j� :��Xb� %t an i&����)&C2�C}.= _3)`a6��(�f_j[�z.��r�� �?s3 n $j�!�� ��!:�*�/ ixed*b-N�u=u_0M2=w_=[21\��ich�vZ2-�]t��'Ik!��v2�.2W�D&1W�TK�jH��9�X.V*�36`Y:y2I}b7T -b� �V @�C" � ���Qq_jZ R�] 2 ~�S$rc j(q_j)=4;��:�[1.] p�v'%X� &�)�����*ewbVE _j,w�6?9�S_j.�0_j'� ��'� �..-$ $ov q�v�6�:�)�Y_j,q_��\� [2.]Ű-�6 ѩu_j=w_j�}��;A�HI�0A�@[3 Tp2�f_j*_j .ś~o x_j,y_j,z1s��� �X_j,p�*�y� &�_Yat\: \vskip .2truein \noindBw@Case 1.} �A�]J�2oi�!4v!1��61Ns &�OUf V0), ^J!f6:ie�� u2� "mD4�`_j=x_j^�Z_jw _j, A z_j �@Q�xI'����y�%��*�A�z� or �>rU�-�j�3.�y�I7�c�;��y�������26��J:��]�!��!���V�-���:�7.�1�.1�%�(z_j+kWF��>XA.%�U��:qx i�� >�# NyeRb2 � a�L� (( D2�? 6�%>PYr�u D,w �m�8m�X2��AH*S&Q� �F� � B� -P, �>n1'>Av�� &? J +1}'EBj�-9}$n& __j=� (-C�l �& � �RA �l0s9c ���FbF�v�D� � � BDI�0��R�!�$p)��6;Q�E"� an analys�-f%�al&Fp �8 >FpjR�AQFNz�_&�!N*�h�*D�d�@�$.�c�'D�'rͤ9��� ��Z&=� )6� �$MY!�C �&��Q� Y6� �+!�53&�(>f] f�W���e2)w%_ze ��[�h� ��"�J3J{|`Tu�4��-P�2q1s3fomrs.�$F�87��6�e�"RM91�Nb=e!�(in b�R�$�l��.�uw(�a_:�.� 1�jN��[Y2c�bJM 93),� 4-{19� �!l.�9mm��8�3}�OE*�l% to��� q1� T � ���6Hi�������6��β�i�\���~� 13} *�2��, :( � n %��� B �C�u�col� � & 2�A� � 1����aeq!R)�|J� �.) � � W��!; � Fr�"�� '� }�A�.~* ��6�� �,^C.�^ @J�� xmRL4 j��%+1( :)!�XwUv�W�FA;:="�dk{F3& N�EBB5A e�` 1>8 R�7G`�$>�^R��#B0s �2 �G!�� %5Iis2P�~"�*y5�k�)�0^�#=&ut*�0�Ay'rj!�:�K�4z�0 pare d a�Y�06�0). A�e!u Vu2�)@F�T�D# ZH�Ghow j�^�%�lso 5�# erty�_l�ts nzfEoc�u5!EiR&�ie�-�� a2�or!2bI� &52�p 9�. �BE�Re4�=�T1&\%�%�by�X ��&�% &�l=%:=T>�nA5,A6t 9� sec�J)�PD-"�bat�!G>�� �llq�s�2{��'>� wu�&g!.:��E>�2��K�J�?G%N�K �Ap�.QN"�v2s-i�P\&�*�/f� ��&BL�byI,�'�\P"�x �i+:�/+��R1- 1-�Bcal[7� i&c4B0JJN8�2�6k."WofZ>?&Z*n�B~X1�-�% 1Y  a� �)�E ��*�/i�ichz�((Y?��+��w"$)Up2& �>�Lsi_1::ZC6�j�2F U)\c�Y^), %}a6/&�%M� R]i �.9 by�� !���-�1�;Y_n*��hat�:�!/:��t'J?>Ɂ�*�>!.�-s"| �pro�l!�M ��:��7A."{-ɭY�k���E�� .�1�Y��/1 9!�.��.4]�9�F$i.{ �*X~9�"  6 U�e��i�.Y6z!�i-1E�j T{aVl (Zariski cloM!/C "j GiV �,s%%-�;^ iu�@ *-x]-͏*�E�~B ��9� by f3@!�A�up �n�-eNC)q� �^ :�?��(A9J_C:L"�lVYa�m?]x)�1�Z% en.�Zv2�2/4�*.R�_%�" PT!���{�3Y_i�Q4"�=�e�5A�A�q��RH�}=n)�H} 5���DICi���s�c�,ap�.�tA}m B}(�fa�p!�[����38 (�� �ra� )u�directlm�tVd1S.�res~rngqN��: .� ��&"ztQX_.nNFdN� nv�0\ . N>N��%A�:'M��17*�3s n�: %�$B� �]�� *3r�2 � �3uN�hX)*�3�Q��� Sigm�r$�F"[5�@&[���b db�Znd�M�i'R=���*/ySrE�C D:7yk� particula�2nuusNx� !e.�Vw on+?$|) |�3eMoe�?�C+�v y"VyqN�:}�Yy� � 3� 1myb�-`0P�� 3�K 3}}�zR2},�HMq�Z om#�f�r]B� �_1&�Q2�T� �Q�e�� Ni�/ EG"$ ��.��2WAPJy{Y��mEq�:�9q}{X�V.!�2>�H��*�8�8eof5�0.�X"�X.%�deb�|$au(X_2)$ (*0J2.9C=�byds 7.11�8JVY �4��+.�VfB�VY_2��_2j+%�vb� %�E12�1,����J'�X si_2UA;�RA�E)#�Y#X_1�$ B( QY�)\tau_%7%�=-\infty�PB5� 8.29����,�L��Le!j})'.�w1�wWzresolu�HWؚ itie�"6 75cy � H} (cf. S�6."���ejb-M}��(���ٙ��6�U A�IE�J���of��A`*OJ-_9x2=\�\>$� V .HXVv@-E�B�n/A�F�� SN&��.suB, ͺ1}��)M 2(3�% doc1�&{�Hthebibliography}{10Gib�8$Ab1]{Ab1} "�m,, S., {\it O��val�8�?�a �&ddomain}, Amer. J. Math. 78M$D56), 321 -- 348. \|2|2V|DAlgebraic Geometry�Scientz!w Engineers |$Soc., 1990���8K]{AK} Abramov� (D., Karu K�$Weak semis�p z inE�� Deristic 0}, Invent�4139 (2000), 24�273.�k�(kK} Akbulut!r�King, H�TopologyA�a5set� MSRI publ_ s 25, StD(ger-Verlag,�~limE9wKMW!MW!y1,% !,% Matsuki �0Wlodarczyk, J�rif �&� "ʜ of bibHo���$}, JAMS 15%#2), 53%#572.#MR]{AMRF��, Rashid!?M�A�A�w�� 6���of�ic :� �(Morelli�x�=C�3 }, Tohoku�hA�51A�99), 489A�537 �Corsion:} B92%0), 62963C�Q�TBrM]{BrM} Bierstone, E)�$Millman, P�Canonici�e�m{FF� zero�<�X�up!#;�ata!.q�"ےI�I� 12e�97), 207�30.�lBEV]{BEV} Bravo, A., Encinas)�8Villamayor, O.,�{A �plE1�+F��a�0eAbr�pp*�in Reva�!�ema}|4 Iberamericana�5o$Ch]{Ch} Cha�ensen, C1_Str�d�cion/w�)6fA^ hree dimeE/al"�/�0,rings}, Jour3e Indian�h.��45AX81![e&47}%I�R2, S., A�m�]�ala&ie|V 2004.&P]{CPBhAPilta�GOq�Q6*�  � �Y8Comm.�ZAlg. ��� 5935� 5952�S]{CSR�Srinivas��H-F.-N�ma��= F�� !}= DD1]{D1} Danilov, V�B��ga Ato�m(},%p< USSR Izv. 21 (8'.26ů280nEH]{EH}6�Hauser*��H6� հ V�},%s\B��$. Helv. 77�EM8�'84.�(E]{E} Ewald�=�BcP%Xsm�t �varie�Aybh.!x��Lem. Univ. Hamburg 57�$878\q`H]� Hironaka�6�6��Pn]g �y}�el��ch2 ��}, Annal�! , 79�64), 10%�326=�K]{K}*� �3s��B�)Bu J.I��  14%�5x6e17.�KKMS]{@} Kempf, G., Knud�l(F., Mumford� 4Saint-Donat, B1�&� mbe)90s I}, LNM 339�� V ! 73̒1�$Mat]{Mat} !2� MLog>�y�2z,ContemporaryI�>. \Y8M]{M} Moishezon�Gm�On n-.*�act-�( $n$-��)p� mer�]c fun�!E�� AM T)�l� s 63!6� 51-17.VMo]{Mo� , R1�:]F6I�i�TI>� 5 (19975�78.+ ,O]{O} Oda, Tvorus =��:� ,TIFR, Bombay378]�S]{S} S�*� RϦ�� a�n92� );.�5R . 17� 72) 29�300^DQe0Sh]{Sh} Shann!�D.L��v��&QG�n%�B� 7�o84�Q32.oW1]{W1}� yzk �i�DeAMosi� �=�i�� �k up� MheE4J�34�_ 373-411.�W2]{W2F��e`Y-%��JN � }, diones-�15�m%23%2= Z]{Z}�!Z �hHvmahne�^,Riemann manix�!3��bs�f��y�f}q BullF,, 4A�04��68�69.� Z1]{Z1N�Int�#zt��ble� min�k>el%��%2>2�� P.1��he-O Soc.Jap� 1958}EZS]{ZS2�%�Samuel &�*=� Volume I��Van No!Rnd, Prđta196e<B>��.5>cJ D>�t� a�� *�J� ersi�Nf Miss ."C�8bia, MO 65211 D*U3�%T&���usl��y diffe�%ǝ!Wsubmit�one: %1!e-$ond�a�a�/z.��u����~&Hch0} %is new. %2. IC]sl} 3 vmail-add~cr \�,class[10pt]{W�le} \usepackage{amsmath,latexsym,amsthfonts symb7$setlength{D(width}{12,4!� cm} >#h��t}{18,6 $YGodd�mmargin}{mLBHop> !(hyphenmin=2!�ewe&emAj�}w} \prem}{P 2o���R}{O 2&�/��H 2&c2�}.�=�6" defi��}�� 2F��}H!���1�,} \title{A�fil}�bB�[to seleBUhles} \author{Lubomyr Zdomsk�&S$ \baseline N15pt F�?&paper�$develovnJ�aE��Me��x Hurewicz !`�� &<1;� cardii$\A�frak g p,a lower bou0Af7additiv�1&W�P$\s> $-�\gW�a�by �@�pYa�5Bai��acJun{p�u<�$ a2IwYX�qJr]!e  �+1�$rm{Split}(z, q516  us i)#cos�ent�ZFCW.�d�gervq^�3% l�j��%�b�bb�1-�P8Y?(%\keywords{M�, ]?, m�#f�,: s} %͇jEV({03A, 03E17$35, 54D20}��\large \�!y��bf{.�@}} \normalsize \Ewa &\�U�sha�3res� two �$io)(.� !ysM5N��!t+e'I. hjb u%�A{~r�� by=�!�:^�footnote�I.�\emph{K-�e�phr�c}>I,U=�1�mj���, B���� MSC.} ^.�%�ITr��to�?\%0�o acT � e2CA�pen ci sOM��i� ed!��Me1��nCl�1!, m�ed-sz J#}:H�p4Y �Al�ai�Ghm�2c9 ifn�6"+4$(u_n)_{n\in\oʪ}�g��`�("!CvBC&|"$ each $v_n�� f��Y�bfamil� $u� A�colѣ$\{R� v_n:�\"$6!q � e�-8F4, i.e.mA!*w 2�mya�ea,to be much we\��3n> _(se�\~K BT},MCP JMSS%��/�s), but�� has AF eres7+-�� itself%6� ��%�qu6ons. O"&Hm, nam��#<.uП e!C}_ of c�spo+���&, �8bscuss=�8 . �/ us r*P�a6����IE��%�+,tE��&ala"am$6�}A���lo�� tak!�TAi countable�E?reforea!  $A� J$ belong^�� �}\ZsU�+J��I$.D'a !g)4ro�i2��� 7!�ǽoaU$6e� est  �[#}�E�u�;>���8_G)=�E4�pJ�dsetIQ$|J|=�#K�06nI=�[nd $X\n�p8I�e"� � obvious��x"! w����!�by%L�rm{add}( %��� I eas!,�(a�,)�x��q�e�ӡe� M(X)%�AX� M�BtE��)aiQ92� Z��)��^2��9AG�(askN�)����{ Acco$ g��ɋBS��!��� �� Ebb{N}^�֔`6>8 �xitu$ etwe� � s I ez�cf-� d)$,")$mat b.4 (m#well-f?n� a AL�ng�s m,�4,��)Va}U wX�ls�F.zu��in &!& �.�EW%Z=.� \I 2.4!XreH�� In6Rano�Wi�U굢 q�g�gan>� $6�%��ykditar�jLUl\"of R��@��@moxof ZFC� p�b2� aE-4 Va})?�A1nsw4Ac�4��d!�in neg��. qcer:�B�sw?mNG�-�yX����forwarp� �)��t]��]E�aleph_1�>lef"M1readerFLA-�"� �� devo4p� tabi��&+ . F" E� {GN� we&�a 7  $u�}e�) Nis�&iz"�o a � A }�$�4if $xGX$����in� l@� $U$u$;_Z�4I $- ^,W�e� E%���K�` � $\{ ]:K�e U\>*�:vH6Zu�A�-Aex�e ��1A From�'oA�d�tb� Lق�(�o2�OO Y9#�X)$���:@,)�:-@8�8$-))��b$X$. AF�U �&Khyp�k]Pi�r� 2- $u � Q)$v_1,vd�.!*T2v_1jvv˅emptyset��up1�u�1����� s%G����!_�g! Roth�!er���p, "� X[Cor. 29, Th. 15]{Sch}. ��Zat� *� A�� the �� :*? ނ $QehA�B>' �'�9��$Bq �Fz -ed�emea(��GB_n-�  v�\s�i& $v ! L. Sub�"�"�"�"$M�"��!��)��,��.�&��01O( $\bigcup_{� rm{fin}}(ij,i~T*� refe�ߥ�p� �02],of Scheepers2j,�o�S, )D�^�M�Ͳ��ne el�Zm%���J��a0F,!s�!��k�% } (�\[Issue 9��4.1]{SPb. "�(6.7]{Ts-new)G Is6.�Q�>1s& Dbb{R}$? #�OC? &�u`�!����' set-��+�F]D `�:��*Gp�!>Vg!]�m� id�t��W �rm�Bm(Q!Za��vn�> ��A�i/-��s�H.06E�2W)6 �N �Yf �9g�. @ worth�m�-onj � gCH�I �:�Luzin.��0} o �2|  a��e�! %k 4x���� E�M ��det��f���&n^ "!l(ofN�� m x8&A� �iu� �jgu" coZrde"b � "� "�:a�mwhy����|�:6thG��A$s�0un|+i/8e� n� b�T, m.A�ed �us#*�DmedjVSems6U2T Tugino,�r&?�)�VaNF*�"T m�E�g�J�I�be�set. A1�)�<D��[C]^{ 0� wbe �h{�x� $X< �E� o�-$X R^\ast Y$*dY:5(A�ArEd�@tlyFC.�AM���e petminus�E��)$[A6�($A^{<�)� ���Ÿ] &�i"  ( [3�#E��A$)�LJb�V�%)Hgroupwis�se)S&K p.�\P&�f �A� BNa�1 $C$a�*M5rq �F!�H-�[&K 6�H6��;Y�� AM�c�!E�estU��/(.#of :)E� �r_ �D0. Given arbit�&RBN ��DM��r��m@"F=\{C�IMD:D2�\}* Q�Fr(C)� g;th��e�Q� home�, cop��Z �6to�#. D�$v�� For "�E��$-:� y!mB�aZis�_)q�j!7b($G(s,t)=\{A�6�:A�s=t\}!S��s ��re6��$C$.) gFore�'A�*� 2[hpo:zk&E^�: "Y)� 6�Eg>H:%M����E�.��X=meae]I.�rQ �7ܿs���!���M}sfa�C�Br>&a �6*��B� a bi���3.�'�"� ��A�:��� }A�J�2v �b D��)�2� �a9.f;�T��@ٞJt%� 8iss��Wi���.Oj<|\geqJM. a��aim� fix�%� ce $(IFg"'@> : �GC.A�mn0<"-P��G ets all�� P"�I_n��j&� R�n� �}I_n=D���y�" ~let�y)e no�� ��ZG_ {F}= \{Gx m:�� G}��\ \}$. Now,�uffic� to I:ya�#72v�^V�A���&�ap��2�}Vc6� ���M�A|��0 llFM�UC�e|<. "  "!? dz E �Y&B s�!ien"�!>eZ ��~ ^�%n r unG4one"� ny�.$�9�F^\perp=9� C:5; \for!5Z%g(F��G\neqU�)A (A��%� .g�\2� %I�2�.�+$ in#-0of C.Laflamme. LaPQcl�=z.L��@:  too. K)U3*.� �IA cal{P}(C)"�2�F:62%Con�zh&C" Y) �`�� F�!�co��>}.( &.�GT� m�� (mI%��.��a�%�q�'ya ��Y�*yof . �Ej u]��Q�N���"����:�u�e���)a�q�xnon9H.�Vb 2�N)%�}1�EFw�� �n<y w= .�Fr'%���^Z�Fr�� Next,�@���P�BM��b�ڭF $�$ ��e �af#=��D�b]�)�\tQ��"K��J�re�2 $\leq�kA�Ն bb N$: \[ (x>�:>(y>!8 \mbox{ iff } \�/ :x_n? y_n\�m%dE�м\]  �2^2� $��U8A�"o Qsun���-5�.�o �  ��.. W�&�g� M"�`8}��K�R e5 �*�$e�Fual�$ preor�-SsL "- F  ���.�$Y%�'�&-I Fr.,b$� lmost lity�rep)2�� � �416.�agi��u�)m�ing*� "L3+�BM}.� �E)>] %�q noF4 -!;.r�'�on}m��R0yns�fx-M+d�9.8�&�.}|T$)���* i�� ;��*d%F!�aW 2{ ,)����)��Phi:X\R%a�^Y$[7 P6�")�ma[ &�$Y�B  $A���we pu�Phi(A)=��_{xeA}x)�  Y.$ i=A��F��fendow~��� es, �+!�/onias2lsi�cer.GA!�i4�:91��(�v���.�)�/b=5�&7\W$��acQ�$-#ѭ!I�v9��$F� h{uppe�ninuouq<2�#� 1�V)���e) Phi_-��OV%�X:=�V�%Uin���v& ��6 \C�m"�N��6 N� map >�!�J�.�A�X)=��T�����!(Hw6)A0 d so!�x% Ν�o с��"pF �w�� � }%%=�#�b�%)�� CA�!�� ;"=\��2�� v):vas[w_n].�� �EkEhRfa�6�,�Pz7a��š�%*� M:#�ZX$2�-�#���a$(c50)&���$c�$� nhM�e�$2PI2c>"%;a (�$i'Eh'vY.�.�} find�2�8$�w��%�)��-� )�p���0)63A�b�Y$,�XI�� Z�M��}� m���1��p6%� oe#ig�H ��:�4A E�*a �m sf Ua�\& U(u,X):u� o(_)�(X�B:� "����oh>$ 2�i;P��E�)>� X$ e ��b �%ra�&S "� * ue��g,* z� I(x,�="�*�dU\} Xe�I�0R� 0b�P�7n��&� |� u2}6�X}\up_v �� B �s��$B��a�t $��ote+QA BI )A�"6�Z: pkB"� A!$A=����e :� l>� _A"� X$~yu$)`)c] %��A� �(w E 6)�%)}X �+instea^BF4%43,1�Wl/�hm g,�[e)hF%AR&���qd��Y"�8�A�2:.Zn%he*bin6�Bd$D�"#���@o#Q. a.k'.�sE ��'s�A��>���� � U(u)�E� �h$. �Q18�+ `*�'�&en�5=��'c}�Bn"���$��41*�B9Abfu�}. 1. E��q{N*� Inde�+e[u  5�)�4=�at �Ni�F��<a"�4q/(?.~:��X%A$f6Af.� %��t%� grapk�i4��o*�CDon. 2EY ``m�''D�yG ^d5&m3y34 re6>�+��(by B.~Tsaba?4�Cn �b��K2J�Viz�8p)y \hf��$\Box$ &['W��k�d�n*Y2"A]&AD iB!8S�� �Ji�}q�ruM�'q�B��a.0�k�X-�*�2�e�a�P":�  x\�Hto �����-:�+]��N� m} �:� J\P��F_, bec�N � (x)=6�A�R�� �A��ס�yYP(u��us*�, OR�q� *)� &v  �� e?t�~ =z��m���(x�4q� @!".� `�$s_ :_.wj_v,)5�v"� G50L!y%P)B��M &� E��bf �0�>� "n� \{G(.�+ %Q}$. P�s=q \{s_vN .#, $c=s�I%!s$U=c$$6Fi� ?1�w �� B(%$���be��' s so �owL�U2m�EE�$r� .EK� �� WI(x_1)�s\s� c=! Bo �4I�.�,v 5� *)\}=G�;fin�M �2��2�v6�� �&�G�V\ &��T`�n�֝� N�]-end��$proof} Giv�^en any $v\in [u]^{<\aleph_0}$, consider the set-valued map $\Phi_v:X\Rightarrow\mathcal P(u)$, $(x\mapsto\up(�U_v I(x,u)$. Let us observe, that $\Phi_v$ is a composition $\Psi_2\circ\Psi_1$, where 1:XZ�,\setminus v) �?B� �6- and `2:\�.'Zwl2:w- 1 < w$. It is clear)$ ��compact1|hupper semicontinuous, while 717|so by Lemma~\ref{crucial}. Now, (mf} implies bigcup_{xAX}�5�=)�|(X)$ is Menger (Hurewicz). SinceE9(property ofF)�pre%�Pd by countable unionsAe �filter $5U(u)=�N�}~�T \end{proof} \begin{l!5} \label181} A��$X$ be a Lindel\"of topological space!�(ch fails to1-" \\ =& Then!&pre exists $u\in\Lambda_\omega!g such%� tn%� not r.n� �� �Assuminga�isF�FP, we can find a seque!� $(u_n)_{n��}$ of 9�@open large coversA!Q�- |Z $(v>Z =$ each $v_n�a�$ite subsetdu_n$ a�!;Hfamily $\{\cup v_n:�\} E(($\gamma$-)�HX$.E$us denoteae$u$YE� $V\{u>W(. We claim)f�b�$ aXnoJ�. Indeed:� =�o>0$�9�%a�of)�),)�u`P�Ʊ^ o_n=\{\{w�2%:Uw\} u_n\}$. �)�!�!�a.($X$, every b$Q�a�,$. It suffic�to show5Ire]nY5 $(cFUi rcj5oA5Q*c>�t�]0 ��5'�t, see \cite[Corollary 5]{Sch}.i��oE�� rary�a��� urJ��F.�Yfor)\ $Y�$:�fi./iHof )�52 !,U�A$:w\ni U1�v-�F} $A33% O $J_w=\�2:)a�cE>cae�0\neq\emptysetEjFroaU@e above it follow���J=\{J_w h�a����of in-(co )q%��$��$.~{a�en�qJ_{�}:�Z \}$ �w�w4 too. But \[ V61 kZ66+�%x%� ,\] �Ej tly u�.]�X$, wh� I�dic�d ur choice�!! hca�FD:��u�-Zofʼnɹe�B\�� X$. Enow on y� St(B� ��A+a\t����u:U%@BFt 2/ 6/2/ ��(be a para� r>. <is U I vided �Tb<�A� sf U;�Jmeager-L����shall�|� possess a�b�����?!��M)�mV� �X�� � )�J![&�a�ri1X.)��Z��� ��X$�D�Y�colec� [�. � ��� s�  ercise��truct� $(wF�����a��$w� U_{n,k}:kQ#bb{N}��� refinemen&6 ,=� $A_2,k}m`~ \Z0_1,l}:l\leq kU�A/4$n_2\geq n_1$ i�E�2 e��%�� $-boundedA��w_m�$B�� e�AWV� J. t%�4=b0 $(p(n,k))_{%-� p,natural numb� Y�� U_{m,i}:i) , n m\}%0ap�k)4 '! p\}=��4$. Without los%�(generality,�=!. D�� mV\nu:u\ri"��$, !�!�� mI@mxbijA�$ve enumeraY�&( wr� չi� !�m =\sqm9�}\O� _n$�E�=\{ �F�.�b .� �kFo�aim) >�Acimage*� F=\nu(U�P� a�2E��! !P(){� OA�wise,` Theorem� Tal}�&1�$ $(m_l)_{la�%�� >� Y�mF2�5a�F$ (and,�(particular,nu(W)� ?@$ X$) meetse�but[ ly mgphalf-intervals $[m_l,m_{l+1}� Pass�o�� � (, if necess we may a�f at $ I>\maxI%_1,p(��)}:A6����z [0,m_l]��M_{n_1}F�C a fun�� $\varphi:)jFD=f, ^{-1}(l)=6�a%5$9�$ �"f $B_lJi\nu V m):m!� � l) Th�-�6J2Y#$( T\unu)Q \supd$[n,+\infty!�z� $$X=� .br ap_{� ]g}�6u&�1$��$l_2A�$Given arbi�2�, Y� $K�hl}E�>9�!�6E8. Equipped wit-ese��&�œ $$J�I�A�AL AY59�AI2���.S�W -.FAmS� B)=G}!�;e�a� ��e�f\ �a<z�b�(: ^A}��qE�4{z(l),l}.$ By 6� ~����_I� :� A� have� Bj_1),l�� 22.G I�P $z(l_2)� 1�� some:� EC($l_2>l_1$. �Ŏtlyn=J&{@ A}^1)cVz |A�[0,l)|1�, $$ w�kI)�.p=\B�:�2)>1)\mbox{�a�} �E>�!��\\����nf�u $u_{6�&� !�$2�A �N� lR� R�Y>C�2A(recall��O�n+1�M�� X� � � )dr�`� � ?Y�N-&� vaj ( .q�*| [ ��t5�kE�nMXɜk���U?Q��2� , �� N��vH\medskip \textbf{P�!r2� ch0}}. F�f�L�s mf}, \*�1: 2}, "q 4c��}," remark afgA�formul�>R�8. \hfill $\Box$�Th� ��v statW�~f greats orta�in evalu k9 additivit7��ofE'gs�� M� .kaJ�*�,osi� "�$sm:sem} Ev�co VjF$ �g e� �9�cxof}�Z��t s(� $[ f]^{.�[4is homeomorhic4 the Baire?ͱ N^ H$a�2B 8dense $G_\delta_>$GR N� .� G� � с!usCa�lalytic��!.$\sigd�s Rr�u�ita� tain�closed!:R<\ $D$ 11p-2N"&�m�$ 29.3]{Ke}{J5�y2YI,6Oso! v),,� ntra%ion. ��+aR&�%EPrUbi�M� enD�intro� a new�OB� s. AFa8�d dAdbe �h{almos�}�b��!�U�*� uZ B�AD:� &[ �*�)qM�Ax.�.}� blemu�am=m} Is P(metriz%Dse� ble).g2W n\\ ~?5� e�$Sometimes A� is m� convenizto use� modific�ofF�$Xm} Y $u=(UF#�i?� �J8 ��Y$�b0 "!  $I_s�",X)F8 U��!f)> /E8� �wn� V"�} U_s(h$�smallest.T.vXain�e� 2y(�6let��$sh!v�="1"N wAJ3weJ�M�sPY�x��ce�Rx�non����Z��[c� X)$ a�� . Again*�often��if�.e"!4��%w\ndm)$ or !�n plaI9:9,#.;��lti�unch�O"�n��m�&�!|only if��1�V�p%� �9.i6��%a�B� . In�on�0 �8��M�i�$R*� �71����2$�i1`1p�5A!�* �B�,a%�!fix'�7.%�}�Y�p�s�\���� �թ4 /NB% be�.T� �tJs%eU �id�' $jWB� ��"f W_n=�� �,{1,\ldots,n\� Efb�%%S ��\ (Y�'Apply�<��e�conclud F.h(wai�*+%��%L9P1�&A\2!"6�3]a!]D'�!+^ �sp $f:w*� �,$ $f:W_� psto n�#Next,.�va�p��sp.u+,�)e�.1e %�Q�2�w���,V�f�w ]�*q# $(WBh��f*��))=6[Uwf:5:W" �on.� &iZ�%��@Z-aA�h6e �`�P �rg�#euline{�AB� M� � )<}} \normalsize \���As�v�(already sai� I�  , one�$main resul�t�paper!!��ing��&�(B� � a�ditar '&S  s�W-�\\D!@rm{add}(M(X))\geq%���v &frak gz�Le.Yusub& $}� !S $|u�Y|< r�(R- 2NZ����n N� A�,>7!�equal� !�u�*)RSYyCY} R|>�1:�+�����Y.X6G � their �>>B�b>�2H ^� 1} o{ a"� > cu=j0 iF,�~i"�,%Pity���"� &[( �rEU�U�E�(� 6+ 2;�k>�"M5�!LSI-a��erN��Ub��WM " ;��[-�r&�)Y�+A�� @ =\{Ws:"�!F&1 6�$&U 2', $(k_n(YY!*le�>�&b��s� Y=(BNF�Q =-P�!� z} � $, belong$$�s��#:�1zuE�q �ݪM��Ae�_Ye�.� LYBRp_{rf}JKR m-63&�2makaVe�U!7�:�n1v�#e*Msa):�" $\{BB� �.�6 &�-�us� r"M:�� $y}DžEZ|�N*n_k6�$7�$A6k_ ib�*b.[��UAJ t29$Q �I_s(y,I� �-f&�-.� �B_mS� �pr���L�6Q Mܹ�X� �6�$ true�!M8Z�FJ?&�*\3)\�[ �T3աSplit}(��, )$jv Throug`&> ragraph�G�is devot�!9�x, -BdWZ1"40v�)�$��a 8X+0&��� 6sub��(� t/*.0 1.1]{Ts3}), �xrestrict�&� Z ones�&4N �+s%� Unw)���u�  g$-*�r.f�5rmb�!LN� � ��e !<2� � &�u}"7  stra(forward&�ce Pa %da0*al!>Lult of C.Laflamme. A�-��=���P$C�� 75 dbi-�_Dnei�<� nor�Aq�1 ()�-, 9.22]{Bl}, {Laf1}) lll} �8�� Y���)� �$*��C$. If6(.�( BE:$B`is 1)I�Jq $(KB�!�paiQ( disjoin�'a)"C%f2�9A � ��U2&� :F� K_>�1:6O( , �t7 Q�FrS(��n ultra�7�/l $)>�vRe�.}%�BH:i0D(VisKas:6$A -p"� increa�&� (mBva">� )S.�'9�& [m_n)� )}K_m:� satisf�G7n'o���Q�!26�..lro�.}�Al��C"�429Ei<�4�erRj�5���� ha '�&��%z� step���G&Z'H8e (��;Eeu2� . Supppoa/A�!�V�A �-d&� sup?;u���v�:.�I��*�~�;iem�e T�9�':�4 @$vE�&( no &m� $v,<�&�< v����7 beca�!ow�,�8q�0y��0by indu�6� vR#��u.2E^�X ),n|,m#�!usNh)d�2�Ta4=$ Two cases�2 ible. 1.-6���M4cf6 J�:%� )�-�)5͉�2����/n_0D�8��j!�h �e&n_0}v,;< s 0"< �fw $u_0�(>L_ 6�u �L>�<�5a�%6�7����n �}� $m_01��0Y( neq  2}$�{n_1n_2�a� $U&�� 6�!k v_m,$2�&�um noS< v_n'H%$< U6Tv_m � 2 !Cݟv'F}jKF] �;A�l�@!� � $u'=�nE nNT=� E\E{�7= ��$u'$ h not ňtz . *������wouldiYtwo&�"qD P*[ 64q#}! both�u_�U� A�<u_B �� B���i��v��%Uc.�B��ye�&�� .�:_;)+A\\}=�-B�e�" &�Iwq�!���?Vf?!�2� , e�$A!g$~#%. Wn9:B,> mean �yv����n) vC?2A6^ �卲�w:!D� %��-�DIW,W=.� 6� .� AZ�n� �) F�ch0}.j1H!;J&� �JE�m[=�'n�_ �-h0}��By�>�e&/ sE�xbe �4�)2?&��:uAeE4(X�Rq s corresp�-5oB��&���TL �(�.�e� �5re "pur 9�&.s"..�pB�- a:re�u� a�� )S�<.��,qB!�o� . More�W&p() S�V��o! kBQeH���ф�"�-u�B� �b~�?"ed%f the N�is free: ��was�3 4�%�(f&��&0�VdWJB��HF�K%��)�Ks multiE:�o =!�2� inE�!hiE6�!�="�&�} �J�$. Ea4If"!@` �<��o6�i; F�:�L� �L>N ($\equiv$�Lhi_R��$K$-a�� tic)6. .�,�"� @<�JR�"� %�BC!VakA� �� � ��s, ia[25.A)/ u]K��y;VV�!i!�U&�>� 0.F%5&d7> �L ExuV�&_n^2$ )ɡ5!�$(U_1,U(7�?U_1��U_2$.~�;�V �1(B[�+)1�B4 1, p. 30]{To}a�6�a�<i.�e*�":*�R`2` ��RW�3��"LH��w�Fterms~ob�-%<� �t�ult<v�1 � {Sa2vV@asa} z3:xAo)W6��6�group, ��� *���#1A7-y F� б�c��M'i� is Scheep4C�1�!i��:`8E�(rm{fin}}(\G�M,�)"�-Z-�a{$�5F!\&c [&5"8_ J$E*\�8M"�(�8ZTJ� ���M&�4��18�w=�&J )�"� ��N�"X�&j�%A)^Fe2��7ZS_s�)� &H 6*(�"1 I�� gi�>usūJ� ��>j2H �j` 6�B�B&�H"�$��� [2� �$.J~rIB9+E �:%���� LB>7IR$�P2�f���$n�lFMZB N�A�� �z�mO=�ϭ�B�F"J�J�<2�� ~.��RMb) J~of>U>����i{M\{K_m:M{n+2} 3})\}�D$& 2=e$p�*%)�2�, nF_{evenz> up\{2R: n>is�nQ@ 3F_{oddb87'�V $�Gn�F=��� 7F&w(}).�1e!it_+1_2n%^2nzF&�A�I K_mq�k�S�� X�x�pqf."� &\Ff�>��6g"�S��(:y6  $Se �.�&iS2�F_x8 �* :I�64FB�F_`.y�>b� �����%$ %��@R S}F_s�2�ba�� ?[m_%�|J)�2IU$S� !�. U"��S%�1�� 1"t&�aw v_k.e,Y�� shes&i#. � � Jz N�8 take�s origio clIa�p�/H Hu}CW.�*it*�E�a2 �9� �A�� -!ndqif=>�u(u�H f:X\*6La� bb R�/$�?$fcj��domina- �qect�a��� tual (l$preord�PWqR zer�mensona�Ae �s� on holds�J��JV�"(>. Tr�4to"|Mz���1 outs5!�.�6rs, A�1�hop'�realm?&y1)�s ('-�FQ'- obviouslyC). HowAa�i�GtacleAKbe �� ��'!<to*�$s  ��23 �M� ���� �-}b_=>  $EZ6!$, 2�*�F3T!F&�%F� Z�V�* v�(^� � u Z/2� �Kn= *= Be^;aM-p:�itBK :K�is]&z �19�!��;c � J�#6��MB�\aN�#deaE5�� stFC worke�perfecxV05 ws:EU:�4e~B>*I�N�7v�Y���*{BH}. u�"M#J!,%Z�ZJ� Z�RE�E tantAꍪch�Vteriz�,2�%:�%t �,t� B|s.2xample;0i+[B. $Z=� R,\taaA!$=\{(-KN,a):a� �\\}.By$�&,U"�3 $ZՈ2�E���i<,E�Q�").�IN�� 1j. N�B�Bs�to�v<`ge�SƓ involv�m�Ubw],�B +�>@�PhiF|�[F� ``?''�'t  q>HI=H[6HLE vali:JA�&� 6!. T1�' "if"jh�Ltr'�V�:surQU �� �Z�A�} b� A litHV repet嚝=#1} � E�� N#"q��) �iz. �:2� �G8 �"q*)���z�use.  CQ �R�G��E�� U&�&��bS�7A+"D�l!U��B*(),!�� � .� A)!y{ >�*p UJ�6��CAA( j}. �5�<�"ioned< �of��e � �(6��` yJ]�G=m T=f( 3��nA?)�.)Bb $�4X |[�?"�R� $g:T��g(T�G6�!0�~��m�Fstrong swJ:�^�*�ET2���Z�5l.y�5x�all2�a. T��-S �$a�2;A�Ad�Lf � ��S $g_i:T�a(x>4(x�i}>�� isUXgen $T6V89B . An�' ally:asB�jsi:!>�i.N,^j(ni "�j{/7>}:\for�y� (!lleq!l)�,A direct ver&�H�w" s� >�tR�$( j\xW g fa)(�H>x��H�h�/$Acknowledg�Ns.}�'author w�to ex�is !�thank;@prof. Taras Banak$6 o po~Qd� o�1A$im�Nt rolE:&�f1selW principlBnF�s� ; 0f. Boaz Tsaba�Gho madnv��helpfulp��s duras�pr�����S� �$thebibliog7 y}{ChGP??� ib>&[Bl84 A.R.B�(, {\it Comb�,orial cardin "s stic� x�um,} to�#T+,in: Handbook��UR y (eds. Mk em�et. al.)8"�H]i T L.Bukovsk\'y, J.Halez � On��!��WiesT*� T�jyE�.CZ�"kM]{BM!~-,H.Mildenberg l O@e�^!�3powerv!� rint2��ST]{BST} T. Bartoszynski, S.Shelah, B.TE)Ad3-Q�e)� �A diag)� s },!` Jour!�Hof Symbolic Logic \m;P68}(2003), 1254--12602��N�B2�He�?y -b�D>�a�A(�-"'Con ur%�pProc. Amer. Math. Soc., to apAR.ZB� \sf{http://arxiv.org/abs/0.LO/0208224}$.�Z]{BZ!�q� L.Zdomsky-�Co��!<" s}, ,Kyq.,\CP]{CP} J. Chaber, R.Pol TA� rk~8 Fremlin--Mille�G�EaAcer�$9(1�y%@Michael + ntra�:�6},RwGN]{GN�8Gerlits, Zs.Nag ��NdM_$C6 , I},c]Im}6UB,14}(2) (1982AF51--163eV\qUHu]�W.�G�_0\"{U}ber Folg�L tetiqoF� en}, d. I Q�9}u27u93-204;.�JMSS]{}w(Just, A.W. )r,�u"�D, P.J. Szeptycki, �,�T�/� ��.} II\/auB(H�H73}(1996), 241--266.DDJR]{JR} C.A.Rogers��E.JayneMI2$Set�oin: A�" (.Cet.al., �n), Acadgq\ Press, 1980, pp. 1--179.�Ke�# A.Kechri�l�Descript/c��}, (S�ger,19952�La]�:*S; ��\valq~�I� JsaD:�8! ransF95|330E5492), 307--319.�HQ�LL�6�C.C.Le�aE F�qgatPon"�"�Sa�d� �; Fund��Q173} �x2A�59!t3. �(Me]{Me1} K.�,1ini+m7�$GN/0301011�p�[Ta]{Ta� Tal�@�dU�r\4Mesurabilit\'{l>rapid %`ri " de�& fort2StudiaE-�74eP��283--291.�To�&( S.TodorcevAP�Top!y--�5>172�Ts�@"z-�R�s�@t �y,} Ann�=of Pu�0nd� ied ,5�12!� 2004a�07--130�p)� 72252pTs2]{slR�" �� � �mslalomsv�[-(E�,} �\�81�]�27!�8 � %%%.�� wi�Pd\$submission.es3RB -newB��V{X'�v!��6Z&A � !�f�DVa]{Va} J.E. Vaugh E7S6V un_WG� *%d `�J. van��(, G.M. Reedv ). ROpe�a�D�CH (Elsevier Sci. Pub�E41990) 197--216�@A>h  D� ���5�: ���z s, I�0Franko Lviv N� al Uni8k ytetskaV*,8, 79000, Ukrain�;G@ it{E-mail 3ress:}I�tt{lz� 8@rambler.ru} %ť it{H9b;:} 4\ubomyr@opari.ltg.lviv.ua�end{doc)6}!X\�0[12pt]{amsart0(setlength{\O,ndent}{0in} :KP}{2ex7uzckageL,math,amssymbfonts thm,�Pics,pst-plot,verbatimITBA C0tbt}[4]{\ensu�A�left(CDarray}{rr} #1 & #2�#3 4>de &V)}} EFronti)%ff.�F!��ft}{\fM\fk_kl lz 0ri>_igek{\ge kdg >i J:m #MJmo  {M-1Hke f_{kA�0Random stuff iBvxA6vis_XE0�modmcg2f}{R1�kb}{K' �h13bb H}^2  collA�C!u%% aL�]Eq!]$ib}{\bar{I�ib�ib_\star!��!a�mu��h �a}i��tsTf"/Us[tso�:e�(\soo�tsz�zfmDCoex�cp�e�pcpo^0ccc�Surfail��S_{1,5��S_{0,4�szfi} 5ot1,2tz2,0-kF1#�5�cp �tf:8f] ooszfo}{R!��fg.�GtiD! � !�O�,et}[1]{\{#1\a. .�:_2a%% List��: bl}{"�v4ist}{$\cdot$}{2��(margin}{.25>�<& B pars�<0.5ex plus .2ex ��0��.� item 0&00 1 } ��el�znd{� �Pic]-�pic}[2]{��,figure}[htb]�M4{\leavevmode ��fMi#1.epsI9cap� {#2} \P�#1Y� S} r s}[3�` psfy�V=#3 cm1p 1 � +N2�z��XbelZ�a��^%t{thm}{ }[s�] \nt*{mM�X"{� }[thm]�gp lb X cor C;} *{q}{Ques!<-�Typeset8(-.be6b&�=c�RaO!�i%pE�{\bf #a� \� {ram%� R� A2input{!� .stytitleJWeil--Pe�� son ��S via � e��lA� �@hor{Jeffrey BrockV�{D� arg5d� {:& ath 8\\ Box 1917\\Pr ,nce, RI 0291a�\�F9 vhHUtah\\ 155 S 1440 E�A4\\ Salt Lake Cq 4 UT 84112-0090�:A:�@ �K pQt�6I9d{($NSF grant Ww$ 0354288. A^ seC�GanJpostdoct� fe�iship �a VIGRE6$�:�8F�091675 @F).�e {b!�@t ,.brown.edu, ��!�  utah6 keywords{�W\"�Y,BaE^c,]i\ppC  g 6sZ subj[2000a�8imary: 32G15; S%V M994mak"l��i �-}\todayeX �2�ab,P ct}W�%te�"A���� asur%} Wolfn#say�. hyper�s� $S"�mZ"kJ.�3�a|>�)>A��JI|an el�7mFQ\ . O��Chandl�Ce�+unt�ked6J�h�(ur-holed sp?, torчA�0two..%5o �kK{In�h�3�pur�L{s���$ll�se;gap�h�erstandATofBE-�ies�\ET,%z�'n�.eLJF��$S_{g,n}�0�j1�$me��$g-�$n$ p���{\em eEoe��>}1� is: \[ U = \pi_0(� pms) \]/8\ts�%Nd�+S �!/Vc. :�pr:�/�!$S` tin �{� ,` ,\Q R� �i!��j�96�$�$ �: {mw}A�.�!X0 gred!�sL�exau+t8u-�s,�"autdmphism!�c� cur�7 �!q.a �;�PA#?��ov �nviU8�uspe��mAduKorkmaze!Luo 6mk} f�M See��a ?&bgI &n-s���A7;aIL�*�$:�toY#�0sN5'��vie�#a" y $I�.)�as��aVan6Q$i *!XE�7� �$S�}By.� !y02+ibs%�n3{�a.�:�$fZThen,�o�eE_Wol& {b�%*cF��H�O"+x"�� $f$ |s!e���we&):�FQ ���m�$\eta:m� \to  (\ts&&5). Fur+%! ker(;() \cong \zt�*aw:t ot,\� $N9: \oS .E= a�:3= �j= ?3}�$� =1$ M>NQ��%iM.&shS!�Y�1�Vvi�mo ao�b8(o��esa�@MtkmESatEѹ� ar}��)is wa�'�,%�>F�e���+I stud�TofRLM6� �2� ' &o*Royden'sA��2�4�Z!analogug$�X.� ��%6�% c �p�p{J"%We_Nlik�"� Ben� Farbcsha��) � � al�s;!L� cH�4$uggested uKV�i�Tto� �B�9[eP�� came�%f a�ic�{ honb�?F� ;a�LO6� ��i�:� Bob Bell��Ken� m$� �%Kcu3 ��c�W �I 4 G".� ase} ��+diD� Chris Leo # AlsoS � Sq�� ta} �&en!~� a�^ Mlad�estvina%)�him�w�s�1ie�,�%�en1We�"�prgQo�W1Lgratefuf$Indira Chaji-E(vin Wortman\us1�en!8n earlt draff-�perA��{Preliq7� "�bg}��briefly yBbasic�p��? epts[p{�!]�M(ŷQ�G�cc�$, ���_Harveym�wjh�[ �2!�ct�1i  flaga $vxXce_:�Iisotopy `(f Je )u �5e r 0edges between\" ��bA�alizedA�I[uon � �<��z sA�5S' �*�=ndesirv-�B w�8: $ �Zsz�bo�Isot$:!��*� [($)f�0"�-�y��� , mods�K=Jzf�SZi!�We-��+%�� c" Ga�re�et�$��p�ai��t�mo�w ubtl�Luo�i� %ri?] iotai3��L ellH#c  3 utioō W!rR�u/'$\pi: !CC sot/ Z� { "nl5� the U_� \cc�t'r K"i&zfi�<�/�Gcg(!�i=�t�#i$ly!#�JnH : E�EFtwo& ? one y5E� threTUe)o"3%^s�6 aut( �ot)}+��P X>of�B4Mz �ngmc. Such 6�cl��yaXA�u��2}es�I�<fl}� p{P��Lph�,�~ţ �xp�x i$iHatche�Thurston��htO a���Zi��q�z��de4Ms�=a�((i.e. maxim>��\��A`s$).�� conn�!ng �6Vm�differ��a!+%�n�mov�"b�rG J�eaA+�E[%]:]WZ5ArE� �A� "�s� �n�v9[!�erͦ�e�!i\o  is 1�2, depe��ve� eu 8sre�ud 'in 28 ngleq\A� �ohe t�!"��) iH.; �KFi Q!Ns��ics }{E6rs.}{1.5�T }H z� !7n� M�dm}&2 �W dan}�k6< th>> i�p�> =�ײ@ 2; \z�B 5fD IjE .JG !�nM[��!f" �)�!7A]k d�I+ab_j �4=��� 7�n� E6&�� i�EN� .} AC1A�z�16� `��t �6iHvGY� ir $(X,f)&4VX�b*J -areV`X�f : S�:� mo�a��t�1sm�m$(Y,g��YC�O�*t�gA� rc fg��� �a&'�9�$�>�y��I �_Y{ �r�J rivial)�V46��isqIly a Riw1nm3��wuni&oS0 �W quot\�d $\h$�k$a Fuchsian� . I�s_� cotang�%� $T_X^u��M.!� $ifi*� =of hol-�c quad�c�� enti�'Vz(.,�$ typ�$phi(z)dz^2��^ � A� $L^2�ne/ duct by:sla�wH,\psi \r 8= \int_X \frac{!\{ %}}{\rho^7]91p $rho(z)|dz|EL� 3� �A��%eVV�e�� !�/�bi3[� �mu,�J�mu� \]!;|u� e�U $ 9�)6�. Chu$Wol 26�V�V�!�4 Rll �tc�sw1ɒ {Aug��edNV.}�g�! $W$ yie�Fa (� iblyO � ed)B5 whos�: mpon�Yl�E�pio WAr��� ex� igmaI�� ��;n� $(W�o)� �a�wM$-�V��)&��!�n�T� $$f�lon͘W$$ sbif \. _{S >�! ~!�M2�!�!�)%�W!���n��� �e�(ZZ�� I:�rking-prE �phi�W�uZ$�[ +e4Vd�nda�6�oI� ���.�) real�$� bb{R�" To descri�lne})e�5�A��%Ne� coor�8t�dap�R�� YJ!VQe2� #tauM5$)� �T� �r`�8Fenchel-Nielsen.�} ��{(\ell, (_{\alpha}\}I��$(!cb! _{>0�+��9%$\right)^{|�|}�с��f J�+Etwist�ame�  all�ufge!� ic $ �_?ViA�A���o$�, e.g.�� it})��4h_h{�ed r'� %{!Yo�Va!�� ��;��  $IL)��A� stip�'Wat^anyF $)�' '~�h�o�Y )_)a� m (0 '.$������EO�rI��RF$%F �.�B�!����6I��� $0�-nd2RoXB$ oq=6oj���e�a�� Ud�Q%N���2> ��l!��i��גnE� ���A� g. ��:acA�@W�9o1�?� � ~-t���Vɗpi�d�S�9"r?.}t thinC= �� M)y!a%T$C,a�n�I+ug:s�=ng� �s 8k$� �.}$\fR�?�I-�D . P� %h!�h:��7ly�B{A��� ssoci �T�>�O <�T���s"U ���E�, s�D��unique.{ �m54~ � nAsNx �msW�, l"�c �48�)��Nsa?*;� own� $d_{�*!m�>��#C Rinher9Qc 7 ts}| >A3!NJ� "�!pr&�!, t=V�9iE��_[�a� trin�Z� ME,aiA_"N @ .���minimizA� pathE~-Qdq e� e-8"sw2 Ytog"as�g���&�(� [Lem. 1.3aw mw})R��Q}O�T����-cs)�os}�Z!�2�r �dZ\p{Negate�aA�.}R!{N�romba��1S!�Z�nR��Aur \<�o�(x)-{aj"k!u'�n-\ 2L�90CeՅ^ amat$-%8 9�{bh;Vis};�&.}  b� Y��A��a�uv.3�vxs Cg7&it 6�� �PDu�$��n-mXene��heZd, cerc_daEKa22��J���Ute-m1�s �}T��I%I�-�$�ay&^]!�Yse) a rays}`De�R� ��. �aA"�R�$5�K y��{� �.!�E u�U(� den�+�e�{jbr&�Dm5jeff}� Y� X= t!� {%���/i��6�$Eyy� ideaI+at-iYt7m!���^ly�t1�� Z' $N(X)C 5pa6B }$���ac?"� s $XBIdO8OkU)� a�W9�, a&�T K�a+]����U� dB Q� e4E�o�_n)Rnve�� M �R:!�� XU-at��H#Ee�%�UI"Va ICsw�'i� mmedw�mpt iDaB�ietr�$:���!3|Z��bf,/0�w �}A5�C� B nvex hull!� its b]P+Y 1,�� in f��Lus��r��X�AL"� t�"q:B((���I<hite!i.�4% % &�+ Edge 1 �4&a��z���L�%�=u.(-1w�"� ��of,T��� XnDI.�e�F �$*]#ic�b�� u<= lw� llC!� #(e��e,� . B:����}j* �@6vM{j $\tf�'[!>5$I ��en$$���Int^�e��2 T���?�G�h� nd odf/Z�N�9�4I $Z��!�M/��'f$ ($Z�Z}_ef $R= �^>#"�(R7zf$��e("��$a� �t>(E�>f  Vof"J-aYeR!|q�wa�NGs�7�q&� N�5%3 M�z Q $p/q r/s$ (%�-.!�)e�&r bBAe���$�8$��$ |ps-qr|=1a���{Fareyl!� $\fgMi�I9embed��e�"�@} ~ h$:  !�OXeplane �e��V�"s "9� at9�(�5�?UX�a?���x;*F�x� m!(\p)b-�Bq!4T1 =8� .8 farey8 A nowa E���!4)X�>� �.�+r_in� ax" # �@�!c fixe�d�5yMA�*X16�to�tbt{1}{0-1=�0�'A�gV�)p$z�pD�- z�� $�v-o�� �*\ !%(� � �2�!B�@#�6�R��di� $s�6 cp�7;:s)�}7]� �N>  .}{6�3{ if>�vs.� ��jECz/��>?�enc�$ adjacency� �gQ�h_.h l~��Ud:e�Qg) tri7,ek!hofyr,!�, %�q�?9!�-ed�tripod}W Pe� nemI[S��g��0*J �:J ti}Le�X,d�oVJ �l*ABCJk ����!I� - �t/1� G h �'�$LA�4�D���e@BC8n $d(A,D) > L/2h �� pf ���at,e7,2B2\�T5 eQ��ity�S&� k9%х�� �=��l=d(C,D)=5�)�l�,O /� 2oQB�� !�p.�ADC=AC �$ADB=AB]4e�%���)t e!�� nextQ�$L%l>*-�ofI> �RGpd���(*�G��)�$\dwp5>mu�  >� !�M�E�}AP �P'0i�2� � $\pd(P,P'A+11��6�2�s��"$W'\ ve � (W,WJLJseBge`1�W.W'A [B�>p�eLR8��leqzf} = 2 <oKu-P�y)�>ccz% �%n� �C oo)$ ���<� vor�Vo�is,���z $R$^j � 29%R8%$Z(�D)e�a�us�g fold� k s�=t-c�BE6Dh 2�,�.R~R/Bilo�3�q�pi&Qcanoni&F<.1FR:C.i�'i!��!R�$�_�j)�� -�Z}5�2 /Z(R!4mx�:d1�de� e�!�F I8h*hͷneew@i�A�g�A�5.v5} �S���M�,�e.&,)�"HEu�U6;Y��$I�!�(8)��\ibp��"]�I�� �*�戡�ek/�8$\displaystyle �lup_{i�~:friH� &I* !Pals/b�:f&;4,ZG5]{mw};9��%���n"�4e�&�-, q|���-"�:�S(%n�Go�s�a}!e(\ft)&�!ft�I$S ɖ&�9)� &�" Q~hu�!��"M+,,B��N(W)It�2�'���!��2�"$K!�ű \kb = K \�\ibATb�1Wf1v��(�~ P����}(_ &sv9c6��&#3pacBu�� 2�Wr� (nam��a+(\kb)�so $W9"�45�� �II �_�|.X�!�Y8���yAwb�2�#+��out���zitselfK���oe�Ke�)aR}A�� V�c-���!�J�2DI!�%�H:E$I=S6XTg I�I�!�* �� ���"�e-�a�l�]�wJ R+iv!�"� 5� fkt$� �e�� �q!��e�.w $\fztatspby�s!]i2]*�YP ��= ju��h�Ų�Bt . N�u|�%�[4��.M �i�$�-Ot�$yT^<���/� 6�'� i6w �1* �z�7by� �EMY2N� f�.2r|_{R�(!d!���� % W$wp bine�m� !���G} -�riAJgap"���9 �A16�5� \|��>�c ���-L!�ibs�_&R2F�6j �8G U.nYoi�IW}m�i6��.I%% sAw6w# high�4levelɊu��fmkV�#f� 6] �J"�)on*{�+)SP� n $2!|�(\�Equ�cop-�e�O�t�"BxU &�A�2#%� u pN4#a >��"m� 4 AO)P [*� a�_{�/� }$ m�b�7e �*F"6 ^Pa ") �ah:�%cQ�y inva^tM�  b�>reZ �pbP>m � s 6 a^�V� �By.A�%"}� n�M�!(�k&qB}, I1P)�� ��os)}$;���y�Esa� a8CF��F��Q��9�n�.� 3}  Bd ����ue{��r�6�da�`��D @� G.j�DBy "N �," As�Y!�?bj4� kernJ�->'7�8!(!�&B�*2�D�1��^"YfD {plaQ.sf{wp e.$X o�6%X�WX%6[pdftex&?X%�6m�,a�worth*�4 ryadd�,��vs %a�HKharlamov & Kulikov��@of Julien Duval, . % Vhe�i+z?mo[�pr�=veK�O��JA�E� a 4-di�w ;st7  �",L %�y8Kobayashi pseud �CB� %*N ebh�Dns��� adm&no,d4 %) esېnGif cu=� t 5 �TŅj %�2�Q"�͉���lt8��. .�Yifthe�Y*�YsubR2+am�YBZ6eu0pt2[all]{x�Ql�|oref} %.ro04ng:boxed( page2^{`icx:2e2�&�Z.qlscapeB=sfi>��/E::-psboxi6�{x� 6�j�5�Dnewboolean{pdfOutp�ZsetF{falsd5a� _Z43 qels{RBq(} { % PDFAks:=7�,!� backref]{Ek%�@.�R!PVS*\drawfileMSr�� �lS-�rpdE2�j=�KaZh=2FkRB� �I7^!�>uCb1CV1Qb1QV1Zb1ZV1Hab2HV2Ocb2OV2CPb2CPV3Rf3RZ3Hf3HZ3Of3OZ3GrF8��ce�Gr4�ft(A}�)> Gro K$widetilde{BJ^K6�GrC J>�_{\C{�E nullH�fsu�2 th{ NV2i8��N�W^6�OI2DSO��):�so 8�U��{so�4SpiFX:z#�V%�|>}&`>� ��EClFC2C�;�HGL H2<GLJ96zGL�]B9^+F�6;g �5}gN�64SN�S��P9mbb{P}\SLaN:`�e%�(GN(slLie*)���UM:2fU�eSU k27S�8su 8� �u�lym-�.�6zpJF:IsRG��CLah2]>�Y[26,Ia�R@�e�jDCnE� 2^{(1,0)��Con4[2]� NN0,1�N:s9��oJ��u6Sym�6�2�"i1d2K:LLJKLambda@)a ( � � B�nFormsF� OmegfH� BL CohoF� Hb�VG Homoɵ. H_�0N�GDF�k{\Ad}{AdH 2�ModSp �uM}be >�@}�!m�>��PE/ {}^t��*0 ba�iHi�>Bbarj}�h\jN!LT`Q3_RR$D^  V tr}{t're.�Re}:zRe�6&IO 2�Im�R�ad}{aR�lm.�Lag �=�6r"iR#1q�:P Norm Fnu%�6�Co��!^*J# Proj !!���I V�ind}{6jON ���E�Y�kO)."�*�{�i�  { ( ��p1�B|i�}�} 6J �2r��^!�lusaa}>�B�5 % BlowupR�2�Bli�%,I d -*-)6�extraS�.�G { 2��"�S!X "W&#1 �hce�> emph{�&�&�.�refer�to�H/b,tl�'may skE@.Vnd6gpar �BY �"�/��B��1�����na��� �!L%% �an���ni:qPQn}�P>� Line�H$��>*Co:Rp�sR�1.Lcheck�>ODN.ha��:FAffineP�46�A>*EpiAP2�6�"i��2, >vlg�b2���cal{A}_n>2div~5^+F7gr!�}�l&Wr�Y �#2,#3�\�4def\cprime{$'$:� Splu:�S-� ^{2+B� Sminj1-B1INF�# �!r.(��Z?Q��i!lSZ�}"l Benjamin &�k*�_College kOs  $, Ireland} J@ail{b.mckay@ucc.idate{�i} %�kMSC Pj,57R17, 51A102 j14N05��{T�4Robert Bryant �"Jz|�ws.}1a�]�]3�� l�c6�*Radon&7:$�> 6BK� M/"�R����OWe�&`k%, of a��a z Ԕ�"�,*�� 6�`$ .�re�PG� �Ks,�h*2�&c'�7 b �colIk;� Ra v�_t*'� .c�V�)B%(l�.B[S�9�&�mi�9�!C!�pa"*incorpo�`s�F��r#��C ,�9&�5ve Jpublish �bf{Geom�0ae Ded�da}Asma�l\t# ofco�ds&9?6kA1>>�{�jb!��o"���$�G m.�*eWx��subs,�6!��1���#e axi�|ofF�g � y. A.;Z � n �J_�B0 $M^E�$ �=a �,2-< \�!?�6 ^n% 0�!�8;�bui�R�"n(J��& =H��@恵ite{Ktru�)e�.��^m>�uq ��:X��2�@B%A��H� t9e%�Z&A�s��AGromov'A�)H0nlip��2�� E�)Jn �����y$.csk�7 $\CP{2;(P&in only6<Q1 �� 0 was �� n. D^�!�k �BJ �0�R��"_6R�,\H�(O  sre� l6.v�0� k.CoZ\���%.+�� 4 or�3$!;2(�'I�>���e�a (�d�~B, A�64 �e.�N���Q�i"�.>��% J� �ef-F�+I�._ys��fBhM6�Rc!ӭ%��y p.��A�h�6Y(2� �g !�orm�G�:e�, ~�P �@ne�PA�s�w2�J�!�2/sys��7>�an ir16mv��az=� je ofNu:Bv5�y5!�� .�� J^ �U�II~ {.�1 )j�  $���.�5��!l :2���Q�Ms��l� o |  ab5-��_r;�EE� z�A ho�W�b; the�2�@mwed 102U+moduli �space \item they are diffeomorphic to 2-spheres*�rough any 5 points, with no 3 colinear,Txre is a unique smooth quadricS(e dual of a:# @>74end{enumerate} Guncoverp0dynamical sys�on�4 2-torus which[$the analog�ofTelliptic curve found i Cproof)HPoncelet's porism. B�4section{Defini : � proj Hve planes} \begin{d/|} An \emph{incidence geometry}�a tripl!_�$\left(\Pts,\Lines,\Cor\right)$ where $ $ ; set (whos?elementsE called% )�}�!7� ), $ lS !�UzSA+R� ^ and $� \sub[� \times z �2o Z�ed Zyw. u$ !)B  correspon)�eL},-*.� 6+ } or ' flag :P. We will say that ai^ $p \in�!dA�a�!�ambda L $ if �E p,\ #M *$Cor$. The �a�}R��]X^*MZ Cor^* YM^zPts^*=-�U  Pts$!�'?4=\SetSuchThat{ � �,p \} >�\inE}$.i(5y5��-�a �>x}!0mzBU��,two distinct)�$s $p_1,p_2)O �re)���%�� p_1 *e�$��B]E�!n%�_11�h > have a jcommon �> -G>�� m �t��$at least 4 Hs,��threea�2) A sam��J���.�-_.E�!�A�: -�topolog��!����) �pre!pact 2iZs,/��map.�to p_1 !�E�=>.| ,1P=Z$!�j ontinuous-.�z�.�Z �3^ � %$ manifoldsayCor�>j:� ;,embedded subG%A vC�A�Q�5M)C�!jJBTY B#ɯdstudied by certain German 1_ sts;�4standard refer�Qdis Salzmann et. al. \cite{:1995}. �� StateA\arta-G>� s} Tei%lHuseful characteriza~@, due to B{\"o}diE�$Immervoll:VbSuppose�Nwe�7B�, form�$�%an!���eblosA� Q s, b� lof dimensions $2n$ ($n \ge 0aY�Fnteger)EP s.���!9�L 3n$-ial 2�lyZ�so)the� anon�TEmH \[ \xymatrix{ & a58 \ar[dr]^{\pi_{�n}} l]_ Pt & \\A�Pts &��( } \] givenA�$ I2��)=p!d 92 m1e�)la�er%j. Call5� � -�(generalizedb gConsider! K(sets $\bar{ k}=� �^{-1}�)2� �GpA 6 C� Ap;#$E�$p�L )N�� �*)  tify2) )� 6�$M| till�{ig �� (:+Es lso often.ed&D� row4 !K J{,literature),a`l� )"�ll beYA�pencil�tb $p$. %!e�!���api�J,�n theorem}[�4\&�3 �� Bodi�GH2000}]\label{thm:BI� ��BQ%%>� justs a��!l �trans� e)��G)�1%j2��4.A�> ly, everyb��= Z n6-C101@,corollary} E _�5�>� ' is $C^2$�� en%�to��$ ! �B;; hŗi� >Z%!��odepend��$n$ funz*�6 variable�^�M14remark} B\"odiU!edi��7} !s�Lit�(not known i;reA� realXyF �B�s>is.na��aF�. Iz easy!S0construct lot�} �}= n�duc 'BU� examMeigen=�( Laplacian.< reby ona�n�ily� .�9 $vector fie� � defor� & $F$ v�B�� <Ae% too�% be accoun���b[e �eYB(mmRH group. See Hilbert :1971}N �� CiI�a�1�I>qA*!/8 �at<� of WiA|e.I���War 5%r!T� ere �in �ly)%TU&n� 6�!�ano: �:i�9�I([Freudentha�o:1957}] 9��Xb�eix@ 0, 2, 4, 8 or 16 �z For!&of, seeB� m�6� L p.258. Ignoring 0,!�s9 ppenanb%S�eq%� >�[RP{2},\C H��O J  ly (N�M�:�AӥL[s);� S each!Mth�four s�IA& model��lZ�G���u. Zer� J�i�discret�� ��forth.D0�2be larg! i!�ed.��1�[1F�67,:1969},V;$51.29, LR weLLoewe<(95}, LeBrun: Maso��8Lebrun/72}] Two2� ZR#Nj!ee�>E>�A�2k>2 car��.� �((ure (a quit'  typ� path"<, &� ing in loU coordinatAPoa�econd-orY ryL(rential equ��A�  i�@Bryant, Griffiths!mHsu-i / /Hsu�5}). G�ic^j �3J` y����=G conna�� (i.e.?�/ geodesics��aD5�pQ w��cK rnedinV�, althJ heir'�this m works!e `= 0as well; most�#ir7!���paper do�app�]!�ppl�Z�\F�Kramer-� !�4}] A��� � f$of positiv ���hom2� its ��,��?� F%�V� >h �'�4K �s some i> deep6�ly� $ much easiqo show1����co� MDex-!�)! �(< ˁNRC;2� e� �ý'95�� 225��_ � a icul\ �"mMr0}[Breitsprech5�>^$p. 257,2622` :c ���P�)�=�ZN� B�sp�a4n!Dh homMy clas hnyu!�y v�� z c7I�=: WEQ� MW%���i�rel� s un�7 pullback, ���ot�� �E�>� Henc�Z,� ==is greatA�han= w��llAԉA pfic�lB�to ori��%�,2� #Y�1��Ze�,Umatch���5 � In partA~ar,Aair?I*.Vrg�i[by hyp� si�ut more&�>ion P� "eAM�~\vref{� in�>�o*  4� t��.o��� % �kof=~�X&� a4A � �sm� >�N Pts_0 \toB_1� !N ku)�:(!���_1$, tak�i:.� @/*u.�_0$!�!�:e:Cor`.<16f_1a~A��;smA�����colA0E��Z�-�6/��1,/ ��.*K!�)& &�sm!iZ�( >�NotA<in�assumedqM���"� whe7 !oC mustA��*� Affi�harts} "4f��!��wr` dA"t-� a.]) < PickI w�!s $0,X�]$Y � . (Think!X$e威�gi��ak� ) $X$ E�Y$! gat$�$xx, $y$ axes.) p $\�DAW {0 X�Y"�  X Y}:0!i�Z}!� ocia���is choic�.�2�},jF}.{e�$}��}. �!e a�alpha :��< \��slash tށE�cv$ p_X,p_Y \{!)� 9!<.SX.�,1Z5J0l�Y 3kby)align*a�p_X &= Jp/ 0r�p_Y.-�-lm�e17!=,%> DRT{)C} :�) %�.��} -K x:_X"�Y � N%&B X.V 0/.X.2A$9U0,^W+1]�-e9U, 1\6,ZT�lemma!�$)Im�.[� � sm�ˡ� ? M�MI�"A heckh  if%�E� (p)=)ZM�-D! then*p"�4YU?.3fo~$`��>& ��,�a:� . Similar�if 2 "� �1w]7 ��h�( % a"%�_X5�Y, \)�2g� a 6vm-g25� �>� between� % �uovzne9  ��$ . A���$, ���% $*{i= $, can� m�� :�"�:�mP��+'wo ways". �. -.�&=e�Mmu�Xy끢.�6Bm~@-�_JF-��G��$;p.5Y/wRneute $pE1k'p_X U��Y�$ (as bE��$ � = p _X��b�z�:�sq��1t &: 2n%�13 �m&0Cor} {p \notiX ��O�ccupX�Dtext{7 }qH \ne 0t"!7]2J�{1uUq>/Y�� 2<# \{0,m�\}Y4E�!Y�X}.��.�>.]5"2���% Y'  .t��.�-�2` 6��:�2� 9dl*e9 comp�(�Bq� $obvious co"x s. MUf< �AI p A�  preservF i"�� �gK� , si+" tU� )��� s��� �cle�H0 enB�,��i f6�of�"��k�pe��"< ge*�!!�� R�"s meet*:lend6�I)�2�$)�w ��?R immed� : w$x ��_� ��_= nd!`, ly)��W�) ver  ͭ� 2� .�. turns��� intoQrw&�*�!�!�w"�%Blowup"�E�'a+��hina+�a+,mA�bb LU+Bl{p_0}{� } ?�<hU#A�-�?*@m(airp���h�|�n${�w ,_0:�.m�.�M2� ��U�>3aY16;!=wB�&�. �ma�,�\R�2L� �8�v�Sp}1� fiber W�is2 adm��� glob���� )=��`��.rn2�$S( imag�i�pk��!-�excep��(al divisor}!t $p_0"De G�$$�$����MN]�2�� �P� t , sur+^^.� :� $ away from�J�M�MtM�m��� 2�6�tt�$X=)!9o�M�&Ungdom�)�at��� bya�a�s2 ��$M E"jne ��=Xy,� p� arbitr�]$��O �aan��&�b�* a bi%�o[ 2�>� 9�2�} � �Ane 0X,XY� 2�� 2x����{� > \Ee*� 0� &�  N�  )@(�maA�2��qE��.= � ��_Y=p_Y$,"fy!�anM%e%{A �|�(a�-�:+:��T�OM4l��QqI�cQ�JO} . .$ To L th�N0 �!nA5e swi*],d0 $o=X,x=O,y=YA9 Now � try1u�+eMd2D=  o��C�1W��n $ � term����X_x,p_y��_x-�@1$!�o�qi l$"�1,_x = o�� ,�5�.\[ # :6�:�� �\��=�\U�y ox,xy 2� � e *� a/uxyH Q �} ���}to{.$ox.�q$o, -ETZgo�Bgo,y� CbI� �p�"� )��Juex� �-a�#!E(-��5�e� = po�3F7M�mapA� the 7oA�e:is. W��,Q�# 6 �we�W'm{:� �$? Q�AiI��#��vice Ca, vi>�O-W�$ve nowi�{��M� ��j�O)<o,o�, y �!&s�� <Ůk8rm�,oM-$)$. Swapp��!_�$y�/ �s � ="+t��A���ne �!��"!&  ]�Y�r�,�@o�-xE�Final�choos���5& .=Ds, perhaps perturb6�=$1bsl9` �(re"" ���"O Hopfb r�&�9�� kD0��oa��!�eA � w>;� ���)�)e!�!qf :���  c�� !���iM�U y�v c}_0��A6�"V sAp,�  above $q �6F$�%pz,ua7��.^�q2� -p-H61 A���( 252; pDZ�� let $U =!B&�0!�qq,)�,A$� �a��y$�/q$-+$pq�-let�'An��phi� )��_5� in U/A�mF!Dp�)-� 2fcUeJT�(A <vim ouw,9�-zQ�{<-�A*&� E�)�A�,%� ͒� E� BA5� bu]p7�%= $ bea� -JTC�����$f�� 6�&{ ---- is esse�'��ame) < .�6� y,simal :} We neg=o� r�.�>:6�,ogube:F.�V�,�-rt��,/!C�t# �.P:�j25\tau \5]r]�4k�$pi'"5#\d aN�ie!�!ar DCok5]�Q+ h�&N5.�o��tau$ ��9M6te $T_��E6y�W �lM�^7 8PtsA�byq<lu�5: �%E{R>$�o�&� MFR�By&�al���� isn��A<I6�z�,� . RescalA )�sA#pz&numbers�6� i Vv�qA)S�S>!� EhIX!��&9�Ea�|Ѹ/\R{+�,]Z%A�l9)O G.v�ҥW2.Y�= Z�/Eac���e �$�A5 �$�*����`!�tak�7Q]&t|0' at �=.Uat 2[j'ma� %'to2��l5W deriva*� :J{�� ric3x!e .�$}�R $..��/wh�7b�(onto. Lets 2:it missa*�et�n ���rQ�,�#�#��cone.� �!�A��.�lor4#G � ��$.�dil�;O0*^ fre�6 zoomb{#� �#. Aq, doa�@AN�� � becT+flatterEaa�ny 9�swe likMfwn�$`�,roxim �m!@\4ly��x)2]"+ g GD ��1$ li�ur%_ (in ZkE�'/ tes)-�� $p�  e��)�%� So ^- has densehicbyY $Sͤto6�$ �%a!�ll. B�5n,� ;�i�4be�7dE�).�2zZ� �sf���lso&�"�Sard's �EB eυ�J��if�5�xfunda�Eal �+l'�,. AgaineS2l%��!�C2� |a� >K n2/a�icIF��% �m�<X!�S]�z.� rM ��tF�:�?B�866�:Two� )b^Q��"<*q/HIn .�+!�n� Kt&�@ �ɀI<l���=n^�:�  S�5:�%j9��is � 4wh�<2�"�p2�( pigeonhol�7incipleV�5U*>(/�E251); �<`ItIis q#re03emplo��!f�y� micro)B>� _" Q�G��; (\ella� $�< 2�� real8�ell"�(T_p5(+]� magn"f.�,$6($.\footnote6 ��e�I:6i tend: remi�e�M/oh s�x6va+ � � &� 3Q $�7$.}�J.:-M��a:M.���EI�� j L Z%�Zi�=7^!Ra��-.�%Q1��� E�t�|A2�!�.+e��"����=6 m����E�!� X �2� 6��1Z #�G new��� to(�! L 6� �9B?>�(.�*hL �� }!la*�0B�&JbL[a}� � !CmD� �1�1(-�B%B :!B.BBJ*�C< Vz" usua�4nd: �F �!�m��Bn.YD9()a�i~�s}!fnQ�b)J0 s?  J $ liFJp�Fnd�I�:6q �{&�6UO"A� �_p$ (Btpar�l}A7+�YI�$p$�(%2<��.��D�<D_*�$�1"! 0� no)9 �J� (e]-� /"-L�Mai�$v2�4Q=�Followa�? \&*�Bp. 66,Ax!#- .� )} ( ��})w*��w\EQ�9�&t_9� $&��to- !3�% � (��A)A f&��@~a�ZA0�#�L, 5it ex�H���epends1t=kly)��R&uZB PM�� �'5B�=1�En�aLJ4MAF��3� �=a6�0�����% s to� s,`� e �.�&�2�"We N5 a (]#) [)�]�=��S ,C�@!�(݈ c) [��3c].s acts T:l�% �-6.�M�. "�$ �F$�2As&O�w$ lekN[5=.6$, �z�"B�9 �;�h] ? E_0=:�CPSoFS��r� T)� ��"@$�% quot�' + l/��x2^_Ion&/I:Aa$Q : E �E_ C�PL%�5�mp�% (p,l�} \oplus_{��Sefwl$Q�/l�W�A�"� w�y �L����V �21]in!i�%�- MN� �5 :ATP�I �&d\�A }3�� .�i,�(���$LE�.l�I� 2 �� ��_�Y eKq * �cisa[�V6't|>�!]ar�}ӂ�1Cq$Q%m�LMnHEt rank1(� or!�A&ZWsub A]c .dYbc� � l  �� eH�R,luI�ub�s1�i2prove@��6�7�end"$ � re�H �x>->�(�nn@� !��nod=necessarO =2] 9 �troubl9=gV"� �FA��� T��WRQ. Ind�)&0$O>g&aܭ�1 2= Radk+�"�.� ��E�b�� �BBv�:$�+s2EK��#�*^)&C}= 0. Tak��$p deg����\et) �$EO� nd��06et.�  *?N.}^*e�taA��$9� �>e _!�1�&^.q�e��Pk ��an_K-�-�.nM���I��A�a volume% c 5l`Cat"� vanis=A`6D) �%K6��^!�T(^22� B,!�$�^* 7$&s �> f| >�:� - - 6�R$C�� -fEp �I,�� � ��=�:t $o.� �U0���.W)$!�aY\`Zo7PA�{Q8�J)( �A�:,"2X�%i�_"�1)*E=a/ $ = f \, d -0 5wedgeY ET"f>! nd $3���*y ]�� ��!�2� A. Y}$ Bati�6~@*�1 T)V . Pu�>gE[,Q'*�4ňq� !�S�Nj,\' \pdQ|_Y}{p_!�, d8;+B"!�"YL� �Pusa��=N�Q��6�)��^**Peta���0fF� �.q  )�zC �ZCY:�"�9�%1M��=�ra-7*�7%eXVdp�] :to �& signs�2L!ensur�Bat��n�1ently�4I�Hk�F$J�>0"�*N]7 �YAp\MX AGU'c.� )Ie C2 D0.B\� 2j05�Bi A\j /I ��E;��� Q��� �Y:x)�-��con?(em'��M 2��'��p�*XO� s5>�Y} �.$�*er�o�@2nWF�+s, N� > P�a� sequ�.=$�1$T0'6"'}&��w�A�~X!4any��"��6"�E B$0X XzX�9 �-��";�V2����%>. �4ny � zW�^� K"�^7=�1,7=�O�VThGd� Ep � &� �- 0��+ir6���$A �^2? ��t y�a&3D6s � %��U$� �w>!dZ 0,4,oQ 16� �2){(is apparent&, &@H"r*vU  Bp.�N� < 4� /� ,� !�1;L"�#2� �� alsy�9cti , up� "Z!-W�>� AMhe Moser�,otopy method A-� = �$\Sigma��4a�� i�&w\dY (�+nb�e�3aqcorners)AX9�$n A�Q� J 5-�0int_{ �}6� � \IN&�q�} \dta5&i�\(j/w@�%� .��11<�r:, � �;!�full mea�� �O&� for d �RX o�9�}�Z�:re�� �V�� �� trac�F���Q�it�� neg�$U%o6�;.0a2�o/�P %�� � ion \K0^��zw�#n't"h(worry about!��%ae�� multiplic�r�< a"Ndof nonm2�mF1KmGmU Firs"NcueU$Eo }7�-_1%�J 2$,!csibly �NS�\]UverlapE�6��ir4i/aB c��J �1.f+!�u� _2} ���'Oy'0 hand�+�">e/T:)� U�(could occur�� ��.!2but po-6on�2. How�\F�q�' W \cap �c�=�A'��n-�L. N�. ,�'��, %�. a�'�+�+f�+S�� )�+Ptx!5�B striX&-p'�3�w%�Cos�� u�so�%�$�!em�2uDZg9)w6u1�'Pm a�+k(�%% �� �� =�/A��V._1>5+f52^5E�"~ �p��� pp!���RZ ``smn%pieces''�S-�� re- hold�o)@(>� it reduce3 a se]&�S&� �")M�n p built ou� 6�[]��of �. �0.G , af�Qcu2</@ el_}6��()see�U��� I�: "i�#��y^ ^� ZM>"e X�b W,�3 �K"� �e2��p� Our�egral iYG[Q<f.5=�5\2�T*g[QU� �M�:%!>0 �%�js prei�at�  �t$3%by� !�a� �0 &�=�1�, �HMD�3 6�' !$�"�V�n?�+��~"A "�Y.� gene�(ind�8i%�yX�nC>O�bgrC�es ]8�,)C�pFMl%s�ak� 6��J$�,l�Z� v�bF$*!��Y�)�W�E �l2�?�%�j > �V"4� E���b �;l��*x %,/ rue� 5��<rQun �J r�Af�b:��� �><+!�m� �N��e�b� $:�h.�cyc�q(e.g.M��y�%�.Y^"��*4 �[[\�]([ , &� a���>X�_FG Cohom{2n}4i,\R{}}=q $6ni�Homol{��?X28r�� �3 s, u"�&�kbasD�<���a�di�b<U& �ojAav�n 2_4 =m�N�) -b��`rWCP�,`U͡>am& 4n2pa�th�alexBB ��Q�m� �qZ�&�4-6:a"iic't�eur�2y3gR�a -,!1a�@we�U0t�J�.?Avp�,.�J.self-��.Y� �sn�^Ih�J~�;!3� �?ic�m, belong  42�`famyof �sE#�g�� "o �slat<����#.�al�t�&McDuff ` / �W6}!�vaMatA ac�$�=�&aic*.� ��6 .DFg!�]фM�lex�r6E,a4au>!5���F��+�J &4ͤL$S5nS^2?�]`�X� ruU"� �n�m�](�0��� ���N�pA��QWmnw �  �s"8�1�T2� -�.�("�TB�+w�� ask%v% `6�; � i��h� �Klow? ansc�1 ntal"8(nalgebraic) Ws-+vA�:$ularities;tu�a����2� �,Gw�(reFV�irU� �fivk�9# ��R�i(or�9-�B�2�_2)�?�6eRe�� !�)��]urv0�i %:useles*P� ��1fp ]z�a 22w��fg},�w��aPO5�)ZS$ �,�.��� b�W u:$8p babl�on�-&XI Cartan'Eor@��rg15�gFhu� !/G9h2he�.�bZ~}S2~uP�Z�&&e]G� $.�B1 � ny vZ�$/�d:&!_y.�m� � ʍ�P!�)��).��!�:� 6!is�on ? | n | � I�.Z7!��" W� �a.�e�vE� ��=,HA�3K� a� � � � � � �c$~ � �$=\mathbb{Z6u��?O� .n%8$tgC .6d�fE.m� FC :=d VNZ, � * ,ger $d.$ But$0 <Gt_C&�  =%�.S*,�e.--*����M*d�(O(a2�$Crf��J!A�[H�d=\frac�~5 } 2�-<}� \Z{+�.� �I 2�-secant} ���A"|]��a !Aj $p_j�C$ appr�6a� limit �GCi� wE�03 j q$*�6&�+hW����'q. ��-�!Ra� �Am�oKb[?2 ion,�I7du�� "pCE�.�$5�)�su"1} $���1 �ADI� �ny�2N@�  $! s~g�=if%``>���q-T�n (q6sf9" T_q C$. D�@��.�@as 6kM�)*!�qo�9ly�Par��in e�tinP?�? ball%( � ~&-#Z�(�B�! yGrassm}}A\�tsX GausA p $F Gr��TM| �gaU4�2 0A���-��I�$F�g act � .���a92�0iDing�@-%g[$�@�%W�Fq} n3 impl�NHBj�16M��m"� Poly�ct�A}�JCeld $\Thx*� 2n$-��)e &5� or$a+assig(to �#o5aw�O�\r&z20 e f�� OaH_P'#3 {�2}'"pT���C_ �!i��p���w�52 ;%���k�w(, invariantg&*� �aityEY�_��&�U- }= ��(JI�}  �B�,� TbU9 ��R+*@*�?+C� �ce H'F��'�e\'.d= &���!���I� � ��f��tia��BJ+B &= "�xn+&.�'9�)!qHv�\jRQ�&EKav:e�_2�,)��)sON)5&.��FseVEK�Qi09�}�G�0Gro��Eϩ��;a�J��+ed(el�/6&��O. t$widetilde{ �u"���(}ANTe�K tautqkp x�hBV_{\Pi-;'(\Pi-.\Pi9 .-%m~T"�2�6}� g>�VGr%7B�h :��e�\��[)6$=gF�N�g]�I:�Dif%Í7an im6� E��Q"�6 $g^*J|Ѽ=8Ev: unwi[ �y� s�on{." .��� .�a����"w2����$ Lipschitz6�QC%�\� 1a64"� a{���� &�T �yr&� �b*/Bz $\vart�(s� )&�Y,Z� �$)�,�#&�3"�3S =- A� B+!Ned�]wc�� L%#"X {al3 l3et$ � �s 8!�(���R $e��Za2[{"]; ?A�.�m��ofu!=r�E��fO.�I�w�NJ�l ` oM�A� t�?�)�)3i.edMhE�)� :QI�: lif�ojPMwP>wied�K$(c"kph� (c�r�'�yE &:$QF(phi'(c) T_cY I� Y$C^{k+1W ( �E-ak$�c=�d)-f-W-e�} By &�te5r2��Ph qE$ed;� �Nam)0��z-��]�8r�G1� � $c(t)E�"� look�.� l�i'(3 ) c':�� �Gy!m:'� )=% O -�(tB\W $.! J|�J��+R�0 I�_Z2yo�?A�}an-io�5��>u��/i.HB._Vy=|Y��B�ga Z�,� ill :DY�- �� rea�is, f>+a�_�vA(A�= �(c!`Nexm+$p=M�)�1�/!o&3F� �b� - -� * Z� ) r6�9�3Q�tz"PhiMl�K�%X:?!�p�bm�5:��m��re^>i�Fo� �o�2<�T1���$=2 @� � � � ��Ae%E\2_$. @�*:n�}�!�F�2"�:�j(�]��4a�.Cp�" z �}�R�Á���q. W�I ��"M6^h�q�k��9�A�)m�AsB}$B� �96� :CE��T*�'gv�u].� 3^�f?_�) FbM;j�ŷN�Kj'��"_! b��ŝ���}A!h>.�^*��k^*U��%r?)�=���mA�mU G� .�m)&E� cor:�Cu)}K  � P^*u��?�u-!�% 321�^/�h��G,u�c�  C$� �teD"E���&(�i\cl1ae\-�91�J�\�� &�.Ck �6Z%��1�2�M+� p",P**ዡ�?2tY f�� �-� ��FF �6>* solu��"J &_V�om� ;9Ik"-&l�� � ����2S �f�.�E�����%=�(�*&� �@�� $ satis�hX=^GInF�lzk�F%sB�.Oi) sy� �f�#crRc��Co*vImap�Ha &=�)�.|e�"� �V!�requir�0� .�� +Ee�0� 'i� angF �o��.�f ,&1�e$4r!".�Y 9EE *�:��Re"y}:�STU�2�K�*-S$. Let $\gr��{8}{n}{.4&5 �)B�9jh%pBn=(�$.�0%�aG&` 5}$] !�5L �%*�S� T_#�7�!z�s��6"�2 �� )�s)!2�K,tY#q=�$*yo3"� �>!�{�anD.q�. A^���r)�j�rK� 0"A� z�!)�V�>1w[%=~� ie� $V�)*�����#n��R�A2-j. I�Iby4!��9�i ]�Dc� �O0ir*Nd��|Ns,%$� AU"he���gle9����A nt s�y�� i"�5����val(to�it/B�s def:tr;f�^A�A@a� $t :�fo V-oY+ W$ (���ru�� t_u$)� $\dim {g VL  W��Q��.�(f"�SH%6* :82�S%�)��r%$�%�\�F,�+�u嗊e� A�a�&�'? % �#I���A 1$A��!P��Yi �'!W! A=WA$�]� =R_uA�(�>kby !win A$)�Ɇ�;%��&�:)�A�5�+9�tsC=$A�1$,\C{},\Ha{�0r $\Oc{� %��'5�y�5�>��i�_�/1u"�~�(a&0iam�\R{N}V2t� � $E1�tr��APy&_dbY� s $E=j� X/E�(�I|s.2�R(�\ale u2B; GL{n�2H;;Epi �n�$]g�E& 6�~[)�ve�?p�C�#pi��sm $T�;�kS�l�O6VU$F�$a�/)Li�/ {N*}U� \R{nI BDa $\dot{E�! �fa "�ia*%�&K"]T FTFo ^�$TW�9x2&z���&k �e"Jaf���i� T_T N�$A*} q�)�<��.T��T� |_{E� E^*B0(W]p-�re�]��A�[��.�R��!efjz$Wly"�a\hY)�ep2��}5�# i�!�a�29F?�H"s l M �;�gA�xi� ��(��m "�\E"xo���  MY &��^�b�HD�o-�9aq6& U ,� &� �4��%tB� �f��.�� � t�5in�=Bwm��CM�� ��� ����Ji.u �.sZ��&w1-^-ln:� �o3�s�9.7k2Y$ abs7%���D.� re !�- �l>I .[OtteT 052}��r� $ )�� 2�c :�m%�m�����<C �-�Ap5�!�1��Ga�( ���Y$��d�u���M) in!�2� (�4�<{W)q6"oqu*W ` U�mag6�Ti�� ���x+��{�9&" ;u�T_R2 ��6�54�*�A�e^:� Ls�S-�+ �)e��ae-:]�Z"��!6�A���"�!\)nd-9lNn�E]B�.�TF�itIL��4s>�}$� 5z"� [9!y$M��Cum2�5�!�T���/%��=����a.BnUpE�P.J��F��mJ`N`�7non� ɲ, 1�$v�'-�-@��� leMEA �G�qpab4$v���% .�2�ikƚF� ��*S@!�t�.] �H2 �|3�6t�ivB2�!4*�p7>��O!`} �W$E}5*�� A�*e+P� �9cap1U6� el�mI�!rR��' �E ��� e"*6-6N'J��k�3="C_A -l"B%pE&��W'!�J lY�A5? '�h����tGell�+��A�-� -M"�1�'A�,va�8�j %$Gnd� � A��+ci!���A4 v-�^^A l%H�. C*�QV�`^K�:u8"�$�]�X6�9c!)as�� AF1^$!�mo]�&�]1D\� �5\ )!�WIt*h��XE�67:2 �M�@!| �e�� R< =xi(v)�PE?nk� xi!�a a"� .: Y BJq�|�~EAv h~ <�  = 6� 4 %��$ T} v�%�$T2^!Vm�y���_ rhe velo�L� t��&?1�(��؅2k��Gpw:T 4�c��S njT}-� 8P���2�x.��,E�po�!���))(0)!+T � S� ��u$�Bs �G�2=Er,�i�HreV�ase �Bl!N'�$v�L�%� $v(?/ zRQ� ���v�����9 i:#6r�Z6_�e.� %���f AF� ,5)�  h� P�I�r&�tog�O�+A91��5� v(00� Plugga� in Taylor�aȮ�xm%~��$@ x,A�fint+A'�%K=0,, Y��.�6](0)Wtradic� ä&�&� ��!7Fk =�� B� �  *rxX Os��� !��Wh �u)& ����Va_A"= N�U .IW >��d�h8A�G*g �p�f� �z s�t� �dE�2` .�0 of B9s�&-�2a��-Aa��?�':1996MF�-��9�6G5�(�pr(_� 2���>ib�8�"f � pB7\G��!1ric��� MC�*W4�8)��-  ( � �jBy5E&Ȣ~\"˞.)� 8*�}B�2�e�C>K*�u�t� �targe� � valu;c�+&�a�2(�sourc! �%�)K-6�*!|&yA�A��K)k.�2OjW|M}O[n 6g-�����; hi�"�T_i �Re� //&� M2��*�?��R�� bi&r "��V' V|�-auD��o? (R al. m� CGGGa�1}3��'!)��$B M�be $t�$V"XU �,9E�C� 4t^*(v,u)=t(u,v~*�92��cEU[��?�2� $ ^_  unqA  �G$v�o���fi���O 1�zFgiv��% = v��b�@=/��2�)�&J%'�  $U,V,W��H"��di��:�UJ9Zm<� �.k&8m��,�Ck�(eR�!�e_U�-U��cI�7 $e_VV6"�UA4\epsilon_U : u/Uge�e_V #Vb2@ V : 3V@ {e_U47v.AWKe�$v_0,v��inZ%#� v_0 = �V t� �(v_0),3 l� Ejde*Q�CIvI�ty�$*�i�dmu�Kvg � U�iv|�� �fXa i�5�a�}�4� �K��s� � �pY���ny1�� ��y Yi��\Rei�?tr)#t_u- }{U��]\ZT(5B (u)=�Z[an� ��h%8(O,a�as * � ��>�0 inN]� to b�+Im(v)=v- �a�end2&m9qH�]N�y�+@xz{ �3�lx����ň 5�M�1� �?bleauA�te>,��<(g_U,g_V,g_W-{s $gi�~ GL{UF etc.BE &��QZI�� = g_Wqg_I� ut gm#qo, isE�"Y5isU_AiI�s}� �sɣA.�� :1942})"c6� un��u��hzM ��ev�<obr s�AD�)Mx�tx�4"(! $� � � $x���L_x :!2: � %�!!q :i!by��.�x-�/�� ty�9c � "� .`%CmamJ��Lend" �"pk ��mv>��~ITA�}qIH }�- y��;Fv �� �e#��7�3/� 6ش& �& � ?-of l��"��al�j<�m�J�{s,�� tern�% or oct� 7 �Z*�"$U"56`$�,FX"F�0.�zZQ���b� 2~E�^^gi�*k&�"Qe�� s-�-ĭ�  71M*=-Q(x�\R{}$. 2� U �V$����� �B�9ant��de�|L_x^2��=l^X`] �xO�.�RA�A. XbQ�� ��r�9\ Ada�c��O%�rr"_.m �[g$xX(� $�= _�Uco'���1-L"����1+=Bec`T�a�zno6% , $x=\pm s_iš�$�C �B�2(�t"q$$n$-th roo߼<�Fge%��Re{2/ȫ]�>V&CV�.��+B�8a�8 hooke�4arrow \slLie{VP>ex`�"6S���gClifford�� $\Cl{V',Q�+��5/�C�I졩I!�e��� ����.G-vt�wTV�&5sum��ir�^�n " ��$$\Spin{n-1�0.�Q$n$. R2��"ok�ells u���/B{�)/ $n=1,2,4$��$8�1PRe� d{g��sen~ ��O~ ~!�����`U�$^�'����"�RM�(aL_.1E�.՚m�io!K"��adapt�; oframing}!�L*�.� Q%:�+�.�1wsI "�>^{\mu�meg pi dmu=1,us,n�8�pe� & ^ �&�?�]$\`I semibas�W��2�>�>>p�r:; u �~/A%2��M="Ay-�.��\��on��:��A)����ny B�,%� calc�P7r� = - p�wr1modul�'.�K��2!4 comb:��YAp5f-�:�vaA EIornE1�_{\nu�t)� \sigm�$' �y H!�t-eN5���H  �M� FA �E ress� $ ]�= �� �u^ �v^{ {��+�s(�� �)AD $" r� NTri�MFA �5a�YGofA)]e*Nq7t5�5� dd��m"�[ ��absorb? 1��qQ:�s�Tpreven���%| ;��.�3ʹ��A"�N-an�s=� �� E�?b� u6�pi�A�� >>�WL�ta�ff� ��pec�6&�y�KM�ak!DK �fIKi�Z*94 $x,y5�/� near�o"_D a�$$(x,y)=(0,a��TJo%4dy U j��a��� )�=dx � �n^! uieUi��D�Oman=M�Us, = dy - z !tW�s�<�Oe@�Y"*!$z$T ma�� - a�� �)mu -rbѡ��6� �a�~+��indzAȅ�u.EI5 i��]OWf *� 9�"<t8"�F�A��%�$,�  mo�]Il"�$vF=[ odz�%}}{dtb:��,���&�x$%�: V 2f��!_o�����im|1c �a"N.�I�r�� >�, �t� Z7��)u:�A� ;eDer_X 5� =�u�d+>Tk(X �.GZI�� �i2�Z5��9�!FaD "Q, $Bha^ �$T$"(az�Ż�$F-nA�cgMV $u=�^mu�Ld{}{x)�� �i}?�.!! $z8�]t$dx^1�5d� (dx�[XE�w%�!�*s �Lq�I�$2� ����!&� DQ "G.~�~o$z�" is $6j!}%�Tt�vml&�claimed�&Eex��5�0k�-�."�yT��a��1$u� v�V":�ifa�ch.uNc� I1to������U�'�@ �� pi �5=JGa & 0�2b & cd & e:Jj� H�U pi6?���*��q�}� ) s�t'� ati�e�u,c�� �ro �*z���aux"� � 1�� A �akn� 1 ,Xm��-�7�-� � � ��7&cM�s,)P,��$dY=-tA*  E�>��7y�"�� N* � Uf^*= �pi� ^*=-t ���X�B-t�5p�@.� ^*� t^*� %y�2�-%-3=E)�3 �i]0q6q6�(J��-{El��!�*�/_ .��-&�NWV�0 5.14�0eQ6OP�G�z2dQ���e!c���.� �Xn�0  �#| e c ��x5�6$7.R_ P.*7 SC7�r\ �. gr�m�)�>� 8&�P���bQ "��$\;,�5&�Q%N���n&�W):S1ma�oveA �0M")�Q�&?P&A��M��� is�" UGM�I�`6m��k���� T6~$  u�v�7 .�e�0gc���>�V�m� �#:e`"+;)�S,�J1b � � v%mooth��a�uF�=&6�G� }V1�\ M�1�� . T6-euAKp}��a�*/ F�Ame�c�7"� !�be "�N.N"��]-&M]3y�� �/j6q �):�(m��(�*�0�a.�! �l _*�!SR+��-,> 2� �A act -4cqh� 1Y.)i�!A3�I�a|AC �lf�ka� �-��� Or� �[ed��Bi0�$T�Ct��zE��>���tmUmF�jNlM&�*�p�~�1!�&8 �s)6� i[B��� Aa��]reb�$eneric ��x,y�S-4c�k ��ed*�x2Sm"R $X,YSI U6K��l 2�-�- �iÇ VES���%&�,�!�s�$�&�2u{t�f� ,X,Y�-�A(��t1�C�"� "��t�2HM-�� M% & =�� -g/-u��A�Lemf"!�_(� *0ąo�(a�n�4S"�KJ�-�%��tf�w"�s��M5N (�&7}�GA�ar� !.�a� worst���2��6 %OD�%�%�!�.Vm� #fpa�? ularŽrebbe5�JU�x&=x(d5N y&=y(xu  X&=X�, Y&=YX� � EN��he���Rp"zit JK� -&QB9m%�� ]s� �^ݑi�\I�"��5_k�i�a*6}<)嵦e%�l� !�K�"5�a �4Or� wUq"f&��mM�mi�, :&�InCYZA^�� 8 ��!,�-A<n.|6�,�$�crx,%w-O�AK&GwCe7 $h^i_j!�Dse �ag (pd{y^i}{Y^ju�t^i_{jk�*^2 -x^j \E�al X^k}�pd >$Y^l} h^l_mBy^m}{2( �A\�6~5�1xhXTD\[�x}q ^k ,`�,$���$ � r7-�%���M � E�%�1�1�o�?!��� ���dyM Z .!2!/I|_{m��xdx.�Param�iz�U 2� � 7(o%K� �9ɇaQue�M$M* 4�M 5.�@^ &� a�}�c�� �U�"�=efy,:��|]�P2�.��� l�y�+taޛ"4 � �_l lN6�Xg9N�;!3�� $a^i �A�i} + b^iE�}e$��i�r=� �@� ? 6r a^1=��:su2�@�*�,e�%�c�R.�b = M�v)& O �)��� �p�I :�Ew �q=6-M(�7E�� "� ���Gpas.����I�����m� "hat �7�5E>.sfIE|_{t=��� }{x}5HeS "�o\I3s�@: ��9 �6x�� y�ɭ(2:"CA�0a��gy� �xA> �X} X��<Y�f�0)GUoncluda�� + Qpd{Y}u y}W X�+D&�R��wg:#9!�:1C!5�oTQ(���2J.�g*ni,6��R�� �.�, ��A/ma�A�cm R� + ing,�??�|-�X-\|eDx^k �3$.@-R�t�8 2 in .�S&�in 2�2 )lR����QX� �D��Ee�%^5� �Hyq�9{��M�M#{Ym�)$ W�Jt*��Z$�  &�]0��A�y}{x*u>cB"yq65�(fixߍ�!wyQ9w#nwQ�*�4.�j�7>�&�!�u]ufor�c>�� ��2x.� "��N�$M�m�WU$������ |streng� �&X A�|A�K�a}�. w ��ZZ :!�� �u$!b�F.�Gm�xu�kj}��3*v�X*r9n�%��to BnI��'aM +Nl�X�A��l��end.�"OI% "�&�da5d�f�,0,8 �2)p'!�2e6E A�i��,c��!��arr2��aoY�t=1,e|X�|=0 Y}+!�w6��"�3:a�~����R� :unpubk7�C � caseE�So�2\1�L�i:6 �{E��� � .�"��`�i�+�J�O�/ F� 2�n4 oZ(re�&��&�>�.!fe � �mmm+�Hg� " ' �)��U�� $� w &�C�~"�*+a�� P"=*i/���-~�+,�!��a�&�R&�|= �"M�`�^�UJ e�2�(��, /�� 1�8 a%F�Ǩ" 0HA4prop:ZeroAdapt��ed}, $v \hook \vartheta$ has nonzero determinant or vanishes, and therefore cannot have rank 1. \end{proof} Elliptic regularity results are quite involved for projective planes of dimension $8$�P$16$, since the relev�Dequations are over�ed elli��X. Nonetheless, with some effort one should be able to identify in local coordinates a de)60ed subsystem,� proveN$for it. We��preby encouraged when studying) curves�assum8at=yF�smooth. In principle, it seems possibl79? �mmersed6nin), ^ irreg!�=�4 plane might b� , becauseR� /never hYT, but ot still  % fullE~4. Examples of N� �s w-� valu!�. %% \sAyPon{Proper transforms} rmk{This ( appear%be usEN . It/ � Tful, if I had a definiA��,%% algebraic)�Ea=P( structure. �(begin{lemmaSuppos-�$\Pts$ iA�F�)�Every1� real \$t \in \R{} \mapsto p(t) ]�e6$p'ne 0$ A�!� $/ =p_0* lift%'Ha unique continuousxU$\left(p t\rAC ),\lambda6 cinA�D blowup $\Bl{p_0}{�}$i�`\[ �in T_( \bar{ f }(t)&\]J�%= \end=�-�pro��$%% Given aN_!RL(0)5�5%[0) )[, w% 8clearly we take!0%(t:%�$,�a�� troua� arisan>hen$�%�8. At such point�plet.d$Aҡqmagnific�mKofEFspaA��t))/S��A/F�an��ATout losa�( generalitydt���%A_8 except at $t=0 l Pick��de @tAqor��%�We��w Yx=y=0$K[r)E]p'!�4\partial_{x^1}%�'@�z origi �x,y,X$ c|-�� \Cor)�I�\pd{Y}{(2()} = (0,1,0]�d? 1tau =8^2 Y}{x � X}(E��tri%D�all o��*8second derivati�Rv��%*Th�1�mg0is $Y=Y(0,0,XMw!� $x�a�bitrary.. vB� line)A� ansv�rA�!�(rec�� a*H $X,Y$ from knowing%i�`angent��!�aI��y)mwhich�???7e�y�m� corollary%H~[H proj�=v.^Ta��ma��,phi : M \to ��$!R a manifolEL$Ma��inUdiffer~ al $F'� m.at �}y�m�dM$|p5to =(mm��TXA e!N���*$\tilde{�}�>ksay.Q�3w �B(m��(m��9E�so>��� � p(m. wher���!� �0phi'(m) : T_m-�T_�(m)>:`��ED= �$%BEF65MJ��aF!H)�; �-� !��WmYof! ab�)�BF�y �Y�Z� rmk{u�(rough idea:�sA�,ve Poncelet': rism��an"ByI of �d"� 4.d� e in  usA�(GromovologyIto'w% sy� ctic na a!9n��a9m� detailsAF�H V g��� 8n jus2 @ arguments explai� (in Schwartz�<� ree�ce�  thinkM� theory�;8probably doesn'eMgA�%i� someJg like� B %� I am� �rely sur� i�are%�quadrics��{�9�)* . To w, I need!jbe   get ridM�!�� itie_ pair夥�,J� work! Adri)�Butscher!J@ Sema Salur. Or I �)� )�'sE��7abmakA#�t)D 4��Qn%^eA�E"�E��%Z��"� A� $h$-", � classical�Hies 8� &� If $A~ n� ,�n $A^*the#(same vector4 c��A� � "a $xy$!� EA�n by $yx ��(i.e.a t!�au�multipl*� G, \otimes A^*œ� dual!<� ~NL J$)%a\& :"-8��<[Buchanan \cite{:1979}� E� "�/ beE ormA�M !ieE/ to aF�y, i.a:n ssociatee�to� �-�s $ 8,\C{},\Ha{},$ o�n Oc{}�d�s%7� �!G �remark�a�t A�%�{(build�on(Yy$p : X��V$! obvi�<onI  thougheof� APv� $fiber bundg;X^{(r)}E�b�y =$r$-jet%�lQ[)�Rat:V�Z(\mathcal{R}u6n26naMof $2k� each!��i�9a�� �+:��A�2�!�� mode� Cor_0 �  �ni�_k@ �I�L!M�i>9��G�.�a!�ting.2�#$5� n"� 2�)!YbU!� A,��.�$z^{\mu��y)�$=.aS�$p�e!+!$V�� @ ,y^iE(�I�D X$ l$$ gd&�!�m$ pul� back��$VB A)�!�U� looks��a choicE�%� $zm �*K�8d{^{\alpha} y}{� �x$|  | \le r$."Mco/ V$$a_j dz^j$ � a co��spa �$V! nsid�{ �Pi�lly�E�A�dfixed�sen.es �z)�fo� ��.�Z�\�|_{��-1���JE +e_j:1z^jfL�)M��+"� $(r-1)� ,Zallei�=��A4c�=n dirzon��� calls:aa�~(i$ a \emph{��cipale4!�}2Yu{(p. 180) Qa0%�Z�a��h�}e!�eCM�a%�.�$,$A e�F� ��ain� $a �5 [�W\�Z-�{combin �of -5M path%pon�Da� 2� cap \��He��$ at �- �<jet�Veo satisfy ( �' of)%�$&�  �� E>R��a�i� ver�&�8��16 �R llFm,AP�l�& .� �conure�It� m��ly�� �o%s4�Aw� ��f!��:� �M ���b9/ sr��,�,�'�)�Tleɹz^IoR *B�� noZ��|�6$Lc . Fix(;ofj1l�examin�!���� ��"p ZU� e�;3 expressI�itselX �$z�(x(z),yX Y(z)[We seq� I��aE.our �a�$z=0$ ��<�i�in<=y=X=Yn"��pd{}{z%�Q matrix x \\Ny X Y E�.1=.JI 0 & 1 & 0 9  1Z 2i�n�E6�N� ` for�5ur��to� �t�4_{\nu \sigma}=! ^2 Y ��nu+n}&���. +2n}� � More�.� l"� e�Um� altOlp �A >�A� Y$ a�il��atE ��E�O�g��*{ ;� p�c!I[2X they8"2�� C�.�e?�.A�{.�y�jF%;]��!4underl% 1� ��sPv�~/��\ Y IY I$�&! F+f�o� ll �sR '�alI first.uE�A��yF� �mTI�a_Iw 2A} !�al z^I.m�intcc � �mmaO ��c!�s�`t *  2 "6)���(dz^I = dy^1h�!���th�r��eJ��iY(,Y)�1.TI*0EiN�F��$e�\ �A�:�WE'*!� �. "s )I^ h�E�^in.&��p�"�A�E>B}I),j !q6�q^ ies;! M�Ge�s�e�;i���&��6au�-n*}"\RBIea�!�:9 A�U_�xe!$n=2,4,8! \f� �&�LI SO{���JE�ac&v,�!{manner:!+-x� ,(g_1,g_2,g_3�� (u,v��� g_3 2,^{-1} u, g_2 v =EUI�Avera���' �!�!%�*�1�sr invatXCD"��B# mbA�tauS!�fX% � l Tco%�h�%��F��6Nn8�x:/ne.V" �L $x"�$-x$� R{n}�( posi� V�]an� a r"K�so��m=q1SL$!+$,$- ��Jͦ�P-k���M xA�Q� *!�a�\GL.JihBt (e diagramma�*})b]X,W�fin|#0Far��check� �(standardJZE�(� �v�visioŁao'F� fFis>inRI�seB�EՅ��tY��&i��)� ub%�,��$�m@!� hold{�f�y�A�$dy$ 1-��E��%.��0 a $da(r $dX:�rwe'to�ry6 u>� ���x^1I,X"�%nsL�Z�VYan c� ��<��W$" {n+12z &2PD-"( ^2 Y/"@%zJC=0En&ņ`I=2n+\nu$, $\nu=1,\dots,n*$�$Z�gag�!$�-&&t2j"# Cha� $Y!u"�&� me"�*�< a�arr!eo%.,))`2� %az^{) }}=\delta�  :u 0.Ttau.I �'Rq\nu2�|Q .=a>n"� y�)J$Y��*A�F� aE��i�BI-�S 5��b:�+Fix�\/��$e/ɛ9Ca$�= Omega_e�����m?*�g ]�e���t�Y(e,v)=v$5A00,n�6�ub� $�^c "���5,�fm&F��Y n=4p8^ ���:;~6avo� �^cm �� �)�\ev�+Write->-� �"mT^ FJ0_{M��+ .o j'j2'��('D Greek indices run8$1�n*hile�Rom��))2)). StarteY�!y=�[!ER_0ba� �$� 8!�Z .�� -a+� +$j!�dex�M� i���u$$a�  (��lasXntencj,we made crucJ�$� hyp& si�".�&Y�n=A��2$�=1�La�$n=2$.# Rescal*{!N ! !apr�"l����Z�� r_!}s�e�n�& quantity%l��!0����:�!6�E&Q5�*� n bq��E�!Ux ���gro�/G� �3R�%��(g_U,g_V,g_Ww �VGL{U}"� GL{V2W}%�($U=V=W=��)$)���erv�Fe"� �� �Uv%�%V W�el2include� � 0�|$a;,ng via $g_U$1�T�$g_W=g_Ve$�*� symbolicN� y\�� i�fyt i!&iq�5�5a�>O%���R� s-T�g� F6m$�enumerat>\item $�8m"y� B".�frac{1}( Cepsilon� ��F��\�8:�&6 Q�BU  +T1%n�a��!|2�&pB\ -�:s�+!wa+�4v�# readN Rn��great sp�`E f#eW show�i<�4F*!goe�+�*R.? A_i dx � X^i$. EK+le�iS4han" mi�*�. u%� ^1+�S� +dX�etc%Q*�+sM�67�"oo hardQu+"a �%%y`+#��5�"%`2��rh���W}\label{ ?:h�lM��-I w�8to re�� 2���i�c�)��stead �S.@6wp6���mG8�!�� f�&ish�d$m�*~&/a�V�&� a�m* 1� F�$��)F?k�.B)%Q%��% p. 744or6�%��%E131E�� ��� �".�1srel },microflexibl�-aaqbe���FA25 sheav-on v1Ns ( �^9)�QCBv�C�81 �.�s,�V noncompac+% M%��&+ �TT��i!8ly��(`!�$�&M&������'��'��'&�'� �Q\mp�v�#��! (A& r� 180;0 see below��!^&r&!�.j"���(��(��(��(�(�(-��M�Le�6�o�(�(�(x���!AQ*+ a�QZ( @�(�( m�(B(x? �(�a(7 �!''z(x�(R+ 0$�+"w!�D & *�$x!��A'� J(�i �(Ix�(�(j(R$��'} ~�!ag(! A 6-'�Q�,�(v(Rp ~(R$���:���(R)1�(v(In#as�5Vs"��!""}C�=�<beF1'f�&|&F(< N it a"orrequire)1h �w�8� �VH"��70 ��m�q�"'�6��+?'+*_#�#e;$< �`"44 d inpd y /&�!pAx}~&<�+3$*�5w��N8(around�!� $t"�? ^2 yF`:qX�%%�fu�F� *>C��+- �st{Ei� �&5�X}V%�;Lgeneric&?,a Yurd:to ,i�&� sui9�D�%�Ch"at&3believ�N&XIE a lo� freedom� ly� ]�cE���nF^6F)@mora*�?2".�.�x9����he"� K(i#Dduc� �(r`6 �ng%i6�U��F�8"V9* �.z,% G%� mua3nd&iv��F�?�2KI dvors�Gd;�t"�<atA^q w2��Y&a�m:�bas1*�-��C9-DB��c�6�+6+ el����E��!��F�: &\<worq.�;6"s!�e6�s��3a�e�&A06D0!"�-&� 1���T1��J.>!� =5" 1��60��than w�G.rovena�am tt�Bnfn2��+�H2��� n=4,3AJ]1$!�2hopiH2 �{A.�2�,�(�1A�K"iM&#��A� deno�Kt%�D% Algs ��A�3vf&OHn��tR (x,18 )=x$.�SA0�$t^i_{jk�;�� 1"�i_j �so $n^2Gdepend�0"9L�tAT$\dim �=n^3-@=divB�M!��no6� exist.�-zZ"8O�"U o��^$<X�8E"%<� �*� w��^?meteriz� 5Cb�'/$��a�mu�&��ch!�a��aIstr EF& [�=a%^ �2i%A.�-Ia�is H+,�( correspond��)�[�y�I� = M� y^.kILatin"� ��$i&�%-$d� ��.,=46!0��4�<A �E(1�e�1"��&� T!�\RfB"kB���( (dŲ&Bwhe��&1- .8�!LXa-OaQ� �#by.�"�7�>EP9�} o $0,a$A$*-xy6� +j�I6*i}%��%y^i' ,L�N 2X6,.�F*�+���W6�.2,bE!�6lynom�!funz@I��P �, �,Q��&d�6I�=y^0q�5=E(�G� �0 `>+K1 x> m% =)$ ]�5 $ M=�1G ;is�� ��Ny)�K| �|^n ��w> `ef"�KAJ$usual Eucl�*a�ner duc�RestrictA^$yv$9vTJadius v�vL$ $�1�3�"O � $ near $0M� �1, �h $|y|%e�!atf I9�)>����&�+Z �by homof#�*(�6�?��Ir�{�1ily larg!ji&$ (.�.or nega�)�� s�!ѡ � $pJ� = � We pTQup eigen H}���Z���ni = -e>m Im<�I�F��!-�}{--}bU:lZ2eM�� ]y^mT)���>�,if $z^0=y^0/ )Mz z^i=�@� fi.f95�3,1,z)=.�Sen��Q� �:p�Ofty V'ha��@to!�]� $y^i�A(� plugv2E�/�-� $0=-��! mu�$/ta��+.]ifa<makE��$I��staC$wayB"�)�2/ D ��s 6))�aS%�1}{2}�Fa+-n A=�+-�.)-N)Ida*�suffic�Hq��Zend*  &) d#����!�`fg!���>�!�B�/B:'s67��Yy�9,3� <" !@3X���<�' �r �->�=&�X��Hembed�/ weak� topy� ival�) �Ho���BB%�!�3�� � ��E�:.t � %9%�9�-�*�  e #~\vref /V��f�Iof�# A�.�#�|e)Pq%� ^6"�uEIj�}ol�(topgQ$!���)[�~]T ��sa&�*��!a�isCuA] easy���UE�&�re�] �y,�#Kramer'{I�./uSu*�M�x#�2V%) t.�$�$$ admit0[&x"[(perhap4$holonomic)F[-y"6^r\�E.� �9��QAKW�E�"1m]Z)-a2��>����1(�cF� � 2�&a# L�6� )�z&� �|Jt�7XllB6�)*iM= �k!�n' _'�M��4���ask�j �a"�O*< X�1�rew a�G#gt�L�aabilizer!oB: )��'�(ku?NY� f"�y6� s��"� .DiRT #Q\"�%Ndescrip�m? �yU�;\to�+o�uwvY�-\�!�)O>��%6�%f/!�7W"��&FN0�%�[ \+,�$T teME� �&ureX��±qB)%�level!s home*Psm= �eʼnS6�a �!��ſ�X%e`nis*>Iy[b ��b�� 9�)�b �Steenro�)\�M�<%�Can#V��xim�\�$C^�m^�)!� $�$C�V��!�R)?�UbPa-{\i_ }$v4&���9%ߵNa.� $-�a�p.e.�I do m�^betC�A�. C!e6�� \"Iu�&IEz�� ��E�n fac�cMHR RI.�:91). . As�yhow)�myiOoe�ZF-Y�s,�]*:ctuWR�'.*=Dby"PT'�brkEZ+ A�a[ aA�k �Q �A�2�%9MW$�I. S2y+�cca�b23l�O�)1 iA�s �$F�!8v!y�.1:Y][է6��(orI�~) �m����r"�,, IP"�*�e�:&�EbyBf2 i? �pencil�ȝsEU5�so �triNQ��� ���E5 2@4n neighborhoodEG��G  i%-%wy�Futeg�h� Őf$\pi_{s1I 4J_{\textit{cl}�%)$. IfaOv��e��tU^)Xat0$1�� �*a2���� za_�4�$. B{\"o}di \�"res u�6!-@�wGrassfi�@T�"V "a5.�� �-m�sman� d%Xsu"�.�z.o. U(0&���v:�i 5��9)=en�[�T�N6'$hv�I2<�p zHop2fi�1 @>xof�)� en�0saffinew"r� �"�=�E.<E�aM�* � `2 enoughr2a>is6b 6.�A>4,��"D]!Qe�CerA�lyA���IK� z�B�u�!�as�geomeAq�[��%f�6�̩R�7� delet�F:� 9$0�;�now� Zexpec9smvuri a� nf�hy�Bry� else[< �to�A� kjglu�[og�� normw2���UFt!�:ih`+ I F1�"���#f!�6 )FbF9similSgI.F�ber �-m.3>hon3fin��V\�c map.AO%�4$L ��$p$��L�?n�$L�;E:�E:��o�g$��e�G'Œ �W icro)��=L�s -��9pm3i5 nearK %Ywell,0\#]"a� ~.�!1�dow�5 >�a)-�ie)t�����B . Bu"\&�[V�<r&�(>toov�ENge� �N}T��t�'d,*�'by:��*n ��57  6�5� "=6!.J�Rb�]osAS厅� E of Ka�0, Mimura, TodK AhR# {L*�1)fyE�Z���� �=q� h. iAB�of � A�� %F*73  (1U$ !� ]g/ɂ�,DW�Joa!� ��Rs( ers��i$@AOJ$ ���n�j)� h(2 �� !6B�_ ��o�[6i�ҁl� k �`deman� & ���\**O��!�1g#46s��� .�L} "�'Carta� count% sec:  x�;er who�o�h� "a�� �mumbo-jqe �ult Bryu$,b &(BCGGG:1991}� e� ce. ���; � integer"?/ ren:m*P]Iji�� a � B�A($s_1=n,s_2=�$ =s_n�A \ � �$ �$.�tpik� A�r�< vert{9,2�p� !�lIs  ��1u�gry�_�/columnI�nAA�ar��Y)�AentriesC r $\va�L%$n$ �"�!�(�It�.t| �r�F>"�.s avail,a(ul� kc$d�r (� a�M� :�]S�PfF an-� ), e��7%$Z�-�&K�P ,\foot�*{Iu�#g�Z&�_s � Aw 2�"�)%_ Y solu� �ing�/ $s$"�!�v$d$!6#e mea�$�0] passm's tes�$ sDQ>m6charac�$s_d=sYV�val analypM$category, e��f')%Z��a��. ed CauchyaWo��Ձ7 al6��, u� �q�+=)o �U tell"��l�AR�%AJ:��j �re!��N � anymp0�at le�E�v, �#:�A�:�k�  �!g%���is�T r coe^s ��d�%x ly C UJ5 of �M2�. QD!�t��v�trW� a�M>.�xN�aB�C> A�h� �F1���out��!� F�-�worth�H�1� k� �i��!~5|'mq 6�6�Q t $plex numbe�6F�yuġ �2}�,fter &�8-c� UP,F A�AR3��N + a2�~/1"�N.a� b��5 A�N8� $�/}�,bE6 align*a<$p^0_1 &= a p^1_0 -0q` (0 (1_1 (06�[�65x!�8� 2-"GNalt� MJM �*vvI-ex� �l.3x �:2��4.sV� ���uuQ*;6J�IA�  AH22J 1�H5 �is"��G lB (rigorousũ!�6F ),`rj7n�_ i�p f s- �un�~ma�Ɂ9= -r=d-v�  See�! ��$Y\  "� is� 4IB��� � �Warning:j "�"_ !:  �v�� not}��!&%%��g�. 4.inЀw� �)r��P�5"�Pv<4 Lonu�� ��&0. Now perturb-3!�~ &v��PHD\ �3�bbDita7l er �\�at6uO^i.D� %-"�7�'no=Vo�f�����e 9 ��m� Al� �p�` E;��:� �s��r�t ies)ࡺ�\�Xi�jme� $n"2,e&�T>�By��!�r=� si��ng&.�5�hA<"42=�%��= �9 a $0@0ty (replace :� $uvb0 $u*v=L_{e_0}�P (uv)$ �$ $� a6> $e_0$;�Alber�9  :1942}). e%JI!$py=y(p1�Sos&we�3`\ P=pE1we� a� y!� x �ӡ�!�$x,y$.< $R_{$}"�6"�=� � J�8 $. Dp��ew> M $*$� [ x*�3.|%g! (y \�}��Jae�6C?�>�:+ Is'eUt"h>Yol� �yam�&�Ue�*Heinz�-� !�1}� SNOger :1954��$a beautifu+of�?cI%T8,Behrend:1939})" ��!��)mmD@(�necessa�1a�( ive)�4m"� ��=�ors�/ be 1�12.�� m�- ��+� r�-� 2+��8\16uQ��ly basic.!� ]o ѝ� � � Our6b( |�$m+ pfield(��M��@ A9�0)� e0��1 *olIWd �8 "Q ��, "���a&@.. kW � f] (lif� ))$,� %7Fw~�ኡc��>-vE�Wbhm,}91-�)7�ic�Q$(p~�)L<�E���-�cu�V�����r&8*�3$,ͧ�8D-bDx "� C/ cor: �# e&�1M��y N�@Ő� g��pu_:rfG$no ``littlA~pia�''a4*" s,pas!.�w Q . WG�Zstreng/%�sl|TlX� 2Iage���&@l -�+a�Ase��n unless& i!�/.b�,E� \��, R~a $%��W M�ga kind�(f *u��-Q�$L!D1�`(� $oughly putEj�)E_�t highY�a����e��r�$j.�Q B#Qwa�cev�,ly unCU a|�,M�� M*�W\rX�|��ernion�B>�$(vl..e�}�7=oct�WF7Rober��A��2 @v�hRG�($didE�(publish it)�� ^{W�can�>7��s e %�!�8-EXl�&�} $F_4%"vl nt 8�dBZ���F�ach�amused (#,a$ easily& �r�. $^�J:ya�ge��z�^A�s.) G/ic���Q�-� yY��! bear6#Ws ^�'W irM� Intu�hM� abse�ofe5 Go"�by clo!+21$n$%a $2n$-� ���$$\binom{2n},*6>:"���le a Z���R�$n>V 3n$ E)bl��S:�%�r s$4ّf n����6to J6!��ed�� ll)s5VI�at-6>!ˁi�B:�@< ,�si� UixѢ1'����J2Qan_[�7urk}���  ins"/ eaI��bp ld1!�"H� fU�AkJO�`A�lg!+6��� �..B�t�[v�4(r� ��}�!��Cs�tef �� a1 !A/[2�d�s�4(�(at�icj>�}B�no/�. sstLJR��!{FP av�4y 2�P�$ Gluck \&  er} *�W6 � / .[3}, imag�+a famd>t$%N�}�2� away \00��to8s�# M b2�enaK: i�Y, !�<'r!!��� $@ ",A�urf2:$\S�u \I8 \Gro{2}{\R{4}}�X١or �1Z. D m�+��?�)� 3 ir +�%,xi \wedge \eu��\x1| nd $ �er�J�;�t-l) �!vp/A�Pi$. As*�R� �&,eai�xi,u g-�ed�([^o.N*$v�| � i� �I;#h_�6��# G�two5bA,\Pi'$ %Q them !.5,\xi')E�'�nd �6ly $0=v "=xi' eta'$�� jP'�#.�>�J>V >0$ 5 %iMk"v� I�� E�i��SpllM�E#4�_+�> -$aC +%�a :z-�� 2�,k#$ &- & nti-)��?%v�� �J rthou-asi!� j^iACF o.�+n fA-.A6�Fa� �{\pm}^Y � j =�@dtY 3 ^i_+-� /^j_- �Bx}/�HGc6� = X_aÁ<_+^i + Y -^i,��A1!�z@y6Q\r� )�wdV�X_i^2 -V^2M�� �!�!M-qsa�!}uni�]As $S^+�� $S^-�9�GVj.>1�#w�map� �- , - � : �ato S^+�S^-!"o ��t\&.)3 h`)�g|�'{ f}g|>G6+ �|}ȁ6R� t re�gߏ�>?��ly ��sQ regj� ���q�. XIequentp i��(ret��"i�&cC��imaB� m� Ų FQe�!� grap��� �ictt7o�C9G!�A�A!�j_GF1�E�e )����'�ppS` diata#-���� �"@�.$p�\n�6�)�*9 2 �e�s�ong)��%y�=T�P]/%V*j��. �el2M�!~E al6HMW &@ J�#��M�^+-�� "�����.m��2�:Z�� \A$_+ > om[ v�*b6m.&],�6nB\ s} McKay .  :2003} dD=op!�"�!! o��pseudo lex "N.�tR9."Pese�"� d ET �*oY'&v�( Qi�KI*: Glob��1 =��"�$!��&�rt��4"#ijhav� A5s��y"H(NoverlapsA>UbNr�.thm:taub!� ��"*a� ~��F>/�)K!�ace"w�!, tamez� .�=*(��aM�=mo��57 �an��vslf! >�'@�[J +�6�Yy!�$\���v.�2WIb�#r,��`�-�  B 95� ��l*�Ft� :?AtHSV� >>pC xie��VH>ATE��4�=�5��� �=c"�=2�BT�Q�F�We `(be brief�[�,sA�a�`�d˗!^�B�A�9!"Lal�McDuff�� / :1996}  �� ' �� �-*I�T� �5v^ ts$,CMa ��rm � � :3�;Aco�4log�K.� t!. [ 2\^ ]�Z�R \RT{� &TRad�rԢAp��iZ4A�~+.B n}{T �}�mP�.��!�preciq5�� | �\���3��E�.��ia��'ה=�O�|L^��5 . B!]./��)e��.uI 20� � rcE��A8be�1.��m. � �ށRaYŒatF :!a� W� (!lhsI��A�s}�#B�5]�Ũ� g��res�� B^�+&*m�4hͭ�4yp |��?+MUb"d e�I(�_� a3!2F arizɪ}V9)2L�OI�8 ]�.A��%� of TN �-��&eV)*@"� i� upA=)M8sme��xing"�� �T�c�9reo�ing!(ur_�tX�!Pu\@oI$A��a!����2*7\.Z��~MseG*VQ�� m�B2� E�j�i @6�8;�'@�.�: stat+D��! �!�MRK�@a�!�a hemimp%U.�J���duc�a�mF� U���F  z4i5�VL27�1�iMe;�-I%�F%_�e~��T�9etbJw[��1���>�e_2Q Duisu2aatMM�2}&�8A��w ewYo�� o !5� � �C���!) .�c~&nFJc�Q�sa ��� b�aw� of.�'s & '} ��ier. AM]lat%ge,::�{r�?a�� predisc ed bz*searcher�.N�3, W�$XL:*A�=�e�aX ;|al^�.} e�ag�F�b u�)�kerne��5| procQ�a�M>2U��&\%� A�o{_u�GF�m|qDA�dD.nc"A7a�:-�@ "N.]:>"цiz�M'&_ ��L2 iX�Aap7�:�hA�iL,��� iY�o�6inu%1;.EI��Moe��l�$�X, $ȧ"�}a��CC {0}{\nu_"`&�D��O 2�5��˜!�$6� ,� ipp%Sw�C.�au6� �^}�"p ��u� CP{1}���N�(�r.��O�!�L1�ET1&�@!�&�U��e��in$��}Oz)zYS)�"J@o/ K-$I0�e2-�a', i�  |%}� A a��  cM\A��+f�D%�)�1>��Zs.[eWE7!�*r!��bL��2m1U�anQ ;"�p. UL2nO's��2De %�!~�6 b�es1PGU,y�� � � !^� g e2M  0 A�&� �"z&v> � 2�FKD�Tinc!��/&bo$. W&�o��ɶ"�e�Yde9*�2!P&8!$6�EvvN|D��*�(c ��\{D. F��Z.�<%�b h�~v6H 9J���:e+%_ 6*�od.r)�1B/�!���* *u :�XE�� T !���� urM�2�z%��(A��iO � U� �[9fi*m��Tac��sQ���EK to ER0 � �adE���!$21A%A�A� A�9A�;fp!p"�AB E�k%�!@j 1���(el��e�� es�Bdap!�PMg2\E�) � 9�$E���e�Q%N�!t.Q� X"�CKiA1�9U'or:a�9�KI�"?%4T(P)L�y+EE� onto��d& �'s-Mly�T�&M]` �$P$�[ boot+hppingj".lQGN�(��a}�--�5 I 2�%?m�E�y�%uAF +�v�,�29��}S!��of �)HG��ll�2�E�p� ous� sE�T"�a��0�,(� )6��Zm'E���d�(� $i(�IJ"�C%ʁ�T_{*�/} �iy �:��2i(�p},h \x&y5p}�TN�B% :#��F� E?!���dot8(p)�G {p}$)5o� p 6� �F �}Gc 2xY�M��th �l}eAWhomRn)�:!��dreason�r�ub��A(0isi��H�2� 5$$\w i�s�."�A��r $6$��E�7dd it� B���B��q9"� &�8U�P.J��5) E�Fi�P��Qp@%� �%0s mee6�1a e�YiJ.R eV�'ion~6t j~B� !~&: � ��CR�q �.; )kj��r!xai2 N�Vpap �:s!ap��� em~bthm:B��}+n30/��GSY-R=� 2}$"b )^2�9���4aR!,�n`we� �**(��:+ Fubini--Sy!<&UG-Gە�5� "8 2�B�A(��-�>Z�ȉ��a:(-m} m.&\ l��Mom.\ NI7l�&�W�of�+ (I0 XI��E�tH�258��^f �T4 ��"* 6�2�� "o e��r� �TSminu�0o \Splus$ (be"�a ]& ; !���U�2M(��? es2�(s���w$A�*�$on �^�IJ2%*�pJamA�*�X ��94J�]�PmV u_p�lk <�:�L>1 icit�%�h 0tam��N#i�L�l��%T� !Ras"e4�L%x�Z6��a�2l0�unL�ial�\�-�VK)Vvar�IN�� Ÿ!X viewa~��ma[1jg 9-�5O�6=a/Jj hidde Ei�92�&n[z)�M6�:v�`1th>�B6 !0�I�#a5��#���+otGE�c"� fC/��`:C2h� ccurs2$ly!\a|N� i�aM�,��������a$ ��:��1B)5�"�d���A><�"&Darboux*�$���an"�8!f s�3v�&�"pas�zi�nOEc/up� F ��6�R!?L��n4[~*0ua�&�}gl� [,�"�L�o����<�wEU0�� ��!�;R'? 0�6�9 {� �t"83~ J�#9�PNach�U� г"1?�����va�T 46 7A��op� I U�F�r o��![�>�pi)���Z�Ӎ�FIo�S �Nkee� iA�R E�n6�$���no?�Tt�;On�bt,4*73�, surv� as�!S�!8$���3�TŒ9H�8E�'Cΐ ��EJ�� i�Z�l6�� ���5!v(�$�Uif���"� E'15"��c&Qh�9�a� a�;*5 CPTwo�-"�%� :�m�4� Z��t� �\�p��?|&��, � . �"�.e\��!� $� u%�fnit H6 $\Lmo5T^*�-�& 0e Pl{\"u}cker&w:�6[�D$orname{Pl}m0�5T L�e\\]5� , u��&B8E �j���a~5&� �: � eRn�hN Gaus��mapa��%�R,%m���c�?l>v��}ma��9�g�U ��}+sy(F�V�2� �� �&� j `�*� ��K��Y�� o� ��:p�6� ng!a6A>�b���is�jk;� �1>7 %k!&C&��"-s.)xB?s�e�a���8B@��Fv����> �C �z�?me`aA>| ,L 2.61��!Y$!� �J*(Z�3i�\�yrR��"��B!�rrǭc*�Ci gM?A � bo�^�M��a$FDg�� !�}-Rz!ZR r�s�(��N&J oedi�� ��3��u&� �M��U�>�^"��v���8������i��� cg�0�e.�dCt&& pigeonhoErN���oug�AK �1�oI!j.�-oF*��1-1 j .�is|�$M�_p, �_p!�aWcp"�c�$-+��.�s�7e17{+}9U $J��$S^{-}�8o$�S�A !7B 7$E"Sard'aHe�Igy(v��Hmea�h 0>~@M[2Bes4\-V�v -�Bi�6*�7sb8u v�\�)a��JIn�lo�uu.A~() _BL8[�p=�5\H�+�S^-\.� E�%j9m,����e.t-�Ay�p!�m!i�'�.&��a�� �^I�NC3� eF�!�^N  B� 2.4)N /�!c6� ڈ%�2r>so $A=d9[S^-\�]$, ��iPP�Qd$.6�"�)�nże�`$S^&=8�.̱�i.�9� gr�{\ell�{{% Pt��:�qa n�.Z� .4).\nw�kp1a�C61ll"d?e6�.a�"<�$/�6 eH�]!C. 2D.(�)�3A2�ngm�Ii�2j���46*��V�&)j !�!����zHS�*S ��s|� �T)�AY�)efA6?;]-i�]G (o-_�"� "4a;:�.yi)> true� w�E*N��m+�yR !�A�ɞ�>-$w�8�farI�q�\�;���5�"u�w a��� e7 H�a�s�nb��/�wayeQS�H&�2mzM��*�\� R#2�GI!�Q�+ZK&C K:#KA3 �a�reY2�<%9 f^16�B��^26. SO�V &�N� Qa'�bo� x�e����j6l%�TE[*��Ea�v6P$0< ���D-*�<1%u'1-KU=n31�q!�<T\  m�w+ rEA)%w}F �#�R.&A,� -1\\ &=� <ڋ �N$#|p�WY$�1ed�[9 �"�Q�j^�*�a�Z2�BuM��a2� sj�u "OAolima�n\05B�{<.��>A���@��2�a�2-= -��: pur�-��I��72 e��ԡ�� c"X�� �� C^k$F� �Qa � �f,�� �F� �� (Hy. {S�po�lr�f+B�:EX�:� $FAB�B�*_0$�N B�,=N"� �)�*!2��3e��� � *e ��~U�G/h@-��G��~_0����9a*Xed�--�4ɞ. F�Ej�""#9vt :a�Jx�N�� ���ߑ\F_t"� *� �<�{'B,(!6in07 L~%N:R5 ak���+_t);>�+)� �� ��1Z!;,!�t$-*T"���\_h��Lo<&F� Ao,�$(t"KWk�"�g<��D&�;�(n w��JE����$�'i�V�Hm�TobI�h7way�$!^bV�aryQ�A�J.4"�B R�d b� nA�['��V�h�* �j m� !�bP���q�!*��u�B�bt��6e��l ain�ց(�`v ������o�D*P1e1�PDE��wo2�Drwo&�>��M��t����f5"�H�-CA /Q%�phism�gj� kA�9Psa�os�v��:ZAe�. � &0b�d� c&qA�)MEG=���-.�� %|em.E�Iso �*�[.^z] d� e!�Ud"��E�"r%+[ [4] �s�cco� . I� "�"?D� wYa%r.�E+%z5RB%FmQ211!T ���alJ� qs,)" q�Z� !�eI?�M �$A� , hy�"6! In 4���:�{k y[ s�EakMKo/BV1EO�m".s�6~�9� �!�aF��w.^@�C�th!�.�eof^��np �_!��"� B�}IP6(�o:U*K},-U~ou9Y�JI+mAM �!s"t\! e ra  poortul�vR�4}. I(surpri�m&!@r�)� a 6�ywI�Hbe ��"�&B F�� �s�-' �%�i�Z��2}�ڵaL�$ ch�si 9�9!�8>��z:&A-B2Pu���r 4���oJ��= ngen�+&�e�+. I���9�h �&�,-��% ��4A0a-g c&IC*� >Pq)& k��[T���� �5k�is P !\sS8 �x��� See< � IX:1896}, Arnol{\cprime}d $�c88}�vhr  :70, 153v ON��>A!�:��X�U�*VT�nd�i+Z+M� >� iV]s�!2�T_3+R�7c>�>s (.�.^ N)1� Eq��+F|s�#�0I{V�]� �~  aZ�0`)�% �p_ �`s !1 �*� ��ZOn �2���s"���t)]Eā�!�IB�.> #B%�thT���"�[f .tC r$3 P$N� (~)K�M )UXse��C 3�eY�alX,J6o~�,�% 4.�]V&�XT$A�l�(U��<��d, a�!ţ� reM���Q� �+��{��~f )�b��:!�it-�1�ӍKAs $DR3�^��an :�� ���sb�,��� M �"Q at�2� �sI��G5�4tau�pF5�}V=iD�ho "> &�!5rY�=jL3 g � g$+ e�!�lso:��� �f�H�U�2+Wa HQ� Z� [ ~6%�$7�L� �$TAq� "QB�4l�/�?A� $UY��$V_�me"U"5.�bU  pg. 2�h*w S nce,al �t>�<%a%GA� va���3a�*v�*� M�I6���{ --RiJ�n�by!�:� � %�jBJn&1�� m�m�m�q� x`,&5$.I�����y!� .j�ulMId=� �v:�A� u ach��!C&T�umc� �ace��&| �$y!�^G�%�� 8���#�I A����hsA�����5�sm�l �o��>�B my {CurE}, J _��ae �helpfu�� adop�m��ge�e�iod$e�I�� a�YTzk,�inb(p. 280��!�a�&��8�Mp�S�h�GEnaa f�) �?"||EspLiG1dea!��4�9$ ���V"sg:N�A!���$\T���Z^"?0sub�Q��+ ɏE�H*E=����� �^}2�:���e�^�.��&�gN�V�\Phi : C ��+F�o n imsB�6i"� �F1�Rk9_� �a $�}��� �+y�-�pV���G'Phi^* @�X�0,is Lipschitz�mn[ ��� by "�S "�(ZFxjb2�X[M,lef)3hite]׫;MW� E�t  3=�&t���)a�a��9%z�/� # �b��UY$�a �t��Տ U=mj$� �3y"e�� Ali�; �=�� (A?��� a nod:#+m*�� 0�)����s�W ��meo54.�>a��U'�2�� /;�ds �!at�� ��@�-W n�F. �,�&"�rno Dx5j�=��ٳZ)}.p�A��U� $1�]� E� ]/:1995lXu <Sikorav"Q <0F1\mY)krɂ-5� ���E��MgDuv*�Lval�9}!I,of Kharlamov�� Kulik �/ �3a��-"a6�Mj� Q��"�u p�����onic}a���o�l��hG}��������$_* [C]/\%!�*\G#�*$+2� e��iat�m�)�C)�Bpj �`a�mQ.�-���nyand@ni){��:d>]!eie1rw4 of lines, or ��is a smooth embedded Riemann surface and contains 5 points with no three of them on the same line. \end{lemma} \begin{proof} A quadric i�xmap $Q \to \Cor$ from a compactB��$Q$ which is pseudoholomorphic �Ltangent to $\Theta$, 8maps .w � Pts$4a deg�42 curve. Split| into�onent Gt= \coprod Q_{\alpha}$. Each $ must� gp!WP or have a positive � . N.o; ping?=�s are allowed by definition, so e�!N� �mBk Because !� total �!j 2, either%has!om WsA -51,5��3efore As (by!Eersec�! ory E\their1� 3), orrone�ofsH2. The singularitie�th�:c=�%�be diffeUBtoBJ !�la�A i�8 classical proj�ve ($\CP{2AT�selfin� number at)��y�at most!|by-�2Dth%<8of McKay \cite{ :2003}�)�on~13!��)� � $q \in a�M� pk @ \backslash q \� to p 2E�qm=( Hopf fibra4 . ReA�ct�� Q1Mesi/ 9� in�� $M\t$�ere $p$!�sJ~e0a�A�g ed��� �"Vin�r�iAwdistinct)�2� F!+��everyIxn ��a pairATFP��*bR)�orA�. Q$ (�4.� �),�nce hig� .$t forbidden@4homology count��W� exte��e� to�$qi B���q%h��b� a bi[ %z� �_q\  Away4 $.�! dentif B� minu��e�)(i�6�By E�  8:secant}, if we��� !EE then��)'sa!M� sm.� ,u�9 �uniqueQ� stru�,_!�B�!s:�m�m� remark} I�&!� ej$1�is�g�� ].n -�)"� � bk A� is nA�.�second |to� of i�� �� s. S2*cy impl!�.�,  $3��s shownx/ B; ��has ir�Q dti�I� �!�(isn't clear�:1O-^E?} IA anony ��formal9� (see^�)�C1��� s bi.!�� 1�J;!Dn ibundlALisF)$\OO{4}$ � � �M3l eM�nes��coF�"�Sn$well-knownac� el6O -�!�B� be 4� it�L��, giv�A�top��u e6�. Apply) � fic�b10rank 2 vector--�Z �----+)spQof:�s! an orient� �real �  o���� $10z�Consi� �2�` $\nu$. It comes equipped��� aT ariz5G�Cr�LA�ystem���s!�Fo�!z(DuistermaatmW$:1972} (orI�>�),�VJ wr�� ed operat7 $Lu=�g,\partial}u+buA�for�L4 s $u^ �)0e, tur= -�Co�lex� ST {)�u�&�5%%f�!>eur�� vityA3$L�; prov�'n.Y57F[p.238.M�q��moduliI� f%�s��@standard elliptic0ory. ����]�E�>Y av| �%kernel$L$e� �,ing Gromov� ShubF E / T:1992}: \[ \dim \ker L� L + ^t, \] Enj{ug���--Roch�,2�=d,�reviewerDs out), �b $L^t%��adj_ M�� duaUcL$\kappa \nu^{-1}$ (w� M�.I�). + t� b� ŵ��T� v!$�u+v+Bv}$�k� ){i�s�4$ Bers simis!; K D :1954a�if $vb E.^t$�N$$v=e^S V$ a�$$e^S$ a no)zero .�N of a triv����-+-�VE^8nl.6�, $\mathcal{Lt C� ��Chern�94es, $c_1\left()�a�-�<\right)=-6$. So ���� &�� �-6��AW&+vanishsso%NdoYs�W���,Atiyah--Sing�dex)��g�eA*R)��align*�}_ &=� d L \\ 42 c_1(\nu) + 210�G� ���_s�(vO Pick&#.$,\dots,p_5���� �,�3A-them ly!�8!����1-p�6 amil�� B"� s or \ti�x \R{}� APtsLines$ (��$\Cor_t$a� )7Ad\{tIU \}$)E ��� s $P_j : z�; $j=1@5$� y0�sis.A$"�!I^�, ��i�1%2�C!�!�our hypa� sis,Q Et$F amed������ ymplxc9q�%9ea��ime $�Xno5�-pP_1(t)MKP_5(t) tcoA ar" respectQ %�M�� �  nyQBd�m[ )f!���5Z�!giUR, 2us�LR 0 guaranteed�exist-H� ��@taubes}. Let $M$b �I� sextuplE�A�(q_QC q_5,M�)� \^5"�!�sE�I��no+� $q_jJ} R Clearly��n ope�bs �$j��nd!�is� ��t w�we remov�B!� diagR loci�i= ��ɫ $q_k!a�VAU{q_i q_j�O� 6P8 obviously.�A�of co&Y 4��qus:r JpD� e[ ten�$1�$i,q_j q_k\ɱ��. ��ilok:! U imag  map� !N(q [,.[�2!.  Pts Q<�"� Q��a�: G � Vp_1,p_22�.u &�\Delt� �p_1 p_2) L�$`  full&at���p%��tAW)(� ž \neY$)vI��B _��<��t�#A]A%�a�H�p�!�C.-) 1<�A�-)N J _1, 5k$�&X 6� �#a2R��AI �avid�A����\text{e� } \si�-��j>�%�>�%2�A�AK}!ꁅank-�p�T� � , re"Eo��=M�f� )[ !Y� *��El-�x� 6�uA~"s&�".C$2$. Our&y�!co�bmO!�.Q���z 5�.e2%�.4.���nd�V�conne�6t>�G��j"@� RvAHe� of͕�oN aM� r 6n�throug��M 5� dependsmc7 n* choic�!h5A�+s �6WH ��E~!�'s � H:1985} $2.4.B_1''$,� some' detailm_-\`� Star0�' ���V> ��>% "�r 7D& *� ,�� -�+ 1$. EnsurGt� 6>u)v& (� AEAI���imFI �llA�VŒ� B��912� ameR� .-�e�act�e�sE�yml��M�x E�#-(E^A6a�acDA�n�n%0va�$t$ valu�  $\R{���D5qu� suchy!/ $t=0�&� -�""geomet]T ��survi ��mo�& ������ �9emplo��C tinuQmetho��e�4a$r�equ� s[ �du� $ho� �6� A5ar��\[ j��/� �}+b��deriv!*�Y�,r!37,�a*M�� ��we ne�.�amongC>with  Wd M$u��P_j  w 0!ʑ6���%y%��assumA�!{!kQ� $u=(AA�� B�,AD��!��+�Y&HXIvashkovich \& Shevchisq q /z9}�Barraud�v r%0}.) 6�� isUaA�val�Yhe in�of� B?,ͤisAYv"�)y �]J-� ^t,v (�� %\H  H�2V�&� � $%�>�. T��ly�` first6P!�я6 :cy �&=F$ -;nu � -2-4 6�~s 2& divisor#=)F+%<+9��z �--�--R_, +I��m� .�,B3F4g�SA{ solu L� C�$\m'$ atis.AY&�(L,\mu)<`$- \deg \mu.k� q-\m1`.��� i} ~�A�n�,a"Q(L)+1$  ��mz�238�x'$� �� p� on� � p%�I�'vol�)} �1!� � =�4��169E!o�]��0calculate it �"� ���BI��"�& �!�=5.� b�".�N�� �.�principl��0 � Pk. �MC4!a�u=e^sU$e^s��a ���� c  (&t�)�u��%& $U M6;� ''m �� "0as� ��,Birkhoff--Gr�ndieck orem� nu'=4� ���%h�-mi�a�[��(5 ! (�e"� )�P)$U�qJ&$.v� and s /!�R�'� !ptჁ)�&V�9 $did!�lySto us��e��!�A4'.`� Uba!=�s;^! enk Vnot> �uI]a�GE/� -�s�!~!yQ�Q�sK$�> g�R�)1: corollary> ����m.� � n2�= O"� 2K5-t�� �� "�i � l�& a .�2&B ��aI�tB �w T � #~ �R�^�-7 � ��5$N��(!�.i� �( T_q Q�ip:+�)� .�$zn�) � � � (&5�V cor:�C30s}�i%�A�ma2 $!X'�9a5  (perhapM��"�0��BA�.�Zor�Z�$��ie��H/�$% ј��woMb����� 5�&*�b�%A�)`[ y.wp(L an o�.E�a���*�F.�1�/wAbaut��d�3�C�/�!�-hH�&�e:"�- �!��!t &��)��� ujg�� ke�5Vorigi�+)�would�7bee�&*9�n� ���M�M�M� �dM44re precisely 4��ultane�.)ny�I�*6ys,="�^Iiplic�3^"do�9� j"6* unle&�� O1r�)��non&�12- �-- �.���!:� 2  $Q^*�  �*+��];s�nU:! � � � � �:5E}:s @ =�i� form�.en�36)A�m�� | � � �4F~,�qj J� �2%Ae6oA�n�*aR�EoS��|-z4 Io&� >/t6ga`J ��ui D,��it�J�f2L,oL{(I�A���::O ��dsB3}))�� � >�.QnF * XiU�,� p>!our 42�-R�lstoP)N#-�ur fifth 9 6���->�>����-�f^����tp!e� "�'��7on0 d1Js� ^ they�.#-g!0�ou'" �)* keep<mT �,yAeoF�V�,16Zn�aC6/V:1$,)�!UJ��,A�0� p_4�QDF4 �i|�$A $*"74rE�ALvi�$�#�zl?}$�5han�H, � p_ip_i� , i,&�"4.<�X-x1u!X }s~� $s1,� J�&� ���$p� ށG �-+4c� �+, a 4!-T8 coveB "� ��  o�ed�/l>� ��4f*d)$2P!zbbe�, o2c�I.�)eas�$add a "�$ �i���/m�9a�2 AH&*#p&����?� 1#�j\labelI�:ik�9 ��~:� , $XX�l s $(pQZ)`"w�$q4�0nd]�� � m��3. �4$\iota : W� X�^� p'rM�eYX"� p,p'�"a�hU�2�u)"8� �@� $p'1�4if�U�6�6 >xi��!�%Ht�� � � �X0��%sm-�Z�"�#X& pi_{\Pts}�*!y%k Xq5� � �%-�AI��to!����sul�!\r�;ality. F �[9��Rr 7� mmedi���<--�<(coordinates��:2 =� ) 4 Pascal's mysN-hex5$( apparently�)$\emph{not} ( a mechanisi/�9U)C&�s;  2 Hofm�AH 1}-��B�� : <Pp. 309 $0.2.B$ sugges~3A�approac�we� akennt�@�O��� �� �O ll genera���srgu� ' 44 "d;) C.(�38.)F�� subtle:@>6seA0P{Poncelet's porism} B��k � �'m^c A��32�+msh! �� � --Wi�% invariant�� hug��ll �!5enume29� $roblems ab�.})P n".. (K>U2%( :�&p not qa�e�search �2analogue��e��in�*9i#-i'F�. e� (D ?2s*%c+ ,eB Griffiths� Harr^� / aW7,N8} �aSchwartz�� e�begin{&�C��A �polygon}���B� �Nn�:c2�>:�"� $n,p_{n+1}=�=$ eC* j p_{j+1}Ÿ�l6*he �edges}!� �b whil��3 @ A�ca:Ever�i*ADX)�4circumscribed}M�"��J �:� G��� .2n linh�! ,�f g��3!� &� .�  -h .� �A�"| �� �8E)Aa �qg-�� �s��.e-y��:� }[]] iTaőne !l^� �c�>�#2� 4�<more,-h{���� belong';�*�.U�L�iT�D!&��R%� d g!�i�![d6Ajs];C�n&x entir"4!�!� |8(emKI=�[2]-�1�1�8�;)� �>Y�&,8!Z16>��)t/it!si�=1e�K of s. Henc�th���B��>�<�4m8se�uv�>unFl� ��!$1��R�� true�- ico2�!�:bQ�16C � a.g�d.�.Q_E�.1 "�5�.�a�G Q_V� -AR���u�.1�E �\ $T�j� s�� d }� &� !9a%�� tai�8$p$).�. � T�  !�akj 81 ��!�"� z+� QY �*i�4-��ed,M�� "�G"+branchedf4$ n1�-0�:���5�0\d�- :��^*5S�map31��< ��2��3 $(�;b):Q_V�*Q_lV�fQ_y*t@!�%!A�!� $T'$!Cig�q4)�^V$5�eqKp=q)�%m!a�< Aa�� a��ne 4pq=))(q)6e��� ��-aUqK*��w$ � �.K$$2$, excep!Y&\Ea�i,%�q�E�/�3�$$Q_V^* \capi"b#Dua*�(�� U�.��� ��p��l� �5F�MBy 6�, ,U2)��"�F9Q.Q�mm6�F*fo+r{ P� n�,1=2�-�-�-�)ȅ�\varpi-�*5} %�a:^o sotopr@�e�H� N� aM�) n\� ���FSny6 � � � � �.8I� Pa�b��$e����OY�ai�2��X��A�M2%$1���+ y��2�$� ��&���n"U, p��P#0$p�!@p}!Jsr�V��sh� �-$so�P>�FA�Qɒ��-BqS�qT:�#_Va�!�cor�;ond�E�!n 8p}=�fL�7j � ��M �L� �#V@ �?p�!t�� ffAG!�8 7E�z]"6e�1��V$]necessar�E1�C�21E!�a��m�)�G��rR! �q=9  &8a.�m{^� !'�i"��B��8M 3>�'@�9\�v.$�% UjP�}wo25$iee�%^�i*�! !mt1�!�ae$p'6i�Y��]*$A>pl5�K$N���-�A�F�Q0]$2!�A�e��E�)�2l.��if������� QWF�=�E�6Qan lastT3agrap$SU < R3�i�&� ~ &� }e^Uby�@ topyB� ansl U8"n:b ����6eAd�qW>� �&�4 > � &'% periodic Oe��v�2�Y��M�Me�)�ndU�IE��D�5 ;2*�!�nex� +F� o3h4#�8E,O2��I%AH�"dB/-�u-]�"�$&,A� )�52�e�ieqb"�͋_�B lwis6�A ,i {i��7AP�Qa"�) ��9q�!*s,� sh�' be a�X46![��� �A�s� e�reMY�entGs.DN��$moS FPthese m�F��0T�� 1�B��~bi2)�"\%e�Lre�=U^A�\Sigm�]%W"N$CWHWg<xEo�@verag,1s�1�,.� +�I�$k$6�z#%Pe�.7�(k$ get largA�I�@inO�[wa"�ict m emerg!�6yco&�%�A�CRadon--F.2,i--Study typ!  \A>N�, but I�no!�ofmO9�iblio�vDystyle{amsplain} \.{p�} docS} F�\�@[12pt,a4paper,two]{gM@cle} \usepackage[��,n1]{inputenc2�AI,amsfo�(amssymb,a4,3 e,epsfig,Z7y," � \def\qed{\unskip\nobreak\hfil\penalty50\hskip1.75em\null2( $\blVquare$ 7 fillR=0pt \fw+hyphend!�its=0 F7}\goodbu} 6,6pt plus 8pt7T 6pt \tole�(e=2000 \new�{\ea� rm}{cmr8} five 5b$newcommand�f{\noA5nt\bf 8�Q{2! P1: }2* {\card}{\�4name{:(trace>) :* Ab}{:Q Ab}}6� {\NN'A bb{N � {\TTTBZZZBQQQBRRRBCCCBSsSBEecal E>FfF>GgG>JjJ>LlL>zz bf z>ww w>b%u bf TBF 4�%�m��}{Tr`emI prop}{Pr"k`}[5!]2C!1}[. ]{Co")3AK $D"�b6p� IL�Aure}9Lthefootnote{} %\pa�"�4myheadings} %\�V,both{\today}��d�$,\title{StabiY�G:?a$" s \\��Heisenberg group} \author{ Tania M. Begaz�Vpd Nicolau C. Saldanha } \makew �absa�t} GXRr��dr�a!c $3�3$ matr�w�= unit"�H. A laleYe"l. �`o-C" $M^4� �-b�Za?)��~9�<�MThe $C^1 V36rin�? a&�7=""�) ��� �� . An W {\s�WE}i �$o% �act. �+�C$A��f w� vestig�&u> �Y1"s�- �perturb �tilde N �6�Kb{.!#9m�e�+� _ �ng� Hf!�sQ��9dosho� -8�+N�, �%�I>)X\RR^n$,�#e� �doR$�U[SH be�4? y 6$Keywords:}B�(, nilpotent�% �,�.>R MSC- 8:} 37C85; 57R30 M60 ",&Introdu�����: A��nonW+ian� Lie��!�&� $3$.�E\Gg�G�-�C/i_lyFF�9 DM7P� � �2�!$4$: a jWm: G��M_0�ci�[�[A'SOD� ^ ��P am��D� :y2IB&�:8mT;.�m9. ��--�rV�!�N�I�K n!" �� aU�L�� are  s( ��� �)(Y��? �Kis m��J(� �+all>���k 1( best ��8tta=is �(au�" a ny borho�Ea���*�"%=V�. A%� elsm $\phiI�o G$ ma�1 des�&�=f[Y. 7�*ETLg�a2l� 2, 3�SRE�G$, \[�/mphi�pe�x}1 & 0\\ t & \\ & 1�, 0,\� {(t�Xa2XijX3�XTi2X . \]��9 '_j(0���=A0! a_{1j}%!!\\ a_{3 a_{2 0 2k;k!�HBs $a_{ij� entr(E;.R �x $A$ T 713} =j �13�1}22} - 12  1}$.�$�dlyb()�� �S X)es�E<.���2IÅ7an au�,$sm exactly�n�aZcNtible. !~ $H"lO&� E�!�C'aG^�X*_/ : $H`scret�c�sui$R$GѬ M = (G/H)�((-\epsilon, )$WIG/Ha({gH, g@%G\�hZ��:� em%E�& ous horiz=l� �=" rm \[M�%x} � : &�� &e�& MA�<& (g, (g_1H, z))�to & (a�_z(g) !� `\]� )-\sfa�X.�� G$ 7� >Xa)IG�N`!��n � $2�\{z\}>�-}. Ww fnot� Jpd]!g�4�� r"#�n by��% A~ $A(z�!$z%�]) ]*�F�D$A�J I$, a�13}(z�[�# 0 3i�)'2 q�1 IÁ�A^\sharp= M%��a'_{12 & U\\  M  p2��$� )�B�0a���%F�� �� is (��) {ar�Vt�}a_T-  ) if�D]+2�EA<:#� n�'> 0.��� �ld �33<"M�2� ~ U$ =�!�;O�TU 2], �*V 3�/�0?(d_{C^1}(X_j$ j) <ZI oi� mJ..�3��i�!iR clai�/$ , wSFs�exp�E:�Ker�0 �86pin4$W 4�%a 8.� i/F�Vly erg�!2�5�s�h�^d foli� s. Fu i9�6,; �G%�3 ���paperJ lows!il� 'sA8s\ o8B}), E/)� chapter�w�'evelo�kratZ@S�}�&�H:�, Rd�.�a�� , IBn a� rary0-"���|2*�*� "q4Ն :�b��S _0:*�.q�L l.6t. |?��$�x6)tL)� sl{H6 V�072a�@%�r��="�8"8 } \item{D�%=?�$;} %!�p� =M, 5�$e���� 1�UJ[�;p6��A ma�<Pc$\psi:� to V5 �iNbMm�$02�(g,Y(p)� (g,p) C] $�<G6M$.".LendE%Y^ 04��2�E�ha�241�eknom�N$0B:[1| �~�)el�PA,d թ satu��dF@V�CCL} or amacho�1�7y|� 6.�2"�Z-l � 2t=9; �S' ���'��~�H"\gamma:V��e ._? *�/~-�F W�= =|ix%d$z�-�p: $H_z.��J sotrK)E��&�3c"{�i��T: let $A_z = H_z/[G,G]V�Z \ZZ^2Ej $Y, b��H_zf!� inuo�fc�;�)-��&ng via� quotS&�}��' r�A_z`ap hi_z���b�a.�� � .�, >! �  Q  1�S \r�#a� �\q`�eTr be)]]&A Kpsi%�Y;by �� ((H,U= 9�%�� y2=u�E| $WV� ]g^M_0&�,r�8en�eft)�S ��P�5 :i\!Jc� 9z;[5-d:AJs8Pra���a!� forw�rchecksK��2$reader. No> jah�IiI)t����2�Z a�u���by }3�� qed .VC b } PoY9��/*\ $(y�y$y_3)$, meay'�'�'���a�* if $# -v$, 2�G�'_33)2U 1``� ntO $s. Alterna�6,-T!Fed� !�0�'& 2 �_�2e^ �x�%�B =�$:&�[b_� = b_{7�9 .:' v2} + @0)  0) - � 1.O�11 R H = &+9!~A�W�z$\� |( = I + zB$:EP�~A �z) �z�� @�z)"w�!$z% �oJ���7*�&'. s ��*H ���E�"�(ligj.hat�} 1SM &� M \� g\\ >��(@& � � :�v k@a�6�)HX_1��4y_3,z) &= (1+zAP 1}) �(+ 21}� 33 r\\P2JP>� L ^22^P2^FP3FP�� x P � " !�E_)j�Z�g�Y6� �g$� �it suff�-#4�F�.e� (p�~-p�u� nonN_|k *�y�D0:�)� q -a�!U+T&=4Q7�1')!'.-:29+�t q�q_4pC s(3� a"�L!%��77���q+q1 +@� 4 (b_{!�~�A7p_2a�0 ��qlU�w�R�$u���c�?_1i�$p�r�W�8!Y)� i�e~" = q_i �T.�A:P"�J�IJ!+ � �m c�M�c��m)c_{41} Z"h-}a/VJ1{BR{e9!{{ aT{2z{N\�Z XB�27�A� D $a bump fun��� %.0)�. AFK ompu� ZYg6 AZ&'2��5C30V- .2�Ho] � �IFWS.�]�4$!_1}Lor 2, �mQ� int�ng�j� �'! �, r* W*�,8�m%hn# �~("  t)} A�Pv��:q �.�)�c&>c���$:>Q�nJ4&= e^{"Aza!!Б� 8B� 82J8!�:8N�e^V� 73R����r>�qƪAqK� -A c}�}:�ZNcN$-wB- c��G6��F�����%��eFB� �KoW4U�%����f�|$c�y�$23 cr�we�=m��fn2�E  smG Qz�&�Ugeit�fl�\\a "] "j'K3Xv_1!� + v_2�ev_3 m�$v_2/'a$�oQQ$: wUo}�d: )ZJ�z. ��w� KiՊ_Xw�(M,^6Y $': \TT^2� alfiK=by�Fhi(z,w(b+ z, zw&�( �L2\pi cV$c.� (CwEf[x= \Ss^1�7]� C "�\CC$): t�%0lso�3qu<"We.:s idea��Van�r Corput��u KN}):�A:,^ �JZ{76�  : !�6n)KFn ��d�n.nySJ��B�;;5meaqvXn (A9 Haar, ���nt �d"63Lebesgue-)!�F�phiP &t7 �,a�.4�d�c�EBa�W�i -� ManeR�7 9.2!�n� s�f2�CCC &�aH�! sequ�\[ g_NA��(1}{N}(f + fdrc �kpc�r:8^{N-1}) \] conv�=!��/qo 1n%��g%�f{}Fur��m�TiF i� f$ a Laur� 0?nom&0!Iv$w$c de�P2ff n*�= "S � 0_n 29ofNvU�ing6�$f�f $�Az:�j$af��6!_n$�Vcl y�/��a$"�0,[ra2 a����.hU out lo*�gen��2E@$atn =K/7$\�-  *,)(n�,bu "&8 \| f_{n_0?/0f \|_{\infty}X) D/A�W��-av��]x� \| { (N+X\mJF� vM� - �� =:�e�}{� ]$N�Q$ �euN��"-�%sa~ _ex1�������k6�A �8 Б�|g_N\|_)�69.�!�=�zCZ�M9�a�,�des� . H Nsai a su�mQials,��C��&�T$?%�$f@z^n w^ma�X�easG�9!G�6�%�!*.�^jHq ^{jn!E\1AU@j(j-1)m} z^{n+jm}n��O$j'� ��B �a�mm� "$ �$nV>�g_N� &=.� (�+�n2 {2n} ��(N-1)7\\:[ g2Nn�11}n - 1!n. n ag��:� alph| Xn�XDN|z| = | & !$ ^s)/t)!�e�bo�;d" $g_N$��:�A�$N$ g���V��y. *�&f!��"� � �1��UNJ� {n+mBwjn+92UIUH+� �,&\phantom{=}FH)�0Y�(N-2)m Rm})A�N��\wwMz\zt �� ��U2jC^!AB�by> ww2\sqrt�B(1,\l�,12�zzZ0z^n2Ian4, a/��N"f3u/�inn���<, $�U(� A�4|\langle \zz, !\r|�w2* �JQIR3Q�toE� u�r� ; =< R_N:� ^Nm\)��!lix:#� �P 9(a_0, A9)�] N-2} # = (r"+ 0)$; Z^)1�_� Ik6�))?�Z%[="�Y^V%IR_N^kB�/Z���ylA>� NR^k_N ozz1�2�N} \Big(�&]� k)km6H{Y:^{k:� k(k�q.^'+ �){-6k� E+FO:.1.�G)�(ND-n)��m)}�); J��$kwexpresٚ betwe1a( h�+�Q�hj" h�!S n%y ��m�Ft�HS,t� xuoV�$ " +M�)jqu�'�] w$M > 4/^2 F��wewe�&#d(4r"�)$N_0 > 2�(\[�MR_N�PY_|,^2R!iD |Y�{M-1}J,� �9M}2�N > N_0�Q:� |�+�a.JRl|G��( :�20), v qeao� �v�hM��(M^!M)� $2M�i =\��Thu>�5?)�ww}�m� 1}{M!� �R��n 2�6 .��� �f |\wwnI�� %+ g2�.� ^�� QE�a�B(u%I�Q {V��FC8�"&��!"� :U fluxe-X�� � NM,a+zA��v�^v7v�8"��2�>.�2?^ irj���2�J'.��}>�g-� ��everynWXi&i!-"P,As���jb�= 1! A�/o$ )!p�sp�WBYX�[� (t, .~)�! + t,�&� 3 3 t2 ' Iq7 !� t^2).!�} m5�"�or25�: 4>s)N!?�Qerves $�  a BorelMbAI�$xY+!bAF\tau(x,Au\lim_{�_1} �T�K�s (\{t [0, T] |1,x3A\eM~�%�A���a#\RR�r4B*c((I$Q�&�3!�S�h-.�m(A�"I|=e� A�9a �%K�$\s�R-a��A�5Ys �1eRi�n��e�e�.�? A�$_"�A>1, D}!${)Bs,A\23)�%j(0&H:E� !D \��1p�E-(0H(a��galm�/D&�  '�6�� isc): $m(N�E>x mu(D*�1�:5it V�. lt�5h�En,tg�).�!c�#e�(t_0,x)�6�<�*� 3Est�s(�/ 6�*!� x�"" i@��r��Mp Z J[�17}{T} yQ\{)� \ZZ,$"" < T,E&_1^s(�%�>%12\%]!�>$; ��D�},7�1I��*F*5_�b*�A�x!�i,�+ �!}//2)v_�J�-���_ɋconju�L �:� 7� A�uss�X,)�/T "/ BT*+uy�}�ADN� =�c[w5.�6. F"-8*3Excell-f#��\\ �-iO�&ʹDEO�)�� � w eN^of�*��$*6Q��[�$�&X=��spV" bc�E�: �a�hoE sub�YKWacZ]Y �r^s �7GBS}!���,DY�see &FF}AqE�n4l�&J���8 ying=V)PAO6aone"]7�9��\Ff���C$M$ whHn�85.���i�{��\}� us, Z�;Z)K�a.M�7genlF %%��DA�Ff$�c i.EDBp�Vi"<�i�CiU��alwaysl[9ala�v^H� �s�i, .� $�1]�2-�j.�Er �E�a�B�/weEZ� aE![6�A�[=ri� A%f4� pi_M�7K �a!d��N:?. "� "��5: [a, b]��H (a�]gA`0c"'� (g_0�*_0�M$�%��lif] �3�be Aath.��� ) �a+�A�2�� . ��L ")6'("�A�/_ Ax "C t� $%Va��C� pi_HX$,"�:�:� nh�t+�9�.YH!!sf:�&G [�F�")��1 0s ͔ maximalN���\Ee5y{aDn�I�domaiU[.D6��$[a,b]�K lm>E� sai��be k $k$-�Zn �lif�N�x $|z_0|<��/93� lengY!��aI�!!Vs�$k$; abub��'lE�= �i�0oodad� � A sk�&ci!�c3AA�$k��'a F� EOa�0 G$,�#�qp$s $f_i^\pm.d9/L'� /2I�V� a"�3. F���� r $iy,'��2sE�m��2-ath&�E�(_{g_0,i}^s:D 1u���� -1}^s((8g��1{5&-sO�5\*r8 /-, .X2�X0 �5cd8 gFVX3�XT h2X*Now-n>�K:�$, an KM�9o$�Ert��Q�I)�#D�,mf@(z�8�G f!i� moot��d�+iO incrV�ng68=ͩa)a�in�OI�`��; � now ��w��eJ� stea�/> 1$. &ɻife3H =N�>ena${g_1,iP ;3�Pnd-�Q��#1,i_ Aح�!A�3})^{n_i�a�H"e"Qnj n_2$p&mea\?�'&@c$���ot!V onglh�levantz = /�be om }1!\�. �Can[fUf_1-f_2%� �f_162 = f_3, [*@ �-idE�C��!�1123Q6 a���z� }��N�CL(�(�|BS}XMt��� 2�c�'n\ ; �1i{sf�Fl2 "J }�.lea�fLl$!�}ed �TX���3(z�z�qX�4�Ll$; !�>��|�E.T��F.� belianw., 2..��E ��iM "m�G�A6a W m0�smA�e $1$-j$d ;)�4�|}o� *<��*p i��g�c�ab�otdS� |z� ��5g �V-c"��,< exac/H>�:��� + dR � x>�ɹ�W.^ �_-!� "�� 1W -�%�%�wE�it9As&�A�'��o)��=BO&�} "�A)Q�U9/|w!F a slly���1d� �� 02�qujAN&w_V6�U�}" "�E W� m%���*,�_{G/H}*�C,a�%h%"zEn\.�(-1d__P�,1) pq]n�N!�t���GGJld:-.#DoEZu>s�le�k�:c2�K?q,nq��;�8�0 c ��C�U/?J�..JA�n�Y�]v�9kQmB�.�^t\JjFeq�a�ŘS&� $\PZ9 to U$ tak�%&m0�,)6yEBF:�r<�K�n}R���n��;Q��� �sM]�~_[ ����F=��z�Gl���Psa��ea$_m�C�on P0 ���,J���sm $L� ,p_1}: M_!� ( o�h \vfil "No"rs:e#0jau_\Ab�+. Abf o� �\Ab6c��T MXiz� q<��Y!0�Lie"$o$=o>w� E-�c&� k4[ \Ab\�RzuTu*�0�%^�Q\f0� �%�%),�d�Zov�Q  \\ v�Q�A .#.o�,+ -��Sa4{Fd� �"&s}�"�.i�.iTj2�0.�"!� Z(�V�%fa�Yi^Yi�,%@9/v*5 �01o�d1u �l.~'$ '; A�*@m>�ş$��A�!-�%p*�G� �t/>r<�V�R�&]$&A1(&J" j'E��B GgC�O-au_ �"_��$w�=i����:�toi# 2 �%,$(v%$�� \bT~zQWxtwym�+'�Cq IŮ,��,_{\Ab�3� � l $�N�%�int_{M�p}�v'n*3 ) d\mu(p)�.~.6 =��F jF�z ��>^+EKing*�'J� h0" �� ��n6�Eid�[��i t>�!�:.!/}I�in�u  auxili�1xR%�_%G-�Mj)�)m & v);!f$'� Nh{�_���z6E��xi}9 � �2�:��u���N?>0tIliNA">0tEK(� (tv)E�:2���1W�b&%FL.b�����U|,v�W=1�ͤŗ\:�3 &V� �Ee%�= :�!�a@0^tB5{p(s)!� ) ds*B69�svkf�* (-�=i&�� v��(��'OE M%7Ʋ!X�&i�%�j#=/e<��A�A�a:IquA�%�0,0�B&hsC�X�S�b�p��� ,"M_RAy�Cl�bF��X1�������cA%d1�P -A�)D rf�2�1j)�D xb�5�5 +w))!�-B"�� $w�$"vDqBal%]y�-n���limb�m�B>�:b%[N�-ay(.c+w�b��&A��V�e%�P�o�i/�� �e�V� , $2���If!�- Nv���6� �� lMdirectZF�FDb�!..or0��h_c%A�%K #alL0���Hver�HirA�� ncI)Ac"r� +�Z3 ݨ&�0P~{D��g%`2F�d. } %���s#=�$��&�f+} �ingy%�s %�$%�$$� -�asA\���#Z$or)�s�)0�Z�^2 �) 2 � ~� ab3}��>3}(E_|6t'on  �� 9*� .A�:�oa�  9��.Q t�E� �!� �:^�V� R����� 2�J.+K�/J� 1)�9B�2YF k:6!g��W�c��d loo�{)]R_> 4)I[)$p�ad�E�2:�of�� >�U �SG�g�2c�{g�y -0(t��"D1q�i){)i��# $p_i� �) 0, 1oe%'&\A.hA�G1 \x��� �E!i� � ,*� ��]�.iga�.�����AR� E��'e%]5e)+1�� �:��W�M"B,1�NG2!��n&'��P ���4ewi24 ^k2:Oe� . On�o!�ABw�a2 a�K2� 2��� �sZ_r 1X1,�Z�q�F5; %nH �gB� � p_$ K�C�m2���.M��Y 1�)��(�PJ%�r�ia�CoF� �.B�L i6 U�Z� O)��0iz5 N�a�W0.<��exa3�seo��p�� 3.2� !�r=Ja%��*�5,D�tA=n� !YNq��7 �e�isKyA�ZNpa�de)�) ��bf�f c &� X.hY�2� 2j.]:z (c,0� �) ���F]ab}�_��n��.�+�-Fn %�a .>T.�)`A,� ��Sqc�� "I� $F_h�R� 2629"%�|A"f�$u � ~u^h = h��u hw "�;�8�� by $z#2�l.yRh : u^hE/�!t u) h ��ſ �(*w 45�1}�� A�m�*�\x�"m� R�>� ^�c N& o!�-^�|e �� K!��I 8|�J� �n$B�M, ���.�414�V1}(%-R!�- uj:ME�� re2�<�wf stww+Y;"imY�." �� �x ab�iV.@Q,64!<6}e"] �ach��@���obn" ������ B�� �  NAMmaS�9n} �*l��a* #n��-��8nkz �!)$ ����'#Q"r��0Bq_s� �&~y�&� T�y�hWe %: v76�!"�y.Fb2���d�;� e)��-�=� � e�"�< c�|A�� �$"�|Fey����, $z_1 >G#8$��<m�c�3 .6 AVl�)E}�'YC�#�*� �|�(v�O�ByB�I���:�i�u��2:i��p%�T ZZA��1 }} (�q��*(pV�2�{p�q\�= �e]N � eZ�t*�6��� Ab' P� �A }^ 1} 4d}{dz�I��� dqO�2 ) (vE.jp�a�"��i ��E��C�F^F= B�5)|v)���r��6� �k3�k "�k 2��j���R�f�nf �\a_�xCY�"Fhz)�)�u��&��jJM=in�@ble, $- ~Y 4U;q}c^2&L):��Է2_,� '6r�{ *� �\x"�2 � #��Y��uv ��\o$�#�A7��c�0 span�*�{���|���)�e fact�beq�: G��� ;�m"#rE z/�l, )م�rCLUu) \w�|u�P|4ll@$�����k����;\ R,w"�+e�x1E� = cw�s?p��ve 0$c dw�NH.5ޡT1eNA"��6��\� \�T�lr�Vay�%@�2�p$s]� a narrow Uar��; ��$� e�edA0�9��9P(���i, n"M � uo�h!the.P�}{[10]+�ib�5B}��cٗ, T.}, �"�m-e�hdade ���e��"R{<�o um do grupo3&t~}, Docto�` diss@�=,, IMPA (2001 X�SB��=p�, N�N#�2�H� <�a�,rval}, Bull � M;1(Soc, New Se)�36(0Y25-38�5.��{{\sc �{, ��,Lins Neto, A�Teori��om\'e�E a da�ADhea{\c c}\~oes}, P)�to Eucl�) , Ri%Q0Janeiro (19792�?|��Geo�A�or gol�#�\"i�rr82D lDenjoy.�Sur lE'urbA%�fin�cpa ��� �r>8elles � la su�Hrface du tore}, J. Math. Pure et Appl. {\bf 11}, ser. 9 (1932). \bibitem{FF} {\sc Farb, B. and Franks, J.}, {\em Groups of homeomorphisms of one-manifolds, III: Nilpotent subgroups}, Ergodic Theory Dynam. Systems 23, 1467-1484 (2003). \bibitem{KN} {\sc Kuipers, L. and Niederreiter, H.}, {\em Uniform distribution of sequences}, %0and%1ied%G�ematics, Wiley-Interscience, New York!L74.L Mane �(Ma\~ne, R.}-A�theorys�differentiable dynamics}, Springer-Verlag, Berlins87>s2bt�CTeoria erg\'odica}, Projeto Euclides, IMPA, Rio de Janeiro (1983). \Q)S f4Saldanha, N. C�XStability of compact ac!sE6$\RR^n$  dimensionA;$}, CommentQ�PHelvetici 69, 431-446�9%o��end{thebibliography} {\obeylines \parskip=0pt \parindent=0pt Tania M. Begazo Universidade Federal Fluminense Instituto de Matem\'atica Niter�i, RJ 24020-140, Brazil tania@mat.uff.br \small�, Nicolau C.5V Depto.!�pMatem{\'a}tica, PUC-Rio R. Mq"th!}6) symbB)cd6��icx6epsfig}�-�,%%% % Makes� equa�� numbe�o8 subordinate to&se�� % s. \ /within{E}{ ) } \a��4displaybreaks zT��(ems, LemmasCCC>RRR>cE cal{EBLLBFF>b<barF84para}{\kern0.2� (backslash} -0.7em {B0 �"a�- {\m ent}[1]{!Es 0par{*}\script�  !�� rco:6k\ }}} :_a�_%AlanbXIKJ  end5 :� \setcou�({page}{1} \ ��empty�2� {14}{� 3)}{\.ref{f�  }--las }��Parame : � , year, 8 r� ,�j � Here � top-� er!your Am awrts1� �a�Pleasa�plOby g data%�� is� � runn� lheads \markboth{A.~Weinstein��8M.~Zambon}{Variis on Pr3 ntizw label= $ $ \big% �� Titl��\� ,e{{\Large 2r :rWS(of a Dirac 5 $P$ � a�\ncipal $U(1)$-bundle $Q$�a�patible F,-Jacobi stru . WA�udy�a� of�lgebras �dmissO fun+Ag�(on various %H� locally (1  respect� $P$) �ed:L�Q$, via hamiltonian vector fields. Finally, guided by e2 a=is!Oin�0lex analysis y cont-gM� , we!�pose an)�-f%no�  of!�quyNc? !�9:)�!!��is permitted to have some fixed point� haUm Hg�Ymy� ingsR , iV$} \emph{De�ted!q�mem !�`rofessor Shiing-Shen Cher� A�L��%�{Introdu } >]!]�1` attach o a":� h%&!�U Q�K$ (or�corACon!  prb�),ynn � wh!�curva  form!�!�.#�� Lie m 4 $C^\infty(P)$An!� s faithfuA�oni ( $\Gamma(K)� C e"�AW equiaDantB). ImA � polar��0 $\Pi$ cuts d��.n)tLmaller, more ``physii�ap� �3e''6� _\Pi �!<&a sub-AF6may st act. By ��nd look t%$``ladder''M.tenA�Ppowers $K^{\otimes n}I6Q$ trans!�accZg%llo negative:^m�"[ re��ent�2i�$), one getL ``aA5to��64 �AWA V5.��l^C @ often goes undeI� name#qLic .�M�i9 D step closely relq�de! �.A(. For syst�����ints >sym��, tph����Ebe ��.�� u�. >',�&�%��%=�T���SB0has been carrUou�these se��m s� al aDs;#ir work� ci�.below. a��eaim!�%�paper1to sug�� two�2�. ��L , Ounifies~A�l�c%c��cas�,nd thuѢ)xHsimultaneous applicI;j�I=U- �EtoI w.�!Vsecond24ARii�?��@�3 .. w�� !�a bou y, sH�`:S �4bec�.s,a sheaf rathe an a2�(over $P$. I��course!�E,M alsoE� new obse�x(ions concer"� 1�!P�{&( %�.�ub �{S:\} O�@&3 4(P, \omega)$, ��w �he Fj j  $X_f���1? $f$�$ Q8(X_f,\cdot)=df$i�b!�!�9D bracket $\{f,g\}=DX_g�n�W{�_}�`�+�� d 2-��{$AB��ed intega� if i� e Rhaa3 homology V $[ t8]\in H^2(M,\RR)LE, �Kdi)�image �Wmo� $i_*: MZZ)\to.[ associ���e@incluh $i:\ZZ 5\RR%p0coefficient g  . WE� �:�&�Ko��t \��{Ko�we*� e A F)!� choo3 Z� � � aezɅz8 )_ !,0$i_{*}^{{-1}}1o$. ��%Kre!Wa ��� $\nabla9 K� "� $2 \pi i � $. A-U�to each6�!f@operator $\hat{f}_ ." i D "0 {Our�vena�� Mq�Q�Q�Y�?ign��t��of-� Gu} a�9�;�se tly jA�ula�7E8\eq8e�} Ť�Fa �too. �q�� ert� � map �Rq�s!C�rJx �s%�n �W2�I:Pa�-, s.} �(s)=-[)� _{X_f}s+2%� fs]$�E obta� "T N} 6q $C25� =���2~ abovE�w len�!�uO , du� Souriau-�So}: letšb CR� .�toaJ. Denote!�$\sigmaD �q A�Q$ 2� D):$ (so $d C=\pi^*m ad $\pi:Q \r�arrow P AYby $E yinf�(esimal genei4 N�. 8can ida&fA]l �� �%"+$�s}:Q .�\CC$ Jarp-Ah)�r C(x�t t)= U(x) t^�y$!E $x��S$t ),� [!�ly $E( F)=-I� � !1t��/�T .T.n*�eAS& �iY�$eqnarray} �i� -X_f^H+%� fE, �-wh!��supersn $^H$ dEi� horiz�l lifE�E��2`ExP$. N� A�atY��A�� ]�!# ��5^H- �ũjus� bjof A�^*f���,s �s(viewed a � "�; see SI� \�6$ecjacdir}):P P2� BS >�%.2� f s 6ZI�N�!0N��ant rankقUn�� y ot� �  (9_ e� ose ��dFe�e w�us!�e� ``2�''�NdeA2be anypifoldo!be�a6 , E" A�%�do�ot���k.} was[ <�j G\"un���%(!�< Gota�&$ Sniatycki(oS�NVaisman Va1}).V�  ��a�!0���alo. eav�$\ker �S�0as�W.psuNu�[ce u u.�5Q$ given[!Fula6�, i�aR$ now�_�i of6i satisfy�M�:� >�� ,uiLambda)$%�" investig -���$Huebschman1� Hu},K ter�) *q > 2}, eT��� : circle� <Chinea,�% rero� de Leo�CMdL}. W���c:O  $[ �P _!�  iI�; !�a(� "� �&JO� ]$ *� U&��e�$ }w ?> %�2� in"� -1}[w �beM��X&A��� !f�� i��$f�f6� �b�(�2�*���)!;$�T!U a2�.� . TE!5s a (��alway&�)�!"�:A :�FW�gni�#h� sult��%$ prev paray$E�ut !yC� se w��ir�6 Cour�4Co}��e u�e 2�d as � ial d O ��mhand,�Y8,had already q6�Kirillov �Ki��,Lichnerowicz Li}, ���m^,A� 4���ci�A���n as >�AU�� l(�� jYZs %ienE,ssK%��#�� Wade �Wa}�EQ��( actu�� 0m $\cE^1(M)$-:&8;5�stick�AJ��in�``4 n'',!�=}�){GrM}k 9&. ToA q��N$�u �ig aTg-�) �P� implib exist�.a�a7 ��� 2� Eith_.�j� �(!�7- ���Q$.N�  (suit�.)��$gF���(achieved ``M-� ''A�A�to $gC ����!�^�E���g> ^l� � T��A�o� �D(�' b: &�)%,> � {4^�ct���g>L�ne sam.d�U"� can�^rea�� d1� �%Z�:~an $L$-Y>"�L!��&� oid�e��e �Oae�so � ." very n@als, disc��lauMBrun. G� &4 pM� ��distribu��$C\�t TM$,�nonzero�G%�it�nihil��w�}�.lA(y$of $T^*M$.S! �]"E � coor�ed�,S  p�)ve half�?}_+�E�suw$. By adjoiB �3%``�M  a8 ��1 �''�."ՅJ&�W�J�on :��!�= a�.6.��� �a ``L%�-�Y�''. If� we ad�=�) %��5� we�E�XM�b%Z�*"� !� :� : eP$�n Bmod�ia� cz+ps��p� [ fib�A���w�5| �Ionents�byfl� e�� G1. Aerreac�^� ��� to%�Zr (ns�!#n�n in 1!<),�UFQ�UNi� $M$ S*2� i���{Organs1!p0}8�s"��� :�!�!�o$ facts�utM�E��s. Inl ZpacesWst�*w>+��["a�2h�&� >In�>�$.� �r2p ��$:�>f6;& �3)� �8Uder�����:=A�Ali'ng R�"sA�&6|Nteclebru:�B�ofM�'s�Us,�$�)-�j>�t s"o$7m�)'we �!m�=q5�s��o�d� thsO.� -l � }< noin{'4bf{AcA�ledge)+0s:}} A.W. wo�0�1ank� Ins 7 l:&�38JussieuE�@\'Ecole Polytechn�3� hospi�0ty�l�" is i��be��prepare�  M.Z.��grateful�$Xiang TangY help���on"d advice!�Ah earl#�%2 ��l v' �� B� l:' o�M�uf ՐJ6�� urag�rwri�<����*by�s u�ub.�a v�4of2cee� s (a$ ll�T�j kb�� ue meeg�elfpi�F��}�e� �] star�� re�h�-'��k� Co}.:&� }[�1 1.1.1] i lindx, r} A�-f��Y�}!��$VO max! isotropic%s�X $L �0t V\oplus V^*� ����J4!ic pair�mj*" �)}  ngle X_1 [ \xi_1,X_22 \-Lle_+ = \frac{1}{2}(ia2}4 +12).:K�6=M_ , necessarily"R�B&W;as!&��t!�a\rho_V� {V^*}4 p<�5e$2:on^ ; $%N% ivel�)have >?!2�,a } �((L)=(L \cap!�)^{z  ��{�,�M 4�286>8�a�}6 ol $`$)"�� . ItY "c� nduceat#"t to)� kew �< neara�' )[�$� a bip� V/�$ (} �5. a"4_(f $(V,L !��NI�� $i:W2� V$ a)#ar� � � � pulld1>p�W$ E,{YI� � xi:i,\xi\in L\}$;x �W(map between�2� s ``uw23�1''�it�s !!� @����target2X�!��"  source6&)i(BuR}. Simil�,[ ��)2 $p: V2UZ�9C W'ushfor� �� n $Z�[#pX-I!F p^*=Hb&* a*�,``j.8� . j$��$ , aF  subbu�.L�  TM ���h!�ed  3 almos� ⥚$�A&*�* �#at~ nk ���� ��,nt .,Def. 2.3.1):�����def�9��unZ�2 �(�,iWofd!�)d*�"�� �9 $6SDis����d�% coubra}\;. [rm]=u1(&��]\;)�\;\cL�q�b- ̀+ݙd( Ō  - 8 )�1).6�F��vpi� � ble, $(L,� {TM}|_L,[5 �&]�� Lie �oid&�R��%�[!��I� $A$,aY!� toge�� I-��&L' �A/I J)��a j���`: A.Z!TM$ (��(``anchor'')��`Leibniz rule $[s_1,fs_2]=!& s_1(fX! s_2+f� '&e�sdiedT/� Y�$Ps_2!�&DK(��M$�.�Thmi���a�� ularn*'�%�(͹t��l� s]C� StefA2nd SusE�S�%� s ri�o�tin z foli"� ���"�� ��:6 (6�)��&l|*A i�h= 56) y60L�$,�P!ݡQi5er c27es5[� aU&%way�:f-r^*M5t��vh�$ tangAi , bu�2�it a8� C unless�ha*+�(!�.�9� , eiaS. (See�=�notadmg�bDB�of�.&�.) Nexd��>�4 '+� putmˉ9a&d!�a� ���iB2}N� \l� dirhamvf� q8q7� ��(M,m!� &�5} �!"e �? smooth���l � �#| �� dz�!>$L$. ANC�b'��fj,�fMe���s�am�u-M�)J_{!�!PO"�3M)!a_5%��} � �d"�6�>$df|_{4 TM}=0 �4converse holds&z%F^c cap ��h g�#E�, aain�. ��words,�$A/i��� >��T#�A�&| -�:�0%j@22 Sincy�b�� �9K2�++ha>-� E� ") �% J],�Z�@�&�9��e�.���wa�VJis�![ �.X_g�fNZ Y ���+�� �42�d.� G Co}I+it�aows u�re� PusualA v�)��6w��>�sDwnY,. %m�+fe��;��iBI �%� �^ 2.5.3&[ �,8on���@,LieAlg} Let ��M4��.e��0�$X_<rE�j�!a JAs�M�6$ghn $-[X_f�0�N�:I�ZU.z �jfo�yazwela��ѿ"�L"Rat I(1sh )z�( �+t�2 $(:,\{E�V \}*� Ѯ.^ .���� %B��aqbe�i�;&j:��.�_{bas��ŝbasic}�'su1of*hi$ �B$d\phi>��8�\7.%!N/ s. (e��#����� s co�-�he^��F is re +ndeif $h .�ndE�is �$\{� ,h\}:=X_h%� DA��d)", s��!~ flow!!j�$X_�H�\�&C*"�2�::)�0erv��i��2.4��u�!feG n. 1Yo�I����,h, %4vanis/<(adap8 proof of �T:�\\?6 how�4:�2C4�8% s fi$~ e fxB����g.>. ��"*& R�C0M$, $\tilde{ %}:TM\r&�/9 !j"�<�($X \mapsto �5(Xi�)$� s�ph $L=\{�6f8(X):X\in TM\}$ 1�RL;�F2 iff *A� � �p ��O8m�nondei%teM�e9y 5�U� nd a�8quf\ 2�>�_ft6�9�&.�as� ��*Xi6&i9". ɋ 7$��a�a&�7� 8 $x_1^2 dx_1 \w� �n $M=�R2nd�#��be� )�� ch.@ :�u�%3 7 %g{excepong��x_1=0\ɒH(�-s <tw�*A� s cl�noo!) (cUSEH�*` &�J= &%)�(��alaL$f=%. $ t2J�=�value�%f�q.l$ $f$ is ��i!FA�llust��; V� � "b M�rov�T� M�aY�k  Am��"� Y��R @} MQ-ERa��N ,�B -}:�52�3M A�64p�R $��S F(�o ,\xi�T(N�4� Harg�S 8a� � �;� .) I�� ��q� �(a2� ��^*��!3�%��Bv%X# ��� _ ?� ��4�Sc� � rl: $�-, D]_SG |# ). E�%9�FS R�2�3�{f=j fe~a���.�$"; �(df,dg� \25B�!��&�2 )N+"��q9n.�1�*���*(v@.�~@)� �+�-�2� c��+�&)��/|Jl, LikeB)�<?�f�asT "tGI��a cer� �m��&} A uB!ax"� �A�a*�6L}� (V\�@> R>a�_1 + �02 +g_1f_2+g_2�O �ps,�%J�n�$V6v&� $\dim -�= $ V+1$. Furs more, E-8sO3O} ��b( too:B*aV( u)= �MVD V"Z�5 8 A�iZ�/,:L�He .�ws&���47i ahN/[�4. For��,�2nF>q�!�Pa���Fl�""�(pX,fM� A�,g):(.�,g)��-~\}� ��@|et �/:= (TM}�� ��$�Q n �)�B�&�����"Wa�". 3.2�"defjdb:�"J^!Ma &=M�:�B8:��,8�86� ���")��nk�-A� &.1�Z��".ex�P�14�� [�(��)�A. _1,g�8;,�$�#& 2,g_2)B�,� f_2-�# 1�� )\\ E�\(�: 6�`2�#1 2W+ f_1�#2-f_2 2T0(g_2df_1-g_1d�f_1dg�_2d�,��g� g:K.�2�z-f_1!�)l~�."ah o u*0J :s4���2)6���)�1a�&>dCA�D3 s. .�?U� embed' "�=q�).��KT(� *T^*))*�9$$��A�,g)�Q (X+f�%\p�' al } t}M� e^t<+g dt),$t� $te�} �/digZoa a $ faUOa�&� $ ���n !�q�- erv�%�!s"VC5%'^u�q�-�y� , toC5L��JL� `-�"#! _-�>� 6� *?XQw59IwIM}.heM: any6L1E��0-�.R����!�2�*s"��V(_{(x,t)}=\{A#R!J" A""�!2%: Fx� _x \}�IEEyp�R-� h�+n� 8&,*p,14�� ( J :'�$�2be�P` 7 6|1 �-5e ^�" (&"b"/�!��� 3.4) �:�AT�'} ��M�M;"2 AsDM> �s!qF1�) oe�a2,l%�al a�&�1h Ha� $<�"� ^&� � $d 2T� �PS>~A� DJ}{  a W0p���a��=. f� �� f�JILendowwu%7*��D�#�9�N�Bw 5.1] A6=�7e�= 5{�Mm  *�}St����h �k $\va�J_f$&� $��Tpf �a� !�u:. PairsB?�V %ut/up) ��� ��Q (TM . i3���Rd6�6h7�z�#b, M�,'=�&) �EN 9 �ѹa�Jc�d:$^*+f1}g$lbmPisd� @B=�|�ɚ�� enjoy�v�-�ert�;�3!M�}�E�L{e�"9s� g�5.2E|�a �&py d}� H�"9nMI )s>)xf��$�}'U�6n1�*p��  &� fZ� g gug,g)]=6 ([,X_'5�- ua-d�,- ),)� �:/ heo!EVag�*YE�!= u� �"!�A(�N<9:!�m���(^a� a"?Q�si�M$���� $X \psi+ f=0$n �ele�3 � �>I��C e��s 2/ TS:1 $(dc,�rh(kz� }( b��t��8�J^;6Re �9"J![��9}s.ݠ�KE��@s,�9harVhej 1 a#i�"ml@em0b DJ} � �I ���v�&R��G� ��eEBw1�0$ll-���~)Aw��' �qm� } It�iFYq { X.�@@ * �>- �| �w�? %��d�h� )t!�.��Ii��a_xFY Fix�ho�5�P (X_h�h)I�!�Jc!~i�t�$�+�h6� }&� t(\��  $.(,\C �A��:isOKa H&�(F!e^th$)%a8 "J �Y*� � 0)} p ^S�N)^*� ;ea$ e^{-pr_2^A(x,0))}͜�awei$fy $T_"�:�F}Qʡ� � ~4&(6:_6#=�(xd)$��'s�-%��?E. �(!�6G�Mdd�6"A�j�N e#,e���7m��Q* 2>3#,�GL �~ a\^�y�[8(see� a��>�s&� e tZ �&lsn S2!r�Q.�OwjnT*!e� � *�F�)o[ $(:�^*(};A�$,g)))_x:= >+�J N/R .$ A .A�c1$(0,0�  (d��e�, h�")\,,\, *�%�#2"= :�}���}\Big|_0>�*(�.�� s:at�^� *6� &\l�K.� �݆psi),n�� "H X&� b�>� \big[ � K�).�R�� :2 2!�)_x� e^{���]=0��u 2t *}���P�\A=n��Fu*^a���&J$W*,h� aE "� �TA is�# . Oni_2?ed cheJ:�'s � 2"��)Z V�&�8' 5.2);7 �!ps�8 o. Altern$a`;�>�+s ��Leogo�eGB� �!����P$.�(�N� �g� homJE} Ji2#F � uI� g� e^tgo jUib� "� Li�a .WN&6��.7n�2�1U , if5^V� d���tv* (X_gu�g6~Vd(�)h# V>B 6�Uin*�!� �r� *�J �Z E } g$. U:5EH� �< !0_{M}= \{e^tf,�\9��W� �IoU��9�h!�rch�C� ţ s.4��h .C:V* Now�ds�@�a]E�>�xMT�oIcone-to-�&�%��< F&R#T):� 2bstr�i#�6J2#in "�+B�:��e� PI�(on*�Z�=�#�wP(X�T��"h<x&�=, `M \RR\ &E �r s; . A�MacF�\B6' "S%,"�#I��Z&�E$>"&�4<�SE*'&�!�NC&=2E� �%�`0T $E=0K0F��p��. Any �?-& $mW� m"k`T"�!]22Ze��4 $\2y(�}hmatrix�oi�,�&8} & -E \\ E & 0�560� (B�&�T%>a6"$E��X n�He Daq;&Y � \xi= 6�($\�z{Grap�q��B�"�C"_)�eLm% u%Q-� �,E"aQ".! 4.1R/��9��q&s�[�b3AOis��A�>c op� �M4H`�6 a.}�+f=�] �} df- fE�.0 f = Ej �����!;u��5�)+f ? g -g p5 "MAB�!@. 4.3�ZR FR�p2�Aak*�%�o�g�R�WaQ\�_aU- �[^0:�"�U${EqdV!*efz�ޝF �-^ci m=�`�%���-P �J��| }k$(M�ee(����6 Reeb�N�n^ k��:�  �}|_-v 3}=�jId�D�_6�-- IW},M�2.;~a6 8�� &�<isn �J�x-Nx�"), LconOx�Ty-�d�0s�(�4`�Jj��X�� ge�j�M�Qs (�Z").&i/:-:�Z6l6�%Z-=- $)��-�z ..���MR�&�-8>�M�,&Kpa�O;P� U � de�ine�Z>H&�OA�a*1&�]Ls awt- scri�2)`/X� �'' �c��5ic ob\}���&�:fiG:jO�!FAP)$ Ud�5d>�M9�2�-�)� > ]a E ��.m��]!��aGC6 |1P� arrow TP$&�" B coch�>� ��FIm�I�zl!en(#B:"^oA��jL $H^{\bullet}_{dR}(P�jto"J b0-�^ Dlat�xha�%!fp? $p$-t �!7 �s)�>�Ui, k^�ul�_i�  Va2},�6i�"^ ]\�k{2�[A cgi�kw:��b]_,K&Elyz >��pois} :e�"�+{\cL}_A �:L� shn�lU7R�.z)Eh mnAss�� isf}Abe� i�:lhmh]� P%N>!H')�CvpZ�F"]�4�1!��h�Q�.�k 7$�/$���hS�h�A���Jvh-ach�h2i(E)=1_ Oi_*u I�.ee�%1Yxe�)^�jac} (-�^H+�  A^H,E) U*����5e��/e�u�N\,0�M6y �x]_*$. (��ZQ��p�.�g:�g,)��b!H& [ -+JLfJ��P$�5za�ia6pp �map. ���n-���yk D%�b�o *A7� )I.Q6 � �a#�S$-�e��1[6� )} (�h df)+ f)~&M ^� �$"DDPn��i)A" Q)$.�</�t�mt��&6 �io%O4 �� �oL� nJ���<��(e��9Yed +"k { �I"Q9P}: L6;P$; bX � = �Gro�Y�9�dJ� X�a� "��&"�+�FA��mT!l�D5"�f" |��2| � �tc�_(�|U:P}^*:��^Rc�8 ��.(LŜ,��I��p��� �����p(!� $H^2_LAn. (W� ~# !1�=CW}iZ�eF�!�fgraded ��; viK �/�-rio�K�}ezL^*$.)DC8!D�IK�?d�)�c��): a�TP�IP$�g ]1 M_&�"Ueq�kymm.!���iSti*.Z� B� � �0��.EU2\-:72�N-7�12�0�It+B�Lɻ$\Uj!��C��%$d_L  gHOurB�]"b ��Z;$ 0} [M] %A�(i_*(�tP,�t)B��!�|le�rBis8WUj1}Zi=z+� betat9� 1E�"p,"$ �� $F$ a 1� � A�6C$LA^.e.:�*E�"�)�D}g%rem�}f%L�Y��ka!�*@-� $@�9�A0=k %) ,xf�A�6�"�!L-jK"�"�<6�6=)-��D�[)d]=Y$\,!W only�:� 4 �]$.&/7E����et��faցha�5$.9@ �oW%e}$5�x })= .# �!IB!�J a��d �'�c\ bundl?!9 zJ Bl$��lrsnf >�K}s� B=dx dy�1^�At)� �=6�}&&�>B b#y}$).}/ Omeg(lV =�� is ��at&3n�d liz�A�2�a�"*l 9�E:l&|s io4(� �0g>5ine; ula ��"` fm�Z�twAod}O�V� �.0NM�pbv)rz �: L�&� s�^*yEF% � H~� ߅� SeW}. If � h5 � 3�1� .�yc�� ��r� phi(�=�=2m x>� R � ��k �`��<9�9) ".s�WFZ& A�8 z]^m%}�"gT�� T^��6�T� Ke�&�L� ��$N@���2�>�a�>��+$,!�m a"�7a�oi�_A--Z���a� a F�?&�X� vE��:J!EG auto\�� z2� (;2�(� |"xd_L1�� orb"E�6Id ��ԅ_L$�=� �-ib� A~&�Ew&_,23r�3_L=j^*A��k $j��]B�|u �3a�%l�o$d*�2� �8lexs�' $= Y=9���= Q�d� _L�V_{ �,$$!v"�b����� �ly�K�$-Ih�'�mx�_��to�l +! y�nd1x:�H�D�.e ��ge  .��7 ct�� �a6 ԓ"-ab��nvolv�J gerb�4end�mNow;"^j].�0B!�7"b Yg� �-, "{a�i:N�:!n� &�i�� �*~)�$;�3� L v�z %eZ& |�"� thm���x�$&g18. Q�9�3e$direct sumF $\{(X�y�� �+\xi, � �a E*Y!�{xi,0): .4\`!\}$�pM^�s����by/-T0,11nd�&9D�k \alpt�0)� a�1��8a�uo HexC$A] ?aJ�m*�E�\%:�W `8!beta=2-. 6V, \ɫ\,15 _+|_�VS�wa�%X�V,����9�3�ndepe�f�&"0 >��Q/"��'7LCfFm(E�*�$ � �e �$) �*63�� n :@. �� -%YI8,�Y�&*�AZ^%� 3� ��V�(n2ffm  mode�_�8 �A kew-��� ms).�k_Q!� &al&| �B�a�],:.|_C<p% � "[NsMu1� Q�a��� M� >U�A�.+$.d,�&�e� non-&.Ob!�U c �c \,c �E�AeisJc�U�i��B��ng�F��is ɓy��[�~�>U e )b��!C6�$6eY. %�4ly5 �+Y�,etaq�a}L d*�DmsO .@�E �w ���Ma��g�<9u+Y,)q+�qz=0$) zLNi \ker��azo�u1M(%��� eoret��#0;I�s 2k$)2iB�iln�:� atelac� B�]e-� � ��j3!Y�p�|for*K8 d\me�>.�:0bh5��9f>�!�B%�CB_fX ���;|i, >� �oY7N�.�Y� Q�a�6&�h$_JP+�soMG�*�NB!o� �62s � ble,a��%�=z�&�Qi^[��� cJ4[e_1,e_2],e_3 �'�(�9&Y_e_�9>1a-�#�RŁ�c] q_+%�a tot�W:���if���L�to�.|nQan:* �, ^3�I^*)"�h IM},�<2.�j Eachdi5bL.]mP�^�"Z� Q)$-7 a�mb EeV�%t,aOthree t&��5N.�: $a=:�� "Y * � -�! $b:=V�  $c~�  0�3"�|�ubm�FIl*��As�d�� c!.A� mmed܊II %,a�6@[a,b]$,$[b_1,b_2]�&$[c_1,cE��W� hm"H*�$�, [a_1,aA�a_3Y�A�5Y"wh :��#"�"X�b bc6`�}R�mV��6� "` 1}�sZ�1d27$:�H$zJ&�rVl�}s&�u�#*} |bf{� u)=q��1, X_2�L +X�Vl%q���.y�v��25�� J1+1+ ) S�3 �3[�� big]1�� !ga�*}]J.�y�IXa�o%8se ex'7��V enough��UA��}"c?��L � ���b}�h�Ef"�$�U���'xactl7��a:\U� >� �=it� &����� �� UA(P,r*&Y^�N�.������(�!,\B�b6j:$�:�� .|��[�� x�9sa)�l�x6�q="��5 x9�dG�:\CC M{; T ^* M�Itj�[�\eڙ!� AggeH�!�d{%�*DGua} lYlJ��bE��}d� theiŸ7!�ju\��U6yn�U=+ IIW}�Ylex� B��!��:wPpUma:� �ya�z5l!" ��}e b�1��M7='�e��:�M}$9!no�\d�A�I{ied�l �8� gA6A�ar �rnone)`FDEQ����� �V-Lwv. �+!�. ic"Iv � APshA �!d)x+^ %({TM"1me�~ ho_1�1F!\ \noti't/<  f$!d_�9 )�sura.ive, �$>�2��v��:"܅Pr'�Ermśhe:�I[l*-�#eE%�iIygNed)�r, �"ea2�OI� =0.+ �^+�B�Q-8��1$� !5� x'�o�'$T1 | a -'�  P�_{ 4}�d tur<&�o�B�!&(Y):=-)�(e���ny $e\&�I<,�D�(e)=YA�wel&�=1F�*� $( �,� ���7v2 cov2Qn �!HA ��S".5+=>��>,aAOnR��$(Q�  %IO��!�AQves %( &� l�O�h �+_*[C(%�4(L)+\RR A)$, %�AA�]�thr $q!��-l:�r�*�x�e�fNBRz�.��,r�"F$,$&F6:{� &�R���` pask> �\pi(qE+�i�"*[A�q hav�:푁�1 \Z�Q} \Left��AkJ�Fr}F$5�.�jP� 4�\we�� dedu��M�u�=qu�5 �)�Fake=pn� Xi0JZ aDEMmf. Aa,W $���>_A-^ )$$ � PACn�T�%�� "� {A Aac A)�����! :[�:cQe�u����>U) ]!i&Y2e'e�a*��*�Ax!x k.s ��Pa\�ea$ (ɽaE�pݬ f�Ky XB�ve? A�  [& i�+��=7.� $$�(��,7!��F:�4'gͦ�E�JsÚ.� )��p�}24 I1c}_L4 ).A;%((pr} Y_1,Y_2A� Y�/� %�CI^�Y8= {) pr}:�� r� @2i>TF)$ �5? �A%�m!�a�m��c!�. * E$�e�h� oEon ��lq1stwo�>�pium�ns�!_L�y6Xa �A�v#� �L)J�Cc��VJA�� ��28 Dsc� �.� &� !'�"9 XTi��qa�V� ������T~r ist ��%m�lR 1W$ %�6w�$a�u,*zWZ�-�P��L-> } ,4� �23�g�GǷ:f �2���:! )k (�WiM sm��!�O#^+� 9AZ*�#�6��ܞ'&�#ha�q�8]0]�c_1���_,-{,��� J"" ���E |=�A7ɓi� expl�9�&how�m2sFy � �,E�M2]z)!Fƍ,>8H��)!:Yqout�)6� d3��&pl4� r �_ >1�. In R,&� qYA�9� agre�>Q:q  }!is��Vk $!�nF7."�ZT�ch��WrJ���[^.b"�D"�%E� NEW}�I���$��I�P$j��LF�� �h���4I+U m ^* ��o� Z�} TwoZce��Bt-�P�)y�62�s i�y�9 re�;��n.�!~gauge |�7Rv(P,A�����Q�4-P�,s/ Li��2�)P)� sc2=�[6f�� ^15 �[�$H  �� quot��A7ǭ�e%E�� <)W$i�$�("�7[N-s��:ma�J�� U�:[i�P(�\�P��!���>�.�;����6s*$K�-�%$&� ^*�rc i_*)�*=0�topu>+ �%0D�1��sws:�3Q�>P A��i���� PNpac� $ 2�.1]!E1X�W�i��"�W�E�ripb (Q,LCx)$ With �<, ��$ 5��!�ll��to�sng� KE@a A8,.�$�4 w@�x~3�&�!z ZL���inHa����Aթ��: " �� *T8^�i_�Eso}�"+F i�54RdJXecaN"A��: �j �9),$�u/N  he�IGd%{ . SE�uG� A�]ce"LOtwo*a)V��TDe� ��߅u/sr�V2' >�K.b/���Ew+Ey%�B-�: �jALWF ��ted4)evnj2NM��h&3 $� T^{*}M�6i�<"�4' $B�!�!)j�P�jP u;Ha`�"Y*2�xre�C� �!�4 G�j�� . "" �p��t,.��$�[!��endM�sm_k(M)��oEeac9�F�XeS�52jX�N�""6=O�d�dhI L�yvL�$���Z���=nd&@" k��!B)%�uytF9�B�� aY. ' S6y)i�a$&�edZ�a(b%��&mmatwo� �) �,Y�6|6"=:P�6 ?���7��ihro�@:7+b�m�b�� ױ� p $ ܅%}.W!�aB ��, unti!DeA�i�n-�h_�A!E�M.q>� C*8�Nw�"g6\cFy Ԁ6R�bit"i&���F%%�5��(�rs"��b�/s.� ����,N-z}sL8&۷�WB�  $6` /� {.�} ,��2�I:.)� !�A�  l ed �.��o*7�1$  JA:�.� =�mZ̈́�Ew��A8G�gk%U 7 XB�X*�&=�N~6] Z��� JZ� T ^�+n ')"� Qc&i� Ea�� '$ �1����lN� � � C�d޷5��$Ŧ�4�~u� �#f�qN)=L"!1�� �)�Ui%��Ct�,��P"�, >��wt���v� � �� mma .����e��s."1~ , di,jAcD 2'. �7�! nowE!]"��z�D�)�$'s+eaQP�.�J� ZX���T.)E�&8� :f� H&{#&�"� �'ME], ��a � '=I+A'*7',u/�*�6I\E�=]P'$�!�Z� alɮ�F$)3!� z $A'*;6&N$�*tAiA3, 2'=d �-\�A'} �h���hd@*� ��"{�%q�2L��e>��l.g�X_i)QH�0L1��(*u)G} � %�(:l-,"f- �2)5*)+�w! xi_2)X_1-21)X_2+A'%�MN@1���� Cl��]E�of82%N2� �%� 8�^*P2%�$�75�C� ��4)."�]e� �����pi��d;�rop[�ly6�҄P@: s%O(neighborhoo�j�,k &T���&�F>$.l)X�/�6 \xQ�dt:=&(L)"�}�T s $X"59f�D� }M? A�uN.#5���B�=`�LM6��pBQ�a+��re�. K=�by mea��� 2Օ��Li r��iv|.��'�'�'�'z'��}�9 "�I.[@iz_�8i� -�F��u9 1�e�!�.�LYr�Na$"P,�䭫So,!�?I'�2e0�*�o28FoERd>,$�mfM�"2 U�� Alsow'x~��:aI^.�.}��$b�=y_��\r � '��C"��� a��_o ay (�� " ��:'$p!by��,k,��Y� !�"u�V� ��F�"w"�2� ����`C(3 i jW��>�]d=�F�% F^{�&�� "�.x:� | } �� by a�@*�"G .�:!A�5��-s= <�%- su��*� TP/F"��2m)��� � $�%ByZ� ���1dV�j� *%sD&�*ly�P�0�&�t� �e�>.a�J�$:�7i3p�Q$\{�5{SXI�NSY>}\V*�F}.�� ��\"�G*z !&YQF�P�4M�*�9�e� (a�v9a�e }#in de� two"�O!���6 "k�T!&�\ "Y8 :��)_�ZE� � 13X%i�i�� !�A�by �� �t.#��/�z>V\5��!i�>`.��!�9���@;DyPA1!doZbyJX mapp�^ spac�!&�bSa!�``"� c�2s''2>Q�tVbygF%�K3>onN�b|�4Q,\CC)_{P-loc}K" ��(��Db:6�lex2h&&OWe basic ��a�&�c=in or��o �� �.6a-�m�)�line}.}&h�r6A��?T 6@s"�"y! �� +hAo��X� u���#~a�*)���m?p ��%9'J %�^*Q&�2"a� :*� (EKljh6r�,:A3I�ure#�eQ^)��ol- %>�ewF�B^'$M� %&�l(PEa: (��,s�*�� �x%\R*�x\}���{� cript ``$U�''�Vh6��a��>9iA;� �!��%o?�~�"p ,U�m$Q��U$~�"3!�op:� =9�We�@!sa��%\l�eUal}.�  glob>�t lj1Q�l��oo 2� �i��iv�&O. p�� iinj�%�vA���;A:{��ita"��as6 .}.>����?�0�A�&{�snd�t�cl�a��f#�1n� re4�� sub6��l�( �SL}��&�7#Jg):B"J�k{�kD_Z�as.�!.)&4� ��y:�?��� ]-�� ͭ$ via BLZ"�G ��+Y&�r �(.l,xSt�/ h\}.$ F<�!�.� Mi*m� $f,g&eH��A�%�ir"� mU*f,}�~�<*�~y<&De"�].�\{�� aFi ��@"i���Qus�_.t��aCm2}�4�1%gV�q'Y�Wpihom}���� �\}�_Q�>�*� �m�, t�fpr�$�[� �)6�t�W� m} (�`"r,d�P}) &\&�1 0. Der}2=J)\\ g.��  &:� -gk7JEt}2�8>�A�.�J��.@1)�}^I�� &�@ [����wa���"a~} �t�7&u�� &)�%$-X�ul}(��-%� 0=B�S~)X�B{E�g��of.�2� �l$��Q_� mf�! ?���X !�X&~!>�~!��= ����!j� Q i�^�+'-map�I�� .�6 �D�Z�'�^�šb#�}� �"K+�}.tEE&�T\�7SG�d: ��^*� ~'"Q"�!<+-҉! &�w�d"B�"��$Q:�K �B�v. %Sh��S.2�-�b� %a1��!�Dh-��eqA^9�a�F echn�(issue, %; �Pddc�<%�wj�V0nN��P� el$ qasic %1$� ��ve.��"�(H4t2��%�qlh}$��hsk.<n"� %R�"�z� $,�F%%f' �� �oi�h}E�#K $d�}���6}f�4 %B-�3Ag�s �."$8 %of�4R�(�f��by�m�after*�V %��EC�B$Co} (2.4.2H[1�isA �AH~j< hi_t�2���$�6&%X*�%u$#T\`Oӷf"�D!�2 $, h^O�`� 3�D�얉WI} %!Q���3�~F?,.���$� be %too. : zqZZ�Ma2!�mak �x Y.�%$[�f}, g}]�(I<&b)v see B� C��� r-��20"q{6nvaGй7� ah#Hb �ZV!\d�� o*L�. ! & ���W�-eigenS s5n/�IvE� 6�.6-2s $��n&� n$ musta=a��erF �'l>|$Hradm�2w.��` �>7BA��9{6,H^{n'} �\"�eq +I�2�n;P"���-fFAx(a8�Jl-�d gd�{yH^03 %ichŖ�& �� $�WT-�� &6� ��U)p�� �FIP�d{-1-��A�^Z� �6e- 8{��-Ťlim�= "i�"��n%1-81 $. C��i��%�i�,s�O�r�X2�A%FJ�@ [�Rf�=a;�` D�. 5iH1��2a�!OJ1 ::x4*E� A��ign�+J��f��jB�!ChB�&� �jg@XE^K��A$%�in >e aElm�~C&�����n` # JE-E��&ral���gn�0oice ���E`"_e��v= �2s. &��)l/�I�::=�3et oranm�*�s"j>ng&?t!U6P:i�)�� ��]Q9ſ* $n$&#$ �}osu2} &n�\~  $(S^2�\RR^+tr=t�c_{S^2�XZ�� d+QLf <:�vduc� �*�!N S^2$V})dard :|# "�B� �`zX� e:@�$8�B0>Lie"�.} $N�@frak{su}(2)^*-\{0� ) &sp1�i� +�jlfAA�!� Ar�q��E�ZGed49�n~ �g,A.u�> Ri�)e1 $b�et `om�l�'�� � A +A�(m $(ct^2-t)^U �a�8 reala�!� t $cA��B60:h +[-tjZQ�]� so[n$qCB�r cE��EA6=�2�"s[Ah*_/$A >f��\�:al}  t}r�Ăwe�6mBgTB[B�$ y}~&to.# # ] �I c "�!a��Bf �nof5!�-U5. H� ny6��<��#Q�C}� �Y��as���p�4%BG2ѧ�Y4\times\RR^+ $ �is of the form $cp^*\omega_{S^2}+d\beta$ for some 1-f*\�C, where $p:S^2\times \RR^+ \rightarrow S^2$. Since $\tilde{\Lambda} c =-[\6 c, ($]$ and $-:' '`$ has no $\frac{\partial} � t}$ component, our first claim is proved. Now, �@any choice of $Q$ ��\sigma$, let $g$ be a function on $:�O$ such that $X_{\pi^*g}=X_g^H + (\langle dg,A \rangle -g)E$ vanishes. This means J|is2|�f $t$ only, satisfying $(ct^2-t)g^{\prime}=g$. For �Dreal number $c$, t%�@exist non-trivial�s.^(these condi!s%>, example $g=)�$ct-1}{t}$,2reforEz all-hs` homomorphism $g\mapsto -9:$�@not injective. T! v also showS$at one can5(simply omitp vectoA,eld $A$ fromdefin�Acis.�%�.�� of} � =�\subset %� , itYenI#oadsidera�5�%� case. Z��^�!!�QK�L$Q$ is determined up!Usmooth sadon%P[@singular distribuA�d $F:=\bar{L}\cap TQ=\{X^H+��(\alpha, X \�� E: X\in L1 TP\�weMyi�%�X, if a $U(1)$-invariant2j $Y$�(annihilates�_�!�69��n< must�� �!+$F$. Waart b� aracteriza!f_�4neighborhoods �4a%�t� rankA�ump!H holds:Q2lemmaqų  L�~U�~n open AAin $Pwm��b�%h TP�@ con ��2$%�U}=��{-1}(U)$�ten.a$\phi^ 1K8 admissible iff&is�along�leaveAK ![ Fur�m $A�hiAmA�}\ker dz = !�e_-\b�K of}WI;$eqnarray} =\text{.�} \Left*�(h,0)m�( \rho_{T^*Q&�}(%1L})>BA F<2, ��I!�%�.� �{sٔ� ula-�La6>remark 3A�D��4\ref{dirhamvf}!� 4fac��\dim (Q$)%�Q%&,TDirac-Jacobi structure�ahas $9.�=1.!�( TQ)^{\circ�so �� statement �s� ���+re�~ foli�A�%�U}$ withQf� l to�:$\cdot \cF$���  a gA�ve a.�|_{ Z8}$\footnote{The2� $F:�!>8 clearly involu�; seeF�Pefjdbr}.}. Fix $p\in xw choosi 4submanifold $S��roB$p$m�0is transverse��A9-�E9 . Gi��co $\xe�T^*_pS$��> findR�!y differen� G$ A\p$,AtIextend�%!��so % ��Q|���5���N��� ~��eA�IU,$n$-th powerA%F�� dard)$�� \CC���w lie�W�� $d_p �+Aull be�al �xi�) $T!B, 2\pi i n E_- n2 oAT_p$: w� %atS &x �:;� %�&� �[E��b a )�-� �Cd��� j��< 1)�,aٖ��,��aY,other inclus!��HaIA pr�� � !l  us| !���1 ��` $V$A $P$D re� s a� empty6/U�8�T �*Z)�$Indeed�$q�, a point of ���NM$minimal am�6!{9�6� , in a sm.^�q$FTa�0  P&� �q� D. \bigskip \noind���it{En�%��VC}~~ Supp� now %�Ɋ ]�F 6�bus !,a� ��T $$Y\notin F�� all 9�&Ip� �� . By���above,A� can assumi �"� B�^H=�FEM� ant\ L& )s�I �E��m�f�.�  ta� A �!� tradi�:}If�modified\:�\eqs�}�i } U PU $(\TT.�8, d\varepsilon)D $H=x_3(dx_1+x_3 dx_2)� th $(x_1, q x_3$�ɍcoordin� o�rua~�+RR${��ively. �is a  . ympl� c %��by Z#A�:w!��8*��#$re=�. �J��ly.4ble�ѻ� $\Oc=0a��L=-7 ^*_{TP}=P$A� the >�"nQh1}� [��?t��3 �� � $P!�!�% conn!D�\�=d\the (�� iIb"Ufiber 9�)�>, ��Q seed�x�E�n� �v,� one dimen�0al, spanT by $2 x_3�\Fx_1} -j2}-x_3^2^# ) }$ �8coefficients $2A�, $-1�!� M$ AIlin �pe�)�,\ZZ$ unless e+�Ta quadratic algebraic ��gerE�closur� f67 d b&.orm $}�\{!.}� pI densedo �'s.�Qp C^{\infty�(Q,\CC)=.bas$�usists�ct�f�lex� d%En$n)�  similar�so{!*�&� 8P)xex othose b` Bue :8.�a%�ssociat� o>� �h� f� x_3}!"�so actsq� �.Q"-i $.\\[|% ext��0illustrate hoTeR icevolved�k.��� :�affb zitybH=2MSS^a �q�'�!K!�$��-� o� d $s%�$> . Endow�� O�>Poisson*�$D&)�Vduc�  zeroJ=A5\R.�Ž�in`of ani�ral ݃m]*S�$���Ѯa��(ble; in Equ%���#pois}!�� :]:�$�� p:P\*��)�a���2% ��Zer���"�. E�$g �C^� (PD�8K D�-)~ nega�� 1itsb� }|=(: ,dg)^H+(A(g)-<����tkernel��)Z:� is gby.Ea��s$.$w=UIB � )>if �+ang� t�e.+���:����. IP�� T>] TE n�� an honestpordb.�9a�. Howev�_e&ia�is op:�m��`�:��is!we I� $AJ�*� �if n,s}$� ��s Bv.�A(Pd)� aU�u�&�A�9`iL G��� Tk� .� 2p!�]�>(i.e.B�, �lently ] �  �ied).A�B7discus ��* E }E�, after�]fix�"�F F -bh Ed��V(] �1reya� L}��q ,A8 �E�fixed�� qRunique�.���'$8 ���)�9� $\cL_{A'}� _L=`%�� O -�ose flS�Q "�s betwe�.� i�. a�a�topology� geometry�HWicm���``A�es'' suc ly� leafhnA(a�� E  su2}~)%�a�!�oG�� $A$'s as �V $TP/T{\cFbll9 coincideVj��Y>i/64sQ�+�\"R ��[ 6[[�:J: %�.��:,�v� JllB�ari )��An.� �*s � Q����bt�j% two7s1 kb Kos Ht's work \cite{Ko2}"] ZX hammech} 9 (34, Theorem 0.1)��oba6k�Y �)��.��/�be S!i��"\ brackex V@�"� $s higher, e��>�is ``cl  cal �anics:J J''. II�generaA�n�%��s�h see� 6�b�"9a ( �&� e 2� A�:� $�])�a:�s J � nto �;. See S� 5�IWay�pplies �����.u o�e �+y�� $.};!b���")UM�'sM� ���%�too.   (P,L��=?�W6�, 6NitsB�� (Q� \RR,\�%)�!�a``\ii''!F2^ . Tor#ifno�"�deU pullback�8=](#Q$$�$) un !obviou�%��s� !�samŎbol. U���me$O homJ�}!�a�re-writN� :om}�B�PA�n N� _{P-loc� or6&b&.&)��$$ g %!� },$$���&qb)�� q�a�2�u �l�P �|k�\ark�}ih��B�%a>�& �dA��)�"n�qc�\c re����% Hz��6�d(!9j )!�fRE� % $. M�&preciseq'AW*a natu�c2 ![�V-�!� .�#��moum �$ $e^tB�c�ctS deli� .# . We�f�b�ko��v�[ion���� call":ced�f tak��� �-c _ N 8'\ ``�in-� ''; ��$�rm�%b�dC'��a "�  s�-�a( Q]aKS}.yr � EUL�%�� nd-�aMJ *��ReA�n u�0 $-E\oplus dAo�6Vj" ��%��� a ``Q map''\%vQq6bBc� by� u i� BlR}AE!�  value 1�ob $L$:!��>" ��!�"�+);U'o�.{0\-$easily� n to5 $\{()&"+X)& \xi,"1&�)  �$*\xi: / � LG&!��pushforw�via�i:Q.P�$LF�� {��A approach}��} ` is&� m~Y��!�e"l �by let�)�.Su_,�)!� ��,aamitian � � $K$p P��� was�takenAq�for�.��8�!�j(HuebschmannmzHu_$Vaisma Va2}a�o�T�s> ��AO��� � izes X� nd tur!�oa�*(� A�$we describ�� si�spaces� 6� ���&,} �F} -�L9XA,[�k�q],�)cLie� oid)���� $Mg!��al�-� 3$M$. A�$-z� ont�1$K.�M�U�Z4D: \Gamma(A) \�/ K)2�/*K*�(M)$-Aar��$ 3�c�e�� s $$D_e(h%- s)= D_es+!5 e (h) ,$$"�$e\in�A��sK��$h�h&� �Mrurv�w �6J�hn, E^2 A^*2Endl� \ $$R_D(e_1,e_2)s=D_{e_1}2} s -  1}s [ 1 ] }s .$$ cA�/!=2�A >�!:��K$��,KZ:�y�6% m-�d,���end. :l W)! A=TMw y6s � �iaa�v�. j,cov�nt deriv!a�5�� � , ) +Hry�Qq$\nabla~K�N%���v ga>Eb����A�= H_{I�}$.% �  WG�h��@F ��adapt��N�%o鍡+�]Va3},-�h it ��seE$L=T^*��A�:b<-� �f-x9.F� [��ure&@ a2 n lo y ��$B 7-E"�/�"� �1} e!"� o��%�E���2v!��/ee8'th!�$L.  $Di�n a�=w'\U�!Ab $ =\l�3�o��|_-|_L{%f�- &.0q0H$$\hat{g}s=-(D_{X_g�dg}s+ |gs)$$-6&9�a>gj���1K $\{��] K)_{@: D_{Y u0}s=0e%{�� } Y��+# �g�ny��4.� �wI�$g% )�� }��-��s$%�}%ly -s � well-eC����fAY�� � , ps�V! r!9 �0�,a�E ``6''��.��[-_X T_pP"�qE"N �2�nqKE1�% easy#e�'e� techs (; � 2.5?�TF}) nee� !�P i��m�6m��,v 7� E'M]dg�$L�#ducE�] hi_t�i P$ ((4 is j]1��(2X $X_g�c,( one-parame�fam3 of�au.x$\PvTP � �-. 2.4I) Co})� �s�+ �t�5L$-path� &$�41%�"� $A$ ��a� B! J"fk'a ) t)!S?&�!6anchor� s2-� veloci�*����e Zpi(�* t))$c.ut1,99�x&mps a� P��1|��too^'g:.'%�^*s)_pE�th�rallel �.la�s�1_t(p)�$"21_ )�${\bullet}(.Q )_p= dg) O/W. N !��6.}�nz|_0 (2�I L�e)� .�vY t YD_{D0)}.g.$ AMqy",l5c3iX�U�M1�&Z�2�y�!inK}0={{ M}_*�s1C%�= ^�% \)}\Big!(�a^{_0 9�\g[ ))}2 &�2�&I�E9an QY'r�15 0)��9/$ c:�baM�%���a:�$(B�U��I�tqDM�aJ (S����q|-,"�)�L M) A�weF�eeJel3�1�eMKM�%�$� 2u�>�y%.�a�)3 ��xr�9 8 ��5�M^n�}E^MT:�bm 1QP FPQct~\,R] �R�� �5-)�zy{IoYҁ��� E? M�U+$�<*3ce "+-�9D� .� .;Rp�} 9U� o!(�"e �"in���J�s��%�/j5> f�'��Eh� �(! re )!� �>m�� ��I�)##u�evalu�=�%9{ \�==��b2�}s-� �5}ZBk= � �< of "�AE�$�[VP,� dg]�np+w u3,�%p)s.$$� oAf erm "4es&�1>c iȕ fa5hatM�t�.!Z�  �)by� 4��� Courant" Mgi:�! w?A�. Altoge�3͟t(ve�!�.- ZJ$5es �� EtR%�>s  ��N� nn/^8�71i�ll)�� F= $$[U f},g}]�X_fb  dfAi5�� �2 1+2 �58(X_f(g)-X_g(f))�)�$-[.b69={+{f,g\}} � $ � Co},1. 2.5.3aO!�9$AMM�$ x<�;F�\wide� m"p&� ��.�%A\&�i�u61}!�/5&1�.�5�-ed"j* 2�DP0ha*S� 1-cocha�2I�-&[ �r�; P}^* I=q� +d_L�Dm�nAcan��D� *�$D2) rN@&� prev�E�:�Z�Ws 2�NN� 1&-H�5�+1HA M�:"0aF(iGKB |)�B^�) 9&� $R_{D}"� ��)!�j�� 2!�yc^D1�QF��A�'�|u).'%�����WB�-2o i��Ee6�$$ �("R$R_Fq.)�1�mAAn���mpu!!�!R*P=9B(!. e_1] n + � (-�_26�`_2#1 #�F+"� !��-��>n�}�[o  ; 1�"71,- 6N"at1GcD*u@b�!}��cH�}-���.�6�-g)] Y �*} "+Cs�!.�E�Z� Z� �Y sBkY��0 �1� >� \�3Not��N4Bw+&�Er F+�F� a��3-�>,*>� M�d"�2QJeK $�1��$X^H(�s}�3�- �_Xnd $E,�-( s$. Here $E�[� \ker 1i00orizontal lif�N6nd $E"� in�HesM<� orA��)�"�" $ (s�3%p$(E)=1$). TN@��C 6 �U1�piBEe�A�"�=�g�0B� dF�E].;:~S=^t�A��*} $split} \{&-�UE (Q, �5z%: ' \{'{}9}Ab Bg!�}\\(&Y*GYu�[u�E) ^:�i�a��� �:���i Mth!�elBhPH�E_R&��in1Z�SH�R� N�Q� bFaE�!g�3�6�A !=)&�&=)��z6��+ \t<thm| })6x9 �! N)�3E>XW byB�4�]� tric< ��2g)sub�;{D�7-�a,>|on�4�6:  �3po:@ viewd"S\)��A5g�+� assific �� VX!Educed�R�D)B �� h�� Bvm *1A�>�6�s�9#se��!�2�/�0f87. "bu�Oearer c2 . R���, � B�� N% O �� E"�/rit./ .�#/ ���!2PY&*�2!1^�0�6 � � %�V@2&�)� �M Fa2d� "�e�$z _�=^*H8rc i_*)c_1(K)=[� ]al!`e*�:��$$K�8*\.� .13A�6�-� %>022>t%:[!sur3,v�!c0/is"�2I;�0f>�:� �(�-�d$ J; !;��=9e5(3�/types;� ZB%�a-� �pr�2pal�,��-ze $H_L^1(P,��).$.;2�x  Ex+ �eh�Hah2}, say-k \��\xi)}=� {X"' "� (�( � 8 �%�F�'$q&8.*�9 $D'_{( e^�"� (� �+'�E%som1es&� / 'A� $)�����ria=Eɖ)E)�Se 8~Uo�]�2+,O>e�2z ���si��&�I%�E6 �Q[i�ȡyka$-%�)b �a� gaug�IixR)he�).G ��*O�:b�) �a�0m� �0E�-[� threeNEW}!�iy�"o # (� )�)$6%��a�01:K72{ine2}) ��!FD'j� �Hccord)�~p�6� �}. Gi�;� �J g/�kr�ex�C���J �ins�i�M���F: toi t*�s��Ts�M�QA��6�,progress. "M,P:cof"%6; %?&� �8.cA% tact"� s}�vDU$seclebrun}�/�5already2��.��"�1�& .�&I2�8s:' �*)�c�c�O^ZIz(, $Mr*�@ 5&���m $.�1$�FK ���mayy M)�ed pureJ�sA�Ded�.�T $C� =Td�: �. In K"' !Z �.FA�� n &~Jor $C^�P a ($��).�.�O- T^*M$. [)CA�,�&�se�G%�� vZ-SC_+�Ei ]�Y={1�s�R�(times known��a�/M%� (M,C%�I@a� @ M$�+.a�C@,$uZ� e�y)*F a����JFtaP��s a"�.&� &�<K9�j<PI �� $(Y�84�� #0Q� *3neA�be o|jZ�Bi#� �on �Y�ic+D�� �DM��G/  t�On� y�Qlq�Bfy,E�_+��Vick��:� f J[iy$)�eIQ�; o ge� QJ�bou�Jy�-�cc�.%>V`�A way,��[��ake%:a;!cq[_{0,+j2QAtuBIby adjoicI!\e��. �ɆA�ar#Q&�)��,B���[0,D6/�s]�d(s�c()=ds\wedge  + s d  �� ex�^�]E !�� te $�.* RR$.U[�$s�ű]Q�� e ch�XsAe.�f:i r6YOo1 �� �3�:�i��y�3i PBN5q=2w$�S2Fi�<�\n�Ir�:�CN]=S$!,A$ed, so�(�} e@-? pheny7on�u0)toaa&DB BD�'Hy defd�Vr22W�1so $��*-"ts@:Q�!� �I�/r���Y�/��-\. a��pro�]a�"l ��A&C4re *\4n ,2CA�n is `$ ular�t wxOb�7teres�%t_QNz!=&=s�J�Ɉ$�O ��@ . T ]m���L enOR=T+eXwe �.a�Mu�5{+�u&�C!@��d�U,$(TM/C)_+$, �z``�7ion''�9j$�A*r'�p��he�C�%h=E(X�. � ts$� HAa{+�xtIfB�3.�� $� d�.a��t��CR ev���M@ via !��?a}����M4�NiscedgLeBru46Le� m9�0r��+:L{� a�ts�X*K r-sl-l1 & =9)g�$i��is"� ��{\bf �-���R:�5�'pU E�analymI),X|m�-!w�<we��e� E� -3te $r=1/�m�E�!� $.��>R!�n suitE� ݑ���&� E�f $ r?tem @$du+\sum p_i dq^iiO��Fu< ��!M [d(r`(>I� �.�r��aJn:i8;"4Lambda=r\left[(r^9+ r} +�X�{i}^( p}G) frV�fuVb#q^{i}} Jf'.x]�6 F� i%HulaALYno�:a:a�7�lsmo4bl&r�>�J&+a�<arS  $$�umf���$$� !�originW S``typ�'';"`-M$ look1�-b) encod� |b �paca]20.s�H?"�L� �.�F ax�un������I3��i *A�0,���:r � �#lo5O rvala�� E&� ��$0$�hV ��  �S%�Atrec(g�W�Qly|m��FwAXe�%E� 0DE�'<Px�0&geOe A� !E�M�Ir ``� �3�r �$I�Afco �J� $*� occurr�� >�1  Y0'�!yn fac�jp:� en�Ey3�2�4 !�*5is ��Y"d �x h0oa�!�U�;'X!e�Va=�. A�?�6�6�  $- d�� To p�g�"� %�A�u* )*C�eV*6�A�o�K��`�c�A e Euler2j4JOsb.KO �?er"5]�'�4Y'A = -b� r*) +0JiPa�che[A�!QmGi�^ � is2�!� $-�|$,ubTrec�&B&or� � $degree $1$"34��E#�J(to $r$.) O�#�M�^*��"#�A�j $v � @%�3�inc%E[o(#A@ Pa�Con(aV�!Ay��IRanY�m $o(�beete4D�q\ Y�p@ t $P� &�taZ&� $5Z� $*Y%4p(�&($-periodic)*, � d.�6�%�F��Fg�ig6�. 10+s�n = m���Z���-���-when $s�k. p�M �weŎ��K�M61 �nE�A^H, Ez i]+qbs�.oy��#"��j�fef� �� �� ��  � -^�)�})H ^& r} L ] ,^% K *)y9of�kir�+E%le��R�!s�)} Inspi��Af� � Engli\v{s? en:wAk ted}AA\�,lex s�?e��`�J: �|"v-�L �``pinc/%''�&"�eonent&�e� �M�a��Creplac��it��p�R�o d�Vi��*y i�)7�unit -T6 plan RR^2 *&�s\`,yw n ada)&.��d" ��<fSJ1"j"]�)���,�sec��o!�[�V�<ve"�R3Q t*�)$f:x \to\ a";kr� $I6 >)p$f(r)=r��m7]0���gB?[2(?�" J $Q'$�2�*�iy(�-���dA]-qE$ $x^2+y^2=��CRad�p&~T-�$(%�-�2k,�EF:Q\to ��6���D7iC j<�5& sm���$r>0$�^Y�5�I��m�j��?m� � &� (0,0!Hn%"fD$�dtself�, ; 7! qfc srfF��6por�>O9Q )2 ar�%�� � Q;+g$� O $ $x=\sqrt{�! cos �Mysin � $r=-�� n� F;1}{2}(x^~ x}+y^ y}),� $^$ �}=fby} - bd x} .$&Q�`ubstit�qi��'eB��&2���po�`�"�Nr, �)$�2i+� aWr1q ��(immedi`A�? �BeMA2�&�T'\ 2�E�'%j� �Y 6;� Q'03�}� $Q'\�J)xike/�LeiZ� ���( &6� V uH"z� ``f�L�) ȁ@''�na7b�J o:q!,secjacdir}.)�b ess� l new fea%p-6 u5.�A $E'r�-n�j$� >�5$" 92�$locus $x=y�� �6#"�:xe H��EA t�Y�.zye �:�Q'$ doe�tYe &M iI�";@ �� < J. &�^�xu"�LA�J^� urninDD��Y�by W��� �Wh,\X#ultip�;�bi-��&1/fir"�%'by!�(/f + X_{1/fy2�Fu)-���m� ��q!F��no�qV|M���2q*� �pr�wQ?y2�]AWE k`- ��ora'!H/�K�-ba@{JLoo%dOJ& ^�I 91��Rt�0have embedded�b�  � H ��""Z 2�#in �Q#ur)?q �e�-!� "P! j �!A "�ha�$Eliashberg 0Polterovich \�[el-po:�i� � � �f �A,i!fcanon��m �O�"/a��8E �v"qhar��q()i:<!<�"m� s![z"�sm"#"8~>X�A�irs8 Q�%I"f�9%�bA� t spe�D \CC^�J&_ �Y�"ie�$Cauchy-Rie�Q)�� -�l !4�r $D^{2ne�It.��Wa6Vpgx�8PIC �zbO" pped�k 3VBIFqf%E .�!:�Q���"� �&�6��i�4u�Msi��U >61�comA�!a!� K\"ahFB[�o! ,�1�a�.m� hyperbol|*. I8o�nw���>�$Q� �,# aI!�/B��< ����-�glu�0AmO>nle�!oCoo q9a6u�*a>=� Q''$�\ng�4�V"�$�S''1�x!B{#fib*�k��� �orbA�24-s " &/�6{ `[ �.�Ju>�{n+1}�- {\emA�}�<1zU. Al�0� ]c�ogu���\�8.4r�� o enlar�xai�Hed pseudoconvex dom�>DJJ�Q!pon�  �� a )N��6!h�6)^de`&s\1b"� !�rOU0��_ �XraxMestorya���!���,]�AOa�+2w0��5�2� a.(,%m�gw�8 f%�::&"G`�Q$ �/ (O�994>fhav�c �W')rA( quot�*.� ;\o �.��-H{Fina�c�Z�Wqu�#on"�ɥs}�$comwdeI�) sugg 2�fu4L� earc*��s )���$R� aper& M�{C/�$>i} 6methods!,e"�,bbfus�<>fic 2�7of.}1�s:2� !`������c �����ooM�My�  undesi�&�0 erti�Day]���c &;�;3�fof� aN� . (*@6Qrej{���� �ZaH} sn:g}.) A,Yal)�`(e.g.!���)9;�,%J.B�%�C%e��:R�Kge��Qtre� way-)r�i�be don(_+�� , paeNaP�> @!{K �s sK*to� � *�S!�M*&'&�&(V5 �h.���1�e|�"#Ne . S Z`�`'r} � We $P$- L2���by��Y�)D B 0 ?wt[&(C �+I�9�e�$by CattaneQFel�I�CF}�Easd��m�B� coisotrop3 &e�1��u�, )�J!�E� !��6�( 2[*ide�(�?,%n.�@�``�*itu[+ l de Rham���dl�� .+ "I 6�� i%!o�A� th=� >is�l 0.�NG�s &$3� &N� fulle,��L+A�mp��� t ms � a�f%2����0y "!�!�| :�.�� .@1���� a Y� �r $L_6�Sa!QAun�. Carr*�ag"i��+e�>�abshe3r*O��a2�6�<�ꡫ�v:NoncommFv!>nr��YW�jCA%�96AU�rI��t ia�Ugroup5I �:�<t�$h�+.f"��� ` 4eA�1R�. B�/�kextra��7�]>BG} Ta Xu}��� ��*� � n6SQR &ńi>�"l �ja@�.�.��&(�>�� s!2� squ��0�!q Hochschil�4"F$�#��ItQlB}�VinVb�~oA:�<%�a�.8y�H� ~�$~t�)ed *6���>s���SX� D�m, ml- ��ic�yU�! �� ��!ש�1MWq/%V 0 bibliography�� the.]}{11}�bp %\bibitem{GH} %Ph. Griffith� J.~HarrJ\OPr�=ld+f9M %_q�}, John % Wiley, New York, 1978.� v audBlockE�E.~GetzluQ./Cof�s�s�|Nceea��A�XXth I0n��al Con&�  D��?Gr ic M in� oret: 0Physics} Vol.i- 1, 2�@World Sci. Publis� , Ri]\Edge (1992), 471--4877p�@lR} G.~Blankenste�,nd T.~Ratiu,E3 "Ig! �45 H�Zt �system5$Rep. Math.�.} &.$ 53} (2004�0211--260. % Pau�CArXiv:m:$DS/03030222�� Y.~:� L.~P&�, P�Z�Ce�$��eV ��aw?+ E�A}�6����nct�gal�(��)!�$1448--1476.;e*1%!�&T, WJ%! g�i| � 2|. � Comm6�m�227���K��41.�F} R.La�rna,A/͟4oids, holonomyS|:_ �e9x)Adv ��170�119--179]�25G/00071325GoS%%GotG>a�,.~Sniatycki,|)>^pr*' dynamŗ��5*� i�ingu�JV� 82e� 81/8!W377--38}9 {GrM� Grabowskie5G.��mo,�( gra�q� %� (co)� �J͎ A1[36}Ii43), 161--181j]207012IGua)] ualtieri,��er�g� m]q . D.Phil.�sis, Un�s�,Oxford�. V�l1222�0Gu} C.~ G\"un�����.!L�>�r�q� pa��(-�1H�b Noz�in���8%TSprin��Berlin�y80.7Am� &Zm,"� &��.��J. re ngewi2�K408E^��57--113.zIM��$Iglesias-Pxi���e�e ."%; $\cE^1ek->\i�Yo�K35}y�$4085--4104jn106082�IW^��P ade,r tact*N a���jY�.������451}�{Ktr< D.~Kazhdan, B.~VojS.~Stern.,2& �( �s� FUof Calogtype,��JPAppl. ^ -�31%�78� 481--5089�T{Ki} A.~A.~Kirillov, L�i��asb em Russ��a Surveys"M i� 55--75.g o1} 9 ,6E !�NJ� &��zrX�# 7�87--2.� iv.~Mi`�co @t]�A�"�tq\�BKEth!�S*5ndq� ��~ (Festschr�Sin Hon� Alan��)}. J. Ea� rsde�!n S. q Editors.[ KFO!���=23�> 2005), 39� $ bx 312252Le} C.~L@F�K icke!&i�&�gra��m�I��.� Q�13d 1), �2pLI~pLichnerowicz, Les vari\'et\'e,u9 et leurY g\`e*de WG\'e|�f�!5l em5�1e 4538Y�8 {SeW} P.~\v{S} 8F� .5���Va 3k1$a� nd. �Progr����v } Sua� Noajbf� �!7 145--15��� b ��D 1�2^6� J.~\'6��N�� ppea��A` �:^1�m� R�5� 1977�y6\ 2_o�-M.~SFau��8 g\'eomAr�.%��8e:�H%�ncar\'�}$. A (N.S.)-�6��67ac36� Su}?Sus�t n, O"r �ji^�V�iintK]��.�"*� e� 18� 197'17a 2�4Ta} X.~Tang, D&8B� .�(�)"I] ��.<QA� 53&T TW} {��C&� 2��Morita�.i M� `[/> Nto p��:��305413, y! Anna�de l'Inf FA:er)N 5m2B(�E�2�YqI.~Bv� Y�2Y�-F " Q�J��&�%� �~19�� 333�4� �q 2���mM)heAN"�M����HesV<118}, Birkh\"aus�&m 94.� Va1}2�ͽ:� o�!�BMonatsh--9it8A� 293--312� Wa"�  lB1&< Lett dB )~u 331--348ZB �11� Y�We ]�B)�up�2Aa�Heise� �A&W Q&Bull. Sc �-11� 1989�3� 402Xu�|Xu,>�Q�� �Y AmerF��j 116} 9a101--125uendB� �%�= %%�  address*�6 \\ Dept.!v��>$California7H, CA 94720, U.S.A.$alanw@�Cb1.edu \v�*{0.8cm+W"��(Marco Zambo��sc�/���0\"at Z\"urich}W�;Prthurerstr. 190, 8057,0, Switzerland9z| �unizh.ch�~V ?P lastpage}�% docu�_} :L'�[12 pt]{D} \usepackage{amsc!Z$mssymb,ams!lthm} \hypI�${Looijenga%newt��2 �Gon}2  \&# 2 6S} 2:\} 2$Corollary} !new�(and{\ev}{\o0�name{ev} �%w.}{\! bb{P�C.DZZ> barrbv1!d.:r r�&arrow �y oh}{ xcal{O}>^com|C>QQB�Lan}{pdV:{R �: l lSe:rR6Teqq}{\stackrel{\sim}{=>� �}{\bigt�agleup:d sumo!X��:grad}�f E5QM!P1� M>yle!ell>8mg9{M}_{g,n?def\scup)� bin{T`@\scriptsize$\cup$%� .az.a .6�bpf���] PP�.} :e+ qed � {+10pt�.~LLY!L>hodge E> ch} �ch>rkrkAyau�[leqno}}��a� \title{A�J� view�A$Gromov-Wit^H�e �author{DE ulik� ,R.~Pandharip�} \date{�h g} \makeq�setcou�A5�}M�&?=I*7e"�_{Over�$0$Vn:a� sim , s$,b($Cv�4 riet�Qn��'29( divisor $W�9%�abs��e}R!-�G'"I@ � �3R�e��� � e� moduli KsJMO8$V.�\j�S$pair $(V,Wq:� i;��Rg$� on � ���r ]�� �*(reav(��8 ency dataG,%C 7++ent�Y{! �� stud%B�Vc -Mu��+ee ons.^�D�I�b6%� not}A vide �7i�Bb ;i�0t@9"Z<%D!cQory� Eof�tw~+*Z� 7or(is guiZ4�? strR/�'E2e�to�. �4rI%s �/�di:!�}sucY�Rj.�$1�am(t!�t2 a�o�EisA�$N�9) ,e ,abi-Yau quin S�1surfa J$��^4�= .�,$Leray-Hirs��>uvm�XN�(0R��{3E�a�-qW$Ɔ�>YX!6��-v&4�roj(LKp\oh_X)s2nd let�iB@o p, $�e:Y � X.$$�+sum L{E$W�;���;�)�e��szm 0, D�',M�Y$�j[4e�X$c�!gWe��&f�5�6�I�A��n�;:�!2% $Y$:8Y�6Tm\of !maAVu!J-��% t�]��!(Y,D_�\  �(),  D_0 5$)1u�+i;[p�/a�Rd��8�em� Z� ��/ I$X!p�6; M�mn}3%�X� �!�'b�6quA!)efM�iӢ Y,&Bro~5J@�[ADAۅM $�dLz$H^2(X,\Q)$+nd��2'"�U�i�@U^> i aaa}��exh$�YnvW�# �cof�>ur�Sˈ two �3 *�%-are�-I (e�*pI��+fL�wi�b� ^*�4 @ $Y$)%"�3�m�hiva� t���Q ���1$<-ear�)E a��!��v�aa��6<T .���ul+N�.� *�� v�4Uf�P�� f �" $$N�� W$$ �1he �mal�Oa WQ5�8$� T � 7.���Kc�/ I>� blow-upVYJ!��,�/>sub!�ety $W $�C�$"�D:c|t ���Jё��/�F�N.�E!�s��e"�^� (0) = V �x_{W} ��(N.4W)$$ �>�"�� $$W)�tb7� !��by�@ $N# 2T  ula �),EGH,IP,LR,L}a�N.QDR��3AWA������"��| �B} �w$(- �eoh_W), W�sJf&y�;a�H$/!�� R�y��s�Q����p�YI S��olbbb+:�qwd}��N���"s z�J�!G 5�%U\$VV9�W��`m�map��*(V��M�H^*(WF�WeJ�wd}��6�� &�9�&�e�R��qu�l)<ng�A qa`#����i ${Mayer-Viesn�c&#N . Let}�:@� V�Delta�a fla��N�� N� sk $ ' �$�o��{GIU &m:Q\enumerat�,[(i)]� {V�_Cn"� * +�k$�B �a� punc�']>�^*= �nminus][2\��1)F3 V5v� � 40)=V_1��W V_2�[� cros�s� �O$.�Q�=(B Ny ��.�rc"�@E�$A�2�A�]�e �~�V imag�:�:!I-n-Eing�AU������R�A�� 7 aF�� �� a 6�a�ultlb&C A". v��6���n� *�uKV$!,�x�MVnd.R ^�6���$V_1$,�IJ��� 2�� -�:���� \��VsyQ)^2W, \Q� \e2� 2H;@sTs} a 8=  �I.*��sA)�2���}���4!`A��_2, $Vg� 8^rB>�Aj6<&`7V$ �S\*��r^;e1b.  ��S�uH_2(V,iS bb Z��k��ke� . 4&* {\mu}���+�'�S�0sum_j \mu_j =wGt_� [W],qY��5ar�,a*m.�$F� (V/Wik, j�)$�am izes *�N� �us $gA�n$-�H�&�%"�D��r )F�@ mu�G�0A�a��A�6$j�� ���nmP"�m�c"M]��!5%psI�"�Q=Ha�2��.%� $�4ta_1, \ldots,  {m_W-�Sc� ibU/Q}A._{��� nu}$� ��B3n �unG� ed} a �q airsE8fT\{ (\nu�d�i_{s_1yv�{ )}�%�el  }) I� \}, Awh=$Q� nu_j�~F�5_�$\iQ� [W]C .0� g�7�t�Aut}(� bf{! 1 per�8onc"�&AB�7-kf 9Q�nstaA } /�!��)�\nu� $$!_i,9A i})>-9i'}}��if�� u_i>!$�:=��$s_i>s (I[2�a_A&[\�MrI�� %�1�=�)$����1 �. f�&�!XeB�?&��J�agains�  virtu�K�] ��of�P. ea$͈_1���a_� �k�f�e_p"8" �^�_*h eft. , \tau_{k_1} �_{la! b�s  n. n})\ i| 2c T^{V/W>��}��\ A` 1}{|.�nu)|} e{[r�.�U)]^{vir}{ZP_{i=1}^n \psi_i^{k_i} pev}_i^*�i}� up <j<]; :^*_j(yj}�$"=ZHere,I^�&�s,  e��j: ��!'V WT�6a���p�z� 6� ]� Af�(P�sign)��"�\ F�s��@����B)Fgr����  �4iEH��ing���ArWwfB2$prefac�V��&t S�7~ep A�qP�^��� �s7}��eh$���he� ofe�r6r  AGj^r:u e�!�� gbX 9 � s��n-Ole�des� � �]+*�B 6 �|�4"y .|.w rw��Zn�C"� "2' *E���M1`U��t�6ts)AJEin`�of"� &� ji �validE�!�7+�B� $(H& &g"� r�z_aF^9ja� I t:�9��=B^���.$  9 :�C� ,�{y�>$3-folds} NA�7, FH �%V� ��5>oddQT�IZ� � is%y.C"�@(OP1,OP2,OP3A~.�s� - 3Ud�a�H3�]�a�GJ���6�#F{Agiv,GP�ye $K3$�� v4 tool"�**---zI�6��� a�e.�A�n� � bl}.t�e�f&D f'mc,�kcu7}pM�6�Y�5bof�5# hh�.��.�MQ!-�4�o6Z 2[�J��)Hs 1j2.�mF� � ca��.c� s 3, 4�  52�lR#��&�o for )6g=Cg�gLan 5 sρ�v ~!1B� have&ư"�T%� B�1� chem"X�.�� �ic2�� $d \geq 2 O�< $f' ( $$h=h_1h_2C u�f_polynomi�@�C$d_1-dnd $1 Q�s�&�Z �� ideal tf-h� Uk]G&� �X}&�� -�[#.s1(�p!#!��r+. v� _$0 v ;u�j3.�_0= X_1 ]I X_2m{6�$X_1$��9� h_1$%7 - aX��.+ 2$ ��Bz"�$IB?��yp�d%�,1J�tow�E�&2��R�*�}ue:2!� B4�t��t�Sv�,�� &&E$I$. �7l8:alyFC[L!��i5 .�$�2�At�>�E�G�%douA# ��?��+I�2obl& 6)�l Weil&m!�)e.�bl��n�mY���V�:�%X}I��EӅI�Ma�f�� ._:EV!a.#�-$S� c�N�4 zP!2��Twf8%� $s $(X_1,I|�(>I�dBy "� e � v�jmP `2�8� ��� 9m�f�Li5 7RmN�"h�T�0�2lk: � 1�app�6a~�.)ss�2�$ccc} below\BX,��o�S.Z�F�!N!.-�N �he2��!��>�$1l|��A�B9�IB�� e�6S� C��.F�3H!%:��!)�RA"pr>A+.PZ� 7�n�9Z�!w�y�b��!#W_1,W_5"V���d'\��us.�Vu�ZE8R �2ssvP.)gis ^9.� �J=!��-�� $Z��:�! "o!\Q.Zx�' �� O�^["�J��+-oneeB2�s� �inI4un. How�;6  opti$p!�L av�@b�QSA:mmG��Z5edd� Eh*W� )�" "� 9��PP:6u  s T!�m�$d� 5� 3AWz�}2�^a%T� 5Y  $S_5�)��M 2g#JRMMT&�"f s:�%� 2[S_4C  0aR�_S_4�3ap-�} $C.��O�+H ��f! >%A' al}A6�=x�adjun�9us � �: primT4 *Zins,X=m7!-:by d���8y: Taubes' tetrvt� S�Esjto SeS(g6�0u0t1,t2,t3,t4}.ò2uexx�\�R�*� �$$�3 1�3(^{S_5}_{6,K�-1C yDa"�V"kCA�6U �!Qo�E!Hera or%L*�.C� t ��!� >h� �g2g2��m$3�4�2tA�n"�(\��ig %�:a �!�^w6!3m3 4$ %"! ledg%lL�%�j}�/��.mQ 3$ %�&lat���^nacce��t0^��)�0�CaD/ f)��\�.(!#�=�c)most mWici*. cap1$ �Y)+% 6[}���I�re� u|=��6@1�>! F�/roj^3,\��2, \ S" S_�� {1,2 C_{2,3 3,4 4,5}� $S_d6,3��.�Q�d"��ץ{d_/2"zީHNFV��&�"( ,d_2(%�1�)��R�.e)3��1)�,�>�\2�zzwe} B�F�^&L2}m2.� �1w!;�E�� :�$] pursu �s7al���M exts"ype"�#��{� a��-i��a9V hem@.�nJ�N��P�q��miR��A�e�1�~�du�YlyC�\1on{Gat �@��;a9�3T<�3ic!ce�jJ.leN.�of���us>� 6�!/Qz$Q6#�3w���5{66�6V� i�� 0%J1�2a�0o�-� 6H�(�V�� �>o��it3�D)��di��I`2� &��:�/�bs u�0I� �=��&�2.!� , �{G`#!.� �(4.]�*&� �bi�kr�.G} 1��.�. �]{Q�.\oh_Q(5).�.Qb9 ��- $:>>*�-=B�5& p] ��2��.AlCe{ �� ��Ֆ"�E������a� ^4,Q&�V��4�͂� �k\b�5�|(�-  �g3,.�6�r��� 6�a_�r�4 ��%?a�� R�ta� i����Wa�e�&e!��:C�)lx andw :38 $N$>d� ��B�=&;CLCo� N1Dem�J��i*�$ R��6�+&35�s�F�EjB%AW ^4, AjU!�6,n�}>��͉�40fo�4��ge�7��Mj1,g2,g4}��P ~Z r տM-6�Y�r�-�r�Q�&?0F�2�(U��"n IFll}� era..Ui[%ka�2Q �-Q�y`&q�h�'Y�so1� ��zyF *� &W��ken2�9�2&z biI?LT� � n b5h�p!���� �grӂn.R vo@�AR A��_yet c=Py>?g9� � mj�"�% *��3a1o�l��m z� A ver݁=�t|.�:D2J9_1�2 PtGr�$und��"lL.�>Z0�:2�NotD &�"�ky\X^/.�N�4��>�"�> �5AZ*�>�=:�N>�>f1X=-�0M�s $D_0,$O=F�%A� �>- ?�&�>."$ �-1�>�.X8 >�.��Wzoll%>%�&M]�&s7q��*���^{ �}_iB� \b, mod}\ m_X6�^{D71, ���{o j� �,as�+��Yx s upA�$Ser� EJ i/m_M@ @kB{ �J�.![}?�*x >`I�a����B� ��N Y$�fca�reva�"R�?�}Y� | �sca�ne�- fR,A��$6{Cm�V��d-l�GP viagv�/2�&hof � �'�$*W@ �i �m$c"�8$�6+� .�%b�4�'N5Y�/DVs lociFr: J�.bi�ct�^p�WAWvV32�4 H#.� |D_0H2$�D��tvut� 5b�>�DGr�.�b � Y+ HGK eBrd&�$TJ�J%?QH8"^� remo��%� ~U$FP} �|��Fa3� a�>�B�s}&�)��י�~k�A�#6�&7 C� ME$�<mul"�2LI5muw�2d���22�(��{l){2�.u2\��1h8athrmO5u)}fs2Y/�keetaJx2mu}x2�rm�2}D2iz2{i}|2�\ev^{\as�5�� ^', d_j .'=r_{j}}��=�mu=�6m2�6r_:�6mu5�,�0b�6 })\}�G a � 1#&�7M�*aXFH�*�9=%_%���0��*MDvaEe�"55�+ˌ.'7��*��:H�)�@i3v�n�#( ll�*�� �� *�2�1M� : $$'5)�i".5!�B~o��7A� Y�&! �G2 �D�Y�. mѥN6edD �I� J 0AT&�Hj�h�S � b&֗- +6 �3> !sNZ I � *)i :j9i=Zmu %:�d�c�c:%R 6Q)R���M*!not>�=�� � c�� �dobH�s. Dis.<�e RH8ly in the dege�Lneration formula. We will treat disconnected invariants as products of conne:$L except in the study,4rubber targetsSec�T\ref{rc}. However, ouri0of of Theorem (pmn} is valid without assumingrp �$ rule. The�/6�ssu �be�8ussed carefullyB�?$}. \sub �{Parti�,terminology}~follow�consta)HHsociated to a weighpH$\mu$)�\arise often: \begin{enum!Ƙe} \item[$\bullet$] $\deg(\mu)= \sum_i 4delta_{r_i})$,%.(total degrec cohom� �s,JeIdc$ equals: num!�$occurences!�A pair $(1,�Id})$!a�F`4 $\mathfrak{z}j= \!�_i \mu1jJ�. F� Orde�Ls} All Gromov-Witten.��$\lan,\ran_{g,\beta}$ vanish if $$\4\in H_2(Y,\Z)$�$not an effa#ve curlass. We � a � al o � on $N asmDs: p'< �$$ � -'} a nonzeroZ� e�setA�A�s $(mM�()$ where $m�0\Z_{>0}$ and a[lt �^*(X,\QA�s�ly �-�he �Ding {\em size} rel��u�qu0}\label{ssf} � > (m' �')M�5% m> m'$ or%�m= andE�g(I�)>�')$ALeti��-��ɕ�Ax�F�of $X$,!�mu=\{ a�e=�b1})yL{\ell )}y^r.})\}.$$a�may placi�)�v�$in decreasa E7 by ![ \eqref%A . A %t4lexicographic} 1:n�y s isM�d :|Dmu \stackrel{l}{>}��'E�, after�^ �)�muA�R�E, !bfirst� � whichFHdiffer!� is l�Ur4v!� ɣa}on{Fi��ca}esQff}I[F]A�yx denot)�)!�a fJ%�pi$��)f * } i&5 of type I% II arWosa�Im�$(possibly a� ) multiplŢ�$. Our-1 goal!$to calcula ��.�of both ��� the � ical.&�X%W$Consider a��" J Id01*P,^�$exex} \LanAI \Big|��x{i} \tau_{k_i}(\gamma_{l_i}) \R��d[F]}.>�^�!ieV q,� from!��ivariantor� $�~ j^{1}$. �A moduli spa� of stable�� ve maps �%��to�1$� to 0��|�5R� /0,dZ���( In fact, $6_Y�� �bundl� stru� 1�T principal $\com^{*}$- 1 a2y $L�� a!�ndard.4a� �6��}$. �L$�-��ve ob �e t� MC26 � obta�Y�fq-2 eureU �� �0onship betwee� 6�@ virtual fundamen e� $[>�$]^{vir_\pi� bB :BY @)�given�[��^&fgv} N��8}} = c_{{top} Tathbb{E}\boxtimes T_{X�7 cap NI� >K � bb E��A�HodgeM�.�r�rewrit��� as>�*��� q h_q�(c_1(�), c_22� + )\ t5T_X / * \ �*}1h_qi;$t 0re polynomialr A��6kcaE�nr compu� by��: .� E�ɨ$X��h�e sultŷeq��integ���X6� b�iץ�%�1�၁��Ŭ, =\\ \frac{1��athrm&� }1� \int_X�(%�� �^j ��1j"� r_j} %�( \pi_*\big(AMDpsi_i^�Y \ev_i^*2a^D)?:,Yi…T) Eui59$)�0 �����d2�`�?:H > 0(p .q) omega�c |\nu"U � }$$��.H : �� >�ser�� g$ P )��uc) A non-ZDs.� \| H\|2� r f vF %L�u:�Q=V by a�a0algorithm. A4.�$"� (\circ{<}$ oi`l6�Jr*}*|�8-�'�s| ^�'2�- !�'\3 ')�'�j��}{<} :� e{0}ID2� )��fFDif on�!�u,s below hold&! >�(1)�' �,�� (2)]�� alit�(1)Isg.g"W(3B)-2 +\| �'\|c \|@4F@3@a�� '�)?5F?46?nu2?nu.?6F?5.?i�')> ~ 7F@6 @{k'B��>HFor any� 6�u8��g,!�re�o8only finitely mH ZC2�low�AB�}u�  u�Adsis C��oEo .���sta� us�$move down HN�:mRe��A}pax1} > expres� >q� .RYer��*sestrictly-:nd5� " ��̙$�Fix $g�e�>0 %��2��genus5� ;�ll viewed���"�}2�e��\�A.�)�J|� Y��= ^{\prime}a�[$7�@=e\ {c$ {and}}\ g# ��2 ���dly.J andmB4fore, omitted Ah= @ �R26�)&*> ��W���X��4��OA��+�&�W�V5� (&v0$  i� �CbigG���{i}}) !} ,\ \nu!� 0\nu_{j/s/? � qwq�A}� have"eqnarray� �z( C &=& \no��cV_1e_ %s "�  {%����-1�{ })� C_1:� \!I � & &-\h�{-10pt�{�(({ \tilde{R}& |Zh }\\5� H:&pR�$\ C_{,R}-� & & >�B�0 u�\|\leq��\ �\mu%) \geqA�A + 1}} 525pt} �5,)�'}uLPmU%�  d_j�X�M�R���Z� \\ 5\\!� - \9,�Y�� $$C��� @�eYj-1)!}MBig( �{�#} [n])^{(nu)}\neq 0 �n! coefficie�$C_{*,*@r>��lsS� stEfor� �Q ��ҡ& IIu��b- proof}&��;6��A��sr0)$&P by r2� J�8 $\nu$ along $Du�$^��Si) s!�\theta=1���B��Br���= b%u� cxsd��; �MC��v�U�u��}�!�!�Pr4" ���1�u d� `B!!� �8% via"e"($tornormal c� $q%y!� f&ALde^K� �2%is a un<:wo copiM"$Y $$ Y:� _{D}2}IuK visor $D$z�rg&fieL$6��f$ �� 2 �.� T%*� 2\�� I�*�, ua�J� &Q�>$&!$MA*��\ i�:� =��um�����f: �%��{\K" > ^�$_{{g}!,�f�m}\ 3&$}(A)��� eta^{\vee2t_{2}\ �Nm2Fm2}}�-ue�*�%su:zgv  ll splitaJs� 6 �#ll& ribu� A�he.]�+ 1 E�med+&.["�!� P$)S;nd� Gnfiguofap�a�onŕ yiel2�&omainiAZ2E�ʉ���"�1'r --- indic�&�su crip�"�&�subg_i� sma�etic _ -Q �mapeY_i��  \{E9 _{k},\rho )\}$ b*!Q� 1O"�*@&ݸ=�C!u"(#� es d��iby  {0}]A[�r�E' ed aڝ 2}a��j�ly. Hl'( �� �Y_�!�A�H. �*�p ion,�{i}_1}.� =. _2@0}].$$ Since weE� �J� , &1-Ueiwa�� eta�)a�� \v� �  in�4 {\bf Case 1:}>1}= <69�p"6 ��9%o1}!��shto��R��q=b9�A"�� � than in�*�$2( M�f_i:C�(� A�raeele%�"~ m*�!��" xed ��i�"} 1Y5k �)Aj �a �i�#y��E��# Let $�%etH'�0{length}!$$� find""g = g!�+g!�+F - 1�  I`.�*�, @,y�� ��yC_2v*t s�ԡ3con� $s at least�9aar}). mn $$�2 1-�a�,conclude $g &�AOth��f�(C!$�*�Ŋ�$m��,W*��ly ram�Ŕ.15a�va�#=.�!� . )#$g> g�;is6�,a��,i%�A extrem�.r/I�5) Z;>� to ���qC"� %ϭ� bm.2�qh Ԇ�These� A�s appeaw'�seaHJ� ofBj �8We must analyzeLc��inuI�%]�F�v�� �%�6U�.zn��2��by � �~� =��Xm�nu)aGs���> am� -� �y� 7e�dee��,�^��yU$6]R <�&co� {k=1}^z*�, i^{(k). ��� empt�.��/s�cre,��\@g){n��} W� i }), \�,Y0sN0s0 +ThA.fori�$k�V�zzb��})=�&�_�jg  ! HA }A���:^ u� O � >L*} ByE��Vi, a � in��+nM � impl�&2��%�c�:�ey-�]�a�� c.|uq mens�a�tra,���6S � `>;xddweta_k-1AU�1{j]�1�)}( �z"c� }nm0eO� q�� �d. 6 FLa�v}$��� a�o,st� $(�1&�E��1 �e�>�,1�.A2-x!, _ ,�  >�aU�=�Ik �oT ��j y���/ }*�2�" I �e��A-,� &A�u.��e`1� $'�2!��V� ��_E3- r!57 /+%�r�6�l./5�%G&1$�u aJ�m�"i�qaE!�RDf , o�(,xi>1�)�)�K�4e�We now��6fab��Y�3a�-��sY�A��ndE�(inue until5�.f EhI3 exhausted�X findQ��small!ozI& /��1�h)� =fS M�lath0I�we rec� Ra���iz� �\$�!��*�!R5�R to��A��Zj} &/vR-p :* &+� �.�� a#y*"6xa�0.� �grDYf�� Jk evalu�uD2A02� /Hurwitz yd!+�% OP1}e';��2� 6fR�2*�2b��&f��o" *�I�� �����third�X��Z� c����5�.�1}$A�bC6�� A3G�3 negl 3ng) �� *� $C_1�U!6�� �s�� �q�ji mi "� �s �e 1?E�$�a��f mu���f b] e�� not}�� owedd2II�$k$th 9aA�)�doe�t� �E�!O&3)!4� �(Kn���{&���� [:dim}_{�b R} (X)�2s���s�*e �p�;d-backKa\sam`ojAvon"�[42�%�� �����(X) -1�O e��n addw�U6!�ns9M<A�F����� $=s -S6*�;� d���*{; ;�A�e�� $�  �)�{Ru�>@6us� rc} 'ub:*�> �~�>z2Jo�2�&X jv�2 loca� �fGP,GV}��*�Inatur�2��w!>�3\ast}$�3��$�u�>in 2{? fca}[ �$�-^*?+�(du�}a�0onY-N+�m*��7sN6Q6E Xf� lociA_\�a�4[ olv�Jx6toA�-rigid1����$.�3�= N�!&�6r D"��#V�5Jn�( ,�:.�(�6��P've��8ps,� le� 6�{K \simN�6! "}7V� "�+.�7b� *�&@ �gs:*8�A&.�.�e�6�BB}-�N i%H/3}.%ۡ�epsilon:N� \�arrow208:$"caQ�fo�Bful�. *�ed���te3�s7).���� Q3{MU� .1�)�$ � paramn0iz< ps�!a�"m�s  spec+� � 5"��'l` data��not made� lici%zoura �"�#�!g$� *� {y 2_ Similarly� brackets���@q�1&># ��M�" -$V�--����no"�/ rule� ng2Z!D2sI�sA">? Cotangent� es]. 6�m��Ne�$ carr$Butolog��coAm�7s�GLbb{L}}_0 \�� ��a��9�"� ��I*[::vEje�(Psi_0= �72n0.@k%! { J' < pla�0 mporVE rol�N�. �!t7D pr}} !�$�* 2�"?p"� �;�#:l�;on��� $$D_0?(�92�-� �� k2: T�eR>6)5!�#&�D^*sss12} Q9 L}_0!9�{2*s((-�Co ."�) \ot!�  pr}_1}^*( B Norm� 0))�"�0��4:($ 3 `( _�!m� ,%mr1 embed� )xey���.� = L^*�7RBO-8�9 6i8L)3 is easA!s=o-n �5�}a�%a�#6"i�$* V� is s�� yd�4>u� ��H�2�7 � *� � if�o ion}� S ��W Lemma�Cyg&f*�=�A��.� "\.&S)Fe:l�EA�a�7 be �F&~���$�rm{ev}_p��Yy,�->\=:]^i>rm�= }} & =& 2 _= �%(\ev^ _p5{0}])2= 2B>��>[E) �+�-� rbIKg�f� �+�a�)�1"� � 2� �0 e�.:%�:x " N+ R i> d&&� $Vp �U�Dtrivial* ae.Fo  �$pr�?ɫ��H�B*$-.��A� &�+M%6� � n'�  t�"� u�Za�u"�)h�L basic sub! &�(numera&�L(i)]a�e� � ���2��Y$ B �?wL(ii)]5J.I��II�.N i)] M'll`{1q"� ,I ,&JGalois �s joiz(i-iiU�9 F�s#tra�OArK( &�urves (i\ AKOwe2Jroper:Kn hX��+g�d""o�y/.is 2 les�AVBV<. $y2qq�A�g�cgt�)i�V�6�[N�R�64*�-�!1�� con&� 1N� cance"�?;u� -R! .��5�i�"|�t�I�a BK.].� ��'E��F�Em<V"�),)�ne�GE98i�$.�s�-&�$�� a�iqu^ ���u�8�0idSn-)Wl�5J9�pu&�A"?/ gt}. More�e)�u�p!�us�6�H6�:��$2��H�2-,Bp^*$EL))+t}{-*F +t}�6�2`]�F},m .0.�q�.)�C0&# $s�Ga�Nf��auJ"K f!׭i5 y�Q e�s)uE&T=��#� 6�G5 �- $�Ing�6C)�TA���t�eis`0cal�0} 5 rbbB_Di�ot da}*��6n���rfr�gd��� A� �`ai"�>�8 � �/-0 �Sau_1(1) Oi�"nD0�E2�EhE&^kEB�A:�I\\� (2g-2+nX*mu) nu)�b^� ��ҢM=)��Q�2h$H�O^2vR, h/Wtakw���"7 ]:� %p0(H���� �GE7Z.pi_*( )} H�9F�D_~֗\=2t  + *|%n :-;J"�Oj�8�H�O!�V!Ll�' �2��(^8>�B�>.�{k-1}qA{K (�%j"�( s_j}>�\:E;:m /�%j ]yI�F�U�6� "Ms�86I�� �N�YBcG�&(Calculus I:.f "b $�es:1 &"� C 6}*V+to6A�ar-"� "�p6�H.�'�ma�:| desce�0$;4�6� +/�B�/ �| �+�qգxxŤ6 j\2X����kA��� ed%0%�"��� F-�"�/3��%�'d s byADbi�. .f� :t1ccc/Rl1RllVoV �NRO2I}.�{��S"�8p� I�  �&�9 FinalE�Vt9,�� >�sB ��0 }f]6U0 tw�'",$$fh�IT`J�#!�]�B��E�N &9 bb%gfww1�8 Rq����6�!�>! .�3p~#M%�A��"I�f Au�a# @��� - �k� "��EZArtinAck� -� , 3-EZ�^ [ alpha6�3 ' )cal�U0,3�'G�R$[fQX6A sim$. a(f��e� ��C_f=\�,-1lO�,(f(p)) C�N�3%M!?Y Zt�RC_f,\ ;,\"&N�OC_f|����&i -�A�^"c �\!T�#�#�թ/ e'!��K=���Top"�recurW���Z24>�"� �VnfE�.�$ A%a� ��$�"$)�$�����U^U =^`c_1(L)# R�2�~  \\a � '� | � .#_1@ �E�0�<6 _{�5 "�.� !r"�* eta)l �$r �_2m=Ay �$\nu^u�<9169@=��A��<.�<"8A5ά<B �&ťXB�%��*F3ej�V~�m�!Q�eJIae I.R-by�Dd$`II��N�M�B[dP~8F)<���;! apg!�! �� �@�R5fati�7$qn8t�\�1G �8q��!�aW�re�%�Do�'R�� ђ��7*= ��)�,���#fewer}��a�� s. Re�/�?�cycled3� �$ f^� �+�"z8�g�o �6�AJe A,)ng�; lato� �. >�&� I:�1"3F$}**� x#=m�*= :.&�3v795��&� �x%�i;&8 ���� � IfB���an am]<�� ��>�}H BG � heB5F>�^D 2 ��� �!*7 1Y��� "�sy;r �ulo>�I�&�Ne8:u�A"LM as�3��`yeGtrt�3�) yrJ� XaB�m-l3*97$. �68�O�-B&�X�.�FdF2+2an fw} >�( JF.fM \�V".L�Ll�L \|��/\*�L)6�L#n&�L)�? ;�\ m60� �L,'',\nu�L�e1�2�FH�N� ^{mh�,' < '>LG+�K/\ B� " )&�ik#E�J��Ic*A����*f5sS0�L"�L��< �5 *� �,Ix��i�&�4> �I��#�e� "�L�B}}$ next�� Qȉ M�y1sqlCCA�6�A! �N�and�N0(��1�d!���� & J+:& Ii�� O B_Z O�Z(Nue4�:)>0c=nd*�!�:�1�)N�R �>�R,AĶ�RF>1��B}�R, %For %�h=�\{ ~SM'0:>Fi3�{b!S $, %!>�S�� %!�&W ������ \uN!z �eVbR{�*�C �Q_J�C+1<E5rFBEx�E M�}�D!J���f{0�S>hmmG �@? �<}>�1+� +��4>4�2+1Nz��525Ɋݜ �6InV -�Q�Q�O� ��5I+1��P�W+�T.��(�i�$:�F0 ��Ŗ r�f*6= ��>@��pB�s�j>��b�S!� step�to us�("� ��,H^2vrQ�]$/$0]=&s>-)��"to"�h�i y left"�$��"61�Ѳdcq6AA�~���� =B�y� �,2NiR��fY6�����.��"�W -�2F�)�m�� ��J�� U .r4\ |p�TlI5>, s�fl.�9f9(�f0�s�&i��9"D&a6 A��*iX,@+c"�6"�m6�9� b"�4v�*�a"�D �a�$\>-'i�fn ? �ib�7�'40I?A5by���%al:�*to6cJ R:,!*�)'b�"�6y6V+is Grib� a$�v�Z�P T7�!> ꉝ2�]!�"� #�#.�e��){(.UV� �>P� "�� fz34j�����m6�E]"�!��� -�^]�.�/ lift�W"�5�4�!aU�>�L�~F}$ &�rN_ �J2�n%ula�u �U1�l� .iA��-a:�j���jQI�H�o� �b6)D;�+'-w��BB�B0)`+Fua�^+R�`G�v�1&M��of�Y��.&3C� tUsub�M�� mappa-�#u�6CM�$BD6�-A+Z"EvJ�%�aQs,�a�luG���P "���6<A}5Ts [L �G.�� })+;�NWheR~�\e�xmDre�J�;A�Z6�# 'Z�et>Z�o� $�Y'  .�Gh0 ;{V4t�7&e`nu)+1�$B2�ab}, �&� 2�%�ah�.:,a��.MY�+ summ�2sP.(6�Ba> Next*�A[2��ʩxcf>6!���������D���"0.r M�� :^y��n,�}�0!N %�p.>�!�!c�� 0N��� �)t�QN&���-�us� ����A�"Q�+r�&�n}?} als� quilj )( out}�B�js�S5���1�Ƀ���J_�."�J+R�Y�$�8(bf 2'}$.} %�����kWe f"$8� *F��K JK ������B* ��J 6��̀q�� +6 /c9�)�ř����S��.}��Pje��>��} �mprimar�o�Na��#6� Kj�� $$(g�p)<*��'<� $ orBZ'=�~$g'x�i*G 2� "�!WeS�11 \� �. T�e�P!1\rŜ�E2. 5�{ 5e,>5��2'��outcome� }B�>v-�"�$M �� �:�-�.�N\Eűv9�ɚN?�A�63Jp�8mplete. A�2� aR ^ P&.W�� �d .���u� >| ^+X. \qed6�C%/2�Fy8"Tx }�&��GyEU ��a|,y*!}!�!*��s "�, �)� >�y factxs�4TcJo(. Unfortunaesw 4�G-�N= haBb%C .H�foundE�a(�me�k] ubjectA'� z~^Abvƌ�"� %T�is��q i�9"��'2�J~'_?i�v��DmZE � �;&.���&��#�� ��]#A�h%�6#> /�"It��!Z1Y.�.�\#�͆.�z9�6<Q� �_bJ4\oR�C $$Pocupv6�j^1La6c�xHve[). D�/�2���l{0,�,0\G,&;�i!\�xubnP�y[ 0��&2Ey2oVB;*:1>�[�)^n$-V v�4^$�3nB/(PB,\  �:�.$$ A"JB'$(|6v�.� "b�$P$�!!sQ��Ant"?lQ8!� �has predi�3.;isWe lea{Ob(etaila0E�reader�TndeA�9F�ueRX�&beV���6� � ��P�� baP esen u else� .Z \� A v� �饏absolute��b�5E`_{NoA@}e$Vf[*=Vular,��� x,���hA(et|Ba�B28q $W�I:WO2VAa� ^*� 73!re�N���&��2�I ^*: H^*(V�� XW`!M8� .�?�H_ H8HX2&�)U=>� K�d$:�Tit�L�N%b�F�IW -!�.g $$�N)�i ota^�2T_V))� T_W)+<* �o]Chern� E�>i��� 6�M9t ma-G t�&_6� &Qa�! $(V,W)$qpt �&B� "ހ123�8 eft. �� �-"N4>\�Q� �1bf�'� Ran^{V/W}."6� ePE {�;.�g�� m_V}��x2& {m_W}\�%E ba�V��A�IMA Emi �= \�%�$� [s>h�x4en2h�sh�P?%x��t$�!j!#_j=z-@ [Wo��R�1�-�>8;=��� ��s. *�[we��2�.���o� EO��i��.  }Vr w)8�:6!0�ce.t� se �RusQ2�o�.CD*�r} i�%��5F}u�.�DѾ�"gsW�M2,�ula�,EGH,IP,LR,L}� �rto 6ty , �:�th�X ��� � a���'~eof0i�� $��D(N\oplus \oh_W), W�K > � &nJZy)>Ka!AO}_{W})�H>�%��MWiiƽ � �22m�.mao��!��6�wd} viewSN�aovi�O��m�Y�"���BuN� -{!�!v� � 9wJ,. 2�O�ing� p�5?<��r��a� ��aM onlŒ�UAs8%:aYofa>*�2�of6Tʆ�5 �-�ʃ >�7F8E�H� &+���������:��nna�5F!���Ł�!�H'kv'iq$�Z��V�k���!B�@.u"�)�u*!�Q��8r�Ju:\�5h62JM�U�!\" 2�r��&� ovl�oSt mtB8 �' pg�a.v����1�_:?r/� i6� PRowdX/o eac~�C m�6~m .� ��a<��&�2 �m :�V$r� 4F2�� Q1A7_j� ��E.( � _{*}B#/j}+>�w{V*� B�"2��S ��JUN..4G{!�21�, w�olif�J"z y� e!O ̎q3f �3"� jNktz=[sM]XT��F. znuF:Q���J�r�f���ul�>">o���jblow-)� map �o̓ F}A V\W:dm�)\ȈiQW�6 F�2�� %%{W U6,:\o pId��*wZ)!� BP�}: _ �� D�CP 0& 5 he)up%5G  transAQ�9��-3�nwq/%:� q�2y��!,N*�S�o�o�5 \ � � .�� ��  C�?) .1n�"� |�  �0  6 ,�/'"dFc"C��j�O1}{� ;�\�5(&L [WV/�a A1N�-�d�N�-: C  �(�w��\ vjM�I~ F"��bnAw2 ։���8 �w�*.�.�B ~=&Q�� istVgy�"� � �(V o.A}�F�&�"�&2O"(A� &�&�6$x_� TE $g$,���A��alЉh�e!&��i1J��z(ifO  choice,R�"�#�5P�* :�|?heF� ��2� ! �"�oL64'-&�$then exact!�Ews�{Bj�� }_E���a2)�cvte. \B�"� CorollNCr jmg6mh�� surf��� R1A<j^rBZ���"*(��T�K�* (�Z7l?(!��^�q�6^e)�j�lear. Irm,��.1n"[) %)=r-2$`Lefchetz�q�J��)?�)=r)MthuB�)R=e \ ::Rj!�:�]�s2� ]&� 5-����efAc�h 6ag t� At�l��%oalw�^ : [�\� \ Zs �%(�qe�jY�~��zg ��r�>�V-m�g��--N��\i�&},Mayer-Vietor�\n)qui�� schem{&B`ex*�u�]8 ss}}H$c�P� It 2��$pends upon6Lmv�r 6[�~*k�v�0#m&�Gn>5A2�� ulaE�� ��wd9���RS��veH.�e $Z)t 7��non� �R"1O�{wl)}$ $$W_1,W_2Y� !�Mk$\widet�V&�� upY�i�$ZV\setcouX�? {0"U(%e}&�4�6+*�:{ is u�Zl�fd eO�6'�L3!JW��� V$, ��$Z�x6:�!����� !3\Q.Z�b� �>� �wN���/�bĢ�rW�|V02b 92j6� N&-�gLBRri��y �e(OA��f�� {W_1Q� _1"�gcoN� �=�" ��.B2! QMz$.fedA $$.�  6�*�m6�}{\long��arrow}N��  Fʩ�fQh6��:�A\e&n^_1"��{L}(N_1* !b})U am^@�?6�w.a�B���yʆ�6*�0�6$�&A�-���nh"���*�!A�M2��PE�N����! >WV�:�N�4 g�U�/ *�s%!z��Fall%ہp�V}�j$.!$�W�V)��re��!o��� "��*�V �dB&�j  [�U K��zs%5.iW��q a$|_Z}'Z)�dZqxG�or6(52iY�" w!��e�� Ju!k"M��Q ��n>���%�F�%�g&Ga�N_2|_�>BT�ea�)v �ި!C��E&�~}YJ�=��i:�!vJ�)!�R� E>,c�-r�.Q>3\�_Z5_!3=bm��<�1aڈz%ͼ_Z2m"+X� last�n�� �#a�*�$N�Nb�,� \ݢGP}V K�x�sx�4^1��xW"���beZ<$�^* M $"H=��� �V;= b�%%=�z-�� !=R`.�c"�'R���2Cw�ia�$-/�%��has 5.�e--- each>XdZ<*p>��!� .I'6H&� A��:� to H�:u "Jv )6I*� a�) �BA dir gx *��J(�Z ��ss}�Q#.0+��ed� ult.: ���: 7(.d �|  �) W_n�D D Ab:��^�N� $$V�� �YW_2. 3g��L ca& +W_i=Z&���!v>�b6��on� ��2.�6�-� RJZ1��f �>� �> � }>� Ie�{�$Calabi-Yau��&a�zzw�� 4&~)>U� "�P C%, s� 3-fold&�Pconven{���e1��� a>�"�D*��)](C_{d_1,d_2}�etɕ^3� 6�)c� �� a�"$( K�&ijS_d6WRc �Tq~$d:�m �TBO4J�):6N=�6'��^3[ �]W!W�+�J� %"� =H:2H�!�-���Z�m/� iagra��"Sk� s�>  denciZ"�R=-� a)] |s.��*�+�ZY"vob)]F�.!kF�\��4�s�  $k,+�or�`a/mtc^tl�t6�F+&�J�:��$$T_5^* &�3F�, (T_4,S_4)^*��[ ^3[4,5], X $$(R2JRT_4 LS_4,$$�4��3,S_3>� 3,4]J(T&��3�3,<T6Z2,S_2>�2,3�2�&PV 2�2�2� 1,S_1>�1,2�1�&��1�1 ��+$H2�zJ��M\9䍈EJ�DAoA#��4,5},:�%� ARNgS 2�-��KE���C_{3,4B�E A&Rr� 2�M�E��S C_{2,3B�E A7Rr� 2�M�E��3.�1,2}.)��9 enԯ"� �R�E�u&�"%VW �)�A  2,�%S)�Y[�Mf)8�)� E|��previous2:'2G"  $S_5$"Q0exx�*��p���'a�/ic2t"? 5V> .| KѴacaF�5 �{ adjun�  u� V 2Qis 6. ) exD(e&p��of� us 6=��==0Caubes'6, ng-� SeB g-Wi:��3$�Xgle 1! L_{6,K}^{S_5}= SW(-P_ !G��a min�1H�!M# , $$.D\ = (-1)^{(1+p_{g}(S_5)+q)a$-%� �* |m!�/4rm{Spin}^{c}$-]ure��uc&�3� xY"uc!� �%$��$�rЗgeome -�P irre�)���� T4morgan�"K*� `Gl%cVm$Dly��6&me�O"XQ�6q.[Q��y[ o[  a K3��4a� �a�� I:��]}ne quR.cI��S�Ԝ(a�C� ,�2Ş"SBuF�� %RF�6j �� 201k�NTF^�-� A�9}I�I�zQ��g��P& #�5� |\muE�gl>4/C_4�*.f51x�)��\̢|17B52�eS&�&!��H%�is&�@[�si*�$$g_1+g_2smu)-1=6"�$*�K_1+�$ _2=K��A�&�-���MA�T!muH�2H,L5���"IN��esQS_4mpBH.?-ivv� E!x2LAqt$$i^{th}$ e��io�=�$$B� AlT�gh%,co.Ϝ�>,!9Q0����<e��3��m mos& @a���9d\Ał�4nE9�%�.G ex&c,_�.٣g5!�ʟ5YP =H$,"�;fou1�x!��e��[�bh[?$*��&�"lw/!�@f ar s&% $|H|�j3�_:�@%�� be e\�_/�f:Y �IN��Dwe%KӒ�'�vP'_{2ax5L�e}i=v{20} I�al);h���Co�=p9E �Nc2E� -\3}-ț 200 A�� |NAoAN�0�#�$�Nɇ�4 C}(5����gQ� $$2pw��3}+u s H�u�unodromy&$ |9(C(5)| "$�mI�=is'Q��:"i0$(B��%�m��\. e iK�ce,Ǜ n $�M= E%2=L-T$Aݡ�0{(2,[p]),(1,1 \}Y A�Z�� :�i!`e��eى; $C_4&�`bf{P}^����pa�~rough �45�e�6AV�ru�|�thm�easy �e/g� ��"l5%1=tUh��8��9��f!�v� = H$�3�!= 3�|Q;E3a�yth�=HxS �..��m�o &= &\{(15�=� %�\},[02}�� 1�n%� XmF?3?&W 2aa/.E26%2%\�|"|��} $[p]e"H!�(C,20 bb Z�1M<>e-��ɮ~ %���$�i" a�q�� �%_ [s����$H��Bxm;%�4j�p.J�\<1}& υ.L2npL+2}& = & +io)\"49>In�oQBR�.=�h�Aa�2}A����02}a�nA�e��>��.�.D�J��ai J"�4d&�����5u />�� �KD� .s�(K_ $;�"�_45 ��*c?lJV*z �byC!��t2�.���- nds $�AG)�2�}B+ �{0"D"�p.�we�Q~� F] �(sss  �.f�p])�5 r"r 0 3,H} =&X  |�ga�.*) .+�zE (0)�K^:@>kP/D�}_{3,[D2]},�JX��~"�'a3�� ssst 6��%��i��Fm�#%F �]: 52t5�%>6B.1n.!�I6BF��Fv�ft� 9b���MUyy��-�5�F�A0)�m!�V!B�N'2=�V G J� !��%]%_{3b� + 2F�j�5 ]y*�Bu�2.N�1�D�D )5Db0�Yz<;$ exist Kah��dL;m^ �5��*���� no&�)�_ kllJbB��Fnk#In6inftyB"e- ly "��)H2�!to� $1, 0,!0$�! ��43J���Q� Q+�a#5nS"��S= -P6/2j/1�:/6 n�=��s/�ced' ��, �4.�� ey%�/  IJlmai�p�u�;5W= |3"� ��A$N5"� iq�J�0,Lwjs� rgue"�-�2#^6ԙ_{0,4}( ,� �H�low�.�!% "�al7$E,�v{(^,pL34})� C�$ C6% \ |�96+(� '"Ac�Yƪ y�9=�E�(��|:�$C^{4}� �7�7�^ڳ 2 eu �f�O;N.��$?)!H�(W,~-� -|\ V is���a&� cT�cu3<��>, $[Z]2��T.gDAXY(rank 4� wR�fkπ$b�$�>2 K |7q-w�]�� &�E� �ZXA�=a�q�2"� Z� 3�643z4�e�8�)L"�]-# Fm�u� �re%�sQ�6��I6���6��!Y�^ = 5HbUJ6�" 5wN*�"( �ccffw& ":^{BN�)�A%)cr P���Lobserv�that,Mǁ����ab � C_{5},N#45at� �$, <0-��%"CalR�%�2�am4}Y&�5E� &1IRy�0(4Ge�: Ion .�� .�B�9]-��P{0}O.%;V%�at� �wo�O�C2]" stea'$��&,5�-�} 1 =qV:� 69��F_�J 0� � �t� �V �Jm ��aga��e7&G65�!E� situ�A2�=�2�%i��Qin��cx� WIna��S��@��s���r�|!�A2)^�"38[$i&ڤC2�"2[�mI�is6e . 6�N�An.�W�8of*G(�05- � ).8Y�S_4�7.�U�F��!�no azer> 9��6 must���+ly�.� !�Om��=Sd�/� ��7Z#��F� y�0]�@7,O�q � *� R4-9��J� F6=��For �4�R�eC"� "#if�vsub��5��? q�q%R�y"�5*� 5�nK &1l�i! eft(4):ib� -��F,:0{0}]}\:)�.~. ��J1+(-1-7�m,1 + 3(1-(-3)2 -1-1\\3-1�S5�atf`Zś3���� �q?0mbi�\+od@�&Io"� �K H�>q �E"*9thebibli��y}{99!( ib#G,{bl} J. Brya�N.Cg"ung]em� �)�� !6K3$�.rh a3� ms},\AMS;�13} (200��371-410..�XEGH} Y. Eliashberg, A. ��tal, HEfer �Int�Q� to symp�c fz�!�(ory}, GAFA z$, 560--6732z$FP} C. Fa����� 44} � 818--86�t3B& -&GrB&SW5&J� )!$:@E ݟZ�51 ���203--33a�9,4f�R}=%� �&F!A � c ]n�2� 453--60� �vz}a��*U��i_qe6�d.nz1ew>!�mpact&6��K:,w]et!sI����1 Rie� ��kL�p*i 2Jz� >�|"�-ycerab �F�*m*�ws e. us 1.� �AN�3t:� 0 %\pagebreak2�: �\n�� D!s"�f� eocsjR�\\h, NJ 08544, USA\\ dmaulik@m� � �� .edu9 �+1��.u�:.F�rahulpJ���=doc�} �\ �[12pt]{amsart} %\topmargin=0.1in \hoffset=-0.6in \v:$textwidth=hD�=9?(usepackage{!.rsfo"amsfontFthm} .*@new��emA)K}�� .lemma}I.co�O}{"�O6<rk}{Re��6#�j'}{Dnj 2b$, }{Ex-,6propos 7bL Dcow{\Loc��scr�6C  bb{C�.ne;D}{\OX�& J1�title[N`��cnesm e�*�\6.0al}$-Neumann ��(ator]{Analy���(\s, plurisubharmonic hull��Fk� �Mrk k��author{S\"onmez \c sahuto\u glu} " Emil� Str`3(mail[.:S:]{ HgliH tamua�9:Q]{iube:/ \add� {bu0\\ Texas A\&M6��", College S�8, TX 77843-3368�� subje�{32W05Se��ks{� � .�Sm Class�U}: @i�a?ResearchY<׳Kn�`NSF gr��J�0 DMS-0100517.��0 %\date{Decem#23K4!�o�a��act�53 &��lex�,> $M�E-b�mrW a�� N/o j?x d0� $\D=$\C^{n9� �"�Fto` ac�U��c,����Dat�s�q@*`M�) Levil s�$b��n@Gma}� .�P$\, n-1-dim(M)$ (i.e.09 ױ�4 tly 2i)6d�C��Z� �$M$).��e��a�}�_a23�r�΁��� �aQ� eigen�e� %7I$ipl�p?).l0i.=E A!)z[���kGpic̀upA��R�!�a$�|�G2=%�I�aryQY� \make���>/*{2�� �Us"�fD$�q �ZiaC^n.$� �q $N$!���inI2{ e.a�Lam�a_Box*K��4&t�^*+*޽J,a�s�6�gr5� $(0,1)$��Im�D$. ItH9"�7"��ye�im�Ɂ�_� ��� 5z���ent 2 &sPt�"PCx v�bles;P�!L� QH�r@[8@BS, CS, FK}. In p��articular, the question of when $N$ is, or is not, compact is of interest in various contexts, among them global regularity (\cite{KN, BS}), Toeplitz operators (\cite{FS01} and its references), semiclassical analysis��(A{�!uq�. Such,s also cause�wlA�Dof hypoellipticity%�R% {C81, DP! The "~wheth��yZk.�is�ma natu��one�}�� answe��ye%� case!>��5��O0n unpublishedmI䩑 �C ea�u eigh��; �oof�h8h4with Lipschitzفi�)�FS0A�(Notei�J� rse+false:0re are obstru��ί )ate�$nsiderablyi"kan-���Q�` �M97, �)!� situI�� !tely �� stoo�+Jly � xifi-5:� 1� (��)��! �Dtains no:��| FS98 � ). I� folkl? ��ŠmethodA\at work�U$e�1, any dimen�= $n$,���Rn;��n����no�D�a�$(n-1)$-ual%#lex ma��,ld. However,uWa%�!�necessar� n.E:D � pen. We �Eis pape�elA�!1ee_qg p9�ax!Wk !#� is s�~tly6i) direQ� rans��e�F��. M!�g ly,�!>$ trade onebositivea�envalue�L Levia�m!o� !E%�-�a�9��.�E"�to5c.Z 8. Although we a�mai�5es�inXac�r���� D$N$, our arguments�`ce��(ia existenc�� o� solu� &� toV� on $(0,A�E s. AJ?$T$%LRBD!2a (&� )�$T : L�I_{x4}(\Omega) \cap� (\oB� ) \r��arrow @8$ s��e�N�,T(\alpha) = �all $  \in R� r�$���� kno aQif!�!-��Iean � >�R� ^{*}�L%Z:�� said, 4 LS 1.1A����). ٝsiA;A� proji�+ $% 9a onto'orthogo��me� D,holomorphic &u preserve�x , sab%.3e E�-3 Bj���sX as ^ ^!^t; r�� \begin{theorem}\label{thm6} Let $\D$, a�� in�x,n, n\geq 2.$ EPAs b\D$� assum*2�� of $ 't $P$�the ei�� zero�multipl� a�8st $k, 1 \leq k n-1A�f��JyJ� N\J�(i21a AR>�I&�o!1D.:)m;)doe�M $kvH thr�� $P$. \end5� 6��2���1Yone deɮt2�at�^6�s �Mma!�!�r�<im6��re no �>� .�.��pecJ5 nccurs imE*~v K},� A��<�  fiber�(a Reinhardt !Q�$ nwu� �p] of` \refiX:s�~2, alongI��9 nex!� rollH ���#se� \emph{)� lat}>�!�( nonempty (�O) �ior-�i foli�by �� s. By�"� � �2(ioned abovef} inEti^m �7їan eas�nsequ){%�=��*is ���dse�!Ta�I�4l much bigger)6m weak:� }M�.�Yc1��[ col1�[�Z �����Vx���$ �*�&V>��y�f�a�M�J;-:a���|>��eA���9^ i,Remark 1.} I�Ln �b� ^� �r� A�- sub� ��$P$A�@ 2&`m� a�'WMQ,�I wnexpec�L  Ze e  Cavo�e� noi8�(Hc d �@ do%#��@is. \medskip Den�by $P.� D})$!�8hull, $\widehat��$ o2 �K\sub *l D}$ aa� llows: $.G(=\left\{ z\�/&� D}: f(z)b\sup_{w#0K}f(w) \,\,{\�  all}ft >;� \}$$��� Ӎ�s�� aken�$re��t!.�^ �ulowinga`�g5w:F�� F~,�� j1�f, or * 4N�8� p � � $C78,C80,HS� T��7E9�$%� Yis` ermi�}A�K� _ :23 = (W� � :�C80*=3.1.7,ZHS} Pro�on 2)�u*� �EA�$K$� 2_$� pickeE�q�ta�.re .�� \neq �$�m�s�1obv  N��(���%i.��i��6-��� seem� ��*gat �)a�nan *>7>�Ey���a* C81},aj3)+set ref�� |� msel� ��af candidate�?r �B�)�z=problem�'�!�i,a�o noth� new:*�ACA.a�hu���U-~Aa�al&<a�ae">4�%3a�%34).D hig�"�s�0�%M~� in lessQ way1 M���"� Q��A7 6R�5my�.:  $k=1a�& !|*e arises�).ٮ�be%��p�qaR� i� x ��mI.��oVRr . Perhap! t surpriy �y�iE��YE�U`�ntof> �9Z�BA�on� hull}���r%�Z>"E� "E$ D=)/wh��� orm� ��!L� jOT� �� <"6aeof2�>� ��74} \setminus K$!��%�if �mw��6�1d&�.Z .YE�%f M��nR!" Zfor�)�he � ��}, bume ad��al`s neededJ��� �3 igK 2� $2.} Sibony%�*a!�em�hw�Z�=.���6�s^�by�Kin � } = $-spaces:{�y2/Ջ-�ed r q �� W$ly square �wg� coe�%_$aVMs�"T ajD�  $u� DnH$ u = 6�"}zRg�% sup^$eyu$i���D}$�equ�"\��B;j��S1� Combin�x"evT�i�efZ{!%ws%on a ��!��Z�Q��feac&"��"�&� hy6�:�Uh!�a�E�!�6X�IXłsD�beY!y#�vto have���M� is\&lic>. \m�{P��Z�C)�} WeO�f|�0ro"%��!y nl&�� ��"�:�� �ac�$l> & f�lW��&} %lem��$, $M$ � �of&\  $k%��9,i�$PqM.$!V� Ѹ$ball $B$ I"e�I9 bi.� 8map $G:B\to G(B2X��$itemize} \ 4[(i)] $G(P)=0$ M" B)=\S`|w_{k+1}= \cdots =w_n=0\}>?A� real norm�"$G(b\D� �at��EL$G o  is �n��J<$Re(w_n)$-axis. �� -�� o�C��d� 5Le12changeMcoordin so�TI=� .)��!f� �(�)�%t ��"�� nsd#%$M$s Toav�,�e firs����.�e.$P$ s�� at A�k %)�(i{2\{z|z>�z!� \}AT(nd $P=0.$ I�s�'5 , l~ \rho� d�aZՉ�A�$ �0Smay.% $�� L/z_n�0$a�!�� s a !a-)4d $C^{\infty}$"� $heZa n# borh�! of 0:�M� $e^h\(0,I� ,0, \frac"z+�} bar -E}6 �5�}")�@conjug}.�X M$ (�q�� onen0.� ). W� 4A� N8 �A�conclu"!\A� BF8�#OnId adap�"se&�" o c Pase!Lre $dim M>1.$ Altern�� y state� �.�� ��SS02}, - ficaA�Mequival $(ii)�A $(iv).$i�1; "�appearA�� 2.��A al, a �-b�a�-f� b$e�V�' 2!g-\ S93}M��|)!8!�%M�6�&�  $d(-h)=K Qe�0e�?of<!\Left*p � �e-%`> �z^^ extY$_h$�a f�2g eh5 do. ��now�!h6�V{�!Y $&� G}(z_1qmz_n)=> +S(z)$? $$=2 ft( .� \sum_{j=��$^n z_je^{h6Rk,3)}6� ���z_j:�2>q�.��G}(M)"�{�W�`�3�`�-�5!l$MS��m der0ve%�&?G}$!�.t��ntP `#`+! �yr ,hypersurface�{�/\}$. C��*�/sB1 (� b$gain d"| $6u n)$)�a� �e� as biD�th�B��agc�t,�./�M�!�plane �� \}.$�ider A�)a�� �<-2 �+t�6�(M� ���$\7 4,0,e^{i\theta}�� U? ���)i��� o�"m�!��&e�w $ Ow"#/(.�G�!�E5 i.e.�0�\.$ *h_1$ a:(S'jź�� fiK&�q� $B�� �s 2�D{n-1},z{_n}e^{-h_162R -->j$}qw$$ ro��!7e%�1�2 !�un"�  becom�#� %E��3 threeX :�"5 - s� �� �er�+ r��� inM� . *�Dp� AfJ� ��b;a�AC��iD#&� � �*a� r�)*�,$�� v(#RUno"�(IM sour(:@ �e�+!�"� �..�A(\D)�Bergman��S "uia@0mathbb{C}^{n}�\�h��@C$$L^2(\D )$asisY�.&I&u�*B �.u2>U2 eV�2�\C^ns�2 � ��:� M"�) . A�%e2�* 9_1�JM)p\, sharM��2[9 s2��A�I"�riI+Y��5�o  _1)���� act.� -Depr2: ;���.ng a *<"� $1$9�%�M+w�noF verg�%m�"!�/� . Le� {P_j\}S1}&� a~6~ps�NETommon !�.��  !��*+* $\li� \*�  (P_j = P$. S�Pf_j(z)=K_{\D}(z,P_j)/ P_j^{1/2A�~$ $ �feuE�8A�A%� �iG7�8�c� allel f_j�   _{�)D)} = !�}4�*j$�4$z� �fix�6A�"i �(z�WI,m"Y�e'�( (in fact,Oa�ell:2 �:�5�!�.�"�$#6�[SA~i�0 stro:MC_ -J���87}53B86&:�1�J�!$j��am,I$� e.g. fH65.<.566� M;2P0&�)� \D$. Oi�}hand, \[!4)�Z� _1)}r'=&a 0 I�(1 E�KY:>}{ /1} �* U> _1}/ /(C > 0\ . \]�^~ine�W4�!s�c appl,Sp�5�o���8 )�_1}5 AP5� .�$�X'Fel8� �o(�9aM/�es�batim�FIDj28}, p.~637.) Bec55�6a��^\�]r.�0.9at %q� asymptoti�5�P�#��,( �E_��h I_� *ed J\.�d�\{A>F_�noa�qZ�s�3rgs5�J}"6  a 2}bN te.-%"�Fg ,V �6��*e&�� b�&$ne2O� $P$)8 �&ź69v{6�'�� leam aW�2�v�c� ed�i]4�1��.' ��Q� � E�M>os� I*M�<4)� 01},9�.4.1a! turn��os�6g2dra�>oiDon ideas.(!e p DP}.� keep%n: ��614* $G(B�s f+�tilde�w)�)�n2?s $V_2   V_1  V_0 ��� � a sm�Teno�3O� B1{n-k}.a $M_0\ti�b2{B t.{w=(?j=Fa���:a# ranka� &� is c$ rved%?.sm5� � >� �I 0$. 6a22��ei�s!�N�*r " s��x}B� �)\� A(S_0)$��Z�I'!�6 �I�B��� ""� �display�} J(z)�5�\{'array}{�#L1 & \textrm{if}\quad�* M_2V�\ 06!\!; if} =not���\t q � 6�e��%=*1 p�Eal} (� (z))<)=F_{k}+]�""j}+!X. $\{YA�k6g KB��L�7�B�We pu` \{� back[' $G�Ch&a�1� �.Q�7A�,aZ9 F@��, (byM�_�0$ outH $B$�Q�%�~V1%o 1"#7�1�5p���O��%Zc  �6&�4fon�0 �. A&, �>68�&!`ށ���and pas>�E2�f"i<y yie2&�:Fg%�JA� 0�O�9.4"�k���R� � xa�R� $. R\�Ho $j�I�pusM*forwar� 2�D�s(#�$\ ~J��"J���%�s�:�%%$J���U� $. F>2sete`$h�Ag-� �3$ >.�^j>. N� ��vh_kh=%2� &�'V_1�oA4hA)J3..ZO 9 V_1}�;�AV$-���aR�� H heri�; hell�� aI6H�o8Fwhole  �&�]7b�:�# Fu�%'�� � �EA#)k z�;2(M_2 N�!Hy so"9VF_N�(�;j�A���g8 nd $EG\`vo� M_{2}R�$).�!@submean ���yC!D�'var?Bs $w_{� wa�/#,k})ile $(P#6!n�0�Y>B� tay�8�F��t�QF�w�t%�!,fNL=%�.p!�li%DA�.B� ek.'"OF >�/c"[*�W1x�&veR?&e $V� a "�8B!�se&j�2/�1ofj�6. �4$mN bJ e maximumZ� AAV� #P !���kr L&/ ] rI m(�=�&As,L)c 7)��+E.finit>m�E���VA��,��� C��tR=m$, heq��9$m$%�)�,x�_i�>:,Zb�/+x�ifo�]of "D0 $n-1-my�64F *F3 (+$k= >)2oefNX$"�opeOF!� ��*.EI��radic-2)f�a"�(�;�(. 6 )AY.�Nh*/} �B�Y�?y $L(Y,�Z�7!i/x �8#vec*Gf� $Y,Z�typ�N1,0a�W�+mil H�n2�� f}Vr���! { Hessia�! a"Y $f� $J!;6��I�ofs4 � bundl�)�(, $F_A^t(P)I flow^9tedAj�a'. $A� $A^{}=\coL^ )A+\sin (  )J(A!$�o�U �A%L� � C78}%���92� X)@}F*�>��� 2c [AsZ&kAL**�.JP�]r�?�I�2N�U.1'$UEVS(�|, "�1�-�A�Z��#d� $U_(t_0>0$ &�aA-i!��* ��A*Rtwo2�"`+ $F_{U }}IM , $0�9tr q t_0M 2\pi ,*��pRa�Ӂ�*G3['possi�J,after shrinkAI��AI�w�Sto*yA�r� $M=\{.��p):.��(;t_0}, � �\}|ctuaA!&�,J�IE�som� a >�)W�:}&7i=a;L���I�Kd�'Z�.s�O� =�QV&�J# span��0A�u$A2X!� eans�'�#inv� nt�8��YG�'[ind�H�lex"�-.a(we "`#�O?ame!��$ �a �" # A3�:J � 6��� ��$f(t,)�):&U�M bse� �\j f} GM"���a[f�A�2�� �:��,!Ñ�eq1~-J/* s} (�� )^{\prime.�!< ��x:|'N� + :xRK- \\ :/J-(0)=0� �{E5�:JRyx){a�Jacob�S.�*rDfinRsoK to (U!p�CHC$$a(t)A+b(t���"f.�, J�$ uniquel�l,���&isU29 "" J2k2ItI� >#N� ��a�Sb�io�f��^2��ɋ�p"� *Dal� I� tituteB:!P :�R8 iLJ2%m :y'n�0eq2} 0&=& a'%�(!���)-!�2�@)[J(A),A]\\ &&+b:2�)A-6G $\nonumber A�vaA�b(0) Q� � S�5�NYi0&%&$��GJ�� 6�����H&�Fa2�6aLRutomat�-7'Epn�f colleG�Y� aH6A# I#?=.GW\eq�G!�"�'ar i�w��A?��A� $%�,!�@&atX a (i1)u2�S FJo: 6o:V7 thesmB� � V;=Aj� (�<�:D dia Niz�S,� B'#M},�R#Y�X_1,X_2y$s,X_{�*�I�N�� � �X*� I+�R %����. We :N3 �= U*�A24)Q.M ]Ii�MTassoc$J�9a� a�R�>�1͏sE$ $F^{t}_{B"� }� R\ w1$3��f $B=\rm{Re}X��"= a+e� w��1�r"�N� = E� J�0i#P�� �K (I ��`V� below,�Ŝ"o �+ ]sHi>h�et.�Vu (utW�X!("�Si� [A�\"7X_1}\ (4] = 2i[B,J(B)]XJA#$ w� aIW�FE�)�=�}2� A�$n $v*wGw]$ j:likewise�$�"�Hwe �lRI�$L(�:R) =n!��4at! ?assert��]9 :C5  Y-9&Y}+\va�Q (L_n L_n}U I}Y�rf�%� if $k+) �#To~��A�� R�e,Af�hspa�#�� Bb�E�] -���%�1% )L=�_1}=�a q�*� in aBb�%&^@Ilat�*e use �&�"�� ). C2F5�)��aJ�.>�;�_� �C,� �!f�8 hor�4&=6s�`2`��,�5�y�Z~n���U>�� 髁U6�2�i�:E�. .U �� so iGZYY2X#A��{�T2�> M$, ���f�|zfj.E��hJ!�"SB�dre�Pea s��o�BfoU��F}. \(�E\enlargeuC4page{20pts} Om>��in�-6�V DK��I���H �I,Y � m2 &�2�@Mact�y>_M2D}$%{a&�Ix��GA, �no:J-��*�4�n �)�E�i*U 5 (J �$�X one)1�� A��Take $V�F�>� )<e�)sg1V*K�EfSset)# �i!Wl6��s�1�N���Ar.� w)3f�in �o"�?*�" BV!&  y���)uf=uByB�E��&9!�� g_eC2$}}^3`��^$��a�ok2�Ep�* $A=X_1+6�t"�G cholaY]*-84system $(t_1,t&b t_{2c,r).p$*:!�2�}&Dt�0m  $r �d�(MfuGi� 0.ll �K*6Q$s#�H.�patch��  �Y�F� g7eclF";*!�1E?$t �!��)Xj separ.8levelS�7s"�+>{T1 �-]a(�U "� \D2!$��V!V6.(�%-]"J>QL ' o $K$)El2���.W� i�k auxili�7�KRgjQ=+I=P1}{m})/(1+m^2(t_2^2+\� +Q�^2w �� P�+ c=\{JR�0):f�0)=c, 0� qA��t>+a;Ci1.!s8�ily ��.�S_c�?b�+/V.�p�Z$c|; $1/m mc! +1/m)*�V� �dy�>�A/� 3- T>�^�V:t_1�*M_t_0�s%6ly .X� .�$ge��57�Mk �I���ifiu�B�  $r%�/, "�oaa`have ap �;&f) �A. Speb�C,AL $h=g+\mu r+\nu r^2$K\mu,\nu$5�d�YSb�� �R�;|e $\tau > 0�� $W =!��8�+n}w_{j}�.CF{j�jat�b%�s,�r=0$)  !e�o au h}}(W,y� W})=� !0 h}\Big( L_{gB+� L_{rBq`|W(g) + !"W(r)|!�+ 2!,| d�  S�X_n+)big(1/\�B1�<|� r� z_jX2UB=,(J0 *�(�Bc7�/ / z_j)gX_n(r)=1�,We expr�S$W& !���ba�a�19J,[ n aas $W=�n&*jX_j,$ �sy7E�i�7�( $2abi�0\varepsilon a%g!>)bO�y /�, $|a+b%I�� 2}|a - | "�V!s|�{n}a_jn��n6!|a-���g�*��*}�AK}A  h}L_n�&�f & �2 }{2} |X_1(g)B�|-k1 +ul2Ap-1 9(A�LE�!�y0X_j})� ncj6c n)jM�\ &+&m �n�-G(� Sn6S+ n\mu!e+ \mu6|�n2�n}�:� r�-& s.c.:� � � - l.c.! � A + R  \ , d{e9�ho*#no����� tant� q.*�p*�+s�%z�T�4 \mu "��9�VZZ �#$|I | \a�r |A(g)|+|[ i|&� =��g�� t_1|� X 1�j2�j})"e�2� ji��ecufore,8� �B �"a< +�). nbig&* "���N�� |WE�."� V}�i!/. So $J�f^ �. 0-z KFuyon� :9�}exa�lR�\Rp. 54-55�CZ ketch it.9 AT2u4 $\psi_s� )$� �d��� #Aorr %�"u 2(>� �q s&�s >7]c�9n� :��"� �{�{s��a� h50c�(rE��-� $V� *� �� To d�Pjn d�R� F�m�,sq�s�d�n�(i�A2� �*3.1.6IP � a^*= (pn our&A,k*�2� b� a�}O$V_[@!b/2T${t: 0-= � �W "V O!e%��� uper5� d"� �%cs%S:\ ��0yZ�A�uit�c1x i"�z&� �Hly�5$ �HsJ4x d� h^Y�Bu�V"�57Oby) ds2/  � :�2T *P2/4l8&i 2+nontriv# Y�of).E*p,. %\new� {�/ `bliographystyle{amsplain}U theb' }{10ibsS�J$E.~Bedford��< J.~E.~Fornaess,S8 it{C�O)%�2� qn`ies,} Duke Math.J. {\bf 4�ZLNr. 1(1981),179--2888S\�86} S�>d\ 9it{Dif�}tiabi�A�B�D�z -l3S "D}, � Z �192} �06), 467--472.!<1087} H.~P.~Boa= E*GO Kerzman*U3 on d��U�@}, Indiana Univ. %9 1: 36},%:3�7�95--4992�S93.�%�0E.~J.~Straube9�@De Rham cohomolog�B 9�V!gv !uinf\(e E� Sobolev9l7.5�(&�/4�#} , J. G"3yAap E73 ��093), 225--2356�} \by�B�Global r&/�M5��: a�~��L_2$-��<y,} Sev-~m" V�*bles, M.B�ne�E�XY.-T. Siu, eds., MSRI P$x�s �7F CambridgeEersity P� , 196�D D.~W.~^x9BK}Fbehav?|o^K=onRZ3�.s,} Pr�qton� Ph.D!� 1978.��,F�N�.%7"�0� N�j�a&�. ADq�5} a�,0), 605--6252i/BB4N"�,f:eA� su"]H�y6�[e �+�_!l��� �}, k| D�opmkuinnh6�( ed., Annale��M Stud�eU10#g6�. E\ �� , 93--1006�4J�if Bf_?arq�"�3u�,u1u�of� }Ee4\a5��3cymp.\ P�2 ��4�71984, 39�#2�S�\-C.~Ch�( nd MShaw,�mP�>MVI al E���f�} 1h(in Advanced�e)s, Am�9n,al Society/I�fn.!al)�, 20012�}M� risty�_me1g�� ir=���},j� M. Sc��e %�!��� ����B�F} �kS.~Fu��tapm�nw,magnȃSۅo\-�?.ۅ�N��XAharonov--Bohm effect},1�E A{5�iA�ess*F(DP} K.~Died!�h�P.~Pflug�Nx�>er��h},�� �D �D%�.�D 151--154.�FK} G.~Bd lla�J�Kohݸ�5N� Pr+�c, Cauchy-Riem9�Alex,}:�-�6�75,lN�r�  196 I�Frem�&�*�nd r ; {2�s�.ooc.e�.1K��57� 7� 4no:2, 369--370&T " ]Ii%4Z� ! q^�bc9����:��WFunc. ��� bf{159�98�\29--6412�01J)6�aa��;����� etry> ~���� Ohio S'V�1rRes�st.q @., 9, de Gruyter,Qlin�n$, 141--1606�d>>h Semi-cl�B�?a� of�( r\"o>c�E)1��� $R�L) , Jour�ofIG\2 �CI I\27�20��pp.~2� 282�dr-d8in.X| fY� 2 2003� 5--196.�HS��Hakim� N.~SNh��|tr� O"��B pour�l kQa�v 2: e� J. A�tO�al 3iZ 127--136 Ɇ��(S.~Harringt�E��1�a�: � zP .�<�  miniK*�*nes��ofj1 re DL|.f E�2W(HL} T.~Hefe�I.~Lieb9m�Q���o4Xv� �,}�. Fac� (i. ToulouseI2 (���ҁ200{ 41�32265} L.~HZ�rma����i*Oa�&�Nt`h�  V���cta ��113��65), 89��2r�JPI(M.~Jarnicki�A':�I"�8Di�ces %A(M�� >�,} Wa^a .{ 1993.#Ke=Kim9In)DtQ A:QY�QJ��R.߁�&E;� ��l�%�co�q�},6] Cal��8nia Los Angeles:i 19972�c)�D�tY�A &�!O?� 1�v�Z�Q2���io��A�& 195}� 2��0--202�NT.~�NE�K.~�'�N��Ve�� }G.�"� !�M�, 95} (2) "�197�2�$R} R.~M.~R�a�Ho&�w��9 �Z% RvE"b�}, GraduA�TH��'� aZ10�Sp�� 1986*�S1}N�H2�\'�8ur l'op\'erateu�9��} ,$}mDAnn�k276e�� no. 2, 292QSNz UpPy a��]ۏ*�V&�\"�! 5A?1987, 29u 120،Zh  .�si� WITE�jM�F&� �j}�� Fourier � 4}, fasc.  2004� �716/S��2� Ś.~K.~��es� E� it{P>D'W}& s, g�i�5 g*���'a cer��U�6|f E1�Vieweg�O1rQ>�� ��s ,�docy�H} I�% Title: G�� ic T͊ � GSp(4�X GL(4) % A���: Mahdi Asgari & Freydoon Shahidi % Subj� : NT; RT�ent: V�^n 2 \�e�,[12pt,reqno]�ar�-4length{\oddsid/gin}{0.5�."axJ#2$width}{5 B� u�ck/} .amsthm}J�8N symbNfonm/F`cd>/[\$scr]{eucal>{ve�[�new� AAQgSh�M} 6!m[pY]2#$lem}[thm]{06@�\ *�6$cor #"AI6!�� b{6�@ �KL6#FJ #E��6 Um Conjec�H-+T3@and{\vlto}[1] {\,�Bpi *$(#1,3) \pun 2){\��_I{#1}} eY0\,>]ne�]0.]1�]�\0�\a�/}{v;inner{\m�`P1mu\raise1pt\hbox{.} 24f7 5 1mu}>5A}{�]A!`ne9�B B>G G>wG!� {\en�aM {{\m�RG}}}^\s=c%� \re.pH WHW6L L.4M M>N N>PP P>R R>T T>U U>Z Z!ne�un n2� BG}{*rbf!2:#M>#B�BR>#�6Gb2jB�bN.CBBbP.BGbZ.!2�bk.k>:bn.F%h�IB�h! Bh�B�h�B�hT}W�IA 6�h�=F�cAm� cal{BicOO>c�aLbN0& :}Z;b}{�\B�bJ��\R�e}{\eJ-: g}{\gamma>�g!=�x�wGLB�gsAqF*SOJ+p��� USpN+ NX��6��lambd!-.�mA>u:�o� omeg.6IoB[ )_)[6�esig!@:GslFHŻSL1�:Ko^1O16�sp^3p3. s!=[16S �_�6hta�th�p>�tFO)J.z}{\zF6�D}{\DeltF�O_ 2O!�`6Iw/2.�Et�c%:thV0�� .�@� a'tv {Vu $\gsw �6$\gl(4)$} \+�[.z ]{.$$^{^\star}/ddress{S"-�(Mat0csJInK�Aj ~ y 01 Einstein DrIt\\&�#$, NJ 08450US��email{a@�.ias.eda9thanks{$ �$ P"!�Iu]�&�SNSF gr�OTDMS--0111298 at IAS} 5 >u]{>%dag2.D!8t�$ \\ Purdu�er-%�\West Lafayette, IN 47907.�s� �pJB�dag��25} UGad� act}.Yestab�~ Lang q� oria�(!�� ic  trumiYk�descri�Fts - $0I�.�-u3D�|r� tor^he q��(d Ramanuja?�� ��r:�_9m.�}� \makeeE�Ap{InE��}&D�} �Ik$e6au6���YGP1)0 roup1!,\Ad_k�5The��necA� o�{@) $L$- =�G$D-h,\cx)$ ��Ja -�embed�{o2l( 1.b�J��X�@ss�It�5i�W�=L��;9��asM�R�G��t�-�E1 �.$arthur-gspݣ U�'}or) Eisen�Vse�+ reducS"AP<h|�u{(cuspidaln�58ywu  #U�icS|: �.��preci�j, (cf�(Jh-m*-):*X: {\it�h\piMmB�6�-M��~Q!we"W@o!��%l]�ic�nUqi$MNu�Qt� cnj4 $\Pi�W2�\Hisu�(g&lyi;%-lyn�"�Ro_\Pi�8 pi^2�9 r te�V,{\Pi}\otimes*{\pi}$�:$%L�� �H[U+ �8>h��D)� 6Pi$6P.� MoreD ,!ic a %�Qk�)cri��n}��� �%�0,!�%��2M�Y;cP sobaEy�}two!�6� 6 � gl(2UE�*tI�q-cri})�*We�nRof���!Wec��)�Q5�is ��Y� est}�Xsafim"���N�e�.zp:azS�� � ram-��eW3�"vzW"y3�T�+}%��=�n~������!ESly ��})�B�(I5`2��32,P or} w�l�3�Z-��I� n immedi��(�B!3D�y���#!�f�:{.�)�entir�{6s  �Vm����re�R~ P)$�D{7Ca7�d6� (or�ducg�a�C�N�{�f �al �RE. ��bf��Yls�4ev<��(ly�3HR. Takloo-Bighash u4h"u1  s ourbaV�@�9�7%!��t3���)��b�,=Ab�iper�4I�n��Time. KT��Zs!H]�8Jac/�, PA ,tski-Shapiro`�lika k���"� � �,f leb�*inciplec,r8�SasA��O�6eirQ�w�=never "���-5%�2�P5:i%�ofabbas�55�%`�FY� disj9y)g)� Our��� PS\ tart$!&*�i�mA�al>Aa�- � icN�in$M|e�=$�  ga��I�a�s �Q�orcI PiGHt�E�U)���B��� SoudO 8#��e7~VL$y7M  twg�dAy �(1)�� 2wBo%!in0  abou!�e>���$Q��" e lAmofi���(%]q^@�ofF%69X�bpr�t%=eZ carrmw�!�".)� �2_ now.&}RI�E�Arut�.�,aZe0hre�F�/�woД!�>�iDprd).;�. ^U�ogקh en%J �th-����a�#n$ * " by Ginzbu)%RalliG M �rs,souq��y� toEg tech/ I��h!�i()of C$kim1,kim2}V� 1�-���{zE Ap� ��wh^�%�icܵ not)�s AM '�c% mulam Y:proS`!����� wA6���<ssu�r�Ds ouβ�;2� �&�T!0� Ja�X Cogdhk�wghelpful��cu+�x#0 Peter Sarnak/�Kn�����ի.� � � �5KU��Steve Gelbart, Dihua Jiang, Rober�$, Brooks M(Ramin>r�du�#e c�wD(�.�M��R�f rv}\Ad+ l "��u�dZ&�.W�#fi4� Oit z�z\ciI7degreA=ur via4�[ �g� =�<�g�Kf 4) \, :^tg J g&mu�EJ�r\},|�A \[ J I(=0matrix} &&&��\ &d & -1\\ &�d4\r�)bA��@(g)\in����Zh�Am�:�"� �mfixE�?08��b"ٶ�V|� S�j�Vr5� $\T$a_�;:�\T!LQ\\{ t = t(a_0,a_1,a_2) = �DfB0 a_0 a_1 a_2 !! !%' 2--& "e1X1# \}"�} �a!��)u^ev��҅q��'E���] �in(2n+%o�$Ŝdzall�ti�� 7�!�AvIa?  in(5C �\p� s^\c_v \pi_v="k�A$-�icF� f{!�-�D�uy, T!� �{s|�&a non-t>CTveYmWk\#uslash\Ada��;i�U�)( unipo� rad��M�� �ruppertaz� BorelA�!�usc�way�A�)�ܥ�do�F�eat�Jn[�st� ��paper.�S)jny�empty �te�Jofarchimed�o�W s $v"/CQ�d��� b�!�!�MP �)SRA� \ ` ���p ���7I����\id��$S�b5��p�R, su�$v\Bx1IfH�A9TJ � mA�3 ��.ag($\phi_v : WA���0aނ^&f!?$W �AA Weilm��k_)~l�6-�i}).ɺ\Prt�%Vbv� 7= \iotac rc �$#R $ :͕� F�d=�B8C!Cw���Qm��I� %� 9�!�a�f� ycunQ� subquot�Ofwr2�Wi uced� ֶ>�( �s�T(k_v� ��. Wriv �o"�g�u\�h chi(6���_0(a_e chi_1(a_1�hi_2(��“/)Z ���_re.��KAW^�tY a_ibk_�r6&-�-j��-o�;duc�4.z�{%�EA%@Ebo l��n)��R!��bachi-__1�<%I22 ^{-1}0.1��9g�-�. 6��+��T��o^2}OooarD �7�e�Sl�)�6y B6, O� }:�y-�\simeq\�_v�oo_�_v}�� .e.,A��2�y�s ivalo�x:$ � J9E7�vBB2�s�:<^Gaut-ind!�t I (|\de&N r_1}\s_1 ��O(t(t)� 9�iRE�Zt�J� n_1)iBpT gl(n_t�Jith $n]W�T+n_� 4�Ce)�sy�i6m.4 Vqi6 Nr_i� rl�EWi1����"�9�da.$r_1\ge r_2 �(K r_tP&��xM �Uj n_1 r_1 +F+ !r%0"Bim*e�$\leBY� � S \cup \{�Uv|!��Qndۑ��r�tbH5­np�} L^T(s,� )� a s}_t�u PiJ \1�_{i=1}^t ++r_\3s�9�N� �� n_t=�{Fa�� �\ �A`� bye����Fc�:I 274$ps�)6|��-n�o $$s_0=1-r_t!��]st S� ;��� pol�hs_0` p ʕthe�a�i\nc��Re(s_0!?!wA!r_i -A��� c5&�XNow6�!W3�� $t=2/Wn_1c�A'$$n_2=3$. R�b :J!vt-Hr� d0� l��ngeA�ii�-r ] !��k e� siֽS4 s?2-Kd �[{�*DP� = 2��icMase� >;�KNQ�) �W hav49�!O �M1.3>U?s�d�eO3�ts�of� if s�rgu!Ohrb�wp � r_t=0$� �k  we eiAIW:� = n_2%� t=3=�1��,. *˽��rul�� l cas�[9"�_d6i=A<e=!��z:f�rs8 a- f�tI r_3 ^�*rG�m�\2 3 ˩9r_2 + 2 FU ql���hbe ekMM*-p2biZp�S�I� .�!�i*�$�(����^��vblocksfp1a��p �2A1) ��*�{��1);3:�1).:� �1!zFnev�tBh'�!��>H�e�V>V>#A9i�V�}�OS�w<�H� $�: (� � $�qc�)a# iB��$�}A�$ASA�.�oqm �Z!�"� ly c$A�2a0 ���+E�by  #[o 8B� �"of�.�� ��$Inot� E$ u,"�k ���eIRF��o :kBQB mus�G�Ydoubl:�t $1�ny-�!-:� 8m�a�e��A&¹^�o.Gq�"� ]h$-8�" ni"ԗ� {%gC#b�ab�%�yA��&1 bnyB��YE "�h�? a�B.�v<$�Vu/ ) e e�ze\,q04�WE�E� 2wisVzeyFы� Ln|�#yy \s_2�{%�E��c3fXa�m� &.�> = �4�# ?��V� @-�%h%=^gHB� f ]��enPf�% $ (not ja�B�a/m!Tize"`�a)]Ap>I��U�k�FAХ�fl �s�o]R*��lif?soY� \�[(b)]ye Lq� n-: + F�%:��&Piboxplus &�eac�P4�aB�n��%8*_'�� m Pi} \ooq �.�PiA��z!)�endI�"j,�$} B]Mopo�ao�%��I)wA1O!�.�buBZQ'"� m>S 1 \ =&|_{9 �h��� } (��1 s_2j�� :6:�^ G�  ,�~ m�&C� 7:liA@U���>�tGs�n{$\tau�]�*7��\p�0A�.� nd�at U�Vb&%����,�N o�l�!^B�q�Qx����� n!*: ���N� =���"c !�'*�npy��. f��,�ki�nB ee they� B���Woby st�jB�lC�) �jac-sha-u"r�DI,Z I,ps-corv�"}!f!�b�+�Nex>(1�2Oand���~�n%�2�;�4$` clai�f��#_v%*�\s_{1,v"�,s_{2,v}A��(r�.}.?^se!7�G at^s_{i,v�_nB� aN Tgmpeߣ:��\k]#i0l�L/;/ $ID�$ |\ |^\aa,q {-�8-$\aa\in�=/�%��$ a\ y& �xsX : �'$tt �Egn&�Y y.�d��leaWx co�q�� pv&�_1 ����1 _2 -bb%{-\bb2 ,\bbR{p =s �a$QHU b�����h� %z pm\bb=\pmP�OA�� le. "��if�-EQQ's!E 1v��+�n!`JM �: �>��EJ)Y)?�v \aay�J QE�9�a�R)2eor�g\et.�K0^ �$E�W"���6)�eta� &� �`��z��+ $�E!notN e�%iM>� .CA B�i�_w AgaiPn"�˱a��;:U��� �6#�*iat every'!�Re� s sam�23.s�2 t:"e4 �.�m��$�Zan "�1:� , �$�1���N �%U�Y�icW�mN� vali�-f:�Mite�ps��-3uB��  F"�,� F%��P4��+ �{b6� 7.*��"��*"�-6-%�TS�.!� Sh�,��A.)�F�2 � �_i� � ��i=1,2$� ��&�.�"� f0&#� 426m1m)*4,A2���� � �n� �����gen�YJk$A K  N an N87p��n�&Q� O P  CAP>��Z*J; �s�ό'a�!� {�",A��-five^,�ŀ��;d &W�G� � }������ ��"�$A�^ '� t +6 I.� �(��7e��.� �* )@� �3 ���"n�chA�v inue to k by�p,|��&���Q�AQlosa2�� � �A��&Bwe did5p&R:"��e09l2�%2a!�� "� �WQ�:-x i4:�3a��4JNH,�' �:W!�9 �}) e�mL�xFur��Ͻ8ŷ!E�!me��*� V5.%L�)7��4 Ano�*�y42�!luO*܈%- ��(R)�*� )� n-vanishi�- ɭ N�9lo~�": � �>81AMJ�/�a��4cF��%:�1�t3W&� �m�- 3!��$Mm�!}�:iߝ�F�$��%��0!�� 挕\�� . �qa�!i�jn�%�� itsJ��o�$.�PE�mjBh � *��5_1mA��f.7s>$&� q�fOsM�.�a��*h6.�%b�D*A�[ � ��B��$2�!%7g:���i>  !u0u� .���sub�-��A�j0V:5��B� l� �V,%xS"mP.\ exp} FixU+�eI{�/"Q M+U�"�(��%b Q�T$ Q�pi_{t,v.0}"�%"01W��A��p��J��k�j �+ ��]!�" F"s�&e�n_iM $ � >�> b �� ��_�$-�*��t>���nsp(2m n.:6�F6  few f ,�]� n_i�a4�z�#&�&�% + m �"3Ea} $m&�% ��nv��Z)V0�a�10 et�&�h�e�>)�%v� .�&!�':I� .CB�J�:�X� !V�!E�>�D:� ���#eB�A� ��� �1�m�[h? mF_��PivxU�2 ��v�2�  u}\,�y„icav}�y�wE�u� �v& (�pi}I�q�oo_v)N-m <�(E<��*}�, FEF4*Big"t->*bPuw6�1�: %���mo (m�y���6:��ux"mH�w �0�Sa@7^= ckpss-�{U,� c���T�6no#8i"\ED�elet2? R; 58%r*S .9admism��D:J�4 �12�am�>Qm not.���A�:wawIa$�8t^  � :�%����$.)&{;� opP�j� <]�)%Z %�.�3 �l�% �al��y �!(0BPVB� )%��O"�Qe!��,Q� �,���(�%"�%���G:%v�#|#e�5�4��s~?�A�\rh��A�ny�XB;l(r�f� B����O\g� X3� r,�4�!!N!F�%<key�@�f"�'A}�>�F� BU@�E.��.ׄV I[Y� ��5B!�I�u�v�5X w� =��U`ɬ Gw\ un"�2ELP*�5.1��!^ :90a+o.$��c�rs%eJof"@<�B'�  $S� = S -�-�-�!gm "p?�#�q� .�7.*��>�.� by&&s�t&�$\g$-!�o)B�jIv)�h �i�?Ew%`a*=r�seJ.�!%� M�\.t&�e@A�V ms��q�"�(!$m� toolA�"���I��%�6-ZYK.�{��7.Fb)���e�+�" b< $m+�5m6�.� !n )=! ��@J%AAg�� �i��aiel���N we���ho�%Fb� T=\{wDŽc/s��a[gle2� $)noe�a���P&u��Qֆ>�%�m/6 07�7w�9:B�H=z��&g�g] f *.��:""f>�*"C./ )�n"� ��~aą;��Pe�8M�o���4=yt�� clud;�&\P/�e "�%�p�F��!^�ƣ!z��( . -s� wby�+T�B�y � w�O�G�b.�_|5��$ W ��m^�� e�L\_{�hi�on�WA���re&��curDa�mu&.�"'J�mn�^)"wc�r2��`K!��!(quasi-split� H� g:!V_gajY*a�� �8�>} 2:com�9�c��a'&�!|��~<A�HE�-U!�"Ha8E��a�I�typ��f��& " }: &�c"�L%�2t!�.B%6�Hll R(H��}�1�& >�E���L�� z2{Es:&MU� �L FG, ]>@!�R�9%.*�"��in��"�I5.� a1R�i64F� j6�G gl(m� &S�Be�E?!}6>�AY��I�1h��@be writ���� V�F R���a���"0p0}>�8{ th $ P.ma�i��W�y 9*�Bd�AU+)3Tt�5,��@��i���Ȑ 1 2 ���b�A�zlyOn �IE�Cum��RM�Fsay| ( n�r6>� �A�� � 2�- �{m^2+Ƴ-�0luo-rudnick-s H}.����\r��$m!n4� a ^](1+ m(m+1)/2��� �b�}; vailB~��4�k u� idJ-�aone%C-a�symu*Uqu��.�);y ab���2� g�<�$�8) >�$N I�0kim-sarnak}) �e but this is only available presently for $m \le 4$. When $m=2$ we have the better bounds of $H(1/9)$A�La general number field $k$ \cite{kim-shahidiDuke} and $H(7/64)$ for $k=\rt$.2�arnak}. The Ramanujan conjecture demands $H(0)$+�Similarly, if $\pi = \otimes_v^\prime \pi_v$ is a unitary �dic cuspidal automorphic re-7ation o\\gsp(2n,\Ad_k)$, then by � muic �)(vogan} each��,can be writt!}@as a full induced>y( \begin{equ�} \�H \simeq \mbox{Ind}(4{1,v}|\det|^{b }- \cdots 0t60}1?8 \tau_v), \end� where�{i,v}-`temperF�\of some $\gl(n_i,k_v)$ E k>BgAiF� K$)�m J$with $n_1+ �4+ n_t + m = n$A/-N,defi} We say�,pi$ satisfieE^$\theta_n)$ V \ge 0$Am0for all plac7vyG$-1 le b)"  �%X �E� classific%�!31uM� dual �eO (cf.Ms0lapid-tadic-mA�,��example) trivially gives the estimate $H(1eV��P again. For a survey�$results in��direceH!�$their appl �4s we refer to ˉ-�\ s-notes,s�U -borel}. 1�Hthm}\label{est} Let��be a 2�� assum��at !�1\� 6��I�4q� (resp�ve�|E�2) IM y $HQK)�:6 2)$)�Qi2.,��!�(n, any glob%�>Z��A��� �6�4E I��7$ transfers!� non-^h al`I�LTheorem \ref{main}),A n it�A�,possibly bet�� boun�>m82���!� Uproof-� \Pi$!�S(functorial � ��to)�5�&���0n archimedeani�=k$ ��u0clear since Q�$case local�ity�twell understood through Langla��( parametriz�e���1V6.1�u gspin}, ��m��mor�Atails)�e&v%'a%�^� at whi��8is unramified.�n,!�4follows from (%�chi}) tam ��is ���=i��`Frobenius-Hecke (Satake) -er�u��f)�ormF �Pi_vP)? er} �(Xdiag} (\chi_1(\varpi), 2 ^{-1}0 41j#)B7�6$ x $ de�� a���izeI�k_vA�A�E�isu�Mv!�$i=1,2�tby ��p�j( \[ q_v^{-m:4ɀ|�i�|�i)(. \] 2not>�2 s�  in�lit�N �R$�S�&d�ev!�i��}�<�v2�SeJ]1��,y$ �5�| = 1$E�refore, BXUO��^ also��y N�a0Next,)c�=a>T ��k$ in $S �n,� Proposi%�eexp},�3-< argument  $bove works�a(e�}��cor�����g�%w� �T� !: 15/3�Ifi�$�Q��F�A 2$k .e$% M�Qq�� :?)�H(9/22T Hq ,���.)M%>@-Z� !�immedi if{combine!��n E� �knownnu�onU�se��al lin�,groups !�ioned %�.���:��R �m!u�at� �>s8 ��  !0imply%Yb^��ic %OrumE�I?)$6Z subs on{WeakY��,ram-weak} F�6 ing ��cog-ps- �lity,ramakrishnan-mrl,kim-ex2� : c� !�ɀJV nesa�.� ��\G��8split reductive)� ov� he6@ $k���:2ki_vka�nnRizG(N. � �)] !!ly9=A��:8 $\epsilon > 0$�� xist�Ss T$!���i!k$N tain!#%�.� onesE�on2E����  such �T$ has��s� zeroSA�,$v\not\in T$ ~>��� $��((\l_{v,i})$-8.�8 \[ \max_i \{ |0|, �| \���1Aar ] He�2$q��!cardin��� residue�>Aq� We willAconcera�%8; )�\G=  m)$ �spe�"@ paperErQ� at (iy)��_%{� areFWZ i}>l} �,��s 3.7%�6.3Ab 9q�&] ��>�hny6H�3, letF .� $(a_{0,v},a2,v})����}�`%�f�i�I�!>�  }))��  6�  AY�� / "�  A�.3 ���>��e :2!�E�X More� , $| ;g � !� �M��� ��� aboutE���properia H����ly�����- �V�< < o e���n%R��#� .# Spin�L$-fun,e� `)$�� or} A��other.K we ge e99% corollar��our mai�,6���=!��=�s Ns A. � 2  $L(s,\pi,)%Zentir., p!Rb,: ��* uU� �2�Z.t Q� � � :� = �Piz i:���!� & :� �/�{B��Qcrem} T��/K� been�'vC@R. Takloo-Bighash�4Ɉ� n} among i"$things. Hip thods�differy � ours���based� integ�r2�/��Libliography{mahdi} \.style{pl <doc� } Ϫ\ �[11pt]{article} \usepackage{amsfonts}2@latexsym} \newcom/D{\bbn}{{\mathbb N}BzZFqQFrRFcC}}%{� \bold� $C$F6f6FR6FB6@qed}{\hfill$\Box$:�$too}{\longE�arrow>#hen}{\Ln$de�Delta\,�{\bigtri�edown>�G}{{X *Gamma> C�'K>Trho>s%�<paBot�it TrB8hQ8h> cont  :inv}{1F)it %:D TDes>des  :8maj  :DN NJWeg>816nFdN�J�fd �fJ:fmJ:$al}{\alpha:�laA� ambd>twPtilde{w}>�t%Q sBbdotJhg!�ht>Rhk}{{B,ua�Ja}I�hat a}} P\ddot\acute\grave\vec6�ubIbI b>�u%jwd. d>.d �/�check bar B�d �6 � 66B�d �6 � 66B�o�vecF�o�Blaw!�a_{wswi�>�aw!�"tb"sE,$stjHsJsL%�t�� {�}[�]2#$pro}[thm]{*II�Flem #Le�#2@cla  Clai��:cono, :?or" 6!fac ! Fact6prb  Prob�2�exa Eh6obs Observb2BA)Remark6df Def�?$newenvironC{M�}[1]{\par\addvspace{\medskipamount}\noindent Z4{\bf {#1}}\sl Z%}~hrm} %�"� eqde��8op=\limits^{\rma}V0 \stackrel (C=>� [:=)<ssum�csum m: de � tial:hal�1\ 2rs 0\gotic=eufm10%�mgoeS\h�!(ic\char'123a�� � 6 8title{A Constru� of\\ Coxe�G( R6|  (II)R` aca�author{Ron M. Adin% \thanks{Departm� xof Mathematics, Bar-Ilan Univer�, �t-Gan 52900, Israel. Email: {\tt radin@� P.biu.ac.il}}\ $^\S$ \B (Francesco Bt i�i�iA� o di� �a, �\'{a}�Roma ``Tor Vergata'', Via della Ricerca Scin O!, 00133;, Italy6�b�<@mat.uniroma2.it:�0Yuval Roichma�Q~Qymr�2R5� Rese�!��)�8s was supported�![ byn)�) ce F]��$�d�the*Academ/S!O�"!� Huma_es b> EC's IHRP/gramme,�e �Tr�Net�4 ``Algebraic Cka�cs in Eu p'', grant HPRN-CT-2001-00272.�<�by � rna?-"6�J�=,\date{submit!8 Janu'X6, 2006; revised July 5 \\ �^ Ded�"edT$Gordon Jam�KoccasL&�060th birthday�+ subj� {Prim~D05E10, 13A50; Secozy 05A19F20� C30.�M make�Q�kabstr��An axioe�3roa�o%�6�or%��� �!c�#�a)�IvnEv~�U-I}. %�A�carriVuA�2atu[*� on %A�:�matriQPavoiding %a priori us� ext)�~pts (�$as Young t)aux). ]j al a��t.� stud�E�is� Inedicular, !! sym�!cOh�)nv�ga)' d�! . Th� sult�6��co�%t�E%{!!� includ�ir�i�)�rY \� {Intro�o"�s.iAL*�Out�}6D2ofQ+ �>�!� b"��"!d 6cU!,U b � \small< �(W,S)6m system�%d�$\C "� e %Ht!! $W$. I \bbf &suiE�M'2(acteristic B(e.g. ' Cc(q % IaCIwahoriL#m�)� $\T ~:C of (a{RA of)�a�%veW% f 4 $V_{\C}:=\sn_rPf}\{C_w\,|\,w\in\C\}$�  basis @!dex�yelee�!I�w��toe~�g sets A�:�T$�$s�)5& �:�#ite{#} \ [$(A)$] {�qge�,t�s�S z� � $� !�Xe �D scalars $a_s(w),b!E���, $$ \T_s(C_wQ0a_{s}(w)C_w +?* {ws}.-�rq�-$ws\we�Qe $ r=0$.% }t�ize�tn 8A pair $(\T,\C)]y��A�8 %��ne�{ {\em a�c Y�_(AY�%ir;} Ei"# +AY:�,1-!� iK S AY cell.}�4C\ne \emptyset)|enoperme $% ��t \C' $9sM�'}z�-inva�tejn= �al� �minimal�!8 .} (��a cA an)�!HeA�be.�.)( big�j%�� %p5� %͗ ڗ � v� ";  I./ it� shM#a an!iF�a~& ply \&���!�dA mi�'z#cK-�> root��.!9�)%H�is�, fura�P)E( valu� �(�*arFd ``�* ary"�i�CM� �:� (see!�w$~?&4t.7} below). %ݧIn% � )s.aGs_Sn} �Wis/ d %�=2�"= . . toݕze����:� . %% �b#P ��z5 %%S4$B�. % Am�/R| $S_n$ %�u.�!��  3i%���3#��� %�au $QG#s�$n�B %$$! igma�\C=\{\pi�#_n|\ Q^ v} !|j }\}, EQ1$/��%]�ob�#ed��byA+lac�\g2 %entry $�,y�(�$\���"NU!�} %UY ��=�*�&D l �howi�every .� :�of� m�,! %� ma�- realE�!5��i)�:Y N�irru)A�6�g Weyl�1s a�ype $B'#�*u�JC. How�-�! A�^0���4mK hold (thesey(=I�B6�F~$e0we.��,s[-!�A�; �-�f� $[idI]"mA��� a#,� ��an.�:;E@� .�s55m6�O�0-�p���$_)c � procedur9)��� e�res �灴BU nalogou�*, %Barbasch-V�5 rul YD Kazhdan-Lusztig %:!� BV2}�>^�5�a  %&y�5x� E�:�&C�; sum�of �!�uR*��p):D/iJ87 T:���� .�s organqv�sd3s&�)M-"R�s"�" m!�*-G5 l�e!�of rel".�y lattic"$A�@ BruaForderS$ts quotien�ee)�[mA$ 4.1]{BW})��b>w�m2�}aU\�N $W� ;� of a�Z�&��6G( up to isom^8sm!W�" $\�4t.7m}{ E' ҉��)}!G m 1:E"� l*}�� ���+N $W$, �x�is�. %�*� ic� .a�- ehavior! � a)D.%B (i.e� 1 $a� ��B  \C, d , .� )&% � %VI#9V%, �T^f�Cassoc�-da�:��)�Wiud.CF}.* !��7" ��es� tinu�*a�/s�E!���:��� d�nguishedF4 s���_ out �[;U-I��MsQ a�11O 22�ia�y�S"�d} ���k:�F� ��:� ???]� I} iBw�e� Z��b �a E�\C� eteq���Won/2 ��hF�u,��.$ .!d�'CEI2c�C O jO skew�t{� �:FS ��Q $$q��O BN \invR .V�9es!8.7m} toge -�>!��� �0{^$tabl2A��&�b���6� E %���PM"�n � ger-��d�a7$VM: %.i��C$-Nic,��s =&{ IO�&�Ythe %id�ty� �>QvA� d��#���� %E~�� Q�!Vend��%A���� biv?� betw'l Z:�s��(2hx1� same shap&#/�0����E��ad��%�͍�'�2!lt�4us�prK5z�ingnw. {U]C* jirrE^C � liL =6a%/���� M�}�-B�)� :�B$Specht mod� $S^{\!$ /\mu\�?$\l[of> � (A8$\mu$&g;�&�:/� yn >R2��� :2ZC �� �!i�!�Q�� E�� ah j�6s � "�3*�.X ��&�% Int�#����� � F��r*�dfQ3dI3t�.%%Def'n:!��."�%�1.] E � W��g1>��iS~"�w]�&�!�s�7"� %�y &X$��i6}�1ve� �2.]� s�g� i]F��m 2sL]6}&6Q!�K%ž5=d39��top�I\^� F� RR�n=s5}�<2 t"� 1:��5 %*�(x �,F��).%�*�1Pfor�ermuti,�3"%�=!�A-%�!3$column wor�a rowZO��>Md.e-"�%��KB(|p&$Note:} %Af�$�_��a first �$�G� Hav *��heV+1,@w�inn?2at"�4equivalA to1�"� � an2[ �,�>� r�&R02; pp�k$KR, Ram03bEP�Pminarie*\p$;r%�necess~ back�n�02�s "{Hum}; oHIvex:� �h desc��de.? BW};! on&�:�.6o=�n��"m t.yof-!�} �*( �O�!��S&)  M) �x� F�M.\{v_Q� Q$n3� ] \}$ b�� ���  m�� � 9��'G?Schmidt�3a����(polytabloid h� -&"�9-+e!+i} \T sH(s_i)(v_Q)= \frac{1$3Pk(i)}\,v_Q + \sqrt{1-: ^2}#{EUi}w b�P�GDue�O0J.\ Stembridg�{Ste};��.,Greene}.) Ma�es&]�( �) musDH�!� rel�����5, beca(&!\��7rue1i�%�!s"&x%�'�Mof8G4E �:dy]�72�+: ��w�G�- $Y%�mbd)�$. Upo!��&�I toCk\F+s S_{n-�(n=|.@|, k=|\mu|$), $Y^ �F�oseu)(d�K� $@ o�8_{\{\mu��teq BeEZ$=k\}}Y^\mu"MNB� O)r�7hand,6:s �Pexact�+� Ad ��A��s^&�H�H8corzKon4( "T on Schur  �([(7.66)]{St�usiH�'rse&> imag( S�F5NM5g S5]%j6� E�be&ca+B�. \qed�#"�;��&L A^K ,A�au�&�,$S=\{s_i|\ 0��i<��D, $m(s_0,s_1)=4$, ,i,s_{i+1})=3���i<���:7'j)QR%�wisi.� B7of�eoi"& Y#e��,%� s $(Mm,\mu)$� �� mbda� 1\m$�k�nA$   2/$n-k$. A�q�W%�r�Y)F�e�>��� �$(P,QTV�6X����,�"�F5P-��A�a*��lzI�f$:� and �%E!�� sHG Qa�_ �&\�"�&Di�aP��I�E �{P���*B-yof} C3Q8 QNe0)}( ��@ �e �sA v_{%�}$�,en� $1'Ki< n-1$�! \rhoe�A��i ?8) = %\cases{% %:[�X i +wv� +� Pi}}, &if i,i+1 \quad@ box{8in��-� x};\cr v_:E &nB&� G,}�")y���!T� ��  $\e$� )�s: � := 5 h_P(�M��"�Oi+1� both�$P$� h_Q�.Q .\infty)2F\inJ�.}�The1!��7����v�~m :�r��2e�!v�O��1�&c �� �h1� 6 �@asoB�0A ~)=5�u+-^1�� -�-f"Q$)f.B �R� AT*m�R2> R 2. v5 .} REGn �Q:6��( the /�"& �8� t�coi }{\rv "J 4 �� ��x ?!H!�Hasse �PrapK�% Cayley s@ %$\G�or,*�;$�3r 6B[!.���07,x+0M-eneK2�,$w��-�J! ����-a�%��')��W�B:��,eqnarray*} TT.&�8&:=& \"�:p , e.> \,wq.,\\EpDAal \C}�E�JI.%K%�barG�� \} %-= JC} \cup ��=%\!O1$.Xc�R$*city)\\ MU-�r W>m& � F�*q�#r"6+�A�A��� } if5�&� [�� i)}]I(ll $t�){ $ \lUA$ f,\al_t\r 5�{ 5, -1\/2[Z\=mvein^^_�/W), $s,�S m(s,t1 ��� wt�C�n�r2�U�}�=:{"�= "$\;(= \pm1)0E1!d�/E?%By O&�<���_�F�})may7#"(Y$idq� By�[K 3.3�!R? ? >$ 11�%�,�� mildA�d� , :�06��&a ing:u$� [$(B)>�1 refl�q $t%�,�1, $\ua_t, \ubd db_t !6�1�EɅ�S$;�\C$ &�1�Kf9� C_w+q.�1�h\ell(w)< s)�d�?�?Cdb7C(1C>C .\cr�%Q�A�M�M�w"Z2�/$6� =0$ %(if F� ) or��2� =0$ ./� ).% `!�Eȑ�* I�1��mQW7.4I���-'6�*y:$').$�J�"m�\ ,\ m���n arbitrY po�v"�e %bi���XR~.��f��V^*��.a&�kA� := �> �:a } \qY (\forAх֩�B� \C})� 2�# $A�t� A&�3$At._41�.��+ A &=& 0\\ F�` F(1 - 1) a�)��S�/u.$fyy-��@6}5o�()JM :=1-6�$4,%"),�� �Zs*�6�aUu.�\�a:A+!P# %6�=� c��6one.�d norm/V�� �Js. $�0H�<�� (a)�U(b)W�C <t.l1} (& $q�Y),�F@j*&Z$" +�*U  ��JB8��N�)�E��&N2�&� 62� 12*� ��5����B�Raυ��� %A*�`��] ne� ($q�:� $ %%2� %).�krsQ�AG=s��tBy�a$)��2�B3>�)���s a%8�  $�"U?�t=z� �n B!$$� ��.�2� � b b\.Ry� e>�V�=�K r%s:X �}.%� n V(<}1ue�* q t.rep2f.qi�/"� %Extended�:ps (S2�ps)m� . %S>0�^yof1} v�� ???� .>6\&R& ")&��AF�-��n&|2�J�D�>n2:i)+m2,Geck%,�P�2� �2V&� B[bI. %3.15]O�W4$)? n}.M� %clos� rK�g�2&] $Sc, GR, Ro��ʽ50� jU94 F� �e�� $P=q9JM�$ $(J&RSs� abol�\ub�,� ,D$ F�$!NA� �q�1}�|n!�:\&A 8&g0 to $ 8$.��W^Jb �!1T .vB:ѻlength)��co�>��n% /(\psi, r�@KAYJ�6C"] \ z& ${ H} �A�L' L�@ 72.]0iE)�A, $� \upaqQ ^W_�s "3� %[2on� $V_{.����� AtU�QK�U�1}&�x 9.7�� �y:�rP ! ei�.$r� , r E<$rs=pr\.$pCJ$bM $ ofi�F, &.!o&�BAT.�*U7�$�v�F�!a��e: E����1n� 5� a�@{mr� "�Cs�9%� a_p(m)#} �@s}, &"+0 $(rs = pr,\,)8)$,��coeffi�HBa_p-ub re�*��.B�I�$; name$ A�_p(C_m{A� C_m�� p}.$IkA^�$� {B9I� C`S*�%5}�6�& 5 +Ss.+:�&���a�qCLi�/B���6yr�6"�*aj � , %�  $)�! 6�:$�5 %onv��2ZAreg�G>;�L��K*!!2f&�"�yR�Bmua3 \bbr�~1_ 9is�" %$W5  >&BJ6(��3Q3^$"Iفa��=�lW$�!:6,�2$mu f}m9%>�=7(d�#C,%discretenes�|">s!�J�!w8!\�mpm+fty9a_s^{(�)�DB� �J� to 0 %>� ��,� W)) ���Hequs�2|O�&Th-<h>�  %5uA,!=�s)$ $\& �� w tR�Z %B;w:;r W)$  >tho�J �I�9��Xi!9���8 �5� O%V � j"%s��2}�,]��4�qm @�:a�~9�r�(on�of a�9 ltho�l"�m$$\C^f_{w_0� Wj"s.5(dpll) $w_0as�:%sw#!] f,*)$ amy��A�1�/�a�""<%*no)a�_A%�L F�,A_��  *�&]s $A$�#!~(left)�) $A$-{+ seC*anB��>1FbyND� :=\{�/A\hI�tw)� .6CF} %3 C�n)yw$"9I���6�2��u�`VE�6 A+�mM^&�  [(1)])be�A_f� �T �R3�]�"�RC$hMO�J{vE5|%:v)=5#%&`B�!e^=$jD� f�����.@-*2)]Iax��a5w�W (^�cg}#E�6TBFA-�N�8"w),L& the "�66*� =�t\,g���^f_w})�(row-stochas�LO�p9�L��= 1v^4�gd8_w$�\jH*��!Un �#�rea}no ambig�=)�A�iFK�P_�0q=1� n�K �= "^2���$, so %%k�E  % )"�=2%(Ŵx��&*�:�_sIn�-%a��M$�-{\em %&� } %%�w �M$-1�s �r�T�&:�z�UrACep*� Mf2�56��A4�2^'p7nX.2 (uA&�sm1����  �t��'f$F� %�!L�JZ�wH N� %��V�\2��z N� �.fla,w� CsX{ ���V }Cr�� AE2�u28() hyperplan�0n $��M!�� $$ H_{t, s�l��. �� \��  !=6���� T� va_�#�' $. A.�% � �� �=r� of ��s. It,%ger� *P&4&�N �!k A"* �ra c� $H��$H���7*�\=�AA0,)�!ch 5 _��a�V K�%�l� H�26�L$Uk!�A = A_L�\� T-�L&}B� \ [rm\�!� \ } ^�\,�TC {W_A^D iDiA\��$$�H �� w)=D&�8S���sY5�!)�!� S$)�8p?$�sM�% S#s,�9MEQg:} V)%�/m�|^ %q,cY��oZ�al)joint:hong �� { \ |\% W!1:A{s %]hr�nd>bchoice�0T2AM�))$�C�x�:)!iwH$N"� % �R�<+i ``imit''%2s"e$*�L$�>q&_vn&E�= T#% =-�%6 8��V"P /�15}r%�K2�2X�L�Tqq% � e��7)?fix.�D1�Q'A�!�iUu!�r � �*�!Ae�,$v,v'�"C�� !n"��s $f,f- L$, $EZv!d(C^{f'}_{v'} K!�6�A��v!��9>�g !e V�F:ll��BL \iff�? f, �,q!��_t@-6� A_L)�`L���|_f��lx��!=!9!��2�A8)U \C!J$� ׁS)\C��#e�J]5��B�:��&$�!��s �>s��=���Nowa��+$f_m� �� \{f_*9f_k,9V#��s!%��(pace $L-f_0E9� EachXL6t {qu>WA/]�,4f=f_0+r_1 f_1+�9+r_k f_k%�� r�l� ,r_k� ��%ut)NO!�y:#�a��of $1,6{VHis"6zu )�A"1�:U �D!�q8"�m6!AZro2) 6� �* v})$; rT�d�/� . 'uh5%PM�E.�5�,��R.�xuW ^f_vI&� Gx a r�A1o%m1�$�v�U$\tr(@4pդ1se B�s (unlik)�actŃ OA=�U��Lo� �w9 ��tx|a�$f!^v�8Iex�LTe gen}ere�*$,5�5 ,disconnected�3F7�? By%. �a�\�B4*�-�BM:_�@�tOin)��avpon� 2��'|NIimuGn�by�B� z��`2T. � YP�]�A' all 2woGm Rs�7K�&�7)/exa} Tak5=S_3=��s_1,s_2� (�7A_2.���4c8$�\"H � LF ${s_1s_2s_1�&= p � 8 %+ AjweE)ch�\C =\{id%8�U I�at;, $�d= P &M �a;(# �\A$.��?jZ�zA�> `9��^2( ! 2�p �:�!�m fX)i7 op���Es� re� goed)�=��� yI!'.,�f��3-d�f��al:�!&� /&{;qE sign�n�ao]un�9.�82.p>8�xS_3� E��Eim:fa^851 hA^ạ3C =e&�� " 1: � f � ^� ga?*mFw M�001�, FRA�J 5�I%p6�  $�� o�_W$*$#=VN%a"� !f� x�5 ignoyOq��)/���_)W ly m��Q\mu�a� � *�%F�.r� :� �>*Cf>� , by{ K)Ht.5}. J1 :> ��7<j :0 = {� �kQ�5z4kn�fn�1> w�@a]%:-"g �)��us *&�>?1?�?>0� V��q�f��0 ���6!��"C�9��4b!'�u�vdi+^�C7�="a*] &�$�+���<x>�/�A���V��V��V��Vn�V%Thm 1: �0�0�S�v,H�rnHX� .��2�@I����25  %"�".B+$ b> 6��d"#(&\���p%R7`le>�IRc1}�V?j !%>� �=& "�IM dK �C�s�Rs_S�q% �#�Y 0^�!kt.TTJC� $' n$ lead��/ �{?tfVx (dVGG@�!WlE6�5!�i*-}d 6A*�T 8C %>�!��V\�*y�gf�3ge3glBT� $q$ {s�.xH6/�a1��Eg� a �/t��*9]-�Y;9�."Q_ �a2�%�Y.B 6m�"%� are*]R�tNrea"Xq1!J&~PdQ1W8�YwP\J1{I�UIN���H�H*Z&IdCT}*Y&9BET tudy>|�C kbS_n͆"�7Z�7):O� aP��!qF�&&�VU?|; "#[ na��*m8�_a!�K $v=(v�v_nUi�^n�3LG$ �{ v:-2-21-v$G1}9{n-1}v k(a<)Z^�KJ $�K:=j-iI? iCis��f�ow"v?XO$j�? CA~$!5((Q):=(c(1), � c(n)$he [%) \Q�� fter'(Q.9 deriO.VA.*paƑi1��hIr" �;�a"� (&+�3�l!�9V� {)��-�� ^n\�"v�+v_n=0&t?$i��� $\al_{ij} V�<r*�Gto%�tӒpi7� �M0a� �t�8)q ďe�_i�6*Rj! 3B < j�����)!�$�u coordinatA.a �~Z�V�, ll alwaysL Y�n�CF � iafKas$��1-.�2N�eA2'n)$%���� ��I��aI� �I+^2� n/\, e.�e�(5L1%�'^!'We�!b�KM �[��&�.$ )CP9by��of *�.�/ $f=(E�,f6�;�� nf!�6�l�7,� : \� s V  bbr!; ���,E]�i2�jX = f_i-f_ja�^�&�' id}$�:;des_rep��J@'�q�!%l$6w UF/%xa"}(.� CF~(V�&�  �H� n*Z;m��"r6� �Pm%% ��%�"-$PW�& %%>$ %� w:=\r(. �\9[�%�=� �w&�E�c2�AYR�2!'��2^n%6"W� "�9 ), %���Q%Y^�#%���"� "0� 2� QA���hav� .�L n: &M�,%CA�s:� aq2�ifE��VaR.48�v6W �A-Z�a�xf=�e(Q�7\ei_U*p$ r.re�}1h<=< M2BBQP7},�$^� , %�J�   $W =��, %QK.2_D)qG�$&I9 %$ma�!�A"W- star�&�%�:0IF%�w>t �nst� �>�Ax)-2)]� ssu�F'mB�Ӈ� t es#� ial.7i&� sh�p>� I�k]�!��hy_fZ��W�� � l��& W % %T�rve-=@�G9-Z �we ne h�^�3N�p V&���uxmonoton�>U���93oR�,� �q�� B�.�e<5��� �:pm �>T5.�EI. dnG0$:5n $�B (i)< jhh �0.�e�!*^ �F2l |��ly*^$w=id0� su�4/oEBE|$f$w"�H��- $)!�j)- ��o $(ws)f  �)A�*. �Rs$A�� dja�Y2 , sa�6=(t,t+1)�� t� �)%U9"Zs�&�u!��E $\{�, j)\}�.Z\�Up�ai� =̈́� =-" 5uMl.A4.@\neIA�� bE,kjG:!0)9�uont݀ct�0�Dp�"��A=uZreu��92*�F�on����6�6���E�%�*n * %u@�e.R1}*MH3"=I=0\�� n\ \�Q\ �"pha6%i$ ��I T_\Cr�Mm� % Consi) ��ea+Z�* Q�)i�<>, :.:"�pr.�Z $$ S in Z �q��$:�m�*� . \aY.�:�r_2 j.�$��<. �sc��LQ`=� heiu�}� "� $.%,B}F�i "�+�.�eE�]�1:} �f:(!$<2��%2=(_UIS$.�J�, $S &KůVP&�4"G (iy�� i��*�#���Gl.�6�� �*�&vz �i+12�%��'�%��_{*�!HB�:�Ga�f�B�2��(� �Q� our*r >��=�<.� ^9})�W�FIUk stepA�a(?��A]�N IE !ZF^� j-i>�Vn����#b K^� $.8 in $CE�erM�s. %AG�*�j'I�E',9�nO�_\�C�# ���gd]|"� &[ | m/..<byt {t&. ,�&ly X=JV>0_�*d_wa|FX�"d .�w(t)=i�  +1)=j$, "�*%� = w� �9 n� , %;9!��ax JLC_w�7nE�.�on!�z"kd (�3A��H G �}B�a� i�%8 r_1= ��1�.7=2$. j$�S5��HB�w 6�9g>�.�=.� �:0Y+1,t+2�b[a=.�.��:�.7 i� :G  (D�>R)S e�3%b1!���dU�.�.�0." m� r_2-��F Q�&� hypo4�i�"� A 'r_3 j.'). &� 6e �a0� ��4,r_5��B��ˮ:B�r_5 r.��CNol � BPB1>�!�Q mpleo��ZU�~� R1}??�arAT"0)6�&B�9 ienc��n_�BrsVHV{. �u�? &a*vo  2% %it&�(F�+f2)Z&%Njg�nb@�� QM��:e�� .$�!uB������ .�~({>l%�� f�:�af2b *U �Nd�  2 � +2"|�hR�>&�0�;� 5�sG����>�a+( s :�>=$&�� "��\:�.dan,� $i:=� N jX,�`��$i!I�>`:�C%� 1l2�1a��{N�f1"�%.�inft.*,A�,"�_� !k,hq �$t=(k+1,k+2{ �<��$1F&�_�O$rEd�&-k)rr!`@+)*_�!(r-*B�F�x2ɷ:A&4u *d� -�W �b >%tI�RI5�zs:(2� �BK =�+J�rtFLr�� [^or&[i�u�:�i0uA�Rh = 2.jsVh \,��j4} "B $c=(c& &c&;$z!"��L�NsK� "� 2,A�ae�4J ^$&� �" � } c_!c_jNB .NCc�1�5c_�j� �} 2 -� I�Cclfw�a�>O����enOxct�� arC\ � jlTL ��xXR�4>��Z\b)�be�K2 K� � 6�`w & �({o��|z�$�tu��ab$H7�" = >�Š Ve.���Q%I)mAO$na~By��Z� j� $Q'*� �'F�{�+� {c_M>* in[n-1]{6 c_n!���l{kGmax \{ 4 5 : \;A�}=c_{n}�*By���� J [�[�4�� $E�1Uk +�a� 2 -�NBk%tN�x'�x �x��hZrށ� Hmaximal��� E 6.jO� Y#t!�P��"�6Cy$�z�A� ����zired.9�[g EL2 �<*-EA�C("|Pe_�) t=1,=_+��Q'_-$,�=s��@hez�#f.$a��� �u�4rger :�� �!an!��E�(i_+,j_+�Yg(�9)p &�'��est (�[s�+A�$)� �!��+!2ndV e*"m-,j_-#--sll�+E�(8lly)^K thea��? �X!4-64southw�!+(is�t�i���vRl �W$!�pc�z5{"��.Z� Cj $2$ � 5JM,� r1�G a�>mok rner�an ��e: n +1��i_+ +1, )�to�CmA�R�s lI9tA!��an shif���boY_+$ dia�{ly (prep� ��Q� ) until $�= i_-�{:�$ $j_+ > j_� $). D �v��x�4%discu�CisN2nA~pif&W-Mn%�es3a�&l#w6>�%A]:�!a�2}."�5 2� &�#iUR4�� &e3{�3&���S��T�CH s.CE�3BB�) � �:} (!�J�")e�S�5i��byR�."�ed #< $�$^ 2r� 6�*aj ��6j �2���A��7�<��bij�u�A�e�H�&��C t2ox/a"R�as �Mu�N��QB�F�i�� 2%�%y1;�|$)(�!1!�g3. %Viewa�f9�a�2A�a�@a2!�+e0,M[c."6�-�)�'Ce 2P-'O-��6�s �ebT"4u�>I�k A��1�5�]I \%�at�}*�� �7M�}OQ3+�0AHo>5��>re�š:[�Fvb4�\i� () � n�g$!j"�.Y�/ t.card}!.6��l$l������9 �:��)J��| uT6�GN.(2)�:!:E"|,&�t !ob�==( . In>FNO,�$Z#���&�,2QQ��5?�*}�ay�F�EءuEh�  /~�RQ$�3�s_ :�"8&\ j/x��"3+oE$i�-%��7!�{7��@[.]>1� a�.�ac~��d=�8 �3)] e!(A��� B�Z1�Ni|>�| q �Vx' �ycanxb� U�� v: $>j{I"gA,U9*U9si"�%�paři� &��e�qxnP+ny ]Q�6\pi s_6S��Q�A �"�\A;_}9+�>�*�.}=(�8�( �Y� �U��P1e.78} &�z�" � \pi�!}}:w���%�)  =6)w�(i)V�(i+1))/ \cr �o\pm\,(f[% } - )Hd #.�9�aA,I��``�V$''!nEX!GA�\p j� �'e REl%�2�6�*%�J�D$1�9�ŵ.~5�m+|!{BplBR�u��}S��ean�a�)���y a��$"t}a�iK#�HKowN.�9)N!{:n4 .1uv_ (5)�~ =aus_E�� A�!5i�"A:�� Z�e�ABN�.�Z6$ si}��&(t*�1ɝ��9}�O��3�en<ty .��by��bnUm!�p&9�(E4!j0�Q 6�1s $��S*� a85r�����F� �rO2��Tt.3�) &� 6*� ���rw�sW�4=]�K E�Y=��S_>>]=ND �R are R?�N}�>e&��%[ C*k}A � I�^> ect [>CD[Ctor�5�=?�]�sd;!��vexity = "�B%2jCorollar*T~. (�m�>Y�_Wvex� ��a��,[�yCthe o�! �2gž.AL�)�Y�A9�� i �9T(.*�� < j������\��C�tri,�o�$f$�6�| ���� �!�&� �aQ)� {St_�n!S_1ny� lEJ����"� $T_U�7 %T*e s(T_0�M G>�� Bro&/+�i�)� *�i a�j� ? ,I�$1%��� *�Z(D>C� �Fs�a .��Ecd k89�a3 ��,�T!�^H)0� * )K=J��A��<)� ��.e.�& I.@BEH�-#}��*�/iwd.2��!!� s5#� Hx�� ��E�� ��� e9C�t]*Siv�Ir�qI^#:FF��� e��"L�TG�4N�bPl\dJ�������\C �Te�B}F %6-7!\�s!DQ�2XE�%fa� �4s"� \C�R�g�� 1 H+ <)vd�ed�8of�b�n"/�U-#HvJ"�I� �:Xt�ory�LAUF|&}� Q�X��[B=RSKD�orithmi>�B�.�;f.�>i extremely���[� �Jsh�z&�$-w"��z <>�4��s$t Z %7�2.A�p=id��w �� E�Q� 22a�N��"�6id, i" iR?�# %�%^��!/j�} �]<2��e <ma NL X!i"d3&, %� !(N� 2���>j2�%(� &��\��AA O$)2OX��.P'�Q TUion�bJ!J��FV=�n �fk�Ӂ*b2^*� .O  %$id7 pi_0%�_1�7�J!j_�h�.�/j�$ {j+1 �m7*ml)"I�_j� +� %($ �[8t$%(B� �6t!Up|0=�6yE�Ys)*q' )qleo�incbo�;!�u�K�oed�b&Y�;"��{}�Lmap�o=-4phi\circ c_f\ I� %f�.��.�f RxaM a fi���qB��%. MQ5 $AY$�M�2P��AZY*�| now��j N.� ҅e� ƅ:h�2&1f n����\C2g�\*LI�E�Q�b}\�2��r22��J��>FD%�:u��� Giv�Uq +e $f:=�e��J:I������1e�%V͍��H���xB2 � �hN� �0�%)��d�vfZn�RZ� "�B�i7" >��\Eh �t j�d s�'aX�?+$H�.� L����bas�g6�d�(�aD�-T f�� �L`�(mL$�5l)�, dueZz�[�W��ro�6�I_y (1%)6�%�@ J��gſ*�N.�:�5}� �lf S3E�),'�n#�.T� 2}� s �X� ��re look; for"� *��a: ���YOF�G�"�JQ�$s explicit� rQ�� �Yo ich� de���k!cp>���$USpI�DynHR� .�T%�-"�}sL6�- stru�<(-���ir*q�� {\C})-T� �"nv Xal2'f n)�e��&XAM�/�!N�N�DE/&��/P, ZfR{B�bV6`PA�iNY1"�j�b�(s��� You*�Dٱr����"iCw"�$yof2}{(\bf D:`A� S�W�U )}\\cN2�b��V��i �,Н�\J©*(�!�)P�d�%1:a|"�  �=6^*1v.:�"A�# �T[bi}(Q)=�� %{��\�}Q + \�2i� s_iQr��%64�N>� .�,��B �:=c�-cQI��hA��� Aw-uvT $f"�Bte*� = z/ AB�  :NAM(I��N� Q_0i�nJA�>O (RP, � �W�� s"�r :#��=d�%AM:=y�S7�fA�T$-^�A�,A�!l�+0cae�oUz Qx� 2V}ݠfrv_"٠ \݋"jn,\, �in {ጢ1,��B4��3a A&Z8n�\12} %>3N2f}�w�! A��" ~�.78}),i2#���a �, $h(i)2�P_i$"1bF� ����V�k J�&7SR�Ak�!U��?�����x2@ {�5�e]����J� ���=�^�����:��a@a7����Y1�Ŷ��X���mq`I &`���&x��m"[Z�}):A•�irr2}� &�l�H��H��H��H��H�RH�!v&��R%On!w �A3V\AQ>T&��&U���a$EB� .� 6�B�Ɇ��+ ���8�*S"� aIU]a�"tla�!o����|�-V{ Nu���1.] Q8#Mn<.nN>��:� F@x%c1�!Z��indCo efer�3??�!O YOFaÉ��!� d %compar��u- "�bUIr� �s R*[o�x��g AY} ,� 6At&�'�T�K"(%-�ind�,*• �dCm�%��JXJq�be "�k� �7f ��: (�K}3�g_SE"2,�9be.9XX�,_ _{J_�<2gs i*���W^/2NJ_2_�!� ./vc2� ��� &�Dpa>���x:p� �Z L �152 :�, (% 1F�rho_2)"݋_{�1}�\2}}^W_i>.!?E���le�R��H�&|!2�Q, =�1ϊK}_2,-� � ��-_6[F �%6}�= =��eI�.�� 2g "!�NeZE�"ܥ������5����U�,1!r�,��, �>�&~ fi�M��"h l�$1sb�t�'�P��$L�6�b�4�De-(S_{[i,j]}$ !��e�!�i>Hi, h6 L �!? T\�}shuffle7#a.�"`S_{[1,k]P� ith >&�)�n+E*1tau�0� E��"�`k$� �/aq(\tau(�c��c �+�Aяi.' pi(kd�\!3h� Ln$ "vjCjA]��>J �� !h1tU\lao�t-!�� ���-�� =>�$ $.�%-� |\ P&V(V�$$� ZR�)�{1��"�+!��� &]2M !.�4}�@�:1.�onJ%pou״pq� $("���S.��H_{S>̭}^{S_n}1�!�^< }j$\Omega_{k, v!�9� .�$&?ck"��AQn) -.P {A�)qA�(j�L+18�O�j�*;zG�&RDJ.j&f �A`.sb!>�z�͠�aCi�n!���l�3��%?c"x'� 5�$ *NM�T���c>Q�.�C�N��Xd}\}\cdot \Omega_{k,n}. $$ The corollary now follows from Theorem~\ref{t.cell} and %LemmasiN./Pirr} together with Le7�ind}. \qed Denote the set of all shuffles considered in C���ind-symm} by ${\cal B}_{P,Q}$ andYpassociated AY representation 9\rho$.�>matrices��@Coxeter generator0$S_n$ on $V_{6��re giveld \begin{cor}\label{t.yof-! For%$$1\le i< n �$\pi\in 6\$,!��p_{s_i} C_\pi=\cases{% C_{\pi , &if ei%�N(i)cDk< \pi(i+1)$ \cr .&or -+12/)$;-L\frac{1}{\hk(\pi,i)}�( + \sqrt{1-J$ ^2}}6�o�wise,}�where $V:=c`�)- D))$ in $P$ if both �)$ !� ��!�$�$, 8Q8 >k$. \end%�� \noindent{\bf Proof.} Use Remark~\refA�ucAJ1}I�$W=E�and $J=\{s_1,\ldots,s_{n-1}\} \setminus \{s_k\}$. Ni at��=mr$, -mA8S_{[1,k]}\timesk+1,n]} �r$ is a mC�W^J = .,$, then $rs_EZ2�!&only if ]8^{-1}2= !h M0%tEd )mh,coefficients�a]A� �not�2� !�damined,a�^�2}a�.�tabl2��FRyof2}[�$ontent vecu�Pm�Q$��8\medskip We wi��ow �Vt!�Ksub��:�\ eq A4 %�minimal�� cell! $B_nI n�mLis naturally embedde�$+ as a maxI parabolic��group. % In order to accomplish this goal we have defin��aE� of %�excepaalF $s_0%(��pro�� B-AY-yof}!��r!�a= :�of �q2!v�,simple refle�s�i$,�q!fis]f aA� C>z��e(6j�:Fby $$��0Z�}, ��a�(�r�j-�0�ȵ,.�,��!X^�ByU�iesB:��it sua�es!�verify �rel�8!volving �(. Clearly, �P��,0}$ commutes�ٮ$ f�� i>1$ sinc��ɲ(1)��p $ 2* . To �!z � $(^0} 1})^4=1$.�$check four�ss:�$itemize} \ [(1)] If1�m��2 ţle k$�n͂���)� s_1,invariant una{5 0}$; thusb�2��!rh%^1} w.�2��>R�A 2��veigen.�!�� ",alue $-1$; %$�=- cA=%#�1�%aga�Z�9(-T!� v532-���-�>-� 2�A�= K2�� = m�)�,C1)C� x5�6M Q�@v= J0} 1u 0}& 1�R/ w�=# =5�G Hence,b�4)31:. mY4)]c casi�(1)E�=�-�is��ilaũC1(3))is left���� ader� a�i�g We deduce"� thmՋ� AllHirr+ibl> � k8classical Weyl �T�}e/�� �mZ�8 As before, let� (ambda$ be a�ti�_�r$� $\mu$: $n-�< standard Young �eau� shap!qcon �,letters $1,\� k$ !b $ P bP�6L $� Nn��� �n� bij� between� paiU �6vx�s=+I7� elemX  i �d >{ $$: $(P,Q)^a�\longAN$rightarrow \inv$,� /��!:B ed��-lx obta� O :$� replac�70each entry $i��# a �Orthogo_ Form �� ProposE ��"V E�� the Y�on�inh& B� , a!  5�"� $ %Abstract �6� e#�t types (e.g., $B,D,\tilde %A$)' be studi �0\cite{U-III}.� (particular,�Z be %show!�atE3��0Hecke algebraaK%� $B$ may�construc!Zus!�!�@AY method. %%ExaA �interest*B4r more ?? \sI�{Top EM��{s.H } % � {I] valsE� Convexity'A {\em�vex4} $\C  a poF t \C ]h P$ suc� ,at: %if $x,ym C�(x=x_0m�x_k=yjQ pathq�0Hasse diagramA�4$P$ %(so $x_i$mcov�[ora� eda$x_{i+��&� 0��i Dk-1$) %of smallest�s��lengtheZ $x$�$y$ %th x_i�($\fo# i$)!�F� t!� _conv} %An te){�>weak BruAn)`� 2ex. %*� %To pro3 E py�~ rec�AVno��H4lized %descent�^e� %~e$[Ch. 2]{T}@{BW, BW2}. See %SI9�0s.prelim}. We��(ll use Titsq� %(T6�tits})3 also8�A��^7result!YL��TŴ.A��.m � W���AY� T$ %��ny I��(��)I� $A$-1$ set}cn� $w!� W$ %� �Aj@ %$$ %\D_A(w):=\{Z8A\,|\,\ell(tw)< w)\}. /F�D�2�<>0responding %{a�g%� ��z}��(W_A^D := \{ � � �=D� % %%"X Thes&s w �:by)�EY(�;8Bj\"orner-WachsT�eU? %%Our no)�s M{BW!�e��? +AtIJa�aa sequ !�p[Ml 2.19 A�.A�e: 5.3]t� 9�� 6.22>q�Z "HE��(A�)a�MN�%#W�i�� ��2��إQD=%��sui�� cs %b3�)���b��0des_diff}{\rm�of�Co�01.4.5]{BB}} %�IE� sA�S��M�M�s)�I� \D_T(ws)=AiTE� 6tws8 \} =e> T(w)>0 /. )\} %\cupA�sw�0\}\qquad\mbox�(disjoi ion)A e�end%!Fz!] �齽G��[v,w]��an�vaD��F����ha&�# $W$. ByNv5�, %�every��u!� �=qv)�O%�u) :w)�O�eH han�= (ref��A ??)�L %N��%h!���\Long%2 �� � Thus� �!g$[u,v]ea!ob $iG %=$D= �M� A=(T*"� w) )I\vH��&� ti�qpler�pr� % % %!FVq .} %�uru] a %CRUu�܁a3� "� 3.1�+B}�@�_des} ɾw_1, w_2A�� w_Vw_2$ (i�&���)� %��!mw_1>�w_2%�y�%V+�, %�. �,;I�.��, A�RfW$:icU� E�6]��r���n��[isEZb� %M��� �A���'c V� Z�E� &>( %It should� qh>� strongB� @ %not necessarily�@� ��b} %Chaerize� alI]s8 �}�1which� �are %�a�b�"_m�G�94x1} %%Thm ABR1� �@p. e+U1}} �!W�Vply lace�a�z n�G&��s �eE�dEi2?�VAK�����T APmotiv�b�*\ rmuv�4t���Kriloff�$Ram, based!k� �Loszoncme{LoA -��9J2�p� 5v KR}} 2?1}S %*� �{v Symme�" G��$ Revisited�cI9 is�\ we addres� e ab� openA�$blems %(Pr Ip.rep-A�1� x4}) %u# ��2�.a i-irsCb �]�E> 4 M�6$d. %A solue�oz!����sxsecond� J!.^�top� �. %j�{.���Qa�_Sn��՘df!d.topADef'n:""�% 1.]""�)�d good�f %�������&���!�� ee D*0i6}Iŭ�[2~�6?f %���:��b�*�q���iYdf!ay�5Iar͹ p.x6!kM� 9::�)E!.�rJ"������-� AFI#�A�QU� R�V�"� carN �Q=�}As6 x1q5�;%��u"o�!��m o���Z��.�row�Q 4 skew�tab9.B� a�!%5(column)>}!`A{T ��ie�W29�larger>$�Q1allcex:sts �2.]%S���0 $\, �&s&�by reaN $Q$ �owb� to� %)W �Z 2b> !$ `bottomatopY ŅY"�exa2$-� \[tarray}{ccc} 1 & 2 & 3 \\ 4 & 5�(\\ R + \]I�� P. Its!3!�apermu",$[3,2,1,5,4]\S_5�!^ �< $[4+2,3- �� � ��gg%��e.�(>��a)��. �� �atRrea&�"k2]a���E�u�|se��M�(explicitly:uT2> s5}�m 11: |(T ɦ \pi]z!SIW.� ��)2 *�8 for A6�"+�e��>�-���.��%��b�C" }5ES!DIx!0 6'=we ne$ .� l8-*g�.� \lN$ m!� %$�� fixed SYT�& ��EU"g ��seF;'} :�AsB $P=Q^�"7�$nd $Tsigmare twoJX4R$$P\le_Q T$N�" S�!�ZP�E�"o.is���,$(SYT_{\la},}_Q&�!p"tle"4"t.s7} % ;\la9En&� i����b%is�zorQ����ouk � |�1�f�iVA�\\��$\-�a0�=� \h���}\}� 2�əZw:��(e�.id �!6� �g�*r� !�"� �0;(�� ve�(row) ��Se[�T!OZ�# M% $B_Q0�Z|\ F(�.) . F� ,a���easy dir� on. m3 ,!Dž� row 1|:�� L2qn J�main.i}�!_ at�� �%.����i� &"*�!�� re �unique5��w�2["�  s�- $�$ \D0)$"de�-� �Tas/!�.n*-o�:g!�E�z�F#�&6(��16�G)>� �{=69J�}MI��% � � ��F�9�2��! B�� ��W!�ncluda5�MF �um -�%��.��V��/SiC(lyI[>  %&fNow6�op|e��AkaD F���$u.�d4$ has at least� �alq:s ((��, Zx)�:a�u��ِ. �,!8��:�! A(a :%Lˑ�An*>�0d�-g4s. Without los�=tyBl�( $2|�\F�(i.e.,boxA�,2)$)e|�1T�#� Gin (\la'_1,a�is big"U 2.� fi�he lEd9x,!%rt������)a�pa����R M��w �,Q- proc� ``up"�%�. %LookA �co*c"Px���m&D stepI|$� �I, multiplic17s�%˥�sD 3.� i��~!(er�/satisf�is,�[� �)csA�b a same!� or$2F(�4at�wg!titut�*$pi s_i:=\p�% Also2K)l\!JA7�� 2n must�.4MM7�0 �I� ��1��Ke8�(E��R%on1 subM(�siQ(��IFsa3@ioneius can!]m��)eI[sau�N *�#:�6 Claim 1.}a*�$jR"� j iI+1�$ � >9\ -+$jm�6�0.�.e $j� e��"� uAk$(ja�;�.k� '_��-^�*&�$ � we&�!nB��)&teQ6aaqfm�1,...,�M)�)�:~As��ht:� "j&���!9 for �A+-R��j� _j)$!sE�6�4 4+1!He���#Bst��a 2�nm�&{75 qZCI e��a%���)G �s�- ,%��.${(a,b)|\ bM8_j� n lexic"�� W1� ��tFY re ��~per�"c*'�� JW�6�a�/; namw by No!2�oA�5v�N�o��2.}4 � o;xe9u-o M�j\> \la_j-1�/re loc�"��)!0��1%b+io�-$.N�)6�3`i�  u52 6�T*�5�`^w A1�� � �y��n�IndX �+c�Yas��!� Q)+Qx�$(mn6)�^%*I� 0u�(d8t���switch���(!��!�)�isNeQin.X��=A$). Bu-+p s9bE%�Aq��4�p�!in re�-eij��us��0B%� Q$  rt� 2i(~�>a�"!�-W�so1"rC1eX9�.n 2�� �8Ij.� �-� threŒo. %�E�duraour� ssD2!�2)�0 (j+2�r-D�=a_j=.v i�O2 +&# $�i�B� asQ ��!+"7I2� them�� n��� -�,sends us outE&� . If J��a�N�� N&��N� Z�So,��1aU�.[+& )�.I.p?2�X| $jb:H)��&k��i!�i�S%) s lP� 4a 4%+.q���$turn, %(by�;), NN�A1�!� )�:�1E{:,!.��;"?7aGll�j"E!T� m8)%7),2+N � i���^�0a�� �=i�B���� 1Q�M�� � ��sse*�= J8-er�? Iz x. \8�Z],>k5}.} ByF�=irr2}k derived� '@ ";!�a5�~�7/\�6 give7.I>�>i:J9empty&v!3 is f�52 AB�=E�"ii�hK�ajK s�]�<*.ZX���Y>som 6a�81�� . *:F�R�( )� \big�0:�$Acknowledg8.D auth�E8thank Eli Bagno�)@ Yona Cherniavsky�useful� G r�/thebibli� y}{ABRabib� &L R.\ M.\ Adin, F.\ BA�i q0.\ Roichman, cA�f7c���6u C.�(�r&�F(s (I)}, Advlpplwath.,: appeQ7arXiv:m4RT/0309364. %p�,int, 2003,\\R)(tt [(0�II�'����]A�*�7��I����ar�B �%�%��! em D�5! .n�]^ tE�t�cs�,T�(�mer!!q\ Soc.��%�e numb87]aj?7ndices(� 8hyperoctahedral�%qF�L~27 (2001), 210--224rU�APRB�0A.\ Postnikov�6� �On&�!�&=� Discrete � ~226�355--3582�a6%Haarceli���* t�(~I�6�!ory!,in: New Perss�XGeo�&I0cs, %MSRI Pub%Xs Vol. 38, 1999, 23--906�$GG} %I.\ N�ernstea�A� Gelf!�S.\ �Schubert�%��Shomology�O!spaA$G/P$�UspIT�Pauk.~28 (1973), 3--266�B5�j\"{o}6����2��sw(%�Sp er Verlag�^\qnBV2} Dtarbas�-nd Vogan, \i�0Primitive ide�:orbital �grin� plexi=�(s}, Jak�;~80! ,83), 350--38��W} N !�/7��G*�7 quot"�H1} f�~30%�$88), 1--376�W2Z��irPe&�"s�" sticI50linear extens� ofAet%�J.-�a& Ser. A~5�9�85--116A5E�ourbakU#E�<fMa| a�, LieM'E]-��Q8-Q8 Berla3200!���BH} %BA< rinkM��Howu , %??2G0Deo} %Deodhar5�DJ}?Di�A�G.\E�James�|R2!N�?> ?>geNl1sQ�5 c. London%.�� 52 (1986��0--522�GR}��!�Garsia�A�Remmel �ShO!�Ys�)g e Kron�>�duct}, G�/)�6�1e5), %217�.3.�Geck} �eck, %H Meinolf(F-LYON-GD)��6inw��8Kazhdan-Lusztig��}, Bul�)(\ A>� ~35 ����608--6:�Le} %!Graham%-!ˡtLehre!��PCellu=D1��6Inven�3x ~123! 9!�a�6�Hi}ɒL.\ Hill]�J��� �Re��No�6iM ~54, Pit�  Boston�\��Y�HA�P��soefsmiA��^��AfiniteM� BN$-"^C%c"�D A!PhD sis, Uni= of BritLCf!bia�7:"um��!�E�umphrey�R� IntrE�Ato2%�6����B*New-York�aDu�,Greene} C.\ ��A  al-fun.i�Oit�({2d�sDMurnaghan-Nakayamao ~3#:�Z$�v. ia.EP2a�35--255.XHum} J.%-R"�LMK%"B^(Cambridge SAC�� I�29,%-�P 0, =!G�5G Ja} aJᠩ ��+R�A$:�0ahLecture>682, B�197 �K:�%� Kerba�%/��4}, Encyclopedi D)0^�)0 ~16@ ,dison-Wesley!+812�Ja��Joseph, �Cy�Ka��.\�, %pers�Mn�j ."KL3 �?�!��G-�6�e�Q(ɐ8ż�}, :�5��79�6��8a�5� KR} aT.j6�� � J�graded {�7},+|~ a$31--69.Lo}���6 �S!2�)x�^A�&{ �e� |~22 9�2} 266� ME3�D!l Macd!�&� "z3F�H-a�$Polynomial!c%fed� , Oxford e�\ Mon(�# 6� At92;OV� Okoun� !�M.\� shik--4A new approach��R* a�*�3�Selecta� (N.~S.) 2���)58!�02�P} !>� PushkarevM%�*t6�E���wreath p�16�� F�0 Zap.\ NauchnJem.-P�(burg.\ OtdevMa��Ins@Steklov (POMI) 24I$7), Teo� Pred+Di[i Komb.\ i� �oritm.\ Metody.~2, 229--244, 294--295; �8io�#E�MDSci. (New York) 96%hA�359� 59a!�]R�]!ia� $SeminormalN^yI�Iwahori-B H3c.\� �oc.~75�!99--132�Ram03I����Af�E� ��%�geC ized� �You&�Lx},�(A� 230" 367--41A� ���b>� SkewB�&[. }, C�Umpa��~32&� 161--18:�� �Reutenau���FB>� � .Q2 �� 27,�:199!s]��N�I"� a2�Jri�of�X>� <)134%��384--398.� Sa} � � Sa�)�ᓹ,G�8:��r*5,.� �VleEhms \& >�j,}, Wadsworth�,Brooks/Cole,�Q�Ky, CA�56�Sc� -R ,Sch\"utzenbec3q<La &n%e�T(de Robinson N� atoire du �e� que,�/N�( 579, pp. 5a913V 72aS!�w SolomoBeT!b� � ���$ Chev78y�J%�L~��6��376!�6L Sta7I7c%,tan�M�Bin��R, MDbiu} i� Ao*� enume� �)G.\�oryA�.~A 2�z7�3�566t�?Z�Efve ` ��~1, %�B8|�XSt2�2%��y2.� Z� 62%6 C� Eف��_sign^�SU�"rks�1,$-balanced !�majp=NA3G  \� � $2005), 8802} Ste� Ste� � V� }� h ��T�Tit %] Buil�6E�SpheriuS Type�F� BN-P7RA`Zu 386JryK2Z6�V�Ver` �Lo�XEat m �i��'s ���QI@��QTop�in��(, Banach Ce��2�M�26 PartAX%PWN-Po�[SL] ific:5Warsaw�: 0, 4�67a�1t:�  docu�}��={6QRes�Q}�2=duce}�'e 4� o*A� bii�al� ced, for խng�5>* to�:�\s. UC "J�+nalogou�Z�' (��%B.��~t 2>�~:�F1]��obs1t.i1}�3(W,S)q:���system/!OP=\la�T J\r �/J&2JJ�6�]Az�J��t $^J �A!sfc.U{of"�*l_Q�]1�Cc�&]Rn _�4�X,\C��*AYU�1���n�9�9 j[^M$%� 6#Lv��aA $r_ic D}_i$%aKR-$�]r RW! |_ 1A �%?a�$P&�X2)�X"> ed28�c{EY\downa4V}_P^W�isomorpEto�d�3 sum $�4oplus_{i}\psi^8d��a-�sum ru" v<e 6� n (1:��BF^��. o%p!� on $"�d ��8!�)��GA�>p.c$ Axiom $(ABTequival�R-F8BQ��Wf-A$(A')$]�u@J�$P� i: y:�-W$ Y. $.G$�(PMO\C�, ``E�OBx''%$wP \cap \C7 "�(NP$\T(p&A�$pO!U%05> (see�J�/� 3qG�F)� �<oFH�3J�A�s��F�foA�2?.�!t, unlik AI�:��on rul��rB$6A0Fv�no�)) ly:P,.�.RdiscusV a�S:7D��} belowM�%  2YVurm&�7b�Ji�8�M��8!� w2s,��$by�T�f�T.|-�Pr�J3.1�QV�dby ck �� 6��fO<�} t.i4�f�^y$ $>^~\V[� t $riD$ &�.A�E!��Ef �С(^�� D}�n�H6<e�P$�'�itoh.%X $W^JB���ah.Jb�4�-e��Vq��)$(A�, ܉�.� pair!�8 &n:q�u�\ ��� ��y.}a�~ 7�a� LBvi�\up�s ^W_Pe^6sa (��)!�.��6��}V�Aec�ec����,a j`3a�#xf q4�s�((*� �em%aRp2��W!�p�QA=:�'i4}5)shA!F`? %1j �]�gon: er?)old n(us� BjoH!bW)�>��!:u� lattice}{"�N � 4.? W}} %�Z[ Pe;� "Ge&,.� %%cB �)", �  AMS 308v 8)],)o�;#Re�L�i� � a�6(,myA� %co�!$te meet se`9�n*�8!�B�A,��(�N�@-%�(i�is) ?!TU��!SA5S� S"�?\vS���ɖQ�����_3"�S�hu�igi��an zC!Uult (to�6 used!2e�9��nUt"�V B<�*X�h�s)=@Sw) �U{w��W un�WHe"�WSi[�l�ng� -�>�*~r)k J=\�*setA,2�6��N� fact �rz �wE�r'@4#mL:�T�� %in 5�j\�(�j cor-M�O�� �J*� $.�R %�, $s,t�SD/$w_{s,t�;aS long�>&A � N  s,t N� %Xr�1H%�**7 %0Z $vU/rs� rtv.I>.*~j��T @ ><!H.��u�UM1��AC�[� tI�,!�6# $ (ha$v=$>� �BUei5�� . 5��� I�a�c "-*> 2V��!e�!�I� "�\ be a�N&`l" rMDM�:�4��Q u [ I��;�> �nFpg$rs=pr&�G� qS�f �93si��.��P� ���!� ^��w�Ars) <�Ar)%VnepN�C��2B�s) = )"[\{rsr^�q\}>H\c��r: fore�q\in% .{Dmg a� ao�Brx2(r �� ��up.�$< �-}J � B%l!v.�s$�e�k9�V� �inR1� �5p=z$,] c�<SR\2 %V�(wg+3�� E)X %g I5j=of$o!k� �spB. By� ��"e� = M*)=0&K�@$r=e�wl J cleo holds1��!� %�-N2b v8iuja� �~( �us4]^s $B�NŪX7pA�,1= 5> �_k3��BR%��un %�B. ,B{l%�mA'Ec2FTFrs�RvA�n� % s P.' . %Oa�[x�=a�aMY!G1a�s� oge.)�B�V �+ere %2H�DS$&GC rsBfBDIe=pF %s_k=prO J!ba!� �F��a0i# s�k!iunoX�6�yc%�=s1��B> �a r���a�= ��$ d�Y.qw�qN;�$ wpAP29"9B=:M�. <1� B�2}QJ!J! !��y{k�v -�If ]� \C'�!u%Bv.C�qA�y��#UY� ��_Rz�.)eJ� ,O�> # %2th#d@�:�N{)zAt last�OP�.72��9F4m�>�� i� a9:%[b�&� � %.Z F�2'Q�=Q�9�.�^.!z!� = p�F�e�#2R� ��! \"0; L� }=�5"�A�� � bc[WR.{\oto} �[P]} W]�ithwais $B= � / rF�, ��\2 �aɉof0vI� P�R Hrho_s(!Sa)=.s mi(�n�bS, �1G�) �|�S">ry.v:��v� � B6Y:� L�6: i5}, � �eo J=PI =V(�!��e6�@an write%Xpsi_p!Xtz4a_p(m) C_m + b {mp�v�e�eq�ay*} 9 9� &=&I�qZpr =\cr) .� r =.�:� �.�2�U�A�nat@~ bi�u,$\phi: B\to A� {mr}:� D]Aa�gڂ =!E�)�nCF� now have3V equ��e.rho=N�!�.ԂmrK.& �;!F)� r5"$2:}%~ %dD6u !#ŬN�1�� ��Ev D}W^J��1: |\ 2�yz!9is AY� "R� �A�%|W�J%V�}s��2O�g conn( vity OCell %vV�T�BfJP�\;yRegarq%b: i�DenougH.&�P�]�$m, m'\i�e% r, r"� [ Yth�\G0 j$mr�sm'r'$�LCC���E,nonzero $b$-.H�!M�W\fF6?is�Dt�E,arts: $$ mr A�m ' r'� middl�h!.ac���\G(P,J�s�TA�Hu�idA�2��p�qq.id :�Z J,�!�t%N�,T,B!�0of (mis��0^13 A�� "j$ clos�"9���W %(�j�lso�).�5*�dR�i 9�l4:�sT��zal2$g�: a�a7>g!Fa��qt�T&�.�F�#�LP�O��8%%.+QV %� J��bbe�|�e(f�fin^�'-�icG. %XW choo�0\ne g��V*>�o�g, \al_t�=0� "� �=e\C�h�ZH{^Ks.t. } in %\h]span}\{�r|r�6}\�|�*!�poIL�) |]al^=$� nYQpac Vx#��count�d (DA+l�?D plan��s9F$FJcU(�8��+ . %Cf, $f+cgI$\C9���c! \bbr���^{5� �t�' %�#rho^f$ mԉib5!8M|� \�|� "� Jt# $w�k)�)A5�p 6�$e�y1u�c��� �x%ls ��+ Jat�+i�+!A!T�BnteMC$n&_a6|eJ %%$gv��Ip@a_s^{(cg)}(w)={1\%�QcgE"�} � }= %>,fZ+�l=\pm 1�q�wy�%�J, !� {a�) ���9�y�:!I�>ztly $b�g_n �0'�]e`��z0vJ�.g �\C�w��$c@\infts~^�-�,1$:(Vi�M%�>!Q�^{\mu fa qP!yl.!�r9�r Dx �\mu�!�\i�e /h��e� %>����V36�!�.�$�$ �{-�s)$ $n�)!�%%Ft~�o�^�,{(�E6MEhW)�en�?�Y�e2�"� .Rh��lla� %�z:�s �f2�g_n�U%6�%u1� 2-$\lim_{n%�ES}��^ Q&�*�%�� �"�n�)f��R�2")�gC2o$KW� abou� �sQ .��J$ ??�>aRed"D�p�Ã�c.��i3s�0aR �:(�&??)_9&lfA�Vy$Wٞ!]71���� ��, #tDT�!! 6g :K1c %C)W%k6y)Cr-c:=A��� ! =� ��-�'X�-�*z$�� e �!!V a� $S�}ӡ�� sub�ftl�S �� �8(st)^{m(s,t)}=1��  $s)=�R 4t)=m(t,s)\ge 2A�ce �#�In : | w occur�R2$sae mak� c%�n��_�t)=iXJ)� called a �$1N%$}l 9� 3 ��sA8t�n5kisPN*  lSx}� roug�`� s pap�e��=� =�i�(�H�E!�� elf�X_� ,9��R�= } (s�L��!�2yic�6E JH}_q(W)E1&%6/*^Lak: Oat��� hat{sN�=�2�8iN��s� ,,nG�Qr�W}\"| _},%e.d�"med_i҅( x-1) +q_s)JI �),m�[�tad�Aa�(usual braid�s:atwo�0tinct� %&�'� � �0t})^{\lfloor m\� 2}\r� ,s}^{\{>%}}�� Wt Ws�WtZW; �� �� s�1�!�~ !�Z� %(il� fag�n�5�� tH $q_s�s�d�^a�eepe����� conjugacy $ss�\$WZ�!�e����" $s� �"�THIS IS THE GENERIC ALGEBRA, SEE HUMPHREYS, CHAP. 7} \-��ience{-�F��v"o�$q_t:=ա�L*'$͝; %�0in��nyYZ (B�~�^�o $�f�~8 e̊i�!T&A)"�$2*����s� -qteE(O!�p3-oneaN.�$qw V��� ��n" Wn at mo6g ���V,:�to�)�l�3G=s*+6� Cayl@@ aph wh�sX%�9): @ve���XJh"�k)���!T $x, m�W�x ���A�e�Ji: .x�(7%$\G�>und^91y�. A��$\C* )I��?%�x�u� ny� 8a��geodes�=(�� E%�-G'evn��"��!���Pir�^%Az�5�P%�Ѝ2�!p�2��. � n�'.*%Q�i|j%�ex�, �X�!�$\{�}b;n�s�eia�?�>kL%� $q .�=n:2 J} $qi,%+=w5n%�Zm �,v=m�BW %m� t4 per,iH1}6���%A 2 F�, nd$�G�Tq�>�m� E w<m�iff�,��\a6\ };,w1mw1#$$ &�.�Mで"K �.� ��>:p�N@*�h�Pb�Bgv[%� >��:!tM�Qa}�leq �����������Te�Ae!`� l@��+�O��A5> =��8e�D� {MB#am�$�.�A�$$a5D��?�*� >� dm[�R�W5��f<�$$�sT s�(� "z�7 {B"e�("� J%�v ���8��a ��S��[� �� �F�2.�g�-}�� ifB� ifa�n� V TH1�:1bW5.�}A_(�2Y� T$. "�x&Nr�Q\�B�a�A_A�!Z��w B" !� \ �� >WA��eo \simXV�J��eI�ɒ�!��eW� �tl��@)�� %alO i�$w$-���#d5�I>���l��se&)c M*� "� one��͸Ca* �?af� dele ���dg�{w,wsA)'2A�MAY�hm3}{N*;0� Mu,v\i��m�2$ u)� v%�5�a�u)�,A(v�&$x.���V�� R�>Y  .�Qe, 옉= Deo}�4c֘�UAus ^��^�C�(]-a( 0s\G)�!N��jbn *� )y!bi� ��iCe�Od+�i!B(\al_st�%-\cos{�p��}�"��8)��(�rp�_�b�cB=$ D�).�.� &�&�ɇ/��mapE�gma_s:V =!�e�\s (v�v - 2B(v�s)�:�EAVI�yieldUfaith�c $B$-rv���)atgmae��aon !G�CM � %�)� ��o.�s� rootYܣPh�"\{ �w)�)E 1 \.6V�$E�:P"��H&� ;[ e��s̞+ �.�}�"�2��rܟi�K.fs�e bis� �2��� TpN"3!0= Ph�G�( $t=�� \�6 \V =:W($ (providedE�0*w $�$*�e�$i \ ,\"x9�n a�` rary7 i�`E �[6�UV�� u! �o:UC2�? >n�ximLie�ory) �n�"!aR��Y D<)F (~����[\S 5.6]I�. %How� ,�^ Jr7� �dnGAp�� %i/.�+ %$I��al_{wt(�} 6H �4WHICH LENGTH? �HONE GIVEN BY (|) OR6 %BY9�,9� ?F A����rj."of"o \��2 6���.li��0mh���)h)`;9it��1!�!�Pr)hvis �8�uniwjs�%URqn�+I�5sAZt8O$B!k!lc mS��-zdQbn�.in our�r&�S!�ory %%�� ??�6w��Oreasoc? �) SguH^m�^ �a� �L&�he]�m?i f^, �] $s_iĉ!�t&au:��pbynterchang�$��z6SER� %�!�(��{V� I�1U ve"DsT B� BB,%�VN�-�,v_{Q^!�}�1*� � se ^��ltZ�%ly�s$Zox<l�o. S�M�t)l�;-�k/\mu$, h�}��`U�p t��5Chi� me�sa�}�G�#\X� "Ily�rpI*N!"�SA6���d�T:�_qp s.survey}���on s�Gn&sm�mai� '+��i��NOw��be����pW . ReF !�oof�* �6 hA� in&@d��=Qo=Ï�M.��{\rm (EJ �Ka}�EG�2a(�&�^*ImInon"} t %a6l>�{:b �[ _\C$?V�� p=�r�Q,W�N�d ? 2�K%J2i�&C  �q).(5�,�%�-0��]�e�.� k ��al&��to^i2D��SIqq�s.mB1l:a s0? rep}A~ �s.�_S���yi ; Q��2�rat�!1Qi m�Lb@Hv�����RMAt�0_Z rEE�:�Q3� Ever��Hk� v #hfA�&�3��<����"�fN .�����2�Ia�އA� �C�F&�1} �>i ve>��.�*/or,&Ctly9RͰwF7c+n .��)(w)Q#0.X� � $w, w�%� Importj e�evP�(� �)6��e� (M}QV�AAj��Y��&�bK!~As} 4I�{Main&Y ultsB�^Qls.? Surpri�0!U.;U lead+KEk�6] �')(ose"W��C'wntiJLin|e#.. ��a�} >>�r� e}E�App\!x yc1� mild�%#s,2�2�( t�E.+more �qi�Z�i ��!��� & ��n�� q�"�<\ ,[$(B)$] {\it@ ?"a!� x.6scalary ua_t, \ubd  db_t, \bbf*�0=;*A� So'$�\C$v6\T_�;w)�9as��f&�- C_w+q.{ws��s�G.��8 �.1w+�.C � a )$.\cro�?�"{/w�?:�&$6�=0$ (R�)�$6��Ff F� ).% �\!�hI1�23 ax.a|��5-��@W%(\Tz�Z�~R2'  &.!%��BI�Z����,$a_��0=a_{s'}(w')\tJ.b b�6\fo��s,s89S, w,w \C�(:�*$ sfvf�@�+BB.$szY� e �"�,/!X&�2 .cNf 11.1�w(.�9Aa_t�t�T)$&�W�!r"�, �#$\tr\T_w8A��-�V�<� � >)pa� r"�:Q.T��ev�.�6Q;��merely�_9giz$�|�i�V=�A�)6})�E �)�-��&O�.��|4�&+L %�w���#�7�x7It�~�bz&@&R�s� 6���tIN O_a�_ foal� ". Vari�_2j�+�MQ1��+ r���:*�( !G;��$),~T V1=�$stochasticA��<D����= 6etc.\ H S"�YD�oH5 a*�"� �MTs%+.,.:= . R�* ��_:�.�%�# $q$-ue $[} �3�. ]_q$vs>l\ a32��m�[�+ �`8."\cb� [12pt,two�)]{R cl���usepackage{amssymb} \font\teneufm=eufm10 �,ed \magstep1 &sev(7��J' fiveN5J&newfam\$ fam \text� =� \scrip:�N%� \defk#1{{\x\� x#1} �msb��$tenmsb=msbN � 7�msb..AF- .�A�C�BFI C=I : �Bbb � �e�renew?q and{�JfootnotZYfnA#ol{2!ORR{{\�~bb ˦CCC}} QQQNNNZZZTTTPPP� k ra{\5 a� cV�85�. %�HollowBoxx #1#2#3{{\dimen0=#1 \advance\  -#2;� )1F)1)#3( \vP`� 0pt� th #3 wid Th� ->6=#1B<3}} � Left�m��ionI(a� Tlb)IiJ;-�a�E��E)&KK1*�c�)BGK KM}.B��K��2�{a� homo�At �����E� $C^2$-smo������$E{. A.��r��i%�Hin spirit, but utilI�o �!�isotrop����0 poһi�F>��IQ�#)8 GK}.Y�in�* �el�E�Dk���Qb_unD�� OIKra1�4$Kobayashi-Gq��lB!VV�I��>eV2 w`V� *��st�T. N 4a9��Ž�F�ad�$)�m�a (real)(5�U��!7�eBJ$n^2+2�ra �\dim}\,2= (�*Eif�T�-�Kd�e:Ko} (|.>*AS!�l��~&E 9 9!�2o�fac�9η7�1��=�M_#�!���h�.oq 9p5�s:�N�J4O9q�G!3n%�6\-|���0( E�)n c�CB��/n��R"deK��P��h.�a��Li� *�B �OF��Tm� sm"�t;#-2a*%� am.8r'�D-Kj�. f�_sen�P�A���al\<��w����#E&c)��� ]�X,�~0 �Z�t!Alet�]�-$E�a �all}\�<^aE�2��� �z��f}y ;.M1N��JB�.]d- ��N� �� 21��G FG E 1A #6� !�"%V�s{ ,}A�"���%"�L��c5�$n$R�1�s�� eff� ;�+E e <e` $U_nY2%�"��*1�in��u}2I �)�>6�}) ".q�End.DF9"��.��95%ly$M$�Me�n�+ ,"%�z�.�9�li% (�$>$�`!c� �;eRR�iA]"&)!��x:b�=#i�i7By�F_����%�~yd[���F*��i!�mg6�fMz=U��fro�qB� "� A�  �&Y�ro��,� !DE+��Iw1�E>� anY}A�� M2N��h8%]�6>͹ �"* u},��&@ �*�\�[�at�lll} I+X-( & B^n, &\\i)�:�6v 6 wide�B�$/\ZZ_m, & ^:'f2) �v nRQ�2. ~?(v��'� "U {0\}� �\.h2;�{�[�N?�ix �x�~}�.<B_r*  6 >� �� sKz$r>1$},9hx->��[.D:E%��f8"�F��1bM_d^n5�B�dLBC^*��|d|\ne��I��"6O�$"�"�LPNN$e�~}$iv)--(xii)�vh� $m=|nk+1|g)Mk9ZZ$ 0.1 (n,m1M� Q�A�2AFn#.�o'Q}e#)�blow-u��~Le orig�3 hn�$D$�FCG���_rZr��radius�l!D�$%�63 Hopf�O��by] f�a6yL$z!/CCF7bdMJ z�� ���i�\�9 � oll �x n#�h*�coo _�Y$(1:z_1:�� :z_n*8i>�5d�(�nYE�brace{0 b0�K%\ti�FV�M }})$�*S1-.��� ���>� {Ad}!8:iL� A ._ T.izI�2>�"j�9N�/ x�Tl u��� t� !�� ���R:%�!��*��8.�B$e=l!(G:=SU(n,1)/��3$Z+!a!O$ (�,6�X)� $G$)i��fN�. ضby $G^c.=KW.W .)#[��I5&e,�8s U��%fYr m-�2� �� acp��.陁� yb'%1�(6� � �9 E�6�:@� .��su �� d��D(I�)/2kBla� $n=2!�n3c�>w�vU6�_��}G^c=4UUA A�JQ���Y�){.)1B*� &� [s:�%#$frak{sl}}_�a$m,. o.76 {sp}}_{2mŰR? e}_665:H8:& f}_4:g}_!�I��dt$����3I3j�3!BO�:4+uF/-�K  u��d΋ J�Y(�E�"f �� ms �  +n q"Y�thZH0A�APeS$e��is .�J`5� s&s. Fura�� F��(��R��!r�  lR�]�m� 9>���T2�*� Next^��a�: �9ui), (xiUba�%=Gi �u2��jby&Y7�BA� \mapsto (IQdet}A)^k�A�;F-s�*�u2�R�E)Z$m>1$�)$F��1� >� $m�W��P�q9tBK$ �V]6�Rfiv!`v)&�a�qu�5py�� {n->�(ف��~� `� " �2� X,c 2"=N9#�>rv�ODK! mp4p�W�2DI E���!D�xU_M:\bԎrel{\sj� {=} ժa2JvI$GL_n p��2]s&�xbTc!-z�i8con�+r:��Ivix�?M8tsN��5��4�P ULIBM�� a\\ 0 & A.� @<\ $a) � $Ap05*" 3h 2+�(* �:6 way a"�,ar��F.�C�;Զ�"x%�:I�\l�  H_{n,�Z2 Bk.g �?n��%vdeg��$m�#Q v bl��fC+{i����Y�Fto�$$Huckleberr���&.}JrR,"�j>�r:�jX��m�ͯ~tm$$o2UCr_� b3!9mv!qed(+ �,vrm�>*k!?D *�&��oE:gj�i�wv%lso&6�b52#��F t����on V�!��P� J�Kźm6%�bn��m1areiQk)w� y�!]~ F1_��=�a� $B_{r?�&v: �(2}r(�*|%>E )r_1�:r� ��l�� s �R*,����IR\*T Reinhardt,"� r:�S they!t� O'.��l�1: ipM�K\I� Sh}.X'm) m<>g�{ABCDEx'b��[BGK]L#8�Byun, J., Ga�er, H.�@Kim, K.-T., Weak-�Fj)�%i�:�$mapping� B_��#�)]�u�!|Hil���b^�ߞit J. �(. Anal.} 12��2), 5)����HE]{E} Efimov, A., E%�l&-�%�%;;"�$W(trB�m� R!4an) �Sb.+�86қ5), 9 �976��1�GKK]{7%.y,=v)�0rantz, S. G.,i���cJ�N�% ��+Var� XHn�2 �2���F�%=��5o �JD ine Angew-:} 5!8��187--19��U� IKru�uR�uzh�P, NI�E�o&Y�>�Canad.�-=54u�1254--126�dKa]{Ka} Kaup, W., Reelle Ta�O �l sgru\?�S iDMe M�) ken auf k�xen R\"a/-?ɥ�3a�(67), 43--7054 KK1]�( ��FN�N1����. A�� ��} 3=<279v�812}KK2�2}zxߜ�r!&rG��s��-v6-VJ��ˑ�281%�3!_1{�22�KM]�)J^Ma, D.,�W}-Korean2O4&�503--516.�$Kl]{Kl} Kl� ck, P��\"ahler,�s nega� curv>NeIBergman*`�A *��-e&s),RH*�*��� ly pseudo&%\�^I��!�Q�75--28.� [Ko]N("�)��-� Hype*&A2YH*?1M" }, Mx� Dekk�Ne�rk��-�yQ��  KBr.[.>F� ~���$\ USSR-IzvaP2�c9), 15>��IP]{P} Pinchuk, S. I., Holomorphic mappings in $\CC^n$ and the problem of h3�equivalence (translated from Russian), {\it Several complex variables. III. Geometric function theory, Encycl. Math. Sci.} 9 (1989), 173-199. \bibitem[R]{R} Rosay, J. P., Sur une charact\'erisation de la boule parmi les domaines de $\CC^n$ par son groupe d'auto)Asmes, ��Ann. Inst. Fourier (Grenoble)} 29 (1979), 91--97. \b �8Sh]{Sh} Shimizu!�, Aut-�hsms of bounded Reinhardt do�� Japan. J.)4} 15(-/385--414.0HW]{W} Wong, B., Cha!$erizat!"ofE$unit ball ]$by its a� group-Invent�41�(7), 253--25!�\end{thebibliography} {\obeylines Department�lMathematics The Australian N��Xal University Canberra, ACT 0200 AUSTRALIA E-mail: alexander.isaev@maths.anu.edu.au } \� docu�} ��\�class[12pt]{article} \textheight=8.5truein\voffset-.5truein 'width=6\ho>&�usepackage{amsmath,amssymb} \def\bbc{\mathbb C}d{D (iI bbt'T  lam{bda 0tr{{\rm tr}\, ker :op ker} dim2dim$newenviron!I�{pf}{{\bf Proof.~~}}{\hfill$\Box$} \numberwithin{equaA� }{se�3!ew�8@em{thm}{Theorem}[ #] v#proposiE[thm]{P2+lemma %L 2 corollary #C2'�iRemarkA itle�< Operator Valuede�@regressive Filter!blem a��@Suboptimal Nehari"in Two V�k@} \author{Jeffrey�TGeronimo\footnote{Botha�8hors are suppor��in a�a� grants�� the usSci�F��e��0by a NATO CLG >}9fE9, two-vM X polynomials, stability6% MQp$ \medskipB}hMSC}: Primary: 42B05, 47A57(B35; Second ( 15A48, 42C '6(7A20, 60G25,10. % % \ab��,ct NecessaryE:suffiAnt [e�I�Dgiven for the solv �Aoqlvil.A�}y )@1�� ad n,aPtwo"� su�-B -B��P when a strictly contᐁ@little Hankel has)!)� ol.E41> \�{Introdu�6�>Ÿ ical:�M?� asks!Z��str H![anZ>based o�$finite set2@prescribed correl�2coe1�ts $c_0, \ldots , c_n$. There i%olu�� to this�ifE( only !�Hermit$�Toeplitz matrix $C=(c_{i-j})_{i,j=0}^n$c�%ve de �,X,in that case]Q*2�8can be read off�1 firsA�lum!<8 $C^{-1}$. WhilQ above�(dates back �Pe 1950's other aspect" ���E�� semi�5 %$ces had al�4y been studied�detai� \ early 190~ with workdCarath\'eodory, Fej\'er, K? lgorov, Riesz, Schur, Szeg\"o)Z5�H(see e.g. \cite{FF}E}Ta full account). Multi�� � ons wA%$considered!Q@ut halfway throug �20th �^ ury."� quesA[s l!�to exten�m.s4 results (e.g, �HL,HL2}LDGK2,DGK3, DGK5}), w%�%�s c�,erexamples ( �CPJRud GK1}, #DiLM -APK})e4 A% ific2� � *l6� was noA�� tely�T(ed until re!9aen �GW} or�2u�atAN�@!Qan exA�edY�Q�ness rjre% �3 a doubly U&E�8x i.e. a blockYD  whose s�> selves:,c� $a low rankA@�� ��sub S is nՒfo� exist of a!g�v!JgeAa �[F ^H. As it turns out, ��J�maa� reformu�a�<$commutativ$ �G��built�m!4f� ��isE3indire�ť���3�i-.0e����  2.2.1),�Q~a�$y recogniza� s esWialM�nowAxis6�=�allowA�r a gen��to0"��0which we will6��kaper.�CVE� yieldsZAX [ iallyI�edM�:�xa5have au0 q0�ple��,!�fo�. !Ya��_ s $ � Prow} (c_k)_{k \in K}$�� !col!  $ st A�aC1c��vec� �ainingE3entrie��k, j$,�5a�$ively. Not���#�g stati�below٪appeaaoa��ve�s�sA| exedw pair��$ integers.> F %\label{i } Letq{k}�\La� :=\{-n*�n \� mes \{ -m m \} \sub��bb Z} \t0$ � s�at $$!� {k-l�k,l%�\{ . O:~} $$ A��*� . Puc\Phi =�j-1� �>l},o$$U_1:WR�8^�, �1=\n�8 6�2��B�2� s9.�!� }.!SG) at $!|_1%.�  _2^* = %  _1m� $ c_A�,m} = K_{n,m}!+\tilde%�w+ M�"6M�K} C=2U}=(0,m-��1� .���� zF^�tKeS�� ���^*��:�B�5� , I8, l= (n-1, 1) }$ �Z � : �́k$, $k \ \��$,q� $= y�\in}�M Z}}$RY  (�nك on $l^2 (<:N Z}))$) Ɂ� Us�{ conn betw� B�:"? co�F} s�Nit�u� ��b� method��,� "� G5"� GKW1 Wo2}) one�tak��e ideasU  goc� ofP � \ref��� appl� em� the 2�Npr<"e*�6�vs � a"mHt"$H $�n&�ly �� $\psi$� in fact��se #QJ $\| 5$ \|_\infty�| H \| $.f � Peller�  Inq  or more"�!Te situA{qu�differ�F�� ll,!Cre' s� type�G- s!iZ .q most!uminent BS��o-call�ig U%�2�^� CS2}Q� showa�at3rz 5�V 1��a. D 2�=)�. R� �)nFLN�!%?mall >3�rpA�!1of �ec�L} reli!}�e dual~ � *�M�, due� @S}!A� !��,Q��� findK ymboQ� of a �1�$h.� \| hA�=6�. $ We 2 �Z� ��a � ���e be e� lish�a| �$ sense. To? E�precise,� v V!.v�< 1$ imp%h�@��&� 6�  $F�J  am orga"� "� In%�2�treI�z���� v obo A?> �%�S�32ga�&�N6$ "."�-auJ�_I sec1} A6_&q $p(z,w)��:%�e} if2#$invertibleA� $=� \over� D}^2$W�$N $gnd�k,closure of $HA�{ zhC} : |z|!�$ \}$. AlsoEqden� DTvD= B�no�  $B���H}E�K})z �(Banach spac��| !$ar Hilbert!�s act  �^H� o �K�0We abbreviaten� H})$":� )$. "��M#�} G��� ��{ {ij}%�6), (i,jM �  := -n,"-:� 6�  \� etminu� (n,m),(-- -m)%�v�sA�Y�s^� pGI�AXsum_{i�>� Satop jB ,O  p% z^i w^ (> ri'=��n rn Zn H}) �����}�($p_{00} > 0� r>0&�Z� cijs}-0^{*-1  �E �u�Z}^2 } A6�=)  - W , \ )(2FTF,:� � somer� �) SQ�, $�ס���itemiz$  [(i)]�WPh�)_1f GHKwe put 67�� 2�A�� :�\ �)ic�� � R\:� �t,����6� %�\{" ,.�Bk�B \� �!�} \�g>g0,0g+�B� � A&E0 Here�A+:�Z0>�.)�)V��������n��wunique� ic���$���� (=0$, namely!gc� = .�!�ɂQ� 0b�0��J�AX, PE�%�tpe3x�,n�} & \cdd& �0.0z- %.01}�0X [.�,>m�O>�� ����m)\} }]�e�2$$!O\v�6j���_9_��� }Rj%'cr \v%i c_{0m}  %c_{10 :"1 ".6CnR7)� %�5���  NotA��(i)A�r�)t��b&�(�%�6������$�mut� hese&� � spond exa)�& a�� �$�%�Gn When&�sʡ� (ii)e met�e*� $p$�b�n� ��$,Yule-Walker ��� tern9elyX �)2 $T j}g33! gn iterH'"�". �� 'x�� > ��sh�)%�(�well-kn}s� clud!Gthe $3i  3$Fi5}�Vx!�Tc�ID&B1�r(��&.] nceNs"~�.�'= 3x3} Le� &��A & BaL B^* & C6� �� it and} \� ?C & D?D>Ee& $$ bA?3(*QZg )?ces���*�$X& $$ M(X)=V�& X���X� �:�b E.g.�X= B Di�C=: X_0$Afact, $�A�J�� $[�J]_{13���.� It�p��,�pr�"I� G%Ialso ��c�liLu$n� plac�H"a �6 DG79":!ACC r[.,XVI.3]{FF90}�Wene�$MQ�g2K)m�~2.1.52�� �4Delsarte et al�"DGK4})A� n*~2.3.42D�M)��mD. i! �u�u . $$! �V A,�9&:�%.6�� $z\&�bbd� w\in�,V� �2 &:@M�!/1;pf} Si�0��>Q%� m bbt$��� writ� -�e=�k=-�}^{ D g_k(z)w^k, \quad �Q , w� bbt,�!� $ 2%aanalyt;1or->�A� s�)���"�� R =0$%T$k ,Tn �{ } MoLL1Aj_{il}= � , \ i.�k-1; 6�, ��W �nn2 n+1,VqkY<rFq.FqIn�( P.��*$j� �*��Aa�1AL0incide after !,=�(L%$s zeroe�)�s $Q�, j$)��e9�*Eed�i�u���AnalogG!�"@ bE �="�.A2# A(z�A_0 + k+ A_nz^,� ed B�9E��Eū.��b��+e s�*&"B {B{ {B�!}z^{-n��z anti�B B(1/��z})^*� $&b � (��"C+R�!Q� )�K _j$, $j =6t$,��nZ u0o��!�>�)$(�^��-�P&". , P_�8$Q%**;$Q_0����ed via�Um�"� !�� & AG} v&"� A_n>?6: >aP_0.O\cr P_n:5=B7I* >;�6�,"�ɼ}���r�)i�=Q�.�J�.� I6  .$$ ��!: = BBA΅}Q_0=CCH+$B� $C$}x�put $R_/P_i BA�SQ_i C  �yR i�� i0 @Y�!$S6$-n}^0 Pz^i��9R(z� i~ �:e�a�- .�8 $$ 8 � -1!E:   �j&a ` A_j z^j,>�T�&� A_j=A� j}^*, j >j1In�/,�j! |j|>a�ism�inL2 qRA_r^*=e:r�>f6s�G20[F  {n-1�J�{-r+1>�\r+>^(, r \ge n+1>Th�$�L0*.�g���18Qa�.: K,a��l#&�,KW2}. O%��%$- ["�-=3]{?% or TChapter XXXIV]{GGK2}. 6��fno�� leftE�r�:Q� i�; s of>�$ trigonome�4�&s. �e I�ien A_ie�aQ -M ^R� N�*' $,�/A�vYA�$|z|=1$.Ep�;ular, s� ! {%��Y#�<circl�$cm-4�hi,$�I� i}^*ai=.�i� "@ �� "�> r�.a�)�� 2�} -s��[ �= M�MF�,E "C} 2�0�F�8H$ y6� �&�ad�:e $�k&U&ca] A��is!�!e*�4-�36fJ2L<.`4G?�-u�k& 2>i�RO\: HE}U5enn M2| $M(0)&->% �M5�0$R R�!$.��ref� �is - 1�sI!e�I &}!�ID. Simil�5A �em�� u�LL6��.if $Nե�� Ac= NF] ,>P Nca"-�� ��N!{!%%{ *�E�n{l0� n _� R  - uiX.@]@bo>!W�*e .} ObservQ0�_i��l_�)$� �$�7!��%$ing compan�'X�3s:��"� Q1 Y.1.F �� � &*� I & 0� cr d�&%� ) 2�,���/>� ]saF [T �&  &,& -#1*6� � 5n!2-!A/9�= (Q_ ")�� >,� ijN�9D� � \deltaL�0� � �JKB4BW��3} ��� = (R�B� J$!|�)�>� � r�>=���8=1�na.jqL9k�9I�: ��#�:.Rn2�"H5��hq�� 1 �B^Upon �*er int7o ͞at^�SSJ#�= (\Gamm��=-1, �l2�!n-�< *ka"4,r-s})_{r=1, s��m 2m 2R�c�,mI���7� �/be�*�- c8"� &/)�SSS�!:w�1,6�n�'��z #1.M#z# -nm}6,A�:s�2��m ��%."�%�1�!]#a�>Ke_IB2� #2_B3� $(F�1]Pdot�06M^*$. D�0%�! �8v� � N �:� �� A2A1 =%s n,-mt&�/\E�:B&�5y$|2<(B)Q �*. View Xa&CJZB�� $C_�% c_{ku,e mdt@dO�A�| .���oryA�$Ft /`C�C8!>6�>I [Fli �%�[U�DN� >^>�ExN we lV"�6o%QNg%�m&Bh��}�:���w� }0 = LL&�L$� ��*�P_IQ_j L�; j*]n$�?. P�:=G*z^n� �� anbl9cpd'.B3 C_jz^�k � A>�  T}J�}qе_S75 7� �$"�H! �|N�:A�)$>� p_{j�(-�:�T6 V'�cQ� &lde{P}0.��&Ln3Bu}6�%� !?:>�;N� ��)�IK�OF� <C��z hP�-�6�W:�2���C_-�Z4��Q$byE�OE���ro.�. *�ifal_?$B�R��B�RN@j�%� 6�cr>MN�j = UUy�U$ upp�"B)�ESe�R_j U)gi�-&z20u��a�S6�� S �%�*e�!)~�^ � ^� &�dj�*>�SQRe�mlu�*� sj} )( %qfQ�&^a�ᨡ.yM� a�.�-0y�p}_{0j:�,a�=� 0B���!u}�V� �Z�IM���B�SF� �� REq��last B�MMa� "� �GO7�- , $j2o:2�"�+�= �F9 p7s��� � ��! � . U}+� �J$( :F� � �BLb ,  bw>2� x� W a� �(zq�2A�=AZm� % !� \� "���PtjK� 9Zk �%!���a��$k$D�8&! c_{j>� .$ %�f�}�!�6�T�9.!< in I 6X>� w � }� �B:�;�Joup&Ie:�V E5% as $(T>m�rR T�!) r-s,LN� :���Tak� �< lity��cp}�per�d$a�oup //tPn`G�~E#� $P�A� arri�JXF>�T� "F T_{- &, �ST_m��� T_:�Ba\Pi��Q Pi_m6 =�M�(� ��.�o:;��; $[A(p_r�A�apEi_0� = (q 60�,s>�- 9�o i<0$rA $i >��$jj>m���q(G$i'iX0 q_{i0}T :PeHm k�E8&(I$UE� TK nti-"*a�-RO4j �'A) 4�+;P�/�J��\Pi (w��-�*} !xm w^min.�=�Rwe�&�$2�$�E a�q}Ls�?:YEE�La� �,!�. �m%^j%yw^j:N�|w|�#|_ B�L m�ri*��z%� $w$ŀ,�.iSs� �Ph ��R�z.� �� Comb"eKs�?!�4Ks1�by6�)�i { �O��&Q!�AѦ)�e?!��'V 3�[*LT_m$. ^m a4 � j �0$$jir32 � %�D $<:L<i�+�g', n\} B�=����i -i,9#� EQ��)TE�$ t)+ �<IFV7� This>3���1�� e�em. F2coa�se,x pM�r�?&��>b�� �YASA�0 �=holds. f�/ug�<�=u�R�=�(�, @=i���� f_i�8 w^i UDT� T0/:= (f� (z))"�kl��fk�u�N}(�(�.j/T �"h!IxU)��;�l?�0}^m r.!$)y;p = !\k7 v/�Dey Y �s^: mula�:  ces � GH"�D#ťk�$m-��B��}�AU} � ttnine"� array}{rl: T_{k!|I�F�p_0�  &&\bigZ# \cr\8){&&p H &Y& 9:� 6� \barb J� *l \B +w � & ��&&[J7.o-� &-:� r_{k+1}F>6 � �%  r_1N9-f\2�1�"K �z) Kiz)��-�1  &tz:� =: Ee�� I�YGAs �S�}n�ue5*j_ !52]�9E�A�.W$ 2! :�u$ft�lfa�R s $M�e{ $M-��)� � $E,W$p0G�(,&�I}�uten} _E�FM�!q{=aA (p_l��l=1}^E8 & �)W5�B�Indeed.w�2e�F��is"d %.n���"�p\.<�A�aiz@.�7c�"�;t to $ 2?i�7 stra[(forwar�7�Y�O=� -8.f =.Q��nce b�` $p_0�an%�65$�;�h,.\2�s�&.^+(R0)<(�E40 ;�$*�^ Z &ame�#I��04q6� must�zE�t} I�M�5��.�k=�>>���b�W� 6� $T_m(z)�)*�6�i� z^k =M_{m.��M?$.�-� $  � +�$A.� th�&/<�'E� maU�C6�6"6� C6�/?2BaJ.a����$�65F�P,� =.�C:� ** zero�2$PT"&Y�0�\n t�Y) i&Z�.9;=%F:Sl� By a q arguF[��~� R� �1�\wide %n�t2�2%+)h!�*�2+n^D:d:�c!� e%��~�.�@ S9�.�g� $� C_k:�k80=`�T8 a���&~ sj}. &�SA& ��<��G@S�C4 � ���"E ��(_1 �   $ re!=C! '2^*>8 1n� -���eqF��� �� J� ��NBR� ��EEA�f)MZ& &#2T. 5<�-1�A1}-�3H��asi�_e\@G1�F�I� 1%�>h�.A���x"�ny\ elKs�0&y�]J �!��5h YR>wF*�$��!lF/i"�`&aK�!*l/ c�` $n<"�\� $itJ`)&H\ 4թ}VeyRre�e&a �a plic" &1%"Rf�;�Rakf0n��-G.�0n�ObbvL$. \hfi^�jr�,�\ .} F"sly�)J�, :]"�Q�Q'*;eIVs} Q2 starjFa6 3*=D��e�� g![ul��RAbe usefuadour6;R)�pe%k _6Ris�% Page j { } who� �bit us�it(`" YtoEaant lif�Y� jpezisX�act�[-)fbbG ) \to 2�[ � oppo,[MYusual�Hq�Wa�SNDf]6�;�oi �`\'!�0 in LnUT, i0$�;6�S :9m~s�� !M)k^ hankel} HA:b�mA �- �$( �?� �1 � �c&�  �AT:!�}K} ( -&�N}_=�)a7>', ^�u!�}�$5�k_�on. SolvE��~D800, D_� 2�0� �=, B_1" \:u,a~: Y>�J�^wYWV} H%CH4H:f;B�B,D)1a F )� �6-BESI� B B�H! !�B-�B_2� 6Y :-���KS"o F2�) , DF�^cr !�h.cr-�I]$j. ��A~65�-+n�-U%[ 0a�}}� $j=-1,-2Qv,$�^O gj} m�]-q�{�01..2 2}I�= �k�yV {j+k 3kB �; n $f \sim"�- A��n k:lo�xto $L l=�a�UT} &I" | f &z_<1 �nAB�MZ�1$?] $f�Dzic*^Na�+s. V6alpha�6A�A_9�j�M"5%Z�>�0�02�1�1Ae1:tMJ1 �-:0f1AF1.��Zc�=�$A�<8�<, Cn� ��; 1�;C>�2�R{J1,10J�M*1Kc�8"b.0�}2�))n0,�.^*(b#bx/lq=�P�"�Bѱ�gjAq��j^�.? 1}^*�?1�@ & {j+2 �W KJX%E.h .C ��� HJyz �2N�&� ���6&b����>�\YW��:K ��A {H�&~� �� 4D:2)��:q �kB�$$��� (B� a!$)&i��2�, ���2G%d^s 1hgj}� �al�n� Q�f&a� ��'>4M3ZA�'2�>*>� -�V���� , u8-J�8"� Z�2BV�% ��yk:� =q�o Js"�U<F �QXSprU dv� .N(K&C"C2Fg� $,coU�8"���{rK3!a��4�� ��,qU u�2} RO��J�MA�]:j_ :��*{)�:��)�e�ha(F��e� L_1^Ge"G9�:f�lit\[ ��[>�Z}m��6.�q�� B���n�BD~��(ithE;!�Z}V�)pI9&�u�i�2� Z�"�'hLmRR=?d&�Q��lle -1�6�M�gj1}. �W`rw>"��X�a��9�zR�02�W $\gW:�/~��i,j�G��n2�Sj H�� $h_ kR9{6� !��q6cVC "b L =28e�:vi�L�B4@-��0"0\�[� N��)#_{��&u\""�-�+��&b���O_n�t&T6�rP_�Q} \oplus,.�1|._0F��w5�� N0 P^*��..�^�S.�(69Z�Q �^2���>�z�>�Z�%�$$���_At������V�B�9 =�^�1|.K��F�fR���_06�WA������z�>�1'>�������Ys>�9:�e�3 K � j='on $P_K�U(M"�(K� K�yeq M,$� �by#k(:� M}) 1e&�" 2[ww � o�`*q�q�m� APh. 1Bx'�t�trF��u�H} �- 2z.X) \cup 2:Qju�Z}V�KC � �xG (� i-j,�@ i,j,$hN}N: � 5�^Z"�z66�`VH6�?�e�}l&bs&PO2 i*!7ZA���1�1-�Z>� �? J�tv�2i�t&!?"O ?Sz$,� "M } or,ciu�H2},� q!F/ )� �E,�=�(\zXA�Fv )}2�) �_:;B4B:� RS�atep �.ofa�to�u9�e�2SbHSGH� ; H5Qt�!�!5"I@-(�� �� &x�8�"sSnq�3Y�� "� $i�4-�%T5/~#e�bt� ��A- clai2&�C Pqtai�jpAi�D>� � @G�!�:hDZcM&B u �}MVW .^>�LB� }6[:BR(E�*�@ �N�[A� #Y"� !X�%a�AR"�N� �! % /bfB5:�H!#�2� �'%!\rm.SAQ{I ..�e�K�&�_Q �&a cerw�.6[Q (variE�5}onx^!�"%^2��}).instance:B2.CF��S�Q%�!�S6�,� �y� >�Z!�Q�H�Wend"��M� $!S"�R?Z}a62��1f��9*Q�,S�>�AW*&b4�IA�*�(] "�!6� [ZN["8(M�` Va�  :��!ĝ�S�(Z0 hiftrcN: ~~���>� ZJ�!�0�,$IH$Q �%;Q!�re, excep.W�=6�A�A�)%�-&�2:�y Q = ���!�9�-�.�2�)�Q!�Bb.5*R ]TV �E.b�e�H e��$Re$aON� !�.�-��AKf & possrz waysu( e�) _1,$ $ I+" :� $ $(  A2^* CZ_1B@2^*)$�� �+deduc`+!� 8X 6�� �m��&_N� .� �:^a4Ae� �Np &� E���!$�pl� !� Y$H>oY� $0Z_�\{�} }i�A\r�4BB�0N�$�6 Y W)�U = X &��U,W,X�Y��5;Y =��B��� �6" �2f�/.E�� $$ W����Ev��&���!�����>�A�-_~���7$ X =;R>yC��Y��7�Qa�5AqM�.n�]2�9�.�_�yAz#Rv�+�P_�FnEZ{i=Fُ\��\*�/->�� Y jrW & U�* &:� r�,o�[5�l^221q� )]�e [+2D,6) 1[6� 0.� ) ] M�6��\F)) ]I&��%lp2F� toge��V�7�!�G(5~) M�(���o .�q#4xVw*�adK �B���}va,�6 .��Ige �is�D�0iD2�B7}"�2F�(�h8;&nFtA �I1muIM���djaj} Vd&�7{D�Q& q_j M � f\j6� *#; �X�B'w'j� Sr sq Aq2� Z!2BN C$n�Zk9�! q��i�}>� K�p J 4 "� �.BJ1�;� .h6)1r �!$ h�2��z*�HR�=JHY��r2�adue�>�E6j��#�-\5 �h}8 ANR� >Vx'"J;{J|'>4�4.zA�� $ ./�Q{1�= )_G2�, O2e� ED� >�QyQI� D}_{5+2B_�,.I��) �A i'p)- F<_:Z<)4^5.�;j9F�6U �bJ*�r�� �"� $0&X>�R�cr�F�. M.rs"BE�F�a�-�m_.�/2y� %%k}.%�k�� \l$Imt�%2�CR�'rrr�}G�n$j}s�B%?�� $j m��AI6�r���>VRFK&�  Like�b,�Hg��5�ţ����!p��� R0|(�i��$:�=P }_AIz�/^b�.+�1�'s�9e!N�fv�P *B����* -�L�CJ<��ISEj"�6we?)n2�"�� c:NR)>�2N+%5.m" = �vJA = r�!�.�1 �-%.�j��I��z::B;��r>�!�>YrtEcit BD!��'� �zns�� �8^g"@�T�| B�b7&} G���"'�a�<�: $ (H�=�<�>>.� �� N ,��H_�r"�p-q�9ip,qVk�n 0)�*` *X0)R�W!x"�,� � $.�,j= -:�5b�&  �l��xstyle{plain} %siam, ieeetr, ams, l�*7�{master3�polhk#1{�pbox0=\hbox{#1}{\ooalign{\hide{� \�G1.5ex +`} \crcr\unD0}$s�(cprime{$'$}A>mth6߬��x��,> V.~M. "V>D.~Z.\>�.M.~G.c>\u{\i}n.b��In�{H} � 4�>re�p�bb/.NX{\em Izv. Akad. Nauk Ar�> . SSR Serڭ\.}, 6(2-3):87--112, 1971�+�CC} Gr�dsene, Zoia Ceau{\c{s}}escu � T.~C;!�Tn.�S/��~s� fA�6ds.6�Lin�,Algebra Appl� 109:1--35�88.�0CP} A.~CalderI4nd R.~Pepinsky.bO!Se phas�AfH��2��"�B real�iodic "�"F�Compu�@Mk���Ppz�ym@$X$-Ray Crystal {%, (R. �X, ed.)}, pages 339--346!5x�a�k�{r�( Mischa Cot�q! Cora Sado:r�dis�u���p��. iL{BMO}I{N}y�-A�a<mAy%*U��si toruF'Integral"� s&U���Dy}, 26(3):273--304�96.���,} Philippe D��, Yves~V��ninI�a�amp. Planar%ast squarotI@�"{�$. {I}. {A}I�E ��eJ�EEE Tk�. Circu�B!�Systems �1):59--6%�79:�3��8Half-plane {T}oF�s �.eu.�In6 &eo1�4):46��7%�82}��� {A s�m$of {R} � 's m.ç�Dbil�E� em},�\B� Acou�$Speech Sig1�P�4!�(8(6):701--7���0),�����.�min7��of��"iwquadr.��halF� SIAM:��%(ic Discrete�{�((2):192--21G�982�XDi} Bradley~W. Dickinso2\Two-dime�u al markov��trum w�m�n�noto�`:120--12 �:]079a} Harry DyS�4Israel Gohberg.nE��V�5\�F�(s� !g?�&>w �UFt��a*503--528��>�79��ğatr#�b�ZI36�H2i�6G5ޝkernel�=${F}redholm�.�e�J.��e !��� 42:5k�!782/83.HFL} Sarah~H. Fergus��8Michael~T. Lace2�A cha�_2'�6�by��ov�{�� � Acta�189eU043--160, 20022�S^�^�>ȷ%D�E$mean oscilr��A� disk�� ter J��w{C}arle!1meaG�b�.� 81:2o267�2�FF} Ciptg Foia��C��er��� � least-squ. �Tit�V{ W2d� recurs<��FNElect� Letx $11:330--33��75.5GW} J��~S."���i�~J*x�. P�" s,��ɰ -{R}���U1V V9�;2!�.n%�8�ofi' (2)2�toA�ear2�H} I.~ͭ� G.~Heini2���r� `"&� ���D� )g{ a non�*.���G B�,Rev. Roumain�� PEA���19:623� 3aY7.��{GKW1.�,�(A. Kaashoeky H.b�� ſ��2s �����Ag5ߕB�J.>e 2:109--1562e ρ=�����:Q nA�*�>|  nd newAN�B�J�8:m}, 12:3��38�:�� 6R , Seymc' Goldd )�Marinus~=�B�C[�]>)�. {V}olP IF$�)63A�a_ >��+�+2L0HE} Henry Hel:� � Lec�U�in�,nt&#2�$Academic P�$, New Yorka4624HL6w%�(David Lowde��g��&�Predic�@� R� {F}o��se���1sOal& RB�2� 99:1� 20E52P�2!��z�_b�%�2�106:175� ��62� L-=�7>Loch Lev-Ari, Sydney~R arke�@nd Thomas Kailath.w��6� ximum-eUop* IcT6c�61 �I*BM35�497--50# 6�LM} J.�Li� N.ap Mali2mA�!lgorithm�BO�J�$V�pe�b,ruan� ~�F,G, 6Hing�n9:4H412 >p�S Lavon~B.�S.{�wi�U���({S}z.-{N}agY�ia\c s>�S.K)�ndiana\��  J��$20:135--14�70/>�D VladimirO BfH�&�A`D�r2�22Sp�_er MonoB�x )�.$-� �W2002�$RO} R.~RocB �i�P|+ ed $Cp$x�F1fB 6:291--29E�7�"��� W�� R�.4��B�E�p� -,+}Wfun��J�llinois��!6!�$7:532--539�y2"��j�E0MZx%�1��:� tich<5)�sch C�%um20Bi:0rm{Bi:b0P���rm{Po60)0Ls%ws���Ls{� {{L^%P_>25K {\raƆ005pt\rlap{$\m�-1.5mu\�,$}SQ sdsubA -.40>B2.2NB %BROKEN!!.�{\cA}-6cal Aj9# {\cB.B>Pow. P}}%)Q etc?6jZ*�@�MH{\hZs}{(\frac{1}{2}I,+)^2:.RRLR}��bLZр} \tiK�Sharp��ese�y perc�\�!f0ate{October 4�5_�� {B\'ela B�,b\'as\t�Z s{De@�mP�d al�s, Uniyt��Memphis, 4 TN 38152, USA� [Tr�9|y College, Cambridge CB2 1TQ, UK0Resear �w�>��NSFp�, ITR 0225610%DARPA < F33615-01-C-190I �^���xr�` n dut  a visi".�$Forschungs<;�� f\"ur&�k, ETH Zich��nd Ol!0P Riordan$^{\dag\S}$% �oy!cociety �FeRW, 6�ytcs�)M"9�Iz�sE�,� ))�5u%m} .��\I}a��}.)�t�l��in~�P{,�S�  crit_zy�random 2b� is $1/2{a by-o�}, a�rt�developE� #m�}!(p��+E`r��v�%,.�inm�E�eX  tili�\iX�so)�. HG�weA�1E!@s�Qi�s*�!< Ev� c�qOs.Əw� � aE B����VlatA�q}t !�ded�%!d!*�f,E��)a`�ue1��|��M�h�w ��W%U. Fin!��. �yQ�d"m N"_ .ߩ very�el.�6+Q�ofM@ N� ]SE{be!gl��to2B+&E� rest):�|t�r eE�freA�J(-df��@%w1p��A%B# z! ɔ-� 8�U&�������y� �!��� shor�<�}r �#�x U�in62!� non}!n�:ha�.�e��9 d%�cor�2�(}l)B� 8"yu�%aa� �ApbelieO�o��new. A(FS!}[a� ��+$G�af@ 32Asy)!�assigg�%va r�V},�� open} or �jd},� each�{ $e�b G$ (/$lu�h$$\sigma$-f��{ ��te�hs). S�L�>i 7 �$G�2�!�:��Y4/�5,Iql �ONeV�)�w;A<� �`re�Y27Y1�ͺ�F $\LtU;�:L9445�Qus�F$nީ�Ln- 4I�{L6 }$�K�Y�-���A]�� 9�^-pHv�oprUe $p�w&|�6�F5F��f�A}��� i1�����GlR��?��� dan#of!�f^bz�1O>~ei�*t�� ��[Ani �cxer}!2�mxim�� nnecsubi��sL$ �rof�nse-�(�) ��W� �C_v �!� t��J�fa�bnE�ex $v7[Jq��w$ ��inPxv$3 ? K !�m�.ch�� $v$�&8&A path��aR~�5�.�C�c?�ofBO,�v�扈/ � =\emptyseeYWri5$|C_v|9*num�of�8 !�!N� \[ � (p)=�,\left(|C_0|=�2\�E), \] :0�'z�origi)�0$.8f�ly,!�2"^ n� 2�1$�i".i%�Mj some �A9�� ���=]8B�.fno such].&~F%� incr�ngqp � �R� � Y R"��p AV#.,de�q�!!��4 E���yp�p.V-a�� �-��  asizP �rZ:w�yi��(:�Jr��5�{!,;7!?Welsh %�  SciProg} � SW}),�$�in hon� o��Hmmersley; Broadbent%HH �t�Je�� *> 2 �$1957 paper �BH. h!�t�SBq[3r�2of���م� �Ka�"�� � b H2,H4,H5}!�ved���!�6,+s�ED0y!V�����vw 0.35AVN�<0.65����\E_�_���E*k !�Y��.�chi(pt}F ����bAC��qAU��.���� immed��m5 f^��7!��n� R�,�^p_T: inf\{p : ]�[b1]�@!$T%�Yv Temperley:"a�!�iU�6TT e�=$~':i��QEyea�N�� A�!�p_T[ =1/2�JB� �1;J�con�Zu,� eems�b �b�yma�xplicitAGbut, &�by �#ou��w�numer��evi�a��F f sl�o"�Inx78, �oM� U"|'A� #SW} �& ific�& progz&�. i�=���tlyp�!B+�hI)d�!8 1980e� enty-��H�'u&�in��a�\?E/2Y�atN�; �I�.�x `%���nshikov-M*�� $, Molchano�wSidorenk1eMMS}) Aizenm{d Barsk�yAB.[Graytt })�T@2�eg%�gn�t��.���� .l _ͯA9ph;yUXK�ss_sth}Da� 8#�%&�EN&� � �&A� >�h0a��) 6� _""@�l��:g��c^�-11s���.�a�ll. B�A/V� m�!er �� �A ��<�ty$`�.�UM 81}Eeaa51i[N�aW5��n �T2 �F  0|��  A $C_0+zcay�k",ly. (Se�-so6�Newma�AN�[Q� �}.)��)�ghS p]Jkq�$ 8 ione�� ve, )'���e� a)BglV�_H�� *(ab�Y�F�C�O�How P.� �  a��&���.exȪ)o&�  ly� 2��E%����R����@figure}[htb] \[\�%{file=�O,_edited.eps,��01.3in}\] \cap!� {PorN!БZ$L=� (solide�s)�q'is��c�� 7 $\L{$ (da�сs)."��fig_self&�H � �im��Ͷ>;pB�����`T-U ity'!�$���r Mis key6q� rr dm�e�%-�%>���e��ro�4t:k!N, �Uh�:ndard�%���*s:i2 $G�"e�a�J� draw�$N =hV5�exT eachx�� $G�k�n� $e[�,m$G%.�- joina����s�� �� �fa�@��(�6��}� .@�$GIs%V�p �B��$[a,a+1]�#[b,b+1]�Ba,b@\Z$���� ��8u 8point $v=(a+1/2@/2��\ easy.&�\��y� G$�Fe�X2��.���� e `<�+hy'��N� � ,� � triv(observ� , o�fte�qu�-on}Za ,A��farsG��!��&� � 6��*sm){P5ina�0 }\la���N ."Z!�(E�Z� wJ�b��+�lf-a��4da�iin��!⩰�a�rp-thM$m�A�FriedguKalai��FK}, ��mp����i]aBKahn, ;� Linial F KKL}!�cer�$ influ!eFcoordinK�!�. �� RBKT.) <� ���fixr�����($N$"6,�h�X_pZ{��"� set a�X$�!J�se�7!��2$xaNX� *1 m�#\� a fam��$\cA\EB et \Pow(X�f {% $X% X(\cA)��Q.`9���cA$� t��Aex�!��-i"�W�A�"�$$�B�X$ im��$B+. A'�6Z symmH�Y*�pe&�U!�p&�e�i�6lym!t�!�Mwar�onA� orbi)=!"��v /[1k%!"��1�InyQn��aR*�|�t|$q� th_s�'�}�� n ab����$c�&�´|X|=N� M? !t1���5~%�9�E�F�VII># n+ Z� Pr_q1- .05 $q-p�I,c_1\log(1/(2())/ N&��.} Fs��!make fr�st��"s'���8b )/�.l_�e } IfIEU�5 � .���/$p���N��p �  \cB)��^1:B).�|0 � �co�� Ƶ  �<�to�e�de }F� r�� a!�A�d!6�EN I�awq�s,)T�y5CPof�"� $as Kleitma� S.�c���e��ZHex�W��=��H* -�:i���a��of� s or�s� ��la?" (acc�#g!Kwhe�w�#iGide#|J4&)m ���b������B)n6< td/v�F��n)�! YwDit?$!r�=A hangWT&� ���6eu,o��sm4 L%��E>_54ly�2KS"�!U�� sO.i���b *M o����-� ���,. AB3 }L.� i aem6M�Q, � � pair��,a�<e��%?k at7 �Ia�a���H$k��1�(be!�%�or-r)I! Vl �er@�of�-�b2T�h�dk=�OP��8�%�� }MnoFRw�C�ee��A~dg $T�e*�;k9�cq � t2N.�!92�Wy,�e��.(T$ run over1���q+}!xAR�.*(alli� der 9em:"��#����~��t: arisI�y natur &!�a�:f (Emx!�ic ��rm�J &3(�Y�X �C��by"�'�/s; = Liggett,No`�& d St�E��LSS�A6k�. ��eir*�+e�1�o"�z2�6$!�m 5j. ved: worke�y� �Wunt#)�A9*��degree6H%�d$)i��<.Fa�(G,k,p)& 8any $k$-dependeTnt measure in which ea�Fdge (vertex) is open with probability at least $f(G,k,p)$ dominates the.ducg $\Pr_p$ o dges k ices) are n0independentlyF|L$p$. In particular,ovided |(individual f � ies hxhigh enough, percolation occurs�,$\Z^2$ underVassump &@f $1$- (or $k$-) ��frequ)�8important. Curr 7$\setminus j, !�lNB$Ga�-%�ary!�$Cj, i.e.)�seV. s jo� + toFr �. Not� at e%KFak�Ls>J�E8Lis thus closed. Pass%*o%Olat��( $L^\star$ �u�L=�@Das defined above, !��s�:correspa�a� a(�;$$B$ form aQcycle $S Ne� surra)�e )ڙ�pfigure}[htb] \[\epsfig{file=�[\.eps,height=1.3in}\] \ca� {An>S � � (doti�,solid lines))��i�!��E�!�BR=�7L]Z$ete]Ag!e6R�!)��9)(dash= . The poi�!arkedɀa crossA in am a�Y�2�.} �� fig_5O}�-| Give��Le length $\ell\ge 4$�S��reŸcrudely�,most $\frac{4-2}{2}3^ $��si�iesA7� (!hence!t): must �!:$x$ ax��t some-coord�� betwee�1z$%x.�3. WalkA�E�o,�ŋstagea �at � thre!�� fo� nextE=i�3 one choicm�e�E�-�at�en}� back.�B�$ may��m�U��nto fou��( matchings,�!�U )Yo�c a ��$B'%�a"E |B|/4=!�/4$܉B$. Now�st\ m$a=�M�*6 %%_other)'($e\in B'$ i��I�:� I\1-�. Putt!��>t� toge \��ee�pA;.J��+���R, )is exac� R9Ey%�d-�ii*aM6�Ͷ,TM$ \[ \sum_eeR ,\,\text{ee$� n}} I�!~iD yE (%)iV(/4}. \] Thi� stri�lesAjan�  ifK� Fin,�H2� nega6 � is ja�$as easy: wpeM�Em�ca�$proof from� Voronoi}. �time, itV easi� o work)� site.Y . Rec�%�-m>%0 ext,�� 2WM��o,Aj!�A�of��2I��"�� �� 7$ by a path� )E�y_�� > ����:} kdepneg}�k���xed�(�  integq1�\Prtwo .� &� BmQ "� �iE� ��ex $va� �n� i�p$Ŕr4 cons Ab(1=p_1(k)>0$&D �� p$$p\le p_1$!�B$c(p, 5�R �e-�( |� a1n)A\exp(- 6n)a8A($n&1$6� \b� E� } If�+n��i�subgraphA-�induced!�A4!�%6!� �Fs a t�$T$I�$n$&:� �. Ie wellH aGai�che� ( }number�s� re�q)� grow��� �i�6)�,(4e)^n$. Fix� K�%�% 1�suba(� of��e0n/(2k^2-2k+1)�%! V�>a,bAbS$Sat )gdiA:ce Xk$;!t,  find Rae�e�Tgreedy algorithm: whenAg� E�a��ca�n� 9DŊ5���rul�u%���=y :5� )}�in>� $k-1�Y$a$, nam* $$4\binom{k�=-G$�#e�[S$�HEu�Mly, s��B�!yFexDT% Cs at Ip^{|S|}V nce,ep ^qI6 p^{2��|Pr�$M s sma����$r=4e>1.6}<1i}�C�f&ws, ta� �=-\log rq�m� \sec {B>�i 1: ey decayb t�C N w�sijB�Z, wri���L��a�.��� $^{� ,\mathrm{]}}Z�  N %�.9�Ag2]$p<�l�!�I�Hs. In�$ourKesten}��shortPof was�nw�Harris- /e��� on�y�� H=1/2$, u�TheoremR th_sharp}DYma� ngredient� fact, $ethod also��^Fk!i$p<u6�� B��`volume'��e��eA{te:  X w��M� �$\chi(p)%�@ .��s� %-$p_T=p-!i�[ below%x firs%�ve�k)t-� 81}!x 1981&St)hQ�th_LsM��� -'%^%(� �a=a(p:�I�(Vw an)$�Ae�p0q�� W{de�AB�-  \�,longweak\ of �]� repr�!#%:as6�@G }. M�� _ i1NR wentb oav)�is � IAstrongercm,� \!��Z);A ����2Rxa%E then��I! �$concerns `I��� O(rectangles'� id�f� 4 $R=[x_0,x_1]\| �X^�U�N p>� be fP .� R_n��a $3n$F � Y.���n�0H(R_n))\to 1$at$n\to�=E�}��[Pofb�] � �� � p_1? bh!q\ �� 6�D  holds� $k=9��� c=21)^{1/4��� y6S5JQ"R\L�$�*Q*>$isomorphic!�. Dn�_e1!a IA8 $e�to�AxZ) $e$,-, ��l �*v ,E,a�*�� ll6B^,;RU8mI8m$Y8T���*�G ho8$m\ge 10$ large ���3 qe���ong w����of�!� !v&�czS� s=m-n ��EfSB n $s �s$ squ��� . Arrang�� ur $� u6���U,�,n annulus $Ae= in F� �ann},��[R L.0.8:F���A}�6 i� |��!ui !i ~ �U$S$. U��6F��},B�.�^4=�1$,� ����A�Ċ  %�E . I�is happe�2��6G =!�!��s�s � (SeeR�.)�2- "* ase, �aU/ , no��ex1A��onnecFA��E�to&�outŴ$AA�Retur�k$,E A�J�kQ�,�� B(S)e!��hsv���� .�at $L_�4-"�$2s>m+1$�AL��hav= UA ш��?. ��u�:<2x t$&��-�:Iy$v=(x,y)���!�t 9y$�b %�+8$S_v=[sx,s(x+1)"e sy,s(y�Es D_v)$ �� s on� E���� E�e3in Z1$A�x� >�is $9$&. Furmo=\ b�� t$-.��$. z0U!%&B m�: A alBH* �� C_0'�SA�B�weI6��.B�".!� n $an"�� '$Ewua&p^ M` / >(6s+1)^ay� &m8$w)��!�i J�.n^>3sq:w$��$wA�S_Mn�M�%!B(I�0 . Thus��V�60�K �$v*�I�� �s�� ��ie� of)k@�� 6Di wect��I�I,i�u� � a'"�a�I�!�ep$(-��,� �5�QNQ _ �n) �Prt\big.%/ ^ &exp({-}a6 ,��leO A�6 �>>,.�(m � {Per".$in� � s sec_} z argu��V! re specif� �����.�{� , since!HwBtr$oŋ!��a �as,couldM�0U�v. Howav,��3�%s[�#bl; m}�E extn>�%AsusJ \ST secSR�8 �%�� ny planar1sI��#be ext8&d+:�%� hear��1# �F>Y;� pres �[e(�  gener&v!vw� l_our O)ue�ej��&fa:�J��develop%S�a a ra�� diffeU%, P inuo�� � 6random C.y1Ba�sEIR!_c�\.�Zf\�;!��2$Y)�yB_%edK-:OA��much mor\mp�&A�th% �q�;a�%o($n� �"em �)�or�A� pplyZ$ �r�&s�#ud!ir9ies, ~١�L appropriate equivalAl��HRusso-Seymour-Welsh�,�+ 2x&hat ifl)y)T s � � � sign��an'<)�'M�ame}�.� B[a��tA}io. A� M=&�3 �=M�sm�r�+sq߅3A e an2�=))s. To il�&r!J��we�two~ T'�n S{ezs �'s�}�  tri}�\A,F ��M\, a�La�(!�A�R!is A�necessar�se�)frtriang +ve��n �geometryJi \�~{SD�#s�� ���s_sth.�5D!hO�.�*onGS$\RR^d$$ e sa��&x$d� men�alr ��}, orI/y2AVf J��� , lo� yN o�#8 �V=V(L))t ����A?.y 2 "e "S $\rho>0�DA���� $d$ autom�4sms $\alpha_i$� L$ ace�T V;translɣthroughV'� *�H vectors ${\bf v}_i� �.�� C��e�A�>�A?)& $L$:�8B�we �Jrealiz�%� 8: �!�la4)'3&�b}$Lp &�)md2-d]��,��DeB��Iar �$. A basic�| pert�!�� �� �-t] exA !�h�" & intoMHly��0lasses $V_j$ 972�? up of� x%"cts)��"�c P.*N�.%�t �Vsl>lyGN(eY#� !�V�&�X�(l�'}�$X1��,�' et)�$|X|=N9 2v, $\cAuFPow(X� incr�$ng. S�,�}%�gr!*$G2 X9[� y orbi"� a��eCG�X$%�siz.� M��� \cA* a un oYs a�"Fb��"�absolut�c��ifs8^X(\cA)>\epsilo"+#� _q1- R�!; q-p�#c_1�& log( 1 ))}{ N} " N}{M� ]� )�:W7 � !�!s����Jo� , �! 2.1!�Friedgut�ZKalaiFK}. F� A� the yn �FK} step�,%nmod�� s&at�Jf-�" vari� �oinflu�! ��$x$B$lQQ� sum�!:E�Z:Mx$, { { jNx��} Enot��1 veni�0�y��)�$265�./32Ns c2�( I!7�s-� fac� a hy�� uboii !�oh0&�ur s separa��e! U�:8� pr�in !*�&Eyway��6H&N y�mW=x4^{L""�}}�r�`���#l�QJ�4 $�'Anz1!5}a+����f wy k9�4.� waB�l�1N$R�LRR�4�#"�e} *� =H_L^ ���v�m�"� ����� ��996�R$ �A\$v��v_�'[cimi�� �6NL$ �mee�4�eft-hLx %R��]6De�=yB>e9�/f� �4T"precis� �"�=H(� h�"#al �1 nea�:�) m4 mat7#--o� Q����.�ff�� �"0 ��U7� vol#A�,5�!y $O(1)wI� q $ ,��yEhK#U+orn$a! � a8we h5�}q los�+ity� bea allel�*z0 axes�,2j*�A9au8p�1H/t����8k))�/)%h�,63$AM but {o�s<,o#9.JL$UdoW=8 ��corner%�:F!�q��Q& 5asl4\3a�a�&�8m� !@natural,��w� m�6no"ceBN��INis unQG��.�L$9�s!�Z" gersbO "�Q LQ >�� . , 0x�U$y_1w4�E1&�?Bn.Y Y!*u�e��"�k� -b�e@B��%TP}s7+u"6gS=cn^�F�c.�%�8,%�mk� � clai-.aq �a�; $\eta<1F>"{L ^T1�I ta,A�U"F��� �'� *(+I_�l����now o�n77��$N=|T|=.}� n as $N/SY���Cby N6 it suffa�!��+�.�+�a P#!�% $�=2n+� ?�|cer��9S� �z !`%��A�� �A�p i�R�!�$n� �_*�C $x� eb$� r7W is `85er#f'�n��F24�{/.0%� torus�� j cove�a1�A $M� Q���� � �Pq�* � !e�a��y!H��f&d�8a��s�D $�&�11mear�!��r�����=N�)a~��. Ia�ll;V !�u���EMfbAgAov+_i&_&!�E *%�nQR ��-q��s $E_i=?1i- (so $E^c\sup��D_i E_i^c� �� 8�޵�. H� ,!2�j-���$i��� �-��^ce��ly l�^��the dB;�&8cap_{jS !�A�k by )C!�Az&_ ��A\.,aujus,B�0(��{1/M} eta ="9�if��p($��#lyz/� �sm&E�nd��:�L �R`)����as Kir�H�_�&r!{S� �o s2�"��"t�J,�\Lsi��M6P view�Ha�+ F S)�&�;��. \LsdZ(non- _) Ee� ~�(�� ��)- adjacen�$ they $t Euclidea.s1�$ $\sqrt{2}oo�1�!gK�$�B)O� �E��6�AR� V� !\�(L�.*� w,"��StwT7�:��*�*T �tL�JL�.!!��h �i.V,(L)��Z&mh�K���I4�cjIG 2 @�-"HIGeJll�5FU%�gQ&befl/ a٦�uEE��gq<�H "'8�"� �C�8�hE�hZ�8A��e�VNg)K �>s8.',la#6!�V%���t3�)� &�&�<�Q& �  t4�4a0eAS \inputb0.pstex_t} %\6LAo#*L2.55�iA�{A:�� �1%�.< draw' x3ctago3sR&"�P row/c[>�)I��;ch�H. `Black' (shaded) R.7Ei�!+ b5 �I��B���/,d&a�y0Gath (��A���s) @top?bottom��D th $W$�:%u $x��"(�Fthick �s. As 0 leav�; t $y+ H_{\Ls}��'6b61�:g6QE�l_hlvl2�Y Aw� \��"`NP���� R��a*� %�J�. What�#!��"^ 5�A6E<e>��0 $L$-%�p ��bN�c�9�6<e�<2�Gw!�h*�1X equaA�1[)Y)p + {1-p}(V_{-N!� ) =1r0J��)�g��WitmC�"gn.i�+�'k��. C2�9Ual til��H �e��y2ndQ�M�JQ9Up: w�EDiɥ�.��2 , colou a� ve�ޅ�white� )�, p�9�m� t:�IE�e� wX��Q�@A�a �. All5k=.�GE�mɶ��SEl.� %��/�0� $# e a ) �I�a (7) {!`�9yend��se o�%&�F��@vOTab�G�de�Gr#$ $2$ excep� i�+:9���,��z)U$w� �� R$!J�4�8&3QG2U�$W�=n�����to�A��* cann�/nd*���alkA��B(e�"�%alway�:� . owI>AH�E� Ad�� <1� ! >A�W���an�h-&~:F aU�hilM+EtB\}S9TTd^U��i�.f% ens0�[Q� ��i��/%>Ay~�R��.�$�� ]A�s�1am��d>U�{6T�EW�W!�E^ both��s�6Ŏw�# $K_5!nuld��b ��l�O�We��J�/i� p_H(:L&)a L=\Ls,\�,�&��X. A�5�'�!�pg���u�X Menshikov�} (y"MS,Gri� t}) ��!� �e+ d�%� e>�I�radiu%"� �Z�a&~G $p_TB�GB�;nog-�intrF�F�P� s Uq�(of^�G or Aizenm: nd Newma� ANFH=D%]*� k��r� t>r��a�Ns.�C$R_i=[0,r]\�H$(i-1)s,is]SW,\l Z,a!L R:t:0,ks]$W X!1d O6�ї��Y�Bing �$�=� -!Z�m>�J�)^!�s� �\*S_p(X_i�;O( $V(R_1))/k.y�� :� A(Ń�al-Pex&Ws�%�of~lS|iq����?)$+hB;�P(R>��4inB��)�$\ 1=P!����K �%�U s )��U7%�I. (bW.�r/�!�E�k�E�l�}eI�� a>� Q$ $Pn^J��ZZ �E-$W�|Obn: �ba3ep%]� S  examin&o "�R� s�%ex�XP} bN[ Bd.)�K+$�"� 2�eI6�?'k^�^'!�)wal (but%�_8 ily l )"I ! $2�0,sk]$&#by refl�!!�aUi*'� $y=js$L )>�G��. Also,�P_j��1�?j�7� sub-!�EP!>1�\DR_j.a�I�eD2A�"� ��$ #e�`�Y�)Lj *� %5P�6�a�9.\al)a�"M,"))&� F�� $P_H��L Anye�Y�m0Z%��=��l @� ��ex un�Z� �8nL6%[ \(go�Z��^griB jj9�1� $P'~/!D� A>pr�7 ies:y6LU4d&z;g[ Jt�i�f, h�ap=t�%�Va"&!Sof!(,q &2� h!(*]0;�&V��nY_j(PV�G:a �exists_:�l�A�a �Ղb`Ye:qcs1} �\j�k͙ �B� Gi^�����8!�� p�_leicA#iI��;��A]�j$��u2em� 7j�rj+r�A��>:�A�s.Tp-2\mid � p�!XD and,\eq�e!�,(^J� J\� ?H�*;��)�� A�6� n $X!# -R��b�F�X_j���D word�2Rb � X_j\hbox{ ��}2\} ,6R�^A3!���na�!ۡ�Iu8`�12b!6 1AY1)�so� u$\�ieqVj��y�%�-� � ~B� So far���,was�0�JruD*v&#ll:v�,cUacA�A1�8j)$�;mm!uM� eq} s���j�;!�dis�5t "P;� �4��67. ��^^X_jB�-b< 1y��P͐s-w� } ![J�G,� ,X �d�Ccoroll�fco"C9HQ�-"� s,���&we" �"�%� %�&�!� Z�C3'�R_{m,n}� !qCR�#n*�# � m* n�Va�W) B&)���� W �#��Pm�3&n5Eqjc"Tssc>L�Q)rho. k�@�1��(" o$c'=c'(c,k,9"�d V&� _{s,s})),u�_{ks,k�c�323l 2&"�3�>�h)����$%�)a�so  �!h� �!��(�E:R) $m>s*B)VW,hms} h_{2m-�^�0ks}^2 c^3/k^2m=�* AG�-HQ:�ded�&A>�^z-inc���Y� an2�nsRn�<2�%Xk�E�%' -Fd #,$�} � i� �BY��($r=s$, $t=mb A�i>Hhe�:Z02� ,�$=[s-m,s}�eE�  $SL&.�^ire4�'*�)HRy�fe role�R*��inF�!��2�5(.)����G.U��f� RSRkZf�� lappAj�d, %$4&)��).�Z� aths3���)��$:KMll`ed.�H$E� 3a�� H�S� RE�&�(��\cup R'):Il! >��)us��E#o��j �' @>��,&� >"? il+' ���c"�!� r�!|,v67)&$ $x=s/2$; a>� �. "Ai ~3��%R.���! ,-��6$E9! !�)uE05ms, Ya�e>��ho"�\R)"*���U&�FS���;�l�i�� �' E_1�Y 5 V(Sd =�� $ B By�0y,ѓE_2� ]�^-r�6�*sb+q�&9 narray*0 �H(5m) &\ge& �� #� 3) \\ )�v �^2 A)2�|By� 5>�YS))=h����p+ [2�5*F�0���)�NuRB ��EHeraPJ �T� U�E�BQg)b=Q; jmas^?�NB Hq9l e ke�8to+>�]"�=�� �f�^ b]��Bf �/.�0�yir�KJ�=�  >� $.�**�wL$�E$p��(�A$\t�:_L(p_2� )�%"Ez�W p_� L_�>� +#�\p=(p_1+_/�7���1�=}sE(�.[4$7S[e���de"Zri%2*6�Al&� �� _L(S_i)).�$H*�$ =1$�?l $\{L,�$ \}=\�&\})��^at�!(a)-��l�*&�$i�L{1,2,4\� z  <Z%�a�.R%�(bZTAM@ �{�%B�L�Q"�C� �,"�  (D0t$c= �N=1�=A# $k=2�k=4$)[U~a $10[@.� t J�!�,e!�l6�&p����*Wbge c' � or }!F-,�v �}"�5'hb>�J&oKSr.��.� A�<�aD!�6�c_3�5itU:b:IojIdecK1-EB*/('�c_3�%9� If~�_eH� �c V�6�, %�# � �-[% star�1� Rl%_"�#�_;"i),� �|i@l&'\�f?0{R�� {8M C_� ����:Av.p�MB?Q�D���sal!,ndard xCs;=uWVa&�O���/oneG`J�. C�cc_3=p_0�23^9�u!�s��5forwu2~�~I!e"Z� ~ Gz,� � i|� �$V(S_�pek �>&v �!�ɳKZ��e��a�`end'���(& R1�2}� ��� m~���: )��a !��X>T}) 9�9^{\,3}!|$Y ��$& `F$Sm!t�t$^(/by)olar�/! /*�p$(a,b*o +1 b�1�  ]$%+��  ��"[V�$j'�'�H$ $(2an,2bn' �m��" �s� alogous. >�fInw?`.� ��.e Eh � en�3G��6���$Pu�t2d6�.1���<V$C!D�Ke�:�aP'�{o�)2�2w �!l*v3 .�-��EBV��S �(�l�X*Z%2ly 2�'�'w'�Jq T�y)�a� term�� �Gpqq2 ��\b\@it� ~�7\u-�(�r�8A�D( \Ls)"� HdZ�S*B5 2gQ<L+'\Lsd)=� l#E�-JSu�P�kpINI>I$.� pH$���1-� By>N��c V�)^(!"/{B).��}(�  ��"a-�_p6Xd��I �@ B+#�s$-� ~(y��/$d% {_{/ zero�/ntP*�X�vI�p ] �Bi�/&� J�� �h� � �g���'��%x�>�X��O�"JD�(h'�H%ꉣQ?"]  one0� L\Ls(p)=0.W dsub(1-"m�O �$ �*6sa" way�'�\�y�of>, \�)h>EU.B)�@>{]�"G$n`�n_{i+1)4� AfG)�9MaI�i �4_{n_i}�Q�S8PrI�(H!T%8>*. *��aa"�m_��2�-��/y-�/old�b�+�] � HA rɈ annuli $A!� �I�fig�k%"inn�nd erY-i � 3 �zX!� Zre"6!�d)N&k�g;9�l6Z)�}�C Rc�qad� $�/� XingY)�ݿ�4z(c')^4$"#?�.+_;s} &$E%a �*� A=� ��y7$. *�q;�/ %��@I]ai$engqQe�S7��<��Jj="k�@��&���11m�JH(L))=0 r9*Aw��!n)��>� uO�G!I�3eE? HProfessor Ronald MeXx. d describ�i�BR[/}Xbx a&p-thr�_�Nb]- 01��pl�W��� "o�&3>b}>F�`�D�%�;`a equi2AT FPA�t�� "���V`.J[ Mi9%�\%g jM� o!�e�4-a��C)� "F!t$. EaczOC5\ ��X *�$ly�2$pT���pI?��F�> E�usual� Lt�` uB�?���.�at�[taa��l'�is *� A�q#t)=�. �4!?i(agr�d e���2s m�uonI�Q.2Ac�F/1�c}04^kk�s)���y.�p"ut"L0ġ5!)t D1+��)%�bC�j(\Lt)H16�l$_��;� �� &+"6Sv)s�vA�t�H�previous!d�s� w"8` ketc� detail��::g )Vec&efw1half{� �&8M!}!%�A eS!D .�%a � X A[�$pEfB� a�-)�i� o*8+X*S�0cJ�8�y�� &8\r�"s;�lle Gs�W seem!tfi:*��the� "�C%�큫9H2:Xk��N�7!QL�Bgl�`��N<l� itabhYed >N��)N�a�ork�) >�en�Y#:s4sI��b�6/en�$��r�ri�B� UnlikE�Q� sF.oA�I9�A�z -!@Voften� alig�5{:&�X!ZW�a YD-^� �eSA�%�bAoJ}5}�$w�obis� �)��L� $S re�h�S%r��)��� a��85��{ �6�@e n��bourhoo��� .���t,"��o.� [#ieE���q+�Z�;�0�Y�&�-G �� �$CVE�ife�ʇ�*�,^!�%3w- *HՎA�oj�![a�*�.F�.!�� &qR (ch8:y�;v"0"�atwo��� f��� �j q "3�a��EU).YV? *�AA)+�Z�(AF)@]��p�?�0,^� self3x@{1/2}2WWend*�F�bf�U�FV��McAi�A�&�4. Wor�=�&�e� took!u�����H��we��p8qAM2�� �bau&Y�� l��� 1R�e�(�  ���9v&8T\�A(��l.k���^�c�F�[cBO%� �"R��I!�to�anz����. A�fa�p � ��!_e!l>�"� it g X5Ou�W%B�t$�yD![Ylin@9 y=is�aw:'4AN�Հ`� � �"�ox��j.R a�3C^�to7!2�A�Ya(8�١ ��h��& �ofY��F�k"%W. &�C6�* $_(A\U��!��B $[a,b*:(s�+~$�%b-a>2$�Vmultipl L$\$K3}� �&R�C!~�>�i� �\&�dR��=�3UY�w�s!<ch"g%lya&� S�,�'�7��s { extr� lu0H�,%��-\ :}(6�HRRp.�H"�^�H'$w�B>�Jby&�H6�"��� B (s2E�!Ka��t3= ?%)�.�)6,HRRp:M( R06V�}R� �&�+��!�dO� ��h�&'ow���(avbZerr2� Yge�Y/2B���*�(& � &�4It$�)R��R.5Pt�r#��AlN��$R'&��R�kic���,5V�ZoFnA�R^)Rp���.B�&�;�� *G 9it6*Ŏ $c=0.0�#sri:��62cR �!�!P any "rR�#�p E(r# fail2%9 <�BWe*�.�zp��$s�6�� ��.Hd $t(�K?�+%���!�7!�^�ptU/1/8�Rq4=(H([02?s])),1/2��&E!ߥqk.�.u |XtZ�)}2�قyc7�o!!�*ob�Za\ �a� 6�X"�T?Jm�A�l facto�A$4$B��98<b"�/)�%�J�!�/�$!�@ $t=6�@�+ �" ,(le�T$0.998s/6|V $s/6�/!P6s7 �_2s�B�a!6�T%4�.�"% ^i:Ѝ�#A%!����--Acu$s=I�*&1 0�6� ����G5$JQ�&5a1/8�s�@� Mh�A2e*t0, E@!�AB.�Vd��-��!,�A�Rp)� seX= &͎ay/Q<��sZ"���!�i�� 5t(40s.5402  .�'0��c�'|�6�S�ǁ@X!S@40s/6 = (40/36)6s;, Ek*�/6Q as  Sn*E r!"5s�$"\��&; � 1%O�>a� e� �/!�/.�a"�  a9������>� f+,Y e�o�thoL�>� wee\> �� �a��/��y%$, emphasizA1<}c����r rec� 6R "FA� �ongru6$6�5~9�& �R:2~:� J�BM�!�6-,aZ�?�n. 3�Q&$.����'}@�X�ds;%Oex��d�,� 0�guarant"f>v%!�.�����.UFl*$c'�(6 �2!�;?n_0)$ �E�� '��a $34�r+!T* ��Y�����n�Űm�VL;[�c'�To���f%�aU/��4oi*� �O�^BM]to���4�dq7�r:f�A, �U�J��a�S:�$ !)F1aN)�5l�c�RB"�ssidj� X�XX!E�. �nN~"�.�q&��G%�eU����Q �Bg . (I&7�Ws%��kisAsi�@ՋD K c u%���AI�n2 ůjQa/(1+Q �e�T >i�r2= � ictu� clearerJF�9r:�J'���a��!6>.�0�>)� c_1<Z"of"RR%�2� "2��D!@��� e���1T�p��ť�peK"S-� _ y $3h�11.�a6x7}�"{L!�&#IJ��(&��G�\LtI2�&��";R�,�%tN�%�%��;+>��$ic environSs��� non}&B@��^�$�X*ֆ&� �Ts..]% �`�EuIm�@"� wo� s:�-A^a�0f.j��1L(m." y�,a�d� �Ye��.on*�I"��L�Fr��2 the model\%��&FQ�*�.�^on�< -~"@Q1!"Ȫ�"incip� An�Mion�J2>�Gp' {r �5�$A�}��m� v ���"�q�;ᩚ. R�� ��mge��*�O2�y� �]%9Ax it�Las�%a�s�{� �!&�K �AE Kpl[I�s�t� f*)!Mf3S"��,�A,van den Bergv�&]>� vdBK*I!�y�k���discu&�p� m6t� Rur@roachg��s�e:�!��#:�(RSW)a��(�*�#A5�ؙ RSW)i#$ԇ�a (=�v7E�p�{8 :k��4A >A a cells�'oci�d� Poisso��oceR�%��n� ��Z. Due4TTM9a5��I�4�!b�'�BPU&) VRSW*Y� �},�!�}�*��a9�M 5��"� %zydk�x=�~ez!W�!�����!a�)�.�(igtruE�8D�,)� �.{��"L2 *��T�!m�e�a &:i�n is��heNWaCeVjpr�KA� 1 Jng����Win.�-+�-����b��Y*>�+u4\bS*)U�=�,*b���a:�h�s"@ �= meet� g ��7m��!זd^�@�'� ombiES�orm4 %2ofE�H*N �!o1om�A*��g�`�!uB� *�"�0�asXF ���}, �&}!P�Q� %O[�s�) ;S��<� ;��C|�ʁ�&�e5AJ* &D.�~(piece�Y-( ar) ߈�aoaP�R$�r�C�a �Sh�  ~��t :3rm{4M!L�N)��2�N.��B��,5��S!�(a?se SU�#th����")& #�)o��_7M��Ŗst � �9n& dra�= }%� stra�!v seg�����)�b ��S&e��vAQ��6�3�)5-WU�%, �!T L) �-V� YHb� 4 H� ��!o-$P$� | � 5�:[͏!9� S=I�; �� phif~�&�� ���@ ( *�BJ). B��"�0� �� 0Z ��.0t$th_wRSW}; B5�i�,�d ��� �4de64#~9�Ti K��Ki� ��/"� �r|m*���Sa��4�A -� ���q:-. ?J)$4a�!J%�a�"�S�+�$�C�=i� % ,[U�8�3>2�.i�AE�ك�A�z ing *�b�0p? �)(i  n;(�aIsg a ��� o,l.�a@�S����d1 spac��oat6 ���+ ?to �ɜchAj`�[�Fw4�A'. (i �set-up2!t A %/��J72z�traB-�Dv{u $(1o{E�.h{_"�� Y"i��X�"90�b s abA�_e. � i) DO�c�asympto ��7&U�!%we `zoom?2'�4>]��k��>� $\lambda=ARR$�;"H �a�$\{ 0 x:x4R�A�~Ef�?s�$R_7""�O&��$�t$�}�&��_0.�� 6 �> ozE)$A�A�C�+!� ermsY!�e�� �A�& _ �2'Os��),&�|\Pr(A_1� A_2)- ) 2)|.�4(iv) S (��I��#| 2�Z� �E)X ��sr�;5o�%r2�3 !�"�.�p% ������u�5�A';��"� 10^C$"�7 �7A�.��*�s�sU�sP !��Z`c:� )8t�ohol> Y6;Ed"M Aq%��~)8!f6���sanRPQ�s M exgj]RE�*c6M"$(m+1)(nޯ џV�ġ��!*e�� �)ah�5"7XxbE}k"o�Q�3N-R\:-R~D%�09?_1)a� E>1�K� n. UJ]� ��,aV�Pn,n08 �AC.>_�ePa� a0!�����">�i y\rho ~>� �� /�} ~j ��1��:�2�A���>�:$\liminf:�Yimp! #sup#=�v2AAf��I�� A]d��Y~8��Tlu�&a�E�7M�=�=!�Jx�`.:ere-^�} ����{D"�]>���M��AiD�;�)uBQ��H <�=���5. Our�3 is M�-� el�>� �t. I0!$� �*. (As�W �awaX����M�JA`X1hx33v)i� \hZs#)/~�$x=hBI�2a,2b \Z$. �ua��\*D �1��isZ�u,n�di�7bu�2,$\{-1,+1\}$-�Idq va��s $v_x�"�� e�v_x=+1)=�F9�{�~E2� �\Z�!y"W ���^$w% �!�9ll{C,b+#w0?1- r �w(0J �dd,Hn�"r_ a=b=�:� m=w(b,a-g��w%�!�� ��� a�Ri":R' �[a�Q�t� 1n"P As) s:��A��R I�Eya midEC $m(e�.��e��� if�*e:�J sdef�';\!�� } w(x)v_{W+x}>0�>*N! ���!�dd� ��� 51n�,�E�.��6&�� $\ppw�~s.0� �2�v&rv����E �=�3�=� �� 6YVE�"�3!�� 0)i"&U j!�sE�th���8���$a�e��P��� A $��(�)F� � i,E�J�Yg{ly*TG�Rn{Lglj:AL\to�� %��C�Fn.�.,:F�pw>~>�.p�� &8J� a=a(w,:+: =V�UBik!,e� M�&^We �$tAsoA�isi �il@�o$A&B� 7~ !�*�9t�8eB�O>"(�;u��sq����KR "o@� $w6?gr @&=\] �}[O�%j�!� .] A�)u"=e 2H�+er**s}��.$ (�^)$)�����tM���x2�4��*Lgby2vE�Q�Y�5�a 3av��rS� :{ -.? a� &ְof� � �s���c)e$��4 i*�aAv <H<{TcK�Y<)"F�dy�QNm�N�t)$, $R=[.�2 c,d]�lb-:�7&��M%%.14'=[a+1/2,b-1/2"(+c,d vno�ak%�" jgqN S"$�!�� *�. Ecur��-uϚ=���,lsK"�i�l}'�=. ��9lb#l��6 �VNk(-�m s�s )>0,�l��"� ��( `Ae� ���S.�>6n.5qO�T-waZ�� +-y� *���+�"3�s.����+ƟA2 Z  (on �1:�D��� )+\pqw bJ�٢<-ph/2�%!2>H: r¼2v��.�$�� "�isdfH0�_&&+1,;=;0�`H��`�W����%&ǝ6":�:� �ct�U9E�sC+  zQ'f1A>cusse<�.w&.�呩�)�LJ�3qa i2�����.�� �eb)� AH5 m . C��e� z e�"�?*��*w$8&{�*m{MaT .>>Y. "](ic2x�o% 7 6� �h���s�� t��$D'~!et�?,]a��z%>&�74 a-5$DV Ud>Qs!l"�0A�� ^�� >bitra�naL��$eR_{10���Y�� cFo� $c''s�� �gpwg$6n,2n})> cy(�2�2O%�%�}.�!��(way as6.�&�% ��|"%#XA ari%l�** A3&�Tm�BĈ&DSR��IA)�DBon>�EC$xdB��tFA �o}!�2��1�&2#b�)� :� "�*i�xb�  ��, para��c ��M��K*jQ2 ��A�;]&�8> >��� B�)*�@�ex }* ^�)W� �.�] �^������� {Rϭ�&ra�c*�} � f�ʡ�mplL6a�� ximaA\!/f�. sJj,"�ds, 0)n�y�E|�����Q-passag6R,by Vahidi-As Wier&�yVW�^J�{a��e�$�:fY M)�a �m!� j �"*Z2%\ a��> Î�nH�e��ZJ*�a"�9��Q a�&)>�:�0 r1�#a"��sHer ��U6��, Zw�"� .vE$0<\p,g?:� e.tB  � �ylsly-IO, 0!`$e.� $\pi����� 9���pi�L_J � %)1jN�(t���$z� HIC V(zpăa} \��$: d(x,z)$�_{yE} y)\}_ �?d(.,./!�F��.�S$zf ' ����~�sa��Y � X�*=�L��� �S�T!1 ary,!�F� 1$ a� ,convex polyg� �,2V���ilT!� ��E��,)�?\Z, YZr�G[)o'd �}� �b=/%�� �&)n>n� �2�B�a�er;E�M x do�%��of o4�*"+ meet!��G. Giv�)� aTp���eM� J a�atz�'��7EOZF�R��|E?.�L pp{p*Iass�+.�,�H-x (!�)��+;� �i�("�S:nV�� ecu� pair;5�aly)*�N3 )�@ "��aO�Nmr ��p��y���2KT��a/��Ba;J Xn�dVC�Q.!���W(f&�3t}!)�osG��2%�2m��!x�fZ���^-O!>\pi>lUA :�a�I)@^ �T  .t$5n$%Ys�J�(-a�\>��B��to �ft�$��caTtqy��rg�HBp' ?)feu�Z�}ki�ߵachY�6&Bit�a��, �m�:�re��E�7-T�!��� co�2d��_� �'A-�_!�{%8+-4in% | thE�e�g�L6% to񝍪.s 97Z ��Puggesp�� Ǚ"�'�5N_�;�fP, *�|B� "�D�%�@ �8i� �( �2 amou7��Cun3if'ex������H�0wo �ts)J]Id�|�Y n�s�(harder�E� �-dV�iཱ�+) v�z݇�cvN{F�g��+ $v_z�+&z\�5n9 , � E�������M-1$z1h�Ӝ8$�*a fI��ly �r�,�-Tz=i;_a�< $p_{-1}=\pi(1-pp_0=1-Z Y#+ # �K*Ѷat%9�A�}��it ,A� ,�i. E"�l� 5�7!� ��� �% %s�=�kno $z'%~$ Ef$� ')<'&v_{z'}!�y �!��&O@*�,A�%.�oA���(z%?V(z��� "�Ja����=ށ���if`�>�/ 0&�/-c�aP$z�$z'-� y=�P$x� 6~0ck&�*��aAYC""s%��>n "�(%���z W84�!C"kA��o',�a��i��H;�b�*���K ���HE�qM�B�!�"�--�W- -up inherj��J��2BataB"*� A7P�.��e�n��:��L.����Et($aHKlikel�at-����`usS%og&)$ �eIin-�]'�� 4A*�� &�1%Te��%exZ*e"h�.{����A�no B)�=^L� $0�!�*j) *�le�e�.� $1-o��!�&����0Z �AqdeA��4]-he�)�#zzic2?2��-3=o�*)u i;*-��c�t�U��&dC, �:cr ��b��*�s+a�u���2"jH �^3� s%3���mee�*@+ ve dV�Log Q�#��!l%O1-ЧE*i�"�`b_*�Xck@. "�0�m�� b3�=B| huN AI�EU���� G�?����he"9�.�8%� =l),SJ�m.I��7��N8ed��(PN>!��060A%�� .}/�. y'f]Vi>7�topolog����-)�"R�ach{1)��5��R�6J��� �� *!��f�d�{p�j+��p��&d�8f,��s�� Y�O_&wd��K���byV�����EE䁹^�pp12&pp���� &�%+N��r�/ͫ*G ag�=>zH"��&� %}$o�"�I{-ffbIo�pSz�n��1�!�( �,! }\�,.+O$_0*$0f02-0I _�) �*92�O 3)�A!�i�a*� �N&j!�Yg $ae�s�xi�p-5#>�dVwV���J asi� �"a}� O���%9�),����ust�6a littl��refulR �he�I*�&�:! achieve $*"nK5we�@�a�7�$G'wM�� m�6a7 # >��� ��n� sa�e & J�o.s $�=E�w �E~�anA"?� � �.���!%`N �nϗ2�� &-52. A@' techn��G�kE�! �=(�:ypfmainJ @ �@wNU�,�b�A�Z ��I-a�*C� �\68��^e\#%B�6s�r� ���1e�UP]�] T@$b@!pp2����W�!��3�!u_2�"��$ 9e�͂!���� &�8 min���A�� rs�S��nTJ�C��!E��el�T2 s�8�7�)A-we�Y*�0of6�0p'��H9pX1 �P=!�. S� ( ;iB��Mw}� )D(v�cpl�Fif-�2o� 3.2v:�SQ Z'�0�$.!�U�)ono�6er qui�)r�C!�t A�.�� �"x�{�%��C��?..Yt��&�"�vZON&� f6w;J� +Y| V� � �"p�)�U�-R l!vo�-4%�gb��thebibli�dphy}{998ibitem{AB} M.~A.��HD.J.~Barsky, Sharp�-5�Pe �:�R-C,7�Tem Comm. Math. Phys.} ��108��4987), 489--5260�NF�C.M.~;� , Ta_0!"!G�!e� behavioEb*V ��e��� J. SSOst6�36 �04), 107--143.���P!/"��.~B(&��M.~��, �%tinuum2� �r���L� disc1R� S�Mur�3 nd A�s-a2�42005), 392--402�� F�8O.M.~Riordan, a�9Q.e) � O2���CG&��3��a%�jP*���]y%�Re`k@d Fields}. Prepr�avail� � \webc�+@http://arXiv.org/b�/0410336�Z\Qa&W �A rv���6d0�em,N�Buln�qDLondonmSoc.}��592�fm~� A n��� R��u5091316�KKKL} �aour� , Kahn, G.~x�, Y tznel�IA� N.~Liniala���$�!S&R �����em�Israela酌m%77e�(92), 55--642�t ��� ��. P6 (, 15-20 jui�K 1958�O lloques I&znaf8aux du Centre N �,Recherche Sc� if�8, LXXXVII (1959��A` 17--37. %�L��=��Y} T.EA�Q��XA l9��M^����!�Ly@1iQU��FQ01960), 13--20.���6��~on boolհfu�:� �29-thA�ual Sym"��0n Foundationsl of Computer Science, 68-80,�ociety Press, 1988. \bibitem{Kesten1/2} H.~Kh, The critical probabilityt�ebond percolation on the square lattice equals $1/2$, {\em Comm. Math. Phys.} {\bf 74} (1980), 41--59.B�816�Analytic�,properties a�Dower law estimates� func� s in2�theory�,J. Statist. .�25}�,1), 717--7562K8leitman} D.~J.~, Famil�`of non-disjoint subsets. ) J.!�$binatorial!� ory})&1�466), 153--155.��LSS} T.M.~Liggett, R.H.~Schonmann%A!Stace�Domn!�by!H0duct measures1Annal%DPY �-97%--92��8 S.A.~Molchanov-* reli)�{��J. Appl.m��2M�5), 5aK562�VWa�0Q.~Vahidi-Aslb(J.C.~Wierma��,irst-passage2�-�4Voronoi tessel�W��@thm6)epsfig} �kcap�X}�,newcommand{\ labelx(}{\bfseriesb-,size}{\small%(addtolengthQ)}{1cm!�.smetti�[1]{\ �{!�=#1}} 2,$Sol}{{\rm  :chiorb}{ ^%:%$Ncentre}{N #  ���(em{lemma}{L[se�]�#teo}[(]{T�em k!�"Proposi)u�&cor%CorollaU:$nj%njecture6oex#Exercise!�\ i style{def�ion6= defn?DZ% fact%F 2�qa} e�Bh��l$�l>7example%E  :�raik6�!�1�R  �U� matN}{\enF aE {hbb{N}>. matR�N.RN.Q^.QN.Z^.ZN.C^.CN.P^.PN.H^.HN.S^.SN.E^.EN.Rb�RR�Cb0C06�calV�calJ� calMR�/M��0ef\interior#1��int}(#1)I�U}$nota} [1] �{\footC �H{��:5GL��GL>JSJ  :8V�- aA��d\titsc=cmcsc10 scaled 1200:+timtil�egin{pi�uH(12,12) \put(2,0){$+ es$} 4.5sim$}�;}!..�`finedimo}{{\hfill\hbox{$\�0$}\vspace{2pt!m2=9�4 %@1pt}\noindent{\it2 of of!�hJ \ref!j.�Pauthor{Bruno Martelli!/add�{Dipartii o di+ �:(ica \\% Uni��it\`aPis HVia F.~Buonarroti 2156127' , Italy% oemail{m �(@dm.unipi.i_ \url�,{http://www."/$%p=/P`title{Links, two-handles,� 4four-manifolds0 subj�p[2000]{Primary: 57M25; Second0,5Q60!L \keywordsvr $smooth $4$r, �dlocally flat $2$-polyhedraUthanks�e )� is %�6 supported&�$INTAS pro�)h ``CalcoMet-GT'' 03-51-3663%�I�doI A� abstr��8We show that on��G$ely many l!d� (a closed $3�d can have homeomorphic co��AVs, up @twists along disc50annuli. Using�(same techni�x , we[ ve �by add-!O-i � <� we ge:� �-�Dcobordisms betweenAI givenN�s. As!onsequ@,�re �F< -1 q4Y! D truc!� from�8Kirby diagram wU Tbounded number of cros!,s,)F,E�!�nds, orQ(Turaev spec�shadow� FYv�$ces. (Thes �AuA�d�#z ak alogu�Heegaard�)�r pines for27s.)Aytherefor)�two� tr� 1�!�f all1�-Q$orientable�u� �I� �Y>`!�0equivalent af� linear re�=in!f and � r cardina��grows at least as $n^{c \cdot n}$. �!yj \make�� \y *{Intr�R � main�ult!�th�pe� n be�erp�dyan exte%�1�(��   decom�s), see �+S}�a detai'overviewElyE�� ,cularly effi�t w��.q ne�!�$1$� , sinc� ey redu omq� colou�e�ygers: iLat cast �p�  must!�simplya�neW . � � �9be (er!G-'>Bds, or� Y^A���y.��general=K$2$.D " �half-�� fa� ayy�t proved re�ly� y eff:v �T �.�)��m I�� se%� work��(Costantino APTK I7 CoTh�7� !��!,a�9 �A.Y�rZ!�a6�!�:CqA!na"� %�,���  a*P ��*N 6>�JN (s �� diff� sm)A�� nite j !��+ � &G �1� �l A��:� ��� �� ɽ���ow�to studyj enorK -- 6,�'aAp�stic !C�",u Dunfield6'Q� didI�� p.h�DuERFor inA{M!it + s sensE� conu to cal��tE��tye�a�.�! be >�� �xEfsy c�(- i.e.}~�dmi7 �ilure). 9�group)� \!�� total} �Q��e $n$-th12!=fi Zt m  O�#e other���  easyi��U0homology toge)�h well-knowv ��Freedm�,nd DonaldsonE�� �y�>W�y@ )S*Z sm}�s $cn^2$�"nya[e� �?l !J0en arise: do] e.��j�(e� :�� m� than quad� c? Iv2de�a6^ha� e fundaal,up� ? Sa��1�4b inA��4$n$A�� y. J�it would���@12�\sN Yeoccurr} for �%val�$n at- !�ones l�Z 7 segց �Y�A�L�y��H �Ʌ an<� low. l��e�,.tworld�  natural�1�)Sly] ��Matveev� lexity, w��dals (��i�uciK5.) �minimum]ctetra�):$�RT�� �;Mat}. Ma�)�< $n\leqslant 10$��b�z!�t vari!;stages� MS,�a�0d Petronio, a��1�!�$summarized� �$survey}: jt 700$^ 5�5!�)Q $�8$`� 2%sl��}*8&appeaE�� ���� $9$,Xthe�� �e A����z=�Nb@n rapidl�a crea� e �MI|'!�aE��a^be.cis�un � � �b3a�r�ed  {��� �i*� )� Co}:� h.�I co !�֥.�w CP^2$�� $S^2� S^E(wh!�m�%�p%e:�m!��) � or big6b. A� A�.�� j�aZw��A�BEL ``f���aF. 6hFM) *G Yũ�do not"[ �to vB� tors?#l%�$K3$ UOb.4one? Of cour� ����'� de"1 rext!�F , lik o��(� ab(l* .c) �heJAwIWx�%a:EV�I��f�#w�s. a� being seem-|:� ��:=e� tue4� less� ��kt��2� s (b�� ) iA1icfA�ut�al eM $), becausN)� t$�%4�2� ���ofeQ8:'H&/:  �{already�.� nsively!��;f��pVis organ�as��ATults ��y% d ab�a���CF�M2�I��"�, excep�c�Tə!� �:sconvergsI , ��ch� �A$A2�!yJQ! |�� �����=�re6n e Bf8��t�c&�a,Tin6��:slideK�*s�,�$ *{Ac�c ledg�} -� i�oA%nk Fran\�is.E���helpful��I�sQM�.� . Tr echi���da� !-pW� MB� !�6i�e.� 6%tegory o  �4� motiv��EM�%@)={DY�1�} \'N�� illuate�s��l�2>��5�G�ZWA2  } Un%�k ~���/,Y�� rbitrxQa $M$ Pɳ term���cd a� . InŨ,#moves m*ansform2� $L$ i��an�lP[ l> ez)aN!+f: �se $K$a�a�!A$L$2rev*r nR)8borhood $N(K)$,��,$M\setminus\���#{&}Mn�A� �*ntial   $D� �A�eQt ���%�$L$[ p1e�a� a full��} n:C� $D$. SimiL,�6b�0_1\cup K_2)}$bwo.` $K_1� K_2$-EA�F�m us $A"*-� W�AB�, �!r�|-�q % �A$�WA�=� !"Om�a$b�$|m��ZB� Le!5$��a *�!%�Joj�!a%shw �j *P,� to 2�IM)x�uV�! � � $M=l5���by�q�}a��� 3$,ahy'� oder�e span� t� Y��l Fig.� �:�+-(g3��a�"H�A �coaxial=i).�eB��> 8 w� I�@}� c���!�torA�\�al N(a nd:�� a meridia��!_2)$, r�2�� �u�!Xey �A�� ��0%p�*win y� Qe�Y�,6�r}�rp"r�E3>���DQ� )ҍ|���l$��E !R1��s�!�6e�fig�, � er} "�-MN.ep� / = "/} �.{Ai5 �a�� (1)�As��A) (2):G�r�3eAd�.} -a)E�i��x0� !� izesm�' u� , sa�!�� ��)�am�:, A��aiev)�)�1 pairs. Ac@, h�W{ a�_asVc vc:n�q  pl8 �5 also��. �-�$2$-UP�3 ./'"I� �! rela��byN�o�4E���C� T&by�3e-�Be~ *G {H1)Ei2� " � s:&� e��&sn.�&����t2�. A top�ical =!ifU8 is i�s�,&�� g�2y� l>8 esen!,y���fB�of� �,. Moreover,�   !.'c�a ��� �;.� typ1�FM!�EveryG�&Pa��n)�. IB $0$-,q,0 ��!� 5�(be attached.D� a uZ) wayM LP}� e%=huge 4�;!8R�du�1'y p�(:g`� ;� 2�&�+e��d via] ramede1��!�ehar6�#.s BF ( says rough"�B� etyJ J�e�fixq�$ is�@!� sA7%�U,e�� i�)amI(� r maiM""� ��$N� �Fu+&nd $Li�t  ��"j� �*�*Zb+� �z�"    (%Os�#!� ing)�S! ToA�pre�3,�Qĩ�M� )Mux- 's [0,1]$�HitsU&�T� $M .\{1\}� we < tify)�$M�f*&,z�on�, @va$N� r- otop��@""k*. ButQ�1��E�.� OqGb� xed,"rin�(��")' $N$'id���A�.HE>��!�� n�otheH�Ea��uier�-�O �X E�?&~ Hopf�?t b.i [t] � page}{.02p8` }`1�#J4.3 \ ing*� �6� .9h, \vglue -4mm�oΣ66.o{Ha�$M = N/ ��x$n\in�Z$.���Y�, cR� $$2$ balls,�I .�\e�. � til  \c� �,.\#\over2-g6CP^2} HoddG�^GS}. � =��9"��-!�E(.��5I�"�&Myt%� usual nK, q�>�. pa�etb�1Un6�(��N;,�Tccord�=� 2 ��&� �E�IH"� ���{< &'%�.�� t!�de�be",'der %� ��M1s�2X. Ŋa�D$k$-skeleton} $P^k �t M^n� �!�5k2�% �H!�*��& �Y��N�F2of�!lf "! hig"�$kwIf $k=n-%P^k�Pa n0Dl�3&�" .�" is- \�)�� Udas $!M�0Mat:alta:dim}� s-�!�co�-a��hop�uat��rs� ght:t)�� 2�,s>� �(1�� mat�0�.%i� . Quit�#$rprisingly��O&be6in=p $4$:��H%L � ure��is  5A�. A 22�2SUh:f}�Y ��4 lat}"{8]5M�7 PL� ion� 4� cD� sur�(�. r heavidor�a:� S"�i�=.@ Wt*iscusN3��}D."I� � s� ger�no�.} if)� ��5� �3�EcS !*.&�5 $1taY A�(2�a�act�oj"�%�c"X�.W ! be:� planar�62�}�ɤ,����- coup��!�(�����spA%)� S^3$at �e�K )E�a�S�5 (o L*|�s�d�endE�!t�_ V�&� ���J F cR�,,�8��; . H�� ��Qak 9w�'nk�4A�DLaudenbach-Poenaru��(3LP}. ! �{d  .��76 6 c:��1`�����.m�).)�i� (d�\-$1")� .gl o eace%ANAЁxs�)m��:a�/own�t&��%��5a�14Wa4fin���w�t}o:�,k!�sum @)��r-IN>.��Ar[BVZy "���� ��*;%�$.��Z.�s 6� :�)�) ��R"�(is�,� %�$n$�Q��A �f"+1:� $U_n(0� b�� >�E�6�1^�. W�9>"{( $U_1��\ldots U_n $q n�edVnK�PPs �-7% AլjW1I�� ���inc7$P% ��R� q< in � new_�- dard_nhbd��if��ee�F�K� �)!three=e�y>$c+ cell�2iz�I#P$6�- 3��R���x "= "2) "s�*s)� )(vertex}A�a 8a�in��Z�-(3�2�QޕR%GJE�u.8N�]� ��+-�*���Z�j� Inspi[&by z%'s C �;Tu;e �N-0� 6 m�a67 ,��h Qf�.�� S[4N��h"� iQ"!n$�t>��+h$���4h �:C2n[J 6s�)�u�83.�>��N�A��7�q2�qE�b[2��>�-VTu �> in �G7 f�W��I4W/ng $V��a���!� 6"� aM|)�.� -$,%42�V<t � ��2�W�ke�[comd#< ��w54�> s in",]'5sV��>)�)]{ &| a�?w9B�?)TBd�+sY�� Q�:�4���q�V_{3n}*!!�U_{9n+8}1!v $n>0��f Pnow��)Iin�ƭ�)L.�@� ��m$RsaWF�% $aAHof&d ��c3�@n$�"O7 s $04�(# �"� #�t%�f>��"��P)6�$�?&<�->� ��� EW a} V�Be��s��B2$ ����� $c>0I(�I1)�|%procf6�)�~�$1;!9��t"QE of��$FriMaPe3},C O 8of Mostow rigid~0�*N0.�s�ageodesic"~..�@-�p%.9/��' �� c% suf$�[$� immediargets:UD�NQE t:O:!<�#"�C $\frac 14{5Yc A�9���%�)�)�q� gN�4 uS%�celebr��B!�"q61���&z6 D}��eas���:Q�|1.` N�� �5{16} %B��\��^bsm) $6����6} W��ia�ee�th� e y�B�� u:y�(q�)? Isbig5t�.&�6iF � +�'%E5AB5- Y+a-,I*w's w�Bb�#m9���J]; *lz"ka q:ng%ori����e� a volum�Cd a Eu�=-7a�;8 geo�zr2�� ich �,�/� UhG.�1n�(2p.Seifer�:��BC�t*�W��.Sp)2G z7, Slop�S�(T"�,'. A���!CaA�� 0 basis $(m,l)ʼn $H_1(T;�^ZT'�sd} b.~is��ase�E�e "h+�'s)A��U y�unsig�:CD$$\pm(pm+ql�' thus~ !x-� $q/p�Q+(\{\infty\}$�� ��g�H} $\Delta(q/p, s/r)!+� �s-#ir�2�9M;crm$,C alx $|ps-qr|$(J�#s�rea 'N%�<"�@n2l�(7Xy d�:�$�C.)��UAVll ��vTher! top)�of � > Zcd6H!�@c�0n6. I1 mpled�4R6e\ S^1$g�;; spac�palla�� foli� E/�.!l� �)�(MceH�LofteneNVE�&� fac*7,�t5Q�SMNz.$\{s_i\}_{iMKN� 'Brs�L� I=*� ���_3W \  $i$to \lambdaez�5>9 �3neq64A $i$; X!�&� ��c�.{"� A[An !�!$����I�� case�p� mM,s_i,s_i')\toi6���  &�/noI�6 9 invol�B��U�)% =q_i/p_i$-*|p_i|��|s_i - �| > k)t-@.�: $B�= � e,q'n '_i)=|q_i -p_i|=|!-sp �.$$�j- � ��W�l���$�lI"�,M$.�%�� $T_1,V,T_�� note�6$M(s)$E+��2{�fz�$APvectoh I� $s=(scs_k�("�"D#Cby tAS%T!�a soli+;ru' a map se�>t"�-�$A�.U iA�2=>ks}~m� 2�W��k���y%G�-&�4 D5�s.2�n�R�-fiber�ovem�,: $FM��. ooR�h'Nd�8!�us $TILt ] �9ak� $m$ ��:�O�I�i)l+�. * F�D&� a� W &�  co ntly u�'l�0. wise�Rcho�q� E��.�0 $N = M(q_1/pYsq_k/pAw �s %j!�orb� $\Sigma$Y�by�#%k$9!�'���ah�c"8Oo|;n� � $2\p�xum $k$ (we ass� idwlog}x t $p_i�� ll��)(1�+rH invab_ �"fi  ,arejs cha�Ter c $ ]( ��5 !�!$ 89 e$�$e��ch?= 8F)+\sum_{i=1}^k 1{p_i}\qE  {\6 nd}  e = F4{q_i}8�  W�1�(Q� , $eIk'Q�Y 1Lt�#�3 we r�l,MV0&w@De <1$. By substituNa,/ $�� q_j/p_j)m� +1-1�!H!5�a��&(is,lDKI�Ie�&�f�b""�&a����@: P:��"e���UA�B:Z� if6P9Y0(7aEon-nega%�QS |e|$Z �ly` $N�BW>NweM0|\pi_1(N)|\ge�BRG"�� �6Y��E�m B�n�Ex"�-5�, �<� � ��Sco} w��) = A��aaa�re done.*Z chi > ��<.�\ �!q��N$ lifta �S� J� \tilde e$�J3eqas�4c�(`t zQ c���E�n��A�oNL�  $AL, �%@eJ�� q_2/p�5�5reo8�a�1us.&�I= � ��u @|p_1q_2+p_2q_1|=1T!�:W$|1|i4// p_2|Y �� [k 3.6]%�!�i A�]D]��Vg[$Q�N� Sol"(s}.1!�*Ha�"��%be��%n�oriE��jn�t\�-"� �Ja"�U(�[O ���A�B�!a���_� 9 APt5~ terval bu�\ .a2� glue<4X+�"�!i�Y2� G"�J�$35` } An2�Gy�G�%.,Z� A��i&�,A���--^#is1tisfies"4O's �z��h�Qurea�2G�e�a �26sc6�}�  embedd�"N�Jo bloc�V�ne�]RG8' ree2�&��l!�� �[�Q�she �`\ " R�&�(�-R)(J��XQ ype f\hT$trivial.},� 2�+ I@�a9F�R��>el��B$K�X�� empt�YAA�e ��%�check%�1;c�R&�+ ��� 6:��v E�F �T �u;a�.�� Kle�I ��V�*�I%��ch� k%�a���f��� ioZ.&�s"�enume�  u�|�_�/�>� %�2�<0"t�f�Z� Zs adjaw!���J82$ $S$ �Gin�U6 �S��.�end)�� S� 6d��mea P�E� he 0le �2�SshhM not ��"R�Y$ (6v� � ��A�nic&ts). A5�u�9w<0^U ��?>�UcFlI�M�aUU�v# M�"� qu�Tt�LVol(M� �4i�;!M s![.�"�4Z�iI3�zor5 9&�  �av$ �=�O%� �""zsum��he � heF�,�u9*B(e�4�1he�I� i� �.:?j�.=��6�eZ�ef.w��MեL�H�R&&  ��!����Zy]=�"oO0 �2�5�n �=� A$2S)�dq*l�!J� �if��@w}t�5 M)|$I�e � �0$�2�:�is.e2f�O��<�aJ� )Umonodroma�ps� T $ �\min\{fm,%(m))+ l l))\}$$?9�>A ���M� ���=1��a"un]a/wof� � %GN'$&w.L, t�#�ax� l,l'��U��(.] �� s $l�\"�B-�l'B'�A���ua< �e:�3m want �$�0m�v53P!Sglus map"9tw�P them� . To�O�I,�+ tarta5e@8"� �%�a�g� �ny {!!Fshort�Rr �_ sqA�� cusHR.���d situw isF�QL@yE}& � �J�ntrins2/%�e��Q!u&2?{-w .~ +s�b��0<����/wo>m�q�5 �le�U:F�9 !�Althoug�v_R%q.-^econd !�M# !NIts)�}i. � � !�5��hhV� A^> E�e@)��_S"Mmax�V�T�s*� $s".Js.J�%>$ �J"7 e�s6�2 a ��:�KW$�!�� �l��� o? @5�W�x��UA�:�!(!6��;% "&�Pd!bW!�We.� -vj�-�!���}F"� :LMFsAF �. Finj .h��m�d<�X�I $I�Q�?:� �&.&�;&~ ���� �b else0��7^R.�F(�"{q"�"; �lٟ .%&� .l ��� E^ ])�-�s��� or-U; G� '��(-T:"� �:�� cM) = v_7 %|&M e_0$, ���$'_  .�0%&of)o!r_H�"�  �o�is2�� bibbia�TS>T�>2Q*Vol_S�{n - (�+s+ Hk) \ \big| \ n>0,\ *�k9n+2\}�l%�_+,$$ �:�.&� �-��x_�x_k{x_�! �H�" SP �#�H. . "d,�%]J.V@fN��/)�)�-�Bp7��q�Jq$2$"�3giv� X$.W) "�Ŕf�1ڹz�M2� ��e6($E�9�9 �� =�Qg�6.�"�a� ing: l� TՌT_2$ Y� ori, �J �ppe�Aa hB?(_i, l_i)$. �Y%$$K= �%u�6�2�)s}&si:T_1�#�F#y))5 �T(� _1),m_2�K" �{ 'l'l:'.I��N"�-�$�!��E���Ey� N one,&�&) b~ellip�X5�;�� j�!�;�� left) �� � �'&~ �h#i�;,K�&i piec��i`s�"� v�"S4�2�/B�z)�*e"]%Jhi�$v�� +v_k���. !Tj�h�[�M%1%;J�"�-� �t#�J%vrO�-=��4� �. "N%�ond���=A` !{zaR�k� i2ztonR*� � 24��.2�S.k' �Ja.,Q�by�Bni���$�- D�$"% N$�m�$et $(��:F))^k�,)�) �C� $T 'V,r5� in�r� a!EA]�C"60"'B�$BU ed cl~vq� $N�%� ssoc0n%-w�d�e��R�%v �%1&KE>�,� ^Tq�J�� Z. ion:�{s^Bf)�u]�6�)1RbanA7say ahnA�sM!@1��(big\{N(s^i) }$oe�T~A� act,!��B�)JG)�n'n\���**0) SA6s^ q��s^i�$�`) = (k))k)�4c0 =Hess�Xhr_j.*_j6�(-{�C�,&O �c_"one�p j��l�*ha�%for'd�A�s|_� 1�A�K)$��7` e��c�n�q�_��7[-{h we �f�s ��tt!k2�-��_ �;pDm%\!�2�� �`a BAaF,,of��i�Te writW6,i\nearrow a$�n $a_i<�+!�$i"[P$�   >�> �6�!;act24 )Y� 'Y �(M!6-�.�W5 of (*�O)�P�Ana(to ��̦� "A#no7Aq�.�0'b�P�!�,%nouqp<.�_{j'}�fN���]oQ=]�"0$N�H1pajz��b1,���^if���~A���$= ,.��)U2 )`'q'orp' e>1V$g'�OA<"6@�"�>P!`fal�-i��ahyp�)02on!\�Dl3!#ii"�h�\A�)�*�+2�D�ua)w���|m�Y 1��6cy)� (,a.�Pa("i&�;aaA�Y�^�*)V=S7%�.UtC Ŏo�j�Iif�>� � � E+2�� d���Pq/p + i, q'/p' - i)$,b�li>nM$()�, )�*�eA�nu�Z  ��e���fpen�1�)�%�2J �W�/y �M� phenomenai]�ko l . R8-a!m�}�ocho ?@.� � �5$|aBM,%cow~naX�/ I-AC�// a�)/p)$-.+,���new� *` F6� �KE�1OF"�?8\ .^�>�)�Y��3sp"s2�y "&#Q�: S*$u� ="A&D))|� I�&4alA�6_/� �.s%)F�7 Y\~N}!3N$Ujn mbig $X" N$)%��>H?�a�� d� !>��e���/� )�)��BQq<02dU�cQ,E E�-+"9�B=i 1xm�$:�@ �M �=�M�a�e>-]h �P$A%��-of-pan�|ndND+�"NjP.d)wo��e�~� $HHH'��;r�p݄;_!�� E"�#A�y� s^i=� K)��H$.�S]�V]/2$�f_, H', ���0��%�uRFu_6�)�Jvk$ Us �*c �2.�,EK^� �h=|)A�Zrs3� ycFlly *7G 0dmlmatch���# Txi j = i. ,j� ^�5l�X\I _�$e#�)�>T�m5T6rB�V���� �w>��� +� a<� devoTq>SV�:$��  ^i/5s_k� %�a����6ar� ��at i,[$jB)e�� s_j^� sll�.�@& �8"0F 0A)�+ ��Q�"�)�2�$e_�̍�4�b'�AN)X6�08 �{I*C �8�jF ����a�"I4ކQ3pI. B��banc�9 .sz"�s^i, mF�&95]e&��� �2= �8VJUr V pr�t� � [�[ } Bnn a�1�� 22^; z�}Ti�ir���=�/�0�,� �x$!ry 3vO �� �/zn .n�mZ s_2y�U~he� 2pg��2&��t1p:Cvno..d AU.�} I.��v� e M\"obiu�srip�.s dou(.%�0A)��0�0 Y��+�F Also9/� f�+_�� vi�e( Mi���l$j1N�cerlʖu\9 a��<�b @*QE�� 'qajz�#e j!j^�<j!�� $|5�J� �<��4_i)\s]� ei � �;�l&U 2�=.�w)C ��Dz./)q' j$,.g�J s�q"^Xe�a�%���5`� �  an�igtradic�76&��a |" E�e(N�8j �>{.AYnd9�f�&��rg�� guarante}.(V exs`6�$�+)# r�q���.�Q� !A�7of*� Q +arej�N�?. triva �A�A"�Ii� \ $N&�N_t�?proce��. � $t$�4'"�t�i�!�a� $t6�J $N_l]��EjeD�.or=l�u��o6�"��1� r`jnoS9�* �VU�Y� "�Kan���� �2��^\&�-�.�n& �$$s0x�u replac)2!�"O "� cD!G} JL:eqn} {�;on\� \5-}\ N_l,\y at\ '8\8\"(%\q\ }kkmbda_j5\ is\�\�er\ }�07 �BdPerr51�"�F N_l(����t ��"X"�J�ћ O�Ba ��%5ill!�"� i�h 1.�m�cup_{l%=t!/(x ��(��:o)��K���0� ,� =e (v� )Z� lBea��"�Rxe:���m6 . No9� �r&ZO 6�[QA/Me�b,��El��.*tj�*��!sb �}� d<;��2) �A$"ME�jR=�12SJk"�%�X<<2��!Ps��%U>�2�\!��I�!�����G��4*�eM$�z:)�#-(m�z&>Sol�Cih�}i��rc����s uxu lyl�*� ��%f W . %\; �~F�D%�.H_i)EQ "�D.]Bw>$�< � َA�tq�, ����"e� �@ N"Њ �@"2�Y��U �e&�=.�w�L!ts,2v.��$P *� �#� e�s $q_1^�ZMuq� �=Q$��  = q/pe�)z �CAM �" �� vC4Cw~*�.!jAJ,�|Ae thir? 2�26��e�9�J; e $-|. ^i +�>� �M W |%>A ��.�\toD!# �� Ga|<i:Y���^��;|N �nI൑�a>. � N_*Gi".y��� modify��@#��"Qs_*^i/#2F*$,a remo� �B9F$, prevȄlʘ&�9�����&5_i�� �N_*J_*�.  D߁�-ai�~�xCwT��! �"� �� is�r1hʹ�'%k I�� �{lw� t�_2� ,.le��h$N H (B�1�}I�+.9!vFa�$ ^]Z� &340(�P!j�z�_* $t-1&: � m�ssN.on HC-��A5&� &� I21&>wP\�� V M7!ba.}.�' �*�g MR9.&��� 9�R.l�w$->_, S�(,���,.3A��:B( �f�EvEe5E >� eD!�7bHc�O�ZE�se Rs.aJB^% G$ suff ��ho&��2K" `a��|.�� $Bl)>�'$ �T:�< $K$)�A\W*�i�yYB%�aq�+��th7s= ��bei�yj�jyVs (�x(W�� G.�i-�nlyaF�F_l = .� ($�a�2:p�<U:���%��d�W �� $q��"6ov .��R�=b��m��>���)���%�s direcL&q�M$Fe ��]&)~�9�N�o|�&�O�2�"�$F_i(\eta),'&� T w7<eta, '{F�Z$"��_l�hT����D��c�lbe�_our�.�a);� E�ei�+A B� �0:�L\pA&&/ .S�%�rB  6�I+Y/l���JE>� )q`R&^ ���-�n�)r6P  �"�0%P]�)a� hx�!�f�+@-NҚ6=]{�Gc-����lJ�0m�)Nn��2i#.&|� ��&�B j!�$Q+�|S�VVE"W&; ^�q4*E�%�u,i��j� � ^i � m)�$|#� ����a�=aN� �Zq ]�!7�B$S�I� �C::, J`8�h�%�8J�%�(.��Z�Jh�%) 0M�p5<.S^� 5o�AOEe�a��,�"�!��gs��#�< tegn�h����L� %'@"-�2pT� a>'L'*�_�ͱL� not >&)`�AeDC[�|',.�>-"�bO. &r2itA ai]�;.2ajY�� $� a6�.)�-,!���E��yv&!mI�U�0_l�If =mC,I�M�I�=m9q/"� a�}�2  p^*=X)��alR�av!� �(iV�&� &�3Ŗ:�� _+�4$6I[�W#!��'c3 te. "�� �bLinks"~�}&όM� ��m"*B�E�C�n2)r�#tSB�TeK� �/A �~ ;M2�.�u# ��=e�$*�`�6is- elf-*'&s�o�6A�1M4ut��,Z!� Acback �A�]��"�*�-�x�dI�L=a6�� �o�� Ya�&0��_)cb42Lw.!��$e�ly 6�&0is :5Z 6Z� $�Z=No$�f| &�AU���v�6`� �(� �w� M$.�;R5 ��P%U�tP"^3 X !�i�!u N�:�KA%�- +;D3�A>�|$M�P�pnecessar�d[d&Ho$Whitehead:��>6A�4�U�r[�'~�'~��n )dt��,~�,~%)%i�s y���TT%�&z/1/n� $(1/n,��xb�$&b~ :T${magic}. A�� -M��p�,7.jimE���a"�w(bans�j�f���R o� ����o�A�&g�!in6� �%'A�WQe �}�G9>'�swQ�all.��qUi iLa��e�.�MF�U"b�W�}|OcLr5*-a�itude ba�2!�:�s.�belY�eH-1m7 �*�  PR\j���s}{.���!$�h w� ��is.4,"uG���z spl�'!�� ini�i��way�Qppo��+"#o#9*>��V�*��^ij��com2�J��a�8B5>��fbO5A�.�+ei�`G+�V�� anx8�h�# )j � <p e�A�$� If %^W3�pP�e�8�h!��_ ~�ndFa�2$M�/4�g)� �i �%� Zx !��="E9"�>�k�P�3"�o �$� �� N=�0$zp�"�  R 3pU �f: I u'Ha� � ,%A�y�u�>&9is�eed. Now"�-�J�*%t�/E���;1,1�!M2 ���E߹�� E� �{��$] _1, 2�2a�  \pm  \mp 1��WB�A��u.a12�Z��a:`. A��&::� s%9��9_1>�fwe!ENj% d.bove..EN>�E�hA�_(C-E('_1\in [-1,��M 5k!CoOo>�E8=�(.UB9�iOv9B �(h !� �.��Z�:A�g�w.��j�>aM�es �,�w��8C-Q . B�je�>n�A�rguD��f5ya� |�f$�.6 ��!,�E�26� ˀa*"�T�a..e'љ�'$M=6-L\if:� : �we��,�c�6� !���(�k;e�. 8���27 :[&sz �Kd)' $sF %�ll.� }[ '��A%>k��A�*� :(V hB�rsI��%�!)>�k1!� 3� 1-1 bi \�bcorrespo�ce1<�"\��� s\ i�' Mz'�� ing\Y\EE\�s� \ } N \rA��/_ K Aut}(M)}}�IX g&a�>$\ \{ s\ |\]dMB? N)}}"�I�"���EGc �a�� �Yi�:Xub>� ^}�-c�,:jQ���� �*b�Ce��)*f*� O�d.y����aDa.a0"� 2�%*not�%�Bh>ΜA7E&:�&)��=&%s,E$5 �<.H OA�{� 5R�Qa�"g u�%�U-. �!6U�.�A)}!�>L#Ps��f�Y%�N�t6%�o5 S��o � !@4e�f')$3$>�e5� -%n-�17_�6�2�@ݤc�(Bg&y!�,���@YeYKa+:�_ ac�0fi���׭92t�nd :(� _ha�c>��� "�6�mǓe�� !y�l>#��"�'In}�:�0�?7�y=r�@�8�O����mL���� a%�a 5c�� e7�3"��m)2{� $��a ���Fh�C��btQ^k�/Vqm�  �B� �U�gG-���$B�2h.�UNd erty�A"� $2$-�FR}4��61���s�~5�L L:�7�}le�"� or�R�NE= �a���a�Q (� � .(~&v am5���$�B=� x,N=%�&:!�8�l |s_j|�iv�t^�^�\~�, k.},.�D,�=E����oH�"�j{"%�E��s� .H,��Zs $s"H H� )��� Y+�*w"�teu�A_i� or� &%�"Ry�E�iU,K�w/�3E� �&,���� �4�nc��>E�S"!�f2ar��@�����uished�ilv�}or2�@:�,#:on�m�*�a 2:�+ :Za>�  �qF epm.' �B&0S,\lyW�'�M�!�NS*o�1:����b5C�I-b6�_~�K��sN�Kq�2&�v�'$L=\{$pt$\}.m�)�IK<�# $�� FzJHC ʬ� fev�;����]"� ~ a)�] �!��i��`.s�s�C�.�(Ud� A}2WO�q,�G.r�k�m�Q NfiVn &k��Ւ�Fv�+is encoA� ����g�N9� �^�y�:��A-�k'�&�yA 5F@ �I�e2��"-)A��;�(�&�ink�'$N2bs�� ��TM(simultaneouhM$pne '8�G�+�6� �e'�]�%F��4!���s�x��;� �a2)eapaE�� �#��� z�� $M^�gi�2�-�Q&=�=3��%5M^{i+1}�[^1= �)JM^{k+1}�3^�yA� �st�k����k� ( �P��.�wHYyxng�a*i�%�C�A/ S�m�3w��� T!+� -Fe�}&�oOSrci��lS5_��g�*aNme,�.G"M5b ^"�7i6Quu=9\wG6��d�@�!&J4�j�d�:(���}� � r�ed�(� 1�.# H.� ��2� �C�. A�9�]J��N$"y ��56pe�w N are pai1@j_#.�s. j:! :� W�vz&�3�l k�F�;fix=1� 9A�"�*B� �&:� ]���< N�!56� �+5uA�dO��a�����U �� 6J� Z�Y*O��@�B^�CX . uep��:x]�impL���5�=� "9:q  .�� vi� iz?2{a�"�9Rvia�ri�Ae�!�ed{encirc��r�HL]d2��61n!-� .�%.��'H=*�$7 F��o-#el�Q/��8^ �( $� o $a+2$�*� �`s44�^iV#���{#Ab��~{A!��0$��$1�I &� �;��`J�&!o.gqx�" �r6c��1~%.�"ț,9�%���ٳ� ���i$0$6�E�Ĉ blackbo��Aing&`#p)�E��>ΥF�!Pe(�w$k&Nq2�x H R�e(S_j=\{s_{j}�[B�XA se�ka)W I�h$j cbA��W�^�� 2�,{�1f 6W��>e��O� M �� $\s9BL=N}r^i�F bC2� �#n�*"���N:� �#� orM�5q��G.���� 59��. ,ޙf�T A�aFR�E�&)Et2�ctop�gEcA Z� be�A!&O� . Per�rA0�% �86� �2��� FigQ��i or�  ���� in�����#�$:{�Q %�.}A/MqM�{j}|com�AN&.�c2Fc:S2 : �nW��#� ni�R'%�:ei���>$sel��� .��u}$ s�yAB&"�e !s�Ake�0&�#sor 4 ���u�Qxb-vA��$Av� ts� �g���(* =M!; �0�T$M^9n"�YA�eT��< $k�= b�cC��I!�O $L^2"���� ��be � "x�w��By!�*% &�=)��ts._�)*� e "m(1 ���6'  eP�B�eD� � �.0��: 1 L> +�{K.������ A(!�"�&"H� E� : :E�}2��!�2�� � � �ޡ��7" y�O2��AJ6_:� o&c�:pa�tr��u�T��)� , $h�e s,�2;Q�� Q���A�)|t \#_h6>IV~ e, {s�����P -��.���E�M�U� $M=F�t��N {h'}:�f(h' =$ rk$(H��*��&+ L)�J5*� �g�(V%�N !>�!�!��c��;h>vBy�-�Y�%Ma ��&0<C ��-�J3$4$e�way|-�itu2&�%:�#e�K�} O|)�������(�"� w�A$I�A�cou�A!�����GP $F I��0��l>�)p�2�-=e�F%�1{L��Ul���>�a"�s��.e�ĉ�t/6u>��Let $Pq�"HVvu"F �5�".[�nes%���+"(�2$1$":� $P^��T�i N � $N(P^����&��t��3�&N��>['��&���E�e!v��6� ABB(��0X�)TI�}� openƗxs ^� &� !��  >Tuer2��p��)��g b5Z� &�37c2ħED�Z:��one5�:IB$5�z g��MR^3$, H��!]mA��"F���Ip�\E� &P �%��R`���zPMA`�� P5��D� th' ubul>o�A3ekBhC!w&0��� B^3\ w+�W�?Z $\{0"] 'X��Mf3$I��C�L�AE�L� $f_i: �I�[to%|� �\{I�h�4E�� valxEvw�$�%� $\nabla f�h q 0$� Uw 2x�� $P�s (2�&k]a�.���5� �s #�q$f_h��dinnW-� F�=(! M�I E�F�7 $y_0�.'ap'Ls_F� $g:�%Hy_0+$,HjrC6et2��]�oEc)J%_:<m�1a^,�7(1-g)f_Mg-h,$�aL&(=�NOU a� hedrA)I�m]B9 E*�*B*h!��5!�i7>�ЅKQ�h�3A�on 2�By$|� mVGIl Qi.h��w�P=O�%rz0am!|mo5� -�I��ca�N�al�!ed�i�h$ �Ul�F f �+ f�ˁ�Pa��>�=�!�.�[.�, .�]%�U ���m�A��"U� �JN:� �t o7ite!�aȉ� C��wh�F��  !X�yyeg!X:7 �U~�?�+CPE��z�o,�F" *� ^4�.�< ae"Y�al|y �4��U (pos}�y%�&)BP� body $H^3", �*w �J�J� Q]thick+�6�) .�6g4$,�l����) �� ��fL��H��� ]"�(�4B!Mk�@� $L=��+3�C$H6s�ade%�0$�&� e�ce�S"&* N^1(P$P'%!) $!= ) 6?���c"�*2�3�&� .�&���'� L j��H^3, L/8n e]$(H^4, �"gThD����6v'�M$)�� S b �-:qN�$M�H\ ��� >�c=�I���~�)��s�%i&|�a !�.��ha?�6T!�.2m�@QHq!�.va�=!s:�� � $v$�$DN1<��H� ��.,' (r �+}7�4��{s��A��}@ �� �/2%���I�?%�1�D("&&m <54st�&��eO�r���eE�3A� �end6k&�%8\label{PL:rem} �LA $2$-dimensional polyhedron that has locally flat faces is not necessarily l&8, \emph{i.e.}~l��ness of the $1$-skeleton is a serious hypothesis. For instance, take a closed braid $L$ in $S^2\times S^1$. Let $P\subset D^3\times S^1$ be ��ldefined by making cones over�braid, .�\every slice $P\cap \big(m,\{{\rm pt}\})$�z]\ points $LD�JDDwith center $\{0\} �.+,$. The proof!sxTheorem~\ref{handles:teo} shows)�if $P� .�� n it�conta%) in a_�perly embedded solid torus, and hence $L$J?' $T1�� )� Therefore� C`sufficiently complicated !W=� �E�.�,even af!AaA~Xotopy. \end{rem} \begin I�4also essential)0I%�e,4a neighborhood)#I1@smooth} $3$-ball.:�(for genericIjsA� .aia�e>�$constructepRemark)�PL:�haa^.� :�PL� ( �i�)�1@$PL-flat!),.w, as follows:!�)�int liesa�ide a �<\ we are done. Otherwise h some2� \{x_0\}$IKby1$ityA�ADeA\Pat most one triple of)�� $Y^W lya�in �circleZ�a3whole� .} \label ^�)��� �cross!�%Y each�%�\1I�l�� coup�` discɝ attaM� any �, we sl�: �I�itrV2). ()�E no ?atEܡ� dd a� frama:riv��(knot.) Fin� ,����Jno �wb�ơwAJ  � V  3). �� result!�pifQ�~�#��>�3E�A��s 9$k$-�� %�, denow�  .aya��`� (hadow repreng%�sa��44$-manifold. T� i�a biglM�382~ ̩�it��aa-sp � n,Yk>K-:, 9� � ��a cocP �-�9� =2 � _newe.��FAa�.�Pae4 from%<6�of�� to5�:-X2�ur_ genus%� and )��,s $\Sigma$ (!Y $k=2$)�7n%6a�/� 2$-Js!�it!��ing{ �. DotsY$�r I)]�l 8>ujy� y,+� �O %-�2!�s�zIz� a ��ubQ�%qise*of�L $0$-!e.:6A !M .E�.� L�plu�(��I��Now�i�) a�y 9�� q^-Y �$we get our-� . E���Oʥ� non-e�d�|pr���C ex� $P$:A0� $P$���~'j � . MoreO,8! easily se�o�8special, becaus�e orig���;�ed��c6 . Concer�r$V&<U_{9n+8Y 2 @ , well-known �3sla�H!�a=6 into>]8~\cite{CoTh}: ��, t�!��29!-he plane BMat}. n cu{�n $n+1$� � rrespon��to edg��c! a treŊ�mplementI�, pair�qI cut,� 2�M[m����%ia2 Dr!5w���1%$!�egers1J��s will � �a2��a�.� 2��gleams}6F-� Tu})^�%&j�Wm�ney�� e�mt��mO�$)*� �I)ABE,� $4n+3.8 N�_r�&> $3(n+1)$1W� $2 E(%�i�%G� �2� �$a~$. \fLimo 6/ FundaA�al group7 pr3 ŸT.� #4 We start($a similar �4�-��o�Da. ��prop}  _�numbee. ��fB� of Bi �$n�(gr�as $n^� m s��}E� n inM{ FriMaPe3} ����5sn^{C\cd�}$� �?J��t least�{cA)�m dspi,fAtinct�erbolicA�" s �geodes�o!0 ry, A쥿$0By Most� igidity,Rq �s have$J�(se�{ Fri}es�7 this fact�(B� case). A} !o=.5g��r��-� �ubsGPR�I�E� } Proposi��v EK i1� ���Y�FAc!.!-�1�!f�YaQV�.� .� :� To rec�sJ m�A�2|,� es (2:F�> passu �� ̓��v�versa, tJ�!&��A :� ?a �����, .�| mad`: ,7 if&� s.A�en�qs�d � a sme0$-�un�� &sHfor its double $DM$�1GS�� ��&4n$��2� lose& , $\pi_1(DM)= M)6�E�M�SAn�� u�:]�sI�s;:"� M�and ,homeomorphic ��a*J-_ >V^}�" )Pd loure-z$\pm 1��5�!�hsome $\#_h\matCP^2\#_{k-h}\A�line{� W� th�p1�$k/2$��57!���B< rang��$1$A�A�� $n^2/4$NEf_B2Fp}A�$Freedman'sy� F}�xp2�II  2sūdeterm up�usm�their� rMdA�m.� mpute how���s��a�7t6Ba�fixed!Nk!?. Gaaodd�{i�� typ<(\langle 1 \!�le \o� h-1 $i�$k+h=n$S�upposL4-h\geqslant 0$-switch!߁�or��  (ind�iteʼn�a� eral�Jonomodular�s�, whil� 6K$h=0$ ���=D'dsovD})�.n�a $n/2� for�X� BKBL2kE_8->lH$!�RohliF\Roh, GS}�;I� $n/16F{ Summ!?up�� �< $\frac 9{16}n+2.&E� 2� . A����?ao*#bia�-lA[ rankt�c. ��e��8$\sum_{i=1}^n (�i+2) = @32}n^2 + o(n^2) < {5}� n^2�wq�6YAe\h *� z Lthebibliography}{99}+ dibitem{BP}\textsc{R.~Bened�d -- C.~Petronio}, ``Lectur�n.$ 8geometry,'' Uni�iRP, Springer-Verlag, Be�O, 1992���e�J� rge}�E�Aa4extk� $one-tunnel�s' link4th� �(}, unpubliso$manuscript2� lHoW�4S.~A.~Bleiler,!XD.~Hodgson, J.~R.~Weeks5 0Cosmetic Surg_|on Knots}, Geom.~Topol.~Monogr.~%yHbf{2} (1999), 23-34.�Co5F.~Costa�!��CxW*�xp��in2��|sc6U!�8D.~P.~Thurston}7 $3. ef&�K 6\}, {\tt Math.GT/0506577��1�D�S.~��qAn app"o gaug��ory�c four2"t!_8ogy}, J.~Diff.~)y�bf{18%k83!k79-315.m DuTh�(N.~Dunfield!WVFi��+�^randomE|��}, >2566FyM.~�!I)�:���B�mb�7 �(2), 357-453.�E %)� Frigal�Hy"n�LF[ �b *bya�irF� }, eogy ApplyD145} (2004), 69-81� {&>J�!�$B.~MartellJ�)]Dehn fil� of cusped.�39�Z�fu64 �Au425-45.u {FM}:�� � J.~W�0rgaE ``Sm�!)�9��� lex3s��8 Ergebnisse dere��ematik und ihrer Grenzgebiete (3) 27v�.� {GU6,C.~McA.~Gord�<L��� �#a9�"�N:&memora� SISTAG, temp.�@., 314, 71-82. Am�"an� cal SocierProvi , RI, 200.� {GL9�6�-�Luecke���� A�N�2�a��A�th.~SocY��8�371-46�GS5b R.~E!`mpf�8A.~Stipzic}, ``2�!O �calculuE0Graduate StudRi.1s!, �ibKY>N��}�{K.�P�>�2�E�8 r K!s 1374r�82L&�$F.~Laudenb50-- V.~Poenaru"hA^%&"4�!&[(�bo!+� Bull-���~Francei��e00�h(72), 337-34.1{survey5��^ �6���BM405250},�app� in �,pac� $f Kleinian�up%fLondo)�.a".:n Ser.~329 �{6���magicN�![26 �.c�(the ``K''�B�204228}.Z,Mat:alta:dimy� S.~Ve^ veev!K��S� �)~piece�%1 !2�L,} %� USSR-Sb.5�21)١�?296�ц:�4 ``Algorithmic�ˁ�cl[f (�=�e;e� AuL>�Vol.~9j(2002�Roh9DV.~� 9@Ne8 � X "� ofɈ.�+5H`}, Dokl.~Akad.~Nauk.~SSSR5N8�195�221-222'Sc&� P.~Scott� m!�H�.���%.� }, e�J�C� a�\1 401-487.iT= * �algebra� knot�$trivalent y s� Turaev's� worlA�� T� ��6 !(��� �O6.�{bibbiaUx>�  `�ra� Eqh ogy !5\,.7Ao mime/ed�s, Princ�,� 72iTu2@G!%��8Quantum invariat%of%&I�2�'',0  Gruy�%^�E�18, Wal(d3\& Co.2lEWendB  � docu�} �*\e��[10pt, openany]{amsbook} \usepackage{mathpazo} %\� ier6[N'�ed=0.875]{helvet} % ss %\renewcommand4 ,default}{lmt&tt 2zTamssymb, enumerate, xs��,Iyicx, url2��[all]{xy} \SelectTips{cm}{} \hyphenat�'4Groth-en-dieckɁ|ileMatr$  \make�x .�[notci�notref]{�keys} %� \��in{equ�}{E!�setcou({tocdepth}2>:s"]2<2^T{chapt!� 2� \qed!n$ol{{\ensurd 4h{\spadesuit}}�650bibname{Refer�*s!H.�\%@%Indexa"�ionaa�#@displaybreaks[1] �H ewenvironA�{U0 a} {,8}[\upshape (a)]"a@ !w^Qi/b�.1QijQt*{! d }{\ } zy# 2{te�g #.�d}[1]{6y>{#1"�)/ }��:� ${main }��o�.2#B[Mf]2'�}[ 4]=^/-Y3: .;-Dqion6F corollary9{C2qlemma'L 1Kstyle{�2>�^�no�+N2Vexample(E N'sF(acne5�a�rk'�06Nnot.r� !G.1rN1+ ,2�Y�r~�rv�r^�rR�>�- .F$*{claim}{C  ©� step-Om�\{.�}0 Y.'D[1][\relax]{\addto�� 31���*{Step !R! #1���_�`�p\nome{2D� call�>lf-#1}6H:|) ��\bref9 >.;B.reff2��fN~({#1;#2})6.refpart/:&�����A�hcal{A}6mcBB>CC>DD>EE>FF>GG>HH>II>JJ>KK>LL>MM>NN>OO>PP>QQ>RR>SS>TT>UU>VV>WW>XX>YY>ZZ�6�AM�bbB�BM�bbB�CM�bbB�DM�bbB�EM�bbB�FM�bbB�GM�bbB�HM�bbB�IM�bbB�JM�bbB�KM�bbB�LM�bbB�MM�bbB�NM�bbB�OM�bbB�PM�bbB�QM�bbB�RM�bbI�2G SM�bbB�TM�bbB�UM�bbB�VM�bbB�WM�bbB�XM�bbB�YM�bbB�ZM�bbM�ݙbQ�fB�bQ�fB�bQ�fB�bQ�fB�bQ�fB�bQ�fB�bQ�fB�bQ�fB�bQ�fB�bQ�fB�bQ�fB�bQ�fB�bQ�fB�bQ�fB�bQ�fB�bQ�fB�bQ�fB�bQ�fI�.�Q�fB�bQ�fB�bQ�fB�bQ�fB�bQ�fB�bQ�fB�bQ�fB�bQ�fF�rM�rmB�rM�rmB�rM�rmB�rM�rmB�rM�rmB�rM�rmB�rM�rmB�rM�rmB�rM�rmB�rM�rmB�rM�r#6h rM�rmB�rM�rmB�rM�rmB�rM�rmB�rM�rmB�rM�rmB�rM�rmB�rM�rmB�rM�rmB�rM�rmB�rM�rmB�rM�rmB�rM�rmB�rM�rmB�rM�rmJ�ma_ rm{a>�mbbBccBddBr(peBfj8ggB8hhBiiBjjBkkBllBm_.rmnnB8ooBppBqqBr6�ssB8ttBuuBvvBwwBxxByyBzz .qfM�bfB�bfM�bfB�bfM�bfB�bfM�bfB�bfM�bfB�bfM�R8M�bfB�bfM�bfB�bfM�bfB�bfM�bfB�bfM�bfB�bfM�bfB�bfM�bfB�bfM�bfB�bfM�bfB�bfM�bfB�bfM�bfB�bfM�bfB�bfM�bfB�bfM�bfB�bfM�bfB�bfM�bfB�bfM�bfB�bfM�bfB�bfM�bfB�bfM�bfI����arr{\ifinner\to\else\longrightarrow\fi}6-x6x#�Mi8{\hookb#lC6i:F#owsim{�. set{\sim}v6noqed:�e�20 H{\op5or��2 cech>%\check _2, op{^�kop .meqdef�4rm{\s�) =� }} =: %.�i�<:� th{^�{t�� \def\8EI_#1 �em� op{\ }\limits_{%-=o#V>big FB2oho!�.�Ho Ľ�curshom ��!)�PH}\hskip -.8pt om}\no �:+E<2iEne6�xt:�Ex��2%isB�IsF�au>LAuBLtor:qTo�s2qpic:%Pi< 2%�7:&�!%�.KodB5:){\proj}:RP:Yge�/te�la@0#"A06- {\GL>TG%.�{\PF&>LSBLS>L\6" .g\rk:�r� 2#i�� rm{iB-p>�pB� indl!o�njlim�2!f# $=� arrtiK�)��'�!t L}}\ / H�H{\ignora2\ {\hsmash}%�settoE-a� #1\h={-D Z�� dash�� -20pA�%w8��iW9a #�9 will  ;, %bu�D;: % next"HQ?�ed)�Pdir{ >}{{}*!/-5pt/@{>����=fcat!(�Zrm�):�cat�ncat{Se�2, catt��T��B-��� f/�>Ksch�N7 {Sch%�FVgrp".��rp}(#1>�aO 2AffJRaf�ca |&!F|s:�R�qco '2{ QCohN�catmod.� Mod}ɀB&qc)�TJ��alg:�.Com>�NqcalgB[-J_ca!�%�{!{:�a2�S�.~(urssheaves{I��S}B)� rm� 25fun)M�H� l(#1\op, �setrB ss{^:�2[sep� 2�pe� a� �peB�sy>�SyB�soV rmFq� rm� 2�ta� rm� 2�,)^rml 2mulB�in� � >� et{_a R\'Jl{_% rm{c�2zp^ �JWr_!S=ar " def\naive�t�rm\Tiny }LR6�${\underhom�![!��55AC}^R E vF zGautvF= 2E2D< �bin{\d � s>� 1k ��%8xym�%@x{{}\ar@<3pt>[r]^a� - _{#2}& }�isoIiepsilV"2�isoam\alpha6�\Aw 2+ArBTHtba{{\bf TO BE ADDEG2egm5 S] �A_ rm{m}, .�(qc{quasi-co�B nt\x��:��/{LB desc$$�� ���r' sub-schem�2@ J&&&;#E�v%�(�!\title�"lEG�'en�'�,(ies,\\ fibe0=�Tg�:s\\U7��*�"y\\\ \\�\�>Ver�W�&May 17B007E�Xauthor[Angelo Vistoli]{6!xdaddress{Scuola Normale Sup�4�re\\Piazza dei Cavalieri 7\\ 56126\\Pisa\\Italy�7ail{ax.vix@sns.i!D%\date{February 16 � ] ke%5#$ableofcont/PI includ�$s!�%!i�'"f9� �)M�2${mrabbrev,-Ref%�p�7%�B�*�^\0&*{Int�IA1 } D �-� UNa somew*B�;id��>7.among�,icJ-ers. In *A�;n? say)E�9 cerN�Ed�Bs�:�?sms betwJ \qc �� M2be4"�U�Uand�n glu�O�Ai�Q�tisfyIatibilit�@ � ; =.pthems^+�{ via ���@�wCs�cyrUco �. Of�N rse,�`` � '' w�<to mean�/� Zariski �7''�D would!4a%�al stat:5,1�lyFCful, Q hardlya�erv6;�a�anory. =/�Wi-�.���s5��OEW�;1�6SA~t�>a�Xnot��.ogy �E��BallLR/N�y}. H%EhACver�R are,&�Xly, � surj�Bve maps1�! a fi�9�[9� So!d>m�RmnPck%!. �An eB��>�F beco�[$highly non 0(ial. Still�>9�!vD%��tosM9 ac�'"��!kt2��12rA Ed �c!(aNI�Ocanon.����.,.)A��JoaI �developA��)�;soY!;>ierK!�,T�<F8,AOmy opidXIDO!�!�distaste�:wh�XE��2.� loo�@d6!( X they"all�5�\%.ls�U abstract![�4`` �� �:aworks'';dN% pairXs*�Q �%�a��A@/H!�n �+��sT�3}9�Oas�@stacks�O"QC�al�Dis quite�8�B outK[ of moCi�ory�Z�!}9�9n mE i�!4oluteAEent�C�J�� jE4deligne-mumfor4 artin74}% Hlaumon-moretbailly}-�sE�es�d bornaMaCmp��y ten �1�A7Ng%Rnd:�}A�! 9Adv�8d SchoolBaLA5ic"o4�LA�placeKCLI.C.T.P., 7--18 July�6��y!)bU�Q �*!��bI �.hNFy:2� ('s FGA Expl�Z},�>�Barbara Fantechi (SISSA), Lothar G\"ottA� (ICTP,uc Illusie ("�B\'e P�� -Sud), StETL. z9O Research)�N64 .~`6J Bologna�Z"�BLby A.M.S..\footnote{��on��c� , pos�6a�ke � T \url{http://homepage.D /S /m� .pdf�F�. inu�]evolve;Z��I, Icorrec yerror�a��eda�A�m�Z hope�it C���L�A)ad !Tnew ma9D al.}�Y ir purpos��to�TbHex���� �U�a���e�]�]��al (s�� �reay )���5Mmm�^d) a�F of2� (i�g*� - �}), otMan�sga1}. I)��!�uag�Z����A�he a��!�ext� ha8 b� i� � % # �\+�D$dard sourc�� written. %��Tat�4x is II�ow=�gz�b!�!0F��/��: s� ��,:er iU f�emmedi?gk@"�;E�probably�ru� ted. O-�^ >A�fin� �s�/ both!.er�4�a�DblQU��\�Q���yEL/U�,agree. Also5!#�Susa�3M.or�T�[v Xnd���m�9���&a���JasoObe!1:R�r�neverUt convfd 4� x ob� sU�W�� � E�w�if a�"tidA[Ow3] itl +n�g5m"� � � isDge)trQ�&� ��ora)�eavy (AJaŪic�K� np��L�, see \S�1� sec:-�-�4)A[� y quA.gXwisUF%0 hoice;�Id e-%�; mysel<AM:y �wa�= deed�sible. AM�unhappQy maeas��A�e�i�c�d��Q� �Um���herE�l �eAai�A�9R YefdO��  du�S.�.2ILnoqinmzG no�niLA� , ei%�i2A�U.4},�E I doD�?im>R���!ag; ��modern ��s@-���I�U-in&( �7(A-AXM>��8joyal-tierney})�MinR���m�v��$noJ!�ry�pLkontsevich-rosenberg�xGɘR(�z}M�E�eM exci�E�j,�tFis>� ll� &X �er5Ti�ideb?``higher1R5>s�cat���"Zp,hirschowitz-�son. s�[t5$).�X�����I6a��< i�Sr@:�"�b9Y�JTiFztorc �� I�.�,'s philosoph��L esen[ JK��gA�)- main io t�veq s� R>!A3Rx�>I-no!HDW�� f �ofpQ�Z �M�,)� �/easy. A��JV� syst>j�ved�S�� �view,��ira y cl%rbeauti�in2rehen��iI he bm=nerI�i�@demazure-gabriel}/ In SoMUec:�AH�; dR�aCd % :!7>� } �6�� pretm�!�tI: m2�D4intuitive. Howa AH=A����kof%J us!Hsie��a�tagmso I A�toMTmZk �e�,�$o �S Ital0Gex1eT ,  viviMTs��a`y barrel�g%��ZX pseudo-��y����,seems less cb^� A>� `}�dedM�6ZGB�}�� EZe>�)[J=�� �xEX�y�csadal�]2x&�,�r"-Aqi$� is"{�)�!A��� 8 em= $is Yoneda'!Fmma�F co���s*� equi�&| y A!>Py (.O��z�ers��� ek��+ lighAr  co�]a *� of2�a�f���he�` sV ! >4[ . A�q U ough�� iQ� data��P1�E)i�Ea(I&)��O);lence)��1Bi��!{eGof�� }: a8ck�JpN�| w [a2�����#؅y`��u: a|� th,e��sfear�]��a itle )eǁ� proc   km��te�BE �be*2�}/)%t����~i& \ o��I � @re>a��)��f�(��ph�)�m"�endow1 a�$�O e butua��dil>�.� ��1�W�cipal [!�orsor� n2's� inyya8Iiql�bٮE�&)!� I��$M �doe_n)S�.E)%�CTw�.�qnte�x!k!�m)�9�&8 r",� Michael A�. ItsM ful��v��n�P*� K$e4a sen�vB�]%V" ���� m�AB�� Mz ͅ. =$��G&��1ea9\�i`��> Ja"g to� txe!q6not�}�Bfur�delaya=h���e��BU Prer���ZZ �����!t acqu�Gq!!�.X)!S� Cl� !H,Hartshorne's��h5I!�Ɂ5v�`Q� ��!� B,pa� A&� q� � ��� � ! FN�i� pr�%��rth re�J!�! ap%r?p�eI�\'{E}l\'� - g\'eoma�ri��briqu�[iFf �Jt I$ e�/vy%*Q��Hk 5�: ss���.�W QH u�E�transB !:,.-=i�R"J% �a� @1��yr&I$r�/ F&-�a�ex� ion:%���D""MQ� $y faithful.>!.8!1�R aQ 2�Ac_ ledg�,s} Tea�`c o#qI�A� �'��*V&��e�]�:(he camaradeAh>feAM rs (B�, *��"���2�ym-vHnthusias^at�6f*�ipantg% am�Qi-b�th{��}� �{&o��abo}n�b F .P�$��`d.aham�y!N�5�&usde� sugg�o! �invol"�$2 �h�worjcof*Y,pdef:s�&�-� ��8P>�l!:*�@--�cG(Alon Shapir��aE�ous nP'of yP �lem:criJon-b6�� Fi#zIH lik! �)"��S�^D m�<s (-in-law, Am �6��led away��a�86� eyI%��� ^He �� he�q�i lear%�d2�%�e�a k�A�r^�p��ya)ձm ��"1�U�la"until5E� da��� b� ins!�A+!Am5�,� �:nz-} "�q&�f�{&�#ry VNh3  �E-�me:"�!��"n u!�Mۍ� All ��i�� �ll�s. t~i_.�y �! w��a�custom!;"� U� a ``� w, 1a+A�e"� '' (��f��a�Lem�D �b�;par+!�6�s�o� �"�+ s. R�<-$Bgxan1n:!!� $A$�sa�* 1 � _ly� enfaHe quoti�0* �qnomG~ ] [x_1, \do�]x_n]$ �$A�j�D,lփ��l. ӀA�noe!qia* e3��"a�MM�!�en�  O �F��te we !$B = F�/I$, $I�m�Y��xF<$�[.�41.4.4]{ega4-1}!��2; }[S� mbox{�525 }] A&�u�s $f \co�X \arr Y�)�v�} /3{"X!�;v'!JZ } if�� $x ۂX$A�ax�.F| s $U-Є!yX$��$V  f(x)�z $Y$���$f(U) � teq V 6\cO(U1s9�UQM2$V�qend��A�X C�XH/ifq��.��. `I�&`I��o�u�T4�o{_�6o u}[::]8\hfilQqe]P4pUe�VDF�-%ŵ,%��!�!�^ -��5�Y$�p��ve!@=B���m!��� �1&!pQ�sz���!y%1Given rtes+u�e\["68X'\ar[r]d] & X \\Y'a�[rY}\]a($2�~�� s $XQ r Y'�tA�.�r !$Iъ�6.6.1EV1j�2���� -!� act}jqR)25�a�s}a0��inG e imag AwŻ6DE�I�A�i�.�8m��%Y�B$,s|.�6ii�6���u�0��}7qs;�� g6is ^!, "�A ingA�!��R�pv).�!�7!�5 Let N� N����"!XMj.�m��)2D�esa�6�!�nV;Z�Nr&#Y%"�4 $Yxr cup_i V_i�V�L�e!�6�͡of � $LFe%�2 In*E, =c�va6mA �6I>^nR�� }y}P en8to �u��94eY9*2�egI�)v7v0-V&� �.alDbsUFo"B2C���O� iat&��s*+a�:�ch�"w 0rad'b'ls�&�aB �%ni�2�nble�sa]XAs� A6n�� �; Q荵 %�Ë2s;�e�!�A�)� obbyC: �!cop�$!�� V:�$U&��N_�;�De�Y�� ��� re�-:�o�!�1._Mq��e�- �Y$�e 6cop> $X$)��N�&�so�xA�2��~qw(zN6.6�!�@ 32���6�2}�\�2����2�:%Pvv��6��^us tur8;"� . ��.�� Xny.  �Aai=g9a�"� � � �` \cO_{X,x}� N�-�,ule[ %Y, � }� .�Q8./2� .�2.1"(2� !WN�r�i|��a�.�f����U���F*� ɪ�� R� �!b"; l��1� m���T ��[p�ȅ�V�_, e� R{� ..���2� 4%��l�uja�5��Z�Z��Qf7.J�/a�lav:V+:5j>Pi|1eEd&�?�|.�i�Bܚ�F:�Qr.S/>�>�i^/�oc� dN��}pec B N�E%6�A0z��s 7.2�<7.3]{matsumura89����� f�n�BN�95� A sequ&!�$A$-m�<^MLM)M''Sexa5�6�  /�QB:Q�O_A1eM F''.$ !�v�ho&PDf��in\6�J�asUBS��6k�1�l����XB �2$!��$M .= 0 e�$M�h$�I8frak{m}B \neq B&Й�al� 2.b� �z�6�fE(��y "i3�z;6�4\ ��ɖ�6:!V->��} A�N��"( v9A[@�wV&Tk tru[l q\%��Q vw;�2��weaker �" �!?holds�3Co�m ire~2.3.1> Xj�-3�-t�/y}JV �26 5�De��!]A�A�&�0�:�is 0 R�In� �s, g$��� i��3ayf 9G� - rmk:need-�w} ! �2.7&� : ��A&H.6 >M� �!, let�� +teg}/\�cz��� �OBω ��,�% disj3"v!,$��� Y,ya�( $1 F 0$y�Y<��&�U�on Z6�4�:a%*�0��S�,a:-�(� �eiic �n k^{-1} @RIaE1, � aA�6�9�c�/� an�MsM �`a:�j� 72� 2w�-qc!}���R1 "r]3*]B72:A7�"6�a�� � w�"$8:�e�e ;2� ;�Y�f�. .�M>A�. e�*+&�!eğes:j�is XwT,�>a.v�.* �. .I'2la2pi�,�2�,is unramifie2��*�4�3.mo�ing2q���>N �aA:%Աs|� �t �Q�?:z�2}� ("�#A.Gv�,�YE�l>� . Usa�.��>y͆a�}�a���E1��F&.I�Z%�A�0>MA�$Y$2���L��&6��$N�ef�z"C,�ow"� �!.��r+�lamiliar� �+��(�d,c�nGC"�-!#Ha�/�a�&��"anjMwe��,�Imac�� 98};)/� �&%� 'borceux1-�c-� AHnd6%3�W�!��Jinguish P8R< larg�+�=i�M^6�(�!%oi�[^$w�t-�3g+di��TK?Td=�0b�GyM)�"�Darg�{c1A�u��e� q!Fw \cAim\c >-nctor,l$I�2M&g#�L�t��&!^A�4�-}I����6k"!G$A'� \c Asjion�A͉�v&V �or[ y-aT$1�"�Qf5%5Ti? %). s$)�� � �dG%"0c�!*U�-��ex�%�or $GY^�%�3N�!���� e $GN�d$6� $\id)�-FNmI�V;B��i��wo&3c�< s agI��*0>Tp�. ular~��($t''a+67�:m �T9L�;*F*� fact�b�Md��f�3ee��EF�Ji�J�BH $�G6�evV�d ��!�� �W!�8I�J� y $a� (\cA�\B) �I��4 ��PhiY]���w;#Z $\a�Y/;arr \PsiOQ�+l:�2�-$R:cA&�A�.�� ? ��d! F5R�%6���!')9��>r51vE, rule:s��f �� R�B<]�� � $9�.s. AN6" 61y�" �`a�Z4ulaj�(+)�)_{A'} �%�_{F$'���-5PsN�V�z5"^0т�=+�� B'$ ٓa�� 3�� F_{*��%�Ւ.�!3o-��kT��h!;� �/�,v��� sh5��5,�z�VDoidѹI�m��k ɑ%�#�tr@*,n�D� mRr3o � -f[<�3!LdJ� �>n arbitr,�.47 ��pul@{+V_2�%a�n��%X� Ben�2 &�!f�'9�\2&A>&BE�.+&C#d]�A&:"& C�e{;9&\]b��"�� � �� squa��ari Y {=ٚI sa'W�WV_p; H��� ��^��,�\]2� y>e |@�A5���<%� {� �12� ``G#�i-1��,''SsXDm)�. stra�@for�Oo check4 Q�Q��� �n"� %!�\wa�d/��$(\cC/X)�v Z/� yq�b!omma!�R���!�e��#X��J!1T�/1!sJ�@-15pt)UE�)r�&VlE� &X@1�) �ɫ)\cC\op.oki'�Z "}�dexJ35v#>w A�. sam'I-2ar�;`6e "�=s�Q� t� ����2A5� W��� 1��!�r%2:5&!,4�anI�1�D�ca3!Y)�\cD��W*7/hi3�/be�A�x$X_1 !n_Y X_2E5Y��.�pr1c�. S < }X_1 pr_2I ^-2I � &�s��EAT<.\0��H�,�!���ree�mi-�:*"�F0�%�A���{i}f� � {Y} X_{3}�iC]q�$i\th$�LibBgj�h1� �jql- rN5 2e�A� $j�h o�P-� Y�oeMsJH �a 4al-y�%�$0$ sc< ��wo8^��i �$A�e�m'w>4:�"P'3AtJ7b��\ptQC}U�D}� y[* C)����to�Drv9En���q� (��:��!�&XC6�FM� $U_1$�3~$U_r/C$0?}[.MG� U_r �UC+� �$ $F(Uu�B7) 8F:�]�$::" ��oe)$ �RV�lq ] �  "/U: E4d4fE��� V24f�"-V!H�r�U� �2�6" ��[r]=�I d]^{F(f_1�h6hf_r)} 3�jL���6LFf_r}�F(VZMV_)�� �F!6Q/A6 %���i< A�horizI�x%L!W"�sm"1above,� o�S�Byzimp�Hdu�Qa�,�m`e$4A�*B�$F�AE>'�R�r��"��i+���4p �E5e81$Vq'F�&x92�8��&x��Ie�dBd��� it= ���0 �2��� "<<6� \c0q ׭w�seB8b�4qF#t�� �Gj'hoF.� n�zch{S}F,o� fi%�ba� �.H� "�;CN� sIch&�S5,%ReEQ:�S%�A��M�=KzRrep���G �6E�ZSZX+&�b�X��)a few�*�T&�&.�%E�KU . CR/�&f � oA�)��s��bgYE=&,A !����\_{\cC},]6 e�!=V� s. F��now\.�  aZ6%R�F)"Gcj#s�y+X�'�WN4% S�tor5$\h_{X}$���� \h_X�I� ��rE�e7] � FK� sendA`�80"V <Mt U�0�$\cC(U, X).)�(8S �U�r UF dros����7h_�lpha  c 'E�0���� � $. (� h�tA2 e���J��?)u>ofEa%eu0� -�!6 "!@X$>� "��}) Now��I� N" yiel!�I�Af!;) `\h_Y U$.* f}$}��^4Mg.���&�1FEfE�iqJ�N�NQ��!��h_I��Z�m}-� �] !�z9{} ��Lq\h! �Ime& 2Y!$a#Y#U2V'}& Y U' )S\] * S�ong6UX& A�!�X��%}% N�A*�@��-) �1`M�!�Qo8 )��$&�nԽ}{.1 (?'�=')"�=.$!.#"!D! (:"���F>$be Il�"�EGtFE�A X, Y��Ehom (!,!Y�Ebs��NK~Bisq ve. .)%�!2 A�!Ue\"� )hN6��Ofails��n&ce!�zies[۹in�C *�be^ j)�nF)/3��\o� � �" ��Z��orm�$6�&wV^�,ull�& �� $.!(J]Zng� �,2;͋� ��.oq�a1\y K;K�!�}�A�2}"YrN{ >�2%2! �}!+5#��5zE��VFu�F &]ڦ$��i�24. C��bepLw�� at�� i*̾� I�e>�@2� ��q�simeqa��7nd6�Cje�!:�OACM�_ OY$��� � a�"q�,*�r> �(,"N�e],!2(��CY.Jc���)Q=��sam��orE�"�el�q7c.} 2� 6q\iaF}i%U9�!2vf�Uv@new*r] �m�$� !6~. �׉� �(I�1��F�$�.")4VJ  $\tauK rr F�nh n e�* $\xi� F �de�J�#--�identZd map �!X:eX$ via%e�a tau&R ��m�{��tru\ �� EhomͿF�� ? q��-�B-�6��Dl,�){% ��0xXb0o �s5tR� y 1P��:� $f-�b X$�p@� � 6�F "/F99Uv4�:n{� MH� �F�b�&k=��]I#f F f(\xi)%�0�)Z[iDaEs�a.�h� �dAi�w=u�#�*�LwY23�.�U]�� �� �5*.2M "U-��# l�]"� i�!se�gq�$2� >$�'��ȅ�iI���� " A<� �� esta �&�&v��r��enc.�2��F X��O � �Iuu�B�vlef��!�Z.:�!� �zepr�M�.[3c�1'�ve@f�n�S��&beB�%� ofBl�^(e: (T:G$F3_Y%1l��om(X,Yϴ� �t9-)��&�y� %�i�a&iL DYa+YmIa6id_ o u*rcy�;S/F�%X6l����e�B�H�� N9(�����ynmO�D�jk HOI��!�a[�V9@S&_{A"F{ .a�5�2� ��+,r�{���Z,��)��(n� �P!�e�\�\6�ER\h_Ux B� qus,: be�+*�#�1e�mt1q!�roqZly0�n pDeicX-�or.E�� uy�Boftoo big� ��to!�Qj� *�Z ly.)���r:�to%f a!�*7 >SAERD��(��� a�v��5�." �,"p�  !! "�N a�w $���i�&0 ��*])]:3�� �A�!�erta�at���% �2�U�B$\sigma�f�M��unS >e��X2MM��=� gma �U�6=�>zA���i2u�a�5�N�F0.2 E�a2�. S�o<b� q��FD� Xs S1S6� �'�� {IJB+�2�C!B�� -�XA�F��a�tor6��SZ�B�!�2�!��&�8�F�R�+A�s$+5F8}DE�nqc�)�$X�:fey�; �&Q-<� )�.�Z:G)�u�0���A�BJ u�Չof����sV��d�9226B!�E�:�tls�,!��1-�I�&�z� SX�B9d set �&'ž(U,X)+�I�)\pF}b��)8  ��Nt01/��# �I�.X,� =*� F ��X"�%�eFt>� . :nEx\\"��;c:$ϧiW&U�!�u�' ofz�2*  �7"�!� 3 $\rP&��F�*� %�S� L\rP(S)�%"�-n%.V8 Qy] H��AQp�� �, �-�"U � 7fI�E�-U� �$ Q!�M��>ex?-b9Mq}emGA)>́mp^P]o��2��P ӑ��lb�qc7opR�,���3bynti�� ��/.S^ ��a xF�a{� � t>�� �col�I�rFe1�5l�{@!.�. E�j9d�coarses��*�/!IC�?%�}61�!|!�|e 3!%� �y��$A� tysew V� 9� ��>k� o5r:�4$�mt��$a��4soAHm*V���Hi-�.)p1%k���\�h�( Sierpinski /o ��Y�nC�B��:xtU��z�M�A!�~;�����:5:��t6r {HausTop}N 9iMF!dorff1�2!Kiik�?�riua�F�2mF�bq'�I�zŏEE!�D�<�5(,2�<*� z>�-S%�/sem�#>K*�discre_rm&;a����� bC"vM�Xm�M�a =͉�u�$�&�!�u xi�}eae� $�� 1�F . AnalogoB�v��$ \setminus��So�.� J�rBu6:��0�Y^s����z9Gs?Lt mus� v|$J�hŚ)\�/�CJ� Ž� pCn���Y� �"�@���I�M���=Gnݙ�9��1T6�{\xi}� a fA��i�w���b �.�.'Q� A��or.3�lat��Sg�)�e�f>���e�aXJbthɞ $G!�P~�sub q5. G H�a D.�J ��$J�uIJH [J�g�5aP��oe��t���$�����ATG!��M2�%�r{q�$\Gamm "�U�� %6#�+I��6-�FE!Bs%�*.WG2RGR� .� ��-� �*�=���_1 = G_1��>be:5��h�r;�L� e�we)��5�\2~ZZ��8�4Z� \ZZ � �6� � �\��$.��� �Q�>$f �6oBf�&� n \��to f(2n)�@��1�6  if黥$�iradic�A��I�=i� ��:H|-o���HotV CW� plex#EP!�V !t�WM��';j"� �� �n��+�number�[9o9 H^Ƃn4�>���at I �h� = a�$n�2co���i6 $c(S,A+)E�"S�aL�2А -3�%��g�*�)�a�,�pn#a Eilz� -Mac Lane�,"�d68$\rK(�, n�b�2�u<�r$UD 6KiaqR";��Eso�K'sE�:��u ex"2 Ŷpec R�Y^:ze�/�}v$ۺe���H h�������fchΖs�.�M�}&) @?}6� �w$\AA^1_�[x]�% U`���#\cO�r.>g.�5Ul�?$S$Ҙ�C�of globZ�-l%�V.e-t 0a��xA+e:O3E}��$pcVK a����3IM f^{\sharp"�>�XV�)r f�>O ��en2YV-W)��!"Fa��!��`� �Uq ��:; m"K!- n.���"ޓ%!xe�zis]�&'+*/ =%2�XcO%"��-!u �3(AA_S, �f�eBX  >�G>M�E�I�n_SLeR0�"N%�^n2�EcI!Y2_%� S)^n�q1&)�} ��@Oj\gma�m(&� 0_{S� pa�[x, x�&a@�h�10�we%^�"�F�zero-M�&� k$. f-9�!�uC&�\gm%�de�7)�`m�[AU\gm)$��-#!�vt*��f��"�� �^*~of�!*A�{s/�$ure5m5�Y���ub�} A�i~bl�9v�Gs /} �w8+�CPA�A $ R[x_0, \l.l*Q?W�1}�(1�%$�-�a�_�U$6 ,~$x���& te ia S2�9�$M�i�2� ��j�W*�#(\cL, s.� s_n)3!wA���a$v�MeUq*\`$s2� s_n$�A�\E�^.�  n+!�"$Z�E�:++', s'2�'_. �Y*�dn2y):chy� $\ph&�EL��)cL'2rry���\$s_�nFs'_iNoq �, s�A� *�%��n$� ��ږ� . E" 5��ŽQ_2� �} � �m}� 2��a�&�Uj��_i8m3Z2J��͓N���I�%�J��Q_{n}�^��<{@�"! f^*s2n� R}�x�v!S�����a-]>���Ad@des��!�:� WqC&�(.�)�tG[^$=�!�I`; | o*"[��_U^{n+1UL��.� e JU��&2y.n.2�.n�(ur�6�0T �YV!�T:�`"Z�,�X!X�S��gV#:LET�Bde���-�cvr��w N� ��� ��j�� an]թ���Mi���� � � m,\�Z.� f B�$(f��`, f^*2� � &��$�5���yQ_�8 ��G��~"s�Ializ�B-�2�willt !\�h6�H��  nʓily? �6cM$ a"}�ɫN In>P�&| �-�\PP(\cM# I�laA���A� tru�, \sy\QO �B��Csymme�E��0��$�EYE��;!�e�i!���� �^F�,6��}��E>:gpiMMv�6�"�$ab �[�EC"S(ny!�"� ��-VM�h aF��L���Uo V9 IT �$ \twoheadr�Hv���24 >|�.B :V1*�/��0sc)�U}$&�$ezAcomP*g, :5�"�phz�w�-��%6} N>�+p�] it6v4.2ce����,��o&e&6���Q�#MaM"�sch{S}\�op \arr \catset$ that sends each scheme $\phi \colon U 4�S$ over $S$ to the set of all invertible quotients of'pullback W4^*\cM$. If $f\ cV �>}[r]&{}} f^�L.] !R�@V)$: this defines�=t�)e V)$. Then =functor!�prepresented by $\PP(\cM)$. W1$!:\= \cO_{S}^{n+1}$, we recE%AR�n}$!�Xprevious example. \end{  } \beginl\label{ex:grassmanians} WithQsamE�up as i�eBgT, fix a positive integA�8r$. We considerT�e*ch{S}\�=$!�Q2��m-22 ^{*}ai��$\spec%��IiA�oc! *� A(>�aGis mean�at L, view5/5Q.\-Wst�5��ra!�al-Q� But �F& pa� ecessaril��closed Y(1(immed�c for af��M�s)Rfollo��\general case, because be%�e�p�Da topological spacM�Ŏ4 property). So)G�ʼn �; but)�(would imply�De� 5i8 9N9 Q �%fails,�� $\AA^1_��D \setminus \{0\} \ �eq )\I-B tremarks\rmk:dual-Yoneda} \index{  Lemma!!�m  &. T�!�c6 vers�� - 's lU,, which will��uAin :!!%(!P)5 �T fl?%}�Th� � :+ Z�U*�ger te{i#,�}!�[d]�� Mw)�-Qo}&�G ��6J�d_G, ���>�]�}��."/proof} I`&� to check: , i�A�>z1.co�ativit�+�;above�Red �� axiomsl7result"O $by evaluat��!:X(;��sofl s) a��y��.��u- Thu>� 6� �� a �$! at h�)f:?� ,r��6� map�4m r�ntinu�(of cour* "�f+giv132�uto0 " y� P). L�g� � � ���� rst&�� %n_S�rS$ es��.&� cO^n $ sen&U 7S�beIcO(U)^n�� %z n ev� addi � ��{ t�SE�often� �,GG_{\rma, S}� lso�gm�AA_S^1 &�0I"�I�2�* 4J�MO!:B �$!A*� !iis%�!�gm>  ob�5 a ;). NowA�%j��J�IƎ�)� M_n\bigl()� r)� n�|n$ �c�coeffic�arA���L��ly9��31�4M_{n,S} \eqdef�_S^{n^2}>�de� nta�pvas".!G V!mdet� c� M&$;6YL �!E�BX�"��gm6W1%:T pe� A� �E+� |*ZD �Q!��6[q��6.!�of9��Z�����=is.�t�1�Y+Q� they� m��M ��!�9�� ���-� ��"rezvar/�%B�$2U�]re2Ns. For��-S1�a�Z����BsV $1_SQQ�Je�via��s�.{�)�2Z����($\SL a���=�~$1�@We lei" !�rea�o%orthogo� �)� $\rOq9\ Asy� ctic>,$mathrm{Sp} 4&'.jG�+d $H$%� u3�e�V.�Rh.!Ap2R2v%B7�~&^G �`H&U.]�e� �2�%7inducedi��� T�Y�F �.�.6��.7F�s" � h :"� @ � E�[d]_{f�= f} & d]^f\\UHH�AH} N& H7� ] � es, .7�,y�i.�a6� .�8(itself. Fur� more�#c"Gof2J��.G��st�6t us,>-n� ixed&IE a�A��by�m� over{\cC}aK�N0 �� rve-p�->�HS.�rm�\cDi��i Mi�67��ptHH D��6lF�Y\&eDM���E��s>���6�k2e��cC� �N� �A�r�yN�2FY�F �C 4FG��vn b |��ine$� �>P _DQ"E��"�&�>-8:�\�� �{Fa�Js)0FG$. Analogou� �us��F�{;F(���F��J�i� $:;($FOGٍ�.�.3��!� $� 8r F �? v#&����� N��I����yQ텠Ams�e� >s! A�!�*D_�loub�{AyF��J +:�!�2 &�&� nožofrU&����:�RW R!�11�R} A2� '� ���m UIHrz"t2�2�R(a� Vg� F bFB,M I*2+ɐI2F, T(Uq�"8n*D#A/%~�o5e3N^I %�r M�&=��y��1���� �TJ�Q��VA2��underly� �U$� '�! In o� words,.l�.d($\widetilde�-@�w 6 ?c��H� G��]J� uu.Won�$V�!.�" %)�I%�s::&� � Aa�{j�� y $g'j��=$xFA)�^`� 7 $f^*g \cdot x =(x) <U)I Rz*M�s� ElLnՄ�� � 51:�-@��� E}4A Q����^�%"�>%a�J�I�)�!�� }. AgaineDD re� ulatw �*3%lerr � s�'.X� : *- �"�! �Db�~�Giva�[��isb�A����q �ZX�4X24%�",! ��0m�acts lik!�*Y a�X$Z"���RX�,&�dAs $$X� 7[�-7 &X �I-��y&��#='�-1 6� �G��5� X �r]"� ���k �&�Z�6w=:e<-�o�o2o �! A��#ah��.�jz 6b�m�����]�{��}�W%�$Y�,��D � \aӕ!i��}m�Y�ged3" $G$-� rian"`#!M"" Z!}=��l�#6%�JW X(K YK �u.�N. .-" , $f�:��A��a�<\�6s%![r]��BW f�eW )&tuHY;r]&Y�7\] �,�r<)G ivenAi)�s*bes!)fl5&�w>E)A��)J��"G y�&n� ay��Ep�� �f*� ���oE���7 . G�2v#:nEnd_U(U�� X)I2v � ApAQ !hrg#���,at9 �!i!Upro��\pr_1��BK]sa>:_monoid" �*�"�*/� ion�.-h' N�i3 Y�end"~e�'r�� de9pI-�m&� $!)/U�3W"���f 5o5�2R�� \aut:�&YMXUJ}~o <Z(X.*2� grp7] �  f��%�$Fc�h�N���)N= \pt)�b"�)l�#-�%..�! "�1J�O*!&;Q�isane}*j:) �2|.�&�V(Vu%�6] �f@*�$6*&"�xX��{eb # 7m�a��%Mf & V1�(�rtesian"�+�*9I \bet"� �kr3V�: 1�W> 6�6dm3a/�<�� rf J@$@/_7pt/[rd�)I 4@{-->�%^{� &�e6�)g!-g&:�[Z 9�j��X=$B�CAd"����Ť!C�j�\{V}.�� U}2�� as�0"i,�52����Ma$,��O�{$ ��A�d+&�� ). I&�#{S stri� to 6��e�s�5O$ F��26}�"aYon !!�� /1particu<7�1�� of Sion~&7ec:R-a�`�- "�*H9�-!�"= � ~J)22� v�Mmor,�2�"�*6��Y6"y �b$rr� B�!6tor�J�� !21E" �%2�we*? Γa�en� bRwer"�!�� ��rf_e�� �:inf 1� �of � !V���+�� m� f $s*� >Xe��  FJA �- &circ z^� d!��#�:8N[ K)O�[6a% ���,�4:�� �%���f' �g�T� >�uA. ��ly�*�9&�m$< ���� Ae��&!� F EE$g$�&D�*� B� =)�:h4WK ll�>o�8a^��[� �&�$� q�.Q�� 2� �T# ach �l $h@�:AxcC����h4a3m�Vd� ��e"C "l!/:. <c�ng!p@R?%�j>�{2} n�Q X$. �'6�6��E@ I$E�VO0!5-w }(V, ) = .n[a��n�A2�M"S��b~yd2e�:2�� permu[,�=R��%s�8al�ngsqe�:�f!sm�% stra�forwardE� ��$�p�?ercis")��.�" >Ja� E�m�.OAkA �.$,�7EN�+�32RA�-��fH0�M-A�_!EKIUR�řNg��1%%�jo�OFe~�kD!a�a� ��)E��d.%V�s�Z�E in��!�%��.\qed� C/.���:�Discrett>�d &�""�a standA�&� �%mS:��&�&6$\Gamma$?�2� �2@^�/�1h69 QM46�  Dap� r =hyp!Bsea0B%�'���Crp!%1?!� !!�}1*���}�$XA?I&/n�.)p� �#6� eome~ -2s� M� 7#al&�}}�q7Cae�.!t>�=�� E�/s%F��s�=�BR+ Oy, � i:T disj�/ unioi @sXI�*9Ej 9)�8�8Ysh.>;$)�w B]6!�cop�%AQS !��C\0 $%�:9A;&�& ~7m:)�V!UDS*0�bH.N%?� &�,��S(U, .]=�.M��I� ����,S(SJA��� y}\!I:has-1O- �s� �� 5�.|s�A� !�;zG-"=*1�!%B&�i�2�iN+ �Ft'��Cet $IF �)��o _{i� I}�% $ ex" Q�bA ��� 2�%�s�,VZ�soZH��^I�B# �J !1 ! }^=� 6O �N{�DIɀ$J$e�}D$KYH� II^J�X�?ollR!aW �95#j%}J-} para��z�0 $I$:i ��$-�&!"�e�tLkBo�:Zn&�?M' e�D�(i) �� y O3%k�� (*� phi_*zZ<� � :ar-Q/1 \p"Ar�6a �`g9�� $5LJ)�K)�1�.���( 7��)_*= ps ��;�>��igk%JK2��ayFS �o�ADel&��� y��FA��M>�e�� e�6��{iR�>qZ%Voru� '>>m�]. B��"���S� ad�#M� f�Z\pt�� Re�S��E�*�F��N ya�%%A'  ����ف-a�v�C �)� I, UF����$M��} :�U)$; fu"9. �b�is T oria5P�$U��Co �ifAfassumV�G_ �jJ��$ ��.��$� ��,��n��*�se�K��.�1� �I uI�ucb��%� � es@6iKH��O2� ���C;EKA_����HF �. nd, accor�hReGkrmk�V/Fi%�j���R�*)�&�f6�D3"4 � nd�arFNrM.� hap[N.R[e��ɹBiAI�6�aeuF)8A�!��a���U�D; &�Q�5� {s. KS��� ���cA�%�FI�UU"�8I�&k BLBy�?%k��.@arr<s ,!�N^f_��v;JS\ 6 empty���A'�Y)5Z:tiM�!aDfact.SP%! set,%�&� of %�w �4� ��@ \{i\# >���K�+r@"�60U7T]�(aH4� 2�� �7iXU$). O��ef hA Qembede�$\iota9� Im.��eU q6g�U��� I �  $�bF2!��96d*{,"� sm�I1 W6q� -{�� b�A|>� 1�9> �2�"<� eI^� ��/��E�N� ,M�~� .,}_!�yc�N�, satisfied�.���S1} ��>E(2} �:�m���aI��A�a݁�����0.f6" ��� ;x3}�w��}�E$ M�iMF��e2�4� 66�)] 2�;�,h���attop$�A6o6p� (>�66B���* 9 )�l�3*o)�66s� $�o ���6 5�y�V�M8.�aAf�<mZa�W�Has�P>���v�Fe�8#bUX%�.2(e&s} �;E�A��wM�`�!M�< v ~�V/{6Z!b � �>� �9r:� j9"�5_ So,�&�A 1X.(C$f�EU ��/�AbA�%�giv; 1|�3�Zų.Bgr65A� $*�P�"�N� 2�-�&� N�MI�&}�h5�1�.�5�5�.&��^A 1'�T�11J��#{ ���i��ue�G(-%n[ 56).��eo�v��� %�$f enough!lrq 6�E�>($:� ��$ty=Q%&lR�� e f�FR �Os "�H�[o�Y�)�   �&�) show�,E�n&���!$J͢pa��(�%Jec&� 6�>� -B2U= 2�-RV\ F� well-know2~ of��MZd��� (i,j��6F] Ai Q7� } \bigLB,�6pt!r�a(J �* =1Z� I�c� A��mn4C%�6�� p #!�΅I*� *�)6< NI�us�=�1w��Z� 2] TN� J^r�"eaEH"T E6_��%l E� b'� ���n& s=%J� ;5f Jo.a�sh� �of� uA.� ���0 same�&X"d%��2�2C�I.� P&��=�� !� V`}^a�3іX�22���� �%�����@n��� Y ��$ iv� ��VB�7% �4,!�VI(.�� Yy M�6�Y5�"� M.Ag��g+�>t/�.�X,k1!ɡ�� !�to� *se &� �@�<l��"�#��.�%g*��.�$�<H b�RYi m� he�.Y�a���]P{i��$W )22P4 unI=-i 2Fk �.� 2�'$��onZ0�#=zE�-fn�Vi2oL�$� $. "x r � �@�#�m y ``e�fD s''a4perhaps mislea�D >to:<.$s�]b�`2MF3iQo�em%�&3 j� . How ^d�6�to�m be�d��mo) i)Kist�5 mMPru��>Z�khold:E/��purIcA8.;D" \defR�_m^@be optimal (excep!4a[=e doe�e�� �v)��8� *�_0#Mz��2��"s I)�in mind)��Qq &�\ Sheac in Gr�#ndi�S�"e&�$ ec:s .�:oC�+ ]thJ9�C#'Samilia@\�&�$Zf�:Jp Eheb#�v�#o�Pe7$"�. D&�H X\cl&� in�_�M�+Oe*%�d� �( ,���8inclu7`y ���-Hn�yyT{�F�f;E�E�0) ~it"s�roa%glu��&-�R)e[g Wl �um[&LQuneM�Gw!$n asko9T�2%�9)�,.�D*B�+��� Q�c"�b�X �1�%�y82� $F_X"�.sub"�-�!�e�:G#C�b2_%`%��$�f b=�!X&�Bv&*�'#21fY�-�bKNyy&<S�!�k�aItheory.b`aVD$ ``I�e�7�e� �maps} 9Eb�� steaZ9�{/&�&to look5Wf�b����&(play no rol�4eh>do! describ} :�,�d��ver�+�&� &Y *�g��topjL%#aR�� M�y!.&.!*�(2 A-�C�]�gtoI�f[I�C�'>�!�!�o {U�to U\�� "�>c.&$U$�}P-B�]�'E�`9c6�+T�*b/�*� !sJeO{-"��mY2}Y6�!N! I �>{y))v>� UK_ _U V��, T�6n%2��?� V G�R�3���T���f $HC Z�V_{ij�(U_�(�j$�T�)�{!wdep�ng��i$)%!:�i�.$\>` �F�A�"32'A�a^�&:�'�Q� �}� �X1��k7�(�AM! Z3}�F`�+if!.iA%j q}e+fQ�e�A>^i�%i�H OimeEu_j:RKa �� In�w�Q%ed %��%FOI-� ��.��,\cite{sga4};\re2 e� EI���differ�l3A{� �9?C eG+���x/oWN� I��.!XA ��po |]w���xC%�H!�Al;�Ae*y,!| sens�9N V-�vq Desp�$its unques�r tech�hadvant p, I� fi�e���9v&�!in.�,)� intu�\��I!f.so avoi�;s�5(just a �fhabit,� oubtedlGl*� .sie�E�M�q4nt�Sn"/%�C_"� !�r�vit�_ eful)��"b0d extensivelym�q H� s�+"� ofR ifYI� �%W"����{i�E��`a/) �ve���2yP(ly sur;v��2J I� set-� e�X. �th��[sA��h|'� �}[=�65a&7 ] �ex:cl� cal-QO�`u*!#L Xq1W8 �Sw a<"� �h zh we--.� �y�- ��uz5�Ş�v/ yR� *E][ �of '2�)��+�cU9EFU�DU_2���Aar�FiQ:� >�4U_2 �ens 'cap#m0Q%"�E6 glob� Q5%]Y3 $-$Q Y<!F8! 4}i�2 U"� !a Ci"Q/G&F %A�1�F/�Wa e�2�: %�"d%�$k )�&�&�lwvis�Wt�4k ?''`-,Ab�G�ti�cin�+2`*� ;��A�{uRue&d�+A�74- "� ^�19\N�"= ��i* � �4v_\'eta�"��� =�]t top-I,-;�2�2z2xs home"�>7:.ž' 3: tremyimport�-W�algebra�^�6�Rm1n�ɰ]s-zy! *"tQ 1�yK!2^Bt: }B�yllA�y�X_{akrm�}x " ch{X�Qs��of��(X$)�l�X*sen)U� !>@ > H��&� 5 i "%�6/�굷�S-�% AM$�� �!H �|ss�-�2 B m�~b�"�1�U�U�at�>�w$V�+a�B%��@a��j� e�(B=��m�b� )5�)/��@ 05�A&$ >�v(�[<zzB R� fppf�F� ,<\�K��� lat��� abb��O�:dKQ r ``fid\`�*�t e� pr\'�� 9inie''F�� _� fpq�&�zy}� $:iwg+- �_Gvto�W]Dcm�A�� A����%�0��7ed)%���* �J . m by t�Lᐙ=q�*��*�Z�&�A2 �7i�"? Withful�lat�*wild Y( t �!#,}. Unfortuna!,)e!(2�(P53*s\ u4�-)Hness}�;ureʂ->%�0es%���B!�dB9-r�t,b[soS ��2�-���>5�Q� ��.�21pҢ{�&.�SF�%|mpaρas��rf�(tB@ note"en�� ��!�b# ded_6[13 2ar�4>�%P)��F?.�I"o sugg#77�&�>�q� ��&:BAA�� A�z*2}� fac�"z14}�[3}�> !�g*/��>�I��,� f*����>�=�ea�M"�-~�=m���jW4}:�$U'�a� a�� X�X�+�x$x�/+�$f;E��A�,p�I �6x�Í(x�In Ciu$U�b{-1}VA`Si�Mm�+,y��>��2S.N>%�zF2a�>WE����Za��in $ ��.V:!U�2%^:��-��)I $U''� 22�!|��f %g 8�!~U' \cup Eis6�J#�sA�#&��>� have-?t�"�1�M��1ۋ4�1Y �)M�I� ��EP�UN�@p%06wn� %X�XsoA��choa)} ly m�8�m,��BHm $W_1$, \dots,~$W_Y�o], 2&j$,U~1T��ق$W� �eq ���6�) '�i������=��+2�$"�A7J��� ( eM W'_j fW a�Ux>_Q�B1,cup_{j=1}^r @�M�6�&#:�BL_j = �^Ѭ.+&F }�/cI � !� n"27J!4�  !J%�a f62 jE��� e&��"LE�Vw*>� �.�RCqc�C2�9Ka?����� �U1*T&-*F  =-:}\hfil&�&�dsF`�[l-�%�!J of~�:.* <1� � � ��A� � 5}6$J� A�<���� $M�k��0$Y�R2� 2�f��VM1q��,`��e�.� 3} A vb�Cpq27 4} Af1E�iJ� ��X2O A=*u4�3�;chang�n�.P5�6r�:A!v�_  ���f�d��i��"eA�J[uh��' �v]� A�AX��U�3 :1*.A�*� y�,t�� B@�z�1�#�[ Also:RB�5&F �=�w ��6�Bt>� �9D/j! 3}.~\4�� ���!�.< bgb6u6Ed(V�x->"}Bf���*�Y6�W c�aral�B2 v`j����CTs z1&�0A�pF�5%>�V-fe%�]l~t+hai�"Q�3ch%Xi2'SJ*urn�.YB� M�9`�*�n�1��AWcodomaie�A��� "J", }c:L/A�x6�! .��h"+nu�b-�D&�y��"a $\{Y~ Y��] q�.6�"�c1�&�1 $JK _{Y}; r Y%�*,�a�!* :"S 6z �!�sef ted,x 2.%Hf�$C �.x.#2la2psmooth, Yunramifi6�M�.L�&�N2��&8"A`e:u�h �AY=!�_/ �t.�Z�  �)��3�j1 M& ��� ^�rC>M�BoqF��b�� 2�� ���V�E/-qc!���}�\!�;?!�:�Շ�$M*a �;ʿ:���|-���O-� ���(�����Z�.) ��_�9�- �%�9[1�\ ite,A��>w!?bstitutftes-�8ch �8m "2,':�-s. (OB���be�<�=AL-��1.�-s.)�S&l�h8 ��.k;"r �"�^"o�$�wo�is $�b� b� $FP � ���Ke���coincidz/&�I� $a = bD �� �"o6A�� _ảF��"� !(d:V>�n B�l !�i��2of�O!�� in FR $2�>\prU0co�\U(ɪU U�%%@-2XIn-j'(z#��7se�A��.on��{�3 �2�@�^* �= 2�IF(>�)�'%�t$j2a��/�3|���!�-�d�Qa�Qi)@2c,=f%�l�re�AoA�a?k%ۚQ2kA�N�%�G�NsC yfhn�iK�>.� A�,A��7 lear�0W. �m���)M�&��r]=)� so oDs|4f ��xA�\�RG.��Cs:5 R%�!;faSit�%8Vv��J\]O� �im�i�d our �"�$ pedantic �wo�@*_z%%-�bc``.�� Qlɤa�sEMaeAo�:�)���''ɩreaso�ET�`:6$E~. *,T4A2J��w ~�M�4 �~�tpossi���_FLEڅ[�j�D:9D* 5��e!T"�2 y"bz�.��E!d�",.ߤTFB-,Z.�s�� f�g �te�in�=�I/�IBA�u.���E thdwh�U-�`)�� &famE�tru�@�altern�e w�eon�R�� �R UKq$A$, $B$I�CaDi2@�:�f�w�}A*�vB@�$<3pt>[r]^gA$@<- _h &CiO](�L:s�b�i$"�A EI �A�%s $g, h��B )C9[Wee�g!� �!$an w?�ize"�bA�#]�a��-�&#� �hMX $\{bţ$B \mid g(b~P h(b)2�B��6�F6�����,df =� Ae1y5 $p1D)B.e,JpJp$ iu���ro�S$A�Nowo$ jor���>�ul nd e+a0nf ��R-�� q؛��weq:%�-a�vesE`F�'\X _iCFA�<lelong{� 1^*} 2^*8 0{i,j} FF�H�vA�}*��Q��)l Ni{�i�]"�P�o�Fs6�* il*;f �1�.[m��v�~i)�/ $(a_�g B��z( �>/bq� c��n@� )Y������yagr!� a��� a!�e -�9�p�8VA_4 i1�%*(pr!��T-T*EaA��> O? �� O"+WiHA� a"�.(�N�)!7i���ņq0iis����b0!�o .�2�? 3�� "�b<;�H"� B�"� a�6oc�&�B�0u@(z a�)%��>\h�fU} *i= \h_U��!$}]1 (T)$A��N�:Q} )��*�N�!��A�{Ab/��qnka>5$U�@$NholF�6W�+!���%�-�Ta�Qgg�Nt�M <Y� �AQ�ҙ���D2@it&�El �U�Y�76�. �Ks2`�I �2r�S�U}u�&$�Ÿ.Jz %(2M$S6�{U�:"�@&L!�S�%ms.n(6�:.B $ST$ � $T$ run,1�a�eF� a�-`AQ!�6�#�*!X�.�� �, ,��e$T- r TuS0n�(j< D ��"_35su�RA"$B��#q�ll �2Dt�\�E�cS���lerJ���C��2j$%a�Fn*;g E�e $F\cUJ��@-���b�� jRݥ�+ "nHs�W  �:��x%!o.� 27 2B *SVo!���2.y�!z-;�*�:D N�e��A�A�* [�nyw-�P"R &�g�&R5� hom(�\cU}, F)�[!20.#aa.� [2�#{}S Q a?&�# &� &�#4�.�-{R���� ] u/� top �>m6��B�M'.Vhcolum"�*� "9 ML"� "��M�As�U�m�HЫ:if t6 {i�X�_�!�Q "��${_6�e h��1�!�r F.=~$� !T��H�=I�"* �U!�n;����n� $Rr gbi�^ phi(= c)r)K��=�"2 afpr_{1}��^r2F� �`_{26$��_ sharpen�N EM��w\cTyfAOaJ�� RY") �- �Xis sai��b�A��2�! E�!� /a��N�>� qU2�y�eq&|�. ���ao��talk aboO�e �% � cC$r`"�M 2�Ast�B�7" Lc�*jl�� ppar��aft-(�$c#fZ0$\%uxy�.` m�J�\�'a�f!B~vi!:5T) epar�&ieor�5e�o*r"r5�e�?n&[�qT$>��S%��J6�E�%��GS�X�B�B!��xTBJ ""�?ł*�>�P:�B=nsequ�cA�C��%Vao ���ne��F!}a��"�1�F�B��!nd"�26)E g"OZ4E&�%� �"��$%���6�*� ,*�"�of�=�/�58F�K�D*�6 next �y���q� lem:u�->�y}�)� �R@:�m�� �>�L��� �� (�F�L!)� ���i2�> "M � ?I(S� AMrusQ�7 � "� %s�$T��Sf��)Ia�>B(�i]\�. }�ir, �% s $p� $ � 68I�� �4J[ #� ui �6N�OY �@ :4:D =�1.���!�M����M;��do�ed/ �o U��-�,�desir� e P T�>�V�+fu�m>8}0�Q�FK9�:�($23E�!%\cVA�`ju�~�c��E�:�{E��A�V_.O2}�>:&�  �>RB�*ac56:Q�h&T serv �O,s�Rto� 3!i�S�� k�^.i.S di�Jed-Žs}\}?� "�+��A0� � {i=�nd!�����2��9&!�\cV�q�p V2��h/qg^+�S�)U 2 q)  �\2 > � .�,?1 �S�J��( N,LM�2Bc).�2"�#w NI\k9ymmP�{"�&( to\-pol\-o)ꡰ�]"�f �)�$��>'!6� �%& �q.�_{4u�_5�s&+r�ly��  �8�oU\}_{a��AaG�2U��  � �+A �#s�  �2� VwR�"m-�. N*d!kchoG�\+e����fRa�� not}L6;I data� �y rDr%�.�n� yrel�b��l'L)�imo �a�2ex�>se�m>�Y � �H@"��U� =�� vF ` ]b,�*�xU]al��|*�!:�YV�U�ġAX�W�~B�� B|Q6�A:W��t7mi"�8�-�XAq B���.2>ozBelfl!:�A.5�of�)24� pre-�R�dmR�I/.09�]��=�9�X��%�C!�6+�-�T'$��y�4�l{��,eإF�i!subr�at"n! Cy!JkyW�=�wr.} ec \�;a� 1g ��72[�%`>-'!@��\c2`{'v�$:��($�)�val��mQ5F1�?Aad2�( �N�B�Y� �Uv^u�*�k1% $f�reflex��nfss�,.�%^^;F�-.Z � Z�%AYncMbW]`]a��lyvQ.;"�mH�8�0�B�r;M/�yr8q�T]�e�t%-Ry�A�@�r 6�:iR� - �]toErls�um)"E iBn��,><� .�6�x�)  �V��I�le)/~� y16 !��.�6/-�-\y}�!�e��1�)O 1� < ies!:�� 1�`� cal !g� ���(wo^e ���"< ���֥�6g"�`t�g-���C'5%�"B0I=�/F�R�>� ���.����+$!=�CS<.� Y&�?B!ݗ�5n2P('s language�(�� dYb�[lJq�:-��6!�=6�l�]�;�s�2�$f�_!�T\t[5(>�:g�g-c�g})�RA! �=��>GB`e,:�-��qRAy�aL�?� � '�1 �|"a3�� [ �.�c�ZbM�n�>M�[]!  "X@}4�C*�:.:��J�_� V"x@sz�?. By�m[�Lire~17.16.3]{ega4-4}&; `"�B�-=fn�2Xg"� *�Z*s��f A�1A1di.%�Aw_^{i�$�;9b�FN� KP � (ip&F�F�&�Sq}�o.(G�5.%���A�>'7 6K��-]Q1I�3��&1S'.�:Y`�5(�� dI��4 L�6%Beqf�M�ͷdef:s��AV��Tb2F9�"]e�� Ae"�= �y!Bhd�%t�1{M*if�9R� �c%1j���g��&�)��%��-9 >�:a :�$\��line{\cT8#d M�q��{f��v]��g=�2�["�O>��n!��0AA7U �^�>NS� ���i>2ݭ&�S�tr6a*DA� � ��.�6~� '6!��� 0�ld2 �`6� �= :eN:a'ebu �::LJ�cY"] �jJ�>� 6�'} = �l��6e&o?ie:�<.6� "��a�&O|O �$.Bv�DCJ� r��b �D�-.{�.:��>7 &4g2L! L!�� �gf *u=QXu�<6R�J���lbl.��l~B!�*� r��[!  � �mou��U&a��a2Œ �&�Es;� a�]U��;�i}�� � /P�p%3Qu 2Q�9<%Zwe��&�5.�.�#f8�f�'�K�>j&p?��0�51�'�"-$�:N� 0b�ZkB.����X%�$f�$��Ls!�i�fF, (it boils dX��'� ��>�1i�A!5"Z=]"�HR�K)�,�8awso�FK�i�A"\(�N� UR� � 2 #Ak3q�J�LV��&��ot ��ill�Bk ��Y�T�6��i�of�B�R� A priori� r*��se"؅!"!E w1B&�e��hlu&� � �y%��M�!��3J��xm}[.�-sthm��`N��6�eyoN�}Mq���V> �!!*NLF:H^ɱ"~I� �}�par"�i� :�� �1�4�*�mOzz]�*��G��+%�k6C�f&.PC�[ &�/V�U��   epim�� . ifsKn� &s wo f��au�|��f|4c&�-"[.? De=I�7( � al#�+�"��ӄquR~E� #�C}(U,"��&��V,�be&+$��n�m�"EL!�� .�=e� ��4,�VfffvHve .]� !):!'!�n��7}~�51i��&^#ٺ܂1���@1}2}'�9] 9���V2�� ;8<In-D��N��3Z"'~�.*�A}{}4' 8.�,X .] � @B5en orem^(2*� �p���qOA1���(5�.a���vS����~� ��reB�n� wF�o�,*�o�/DalN A��"tEe bF�)<ofB��pqc},a � ``�''6/p���� DTZ(s  �l\r����� �K%� badl�OKd��2�allZ �k��v\ 8�8teg�v� urveA��n&fy!��R�� Y  $�nd�'$V_EE�k� U,p}�1�u��hs�Ein U(k)a�EqI�A.>qO �{je�d !2*�ũi83l:�q. j�� nOh%�l*��$p��h*��p\ $�M���Hic �!�8�8*g�T$$U V_q = V_K�!7q$,�Lwis�iB/w�h@�a (E0 non-"�*)m���by  < "��!���$TD$a[5;"�:2"p#to��-qg���� 4d2�&sK&����5� �9{p}��%$s �JF(>p,q�_X(%�)%b�9�. }jm�no��r� ��))-�hC|a���6n�7([*keg�a�Xsend +$:~!T�!l�Hin!*['!�!�6~F 2�L,� � 6o�&k�G� �e&_ , s�_A<�� �`A�=.��� � L�3�|W�.'a��Z Q�B�R*G�V��+�}�.C����"7?.1&b��J2} )`or� �l �W*��G}� .jx3�ite��&�i"j endoO�{a!��Ո: =r;a?� �EbFA52�(��U#*0EinB�Z)��˓� had deal�Q �� 2�x�nO(``.�''� ��#�E�"�1o�25$+ "Q, ��{)�F@1�7!#Y@e&c]� ines",#*�nd� ��f.�$ 5!��Nk�w =�}Uc@a&aAz)!�,� e ���!WS�-#oB�1"=k! 8}\index{comma!t�opology} on the comma category $(\cC/S)$ as t 1� in which a covering of an object $U \arr S$Jis4llection,arrows \[8xymatrix@-15pt{f67S$, and &:�nduced b)4 fpqc�A�2Ef2"x. Analogous statements hold for1r��g4clear, since $� ,X)$ pa\to � $, $R�B29(-M�.N>gR5becaus�_{X��sheaf. O����$hand, let A�upposeIwe��givenA}ele $(a_i)$1S�u���!�)�$, wit�Ke* perta�atI_(ll pairs $i!'jVindices%�eq!�ty%C _1^*a_i =A_2 j$e�!u)% {B($E�re exist�Pmpa�e $e�� U \xrightʼn<{a} X$ coincides �$a_i$��,we only haveas��$ai��a� S$-o�s. Buѓ��ivSB�a structuren�S�!�;.�(-,��at ES�dQ���� , soIJe'(U 6e�!�e%A>�E�SA1th�� mpliE���Fx�iI8J�!JUmQcco��teE�of�-��� of}[ProofGPTheorem~\ref{thm:rep-�}]�Lwill a!follow�@useful criterion.��lemma}�, lem:$-%a } \index{0!characteriza���' b&%�ves} Let�]be�|�� , $F�0\catsch{S}\op)aet$ a�Kor. S.5$$F$ satisf)�e=two cond�s.1^$enumeratei�� itemF]_ie� global�.z 6(Whenever $V �UmM8faithfully flatY��ffine!-)� diagram�)F/ r FV.�\p��} 2^*? F(V��V���<a.�� 2�Th F �%��!�� I6UEpA�}�� I�,be divided iars!!al stepsA�  [: re��` ta�e case%(�gl�,] TakA:"� >!ofB� R��sA�V��co�_ $���� ��2�!. S�1A� )I, I��$F @�� FU��*J restri.sE�n iso�. We ��� mmutativ!mE7�etN� � EM([r]\ar@{=}[� A[ ar[d$<3pt>[r]^-E[1M[0<- _ Aw &>v K\A�n & {}.�O N�jD� F��Y�U_jE�e \] wh�p�columnsTbi� ons; h2 An&z /$bottom row-} zer i� enoughF9topN6F� w-�x�aatBZconsiderU�sA�M:� "st�߁M>%A�milar 2� M� sepa��d�Hmay limit ourselves�ed-qms j{ T�Iargument how�"�F :�  Z��,* $U$ � +$%ΩCea!HuA{e E�rqlao�II�Eg ZhJYofact,�lis��AU �(disjoint un� 6qEpF ر%[:�X>�] Now!��g4 ����f�[QC $; t�En open5�Eg_iU�V$�"quasi-�act� �g , wh� imag� = fV��s 8!� � W� each $%a!�) of-& ly m� 5 Esub�%9{ia}$. Cq%!b�J �M��s %�"�C-�E7�&[d]�&����ñ��)6� \\�é��� V�� Vy4I� a FV%�N�k�W{a,b}:F( `�^b}):�2!cap�� �H�� * �Fh< V_{jchsmash{. � \]a�i�B� >� 5��ŋ9E��U�i �9_� �Y It��TY ive,&� 2K t�RA�se� �M�JeeGof2.�m[s $�A�%{b�$%�\[ q{J-5a!96k��1v�^5�� � ive. H�he2�Z� �FV�K:-����^R&n 1? from a>��  o� an�� ] � f��/r ab ��h6`�6��& . Zb*�8 n""0A�m%(pr_{1}^{*}b� 2 E��{U} V).<]V�C&�y�FU.�$fva = b k V$. � {�G}}$����z:p ���;�m G)� .>���TU��BO, heJ@FML��i}�s} >;-e}- -c} %MK ��ir}C{U}��}� JG�% i$ denote�$b_{i}$!2!9b$� $ ���� %�I =)���B�e5!.M\F5� nZIilYx�j�2�Vv��+.��i}: 2kitj?? � some.��pullba�o5yA�1��l�K� =]�i/ ~6�"�.L�� 6ae$�w&u!�J�toF�i™ԉ�en��!�!4apa�.�����f��p )Rl 2�� 6&& .+ !�pro�/ �-E�surv2W. ��v,�wE�.��M$f\mid_��}�"�Щ��AO��Tprevi"ep�ي$a @in>�(2n)ő,=��"8owever, I claim^ 'a_{j}R*� !k"/$ �cup� �)t� fqpcrB,%�2�:ٟ:���wN��� �f�b$(Qˑщ�! k.���dpo�`��)> resp5ve���_��j j}+&� �ņa \eqdef2��v;Ws�%i$�5 as desire> gene��]]J���(n arbitraryE�U .� �{i}�2��eɩ,2�!j��E\��inverses�Uf�$V$. K%�w"2 N%rU ��� �} &` U V� N� f�N3% /v&�/>�6Lu,�{%J}a�i� |�  :�2Y) ]-� VQ9.�"ps��; fur� morL� BJ� �ze.b��NM8] � !Z�An2 6 �26J!F� ,R��!��ro��my. Final�`46�*"��"oresul6s� #"Y chasingD�} To�rvej���� *w F� h_X7 ��$X��an*,�B !��!!L�N�!6d!3rs%Xall%�P&9" E�!N7"�Ris*pr�!{-@in�9 $S�� x#��2� "��%h���%�&�# . So m� %�!`�1e workɚ��&wout'ryEabbu� �W��$ll assume = %;��-�� SFU�AW U%BXRGt�1Bs!�Q%��"�%����:rhom"/ &�A \< BW r�ng��Y5'&� yB.W#PA$-algebras $e_1, e_2� B n \o�]Az?&1%1(b)� $ 1@e_2 1b�s1���&� #��U��V%9}*�exact-)�}��1v���#0 �A \�set{fC rr B%.�!e_1 -! }!9)�r�F ��E΁TFH$$fe+ $��B>k�( $A$. Also,m� $A$ �� $�A'A�2u+6+f��!+{A'[ o�+A')#5{M ����Ochang�]Y=�GA'$� before.�PB'!s�A'd!Z!%�+ natu� *% i'.�B'F �simeq (`!�)'Ao, mak�&N_"%@C+= 0' & A' ^-{FE� {� 6&B- 7� e'�K'_2T &&�M�%�9� ��~t�--{}�15� .&r*Q(\] *��A����&� r i��Q���&eas*� G ]hesis.4 AQ:�$� �'o�dF6�y#�?*� et $AE���� 2�q#���ia�)� b' \maps�Ub'$���e�1 xgeome# term*2% onal"�.�R5U!bA�� &7>��26 \end��%-is"X*~�'��n� at"� 7 , rec� Ŕ� �S� �� � X$!:�*. B s $R��� B Rq�)�t*� immediate+ ��J �" !��� A��)w 2G �. 8not necessarily', wF N cup_i Xq �`"L )``&)�r,"o.�" . GJ!&�!m� �)t;!v 9� $f, o�=X.!!3"H� S)�!����v!9&�, &$g� �+�&-t%*t�/so�can=#�!^{-1}X�,g � E��!�2pE��#�o� 6�� 5 VU�_p.>�U_i}}{g !�C�I ة $%���e<�%[= = K2�8"�.�T*mplet6� T*�.3 )�I�*1-wVo.!Db 2� *�091} 2} VQ��y g} \l!VX-'U6;!�]�g$�$ora�r�&$UKU�jk@ :g�,-set} below,E�fac>lA}6�U�Uu !(quoti3&#!.)!qp.�(V�q+->R-R}),!%ge�.a���&M "� y��%ontinuou�J�eDf eEA��IA�= g �$>� %�g7��a?f_i:iEVaRE!W&e�Xm�zVi'K IYMuniqu�%tMV}$f�i3!%�*�� �f_i �*_a�f_jN XA.2 e,\] "#�z��=AU�$ glu� geE � L' 'M��.�� u"7�=&-�!��5�.5Uf_1�X a�YMGf_22 kYA!q ��-. �5x_Hx_2*)pv(s �$XX ���Rf_1(x_1�f_2(x_21���2X $z�!Lfibered�C ��{Ya!2.�1(zk���221Y)J:v. i�y��>�� Y>)(extens, $k(y) \eteq kB-zJ��Bor� 9"4 {<}O2}�0&� JD wo ve�; spac�mU0*#eld�f000$, unless on"6;is $0�V z��0maximal idealn#��f�$K��1F�%,�>�H bothAF5PEH� �1X3�,%KI� 1TaEE.b f_1}[E� 0B=2wr Xa76<2<���we�.�2WX�#��Y2FWe a� �1&� DeN .:_ 4!Vf�3!�now�A�. :E�70{H{( ific"�3";3}�-e usual��4�,A�7hea><pre$�+|5"�;m I� carr�3E��1��"Yontext�"�:��) def:n��,�<�.t *54Cr.4A \emph�4W.�4�+� $F\ass��\Jn, t�? &� transform)��A�R� :��2�3\�4��9�7� �%a aU,9aSx� \eta +&3 E� &�m�* in �{/Oam�.c!�a�($\{\sigma_i��U��'� $(^* \x� .�� �: ��8F�$! lU5T`%a (UͿҶ!Z2V�s"�22�9 $\xi�?ss�) �!!� {\xi� T.�}e�i� mHll�7>R�!夥�R8 $ M2:*�7EW�$>6�7rjj��81}�)�M(NN��m|u�E�FEy" � a��& � � B� yteV�2}�l.6bB�IBis ^ up {"_?.�!a�j3j"�r`"� (!?E�&� �*)Pn$7)aA��mX" ��B�M)>o [Sketch!�� ]�* part9 N�{1}w le{<�frea�4"�4)�n��.)�r . lU�=> $\ph"CFAG�#n:h�:0$GQ�R�.*�:�!I]#we want�e�B��DG�.�NS�6T!�R�V8�.ND������M9B4 \f� ��� _i= !yH�kG<#� �%�a�: 6�hpF? j �AX&< hA(a�eir �!.�{+AFl �6k*� re�.��%4 lpha�'�Aj�%ٯ.go � 1�ۡ�>�xi�F !j\ b" ���$ :�EՅ�d keep�^in mi�DH!�8aZ��=S$Ge�e�seA��1> �et6@AV)�jj-G ��'2 ��5LA!�BA�.Ej"� WWDQ� ai7GU$J�(��AA�AK �. �>ZK<8fI"�7M�$� depend� a -i�bby send!q e�� �Z %!$a�m�^�� G�#47 x 0 Ag� �:zA�I!U1us��ve��2}*�+JK E�2>[Gc"l� 5!G� "y�#6� *�.g F��a� m b$��I"����.8!+6�ito-��,yu)|%easQ%��#uV�iLw�f[ <$F\sep U = F U/%[�+.�p-�2*Y<�2cC2 � I0!I&F-A$atibl�$�D"�H=� s, y�A�a5�E{ �V��iѥcPor 1$Y�&rN�sep�$�� stra�Dforwar�#. )8E�"~)\%�eFJ��"�< or '� G&��� ���asy we ���e�JEm�of�� s $(�<}>o� , \{� }g x>�]!�Y� �$ 5  a�̅�E���I�V��.͌a��9� ��H�a�H� ��[(*63�8is�w�,�GbDby decla(b?a�beY�? / V_j �I!nb_j!n!mn�*�,����bj V_� - T�r�uel i.�I is r�?we"�"�Eac�ůF�%cp�? a?=���n6 2�.,classe$R�2i^��Z�F��2associa;E���hA�ae/%���B.�] �<IU!� >i�KV\}, p_YJ"x4 P|O0 �� Y"3A�ce!Iq ��L)�:s well�d%"�$-"�6! }N��� �;n+�_���� p:!�ajK�e��i�:%7 =��a"�J/����)������!-���J� V�n<���P��kWUuni�0al�v�K@Be�Mr`�" "� nG�;�~�. P��3}d9_ ��ATII�A slicke�.uty�t[55a�.B 2�@� $\{Sp/ 6�,ie�Ckngi�+ $\cT� �AF Ezsr m a orde� set:A�ei \leq j� $S�3*�H* ccorbtoZ2. directed- �}�'iEa  system� s,� 6 J= !ei7s�9k. $k \geq �� s �HAse�K�Q Fv.� -�� �lE$@lim%�$hom_{\cC}(%,i{ad�, \chapter{F �L ies}v,ch:*A, \q*j3sec4.�DYP�����/ertt _)� S !�`)fix%q/��/ ( play�)rolG >study ��F=��F$e ppyF� �G\p!XF8\c�R+ .� x draw"PJ*l'"�2�"olva!iŏ�%"$\cF$;a1a� go+e�}E� � .A� � C- ll�� ype ``<�&U$'',w��+�]��= Fu6�3�Y+ah��5 "�){{}\x�A@{|->�IK)]^� &{}C!5 6)bL [r]^f & V�(f�r=�+�6��6!�>-�y]�T ){!h/\xe4�His� cartesian�E!B f}� � �3wsw zetaɥ y� FI-4h��M� .;�A��P=�!<\>. h'6ps�e`�th�U!.|seNj - = h �: { �vaa3|]qnh @R=6�X{��+Itd]!L@{-A� rd]_ nE�0ar@/^/[rrd]^{�}M� D2��7[r]_{!4E�%et.�m�+{}9K!�E� d]_h.t,|(.487)\hole 7S5�I�[r�,2T%yVF u! <rQC�-:�a�I�map��M�"�)VQ� U0 sa�h� �*���;V$U$q#^}l}�"�remarkѝ rmk:Iy-=3;��5�CofB��"� rTha9K�.ak0\cite{sga1}; �L>M�M�(ed �strongly+j+ Kgray-�_. "�=�<d5��no� � ,��"�� -��%*�1)��b��($\widetilde)�RI�II M =��Z 6�K�Q�!� fiU!�9e�6K2�R�aQu� ��Aph��B�u���20r�,�Ze�26��[r]���P�5a� "17�"�*�45���2� ex�1Adi�:� 3b5-� ab6-�  Y�]}�"q," i�6o� Q�e�&48miO`8t�:,��lefuA�#I�S  ion�':p-��" V%4��!,� \UV5)a6# hfil_.�&�J#*`�k�C�2�:v��E��4}�9�e�)��� �v$%E�X6* )N*�e�MaV��"�G�6����6;.� 3} A-nA� �EB�CB62�>��2J.x2 �kG&� G,r� �#�&� ��s�\&�14�y�P �F�f��9RE%��PF���FYF [ RG�ph~T�F,[-�2jM�A�jZ� ��.A� a�q�"��}"/%B%7\b� ! , ! �&}�I~P.�X�$eL B�-0F!A�a&� � � *l $V�>R�O f!hQ5�e�>] A� %O=:F�i{- &d� �:�M �1I WJ6�� �&� �C��.�E�7ndmA�re>�.�t�+kE+'"��Sb9-�X��?1�!7$!VJb�G m�&�V''���!"0�9-�(er� Q!Z:! /��u�s rc FL �$; �si�uE�\W6}�\R�#.� Notic�A*�D!�cal3r� must�(interpreted �Dct*�4��2(B �UH}�`�'Xubs�J[!�pseudo-1%�YX����� 6� ��v!�1!� Eq�J�D�(�e/6�y}%��)Au)�)�v+ �f��%��g�+T R>�*�AG Jm�I �Q�F$BE�F \id_VaiB7-iF"F2 �)�f�:&6��-9�6�M )'��![%g{K\cG =/h�%_�;# A_U�(U�g B.6�&-llF@coulde�%�~,.��u �6���Syy�,%��EB� �Z�*G�'�end� Ea��1Xj#"�jt c]v+kPhapw[wKC��U~\#��*x*A`"�?c, _s"�'�!�Aemp�A�ScF(V)no;> is kR&� thYm does! yj7)cedq�ies0�@wh��V�$q�>i���>b7VA�i:��+-G�)"� 3� we choQ%*+ey_� Qf^* � � E� A�WM`]bUKf^*E)DQI)h>2&:���)zf�t&څ- $\b�� &W eta'��%��&� >YA�E '��E"��A6b%�7[&��zS&�i'� D ('\\7\]�mut�2J� �1�F vage�!͍ Y��i�&C &ns�i�;m �4F�*�y\C.�J�2� ,6 -�eAE .2�(K�1tar�:� .� �G ���� �?�� axio�choice,m%:"y�a 1S.��F)a�qth9$!a"�&2 *7�VA��]�'Q�Q��r�-��,&�4� ( . �&��t�+�o^g��e "aŒh��%dJ�;���!t�E[zies*�F�i�kquroc^*ct>�MZ)6��M%<�B n*8Ai�Hi�#Of�Vrs�"�`j �Cllqq?�be.o�EK� ies: ��'cer H��orkɰ0�%S",� i��often5v9k'%Iն�X�IE�}" {ex:EJs}�}abhs). W� :e�gT�atb$H�=F0 R/ >%�eE:A� $\iso!]_U(\xi)��5�"��� 2` &L:of�! 3}m]A�I�mN"Osm$<��Es� �� A�=H�{�U)�4A� �Br�Wproble<�� ing:�k. )� N]7"eC�%W��� "9�$�$�W# n $f^*g^* &!d9�4M�1e"tJ1�JAƩ� I�e�Bsoyvy:lshB hD $(gf)�*q Ra"�s2�EJ$ass_{f,g}(�)�1�m-�Ih��z2?�1a��]9�B76�6}6x�]b cF(W6T $. So, afti� ��ٛN�almost�`����!˥�6%�>�!���E��Z %�t�J!���y Tw�]k nown�� a 2- <y;�fs�OAOr&i!y1! E "OaR  S�n turn��%  wm`be!T�y�*{ � un�>s! u�1re 1- C(#)��s ( t ies) ��@�2EZ�Tp$!Lv$et insteada�9��$]l0�6�}, or�i�=�. dernVJin ,;lax 2"}��A�:�<:i"� :�: $\PUo� �� !�B data�.� "�])����� Y� s~$B9%�V�Q���q���� ���2��L�nvPhi U}>O \�  �O�5Z, ip{2"@}�.g}�h6�G5is�1 �x6��W.�M ] of1Y�|�2&�>&�seEe`r�- �Sas<"��Xa�c�Ue�!�I�UAa��Jx �(>��y� MuEq�{���n 19GU, f}($DI (<��B )N"] and nT�'�Vo"�V �M}B d_V^* �6n.#\]Q�"t �iIs�h 2z h} T)_a&�~R%E��1(T)�O ��"(@C+30�%I�h� &&�^{!-"g}(!)�&r^�1�g,h}( G )} &z`>_,5f.6"" (hg)r� h��)} lh��&~ �]�Q�Y63a} ���& e!�n�Yi�<(�B$ravariant)>;F�tA�� .&} ��m�m.!CC>6' valuen2J� ߀��*�c2a�qlZW�ZI3$" �}30�_ �:�w � 1 ��6��O?�5 i�$�aW��D4U�V7�fg�c =Il{*} usmhO~o>�J�oK�O�.�, %��ca:�xMst!x� oK2� �� �w!�Y�����i�b���oP4onKi.��I*% ]� :�){c��1R��� �, us dai#:�t�y~�[(�""t!T5 ~(a)A/s�t)� >� � �h� � $� r|>Ulw�analyz����a�A#6�!��h*�� $Ww&V~L�^�1!S͎� G3e"d%QbK,41�a�� �a D� N�>�"�x Vinq%%Bs�5 � )  B� ��;(g�6f /�R  g$.�?�u "TTa0E�Hm g� � J�a� q���.CB') �o��� �+��l� 'EPK@�AP"�<lyg)}�A�B��y ^�Lj#�=�$C , U)&$�?f"5 5C-*V.U!^ #"%0 $(a,!�M�f)', V$%[F6�"'Ne 2�:6S %G�@#" �fw)-���cSV�B"�F�*8s: if� �� \quaE�T {anda (b, g� o�_�! E��, Wo�A�I�Nn^ �MA� �= (�f5iai`%f{�>�/ ~"�TEQWu�E� �M�at�Td�M#]eL Ad�9� �!�5f$;6_ueqrmak�TA6Or�.�,fa^�� u�%��`j05���R%,as bigl-p)� ), Ur1. iNe͉�� � ID�a�i�Il(�{)� d }, fe� "�+I-&f�)��BC�t �Bt"�߉�Bt�!2]6)2"t"i|AQ"�D�Flev7lI:s� sXM]FA%��)C><i'6;a���=9Oi�l.��ll� A7?�?��? � . U = �e� �,� &�confu����F����!R��A�for>%* �1A5�AR�Jx����I�. Again!�):����:�f^*E�a�!8I~" �Y����$�v�CbN�"-�%��meD��� (a,f�3%�  \cdot��fL��i @2�f-��)�� C`�7�V����C�* :a \'d>W' �b� rr"gx�2&.�N�}x* 3] 6�,us. ��j ܃60 threS*c"��*��\�*^{�f�&9�b,g )S�m|V, T���] �LRha*g� (c,h1���l(p-�E rS�zl(cM(!�E)f /] ~3. �.uor2u l%� 4 pb(po!ByEXE�".j ion,�6q ^y�align*%4i� &=,Q�) 41-�?A�? & = &P�C2tzT,Y�5/B�5�9L>�f,*� ၿ�!}:�-6�>> �g g*= ^� cZf^*A[ a;2����m52�%��><~K��[�X'cTW[2�f��� +h^*i�.CY1�Eea�FWh^{*} G�!u.TJ9=��DI���k� c>� o&�2�� 3!W �*� Bu)|R�G�I squa�9�!"6a� r >K� Z�%W� y*2��UR.h�in &vJb+J�$��&�*� �6+"� �!O)��A��C �*"xi$���9 8j$/{A,U!� D !�r =�x60=��>��i� �erLT:�yLs neut�s|RSap�,�T&� ��2xx "� �����e��v�V�F� ��bigl(A2��:� 56�2^#n9!E��!^U,�#a�^*H��1!�-�թuK}0of��HG� �pV��Lals $�*�$A�m'zn#=4o#{} �M��Q-�,�.-dA�a�7�KA���a.#T�iBWet� {} !u>|&Q.}v� ^<��u*�7�^? = a$_ d�\r� � f°I�� A��&N � 5�E�!�=kEL6����*aE.�>. ��*q(!k�`g>Q�<F"(6�4:��.�.� Y f�4��YJQ� e.�<%�raJH���, 2�et( �)[ �7.>�� Aw��a� F�A��Q���A��n��B]�" .�tgt%DB*�qr >�R%�G�-"[ $@R-10pt@C+i  ,W�&�H�*�L{� iN2�L� R&B�Q��L::� VB�\�W>>�L^< g I965V I_" & 2I(��;dot45�)�bF^r�-a:#%$�[;4 nserR�.�A�� J�a�<�)�B"�;i��e��"h�d &c, fh),O]��E1 tells�����A��� f-F�& �$Nv�e { b, h���?ڕ��Fm@uslsou�`ag�"��l�6(B�ll">�Nq���$� e�>�,��v %)�C�]��� a�"fK����"� �C�l��7),�)�J�,��^&q-s9 � U� I6���fèX[ � �AVvia!72� �;�{"�[�)b��A.�&� �6F��i�start �> - �)tr��[Hed��-[\!&(�}�*�x��7d:��)�"� ".origiv{:+{7Uo���Con"�:��d.��.�(��2�b6��N��hx2�Xth�%j~N (al�:, S;6givk>�v!esa��s'~y . O�9�8 ��U��T*+)�>�(u�j �sm (ReAR rJ?R),^ q��4eJfYb 2�!aIT�����:��pcisi�!"o�,:� Bg!!P�j�,6=�-F7 as w -l*Oy tO��te[%Dque, pp.~193--194]�R,�:x�=�y� h&Ors.=Sit hel@�&3Z�:�*F��%?Z�"s&3Gf�%�bs} .���-th�vs.�+$\AU)C�k�� *�%�cC$��sաAh1 wam &J��b�"��~�=`o*�{Y���4oZ@�*�6 � XO � n YM gr vRJIR���P� - "�N ̈́C{nds2�S � �ncodoma!3j!���J��i2&��'.$ =�%1�9�" /*mit^��/ i�pre�%,V#r�Y�� n"��)�A.�!)Rr �1M��4��Q��st"-�A�*�a $\cP� Yw27}"ML C"?*AU�!6 !~�wf `+�����"�,��� �~�5Y��eXPaEqX'�6E�xYUU~� "� � Am`*a5 A�4�H[pWU'eh� ��^6�u�$ehre� �E�U#c )D �7\P6t�NQɍ�#$s_V,{�'"�<�#&�UgVi���=M�=� Ix]gjF�XedIb�P a C4A? the M� R � I�nKVL�X�/P$�G6{Pq�, ud4f��g�U�35��hYa�`=��J�%�A"&Y�W����r�K �T & V _]N/� !��Q � ��l=.�)�%3^���USB* Z�aex:�ify�9MG�Dt��)y�*)��[4!�ck2f M A36vyMGi�*B $\cB�*�(topA��9."X��s�|�`IQU�'pr�ppu�0G$ bundles $P!�aEn 2M$(�%N&$M_.E_Q <V$ bJ_. &�� P��` d�YQ Mb �`3QS�!���< $G$-S+r�7)�(�gNS�A�9 )= "C.%k�,��dy�.7:��"*65�R��?��0&�Iof5m ��B�,єqHE�?Re� � gges�bF-� �articipa�s�Al*1#)fo�H��5r*�NaA�I2A�s�� "���Jj��t4nder�54!$F�#i �H�9� �A"�uҵ!Aelf>n 6��$u���a�: Eyou�6�M!Ya[ �"�BF��D��!����U���ڹal1.y}�&���}ar^ &(]CY� (^0$Y�}��!coarsesл)�� �F*-u�STe�JM05� $T \!��DX!��T3+*e6 =Yk9��72� 9f23: � eQ)���'"�3 ���r%�a�eIa�$Aӹ�9��eD *�i9Q�!��H��d!� ;�(mxu�wa�B[V!i��.dMρYU�F"4' ��a�BLW��e�8e$�a��|v�JY |/A0�-B�9�6ѱ� �|� W�:A��j� b-�0ves"�^ "�Z�X>$12"b6��V�� ite�\�k��-�y. �� refe��aif1�f�)cC/X)�<.7A��Mu>y (N�$*(��a��n�$X$DJF ^*�*�lAXz� $\sh �.�8fb>q � � sAd"Q5 A4"�i��.� sh{YPr  X}Ѣfږ2��+1V�Y{  �O&�Ih�%l�q[�F(m�x�eqdef Y!�p[�m-�f _E��������qX� ]�� (z � C.w�Z 6��+ GY� ���&\$�!����&�f^21=., %|I�!�Y)p]0 kX�P�^�7^*F��v`�e�~A# �B'�r�Le�&xASF�%��1T;/G).jm#.�EY�q�VI�.z�)+f^*57BdE�����s��)G !5�!16T� eS )�w"e:3 &�.�X���+E�"�M r ZI��8���)an��)it�.,G�%I#�*�c%cZML E7Fu&gm�#XY�\sh� %�a�)t�6�)B'9Qsi+HrDRn{�}^c�2�q3�ha\S1�� :�7�=z!�h�h�pI`� �����G5��1:j�9LuQ��$ *���ip�Q��belian�s,Ԕ� so o>� K" cu�?&�"~1�byz2� U�I��&]��/�L � �!?e�!?��"�!�E ��"��� &o�'e� inhe}dI8!��`2�9%8 creaC�ss diff�&I? forc e� FOunpleas��machin�ZZ6^�0z%v(discrepancy"�MY�!�a� "��1�L 5 s0O desc�Ҕy� \qc9so &w1 �=xerl�Nlis�f�.�>�s�Q9^��=E�&�� �(if'Vk;of.2} : 7: c- �a$ntrw 6+13q�.� ^3���Q�!�C��7w� ��5xWI; ��*�[z�B $\qcoh�A�q6-A]�[<F��h�V��u�v ;m��=� wM �8(Unfortunate>�i��mo l��KV6"K�S6�M1"�A6T%�&�4-rJuQ����#;Tly "��i���aq����0u����aty�>"�c:/\u_#�nd��~s�� n��t�j&�%38V ably��exploi�5xfa�Q pushr�$f_:Uͺ%_� M iaj�m�?_*&�)g_* fo �noT��!})(adһ!2M &�=,MD�'aHM�5� $\cN A�& 9�9�s>#�.Tt$_f(\cN,\cMOX��xO�NcN,�#�6$U}(� N, %] \��T�� M` cN$. M�L!�ici��r�aB-{.�%�U� �!&ohu�catgrp ��$byg (\cM,\cN)E�h�yB�]�% �B>K1!e�-u��B 5!&I���/to A�]/ . E"�A�s7�\a��u�cMM�cM�n�ib�_� \cN!N!r6 D�.��QzV$* p%fv����9("q @C+2�,vj.Pa��,-|�51DU� } &x5�>� ^:Z1<�QA�f_A�'<�1>{'72?:{ @ �:I�!'u|�>�'e�s u {- /!�.N�'}�-;�- >zb� �N�{*}%`�+1N�a��3oj S�= kq� i� tafA�.��G�)/)A_m�Om yC� �Gis�K;� �jl"�Y�amT)> yX�ruh����"�A2�b�j�*� �A�a�� ). NE���]�R""~adj� ��|Eh��M��1}�: -)�d'.q�YN+d�-~V$C ^F=^*J-I\6�V1��C��3 �8 ual 8(�(of Yoneda'sm�Bz&0- %})� &=�`a6�**�0�O1�2�}�A���+mRIJM�\�����=� A@V�|V&1E)=���{-*} )�~Nit��x�A�� one:��A����& M(A)P+ord��>� eqF"AG\ �O85 AAQ\d!-=�A}�O %Ijs=���SpieceA [ � �.6�+�q&tG��� �a}�E!e�Z`"3S� h�%e& �M* I����$eK$�:at*}{3�[}��2�\cP, -?<�QM�2W 2,7_*.2& �DDl(�D���{g�5 cP,-�.$Rr�;{}=Zn g_*fn�&m�>�V}(�a�0�6����P,5B�uF5 Uh�k�hf96-h ($5�� "� >�+=1T.S��1o �9  {}&"6���-b.�)�!���6-B�N�*} �TW$b��D"A�o�����$�� 2�e��1f<cP!oSG�\cP ����\�R�Q- L� J�>�:�ce =%,�S��A}�:�(S��P�O�zN9*8 K*� � Z !"�6ݧ Ar3gf)�(��g��E�]6 H d\cN@I� . N��*F `#�^*��M�AC�ES�E �s$�E� �)�-��0$\cO_U$-moduly*��*��5�yU)�)$ �.l�hDFY;� �UL.�VD)�:�N~6�}��75d�.��� �e&dG1'�b {F%>0 +%@��wo.�s"�2V��5�*V�D ro� B8�Di� �qx��V'��!O�U�o�q&� .x)�x �it*5�_�5=)��( E��A�">�Ne<SisN.ْ:��V5�e6eJVAY"}�Q6�a n�1\6њ�� .� � , - (."6)�b="�XT �V� �Q*"� �!v� { ���|*k-"�7w�/p% Y%�e_;1> _)�z`�<� �s) J" !� = i ? �2�1>Si6�<s΁ks"}�k�-�a3![� )o amt./$&�|A <�$����S�6iA�cx^z�)�^�noUb qc{S�R[  ���B� �y$4RK�n��I�N�A�!\cO��_�.H{�e�zr&*�*�XX5ej΍"��C�"��i�oidZ?y"�r =&�=.; �}"�+ 0"�.0% �&�$2%!�FST_FF�(i&�R!z1.9 Huoi���/�M)�"V`�~^ce^����o�ofinz�er�;U� �27s* �*+a.$|har�4 -in-�s�-�;i/�����!7*q+.d/�a�ri(�<8�T" ���"b0i�te0�1} N[a�=v ��(l(C02}"�$c?� ;�a�#B7\p_�@w1�� a�I1>.�"�B�� <F�$5 A�z��P 2�B .�"�'�\}6��s;JT�Pnk8rlI�E�Q>.�A�f�$2��`52 �e��~J%4f;�:���'9&�}b�!��HN&Î (%�=$;.usd�vnphi�3( d*y�+�e2v��)r� in�e�?�[2�si$<&i�F&� a6+�^"�6G%rJEbYhG�� G �!^��v�blC*�<|�dFA�}�Y+ �L.aH% ��O�.�%��"A�p:j�2�� triv�+��d�BK%66�Vl�D4!�H2�t*��C$�]pi�oF=��� C�qXr!�hi'l�A��|�RZJsBZ rsF��>�Fr�' 9�ټ��'ߐE)R6�a5�w+����*�)�E�6�F!`�[������ɛ corollary�y#*����'G!be2� 6�-��2�E��p-v>Ie:�E.T�:>a�^r^�O�b� �z�eV�<, �&e6�w�+&I7ar��� lR��&B<��9�N5r���%�?e��_N< "6 F�~��~g:C W1F6�= V0�C� By�i��#��80Dthoughp (E"�%2���I22)"/��%��/y !b��u � �z!!�gep��E.b�iB& }rO ���% �.J + �2E  a&} �D~@ Z %��M�Ise0b�~J���J�� S!R �!��9B.Y t&ş.��", ?� � bBA,.Qie3 �BTN3�')\ʊ �n a]z >�ɀL��+!��B  �z}.�' � a'C� � � ��uB� h� " !�� >�S.�J))*��ae�A' ��B�&� �� aG, pickE�6�4�G .���Lf2�!ny6*)\1�+Y�-IFS xR�|��Fm��:@m5O��K+�m(!" m��P \r]� BB"��)H�A��� � 2)!G��4���`9|� 2�Q %�=%�&(. b� g"D t"��vM=��ޙ�ޙf��ݙ�ݙ1�642� �d%� �uq�1Nm.A�I�hZ �`<Y%��;�,�dB�\:U�1=�2�B����,c6� k}�/ JE�"� T3"_��,�"� unAic�Yy�q)e)�w^n��-P��iFbe�>� ��map�1�FLG �l����a�%��+� ru����cg$qh`%]�F-*���^&�*c MQ ���:��+*%h�,�l2�2�L�Nɵ^Ј.��� � mJ�U3� !?!:j��!&�3R4*>F1x5 qf�& 2"��I�9&��JIMn6, ٥�NfBs�)FG��KaL.�=z;�ÆZ�5iX .�*6<�hi_9UPhM#M G!�&=f1[(Kfg}�� � A�E&/ 1�� 6�.�0�1�NA0��EG��s�E �R.=�2-6N�V) &��A>@ 2x�mG�Uj �&; �J [BlG(:<"~a6��Q� � N�Ɂ�1��(b� A���:" fTw2��1f�6F6qo�R�cf� $˨g� )�> �_P$� ͆�Ee�E��� &q�qeU,�)Uӡ :S�0� .�s`2"ZkE�$P�(V,r ������rVE]�� z�'c1%F� ]{nm�$ZB6�*�%���'�0a�R��4F_7Y& � <cFsi'}�f5�=~ɢ 5&��%��)�iz<5�9�%x�^�.��g]�s+r� 8AKv� YQ)xi �d.��E '(f)�K_V2 �Phi6VE4"� smRt�e�)N�% W6VM�¶WeƷi��f�6� 4this defines ap functor from the category of s toB (�ies fibered in sets. \end{proof} So, anyM� $\cC\op \arr \catset $ will give an example�a` sy ove H�@$. \begin{remark} It is interesting to notice that if $F \colon �.�$@a�and�F$C$% $associated�:,)Tn an object $(X, \xi)$� $\cFlDuniversal pair for9�$&f� only�i�$a terminala;W. Hence <8s representableA�M1 hasFQ-�1[8 In particular,%�2�X�$C$, we hav!ue:�Qt \[ h_X\b�,#(] defined o1R s by%,rule $F\ U = \hom_{\cC}(U,X)$. T.�:�]O.� with this�ismcomma9�$$(\cC/X)$,%WaD�]< D"E�forget ]arrowA�$o $X$. Si| situationC(ollowing. Fa�(Yoneda's le�we se!~at�u=a�Exembedde�J� �s0a�\}�!�hil_Z2is~`�5 �ies. �now��identify}�z�-�,e correspond� gyj�)�wT(inconsistently) call =����$ simply ``�90''. \subsec!�{C�Z.2�ɕ! } \label{ 5: e-&}M��proposiT} 1>/L�V\cG$ ben�^%�$,$F$ another54,2t� G$9�ebn @a3-�]G$>w��>(C$ viaI�om�a�pa�$G} \circ F���� Fur� more��(in groupoidy�R��R2!(�@6Z��v�U2-��1� ion}���FOne�s immed�xl��atA>�4of9cartesiAZ�+it9age�IRRz7���8irst statement ��sHie�.�o…� Cber����-U�M!l2disjoint�3 on, Ŵq�,K&%is�� Yll ^G$  $U$;se > areY- , or%�,>7their:� �1� T�E(can be used�-0. Suppos�Jat $S�9)�1y��de � �����vS�v,: ��6���GSybF�. By P��~\refA�:�,�!�.$ !��K�7S)�!� same!J� 5\% togea��$a morphism)Ũ]of1)Bx� .B�-X./���S!C-1 s; hm we ge�mat �v�5�BJA�equivalaHto�ign:?R� >@natural transform1�2�8h_{S}$. Describc�process��>mMssXhan %6�!,�,,eneral. Giv M�� -�B- is=bu jr� Q�chqh�>edI#A`f ful� i��r0b"F$ whTaY�)�G1�5j�a� ��X&lo� ,y free sheav� -1�:��H-�y� atqc� � $�ch. Here�an�e� �&�]�� def:ass-"� �@%��*����"/ *�EPe�/;�G!\M # U!+F#! !G.ZU'�!�� A�����5IE�s/f�- 4N"m�q� IaK2�2 �E\E�)mZc�-"2w.D a�FI�L�A�q" Rh� i��d��.� �!i. ! ��i@ �12�;� ^"�  V- char- �-in]���: g allx:�V-5� }{4}�YmES ce� h1�ie�c.�NR< <�2�!fac� FUEU-�iesIvnot s,jstrong 5ic� +Ldoes cause difficult�$ As usual%� main!n blem!pT� between� isoI%ce�out be��equal;!��words,FStwo fix&� � j *3 �mL _�n�V� A�mYV�mor�} �����Sbe�9z5��nD$��$G&� �bG$@)sms&B base-?r� V�� V!:E}#� :!V?s} alpham� ��KV6*" ��& � $�a݁<=� $ g_��colonlG��܉GQ ���� eqdef �F}.��(F).Q)�An͇U�sm����$G$�a :4^� G � �y `QV. �] Ls checkip�(n�e�F�.�~lso>�.�9��Q�yͨ)��TmQ��%���ԉj&my� �+s;�denoteG b�B\cC(\cF,�l%� 22.c&�=Bn�J;y�. Um ceqd!R�} ) I=�$!�9DA I���G>� re exis!�5�.HG�́a6�]�M7��th $\id_a���a��"A�"�  W� llauau�hom} 1�]&� 'ca, ��acteriz��:-�&� �:)V�!Fu6R!Z( F' "� cG'$e' ��� .�Pi�%�� \cF'9�%�%� Ug�sz na�r�&�A��$"�u�#2'e�')]  sends eacArPhiV~�Fc�D��8A� > A� �9 G'.5]�SAY"+ A "' left�n exerci�reader�-�P basic criAmo���$wh}�R'Mz9{&g .�.!An-2��FVN��1R�M �聠n.&� j�!�ri: $F_Uy(UI���JQ:or2*r� ..=of}uE^R�; a��&��J 2%EAUG\simeq �{\cG}}\ F6 F}$ 5c:V%$8G_U6:!&]'F>'!Y}�o $G_U1X�nr!��Co �ly�assum�� �q-��.��� truc�Z�!tASmM &� we�goaL<"eedy]q lem:fully� �e*� every5�a�D� faithfulm]�� qi:(�� �>�We !! showE��!A�� V �Q� etaI�an� $\p� �GF 8_ � )�a�qu!�!!D&Tx   y A"bF s'{ hi$. Sx� � �$? =H.�  _1�m���pullback�X<'� U�jeta_1N_1!�a5.Z�;- 'eu"� , soM �^!�$E�ors-7ly�h6$2x� �B B-�)Y�9� alogous^ !!��>�a]or�throug�)Z $; s�I�HN�n� } lift�7Y`6�_�n;�w��$proved�L4#m� } F:*6G$ pickA�I��j�M���1S$�$A�6�6� J�A�\�F7.�����i�4�$�  be\�J:�2:. Nowe�J *!�E05�)�a�b�e)r!|V�Ge���)I�G ]&$%ph\ �eta-"8"xi^{-1���is>�diagram� � p\xymatrix@C+8pt{{}\xi\ar[r]^{b} d � xi}&�&{}�ar2eta}\\a�xi)"N�}& eta)})\]� mut3Th� �k s � �#��� �p )= . IZ�by, ��. Q�EX� *c��we�6� b ${\mathcal EM�-��*GBWe) u(Z to )�% K%*�� �c<� �&tid2�tFixA�=#.�E &[.` s�a�oni��� IJ{ɡ�$� � X'))2. S�Ra�e�6��:y6}b��{�Jz xvu��2� 2D=q~�$;)�� si�$� I�n� $a�{A-�I16�G}*� �#2�J�'i6� relii� �"u'eq-# AsA�9+�#\S�{se4&}~no� �ey gM!ize�e#set�"e�Tpossi�+E�a�z .����"� 0 aR:AseA�#c�+ �. :]R C4teq X \times XEp:@1 q�*] %produc���y--RI_e!^,�1.ofmws, $Rs� CTour` nd tmaps �7 X "�3�&2second��-ionX /$x= yi X��is pre�lyE�� $(x,y�f2<!�I"he %.�classPt+i�nT'if�y?not �$ itiv��� reAIwA�"a)!�ro!,w^reflex 9tell u 6��2x�!<�>� (x,xr �ޱT. F�.(ly symmetryq��63�.&P$(y`. So,E1 E2s"�'��Oa-���6 ��t most9�. 2�)�a�c2cI �~Xd0M� �� dR2%!� Z�ini]!9E�vBpY�y�Edch�r2�.��.�.^�a���$of� �767. "�ts^�Y9�inA��#2%CM!" "to7+el�2�.!"�.%u�tset} A��/o�|aāho6�1V}&� |.���IfV��yZt,�i,P,�"10�-^� ��2anEZ)�$X/B�.k���M���3 �,�#58ce4,e��>B?36X� �a��"q �i�1��8�es23iasurm9{N9�!���� )�ul.-rJYZ��%} ]?��� &�a �&quasi- �+6�,is 1�f�('�"�"b1��) ]��5�* a�r�=�- a�:-� �.p�e2�=R.�.�>D-A-Gs�~01x>�6�.J%�s hol*Y$enumeratei7 tem E+��-!� �3A]� $f,U �\p_� �&� ��"����B:� <"M�� �= f$. F.�#ada�yL! �/'� K z ��$F}*Z� aG �E �xi'| \M^*ML �  \%b-c!��|v� ��Zo�� � � � AF{>h{ B)��1$f� 2!ea9��# easy� oŵA�"Og"^�ftQ�A��!�� ^LjD2qJ�A�ked�w)Jj&av���9 �"�.��={9T�1��app�$A*�%~ !���2S>f &,*1��G��Z� $�nV2=��6@A*u > �sol���7..gb^"2:t :\ � "1����^+. 2�:-�6"�)�.c�)J*]b��-�6�'. .��J2�,.� !� U2� Z el\5�+%�.��f�V� �swo^c ���b�Ӆ�&�(V� ;�2&W�o��BF�����>A�&�'-�A��� ik,a w�ed�� f^*ձ�V�< %_at�� ism>  $[�]1-� "�F0of=�M�zto&B � �%�$?!e�(uctur� �VadNh5If� thincPh��� u�]�Q%v�2byl!0* !�9-�� &Y)�$!Q��u�c� rj��%^eIK}�{*�"�(�B{��m ?.ARa fewf7�3ac�@����\�.��->�#\hfil*.l,ref{1}!�"M%=z�ct0�"6@&�*�X26X:� �ZS^F �3>`� ~ZAQ�m.��&�" We l0�i F�5�V"�In 2-M��terms,X@�, part]-��say�L@11LF�B!qin} just a 1{� �oVx2}rx2�lU�3m.:(�-O�:sQBĥzhe 2-�?(�qa�{R2�AFF}�8*rrep-�s}�S��s$-�@.:2 �4� B��hA��%Pin.x ���Jxto t^-6V��6� X5!�&� �:c�&t*���% eC-�0�~k:�}��*�BAp3��:��*B�Xc>72: J�� Y$ g/��*< -A! �8f)� 2x Y)�."�? �-X-�&-W�? 8X \!z6 f :8Y� U. Cf)$!��:]-15pt{Ud]r]&&V ld]5&X&& �J�mutat�� obtaBD��A!$both sides�"K5}�� !�U#���%�co� weak�C�C�Db�Fnamed}{� &>�s6!+ e�� !)6# a��-�s&�(%~ J�B])T~G� bi o� ��z� �:�.�8N�2�>�M�&�R&2�q y}�V� _1��1)X.��.�:H?E(is necessar�B�b �I"�. How� � should b�r�:�� $�A� :k�3_!�� :eG�) �s� "Y�` hena�m�homY�0 hom\bigl(�sX),* ar \] ��accor���V+�>�-����: &Mie:G,}�6��\Ds ��&s,; ] buI2J!$/'�4%&semc%��'� b� 2��06s�'A$��ca�1e�op5�$a} onger�.�f[.:�*�aY�Qbo����m�� "���$.Z'�be) n2� FR��;��a �a�KAI�$\id_X)�� a� Also,Ab��!2:x<  >1h $F,� �!E�{�bV*�!�a��_{�"k!F�AG �Zi�# ~E��LU�I� �/FrI�V).<]R�5��.G�d*�Fg&b�� �Js*�1���V~���x�Lj(5�gphi {&} cCSQ �%! &�%-6:m^Lhrr]^f&t_\psiRy�-c%6��1�theta1!i�%�ps � ���@�A0���R=��& V}{�&$@{|->}[dd]5ar@{- rd]_ � /^/[rrd] � ��&G%]�M&> ;� _fpX4|(.505)\hole^>!m�[r)h�& X� qMu� 2"jiſ!]a� �{E(Q�Cq/B� G V  2-ySM"6'!�:v� :%� �Wm�s abov.'��alRFj�ɗa�l^��� cF(Xu��:� �} T2.'!X"� !�i? N E��p5] z&�] ",�="�Q� "�.}�vO2�te�.��$ yield���8�'X}�;� i1�c�"ca�'mQ2�Qv���Bt� s�,2�%���Qar���] takm%"Gjo� � ��.ٍ*0&�%>S5B6q:!�3��m��$U 8M&'.$Q*%"m ��,�IB7�Bf���.��/��A&2 learl*tEO2i�G�'i>�MafterE�y���=&�-��&��'is mean�$F�� )�%Ca="0 $ alY?�SB��U�2�)� r2^�  �٩>��� u�D 1#6a.��B�W�/�=fa�*�Xe:@m��LX1\Jy!�"D �F gBTl&*L!�F�: � � "jR�� ~$�R�! U��&we Jw8%A�%�* �O#{Afora>�6�A��Nto(ormulat�"� A�5'$ability. A�V �/ 9=�P� �֭�ZKQA� � $FO Fh*K�`Ri�"B�v orig�ZX��a8'it6� :�)�H%[&�� sa���;po"i��-=!+�>&�/�E��e' ;h"%<U,�via*Nsm�AQ�rho��d���U$]�!]"3�5<%�xTa�i�! *(5�C-D.�e1i&�C6�F[Uz$�q?�M��7#5*� r��S �u*5� ]X"�2��}�lFjJ�! 85&?2Ij�!�J��9J")Z&�!e2�>� 1r�)qI&6.!�AI�I�.�4!�2� rho-�R*�A>�2�A3��6*�2cSplit/]Fo""�0E&7 in E�M�"ex� -nosLVT�G2dmi�<*�F�%ilw"0 �sa A"�Q0Y�theorem� thmWs t-"� ,!eH� �,ZcB��nB���L�2�"� ly�d^�0$\widetilde{\�'e��M�5=�B>�K��6G�.Y-)&�� }� *a2&aL�"�����\h_{U|a5��U% "�� om(-)^� 4}$.aB-�\opaO�SAll�J-U�Ty��)�k\��)B].s � �� >h nV�KKF��V.�� Z>�!v I9 h_{V�A=%�Y0*�1�� 0 �B2U ;@�Ju��G1Bv!��91q�<"�aK�-a:H: {E>�co�4:mء�"�-�T&.:G ��F!�� 9�2� !U1 %�#X{U}&�E�A.!6� B &DofZ@Bw#vi�� �0`#l6@2.�Qe"�Dfig�$ ut wV%�� �A�� �6�a &Z/$ hom� 9�:HU��v.cV \r!?Mxe BQ&�_�7 unc- .K G"� 1�> e6�y;IB L ��eH A�K'& "�4 * 4� U(\xi,e,�h"*1 ���_� �'Ao��U. eu "a� #�3wo� %&��0 g�[ ��\ �� a�$uX@� U �tS$ cu_2�U  %�%� �8 l��R�S��:�xi_Q-� �5t# -W@u$� ES$� $i=1$, 2*�)� *� �U_2)t� So b����!<|� I�Uwo Ts, unique, �_"� ��Bxio ��;&�;' 22r 3!Zxh��"�>�!h1 �>�fqZ�&&�2 &�!0 &}\qquad$ \text{and.>j���{ �>k&2.kj&6>e$>WjOS%%�� a~P_fq�)^5:"� �=�o\5ׁE���VI]e�{U_2}a�_2i�_2�13�4U_1 "1 "1 "�6��0�� �dy!�.�� �xi)e�D_./C_1)N���5��#K!�Af^*g%�*Af%�&��IH)SAH%�HE12{B\]e�6ar&Jthird %� $gBtU_36�1�!� xi_3��:=3A�)+�� j7I*rGer 32B&E�Y _3$;�V.�7&X!-� r {gf}� Z? f/F��N�q�%�[ Z2Y�e�)_3v]�!�U�>a�(gf)^*�3 ^* g� �M�3I�3M�3I��:"B"�Az choo�%a �vag�,���]�:i3&6 �I�under�Sa� �"H ���`7�l ] ^RCuU�)�W_b rsU(u!�� D Ms"S �9�; � ^�=^��/Z�� ` �]"�k!�:�2}�_2�_2�4:�u^*_1(1(q#ɥ*� ��effec�R�*�`"5A�/yNL��o� ZJa�ndepen���cho� U^,1�sen�O QzsAr�C6f �w.fw�c�[�O6=� %MV�a8 $\z�x �0�S���>\vee , K $�"�� "�.9 $Q�<u Q2|���E� J� *2a(v.�k�EFi�^-�!�8iTŎ"�&E�� i1�!�1�%�� �<�?"I 1[Ex�.� Z\��bede�*��12r.� � curs�6�aZ��qB��"~�a3%yAWM�U�|]Wn5poviof view5�c�)%$R�2 som-N�U" tripl.�'�s�X!�AS eta,P#5�w1� %6� ݤ s"� I��F �$uM����J7 �Eun� Z�r��} �ZU � N=5 5 _21�^�.��Y10B� .g;� _2�phi�N �o>u �8.�=-E�q[�)s�p^a�6-/_�E erefn�p+A"^ �:A� cour����*�.^�.�.�)preg.-�U i3l�a�i�qs����M�VVa�o5h���"���jIg�1i�tNlphi, B�): !^R�!�" "[!R*� �9��� �3VMlso�I&��Ah Le u^*P ua fbY)Ui�&W` mry��&�G!�E& �l2WN��o" ��s<�VbRR. But; �%�V-!���6�Z��#��QzM� � yj.�"��Eriant �%FF6�ibered-�j�&hK!?�E Z�ff�modul�D�schemg! ve*�j� ",a�� ,ite[Chapter~� S~3]{git}�Cyx ite{`\ason87})�somew. invol�Ra/couy intu�Ie�!�v3E0:!N|!s)�6�B].��JR&o0a-)d �^>�Rm$-��1�N}�I\cFA��!�m mpat�LwFk JqH �N�ONA�2�$MQj�1!�W<of1�% e languag�;:8A�is�)y�/ suit�<�:xc\) concepA� G"-:g$ grp$� C or "�:QF�,!6���)5�,h�!4(�?8�v: !s})&E��;defe-��3�3$G$�; m��3}T! :���!����  �/2�qn2SM A�!�&!�S , �)$b B "�.UAt&DD"� ��"�$rbsatisP&.�<�)p��������|�Upp���L :*u ��V!ha��K.�>c.+�(g- D�  rh!$Z'�way0yO� grou>�*�G(V c%�ATVE�<�o. ��$V� ��{ E' �p �e�$k.�w>�<A5Q"�� o\sigm* pI:�}�itxN!�#&Cn��Rp {� .��J%F�I��bU? *)'\ �-}�{J�PU�`���.�%� data��>O MW ���F���׭�i�:�**nHdifgY�d�x�� e�t tic�#&(>�)�)�N�A�4.�_>]&u�;a68&g�b>*�-��6+ set$n�MS�," "�ak�RB�t2 >� �? 鰭���Ip:9-�F`S!�I> .�!\cF^Ga�;/�S��.� ��5�h_$har%�I7?:�b�T "}� �69!8�"�dB=z Now*4&�F�j�q)" �C$%�ngaW�;X�Kk6I tom)1q�Gq�<�.YV�H }. T:0BI!���cC590 ^{G}!�Am.� �])�S�mery�+p�H. C����%`��t a�\ "i-��. Cs-I{��r_2^*B"792)&S��,�67.1�:U.���1�&( NŲ�� fM�w��>� r0(2�>j) Aʁ��r.�q&%{LJ�"N�d�y�^(ng". �<�9[�prfW�[SX ��[�?i��nR�$�$_{-J!s#!� �.(AF�Of"�p!/&�)�$p5�V2�A5^.� �� �i���y�1 �5� & �.�E��3�$�B"*^$pr_{2}^{*}iU6x2�Z`V/�aEa�*�#F�6��! N �ba�2b�7p3,A� =��s~&�%�lIV\h)��G'9��k )�!3 ?ao�S�Q+p�FZK ZF of DΆz 2^.A}*&� as2�y��a� M��R""�atmE!��YՁE��Z)�rh�YW $8%senD��=in (� �$A�e*$(1, u'G(]�.� f >%�>�epsilon 5u�r"/:Ykw"91 � :2]a'��*&L`!>�\�w�0u�T�s�X}M�X!�pt:�.V� H �_{G�;R �WZ$�*.u��woAI�s H(���6M$�$lu-�LQV ?I��2�F�������))=a�9�ʷ-�Q�Z.�;���"Sʁ>o .�e�͍6AJ��c_.y 9I�m�b �=simil�8��"�] NF�Q_f5�cFG1�� }} &� s&� A ["i'g'V&���}KrhoU�mq��m!Ms�L,]�)�&`P (we�A!o%�detaiA*jd�r*�q"fPz� ^. T�5j�.�._Z�A.�,-s"��6 Q�i6cr� O^� ,\9��: 6ijz�fZB=I@!�}���M� (�XU�)M�\j)�*�\6Y�ia�����@oreZY&B=.�.Aa1JeVI��g&�o�8.'orh�!�&� !S@ �n R :��:�:�;\-@a�1u�+~Ry��uih�a�q�u} ^EB_�[u�'K'�i�])+�#%�2W�Nm �<֔fuL���F{ look` e likRc�fO�f� �.B%( �"�Z� �v��va���!�� ���AzmI� 6�Ei.e Jz?U����Rt� ��:YiE�\��[�2&.�,̑rt4�]} ^��Q=X��}�rσ&�ԭW~B�!)o"�S. I�ri���.M"O60$�/�� :` 6RA��C heck�^sayal f<: q�on&{�)p iF<b9r��-H"s��*1F� F8� !�e  $(g_{1}gA�)x = 2}�rr��_4 $6,=2̓:� *����). �.=�v>� ��-��>�A=���$� by m`�p"�a�t* tity�Wd,"�G "�''�P(a�dempo8� end�$��=�H�,M? Re�6R)7"*Krho�� Oaedha�>4n�42�*vf �>uXHi n�a��Rz&v5�o�0� X~����s��"�&sm%�E�4=�%7A81��K�*�n�FYG)*:a"�)y b�W�V�� � � 9\M'5]dF.�!�.Tr�.�B! ��rB F= mx+� & �~'H>p 0 �- �- T�0�- �- �- �- R- PEnal) ��is&�,vqG��A6.`'pseudo�Xs. Re�aɡ� �N� .�m&=%BU(CB"Q��W2�2  iP}Ń`�y� &Z[ >A��k2/.�l�!�!1U i��*� ^{� 3} = ��(N"' ,�P 8+ 3*�+"�  ��Y +�;> 2�{���%E�b�*� 6-��)m +��ano<�B ��s �� ARq>� 9�3*  "%cN�T unwi�vhe var.�&R�.dB�6� ���'yF"�"��V�.or.c'�F� �?>Y!�znz.�e@Q)��aI)a� �3>�6���EE(U� @R+1b�0� ?-{b��phie;3d]� {2! && A2rho$WBar[ru]_{Q�6!'5k�W���l�&A>B�#of.<-some kA�(2 ��, \qc'), 'Z.y[ȑ]�[R/0 \cG/{Stack"{ ch:s  &,0 Desc3$&z :�F��GluaFcontinu��z {topolog� spac7�� 8"�chetypal1}�$ent. 9%�� {ConiHtoaM!.Y&>�(�  u.*�' 1WtopNE:�K +})F*�Lo�]aI����a{�)a ��6W � ��7A�!�"6����codomain�s.�:&��|U> �>zY o� ? !w% �2��s� ,XU �;Gwl2h>�(2!h�\ �a%D8o5�"~f �(U�!-4{Top}�J:p_�&�@ n op�%2!Z$\{U_i\}#vA�6�lhE)6f_ U�Do�8U_9p�o� �!A$���b-� j�!$f n(ncap U_j - x6� incid�2�:�6�)��F�X!.�tha�) � c vf�iLm&t�`&' yM2tbZ�Df-��\rA� :�, �xA�:yq� ZO��&`!�-($oo $/p�>��!�.YVB _U1`V��*0A�Y�e�V"h%�q�:�Jq)45��uMa u=��by .E��0!�-t t6��]c;�3 <�"dG ^i:=�2��Fl�3 d $Y")�Ť1=Sm~�S�&�h�zJ�!.�7X,�e-!�9WS��se�BY(A*�IB+�TS6 Sm�&>fKaSi|�%&=��NS�Y{4�V2���UǢ��_S X,W�f��n&�78$X&�y�:62�]"1Ay� g���nd ��?E]-�Zk�iEY5=� � Z� ]V/`=� 66��Y�(U2;�gS Y"� =!��� J�g&kp((Ned"n���t��glu� 6���qA>f%%o*�$���op)ta Y�=8f�}�&�M�07� . \;"V�C:����focR"}�:+KlsoI0�� , al�1%E�o�p�..�.� g -top}6�N2�a�i��aJC��V�;�e��Aa� indices $+Y$j��k$�B_%� ]` ts $U_{ij�H.R 8k>!�xk:u�  /^E2�m"�*NX3 4ɒE�J�*{{�E��b home&e� �m�u_j5 �}�6 �u_�� &� !��8"P"cocyclAt)E��� {i%( f6 !D �7u_k�k� �  �k"�4�.�X]�)ny���q��*��͕�u�!�16X_AZ&�=n= �=#J ��>�t c)��&u_i v:�7 jVxY&6]S2�2di.� $U'� �o�  :'&5 3�:N�ha�I6��:$$Xr)?h* U'$;!�&VW<tH� eq X� K��&�0a"RBx_i, x in!� � X_j.R�2K=�x_� !�{A� x_j$:&���6�_"†in�z&jf!B;U5i�[ tiA&U8{ii��lp ��n�5-[���ho��"�*_}��� �_Q�.�>�i�) rE7j67eG$,�wv� /q��ic�,f��@��s direct0�Q�ge�FZy^r�b&quoti�$X'/R�KIf# �H�A^5,�`5ir L/ $�_X; s� Vn��uc+�2G &���i/:K!�2�u�.D X'�=Xx�4>oE.����j�o��9�a+�� )6a 2X.;�.se>��Arirc ����W!omplet@e�o>e fa��an� :��( &:�2ae2"���"�}L $]  �t�@{�.� w �<���c: -WcC�ag�elh���^��F�A�C$.&�s� GED*� X#�Ah�O� �so�@_Bhe�D&|. A�ck4mor��5z7�F � ^&P�� !e�f�"�;2�:Ej�&fTz��e�("� w/��,Zresorq[5JLO*O�c��\!͏_.k��, �� &c�Ye � �y�~�� ve���)�"�7!D:��Px{M�E��C-}E\�Wi\y]XU�@\}�'cr �7 colli\A� tr xL�FF��� �T �2^�I��� 1 �o�v `.�jm&Ac�wAF��X i� �C��T�c�y� D ��(rm{pr}_{13}���EN62jb�t.E*��.� !3}k_kA&1 -q\]�N�$2Wabߟ5�Nٚ�� 6 a\thmb ���F�� ! a�pAv&�5J� !� K�ed��6�H" sAF^A��I�E�2��j�"� ,�.%L �Zi\� �f&� =#�VuJsuJ�4>E�aDa�9_�mS%�T&k U_e`e���&�+ny,v�n�C+"q}Z.}�gК�: �U �2I�j�2&.B�j(-2u2u�!T[j-�. �VE�iF]B�.2sIn Msta�!A" �<t may�uusI{��� emp&�lube�� �QXeq:��-) �2!&�i!(�>a�'�3pr�J.�u9]!12-eKjk8QderrA�&&��%f,G��A�]ar'[r]9 2U_k\͢!O �end9 "�\M�� ��b��5Tio�c+��c�6&(�0&� o>�wac� �Ym�����sI�b�E�0"�,o&Qu>(\c�F(h ݀U�+���qrk�u. � y&bU+X� A|&�:�"���%�k��,�9n�;& � �C Tӂ�y��c��f�1���) 9B� ��W� ����U �gB ށ��$~�&PQ X&�E :�(� _�Jx�!F�smsjK�jB_ =j�W�@:h [E�B^%qJA�  � 5��W�4 P n-�aՅ� 2m��߁z)�}��O3f�;�� LiE^j�PA�omm+ done�����) os&&t �Tg'5g!Tѳݱ� ��$ �Et��C �-��r�gm-�T,k\� �"}I;)Q�a:h5[!�/�F!hA�*Z\&� m �R gimport9 .�4�uL���HK\aB�i�A&f "?)&� s� "E}. le�^,�"ri�.1 ��to���A�_��\.\��re��!����%:&ka�� f<a\mutKA)("�c�6ً� ��� ��Q��e�"�Z9g"`��-1.�f2�_{9PI�?�� ��4N� ��#a*n ��:y B L \k, � : , jk I}x)k, k !:�Z��A�_itR:> � � }a�plu�Q<�( !!�a.g��" :f&�{i�c � �ag� & & %�!� B�� H�j % B6�� \k &1i&&��]&����A�ca"�5F&�wv?'�"�;$2AFa"ap� r���  ���(&`/*] )���C�wLI�a�t��a�\a(2� 2' �I� 2���Y�6�,2�� �0� d I�@ A� 4] �b�b(�%t� ɥi\�%�A)edi �0 9�E�vH�{b�t%�*�=pr�� k r_2 LU*2x���"� Alterne!l�I�erhaps� *�_v%��`% 5 �J$(!c�2�%^)m_{�=1�iv �;a��[B�3.p� �V �&��U)�ap%3 n $I$, $I� �9 r $I�  ��Ta4 � ,Xnz�WUFM-*>-�voIYM %\�A�����<t&VY�ɩ�#Ki�, � ��v-O��c.�"% &y�u�aW��IB�&��`2�M�m� e�" R97 1T�ZAim���mO  ja�e._ {"�utRM&� o xi_j�m�E�  a��)a\c)hF��lӄyA� ? 2Ba ~ N �R �H#X62y�2�ME�hQ>�f(�b��,� �a�N� *�wl@tn��� �e���omp>4 ��tI�Y�jruVdaY�.Dd!�B�U�:��x�u � *G G�L�D :aG  �J 8�j�dNT 6:�6<U��^*l AY�(6!�y �S�� �%e)�c6� nLM![VY }���ON�@��24JB���[{ 6�7 �z)$exb�[if�:�g�\���m���&�VY[_�%P-6��9|^�r&��� 6�k��$�H8!���*bI&V;2��s)�^�1c�a"�A;����a��%F$5��c�!R �'���q>� �fo��$�U+ ��� _"@�!jplL ��5IA�?:��d u�`!��BOf� rs�fUreally81�EIAon� ent��Db�\[0�����C��c"7L�=>8)�S2;2TJ� kA�r&&rpriori,��=,m!#!�rbitra�Nd� duS��1!5� eleg��"e I�� � �"&9;nd#u�sieves�q"�q\! �any�g�cX*! fG)!e=�@c�z� >�blU�U�9E*E5�1$QhA�lF�� h����1!!���T���0a�z�:�s�6'&.6){our!�ncipl-`m�" ��>�M����oS�� d*�|-:a�axdv�sc4pr �>�:C�~/@��cC!V\`!� bigla}!�c}r&m�T�*~/a5,�@ri4�P�F�k �)p�#AyD鵁z��F�+ 1�.�,"8 !�)i��aO� ���v ��2�fZ��0lX UI��acjX� � ���ra��� "� R0y @C-2ך&t��2�C.� -jk ,>ij � E&&j)� Hik�Z _rr ,Ik + i)6giv��B� Ebcp�bEGext�1�dqp�-��1[E�N�0� a:way����[�Xm� 7& 2{���,nh%�2e>!] A�( F&bkU*�' a�^fv"Gn��to &f_B�Vof�*%2�UB� 9W�2�� �  ; �]�0"A�k!n �D.� ^_VMZ W)s>km`fX1��3*[ !(22��*gc*,�>�F�0:funnycq��0$����w�.13��2(g%���2�!C�b�lv�%2,�1 ��9�!AN,��=2�.�.‰r.GSu {2u�� i�E��F��:e:"z{ikB]� ,� ����.]T���a��8�2 Xw�oA*5Lee�"�$� B� ��x�AV �� *�2�U A���a��8���{T�1f $T$�G��@(� !.&�Xr����� N 8,E ;%� �2I�� ��/�d��G1.i'%Xp�;���3aB�rRr U_{�)�!Q��/ $( �HR�5"�J/���� �I� js1i�� i7{n�{ �[rhd] #�DU[� ��ET��<  <�S�y] \hsmash{.�\] P!%M�)�E1�-%J�T "o6& .:T��!�:�O*�;E>� &�L xT'k-A�E�A�L��i�"�]E #6}B���a �#� Z:�?;Y9%�$�1w)"�PZE=Dab.�aq6�T>40Bh[�>8�E[!�2�Iir TmVc�2ɇ>�j�M!�zR��o.0a����2s��'� omVs�$�T .� ��-Uc�k*�che.�5�.��K`��*�2�GJ�J: F��] `F�� �"� 9,0traightforwar��NQ� ߌ"��#��E)�5%af%�o�� �� �� �� �� % %.�1v#��5�"����E%*�WZin&Ɗ �b�)!��Mũ� �� !l�}&"�=!�a llAT*J*u�%V�L�o�=*� �".cal{C���Um�#}��%�cEQe�X}�Kto� Y}��!#A�n�lN��(��?. tY�)2�o�s ��B�,�Q�sub�ooY��/"'H�B>��F��BP@!^en.n�Gl��) Km44%u��l.E�ctu�i5(�E��.I%�6�7.�X�!� a�6)�5�)M�S�mnic&l� px�=.�b�hu�)?�n!C^I�, �,!fa�4��%�. %A"!Zs $f, g�6Y��6a"C~ 2�/TM�Eb�� ]�S�n��h_{Y}T qc_H s $h �T��X�t��!$(fh, gh.. �J3�I�i ��cx�"Eo GY]6���&�\� %DN�Y�!Am3. % %~&� }de�w��} %"�3*� ���52K} ��aE*ʍ4pa$R!E2� Q�%4'� 4 0sou_R, \tar_R-lR -��-0."T^�.�!6Y�u� $R(T�[o X _(T���#"-�:�10 �]4. %�=b %&h�i�� ofQB!�5:$neVA&>.�e:�>AM�QP #� �:A�����!!g-�5(i���B:�&ona.�bH)�B�epL60%�"*��is happe�li~�n�9ar� �%��nV�o*8evto A�XV!n� VXenM�A�:BO� %T&~3�L�p";,!82 v8� H.R2{2A� (> %Si�i!!e �=�*25�U�/�r(Ec~u2�ur �Eh2t� switch<�d%sV \inv_{T}:E EBEM�U�i��B%JRV��R� �"��I�=�nv-�R�5A0�F *?� 2!`6�-��T�MB�!o$ :!�J%�T.8?W6bj��;s^�� styl�uv0��! litt�rickier{p&�A�5E�A%�_X�B}ac� ��d7�0&�o�NX&P�� )��%7�i a9;23AAaAM1�hs6'1� �{X}-�X2xn(Qevn2� !��&Ks!�5�kF�R�F ��I^!W- 2s�1{2�^Ed>^� \ Nl �f�:�(!�a�A)�_- ofKZ�6% u, v#(e��e7�U�� u"�lsy�v�t� -,'� $(u,ai� 9�mU'��� tvIDf ��qlR�� F$|(1� X R)(\tau��r�.�vYT1�Bi.�If���%� n ag5�!4�M�:� ��mulQB�צ��<ul�΅��i|NQx*B !E�'E} %S&���&�2a�,e ��A�r� 5�� �� �� y :&� eAkax �k&�+9���_{RQ5r !�� �.A"m:V� �5�U\item�F there is an arrow $\inv_{R}\colon R \arr R$ such that $\sou_R \circ \i 1< = \tar_R$ and $ F%=$,& %\itemR�mul.�$\times_{X}�, B� omul�sou�pr_{1}2� ,F%.�@end{enumeratea} %�definition} % %\begin{example} %Any )Kin $\cC2�Xthe fibered product $X �,Y}X$ exists je%�reQ���(widetilde{f1�q�X'$ (necessarily unique)B {R'}�.O = ۅ���{R2�7��71�.D!�$Now, if $F-C \cC e0\cDe'a funA�e�a�R) nR�!�!*I-inducedR*( $(FX,FR)$,!�whi��ev$F1 , F� �F-z$FX$. If $f (X,AarrEE �)�ineQuj4�-then $Fb�'1 Y�)T(FX',F ~roA�~sD��$Now suppos�a��cFris���ver�ܡalet5�b�tV��4. We denote byIF%H$� subif.R [4F$, consisting�ob��,s $(\xi,\rhof at map to���JFI:},�� M)� \xi$�]Hboth cartesian. The)��|%���-�v��pحf��tity oA�Xa?��proposi�K } %L!�V �U$-����Y=E<$\cF(7)$ ov5R@with descent data�,E;�t�� Y, V�y U}V)�M2�"dproof�0(\zeta, \eta)� �!�$(�:^)$. SiC!t�=%s � )ֆ���]?X .  2Q.�)vV$ respavely,E+U&Vey�� iso�� s $s2k�Dn1}^{*}!! d $t^*2*I�F(.�%et��Bphi = s% t^{-1�L ~T���. O ] %I clai� �Z,phi$ satisfi�cocyclea�dE�. !�� -� \subs!Don{FiH MUK.�0} \label{sec:t -M�} F� e%\cF)�� e)Jn a siteA�Cav N"0 ib� QeXa \emph{prestack}\index �W�:$for each ca�$\{U_i �U\}�^a A��Nq(U�a 26)�@fully faithful. Z�2� ����: of=��A.r2�Concretep!P!$���� 1� mean� $following.I�,�I�� $��awi� "s #!�$� 6�a5�xi_�4D pullback H�T � $U_iYxi_{ij"� eta �C:. S.� arծ$\alphaAsm��mpiQ�F(U_i�.�pr_1^* E=�!2j_ X� \$%�all $1(jݨ�� ���[U��wh�1/A!��� ��"- 2�. This�� canAZe�ted usa�.�of �%�S��~\ref�� unc-ɖ}�<0comma topolog��� ��C/S)$(D"� S def:=-= }). ��2f:�,!characterizo�{�!$�N 2����utif A� only a�anymF $S` el(�qf!� m��S!�!!!Mto� $underhom_S %�)Q!(\%>\opM(catset�'a sheaf\R%L5�.�p2F.\11us$vX �u(part. Assumat ��r. Tak� )~ �of)�,��͢e?��M�wo 9aJ:� G�.Z w2 (\{�i\}, (m��)� dA�{i� "b��!!���� associe�)BDr2� $we see easd�Si�A�NB^�@' colli�e� 6$\{��dZS�ٹFJ�Ori�)0ph�9 j�-�� *:n� U%!$$ coincidee�� �$\u0Uy0 9qensur� a7� mes from B�x^� ; bu @� precisely ��y�E'q�Fz�>�| A !9No�� implic��$is similarI�lef"� readery�a�� .lA"� E\2y2�MA�\� � BIis1 effAIve2 m�Bh!*�SitDiL c!�!image!a�.���.�  �o% waWsay��is:MwB�e��z.(-i��, toge. �c�y�*�a!ŷ$\sigm*�k  U>�� ram p@xymatrix@C-10pt@R{{} �xi�ar[rr]^� A}A�[d] &&1; �\\j0r1eb [ld] ' &\xi/}\] ��uta�orFQ In fact,!d�0cor�*4toYas� ��-S� !iQ�- ;��A� � ativ��Bram ab�Z 2�v�NR}!,ioat sends�-$� \in %o�6&� !�2� �\mid_!�}� +to�O�m3iooua�9a'�or betw� dis�*,�-6 6-s�atmin+ ive;Q6�m;6��   biEon. F t �\s�qimu,remark}� termin��, due!+Gr�ndieck�Ta little unfortunate. J"� aJb-X s: howeve aXe�!?s1 y1�o nd thus,�ana� ��tbe=a�ed1� y. W!�w!�ll�|=called{ ��c. I hav5 � d!stickɫ.('s.P4, mostly becau�"P&�``t�''��A�theor algebraic #ͦ&�more rj al�2X� '' wŤ�2"zpleona�M"]�-p!�E!o.MaQ]}0(9^0J ��n 2�!* K5��atsh{\cC� r��,� ��EP!�ex"�A�ve� �.*�  sketch�/eY��nd $G�� I �" $X&v:EKhowi�$ �D 1�A�wa�.1"GV F,G)�rXrr . F�: $U��X$, letV*B F_{U G !z2{# = $- �{i-��a����g{i�q 3t$ aA�"� =g�C/'����{iQ!� j}�dJj�&�D*T �j:�j:�j}S��=,�$Ti)�= ,$$T� = ���{U} T��� !�.� 9�$T\}$. EachO� U$ f�" thr����!, so -!�$���MiF p6 G ��� ousla�1+$U�ion�2Uj1�cj�"�"&� "*A}� row�a�$e�� ers� [PBF T![r] @{-->}[d])&_od!$),\ar@<3pt>[r] - [d| 4 �}).NjO �26j7j 8tG�F�))%6V�>3j} 4(j}\hsmash{.�\]!:1�Q T=��rRe at on�sn insert��uwh7 keepit.���i�s|(ness. Also,.i& sy�dcheck�Ci AM�T]~a natur�-ransform�>,U�evI� � �}� �A%}r.��I�}\ "�]�� "�E�2�F_�B�s* G�a���_� �����a]-n.j!>=ve��: !`= � F_{j})~ Z}�i!Ղ���JU�% ��8 j�beforeQ��� A����� U i�%Y�c�V�"s!~.� �ʍ�A�a�erte Mx%_car?&=0 $\%/�X�,3# r_.B� r wordsT%�Seq��!�}q��_F�I�\ j=j�� Y3� �R av&�  �wbigl(>�r!�A�D� bi$%l(m7j}D.#r� A@��T' �!![E�m< e�1sS �!#+ĶD1C'A$5�$F�!�F T'$;� `w�*$e structur2 wV �B�.�%le� )1�Ej�� �. L � }"} C"�7�).� �A�\UX�)H#�n�.q �! $k$� �%�iT�*�.��� U_{kX ezk� sR�kl q =� "� of�> 1 , $s�"�!F9 T6V 5&�!�_kaBso!hI]�el�:�kE�a�}})I�&  i}E9�#:�#J&!�:��I�� nZ 䥆���I�e��dir0>�ͶXaυFF� }$teq��qXA{ $. F� �#��!yh � A4*7-!�k ��d8�ki%��JA_k�"�_^B �"%�[]�� �.l���`)��� &� H�/|e&Q].� ��sa�j� Y!� �%)]i%#wni� YA�b��)� J.F� ,�a�_�j� U]�FWe��theuwoZ� inve�to ��d t/( �A�:� .��%"|&�.� M�" stit=:� ��S��$ ��.� E B��A�!s��n��ch!�El\  e-"  26(E0orial behavio�.� }=(p(:2=(-�*"2 Lity/2FX.!23Y# D.J+�hree kitof.�� ies:!p3e. �&@*<6viJ�� !)��un�r]$�&. �F&�"3)a6T�~�o�� ' cP $\cU-&�H����3�E�\cU&�* c� \cG(�d E�a�vel! ��)�2 rule��F_d�"%,&�$\}) = (\{F� F���})N] �P>� �* ln j�\{" #}\�|�&. oFura�1�.x"-�G� 4a base-preserv!�Z�*�3|3�H�1f9MR} rho)VQB-e�LG *by�(>)_{n�) /.)}}\5��9)���*l6Z;�VAx)<�68. �"u�6�{}A�I�� �M�S d]�/G/�5 /iiF��92sen���e ��comK0 s �� P�i c. &�we obta ]&kuseful�LFm����:%�to�->}\hfil"6"a"y-�3���>c$c�0t 6��7!�5w.=F#A[B!�If%q�'"�2[)��t� �&ms, �!"��E%�R*�e::!�"W2 All4�b�9�d�e� gane sieves� !%^G�5 �9ew*�3\hom(\h�,,�.)�?BG)$A��8U�� $B���caey�bec�&aL��B��U�:�#�N �>�" EG�  �#EG2�� sB(ly�mul#eA�I�Ey5 ŏ,�.�"� �=�detail� ��A�not go�_to ne�+�iaA A�., �&-�� w!�l�ly�$idea:�!&�<a�&b��4��"�tx �7�3&��& �c8��� �5\{V�  � �V Qn�� �!�j q$^s ~ �n{���ed��!!�d0�� �P�v� along(.�Nq� I�VO8a��y��� ��2V� _{i I�5��cV* V_{i�:)� 0'1&� -Y�w L�i'$ cho>aŗo"�.$_xr%a)@{ff}}!�\mu(i')���vcer��$ �-i*�>���)� I'I]I!NJ\cF+ %{ V`!�2N  F� E%s�7&(\ �]68 � : �E( j'%)$�%�8� *�Ya�ň�7.. Am�.$ 2 -7nc%(��R:=. �\psaj� 6\] �*WAME � &� ` %9i})� Y*2a)aρ� �Ba�a�a6o`=u j!pAu p!.��.�<>�h���,!�verif-&P $2#>�}$ yieldT �%@� .@.�, 2Z[!PN6�eta�>H!� �M�,E� E�P���3ͤA�esa*ia� �; penda;} *b��sif��chang�'d:we��k or; ��.�S.�5$\nFI�a�-l< -� �f�~*sV�g��n6�� 8 qI��a$ :a 1$( %, ,"U_1� hI�)�y 5(sm k��.]� ] �$����V?e&� (EEE�"� @C+40p�- �n�'\a��Z�} &S ^� p>3i�E . 9�.. ]^-{V?h��} &�l)D �5�\g<g-I] u]_{ �v�J�FH2�:=�a]."Y������IZ�0%$ ��S $ (w]��0R ). I�10 toB^�e��u g f- W�Wa�6   ŸB -{�F"' After a�#mFd� �{�'-e�ͰI�nd�vI�Rt , $5.� g) 4E�.� yV8h.8rho(i29��%o�N� � @"W1 >/W% .'?AC��t/��\�.�third��YX� we may2l:�R;v,:*,��we�jus(-e�,� oe�G.}.� clas�-N-7�'%*W$; h\ �a*<9EWam"�Jn �@Bh��$ �M��� 9�$�%���hUN"AMiq I$. Given��� �c�-&b �m#��I/o4i>� \A:�~*A$ w��ͣ� \�����֡�i''��8�.j/#�a��� ')\, ja3\!.\] -��le��Y� .. .P. W��-���f_�i�R�j0�! ���}canonica�/m�:5�hz�2�'�b�$�KA�.p� �BI e})dW��2 AJ desi�.:Im��OWEagainrI5languai8�J&th�His much�ier�cV%�R�: e�VA � sub ��$ U<���embeddt V}�to -� ucv�!�m68>�-bm2V� cFQ�w}%n��oic^ qu!K�D.([ is9/�Y��� �f��B�W6��1m$B4�.�2S$nnos)2�7ndM3} Uy! rip�!�"8Q�%t,� �+P&IU/��ny�@6��f�� g&� very���>%ANs��ch&i2,=eV2h4 snI$ Corollary �cor� .}�6c/}4:1e8} A"q55a�M�7iR/�!�>�A2�Ŵ&��6��C�! o>L\cCeJU},u(ar &al �"] �!�B���#h��N2�4.�93�C,an sharpened�in�4F�AU-�.�!_s" F :vi�.��)�i!�)�{%⥛oCn%�be��0 \c$#!qm�:�1�n�S��2�SR�6�A� '"�>�� M<is>7�gFU)$S$M*!�1�"n[3�6J T i�<-(e6{�;" E%��[:Au� R�I<e�Go��;con5$(a��@�Ior�"�*�;F�4Sv(MF��V�. C:2"� >�!�#U.@:�:��""!&1Y�{:y��RAI 2�i�Ts a.�.FM�:`I�:�u���  A `����6�9ߡ�2� wF 6�7W� $ !\��%Wxn.sur :v sE0.�E�. S�*2�,�kle�Hsufficef ���_ lem:�"a->�L}I��6�Koz$A��M,a�� $S'e�s6�Et"�I{C$j$S'**S� eX dN�JHRsS'2>s ㍠) ��!�&s42 of L!I�Q!/"�9->i�;*O�� V��K�E�Z�,e�6"&� m�W s $SmK�S *-��$.��$�<Y���.ameZ�$�s&�*�g!��.m6l Y8�64fD9 �X*"#N�8$S>�a.�9�-�$��F( �mG�aC2�'�9"�-�??i8\Ui " 0�J"�Y s $p�J>ES!%1�65Ή�NE���ŵE7� �(n]���c�E� )L��F(�)�)6�p1) !o U� andytG:O)WjO !.Or@6"�U2��%�JX�8: s"�Tc&[Ft�oAm�HM�� ~�Y^J|:oV"M�S -NN*2�R!Q�".��"F�E=�"T9E�Rb�=SG-�)!,N*�8 � 9MZ�&&-�N@ j6QA}� �AX�G.�o UR&-N6Mz�G=Pinterp�RdYs*�Aa� ��F� a�I��.{�'P�!q�m�_�� �J�8�<�7,M� e��a�A�mp&r0��_{��::�a3&+6� 2Ved��Ŋ��end���~�4�&�KXwo�ia`�5hQ�,�Ce%#&4�- ,,a�f#)EFTJ�V�!�.P�. .Q 0�&L�!e �!ha)*0u 0'�iesV2 $&�#�cT�cT'� �-@5*.iF;R:�Tx'a subordi�CE�sO%->yx#%,)b ���n� A�t"]�n;'VIn�Q icul:N�6M�-�aN�b�La#� if6��B4�s8later`+E�e]e�U��6equ� F� q�*M &kn M�L pass-to-&^} y+F�aNx Ei�a��5�pVg6�dv.!>�*�,F(\cV� 6 =�:/�+E-2I ��)�D}�Q {Sub%��� � �Z"� :HK6zZ�+. AP`a�P!�=m .H_y A�I= �.��"63y�A �KR�%�G�B2y1 E �[0Pe*� )��[*� "�-&K[[f"( ɞB a�W�e�$ � %�A�n- ��Ib U�$�Q� 3�(�NY� �(U)���O$>�2�}�Y�� (.��{�Yt�9$�2�-!T +�)�Mt-�5�)�7 re m�< eg� situ*ajO:� %�Uh��(T�GemN$thm:main})KQz.`atqc{S�I~ o�:6ch&� pq�;�yJ$�RulNY^��&�alo4Iy fB5�'@f �h�HnkM���!6�,m!A�e{.a�q*2�p :cri6Yon-A�z}25�BEbZO>B . Re[i�A�\Ve��a&�V5uD4in groupoids (NZ��#}��F|�Z1}�0��-�� IB� artE�a`42>4�_���Qm�lsoN e.�.�� u*��% �aA���cf ,��))nB�O!^%��<1}ANZ(2U 3�1!B6S �G!�e�8i/2��,� WI�enough��pr �/�1�5�5v.��7�� �eta/a; �!somC.c�.�d�=�W=P:� � �<�V =�.%e�*�.C��2�*i�� r\~� �2)�T6���^� g�.7H��q0�i �z�^���t1"�_.�<i�;>&^A 7e�c&�B�YA�� �%�A���%�inI/ _iA�r�2wm\Ahs)k6'?A�%�+6�d!�1�A�3ZZ\5�eta-�xE>���6 -kE) �-%Nk&�� �Ab�g�F �smy m&%be:3)@�e�/!�� 3e �"Q�~A�@le�!:  � %.� Cq���� % �� ��M nher�$&"_)����7�h��&� fac)often� f�d�m2�%S6�,� it_ .n ; )� $\cGM�H"y�%P�A�.COCknC��/)<"�f%F�%\tba? \�fDe>iKQ quasi-co�-nt�%�.�:3modul� V �9KYe M=�g�>�6- �[u_velop� affine EM!� 9 o�3or \qc�. �*���5�V5 bSNo���( goodaAH postp�8rea�#$it until a�*�nex|(� n�>� �A�����)26w_6*`P \catmod{A�C�MW==�$A$�#"a%� hom"�% $|o�(A �B M �nF-)��.�iota_M�� M \o�A B&BM�!usu6p&�$Af�4^!$ d(nH b�>bn�D.]>E@j�m��2�X)�{A}�2�� E(m|1|m�;"�5,$r \ge 0$ se*]B^{- r\abrace{�A B� )_A \dots  0}^{\text{$r$ %h}}� A $B1@ $N Ʉ�@A��2 n1 differa�way�� s $N|{$��$.�N$;�ZNW�:�e multip.�`=Ga�ula $(b_9Hb_2)(xx_2!jb_1.b_2x_2$�5�Vo2Q,z�� 3h>��,:�2F.=N$ (mZVgen.]�]��r)�!�6��b^:�:��) �u+ &�ey a6�6�m�*6ps"z 2�� =N6 U �a&� 2A:x3}xE�b�]align*vpsi_1 &�2|� �C.". N,�2R2R:F.��%.F. 6R3�R��ti�J1bsoR� a-� q/�T"xj d/���g&�o. MA�explicitA�Q"�1#id_�%1a%93E )* ,")-6L2>�1� x_3a�\sum_iy' Ox_%z}  psi:KZ?zKin6��lternu� �2E6�ŽN)E (z �){B�z (5� 9BVOm��������mJ�~b �?�,taKpai�1(Ajps�lZP�F ��!���z���NzN��i&�->�2y�&Xah|,a�!H 1h0 3 �,:�)� �~d��� N �5)Q (N','EJ}�q:KN CN�xmakqofH7�:��6�;h1�� U�A8BG7ue_AJa 06��}��N'H1?[�es]>&!m2T'�I]IEe�@�"R.2�BM )"] B�!rR!%2 " �"eE� $(.�M)�_ME��\�8AK"7 67)>�B�:0W=i�7 �>6:I t(&8 mi b'��b'mQ�In�DST P�#6��VM IB�Mi>� B%��/ @(2k 9j�*i?g!��ae�F�z � m��  M�JT&� ,�EseeBmed�l*k�~.W? d2& p2 |��M�U��5L| 25 $.oMbi�em/--`"- '!� !� � �c=x{R� B%�'�l�% $A� �E�e F15�^�4] �d "!�6 !�͇i�(c �B�>� � $GB�1{ �=�#�Ms�ɑ$A;sub)M $GNbs"/Nn.PX�Q s $n 3!&�^$&9 na�3n �l 1�"�6a�%$�[�(�f �(2K�>o�D� Wn�b%�z !uU�i�r$ t�GN% $GN"�V>M�9xA�We� �3e|A�6rZ  s $G�(F�.��/A �NK5w\2�� g?�:�)exactq-6  �� �G. �Aa�c ee_1, e ��� &=M�by $e_1(:1� e_2 Y b!O��/ �2�e ���.�.�� � ��0IC���et DMi�l�O.� M=.<(e_1-e� ��SM}.92}  ?���Y �` e�&+ple varicq7 !Fn!Q19Gec(0*�N� u8bi�ZR�r).u�&{�q9�m -"m�& 9a�_V�1)^A�end���o$mM?b�e'20&<%��l(r�xM �x1�>�xS]�x��.)M$�^ /G6�6�a� kernFR$V��,.� $MI�y 7M blisۅa n�X.: KUa/� G6�!GF(� := �ą�8� F� �_�7�RJPX� �� ��^� G��+2St"y ��ٓm*h | �-�929�2` th*� 5O_A��N�/!�� ��92# = bm$. �us< -@ hh�p^�%rs? yf� @C++r� .�. ��a�� -{��! �  N }&A�5  Vd]^a:i�.%�`� 2=D zuly i2� 7��! Pcal7'�m"�J:4.�at*}3vjx%�.�.J ) &=9�<�� b'm) �&�|si�f.") (�&]5:+`2/\z&=>)2%#\qquad h(�k$m��M$b,J2A b)ͯ%!.r59JA;)y=`\ � F. ;m�-��!� S "%�$�n��B�did�^FG� D6� :���sm�s�  1.>� ,A\ta���N��� (n�"9�n��q E&21Mby �� ,���R�> � - ��;Z  a�=�!+ � b!r.(,_1 3 .6vbB02�(� B!N)Թ b>{B%���L%u$���s7$��-�iNd�( -� P�*�*I��*{ A+"� R� &� Eh-�!b�!*%!}o!�m[resul1��oNa!Itj"�#at.X ]-CO+r�A��2Z+II�^ they+k)BEeiW to&�+W  quM;�s able"J2�/s�B�ZariskiT6CFcoarse<8�1 iori)t�exS�B(to happen. � sche�(S$�&L+in \Sy�&"�6�#}�� b,hpg+�Hp&�,of.��XV3��A�9!�Q qcoh�76O�"$U*gkiirb�Fh$JpZ*���-f"��be.H�=��-|�t�T��x�&iI{�rmk:re�S- �-a�t�o5wild 1Q�\1!#�AisMy failAB!�``$''6I!�Re�x*/�>�: J�m[ %!&8/E�ML.�+���"�0$\{V_džU�0* Z�1�� f $\oplus5 cO_p1Ai su�2I�lq��z�]e closϗ oint�T6�A�:ga�|Y $V_p��Fe��A.g~8&�+Y \��j�"�B� �cq�� zero� $ $p \neq q�$or 2p$� "f &==��i%Kolon [!�_ `!a;|�QQ1��o�AZ r2� pi_qDQi\U V_q ^(f_{p,q}^* (-l{yt" U&QE-�L� r�pA�Ok�dm�?. B�!�� no2r A�O_U T>��&at%�s"A+$�p.�,p']y-: �co.��a� X]z5 z�mt)�6\i(�o�P���PX!e^� Yt�����70-+ ���_m(�{��"I2T|F.E9FQ6N:fTb�,���!K:�E'Rb& E�J)�/{+�<�*}8'!$6B�1:*:(�!%4"I6pd�� | F�2A��,q�R�>��2�2 Whe�D�PU��a�*EqF!��@-�s, �u�*� H1mE���6 �v�� 2�.�-v�%\2�5 OlPD>�0 M�Wl�MJeQH�(�s�b clar@s'dividR�s)Bal step�^cc <g�=B� &�<-split}tVl=,:Nf��,6XTMR�H,oybbea�d�!)� 3 � � [:.gV3] G%T$SQ �parrK���?�T��� ՘FKun�T&׋�%ͮaebT}\opE��� et.]&��"9} !�}��6�� H � *��.�m]�f�!71 1X1�:��_AFch"�Alwk�H�� APs e�51�[: re�u%/�#�+�ngl&�f]jstart�|yz���0�Eu' empty_  $A�ty���bf!m�M1.0F(-)4E�als,�0-x c/�Atm��� h Ei�(�Z:A D�2�?>!2�4.&� �"j eJ� �@)��*� cqL%$ B�` is I(0lly��� Dset�.!no�shal�Bnd� !��eis5*�&�Pu�*q!.��I!m)8)�2z$9C��Ase%�p !��>i I1�3!b>��tself"�L��6-��/E- O.�*��� " �"�E��?�)e5�t! ͈M/��I�n disj� -I�@�C k'A�o� open�;=<%>\Yf��f�IL��.�t&�f�ZB8(D}�!�, ���7� U|.V _b7!%2�@Ay-�i"�$)5"-1� �6e�@�b&_:E�j�.}2J�9their.��8�9ac��6Ղ*Y�V��F��:2`gTio +1ho}V�8}2�+)�i�N{�_i +_iag ta_i.d &؈I�� ��.|��q-�!��>2i�*�]�;�(s&Sd&1 ,F�%���a�6a�*8XxG�=�|*n��j�9*!�$= j�L�H� e�� iR �Z�Hp\;*���b"ڐ$�H�]5%2z���F�)aY&e72^�q\%%A_�".�o- E�s�G���<�:�z���"�hiT}>�B.��we"A"5F�!C_@� %��t8�!����A�NRQ6)PS]�V{:`"� arbitrary.v�� \"� $�kcoE�iEU ~�M"7&7 ��!Ap p.JP�% �B�K_F��kK)%::o��j2<2�B�o���7� Y#y.��-c:�6 ����>&@.] &u)!6 o�:LN�"� Z[��8Enb-N>`IMb� :is��&�!.p�V�$a"U� =&�wMU �1MF{i,j}AJ&�U_j�`!5o>>)�����As�=�� �6%W �L�VPeq: 4->!�1.M�a�PendN"�Pbf�BgT.! sbv%! y2$-�6�*��!�8]�Ni>a00?�&h.!3 '��F�?nd��h"/����e}?-�=AHB���Q)%�"6HB�~.�D��!no B� � B A�"X�f�b�a>ɓ�2"�џh�5#�� �z�%].Z��ll�<$&~�� E"���!2+(i� JN v1�way+"j8� 5� \e��EY� E,�d%�Ni3�.�d>�u:-a&#[.��O�4hi�4Z=� 5 �0N e�$&�.eY�U��!�A��E��6'E�'oG�EJ��]�';$] t�I� �J�1AM*�oof.Y) #yx%s�J�dckI����9c{ >F� P1qS,��_�1q�Con�-8�a�A�؀��ͅs�{efVm)� (�eqN()A�� Y�!* e���1� �#�"� :E��k��'"�w &��� �HK e�6�&2 M�$!e�a�!\f ���POinǵ&�!�EN�[��@s%5a�-comp� "\3�rM] !�w%l Ю&4�! i�VV$6�i%$�Xi�?|���4�I��V�o� R�� , $V�R�y5&vy3� �0.# V'��B��hypo!si�xby>�JIQJg2flK2b�v��-!i��C)li�Uō�N� XTg.�. %oQ�2�9�a Ue2.��of��k�!k � "AA�IzN6a��1�a&� ,6�.k^& �`�edexO;M,2=-�%8%,iDMW6�havA�N�{"*�N � ɯ&*-3*�_���X�A� �ldM�& :y�Z{� �e-�F@a�.D6�&$$Apre󂁈-FT.P:Z6s�" 2G�vQV�^ eNIMP��G>�:� �: clea�-B�V�jNI &#.$/RJ0)T �Y� <9�J =�S�a&�K�*f1sn_� ͬ2:H!,� r�a5j܅E�e��q��* -p)cup V̑�6^y\nba;�V�J�ar�d!t�Id��-�Q'*f�Y-=;a = 6� � �YC!��S X��=M:f/\�co>-d! eE�d E�&��! i] ��c��/"c�pѨ&��V���"��no:� i�V����& d�h%��byNZ�Llet%�b�e m/BA- w*�:y�e<��r �H�F�hN�"%���w�U.�d�rdZ� $\Phi_{U'�/!�j`< �Qa�/U6���\(:�!n �ByY��#�4�ra���m¿�w�y.ca���i�):Qv.O`('U@) & �7 �8�rel�N (}{Iw1E~2JI�2�Ԁ��Y�Z�5=���>Mj} �:Bp�i���1:W�]yc��i2>r*�A�&��w*��qu]"� ��%��.-i�I� *��P&���^IaEBy appl�.���oe �F"� B�u�kp�eg j\�i2ied6�1!&�����yU) .&�zI[�B,�+��*�}1i!@&!�݃ |.�  /�:��]�y�� �n}��m��;-�"+"�s Fp�E�RWa�$,& by�����h$Q� �� %b${6�N�U��Q ������ t�3:�o)>{.o2�A�8��)w�1�F$ -,�ʼn�!\l6�XALc*;1�#>�,:��Ia5$ ndarM�iRK1M){#c" (�>X$;�*A��)%� MA�n d!r�(X-z"�,;��X�.726�4���W�� �2 9f&� }T&/A�b��"lat��VW��f�'t-eb� $�4rn\��G{�>�($�V�y ]3 r@M5e�XH2M�t� 9y a.wF�=e�6���J� ���1�&vB�R2U<B:2.�0!Nm,VsD�9 =b .�<QDr�7A±�:������5�.�F .��9"J>�M6�>ڄ"���}��+ (\crEta<پ��7{V�=�yB�!psJoq��_1%"pS_2��5 % !�.�MӒ}�+� 8 3 �I��m:�v:Q��L ?�R��.n7"�:ݕ�}^".� �Z�1�B�* ]"� �I>�F�� c�n��m�[)B�Q,=�( is��;13���.�te��A ques�*us N:�Y�$A�P.�a �'h�N��m8��A�6 !K�Oae�oXpJ� . S.!_��$4g�����.�1!NB njB"�"�.p( � B!,s*�p��� �i�1I�!�J�1�bya�oF�h��V+2�-��s��)a�cH/�uw�# namedr}{O+Q0 } Do�>�s� �z?�"not��:�N�5Bp?�/ �x/�%�2T`_14iY9�T��5T� a�Vj�LpB�3m#j�Y�pr��)MI �Qnd�^)]-�2�; ���EW�d� /4r��,�&4� $ u�;by 6)F.�� � *�2� �exr2�:b�9-�4���as2��typical�Emple.!���{�J$ �4"�.�a&QD5�!>}�Z�$!:U$"#P�f.��F O,�)�'Z\wP����^*�Y,FqG�� alg �>q4�pseudo-��s1=!8!�a���;�S�8p���%�AFfi:�>!�rqcalg�l�� 6U1�Y"O9 *2UZ\2a�nt5kKm�KU�C6�M�� �4 �� �:�BkPBact9 �0�ll :��Q}homR\{\8�~ U�$���L6:>ra��!.22�8�9[$"�lA$��$\cn r6�B�>ֶz�$� �\cA�B-'.HC}�<�:E�� �^*�y`k.^vQ_ai�w�t^&�Z�7!��:!-2}O$\!.!w�fe!�*aj�Bg���!#A��N� %4a�R9�E=h�� ),j!W!@�  %u��s6AR�D.��":*:��r��u Rb�%S �Q�z�� n.G"ok�5!�ek,��i}��iw>4� partd (F�{1}ŃZ  RE cA�{�da�A& �%�UmuA}}�U #�3cB>X f\.�U�HeY� cBF� g:�B2� #] l. H'�!�R.���O_31 2%�E� ��^*(V��6�s 9_6L1d2+7ph-)2��� "R���j�ph"9bF�(V��/BF�B �9�&�$$=�-R?>JH��we kn!NaL.:L .�on�>�����Dly�a"�F25 j��^�0l.�&�G�b�68"�́2~;2}"�%"� ��!� n E�emuO9�a26s��IJc�����i�Tq:�j\cA3R�!�6�!�� ��:�D� N�thl.�i�AY��U�Dbd'm�;&�#"JwY�in%�i�U�!q9���&�M�v i4Aki&r> prov��&9!�����6�{>�\cA!e"A!�� mugı��:*:� ���x��_1e lo��M��.��6�D "(!m\cA��� "�qC7me^��#"�A��WaCso��&$�&� .��:KV � 0AnI#2���Zh!�w� "�o"� �2öAX�j�E*� Il5>�: �!::qQ˴m��)�[d\by look!����c ��~�� &Ԫ�IdBeF�Q � .�"� m��a�-�� !):� )�%{M]F�1� "��a���1qf� zY�"� J0fo0�AY �.�>A2��9�"�it?N�+�~������%�&q,��� �'*� � b.*EXA��t2!�&�t]�F��d>��.�6�^�#��b2W�Ć y��-�U� EWbt�)�s�+�5a$!�:�56 �y of (not n*��=0)"96e�K,�$?Li5Vm�so ����-�l�|�=9+����FRu� ��n7 "uec"[)}*�2�E�u�!��R�Hs��cPŃ��i�e/��JQAmP�Te>��m��ed \�P"��f�0y;6)w�.(w �:s�->��lcC�'a /�n��r<�KP$< ���A�L@\.��a�'e!�g5��~(N�~.��5�_-����ɐ�Gre�en �$�HEqf��!��H��>!�20 92jF�rep-fppf�$=ym~\C= &�:,����YI� w"�RAf �I �#s � E�UYA,%�%?i��91&�P�Se��_]#l�;X^ XZ ��j��U X = 7 1 X X_(a��Ho1te�$Yx;$YN$:�M�I�f&� c�D-b=�"H���> � 6 !�ifJ�f.8 �2d � "�h &�@��5)���q��0$6�coi���, �����i� a�&a B.�f_i} Y!/!$�4"� t�*B\h_Y(X_�=67&� 9g5g!G$)P� �&�h_�! f�7{�X�y%v PN?��.*� � ���d � 8�}-?!)X 6F}!:R�&� AV�*xx�� . �[.p%��1��1-��-E+,f�^Y&�]Gp"����DIz *74�E�At�0-_F�!QtEU&�XIoed�#�D>���ŐƗ�M!�6>a J|�&5��g�[r]^f !a � )\h! @{=};/& UN` �$fŲ!I�%%N��|�gF�6�E18.���� "+��en�xaE(ll��#�4-�_ *G#�canx �S0 unless� �� �&2"�. կ� �&'def� c��} A>� ���C%:OGh{� � >�G%Ms!2 >X� | s�bleZt �))�Z� holds:ayou�6�K�� �3���A�^��b�<8��.Qi+�?A�����A�+!�2E�m?a�)MJ=�5�i�N NL "�VgI$Yy, e9>��!�.<0isE�guarante �ApZs a%��9���!'s.6 �Y�T��(�"��2Js�s ��"��typY}D�eld��,�bo^Ld dimen�c,��� � be�"� 6jo�\k��u�k2"% >-*I�!3%��52� y. C! $�PU�a�F U�o" U�w 4� \l�~�unB�u� y }!copa��_= |(�<":Do��c�da�� i�d|A5��q. O!�L"�!X)> $\AA^i_pOblya v �P$�$EeV|L� &~L�w��f��0h��.�( ���possi�D��!*t _{ii��� �"6 i� ��FMA�C EL1 i>pL�6͸nzL�A�AL�CB ^�[2+eRAB(M���� :� )���6��M�B-!v!�6 _" ��`M��� 2>]�G�n�:�,V� &� ���i}2,n� �F>`|&a>*S4 cart-z�$� e"�C!a�.%��""�j� &�%O&{ �|L ap2�urs@2_XNQ���ve tr�e�-��E-� b)���� ?V*�Zr n?:ub=f�|63�$��� �U ��+6�!�5AcA(n� A 2�6\�u,9� &�BA���l>F*ZR!.��p,r \cursspec_��U \cA$; this is a contravariant functor from $\qcohalg U$ to the category $\aff U$ of affine schemes over $U$, which is well-knownIPbe an equivalence of Z ies y�{U}\op \simeq \aff{U}$. The inverse�sendsX �dmorphism $h \colon X \arr � \qc sheaf��ommutative algebras $h_* \cO_X$. There)8_$of fibered� \[sall v riterion-�6 3 {1},! see)�>? <�tog->} �]��y �ls!�(,�%U concludesE proo�(F�ffine ��&` following corollary will�W used�S\S%dLsubsec:descent-ampleG\begin{@}\label-,embeddings} ��PI�U��Yofq���4{U_{i} \to U\}�rfpqc ca�<. For each $i$ s�8P 0eqdef =m�{U} PAd %j} &j6' . Suppose)�agwe ha�z clo!!!�6 $X~�vdA�.Gperty:S pair�indic�Si �j$%��> imag�Y f�� j}$!�rjsthroug��first+secondA��re�}�G,ly, coincide��t�BuniqueF���P$ wh!)2��}$Xs) �.T. \endA0I�} QTE�} W-tm{-� to PA�LYi- = /Q P}P_!4� pullback�pr_{2}��X"%7$1�to\� asY s)_{)�!�e� yiel�$ canonical:�phi5 u���.� �cocycle� di�%utomatgLly satisfied, becaus� y twou|�k}" )u are iĉ)]ka�2gYFH��e� nF � PA�at%�s !�%cE�e�!J}$23;9V2SQ� �ing�ofZ�local-A?��UE�nesx clearD!/>�-7 �!)" cA$P9Ln fact�1alM�M� \�Nec!�{= $base chang��ŧ�_ *:"- "} �� nexta�ult��xgo��Tto need a particular cfof:P:r%z� ves. 2 �*� diagramX� m �- equa��eq:�> 5}z xymatrix{E-[r]^f�:0[d]^\xi & Y\a eta\\*� *aP & V Z�o� a�a� �8$G Y"� Liin!"a xist� natural25hom&F �$OUO�� beta_{� phi}(\cL"� ^*�_*\cL5& \xi_* f � � is de��dAu�� s. F�� ll,:rt�E& �adjP� 2� $\cL!nr f_*r L$ (��i�e60��cor�Z ondsAn$\id_{f^�ɪZzu6 \hom_Y!,|) )"e"X ( Z, )$)�isz 6�1�VN�!�� � � =%���*-�)�.]t� J��'2%A2junder%=�=\index{a�m�!map}J.WI�� !/U(�QX!O,IR �)�h�1V() +�1��6�$V haI8I���useful�sracJ z� a� level!��$s. If $V_{@�� open�et*$V$s \in��t9) =)�{�L( $,!�q�[ŔŒ ~hi$ [ %' M -1 k�;A�.E0form generateXJ$a�at6KA�Q%�%�� � cL(f�O ��cL(\xi�s� can� consid-a�elemen)_A�{*}pN%��2%��� � -� only�u9linear6W he�� suc� a�%Utn-�*}s��%$!8�xin�&\all $s)� boveA a���.|A@�i� %��Hat isElre�W ,�o!O��� ��$��qc Y$�d� UQ�5�I&hձtransA�il$.t� s^*$. i�b��a �Z atibilityAL� ..� ��om9-q��} z�!2;e%�I�J�8g beta & Zzzf-r]^\ps&~ & W���] [!("��E�O�p>�{Z}տ� ��.A$�1Rs2 {�*�^*���V 8rr]^-{\isoass_{A$AQsa�! -)} 0d] %��g0cL)}&&* {} (rO)w��x d]^{A s-�>})��gs�[r� �>\ g��E� (gf) 9vlwA��f,g2u&w"f^s�1��  a A�`ionB�T��$mmediately�ved�tak�an2�$W���Wa��T ��%�͆-���� >nd���;ps��U��Q����of} _inZZ 2�2�Z./��zi. ,5�$�Jalway� o�geM&v"�����cor_ ^ ->�� } Iiusit� !�V�f, assum� �bRM��2Q�I6<�/e.?J4 if A�~i�V=J;I99 H�� .�t�,A-AV�| whichBare:�it�a%s�*plee'standard>Jnoe�ian�4eaLof reducF��a� tech�� at��� hY!2�J� �լ !!��2:�q`(e> )!Mesian5aheta%��er)��nit� esen"on � � 5�%�j2 flat}V$j,any point $vX V$ denote��$Y_v$��a$ �ozv�tb� L-�|����bO. � \H^1(Y_v�L_v��0� �!s �Iis �ly free � !~!�rreB�C��"*� �xrJ "�%j:�i/!��:���s]� ��re���s L\cite[7.7]{ega3-2} (xE� LIII 12]{hartshorne})!]��� le?lfis easiQexo)`iz��@Zariski topology 8$we may2� ��. Set $V� �$ A$. Accor�A ҽlh 8.9.1, Th\'eor\`eme 8.10.5E�.~11.2.6%*4-3ň.� subr�{$A_0 �teq AA�� A�figtypQR\ZZ$,���,� �  $Y'_0EAerM� �_0m" 7nt�a?!K6I}� Atog���6��$(YeG)$ "!� '_0# '_0)_ 1� By semi� inu� ()�2f7.6.9%eA�)IU��C s $v!b� ]!"� �J%��e�g�$-MvHen0!iv| �Ae��� w ; obvious(it does not� �!$�%! 9 $. D��Vw("�)��y� &F ��t�$YJ��!� V= E� �'1��5� � $ maps in�U��]�b0 c1^:MBq� �o2�CU]jR � LyE���:w 2(D� via ��tibleeBves� %j>� C���&W very� , bu�Y8 limit$scope. One!Zmo�_�3 inte!� (X vls, ra�A8nA� �on@!� work!�MDaseJ  long�!@N]�r ppedi�^/I$the'uc�: � data& �1gE )(0 )! !r�5�-XSQi�DcF  clase>�5��m~$ ��p*@ !�msch S��W!nf���(D��I�defe�})^`"G$xi\co6 % F$A ��["z!{Y�� cL_\xi, $X�)�rel=%�I1 �Ga each&� � ��[aQ���] a��rho&1� �_� ��-f.��IX�*sa���smi%ra&)&to ��6-!�: whene� *ar� 10!�I�.2�b�r]�����column) �+cF] A�� J@C+15pt�#E�}�*Pf^_!)F��3 )��"& �6]�E!2�5It�I*�5� }&� �iG� G ] of? �� X����$B� ��!DcR ]2l#K $ed-quasi-c �T���$!�^2��<�y} Ano�el�cumbers��ayE�tat�P *� �rus' mormala�P>b),�U$fre�\$B�: s�%(�{�_{E7W2�gB$�Y$,a��� cu�! $)�QX�lJyA%r 3c�etac#y t!��X#��!simpl�.aAP�-Ej2�� Q�� rcI��Ga��6r��{\xi}"�^ex���ex:E1s-cur 9 �fix�)���'�non-neg�?�ger $g (Bt���=F_�S%�xsmooth�|E'H$geome�(� ��connec8 �Ajgenus|� s*E ��m a�� ���a��{S}Yg \neq 1�"�hE� ( applia�R!) ge 2�tak�A�� r U}+ bB�ccot*� 4Omega^{1}_{X/UAMor����ts power%il�r!` =�we%d|*d@" So6ce*%�% $(\5�)?*V�0ass-groupoids~usually�� $\cM1�, play)import�.rol� �-ic1�tT��no"�E��[f�Y fami!�!B�1$, s���&� !� y. Ij# _{1,A�+ �2!it �, �t *:b 2� A%cou� iU�Raynau�(XIII~3.2]{r ݡ�$See Remark rmkq*$ic-spaces}A� fur��$discussion�� y} R#�E}Z�)E � ]�fa7,T�L tacVO6*� �a߁\ble->I }. I1 L eas�hcheck� �}2z>M.�$� *-  q��)Twe-� a�� n%edMqIӡ=7 U�/*ўX�0Giv� *% square������ \��d��$ we�a .NA���� sigmu$��� ^�M_{�ŗ�O�� Ŋ"�$X4Axi #] b6f/nge:�YD2��}��  V� �@�6� �\] �a�*T $ �tf:~ :<t�$ $)&���2�R @3��]!  �66%�} F�� A��.��!m�� �� � %/G}i*XE�A�} } \xarr�%$���# Q�6� 5 -M%� %Y�� � ,g-s��,��RP.���…�s� "b�$  nd let us.VA�M� ��heVd � g) \bigl(6Msr)'I��I.�#Z8�] (� A�Q%��G "� s$� e%6�)|%ץ�B!U&!y� enough(";% �#0 s+aw"x onVu�!uI�align*I#QP�]&"d(A��&�` E�`rc!P!��--�)j��R&=9�%�J[E7B\%��sfr�Q(� 3;1%4��|-5�E�M&= �&9J:V)D 2�1�J'6�9Z%� H 8�2-�b=\)aN !�u�m�o�qN9i� �6o!��%�A)%�.�-���.\qedF c&"1� �  �1~0o�5ag>6a�"F5a�LemmaP lem:- }. C�(�6l�9ur�2*LD� I$&�8e�"E �%l��r�t(V�)Notic� at,} ��v� t N+.e�E*��n�a�� t"})!,� in� rj ^{\o9 N�:vw�.!�+H#*="g� ��"��� �: N������6��e�E�M �0@C+30V.zA�X b.-�*./Ŏ�(�J&4.%�ZB.(M���N2<FZ.!>\]"J'&l0C4�&9 aa�#�2a=���U�g��ɜ.�=�Ž�Z� �t��v& �:�i�3, 1 es��;!�*� $ ag�"E�m�ey must�� �!�ubstitutw ��  2�!=o U "b,-{81E}+�Ʃ�\id_VeP&=&\��\gVnS�1*25@qquad \text{and} H6<V�D, pr_2�� ~�1V�~�2}6�5 ] ar$} (ref�.<�&~ ��>er.�Vn A&&M�1C,%y�"cF(�!�)p$nd analogod"5& "�A8i�.~q2vq.�n.��$f$ a- th�40 ons9 ED � a!i+%��7� AX%1I�6f&Rg/kCd 8!,M-�9E? $  gNIv� Bq8\A�2�uadI�6}I>�V}`^ r .~end5WFl9A�"�.� 9_%E�-� F�!AMh";�)?YH557)�$�&9W8n.�\ �"$2XV$: �yA~B�<��i' Xoj&�ݭ+%*6n �*6r1\�Y3A�ar[�0P=23�=  \ =\%�{V2>��9 d] _�z{1:#&&6~6?~l0,-{\hskip10pt�1�=q �phiI[Ag{V.} �:Ev�2�h�\]m yr �/�!�truct2�#�!v:;1T,AU�3V$. F�D?��c��1�b��U�0!_i�S�I2�2<��5�����1}An2�]�.ALi�EI2}, � )A�E�I�5�q� >�II��D�.~1 ~1R~�@ lA@6~�=E��};f]�="(B[%)w � Ke"�vQ {iy��OB_.��%/MwpEx@{=}[r]Q2 9��!=� �5Yhi, �eV}"�1� )V�5!��$B��q] W�Hse, :?,��6?E�r�4Iz1}}n46�z�n2�C \2��� � �!���L>u9V�#�;�0��V(6W$����B� . We�|our cus�Cry no�ԡ9 �b! 2J Z1�Q&�  o�+B�E�J f�Arod��DC eS_{Y} X�D� $p!�$, v� 3mCh,G>F" thir2HF�a�Nd ;tripl�:r��� �3j (Pre�-A�hpG�*)�Ksv21A�!��3��+���0IconfuS�Ims�"�!al.) "`3�q @C+2�}� Y1|U}�����12�!(ar@/^1.5pc/�{p!��A�Aޑ{��� [2�&6}F q p�BNe*+*�. oi. 6e�_F��6 6=2�O&�!��.�1Vq +"; &E;� $\�%a,�@ >@D �PB, �5z"i����R[��1� �E���%2)��U �� S.G 12}.< JB>NI,� ] sou}aAit.�&��B15��A/��� �%66�����Ind3mR8"� fash��U!�i.F�^. � �3:�-�a� -��! 1}},i�@� 'zs23 s232�Js2s2�s]�N��s3s36sb ��1�1��1s1}}� &� =gN�z����. s.�We�Itov{eu�-�� �A�Q��j� si$;�+� �*���e identiA��=�'dFJ��* ificDBl�C�F *h"�%�4�A�a/TVt�}h�_Bf (62}+����1s� F�c�BaY + CM��&,86}A�u�q�2y^h�}6M }R �7�|�|�2��?wex%�U�am+AR�"�1 F� �U`h!��  Vb�E,2 �"���F �5F�i8M��)B��fVA �=Be_:�� "��� Z= ])~rDR^9�� �Fx Y��r�T �69��AN)D]:* ~ > .q � # U�Ue..�%.�<�.=n(!K:�60!��y�W� MhU �YBdhr;SFl% �F� �.V�JF �eRAFE# & argu�Js�MD�� i|.��e.p r2*�V���NF�Ec�F�2�r�2*j�"g��l �6" Dse�EBZ���@q�^VKF��E�%E.�a��� 6=� � Q�But@ � s *4H,6G% anksᝮ%%z� Fh�hiSSoD2��()�X/j.fFeAit H<ss�*�j�*$U�Now�* go b�0�:gf!�B.�/s_�N�4�8wQ;�Yn.~Q.�-EIJ tau_'0 Q(%*zxi/^O*dJ8/SL @T&�S:O!�eF�P bu%�| ��(��s!Es�!n�A#�*� � !!�D< ;gZ&:|J8%�� .�,�[:�&�RN�.�'1{f9 ^%x�\ � )L�U�B):G���0t�%�,P\x)-LA*�f()\w�#-�0w h'5� . (�@+5�Ma.�^� ~Qn���*I M�e�E�� �xf�"�Y"�)�N�.y?sf?q%E2 v�MkJV"VQ&/Aq)?!�6�a��#�JB/V�# en bk89�� 6pmWA��]gRensF.hUs: sQ$2��+s)*�/�BoGs.4Lӽ�"k*L2isF?%&o8to�"�� b^�$")LM6���,B�3��{,I��N)�L/2 .�$06�>gE�C _xiY6R�P�*�+V=U V} \PP( Wg�!�q /1xi 16� *A�.Q"�v�{}6\�[r]��d,�Ņ�����.; �� 62� Also,S=)�%Q� B�#]R!f�I�,�o1�Ba9��P$ 7s8eta� T! �() �&�-1��3OYH"�By1��B6l �ro?&l�a"A^s..��.�'f� >��z�"X!�!���@{^(->":2�A�!(�1�nP� QAh:-�R){BO]' . G � ��#!�HAa ^ ���~-.� ^���� par�B��.e(qd./ %!�c! is�B2�6�Y��U}&��}z�B1Ŗ�P�� �a6Qu)�H6�L��-�%\o 6=�=��n���+I -9��nta8 0 1��fK�~% ""Hj�, show6'2������-�N���� �l��AG>� ��n�>$$��)�D fO�,� hand�6�D^� 8 W*/"�"RkL!R`L $�]f�Be�r�3aM)� , $F*N/7m" �&o! +: p� V8m#B6�,��.iI M).~9<>dr�3 a ^�g��>)�BF`e�)�it�oA45�)�]*?F��J"SC!.f.�JI!1���!�E�cF� ��)v�@TLRocY�L�Eprecis�?$(�'o ,phi � !�/V!��"�A&� � gN<"dN8- orsors} �M�* most 0esY1�AE ��c@k�o�--O`> �tN�_ vast�i4a � well know(hce betw�SB atr&Wal ve�# B& >')Tx:*U?9nti�_involu+. T �s � �%pr�mpal�1bundle�6ATN`I�Yfi��t �nklXam�N��est2-��DGalois field exten$s4UE�C� ex:g--'}C3�Iw�2ly!��$�; $re minimum!]ma�baF2O2owsP&ZLhI��pr�maA2�FvW fulld reat��%e gD@{demazure-gabrielaDgis"�wafll7P-� sub&�Jq $\cC&.03e�%G&� a F"r.G`.C$&�&:�C$�N$a terminal>\p�pT�)ta�a�h�#in!Gd%���4cattop$, endow�!!� glob��Oic!oM>J�6�A�{D�V'�� e"kpE�`m�9T� r S��1 � .�>�`}{m} �w�in�cE�emR�ac (0called \emph{y4m.}:PPr n�tXQ@C$, �a left87:�sG�'/ ?G�W"U�SY%2�invar�v�f �7 !}762�E�;!���t6�:d9c�#$X(�rY(U �H � �r�na~!�&58$G2�F��Ma�0UM�C��%%�JUC� �Fa�u$e��(2�c9zYX�9"��]*Q �_"-l$Yoneda's lY=��Yet a �e&AG.��84isaJ- 3r!�ean[7vi6 t}WG$--h ��G�c r Y��Z\p"�22[ 5� ��=&�vY' *I�aM��8 �SI6 �gGa>& �**}y!�q 7�tmak��e�+&8 �1�:Z �'�@M���hF�q66RLX$>��Junctor�~erdM�_Ue��!��,�Lin e , $x�]e)iy'Y'e,��hG9.w same-Y� e�&�)IM(cdot (y', x� g x4��,��a��Af!)� Qf��}�327 ��2i�$B"&-Y�$s AZA@��~ $G$,ieM@6Z�� mula� ��(h, y� gh,yY#&Lh��s�b)�q:QOE�hA#��y %[ . M�8[ �ZaV\Bl))!-8m� })(�nYFF�{6EAJ!(6�aauM�m�y�q ��i!]m�!x.m ">V*�69�Y X�Z" ej}@-"�TEG#6"�[Xf4!x:&!���5fE&e6A]@. (�.�itselfA�j\p�o� YY�[ ts lp�<is"�V�.A%)�y��5!�AR-�n��Gi�F�\�m:*bj�� ly�#�a�� �.�T�9u � i5d(&.Z�g} AM��( HU�; }�H�e�������%���,6�^�[�q&�\{Y_i �n�v!WY-m�"I%<"��wɾ���&QɁY�_i��>k�.H� � 6�Q*��)�)Xs..�D �Xy .? �� A6�����&!��delta_- 1�u�-�X� !5���n"YR:�l�fo�� $(gŌ\)_to (gx&A��.� �y���4.7Y�A' ?\$ �|)�"�\ !J�}jXjn�A|e  !?.�. AJ�bd 2Uf�h&LV nume�Ki�j item�}1}��.��Iw-�e�Y$ L4�zR�7  �2�cO�?q?&\!� end{.�.� *H��@��(2�!)s,U���R�b/=ury�he&g^5�(Np^s�uEp� &�!�A*^Two�]�Xr�Gied VS%/*�$"�EtoqD��*( .*b%��te��Ok\p�<*�|5� 41>6�E�Bj9�ix.�5��M t�O VB>dw6^� R� fix i�=927�=�� .�o�F$� a��V A >aa9e"5IVW�7�z�eaX|�O!m.�{Y = � ,sogifTMjn^�/n&rK 6�$a0$be written��A�c�#a}�s� � 55 X \xright�~ <Y �(�  1pV(Y)ً62h� E��Oc.�)�F��!s� middaYsc ed!~� rule��� ���Ml((g,y),� y�O�, h< �$y� ��V I�':^$ necessarrjm���Bmf!,p:: e�;).��c2�&lN� -!r�n�Z�sB4,�&IW\�@-�A�0eUG �|;B9 �9 {&SAJE �+A�m�6!��:�!ZeA6ve~ \{S_� S� �p! 8#Zrow}\IS_i�;&�FNE� _S X��F2]C��&Qc�@n=�; "� )�"e/P7 �(\cC/S�2�(*?%�R<�!ma-.*})�[ mean�H�Kai� %s�Is.�hf�ZY.��+k6y,+�,�T�'&�m�)Nl !���f6�of>��by5p biQonn�baA��"SF� s�+0$S_i$. By hyp"s�;ir]6�2�%2,T(U)Y��S_�r�U�%E��!t2 f@`L tysef���4� f_1=J�\!5x �nwehE=� �G�0*y� _rbitraryImw�V t $Ua�ΆynW#t�($"�i  �Ua�E�* ��"�L�et.�����(U)N"^{f:} &a�zwrod�!w_i%y?#od_i /_i�#<3pt>�$@<- >Kj}!�_2�>O R U '�Y ��wJ��{᱈in�0!ѡ+�qua�p�aJ�Z�B@!�ami!�mk�1 �M�FA�� $-`$ 8%,u�+��, a*Z"� )  &2 ��Y I�cho�c6�&� A�٪��45 s $X!;i?e�%�)�� �JO2�o[N�Q"� b!�X�A�\]�$��{IE3��RJ��_��C�2:nq�]rw#*~�v. s $&o X�_�%F.�M9(.w 8Y.6%)_�)�!�a6> * j.�M}��'�6)H)G $�TY�G_�9prI��6� 6�6/�3.ag[(0 z9�N�� �"�s�f6 ��Ƀ2�E��aցB{ �)JC:�� 4}�1R� IK*�tLU_!Cx%!&� 6 762N G_{K�Foscrete * $G) �rK!�r $ as:�#MY6kd ^�f( i�����L�x�� m�"E� �~_{ �?Hpec L =Y6 L.�L�D�$ %$ Z� �-6�"u�6le $!C&F% T.yKv�. (�hconveni���M�" x:*V ��}hx1 F9 �E�B�lyk�2�B�4pr&s.[8k�", !�?�e�nY��K$� "�&F $u$;H!^in K[x]$hH"8imal polynomial� !�(/f(x�"M�AOactPX%oo fe p$yci�7 so $M�"�g$G}(x - ug)L�h&�j�d�L��i�2��HQ�3��-� F�)i;pec(L�[a L�:���. 7-�-$� $L HM�L^{G}q~�{ �a/ b> ag)b!�r)_{g!�G"!: by $ [fXea�+!c�J��op{/!�A�6���"I�6��2�e�]�A� >� �= LH �y!�M`vBB?� Chin�Jre&�i.!�&n �[x�k I/!8_�>(x-ugI 8%oc] _ 2�a&u"=6 $6`5E��S�[P|x6��2~Y����4i'��}e�ud#:�`6�Z(�d��-a �es \'etal3� h�'�(3Z�F o�G���&�51!ޭp&�C_&?�"7w-*� &f*>�7���&�� (V �cC$�7 tack!��#2�"�r�N�m*X(Y)r !�.z*� CK$�!�cFA&(X)�D^Ysec"sɟs�+-(BHB��b�sam�s*:L��%cU�mF o Y)� i�ofA�aduc�2.2 B U�"k�\H�&&@"z q�+�yi�h+� X9[3&I�bon��znU��cY��RYb�(%�I�a�C�I�16�'B��6�:��6� � �'\]  �6*%�A�.� >�h = (ghx, x�N5-  OA,�d�!�A�?},o�Q�)'�I%a�:�g+" H#I9V ?re�I��Su u�-A^]q"�~depend cho�d�">,*�MJ� A]_2�&J6' � c>6= % �(ndB!2d*� Y0$f�Ka�)��6rqm6'� �@!6Ky�JE:@.�\t3oh:� �A�E�.�M013}&= \mul_{G&� �Xq�p �>Q.Z2 ZJYy*ml�X+��w�t�"j=�^��X:��*=(&� &�'� Hr !�5)A.�Tf�TZ $}W�j,y)� �_��…�"Y!�=&��F�&2�p�FE_5 rho ��)�^{*jpFVy��1>ʙ: �XJ�&3 >Z],F,�J[\ur�0 �, �pSQ".�} �6q��2���&1>6!��� (����oc 7/happe�o aRs��2eftA�.2)��*Z<��L�ݥn�j\-�/ Fail%>f"�3��.�� � ?:f ;="w�con)�v1�r 8� �F>k�"erOy 2y����]&���el�� star��e��v� n HironakH.famou�(�e��nonq��Preefold\� � !E�cite{h V62�OP[Chapter~3, \S~3]{git# A!�dix~B,"�33.4.16߈�is�+b�4al�y ~|to28e,%"a-Jx$ee-dime4al*�xs�w � -A�b��tD%s �4p.~14]{knutson�#F�!*y`yz>2 $\kappa� e�Y�M!8@{-�c"!{t!x .� �$HG� Z��"%Ɓd�y rouporzwo $\�2rm{C}_2�{1,�� gma\gY�ain��P$� $L_1�CL�0� \PP^s{5.Lyv\-�W�a� �=�1-�e` + ]A���3ly&q �1$0%N�1:�9��BD+na�)���My2����߁g �$simultaneo�e:q/not �"�?RE� ould� surfac�2%��l�D)Pq}�q�nu�Ye�s. B ��5�% zero�? ��y:!�GTr�9M"� OH�:�Jpossibg"Uf�.d'w�%2�"t&u@ (a��� I�6D) $V$ ir� �!iiu$�$M� _iB ^y��s*�"Y�Ssq�PI�. W� ���-��A��ց�!Tguz*�o��u�6�� gk�O55romha� 7�A��/�=[r]! >�j] r���6�a#$ w-���!}k(9�n2� >!/ �"< L2�mB�V$ (keep��8e�A�S R�sB}m�% ?�g )q*I�=i!��Ds���=�s����!@ |� 3N|��Srk"rN�� M�:��! y!)s�eR$h{"�3 s�2:}, du� Michael A� �>�{� t| �rep?� &i �/:l� ��7 n�)�Q� �op �=$%� sg&sen�E�mE)ly" �'"i � u �v%e2* ��!Sd3$Dmp���;3� moreO�a?rk��e%`�'�A@!� fppf&f/(��probab�ls"��2q�>pd I do�-�Ajsure:� �0,7B applH] ��;�)n ^$ed). Also, 9��ep ndFҘp��o5K�d��=�� �)a�s *�8��4X-���2q��us be��X!�ea͈ \1�>��bJ(%�[q'in+u�1s ��E`��bils ;�,�>wa Qſ�Fa����vk�z3sed�ac�ed{15$%B!Y,shed{7 April=2ona�B� ] � 2"zeditoa�\�=on%t$arxivrefer'{�(.GT/0412513�>E�f:<%�XEUHC$macros (de_L�TunM) \AtB �D��({\let\bar\w tilde\w  hat\� �)�7in&��!� ���user-��d��� \aDatletter \def\cnew� (em#1[#2]#3{�A ${#1}{#3}[s/] \expe� fter�cs�� c@#1A� \c@thk!renew,Tand{\mX!�Dstretch}{1.05} % _]s�Eaa+ length�( .�]{Ÿ� \�%}[thm]{:;o  % v6Mcor MC��Q6&A� '*}4} �l�# styl�Ks�=6B defn B&�;j6're�2�"6'exa M� (Q utoref!� v.q$t�!�m�L%��Q$ block %%T UserMzT�y�$own  (!�M<'s etc) below. %I�ni{{\no% nt}}  ce{\d�erAH S{{\Sn&r{{Zs{{\s. a{# Bt{{\tauG{{\GammQA{{�?{G}#(e{{\epsilong{{\g.6 d{{\D " l{{\lambdb{Ъ"Z{{� bb Zq$f qQ Q<V ngle>!2oK5 ar K$o�GD{{\DXAT4f T!�iot R�R$��w{{\wedg� m1{{im8 ({\rm mod\ 1})UL{{\L28n �5|R!l9 R}_] def\Sbf S}^D={\ {\buildrel \cesH\� =}\ Qsp{"AH spli�mponeY� tsps^$' � �9j�b�{� aw  asciiabst �} �6W . � coll��9 orien� alterna�Q  ram` bo��U<NPc the :^)QBveI e^D r� �� 1.2).  �.rK� sser�&w$ hold��milar;-if PV���,an*"<=, �-6S*�!p>F /0 d a �Aa��zr!{02-`�Homflypt*� �O6� �:�web�*�*�*�*�*�*�*�+r+2Q)U&�lIfE��R�R�R\�T`F emm}�Q�Q�QjQ�'r'U� t�s�S{In�V��} �$i} I�2(t{?a�# ���� x coe �s, $$; = b�Ot0,i=1}^n (t-\aB<�� $bb C[t],$$�g, {\it:+)>$m�$} is $$M(fj|b|l6k\max\{|o |, 1\}.$$�4ŝn�,e*6���>�i&vCto͵]"AzY-�nM�1B$Kronecker 2z"��Dnic (ie, $|b|=1$) S ger &��$:�1|4�I�a p._mo�4��0#otomic=�s�VLIn 1933, D\,H Lehmer��2 �3Jic�?�dev�$10, $$L(t!��t^{10}+t^9 -t^7-t^6-t^5-t^4-t^3+t+1!��:i� )e�1� us g�X�Xhan 1,�#alL roxiYYx5$o 1.17628 �l��( ask%Xhether�  *5k�  >#��M-Kˑ=�E�$]� $1 < Ap < 1+N$.-='s qu\o�1�sP.&��no -�.hxR�&f� iX:���%$M(ǭo6*��J�n'"�R motivat� T�)!o:aH��m "t0"�)qm�nOnoB!!@_/&ldoht_d��R7a=>����bW8&�E%RralZFi��X$y*!gu��!0��the%M�rgent:�E=�7t_0^1�M�} 0 \log |f(e^{2� �=h*i���Bd})|d\ ) Sd��ix.;J�!`higA�mx�*�2t �*U~C1�].�(Boyd-� boyd�_*()er��  I el&dJal�eK%�] nfor�Zon�":Q(is encourag��*�GEveZ��War�EW}A� %08/05:�d�X�2�ͪrem1.1�>~m Q�La�.� $t^{-r}���V��"�C}[t]S0.���pa�ikewiwT#�&^��/2 l<beFThus Z8"� .�&� �� >� �ny&.k�#orG Z(`mN . S� e�deals��s�%` ,� FHs. 0!�F1�2D ���d A��)e� rpre�of:��}�-� ])i�-9.�of��[�GED8�� growth%branch��� s wa5�n�X�t"m*SW02}. '8,�:�^!�N��)be�Z�aea suita -��(�hQ4Lef�tz#�efK ��dromy�4a^l��d��dynamic?0pseudo-Anosov!#e&�IA�XA��� �].��� �!+!a�~ t �edE~� � � ��=r.i their{������'.� t,$ occurs (up�!��Y, $t \ 0�>00 -t$)+ +f�a4 . Perhaps%��!\��ng(!5N,$(-2,3,7)$--A�zel , a %�ed"H erbom-; noteworth�u!\��e� Gordon-�g },"�/ Y/��If5�9� has �%���t swer�{� }U��)"uOc�n!fbe a (��)jJF� arbor�((or؛way�$��ic) 2--"�e/��$S^3$ ("s �� 05})��ydhy6i��vs�% $L(n,1)$ ESWi:TAa)��\s�nee�ane�aS".Qs!(1)q�m ��� -A'inJ�is uncf�Y!far0A(Callahan, D���Weea3rgu�' �CDW�Ta�Gr>��t� ve ``s� e"T2v. refl��&u�y�e� �t�theI�o�a>q!xa�_bw-n?Hed/p�P� ѽ 8 +t��� iel��� few�7�c$etrahedra.�"��� !�} suggf� � 27b��$-��%� sm�E6�. ~of�:k� �CKP�a1��"ܝ� � tow�0My. � �� @s��\�ډ�!�2 �,T BQ�WO>� =�*y�U� �{ir r%�cre^�!o out �$. (Dasbach?L�DL}��3expV'e*� :#!�.�dia�)�f!�>a- gi�o A�erentW{o~o:o%)� � �.�#medΙ {�Acl��sa�e�b(�g� ��to� shima.�(��Osaka C)Un")�� hospiti� w�?� $��per��]!�is��w�f�!pro!3 ``�W�o؁ de-a���ls=8ocuse,JSPS Postdoc GP04300�l&  2. SpA>!�M�� %�% "�21u��} ��KN-E�ing52&lin .ellz;e� cut*!\air�� adja�# arFa2ek $D$E�$ Ein�"%2i� $q<���s (�-cv:f $i�sSM%�� # �t)t/- tachp!��&�wy0we9 a ��!^��ell_q�4�g Ľ��̭� m=-bWs� { S}$��ve4 (ChampanerkarxKofma CK}�>h!�surhN{s $\Dm +�G�,ave0� u �-!)��`��ga"��X �Xw !� arb�X-�s $q_i�!�Ifs ��?�[� nxV 3Xw��!, q�gA�uE�nce. HoC3�s �:'  Nll�lly"�5ely m$dx.ncdmi!ints (cf*� x5.1R"�aeJ�}lC%Y��egARQ%�b,3e�sre; J�NrU�RA�e�_q�|ou-p. TA��Q,��Ts. 9xweEf "� ���w� ~1*�$�h we replacQ�qH�[^0 exnRI)]{Bi��%n p%�!nIA1no�@ojE/!��3�n�"� !{ ions� =MDH�R�$ �. A�Tbig�g�)�� x�rE�!Lcaaros� y E(ary[E}Tei� [n �ڈof2s, max�R�=�i����;a loný.Ks�5el�W���� Os� V�o2����k�I�D )t�Ś! 19\�� $t(D� �.&Wa��I�WP"�SB.l��-�%��ad� -��'{}}f 4 �{ (� ��m-1#s)�RjA�X�0O M5�Fo!a n unT �c�( 4r� bf9o planeVmA�. W2�%w-} $||p||�a:0&]�c�s�x� absolute � ;.�ics��9triX ineZ]ty�)�t!� log� �"E�( $M(p)\leq �ioL) adle&b#�s EH�7inj�Ů<er}|�� �� ,�<�0[�. 6�F�3ѽ$p \Z[x]$i!wP��d ��� 'R'Z �]mar� ���so-*'"�G�l%s� ��PH(v,z)��!E"�(skein=}��� �on $$vB>Pv+}X-v-  = z0 �!n/���us�!mwֿ "�WQ3O aa"$1*~zYi�a $2$.�ar.�) $${1 P 1t)\,=\,5#�" /2}- )�$�<)��a5i i �erv� 6�E�io�0!~� $X(q,\7.)�?Gp6:in�� jone�Z%�>�}��"�Cb�� $q= c=t'r[E� �4s!n(-)')&t:&t,t^{!9%\,!�����N�}�6aŊ��PofU� )� $� L N�1:�1N�b!H5nnGlMF erm ``N�"�$�$�� one}�Mg4;�Vm~i1v- �8�4red�G?``�5N�."�a� ]@ !�,ed UplW>A:[t�.b3�Dmain}%2.1 {\rm(1)��1 D�^o "# �^��s�2M �� 4$�!�no�� �`ei!s!�({||(t+1)^nV�f8(D)}(t)||\mid D�# � \}$$Ay9 \,||(v^2-= DM�� Iv,:K .L:J %2�.� ! <)  2�=1c^ � {��) �F�&Z !�`#5/08:���[)��ok�^ 6�s=%ot ||.||QG55MG��%21V�V>6�)�I�V�  $\{M��"D)J  DA"E}->b={�cA`���Ked�:��)?� 5p!o+b2JP&F54 &� fa�Ł�6��2�iswa�� iM�lply��29D R* "V��V6��# ���M cor2V�K!��� "m� prim�&�2 � "!aCs�� $5�_q}"r"�E iss��"�ERn $a�T Volume}(S^3\setminus ��Zls��:G.eR��)  E��� �adm!�.� �+�F $D-�%) *� aݕ�HPA *  mee� Si� &�6di>� "� IS����Ono(� m 1!�Lackenb�$l6+D L_3 (t(D_q)-2)/2 \le ��e&B v_3\ (\ap, 1.01494�.the��a�u*]YAl 3--)Hx'n̅6��_AQP>O��ref�O,�'%�J`$�VV:^"��<3�a� &�i�WiyAF$!E�!6��establisIr)�uL!"�,��Ts:9 �an 2$�Cn)U- �u&�i�ap wir�1}Dm#u�narA���--, n$ vo6c!|r L)��} $v.|v_n! tGS=,; s�.95O�+c"�b�ie�7rcs��ex�\v� �U �Wlle�}�a:@coou��JHh-� M}.�^Ty numbv�f.;+��6v*5 fi�D}[ht!]\s#02list \�D (1)� 78 35.2244:3403endlabe V�:xer} n�lgraphics[width=3in]{\figdir/-��2cap� {Ver!�!1I�:�,u1�0 w�� "a�6)!�%I � w��$$n$--tuple�kq.{ q_n)v�0|=� ft�fA�-l!�he]D;0] ev6!F-M1��bb2odd�$v6^0�RK�6���J�ar�a��m h$by $T_{-q_�F�y!�.-�- �2 �h�^�y?�M�sig�0)3���2*���k퉩���.)�gyl�?pCou�rmicE� } to � n�(ed tangle $�aT_{q_i}$. Clearly any oriented link diagram with twist number $n$ can be described by a wiring dia;of ord 24. Note that a P$consisting+0a single cros e�regarded as either parallel or anti-p , dependT,n the choicebw2��. \begin{figure}[ht!]\small \labellist \pinlH {$q<0$} at 146 2396= 429F> :30:9\infty [>!end� �c!��}%� hich�!�ten a�W = {{�+A�(p �-Fo)(�{1J)x-�}!>A�ytial fra%}$ decomposi!�5�{1)t+1e1[.�M*� �{1A:A9x}�{{t�>1I�xx}ee�Tak!�@series expansions��$x$�these AOon�MQsɭI$ng coeffic s, showacat }�0= {\textstyle.��������%�>�(b�36�Since . = q+�0),eMseiM$statement 厉d0$. The remain��~ollowa!sete�$v=1$<$the Alexan� $polynomial)J0t0 Jones ,�Hq�<0��handled!���0ame manner, u$ �� $ga�� �r2 {1-r��x^ri� then�r=1-q$.  �ѵ�\rem} (1)\qua Champanerka� d KofmanE) � \cite{CK} ��@-Wenzl idempotentMU!� full�, $�eR$�express aF�A�$t �$t^�In fact,�ir-�( holds more-Illy���� on'  ,of strands (��arbitrarI �%). (2)+A spec�@��of� firsE� mula\v��b appeare�Bhatty-Sb }-�!�5��.� 3��ʧ 2�  Z}\cup\� fty\� � 6� 2� anA�&� qN� � � � � �=� Z� -� � .�$,��"u E|� D� � + {q��2}Fb,�2� , � * 2� = \biggr(2 e�( 2"� P 5 )t^q& X&�>$$6l 21a� = Wq�,a�q_�50  n/2}et�  $W(u, w=W w_n)�r�T [u^{\pm1}1 1)w_n ]$���ly��A�6�� ing b-g!S itie1.�$1i2=iN��m�W��^{n-m"^q� {!j ^{\d_1}\cA� q_mm}�� 2^m} X_%9� \d_n��-�{m+1}/2}9^~ >�!Usum rang!� allP)- \d_i%�\{0,1\�6 $i=1Ynm`each $V��{R  wY q� w_%8�  p�����  i� .23]��p"� n y|BW*}�split} ],&(v^2{m"B��)� 0\ \\ &=\ Y(vqEi���:�mEEU)5~i��� � 0 on*}q�Y(u,w,u_��u_m,w VSR  �w-�3� N�� � ��k"h   U� �6(1} (if $v_n� �� ) orF,2+2L ), w! n�e  J;$,a.�in -�5�$ �O "^Y{n-1},0� , h ~��q %1%~ .*UJ*] / (o��twoa>��.� will )-}n�� �parityK $q_n�ontinu�i$is fashion���k �q%urn%xrebn)Rt $t2t1a\59�ً�@s9�\e.=\en]>9te+ e ]$, �A�.�-p\}.$ T!r ha�� iredP  .^ZqQI%uNMM $. �argumy!�NALis similar. We provH e seconser !�ut� . Lō5pm!>t ź�a� \e_i�� �f�1_i (($q_i$ evena� 1$odd). � Lemma 3.32��� e7�� !���� \lfloor ��f rF5mf5*xB]m�C��F�� Now��5t"�s befKtoq2�j��0linear combinR!�Y�s F��Zi�at�.M�6�(>�m�7����*� Ihe5ini!A� orR� s} a fixed*~ (�/wer!`$t+1$)a�.�=z�3a �&nonzero29.:-5}!-a c5>g$fg^N$����� o�0��rivial �s&��.@5} If $f(t), g(t)^C�A(\ne 0$,Pt)$ no�uniG,v�� �te0to infinAuas $N�crease)VoutIq�&�I� W y a^�6lospge(lbC� = 1+a_1t+C ��!(= 1 +b_mt^m *^ $a_i, b�D*� ?b_m)#.� r��P$k E�.4 $c_{km}^{(N)}��/km�-3isUPS� su�ly large!Dis2ais �nA� the �  $2x �t_{n+n_1 �L + n_N=km} a_n b_{n�jN}W!x $n,n_i�. S� �rB ;  M($p�q' $n_iɚc�  it�."�Hp=1}^k {N\choose p}�b�p �%���?��S4 aken �!c$n, n_*Hn_pa�(th $m\le nA� ��p� $6Jn_p=km%��|�{|.?of!�%�I>Vso$N!dk�may">GasF� N lea termk!���geg �nd-spoW"p=k �it� Ee$�+�!g6n�$�)u�$. Zg%kno5_,M�x �N$!MisA2�Yns*normalize�,I�. � P$ (� para�# preceE�"� �}).���= Y��f�]� prop[ esM�i012L\j�}. 3 [A e�$D�U5V$, fillAgapM�* 5���� they%�7:5D%5 a *-�m�} (dA�u�)A4:� D= D_1*�APA�e�is)6�%�it doe� �;&e�~�=�)� words,!�^o�fL�no=}Q� I�. A V~r b� �dMsits]ZVM��"to� 8,1*�  *D_rZ �1s.�aP!Ri$!�2  (1)�V ors})�$Ii-� lter ng, so A�a�$D_i$; I%��5�}. Not/"n �P u!��ai� �� or. �(M�1�$f2�\� iE�2 , add=( al backgr ,p rea�is advi�(tVn.U0� mura60,2}[ Crom�" !c }Nsh~?Bh���&ah%1r� " JRia/6 its�� iA?n�FK� �,, .� < Akb< �j s re&&0d by $D,a�� A�,Ap� vely�$n makh+�(fa+&3 �'� %_M"%!!4S* B��5 , up!�sign,!�8�d,JGsH�_1!&nW_rw �V�&w�V5� homo#ousU�uE�PrzytyckQ_MPQ < %08/05 AssociaA�  �@u�[xB��N � $\Gamma$�)x!&$ m�(0. Checker-boL$l:- re�I-�q��black�whiteI���dv� c� �&R�' D f. Two:��� x n edgaXr��a~b�1ga|]��A�a�-isAar, (!�4y) �� ets,��changZc!'s �(sls9se��dual %��(26�n�Q�U e to cJ�s� at)w!� ���&� ���H� � n �egree!�g!�ex5�is�)�C��A!���Y3y��� E<� asHtrave�(��.~. SZ3q��unique�globa� #(reversal. (6n&%�B=��,Af�4ei�b) Fix a1 $v$,�?h�root}%R-  ny&� t!a$$T\subset Q�= ��$A7``towa�c^"6�1�e �Jn�%� exac�one!igoA�!�_ Ds&�0(T)�0��&�+�8T�a�isaE!�the��)qo �� �a JF inco` nD � F�� D�8 (resp.\*)� llE� k�>n2. �$ � Stoimenow� MS} 9h���}�E�$\Z:*B�2 \Dɽ-�5V2:�}�\!�H%!8D22B�2"� �br"CAm)�1�x1cul &8/ae��pu-�d*�� & 9A�Au�9�).iWA��Y��� coincid�* Euler cha2eristicuc>� $,;��Q! trai� ) jR�(&U)KyYG XQ�)>i@-i�!in]t-nthis Z�-�"Q*t{5 reciproc�0�qu�#!19e%s conveni! wor��:� . %. 4. Pm6!n,Theorem 2.1 % \�* [)�4main}]{2R} �k�y P+a�*�${\�D�V � � �� +g 1V $t(DY grea�tha�k*R0��ger $B"�an� +����"�B�+$X� �< $�(��(1)�_ (3) impl:� lengthi��'n Vu7 $*�' %�(a3 -�8�+��ed�# $m$]�AD"�< %@,A�XM�* $ .�)a�!�6 s a2� $Xrn .at!�casm���of��,s"�Z we y�=-* +1)^re���ely m�j6�+%^%�!�ɹ&�́�.part of9�E�a�/$d. �we per� % Aid=��.�kat�{r3&�an �8: ?��)9b�!�F5c )�[-� Mah�Bmeasu[by�>1} toge�t)T(previously M%ioE�acA�5 M(p)�||p||E.?y��� *�!. How~ gN-2�I��N2)�we���le�in&�(ex5.2�*,he euclideanB #h�"�:-�AV�� grow%7� %t. A*� .�eE�$behavior u�6 evw�9we �� explTnext. *�:�aEU�.�� m���E'i�F"�I�$&�md�.2�%�m�!� 77 llelZ �e .�D}F�uag"�>E2)�0��ρO^ ).�� A%�& s $Z;.:�0�%�%60"b))$` v&<�� . To*�"� fami� f. *z �E\edb�.T� �n�a"i:Y�mN'rapid�C� �:!O�.�q_m� ��Z *G !� t%,;nBwŴ�� $(\d:2Y03\�/ /D U $S$ M��B($m$--tuples5d}=W*e" \d_m2Tm$(ep A\delta�*=Z�0 ��j��.�$e�9�* {\d}E�maximalA�$S$ (5 sen�>�r}1i'}\gZdcE,aX $i��RS[E� 5'}A<d}$�'$X�%��  ^��QA�&;� !� F`9l� i���`n�%m:nol esish� bove w��concer�����thA�]�sVQ��uE� .�,U�#��aB�+�tA�0st 2. One easa����Fn�F*r5��%�D$*�s�a 2Y&"1 while a.JFCch�"(%sisa%� subdivi�4��umb�)&�)!�Ih$"- t���a quot�>%$\bar"�byc< ntif�@ach:��� {Gbi-"� �,!��E�&27#}. Ed"4��#2)saiFbait� inar�;We*+Hi�T):�to>! V�~�� lif)�-�!CRHHA*�1�3as vari�%��%ni- a mo�>8^a�1�5=�(\ ��=.R�.D@v]A��<],th�'e=exponev!�^ =�%c�9�! aAS.%H \SigS�.�!�� '`%��� cycl*� ac��,For�+g| Qwould��a Ma�2R!t�&Bwistx}a'd���  _{N4y6)~is&� bRG , �be �4. � �Ivent,�j��.$ o)#R�A%) vanish,%gr".$����p� )���I6!>!�!G�lE2} pibu��_J&�| �^o$�q�:� do�0cancel. To en� ԡ�e6RG ǡezJ���A���I�M� �$)Q�E�)&��? 2�.&Q(K[ht!]6ce�/}f�K.5i>�K�D{ !�{Ay67es:�Kxax% ��4.An�Aest.($�.(Z ex"�.96� \ T$j�.�2�+L�FA�*N6� ��- �T� b� (�exist�0our)lim�n rk�U B�͎he�?qa �zex I6!)Tw, m�a= distA�!>ES 9�"heeoaL A�4|A� tYH. �a�� $e��U����� P�qn add�to 3 T reby Y0� a�� ] C�I.an��>ei"� �I) �4� �A% �72�!���Udiffer;.?e�2� ��W.%xdo. C�tly��! C� ED z?8�paths +�K"I�(��%��@in-ICTu�and an P� 71+�m�!�s. ($ W�&tubE%/=e$ poiFa}�.)�CxE�AN�Y�C�� Y�.v_1$ E���$e.� yK�"l�G�%YB*0medskip{\bf C�K1&Z@$ BG a[of ��M�. F*G!^?�%x.�, "e'�oB!/Qx%ӹ�I�C&�%%� r.$"o@ must� � = -� �{. Dele�9�Y+��e> � ` �xjt�[ceda� '$, &cC$ea�FT2JT� +ŦE�^��L�]):��By$���; �yJ��Ne*� re� �nM5D is=2g)ewZ)"\ )��� y abX8ofB�' �J�& ;1�8 �8. Re�i;4rocedure until 76�$cq! TTZ�I�i[\sf,Ti� [bl]"221 394*�S$a�8 [tl] <0pt,2pt> *@5 218 \hair 1.5pt.6e$ [brT196 3722 '$ [ r65 312 H82F {oldg } [tL59 162�T!�%�#397>$�+�B!�}z164 81�{6�B-34�CrUME"�iIR�T.72Y A�, �TExeε�a�e�e>uiT. UD�~6_ GX7"!]��obe� &�K - F&�2pK.T&(�" (NI� - ��at|!�q.O�is6X$1 ��06�z .� �\�' Ag�� �'�"� z� r2� U�5*���r� -h���e�R!�&7�GyIt*� 1� part�'ed"�!^� $i$thB�ar,፡�J �0�M!� i,\ @0�ru@�r��a ^,�>� {m_1s�2re ing�"$me%�O rT!?�J�$27@e] ���l cTA�� Q�)��1� D$2�! a�"�nyp �n%w%R them�)a0 ) VP"�$B q�2d_1>�%J!KN5�JPQSN?q�2,�M��jvYosZ!�1w� rk aeyeD� Z�L `>{}��� $M_e(\DX))mplet � s u{mN E ���O:(2Q> true�G�. B ��g�hcla�%��� be)�M�9Qm��! .Y.�yelabor�*oG#$ eme , butK!�"4ieIA\%ESN03}E� a biM tra; k�is *�(�@licit (though lik'st�E�opt?)=P�ba2�$�ial��|%� 6�" 5. ExaA�s&�"�"{}#�6|0N�.`� kno`b* ��a�nE��0r} e�t sYaly�%�@!'!�t t illueS+i��ur;1}s.� >��.^pretzel.A P *~(2,3,xF fty)*8 =)�V��exa�A �*�OA&���0g �%i�el�0 2k+1, 2l+1)$�?2 � �,5%D2 ,?�� thirF5,�!"/, $k, l�0�If��fix $k c��< �)-�y�byA��%*>;SW04}�U�*�!E�!&;"I�E<>�t��approach�HIN$M("�-5�}(x,z)M �(?$&A6%�a��$2$--;��I�6� Q �7� $k=1GRem�� G�#�v% � gu�z�$5h3--���9P.�2LwJ2 y,z9 9 :*%2\brea�5> 7>Ryvv�"h&�7���A�7E�en�-6kDj�v-%�d w�A�E�<�7"�Qx.N"*1B�I\,=\, 2&:�(x^{-2k}"�T(% (???) % IV�you? �Z�wo=�s��5� otomic` , $��= 6�r��H�"&W"v (x�FwYX,�ic� �l,�$%� -1)\�a [\ (1-P]0-x^{2k+2}) + 4}z6_}-2  k-2} C,]. $$ A techK/ of D Boyd-boyd}#@eX[�J 4.1]ic ) ena$s uqj�)6U\�.3"LN)e Oley�.kf_k(x)=>�C �)gL  �I Rouch\'e'A]e�;(Br�-��ChurchY�{BC})��s n���]&S/�! $\zeta_k�� �%�l1 , a )�TiU5�0��� d�=6A�moduli!-5����( �WC)u!absol���>��7($M(f_k)=1/| � {k}|�z�*kQGk'�emN' w,(x)-f_{k'}(x��� t ti�D2m9�, ��$ ?!=v;A"mon��A�-0^p[�., 1a ��'}$�gn Hk'�.w� mostfreal ��At8F�]!ju^(A�he:�1[2E!i+triple��in�6AO�3"" valu�a6]*j!ZM\��"� X�} p� 2]- 2$�� / t �* 4 *zL8 22@KDh#lu�QA�6r} dx;�]�$5hyp�s& � ��M2� is dropp�"�F.w r n$ [�67 297+ ��i>K32� Non-.8 kz ��n*� � 3ʴ 2}���7&� L&. z�Sn9� ~,~me�#���$n=1,3,5�'a�2� 6upp korG<hV�"�V6�! s $k�He+%|@k# $4 kCX,)= t^4- {n+5ZP t^3�h n+4) t^2 > +1�B���q�>!��X�8. "�,A�f ,=��s<��m�y,�$c��Dhaur��G $(n+5)/2$�sov"��� at� Z 08$)�&T volu�p�5`f3m�8 (by Thurston'sa�erbolicBger���;!� Lacken.. �9 en})�#Sly&V- cor2w^p fail�/�,�U��assur"2�kR�Pd�� A��D�&rs$zk{%*� C�5G"�`�IE+4}.�r*�ka&F:n i6Nmn!ua�foi�d� n��d � a $8_{10�Itefngp:, alway �l�lYs)of ^iteness)top�.ya .�I ��'��5�ng�e�1 = 3�k_2 = �, et ce�!l1m  T$ <1pt,1�320 566.�$\script  tyle8 <-.2.:37 376o^:r.5 s876 427s)$ 80 2>2336>-8610 9.� $D_3888e�ao4B�42�aoE�Z>�5�g��Q��Z:Weimi.� Ij-1Rh-1})^{2�Yu,�252tCone l��e "�PfieldA�f�7�E�"*�Q[t*�Xvi]$�tu@ "|!i�\f duloCNre�ls n_+ - � _- -�--";l~S�(+ A- 0� �;k�l� � �%�inducHa mappa[<$F:S \mapsto F(S�WD_{D(T�C S)�0"�5QN�  de'*nator �Fm͘ ��T<G.�0�C��5}�+�5��Ku�0K"�rpB#112�S$6#5�5.�!'"h487 14.�{2%} N -��40E�e��3B~52~L.Xfunal $F>� 5rk�"K s $S�kS�nB� 7�m a= ��� E�iV��-G T = zV S_1+}V S_2,�R^ scal�h�N,gV�V�[�_m{T&nQ-9 a�} !� qI�I�S_1 I� � "2  ", ��eq5.1-=g�ay)5Ab� bev�� 02� !s!� 35 72� %�� 200��1J�)72I B%��,E:�7-V���an�d)�m�!�$f �,ubstitu2psQ~!Wa�Ay k)}Q$S=S_1�'�@��sI�quJ � , $D.�$ ivO2>��4U 4 n unR�T $(.{�A�I<02Y��so %>�27W� , w3S=!y N!�L2]�av�"� ,$]�&a Hopf�f�4 . So>Q>�ca,n }& =2 3R(�(���T)$,+\, .5 A! \cr &=\�B.Av. a{�.B�cT4�[=�Q!�L.� $T6�2-~1tE�:(%kbI � /1�H= Y2�TZt #)<)V�� O� !�"6 a%a�A4} unn  W� �,a�2R 5 vo� qc�3n"�.h�! (@au����m+�.�!O� ��e�6Y2� zH:j�(dQ�# If���"} 2� iH�a��i;kLr�i�)a.� #\tilde~Yith ar�oi"�[)4%]2o)�!C {\sl�}\/ NQ`$1YY2t��97���sult was!ove*�Jkalfa�4An�r methoJ2an.tOs�G@,(admissible)=��}�7fa5� intnt� arbores� >=6�%ive"! &�DA��y5}Hlnind Whi�u "SWhQ�s�5 yeT J-4�%�!��A�-���jMp� 9���bZ^� o�L�+!� s`}meridianw. ��Q!to M�A��?\biblio�$yR{gtart}6{�3�end{doc(} �^\%"$[10pt]{ams Eu�Qckage{x>,xsym,amsmathsymb,}icR1/,[all,web]{xyyddef\urlfont{\DeclareFontFa(<<{OT1}{cmtt}{\hypa� har\/='057} 2\�Y \tt; :0penalty=10000|Zorsfs10}{�F�Shape �!(m}{n}{ <->  .5,MathAlphabet� �}JE �6 Oper� {\im}{Im} �% \im D= immagine (di una� z�@)^Jd}{id.Jd Jfu 9�8ta'ZBSpec}{ � = � anellojAm Bm}AmA ei pA, chiusi�RHom}{�RHo! = gruppo�f!!ritto^Pic}{D Pic � D di PicardZ�Aut}{@Aut2@@egli automorfismiZIrk}{rk G�rkS=qDbTing}{ 5 �luogo�oaSZtcodAc !A  = en�e�.Ltitle[Geometric TranoQs]{RA�Tauthor[Michele Rossi]{2'dd�+{Di�nCo!xMAy$atica, Uni�Lit\`a�Torino, via Carlo Alberto 10, 10123 $} \nyl{m �.�X@c o.it�8thanks{Research%% ly sAHr{� Ital�� PRIN�ject ``1da delle Variet\`{a} Algebr} " (G.V.A.��CRS f�M'�{a} di � (l I�" � grant: ``.~!)che, �Oi�%i g1�D�O!Y�fis/").! def \a{\a�� } $e{\epsilonG{�* g{\goQ 4$\so{{S _0} P{�bb{P}pl^�bpt- . ^1 \p/ P/p2{P}^2 pp3.�[p4.4 ,r{\bold���"cal{R}$!loc#1{$ _{#1 @pxb{\pi : X \to B 8co oNO�coy._Y -Cod2Dc2C ,c{\chi _{top\kb{ K_su{\o�[name{SU) spin>pinB }} %%DMW:MW7rk:rkso:S5GL:GL6f{\:{1}{2Z) bb{ZHHCCRRM f{MQ  b{Q}at0!S �F} \new { }{0L}["L]2'��`}[ 4/L2/coroll�?-C:+n��us�YC2-lemmaT�"��*{�� }I& `) rew&6` �Rb%sB&sAc�M]RNe�*N�*6� '.v (s2)*{&�s}{oxX<��2�io:9 nR.1!I�*{cla�C.�(*{step I}{S NIV V!V^V�< ccofP{\cy}{Ca\-la\-bi--Yau��ne#$ka}{K\"{a}tK �A0hookuparrow}{�}h90-4.15pt{ }^{{}v"�\.a}�� !: ab�+ct}c purp�A"is pa�i�%&,�-�'hand, �11jl &-� A� �opologZ`� �Calp�W$# oQ& t� 4zquick�T�o pir ,| cipa�s�&s,�Pin ��e�s�VQhysics�9 \\F�  \MFeof ! ents)�page A��!6 a bi�o�:�9Y�a2mplex&\bW3!~�s�-n�<�$�b,�1Uly �# , \c reefolds�\tMreasonR� s at�}V�P�?of)895� !�)4�Wno�Snt&և2!�o$Mview,%̡�ertu "7M) y candida�1R�S 3--d� �b!�nalog1oVDaly�Sd�q!�e� betw�bK3 �Ss. MorB'ecise�=K3�� ive� fa�zMF��K}�Yenu!%-�N�,2� -i�Od�'sp�c*�=A3!��$A�ly9� �9s�/b�e�6 w�b1a�0~of ``"�X "a``` i �"!EAN3--ML�uis ߃n� 9fam!uReid'�v ntas �8�un�2on deep�5us du�Z H.~C�=sW <83}, R.~FriedmanS*886}, F.~Hirzebr�Y��A� J.~Werner C 87�0U�On�.p�'I��'Q�b,IM2� tool!^-pQ� ly"�' �*actifi�+�o4 U��106�@type II super--st�7� ory vacua�F �_0BN�F T P.~Candelas, A.~M.~DaYG�P.~S.~Green, T.~H\"{u}bsch, C.~A.~Lt�o![4R.~ Schimmirgk!1)�CDLS88},-rR-HuJ88let}����6CGH89?CGH90[���Lterpre�=A�aR$1�a��-tٙ=��"%D!9 ��n&R�c 1995�A.~StroRAer �95*Ht�%� he v0 �\emph# ia_}2;.e.^�wvIa&'UZc�6�Cat �*"= doubslin�A�9�%pivot����eV�� e b�K1�ly�Rstood-�BKK%I KMP9a� BKKM9:z_s4R�i{-!dl �)��8��orizE� sabL#&)tQ_ &�oa�ᇭA�de�Dses \ksK���'$mirror sym� y ex���ZIB8�6(seemed natuy5�_"a a� B6-.%^��}]� �|ne�( a co�PF��Aes.�� n�C-�4Morrison99}. R-2z.�ta��a�Musefu��ol�o�T"�N�mD,�.!/ten�6, �)�to>deM���}�eBatyrev-� 5���)-�*d��a�S )ej8-BC-FKvS��M� ��  s0469Inms,V�i7new�Xa=��0po�-gh_u!W?�= Qqn��5Eed open/�#<>� dual�[ �8Gopakumar-Vafa9�NOoguri00�vU  .3cmW0es� \isD3��E<.  a 2�� �E  .���� �;graN)!!r1 to 4:a�ep��%Jl8Z*%�"noA@a* � �<i"% ys�K[t��rS devo4 o p-)a,� m��b�O self� n�9treatme�MforheduO9 stud_ �<b�"a�F� �%Ehgn �7 s orav1H � elop�detw+;) � �%�! l'esempioj;E�M bis�k%c, < cambio om� o"n���1!F-�!\i  to�e�� te Uoun7 !��[a0��� �5�l�H�G.nAw E��Vl�iy)4@ twenty years ago� &� ,%���%p�*� ian%� � �<I7Af �4@fi0�WBi+i�3�wte &���9a c�!���f��u?ds AA�CerV�%�is� I�:fer�fto re�%-TKel&mIrgDq�no�>� L&7s�a� aic 5����y2BL yC5,6,7�J-T6� s�kapp"�� ci.is�F� &� $r�aAeE~%`ly �!EoE � fac�Und�%}�s�� topi��alY>I F1  r!y��5�*gi/p_ E;,e��,\e��ed� veys�)!�A99�sub�~>�]a^organ a�Cl0"� Smk on 1.����%ݍ(�V .��"n5�funda�alA�a non--H!coB� invol�: quin��� $\P ^4B%deB�2��2�a �^ sed o�sAjiZ ``M�� �N3�(s"%)!�'��f.��Oa!saxn�až� �.} ��lgc1�)��(PropoX�fe�s �)2�Inqa 3%�gl�h�@!1car� � tudi� re��ach� C�"z"A+!-[ thEWpof[��!^��.( �>O) � ends upc?%���]=��e��gen�k�J~s, .��(Y.~Namihawae J� eenbrimk-�!kawa-S  nk95Q Bm4EFa�.����oE;cs {AA"b a (a�O in�:)�/ss"@�N*. Mail��>� �R&b, M.~G��-�2m�,�i6-� Yded���s .���M�{5 Ks how9��� �"# h  employA�in*� R�la��6- m� �l``i�Kuc� "!�� M``unify"�e"���ac����}�6� :� role play�N���B i)} , st��ng!D�Nkeb- o^ �.e��-� 7�fur�GiM� 6�t f��.�cA6ͧ4cml$1� bf{A� l�I�/s.}D �Y� to esp�L�Gank}Co~vo!�Grai�D( sugg��E� stimut� scus9B�AA�Jint Med �Lo t\ kin�2problem�a�Ix�6mQ M.~Bill\'�( I.~Pesando� k:� ab7s� �W -�V8":>�!�� ���seWeN{Cala�"$by .~\1{cy-def}TY$Sa"���x,!�ive VyB@$\dim Y \geq 3$. C will��Me�z�� �yJ]�zLerate�&\item $}�wA<^{n} \O��_{Y} =:D3t7 $K}_Y \congO}_Y$' J h^{p,0}(Y .0 ��d \fo�F 0!-�TJc�2�)�s)Zlm6�<val� nAI@�) r!"���\"!fy�� n.�ISSq�� izb )X&Wv��=o�  ��120]�� ellA� c cuWM9w�[2V6 $K3$�  - �+.} �%"WG.b2 3@2^4.05�th���t�M<m \ka,Qu,Yv>AQ nomy@-7sub&N-\su (��kYSK(cfr. >W} ! �������ͅz�Smo+hyper�A9fʼn1�= n$ (�W Adju\7C��A�EM(Lefschetz HS(��*�2�Ry(if�!�k a we�ed%pr���� (q_0A,@��R �5 $d=\�si��{n}��MSE<V m �!aOS-c"�rsys���\�=su*��good} 42� � FanoUb�6�94!߁ � Suit��̅E��s.... (�A�SnD1�2t�� covez�:�31pmif* p�lPM/)] 87;(oc4 ]solid)�`]�I���* �*2\ ����.*>�Cox-Katzy iAGR02}J]H ����$$\phi : Y\lVa�# \!&�"{Y}� q�V} +1%�/}1��7�.`3)�x�����V (MWe�7-a  $6��U2�$$\widetild��Y�" of Ix�P! to>7��:3 ��+�}�@shortm5, =��~ T(Y,.�,2�a�rXat�5"� �W*��\xymatrix@1{Y\ar@/_1pc/ @{.>}[rr]_T\ar[r]ψ hi}&E�..�A{<~:]&2�}\ Q��A*� ��0U[od )�t�4a NwE-Ya�Y$ �d�T)y�ߵ��}g "� yT y�s�",occur}: e.g.T�� 4.6a�iBWil�2}�?a.$ � ��sc* as ex� �%divisxrVi�$s/Wdow�aC+ $C2�I�j�ly2yT�E=Y�U�! a-n"*0 $  &`|Ï)HH?re��K*Gk "y 1 (Q B: B�M��C"@/�~.M"�2%9�%2� s $V-��at wors�nod�T ngul+�� )�&d:A �y+ 1.11 h�ao&�Mut ``a��AA� �L���EqA�V$!�2Pe dard $S^3E/�C��S^2 ID_4- �"m2}�uu.q/.S��Qm�ove�3= 5Xlym�" �,%?$s} (nodes)�2, EN 0 Z o?\c���(� quadric� r�X +1$ (3��' �: V�%C.2 .�V2�:%�1A:'4$�l"� +&� ,� "9GMS�"�H�at�U��Z (t)}Rs�聹a�X4 Let 2] �t 4���6X | �A���4Qm1zJ��x_3 g(x"�  ,x_4�Ax_4 hF= 9CHaW"k�gc@h$E � ic 1 7(&�:E� 4.>a3�T�GBN:! gT!� $X2�=� = 0$J& T1Q locQ2��%_A��-X1HD66ita)J\V6(.�[\{ [x]%|%� |�=x_4=g�Rh0\�Ae�,y(o} Ilng:d�� o�by 16�W��e<2B��p�J��ih�QtoCD�4�W5^RA�DpyC"A�K e $p=[1,0 ]I%"N >y with�  afX] �"�#��%D$�1/� U_0 :=9r-%q0\neq Bg,*} Set $z_i:A* i/x_0\ ,\V�\l� , 4$�e½a�c U�isdb�!y� ��>�QPeq. *IN z_3 * g}(za�z_4.hf�x_0^42G=q�> h}=h$. Be� s $pEX�or�%��5�T$g,:�Ny2���=*S (�mo�) IT[&G g2� h}:\C ^42 C�isubmers� f�Z ��! a s&rt $(UsY 0?e inA�0eC ��Gs�#W(j�e-�Y(U}A�:7 U :%�z_1 +%�z_2N�ع����em��.� [�re�]��'lu��ZK}?s>tan��7!sol�@! D ]�m~�����hbƳup}9X({._� �of} B Q��EA�j. W}'tA�&�1I�sbA� hat{� }:P} ^4\x@.�� �����os�)F� %��1$--bundM2$. Let @0)W!�ery� ��:� !�C(&A�.�A�kM�Z2�*lpi)"vR 9%�B �j2i--.14 $y_0x_4 - y_1���Af!J (x)~ �N1 (y)o!i~YOSllo.R�l�rio��narray��e!-�a%i��>�$&=& 0 \\ ��E 'F ��y_18 ) +1� i�uwIv.O iz�= �m� !��U2�_{|Y}C :�� .�%�an is�sm� ��!��62�)$6�*=N<PphiI@p) �P\^1a��H��P ��F�* /.��m�m �md{2�&2oœ60 ($1 < � Y -1 =2$��To0�&��r*�j}aL!| a�,G:b �K_{9�eP} \v��^*(,a!}A�(4-2-1)E .%o- 5M� ^* (H)+ EQ�u� ��&$E�%-eJ�� 2�� $H�~!de��.�I  J�t sZ"H>K}�MN�,cal�)/\on'%)O}6X^4 +2'RD (EekM�B\YBPs6�n��^ :u}nneth��mul�/RH� Y,\C � . ^46(%�@ 1=��U HFe )1)=�dF�)!�Sy* D�.�8et 's= =d R� H^2 �1��2�Y,�^8B��2 �( = h^{0,2}  1A � N�t � ing]>�a�iOob*-E�k%J� :��Jd(�aVIn*{-�,9b\�x*/e�Y$ �!��*n�l^ 9,b� Apply"Hle��8e`s&p ��B,�yMxB� $�!q!�8 ��i_nmb�=�� b_2 ih1i) ��AG1,Y !2�.2Ih�� r���nj�mY.�I} fib4� �8"�:�I9� of} P%$L�����(|<�S �!] 1%disi�=a ��.T2 a"#2{)"Z1J2ƈ��"�mgi�L:v>,p�s٤ *o l�A�U�: �� ���+isu��&IAf�)F� �$�[�"|���a �J��1�-�-�� B� �, mean athbO�* ;% �.olo1�, ?�'Jh�'�,he�VD2Vimay2^( N1�$q#h.�"y� U$XxnG�*� g.% � U�Q���x�&�U UCš|>�Q� 2�z_1��2�= 0B�!*�M� ��P!K-�F Ti^i� y6�~ E�[.�S �,.`>Cu�K�!: - *g � ��-c5 w_1� *ZF(�3)��\� w_2.i}{2}(-n/3/�F(!b4J]4.]2 /)�B<# 3A�E"p (e/2�)?-�1� �!jޤ{4} w_jsV0 B *} DП x�6Au��ri�N�xpar)�"��v%�$�"52�v_j#&�M� �n�g|i^*radiu"rho��c.�a7--sp� Z� S^{7� rho}:=\{)#�%2|>� �+> �= I  :�*} Cu���� �!U}^�2�_{I6"U} ��S^7 !�f) =�Rgsqcup 1`0}*�Uj);��_E��irb�.� U}q *��� A��D[F׭A�ZRA�"�/�!�A�e5Y��� taglio sf&o��F{^�� rho^'f>#%�6�:E"E� K��::8U�<"j Q��Jt� � fib�AQ%3U��)�, / \sqrt{2} I�vQ�:� �= � ^2/2 \AiPEgL vn $v^o�n S^ xw%�"� y� �E:�ig7 ZQ6@�o5RI�ic��a 21#� .? /1'$2��� k4L�u�N�.� }]��3aM duct<is�CI�� N!\Ra"6�>hex � U)J� 0t \R^4 (v)$. ��@ѡ6p$\R^8�O)&r9,�qu����Q:��5�mMd�:�-t�"V��&�<Z;, $T��B�}���N3g%�� &1:� 4&�$ L;��� �B�7ritz^ M� \ .}a look�V��� ��CG��U{ � ��I �)� (z)J!� =�-2&��i��-�.$ y,2��� I�A�U*>| !!>ty_0�- S��(Y"m 'G '��Bds.0 � %�-k(q�a�0&#.-OR�c� { .a.vof>� &�%*16?ag% 2v� aYyN 1_{\C��q��apliy%$z_j$ i8aR� ,9�m�9�)�� ��T 4_D�"# e�� $� amj�<,by $[y_0,y_1 ! �.@�%?\em!=�"�5 &� sA�ng[/by �F� *% n�& j: � � + i � E0N2e�.�^tI b4>� t��-�� MR\P1$��uI�8ri���Q�1�� "o7$u}=A\left(9��)�7v:� �#BWm/+ce di���( qZf�%Qt{cccc: 0 & |y_0|� |y_1 & 2 Im.� y}_0a�)ReV� -P+Ph-2b9&^r V֒1&N�U^�v�- -3��#)d% -� Y!We��@C%�x $A$ (Arɗ�)' !�)3A��*h Aa��ingA�A��(1.18M.F��B$+$[y� Q�,�Ra8eaE�Ȩ�A 0SO (4��nd�n�^F1&Hic � $^{t}; + B�D�f.y$\Phi&�U.�� .��#�Q�5�mJ���\ov`�9)�u |D: &�s�#lon.z &&%U}2� �`  �lI� & (v,[y]ak�l& (!.v, \\IU � ��  ��n�?��A)usݪi�Fifr6!`-��Z ZE�� �rW�}th�qw & ,���U=�B  =z_4��!�s�a5.��$�1 *} \*40\va�$:2�a10&.� :L6� i�s���}.U $ e, bire�, 5 !!y=�!��%Ņ'"\ � OE�(0�U,���ain�nU�phiRD#.2 s-� �r )"^1>� congE��@ {0\}SW�6� *} R���B� � �,6� 6Tw (} )6mH 9!>%s &N ask w�""�"�/1p @�w%gz_Ar!����n'|fpYWwe e.["1�uesten ?� �_|*�.V���I� �2i�� �� �M�2nF1�A�9!��*�  }��" A�m~�v���m hold*o u� .�&5 U} Ml�r�A�"�/\ *� Y)Q�E,@{^{(}->}[u]B�Z�miHE�4>:B*D �Yw"Vit 8 roh�E $� =(Av&��%:r 1�&� >��2��s�vZ+��facN�|u� - |v= �v\,A\ A\ v -\  v\ v�6: *} s�Q�`�rthoglYb���K3ZJ� A�6Lu_jPB�~- �v�z�6fA�.n "kng bi!�ar  . ���./"5� b�ff193-%t�S�: x122�* vect�6\( &�a#4P^1}(-1)\oplus"n!2$u�2f5e�a���=:I"��a� �a!!a�/�'xCuc�?-,n`�,}���67:")6sg 2]!I$Hit�{ 2{�90G���51�"N} 2�|�c^{1�n�&�a���c-��Et325�b|b= ��GraSndiec�Neorem!>�[�{R_�r��T}]t�%Eh;�}(d_{1}M��*2��M)�� *} C�ll&e!"$S^{2 � 6{) a[�En�we�!�south �J��vϸ�30tau :=y_{0}/y���sigma 10�;Uassշ�.�. LifC7t�R�>��B���PF,�s�mtwo43.Ca"��TN(! ;t�,t_%�6 , (- ;s"s"�=� patcT%*�-�l�E!  �J�!$(%r:y_1)=� : 1: m(J"s_{i}=� ^{-d}tB�wh))6+$.~"T�f*_9xm GL(1,1�C})=%I�$bb{C}^{*}$2�ha�]� seN�%�=z!x�2%�4}\ ;\ %�=-z!�!%�!h:[  � z*}!J1}� G=�%�}1}}�)m�Vj7 z_{3^646�h �"h�wepE�$�E=d�=-"z,\2R8V]%?֙�!�́�F �GaM^��U� �p�" 1-��Y�% $f:ED+U}�?@\R�rb�lisci�Q/ U_t:=f� t):\�\{-��{c�FM �:�2imt!�8Bu� � %%� r �:�}89['�#U_{t_�K�xs�Q $t_0�$ \R, t_0>0eTf:�#)� F_H.�c� co ;S  $T^*�$�@!�"�.�& �c� S^3�\R2��.% of} o����mbe�Z$�q,p"�"�<�c��uAB�q�!�1)�!� _&�!q_j p_j#2#T�.Bs�K Psi 2 1Eat|\<`7'#Js ���mu_j}{�A "�!}I�}�q �v_j��2��)r"c����lm^�W3>+�E %��AR�!�� !%SNva���v�we�*I�n e�.L�?�Q/U�SxC�TSm��T9��QH�ciclo ɨ�vhS�_�U;i�{&t = v_h�\�94� &�{if}\ t�"I�[-=u6=uV= leq =�n0BpC�A $S_0�#�U.��(fin ��S}:= S��. &��NGHp�Vous1]��6�eA.�,S�D&e 0--�*>�}E�A�-M�U�%�+�|L�>a}9�M�HMfsympl c"�J $(M,� B"�D �l�ngian} iz P2�3_{\R}L!�di M2�O"�4�L ,"�OX,YT_p M� �_pŬ (X,Y�0*�' nume�PE6.Q��q0-sez �>{)zM%�1=5Q$M8CJ )֡���} .h7�7q�� Q:=d�theta+� va !�An,Liouville 1-zN��6@�oM4a 9�2 � -].�JU�qq�IYx.�B�a>3]vZ  �>@.�S��^� �2�1��mI>e��Sa%MS��D >si^*( I)�,%�"R�t�qU}�=�\mp`Y�K%�-�_Y�.Z߱��%-.�|�\{S}!Es |_{S^32 "f e?-],*5F=T[ le�qL D_n�� \RlN_;+;edk�bXAOc{*1%"�8� \W��;F[S� �)s�z!W?�}{+})XU}2�D_�5�Y�\.Y�96Yu)���9M�YHD�*�(�D_3Gn�4P- :�(2�-r}a�%ub}G naOborhooݞ֓z� ���$� ?.b) $��.=�U����.�"C-�e�st� 6�Q>'c "��\a%x' �(!� "Ƹ\}�!q&=�B }{:�L*�&Q3BQ! & Yp�& ( , }{|u|},� v 7e� �I0�!x�Xric !ID�B&%J�ncB��Pp�ZalA/E�)=.�! = +�A�B�Y)Ox,)q��Zl}= \id�� ��E�< E#�Us4�N p }��-�+ Va��"F3BtA�qbe!�ed[ͰM��-remov� eDdpa���.�$�l4i1:� $ ��#q�\� ' Phi* n>sit��8 is described b�ay the following commutative diagram \begin{equation*} \xymatrix{\widehat{U}\setminus \P^1_{\C} -Xar[r]^{\alpha}_{\cong} d(Phi=\varphi& ;$widetilde{`S}Fs>\\?(\R^4 \�8{0\})\times S^2��'~  S^3 .K3BK} \end{=Lwhich implies that $ �L$ induces a diffeomo�Dsm from $\partial(�D})$ to :hat,. The claim )�4s immediately. �4proof} \sec!��O{Global geometry and topology of a conifold transition} Let $T(Y,\overline{Y},\9�Y�(be a \emph{G} tH�(n, by defin] �@he local analysis�0the previous � we know%c:Q�itemize}%�\ $\SA�(\o�x)= \{ p_1,\ldots , p_N\}$ where>$p_i$ i!�node; St% exist simultane�resolu!d1D$\phi:Y\rightarrow.�pE/G bira8al QCcontract� $N$ &0curves $E_1, �, E_N$.�$]M$Y}$ admitsIvanishW cyclJSJ|S_N�are 3-sp�sMY!a%oaSJ9xU� \noiEE For5>$ (1) noticA�at if F�,{16}]$ would� IM�!&��  have5�que��`bA�)=2� )+16-�1�s s cli� radi�4(%�,betti_nmb})..�On� o�� hand, f2� 2) let us0pare $b_3(Y)$%i 6�$a7Ś}2 =174!�@63=204$;�n -6-2Y)=30$�z Y1?��89P�;statem�D i�;�y�Q:C� coun�their1(!�-�GMS95:q Actu�^ prov�}!E� do�_ needB� ofaE{s, u�a verL epera���. Ii� �A�we pres�!�us!�\cam�. Here�f!r most:a cedu� o� $F��J5�Si�W$�`N� .z \mid H}b *O* P^4}(5)\o� 6.F}=:j(5)��0heaf exA� sequ�܉�Z�\= @1{0�r]&rT�2� "��.63ކ��L%*2!3a�&0F��!�assoct d co� y long>eM s as�B%� 8coom-succ-fs-tg� 0*I ( H^0 \left 2t{6� 2 ) a� BKH^0RI�U� �bVk�L1R�2��I��BL2i� � } All��e$ form� SAFn/ de$� AYYN ]d withEuler:c>vQQ ,ARILr�F�mB�u�3!;0(1)^{\oplus 5�8e�8\�� �>�}e�5�� tensor�� duct��?�24�� of%[struct���� ��4.>.� ^�!}a�str��~�5)--z�.�! 60}F. }` �S ]Q)>�narray� RjC jJ|%�P��1mN �RH: G�Y�w�:3H�pZ�2:6A}&&� \nonumberT. �B�^�V�����Yv2�p�\cV}&&�U Botta mulab� botti h^q {p$,} -� 16: 3 = �7R7 ~-a+p}{-�-��6Wq=nb� �%�P�G5q.�u��."K 9 >2��GBRFGI�� �, F\ Again 21-3� � 2� w�.W2Ch� �� = 126EA125F*} � ^�2@ �= ���2V� e v7^�J� �5 - 24�01^4"� argu<�"��N6�, s� it i�B�LnYC bi--R � ous N Q risol-zioni})-1�a =: \P$s *sis no|an �� likeMw a�})%�I\er��"i�z�1�Y�A� urpose du��6T�to ge�+u8 � M*�4\n_N}^*_{Y*\PP B ��lN< Y^F 7 F� ^2�.�:="L H}om ��y���,*O}_^)?I}_Y/#^2$, be�& $%xideal� � Y"� �٧)|���:X�%V�['� P}(-1,-1)$ R4��]J� YZ6�YbS 4)n�Y�\cy, c�-a�rivia���0fourth exteric o}��Y���%f&� ."M ^]n�!�(-2,-"�M^2U�%(.M�{\P}^4\FoQ�F91� wZ�1km > *} Ta�q�,��Y�Q%2,l�%@n K� �9Mone>B���essionqNT�� �F�"-8�\�=1,4J�Y(1,1^9} !"f�N�Bl�C pass�t*EN�in &r�-� , re�>!{6u; �i� � !�.�� 1���2�&&N�*� ��n� � ���UE�%� :�BF] 9�1�z$.h :�Mf H��( �e� �rJ�. 2��2Nj "i -���ob/i�suita`w#of7y�69�"��u�R �b� �$� rAI�B�o)U.�v Bl6(�7>�}n�I��.q��4Qdƪ2���F��{�a� blow�Q $ a�A4plane $x_3=x_4� wh� � o#�X$\PM��"n� B� ,e:�1:=>���2�Mm}$� *�!I���t29�z �P5�)� � by $i�Ed^�6$��^(��-eXIj� 'W��I�6�> B1 6  ,F�60 MF7{1���� Ϊ� Z�1� ���2��MfNZ � K\"unnethE�n�k (Ih^v2#u%� (a,b! � \bigŸ_{� �$-��{ p+r = u q+s = v*4$} ��[V�1*��j �Bh^sH��^r���ɷ]Uu�D�i�pf+�*e�&�R�ofm�.�� Y��� *�3�q�\���{�6�FK *-q.pe� % = 27�*�FR��!F�Moreov�he� by :�� ���"m�6�m JvJ,�!�RF���]jat � .x%resultB�EW�V���I =�hV %�� I0J� e��� eref�#A �"�Ez��) ��"�%f��"ri!&ati��o��b� i].� �g�&=A��=:o5�-���} T"3#� 0J� u'c�$!�6�K&�H�O �.e�2��$&�-��M�\Nf?w (0,3q�B^m�E�.6-2 7>�*B� ��.c��2��"� J�+ .-�.�R 6�Afirst"� � ���e-&�2�. )lM�%�Z5P2+-z+E V 140 -35�Vd F�se�ꕗa��>�F�����Na�4F60} Analogously!�V� 1))$�)>�-�\�CM�6�%p"K%o.6-:�7J�L ��2c0,-u�ڛr7aT�Z�^�Z�2��\M��Z51� +z� & = 10n 9��u�j'fi�+>�J�j�1)A�9N�T��, &��*B�)$�sV ��), 6i � N I}) J*���/gi->�m:�*6, = (104 + 9)�7 = 86F�� �7m�2} "�-��"� 6s� overt4R51%maxim- .�1*o4 >�5i�2!�-R@&�2�55E�9�5turn �4 to be deeL-related^/is� chaF6 erizO gl8ch�/�3t8�8�'R 8(, as explaiin!,�)m1� theorem}[�0Cc.s83&�0 eid8&�0,Werner-vanGe�.90* 1 92},-1PNamikawa-Steenbrink95-MorSDn-Seiberg97}, ...]�4cambio �1gico} �-��8 �8"�4&�8%�l&�"7�z\q7b�IT!�IS,o��866�8$76 Kk$KM8S+l�A�!�}4V��2ic�i���#�D8hen&Q &�6=D|N�9|=:N=k+c2�8(B�4-s)�4iB4b_i6Z ��qT)$�i\neq~ 2,3,�4andZ �4m6�2$2(Y) & = &�5\�B)+k.2�+k*�(parallel & b_4.m46mk4:F0.k & U�5=36U-c.2�-2cF�t))G��:P� vertc4A liti5=r� !"�0{e} DA ty; UAP (Hodge5� )�:q  �{c&9'Vl1 �Y)+��!:�= {1�46CY)-5�% � �:" y�e�v$remark} No�3t point �7�+"�"&�4<$!h�>thA >2�9$�"satisfyR��xe er1$A�2� -F =k"��ed �:�defec�6�} �XV �`1є � px<->ka}� t (3@#-T@7>. �4&�I?icK4pre� on: �RG increa�<�*^8b�%e~�2mBr[dea\k�5�8 ] �<R8 >=}205� rea;<is refer�to-K"�8�da d�6 under�6ing>=4!�)>q�8�6's}*g will�quickl7scribedZ� [PAm� �>�] us denot&�>�hŸa��v$P:= ţ6�=n@ �? o@ \}$G%B ular locup 6�.�$EhLbigcup_{i=1}^{N} E_i Q2�Pf$Y6ISRISIYU6G2�N�.�@�<xBh? : )a�3.$A�%C!�is"$Cq���q�b'_iso} kA :Y&�CE [setsD{\�� z} !� 9P�ZlF�*":�7$i=*GBN: Proposi� �;�  lemma}�Bcam!n/ �C6tubA4 neighborhoods2r8D}_i$M�=�$  $!� �?.��-G2DN i�]BC&� ��5�b��E _i:2r5bE�E_i%j�>� �@A�6�"�*we)Z ?assumx �E9O$'sp9  disj�&6x�EA�s�A�"D5C'siá� osedG)phism!�phi\circ) _{i}^{-1}~JQ�)q-�>�$6Y _iX : �J0%pS�p"� ! 9o\{p_i\+�}"1 26�S��" �1/�$. Se&�Ee��2�����0��2$_iq .�V8."_U?W *} B�t4Ehreshmann fib�A�#�;"�E)�"�EL 1 � .�Y�d%�2��j �H6��D:�*} ��%o �(nd:�W �Qe)� *�l,jk' C )U�s���� S �j�)%U^.=B�1~,step I} $\fo0 � � \ \ YCi6�� C=�b� =F� / Left�M �@\�\6 +N� J|@� �f$T, a0U}_i,O ��)"��ui�B.�(no�  a��>�eIisi ?e})�}d# � arou+� $�$ in P%M�0 � �:=F�a�s(F k($Y^*:�.�-45$.E��E6 .gR�5�!w �Y� GY|n��W ��P$;I+"s 2+*� 2$ = Y^*\cap. %�4$Y= up76 .�^Q� \�]Y}=. �upUte��~wAda�*S ���!\y Mayer--Vietoris machin�Bt"�Cp�J(Y^*,�i� $2�#�|M ge&�twoNc"ea�b�MV� ��*�5#s� & H0.^*)�8�N "Y^*P,  .42 H_i a%�C-1>g#�4:XBI�MV� ��ovDU^�#Ad>�@>�Y6�o2~�Bypa�M �m%� topyA�N�I1 slh-=�H�x�ʼn�) *1E 9 \{B�)Y \Z ^N"�8$if}\ i=0,2 � 9 � &�� } as��/k *� �;`l-�}% >;.Y�=z�P ��� .c���-top}�:W �Qh�g3M�eso�),��a �` *��T phi-!�e�]e�8�3}mx8�F(S!�S^3SS^2��,I5���  b�nbw-,�N-�*yq6b%%>� �?tr)J;"G(glu�F�8�Vse ALy!U�c pol�Jthey rea+��y(F�V� �MV�V�&&RR! H-�B�'�w>� }I�"& *�2{&H� 4 d]&&�RTeN��] ) T. nPA�u]YK&���\�iY} tu �.g �.4 "-_� ��F yions on 2��" F�- )+C : (� ^*)+N) +� J=& �:^*VC2�+N-M.a� U.)@F+� �M�����"�!!�oYR�eF�  :P+ NBR*&�3F�3,4�� Y�i6�� F�!�:<oO\.M�L>�:h=!�6J +N-cf�!�� 2 � nea�T��W �� b�*. �us �1"� !���UN2 ,� )�766'� :=2"SS71��21*&[ SN����� l� � U2� ., z) <b U}$J� Maey2� �0 ~�Eco�  $6^� �U� R��smV-�B� ( & 2Y.1i.�&� 2U�M�F:T��m{&� 1&q����m} B� �&� ^� !#Q�" �=$&X �*N (S E�fK & �� ,3,�5�� "�AT��"��si�nz� %-�.Y *�"�in+W]^hpsR� 1e��� !���a�-Nzt�� �� ʿ )! �B22�� As ��,;!�F+ �R%, !^� ts 3 �61 3,421 �<��N:�)B��4 glue��&� _ 6� i��� *� 2�a� q�% 2�2� & 6�"� � 2��J� 36&6sy�0Z] FtY� FT �.� J6q f��6 ��=V� ��\� "�LN*� ]} 26!��^2c �]&0"�%F�� &�� ~� 2�� 2� (BU � � 6.-N+4 2X :-� )�Bn 6. :���.)ʈ�*��. :�: :��C>�'E :� �E I}p k *�)�t(meY�%�+Steps I��II3Xp�vsd$"e T�  r�)�AY� 2��Y}R.B�\�.:��-b I} �"C(�Ht���"� �AOY)Zp#>�BRKC�~n:H�|2�H� �&=& �\ .� & !0N-c\\ 5>�]`.E�( \\B�H�'N-k-c=�_� )]V} AJ1G��&� �,.�" ual�c"whileE�^` }<*6�c>(#W.� Y"�$�=�:! �!m3\- ,} �*�e*VF , c*�7N"�1`qJ�]-���$�� "x"|f .! %!�jv&� .sSQw Lefschetz�Kty ensur FFeOH^{6-i}(.�) &� ��c, a�-2�" Sit>� Y},SFw3-�B;�Ifkl�M_bn �:v~1)C=�.9.^�0y*� �+�s $uMr6,S at";-.� � 9-I�r�)&t/�&A " &F�C+~a,E� �k!!}%�( :2U6:E. %r2,S ~ b62*2(2D�"�1�Byj� �e�"75�DEo}.i�� h�a�j�(/G"LF+r�b� k-c-Z�&0)o�W� )�dJ#<0 >�U  ? 35�^{\ga),\ar@{}[d]|{\gllel}w2�Q��B� !�* MJ( � <�E��r]|{=�I�kappa}� ��.-�1nN#F�b/0&BsS&O4q��B$ I:=\im [ � : �=3 E):�*Y):MC�? n $k�'rk (I)|/A�&�4�ar2��kof .7* .���'�R>U �.qQLI!RE.1_ FI :2*}USa shorOL+<�O��.�i� �h  6M k6�*J, sb� K:=\ker [I�-�� E�SJ�> ^�N-c:=%�K��r8� oy9�V' Bl��ZOs&r&KM��V�iZ+ B��+0 9q}&�.{WL,�mmC�U�n !eg*�ps?�N>Y07izzato} ��'�Jf&�qN a=Ya@i.w�v�HH@/_1pc/ @{.>}[rr]_T)�^{< �s.< � ��<~:]&20Ry=�.a�hbe� !1ate@ 'm M�Qpe�j�q6 +.��.��0 �L�!.�mW|3on�V1�r�< simi�1toF\:�/!�z/4�6�r(n. Anyway, �2 som�irong) koAoSin>�,2wA�!Nbe said2�3F�A ill�:�2*/ Q3NQ�op"s ,p_rs�hom�.only by[ _<2�h"�2ity64�jHase�Sn a 1--��] flattm@<&�MY?!\Delta^1"�0 -1�6�*3 +y>%��B7=0�&�<5Milnor'� �tj6 68}. C!a$B@WunionfQ ,'sG.es $B_F/**w�rhavdM&" typA�$ a bouquetS3-"vs Interp%~Au��.A B  ex.�N42>,J^iR>X,BNFZin �ag�  /�2>C5Mn��D�v 9�!���mP8>NamR�= ' (3.2)�=NS-thm}�$.�--a nwfl��k �oAeA��i�"aJu�mafkr�n(4 p\inJw$�88 $m(p):=h_3(B_py*he�6II� ns$p$h!yec�G:�i< i�toM� G�i-yb�>� ; 5 b_4�2XR(�2f F 3f$ +h-m_{Z8�!6�J.� �Jb"�ifm�%L�Rt<�7ove���.e&�thb�W�N/Cb:2.:3\langle�O(Weil diviso�B-2��0\r1_{\Z} /%bFICartan�K *� �x�yely�9tAr0belian group.��a�ic��ifKc>*c=Z)cnQk� �(�^)'""� mD a fur�3 i�er�;Aa�^�<.)"��} a3m�G4�� ~"$�G#"�t��A�lly��, �=1��N���v� E%��&MJ2^�< �ico6��;lasL�NG>juvD2 emplo�'Y ,of A.~Dimca �S 90F,$ J.~H.~M.~��C�C856�u�-��,�, �7w2l� M.~Re.pc{u �D15�NM�#v6X)y=&�[! ��� U}ic.�39P&�{�)�{on��a sAFb5�$m0s� �@ �~E�F (3.8.ex�T��}Q 2��P�� �~�|�8.�!,E�I primit�*+<s��� {2-V� uces nente C_idcf [ rank�"Rr�w.*Mi�B�=� �c}��C&� C_r� *� "6��2Fa-k�F.7 $3�B\sum d>r n_i�m%1 -2"#�CQ� �!far�6I , dropp� � p�� N� $ leade��dtha�#terr~n��n� ���IIK ��es!kZ�@� R=Hs� 3Xap� x A,�T� }3{�zal v2N"� s $N,k,cqF2L&\Hs,Jo�0KMP96?AA�wAthese.`in m5Q"��s��:2 � s non-Q0e=ői3 D("kz�> Szba revFw}A�2?:)��-C{CA� ific�W�Nms�d" �,�Zx1�8 neL`arily�B9)*���8�� lway �t �5a� V�� ��=<ree9Pdto a l variety:m��!) ingredi�Ga�e�5*}�>�Fol��:1 *Fa��*�$)l�^�AY*~�� may occur.&Jam�u them� sel�Et^a&$ �;`�tar6�M ��UTMnt����y%�% ��Fof our� �$Eu&�A~tl! MoriBorye�\.�ALet%��K2e�co*$�WPicard *'7� \Pic�7&:=& � � � In�aaShe?a� 6� -*� ($P$)}� "UJeDK j[\ ar�I ival�$($\equiv$)" �Q�^G��ya�1~Wm�0Y &Pic-cy� 1,� H^�\Z:� �3�N]ka}isMn�is �~��5��-�\ H^1 !�c^*�� A�R*kT[R�vIexp8h/]"� e�*�,0\�&�7 � ^{Iexp}}2YV^* "&�3�1e*}� �5���H�aCaVA�EU� Zf�_YF�pY�mm�QA- Kleiman�G}!�g���l vector $^" I-vsI&MR)�Z�]\RC+\R ^{\rh.F.\K�B�bdimen/h�CD$1�.(Q9c�j���&A$Y$� � ��} A� $D�M� TIBnef�;I��K�" ef�ive})�ny� $C�E L �tsb�� nega7ly i.e.>c(D C)\geq&3U�%;.�I[a;clE|J cone�4cono di kahler�- �:1}.U�K}�=5g a6M AaM.IS $U-b Y  nef1���~��O�]E��n�G� Ųre+'��per!� pairM)}��(\ %� \ ):�\�\�,a���arrow \R)�Mi��d^ U#�pr�8t�s *kkM�-��2�NE%��N7 [1�Ampleb�Cr��ion� "66}Q2KAC} R3> nei���nor?u�al)a� �nd�fZ{�-Z.4&� �"�$\{ 0\}�-m?%� Z)>0B�e?1UWcorollar"�-i-%�@ ze �Y��] N )��n$}.(��of *k  i�A�}Eb9 \ka J 7'A�-�FXM��-i�c1�D %�.;&F�� g � ���AUu�� }� . A FQ ,6pfunda�sal m-�Kve��n�S4 mpl>J $[D]A/u�d!6� �!T\�!��u2Z��C��>R1r-_Q�Q`[� hey�Ga�82}���b�At� ]2I�$ (A{ not .u �t"�)Y(polyhedral ���r�NQl�lD ��$\{ C{J_{i!TI}��&�*x"Y$��R�!>�_{-�7"� ��6�Oa�B3|(K_Y�� Z)<0\}=�^_{�4}[C_i] By�,1�b��4-�Wilson*�� 9!®� cubicAe�,UVR�e#(A.cup--�QR�H}(W/W�F\{ >� |D^3����> (�pgon�&�n� �.&� $W:9 \P (uU )=\P� -15�R}$?* ��_in_bd9 W^*�8��:�bset\�alf*>��Y}=:X�lh�ly=(q away �q $W^*Ine�E"�f�Ւ A��c�b�  15 WW�Ii�1 $��B�� �W1Q�W�z|�Ac>T &z�.>fa����$Ie�i�� K��tr�Q sho����,�V��V $D^3>0Qc`�6.� W*})-�q By C���Z�,Dڕ�n���%�par!i�]O J"�s��de�!����Qm$BY$�R N�" L3F�*7PR���*� �5*9��ej �hVgA1f�A a� ma4.ah�Rs6C "\,} (or altern -Next!�l}y& "i&� mark� 1:1}.(?ai'���beE�o�Vin�_Fȕ��2 i�Any�:�9E ����� (or I*�) �!�Y.�Q�pro�on}[Ce�&�C��:--Ѡs"{ view� co�_poF�za� "or cew� �U�{>I�� AJ �0&� y\Y}\Mi��}=�romr tv�AH#� |F a\}�m� ( ��>�set�W^* Q)_{\Q �FZ NV.�.�O�2Z�=T(\ {$$ means ``"� C�''.�����9�"�)�1h��} &:B�SeE�)S�p)�it Y�a' ���Au ior9�%�K cB� j}I %$ � ��~�O)���n�S�o rN{�.�� @�1�5�.�.�$of}[Sketch!  �Z$H8ab p�u�6� Y}$.r�.8;'/�a0 wkW�B�u �� ita'I�H�� %6�=)=��tyq >�7} Look a�O$pull--back�� ^* HO�nh*T��BcY�$ �x5TZ n >���v� Z^*2� ,�9$E� A�B�*)���UX!h!�� �!,!� =_"J�J�=0 :�M�$Z���a ZC t E$R�+e5$o, \?J)$� r .}"�� $ cuR'}���$ ox.@D�Byl�9$[!=%�]$"��NakliUhrb> b!�*����� if8\R&� �-3�2Sia�+>H"�N*�����iZ(T�faWu�to N�A�6.�urv&QE, $Z_1,Z_2Nji�= Z_1\neq62E*M� and} [C]=Z_1+w>}�:Y�� ɡ ��m�Y� }\R.�]\�~�)=i Eko�QF=M4�.]N���� /�#� }��тw�n>�s>�:�H�o�,b�phi|.u��aaQ.� cod.�Zh*E?����*\���$�� 8`&� 9���a]a" *� .�%�2yP B �~Q/ite �S)}*="� .�s�=Q�V�ez N^!�h� izv!pro4!�sv�, $ VR��O 152� ��:�=M �&� d�:EZ&� ^)i&R �.�@#z_!�F� �bo�C3Y��)��t a 1:1:�}.&���e�+ev��d!sU�-��)2� ����:���5 � ]M 9���� !�1I:�t#"P$".�FvR")%�)�J' � weenV;8e�2 Aye�"-.5�no��&P ����! l"BOX)$} (�%"H,�t 1);g 2!49f=[s (&�s)�#����2��}n? ��99}.�e�x.V$r$֥�!��XaCVS�,�;1X�$ � "�c��r�VJ�*�#���C�E�[FE&R[�5�"�%icU\$� b�f��aVi��) t" &J�(�M�&!Pru&chde�h)B item[6+] �� I A, �!B_ %�� <1�of�,ly x��� s]� yzqb X down ���;�(uq7casSf�i*F+Ani2�$a;(@�-d) �$del Pezzo M�}�mG�-0}h2.5���~$C$�F�stillF��e��nicAbundle ��-vP `\�.2�E�Q�U�*�r���] A�)2��6�0I, II�m�- �IxuzI|�*2 .r Q3�mpf jA�N�,G!rH)0=�0s��{S%s~ax(E�. Y}$}|Tu+w�&�SzE�a4J�E�prv(c%n��n|m���� 2�� G n:'2 \&��i���one�~�ble�to �)�%=�sZ�)2F:!2�To��֤�R9zV1*�/Z,o2� z �"3�� ��A�^4� ZJ�q< kind� w> Lo !� 0 Du Val (cDV)6��S 40�8�x&�(1.12))!Myi1�>+a��.�:�!� :�%1�cdV��(f(x,y,z)+tg ,�6 A� C^4$ 2�B� L=0�_Al�� K ^3$�^"�p�9� y} (� e+as�-^.)y ?=V0}�BPvdV84�^��!)��A ��-3-.�%.z"��� ~�Wa&�!�I��3:�ES�} (inH$Ad*�s�s�Z�1�X�?�^����n ord�f|dou.Ɋ(1�Y8����yU�5�$x^2+y^2+z^uP&t]h)Z2Q N͓fac&[ETAS"� : .��[)��=94}j-��B[0eq!6�{,2.4N.02.#7QYGross97a3.8 ng6>��a'2� ŏsup A��:0f0 �wZ:" /!�EA�:��4��,A!W al,M\tiIiM�UU�<��� "d�\y�ot2�eg�*at wo<�Q�M��E�s. E&1�2�� �io"=:B�xwm�~j2X�,�K2@1 cDV� F�4i����2R I).Y$s<.*��A�� ��(it suffices.�1Cr�*e.-"�D�p..ws��i�M�&Q e�"r�<by M.~E�� .�%G!:9"�<Rki�5:)!c� ��*�F>*f =�1�#��!�In-*�,�M3.10,%�!���ҰI"db,.$\Q$--�� oria�wP�$�/(W(Y)/C(Y)) ���6T���%R$<����E�termi�R��E!}.�pI�� �!Y.~���$J2�<�n��C94}h� %�qFF�R}��R%J0E�.X-5 a1.^E��a�' 66{ ,��A.m�3�j�� �9��z� $� &��6�Q�42�$%�po%� �9$tn��=_t �O>�()A�� ��o,:G�6= bu����1crepantAHo1��h_t.�_tR�:����sAveѝ�E��GU�RD_t$b� itemaI  @F�.� � ult essen��{u�g�(R.~Friedmanr%86u"91�H�Ad5.1��f l��� a n�y�? AW6 Ea|�st>юt"D!�:;U�I|$:�V�Aј�%�$ (����is:��0�?Aj��9W0+1I��P 4 �>�8Figid)]R��Fk"��key�1�*��� Vr��=.��s�&h{�"� must�5?,5O"gX�> e?K8QK�P16� "�;.�`�A�.yuniquC�@z $2FE_i B$q©�i�!� n--t����ar�cx=lgu�.7�6�$,-TEIE@. R�Lof.�,B�G.~��*.I ��]��q� 86} �� 4.5| 6"91}2Up8&� l9*� 0.�2 6� 5.�I� *R� ��7 } If�a � &�!�n2".�l�>dby $N02&��T#s.�p�O�PJd $TŢS`>.�>U�ngJdq<�a�s5" 2�$��n�?aQi�c�3�K޽1�.Q ���]���<�EMn2W[!W�� a4 B� :1�]���:�����u�O� $pD(E�.C�+��c&/�in;OM�40��E�7aP &��� U-w�!�upa�6���<p� ��.��%8isv�N�'&E,F?[of deg�D$k �9$An--UBz��s$L� 94}}�XM$k=\deg �)!&'� vari) D=dZ=�BRwewNatJ,2�2.9��*� 2.10):e� 2�AI�[-#2$]�n�M!ua2s.��CFl:�sJ�;g�;3Bg=!*��iplic'?$kI)min�� embedrS&$$\dim �,(( m_p/m_p^2} |bk+a�N�B2Q~ I>B�A�)�e@R9 ]�V,�A�+ry[!5mp$[���3J� BaB�W�*� E y�^ BC ��d)�� ���e�6f� �"� �w�!���"a�A��$i*!� q 4$K�p�' �9 ��.g �WR\a�)G � } �}%�����ba2 !��Bex�!~n�$E&r!"� 2��5.4�5�% E�.SQD��C����5��I�9e� B� precisely��=5B}.t!3.�d��C)�,l>PFA0a Pfaff�O chemI���0Kleppe-Laksov՚�b62/��!�c�D��+r� zX?��e�!]by t$Altmann97}��)nnZ �k=6�I�)M�wM@stinctM�ingB>Z h&e�$b�<v �1B(/]���1\��P2 !���7�DrweN�rdns2s2i8�5I7NI��i�i��:02�)<�h�`ne'N�)3$�n�at'p ,sy͟&D!fb�8�-�$E��=��.J��2�fR2<���uiL��2B�3`��  Hirzebr�ō�65F_1:=\P("O�^1}�m+(-��2Fa�6m --�&U]91=x2)nZP2xw} (��Js['At��Schle٬er71}V�Z� F���a1a.�� I�'/��}&�Jca(8�3�EE-���7 i&Xaj�gnLv)��� traiwP �U� %9H; ��p�l�"��)i�� .R �!E���2j�$F_a lb��a�ZhaU+ $E^3+ %EE=7RW� 5.2). �I!'is.p %'�HB�)�!?: �6�5S**�L� 5.6M�E�5�*��U "�\ ��I*��H�CQ�rFx a]5z ��"/��.Y.�.YS,r$Y 2�'x6U8�� JU q#&� 7.d �k#%�&�EB� E�� &8 6t �a�� rEe1 ity� M=4��NI�� :R&V 6Ris"� &� �ub� 2J.� � nTc/� �����\ ]c?x �"m'scr�*2� AjD�\P�or ���^>A}�8)&,. �z%�r<a�]T " 72�.�~wC=N�8� �y eof��"c)�"gies�?6�;:�2.26�\80�X)N���*Aq�r,A��Kofn2~�!sa%c&e*�a�O_n0?NI�>JJ�n$ it�Ib"�aln[8I�C e���'n�|_E : E�a  C} hibi���a� ic2�+$C��;)fib�>M��Ac�!�Tu.b �s meeiqtb.oint,l�#@*�,p"�4!g� ���QG���C�mh"/A��2.2�  3});;)@lS-XˆEUa� Z_4!�38�$f:4.h���Lmap; sa�$Def(f)$Bc-%�sM%hf$)���`a)G� ;HKD Kura��AQ� wf��ap@6 N'�$ �\:tM Y)\ -3.cP 8!���gen��Os � !�o�d12`![�k(lf�^E��Y)*�2�b6o 1.22�� "��� g(P1%)29 MqV1 �6�}Q��� 1.3)E�faB+�$h] W� 6 +fI1 zS�\6�]$ yield3 /�.� fE?5I.���e�V#.D- im )Fe�zq�b�9� $ vi#�}|e�6aR&�9E�.�"�Q%b� KUO-�D92>1.4�55�2�a�n=6�!�.�L!- \-�K;!�!�-n��}M1=w.�]\A�bz>�pVyZ���� by a��quI�:�'; s�j!& tech�!7=1%��IwɁt�!Xlat4�doen1t oWZ�9�2�i+#mail�o@ks�� kh�]�'� ��=0)�$C&$;� goal!���'�S ��R'�%EZd]�Q�RS):'% imagż! qmap $ FW~��.V)��=A����S&�4Y�Ee�VJ k)�4f �2�qSt&�"Z;#:�'"J'}2� :�oC�>��HE 1.6)��A�&�cB� 2�'� a':N,it"�)bm�uarante#)�<� � in��;�]sho�6hA�?^�$X3��carefu0�l4t�  :OW 0d��r ^K;:I��V$�p^3t6[ cok�l�abo��fN�R&��"�  $�2$;R�"\� E^4jq 5�h�h ��Sef>-�*a}om�7bu��set--�e$��6 ;"6&ne� � io.~�1o�?U0t��n��h a� desi��=i��q{h n&!!��6$v� 7��YC��"�4%$ype I���a9a&�A�"��"� $� ers%M���"V �:� \-��& � :$*�#� a�� .�.Z,�56 a�D��E��pr �3��- 6�*�(wa}�HE�<4.2% � 4.3): a�u>Gw��5> �o&j(a)�.�8)�soJ,9. &�p�u����by obser4o �]�]M��*x�*x2*x&�M��!�de!�E�! ��ib\DI� %�inv8&w�m��� ]ġz�Sfacw�/tqthroug�v��| .|&RF' jump� .w�Gd&ײ 3} � !��� .07C)�)�5{u-\cO4b+*��vv�sy�kj�WM�iu�n.-�iraa�tar�e�h��3y65�*=>h=؀�8t~��- d�!H)O {���]�;!+>� plent��2R R. f!l!�!83-���F�A>4ms to!���exc�� t�i�NJ:I|<of ``"�B "�C"Ŋor� �epc@m�� 6:V\9�&�+0� wp� newB�2'i��l��d�dr�a�Hof ell�c�)K3�b�SZqE6@]�6�y2mom�lex�4ma�k � $K_Cuh �<biholFh�, n algebraH#� �#O\� o��0 q toruu?nd vic�,sa5'6< ��6)�A�.�1}(x&=sJ ��]� � $S�<$ASb- S�5d&u��_�" ��UnleG!e *�h��ar)}� �[K3 Sur�Js](SeOE(Beauville78W ["�=��{�!a7s wa�m' to F.~EnrNs B46}�2$�Og  30.�PY�a|� � $2g-2RV� g$;���ѭA��is $g*% N�w9 n��p�&0 M}_g�]p�^veQ=o���so8i3NBV�Ra�M:6k{g��an. N�al�)\��n��+_{\C}"�M}L=19Bte Q�EPq.� ^{al�� Q� K3��!m�r��lAi ��E�C#< �untXn*N�!�M��i�*�+#�� 20^����"�>: UZ9�uni�szamsof�s:�\bD>2Za��a����.:P�R�=20�:"z.r��.�s&/��nseA3se�[2RM��&o In.� word�D�u;� I:�Me�c:*X�le�&4Y-"� %�gor�` work� !�0lLsr#�ga�k\ka]�_ s.}� factAeF\ \ka} c&�Y�s�|� "�4Ricciȃ�0\ka--Einstein�b21 *� "@� 87}�@  sugg�w��(* ht approa�goJmce�M ~ J�a`,e :�2a ���" �z! !K3 ��:�9�to1�,r0�1�$ ;n�a��)"sg&< �eR.Q9:"(we"|!'=C"�d4.7=w"| vs.��ka��cS��=L.F�T\&� A�a"E >�*�DH^�z$ag@.J� *# &O9e��J"��##�O�R�$��"t9 3 E:�8 �A] y�%:t%�$FX{� �>���Nern�y6H�eg��7H�m81�U &X��� ``R!�"F�8 � ��\ �,%�U-&�,�D.�n ��>a�7�\�@H�]� ���6<X n ev(��tr�g5ie.�.�}��� 'a�d �y-d^sw�8sum‚*� &7�$Yl� !4A&ih�ast :+probab���=���Ua�i�bu����!1 A ``\c9�� �P.i�QU zeroA� 2m(ype complet�Rely determined by the third Betti number. By results of C.~T.~C.~Wall \cite{Wall66}>�us suffices to guarantee that it is diffeomorphic to a connected sum $\left( S^3\times S^3\right) ^{\# r}$ of $r$ copie��`\emph{solid hypertorus} $BL($. Introduc�enc of isolaA$|cDV singular points. \noindent e by orem �ng-thm},>�!` be deformE�$ a variety6,'$ �)c@t worst nodes as �0ities. Recall�xTh�friedman �A�secondA�t!J:impli14eia $|\SZ�U .I�0) |\geq 2$ orB��Ѕ��2� fi� caser�4or equivalentl5b %� coni��}�hvincolo!� � �-2 � =2r- N \la�r - 26�} ��Y$�i ar.�ir2� !�Pincides\footnote{Thisi5  A},V.~Batyrev \  99}, obtai employe�p$--adic�eg� � WeilA�$s. It seem�t� |motiv��^k4lizzato} ensur�;a, ��argumE apx , �4slight modific��se_an�<yQ� /ou VB�T$ is!��>� @ last step should a so ��gluing}!U all !�:]'s� serv!R" (ility postuG by �((2) (to use�qHwords: ``let's igno%7D s�R4inor technical�&blem")�nremarkqL � ke�inE"� u�y��clearl�6�: �little+known ab!}M�*�I�:� ��Gfew �qua&re avail�-in dea� E�^act5 lex&L ma)�s!� �"yThe}�beaut��J��).�is/ n alsoal;evi analog���  lower >&�6ellip�ye�,of K3 surfac�� as!QA��jh*�Ikof%2tis ��n��&� =&u s�� a�5��^ra� toolsm!to le�~�-�(, \ka categ+toA�k�Zo'larger !�m!�,Clex, !Wy!$5�}6� ��9 !L1^ )^��-pre2A���.��*>IΙ``Kl�tori"�Qs \subs�on{A�(``vacuum de =c�e�!�str�@t�y}_R��oo�E�c�;� � ly d�wnct.�Ii2� q��toA#concep�! a��s��le1Hs�due!�!��MC"� ZM sugg {% ��c�� in 6. \"wm 6�pla�funda�Xal ro��n 106� .ries: loD y 4 u�i� rise �8usual Minkovsky) --a7lm*emain�6.O(!,so jed mEhidden(}�!XDir microscopic extt ,A�L�orC a� e Plank!�stant)e�m�ifiI�.�model �ch, esSi, �crv�quiA)supersym'y, tur:�o �G\��B� spite��f� h9 �% �ist#B��--:�, ��$ near--un�f v��ual1�9It�ces)� %�!��8��hoo~(appropriate�%L:W���'re �r not �!Tcr�on%�makA*a(cise choice�� � RQ8a huge multitud)T. � � . M�� n�Bwo32�� �``�i��*� fromJ phys��&� view,� #��|F-(s (or bettee� �(s $h^{1,1} 2)�h=�E�Actl� �(n�)%Fplen%�# vector)j$, �7p��veW!>h�>ei5��6 6��b,} ���nE�orBVe ideahCle�1mNF��, �� ���� A� �)&��1987 ��to �Tists like P.~Candelas, \S.~Green, T.~H\"{u}bsch �g ��at: � iz2&� \�_� � , at�st - ematA�ly,Z�,ed each q� " &�(^). }.��nd�n��webw� } dea�bed!Bmany insT ful pa�U\ r�eV1988 (seA�ite{CDLS%P-Hu!H88let},�6CGH89}?CGH90� A�w��ver()�D � will�jn aTr�A�M!�oss ��cong.�%�sXe}� .�a"_��-�6�})�2� �: even�UN� ��] ��!��'�bmerely./al pr�': w� �I�y�"=}��we� !� 9 involved?.XA ' answer waɘn� {� rf& x� 1995A�$A.~Stromin} ]S95}a�Q\ MS95AHis3n� Ahowm�a�o�l passe�ly� roug��"� �U�U!D� ` of%���a% insp�r H0of N.~Seibergn E.~W$�Sie-  94}:u�1!����E chang�oI�t�g& Lens%&@massive black holMol[ ones�>�aCyears���=�b" �!�a'A�h,bAxQt4ly understood: �� exampl�dBKK�)4KMP96�2BKKM97}�:� mTedn�*�\�R A:� ref�2��y:OA L "�~��/G��97b�5t��rI !�K3Dfoa`�a�(gebraic K3 �E�bef#�4[ v-a8onh�E,A�K N�!,��u,A� stil�y��ive7�hardest�� C"� 6� h !�o�i:s���Fin fin-%�)M7� s ob��R��8�" c� skip s �ba� aon�� � iI�*� "G&A�=�)�think%nE�giantEZprediA$by�6�`co�Ac��)�es� �Js. Twors�#�,  &M M}_1� 224re�\ud}!%A� rrow621\�"5#M}_2$� �A7g�< e% E:2z1Yr9 Z 66~2$�"S .h��}�a`(: aq�]m�%.�1$+re exj a b&%]�� yr�� �!."*�% !lH �ily.2�Y}}.H$Delta$ who� e "l fibr�;^A_0\� F�E)��b;t%�J�6�2$%_-� $t\in �a'6�}[See�:?�$M_QQ2\!�V6Q)qL by��!���'i "� t�%Iab݉%X� if���>=� 7. $p_o$6x(a �� +sm>��!\psi:2g\dash�A�6�*"�*�o�&1M8dsW"� B��&si$!�a�lif|da up A�giE�fM���&�sU�$ hat{�}: .� �$��NlZ&25E� 2:1 I� Ak 60ic�${ p_i\}$* �x$^{-1}(p_i)�� y1$.y si�aC Stei� oriz#�H$=f\circ\va!�qH.X*R, mutaEndiagraB�1� ma�M�Dxymatrix{Z\ar[r]^{ v}d2' (phi}&]?X f}\\��.� \ar@{-->} ppsHAl}6m} �% �%�!DZ�of�%60�� ^1��$f$AW} ��X}?S4,Ba��,�ed��(6$S t�$��.,*&)>$9�0immed@ &S � �,��ٞlocus>,'po�to  %zDM.&jD>��oՑA�j T�"f�e ., famil)6@ Q,2�2D$�? !��u p&� graph}25%�� �"�)E4.D})}:ݵ�� 3web-8uT&2�mQl]&F#=pQ&2<DB}.5a�proof}[P! Pro��� ��]�b�is!�n&= a��Bfor�,p \� �32 \setminus�7o\}\quad�s (p):=El(p_o,p)>�(L}_{p_o}:=\�/\{\text{Y s $l(.� 4a�D�{ \}�~ ) F��V~�Wc�%ab$p� ^�Aado�.DYF� ���%�'�Ii�of� �#EÝY}$, $ D�/ natu!uy�=a well5��>X2� �� s�3ng9�narray%�1�q!�Z5� E-�2 (q) &=& (���phi) E�2NrCl_qI�e�-�E5��| 5P�loJ!;B/��l_q�# tang@%�to:s� T "�%d!(!�:dir-on>s%$%*E�b��[#� ����image_&� qE��dAD.> i�� 6�+SZcm���k�N,e�$p}��1�u�? !$S%a.A $degree 8}."�q}$� e(i��,be�$ b�origiu f�� � $\Ch � 4-�k�� ��� then�@by $F_5+F_4+F_3=0!.�<$F_d=F_d(x,y,z,w�_"�  homo!��, polynomia�-$dk.Xf $p=(x_p,y_p,z_p,w_p)$�;n 6�.�"A�Z�4x=x_pt\ ,\ y=y z=z w=w_ptB���w� !�fE��.ifVw(=% )|_{Q]<}=t^3(at^2+bt+c)Bwm�a,b,c��V::)a -P5,4,3,:��sfB!�"�/I�cy d�8>���d�=0��(b^2-4ac=0\ � qj la�,* �82�2�}\P ^3B�e�&�� �&Rbc(�R� .uJ_�$a=b=cAڅE��s7!͕�Htn�.�.>. H[, v2 Ŕ1aJilh22]a� �X3 ّi� w�g �1a� �\�*u �a &� "$le�t��� })0��E f$ oH7+5 *$ (&sit��i e�4zco" � � � )�29�v N*� c!aȱ#3$�]" A �$S" Q�K q$�!��i 3 (S) =!�Mg \}$,.���6o60�/\>&V��' M���"6-u1�ed)j!�I-&U 6 5�1s.f-*H:����5$ofy�eP^�,� �u} �uaT me b8%:� -� )�E� �E�is:�(8 �%enq)�9m7e<big# � .� ��A�s�3y�\c"�5s?"� *�[�=�(E� �s �iNe��$-Po E�+ce4rB4�.w�Uly-�in��""I!�.A�.�%s!�.���<dlet� ter*ŹpF3� C �9spaceCp%�ea�"2EM�9 sign/ve�,��I�� CGGK96^�;.ced!} w� up�9u�2are�Z�%�c�3y��y. S�a� v� developa�ta*�"3� al�0of D.~Morriso�$worksa�d F*%m�/!�combina�al c data  7reflex!E� topes�� ")J6��$%�e(�7*� ( Yif� �6 "�5�[*�F� too!i� Rf��-�i��"�two2�2 &�$&� s. B(� !)pul'search,Pautho�6 heckg�" i1�5ށows!^lBl!0 ��e7�hPA�Newe�$��4$ (7555,1s) z>�=g����i"A7AU"�)already ��*�&� collaborA$ s, b�*he new�*i*c$�(��*�7)��q�M�.w��wo%�nI�2e9noy: n ge�,�-(..�ra9+��i�x6e oc a�ͩ-"o�?vu=. W� �; ��%\1l��! 1�Z� �,dEenglob0;n�: �!�6m �-3 �iet'*" �:�2���$ ZW?�VV�M��co�!�w�62C``g�'E3C"5�!�.'*�*byB5~"O.�* e.g.Q 6N}?� �In!�ens�*�i �'� is9Q"�7 s a �w�4cA�ppo�@A>)d! -As&�2>�&D :��.� N�)s%�i.po of9 �E7�!�4of :A� ���out, �cop�t�p +.�&�we �*( � �(;)6�A�:sm7fu�b}8a$2of�;]�1+�.� �[er w�2i!�deeper_-�t�1 k8�ul��15( mono�{s�!Voisin*'$Cox-Katz99�)Yreo" 2$HKKPTVVZ03�&�!9� }[InNDs1�E��9�-�A�QRU�R�^�2�JB֨� ^)jn5�A4*+aG3!B��ms-"@}%R5�{R�E�R���h�"' ![N!�Mc^q-WmJ�kU%�.BH!�F� �q}' �ru�!}��.�r���TN�}JZI.�G8%$p=1=qe*�)�5�� -,P.!�B�':=�O6E�1� 2���6#�r�NH`)�J�jt'2�2�OF��l�2�m���n�<&p �V m*�O1�cy- �<�M_tR � ��I$ fix al22$} $(Y,J,h)J�bac6� }V,<Z@"�N } $J�'� a� (hermitian m!O } $h)�+re^art�P&Ricci [,0} riemannian H,f A�in�02Fclo2J $(1,1)$--q0C�,:=-1/2\im h$���/+} �i�3�-v�P*bT"&/9;!)�� }�NatW*�9C!5~�< 0�P�JC*!�tB�)��R�uQ bihol�Gsm�Bog�Jy�m�m�assoc�'d6�Aoco�log1 toq�$.}n D5�[9�= kahler)Cor�ryn3 -�,pretazione} ���;( N���C� ��#>� %�!gc�3.� (Y)$. F�F]reason ]�B�U�thought�c���6o��Y����&g8$Y$0"["!?��%�m������*# H^1 .*Gb�tu*1���ed!(�H"�V}�� 6�4F?R+> ����um+�"\&9=��"�E#�LL $R=3$, do$��t�*&�Kz�"'N,orac�Wo� . ToRE an$ra--datum,+C��he $B�� ield5N,s needed. Ph}@ly +a ��LU�!KsvE�on. Mat5;F�G"|q#7&1Aa�!eVc|W $\be4�6 quoti��R�C/�MZaOn�6L= ook �]M�WZxM:=+?ta + i ��i� - i/2 �)� }C�Bm�# +Z)2LtsQ��,�7cKMh�!!ra&!$ �& A�-"in5 C�>a�*s�;� & $��!*E%wI-bA�\!zs7 %&�I\Ite��Q�.B V pola�/}0A! m&� �.'�5�26�� ]"Uo(H�!Z��"q1*�� "�K}_{\C�=:2+E�%-�C)|!�!@5�@(Y)�\}Y�Bq *�Z�m.� ��M}_Y^K%�!�rb._ �$� *A:�� aut&�  grou�)Aut�O� q"a%%A\1�� Y,�D& @ �2�CJ�K$q�2�:~>I�.6AB)D�w67ev�A� �i�=to�HE 1Q8�(r�Q.U %��"] %!� 6Yj�/� 3end_wE�c�P�*ki�e�2q^A�$C:RqTi&�*Um|5k<.EF{>y 27,8�� = ��,P.~M.~H.~WilZ prwT ,�wdunt�NunM�� ��!>��,� ��K�9%�s�X.���u,U�� : �92"e 3 $a0Pen �BlH� nB �_)%M�!�!�Ej,2U)%�!���,R trivialI#w+ � tJQ�D-��eb�@ly�e3�a3@�n.� Z�ki M)�,$U tJ�!8�(� !�Z6Z�� �!h:�|_U~@U\ Ls6tKB�TheB6$� mB����be ood a� ���erVal LA�%V �onF(L=:  D ��-�*0%�(�chi�  ��e7 uple�Z�'"�$.8? $A��s�!na�r�-��~�<��.k.�im�= &5�2Cu5R�c6mb=$=�$(���7},! \)� d %=0J-,h )e/a��;��%>R [J!!.) ��s�"}f 1�U}Nm�.�(ZJ0*�.�Ba��}sI e$2D]�5#=s:�2A.;� �Me� theyzinheriOe E��>�c6�6�)�1%M2$ �>#m���o8U2 U �a U_K �, HjU9g U1v:B >.�l �%.�/$m:pl 6�B�$� � l�tiUM map}!����LFf<)�di��V7m -.�=U_�%0)6.-K �,�т! 2<s�eu Ian�, '��� ��), zd_{(JE� )}(mg-VM '^>� numera�h** "�+�[� partne;A�)d���%�-cy>: x}9y���" a`e?_��:b n" q� Z-�OsI� h^1(U�,T}_Y)=h^{2,1 =0 �H�`e.bR ?M�1�,beC"�$yJ�E� qU:-���{���v�m.�d�`� can�R�<)�y: in�].9b�R.�6,�<�%5List�Tw-hJs�-�%H 1986.C.~Scho�c*)�N  86})%fZ�_ec� erp*%��d� &$d1��&~h sbi a�� l��:.Fr�R�b"u�6of�R�&ptrabH@ �Hbe�ko�M�t[��I � $N�$iFJI�I}1�:, (rgNxI):6*I.2(m�/"�Anyway,*�'hX>��m".ly un�8 \�jd�Ny� bt3vfi�ao�Gn�QB�&�N�-y'�a ]c N\a]�>Num?i�� �(o�Y�#2�(m�)z?&} �(�&�+ !%��ev�eAZletB%$ 5�g�m�E �.�$Y$� 66$�3&�T&� Q#�MS+��t&� Y�A$/^1pc/ @{.�Ar]^�> r]_{�;� @{<� M.Sg.&\�36V% B<~K]&2� 2IB� "� &6=1%�� j� -=q�O<h<"|Y���Rs\if $T� _R=�,i) (3 52�j>*a�M�j,cpx<->ka} al�<tod&�aIL('�:�=$kf��3* B3A .i�pi:� ly s"k`�a�w�Z�:M��h��be es�is;�� �om�#�A��1�-t���!,&N ,�bab,Tu4 *�6."k 1>9Rz%p"\L,�S� 7�j� �W&�Y�7l @Lynker-Schimmrigk"�Oc�Y1 �-T���,2���-�-�let2-�^�$4K^v$/:6:�6n��?�lin�6by"� �R�/}����AX�d�K�� v})�=��t)�=�.la�1&9I ]V�� 2am�We"n���: e--PzXqeop io2�:e"90}A��8:�k6J�^E�`des0Ki�L8�9ctic R�6" $\P �&,2���3�generic"j v1� ;bi--dQD$(2,4)RQ^561AF�9e"*<v;��1)�$BC-FKvS98}�_ -�]�{�6 ,9Z�.2Grass (%�N!�te�"&7 /Fan�k*�7-8-�d�e�r!;J��&MXAG� aAisS�1�7 A i�f*�� .-*� R�\l�x.4-6 DT�j5=i�en��.�\-�.�:^�J B >r7Me\-+ �\-si\-eL& Vg�% F��21K=!��"�Y��A�nGP.U"�  play�"F� .�Api K�[&�of*Q<*�1�}=�s��$a%bG!$/E�.Q,��U�B�QA�&� B6� : ���"� m(A& t�SIT!vT�. U@s $E_1,\ldots,E_k�Fco = ed d>m�/(a "@nlel $C�,: (ound Du Val"\&=_8ype $cA_{k}$. E�S"J-� 326 �~"�=oQ3V�@���T�^r !a�9�� �QY�:W9 Es glob|hd�(A��:!�Jx cS_K(4Aa.��<�c -�&�K� J�`hibited� du�5*) � 'f'%�kZ�Fcha�now"�(0|}Z& (a�.� !� I.�s)I�A�"� 2zS�t*�i�cEEF.�% n ]�E� ��ŋB� $T'>�x'B a�Cl@b{T'�Bp 3pc/ �d^uIdv2P )�B�2.�?�dr�Q d]F�Q :hB�Y'O/_� �u��_ ��{M8�'r�X � ur]&B�2�" RlI��K�(inom{k+1.u$ �@�� $2g-2$ d|,>��'Y'��ere $g�2a� genu ECR1�C� $N={\2�}(t)$I�`.��|S| B�sp�z44a,@ �Z��N ?Y'�)S>Q $c=N-k�1*�)kqJX �b%. iven:aQ��a�. NT" a-�J> $T'&T(�=��� c,k$), asr� �}�?�s%:!D�lso�a�F^ �Kr�eeu�ite>�9it��hap�@atVu� ׅ"a-$:SF�G<ݜ�w![��sMR��@�� F�F>nu{V� g=1+�x}{2mci� }\ ;g��LQByj/\%�=� Jref��g.-=�i5+&��&mru9�. AR<�� sat�Os@Ig�$?g2I(DAs���E��s+f�2�?5� $g>mNosJ_# 1 k$6N )}E�6� M.Fa��:�MT'}R?7��{T� 4tE :!6> �"� &;u MethoDKn� .�� gelF�,>% 00} ��2���wh& flagvX� al3qac�(�� s�&i�QC3PV@J��i7s� �Bb$�p"�HIzi�5C-DA|� ���&I V �� v�+i�"��9W�94}�m  -vSt�!n95} �M� Bo�Jv}{�H�vr� & �"UG^l �E_a2th���i%�2$ �04}71in�@�z�ze&�[&� e�}[ �D,.�4 3.1]�X& P ^m"�c )b�i"�u $n� n�eGorens�_9� $P6Z�Call�P I� 3.! $X$}M,yIA�i�pas*  'n�I borh��$U 0�'CPn .?sub �*^9X"'!�#U.�6A���fi&~%Xa$h6��fAY8��A婈s�ld��*$I\�� ;dm $X_t�2pkat)BXsmo�!fo�%m6$t�0U2�SR;:e��,em0:=l0:lhA�+,�.��;nB7! $X�gPB�cC 1gZic�&X$ X}/UZ1%p\Pic(X_t�oL.�(! ! C- �=r}6"&�zO�IJ��!�~w� l4.� �X?,athbb{G}(r,s�3embedd�#�^� s}{r}-1� �/Du&yPl�s cker @ ing,"L ^fC$P:=P~MU3VBv,)E�>�00} �*�/E�.�n�, �F(n&�n_k,n��)�;)��( e�$����"�^mZ��(���2N$P*-�%�u�E���� T ��6d2^n$;V� z_1\c�4 z_d = z_{d+1}{2�&E�i4*�,n\*�d-�l�ms1��߁" �>x}����[� 6X�oN�R>gyS�#$X�hze��/�_S!�P$��coوDleast 3*�F.%3E�!�{P�,�nsm�� @�� ���-`$H�%1"R�M��Rcu`� US2O͋ �� \1&z% Y$. �X�� Rnd�<ve&$:=Hg=P�C1\#Bm 1m 3.�e���� �#&�2 = 2RDZlW ��6o*�?}.  mV�gP� E�iTzanewR$P�f8 a&�� subd`kt �'�� (<>$P$r��e N�.�\�,Ş!]aF�7SD 7Y$. We"�!n a*&L&-!Y6�,Y�K�-"T w;-�=[V�&0X|{ r]&P>#pPjl]F�2 ^{(}�hu*��&]_:(&�u�\ao#0�#�#*'@n:�b96c!�.{Y�9*� obr+�.; �d "; ��6_.t&O�<m)�d��m�2�5"�Vbn�lar��_�@ "jWu3 m= �#���%�T$K  P \hook]� 5�au�!s,�^MOoa��ncorrespo��cY7AGM93}cU&� waG+� �>R"a"<FBv��5�*�}�2K�1yk.ҋB�e� sB'^!5��>r]&&P�}AJB&6Cl�D�D� .>}[�q*F�&"~(e�_�*:�]r�*6<': 1�I�lUtY6 �ZdE\:r&&2b6Y� uuu]5(7tyB�'*E1.����łJ_2,�Mq.�T$�ep�[�Rfor�*Er�6J"  ve�S�I� �:��"n!).d(>�*2Uox"ke�h�&8r�2"�0�N�"�TkX�$%HB�0�in2�+$ -cy}. At � &D/N ^ 0a�F~Z.-.Nu!!yX&3V�U���� 3j�.*�T�R.A [�EZ :�)7.�NGe��!t�!�_̃</)>.�3$M���%� &�2%�.�?le�;ed3q�mB  �23� u?6�U,.P��) �%�F�my.�!$��v�iZ��PZ�&5�� T�2��N3"� �J"2�io�2A�"�^&r���)} >�1A~�1m�!��.�a&Q  Tof &��"�aQd �&+0(��iXEW� wsɂ \�wFT"33��!l&" �b�=U4�>�q}E*G% +:>/�Vat�AO�0P^1}(-1)\oplu&>6ar@�&�TE;� ��! �1U6 T^*S^F�s stud�Gin��E�ߍisi���s ��Ml�5[3�A,e�eset@D'@�_��/�A�G)�+�&�4�IA�#v,�A� ?@Z^<1974, G.~t'Hooft� ��iw͎�,ga���4�1a6x� �S�-#� \7LLater {92,*‚ show-5ua.�i5�y, ���� $\su (N)$� $U 0) Chern--Simo��y� ! "�-��$l(&���)�-e�? $T^*۔�yD--�nes wr�dcN�$1��5lD1998, R.~Gopakumare>C.~Vaf*M-��5�� � � j�suael"#2� 5^���6"!�!#e�.*�6cj$�-�-�9>P� Ooguri00}gx!$�j�s� �l"!�V �4e�o@) ̹�"s.�5�ewD* details8 nN])]�?fee�!=.^)S��RN �GR0"%Qs1yA1th�F]����+�B&}ݡ\EeΐJdacךbL����,�l��to��,peZS, ��a"fnAYA2migae+ies� is�d�a�2"&Aganagic)�16t;"�'of"1 lq�-L'�K�by  ."~Y5�9�mab�, ��AcJ)�DFG03� Jk�W � m isrcri�!���_ SForbesa"�thebibli%_y}{10�'0m{Altmann97}  K. ``A �+al�$"�a�il� &5s"� ity"HIn^��th.} }&|bf{128}(1997), 443--479;{\urlfonxV(th.AG/94030��:�  M.���  C�$G_2$1@�s,QN"�8L5�~e inee�s" �0hep-th/011017IV�G  Aspinw� P., F0 B ��0 D�!Z mono2hA map9714 RA�Not2>} !>,3), 319--337N>30900|��TBPvdV84} Barth W., Pet�@C �VaBo Ven A.-�C�� ��u�} vol.~1�,4} E.M.G, Sp!E�Ver� (1984)A�-��9��� V!!D�X�hedra !�B�U :�+~�!pies1M,J. Alg. Geom=F3} !E04), 493--535;=� E� 3100a�J�9!H�B&�6mU-�U$n$Ws� l�� xA�N�reh�0"�M�$y, Warwick�� 6} London�Q. Soc. L:� Note Ser.us26>!TCambridge Univ. Press,! 9), 1--11R710020�^:�0>�J�#��5�!�' 6"ng1�bs��aA?Con��, gno 20�(A.~Coܦo,č Cont�PM.Marchisio eds.) Dipj� Mat. ��'%}� T,  (200A*109--122= U*7120346"� M� V., CiocsYFt,nine I., Kim�7 van �" D. ``CM%s2x% �#��mm�t:�in2�Y{uclT.�� B154i&,8), 640--666�y&E2N�00�����i�.�E[pwI� lag ]AI> Actai.䁚}%�0I� 39; ��5�8031086�i�.J=��6� ``G"5%p�m�ic fun� e >�+o� 9� 4 y T&> l�T Comm��U.�68�I5ᇩ3VI701:�,eauville78}  �4S�$�[\'{e}bru�M�x�!Astrisque��5��P�N��782�jk� Bergl�1�q�g S)pKlemm�`Q6�g%�; m�S�1e-g!�ic2!RMd��1Re+ >W=LB4Y[�>5AG53--204.+H9506096H%�R�,�A�Mayr PAJ�- Higg. �1$N=2$� ��2�> B48�7), 2��228N�605�2oJ^E   F�Hamilto�_'B��9&HDokl.Akad.Nauk.SSSRy�243/5E�7��� ��046�' � L.A{Towar�1h�(�Cr%V�J1.S �� 56}  E��r pace��\k\.�P`)e#���!IqC�al��gr*�of��Hians, Amsterdam, 19��2� <2}, North--Holla��2A�56%�6A�7.ZC=� ��eoDala�M., L�$tken C!tA�,=irgk R.ŹJ+B�eYM� V B2X:A A��252���6��  P.�&=� T!�F!�di�ceu7D�Z�Gaq6e�a>. Let.� 62�#86 956--1959:�90��Ro�g �jg!. 2�.* 5*330e,9��4�026��> Chiang T%�%*� � ��G KD�r Y!/B��Hol�J"�%�a^��of�=�m��%>A�.Suppl�846 �A�82--9.� �4112:���� $ C.H. ``DʎSolids''��dv.��\.} 5747)�3��07--23026o"Cn Cox A.D�lat�x `�2pA�  GaxJ.4 � � S���M"�na� er. �� ,���= RIa992%] DiaCW��d r�Y#Y�mo bundlea�in �!3�gW � Li�0oB,Sundance, UT�/8*��� Sy%. Pu б\5�"Aa� Sn� 1�73--132�B� !l�+&��e2�/� 6�#ё^{�3%{�( 1415--1443N� 811136� GR �"�Rossi�``L�--"D$.�y�Dy*��j)��ice�Brane�om�1} Se�A| H.E.� CosmaD >Gravi��8on, IoP Bristol� 2�272� � 0209046�� -.� fHP!|>ph��.��U L�OcI���ZT1%�� 116A^166.1����CX��* ul�j%^btulQ`n819�431--441B�.&E)HfE'aEM.�v���j�2FE0.�B33��A�32� �G},.�R �S&�6 ����F�un26gs1F� !u�B45)�"c 120N�5041452c (Griffiths69�  Pv `�? peri�6of cer�]"F�($grals,I,II1塯/��;�F (196� 460--5>�oss97a�3 ``De,@�J#YQ"� e�"" 30-�7�G8~ 6q�7:a"��  ��P"b�Z�J. Diff�4i�288--31R:951j.�4Hirzebruch87} "``S�9/!o9�,B� �ڽ8��p},},II, 757--770&yc872�*�x Hori K[� &d(, Pandharip��( R., Thomas Ͳ, Vakil��Zaslow~E0: :'1} Clay IB� I��`B� J .xJ��20cJoycef�  a*�p-kSpe�G� �,y}, Oxford S:ace Publ��--n York�]6 #D 5L*��d�� ``Enh�d��"�inBE�U�"KI ��B47c A  10��RU6�82�K7�88�C�� Crepantv�a�upY�&;8�O�5 "�J{��2��toF�H��Z�12 �� �163.(Kleiman66} `+W�[pc-Ra�ampleV��~I�� 8196� 2{342� 8Kleppe-Laksov80�ppe H�\ A�U&��h [ �A of Pf��an schem"� �]��6 �(80), 167--16a (Kodaira64} �q ��4o�!�C s$R� 5�m[Am. Jm��8� 196'751--7982�|r-Mori92�ll\'{a}rL!)�Cl�˶��2-.�Q flip"�!:� ���(2), 533--706@"��F<�PM�i2-�1mat��} (Dec�/r 7\ 952�FNP z!<hP�[&� &�Pi[�b lies",-�NR�4M���562--582.�.9511056&$Milnor68} !��S�N�0�"ADA<2�}, Annal�P��S�&s��61}���Dton�S�ty � PAd6A9 82} IAT"� �BF4o&notN7�! ef=ive2 �YO11I�8AQ1AQ176.��   D� ���8mL�_ glas�� �.6�y III}, �i�K!Eal�+i�AB24�!1 263-277.s "_ 70502:�o@�-"�(" �r  N�� xtreA�2 nd fiv6��Q"�ic �p!�qbNA�J ��8�5 229--242�Q�609076�Namikawaz  ��O� � ���uA 86V=ѷTB�yY"3 �� 4�442!y02}:��5'8&� ^F+"vF|4e � Q 2t126 ~(-Steenbrink��!%�a�``GjL�8A�6�1b�#�"40412 6�' �Ix ``Ka�in�an�Dn!'�[a � 5�EAB5  56 9 �!!%43.� "y91212��",Ran89} Ran Z�� E5�ma��u�"bE���&+iv"�+� B��co4�Cil6@8to C., Eds. LNM"� 1389}&� -.l#6Ra mn�$-# toͰr neg@��2tq�J.[#�.!�p27a�92 Reid, �dCF ]�9BJourn*e�r g omtrq dd'A���x@Sijthoff \& Nordd  !�N��U �M[6y) r�5�&�D%�O &Q��� .v9�B����w182��8� �Young(son's guide� �2� '!wJ�9%et=,Bowdoin 1985� 1� Sym � ��&y$46�MS���354--412I �; �4�uL;����$K��may n�Yth�) be *'DQ� �� ��28X ���36���( �Nuc*E del Pezzo&�  mT RIMS&d��695--722�Sc�s�7 �Rigid of ".w1u<: -�^�2 7�p6.�SIf (� . x �=ip cyc��on"C�)�arJPZx5�+"7"792B�� q�&W��hE#romagne���y,t)pR�confine���r8!+��0ic Yang--Mill1po��2! %��]5.��\407087}2�t 85}  J.H.M�nVap^e�nUi+��A ^#Y�13�330-341e�6� &� ``Mas��&4��-̀  �Sm�G\a�� uni� :P-s"5 act-"!E�>EWeil--�+tu��ic ��o" aH� )��ox(S.-T.;�0, ed.) World �s c,CRgap^�p!�6�66� ��.� ty ��tZ��Z�C٭HEssayt�  M�}"#.! H!�K�2� 58Y..a&k� I��n%i9h�1�:� 43�E3.4\cyN�L � Comm.!�!� 1�&9"325--36hV͎ ��Sy*�Miroir}�ora�JmS�qo�!�o!l$A&��y�3i�*3Au41N�U>�4 doc&�} π\hL{amsart} \usepackage symb6�4x7�%, [notGF ,notref]{g:key�<% Roman�,ent7s \newV�Pand{\rp}[1]{{{\rm(}#1)�B % Standa�set:7Z}{{\� bb Z�j.TRR>CC>DD>TT>bbv{R�2�bb\{DJ P_{PJ �{ZJ �{CJ Q`QJ S S  %�&X�nviron )�@ emAor�}a� �� rk}{�n6lemma}{L[�/]2?�}[)],?6I coro&C��6$d `9T P& �}��� Ope˝ Declar� \ e#"{\supp}{$ \let\Re=\J}< dN4*{\Re! 1Im�1Im}{Im�S�ue list [�0(a), (b), ...);�t|T+)=�{SO List}{% %$K+{{\hbox�1.5ema�(\hfill{\alph\} a�%n@ZJhssa�>B)p}}}% {\setlength{\topsep}{0mm*�parRB%MA3;fwidth�9Pu@�uJ..� % }{�+�$} \makeatlE�\re.a��!F+{\@!\c@ =�� %�> -����t0title{VerblunV�Coeff~)W i Coulomb-T�dDecay� a�� {David Da��kdd^/� M \s 253-37, California Ins;���Techn�&D Psadena, CA 91125, USA[��l{d l @cal�� .edu dateAd �b�bst� } We�@ �@� a��measur�%�Nct @O��_{m,n}.dWu-soA�sii�A?m� �2ogv��&Oh �.��y�8 Szeg\H{o} �u d\1{n+1}(z7~z �J�"�E��a}_{n} "^*(z),D�U 9V^n.g n(1/Rz})�hThe $ ^_n$��ed y� 2��they belto�,disk $\D��{�Lin \C : |z| < 1 \}$.UK�e��ev � �,� \��<_{n=0}^\infty \D�U9Pstar�7�� . Se�Lsimon1,,szego}�5׫gr�i��� �rtN�� un�(OPUC�I�!is8'A��ArC9>"6�Qf>2] ����j�>��m:"�B our �Gy�rt��!�%�"�Pp/ a��AY �:�",PDmay�2���s"�d� �}s {vcas`].�NN�\=8 \log N�K �9�d$AU���}&���/dO��ImT�25of ^Oc��r��$Q:i�&�_�� simr� \k{1}{4a�}a�V2�a� � 6�e1e\m�a� \notm�u�HrIw >-f(lmost sharp�b��7� 2 ���oa�%�Ӓ�!Wig�on Neu�F_�exn-W��igenvaluA7 r a half-6G\"og;er�6 �agx)$ po�k�pWvN��}���� �d��i!I <��+��o-!�n��;7(em~10.12.7)�f1PMDholds%�EJ$A�kn)��[�� $K$ ��{$"h��! �Ke�4A�K + 1m��n�i��e�&� -�Mx �a�Htrigu4o�LquG V�>�� ies .d�= 0i�re�two�Is7wh�JBd��i�� vQs���is"��Stu-��it!~�� easi3�o��QA l�:y=��@ JY, s_ %bM� just��x�xN,OI�Ry�a�i��e�.F�ADselev[_c$v�\ abst��JD���� ctrugc~,sV� q- u-��ka,Our goal��a!/h)� �,r0%2���'*ë�mp�`��& gA�:� V���mai}�!l��E�is2S�L�m� $ ��B���n,Z���� 8�mlso!�wa ��ba��."i�A = 1/4$!�aiܩ~ �~a,^fe�s 0��C&Rm� �:�ma hve+t2�$������ ic�sopdl�\� discuЮ�Z �]KtegnwS ��A�J�� $ns"��Ki )�k%�i  ll r�ݩ`p�0�ygk.�_fE�(�Pr\"ufer�%��� Bern@i-"H�roxO� to)��  ST~2]�a�U�on ��P��(%3HChebyshev-Markov Mo�}$+�M�� �a 2����w�3�e2it�_$ Hausdorff&2 zeror�� a�a !���fZl�#)�r27|o!��ҩ9B [flavo3�T�v� s. F�h��w�T��J�4�O����heF�M:'s�key ���\b{\��,it{Ac�� ledg!�s��/�� �nŹ,ank Rowan Ki��!| Ch�:2Re)8( us��!���. ����U��U����'v'\u_n��b�3b� o�no�r�Ax>Vi$W$� D(ms !�Պd���S�Hd)��r���":� ��z)���.�(c]A��=re� �&�*�$A � baٞ�[0,�Fwf-�.�,H���*'q�[� b���&6y$\{ e��} I _ns��6�.�n)�U� .b�(bn)c^S � = R_nA\ex˰ [ i(t$��ta6,) �b]Ϳ� ,$R_n > 0$, $46��U $| ;*thaf\p��se., �:%@�遛pai�&�align�t� R g^2.�}{R_n: &p + |9. - 2 \Re \���!�!P[]!V + %� + 2 �.r]} )2),�e^{-i( )%.-=.) � �1% �OZ�R� ]}}{�[���Zc� �]^{1/2}}" 1��� e $r6g = |&!iM�|$. W�g{9�\}Eq\ell^2Y Q$}� fs} >j \simFy(!tsdj�{n-1}A �a_j-�j+1B1'j.�]})1(-� (WeT $f� �g�" 12� C^Jqg3le ; le C <f{c�r)�Y���=~� 2 fD"6�[@s�1��3]� Next�Z! gF �} Approximation of $d\mu$. The measure �<_n$ associated with Verblunksy coefficients $\alpha_0,\ldots, {n-2}, 1},0,0 &\$ is given by \begin{equ�0}\label{bsa} �D_n(\eta) = \frac{d0}{2\pi r_n^2!$,0)}; \endL� compare \cite[Theorem~1.7.8]{simon1}. I1 and! nu$ 8two1@s whose first $n$1sk:8coincide (i.e.,5&k(��a%74nu)$, $0 \le k�5.5.(ii)�<). Consequently,-�\a Laurent polynomial, $f%]�\sum_{k = -n}^n f_k e^{ik%�$$, we havej�,int} \int_0^%� } f(DC) \, !#sz+n +.>��lemma]S est} Supp!�E���%� 1�X. For every $\kappa > 0!�,n \in \Z_+$,Eg &�Cinterval $I \subseteq \partial \D$ of length $\delta \ge n^{-1/(2 + i)��,munu} \mu(I)El!C 3I) + C \]^ NBSeZ)P� \noindent\textit{Remarks.} (a) In \eqref{q4, $3I$ denotesA��� $3 � $ that ha *E�ce!' as $I-�C�G$a constant 6 )$. �l ider�P Fej\'er kernel, $$ F.��c=�a$\left( 1 -��@|k|}{m+1} \right)݀"1}{n+1} > �s!�t@ {2} �t{.1b�A�0let $$ \sigma�@(F_n * \chi_{2I})ٽnT\pi} 6��tau) :9�� tau.vClearly,��>- fejer1} |� M)|!D 1 ��{E�a �B� Morea' , by��bs�,a�followi9r�2>�� � �m��!�2�N-b�NotI�!'::-9� yC 1}{2� 5�!5 ft[ )�Z�+:]!�ECFzI�] \, d(%�W��||A�|5� | �5 ~U$�u9 s��{>X}^I �i8[Q�%A���6+ �%2) � ��&� �p��.�eta��X a�|>#^oI� �2)�~ ~I�tauA A�: ABsin^2Q&5�}4sssim+ ^2 n-j �cwhereB used! �pp� "hL^F� ��Dlas��ep� usv/3�/%�)FH%A � ��>Q$%� satisfy�} ��B��asser�of �� m mmed��ICc�:\s � --.3i��%�N \sec�8{Zero-Dimension�O�4Singular Part}��Z� In� �Ad show/ A6s�t � must�s/ r onk e%@ zero Hausdorff d� i)�3Bobe�] vcass}. R�of Q kind waobtaine��� x�b by Rem� ��4Christ-Kiselev ck}� 4Damanik-Killip d���  will� ( ideas from2 rather 2e p�p31} AP M�1 T��spS��{�B [0,O) : R�,\b ��is unb� ed� some��& \}�G5 ^�>E_{{\rmE+}}y �m�prop} "�6�, implies $\{!n\8  \ell^2�4refore, becausa� -D fs},�  goal!toY�� A(n,��12=r(m_{j=0}^{n-Y �jZ [(j+1)2��%@,+ 2 \theta_j�6 L]%Xis a 5|un�eSnS~ $J$,8 vi!���D�away EWaAab�"� �"}=(klstool} If�\hat{ ���,nw $lim_{N \toA\ fty}1 = n}^N 5- jE��exists  a�sb sr} � j=1}^� ��� ,j)p{j!�| < �,~"�  ta'%2 \notZS$Me) 5��Wei���$:%|1�(in�)eB��Elq�iU�r"������? %�3� ,Write $\gamm:Xh N� N�$��.�align*}B�&R�] [V�-2E1�a� ]e0R�- U9 \\ .z1uvV �bZ } - <( wE5.�a��� �-�+ O(1<1*�Q�|n���| &  | �2@| )�F�-ewa4\%�2 J� -QFD| =\l� |m�*|m`�mne F)M�mqmb15i���SZ} Let�FT be a posi��X$uSCac�Dvarepsilon\in(0,1)�e� �able �m$m:K��q�Biggl�Mint\ L �n�mE?)} c_n!�-inAC} .r| � Dr\}^29Z,\mathcal{E}_� (��`n� (n+1)^{1--$} \big|c_n^2\! �' $Zd6c$Q$-�g{ $d!�: ^F �=��t $(1+|x-y|^{2�( nu(x Y(y�6-b�M'T�MA� sl� ly adjust=  calcul�2@p[\S XIII.11, p.~196]{Zygmund} also� -4V.5]{Carleson}q� �Q� [P0�ProI� on~\�� .]�Dapply ���rSL� 1�. A�us6��b @t�$ of Salem- ��e ser defin!$.($ ver�ff ,� J� ŕ> w�exclude)bJ�)uth>�  :�is� �ed. By))�!�@Cauchy-Schwarz in��_� 0dyadic blocks:=we se)8� / &2 ]�/4}KwA 1.� �Z� . HeG�� ��on4I�)%J� o:we9Na� all .�i1�� � �-Tn^{����� ,n)$j &� i�J� no mor%<�$. ����$���R� ger-Ed�aon2�BB� )�,.*SZ5�qt�l �cF�m_l�)}^{2^{l�- 1=���  t:����) &��F_� \tilde{m}kQ6r-1-n}i-~j��_��l�^2^l�� R� ��훱��f{1/�sqrt{Z��j �2l}��26� l�S��1�͉5�=\max\�A,2^l\}�Bc�Xm�{2^l-1,�1� - M�=] sumsklower vx gre��K�(upp"oA�t) d asC . Multipl��both ��ň$22{ l/4� summ��afE$l� �  e triangl���o� � giv�2~ �2{e�M8 }^{/U��U�M$�Y�*�Ev5�T��i��any��E��f�bigu B�2)" �\n�� ��is�[���n�g n)�h o�e:b $capacity �!it doe�/ a-PeE��te2$� ). AkeR�ofѥ�.g$�is � !n � qual t:�8 "` IV.1.4 �� is comple�3 �!\fact %j$S$��J�. �secona�!�bsa7"zsx!� $S$;:�#DCorollary~10.8.4]{�#F��N�%&�AbsTo� "�DContinuous Compone#��V�N�employ��6k}� &%�eAHno!�� � �A� s�.!.�_pa�y workM !� previous "�c$be crucialM3w% step��tudE numbf,on� p� "c0unit circle a��!Hthe Pr\"ufer radius�large. U:��� I_- b_K� He�$a, b$� � s, $=��� -c� ' d = �-�-1�� i�!�i^�If $ga!\l# �e $|�- g�M B � {j-2}|� a suit�$B&(��re%� s $Ca�C_2) such�~iJ $\xieH/��?sa�n` 1�f%5�1!�jb� i[jM+E�]G �0C_1 \log (\xi2pC_2E�2o6It�&�%o�i$$ � P + 1$.A�E;= �k = j"Ok�� ik\xm# quad��}!�} 5aS� &?" �U�Q j��} |��� ��+j}^{jllceil6�\r}1T&� log ft( ��� .�}{j1qFCz$smallj%�a�r��e^{}( i[j!�Q �ar�. log(6�F�OE� oW hand2 " .�f�A }^{n5S��=)r�iqǍm ��b��)��.;%�G�Z,�AY l toA� �VEv��bJ( Io�i&!�J( ()Ln�3V� �e�By6 "�q$L� ,(p�g$g ���*res3!!=e�e �2 �+�+��A($B$. (Split�sum into>g�:��Zq�� .) Comb�� ���\ *mx�� mma � ��7 } ��)�,0�����#sit%1�0�aG�  _1b1�� �� b�'� r} | �_l)c g�$a� n}{1T�-H(} � qK��A�!�}4)^Ts io�min28 d�_k �l)Ŭ�1/(3K^2���^kOu2�)�$K$�  above�  s ac� lishIPA�)�ADZUl43^�!)�%�A�s $n_0M�K� max}�  (A)��%�� �!�AEPre can n2� H X$� in $I]��Q�-��Q�9�� M�%BNConI�Zx&& ^�qD��E-l*!�*� .� _n$:�Le_l�� = E_I&2&�!_��:1 _l,0�(1+j)=, 4�e l�� K���&normalizE�5� $E_n c-n s�.a�t�| @ one. Ob��+>ŕ og n��N� !B$kP &� n$� enough"�'��b~ �fK51}{E_�(6 "� 9! �j- ._k -B_k!_ +2(b�JU( v�n �Fl� �#k�U� "� +RE#�.���1�C}{K^N/��1�We�\ied. stepdge��6>e#����2�)ey�Y �2����2 $AA= Thus� 1K > CI;�2��L��"�i߅l'E`�' �� F�_n$Uy��8 ��S�)��6�B|�2 �>&�%z��us ��6$gR#b0Ѿ ��zDue- =, !�� -� ���3"2��Os��2�F� =Au� � uqj��Am2 Ao  n��FH � ��l� �s6NJ �mi*&��!&�- �)��'1if M�Ae2��� ]K ( � )^2}{196��} N` l�t_!A�i�4$( roughly be�pe$!�$392 aTTl fu(we���$K Z�C,Q \hen�"�-���.� holdez}v�3 �us turn�A�� mai_ �:. Ga;B4 ��&now&7 - arguA62�!qu�&�5&n�*D!l;@!�A!�*%��a-*R part��]non-triv  Fix �79_(b &�"� 3"Jc}}�8= \DeF9�9.��d \2*z�p�%7� achie�p6_+^J)7 as   weH7A�J ny sub��=I�9s"�7ly Bl�9�<n%i#r� find2�_0*�)i�/I"!s)�ing�di�ns (>F 3� > .� E9�F ):� itemize2  [(i)] $�&� _0^{-3"�>�iz 6 72�(J)*�w)� }{32I  ^3}� !1c s $JQ& eq I�$|J( e :�2R ^{-2}}2� � �6�1/2}}{�6J�. 8E�� 6n32kv)]aIi&Y�/se�xm�} b�9D>I�9I�, "� ��ay�� J��Kend=�Wq>vat6�Jre�ILlongs��20it{scale} $m$e !z= .% m :=:�m�-wo=��IHA�ed fB ed}fA�di1 ce betweQirP<�:ceeds $36�^V An� a�2�%al2�[1�F- >2�m�!AlWh@��i�/ �v5�]yat Y)%E. :� _�2�$vVof Q!� : $J&�J_K��Mm�z$}m.$ 2!E� �_{n_m}6�(@Bernstein-Szeg\"o� N�B�level�$� ��bs@�S&g&�( �"� ih ���(3J� \mu( -J?.�V�F( ��:12N�B���m�bsa �qR�}AC# �* im R)e�� ,0oO Y|�l�e��3��K$,.~NX \gtru2&�/2}\!� � �?@ 1 �>@ X.a@D word�6���� a'=�0$a�. . M"�:$>� R�.QZ'"�2��u} >��u��� Zyieh@�t�I2to>x. . w�* $S_m��yun�| llV �a�}k@et�bjver"at � $8:�fsiz�0=o9�E]S%�"ls�8R �*�(:f5"J� a2�B�@perty~�D�$.��C we g\5e�{�4� S_m1% 6�: mes� ��6#^3}��el$42�^293� y $m��NowE�� := lK/i �Pfloor m6.� \re�J_l^{(m)� v͡ 1�!��V�3a6� J>�V)� $<>� a �D�,$S*$!�ce2%Ac� be�Aen�to?b� 5E�iJ8,=S_�etminus b&c $l < m} S_llzb� ��� 6iZ�����:s/(FsZhnE�2�Bf:�7�6�\e( � xs: r��E�1X+ m�.rrespond 6�^2$.`.5�K MR�5�mG4) ��)n36a� z� +Z9� m9}�" } >7� -� m}i-, 60x1B.a:�^32�0^5��@��b 8:�3���0 �n� 6cB I�� �i �>h/�� (iiiN�E0L(-"`<20(cf.~R�1)pK2� |_{I���)���s�D!)*e; I : 9s�%�?M40H;)� mu(k^?,k+ )}{(2 -B\�E \i$S�K�F\roger=t "eOkn D"�&m"@_n �90$& �.� �_n�_n�_n�K �e��J"t,�1 $m�byh]B{m_n}B� %(_n �:+�/=q�"02�[�We��)�F5 /2,k�![M/2!.06��9&i ߎY!-ft)YI���)�^��A\J�0�Ae2��6D��6�q6�^P\))�s!��g:� �  .U Hthebibliography}{10.bib�&�5 L.\ Ca�5,"JSeleca�PrIJ Excep� Tal Sets}, D.~Van Nostr�tCo., Inc., Princeton, NJ, 19676�ck} M|h4@�A.\)+, WKBspectral�Iys 0f�.� SZ�I� $slowly varH0po�K ials�TCommun.\ Math.\ Phys.}�\bf{218} (2001), 245--262.�dk} D.\ �@�R�(llip, Half-o(bQA�no:&Ls,� ppea; 5� Acta �.�gi} B.\%� Golinskii�I.\%[� �#doc@ } D^W#:p _�1�4we3�Aneed  �410.12�4I�"bl�$�sim �# $f,g"�#�W1 D(f,g0f2�H�-4- f)(j)| + |f((2V; �1<" =�@t $f(0f�)[K3�2�&a`�B*�1|%�&_�1�K" 5p�@�*�.�1.4/i(j>+�1.�& le 4� �'1'�1�'�C1} )%[%�-`�%%%�8 e#�R,tmonout.tex.m* ainsU# tine�,n7 autoRly Dge`Vte:  (1) �� title pag cDc) rmat +$2) TeX fi�Eo >e u c� (�) 53) E,Ybatch ?to renH]�n6E`J .batL4L data $ paper.dat4JKfi�publicH1 �5D� {Z� Gtx G emai�$:c�Xr� ab�c16Kn html>Lhtm�!<.� Us�_makemon�x,�om�;�E)��3�+� @�6�of GTM �\cle �2U� �.S IX.8.E" !�instrus�gtoutpA�x � �C�\ Rourke 26.7.02 % tesE{ �Zx or plh%$ex \def\ifXtex{\expandafter\ifx\csA7 �c�aT \2[x}g get 2centerA�]%^ \hoff�(14truemm \v 31Z \h�7Lep 23pt \footskip 35G-BG 12.5Ifi �gt{�8 surr =0pt\i\% G\m\-2mu$e�sy \&\ $8T\!\!$opology}}1�% joura i�in�:omm�style�m��� �M �1mu$on�s �% ����s�p��>� P\!$�� % GT.�~Add� esr{!r {\� \par 0pt�� plus 1f�6A�\{;�+lPLa d \med7 E��:\stds <\tt/��\hfill% Received:H/\{\ date�}u�������recd{1�f�� �>se%i� e�\q�8Rev1; !:\fi!�}} �% J35?, new ingredi'dXmT�E� �U���ѩ)ŵQ]logD?#1�]f!�{#1}}� vol� o?+.B.yeaF,B*�+FVame*�eB�2,ge +s#1#2 �start!)E��Csh 2��#4� !�:-Q�&B'%�&:%ac�e&>' scii�3Othe��>*>*autho!+))th , .m >� B.�ZB. >.�Y>,>*urB(ur.&� �R. T�(E �^ 41i :��5key�$500erratum* {�,emptyI� I�A� F�.>.> , *��cis�|let\\�� th���"th2 }� �0�>�5� 2u�  -y� *}�.�  CB~D.b .1�%  Fq21-� 36I� ME5QM 26Q8 7.��QMH 0�eY cER�^urI� �7 a fe�*i,� S p�fs�Z5�{1}e<9�{15 th.O{77: %%% Ed0 n\three ��� r Io s (o��P�Oi� | %dE�s�. 4m{�b ���eex<W�aKirbyfbj *A�{1999}�I make%Dp{ % ���($ \count0=9+ I) m\nl*T  GT� �  (top~L) "- V��)V ���:.ameW �th:=b  E�� 6�\nl8 Pa�R�--=�\nl vglue 0.� in%�margin��%" � � v � � "� E2�  #}{*= \nt L�G[ b�h}��� � �0 in� m : %��lfc!O D} 2t% .t3� t"�� EifR)�s: 1�9$ 25pt* �A��}*� he��Ibf AMS dk6/primary�U)�K�UE0;E_:� �K�<e2k !*}-�7pt !�% enda)j7� Head7 er� font\p)=cmsl9�(d 9502 nt\lF10(pnum=cmbx10;13; p{bkF k&���{\vbox�0pt{\vA� -4.5mm\  �\ifnu�J>?H ISSN 1464-8997 (on�6)  89 (� ed) �  {�\folio}%�\ifodd��m� }%�=B2�Z� ?th."fi i2hm�S \{e}2 3��pmcM�A�� Ku w$fi\fi}\vss� !�)K6k��>h.)h-.�P�K .�� copy�\ \gtp ɡa���umi .�\ (� �f) ; � � G�latletter�l @oddA��I�^��'a\��-J/ � \{ }2�I�bse�%�!�� {fq67J� D2�Q � w!W�E>!~�@even%d1m1A.6\e�b{�;�;)�����2akeatt1 �� , %�@%'#age"N &$input %%%t���cr�U xxx !eer��new 1\�w gA�1{Yr{ +  \{, )�s{ Ij�h\op[7tu�.xxx \&:�C xy-fo| -���QTE|R{2'fi\s<2A*� U Q�< fi>2�>�\no�\\r(A�\: 2���}5h�5]>�T�<:lIC91 2� fi�f]Subj-�D: GT or SG, GR etcrMSC8!t. 1:�����qUaS �n=J=0-ref: Geom. Te�4�.��!��s >5 *� *� ry&j:��by� etry��ogy M�aphs atrW\s0 http://www.4'\s.warwick.ac.uk/gt/GTMon!d.�/p~ � .abs�lvz��EfeQeC/ )�n��.��.�"� fin1�b-��E�?o.�J ebp �,.�kes��?k .�Nt�(�( I�� ��: m7-16'�7 "C Hom�'�esent�",Iwahori-Heck�bgebraB6> Step�EBigelow�FRN&9in�7�%$4) 493-5078>T=�} 13 Dec'r"46>;  a La�06 8n61 \2Y{gtart_h^;� ��{7}Z�Casson FB�2004}�pe�e{16"l{493}{50f�{9 Sept5C3�O{25 May%Y} "�{10.�ed{>��u$9 ckage{ams�8 , amssymb cd&ldZ{�} 1 {thm}{�% em}[�Y]2#lthm]{L�#2prop} *�36$cor #"�[>!nj"njectur�'ne�qn !Q�@.I.�,*{clm}{ClaimB�&):4defn}{�:rmk}{�|Tnew� $and{\Cplx}bb{C}a.! Real!RB!Zed Z �cHom!rm{>dBM!BM 6CChain$calJ���.#HG2�Loc�FLB#Sy�frak{S" %2Gco}{\co�i thinT>Wsig�rm{C%=��2�9I1P !V^�\\U��6�a���HHI {:a@{D�Bt� �&�(s,He U ,0+of CalE?nia�;8Santa Barbara\\5'$93106, USAy�{bɌ@�Z .ucsb.edu�(A"� Re�Sb6;�type $A|K$ �Cequival�~�%RR4braid group $B��[�P�^&}s�vO?er�& u�hc � �D.G6mCu�Xd$P7:� Gh natue-a�$� �o�8h3�0configuyonT]"8p-rur? disk�c� C8 all irreducibl�&*�U=i��7�/be7Auis way, ��n%*ic*F1 $q$.�=� �1�{% z��P a !%�-��@ ��B_ �5� �t3�� ۀ=�Ij��HV��)� ���9�n?z�!I%Z_nJ�?w!�d@)-V�q.�r.�{20C08 $2�({20F36, 57M� \�{�, �1�,:+,.�,!p>V��}y�"9 \v�{-5pt"�� Ait Dedicz�Andrew� , wh�l�Ji�7G@ccurac�elegancewWhly influ�2d m�b}:H��� �0pt"/z IntrD`�u0�X �|+cwlra�wit9V>A�+5���N.�, si*s�lem|motiv%|&[ A�� ob� s�lby.��6�zs ]F�is���m�edJ$\s��1,\�b {@a$ % �ngg��e:�L\ Li FjL; `ji$PJ$$|i-j| > 1�R^> <iNGjP=1�mR�4p$q�.Gt� a{J�6 doRO�X)=~�$(K,q)$, or)�y=�,!�A$K$--��6pT5kT-fIt�fT_i T%\TjR*=.=4A9�(+ + 1) - q|/��5VE�V* plays!pG l ro�k:�!'ory. KEq=1aOhU�vis$M�-L $KS�F sym*ic &$ SK=icharacte~<icAe2Ais {\em)�ic}a#�o��H$isomorphic�� ~.Qc%�ic60ns $q^i \neq q $i=2mUn$. Most?Rearch��6�>R6� unktan!% .� case�gUh an oY map�n? �� *�ei�i! pstoA'eSB�/HF^ t�!:� !�� ~T  $(�E�]��6aib6�I�� to dv� a� "� m�6of!`��� such>�)P�S!K/A+)8 in S�� �S sec:6�}. Brief�!F�;@aC#�@. A��Y A�� a� eMxsm)�K6�  $Da to itself���] nduc+0JF`@>5e m(D_�mFN$UVn�!�K  module �Xed �$C]u>�!��P�%�"� E!2�ed 7a l3.5� system� &�YKf.� � $B_mE�-��UYH�5e�8%�,thm:hecke}, ы����f%�5�� Jd��i.Gqui� F( �pso�n!� �A�R]$Z��s��f�a���Tr� �al� R, B�HmBM} �k�a ";x�r1�i�06�,��F�� , it"8n� d�}�E�� 7�n image!za �������{ve[ ereas2keDatrwelΏ quot�0e ond� ps�1[�a rooE�nZl0:ULmfe<gV8 ic. F#] >A�5e�@-3E�preciِw�A6�s�m�ed9 E�EB o�_tsN *ly inr e��A�:d}�ous��a�|a~no��th�\ouebY��"� � D �!I[ `6�^t $SA�A�mplex�6ne.A-1 < p_k n <0 M distinc4�in4\ M realM&I�� $n$--�MF \&�O{p"w p �B� 5;��� �-ofA�&�$s $f \co D=;t$ M �\ $f |�4|G 95IA�taken��isotop�aPup�8a>e�I��&b>OB5 � exch��$p' �x $p_{i+1}$��pIu$8c-}wis�lf twis�|blsoUFž�!� \�fundaOal9;`Bp .� XEP4a surface, let- n(X)�W%�J� of un��e�_Aup!:o?�6H~�X)J)�N,pi_1(C_n(D),BF=i �vx��oopa�JNiswi!<pla� by%bw��nyoneA#v>?teUP� le�D !�possibil)�y���sQ �h�, a&��hould�� techn�l�U�[�]>�of �.!7B7 * �W�� ") �i sugge�6g�  r ks �cBb! SsenseQ soph�z?ha%hI ��~ � A�a�>UsrNa �!) $9mH!�.�C�!jJ �5� /c�P7�Q !�&�x$2gӊ/2v m$�V$D �eo$�P,c_0)-ɼ2C�no a deep 6��b2Q��h`� mť� yP d�cT~ �e sub��$B_{n+^�!�ng~g|>D�s:�9ya17A�Va1 �r�J%�,CS� .�0�eb��map $%�{z"�z_m\}�\prod_{i�Cmj4n (z_i-p_j).$$ ww�.E �Zed$ qi��4��:��$C%�Axwi��"!%� irc l��\�? Q�i� �)2}&�i� ��WEbDIIn $i_*�)4a�a�Z qMH6<��e~m-��c�qafxT!{g(v!kHq^{w(g)} i_*(g)(v)$�P�jIxG6evaEVe� e~!=,$V$--bundle OD!YO@dromy�/��z��i_1LH_i(C; Y)Z�)�3�B(&"� $ B$���{b����ism� d. A*�P�!a�al s�er��9P{h^�` E�S/ to C1��[$i$--s xA!-%enF= � �lif��@ ~���LΞmap%ms r� �*i!F� ��:`� :�%K�p� cular6Z es�i� midAW $H_m=�.�{:� F�k��d!&Ahusual��"� �0Borel--Moore}�,CbyeH_m^\BM�- li�Z5arrow} �,C��AQ�,$ɐ�gin�Fe_Q!��lniaNcT�c!a�sxn%�C! ,k5u Md��f  Š��$ 1a*y��.� ��:0Uac���:� l2=<f�4V|$f'E��  _� s �M��.!<_*)�u��A.w'�� = ��$a�%e6� > ��(ZADL�qu!�f�et܈f} �iu�Q��v-A�fiW�ver�i� ��G6�a�6�a�is6&&�l%�mV}/Hf$ $nko�#a�c , so� aiU9Ut^d��WEB{ ��� :��qij,UL]�)d/ ����$I��xW1aLlU�our�"��:( !_J �Jd �3 �@�[impro��a� , �Lupa s � ]M��oE!ri���� % (�K�Iea�9!�� $. }�� &� %)�����)$2� ��"�0�V%�ai-� wF!2���le�m�1&Βs��B� 6�}.� �s&,!�u���.�x"щɧ��are �6f $W$, but%�I��n easi��o*� ��'�*)D\Pi%a s� �qcL �~= (��% w!.�x *�a�R����O� ,!A��5 �E�H� �-� U_\pB��� $\{x"� x� ;C2�2" (epHand�P\sharp (JQcap2i,�)��!io $i=1ǫa���*{$mX all, �lemU��I�.!J!� dire�zM$\binom -1}{ pa4 V$, �.l���YQp%K�t2k:!���M'CKi� M'��%�!.�-`� disj\��o���+:���C_�H2;VEG �� �pYk.�_�b�Bx �p=�_0� 1VetT6 �a"� >��N$\��rM�A_>� �>|E�6�,|z_i - z_j| �` g&% "�$i,%1m�o� CpfC$a�8aQ $.LT".�"� each,�!/�"act��5i Mzi�Pn�+Y sk.7AZus`hsds�*���!L ��F�B�Q}� _0,C�"�9�U(:z ���. D'�Ret A$!losX1A8/2$ neighborhoo���Wp�[��]C' = �'�!4y �� ',C'.A �Z $,2c "$$��To�Q�1, n��hom�shrinkA ( C'h  $5� �-$j�Ei�")sU!d!t�]Zs'.m!n � �z2$$Clu{ehli�9�=qB�)�n �is�ba�ci� 5� ž C'$.9p exci�,�� Q�U,Us@=�f��� � n5�diy)Vo}'t' � U%���%�B� $B��$x�2�%�z_K&��Yd.@* pair sQUS69.:�QTť~.u�F6b=��x����B< �ZF � Kramm"�2�}��a��a}R 0 �mlo�#� ��6P � m/��� dK00��da�k�aithful )�ji�V��$,� te�&)�K*� � gene:a�B_2� � Vo m� p"�Wby $-tu�IEE&�U2�f��e�"Y 0 � �� monxa*AI���J" h2�F��Fe*LG5#p �j7�a _4X�ZS�ak5 (4�l�Y*5"z ld>�q�By �8 }{2�H~ 1@U ij� � U_{i,j}EH!_s" �l,y\Nv x� (p*1 $ ��$yjK j+1���u:gҳ�$H� uBi s��X2�����˸bg�bas�>f6a*���o�hfRy. Ʋ&b� RA�]�2c<1a1_T��Z�a��!�p_j����ior�0���h!pl�"%RVZ'-�r���v:C����5����%pri8W choi� of L ordinatesv^ ��I�I�kE��r,j}u_{k,l}.$$�n1�a-��.S�)��har�gr ut�4 Q`YO!J:o��q��&is mEtyv9so]a�1mVu� by�t"w�����`auc�n� ua:A�3�us�h��џKyѡ``ю6R'' ny ringYi*ove'[C�)(e 5.7]{sB03a%ª &A:}*"2�-&�* ee!b��F �&,�.'"f_&.�>@&�! �",&x"}/\bar{x]q:ut"�{$K$c:*�4�x&�1q�K$�7�eqA�1�=q�0�S�.u,"v�V�V�w o ����7"�6�+ �"! nva��yH!H2"�5L4~� Bisj}= bG{q�B�(�/V �' 6�%l� D�a�ex� itlyaZ �u�)o%Z�15>�E�e]t"+,sults 5q�3 . U1seI\^s �� F=-� ! �Y<E$Ŷ�"m^VT� licmzV��*"���1of� !�*�$y'�� �����a�FC� ialC"�����,�*vc/#probab��Wlet� elim��dd����$� �2o E� V� � 2z%ap&w! I st]eex����%;�laya�imporR}�4 i�0 !S��[0&�*S�%s�{pi fe��m?�up�Let�f"�f_w� o (I&�I�2D be{ Jver�-cs7�ed upwaO~2!2E!6�O{��>4:�!�%r) nh pas�d"���e�Nť�fsF = fg�,+�+ f_m"l^]Ddv5qq3 o&��#g�lif�F$���� ub� 6a9eC��G9\:'� y$� \m6:aja�2� n!h:��f�a2�������N& �RF�1�<)p��'vye�&%+eC�V%�cee��60 523�+���!jE y, st�&a7'��familiara�!��X�, D  ��"�$�Y�E�A�! co�$H^���MpI$�"co"=6>!�a�,k!�hiP9Y�s�Cs!cB;j�" aE� P�7)2�""t  m�� io48FE6�&(�* ��5�5N�FS!�T&/6`� t)�%#"�-� :"55�($H_{2m}(C;Ka�Nv�� �Canti-">:sm�N]� 5!�s�2 d-!,>Qi�t8e06heff~ve:� 0�%�se�eb�"$��s�(   ~��Pco�(�R����K#fQ2E_?4i-�" VQtE�re2y , sesquixVa%i� �Hc !.�R 0V�(� $ a*���u,2' �u!Qin-Q� v(2t$v!7.7.)"r(*�u� v$�>�� d5*s!--� �}�_0s � u_1,� 1(� s6�F2UbO,� M2.M"T , �� $necessaril�-q��n p� ce, >xC ofte!�!0j! i�sed��o�U�� fold!7 , to.�� $:$u�� vW<$&� g- Ni$�+� u^ .U��!:�b��[?�w�����.��� $x� 5i�"�!u_xQ2 �Ln��_ D�P�u} 5-v��4f*%xD ��QKa-�U5s�x��.&_x,v_x"�{)P_C� ll �N�k(a/��$ ie)��!UXy� ~ i�2j.�=2��6�W�6W�. j,w_1,wm�WI���~ $a|u "�R=@)mapd&A�.��'�Ž� o-�W:�i 0a�ۧ��N �1�N0� @�q5ve9%� �C�7eH��rTWO a6�&���;��S��~�0i/�i;� V=K=w"�gR�˒B� ,ty+a.� ��. %??)�.d�!xV] @ +�W%f�9E tIhvC�2inm(ML�6��n�a\�!�n�E��!aty oB��'K�=r���r>/�c�,rB??}, Budne�oS%�| ��!@"�3\it�3nd�%]:i�i9�.5.�:_ V>}�7K� *Ѕ�--.n4EJ Q �m 1P� eZ/ .�c�"��F��J��4��vTo avoid� f�0, d��%~uL����$Q�"� {�%aKn\>B:�!0/<  {n-14w�Sw&B�9aq>L�V*k�Q(�*$ 1)(q��_��1�&0"�&�$-1I�%fR�]2pn�-WFp � r+�G�$2Y$��&���}�%sR�#�V�*�B"�Eŕ1)�1�*�.���� ��1�9e�P �IIn fact,�$�v}��,onȐforUN���Ua$ ����S.�� R� "G>k&� ��������������g 2 be�)�a� � F}H :)$BC&�,D? sk��"..��Y�eio&CIRsv = 0$ �yU�� V����9. Ca�]�a$� 6]� ��1?).>2)0$F�o}�a�. (oX;�dj*2 �i4Į oֺ) � . N��i_6��@ �Q�>w�Ʉf_�Kf �$�(�m *vf� �2�f_mI W� top�e�Zf_�" keep��mo�W��fk#nd $�end� %E\%;a_A�&y � oO�,paths=35 f}_10 ���g�� f_1(, 1�pzng.� $58p_3���c!�FO�r�*����.a�ѭDeqnarray*} G &=& gZ jq, \\ F'/ �_1��rn70s6Aed u+v'5,uv'T "= �=@r� 65G:@F}'�YG RF(�� !9!.s �/,$F$�0V %o��ite�)TI&0$thEmp�06��%��F; Co��$�U\a��6'c�9i1(t \{(g-�}_1)(t),!�(0) f_m(0)\�!�� | E&J$�e .F*:3Y�8 I�-��5 B}$ E��(F!�:9e\ �.? � L.63'a� �FY%_aM ; �aX�_uA� UJ�)z $N 6��5 +>fa�%�?$.Id m$FE& , so �F�<d��Gv- -q v�6 ��u�i3- 1)u�O� A�p 繡�11-*] +qVS8 FT�Ob�/2�-/0��&*w s+ZWq2�� $U.R,%isu�@F�+E�C.�s�&"�(h+IXz Uar=in$�W&u/�>�"(, O F�Zi :2a"ZH�&t!��E�ui�H�U \cup&H9isH�0he���eRGJbD.��gh�.e�4,��$f f_U,�=yw�;�tr&A�,-�To��F/2Ip$Y�a b@=�Qp)^�U��0*UEY.PR��Pj�$"($UJ5!2Ov��$(1-q)v'~�! ��is:�I|��f��� .�26�"�4�mf"m� $g_1 gYg��-�6�go � �*� ��$L-H��� /2)i��iXemiAKAf rJ2�Lp1 �y�!�a6� �B �p_1+(Y�)L� &8 ����G_� 5�!� f_3 \ZZ f_mG_��=T�n=* ��^t+ v_2"q v8Fn�O*UxG�0} si�aneously]h%>% �f)�g%hby ``pusJ% down#''��onh�� aϥ�e� � =c%�a|���QG1�$-->�4!�O .��.`su�?!4�()�'%�=�- 9�b�)�is?�� �?��G��aso6%*� .1�F�c&�+�*�/ed5E�_)bY d.b�*�8 6 g ��w!�rC�`)!f'?B Ga !�i"{Z  f(n��  3> � I����F � G AF�' �� :*&^ ��B !�f�' _1� 2 fR�"{C�!��*m��h��O e�%gE/ <2ea.<$3K0�2� �N� Rj>� G}%?��1i)�;�%k*�y�[)�>�'Ŭm $ N-�* G(� )� e�lde 8u �e %)�m�} �I��]�a�#NMe �) 2g)� � .i3tE�4 v�� _1�9� ���K (1+q�1)v� ��+e $|fA�-�(t)|õ�Z�$�� I�%T�%\{(t_1,t"?t%�Lin I^m : t_1 > t_2\}�!T��9< 9�f}�G_1}|Ta !r5O 2$�� &zw/w#��b�  h��"=? + 9�� $$H��� f. | !5 I! E2,�ESo C9w�1/H}4)�8.b H!%� }0GaiHcV2n2р&�(���3cbMA�� �$�*�Hei�6�6,2e�ш}�y]oC ����6��5 Ш�Us�| ��aE4 7�6}��isi��/i�u�� = - A\AV(2h�QJ!�&� JB'� }�(1 b)A�.�f�T"�/,c2�"P&a1 $RT��jM J�!x�+�,%SLOPPINESS:S%68Y��Q!!F�:� "9gC%^�)"3)u %�an�/��em�.&- D&b7lJ!�V�aCR3s.&:�1"h K%��b12�(aB�NEH&�b-T_oŁ8&�HJe�42�N�U68}.`9 r>!�0R�� factqmv!-�\��q�c^{�r(nd�a�s.6�./�AthɜRndbreak�p�] L! DJ86� ippeqFJaKD+ifEfPm>u TheyFn2p�VN]�P\lambda�1�_C y��$,�]6�$aL.\ �ter8!\��Furmm �ey%jW�O1 Uio7�1?��!�"s+N��F�)IL%Z ��U2 \L2 &� kn�W1 1 �ge k&}%!k� *+(= �eG\mu*� �T$(UA�����n-��YI �� :d*}�"�6.�!�)!�:�$D_�l�3� as��:4,n6�by^�c n $;'DU�h!�}z-p�4�m�pFX�=��du8b�R9)�z�VQ~o $D_�Lptyset�!$&�62�A�"�nu��+K��� njeVv%< rue {`K �7  J"�7genericN>&, ��Iis�6��AD-�h Z-�I=J�b� |6edsom�bA�a���U+33ly�/lX�d%��Xi�a���s�u�Hde�q'4o��behavp=toS6in)a�Ѯ�: >eBV�;&m\R�n�ma�-lB��r�_iIB%.),6�s/ YX�aa1���  (*RK dse��Pi<H_0J/=�:� !E�2� �zWEb':� m\m�jq:Y,=A d�d<�����Burau:���-1��%_��m!o�, $m=�%��C&!mJ�iJ E�y�!+�2FX3"�6G&g<�*uK.&%apw& U*�B`Bk��5 (DIA],an $(n-1)$--.�(.�( ��I:��pe-#_�%mkf*!�9j eR�"�k6mH_��H_1� D_6 9K a��*sm exx��;� $n$th6�e�"�*�1] map%?a#2��) !=�s.r� ���"�*L��P ch� if�fi{�{a`9�-�.J�q���q^Pb�m���$QN{-�2>��fv��a�:�*�2.�o:��l�> ��W�G&L68 1�@-ql ��u6eGQo �1 �8�2�dr9D�G�[�o����GK�J�$ B}GM�v�A\� ! U:�$ by a coun�^terclockwise twist has monodromy $-q^{-1}$. Let $W_0$ be the image of the map from $H_2(C)$ to �^\BM(C)$. The main result of \cite{sB03} is thad�`dimension $n(n-3)/2$ and +�e ``Specht module'' corresponding�\\lambda$. However I used�assumptbthat $q$\\not a square or cube roo��I$1$, which I now think I can do without. If $q^{n-2} = 1$ then the kernel!-; f%;W!^to $W$B,-1$. A basis�4given by liftsLannuli V�form $\partial D \times (p_i,p_{i+1})$. Such DexAbecauA(he loop in �Lone point goes aroun)Iother  !�4all punctures !�]Tq=Iac%�(of $B_n$ on!Vs )( -���R�J8symmetric group4 is sta�e �c,understood o� ,non-zero chaA�er�iV ideaDto � >uv6��b$\�% _n$ 6��ĩ�iz��t $(q-1!� Oa��  effec tak�Xtquotient� B �m� 0difficulty if�G} seem��Ain)�V!��u�P$Hermitian a� ^uo�at�0universal coex�theorem�ׅ�P�rIG�T I�toru �$l�^��!{(inspired byM� duea�Zinno � mZ01a�- state� Lawra\--K�d>�a:�Q\.1./(BMW)�<)&BMW, likA�eZ@, t5��braidI�K byi[�on� !Igen�8ors. By analogy�  proofZT)�i�thm:h�}y shouldApos�%Zshom at, up!kse�ild�4caling, Ad$V$ satisfi%qv ��� �=�n so d� $W��s " |thebibliography}{Law96} \let\old \bib \def #1]#2{#{#2}} V +[Big03]{.T{\bf S Bigelow}, {\it!V {L}U\{K}R^},�: ``T�!�d Geomete ,Manifolds (A� �s, GA, 2001)'', Proc. Sympos. Pure Math. 71, Amer. S(ProvidA�x, RI (2003) 51--68 \MR{2024629}.� ud]{rB??} �$R Budney}, �OTi.��f�T arXiv:math.GT/0202246zDJ86]{{ Dipper}, %{G James�R2� sAh{H}A�q3il lin`�D)KLondon =5(!#<2 (1986) 20--52 !-0812444.-(Kra00]{dK00 �D �[��.� {$B\sb 4$� � }, Invent1� 142%� 0) 4!�486�1804157>�2�2^�B�NCew Ann.!9)(2) 155z 31--15z887aS q;[ed ]{rL%� R\,J�f1~:\s ocia�� {${\A" frak{sl}}!,$m$}}, J. K����y Ram"Js 5!�,96) 637--660).414092..Zin01]�' � M\,G�C�On U�'s:�!.�U=�}, )@%N321%A(1) 197--211 �85737E?endB�, \Addresses { Hdocument} ��% % L�Pmodified 10/20/04 % \,,class{amsart���^usepackage{rlepsf, boxedminipage, amssymb} %\input tex/macros.tex %\oddsidemargin 0in %\evensi: topm.%headhe� 0.1in %sep @ %\textwidth 6.5$ 79parski5 }parind (0.2in \news{thm}{E& em}[�]2#l(thm]{Lemma}2 cor}  Corollary6! prop "Proposi�6$|bRemark6 fact BF .� *{tt�.{ }{Q_6P}{&�6� }[A]�b!.]$*{claim}{C.style{d �0{7pt plus6.3p�n 03pt}% {\rm}{}�&L0.75em}{\thmname{#1} umber{ #2 (ote{\sl\std#3}} \-�B�.J-fEX2�{exercis$\small EIV,command{\bbr�t!�\em O"ee"a� >@krn}{\op� �ker�neD$la}{\langl �^rr %�bex��B�#�!:EhwE-)>L* L (�> 7 e't e e� � 6{s}{\v.�$} &Z6=p!s:�be�num!zeF}{ �."re.�QR>Rv :��0vect#1{\frac{5�  #1*$co{\colon\�e�a-!2$dfn#1{{\em 0���Qh�< \title{Invarian�Us, Embed�s z Imme�s viaPt�� �Hauthor{Tobias Ekhol�a��{DeA���3!e cs, U3it�Sou��n California, Los Angeles, CA 90089-1113} {@John B. Etnyre} %}Sta|d k,  Q4305} 2)� Pennsylva�� Philadelphia, PA 19104} \email{e@� <.upenn.edu} \url! ,{http://www.6$$/\char126 C!�4\thanks{Suppor in !J�`NSF Grant \# DMS-9705949.:$keywords{tr,%�(ure, Legend!�vex[!> subjB 4Primary 53C15;�ond7M50}Q� abst0} T�papan X view!Nt�Fof co �g� to ��]�iU�$eU�. I)�ar,7$discusses �o&b  ab%mfvand a=% subMn��. W�n� rec� work�c* es i2~Biw�-)!;9��!R#asH .�.T 9� \x� I!�years E�.VsA�1��%symplc9�has been�"� s���^p�s. E@E$wa�� Arn� Aronld94}re �btudq I<u&��Yr)dDed plane curves. M�zally,puA@a�@an C=!!v Pto (unit cotang!�bundl$\R^2$, �is�eomorph� ", S^1$%] / carr�a�fI��!=�f?2�knot p6 �s selfkns��d�demL���1�6��.srbuseful<*0iI`. )K�s lre� A�top!res�� cert�ways. SiLt9s�pickedSon �'s�!�]toM�co";x)��in U&]sM� Goryunov}�ivGan excit��G arch%M" A�n Ooguri%� Vafa `$OV} sugges�a N� ha� leva%o%0ern physics (�D�)` ``large $N$-dualities'')Af ew w&of inte!r�!�AIvbeganB�aeǵ�holU�-�$(or ``bran woLag� q��a^a�yEZ��$\R^3$ �ed #promi�i��|,)develop�� ��FieldM@by Eliashberg, Gi�al%�Hofer-� egh}y�d�l�)��une3s�>�. R�jlyT es3}�72��ytic npin��!c� _��, ��edr5inS#-jet �%s,i� is necess��to��.�a⥱e6ofB�ha���Ng �Ng1, Ng23}han�]Oj�aqdescri@$�e '��#� �wut�����P! @.*.ya�S�"a�%:A,Z$o�i�v ongoa�u�to%�zis. N_#e less�'A�-V!'�3 on;Dbe amazingly power�L�$Ng3}. For ��a����AlexaNE�8$A$ polynomialsA*��� uishEYun!O f%�G���moeOi�L&1it�!zlet]>!p]�"go5�[p; toI ��2s�4iendly introdu�!4EUI(%!I�n�� betw��Y//d� Ng%0L", )UctU;Aora�inv=!�beauti!��; playp�y,"+ ,i�si!� ombinator��a� `#Y _!onlNg-�s}� hop�kA*�����nd}�#�reader A�ick�Y\� ��clearn�a-%it:�Wtwo)�s conP D���er �����(�B -at!fApE'� the �$�'"K 1!i")w��p) �A�E4 R%bse"m both a(#rt of a� f� MbE�� �y e far bey�"E�is���E�8 liter�% #Ac�" ledgaMs: We w��XI�0ank Hans Bode� encourag�lB!o wri��is>s  ma�3 � a tal� #� � ga$ t ``� !X"�of "�''!�%�c� ld�McMaster*v!�Ma� 2004. TE!fs e�&^!� Swed��0Royal Academ?Sci�s l*so4 Knut�,Alice Wallen�� f.)�# . JE[ sJX XCAREER _(]-0239600ID0FRG-0244663. ��f \�{A -iica"[ �f To ;%H $M$A��͕�"�0$(W_M, \xi_M){ n� $N($#>[2{ .K$L_N$A l k.$�!�V"&D)�$$briefly re�'&�A-&�)8� A�^��� S"�)~�)tmfd}!!�j�Dctf$.%cz�x �!� -�sB_�Y$%6P8 �ed,Qp��v`(� ed, 2^9� .$ T���1familiarbܵ/w� �endZ"ing� �� fCI�z, Geiges }. It �&"�(� to look�%��* -Œ�i*�'��Q��=;=R%�+6�w(I_1���K!��� 94� %+� i"�{Basic�} no= (s}%\label{}�pp An o #=1>u}��'4able $(2m+1)$-1cE�x(� ly %�gr5f7 : � hype�nes $\xi �t TM$& a , a9.13*n a :=#{\alpha}0!�A7�vanish�� $1$-�% $ ,$A2� })�such �J�!A\wedge(d O)^m (a volumeL!>$�No�n�f@ /�%�[�$ S |\xi %.3( . A  #sm!\1�1�s $(M�7)\to (M' ')S� ed a2N } if� m�(!��) \xi'$. An�Sion� n $m.f� LxM.p%ny�h,$df_p(T_p L)Q��{f(p)}$ ~ b $p\in L$.��$�2eAB1<}mi���/6 We��1i bA!�&=$m��he6� ��A�| �1�.�0 i��ro90iv4)co-q|d$W_��E�s%�A�� of Ns#~H $T^*M$: \[ W_M=\{v!�hT^*_x M: v\not=0\}/\sim, \]�)re $v v'$A]$v=cv$A� a iT���$c.$ C@ ly�(a $S^{m-1}$�over $� 2s�.T h�3U0 W_M$"m�*. Fix� $g$m�! n�+ �g2�,M: |v|_g=1\}�t*!;�>n~�N(!�3 n ob�,(-,\[\phi_g:W_Ma;W_g\] seP/]equival� Xvm�fDv}{�}* �G *".$ a%�a 6C&4usu��%-~}V� , bu{.1~�� rea�+� $%�5be� ed`J3 choo�5� . R"� r�/=on1��l86,!��� Liouville /,%�A�il :F%_ac n,b/ �"ert atI�ny V��:%�^.E pull-Z%� �)�M$`Փa��Pab6!equ� ��harlam���^* R = <�8���6exp*% �in %3coordJ�?8q_1,\ldo�q_mK8B,Athe o�1� $U��-`[1|%)*�7>p,p_1, �p_m.rey�6�/et!���_{(:� )}U$A0Am�tena�\7d =\sum_{i=1}^m p_i\, dq_i.a�Set $'=\pi^*,$q��\pi��T^*U a�UE9a&�wona�#en. A��e�I�!�V�'�i� easy��verifM�jr� hE side &J,\eq+6M*i \sto�� buse no�7 F� ���)� le���i&m��meagE�!6e[�, ��s!� conf��1dopZ]ta/d �O�1inx�5&�6�%T��� �^�\aD#��:� (hav.fixed��)�IeT!�)�|_{W_M�㡰�&� �:�Eiq�m�=.}-���!�d [e.�dA�T  A�s*/� va9��.� $([)^m�.${ e j"or�z.w p_i �:\e ial} a�2U4c?� itM�%� s.to��.$ ,�6 �!��in&�$ y! ��.$ So!-1,-�=�( 1m \iota_v!m5B$2m-1$�� �ot �2Fny*` ��%ab�(v.$ (Here $w $ det'� �on.) Tv4�.oa�Q���.JM>@v =\kM2��qY�"� � L Justawe� m�a�e7O5 #*pe(* way,J>j *} �$��re��i��bofcA? vis D!A)� � �/t�� �? !;� �1���JVA`da� !�a';ly_�["P2 0��\<QE4&�iU s al�6��y�bcta* $$ w eq�9T,\quad a\in(0,\infty).% n �%!it;  2co x�it~=���7rs�n/&<1s ?whose�7a�a�. may&iz!�is9*byP fiber�@: y �-��:� (q,p/rH�>ci&A�!te aboveA���*� $$ (q,[)\�0p_{k-1},\pm 1:?k+p_m])-uk=1 3m,GU� tran� on f?. U� t>� patche���t��Q;M� y��:gas af+8]X9��t�Kw�A y ag�crict � _A�A� aforward� cuU4�w�!��6� !�=K=J RJ have!@��������pm@ k ��1  dq %�%� 52�+1 =%�;2m p_meO�Xer"�&2�/}[l]{3i.t -�> ��*bf smo��?}e�\break!�a�%� �-�3:\$I\xi).H}`+6� !�� lS&�&s���*se�A �=_<"a� h �q� -normal��L_N= \{uj4W_M | u(v)=0 \� { # } v $ TN\}A "CgO $(m-n<: -sph� �P�:$N� eo:52�in ��^{[ }$ S  se $�nR $_uL_N)rt T_u5  I pi&>*; JL�B��e\D� ��6e .\pi_*(v)% 4_{\pi(u)}L.$ H8!Pm�_%Fu(2)=04 �.�0�� $L_N� nU�"� Fm����A� L_N,$ or "%{* $6#\xi_u� �1UY !�n�&foŵZ l�% $� "\al say��, &�hq��2�6 6�[bC[��>}} As� M$�0 bH� :IEvK2�q0�1 6� !&� � imN,�to� � %pa��isc'����-dg�: through a.�' :y��h2P#  typ �%���+�N$� to3c6��2&�.�� %4��oD� p�@6�pur�u onclud�[��ta; ks m�*�9lya���Nz$�2�L�I)h� .���6&&.cA|�� Sinc6�m"0�& , h-principle���littlz!o deriveh�icY N"� 2x:*y*6a/. HlJ, �� m�0ed��<�kat�(dou�p�}�2 �n�."g �J anni0\?+"-i6&!D�� t $p)��� r, �2�>�+9muIca��V� 1*A�q� OK�@{�x #$N� �� ��so&�on��' Lhalf''�A�co���I:-�"# two Ooneq2��� ��$srFbpt�!7e$ɷ&� each# !oA �#beK/s � gN$t?��.s�1�&� $N$ CJas �ed.� e ~�2�u!��e $e�9%��ne��6eed�co2 >�M�kus���!b�4�> gener�lyM{6�~4 !k.] �y�}%�i���`ќc3<9t-g"�)AX՝�� C*�. avoi�. :J$IEc�.as*� �2��Ev)�!:cy2{ a�#'cC2��F !�:�m?be op�; e. S�/ G�w���.^Omr�l�{�6dNrou\07]V!� "0%�:����2��#�w�o% [+E!P.D��E@"��� ��&�P!� C�2�A�si�3st݁��id�sm�+of�/�5ed)�1� � �2�Qe� IDt } �W='>�2!*o�u O0\a�='Q1� 1 + p_2\,2)�.$�&�4s $(x_1, x_2, =ta)�W,�A�x_i=q_i $\taz9eta= v${p_1}{p_2}3A�5D�'align*� &= pB��2 2(:W�dq_2)\\ B2 (� � &,x_1 + dx_2)=��0:s (}(\si � 3 + \cos � HgJ- F-6 �A/�&in}lit� �)s� $�26�� �f��8p_1^2+p_2^2}}= =1EO; F aW) �xA�:7 }piEz�e Figure (fig:UR2p&f}[ht] 5H�% box >��0psfxsize=2in\�\�{\boxE0/UnitR2.eps}}/� �HbeN� \ca�0{!Cm_ m_��a]\%A �4r circl�afmid{6� Ic +Ń.0origin. A few5���1 d��ind�ed��ey�Nc� �kte turn��� A�rau6d.! �#1��-� All�F�6 �9InJ�ia�s�y� span� b�Dis � � ""iM $ $x_1x_2$-s{1�&{ valu� gjisM A 6A!�. A(t��$��*�U-.%{ �r�Gr�, oncG�H'&�'��( s5 $N=\gammfEC%O* $� ��)!e OJ\ !{``�X$ed'' GaussA�8 w�2t $R( ؁��+1�i}{2}��g:Ns�8 :X�)� v�$R\!# g� nyEify�T �Q1  �� flat.� .$) SJR2ex}� L".�#M��.3j.i�,�J left*B ! �,E�Is.�G�>o a� heir}�c2�Y]%!tlesV��:� %�61)E�_0M �:Hwo>� :+�aL%�E�A�.2!:y Pt�"t�3cnd2$e4s�$ap $C_{ �t}" S^1�[0,1]A�W$Y* �4$C(\bullet,j)$�ameu$saV[j�*$j=0,1u)5st6�@8hec�1aM!�l�9_ %F� "yl��T ��*�>]y�s%MnyZ� y �53>� �* ribu��$(1%An�B,:��9usA&�3icb0��2�&�?a�&���ofB�t�]sam� lds �YH�2�}1ex� In�0"a>,  =� �!$%]�, 3$ (!�E@��"7 A]C) f�9a2?o>�a-&scribW�. His�Bho� " ���"z/re"�e� ���?2u�?��v`2G� *�9 (��1�R)Qa�wh�llu�ot^�w"�2��.�5 �9"Z>2 )�}.�iL�d�%�Sfro  ���one8D3a� ly. While�``�s]�''�1u_guI7� �}|$S^2$'�$.K�:?m. S�, I� mpcdA� %y�; � ���� nM )q�! Two arc%�!u $xy$� i �$%�Varc��� $y$-axis.* 9v s $S5�S!��ob�Bed!m s�?�1�� �U;_� w,�p!}6Vy )>{ �AA!JAh$R^3$��A��"�YNGedA�e� _?yur amb� "�1M=�?ţ69 '2�Bs%Q *�#R�3�  S^�qU�6���",�"1+q� 2 + q_3 3�Q]S��f��&z"d..� L_K="� 6 %} �ta A `-H�#�$"�*4� toru� K=T^2�N WgA�A�N�!q� C$?e# most"�%�n)�@�AK�2<��,1,���  de�c� y $T^2� ��yq /ic�2]$ i�W� �� [*�!\�] `."~+� ��2. �k nfinitesi #)p�!LE�h�!�q s $0Q0$-Bonne�`Y\�p�K *+e�� i�g� a Thf� .�"2�Sa��qud!Lis}+--��t(/�L�! � to 6" Eule� ar�1 stic!�j]�� . So�P)�$ ]get 0<ardaC* G%\EdO taMM�)4n3xN�/_�Q�6� ��8r(L_K)\co H_1(L�7\Z.w#r�ashs:� �z $+� "D_� �le@!$ `�a� findHg $\Sig*�]�$ b)eda s.$j@H *�.trivi�3�e��8Q% h,$.�=�:$�8W 92^"�,� at�m �| $x�$1�2�)* H� $T_x L�%j$x$!laB+f =4th [+"�0=�So12$�$? -�iofBb� c�/�5 A��E�7$\�OSL}(2)$� GrassaRB6JX �� 4,$ p!ie pi_1(6T)=U���wee&��teger $I�� I��t�4���+sh�6���IC��nd.pM%�t�>SE|_IM),A�b� 1+}_e'7 0eW��?e�: !�2�}�evF ��dng*F ;��0 $.����r reas@F)i �)M�F�A eV�Nq us�"onLn5��Dill�DQ E8�w�by�0o%��:_P6eZ#�.$ BefYwG�:n>��Ew���{ anHw�Ce��aF!�A��_++�d�E<~�&��4 next�E&E.+� Eucl�Kn Spac�R�[&6 <2!"1��{"x$9 m�<So � B� ym"� q-��P%4�m�  = .4�3w �6$�P��r�P$�a z@+�*wD�%s� a �iV� $(W, ��PToa 5 A �V{1L s%�!�< �9je ._� J^1(B<)=�7 ro\R�3}$.-A"b+a %*�Gi�G 60( $f:S^{n-1} \R$�F �� �D$j^1{f}(x)=(df(x),�f6�.$�� ���� 1Louis�:-�84_{ /1- dB�V� on J)�a�%!� Mt =dz-Jg .f,{ $z�!�c"2/\R.X �llw5|�pe5Vby $(�+q},p} �i$q}=� �: q_m� p}=(l2;p � i�Pni�lngth (�1we�3� �zH &H4W�N�Jem$)� �%%??in'7�d�(\R^m,$�;]�,q}, p}]Kw�� dq}$��;5�/�ec�s-,��  q} -�nt 8�{ 14>| mpM�do_�S?$ \Psi: W_{! a�o .u{ by�)I%pM%q}) = )4���2� �>�S �J���+A(instead 4���582/IJ�� �*sn)(al advantag5�vi�7�(1  wo v�oBqful"-7% JdF;r @�0 ^ e7o�<F:2��l-�\RA�%�j�'�@+th��qedir7oW�2. q_d�rN�7� z�:�>�<*xI��+�%.�B�?$�Nsu.C �sN�$F� !0�$p_i$-�_Eif weA�� %--� $F(L�.* $LEY P� eFaExbe ree�aloo � lopeA !�1���� ~(s_/-2|_L=0�e a�>"�  ,duc�"&�� 8 r signE�ntly (ma�it ��e~:%!)&�Clo�C ny iQ_m� !,[� ot�3� ! [P}A��H1.��Fon,��iFT^�A� 2]� �Dor#Ae�%*N� L$�* �MJ^1"S I� $\PiE!is.�.�A��9 � h�9to*2r���zU/(�Z �:�9-I�� �,$E��Leess��RJ�be �&�Mqn�+�_�+��"a��+�+=eC�%H�s��Pt !>��_{S�RgraaNU (DGA).�>�2*!�P?� E�B� (A��b7aRly�iz�2o 6M!�37dQaUex��*�"4 cros&R,#It��%i~ �`��w�wl��` A�" �$A�n����FA >bZwe� d ^K[(SFT)��E�Q[���Ub�Z(�Uof SFT��tbeA�sa!1ut��!unT�=�B;in "w�]@JQyW�Eor Z*u�4}.�g!��RoP �. �G\*� fix�a��e�7lex*N $J�F2s"�KJ��0  is"� !$T(7I2�$ J^2=-id_{ �ڥ�>"[a��Z�n.\hfill�1sna3Ai� .} D&36D1��R�,�by &]C�WG�O $\CC-'f� �HZ@�*6v.�"Ysh� f@~a�9�6� . �F\ZI��)�N�VGraG2.} To�A"$c\in�? �  ,s $c^+z c^-�L2)��a"q �R$c��D�Ma�^  .` r $z.g . C�Ke a mC'�_c:"0'Lqa'r� A�rc ru�^ m ¡'c^-"�) �cY��#(��pGs)]ach � �}*S� �J$dH�'7}(n=�(, B�� t��aa�$ $\widehat ^� #A�]�3:pacP \ ?Lag}(a�\�p� ))�=5 c$�9�BF� B�(�%| Y�!t>�(�%i{�IsR�'��5D0)}�H$ (unrele lJ$!�&at (1�#� s�s�'*|4".W T2 �an>[(2) $J'(J�)=B0!cU-�)$\ove�/E}Q= e^{J'�,}BF%DE�Be6�Fg�� clo5wA~�=�) nK4=\Z$ ($m\ge 3$!�X �.zB>, $cz(c��+$Conley-Zehm` or Maslov�*x�4�i(� 3x ��utA c8c���MgL�+mP)���% *H.+\tor��ich��� �M� verti"�e��%ץ$. J+/��E�c%�\[|c|=%)-1.\]���9<%"�= H"r7���[�h&�.�*�%h�O%�� gu'lt�S �-�'&0"�D*�?!1 (procedure. �Cnd- �X6EZon divis��f�#s�4�k2 "� onv��one(%|c|%CEs �fulo $n`ERUDif�J� .}!p� A�6�$\%ial��\As!.E�� geb|��)�Ytext�S{"m�#(ibniz rule:� m ab= &��8a)b+(-1)^{|a|}a&bR%l\J s �2��O $b_1� b_k%�a "�!``letter:(\CC%� $P�G 0$k+1$�Pd 0dgo�+J �mes 5e6\u+h&؊ $v_0� v_k.$� %�b��m�Xu:( �&D� � *� , �)*� $u|Eau� :"�r \{v_i\�0�)� ���L( 2u�V.a�ex $v=8 mappA�.� e�s�c;ive} (�. neg�-})�aX�!� �9DDxa�U �$>�%n >��� ~T $);ov, j>�q�j[-$[+$)�l(ere $c^\pm$� a�piN|a�ingR*�\M^a_{2�}= \{�DH'!�1.-- 4.O}\}/ �MC1�iho&�ir�r�1�(�mi�+lgkt!�$0\le k1$)�Wd�m| 4{��%\ [1.] $u}�yJ.O� ��M�$\R^{2n+1}$ Z2x(v_0)=�Fa��Q�. ,3,$i)=b_i, i="X k(I�4>Y $J$-=co:!%W��n �VE0�Hq�ahE'�ULb_k} (\#_2\M) b_1b_2��,9�A�c� aken� a��H� ��O�m$\dim(F�n})=0$eT$�&�IomoŨ� eeA��%e$\SSe:�{[=u, caEI Sullivan,&h1, ees24}] W�$q&jB�:[&�w)�x���O%�a6fLZr/�l at rhm m���1-�W_e t� .��#! $(\A���A�.M2$L��AS"�"���>end2�!c��e�e - &>w�U���� � \;�t" %�&�B�E�A $T+�2���#a!$$)�fRV u�h (new?� va7vuS�c" �.Zw�explicil.�>M&{ cmA~l"\ y& �S2���BJl  u'�C,E| 7)Fn"o)��of�-% nnylsd�AFalsji�3 Ng1}�predi�rj!� � .�-t�nb �B���J �H�n� e�l�giv�(� -�)Ba�!TV� �yuDGA�4� pDV� �1�-L�&9T%n . Afj5;94ees4}Sis*#) B�AoL_A��) -�$� ��'] L)>�o4�,.[N�o�A�E�"5�DGA��&&�&Un!#}�>P3uk�\16�b�0� j9>mf$U� tEc�&3$f1o�r3+bU$draw K+f�41a�ak�'QpB*by!��$iZ�$Li���1o�W �E�"W&>�5IS��An�=I�2S2}4��A�A tn.^�!C �# *#_A (-4)1-.`A5"�5C< ot�Gnt�#(h6)VD4!3 �0�> �a!)t ^�O{2�SME.w̕< w*?% �he6W)X*�a�Q����vhUb � (co)-I�%�]� a ��:)#E.orthogoXRU$���RZEԁ�2C�=�K�:'s. A�. B�i1U e �U��C-��S�3aGgo xQ�n�s7�� A�8XCe�I ZG&s rBB �2f now e�c>�A�J�'�$T�A�S�3 imesq)�+&,�.!$ �M!�Hm~D removPDo$: \{0\01�A��R�:C9.1p1>$p<k@�J.CnhY5 i�xV)%M <>0E_1D���E�- )~ ��>B�QB�Fgn�4�u���he )�i�!1�9�.F# b�-q��qBqB��F�ƍ��F(�"�F"�8"�Fz��%�m� �� 2�9 I�8 1x2\R=!�.�(0,0,0)!�v�FV�!�\RD"a��=�)�om�P-�.on7*f{$U �n�B�)]� J�*.&i� �R�aOsA6� is 0E��Gd;6�apmagnitud�0FA maxiV�j�_N�eJ���s &�n�: r�#u�eI�e-�X$� N*�} �$ "ʔwS�entireB�� �F�� �U/��!^?!he �; .�No�JJF�9�x1��jJ� .z�T< >�!��� !�� r��=�x-��_, D��ud � � .��5*�P A�(a"� ��alE�5kiurbedg� n ellipseZ�U>�� !w�Xa n�{? -o�P��N� R�? �Jr��&%G�"��i,��� "����$. /a|" llel")(�"�(22F�x�nP1$A �O7 x�q�"{_1iΠ�y�:�a��5![fix�{� i`4S �iN;9��!^&B �'�\Ei%�$�k#Kry�ei��zl!�� are �zf�2 �-Wf��� �26 $a_1,a$Pb�? $b�!�o   zB�'*C($|a_i|=�A|b)U/i "`, a_i=0.$ Act�l)�63}/ ah is 1^)  n odd*�G�� id) *R diskIk�{�"�� $a_`+EO�("&cu oa&�&7sTsnn�&%�e � \$! mA�!�(�b��mpolc �B*d,&� )�T/&U� i��!�$%2�� ! �AEPpoܗ7�)@IY �)D�P<.6e2Ccft} �7� !6�y!p�1�>�:� �i$!� ataxcanB&nN Ay)O�z�%� 1^JyPn %�beB0 �EBiF�2ds��R�2Dslice*^ [ {1}{�$s 2263}{$a>4 ?z� :9�.�M�&;5 v!��@� .� �fig%96=�c�W�1F�ET�>v�2L_Ug IZ) ��.`-� sN{L�A�2� � $b_iO A�:�no�B�V do. F��6���, \j q�(b_i=a_1+ a__UD�#�plet`cj�ee�.�6�n� ! U�/tun}��Z td^� 2�4��)�������;� ��du%Ea�x\``�`inHdea of*�+���+>iu�(,�"+�p;�u�f BraiuJn)�ad'Ffl�>ree2�K�}�xW@ U��; arbitrA�!@*D�%�ZMr��of Al��~\c��2����B��be)<�-� � j��/wA� Pa tubular neighborhoo�g=U\�D^2*HFD�e�1�\�� �<�F�$��0p(3 \{x\�4LE]ll $x}Se�Onc!-� d��"�nshr�� the !�M(D� $Z���<�H> �6!U�L!��$�>c�'�^$K$ wrz"n$�s"� Q�ng<}UH$K� ge66)'! �{qOV 5� �&&�f���"=�� �9 .2�T)� 0-z�!�T^*L$ (�1!m�9q3� =�$7us?Ktur�%t�?�eda��A� much;)�7%;%jZ-B�a�at`L_�We� ,�<e�Apei�L9��1�A```multi-A''�*��1/:� a 7&KA!fN6��:��Tn$7 s $f*�zf_n\co "m0�!�� $f_i(t)=w f_j(t)s- r $ij1 1A�sets5{<0LZ 1 r l.&l-gluAV$��d$a� $\{16b)�"�=�>!�s > ��". �[�[��hN$ l $B� aid *�E B�0F(t)=(f_1(t),<%,!W(t`)e1� BP�([of���� $n$-tupl�9*%���7h�'8h�;is ��[�9n^t�PGtala� u: an h,,t�.)A��I�b�:N�!/F�r&d�\[ g_| MXime&Z\R�K(t,�/)\�*to ngle A7t), (`a 2\pi}^, �a <%l+'] SGJf%<_B,%A"nQ<%DQ~��te[O��8��<�!% . !�!݃&�. FV�ia8��� !�v� k�2_�$\Q;��JtR5F('ta�}me�D28Nu f>o��t� Y�7is hJal� R#a��, $dg_i=dg_j,�<s`Z $i,j�EM �*g_{ij}Y =g_i-g��Q9=\l.2-���9�(e%!�n��*d ��So cri�0q�-�:ce QT $ :�4.76�.$��/"��:s occuh)X$|f_i!|F :.&6^7:�a�R AS ly�X�mum��x �um �+we��$a%év$b �Ns&~U�()o�a�6%,�4their�,1dex��� /�&@��| �|=�nd $| �|=1� Mo�Z��1��0�ilyb .TA�Rsi1A12;*�) �by!+ ��"�B@'W �eZ�m�7?��� b�i� a ``Ze'' to�����Z by Floer.&�u���'�dan��)�t ���8Q�*�Q��UB��P�h)s $g_1:�jo J�� $g_2"�8b&ݹ��r��o.�A�can] !�"�0!A����+!?�=ign![B suPqty eJ�Ze�" � ]%%1b��9*s cjUct� ) UM:�*2L( 5�[/6� $Ee1� unts�_igi>��c Xlltf� 1i#MUno.��A�u end� �Qon�o�\��< YNb} �. \mat�RF}^a_b b�~�Y:!a�I�0#cF�/@e�*�= y$!�sis�z)g. Ha�!W�i#�er�u��w�r��fE �i.%s 0�� Qm(> W��}e������VL�d#��]5A�.�6V�3b0J��� current su�)�i\� m�T0wo���boHo8D6qu.�.+ jaJ)i�3 $Gi�K�u� $f:G��e��b�0@�� 1, 2�3 � �9�!�`<ed �;cb aoc�s�[: ce 1�C 2Cex�W�a�!�B PE(s)i�%way4 it \�0$f$� �1�2 ltc����G:69x��ij�g,�1a0�� �)ӡ/n � **7�$ -��r ayJA�g�z� �$)A� �s �l* a��d ��3-%^ �ex-�����$t�r.� �� �,�9 � is B!~ !�o is"�8>�A�!�s D 9�$H 2Z a $k2\,g_i>g_k>g_j$�g=;j:n�q b6re6�kͿ�kj�5�aAK��U���x�2n it#E !No�4g_oi�~�� � app� >� ]A�M'�yny-�E-ce�a��)��a ��N�4E^s 5h^1!a%�U]��kj�E:C .9vE 7*�5N�lft�l�la!``ax�[��γ&3.5j�l Flow��*�zxVar�yp���� sZG�8 *^i!fk ure}E�>b+ftd)!�``Os l�> m�n�2��T�&4�$Disks=)��g_i���t6 `` �sourc�>r.!� 2�d:� � A}D��EB�corneeL}s�  �e)O� � �$no�\by�s��N� b.�A"� T� 2l=l�?9�# � T�#���>� �K�O e*�?_0W&�!� i�>��''�rɢ) ��a�:�; $a.+>n.$ F�c�o�s "�FO}EnE{)JL �^M=(�� ing  �+��'� F�kUl7cis�!{ �*{gؓ�' �p�BD$\{��P�<��S�A:` u}�*�\t�mbda U.�.llJ$L](��c.�Hp;F��FVJ 1-1A�.Ao��ce"�ni.��;� Y^ 2` r�& >J� �!!-���]1"2<�:�rE�2�s"� A�AtehJ� a�dM �A4�M1P�'io"8�gft�}&���&b F}^{ ! }_{{a_{{i�zj_1}}}� ,l}{j_l}}}}) 1j*,��!a�oN$$�O$:�}�A{%L.5.a .i)\L $\s(eE� (BCbk��'6jkZ�' k}{$:\p+:(n}{$n�zoAMe2#sL9%(o�coR�G.J� ��Fs�} andsVb�a=?-}�&�=%W=�$6=-�d>�*�u"�I� =  - ��B( )0 a� *} W&����ds �+:;�93]%m� �I�pa�zt. &�Pnei\ Fn� F}�,Reeb chords 3A�6FA���]m���y $8U*Njle� iQ�� � p �A��"(shifted�Ay high~2�3$\R$-2��&As="TR\RU+ +f �90would�~=\� � �� link[q �\cup .�2с-Ca � 87k�%1�NaMf�!��r6/R|!�+!� -�� $b$*�$�-!i�-Mo�&�6wA="�r a_1j%4\pan5=0%Su� RJ\ %�9$��l�%Z�IX,� ra$��� ng"v*8 ��6or�6l� Also4�pF} i�8-��8%�6!�B�2� |!eq�1)b$�6�J�E��4a3 s $3=� z engt"$Bm| b%sdeUlZ ��r Z Fm .�tr.lHN>�2�&2�2,�K��!Wthe�?�d "�E�\%�sMA�@��)�> X K J�mhE�1y :�z\tl�.�2$��.a:V�#c\���"�� Cuspa�w T.1c>�&Ira+�5z1!O&:ca��>�3a A3u2&��f�0.��žve de�IiESţ+=��,�.S+soc@� V<t�U _iP�� y$-pQ���4.�sa�1%:$:�iB�FR! eq�s��#iN$:Mor�m�0E��.�R8474$ In S)v&y{uk}!,��Xa�@�44`:"A�� aui�fM!V�UWa�w �AwL!��u��pmade._�*�#{` bser-6�K Z>&A(a�!��b�qJ� UF},��ill��d�ver�}"�w|�n��uthO:�9.Om�/s ��er>�Wmnׁ9 �� zvr&*ta( I�n3)�����QUA5ra$ %&�$z=�$ilon(x^2-y�M��� $%�� la�U�:!M�. �)essA�M+���:tEb��except>&�;6KE�re quU� a ch7)eXs;)c� ?<B teMsK�a�Q C�� s. >�sw}�w�3 ``swH� tail� lar�X)XC}��``i��� N. T%�k%p���p� -��ht%�F� grey�eY�gi@�+�  cP w [2I:� upn%�D)H)Hepl_� ׅ���st�u� ׅ �Kq�"�$k�D�@ly��; d�rw,�.�>��7�� i!*f  �ݹ2�+�].P)\}��Gn�SiC*s�%.v5� ity,en"yr���aYZ4�x� A���I�.& %fig�C-�BE�.�zSa�YA�=�UB8rth'' a�``Y"''Z�T:�,|I1A{�f.lM�grZ �wv/&�v��s �&/Ws���"�&� 0nA��R� �.por7��� ���H cusps&�*��B�~.ed 6�''@5� �Zr! di�/*�H�usFL="w=w phen��aa�.:7;�es� �&dge�va��"��!tcei ,!o}#th�z$�$� �&!7a�)s split))d��"p,*d�c ��Ao!�oNly��we���N6 ��m(�"��K���J� cft� n�cf�_LA8bo��L��!�`N .��t�!j��h.$ 6� -�@ bvm��a�A�dot�_O)>�e 8'A=x��:!� :PR;!�c 0�]T2%E�$E' in�w��A�sY�tP�topN-z59:#>4z n,R�A6��"�ma6� aD��*�a�P� in E�~\ް.�"� ow�6m&t*A��!7ed}%D� W+ %J �kT4S u�ds),�?�a�@� *2f 4!\� tYR�G :-7H�?�$ S���b�Su���s�!]%_&&@�,�\� rQ�)�9 �"�4'-|#1��x)AU�$� 0WKY$4n{;m2.` $c_�, d e f $� ($��$ -�3�%�b! ]-�.� ����ng�1^y� .�R$ � z �$8/ ng 2�IE��?fi."Is�$"EA\Z]�A/��o�}f�+<2; �*����h�lu����)<�&�"��;e9r�<r � techh�]u/�O s&4X8me��0sketch�5 in� ���B^�%���5(-�"�I��m=C�w�Psh "�/! _!8Pȧ��t�,edB+ D*t����� e�Yd�� e� �ll�K�&*�82YG � $1-1.�)"�8��V�(F�e �)A�ob�|""J42g\  GBH6� k A�O��T.f{� %3� C�.ic:Z�/ e^e�:�their;ie�a \�� u!f�&1 -m``&�� �~M m�>G :�a �Ƴ3 i9�Q"�L.Y�co^%1Fp)1�SB}U�AXbi� ��twoe4&#,�#I� "��9� &3+� "YA:���B�ELE�� i sp@ofBG^� . %%� � B� b���ood'by pushA�� .�V�!s' $��Nlos^�b�y�FE3U.s:8 e>D;E�.yr�� .  %.=d.��V� ��feǂes:!�M�n&~�q� �]_�.)���i�Y<�_%[�N#people (6j;�iSjul��irm�P�d&�ez%"/z)>}dHB� . (Ng� veAV���iA���P� 6�&�  !"&��al fashr�~, ��X!�>s.)*Y brin�*�8d=he$  (��*ees3})�*�� LaR�Ů�I.�> %�u=*��$[H_q ]ȵvZ�� ]Nef��lz"�'�K*՟,@a�extrac8"SPO�� !�e>8 $A$-�qn!��!� 1K*&�u� Q ��o8)�!=�!uF tron��th�Va�$l����P�a6��I4AU�R�>C6��c�Gah%k橁�it� mA,%��5O3Xi�9�e]d ��&m�S��!a�e�s�dF�je�Ci~�oI  BT+��$a ��7ber� ���8�:�%�-�sV;%G %Bx�xE_$1-�{ $2t'��al.�s&̴!o $1���aA����'er "݄/�abs�ofA|�f"%�E�Ab� �|�_*�AcF�i�\i*�MgiZk� ic� A>to%�  ~3 ~S�8help establish �properties of the DGA and, in addition, understanding Ng's )in term=�Icontact homology would allow generalizations to other dimensions. % -----�d %\bibliography{../../refs$erences} %�oo$\begin{the.w}{9} 2�(style{alpha $item{Alexa!e,23} J.\ W.\ d, \textit{A lemma on syste)|hknotted curves}, Proc.\ NatG8cad.\ Sci.\ USA NTbf{9} (1923), 93--95. � �4ronld94} V.\ IIrnold ?it{Plane u,A>hir invariants, perestroikasAU( classificaE�C}, With an appendix by F. Aicardi. Adv. Soviet Math., 21, SingularitA� and bifur X, 3� 1, Amer. 9 Soc.%vidA$, RI, 1994.��egh} Y.\ Eliashberg, A.~Givental,n$H.~Hofer, 1�Introduc�L to symplectic field!`ory}, GAFA 2000 (Tel Aviv�\9). Geom. Funct. Anal. ,�, Special Volume, Part II, 560--6732�`es1} T. Ekholm, J. Etnyre�(M. Sullivan�HNon-isotopic Legend!�0 Submanifolds�T$\R^{2n+1}$}, preprint�2:�2��The C�FH�Fof�� �3��Ori!�!��= � �A�Ex���2yICE��r y�A�$ory Lectur�'n1E�etE�Top��! geo!�Y;(Athensa,A.01), 81--107, ��0Sympos.\ Purei�, 7q�\ \Z� 2003.�4FO} K.\ Fukaya� Y.-G.\ Oh�PZero-loop open string%��8cotangent bundlm> orse��topa�As!񡶅jiS bf{1�_L97), no.\ 1, 96--180.�Geiges%n} H.\ �Mp.pto�2a�p�Handbook!tDif��t�/�Q!�, vol.\ 2�Goryunov��  , �nLocal��^ mapp%# of oe%$ed surface!8Pto $3$-space}, C. R. Ńł��(is S�r. I)2 323��96)+ 3, 2A286ݒNg1} L��g9 Knot%�braid.� fromB#:�22Ng2�`` IIvc3FcFramed��~�2�OVI1Ooguri%C.\ Vafa: ��&ti� icalQ�}, NuclASPhys. BI bf{577} (��9� 419�438.��@s�x}, AdvanIbM4�z bf{6ef7�P329-346�endB� Ddocument} N�%\�8[11pt]{jdg-p} Ramsart$setlength{�|width}{14cm} \usepackage[dvips]{� icx,color2#Udsymb,amscd,latexsym,epsfig2+\[arrow,matrix,line]{xy} .qLmathscr]{euscript} %. show �]{refcheck} \DeclareFontFamily{OT1}{rsfs}{}2 Shape.Dn}{it}{<-> rsfs10}2�A� (bet{\curly}F=� \newcommand{\rt}[1]{\stackrel{#1\,}{\righta!}}62RZ2 long^6X\comp{{\,}_{{}^\circ}} � \B{\' (atorname{Bl6y \C{\!p bb C6:QQ2�\RR62GG} \re9\S scr S65Z a�Z6hPP bb P} 6P 6P26 {\T} 7T6lX-� X24@\XX{\,\widehat{\!)� X}{:NYAY>�LuL6uLL5L>5O5O65I4I6�$into{\hook]2�res{\eevert_6?To{>Q2=,half{\frac126:iAh$mbox\,\_\h�#@{-1.5mm}\shortmid1.5pt}Ai2_{^{\ }_2t{A(}[4]{\left(�,array}{cc} (\!\!#1 & #2  \\ 34�" 8\%)2�{\rk}: rank�Y�{\coker>) :Pim>'im>$HoB%:JExt>K:&vol>&:&Pic>&>&rojB'\,:*� >*B* Hilb>*:Rch>&ch6i {\au!��frak{:FGrass>I ��pmakeatletter \@addtoreset{equ }{s� on} .o�6�{\the2 6.\arabicPw$Au, Y1}. �first�w2(Aqb) came �((holomorphici- sm group.�A0e most famous � i-Futaki&AW14)d�i;a �ac on +Lia�gebra $�h��Lv��, must vanish�?ILR8)�Fut%Kw��d aA�er2x� ed K-� , arising$ certain d�e��s (or��tes� figu })� $X$ �PTi2, Ti3}. Moreover i�h��Eure� at K-poly�!�,a necessary ����?���v!mb ; se< p�f� :�u$}. One dir� �e�� � �now alA/ �d: �knA��O�qlxK-�Lb-� Do5}A4us J?�Mq�.�E�^  ,. In particu� th��.� AsC^�$-a|rec!�E�6�*� � !Tse ``p�!=�8" are currently. on F)have beG�ѻ, studied. I�ց� aper� � ider^,��$associated */ oh , ygA�a new.���.@ !l� s�*se�=! m����I�%��>16 2� e central�Ign-normalA&e motiv�Pan analA � y.avector� s; j�=as !hea) caa� 7se�hea� 7!v� how=H >9$X$E�Sm5 \ref�:�r� of�}S e, ba��6�,!�o�!�> (aF) �t7a ���{B) .*i in�| �kTime�p}I�� e an }%A7:�i8h� toe�UD��a��:5�0"� �4 . AI2alAMve\� n�T  6.1!3�u RT};:ltwo are%��$be equival�AB��]trya/to@m moduli of varie#���ic&H u�AZic In2� �y, ]�co��aT ise,s �� CE�"� "�� i1#of->�!�nBtha�in9%� L!KA�%A��relev�-�{ (*� 4.33E��em 7.2�5�)��S>"non:vi�Bk!�� "^ ��:a �-arbitr�*!� en � � (as expec��"& .�rir"�" �v�!2� >!�.% �� comp!�!",ome similar ��y�  result�)hWe}. S�5�A M� is��E���6 2i},� | " 6.7 of zRT}E4��|a�s far<we�FM �& n�n-���7f�#OB�. !�ppM��!y mula%;tudy u� �B� in 2�#�p a�� n�mb=x Hong-Ho}. W � �iM%D,HNarasimhan-Seshadri� a�/*�o | iv� of anya# *�of Y�o)!� any 6� i+we�%%to�-�V� E�let��)(�e �f$discrepancvb� SA�stric ��!���� � le until! =^I�0Do2, Do5,Mab}Timv �:/ �mO�&includh�m(upAF�ups} i U>�\�r.=�L'a�6� we)d*�:��n&\� triv�!�2� m�do V� (e�0rmk:folklore}%ne migh�)pd�Il($inu]metho%daY�,5 multi/r ide" @ aE �a @$C^0$-estimates r�i red �"osednes�(il-�Na}' a� < Ue� d��!6h�[e�6v if o}(e*�`�}a"6 A�3 :{en��%Lthm:KIC�$ie&* le}a4bined %�Nadel'��*sol���\���� FanoYk� !�A*{Not A�TerminX%0}\ \vskip 5pt>F ,$(X,L)$ will�a'�pl.�of&q+ $n3th�� {�(\�i.e.}\�>J k �$X$�0Fura�m) $ZUll denot�y���)�� 4 �an2n$\I_Z$� !�Vis � $\nu_Z=(#/^2)^*6x�e �� e � upM� X ��$\pi\�!n� X�X$,e� excep� al d��or $E�N�%EP_* \O(-jE)=\I_{\!Z}^j� $j\gg 04Fora� veniT wte�-ppra?pullbackx%�u�he ��to � a�ACaA&9.�. } ����$�{X}�eS$$(\pi^*L\oY(O(-E))^{  k}$G$L k}(-kE)��interM�a=A-CDs $D_1,\ldots,D_n$�?2�l*_X _D_1). 3 n)/ � ��bbrev6!$e .D_2 5 hin �s���}%B� sec2� . �%"�wB- does�  ca!�confu*,!k$ may % �%�2� L!^cap!Y��%2),�v , %aO�,� \I� L^n=!L)^n=!>-=$. A�at!"Q$\,- �Ga��m�um.�e � coe� s; s� �C��^Y��H�&��[` f�sai%�be ��if!z�be writa@q.:� . � �p�veV��eQ{e�[f.G, T)!5one w�2��every; AwM�nonnegam� A� extend$�bb)�=)�B� @Kleiman criterion�Kl�% ��} ecisea W(losz+of )2con!�InA��#(like $H^0(L.�)$��4always tacitlyX - a��$k���65�n honest2�y�ite-d82al bsr* $V� ��$B spl�$!�2Gwe= GHs $V=\bigoplus_iV_i�a� $t\in[ ac� n $%�t^{w_i}$�m(egers $w_i$� ���b us}a`���I,$w(V)=\sum_i;ihe�ota� B:A; %i��Z (hinduc6p � top Ay4rior power $\L�^d$x}V$. 2�Ac ledgT)s:�We VI7o Hank Simon Donaldson�� gges� look� t*�of�=8 �s�$ via�.� � ione< $ext1}). AsA�� us%\r� d���!� Na c?"p� iC�jaN� sp�1ca��it wai$�Ued ou5ud!�u;�D4out his invalu� s)3�w1on�k�!Hed at*�.����w��%�d\'ebastien Boucksom, DavidA�derbank, Joel Fine, Jun Li, Sean Paul, Gang T�(both���fu�9m!�� invit!��%�!� a�f���kH=?�3 ���injR���( i"ba~o  be�pw�aT gets�dA* 7e parame�sub�!�p&�6ar trans� �E�8e Kodaira embed R 6����wj#�˕�FRia�e GITr�N a ��. �<J ttemp�Ddescrib; is f|  but O ead refer�A�e�7eafo-�Do3, R%��$�&, \label{def:!�)�} Supp*��m �a�c��� �(er�$ ynom�,$\P(k):=\chi>: . A {\bf v�fY Q�aI �� nsis�f�,enumerate} \�8 A fl�%Yf�.%�2^  ed �s� X,\L�#�!* C� Zn�%*q� ( :$ coverA�a�usual 6 �"�8\C$�$�+� �$%�If $�0_t,\L|_{\X_t)� i� is" �3! a�aJI�so�r, �\j$slash\{0\}�endA n}�#%Gn�c�A6�!3 �_t�! ll h���b$ (��Ha}6C$ III.9.9).M� aN$aI>R�}$ ($\X\cong X\�Cm� :�I��: = .�� ly!��e! fa���� $00 d Ca5 fixed�'get�6� P6�AO_05�0!� and �� � \ $.�I0�e� $k� .�}�f"} y�{a�V� 2�R(Is. Let� k)$� !,n� � ��.�)e$�b  �r�(Riemann-Rocw>���� egre= $n+1i $k�, a"�:n expan�� $ �/{w(k)}{k��\} = f_0 + f_1k^{-1} + O( 2}).7W^��^I�fF� N� a�,be $F_1=-f_1�(s� ha�~o��itog !�|z"@�K W[=ng��(=a_0k^n + a�n�n�9'! = b0{%< +b3<%;�t�M��'�D} F_1 =-U\b_0a_1-b_1a_0}{a_0^2}\,.M�fE�_aibi�5H��e>�}\��iz�2W)AVat�kAŢ� av( '(resp.\%q1 )\-+"|)})��q� non-����(o�sJa�we� A>0$�A�(F_1\ge 0$).� ��&��:�le��� ��6=n�6��ŭt,duc:D� �`@Z7x $es���I$s�L��I9��� U'M/MbrmkD!le}!OM�A �=0er�!bea;K-�!/!F)* �ervedUCE)replac5}by2r�so �1s sens2�(L$$\LE�a� �6�Q (}�x%��2w�nZ � )k��in &�0 3.6X �� RT},� a8�q��af� twist��by6q(,)V�9�",EU! , up��00�� C,B� ��F �^�lasR �$,!5{�A��Ɏ $S^1Q�-�`�A7f��� pre� �pEy !mMumford �Qf;B� in� �E(@(�!3.9�5ˁAa0U�e.�,I%�possiA�to Hnd']m s ab��  R$ %DJs. (B\>�R$-���m`.� %$\L+${i=1}^m \ap: _i Dv�each $���WK %$6$��"eal�*�Cq=� ~wchoic�y�"�  %M�. F[strt<e5._!�ɐ��e� e anř^'y�DF�})'gj-` X^*�A�e�w�A�MFT�� e�to�  mple9 9�^ #R� ~ 2F�,I8B; p*� 5��h�g�͂�1 ���( $\O(D_i)$ � F2/nyJU%��; calcul3* �7�vN# r6�9.e.1 �Chern%Ar�ea\F�.;"��ex�E 2�ev�'a��-��*]�we takC gEXA�E�� �F_�!4v. %T1� � uy:r�� %'�g�* $a_i( w���. %��y�YD \O(\��� %a_iA� ^ �  2�  $w(a": a_m)$�otal % ree at %�� "�4 (k) �� !GheN�!IL�n %%.$ !��2 % $$" �U"�m&4 r3 ,$� n��)�!�e B�0I!� . Clearl� is % .I\eq''�L }��6M�9�Q�."* Q * defan�' nc � ally��>< F% emi\�0le}) if%��.8 "e'��FA &�e�R�5�!D > &N L  ɖ na�R �� � \��6&� &�zB "R� ��3 a�>1 �%�5�E; AA! �!{� �+��*,`G�aic�6�-�� drope�qualifi�/�8%��!k@)�B ��.P{Re� ship�0�5N�:g$�%D;Q�sec�$and�%O1}\ ��p�YG�/ng!"�) 2<+Oo!1�,follow>+ Y3�'3Y4 j2}[Yau-u-ռ]mA �2 .w,�c�'� ��ere�+A1/,ca72�)"<.1��hH6��'!$A��m�1 �is*�(le-��} '�*~ ��p">} at ��#x =S {&&V,��)X2"):�)om3�  how�5at� &�'Y)�&!�.�. B��L�2c had T: ly weaker��� Kbal�.dQ:%)6=0$A %�j���]EN� "��,%&�r��! ``�"�$r�12}~�61-,a�Otor-ly&�/le : Zh, P, Wa'- Burn9%N��A3s =_l�1�, a%X FX  Mabuchi z+= m3-4roAP!9 lds �Y���)�8$>a�&]y��' [!�0 patha�&rough)�- g 2lso��e ���3� 2Da.� 1��Z�&v boun!�/ 1�4,CT}�aL5!�he"z+&~)r)n��]� P�);5�#�:� 2P~ *o � 0$�AI a>${2Q"kACGT}��a��sV4&�2no%�$o guarantea�>b.�5) E����S nger�l6- x �&b�$qu�+. (�aKA� sE)t, V�%postolov�> D.\f( e�A�u� �%jpoint^"N'it�be ����*�!`� �s�S��'eMo k��Uex�E�a�� deep��s � :"��~ingym4!�op-T�:�.��Ce��How�!A�fac~AR>�is ] �&a >�7a*+ "|+� X$;we�9w-V . "k>*�o26�2}��pYE7 Fix� o>��3�c�'I�Jas $$R� r*( k}) = a_0 "� k^\k�l� ��� �[��$C(X_\�B,L�� a_1���~'2kH$$a_0= <1}{n!}:�),\quad;N{and}e =-72(n-1)2<K_X).� �# so� BntB8}{2* �.F �YB7-1 X$ l�.9,�3�ji- (>0$ZF'�'^G-6� Md� s\3)�"o3� )�Z1� eqnaK*Y 4\epsilon(Z)&=&,%�H\\ &=& \sup\,\{ c: *wk}�,r.{ck� �Y{�8lob� W �S+}H0\} ZY0 : L(-cE)\,\, Ea�a on }1R X >ma8L{ ^>nefJ<,� =��sae �"-%��- �$)ksD R!�/� they �6� L(-E�QN S;�Ei9Y �A 6p0"� �,) >�_ �ly=s�$�6& 2��E�� $x*�Q$� e�(x�yYGu�Q�aidef} F�"(-xkE))��(x)��(x)N� E, A, 0,xk�N5�  T NxrE)� 1 �in��o$r*�$,��v .Ex=7 7-+ so9a��n� �ER6 R�W�BZy�1Kofa0x} ��!H�I{YY}0 L(-x�0n,��&�^ � � o"F, $p$��_,� ��2�9&ula o"M�-1B� a_!� =��1}6�B�K2�� ���,N 1xB�w$6P$=K_X((p-1)a�ip �&(5"of 2�53�ev � b�U+2ii� 46���3Fixh $j_0!icM [\pi_*"'3Z#3�'3e 1(1�E�mH��[=���n!� $eM�Nt@/N3" $x<��^nd��in.V>$kx�� ), UX�ltern�/HS} h>/\=3I_Z^{x�F�B%�=a_e"�aNJ. 4&�.!T�C�(0�!e�����Z�.)U� !S� -Ua7A5at!tE�$A�W1W� t���t��I)��3�,�%���Ns 4.21J 9��%�͊� IZ`� peB o $c$}A �b�a1  mu_c86� ,L)�] 0^c \IS� x) +" 0'(x)}{2N \r% )dx}9-�dxI 6�*m� �2�QHdef��� �&v �C��aC)is. �le>$%�$Z!(l5)*�Me=`$ $c\in(0,}1]�M2�Z�t�.� re9� ~� � ,L)<t )�% yN��>13 �$c=��$6s �4E���D-0s2y!.� �7{R�6 �e�:! $��0�4&?j8�#E*=��!� (Z,c!�y pair&<*�9�=� !Tt�2H*�QD,c � - #."��!Pm�$1(�.B7N6DI� $\L_c= P ��8� �8�&$�_&,F("�)��$Fin��]�*<6&7 m2�#&�$AoB�a*P��i�a�E&+!m�q�rmkA�E&0Z&_.�2�ta�i�"� . .GV5Qn�#\ (A])*�]/sl��j0t�/� �=%�1DX7!���a��piruc$c��|0/�2I8�/asM� ��,�>mO<p�hlyq�.LK��as��}VNm���E�� JA�"{*!9* :d�-�%� �6"��i�!k�le"/�"�NHR^n$ (08Fubini-S4me�2�). �}� p),\�0��pi�\PP^n)$ ���F�4�� s;$p� ^�.ll"�4 �*S-��;3"�(.5-�&"�% i"IG 0. GialC�MK2Oim t%& �Bof6�5.�"5�'on%� s} \&?u��'2�.�@�*r*C�w�5Ail�@}*��J�ble�\ B� le))D6W.�0F:�(i`E�e.�(*�'L$ s�.��,* r�r.�-FV�=r�Y:7t/���{c}� � 1_{r&����U0< :� ž�/A�f"S�x� aa� Y "� n�; } \q�� � & frac� �.� �� 4n>0, \nonumber I( aR S-f Z�.U .E<0! � ��e �;p"=OoJ$0� o)�2 V;v� 0$\lim_{c\to0}2V% @ 0)+� 0)/2><% " >;�95�)�S7 ^�4,Ang B� (by2R �\�SRT}),P+% �"�?}�� G$c>0$�,)T ��ngAA�E��4�_{0\le xc]��%pm�.�F�q"�L� aDZ *� �#s�Nit was?W%en}� he A�Z!�M&����)m  n�I� �i&�Ww&Zy assum� �:lk[o� �F��:i*A�;ickenp�@ny �"c ��� Z=mZ'�m�1$Ye A&�.0m}'�,B� <0I>|*�i\*�emu_{c/m�� '}^mi�e.0{Z'}) + (m-1)I�.ct dx} }pqy}  Gn��E!ťZ$�a.��nA�E��cf@M� mpon�G$ ��s9[.a#�T .�� 4.2�n� �tA�@Y1@#maA�V4^0�-!&p E���~ &4 :quo�<tE��$�4$\tilde{a}_�*�by�B�8�O_{xkZ}N�/6�82I�E3 }))={*��N�,$$nA�2�qi-a Ʌ%2�i�"$�  2Ac��(E mislea;n�H)�1Q��=q-]mO_h��O_��� ����q\w:"��'_0 (��qF@!\dx}�6g��V�� dx - c�+��* Soi!} * ]be phrasJ�6Y �1_$. %� o�^t� W�t�,n %2C�� �J}Last's&� '���e��%�.���BN� _{\,>0}$,�s4�K� "MMb ��Z / +1}_r W6� 2a���2*�3})���F�7E&k�%, �mN$. (So4��-���ZdtJ:��qB|_Z�� S���L^*. Ѷ�,  0,\ 6��a*�b�(($S^r(\cdot)��.���-th�vI,+ .) �nJ���"= ��(c-x) �!�dx�� c2 1(0)} V5!��*��� E���&F"$a��lm ,bar{x}=x+1/k���-*���R� 1��e%�A��+1}� B�F7)� �(T. ��0*} Bym 69)�5 Taylor�$an�$� q��F a�lg m$"� aligA([X  &-ŷ-=)]L[�1.` +E\s�  -� &��� q� -a_1R��� (&;O� UnT�/n=�=a�� Y= a=�� HR+]IZ}.����gg#y!D �cE� =�- ��=>}{.�<eq:7sandas�!�j�( ��MminFp!�!屬�y- ��is�$int��>�a� x�E1(y) dy �= c2�m�.$$U%4�,�M�nACoN�X�.m�&&&j�t�"�`"f*^*`ѱA&�=�t�*�S� ��&K��.��].,S �>e�W#�&T�R!w ��V X"�$FJ Pt<�4�!�2%%B6 C$% $Z sC� �OCexFqRby $P� The 2)�Bc ,c1%�"� X$ glu) o $P ��R:e Fig!0�fig.B�).�a�_&?!$E=&i\nuo�V�*�cf`e%��,�3 !�!e��L $Pk��M\9,rY7�L�Cu@��< py $Z':= �V/ oq �6 zeroS$."f�e}[h]z!�er�put0$e.pstex_t}� �Q�{�1�FQ.Q�:~�h ~ CGd�G��&�:dId U~*X!~s=we suyT!pu&}T�$L!� �Dtri�XlyBNm=�=~1e�MY�%}%71�! x'm i�so C7�n��M&X ! q +d &F;�!�",i=�#[' cup_{E} PE� ��;."i�$�g�{d�s7��AU$ɀdiag}(7hO)u#W�.&*s:B�Q%! �\.D��$� � QU� .q� thm:+OtoI{�pes�I 'V&:W6 A!mapq��%Us�;{��G�3ptW X\to��b����=o f�/on8Nle�$c=r/q$.�1ose $qI%�&s*Jm large "E=!&eBq} 7 q}(-rAqgB�)E� en a=��Z'��RZ��t P�.9�'d#�Ap^* 4G2/� � r!� whilI;EI .K�t^r p^*�G2N�T!9�CB�%�1" ��A�6F|%so�*foEb[>q" �ca�L_]Y4k2��.o* A?E���5vex�oi�X�R� T+a<NU��J�!I0<6�m M� I �SRG 2l�&Z? �"� � *�e�F nopa�keak*I\ >� ��6T!)68l�:� �_�!�� Ji�7inmk%Q�oe)#5hNH .�*&&a18)M��6%�/3.L5�%"4�. �&�M, � "{3� ��a C� 5aa"N �' � K-5*� Q:S� r�h �1��,cA��� K?a�ch!���eou"�[�<d-Q�!uS b *Ethm.f_2L:/E#K"$;l�Rn- �1��&6y��2� m/�B8We ne� E E ��\ge��n��m�\le&��Bya�$ah \ uB�{�oi�t�Z%Son�kI� al $:� SP��4t���) �!�M C�|�O0}" �A2�A��� .�^u t }����/ \C}�O. `: Z+(t��c C[t]�m # cal O_:_�!}tE+�coordɍ1 bb Ca !�$��c2/� �T"�fnsA���Q_�Mw+� /.c/.2Y4"��-5.� " (�I_6P"2) 6O ��R�!f) H�&&�Z{i�F�2 t -i}WR���iL ,3� [t]%��k� 5 ��&5oMAr�% && �~-6mm}cR�=R�=�� \Z�% �R��~"�!%2�5��_>�*\=�%��n�^:�Si>jlylX]� l� �7L/1$�0=H^jR�R�E*E]j��.+m�M] 6\ u�I\j:\�����&6�jk=02� for}D3 j\ge1,\J3G67,\ i=0ebck"] vanishingW��)]]W�>,�Ej�a�/F� �.%0{iAz/VObigEx^i/4c0@6<2�i�$��� �p�%)�!�T��__,&R*O�a� } a���. тd -T:x�/t^=�lj���Qf O��a�0�n -1} Q��2�2{i"�,  $eq:spaceofgsM���>�U$; A�{�&e��!c*n Ys.$%�$-�<xP$.%tp"�% $h^0fs$�Dal"�8"U 72.�)M&+� m2D�v=i}A~-z%A����F�)=�;� �!8�)�QlatqX�%MZr �P� K � �:+Z. Now# ��2� ��W��<s$Yso)�nu^*_0334L|_� but w� $-1�Yt$�V$J`1d8 E >�b de*�Ay�W:VuyU� e pi{AL Q$-(ck-i���lJ !M�&;�lUn�MJ] -B;6T �F2�i e^*I/ & -\Ku�IFy�JI��1(i/k��W 2 �+ �V3}Q�"�"z"[*�$^� S��H j>  ,\2� B�At�(Im��7 $a�j6TVH}���_Oin Vi S ie6�)nEe $!++1M $k^n$&%8&X$!U+�� � la�^eq:PX�XI�6FQG"�"\!aZ"$,&; ���eMIyVSWU{-�Sq�#)dx�J&G\! H�+F#�%25�1,& :H % Q��`"1g�]i��V^ A^a�4*d%be2&� Donaf-�M*0�K�EB_�L_�*Ii"'$$ �+[)1%, ^2}(2[Z�!�&-biZ})W b�A- &a�%)�= B>"�&)-�% 1� )t� last�>u�X)[�@"E>zbi}�Ua8 4:�,�2�0),G�RE�&�� qvAr�6g/.`! u���e^b_0<0A�X��&�as >r !m�8m�y�;f(�?+&b �s$\ZEf��*')� k^2e�Y +� ka� f(0��f� 0)DeW�� �-n:�T=i�!m c}�� b!gGR!dl EQ 3�ck(ck+1��Soa�a�arA;2�-�nx^m,\ ,-. I. .k i^m!e 1}{m+1}k^ ���>}�!m"�%m�Uyg;t;�z}�_�.4�����&� 1�x^m.�F�as�6:W AlthougA>wdeDgiZN icat�Y;:�s �@s to *�."�.8a��6�8 <(�:)4;>�(E*�N%m/w-}Mt�te���!��Fh;s�oB� (�AFc$�Yy i"�7�y6vexA~F �4RYv0qfS���e Fe thua�)d.dko 2�!>cX-u �=�.*+ s ��akd$ cl� y1cE��8�� viI�%fR� �do!��� �jarian�+F_1(d%�evN< {d}(�'6>�#_�NUE2(  $m!�l�3dcc}��2j�Z�=0$$ -6  4aAr>5�B=0��� x 2-�65� if�"�A�is 5�A<.�"4�j����m"�#Svf 4.18m:y�not�a*�ae�$ A��(N� eitheFJ%ubt{ToQ�A�aD&��S\*x�+t,AS��w�C�:��"X '�;;.Ou�q ��^ ��urWk��-AL�:'��e!:Zpa�nge+order�*3 .� X_P=-J��o,�Ga� 7l��top�$P�\RE &i$kPO#fZ^n�g�X6�,�%��fi  P\to\R$��l�9��i�sQH,!�c�hAQ\wis��x" 6�V��X4(Q=\{(p,t)\iy imes"�#R : � ,t\le f(p)\},�;��2�bk�X�ufM�Er J�[tn\"\bsQ�� \PP^�C Remo[ �c� 2 $\�$ fty\�L .�i�N��� ��A�j�"�$&�c�ngt�m $(s,i%GkQ!��_m�Z^ofY+.���$-i2�' #(kQ"G-w�9A�lattic!�int!~$kQ��W�!$f!i�>Q�}W� yp�waPsP ��@�2�$w_k=�P)-Q)=b_�N� Z�d !$b2 E� ?�H@*
4V�e $>4} Retur�8tO[E< Ecwe�]siderM�A`!EC0a\ \bed � J�mixedK6�defF}) ��fqFK@2&;� ,b�B\b�})��� e�1}{2\piX_0^{t_2*} \[dt_{2j}\]_1�,J� K($2} u3,^{� 4��F83�Cr_ )F8e"ta_{21} j1}�v� E2&Z a_20N� B�o JU2!Cac� �R_JW)��}� 2]+R�%e� �b� bJbJr_bJbJF�E\!4�3})r_�,r_b) �eg!*})recE�onv����� �*�def(), i.e.,a-�=v%�<1})$. Subsequent�*��IKA�to2�*P &(R r\]�0,A }we]6 YaWP&zQB�e�&��"JEZuuA�6?'.@Ft�i)�N&� K(u��"��&��F�"�C���9�A���1,%h1u#M1}; r_3a>E� ,��E� bigb.d }a$^� m&t�n& :=&)�p_0�E�2�r 1} dr_b\,opsi_0 (a�|^2Y0 M\b�  '=de^{-i [ $\� E�-%)� A'-9�B�e� bj ymbol{a�}� Z�p) + B('.) gN�=;&: ��$� v�p_0]}J�`�>a } e�2b- � NYˡs�r_b)���b}} {F>y[i��]5��NՀ��� �~_1,�R_2~`A�R_� +1}JS K�%Vv %�Jv���%'_J� J+1 VMG &�$A� ��_2�� |A :Ur�9qU!���}n�1�96�A�J�B {oū6�\b,�>�1~ 0RQ�� C1��{2K} oAͥE� BaEz!6  m��["�.���.� \&�"b�2:��1},&4 )6[��B*9X%��RI�2�I�6m&Z$ yE@1,"o %V]2V�� $�� :=�7a_2�' a�Q")$,]>� := (���,�$( )�J�v� �eta�W)t It , $a�1, p]$u (s regularizf$D�a,�qas ?2,~>� $. See"3 8greenshortdef})%:a� ilarl � . 5$d��DK ;!ymak� dispersiv.�a�"�rt�proof� 2 4� 6� .� �� &X� [�| L�� 0 {22}� s_j\]_3�$in "A/#'2$F�C;�J"� 2� �u36S% (s_j i�#jJ� +-+( }}{(�j!)^2} F��� �� �� �Q|.;� R)�� *� !2!%�!F�1�� : �`��% !�-%�9/2_}) &��|\!����f�� 3�)�_{d*� :�� '&��| asA 1$^}&, \footnote{MD%4careful analys�!�P�%U)Lof $m4 �&�%by argu�K�60�) D��TB@$)"Fyield a6sninsteadG$bbut3"we do�� �!he�*meqp�.cru��.} ��N�%�& ��~��$ t_2^{2\| 2m\|+ b-4��b-4)!J�}4$>C \|* \sum�"��e| *1 Repeaom<2�tdivf��k&N��  ^�!l6o&�,F&F�&�F��:���.� �:�2���&Q�6�\|!1� \| Q�\<��3Y�\<��F�� \�%krel{�xi���� 2}{ZB}Jf� ��3 =>^{60�r_3�48��F�grad_{b^{�} Aj3J�Aj:��&X uI�c{)f"42\| 3�N � )}>�F� Big(=!3!48-2/&� 4v1J�"� %mj-1}-r_52!4Big.�!�Q\B[>Y��]^\Y[ V\i � 2�3Ai�N[8 ��R!L�i�i^i\�52m Give�o2of $AI�$A9derivati.�,r_3�m!,$ pass onto;��"�9s6,�2{�9 �&�*ly smoot�)Hence, �t�3 t�*absolut�0M9i���,�e�[3cs &% �)s =];p.�)� show�*f�m$a�3,��u�1a�}&������a<&:1n_1+3�5|m�0,1�4�bF�-"4 25+2 5j&-�,>5C[. t::� B+(*x�%�Y ~Y ��|6G m+n_�1Em-�4Fh{x \"g �2}�g �� ]�����R�-*�.>+ �)#-�b��,:8 �""�2<�< b-1$� h�4 .&�way� We start��"(� �/ both�&,onent kernel���time-�!ded  . W�(nH6O���?.1 )�-��U{�t_1` t_{1&�!w 1*}\[ �  @2!?"�U�/NEZn {2,\�\ �7� y J�"T !1"q U"� N!*� ��F9��&��A����:L!#�K})+8-g.1w _{13};� 2, %kHv�� �FF� ��fFE"A �2�zIVWa�s*� {11}^<���%2� t�  )\;*�<F2J.^y� �){aC��.%1iv.."*d�$6k| :"9 E\�&%B�B+ �rJ.' !�" ]FT.�S zFutB�+nY �%}�* :��1U?U��!N��$3�r_M$j�  j�$�B� W�b�A� \&CH NC C �@"�:�N�F���1� �"�j�V= j�%1�j +^*�  NJ�rZ��>.�{3 ���j�^�J= �' �$=�<�&1��&. ��&�!%&�R'�J.� F���wR�-��00,2F%�� \bJ6Jy�Z ,r_2$'M�.Lf�?i�� D���w>B�BI )N��!e^R� [v�����6q����^�'.7F���<��z�m��(=�qx,5l6� 4.FP%��&���ѫw�i� � proc�:*-'Kn eta$h 6�JY)�6�&22�IN�� gejF��>� 6� E�� R� A�.A�� � � &V�í@C^b t�5 +2 ('� + �  \|)Nx% 5)!�_�  1*o�2*�"%R�\�� J uu� �FF��^ �^ .^ 2�� !r1�e B�� +aխ�)!x\!"�M,KU }J�, giveBA�)�&�� K �\ �\ �\ �\ :}�:�|1� r�^< %M!F��.��'6b�.&AM�U\|R�(*1*��"* !R.0]:��`%,a40}�"q236�9q�9$"�gIxi_�"�mA�xiY -1R� / �!G�?  F��-(\2�$Ysupremum��E �3�, � �?�EB[8�O$v�c Againn&�5check �*�"`- affe=6o6#S���N{SfKE f'F�&c;6w�R4�� V�'6�n='�.^E2�:�+m}�:"Z!X>}��P*FFi�F�Db-1�C6G"� )3$"� �5* whil�P!�j2to writ��(\1&@2F "�+>�3�.��({JA6�� ���o��%�#�j���[��._ 6 1 \,� S 1�O�� 1�%�b) � �0::� }T  =R�@.��A�. 1�A$J=0,15�2)~��:%0�.#0� B�K%b�M ![As32! r*�=�Yis" � �E2�=�;$\�  "co"=Uat�9�6o��&r6QG2�&+ uB�+vF��&B )^6�nL ^NR=4)!- u:QI6� z�: 6BH�N:H"A�:BHneq2,"�6�:%��O fun%hs,��*6H,�<�JBI TImp�-�*�H$.�$t�Y�;t"N =nPnt-P#AionpM�HiP(M�b&S0b!8a4)=be�5o�(�  $SU�CjQ=/�IOJ.%)�=��%!#0costly $L^{\�@}$Y��n2VY�Z a�&�< �er�2)`$�are�J�.Z =)�e+. �= �S mechanis�utiliz!q�s lik&|/>tBq�V� ���JJ*q[M0� n1})mCSuppose".= at $KL<K&>mpl�K$ ECn�A�Bs%#nNN.� {\b}E\b�D�X+A EO�La� A hoose �["�[0 atk_�[kN�[�[3�L�@��b;[�!Ё�A�6�i�, \, L 4$A#r"!�&E\5�Ex�Z6�[>�,� lat&A Sed F@$\sigma:�\= .�V:= �61��2^�"#e�inar���L&4:Pi :q�uH6? ����U�X�v�UAm<|&6��|� �x r�&=�j|}�Sr"93X6G }-�f�F14e_ A�j�W�T0,�N�A remoH%EA orrespondA�M��t�$q��] K�SjA�j \\g_j , bEu�\q�2:Sa�+��.b��$�.Wa�*�� &)�.UU8=�8gdd!/i� b��# \>^4F�\�Z #:�]J2Ef�C�7\b �C2C+r/�)B^\<%\>�[E82�[B5M�uK)"18}F M @A@e^ a� *� 1& C"�2(%x �%m\b�1 L!] )2���<uRJBV�z�(�_{ G}I& pJ%B< +�Y��)-"WT�\B� - &� 4��� � E�U�^6zAXAB:a2=Xy��V�nei' .p�W o2�v �]��\&GV�Xa�on�[a�f�$!��/i7be5 $ wa���$y�ft�c"�ImaQQD7�F %b&��]Now\�� $\b=a�ZBy�SN ,1- \�I$!1AcgD geq249iK2C2B*,-g.�crVr_0m�0)$ �cm�A�e�W � ) M: $,/ p� vel&C  I*9 s3�a!�1wQe 1})2�=0�l�H9!�same typ_��i���We$r�a1��N!�W"�K(U2?9�Y� �_�\B� 2� eW �3oi�'OGr� ��\t`��K�H2 �� REeW�[I� $r�a��o%����)V m�+Re�'!!�N�I�1 %�%�H$ 0�T4(����Ys�5ogously  ~rea�4" . F\ .[\bA�U 1$ requir�,tw&�e��8%,bR- � &�[q51�MBR^$Nm �Y� e�We omi� �M,� #Kem�SJZ�MbT>�&�R dWRSY m!V2�C� �< T��*2.�Lm�##Y� &�36�X� U � �X�< %�!uB�Xn6 E, � e~�.w.:,is eliminateH pa6�P"� F�T� &f�U�J3We_2�eMR�8s��� 0�kA i� E$ fre�/�QL �*their���M�L�-�]Q�.�P��#carticip�Lin7V9:d . E� way,�Q&:/Q�&�Q."�)�nd�> $CA�2)� I6���y[�Qe�� !�xploi�6Z*6:w ��[ch<1dF$�;m��N�q�r�Q������4v�SummaryѱQ�U]{@(I)} +�)K�K��2632�=4}), we �@[2�3�ill� �2n�y����^�3af�bގ&~� Big[� ���R\<��1CZ( \chi_{64� 5 >&; 5)!}sZ.�"&�H m! o� Big]6,�ch,{4&�R"�]!�$sn*�nI} IDa(Q/@���"\gedP �skip d we �P��>I���Z��^c } ToV$)[ lici �^o/� � �aw� \a_{\kW2�l B$ �=$2}\notin Bq 3_ j1�Ced so7 b�&~^U�2 02j0 2) <0 2 < A2+1�A�,%6!6 ex� �m�"R1�(invol�(random phas'TEx)-l:�Q*g\bE_{B}&AA[ ,A\setminus B*A�(ur8A}(n_1)\oplus An�m})N�*oveJ\ a�6�RrU@B�M�ZmL0�] !�6R0=& |\L�b!X(z |0d� -4R`0k=1}^{[n_1/2]G`{}kN:o^k}�L(jk_2�=-UBb !}`;]�\B/"R&{z�'2� �3 a�B�'��%k[ 1%2�H&�_�wa�]6oae?$dua })�5�.j51l&�!�J�7)[[%� b(j)!�!� �/):%�%!})��0�k� }^b!�(>k=H+� (j+1aF�%�AN�<) � j)� aoLB%J2 {M�- fr_{j}%kN(1kI �� �^G \;,�Y���II6���["P]�}�<le�P*Wu[Zu_�D=�+ :=�0$�t++9r� $�m} � \{ [�'$(j)}]_0^b �k�r^ ir prim�Wunter� O v"O left�� � IF \to�/� � w%�4 vj�"A �D ,hat{r}� ,��2 �to " ��Onp<*$�#re�!9Y+ ~^sn�b&I:A��;e���8J�2��?*pU�EPv�\u��a�.�2�r_0�0��F>�\r5��01�qG� � �[!�U2%]FuD@e���� L{j�N�� -p92}zc1.w Y� �)6cW�w.�.>q �"b I��iu� E:K�W< Y� B�. Unl��(�`ifiedY� R=2� � � sepa�#U�: �� a$��m�w��6-�8e� Each� s�be 3!��"q�1�"�*�V0net e�'i�at � �a��, ^2�-Si2O�I�Y< vali�<�� �k*� w %��)� Ro4,�0ś9)!��-��FeF�"� we.ve%�5�!�!�1�!J e!�groupB�Al!�.�,��no-�Ls-�`t�?v��,�ioJ)Gti e D!;@ (D &b=]�s8xks]TQ��� b�: twi�B(h[%��"V�"yH6R�isERsjS.�o�3 se calcu��=10�� � nclu�`A�� �aNNA��:2�%2/* box{!�}��^�&2}&�"�{mc: q�>��e��vXn<(I)OS�n���`U�Q�XE�V�kE�.forWw6���ulaU#�jl�of<"Ni\nuv>�l*2,'-')r�(# e*v^ }!ʡad�Ton� nuaH \N]FU �tm�)� \.�a\�ypP3)�7& �&�I B: |B|=b}XLe m;,2Q- "�LA: ) {B\prec AE &�W� �BRC(N,m,b� \,B#�B%�^:�J/�5� 1� j�%�\&�1B�CF�IMzB^7u&�}9?N bE�8%8j7E�Z;$5��=4inom{N-m}{m-b}��m-�e�2l�Xł DYe:$"m -+*  Compu a�*�kK4f�yja}q,b.�39�a�� b b!a�F�*<1��I; \g , �M�+l]6cr�&nw�W:=&�2��#�|�t 2�Bb�&b�$, ���B �__0!bJm9?(�0�,�!.r"���1-@%qF^)�)GJ�&��jN{�} D:Q}-6R @ ��� ��8n b>5�v.� "^�W�[��#j -��]A�9\g*2�j=r_j)\�N e�E:�n1=6�l �j�ei $\gamma =$# >"�|���s��ly�Yx\g Tn_7} � \g =�#� a�N�!�1�$12��, b� �O�/�"uhL,"!&UE�*� "z �� ��k:7�/��bq-�M of S� 6!>4} .x%jn5l� �to spliIzk�K�&W& en5t��'ent=$�&}mf�'BQ&3m� n_� aROnbe ga dq"� � �6ZhJ_ :Q�=2$a�-pC:�m'!#E+maI6�E��[k&� @tn}B�j~?{\g>e:Q�R�m6�)A��^! E���(&=!Q J!@Ik�7�(\gIp*���iM�o1 � �|70r_27("n(A��� yCQuBI�>2� �p a��-AWN�2 s (6�ep A�)% �  ��(llA����A�vM$��� taԁ�R\bl0we)(h�[�W�0in plitf$�y",_vV�intDd�)�,0�,r�8�-� \>^8ى g1+ϋC�rx�j�C�0|�-+0�,��2�(0?0*M ��g |dr��) �1\>^4 � \ 6 ;� ��1=r_1A�I�) ���1�.2�1 1:!Ka-dA�%K2 �>>� &'.��2=r_2�Foa1 �2B�2 R4���t6 �)R��!� !��fQ���/ . �MR�Q|�.A0|^2+�:^2F2F#B�9A~,"�"�double6*}�e}E�yy�7s6a��a�wm�an&�4 sBh�5�s";`Jb��/`�N\.�/��c�'Yy��� e�way (af�4a 7g�va<(�f�8� �. Qs:MD�� Ig`���~O: �q > �J� 2S{�J�0^2�*2AU�{m+"kw=�*}�7=c0�7M sec:g1n1}&�,�"\-&Q,*xX=N� forcq-_j=��jNb9:. &{�Aw�7strA\�) }�4wh_s]6ell_0>0$)�iz. Se�>Xrx� ext � A�M6  hUN>wb �.covb%1p"�H]u1j]u2�� �T&]FZ6ސ��Tʒ!��U��F�a R!�S:���2 '>6���^k�I g�g&W{@1g })�S�k�nl߃, k_m0Q�^{-60}*4K�Wr'� �E!:!&*9[E:g=1� �2m 1B:@b!Ji�db\{!�0.@$m_�q�+n&Z2m? cons�z`-2:!1/n��"� K:QHs an i� ity "� o&h�Mdiv�2y�&�wu ��$�<sq?_s  'w {-8_$�6��?�.7%�+� F@.g�*qf�E$d,J$& )%B.&.n11:p&� L _J\]�'�mtW-�.Br>'>?>`SE^ 2javbEh��bh�g <2mf�V ��(- '!l!k,HBd @ ��Ț1��W0g )�NJK �M %�m0�p"�1; 0@�Ia�JW��F�_j �'6YY�* ,�q>^��t ll_j �.B>�YA1  J��=e%�.<2.<2NGg]Y<5�b-��9b�+.22N- �F:-~T�2"�1�b17"^[�)�bB�=*7^^{BN1GͶ-1/�� <0!c+s�d �R %1!\%|F� " xu.� *�[uX 2�F�qjq�y�i�mXF9I{)&� �FO)���)1� N���)iA�s��2 F?;w*�O! gralz= =by9t.$#"|E,2�h.viuseb=E�L1|01��T-܁@ )�1 + �֜�5A�U^JOM56J5Bb�"$5-�-u0 Z�F��0�J�!C[ Q�Ig- %�y ,].eB:$$ M�)�.� ="-PGPut%�R tog�@we>�Hg.�� 7� ��"� ";L2�o��i,^� F� F) &� �� �� :� )�S�C� B�� � ; � ��L}.�!��2�ma�!�&�X\2Bw�T62��3:�'�&�*1 �(&d � l:@dl��)�%. C*% �vʗ. !&*1�*f*:� V&�7!"� Mo�*Vm5)��g���2O7)7 7 7ym�� $b(0)�1�t��Ep���Ana6�&T.;�" (I� ��*#A1��1�L6I(|)� &)er�Q 8 b� "'� ��_ b�; �;R|D(*'p�@6&33;v�v��n�m!&s>sNqT]\>^�  ��\<of"L�,��s(��escom&��"� !��^��!f0)4. $\;\; \Box$ m �vj) plus�� HA�w�$( a new coll<�� |E*rval $[t�i�+�$)$�� �vid�* extr2g-�<E*he\N f&�� �a�%o:ofZ pagaQ�es�i0�0<y0Zp$ !Y>P%K ��9K��;+�p�* &%��E�&�l�8*B6^bcd}. S�laMu}u��G�1�b�h\Q*Big\|&��;2k&k_2�#k�J� 8 a_0,�*^{�$rm{no\�5c.�L)t^v,k�*n_*�*;Y A}(s,t_&�*�=>&� JX*Y<�e�m}'' FE�")Z�*Y[F�\� \in\operAn$name{S}(b)i�Z9(�"�;2(<' ==XFU-�(F�*R�v%�%� .�WDvP)f\�QF� �M0, A'J�J~� aGsumuK$R#1")�����512o�� orde�S4 sets $A,\,A'$�size $m�P�30,l(!}$ s�Ct24k - ''$& no r�za�elea�s, �- )\capDŽBT* B9�,6�)^�Id(B)�ec'6,g{�6�iin1%%�our{Vtڟs,%dSchwarz *��zsymmetry5rebE\| &Z\1,i�M^>:�a� +��e*h8q�ta�zab,B3.%e1�)Z�e�1��_�6��f�Z%��8 �!E��:\!ků},�.�7S= eteq!��B�]%�*�* :+:]I�6\.E4:�j�B >IE�>����[��\n"]:�B�F�e�B� �+26�����2���$�tX"1-1}�  1R(m+1)! 12)}{2} �I��$-5�/r()D$1(�=,N)6;kR�"_1"�k�Y2�� �Rk ��=�7l�:� s�$;�AC:g �Z�  d u9e��� oric�2� � ,�Q*f���/���1!t���b�M�g_2�[?�pb!B U1.��|\{#E�2a1p�(SZ�= ��1n�����"zt#�(r_b)*d" �� F��=BУ:�Nw%�bEa2Utimes�VhV� -p�z��Fu*�1\ AH*. k v|9�< 6&S#jZ�)TQX��1*� +�{y^a���2�2�!�.p �F ����%�5�"�x| !�0%%RQ�[��V�7Q2<� r��-�� Jh�>W6 aris�c}���iOX���˅ȅ� the ���g6�v#U#�! 6q� �+b�;er �2>Mp���֟"�@*. Our�*�/arj�i�&6�:xy�5i� }2rE-��IF�I�~�E�� mH"I2���&=�7gxJ�-05.�Da�a0_�JN�2@�M2�DjV,Y ) z\.�D��5)T�2T��R*B�!cN�o g0'> %�#I}�&�! �.IO��.�H�>in��i&gthroughA� �>��$ �,ppealPto6���. 6��4 -6�+rw>,�B!as( veri�Ce��+2pM+��^Y:WR�[� ��Q+*�&�m��]� >A� ��!)�*n �$#&t�z�� of�C!&B��A"5:W�.eJ� =][I�� �� &r�p���E�H % nested 2 recoln� 72js@9 dFV���A�aAfr"�toM}�� ��7at Rbe able*�i-��4to��4�GJ��.�J!��fLgm�e�W �@��D.�V�H�06>8":/%%�SY�9g=o�gu"zga � non-*\BD[0 A!} *� $� �A.� `4Zq[2]�,A}� �$ �2- !�A%oetb��9� J0 � �A6^� 2&-?>e�V 4#� �  �.q(w�erb=- D�W�6r2F�%&�>26�AF�2OB^f��b"�FC"k@ f�NzR/V�A��!�C;>�!�2�1���B�B3���7�U�1 J��n�.���BR�B>(}d>��B21 �U2�}K-�|I�B6| F�G � �W[" �*�B (]1),2)J (%n,vW�~/I1�(e���F2�Z�A2K�k1��4a� ��b\\�4�W�YJ��B}""V0 # u_0 ��{022�� 2��r� }\\� �.F�� ��� .al,� ���*_� ��)J�6.R;�_B ��:M;v�, O'>Q�BF@2��b% MR� $?f �@2 � � ��VqF�a = 16��K � LiW 0 e1)B8��;'>�#andb5�& �a�)&�9�*5=�[��0��S�(J<� 1)]A\"mm2U.� �>1?1J�.J*�Cr_:oj)F� wMn� o�92�O"k�Us�rB�o�M�=$,�N� J�:��(>�Aisolah�moAa b�P c"n%�U ADm.=6!7B֯" RӫAh� defb��J!,A�_>0$b� 2� &��: ,��1�/��1"r8 .c(1g"`*�\A3:�Z�b>��*!+2��l! }}{4\piN>=� "?��w -i \N�2M�5R�f0%w��8)}{_�1j�0]��*\!�sq J�"12MR_: �}�w�w.��F� m�� .Y2^Y: ��jFZ ��\���@�\b�ez6�8�4)\=C�a�M�B�����),K����3�$.��ib��E"���_$B�� ��fB2?�aa%&�expan%ea $��:OqN'j� }$k��Zd&�3~�)L'-M'\#_2'�rnd}rQ/!]�%S�'��5�@'P=&04<9��d�e>U"��R}�P�M1 <.c%+�: �g��,  6� a�?~H&�D.�D-�p�  G�ants)�#l1$ZFmJ"�@A���Z�v VZ,���xbu��t/t2��"ږ1,b}\|}$�:�a�h XCn&�"�.���.basic!�Gb3�^.� >c\MMbL�0��0S�e�?��0z| B] 652 D + 1�6�=11�p�= �6bN_9 f _�C6�pr&��� s.�U$ �� 1$�e$�� 1}$ .�1�am[ 1�^�2kpm)*T�U�a�&T)%�co��_�J}$.�2��&ZU�$�MaN&�EY91�M1s �: ���G0r-2�e�w� �9��,!e�+AeSNP"S LD�� @ ra��:(�&�2��� �%K��lJ�/ZG/),H!Qg_1 >� �<5�^.� ,�"h 6\ ��'^  (?`g0ge !�6jY^��<v2�]�J�G2�\�>i\t�{j�1�2&iO� r� �+� �>[2T.� 0 jJ)Z,4A��W/ uc�\c empthsZ�u�/�m4F�N�Yb"�Kw������*�/M}c>"[�2e�� [3� nfor�)s��HZ��V �O!2�Zioќ�t�0usual.��K�F�0�������ׁ�^ �] $C��-b(a�"�rAt"�"s.sOke&]o�s8�a�^� p_0&Zm0�>f ��f�� �E�0 " ! 2F�sB> K(s s_2; "F ^��{01}}��2}�!_ ".�b*� K(s�,s'i�F �[k��mF�� q:~}.�[C�:�i -3}� | f�_{!jri}JN n�V1)=\kapp�G A�������p. `{03}},�3����:�(/��4��f�> 5�.)Ł���s $-J1}�`� {0X= +1 =0$A2� afS6�I^" L+;Jz:03b2�Yf�Q�5>�h>�J�oT o�/���k�F �"��D��  ]� sums FpossiF}; <02"3u 3}� �8��"�at�)1 t c1[m(�:�# =�{���L =![vs�2!n�2"�5\;�T�,6ZA_ingpongE+&wA �(d[�� }v���!omH�b  \|�M&�\k_3=:Bk_3�L��,!�}�^F\?"E��V2u6_/^Z'.Nu�3}_{*6G-;AF�Y()A ��L�=��aZ66b�&^*�dZL9�Vc�7!�^3Z��-*E/O/3} O/I�x-F.Bm"H N�b�t^��6��p�p�p*ȭ# iR,ad}VY6�F�2t }5��)���6�}l 6O �^2�.����7,�E���y�r�Hstric>$to"[S�.� O2 OB3�zL�^ .5uh.�), lead�E�6�.. �`*/�/3|*�6(X 2) 3Bi��x>�.m��\�!���2< b}��\g��T�J�Ubaj\fp� D�pF /�u[-U�-FCFbY,/N�zPw.\pa��++r �u b�"6a)2 ""O2�&�`���b-b-2�t�� �,�.� � �'�.q/U:�(.3's�Tv�,m�nto alway�K>g@ >s:[ f��n�va�VE~>2�=�=i�a�n'� b $%� 5- K%'���&h�&W ofu � ( 6'2�� ( "L"H� �� 6�.�ndy $� >me$ (�) ]n*�1h��N,Jb��� "v?&�`Qul>;S!?&p,��?c��c&`�InrHics���9@�as"� >w*��� })� N ZA� th`�� YH$�L{�W{g_�Sr�!�, �/re $gMf$g� �q!� !�~ s���Yt<%�(�,�0��g�U.��1�\�C�pr�W+��pn&C�ta]�*C step!Zu���� Q�O volvyp� ��i;e in� � spa�o%�A"c�m!�D}>�- -?J� �_q� $p!�Y$e�$�,us$1_[o{&�.QA�,UE�`A��"�b �>"�`R��!U����aCs#��1*βax��"��2S��W\Ic���ř��W�� "2"U?s,�S�A0>D���.O@3�2A��T�<��Q��.��@�$F�YV@A_�3id�AM�.� )k�[�discusWf= E>z�����fZ/�"��L">]/.�\UFE�uM�|�� .I]e��#I� $\|f+V n,n'],BV(langle x \r ^n3U�x{5f(x)\|��  w��1s�$)�4*[$f 5i��re�|5y�$ent�$a�paramete��a bb{R}AiI~T]]oab%<pW����z $�f_J|_��Əao@�_{\a}5�$0<� < 1��A}$wi2�,]Ig)5apo�D6! "� B_[0(\a,u)f (p) =�  #&:=�]�%1 ^3}d5�),-q) f(q)}{\avj q+u)����s\w|{E� �B2�79W%��lyE���%��&\Hin!$ta$ unless�3be crit�4��3�"i{�eRu��L:�A�W�NY()jAЉzNE%f�_ 9!�N+2,N+xA lamb�� \llSt��t�/ exisbQ��$stant $C$ �%�nlyA�$N$ (!� Xcit A� dime�#$d=3$)���]6��M�O!�, u,\��|�hp�hn i�pTa�Fb��& C!��| m�!&& xrvp\�~ialE��j�2�af7�)E�aWeqJ��2����&:�n�C�Q�|� � !��\a.����:� W�h�y!��=ifo)|6�PAWC  $:u2�.�I6\�URI�� } A�*�� �0Fourier TransŸ Yukawa&��� irC8tie:��Ql *6#F}�� MV� \�R:v� (x) &=F�C� ac) i|x|\sqrt�[!�}- ixu�|x|�oG_uL �/GU]����nx���xp} V_0�x�_yG(x-y) �eck{f}( BN _Mc#c%b bran"H} squ�� rootT  ve imagin5�AtD �Smit�$a�*�7цs. �,��use1�E}V ��< a�n H[o�i�� � ii9�aA��f��x�Cx�=)G-a%H G NJ�4_{L^1(dx:�4lA�(Leibniz rul�ahb� V ( �x )^n�>E��)ni��}|k�V � i6%� �:( pro4�&EK. eE X E� same A� H�u�!� $ܷj�al�DG��, u� qSCe�ł,|�1/���9U Ts ��j�manner����� ����LL=  F�fp,r � defBJ)let $N>`��)\ C�|\h~ a(r $M$/5��> � !�b�A� p_1-p�l��{p_[)�\tW9A ,p_2!�FyrM!O�\%�.m V�> ���:�� "� B�I-IU-I< ��~iEJ{. For*����/jQx alig.B(kYP,(%^O  d gk}Y51-q�3�0T q�H\a- q��"�2O ds- ?kA� q_k� ? B 5�A� $k=0 $��� K=o�=$[Mk$)$. Thisd implies: \begin{align*} T\<\grad_{p_1}\>^{n'} &2L B(k; \a,p_1,p_2) \\H =&  8\int d\fq_{k} ( Vf0\hV)(p_1-q_1)J=$frac{\hV(q$T2)}{\a- q_1^2/2 +i\eta�\cdots ?Rt q_k-�P -q_k.P>���p_2 �=&\time�F��+�.�FE�� ��BR . \end5�^nUR@{n' } B(\a,u)^k (M,\hV ) (p) =JVR4} \underbrace{^\circ5� x}A~BWj�>0�We can now apply the previous lemma!!get>v|�@| \leq C\lambda_0J.|�^{k-1}Z�0\|_{n,2} \; ,6!�8inductively, usA$�%�s on $ if N8n'}$, we obtain:$� Z�A&)(=�+1}>�-0} where $0< ᇉ�1$,E�$B$A�e�edA)=�B}). a$$dependence�ZI9omittedi,A�!!Aw airqls bel��$re uniforme��51$.����H} \label{L:Rest}LetU� � N>0$i�n�`re exists a constant $M$ ā! only�,N$ such that �n) N�& have^��)_1��$}: \num � |M��J(M��4I}\�-q �� p-qi�e#(q+u)}��{\a&a"b� f(q)a7.5Ede�R} O))S g laim.8$, $n'%� N$f5_!�  \� � .A=�NAmleqB� C=�].1/�Q\|f!�n,3Z *aLE:1�eT.�0 To show this'proceeda� in LA �LFBa� , except)we u�6 *� eA) &\� A| \\�T!&&j+j'=a�Big\| ()_ x)^j!wxaI5 V_0(xN� ŗy \, G_!� ,u} (x-y)KDy)^{j'}\check{f}(y��oeYL^1(dx)2� R� |\hV)�n'a�5�K\|\ �-a�� ,0_{L^2(dx dy)}I\!gD3 j��2:f �;x!5=m�,1}{|x+\nu|} �<i |x +e�$| \sqrt{\aѕ- i ux }��It�q easy�)se�Pat��nee](�: !z C>6J ,which justif: ��2# ). & ��  of6 eJE�� e $p� ��u� 2$ � �b�Big!��n (c $^{k_0}_{0}( u)&; E�  &�& "� O k_1.1�FC>;.�!�.DU�>r�1} 4\hV)�� �.m *}by� �mV�( repeatedlyN�B��" WAnLen sum over $k_0, \l�, k�$A���let3)� 5��%��E� \� ,Wigner Trans�0of Main Term}6 $Renormaliz@ } RB� B}) � � 6Y� \phi_A&(t� ��6:= �T\fp_m��$\psi_0(p_m!�hi(A; ${0,m}) K(t24 \prod_{j=1}^mF1BJ�s0,p_{j-1},p_j)(2iphi2� �no%wat $B=B_o �� quantita�deriv it � � 4:=(t)$ (�jQ?def�,)) throughou��e whole -� b8is fact will bef� . A Fend� 1usA@a  necessary�� � 9  in �,$. As usual�)� $!�P^{\mathrm{no\,rec}}_m!�n(m_{A: |A|=m7)� }}M$H� ��a�A�$Em = E#Rs$ � =] psim< !�%suppres "not"!�E��~ya�-�. B6�/�aSreplac8 �$ with hi_mfU 0phiminuspsi} �� b�bE�Ma,m(t) -)F \|^2�q:� 4m m! \varrho^{� �$(  t)^{m� (\log +\O(1N;>5%1 s Pfixed $m)�our scal) ��� X_0 \ep$, $t=T\ep^{-1}$A�v@\lim_{\ep \to 0} � = 0b *m *m����� 1{�J!�b  by appe �to6~ Kide�y}�6.MAA(t;p�=&� ie^{�-( t}}{2\pi }.& \, \> F\E�I ?p d\a�ie \ f� p&��J� 6m P�b�Z- p_j�t + J)\6��AAq� KF})!7i;A� To��ute $1��vU(�AqA )a$ we��eali2E bcd}i�1�>� G(݊�) i!M-� 5���1�\� \a�{ E%�%�T-�-D� �Lk���(y� .�� ^e�!�)�5� 5�\*� �Dp_g ,p_k��A �omQ k) }{AkA8q^��^m�pY��EoF�� )6�We �Eb��ing^�Iib�m \sigma!� \� ,name{S}(b) } 3\ell,I��^{2m-bNTc Ifp�b}  '_b G(� b�Abell_b}*�$\overline{ 5{\fE6'7N�Delta_ �obv '_b)Em|6 �Propos� �P:crostools} �"�"&z�is time_o�T exploit any structure�h�pairings� crudel5��(integrands �(variables $%{b�h�L"��wHowever�el�ate a ~ o��$t�BI �result��bH|a� ',p'�9'� -�pM� >� C(M\�) �JC[ |\a'� U|}{\<v-v� {30}8 ��� (s trivially^ 25"� Ind�!� nume� s Lcancel its correspon�A( ular1X $ | �9> | !o8nd consequently' 2�totalTof9�. � ��L$v\in � bb{R}^3�fin:�&. T_v(p,qSB ( ��+v�$, p-v, q-v))J�B @ ,p) .�T�%�} �we "� ed%oj " p_m$A�atqn $v=0P%�als�anveni)M dropVsub�T $v$ altogether. More�l,)se. Q �"� $.? �� i�{\it r"j ed} �Q kernel:� 9B&� ren}}(2��T� -�G+\Le|J76 j)\d�A�_) ,.�Bv�ջK>�6�< (-i)�G int_0^{t*� �0��ds_j \,F� (���W � )} .�.��*� }� "p mo�a$on a discrylattice>�ltadef} "x contconv�beforeA�take $L� >a��benefi�=Y� � at6KY \bE_{\a}f!�� x_\a!@< %�} . yy�c�[:*� ��o'$B���:=� .� mf�� ɦa simi�e/�^T $Tfi�"iQ9;,ed wave fun���l�an� external &� �!b�� {< .�AT}A�� :#mA�FJd" A:N;F�" mNi=yn�FW>E ).4 �2 :Ep:& % �: %�m":"L` PL:ren9}�$q�=q� *aLn7"mij}"*a~)limsup_{}�Jzhh*q%�_{�Bt 5\�!krel{ E {0,b}� |.Y<� NJB 9b% ��� ZJ� �2)b�b}F�y�bNU b��hb \"���)^� _j}� ] + \O�(H 6 7 |^�m�E: m>&� o� agx$Fw�@j!�b B_j�& Alson `^�K(t9^^{6�=�b!�"�[z\]_0^bN�&�bF (-is_j97}-@!F2&���'� � *}:�^rel��62UI�%0,)b !1��%�[v .6%Ff6A*] =j�b�.mU0K�R.^}p"a Ub)� hand6y)bFbE%$A�S�_JF�_.t{f�\2geq m -bJ(!A� �_b&2�n'FUBla �u>:�\(�F"!�����!�.5���2�Eexp�A�$L^2$-t b�%Z b,b'�S}S �9qA,A'}{Q $b;|A'|=b'}� `=� , '��'}N����%� '_{b���b) :&�( 7)�6efkFr :- �9�tT(o j})}��}}� � 6H' �e)[Q^� �Y ' � } \]F,v�F�g� :�'_0},��!�ag } }N�BM uJ�zB7�?'i-B.:�  #B_\rDNte�Iv.�R�tbe��uR�bpY�9B�B�=6�%AubeJ*A$e2� !�u*^2}agB��-�}�E��q_�_r: F\��; !&�Exp:C afterR@expec�s& prLty�2�fc�) of BZ $bceo�)Q f a permu ` $I�*�) $ A'= 0(A)$ and $f_e>b)$��. v�" s=r.�t�dis�Luish between direct j-s ( �G!)�Id}$) � "�:3\n�)F6�-��.l,NH[ Pe Schwarz inequality:r:� U+\mbox{(D�)}r4m^*@ w/ F�%"� �/}{�|\| = m^*V�binoms }{b} R :V|:M|j=�m\&B�� |��� |^{2 j} |�b8|^2�.| N�2b&�/O-"�defT}),�'�/�/� L.�)�-�6�. � � I �=� 5�{2I/Fx� #�p_{p_A;:  !� (&B4AJz 1�_b�)60�F� (b"�\<:�>BW&a� dispersivY ��in� :(�� .2  0,0}^n�Rm�BD�C^%Y.��!�� T)��{(%� )! bJ��� �>v J (C T5# ^*}}#!2�*�*�)vanish)Ewe�� e $m���� -� l�6�,ч��e;���!�right? side B%&<n�V), ���!�as1�-�1��An=!lic�!�nF��f0symmetry give:�F�C78 le*= 2� ����Ido:�y3ta���b:�b[ >���> R�FW�j� ;6BI~�F2�@ 0}^b�q Vr}��6�!�3conjugMm*k���3)a A` �s�F7� # step�v :��get^2i?��='� :pJE � (C~&4�$m!�4duea�mw�numberar*� s�,3 �'!"�'R4w(�&at domi� Qverge�theorem� ordh o passSlimit$�'�*5 in=9�m. �%gen*5%� retur�s>��6 $K$M2H&_' . A��  �L�i non-� ity!: �)ll%11� a fac�!�� N4d17=eR Fin! xvT:> ]B��(����f�" m!B�R�.ba, \,�3�1"63 �#y&�)m�S!% % *. Comp@ of �.6&  %6�.V:"�.} A�e}#caled Hu;�* associ�T$� ^2*$}_{\omega,&[�#2�-hO2� �)teY>�5}(H^{(\ep,\muF>r}(X�/ V_0)8(�( W��+ *_{X_0} GP u}}*_{V]2&P) d\&X =&ͤx dw_0\,>x (x,w�2R (x-XF w_0-�6�)�$Cll}�ȁ`Gaussian5��!���r-� g 0N  $1$!#�'$,3} W_-ax/D,, ��rekedQst�0. "�0(#decom"�&�1st A..4ha�(disadvantag� atE threshol�,_0� #ent� �2���*�&�6$fix $M^*>0--Adf) � tH}!_0�ɓ� M^*-1Y�${.�no�/(t)#5 <M^*f _0a�Bl��%fJ LPsi_{m_��\z�m \,�(� Accor&>E-7�7 AF@?�&C � !Q�0$�c(6n��0set $m_0= m_0a�):&�15�m0choice%�W\%q?�j�F|)cma�a61("��6�/ .�'$ X� m}{m!} +r��T^P!�/]^{m+5�].l*} �'is ess�.���sam&� � �C.B A9 we do noM ve�) div"@�h2sI7i-rov1 ��60]��/M^*�� � >�/ L\to#!�B]9 ��z�z� M^2 =�<\, *�:cuttail6$ We ul�A ly n)oK !,��.�*��IY�:nd  tinu�A�  $J� $eA�(6�FT1 0&� .�8, ���G}ev��s �E.{ ,�) imSK�����o5Bj4,�^q�V* E�B� h��6�=��%�*h,��S6��2%ą�'}$q;Ro Fourh i���I!�o�f�;�q��N�xi 9�oE5�_t� p -D�\xi}{MBigR� a�B+ � 65:� �.e5�"���y:�� �<�4. O+JSZ�.���V�N4,I+r J+mC;  ': �$n.�p DmM$nAaL+!#(A;�+ �;p!t,3m!�(=�ch E'F->F \"7nH]%*J� B�'?(tb�=� � � f �.E �K&G�'2W-Q=e V,A�p'�A�&����0R&3TA]�jA q5n))�.� >��w_Y��2�F~bR.�)A%@�:F�extOa$* "i7�x� �,,�Dwe�" &<1< fo "$n=U@� $A�'\~ �!�]TA�F:n)$6Pnor"�"). Re�!u�s $w_j��p_jF�� $w' $!�j >�nd[�e�7ing6� }�>�_p(\fwk%sC�4"2fC>8( w`3+�� j +p�UF+J,:=&A2BE]M�$(w_m+ p)^2e�F6-f;m��-\�5�S�Q6 �-w�9}`>�(�-3 \pm �7}2N:wj4�$�E ,wELC*� *}��} "F�>�l��rhorho})�Ga chang��1s $�2pT4tAe24%JB G�} %}\"@NA� H�hi}.&!&�) &H+ed}.}1.� \!�qi�2�$ S}(m]! \&)2�J i^m��N!7A^ �2  2 i  F��v�2A8V�} Y��%ta�m 'Av� vq�)�� B�*_{ [)w �Jf:4 sa 0}(2 ܁��|;S%�}�}YG&9� j�Nat�!�OI"arise�=��ՏV�',�9smallerAa �c�> -1}=:�O� )�~�"y .� �t�hCr�"� .)� F M^*$`( B��state�isB��"�of|e),o5� t�$�it"jI v@-2�uG$>�X=�Get$KQOne%�p� a renen2*��&ded�< ()�differs)�%� perturb�� d�%on"%*M��ree X)�)X>^K|�=eK?;Q�X s mi�%Ohos� ��An�UBx�h� y ob�� ��pe&�J �:=8%pb�mo"uK!�+ag�*  �e ���k,���DfY='�W � *\�T� C}{E.�S�4�@|}rc JA�Y2S*� �H1�7T�� ", 8:��6|.F&\qquad̵� ��  |h*�E�A- ([�3 %9++D,0�E H)G|}^� }nQ:y m���G'B%�Ca�C�-u�@�,�� left��WA:6$�;F-=!\'aTu.he2�ll . Our � �$��t]L�/A B�m��/3� .q =:�N>�A*  \pm�% � A ,n jA �� T.�2�:82� � �� E&� ����q�%��C�o�64potential part�:�]w�� !!1b-a)I5b�I&-k� =lLJ�=6I fBBel) p( Bk2`R � � � � �)� � �� �UP: ��*�*} {F}�^� !�6��&2� �B* B�#re\��B�1F�  E�$A��]�&TQ f or�&$"C�T "� e �L�  � .7"isor�[t�HeI ��".)M�B|C�] M� y��: $ (� �T/ �)^�? (p)�"Ine:ic�G,, higher pow�obE"{dat may� a�!. uct �h harmwB��,�-evol�!�@F E&be# ten,� !2�#%�t2A��*LA!� :� ��>� �&"* +m*�5N10: r&�?.F [ds_z=mm�t*}'"� 'Fu�&c=[a�j��O��ue��_:K\; Mi | [ N �:M&�T&$ X} ]2��( 2^{m)>p �9- T*} \[da���>m��0[ 2��pu'#IscbT�j;!�p.f�:�V:p�{-a/%� }^{ } db_jFN!� i \O[(!;Cp)�T]q� \S�.,�6� � b) �w_^��ĉ�!� o�6��!\*JF� Qw� 9^�(UIE JzR+Nw-)}�J�e�we.roduc!�=I=*{2}(sA� s_j'�C$!i= - s_k'` !�!6�&M{4(\boldsymbol{a�Z ,m} �.�,-�! �:M;A:�IIn9�8 U"q> defM�JnN$memb�\y[m� )_{N�-1}}( br:.� La �[]X!YA�E�qm]%��`J*ebch��b!�F�;� ( -a_^ ��H �; �Aya_JsZ12 F9� �Z()%}|(-A&: ]fj:�R NeglNgng� w"�6sK�{&.�� i r�"d&&z�_M:�*�)�:��)c2�(2��*)5I� dV_0X**�&& .pR�Me^{� �iHŶz�p�3Fv�.�&\mks �{�*�*K� &�} }(2eAl mN`A��"�*�{!��Uo���~�!D�����2�J � A�[��"��� T!��)V�M�}��~ 1޵&�%e�Ced6�!We would�Plik&' &{�] p\si ^�  Q"]'� � e� st�Rs �J%�f  \0$�Rc�'' ta>&+$�� ��r�v'ri�M $�Ez�$"d �2oY  Nnd� $��7U� t pick uRonshell: .�8�b^$is�8orousnw�?3� �" *M."#M��%� @P:MoiAJ�xT�? $j=�C3, m$, $M) $ b`%e�Z ��$fA��SA�S}(�#�$.6G*1 �&p���'uZ�sf.� �V�U�N��RVF� C(T)�t�#m |\! f _{��Υ8Nv $IT*in*�0f�Q*�S� each� valuM!�>fTFT=@ ��3R!to9I��.�\,6�F�2l]$� - wxZ)6+5/e�.&$.�sW/�O 2 s if $f=fm $ 2da97,�a $ ��, 1� 4>�$5u�llyT.�Rend2A�_-Jlt say�$M �cr�de "on-e�"�+d�(��.v �} �Pep>0$a���6>Fubini�LR�2* �5�&B�r0R�.iY pb 0� F6�T ]]lr~"� �� h 28L2�F�BL B#d�[ -E�&� &� 1R� � 2-"o 8N� }]S :�#�o"�*�v*�2iteraYt(�E:basic.ſ"d:�f��%�&=�BuBAƆ iY���&C{��b���1}I�\<� >^{-3�m*�M]�I����\!.2�iU�G �t�tQt �16�:N6�A sY,e�0�:EX�&-�tripl1Crm� $�r\!ju� *J\<� � \>^2�\� 5:��C%v��� |b_jl ,� " �*&%ep�[\vu�Wcom:bj\� �v"�* *� e�� *�l�v4,�f�w*tilde{M��xz�F�&Y�� Ne1C���0^28iu"M( Rp.����"�Bo�F�*�u�. ŗ�5)>��/�9� �?3&�� >� 57(�qFH-H6PRx *G�b)2*����A��\]2��E�VB�:�F!Jd� 6SM!6:�2� ( 1#jr+m5�Bj��i�7[69:$���jZ#q!�o*�>m #�a�:�:�2�-�� K&�c|\log\ep�!)G��A�����\!c"�J4Q M� s"�7fis�.ed�$��j "�K��$�4��AY���o$."KB:[5�% �j< g(�`>d ) -M�Cbi�E.��&(6E�!�2� !F�D6[amr0 e( 1AO�� �B�\��� UX|�\H�R0)}:��  :�@"ByV�&Y ./6h&69 }3TT� 2�E�6[ &-�p*=,A�*L=Fr5,\��0,>MFPe {9~]N�l\ 0^ �aI0N�!![F�B��[0A�.�& \�&*�Y�BlY���0}*����� Big]>|:0>�.6�/d LQQ �a�O=n�c J$a$V_0$ �/,'"&3'squ '�ke�ianl!�r�I# #2t['�}ep |p|&| pJ"?$�!:1 a�%�expone�%ly�*ter�,�:�atm� TT})�es X \muj .��\\ [6����Z{. �wF~6͇>�0) }=g�)!��{"_mJ�� i�!2��� �XXBbM R >S���d Iou>�;oVT�ELE�p��;.� ��,6��n1=�$�xA�2G�*4 -x� j!�m}%~�##J� >�^c }�J~16o(;our�� liciy� ��Gi�?alMi"�&f#*� (x��^{�h=x,�u_0 x.*} itEbe �fi0atf�=�5���/ b��5��U/N�5b�� 6�"V�%%ԡ'��z�!�T*�"&L F��mA(V_0-w_0�7 ��q�F_0A:-m�U8<{ T�F686 Im}T�:��B 94.�|-elnj� �2P�"2��"�E40(X, V) =| h(XB� (VV��A� Q�&toFG` ThM^*E5"� Pp� �{E�@<>�RR�G bw ( 3O6�kime�%eg�onOm)�+"�l�2 $!n9�Jf$�i�Qw�-!+��ߊ X.�p�4�+b.� $$ :��-~��%-X�&!�9�")\k$$���.m!�eT4 $BJet؈control�Nby6Z3�8�� at��BD�+0} ���Ne�d0�scatte�3 T-matrix *-�!rm{ }}$&�+t). ɀ!�:u#.?��^2�.!8j) ~KI�i,G!uG.O}"|�6�n_%��j^��!�2�e�M !�\�=(U,V): =A� |P2 �UaV _,H%��Z!{opt_H �Ct�-F��5�(V,V) =�,� �A� 1�XU�r�>� �bonclud :1��GF3Dsi_{T/�)^���;A��K�;�G!J.} a�V�}� *E}':�I�Z��qhG+Kv�hR�K0M6  $k)_G&.9�!��i�vm3�� vZ�HW0. $\;\;\Box$ ��"�� *{AcUK ledg�s� work�[�Jexjo�` proj�a�$ H.-T. YauEXm�Ho�/ideas %a�#-bevelop#�gabo��P him U�confer�O \A�announc� �J2� � 6�$thankV."!7�K�advic�:�9� #2� M"�Pb�pazblaP( %\newpag�wHthebibliography}{XX���bibitem{Ai} M. Aizenman: {\sl Loca� aXak� : some el�5��}, Rev. Math. Phys. {\bf 6}, 1163--1182 (1994���M} .�%S. Mol�?ov:V�large�6at�%re� nerg���L����%},�WmunJ� 157}�245-278 �36�} P. AI�son �AbsA#�&�:uiC��cer�d �{omCvs},-+)=%1109!3492-1505{582{BBS} C.�d�^Pini, L. Bunimovich, Y�Oai: O6& dJE�A�LLorentz gas, J. Stat2�032}, 477-501,�86  Chen} T.  RHLength�|�L18��T1N ModelA|S�= DiI}a4Dim�P on 3!?c<inv88 xxx.lanl.gov/��(-ph/0305051X'M��2B�$L^r$%9"�Oa Ran!�Schr\"oa�er�N a LiO�E�3 }, �V�407037�8DGL} D. D\"urr,aG�/teii(J. Lebowitz1a0Asymptotic mo�(�g class�Hei��EQ} &%8� wo d1S(s: Landau m!�.}j#1! 209-230E72�@DK} H. von Dreifu)�(A. Klein: J��m$2u ope�g�~c=}l�Z�aNCo^�4&l13��47�912��P( L. Erd\H o ��S, {�{B�uKYw�, coup�5? !�ae � 6�A}, �. PY Appl���TLIII}, 667- 735, (2000:�2��Equ��s��ng�qىum.%�NA�YiN in D�?�Q)B�ema� �ic7 Contempor�B$s�{�21��137-15�96$FS} J. Fa�hlWd� T. Sp�� r: {�έ�!�2�!��pt&d bi�E�E�:dor .��\yn@88� 151--184Ao:2FMSF�, F!�rtinelli�ScoppolaV��= �,&��9f l.�in �n�n�101�21--46�52zTGa} G. Gallavotti: Ri�,!iory!�!s��Q��݆. Nota c�{T n. 358, Univ. di Roma�76HLW��G. Ho��7��AA.Wilki��E!� N���a Fermi�!J�F�w}, �E��6 E�5!7�"98�9227KP�" Kes�98G. PapanicolaouTm��b�stochas��accele� \B�FR�78W 9-63�80�{ "� Kl} A.��)a;�:�Yzi�Ysbnruc!�UVi7�; B#��},- Res. Lett (1}, 399--40��46" l2} >�Spr�f�pa���heZ� � l�r�7�| 755--77%/962�La�kJ. �114O&�CA�=��,a�Xspace-� �w�RB �259--309!�:(RS} M. R[0A�B� m� Methom-f%�rn  ��phy�� III. S*�� (y. Academic�$ss, 1980. ]9Sp} H�uoh D��U� �Q�� !E� doceY} ,. �%�_ edit�DSN 28.9.2004 %fileZ(5ZLby Yuri V Lvov Septe)g 18, 0\j [10pt]{�m cle} \useaHage{amsA&�,�!6(:23epsfig� \oddkkDmargin -1.5cm \top 00.05in\texthe%_ 8in width 183 2asuC6�feynm�\def \BE@�U�a}} E!sBBEA7narray7 8:CR {\no�h\\j zer {^{(0� ��1{ 20kp {{k^\prime�e {� silo�Xnewcommand{\todo}[1]{\v�P4{5 mm}\par \no8+ nt \){ par{%hsc{REFX$frame}r�r miniC}[c]{0.9=� } \tt #1 % )}By�� J9< START OF PAPER J#%%R:���E2q!(} \title{ W�aTurbulU t} % \author{Yeontaek Choi$^*$,m�.e�0$^\dagger$, S�](y Nazarenko.\\L���,s Institute,\*�erz_�O Warwick, ?`Coventry, CV4-7AL, UK \\ � Dea>%C&p al S�^ ces,�SHsselaer Polytechnic�sDTroy, NY 12180 } Abke%50 \abstract{I� is paperT�[ew rec f��] � +-i�a�� Ybonly�0!ves,>sub E� :� (WT��se WT9� CIa g� alis���-�� phas8�rox��� (RPAl%�c6>�8E to accounlat�"qIUs5pamplitug��EɆ mo�! �j���dc�N� ``�P � nd Ac'' �roach. �ap  a/to systI�@eJe kine� �X���!Jgy&3 from�pPeierls-Brout-Prigogine (PBP)FLm`d-��"�ad ty"� (PDF)�e PBPIwas orig �d��he-!e ��T �NY� �&��.�� four Pcase. "k�!� PDF@xbe� �:valid!pthe2assumpA| s ab#pNEF%�U@M!%us � WT clo�b Fur�;iB6����sde�eedsu�inC�e*, bey��" a�vJ )r UK study�nk!�A�� rm��ncy!}WT,�it1 de�Cb��2�. :�Gwe :�%��o_% da�*O �aA s�,��)�a fluxa�prY�M#�O:9�s. � �c{I�Hion} ImaE�surfa=a�o5�aedDby windyarA streT, s�!JH��cd !V!�enoY(tecaps. Typ'�<%& ~exh* g9 dealy�hEGandE��yRch aim< 1�ir2-�<er$�5�� V�$More broad�WT�M f:�of� �w�A�engagI#=�BFEoa:>s �/ a w(vrX� ŞE(�h4 0al media. Pl�ful exaw� f WT�f�� in ocea�}atmosp�s,BSsm�(nd Bose-Ein�ay��ates~Y0ZLF,Ben,GS,Nef,68,Zakfil,ha�Tman,DNPZ,llnz,davidson$@harovPRL,jansen}.�-�h long!�Tils hist�)Tstg in 1929 ��C pione/p��of�����)d a R( phonin� ids �p�}e�a�1960'E�S�ave vol��v� in %w�9.-?!V5S-#% in pl!�-�s CGS9`,lvovzakh}. F!6�ll, bott��G� Qs�$ik�typIA*�a9aga%�E�,Ns�V y key rolM" 3U� t*~ phenmva,�ularlyéaɯfLA��� �anԍa&M� rmo-}#uct�i�okamak�Thus, WTBA&N ed�analysɮle`9!�% . A-? BO }he � xM�d� b�_�E��Zai+� Fo � M�I- }. B�Bt� ���as� ly `� stoo| ���Z =�Ё�*� ?Z/# thou�z�#% a ``gas''As.��E�cl�V�$rmodyna�,equilibrium.�%w�M� � w!�!,fE�to argu�� �~���m��lFDKolmovU���is`���Bbym�� �#M cas�� ,��ra��!��aB� ``qera8�''ѧue]!+ i�ME a��  pi�!�su��nt\u��Dark_�a�c�X� an�"ct���Otoi| ave-B ��Ps)�=E) -���i�RARY>,l " E-U� (KZ)� E they� ��nucleue&A"7 . Di�KZI)"oAQ�"E�it*x1N6de1�erejV. SuchUA��YK P�e�x ��sit�s,ɳ( umE� stro*�$�}s� a�X effort�pu�[ir�zerA � expe� ntal�*c 4��db[, i��. = WT l(ure��"z Cse �s��hE��> ZLF}MAKgE(book so farC-�(�is <. Wo"APps& 7zA[�.�5� in ne�-�o�ua^=��Zgnnp},�x � ior��LT�0even cosmolog��0Micha_Tkachev H��Ab9f{t�G\���ry*K �<�H��s��0 ytnot�llA>is$aҥ��M �  or7��f ,!w�Q�� Nqu�5on!�of�b i;SI4� lof &� becaA/ � a$3 %]" �-����ly U�"vd�# flucqbm�``burst͗1Ka@v)�Vr�7edict �basedAsa�m���?M� bive'n�Ue�reA�kA�o� ��co�<nt& �rm �4p  on sea `�N}!�collaps� "�(" 0k }�I�C  lems�ili�^ �!�B����!� not �7Br��� tI al �[l] qab2�s" s �V�;,-6znp4!9��appear� lne�� =  si8 aneo�J QdF���aq�&� E��G�XE`l�go����!4Q�f:u�!)�� :�ha�L��teTsA?9�research�Wuntili9i!��Ѭnd� �,��hap��Ke�gg%5shade1b�3um ".&l�[ �y1inv�� on%��by ?A, &C�bp�A9���$�Ş%�!�!�`A!c�3"5%m*����"6 !��R!^��e�of\doJ) l, !��� Zaslavski� Sagdeev �zAl�iz�s,Q�, �<9!�VXA � �h��con�\ �"� ɝ<�Y����& � � (i.e.!�~ >$Hamiltonia��vo�+co|not [)-p�Ale� capill_#wa!�eu, Alfv>Z�na� RossdB,o_�oY 1A�ng !�%v��E�$!G�A�Od !�1R!+the�st�� 5~�. i-�� d�Qs �aa� YŅ�s�obe�KeQVs U��Ui"� t ` is� �WOZ�]ew�P,� p�\nt,usM ꥡ�ri67u�F�):��Wa�g ʞ�of% r� --FM9q��ve�c� ��,�tWTFZdeep IKd grav��E7 aY in6�!���_o�/@*���yb+'oew) (NLS&fb�R� %]�Kb�aly=�y��9�xI?.�*T6�2W��.!v �0e� !J��!+� ��z � bp,zs��a� devo�m �2D�!�!�a��s. 1 ``a|�''��R{`a�� mis�ce�� VNsE�ve zfas�J�. u1Ia�9�:�E%7 $3Հ avergC_ be m�* �X �Ō``forget!''�Oe.��.� too�/ e.g.�O( .2"hib�e �= ob%�� � ��sSo"� %5"�i]&g��*Q ��ar�$p� t$��:�"� 6�� h�  N��B�S��. eit3 m9�fr�hcy cor,����helpsM�i��n-}i<�s /'�h� �}r��I s�-o��6~�\J��+ �i5sOR+R!^2$�>!"jJac)$ �+ E�zt7����, �5%V can� occu��qEy[��a�y"!5q7SWhop�� ?"���bew6%N4�-J A�� X�5�:7��$�@56:�V�� s egMk9K^4-t*� \Ato"�E �o�.��G �(~ X2$.�� N�j~I�-�/e&Vl9i�tainfE�!�'9�s�., ��,i!`EnEY (�$1�5)J4$)�T�  � firm�HGnu ELE��6�q`(akhpush,cln� V�,caŭI4 Y �Ay4 � �m5$��t��F�����-��0k:ch �c�B (or alm� )%t.� O1Caޅ�r�l����y�z^�A "C�&* p+�-P��� m%�� �v!�u�!�nn. Below~p\bW!�/Ztr� jaw"�A�����-\*�v�EI5 6I&� �E�9/"� ���er-i�= P9�_U������)"of&@�sI*I�]Q� a� ``no�aess''/�� g)"�ua�er $�t� �7�ndyf &s:w �� FTem��>PMqone|"W z#�3pces%rͅ�YA&]�, )9A� .X� �hus���)P�'�6f �2#� &� 5��`)� �ISZ TheSЋ} �s I: DFa.�1_,M}�*Q "u ��a].� 4 u�nd�/� ity.��atic �#e��a]� ��� .Pu"�. HL�;���$%6 %q��ng%�s �� iodic boxm�V ,�'@BEA i\dot c_l &=&q)c{�)�m{\!HH}} \bar.}#�label{�D$OfM-p\EEA % �; c_l$�uoft$c!%�Ek#� .č�HEb&E �U� � plankBe2Q���s�� an�8&@k� U�-%5 = _�Y1 _3+ 4*w5�Y+zV0�`�}!)9(H_j%(a����.io��! $j$�s %b � �j CT sum\�5� q_N�$:UY:AKaU $n\2 $Aty�. In�=p���b go�i�@ �o�cA����s �bo=th ��i�v� . U�<)1F�!��0d�c��a.k, ���s���a�F\,�",iaga_ isedM��'y��oZ�n^Fi 2$_n|c_n|^2.8AQu �=q�Rc� :��^U ng (�)Q �#���!�q|2]i,)cubic t,# U�)mW2�� ofegli'k,0E�A�@lu�.,in�= one.82�� h�r-~Af:Ɋ_3=`� )� l,m,.� V^l_{mn�rl�Um c_n\q +n}+c.c.,�=�J%VU\ U^{lUc_rP, �@&v1Y biB�\ � \ll 1��A /uame�%�E�A G� mall&w ity (&�G�%or�?!_7���Cc_5 �g.R+"Zgc�,P1$.) MP q��%�&j]`B 'L#T#��!�::KYW�t� ear�gt)u� vacuumUb qw��z � % $XBHr� _{l+UC $$ %y�2�Qh��� s� a[at�Dd"֛\"� reson�V# �k�_ribj�to�  ?%�~ k.N�"B chor%o�t/|=*�1�9�#.2��%C$1�,3$, $3 1 2�e��40�u$04$oN��the�JI n?1iexGdFF by��ropri�canon #�7A�� ,o"bw�!gN��%!gz�E�%4A{ $"e 4$, &�ly�4.�4��^2��m,n|����K W�h}>Hu��"% l ��$\mu c_\nu.6�� Qu�"=��w�oIt ٝ%�&a�!lyIVZ "� QW!O b��pa'A,�wk jor �7es:A{��s^��>e� o�#�i5U⽅%�llR releՙU�Z54$ � negle�!=�em��tNzAycdb�tisfiedY8T { H}��"��M�6��'5�Q� �C-�K��^�� �shuU-}. i?;��m�purpos�/�pR� -$ ei�) � �o�A�an3$*a���AO��o,�@2� . E*�.=~)� i"�J�����c*6 ves, X� wV �,�.:��> pl�8"3 ���jTANLS1laBu7 RV>O/EmenO/.�ireS,�*!2B'd rese 1�h�'Z�"1 o�/e���#L .��a�F' ! �Oo��e {\em>q}�&����/�+, \BE  jo��s?wk^3"EEa�*"� = {1�Y 8 �Q\92 ;}q omeg�r�\ mkn)G` �Z�0[ {L_{k_m, k_ �( k_m4k_l } - .l, -k�/l3/nF/2^/^ m } �],�f % 2���Ak}_bz��;fnۂ��G!�$) � !�Q�te�  c9�>�.}-�(zakpit,bnaz!�6�; ta k_{jx}-1���2 k�O6V�-{i��ta :4!��Qlx}m nx}C�1/[A.� ( {1v�%�2�l^2} - $mJ$ gm& - JnJ&!c$)�NnEE)� $\b�Q!p��aTa�Coriolwa� )�rho1� -zd�� radiuay� s�hst 2�*� m�i��p��1�ZMR85f3!�=�0=|k_j|^2, \hs�A{1cm} *l m = 1.Ec�@ eQY2�}� �+nex�L�g ��yrR�gk}\!9�RM/��&/ not!W�'� &]����op-����0krasitski}. �l=� bsT����}�@�b����6-$�G*� �&� �?��j.�� u +B�m_F� �( �{�Z m ."cA I �a�K$&N|:alB VLe �l-*��*�! #��� ,x  i)S? a_lAu"Z�6.-Ր,a_{m} a_{n}e*��pO ^l ti6E��. %sA&& T.uk3cm} + 2%q{V}UU_.%�lrm}�X-i t^!� n}t .t+n} q���I&w!} s��me =c_j\iQ5j t)va�c Sx�K "�-q =q:�! , $}�T)� Z}^dEZ es b�7!Á�_,�"T�4�2� m/L KL EI�� lV:�S�n}\3v)8��l}- m6 �@_l=)l9�6dF͋. y, $U8��aa�"� .��M�-A�r�e�"�al�"D ity��ws��*G�� Co")B� �o>� e �=�s, �$ a'-R~�xh"�9Osborne�9�.$, Langmuir�� q8AGSI1!��")ed9 AC5 2�'� M/��6� >)iv�f(Q",1��n"�s) asaV\5��= 6�4 =�� Q �FCRf 2" A%�*� ��!`��� vep�m �1a��,!o�.<>�� =b_l��-���W$"(>��b�Dl}���:=55-b\alpha\- {� &D}�hb_  mu nu ��^{B9t3GlSeB1aa&>��B}ZI�"w �} �~ �D A�fE���F���ɴl+ -$��~�!� $. % % U�a~&� �de $l� @X&�d iv���� HM|!PL beha�((��7v8?W:bae�2.?$o��?ur��vC��a self2*s�% l�er����"���2�(�gf� ) as!- ^�Rt)펦aQ�a�a�M�tilde)�J�n�t\OEl�,~�Af� �a�a: W ;\;$��kJ�]b� +T )=- \mu nu*�nS � ϕ'�& \mu � A�_{  A^2"�F�*RQ#���2e�A��}Y:shift �,��!E�.Laf�J > " #J�"I: �Oi�Hsetup�� F �5* � y�to����"to�H� sh�(F��$�%%F��,�$'�!d �HF- B�al��  "� P*EDis@ion Fu��. �4 Z�uS&l D8 $a�x}, t)$��n,ic��j$ � $L�  l����<�"���%�� b� l(\� LMx $i in }2� �=!���dPth%N$ = 2  l /L�bA�griy r!F<i7pl�gy�u��sumT��h�$�maximum:�{max}$ (@�x �cissip� ) #nojs%DGs=erѕn)3mvalue1ex)d� '��/�� -�� ; $N�k �-�pi L)^d$zQ*Zo4%� $lL� 6@��/ �z H�nit�x,!�!�S B}_N�� bseto Z[ � �+XM6 t 0�maxAM� 'a���� $:� = N=3J��oM� homoJC�ju_N% �8� L$!� ! ��j�(Q" \{s,' \} f ��*pdfL"� -�6$ ��\}$~��&$#f$*je%A�$'�9aJ'�!~�\{+,m�;> \�9�lIj ��$\{E� cC>Umetc�;/ollA;��]"ai͑B'�aa *SO &�.aT�J��i��e $x$-��� �8�H�+Z?-��Z�#)�P!�B�%�_kAHi��*_{.�}�3N�,�i% �<|B&.�q<cy �!inu� � s0�$,a/k��ek$.�@��4|�"  a path% g;KUo_�E�)mOA�nN = !�;aBD}si" |)AD}A�|2.  a�y]mean-�[ %�[�z��d�0v�^vol�3ll����(��ei� ��e $N$ o&7!"Nw ). B�Aynng YtU9rg�Zs� ep��$sen few,x"Ec��re�P]� d* ɴ,w �"�)y�9 z %�� �O��ut $M.�-,�nan ``$M<�:# ;U!?-�.�M��j_1, j_� *- M�,left( \prod_\{ l \ne j_1, j_2, \dots  �M } \int_{{\cal R}^{+} } ds_l \prod_{ m {02 B}_N } \oi6pS}^{1} } |d \xi_m| \; \right) ;0P}^{(N)} \{s,&�F \}, \EE % which depends only on the $M$ amplitudes marked by labels $jR� t �\$. \subsection{Defini � of an ideal RPA field} Following �approach/X\cite{ln,cln}, we now dS`e a ``Random Phase and Am �'' (RPA) fH.\footnote{ We keep�dsame acronym as in related] ]A� xima�'' but��interpret it differently because (i)� emphasisey5i r� ness� (ii)Y!"is a �$d property!!)%?8 to be examinedCnot!i%Ix �4.} We say that@$a$gof qtype if�posse -5�statistiA� ��ies: \begin{enumerate} \item All�s $A_l$ !�their !de factors $\psi_l $ are inI�ent-(< variables, i.e. Eja# PDF�equal! the aVuct15one-mode,0's correspondEo eAz(individual 9���, $$ i�Ni = q�l2L} P^{(a)}_l (s_{l}) � \xi  $$ %-?The x>$%#H uniformly distribuA�m�0unit circle ii�0complex plane-D for any %$l}$$Z�$ = 1/2\pi.$ \end.�% NotA�atE� doesE�fixcshape1�9^PD!�Land, therefore, can �/xwith strongly non-Gaussian wavee s. Suc(udy of2(ity_i�mittenceK0WT was presen!<in 2x7 will�be repe�#�$. However��(s�\some new objects describAjuEs1 E[. In6�%F�{\e��sumed}A� hold overA��$linear tim�I phys2h�N@p��T�7 ]a�$teriori}, e_basedQOevolu=ac A:��multi-pu� obta��%� RPA �al��s. Below�%3-A: is work. ��seMRfails5(in its pure�!" au��above��$it survive���leae�order so�WT closUbuilt us!��&$is valid. � also���cU�=%�u�is quiteA�a��$forward, wAZa�zy$�ce=$be conveni�  + mean valu��sA�b�f��. rateo� @no� frequ� YK> �. T��on� uld �.0ye+``.�&R 4from $-\pi$ to!)$i$''. More���m�fluctu�y �&� %�s(gr�a theyHckly spread beyondir 9  $��$-wid��terval6�L But perhaps even moQ),�Ey�d mut- %@l�s > 9iT �0a� A� rema� &e . Le. giv�simpl�0ple illustratI how � FyAvible due!t!J��t �s� e between � !O@�!� a bi| ion �$N$A�a v �ge� $d let $r_1i $r_2, two.C (ofGnof1ok)UnumbersI�MN6 �E\K $Af . Let % $eo_{1,2��%� N + r .$� Then .langle a� "\r= ="N ,DandB! C} 2I4\pi^2'N d�u��$$ l CBK -F"�:~ = 4�� ^2 ($�SNL^2) > 0��a���at�-A4hi_)� )z2]qed. OG )� h�)we�roduce%I�)� �S{i� ,2}})t then ,5�s 4-S=0 *J�*} f5 =0)�A:5 $B,-=� M)� ::^ �� bEs.Esi1Eb3 .���v�-� is cl�!�� b n.[�Fies u`Aae`!�s rises��Pfact ^fun� *(:)$&�hav!�verse!�,��sŀ�inၥF about�) con i]h��l� o$. Summ� ing,�6!�"(��c�á�p�wto �thahz�  of%=�*�"5�E�$�Qis9A ,��%I��smWiH��obs��bl%?�~res�.g�]��4be ``tracked''!>[z siQion�ntinuous��?!�mak�k jump4�qw�:!�� �exceed��K!� [$k$2' hi(k� an achie�� larg�g�� �Ais��!���&(�v rokon*���-� kind!�U��oafa� &�ng��s �i�i 0mechanism behOde-��|I# %)U~a*�����SS .DW"�)long spaY��A . �P 6 Ofte%�WTa�ud!Z[ A�ric-to%� �-|decayA} �� d b(Ben}. For s� F,Eu��Fourier� (�EIbeh . Indeed,�BAd.�length!�mrsmaller���sizE�8box�isq�eMo m:Ibox�Ve &�J�A�e�trans�B" bigx��*� sumM�FC*I2�M�!�5bB�quanti�K�� e, b=8e Central Limit� orem%) big-boxF� has a5�&�  C��}��1��re ��!�= o �.S �mE'� . N�!��_ +Aaccoun at � (nonzero pow�f $E�$ � Z  aft� e �g�on �=�,�an"I LHS=RHS�"`��'C . NU F easily reA�enR:n ter.  �U�alLB%)a�&_'�R~ \!31$L}_�� ^{-1APMki�n V�\} �$r^�>/V )���/%%pdf����b�$�"'(�!i�%�Laplace &� ESK%ect�am ��%�� a���� ���q�� ��%ce�&� w|��� $Z$��r�($�f�in( cX(�"��$P$ �  fp�( MellAQr"�fe V��$'�Wei4�"b#hR$E�,eLnT �-��indb)�Zm��e�!�all� -e�er�. �M�lCa�m��)�y- ���%R� aW. � #be �. E�[�zU�)e��liewed�aAXul�� the Bg�@a�al !�"� |� checkF�2�  �1�t1 ��_%� B �*,AH0$�!��( $")B��^ � lyA��Di8��A�]B�'E-�Z�ch�%� &�)w� R� Z�f! = {!&� ���(e),���z-rpa} *� � bf=\Pjx R�  = [)9-��� \}|_��=0�;�n��$J2!RET&N5�s. HeRAt KronA�$r symbol $2 $ en�&A{Q "- ��rJ�mv" � Aa�f� stepA��&�E,A��e`,w���.tov�o J�al �peELi�)�) "1/N� �#.�&s ,!"] �(�iptI�fat $t=0?2pO�+9t����� ��em";, dens��� 2� T/)� a>Y Nd $$ Z(t,Mz)U�Y� |a_k|^"��re �n* ���v. �n� i��� �$s=`$!Y� ${\bf k}$桘wr<+��B,".q!}F,a)}(s,t)& q�I� ( � -s)� = "�%�l i10}^{\i�Z(-* , t)e^{-s\mbda}d .�|-iont�,��Av!��*momentE�9�wee�narradM_k^{(p�<��� �{2p� �� |a|2�=��w�=0}=\non[ \\Z_�� \cc2 (��3 = t_28s^p%(mxdsB�y momPDF}, %�~pS � Ni�1cript]�means&-i\B Y�$p$e�s. ���I�s�%� , $n_k = )p1)}$, !� .a�,trum. Higher5�$ 8 p)}$��Z&&M q.L$k$-sp� .Fs��� ��lMIna��N�r.m.s. + l�0l"?$%o \sigma�\sqrt{ �,2)} - n_k^2}�& ��� \�3Se�;a.�$imescales:��l�3�S� W�!�yn��_�'.eak !Z< p�.ds, d3� /$ dynamics,��.n $ charac /�2E��8� �vA�d�xFge ugym� $�.��2�re� �� ag%f s9~� =goal Zb�*0/ e slowly �� ! ��!&t�e fast1oscilP. To fil�D(.!*�0 eek �� so"0-ime $T$� ��& / \omega�-T \tau_{nlH��!�!�N��1)� e"�%�,���^ �,is $ \sim 1/� epsilon^2nthree-)Lystem� ; F;4; four2:. S= $t=T�Tsought!3sere�"� 65a�� $�$�a_l(T)=a5(0)}+" 1^2 2)�Hl��E|�� Ta�wee.goA^to ite�)!'�H!�mo�3�In&��})� ��E�OfM7A}) too $ �0�� �� a 2��by ������!�i � termed�U��F7�o9.F %�Y�Io[s,_2d.7( 6assocud % D� *�!shiftti�nee� n� �? to %neglo/ Dur%�analys�!cer�$� gral�a t�7 3&f(� c \l�s_0^t g\exp(iq�t)$z(��(play a crucsro�2Fo�9�� A@i�e �� A \DNl_{mn}={ _0^T� ii� Dt}d t = \frac{({e^:! T}-1})}{{� 9}}, *3 r {kl}fujx$F{F~i`Newells�ec$�'E(x,y)9 )$ (x-y� i y t} !.%�8b�&�  a �E�asymptot3��&�s, s�4�1���%�b��:E4A) its_{T\to� 4E(0,x)= T (\pi� (x)+iP()�1}{x}))&�(2*iRM|1)|^2=u8 TS)&�WuV#I��:.�� .} % S6+z(pa0��� )���6�w/f1e�zerothi�%&�b0)}��(0)M ��ofa} )�&�.J���%�i"�*�s-! �� �rM��y"� ��a_2s��A(sV0�?��6P< �$Lic!7"e $a^ł_�=! $, u� \� �*kisren� $T=0$ �<s � argu '�� io�<exp�ly.�@� S� 2��T ��[ � 1)}_k (0)\ 2� .8is �n by %� A �9 l (T�-i �m,n=1}^i" � V�� a_m a_nm� ! +n}\� .\CR@8.\hskip 4cm + 2� {V}^m_z a_m� {a}VbariH iB +��Z&z�1I��=E���SBSPer�Aasecond��,!�!���te� E�"� calmo<5 Ee,M��m i�A{ aA2k="�:� Big[=�-+��+n}Ş� n} t}%� (a_mI�!�^{A + 1)0)-�) \CR \hX{3cm}+2!�9� z!� zEP7 B|gD!� ��0�baI �-��]IV S%F-�TimeD!v�? EEA �,ce�22�+to nOd��)�i�9�%)� 2)}eZ &=&yZ�, \nu>d[ 2ud )� -V!>}nu}ava�#�#E[-b l_{n�X}, mn}]�#� mu +$ -2 !e V^�{mb g mLnu} s>oM T n-��Q� !� &&�i . + �AOn9g:�� ��n}�,-- Sb��6:i F% E[Y�nm l6o n}] � 'm- ))� + n}1 aw��V^n�I2 nuo -)���d&mu6�ȥ�1�Bi>�Avl!�nu m}, 12gn}21n �-ML)��],�VF"� \nowntw d�D�Q�,�)�&(drop super-!�V�! *� lik*E "24})[ brev� ��(�� �� }��1 vR� n�v� ���� 2} $��� � `i(!f �n��"&b�E"�a_l\one� �g(\mu�v W^{l AS A� AyB))Q�N5� ^{l 8Q+~O�_l! T. s.@1"�[ % % ɑ!��9m�8w�tB�� two(T)&=&� � � v u�� W�&! _ % u)��v\bet��R+.0!< N��v!KI�#a�V}%g 0nu} E(\tilde�Z{l ��v E}, :)$ �) �.a�1 \\ &&�. - 2!�) v`-�A M j�bN-�:2m+ 2�u!���!{�a_��] Q]Z �*�)� )�� -Qk� {T^2}{2}= \\ &&+ >��E� qM! KE*B*5!J: 1�Z�9�,0) -%�: zF{{i R} vm9|( � ! -2nuAB int �0^T�� '� [%���} ��M�).z F[N��q?�A"� �R�� ��=���an*� -V��F� R� $Z"0+� Y)�oi��B*= ��n?+�?os. *M���\o�2��XN$ �$he&!o�H�&8bG� a/*fu�.} To doiKh &� �$Ah�6�; via w"�(�itj(T)$ !�>��"�"�n=! ``ingredi�t8�L,�a \e_j |a_j��;6,\zer +\e a_j� +�Dtwo5 = &�_j x08 2}} ( 1=�J_{1j}}� e^2  2j}}&�i�6#!�%A �*j^�J _j}=� ��:��^2 two}{�M�(� �2��^{ c� j�y}=��$j�  ( �� �-({ � �( �1�A9%&#1�(�one���one� zer)5\F%J_ |N {(Q + ^2,2!�2}A N|^2#G@^�two�+-4�ɳC!n.C)f (? ��^2�+\ 1C1H)z{2Qo2}}cOG- 6#Y%�! �mAbFYtwoL�zeY!�� D4�[�M�  2}-1Mf>� one}Q�U�2 +.(F+NF��K�P ~]-�^2]}{4=]��2t"�s��Et� E�Sthe*5  $Z$h �Ci� :$ , T\�, X6<,+ ISX&�',NAm R#"zx  %�!ar NO=Ff0\�� "�I2N}�<&Q\|l\|_A �I4)�"wxt ��+�A OA�� ef�l�)le�A$l8�-j y� 6�)� �)A�>jI+>[6""3j1}aG� �&�$6 ��+!� mbda�6E� �6�}:�)on�� Z��\ J_3 �eG-�R��j 92���!T� x �)3�ev�f^�3-54��-��D[ �6\6�4���bz9O N�-W]�_ioA'��^�4 �5 ��{j�Xk}� k���� +.�a_k k� �u�1��9?2})-pmu_k}{ '?a�(JW �nq "!#!+:R^45a��ww3e�$'-�>_A� $R�$�)ot�JF:#"�I"B "K s (wkY�2 be d�EWCe3=).*�0so far�# ��.$Z� ��X *�"� 6��/3�(to ": �re�5sX$a!oNIaa�$N#*�$m6��:�� �. ��.�}), >� :1f":1 T%�2ively��B2�B�?{Ev�#of.e%m r:2$�"'"'%%[� �"�[�#5�Rv���con=8E.iaV� k(0@P0�$ {H�0%h�@�"aYWfi � ."P3pc J�&.P6���"��&`&�$s,�a+a�t4%a�WXQ~-. 1�8J a grapht@ classi"aU �� v.�#a�! u��<�1�al��aNH"�-X%s%^domina[ ^"%5��W"O-MI $J_CK  2�5w9Y.�}%�9(c method. C��� �mE �,`3$4��5$, �2�K�\(me principl����foupn �+-P �b, ,/6�Ie$ {%#"B!e ; ���, upon�/��S���becom�BM J_1 �Ũ &V �9^=� {j,m,n}.U �^T n 2})�(V�$^j\ � �_{�^j { V_{jn}^� >  <<j+,� )$ K � .� <  ineps� �"& +[yn�eEaI�e: ofݎ�I�/e'�+(7Gy)�-QBe�"E�I>�E mbin!#$1J�16g7�1m")a a vertex �6��EJs �' in-cab g $jE� ou�Cm.$m $n$ dir�p�Com�]conjug� $!r!�mn!�1�)� �uraw�u��: ��`� opposite ��)�2�P*]�4$a_ � ����&dic)] by dashed- f1�awD(%��Z� � M:��~&��>"_A�&vi�-aOA :A�[�not�!N te m"Z�M�%Q-]of��m��8d.}MT,����� �"ula�]�) �pschi.�<�8Iv=Q�4figure}[!htb] c�^r}$tabular}{c:} \ \v $1cm�mP C_1= \parbox{40mm} {; fmffile}{��,�mfe�$*}(110,62) \fmf��{i1,i21�{o�<\&�$m$}{iFn@ .j$}2E{E>,s_arrow}{v1,.LJS~: o1,v ��`��21$ } &\quad e  & C_2�?two%�?�?�?i2)$�?"x+D]�%�� e�%#eZ*# I �(orej��set $\{� �B �O K�Rtak,9t.�'*1al6�_�}G; dis�E��O�;o$�1&�E|D�CE:=0$, �4��m!u>$ bar H)��4^m_l$. Further�@uSbU1�� odd"Qb�A�RsZ re alwaysV*,~amDO!P&X&e&ClA ose, s3a h=� l g= )hn� z�.�4f" musti cel p8�w:J`osXi�<Y C�` matc�UQ`pairw_g�Ssimilar�ie �J���M�"?c�*th%�*ard1,�?d6%OU+er5 ists�Xil&�"/ �&r;(�e��{ !r sum) �ing�Yt?0ext 6on05;qpre-f+g $\P\VE* $. Obvio S�?K,;U��L� pT�-d,ed%| A}c�Ll eiA�~�&DZupl��in!l� o 0*7� c/-�o � $l$-M��:r<� �Aih&{ e �6t  loopA er�Z!�1u EM�BSbe show� a.� pinl�L blob�endIVs!of!T .J� f~Pe�q]val�Z}@� ��]&�B!�A�l� no�-5���Q�=4W � a�a*� 8a�6> �j"O8�>$-�>,�#� e.)�20)��Eas�+e�m0: &� IS/��@pTd�"�o��sTly homo�ousq turbu%M�@��V1�A�<um!T�V��{rQM naQI�Q�ef� $k=0:\ca|Wsuch Q�=Dvio�6g�WgEEsR��7)G /5�%�b5A�rix ele/ $V67��to�� ma2)j4� ly(�ah/*a�-b�G VA!� =r27H $ V^{k=0}_{k_1 k_2� =0  = =0} �Z}�w$V�/�5qeŐ5?�=L&�s C_1H>�}�= C_22,$+ thfD�4z9 � �� �� �� Y v;  do� } S%fm� �_ +] & %>e� � {[} %] �(&� (� � � 4 �7 8force{0.5w,0.5hW Zl6� 5.� K M:i vi � !p@� %s  %}�� �r�"q ef)�.!8N�-�� ��-Z� 2� -�/2, �=.4, tea5=.3!p%"�:3�:4 5�26 ��%!!E���:� �f�E6n�Efh1!�b�1/!S��N�@5u�DRD>C9Jen {six�� .�Je2 EemI2�2i�W�K2�,^25�22e.�a. ���� *F(:2�� &�8Ot �k e"L�6>aM ��:� 8�m�q3e �$� A_m A_nw'~7V#��J m +1y3n." j-1)�� (R ne j� & 8 l) 5? "&+&=!{m&�{2m} *�}`% ��m}^�^2 A�  ~m +��AJ�m,� (�\# hahaa�t�`#�5�F&=& 2�� ��'�� =�2� �_� �12�n � �"���]�n.�n%�n%��nn!�n}%�n^2�"2�{,F�2B�n,* �1�"�!�2�B� v e�:� s�vol�\GP$'s, {+|�' e@c&LsT�&� tQ$R $Z\R �Q> e1 9�s.8 �V�"��<�tple, a &��P��i3! 1}) mayX"Cif j�'��se�H�o"w 1�Ka��m(0. �k��f��� sum FL_!\�dha�Fof �H�Rnwy)� �R�to!<�Hc, �ut�Z6�j both�55G�(2})=%�5H�ultan��=I,�o.G"�x�4of ~���Roves sum��n�4dezxd,K^ce .j*T%�^=A�Igdiagram�.!�s �kWlI]��? ��teVL&�F O(1)A�"A�4cX/&\vaG �F�at %�"� >�  }qN^iK. AlthpFJ� �a�!- W$c.$!6y � mJR�DII�31$N"RD $.�\$���Ha�?b�yL�\0$�."�ni�/ ^2$-� 2$�R�<�fM�6� I�j2�$TN��)u1�.����l�2;* ����,\kappa,�3("<'.F.�B�)})�: &&0>1cmm3�K "�a_ma_n�:�$@ 5b"@ �(�:) ("�w ��^jV4�s4nu Ѹ ^"y  +  +2|  BN ]gXa8_{:,�7�$C)q_,})D==)BS, BO,�) B_3"% :,�T� U( \\� @="�?!�"| 35V]n7� &� W (60,45)� f� (0.w,1.h)7� 0 � 12�  2o62 0.25�) � 50.7>85�v3�] �  > .� ���� .)�:�nu�fmJ� .jF� .q: fZo2, tot{, �=�2) �% & A[�,8%Z�,�,�,�,�,�,�,v2,A��,E,A E03�09�0�0�0�0�0�0�a�F�v\�0.0`! Ŕ\!2��90 �h�%gb  eEcoeffici�8C� � "�. 1�� sb)a �*/p�A�6-IHdot�$[J �!x�  �, "ii[*k �R;' �&t�#no2��&T e*~< &p. X R�p*,Qu"&Q">�^(-9�g!%� "�"�� �5{o�&�6�$^� Ww�B_:9y5. ��10f/50)�'�{�5"���������������!��  � $   z��F&�Y�F�706Y fish:s V �"� � � � � .5� 0.23�!6 �E�t �� :M 9 �LJj21.\  $� 1� Rb�b6�{J� 2OI$}��1A�3 :%��:�Q �)b�5�� � M "� !1�M')�!,2�� %b^"< F0JA�6^cN4!�V%Ii%E � "��* +2՞.5��GYb.�Šth�G�U=1y� �9 �N���.7y�=KR�1�.4-�g,R1B_1� � 2�9`2�!. reuse{x}}�.�`2\neq mnI� nuζ��0*V_�N^j�!wu%��0 "�jA_mA_nA]} nu.�G\\ &&�kmQ2.2A�BI�3 U�m+1!Mn6 w#4�H-�!0 m,n.�0l)B3\!���@9��,%�B�.�.�{2"c ^2^.m� 5�  �3 �H6� � \\ %�T 5cm &&\� 1�A 6O)�� 9�A2��nu}-2) F�SEc%�V��5>�b���} =m-7 amkyR{j=�j)� %*)�} ) |�8j}|^2 -Y�  �1�j!EA\Nd��E�e*2BWg'7RUten,� third wn I��) iM(j�-ai:�4�Von�z-��a-0 ��p�Y CJ��*hS42h��F��due8� �)s(compn�,$B).2�{ A�!F �!C-�c:�s|�lynmv*i�>7*$O��)�)6�y"� 1V����/�+"�#D �F 5}u/5_-�,t��/m:��oϓr�6�"K%*�\��i_lI��]�]B][1+O(1/x]! �rA$preA,dAOu"�;<=dalu:%g5!A �8 6I: �J!�gC<g8minimal�M.,U�d1Q� �. redu_tG5�&vAdoa�p�:\(38g in "�2�!��,�a��� " 3�F3r[���9 scTta6n"nR��v3�Fi*�. uas2�6a9Wit%�aind3I�ce-.M=hav�n %% %2b�a 92&}� +#�@�h>< � B�& n19pZ�>�ů># �> �> V> }F= "� �E�F�& .�2�&& %YL =jlYu��z��${m� �������m���x2�" b3 ��2I��EgJ_2W�����>[6��&��� {j} + 2 8=�% \0,]'A�..)]�KTŔ�lo�B�d ��&�i�m�$edB$J_ondBE@�78o:A� ����me ��F �� they�%�V�����7f4ism1oqu�B!h Wg�B���#�>�X�'K. ~3�Ft�5ow8��afy .�F�=iscarL�?g�*�"e�͈"�#��ceF�A# $J_3$� $J_5"i)`:�A��Bwe�$!4� rPk,?�J= 9�a�6,.�!}�m) %+q�A ?q�*���@�C)��4$ J_4 = �$ �g(�$$JcCis�$N!k F:�eor�C3$)%�5�5=�qF��*|k,nT#)�%#k�L`_!kR!E�(k�(j�&! %+2!w6s2%dk2! )e k}^n.aj+/!1_R.�TkA�o \;\;=i�~ Uτ our�%ult�B& - E�i}fxt})F� zx})A�G��J - Z/G�"e^PL�zd {�@z\ �K{YT-~!yA�W9 1������^2�^� %pz� ��n�X\�+ 4!#Qu%"}�ɵ���bMn}}M_8EA>�9v �(�^m}} -��!�*)Q� `EK^ij}*�5S2 .T�������Yt3% f J0�IB�ki�; +cc"o-�EreteZ"� �;d"re�F*?>� � l$ appea�m)of�Z|�+ ors.��% 7E&��z�y�y4)�Mq/6'�s.*�<wZA�<��%us�Dny�nump�:�J�.�As�G$A.�:'*=*22pIT�q�q �,*]i $ (w,-BaA2-� � �*�s_<ial). T&��2,j�AV�la�&�l �N�l$wAfI� (xN�l�- , rev��$(��a� )/T$� $�h ���}A  I ie� !0t \big\{&�TB� { ӑ-�E��Z" *(. {j}s1 Z� :<�1{m<�{�� ��(m�:��#:� J!2~>��>� �Z6F  �5.�B � �� ��� R$�);6 4ZZ�V� |j m �&� %$�� c-�RK�')�&mB�  B3'�`: 3j� DYơ� ��!Gi}\, dk_jmn��Zt6�var�z(��ȵ�insteaItN�B�N"Zq� ��N0W���e*w� 1M3�P"��L�2��z|%�_�Q8 ���V $"M6, $ w�be� rv�� ime.ŋ�u turn,�A&H>U hƀ�-���1o�at3.}S��?&\U ���aI�k� �t))��G�GBD� $S^1*Ctru�& �uracyh� )$ (Y���" $N$-�g�kt�0�, 2  ��x��0 Ũproves�&sis��c� ?��`&֥��''9per�s. SG; ult A*�bR H>�TF�?'solidGt' ysics was!�dF�b�Br�� $Prigogine cQbp})� �!�B����0C�b؟"E�W Z.X�% "�R �*�(EB AT6>w�  b"r�!Na�r��D�(5i����in fut�!Z�FD���I��G ;�Cd&�(s�2��U �f�Um5i"�T}�fefe�d+ � � �.ǗT7�+"�8� �32�S PDF,��{�P�(-���  F}_j6�s_j} ��"'peierls���^@*$ ^C$A�a�xa ��a�Iq��*+s_j$,�-{Q �*y ��! int �  (:bɑ���z@ �;n}�f< &| j�K�� ) s_n s_m:OP} � ��>, �# � P} (�ʃ&Q[�� )sj6� +2)KҌ2ޅ5I"� 52� s_m�;v Q�:Ufluq+Q=� %}A�"�G+A�Lorigin��/ by PI�~Q��I8�fsc e1r�Q��ex���8WWzan�� crystalsei�9= {16ˣ�� }i��xh � :l}� ]_3�` (s_j!� A�:<6�.;9�d ) �V )�>`QEE�%,c[��=u�:����� U�!�m.�} -Z__nd�(M �&,EE ZaslavskiESagdeev�}zs}5�Aj�Aw������WTQ .&�=&�~� �,bp,zs}T riV��:"�J HamiltoniW��``potea� �gyܮ,&J{MO� � X=_coo�at�� VmoDKa&��J � es a�\�n� �"c�!�Js, ��Scapa�r��ossby t�!%}MHDDK s. O"9v�>1uߑ � also�1�md�g!�!93� �.��5�V w-�1}i2�=looks�Yw�#$more elega�symme!=!�� SR�� ). H��, �6oB/�� advantage": � R��inuity5)[. P0=zrly�ady� ńs�N�Wim�l���zit oncAl�~���4(F}\{s(k_l)\�hyW curl}_s A�i�e�{m}�&e� A 9n96�(k_m)�E�:�\%M�%��$A�(n arbitrary*ܔA$sǤan��5A���=�ensor�A -= 1 & � k_mn�\; #! cyclic� mu�4� } 9 \; l�,&N,oo-2p�%� zsE| jI0�if >=:,�= k �%��\;#.�!oAΨ"�wo�@.C !� $F"�2�solenoid aA�!*�"| -�. On�UeT atm4U)� ���3� e"{@n $s$-&� . S�Ca7��w�y�O�6�B��!�RcoM� uZtZ��* sр�sa&{�A������*wP �5\ X�h��ag@&����&c�%)-�T@2�@��$\�@�'. P'� �'>�fr4�cy�onZU!�,broad enough�� gA �`[R�U�autho���_NQ, lea�UR_�8�U X*���%-gi�EFB^ o%z 7bA�r,!�WS�p0]����%iRe RHS!nilSC��MxI�$ a��]yono�Ect9W[!t �A�uύ)M (�8�!]:[����)ATree�nite-Y� p-��R1C�Eond߃>+S";���C S,yV����!ool$h��YGE:e�'is su�9D xc0reEmԃ"�9s. l"$�֍��l}':iI�� "hW�!�V�R�alʲ!�@��.��u�u &�uj�gfo:��}�jj ��!r�a�g�)"$�:#��e���og/ PBP q�.+�E6i��P�Za�spiri!� th�[�"�$!�o:v;,�`w�Z9v��m}��9jf|�.� �slg� ly m f d*2-]� renoa�isE_ �itL&T$ly �$v�by7!"��M�(��s�<�Yon�< "�a�)a �I"w�t�%�aq3 �%e��Yf^a@ult�d[� ��$)^ � ]@�h��lb�"�%m%���*")c of lF��*��&.�Hc T+uag � dmean e��HJ.�>|%.�l�% ���Dx��w>�=��mr%-E �5��w���%s�OA�$m���� w��6�!i&'c����'toU{e $�start)�@G#-E#!�s�Gj1}),� �G 34 53 ��a�pű\mu�Y��tx ututa'toz8>*kKBm0 Bm( zF��hX W 2�l1}). �X��N �io����29>b:�],:Jo�r��n,= 2Oj1�jw"�{��>'�x  a`| 3�ɂ.w-2^FQ  4 ^{j >l.L�j�?|�y"�G?- T�\\ =- 2��!% V�~� yI.�g� T +AOȀ�y2 T"E4!T�(,S&�� ��L�]T��$ �x�T$.}3"� our choi&� &:U�MFj R�tz�t}) m&cAY���(NV.kF.$�a�� � �*h� in������ �. Als�\is �=ޅ*G�� p��$tL�LaG, . � t̠e� �e�thm�$T<V�1 ��th }I� >0s) )�6;�En=�W^{jj }_ AG6 T|)M4 -4 A@ ^2 -�*A�I�(G&� A�U�D T )^2\to 0 {\rm \&\;� \ }&<! t.u� % F��lyA�get�Y]X(0!�=.�q*\muF7 (1�[�^2)|W%�}y�|^2�"V�J!mu^2�A_\nu^2,C�3�fT)V ��3mbd�0Z�r|!� o�+� -2&|� )�'�� {\���+9)-X�v1g�u1g neq R�uT-2�k!�Y8 5^Fh_>�a�^2 + Y\)� ^{jkVU:R.A- :]A�!�k%�+[MBy�k$g�yt�c toge/ A��#z+�2"%+�oi�X�ezeries2iqdF �9"� & �� "��wT :�eB� P$T�="o�<- \B� Z = &v%�a�l}_{n2):(I.I,^{ iXA�q_3Arac"�(} Y�}�P\o"J$l>?zHC�~$�%�3[&Q&�y �� m� n) ZQ$"] dBd�dk_&v#dot8)A3 appld�� is"� %�b�!� ge n& "� <.� ŽA7$*>��5�&%= {F���)TZ�&�42�l���4�i�*�!�l:n�4.n)E��n�+Z@�}�   brac �6hT%i�a<��:�<�- NQr -� "tlux;e{�T�by%*{� {  = -{4k�@>@s� �!���^&�Jus*K�of{#�� Var � �! do��e ��W�u�PDF. .�"{�=�P6�֨= :�_�w�Nw�� �C-=i.i<&�Z�� ��A;AKeXt��u�5?v ẃ��&moݠ"���$e�w�p+=:�: ۛ�0j�"�not��55&��!> 2\��:O��cascade-�y`Kolmogorov-Zakharov (KZ) �rum�j^{kz٣ .e. 2d��1/n #)��-�$ (7 e��endix�nor �n�noa�%F� �EV�ofm-�%�".a�m�j%�,�a���"�(, "&�9� &�&�( �N��?a�� . DoO�y%Yex��ng WTo_ in^*culFhe*� eticu�ne �&? S�ansα�Oqu�'on�u6Υ�F� SqumI�&&��hp� $'9getW�5M5D�R=����)�at a� HE�/_Ō���  Ai�� {j_2 � -F'�gB28\"= 71^4)�h (��� �`ζ) ���� !�E�s h1�r 3�=J�1j� FT$ �p!ysVac�*)E�p� c*d��a5��^���2,��_$�}��N, s 2}!!-6j0�j_/C A2 2.���J�>��1yX46���34J� �3 4})!�G �1 �j�.3 . 3}) .4 ` ��1�74��� $, I�����- }. are��^ �-, {�4:�M^_1ql݌�,M�,  +ots xm�MmfM a�>&� "3 \\ z��, ��-MNfA.gM+1R�>{M+1}}�y^_^��# 8:! Mis�t�0��a*�x����he ZS��� coA���R/j�x�VM=2�:�d�WaV9��>�/ �!�err� s �I/z8�H�ybQt�E2�8 )$ (*�I�6 ��A��A��$.u&�.�Fch�s�'q�@*� a'� B(to � )g �a�%(ly�eeed#\ �c{ &�lydM$.���vpr{2!� d�� ��a�2baq�3�or�wjdr �et�� iBc�3Y2�� �Jlet@ K �bC�71!�i�z� �)��e��M�9N$���#not6%ry�f��E�t� loss �!$N"�&biggest� �M� �zr� (�zM box)5�%8 "����U $M$-���umat���%B. TD!�"�2 al o�!�v.i�)�wfi?"}]o �ar�4is�4�p�t^ e�< c�u"�K �*th  "�Io !��D!�.N�. �i�L�@Z�5whre-��ed�!m its rela.�F�4N*. "g%�i� m B.�".� WT ��e3�7��� ���#���J� 8��A!���)ly!Y15y� � 2'y� , as���$.U49�C<concernRa@'ing� m+ki> �PE��� �F!= SmA�A���"?'>,clu�3�KZ"�pl�}an "��!WT. � )i���I����%M,�4�A�VA� �#R!�tv �$�R� m��$,-J *�!E�]nZ0?��i^r�7%e�so unQ�7x%s��I�!~ ��pl�-:� elecC�e1 b#)lasmae�e "%�p!,le6Efu$����"sfies� $Liouville 5�-��in�-,�a�ble 1�E�I�H*!��Fv� �,!*be"� as aA�d�$N$ c~zLs*�/an��1 2Z��9|?&�$ac6}Mr}s[ $M9N_D�:\$ V�E)1 A�%"Debye sp6.uM�=�F `0�����'o a "d����colA-�� beha�8rE�gR���" �%�!�� �D�͆��� "�'8$�<famGamean-_8 VlasovF[ ��i�Ag1/N_D)2c� ("��! ��is).��&� &�Ont��s} �cc #!%1establid��1i�%m�AO� hear�4%q"J. AllN<��E�T%eri�<b 6 &��1%y�I% $$Z_�ql_j��B<6h�?�> $aJ&f b���=ed��2�3% ��BE�$ $'s �d*�,� p��8Ewe"zero. 6Иs4 %"�"�"�'t:�' �2��)-u�L5:�aKfol+�,�� !C�Aw�$uE } \2� Z_a}" tS5| \et!�+6�� ��  \gamm%�rc^},� za�X_��a �1G�:*�:8��LR7� n"Y2m�|V^j_{lm�o E�(x ') �9|V^Zwl.6 >6 ) SH ) n��m�, d {P1} m} , !! RHO}S5P�86�� j� �:�� +� &.;�6; �) (�- C�R� &٦GAMMA!E�%il<.,�:U���Uuw#G 2 :] �&0 �"1&[ $ n_l n_m n�2, -�.� n,Y�B8RHO�� Q�� "� 2� �F!���(�+��6 n_n\Big0 �N�.*5 �%�1!iv5dFw "'"a|�/-|8���,ay n_jG"�$t�" D� Dnga za�^ ���an�f� �8s�Mh�B�{2p�$�$~;.1-pyf + p�6��-ʲj.-=MainR]QOneA �: ich,��$p=1$� ndardF�  - )H-�+��&9�k4��-�PDE.W� &�s!�d���(e]�z chaO:er9cs�t�J�7 !%� Z="}�1 $�� n_k. *��y���of-��BE %i)��p!P ^p. �&�t0"� N-i��12��� highM���/�&Fs��|i�$)�Gn�19i�t��, s9 |�!!/��*�s�4:z� t o� na+C :| �$- ��>!G$s�� A���"\ P6* WT�$icS %1mi�Z,���a�Uts�;gregB WT fj��0�\o cle0:"` )� 8 �^be!�orkw N�L�a6�loJ x��{"�� � "�B2� $P_aLE� ?;�5m"�:i!(?%h��� e�C*������!i��s:2�"q &^ P_"K�< }+0%F�:�>s� K�"pZ- )]R9'npr9!=!!\�s�Á|beg���F== (���+��$��;�' �k�?�W5% N�x?9tVGu�N�dot P_{a��$�� �3-s��10_{s}P3 F`ta<r9}._ ff��EE*�Oi�6�$-/� = S0E�s i^ >�Mke%Q� �6:A?I>ff�is�W(P=P_{hom} +�!�  �{"6�w �"{(-s/n) 6X!�N * �*= FD}$F=0$��$P_ �o2Ǎ1�AWBE��$ = -({F}/{!I(}) Ei({s}/{x/.�, ��n$Ei(x)e��;expon=t8}�A�٭p5G $s \gg�M$��"� s#+� $1/sD F%1�� F}{sI2}-� eta F}{Q�s)^2}+ 91sm,P%$��:.�3he:K4asB��=P<�i ��� d��sMsl_58d.W(��)%�A�Ŕ%DVc�%�b;���%��<c2 .fQwea��2] 0LS�5*�L�3s �ftyb= �4A�(e��� itiv��1P����rge�o��s 6�7 $0PaY ds =�I��$y�= n'.�-t � +%Z��6�e$*X�q �. & WT��V���the*_� \geG�#��!�5��Z�.m7�"T �&a6�%�p\� �o'�7K,e[exz ( a cut-off` $P(s�Sta�=�. Estim���5 of $s_ �>�"[�'al.�9�FouRY�B}) balan?T�a.�#��U� �� Q��8"u � �>$k$ h"MXV'-] critwv�ue�) �t#��9 also� �O�N)!a� $k� of widt � �\�$k$) & *� r�ed� A�* ȿf�9����'��sI -�>)/�4 W k^2 \EE Th�is cutoff can be viewed as a wavebreaking process which does not allow wave amplitudes to exceed their critical value, $P(s) =0$ for $s > s_{nl}$. Now the normalisation condition ca�$satisfied D�the finite-flux solutions. Note that in order 3(our analysi�giv'@e correct descripF ofc PDF tail,pnonlinearity must remain weak� 0w%9means � �%_Pdown happens far from`nhcore $s \ll s_{nl}$. When $ 4 \sim n$ one h%�strong^ predicted!,\cite{biven} �(is hard to �Lbe rigorously due toW.�8. Depending on� posi!4l�AH,number space),confirmed by%�di�B8numerical simul��%A!�E% Q%equ repora\in �� cln}3q�ofM�are show�mhfigure \ref{fig1}. % \begin$ure}[b] center}pincludegraphics[width=.5\text ]{1.eps.end.=ca�$$[]{One-mod�b!C's!?two.q(: upper cur�< t $k_1$ �E!)�#2$ such��81>k_2$. Dashed ��]���ORayleigh6n�label!!1} �)H$} % %� %m���a a�AeQ/A�"Nb� diY�, where��t a-a�itQU��J�s�i� i!�mittency�tA�8scale. SimilarA� clusF��.�$ turbulencE�U�low raŨ than ��֑Ewaa��|d�ba_ofV  in�@yoko}. To underst!�!��)reversal.���ppear�6 oQ�st( tics,�W" to c�� luxe7 multiI�phase�-s will% d����next sec�� . %�  \ T{I6��Xh6���v�9x.}��� I%PB vious�,�establieyEP5vPDa�U deviate ��eU�2�s ia !�A..�-k�_itude sG a� equal�� zero. HowA,,6full $N$)�D)�,� t�9s�Toriginat� term a��.�, ``sources''��``sinkPre impossible, see (�� curl(}). Even adŅ forc0 or!'sip�A�U  dynam�Y�A}s"� �ۉ(fact becaus !�$only modifɯexpres� Ab� (see%#A� dix) but�� can!*l��a tinu�� �peierls�Thus,ASs�j\ � y �e�pointQR� ��M]��Dlux-�Uq straight )�MN b$. The glob� truc9 b�z a [ KU_I�:�a  dimen!bal .8m��eFA� illu�ъ?�� sket� itsAj�� o' (a a 2D plan.A[ ne��-��E� one ��2mpi}s. Ta� 1D� �is �B( observes a*� ��%�at�B���a"�  Ci�+lo e�a� � �_A�&l zmof 12er fig2�  4. 2� Pr9���.��I �70a $(s_1,s_2)$)� � 1$%. 2$ �9�!X9�s% 3kbA 6 2R  W $uld say, h�l�� exise+�.� � u<(s, although�5s;t)�-�s,O$s hypothet��and fur�� work nee ��to�Ndna����sn �-�<m l. ��N�Di�ion��F�is paper�re�re� )���! Wave T&� devoted �udy% a%B!�AZ2U 2� , valide|k2I e�E�domness,�er g(ral moments2fl�~Os.Aalso ��� !�me new , icular�eri� ����og�Pɕ-Brout-P� gineٽ͉ four� system]filAwe dealM�are, g�"oracteris& non-decay���2al� certKJ� -�co���p�<�%�sz type+�WT,�� .�,%� packa%_� ident��over �� �xs. Onq� �commonE1�18-�ed�isrn3 � �ial�d"H��*I0 %�Ed �raA[� the Ut chosen�!b!�� i E_L�*ave-T(can develop&� ��i ��4:�sA�I""  c6�2C. S�taneo~,�Ё�r.I�2IofB�� ��>�q� &% .ae. both} ��a�e�t�� rAĉIEDG of a=+ya�x��5�I� (%A"u for b�F!�.�) �pe�AmŚa� $N$-.� e;�$N$�)Xs�  5�A3an.2GYy��� arguQH. e� � romp�bya�-2Ca ��-5$��Ӊ4 �B KZ � trum%� de.{Ls. Fi��6� �� �4y�}ly��a tas�fu" . �; "�Y :B�E�soS %�sinks�� �� � �\C��a�inFta pY$-law Kolmo 8v-Zakharov (KZ)ͯ$um, $n^{kz�k^\nu$�icYaliy emsel�in2A��&gyF� separE�by� iner�!�A��� he� onent $�a�ends 4he *A. propF�����a� coefficiGaq frequ\. M�"�  WT literaA  isUA�sUofY�a Xa good Cew t��� � be foun*� ZLF}ma! t go� C @o�M,�(instead we � 4to % out� {e^�tu ?Tevom"8s���[ I ���( Hamiltonia:� E OfMo�g}) let u��d \BEA i\dot c_l &=&\frac{\ al {\�<H}}\bX_l} + i \tilde \gamma_lG, j�4 EEA �$:GA�DbesF�!A[)l, e.g.� !�a�A+ visc����(ively. Easy!�R��isar ��%� :�2�����e-p-�"�IKt .yre-def�oe O� :!� )xF}_j \to-�-:s,j s_j P. \EEu"/�ş�imp�N renor**y)�u :q i�� arr�y]e messag_ a))�J�do�� duce any���''�`" � 1#A�@."m6��Cs%\i|ic E ��easilye� $Fb��nu pa})�5d PDF,%;P P^{(a)}_{j} = (1/n_j��) \exp(-!�,!� q,$���.�(solv��kin�5����:�).*�tVeM�check�substitBe��pr!�(��.�1$I�P�\Pi_jZ� �!�� � ct9`�*CQ� -xm }). Ey1�h�t�p ņ��i*�a - to a�� E,� "� NW A�� � N$thebibliog1��., 63ME 447-488.� krasitski! P. K i, On re8 d"/ eb�y*xory{��ly 1�ar���s:�(. 272: 1-20%�4).� � LT} Yu. �}%"0E.G. Tabak, uU8��168501i2 1); ��K!�Polzi� FDmt92K2E%1�U*p  R.��� alenI�kIo3�� 029) 1055�Sbp=��IVg�in�v�822F956[1-636. �zs} GA�$ZaslavskiiQ6� u y 25X 67) 718. U�&!m��NSergeyy�4, ``Noisy'' �a,A  � �"�$w,I "�,��aJv.��6aK066608-��% �4). Aa��ttp://arxiv.org/abs/math-ph/0305028`'MK�'Y. Choi,�a�V ��� B.Pokorni!�omalous?.�+>MJ�� ������4040229�� d} F��:R P*q$d� !� �*�& a���N� accetoE�� A; ��J"s4 "� �w�%~:� , su9?aD;�'u�A shuu J E. S � : W.iA�A�gr�q?� by�) :� � 1, p 1��)MY� push�(6 �MGuy� ��N.s ( F. Dias, �y!� *Qel,��%�&<152-153} 573-619e41݂Micha_Tk v�~EI. ,�Ft* �zE%(, arXiv:hepeY403101��r# ! 6�:  ``R* � foam� a �e�114�92� Osborne�  M� orat� it e�1},H8�?144�2K4jansen} P.A.E�?Jansse� &4 &MA%wI�freak '' J�  Oceanm�K33} 864%�3.� cnn} C.naughton� " %�d Ne�5� [184\-97 ^y61 L. B@1R�.\ ''B�g/�,6���� onse�%��ncO ��, ɺ(80}, 28-32��2v:�f� � �M� , 520-550U.��*, N. YokoyamaBg50�� , 169-178M"S,>1Kend{docuM } i�%Re���'p�!l %Last SN's edit on 1/9/2004�%ATclass[10pt]{article} %4style[aps,prl,�Lcol,epsf]{revtex} \uq4ckage{latexsym6sp \s6�feynmf} \oddsidemargin -1.5cm \topm 0.05in�h�-t 8�."f. 18 3def \B� �.K}} E!CBBEAa� 7narray7 8:CR {\no� \\j$zer {^{(0)Fone1�.&20kp {{k^\prime<(e {{\epsilo� \new� 1 \\ %\add� �emaS/ �ye,�� Uni�/3$4f Warwick, Coz3Hry, CV4 7AL, UK \\ �D�t� �)e al S�c� Re�P� -^#tra%al forF4(, RPA assum�4at%of.oK&� qua�%ies� us5 ignores )� �ir*V . R\(E5�4!g<� �a �5�ak~ �ccounL&�%.mC is appl�:"�( � er#(aIpR� !|l& . &Htoua CingfuB�?*6 ��* uni�,~5ed&�. IaB"�c�{eS�*.\" ()1w^; arbitrary~$"�8s)Yy� �2J when"�4iW�8 sets-��"mA$les!�a �total3)bera modes. &3�. sizeaSXof >mmRH[ g)�F@t� eYnot-�is" intoI>duc���� i�$�4)ord-�,+s! �!involv)2a ``collSv�(Ged) mO#. We)˩�P,typ%0AZd�"��A�IwY�Z �]�'& 'Int�ion��& �&� (WT)!�aa��+nam&()��ofA�persiv�=.Pengag)>*��ȕ�!�"� R'��i�<dl&!�PlE,�a"=�WT%��% o�0tmospher��3�.Bose-E$eie��ates~$;,ZLF,Ben,GS,N�68,�,h),�. *��C05@ve beE� ree major��ro�� �T!�WT!�oryQ8bas�8a diagrA%tic@�;�,�,��se�AGcu��nt� a24s C��68,�, ֥S�thirdaN _��I�aJ�9?GS-2}�R���-I)aI[ore)* spirit 5��'s � que |!}s�3meA`e x n vfic�\�,��cK#�7,a1+ lim(#|n�| end ��%�Ż. I��u sai�a�y�al��2) Fi� ce (� ity) % affec�Ee�0�WTpBl:e�&in50�u�� ��7*($�٘ce�=f�B�&e�"``seed''!X%`�#ob: &L8e-jof͚� �aken be @\)�0�8*U9  � s ��greMAq<�.f. ��ula3D>'2am!J�� ctlyE.i%A�]� EF1� ?*y)� Im;Fleaf2an artek9EcisQ�1.A��@2J{r *bME�s��a��  a���A 'be&|%2 ques�^n;d .L, no mat�Bhow)�, I��Y�+G YS.QW �< ��B>=~=�n answYC�&A,. Th$:.� ��ach*?6� &�,} o buila�e a&urbe� ex�W,286dK�A!-U2e iS&KG� e Fw�9ext8-��A��senFfG�&�,�B*B&� s92eleu�:��*be us��tprU;t=,w�A� �pE� �?as A�uxili� � sri��� � u)!% erms�&F��i,ach differs&�;� ��s by �-��4l t�A�'ntinuw>Fouri!F rans� �,�D� %S� A}<6&5� �if s��=(box-�med�>A�pi:w ideaW.a��]�!} � �(ill#,e&�Ie�� b *�1 homoge�3*�,i�+l�f��Wy1�s���ddI !'9 r6( rapidly en3^X6[-�� eleg��IT r��� ople�=m�7��=�שVq+``fA� '' (�G all IJen�3:)^?r�'yMal *� V�qth+) rd (if1��?)a��-UDnC�JD�JD For 8 of �`objects, $\langle |a|^4 \�1ler+��Rit"�J!@t�\ !fluct49ɐec=-P "��of � gy $u 2 $,3 Ply $\delta E = \sqrt{R� -%0�2�^2} $ @@� ln}). Fu�;m3Hn.9I� $x�2�ten� na2�� NLBw%� ��嶩�.�t|2.t*�7A� �yю. F  !����by�L&9pop�*n^LK7�A^ui�0�@�N�W2b occaZ<%o mgra��j�M�"�� Qnterp� ni�Ѱ�7 !� ;M�2� ��>��It�Med "0 RP�%bem)ly a�� icisa had%�ʁ] �r��1In2� itq4@:ly���!��sve W fas�th^ ��2M$�  �� D2��:: e tal�a7ab�=��� �$$\omega t$O'  e��m�(on re��  iAL�bD 9�f�6i��� help�is!�� �),zs}. $(�h�L��tM&M s8n��e�pq)%�periodAyoc9d�.vJ��f�A�-"� $\^2$�in� J_ )$ !h� -�E� 2im 2�) iGRon�Eoccur}E�zZ �y� �m���StABoce� �*�ly�-�stbQ�� k" ) alreadF i@(,l��l)%t.i��Ta��r�oZA!���y�.��^mrd'�*0� V�A��E�a]p�!e*C!΁�P!! ��o)�� +{Gis �C>An�Ng"�_bke  ���� ny.2 tfHiB��51�U�5�E�-�&�!FdeeR��%�s %��v�A �E )�o�G�5B��,Aqg &�+NR, %b��get wi�� !�Y%�du� N#.�c�ins ( �) ��s. Pre�n� stepYrxIr��\c/Wlnq�' AeCa%'l� e �ڭX {\em�}H � �9� &�!XP��� m�� ~�a�"� "� �!D$unit circl��expne�kep�� �acronymE�Are-��> |t!�``.L )A"[ �( refl��p ���, first�.5�c -�0,�Y�a�a�2 � '' ��Q� -��-!6�%�. S��a2� RPA �� "�Q�-�?O�����,e� �E-2�.�?� .Yir ``&''�;!H!�� � �=ZL�At� �"� %/achudA�Randle) s� longh K length�J�0��&��E)�( iN�0. Of course,*�[? O$trustworthɣshd ����;�-��! holdN]��!hA4for% aE� E�.�#�\:�Iv��FSm� focu"�ś� . To*F wVll < .�� e�?��q�t��Sal F� !�� �-�q��v.���f:��!82r.?��Ys }�(!h)��Jw �nG%� �vI!p�Cob�! oq" exci�o43anharm�5 crystals�R�?bya2��"{2��)r� �^y&S2&$KI�t26")2�;M�m  A�$se�C�str�]to��e !�a quite �) ow c�*�QeO . 4��� �Qa po;A���Sd�b*OK%a�a* se }d�_-Y"�E2*Scngk�,�A:c�7A�teN5, +7!FAlfT����� rk8!d� 5�U'turA�ut!Tbe���'alE��g!al 5VF�*�A��";6� F�,A�"cT�o ate ``es�$ial''�<�[)����' i���8up�a !M�"in& ity �G retev  F MACu"�FqLWT�^ur) is � M ��&�a c��a �� 7 l, �!vYCic�A,�e� s,�a win� V( � ]IAo76� LWTX "ZndL"�!��co� n+�T�I.�$Lj������WT"�Qb�y�W#!39 ���)*�(.*a�qŮ,._a$'_ad!VA�gy�I� ��concerE�WT.ory6cen�(wn$1UaQ� 6�Ie���}����H� � ) Mi& �P$Y^y�%� k-�``noise: qN� %-�its�(a~ueE�"hO)0�um2(!�e�ed �� a l�P algebraicNmEnd�s!B��U�bKT QQ"2>0QM�p�+�und!��O�#= A�ɍ  k "ATFla%r �>�e�+�e�h.�d�_V�a /II�� � j!��%� it yield�a �al ���iy  ,or�D�s~6�MAXhe 5 � ce��m& "�MF �B� &� . ��&. Le_,a��ف�"e$a(�3x %)$�aJic cub�"� = $L�.le%�qr"-ig � be $a_l(\�JQx $K in }�I$Z}^d$ mark�:eOw���D$k_l = 2 \pi l /L$!�!�gri�$ $d2P�e��or ��us����Ha maxim�Oav�({max}$ (fix3=.g.�hd44pŭ) s��at �!o�.:�sU#  � m�e be_ edf � ca� �* -of%6s��$N5Ik � / !1L)^d$�6*��'�x $l$ij��� ���2�,!�!��H,B}_N \subsetjK)̉�#entK at 0�;�AM�� 'e�D^ $:� = N^{1/3vh� ��!^�a��OT dt!\to� fty �� ����)%0. \footnote{ � �Jto�U*!�in� Qs_,�= y$.��:�.*e [F�� b)Up K"$N�$ �4n $h_MK~o) \V�� �l�� | asI�%���)��E� "-yo u&GU.} ���"ao� mplA� a_l$� , =A_l \psi_l!�/  $A"i&re(o�# "�$7+���osR!�0uA�n �K(S}^{1} $, a� "�]�T�%�Ŕ&��g � !5�9� jP}^{(N)}�+.�-u �t���$es% -�ɂ�ge�\ l, s_l +d)$� M b��-s1$K� �-� seg�o betw�+$\xi_l$ %c� + d $ia�$lA�$. ?*� isI�^!�es�O*"�gr�RHa/2� $s_l$�fnd �Y(1��p�v � 's, sNA \!f\{A^2,E~ \}N!, = \left( \�M_{ ��$2�} �t_{�$R}^{+} } d!�\�1Mj} |d %@ | \r a ) \;�KVQ% \{s,' \} f �7gpdfn} \R% i+no� $ �a\}$:l�c�gf$�� ! ab^2-L Q* inIL�0$$\{A_l^2, \_l;>o(si�f�i$��_l.C�[]>F, etc)� �,���"c��)�6���or2$3A@a[�> � "��e * #�pg ood �a�m-�j $u� \{ s_k%�_kAL$ = \lim_{.�}�:N�, $$ { ha"4al �&�n!�'@4*-/!)�mk��ekѕ���9 �3 �K |C` g��9of�QA�),=BEA��$M�>P = !�t-�D}si$ |i?D}A�|2.  Yy'Umean-�e %@'�aA5���o�gsI�N$�� (�4�P ��oq1!R} ). B�4t! out �hANargc>s� �c] few,�� � �G"�cK'5h��1,| � z�{!� �C?$M2s[w�1�* ``$M�g''&z!@�S)�(P}_{j_1, j_�,dots  M}��)�( \ne R.v5BmM&�j rPmE7�S��t.D7TM.�� �%�6%� ��ls $V� r �$� # h {D� i!�a;annal��� } Followa��"%of � �# I� a�CP���"?�)RQ;hv5sa5;� $a;Uof�t�5 if i�ps@�C-0�.�&:"�;�| erat=�S�"� �$ �GR� #rD/�&�� F&y is"a ��a�Dm5o s�m!�� ach* ividu>T����fk��y (I!}"�V$l (s_{l}) �V�W)}\xi $$ )?�%�y�� �f�}D �;})B �0%$l$}V�$ = 1/2\pi.$7=�% &�v�"�fixasha�7!�9Y%�� W"r�da.Pevly2���s. Q�oo&M0� Ap��&/of WT�!�!([ omt7��bBp!3/%. H�gw^�"-n,��-u@� ! %��Y�}%E3P}A����A*� imP )inf" find�����rtruF�yL=sv�6v%*�"aL7 �%=�1WA fail��ix?pKs� �����it�� \a�/��&_�2*!.��%q. W-��e)��xj9%�u�is 7A��lforward�`\r4Y����ch Kt2r Name8 2�,3�Fly�( a $O(M/N)$���o. B9 $knowledge,a]!/v!�i"�[���%C$, w!u�=5�%?!�a�:e�wm�!�I"�*A&A�E"� s�v.�e� $M \ll N$-37 $*�\P��Fn��nly���} 5�r�!:B:,�#R�b��u��nQat%V�"�>)� !� \e^22�� �z�{1 \o3 (2))^{N}"�� ,a)8 � � [1 + O v]F 6p��F<=�`DV  }z� );�� �&y1Q�2�}�cA-�( =c!�[(.�[M6�ate1%Y��9( P a� :�9 �?��:�tu���$o)�$�E�s�� "x� } .2} � .M}1� �g]�`jK����G&�Bak�B�Kf�5]*s�  &!|B@?di:N07T&� box. Here��"t quad�cF�All�[U/�$u�/}��&�.��o�1E�| �;�� "� �[&� �"�?],2�X}, � *�WARG! !�@�?LT'>In"����0f" .>V�� s!A�d,Eh �d &=& �,S0m_{m,n=1}^\in�V0V^l_{mn} a_{mn}e^{i-^^l t} ]A51+n} + 2ue{V}^{m}_:'�ea_{n} S e^{- O^m$t .O +n}\�,|'x)�~A ��=a(k_ld�t !��z�m� "4 6q.,��� l/L � !yL$vector, $�t3')/%n}\equiv _{k_l}- m6 $, =_l=&l&oc�&0 , $1����:�h "�/-��lN�1parT>.xLI*<fil\4�#g42:_�1.m�,�gseePk!"�d�1$T$@&�  $)�/ )� T 1/&K2O3e;*�Pdia en�"A�T$��{!t.4e�o*�&�. Now��$a .m=&6A\�F9cm�a�(T)=a_lfO+�^{fO^2  2)}.Q�E�=E� % S"ek+��#��d.3)�Dimlth� % $ u0)} �(0)��%Oofa�%4!�.H��y!:.�^�"sw?a!�3^�I���s�0�7; ���a%�t o#&��M# &$a)�_�=!$,�aAnE��'aXLy�� ET�g�s ��'�men��xp%�!e� L is"�"�A �1�T-ij� �( a_m a_n \D��A:F� �����un}a_ma}=bar A  @ �ﱡ M'F�-I!�teE���6� =\int_0^T� � �w$t}d t = ({�u  T}-1})/{i� }.�Ne�Us�} $ % `A��<ea> 8]TM�!k (0)=0$LEe� �B8��wea[ XY�Si� 2)} !��|s�s$, \mu, \nu6{[ 2�}\�  -V!n\mu/!�a_a_\nu E[�! nV U,mn}] 9�:+J -� V^\mu_{m a_n `!� e j{l*_{n \mu>l k S kM&�!�Y=.�T&& �."@ �lS) 6�b 8_�%�j!Hln}] �m # � -�6:h! %zW�nk l}2m !}�'m +%�"b �l+ a��. V 1-� V^n ��a_m )� nu� - �E�a�\nu%���+E���Bg:�%}l!�nu m}, :Q � Q � �) zY&],\CR�eSLJ6f % "=Vare��1e�2)}u� � $Ced��E(x,y)����(x-y)�� y� ��.�V�v �&� Evo7� S&��PDF�� ��n/,���� apo��N�of:,��0)*: � �� 6� via5��N�3�^al,k � $weak-"�&�!�*� � 8i'@_tL)�l|0e[Uqu�uOr382tw�monstT��&�c� �IT!B)7ls|9�Ue1 �lHF�Ht!2n*[�:,&`Gd%7&�*"�s1// �l "�? ��U� .�G\+>�. ��U�A� +4 AtgNs�ten� f�#= E���*�%"kEly!ysu�6� [} ]�DK�G$lem2 �:use�OA��!�� Y��%�A Z"(\lambda�=�� \F� { JF���>$�Te^l_l V"} �� �� l} \�E "� Z}�q*� \D�� "%O �"j"� �(�"�"[sF! _&�#R�% nd $Pb 2 Z}�  % %\YL{e�SFP �$G'���!�h8i� �&��yl�|.�  8ly�>:e�� � �d&~ �e r D� �(�de�� 4��a�l%�.�_\Phi$)% ��M(A$).\\ My m�`�/i>)!E�-� you��e ��*pt=�W�C�T�/AAbe*�P,Sim";}� �.�.�X2oZ!1U84���� ...}%�!_ri)*�� &Ua�� %SN:-�s%�ne �O<�.�!"0?wA.rb&�- pdf.>!��Dis 1*A1EYeciese_�lacɇYi&� cur5J97sMM��BE mF7)N'&�#;%Jz N�<� \�? \�  #j�� �l -��)Fp�*6 ���(^{-e�, X`�'-��E �'��' }������ Z}; J' \�Y��*�u�2ver�a�Gqi�]ng!�Ša�� $f �(�\' u"9�rul��%*�[:(%��gu֎�8�).m;��m�-�Z}$ (���yo#e�*�))�)�%A^2�V$-�U�$g\{m, A\} )� rod_J<�Jm_Hf:�m2�mv,i�*%�RR���"iU�!v�a>�= xVA�w9' �g�e 'pdQT�H:+B&�]@n !�A���'�/[ af":)�2h+�=��"" LHS=RHS,"(܉.�Qct�w��A�S/"�9m9)E^*�5*�U;} �6oN8N�r�!2 L}_� ^{-1AQMli��V \} mf�>2�+G&{��pd�e20b�$�IS��in�)�~La��ra�3WC*��(��$*��J�G2��jE=B�3a+�y &$w0�m��$Z&Q.�-g �,=3�=aS$P$ͭH  %f 7ene Mell��1eZ26|�-!muS.. % "A�be�r��z,eP��� -- �4id  %ZZ�I rl"m^e�!�!��$e�P��M�� 6�a�me��ny��) �&1R %P��7a_�a)*b�. E"�� %i�U�)e�be2���N\�>k %�- �8� !��O��4as:~T}A:�:]�b��ege�� "''A�B�9f{o�<n&" ,&`!$r2� ��_' *� 6�2+�0dR�`on?�e�#ch�"s�;� �""M� -e׊�q�Lal�Z�� � ���!& Z0v��(E�&�z-rpaI � � bf=" "�+J Rf  = [)�"��� \}|f=0��&$N3!SEW&� �[=�aeV�Kronec�$symbo1.$���&�%$��A!Ѕ V.�). Aa�� step��&)�:�&]+y�:��9!�D�.�2>"�e�m��)�) e"1/����#$ 1�*� "�l V+�V� �K E��t����2�As"�M� �0b.�  �"Y;)��C�*�N Z`+b� $Z"�M�$�loi%�9��1}"and>f'1#. &�8�" we o�_su]So� $�6�'Z$C%�*O&�+u)A�a� fޚ.}�9 dp-is�E�dDal+^^3Z$Ac��"�Y�$t=T$�)]�ng)oAa$a_j(T)$i[M�&�) !  re�E8etU M�U� onlyhD� �!V"�9h�jend�,?��z:�� :� , T\�  X6�,+X��, -_zp �� NO= X(0�%&�'2N� eft<� \|l\|_A&4)&��xt���)A O�#��l"� �v 6| j (�� _j +Toc� _j}{2|a_j�) one�  +p��"1j1}�l� �":n•+!�mbda_j^.�-�^2>��one|^2 Z��\ J_3 ���sj 92�f~�mZ3two23^�3-54��-� �[ �I!* }{2}6�4%zer|^4}6( 6 �}-1)�)9O� >-W](AbW.�)fx4 �5 ��{j�4k}� k�.� +��zer)a_k k +f=?2})9: k}{|K%Y2}( y(W -e!(" �j ej^5a�.y:$%� < \c �)�>_A�Va� &����� al&� � "e T s ��dI�&tly�Y Ou֧x�epD b?��erߧ�0b�0ق0��e"��AR $a!8 �aac͝E 2"T 63)�X��`��0 0 a�bF{.��9p� �hDb"�?con�%`1�f(Ds��k��=S$0 $ C%:m/g()�&Q2pe�*ZU@"� %���6���$���M� &GQ0s,� ��n &K 6I.ޅ%m�go6p'erc����o�d3�7%M�>}0�:� .5~8 �G)�dYM&�1� .�w5A�?a�77s�if=8*6 a�"�]APt.N�l9� doءn*4� Y+here &�o�  $J_1ik 2Ȫ .�u6ˤ�c0Q. C*� ��A"�*� ineps}͙�2� �Sb���U.A��Y per- \2+ (0)$!O]noW2 +sM{p�T��;o��D}�n�je���l�Na[�Pu��!" :Ő�� Z({U%Uy)qA7��_`�\Hmb_�� $1�1�, ll bF8rkI�a|tex�d �o�!t4;-ca� g $je< �m $n��r^.�xF�jug�8$!�A5mn}^j QIT ��� draw9�Asa�ve�-8: op;Fe i�����L�1;�H�u �� a_j$�bemi.]�d& �s�!!aaGmt?�� �����~&��t $� y�!BRU'���n%�j0t!�t&IV6��r��Ad.}*l[}��AJ�}r)�`! sci��tN�9A�5, %z{ figu�!htb]wGer}$tabular}{c:} \ \"�p 1cm�*$ C_1= \par�}40mm} { tmf5�}{one ��fmfe� *}(110,62� \fmf�6{i1,i21��{o3&$m$}{iFn@ .j$}2E{E>,s_arrow}{v1,.LJS�: o1,v ��=��=1 } &\�44  & C_2�?two%9W�?�?�?i2)$�?"��`�$]�"* e� �a�*� � "wZM�ps�G.�> K�R�/a�to���{&� �Y*��}� .VD�j*�oP.n#s& %E!�=04�#&�m!uw<�bar;H)��^m_l$.�j�Zuc�0��� odd*�W �valwaysa,~amGS!q��� Qo thocXanT7|h�� �y� h!��]� se�>" m jc��l 0:�wc  �la C�cO2 matcb��8 airw> �SshI  e Wick's�� orem�"?c�>�o�2 dard1*P�i<�2r�Pj �"ж�`%A��(�e*q!r sum) �ing�(��b6on05]M� pre-� $\Pi%j&($�5 Obvio���V IҴ�S�a������%|�G}-�>6e�,� mu´ coup˟�i�sum or0)��/� ]' ��Q-M�-61W<� E by*{ e �6���looXbG a� �EM�BS�&Ŵa.�I pin4�, blob�endIVnY�ofyp�0x�r� f�>&�=v\�ce}@0�@�G)*=Dt�Gn@�5�q AmJ4�N } a��"*� � 2> ��"��8�o$-$# <�)�S0)�_�SEr�s*qRIG + �(�"7o�AsbT 2�Rq `uu9�8sreZ1 !�m]um�v"=��{r�B� Q�Q�ef�> $ka6-$� -@(viok*g�er-EE)if �)G �6�w!t)�b;A� rix �u $V/:��to�� ma2)ispInty �x��c�D"�A�any���!lFr =r�=$ $ V^{k=0}F;1 k_2� =0  = =0} =0.$}�$V.�-�eŐ $$�=p(�O C_1�P �� C_" r,$+ th fD �� � �� �� �� Y v;  do� } 2 � �_ +] & %>� " � fou ] b7�&� (� � � 4 fm��{${0.5w,0.5hW }l6� 5.� K M:i vi � !��� %s  %}�� �r�"q ef)�.!8�y>�-�� ��-Z� 2� -�/2O>ft=.4,5u� =.3!p%"�:3�:4 5�26 ��%!!E���:� �f�E6n�Efiv�D�D�D�@5u�DRD>C�(en {six�� .�Je2 EemI2�2i�W�K2�,^25�22e.�a. ���� *F(:2�� )%s=P�t gk e"Z)�6>aM���:� ��mimo���, A_m A_n A_jD:V���'m +n�&�&n." j-1)�� �/ ne jA & I l) 5?�!&+&� {m&k{2m} *n }{2A ��m}^� ^2 �  ~m +��AJ�m,� (��- hahaa����.6�F&=& 2Y%���`"-=�2- �_. �12�n � �"���]�n.�n%�n%��nn!�n}%�n^�A�"2�{,F�2B�n,* �1�"%!�2 B� O�e�:� s;�la��.5\ �%|�' e�,&LsT�&� �-$R $Z\4 �3n We1�.8�)�"�AD&XF&RP���Y! 1}) /{"Cif ��'��seٰ��"w 1�>lL�m(0. BuIQ�c�.Vf��� sum :��[!�GTYI�7*�!nwy)� �"$to!<�Jc, �u��t 6��aj55G�!2})=%�5H�.ar! �oQ�"�x��WAD�� oٽsum�\n=!<PYUd,��ce�0A6�S�{���)&[ 7no!� ki4l\]��\A���ti)��is�N1)A�"!�o\$'Y��� l1 �R!zat3 � "1 > �`O(N QiK�nt�B)3�Qa�e z"6y �ۅm�/�II�$\e^1$ �"�8]:'\��q$�G �� $\e �d0$��  %.?�2$-�}�T$&T$"_""�!�f��z%wE!2$�0*P%mA6� �6 j2� N8 �)� 1f(I �l�^&h* ��,\kappa,�D(�'j+ ^� B�)!E &&\hs�e {1cmיi�"!a_mv!:!�H 5b�H4!����) ("% ��^ja_ +F{�f23� 3 +,^j +2� /B]4nu}T:, Vj PC)_{!�})D=&"NB�, B|,�) B_3"� :,�b�+�H >= .�"( 35V n7i &?  (60,4�" (0.w,1.h)�:0 af�(12t  2o62 0.25�)� r 50.7>85�v3� � �� .� ��h� .I:�nu|yFl .jJf<�j2,�{y`',�_=�2� �� & AY�,8%Z�,�,�,�,�,�,�,v2,A��,E,� E03�09�0�0�0�0�0�0�a�fm>zv\�0.0 " Ŕ\�2.�(. �h�PH e�c&�s�{ H a�Z �c� s�&a� �+//p�(я .IHdot�%� L �'< at�Tt�q(* �,- n'#no2�_jgr�&*� &&�,B)p�-2=9&�">r�["!%T "�"QT �Vg�"�6�$^� #�B_:9�5��10f/50)�keep{6������������ʗ!��  � $   z� + &�� 1MF�706Y fish:s V �"� � � � � .5� 0.23S!6 �E�t �� Jk �LJj2�1.\ ��}rD�b6�N� 2"S$}��1A�3 :%��:l� �)b�5�� � M "� !��M'� !,2�� %b^"< F0JA�6^cN4!�V%1"� E � "~�* +2՞���73-b*1Yb.�Štheta:H1y� �UX9 �N� ��.7y�=KR�1�.4-�g,LB_1H � 2��B�.2�!. reuse{x}},.��3\neq mnI� nuδFL1 B<�Zb&wua��1 "�jA_mA_nAR} nu}&E& U�2.2=���4 U�m+1|Wn6 w�4�-��!0 m,n.�0l)�m"\!�R9�m9��,%�B�.�.�{2"a f *kE 5�  ��3 ba>� �L\\ %\hskip 5cm &&\� . 6O)�� 9�A2��nu}-2) F�QEc%�V��\ >�:�9���} =m-7 amkyR{j=�j)� %.�)� ) |s{j}�?|1;at  �1�j!EAn�.�+2BW(7Q{ten�, ��u����"Փ �B�k�Cm�{�y5��a. OV�  ���pY CJ�`$O"�42"Wf�� 9 lost���� �*s(compn�.!>).�y ha> �!C-�cߏ$�nly�K�.}�Y*1H���u*�*s�b"BIH�/V�!��0b,"�#D �& �}��h�K-�-t��b�;��ManEe�C.�) \psi�olI��]�]B][1+O(1/!�]�!our.�2.�.�h6� ]�-� =�� �� 4��>/ · �� �z � ��Z � t � :W � :�S[ %D J�  :� �+7J� N<�!O� -� �  1s �� Fl&2� �L5%=F� 6:�hammock:� ZQAR8��:�Z-!,/J�j�2"�'z: !�2[F E� /!�| ���J�6��AB�i��F�M� ���85Q+dm�a� .!��1� .R�2��nJm����[� =�=M�3)`N�2$�&t &� 1�+"� ��^�N�a(�5�1�!�:M9�� 2a��F9&�>Tr�5��> S�: �+!qF���Y�2<������^'45Z� 1^�856�scorpioD�%5-�� )�!�!l n*� �3.�2�v�-�.�O� R*F� .4�NI2.�ZY1'2��1Օ�21R aWA͂�V'f^p^a8�-�����!!U�:aف�!*>���6�3.�A��m!��� ��.b��}.\\:U�FT1}}2;0�K:KG6�%2Hj6$'"H:.&&a�'bJhI�&H�H1�{�H1�BG� )�1j6���("�%�-1n"�'�j*� \\!:&&-9 %YL 5�F%N1�A�%�{-��:kJE-mM4R�&. 5)tuJ)31P�Jm%`n>%5:in+26i3j  �MR�lb�:i-� ~!��"^+}3*mZ.YZ I�A��3VHX5*—K1�26P1�2m�1�A_�m ��1�2� aW#,j�^� �%�kJK)k�,.J�r�& ��mT m��R�!3�8��N8A9�3mQ4m^3W4W.�32E3mN 3���@2}�@�@ ��m��!2�Q2m \,Mh6)DJ�U5I�-mN�H=zF�(% The secon�@d term in (\ref{b2}) contains one summation because its graph has$tpurely internal coupling. This c�s $N$ times smaller than the largest �s�8$\langle B_1 \r t_\psi$ (which have 2 surviving�8indices). All aothper _� � noBat all� Ttheir dashed lines are �ed ex �8ly. Similarly,7 lead�k ribu%Oto.�3:�92 6h{dots_arrow, label=$j$}{v2,> � fmf{E{)eft=.72 $m31,V�3n3f \end� %L } [1+O(1/N^2)] \noIcT\\ && %YL =2 \prod_{l}I.|(\mu_l)\sum_{j,m,n}(\lambda_{j}+ ^2A(^2 %-\frac{<{j}^2}{T} ) |V_{jn}^{m}|^2 |\DA�2 } _{j+ (A_m_n^2 \; 2�,A94bel{b3} \EEA S��risa��:results eis sece�Xwe can write for $J_2$:I�J_2 =��\A[!m�j61m%j} + 2 8�L \right] VU)].)Ge�%% onsidered�bdetai��differ�̱� volved in)L andBfound�,t%�dominant2O(s come from%B+s��!��=mor�� �6 i �Ѿur� ut�&be?(general rulat allow�2Hto simplify calculaE1 by discar� 4a significant iKAd�h� non-� ��ce. Aft��A�observ [f�ng �r�IE�e)Z, $J_3$�$J_5$,! o�4a routine task1p�+ef!move i���< Appendix 2. %� \submQ {Equ �aM Z$ \� {EQZ}}�o oNowAQa�)?)�ł.�s!,the evol�of � (nam�$J_1 - )OseH e previou�$A�95) eain fact� \R1 $ �mea�hM�phase =s $\{  \}$ remXa set�(statistical� de!�am(of each  and �\A$'s) variables uniformlE��(ed on $S^1$m!is trued accuracy $O(\e^2)$ (assumA�� $N$-limit=daken first, i.e. $1/N \ll B$)��Dproves persistence�a�? D ``essential RPA''9 perties. � a( ult Ana spec/class Hree-we system� �inssolid%i0e physics wasUly ob!�eda�Bak�Prigogav(\cite{bp}. * �l!A est!7 b� it ha��en[ with�� any %jp�n��� U �e a�� tudeEB A A@and� a�,k0is valid beyo��e!N@ approach. It may$ear useful!futur�4study of field��randomI�s  correlaA^�\. Let us now derive an y�� ��Ag��%6fun�al. U��ou1�s1$y�� xt}Iq  zx})�3�1k (Z(T) - Z(0)^ E� �� {\parE�\over & })�����^2�^�m}J�n}^  $ \\ && + 4a�2"w  j � -��Lj|^2\bar E(0,\omega_ )2�j�bMn}} +�m1 U-V�mV0 m �(�^m}} -��!\8 ) ] `EK^ij}}&n 5S2Ew1T \neq k,n}QFj k �[ -2%bkn}%b" k j&I ! %+2!%k!;1~%(k2!-j k}^n6//!1 9 ^3% f Rt� iTqEk}}� +cc.Ak� } reteZ� % Here q��`ati�a�T��pec��E�l$��ԭ� of �|$A�� s. %��$expression�U upd�& 4)$ +,psilon^2/N)$���s. Nothat��still�� no�%ed: ab�������a�ar�N: as usin<w$traded nonarity�Lhigadimen�s��e las� h!l$``spoils''� separ��of*x��!T� (, puts a qu�on mark��i"� &�$\{�� ��o�_ ��. 2o< $N \to \infty$ �fo� !�0y $T \sim 1/\-�.10 (we re-itera1�� rd��WsA"�). Tak��(into accoun� at $\lim its_{T\to �}��(x)= T (\pi i�(x)+iP(O01}{x}))$, andfIP0(x)|^2=2\pi TN� , replac�$(� �� )/T$�$\dot Z$A/.7  �4 X� !a t \big\{ f { ��&�" e��$Z4 *(��m&) _{n:<��{m<�{m& ��:��:��5:�N����Z">��J! nl �%F "5.�j OR\�n$�\J 4Zf�J0 2Uj�m>�%$|c-�j>�')��mB�>3').�b��b� D�{n}m�m��a}\, dk_jmn��Z 6� vari�Yal2�ap� �stead�xNB�N�l� ��� f�PDF��� %�RU$inverse La��e��ns�! � -R"� 8�� ing %p��<S PDF, ��,{\cal P} = -�� F_j6s_j} -�"�peierls%� % w�=$F_j$�*a flux�probabil����"L  $s_j$,��6�� Eh { (0 aOI˕ nCm}^{n}yi< <jaNA��� s_n s_m9Da eMJ9 (s_jB2)�U*�7  5�R: i�f� xm " �� �m - Mn�B -2)��i-2��)��>zm}bz��Mѕ�X> �be+ied toI�-{A��W**!&} A�\in���E�Y�I�YX.a�>� +��!(��@&0�� )s�6� +�c�c-IUk^Im} ' B^'��1AMkO is i� t ��origin � by P�|���5 �CJ!�e1r���^ex�� 0��danharmonic crystals. Zasla�xSagdeev �zs} wO ��tjb ٠�WT� . However� analysi� � �,bp,zs}��ric� tow�a�$ Hamiltoni�y``pote�8energy'' type, �DoDs onl�coo'at ��momenta]is��lea�al a grea� ny import1WT�, e.g �Dcapillary, Rossby, �: � MHD  s. O"A\ve3���Q?Q A�als�i' most�l r!932p. �,we should ag�emi�! ��WLb�^,>�I4�$\e�0$�ond. P�eAM>� frequency!~ona}8is broad enoughA�e .�mod}0ome authors, %�Nw, %��sumA� Q�PDF5b even a� �%-giv�����{)$. One`to��car�terpreU such� mulae% C�"I�RHS!n�in)�m!��cH# hBb� exact9W*tw�A1�t� $k$)M (as�!]-R� U�I�$). In real1 ite-size �alu)�Aie[m6�a &Z s, al�gh �#,Q�a�0oo�# s�;�YGE:en!�^ ufficient�jV�reEmti��ys. a� f"�g�noQ1I��&a�i�!�>I1e already b%��.��  \�A>xim��y�"� s.}�`  V��  do!se �ab���U��ud>e�'re%�!z�(�$'� get"� �M5= s. W�$easily� ate�f_t�(/'u%_1}^2 2 o) -F&��)A27\� =  @4) \quad (j_1, j_n� B}_N6� spli� if% e:�y3.�=�L:0��� FRm*!�!qsa�� )A�$t=0$..�)�Sc*of�'s�-B~�v2�7�,%R�:, s �+ -.F1}(1}).2 1=} ^~�.�%-p�46��34J� �3 4}!�F���.3 .3})2*4 _ $ at1{����$, H�� 0 �- }) $ are[ four�, two ��.&'s&|�$Id gng �(+Dbut 3,2 or 1 argu  �ive�,� `��� ,�Ra� ^2$T�#e FourierV ��O$&\� ��in�pair  e#6� i� y�+ �� �ry trip�G9�.N��ho ��a2�2[Z���!% $Mf aiMMN_1qW2 M})� lotsvI�_MmPM ��M/N) +�42) 2:�, ��NLA�MM+1R�={M+1}9 �^8 # 72 MismatchB�$ �+es eTst����he ZS���� coinci� % %j$. F�' M=2$A�re�A� WA]V $N$-���6� errr s $Q-)�'� bles�an�\^^M'due$ the ��ka� �*��A�L $).&� ,&n*� s gr�*as $M @*� a��to � )g�(a�q ly exceed#.�# &� ly�1l. We��vpE(!� d�i���2���qyis wo�� X2r i�s%�Ni.9 pr!(y is com�� l�IBA�&��!B��O,et, $M NU�wor��oo %��!isks"�'+3X)he big3*!me�+M� �lem (�Q box) � des w�b��2�all $MA� bsete' mata�p%:husE�&"$al objects( olW" {\emZ}]d%��#is�Ajproduc\/eaV�' `�}.J"�  redua�to �3�r!�!7�f L. c)s�#l�4wh���! defi�)RPA!d,its relaxed FR*1."!%�i� m @s]�-�WT clos)�%�[  hitM�~)J� time�pK(� ,��U�c Q )AK4needed, as far!~!&&F &#$.concern�A�%�4�F: �2t% act B �3� �$��4ts"�swclu��gKZ�+��g playA �t rolA� WT. ThPtu+#E}��b�5I$+%�+ywhen �!�!�tK �a { m��aI HEi�� e�iNr�-%_� so un"f%� s. C �!x ex!��di�-electron!d i � lasme full�H-I%le6D57%�@ s6. fies%�$Liouville 5�-�i%��,�a\ ble 1�E�I� word�K�)v� can!%bea3tenA�aA��2A=$N$ a�vJs*�an�q1 2U����%��'en)� 6{Mn{s/ $M�.N_D��;$ ���A �A�E�Debye sp5�� � ��� rans�7 a !dividu�7colA$4- beha�0rE�fN�����%�a�\ /0�.{"��h4/�;fam1mean-. VlasovFR �2)A1/N_D6) (r1�!1=�i$s)�&�O��!� �%+establiX:��e�%e ointAD heare !��. AllN;��E�be��ed( Eq �z'0m�%q�6, $$Z_a&�'j)�6$left< e^{\d&j A_j^> $$ ��aqbe"���$Z t)�6$\mu$'s�F*,,| p�n�"Ek�zero. S.�sp valuKo�8.$ge/ fo�)��ݡ� !$,�#bD: } \f�8E�al Z_a}"\/ t�9%\eta_j$ +� mbda!8 -.,gamma!qrb]}"W$za�9�]$,�� = �)B 2'A� %� (|V^j_{lm*�#  6B# )� |V^:l.5 >5 ). ) nS:l)$, d { k_l} m} , �H RHO}�# 1' = 8o*6�� j�2-� � +� &�$�6: �) (�- B�R� .�GAMMAA % Cor.Kd>� m��| $Pa�sA(2�+>�Y�1�"Q� t}+ *�0F> �" =0, 1�pNd� $F�&� �&�� e s-�&, B�F=�()��+mZ'��#�)"%)h�=�<.�% x8sm�za4 p�:-0�7.�5and stud�$in�cln�!1� :sN6[ e� Bc35!�/�sW6&t e"O0q �ta�$)!�Jt&�6K,6�"�bq c   6� 12s�� �!0r�G s�;9 ln}. In�� ular��� 5�7 T��notb|the fc"iarBv n.n j)� n +��$� DA�6eta�� %$}� +y�be1� O� b: ..Q�=0yc Hj���>��!;�$� >� s*:thF�i�3 K cent&3 M�(Zakfil,ZLF}*(itE|n9�E��Ve�"o �P$F\ne !�Cdescribe�� mi� c/C�YYP;&� �>IZ#t�_��=�$� "� ��#� s} $�; = e^\phii�ae, s} $ themselv%#Faza�Ts w$>�ven&!�", wA�ll2 Hrimean �� UajM9vL a��ci isa�"k y�C``"3 ed*<g$-\pi$�!$ ''?  ,�a %� QD � fluc� �6�is @���=e� R�a�<�@H%va�> . To"�?it you> � rack��U)�#0 %a vrey long= ,�m �wA�w�Ftal{5���it %2@�~(hard-to-mea�Űs?}�7 SN: deco:be� % �<�be a r=�gere�  $r_1�,$r_2$ be@�Q4 �?G!�of &�)U����?!��?E5�e�K e� . Let % $%�_{1,2��e= N + r .$$ %sn .l|�� "|= ="N�-,DA p! C} 2I 4\pi� jN I�H $$" CBKQ , ""+ _ ~  ^2 ($�SNL^2) > 0,�j �Jm&N'Q�s i_)� )z�aJ?. O�gQ0fA�intL�>!�s-� �}{i �!�})tt�!*�4-S=0 *J�*}��_9 =0)�U5 $B,-=� M)�� -�5~d E-NbEs.Esi1E"�*i��� ��,v�A�j is clear ճ� c�G.[�Zies�A�)%�e` s ri"��p ^_ *(A�)�'e�����4!�,� �+"/in�^ ��$N~&n�Bi]�tt  si$.B./�6on&�)�\, cap�A�e�*a���%hi6 q*�4{������ below.�uq<1h�7=( �.E�Lhi_j = \Im \ln {a_j�� .� Exp/on}Taylor-epof log�<h O$�$ gets " !�y4\Im\ln(a_j\zer�  B +6 two) =5&B'two�#A�%erel ]&=& pVzer,\\ Vp&=&�o �} zer},\\�Lhie+�(gK1}afZC\�)^2 +"twoe ". �iG��u�EA� averag� "�!y<�0yo�Fps%1$. AAual  s"�Oz�EA6o /�'B'�celC# &>ir�" wise�cos� apHO��"�UA.�!`�.GOa��| '�B.�E"�t!thea>&. Easy�sYH� �$e$��fa�ree6�c ��)z�  TAd��BEA(���_j�� =� �%�� A�AK<]] (E�one}{%A�A� rEde�I`J#>QcFc� � &&h = 'AC j +2l�N/m a_n  <U=<j}Cm �9u ��^} a_\nuH �� + .� G��nu Zn�A�� �>&+$�) phij�)ra�)"��'e�:a�woE�� el}> �'�$.P!� csT�I��x $j$aDT1 �-�<$V�if����iȅe8�N$I:�a0$#=� a�NAY�0 KN"�L I'al�ng�H3$3hav a��~p�J4\sum_a M�ҔGAgQ+�8n}�sG(NP ->)zF�:�A ?1]�qB�atwoa�m:C�@%�C��a�S�&f�C�U�CZrCe A� hi�I%� "O-�N(0)�K 2=C? hiM } )�W�� \BE&K dotZ�0.w=�0{NL EEQ>�0|ŽoEfrZ cy�7L�V�o B = �I)�Q"�RtA32I�m1}{D�T� `R�(elt�^-6SM iFME;M 6oInMm)�]�� �k�n_m- n_n1�n!h,VC�>%�WO12� mVJ2 y1 chan�  A$yT�%�M�� ew��'twJ �O�  �  ``)^�Q��.���7��u�c $tŶ�3<nU� rease$.'� P� �  of��� deN&9 $*[� o y �FqR!Gunit cir�$Z\�e�q ���, �ct3peR � 's 7 stay de-%��d�f�*�do�R�n b%�).A/48saw%�) � 7#(�J�%� s"�&:��EfP'�map!G�to  *���!{.��� now��.ch#�up�*$"�&&�8E|s�;Iw �la�T �&F�2$,k} \equiv���_j�!z"O ) k2k���*=�� ;�G_{k�"U  <3>..$ Ati�$T&��扫� (T)=6� +\e:one�:� �4%DQ[or}�g�zA:{i�1D �zer k �>�$ 14.2, \CR>qa�pl�X5j .? +� n d |Rd� ndI �:dd6�.�k_$.�>!� c6<96:�V1.c�ZWP��^ B:�M� (ed earlier,�M:y ��:��$\e$-���Q�!J$>.+ -!g!�2L=jQo R� 5���A k�]:-_ a_m@? C-��] � �Mj :VO Ln :Ti Z Zsi�jbarjk�TE� I���"c!9�a��op!%6_ �/er:re�^, ��via!�O0bin���_k�� �k}$. Po/C�vX1�0�>*�,"30t jects�._k��k 8(>$ knowledg����� �$��&�1ށ$P.�ei,E"BZ-(. FortunaH1,}5�i�ne� causD�0sp�U,��0����30H A, �ce �_# ce{�Y���2Y0�E"�c KuZ�A6�X��:��3$!Wrt��2��M�%-V�� =W% eft<X[*XQ&�VMH � �(tF�]��| > =e� {.x* 4}R^2 #1}{(2} ue� �M�FyA>4squ0b��7a�ejC�_� � (B%� six)T ez's�Y0�0. �`in4E� !��aUre � Gm�dc�DZk$2� T06i��fI�na"} way. � �a aWp$d�k$ �)� $) dq=e�any�A�Q�i�s�X2t6�� A�ofZ��w/ �B�/a�q�� � \CR]^ W����6s.\foot9{�Iof� rsI$aw�N��6h$imultaneou�'�@ot!O)]6�:)!%O2� �3$�UN$ j7� >' &�1 ignored.}�co{%A�:��B*�Ei� ��a/�& v!*- drop�!MN����!,N,�65:�I!�c2�&=&'@f�, 1}{4��<�4^��Õ���\�� ^�<* %�G N�� 4.��T��a_�"�m : ) �Z- + c.c��>d !'~[(j-k)�[|�.�@-k g+ 3j(k-j)}�[3.3k-*g + {2}�[k}^{j+kp-8.9"�2N+&W+^j_k ��g 5l,m��l�N:�f l�Q.�flJ�g8j(� A_l^2�H A�5S0now��e&&"��)d�5.�*�Y� $\"BJ�gm�J1d e//!J�0 %�.� �"zJ) n_{!� + 6.�>66!�!�m2�B81�8!�M�] &)9/%��#�)�.�}A&0> 5�M)�_r:=M &l> n_l n_m�] dk_lm"�-��cmA Pres�&� 1-st�2Udj s &vGe �g$j$-thEk m812�e.e#6��� �#�%(eek��a sen��[ $�Uq$ sharp �4$j=k$�# ����.� �$j �+k$ Q - �DU>a�e �~.Ho u �:Bd� ca� >7� �T�mtr2/���f+bas92"f`)� �)ra�!��"s�)p� 6�6B7*�e�6+"!�A.) �s$# Ne�e�  i>�i"�%� disp�f�_nME�\sigma 6�^2�a&} . ^2$$��5��.PL4k /n_k,�"��v Z "#63# $n_kh |a_�a { $. >\D� �Na !&alwayZ*i~8>a!ge.�+s �0erie�an un�@ed�+th. OnIonagC�DraQ , �,sim \sqrt{t}�e��*� -�!7m t$. Re&AU�� M�m ��,�a��OL��_6[�EoN�� M%<�`Q�= &�8 DiC+AK} �;��t pap�-� sipm�-�L�< Nd??7m�g�S6�7al�thep@a�  de�:y&�&�%�Z!=:s�0t#�+�ors. W�o�8��=2" , bes7� ]& ?-�6!d $S^1� vL,� so& ��9!!o%w�b�s� in�P7ity. IYs add�;��L2�K.&n( tooA�m>hey � V��a weak�. IF�'l j%9PDGH!��of 6�C�<$/l�N�"�$M��9��-�>��;�CA��d�D�C@yA\l( H PDF "�)�j%as� .�=J|nT6�Ha�e0jU�Swh @!nnot.D*�=�A� �%gy>�A%8)CE5O$1M 1�$2 "B2�@%�M@��J,EvifbV*�� �*�n��. G��&�ou�Y 6%Da$X�)-i�!Ur�����7�l Y�"< A��$e��>ate& �!ri�24techniqu�W�-d " 8ln,L5. S�V{V-A high �|7a1E��s]donAR�5nI*�5�6] ��anomal�?!���,#+�yn nA}�+a�!A(Laam.-f�`�6!A"C s�`* d!�ad-br�*cutoff= A ader�refer�8 2e`E�8k�Qu�iMDWT � *�6A�V2=O�Qa�v"� &�W�MKt (�&$�pN$)�X:!�a( [eLE�`9�t�)22:�9�z��l"yoa�tr~eS�'�Sb4$) b5Wp0!=�e�Ey��4]J�Dm�"e+�(�C*�-aM������p!�"� s.<6�i�[� z5develop�iF~�%R� rR5% �]PNazarenkoNewell,janse�:u �6coՂc!}�'�a�we� �!3ZFoe05ea2B0I��.��/R3 `�X� ps �P�\e�7m�""L N�;f&7s 50e.Y !C�ŕ�� : noVb7=B T ��"� V�!. Moreo�^5�!bec�M1ved�S�1��v"�)�li��~"FZma�tld�K�p t mak�.v9y in�rpYge"gl��#A���metho`gWT �:pa�R�3�� work%�|� �f� do1I]H6pW A7B% %� �qe8yz choi*�>��#�7�*2�"F�!�}1]ur��5����[� sl�ly�\*�[>ɫ!j&� &�(shift o�Qs� a lo�W� 5ity�XMtqO6U&! i�Ś���8�a��vt.�:�� �!"p^pe%1 renoN^i�Io>A�urb�  s(sZ Aq� &&n.�::%~is *� �3be pu�F�o ely,�r�:�we� �Iu$�;�TMŠ 4)�J:� P\c�-AJAV%rn\��,!��qinu!�1�m��b})��:&�y��x"�Tf�E8\e^�,$123} W_{23.1}|tilde�(^{ji}")t ^{j1 0s_1s_2s_3s_j(K A}  �B736 s�RXB2"sB 3})P"�Eg�c`g�)��!-�inemb coeh_� % $ �,,(^{l\alpha}_�=0 "�)R+\O�ul @- \mu nu$�) $ l =$:e�E_8\mu W^{l \mu}_  n ;A��u�B�<4we]R�!*f6bm�=[!ar)�A��Neog.k&�ot}B�\1"eW�>Ey�4ts A�a�P ��Dd-�Toi ���� +�� �1�"�t"ZD �PA  % � n�}1 �*�"}1}"��g $Qr��"Q ��rSkc9� ity LuA se�b��� Ea���ed�] step%�zD!�id*Tepa��c��%�b ingredien��~(;&T(aB&G8l8�/a$�+}.�8��� ir*�8�J\ A &&2]K|a_\/}*"�I��8v!�(two|^>5K4�H+\e�m�JN�! + j\V zer)�'e^2� [one|^2+N�#@z?9 _O�]}\CR��.�Uze�v\{ 1+\eP����� #2Є}%�'ba �9�!1U� \% N . �2{�|2}} ( %{��_{1j}�� 2j}})�E���F% �AI� q� $cxe��.E�e^x$,���veriA$x$m� nice��a� llV..�ESN:K�d � "w$9% &&� c�j}�7�{-0A�%.!N�P3[� �#<f�!r�J,�5�&A�S6:-A-1-�.Q2U $=6 ] . [1-\-�P^�-� J,���+��<"Vl\{e� >�=GB)p �w%FEj!�-KMcL[Ra wb2bT2by ) +�Pe@>$[uF �.~� �^2���>H։��^2�{��}{4�(aA2qp] �\}a/ŹB� (ac {\b������ ��(��� �Ρ�,9,.Y�$ $�O~e u� �;�pon&���6  D� �S�P�2�bVR�v�)l����), �"���N {(Q  0��^%j-�=�#�q.�.��AM[)���6�2CE� (V?��G ^2},�1�1mPEc}��}�,G-\ � \2Y5 6�]�Y�0�zeY!Y�ay��f>b�� +����e����^2m}��"�1.8D| 2DR# #!� e�)u� .�D$Z$` �!!I2W � ou�*cGa] %vBi/Eof put x x"�*D6 ~� . %��pof a ��86. �K1 an go d�0�7a�o"��)?� � � 2O8 : 1.J"�H diagra�C9�?N"� . 2."� K.Kr. �"A � {1z((�&)^{N}.V��<":�. l|a_l� $M�a_l"@ lU)*� l�  > = Vx"�/��V2y �(�[��"� l}�  2l}]�l1aUl 4�T�<3�1�>��  Z��-!l.5 l5) �B�7� �3j(�1��A�Ū)�:#2#2j�WP 4 jP 30%� F'nGX>< + �X2l Y. �:z�\�:Aq&�>J $JZ�S*, X(T)}-+ &X 2N}�6{\|l\|_A,�xt�]�F)A F� 2�l4.# �j��.� >�3M5�� j11}� � �2�*o ��+!�i�- ��k���@2� V Z�2��[�2�sj n:y �)5>@^�3�4-7�+�S��YC�_^�4�5 ��"������j.��WY�k!�6��`Ae}{=@2})�k}{�/?a�N� 2��O�������^551a� wD "�>c�0� _A�I? 6� ��5�$��Rz-k.�s .�. |. remi�at/�'AZ";16�aR&n?6I�n�"^%; �G�<';@:yG�ddB�2�T T&�0"�2��au"�C*3�,���n:n�RJ�DIu�R��C� ev=| E j3p��M=����  %S�C,2�R � [ 2 �gm� ��( -V^m_{RYRa_sV ~R E[" j_{n X !"�� mn}]�7Q+S -c V�R_{ma_n alv q v�F"n �>x0#\ w\�lE8�+nM:.!5&!�eft. +�"AD%jn�8(B &n%>2R|�!jn}] �9x � -� �1(Ft!;n!���5n!] j6y !�1�_+%�}5,mJ� A&%D.�F. 1.I`(� V^n2IU�!�kpU� %�1 3- E��\nu <6��+E� E�nuNsn]U 1 j!�nu m}, 1Hqn}>Wn �)&,YV]�j�Be���. *E)�"�6`)Ped �+G �mraw�p. �p�� \.]~̦3^̦30Z˦60,45)6�� w,1.��i� fm&Ӧ��2�l12o6202o62 0.25M5N�2g7>85�v3� :�G1��  n$}{�:)�$}�>nu2c{.z�}{i1,�7:v1,.q>2,!(^<2,x�{�{:�6��jfm��>��]�� 1�tkR� � � � � � F o2,q� � i � � � � � � i2r^�@�@"�$q`h�+΅�W���7�7�7�7�7�7�7�W�W4�w�w�w�w��.&����oj8�}~ d v����&�5� � � � � � � ��� N�� /:��TR�IGm{�&�,�i;�5 l �1>Z�"�""�6�<st&PA�?6߶mTh��h�i � $V�V�es (V2$G3r��d&6th�)�8-G\>amz��>u�;=f+m�5e�Zlso*EOi2to&�>�#�S-'S^� dOing�'�� fpnt@-=BGcaB1/���2$`rB2}��\!�L�\b��b�28Z"7N��M�fo�������vq�/2��e jm,J4j���+2 Z�fI9�I"&0������I}FH2f* �H!H�Gp�H42I�H-HE]��|F���\B)w�)*����[ {IOA��B�&] %6��_ &#�%5��(���i��i�f��f��f�f&� �&&q�7c�d,3s .Uh�BB~�4��J� J�KnK��E=&? �#"�^:@:�"=&\XU�l"� �l}.�6�M���$D ��%j�%6� & &�lmF��m�m�m�mRm.�e�Graph}�R? 4H �P��@�-*�(a r\/ .�< \þ40Zþ2^�80,40�����������^�����Z>�1,.�J?R<��w� }{v3�� >p3"$�&�> B�fI^ �I�I�I�I�I�I�I2��IFI")\\�1: �>:fqi2F:�q�q�q�q�q�q��"��qFq�I���I�I�I�I�I�I�I��v����!5%:vN";�K�Us�6dotbS6;;� se�" (�6�sum�}Vx. J0J*ȋ:ZJ^K�s,n+F�{�fR "�U s" {y�f someFg&)M�4we had so far.�� gZhT�Vgaf�g�� �"�)i�Jac�A6O;��L�"�. R{d�)d4� ~Z}X#anF�8����]Mre��M�.�Nno=H��0^�Rm.�o�dnwTse �.~20e>M*�0 doub�)D"�1�V%���\�j�V!C$m�I$�"�*�X n$, �Rz:�OP$j7y]-�_�$-symbol�UEJ�UF!�!nill.} �g $J_4�n�e.���O^Zh+EYT6}�XFmi�ie�$���Q*�%�|0j�*5$��r221<L� se�,gev�}ͮm<�. H&ȯ����&4&�t-[WdYUa�f_�W�uHS. Just�E�%�tT[oN�IJ���O!Z5�K���z %�sʐ�*a@!en��i���i N�.-ofy��\r��>>Ua���TPi*KvKn��o��D�P�M��N5UM]��ab%�-Yԅnd!*3>Gj�8 3�BJhA�2EnoF��PA m p�.�O>�2��=Pm!'v S�LiJ�:�9��b>� away�;}"Mv3$V w"�IRn:&!% .VV$�6[usAi�[.8? $1)m. FurA�%5 =S���}RA�ס�0)��t"�� when����##~��}��be no .OC�z!�L�:AH�w'� Q��$mu_k$ pre-�%?V6+��2��2N�26 2*�,p���t%B�mTF +!�:� C�;��1"5b^y"10���"�F+a+ �~��4�4 zk��>��K�>8jU+�%:<jb 4�K "H �E�/M�5E���� psi_.�8�1���� \mu,�."� k "Yu6 X/�0�AL� V_{kH^[$ a/ _{k+<0�/5a_/���f�l�#2\FX;�C?-��^$������������v�:��:�,�!:�����^�eL�q�2�eI6�a�q�nu}^k�3A3i�ky�i�ia���4q��x2Wn�Z<.��R6Z� ������������i��2N�1,n�r��R�R= �R�R�Rm-�Sm�eO�XbT�S Qku� w.�.SV�"]D]\`C)!.��� 7������������ҪjS�a��S�S= �"j���a�e2Z a� �<j-2u� VZ Bk�X �� ?c; }^k.*Si�>�BM�K2���J@m �%�9E$�qX: = & 2 �.6h b�)4^*"RH+5��(*,���C(F*rJ+B5*3�!!&� 2Q���(@{� Rw���"K� >w 8%�[�HY�A�H "�y4JQ %"S Y2�I#F+R6��B���*B3����kT_Q]kr4scZ�f� 2: �= & �^�!R7�Zu�F�N�-6��4&?-��mN��jk�YUm�#k^.4 Fl�" T��$CKd*�t\��& z�a t��F���Z. Summ�2ing�1 J_5=�B��7 2������v�� , *.�� \;\;*�TX�-J�GD THE BIBLIOGRAPHY "�-.J:� |Vgin��biblio,y}{190 Tbitem{'�V.E. ��0, V.S. L'vovc8G.Falkovich, "K"�� S\r�rT"�u", Sp��nd P.Saffman, Proc Royal. Soc, A(1966), 289, 301-320; B. J . BFA.C. �o Sȫ�Appl. Ma{z�] f 48�]) 29 _9]�b �,GS} A.A. Gal���R.Z. ��ms``Revie(� f Plasma o�`s'' Vol. 6 (Ed. M A Leont%E,) (New York:!�� ts Bureau!/73)9/ �68�C. �$: Rev. Geol�.�{6}}, 1�8A�} !�1��F��q , J.)# Mech. T � [( 4} 506-515_7..8hasselman} K. HnVFluidV� 12} 48 �2). ``�Fre<"decay��w$y#mu�wsea��fac�v,h-u s ``9.8DNPZ} S. Dyach �E)H<, A. Pushkarev, !U�:-�Ha D \textbf{57}, 96�92=VPwyld} H.W. Wyld, Ann.@-3 1e� 1961) 143} llnz!�,S. Lvov, Y.V � �%�2�, ``S&�L *�psacous�_9;''-�E0E)�56 A�997) 390.�vovzakh�E9� �8Izv. Vuzov RadiI� vA�XVIII!+75�70ymU(davidson} RA�D  ``M]qe�No��mRTh�� '', y5Ag� mic �s 1972�Q� PRL} A.N.�:O A���!EcC�� �� PRL)9,76}, 3320-3,�96'�PhysiA5, &135A48, (2000., bnaza�M.Balk%�S!�Naz�t ``� V l Realiza&J^(Anisotropic*h� ��WaA� '' Sov.U.-JETP � 70} �0) 1031�T1�LT} Yu. M��E.Gabak, 58a$168501 �1})p'p!� 3pe-�� �k �3A�029�55=�bp=Br8�nd I. "w�, Dca E2|�01956) 621-636Izs} G.MA�����6�5( 9(25�967) 718.&a.push}6K, P. Guy���t6�F. Dia lWa� �?/C}"{�al Dnls,Yg �<152-153} 573-619Em.y ln} !�a�%�SergeyYl,��l]q���n,Y��#R$�"C *�n �Ye,��`=z PRE a4). AlsoQ�http://arxiv.org/abs/math-ph/0305028.��U{ Y. Choi,:�26AQ�z .4rof j{&�$�e�6�#, sub� d toaힱ404022�u�Nenx} L. B��,:�%��� *, ''B"{dow��:�0d"9*^"�$�nc� a�� t A,�d4f 280}, 28-32q�;2vN��R ica ��Mq , 520-550U}bj`y P.A.EajJan�� , ``��f"2v�aj>Ief!�F � th6� doc/�} wP\��@[12pt]{amsart} \u pckage{�0xsym,amsfonts A��(} %0([notref,not�^]{�y keysR�R R/sb�R� 4 \newcommand{\��s}{{\�bb{R}�" Disk!DB!Int.BZB!CmplxCC"6�UU2�SOSO 6!C cal _2@E.E?2Q.QBPP. PB LL. LB M.MFV  Ex� ����ExpVbbJ�Ά!rm{ >�Tr Tr�;�URowan' �sD�,s�Eu,{0slisA�$newenviron6�{SLe� !({{\rm\roman7)}}{%V@tlength{\topsep}{b%\sparR96K$$width}{2em2O�margin use �e.�% }}{e��Fe em �sJ�I�t> em�Corem}�� 6lemma}{L[0g�>eBC^}[)]{Propo�on1$& coro&Corol��} \ �style{'��l6>jD �i%6Fre9�6B >R #F� �v�NA \let\Re=�dfP�\DeclareKOpe?�� }{Re�< t\Im�0Im}{Ip�RN�E}{��Jpn�}{ �llleQ=\f {{AN\�*within&;�{-�FpzRZ enJs��%�sR)f,�i���� title[Lax� �8Ablowitz-Ladik ��]{�)B0orthogop ,polynomials H�*��} \��D[I.~Nenciu]{Irina !dd /2\\�'A=e�.s 253-37.Calo�. \s�@on{Introduction} �h>h, The aim of �paper is!0p) new!M ults!D|cerning the Ablowitz-Ladik (AL) -; MoreDcis%�we use7Fn � betweenAL = andtheory��orthogonal polynomials on the unit circle�F�,s associated"�,HamiltoniansAVIdefocus�xAL hierarchy. Our main investigE2 .e�?Dperiodic case, butse5@-)6%#92- 2�(.22()�Here,� throughoE�is�?, $!�0 f$ will denoA�4he time deriva��Q-fun�� $f$I� 2ae@ name ``Q��n1�" t)�`!� for6is some�s��d��a m��generalQPe iq[�w�s�p�&u}��over,2w( also appeaE(B literatur��der�ID!�,(integrable m\e�I$). So far,O stud�7 t!�1) ��d�$ly aroun!�e��8rse scattering ��$form; see,%1exaA�, �8[Chapter 3]{APT� refera/s0rein. Other a�s1�Z�s have b�fur:�ied:�"  GGH} �{ )� MEKL MSCE R V1}I� 3V2}I�E�try�0u!�st��2q$from a dif�t��ive: E��[�~�!-�C��0. We concentr�4o #�fproblem��it ��A�Dfirst one solved, �o��re��a$ /Ff�3>���s follow)F6� d!��i���!\ hilei{
a��6�isA!$ a coincid��,)we�&see.) I� rT %�operatorl multiplic%|i $z$A:@$L^2(d\mu)$ in anA8 ropr�  basisE�obtA�a 5-dia Arary( x!J�8cal{C}= \left(%^ array}{c } !�-� 0 & �0 1 rho.I� \\M 025-Y2P&01 &I>M!?2?>-2-3�2e` �ag6[>>X�f[_K3�4�>.� &� \\� )�% \right� T Ox�,�(ca�edA�Cantero,� amz(Vel\'azquez�VCMV�3i��llU he&� x. F�a ,� � Z� a*; ��very n* ally� hext:!x��atA� E$ (2�DefE}) ��(its Floquet��[��4$\E_{(\beta)}$��i�  � s (see �~11a�8y).V&�E^��)��0 by Geronimus��,�/re �0by PeherstorfY $nd collabo�ps�� Golinskii�2! (���ed .� o�ir work,��>� ��D� 6� Hill's "v to fu)�velop] �J  .�%cp ~11]1o0. In particul� heM*�A�rimin��($\Delta(z)$]Ya:� M� "b nd�d� at �O��}[% ] & p$ {\rm(}Y?A#.�$$)} be evenb���o$E�%/ eigenvalu_���E}y�(.�.4)15�B6 u6j)$��E�one�$� \in\EkalW%^2�Y��ڸ-�al�# !���$\� (�)dfZ)=R-VQA~Y\e; Whe� sdi�� hold�say�E�V� j!iso�(tral. Next^ two�s which&� ed a��8ep in establishaJi�� �� �5 "�. Fae � Iuv xjustify� claims��Eys~11.1.4[ 5�� ��4igskip \noind1 {\bfB 1} (�\). � %]A�m"�%Z� ~ _j\�7 /$Qk $jr �a=p manifolA0se8a( '� =(1-0 P^2)^{1/2}e^{i\theta}: ,\in[0,2\pi]\9 f $\|\neq� !zda point (or a zero-dimensiFtorus), �=7.K=�\~O@2} (Akhiezer). Co r51{2j}=-/%Q p+1 ^{\prime}J ith�, :6��1{�be�Nbm ` &$ $p=2$. AgW A�2/ is easilyQ�bl��d����}� D2} �=�)=\� 2}{!�'}[\cos()�)+\Re(&! �')]�h�c 6_{\pm![0,\pi)$� $Z $)=-6a a\pm�'$. N�at $|Z2|+-'\leq1Ͱh!Are�q alwayslu��,)v$05 �+< -pi$. HH~�.F|&2$A�A�o� if $�e!a _+, -]$E� Wres��in��� set3s $�M{')2t^2$�"leaJa given \ $JAJ: ,D2}�e��$ d�ex i� �6�lua��#@Qm�iz2�T���(no open gap�r�=�'a�]s� Z�s�80.0�N�4.� �is�@ ctly2�nq�=!��f'���k!Ip!R:be!�a�\ e �!��9if!VQ)f^�twJm5z��d4s above sugges�a��A^p$ fi#T ori, mic� of�l ��$ $p$, half!re2 oA�.bMXC prov�� A�7 �ReyEX a H& vec�$field $V_HS .ed {\it�tvaKg�}� a doF$D@ n�2a��of :�$2ne�tE�exist $�f m�( $H_1=H, H_$ ,H_na�ose grad�Enardep)n�ahIwPoisson�� muteH .�FPLiouville-Arnold-JostA orem  )aAKN� Deift})� 1 A�$N=�NHcap_k H_k^{-1}(c_k))kompact�� nect�t! itE�n $n$.�i� . FiCA1sy�ctic ���2�-[���V�#ic*�6� Uio�}�it�dm'A��E* purp!��i NenciuZI�%` [Ch.11, S�on *�!�at�"describe�sNgiu� �R^/�3c�h�pofA2 .�.Da�. So wN�a.��6o�5.�_� hasFE�Let $\�A�N }=��_0Y,��_W:�p$3l�u_j=\Re*_jl vIm� �� j� p-1��en!�%pe� ]��by��"�L efSA�} \omegaE 12 \sum.� ^ P�Xj^2}\, du_j \wedge dv_j��f As�M���t�*� �invH�JA�cor*� �Ibracket,%Au2 at�$f-Dg$ �8!$>�e �1 alig&b 8efPB} \{f,g\} &j- [)%� f}  u_j}6 gv_j}- -fA .A"jA`�]\\ &=iF�n�.k &% v�M�~�'f� 6t �R!)�O!a $z=u+iv\�u�$ao�CsDard�6� ! 1]=}z}9��^* u}-i^ v} �@)\quad \text{and} b8��Mb/u}+b� �C!Q�lemma}�  2-��.d�\�!� � :D. E"�!em�APB}� e Jacobi �t�����nde� ate�2 ��proof} $��� a suA& �s, each�Ziac�� �%� �  vari�s" �fEE�K .KBuy c�closed.�@R� � � .� 0. IKlso n.� , si�#!?�� $m�{-2 $ posi�x&xD� or �$j$-<--2 CsQ& em}[��-��]�comm} W$p :qa^.1��\{Hz), w)\}=0�)�any $z,w*� C��� :m!���%coro}�Ha"\' flows ge#~by&T)D $zwp�2\E�0I*)�$��� � sI}T =leJ"�(wl nvAznt-� ��� q %xAgT (Aex6���$ term�"W.�(a_". Indeq� \lambdS S^1�$n�A?$L�mB Y �$\phi$ �2, o Gp�e r=(L<,j$�<�΁�!�{ *� dot{L}, 1+(L} phi,� urQ4� *} �C&=(Q ,L^*d:l� .,�� �,)+(.�: [2Bph7:j] 1�( #/}N0.� *} as $%��So,>R ^}�.|=(eTo)zs(P1"-(P=�.">-1 BG)=0��1���< As*turYutJ�$ce � v Aep b%ed"e ���,) r�E�.�� ,be5!���+�aril�� ly�'?!�m. A�6"i. ���2.2�# 0ula (11.2.17)X%��Z�K�0et(z-\Q_{(1)}�'��[��-2�?( $W�`���{rih#�8\E$�F���p$-u!0 $l^{\infty}$"�'z#6# +;qd)qn . 8*MainRe�)P})���+"� show+"�bf '-2�* � I/e�4o� V~Z�3Z� trac !!8.$$��$ pow�0�-�$:�e�ps�(�Pj Pro� on)@Kof1})rZ��zA�A�.E W.)�n�%"O ��i�.b�?� f � ,� �&\implie�4�`� �X1"��89A9)!K\ɼ�organi6�2p�/*_�,s: In fn�E�) objeLe U�.i$b e� .7,�)�LP}�n i�5�ch2�P�P}!z�r e�a �$o"qq� Nrw��in 6�- Comp�@�%a&N6�is y.�s �F�.� e�I�4} d Aj a)"656�75 ,RV.��@e necessary backg1�-%R1Z�-AN�� e7�&8~�� ��9 P�& Case� ) (P}���%% t6 must�~M�our6$K_n$. E&� 剅U2�� per volumu�6�V�)E`""b!!ou?Ab2�8qNE, %} .o$p$m.x'�n� E� VN~2%(!�s��a�6 $'s;��p��oddXink�{q�&*:Ms��J�2p�thu� �:B�v �*!F"��/1$-��z� %0af�7 Kndefn} K�7f�/n}\�k"�(, \E^n_{kk}\,� &'�$np#�1�$ K_0(B�.7 Fim��}cal A$ �ubly-����a��& A}_+� ! &I%entrie?7(2.)_{jk}=\{%\ a-{ll+)� a0,�-m@\hbox{if}\,\,jk.V�-p�>c�a�X ��ur��"*��em�L7?L6=��60$n^{\rm{th}}$.][!bI�ic &Q4>��Z ���1dU4�LP� {\E,K_Av8}=[\E,i\E^{n}_+B��Z LPKbarJ\E| {KN2}T(U)^*BXA��qfM�17 !9A���( E,f\U.* 9dR�E� $(j,!�.{�.jk}H;/f9af+$ U� E^n)_+\,� � =a;�TI�qI%��� idea5�? w�$inspi)0!��:ous�30van Moerbeke~� vanM]5Q4 Toda lattice.�n`� h"�s� �v �..�.@ =.[���� cal*.�/!g0sY e due� tri-e3,�me� � ���J�J��m61�͖' -=uKJ5e.�@=) m�:ZicF &� makes]�?� ):0a*� muchJ � M�M$ i�m ���}o<"�alsblem,R% 5�&k4e&ap�+�4� 2HsZ1to] ch' �68%H5��4 a�. Also��w�/t�+T � 2�EC� thes� s!�E& �8! n immedi�� *�A9�� \E$;��X)�)�$�� in�A7��0b7=d&4�}�nzE)��\�M$er� � E_{j,k}^n��$y"+A>a"� qO&�6�}�5! �-�O"@&�.�& [] $|j-k|6,2n+1$(or] $j-k=2n $�nd $k$e� N0-^1odQ��:�!�&�ve$��notB, �� (}as50Q �$'�1o�7y row!T"� {E1�b�:�$4n�S)� 2�� I&�%� "par��g $,#6|)ainw.ya�ne��4�Fs2)p%�p$!L sepa#l8\""-3u�"�"B*� (bb{Z})$ $$ 5 =\{u� &E.*D\,|\, u_{m+dp}=u_mF.of"� %�ɧ $d!3A�:^ar1bic�/>p� ��g6 j+p,k+p}=q��j,k� �end�$��$�R9- for �inB�$$dam�&JB?�$$\xi_k^)|, $k="9%d�$�Lb��&� $$ (R)_j=1 �! when y k\,( $mod}\,dp),/�! ,\,0 ' wise, 09$1i{{0 �,  1 Y9,{�} \}aq;�5[i�E^n9-& !�0 >}= l2�}B�� +ldp! $$�� �umZB�~��non�0 ɸ%�ny choGn,j,k,A�A?$d m�}i*<aj�x:UN�%��0$\E\upharpoon$ m~�Mhe-E� xi5�  ��ͮG>��(e~�;=�$\Q��, wS ���~{ Qdn} D,�r��"� 9 �",kpA�!�� ��$dpa� � ��!E�A2"d}�� Tr}(1�^n<m.,fAE�ls�, H |�� eYzk�%�(d2 �.5 $$ F6CL�$� ��� know�Aa!�!h0�1>2\So)K."@�N41�sn�k,i�=i�:�J a=��ic�Qw�6- nclu�G/2$�$�kgEUNJ =nK_*-�D��,)�� -���If�ris��EM2�e-��Ibov�!a�extra�D MU5�!d�_j $d$,"3"�:x/��  2s%�4 �|inR��u�1?#$d� �a n h ��%۽�� � keep� in miat�kX�!o �7 �($dpm dN"\cdot�,q$ refo�D"d�  �,large enough�J�2}U\rB� r .Rm�Rn2j<6�$$�laOFb&pwP0 |AVE2��3�bA�!� obeyV�A�E_{k+p,�C*qA�J\G!_$b! \LL_*B Mo\,,a�( $\LL1�M6 sy�.f5$��Z(n#l}kl� V, - *j^'&lkPjl�|2�s�9ed. AAa�A forw5+&#���-�-K��jk��A� �i�6�VCIF12.B:&1 r��%iF ,aq long�JAGU�2���:SoA�6T \7wm�dT�,A+�uG����}D KnQd:�dnV^�1@%d��greate' an $��. � &�Lre�Gs*�N�%@va sens 5&;1V� $.* (AJ^ ce� t��a��B�con�=C"\E$it�s �to�F -�Z�+��A�&� By do� �we��1��)-� LPd}8 �@Qdp��##f;+Dd)}*li ,+}zB Nx.R�" &�W� X)^*^e!w*� �� 7x%%�J�  $� %�� n� i!%� � � F�v.�- uppa/riangulanS trix�'i~7��T&��'� �S ts l! :0�2ne: źan .��<�#  wcan&y ��NS Q1)}Iq����'� 6� changiby�a�H&G-^� most6h:ugq�!e�~I��*n~ �A"�*.C�":�l {Tr}j 1)j �zbu0 P2}S6,e$ )=K_ +2K�?��S�.� of} / �$~�K� �JG seIo+ $� ���' 1),j~�j+l�� j6Wj&%$�i��&"V0� $|l�1$ |j-(X) p "� % >,z. �����n}\Tr�;)��� �&KF*�K_ni n 5%!: jI��-e��!�, �EA]}"�REodd}22: � f�,mpl�paB�)2�&V|  j)�c& j}+)pv( &&�q0kI�(a& A�+1,�Av� %A_>�� (� -F�F6V����J>� Yaz�I�%' Nk+ &p�Z�J�* )|&�.9. AnT�"q$>$ :(_j,2\Re(K_1 3i%�j^&�Vj-!h�!j 1}M!�3 F\log(K_0 F 0j$��F�4e�q��Xi_cj)n ,�5�&�.z[un��3�0D�kI�f $5-2�X"'��>E��Cor�Lry�� �V."+l�.@2� A�Jl �26%�n"�I Im(K,��g�Cre��LPR� EQ{n}!�2Y +v A�1��LPI_�_b -� � Z� <,!�6K/*/\Apx�, � %�� ��,>~� LPRd�� M�: !$ � �i�5z*>x61 ]}, f-��dvJMy� :�J� RdI��� LPIda�4%%Re�2Q�� 27N, ��Q&�� CommKPR\{K_n,I�mA� %0,�_� q $K�0a5 0.#�\t DEEOdV�"$\PP$ H$ \PP_{lm}=(-1)^l\d>O��i�bi"&6>/^2r1�� � LPK06�>}A�A�B� $R4&oS}5�'��for�b# ,K_0$ \PP]�pYE:9R Z.K0KD{K_0,K�W%�0n�9�1tor,��i�Oly"�1#-J bRIdm�nQJ5KEK0B�E'%�.�ofv�u$)I!ucheck�a�"2�c���; base�F)�ac�!e%�2FѰ!�$ r�W�Fl�&*q��� anglm&�-�i!���=�a0��A�M (ek,k}- j,jL4Ų60XF\)�Kn�)K %�D!�)previd%cases,�"��]h�-HI"6�ZXI�#�7aS #erves2?/�:�d�M.} -�V2, :���LF[0e��*��bU9���2�1 $c_kzJ $��:[.�2"(1 !�G 6��%w>��*�LI��F P� $K$')�cP "K �at�own�_# -e�9�s�c$22:w=�4. %TK: How dRgo�.&v&�)�4��E���e %�N$' R�J "g�*2�.: �0�>� �!�//:i�0)technG% ingred�I%�4Gh+"�53�+�"7%&����Par�9K����0i &����>#PK�7 � er G\5al� +1}}�&}= &- .b"^j {�}{[jL�} N;rho>5�+2,r4-�i 4-oU8q�j �� � ;� .�^�l} �R62 :�;9Send9}j�/Q=|!�-E-�!������)� ��!T1�:��60j� 1�2 �Z�%j�x3}� <)� �R --2�u ,�9�&�>?5�- i �>>.: @E.�.3AC)�f=+.6[,Eu @ o�4Υ.�Ak= u!2�!-22#6�I]� �B�3)�.\.<.�f^>�I-Tq.�!�6;#�nM",y 6�ɐ��$ O ��&ɛ1͛>� � g -cqs!$ K_p a�t�J=\ove�M�:�IB6ar�[_j�I_"7U 1�Vf�!S�j*$�"D'pe� op M>W*-qj$C *���%N1?��lU �  reduch&K � A�*�lexa�V $6d$6�# ��Q�1���F'a5 by aB�"�M�iGu I�"�6� *�%��j} ?P)��k�#E�1� � ,kl}& D�d),lk��:� ="9 ��{ [��>r �� �$j9�+"� � �3���� A\ N1 k ��U :��z/ b. .�� �qe.���4�� embark�"2d  � �6�q,$ide an1. preldr�CB; �?"X�aln cer;?ly&j newXe�a_ofe@~reader'�@ veni�@. &�<$N\�pN$�!$A$��E"D \emph{stair-shape��Ar�i�:\starYi& �i& ��i0/h , 4z,v�l& O dX � T& 2  ) 0^� =5:,E�;"�h�D!C!v0'�8��mct6b" blocks.+!mE"�at mea-Aat%���3n�s $�Hre�Bs + lumn!j(�^�a $A_{ij}�,�j>$"� &yP i\mapsto "A�non-decr:6ngB�D#Yk'tr�8.�c ����L��$i(j)?_� :�$i< _in pas!wc �� H3-#a�l{XS#sagD omew�inR =oq��$($\tilde{A}$mha�(�&�Xpe~&A$}e#05ha2F7 1i)�ll!�T( � mSid$$a�be�[�$m- �B�  arbitr�I}��? "enM� ! } [A,B_+] � I�'��(i,!�w�-�\.E!�� E�am�9d R?��� ͮw�_- �^%)2"� � 3���"o7Lh�.�?nd !Bnaqf 1os $�+]!jd -]�)���u�!�$A�ga8 A:byqBns�F�zs*�%�I58 typ[)�-A2 ``lG&�&lM}s."�� �:>&�*Rm�E >�j .�5�@�Axr�i T aL E,��i�)diJH s�;!��)u!c $[XA,  B]��V<k*�A#ls@tJ�VK A�1�`k Ak�- W msel���B�9��MsU�!W+ c�.by F< : e�mRa�n "3x�6x6va_i�.� *} SiB$$B_-=B-B_+�0geA@�2;_-] C-+]�A*`cse(,"��1a�>*=�JonwX-�!�A�4Z y�� e!�ore&O�� <We�x [�>�Drs-J(LPK� r $�<,�0$:�{ \}=iE^ �a��-h� |��Ųwo �R�*:A��s out2 �� of a&@�Dh�^!>�="9L i{h\Kd2uk T!t).�b&�v *��}d-R�-��7eʍ�"�E�c�! the�%f;c]��third2�+�qL.�lE?#+1!��R2HA !?AE!� �q-� oC=kBL&| [ \Aing�GN,r&rt.�*j the R�G?F U$W @E$2=�!j,k�$$&'Q82�;!�/C�Pds1DOS !!-shiftM ^<0z0�T�is �6�&b�G .�95xK; �{U^*BUK; k}=Bj,k�AG:�]�= cal{UBU^*.7+1%�"&r $\E=\E2�n)�P�>�}z.A8kA5�G�m L} MG� >Q �� \LL!�iag#l(�<T�l" 2, 4�<.r)��e���SnB�klMjkwee1 32n�oI| ly`-2 &�+)5#U^* �L0."�! \})^`��U= &\M*spm}) RJdM�dLLJe:u#*} "ch�%B!�>�}2�EVB�.|�6�}�9l r���g is � foraJ9n�^*:���"W&��" {{� $_{kl�@�6$(k,l)$�AO �U.5ɟsitly��E AssNwe ejZs?x|ai�ZZ� �G^BA.k2 3��A�E}.��aB�"�G�e� B>remc{��^:j)%J, �3+1�B��B*p�sB ,. B="�p:�}�G�� ��*1�{\r�(�}�C^*�Qu� U % �C:le�>"(]�R*yfV-@ m= g�Em�1 �U-��S� tPH� e��;1K�]N�� U &Rk� U^* � ^t]a E)\}PDcal U!EI����,E^t_{k-1,l-1�6E�8#{S _{l-�7"Q[%,&�J>"*� �Q� jOq"< �Q2~Q)i�O�QM�"S_�'N2�i�o�w2ve it� � .�k2|k-1 � ��()�DL 1��=�]� m�2ap�6m ro0o"B��*��U�t$�9�;o_Q� anyt0znew})"�T>v=��d�7*~"H /K!!24,sR�BE� Comp&��aa�F6�oJ�� i b+�KS^ H3�e�8 )^*]�1WGllx�i�sr*�:s�waJQ[ .8�G3incorp�k�ne�Y6ad}_�&�?E� �"�)^*=(�*L)_-�So.�Em��LPt �sMQIhoo*c>GF�>.Z� �Tu���U��neA���>�!�@�o .�oMu�E%�2w �2F*�BYu����MAO$'X�P/a�+1Z�%���2�Uz�\W^_#W��2WJea�{wlymA�1 "a3 s;%�o'��ce�a ,a�tAx0"�;8W!�� 1}$,u"ɥN6,�J8T�i�c��b���ly�.@o verify��.�^�:��}��]�]F 2�.�^2�] ��]�]> �4%se�TA�L"�/:^56EAV��,��MT}2|J,R�xsystem�B-.��j��2_;.���"_;�20(k-@kT�DeQ�R���"-"E� }=|u/a behi���L.�ZTD �{�0aka:�"�� %�1�3*�V"E!f WB�N�SaryE��nՁ��iK&mf[is���ite�� =_@nUclysG o bo>�Ab2_ � oR@� �`(lӌF��}*8tF"eL�|W(�%;~�{�Sel��e�v!GN~a�weSY9�jXhuppor>meaf����F�j%*iYb\@� -�jl�",QAk�+&:DrS-d�k�Y&A31��% " k $k�#kI? O90C_f=\LL_f\M_fA���#b"x1"Y�  &q#rho��>! -�#9 &�+.U%) e,&r)�q:�#��!M_��1l ��9 !� 2$�1  .! &= ] fE "N� If�3ad����,�hV� E4�"U�f��Eڥ�"��]SD��cBq�A��e�gq�is>^4�"k(Z 7$A� az�2 �. D�J2�p^*Wby� ity:�nk+j}=MwC-���#n}�Z}m0�qk��iN�c� �'��s,��E���.q-Ud|�;"S � � � %XE�oplus_{r2�}S^r(!Z>kjC&$S:V�K),a_Z�X�V��$[��o� &�.Co�""�V�#6�+2��cd-1} �iGe� )KI�}aH(\E2�FS{9HC_f�TetC U�XI��\ :�$� R� � -�q)j`�]>�ΓJ! x{r 2�'6�� � �T 3�F: M!a  \M2lJMM_f�w B2S�wa~�i TLL~U�� VS"�->""�Q eN2�$. Like�Y6ld}�7�I�&h_G u j1X%[.{$�;Q�I�B2�F�A?$$A��|taZTa/1wPNwQ�MDQ5�2e0%�>Po=�br�~A�~  ]� ��$'ʑ� � n� �(�[`s�\�M��V�*�� :Ҁ�O$.��"^*s.�8^on�Vp͘q��vr�` �j^����~��� *� *!rD�-��������s b1/�!IFj=u_j+i��*+�Ow . �A�n�wL/a�aj�b>�=&q A��LP�����in^f=K_n�%=�01}{ 6r: .�"��|��L"� a:֓��H.OO�Dl#Z��KGC_f�C^f&Di�^OQ��F)d&LAM�62_`)��h Or� @�l-vqd�A�*�>��2\Re OI^f�[�� +iz�� f^ImB^� -z\��1�Qd vI 2 ,�OAD n^f$A�A���Xn$�B���3+iv.MY�hG�� m, �W%w�EA� Fn^f�G)m�E 0/!T5 %H^A�mE)M> F�G-��}����5�!�3�a-1 ��)�� 0$,��)$B�G'rho��/�_bW�՜qhj Q:Rf6n��S�1" Y$m�E%�E^f �m.(#,�L)vi-� B;x though�A3a�s2-1; Mni� � ;�!' $ do"mW>�2�1no ��:�~M�h�h� � a�son�E8 Tr\{A�5'-)((A:-0+%p)%;)�Uil^�Bl0h�B��j�u`^eA!�)y.Q!� �bm�Q� ��Z�R6�Ikt2���Z�V*�pM2�t"�p~Vo. �~�4e�Rw%�(co Oz$$ V�&�f����YA#�2qS_�0I� �n��t��q�4e�A]to �W m�ALf ult. �.(�!ykvb&owec&�CMV�,x& |=* a �ed�5�Be � ���+ ��t 5Ɂ5 Yr`�r�I2k�"o �``?"2��n^i*� ̓*�xpl���h�: F�,n_0@QVj_0,m 0$.&U+� ��n,k$ Qo�`($kN< 20(j_0+k_0+n_0)�~ suff����ia�Xm�npr:�)h-  ��{A�%8��\Cj,�N���#A�"3� ,m@ _0+4�+4$A�?.�.)Y n_A�Sa-k"%��x^!n&e3yZ4�?auA�k! .;#�(�.a�Tfin,�� ���N repl�?``)� " by24&O$&� $_{-�k&� E� .%&+ &b���Rl��KE�!�e $n^{�2t}$.� �EWQ�QY'Na"�-}� l *��՝Ay�ofm�,K�$f�y��,l�a�a�;�ay�I"r�9�^ysatisfy�F Ae�&f.0,�_1Bo�,0,\k \}) � ^fN?�-O] =-1�+G}�2�firF e4a� gues�H-� wouldvp� � :S�/``Tr"|-C^n;? ꈡ�!%n65!|so!R\� clas�$netheless,� �sa��J�ړ�xC�Z{ !�fi�ur2]�"Z=�@ intu�Ue~̖ u���/oR#�%. k^nS���u��n4be�orously�|v��}�iZ!i^�C�\}0sex of B��9at�^� s&�3� A :9,� shifR��:>�{ 4)�� �<of ``mony�."�a"a�a�a�dm��N��Z� 4N Al�QXI3tB%�� i�B-���at��fIh m7for���!U�2�)5$absolute v2s A��n 1� w\�.$l^1$�=a/)>�#��)&n�)�O�� ����1IGen�converge RA�who�:E. �%�(&�����`�L�h&G2B%]� �6!1}��^� �7��iMof6�� u�^ �."�9e "4.1�R�ql^1�+ bb{N�3�3�Aqc={�I_j*MD�0��� .#:\C$p�.FT .k�4��e )�xN �KinfS%�} :{( 0}�H_eT�9^RE v�I�S1�@*� &�qa� \�$��4 k,k}� ly 1/{k-(2n-�bF::+xA!HA =� ne.��)�>{asaD�beBYIU*E�}<(p6wm����gFm�wo im? �/o&�jq5� ��"w�Yal,B6E�A B�i*js}Na.�<pl2.��,+�Am]bC .�xt7ic/:a�Y��ŞEZ c"� #�A"> 4s $f_{1,d_1}^e� oA �D_ q!a �^3D+$9kGx=8el��#�j "�E��j`b�V�wd_s�wW +1,k.eo�e(j+1)-ki. H!$1o�:usE��v`` (" or ``odd"N) *_ eq d� {^. UsS � 5f�1\�/��I�b~�'i' -���q��;N�<$ f_{n,d_n}^{e},o :�1Ed ^{4n�("aL�C e� $-2n-��2e a�$&�  H)�n,j-k}2��->� j+ U6�-2 sj-k� z� qUs+1}2  \�u+1 w ����lT�Q�a�JH��$(l,m&a:~$|d_n��[��+� a|5�/o�v� t�g $4�{%Pa�9,AIAA尹z�i � |B��< sV=  fa���� t A�;*d��!,reme one&|�� 3f�I=4"`J 2n}&�^n,-2n�d�#&�({Ph�USH� ��Aq�r�zJ�!P���f@ �>VQ�.�.�U���3 B� �A �2)mr �jO�6�Q�q�.x&W Ea:�� � B�� �ekhe 6N ��� � ]� ��I�t�AN I�e.U� I�sum. Pu�(�5 ] �a,j/��J'� a�|-�,j}$|, ,|9� +1}|�q4^n(V���-�|jPIW|*x1*�8 +to�e!\or�eoalcfv_\ & e ~ *U :e�mI\le"B�)�s$rN�e� �":�2v+� �x%  ^a�discu�<&%[�k;�!hx ?-_,kňA��@geq 4��*��s]|� '� �%&j . (As!c\e�rlier�Us^�� not optim ��"�M*�^ u1ʣ s.) �gAq-"Qv�|�E[,\,�AY���XZ)412�k��!�* 2vay �%��m&�9%-fmR� � � � �NA(e !<H2�r. Def.&^i+�iG�#1� )j� ���a�)�well- ���phat ��9 f $� ?�&"��)x�M�[ u@jC ��tk-t)m���M< � &o &ъLP(nD� n�6I]+ a:� J=ve?*� &8%G"}�"�=�%��!�u�&2_=se:?��i1�!�!i\}� ,iE;��!Q�3B!�nY( Z��!��!*�!i)6��!f�z ) y5\{\R�!R G -jP��� �Hm�Q�>�For��en  �qy y�Gl�9e1"uQ Ql ,{/��{AsA&���A�Dp��eM�yFK�,�B�F !�$j#r�)lM�:z_Z-nda3�*$,:L&�t*^�xy ..d s�K\C���l�'& i�t%��N b ly m����9��( �( hheEH�? �#a��cu� c� u+l�:�l `W)��& @���xA�O� :�&q��+ �-ly �*:. e&�9*� ���an�c�M� Y�vm�)�.��u����"i6�"��� j^5�JE�6*`� j|^2O22u��E#.(NX��)kA0�is !��>Rv ;�A&�:�� s XP��&�#�d-2�#j&�#a5�)�E%I%ghop�8f�5au7:��� �lo:q�#�nmXC�3i`� $�~ 0}�)_Zub#i�#b&�3�/nok�vig wH6H[\C"�Q{A}�jjW�s !n2~#�anC-mal4�KAA��#th�_"�#�L�{M�Q�*=��it{Ac�G ledgE=:Q�,author wisheGank�<8 advisor, Barry`�R � encourag��EF0c�6for acc�to .�Y drafi�Ff�6com�òT�t}}�.�1i���$Simon2}. S�l�P anksbhcy ��^ sݲar� �P,Rowan Killip�!helpful )R�*.���rХpis�� . \�� ndix�%�% .�:2UQ Full ?@f@so �%�%G 8J�@��B &@��!le#3=l ���"�.��.b�W"1iGkka��@��� j"�. �[�,\^A ial(*U'1}�k)}%��_jZq=�E.*b�QUT$^�l.B6AFp&�.�]�F�]�)�q�k~M {?}P�_)raL� 6G�J9 ,q_j� Big[�"�(m�HN* =�f Ff� H.Me�ep@2 H�g.�9"{k&�e@��)�.<�j6R:�eYD*�er!ABi)�V�!@��k {��fk7�%�?N�`k �+&�kk�+2No)�g�k4-�QA�1.�=HB;�@6�k�-�q+&�k 2:!]\ޚ�'2X*��JJl\�SjV*qI\�QJ!&�{'�RE]E!�,�r �+�%( :.,5!U}+�� *!�k$ Y\ B�b* 4^ !/[�ia(I3v-2}6�w M%1�)6V+.N1 s.�Fa)�1�J�"�%6�B�b�+1:�= �5Mm�#2zI�%�2��� ���Af��a few���pu+Dc fT Z $iJ+v�f rlB�J>Wh}�=%k�x��9�xI.��-(��)2-!�!12*N#A&ZxUN�&- (>.� lA�5�Y2�a�n�Q)�J��'^�5$ �ǒE  Pa))8bi jvz��b>] cv .�K"4LA� "ω*��b)c$ii"�L Cź� ��|��E� look�!V�VZ� X*�N`�� V��� J� �iYX�I N� cDftJ��jAZ8}>�mfS*� ;K�kF�%:`� � F � ]�8 *� �r v IF�I�8uqp�V:�e>�� !2.!�am ��:� 9B,�(6%����t��B;7[Yq*� �͇ ��.��K�z��� � Za�� 2 �r)��)b.0�pbN <� .�� ^T ����%�].J"U*���#�  "q pS��= F�&� %%� �A/��(3!(���MN\A�z�P-=\�2T plug�apJ~���+e���$&)�Dqd=,>�& |>�+Z2E46�=Qwb"E� &2�-2?+�k E� a�aD 46SGW M�I@�mCQC.�*!�} -'2S?e&%!2.%1}RL%9�NEB2CA=: [(\E�>AQ n \E "�7�Z�. Ha�1*���+ som�sE���w��^B{J5s� step4�c&���,:�!�z�&��BA-( ful **�# ��K ���C9�(&y��&� *]t[6D#Lm�-�_ Ufy�by ��V1kC0�&�-;�1!� occu�� m*�&{r� !%!C?S��F� '=�aE� EP  (AąSE� -��Ie:� SD7Ͱ�}we"��5\)>�B�FJ� �l~*[����� v !]6cb"�� :7 F�sAEa�[ &)�5�2}���%,�,�� �*�F, g +.$�)��A!.V~6��K&+ NB�)��U2,���)A�z��'!JU:G�"(&�|^2}{4)FB'�u-2�u9H 6&�P�kpE> !d�-� )��>eu>"b2m�9b�a+JD1 Dv��~B��EZCM&%�- !�!G%}6�!' *!6%)P-B��.� W)|� 2X.�l�L@9C�+( QRy(y2S^21��� � ��@y\Eda%/EA2) v�! \ &!@N  >�!�- .0d \f�=-b���&�[2{?J#&gGw�{ޕ� e&�g����� �� 5� es &Av,� Z>����F\j -!�Fi!1�A\.,*'�.����S�Btyqf����sed��F�-zJ.e �f�j^2A�>C{k*�1}�LfLfgy��P�P=�0B��}/:D/a4yU -1} �Ϲ�A<}1ahV�VQ�B�QAfa����=!�a􅮽E2E�H"m�U��{pA�N��0.J9�2P2O>�)8,� uB�m9 �u���¡�a\�N w� k62c{a.� )yz �� -cA�yQ�++=NJp1w:p U �Fs"UFpV/��<\:�f6��e7�g-W �� �X�JgJ��n5[ &-]e7n*=S6�t-�Aa �EM�a2F!_2S!�:�2��fM�sd >�b �AU�F� B�.� �  ��hi{!� ,L F!26��*�! �����]�����!*�9!���(.#�( �jc&�tAD�Vc�Vc�VcA{`��1X3�%�|`](=E�#�&w m+%��z`�z`"z`qNhQ�\�<B 2�@����*,aAR�9C��! *��_�t�unalyz�&>�<� !�  �Ez �\pl� �jN �i�I"�BQ*� m�>F A�F�1"3�o&&�s��j.`��2�$A�:�$k12&�.c����>^��:=%HJ  �:u,�,��*n SoA%t?Dwp�>&���*ajP'e� 4J� :� &��.++1>:� �!A�6<F9 ,�?�2�:8J49�>�z:��k n'E� �:E�b�!E�!^n�:&QIB!��Y"�.35.-�be 2?%_�+ !i�1�:* c! !] B�:M.G *- >=Q ��g� .7-\ 6 �C2��%��A9M{�f.3!��'c.:oR435� /n��' .:Hi�b�JIq�+�d��y��� * �4��1}"� � I0 i_!ove��E�1,j�IEJ G���*�~G k+3}� -jIW2V A�&.�� p�A� �a��JT  T.U 6gA% �&!�2�� R7/f�*d��<��:8=��N�N�NbN��>a�A.%��[,{k-1}\bar\alXpha_k\E^n_{k-1,k+1}+\al}\bar '%,\\ &+\frac{${k.2{O }{2} a+1,k}F5k\rhoF-2,k^g2-1._ �- �Z�� �DBig] \end{alignedw&\begin+�+1}>[ &(�\cdot\E)� ,k+2=L,9L{3 N+-2;+3� &�$k�+2 %>)1 J�= �%�N:o�>435� in��!q.:r 2� �equation*} Therefore, we get that $\overline{i\{\E�!O1},!n K_{ns} +[\E,!�_+)^*].}$ nls -� | QB Mp9�FBig[ &--D-1} qRM�6y!o!E�.~i�!�� \ &+ 8�e�)i�[ 2'6mA�) 6#3E�])�1 �=� -(\Em5^nu71}+!�BOin]=0,\\6t =��which ends the proof of \eqref{LPKbar}$%%]D$. We now turn toJ, *:Qp\U�Jg}_{ ;= %H6�I�!��2 � !rRI!251}-\E�6Big).B`The left-hand side become���imi%:g}&=6) �2gB�E3:f=m-.,Bi��4}e�%5 +]�A(E9Q7)��:c�� ���!���m �mLfd��6r3 �+3%m &-20!�3i�`r�J 6Ha_bH2>2�N - ��`��Z� �� &�1 ��ij) 6:�e��=�A�n�� �h���B.�MёhB�So�find w�4we wanted: $$ j�=iJ�q�.=e;$next entry�|0we analyze isV.2�XConal ring�� righ.�first��N\6�}�b�42}} &=\sum_{j}y�Ij}}�u!h�I+�|2,j}-5j6j�T���JjeI��iLE�*bi� jA�7>�b��b� If!vlook aB�now�J��2B�!K�*�]�>a>� &= 7^2�[[q�wM}{2 ))�-Xpartial�}{ A{k}�M>� �Z J\��k�G]��&c%�R� � ���+1Z�M�`�I �J�F�:n��  &-�=���zal �%Z�I*f� " �Xas2w2A� !�T��A�B+� � Z)� ��1B6,E+:2�| xk|^I�X}{4J[�Bu٩}]��q��)& 4�# �9`Š 8-nr��� UrW r� .� r >\�z0�14k60�5�!- �.!�\!_.�2���*� Y8 Bn�Rn:\6U29^6] :X�����!���,k} �!B!+&� �%IY4 ��-�2�� =-�=n�\,,�b�� Dimmediately implie� e.j� Finally�#�  last rel��c have prove,\ Z@ � As ab/0we start witha&�  � obserghaR��s16n�O E�25뙣�E�>y>}A�60 !�!�� i�E2Y +1}� 1m�>� :c �!S�� j �N�:^"3 .V@ B@% 2�= ^2 A�:���:��oJT��!� + 19��U>?�N�� ��i)[k>Eq�!~ᩉ� :��W��a�:�� �}E�*�Fn�}N�K�jE �z�%��ɗ�=��2&��&.+OB%�2>o:�!bݯ9+2h)�!/N��wuU|^2�?&�1 ��6�)#2�6�!B �- 1�W}zt 72` U^yA�J+��js8!�!J*�1- 6 A�!m1�y 2U�>"I�.V�7��Y>��o�1NF��at�vD=-:[AbAX2},>�henceJT (($ holds. %�N \sec��{Background: Orthogonal Polynomials on �\Unit Circle}\label{OPUC}��Z� Iw(is Appendix�,present somex�basic no�s results z edq )theory7o�pF�u�c�.�4reader interesR�Iin more details can check Szeg\H o's classical book \cite{Szego}. In our p �! ? follow�� upcoming two-volume treatise by Simon~\cite{ 1,(2}. Let us recallUdefini!,! !\Verblunsky coefficients."�  a� Xbability measure $d\mu$A$S^1$ G s suppor!'at inpV many poi] By apply�,Gram-Schmidtocedexto $1,z,z^2,\ldots$, one obtain� monicZ�` $\{\Phi_n(z)\}_{n\geq0}$E*!E normal.a�\ph 9� I }{\| \|_{L^2(! )}�These.L obey!�urre�E�ion""� } T�K$(z) &= zk - �%{�� }_k ^*(z), m�PhiRec��O"O.2 - M _k z:M*N*D } w6%=$>$'s ar re�.R!r $�$k^*$ denotf reversed=6B�vrev-*� = \\{l=0}^k c_l z^l \quad \Rarrow!�)2 :;%\c -l}E:� ,} Equivalent� �!�= z^k &^ h(Tz}^{-1})�I=#� swy>� � PhiNorm} � lMk r6�! prod-'!l%\text{%�} E��$l=\sqrt{1-� l� A�} fromm�aB�U� for^_A-�W�Bfin�7 transfer )6�Uw�� '} T��F,�' �0%@endJ A��$�1$;� !�� �JF1)��1X% �mA�(operator $f��mapsto z $ in $�r $. W��+re! t: G as a-VieDmost obvious choicO an .�set%vectors:ya� �M �@ *N , �z�A.w�is leads� � whose z can be ex��s�y�terms�!*�$'s. How�F, �IEC typi�/y% , sparse: Allvn` � includu $he sub-dia ��,non-zero; it[4also unclear h� o extend%� �,to a doubly- �,�Hwi� #!ou!��very imM ant wheEc�%cas%�periodic� .@. More�Z��M !� ]c if%on!�f%��j!�j"Q r�!$t in $l^2(�cN})",An alternate� roach, duCSro,�al,q,Vel\'azquez � CMV},)stE� wo�e�6!Ah !�h Zi $ k �r z^{-"y �6|� duc�}�i"� �� \chi"��^!�s�! n k/2}�4e9� , & �$$k$ even;}�L3(1-k)6 3� 21odd,}�q k �� $k%�$. *p$ S6� 0$k^{\rm{th}}$2/y�%� >^*$, its� al (cf.~�� ). � E�pro6 -�1�2 instead,:e! a second2�.s:��9x%�*f#-�1/�  z)}= ��B�F�-6��B�.n� I�~natural�_comput���u� ]�1.N RNZrespec��t� bases����A����  "Q 8cal{L}_{i+1,j+1� langle %P(i(z)| z x_j�r � I�and� QMVQ xP |iXRQ$$` block�� ; indeed,B�ZLMdef� �=\�f 4l(\Theta_0 , 2 4�*r)R� WM2W[1]F1 32OB� e�� �k� �PV� ��k�� k \\ &&� �:�� �}enVA*��X��� j\}$A0 is is jus0�C}= LM�'�(%1�array}{c�a~ �0�01�.& �0� .���1 !�& � 6P.!51 &I>M!�2?>-2-3�y�k �ag6[>>X�f[_K3�4�>.� &�  )� % \r�)� ]*iV l� AWCMV��ieAnx]k�a i�tilde{UcC}]pML}$. { ��$roughout&paperq�2x rowSc�ny�f� ��� 0:� exampl�LL_{jj}==aj$$� >  e ( )�> $\C$!!vx")'us�S�~\�+F�e}  $e Lax pair&�fl�genera�b�w`Ablowitz-Ladik Hamiltonia�)zc*#~ _j$, �O&�proF54!d�.3 $k-1$ )�� �� Ew � &�A ��0\leq nk-2*cor��on� OF� Ar bP� y st� �the samZ:�� a�u identif)�&�2� 5t0�#,�{�\inE�� anq�  \in �r ,!HmPQxO �">�"J,of multiplicXby $z�!�_ � dered by z� ag"� -A�M��� C_f=aIf\M_f\,ŢNo�(at, since $�� |=1$�V�#v' #��\\��!6%�d�-pos as�dir8 sum!)� $$1\times1$ �cH H, if wApla�.�$!W!P@ Am�� tA5p �A�y� b"X4�$�7discardAn im�  $m�  k$%�fi�2 LL_fEE $!y�nu ly4 � k$ 6j �A� �:d9��tasm�sE�:� hierarch� � q��im. NowAhato} !�J:2�a,1 &l 8��  $p� ��a�� ey�A_{j+p}=m�J 4� .��#d9K sequAM�2�by �icity�� �ed}^�59 1?} DefE}&� E�I�fL} M}F#� Z\LM�a_ J L�(4igoplus_{j\,\, F }} m$j�7 !8 &> Zt RZodd}}�&jFk k%q3j �d�.�Z})a�  ( jvnj9 � j�o �tjFp�spa� \delt�}�� {x m��Q�(0 otherwiseE�6� E}�ll play&�rolvde�in�a�qts assocL'|.K}oeUU�>�systea��_V_Q�Hthebibliography}{10��Z� �@bitem{AL1} M.~J.~z , J.~F.~� , Non�7 ar differ al- ce&>.%�it{J. Math. Phys.} {\bf 16} (1975), 598--603.2�2���E�Fourier�1si2� J�7} �86), 1011--1018..�PTF�TB.~Prinari, A.~D.~TrubZ� it{Discreu$nd Continu�5] Schr\"o er SE{$s}. London%N emataJ0 Society Lect��SeH`, Vol. 302, Cambridge Uni�;Press, , 20042�@KN} V.~I.~Arnold, V.~Kozlov�4I.~Neishtandt,6�as�� " %�celes�0( mechanics,9" ynam�iw@s, III}, vii--xivCP1--291, Encyclopaedia. Sci.,Ij3}, Sp�38er, Berlin, 1992p�M�" L.~Mo�L.~*�, Five"�"^���V ��� .�!�Lin�Algebra)q0H362} (2003), 29--56.�CMVu0��Minimal&V < ��a�"� ��.T �4> .AU!nt.�$Deift} P.~ 4, Integrable H&� M�9B %d"� (stic methodg �* ��EaJ8s (Berkeley, CAE4)}a�3--138,qEL���, �� 31}, Amer a|., Prov��ce, RIW2� GGH}�G�Geronimo, F.~Gesztesy, H.~Holden,-���us=�� �D��, 1ZComm. P��]n�"48Ł9�"$1369--14402�SCE>�(A.~C.~Scott� Carr 0.~Eilbeck, Bi]pg!_�� E\n�����͉�U�� Scripta�4 �1), 50��12LR} D.~E.~Rourke, EleA��v B�acklu� � %i�}>_ igenvalueY�1hJ| A �3����M693--2702��&1}�� �(,, Part~1: Clz'T�'�G MS C\'quium���^if �>�, >kex�_ed Janu!@ 2005.#�2��'�� 2: Sm���W B�B1�� zego} G.~ \H{o}yEV�.}vL =}Pub?4 XXIII.vC:�(hode Island�72�V1} K.~Hani�( , Sy�c�� stru� �\v�9eiŎ� fun%+s ceeKcubic4 J�9� DukeEW. J�d9U81998), 381--402.?U>�8dd�)(al Gibbs�wt� r�7 p�r5�V 20011 37--582� vanM� $van~Moerbe�\9� rJacobi"� .��Invent�b}; �'19 45--81!�#>�  ! docu��} � a �� \title{NARROW ESCAPE, PART I} \author{A. Singer \thanks{De �<�`iedEi�(s, Tel-Aviv�F, Ramat, 69978 '�, Israel, e-mail: amits@post.tau.ac.il}\,,\ \ Z� hussR��s,b2�w �, B~s_:.E/\ \ D�#lcman��DWeizmann Institute!5Sci�8, Rehovot 76100� )/f @wisdom.w K) . } �K�- Centnde.��H@iology, UCSF, 513�@nassus A�7XSan Francisco 94143 USA1��,phy.ucsf.edu1< R. S. Eisenberg�6&HMolecular Biophysic�� .�Rush Med� �<1750 Harrison St� Hhicago, IL 60612, eE7 be �@rush�8 }} % \date{ 22!|May��1!@qUC[12pt]{*?�/ %styleF(usepackage{�$espace8epsfig� .latexsymFa4wide} ..float6ams�o,input{macros6% ~, g�$icx} %Work�figures.�yyL \newcommand{\mb}[1]ox{\bold� $#1$.*p}"�@}6D,ds}{\display%~: beq}{"tneF$F%*>&eJ�zeZHeeH.#BFx}B�xB�yF%yB%zF%zB%wF%w%�%}62emi}?1)W }{� e�-ne lem}{Lemm�conj}M6T,prop}{Propos��68coro}{Corollary��< \font\bb=msbm10 Da� bis.0pt 3ten6 \def\bz�N{zAYrR{\hI�b R�nNN,pbis~0zZ/ Z\qQQ\cCC,sSS,pPP�3��he�  22cm2 $width 14cm�E��t\ns�rsm�,�p!} ds#16O{#Dov0*�wt��tl!3 QED{�-�!�"!*=�expana> �=2�� \�![1�Aa}� \logS R}{a} + O(()�&�) ]�$is�lemA&�in a�rs;aN� &!��8a�&�0of B ow valv�.ata�trol a��e �+A� bN � Atechn` IP7����{IVduo}41��exi:� of a��m�; �6a�Eed �}d%o,;���ia��r,ri i��iM�passag�y�{�� (MFPT),M�/i^ � mixed Neu -Di� let �^5�(BVP)�; Pois� m, know�teTcorner size�x'��".�0c�� a siJh�5)@BVP�w���< M���prE<�=R%bee��XPh#Eliter�$� 3a few2s, ��!w�5�� ���)MeA�PA�couRs)�o fA�% flu�%rough�x� %� by u! a�,of Helmholtz-� }. H5H ted )��T} (p.176) ``{\em Among��eh ��/ nels���L�& must�4p�Y!�teue�s+of�5e W+6�iunlimiN plan�6llqMMes4thicknes�%�ma�al�S"F�5 suff�>"+a w� be K5Jn�3Y or��m�d���@'a�� ely �z "ta�!��e��iE�6o *quant�%''}�4 (�qly,U6'���@����CW fi�ei��ted "� dyn�a���sM BereAAn$QIwa�7aAI�I1H�},�% a�(-52alZQOE *�*�7 @���,l9;~. A"cm�'�of m�)g�wEo�5j�n ���e,�joint V!�*� 2A��a%[��ree+.[%ein]{Pm�AtmLs[��Vz�+���b s noJ��{p ,�layer��2JE���e� ros� cs (e.g.��� ectrif�6=5�%0{Jackson}), e�L)  (punch+�� = ��5uci16y, hydroQ�, E� w!solved,�(E ,� spe> �es�$�� !� vari� �CK �M sym�<<: M�l&�:dual s�#  ��t� ���at�)be ��� iques-@Sneddon}�^Vin�&dov�b 9" &O Z e�e��A�._A�6).�J"l9M�Q4 ies a�not donjm�m{6� attemp�9)Cd -� seem��be ��RI�Vdoea t?��f�ʭt�I< "& devi%1_DZi�isE��Յ<0Kolmogorov's 2\ I�MS77}!U�fM��8ss��noise Aan!��or:�drift mP a stA�A/ilibr�or � Q%e). Z� noi!� )�2�+�Pi%� 4ula� of .�Z � de)�%��H9 order � ope�>in� error y' mates (se�Q�bIlHTB}, Freidli�R�����s s exponͅ�a dec!M� %_`�ntra[A)Q�H� Oa'�ly ra�_xn6i32�Z � . Our-���iw@gUL��W�I*D,�5nAw� *� �J�.%3�,i�a:�M*�A�nU�a���a2z$!�/ muc�e)% $�, %<q zt K(e),j/E}Ueq` ��, �2�%C��%g�j �j:�(Y6E})*�v��. �MR��&RA��;5�de�K"�(sh�*� ���j� on  3 areaa� "5 >1mr" ��oa.��h&z z) * (i�he knew �/e"!HsM3A�Mg �Nn� omp ,ibl� i� � p %��  of .T.L �=) �0]� Sa� ���:�/ �ux�I�, t ��!peH6)�"� �ich g�� back�"�-�}��scuss� � Lure},&� a?$(a^2�Q^2)0@/�7� �"��M ���$\rho"�di.� �� e��.� � Fabrikant�V.� �s]�a�iN MR})A�6 &j�0doE�con�L!�6WyRX [a�by (����!7ert( of�#'s �-�req-me�"�j;��er�i�to�u)�1�9 Rw64M�D N�6[U!'@I�"n,u }ɖB�� *Ő�6e� Ell!8 radius $R&3t&�c%!jea�)a�!�� *�@� ay} �6�n��B�8"�>�B})Qq s booZ.#iY*, V�A�H2 E��<( ins's  1, 2� ��2� .�7k������ &�  $*9 =a/R9e"� !�!� �A�6ED8s"�Jbe $O(K�&�)$,�  a �, �.G b$ Eheq.y��+� { �j<��LqP%YW Q ���HJ� :�asY� z ball. I� &C touchm �g�Q1BY�s9 �=�or cuspn>����N"@ ��iio��*� )X�t��.�� �`isom$�imi�S�!� �er����$, sO:4[I�Na�EAN3not b�.er��P� forw�;�`�re.�!� ( �invA=g2d 9 to-�s��*^��KJ+�Jfu� p�. In h@  sec:M�}{� 2�6��!_�A_B� � /Ijl2^e�!�e")L��"La��toR?��q��Tl��l�ly �n"�al�9 5C/u�_%�6�-q�;��t-�`)��� :^F*�`i �a�>m�a>l�GW!�*H:�S�P�TX ��E� !1aWeum�~I( cY����ow�D� e� mply:nec�atar� a� thir�j�):j2)g~!)%uF�)��� B Riea� �.)���� [v(\x)=E[y@\,|\,\x(0)=\x],\]!��A  quit�a��0�Sh. }. A�+ FH� diam|>)�)��!� � os bUQ�C�$r!- �)��si[-*� in\��Fi �[�\��� cA�"�� betwf[ surfY2�A�5w� �M ent.� , $.� *A |Qa Q�a|} |)ll 1,$$�hLS�[ath"�!�H 8�]��P&�O2!; $E$ s�\fw��� 2�@ M �&&� \D�@8 v(\mb{x}) &=& d 1}{DPquad\mp* for} A� I�,�2eq:v-�8` &\noZ'SW6d0, \;eBR\e�al d_a�eq:�-��+-v}K:q�#I�}n�}�0, �n�-� _r, �@39W&�'%����*_. Accor�o�^ assumz's-�$\to\infty$� !�e�M�B� zero, eas .�\to0$"�#�m�� �=2�. � purp�p�o�d�*+ a"�ion� Q�B ��. ���$�-B� a� B�r0%a�� } To"�"� y$ *we�N 4"�  $N(\x ,A�\xipDOm.m,(���1�Q�6 Jr �eq�i�_{\x } :� & = & -�D�-�,N� .� �JiC,�":{}u( nya%�� � e|}^� \in>�, �6��6>Vl �7Fup� .�7ve��xt�Q>� �aAU -� Garabedia� bX,k" 9��h:%�Fre(1}{4\pi|\x 5�|} + v_S!>Yl,�T`$ )(��$p har�a"^of $\��)��FoUXmbE�&�. Green�Mty give*XWD 8& &!�t_{ VO)>�I��Vx ) - �� )B/�P ] \,d\x !71�F��=�� Mb� a��S})95 )�6�']� n}- 69 �`y n})*\,dS ���Zj����*1*���|e`t_{>�}:!�S.�Q�QOneA�$h.%�JI�J�q�hu9�&&bfQ�( B� g =�-vxP u1\ B>�F�: i�'6�^Nm�|1#�N� \�&������[ �-Ea E��"�v� �n J�Set�-� C&�aF�Mj��� CoPwr} 6�a�UQ-�$eq:int-repez��2DDN Y�Q�+V_MM��.:E�U1��j - CJ� n9�FA%� �Va� !�") �+dtF�e gQ�� ��B�cho� $�!7 5i��]F.�a,b i^~ )��h&0$&� V % } 0�t ��e�9ȑz5�:9Te�N�Ill�1."SG��A� �)m�u��&|  $�� $C$. � ons��3�&�,2��!~�|inՋ>� rg *^ 9$���ary$d] ta )"Y>} �hav1� (})n+N-eq1}[ _<ź�) = -1V) m�Aom ��Q�/n -eq2"]�͊}�cne��e�mirB�A��=] | ).b� |�6�:L &3QB��%]�E>1�N i�Y�,2,],n[#.�.��y?ZA�U��>x,F� ��� ,%e:z.q*&F�y�*. , away�.C�e/��x)n�t�+��2B��W='�nd�C���$C6�"�(z�!)B��� is-',for�ji� -�_ai&{&*9xin&N�%�})�1 alsow�"@1�F&�, beca�/>p�2._%�r(��UQ��:�to6�!n�g-int3e��Km�m�j&) g_0e�S}e�S = C_0NB�A2sB� W��)9^H�:+ $C_0>?.|A�Zc�Kant�\ Fur�)mo�0t4$%qí��a|tribut927e�we.�1�"P#n�--1��P1X:9é_�@frac{%Rx )� x -\y�$,dS_x = C_�RB��-�1C; �XW"� �%��*p;� mean 6�7�7. 2� "'x�,>i>ZBtwMkas la�;S!6*i[(%�}��%%�o n��a (!�``imag�' rge"�i�Ifa�k $\"�;�}fJ� � -v})�(El�\dC&6G2\pGH�"�QU=2'1Y+)�.expa"��1should b/ �;numj;ly�RR��E�<�.���55%9 �e ^ } W�k!�i�^�&,�!�2sB�QM5h5���1�.his�*�"R-=q �9LL).gNif�-�-sumK� �J{n[3 \[i�x�{a^2��yb^2}=1R z=0 (b\aa)Y�iJz &{p -� tic}���=j�B}{\�rY���}}!RjR)�a�� (t�b"�Za"elow)��� of, origi�-2iF�(�*���<�*M[# ap:l)�Top%�*�"���C!�"E.ati�wS}n��,J�\�a��-�&� DFU`�8!�M���"�eq*�) zDH $. U��@%J�i4�qF�4 0t_{-a}^a \, d�bU;ťU7 }}^{f-I1 g_0\,dyr�}]�.� = �\ ab N�J� %!�J��s!���J.U/"�9��Dab>��} H)�7��vKs!�2jJfCaXF�C_�GF�)�BF |A� $>� av1>Xb��B �B�$��1F�e!���E�b�L�\F�In� word�D� /&xcav��21$"�/^E�`ɛ12�F�E�!(a,b)YDZs-rB�UCI -5E6q*1&�&�)&� $e=0|K\""��{2}�C�)N��a) �m�1}{4Da}=._C1*+ &�3Ta� 6@�/i}B�!]^{2/3}� ��|}=O(1)\N� v"�H\ll1.\]>�-}� �d�a�=M6 WeisD#If�qmouth!aa�G+nel!�E3U(� ��r`.Z��Xc�6N�56 t(toAT��e $ ``sees'' Tcr��aN�e�;yG/�A� D an4quoti*�a# pas�o�0�; c fe�A�hd1)VR% $are illust2.ktwY�1 0 s $e M#�B&�ec�k s al~w9ur$1-J7i�7 squeez�&I�ei2.m��/�!) �l��G. Stegu�b:bK(e.�ia{�F \{1+ �F��}m: ^2 e^2 + 2!>H 35cdot 4� 046O $3 56 6>3 e^6nWsK\RL!��%�6�&r5�],a"�= behavior~2,\lim_{e\to 1 !F� )(l"�G16}{1-e�]=B eWB��� ��B�� a}e�`dV=$ 1-eE�B��%.�&e�is� bJS��pi�, ^2 \��e^�:J3;"H7J aJ�(S K2y�i Ia1ZQ| {1/4J� ax!�e�h�9��* #�9f�C�[4]�,���6�{4.�� S}N�Nf�!,� "�IE��.u[@23!&1C"a"��"�.���E^��siM.fp0�Bt A��j�%��� �w mer�, 01�M�! next�/ �}]6� 1A5� �m�|2�f�6�6�DX31/ou&�G&�8e[v{.�i"$*o�?�magnitudms ��1�W�0F�>% ��3�`.m,�0%�2�K:�BF92"��5�c�� 2}3+us�:o�a full.��)�W�b�=e LQ F-� �%�7R�,)�p-�G�-&H.i , JF.cap.Oa=*�  R� 2� $��R� in^2� ��;�c� Pitp@�=AD4@Yv2A �!& r,\t�x,�r)$ n�+k&11orvL's" MY���-*� �# v:�1( -1Z� r�ng|_{r=R} ��>�h%J < =s���h�*��M}F�1�E�alB*}"� r}R�)(>��-% ��!B 7 �L~BC�1Ρ�% �Gc&v�MLM hose�)9D=1$. D���cylindr{�G"�!<�o./:JHab|q~=q�A,F� ==�)"��g"�1�)��4#te�/"w )*} "V(q]]�-W>�Y� V�&9%A$Y�V� f>ev��(�%.f�]~ 6~ e+!/�>�>~B�6[*}�!�La�W5.g $$Jv= �1}{r^2}" qK6:nS(r�wG % v' r� )J ( Z \s�eBbf �� 27 u�s T� ).$$ef"�!$2�] f]s� R^2-�{6}i!Du?�:B/Mqkf�f c11Mi>�E�UCA�&6Rf N�"] uJ�Yw� $v=u+fe�e= u�*]2�]2DQS-�Z�� ]je"�>u�{�)i�R �E7�y58B�gN?X:�n�&Xbvp-u>�!�mCU��}R�i#R}{p�:�B�M��,i*y)I} S�c"5"�M sugges�N��a!��n(��2 a_�f�rxW� $n P_n(\cos �b/()�"&reISKKdre.�|,�3s $\{a_n>�=o�2bu.@q���*M1/=�J;ary-1}.�FQ B !�1 =��Ik B \>J�29 Qp.�bpmu�1}1�n!�B�!���RUU���>��H*7.=_),&A2}�E�B s&=<�����46�c ha�j6 <`r��r� v���M"�� ). D*�PB��J >LV.6>vA"u4s)Qu�FU>� (2n+1)A U�het"� G(m�ZC>� ?��]��2BQEa�J@!��4[eqs.(5.5.12)- 4A75.6]"G. H�9A!A> >>&�� 1})-5�U�����Z�HQ�I�c"!h�&at#ea#�Q@Yg.�P� ed by $n�'J46vWdHR�(sl-C"yce&�Eh make�8 task�Cha4N�f;L�Ck%R�P!{�X=A�s Zcm'�#��V�iz��c�$� N+��"�"��be]n'��Ǚ�col�G���� .�E�reC��VY#.��+!F�@1+H_n) b_n T_{m+n"�m}2n�= v�>D���Y >��22m�5>� �� �B?B�v"���"� ^� $.$ Ferrer'2O~N&�Erdelyi"qRoyIN $\{HZ ~Sn�NJ�$ $O(n4N}!�s $�F�da�G9"�<�?0m=j#A>�"&eqqY� vj 6n=�VT vDF�i��� F���E�O I� �.\JUM�piB\ 5>�a_0=b_� ����}{2n}b_s Ǖ�jр�� &J n�bR� .�1�:-�N�b~��6P� 2 +)]�j�m�e�f�N 6�� e"�2-"�͆66�wmO6 H_0=!` H_nU"I,\ E ���� L0�.Po��I.*$."�N�D��c��ig,�y.u6Q����:"��7q h�a~j�5�QfZ8n^�8q �Lat�� b_n}�qu!S(0^2� h��)�.�4 \a�m#n u' .R< �'�9}^$}!� HyY S \, Y�eqq SubZt�!� 5No,E[ Y$\E� A(we  or $jTZ%.��/ 18} q�= q�%R�0^�9OF3�m1 ))Q:! -"n�= �>+�$��^�G5�J���-�Z� �]B���" �*�"Q5�.:s�#g�YqYqKK\"em$To facilit�yd *�fs�&�Is��0$�Y $H_n'A��8n�w_oll=/*1\6�' termYQo��n�a$f �d ! � {\neq ��l�_"SWn*4 �[�h/���2�&�ajmt�e�8�Ia���E6�JNwg/�q�}_�now sum�N� 18O ��6A. FK� ��ll Mehl� �,>ڃ%��� *��� a%�'Magnus.6r"yJ��fM3\E#�"�H%ecos(n&fA2})u\,du�,  uM@&�j*#"�CZ �&3 ��F�B {\�2��u�H�u-u�; u -  � J�7$H(x)%�Heavi�?�� step�� . TAGU��!$u&� 2e Ň$J�&F�bNF.=�bZF ��F!1��:����Y� �Qr%���F���F.z�6k(,� t�o.'~ 5:� �� �F�Rk �}"#_ eq:5 e��9 Si`[lN,ZJY�E>�=�%^��W��>!q�X-4�pu. :"i .nzDE��l3B��0 ̷&2� �Z� ��>2� :6�Mv�ML}}.vB�&&-�� kws :� �^�d Rg�d\AbelTzD�q )�9���j �Sns� Whittaker\v-���h��:�J����J�){�FNF�36 ��^.�=63�uej��nv�_ble�Bst5lWBanC -typJ`8,��&�is'N�+"�� i��1}� � d}{d !"dA� }.� ,M umA6� 2EU�u}�j��R�>�oJ3&9h-H�� - �2a9i-9"� H(u��F��l-B� FV= -G(u,=>TɎQw/"�$>6.��z<)%!� �!,�� �� F�/� j"� �. 6Y�d�O &��.I�2Jk�G(\psi`)&=& =� ) {�(�[" .d M;9!� -�2$w:' }Y�G�K6 �#\z �J u�9� n� )�\,U = �0^� � � &��13�2}A! ��++-_0ps1*X RM-<�(f�"In,�c,%�c$�R�GJ�?u�:"|� eq�3),�v�!_0�F2Y IYf�A@��EA0 6� D2��1quJ%.� ^F�=&5��>�He;)!�Q�ps%��!�+~+E�^2 ���An��@%ʑ99�G!�&�q�yf�DG} � M�)V:��&&�� Jy��)Z!=RZi�v��UJ&�}�N�Q �!�NH-�>�-0.q��F�J�^G!� R>FY.� �.�e +M�=�e�_4 i5X2�sgV2ej�A}N�A�,�%�KE0i&#�RL-s^���Q�Q�Q1~�f� Comb��q�._0��`IG})>��y�b_0-exU� b�>�QdM7)�,9=Ձ�I,Yj }-1 m�vJ2�K2.9�(1):=�6}{4�,1jE� >V: :w \�R�23�)"f|>o�<$2�( $a=R�0�3�,5�# �[65"� �% Hn0��"�"�� 6b�oo�RY7�$b_j*��+a��Lif,�a�Ep� �:�&7&�`�M�<&�<�-rYs �eis.\��%u:|F] 6uDNcRJ[ >Cc�*�` n}}$.�f�blWet�xBx�ge[S�]]XnI.��:� 2W f�2� ��R�A�m_2�,� ֩�>LaX�g�U67)v\,dS0� v" ;�I%5 #>_� f_�?�@��x�� �!́�n7�8 W"� 3  P�� � 5K(u,v:Y6tB� j�� P��.g�e��) �v v.`-�"t\,!1)a% 2=Q$-�}�"*$66B.L \beq� 67dE!:& "� �pi}F*H_�son�A��CNv� 2j2)sX?=E�!~ }(v+:E\  ?2Z|%:'� |" \>H%&"R`Bf��f-ufjCV^� v+u-!J�k}N�`A�v-r+-u)*+ �Z�l]��.4J��jZj� :be,:�o E�:9&!�% Q68 q"F�F 5e� 5u��82B!�i�0��m�f��  j�z[.�"eq:68B72�#"F&w 52j"� 53}),&d66�A"6�w�� �yieldJQ@Bc%-1b-�Zb�-��ZZ�}���F��649�I;�V�V}4f�>{$��:�-.�.�&������>����-P*] Q��� �9�z�5���" agΑv.Tsn�O� "V�5"&��$!PF� ��J�I�2p��"� -"V�&� %.}}��8BQ&r ��"� h-g-K� &"6��� �U5%�_]62BBkIe>keV�)�0^)l-�z�-�!�0>�0.Y9��)1%e26 !66-"�6�A�H���wOaN$&�ͤH.�aF�]:T �] ���N9�U?u !7B& V`%uJwW7ynJ�� J} J�=d + >3Bo:� a)�\��1noFredholm vrbN�J(� v = M(uF�� %�f�y?)$*�.4N�M} 0^E�.�\�WG(vpv"+�:;!eq�� � B��( $J$�F�b:ENiH remad�x:��$ mIe�\6\6]-^�6l2}"�c*E �*�;�)z&M J�Gny�J�H)"�B��D�.�A�e��L� -�2}>5+B3EA2� eW���u'�VuBSI�$JE�N�UDq}9**<Iw${�+�����.$$��r�=b_>�4�.��%��6�O.+qk),$�:e*T]ݎi�:�aI)v-u�\co�J.Ji�6-!|6a Y:�2 ��3 >"J= �,M �|Hn0E��-��r�Mntuitwp�4of� >TM7>Tl ��s� q��-e��2�Glogg� hmic"�`�V��% $$�rYn67}))*"`� $K$,�!dRrKf �bF%�`f��B\� ��[0.�"]M6toR� ���)q ap:K�}�10n]8L_2-K1} \|K\|_2A�qmΉ30}�RA.�� ):�B��/.Su�T. Better�"�x��;x wXNttl��Qd�N�C�{|�u}�ey~ �uB�/E"�/�h|J!$}�c�!GQ E��C 6ɭbeR�I�N$J = M - KJBi� triaMJinjlA�>FK �-�|M���|K�J" 7B�k toge�c�4%5f"�M5��J%fu �� �lTM~d��$1+�.jH+) O\JK86Il FWT���>�:^%�$���W3Ice�P6&�2�a$-.?2ev*�kker�Y6�Oe1n7K-0 0� �K* v � "|: "�9=4} uBI!lby $Zg�"rR����p ��_�F��pin������piKM&�EI� 1}{n�" ��2?Ku�pi( J, M�vN=*�6 FC"�1� �e��(�Dv+  nv����>fK&Nl*2 �$�_M, Ao) ��.�8� "�MԼ�-�\� }� ׅ�I �<-�Q*&� I�)�7U�B����/M�/�0�/�� �R 5ϱd�)15)�N)�J.@%^{3/2.BX2u F!+&#�U1&]�,�(Y-),�r ��9�Sy�U|J ��f � %^�oR�*q�\,��=� e.>O2� =C�)�0eq1&�3�6X"> 1i} A�Cauchy�wartz.fa^� J "� pEI0�.) |FO��L T5du-&|M�Z� &).2Mm&:�B��=ng\+_�u6�U�h {0r�b-final��-)6pi K y��1+2�& �:T M�$2R%�DF�"�Xe�[̊I ���<�w5� ��N7j$a�JZ(I+K)3 F�h*-�5�"� M� $� <��for s"��ly(.� $,��B � + �c8 l Q�J�us,~-JB M1�6�q�*�$�$�6w".YE  7M�"n�( &&Z�a�I�u�=F+�+B�90y{6; �F\,�,iIJ��(� �tL�D[F� J���mi�.����$vR�^3e�^2.6Q �]*� �21}Fh��aPδyNas#q"� $varepsilon� \int_0^\varepsilon K(u,v)\cos \frac{u}{2}  8v}{2}\,du\,dv = '1}{\pi} L^2 \log 7!h} + O(P^2), \eeqq hence \b u\sqrtx pi}{7+\sin.u} J�J(u) � ����$left(b_0 + l@2R^2}{3} \right) #[v��) E].��Now it follows from equation (\ref{eq:b_0-J}) that % �1n0|\Omega|}{4a} �1+.�� �,].\label{b0} � \subsec�p{The MFPT} Using the explicit ress�8b0}), we obtain.>� < center of8ball as \begin{1H} v\bigg|_{r=0} = u2+-�%�6 !'1�IF27)�1+��55 \end{�,This is also�averaged-por a uniform initial distribu!jaE� E\taE�e�1}� M�{2a\,d\phi \pi a \theta  i�R v(r, ) ra�,dr =m�&-R:� :�=&m�\QODSummary and applices}M� } AxTnarrow escape problem )KpBrownian particle leads to a A�,ular perturbd:A|mixed Dirichlet-Neumann (corner)/(with large $t�smA�E Q� oundary. � VU,e� arises in classical electrostatics (e.g./e ifiedA: k), elasta� y (punch -& s), diffue�!n(conductanceA�\ory, hydrodynamics, acouOs,2more rea�ly�molecu!Xbiophys6h was solved hitherto mainly%� specA�0geometries. I�is paper�0Dhave constructed a%Ёr, a� it�vary # & ~� i � E &� �,sb!�bso�� o minimiz�  kine��gy� ��gJ�A carr6 out!SI(Kelman} by � �Csam"l  gave!Z�I>[ �; �a� W5�Q �)�heurig  means,ailess tha��per!0� i"xz $ion, based�D Fourier-Bessel re�en] on��porA�as� e � �f%2�k >  ar endk2L� sum 6'v �e�:.:U�C�T  la�� be�y��1a� -dimen�al1�)Son~ f7���$one absorbend� %5�-�{ ,a volume $V$)i��h��v< MFPT�� ��orm} ��m݉� V}{4*� D} + Ln2D}"@,-extenaJE �.b�T big Ues)%�Ed� � h:~s)�!7�!�) $V=\ds{ �4fR^3)� � ay open!p of s� .�$& ��th]�� Y�Aprelevan� �� micro-"� s, s�� as dendri! spi�in neuro >yjd�!�z � for I ���ot ��a�.R hea"�pa� ue .* neck� n@-- coupl!)�PNA��AMnvV�Fi��ofa es5synap!p& a0Malenka}. Fork ��E�)kuseful Q�L pre@ of�era�t�*confir���6ve,ѾjP1.  significA~� �ف�o� vid� new d� i19!J(forward bin rat!�n� Ar Igir"� S*C.F chemx��is re� )�!��� a gi7 p$ Ubo5, A'p h�bs� e lo62� # � 2�� �6u�Ou,2�A ula� correspo��;�Op%FF�i� Љ@ immer� �f�e diuJ u)�es 1" Pq . But� 9xreaII-�."e a)[;�con�bly�ewx�WE !1�&� 1asit��d -|AU� ([ k_{\mboxarAy}" �  \] ��to�5��c$)$-gYq.9y ). %�  ��endix "�E�J |K\|_2$�ap:K}�zzv� .�.�A�kernel�� A �"�� F,A�( $0\leq u,v��$,a�"���"E )�eq:67})�� q K^2`  &N& F5 pi^2i 1i (v+u)\� N  2 |��'�| )^2\noI�\\ &&2+& er{-7 |{ ^{-u�{�q FurDms&�~ay*} &&"�v&�!*� ��( r�!-:u�int_{2:9v}Esin�p�)b % x `!_ ,dx 5V )e \ & )�-/(]6�.\-:v `)x�Z�v *9u!"q ^%I|v V!CV�BT�5�andJ�%]6J#n��f)Q B� �)�v & = &.Nm=�12nZ�Ax z!�Yn^2!n.9�B SimilarlyN� &&N c"O$M`6Z%�|% m�' (().�x$Mo}B).Au�!%�]�) +JH x.�$-u)VEI�� ��l && 2u-Wu + 2:S :"J"UlI&($ᇭFR2���t)]) %� .� A log^.]���%$� u� � crea] "��N G$0a�q ut, e^{-2}$. Al` �]>n} l$eq:L_2-K} �a'!�&��5& 30}}(#]�Z )12T&}\quad"� .� \ll �,6} w~ ��1�v�� &�lli� pa��%ap:lure�v W�est�� 8leteness, Lure'  }&�tL!�gi!FU� �e �O� . We� � , $\y =(x,y)$m$ L(\y)=1-��xZ a^2} yb^2)�(bE-a)�$0i�duce p� co&at�#d �se $\p�'_a�\x=\y+(���c%,sin &�(� orig �v�$\y`!1" �� eqR:�P y7-[��{�}�+g_0(\x )`&4x -\y |}\,dS_x60�\pi đ�{�?`&)f4*$\tilde g_0|& rho}m�L iy7�� $,O$o!{!x#'�$�A$�v 0� 1�MPdir�( $ �$. Expa� $�)$-pow�� rho$��fi,atJViyeq:rho-eS�} S Y�(x+PY)A�]�(y !Y)!A�= A� )-2�'_1H -  2 ^2��:R &1 *�x�}�}+\"�y�}}}%c $ nH�7H^2)OFJIȡ�Solaf�g�cJ6M)A�I�ak�#Apositb root%�>51!'E~"E+��phi_2}�>\{-1�O[ ^2+ 1 (-�!� �? *^{� �U\F� ef �fiy(Y�Q�*Y �d.���$ iqd� )}{�� � �F��!f��^c"�� �d&=& 7jf$ds{L}(\y ) ���B�QӅ� g_0>�& � \ � Y �� J�p \,dztEpYy z} \/M|z}}F, Situ�$se�Iz} 9m� set&a�si)w} 2��!s�e J5�� ��=b�:F� %�2}}1s1M \,ds9= si+s131-s}}=F�� G2:�~ 2\arA+ � / w q\,�.0^1&� � .,�I�.F���(\pi-:spsi�h� �� j6� a< �E�h��q���}}� �.�Q �y} 6B�:}}"�1n�*$-�$ �+8g]ig�'e&@� replac� �� +\pi��2 �� it�t vb**�\wV-m1 &\iWҲ &=� \pi )��2}6��,M>u@5��nA �&�/=& ak b ��xpi�}m�:�1-*I&Z_2r} |N�UB� K(e)&� K�1�� K(\cdot3 s  x ~�5V� kind$$eEC�`ec�!�/ /� Y e��� %J }, � (a>b&P:We�_#n �"�K� A�u�  y $,�#w clud G: -�tic F�"�! ��(�.&�A path�" example~P}�h�&z/�/xm�"��6I/a�G,��e� ���Oc�es � �PI �"� area- � de 8�0zero. However�x does!�Tessaril�1 :9iXy1(he �p r!� llusZ,��6}-r. Consi�!a"� �*�$"+$�>� � xr"� , excep� r on�A�'$s (at $z=0A�ay)�B�� �%,��'%&O.!7_��ea � Kluw�} 1989Ni2^iv�ofz � ��Their6�$in Enginee},�9.@� A� Lur'�Three-D).� u� E"�) }, I02s� $publishers!�!x4=Vi��(dov} S. S. ��(D. Smith, EE`�� Canon�( "Y in Sc|-� !>� , Parts I\II}, Chapman \& Hall/CRCE�2� DZ} ��Dembo;(O. ZeitouniM)LaS@ Devi� s T"�<2 .I}, Jo�+� Bartlett,��199.}MS77}B.Kk�0)�2��� exitH+. $for random�:6A,(ynh@al �;" � SIAM' �kh.� bf33�C�(365-38277.z> 1} W%� � On some   se2@"�%�ir .+�3�98A�s��)oidal(5��A c. C�;4idge Phil. Soc  57�$p. 367-384�. �2J�p ũn2�Acir6 disk@)u6  i]J!ea;&d�3x�"F h2rAAH(p�7�&� m<$ L. DagdugZ�S� Shva�� G. H, iss, ``Eo>e[a�V�<0aA�<1T J. . � 119 3 12473-8 3.�S�} =>  !a8i�,�'*n e� ial *� � Siin!�babil�AT�Z9s ,�J 1980��8Garabedian} P. �m�!�A{.�.} � ]2�Stegun�(Abramowitz,�'AT dHandbook�#.� g��-  P�-+uA�7.�ErdelyiŜErd\', W��4gnus, F. OberhA�(F.G. Tricom�� Table%����T�@X!�V*3�McGraw-Y@�5.�DRoy} G.E. Andrews,!hAsk�R%y-K!k.�u� Univers!�P�3�h.�M��~ N�E{�0i�E�e�8B�>�� �Chelsea)�sh�CompanE!�4.�W� ,aker} E. T. ,a�N. Wats�;�A Cou�8$of Modern "n ,��FN|7.t !�e} B.  -tI Cha�?�Excit!� M�( U.~Ravaiol � N.~R!�uru!�� d*� y{:�(G�G���}a�m s: effect%charge d*�NA�!Xtri�4 GH�T poriA�q��cu�7al &C�  1!>(p.~335--340%D2�EKS} R�9�0 M.M. K\l oseM�*� .�as �@�6u5:.� trajectoE��(�%6g?"� a�Bi  10M�41767-1780 (1992�69.� Z. w K�tiCal�9�v!|den^c�9�� �9�8S � mr��-t8�T81-91 �P4) �x9R.C� �9, J@�P(D.J. Perkel" A. NicollI�F7p��<8o*��:on "E�mi�R--�role in�B-� p� �TrgHN+;sci�U1�A411), pp.444-50�489�>�Q>�. docu�} η\c�[11pt]{9h} \usepackage{epsfig} \setl�>{\texth+Nt}{195mm63Damsmath, amssymb} XHewcommand{\Eins}{{\&ba } \.!RRb R:!?ZZZ>HHiHBXUUUBpQED}{\hspace*{\fill}$\square$�!�End,88 >�Hom >i=idBTr; Tr\,BA<AF<i�-m�<}_+>z�} " >!inv -1Brest}{\! ��%e.today}{��/�/%%a�|UQ�8} \title{On Lo!�B��CFT \\� Non- �  ,$\footnote{_ H@�Ad at ``R�� quantum fP �or��os�> n hoEof�2 Bros�is, JulylT4.} } \author{Karl-Hen�?Rehren�Ins.) f\"ur tisch�ysik, &\ \"at G\"of�i\\ 370776Gly,s$ e� tt{rw@tie.1SHk.uni-goe.de}} \R%qa�)�a�<ct 0"�;N*H�^l%�g! �Q�al6\)X{ (BCFT)%āar�BGA�M�s review?O �vacuum N's�!owFx% c9L ��u�NpDously,#��<ed. (B�Ij work!L�O LR2} R. Longo)�q5) {\�A PACSA<3: 03.70.+k. MSC40: 81R15, 81T0 40.?"c3I 2�&�� {E$}{0} �@nt�W$ highlightUCR(S a��R;A��#�!-�QFT� i8c#�=a�9.�e O(re;S; !�"�!)�omT�� ze�y�ne� half-�� $x>0$�two.5 Minli ) -time (`` rQ�6�'' orE@� short)�CrUQ3 I�2�t�E`,�5�@AonM�chi��Aora!e(``" � %y?ise x#E #'')3 vice �a�$ is f�may b�)garw?{ ``�&" ic'' &oyϭ ��oe�in )b%a"� s.�KA q<�Ked state�%�hFov�# fPing: A �6��2�DM_+=\{(t,x): x>0\}�DI@a�Ealgebr�&-W).�!i�L)natur�# io(if�N� � e& >� i.e., X���}� l li+WRA�\ fullIjBO &>2s � E(W"�7U, but-�v�' ��A��7� �sub�yA'A%e��every$CFTlr��] R]"�A >g,�uc� " ��!�!� $. U\Ia(r $r1�)W cal PQ�%rMf%%1�s aRK��Ees �h�!�&@AsC�Oth6N he l�����xim!�%�HVQ�97SR�Wy�D�PHilberm!�F�BqO,-t��]9�[A�[A1bd),[a�� %/U1uCFT>K$is fact gi�V fres�Oti�YtoBAV� . E.�[oar�F=%��i�& 7{* prim�+ob�s, �H!�Fr�(�� igF��H�L�cu !�ul��nF��L{+�Dd %�j sequ�a�!�Id%�'�)n�ir!�-� ). Whil\)F�.�amMF+aeX simp� �Z]2.8) bel�Pa�pro�Gs m&bEIt �P4s out advantags!�wap"y n::[ �*.% (m�� p�of X �9> at� d��p:A���8fu!:�.b�(��Mod'� y (  B,T}, see) )a �Zto empha�J�X�e�wV,organ�J -sA��9�r�arg�� focu-�_!onM��"� Am �. c�.rplay\�X9>8.�,1�than do2���Lach ) N .k �N6/�*&N` ���<$T} (briefl~*!�e�Eap;FSJ �O ��t���| Sic2r�aD �H}/ny � + (great gener6^ y ab�U�%;eIW��� when %�eZ�[slF�d%Qed U.& in sui"*� �Oconju $I�a" v�TBJZ% promin P14Bisognano-WichH (BW))� yEW}A'�]�Aw�0mM[@group $\Delta^{it�:&�)���on>�A= AF a we/ �E�= ��Pincides_ unit/X�YLo� z bo�� rv��j, h�Gf +are����e�ŋ�avreQ+car\'e) (i�1ing�].&�$�#Aagy�_ trumM�W}"� ��a���EH)�M�q9KW}��;�Oc e��:� Em�A��3�&� t wa�aun�Jb���) �GL� Fo.� de#i�s� n� v�q��W!9�d�!@X3�B�y�&�u�M� DLR} $\ZZ_2$-�/u�(� fermi�)� 5�N;�[erty.DA show��!� � �TgZ&T:1 CF�en� kseA �� "�  ("M auto~.� %�)I��]M 1_P37ex;a��'3�0s tru�3�%�xhe��ssu"� u !a�!�a u tern�$mmetry)��: �VSect.\ 45�e9 �>u,"�)-i` �"ew e6M�"� s�]U.��``nim�k'' (N neg_4A{ger�brix�8._=U��rul� %,%ly�/ ��� . By:*�-��tAJF� 8tZ;`a�''�c� EW)� wer�e� )�xis:���le��a�ca%.="+�j*5�5!� �ex�gAewd�rPGir�c9��str�en�]c�elism" E�n � Euclidean� A� �al "*�>4 ogou]-N�[wi�"�ideE�6remark�q� %�iri(��GLs $\Tr\exp-\beta L_0�A!�ir5� t�[EGel>%@aB� h�5N $Y([9^2/a4)(L^+_0+L^-_0){Zin tempere,1A pairk���^�P%!famil� F2-* d im�� ``�A] A''-�Z� �� &�A�icY��ZQFTn��F note-Z!F~+, Aby $I%[ J 8set $"X8t+x \in I,\; t- J \ICIf $I)�$J$E$� ��|� $\RR�5�<O=m�  e��Z :�Y �$O\ n t M_+$ if|>J$Qwis�TM�\e��!o�%), ?eriant�|! ;�IM\"obCimes$ (��ngF $t+x- t-x$ sepaoRly)��r���Q��3he diago��u { �will be>�I�ius� e1lf�-��7 cer �x�T, &�k�Yss�tensor �Zon�#*�/s. Du�* condi�at $x"9�lef� P��� $ coalesce A��p3"�"f�>C^�#J1^Iw . LA�A(I"�G'J\ s�n�0b�hl  p=6 sme�f over%��A� $IQ�A�!��cln%-M A:bmgn$$I\mapsto ��ea�ga �& �net�  $A�=I�!;UY�(in ��d�aSA�!; circ4i�]" e��embed via a C�4y����)� all# forth�um!v� 1On%�^ �om�K�Pal�Site{KLM}kit$;split (%�8\vee A(J)\simeq%E\oe��->��!�ith���� ��s"� four-1�!� or�\�G:x,��str�bada� ��LX��1��-�.�" ��Q�&.P.o Q��?a_( $$A_+(O)=%4 5I0.\eqno(2.1)$$[!�ula��)�e� at �A�AJi��e�s e).�%�--�oaSB2=A�E� FI \cup Ja�� 5 �z�5����i.; beyo� hqGsx>�;JD IE�Oq�B%?$ �A6�au$#�� -s�s2 "� �o�'2Em��5n�$ reducible!Da:� A'q$e��U 6� $\p0DusA \pi(I)Q5 �U2Iw A"�f;�u�m�%�a�|.4 I�1�%`6� mquE�h�`��?� :�%uN��-u{��� (A)$&mk�( @n��sR =5� acir1�"6��BB�(``��3i�$'�Y7alq�� d t��1_t)�� � (Ms� Ax$)I�lyM=tm�tX.�2�%y y>v:`�8net. Our aimAtov sta,a�: *�kŮt (2.2�I�-�*| �j!b our �ha8s�sa/<ter�>f ()�.�)͖��}�"-W��̝_���=�}���aNdA�ofL�y�(I}�(I)��3a���:�sB�B�a}$B� A� ��z%�k$B(I_1)U mmut�+i(I_2))$��� $I_iO E�.i-.s �}i�*!�-�s!�3)ś(:��c,�� r�~�q (2<su�s�\6passagk2�As���"sa!4�3basic ��s: ``*6''D``I ''.&�����)�!�(�A�Rs � : )�q�� net :��s:  ����s a4�w@bM�e��E����u d �  $W_L(I)�6 M_+:*C"AI\�M!�a  DR(I):= L '$ (2�i� E5 causa��mpĺ���%� �kbe)Lyc eitvs, let '(W):= 9Mvee_{��W}��i�U=� H� \�0_+z i�mf�oby =]H���V9Vs,�pQ:=�)$��4� OAY�mbei�-we��iM$��e�!�:�'� �"d� $$\ � �!�)'\1 5�� we s �ur��|�A}c6�`�$. Bot�rq2s $B=�# or $��~M��7�� $A$;�%�[�i�n)z��B %NBV.�bal= ghDs�A6�E�' ���&� B�~!��Con��! let �-%�T�"� B$]�E .s �`a$ �DJ=(a,b) < I=(c,d)$e  $K ! L$ d[ATe�va��K=(b,c��nd $LHd2�}ed�} *2 \ind(O� 2Ac8:=B(K)'\cap B(L/OM_6A_Ev�lf�^�#)� b| %Ohj��.� 5�!]t� 8satisfA ��:. �$� J 98 B �D On�&e 2� ��3�/!Z�ngq| . \ZCp1.0mmbfDem:} �)�an�"� Y#ofA�� AFI�= �T!$\\[0.4mm]  I(T1)}Ab�{E��M E�.F52.5 (%�JBN-3-(.S)!� = (B_+)�,$.. ���,!fa@(T3�͓g&�~ dly:� ce $O'E�Iun�on�dźI�F�ie�(O'A�_+�zw RM�nA��(O�' O')'"= 7A��� �M �%�dyI��R�o�M�f 4�;N it ��a&t�>�9wnt� K@7f-�/ AXus(P� cu�w far-f2b9�,;����em6�EJ Coro�y:}M�(CA\EcE�yv9 ��ity�)� W')=%v�� 0$WJdCA� jy�"o%oj p%es����� some4 F�CA� \s�5!F �!��% R� a�GR.�F �Jj4)}a�%^E8%<i�v��JG5)} ��e�$Qisr:6 �/ $B7e�$��&2�f#q� �(=_)� Eioa��� �ne�'nd��F�:5 Af�7val�!iuT1)!�w��s. A+/obv.)�(T2N !�3). (C4\�y,3)"�b��'�[e�.U偅�pbeWy (C5F$�A� =�*�'�, �� s weÆ (C6E1�2��~}akg,3l���%,e~J�,�(=k $Aa6���8� (B� !�co�l�5.j ��.� 7in>6X'fore). �~re"�(P"�'- 2-��-Fk+�a8NS')#:e�!�`� �� tely de� �>� �*'S�33'��BA.6),:9)�6�'612 c6"m)4n s�Ba��R5� f)� �'i�e�posses���Dly 2s~�~*��Virasoro R� $c<1E� !$SU(2�)D��s� �:/��e�B�s*5#�-M�KL}I�" A�s 2t1a ed a�z!�s�|�(�� A*��a.�i me�*Q�y _+)$"*i$yM)�;,�&a#7(O"B 2��nbyAn8)e�)��&���l1 2�%�� lso 6A�We?n.A�*�.uaXGof lemm!� # ofH0or�})esF0ir ownJuLJ:} (Al�2V:�dsPf� �%� "?. A��Y�z6� :&�9va�EJ. O`�,I\�x �13s1�pf?$"f�.0)�cso![�2uUity.)B{ LT I� O m��6{�a) ͮ"�F]�G��I �.>7 Lq  B$)nd�e� :IW�Sz�� 9�,nsAAB&�yt1O$�e� 5' &�Edi�I`� �f.)B� %�=z� ��" bigcap_{K�L}[���]g � [N-,4] 4 = <$F�; � �!e!�a m�0]� I@o$C�� �}un��*u'%�inv>O! gauge� �K Clea�mTs�Ni�w�5a_ )�?�&.�B�� A�%!�J� F�,Q&�%r� k.�"� a�}34 G)\to C F� L[ ����:t� �U��%1 ��$�LN�7� Zf��H!�aB8 (3'� &~r� | L4--L6)���9 t, iH5�'e.=���sa�"8 �я�C6= ��sId!��=edl�9pro� o%�Ns > $\�� {Auk%F�8)}6�B$ejB���t1"M�q��BW̩.eP$�]J}9 �N]B%ޡ��*.��� $B$ :r6���1 ILP}�&�% 1�1loy!mfacto�%or�ch�ms  �Z 1��r1�O�|;nd�$ iwtU-). Pro�#(Lrnd (L4� f("� �(. (L5--L9)�7 oke 6�1. �fg2Q9tep�vmj:1 ferra"�1BP�wE��-�d�uL5:L6~ ū T�aki's SK�1b��9. sta"!�q0' V![>Eac�Hz.� de�+)+2�n��� �.�I Bor�Hs'��mdE͜ ons:�L5)�9�O2� ?,_F"�'$(a4,i�)�(A.I!@LJ $C$, 7�8,*�:���$���� . Sob�a2(i) $\R�=a Q_iAzN�(E5�&�3 prov�� im. (L7)AH�? N? �mF)�_ in FV"XA��_� cocy�H��  tri�01,�&$z(t)$ -BK -qCMicl%��<A��"�2M�=�!�$@#�/{�! )�- �b5 �6��� {��I7}�� a�P�,I$ (Reeh-Sch�4eE�orem)�. � a�67��in (L8J1�!�G&}�F^z�� �Y� one-v*mQ-$\Ad_{!d}5 �0orphism�G%� aG.��x�!�!��av�&z�%�*n�11� ( quotien�9we must\�^z=��"x �4 I0. $)���?I&MG ��A�A�w <K �j!|=�8N�8),�s (��Q($A~�� ,�!'��. .N�2lA !4e�n �v ly. (L1--���A $� v}*! �IL� R}HmI� �Ew�x���wa�k!5g&NS!ncq�64f�6q (nam�di&B$ $I$�m_>k"��\�5��=ݥ!M��c%��2�v�*k)�mm8�WC�cis�j3ti  by w�Jng7)�6�K�ap�!:Lb QED A"�way�3E�.�^�vIr(on (assemblon� "'�*,cc2<!�����4): *^�Pro�&�PT2=~E��'�A~"1�� {�IE}^I:a�"� F� PZ"� ��;���~��k(aɰ ;a�%�E&�!7BW�A �8e��_�L�%W�,F@ �f�*�,�J� P3� :�is up�� d�9��:p�| �6R !�N�c��iE'L4-L7aP2$�%,*��f�*�� 1O ~�EU2�n� .� �'���&YMvl%)ec��sw<a cru�5�=B�i"Q)"V�i�sU7 pri�`/�s l*�(� .uYts 5 }q*� f>�(P1--P3��y�a�ma�� �%a����*�6Wa�� z"�=���yXs'&�:9velop ���q/:=' B`I2� �3C�v�1CF�1�6V:���JCHA#"�J�żM"un�XalW 6A�s_(kit*֗$ !�-5 *�)��A�:!C9A:hA��/vm�/e"o f $O%) two � like"44d 2�'��to�)each  �bWne �0��.�#��J'?n�by�4 2&<�._1@)V_2iO���&�0)}F9� Haag��!鍌u�!s��~�FC1��Bu��no DHR  o�).�A��os�i�*���&&� �ev2(a�* !�J�axen {�0rue�� eCB .�� f.�,M jnzu�j$�'a/, �#"'!��)8ڑd8,E�q� �A[f&�s�'i(A(K)I\L'"L  �"� �X26 GI:(< dJ))'. $$��:.%uAJ�,!�raK�( � !& ex $[B:A]nd!�9g�<&�G����i4"total BjM�&d(\piu�mu_A$@ = fi� !!�he ``"KeLQ(E�up��+b� catego�8܈"suma2��RN[>�f�B $A$. H�o��[J e.Hi�;�,� by J-� �A��� . 2Xs�uia 8�+A�� d C9�!0cH3�A)�prO_z9 ly o���[nb)_ �qBy�Gi-�Ra��: a�(E2�2E'n$�D$Ee����s'j��p�%��"(2}!M�h GGJ$[("�& :B_+A��9 1��3��,%Q%a� � 5r2is bi-i� �.x= ��f 2�2!�n#�of6[?  r� :�.a 6� �E(�:� �"�A �f{2� - �*AKe� es�el�vBA�U��-+� �% I����7 hd5j7 si�>��a�C tertwinerA� $\sigma\;&���E ��bU�$� �ce�h"[�� �%(!�2�,MI� ��� �$Ea���\ $[ �]$v>T.) �]>,9!�p��#�KorX09�&�G%[A�of�)a5�sq� d�)Y"e5*�.``M� vertl�Aors''�"b7RfF by�^�a �>*�n �,� �MK:�! .�,ET�*he%�6�>�uQad�[l-96]n%describA1a: &wm�B $Z_{)�,\tauUI-(R#,RA �R2}��9G�� M *�.e%lcKoI�cZ2�>)N�2$B_2$qP�7J�A (wZW6�8�i�/8?2+>� $Z�4J�H?�T.d�P� TI�ioM )CTP�T�u ���Iаsub)netA �3 suffJ��&ar away�A �N,a�� )A -e ^(�%s*U"��s%�s)i"u1Dxabs� �$ /dW.�E� "XN~G� # E n�g{��r lo�� a ga���J{"�@:w. �can�I0Ia�6eKHE�E�q�x �&\ $�2"ME>���b$�a d /�^�;s�Qi^{ab!�b� l��s $�� b$ (*�E"5s'') run�A!�A� t -E� 2�V 3 !eyie�GA�.�* ���a�'�{+,�. GY�� �$n_�^����.���!�ors $['](-[:�%T��\5*� a n�X�k�I'' ��I%h:�I��ae$�  $$ n^� ـrho %`$style\sum_�' N^�;)}\;3�� \qډ\�_"�:}  n^0%K=\d�O �14�@In2�un� $a=b�Fs< i�� s �g4�m�)�.)��e�=k ����iE9^,I ,IfBQ2&#( �Z� %cA��$IL u�d�� �12�Y;�n�a��� a\r*@ b !"9 i|V[I }� g''N .[Ie>2�st�o�c ``ac��),!F��R���wBE,�:dF\iota2o&�-hom�sm *:x�� !xB vau;o:WU�qr2Js K� � :V:�  ru(�F�e�� ^X!�e�(�)�!�|"b.ce-A[a��2�-sub.s&�aA2� $�K:N!+M{ 2,6? ( '\� \alpha$��J� ?,:� .� � $�c(o, D):=\{t< M: t (n)= $(n)t\;\for�\,n*N6�\n��metry�a $t^*t=1$;� �Rt^*U$. } $ � EX=��0&� va- �<P5a� $a,b$�!��  a6cŕnjugate^� �ar �:M!�#�fU; toNi: id_N)�D �%��(M ( $3&#iAUV"��uM� 7�am> � bu�a�A��> / "�#of) a��.� )�᷁ >����/}USB�H�@A$ guqlteeaX.�v0�ECgloba�Y"9s,M�tiGof2JAsub.�5/6L t� 2�� "la �*�$!9<n ��.dimi� rho,AE5~) \� $)�*  no(4�F  ni 0abo�G!g�) � �0e2z�G��c�vR!� �oSY �now1�G$��alH 6�)�9(RKLR}�4re1 a 1:1 c"� D (u��2;)��.\�i0�i psx5") w (i)}.J*..-" ��* ,�ed�Q 6~A��B{>|"W�_1=.A(IR(Ak��$Y,�_0$) �"� 2��=�-NZ M$ fE46.� �A4���2��$�n�"� c� in\End(N�IA�V���E7"� EM)�Q�:VG .} i�+B�^���� $AB�_0Y.�Mo��ly l $[Cor.\ 3.3e0�"4]I�6�3 ��Bv{:A��B$����= 0%)�._* 0��!p,ngM�NKA��AZ�.UT)9�5�0��>+Q:B�A6��k_{U }:�_Mdto= �Q_�(}՝?,�G \supT!�IN-�=zEWAS%J�o� >�E�@=]�\eU���d#_)�z2�HVD� r�y��!� btl;Rpi�N� �p�t��$�#T]�ce�aA-"R6�@\UUi[rQ"L3c*� Th�� ance*�63s6�M� M�Tiu� -" !*\UU(g)}%�E4g (� C* \UU_ �)%��1�%(� ) =&k:(AT�(�D��3.2G[) A� �� 6�E2u�;�pJ����A�n!� x A_1 �Ga�w+._0)&�(A�#"#3�<"�KI�� 3}�*Dj�,_0��_�.�]�}JE�"K� {Jv:lon"s"�6{4��adsZ�@8 � �I a+�A��&ta��"#6A�_n achie)V�) help5kN�uers or*T&Q�} � [Thm�\.9�� � ��0���"��a�)GNS>H �C:eo)$. �+Q!F\E�(.��E_ . Fi�8:>�@�!�h_0�!ju�Y!3�\"2 .2��evb}-3 H���/ �T D$Rܥ� e*, ^&� �w!t��+Fan. L.-.�` bc; �! 2Z{1,a}:� u�:n$V��_)6 a�N l,tB6^��#� ~W6X%E������)VE >y (iii)2<2(i� FM==Y*�N�9� �ua.�_q�V���,�V�t�O/]F� ifeirm�:�s (k.-``�I�t''b��; m@�n*4$a�X$ � �:"� s, e�j�'a_1=a_2\�tau reAG �%ť�)��" Each{ � [ )ge3gxSw7��YA� � #��9g �BE}: n�/,��r�Q�c"�%�d��$c)� Y�4���P B_c͚X+?�ڕ�>� � _c��.Cndn] qG_c=E� J)   c��6 q�i6c�=A�3c}7 C(��!Y mappCe$��phi_c�b !!v ~az �:?� -QA  7/O)SAn*-}8M%"Z$N��3� . ���-� -�m9�*~�ead, d�'by $X_c� � :�c�CH&*D��.� .���*-)(���DH:��M�_27��Hva)�P :yM��p�Y*)� R�G=� �'ba>�Q] 2+ =  ;��R' $"H$cE!�AN/')5s�g-)'uG�'��E�3!� �$X$�4n",Pif<>i>8^ /�A�%&2�%�6��}?Pz �%( N�_ m c��rc Fv��ot=���7�!q=_� is[5a1�OUa$�vkby�c za "�J �.})�O6)ofR��� �/a�$��2tX!VU.G�� a12I. <�,iA,��M� 5Muoinv�6 % "b $ K%���2oF� ��Ai� ��!77*�B . ObtK�Q9 d.t�\:,L�1F"�tlyikl� 2@q�"��n2#* � "�-�V-jo� '�$6�F��la�"�ily���n� nEkI�b($.�Z"VN w � ��A� :�d fk y� = *c� 1C.6�h6$v�DV#�f6�2��ia�"�5.�idRmz��  �(l0^* �)= { ) �}$�FR% E�ed>�i�~ �Ed3`�� a,b �K l I�B�5�A��+ !�e.�d" B�"^t ". ���C@ E&:X%"1� .M $"�k��At $y�( $�! a, W)Zb"v ���5w%hyu"�n$tA�!�s xZz�$�>B_b$. N� ]!A^"r"= aF�.����>��+E3%q =��;%[) +b� %! b��`i&�(aJ'EU�rj�on $tt^*� pbyeu 4 g rٚ :��_b(B_b�y))A41%ly+CX >Y = i�X_b�a(gl�ly)�B!�`xM6e� %�& +$,��S�^��k5�usDa��xB� hat\�%* &y�t^*�V7eFAGM�R�_�)Ij�!f2�� & ]], �&��2"@>y�(2� bJ lso}e�=��+.\s �ȡK, $.Z��Ct%��_{ ��}tBQ}oo5a"��, $Utzc2# �K$n�� k& ,�A�aT\HH�^oplus_�d �k$22� desi�o1*t&hs"!�r�� Q}A��5_A�^ayA6�)c Ad_UI9��� . \e Zb^T�qA��q;~ *,6@�.6� B:"�.F m��m�q *�,i�/�b� =��N(4.5)�Aan)�wrE�Cz� nP ��� 1�gm�Q QR"5 o,;�Aw�} s;�Q$�>2�)7. N�$theY)� �� ]E�1�;Q#�� $��� !� cho�o�%Ū +�1barR���ia!�rue�A�E�I� = !WB��:;�5���J:t��is "tTby�F�aUASu�� EB��J!3:e�} �*� �@�*�Ea���-^tTG%�$�&��u� %�a!3a�EH?d�4ed^:�A  n� 2B:� :�@�".t>� s�D6�W�4''�iX:e,B6+(�] �b� b(K)8R�:YL ��6) $$ +"llh': mef�s5y t�# spi�T_+)%�!'2�"� ��RH �"�5�?(i.U!!*cor�]A�&�Dv��T TFi����X2!�Q�D\rJ*�06M7QF!i�fn�0W�ls�D���'��u�9�HE�����Cl�x��!�R%Y�&qc�p�mme��VB}= T}W�e�-da!B �F�!Z!�"�%N�%omita&�M�%[ʟ.\ VI, � 1.19]{T}:�M� a J�ra�a6:�*HM4$�cl�nd �t�K~"pGa��R ��-�Par"� $S:m{I�]m^* # losx���7�?�мd1���A&XQS = J0�12A�y# $J=J_{(M9M� e nti-!<�ɬ��e= U2?\geq �#c �.�5�GveCBadd"� .@!.�� � \par.�K%^se ``DIdata''�>!! 0�'"�& pA�&3� J9(�q �  JKG'.6$�0MI��NQL�/}����_t� M_- � (M)=M\*�1%��1&m):-��m� -it}� A�15É��$ENJ�ps a/oW#E�oS:nzM� $$j�' F�  j�JmJ�!A.2)$v�G�Y$ $\omega=(i,�2\; �'a KMS�t`l8�?.~z< eta=1� ��=6#{aE``:�''u �v�zQa.��#| _{-tA!?f.A�>�^is*I6F.MA�����y�?i�%�a<� �i|�7AnNu��!�2(+|~�@ 6<2%��I� ,� �����al 0�� NЀ3e��BW} graAi� OA�!��"�w� !�R� .�5�9a 7G ��̭�1�E(NLa��CPT���n*���7cL/!&8re�kd��sc6�@g4)��~j&2_ :�k/�� /of��� �:�-�$$it}_{(A(W)�0=U(\Lambda_W(��i t")mA�%L�E�� (iv+!*�J%T3)�>lJ{�UnruhR�|W���$ cele�{dg7er�s��}�>-;boost˅\ Rind�V� sen�M=� gBa>� . A�- Hawk!�e�� c*bA���is way�T� an�e~black�8�ak�sx!b ah�(�5{j�,�in +ZaJS�1,� =�syE�� ��[|ng> ��Pr ar\'eIP @.�Bk7M�J��>Q��`� ͅ�U�=re amb?us��gra� KW},�Q a9mpAd��:i���!qP�N%�Q#�%/f ���� r�"�"3!�a "5��r�/b�y�asa�en� !0cA:ons�Պ���@Re�E�3�to5�Q>_.�%�\!X�/2r&�mT3I�E��� iM�d�RS&P�� cG�_i��Ai�Van�v$0�� t�}p�!��(%��E��-� �M�2��-�!t��&-�M!�=.a,�!�,�faR��uk�.+u��a�%�Z�/&E �iu��vw%9�E$ZX Of�}ev�a� � A�m���"k �@az�EEBemfe.CF�X:� IX� 4.2"� .�1�Pal76�F��>� ��<\� a��"y� *� f�rM.� 9!a��3t:*F �(E �7g�5 a>�M~JA �&� "� ^^.� _{t}(N)=N�%"� ���ARu ^�,"#T"~8%% um!��~� �O � 6ݜ_N(�T(m) !� (mG In4 ',�� �\e��CA�p&L`4J� � -�c'pa@{&NIw�  $EmE= �E$>.5��&&>6= .�J t�-�>�= �FFN\ 9CE� 2V=x2EI,_{I��nd $E6�= 6=�� :�?:l ���$N$��n $E=��m�N=aJF!&�^ne� � II.5�B:�� :��f��K^Un< .U(s=0e "��Zq!; j*54 8MU(-s"�M�%$s>�5IfE�g ~y�F}D#-Xvjha.P%���� = U(�A e}^{� }sX1A.66�CD $M=B(\RR_+� �x��"\�QFTR} at�#� �}�0�a�ɏ!��6� �����e��by]6�}B�-���}re �si�a�"�) "� (sca-k -�%\�T�#��GL,� >l �jG� ɍ��!Z ��9G>:]�:�_ta� valu��M ��&��ga>7hXY`_{D)��.� I&� � z(tYgC�� a��`� � I*2lok�_!���$"�&�&5|"�!�*cZe ds}��%"^� B\"ockenh��E.~Eva�e {�g"\L�;dA�por1� FyIf� .\ Cn�30}��01) 11--37 [e-�[t��41 �(0) 3604--36�2�)�41,"6�8DLR} C.~D'Anton�i, R.~Longo, F.~Radulescu: {\it Conformal nets, maxi�temperature and models from free probability}, J. Oper.\ Theory {\bf 45} (2001) 195--208 [e-print math.OA/9810003]. %%CITATION = MATH-OA 9810003;%% \bibitem{FRS} K.~Fredenhagen, K.-H.~Rehren, B.~Schroer: {\it Superselection sectors with braid group statistics, II}, Rev.\ Math.\ Phys.\ {\bf SI1} (Special issue, 1992) 113--157. %%CITATION = RMPHE,SI1,113;%% \bibitem{GL} D.~Guido, R.)�:)�The co1� spin%�sta � t!w(em}, CommunV�H181} (1996) 11--35.6�CMPHA,18�6sGLW} F�@, H.-W.~Wiesbrock �0Extensions of�Ag � uper=� trucAos~�92 �(8) 217--244V�92,2176�H}aHHaag: Local Quantum%��@ics, Springer Verlag, Berlin -- Heidelberg -- New York, 1996. U�,IK} M.~Izumi!#~KosakiqwXOn a subfactor analogue!+Lthe second cohomologecRevZ�4} af(2) 733--757:,RMPHE,14,7336ILP.��-S.~Popa��A Galois correspondence for compact ga?%�,automorphism� von Neumann algebras with a generalization to Kac &}�_8Funct.\ Anal.\ �`155} E�A 5--63:�,JFUAA,155,256�(J} V.~Jones�Index�5�A�Inven{ Math{7I�83) 1--2>H INVMB,72,:FKWE�0K\"ahler, H.~.>,i�ModularA �M��ArAi*ionA.four-dimil al qM�field �iaT JV>4�20��74--86>B$MAPA,42,746A@KL} Y.~Kawahigash�m1R$Classifica�leu�́,: case $c<1$!�8to appear in An��[e�=(-ph/0201015>=EPRINT �DPH &>�Mf�,a�M\"ug�@4Multi-interval]#%�m)�ity!�represen���in �%�!�ore�n�219i�(1) 631--669:���219,63:nLEm��5��Fub!}��mediate�!�r�37 �3) 7--30V�37,:�LR�, K.-���?Net�9:�b�01995) 567--59V 7,56B�2z��'%�sA�boundary]�QFT!+b�16)'$4) 909--96>*U� 4050B�X.�F.~Xu-'Top� i��se�L)�(a dichotomy�^|v�5,20�32-6>i�$OA 03093666`TP} U.~Pennig: diplomaA�$sis G\"ott�in, work� progress.�JCTPS}6#� anon�kor? duct25v�1 �$0) 395--40>�q^ 1,39:AT�: Take��T� � a��A��II}*\Encyclopas of �[ emat�Sci�]s, Vo��2M 3). = W}Z� A�ment onrec %k of Borche��Let�� Phys��s01992) 157--15>},LMPHD,25,157�4Z} J.-B.~Zuber5�FT, BADE�y4all that}, Conv ٦��29"� 230--266�4hep-th/0006151>HEP-TH I�Tend{thebibliography}  docu!0} =�%� x \title{NARROW ESCAPE, part II:� irc��Ddisk} \author{A. Sa,r \thanks{De8�!�Applied�I8ps, Tel-Aviv University, Ramat, 69978 '�, Israel, e-mail: amits@post.tau.ac.il}\,,\ \ Z. SchussR�]�s,b2�w �, B~sc_:.} �$D. Holcman�� Weizk Institut[ mX8, Rehovot 76100� ) h f @wisdom.w K) . } �Keck Ce, d2�aEi���y, UCSF, 513 Parnassus Ave, San Francisco 94143 USA1��8phy.ucsf.edu.}%)@ %R. S. Eisenberg�6( MoleI`Biophy� ay %.�Rush Med�~�\1750 Harrison St., ChicaK,IL %60612, eE; be �@rush�< } } % \date{ 22A� May k !Eqnc# @[12pt]{article} %styleFPusepackage{doublespac8epsfig� .latexsymFa4wide} ..float6amsmath�,input{macros6% ~, �dicx} %W��� figures/ �L \newcommand{\mb}[1]ox{\bold�$#1$}}6* p}{\�Pial:,ds}{\display%~: Lbeq}{\begin{eqnarray>^beqF%*>&eJ��^He H.#BFx}B�xB�yF%yB%zF%zB%wF%wB%nF%n%��%�� em{Defi}niV )� }{�em6$lem}{Lemma6conj}e�6,prop}{ProposJs9 . We1�at*E�)�passageI��K� M the !2A_$E[A�L\,|\, \x(0)=\mb{0}]=�R^2}{D�� + ! 2 +A 54}} + O(}�1$.a + A�1Y� is needed real life]l�4s, such as tra!K king�0pt"on neuro_{� because $����}}%�|not necessarily large, even when2�2��.a�alsm�!� sing-behavio!���babil fluxfile iA�.]L Kendpoinf:a�u�val&�[n�CU�window.Ka��2�\�{Intr�� �expec��!��#E�R��edqq � ����� por� , in�� inde�e ly a�Oe��shrink�� ��I�ލ �.N!gJ$this limit|^ ����38s has been studA%e �peAT ase; \cite{Na�E�k1}�|ere!lwas�ver!��@ mixed Dirichlet-�%�!�IUproűforEB PoiskeC �-��isr,a well knownE!FJ�e��ro cs (e.g.,%M if��� � �DJackson}), elasticaR(punch+s),��and�xa� 4y, hydrodynamiaT acouSs m Sneddon}- |Vin� dov}. It 9s back!V Helmholtz =}\ Lord Rayl� -� "1� �sivA�6 lite�!��4special geometA . e�7�A�tw2�Z  bega!� ��}1�c�x��y 2�n bQ%�membraneQ�ChoqueEwE�a lead�� rder*�bmwa�]ed%B�2�. Iaa is pe7w��� �orough� ysisA�!.V'!n6� A5 " our cal���s���nF $any simplyA�n�eT 1|� dz7 e�a6. Accor%bto � 's p !weeqV0Markushevich}a�i!l� �A ��ar �s� �=A+ t!�s�e �́$e same�cl$ h 1cV�w 6�j] � "Sly�� ival_�1�1 �]��rA�Z�Y� ��2ly-(, but globait�U�-� ian  �Z�f non-2� ��at!F!l�!,ners or cusp)nsLir9�is treaaB�Zthird�8e}isfY3�Yo 5cUWmethodedeme�j����ficY&al5 formud��(follows. A �fcle��e�&e�,� A����"�arc2� )�ra� betwᰁ arclength)J*�&�4R,entir}Gis�8�0 parameter $. � � "� � _a|} |�ll 1.$$�+m�^*c to2�,B� >�!�.� \to0-+����y��!:Ig J � p� _a� asjA fpona�of�$�!��[!�refer�d0rein]{Pinsky}!�#� ah� � at hEeR� E>p� E�2� d$t���A�er  ? �  � latt �Kc �� shg inU����F!�_pprox�� �h)(cE�\ givenA eUGE �� rasta��$.�a t6� al �az$radius $R$c��b��'=* R%� �6� �E^*�Q }{4D2F�1+2� # +�,$$ s�6)�s m�/!�=,rr-Y( iA�9�̥�Aj��e�{a�A>c���$ stem��om*���ۑ itie%�I� fun)遡woe:�s:�(logarithmic / *���� a po�BH. �compu^'� based� he�:o technique� )�� %+y rev%C�yA^EO�s  �A�UfF�.�(llyE� .X is $.�4^2-s^2)^{-1/2}�e$s%� (5,less)rmeasu��1�&�.��at� �i�s $s=\pm2I�k "+i exit(vanishe )"95| o� j"<951�� it�E�Ealmos� stant�of � �ds�:��^� U \����P4``jump'' occur�-� lay!size $O\�.� a�f��)a� | $e average 5^�!�EdZ � g� fu�r�i�p tribu�vM�� E{)�to)�:'%�%!2umAQn +�,-�8 <antipodc  V Uv �ur (MFPT)>�!�!� isb$main:mfpt- �} *�2� =�D%�[%�N &�.� Z�B>��,1�dɠF/ect!8a�%�5�di9� =ʂI*ed"  ��8�����ECali�1�!E��{�� -mͣAgCV^��%hole,vv_max�x_{\x\in }2 ] =  r=1,x'eta=0I�C2AK 2 + 2��!&^ �(�f �f2:!A��a�'mt&� 0!�t eigen��!�� �e �N�1-"�� .cw�1��.i����Y"�ariRI��s�3ҷ ���.��consist%A� Iye1�Xs)/�by a � channel0Berez},� ${Weiss}. 6�I easy!�se�� at % � D=\sum_{n=0}^\inftyEc<1{\lambda_n}\sim: 0}\,� v} \eeq� 0<; 0\ll 1<\cdots$$ A9�)U5�n�0y�lsof�@�'�!�eR}$u_0$Mt� t�k *| N�I�Q�?�($v_0=1$, onQ�qVbou�cE�M�. ( ��c perturb�@n (in $L^2$ norm)� p- MI{I/1�0$6�q��!D6�.�,-Sol��o�i�/2�" sec:A�}��"7 ��ria3)yQ�D -�a cerns ""�!/: unite<�2�!j~!�1T&0 of �  $22} (a9$Fig.\ref{f �)0poa�co�4ates $\x=(r,\t��)$��q \[v=�� ],\]A�a%s1s�a-u�q�"in�7geneous9�2��, � u �,})ٺ�l(ay} \Delta � & = & -���$ r< \m�& for} 0\leq�,8eta < 2\pi, \no�# \\ &&\\ f,\bigg|_{r=1} r0, W>f|)d-\pi|<=�, \Fk9 <#.�}r}.� ��� \rangle.d"� 1\w�$reduced��%�ub#.ion�� u=v- �1-r� 4}�x q:u-�|zqNA�kLaplace0�RbuY�:� >�Y 0 A�Qn�g.zzs. <2t9%f-d�}��}z�� 2}��M ]�.Y��Q#!# adap� mofq�n���% of (��eq2� ). S0%�Hv�zsugge��j�u-�. C}.(�� (a_0}{2} + \T1T4 a_n r^n \cos 81etauI�}AA�*��&{a_n\};oO%d%mi� by3���<,*� 1XYѸ-12�J~�� �.� =�->& \pi-] a�F� Legendr�!lynomF�}tegun�-��,6e�= �A ex2�a�J�M [5[,t) + P_{n-1})mt)]A.B�e�n> 0$@^�a_0�0�6h Fi �vV�E�I��.� �dUo�-XA6..|U�Q�I�w- !�F�2})�p*<\R� \sin�R=�2�m, R� � �F B� ChanA��7o_@mu=6#nd mw�yieldN�ZG �UJzJ�~l.A JB�U[ i@0[eq.(2.6.31)]"�f,N eavy��.>F�� V/.����>� H()�-t� E�) tQ� J)we ob�Jy1�i-�)�!R./ tm) -} 5 {2�B�},N�I�q�< \pi ._.X �typk76��*\ E�--.Q�l"�m�"!})��F�u�"� h_1U�1�!��;%� d}{d� )Ld7�$ui�&�u� �~9�u1���uB�Together� �Ga_0})��N}�int6R }:J� ږ�+�v"v!� J�c �-%�"  $* $, clos� re�&?�,Lbe�N �*g2�4H �NZarc��=i$9'G a_0$k%�0�)o%�Z � �54)�*��e oscill�By�CT� {S�2�%$*� s}�4�G+|3�"����/p94�Bi�.�! $. H� w�.�*� � �L =� �& $. S"ngJYU�magic-�b@�0 s=I�If�6 uNGA�~q�-�ͅl9pA�)B�� �a@ a_0 M�4}��}m��.� /2)} �arccos � s^2+��^2y�=-�u�- n. \,dsn� � 2�����l.yf��B�t-� sin� � )�L� 1+AOR��  - 0sinR(� � � I-U��:� + �2�tEM� MJ1 A�� s}{sI>��� � P��:�6". q�46 $e%�U1�ar� �=.Mpid} \� .{ ��J� ) tu�o��extrem��useful�*e�Oate"$ ���:�E>�4} Now�at1haQ9��&�7�� (� E��))De ��N�eed&'63" t�0&[�.�$)�7H;possible��J $r=0�+"X *�u-v��nd��u2,�n� %<exp�J� �m>�")ŀ��"�":;#� . A"�# J>dA .M"/fn$"t+:f Q� (��I�q I�{\A� 1.Sr\,drX 31.[����*N#2��r��r^3A��}rr�=& �A;i��8} = -a9 B�� 1}{8# � 1 as asse�6iA.)�%�"m#).�$ aximd*69%�U�"B%0 $n"/ =I"�&#) �$a5a�Y��  A| ��%�d�� u} )�}}r�4 an bN;e)�4�y� �F 1 ermuV�$ a:$ rpw! � atFb v_{�#= u(1,0&�=�>J�Y infsu )Ɂ��AX 6N!F1�"w'!��;as>�>A 3p>N�K FPTs�?H oney<#:&�' &i�? su�'-P �)� � &�5�dPin Ap ix �)ap: �-�-�'"@3-c6Xv-max-a F})) $$=oy#a����b�=B�$$!6$)t �e*�%a'\�� BKQ�$s}�<�%k �6�8! $vI' -v_{ia��2-�`f 1}C>8= .4431471806\l# lon�W^M itsM m� Rqj��K! words,%� vari�9aO�"a.z=�,� r�q 1�+ veryf"�Lwever,�bAbopjG� �-q@�, �R��a�R(a8.R#/ .>��3ti�2�aA�Eee=��*a-�9d \m&%j2h.15)�FI� $v(1,\pi)�tB*.�aeuC�Qoo>A��*RAN!((r) \equiv*q !A�S"�ՏaO�@>e\(-r)^&] I�}s simi�"��a�:!�F��isf���1J�>$1-r \gg� .zI "�?*u  2g v-ray-#� ^�eq)2} v_5^nW +� (1-r) +m�-M!� 0log(1+r^2) +q!�F[:��3-aBQ$zC"p*C�W$[0,1]^ s��eq:q-b})-��q-end-�<(s})). Clear�/is !%BFE does�+ hold<!�waf�;E e�E/�$a��!�P 5"� conG rA�res��A$(r=1)\,=0$a�steadi�J=n5/s"^�>atr-\Ay�.E�}$}F-�\�.D�j>@\,� ) = f} M& Q �VO� 6[3]6f+"u q�In2�%n=��@Uy�is��outer�^ �B�r�)W�oceed!�c`�^l5���a�m�llN�*; \d & =1-rA+e&J ��39�� )>yi&?& !� V -4 ^2r�% 1-2r�& + r^2 c 4v^2 W%t,A-�[ ^2j�#exU^����a[ū.jy, .8$v_ray2}), � 4"� �%M�( �)&: � .  � }{4 �j1�va�Bm'&&1sh\pizQ��� e; *n� s^2}{ix&Ff6m�^{3/2}��2i�%�)'.� 4."�&�,EVi��5�%Fa�b.L"!R!IS��F�J�=mrH��C[�vf��VH�+k2 )�]B��7�H"[eE:��/ur*| 8m5a�-:&8I,�(�� 6K+ QcE],\,�l4�In*�:, s��]_0=.�� .v��!�}$B��f6V_����{:J>�66^2.L)9�d"� aCe�ɠ4�6co�Bd^`  w�Q:1�͖ 1n���:q�$. Fur5 more�a9at�=ce!Yy�3o��j���YBF"�5�*lux}_�U Z}*��'� *�6\, � �� 31�3Ix"�, =0om�:%�1)U��2�F*�K} Next� �!�N�K� �f'6� Dif;5t>�&6�%z�Wa*E�f�&( 1'*I �1=6^]7.�*9_:49R2=��+F� F9)���o:6 '���\pi$. 7!"8(" N$�ap.+%��Y��o9:y 2�+ �A8 �K��6�"�� J6�! B�$*�+:: :�i .�  )4*���� t) JX%�Q(j Sinc:-��/!�6�t$ I 9�&�" ) imB_J�:� h1} 9ו9E�") 2'�!�)V ��A^��hR0*F#��Fi6 ��$��3M�%l�x�im�e���Na�#}�QSat6D!��-"m 2Q} alph��Q� := � {1-&�A�٦}"�+"L7 -���%�02^{n+1}(n+1)! )s(2n+2)!}gm(2^n n!#1)!5w(1���?n+�?:e.j3 &�3mQ .�q�V�(2n)!}� � �, � "� ��� �� �� :D�91��$ *�"X?e�e�6� },\, | 1|<C!A�A�AUj9�0,& *"�3 half[i�powGy�$)d) a reS�r�F� (��E�er D.) ��Verm, $* �A=�JzV�J,9ost� one,T�it _"� as $1)�aGQ !%N�%5e�fV9els@rge&uS"� e�eQ .� spli�  iT5�a�-9%�TQC`o�>���M�B ellip=Xx�`��Q�/"X;O0co*L�7 �6,/Mazya1}�PDaugeA, T �%� Z= to60EF�:�* 2��0z  m�:N� m2�;-ft(�N� B� ���Bi�a��w2 2E]zF}�< gree�e%_"�!& �H1�ks Mapl�o Q a'iIRx.)�B-v5��iry>x$":5Ua�Nto $1/� �Ql�J-�end�~E� nd�W� ) �"cU#oE[�; eref"h F�shape�Mo:cap (�n� 2D e(� �NWE� curvr� ݈$ A� *�:�-��:vO�*3 &�\ �U is $� rZ�G)�ven wAX,taken arbitrdXk(!�|���2OX!�.k "�E"�E 1�: -�`uHT�F3O p�L��JIra!�wt'�' M�AS"T:��.uA�u"�"��JA�ea5N�$(� G 1!\� few�G3KZ.�tqslowlyrverc.�:�!�,=�(aɢ �Z> �_>,should be us�Z���� }n �ЁRBF f_{ " ^{2n� 2�G�% .� $f_�)r�F.3(�H}a�E Bs&a !a��@�kZ�QQA t $f�"k:�}$. All�2�C fJ!Ga"�f�roN1��_ 1�*MMnvrV@s 1,� -��1v&J,\�J.� \(MW"eU�)�:?l�*R 6�9��w�!� i���!/  q�2a^V &�:a 3U�"�:.\Z�3.&?>Rec�d� genee;ng&M��J�4"�Yt�493qR-�eq:YRA��T2tx+t^�4=�& �4x)tJn��5�X X� �-�.� +1*Y��y�t�}}B�6�/VMla�/"istJ}Qm�3*.&)>�; i�Iz�iF�-1m�ht)f8"gf� ,h2�JcB%Combi� \ :&�3_1}) �>� M�by�js,�getYx:�&=& ��y:Adz~,�'9J�M0�^2A%-2\,d{&�E]:2tF�9&��:2}\pi{2a �M��"�26�z� �2CJ12 &���.� &&� #4��3��-!B�{�^*� �E�-����3 *�X!Q6��m�eqs0A���a�)��FY}��E91}�9 A- z3�- z��1 N"�3I%�-i�1+!B[""� + k(t&���F�,xM�S.1�9!a! ���j \�-)bcos^2 2�!&E7!� t�}}*�BKTN  �1�\lim_{t��x0q� w/5:�t�r}"�����B� �=��)@ �+ %�)YV� �1�iF>Hn�b0B>0-�(1A05y1]H�Y>t*��É0�'-х'co�.!��/ eft[:� 8Em>41- 5A�1R-"a-MэXI�bc�# SI��"E�si2�>�6�-�F. �A��]���-\ &&.2Q���w.��.!���:B*} jY$� $YU��URT-��W:" 2 .a����Bs 5�CR�=" o(|e6�;�!9! b<��u^\piQ�a0uj��ᭉ�F�I�6 u s<t} 2`F�82Z�8~�uu7} "F)n^=�976�#*Md�N � Ru=Fq bQ*vjKyq��MP�7�!�v? �yY&� taݓ � a�N���9[��/�Hlog  v \, dvB$�M�-�jn�V2. &�:00Q(1&&�EZ�eon /�N"�' A.U�-&�OS�F�F*}!�J1,&�-&*� M�)S1"r,�3� �/"�"N��-�d�%�L ^L *� mNQ 0"�6�B� ��a. 9�6�*�^�"� *�)�N�E��2Q"��!�6yC�Ev.'.^A1-ra�i�j3 @)9!51+�* t + \.�f��l,�hng&i ~�E�*�i Q��FF%2* g+.�N &/:�=Q *Urg/1*����06 ��B3-��  t )�(.~ ,*.��i~� 4I?�^E�/H1xi?2r}\,s$ @a:b�v�f#}6�AQv�5�q �+�*� .[@�0 �1� /Q�:�*�O�V�";:�"V�)&z)r�iO^�� n�\.�6f&շ � 2}\,U��,a�\�I�.� 2�Z� �� i1}�K2}U�-|�}f�.��7R^=��V^����4�%��.p4)&�� � !3O�co�B$\, s^2 \, 6�(Z�+4r�b ��C^� v=�� +s^!�J��6�,6"0�6�ncDF&&*a �����qp!t�..�8�������ᄑ6�b��h3g� �$.$"$&k`.e(l9���r�j /D8�*y �Asa�s y s��8M�J�M$�0r"H �To"J<g �Ri�y 8g@ writ*yE beq:�E} �Q�́-y)s�cHaf>� "�i�1 U�i1-s�r)9 = HC��/& 8"t��"�7�7, d�w�!��9 q�7 48�,�F�!1% \,� F�Q�l"+teq8�;XV�7�h: I!�$J�.�*�8 q�$=&�Vq�!2� 6�>N �a&�62n]�7-�)�&?-�"�9%mB�BiQ'#�-�  2�& 6j#�k&�<=��1/3��ja�,>:`8,$�K.�>B �(2lf�>�>2�/1{ap!}�qh����%�G!�W0^n[AF((�,jZ*�JJ*R�Rh_�>�BI �YDlu Ots=_d"�))i�Ŋ%E�}� .� �"s.-���:�"��i(l�g� g8 H�Uu:�lk �2�>�q��t�� �} �]y]2S�E�,d$a�"dRB�>2 &J-����"I' {&e"�W-hpi��! � \Biggl[ '�%$%D $d .  (:�)a�.-c!�2� �bM.fy V}|}"�#- �EY-R�j# 59� 4uF�1*��"�~R�E  &�)^{�-})y]npWe>�2_by mak~A=.} "��}}$,JC&u ��j�"P��6�I� `X Mu.�I ��u ���;q}1�E�ID�0>0 �Y� -n�#&3:S�+i+T :5Q�� �; �.� �Rn" >� bZ\�<]�:�u-+mO�� m6.��d���-[��l�.����U�_X2}}a_0 -�&4F� &��. �������m-��(]��=qaw2�&3j�jq��N )*V�!G RY�����)N}2 ���,Xa/�+] � co� U? �V?e�^2Q�E a�)��'s��S\,}�1�!���L� ".1:*m9�*q ��= & i�V "*tր�R�\�*s).idNN . m� -��coB�T-V4� A& ǚN�$A-�R� �)� "!)P]�!�4!,q��)�  ten N�;&� A^5ral-phi 3)�+:e -8A� ���bM=�4� � �81-5�bF�\.�6a^2' o�3!�b���)F:Hu� G�/$a=!�=��%�� $2b^2=%�)4 , $. Wyn�yg&W.�0_n 1�~�-eR�J�� )6��eN�>r|.X �:� n=+c_n!�a ==1yω�!$]$6�k(���t'^s�"Pu�� �A�:�uE�]��B:AO%A.� (-1)XlE�*9 �<�4!nM�.� �&� F��@-��"5!YwΊG�>L��9��*B���1A#eq:phi-���O��dFm}2 � �=��:+O(a)� %2��V"�9�is.] &�v!����� �M�v��A]L5a^{-2H��-phi2nq7.�T�8*�MS� 9"�"%VE��nph�$`6V8` &���lZ�#v A ;'uq�5�int-for*&� �4' 5>]\"u ?b^ � �te�?to�I����-RN^��,=9�yet-anTVE( rgalR:N)� ���[6�VU 5xi:] + ;% !2!j�. &K7�g�  &�� ��fB�%��QI�)�-2j�a{2 j�1�/T)L2�{bfi$�)B� 9�u�arf^"���" F8Iwm � �!u}F>��^F�>g&R[�q*]Cb���I��+>� �ET+72�E]� � -��q�����Bb�/ �/PE�m�16�0�Aa����=��sj� q2���\,Ajm��26�)v �\,�A;x^�n+ (AS)BxEh |m+�=q�Q�U"� Q>� f�.��?Jm&VD͒���J�=Mq.� 0&x�7l[)(������ �rrb RearKEin6��w aNu_R��2;E�2�beta_n�bJ�<� C �G֋2� aF^R��Z��t�2}*� b��� ��. HM{ds%�m�h4}\,a_�]q3� &�+� ta_1� ���(��E"p�:�Z�wFZ ��Y-z&C.b#b�-1}�h1�/ �hi �2J�|R4M%:-� ��'ds��& :s:�� -) 6%$)"re�cU�2C "B BN, ?{{-U�h�U�{g�` !�=� �i�A4.(2j�Kj j�K� N��O� j�%2�.:d.�jH (1�j"�{ �n�f� ~:X .�lA��LMN0}^{jAJ`1�Hj-2n-JV "Nb<%cj � (jH1� !"C�2� � ������ �-��� ->{.zs � ) ,d����"� " W%f{.Fja effort�F put���n����e��2�m��� $. E��.a�Z�u!�6�e #��� Qa�Y�^�m�F�i�Aa�O��B���noJHI��&3um�'�N�N�"��J�l�=aI�pV� m�jF�2�F��$��C_jB�� $C_jsc�^a0�(�xG�*� )er�] hyper3�c"�)7���� lternativ��/k.��&Q52�r�R5����-�A�E�(7W(�*F� :BJ$�~�B\� (-C_jvH��+*�ZZ �"��FT}-.j �/}V�.�'Fv}��. Ŷ/&B��!JrN�NqR��W6�%X*�=Ym�.v��)���YR��3E`�� M# E��$(j-1)� !���h &�]0 Aqr����r)$/eq:�.-� �s�"Տ.��pre�*�R�c��B|in9*��b>N z�&�) �%4�?s ! \cho��M� - �u&  {n-jMV�w��bi""k�*U.�]&:u���%k���k �{6�� kT  !� n-2kF�Alt�y6o��1� �(*�,&�f�b=�Z���M�}>J��?%N!�����= F���Z� 2G�� �Q�  P.�Q�a�m�U�}l���eRd�/m>nJ�%\iAok�F^ i+1}{k�iE��(2^k k�]{(2k+�YB�� �O�2�6I .HfAh2YJ��� �Z��2I3 ��*�ឞnq�We now ���Q %x*r� s�#�U;0�0�/q�b.�5�&&Ez ���)�! *$ �~.�$�$ �$^s 2�c+�AB�� [ �&�t�&�N�M`k "w&�5�S"�d&q$ �@- f$�p�5 af�j some��p���Vq:�,�� ts I���K@pman \& Hall/CRC, �2.�&ְ H.L.F. 8��(relle, Bd.}����860�91uRa�aKW�Baron"%� LZ 5f S�w}x� 2yV DZ, N*��42\H6�} . Z4Ł�i��of"��s^$a postsynaka ް:�Y&]�^ope�� III:I� surface,:��6r�b(� R.G. !�As2(���!�cip���Wc��"8�hi#df1 Azi� curr/zel�c[�� a�c�XQ�p��ure''-� Jour�of5�al Anal̠i�a� }, 1E  177-197� 3. m�� I. V. Grigoriev, Y. A. Makhnovskii, .�� ezhk8V. Y. Zitserman!4Kinet�of�"�`��_�. Chemq]�bf1��2I� 9574-9577��.�!�$ L. DagdugZ�S� Shvarts� G. Hwi4iss, ``EquilibZ�ewon<mb)gcon.��cap��ry�K.�e�1Y�3 �12473-8�32�S�� ���m��2! of Stocha�.�nl&lX}� Sf�in��ȮT��iCs ,�� 1980.d�w CA nder<e!TOrszag!� em Advanc�. MQ�sa R qi����(McGraw-Hill687.�^@M. Abramowitz, I.7 ,^ �Handbook!*.� ��}�ver��?���k 724MYgVf Kozlov, V�+!�$RosA[na� em Eq�j� Do�@si�PW��m�i~x�c2�Survey)]Mon�,phs, vol. 52���& �26�J.��)X��t��"�Assoc��d W��C�h���j��de� 9"[},2� � B�85z| �.9i M�(u�e_Z�&� on�-�: S}nes)h6$� }, L�� NotY��s, 1341&��- � �'82�,A.P. PrudnikA�YA� Bryc��, O��ich���� =� � | 1:� ^rg.GordonE�Breach  . 19���&>�  %��pag"IG��J+ clud�8phics{disc} \ca�� {A c.rca��R�h arcl.��*�}�f (dashLjne� $.� K solid lin��)i *JBh.�z+� ���\i:���h�! �i-Q �d�@``BL",�S� area� bP�I6��)�!A��td56Oi.�vlo.�w:}�$=%U�w$1)=&%�:Remark:}�H�ru$�"� "�HA� c ���F)se$�s� $S_muat2�iz-�� $_�\xP_4� u()$,*I]q)$p_{\Sigma-��.3=?p_{S_m2V��j�!� �.��� �de�� l�� ��ed�o}��  $ � _g$,&��\ $\p �_a$.DGarabedian} P. R. ��eial2c2�"� 19"��e} B.  PIonic �Zn��of Excit_ Mt�m ed.,�au�Mass.���ao��� �� �� � {Aubin}#�sc{T. -- Som�Cn��ar�xin.��GeA�y;"]�, 3�8 5� McKean1}H�K , Jr.-�*T �:� cademic Pt�$ ],Collins1} W.�  On/ dual�V"�3Ŝ�sir w�� �L�f��Iq�Jspheroi�caps'' ��Dc. Cambridge Phil.�� 57} 367-384AS62, �2J��˅sn ���6� situated ��#ea�{d coaxaO"�$hz� cyl�r�!�c. ��623-627F�Oksend~�B. \O )(.�7e��E !�5thm�p�er,lin H"��x98.Ve� 2} E6���rj���� 1,C lseaf�C��n� *76. ��A؊A�I:qd�fI�F[��ut�X��X��X��X��X��X��X��X��X��X��X��X��X��X��X��X��X��X��X��X��X��X��X��X��X��X��X��X��X��X��X��X��X��X��X��X��X��X��X��X��X��X��XغX�W~W�"H�&��:�j .k� $(�,gy�' ssum�a��b�"Ӕ)����tra���s, 2��%&II�U_a\1Tet��/y�p"Y�shrunM����?(�����Gb$ h]"�&F��.2{�C �2 �1"�S�� "�lif�, d> �as .�&&��"G|_g&�� )|_g�BV�� :'�.X)a"��ion-� *F��_g���$.i")X1-�be"*V]+�zpb|�ʼo�le�proA@!hsterec���%��ex���d ��"o� -a68���3.� ��d( �YV��XAd�nulusACd�:4���a**�� re��oN!ne���ά�I��e@��is��atB��� ��$�($n �nj/)�q[�A��(>�+�}2B�if�|a��2q$��w�kg��I3, *� lo"���'!�us EWI�����5�angent �lesxF�!)�*�J&m�(dy~-1)U�L1:�z^16Q)$�(a���In�y��v"�ne��y�."�-m"�� 2I�(�hHa&K�)cl�-v U8 Q8)X�<wis%7&R��$�WAF25z5�!�G��X��,�exa6#5�perme"�#� o$proteing "cx��$}�R}~)i�t6K�2H$�$ne]�6OU�I%8��$����(6@ �A:A@&I�aU��cG�! wo d&h',>}6j�lvery тj�*��h��_p����0��:V !h. A>�$!�Yt!�=m!�Vs�-X�0����4.�$1���z�L�6�J52}A3e%�R�^��"BK��A�!Z95M�)���=uE�s;mHT�}�!��rel:size i" ��Uu)�la�� {6��, (��.�sj~�� �is quoti�� �c�%\%%%�magnitp�Am ����9%s"s�H�U�'s&5�PL+�'s"C��he%VAis. WuJ��=�B&2)�a�66�u�p eE� �iso� ot � ��so�2n,5 �-�,��k����5w*,<m�m�5"�X&�"�a�B �� >� !>!�zwa$unm !d"�aV?uB�2����{) ��!�all� >:� �a�B Jf��%= disk�({�ly,!��bewB`��s ��6��N� �Da:��R5 0 !5�����U��%�� �a �# cu f�� edR� �+ f�sA�.!l�V� for ��-x%�u��LؒL���R� aB�&���i��:�.�! $\p\Ome�iga$ is reflecting, except for a small absorbing arc $\p\Omega_a$. The ratio between the arclength of the aC0 boundary andV,entire )is��> parameter, $$\varepsilon = \ds{\frac{|\partial \Omega_a|_g}{ l|_g}} \ll 1.$$ The MFPT to $�, denoted $E\tau$, becomes infinite as .��\to0$. In this paper we calculate the first term i*`e asymptotic expansion ofz-�4general smooth)*8ed domain on a #two-dimeJ`al Riemannian manifold. W�-�second �E n annulus�@two concentric ci!�s, with1�$ hole loca!4on it!*ner �ary. T!result!� � ized! @a straightforward�Ato �$s that are�forA�8y equivalent toI_ �. %�1�-W!� � �involve]e solu)L mixed Dirichlet-Neu!K problem%.0harmonic func=� $i1$. While�zthree .�casAis!,a classical dHin mechanics, diffuA#,, elasticity[8ory, hydrodynam- apea�`rostatics \cite{Sneddon}- ,Fabrikant2},L!� .��\did not draw as much atta�!�E�L literature. First,e onsiderbR ��!}.l4}2 + :q*^4).��q Alsou�ew] woM1u`s)d2� u���belongs�� sing��perturbi���a&` layer�إ��,� lmos�}stantM"� � h$fluxes nea� edge heM�a�er�I��6�is jus��\� $of Green's"/ m4 origin--��� a re)�a2�-JF � aA For examp� !���� rect �E�� s $ $nd $b$ to a�"� �Oof siz!&�"J � (-! = �/ ���k ure �m�})�  $� { 21}{ B{a6�  + �=��2 5��MB{6�v b}{a��+ O_( -�*,�^� ` ,$$/ "� =ab$E^i�=e^{-! b/a}J^ i �*�tur u be simi1 Fat��eE �ځeR $-logarithm�actor� &�.XMk$  e� �ynuT�)AMq\ aI . It�Qob��by eithhmethodl$images, or#]co�X�iH$z\W to z^!�/ ��at fl���a�. �e vicI ykae�q� \to 0$,� refor�R�"� �i�)a�invali:��| o�e}0grows algebra  fast��$\5���Y�$^\lambda}} �� $  �M=-���. 2 .q!�2y� �"� �!�LI^�gef# �N .t�thA��@� one� ressNA���enter!�-0�rO Brow ev��R� � �du�ed "�wo ��ent�ll�o�����Y�mmon �2" ��![%���5���((d^{-1}-1)D�ɍZ6����" )9�d<1!��y!v�radii!�"la�.c�!L.�&�uV�� upperP ��I1�j�A�" edA� well�>���M�y]� n be*�any1�� fn� J��2�)G��iso�d�M �2oEba/h�%W=)< X F�1}��be2X inA}6V way��is"�� .p � rc>� postpaoA� stig� � tokaAE:i2> fuHN. As�(applic2ua�a�-2ym- .x �"S coefficiAu�:i%� life of� >or)ocor n";) neuro�spineu0Choquet}. \s�{As�&�!M�����.�} %�O sec:]},�9$\x(t)�e�jector�� �Hmo� E��'�6 �:� RiB�4 $(\Sigma,g)$.��a:M \subset )$n �&-�"�$ (at> st $C^1$)A) �f_g ��>� and by $|J>a4ng%a�compu6" *�!�mett$g� 7.�lrti!red '�"T a��_} ^remain�� &�-�-�,��2trMies. W�sum�� �eO�d sF� 5E_!G�&U V4,$$ however, $1�Y )$+independa�V*�$; onl>�%C%!Rk[9Ynd &HC s va! %�6��passageM$cy>E����2�ha�a e me nd�Ddefine \[u(\x)=E[f@\,|\,\x(0)=\x].\]�^  $,$ satisf��! � -"�� valu a�.�� McKean1},��Schuss}) D\D0_g �&=&-1N:] \x\in��D1}F.TIF\p O�  n}&=&0NU UQ�} a �Ff�RV2U_a, M5An -"� TLaplace-Beltrami opera�kon2� $D5R� . Obvious)�$\to\infty$�.�2! $\x$�͡Klk6�8! � 555 ��>{Ex������u- E�-�U�����&�heBWmBd2mbyI�-��} 1�8 N(\x,\y) &=& -�(\x-\y)+I�1��OL"u,E� F�,\y \in *B�~ \�S�xE�\n}�0 _ F_\ Q�,\ \ym. uF��">t $sEy�m d up���dditivev��is sym��� (Garabedian}� >j exist_�:G�"auD �(mpatibility|��s��$d (i.e., bH"�of eq.|)�)�Hegr�"o 0 ove�%�$ due�A7�(D"�B� >�:3A| truc��byM�a�Ea%! x $HMN$-,Aubin} ,I� = -I\h(d 2)}�� ,t �n $%��*�� ance"��!�$\�0$nd $h(\cdo H�"��,act support,�l!;1  $neighborho�` . As�onseque�� %4 ion U�-1 �u0��.)��oB!k %���ven'"o""%$% we multipv#M0 D1})!���;MM �+$,]YwB$*� %f2i�!A�J's� mula!C�%�i�A�k \oint_{q�}a� (\mb{S}),\xi})I6\p���+\,dS_g�HI_1{& }\ `%U}�\,dV_g+�omb `2�6 -2C��L7"uC} E���i-��C_*� =\(��}�� Ceps�A�n ��It7A�a(�AS *� � vanish"&so� re e�b uC})�t)�u%y%�=6�+�"+ #p)�_~�!�6� n-�, - rep'1 �, $!�S}e_�coordin���!.� E� $AE9& ele�>1 associB'eG#� c �� f%5S})- � Q�,\]& choo?�!l��15{a�n9�%id-�0��f��iw.�Seq5��)> q� �l ���co�v(*� j!.� �be�=d������ i��})#�Q�6 )6��� {AG!}!~���>N�f� �\B intNF� ) \p}��nE �)A� �QC� BC�8 q w�!�D�Yy5�. ChangaUC @aUA�5�$2�$, �G� �-���oten a\{ 6d�3C b4 :�+2��rep �ejU $:�2:�d�,m@b�*�""J �&1 -0=�� � � : ]d1�_a юSeq�E& �)�beeM�).c'H"�(Z "� S� t \r~%�n u�u&Z zb)ctu1h*i$��� ��M7cA��"��: �(�" d $s$. Unv*A�� �assumpA�0� �n�,� a$ A0s� J"� 0, but develop ��� 4as �a�C a�*ach��E�aY.��?$�$Mazya1}. B -]�� �.2 u��:if P%� ��@I(O1 �analyticV !� �G�seg*�*n powy �rclp*�i�p%t�.| >� follC� same step!nyA-Q����LZ�,s� 0��I�our^Q�,�J6 2! r 2f /e6ApB%X$,� I5�P ) implie<ah.� 2�I�2)zAf�rI2c!��i6{dec�$A�o $a �� n ^$ $0�"�� �>�.e�er�#4by $(x(s),y(s)�'r�.le�1&=\\.\{7\,:\,_ 2,s coincides  &d o"� toy���We��$ose unit v���mb{e}_1l e}_2w  �/og�bas�3Z� h1e!20q��� ] field � X}=x_1l +x_2 �%A�� tens9$g$Mw Bwg_{ij}�& +]��*$sum_{kl}a^#$x_k x_l +o.1/^2>H|x_k|�v�+ 2% � łm$��,� $�KA �UI�rM�6W, .�!��, "� =d_E� +2�+^2Im d_E�DEuclid)b.E an nowGth���@ �0-�>�%:� To �m�p"�Bu T ŴV(a�E�when % T�E2�R�@:��, m�E�')$ �8 s �[p.247j.(7.46)].d)s��<D gain^ .$or�2,..v ofA``R&�$rge". D39� �( \tilde v_NA new � �9 ( .1A�g9<�eqq� }�t_{|s'|.��9�5 u(\x(s')���-lo�a�!W.) }�&}�%]f$\,S(ds') =2���C& M� /U�induced�s�$*�AB9�V\x=*$��P =(\xi�eta�$~&�-�%AKA��kg�!.�5A),R� , \[ f = K\sqrt�')- �)^2+ (y!1-� ^2}\��!�(1F�)f �)� !E) f(s)=��j=0}^�, f_j s^j\,ds�Mm ɾ�2�M'JI v_j- L'gex"���:C&@& @i� know�"C#�Xd $f_j !unF#,��be>a &� A`Qo� �.e . (�%��:VGB�� '� '),)�$6:$-� �� *� �ir argu�� Q�� s B9A�6�$,8 ,/ivelyy7(*M &&�-��}^{.!�^nE�� e(m:) A.'=-�expJ3�ha)Z N~,d�*. 6 3q�i�q\�'-s��ft(1+|-(s'-s)^= 2�\�-n��.��K keepA�Taylor'65p"�> $%2!Җ$&�"�%E�&�hig>(&�-9 "7 pos� &!6�t8>T&c0�6ay}� t_2| 6  $ (s -s')^{��ds' =4]� %(E�-1-� +2��1_�  }� 0{% 1}{(2j-1)j s^{2j}2�/ -1}}.Y�2}�0��+(ven $n\geq0��e haveF�NB�aa^eJU,B�&&41f�== ^{n+1}}A<  | .0 (n+1%���) -RV)= x%.�=z-2j}j( )}�� exp3BP��a�odd $��bRF�VP{n �(s:T-4f'��� �:(-E6]'4B�U� �� abovd�"�G� e� �c"0q 0"F�A�&v/�q\�C-1� c2E[|��|�;��(1 B) ��]+%)m_.I.�?\}\timesI��8F5~s'~ ds':�q�� d��w7A�ʅ�%T2m &&=(.=. �>f_0 +Ep %;(� v"Y=� pI�Y2(32[f_{2p} r�M�pi�=�  v_0�M�f 6\. deg0Z�� �|�[1�p � )s0Yp A=E^{! }��p+1)}-�q "*e:2�ŴA� EaNO :�$. Indeed, � V "]r!'!ID !)EI6o!�"t$��# �h R�� .=-& !M�E�u�1F �o3�� -�� 2� "O;02W:6G2� �99Mi�2,K�} �y[a+E 1=BD&j&2a�+$.��!�9R�(v$D.K#i.t(�3� $\�&"�out"�g�(i" 2+]= �"=�;.  \pi D���&�'6`)ll=�5*0�a/@ �<�IE�/ �/ck a&>,�icla�a!OO,dq� A>@.$>=�;he�@�1 ough�a�FopeH. F�? �?�9a �� h&2$v�x}.|,F� I  v �[ -1, N� 2�@� -1} ��.� E�{"F)vA�K/&C)Vdr=R_2,&+)F\MC�](1, \;|\thet�,i|>}yvyv&=&0j�!82[ <.S.*-D!� !�fV'$w&m%IA(^2-r^2}{4}}�a2A?"�Q�B��-13wexio�GMY 2XB@$r>R_1$. More spe*�Bit"�)A�& 2�.bcw�c.�r�v8���2_ < �`B�Se�C�of�2 ableř�ic 9�u3} u(r,��J)(a_0� ;?h {n��t a_n  �{r�E� � + b_ U�E{r#{�/� ]\cos n �ta\A�� @c�*5),Q���$ $a_n,\,b_�$�@ N,to:��$"��� s. DifjBi� �., r$ yX}&� �^o=� n9W n�[ 9a_n-P>2=@�77 b_n )a^2r-7 } -7^{8 :y�%!�.>c�) $A�2$� F�B&� R_2���[FY)(a_n - E=)�R F3Kt?�?,E =>��S�^�A,we 6j1Ͼ$� �~%&6� �!�} :�m���G^+ ?)B�,"v "�'sC%�1$� du�S�$ �&]��)�aj;9B�R_1�^n�]�E;U�n - �< n�.�6U r�\Bnz� �!�+1�Ir�b�&=&-Ta6{2! K%��JmVS � �D| 2�*):J m�F�c_�Ve���I�V�I��  �]��� *� �"�6/Oa�($c_0 = a_0$A� vert�]�"�)�>�6�cj�)c�� 1+H_���M�R@\pi.'A�tF  pi,N= F�!�.q]*�. Z 0r{-.c"o0$eq:c_n-refB��nH_�1 , OG{2n}}{1+6G,X$%��!)� H_0=�it�;�L��UdN. &�Dy =M4c)$ which�"d!� zer�one@r+�D (�AvE�A�$n�C$�' ay r�W�$g Coll� �)�* 1, 2},� also� 2�S1})�4hzYse� \iv 0$ w��S4"now tr*Bf'YcorMI"5at��X*>0 non 3 ing !C�5":*N2fT����)OQ�j# �">  � cO�E� .I�v � ^�.4}�h_1(t� t}{\� NI�-e" t}�3FF..W 0< 7<:�&9��I&d� 8)$�%quelyA/ $^Q1L*�Bs ?�R�T,q:c-h}2��{ �&Q%80F1 �t) �=[P_n(%*t) + P_ŀ��]\,dt,� "F� ��_0� ��)�� intN� �iB�IF6Z �#h��qJ�B3�2 sin *.� rQ��V9 )�B�ITBD 2E�sumA�6�Substitu ��+)a�qv�-h!#�Ia����� sumNZ� "�o�[���[�2.6.31)]"m[,JG5�heavy�}m� es2}}FnUc Nc])�)[5�A�� �� F;e�-t66r) tm�� }�6awe�a� $>�@v"{,$��aBv�I�qjV�A�NZ� K_{Ū}�2,t) W9=��e�.�m�M�8<cos\ds6P �!�&q:�+K��A0$kernel $K_� 9��J�aF�� �)�.�F� H"2� V�) I&-�nB�I�%2}(1+� t)B>� \�O@U=4)q�KbB��"Wasu$aB1Kba�s* HsLyFF8 %�Tg_e�%�`G Legendr�!lynomia�$8P_0(x)=1,\; P_1 x�3�Abel'�$�Wfow<rIed��@ �Y)�7at9��f"�,eq:fredholm-�P-type�La@Z��({K}If (t,sE�sA�s��o}�� d}{dtL)0^tMwu!�]muI���%�u�� ��,duB�F\*�V:%�It ȡ pi�,:�m�mq (u,sE��E��.� &u  *v%�I�2\, z2 BY�s��~�!Jy�)I \,j� !S+"p a3�'�Aa2�I��oJs�Zmagic-..2} s= � �>!��sQ�? ��M�QE�b��CF�A %��!^Mur sin^2 �t�Bu&�JkU�a+ =&�T�`s` r �jO(I4F�>�8^��<Fm� 8l"�[�8� km  � $,�F�(I-��)h = zB"e�?gz(t�9��"��#>I�1�!J2g�u.gg�)�$h�0!DRaJ[��5�� J^2 ldotsJ��co���Zin $L�bSince�I�P l�Wh,1 \r $ (Ւ � )��3A&�N2�!!�V�6� �[}z, 1 ~! �:  B'!�F�X�82=!�"�i.�)'+P3� :�+ 21err�Ferm�6%?>�2��"%����!1$q}2)[\rz#�D� by�i-"� ?� -�>J�N9T�% e(�m��F.� t��Xa/s}2�$�L��s�ws͸eTy�nSsiR�� e'�Z���!�s��ss. >���.� u -��ѴBi%Qqe �.� �&�1�T"pFZ2` �w2Vve %�%�! t = ��N�BQr6onclud�v� �"�6 -[�dM& &M } +  d 4 �`[.�5� 4)qB��#jf n�a i��1� E\ta��*�� | A�4��a�( ���u 01]!5�� {EtaubJ�Ba�JR�% �BQ !Pq��Ft�2C ��RbBRbu<} 1U&���oY<&�_22c�.io�5 !�. !�``W"rk"�7�Jaio2�&�}I/=�"� )�� sym-GH-a.<&� %`5H.�B�*��W ory� �&�h]B)),�aN�����h��x9N��; A6�_F�These2�Y)���a-)orp7�9(they accounf: /�S��A"\s)�!~Ep&|*�1�)*�aut)Z.�XerBbdu;u�I�P� dHN�qQ"an}(er !�e�?9� �s9�-m5 n immedil9�X��_n%�8S>�=�g * Mlux�'S( � �' $&�T)Z(Z�\.bg�sDpd%�pplyin�complex  Z�g mapp $z\to 1/z"�y_ | �nU itse�ikUpS %ro�"� p(!z.�s- b=�:,rN� limi�=A��ClE\2m9!�ico,edmX^&! sh�6"�+v&e�= �e�i�f�&.�.� �58!!8 ex�-'B�g 2�� Rffa�@�rM M�$=�"�is> {!4�c%alI`H06"&f-67 �fe1�=\s.DfdeWclo@k�!)$M,�nm0"W somew��T`tu5.���Se�qaiJe obDU modhk�`,%[>S^�jo^bly��s:�a)..�+DX`m��Fs} Co[>r.�+.`[ e %X=(0,a)�1 (0,b)$�Ka�m$ab�+.�*�N w��>Y seg�8 $\%+k-_a =[a.@,a] \{b \}$�=,l�>,&A6�X��)t& ���*V, T&1L:�!M,f(->�:8��&.<,"U] �6T -&�U1K"� ��&f��P{b^2-yt+2t+55bf "9-��F:� .6 F�:9:f}9': 1\{0}40[0,b]\cup \{a2 [0]_ 0 \}�~-b>� U.�2�"� 1�� &a)9��*f��*z�O �)��Q���ƉJ~��BAx�m4u�2%�orm�@sZ�*.� u���*�}aa� aj~ �% cosh� Fny}�i n xUCm��2�[*�H*�G$y=b$F�u(x,bL���jV� =Y��](2E,aB+. �U�.y}>�!U!<\Bl'sin=� Z� %� =Ym �0,2�&�q��&�&%� s��4n %"6i^F< �* B�"n�$^�%�OA"� <S">BbR�% xab��i�\ 0 X�%M&lU�1 I��pa62.�{a��� $� tanh�(661M{)���%*� X$ = �?� �%�) &oexpn\{-6p)� 6\&�r"� �"� �.7 5")l wr mathe:!G.�},%F.G0"�"������(J�c_0��IK21��L �%�2G &G�!>B:z=Q@46m lB>o1m��� 2�#oB!�*��&"R4)�Qly� Zf�b,a squ�Q$a=Rro}"�N Il^4\�Rx 3  10^{-6�o��m In�6�]�zR�Em�8�a��b 3�� :!�-�V�7�"�{��p2�p5��!�^�38N� �{ �� :���v"/twi�zs lar�e�k.��Fh"��g )("�,prnu�a�<nsm�h&Le(:�h. H�f7��Q�H �  "��=N.���\�M�<|!N'8WFwjr atC jOu is 4 -L�a�&{tOZ D .@ H"W|3�q��--- Fy�i�q�OOsees rL�kn)��(wo perpendi� mi�p�m7gep���#)]lo�at�`r�>�p;��2*��t '#��so 2�&� Q�&l4-)!} �M�Y�D ��(y��6Kp�(J�E��Xs:�am:esE��erq9 X ?r!A ���E non-5b+ ?a!;^&T �s z�*6�s R�sa�>�pJ�c&8!@*� og z�K�%.�(E�q + �PJsi%S�fs.wmr"�P.��-{\bf ToA�I�Z�m�"�l$�k s un>d u"�Y"���f: -M (F y),v�@ n*���v^"!�"�A&7��G.ey�t�ICral $$�{�} �_{�(}w\,dx\,dy  e"� } }}.l� w6k|\,kx,yky]*� $:h = -1/DBLa�|o"�rs�ag �W:A w = (u_�u_y�}_(u,v)}w��$he Cauchy-�e"( �!Jacob~��&&s�!�$J = n ��"#�UCf()�)}:� \,dv�"�ueaz!��2�Aq9�f��n]�e?iUE� �~ni%qjE �ed2��sZ-1/2)�=1/4$%�$(4 16$ (nFiF�v�J���� � $ i (1/z-1)iE�}%� �!�>�*gO��-��6{ ��uspj��� �F}�B}���� �C$$b}.edv������"�w1pX-�)_&�Q��hen����anAY*�4i avh^ $)�8/�\-� 2\p:�K�FI�!Y�r�a�8F�xb**� two �x�$�x%�o �gal�a t!5�tM,>LQ�͎YBYia�&\�zi}{�y}}Y�p<\}$ (�T$d=1/2�ar֋prel� )e^.��0 usp2f�.Mz42&to���C !iAa�wu|k) . m�-%"-�-9 2}) a�*B�� erm. $d� stea�~��. .�3 "� =A�R^2 (1-dK(�CF�H �9d(1+d)}{��QJY�p$R$!m�a�^� ]2��&�# althhHX��d�KK a monoton]a� P� $d� )��68in9a:8%m��I��}iuC dd\to 1$��S@�cs~!�"�IACe�"typ !�� !�A1AJ��+!)A&�proOoi�h 1.t^{\la�!�){ -6pT� vdescribT ;*r���:u�d techn�8!�B�.�z�B���[a 3&�}?b{S0"hwcaprE!s��eZIn A��\(Oksendal}, ��F� pherAP &`_s $T5\phi)$= x=R"?42,�y: \)  z=R 5 6< �x�KA�%ed�it]b�f��ap�,V^����O.}�$ p=0M{ur����+ FPT2h�j$9 ap�*Ol!Z$�� $�$"<]rot� al"Wl. Let�K���IE�to R}� n $v*� F�� M v F�?qv Me�� e-Fjw:1g1Q��isj@ M$ r2�$�r� @ ian,.'�6m.ccurs �}� �[Ure�^c%Irein]Y��a"b%DJ�%��!hi�^> oxis�!ApDx� ap:le})z� R^{-�*; v''�/cotmL\, v'��77ODEB�3�� "� %�"� conJ/v'(\pi).�v(�)=0;NBCBzQH&UF6@2CA/e"(#�va2H{8�),*B;ris�4R�=*%v�\�ik = 2Y ftXsi()/2�5sin-B� Not�ipri�/��a�%ureʁ�#���� ��\pi�4�F7v7pox{max}�v1�-��si*A0)��4}�. �Ah+�� %�|�,O �^2f� Qs, fR�l k �.�,�5.%.�^2*U ��#}� �/ v͡E0)��/ .�&&\\�:=(Ilog 6-A { �+ -�"�:%Fm.lfqN�:��=� 9%F��B�mA\-�I��0Q�E�arJ|&q�s -no-q�} }:y_gD=piE � F�s��^. �_gF�� �6� R����ma��}arO �9 n.�q�� aA�k���S�iP-� � ���*��)r Id���s@1]_��,���l1n"��y �f�ۙ�6l c�* expl��Ya*Rt��"�%cle ``7" V�!+Q�s]!;>P0��:}�A~�o�8.nr� �w*�eu���-B��fW.$h")!,p�Sqe�"{!vS��� Pno>�(4�.#s�nyAA �v!�+ODE��r�M�-���#e}C4 pres�/AqOt>r�q �7fe� "�1�E u!E% a j) mayp4 ɠ ) � ��$� |sCloF��j�eD9�!ar� Hilli���Q=�f,~d,\zet � � e (oft^tall�he:G)-xi^2+E ^2+(H���$�proje�~��f-$P=),0� �u�pa�B�Ex"� Khi���)�R y�<etaB r^2=y^2(>G4 aE�: selyF�\xi�xR%�P� � hy: y 4{1;B ^A1&�eU/*&Zs J7�6�J!i�)��J {\em{�e �Aa}*. An�not�isomet�G>� � s�&� � M�@a��"l") $(%A)�6t ��Ij( VE��Cartes� �iaO�� apit|z��z@r8X�.��&pB�r_EA/� � k N�A������6��)raКed�;�!$ar Poisson�alQF�)@ V� �e1_Q�:�J r<�BEsuba�a�!z����"; F� V(r=ZW 0B_# �}V(r)="� xrs2j�i&T'R�#"f7)�-all-�} c!�%�1&9�  \� +�%%8"� F�1��g back1&*6�Yg��b:$��v-��} � u �1�9o�$� � z z� A�ac�yEL&_)4A�r�(!an�� Ղ�.�?�‚ (2R)�T&:at&f7./M?actly& "�>�b�6�6��arc.�g�N�^a��de�. ! � ��y"� o�%.�.��zl:�  � ��"�2Ve}){�z��G AdC>{. �G�b� �prece�$�Dm A���e�mi˧�oFn; �n3�p �p0_s < ,"~F�F v*Zc\bigg|_{�gr�_ |6 -\pi2q*-B�F�\+ alz}r}f�V@]�.�_�`1_@�Lw(r� .��T*%-N���$$�y��6^�,*�5Y;&noeqM�:b&� �2w$ 6w�f:�2BD>�YS >SB�WY�Q�Qz�QM�ѣ}{2���^2)Z�]�rp Scal�N�Jr}=r/_&" #� J*u7��b���)a�3;,Nad�S�the�n����7A�&tc�h �Jnow r/dt�*'���>%J(&.C\q a<$V6a_0 = ��2.c2qP[&�*� - >�B�J�,^_�'�}oG&�=Bz ��"�gV ��/MH��"o/�-;/2}��i:"i iA->fB�D[E E���B�2a�O�^� a" :�t�$!z/ $]^n� n\phi*`B�h���*��=�lyA�t�/Hi�/" �A�*n)�ek�B cMi%��� !�Rv ^�w+ ꆜA2�$�KU�M EtauB�P�5\ �E�8to� E&.J%J 96qC 3W4��d%� A�bZ\ E-}�&[�t��t�������`���Imi&�D�� �$2Jj�"twm�!�< 5 %Fe6[� bri^�i�.Hwc�D�Y�i&1:s$��E�&���i�z!{Y\}�"�0��?�y}e��a H� onal2��.�,Qwt�B�v :�h��0= 2"V);7 NOs���Penc�Der��a�?j �C!X��@pj��^�h� N�1���]2R@�5���"r/ �? - 4R^a%/>=.�NZ/��R�6lo�4:8 + 3�6�6��6Y~��O� ����#`zU�:�!%�i!�%�i�ximal.EL/�on�.�,*�\%�al .4@��}}�+Vz�aX6phi�^.H� opp�wA�-di4}�a\erqW\+ FnV�� "��6�)$�$2<+�ǭ�4�2�hal"�I� '�2�*�S=q Rz3��h �al1��'l.le�F Fina �w� mark&s sa�J�K �%m-}�r�" { s����!�R"l�.�5asNcussed SvR�6|��@ aprG��Fd��FE��4�A�2�� �!9���*E(  �B�/ .��865x&_/�e F;#on5}*$"e.r>a&�"v� [_M C�Ё@s�Y\det GC\i,j�Ju�����al \xi_i� g^m� 2G ];.�B<]�+Z�F��}t}_&�\�d{r\T6�Wg_�ވ�<J, j>S3G� 8�c �= �b��}ѻ]�"� ��:5{2g_�[�#�!R^/q phi  � &��]* ,�5W0B�] m�7&�w=wC 1 *E=�QKAJ�$6� -�^22�D �^���  \,q"8J66IWE��W�:m!]p ! b�IpB \no�%nts,Ac}�led�G:a~�7earch�:i ly s��|� $ gran�����FIsrael S0� ce FM�g, US- B(��R)"� NIH G`d No. UPSHS 5 RO1 GM 067241G*b\thebibli��8y}{99} \bibitemW} B. a,$I%, Channel�Excitao�dMembranes}, 2nd ed., Sinau[�(Mass., 1992�gnO D��ֺ, Z. Sנ , ``*�*f�0eptor7a>�synap��m �:;Kh^u W&" �8J. Stat. Phys.}� prin�k9CX� A.J̐$rgdorff, Dx�t��R�(!��� AMPA� �7� mov��s�NaY } IZl417} (6889), pp.649-53 (2002�12.1} A.�Lg!c=7.N4R.S. Eisenberg� C ]8, Part I", (pre59 / .2�r`:aH II:�� N�!�>u�M�H.P. , Jr.-�Stoch�� �dlAwXAcademic Press, NY 1969.qIY} =-�ThR6A&�E�mA�e�.y ��zWiley S{mProbaA�TAl��, ,� 1980.�*ǟ P. R.  �!�}.� B�^�4^ �� T. A� Q$Some Nonli<#�lem�hian Ge� }, SA#EqNY a�8,]-M��DV.A. Kozlov, V.G. % 0J. Rossmann, %} Ellia� B�� ry V�).�2�8P�O�]�#i�}, Ame� n M��9c�1ociety,2 Surveyd Mon�$s, vol. 52��7=>"�e I. N. ��-EM�j�Po��al�Zor!HE3!�l66.lFJ� 1} V. I.  q>�`Q� in M��}, Kluw�$1982X2^jv�of{ �%�Thև2� in E��e9Pg2�9��%u�$Landkof} %!i.  ��"e�Modern�{%a %Q�8-Verlag, Berlin!p72�C1l1} W.�< , ``On �!Z�n�/t� �SE��4lectr0� 3( oiL�aps'' �l Proc. Cambridge Phil. Soc.}�#57}� 367-384�6!:59 �2J�4] n<�ctrif�d2� situ= i�& n ea�0d coax� "�hod� cyl! r�a�c. ��623-627��"Z2� \O ki2))^�25th���)� Heidel� 1998.x� 2} E6�A��F(�.}�/D1, Chelsea Publish&CF�na�ew York�7e�endB �� f�;0�\'s{B \c�on{An":��.��ys�5�$2x: $2*�z$$ (dashed �) NxT��&�� soli %�3da(`*�*88#m&��C�� \i:�� =R"��s .�A "�"�S 4>;w��:�D�.�!����>�A �� �ak9u%���>&��!:gl��4[width=6.5in]{�6=@!�p�N $(0�(A,�6 ' dot� �;)�� *:�+�Pl$:y 5v6t:�iFmGus �=��7�q!5u7��2�"RE1�Z�*=�"I �Jof � %��>w�7(Z "� n%smat=.}.��6�doc0�d} C'% DO-minuncert.tex %p� ac oscill�e nonzmsminn�Der��ty�p  h % C. Ques��Xnd V. M. Tkachuk % subm���jJG < A (revised) \�c��[12pt]{cE�uWR,ckage{amssym�oddsidhp�Om^3\boldma"up$>'xxN(XB(pRPPB(h�}�ox.{ \hatHF6#N}{ $ :�sigmaN� BQllN-LB(ssN(SB(jjN(JB(tphi}{\t ��>�trr R def\�#1#2{{\A) style{#1\�#2}(.�tnA eNB!I aB� bBTn}A�`sloppy \title{ %\hfill{\�ſ8ULB/229/CQ/04/5I 4%\vspace{1cm} ���0} % \author{Cm�$$^{1,3}$ � V M�4$^2$\\ $^1$ {\��I�<Nucl\'eaZ�Th\'eoret$ � \'� que, Uni|-$it\'e Libr�,@ Bruxelles,} \\ l4Campus de la P�2 CP229,� dlevard~du Triomphe, B-1050Q8ssels, Belgium}W��mmu�< r�J�U^ tot/tropic>� �ain��s�� *~�Dia7���ext+�a�A r(ime, namely  �ysp";�J- V�~. Super&��quantum"��alef,shape-invari=� N}xu���e�D��energy�� trumI wave�5mo|^umF=$4�. A�M2n!nalB�(rw!ne!�neg��-�_0P $E=-1$,:?"�> .4 $l = j ��#�" +� ��.dth feB s be!y conn�3�s=oy or,!� ivalently� $\omegao� *8�-InkMtr�[B&�, "G� 1 plum dox6o���5ny deg(acy p� rn a@Ve�'asBϭV@��un�Jed�iU�e8s �4m��!�u f&#-~:�-�B��, 72me^4ver,��S$j$.-U� sens)@�6g ones:�&�Lbroke�-�u 9�p:no�+ �)~�. u�� �F0A �� {PACSS0s}: 03.65.Fd, ,Pm, 11.30.Pb*, {Keyword4� �_; O"� ; U� ��!l%� s; D� V8 m��.��z$^3$ RexD� aNZal�LU}t�c0(FNRS)4�(. % %=���newpage& Intr ��| } Ma#W ter &gby Cook � cook} to �� unus�acc̴�O�c #in�e�(�:i��� disc -ka2}ic view)by Ui�Takeda �ui}0by Balantekin b}.\parAL-�R %���es"��!!Q��!by Mo�sk�$Szczepania1bm 89�- ho g��EMr�� (DO��K�& nonre�v �Hit�D�� a&�8K8ka�Gstrong��-U��(uplE�ermc�P�AoDO#=ro7 a lop ��!?.�K]Y$��B�Efew mp(j6���olv.�b�ofAo nume� phys( �<-s�j % A![2{Jx M-7}� stud&�m��us����;co� LmiesM�moreno}!R!FteB] 2S 2� H benitez},&I Li�2g�� % cq90" hift^u:Bde�" e}, hidde�kp"� y B gBG$kers, cq91��O i"� J���n��od��%N& tene�N�szmyt�j % R.�!�-body��� DOi"aŇ��veIN�nsi^�U3� �empha�Xi���truMmes�,(_k-�l �0ss� bary&t�-6" 7, e.g.,)2��93a, b��re� s quo�t�@i"<yn�� ofExpacket� a! gAe d"l�M+4toyama, rozmej n\B�)4the Jaynes-Cum :a(del�wa,eP H�$2+1$ ��7�a`*� � �v�lba� W3a���(st� frameworkb ����%�C; �%�new phen. a (_�a:�?$Hall effec��5I1al & ��s"��0en� m� �s�)mo-�A�6:p�Lco}�H�$16-do!] uez}O&)&� ioVBP�ren�<�ܡ��rk-gluN� lasmPdel��b� % VarJ�qUA�i��qt�4id� �K*� Mus �Jalterg*ve��Bba!�� sca Dc�=1?ixit}Қ���g� liz4 �*0 arbitrary sp"�yx6} or!pquasi-.L'%�4��ho��f� %v(A: pap w�@��5!w�!j��0�3DD�2��8t=#a a��a\EBcHe|$2m�o�3�v� h N@�xhU1stimut%d� seve��s+�'�Amrsto�i�`�1 � q� grav�a sugg4�hy~ istew � �RA�2"l�re"K7of �WB X_0$�<6�gro�$maggiore��w|n =In�ula1beCll� � v5 ��U���,�qedV���! drat��or e� �c� WB�mh$kempf94a, 7}. Ano���!^_H�s�q��a�yw�� E���ivC scri >La� like-7] ��e�p� and � ou �l�!Ve�( �A7olids,a��BR]nucle��W i27� f   % Oka� >� Q�Z&HC. 6�)9�(so far. An& [nM'one2W�"�E&� !�� ����� i�olvA"ZE�"z�ed=* r\"o�Ver2 "�(�%�2�5�is�>{�ɮ�to .�d!�Q�b}�#meetn�v� brau�!��i"�akhoury}� ult-p"�&J���gen atom�C fC N=��L�5�atd:,��re�� cq0� b}�<rB�fu�bӾ"W��.�icB�$s (SUSYQM)-�coP , junker� ^��ar^ (SI) �c*�WY<� Lgen� $htein, dab�ka!����M4�@$.: ~ , carinen&� � o��I���R�Mo � d��ack�Sc]� � schrM� �Infeld�k Hul"1E�T-h�alism��)E9SI$5�2im�der=&I inA spiridon�)khareſ�� ed e iI4 usefu�Aad0A fh�YH1^� nin��^���Yq�-�g4b}� �"����nor^ �fbe�d�mVm %"Nc0will avail ou�Kvm[݇e}to%iida�ZzDO$�YXvk 5(5E~2$2gH Newc5?X�_2C3C��uE�(E�:^!�n�L�=al^2?<�a>aG6A�A�tnٿ��h� �ly acj0� 6o6[� van�'. gZ�E��m�x)(1O4� DO9a&Z�CotXb&�a Ks~5�6:��� al ��Ic�6�7leT~8��Է)U�n�u�� �{M�]��t6�},�a> !Y�c�R�YD $\hbar = c = m =1�8(�I:y)a�!��B b�"� 89*71=�$H \psi = E \q�5H5K�# \�� (:KIxxbN)��#��"0BDO- ��%z%L%t=��$4ɉ�(4$] rix,!`bH*@ �=�5 # array}{cc�0 &E6$y�  & 0 �& >;5- l/~kIP;Wz-If_F7$\�$_i�i%�2, 3,E�A�Pauli5)!c�(H�wL�6e�� .H�� s $X jP q p�Gy&O R A�� typ ɠ7 5, C .�b=D [X_i, P_j] & = &"�p>�=_�9��ʼn P^2Eq!�' P_iC )�]"�D \\{A [P:e0 Y�def-com}.�X�&B �2wK + (  �')� �M \��$_{ijk} L_k�Q1q'M�Ma�H �% dumm�(dAZ+L*G: 1}{1�!E} :�X_j P_kM� i=1,E�u��!ͭ�Ap��Q �a�!�2��,QU� �RY..u t [L!�%�=Y*6RX� /E]b/�J� %�a� '�{woi#",��b� �"{ 6ra�&��M� ll  !%^Ds� �Rv&�@�)&1�O�*&J��}� �meri��o�n\a$)n the*�&&7"V��= X \ge.I%��*�j�? P#DE~t= �().UR�/&e%0e�g!g���a��Yin�y?p�g sed UV-IRO&\J� te���8Y�URfCmpDa��.l*�G5W X$: )) �X�Lm�a�}�m~m> % {}�u�a��` UG�sm���uOɒ��:� &D)Ye9(_iQ\N>^|Q� P_i]��|�� isZ�)2u5�!�nX_{0i��} �m�'�24-�3%���'}}�e:i�4�Lc��ne"��z�_i �e�, 2�� IA' i .~=�i$2����: % <;c�A�@(#eeq��, i�m�7�m, momentum co��mponents remain simultaneously diagonalizable, we can work in the momentum representation, wherein $P_i$, $X_i$ and $L_i$ are realized as~\cite{chang} % \begin{eqnarray} P_i & = & p_i \nonumber \\ X_i & = & {\rm i} \left[(1 + \beta p^2) \frac{\partial}{\partial p_i} + \beta' p_i p_j \frac{\partial}{\partial p_j} + \gamma p_i\right] \label{eq:mom-rep} \\ L_i & = & {\rm i} \epsilon_{ijk} \frac{\partial}{\partial p_j} p_k = - {\rm i} \epsilon_{ijk} p_j \frac{\partial}{\partia�k}. \n1@ \end{9l % Here $\�d$ is an arbitrary constant!�Lich does not appear McommuI� relations (\ref{eq:def-com}) and only affects the we!I func9U4scalar productmoM�space.<usL} \langle \zeta' | \r �= \int \frac{d^3 \pb}{[f(p)]^{1-\alpha}} ?8^{\prime*}(\pb)^V jb)�sp}1Yu �% waV�o \equiv 1Q�0_0 p^2 \qquadI�_0&\beta*'%� $��)� - 5'}{= _0}..�fB� \par % %-�B< % On separating�O wave5�$\psi!�left(�gin{ar� {c} _1 \\ 2E� \rA>)$ inYr@DO-eq}) into largA�psi_1��small v_2$A��,� DO e-˥`be written as two coupled's.�n � B^+ �� & (E-1) 1.��1} \\5-#& 5+52B525�vr{BA�m}!kdsigmab \cdot \ppb \pm {\rm�Tomega :&xxb2F B-deFJ% Apply!�0$B^+$ (resp.\-$) to ��2})$61})�6using:�1b72})��get%�follow�factor��5� for&E) coM M 1�I7>!2$)f�B2� A^2]5�6+>)2.�b1���f� !�s show����ndix 1i# operators!�+iV$B^-$:1���屼 re.>9�mom-rep�%jM&Q��.\{��p}{ }��[(�]�[) ( /!?ti6} +:Si$e# \llb+2}{p�r�����|J�})�` p��]f��\}mg_p.�B+� �6��_p �J+ >x!r -�$ j9^Z����LB-}J�jM �! �Q �%"���.h N�,is such that.��� r^2 = I2 V��5A�\V\8 % Some further� plific�s � Pachieved by transform�a��� � s���s accord)oZ�Y�%� 1}{p} f^{N /2�� hi_i�i=1, 2�psi-phi��18�� $f�b�$�defined�b�5 f}). As a� equence,��s*�y�Band:X��becom2� �y$ {\cal B}��hi_�ݥ���h�lQ� j bis}��>��+i�(��Q}?2?^ $T0{\pm}$ denote%�5�ed6� +� can*� ^�i+ ��t b! sR_p].>a�tilde{b%35t��X-6XTb^-XO-".=3tVF� A�ݽb-IR,irectly obtaE\ fromY4fWUlB+6-��.MQ�):OQ� ~� mp f��^F��12� ()-��llb��1)�i) p>�� + i�=Hb+-R�ilI\(alternativeE m2��9�{A���+ ta>��� ��+1RE�N�W �% result:�! � A@�Z�6_p,M�>y\!0.j anti#F�pro��in*� . F2��p� U�a] �-A�it at � B�t:C��)�3re :��0��$t����j1ter !ىN�\?1? S]� �A1P � �RZ� K=-���q22�%R�a���=��se{L�J� radL 2D�d SUSY �?Dners} \setcounter{1�}{0} I�p 2+ have dem�rated E� solu�to.U]%t<}) with modifiedM F5*m�s cat ofksystemFr6{E0R�A). Sinc��R���onz �l-h%�ide� e�*s)1�prQty$ G%$total angu�1� $\jjbAj�� \ssb��ssQ C e�$as well!m$C^2" ss !� may look��5�s�x1A�� �. eigen�s�p, $m�� J_3$, cor�on> %ODvalues $l(l+1)$, $ �3}{4}j(j !$m$, IA�0vely. Instead�l� �use $s$," (by $l = j-s �tak!�!� � $� ~,1}{2}$. Then^$' ex�s} 1�0 spherical co4 at�p�\theta varphi � spin variw $\x2G���%��� ${1;s,j,m}(�kb, `$, \xi) = R ' }(p)h Y}_{ 9>6"� =&� phi1� M/�E={2�� \trr *ʋ�s&c - z�a j�1/ \sum_{\mu�}{Tj-s \;  caseI2 \;!�e�( \mid j \;ms(Y_{j-s,\mu}>m) \chi_/}(%tn sp-harmo��u� } %�aI=Uu ,nic~\cbedmonds}�J$.E�6�$ (or,f0short, $R_1(p+2 )�͆.� s. Nq a����)a�B�$,� $-@=�.�a�� � a. or. �i��: % We��-aN.�0�Isam;��-�2�O $i;true s$eĵ�f 2$ s��,: E]� %�5^a �)�latterigiven byXbMѹ�J2!mY�K 6& �B f :F=-Zye�� Y��E�!l last step�ߡ�d a� -kn�.�%�Fsmrose}. H! w�A� ^ %�!3 {2;�vz (:�;r|�ph��:��J�R�{=F�2� R-RRJi In oTwordsa�!U�I7>characte^ghM�$l$�p ($l=���a���0 $l'=j+s$.��n�-<Inser� uZ��Jni*�� z{ a� *zU�V�R� 1F� = (E ^2!�ll  ^2s(2[ "��"^Ybi?acB er�{B� ��g^�� _p1�%aTR_J�B  _p^-/=6J2�%�2 ?�X-"�J�23 �G � A�� ��$V�S = (g,k� .� d}{dg&� k}{p2�bN�e: weɄint#� Ź&2�1� g��W )�1Bs I�k =2]g-k5T\��v�a�A*�}�<),� ey��#!�:] u�s�in *� ace�Os rise�a:?V � R� R � ,_0^{\infty} )� dp}{ } RA�w p) RM& �Q�1~ % inQ�6� . It,easily checkE,at�\ �!E .�a��  -� F�bp!�q Hermitian�jug of on/ �U��r�, % {}Finally>P ��\)��Y�9��eG.��F e�+���e��=��1a��%>+ L e::B� v�e"MYo-^2}"IY:We!� clud� R��rr� `b(ry N!�=8ner Hamiltonianz coAX<, junker}. Befor� �is�#to�ve�X9�h1)�& ��Bigl|� r|^- |)�(pB|^2:= 1c"��A5N�m#�$� vergo ��r��)%�$�� = R'������: ��" ~"  % da�NXquantum mechanics gover�� gm}zedAgF y�" e�has beenA5(wn, howeverA�at]@iaم��(be�$ufficient u�%\a6�to0R�" kempf95}:�9M� indeDeM� doO+ofa%p�I�Ymea�XitI?4a finite uncerstyY��=is lea ���%Z�(pA���o� E�(aFE�efn0$>V"��� ?-7a i�o�1bv(.$s=�1}OF�(mor�� �6� � $p^{-g/M�sC��O ��be ensu�H#a}, ( d)$,.*K !g&;1 >c� �>�!�-�.1U�J�( ich,)�6,��*al� \!Ij� i� � j�a�'< 6�)-jJ��]$$��� )�%�6�� Y�U satisf�/&� M* -j})��N��� $ immediate�l�4� i�B��y�.�p� ).1 A� a4ng!�z�I.6D jBZ_ � expl�lyZ�6A!��~Vw � �*#E�Bust rA�r��th $s� y7>; �!Z � ><��@]@ % Co��o E as��.�$}kH1g2q 2<�twe� O%is tim.� �~<��!:� %<�/E3$. Mored.�� iour)�:\����al!ˉe $�a < 1/2$��7%�!�6� :�in� l$ $6�N�-2$. �%` very�IM G�э�I1$Q�$,� �- �can��i�y "� � co.�!��$ 2��t]l��V� % y �4os�Q 9s2���Y*[.5 q�y�se� *�  = 0$%{�6J ��� 7BL.�!�%6w��*�d�ofA�*F� *�� � ��&-E�ed&�  $\�(�x \ne 0,| " = 0�N�&/ "�E��pm 1$� = B�2H �������.W�&go�� back.#& ��u�8r4*a��=��",&�*/�!�&�'U `U!�^� � �derivede�n":$^&� ��a � $compatible� $E=1�a exclusionA�$$E=-1$. So*d"E#�,�.hough:I�N0- �Z��">��is unq���sense eEi���a5��(%�9�:5��� V� � � �W!U%�%�;8�as�!V�standarZ�be z}, 1!2[2�L6�,�)E exis/r posi� �g�1d>� �+AD�S*:�!�.��� -� re"� occur�-R�,E u� �9^ase, nam %�V�,�*b&��o���]� �Q9u�B-�� B� .�Q ��=is.f�"nei�icl�@r anti�! E5�", vio�@ng��,�#3ifCrka�Er�'�x:whedq�Wie*VR�D==6Goscill�" M�s`-rumn50W-Vnow��BAT��A�Jlf!(aSultim� to��V6��)e��$rdaw%� 4� ults���(nguish betw�three��s (i)F %�!�, (ii) :/, $j$,�@(ii G-.i��+� \sub �*+C� ^/E �� 2tr &o�� J 4�6V��Q &]M tau�6�UM&bB%;p).&(a��g M�$e_0=09X.H� !xThe & !*��:%�A^s>,a��cŤS�by��� $h_0V&u"$�[G�membera;a�!,QM hierarchy�T:}!Vh_�;b�# (g_i,k_i)-+*/$j=0}^i \ep�Fj� i=0,.@ 2, \ldotsJa(g_9Hk i=#<,~ :,� DDm�s�1Ŏ!"� Z�(k_i & > & 0�i�g_i2� e. *�SIb�Cg_0& gMk%�k5!�<"m IB�#�� by "� a SI�-�Xgendenshtein, dabrowskaZ�!�=�=��({i+1},k 9�:+�pB�21(SI#Ne*E/&I-) &� r.�& � ( U8�!� (k_i(82�9�� (g 7G_0) Cg_ii��2K�55� R&�BW(2 ��- U 2k_i��:_0� =+�6s)SI3"���FzF %�޵��7�l�%��.IF� I2H�e�aI�*�iJ=-AisRZA�!� = k+"i@!�= .i2�kNr@��7��X �������p�Z .�&��i$ � 2� 1O.��Wf����$�4Bw��Z� % Us""\ A�� )� !.�� h_0$�.�9�e_n =���Z� = 4n [.�(k+n)]2�eN�%n"�( � &B�� yields $r,-(j+�))(2-2$� :lA;W9Mb�N�9)E_n�/1�C/^2!8!  n�#[1��C (j�g&�! @��60 n + V4 ;].J�*U<6��p�>�,�assoc� t�.�B.n)}* n)�$A�A�BC<9�:X &� "FE�$nB�\z"n=G.�.�.^#�e�y�7�AnegLAZ,$� ++� �]���$$j iV� ;.�< B@ \&�Q�%�in��!hm��> 2_F�Re�ZnoVm2e�� a!�x.^7ei" 2� ���+Y��* �s a �t|V�h� b� �2 -��-�0f-��2i�)++g (g-�4)E'+~C�]@k(k-1)}{p^2} -2gk�U;  k.< h0"�Y �$e>&@&>@&! �� 6� #0xis pur�-��)��!nQ*��re-"CN��0$. O3�3ingVvg' �7.� & g'J ^ 9� h0})�<&�*^~C1Q 6�'=� +� � (- 2�^�9�&45(Bw,0G�F�2 but�$g$FVlac�$g'��N� % IGBre�a$RS*"\�� *� ��-]V�mN%]L�%1�%�}n��&]�m�.t��V �YAV�ee�(2R�6H N�Ty#is�-M�[Qs%&7� s:�3Tv�.1"*&*�&'��K2�&F^\'C$ >�A�<L!Z"� ݦ)� g'�rw�H0% �=>�. >Z#YI is b!e"g#�p  it=ntribtE��-p!V�- nvQ0�'B'� )Zy.� "� � be ~3K en})�� titug;�v a���g& �C2o�#o�unt%)� AV extr%�9,=e0}):^6 n [-2� (k+1S f"�*y¥�=�9v?`6�qua2� 2�.M ,L 6u$toF/ �S&8�&o, se, �)� �a"�D.� �"I�1 k6Z 9KNf �M�]�?b# k# �k�J��S 3H-F��qygJ .�S�AA,bBFh b_p ,k'"� + 2(2 �1� @� k: k� R �O6$2�^�0)�' ��h_�B�the݊Vw� 2 �^=*�%��.U fѭ�QVt!��')2m J� �0mhGte>�Q .�2=2� {k'+2:�2'2� JY S�Y�& )��25 { � $k'>!�� R�b B�� W��:hq�1?PIn} ��+(� &, l 1�* \��B� VWalsa`� ��&��%-%�!&�`%2% J��<2��j > �FuIis�-ed�� )��}Y�gB�7r"6 �1�PiSQway� �f� 5.�Rfin �az� � the 6�6� VL�R *@ (1-��@�Vb�� �� �� F6�6& � i�llA��~ �~� a,6� ?^{� � ��b� b&)Y�� 2&� : A/F �N� u�%� .";B�%�+4>25r�:9�s 4e5�f��7 �Oa b0%"L<d, thu�Cvie�u� tI+� c"icn�%�a� lowe�M�� LF�;.A|t��R planq calculEV� �a�; � n��)dW8*�yY RqU ���)n� 2�7���$ ��r�S!0 exciEk%-�B� � * !"B?6�Q]$. 2�Ia 0�O>&QM�+SI� scrip�#6�$,�BR-#I��H�rej+�; Y���f"�I;)5(o7.v.\X n)X ;p� �G4sqrt{e_n-e_0}}eo+� 7m(g_1,k_1=�#n=1�U"{%2� �oN/H��w�1*�Y�$y$-dep�$c0t�& fEg.6 i$g_�g +�ta2 $kk+3�'#�co"�E5\ki}:F]uJ�jj:A*x]2� �6�2� �|�9o)H 2 ) p^{b.z _ U3\2}(a+b+1)} P^{(a,b)}_n(z�&p� -solJ]<6{�G$6W� a&� a�.�=ELa Jacobi polynomial,2/@Qy�c��F�a!f�ma" �Wk�% qb&$�*= �( zc Az-!a"Z �m } \q�m$(-1 < z < L=jaJ^�9tseb�9� ��n�:�k�� "��c% +z/%� (1-z"-!^{1�e �8p��NF\�4nn4n{}�� Qi{*� �,��6� ��6� ���$vanishes. ���* -^0$E_n > 1�_n < -/& m�Z�r�+`5a%,�,.�n6�),mJy6dZ"8yY�j$}{E_n+1�~<;32`s�=_N�)|�s (see9`l2���B ��!\tz# \ta+%1)a ��\ta,\t�-{\tn}(z6�q�, J��-V�\t��a+1q�\t�}b.�n-2�Ta^�W�R�F= i��;Kr%� (�n�1�6�.�+"�,dreN$&�[a|e�X'�K be s as[2�b�4� ��=W%�� �e=�-1%��:��n�MO� �D 4, 6� ;p)*w&����a (R )"*!@b��u5B6�m4n�. cO ast,�J�B�&>I'��m`;O�*�&��"�8r���B�g�C�T� s to�Tg7*9iszn %��2#  easy� ���]�(sel&�DJ> 95�:�!59Q2*do�7l�ny rol�N*�^a�s � �9W^�?��S�w:� e$nco analys�&!pr<��.Ben ��2] ��$n�"`9r��K�96NA�Ic& � !m�is ob/for�ń&��7As���!��"� �F�'�e�e��8^{(1)}_2 \sim Rt> _1/p� 2�A��~��&�V�B�v2�2� B� �J� >F����w|e/Ba&�g��Yb2F}). UlC�i & orthogonVB=�koe$, erdelyi}En9�>^ :� = [(E�zE_n�y� A@* �$2A[� �y�A� �(~75�����*�R�}��:s�7�e|1�:� YJi��(o�$.;$>� ~przr�g/o $;o=�́k"�� tov�'�by  $or"#k'�ym(jO6I-ich%6 li� �>t��T* Gm�~un�Tg��"�OP�Ti�@nND �#� )5��B2B: % ��$ ��Yq]*5k-��8y{ �� �est�valid�CKw%J�$=I hang���)�6�a!��E� ~ya�> ), a[,below listed*� itemize�6 !сv�a,J*%�QK.�!:!E j e $NF$b$�� \t�U�N͌BY A�a���5 a�5*2G����f6tga-1~V 2�T *�O�O� �6�J9 n)}J5 �*6 F; s"M10% \:�2�>�k!x��Ux:�a�>��I��5�T �yB!/�j:�X92.�2J�*)cZ� }2 bZ��!2�q� cF� !�e��rA��� ~6.1�$s��zDu �`.�:�so�d�^rZ�S�Jcargum%�.6.11&�to� uT�!�6 5 m �{������� ��s��*��6*� B0)��)i%�2� uz@��h&rGt6� �gtr� 0"�  p�b1� �":L4o.� al5G1 JG AI� �G}� +2�!6%:y�>�!2�Rits ?&�+��V&[x") t "%����u �f[6�4�%vF�ora8�<ؖ�4EF�"s!>:�Q�(%�J�4�e^e %�46*MR�"��J�F&&Y7T(!:� �#.@\E�jN27�� �6 $s B-_ R& assumes .A*j��.�wDa�a��r 0"�E@Yj$�r�n �8V"=* {) �/Zb2 -:�Q�>US<: j)2y ���Jp% b%7s�%�.A��q�� a���{� r� W%collec�PL !e_ \s 5E^6E}!�ene J�G2�*�q1Bq1B % G"�M���*`Fd��* Ct&��%��e���DO�V�c � �!m� � , & &E_{nsj}~<&K�\��&� F�<q'[&nU��&�*e"�t�g0� {\��f\ } :V, \ j \�A&/��^ 6�~,1 �J��)����H\鱲�"�1m��f�2.2DO-AI�QBY�n$ ru�'ver���"F"�Eex]E�:� ,�� ��.�M��=<2R\��. S�8!h)gQ � ~�8"n)*�B{�LK"� T�),�n*0*N2�/��Ho>)fo��� �v ��)�j��.V�.F�E1�)6&�:�)� ac%�m2�(Q 6R'E�B�[� (/sUxbE/� �. $] \biggl\{�Fe�Hq�q$^�hF[\mbox{퇥�JkZ �1��s �.�j���r\&W1W% 7Hn"�! = & &��oaW�2�e)�Bpt� J �,�-)Qc�v^�{�=N~=�IN ->I��7��E1IIEm2lD5�. K+.�A6�(N2�C�2 ; ��" c���@Z�>.|D5.%&[- �F � �.M�.�R]�!d$�.�2^ ~  =r.�-�.K�E�I� 21JG�rQ.��oa�J� E_.e!3&55[A�# �E�7�;�Y2.) j�?*Q=26t�c=�&� �r�n7�Qqt6�=�S�� � ,>� ] as" , $N$�!r�At �&> E� $ in&�Nkz��:4�: ^: Q6�[.�<$�6)Id� � �'H (6P+� ,G�*� p� wQ|�K� %&\VE0��be V6QG6��}SpS��}(-+�6 �=|(.|i6�%q� �h}0(�$F�*ifR"}>�-" \�N�-b� �\tF�$�p^{h&�F�+*�&Z�&.F�HaoV���a,bN��H,1}&2n�*n!!Gamma%M9p{ b:�*MAn�) �a"xS�)\{��� )�[ >!�C �|�{"$ !�f� 'F�F +q�]�'j:�- s��*l$�? <��5s�D��8�I�v�ͫ �q {| |B� ?q6K�@� = +1�f$ �=�*�(BE�(j(�"�%�-�,6�"k _�#@"�[ fi�~��``�N8'' category, as�Eb&�!&�2�,)h�n*�T�)��& �n)rJ�n��5n I�fi �"�.� ^ � ny �Ri2";/:mQ�ikF��!%&� &f6�&� �a@�~]��=.Jp ed��&�(smoothly gofz�#n9on�u0moshinsky89, {`A)4*4v&1Na�K�u���u)0 of deg�p6T*45>%\C�.�+�6�.G N-j<N+j$)}50%�}.�cRE'n(al!I�eanU�@rm so(4)} \oplus (3,1)$ dynam�z, symmetry Li�Cgebra �cq90}�AjA�Bnon�/�#2O��.�~(>`1�cy schemP �-lAV oilt�AS=7N:~s broken5��6:C"kc&&�Tpaper,1���DO��e s�8� solv� *��%resenT� after�b�,canonE��J"�'s.4re�%�m@isotropic nonzeroLv�%e y�? ��o�("Y�Fe fН vmethod̊&Okd398��98$techniques�^�d �-��O� &vAS��a�gAe" ::>6� ;Y�X=��>+U: �:� �7utј�,lstudyE!!�m�c embl-a@)�- �C��j�'E�tOO,;-�rnoydun�ux�&�<:�("<Y2L.YBdissy���c<"�:�>�*�L�$�to-�-� �+�xxb \h�e$��I=uss�{ truc�KAKDO.=Z2[��a+�,ps>WEMe �[possi�na.:�\mpn� g�ur! posal�R�) �OV�e��/$q$2�E $- V9M_Bv-�b_H pm}( 4,s�+�x{\mp}( L ,-s)wZaney��i&Wo!vsta�=>�t�(�1D"-D�!{$Ew �#_늡�*dC $-&-6#_2* 16�.I"�}bEresA����.P @ m1< - $&�G��Uj1��nCa superѨ��1} �"211%.&g�#o�K&9g tI�� RmI 93a��n�*+nI� s�%�3.i�2� too, 0,1sabs�J�-����g@� &W $e_{0sj}�|M�-1$��b�pkT���=" mpor�� differ�C�&�f"� A�.l��͈��j�U$o-k�<er5D,ex�w:n�R͡� mM"�%������!�&� &!M.�s�d��cA"ki&OlinearE x&?T�.A paAnn obser�py�x:v>/ 89, x  ge/Hm6� &� P�Noa�F� a� ��:� AO�2 %�t un1�z�Iy�!"�11>ewE��es�featu���0mn�trum:!I>9 %~U#%4y!�uoubm �ict&Z�;��as gb >J)&#!�2B��n4 (A��.1T��� p)�*�26��)� u �7�VA�>�32�ynsa�yiaNB�acquir� 6Z )� � >0$ �^�[�/-�$s6� �Y�� � �. F�4�5E�y.� ['&3 .�E��!�:pQ);d}r� -tz` 1�+ii*k�nw%to �esb�V"%h@�3;�):� ��2�}S��!�AyecB* �� @l��ple�,6}xa&�  typL .*�D�� b� t rV ~3D2�open ~ ��!�co2�!5 � ĪE�TA�DO-���.* �2_DOA�@Lorentz covariant�I| no},�$�<wIrK 99i}aeAL�R �([; ʥ . A(- .r�F�3 a lo�X3zat��ntM�s��-mayS �.�t�in �csnyder}u � 6'}� alism bas��O io.s4"��Bnot� al�Xy �(tPmaggiore93b}, a boost�c squeez� y ``W� '' length�y,s $\Delta X_#, as m(Ps%�lik���a *�e!j���poiɲAY{Ԁ�:*�I r�"l�&�^ �)�ed1� a (� ccur�m, e.g.6.Tthe $\kappa$-Minkowski�t�53�v�Gac)�Q�ajid}yHs% �`XwĎc6� Q�^ �0�DO �&�o6@i^%"f a9Qof�yBPte��{;ch��mA debaD�� ecenM�um-gravY|liter*�te &�z�P�k-t�� parKQm � �t�X�l�ntaOt�(i~ �reA> se2h!�-�Uuino*�'��� �,**�qAp C1��M�sj�ya5"�r2Q�} \renew� and{d��0}{A1.\arabic{}�"&�-%�f>�R/cI@9��aUoAbV��7�%�"?)��a&ע�&R�� ��[ n[ �� ��ng�&��ina.�-o*� �)!$B-��=f V 1+0sG�"3�pb��>ׯQ3�\a�  \pb: >k�pbG$��6N6K+93�B� $6�kB-mom�3����'^�'!�TE�GT�\� qU�a���9.}N��ioZ[W>M*&��$O_1$��:!F'2'=�J1$}1�R: +&�.I (J2OHsNm�>�%aiXU~B�vector.�Vl$HR�� ose ��"�>�tx8R| of�b$D�?%��Aa�O:.m&�">�]�.4�A�eJ eGI�"b!a�K��!r8^�i�(`6��4rHm.1 = pf1p�6�llb.�!r"��~:.� >4!\&l�nFQ�pX!{oa:��MrFkM�p���!�v2!!+32$2YqQW%8alt�w%&�(&A��e%Qv�5)oB�j� �� V_p �r|6�k�+�B� +3�="��y�pSnG�� !��.S*us�(� a��$ �_��.U@�p�7P��"� 2})�Fnfow� �crit$<e�.l�r �/ ��"��*�'&# �T�.{�^Q{jI p=\'.�vt%� ")9cllEk���Lj��f%�O m_p..�opF����YbYZ {}Fu~�&� �  $N.d -�2��F&.�J�a.����>Z�\N�-���fzA1�]%�jAc^Up� %n"1�6�2&.Q�%�%j��v� �}�n0�R�Ois@k�5�� >*�� v� � combi/H��Y9����HaS:� o��> then stra��forwar����sOV��b�&�n�co���&m:h�r1}:r2!'Avq��>B�_���i.>�� p 7ɫ��2�n�:�J>b.;pdu_Φr  - 3&DDyzp>�llb� �b� V� �^�.��)R���RF\�c-S��3v.J�T��#s@ �A�q�Z;��V׸Ӹ�[ �U�nD,"� � � �AdOgma_pFi&� ���u�q�"��%�g��!'*{"� 2. CZ`ofvQ_z�2�����N� tail� EP��A#:(2 6�& carr{�out� -% 6 5s���J����cf�>3J�>=&�x%u&m �L�.*BK�Rit%Ys ��%:2".7Y�gs��� s�b�u*[ irr��U�>�(� $n:$n�Zg g"ާk �&k_����6��Fd})�9"*(Ns &�&& �`)}( nB�.��+�X-1-_�` )}{\ a}$2[-"0��z7 }'�X�k�1�~�."��)�U 6a4{��]�3 /F�3t43&%3JZ a+1,�__{n�X>{/����_��[- �]^��f 3!$z!$�](� 2) z)]Ƽ2n;Zj�¿%C"�`��QNSB� the 6��,u� eY (1.8.7� Ref.�EToe�T�u�-o֒�qa=(�*� >i�,u"a})�f3��G�@%B�� v� �؞Gtu�$urselv�o=%�υ�y�  OC(B8 $I"}; ��-�R�.ouG�6JbF& 8)^{�6��%6�}�PI����XVZ^:�f �3J�aG-iʖu(1+z)��m����H�,�+�7Z�+ ��$��f^{.�E3�dB$� y�&���aM3ctnes�I {\bf 1} 42Eui} Ui H�0Takeda G 1984 LPProg.\ Theor.\ Phys.} L72} 266�0balantekin} B A BR5 RAnnI , NY M164} 277Nm489} M �9$zczepaniak�89 ^J\8\ A: Math.\ Gen�22} L816hr�+!�eno `Zentella�] L821 ��1L Ben\'\i tez J, Mart nez y Rom�:dR P, N\'u\~nez-Y\'epez H N%�LSalas-Brito A L 1990 �%�\ Rev.\I-Y!X 1643OB��ރ$5} 2085(E)=k2Quesne C�.�ۂ�3} 2263\del�`} de L O LSm"�S4} 66.%b �rs!�ckers J� Debergh N]F�} Di,(42} 1255\\ j���V��=�\!03.�cq�75\1@In��Modq+�e6} 152�ma��ez}2�-y-Y�%:�r2I�li��M�33} 1831=�szmyt} S�,R]Gruch�,M 200��34} 499.c�So82o�5Loyol��93 �F]�9(�DAp19.Wb6W1JS�@� in Sv�(ce VI} ed B�ber (New York: Plenum) pp 503--514 A?> (mirnov Yu Fo6 �v+H�nic OscŸin!�ern%��ics} (Amsterdam: Harwood Academic.� toyama} T4 F M, Nogami Y%@Co�� ho F��97 �A%�V� 30} 2585] rozmej} R IfArvieu R�9�[ 32} 532�v! lba} V V MT��hys�Lu49} 586�FJu G-X�Ren ZA�M/v_18} 575.:pa~` o} P  M H,��dim Rm0Almeida C A Sn ����311} 92 om��a�Dom�tguez-Ad�<F�,Gonz\'alez M���� Euro�]6W 13} 16gixit} DH V V, Santhanam T SfTha�> W D!p�#�4]yi66ha�(Del Sol Mes�q z 29} 422$ho} Ho C-L[Roy P!zM"V�31��6.qgross}��ss D J OMy P a�88I� Nucl�iB�k303} 40.2& 3a��-3I�M�6J��.bw��} W� 11 BToday��a2.��4a} K��I4-!qN�5} 448�$Hinrichsen| F��^F7} 212.f �72��{ �{02� N5N� ngano G)�ann R� 95)�-1~ �� 52} 1108 ]�<@} CC@ L N, Mi��$D, Okamura� � uchi TAvm(6f ō\ 12502.$$brau} BrauEc�,7621$akhoury} A ��Yao Y-P�nu5# 3.�cq0A�"�a�Tkachuk��20Q!� �R� 36} 1037.�^b}z^e �paR:QM4'roa��.h�7 *�� withh5vF"{Fand/o�F� u*� sl P~3int} p6$-ph/031202:� per� 4per F, Khare AS( Sukhatme U�>>|p\ ,251} 267\\ C@�jH&O S.�A(Q��M��H} (Singapore: World�tM:.+�� JunkerQq�.g ic M�GfApASH]�al A� Berlin: SuTger.s.�} G�b�� L��8Q�is'ma ZEksl�T�Fiz-C( 38} 299\\ jJ JETP�~e�6356 (Eng��T�Bl..�&�� D��b�� 2 �^.�1} L19.� carinena}i i\~   J��Ramos AA� ��\N���27.�schro��A�Schr\" %m4 S ProcK .\ Ir.�Y .}�46} 9, 1�JG� ~G7� �h infeld} I ��H��T�5 X �. %�� 2b0spiridonov} S  Va�F�:�9} 398; Z;�;�7842��}^1P�M�231�.36} L90,� Barc$vlD T, Dutt R, Gangopadhyaya A��, Pag*�ntj e�2�3 �a�!�ev=�aZ78.��q4b}.4�fc��oryR� &�_ .�&�8 ���0 hep-th/940502! "�E� As 5SA�� M��in��, (PYeton:   Univers�:P�G. rose� s� rEl"�?��:>�}*= Wiley.\� �  Ku��(Swarttouw R+4b Askey-s�Nof hyp;woKic &wu.RE); $q$-�w ogue)uResF}�b94-05� ft.  of TiMology (:��1(.CA/9602214.�5$ Erd\'elyiA�@Magnus W, Oberhet�Q� Tricomi FŚ5m/Higher ��c�@tal FW� s} vol II.g(McGraw-Hill.�s8? S H S 194M?2�n71} 38��m� ?�?�� 19} 8.m�= M� Ruegg H�'� �G0 >34��Lukierj>J,@a�Zakrze�>W JS� X*�2�90�= Ame =-C�20l New. J O})2�8!2 end B �doc�o}��\Dclass[11pt]{amsartO�\u~�@ckage{draftcopy} . curvZw.euler6'euh�6m��col�0kamssymb6,amsA�:+�6$} \sloppy �"�= im}{,90upshape Im\ }C.�=reB(Re(6OtrB'tr't em!worem}{�� em}[�)] O(lemma}[ ]{L2#d��I(D2- corollary,C \�^� in&�>"�>A�ؔQ@} \title[Lieb-ThixA "��ies]{6 Iͼ�r�)�> O5�DYK : Ope�?L} \author[C. F\"{o}rz,A�<\"{O}stensson]{C��s.' asJ 7gen62}�ab[1ct}�lS2kUZ��(the Riesz m�of eiget������$ {\ge} 3/4�|a��)� & � �@�a" �d�]K s. W�Us*�}�Kex�?D @oly� "31�E�syste�`�Bvs�' o greateU~an�C�G�criti�C,I�,{=}1{-}1/(2l��nL $d��$l% q} 2$:p��XU;(y $L^0_{l,�>,d} ��{.�} V_-^{ 4+/G }(x)\,dx,rgVEGLB&.H),G�Q,y�A��X�;I�0� a[0jQ $6���Eng L5V l, dM� �$.�a!�in!�*�@=�abbzF~,� 6r*} )Z4>H(d,l) :2=d}{2 lq�i\nu*nu':=i� \f.+��1*!�-tKL�� w yql�Iy !���n ��LT}�Fŗ9�L\eq"�]2 �3 -��l=1I��M-H��max (��nu)$ ;�"BMc�� ant >��ir argK 6;�1���ded��p��.�!oS4 �2k��j�fZ3A^�̈ if�� = 2lI$!0iI/ 2l $ the boun�Cd \eqref{eq:PolyLiebTh} exists and is for $l=1$ known as the Cwikel-4�-Rosenblum inequality, see \cite{C,L1,R} Ralso (on,LY}. The u�@ence of $L_{l,\gamma,d}$ in the remaining critical case $d < 2l, 3| = \nu$ was verified by Netrusov�Weidl�P\emph{integer} values�lz �(W1, W-N}. H�,�~+%4Rbound typeZgwith $ �t\geq 0$ are completely settledU �$ $l$, whil l non-  � only� $2l>d>�>is still open. For sufficiently regular potentials $V \in L^{ �\+ \kappa}(\mathbb{R}^d)$}U ies Vh�ac�an-�!� Weyl)8$asymptotic!xmula % \begin{align} \label{A��asyformu} \notag \lim_{\alpha\to+\infty} \frac{1} { �+ �L}\,\tr ((-\Delta)^l+ * V)^)_-&= ^ba |B` \iint_{.;\times.,}(|\xi|^{2l}�_- � e�dxd\xi}{(2\pi)^{d}}\\ &=L^{\mbox{\footnotesize\upshape cl}}2f \B�} V_->�,\,dx\,, \end1�% where%�so-calA�Lclassical constant $��($ is define�Y�jtion}]Ls} �f= )L\G�s()�+1)E�D+1)} {2^d\pi^{d/2} lm B1H}%1quad i�\,.)G� %a�E�m52� can b!�osed to�� all}.� ��if%���t:holds�(,urthermore w��nsiderA� Thirri��-�a�gr� stat�<at!�a�smA.stU% $L^02�$��$ch fulfils�59Meq:defl0�var%�_0m1 \leq >^��:�j�B�$ for all �u��ere $-�$��!.+ �.� V$. I��~��$6P�O��H�nu�U$s given byNR 2/Rf�5\pii}{\sin()}�fs �w0,dT1}{\nu�@ �F� &w� It!X�" restA�to �u��5 !-sharpY� N�m�:&��DQ����% 5�" %� view!� �68 ua�immediaO obtaK atJH \max(�;,Q'�)mf2�B6y5l, d$� $. OnE�!Nspars� 4sults on exact1f a!6leIdue!遖\�� . In� LT}by )h 8$d{=}l{=}1$, usE2�he Buslaev-Faddeev-Zakharov trace���� BF,FadZ}( Rn��L=ɴ1} 6� =zOuK5zVe-V$ = 3/2 + n�+n�� p N}_0Ig� 0A-L} Aizenman%C%Lf��0rgument, how!l prov"� �� $d = 1$��* � �(3/2$. Apply!ma ``lifa�'' gi_respectn!�no:�s� k� , not � in |1�e<�paper-POst�  attemptu made~ %e!at��]X%qI , l = 22iE"7/4$. '"Xappeakiq���i� la�( Riesz mean�Ior�$_,!�precisy �L � , but whe� x�b�true or%R�sI#B} �� o_EH*N ő�S�N� pres� -�is!Q{=} l1m�c5�1/2$,%whb 5MH�i)�%�@n by Hundertmark,��wThomas tr�eq:hlt�� 1,1/2,1}=�;!�\,�3 =1/2^D %�*1ase�e)LeF!Ɂ�F� sIi itute an .?5! blem ItaRll be �ionedM�at least%bo�O!��Ls a conjecture about �N�B %�s>� ��m�LTbais ���each .��re �$s a uniqueQ6_c(�so%�*: �&L_{1ٖ��3 & &I for}.8 �x�>� ,and�Veq:lt�1R�02�& bx� .z.��:l2�- Comp�� this��A r�ab�5one0-�*06�a�m�to�? Q�O%��T%� all ����E?!�&1 .i2i&#�support���m�. % %A �w��i�� is issue�� o< %$\Omega\subset�?� a dom� ofSitaYasure�/l��aq } %!�& } %V(x)� 0azs}-�E6McasMb x\in �\ %+b)5N� \setminus ? % r \,, ��the!!enKS T� =0$ id��( S P\'olya.�%�e numb+�eigen�WPs $\{\lambda_k\}$ lesdthan $)1IMA� Dirichletw lacian�6-�$ (&� ,Pol}), %whos��idityA ũ����til� )�zcer�  %ofa duct stru�/� ap1}��IVcA{MAFqk�is�.}Fs ( \lt"�ydimoneA foll� he!saG r HLTW�d extend%� E�!�Za�t�6e�>c �y$leads to (���) �F!�DAX. See9 orem �th 1} *e , i~as�E�$biharmonic��5  $\par�^4+V$ed[ % [2[� �Ou� s�� �o*�  op o�{�� kinds�(rai�3 e)� )oLWR},well a!-.� $l$. We �discusAK %�) 9�W1 !! $l= A���E=)V(sec:extnetw1} M7)V4matesfrombelowE7��c5�y �� *� l�1} <   nu,1�L.A�� $l �IEQ ina�trxtoB`��Ta answer��qu� on p\in� 2.8!<[19] a!� in E3c&, show] a��y, (0.10) does�M to high��� U._)�:�7%`#!_ q�! -�R<e�{u�s�\i8TiL)�most-g� ��\ d{6< 5�q�&l E�.r%� polyB�s!y��4} i: �2�No�v� $auxiliary A�rial} GA� ux} Let $�cal{G}$� Ha separable Hilbert�ce�h rans�it��onj� �$.* simplica�of�c%�en $u%fLA�}�U�V> we f���� $\hat{ue�(�6!bfBz)\,u$.I�Sobolevi� $H^{���J�J�,�,$�0���t� &LN����� %S\{ =f� �.E) : 4(1 + �2-�^{lV,-m(\xi) �j�F3 M\ � }�lmN��($, equipper%�6�n^ �_�x�� :=!J@%zVF}\,��.L, v)ZR�\,d\xi:X*}�a6�. A�= M ��G�%�bb{C}$�e ��at ifA�\tB"N�tJN�9 =Me��� al^�!}\,]�)q�R}�/J�, ��|;|!�q l�YN� %Her�deriva�&� _{jE J� %I�aB� , $j)] {1,...,d\!^i&N!a�F�%(1x \,u)I %��P#h � t 0} \ u(x + h e7 ) - � }{h}q� cU-A�K"y� 3!$K��Af(unit vector��dir� $j4&7 %limit take�C� �_%��. If � =!1$ _{1}%9d�2�A$Len �m�NH!@ [Qd } ... !*d*�#�W,\\ Obviously��!�!lra8%N�h[u,u] \�_A%J_��{$\, ||�:u�:|�$:j �9Br�emi_"ed� %� c�"�-� �� �t �#V�J�!�E"assoc#��0 self-adjoint"�  $� - \D&i|��}"3F� �2��. � V�� z� �� -�d" IHI$<()^{*}a.e. $xA3:� $, satisf�:>�� �Vcondi�s} ||V(E�6 f��# pR�-�6�} # someR$p>� bec((rray}{ll} py1� ;if } |* \\ pcR" = 2l "� d/2lR(> 2l.&� 6�* 9a/R�nuiށq>�'�C3)� V��, uR �dxB� ell-G �M����>u] �+nesA ��FC�M�R�AO��p.�rL , dxM2^{1/p�����:� !�>-=s��analog ��) dard" imbed��s i����7w l . �+i\)ce��AJŚisn�H9 lder'� �w�� `����� \hooka���qR�2 -�q!�q q�qA� YH2d}{d - 2l}$. Moreo� G_0$\epsilon > 0\*Y�!jt $C(), V)$ f�} >y: �:+ N V)�JEB�i], + e �t.V-nd"6 Mpi� ver�!�cor=#onE`"�y��q���4]jQj� .+� B^�5Eq�Ng�8����nduces aV�j�O�< Q} QA��h J  + V6�}!w&� H= f�X� qA a"�"A��i$ guaranteeh$V$Dbe a weak Hardy we�, �+�perq$capaci�,0$U �1MzF V$A�� \n2.�uhaC S_{z.96�AVz�ynegG �rum. $Q$A� -re�!d m!�0u�'te�to $0A>n�#words�  Q_{-� b*c�6���Bis�Vn� ml.�clearl�y� ume�,�,4by�$!*} xsW ��%�2 d3�. �^{-1} W:�*} � V/4`6Fe+se"�$B�=a�W}\,S!V�&9"" =� *} $AEW �&4" �J  � K*�2Z�/2>m  uIclaimqA�m�P E^�� �1 2nEst�U.�aA?Njin  +z�4fourth full�� �s�we *Yi�in&f �*E V,�6>2�%�Af( �j:��� R:Z 2�1q�F�%@hBg; *�$\tr V�aD�BL^6_�Md�O"@  �* j s�)n�better�*%utrQ��^4�� + V ��^{3/4� eqT3 }{� %2� v �x) 0B� HM " �*ig-�JofA�A�� �@ :1�! S^v,�$-�i.V$},",the p;,by rK*V�*. wb/!� 4^"he"n#aYpr� samee te�) ��26{>=."��#.�2jB`-�ne�5int�ek"���0Hno�6!p ``majoriz�H ''. e�Aat � mpact&conj�$H$. 0u�u>�tA�n��(\sum_{j=1}^&{j}(A��A)Fk3m$(-j+)_jX �seque�;.x�� ^E/ �# creau1�� or� ;% ir multip�ies. A��Ky-Fan6��&��&M\G-K})�als $*� n�p re 4�&� (H���\any��# .� U n!�A- have>�*!�\*U�p A 6-� = ||-�:�*} WeyI�h*�2B;�0�1�%&��� �e� 2��'"� �5a�$HTy)�U}(\o+)\� ��T*A�� � *�!amilyaKary�*1u,%�$\mu$ a�! babi� G� "�). iM�"Y�-�*� B� ő{ �&II��B�\, d\mu)~eisU!d�3A��$A$-�-� ��(}[\textbf{P�.}]�*�i*79&J<BFw6||\&�>i 9� Q�, ! 1 �,!OE || m� a�,M�B�B9L0 ) � B��m.E$E� posi���/ F0�t�� u&r*"� U�:�u&�*f9S G})$5�`/at* 9\La<} &:=� [^{3!�\&� +"�^{4/ m \ # fb� 4] W,\\ \tilde�?!�Lh?~6� av � 6C 7�" b, –iY51Q"0]%-* ih%&�'�6�'K?��N�0I����� . Bhav���*Dral-kernel $A(x,yD a}{2�bR%W� W(y� �*I�� ants $a4  $b��3-fqBl�'Y�O*al�)((�@ to a�1�6WN&�� j� L.1� ($RU1�:: v2'���~��qr�'�!U��>0��'ASM^6����J��J�E��.= L��+*: )r. I"� a�pN��0mu_.iC��` $�6�8_M�\delta�Dirac�G�h�=$Iġ�n}{h#� 1-Y�j?( @$?xiY ,^2 b}=:gW3%�(���m��$�'i�Lebesgu"u3�OF��A�>�xi�xi� %G!H�"�"� ? ����&b��  $ '�d�Sxi)�"= e^{-i �x!B �"0\$�\tB�*� �(re^9��EFL!J xi) >� %� :':�}�r i >raq��Iq8� ye4 ^5���V�-.vx}nC0�Si a� g�;�) .�B ;�� ]�` .3)D=mQa0�2 \pi!�,Ey b%�,�""S &@ }1> JGi9l�6�ny!�<;2>��X convolu�.} .� =.�'E� * \,. �'>� } U]!�relE�1�N}&8-�:� V�Dp�q pert� �m�}��j}�$o<i'2wa��R�r�!!� Y ���� k�(\eta)vI)[E 9 5 .�2j !� etao�r�'F� ��!M last�+)��2��5N �3w let���v= } 0�now!�y� o�t� �5�qm� J6�a�VO� First ��if} ] $a]��b� e�b��1}}{2�nymba�nZLi"� b/ Jr�BO!�%f1�BY!6!�u�C�t"� {4�#Uo6� \, uR�#�0&Nt-=� }{?4!O� ^4} ||(�I� �J� ŝW��l �1a#� 2R �L)P� &q��&� �2����r�=��4N� ��bb~:�!RO.�� ,( �!U*�# �GA>�!Y�>�.%V�1)X>�)�-�INS X] ��1�1, �.�J� } D$Ea� �t&Y�Eq}�K}_{E` � 1}{EI�Aza. E^{1/4}} &�6�E:8E�J�] W:} DRby $(-E�!�"�:�� �E *h;�!�OErTB;:Na .Q�W.h0 $T$, enumera�?^Q6=&} �!��Sde"w&$wX7i:�.  B " F�*�>7} 1� �>�.&� %�})>� %The: �s>8$)� h$�� %0+ . MZ�� " B�!� $�I� f summ�2�&�.w2=tjj .� Y5rB�F"U>�V�} �!]� (iuB!hmF GBb9N36A>�|3��M poinw� ; althouge8e�Rc�>~w * indepenAA"($,� ' 6�%t rsp)/�+�Y�(R��v} �*re monot�?}Y)�' >�e$&S %�Df� (V�6� � � m_{RjIn:E�G0} "� � � ll }J���@�fa �6� � �f!-�E8byALu�8 i�B��$se�&Ie6H�2$ly. Combin�I F� Y�>2}�GWF�)�6���� N�0>s *} F6_}�eq:��b�rV?0�eT2�a���  x �N� 4"��/tF?.!J2�*M�&iz!e�F�, h!U�T�-]��>��� $b$ �CEcho�F$b� 1/� 3{ X an eA1� [D�I.w+� zv "�N�jO-U@&� E�b�O,�J�P6 I�� corollary`9)�2~s@��$$$$�� �>_2 &2�%$�%$%$\�R+I�1� .�$� � ��s?2$ 8�13/�N)�9��wrR$a\>�\qb� +:8$ �;$ �4}<$ mO2aO, �`M2�KSF� ��u�eq)*Zd� )Vk dZ�$]�\no��nt �ReiN.!� �calcu�yield�nV�,approx 2.149�iN�� >�!�1�>%�>�14%%0�7�} t5 -� 7Ec-�t +�;mbd�).& , dt� x-YE�!M B)~ `3`,.m-�:D*}b$Bh���ZN&[y)}+y)k �Beta-9#. "E_{Q}"��u-al�,2e7c Ze7Q�� ��$E ���$(-� j}(x&R �� �($. �N�tr �-1��a,N�V� d%5� +.��e���"38&� a��B���\�/2�2} >�F� ��} M�>� \}:=�E��.]dt \,fre��=�`}Bga�2���\g! F.vfq,�VQ2P,�\  ��2�)Q-�g ��v%%{D1 ��@E�J�q�R2T,d�9t_2�j�� =B(���- y�.��%^�n�/B'=>��2� % �B�q�R�n8��J��#�<u�Bl5� ��j�J��,VZ�"q�[6Bo�}>&�i��N�. F���30e�of end+0�+n~9*y5u�p�> �-"�S��+ 1���i 5/4)&�"�a# 3/2�,C6�+%E .7/4�Z2_=�K-� Sq2�2&!����� S3&� {16} �o ��p��:k .l�� r' �� 6)<U6�p 6C2RVb+o!thoPNF�hW1,�`a�aZ$�M.�P %Fromx~��18Oconclude"�|�T �E*L 4ord#PQN}pUL�_nNb��J!,N�Ty"l=2, d=1t&o�Y�6s�(&j"� ed an z*�_m)1*�i %��i7�en(POion� %Ap2 ix A. Witwk% U we achiev�e~N'V |L*�,|F_1(105)|^{e�34�4 |F_2>}{105}z=!<�$$F_k : [0,�)M��=(- ,0]+� in<�J�Kof^�� �psto kM�4\mu^3 (dh^2! �u�E^2 �'sinh (2\ ( A# �*��A�-\mua�l�?��- ���P-L 14}.N0IW5e!,1562$&YIE� %$$1�, > -787.164,�F1�(315.022,$$ I{�[f g jO:NP2,3/4T01.416+0.713 =�29N�M�is basoP'2pe�R8 Neumann-brackeYa tech�[a@ tog�^!�F�8&�'�Sra� �M �A�_Af�N\]�U�@ $2�Ld�)thR�^-)�d}7E�_0diplfoerster}5Zetailed �4ysUa�XiGY�p�4don�>E]G��2+? V��_1�s@�#fGN� �GJ <1�2 =isb!�m�Q wors��a"�#.�6�fsC^is R[A�RI�gan up�a�b�GV�� � L^2\big((��)-��oM�}���>in �S. N ne~at *.)m�a� #�)t�(third.aK$vanish at ` #4`rk�Oma�%3� _JE .�i+$�R-S*�i7V , aJ�H6�I>vYXh^+& F| " D2 u\|^2 - |u(0)|^2���B HV�BJ �k$$"�<_+ ���#2.$$ Soq_ half�OproFa%[*2�fE@(;Q�WqrtnT�>L>�bV% �. %O��hDwe�&MH beca�,�P�7K"�a>B� %��of�]��D"37�ocan�e�Agood %�1Uml6U�+֥��A�B>!S6> �K s adi�DT(accuracy. %�$- aiordmi\raw`-0m�&� �b!terva�:A ,ɐA�CT @�BS� ��in���t�6#!�2]��T6�]of&_ �sSL%�v�=j�Y�h��(t diff4[q adap�� �V.'^Ze-agEB2�ft.Q2"2 *�L�F�Ld"�$�1B�W"�!Q&�o "�3 O 2}�w�w�w�w2�>�-��h��R&�h"��g powe�an 1 -�gl�qR)"�N� u�V!��9%�$, �i�%� J]"�� Z[�� >r1-1/2 A���c_E�>FdJSH8+c�UA$a��9LFJ} '��� �ze�1l}^{l!j><; $)ka+I+ve roo�"bJW� l-1-�$ + l z - z%�= 0F�+ mV"�:�T:�+�D�5�y�f"G:�?:� JPQ*�<&pZu�"�{�*�-b$�"67^!s%e ��Uf�+ 2:qG�7\��7�c}I�, +!���} 6�V�%"J� IV8)�5X�b�7J2�A�"ZasJ�� �:� up_{x,y>"�UyT�M� ft(xA) + �}{l�al}q} As b0we�z:Fy:�ev/+F� �?MO&| z][�v.++�6�lW��C�9-9�IH�+22JM� ej�4�VR�-�#.;:�*}���; )�pro0qV]ilSJa,"ofE%,1#�">\���)a10� �-~{ $!B0*� � in��TDo��*Y�6ei1}ť>,F� But a gla5-eF $f�Z6�6> $��Sf�we\ƌ&8x,y�-�f� reveC�it�q%)�\�$IoIlinT9y!rho xS �Q.e�fact,f�.�k�as - 2ewrha� =: g()"� {B� AA�pl| m"�1k6�.N� g' _��2a � 3}}{�]t})���'.�- )�� �7:�e��h%�$g$5�(its maximal)� i*, ints %�I^�@Nsl6H >� *} (!z1���1x���:� )6�� pg ��  j�DZ o beJ�)��9�m�rh^{2!�"�Q�*.E�?   put+&� esR��m �d6�'��'"s%�s"0 *%՗�y��'��'��'��'�'q�$&�'�siS��2C �Zs>�' "' ,)]1.m & &��'.� M \o*9eJ� n � �!� � q �^� }{L�Á3 l,1}E��'"_���'�'!�Ra}v� ���K&d�-m��} q�ip6n8� a��4N�A�DS*�O � 7S\nu:=*aRKD��Js65#.2$(1+\nu6 �#R(#=� "(+%i!jF(,n�nuM[-<�W:` �Ni*� -to +�Rf&� ]�{2})^l��� q�bG"nu"�#B?"=X,6�a�0"b� *} F9Ol)W1,^ ��)��= ��+"'p� �0B� �8B06�� N V#�<�ainZ�n�*8q� �1 m~a �J& 0 lbiggerl0!,�|.�' r]$l(�b�f8ɉ"�|"���� l/�l�� }�U~[xb� �`�a��"�!1 \.� � �|-����5lz�ere� kO"8�t#2�has�%L-Q"w�.p�s.SoxR�>�  iBS," 2��[@nD�� �+&,2��.Q�no9�HwdN��r?s \49��&�u��cou�exa< �Ho "hide"�M^aP Y\4$4F$-potencuA�t"s infl#Qepre�e2� ~Lq� new*MR�mwn!3��#Q|v A`!�'wt#�� � �ra~� i%atQ5!��- $$H_l(c �_0 �"-�$}'A9�i?�-$ceV& $, gws$%%�S$} �:$$h2�&�B|U;l u|^2�M$rm{d}x - c�!�"f�|;%i�rm{C}_0^�**� ).$$�us �TMA]!ao�Y��x�:P$)���|ll"/ s $ � W^{2,2l-12~ \cap.D \backslash \{0\})�":�E5({e u(0+�#qz-)� 1)^l\,c\,[�wAy!*} �A�c*|in &�%Nv!e"�Fa�exact�P ne n�]�H� *�$ � "�>��s4�:C�^{� =:�\,c:�}"� �J�2!6$uA.�a��'� 6�GG6�$%+2�� 4 $x_0 \neq 0$.�� �1E�Fg �"�?assum�at�!��t�@n�1Q)�u�,strength�5� �gA7F"E� >m�I = &i^ >��4 �.@�3 ,0),e.@c �A��n- $ ei6XB" B6�D FC����'}^x2'}u(t).�t���V��B�!Zj  �n&�#m��@so!�for �}l{&�n s upQ�� $u''$!"I�cf� # continu�s1�6K}�primeA�a^ u'(�z:P{0}u''�u�0E��2B�!!�S ay' ymme@ �c2�%U ""�H }���� 9-�^(modulo�N�n)mA1�aFi>�'B9$��i�- X$, radi� !�&� 9J . So�has�in 6���*�7On- Qd [� �= ab�Vany��s�? � ing !uexp�Y8=-�1%<��� �\neB��Halready �xtov� Di�?�*� :��.%�#Aw�!ѥ�1� $uZ*2�  !o+)�զ ;��ݦAofA���vW $.:�"� ��!(�UJUU &�%1��2�~R7A 5q[�>�o�RFx�H_lqMF; �� aŕ�Qx_�> 6�V�by�(�9pr�o:* q�A�G�ZnG.�sa�e/T'd2a/[�kvaiio��^$!9*�qI#�inIU=��5V�2�:9 lAl:' ELY�we referA�as2M0$� K&�J���Ej2>N nu}+=2Q\Ts>�B mustũ!v@� _n>K^.p"�,: I�$\phin \|\|�%��6�2�!� j�y tauz#Y�i�B��J�B(�.i�� F"eDnd 9إ �&�ss� y; �Q^� zW� �rBb^ splic-!5Z�[!�,]�|"( l �* �%�(x_�*�7a &n^; 5 3-RI=���a��]�B8IV�%�/ stIk��F� is )r.�( la�AY�&] ��enl0��CXau��� .&ql�� :%2}ersc-���&K ��&�*Ai>h.�6I i&dw�/. aaF&XV��g�u MO!�Q� ݦ�X>B� I.B. @i2ho��2��M/a wayA�ata�A�X 9 $1 �*$possible s�T2� c u_1\l# ��2-1}}(x-A���$x�*R� �6C}!C� � �_p(�Q%c!Ra���g.�- .B� x_0 �1, ����:o4!��un� 3-�&% s. u_us,> ;.m}">�!Y��2���~.Ey٪!D��~@+]T�>6�(1x�)a�BV}�A�6�,��y�"4W G��u$�$&.s�E!���$*,�X>,!q $$8>: ���fnR�*�$�er&TsJa�%lt9rdim)RRap���4NBhfrom �1��$|X3i$q"���*Jnone. C.$�; �WJ�& "�'C)&u}i�2�7Ϡ&^ %TA��"<55:�@���set{}{h��sum�!��"�(_j.��� jV.> =\�� \i���*�.jmf�\xi�N2{^? �x>\x6���C_>N }�/6�-&^?Yx,5�Z�JngR�cerLAwU�`6�$;E`' bas�Flyx`(1��d�#2�:ed5.��G6�$q2s >~aearA���u-"� Zobe]Y�/Qu.�MLC$}>�= = U�2, d-1,>',1�6�*R��v�(xps&;F�.u6��2x� lz� \,2�+1,M��8�UI�E������I�>q�)) C�G2"ldZ@ ZA l.r"�>|B�'�in�6�G6 �%q�T% �r#�<V]&G used +O,"h5�}���iow7jo��4Zz ble�8 �97� w)���>[����� .n..�l#b� Krem�:v��a{u� I6QM^d2��x/B}M &S/ b�zq pMZ Sn�fqK �B|qA7$ � "�C� )�=�cu�I��O !N�q^M� � K�  �� 6��?Kz!U6� h�!�a�|2���Y�va�� A�re^��cv�)N�M:�"�Nd"� a�a����d! aC>Q/BJ&QA�(�5�V�) ��CM� !��ly � �hN *�?x &x ,W 3x � { �U��ʩb�E�"���%+�in:� sense, qk*��L���9vaq ��A8.! &� Em52�iFV�$Ujt$6�4*7n%�U2K{�U�!�w"?D1�Q� \j"V���w�cpP��"n��A�I�K-'Idk0l�!heMrA_�i�H t!l �6���*:�*AE d�ei������� Agai&�!f*>*" �����'� bf&AS�.~[t=�H �/�Xs � may��mod*man�i:H��GQr10katN�y.���t>�m $ ac� &#fGa�.܀�B"�A� any VJRZL9 is�4n , i.&. eF"�A x, xR)�\,>\,0,�F*:h2} e!p �e� Lk?0�(.��@)a�m�N��Bm�...�Y^�A^�� B�m�>�&{. :�"a.fg�\ A^{- z� }P xnL T�Be�A���A�a-h�a��\�,0c >�- 1/26� =�at@�p"�;Q<itx�3 >�(*} 0 < m_{A:2,inf_{||x||=1�l�e AbY:� *}5UI"�=�6ve> ��2t$"��zju3� lis4>j2����(�CV|&�!�}"�E]mA�M��F ����i����96 D ���.i��b-(N� qZJ0j:B7#���9��eq;.:\+}{Bz:*��i�!�U�V�$B�D�e�s�"1.+j!�.�k6�4 "�works,,=09�;, �*!k .��tor \\ N2�E("�J,�li[}\�J�}*1�B��)�Zd^2}{d�D�1L�0���LVR�>,"|#E�>_YWA-e��� ^���Z:2'��1�J, R�3N�v���!L��:��>A��\����ali�_o ask"� s� %'��m�=<. DP�itEz�� $A =.�w%��l2���),+ AZ"�"� ��.?&�C� QXC��Ȯ?!�His &G�A��� ndix*+J2*a��2$B~ �6* =Jw &�- &+ % �A�b�e A�*�^�0* ^0 cJ �%- �2qnŗR�*A�.w�����S�&&�*:<*$ �he�� 1;�:}$ g_k�=exp(r_kK[2l]{"h%}\, xV�* k=0,\dots�-BMf"�A$r_k$'¯�$ FR'lexqDE�1�3ş ) (�- {l+1�Iw#f�r_k�!exp��� 2k+1-li �q ���M�J�8E �esed�*�h��oA�r_{X],ve�"� $r_l��%�. &�% reaK�,�%�!9�% s $g o m�g zsquMb gr��|2�0�ne7,9G��g_��&�S�^us ����frak{g�%�FO (g_0��I<P�*bicO~&�+kbG"�#k2Q. �["��� F5E� � �G;e!�^pmatri�w6�\\"-Jva$ $A�-1}J+�e%� 0��~E^�0oy 0 \\5)�2lV���Ya�re�Ak24���B2�&� o!�� AuDMs�f ~�0),]~ � nea�"c�hD E� ��, B@��� \sJDN�0)9h}- G}2v���l c]*E>(VRH8� Eav}sq hy}b��A(�o� coeff���/:a�!��aJ W5{*�X*I�.��%�}Wt=$g)\P�Ade�NinantLF� L�Wronskm�.% !��os#.��l��r�� ��(1NFh%Xq: �ev���SI +N�G}rI!�=w)��{){%�%�%�h}�e3џo�I%,��-UA! %G&g� �F�V���,big[g_k^{(n)a�]_{�� suba�}n�g .�\\6� �6}F�=eft[(r_0N )^n>PnkOF.K�Rb���! �1q% �+oB"6�1�-  0�[ >�(2l-n)>�}{f k�]_{�� V�: :M >�AIF WMS&��geh<�X$�)��5 1 c(2lpLf�{1-�;a�af ScyjV-v�� [>dn�@%T�9A�tau1�bi{} ye^T &R \\ - & %m.B�Eim�y,e�%��"��y%��� 0�)� {leO ))^T`r eF1 21A~ now)��hS 2`_l!�= ���v} !Q$�'�-� h}_01B9hUN�"= ��S*��2/b��Bo ��,+ �{�{binom{�� v}}}p .�h" �60}F9h}}�%�!UNZ,Bh9*�* C}^l!.!l"�H���.�� a�� triv�� �!v�*D/�*PEf ��E�A�)B�v}%šB/�*V~.�4it�R�%S?"�Use*!�-��7if.��:>���)ca� �-`C�/�K)}c��~T%�T��W@a0Z ]MB *{Acߜ ledg�s}=_He authors would lik���k Ari.* Timo�Ywh9c����m�6�$ �Sf opice�ir guidN�y�y��y a��2�� rst ���@���S ESF SPECTEIXDAAD-SI, PPP-programme,g|l]�-p ��dee+��g (Wenner-Gren�{nd7 �Cir ��ni` ��b:thebibli�phy}{99}a4ibitem{Agmon} $ S.: Spect6npropert�8of ��� �erlb|&�d�5%j�@ty. Ann. Scuola Norm. Sup. Pisa@Cl i. (/g0@2}, 151-218 (1975��%\� B-S}aL M.S., Solomjak, M.Z.��Y: %SI�AI�O7A"O�S�H. D. Reidel Publish�@�nS)142��M.;v. E.H.: � it{ODRm.�) 2%��W�2� :_9\.} Phys.�t. A, c8bf{66}, 427-429%-8) N�BF} Bu4� V.S.; :� L.D�Fo �tL� a ��uH�8Sturm-Liouville�X�DQC�.} [Eng!9Hns%rd], Dokl. AN SSSR, {\bf 13!�4451-454(1960) �CA�ConT�J.G�A~C�\A�a�J �jum�$.} Rocky M$1(in J. Math.�5At17-122!G85.�} ] M�Weak tYЁ]�g)25/-��`$��o��~0�0uXoiV5I!�T��. AMS �0 224}, 93-100�77���2�; Z �, V.E�@Korteweg-de VriesZ��T: A��ly �Lhamilton��.} Funca�a!�ppl1S%R8-27 �1�63dF�T@d, C�Z�1���0�� �28$Diplomarbe�Unihg�>\Stuttgart/TU Dresden, Ge\�y (2004�Glaz} }�I.2DI& M�he�Qu�EC Ana"eSiniKDify;��.} Isra�{�,� S�ific EiRs Ltd.!\6.�R�H Gohberg I.C.; Krei�+.AI�.�&�B��FTa6�n-�a�7��.}Q�eE Mon�\s, Vol�� 18},A��9?m��H��*� D.C;��L2��D�b���Y�;el mo�EaS�on6�ǩ`>g.�!Adv.\�..\ ԥs\ˁ�719-731�98](��F�ӚA.;� T]�New��s�6��$!kInv�H ones` hemav�@e 140 3 ,693-704E�0)�+��: A&?���-cE"�� Pds %on D ��.Euclid�e�0�J|��� 151��%531-545%4.��N#S%�6"9 � in High D��� Acta!�-%, Vol.�l8�=89-1111,U�ؾv�Rec�l/n6�I�, ies}!Cc. Journߡ,EDP 5-9 juin ~ XX-1-4�@Y} Li P.; Yau S.-.8&C6�V %� *[�%C.}�m��I�, )8a�309-3r 83]�L1�e>�Ba�U�"e�� aLa:, �6�.HBul�9mer�S!78eu51-753  6). @d&g  f^one body^��� 63s r�A.c Sym� �J ���3~ 241-2570kI���A! ��ir , W}�.4��� ��5LJ_6RH��a�ir���,����.C�� StudiNa7hUEssaye� Honor�WVal��ne Barg�l., Pr|;,ton, 269-303a�76]D,Mz} Maz'ya V2��s| �SD@V�VerlagJ2� O��,\"{O}stensso� ] � -XulaI|�"� �D*� 2=#B� �fN!'� s�&7EZsubes.}_�m.A!i�;ics� e�355-37� 96� u'R� z��G.V=�Di9Rb��_adis'�)�Q�&� b�N} 20�a$ 1012-1015�d<2), Izv. VUZov,��Mka�}, 75-86A�2����r2�M � 9����;�" ,1}$%��#�"1/2.$R���17��135-14�96.@Yaf} Yafaev D.R.:�B l Sc� �� ory.� �8��� Vol t05}�9A��>a {\H� \M$I $sl{e-mail: ��+0tt{Gp@)t.uni-st� .de, oq�0@cims.nyu.eduW;�doc�} ;{\[$[12pt]{g�cle-+0enewcommand{\a�e }{\Roman�u tion^F,ub/<�?��new` em �=(on}2 .&.�}  %:`r� �Mtch}{1.7 @�imag}`rm{i}\,�$title{Unif�'+=5 �6%$i  aqLer& � B� ls qua�Din ɽa �ab@d� ��anifold "�{E��ed�W�� paKAp�e�&��c.IT,bf{47}, 0429 6)} ��D{C. Daskaloyannis\�D{e:mail address: d %E.<.grA� {\it}8s D��%8� \ {K. Y�antis&.K�i2H,./% Aristotle.�of� ssaloniki26> 541246- GreecP7!#Ldate{May 2006} %\uy�ckage{S��2�\NqR- x�t tle E�pag +absLt&@)�w� v� �B.'sujx.nt�l��mϧuuQg�6�Q��6us��N PoisEalgebra!aY�of X7re � sixU TdaaCaliA :�1��ula&� iv�ved����q% | l�i�0�casKAllTn^v� �i�as�?�cH �se .� 2ݧ�[9�, \vfill RunP?A: Ck�fi�A�� PACS Nπs: 03.65.Fd; 02.10.Tq; 45.20.Jj; 2k�f2�D!�{AlgE�In ��mechan�a2OEGIF���aYE1HN$&��s��a-��2has $N$2<Q�i��oS�.U (or�c2s)b�L�|W' sessQ��cum* &[o�, iY3 $2N-}K �.6'FH �=stEwAktwo�al>�5 B�chE���a=�d}�&�'4eOeq inv`gՓ&HZ^)�:t � !F quiO�ld�, �d<19�x entu I��tsS/�xb a��Qgeometry%� cBenge �to�d>�Ufs�`��ode�#�(curve!Dpo%����&al]r��%�free *�i5��s� �W!�  volum��eatis��Darboux�=0extit{Le\c{c}�}Lsur la Th\'{e}orie G n8rale des Surfac\�� T�\qli�E!�����z�,��{ fiveiȥh��orm��!�e�)O%�g5OF thre1�fEt�  (! =7 AP&�uU�A ,�p�uW)!nesL�� �4B&"�eFzielles"g�y @�A�!� param�&�9l�� �ˁmoD'anEY�ٹ �(b&t�gse+F�V��;�Kn.�Q6��X��O>� �%tabB�I�"T�~au VII"IKoenigsE08[vol IV p.385]U? ���v�M�� �5uage,U�� U">H can �glq�searc� �;J�B!�e\.% accept6 B\E eabEk� is��C(�#Z�|*�".} ia$F� plu�Qpo�^%� �Uw9�J ]�r[ . �<�'Mp�:an�6�s�Ns��|�7�treal pla�IArehensa��_r�a�* two-.. �� A |o�^��Tin Ref]J Fris,HietwG ta87��� x^� 93� ͆fla"�с� r@ly cat��u�  KalniRMU@r, Pogosyan et al � KaMi96, 00,KaKr012_PAN �� \�f� � �g���WI�Drach UE)� @1_=�*2 9ur Q "+ Q='9A-�.��*%5( Ra\~{n}ada�RRanada91�:A; %�AE$hyperbolicM%��t! in-uRaSan99,02}��sY�276 G"ly��!yE�connec �o3� co�GG����s�9&�0 D"��N� �r-��onm"� schem�c= åaF��# ��nonEL�AL��A2r!�e�=�ion)0>�5�m�sp�Z!L 9��)�)�99Y�0b}�s� hrq�f)� @y"m n B��0�I�G �I�.NE refs ]E] l:{Z���-Y� ��! U��an�6�A'�8!`��A�1����!�-F�M /eFe.^��t�w�by�"] � /s� A;r��M2�W���.� �t� r  onZp� ��4���(� ,[n${ }^o$ 5,� , IV, p. 377]"c $ ly ��%�c�bo&uo{&bJ�-�9�pA�Win02��Mi 3}M!�9�)�A*!Cvi?by�Mwo�uws �, s ��wM��Mi05a �05b} �1 a�\��a�y��>�FL3�.� %{hb}E�8 .gqfl� e. o� K ]P? �/?B0J�s �AlE�eyR ��ow2a��ry��I'�(St\"{a}ckel�iv/��{2��Sde �tB4ͱI3F��� . K�1T ck]��f1�E�-�!�ied��R�c2i !ZF��sa��AF�,{tNghN }��%9�),.eQu�xA�G1Z Y W u�u݅�� �qat���3��Tsix�mwsh�* �day�Q �a+>~�<�p�w�� �<j� �� )&!aVb!���A�*nonf^͔-R�6,case VI${}_6�< q� A'K+&��i�e!�Eregbldvgym��>A+ZT�*\ c"�9$nyJC obie�[xJ�Q� 2��;<s ������d2�V^ �!�* r�Q� rive�B"in�_nt%�icheJ���pec!{�. �6��+]a>N> 2�-&,�:I!pJ�A��^^ '/A=X Ped � aV'1edm�zk�,�1��%.O4�`[�cani��͔�@]=) )�Sg)�M��E{:�A��! *B%; osed FIA^�Y$�3&: �S��tN��;r"� ��)V|�N�  perm�d&� , �. �dTF��[ "��d�A-0 �#rrganiz�f�h:A��+��I bble�Oq���� ��B�Ũi�one FS F)��die�4a��M��e5 ��:l1�q�y C graph��"y 593{ ,. III, p.30]՞,I�^. 1.. but ;�4a brie� dern �\�!�!9}NLa5�,=�in ouro!uM�� ��,.w̹ BV2 [!t-'s : carre4q�!ja &Q.t\ 1�+& r~� e�i==�s%�i a� 7+*j "�B�6��d�(orn�{� ��e9e"\��Am.56�%�2� !�8n and the actio�n is calculated. In Section \ref{prop:Quadrquadr} the Poisson algebra of the integrals of a superintegrable two dimensional system is discussed. This algebra is a quadratic algebra, the coefficients of the quadratic terms are characteristic of the carrying manifold. In S.�sec:P �LSuper} we prove that! coe��� 45impos4,e classifica%aof 1>(sy!(s with two %zatic 9bDin six fundamental ^4es. The method�analy=1�!�of form�ppermitted carrying manifolds,�potenti!�and� of moXare d9� In this s-YFBgeneral�Y >|, can be wr�$n as a fraI�($V=w(x,y)/g$�%d!Gfun's $ &r!.ric $7rI� solu�5�same par!  differ) equ%�. %� existence!k!�>(was assumed�4obvious by sev%hauthors \cite{KaMiPogo96}--602_PAN}, *Vinet%GLZ-R3}.!�Appendixi�I�lyE�,give a proof�~�,!�%[diu�B�2�N�U>. In 2�C26}%NU�A�ula1� U�!�Y�E��n2 allGsixAqC e�eM>� �. From=seF� w�[n show�&re~new^U , becauseA�y.$defined ony�� which have not constant curvature a�A�surfac �revM�F�!d Koenigs} �^�@ corresponding to- ; essm !�%D Table VII�%VR�QQ}!b~�q�A5�_8 studied. We fi����re��a)��\-Iwas%)(revealed by�other�O��schem�^>"!?QQzero��Q���5� ?.�M�6�jC-�CurvQQi �s%!u b /kAl��d�mo ��bLinearQ���t6cŔa l$�a F�!�V( Finally, ��B}D�<iom�resultEM�Epaper�summariz�\�j{I&x.>�5�}\label%<} Let uA� nsid|n�t�A� \.�Bc%�\-�L)?me�mh: \[ ds^2= E(u,v) du^2 +2 F dv +G  v^2 \] ThU�conaj�� oordinate�w'!3 n�8 �8 : \begin{ѹ} �� dx dy -eq: G} \end3k passage f� orig!� F�$$(u,\,v)$ �> �one $���� real!��us��Beltramiz�� musta�ic� � cho~ �B� �8�J,unique, i.e.����jCs�  a�� -�R s1�ɜDlyK ivalent. � a F�� gFG ( Hamiltonia� J�LH= \frac{p_x \,p_y}{)� } +V%�Y�SB Ys&!Ba��A��!�mo� . ifA uf^ .�L��isPinGw  most6 QLr� I= A� p_xa� By^2 - 2 p_y )3\beta$54+Q}5�I lOfM B4By�;ie %Pr 8 bracket betwee .X��t*t ='is�OJ�9�xPB} \left\{ I,\, H\right\}_P= �p� I}{  x}6 Hp_x} -6!2>!62@x}+M�p2>yn<A�v{r? y}=0N�ab� �% lity� lies ����!��zA�&b (involved in< '(�eeqFM)!�  B9). %%�o!� hAa,!�{�kAan odd�� cubic or��iITq� a? >�$p^3_x(  y$�Tbe �rdAB}�d`array}{lcl} \displaystyle:� A]M!� & \RA�@arrow & A=A(x)\\ nJBJ x}=0:I B=B(y))� � !�!C} -pJ2_xAo52_yA�$!U5� PB})1- indeed-4%Bzn��eq:�h}r����y} = 64��)>ng6 x}+ 0g}{2}A'(x)=a(6 q��8( �0�;)2O \\[0.1in]�w�_1> w`'2L =6�!�:H.�!+ � B'(y)=b(y1B� � F�yU1�%: ��� A�$=a^2(x), \ � =b^2Ep]QX�], $x$-derivat�o ��}�in�%)a�A�lK  $yvI �0��Y�R_1}), �Mreforer�Diff_61} (A'A,-B'!f)-E+3 EC)�1� .��, 3 %�6':�+ 2%X6%^22'x^2}-2%m:Q^22wy^2J�ory��}]��2}:] 2�m a6�2'�zNBQ|=gQ&?yfE�^f yf]�M�f>��F���i]92��C/_px_paQ ��{~Q2=2��6� V$ x}+2�� � 5O.+!P�P.�x�F�2�y��)�) a�ɇc ��rels�yN�2Tr} i�IoN4^22 }D:�:)aDZ�.[j�.'y}Q�+\\ +4 �J�6�: :z-%�>�.�> 2A�=0*� �Q-�V�Ais point��totinguis�ca�#�rst $�C\Ae$� both&rmaq,�asa� secondK @is kto?9. \no� nt \under� {\textbf{�  I: �-NX$ � �$"H�� ��"�q� y simplif�A easi.+  u��� q�replacAn$x�-a %;y !i> fix2�=1 e=1$. For �c� 4reasons we omia�e 3o) � $R\.�2� $. EOs&o e[*��� %����2 *�\xiM�}{g)�eta)}+ V�2BI=5xi^2+ eta"Q ms� M:hQ��H"� Aeq1Beq( 6nW^l�?pec�]�s:� \un��Liouvill�Q�sRA =� $H$.(�tA�"�$I��-��it f�0e-� ��Y�)i�V�, ?& ��� 2 c�abafu��ܩS :I %�>K6$eeG ]��2 ir[ ]c= F!�+A>)+G - �x�� $F(u�Wnd $G('� arbitrary"��)Ji� chaerizes �&6called=R!���9geoKy � ooks ��z���atePis Min e� I only�1eq�Uu ��$�!�6� or� rotE><�sSF , bu���F" V��Jt!�th�$B~A��  $:$��be�l"��4"9W})�6�� }U�A�}:�.� E�}�'�~Meta} :O28\xi�# thenJ,�A��=]�-]� *M 2so� 6�!J&� $��b9���sHA�u�of5\9[�$Q-\b��} Y( ^�4�:O^2.= � �6s:C !q^2}X� �'!E�% �6H2; !�:h. Id 2 G`V�6@xi}J�/. �`B)U��!�B���q�65� 6�Fn]� f99\,+\,�{�b}{]�]�.� solV� �}�q� s $f��g���$% $��$A�de�%� ;qs��.1)��.dF �$e��I�O} y= 4IM2-= \,-2:\, =;vH}�sol'�Usu��mo�&onveni� us"�.� $u,\; v$,���"b, u+i v��uadE�= u - � �p_up_v�,8 "M H � 3+ < 3Q�>! �, �l��& �"� �}r{� 4\,(Ae + Aa)}{ + A�]�!I �=G -vL4!�u:} +_ �d 2iF.�i��  has b�investig@ in a*�conH��%Kr�%02}. � s2� E�&S�$ satisf�"f"sQU!N>�*I ez_eq>�c} E=Hb$,p_u,p_v),)� J=I2\\ p_u-i�S} u�eAxp_v:) .)v�[� 6�A;@%�#e>  sepa�"on�I variu s.AS=-E t +9/49E!�+J -4\, !� }\; du}+ /.\,-A-, �v ,�]n"v9Lass I:6=4� n��$y��!�\��q�Ras��B�!H]����^�a��!�d.d $, $.e�aPje0e } :e fe �e be�<7)���A"g Fd�["$�e�er!�[b[0���G}i��[. Li2� UF�=�O.��O=.N ɛ�9�N0"NL:�3Y2 .B����2��6� " R� Z eta)\xi  a�"ic$G�n �ic v will�"2.��� ��ase 2��R�e �. J�mpV�� . �E� 2�6�5.?!Y}B`g }5�!��B�[xi"Z � \n$&�!� \{F�� ,� 0A�� �\:t.o{�� }{\,�5'm�2�.*� gsol2 %q}5�yPaQ!�"�i!�6 v��Q�x\,:;6/�  �) I:3.v%i]5 ��eN1 JMf��g J �m�>@F��*AF F� C,\; rm� rP R P%.�!�of*���6Yis�TP :P &O E1:P-21�E �\)" �i)� QI, d ^W�int� (AG17Y�!_7 ��l� z3f beR, [ S=!� \�J-2� eft(>|{\;- �-� qk �}- 2m -  - E -��v)? :5F C�u� �>@ )�i�� \K, !�2� V# � :.� ��28�42 z�u ���%�o( ing�&�.)�e& Propos?*.��-Q��7� bi�(1} A>� � ^ l6cy2is"yon a bM/ poss2s �(U�o"(6$I$ Zm4�woE�s:\\ .q >��!?"`1 is a&P�w�-�22c" �3�;%�)�EX�V_2�6:� [ ���!� )�H_("d� 026�_x�8]e"<E�cm�Gx:.=�'��*���_f;A��0simultaneousl�J��a�I=�^2+i22  iQ*b.,f�+ ��j�� aN&=:qIfr�l͟ �l82]8Ig�-MV>gZ A)Ef���xi A,� \[ H��%�-�%�$:3�� \xi AZ,5.g%`FT{U2q/6I(M���`\�^gn��ͳ�����^[+23N��30&�r2�mM�m,�%)$ J� �� 5..���q�� ��s belong�V I�I�7 well know�:�4�;e Ref. &�Win02}�2�7por�$ ^~o3�� pmN�3."A%� .jan �&J�3��"O (or�)*X-!u� l"��% rivileged -��=d�0n�1����][7 ext�<\"shg work!�� E(+Պ p2y4noted exclusiv��8s $\xiD a%$�-�F:sI+��\blezl�=I�3�<no 1� of&��� .0�7�2�?ofA@2'@ �s wn�>"J2��8�} If.�Bgo�b*�<"?A�at mean�96|ree"� �ndeZ=�Ml� �4$H,\,A$E�$B$�&?'�'"7<se1�L L�a�?&V U�1k �no�:.� R%�chY(arV52A� V. Regak8g.�$H �/f�(� $A$�5 �'&y�Y�-��:id!n6��:`$*���Aav� �!�2prer?M�� ka -)bleI�a squ!| 2q5nEIk �"%UA�!n�&C �6� r, 2�A"�% + b�a�fl \sigm*::>\Th2Y�ja�3!O �b=� F�lll} 1&�&#Asere}&�� &� (98)�)�i� 0Fxy*< �!Op" .wQ���- �.! =�m^a�!�i�d�+�1�Ay�&(��9��u��:�9inYC��"!�F4B�8\xi�8�% �8�mDA0�8{� p_{}� :�"62 + *`>/ F�8"� &�.aY�iR�Mk H, A� \}_{P}=7\B20*PB�lsu&= �A5���5�A$�d!ș�V?rucZ%��%�� J=Cq/ A,6��9{>e8icalCAk�^`CE`�%N-A\>��@a{�� 8�D�����2r$C$ i0A1B��!Cqs��;�� �.t"���{Hr�  fa%UatA�9�~� F� �,1iei0� si� �expresD> !2,as a polynom{ �+�B�16 are Z} �. |� 6-H�Ax>��9�i7 d�  comb�?��%�. St�;ngFx�)�!:Q�`=U� (no� "�)� $qr A, C.X��B, 6%�s9��!4rn��1�e�fourth�:6D^�F 6 AJ*; �vbe M�v.A>=cv!�5dQ�,� � �A7*��*�3�� valiN�$9W68$= \alpha A#�r B L2 \gamma A B + \delt $+ \epsilon\zeta*�ACB�and��V�AB , C��> = � b B �c�$ + d A + ez zwBFwBy takA��I ap�rt1 "I* A�:{�5!�!�alway*�C2v o* r �)~�H& AC})-" BC})��evi� E��$ 9F��{H��I��I� � mechanic��R R w�F���DI�an�rN,�4,,in Quantum M2W2A d"� /L � xic treat�1�VCIGDas00*�  p 4!�>6|Mm�&��N Lc� Y2 &"DAbert�  :�%�6�J���a globalF�?Aju � Ais Ů is reflec?M he>o �vurXchI��:o� mathem� �of�5� �-�n�A��:�6l� 5^ foun� <��&+HP>L�-JacobiW _s-{ �B��uc��re�8� ��A, �`.�ՋP =��\{' A, C"v_P2� �����(s $$ b = -�o�c��B')me#��$$ �be "� 1$M� A,\;B�NC$ +Z& 5=1�JZ :� cA->k &=&C L!>�&=&݊ ��}�� �t ��. ŀ.[BP[�R5c�W- 2)^ d�\ - hB + z6U "- MYA�RB�wc $ \,\; �,\;�%~+]1*NA�6Ik�k= �(Hj-_05 _1 H)R�= 0 1 "3\\ %1=)8 (H) +��(h (2 H^2\\ d=dY d_0+d"\\ z= z Cz?z+ z 76?]5 �i!� q d_Kz rn-5��a(�@��+ �R torsQ�N�:�),�S�F ?l�J5H clo� 4u�y`~Y*&� *MHF>p"1 AM�)�$ a Casimir�q "� �2  degU6h  i�% �%N� :� K=& C^2-qKG Ba[��AN � %�-a�&-}�E B�02}{3}a�3i� 2 z A=? =& kEtkMtkIt+k_3 H^32|*( "�-%B�OT l��K,A��a3��K,B22 �*�Y "� aB� two .,�MY)NOE� a a�0���MQg eQ�,"3%Er� �%A� E}) &�s 6�:Z!�is>�) fic � each>_-�,� q�iXA- u�;fC9 m�f&�Y��"i !NM�s. �3 /r�#ed:NE�ZB�6 umed A�32x"�m"^P(were fixed�)� Bf �Ag �Za:�ٯba�o� -�"� .FSZ�i�  describ>aB]=�wou�%Em�*A "v� o)�)��a"�Q�@W��*|6rby aes&of�=�,�it "4yG"H�Ma�t ble}��3��z Ja�"� )1pa]} \item[eZ I]  I} Ta3_�tainsm,2��|!�� "��$!�M�2|.  . % au�*��"\ � eq:S a1"cTg'.�", \�;:�xJ�$Wj {��1}"A�* A*�$#"%  �8%6�N|�A4+2�(� A=&�#nB%#��B%jG&�9$#1� # JW:!, 5���FQsm�a^��g*�TraB1}�� 22� �&qY�2�2F�B�rAH�,6g�,�{G.�:�V��4-/2�w��1^��q�2��l.�1A&9Em}&}�2y�e#!��?a a,�+"�N�& V�& !�CB� ~�2} A=�^v�&aCb��&Q�� �[.Z (=�'x-��-"�' 1����2ڨ��N�%Kx(�B�UN��A�2�" aJ�"�B$��f re]an_&� F#$(X,Y7C.s_�  pair� O~#�I� ]$� 2$6a&gI j�by*{[&�].z.� "�N1�w �?��$s�r�I�(�J&bsub�#"oD� I6�l" :q ! 93&�E� {b&� *P9"�--� �B1}). C.��^�� �IZ� � I] 6J�*�?F�&r �2} --)��2} ��26�*/v���= J� �=8R�^2J��d��p36�bp �W5�s-�2 �%�2�iall caAm'eq�c{ �,ic+1�� e^:)+e^{-C)�� ����.� C#1 2%�| A�E�*z � ��Q�8t6�1 �U�1����ڤ=0"�Iw�X�L�� = 0 -i0>ZJ� )uYB��jQt� `.%qj� U)� �C�r �in�ai?< �6 it{S�o� �l 8}} \&� {� ^�} J�( 6&�ZN�4eca��*FJA&� �=})�Y>�� fu�g&�.Z procedure94$ketched inN)5�4 �3�Hgraph� �f start� o59� �?-�$���0 *� F�KB&i��C12�@�V*^2IF� &� =O)�_��"�@"*��K"J�) �O+ `D 8Y�O+�O-6b-*` �u .6- �O66 +\\+"�>i>--_�q�.� G 6Na�a\p  5K$:�A�eh� ���: � 2$�JEW�� +&^L�,yJ Ay uf.?�J1 �J= XQ{t#VY qn|FG�Rb{>)/ z= \lambd�"\,F_1(u(22 +� 03�C_3.�KF_4\�M8=\ell_1 \,G_1(v _\G_2 \3\, G_3YVG_4(vZ ��1"<F_k&QG r&6s*R�-nly �%��'�/1�� ���V�. B*.je7gqamiQ�-)�k$�+ d $�k$ �P$k\,=\,1,\,2,\,3,\,4$�?$four among mE��& AfteE�:�A�n�a" can 7\-u9R�x,y)$�.1�*q��)��Y�� �Db bPUs U�X9_sS� �some ele�*�X(but � lengthy)&�H^y�ѷ�\ &�Yt����lea� .WP.�� �-,N�S&�� \�@efi}� �B9B��&�,\{ -3\,"�,%5(5.�/ -��(@�& + 8 3\,A��)\,VC�-JC�$ L2C� -�iwF�}�m 6%t.�} R�RZ !��R+� � \&-�+(.M.*6�zHf)�1!�- g -vL)�+JK:FM( fNI��JfM8�+ g :� b\�I_ъ]2?�elimi�si�>I��� ��,N��; I1 f�sly!Z:MJ�"�s m BB�Tn]�Q� ��Y [ 6� ^� IR9E`6:N� ( 6- 66�� M4 M+ M16Nv� This��&`6A$sam�d��!k2��"���V `("eq �n{]^�1o}Y`=o�HU.�B':V_�I�BB��^9; ^�$� q I!C�E�.}ul�/[2NM ^ .�]��x1�-�&j=�g!��" }��[�s�Xe�Aa,\, 6V0%�R�~9�.v6 QI})Z{D*Q+.� JcIB %M N�,-� eq:f�OF� �W= \rho� .] � F2Z BW � "T !L=rS*Q rP2N rM.K rJ �H �� %��"don't �9�!� shif"{ �Sby1yc�/TP expl&phy�E ��4Rj &Y1�.#/.� �'|&&i$$s now stra� forwar�|B( A(xQ�B(� d �(as"Q%A!*&�Ssk:9a��:9a�"gintro�4L�&�J4Q�/|eq:NewCo&Qf XҷjYj�j� �kQ(z�m�h-�>�'� Pyn NewMD} �L\,�YGn,| itilde{g}�  \,dX dYR9�J3N�j\,!��.�Jx �w>�z�c p_X p_Y}{Fj�&wid �V �=a��� 1?�*v$�!գ5BJA1sum}J�=�F}(X+Y)+G}(X-Y�`� �"�'ViE�[1�. hw�g rɎU+V}{2}, -&=&8 F}(U>�VQ$>\d2\�\dr\c2�cv�c��c2�cv�B\d-�)AT c�d�RT"�.u *� =i%� P G}(V�6jed up�S�"RK4Y�FGTildF7>�l�.��� �e1A T6Cn� +\mu8)Y��f�n12�.��� -\mu��1�6�M \mu$� b %.�)n5�.F�A �M*R� ���Oڈ}� �� ,=f(x+y)+g(x-�z]� V&�M�zY#NewPo�>� c:�y�9��r �w��R�,*+di&2|.� :.fFR��-Y)��p^�h!�V��V�f�F�gu� y�i}B�2yP.�w:��L���Z2� 2[6��n]6Y�f��Y֌6U�7ZfZ  . $X,Y$z^��V�B>�z/Bz/Xx/Y95.X p_Y� =d��-��2� 'J�}��/F\M�F[.nM�% l��6pa 5+ �Q��Cl �5 lb~yF �_comput�a��:HI>�" )�:v2�J$x,y$. BN�n��262z�x1}~A%&t (y)xV.�x) #i@"G y) x� VZ,;(��-E .�y) <.=vI�"�.� "h &g "IBr�6�b�GB3l} !FHy�l�2H� �� �y��!�6H / \� \3HYV�\aHVTH�(2H re��*`6uH m:o̓Z�CS"7+7��1�1�D�\Rly.��7% %- M�7\"-2�Rk �q��3.�;r/�l�:ed�3R��6tQ�!&5nV�N65]g 'A�:��7b �*R �*Q�>f�>��:>$9"�>f��x����=��x�Q �>2�45��:�&P)NewB})� 6�B"*v�21EV�>�-��ZZ A�:�7J�*�D�6�*wu �8a"u *F ��U": ���BMZt��&F.m+6��6s, �B)T3 &�0��*R+}ZK�+"7B�0!�Z= }�#z0�?%)"|0f�$FGfgVa1} %fme��/ {Z2��s=4G(@ \,u^2\,+ \,\kapp �4{\nu}/� &:=��(=-� \,vDd! ,{\m5 v^2 }6G \\ :�K4 � ��5$ k\, u +{n�:8,-7\,k\ }m}/{}\, +\, @c* %xqx!�B"lFc=�\x�e�c!T�cf#5 *T~\:@6O]Z7}�i)i)}2N]&6�*i]�w�# �6GAW uad !=Z6��:�WA��,�l>5�6�"�=.�f:�6@o<*�,�WA6���fr�f]S&$6�"�n�a��e�m�q�}6�6hu1�\,\u� u^6 }{256x?i� u^4 }{128�2�2c 0nu u^2}{16} -\mu }{ eO�'2�. G}(v)=o&��v^6 �Y �v^4 ��&<nua��+��v^1pN3�&�f}6l�� �N ,\ k �+ ,\ n } �m) 5 V)dZg) �,\�5:�k�9 � -6��!�+)m} �.u ��� ���Ʊ B=>l p^2_X+Y�Np� _Y�) �=.'ʕ:#�*41T2��. l-.���:��Q�X=2�o{6�l! =ᙡ��TY=2��q 6Y=\ p 6et�8!�F� �J�, :�>E �40 ��- >= �P=16 (m�H -k) : "�P=256(�pD H� ���R =-32�,i� C (a� nP�9�d=8 ( #H!\ z=8  6�C128 (xH x)&mu mB�\[ K=32�.nu� n)^3QU512FK LmXnXn) -64=!^@ xw]  ^ 2� ^2A/�2 h6-�e��� ( �%��J�d�� !,%Å�E m�)���� ��n�2}�6O R+ O" a�o!+��BQN� =el���kB�n �F�( �E� o, �m>� H6 6fB�!\:~p�* �* �* �* �* �* �* �* �* ~* F�: .F 4�1m�De^{2\,u}+\nu\,e^u ��and�&.E� i7��e^vsh{{!1Z=v }]yY�Bmu 7 68-N9x �.�.�� �e� � +n\.��� �z��:�:�miv} 1>�0nP���� �� �� �� �� ¶ \ln�k� �� �KL�DB Y=\lAO� p� et]F�!�� � 8 �&� �=A0tA� >� " � )aB"� � H  2+256�l��"� (�-i�) (m ~a�; �dF  z=3&�3J ��mu Ik+m�� JJ pnu \, 63]�wK= 256\,"� \,�a��3��6pRo^2 O 7( �'{�(k ��\{%G~n��!�9^� 3�� �B���B xi})J %�B & )� 3�.�) �1�? }���� 1Ձ�%h @|<C�S!�`>;A�_F� � q�m�vZ�X�M�F��v��}�v}�^�.$^2}\\ AR �k!-�[�e�X=X6�J �m��Vn=�T5T2'F��� �� �� �� �� �� �� �� �� �� � 3>�(�� ig� �w�>�S�gg��I�tan^2 u.�-��,- }{(cot^2 u�� N\�zC��B�l K.U �X{4} \, �v}m��W� v*2 Y8(�Kz\d*� F .�k gell�� ��!"� 2\��- �=5G+ *\ "��.�.: .�!0F- k�1�)�von%�m4>n�2 I�2:�� �i �i �i �i �i �i g(4 $$ X=\arctan � � �J p_X=� � 2�  � .G� �Js5 G H �� $$18�(�A�� &� ! � � "� +*� � &� \nl("� H�u���Ta�2y 6�� k a� )-�H� � &\,Jjz� �x"g 2\nP aw� E@  -� �"� �k �!�2  ����O�3i��Z [ K.� �W 2 x%!*q X�9� - 64ٱR>C}^��� N�1*�*� !!j�-.N I$_{1}� 1{Eo !�N�^ bF�%l��.���&=)W\F�nl�kNb 0_ ͝� 6[�[=kV ell,\�d.���=N]���[{Q ��� � ��� !wf� � �z}b� \,,:�2�?��*� 6J>�i2� �-S�?�>,���[�A =�NF� 2\,{�xi}�" �h i8�]-M a^ � IU)#Z.iif� \, � )|�\ ��c\,ve ��vu;i�ɧ[�^>5W�w*�=�� bFg��)Wit�#� ./����a�2 ��\,� 221 �� � �H$� k%�:�- � ��2 .� �aA>D6�"�!� ^�� �J�n� m�� ���%{4F�v- md N�� ���V�a��n n B=: � a�+ eta- ��w�{eG}}i��G~m&= F�!�e0��$G}i� ta � >C+R< `��+>\�+,Iv .Ff��H �-�Gta 2q!g�{:6:� � ��!�] 0..] %��m m @ Rk  � 8 (kx)-v^z 8�G6\ E�q�L\6c !.f )Ţ � ZPqC^2-"Q "R j6@� 16* �  n�r��"K 2� �#2�C���Bw� v� 2�� {\6� E��� "�& =/'Vb2��Z"0')4c"o# }}� lz� 3&+q .>Š >� %�&��l�\Z5 �� J=G >;H 3\,kR�&� +�!�Fan2$�ZVZ� ̔�� �� �� �� V� 2. u �� �� �� �� V� ��5�{�� �n�e�r.""+ny�u^3>+6�F ,`<+ &C\,u\P ��:�.%_!9��v��%�/>*�.� ~� 4W*q� �� 166 6�*_]!�:*D,9"� ��3W��*��1 �2�.A2�JR+�2m\Nn!D-�2��Ձ��� � � 6��\+�\+�\+�\+�\+\+��x*�!z\+ 7e]+%��� �� T�A�W �|H+�f� ��� "� }I � -\, *U+ \, 83! 2n�  z= -8"f U|!&T%  "� �|/ , "� [? �J� 8��1� z\ &��" ">w ^2- * �F)<"mu\�m"� I� b v� 3�� J�!� %]��Ɣ!A�)=Y=~ə&� }^3} j�n*�� 7�l��R�5$�6�+6kY B3�!:�� n�m2��]9�x �x �x �x �x �x IO��������v������$u}<��e^u��+e�*!�vG�,�*p d.bF� e�.�� �{� 6�F� H C� e^v= � �I �I �I �I �I �I ��*��*j�*Mn� S9 &�*�mV& ( q!(��u��4 )�NOni�* T�H"ke�H-nJI�q �*� H��+ �)� �H f }^2 �4n�� :"# �4 -.� AlŽHL^�>O?l>� �Vie`\nei�?"D  c� n��r@y&3�of &D�. ��iV�?�6�j�� �oߟ�|or�Y��� .t&�Sw>"Fa^�r^@newZIv��u) ot y7�en �kO@A{SZ�c.�v;TKoe�>��"et�A $�>�t�|}[pEd Ix{|c2 } \hJ ݙ�} &��IR  M� A�&� @E� btabular�Es��\\ ��\<� Darboux} � 0} &^H�es6FKA�>D��� 0 I_1 &16 A_2� 3&-A_0 R &4 ALR&VII.4!$[3,2]F� 2 &F?&-8 A��-2>��2&[21,2]� )  Ih(&2(A_2+A_3)8&A_2-6�&-'0+A_1'%'�1&[111,1J�!�EV6�J1&&[0,11] B�I_2 &�;2}1�I2&�$2+E2U% 5 &[3�J�3�8(A_1+\imag A_0)-%�&��W (A_31 2) &� -?A�3E0=�B�capi{Qtab�K \sf u��E��f &J�in *��u�N"�sck�p��"��i� �� ��G�Aq[\f�D�"v ] Us S&rT trans&CEx p_y +jY}�Y!vB0�DT_=&�M [)�1}{�Y^"��-yb ]+ �� 6.{�Y�1s']XV��2*4}*4P ��6&6&6&:MR�iZ&ʒ w��)p2��a�L.*R�a_��8+�nt�Na&� $a_0awa_.oa_0oa^54x*�Sלw�Kput�]IoAMm��a�{��W*� (51)>� ;rjW$x, y$�ysLo&N�{b$GA�R=&b���"�V5�2}yV�x}�"���5F \Phi (x!yXms}{.-+V- \\ +�42fp9Mc� � psi �.y��B�0ar��a�E#F� � l!=�l9Q(!_e� + 2 43 6[` � `-Bb- b1B  - �(x 4 b 68 a-m ae�%��� + _+aO 6�a��2�p6�>b� 2} -b  - a�.� b 6>� whǪ��r��s (50�YP�Z�)F��>�.[��eI!=5K��a_2�%eadx}{�d}{x\,�� QX\%�- \M}{6+:eU"�F-�:2GW-�u y)�\,y\,\,voJ��V2Ku�.92} {A_1'3��] !IyR ��--/� +N�M>N +22a e. BN4 N%T {A_3� Big(>Xa 0<6>�� }a �!��  4 �� - 2 4 tN���E�!�.b {A_0�)VI`e�+�� J~ ��A� 2}b� .��^R2Z-!R-2R�2ph2� � {��gMga�gFga�g�g�gps2b{a�gUg^��g=R�gقF*2$�** {�M� \cos(2 x)2�"4M�5\s�2x�+<"CZRy,"[1Uy��in (2 )߉`  6�Z�ZZ� �3(6lh%� MmuA� (nu = ��bF ref"�aaZ� �g6�JuA4^2esP1)�-!�ɞ.}�@A�(+y2>co.>��� �z: x22�R 4 �..��6a_��ef*��&��� �� ..�I1�����S[U-| Va��weN�2 f�srf5Vk �\,y2� 4} �>�[� � 5�y) $� =�� � tanC\ y)"1��M (xJ ��4- .'(���F(# �1}{�z2� z N�6 ,�,@� �-� B B j�@�  y)?2 [cos2(!�y)- � � N 4   �l} t1�=6 D/1}{si���!� ��"� + 6 -�>D .D������ %1�I!^1�; !%�1� t2� �12� �1-1Z�.s�n�}+ >nIF� Fl�:�j �AEl2msi�m 3 (e��?& # a�U�Q�>kI��\,BaAou��)P.r- A6 *� � ��oE��(5*(�mYipY� .p���&) �t+�^2� 6� 4\,A[c Y�)\���jK��5��N�ID�{/� �� ��� Y �����&�%�-�j�.�j�=�a�����\���2�$a_2}\,\lef0t[ cos2(x+y)- �-y)\right] - \\ -&4\,a_3\,sin^2(x + y)\-lefrK�^ \end{array} \] \item[\fbox{Class I${}_3$} ] Using the coordinate transformation \[ {\xi}=\ln�(\frac{ wp(x)-T\omega_1)}{\Delta}-1} �(+1}) )+ V1}{2} bqj.x2bx~/ ,\quad p_ � � wp(2F�2 �p_x!k%(eta}=b�y2�j)b)��*�*9* �9+F�=+y!+where!1)B^2 = {(!h)� _1.* _2))}.! >!3))E�A�$metric of 2�� superintegrable systems is reduced to 86F�messential form VII.1 \cite[vol IV, p.385]{Darboux}, if \[ \kappa = 2 (A_2 + A_3), \quad \lambda = A_2 - A_3,E�L \mu = -2 (A_0 + A_1M� \n!UTha�rresponda�V� (us�y�s!1ref ��)!given by3,Hamiltonian:!�H=)�Hp_x p_y + w(x,y)}{g �9�begin��{rl} & = &ύbwp �, �, ) + ! :(+I8M (x-��](\\ + & A_2 Amb:2Eq::2)43F43N434:�AB�)'�a_0:�Z��a_��a��a��%� onlA<reeAeIx8nstants $a_0,\,�,�2�3$ are independent, i.e. we can put one amongRm equala�zero. �� rel��Ls (\ref{eq:FGfgVa3})LHhave that in $x, y$.�Pother �5l� motion iseF�A(J)=&i1}{4 �^2}EJFS$) p^2_x + r7I�*_1 7yE <\sqrt{�RF�\, >O}\,p_xy}{2\,�9��$Phi(x,\,y)wPs}{.+ .\ +� �}{2� �p�\,w - \p�(n�>�E�V��=&�\1A�d>�R[=��^��b��9�=&�������U��*ތ>�while �Z�tildeb� 6��  second ��Bmѝ����K�� 1ѝ\,F,�R,3,}�|>�3��� �&1}b� n�v �,>�6�� y - � 2\�^^O3�0>Q2N5$�)P��P�E( ����.}{ 2)+ u��4b�=���v��c\, ӽ !�%n !�(52FF�� B� FS���i��F�� A b�,^q u \ � 2 ������F�>~V1�U�!x��� � 2* q�2d �;+:�2�d�d�d�dyx�G���=I�2�W +Y A�a_������:����I��c�c�c)cV'I(<1$} ] This case (not coveredTJVIIKoenigsF[Vol. 2. S c�c"�s�!Kress_{ }�ivalence 7 $[0,11]$ y50nondegenerateZ� s $E_{11}uE_{20} A&�0KaKrPogo01}. X*� is�nH= irp_\xi p_ + k  + \ell+m +n }{\2)l +�B +\nuB�� ��'R�\xi�.�9�xi>fB�%�vvE�s m\xi ���B�� V� j 7V� yp .�>�� �V�6$5����.� 384]"G�0 studied sepa��� ses g $I�=0$ and\ne0,\;1�,=\mu=0$. %In��.�s��Mi05b}�sam]areN~c they ���0%St\"{a}ckel "���iE3 ^E4, E6��ref. %%+��f\F�%i2ń��*���� �P�q \,x^2},r��Wp_x}{x}� {A�FAy:A� By}{p��6:� �b�ҁ5)���� 2}D � �� = 16 1'��=*13~4� ��y�y�y&y [ � )^4-� )^4�b]+A� $3 $3$\\ &+��)2 )��M36$ "IByR�?&=� 6rF�"��Z�| 6MF��2$v�����BVb2b  .a�� &#�� ��w{"r�.�-O*��.'�.' + 2\ X *�J[�/ !.��y>�EV� q�=� ^4�1 32 � A_3 *>pR@j&Pq�-�# 3k-y)� k-y�k*$8��a� �a� ����*- k�4 - k� k� kJ����I����\,aNa:"�qC�a~"intIU) dx -/�G%� \,:/+ %�B>�n�J��` ��= 1\\ R�}  1>fj��$�$ -6% cos(2 y)^* ,1}{sin(2 y)}� A.3 e^�"imag x}2G0 -� "e^{-2  /{2!�M$�ofH 3nH ��"36H ��"V�5 )" 0=�"�@ 1), 2�"2(+R2Rn ���-+-+� j�b":�\sin 4�- ���2�\cos 4��- -y.B�T�5�' >`& S (J,> R�a�y���Mv��/���93!Jn�.0 `��)��= �= b= fF"�= .= &}*4J@ 4} cot^2��_ y���2\,m3\,tan-}m� "!�g B��z�Y�~&g "�Q� ��"���� b� &) y)=�'��\,& )\,��'��\,x} �)4 y��' 23 2�2 4����)&b#��2�-r�23�-���1��������-b��g22����Ma�=Y%)�f:�23��:�W 3})weN�&Bb�V V }.A��jY&6 �M�S, + �%)\,dx}!l���+r5� int{I3 K> j�f i=-8�� 4 xa�1i� x�_Q�yPa_6P�3e�JP� �/descrip+(} \sec{S:�,pot^,0s on a surfac-) revolu6$ with two �.ratic2 0}\label{sec:R=PQQ} A manifold whichp �b�a:o �,fds^2= g� : dy H\mT0or} + dx d�-jcalled 2� �e abov�ndi�is possi�->forC,pecific choi%%� Nmeters1�� ,�p\muQnu$. In!y��)V1-�n bGlcula �%� grl !4�!`.m in S)� �*!���e I�m�these"�.by 95Vmany iJ+cest 2�-�ula�**�$\, � + f(\xiV)+g - )}{F }"� 6�nY bYGY f� andAp.MX � Y}+ \wide${f}(X+Y)+ g}(X-Y(F (}t � M�HU p_�jG ~�(But we must)A�`,A),Liouville or A�z3)�^alway�'appropri� ones!� conclu�/whe�,�6 is 64. Amo0- R0 f0���E�]�A�da|mined )0wo *�-n. ay6etab���恮M�a�al valu r!CR�B�AN $a�� shown. We9�!x.,1��eC iVerp��MiWin03}�82e�is �u� scheme�!�at�re���cY $R�$��!�A �a�(�!re��itGa new2known V�. A!�ai����ş�theZ6ŕj�� furE�inK pre23���.�'t0! }[p]a� a�6{|c:$} \hline &�n�7 } & ��D  M� mu6 & 6 e,tabular}{c}P�r\\A�Y�\\ from!g=�1���H}&��` `I>6^�  R_1 �I_1 &0  \cdot & 2[A] &�& C R_2I-I[%nz(1)M SR_3IT; R�BV�4I�J@R�3^I5I�@& 4^(6I-EYRI2[C2�5$7:I!+�1h� ��Z$8I)$�nu  ?�IZ�9'I6L �R� & (2] ��0} ����W& 3:q5( {11}�2@BRI � new}J�{12U39 &-�>&->>�D2� e�3�5}���I6}>� \ca��{��� B  \sf ��6� �kV #%G �w �r��*{ $R_1$: �' V =�5�q=0� The� �I60&n*�.Sis�; by� H8� } } }\, (xi} }} {%�;A� 4=#�#-�$�"$ }^2}} + �k�0 'Ixi /) �ell�4 Zet�%b-}3� �&.xiJ� *�m�� + n ���� u7�a J/"�=-v��u}{2}\,B �"� "O" = p_v p_u@c `p_u�� putt�:$�#-8�=1,r .z($��$Ad" &L#�AX obta� \[ H�ux'uV1}-�?u +�k\,M�( L1}{4}\, Bv"� �mm!�}c}U(+ n� \6b{2}$::c$uV%y�$ }]�_�_{ �N$.�&nu} + �VPq~+ -F}AMJIA76saE�(Oaq�@{}=6�:�+Ar �3A5i-v,\�U= u�eGvu��p� \, (a,a=)0m3)g1 pv0AZ6E =1/G;�E'< 2H(1)bG� fEm1v}�A�6\,!� (4 u&) & &a"&e4 ma[}{u\,v^�z+ 2\,k�>93672b�,$�;�;n�eta�:xi.�͖-7)k�a'A�.���ѣ!e:VJ/ZWI�q�}^œ�� n }�1ږ�!������$,FS2[B��~�)�(yZ )�eF.z1�k}{aM5�^�4��.�2$:� ��.� $(X,Y)$�J""� M�:w4H I2�}+n e^{ �k�,e^{X+Y}}{(1+ )^2}+m3&  }{(-2"}{4�.ea�g�WX=�����\ln0 4}�� + u�Ka�m��YjP-�RLV \, u1�.Taf\[ p_X2}'��!Fu)��(&� v}�,@Y=�"�BL- 6��(\� L��6�5"=� \nu=4J� ��� rJ�AmV� ���=�%�k� amm3} -�l�A+ys}\,+ l�:� 5:2 ɘ �� �0ѓ�m �F.�in�D�DvD z2Fm2l�1,)db�!F�X="QI�;I(x-E` "�#A�Y.m6.+>.�F#q"^�F+q3�&y)p_yQ�,\, p_Y.fCs Cy �x.A�P" � );2-\alpha  +ɏ .G$�a.&* �.q 4 x^2 y^ia9�]Gn�h ((2v"�) k%2  - 2) m)�0 �1}{�03fOL1}{�(M����+�j%)) (]2) + &� �",+�m!_>�6bE  =�� w& e����#��HH=:�6)� >� {1� \mu �[et�5:a !��~ :) � ��� !�F+� B* =%�2�EF-} )\ uI 2�6 E �>� B��6� )>�:)v�R�.{n }.| :| �Q��� FR��.,!8F+xi4 1W=1}.�R��� Ira�l\xi�t#����xi"4�c�&p_v�)�� *e*�R �1}{16�-J�  $|�� c���!4\,�� k - �3�^�+ >! +"� 1AN n1iA*A!>�76�3&� = V Q=���4�%>���V�Ez�D1 !�axi �e^V A%A0&� }�C2� Dnu\�eftJW+ b W!Ymu" CFڤi���e�^�^�]nu �\Big( k � .Nxu�\,�K-1 �:2�2>IL+��M�!�!{�c�/ ��-F� '��X \,} 5���=!�E�!�mM�6|J�Br!�=J3�) n5r.9nnT \,} fr;�A)>��}�|� �!�= *� � �FSv�}ur}ep_uJ}mu=I v nZ�4�“ �l(\,u" �.�)� i k A�)�1h^2(v�H�  / (AL0ell - k)}{cos 0q�A@, � -��2\ 2�T A�R�8B��< �m!��� �"}SB��"�%� n��ya �q -�>��8�)�@"x�A-�ut�!yI} -a�R3��-�` R{ + �s{-ekABta) }�\, B� & �9� 97�[��I!\,.VA&% � T.T t -1 �V2�� % *� hn�!���J�2�):V�M� >� \,.;=�'Fj63rY:�+ \,n= i�n'Fr:�:}zaY� ��-X�B>I�I�E�A�e^mQݞ:e!fe.� �) {�� �{{e%(arcsinh}}(\_2A-!7�\,@P))}� {%C ~>� .>% \�!}2T \,[4^2Vy\�Of �^(G ,(p_� �(F�\�) ~a�j :�^>(2&J .% �!��C ��6^ ll} K��-& %"��+ 2}{ 6�r�[&.� (- (�4\,X)}�� NTc_Rco1�Gc_@��e cO_�� DBv d� �@u$� �+�,�^��6�q��2d- ^IellsW iB��0 $c_1Y �m2�ty M)\,(-� QCZr\,(w3� )}{8 �!c_�]1�k G Gf�cb!��� Ve�/c_3uE2R:�(k+ V:o.�$w16d!9*�I�$&� ?&>0}�@@~�$| 6A*� ��nu?"�$ ��v\,�/ ���]l]�K�� � ���o����.� N$$(2� R��� ��B� � q�% \,(a� - m)\,v}�!a6.!a.+V�{10.�Y��� ��*���nAa\,� �+��)Q�!�# +6�A�Q �QA�=0��&A~�>�����&�4�Z3 $�*��6�I�+`a�s%a�U��% (n -JDU�[ 4Zn#�+>F& A�+m�b�+"+"4�w 6 *{q����2��'�2_7}o B� ��Q� !��4I���W�#}}K m�V�������2f �(���A$,�4Ja �R A�BL?-Y�<��\,"!�7-�&#'�cA�� )�4\,@A�"5�N&ZE%�F�5is2��|ad�8al NrR�(�,�A=+ �=+{X_1}� Kz*2&n XaE7uI�A�1M�LAt n�7& %&  �v�!� \[ B={X_2� 2\,v"���)T�!� wv_5X+�(,^�!�a �� :�.�\r�� K,\,X_$"X��u6!�tXd2�fnd; dre75&2,0. \[ K=p_v,8X_1�,u�!X�! u� E�u) �Ph8(and}\; X_2X-�vo-V 3]A"4 �%�Z`� is: was�5i8b;i*�6F�T�\foz636V)6, "&<�Q;A�)]H3"g&� �7 �Z�R �1�,$*+)6?6c02���N%��en.��u~hS���^3�IF�L0 �FE0hJc\muLn-�2�� � �" \, v� �=i��P �u}{�s"v,>� I� Q64A��l  p_��[!� 7�+�HJP v^{3/2�K_uVR�, � .��/��= ��E^q�� a��Bz&� D� u���v v �@� - k��)� �:$��\,s lB�A���(!Mv)u - #2\(�!ll�J�3��mu��X��i�+#  %(or&�Ztly"A'A�=0$) V#�Z'i�A8)2�iz�m���V��Mqa-�� "t 6��� `v-u4�ie!2���  v e��U�u.i}{EyqLv� k#&�0a���2� .6�%��aa��݁�>�q�-4u�4�&2� $3δ� �uqj>w '] \,q2a�n���B v} F��(; -a��!�0 }q{ �2a{1�k�'!:~7sB�D�C\-�C0ith curvature�l.�CQQmxD4Let us conside��HFc2?t�p zN�= &�@c"J6SB�C/Bi� \,d[, dA6�� �is def�5 by:b�m%>R,9 eq:C�Zero} K"c A g"�Jpar�q^2[ a�  A�Lt \,g =0)�t�>�W]?!&(traint impo�ZresPr� ?҂{D"�Z�ZFzDA "A�0}H �nsef &E u|A�A�> �param�As."�9�9�o?c|&q?�>�r?"r?lane\\ &iAVj?[�&"i? �;�{c}Drach*�AFVRanada97FT �FU&r;NOSan99:NX�<  F_1&�?"<+< 1<& E;?_?P{(a)}\; (r\ne 0)&V^{\uN_2t?P W .^6@ & {(bB^bY�: F_3�=K�<Y�<��'YgBYcY54�=1�J  �bYc)}� !d} 9k F_5:� K:>Z11 Ze �=0)%|>mAF_6�29 T 5 EJ?�T-�T�7��0�>T5V8�3B�� �;@�f6VJ�9v�T{7} Ti-Pf��W> E1P �{17� {(d)5�- F��J9B{(h"}YU�&�"�?GK�?.�:�?����t�E•? I7EikJtegor�=re��fwwi���D �E� ize}C*^ 'o_ >(mplex $E$ p��R.K0�t�RX.� � HdxJX �U��! �)+re� !' B�E�quaJwNdpA�%=TMy8real hyperbolicM} $H_2�.�I� HA�2fzE�-��A�R��i��e9G�MM�As�N":x�Z� )" �Ie :� J a�x� �; 2  in oneV4K-jah� 0 characteriz#  permit�N� sa'$ q�fNM�&�N� ^�N W�y�e&a\�Aa�"t d.�PE��$FN\D-"!)$=�cy:��^��)l�@2q� @,j"�44\,,� /F*�@'D6)(�& Q'+�OP'j z}ny=Q ~��t%�= {�5i \,y.�%�%x*� y}} &r,.f�B*%x����)|t V.�p_=`]2�M"K �<j=cͷɳ� $E oV�6��m2:= �!���1"45g{61� + 8�xj-m�6�4\, ,AlsH� $&� R���isRted. ��%�{�%� � x}{rB�y�!�, = r i^-�-��8; XPre } rWP��}\] and &�E nu=r-��?=� $(a�+� !B�!��j1��H=a�xy!l �k\q�!� r\, "�9}{re)a9)� \, r�eYA�606.3Zi� 16FrT�8Qg3�108x� y&E# �n!�> Th&��ŀ�Ʃ]�Us��E�" V $R_1�PRa,RNSQ�s�T�two.0Ua"R��Š���>:�so� . Whe�Vthird&}� t��=&6kd ��  ���:��u0�p>M2*U�%&� >M!��O �}/�A Z�JzP)� k}{("Wxi �@-:!���+�t�#�JvJ�I�I�I6I��K1��* B� ��A�6�V^{b}$�&K ;��E���� K�J��u�=�<�p"gk>=-DFՈ�8�]���<�<^<6`��=�\aQ� ᫭�x�6���.��.\+N\���>��H:�E���ˁ���nB� ^ :l% !-� �'�+t+ +,)T>�=!m2)%��V0 �7J*T .)��*� ��63 J*�nPOZ�吺3{�$)� U {2 &� +� >6�.6a�\�0� } =A��ee!.o �hJ� �� � 6<m��MEnE9F�U�� *�x� a2�4 ak-�.Eb � Ք��� E~A��a%�yA�� 2�r � ��6� 2fy�N`!z&t Q�6y 6�{��=V�!� 1z � M7UiA��H� s \9 �U5� 4{(m�!Ep \,r} �U�> &� Mp* Ŵ -��"1>} � �Ma�IG �qA.-2�:jv�2rI&:�4&�:q 1�@)���v�m)����$�Y ͟\�.!�" n%- !�)ya�*�.-}����N"�!�Z���1^cG5 �"� E5{��A?{2�-�A � ;2�i!��1, 2�>Z� � �>Z% ��\[J�y�I� QNy.y � ���5I&�; W-x1�%2B) au1)j^`�� C�"�-@ %)sT )7 ^9� 9My�Frl} pE6�2�:�a:���&d�K�=�kNkB�6�i�= V`2C��N�*_b� d�Jv�B� 6�!�>�&+�T�� {1��.�D�{\,� �sm1�E�UuU�]W,� �sr E�@IA� :I���) (k>�D*Sj:+Z�{���� <. yx��� �� !N� �!"�a2�~�Q4% ){4M{.9 ${G R�ns���� ��Q� )�2\�|1� !!�! �i1�V+1J�VF2LP�e��c�p �� �TBTB~~3�.  �F�o�SA+� \�6�8�,]b�a� �E}=znu.e�!\)�I�2 }}=c \��Hd{zJ/))�Y&(�v�O��BQ 2.E{+P\,� AV B�76��,AI�8Q�6` � �11V�.is"� �>��zI���z z&�4%[6:�  {� n # -�B/ +8\,�O �� >&H(vg��.W.�aD�΍;S ?|$�% =�l!�p��]>�4>�21�J�{�# (6$�Q1A��ޡ'\>`&A% { x��1h-�*%[>� �PJ�?2$!�ZB�AZ�h1R *�9!Iq �f� nu }1�K��!� !�&]�� M�- � l3%5M�C J i� %D A��= _B%� "v @���a���A�&$y�� �BDA�E� ㅞ �\��\q-I�.� .z��/%!��4}$\,�v9R��5{ 8\, A� 2\,���"� 22#��8���cm=%���9�>6��/%�.��l.�n��9�qAN6%�6�� �� (r j'!�J� ��m�iE �b�aa9hHR\, o �W�v)m�+�`��3�9/�2_ 7b�PF�j� �  �^�"�9ay�o! �1t �a��� Q%O\� �!,F)3"V Ia�VJ()^)�{3D+�� m�n\ �� 0A� ΪF� �Fzq��ae�2�y� 9p\.� �\*$-]�'\� n(�"�1�ry�GFgo2��H!�96-yA�btµO b� ������'B�Rp��?(.C -4 <6!�*� � ��] AY(z!*% E;>?^h`i� a� z\, 2e�2!QFD3�C|2r��T<>H����e�>� ��aB .*�� 2� )�"�.�(B .�0!�_K�"� ��\V�Q��2\,l\,��� &y*hh+ #n\, P� F"&k$B<�3�'2a>+"�;6L �!*�PIa!&�;:�@ #<��PW!> b�A eta }^�A� * �r=�BB $!�V AI.� ��:� � =.Z:� �E��� mTS'.A�� e�./z  0G!}/^ ./.��8�B !��z��J��� ��z}6*v%#�ޝ�^2向��7F�� JB� e��{ �^� BVs � f)���  �9)Y1"5jk��{y)Z 2Y� QK6 z  ���;�F �j�� I��vN3?�n"q�A�b Z� a1 �).�B�7"NNr!~���}T2aš�e� y�Wy$����(3)�*mu\a�}�\nu�<�) z� ;!Kye�p%S�)P�[ +6`������>��cD;�F>5#$Yvd 7�� .a J = &2u AK�� -2 �NniX} ��wb %�.Dr c�r-{ �? A�)w4 V8�.U!�Rj j��W�� �J}{ , w�Rve1we.�C@��6_`�Pw =�M�%�2�M� y$ �I� T�qJeB�7�g} I�I:�E}':� �E�M�MrkaS �6�� a Yr}� )�q ~.E�F� 6l7A֖�A�ř.�Ai� x yAA%� n:"��& %l r}}* /k?B (2�(r�-yQ�9a�>�B�7 Bi�9 .��o o �fn Ahag ambd"���: }^zM %2;&�La��я � 9�h2(~ R�!;ҏ &|J��x0|y�zK0q�5.�2EQ � Ek<��~)l� ME� �Is�t�@\8�թRI5� \ I" nF�"M� -��X1xd> B�2� �:a�z� 2bF� �AW%@����*� m}{zm�z2�Ui,}{\{z2�}�J�:�.&$�)�!�F���^L�� J�*� K .� s�=dJ B�".� J�5�!4�a�c 9u�t5sy�x:�-n"�*-�!4a>2� �1V�GN�9zaGo �cGu%��򁡁��&) )��"W }q r���!E 8.Ea@"� 7:a�ū�Pm1�K��[E82� M?N�!z�� aI��]V.��%a!5 "�"�*&� � -4i�^=�&���S� a`�!F�%+;�6Z� - 4"� ��%m�J� 4}�}B�7%�� s� ��-��1} we"qQ2 �6V%9:��*�!VA�V� |  4)R� �w�� �Y�j�%�m�w (�{V 2�\+Q�%��9Oot�w-F"~���C U�M"M E �� - �I�e�!�?�� p6h #AA}?V7}^�8f3 2)A*F�8.. .����A.y8r�6� y88*x8)��Y\,r\,+\,��; ��+�y^r%���%�A-�A+ AQ-�� G� r^)lJ\ "�S:� -t!��CA-A!n���J&kJD@@: "J.�JC��7 � n�J R�J?�R� e ��J��J���J.�J`TZ�&�J���I&�I \��8Es(���qx& :�jd� 2FI BspIT(K=1)\IR"v�����I}�ʉ��O76L"QFCGC"�I�F�F1/KWG & S_HI�\6�IC_2�I*H-2 M L?�2.?!_ CpI:>K>4%�F}42W� o &4.�  & U^2�I  C>I; �2B � S_{9�U^{a},J:JC_6�G]� =- J�G U^{e*$J�"I&-�:� S_{8�9 i*�.cX�N�Gu;V�G����R,bw� dX(/ix+��MQ�RN�RN�w>n->D"]��C�z gD  �NYNf�CC��C�&1/�Y�S&{�O��r*�,�&2K� I{r�f=&KU�� 6C2� �X�!}Xxm  +�0&6�v P 7[ F�8\�6 &�$Z�j`�� �� )��f�$ y��.�. �F*}e���� B�p)] $K=1�e&��v�)6~?h @.�#k& �ph�k tan �\th�#� &�ixiv � \cotV,; � �x�it � b5 in 5;F�B��<�= -B�#f�,&>�1 f� �1(�� �OhB���is �2e&S�5v�"b �� ical2�$)P�.!�$RQ^2-�<phe�i D} -8 kA035 & }U sM/q in^3 :+&� e^l 1J @, � Q01�!Fj3rI�*w|�;�4 }B(.�nD E�U�}9 �9�!6� $C�B� ��*�B�N� ! f�!�>�.x2�~Div��6��9 &-��[#r<a��&N7e�o FQ�Z-!� 1�)� ��Z6q�*RF2� OCh�M ��M�?!�R�QbQ�P�32~%��ma��B�&ot Ji�R �m}���F� ��-����}�"pm��ga8m6�h �wB� \ ��&�~-_ \R�tan��A=2�BN�Q��ŧ +-[��}R�>� N{2�Fn�{�i��~zk�Lg���!��i% AJsc��-BdseVw;V;�){\;��6�CN C�f�B NB H=K�Z��7��@��"w.� &�e.+A�J.��)� cZmP�e�%��b�bC�bC �9�56��� +J S|�· F�� {�8& "/ B�A�Z4��,b7S �B-� e�:}{� < B�i>ot �I {2})�� *q-Qwq�N�^8:�A�.;��+�.J�� �@B�.V=veSG܎>4�>�>� ��SF� "1# k)\�%��c�mn t � #6�he� [=�?�@� L }8�".� r2Nr*�Ar�+,�=4/K,�|��*1s>76Ns �$�F��-E�B?�g�<\,�V� ''Ѣ�� R�����Ҁ ���� � l)��*-� �.�D\, |E A.&�� <� ^M�W�ll��f�iFBn �m���� �)L)Ms }�2j� (:�Paf�;1 ;�5a�2:J<�6�&ƕ��)M� {U�(�hZ� Z�)S, &:� K ��(b�:M2��V����V� ��U ��!e  +�;2O :��u.�.- 2����phi$ ha�Yx%��# p��)n� "�-2 AA� x��JUm�|���, , >a!��!�-�{&[ �%��5�_ A�� This�!*2%$�;RefL�@ �Z"�.E�Zi��^]mis`��Z �of.i*�.>(CA*:�2X"1Z2/KH1/K�.%�s�6 R"�fD J)�{�B �S 26& �M&;�F�0�� �P�5�0 a�&l !���>%�U� 7Fp9/ �,\,&�D� M���e���A\,kr_�4>5?aP1 ! �Y .� �> .VJ�#jeh�J? �-2`FL� �N�9|Q -� �vU4J�\,nF�W -Pr>�b 1� � i$ 1�� �>�%J�r�55��DA �B� �FF*�A��\��ZM)}}, &��HA}"RNzF�z�\\�acF � i�B�B`A) !�<�@KG F���Q���@�/ �.&�b����;�.a2Va-���a2:b6� �Y_��t\ �cYy�*3sJ��:P�C &�varphi "�~ .�aV4 �r%�)&s `2zq:V�.F�.�᝾S. e�M�!ai�� �QZq9:}NZ}{1A�mg9-ء�^r�E*SV � f�**�� � /�9�:T R�O� �C��-M u��I|b"G�-ZE\!�Z�Q]� �BI�� �))� ! �eal P �E!  < �A9��:�b�5���6:}���o�l�"��IE!am.r J�2�A' �.� 2# �L !&)8.�:!{�{p1��VEj"A N��} �YF�� :cB^a,��an�Z ��6�)�2�1])��t-m1��c&�!��A$/ �-x�l�V"/ �-�-a�s:%�JVz&S$%-mu�nuz��-�8: P ��=F� 7I 1� 2&�  T a#&� r " �T �� �9.�B���A!&v�v �{ �2n�V�(�a .�c���� &N�n�_ `-� 6��rIU�� �6G��\m� .�F5} 6}"i0� S�e� �2@F�- : �1��2�:!/� ]JY�n Av.-za9!� T2�n}{� c4��YP*��B� wwnkJ1;� !�-��r`� �!S%�B�!iA25b:�a�Y-V3oo�b+3~B�U*y�J�ab;�B��JB��$ !2� � �>)��1�!�>XT R�)A�yi:92�+2� � (="�  ;^ � (w co")�x� :�^*RV� N]$b��-Z��--�-& --F|1->� �2S�SC^PenZ ��$.�b�36O� �CI�Pt % 2\,`��8a��M�F %Y�"MsecY�!�{8aM.&�% PeE \�.���� � !��9i}+��d7a�*� �+ \2� AO��R�+ � �a2��]Q���-e� )���IN�2�^6� �>�2K&- FRZ- � �- S>R+�PR2��T+ � ^� '4���k�9�i>' �&.� �+PK� l���� �� � �WaJ �*+2�,�� J: �= 9=_�, �J@aues6�!� ~5� �C �J�B4:.-\xiv f�% �*� 'v~� :  "R�2�>�!: z�6�:<F�>mF!C2��!�� :}�� �!�fI"/6p��@\,� �(�Ѹ\sigmaE��y��u}-� V<..X29}-�y�VJ��I� �L(�.AC��N�&#\t��?sq9�&!\WV!�<^y(-"[tau�s! �"/M�u)?:� �!{��$tau-@�A�=���5i �ОB�!�Rh)�-E �)� �6�J� ��Qn horoR3" $ �tau2 4.!~R� �r��V ��A+!�-F{ %g}2�U B "2�V Z�EQ�* �u ���\mQ-S�` H�&�U��� >�!� ~Ago��,- � 0n-\�u�J���B�� :��[&�F T2<J�Rd( z�h�!| � �n 1�(0/9 .�+E�hB��-/� U1]4%{�Ze5�!�i1B�"r# k� >���(descriptionD} We use the inver �^ransformation \[ \begin{array}{rl} {{\sigma }\rightarrow {\frac{\imag \,e^{2\,\eta }}{1 + e^{4  }} - R0xi:/8}} , \, {{\tau 6xJejr r r (Y.�}} \end � \] for%#verific%| of Poisson brackets. The above 6GXs are more appropriate YLcorresponding calculf s \sec!��{Superintegrable systems with a linear and a quadratic 14l}\label{sec:L+Qu $} In� case�N>mo� ^a#,L`re is a Liouville coordin� � where A$Hamiltonia a �N�4re written as:A�DI=\left(p_\xi+ p_\Ay\E�)^2 \!( \mbox{or} A 7 8- 87!�andaH=I=) (}{G(\xi-l)}+ !g2 Z�2Z�eta}{FG+ Zf2 � From%7a�s!�!DF=, whichE�$given in SIc \refE"ClassU�@} we can find all\0possible subc0es6� toYJA7!�E�.� MXinR,s. Inte^E�s�(remark that ��tential depends on two parameters among.<$k,\, \ell,\, m$�$n$rTed%tabm3% !6@5ca� of s�B) : �vt� }[p]A�6�|cR } \ha; &I�%�$} & \kappa lambd munk 4ell & m & n \\ J P@ GL_1 & I_1 &0  &\cdot 2 >\D \2&/ CFe O & �\ �(\simeq�)�24 8 6>u d  GL_3 �)0   2 7N]4 ] � 7�-&"  ]- GL_5!32 67@ �   .W :t&I}=\mp 2M�=$&\mu=\pm 2E�k &ell #&0 &m ! n _�� ��6&IQ�& oAA�2=��ell*m(9w5�n7nMU*Se6� J�=@3)_-�11��2�R_>� \cap��{.�(\sf GeneralB��X����1��h ���In>uRevolu�}T�r>� ���defined�a surfac�rT69 �� *9 J��4listed.��� î�cb�i(U�e &i, &l &m &n & ���,tabular}{c}P�s\\ by� \\ f$Tref \cite{KaKrMiWin03}� H}&) �` `^2:^>C RL_1��1Y�2�Q� U� & 2.2[D]��Ѽa  c2�BN FmX  �6M& (3)B R�I��6J6>p& 4j�4& ��4 � � >l& 3.2[E2-�}��!Yp 2nm] �arZ v]B� :� (Curvature0L��zero cZ¹:y3l�� lbº f�p.JPogo01z�F6�Qyi�M�6M� E_6A�y@ [m�:A�RE  Z53Z�Fa�i�0u a >6L6 E_3,ZFLa�HZ6L E 6  E_{18}Z�5��m ERL6Z4��Z# � >  >    �3Z� � >  >    Z4.Z� FL_8��:!s 7  S   Z2.Z��.s:�y�9�HF"C���F �Constant>� by� c S ɾ�� * ����"� ��  mu  &�l ~ Sps\\ 2 (K=1)V �k U�M|1/KB0�Q�S_5B���-FA[ =N s S_3>�:M2ZjM6��*Y�D *#EZJra$�6&($Discussion.� ��ing,is paperA�P summarized as followh @enumerate} \item �>� �s �F�x�\be Fified six &\. Each� on se�*�. Four&�se ($iP� \mu\nu$) d0min�metric�X manifold,�e� �=d6�.m%A7 know�dimena�alb�GIA�"��� ���or!�% &�.�su� f6}th ix �e&A�Y�zedj!�value�1:\up Jp ep.�y=U Y�!� assumedU7 . If fix QO, let us��po�'"�a ��negativ�l9WQ���of�oIf]v� �!�"�ed�6Ae�ref<�"guess"� ex�n�! permd�R/eOo)�ify�Y �x�s. Usi),is technique�Eify�B&�I�^� }n stig  the J misvu� s. W�t�metho�newZ2 wűun)L!� I>�"42�,i�!.)Mi 0}. m�ly%�anyYvR  J�M �assocY�;neither .�J�nor^���YGhav��v1�b.}� not yet)�(. We believ�tatA �5�:5pegtwo���aGa.(s\n��?�? 'non deg�� ate'"�5�Z0)`E#yb��}�Եc�!�(Darboux equ� q RaSan99,KyA�e#1�E��. �re�!�}0)2hJ�f�is�naU�!;��l:� �)�equival�d%'�u(St\"{a}ckel#t>.�F *+ &��di� � f$open probl�arise:N !�izs A�b�"X � cubi&��]dunder]j�! HRanada97,Tsyg00_TMP 4JPA,KaRo00,Gra� 034}ep I�l struc�!q)�)��Jrecently�edMP� 05a} but =V��Q heir)�"�A2�/ ��s� carrzVV!o� ird orde@q��)E�A\Dquantum counterparY�5 2� �?^�E�Y�{4 |�%not y�� In S>�I�7se��!�� vari�Z6�has beeneM� ly{!�!Wm5 a,2V Schroed era% p� w�!in a j%" fs�!!j rd*  T�A workAE�� rent]xio�!��>/ � -�� ��� ��G e �I� 8  eigen/ ~ Nly���ud � (oscillator "��|$BoDasKo93, 4,Das001 2}. *"�$^�,E� � p "> �dg6�� s5� u��rooi��( polynomial�(�օ�-ET Tv .�n/ v/isa..� The :�s�U5�ed!�Ap6�f!�h��!��(fully studi&R��} KaWi��MrKa02}E��b�Mas �e�q\dow2�#z-dAilos�9�N. A-�a�qJio�1N�� �ic� s�@x�� ��ed!�.V��0 \newpage \ap�# ix \�Herline{\Large \bf A } " 'PUX combj&io�2�;.0} Letki�aZ^ �v 9yUA�� �-cA&�%R�&JC ^%A<"x �eq:HAB!�}1�)l} H =l)�&\,'}�&,�)$)}+ V(\xi,t&\\ A=p^2O'k  eta -2 c&�W +q1,\q!A k=0\,�or�$,1\\ B=a^2.)q�'b^2 ({)� 2 \beta+ ���Q1I|)% 5T�p Qf zonI#��E��6�&.+ � :=i a�A A�a� �.c Tb ��! exclude��� T $H=p_x^2+p_y^2$, beca�+it� es� A�:i.�B�,�sh�'pro� ���*osiajU�ProQ�'mqap$M$�ah>�,� >*A��,"�mmoment��� =l1�i� e� tai�� mo \-JP, i.e.qSU".#eq�\Int} M= \sum\limits_{k +M=��T}}^{2 n}\, \alpha_{k,%}E� E�\; p^{k}ay\, "�*>� Then%L>,of)�( ���l($H,\,A,\,B$��.�V :Xl@&#impliE��)%�7a�q"*', !_�/,(some smooth; $\Phi$ (��[ ly a. one) such%�,5,(M,A,B,H)=0 �+)�o",M= f( %F+�!-� $$!ea� evid6 e�it>�d (>*��) �Ian seI�F�)lcl} ��&=&S,Q���{|c@$@A+2 c H -q -  V �K+�$ H -Q-2 �2  b^{2IuEtIXa�/}Vn�#Wa6:�nM\\ �eta&=& j�Z*& b� \\ >} &b���f� �q�e� &=& g\,!j 2zAS��?se8hm6��um��$b $ iŋE�sum sig�IYp���)�  as}6��A�q� s $e $�(coefficient" i�^ $\xi0 eta$��ec.V�/$M�s�: \[B9( 0\le i+j+k (n} c_{i j k]�D A^i B^j H^k \] &�}.� $A$ should�}��L ���2.�e(.se�!� non�\Py��!')$�n� hoose a�ed  !-���.�_0@_0�n� -�;a: finityErajector��p�/� roug�%��� �.f�Hy��2�� a special2�YR�lA,B$, ����F� fixed=��"V��Y&o pair=7�1)61$!r" a 2choic1q 21iRLh � ��|A7� ɀ. 0 A�.�\�26��)-:1�)\rh6�=06g�s mean# �gu�A!� 1�] �����*�s,� %�contradi�1&� A��1 rega�3g% S5|��C we)�u d�n!a* expa@N��\Qu� ed u�, w2B � .a D��0a. A direct�5l. 6&� 42&� !*�F a�-:��^ C}8 F�� 2�-);�qua\-� j. Eput $C5\{A,BIr\}��C$E�$C$:B.�݆&1 9�E�!*�E $C^2� aJ<1�;Q�N� ��!d� :tak�aAܡBu�_7previousG�k 3}-- s2} & Higgs79! Zhedanov9�H��we�v��e�a\}I� dA�true. A��izR�{A#�v �E�M�D��B�VJ�" ��E .� n oddF�inq4-A6 TMP%is2�:�>�n�U�I�] &`9 �6Y}:�����"��A�>�io�sit�E04 2�Z6�cl�I2KB�PHbigskip \textbf{Acmledge�s}: On��D authors (C. D.) w�$thank W. M�9�Ad J.Kres� �:ir �J\e�!ind��ng[ )b���fer,,s [14,15,16]1WtreE�E� blemq�X&��,Zpoint% viewV� .�"z;���^Hthebibliography}{99(ib|{�} G.�4, {\em Le\c{c}H4sur la Th\'{e}Z  G n$rale des Sm2 s} (1898)��on w ed-�d%is�8n b��EBe Uni�=� ,Michigan His� cal Mathe�s Coll�site E(htt{http://www.hti.umich.edu=1�Fris} Fri\v{s} J., Smorodinsky Ya. A., Uhlir M.EW�nrnitz P.)0 O�gher Sym�$e�� Q`Mechanics}, Phys. Lett. {�816} 354 (1965);� �� J��y Group�C�:%?? � .�0Sov. J. Nucl.�ics �4} 44 �7�, Makarov A. !#R8Va*  Kh. 67IfA �IlSearchemNon� v��S�ީ� Dynam� 9k$}, Nuovo C\% to A �52} 1061%[7)�45�HietaY>a87} �, �D�M�"�)�( 2nd InMnt}, %8. Rep C)�47}, 87 �8��1 D96} Kalnins E.G.,�� W., �" syan G.S.�S.Yila-!�A&M"� SI 4,Euclidean-Sp!69�zS(,a�2 D!K�&s.�#!!avI.�37} 6439�96!_B� 00} �� Completen��tul�)� �?F�0in $E_{2,C}$ !�J � A: �'At bf 3�/(4105 (2000�.�Kr!n01>� �/J.M!� 6�!D$�`W #�M>�V� two-.9�-V&�.s!�s} �-)�Ge�a�705�1)2�\go02_PAN:�h�UjB� R���two`� s}, �  Atom. �tEX65a�47�2!�UX�!} Ra\~�! M. F�� 6le N=2�?,��&  C�'}  M�A,�.�-$of Drach}.�!g m��3�2 4165ea���_$>�eSanta�"M�2�*�BonF$>si�$S q�Xhypebolic plane $H^2$},A,�q� 40} 5026�9:eSan� 6dhJ�(On harmonic*��@��rB�(, Part II},a�F�3} 2479E*3�.��^00b>�}�6��_m���A ; plex 2-)�} Prep�jARdthe Waikato ISSN 1174-1570ĉ�2�KN:�H G���AGa_2 e�2[�*"JT� of��~E�}^K�S970�Re�:�o;z�=�x6�F�}&in� �!>1 I�4} 5811%lA0\ *s%ٰNh.� �econd-�6�6�con'c flat �. I. T>�l�� &E&theory},>�e� 46} 05350i 56��<05b���� �J�R� z�1i�=�� } �!� em SO brieA�t�%�.G oF�D&},AO2t���ib�?!he� e&r+orkshop� 2rleقDubna R�3Ha June 27-July 20052�V 2<} L\'etourneau P�� Lz;: P&"A�0�$Quasi-Exac�& Solv[ *�HR Ann.�� (NY)Eg 243}, 1 9!�uB&� Bonatsos D., Daskaloyannis C., Kokkotas K.@ �h$- �$ic Descripb!�� BZ1[!�.�  ` Rev Ai�8} R3407��a�F�4ʼ Dmed O"�&9p=2-"M al�>� � �C �50} 3700�4.�x0} Fee�]:�s� >W�x��2� ��o&��!o�.*�' ] t!�^K} Czecht!�. If�12��B�1b�!`� F��1^j�n�&?J�(H A�&ZIFA �4�;11!�20� ]��2b�=�Z��>q+��a�)� Nuclei ��  1008�4��u��  ,���E{"� s2<her��geo-y � �� *� 12}, 3A1976� @GGZ91} Gal'bert O Grm skii�I�:� A. S�@ B�K�, � �q�I E� "�OR��Ftoi |>ed %�1&�,}, Teor.� . Fiz�  91}, 25u (in r��n.��2} B� ,���z�Kepler Px1r�39&2v�3F��A.Si�UZII%��� I�HiddenU3A�w Hartmann��N�5&:* -GenMU4} 388y�} � Po�c�� .3�G��2 e seXi� d��v�t admit���OblOJEfhq��3} 3592 �0:�*k  � A.V�� D"05 �a���, A �,�� 0xJA8� 6� �1!x 121���u��00V��~fL!�2 2 }�7� "� %�2(�3B rlovini�%%SgI osquist K�EAn�>�OA� 0.at "�� arbitraryWr0�A�Q � 41}  �2[�4e� vel mx2Oix 2� %�t�3�1��L��"0  m"�>o �3} 5902�:� Gra0�= �,~.�]�v���!T�?.�f��1�20!Y��4=U,�em27  4� in Cartes�U&V� =`�9c��B�-G03%G �K"@A�L� Williams�� "� Jr��*� J�I�ree2�"P�� .���0}, 7I 19:r�1"�k!��G. e^M* �!�2w �N{2� �� 12z�6 9 �)>� +9 docu�} �R\E��R%[10pt]{article} [pra,aps,twocolumn]{revtex4} %\renewcommand{\baselinestretch}{2} %4width=15.5cm %h�@=22odd�/0margin=0mm \u��4ckage{amssymb}2,latexsym} % :�the* }{\a, c&U.}3�,newsec}{\setP8,{0}�2hn�0Z}{{\mathbb Z>VNN>RR>CCdef\be{E <ee{%�>bea3nat, Me6;:4Tr{{\rm \,Tr\,btt�,d{{\,YdTvol{|\L W�M�Ly41W �a{e"a4b bk ke ei iq qn 5J� bf r p pu uv vx xy yK KP PQ Qsgn{\,%�sgn9�np�|\n\|+8veps{\varepsilo�O!R h2m{ .(\hbar^2}{2m4p0{{P_A$ta H^0_N�]8pnaN,a.n6+nl�&( u(n_0}{N}\geq�@_N�&)� nlam�?:=calN{{ic� calH H}} %% % qlimI� q.\!-\!li! %� ,orem environ�s�!�em�K!}{��em�?[}{R��k6lemma}{L[_^] %�F@@&}[*]2�(6' coro'Corollar�6neK�U�"*D�E 2�v6o.Jng��#�6�draft���#[\hsize��w��\�; csname@4false!�end ��0title{{\flush�+{\s� ePublish\98 Rev.��= 94}, 0804 5)}\\A}v�{1c!�l�8a�E*�@a;#Dof $|\langle a_0\r |^2/V �^*# inF~ f�, i�bec!4$*i6r abs<(f� . Be�8!Ier�+*.=�to hol Gabs�#el.�A st� C0 � A<ion-� latt!Cs)$l�Fid�A��` . Ap��( MO'(,,  J roofme �6s!�ea�vex�$in+ %�due�Griffith'?�2m�U�XPACS: 03.75.Hh, 05.30.J%*�J:1%E�$KEY WORDS:(s au4%\-p 0.3-,is]] \make��� @ INTRODUCTION  ��la��!�i�Er (BEC)ePeod"e�-�?@� gaugA;�(.[� d!}A](a global phUEfa[3Ac�*?�hi�Fper�A�DanAZ rigu�N�E�: appa�BlyL<ngH1?sol~8rigorously. Mos@� time *� �JaciPF.ed;a' exa�Q@, Hohenberg's celN�@result �,Ho}�6ut one- ��>1e�8�,of�e0! ider���I�m�m��BEC!Blow*� altho�4�<rov^:Wg�B�-=m^�B.�066�Q!N�M u�of �Af<Ki�4e �^me-e���rmP r gr,s�yaverages�3�0�D-e5aF��v|,M��^E�U bo�h#!��icc~dw*ngu� b�8eE�� i� ccup| mayt>u macrosc4)�Q�A�� Mfi5 I+first��Aways l)�.%Psi" ; if!��4 alls=�a"��ue�1ofeTY  devi� �$ cipl�a�.-g:WcerB>%�!�"ensem��is quXL on, cClBXvalid�m&7� &5 (BA) m�$BogA}, rai��FEZ/Tteres�Lm�  @siv}�Rma).��ysicisS c ` Gin}�2ZB�1Boa" "n�"��:s!�r�D I4 pE�t�0��sE( odel�,a�+��- Su},�ou�P!�BA�gAQ pap�t�overlook��An�.�� aG3 lng�� gas HOa mxPorI�d-# sequ��=werful�Bab�BAa1  , obA8�)� forty yea�hgo �!�.�1aMsaaratF himself6� 4 mpor�: V�1o���HM�not�8to ena�e necessb arg�. %!$!8�EWcredit!�E; Tto�.�_vf butw widA��2njW-235��a rA�r5�� 5�o�uk!� nearS= e minimum��8#(to guaranteq;,non-pathologa©~o�$ behaviour�>sY$o�@p�@isg? �m8weakly tempered>B!� $n$�:�]e<�{x��  $V< tota�� energy�P U(\r_1,\ldots,\r_n)=g:_{i0; bj:� pe��u), $d$!Zs�)"*-!b $ � $, $ [R [ �vIVa s. %6$eTh�Qa�+l<re, %l��Lc=$R���nA��3ac��  .� ��E�e+fG�A�j�6ctP+ BA 9 st)�V ng� �a_aem� x)f !J�wJ�$�phi_0\�4 1/\sqrt{V}$ (a�"$�J9?�Fu=FT).q�'�Oret�e� A!�a!:AFs. F F_0$� ���le-� FockM span�>�P!Qduct �s� ^{\o s n}A%n=0,1,2m5)KW $F'$�  z� rthogonal�{!���Kl ic.�$F$. b� �builtLb.[c 5�$j.\ Hil�#e( \footnote{�N& QVed &oZF'$s�T gree�X�{'s origi�'8�-a@r�<��@ o!' doneG�  PRL.}.�#,�,�y , $P_{F'}5��proV;Voc"�pn,�(S:"� B$!:$F)�a )�Q� $C�3B"v:? !ZB�O���G(BA} B_0(C)= � A_CBA_C^* �)w�B� is,P stoo�>$ > $ ac� � on elE(�&��S�( A^*_C=e^{Ce�-\!-l�LC}a_0}-|Cj2}' B+�ap}G�a $\psiE=!R�A�co��T� �|C�2t\sum_{n��0},C^n��n!}}\,U�.j\ ,�tensor- 3ply���.�Z ��psi_2���4A��Y 1|)h|2�2#\m�C|B' 0�=e II�^ � A�p5 ��5Qhe&G:��a@ BA})I�#u� matrix $W%M�L H0?.u83 i.� H} H=T+U-�bN-\nu��(a_0+E1)\%dI�$TA�P*_&!��_(is real, $N*�� SY���!itude�Y� :&F!���c�Rng bew. �$e\�unitary,� # s� tran*�x8 rv�� orm,ce ���$ity. Togett:!� �g Vct� �Lvy�t��de�>se. SoA��4W�} \Tr W�;\Tr'A_CW� =Z.�%��Q��thu.p e$V^{-1}\logRoa Z �Il4p_V(\mu,\nu)\ I��!^@" 01�!] $p_V$��!.�} �L,_{V\to\infty�(p_C\, ( �V)J� =B8� � p�%1shoC!�e��a2 t�F�ht*�$C$, BA � den.�d4Te�/�͹j&� %. �J.!:� to =.�T*70&�� �oC $,IaG $H$ �0�\maln$ed.[.of���8A�annNjp�z ( B���s,"V HEWE�� �EHPam�out�/��w ion. % :$H/J�I� ��z��7H��$. $. %��s ���&��. g� t�P6�sH���n e� !��2act�6�c� . While��W})Es ?Athard-ciKa�F.M5_(meaningful,5� e�Q�Co. �d�UWQ�adg a% s ���yg@"0� $,F��. alog% Eq.~IW}�@�uBie�� ZE��e^{��}\����o�p=F W2p_V0 deri��i�, sugg���, again,��� E�� maxi]� mainAs��e 3) o�r]��\be��p0n��,�[V���=:�gis��BdeA�ur)N2� ak^- ECe%� �x��udiH^e�int�a��.o (\\ (i) Whenp*�convex&�I $f_n� nver�(&ih�{ 3 fuf $f$�k YE'$�%�Zd�so >Za!<��T|y�t aUmmea��.�\,i!r��>�-�<} f'(x-0Iw��inf� ��f_n"!supJ! +0) E�P ee >� ��r}�0<AAHs�*C� unr se��$x$&�R $n -0)<+0)$;��wis�d��fCi��)� ��fU��s�bow! subsc6 �wil�z�on_ $V$.E:A;e embed��i� a��N f�  auxiliX��gH'&� '� _0 N_0Z� %� N_0= &4N'=N-NO Id easA� chec22�'(e� mu_0< $ �s��&to $H'$ _alkO n3N�"er%t�na�-�in}�#R _nu)$. E'O ly, �C�,$� � nu� p_V'��A'e�in� �)� Pjy{��$ (�%��inuous�>��=.8 $), V�Y� �^LB��A �nu��Similar.9are %!>A��/-� we���one-7h{fU:s_5!�,.NW1,� Tin:Y!O-ity, �]in�5C� e (� ing)�P:0  $pBC, so -j. �k�f0�la!*l!_{2�}� V}} ��5^*��7 1}{2�\�Ik]m }\numn �UN" "F}V}�nj kAf mi�%�F�"� :� $*�'}/�2$�m�>~A�$!�)\neq 0j�%$t $\Omega_e�of Lebesgue� �� b�X$�'/ ae,V�� y by E"� ��*�anul1N��J"� =(1/2)\5�>�.��~M\laF�nz�f /V =�w!�" "\iexcep�� ��#�f �Lo#f�=Q)@� �Et=!� %(��t' 4r.h.s.���x$:@A>e�.9$) ��iszeZu`'�)N):q.n� �& ��  �&�- "EEma= �$-&{ !.$p'$ doSt�� -� �, how�&,:N� n:� Gwce�al^!I�0 any}.�5!$,��/�}}$!�m!r *�y �eF,�1 �$ 14��lYW��!�.�_retur�/� �#r� i) A:Y:H'$�� '(C)�Z_ i�p � s !f& ext�������ur� adof�case,� ��[z ��r�p0primN � � �=p'e�!��%)_)Si$"lne-� AM�${AXx u� attbk%��� , $C�g�G U� isE�$-{C��[d (u AeT=0,0)+�?C>. V}+2|\nu| |C|�4�F�s��C%K))}� . !ȭ��4 nu$;!� %g{C} ��_{R0 max}I�;�J%�Zhe upp#invelopa� $\{ W:6|C\in-@\} �i|�^Y,�Zn%%�I� PYe-r2 A�q!f)v-� !� W 6� C$:Q�J�eroxI�0+aC�Iq� $C=A/Th� i��M}AS9Y  ei�� �Z_0�V T��C=B% i�]��ځ��f� ��%�v�:A %\$..RS%%�E%6:\�+|_{2� } =2�1ad, U|�2� phantom{a a ��� ���A��-��G &� a�e��3�BNk$��M�c�x c'b�F�.;�=|&0 � b  s�R� iB�� �� =U�.�=�Sm4E�N�qrtU4 sf� }L QD +-16\- (iv)��&%mim�!�s%�X��%�,\��)Tnu6 y Wa�UAA_�  in Eqs�� r��a�nu}�,I�%� ��X�ha3&f*q -�)�-� dp/d��1N*�}&� nu}=J�v�n>�!�nu\,c>�*�H $N"=.- �$&�aYf�venu�鵊���\be %Rp+2FEnu.?%a@%T $�} �"�!�[ izer�:�$.��fix Yr| � nu$��-" s���}mu pt%)� of^��reI��'*����a &���n\p/arrow� "�g��n%o2<$�a*� �[ P@ �� @�(=Oby ����% �(!r.� C�j$f M|coter*$ %2f)n &�qY.2� Lmu j.#�a�d (>+ �2 2' �7m��Co�nAf5�ω5m�� e�7=4�A& EZ���)�sa�9Y2N� �.>�aa}\no�\\ B#i�n!`�J��4E 24a %�� e@! proc�.E��%sJ sen�%K��e�in�("9$, EL=-�-a)�%*�*f�%͗ c �<  m�ra��s�u�'inter�[geA�P "��4aN8seen. %Fix e.g.3>0$&��Schwarz&�y�gJ�E |�a_m6_nu2� �)�2� ���pV}��Su6udRic�Wy W . N8-!� "�6f]%�a"�"#�� ee�x /$\delt"*+i�l $V>V_ ��e�C`�S���L+ S <\�? leq �2��i6 k �wra4fis obm-s"C�:7A�:f2�� Our 2A�Y#��.�3Afi6�)[n�Z� J� %��J8��$%W5!���vb� few]� rks.R3})���%aA� opti� d c-��JB<�"! ide�R�# answtbt leas��&z5�i(� �"� � ":�: . It&�tטanyth���1fk% ("v6ax.� they��a�""Zq1,Y"� SuN e&�gir�v'<]$ to� 4!�v!; "�!D!�8c��*�8  ,� �A�iB*�.s�# ulta#9�{�"�7Rc>�1aȞ�<� &���o 8sta�|O�canon8:�'/$=b_0+=��$!5�<by*�,a�e �ator $b�k���� n;��ɧ�SzK�4��;4 made afterwaro�b->�hyp$s�)� fl�~%�2� �Enegligv ��@com�9d) ^�$fy just5s��by%�U:Xb)0bJM/�7 s $  $.iѥa�xA�,�*a *u �� )=g(B����)J��?�3\\ ��l9^2p M�.$:"��a Altere�l +�Ato !AsfQ5�6%��;��diffe�)�&� &� �B�=�| 1}{4"%fgDjD��)^2e�'' read��A��!Gof> 1� &�>/f�&��*�&T ��#.� $,�(�0��T0e�&.7�fcri"by8�ed.�!O! KJ  o>!�8�#�  iAP %.~"�5!C"[-mex~(�(o $si��j�%�r %%� " 1one. �%or�np�d�Y ��=[ 0�)pq}) m� <%�@� %�ML"!�+)(a�%o��>���riP% a�nu= �nffeQ>�A�c�;_41&is�3�@�f<4in Ref. [12]. @�5{P@&�@O@&�j,3Bx�sork6+�ly/7�8I� OTKAoU(ts T 042914� 6129�i�C>7L�i&�N Ho} P. C.&�>^hyE�@$158}, 383 _h7Q�bZ; N. N�D�C&VQ USSR E�TC4.C�#�Ox-,S^KD,&LD�4BSP} E. Buffet� . de Smedm �k$ V. Pul\'e��g16}, 43pU83Y AVZ1�HAngelescu, A. Verbe�n�V.Z!4bno.�.�X)25}, 347%�V"�RAV6h[k�w<a�2�38TU56�26M��30}, 489"�d� ZB} :�� J.-B. Bru ��\pzP35�O29P5x^21�64?�a(Sz\'epfalus��$I. Kondor,jX�G . (N. Y.))�82Va7.SLSYE�DH. Lieb, R. SeirinԅA<(J. Yngvason�fet�Yez94�H)35)�8 em J�c匡�$c$K  %�("L in�@ic.Qts}, lanl.arXiv:math-ph/0412023bsP�D&*J 6�� �ad�-} 6+=sh��!nu�� pt I�>�,aVU@�)%: 6714� LSY} ���2,s�/����&�Is %a soph�@�d/-�5s*Ŏgiv �� p5Ar�/(ce�"��'�F.���Berezin-�*��prex"eRJ�]#�)� li�'.�b then2& �z ���v��9  Ig� AR�grals �750� tes. �Z:�R{�"c�Rњ.GtLPa +:Le�UCL+l}wRandom-�jrix�\els�G)�{H�wA�"i~m\"ul�Z<\\ Max--Planck--�K, f\"ur Kernp�` k, H:2: g, GXDn�*�G \ {\it Deda�'  Lothar� \"af�T. occam!U�!8ixtieth birthda`aDH {We + [ �l�^ ic l%c:r-H7�N�,!�� =2�#�,a"���&�etw��tEadvancpA�,� etar� Green'*ӔIvJJ R n�"( � Ye�e/r disg-H;ed �@ier� SimUr�Altshu!�is VA�*gra� &e �Rmut�M�saddle--�$ �J�"}� 7/ )h)�� Z&IBj0ac�^� qa9�>)9streng��I� rs_�!!%of� %�i5 t��� sol!� �$Goldstone >/es�Bi�E��en/JbEa��<4re strongly mi\|a�##l!A�er Q � can �be �Em�XinD"I/.a�s�4 on{I*|1K-)i ��kmrbcha�ME]D� 64 ^E�bmuĭ�%��A`$y 1990's (f��5@u~ GMW�xre& c)� rein4%�velop�  culmiO"�-sel � ofR� lSIM} who�a�!��j/�a:�ta <c^��3FI�.Bu�sa�N<x�@K I���t=p�, Ik.a fresh >F7$W�v4$s mot} � �acircumpBcAF(i)�S{E�m��y�&�add�iI�6!of�!i�!��AEofJ�Q8/oN�)W s��c.~] �]do�^�3ro���8pY�7-��a�ory5�e�iG}�wconcern�Brr5�of �s���1!�spins aa tomii n�earqM[PAP}. �7�d�ˡ�}^��U!�)�-�Ah9��-A��7un��EW15�"��t d+t�J�Fer  6ggt� havi� �t5nec�:)!��calјRi-A� handC��()�p� ``�" velocb '' 06jneeds�b�� ept14b��a[�R�Ttr�HdEof� ��<�inM�:]!�not infl}Id��)upl� -�= �=)AA"mInv s. (ii) *� %6sS�;*�eO �\of &zjU�broG~;*� � �n� I ai%�Y ��O EX!Spl&M������"J7sB.le.f:��nsight"�< d��aF1Mcy�aE��L�M straDfo<G:3c4a�llA%�fkGOEeUE}.���9s x;6D<�P�Rs T0OE $\to$ GUE {zX c�.EE1F--ri.�1�" � ��TI��l�D@�-9&� acts ���",Formu�1o�f Cg1 pro}�`MdN*.M7 $H$�hV0m� L}��\H_1 \cos(X) + H_2 \sin(X�8j1�end8� $X��mey6�%� +H_1�$H�C unQedm���belonga��%s�5FCL�;�5�vyso� *c"O1,�a�shP"8!��:~ �a��F6k5����E �tr} [ "D1}{E^+_1 - H(X)} ]N$ {E^-_2 %'&)w2Fw$xbar�4o�Qthe�R�k� $k�;�/s �ci�%�a҉1"� wa W�B`�tra aLOr� e�`IX-�X'�E1D�)$X = XkH$kH9inc��~ dard~��Ath���6N� �8� � .,A. nѱY!!onl��� �! |X - X'|$�M, �9urb�<ly)mre��� we�� # lo3(� yn g;V) H? �)qu���Xinv�U`e�MscY�"x$d| meanͶ�ing�S��H6 B B BN dX $N \to   �*�w� :�%�.� = k(�M, )[)$�>� %�up\�cc(e)` = Ee\E�I��%  twoJ� I� A�:-(X�'H(X�i.�'1a}) a�U� mid�d$X_0 = �5(X + >p�Q%�$�.' AT qAfX'Af."W4.,C!�d keeDuPPrms up���+H�$(u'�. Thenk%gin{eDc � &\�& H_0 + � = V \ , "Q'm% :8-R8Ѯ3��n�c�Dt=�(_0-�2FvV'��Ŭ_0)�:��s�� \ . q4q�{eBg!�y$�\re� �ed=5H���V} = 0|{��:0�/f�N h,A�� �/:<�<.7���q�H_2x�o ti���&6 iI����M e (a! ual)E�spWwa �@��� on a�5IK5Gamma^&�+ =��piUJk��V^2} / d.96V�>��5m�Aݥ�pval�]i���� i�H�ge�N99��!� ��to ��� A)in����3B �UichM>-�i�a�d$�An�zd$)f�J aliz� ?G��>4��u!�� nerr�{(H_j)}Q))�} nu�}Ac� eb3@N} \ ; \ j = 1,2 mDeqI�0q 7F�e���$q !O%�vHn�� -2 �ш '(u%�A�yh� % mB%i%�-(=�r��6AA_� by $d� pi / N!�%tg�� �1havJ�Be�cal�.8F;= "k �.Z]� Y)%`V�is�F�a�,= (2/\pi) N ��/_y:�G"W�My.� must)$��I�2$1/!i�8ju� f��=�er~ on e"��չUwe�( �:ar Vjz$. S���dq �͋ ᥁.@/3 �D&z*2a}) fc� �i&&N�6V&&Am�"N4 &X _0�r1C��] V� h ��25x 6�� 9Y���9!dib&IEm9�A{.��h@t"� ."�1�� "�D��s&3 xsqa� ���dN� ��S.>"zsupz6^me���efe,vwz}�be1ME.a� oo�� 6��,��r�;I�ݮ my�[�Z"� "� stepE�!p�. I doe0� �Z�<>� |iKGOE���' �S#� I c2Na�$$-! ,��9Jor�z ^ar�K�$R, a���g��ae��J�Z(E_1, (; X, X', J)a[ve : �� D � 6C !� �- .O8!O� � \[P�� �Sbi5\�~*}�BYL 9Qf� ��-�rj� ��m�s-C�!M.�. ��5!A "�28u�q.a��i� �o$)A, t$ run�1�8��atq�, � "$� I�;�sA1~ a} &=&�Glamc�5�} .�%�Q� �\I} :% 2E v :��8&�^2V�!�t�b����2E�o.�2�� 2���!1i&���d� � s]Ua�4��ibuA-�l%�/�m--�i� ��V L$. Un��3� of hؖ--�+ "e�F(�w��'~/b�"4� 6z)A�&7--� �?o.�128}) �ex�s� �fA$,r4"�� �K�K } M�1}{2N}�trg}_MJ(A^���3�O2� a� HubbLY-St�5novitch� i�o now)9Z�I1F�� sigma �}! !� N}{4.���9 9�-5 N}{2 , %,\ln�f N}(J)�@ 6q Y�1� F�2 I= E X� �v�O"� .� -"�\S� + *�SI qv1F�:AFG N=Dgm- (1:m\� %,  .] +F6 We16�( �w'iNmoڻq�s% Tof i�"R�a�i�UorIal��$� O o $(�:�Q  source B�:���J$ �q,�}{6� -I"}17��Q�6�)]�)^{_G = T�__0 a^0_D T_05��Ch1*$ �/$� g%VV3�E}{"�I,i \Delta_0 L�F!}$*Af�?i (E/(R ))^2�K|ll )r`P &o�^$]A� _G +� -+6=I�  P)G*�F<ItS=in:%/)u�%"�]��!�2�$.�6�$.�t�A�/KM�$Mod!��Tmae.I6�*�5~6��| lismM�Q���kip5���'S�*S#6g��nR�!�n�9RE�x�%nA�t�5w�#,{ *�q&�'�9?-�v*�q�� >"o&of� ric 8"� �"d1�o�&"\&= c҈& Is+ a m9�smD�<�! �r�%�? T��sN?�a, ��aAi.�9�ndV1 10})!� $���Wm�* ion~%F31 6��D�$�i�Z920e`"�*w�(�Bmm$)� �o2��, ����.��� =��8�seN�,i�?i��! .f�U �>rx��?m"�B _�$�$ce'i' �:R��&�oexponadLL%� va���1 &&f�P>�� �[:�r]^2 + &�4�2� +A�E �-P J �_ � �!}{4��[L�� r]63 .� d2x�� >��   1�bf � p+Y 16} *�>]�l[ ��gm�[L L2� ��c J=v d .�>�zx^ 6\57L ���F� p!K%�r%�!�V�5[;\�]5] � �>�+ _G:( �_G!'%�� Ђ9U z�:�bvY� � � .�"� ia�� ��V� ��5��k5}~pI�an �_i�� &� 2&� �G�l�A��9(2T5 "o �;V�inFT21�T� U�"�y�!s�y�.�3 �W-�z 0 $N (c'�RI���y�JjO �inNI quad� ��F�r.�V ���!2)� at�d"� �Wr�w-ji:E  y ou�k6f  $\ N� �3�L!.�(�)JMX�V/$ )�f[ )}�P&�1��Uhow�j�E!�iv�6s3n� +;f:�  More ��%�-�tZ"tN M[����M��v in>n�Z-�e/} �u �\C"�4HEcW �(�-d�8, ��:�g theE�!Mp1s��^"�eX�} iZ2n0�!' �Fg2)V�4�*t��/��B+�E$$�*�d. {�>} �� L�6w��6J F�� D:V�d �%8���'9l ( � �[��F �% _G ] Cr�Y.��Q��1IT�ArA��+ti�b�*A$j"60j_k$Th�2R�J�!%�: �����b�-U� =� ��%�\pi!�d!�Z� I(1)�� )_{1%�1�0)f4�%&_4 2, 2 2.�&!1�&�2R���"�gol} �Om�&! 2�?I+�A<60��e�v�3N�by=/*Fo�� appe�g�Q[Z . U]i� 8a})�&reC��erm<��&q ;+�& B� =>�e>g+ }{64Zo[ ( ["�, L ]e�]2�F�!Oq/a\o!/T-6|[��s very��'>)s**�%7.r5he*b1Or�I hree�"�>J�-�30J�*�&AL��$�:��kpseudo�ary&�78$aN$�` 2A(T Tba�wo:�in^ QY7 �"�0``*�� '' ("� �|var��)�%O%&�����% Refs.�%��= efe}�g"��'Rmi5@� ��26&.� 1$. @c("5 ��:& I findy#�7R�\�to&��_0^�2ɫd}��_1 ��f 2@1>;Fg .[(Z� ) �V��2 _2|}{((1l 4_?G�� A �%# :C^�� ,2A��. 1 ��&��}i �A"�d� [_� 2 +�/ ��݁g� Ձ J����`9, + "�ł.. B���B� �(ejG^�."- 3*i-Q��6��a@�Ma�����u��Z)B-�oIl}%�1}"��2)� _2) 1�%�F){5c_1�>^2 /�f� 1A!/� ���. � !Le�7 Efet��95.35)�e!Qx2��[$x$*�)6R�Xr�iIrX�Z*��FR B�s��]2T:a*UE&;&�?. Hope߁y)�5kon b .�,AN>3�1c�/.fW � fi�5/�@5 :�~E^�n�nT"6-:A=� edM)q"� �-or�<�P*�*-Ri� {& 4�3 (4 d�+E�mo�Y/��@ [ C/ 4{\ �, too�h{t8nal= s: �0:d+:74"F �.9: F� & z�,!l�Jr�-u�=hanwM"$X$�b64:aAMi�19an >NFA���m5�2U/�  h:F3.GK-l A��cu� B� "� sym1 �i!�Dm�ze �F3#&�_ I�!den�;�"r-F�%�2&0wo *�9"�)�>")H: (sym)�a\Rd�+�?55 \[>�, a�bQ7s5+/�D]a<���ޡ߁s�3!sexh.R5�k$l�s�t�!�� _s..CT� �/s: *F� $J�$; �B�@Z$UE; (i�BbI �/A��+A�`=qFh�]ly do��?A�O�`Q�?�c k` �� pari%PIU�hg-*� auto�9��"�w!� �F�Aalt}.OA�0!�aAb� ��Ze���~%"�Zeff�ve0w6(��%@ *j1:R&1���iI�" j)Gl�Z�.I�S{ �I��o{�* cu?or4C:�u�(c�c antia)�h"�"d � �;ng0M�(��:�?!�A~=�1�%&�e$is (c, a, )�MA��&#, � ۫iv�"� x&M �| T}_32�/ (+u/ ; , ).4Ff1C�Ma�r#��q�!bov�/� r2��V @W|�a�]a�rm $S_{(�i})6/ �{& ( [\�, L] �\� �id{����|�w��2!�a��5re �2dI'$mIi$L�1v.�? �}�tha1�E�<�r'f;tA%}deqm> GOE )��o'"�0>�0�ima��ry2�=xA��@new�2P"� �`^A�A�i.n Bn�u�,GI�ret(P��vC5$"�!sE@?��)*�pn�|��8A-$$\tau_3$[sig�&mDQ7��of!Z�qmsup5�% CoF"&�Hode. As a result, t�he relevant term has the form $S_{({\rm iii})} = �trg} \{ ( [\sigma_G, ({\bf 1}_8 - L_8) ,�T}_3 ])^2 \}$. Case (iv) leads to a symmetry--breaking �ofR�v~�y] ylThis obviously differs from >�P$. I observe that all�lse paramertic correlators ha+e sam)>, $�!- )- 9.T_x} �, with $l$ given by \begin{eqnarray} %i} &=& !p@ \ , \nonumber \\$ %L_4f# $(1N�>7 [v ��%�H\ . \label{45} \end�< In summary, we %6shown)gAz)atr=aion func Hs in random--matrix7ory N,a very simpl)�(. Each one Etained !�:L standard two--pointna level5�� �� docue: m\(class[12pt,��ican,english]{amsart} \usepackage[T1]{fontenc2{a4wide6e!icx6v!Wtim6amsmathB symb6%�on} %�${manfnt} %r Tex �8 specific LaTeX���ands. \theoremstyle{plain} \new {thm}{T & }[seŶ]$噡���uE�}{ "} %% Com!� ou�]0sequentially- @ed>Kfigure�I �f�@pro}[thm]{Proposia��Delete �+re-start�ber�2lem ILemma�Ccor C Corollary�G.�remark IR 2!defin ��{D .�{b�new��$and{\Cy}{\A�cal{C}jv Brian ps F��](coloneq}{:= �lt}{<:\dimostrazione}{\noindent��DProof.}\phantom{X}:>OpW}{� Op}^ W}}_NF(RJ),\IR^2N/AFXAW}\!,\M F3rmd ad>�be bf eBq qBp pBs}{\bold�[ ol{sB!ga6"\g�B' alph>* := bbet>)} \re.X }{\var >!Th Kvar >!Psi @ >R%IA�frak{Re}R� End� �� �S} \inputac1.tex�v@\title{Quantum Vaace�Ergodic�} � �baker's map} \author{M. Degli Esposti, �.$Nonnenmach B. Winn9dd��{D�t�u8f Mathematics, *dof Bologna Piazza di Portah8Donato, 5 40127+, Italyts �D@dm.unibo.it, winn.}) e� line�V, Service de��,ique Th\'eor 0, CEA/DSM/PhT�t\'-re�Xche associ\'ee au CNRS 4�Saclay 91191 Gif-sur-Yvette c\'edex, France � n%T@spht.s> .cea.fr})� b]0 , Texas A\&M��4ty, College St�L, TX 77843-3368, USA �I�.!�@A�(.tamu.edu})EVLdate{22nd March 2005��Iab�(ct} We provAp EgorovAg��, or qI�- � �spo�Jce,Q� * ised.�,1 id up�$A�decayA� r um vm3s , aIc�", a)eiOJ�V t map. 9 \makee� z: ��PBP \G {Introduv } The! r9� princiof5mechan^ � atE the 9�limit behaO�1�(systems rep�ca!v 's Q,dynamics. It5becom  clea!�atA<under�)�0process fullyoesent%�@hallenge not onlygmethods� semi�,analysis, bu�so�modern ory of�al ��(For a broad �_4mooth Hamilton�1itbbeeoved `ifi '!M�4n,-� ca� %� , al� �eigenl�a$y�!S1�1�al .� operi%�@e equidistributedWAKec%�A�{\it natural} measure (Liouville) oveage gy shellm�iAgA�nt*= so-c!�d {\em�-ityALa�`} \cite{Scn,Zel,CdV,HMR}.A�i�%��al�ult, eTif!�can b@sidered quite mil*!phy%u po0of view, stil nstitutesd�ew ri�Qua{ s concern!�!�pr!rti:y�6� �Y�1�nd� � leavFpeE� possi� exis�O%�e�ion!�subd a�of |sta�� might�vergea�otPin�wt1�a�}P last few years a ceru hworks�explo!{�� ���� �1l��!A,issue. While.� 2�-�p���8some hyperbolicmusE�8 extremely highU{de�c!�ItFDBN},!� is believ���hey do�%�xa)�typa�} chaoG� (by, q�mea!Y�a�bum%%mixing)aWeo8�M�:>�M� diagA!�Rele sg!�e�it0unb �$ity} (QUE)-RS,Sar}�r���C!�reca�riI�is dir4�Hecke2� �Laplac�\(on compact <e%Vurfaces �Lin}, usy� E�� binea�idj 2� �,-9?��I. purA+���!\ory. ��e�K l studied��Q�pa�isE.a26 flowŖ r���k�rete-> �pl!.c� oA' e 2-dimen�arus ph�space.�!��E ised}0 automorphism�N2-tN(``5um cat| s''), QUE:� n along a.k!�Planck �@a�iX,DEGI, KR2}, a�� �C%�@�&��(a�M�``E4''.#) ] KR1}e�b� rictAB�. �]E�) 5�1?�Pilyq� mapQ|(MR,Rosen}. � (��y non- =) AA}. nym 8ve ��Lger $N\in 2\IN$ ($N$��M in V  $h$)}� p��%���inMlary"�  (��ag� 0) $\hat{B}_N$�a�an $N$27Hilbert�3 H � qum 5�q=�� averag:< �͸��"�  $\{ �\phi_{N,j}\}_{j=0}^{N-1}$7�:SQ`} \lap]d, S_2(a,N)\3, \frac1N\sum.b \Big| \la2�,�(a)2X\ra-\int_{\t2} a(q,p)\,� q pO^2\,.P�H $a%��i�&(r ^)!�En�$�\cdot)$ 4 Weyl)�is,�sp!�a]�T� a V � A .0%�ES.(or �)��it)A�a well-��exa� � � s liter) e�e�@haZym=xBV,Sa,SV1,O'CTH,Lak,Kap,Zycz}, �motiva� �desire��� ide "x p�s�C bothady*�9 ence�u��.� ���w�Z9b�o��r� (see"e� �-mU�I)�� iesfum��� a byɉt ("�~N: ). A!i u&\ was fir��b� �,y Zelditch \bZ2}>the geo!c� a�aP � negativcur Rieman manifol�nd ��Riz Ro�~ } Rob}A� more)| 21  s. B!��Q� s� ��rolA}� r�df}19� (1  A^edNCEb 1 er mo: ��w!Q ). �L!�:�ingredi e�z$M�.$��isR�6� betwuQ�!w�� evoE" �4s, na%B\emph{E�v � mate}. A% � � � Fa}, suchE2��� hol �z suppora� away."m%�� :� .�estab�i�:D A�1.�i!�� i5s: �},Qpiz�[pre�"�W 1 }a� %Y!�.�(a T�e�A�already!�ven�3M�ubS��a ] erA���bA�� ). SA��&ed"; !kb%Min eBGP,BR �IY ͚.qZ To �')d �Q ,���$z coh �� Gar#an wavH ets):�)�́R nveneway�� ``avoid''+bah:w�Eo�im7~+"�! M�2�}~qu"p"�'E}(>s{\log N} $2} \eequ (!  $2vpob ve Lyapunag:Y&E\, 6� Equipp�ũ9��&couldL l)��r �ANI|MOK�o��&�'E{*o6�ly"� . U efer�� hisLk �� nSch�# applto Bor�[s) !���"� Z=�  `3spiXby ��4earlier heuris$cal'A���(P,Wil,EFK},"� j�%� ce�r  ��AU9�E�l w(�!mperty)!i�el�, yet �valen<�:����$ us�-sZ2,�S. Ou(in�)uA�follo� ��.��agin#m%��} (ny�L $a\in C^\infty(\t2)\ r�)e��4t $C(a)$ depen��5onN , �\f�o"~ �yofU  B_N$ ? 4sfies: $$ \forP"� ,\qquad"R  \leqN {�m�N}� @end%�3W�=�Uı�extento !EpiecewaPlinea!�p �y��a f�IYe���0uAUm�Pi0 w���tC ^oTe�{thoughgat�>A>z�shkbszI�� detail �# y})(��*� ���$ ,Er se�far9 be!sharp� Z�� %3lF e�� ke $V8 ,N^{�w��)e�*#�� �j��M}�$9&FE��eab%�!Hra>e��. has Iconjectu�txhe tru+ V�8p``��(ic'' Anosov)=�aEB&��",����^j���� �BSS #J�;As� �s�0%)� �ctw�-a �$\asymp -�(; however, k sc�*nc�ar3 10\%� noW N �)�ed8.ep1�s-�� t"Nt�/V,�3f  (or,C�!pb s)j�. Ai>Q5s !� �ZB , at�e li!IMrevealW (sm�r) devi͵"�:"ksti�o"J B�th� �Ts an im�.5E�pr�in"V:� sar2i �*� fe 9Ρ�~o}�"�:�O�$�*� � each2~�?is��t $J_)Dbset\{1,\ldots,N\}"�4 @\#J_N}{N}\Nto8 1$�� �Kny"� {� }� ��� $(j_u J_N)_{ # }$, �"O �$e:QE} \lim1to c ngle2[_�J6�_N�/ =2� \bx)�\bx� � � cor�� T� gi�ise�#z ����G�ny �X)B C>B(�ly �63� ��#a=a(q)$b�ndled)���< Ao�gA"�``m#�''�{r#/���qmwI(i �NI�!fi� �E��s" � ofM�$1 M�ID -�  � 9��.��.*���::~�!\bigskipRk7s:}�dg: C7$to R.~Schu���0u!Dk$to us his ���� � prio2publi�Z �J<� ��Vents. @f�>thank S.~De~Bi\`evre, M.~Saraceno, N.~Anantharaman, A.~MartinezAI$ S.~GraffiBqu�N7��"is8"� A�3 &��9Eu�&an�3io8 �)!� Rese�, Trai''Net�(&�. al A�t��"Y�6L) HPRN-CT-2000-00103AFAtIHP�1 gramx,�OB�6&�+�R���.��+�,I�\foot� H� gsAZ�cutE!�stretc+ �)sm�(d/ J map�wminisV n+ duree�m�>/;d. He!we writ��word `` �'}lower�  ''.}��prototyp+%A�As�" ous & &� �.Q+(sis� OA*|. S�bas� �5� ����EIV!��e��Cab�&"!���r; tailw"*�*"��6` k/��identif�tW&�I.�squ�_$[0,1)z  $.�!�C((horizontalordin�$q$..Q``W;wh:*� second (v�cH�.P. 9� um''] �ino5�$\bx=(!�ll alway��'a.�'I, , ei  $\-6$�(on its quot�%�he. a�:7edO �Q !�"�"bi� ive trans EDnaY"*���.d4B� =(q',p')=a xases} (2q,p/2),&\text{if}\ q\in!�4\\ (2q-1,(p+1)B*1/2,1).^ W#ThB� *�&� h�N �< ��.� \cS_1 #4\{p=0\}\cup\{q. 1/2\}, \��`  y�else. Ifa}"& der �!"w A��2�'y�b�0$es larger:e�$n\in%9B $B^n�">��W2"1 set� cS_n� .�bigcup$2^n-1Beft! �j},}\right\}\,,Ti1A�in�%$B^{-n}$ ^��S_ ':�wD�$ex2g!�!�a���$p� q� s. C2lKAr2)� 1\ densn&Ia $|n|" $� )cis� a}�D�yu�! rmly*+�<s�F�s)E B�s $\pm 2���a�op$�| e�3pybelow�s�e (e .\ u�ba1M"�mad�,��tO/.&se.BA�dota ~l$ 111 $ U] 1sam� � r!M$p$-cU��p=�Ff {-2} Ze�a�D�z�t25H�edaak doubly-in�&0ce!�� _ nep ~N�4Th�4!1[easil�0eck� � 2�a� e . �7syMAshift>� } B( � �2- 1}R�) �B-E9�-��z{}Froc]$�5R%�,�ge)7e Kolmo1Sinaiq�Q4map, $h�H KS}=N+as >(fd �V % ,^ : @"�-F>0�^$C "�j��2$a,\,b$�E�7Ʉ*�"�)�qu "�?( K}_{ab}(n)�oBE \,b(�*\bx2*Ar- J+H*\bx.b�k*\bx-�y3�  �G e:�} |N�|�D C\,\norm{a}_{C^1}b \e^{-|>|n|� AccŘgq )�!�Iat� a�-�!�y��Ua(��"#2� Bq��PBP&��&��l�,s"n}�% qE<:�%2K2p&�2�� now a-�HnŌw�<L#�ap to-tDEG}, d!��!! the &�f�~8 >�an-��r��7,rusAklP57= foro,�in���ain@ a��r�esXFh �lecnw3or�aDd Arn<(*�3*�*� ed "�HB�!Mn non �� urb��_Z� tre�NBasOz} (%R6�+�*� thesr 3i0 BDeB�E$scheme!�%�nt�,�!ieL!�V�,gi2 ducI! \V�W�Lrt�. A��2�/.}m�]�&�0$\hbar�0(0,1]te5t2et l-U( +!z�$Heisenberg}up) $�0#O bv}=��\i(v_2{q}-v_1 p})/�# $\bvI,�m�$L^2(\IR)$ E�by*on  \cS' !. �t %.� 1�" < \cH_�=\{\psk M,\ ��(1,0)}!=� 9�Z$$A sa5e6m< si��0\IZ$-periodici����ir!K bar$-Four�&%�� :/&-FT} (�F � �)(p��͕-h�%' (q)\�0 i qp-�\,S ��0q}{\sqrt{2\pi%9�Dm�a' �. One\ l\ ��7�6ntriv�iff $(`)�#=M\� chag *� assu�Q�now on" b��be&� a� imagEYb thro%A�``prox or'':p} %qPU2= \�2\bmE�Z^)4-1)^{N m_1 m_2!T!Rbm} =u2( 8m_2 8}#0,3Big)\;*1:*m_1,03)\�2�$]�hn��mB >64v��rZ2, admi� &�:Z B,q-�s} A�(q)�1QMN}} �&84 \nu��4A> cano9l (9+ '') % �%�N8 TB�n�6"�@",2 � miti� nner��ducq �)&�*]5+e2.a �%k\ra=)Y$_{jk}\Long%Iarrow\5]�% ,\omega\r "�5E�9p \�)ᕥX_j}�\<_jI�nYTEM Si�$E��he}�\cS(\�f� \eq�8y�;yvt�-��ina N"dc�;�#%�!Ga��ws�/Schwartz"< $\P�Ɓ_A u����RHS�lJ�:�DwPy�is"x5$q�7M>,���a.:�_�L�f;�Ia�/f{U"�� J+ li/ _ ��(ylgLr}.7$ $\Cy=\IT\}\IR-a N$!f�$� *�4��%N �$� ���% ble;E�3-ly,E�d'%y�U�yD ia$\q�$�n.� samp`is 1 S'�'Cs $q_j���adB`�*=�86�,A. ॸ $M)\,, \�,0� j \lt NB|8v� J at��$yn��a� %8A�aN. ) wC��m�C. O�si�5S9B� i�II N$ �:[!T�N$ �!7=hB� @5�"�''><.�]$kj}= -P2H;n (-2\i\pi kj/�-,\q.k,j=0" %-1���� 4 $\ �#�r'x $-\pi/�W* |origin, $F\,(q_0,p_0)= (p_0,-q_0�&Aar0,.me?E`"��''2�o�" (�(Ʉp_j\}$~\ =��k"�;  O 1C�k! � �2K �u< *� by BalazNd Voro � They r�0ree��+an�l�F�#W= ? �X�&IN��B�E2B��e:t W<V � Ѽ2 {F!%${N,�  mix}Di�\)with}  B:/�7 �p � ]4 F_{N/2}&0\\0&�E,!���)� �R%�sl�ly�Cif6by 7!PS�7in$5!�xow;h�%r�HZ��Ds�� A10we } Hnt>"+;x(k$1t)j0l qis( 04�)�mo � se` .�� %�31)�${Nm�sMBs:".}}$ $ �1 b a�SAmH�.�2F�Ce(plus "SC�Hp�^ ters-C�.tsG�)��!�thF�L$N.8a�?$A=`+B)�$d $A\ll B$�,m�"�%2��>��3c$i&-� $N\g�-, $|A(N)�c|B $. Wrif ~_r6�_r�}� ,��s)S35* $r$. Si$=ly`e�o}b<#+F�b/We-6!�a�v� }_or"��a{IN:= !,2,3�\. nd $\IN_0I�+up \{0bAls�$R_{+}:=[0,M�5 as usual."!�%use� ��s.�dD %��}_{� }� e /�H� ��, 6psi5^2=\l� ,� $. Un�eb�5�g �� .P���M AN ���so �W�B(\hn)}6 �,-Schmidt sca�?� uc��0k$A,\,B��%\�v"�\b.! HS} e \la A,B ra��&< 4N}\ \Tr(A^\dag�DB*? Oa�%s�.�0.�,(�Q s $f �t2$9* sup-!J�1�f�0}$� Z>�Xj>0�$C^j$ Gi��Fa�^ Dj}��h |\bga��j} 0\p`F al^{}��$$ $=(�2_1, 2�IN^2_0�8!���e a�iL x�S�1a�J: $:t=�X_1}_q\,B 2}_pAta� �o8+ � Becaa�����to� r�!Q* "E@"5@� �!�{ \�N$, we�@�8C ider1�)=����aBB�J4 $1/N$. Indeed�P!� ng f�a\c�QUD7 �!�a/circ �$ fluctuPm�S�� strongly �K�5% "�Mele CmSerE L@h"�%Ra%1�0$ (��&( sU12� 8[chapter~7]{DS}r�2�M� �sj } d:S_ [�e�\b=(\a 2iR_+^2I8 �g 4N2!J�a* $N$-I7ent-t� $f=fNG,N)*�,"�}y$i��\Ii�FB�6$$ C_�,a�}(f"2\sm$�R3 ���}{N�O% ��]}ri�Enp*I@:'=-C1m�1+ 2 �Q�*orms $>��Jt� �) endowN�� %�U�7Fr\'echeMJ� ]n��� ^nm�� � C:�B]t2$M�s:CS}}u?�E!!0EKum-&1 z s"L1审�>+2b. B*%��%Xe�mcS[ct�us�/�7�i�TM�� rehe@,�=��#3N%,LFo,perelomov,LebVor,�,BonDB�WN�_ a� ane�*�a�O 7 IFsqueerE�h>0� \��wav"� 0A`A�"�(���C�omit "C !�3ce)vp�CS Psi_zc�a d) \s(m}{\�k^{1/4Ii! frac , q^2}{2&m5&��(�^P�u�+X!!��*� O�f&.\O�!# at{T� bx_ �<-�-,���\:�align*�%*\bx1� (q)&5-�. �&�"i-`p_0 q_0910e27.!}{-O%p-)� (qp.w$ \\ &= (2N $-�Z� \i Nw~+ uq WN \pi ^-�1(7X�-�,a� took!ybar=(\ Na� s!�d�'� ���b). �%ay])� fCu��!�b 2u &�`axi9�U���e:cyl.'9�,'e(q0Wq.�5ZA2 J3�_ 2FR5+6&�%!7 �h fur� 2���M�P ble,�.�P!2 99.�:��c&!"�c"��w0a;*�.�!F�,(�mqF,\t2})"m2�D1Cy}(j/N)� 6�A��v�ch�(o ��\bx+\bmm� ��0�$!.$"V $*� $: u�8�%q'�P�B� F8!�M�"�!�)�+`0pxm`�^l�_��oftfq��6approx=9 aiB�AqBt�5:_Q��ar� b- !�) i m8$lem:uno} L�=q_0\in(a,1- ))Wh$0\lt �1/2!2�;�:���u�.� �� G�([�"�F�u�=HJ� + \cOA�(( �I�����K�'�$ �^M�A:���err&Cst)�is�.En$ KIA�nd!Yfl 6/i Ext�W�(h�nu=�eu�1���(get�)!�1]*�K=N�) -LBig((�і,!1R \min\{|�ޡ@ |^2:�iWC0 \}} O)-%�N[if�V� ��8$ _I� @'a�1MOyUO :-\nu| �| -  12A"AnIqed�ext l\l"gs howwso\6& 4A;�!� \��LXVg.^K ^�due2�x="���R�la�F\x" *&�S�\m �,.�Y�m&�&)�I:>1���L�.��$F�h1/ @�:U�4z�>�a�I�.��[�> '2IP"�, &�wco �xK ���� 'u r- $: a�.�*/ �uA(&�&E�-Cbx1��hF} UFIZEAWw%.�&=�H+ A�I8�or NA">Us� ina��G1b�2���6Z�$H '7a,N$:\�o!QP�&\,R)A^'�M�?e ` 5�c�' carr�'$�a�N�s. �#^���QFQ \*BAI��)U B}_{�on:�s6s:~^}`Ws�(�"!��4�\K?ger%� Y<c pO7!Y6:^� , se9" a�!$-Td# (�<� *`#�g�Pl5�hN�� ``fa�Jp)'' ��$�Ai.1$uvA� �-$B\bxHw�Z6 d). DQ w"�]*(��5LPt� :K�&�0<��<1/4$ �<� -Kt@*� D�8cD_�Gdel.*��(\{�:�kt2,\ � , ,1/2, )�9(1/2+G�),\ pW � )��,\ } .���&<>Y6�V be�p�{� s loc�/E et��!���t% s E%e "��r%4-6$ (�,may*Q $N$)�"�Em>>�T^�U�ej9 $J�$�Bmoa @��6~oi�cAB� ҡy�E2� �q �q�3�c�nA�s00 0, & \mbox{J� Mta),$�> \display�u q_0+p_0+1}2RUQ@tE,F+)$. �E" � ֙��L!"� � $%��-��� $N$,��aCI.�:terval;�[1/N,N]$�$ �< I� Z p�� the U-!�}xtGs wta= eRtaMN�&�m� c}^2 (^2 � XT48UI.�m�!$6Q^qe� ves �I"� ,N_.�8: 6�a� -0} ��B_�pJ� -c #']���-�Y-#/4 7 hn} ,"N^{3/4})0�\,QQ N)q}63 G��a��!*� w<�t\ E�%���$,F.0��% e�. R�I؁�z�� not��U�e�Y�0�D��T�r�3nQ�5a�)>> �Xch�sf#mF>>#�\)\<<rH���� t9 �!Yi u�s.SV�4�ter6Q�E��#"�. ~k ��� rk} K@�Dl �p� e]/� �("�a�� 2� �x~"� ��A' c1ar"q6ic& ���* $S_15v2 L|"[4 meta�6ic&Q U\ GS}2�}� D}_' g*m #1, #; }(-J4�K9 $�$[* D_2u ]B12�(/J2p�./2T �/+di�� f܁ $7 Such9X^��+2�on-�6�6rY\�Cw uad\I �:=B'=QK�}��%<0-<\,FI =�S_0� v��,�CD1�ZD]?\i"v �6N��C"�p�W �C+����c�7g0ine�40�Ma� �0ref�)a microt �B�eJis�ect glob�ce �q�6�| ��{DH�� �`� K��k#uR:Eh"�CiZch�Kter �VD$rF�!�&a n"�9 area>�:$M&3$,>p2�c� e��9v  M_�ua ��ge�l�>.nT \,\Dh4 bx^3�&'4$x R ``ma!� l width'' �� m�A� \max�M�a��5/2}$)�j Sch}�kre,,K �����I$�=s �XͰ� lex half-�� Re �)>�'�e�son why= �8��.�Iv�$M E�v#�Z��]+orW5�G!l��-'s"�K:�v� ��y. !{aK�oB\..+*�+�ck98eI;Fs(�0q^A_F�� on onKK.a��V*W.$ (Eq.��%�C{ !J��B�-�``K''� ip $� *@�%�&&+$ �F�$.sik�``i�'' 2 A��ܡyR �7O $� �� �' m <�N}*��6.l)[jM(�i��\�6)_m �31�:>�8 /2-1A1��/)_{mj:�B�N�8�bj}N m�:c "�CJrmulaYFT�hx8�=ll/ eq j,m� " �!5��n*"��U4Q: tro}6�q �F� )_{2m} +  1B� B�&�y�-n�DzvVE�e��eA�Pc�n� s3:/A�.Ѩ$%J�.��*$N�a��[ it�sM+]Xq�;h��Kpu0 (J#:� �q��$\� �j/2l ��;D :� 2q) &7?X@}R*}& I1� (�)�N$p�%$"�^!\\E� �/2,-2�7,4-<�"�czc�(q) +���>��� V�,.�F1�� �R ty $2�=F�$ (vaɂ�E�Q-; �9) inse�m. ��qZ>!&b� cinq0\Mm�•��V��uadv���=~&�n�5�r��� Bz}�"� ta}))b� (�� P�%*I y�wey�a�p��� N>1$��e~iDT� � r&g � 2p ���Ot�\&�2�{>a�M�qu��!�^. �n. 6�$;��8^�u./2xw;�e�. Cyb5 F� tre}�cJ?5���"P^2��!�< 4 hand�mm:�.��"$Be%G�u�#9��#N$ 1��T�$�&eL@. �X,;l@& m�qioXB& m2�<$>t&. .t#� J'4/plE*gomb-*58 2O��N4  �Jap�ngSF���œ& A�,a ��*�3` *he�\ d.h9>�U !���>$B�V&�H]Aa�i�5� -Js{qJ( nH o�No�W 2Ud� �Z,'E _&" j��N/wO\u*block�f>�<�A� ��o:}�' %:Q�(s� $��* ~ zv= Pseiii0Z� �w#S 2NZ)6y 2mF-1 �B���d�P��eTa3��� �{fy2 &�# [1&XL" i7j�-1.&&=Kp�,R�� (���X ,-(2-1)6� 6: �\>P� �&+�O(��9W�} A�-��_f0w�I(M���. ."v?��PBP&�PEuS�?rs:�c}o2obj�2�~���2��7y!F R��n<.�9=%�,�7�ler&*�&�2!�c"�]. Nama!*�.N�����"_a$*�eg�g.� ^{n}� {\rm��_N�gt$�7_N-.? )} \N�h0" ���9.0*q %*�Qan=)V8i�g�<�h. A|p9� �i!~�;i�7mfvoi��9�*Crojs* �(o�7&UNB&�$0f�GK8$sZN8s�(�Zof)Bf ^n$.�;��,��-K�b.�ous� 4�32Dpoi%\�. An�d!-a�s*bn$cQH �|Z8yI�=�!v,IQ� � :. In ^["�k~19BDE>��D��[o�l�lt, LK � .\�� $�i�R $a(pJ!!aS�1"u:: ime) _el*�.cA_GSooAy�$�9@�'%�@� $m,o�x��w�A��y�=:?J/v�h�/lg�L�uQ6*B 2y:z&�<he0FV+h3E>"�6}I e�%h d:AW� . Ho6r b!=hquasi-*�" ��-0}�nec�DR}o J/42Ia� be6�hr'x~6w.[p OpAW$E $��ؗA*��/4��hn� � D,i&�%d��h�xtEG�b��bqx.�e-xB���n*Aex Be� �+e�� �u�h�1=X���lyB"� ime $n$=B�~ �!�ga�r $n>>1"6~m$s!/"6> F�6->��$6�Mw�c�>i��-W�_�bl�M� ��. Like�v $2��)^��`,�!��*�5p*:N��l>��� -�E�!�lAc!���!=K&+6itemize�tem�ա�AF<,%���6>�9�on�m-B)H�,�"Q�8 a>�����I $aw 1}{6�$ps)\,mS rm Err$$\eps�:fixed), [Tl:su R�ŢA����G�&} (�E}=^(�>�&8m �&�"Pm�\%A��19S�8>!?��Xn?!`\[?%Y  B4|</+��J�?��{�"Ao3�th$ed$"u�.:Jpus��e-�a!�la��s�b%�1-!lilon)�T)�� ndYK�e Be �� v� 4,�-� vs. >�z�I�X,"� o�-I� PF���&�!O�}2>k)oL@/��p2~Vweyl-AW��1 "5-"���e= repan>�b��S&2��>�6��^�by 2�i ��|�.X&?� ���>=]b�3.u �,%amnd:!^ } AnL:�� $J��b&�P�c�_jOf= \bk�IX\t�x({f}(\bk)\;ea�kTN+%SNf!} �P "<,"F4�I<6=,bx\wedge\bk}& $(qk_2-pk_1�$��2U)ni�� ���&"/�7R9M�e)2�u2(Cm�cZ � {2}}>� T)�Q.� � cV<X 'h��� *�J�d&M�($��s $ \$ �nga6e�j8 r* Z;� he lat�$�%,E�!J-M�ed`�IdeHdA���R(fy �]���%�1� { �\,;]_\Q!c+ 6�(P �Uz;&>\jofq t�f`.NR)4i�-]* )V+N\bm)=�Z�M� m}\, �FY nce,m�n�$ IZ_N9�{-.`/2-1\}�E�$��6q^_N^!�sH�a�T� " ��K�c/>g rtho �%t�+�q Az�K"% HS�Rr��*r*���1Liy&�5�1 3.9]���u���b&}F��\f<�FH!�OpW(f�F\�L���OpE�.cB(D+�p\e�� J al!ua 4�ai�tF&aY2�M"!��%E!��� ro��f>VCV��0�%e��Dfam�g�FV}v�W�WAW�2� B�'"�L~B�a" ͏L^1�A��Q� �gA!��#MS �[o���[8%�-�\phi,\,'��hnU#\u�� &r&DN N��O�fɬ, \la :N�%\ra�C^J�0e,g\bx& ���@G�EXam5m2f�c a�(l*htW a Hel]1p oppo��^�,%�Vr enjoy\ "�e � A��[�(v��. nV7q mأg���J�A}$N!��$=O�ŠA'�ET oe�qs�s� e�b�ay�,� o�"w_ex�Wsed ^�!.l%��� {H.� :� vA���"�Hz}*�l` ra�/�$Q_) �:= \,k_1^2+ �+\,k^2_�L��&at�� ��s�:RKm� �eI!nt�m���q�u�myJP V erN �if|Hp�.N}2���&A Equ"ESm��^\sk��� ��� $ E7"*byP��A��(B?)�L"�=kernel!�*  1} KUY)�: 2N2�#�  N �x�28A(vPdi��k�%��is�S��,�P<>%Eeo\bknA  �2:����)mode $ _0 �vad��UOAuI�)�5) -f_�f;� _0]�a-ulaE�N�[� 2.3ϧ it ii})]{i��we�=.*�a.�< leteTj@i idea��tGU os97E��"�$� n , !��  TOO�w`0S mputB�le�|&iU%M), AW�d( \ra .����8f V�U�J:�Y�g�4� 50lg^"�JMCCU�y�"!2>7 p >�4��$ey�� gral���#bym�� ��\byq�B�H�_{\R^2}=����byr `"�3�8il$0W!��bx-\by&6"\r�g�� �.�_ )}{46� $$ݜr�AZ gW>�� �FJ< spliA}laV�+,k! �k a^�  &=�@�m%��� 2�hl%.%�V},u5%S h5cB19a�M2f{�J)�!q�aa> ����E!-�*}{2.m+\�+�+nd5O =mW�<)8���h�%��\F#e� (u :�C��even)/�la�:`M=$�&t_0,\b ��/oj+�j��66f��"��uJ[��=��q!uS� �!�l^2G3 s.t.2_140%��Aforޓ]L�j^�X>�NZ*��*�,ba��:qGs� �@ho��H>P"�|1._1�y�N?�3W _1) =�00�HA�8.� ld ��U-��a.Ĭs : �Jes�� F�*D:�m� �z> pf ]�A����M\�_3$,9*� 1� z�� �31�%\,�\� ))�<k��+�/_MaK���[M�WM�/& SY^� ,���/>� AW�:�B� Ŗ6��A)i3>��*�L�uJ�*�@"�I)[%",!�n�  >� hey6�&tesE^&,:� b$"���1A9 Tr\,��6t 1& \�l \bk=<\ C some�^���;0& "�;.}���s0=�3�9n��%�E�aIUq+_@:� \setminus�`} |"t �)�b^M��� 2�-[>�Z�:  @-��YZiO1# @ "�^; a1 �\|\ll_M)�B (1+|\bk|)a��A.�{�App"��& �3$)��)5sum�Nem�._!�, @� $ � f-Sb6��8!bnis�,IBb!�J* m)�J'RC|\bm|^2tB�q�f(&C,Wge�  �Asr|D"��/&AA�-s =��?{6�"s PxV�&A�. ��GA��pro"R>��:P g\�� I)"?�$�&K�T^�@) 1bq*�D'-1"�D�)-��f!�lvr�a5�:��p=\{\�  ��*W �'� "y�nV%K%�I)����.�g\ � and 2V�e� >0$ B�H*]gANt>@MNB�tbar �}(N �*Bmaxt �) N^{2X^1-1}}-$},�^F_&y^-1} Q�9�|23!�go8o��a2�hAG�&�}a�A��#N�$:fF!s�B�=&~2`!�B6,lhaBKAg��"����h!�rm{Mn"`E�W(}\ll\�%?}(f�}b�����aS�� �+aMa�$ rk} �0 �iv�o�Apoj{n^�$~$LB:�) i� rec(dn�A� * i� ied:-� #*W$&�""a"a<�E\1 $.�}<):�6�"s�"�$�`�� �<aR�J�vsatis!�>M_�Y ���Aф:�A"H}�%!�\A(�)A�t. "O�*̧) "s$. By Taylo�,�4վ�GF� :�}{B�= 1�26�2*�k)! �2 = 1�860��f�  ^2 D\,,�#�i�5�&i:utEnJE�'a �.\bk�mubY��"[9o>�7�� + G/P C�p f$. � e� s&o':_ E $M=5�(e�!�MpaӔ�=os�  ��| \|� f) - -&n�"z� ^2} p &� ,-� 2�3e�f �(|f\|_{C^5}}*$ @ fu ;majc\,\| f ] ��.k0 \med�7� J�3^ -�1s�( care/ i��E*w,Fnf%�E?l z�1�H*�CV} T���)bb��<R^2_+.� �� |=1$�:$ .4C� �T.e. $\)_iB_iC i=1,�K@ �7�f�6iZ�w��*�CV-hX :Z.2�{N}*��Q�l?_1! 2sv1RRi;�H�h��()--N�A ���l�$,-T$��A�!� B����a��TGi� o�\e Calder\'on-Vaillancour!e +��@��4O2X2��0Boul}T �WfUF;v 3]Y $\��*�n=&���V0oUH$f-�,��}(q,p):�m.^ q�O ^{1-}`��*AL f $U6H!3%dil�5d >+�uf= t{dQ psi(.}q))1�� eh([page 60]{M��B�} :�\, B6�A�\, :8V vv.v�6<E�6�n.�";"= CV-Rۭ$:?.�!�} !��Q�m��eg `�jfzf�-�q�+0��) �JE(/r?�R6J^2Lz)o.,\bz=�htu�A&]a-o% �2� ,�%.���p6� $�.%<V�P+%-�~�*}w8\?�L1�ˏu^ 2_q D+2 ]_q p% bJ%y�{$$:ere��z *��8 co"�%Gj �}l #��(B\com�S"��rI�s"�&�tہ9gF�&-�,C^�I{w+(2,0)}9-:R&1,1.&^S T0,2.5\-q�� �� %Oal"8 n-!�> Q �}(F0&e7���iy!]N �M� .N.\,:_t-E�.�M&\�n.+x� 6PJT%s(f)9m�2&�F�%y�B&���oj�ř&n(&.,#b�+ B� +B6�v nd{C|  �:��am���N�Dh�sd F �q� 2� ŧ&* f^{�)dArem}}"�&�1:�nEN�E9bigUmE���,N��) �F�?�P*#"F��E��v dom�d�Z "% :�CV) t��&|t����.�, .���%�j��) b4A\T |{a|'}� 2�Z� B� =A�8 :mG�;-���&�R<~IEa�l*N_e�} ��0m�5 ��F��%����6�9ErE�c�7�b&.ĭj"G��We! t*���*� Z erty&��>.pus!�rtI�  $n���* B3|-�5c"�J"�bfq)�in&3L(��D1����di���! Z9_�$B~PWh� -@! :1-Sv2q�p@S M*Rgi  Yg��e�!.?4�� 6���cM���i`-R'.�� &R%a��!�R��(aX�"�,d�  -";_N&�A:-x (*�?�[| .�ca�� N^{5j^� �R�(nc�P\<*>*} & w.r.^V2(��)g <\i�J�eՕ�v"�J Q=*=!R^F0eYA �� :�/ ` !sha8ˏhi7 hn���i�bAk�cA��PA��4Q: B}_N��29�)�'�- ;P"�% 22��K% 9���"8euR ,5�-upJ�- ,P�- �&�ש&�B�DJ�N-`ךf�v�E�%h"�K Cauchy-Sc�z &�8��+N5nN.6.8H�h!<% �TM�lf!6E6�_J#.0-/�S\|am0}u+sU=��1�/,�� give98A[5#�-�� M�\��EK&�V�(�71�{B�)A�!{L�(���PTgHa�23*�p#%� -adj�AMLF���n��A�Y�]�.8�!��fF\ ��rg� D{fari6"�`!�s��at �&_2 eh\t*!(�- (@+-2!S-�lo�v&A �%;�MB2$���E }v cal)rw�7� 3*Wd+ a�QNm4&�/��$ �yHclX3CJ6�1�x�^o, �Jw=.�H�G* 4�omKt�1g F2E����P  FF��!�.G1}s"t�bx$"�t&T;A8h(���=fnoul��)��D EChap.~4]fcGB�,�Jc$.�sE�ndUg �cؿ�mn>1�H*�>� 6� "~ n~ .� �� �M�"�C�$7+?m,\0,&hn`$�����eh4h� �%�"�8a�n�:A�"nD1}�0_ n, 7m"�p�S:�p".\��n|͙k����> W p���% 2�p�0e6�LA�set8A�.* "QB$.DF� �T� e:curlyD"��`��`n�@�B^jRz'tt -j,2^j��/2��,�L*� ���!s illusx��I$n=2,\ j}n fQ��]fig[hz� E}[htbp]S�er� et�� th{\oj }{5cm},picC�L}(3,1.5) \put(0,0.1)�) clud�(phics[�x=0,Fg$=15.0cm,heؒ=7cm]{� fig.epst�M1.4\05){$B$} b1.195,0 )V34,0.291IE7762>766 2){$2~q! H}2J!�� \cap��{Y��(mi�Z�Xwe�Q� �r2eZU�Jshe�� ������מ*��|� b abel!�I{(5��-�v�  IfB�v �����n � !.�j�X"� "� b%�bb�6eL1VJ�$o�����@edC C��VZ�"��;�X&L3>��r����"X)���\",!,� � $U[their*&OB�iatTK $j$;A)fin.h63� B�j� 2�ien*� {n�.:v� q�?��n1J�n�n>����0�h�5}>��3U1Y>��:�*,�*��ov-n-� "� ^n\9�rV $� - 9RT ^n}.�n�Vll cF \,"H � ^� ^�" �1n4Q� *� $A�2U}9K=�ang�nd%�>"�D 3��:[���{N},N]�E Mj!�Z� �Zr:4N-wi����e�%�  $��Q toge� ��fFed �A���Up$, P��k�y�� � �< 6>~T s {�&��-n}�b�b Z�a��b2( .�2&for�͵=F�VG%���1-1�1eu"��͹�GF��W>�p� ٜ�o\ &u1N|�(�!�k��y� d 5} +*\���K�S}�}m��� \� J.�\*5jm�56�EOS�.�2�8On� �� 2u~ RA��� N2E�N23 i$�XK)� B�dp]/�t�;-��l�G��oMq���Z ! y�#�p�E�(``X���'':�ʫy�;4gij�� n|É��f{��-�-����N$>�well (atw�'3c��� �>?)..&;�p�2�tۧ��&�M��R {a_n\}_{n 1���p�I {ed&���6����Xut�u"� ����[� ���bR pastI��;T�g)p$replace $n�>$ by $-n$ on the LHS of \eqref{e:egorov-n}, and replace $\sigma ? ^{-1}H4RHS, including[$definitionb4$\theta$. Now,! funcX$a$ must be supported i �\set $\cD_{-n,\del,\gamma|0btained from %:$( by exchang�roles�q$�@ $p$. Indeed, us) unitarity-h\hat B_N$, we may interpret� estimate=L vol-0} as!@ quasi-covariant u%of!, coherent stH($\psi_{\by,)r$',\t2}$ (w(, $\by=B\bx$,1�'= * /4$) intoX6OB%�U4 , V,% A rest �� proof identically follows. \end{remark} %%%�.�PBP \subseEp{EgA� 1�,s for truncaAy`observables\label{s:opt}} FIA familE!$admissibleU�xs}$ $ For future purposes (see%n%b-oorem~\a�main}qnext �), anep)\,,\\.L-�M9>Ma���a� �in!H�� spli����Tits ``good part'' $a_n�� a ,F)� Dba2C ^{\rm bad)?=E(1-FH)$ �]���One eas��check��at �$ a���oA���/2^ mwla�_�$ .?< on a neighbourh!5of�فC areaO(A;� In lighųɏ �Cr:past}a� can,�out los�U0 generality, �e�@only times $n>0$.U$multiindex�yg�\IN^2_m haveA�qu� @e:fluct1} \norm{\!�`ial^{\bga} a_n}_{C^0} \ll��ga} +a{|)|}}\, 2^�|� _1}\e�t� | M|}\E�equ Wa�\va�%� througha� map $B$, Tderivatives grow along �4decreaseq$; af�b $n$ itera�s,h\circ an-�(till smooth`N!2^!(�uS)%0} �/2z/These* show tA���$C^5$-!�E4)N�i .� $ (appear!uon =R\ equ%&~F�)A� both of ��$2^{5n}/A�^5$. W��our�:v� o!qaparame%�^ �? RHS oJ� -AW} read��� =\frac�� ^2}{\max(# ,4^n/ )}�AF0$ (�pendent A�$a'eps$)�� $N().sucatYm) $)&!8A�B�.��� " ��@�p��I^{�;6�  -n}-6� e+C\Big(.v��3/��^{�/2}��.6{4}��%X)&L �A��rH% \dimostrazione We�T trea6 cP *Q finY invo"�!gP-reversal symmetry as��JD. jcom �+8i(E�e )�)6 �I� /4}=A��ȡc�1akCE�E)$�zA$�)��ime��]+ͺim�am�ov����-n}�5a��E�he �s $)� \OpA-\Qe}E�"��OpE AW}l/4^n}S2I2����rescaled%� $tW n}�J �.�2�� ���[ p .� - a_n$� : $$qt�R} .N ,)9 *  u~ a0+ ep}{4}�  =Z? N^{t�?av$$ Thus��R�%\R� of aA�$-d��"~  spa�Sc alpha_t}1, "J :=(t+�24, ��Aew!�former�!�i&� ,=N^t$ to min+ Aa���re:f Aff� liAZo a�N�, yields a ``�/ / �\hbar2N,2^n)=!�!/2�, sE�� diff�cejwe�he two� ntis� *, is� ed as!�I$u�-R�2m} )}\l6� � �s�M8Simila%  ��"z e82}&� � �2�^���}(6,}e�ed �!�� qu!ty9 e argu����on� al!ȱ�F+-AW} Ac|e� $N� NS� ��(^{1-t-\ep/2�B.� full&B.)!�B_�l )�Df� ���.)-��T5eR%u9�*p�a�!Z= notic�� �7Ũ�  w�IC, $9I�1\-X(. \qed Our!HsonRbelie}e�"� i&< lie�\ �r"�- �}: � volv�s � stay*hAq$discontinu�set+S_1$ �theirx . Sia��sa�sf� $\Delta q  p\gtrsim ��12�?$ due� DHeisenberg's uncer�0ty principle,'V q$ dou_ at I� step, it!% impoN !�� a �to�G�$\� du�a R)D largY�,&[ ?�-s,�!B�#R scillatJ n a ɘ$\approx-́hdir�,a�5ehaves m�8like a Fourier Y(gral operat��an.t (pseudo-���� 1)�� �� �M){Q�$um Erg ity? �}&�eve���vldenote by $\{\varphi_{N,j}\})�(eigenvectorɓ�� f � $s h>nA`be de"te'2seems ru� ,out by numerI�ul�{,an"�y ortho� al y4basis). Let us*G � �Wl-���i�,ying $\int_{/"]4 \rmd\bx=0$. -s e5sgs v� ���n!�v�c� S_2(a,N)� X1}{N}\sum_{j=1}^N |\la 2��)\,20\ra|^2\Nto8 0��zmethod!x�is limi��es�{aker's�would b��apla� OE4\cite{MOK}: on� needs� E�v�(t��2� )��� e�E@$��u"k \emph{9w}� $B$. How� ,�2 �Mtun�!gX in��Eg ab�d rate� deca�1�� &31Je2��\2�m�,���(rather adap� �u!�in-VZ2,Sch2}� our ٜou%� is=requir�)$correiM"� s}��9R�to �s"O� astq�i9 ~/(&m r e:mixing}�; \bigskip � � nt{\bf P!!�TI j% H.}\phantom{X} To b%w��"#��".K� } ��e:gg(x&) 2\left ( �{�0os x}{x^2} \r)�R�B�^transAA� /g}(k)=�4-R}^{ �  2\pi\i kx�rmd x=�!Ys} "�4|k|), & \mbox{��$-1 k,1$,} \\ 0, & $ else� .} � R$$"�$T� 1$%Quse�Ito%["� &/BZ� f_T(8 5Y��mZ�! + m)).�$f_T$�!tEJ5O deco�'^= Wk W%k$f}_T(k)\, �!.!P �� %q./>f)�> }{T}E>�|k|I 1^)�T%|)� T$,}!�6�|k| >T$F��isU�,�5 may �V9�lemma��.�IQ] lem}mlem:rom ]not� s"�!d�ve,��� 6E<2$ aUJ�hao.�*}��!4 )�'}%� AIn) \;)y�� ,\TrF(R)\,%�T n!����"j -n.xndu� *} N� ���2 �Fsum�Q��%�|n|!�iJ!?�vd2��*c j_ �Vhe*��` �$���`B}_N ��j =.�I�_j�R� j /$en �V�Bfi�e = )�,j,k=0}^{N-1}.�n m�_k-�,)}\ |\langle1��"�k\r!��6�MA pl� � !�n` summ�$n$��getT:��$�"�' �U�E�^ \; B0�� &N2�F.(�'�&�&j9�aX0�Kj9rK\qquad  +) j\neq k} W-�=�ʲ�IN\;� 5�)�5�*}� �s"�!s �*aJ�v�of�G��r� ��!�' 1$. �&�T*B:H�� "�$the traces � in��� �f. D���#�ert)sA�!_$�ly +���$A� [-T,T]�'ll�?h ed. We) 51T$ �e � $ preciselyHT=TD4&��"�}{1'#,�H�Q2�  Ehrenf�*w"$}�#��\IZ\cap�e�%[&^ 4 !!|)M2* �first :e��o�,&''�c%Ų`&.&&h .�i�'� �"�"�'A��#�=�*e:{R& a=a_n+2�%n'aa�$1y a.2n&\,,�t` We l$- *tay)���$N$%��4\asymp (\log N�1w"T� ���%�UZall�%$I2^{|n|}}�"N\�� As a� ult,A�fsY /1}�SA�R�C%W*�%�m! \forall e6A,��1\b�*& ,]*� "��{108&HFur� l� �� s art�d��Z�]qE�j\*�%P \med9 WA ��v �qofVg accore��.h)t�u�Q�%n��)A�U…�gb��&= �>_s${&� \ 2�+�O9eR# .Anumberig-$�"�y�!� ��bx, trol�byU$!^$�.�))i$ � �-Wickc�45�y� �o2g\&� 5;=F� 6�N1\!,1}�f?$ +\cR_N(n)� ���!D��rQ /�*dealt��Ra� $I"�f�, toget3�!�iz&��/�Ji�a`�:C- } \|�| &� Ai*b }z l�2zR�NF�*Ip\\ &\"�e� j2e�)'e>�69-^{1�!\,.y�curlyRK+U M��$3)mpute $~��?E5�� ��%�f&�4.^��a@Ive�1negk+E=s, .9�=a_{n,+y�---��Ac-pm .�!!An&�(&2Hard) linear algebra��!I.& ��:�;�@ ��=3L AB����NA�$B$��,self-adjoint"�:0cH_p5�assume*� 1XEen5 xy� �� �e.( |\Tr(AB)w'I�A�)B).OAhM�F]!��F� �$n�:���, RXy���e*!fA��&�� � n\, ��N�[| R{ \;!M� (�gbi��C �!�s�ly:�e#.5��m2: . ByM�d TF=+O.8=|}f|a�e�] %B\�gZjeJ��cB�)%c�{}F69Q�ٍAWi�*  � A�P2+ qual�"$N\cdotiC:)}_{L_1i#}u (1+\�1�' N/2} �$�%�=e�tB2 ��)>2Ms $L^1$&�of�56OF26�$0}��8e Calder\'on-Va�ncourt&�9&n&W(a�" eq C6T�!we�  thus*&0��"l :� " %�gb}: \b� � 1NJ� .��.�Mo �"~ l ��2^�.6� 0} + ~{M��{5T)������ *�We�72s"� B�? writ� A���u*  gn" 0)�Fv A_2� )C '.D ����W�!role16P ^{\prime}D tw+e69 ��" an},$"e� � Z"$n�"�/11B& -�\c:}}��1� �2 %>7 )��#�1>1B��\n>^ ��^2"5UR2/5��� C4�align}1yW�*(���[~3.1]{)]*�/ ry1��buma��:��a*�one���M � �:->�-�"!�&�$pair $a,b :��n$,�bF&P o\�1�% )�M\�@b+b)dQ��J� 4�EHb�4i-} , %�y6!�j .�%���!��ANW �get1~M)J0 �:�E�&=.���as.��kq�.�HF]�\text{}\�s� y�.Cq�.'I8 4}\;)r:�=��+:�md /1mdM�emc3�-:To�ly��!�ŝ�dVn%G use Q&�FWeyl}J<�.N��%1N� !!�n�ͦ"9#F��;H#!�O!�(q:�3A��>��CIt��^u."he �%*h .�k'n e+(s, 20+=a-2��5"b,:�5bei+�q1�} %5|�\>E$2b(�9\bx�" \bx)L|.� �JU�&�( ^1.яaM�0A�d�(JV whilM e2+�B���9�"%aV� = �88thcal K}_{a\,a}6M*���i�t�'\ !�&�" autoN�""� obhB $�=�$B�I�|C, Axis po-�D6E�dynam�&���" 6�b*"%<namp�1# #.D(�Benda�s�'[s:�}):�Y'$\G�<> =r>�$s�Dn�toq"$)$ Z�B'��- r�!�$$ Coll�ng��W s�/�!]�&�) f_���o ��� �3� C&Ew*�:B�AX�rQ��/ M'=�}|�(n)|\�(>� +� t�"��� ZA ��2�>u �c1L"+m�9q� '!D,w�&okY!��*@ 6��co:H�%>E.f%>�\nR�%co�ary<cor:�%Ws,ar� pic}56d+NfD,�"g)�R�^)"�$d??A"ZE$\k2��(4$, Chebychev'�Q��%MQan.F &AA��a��*�*a�I� B_N$e�0.$|\la� {'+�)2�)> �FQ MQ\#�Q\{j�$D{1,\ldots,N\}\,:\,m"�! n� �+ t Z�A�eq rq.}{��a2�} �!�(Y},�*G1 9�>>2�21Bab�:a`A� vergA� o zero. D�J�>J_N(a�!�comple.�1�/ ��2Y6, � �0 aY+ofi4� `�Ht6p$ �sfZ"�\# 1}�+to3' "I �E5�)s $.�_N}� $j_Na Lh&��= � �/n^ diago� a�2t 0{CdV,HMR,Zel}, e�PFex� t� �Z���:I32L�6H�C2=="zQE}��)[�W%N&NAY�AZs.7"$2��=~� Dthebibliography}{9�Jxbibitem[ALP{\.{Z}}]{Zycz}{R.~Al��T, A.~Lozinski, P.~Pako �K.~9Hyczkowski (2004) ``9.*meXpy9� �W2�,T'' {\it J.\ Phys.\ A} L+837} 5157--5172.2�DA]{AA}{V.I.~Arnold^`A.~Avez (1967) ``Probl��ES-que !( la m�canM @que'', Gauthier-V�rs (Par�/.��BSS]{BSS}{A.~B\"acker, R.~Schubert �P.~StiE(1998!#R�Mof� um ��0�TEuclidean billiards'',)'%# Rev. E-'5!'D425--5447; Erratum.1\2\38!Z96TtBGP]{BGP}{D.~Bambusi, S.~Graff)�TAul�9�L F#20B�rox�NVA�fN: a2�:j#QA�!totA nal. �,21} 149--1606�ar]{Bar!� \ BarnettY�OicEz.�I1�chaU)V� submitoto)� CommA��M,Appl.\ Math.�2ulBdMOdA�sOz}{M� sili�.0ox A>.\ Ozor Almeida%u5!uebiz��Anosov�.s5;nn�aQ16aO46--6565onDB]{,} {F.~Bonech)�8S.~De Bi\`evre %M0�Exp"�8 A�$\ln �4A�4�I�8ized hyperbolic�� toruE� �!Uun.!h.I��,11} 659--686:�ul�ulA,~Boulkhemair%=E�$L^2$&$��J�%V1G��F�:�0165} 173--2046�%MDeB�zouina %%N~!N{e}!P�6%Oqui2 iq0�l @+� zed M�NBY�V@(178} 83--10E %Y��� \ Bo�!�S.\ DB�8) %``�distrib58g-:eur�p�1etyd� %�/-qu $�@pl� mo�5s��duA]4ifi�U�C��8.\ %Acad. Sci. ��(, S\'erie IM2$326} 1021�2:�R]{BR�A1-��D.~Ro����2!�Un0:�"rEN!�propa��T %��-"��Duke�h.\ JQ�1A�22A`5���H,V]{BV}{N.\ L!� alaz�;VorosAX89��"}A5"�"�1M�irF4$190} 1--312�(Ch]{Chernov�I.~ x92x�7%Hs�/sT%"*$ piecewisex.Q E�!W2-�& �a�Staa�.� 69},!D --136� CdV]e L}{Y.\ Colin~de~VerdiA5e�85�it\'eA�fo�VY�(du Laplacie�2����M�102} 49�0%�uzDBDE]{}{FmA��,Degli~EspostE3O ``6S*I .52�of:P � !UY sawtoothqB�`'�SAnnal> P'Institut H. Poincar\��,)��)or�69IH6�DEG]{DEG�6��! }a�3��YeA� cal aspecT �um�inJ16T, edi�9IKa*mat] Z]0}, volume 618�-Lec�UNot��A�ic��p� $2003, pp. �9BI%IJ � \1� Isol*C�K�8� 9��rtm*kq]1�r�,67} 471--5072 $DE${}^{+}$�O'KW} �2�� O'Keef�$B.\ Winn%�epA>V stud�8 Cai -Pros�;riJ1!��Non�$ ity}B 18} 10�1096 0DS]{DS}M.~Dim�L%]J.~Sj\"�GndC SAe ral &A ��Semi-9�Lu:<}, Cambridge Uni�GR",Press, 1999.��EFK9CEFK}{!Eckhardt%: Fishm�R��Kea�*, O�gam, Main, K�{\"ulle�)\u>ach� :�in՚wav*�X1TA��gev.\ &? 2}�'[$5893--59032Fa]{FaA�~Farriɒ1a���'/� a ma�Zld)�>racvRr-ary�U� PartCDsD EKQsM6* 1* 6�FP]{FPM�F�X}a`� Pe�(1986�D.�of�'rix e�ŝc3 systemV@"�4} 59aL9� �FDBN]{,} {F.\ FaureI Nonnenmac'*��� � �"$ ``Scarred���|e��um cata7�zFal9s' 5d�n:�239} 4��4:A,Fo]{Fo} {G.\e� Foll�� Harmoni alys ph�Js�G},`+�d ���s� �122�frWtonRc892�,GL]{GL}{P.~G��ar04\'E.~Leichtnam!�93!D�� "�)R&� �@Dirich�0pnem1GR� 71} 5� :JHB]{HB}{a�H.\ Hann�Cnd��V!U erry�80A��f ��-�8/ $---FresnelyZon� ; gGngqga�ica DmI 1} 267--2:�THas]{Has}{H.H.~Hasegawr$W.C.~Saphi�� U"4_�ir�Libi�BK�����qL046} 7401--7426�HMR]{HMR�P ~Hel�H�M�9nez�*� 1987) `1�"� K@)m*� 1)n,,109} 313--326�4Kap]{Kap}{L.~KE n�E.J���8!�L�+ nd n���~ory�2'Kr��*� \ (NY)-�264�1�:�M]{KMA�P.~�j�( F.~Mezzadr�E�PcDs�Na�of *�;� �A�� ��N�3!�7--776 KR1]{KR1e� KurlPFbZ.~Rudn�0�1a� Heckor{B q��&P6H�IeH1�R�103} �2{KR2�2��O)6�2�2�� n�222} 2a&22>�3�3��yO�U>X ma� el��n"Y �r�I��[M�161} 489F_ Lak]{Lak�4Lakshminarayan� �%�um"��Aa4� unus�*re46��Y.��272��6�$LV]{LebVor%2 Leb{\oe}ufNdV��(Chaos ��al&\ plic�/reen#���e�Fa1+)�� ��23a�65--1776� Lin]{L&b{E,�a ausse&� InvaM t measu�!4�dhme,1Wu)&? ''�#a�Zq ��.�.. LS]{LS}{W�uoe(P.\ Sarnak &7 �cLVr i�% �Bs''a�4))l�8Ecole Norm. SupQX� 769--799}�mez�%mssR7 %moduNN � �u�B  M�(56} 874--896T MO'Kh(Markl�Pd� ; �e��'s law%K1�9��asS vi�#r r '';%� ndix R 4Zelditch ``Con� }2�q@N� 8} 277--3:��d .�:��V�umMs�� � para&?��Geo�� *01� 554--15782�Ma]{Ma�]!stM� i�du�to���(and microlo � } �-Verlag,�22vO'CTH]{�G,W.~O'Connor,$Tomsov+ dB�Accurac��d�#� presmofZ ���MN;331!,6�,Per]{perelom�A.M.~) ��8�G6a�6�h thcNap�on�14 )4 (Heide��)2;Rob]{Rob�*�4) ``RelhQimUp�X Schr\"o>:er"P(,�&� �:�xin��A� �H%eqzmechanic!13�$58, Trends��Xs, Birkh\"auser (Boston>�s�sen R zweige���6 R�?Xe.} M.Sa�`0is, Tel Aviv &�6cubSal]{  Rubi� N� lwe�~�A Can� al �&J !�H'!p\m^nW:� 9� 186! RudS� RS}{�4��P��GA�9E �AOi�Kof �D�Oa ��*��U���� ��195--216z RuSo!@SoB�K.~Sou! araj�ina������4).:Sa]{SLSa�no�_"��H��E"E�e��'��2� 199} 37--:e SaVo]{SV1��!�A.��^Tow��!.O`Ao�NI"�6� �b�.�79� 6--26��&�SV2�2�Vac!) �\&�\kS {+2 title}�L� �� 2} 96M Sar1!� �%�3), ``/AfH&� Surf.{ Bul( Amer�/\ Soc�<40}, no.4, 441-4:� Sar2]{sarX �nakɻ�ves2PU"�@uEg�$�(�s �}. TalkENn�Rmeep:�bandomarix�R!�� Ari0 A� ef�%P''Q Isaac New�He, "6, June�9 4.\\ AudiO.$le availab Ht {\tt http://www.nR4.cam.ac.uk/webAxnars/2� Schn]{Scn��\ I!B chnirelma�197�HR �M" Q6 Uspekhi!.\ Nauk1�2��8�W86W SchuANch�j"s1))�S2<p�d�>&D.} Ph.D}��U~0\"{a}t Ulm. A=D .D4vts.uni-ulm.de>1uaa�O%$�``U&�eAWa�j`!.'' P� �,2005,2� �TarXiv:math-ph/0503045}2�Wil]{Wila�~Wilkin_W� `NY� K�SB >�of *�nV�2 ��_ ���41�>~ Zel1]{Zel�~"W �J>LŨU[��compactݨ m�UzR�(55} 919--946JZel2]{Z2B���Nrb�$. I. .�q�. ��)+-( 160}�� 1, a::ZZ]{ZZ6���M.~Zwor_&19*!&�TB�%� *=%iG �\ ���T75} 6*6m��/>C' doc�[\} � \newcommand{\nwc}{} t v*$} %font� nge +mf\i4thbf} %Latex (�a\bf�N til�$a" l�qs)j@blds}{\boldsymbolE"ml aca%greekQ �lam}{bda�dA�tDZ(L=La =$ %blackbo���mIA �bb{A}} %�@ic�IB"B" ballCCa?lex D D Dedekind!E!E!Euk�'s!F!F!�Ufj?%G%G%GwHHHi� ,t\N-subgroup+N+N+natura�P P prime>QQ�x+!R!R!e\SSsp�)<TT%ZZa4erEX %Stra�T (�.)I M�A%lower�SI� va}{~ a}Ubvb bc cd de ef fg gh hi ij jk kl lm mn no it op bf pq qr rs st tu uv vw wx xy yz z�AoldY) %\b* �J�in�Z� s �in� . Nute.no^z�XplaG Yw�at.A� %I. J�bk�q lds{=�b�5=�bn*=�bv=2bw=3bx=4bxi\x]xby=Mbz1Nc�3#.�b�q�c��l���{l�w�ql�m�dl�`�Vl�R�Hl�D�6l�2�+l�'I�Zl{IA�cJ JK KL LM M�rl�nrO &O&�xl�t&�ml�i�_l�[�Ul�Q�Il�EU rUrV VW WX XY Y��l��!�(%miscellany)Tad}�Ea&�epZ�n��gBvar . ilo1 \def\trNit�rT Ti %I�$mBe #��#(sq2{\sqrt{2� n N�j${\stackrel�def}{="t2{`8bb T}^2�NtcFR{ bb C0s0S0hn GcaA�_�sag �3-LS3SAAN bbXTT(RRZZC�O �i!Sp S}_+EHNto8{\x�Carrow{Na4�9i hto06&h&0.!o=� {\v\/rBPrP \re.� qeA�hfill$\� square$ �pro-"� Dabs}[1]{\lvert#1\rA>*�@ +V + WnwcF �a(XArXlp( eft(r�)Qba� b�A��.Xequ��48b%2wbe :*.�=narra)� =a�� \ .>i� l4ize� �]e�d :�F}{��e�6re�  �.9�..:�2�0K\�  [12pt]{@"cle8setcounter{footpd}{24usepackage{ams� ,amsthmcd,)P %.*pdfsync}G6�th!)�{c=.\ic5}�A et\s !=\ > }{.�1X }{0}C�tsetlength{\voffset}{-1.0truecm", w�r4=150mm %125mm�Bh�{ t=21%18p ydent=8(�]mg8margin=0pt \odd:$%%%\french�e;�a*�bP/ P! 2��� 6R 8RF8���b�@:8C 8CF8 8FH 8HB8N NB�J�� pZB<O VO�2on 1% 2S� $athit{SE}}B X LA2?Irm{ad>�A�� AFf rm{ :}a.  : � )1��A}B %� CB t!� wides�!6��c��Brm{ :$�:� at#:"1 �DB�ce@c�2`C1� rm{C!�2A a�BF :MAMFzE5 OB C �CAY6|E.^EB>�+�:�rdi b :!D.  : rDaB=:B9 Eule}�F"n]� :|� 9�FB�g�_rm{glB �* @rm�*>`Gra[">$g�drB r]�g>=r� )�Ga�6���a<HB[Ho rm{ :rh9�h>� �]IB]I={IB7Or[B�Po2 � :�� {QB{G LB r�rm:��}�NF=X)sB�rшrmF�rF :T>�Ro�� :�Ri� > : ��SB��#rm�#2*�!�!6=�sl>zS�bSB�s�BsoYoBXN �Sp>sssBS�)lSU>=Sup>:OSym}:"T]�63B~Vec=�:>v. : rW �W>N�PY��6�hal@(scriptstyle")F2B8f� frakF�f����2:f�BBDf<at Bg s�^��.�:lu� :� {\�  $def\mod#1{%K {#1}� |.w cqf��� e*{\�}\�{3A  G � ase� L_=17pt |a{\@F}�b� tc{\$� d� ,g6om{\omeg.r{\rho ,s{�x vfibq l�� ]m{\mu imp�t{\R%�2�  .1] in%�7+c}{]m}[� ]2#lem}[thm�+mm� �m{�G CH)�!pro ! Prop�]6#ex "Examp .brmk �&6<y F� ��C V TITLE V  \�""es� rabi�1 �Adra ,K�B��ensors��Q^f��!2@\author{C. DUVAL\�@{mailto:duval@cpt� v-mrs.fr�lC�D e de��>Th\'eor 8, CNRS, Luminy�7@se 907\\ F-13288/*Xseille Cedex 9 (France)�$ UMR 6207�>UJock<e aux &�!'Z;'Aix-Ma[Iy< II %zet*�!'eSSud Toul|Xr;( Labo6Hire �Clo \`a�D,FRUMAM-FR229/_0and G. VALENT�-A(gvalent@lum�Ch>H.lZM�hdes Hautes Energies,\\ 2, P=�@Jussieu\\ F-75251�7is-Z5JZ%Y 7589!�Y@ V%P I} ��date{i�: \makee \G] page��{empty1��absM0t} �$B84-,l�@"8c%by�&V^�! urveÄ figua�on07s}Hinv|@g�� . It�e�#��N a ``�7''qn"�)scheme, ud�Pm��70vZABrg-G� � e� ��9 \v�� 4cm "�M"$: CPT-9H/P.120�!0LPTHE-04-33 % > 1cm '9ssHt8bf{Keywords:} C"�&1t��$, geodesic�F, St\"�G=�%�-Z% u:.�newA�I \tableof�Y ents��b�� �{I*�.}\ Y���'��)u goa�9aj WAu��.t;* omew�[gen��qMmework�xQC*-�cM�al*�KeQa cotp# nt bundle�N:polynomi� '; ost cubic7mo�Ma.��aS=e{ws u�U}� '2��7�(ly Poisson-jud).���h�/to ��Tg:�"�=2�%�jaso�y�| |7dy T�< . W!c shouLKctut��qd�N�>�>!�a � Dd' issue,�x , e.g., \RyWeik* he p�T0of view espo�Epa �i/>&�[.�0rpg!�� �9tL�4�/Fd5�Fnuse�T�QP� !�geA��U spon��O# n!*�E;�Mt=�lU�OOoMb\R�lij2SB%_�Yrlt@'the(mutA,)�&�ia�iQ+(�0um level. ��e9c^LZn_/>a�- quelx earlj~�'p��er!ҁ��Gs-�(BCar3, BCR1(2, HW, Tot}�\A�Pz�>�-!8persistE�ofĥ� "�p9�a h&�4regimea�rc�u�w� al)T�1]R helpq�highl� %6�f"Q/�1Kcor��2oa3w���laa�uBtu�"omzyet�'a��!�r��ng�D Return ��eP�M�,�"���  ^S{ S��w� 1!� cedu\@�S)X%AL.-, doesn's�em�r �ap�?��sq�%�in"�7ork#i�{�;3 volv�gA� ificJm̊. A7�%�b� only!�S!1 l���(2�onB�s,<[h�Svirtu%_leae�)E� �-�si�ost�ic}�%}guaranteY�m�ZM�A any �& s. I:z}id�>���ѥ�A���1�� �)�^%�z;Y�,!�Ss�Ry%cicV<ՎnY@e� C@jXI3c:<�A�U� Osa"� )RieU/ian85vi&ɀZ rom�outseiq !�ya��ho�E-�Levi-Cu�..[}exedfy ��:�7%�ic� *%W���q5�*� B�mir)s-�F� ip4nӔ!;���8.nA���1�� &xinŊ2��os�: oweda�t=PduzYl6IMH��to%��Q�AO�\)4$Kerr-Newma~lɓ AE� ein-Maxwe#�q�b:!�smolog� !c tant~]dz�v�j by Carter�@1,�F23}. Also�{%<%"-\M�e���a�C*ten�p�g6]46!�B  origm�du��Be}�,�2nu�Rastelli���}�c��organv�a�.��i�Sml\ref{� IntSys}a�g�Dr%�&x �.!�Sc��en br� �y�a�tra�s&g� �,� coBI , $M�WNIke 0of Souriau's �pc�/ApQ:L��G(estly gauge��t fashio��~ coupE� �v$n external=@ct/]gnej�;��6b �� a� �* ic 9)�!(so��ed52U�-:6B�ed2k� � A�� �-��n�H�x� X���p5���E'�are�`�ba8Ek31 � �Di Pirro mq:�n �P!S�2��Ks�h��J-de Si s�Ta)jMulti-C�rQ�a�"� ��^tr�?e˙2F��F,�peP b8 : Q*� �8�>�Q�>  $T^*M�uw̞ 1�\ c���a��c"� $\���IzA�a�|ev%{p�alQxu Dis6  mapp=isE[e�be*� 7re!#"e*ne�upA� $(M, ��n��J3�% �]�����6�T��]�L&]� !��`"� ex��s@e�L*� . �aaA��AEdetai��a�A�@�=Se�f|�٥�q3%��/he�_ list� ��b![w  %��hC�}2 clu�a���p nd bE� �wsЉal�grksvu��>u��8b��� be�;�.V q�� ~ M�0f�.B%^opens�proE()���&�%� �Et�F�e spiri��� �S. �1� N(0bf{Acknowledg7}:Er� deb� to Daniel��nequiAg1\very A�|!�sork`$to Brandon� A#fruitfu�ra(o�( ce. �=ia�an!�E* Va*(in OvsienkoIaA�eJ{h~m: manux:N a�ׅ�en�esug�!v%9�| reak����"v� � !p� &"�$I� �w��%%% %gxus.| m) &J �notv+%p� �bNF{:$ 1KT���us�>���QNF @l&"�hsOfF�(��,\% =d\xi_i\wa�{}dx^i)V~p  C��xzdhomogenej �4s $P=P^{i_1\lEf{}i_k}��xi_}  k}$�c $Q=Q:6 \ellf9�d?~$kJ $$�3ively;� w� ��fy!kse6���!���&6&&� XZ� $P^\��Z8^al- o�Fsvws "9Ub#61}K�wNX!!}$}heF^$[�,x]_S%j!Az69 m 5-�I$ (of-� j�)� ]6u $(k+�-1)$- wQ���UJaV$P�$, 2m�e*} R=\{P,Q\}-�. �Defq�]qI Tg%?he>� $ T=9�ai}PiQ- QiP�jnd (�.�)� ������ *� !��5-^b� . I�2C � n�E z� �wr� n as&� Ѥ�clel r�G (��. 4)�$ llZ�QIz�"3 kew-6)��w pri`Acombin@ U fact4]�7:�{Q�}} = k\,�2(24{k-1}}� _ie�k�:�RA)} - a \,%:E.Hh_��>MU�Q Nabl�%s3]�If/ �JoJ�,� ppe[�^V�eZ,~$\rg$E���~�FPH=\�($\,\rg^{ij}ejq}HBsAS2Fd� s�#a� ��| tqur�29� >6$H�| noth�j�<rB�nlAU�c:���E }l6):Xl0 $ \{H,P\}=0 ���e,�(or -"S) j;i"0��LR�"�!� �X6)����fJ�sI�^{(i}E. )}=0UsDef �B�3 $}gin�' S  {\rm ��.�� in*���_2:K +P_0�P�F$Q_0�jiff� n�#!`P6S2�-�c���)k2��I�$y� %%% V�[��,� ]_��jk� �D5Jj>kk+2(\e�0iQ_0-g6 P_0)$j.>�3QOInHom �6f܁iQ�B+VR��c�e�$[r,�]_S=0e�W|1' toRZI�_�: rut}I�AjE� 9�y�\& ���1-jP_0=H��V2 CondP0b�* �a"aJ� >O `u��u D�ubz &��} (�aV�� !�h>�, $F$, �" Sou}�� "�[c"#Q�lY��#��E  �f ��(;tw!!dR9 $ 8_FJ +E( {}F_A� *� jB� (�-� t) "� i�E��� s /� pi_FBV ZUvi-2|f�Q�j :1j}{B �&�% .�$P,Q$��-/is�F� �0i_F(dP,dQ) = >�� - )T\,FC6 j}Q,WPBFB���!ꑽu:�.�$&o �����{$$Rk {S,F}:o _F%v~ �^w ���C b�tc��f�bEJ�i+y> {rclV? � =&&R���.&� }9�i_ -z:.:,\[6pt] && -k \,I�:. s H Nm 2})j}]����2�2��)#Qc1~�HBo� e.� ":� )a]!� Q�$[��؇,, �.62Supposą�N^a�a#"� e2; �� � AI2�_F)�xh.r \ ��b�H} /3Lorentz��� �mo��� a ch-d t$��cle mo�$vW8rg)$ dTX infl"7��Zr��b. �� � .���� >� �j1 ٵ _F=+����-) %9� , j.~6HQ���m�<3�^A�&� �\& 'V^FAk)}_i=0q �MaxEqs}�O~w�L $F^j_i=L jm�*mi}�n ?��#I�p�re�2�(} �y&�s�lyreeAW� �*� !Y"] sm�6�)p of'�m�����3$*"�.�NV�{1]�^����zed.� backg3a�j u"G�Ss��O>K *| A�tra� al ough�P ,�`Ap�$�)�P"O"Z F� $ $F=dA$ (l�] ly),�4o keep H"� $1$-��3�I7=i @ � np un�[ge?��'to�I4�T$B�1��D,\Aw� ��p3@.�i^��bJ��*�@H}6� (�-A_i) j-A_j)q*HF�i��@ 3sm! clea���*.�toA�X'�E..� MO�91s $�˸$i=".~n$;E�e� �}la�1%9nk��E�T{%� Jw"�AP}NZ C 1}-AK1})��k k})"n%-} �qg } e�.xՕ!k.�����a�>!��F�n�dI�h~�+agan�Z>uu�9�r#&' via96�:� s, viz� � {� 2�,Q}\@ � is&(2"�[���,*s,��H%VM#)d &` �1�e�YNH2�P}Tm �;��c�*aints%',1�Ui� ���z�����^'�� in o���,�M�w�o�!�$� $-su�/�=:�1"s���HolE��VmI&86�*�&S%\=����%"�I�6F�Def������2~�c.�d"@�ilIs�_�"�(at#:~4 $(\cH,Hin(Liouva;)�le%*�(e exist $n��dim{\cM�* ,�U*b5�s $P_�iP_n\in{}&�cM)$ ---� is $dP_1��s {}d=neq0$iA| _k,Pe�e@all $k,0.�d# �=HaWz &2� "�l,�<f�%�Dide:s�e~as�)>� s, %h=ax&�tu�)$W����� N�c& �rofV��P2U�V3 � a�:to ^ �|� �a=�����s. MoreG.,%N� at"�1��b�0by.��de%2Z�re��i6j� "+e)"�Sta�nlS��ib�6�:�`��!� g!O� ! !�*�JyH=\q�i��n a^i(x� eft(�B 0mm}{5mm}F i^2+f_i(" C&{ 1B5 &� $i$-t*K� $f_i���co�U $x^i��`+A�B'y�$a ���&�.~�B`n=�M�$GL(n,\bR)$j� NCA�M�u� �PB(x)=(B_1(x^1)B_2(x^2K 4{}B_n(x^n)) $$;3� �cjz n $B->�p�,p� (64 ); � �/t�c��B3,8a Y� a�,�0�a�\p  {a^1n# cr\v�#,\cr{}a^n(x)}-to\�6�A�$ M $A\!j��a+2y�b%Ir�=/� o/4�� �DquK?*s B� +m��/ef?} I��6�AE�\��.�L�� nH=I_1��27�We�=�"�.��ryU�!&!Z�F�:�Po�.} U�!�.�{�q�}�:�;>� ��appear� � �V�L(just $U_1.$ĵcan;��W\.<$Per}, p. 1e�&�!�.�7��$)�$e�EH7 \[ \{ ,I_m\}-s,t��\,(-s*�s A_m^t->!^�� xi_sM!� xi_t��t��.I.{}m. \]E�% K $A=Bi, ���3C*i&ty&�"a7�5�d�8on�$ �!m�\�2��T� Q#idq&�0 _k A^i_j=-C^�,A_j^k �\al 1D%B2s�I4dB^s_k}{dx^k},>0y:J9ieb��bis} Ҝ=0, �!�-y %���n>��<l R� T4�3�@�s�Q"F ls,+.��Tm�RmkPaBGo �*;!��6t*�,r�67e%:~102)_��4w19>|�4fH5��!2-�3Q0ANs�l� !$�;i�%�"��is9". ��� *�;.���P��8iteL@j)S��l�'�� y doE� exha�W����%�)33 �I�&aKy&�".^ �wasb^9d ".3�� *�7�,DiPR3}��J 6J -�= �O"a4" sub�� E� $\cE� et\bR^{n+��bi $n$-dimen1�4ll�5u3��UL($Q_0(y,y)=1 �?� ,A� $y,z?�nB� } Q_�f (y,z��  =0}^n{��y_ {}z }{a - D}��/EQl�L6��$0R cE�m����M�? 2_1i�ru�a �E?*!is admit5'>���Mos2}) N.3��I�, pri� ���u,� >� H(p,y*�2}Q A,{n}{p_\a^2}+I&a�[>#A;^2uY�)���1a}� $p,y2��0�ޡ*ome�*w�. Moser%�8,� Mos1MC!�f":&� " FM FM�) ��� ^2+a � �\beta�"i(}{ )�7 {}y_*-p R��uYa %}��$vSaI}� A=0,��"4!� lsIn��>E�`B|�6UE- �H,.�n{d�"�!!$�T�FC t��co�EaG� ��]!�IBoG�&� �HakQ�F.�Ego�dA�euCM")5<��z9).D 9C 6C$I_5�IN�nPT^�,R�1"�A*�$��dJ/8\iota: D\hook�`a5b}��" $Z_1I��B-1�'� $Z_2e�0b��Qs ���3s $q"�6 {\vert}_{� cE}=T�$D!v ��s6�9�1�.)nd ��of}�fr�ac"�F��Dirac�} P+"{� {�N�,F_\bN \}= 7 #��>/#\display>O�T{3cm} -�X01}{\{Z_1,Z_2\�"`� �} 2 b\}- 1   a\} �x]N�� �:�Vsecond-* � �. Now�CHnou�to���=-26F(�5/�����:GHw�� $ Bށ` \}=4�Z AE ) Z_1-4 [^2Z_2$ �!zero on~QH< o�W...,n�fOr $2�aD �;le�QA�j�� =�r�}d2�!P4��鬑��F ` pdklyF�f�A"��F� A+59��Ɇ^2I )��>��'vX5�BiB>&�0H� A*eF�"�� �u,�resorb,1i 5\al*s ��x^n)~` ose�� � �t&�.\ � -)?� {}U_x( )}{V [ ��alC"�Z�#F._=mgd_yj-T"D�Yrm{an!�m�Aq}^Fa�a_"�UV�:9 �^[suH�q$ (x^1&g�4}F6�x�g� (�%J.j)� $��rc?� hea�m&� :):U �� ��(�)^2>��& rg�)=Mpx^iG�I} U'_xKAq!�UmM4UsB�ss&�M*�Jbec�1t"�%inAl \�pu�K�*ei��($=1/���7� �6 )� #UV�we find��$�?reA$1�(\M!�uK�>�.^2 = 1�M 2� 2b:} }V. .5 YD� <�y2B�aXt|C' ��e�V"��(J� � �#,E:��a�i I�q�'i��<}�IV�pBB�giWF�ini�FI& $2}n\,a }=\ ^*�� '����{}&� ��A^�*�MD2�)�� cZ� O !�f�8�F�H=M31& -N2G&��K�[�tn"}-  Ia� �]"R%H��B�q����&|&M�IPed&� R$Ͳ$*"� \[Q_��}� \sim�r �_am�x �=�y_ }^2 �0^&m!�� �3}2<S ]���o��d� "(�.^Q. jW gets��-� rule� 4mm}6"m������W��cone.b ł2 to�ir"v .v(*� a�)1ing, em�)�! y2�lA<P��r $9\;6��|d e��R�$%t("q bFq i )!�I?"�}$_4C�����nM"� � \,G_ "*,x)��$$�1 �:�}� GenFun} G"\xv�� � �L͐��{}��m�-x^j)�H�o} + a , A)i)� W�!� [iGPato�bJ%Yn�C $\s��_k�1�#A:&'" � $k2�-1"�*�* 1� $,*->excluRA��x a@^hfct��r4 5B=j9vk� {(-1)^�2ᮁ�^{n-k} �� FRWl(!5a���aȨc j&� )I0J=1��I$yHworth*6�o�=n" R_k 1*az-�^07-^� J ! tùh��_�I_1^B�<�, b1�#Pro1�� *L$T^9<aj�^Ei2s�# To&)R � �#F�B�(x^k)=E�i\,�{�-i}}{4 VeAwB��6a� &� UjFufa�sa>lNjfa�6ju$i,k=�DnS�%����of}�jobSO���%A��P &'�27�"KY�$�a^���! .$ T�(Eia�! ,a�!.�!. `u��)E�Oa��m�lex�~ne�"f(1{2i\pi}\in���{z}=R5z�E }{(z�9{���.f}z�dz.�".�$R&~�� . �Zl�es"J� �nd as $1/R^2�F�  $R.$�V� ���iZT ab6!;�fiduA�{Ue� �-#Q�miu��&� � %XU�E�Uvk)}\ �B� k6U=2�:| E�"�DO��]�/I(e \< � e�$\,A^k_j=\d���#.\]2@�Z� P" by $e�{j-"3��j*K;$��$j$i$1!�o�,��G*�@cZ�� �� Z� � ��2C," b�{�,I � .�.I ):Z�g^5r�Z�!lU��A�"��� $ Z$�i�>� ���� p�6�k�pU/):� UAaE��'de��oK =BN�"In� to5䵴 $ ($a��24$l��r"� `P�� �s����un�nd.� llo>q6W 2*6Uf@@TVpl�both �RseB� $,:�i]�Q�O.h!+m�Rg|*}�� &=&�4� i��i(x)}= �a�Hi% 3Et+-k�s.A��h��2F*hi*� fL-��8^{n+1}\right]. �\end{eqnarray*} In view of (\ref{fctgene2}), we have $\sum_{i=0}^n{(-1)^i(x^k)^{n-i}\sigma_i(x)}=\prod_{j=1}^n(x^k-x^j)=0$, which completes the proof. \end{proof} \begin{rmk}\label{potJacobi} {\rm \begin{enumerate} \item The fact that the geodesic flow on $T^{\star}{\cal E}$ is a St\" ackel system was first proved by Benenti in \cite{Ben}. We have given here a new derivation, which makes the link between Moser's conserved quantities on $T^*\bR^{n+1}$ and the St\"ackel conserved quantities on $T^*\cE$. We h!�4extended this �to !��case where Jacobi's potential is admitted. \item Checking that the unconstrained observables $I_i$ are in involution is most conveniently done usi]eir gen!�,ing functionM�HGenFun}). Indeed it� easy�verify� rela:` \[ \{G_{\lambda}(\xi,x),mu,\}=0,\qquad *D,\ \mu\in\bR,\] whA�,implies, via�)EaN8and upon expans� in powersa�$ \$*$\mu,$��4s $\,\{I_i,I_j�d$ for any $i,j=1,\ldots,n$9�`Some authors \cite{BT,HW}i�quantizE $e full set�commu%kob9�qA)geodeyYfdellipsoid $\cE\subset\bR^{I�!� ts u2,form, namelym�*48. Notice thoughIeino reduI8process from $T.A!�cE$ �um corre;s may@ve neEaryaorder=Linsure self-adjointnl �9A='. Our p,(�dwill beSper�� classical� �fir�| laceE then?s.v di�=G�A�$a specific�ced�ta��describa9n S) �QA"IntSys}.��,enumerate} } �� %� I/%�{��@Neumann system}\l� sub }�o .d(HamiltonianE�(.C,\�\a�Ldp_{\alpha}\wedge dy})$ is \��equ�j } H=\half2JH\left(p_\a^2+a_\a y \right) �H���Twita4e real paramet�N$0S U'_x!)}{4 V b�not����UV��A��putezcce !�� )=1/|��y go� to d$ e A�knowl� "�r�) �indep4nt e� ���u�I_ne� L b� ic rmul4p�\})� ng:0 J"� $ed momenta�1a�s $yield��QTpro} e�MH �$@��A�.�A�9�r#� m��retainm�2� �HnX��yAO`}�<}{\displaystyle ���A�Ɋ}{�9A�% )�$$ � G_b Z�CiA{ IO aU�{( 7eF ^2\+�j�Sj)�9� !n ў,��, posit��(i {i-1���^{pI_i�} +\l^nN�E�.�*`Iy($i.&) i6�I_an� written aJ� �� ) { A_i^j(x%+ j^2 } -\s��r�7=g >sV%" PiM�FO�a�sym�0. �$�a0�o&�. UsasE(s� s_1(x�I4 x^i,>�and&3 2:A� }-5�x - ..[$$ one !�check��.] �5"()� $r {}I_1$. 2�v-F � on ��H)$��  St\" � l�- matrix�B^i_k�)=E�i�UI��k)� Ep&cU��t@ } fZɧR2P�- fkbiF.� $i,k.�e��p� } To.t($A=B^{-1}$,[en� o usmzd(ty-�useful��!wu��`J� $f_k� ocee��loD li%�E�A�OPro�a_� ProJ��+}U� {\rm���$property $Js>o(, similarly�u�J � "/ ,A�se�[ ��qqd ��.$6��2�e{artic� in g|l, Kerr-Newm�( ackg# }M~KNS�� Plebanski�� Demi h���uc� iY Ple,PD}X R!{�s���.�sol�$n $4$-dime�al space&� �lsoL �%�T4-Taub-NUT-de S�Crg�A @Einstein-Maxwell q�s m �"; cB� - Dx^2,x^3,x^4)=(p,q,�; ,\tau)$, 6�*?"IL G0X}{p^2+q^2}(dA  d RV 0 Y>(-p^2(+ PM {X}\,dp^2BYq� �g}��KNS)F�ith���pX=\gamma-g^2+2np-\epsilon p^2 �\LI }{3}\,p^4ٽ&��Y G +e^2-2mq+GqVGqG �XYF�� $(m, ��e�voEmas� angular � umA�A/A_ black� e, $(e,g)� e�rice0Lmagnetic charge; $n$�y)NUT ,,$-mcosmologihantI�remainaCpk $1$�0be scaled out� 0$\pm1$ or $0$�a)�,� $, F� �o�f� , loca�gi� $F=dA$�FA�*1Y�D\Big[ (e q + g p) E�4 + p q(g q - e � 1]"| AB�provid� exactu�1�f�}2r ��ant9�. �n��fur��yatF�0\nabla_iA^i=0"�DivF� U���e $1$-� *�"4 K&=&\sqrttY}{2(m�)}}\,�:-p^2\,�;+.2 - }{2Y0dq,\\ L�W-�WM_1:Y~X}p}M_2:&� �2 7� *O � o.uct�$2)JJ�cY= p K�L-q M_1M_25� Yano�U qOV twice-& Dtensor $P=-\cY^2$m $P_{ij}\_{ik}\cY_{\ell{}j}\rg^{k� (s a Killingն ] (see� #(MaxEqs})), q�F$P= p^2(K\o�gs{}L+L K)!r(!M_1+M_22)5'y�QN1W� Hus recover Carter's�ult� BCar3} ab�� he i�bil� � .� D a�a�\d t.A �I�D *a differm{. Z� Q_qYq Q2)i� es w�is usu�E�Ked=�35�)(GRvH,MCar}.6h � four�#e>�!6Q!n��are��tively, F/0\widetilde{H}S,E�ij2_i-A_i)!_j-A_j)G�=P}=P^f4�HP-NF�p $P�U� )wF�)�fr�S}=W3-A_3&��T 4-A_4U�STR�, \goodbreak� . 8he Multi-Centre6� �� ^"� 2gEucAan4� $4$ "� a�{) a#.- M_Z,i)=(t,(y^a))�"\�v\bR^3�"z" H1}{V(y)}(dt+A_a(y)dP^2+�  mcmB0�  $ (=\d_{ab y^�^b� flatB�aW $3$-� EV $dV=\pm�% (dA) ~$E��Ho��e� $� sea�d�s��!!;� M��^Ricci-�. Fo� med!�o1%s $!-[63#i!�baEshown� �} ,CFH,Val}��q� �rFD-�EgcE�&� ��ij}a�ij,�; K=K^iL=L:P�S9,j,>� K�L�twomm$�C vect�$��j�{���vwhose*�s� f��"�Re�Vces. �,*,(he Di Pirro��1gC�M Di�+ hhas��'|, e.g.,͹4Per}, p. 113) U�.���e�F�H&< 2(i��0x^2)+c(x^3))}6[!�1^2+b+2^2+  3^�"]�"H5:� g(�(Z d on�$ e adi�al:w!U�F�P�z� ��(F� B�-: 6�. �P^��+�m4i%�|� ed� H*�5=)Use a 6B,K�b-#� l �no�&��type.-$is happensQdif (i) $)/=\� $.,�(ia=bm�)$ ? Awr=� A&�:(AU^2}1ly'�H&%�=\s% on{A�z~ schem��r.=)Wsq�.+'���� wish al nowmAV>(um+.�prece�#exampl�$z�9t As��prelimin*)!� ider%&s:6� Q*/(\4,�re�$no univers� acce�!�)�(of �-�, i.eAjf�inear ixfic�X cQ$,;�(ace a ��22)��s) W&@ aō,on a Hilbert 2. �--- am�m�+& pathways!�!,t sc"a %� � mapp���b#dem���$$�pequivari4] rD q� Lie �p�v%$o\-morphis� 9ph.%��%�S��Mv��o��umu0>$. However,�%a}��i[�"TPTa�ic!q ifol ((\cM,\omegat !9a �>c!?0:P_i\mapsto{}o hat{P}_i$u  w�%sa5.a5� �6� h�sense�& $[2Y,.j]�&allBR.m+A l� number!�B$I 4volve \textit{�.a�c}.� . We �tcho> t~ n &%o\-� mpor�A�yet�1y"� ��, both&�YJ!�1--�e.�possi��,1��sEt search%/1EP-pre\-�a;o�(if/)R uld b�funda)!l �c�2z�)5A.@ we/- $�be�)m�+ �� �!7ng.!� si� programmew� ��*�ňi��!� cubi2�ѺS��9���6rec���SazF�&M�&fy"$-densP#M� �aG >of�(�"HPlex bundle@\-�%�^n<*M� ^\lH\bbC$�)�"A�*� configuaQo���pis oriz#b�M,\vol�z-� $\�y� "�,gtA�y $\phi=f�M ^\l$a�Dth $f\in{}C^\infty%F}2mea#a;$phi$ transVq1�-a%=E�$a DiffGacc*)g�$f�a_* � (a_*�)/�.�+)�!�!�HS�5�$ actly sup�^ed /Y�l� $, r2o!Fon�� ly attachlo A7�&��b74hrough� is a�clm��ara�H2�wo:�]/ds� \la!YH,\psi\ra=\int_M{\!\K5{ G'psi� w�u barG ndC*! A�conjug�I*�assum� at"]})K$is endowed�0a (pseudo-)Ri1�0kuW $A�rg)$;�denoteQ %�!�_\r�(�"3 spon i�y=b Gj;^k 1associa!� Christoff4"mbolsM&2i� in" )%�!Gac D-���3!K)of> ��2�($P=P_2^{jk}�$� k+P_1J$j+P_0(x&@ V��9--4"��2 $\I��5z $A=��=A�n�j k+A� +A�\bone�� cov� derE8v��64�g JA�=\� al_-\.1�jk}^k&$ (or�� $2D(Ef)F#^U$)&� used`�more r� r�a�9 e princip[ Ea��NC��U(�" /S.2NR1})E�R0����!$=�C �%� .�5j �7!2.� a�laM &��7l�mB���Iin\�!��4N(re��L �"' P>$ Q| &=&-q \\[6p&x:515 1^{j4ia( {j}-Mk�D0D0&=&P_0� i}{2} FjVj�M}�%�a�alterna���=o �.Q�s\1{}� k2�(�2%j+4 M1^j0)�/e��belc ��012F�:makes cl���Ty���� peb�9<66�%A�u"#,Q�7* } ) wa�ginE�a���� Q�� ���he�2X �`"p mo��of Y!:�� ��!-%`$:BB�I�;worth � iol!e�~�act��9Ŷs �sst0��� proj� d�"?%�-V-3LO,DO2} �=o? or�0 ��v��J?D@1}�-(Q_{0,1}(P):a�0(M)\to 1a��-S4!VoN�� polynomia�FMhE2��.'*8lE�s:1m1�} 2�0��Q}_1]} =-iQe�SDP_0 = i[P_0,Q_1]_Su�\{ \}}"5"CommP0Q�,e@qͲ�2.�m�m�(Q�n�kP_0)�+ Z6�\\�O���"6b �2]_S^j+26H �0R2JF:z1>��j�1-� ���1\}>*�%%�1N���u6]=9ar� lici� when $k+Z!>�!a"�s�"� nex �~�62]B��!� + Y�A}_{P �X �6�� F�AC&p�� )p U�2�Qo! �� "�A0m�y�- � �y2x�6�>van in ^ � |)a*�� v-q&~$P_1��gence-fr�"�@K �' if i��&�.HV/#"��@ul\ae\��b��un,_"s  guise�.� . He� �go� step ~ ��comput} �UB $2�22O2]$P -ve�3irv . T�at� ;<-[%�ize homo�"v: c���2F]�a P}_3�5_ �J�3 AG}Ik{� k:$�2:K .PfRB���'� �M3B�a�(``minimal''��AoA��@�9m"�re�$�0 �/ 3.(recisely coa de�(eB \-j�Bou��B: 21ly 38Q�2��Y<d r� &=& \no_ [P_2,Q��{jM?2 M Ab &&M�A2�A� 3 E� 8jRp�=) #ni�+X[v-1i jOjr�2-.�k B_{-}(��] `! >� �1E\ skewB�(F�m,Q}!�}!�9�P^�([jq�p { m{}Q^{k]m��)R}_{~m,n.%mn} -(P��a]?Q)9� 5{}P^{mwl} -n=)mh�MB�Q�satisfi����, $-$=-B_{Q,P}$Z�0� a�f*�A nven0 �Y��e ��#*�G�R)I! i,jk�J��6��* -(jB* k) +9$�$R=!p Wkj}�W� reN7IE a}&�N�5iY� Ayk� �1��xiE�Q|AF| A d:�.�.�&!�w$)XBuL'+<"�%)�6� }&�*;.0,2~ oB�,�.&�� )�=(i/2)(=PE�\.z a�+�A {}>5[=.[)J,e�th" I7� ]�E�.��P}0"wid�Q&T��E ra%^F"��� U4Q=Q_2+Q_1+Q_0$>QQyIj1}{i}.4.! P �\{P,Qe.�U � } }-2Q_1,P_:3Q�-�i.E�~� =W�� g"72FQ3}G.� %��,8!�� �>e�Q}�>� s trivi{"� � g � d]�nd .col�3� �anomal( =ADi�;�1Q2m� �2Q�n)4&g ��>�8I+ &�)*�$Q_2=H$�-58)7H�>�a0 � t�&!9?B��_{P,H���\ ^{�Za� P� } -  [j��R!@M�FoJJ>sZK��,A%}_A *qf�)�7a&�2� :�beginFq�m=.tH�{y1���j-e�. k keK%^ 2�(f>>5 coup�1, �/����)�E>A� =U)'��6.16)A�j�a1purofw^cl�$� deed�5 study, uu>exp& �%, how*R!6�be�}.�.R ��  rule/*�d1~.�,,$$1"Rher)�se<�be devo�A�o�-��$2#=py�u��.D`1� �&%�hi"N.�N!*N!!�&�ceR%algebra@!E�%Ch�;!So far�"t�)TT�=-]J�)CB(%�F u �3ng\&h;�)s-c ut a�'. ��&� �=investig>$ie�seMrar| nsis/&H map:Ph � (=�' "AB9,��:Ak I3{�2,_1\cdots\i_k�.{i_1}� �T{�5Z, ) be�_9� �NK'sub"N'A� �om2V'2:"sb(,� �4R�yc!#"E)�inv 6\{X,P\& 3:�N^X=X�1U P�L{M*�%,�IE�l�<�=E$j"P C �� �$6�$TgeC 9�*�K��A:91:�!!=(Xf+r rdiv(X)*� �AdL a sl�'abg<of�*��,I�!�X^Ym! c(� _jX^jE�(-.| j+) {}1E�aS� &� Qc*� �=X� :� !�,)�qNj y�c��m:�/F�) muste&%uX! 6�A]td*��lattJ�&j X*j P}]=&ZM�"V�BM6�Q��>8a�W5a���>�}) �acteriz}����Lwe��j��for�' ��(\XuA�� of��bincrea Ddegree: (i) ReturlJ#�Rre� �� n),.1Q1}):k@$X=�!�$P=Q_0$iou"ily finds �a`.�  span�b)-e"���9�1�A9 *!�! ��i"fg_1=Y� !i)&@w &G�81[Rh�P� &M RJ)8!"i A0})� )p>G2WdefectF�b�-J�=�i��9 \�Q� jk} 6TX^6d&.B�~6� �B �De eL�*$�;f�+�Vp=0/I�1F�d(��)*�AU,�>�� .�*�ak�.d"�E�g(afs� e�_2�GtE^$�i*� an" "l;ale6�$]��f� � j�!A�&� YDF� a�"z � >~ � *\'0volW*upa)a m�<qp%nonzer 0%H.ehyifi[$!hiO,.�>^ygAw}kauD4 ��c\a2f�`ab. A ted�Wal=l' �[V_ytZ�"4? Z=Z^�%�:�U�F�(F�Z^ja�m'K[�6`!qQ{}m[j}��� {k]}&as"M9ZjB06F�.SR= �� �,mX^k-R^k_{\ BX^n�CLie�Bzin� 'ic�+ conn_�* *� A�.�� .��a>�q��B# i)]b�(�*�X6 $\�U aff}�-%_-0{.��6ffine2��O �- 9.��g�!2N�]Z�,���H>�*_3$J��M blenj6$Z�4iBD e� Xb�ic9x�At��.�Ynka�-}Zj��T_k��0) I�� - z>= 0O���.Fj}=( Vj)��#' i�c��S42\delta^j_{(i} k �%�_{m)}� + " /V�)IS VkV'jy�)^0�T Summ� �0 $i=j� n�Bts �2nQm���4"%m" (n+1�� ^{.Q -?{m.�i�i2%e>(m{% = 0,���$n=\dimh�$�9_{i�A�� �.��G� i\va 9� 1_ji�-"J~$ $�f:3 "� ]�%�>�of2 m$I :� . (N�3%�if~$MP' ac �4b.'ary���^�0J}& -�'.Fs.) `picuousxHB��>�s�Nbe=U �.� a ra�  s+-E�.:$"y6=!&�-�"� 2�w�9U AMt9&&�to�I�82u�o sole2t!U(GL(n,\bR)\l:.!Gn�=v>�E2s�=�&.�� ow�BV niqun&�"�wh{H�. �2�-�q� devi�6��cu�9>��>��um &B=� QStaeckel���mh�ge�klB�24S: � � })+s-DN%�\-tak8d4Benenti, Chanu�0Rastelli�) R1,BCR2}.&F=��e,)�Av�e�| .��2 .c"� ^� ,� A.$)s��� �-)� }. De"�70I_i=I_{2,i}+I�0i}�7$i$-th=o��e�5�it�L6L\~��1�6�$N�indicesS%m$��fe�%�f"dwN] �pecs ! .� $\xiZApply� ��@�, =Q_1Ŧ $P_21 ��%j�D*, &�I}_*6 I}_j"2 %T&9"I}j?"&g"li},j} � \^�$B_>0B�(�F   � �potnot"c!}!��IL6?w� !c�Wre�C%�2�R�yd�&�$�! . M8m��[*KD�A stem� D*�^�"2-,~�#*gm $H_"BHB� �@*\K�*G �levels.�a new +�*�nl+U2p+Utn ��(�?�j/!s $84;) l)jji�`l"nma]P&8L �2�.�!� F)�w��"\to� i�fM)Q1proQ1q�A"��2 mn�"�&-��D ��~!!+�% /  @$I9iKcb^]�@���YjDn(2e� ��al�:mpo�����.�*!T](m�fa&'��0. #!?2"=�* As a"�G�Xrk, l�I�AMa�� �&�T}%H5 ), ne�^TJb"�+ian. So�+iJ�[:ai[c{��f}{A^i�a}Gaa (0eta_a(\theta^�[5� ��=9�-�;=dx^a/\s�W�>{}A^a_1 })_r"ns&9�8on8 mo�D cofr�8�v!�signa4 �\rg� g�'$ �=� /}(}) -%>'a $(e_a=^�\p{$ al_aF��]K .� �E^:�)K ��Q= �>$�- to rais�Ml�t X.:.DE&zsfix����d M�*a' $\�G $ sV.;&� 1� $dQ + 5^a�b�q b!!�ew=%cu/n� y. OqH$.$ Y=d6i2xcx�^c �O s�ed�R�K �.�by�?�v�{}R ,cd}\, �cgY d-� $aQ�d�:un�)$1$�8M]!A>�[ summ%�!��/oW�B�t$no ambigu� arises. � �by $R�!�/� lG �1B �B-$ &$.�= �$,:b@\,e_b^ie_c^je_d^kG�offi�.u-�:�A %�0of9 �6�cZF. Strax forward�ut%[, (( ��uid��)a$enň�non-va 8!lJ�"� �q�a�,agX�[b\,C^a_b���|A^b_1\F2|^{3/2}}�1 RBy�i b,\` kc}=}(e_c�X$$e�oMnonj,.�m��b� re&� "�FZP�U!5,GNength 6�,%j ���B9wa.p V �R* Dcourbure} R_{ac,cbS3%'( -%Ba� ca,ca�.j $bcb2$ ba,b�i!�c$6H3)1e1tF��z�Ob� e|�Lse�%"wo la�H gred�HsR !Hq)��A��96cvar� objects. ady��9:W,$v �(��. j}�js� Q$).�Rei�`F^{b!ne!\�{}e_cm�&�f� Q!n b"�0>�� �}�bc}=p_b �Xbc}1yp_b�#AL^b}{2B{}Fb . Q�=qFIq.Ij^I�� REF�.!y�.3< \[ {\cal D}_c PaZ}=e_c( $)-\om^s_{~A~P_{sb}A�'s�]���]As��aa�i� -V��Einow^s� 3eq}'larray}{rcll} e_b(p_a)&=&2\om�,_naGa p_ai�b!�),&e- {}b, 7e_a@0,&iD a �}E !R repe I�R�� �'dver:R.�A�y^%true ��S".wal$p_a$��na��.}�+=#St= .2"�l���p^$ino�;��( Xq� 6� q�piU}6�1��$B�^1 Q}.$\E�suc"0%A��s)x{leus[is\neI8t Q^{j]t}- (P\ �{Ła�88\ Q)\ =\\[4mm] 2Ypp 0l\neq{}i,j}(4E-li,l} j,l}-3E8li "ij,i} 2#j #; j[�?eft[\�/<{0mm}{4mm}p_iq_jI�lpdq�A�lqp_j -(i:� j)�m]I�), \])2%D)$s.$t9<-4s��y l���R;��F��.� Comb"�J.e�&,v iI��r)� get�bu2)�,";b3^N \hsn${4cm} � -X%� ,:l,l�!� E vT�%)!`�+.a�ute!6P�i}Ra@}_{~u,vs�;uv}+("66���U�m leav3s� �<�� ie>6�]+n,^y�M]?BcU=(�2p_jq_i�71�!���� sum�j>��9E6��� $�$�rtA�g ,$ s�at���"!� >? q�^�cunu4���zZz=V��H9D]�!B�o7i�!P,Q}=-2Q%_�͗,8%An�8y22BE ?�+KE� &�2 bnd> ,oof�B�q j� A$$ Now!���"KXl �WX  analysis:A9Jt +� �6�?� answe�B^ �A$"}"�&cor}(>x) A�2�t�iv iffF�aD j}=0�0\mbox{for}\ i j,���,.c�5�RicDia�o!`Y.I "@_U /II c.kituG%�()� ! �-��� mas - Vdiagonal�2F�%x&�&F |�j!�s-�_��{&�{ �,�j"r&�.1%rxkno&9rRoN]e�6)�HPRob},�;!�rpreted+ Eisenhart�8,LPEis}. Quit�LA�p� et al VBCR1}��r��+ht*� separahZSchr\"o�#er"� ��e�!)x9a)��ZR�!�&�^suffico� %� �� . As*5F in RemarkRmkPars}-*!eg�h�5�'!&N�H>�-Jacobi5; 2it�>�sQgs��ab�6 an1%�q�A�ram:d`%\vk 2mm} \[i�"xe6�}\�\Longx & � �leB�}n�BqDow�Dow�M F% ded} �r uad(�f)RQ��ᬍ� ilit��2��O�6!w*:Re"��A�YzM�8  DQE' "�/"�:GX�!uee�E<�6|i jV�<8"sub.O inclua�Ipo�ɻin"�M�ianI�=�<�N. &h| ��s~�k� A�(� ian)z ����MeS35^�oVq 2Ua; �  M��N}{x^i} � {s�i}! 1{x^s�rgd(�eMBN} Na_0�; a_nX1 x^n ]���:6�N9��al�+$y emphasiz\? he occurr*�Yan ���1�!�rrelevan�mS�.)XY�doO �t&��Ts�$.�>�!�"hc� �8�2 �L:m gS u~Q�qo)=��q_S^nH"^ 9�)�ccJI3=Q�]<(n-1)UrpN����5��?��V�gD&A6�V~!QKNS}�l� %�:�&fM &� o*]"i�pq� �pvn st2.9j[c�f s-�inQ ���Ȕ6��!VNs�) ex�gEj$&�$m:�r}&�$P}}]$��aZ s du_ Efa�%0Acon6W&Z�$JS�nd2T}$E�~6!Z  "�u6�* )�a} &aF� "�)��@E�$A�JH_2� 1 �� 2,H_1}$�!]&�@.Po�` $H_2�Fpo$�@_1>: A_j hH27P@�.��Zkq�MWA1}) "=Pv%�e�A$cause, cf.��Ca$vA%4y�\�j�-O! =^�FE�c!�qu��"y�-�)w;.��A:���-)�.�Q>�E�1�� $FDmp (EsiKV.Gstress-�gyBU ��)9.!�2Gin2�U�"�_w[he two�>�I�p:n)� t.�-aM&�_A�/.!�zaeHj(t3 }A_k%1�a�g`on����}�,s&G-("r.b^ol^��!aeFshoAVIDneR�Sȉ�|l> �!�~�!�$68u�b�Orri��do  mnt�\k24GHY,KL,SY} deaLHI $560�&�~s���_tases,bg f}']�ex/Ec�1$3$��m�)��!J �fc"Q�be�(#*� ��se��a� Q�ab � argu��I~h��ly justA� well!�su�K�j2��is��-n :�!�  A  Lapl�m9_:xJ2�N�� %%f� M>;x:DMC�C� �x�o too)�%GXis��./"!Qe� gle�to�?�e�ADBKis)�!_�n���H�� P}],�h26�kRc�~��:Hْ$Z�L .$ �Y����A�"iN�4th.�G��-�1.��DV�ui "�sAJ� �)]>� "�hI"&�m2ki:A2� �;/�� th�[)��*� :' !�Vh�HH�y4��cly�o"E *�t5(� "u| $T�{$ cN2St./ :�ne�(6�$JC 1{}x�� xi_2 �\f �t,\gn+�� �t"ktA*ql.)H��v� $p� x� J}$�%mt\)H� .`k) �01"�P ����s4 )�>�P}�H}]#7!��� ����@t%�" r:�, ���W�P%�{1|B�WH�X\,\_*jR(k %\Z-:*'X�>�0nC�#Aw�Ds %(M]6� ca${}^-+TM}$)*�I�a� �NY�3}{16�fA�c'�x�F��v2�x^3} ( �1\g-�ɂ'3P"&&+\;b3112VH2:X3 � h*΋g&�~�=e $(H,P,T)UHisI!2��^�T$- %3"C EY>6.&�sA�A��` wJw` � ��as�;gK\ i�wm3UvK:V��� `5^ /0z�"K!s �`� �*��.�� "fxDiscu'6�RoutHH� ChCo�G6�-w� j"w9�gwhi3pvPWj7)o�T\c��h�h,�h Bor}e�a de�0�ccounth9t2�)�m�4� �-& K&/?�$G"�0SL}�>�; QQ^1:,$O}(p+1,q+1+^�(�  :�^T�2rn�;de�i99}. �cin�=wQ���jjxx_{�!}j (" j$� ��'.HY�l&� �DijaL< LD} *� ;;-�,s F���CtG.!*~� } \c�(P$w�[P}�Z� _3\,mi uij})+ "4\,\rg(/2�C25 'C[5\,�_ O 6\,RHij m!Q2QBi!��F�*�\J��=$ai\�K'a���ourPha>6:) e"9 > ���_,X.��$) 3=-n/(4a')A� 4 (n+2 5=n^25-26:6=-2(n^2-4) #�t�$"|C>2$�� )g) we�-b�1�1*n�9� � E� 4 /�h c-1.H"�* o%�)�H� m����� ia�2�"1�� $R�V". �u�u%�1�F3�W]C�Ex�b�z�J�6� �&D� d5e�Y6�2�� Ś� � F &���B"i% zHY�Pi2X  $[.I_i),6$j)]$, fail�m�!� $�{}.M#$. Had w;r�!"G^,.�-e-��Vad!��y coe3!9P�+3�4 6 � quird%!�%� 6A�mu%*� �A�6|se[=OX= [. �L, us ���� %�M?� Ց Desp�"th ni.�YX@er[8��2!~�E\y/ (%I&[pntum),�b� � �� :�D ho*H�CJ\.Satխɑ?֓ag 7)��Sson� ru[ 7vg{b�waa(� �FF ic na9�/qu���2s���5�una�6o�D!WnuKb"u -�� "�D chalV4e�f�KNhm�A�vX �np��E�8 �AP2&Em~ beBful��A�21Zb�F�Thig#��A!L�1 (.�wTc2�of� ��! �0�aI�l�DM} '�mI?:� . A�*e�Z� appl�} ye.�co�*R��u&�(i<�y:���1*-�� ��w� uq �U �DWly�DEAn%`� yCGLP,VSP2S�a �per�CM %�fu�: work&� � ?E�;�p�1ᎁ�\ oi��+�"���ul��6]�)n�an��ect>ɖ-a a� gaug�I�t �In.%b� approa�[re��EF6ML�M,}� -�p�'�6R�*-�mE��M Sc~Ien"�t�A��[�=�0thebibli`�phy}{99�2�2 \bib<�${BBT} O. B&on, D. B�y rd, M. Ta {\em I�aE�to "��( le S�$s}, CambriۏUE��4P� (2003�M� T} M|lq2{ it S�ruZ5Uum"`#problem�$e�Xtt{arXiv:hep-th/0407005a�ren} Ss�Ai�$it Inertia� �<dF+*a$�&��(�)Rend. Se_Eat.�. Pol�rprino {\bf 50} (1992) 315--3415�+.� C. CI�G."I ��$�J�&3< betweԟh��ve �%�mA�(* S� =:�VFC2�(�2a. I��e�plete�� Nx$}, J.C. Phys.)143}E802) 5183--5222:32�3�3�3=3 I. Fb� ��lI�"�]�122%15321oritM���MJSur l'&� d'un� ���d'ordyH� l�"�{�, te}�8math.DG/0208171a�Y�ou)�,ouarroudj, {a�PYlj|map},=5tJ;51}:4E=(0) 265--274. ME��Cariglia- O(um Mechanic7���s:��u+in�>ed��<}, C�/a�� GravM�21I�04) 1051--1078.��"1} B.�6 %>�aM6~i����!�O 's�AA �6;iw 10} ��,68) 280--310�$9� Car2F�B" �h(ilibrium stc1}!("s/L�#*lus (Ec�Od'\'et\'�� Th\'eor , <0Houches, 1972; @pp. 57--214. Gord�nd Brfd, New Y� (197�� 6�3F��-��um �ui� e�Mc�*t�+"QA��Rev. D� 16� 77) 339�2�f } Z. W� ong,�HW. Gibbons, H. L\"u�(N�ppeM+S.(1!�Tem� N��,#Hp DT A6 ^n5066�CFH)Q0ordani, L. Fe!� r, P�rv\'athy �"�YO}(4,2��*A�mZ5Te Kaluza-Klein monopol=iLe�B%j20aq41988) 481--486.oTDM} H. R. Dullin, V. Se veev �A2 "d "% w�(sp21}, . Rp$ �mT1aT20a�7��7222T- C�v'4(V. Ovsienko �Co�=lNum�ia!� S�'a�U(N.S.) � 7}:3�(1) 291--3202O2v���AwT��Eus: non=�hyper&5"k�}a�!�)Ni=%�57}:1 � 61--672�LO.�$P. Lecomte%ծRk : ����}, An�nst�urier�� 49}:6�i499) 1999--2029.�L!5 L.�">5, ��m�Uh��"�4�R}of-#%35}:2v34��4--305.tGHY} G�S�F S. A� rtno &Y. Yasud �8 e�( five2���a a�ic!�� 4697--4732GRB�P.J. Ru�m �)hiddenAdw �2& �om:�%1115���267!0:�vHB�R.�zRietdijk� W.� Holte"S USY�� ky}, Nucl6� 0493) 42.�HW} J%�nad�.W rnitz-%bx�E�*1]9G�#$.�!��^,F>��i� Ho��V� �Q82�QU1S�J.-M.~S au!�e�\-�Qdes�\`e�� }, DunodA�70+�opy< 1969);�SJof�Zm�ha�ld7c V>�Ap��"�nd�DC.H.~Cushman-de Vr:(R AC8G.M.~Tuynman, T�uA-0on Editors), 2�ad7�5TotA�AthQ�V��um -��9a��eb��aO�]!* J. Fb�. AY130 1�� 2�� G.Va1>!�i��]�l�tusI�a �the�L 24�� 571--592�VSPE�Vasud�9,A`Qev̠D.�agR�Z�!�-�E�}�>A�!�S����lass.�..�2�5�-36cWei� Weiger"� T�C��1��(%i},ica D56!�E82 �#1ž�">? �Adoc2Ⱥ L\ [12pt]{cVc�� \u�x4ckage{graphicxNk&\topmargin 0.5cm \def\beqݻ6|�*�qe�> to{\n U1xb{&��x}trenew and{\baser�tch}{1.5&b��title�-p�T��a*��imL/ed� turbTmmetho�nonkar oscili�s } \a��{Paolo�(s]�nd Alfredo Raya \\ %EndAName Facultad de Ciencias, Un�nsid olima,:oDl D\'{\i}az del Ca�o 340, .Mexico \�dFrancisco M. Fern\'{a}ndez]�$INIFTA (Co� t,UNLP)� E.��8 y 64 S/N, Sucu�� 4,�!�| o 169(1900 La Pla6 A��tinol make%���%�ab ;ct}v#kuT���l7.�j)��p^�p the Ia� ��periom5��mem�!�#! Lindzf t--Pe�,ar\'{e} techh( illu���'h��� one-2�anharm!a QGo�Van��Pol" . Our~* ultsw�"�3Ti65+��T#w/��fmodel }ide���F9x&�,dK sec:�}�r-`!N}�;A�Y�ve .-re=[�secg��%Bs` !?!0W* �2�ti Z9�Ԕ/) {N81}.ӣ�bH��� (LPT)H,F00},N8�Ñ#bym�\�@{�F.}:$AA03,AL04, b,AM�b�� �a�ta%an%a�� cipl!� u$��itz  (PMS �{S81}�&#"�Y!ELPLDE-�.1��!lso"} q0IM�m� AT �{M70} "weQ��.��ZA%[�$�Con�{&c�9IlI�{p�a�%5o�\���esd4�%i��|%rބ�s 1 c"�Xe�I� .pAec:LP}�&briefly p!eave L5N8I"!��.)vE�Vk)Se.iA j 80in�*!- G %7alg!�!�c� DlHng�S A�}�9anR�[� �5�O�G_AO%a�x �Q��t�< V�\�@\VD)X Ww� �5�.VF�t`g=�R)��I% f�$�Y� Ӏ�("5*a';�io�&I Aށ��"�%���eS�R#!�� y P.4T�4�8EE��s� a�si<ane�@e"c� �trayYor�.��y�&��T2< K`�~r� c�K�A�ɱ7QNaN�JN ��� �0��*�5�} �50d^{2}x(t)}{dt }+H=-\mu x^{3}(t)\ , ̓eq: �F.S���K�[} s $x(0)=1xA |x} oe9 �� �aaL2Œ-~�m�" �w. >�]A��&,2���Eq.:*�)���g`Iroxim�FB!��� ^au $--%�ƦA�$% %U\ V{n=0}^{r� }x_{n%dmu ^{�b�����miA ll--�M&��"���6�+]1v_)son�G���+ aftEPWa}��e��non� i6��b�@_(� Such Y�unWoU&�+-�f2�D5K$!#!� 偃be!�io}�4�vE >-1$e8ɩ�} %!�9�ve ]f_qat���/�CT} �s< ��%%�$ / :j@e��om 6[ 5�}e�a�!!mio) Liz� �.�+^�h�}D �jy!ni ?caNn��Q9&. a %"di( E$�� = t$�� /$u!-e��c(%��.Z :�o'-} b�� \ddot{X}(|)+X ��X�� J[T $2\ , x // d*Ldot�Ce )s�  �on ��*.,) .H��Li'!QwA� *�k �f�! �W���7��1�! ���S_e $% ,r?Ro\a�� �u��r\;hL)/ )R:X4)A);�9�%0$g0}=�onCbI%l7]c<} 1�v+.� &=&-�d #K�P[ �dj�d n-1} ˈ-j�ݻ tau )X_{k�^-1-j-  \. \ "5��&&n. G�j0i{n9^jU� _{n-o\]:Nn�0,1,2^1.mLP_PT�k1m5$-Eh�HeaviS"��Jf�y*Q6$5��|in �o5�z�9 �9 3�(�a9�=���iic,�-�g��1F�.CM�-�A�u is expe�be valid)wI|�|<KT�1�%&� limit��ofQT���v1ns9�W2�� �b� � ) sub.S{T�Z�"� A��Lin�Delta E� }�Nu� 1PT,F}.��B 5o}p�c@`) ���arB7 (LDE�P�!Q�b>%Re��A lik �on�*S��"�ago!Fa ren�<?O 2Tseq in"��� K81} w7e�Sg��sui�6!��treat�ma w0?X!et` �.s � $F00,AFC90}�v�J� �x!� F .%w�j�o"� 68 N;�i�J� ť( 1+\l��LɄ) o ��)[ 2� 25- 9cy�ы cŌa%&5�"��A�$\~ )n E�--?� .. Wa�w�.t7{l!FA1%3c5e��%� �82| � A�*� !�$�. FEL�Afdi�xb,gI�E�AX!�AFU�B�<�T +(6�)� :� !� .� 2�5-� .>� Nex]`�dz ����Bs 1���7edj����dg5!qC^�"�,S�żi�s-eU�&�Q 2�lo\ ing 2A-Eof�!oor�9�V 1���_Nt f�Fz z }�� _{0}ſ�� V� ;:: �F� .OX�� -M� !�v -1Q�Q9U no+-� "� �;QW1;Aa+& vo y�LP0 ).�K�� J*� =�� ��9�e��&��FR. �J.� I, s�&ng�t� %Y/� m.N Z  !l}{128>�}+%��(( -4-�<)= >=VJI W>�&��! optim�� alueaarbitr{���a,᩵�$%pAmbd��"�?=."�=BT`JEeOd9LN)}}{d�}=0\;Qm1y���: ��_{PMS}^{C��a6�e2E~�y�NN� J���l3)�[\�v%�}�K>�q# � &� ��!:J)oJl)969Q[ +192 +x {32IC+4)Z7;a�[�@*\� �^�--� --� --"� �L � W�O�[1�noa�:&! pr.ScQ� !2S @ .$on.ALP} A*�^y"U }�rD�����A� .����="� 6}a� M7��k��j�\��( m(a�-�n|O� ��!d�u� > "�F� %���D�Ra !���V�.>$ :Y M�R����veV�l ��y��lI�� �2� �!!_�+x_+t)x'"#t�+. ��.+F�2�E*� �Th�Mj>M ��t�b*�� fulfjs'�A���Fs#B��!R��)�tB� Solua�>a�Sa6���D&�$�ۡ��~k�T2<K�� �;�B�E�,(��j�;ytn� �� 8AG� ͸-E�~�q�1!s��6d!� ��Y&5i ?P�"�F�-yC&�a�bxB8}% +03�F����i�� V2}+96a+64}+ݓ{16n�earlier�%M�A�I��Z &3  A&8Po�bs:3.�i ����*� }Ede^k 'plF> V(x)-1TxAh$!/ }{2NN�\;N=2,3:z 2 (GA�.H+�F�)��D2@�&2NB; tfeq:!OnP+:d����s�t��!4��1?eL�f�'as�"QT�����Dtic�$w!)h $N=2F��� >)h2M �i���F� . HSw �V�!A�s�3�x 4$d#�0dX-� 6�b��dd#Hr��� � al� r>�V,���"sR�2�Nz~B|a&��"TF�RpZs�qB�R "�"�IN�":t�H!�N�е!k� *_w&�2x(VdP)��F v��\ [1-�,(t)]\ 2a�G!"��eq:vdpB�b�b� beha�� ��&Xomp�Aly �r�G1&�SR�"s>&  VdP� exh�DspKj cyc:�nd�� �)iokR]"a ��it K��s,*�H��� �<w� , unnZ&%%2� does� �V ��iaY :>l*�Wa AdU]��erm ei�% dampT� ho+�k�� �8�Ax}iA�$x��^���� {S ��Sy0#��De�U� �A);w*a��ands[�+$��ALP&�(B�� .V We � Ip2U"�A�)!7B�Ji��%�x��B5�&5�P A u>�]�L�hH\N�I�a&�< d"� $ (�Pea }V$�*�% Xb���66$*+ A� ks \ xR9�o).:6� exp_!�>�a���v�6:��� 1�� �+.�� �ކimu"�h �J � ot{xi�5b) *:��R� P-\mu \sum_{i=0}^{n-1} j-i kt-j}\alpha _{i}x_{j}(\tau )x_{k \dot{x}_V-i-j-�Rright] . \end{eqnarray} The general form of the solutions is \begin{equation} x_{n} �=2�`}\left[ c_{nj}\cos (2j+1)�+d  sin �\ ,�u j,that satisfy�4initial condit� Z�$0)=A_{n}\ ,\ 9#}!H0 \label{eq:bcvdp}>�8for $n\geq 1$. !1Xappropriate choice of $)� t$ and $���-1}$ enables us to remove all resonant terms at order $n$. \subsection{The ALPT} Proceeding as in the case of the anharmonic oscillators we substitute the expansion for the frequency $\Omega ^{2}$ into the VdP equa!|� obtain9�Q[$\frac{d^{2A� n}(t)}{dt}+\Om\x!1H(t) &=&\theta (n-1)IJ!m_{j=1a.m a8-j:+ k1i}IWD. \nonumber \\ &&Y. -M� _{1}qjmz j_{2-"o (t)\a% 2� 02�]Q]1$ANz!�is casej�tR�\{.�[ms){t].�>)<\}a�}$_xB �� (\refyc). ��H $:H2G secular JB, As before, A�,coefficients:��� expme�)+A�($ in powers w!�e�ll �sFva�0ional paramet��\lambda� PMS}$ cal!�tedDthird F. Fig.~I60fig1}) shows !5error ov �fr��, definN!�4Delta \equiv |)� _{exact}-E�x}|$, %� func�!'$)�(�80$) produced by.��rough � $20$%V bothI�aches.!�observeI*�)P�technique, which yields much more accur�v1�tha)� stra��Lforward LPT, is less7/!�. A simia<8behavior can be�dA�:�a})�erer�} plot!��C-1 \leq !V 0$A\Tterestingly, close to !t =-1$j! $correspond�AaA���!�(unst�a) !�libriumi�)[,method perfo�hbetA�6 S-concluaP�y%drawn!!���of anVhith gread$$N$. Figs.�fig2})e|U�3M�^^��I.��o0of I�im: %tqu�`c (m� ), sextic}oc N� �!� =1� 00$,Ap�� vely��sit� !� different>1�nonconaative V*Q becauAh� exhibit�C%R!�Pvergence rate, but itq.a wrong �% � >\simeq 2UXsugges^6��]oaZ(is couplinga��. O,e other hand.mm�rea� ble!0��L any valu4 �G,!ځ�Ea6p4}�.OurE�A�-(I�!}6*a|.o systems%6fails#>� onese}le,) B� i[b�!���a.$s. At presAwe are u a�expla�e�ur%U�>��andQbeliev��%i!)bject deAmes fur%�inv�tge*�hb� ,figure}[tbp]� ce�� } \i�Xdegraphics[width=9cm]{d�5_high_e� .eps) Acap�Z{EZ�Aa2�A�$. } ��� B � � � �2���,%�V�2�a>����C_mu_1�� �A�C ��j tak�!��$A����poten� s6�2��b�00����0���3��:�Fig_5n�Period%�he Van  Pol*^~.�4>�%M�(acknowledgmZ } {\bf Ae  P.A. -e��pport�$Conacyt grDno. C01-40633/A-1. >nd A.R2G sF�0Alvarez-Buyll�S�$University slima. %� ��] thebiblio�� y}{99} \b�|em{N81} A. H. Nayfeh, \emph{Int. ���Perturb�w T� �s} (John Wiley \& Sons, New York, 1981)�� s`F00} F. M. Fern\'{a}ndez�zheory��Q8H. Montes LamasbW 27}, 158 W46W A03bA| ��0A��lit{Preprint} math-ph/0303052.yAM6�M�>�(3!K),g% Ni10060.iSEUP%�Stevens!�)VRev. D Sbf{23!T916 (1>*M7A*J. MariBI�@Classical DynamicP/ �!�S) }, Sen4 ed. (Academic6�76K�J. Kil; beck, �A� 14}, 1005�6E AFC9�G.)�teca,V��E'CastroqLarge" p.}ti8sum3 C � qmmu (SAXger, Berlin, Heidelberg. Lond!j�Paris, Tokyo, Hong Kong, Barcelona, 1996� BK:97} M�� Blenco. i]P. Kor� U�egEB} (bf{56} 9422!V972JPW:0��H.!LJ� P.�ki�D. Wind�RahDh6Az125013ez6�KPR:02} !� L. Kneur,�B. Pinto%�(R. O. Ramosy&u$ Az0-mat/0207295.��� KPR2�b� %9��} �,bf{89} 21040 �2). !�$r�MP:96} A�KreA*D%�Meneze�M.5��� B�370} e#962�PR:99I.�T]I+D\ % 60} 105m�992blde��,Okopi\'{n}sk��\N\��35a�83�(87); A. DunWA�M��she�*\)|\ B)c��1C35E�88)�>�� � docu�$} �%% * StaW@file template.aps"% %  T0 +is��LPS�~ pacs6A(ke PACS cod���23keyF3keywords-%�\q�cz[aps,�5 ,g!�ed-� ,ams� 8symb]{revtex4} ^K1a�J8 % \usepackage{� ic� �}2+d)�$}% Align t� sA�0decimal point2; bm}% boldg ( % MATH -� H \newcommand{\h}{\!Dcal{H}!9.sSBAABJJBMMBWWBXXBLom L}} 2�bx  bf{xByyBzzBuuBvvBwwBnnBppBqqBkkBrrBttBaaBbbBccBeeBfffBSA�6 PPB:DD}}�.iQe rm{iFa% hati^bf!:�a%.$b}F$!.$cJ$d}{2$dJ$!D.HeJ$!J.$fJ$�.$sJ$A�.$nJ$!@.$mJ$a�.$xJ$a�.$yJ$a�.$zJ$aL.$pJ$aS.$qJ$aZ.$kJ$aa.$rJ$ah.$t$6�ri!��� rm{R>;eurm{ :in� >iB]ou�  �.aQ NQ N�1� N�1� N�1� N�1� J�h�!P N�1� N�1� N�1� J�h�ta}�.>h�B hq� B h!�6dF��&� {g%A42w abet$ >agamm$ B%epsilo1�{\F)p B!xi�xiFm�Y� {\muFnn6�r�rangle:�ll 65intek}{  @ \tilde{d} \, \bk:G,pZ,''.�,qZ,q>_ �~t}>&>ytw>&Bsv1�{\bm 5�6v75�(:+%�#xiB eH .#va� bm y>0a� bm z>%�bm ~2I�� bm t>1A� bm n>� bm >'v� bm f>0A�bm B�j �j>0�Fbm >@v��bm >�v�� bm q>HA�bm  2��P bm b>0�M bm c>��bm �2HaP bm u>0� bm v>� bm w} %6I�Nsig�mA& 6DT�a͆TB� iiaO � 2�jjj>yke� no)+A)-see ncolaped)�@=�$u$  not easy k findPigDterature. We assum!�atreader sl y <eE abou *^�. All|()d�#d �(�(fou�follow�*��:ysmally�e(P+8% \item[[ 1]]� W. Schmie#``I�-� FQ� '', � Opt.��.  59� 7-30�6x.l2]] S.o$Cloude, ``�EGy !�polfE� q0 xOptik m75m6-3#Ek�3]] K�m,�Mandel,cE��lf� ``Rm shipu JE--�A<ric� om medi�= � 433-437�8��1}4JCo*�A�q�Ajlisabil� matrix �=�W�)Cmetry'',A�#P%[z%[�!K-s��#!bD* II},!�$A. Chipman4, �1I:Photo-�,Instrum. EngM01166}, 177-18G>5J Lie�Ea�romagne�) Wave{ ropa�&%�Sca+ing�JR ofRA�AuApplic) )��947-974!�92)� ]a6]]G�A\so �$R. BarakatMcN�ms]'�/tŏ)�aa2qx��be�#iv�Nfrom aI�/I�.!�)� M�11a'305-2319�4�k.�6% D"�*���3e &%�~s�-��s icul recogniz�+e s6��F( on4Z+pa�.�nz p*�[< ried!simplif)Oun a(� by ad7ng�) �4seems (at leas� us)Pb ��-  the iw s (ei�g�um m�s)A_problem�$ example, ��`��he awk�. ``�cal''$E�a��Pauli)�c �-��%e^6X) i1} � _1 = &pI,P} 1 & 0 \\ 0 & -1)�" , \qquad E2RE:1 EPvD3bD -\im G & FI� g-% ,-weI"._st�$r!`-�=`^(e1I2.IFHv�7�H~ 6IVM%�)J�>�� �:I Of course�-a��s�2e I�is8, als=7*&3s"�2�,"� c �@��a1� .one. If�$� Tbf{E} = X \vx + Y \vy$!�denot&-e ^ ric fh2�\an homogeneous plane wav��: ng a4�axik3vz$/n�; our} �� 5/)8{ S_0, S_1, S_2 3 \.9r��f�3Yp5~Qb6"� �:{lc a�S_!�4= & |X|^2 + |Y&I  S_0^%&rm{BW}J H} ,e�S_A&Q4 X Y^* + X^*Y 4U  S_2JS2H}S26 \im( X- X ) & o-V & -S_3.\ �2�3 6)-2Q S_1JQ2H�ՁH)fI�5� % wj Al�hre���� spla!e tra�alK50{I,Q,U,V \}$)E5H ``Born-Wolf''\footA��?)[1]{M. -, E. 1*;$rincip�'of cs}, 7th� 0(Cambridge Un"+�)l*99).}� :*,::,:�,:� �4 !*``v|, Hulstv� 2]{H. C. .3�L�5*� �!S� �&ti�(}, (D� Pub"� , Inc.,B]+J�H�Y*Y�Y�H}a�) �7� ��� >@4 It curi�vto��U=J9t�Ian�(f "�w�7Cs�3�6!k(sixties [1]�2ia# s un��.]�B�T; LCartesian coordinate{2� m0Poincar\'e spe(�3 1)g��(�? #�=^1]6 M M �we wri�= m� vectors}\��E� hB�� a��"X ��� 7} \vec{S�}FS_{0}�sS w= 2 0"^ �� Y��Hjd.%�� oN2R3.��� � %� n,�Eq�7 i6})Axis(toT E�$ �$!u �$uk:�:(mph{unitary�-rix $Q$,j�8.�Q wiu ��.���jU 9} QR� �,� !x & 2&:&W � )b1q. .�(Now, let usy �<a6! b �6 crib� two &] q��=j�105L_>= = M1Yin}Q�q5.�= MB/in..J ThA~i�D�to "[=n�� b���{rcig2� =Y=2� �Q ���A�Q2 Q^{-1}Jt6  @\vDVG�@]N� B\6<v &Z�I�)$ .�� �=i�hrH 2} M%Q.) �R�is�E�.sb>t�i+be�ourI iof� ��Bq4  �&s imA;be��. p�'Y�� se2-,as possible;�Dula�9_&;� omit��y�s���n��= redu�o MxplicitU�ion2�> y $�1��=s�_3�@nhb��demonted! it m�,be check��N����&�!+�)�c"HowevY03A!1NY}>, easily done�f8�s� mpuo>pr�5m like M&�. As"4 ai)�U focu�)�%.} ��|!qk m, s� ��asI�[�+any%*r��)�� ��*+F �;�-  2lmost ex�?�> d^C�-�q<8dxBminist?or �-�)�e&�Ququire�e&�d?^�amoune:���L�m�AP ral �.6%=e'e :�A�� �A ly extendQS� non-6� ���\*PHNo=�AES�,"����.� �:k�of ind!>: Lat�1Greek� lig4=.  .H $i,j,k, \ldots$ rumJ$0$��$1 �I%MLnc9�$2�!mes 2 $�w$2$-D � . �x\mu, \nY$j�3z�4�4B�42�F,2��Bat�,A8 B. C} , Z, $15z�162�In !Sq�E�Einstein*6 conv�<o�Aus tensew�axsu rep�BE (r)�Hu tood�� &����w 3} a_KA = \LeF_{9%, b_\nu \Lefto2arrow 0�M$\nu =0 }^3^AB�7 �%Eoften!$%Z direc�@0F�*twoY�$A)�$B$, E��y���/ ol ``$\otA�$''b�B4} C =i8 = Bz��1��m� �x�Oduct, �s&]� �(4��"q��(5} c_{ik,jlr a_{ij!�{klF 6It��ths�9?A� �A�+��%des $j-yk�I�B A �T%1N; will ? im�=�=rol�these r�aE on{Ml bases}{�dv�� "�studyE�T�3$N� $2 \E 2:��%O" M t3rCa >~LS1� Basi �Let $A%(a thbb{C}^{�p NH��� 2$ �� lex-�D�1� �_{0>&U�9ra_{10�   end5!) % {e�Q!�Any2�q2�6 be p�Fnh -to-� co�H_FbG� lex �0ɱa}>�4$ ��ing���e2� 9  VV1@}5T2 B��=R2i��Tn�(�a�Z�`!�>�\B��ZO�N6� L>�B62bF� s8ru�@s very�&8 M>� .� $nl nMl��b� finv3m�Pma �n i + j}B�3F���� = 0�, n -Sis�so�)��  rema� ��?��� sh �#�U��``Rule''!aA$�:����:<wht9a :a�Q�&�e2b�L�Xply �$!e �txmp� $M , \;�L==!A rJferred /%�so-�(edj �[ '� bb{R}^4bm n" +y"!�A�b>�&�\\>E +�}J1? F:92b9>PV93~9@ ����A2�2cF�(Analogously2� }) n�&� sF��<$to �un�F)g({cLA��N��ŐJ� +9Z�Sf9a�TR�"� |)*1K 8Z�8�:�\\��Z�h�0 h/ _{(\mu)},��e-1,2,3)6h�%�/4 �B/*� onF| is &\ a|ec"� $B�2zR>�ar���e5�Q0_{(0)} 1$J�%�b�,� =T1.QJR%��R2�R ��)�Q?-�.�3�Q�6QB�5 .�%��Kf ��\}�3w�"* by uv.A �X Eq.�Qe3���=�K�$���-� � u �R� �E` $\"<4q\}�R� to *u| ,��"�.S> a n�[�L� space�!J� ��f 2� u!h % By[  Eq-4}-�W5})!LP&y 2?E � ��(c�+%!e  �.. 3  �v�Bo &�-��"F� * %��scalar�}!�A,Br"". two5 %��$BjjB�"�� \ _ � \d !T0�Trm{Tr}\{A^\dagger B\}   664 j}^* b_{ �  �Av=6F7��=ag�Q6C $�Y�%s Herm�]nD0jug*!� $A$; s=$ = (A^T)^* *)^T�SuB $A^*�A^T the Q�cob!�j"nspLB u�a��. Moreo|si=T$-�^*�Bh) %} !�=1�B5�A�q� s�).` \{B,"a_ B�pc .�qS�.s�D:/�V� 3N^�� ortho�,al ��1�L� :j��b4 ar&`I�Fq,ݍ\nu)}\M� 2�.&^T2q 9Bi%\delt*�r7^�"�e �_s� n�V�� �q�= �}��^T 5��*. 5}). �?Yng ���E%i.06�`� B�A�E�U �0�xaDJ�eI Jk�#v08�685��A9�5(1',Qnu.[:�a�J:N5� Iv8�e $�X~&-��e)�� ɂassoc�aeG�5�2# Bam�2�iͽ4~nE'rn"� (�+�valent) .�\$:�:ei�5��y��inA� ��3})j�9N� = 2!�(� j6}��|:� 9F�[\�]"�lyj�p!F�MI NOA\�M!L��.i��A\�\mu�� 1�>�1� .�  Until n�" a](ft arbitra�7!��`!�\� ) ho�] for � any}J. x� Ifbcy&i�HE�e�6b��< /$.��)} eE.�E0���l�� $[JB]s$ $!8.g)$,�i/V� �N; N�\}$n�10b�GF0b�Q!B=Q"� 1.�TJ+2?.�%� v�10BH� rf,vU��fMewH buil�kI &m� 1e���)B�4�J� S2.6c RcɁ'Wu-�10c��B��#2�Q  %(V�0,V1Z2Z3)\\ % %n (1�0 ) },1F2  %'3  }),fWS FQc 5&�f�!;J�=2�Z\\bvb9j>N��[Z�fq2f�1 J�1�9�N9�.1� 29���u� �L�*�c:910J�- triv�j2}&*� A)�A>mZURux1awu��= (1,0)�"j= (0,$E��#2)�(C1,RE = %#0,1);B�1�Ah6�B�E7EW V�}I�BG=L�G%VGL�G)3-�QQ BG:5NW�U�,K 9 5C �58�16� i>�.M"sFX�wm*Y �Ua oneV*��8��eN2 :��[ 6JJ�>I4�� *+%(�'.%A�S�, m�($#�Z @s ���+�J�@7nstitu )b)o2!id~#tyI ��%J E�e!��%a}alized �]on� 68`d�MmU-�42>z5cc|5l} P)�& 6�$m1}{\sqrtm kU� U�k9.:�}, &&na�n6m�m.n�os oJ�� ��2���qz�8:��bt��� ��>�8[#Z�J�An"� .�e�: �y2�q"$ multip�4;T:�Tb�"1e tab�m }{c|�7� % af�*\\: \h�) 7 c {col1-col�34} ..�?$Q��;�� $ & &s1,I�$*A�:A(: 3)}$)� � �,Y&$5Fo.r1z.1}�B6sG6s�X" �*H-{aI��2���6zz6Ea[2�2�1JuD6uu2D2�:�b%-g�oQ�c0>� "Q�%*�sa�ds��g v��O�): 6})r`�"i��)��r{5�?,aC&22�Q3" ;�1� ��Z$:� -�I���mplete;��E(y���c=2� ��622�]_D$�-�#y%bT2_��way�learned pmHZ9&� ([29 ��n$A' 2�$v6N bI[6L1:U�,] ⁼�DN� <]2�{��*�+1;���'I�B %1b?e I��-,3�m&|Hg:��!�A9 q�A"D. 4$�P1�)I#x $�,�*}jof>A) $]_!S� �  �!:�J�JM$. An N�2e!@ �-u�"H ]L�-�f$x.� J� ��"2�"��A"����>�F�bR)5},1B$!� bL� = ^/RzoK�KkAw�C>�� $\{*`If��v" &&�� �ϝfN�JN�tr.�+!�";%�GRnow��sUa� \"in: � BX��.�B  e$� G� 2A�T3v;�qPWwa�C�#e~f;76�����'-�2�) $X )��C��,ZZm�^)��r��it���IA�&cG2$]B:1,B�8:&>3i�_Q mu},1��2:3 %1\��B: 8�#=91n-,"B�3 B/B�> c�W)� 50!P1B%2:%6:3 <6mF�8 !��2 2� $. F8K.8�>s c[`a>�*u$-th;Pum`i�2��dem(�p&( &�FZ�mAlternLvl� �P�_i��N6�$p &�+: $F��N +j!�B�W-!5o*|A�y�q =2�t�%a�Qy5��8�.QC2O������� BJ^� �2)�  &BE�F+�F>?:�J�B�%.C=wH�;harH8c,?e�)0>`>�0�U ��>)m�6*:� =N�>��G1�!�\\ :�A�2�,18J% B�7a��7"N"he�fyR� !S.M +OB&�7k &� ���� "&G I}_�.���rm �7a�2� :�.I� F)-� o5��at��V�$ b�Ue�l-�F��r��j�g�$ �^� B (u8m�x}^.u8 =m�Z ��!O "-}\##j[ b[ {\*_�B }^*}h #jV VB �> ^*]_bzfJ2"u>K !�&H �R"iE e19}� Dt"%(ten�~Q (ZG�d!~�l�lS;Q��#seekingn20%�i�J�)>��1�_NSB/2�PU� % B�,.(6�3�U�+b 3te�=1� invol�>�v2�F6�)��ZN�U� \}F�*�!a�(y R8 ,N4"�&�(m�V6g>� 2�.�wC� asi�o�+anh���Zr�or pur+ ;�2A�v �2 $erm�s``�=''� e&�96I�9, &�9..| ��m�<"�r �; Q6 ,k,l�  1�?a�tw.@>&�"!F *&i�-� 8� j~2N�S-�Ig2i+j,�V1t� 2k+lr&2J-�0,��\Up�N��� � w} = i k} j l^Sre)�}�20}) z�8��� N��=.�>�F�R .��A$�F�(}��(1obv�!Q �mCIx�v�� VM>!l~$>J+�1saz'U�N�~�&V)66ZM� .d{ _�@�� B&I�>:2Mnu"Jr`-1bx5� FCe�q� �/ �J�5�]&R0. P�� a+>)�Is� &B=x>� � e�&!�-�Y ����� >�%�%�"� �*N�]%-�&�7 � fa.Ab0"�2! D)3� 3[ =^&v "� e*�WuA"M4M6o�Z �ř)}*� 2� =F,]>�F� 4J�  8�(:7*Qf� �sQ ��m!_6Rif $U6�20O tran*Y9KA2�lE:B` = U*$%"-}/.��Sat $U2�a�{� (FI,BU)=N':Y0)f)`�pax�W=sDD $ \�Av})Dd�]$څ�R0ry Euclidean :5  wȇ"rC}^n$je 14x} �tA EA}� {u? ^*} v B/14xF�So��^ZQ/%�o��,!�'A�� J82V%�JNi@a�J�R�"�c� �I��alism rC6�Pdoublet� stocha�J vari�^s�jM4d}+ Z �"{ E� | \6�4dFz� uY ��!h a{yT ��R2�J} �N devi%xv�C4e2��O�Ge � '= TJ�eN�1a$ &�D$- "�D����eT$���dn�@ZL!"�Ein� 6�. We d3Mt `b2 hyp:z?M��e�>"=| can b�c0�Iev_�f $Es[E_1a� E*7 4d})16v4:�cUd �`:Sby"G0 ensemble. St2�m�om.j&&�pco\~7 �} (or �ckc  ) $J2�'Bc3whose "� � 3 ��&4f} J� H= \la E_i E_j^* \rag= � ��N�214f^I$\xo \cdotQ�o6�1? averageB6�]8%is has��hE= o doE%-�Pe�at �H stagf!j�Pcon�H?b��&�a�th%Bct*,df ^as/Nz.*<%k� , $Jr "�9�nonnekdve!�,Y5i�9 semi ?�k� G^(q� x},Ju�x})}�, $\fo�AA%��< 2 $:rg" (ar&�8f}&3 x_i^* I7 x_j\\) FH.$ (Ylx_jAH \la(%)(xE�E_j�:\r2*�T|0�|^2^,.�1jE})>:�0z gb�i,m6�uv �* *%�;^�9!:�4g���� oited� � ET,���M4 . $x_i7; 2��ޏ>e\6Taffec&�+ B�rS���G�Kx, a<�6��� bt�z.h} J = S�5:��|"�GC>�&4h^���J$ k& �>6�J�of%�B����2J�3�\pG�s} �6��. EB=vM84hb)Jr"J Ib+ SOab-WS�a1 +&/Aa�H J hJ 0l%S ulamv��s>r�hc % J:e-�J hJ� whHq"��7.25fy{v�� 2�$la |E_0|^2�m+ ��1 �$IN�R� � w�&Ihd�@�6totalHBensE/M9 beam�� � ng 6�hc�T2�h/ we יtY�%ito� $S_0z|he}Tb%��$IOs-�R/J�  U.SE1:� $AAthe�l2Q �j&��a *SJ'$G�99�!�= )0on*g%vF��('�V!9�ed coA�ncy"z>!��3t�Rbt �c6rP�>5J<Q J'� By:>��.BS'�r�F;xFF PQE�N['�)� j(=��1�Dha�ol"iv� mR� {=OE-R�^* a66[T:�9�7�5i!��+\nvZt.� �>~U�qv6�U?�9��:b���:.Tz�m^�WcyclicNKperty"�0 trac>'.�{A B \}=2 B AV��� . En passYYw?(ya �n�*f��2a$T��6 �T = cL=�}�B�&$$2�  \{�l 5!�} � :Kl})>� z� lV9!}�qk����c�#�^*24mZ6�= ��.uۥDT!Q�6�C_{Cq�z�%�� |BL~�HmV�y�z|[\G��7 �]&�]�5��F�C FA}zilt.! I�A�>j� ei6=b�?"@ &2jC:J��F��B`���4{N�} :�U� =S^�=�!�] !�Ah6�5�uR6vX>�`�\vX�c7��c( Eq"'71a�)two�d"�w�]� perhr�d"e�I� '>V\-. No�m!�rom}"� �gi�fh�2}�M[:�ig9ZI9ݞ� q�E�1}�WF T��9�L :LlJ'#t� ���Y��"�*�1K�q.�.�,I_2��-lPich�Yv�)4l3=M1.F+l�.�T�ieI�``mX\wr��m�M�..x@" #f q � $Hm�xZ.X (3�fnot��f j��|�r symm�|��"�fAii[�izex��t E�it an &�yH���8a goho how.���start�%��!�in&\ vJ2VR#M�` ~` F�! {mn}�np}.�!,]_{pq} T_{qm"�Ş�P 6T_{mq| Fk'mn2t%UF(T �c(T^*)_{nm,pq2��E]�.�%:N� & FvE.�ED _>+2bR${{{QTF�i��{zg 4}$�reu�\9h{e2 #F � ��eT^*B�2V�"�(�s�Z1��(*W����s"[D!�pFV3�$r��� $FPnoty^ , ho:l\q�q:�>� a��$e�a p�al} e x%}I�� ows} �� $Per}[\;]$)5�� #a�wayn�25} H�K.S F] \@}:�g  H_{np,1� = U�F�JZ%�i�s�*��[Eb'I�%2~}:2�25J�6&� iq#fpS $m$� e-�d�iy�a} E ly r� �leOH OF<+*G�m+�g�oי'5r��t�naZ�h$N~f;�, e.g.,.;i-ZiUHM����"�Z;&"u�a�Ca carz��iiw|��@2�Z�P4-lya�viS him�po �  KE�e��``"�U�'��e�}!an&�Q2��be ſ@/��pl^�%�Rz�5�'}�[��O�fbIw&޳d\�CaYw&#1+c d#�eb_ c d#3>b_ c d\\���& ] F�J�b��6�nc�&^#��a�V�`�6�%�V�B� 25J�� e1�1�U!k" a�e�A�th9:4 4>$a&�8 �qA�*q�,.��e advan�!i A<)i�*KS*� e3i� Mt doeW"�Q�2�M�toY$� A�"heb$*�sub��r��,q��6app�G\W�$ oc@k �tq\��is��:|Cmsm�sv?byi0��$}����.�0�$Mj}�=�%fR'39} F��b�5U�� 00}TSQ ^* &� 11>" "E� AT�j6G1% X610" "G1>� %G160G "6Gl G lG."X"6!B.3J�5�t, m& pplyQAu6� �}Oto%�toq�A:n�4�y)�� *? H:o�F] L 7��%�=( 2o)�=� %%o .G9o:�G)�G G i5�[.G %� .G"G6�)CFZByzTeWhT /e*�mJ�!T^*e�� � K& >J%� �!-h7Ah"� r�4J7&� dias^VX� ���b��F&#h}$�k�xj�4 Ys=N))'1�!( !) >*B�40J4w/ is�(e�4$�n2+�t�n�^zR34 WT = h~23�B�4NdU�5"f.�E40e!We��!�e�kS�RU v� 40d} H*��{h"_^*NfdiR�V�-kt�(�2rac O:8v�:.&�vby�b�mE&,���%^!Y�gen�$3V eF$�h_��&U[!�"��2�NE��{GV.2Q>5G"�.~.-2F2�+��5>�3R&J8� �j�+A�u  �.&j42�z��4 �b weNp�inu� �Z $*&CinserD A"� 4b�2�24;* %s f9 4Vs9z-�R�^�j�=�B"!1�>{nm�N.N�JR �utaN�\�v4J!�RI �}+wPa+EUfac N.�NT c�ure&S �}$Vx=.b.D�HZ�Lus��;� F&yOvn+m�% p+q$. But67$>z"��\Lambd�74V�PF� _> �q7 F� �!� 7"�mu�vT �R_{S"�Z�M[>L�!Am�zxJ�oB'n�4}܂:�^�F�J��+���.8e�C1�ip�j��]��l��aO�g:�$is non6 .!�e���iIaCW�im�Da�P)re1� �s4�Er' 4�6.�>RFF� 4J�+�KdE �r>�a�i�(!3 d�r�d�^�L�6�J�dF�I��e�spirit� � �D %.��O!d �23D=~��A � b�v!�� =0 help� .<�z�e>�%_�Fs&�R� .�]L�b%��C�qp�E"� \�U�E mq,nFH���>�nM1�2�Tr"�H (���Z B�)�\JZ 8� b.f �w���_��U� ��� n + � �� m +q � (Y_�q|�5s&� FW B�C2�8�A5�20�hn�23*g��F{ij2�!qEkl}��B��AJ2" \�� �6�6E&� 44e})��S?U��i.tU�jlrksum�y oJu�nu e� j�2V� }�:�)(b�� n�:?�.�]_{ki}^*.- �C E/.��41�m&YDni}"�Fpj"q�+\&rHA ,k lvX2b i �siNs#��:vpR���|F@n�xV}i��=)!V��:5 Gk>sJjl}�K Z�F�!T , k~UR�Vq2 �n8�i )���_{/ bdyxA`m i �B�2J{R>� Q7 ~wl��b �����s��H���J=�,���~��run?j��-�����K"�] the fi+j�S� �k+lRi�,�Ncan rne.�2gSrW29%��ub�2GBJ 2J� inm�� j[30W= �Aw�}^{0,3}.�,�gB]3J~W�l��cC �� T �� \ for &�J�%m%C�31 $C$"�DeDV_ �$s�ar (qu��nM��b�e � a .�a%V� 6�SMf�30b�2lcl�H)�f�[[cE(( !�b( + 3}�7M_{30 ,�� ),\\Y��^Y1} Y31K\im q2Y2kEm,Y�jY� �13}�9L20M_V�1(YOnY�2�L12.Y%�%� w ɗ ��!�r�B]9��f� �6c�:M_{!B!c�)��[0}DNU!� �2�!+~[ -@!g�;!g:[r�)!5 [.[A�;M[%.��B�9�vb M*Y��<�exq-2Fy!rW1A�JU�m D5I.nWA�'-!pIA J�n�A^��%urA���sBp*9��n!Z%!,U]9Z!t.)Y�rV��!�ei!�I FX!nV2X�!XUjC5W �~��!��z�E� �.��&-i��&w�@a��ٵS*39*Y \{H\L 2�00F� 3N:I�4c��&f�-o! = 1$�G 8)|N/$3�M5l���pf only&*��*$M ck'h/�- inc(4]m�B::*-` (�? �0B H8aiM�2*iM . A�At��(�F�i � "a *�2.��:ߎ�"? 6J�Q�+*� � :�O�gU"fiNL/W���z� �T� Al*�='1��0n� !��F�C� & 6pV� n�33}'}*VAd >��sG�Oi�a6�*33F��t�#l���{nxBA<�"1T��!�u c�2�.{ �R*.��NGV0%/M$=F6G�&I5Z-2D EzHJ"��F� �"�5Qn&Kr/5} 6��Y?=2 &�SI%F� J�-B�+mpa�J*�36` :hC3[2pC�s e� ��f i$�,r�(h�6Js�: ��3 $F�p**)��enti�|�GA�y m�be� *-VR:��w�:to�>it. T.�fm're�5�bj 9��TE� A��( ':�A�l$��U"Rtirj-io�, Es2�V E��2�{A��?!t�^J15l�g� i�% ���! %F�.�ka)�?%&e�2>�^T:c&� %�HJ�� �>�!1N�/ZTA�%6..�*-��h��2�c��U��o�J8:�� :�AI�p�!2v63�)�6i#!� =�-J9q�>L u = z��>J�:��&U�6����m�b�%I�AekC�$nge��K1h]��j&B$�p1  :;^!,�"�N�b_{a�Bn59�I� FD��C}7 j,�V�3J6"���Na�7or�2m�F 6h�m��TbJ �rI %�ou�ecificC� T u��� 14}sb�V�"6C=.9d!���!|^22@}z�"h<LaBx"2-B42�%)Joc�.�1h&�>mu}6���FZ&d2�R�� %..1a)6�p" C�^;�b"%*��_.!X��.rJ�E�rir�6=1V�$7}) reveal0\r�h3=�)�FF! J :�bin��ultw}..3�sc��)39to��u^,�$HISC�w ^u4;9 �u�<C�5> H %A���Vj�J  >UZ8 y�i�)-�E�&&� ��F�@vw4V2:`7N�:GA&l��c8\2RA �����-��d�4�VF��-q��LB�4N�V&�@�^��.�E�LRw> {&]8Y(;69�{9�.�B!.��K8q4:� ">< 4)BMB�i�� � @T� ny:�w���I�eg $F�$�yw �`cT%E(o b��-=�<Z _x ruln�44f�8�A�B"�Q^�PA ��""�B`Y��U� %S� �.�A��c<t�*�)�2JB )iJ.�*. =�A��%#D� �r-'j f�[X.���.�2�C&I-(�J"JkW��f� 4�UJ�� CwD/� BDJ�hF�r�.F�R��E *�|r�5ZeR2[Fa*�Gl�rr#6Ai�Q��*jj~x��#c ^ջ��6.8ޜ����>�>��:tBN �N2��d�c\6�Jݔ���1�.j'-%"T%"� ~gJ�T B� = I_dy�eJUJ��EUJve �@�/&D26�iFno� ert=�"14(2nex1s4ax�*V�C$|WB�' memb]�* Tby.K%@��t�Mq�ack*!���i#�2r0j>�+2� bMC \�n^�nb� 2a��ݙ�B�L,�e#�s]� hS.�n2� M&�A�� JW�ivCkhIe'nu�2'.�w)}%�J� JU_>6�7U�H 44k&�Oq(a�KR a? ���Ap&�o $n=4n#f%lg ��|a��42+ %� ���A�`{0kk 15 \N�J�T^+� �.u&rm�"�%at��s{15._)} m!� �JE^bRr�n>Y �zL2� �MJ�nF����Qr�ovxmE��*>�}" \vذ ��*���+�&)7 �%a �� ! %� ��-%Y = !E0%U% %Q $a! <%O !�0%�%s%�H&$[$d���0b_3*1JJ=qFJ%2�O*u~ ^��I|l"�8 can be found a�nother method, more geometrical, to find the mades $\Gamma_{(\mu \nu)}$ an &�Cresult shown in Eq. (\ref{e44k}). In this subsection we expose that �H. Let $X, Y$ two �din $\mathbb{C}^{2 \times 2 ��MMIz%}&EMr!XM �4X!�IO  4x_\alphaA7 betavy Y�6)�U�@ )} \:g\equivI�6l [\Upsilon��)}]_{ #M},IitB96 F9we hav�6fin�he four��$>z \in %u��4 ��4 !�sn�7} ��1di� B�9L%)Z_.B 7F The��caa#E� .6})�� a compacteA�j48} z_{\mu} = (e.x}^*, FNaJy})F�8F��gus notic��$at becausea{!�cyclic�Aperty tracrj9})�)pFe�p \�=�2FQ�umu)} 1�rE %7RW�MB�9FOwe%�%�j�50��= %6� �a�~�}F&i�1 A4.>�50F�We shall�� loit�^pr-�@in a moment. Now,�uk A/��ial case3�� $Y ==�9 .�y_�( = \delta_{c } �� hen, from2I,8}) follows @ ns1R�.���nQnu}��2-�:�Vz6 e�x >v~51F�鷝fP50}) has been used. A� 6�!<@e transposed one,%P is w��$X2�g �o&` �)1�E� /} An�2��2ma�!m�ͶQJ�n%�691:"�9^T)�y mu}.)�V,52 .,,The previous ults�:beb rized asQ�$  H" 53>8" l" \ X>}> E~z4 = & .TA� xA�R�h!�& ] _��RQ09Bv;3F;Nowe are �ppeo��Ŵ last� st�clic� ��$Z�f25 T��$,A� T = c� �%a� � 0is a given $2�2$�x 2% � ? � cjn3b-�c�b( px c_{0} \\ 1   2  A 3F 3bFh �t$by putting��>*2�%�y��>A �i�V easy sevn4J�-QaB Ya�x � .�Q�* A�r 54F5��s"�53��ve.�Toy�,A�* �55Vv�a�doteq � �B�i�c!6&7 & F�9" E\Z�b`N' $16$ i:cBmj* ~) 55aFJR�Ev�B 55N7$symbol ``$)� $'' stand��r ``i��enEby''. ��7� thes��xsa7calcula�� ele� s $M* �$� Muell�,atrix, by usa�5 � 24})��we reE�:n� 6} Mr = 6� `Njn}"km}z� 8c)�". % s�9at.l��becomenh58dRh[��U27Z�����I�&�2��{ {:Iu0jq��{2���2c.0��kj�6� �� ��D." y.r� }I|�B{8d .� lityrr e�PB�2�����} =.�\�� �F8eF��Tbe also easily checked�explicit.s a�b�.� �{$sr�  .�4N r�8f�� %V�% | Lambda"� (�.Ad \o�!*Z!� ^*) : B� %j�2u�o�0� Beb�*G vareA ��ta���.ev )� ����am��� �v�8fF���d.a16`�#e� lineU�us� RuleZ pass E�dummyp#D Greek"c!t��e !( $2$-D Latis$�!V�rHg}!�gin���� v�5i2�ik��ik ,jlEYP)�A��K% ^0M�8~� *M im� ��:�SiB  �.�2�:�} k!�^��N�z�8gFThi�&m� our*<ion�&�& clud 6'by��ng �)�ea�`$� :( \}$. First�1all�2�i�in�one/a�imSis zero,���!n_� b:^�\,2�0���%�e :� D\frac{1}{\sqrt{2}}*O = !6�).�MS] }R� Jh~ mHH}�%>�Ž��0 '_ ���� ���;!E� !�2r� �:0 �:� N+&�1�. W*N ^D� g :h j��G a�%i�Zu J�"IN�"Q�!differene��ѿ!{ well�n&4"ofeH�)�crg 60=�i!Q�j)�F9Q��3$0)} + \im ��l}$ld%�)B� 6J$#��0$i,j,l = 1,2,)$2e123�-632} =2312F(3212)23 6Q 213}= 1 $����S$ly antisym�,l Levi-Civita pseudo-tensor (!�<un6tenFonentsE!�);-�,~�6Bi#��.�!i��j kM�.�u;1�i5�j k� \}\\�N�F,��ij2� ED2 A;�(kU$\} ARY\im�� 6�i��JcEzQ�k)� ҩ;: �yk} }.r�6J?$"0�toll�-ng�tBse�� A,e"� ly:�������}�"6N�#�-��!vŗ:�J�b� � $ 1 & 0W: F!�c },& \q9-2p 1k.F�N�R� p� �� *��� -/ B��,0=q2���� �_��  %� %�J�Rw3����1.����� :�>�v7 6J&% \2{d� posiaPa�orem} %�. a�o� ��"�$6� $M$e�be a��� as a�ar��bine�9 x(ve coeffici�of at m\%$4$d-J���. H?%Pwe do \emph{not} adop4 Einstein #�conven ~(er�ed"� must� ,'�(llI�lll�*4 as� ���� 3�& i36-)\2�- 35})��  de&�. Hermitian �x $C$ �/!� n it�!l ��$H)!�. Since;@1Sn�diagonal(��3u}�/ )}, \, ( /,�13)� �r eigen�&s�$C$*�&&��/ real 2alu�#l�+0}$A�Z�118} CV!2�"*:HJ&, \�2R�B� 11RA��5e! ]�sumN�2.�& >$anF��alway`+X chosen orthonormal, soA2assumn+119} �2%�5 � )})!9�-�>+, 6B�'11J By tack��a)scalar� =6ofLa:E>y;!�})I@$�!.�P)e obtainn2206  �,NE% :F2H <�m() ::5W6 + !�.�5Y }]F�2J8 IfA��.5 %e� %S!`�47 4getr3Bo �4.R�)ZFVi � mu, $^{0,3��+.�O�#C_�2/� [/-}X nu} �G ~'>� V�U�$I�}.r U�$-�D ^N T 6�U�"w0mu �`[ > C U�!p � a�eb�712J� c!�Bo�_ x $U��r2} U :� !�"5^�,�R� ]�FU2J���$is unitarym �N�nB O:�E�[9}%{EfM J :B YY =� QT ;}!+W%E��GNIu .X�e4aR`.��) '.|)f@��=-.�2 :12Jl/By par�.�2]2�21' immed<ly ��4} ~F��n�-�f�.�J�J�-or,0 M��:rq5} 6  = DJjb-$D�C� }\{��;ambda_1�; 2, !3m&�&� r�6} o� � PQ0& 00�  xe0 &<2�0" 0 2>��012J�+.$ &� semid� ite,�k � � (are nonnega�>: $ � �; \geq�<, �4 &9 0. Moreover, s� �E*P*30c},Q*3&�6~&126-'-�Tr}\{C>�8\{\:)H  \}=2?H\}=2Jq6J�$(1 _0�-�1 2 3 =2$� �.�D Jerm :�;�is�=w Ninver2�#12i �3�f;127} Cl.U DyzJ7��U >a*i2���B�+ŀ+2d� [2�2'b�N� U*.)k [DQ��L �ĩ� �%\\�\6K�6� 2������qr� ~N� nu����G%� ^��{32l n�Nx��w x.vC,12J5� �+��$ \Omeg�C� k-�|*� V $&�>$&P diad w@&�+arr22B^E�[6�5�I�� � &�Y�� Ea` E+l<A%�1r]!12J�wL=�26i�ii"ua�v??131�=Y�Jp:�F� 3J� IR�6� ;�6��!�1g�r� 3B}S>K{�%�U�!�G,�)�>Aَ \{ : M1�!�W�sV�$9w,��O %� eA�nu��6 hA\nu� %3V��I+qE�n"(yE��U�v ' �_&��nQh��UBG��M�5��>�2E??��:� 9."�@VX13JC�he seco�Eine��� oi�"faca1.M1>�!a2�9. ^F�&-clCIo h"goal;�@.�!"� �644c 434 (�� j��H )#�� % M�6f>� F� � ~']�A�x:+ �Q/2I�'&���  G �4;6�Y�b�2�3cR�R\j3J=�=ins>, 3nin232�2C r�� � >�!�N��em�"� !�Vz[�3A-�V2e���V�Qf�Phi*(!�' r�J i�� �{?hZm:  $:~� R� Br�3 >6�1Iu-4m.���wA�63JT�⁈.3��r{Z�=6�^*E�B�` mfb^*Aai�>*�g��K&1)Ś cF�6�snJ;��6$B5bB��J*h1�. Actu8:U�stQto ^�7:�� 6 b�7d�+atcneaBwo si() p�.alm!� f�(�88<4*s58gsMMk�Eav}6>IL ZM/00�. f;# �n0).�\I"N� *� 2c VW I/2I�RL�> /2v�13J���#5�i!ze � ni",K $\J'v� ^�=:o, X � b� &� � 6z"� N!P�d �$�7,\tau&} J�.�b� L L�J2�y�)��"n:9�9����N�2��.�  !C‡f���fl)Fq%NK1�6l%6� �)UZ�%f b��|Y��%B�U�"H ���B� ^��i%e ~lJ�Y� o>*�@O 5e &� mV( �136})r�BK�6f [��� 00}}bڊ 2���]_i  R�Y�� f�A]mu}/2 O�P�=�  E�QmW X1/�r�-13N� hileN��Bw�Xt XL>a:��H6�Q,1$. A necess}and su�%~%d�O a� x�$Ay�7 J� x�:�M^T M{ (2M%�)^FIn �w1P !*� "� \labX14.t+2�ծ%�)V�}{ (2V�)^|-Q.�:* 6 4J�!d$�F �26� genu 2C. ( stepy>R&~ �'V/ dN(fZe next:jZ�Qder�'j" �o�&[by��9�Bu"�W�� �>yp3!�s"�Z{A � backTE:I�$MEM$T$�F��GA learWh�>oCco)e3,!{make a^ ^or�ZoZLifE'i1sibi7�Xsuch a k�Xof:KfoGNN�M$J'$ intP[�(� Q14jJ�Cseek a.K1ormf5�!RM�I� �4�St�Cby�2w3�I�!� help���)r`4BK$� 6���D6%5V�J� �&� )A ~�a�k&�$� l�$Je(� nu} ���Z@�;&� Ũ^* ?�! �A R�bq��� [.f6��p� E"~!�B�G� F�)�& :�)>>T_{�� �<.^^lv/4J�z�2�J2�,ay2�nv,2}:3y5�JvQ�\2��;:j2�� %���:�4��aga�XB�$�R���. A�is poin���*N�3�Dz4 3} M&�E�1'� ��V:sIQ2fFQJ�J��-�k�it�K*h44���M it appear�at!� the gener�XJris���@nonde !inistic��5iC0le.�x�#�.�.bstitu8b<*se�:���- :�A�2E�&�78recipe�T above"Csam�_y,�Iwe A-�,$ a priori}�Ek:=A�Z�3b� 4} J'�56�J2.��JJ�AY�&>N24\ 42&1})�viy.�c14Y0\.�1:�1�BUw re loo�- �"�Y@L�#xL�"�#iN�$* vC�.�"1A�~�4�$)�%r�<J'>3��r�2�Z�`�bef�=BI:�J�7!�7U=? ����  A.  J 2b vo44J�%V�$2aeCV�2�$e�quant$1 ptic7Nin� �2a�&� 4b�Bs<$as ``Kraus6�''. �W �W> ŏtwing�Tbe��3y� abouFjz � .@c�2.p ��, B�Xv�c>8e :�.l5�. F�8:�� m&Hf ��2Jq�* Z>?&<�  �:\}_B%� 6� `��6)^*n"Z-.�2�a� :��.{�v� 5z9'*��%}>� ZH.T} =1.<\j�44JqL�� may m surkcifa 6� were +/7�> Pwould#0�_:}2�b�= � Howe�*�or notwiss�Crrect=2 sist@"{2��%�7q�<ta�Ne�Kd- Yrv4 pro�es. A JC mainL48 @q�co�5ncy\ x $J$���only ifv�d�A EQe2O1R6� = I�-:gi 144dI=.� �� $I_2�7I.C^id 9t�.�SAE<�5!Js!Itru}�/� our^rd44eV�di*�Sq�� )>�"�2P� 219i.Ge�z�jb �_.�".�1=�\muB`2�1*����L���D%���*!OR�6;f�f���C_{��mu�.p$~�4e^E*� 2�)" fK. "ES�/5�35� ��.��#a�\la c_!�Y� ra$,a[rubracket7<dBbe�average��reKe�lan ensemfr�]�=ic 3um ,��e�)� be� �=v�B�N���n�Q�^�]%l]�A�; z�rZ5� =��d/ E�� 2":f \rar�>p&� ]U%:���x �'!F�|T.p\?�,!�v�b�N}��:�� b c�%�a G non-depol�f ing}m $2��R$ �"&#iezg��mJ�4J�L(@qry,� � any}"���."��F&>s&�*�O3�!by*�? k3w$nd &g3�s�F��a0cL�G �Lz:9�.pEKMU_ w]IC;j&r�P!�covariaazb $J�:>�b A sm�Hcom�b�in�. UntilwF4� g\C$ YBad fA"d Mexh s���4(measurable � itie�B w%!>utkal�of vie',�K�� H$ reveal�d(advantageou�%W �Aseen J*�manner:�,multiply�&"�?a���11�3 by $H$� 8�me i�$�s�;v9 �(��(��_>�,�e)*�6B��la�8�QF. \LeftVa�uH %v.CJS�2&\B�"�7:�J{(� .!t2%uwM����-�8u�!2��eA>zQ�'B=e)�)"�4� �\��J'6���jump di�Qo.14�-!e :�A�=8$F��/j�/t6��2��V�� *iJ5�>� �  '�`)�^"gB� p:��p.�7:�qf�_{�  )2��#��&�\(X_{.(&R�eE�nnJ1%B�12�. V%�Ur� a�"� ���J�he �z�".�� �!is very�+ , bez�:�u2�=4&gin*�=�>�0eM�> nZ�=Z1!}>%��4R4�y1.f_!��`� "K;#�e�=g4[kard)�a,�R is S&#K"�! a new"� ��cal{M}$ ZedB� Fn�Iw��i�b� B �Esdescri & inpuUout l�' beam7=ter� \lea$vp�$al system,�{}$5�H �%"�%� �5 ar},� �Z ive}Z�:��]a1 9 map}-:r=�v=g:J� ���  L[J]!]6�5J�%o � � � } revKb  �$lyŋ�in �~cartes�K� , z��T J_UR�� ,kl}J_{kl!`eC (=Tk,l�n$ \{ 0,1\})ad6�NT�>"�mA�>\n70}��B���J�\ G �0,�T 3 R�7J���$b$= 2i+j$, $mk+l$,E�$!:�}�I2T� J>A@�V ) ^T J���!=�V� w*���@<6O>� q\} B�4 "G $. E�Ip8!�)�analog�u( "� )�ue".&ce�D�6�j erGN A���'pe�&6��tY*latter5�/�2�W���8 �2a~*i�&:� j�OH:��R�ii}jt�pu�*b prov�tBzQ8A�6  ?A�� &:B�, J�&�Aa�e+6�-; 43� 96D"�n:&F>? S�v %8b~6� (4as2-�third�Q (in � xJ%�9 Ac.� 2}))� wYw�{s�9U�8"H�5J�� muF)6% 70CNeH!n�9,2.e�%1 '�is>�z'��A)t 8#0J"9R`�reads�7� �5a�j�2Q5 �h S}B�� !*Yy� 4 HU�Em �CBE20J�dGw*zj� qMO$��n� Eq5��)�2sBKqu$mdesired�� betw�|2� �!MrO210T&4 In F1J" Y�.�G25"�#4c ��rv721J.� = F,��H��mPer}[ )�F�21J�� po&�,�s�pX K$ "��qth�,*5p�$H��!� d"�:E \{ E� @����6�s)�bb{R}^*�*k r�21�w[2n�e�q�*A��&7l�a�J15JZ#An"2 �ong)� n�155"!�rm)�6��*��X"�+.!XJ�5Jr H��/"Rj�S also� 6XA u�Z way:kEEz�1o2$&�n:��1�&�QoB9� "@5;"%�n5A [.!2[�=N!5Cn�!�bP,��10�$:P�0�y� P %= $I�� i +j��� k +l �ker�E�}z�'%2�B�i� �uijVqklz<U�B]_{ik, �a\�Q&l[�?qI.�AjUa]j, � YQ�^^-�%�!Ca��D;2� %� #F"]u2M:t2�Qe�">�/� �� �of2J15c��` ,�U2�*�{ɦ}mz�. =*z�bF%�9 an arbitr�6m<A��TB-�}iK ��"`s holdv��qVUa. A]��A��A��suqB�b,�ta�!A>�%H*`t�IO6dFts..�T�F�),Uo�%���zv�eV2�/q}d.$ 1#H]}. i;��24f)H>)2`N7]pos6�D%r:�Fs�^(2�8*�2.��O�)}r� 215eF��sb a�soughtU���.D78 )� {/`v��p�^�&z7� ~\�i B����r8lyJ iD (CP)0."���9QEiZ>�� =law��KF,n&2 \ ]=!3a]&T4JV�'!B6o2J� %5e:� n73Z2�-=QkA �N-�L!�A1+ Ie[6�3J�Nn�#;Bfeb[.�]~2t�F�"U .@ \J� N;QQA�q 2�3'into 2�Ara�?X2Q�u2�n{� JV�0�Q�v�j>;,FP�QI�!�ERFB�U�) A�6S'BT2�&rA�LUv^^&x7f�2�,�, H}�)U�Ym.�r�UK�*E!+�C��.��|=JVH9y�n�.�� Y"^y=N�Jv� �)a&�N��c�K17 f/��v�NS�uS��&�$,�*s*�Y $4��4�qx $���r�P)��.�. 1�F�N9��J$u) 2�5��N.�)�.%  �% KEP�C2�JDV�y:zR�Y:" ��: M�_� I�el��Q�X }�A�]-v6�ezy��t��a�Z� �EN�9��2\ �#�l��\}!�k���N�;B=�qM"{/�!�H cV_x2�&�' deal� � problemJ"qCng2� dens&[9&�5-$a two-phot�taZf�u�� pai�#scL#�" a ``�5''�ly��'`0byB\M.P ���$� word.LGs��anyw'�'( device, ei:�hD or random$ch �� �s��conK0r�� /Kconfigur�s:�M�q'�a�B�D Z�$�(act�sthu;&U �?z�%^2o! r&@spati�W separљ!na, each!�͎Me~!�%R� u belongK� %��$eUe�1 liLtur�1�4e Qb��%6% a\l=d dw*��2"n;�)panA�L \item[[ 7]] A. Per��,D. R. Terno,(mC J. M`�dOpt.} {\bf 50}, 1165 (2003e�YD8]] N. H. Lindner,h�'.iu�J. PhyH�%g 36}, L4492gi9��Rev �b �7^93\4:�10 [Aiello�k�$. Woerdman�S cAZ!023808V^1>"b^9~ )52%�77_5��Q2�M% ��a'C�yleM�s�B�'���LN8dactic approachqt:5Fm�I�ulaa�w*�*K'ed mPbyJO��.zRe� e+ he d�O&Rth"�xLs�WK�7*> qF}"��QqS N,���Q �p->S~")PF.#>lqNS R�!��F�U �\�Rl�4 � }{2 �R}A 6�=�E-2�7B�N-Ny�Pwa Jaj�"q�rY&S  )pTNd :�y ��7}� @u:�B�,qb�:KcV�}weݢN�(P��6, isomorphism"� A�&ecR�8e����:1$\rho�!�RTansatzm�u1i�r����pa2m�bj Y, aft�he �N� ����um�&c�{y=+aR)V>�� $�N�'$"�ar�srho�a�7g.�� 22;q���.qN\%A�b {Si�-)�&� 2b2��U !VJZ�a$\{ | i \ra#,= \{|0 , |1 ��'(h 0,1F�Nf!�p- k@r5@�>* R^#j�3=s E6�:a��s�v �of�+�'W�@horizontal $|H\raI� vert� $|V:P2� ad͈A�c"�}jD� |�r��|H!5!2�|1 s.:!qN�BT feTo( ���;"%8n�_E)mn�6�:a i | j�!��ij��i,j \i�1�1MA� m_{i�1 |M6 Q= \hat{1B� q6J�) As u� � 4�  c�GspWP!0A��En&5�2*u)2$ �=}7f7;b�}nb+q�1�.��A 0)}={("�9a�${c W�0 6�o%]?13 |-a_���1��jd] >\] �dBQNYIܪ simi�|p=�, di�%;-�\A; (i=a�@!&c%�/�8%)$i)}^{\, \d�>rw�la 0 |Rw6N= F�-��u>.ye1Ne1>�be�u%�� 1�FzNQ�5��.��5I,}-�y"be built��.�~�,d��ZS� �4,n,��r�|��)�)�q��T|jE� a�'� uad >/ , \;V�F <4Vh5qN�� �D 66)(�� U �$; s6�/1@V�j�1o�.)�q= EL l|Բra (Aj�U11j|)(| k%Q|l)A�&9hiy ) : (6'��k&���� �$!� j,�6�NJ" ��}.A�.�>�1NEIş.I� ��H%�so-cal-Be� ��B |b.� !M`/�n0/q1N F@уB}!�I\rE�A�&�  0*�6B� 1fD A��N <�at���B(6&�fHIf~7 |�%Wh� $Bj��q1� B!N`1.��Zbc.G�K&���q ��-�����͘-2%\$"B�VE�*�0�wa�vjq1� � y��U |\psi^+!�m E/��Aj��J, |00' + |1� ���]-I ]��6�]-^]hN�2�)�b� |0���>�hiJ�q���]�>]2�6-!� ""��aQscolumn d`+��0GonP A �O��. Four� -� q��o� Y" ivIv;N]� 3)e��Rb&m�F�;2���bra� >ket�ꊬ+da N� ��la j|�:�2 ��;�; >� F�N�T p9]�:rly� i~ (one-to-one ^� e��<s2�@gl*e#��a�tn3 {2 b�2v� �?fQ� Jv=�8� ��& j:` F� 2 n�F�Na# n��B"?F���l}��SQ�� ?.j:D]_k.!"*�$}2�"�n�%�, i4ZGI*�2#�m2�R�@%b 2�4 �?A�gre� .N5aL.pT&�:�Zb""V�% A.*2*M ��q{2�a `q� ��e/n2J2:'�Mrho&^%B#*(,-��zt�+D5.e� !2�  �  |�&Q�6�!�+}Bf1:f�5�� [klX>�̀��Y�B�zk�":  n�o,{ \widetilde&v'D}}x'kM�"�lav~}�� N�K# |�6.���8]IFI�#1F�8k�r8N�q���j"��nuj a�aSn��ZT�)%S=.�_Q@\�PB�M^��/*� &� DF=qR�@6�% 5orkly��L - &� 3 �U�]5:_ �5 A����UG2Xnw�@�k�3"�c=m�:w {Z��2S;Au6 ]q 6AmFRfu��'Bm���g�� ahea�"�v� �lwo��q��\De� = �''w �ion: B:��om(U�-�*�DM c n��@ \"�C��T !Q*_M&�1�M3 K&�6!�'�@;R�R�Ae�µ �j�%Ab�m�"�� �=V�9�"2�q �=SɰFnR�A�]me�x:;M"��w6��$c9)�Gm�A*���X r<�A��N Bi���=c%B2ۡ��z w�mA�2�)�U�Z�Eb.o:D=�?�]�n@}62uB� 2N� LJ$�FE d{�>lso[� "!�C#�, '&� ��6�%n`W.aT� � 3�)/M�}V&K::R�8e:���M�"=S!b7&�*i.�_S�����]�7�52 uy"�A6x6�  } %)=��![52�T]�_~��d�8J�Y�Aj�.� ��V�� :=>�N�+e�F�M"r-*$ E� ��*�y?.l ��B�� L,)�9? 3}$it '} .!�&r]��:B�#6)}E��� JdZ�,�L� \"I_F ! �e<p_ �� � ����ig�r j�2m ��6�ݍmZ�=��%���%�I/!���("z��2��J%����%|}^*�6�� �7 � -�ta$�.��taՃ 2��I�&�BqR >M"� �j&Wo1&Xo��o�OL� �Rn��#�>-S!-�W-'^*�5n6 _FUq�"/(ev*/(.6aEuG9B� R-6�.P�p ��:F��) S9^*�F ��� e, J �>� �- L!w�{,�������"W�va G�ڣB6�1%��x f�CB� v�RM N0�|M�+.� a�}v�Jq�=������M � Z�Eu�>g�^�^6���ʿ�j��B� ���dX�:C*=|�}& j����_�- ��xNf .� �F��ta h [� M�@ � `��J�n n)p�(>r[z`N�)�.� e����� ��\2B�>�; ! l-7  1 s*��to*� exp\:�f�H5��xr� �  rho'����J"�  .� "fI_2� A)�-N1Q;N9��eZ��=^tz�%�S^�_{A� ,&C ��A(��&�w*� � �.�q#� �y�� !� 1-.�=0!Q3}&� �2�2�). 5�Qn"%���.�b<Z�_{6F����)i6�\R��^��^AI������.P�P��)2GOf�.CE�[M��E1E>�i�.�O�� [2q^� ]:��F�fM&�Oc�:�V2n�}�Fd���I�� triv4�=n��b.�L�'>��d � �f�. -'�-.j�k�.� %��Jڕ.�iN �qf_�L?[Z ']:T�FQN�.FHoA �Y�3A`}qB)�2U_ 2�Oq{FF ^�, �v� gl&� ^_�kV�!z+ Vqi�:�? $\de�IV^ nԥ$,���h�j�o ��n� KE��:�Zp' (Z )^{-a# H�$2J%RsET�G� �/�  �ledge�g;a!1�6}Ehum�$("Q6�pb�Sbp�$!�D}�Fs.�to]-que^8�Fin�&=92Bx&Bk4 �%er. "jH eE�)�B�r�hC�g} coord��e�4R2�(�B?i� �!�B�!1 '�q�B��.&}�9B�-Stokes��malQ:�observ�A,�refer�9".{ raT�n�o� To illust�@�]!�la=con@% V�^A�# �^B$%"c!depenS|�:n�&3;0�;^F&��?=� S^F�<*",,S+ (>A,BF�)R�F!���31& +ER^( %�^{A_0r187=r��N&rh O� *� B> 2�� %.�1Q^A1?S^B�U&24�B.8�Ay �,���D%+_6^�v�R�F�w�0�!������=�ii �am�y�kv�2}%Z��5NsF�N��m|now3��AupEv�super�Ept $AB"����B La�2�R&ce�-���XD}�*ZnD&�=31 �ajv-R2�=1:C j�DQCaDFg��*���=5*D�&e5� �/&�2NmPv�33J�1BA�� ��6V� j� 3Z��d��֒� ~O,�}�� d��%y}Y'1�6 2�i.�{�F'b��oS=R�_�&<D�=�h"*)��z�f�(�)��z�N�2So; BLn�EZ^ =1� D n�j�+g�I� S*,: %3N�%6Ra"�\fao+R$QT *R~4$.2� T{g�l�I_ y�� �y=#<{�} #h��$*Ӈ��lq3�2DFC M D.:6 NJ6 �riɘ`` -��alent''x &� p4�9ngFH ��l�+n�l!i*� � \}�Af.K:! �}h� v&"wr�I � D'��-7A6F N���p5�galtern��ly.�� ) M=�p) EMe wAH9.6� !l&P�_  Maxiy E"]OMixed S�N (MEMS)a��Lc� |3a divi�@�7�L" M„�O�NB�F``mt� te'', nam![$| �<%9�[�� V�f�8}).�& �v�!Ycharac�v ��2� x \footpmark &M{W. LMunro,�K F. V. JamQK A. G. Whi�OY P Kwiat�e�P%piy�A��P��[.��% qubits}, �L{LHM8bf{64} R030302L 1).}1"�=n��2� �%�J�A�<g(�)*�< /2� �<-2F)�!�<?&==>jB�)�N*$3N��n�Aj= �ͤ6�/(�,\ ��2/3k) 1/3<*�) �>�Z�]�h X�E2&A�.~6j�4[A6��b�9�!�%�1/2 & - 0 B4 Z�:4R�@��s"��2^�em�s��X tuT��"�jF7;nC�M�7�?!3& 25B-M9 $=C!'12C2Z4Y��YNZA Ha�E�@�#���DUnF|Werner�ct�Z�m�nB6��i (1 - p)/4�=3(Y� -pE� .%!ocZI:f42J� ��?Wg>2�e��D:�h�C*����rX �:zb50ten�>"IB�/4���=p5lE�!$ 2 Z7>�N��a�yW{M�� -modsJtVM2�� deal�-th��M�� -dim}W�� Hilbert�U ces,�c`LQ���&?'��7 deV<� freedo�W�.&��s �1u4�JB%�,/ h�k appa��0�rreV, �@pla^� import��role. �E��"�N2��s phyAY�s� man�L>�o �� �a2 Ȟ� h/�regard�M/U�}2. �1h��OMe2�``b?Nbf''� � � he ej#romagneԜ fielb�Vst%�$2N0�&~�@.8harmonic oscill-Fs 2�W> y � numbers:�``A�''  $n"\I81,\ldots, N-1\}�y$ and the ``polarization'' number $\alpha \in \{0,1 \}$. For a given $n$ the two oscillators labelled by the pairs $\{n,\aU =0N�$\{ n, n$=1\}$ ``os O$e'' along e`mutually orthogonal direc�s fixed u0l(possibly complex) unit vect�8$\vepsilon_{n0} � . 1}$, respeHvely: % \begin{equ%6L}\label{q465} \left(2F �},.Z`\beta} \right) = \delta_{ - $, \qquad ( , -�8 0,1\}). % % ,� \end�"A third. 6�3} $ =]toE$other%R@remains automatic!�6yrel%r( 70} .  2} =22 0} \times21}F�70F�8It is important�,note that in�theory re/0\emph{not} a )*harmonic]�2�$\{n,)� =2E�c U�sM�:hp2} $. However, from a geometr!U4 point of view� introduE�6�R�2Q 2) ]ng onm0IJ phys!�} ��ofUL�of�xsystem, can be easily build as jq9!���,array}{lcl} 6�L& = & \displaystyle{-�a��=0}^12� 6� 1���\�1F!Nj2 26 2Qi� �%B9J!�$�%�+9��Ig$. Eachu�u�ora6(characteriz�B$its annihi��ūcre��operat�B$hat{a}_{n - �FF19$ .P,�2 satisfyEcan�ualA�mutu rules:!q)�F}4A �}[ F~,m�C�̓]݃ nm} R�.:h4J�4The Hamiltonia�qI�!n just�sumq1s m $2N$5�u7orz�!�H�Tfrac{1}{Ax��nA�{N-1} )� $1 \omega_n��J2�1� JeA}1 Y}J(D��,>XJ��\hbar =1Qh � \geq 0$�!!�Lsingle-particle stat��| Q� \ra��are�otŌ �avacuum 8 $| 0-$�/ usual wayn� 50} :m=n|d>d5JdFinza=r��Q�R� tenzM6aAi^���Mbb{I}VJ�_0A1$ldots} \\ N-X \la 0 | 2:� INM�|6�la9�D \{�rm{multiU \;)�s}\}}.vz6J� No�at our}�Lwell defined, we try� ��( Positive O�ET Valued Measure (POVM)Ahordw $o determin� e �^(relevant} d�ty �� pertain�2�1 .�  degrees��,freedom. Let!vf_{\, �}$kotes ��� normal ��2te bas| n͘bb{C}^3$n�50Ay��( t \ii, jj��)a:! ii \jj} Q!ii��� fC Bii�mq % ( fb in \L ,2NN 50J By u�d, Eq. (\ref{q ) for e�mmode $n$Aa�a�ej051!J�6�!� -�V� I_3 \cdot2, e�%R�mcjjR� jj6�5V�iBiQ&�pI�Q�\equiv^� j�F_{a A�}� 9�B� 51J ͙ Im. ��� \�$. Then�7�C�li�"O &�bff_{n�0 $ associatedq�U�rE 52�x m�Vw��&P i�5�v� Ix12, ��:{� V~n �ooJ� vU�j-�q-�nh j� E>g)bA�%v�2J�TheseU"�no �( length nor"L*�r�3�$-;]+�E���56V� ?B>H,&� � E_��i;5�Jg VI��H2�� ɇ } %�r73J��7,�e�i,�6 �fiiA�� {we%� read`�]�/��le-�} �  $� %abf{F}� ii� ct4o�n%  the � vO� 6� Jv� !�� 2�cl�2ER� � .p}{\sqrt{W( .]�.�}��Q�ii} a�ك� Q�J� , �& P�| \n� ,I0 &< .�V��M� 2xi2U5Z��k�usA=isU+�C� � ɃF IS H� t�p�  semiM�Xint� ''VM�F}� ����)�B�5? �� 2E[ PZU:O )�J�6�b'}%�N� Fj{��,�^L%[ F��6�62[Q�V�V�M))^* �V�IN]� I�[!�Bur�2�y�2>�2$ %� �.] ��)� �BlN)%@��(n�A�*��"5�2���~m[ F�,6��1 1�c r�����B�' � F�����1�F��50���� %�b8last step trivi� follows�%fac:at :�R�= R9,�reforej �g��5^6�iN�A`%n� 1���B VI: V�JW��VYb�:qV 6�ZZ< �Z\.����2�:�5NrA!� is pitKeas� seAFa" ree�s s $\�&0 F}_1 �form a }|� on.@r" ��̂�n���8 F}a� � �+c)���� �b�JFEheR�n�� �22\ (2���a�B�]� Х����2�Ř ��b6��V�1x6�%���%�%�� A�� �R j�GN�SN�W � N}"0�-�"�Eqs. � 65}) �() have been+ d�� subsX {Reconstr&�6 6���Z�nR {\vx, \vyz�be :cLCartesian coordinate"v*lRl�l�k U}$,�5V�*nW}�#�9f# unbias ases�" B��ez�5( ���{\vu_0!u_1 ��Z8BC}S:^cVcv cv cv c�~>;�&\{� vx�vy� 2A�-!�. \!��\z�W�w �w �w��i�F�� vx - ^#.�E�F$��F N�!F�""@��"�jAiIWcoron� tp6&ofY�s�%6�"& (& U�!LV}, `W}$: linear horizontal-ve*al, 8 $45^\circ$-$13 ,e]ular %�-A6'&), selec� by a�Ter whose planar surfac�$�to�&z$. We w�$calt�#,Stokes param!*a beaSlU& (ei�% clas�"< or quantum). To�$s end,�/u4%agio repeR N�* out!Jd3 $ previous ��5  �se.� ����R�A:us ob�M% different�s�ro!s with�Ulb�WV :"W 6��( exa8( , if�Eq�&�)��titut�t&O$�vu% $� �F�Fs 8� 6` � �} �!F�#� ��f �� 2 �,:_  \e j *�o t��(@&,1,2)�w> 8J!In!�ctl6# same mannac yM.M-�a��-�. As a%�equAL�w&s'A$alogy%� }Sptics, f&``i�*�A�@�rR ^�%6�AS}_{(0)^ ��1ݓ1�=U� I U}_11�VE&o1�oVo- {V�o2�oWoW�o3�o%M �2M.� rPN�&For sake�Ac�-ty�H *�e six"� �(!�E}_X \� ; (X2, �", 5)$�� 6"� ["�( {c} �E!f\\1626364652+�_]f j�%��)��E�2.�E1I4\R�;2i6N+! in such a0%�'we vre�*D!a��"aS" act �n+6:!!�e�"�A})P �X� 5 P_� A} X}�A+*"9 A}k.Y:3 \})F�f we> �he $4�+6$�#$Pz6�PM<.���B�A�1 &j%�#- 2  C-M2+0& %V0J620IY" %�P P<�# 4$. �.ive) IBexplici� 2�*{�kF\}r�$6��Vv = BG ��n'>� zC� 2P�,vxi� xN � &���?%R )� ? ,!�v� 6bD, x�/�(X)m�(\vu,\vv,\vwU�&$x = x$ A2.x#Z�A )�u^U�,6Z�Fy� :��&��6�,�(^�%&)�  um�jA&� 9�9- ��6%N��a� i�"� (0 sh ]2j��2e#�m�:�O �c�w��!�igma_{(&I"A})�!; ]_{00_v0q_/1/0�mz5.e1�e1.e0 n&n v��&��>a\O�.�� (A)}v24>7 65J^Iiw7\R�} 1 N ? $�#��2��2$ Pauli��ces1.b2b��Bb �-?�����bV|76��r�:�����R�G#FY.Uы��� .4Q3F�%��L \vvar.��,U UEu�22���2� :�6NI��6������ � {\,2��  de!A�resn7�aof�F.�$b a two67ub�6Z�.+!?N:�5� �3F�Ѡ_:�j*� =kM F7:6NP$Of course,%5> &�+�5:IJ:/�)��). [0" "�%resul�9"n �t81 nu |Z| m \mu�2�lF� mkp\ ��.!p"��kpA,K#)�&N QF5pm.��Re ����3%���nu�&��<%�5 i3 �%^�b17e .�n �, �6�dE�B� mu} �}{BD6ND6� �� alle�(ingredients&�;��y��ex�><8 valu' biglA:%$F� !r\ra$ �c�er#>generic+ describer?$R \rhozT��, �� m,n(.�7mu,%t3( 2 _{m )� ]�B5 |�6r NZk0jC7�m��[;6~�S^?��rm{Tr)~l�G9  b���W JWN�Zk��ڢ .�b��i��:� ��&- Ag]-(n�Q�#�#��b� �.�F3�7��D�>� �at��A�r�A�j�7N�{ H 6�.� *x/" 7 �� $^�n7���[I�y��]:cC^�rho'�!� ,)�J&�>x:x�� x:�JTF �z� )��)7N�& s�,et�3n*F ya/$xial regimj1fApag�y�8a ``dominant'' �1t ��,field, say $�?n_0fon'assumn� 712} f:^_ :�-� ) \csFBQt -�ZS>M 2!D} )"] \for��b))Y"�N-1 \2�712E"t % Sincealwaysc%P�:hoose �re) ce f2 , in� caseN)convenZ=SMG2s!� [)2A�)"s^�7_0J> :r��*� _0 0�=�I�!F�O  ��^�;�6j1jyvj� .q2j�F{ 7N�L#!�:i��&720'tF.-��U.�7#6� 9G�@N�2925 _09{B� 7N�� ,/GU 00},y=� 7Mf=/z4 714}��*��� N� � ��2�7 ��>F�6 &4%�5 p�Fqj >� ADU �&� 2^A�2�:714 u�">1�� A&' D}$ v�716*EH� �:�Bg� D}_nD�#% rm{or,}�e [-uA��=B\�,�A�\!<616N-� coincidesE�]naJ�c$of reducedP&sity )Ca�.�+hEr�B+-n!� B�"�:"��b�B"�,*c^R$Y'�02�N�BHfLb�2 do�:so�' appC%i ulasl/Eboe!(s�Z� 0n w%Pa � Z� aga�,��,�1 xcited. Ih;is :! ^Q >� i��A�r2Nf%�F Gu�[.� >�4m�immed�Dl�*n,����NC�?�1%�^0A>efb� $@��nu8r�& iE�l\^0Zk�a�N[s6:p..�{�3^�V�Z I8!�=1 �.ed,Fy{0'T = 1/ �A�av/after a�\�/ion, �<..��%n!:\\doteq�=J0'gF34�:, :�+ V&32�&Z&12&�2Z-22-��V|6V+�2Z-6Vb�6�-ZM6�ZbA�6_N�BKlaApurpo}5�:useful�� : y.scarY real&2 ,s*6"Aw@ajH800%vXs_E�� Ae BJ. R�<)m�ra},� �I\Aua,�9 R�"�" N�*8N�� Jm+a3)v 8nrh��DsPs_3A[s_1U� s-% Q�&0 -8�G8N�(Ggo backA7� �al &�D.�N�3upAt9w�m�OdB4"� B\�0b!ā9� %�2E)!�!. Two~s �[e: Ei;n� ,Fl0�$bib ^2 <"�aBA� 1}^3J<�B.n^2��[ �} ij6�:��H�T� �J?can:�B88Nt INX firs?(�ccurs�!n�D�F�Z1o to 5� a^� EBI(t�? may happe�Xca�!of un�6ed��erZZ,u B}} N!�:fF�38NfE�!�Pmal c tV $�$ ens�VA� cond��� .� = 1,�Rnd .�:t�y lagrange ��r�=J�,�WY���1,2,3)�@ *]�#jc�@a=`}d� ). An >4U�Alit�:8N.�1���D!��A}-'3 6\ V�F|N����Mur��, nowA seek��� betw�Ainput� �< u �A"y�9.- scat+^ng prooa�.I] ou]sa0Bus%�i�X��a]%�U=ar}lWl �� trans�E� ��-photo�X�� .{%�rm{in}�to H �RI"S42�Ioutv�%8t�*j�YN.Z*!:u!��- L}[J: in}]j��hikA} ��}}in7!^�b��nz8N��fn� �~.��~aP!&IJN�2��? itie�H٧���EW�� �> itudrJ8sla � |�9-�=A_{i,\N+}(m,n)FAN%<��$F} > [Z�E.�- .�$�vAel�cn L:�� h&R J6A�z69DAL_{aB$ b�+U_a6&�m) )E 9,!.)I )Ih! h*(a,m)�_!)rqGin} 7�7UR (n,bF�9NH�A*algebra� P2�1�EXB>�Kfor any ?j�C@:�{m, n�"�#�"~�19�_F!0.z �{%�:S}.�E� [V�]IB�9NM�A�["bV�9��'�5�/ jS\6 >j$%�N�!�UE M)�A�MD��,� VJ �]:� :�$9jK*DG9�r of�B"�JMueller� X� DGa�^I��1d%<i�)�)��v�.B=4JI"s >�') � (�`��9�)>jCF�UA����A�Z1B� E�.�':� ( 5/�Z1VZ1F'!�a&�����p6p PaI6f (n,nR�a���@ &� n6S$�Hmn1 �5���B��J�.���`B��"�:�2��.mDu�6� } (n �^{� :�2o9bnP�������H5\fFZuAJ 09NN>�t��1approxR�()Y*9, )) $��k+.'�!�3 1�B}�t #P�sJ.�� 2@��UO can �� �Rz���2 ��>�*id�Q�A���yJ �T .�:�+��6�%A����C � p,q p 2aB}I�AC} � ,p,qZ�C6o ) �K��~�&�SC} �37p,qL � ���.5���a r�N*In�alistic6AconfigurN!�2�S has a .�o6�3isU�Xv"�5 spat�5and te;y�tzwncyp"U�a�sitself�kis% ns��"*a��]��� widetilde�_{m��N��R } r � ^�N"namelnY%9�rhoj \ot�zrF f�$R�8r8E a $N6EN a2�K.ces, �=�|QE�/�e{ x!/a�r \} $VA;V�Uis Lao�} A2�Zmade upi�. $�$Vresen�(AA w. �vk�-&�LM,, it would� |ea�qless. W�Ub �um�\�~10��� !)��.! R��J���R)�@, q)Sr{�R-C}) .#�+<�B�ap��\�at`6��0,�6r��>>N�v� �� Sa�a� C}}B� }, 2�HBFA!�i"�"3$~_"�u7 rB� \B� ! \} �:�A���Q*r �)��)�I��@11��bv�A��fg���y�g�g*��5��z�R_R���u�J~:� �  0}^{3�[ !>� E��B}=0 6�� �( Z�8]��^R:�.2� .H� ~�Ia�^r:��*effo &�T4$��hM�@r�v�-.)> ���� 2�11N;B��:( ��<&:�h&!� rZ����o)f���a�:9B6l j���5�.�B�Q��in}� j *Kޗ1Ia�M.k  RBE _{nn��4>�2�6�S6A:�M�*Pf}beF�rc-HH){ F�k ]�^en/11Ns"z(b�ar:�4��XQ *�Ne fou~cH\ought %b"/%$f**j�-2H �=�$n*11v�"�2�AaZwbYB>| oN)'+roin�:�b#r��J��2�J.�6��wbhH)z/C�+C��.�C*"!R�"Z+.� 6���3}v�W2 �^� �,p�F AF�q) \}~�� �ACAݞ��.�V� #&2$��v�N� ��r,*�e & l�,is valid onlŊ0imi�{N?"A��S�cs&�kTwo2)&�)!FN�)c�>�G l)s�HA��B$^ratW' V�.5indepen��,uly se�21:. WeK�-�&|uI�ra k|U&h'�ke�8�z �pg��X6 s �� ly,-$a,b  $* $N�^����,�HTe�J� will�1in"�gly�r@v� �|4!�>�5 = 2$:A"�',\ra= |A B\raA�:�b52FE)cuAA��c7mE9�&�$�c,5(�IYnd $(1�)B�hLe2i�)�2;$ �(zE4�B "��/ bingg3 �UI �QvlF %B�R�|�(>� �n{Ei(atop a', b'R)� :g* '� 31Z:�%� ; a'4 b' '} |ahYU aI�?R2| }�7: N� �A, >��{A', B'�$AB, A'B'} Anl A' B\A}2��C.�H11N��29)��%�*K-�=) -:, �&�+P2� |V6e��)�)��(�D5�$(ab,a'b') J*N-A�1/ duep>| �F|,-_/iTB4$0v/� �?�8\/yy�Z6�N�/z 8)�j�F�[V�(&��Z/{i,6�0%(*.��� B}_jKO�FS>B"� J� J;)�$2LF71N�Maޞ�/aJ0j.�!�.�J�NM��/r�/12FtcNa&~6�/a�q�r�@M , �9'} (a,a'&M A A' \!�la��\!ᶑ�)= B_{j�w�@Yb,b') B�j�C*t BA2N�.%�i ��'�i |} oFx0�[.w0��qRy0%8́'r.q6� ~>An 'J�0A�i!r[ 2Y:G}B�r�`It�1�l%���E�EA92�,7َ= Z��ay{a'',b'i'k':Bm'"Z2)�7�;1EaE� #*-�') E<2�A�'4)Uk�� �h� �-c�1e�4�, J�T*� �E�yO`k.(b�b'�dbm�=lA'',B{!lAG B�a�%+�'} �a�')A' ' ( �x�W�G�� N 5� �tYt2Q A�6� 2b��63if�>)+�:2B��h$\SbP.S(&�~]2JG&G "bFq)} �J1=��:3N�the�r�"�<(by)1,;&6w����dv8,!�NEAd"zn4zZ 2d�3Z rcJM��6,�E J$( NJB'�B�\"� Ft 0�~(J��F�>�s�uJA�rG!��6�A�.9 Ec��^��� s\M�6J�A�NM.�~�nA'>"!�-�}��:�:W/A� ""�  %��k% cleai��>7��%12eɐ��&bE=�o�A} &6 B�!0,��? A} B}& [J .+ #���+, ��Nkfo:�A�i�5q"�!2� �3WV�!��!�� >k� �"m�[ "�9��k�1m!�U"FQ! ��� 1)�j*� �r�A�6Ji; (� , b' ) ����e�r� NpILT^G.�a�JZ92#1$"TT,"uN�hty buz�2GG">�NA�b ��j�"�  &��]I�!ia-SB'�A ( r� nj�a bb{Mo��' bD � � ѡ|1�.i��A'�� �6�:)�Y8a''���!`B�b��A$16;*16 nx��Z� s �ADK ��r�2< �ZY2M�' M^�Z(a�� })�  B)}(b b� �R N�0�, aY0"]6RH.16� &<  417$ $�A)B�� 2� %��Q Z�B* * ).�H>J}L R/R�J  � &�F\ �:&W A�F/ � Nt��B).�> >v�jI�6�J�� �7A|B� � &"H"���r�NG�nMr�� q���C��L*_�1�X)�/�Ehac �s/�Hd$Jx֎*Y�s�mean �O�&��*s:��o�T?�epa"6MeJmON�J&���Z��#.��O��6 !�v�2�ɚ.� 6@ �!�O{6dE�z�"E",Bp�rI�k+�Y�H ? �}= ) �j!6�"z J�m��f��G�F�^�m>��J�i _*5=l%!lN� r����u��2Y�FS��"4f#m �M ��J�|AE(B'|b�|I:����S 6�  �� Q.� �� 1n�z3�"�jj� � z �a' \�+.�]9'�NB5�560�a����/�; b' b�.h5XRg�6/If %i^i)m a,bB�MRIgY33��J�I  �AfI�'Ee��a&Qy*R��MN�-VW�=�*� B�!�C ު5C � �&Fia>0Ea� e��3 %$:b:! ͏:�)�k, �� � {F� by�B4 "� f�1$�,-o  ����&��I 2�&yZ�"� V�&3:x JnN!=0&6�>�L� A F�3F J�� f*EKF}��N�0%H�F}'���Z>�/F�('}}(f)5�Y� F}')x�[:� �R� >:.���\{\&v>�^�ms\} 4sjst!nd 5�&�7f](AH���%�} A�W� B�|. B&mWi�7J2.5A-� R�Ou z�O13JLF9� l� � e�WB� � 6!� ����E�e �6�jc�!� A}',B} 3�o>�F5)F�-B:^�(b) a�y�Aa�&� B0 B ź�����-N�}'�-�)f1�u��E�5�� � � }:���!�H ��B� M� (A���E� (1E\�Q�f�M��aK6�:�6���0��fg.+ev/Nh!�n90 hold2t��rax�B:0 A$2ol?I�� 9w$�S�FA�����u�)f�%B R�n13�!�����"��}��������2�2�E�R� "G��{�����y2}�>��y A}�&B}%H \B�d{l.�� �&.a5B�A��M�(�����sJ� ���4 B�b~�b�&J�:#.}2'} �y�6�>,9��b�)�%P �����������-���!�R�a&��f� ��>�� eFrN�$ �Pc���a)rk�? b;ݿ<�5�J�f$>%a�a}^�F( Bigl.&��J�%����2�����2�jjT2RJ.(�2a#m ���ъ< Nq)< �%3).�;�*:�-����= �fU�����f�� 6�*3N�=ori�*act�+Ukmr�!3�'Mf0�'�'�:�NQ'.@aR�0� �De'~�? FR��r.�?� &t$� Z��  2Y :�r6$"� >�J�NS&Whe�M�6%<X=�f"n hype_�aT<d,"�a��M3&%JA ��|�2� =?86r6�L�"�).J�f\%$R.;�#$r:r#o$Ni�PN^2P�a R�/,6a=�pKDEr�gPL= N�O:&�!�"H}a sf�'�E�13��2sJ�;��2�"�:)�%&� BC �g, ZK%B6�>�2�J>�.�EX*�e�%&��!F .�%��2�2%�a`)�d"�,3�' 8%�>z&S!!Q:A �kb�ɗi�2lu��%62l �nN4�/R� N1.6�*3.C�< �}TF�,��Rw6"j2?������r�er��:�F�2>s��>!V� :�n����`>H1:�NK*�� �)S.a6�6�=�B 3a��(��FaNu(anvF2'�6' �AQ^�� 2�a& b,ab26�#a~ ��"� ��b�=;.F��&�>���"e!�.� �+ B">�*},E r*N�I��las^Gn�G"f��$<-a&^94��x >x �l= 2yQ2�2�F�4N�=B�Lb��*�B�L�.�{U4�6=U�*� ^#b�*Q7r)^*�&��'f6�L;64N=FS�we&Ђ2�k8�0r.4� �V��k14F�J�v �8,AF� � �:�] �� E"5% �6�6�j�11uj� � bf{M.0.H~� �Nn���hn�4�)��ɔ-"�K */&�3 16>�U %%R2r4w�U��1dž�����!�2E 4NGEqu�H"^�U)�our f��q ult:2�re�^!� Yw�1eBx�Gm��} &�1�`t y�=�,um �ju"1 #B�j-$�� [ simi��CbJ�(de manifestX�d k|$AU� WRN�~v�C4crf�uR��?�M^��Phieg:�N7�.w�iW6TMea/Ph���6�f�.�r15\.�.�I=qfbe���N4� � "6]�'{1ӵ. �'A� I'JiN9TR �~�a��lyA� ivalɴ��Yx"�| aI���i� pure:���q�l�.. Moreovm���r:�{ xbboc��6 Z$mixed} (oraIelyGeed) gs.}�C-B  docu>�} �� \%�[12pt]{��} h%` 150 mmzhe� 23 Lopmargin -15 mm \oddQu  def\be{>� }� f\ee{����}�A�em{ }��orem}2lemma}[ %]{L2# corollary'C2+���C,D�� 2- propm�o..P!K �1s0\title{Pseudo"wR�#"�6 \\�� ultr�4����#.wavelets\�author{A.Yu.Khrennikov, S.V.Kozyrev( �ke�uxab� ct} A fam��of2�D%�,��J�is in �L8�w&h��A�gr]�~ lex  8d funUsOc�Ra qg�.z) . A"J��pjb,�8�Zo��mR�!�t��Fs6���9 59�� diag����.".^-�1K!�rFu�9 &���eigen%)e 6�.c F�F�"�R%� moreQIFts � doj n����� �a group�ucture. ͠��no1 ���A!M�Fw�!�v+can�jbe6��pis metho��stead!_ec6;nd�Z=� 3A�.�m_�-In I�}�w��.�!���( $L^2(Q_p)$�b���!1Af��YoQEw"� �)^!�? U7 ��� is (:'mV�2� 6�h") gM�Me� Haaru(��$p$=2)�+ $p>2=e� �"��b� %8t�v*!�U � �� R_+})$�I��� �"��� Br��Mx�Y*�6��r�U�Iwise 5`� t��$p$�T *:s�%�thUlex root�i1)q���� a�U�U�)U!�A��N�%[6�M��^dV �sur��vTXoIYo&����JX full�JcK�)?coyuou�x=�l��sY"2�IJ%q�+�p2�m!�0hsome newF�\]O}_+�8 �#�j� %m nJ[� .3� m˧�\Ac,!�E� i��he imag��anN� }!RX�N"���are, u� shif�n� Gf!b�9 �s�Q�t�y ��p => > ��M.L6"in�i�-��78Q � me*}, unlikA�%w%Bm�e�m�_q�of6\ous.�is�b� &� �NM!E� �,�� � �6�z ���i�Spk 2a�a��.!U.�k "�$ i{��m��LBs�K�6w3w�nk.�.w �mu.�!��on�� i�96�46�Fw &� �4s%,m5�%>��˫e ��j�av"J--!:k ->:56�!.s�K�vl.2/ �IELideI�6�S�*�f 2���Z�v%� �ixa " CqN4 m.�s!�}B� H!�e2BAs.; t��.����aq g���� loop� �1�B*�Serrem A6�� bb ic wy $|xy|$j-b_�$x=1y$s'%���B�A stro�lria]2 in��o� \[ |ab|\le\hbox{ max }(|ac|,|cd|),\qJ  �r�~c \] !�i>$an arbitra|�!1(fi4� ����q pathM�%o�Lwo (�e� JIm� �Aedg#l����M-FD. If a � I$!�.?$p_I+1$ Y�)Io6��branch epxn J>,$. Examples 0of this kind  drees are the Bruhat--Tits  (when�branching index is constant). The absoluteZaA� will be an ultrametric space (with respect to �Dnaturally defined 4h). Consider two equivalent )itions{F.�� �first ]4�,as follows. �$infinitely�,tinued path �Rbeginn)( vertex $I$N+ R+( $I$, which+,not a subset�a largerzB �s%Foff�s i)�! w � some�,R$ (that is,�root)�called RW$ Obviously$.ZAb6 � does� depeA� �choice: �ak!c$any other 1j(A$ leads toA]Y�Q�Rc��is]:�is9qR ce classeEzY7 co.7:�such %m�A�A\% one B^8 coincide start! from2�(i.e.� tail��.YF� q�Hsame). If we chooseA" each1)B�e)bM\i iyRA�reproduc�n>�. Weaom䁛iDaPrtial ora�$(or directA�()�ereE_p2-isIed�!i�!Eway. FixIZ AwanE�D point $\infty$ at)Q2. To f >+ ^+ mean!/at haveA�:b5 $Rz%�� �eto�� � 1va�<i � , or.y.!�K-��!'��:Ym���e�ici�!�: $J>�,f $J$ belonge�"A8 $I �)�denot 1fQQ4 by $X$. Let ua(nstruct an .`!�a!u sure�6 F �%*$s $x$, $y$cs�j@e exists a unique� $xy$QI�%{��a�� should�� understooQ} 9VE}Si�C%Alj�4are identifiedi8 aths $Rx$� $Ry$�� �텅�a�Sin2( \bigcup RyIC��J�Iv �usatisfyA�\be\label{A} Rx=RAx,\qquad Ry=RAyAxi(ap Ay=A \ee�enot-5 ABC$!�q#$AC=AB5up BC � \[ xy= O,up Ay \] &h)�!IMZ)y %�F� sm�� st (�2 intr�����~)-���� 9 I} {=xM�1 �=y % We�� �8-� ),\%W@N !xI ) ` threa�R)-fFap ��=I!j2g4(non--maximal)MoXRI=I_0I_1\dots I_k$, $RI_1>% >� )s:]��2>�0� -1} �^{\ee W� $I=��et abov堁Ds empty��4 multipliers, �}w :� as $%�1!�31m-�R$��8 incomparable. 2Qt�嵙 ��supremum�fm� sens�<iZ����:a�J=\hbox{S }(I,R)A�[ �� �-M� than bot!� �I$XM =IJi�m�q]R l2dA^��J=J_0JqVJaV $R^%3 take� N $+J and H�!{Hde�H $-1$. Hpant�B� � F, i�e  E]s E9� a)\�w,�O�� oppositee. �I�!lemmaqprovedAM)kEJu� . �T gin{3}� is*r } func ��%�:��if0 nonnegative,�alaY@zero only for $x=� sym �� �!�4strong triangla�4equality): $$ ��ϭ�ea�d�B"��necessar%P.% ity!ob��16|6� , $zBE�th[ �@e�*� e �,F � E� a�V0"�,j�$I$ (w��� thes aWqj �tk�"� ). Analog�&D s $J�� f� $J$;� w�@= �r�K/ ,����$7 K$� � ��!Wus�AA�1J�>k  66;!` wella�4J�'K)� refo�3+$J!Kq4�ed,�re{-.� :�$I=J=K$���F� doo5��5t� by (\ref"6 1}), 6 2}),:&3})�0�d=�T=�T � $I>J �E�>�][eJ$qb%&a Q7 "f>�6�%dwm� ᆁ�I=2� , by:�! :�� >1 = A�� J��Ǒ� d. 2��*!TE'� AX$IqQLwe againob� +�4N���sh%'e��ofQU��P %�"f� �he2�o x"cM�8 � a� topologt.Nt��Z�v��&�$X$ �be logKmpact.  B�{ Jioe re�s exact���p� $p$--adic"� . .7 mea�$\mu$n�%�or �I-.B� � �1( Haaro on�number�o-NE 2�,�$enough to )x8+-� disks $D_��y  A�AA�of all�%�>�:��� m�ntersec�i�V!Oly�:6�di}er $d_I" ±�"G)n � � ��� s $IK I���  1 b! of radius �e�lce�!Va�fY \in !Yai\� {%�Er� -�eq X� Ek(D_I)6��& Q6! 1$. p �~�+ F�ains $p!U �%"� byIF�C H.d���"7  a\m �e� �%nad ve!N�. By � ��extp .v@on algebra generaa�E�($\sigmae�eOI-�le "� ��lctnes5�� "{ 1�}� Lebesguh).8/0$L^2(\mu, X)$�sp` �squ= ntegU 2yo%�o��)"� s!� �.*��}i� �group%�r� no Fouri� ransform� 2��_ nea�hel!*2�$e wavelet Ka$*� enum!����x��� ed�s= j� edE ha� ion��is~uis�S and AO-tU)�uDщ��At��SE�A� +1$ 7� �1� = , $0� p_I<"C B' eZ�0F��z 2T��.~E-4��� �A�d5Ue �������x_I=0,�,�-1� an arbitr� �N�U-~%�f^�4is important:  Ay %��!�iend��F�uwo-�Y��!7 "-5�)�� 6 ffer��-&k!I� lso C5�:�$, ]ed�"2�R$�Q��0 (�![%K9�-9P%8�way�.���d=qB�a� b�qu�!T.�"% 1Uq�.:Y>�U�T�:x[m<*p[ sI&s F=R��IftJTmI��&���&", � w�A :� $7� R6aE�!+�HaJ�� `$��"e � !VI] 5!H $IR$�"$\gamma~�1�� �E� >yAL $Ix=I_{- J} +1}e� ] sM :Dto[�\$be written�x=x�Z}2+1} _  1}}, 0+#\] P$x_ar��ea�� !#!_)'i�}m higD#� lower%�%i>!�is���w�ޥ m A�,u�� P�x$�p_J-1P"g="dw�ɸ �>�� $R!�"�~�e�)� 6�0)b0)�1-� \] T�Q;��a�u"Texpans! of a&f Q�in& ser�ov��hj�� pe)��PN a real-� K= �r fram? v� Is, As (OP� )%�fmeteriz�n Q�EKdigit/ !sugge!�&� K� ر� RaJ"x-�&M*f bf Remark"g%D(�>yo ow��p�}����!�A`�W�� �"� ��I�!� $I 0��l#� by�TU%�bol���\se%�{�w� bas��n6 }&�"� ��5,� �&,\Omega_I(x)$�1��is6 chaARer� cMo�' � 6X.� �a�LeC$$\psi_{Ij}� o� 2�� ��mm ���; $j=1[ p_Z , given�W ula* �Z�@={e^{2\pi i j x_I }=;\a�\sqrt{v �!�I2N �1b�a(.9'of q�Fe�T(�.� �) $1.$I�n 2�"�0 or 1t)��o C�,A��isnT $I$:6Q .:0"��=�%a"�$�s&� o�- yb j�l wisV 2: i -� �� .��dA1�%� � (bucsupy UJ 6�*�0t �theorem�ba�} $\{u\}%�Pan orthonormal system�q�%�"- X)$����:�,)��$"&���--|e�A3F�Z�� rC"�- he scalarNduc4%VA�A{1((pairing} \l�5/, 'j'}\r = {1J�i�{I'})}}\�) e^{-^��' z '� I'� .�[(x) djx)1ʅ expres#ɪ��--&�b/$I\ge I'G 8I'$. Without lo5g���t�+02.#�" �� �= �&� $I<{� n�Re=la�!�RHSA�1�) we gety��Ju��1uR�,"�� .�-�=0�)$)�ib�a&t��W�e:�>�B� &� I=I'�z i�>"\[f�]� 1@�5A� i (j'-j)E�I�M�.-4 =\delta_{jj'}!W%�Ÿ.vS II'} _ɣ���a� ctor�!�\�� 6Dif��u ��� ��E�� os�F�n ���.� to� >� z. e usg Parseva� �+ ty. �a5 �' a%(6u ��)�4w c��F� X)$,%mi!!nNa 9�Zr�r��9� heckpJ�E(��6�!�WA�+���di�&~6�(N { lete2}NRJ���%� {J�%j�#RC (x),�� x_I.y l�;͆>�i*( a�{.K J^ q�.� .pa�!Z $J< jto*#� � &�e=rQ�:* $pars} \sum� \left|�x*� R#�5f(\right|^2= �J) [> J;j} Y*J =>( J}{p� ��*�*6J*� � $F)H J=I_*�(�U :� We w�6 ider"Q�s�� o!�v  or"� *17F),�g(a+�%st�� is>�I_fI"is�exь)� fied&�6��� %p� )��$f$ is�<lengt"�3�$9YA�F��F*!��sa#6v t"�]�propert6 aDI3{I_k})Y@L( _{l=�-�,le62�� rs})�t^Y�b�=I�krfA��-Q�R�}}=mn8 et[(65-1�iY)�-N+N) 5]�:R�1NJfNJ C" )�I�� t��$\lim_{f\toIk�J[�c �=1>lQB. �*D5�.F�A�"�"� bY6� � a�"� �thus  ra?< Z)\(�6� is I+ SYJmsfa�"�i��� ?"!2T2 ��"�2in \citeFs}�� &�Pseudod�7per�}  1>#es=���hp" a family�� pj[��L�-iagonal���Q��-2��=5�J&�3w ,tor} T f(x)=� T(x,y)(-f(y)s y)���-J�&c]/�"�kernel $ G����%|[\�O}�+prob}!a��!Oof rss�$�n&�+ b�(a � E vari�s�/$y$) P oShm*Q52�1�9 �%���)ѷA%\$ ll6&�"(x$�0|"�� �=!A�2�+-101��5��&r,F-R!�l"X%O�x<1�#o!�ja�9ed   (out!��"vic\>E� $x$)13, 4.%fi ?�&> UIᷕ�.� �&1}M��2At }, \�7- if }`6�( .E�2-U���5O2}49O���A�-v�3� $} T^{(I)} N |I|,�2}�w re $ 18 0$, 1 s� -st \�)01}��t&�U FAsm~;1}"��<��� Eu�Y.3a�%31" �|I|��$�u$��A�� ����9s�:-R ��6� � �A�"�i" ��fyi��s&�/�$��).�in7=m�1S B�D6�-.T)2#\j/�h�0i�$.�o�.. �+usb v� u��$8� �"�T-T} �� -T(y,x)= ��[ (*7- y)�I�IO t.N0 ��*O"Y 76%U4�mu� �3P9��"|@!��VZ�is �9\6 �7 2b 9)x-n�5Iy1 |I|e� If $B�\nee��-.AyA(y|= |I| \ee�*�smlc"�-x-y})E���-� � � =� ��.�r2"  termau ~A )� cel-� �mQI ��4~ �%%��g.�;U�now�!it��ies:��>ix�/ +)�&����$2Jsp�ɾA �)���>r�)|I|N@a & O��� Also6�6yE� {�05*� >6��E�0��:?��iL.E�.�m &����W�3�`F�� _ 6.�T�ZV�Dversa~%a�ase�se�kM� : forK +3� �`&�1�$#9� %��� �n �+=!�,�6� valu�C�e�� e@)$x,�2$ X\times X%�s disj�$un�Iof �Wa s�F�9)�w�2����<� V ��ca �A��->�:AWis�V�/-�!� "�3}e�� s=�1})"y )QU=�� conv9�$"l�-�*l�F� ambdagn})A &�| ~* �_" lfad)�(' more�,5c)E.�X)$i�a�se dom*1q�"&��eigenvI�v�B� 2} T� =\)_I&�Z���(` uA�s!�L 1? D= � <_{|Iy|>|I|}T(I,y� + I1 I�vR� m}�B�>Iy|a�Byu I1 sy�!�0!}� ���:�1*� s 2( r�"��a+S@" 2. VyJ1z!+ �. ZD ��O,�>�>@*�&�", �.6&�<byg.ng13C5 a�me�:2C)�^1��T n� & &Vm� � L�:� :�)M�.��1�B:�5T(xy)� � (x)- y) � o]*M!^*d asuC"vCx$�7s  �G n 6��\[:�-� I)�.� �&3!"�6�� �� V�K *� !��E�B��T�'x*� ��5by:�F� -pina�xm�+q� a�+ "<-�! y) (9 :�5n\[ �q2` �`];���Ab��>� ��mz .��p_m2�Y��(1-*  l1!S� lastu$� is�-:��oX�, )����.& -1 ~�mod }p6� .�-1�(ef6�pY�=p�we � A#6}fx�I�zi-]MIf�6 � ���D et" $T��v;W4edt�:�. M"a� �ed �U{ n&a�nG ���$a�\��%� nextq � on �a s�e&B�#%�� .��7�{ *�&� O ���QTJo")04&� I����+A�� .� � }�J>R�J�%�J) �2�T~ %rJ�6"to!Y � .���n� �/i�f� * d�3e�-93.��is E�.=�4az� _{I}=&�%7I)+i�J>I} �.S(1-p_Je�*� .�.(n� !�)�M0 5�%c!�!�9� A� %J�Av�� SubstituK5B�)I�)1 &X%� %G:w-E]��J|,��"LJ(I�+Q�^7,I1691�= \] \[  J>�J)}�J2�+B���36)�5~.A� !��a"��6��%�&�$J��JH5�PYCq(go� � �S:\?s&HU$z-� �QHEdOYd�ŨJ=B )fJ) �R�3�DI!=��V�}&�� "{.Rel�to �(0 line�:�%!r;�aWe� "z$B3 j n�*��y0o�� <of�Me s�9�Nrat�m�bl&ls�{00}_+Mn� half--� was�cussed��e �:� j �1a�?�F�,�7afg=�+n�X map�3�4!r�Šv�"�1s (u9chang{va�� "1map U� �()V�of"u2".E 91)s*�b9ea?\(� p$=2�9$p>2$��n� �Y:."��tl@F�'�)�_+}�O is "mge�<lig2gt :�}X � 85f�complex �dA 8.�tep�%9i�X19�3": H�I�%Ath]l�Y�1.�j 1�)�6i �X i -1shifts>di� YvmS&Y�, cf. �,Daubechies2}iD� � xa!!2A�A��A ��N�'$haar} \Psil chi_{[0,\�4{1}{2}]}� ,1�&�-�)�1tfZ�Z�I�d)$ (or-ao Qre ]ionQPs]!`%�^�f P)+�G n�=2^{- !' 2}}(( + }x-n�J uad  \in e$Z}uPn>&�Ew�C-���% S ��(xaqseeM+^r�1&#wayA#i�/m�d�5� �!&� YA�!+� paperJ9N�=� �5E(p^ -1}j �/O5(|$} x-n|_p); �=#,)1 Q_p/Z_p, *�4-1�A"& 9=F��L1ed �(eta:Q_p \to)�a�X�U�� W!�ta:8i= �}^{�% a_i�iHaps�%cf+ -i-1Q#a_i"�>p-1I9MQu �Z�nd�k&q%�MI�6�.�(s.:L"�a�n:� iuG"* �To3.)� {\sl4 $p=2B�$!r$,":"-Y),' �Fw*��0$e_!�� �U"�[.�##i* QG QA�$Vladimirov*U\�U:^'mapof�N!�ta^*:�,_m \rho(n)ao\!�(to (-1)^{n}�IT 1 �~>*2OjR �la��J  , ap�Jd�9 6M>�5�+ _te ��.� -o&�/ ,'To"�Vc� by� ,��� m $$�v^{(p)}5-��>h �� .�mF�JQI��� E;Z}_{+}{CH�A<0",  er�;!� ��&e�l�W�&�l �O>�Ul ,(l+1) �@$$] ED�a-�VM }, )ted:A�.� 5�F�)/= n;! -��D; n.�!>V>�'3Py2B ^$:�1 s rise?a new *.�m�� V I�=� M� D�*N�we buildbW.�E�3e  �*� Jd` i.!�$a�:X2g$"<*��9���@��@ ��@;z&F$EiRc]%U) rho$ look.�c^new�� 9: x��ik�7-1}-6_{k&�Xl=kU5P.+"�-?[�i6"�-"�-�>;2 �T"�B!��� rho:��)�&ޗ�_"NC  BapA��f(one--to--on� 6;�TaB almo very���.�i�tinuou��*�e�/p�VE�&o ^I }+ l3}R�E�$ 8 �A�� \"olo%i"3Vb�orm} |!(Q�?y)|�7)>�( � .�$|\cdot|"�#LH*J9f"* modulu �argum�:m��9I(.o�tu�c&�"; F�V�F ider2� alphy���t*< y=y_{J_{\beta}} O ��, 0)��X`. EJ�assum�AZ+;�/�\le}$.��i+&-R KiJ>/�'�$�)0,B 0iq 3�E�E,��k= &"� <k}vD]sysy_�`�:rqy)&n2 %q)VRqJ_l�� Et2� �&�2��]"S��y,'.A.{2d6E"k>�C3�D-���]"��T ��)ea�=%!�B�9�b�ZI-m$.�6+5� � �a;\�<e%�z� �n-1I�46wIQ?z��R y-�= �B��i� -�N�4(1-F�"25%��A4!g� f���b8J�4z�"�b in�D_I� e�I)+M|]ɬ"h^outM(X\backslashY"� \{Nn\B �ao01so� Q f". �%-2���-f��$�$�&��G�0& ,&[&*�$$I��q �-VWw�A}sarILm2�� ������ BL�?_��( �\]�$ \[\tilde �nn ���n� }}�A�[q�.w"�OO:�.B whil� seA�S `5��T�XZ�nA8$R�%�[ɖIJ�.� u�r ��!#~1�z�ez� ��b�.�)�N� ]�8hav�� � I)-m������e=��F:k���b%6��I�V�:2� nV�H!��!N�6 � �{+U�d���(l3}2=�#A�� oF\!;"� 5B4�F�3Z�[�aFLe6kW $l�K �i$:�#�Y T�s�- $S\ /.w|ve�mu(S)=l(%S)�ow9?+ic_��1(:�(x"�dx!42] j� *l&l4"C) W/�-6]"% clos> terv�- �� ��~�!��4X Mo>n�� surj�+vnd3b3��[�$ �I��� �J T;�@a��-�e4 (by2k4�� �<�.EQ��A��/A#:�conjug��Q�^*:�Y5:)X%�M�"v�rho�Ai^*Z;=fI2xA26p� unitUWoe%)�in�1J0��>!UbamOof.e�"�<ųon�!:�/�"<&=!E!<�ndI�sm�4}, 5}]Q%]"��#:"" &713�ts}��"! �$\{_�OqL*^A�{=Au$+=a�� *}vIj}E2"2!of2((homogeneous"�!/5%.%��!"*  s$"_"s"b"=�is)^�i��!�e�e��thhe�Paz4�tu:�t"�3u��R%ym�zi!�!mwCDn)�i>`'�1��ja"q4%�E� nam9L=n8me.�U)� �)L:�R l� S\  in�!A(�5 � �!qnfh�?a^>�#or us� m(p&)��!�o7utru0U I�Bm<combin�ELSK6f1*A$F  txe����X$bf Acknowl1P��@� auth�J �lik�rdank I.V.Volovich, G.Parisi� ,V.A.Avetisov�Lfruitful���$a[* `"�_comy. One�u!��(A.Kh.)R�S.Alb}iol bl�"!l&��Isti�kon V p�*b�spartly@JVh EU-Network ''Quantum Proba~ty�Ac�G s''.�~2�S.K.)lhVBl00Dynasty FoundR�, CRDF (grant UM1--2421--KV--02),2 Russian8!%L Basic Research (pro� 02--01 084).g~d�PrelNf` Fede�&o `�=ps llific schools NSh 1542.2003.1'@ �%oA� Swed�_,Royal Academ^@SU�y n collabo �E� t�W&4ormer Soviet U�7e�Hthebibliography}{99��,ibitem{VVZ} Q.�V.S., q e@, Zelenov Ye.I.}i� Adic�ky��4Mathem�' Physics�H4gapore: World �%@, 1994�+ �l1 �V&V�} O` s�ArusSs�)ps>�D _s��!� fielE�y,�' // AHc�Ana�.�X0. V.2 N 6. p.107--124.�y�2}%EN� �BY"I�.L!r7E*�Schr\"oV&>ype�a .A> .Sci.Izv.!|�(3. v.41. N1�55--73�Khr1cL Khrennikov A.Yu.} Fa����Tolu� s[�fH bH!I,2. v.4. N. 3�248-266.�AlKa} I��I�lKarwowosky W.} A random walkB�,�:,''Stochasticp]o--M�%�Geo(y II '' (S.{�, U. Cattaneo, D. Merlini, Eds.),Sh. Locarno (1991), pp.61--74F�i�Y�5.�ochubei15 A.N.} �G--D.�GEqu�@ ��-�N�yArchimed�7Fa |s. New York: Marcel Dekker, 2001J�2} E�>�Z0fN�eqi �, �,R"9� '��c��mERIzv��a A�8emii Nauk Seria�o.A^8a� 62.i�P. 103>�OS}M]Ogielsk!XT��, Stein D.L.}śmi!@2��,�A@ .Rev.Lett�85�55�15.� 634--1637�-a�eck�� Henberg M.} Long run�uWA�.� _ H// Zeitschrift fur�ik B ---dTyd Matter�60�483--488�HuK �,Huberman B.A! Kersz�U�� �{+ !�x%ܡq hier�ic�E Y%9 J.%<AAuth.Gen �D V. 18. L331--L336� �8Kozyrev S.V.} WF �_ɇs a���`!//�=F�3�=A��; . 66. N 2%$�367. http://arxiv.org/abs/math-ph/0012019�.m+�� I.} Te-: cturP n� s, CBMS L pfs A�%yHSIAM, Philadelphia,A�.�nh��Ɍ-# )#e`�F)"��?+M* 1u!/�'.-.!���!34E�138A�3,A�$322--332. v93030456�strKZm�2�} ��S'� Cυ. � GraQF. 1987� 4. LA�L8}� ADFV-�LAref'eva I.Ya., Drag @ B., Frampton P.,>�Ay"��uni�I5M �� Mod.%D.�@ t. Aa91�e 4341--435}� Andr12�.} ed� trib� in A�"� p� @Dordrecht: Kluwer� �) ubl.Ea.��1Z�BfE : 1�ParadoxA�� m�S�!/BiOqModels. z�G3rs�7ݲ�2Z�E0dsq� �mwFreud'� eory!�unGc;� ��// Eu� an�� J. B%�0��14.��535--�V�.� 60959�Carlucci"� @, De Dominicis C&� �F�oL// Comptes Rendus Ac ,Ser.IIB Mech$ Chem.Astr�|�)$325. P. 52^��70920=��W :�P# D.MTemes� T.} R-�F�6� �8%� block--<iz��pE�matriQ//Y�I��nce�# �7%�105--1� z}7031329� ABKO�,^wJv , Osipove�.Q��aQi aGic � p � str� by H.l 8Energy Landscap� Z�20�  3� 7�89Z� 5�010650*� SpinG�q�Mezard %�6�Virasoro� 8--:c fBeyond�;8.�KIᡩR`ml R!j Toulouse��A.}.h�� for ��n��ev.��� 1986�58E:765�-7.L SerreM � .} T��&}, BR : Sp� er$G lag, 1980D>� �ocb)} �B\@U[12pt]{ �cl�3�usepackage{latexsym} \textwidth 7@WThoffset -0.9in \setcou_{foot�}{0�e�,(ommand{\the \fnsaH3"�#�z itle{Notea��eE�-mo� um tensor!��. mifT -spin �} \^��7(tabular}{c}&$ Hongbao Z�:\�({Email: hbzH@pkuaa.edu.cn}\\ \B�;{ De>�a�Aics!�ij��Ng&�0, 100875, PRC)���>ake%�aba�ct �ntXvid��_Q*6m"@ce� ,Belinfante's^b� �k:� )o��%�"�=IaXQ}"[D���at2BuitB&sz�:�M"m��6< many yeartPb $T_{ab}�#�Ru��s�&Xpr%u mea�t��a#xnXedI �� �iht act[l sour)� Einsl's 4alXa�1a flat�tim:canon� Z�es �5Noether'�bem�emplopOaw� er�currenE ssoci$|�Yh�� ies`;,Wald}. HowevA!870^=ce���turns o�jo/[s oc6W�Cp"u quir� �h. IndexG>-/MaxEx�f;�^di��An gauK��ant) procedure wBa��:lth<? j �lyg �|dA�8an {\em ad hoc} cripa� PWeinb1!RmoA? ha�wa�p�dly fwapproa6bas"�G powera0%(c �B ple,&�A'�{Z~�4natm�&1ourqѡ�s E � ald,�2�IcertaiJf�"]ng� ask�X%V�5Z�AAw&}E�>��B. Desp�"�6f�ie�?irSca�o� � �$&cono�>BM�liter!3fscep�!at ) SaraIa� WQtai8Bconfir�� Q���p� ai��"!to 2iz�i�HSB)u� ,j� . Accordi�i�= ent �ace�s pr��zce:Ljjusw es mTX:�?s-,Vollick,YW} �reE�ceod reinA�!�!�.$-� N� fermZ?)7!!�a(a_ ~.�3eA��EnaPs adopt� Chap�C13A)�a} O~�#,&�A��a?! .���t~�Qxs'a�U wt��riv� s} Fix, ov!8A!4all, a 4-dimen�aYD nifold $M�8O�a� or s 9�$Depsilon_{AB},\bar{}_{A'B'$&� dx,Msh�TakAy![05a�0 $�^a{FA'#T%��d���b���!쉞 {9�B $g^:=>P b`B� �^�6�^ �$)�(Ashtekar}.}�3ܝ� e�,�#6�!iQ �re�&nveniX9�: acute-,y2!�K�$ &;�M��$mapping,.>f� �&rU"0$(i,j|k,l;m,n���eld"�hk $(i+1,j+1|k+1,l+1;m+1,n+15r�.|$�a3� �8� � l !U{j&}^{acVbd} ehn hJJ'}="�C4}�Q ^c{}F�J�dU:I{}_J>;I �J'}�S 3 |yOk�O),� �bN 8eqnarray} \grav��&�8 �a~%�I=� ���Ev�+!OE-!�RORK �J'}\no \\ &9X�Q9JH2X�\G��2OGw�L:�O^�H'=�1�т5�} \hat����+�YWI� r\0e �+�%�l�;U.� �[s;�� g,���Up�Ot "& van6"�JP�no�Y9pexwb_J plac�] SimilarlyB@j2 j; e�i%��BnɆ6) �� A.f& �pū2 : i)�F[2�-ii) �%0Leibnitz rule Z 7uc�B iii)�ute��ev�);eRtV Z�iv:3h�} x-_-io�WTR5ddL/5g ����c&�v!� un�)y!��@C�9d�� n�� v^ $�>22���rI�v��$noCA�!������~*a ��� �)! � �%�(�%�lso�sfulA�!�� m)"�  F�4E� ivenp V "�$, ��$$\nabla_a$a\��co! n�z �or >:s _MVk0�� ����(� b- a)�&=&-(R��^��_I{}^:F_�<^��3�!R�+��_c{}^db)�^%�\. R@)2Tڧv�)]�R��{1VFur��mor�_\xi^)�a KillA��G�{�&6j ��GerochJ�\�$cal{D}(\xi%� =(\p +s_\xi-�F� c��^� de�h�� I:�C{}^D6)_{C� ^{D'6� B6����2Li�?&� E݋$D5}$�meY�r�~*�Q .�>�.���: �b!Fc=aDdab' c� e����NY Qa�aEE&=&gb1|�(2��b/2�&+ a>:�zN2� K:�]~�2�=&eb��bc ��2�R_{baIŨI΂C2�&+)TG�b��.�=&0"� ��� ���Lie-dF� viaZ� �s��Er��ext"�n� BU�<{}��@ H,�)rq $LE�}_N�8�=HHZ�d� (>7uE� =C^d�ac}~��/\G�_{a.z\�3,��V1VF FH���w��*�&p2}-g}^{db}q�a_{cb}q�cab}13b.c})B�2B&@V� N.�[>�2AIA'}+CIM!�6d��#)6rJA':�. +rxAI�x#RxA�e��B]Ѡ5�3B>"4�"fF a�UV�s} Starty�la2g�*$"yL}�rny��V�/ �g9 �a&%V� ) �� B? sigm {�'aN�Ap�t@��,F.= _p=[5��(p)V�:�psi���]"� q��H>A $(M,�R� %Y� F� 2�%"T J� �(I�)��.=*\1m�\ ial.G}�R}.A psi+ ~: �22B�1K� C d�B� 1.�:�=�f.V�*� q�A1=0B�E"o$.6�= " !�a�;asmo��Rs'�N��Y1t =�>��23^��}F�&�e>1L9(6gV�.! 2ps$ K L})=0�[�BXNo�?t�� , Eq.�an)��i��~SF�T_�CVb>n�&%�^b)#KV��YL}`Ca!6Y�O !�9&J�0$�% le��{x^\mu�>b� e LoP!z�|co�V',�p $��<�\nufe rh��[o�PN��5.eR�xiQ_b=�, (dx^\nu)_b- m��Fm t�J��Pbe8� aN%%�_a�\v�:�Q�"�� +F�6�]y �F� �D"�FQ=�y�F1}�u 62M�F�Q>�[Anu]}=-i�^Z%Vx�%"g S?#yF�D�\I�t�J�Na?c>�5�L�H�az}{\cal N�:��� x%�}})�2�% %n%cQ��FH &� ntis) ]7�� lastL ,�eSF�F2%�(-8-N^{cab}+N^{bca& �F{ ��ies $F C=F^{[ca]�&e.c[ab]}]A�c"{&,�E��"Z# �Tb�� Z�}B����": �:# (ab)%N^c}ѩBe��6��� 1�e $-|$")lyR� (=-26N I� b�(�e�[b}�Gc]d�,�Bdc JsII') {c]8.� e{}_BYQ�NB�� ���)��E�A''Q��4 A(��wR^�#5"g&wsor��6���A��!N� :.#; a�#�Z��:�})6�N$]{M�$ elfZ,rse�2N s.*��Ld��"R?� &�"� :  �^6� !� its >� �ea� u��J�c*�*i�6)*�&.'�\$i cu�)�;Z*:�)^2���)yI[| :���+v�*�H#$aF� M thoseF/g ". N�(per�#I�e�# �r+j%Bu S�5�L}\0�-g bf{d^4xR� aQx�  S=&&�l:�V��� �� >�'2k �" 2aK L})] 0 �$]V . �D��[:���k_{b�-B�)2�+:�Zdc t @% Z�"�1�A&E�>��{+ *ev�A�-&i�2JK has �|gT,-E�RL &")BYD�%� -^ /-��mGdBB*Y�"�#YD}iB�=0�4}I,� Z�E� ��3�A.cr#J'�>�g��2� V�6� [Q~19psiZ2y�4��Q�d;)��]N�6�5ӊ�F�%�M]-�1�.-�"� �Uc:EnG_c:2��HO W JJ'}50k>g'�1̤fa�B����X~�e� �t%me� [T_{�C} ,m���%2���r�>i("�-�"� "%� F۱&�.32 �2���6� �q��?P%�*]�d�& _" iR#\�6.��Ywg_{ec}(��fm�^ lAxefUxa � g^{de}-22ef�.2�&2�b� ��b���[fI"N _{e]�� \�3BThus, m�>� $2g/EQ% � Stok0_z�V])�"3 =����m&����I�AE'*�+&-2 �^��Ѭ��_{[acIUI�=_E]��=k ֕�4"� [�&Q� ���_ .ma�ab� (J�M ^cN_� u-Vl B�"��Fk :��1V��dM}�9��in�N� � %� S}{ �0d!F .�Bd=.vF� �)c$+�A�) proo�tYion*{:�S$;my pl�Y�a&�S Prof. RQCk'+�:ive s�H-� help.*di&�Stu8� �whole�k. I �*�:�*g�Dm�an�,o Dr.C Zhou��5en9ag�7|t�f�,S,>6w{Swas,or�min���+NSFC(�$t 102050022373003)OF�0>7?�> bibi�QW�:R. M.  ,�D�9$Relatvity(&�=� C�Kgo0Ss,~G84)&B :J. D.  s�CA�6 Elech�y4Fs(Wiley,"�N,1998M�}F.�A � K[R8a VII, 449(19408�81}S.  erg?T�HOuA�I�hI:�C�T(s(Cambridge.�GP�-, �95>z26zG�J�A� Cosm�H y: P:�^*�F#4"Ga�al o�H%�:�B@ 1972�<5DRicardo E. Gamboa v\'{\i},!\�?8. A37, 9573(200.�8}D�Q )�K�,v. D57, 3484Q.� YW}H�H�P. Wu68$69, 064008>u"6A.  6<036, 1587(1987���, Unpub0JdZMs0:-'Ope �Y�Y& M. H6<et al}1 -qc/04090�M�>j� &�AmB�B0p�Bmsart} .�BamspBVBBfontsB(thm,amsxtraBJ2 nice3 } %.�showkey>Y�B� style{pla�fnew�u! }�$ [��] .'cor�Vry}{C V+lemma}{`Z#WU�}on}{Pr"ń/%�C� body�{\rmfaŚ} .���}{®�nD � ���]}2�{\ $I2-�0}{E�{Z'O2P!1n T:� �2k B�2%�<}�D].B@}{Cas.!%."prebk% %lenviron�>�%�FɴE$\upshape}{ec!�set��r��}{1.5emB�E�?N�stretch'2B%thec#}E3M�.\arabic&�5.�ETq1�g{q�D2ppBa�o{�( >^PV}{$A� P�vrm V}\:$)��+�FpII>'IIJ(PIN)^*aFT$I^{\prime}R^B�IN�PVB�VN�d�d:�E��ZZ}� bb�z.�RRR:7CCC:TTT>��f}{{\s?B� \�C�>�Qa}{\�h %6�t>%3::%f>%5J%B�te T.q4>LtJ(3}(� �� \t�H[Di�OPEBev\'e"�& s, ...] {�_r)( *u�A�-au$-f��sk [#, $U(N)$ aveT ő�HP.J.~FB`�?_ N.S.~Wз!�add� {6�H�USy S� &Zs,.� �as|evO?��:�(�A�)})���%piece��co"�~�[o��;i,)1 .�, N�A�a�$t^{-\mu} z 0-\omega}(1+z)��_1t mua � ks 1 &m� \n�0��i-\phe� ) \\�@ 1�:-i>*'e� _ ,�VI_J rJ \mu,� 2 )��x�< ($ .=  _1+i 2 $) 3 $ \xi, t��phi� �AQL bl4�$ !�[0,�) �� By so s��1 )� �)��P�A U�)a 1 begu�l2]3b}�.�s,dA�u�S A6��/qHRA�viewpoi��ErtFN 'oryChe[ �B��V �&y a%:etx 8 lems � � TP �Niʶf�k�e� �aq a $\2i ��*� VI� 2V2b}�%  to �)*�� !Ht}�L�;)�`K!D:A$-U #6x�HZga�N�Ufic&D<<*Ma��+Oa $(M�Y� ,\mua�(0,0,0)$u 0�OEUf�7��3 �\b�sf.�$< n_Q&��$k$��Eh DysoUf� 0 $ {\rm CUE}_�+(B��q*���6f ���t). &�G1�!1,0?Lis (a Iva �� e factor͒eT+�>B�͍ev�M)\wo2,e{.  {N+2�`��B�$�U$ �� exߑN}b��.P- \xi = 2$�4��2 =� ~w� 1 = 1/22W�p�-AF���xU@impenetr� Bose g���+iodic b�7'c\4"t� �A� in d�R ŏFFG 2a}. F.�D2@ ��3Gsse�aBy includ! ip�WaJW��align��&� ˹:� 4z_l^{1/4} |1 + |�r/2:(kܿ}� *2}- 6    1/k^2�  1,9� IM� �5n�t1/ pv'}q^2�)^v E� 2� �*<qb97IS |& )F��"�F�"de�1in =n� Onsa]��z� -�two.rR.� ��$McCW_1973}V a PVI>z@��+]�MxJM_1980%T.� 2b`��n��52)��ay cumu�ve�ݱeden� ��p�W��r��V&Z� �z�� �BR6 1,BO0}WZa�A�� =0 $�� ��,&.5�t�re�S��A 5-*��ide�by^! �AvM�2}, uV �2A�*��Ms &+�t���2"2��SN����bleRO. � " Iat$ ��� ��f[le�!�very %mN��fa&%��t"kL^�y:F3g�k".t5& "G=m�, g_{n+1}g_n�,0& = t{(f_n+1-�_2)60�f_n# 13)� �UdPV:a} Yf_{n-1}lK3 + { ?&g_'+ :+4 t �-tBwb� ��2 $ j�~to+1, 2�<��2c�a�_4>4+1 $ �$ nn,v dVm�6s ����tn� shipA !�fRmlI2b4\n4Ba<3?Ide,4�r^urf(4 $ D^{(1)}� $ 5 "�d4B0��Ts��Saa�u\a�A��in��"�oJ� (spec ��Ĺp) R$fO ffQ��of BorYt-Bo �,��BB2}@ ub6�l8A�O��)]3a}fd�&�"��%�}E-#a��5)7.� A()�{ .!~se�`���7s��!1%�)K� +L!E � 2���G^ory�vus ra"> quesE�a"j �oI�� A��� is�� answ�_�aiq�S�it:��ulaA}A*F\����E60��q"i��o �r%)�A"xT&typ<&"��typ"&ly�\j �<a�.^t^am�:��[t!���$�qR.��i ��*�3v&)��.Ac�$6� �h` [z� Bzj��"X�� l�%�I�i�i�9r� �in��, t��A`s !�re�Jl�seSu-lz3�v� $N$-:^�!_!R��f&� �Zr�eNb!I!� �i��4"T�bl �� eZ�q7���c�m li�:� �, a�6n�$&�IOkamo��:q��.�3��sta�& in5k4..(!Q�.qto2�c� Xhe *� iX^5.|�"{B2,P",�\� ��&id �F��6/ur�?.�4��R!a ~i� �g(semi-��@>�)����,.��|_e�& \(ir logarithsE��_ �� �!Y-d}{dzhq !2V(z)}{W Usum+ #\rh%{z~�  � \CC2scwgt2� ��q � u���s-�� deg}1 < m,��:=m $. W^b�sR {� _n(z9K\}"Ԓ_{n=0} $p &ZU.R � ��3leR A8&���R�i���# {d\zeta � i } w( )�_m a � @}�=�2_{m,n}&�Az!�B�a $ \TTJ.0 circle $ |\z�eta|=1 $ with $ \zeta=e^{i\theta} $, $ \ P\in (-\pi,\pi] $. Not:Tstanding the notation,O�i-��!�aR� {I_{n+1}!� - I�()^2%�= 1 -6�n ..sI0BqIntroducI�Preciprocal polynomial�c^*_��$��0$ n$th degree0:��$ bR�!bX:= z^n2y 1/z)6��B� Fundament�,`our study \cite{FW_2004a}a^�matrixN5 Y�;t)�e��Lp 3%h �-�V(& \epsilon/w�\crC 0�& -0 22��sAq�sYdefnB� ���6��&:=}�m�MP.�{e�+z -z�K>�_n�"�'.*eps:a} �1� �N�-!�����6�.� �}A^ B�b-`-I gJwgt}),e�funs��9� $`  � %%�� nd8' &� �)� �s���$ {\rm} J^=: _ =m-1 � �>552�(independent�|$ n $. Explicitly, for large $z$��9i Xml = (n+1+\sum^m_{j=1}\rho_j)"( m�2z^{m-ua�,+ \bigg\{ -[^N.az_j - . s z_j6H r�2�+(n+2j�^3_6�^2iI�2}6S  &2a�12� %-(nV{.,2�Q2�Z�1�6�-25,� +16� ��)�)�3�E�O}(%�4}�*rThexp:a��YK\bf ]�E\1+\halfF�)k1-@]B0(J12z_j6� hZU2c-.\z_j)�+aR@.=-c^2:LI$.�%h�H-�>�_�.�36�3�=�OmV�A="�in>% , �relevant| pres�vX ,� �~ small�l( expansionsJ:v4[2V(0)-nW'(0)]1!y6�B'[2V9-\sA_ nW'�H+E�(n-1)�nm�-1.� z + �s( � R-�]{e�lEZ�.f�N�FIJ�I%�:���.� � U]a 2[2V% ��%q)�h }�N�.+-^Cm�J�16z+[8 {]@J ��1�}}� 2u�jE� :j� �J� - -�6I1�+5�2�2� B�F� Analogous)$mulae hold .t^  (these�be foundJG ). :"6� O"� , �,.- $ $ satisfy�� &� �� al��Fs givenJ�. R��8 2���B�N� M���i^1�irA?}+z�zA�m� ()�yV-�g{nE�A{ EU� q6�I � �}B i( -�� |21�Q�M�Bz�M.rA 7{� z�06x rrCfJ�\F�9��Jx}!�a����B(.R�^*).��N�.[f�2&�j-`i9b�-1�V�&6$�Az 2b9��+�52� Jte�q��!�;!�%�A�r(-�w -F)>2�=R�g�7�%8��-Y,2�j4-a1+%0 �0q�.�}nW52}�P���2�)zR�h}}.pAԂ�5�I_ V�h^� gath�&) ��� �ec j h 2�B�-1�z e�= :m�k.�q- �Ce9y2Rs�E5i��*_��i�i�-�- � =2�R9u )~:"+n6!N�j-�1�\�&�B+F�-.6�Ke[u2C.�9�!��� 2�:�!2�!W!+ :. B�k-9In addiJR abov�B�evalu> of *�"f s atsin�poi � bi�a�� :�1�1�5�2� �A�EnqL6v �!e�myn(U 2 +V^2 A^.N OTeq"�I4 ^{*2I A�M9�.j�2'V�i�_j �ea+v�bq�� [ ��@)Q - �E�>N}}U���aI�[-F)S!�~]^2- + ?2�>P%� r���� X ���_jz�cM�QR� &�!��)2Z��F��.��z_j�R4NY���2N-K)X[s)E3�;� z^2Bp  Y�Ib� 1[!�6&J�6�y�5- �%�:�EQ:� #1�i�2l%BdQ�R�eq;phantom{��NwN� !�=2�'~�59IW��"����f: w"��#� ty"0lead directly�6one� pair Ldiscrete Painlev\'e&�#. Deform�U( derivative�z+.y�) w"�$ec�Larbitrary trajectoriG͉it$Ac(t�re  N���&l&SchleLer� from�"�!< isomonodromic d���� �s4%partic�("%k0we require h�%i"f���1}{r_n�#}{dt}�"&u D.�`;z_j2;�\{��-_jq�V�1~ �A"%rdot}��>#1 S#2k��=uʭ7 �e"��� }e.rC��#-X \sb${�S6�C� $ m=3\dPV}nPVI =}Gtcounter&x {0}aub '{Co RGC �AT R&�$Co&[' } HAwe will) side 4,)M�E�:d  revised� , appl:%M�s�'in�)cea�e�6 �}�"� namely5'a:E� e��'fix��& z=0, �n8third variable % -1/tL* E"�!co= unit�group fp'inicas� u2�VI_[. � this!#(make immediu*sense�q�$ tV# \TT�but it analyt�ly� tinued ofS �( circle. N9(at whe�).V�mu, \o71 2, \xi �(mathbb{R} $�!$< �+b�% real%� posi����co** N�&] }Nt�h�(ti�(nd�(a! sequ5# $�"� �+�Bf*A�$�'$, !Yg,��!�2,<ase. !�param)s such�_ $ \Re(\muT -I) > -1/_2�E��'& eleh&s!�4w_{j-k} $ say,%�be: e�)��H Gauss hypergeometr�)� %so^3inm�- � spac)�,r-r*l�m�\2;U&}VI_toepM69�w)En$ ! $ sign!�tak�- ccorV ly�($Im}� $\gtrless 0A�T��V�-qx %.? \{ 1+\xi{)�f�' 92i\sin\pf�X \� =�E`_Y�.T-�6zQ Nz)}Ey1�޹ -��:�)K��2��i�2� �M�t^�=Z�1VeB-�2�;t)"�'q2B(��proof}I�follow*P ��i7on��Euler��eg 4�rNH ���H 2�st�" phas*v (branch cuts� kťhe :� , see[ 8Kl_1933} pp. 91�( 17 "V�4,lgemeinerung� � scheu/�e".)*-1+remark!,e firs�'�C s waZ�3a} SD�4��descrip�!`>�n6� character1����2scwgt"of -�^�)we�y�&7N �1\�\}^{3}�({ ,� \2�1{�>/����,��,A�@�5�#� �2t^{-1b; $ =af B4e'V(- (\mu{1-ti� t^2eE��c%, ��D )o!>P')-�%b�*e� -�o� V�!��<se*3�m}s� ��)_N�= &"�N �J_{N��S [ (N%*f.��a{r?r :(N���-e�?]�Z�6���Nh-mV�^*����-3r}���5��R�+9��b�:�2�|)�S[�+�&I�.�]za�#+��(N�(>�(1--�E�){"�B@%$7!!N-�c �jeft. +� J�{1+u@}m�_1-� iR�\2- [N+�' R)�]i��YH��*-zUX!|Y( h.{ZzJ8^&-N[Q� b�|%�5��J�2))$})2p��_�m^p�1 +[e�E�-%[5v&yVI-vQ�Y��;�e�[a clo��GS2* �N" �e�$,[ ce Z^ I0})��se quant9� "�ant, o�ivalen�heB�9. OneU�� $quite stra�0��ward.�� ^^�8�O�V�"O� homo�w0ous second-or * '��9� �(1��.$t�Eb} - (N-^,*�- \\ =]I*O+1}c6V>%#-1�ScVI_2ndRR�E��D-Z�I N 1W &�(�ly+� !Ob C of S� 2�a�<ways. By Xng.��$ z $ �e"�al-J�-�L!g}) uo � , 7<b},%=:a>H'autrivia1\ s1; excepE�� �.�* is pr9s!-U�)�8). Similarly st�ng� *�h})� employ& !�a���on nd 4U ). AlternR ly +could � �ei�# ~�i}) oBk �arriv�A(sam��;IMp���us�cis�M �� a "of E�"�� uw�soughtF1u��s�n corollaryB sub-W!z*D � l_{N� ��.N�tb+�l�in�u(@H qvqja �B�ti�O E�� x��= Nq \mu(t-1)+� .(]"� 6.lY�/��/=�-�By!)stitut!*��ex,�0��� }��B l_N,ɮ � $ .�Aul%�Y�]�Bbe su�� exa�yield��%|N�n�&>� y�F�$�� )�AB-�) p"�� Ail+lE IjV1=~ .�)�D-�9�^9OoF more� %Q%�st�B�KM"1qZ �da2}A?eed viaS4Freud approach@$Fr_1976} (T�A .�3b��con&�in8�Y�H &<= {d�=�,z} (1+z)(1+t�&mhr  y z6"B 1+ mu tL} �&w+�"N�&Ez<N}(z0e���recogni�C$e logarithW/ aha�' "��i -#nug Dw' �we�� �B B�by�I �l�!P fi �j�  $��� `�:Q��LQ�Q�Vzre�E�^� b"�A�34ar�$}/y� + ��.-N(t+1� "�Fb �=�*M �- �4V^�� �\� �^CM �1%*&magnuso� {b�E� Z� q(�8+^? '.�I&� �O 1x%�-�1퍡_ ɘ%�n2i�mparis�aH2��z $���Om� $�5A�distinct�a�7W �byM����oA �resD�U�%A%aDg� K�Eal�of.� bb ! :Vi?=� argu���!��Dr�J�  q� �uv=�0O � earsLME�.9 �Ma�D0}%�!ge*K�! Jacobi�,� $�K_1�Kpi-��,2 �b�alphak bet %�s g�B 2T�Equ  (14)!��work VG M�ab���!+-1\Y6F���I���6��"u !-F�$ method. I"is{ u��e;by]� &eV}v|zd6� w'�/�)z�>!�}/ �1Re��(term involv�m� hi'_� `$�)8 a��@�g!� � nd9`�),E!�U��F"�s.M�!f*F to aW(�+��-�l�n � �VI=�. �Q*��A9Z� �[a �J�!� �u��b����Z&��lSoln� 2 Bo}}j�&� �aij })t(�",0��}}�=�7,ɡ�g+&�%���m� =���'-2K 7}�B��B��� �)t + N-� :�l�N��&� �5���o�c!>� �- 6�! >�2/- RF !46j� I�I! a ll �"�;M��+ �l�$�XM�QqBDM�nae%6 $ z^{#2�y��/2e�A� both��V"������i�e���iD�n �()��taso�#�;$���--"�ref#)n$#of~�I F*�� s�?�"�(�%r_n�r2N�%aOq/p$�+$ qS�'$Z}_{\geq 0� ���\$��$ pfA6@ AE* �.U*����c*f*!�OPS%� h )�N� $ 2>' �&�5ߵ� �"aM6� +���:e�} -t-11:J�9 � �1�x2B��x��r< 2��6 �:< 2�N�-*d�!�� ��2�m+ #}).A 2�9.� ��rRj,�~ �nx j ��"�`>�>D2eR) �!@5� ��X!�jR2�,Af(N1S �!F �ŹF>>� a�those�(f��oluA �Ai8��h�(aWin+l g7eu!�|)� r_{0��!>~)� !8 r_{1"-w_� /w_0"T!�5!1 {0}�V.�I �4�w���"1:+B�(.�-'2"� �}:�S� )&2� %>|combi� ��l) ( ����s ,� �sP.iu)�,is how5+�of�� $ 3/<-y,2L HwC����i��Aa�of��$to�0�$e other mecX5!m3w �%^ � i�$*�manne S.��#9l�U�?y!U �1�-�.->��� ��BndX�.PM%+}�!�� �6I zaY@  aft�3"� %.h>:%�fr,=09t,�l1!��� d}), �.�B�9�1� \s&I2R�% hipAJYX��Ad>'��4van Moerbeke}  <$their mostA`�Y,Z8�AvM�2})� �e� cu"�)5BY 2RV (�0.�/)�iA��UW*Y view .q%��lattice��VirasoroK�nts�e/�-ir vax2�  sh=et�P=P. 0, dx"/2}Gt^{K!t�I/los%��tyU I''I E ,|2Q�"�/s� -�� ,  N"� Z '= T��is l� �7�A &eP9du*A�F>al fa7!E0�!n �2�'0qficY$ x�, (-1)^Nt^{N/2�!> $ y> -!��'%d$ v *J�$. G�PI��"{�8 &� 0.0.�5i��&S� V��+1} �� 64 3 �Z�*H k6� -h= 0 �Now��trans8*�to Yi �FT>>�cl})R10isAAf @ weIwVs solv�[�����i�+.g:�5) nowZ/!�e""vW�!�EB�  � }%<-� -1}+�"^1�M� G = >O%� -2}+6�"W -�!� +1}(. +�A�4}) 3= �1�J x_{2}2fv! v o1`��hB:Upo�\ca��a!��4A<���manipu�AX3W4n becomZ7� %@� !]�(!P� -1}^� -l DJ4�� &� )�&� +�A�a�>�&� U?� z =!&� T #B� 6�� (���I!B1}) oN,!~v- +^ (0)��0� �m�FBHP ��6�ty` q�*ec�0a,b;c;x) e24= [c+(1+b-a)x]'+1;c+1+-�<b+1}{cJ1+c..-2;c+2-M~w c���D�-hA�|�� ��`y zero�} �> ][Es.3 \ !&� Wno� uin�$2f#Mus���a{2aoon �E*�� S .* T������<> seek2��3Nx �)P8G R�f @.@z�dPV��� �5urpaa oe /"wkY !V er�%be���Ted&pro�:on^&'y "'a �" =��>�*�2+05�rBi-Y(a�NqGN)�"b�#%2r��@\ I. 1.m&��}<��E��*+ NF. #_1)�%�/��\�4����f��<�� �mu!<� &�7V� -(2N>.^2t>��. �.�!j+1}F0&9�1�!~VO1>MK6 c=�>�} A�0v�m�is jus�=VI2�)� ex replac= $�>I�EWarrow� ��Y $1 59� r_j \maps�;p� r}_jH'�y�qt�C+%�&�F4 �{�  E� � at h?$� : &�@*=�@%Y� ��T}*_BK~aG{00:N) !�� e�t.*�I)���# ^2_N"D�rbX+-�_1B;�) �}6]2�i Um�r�. >{ �t �� � NE=a2&� {�iL @tmV� B<NFj=- ^2_1 � ({t-'t} �)^9HE�5� by�I_"�B�-�&8- /2� e�(2C�("+|Nlb�%�fl.�fjf�+E_-A A��a ?M�hRg>f%��^ _E\2�]� _�e{R��*^2vNB~ r��^q�eli�kC � betwee*#�v{ &s2�aO� j&�"� �ysE�# +�7��� P&m r~ VI_dPa}M�/� &��"(P qtB ixhUGb�`]o�D~� �N� $ 1�b� s�)�of�%B�&W 1+1J� -6�>U�mb ��*� NE� .�r&Z ��Q\�]26�^2r�4Cr} �}e)^2�)YNi�->MF 6}? 5 7 9+Q62\>)Fq7B�ˁ2% I�R{�Y�Y�YNY+BY%�%:�% � �C)-M N1)-)G� �O:.^+%� F"�1MN^2>�%�* ��V�� � ���KN6��V$ 6 e�"(�k���.�* r* ����e^ J !94V .!������(�O� c79��J�wmi&�#z *�>r�cA�I�f���.�� \�<%^) "�� �� Z� V���Z�5� mR .�&� &�.� E��V$Fj�� �� � Av�� � d�MnG�A�� � !��!j�$^<rJ��5Y5r/m�� A�xn� �Di'eE.s� Rm��2�>!��"� � F(way:{ I"� d"�"�<�K�`�Q�?�w"�:�a1Zl � ��m �  ^�&� .F�� a*\\�&�֩o? 1iU��� &}-�.��*� ��.������� � V�G 2��)F��^�1w� �6�O2��*� ^|� �$"� � � � �{� �  uA� %��&&Y�id�7>�<%�iA��&�+! iI8 _2)t {2�=��B�'� a�2�N�J�SR�N.( �h E�� ��j�A���f%�����=A��6?B}= r��8n�.�.���~ł]I%�zb�NeLuL$"%�oo��6�of^o�'&X�*w��V>�aits;&t*is GdOc h)\ ,� @ U%%:�J#(,� �Z� N���,��)T=&X�$�$J���likew4>5 & ��.�s B�`��!��Cnde�1 hem �SusefulBpO ite��rthai hig�+K)#� at("PC%B,st*�'aFraiw# Iof�&g&�#by,� a.*Rr&+-eTQr� *�-�� ��g2vPf""&9269&� .�Rr B�A�" V�/�{[��]P-[V3P2�F?t.^I�.�r[VA 3?-�S&�[} 1-t)�&t2C�{ big]��j!@5keZ!��ZM��[� "�R y�.�Z a�%tZ$� B  ]�Qe� A��1[ev :��x7��.e�� si!Yan�K_a��"rc&�Id�=OeJ/f})�D civ3$|#�1bBY%it{l6 �I NP=�6� BD:�r� a$.�Z�*r:� Y ���"� E?)[mqm  t2�A�e�JZ+( A �B)� �\div �.H4��<cg3A5��"�j V�j� {:��*LN�l"��d*�;)]13{"�)Ze��Z-�4�P�/R��4_) \text{i؋�W \neq�  $}R\d} 9L a�2�`6;�vja��DUu>g'2�. �,+lP��&��en�KsI�2&������m&�&��N*L/�3a�in�0f�Pm� w' J�g assoc�bd&� de�0K2��G� al surfac$N0D^{(1)}_4 \to56 w]g &�(demonst J Xis ��0"�L.�m//%$ N $-9!k �&/eN�:orthogo�*���"��#5�� is g�8��5it� f%� =�E<��Q iJ��@�(a&YAV �J M>h � gr g_N�M M&D{(f_N+N) =',,f_N-&�>�gR74}E  6+f��jF+�} ��g_� +"$$aމ�}�!�+t 9Mt VI_f �I�? subcjq_F�+f��5g�3t{�L��,�.�rj$��k'�`V6t7-HO f_0� �X��"�1e��Pl>" &L t�^T are >k-% AVN!�ž Ճ�Q#.�5F9�M#�#!Q��='�`t�a1L"pT gXfmA�Cf �!�{ &1-t�1#Ve - N� M�.�>7t�� �E ��:'Jf�2�!����GRG�g� � g�B� �C= �(ef}�^ * -3'�d)m(9�e�C!� �� !�h �a>} mu+{M�I�)�3��|R�  'B8 R�C6�ҏ�Jc[ � �}�c�Q3r}f�!1 2BB<-|��f}������!��� ��6�.�-a�F��?t &�nEG 6I. BN>� *>~l1uY�XfmE�P�A���^�-R�+Nt5Z� F�sN<)1f�6 � , "�'�Z . olid�� each� "� "ka�FB�6� 2<U aE:6:�  N� �pa�> util&�defRo" VI�~"�>��6�2@ * ����MA:pe�11&3 0���1��Uq^�-JR�CA`�[J�8EU9�+1D+2k��f �N�(>.A��Nj Rv�-&L  �T��(NJ;U")F9&�P�O:+>�B5� 6soM�@n�VY9Q AlM ulpo 6�!�."NIZ+T�reOI6�+ ��1� \>mQ .U6E�.E�f!O?ge"�P^�n�r}O>Eal �?(xi@h J�_�D�� � &�� ,����AQ �2b}�n�&Q7.�a ^\Q^��k}^{\v0x$}_{2}F0�E$�Cpossib�qLet�[� reW8�?.�-�@er. G†a�i�`(e�at _1, r��,"��R�o�- +1 �J 2 c��.N 7n ��e.&, �Ii-U b6throughf7e�wrec[en� )� Ya_1992,K3"-&�  R~p9~q}(%)a_p;b!) b_q;tt_N�v=I�{�p�K)j%0�p {[a_1]1� "}-9 [a_p>�N� [bf<b_q><� {s_h(:� ]h!z  pFq_Jyi�9<�8$ p,q�R \ZZ*�L. �Ya�.�Pochhaml9symbols�/[�a>��� \prod^{N}�i(a-j+1)�_j��qL�(hook length*� $ �!�g_{(i,j) �%� } [a+l 1�:pw��#, +,\he armleg ��$ 5 $th box�Phe Yoliagra#zaˁ���{6$ j�a+@Sch�ymIt&LG�= 4&��e supersl�1�R;guishi���t��� mleR��s"�Fs��ind�COH7K�a�, ���Om�]MeM!a�u�}by Q'"�{(v< $ d"5tF�i@Wa �hed��]��k�(�] ��Fo��{aJ�5A~� \lan!"E}I�l=/ z_l^.�l�]_l�rx _1 Vtmu} TrT_{K��A�^\ _{j=0}{j!`q&#aY��J 3��+j&�p�9 }+j��pVR2�1}kt&�0;F.TJ�|_{t_1=�� =t_N=t�$"� 2F1���{T*&�w�_�ws|a�n�� |t| "yy(e new obser�~onB�v��4M�b'Th&��)mVs5e�>��.xem$�Y y|RMi&`�f&� �N� I"F1��25�Rle�p2k�G� 9� � e$��G {N}{�&)qM�(1A'2v@*g${�wQ';N+2`Zz�^`��I�[gR�Y� genHA<Ū9]�w'�n%42tV\ �2�u-%g5v �v�v!v nu@A�Y%u�Q9d%�2u-�# �|$ ޡ=0,�>V6 e]"�L�0ac{��끟�{g&DG.�I^{b}_n� _ �ѥS:٥\�NӥArJ lũ��n}_��z.�lw(��>�n���� FCNSzeg\"aor�� 1w2�r_���fnF I^{1)#} 0 'S4q2J:-N;VfP�Jz; �qVI��M+ A z|B�"� ),��� ni���MR0�P�G:p J��T!iB 2F1_��9�Ate�"��O��$ t_i $�als#�y�  [� ��xi� � ]O&K Q?��� W"Omu&���X,�M��>, >1AiJ9" ;o$� � 1}{� jV*�Bz� �N9JLF�}�9�Gsu1�94%�g "�76k .�\ReJ�}��P �mFi5UB) telA !�I)� -�Q�&ZZrN=��j ,���K2QFst2JG:�"t=zerom� whil��%jZ�1 �yVh 2�9�N�� d ��Q>8j����W>kK2d Ya��W�#�acal1�x^aRr��fn :�&= -2k N�F� )��NN:B�2= Two t+ W��nclud-Qk �| ,�9�ig$�Bt �X�<KmX�Uav��`wR�; <�X1&��to  (on (4.1Bq modul� �ty2�5>g,Q ^>=�J�24FV�� V126B8�:<Fm27><����)Ǚ�choic�Z&�X,Q-V�����sA"���1a�FdjƊ�!�sw��y &T2n=/ $.�supoPfurther���L_2����Nn�E$ t��p $�PV�yr.<q� w(e&O�`�|2\cos\u{f�|��}.( +s)$7.s real!5�vI�wa�� e� �L`=tw�)D!.�_&�R 6� 9`o" t r_� �s��`, toge!k)Baw2!"X���Z�, a �a "ӊa �ula�Ɂ�de���t6l� &7R&O0 !R RC} �6��� �to!6!���3*h'.Yj�DYE���dR9^7bU��]&�Y�h�I�� PT%n/2}x;^e��[N��.����� Sett��6!Q5*a�E@� rear��r[1�a ��Q"r0''n.''n6O&b"�~r}_ Q>\����Jlj Z�1 r ktl-"�k�l �3B I<� easy!�verifA�5�b-��2!sW� =t^nIʩ is .�cQ�� �,q_�F$ Q x B��fax��6~� 6�e�e7��MKM9 2h�$\tau$-l��for \PVI"b�tau nb�ޜ p�ަ2 y6� a�e� ��e� !�bcMsh��ca&{&�s &�oLW,[ct � �Visoi�inr(M.��pre%�"� � a�N!�4 $s."���9��d'&tBCb.@B�a� �� �+itr˒ ary �mble,%�f� $ :�{:��2b}, �8us�d=t ��F��6��Fb2e �baY�qOkamotob�ofF�XOba ��ofE�,, a Hamilton�$ H��ed ��4#co)�ate%imo�ta"m� q,pWa Ҏxnd&�/\a�s_0, 1 2 3 4hlCC�l2�.�c3cR�e+e+2 23 4��B� .ȃem*�K�t(t-1)H�%�8 q(q-1)(q-t)p^2�-�6 �4%�39 t)+( # 0-1)�R�p�j;A)I221K2 ��#VI_HaF!� %�evojFq��pI.o2ANHM>"�F.zdy��{d(5�dt��hal H\\p} qua�{dp�� 9-{)>9q� ���d"� �Stoe �2�e�T6H! NqQsixthNC3�'$!A. A cruJ��y!?developaJa��&9fH�Ok_1987�>:�,q�QQ�9eH�_"ٸ&0og��A&6�"It Ǎ����"�&�:f >�  "� ɺi�F��f]�j�)&'�JN�q �\�%( [)"� ,�/mu,-N.N �� 1w)uh CyUE/B� aRso�8�7 writ"�.W�~^� VI}[N](t;� r�-o _2;\xi�c=�6���="\�i l"@". Uint->9�� algebraic;*r���|:��?!s���(�Pr shift operator, or�$lU�:�$ L��� ��ed�-�#�-_xd�*C h�$Dyő r%(automorphisc9A� E�(affine Weyl�&L%yG� $ W_a("�8�1�ps_0,s_1,s_2,s_3,s_4,r_1,r_3,r#9)x� Appl%"�- ��a� .����! uted�+*w S�m�i�%&�auxili���. � ) dPVR . E��S�#���ert�� incr^�� ��lea�zC �ne�et]Cunchani�L_-_{0�pr_1s_0s2s_3s_4so|O? root��U$ ��5^.��)�f� �a�"N��:[ R0"�+fk 1>12>2-1F )4�3"  c4W em�5;. S� !y�Ah $.�|[ta>^� � on{=; � � �k0��4H�K����bB�Y[:%]��L01Z�\($\{g_N,f_N\d6=0,1,\�,}el| �N�<�;*�lxpi1aJ=N��1<<= $"�6{qa�� q� *� ;�.M(+� 5)*1)1)Z )-#q(.� *}� >��v�=A 1}{2�� 1+�i}�7}&$ %\' %!muT_1%1��>��2� L01T���1?} D +eaXq_N,pJX*CD7%vq_N� g0%vE }:� *"&&N p �Hq_Np_N-�.aPhm.�"!u"� A��M��esg } An&Rv quesV �2y.�H��2s��a E��B�`�Z��b�+VLN," � �#DO:� as �!�in"r�3.�u�aƔ� linky� q�*��B�V',�2!l2�Z?$f> �a9>�*� 2�-:< 3� o�y"�C.�e�+V�!4i�imp&�a���# �p_F�!=&pf.�r&�H&Y"iu^'���Z " �ea�Fo�0�*j/��j�m��-V�@+NA�a�2��9&6IJ�@N}�t43�!q�H_O.��:B`cR�2<)=3 ] ��B{ ��ɋ2 q_�90Rt&=l i]3 _N}-)*�HtF�>o=t1&�=Ni5!�� ) N�-�UW�W9$=.�.`)$.��22  ��- V+�--o}'+1}�;NB�>)c�V ={ѓ�2�9ݞ2FM�KQ>+R�>M<�=&)�X%�!@uK2t.)#u���F��VW��q9�~d��u prim�ozB�5tůx;N �$N+�.C!c��K�ch "uW�S)�*�Cm �e�F� $ T34� *�� �;:F3H%�3*�� 4��.T��1 �c&Q��ySom�ń y�2� , T_����.��1� { �\�; F�- U-q_n(q_(�p}�6 &��4,(e�-�&�)&�>3 n�T I p_n---3 �M� -��3-1)q_nZ�4j�4ƍ[q_n�45���v�c ~�= �&� t� {�0 �I^�0��^2t ,� ~A�we�{Eu�Euy rd��,a�*/�2q"��&>��F�n�%���1 �%�Y{��� ��IuD� ��!�Z>��g EY05*.�p}"� ��PLޢB�+���Dc �f�!1� ��w. -aD� all���!��7*M&&/ )}i��">Y-06h^i�Y[� �+][E6��Jŧ2|Y 2P�s���b�V "�A�nE3-?��Qr8yä́�< U�R>K w��a � :�}"4be�o%providl ���� 7  on�!���a��jS��2��ng3, hextens�U:t!�oyJ� |_{\�(�s69-n�"��pro�N�$:1,1)�%Ѵ�3an.^�! �!�"�&*�*o ) to��|� "� &��VQO�(Ѡ�v.�8*u U 2>Y���Big6�JZu Sa*c�*Ah.�&t$ \� $n,p_n,H_n,��}_{,81,�<%���w� �[6� ��1" 37"% 3:I�vD3e�* 142���,"9 "8 4? . UsA��~�ɰFO "#�>n"�l �"_L14seq*T"� [@"�6�g_n,f_nJt"�&MY.�g_n�"{ ��q_n - *�gDN��: A�f V2]Pbigg[@n-t� � >fff��\�FJK�D e=� 0� �"d3� :�-5�{ '�5 q-)�]%X }-Ff�&�A�$��A;N�*��6IUNXUšI=1��YY�� A>ofuNl�c�8�!T�; z>oa�-$� ��y& way,�1p *} {$%$(\hat{q}-t�(@%1)\ t[2Z%"J & )q�h6-(��5 2tQVUp4)q4t�\ &���NzRqdiv �o�J�J��n1a&P')Jy�3:�:��� q:=qҔI!H-$. "�=�(1,*+L1��"�NL1��)�-� V 1ilyL ast�72�:"Per I��0[Mpu*J� $�E��-$�{a�:, $ L_�Y:Z Ma�Ou� L�b", �`>�0 �a�kZ  J asZ[tai��N� � "�M�&to���&K�.!)��)teg{!.B 3a},�s�-5�v.� ch-"!6 3{\: �n2&��{.�2�%��t" ��& �F<dZ&1*w 2)bar?&)>�14R!`�.D4D l��S�"�%"3$>cZ|^, =���2�+j(-�g"&*�0-(?$(6(�r=X + = b5 0�h+-<q_0"��� Q.{ W-�� i�4� -i� �%Y1�2=M':<�e^&�A�Ť%&�&��Ainz�� a-ܭ�!St�� J!u�"�Y-�m�1O *rk}^0is)In�>) .��7� VC&���D��&bnBy�N@01@)�#2��Y1q�2 4�!�3->"�0�B�F� 01mH�8b�&��,$�� � "�e{��gi�v�)>B*n�N�2I*.1��!E(f��3B 01�\5u"S �(Q3�R vLg!t} +qG+0�B� K*%�g_n:tM!e� -f- I�hA�*�8z &� *l�&�01 Z�rm[, & my�%)�"Zl�.p�$ Sssubq� U 00F!s$:�0s,¯AM5�Mx^3aR O�4Y@*�;a�.V�Kx^3"�0��6arz�I4,!~a�{" �,9q !-qm�# p-�pPQ�Up J*�eʱ:Y&.?!��:�ih),-���U�>+R� xp5E`.5`L"��!�F1�\ly�m�^*�<A&�1s�8Physical Models"�< �Gn�<\.�andom M�� A{;0HA��M�2M��l�s M gre�terkte �< r jmj�I�KS�0b}�.KM4}�[FV2"�SY F�(CUE}_N(u_5)��r K3*�L/W|u*H2� *M3_{{\rm Q:[ f����"�nerpre6��"�<��$t $-th powe�4Z#cmly�%�;,!AMb�?�;lue*I�tic*�(�9CUE��hF�s�I|u|�KM�= �V�B� XX��$!�<9%�ee �5n� ropr�oAngE)&�� 1������aW��{l}"(F!�RZm lR� (1+|u|^2zQ&�81/. AR��u:�)b�|Q�9;N>cQJ[Q��$� CUEp�H�+)`-�a}�&a�al�I2w�WtI. �U |u|>-�= BKo,.�V� 1�u`����2�=�VH mu Ne�R���1}|{1\over u}+z_{l}|^{2\mu} \Big\rangle_{{\rm CUE}_N}, \end{equation} to relate this case back to the case $ |u|<1 $. The weight in the first equality of (\ref{CUEp_genH}) is a special case of (TVI_wgt}). In terms of } parameterform 67� we observe that $ \xi = 0 $, $ !, \mapsto \mu 4\omega = \bar{ } mu/2# i.e.L)_2 Q�a and $ t = |u|^2 $. The trigonometric moments are \begin{align} w_{-n} & = {\Gamma(\mu+1) \%�n!.@-n)}{}_2F_1(-\mu,+n;n+1;�@) \qquad n \in�Lthbb{Z}_{\geq 0}, \\(w_{n} � {2n} �~B . E?a ��result%�@Section \ref{PVIs }!�n allow-��PVI_CUE}) to be computed by a recurrence involving A$correspond refl b coeffici!t. -q$corollary}�general5�Md`characteristic polynomialA�,\det(u+U)| $A|H arbitrary exponenAoEb$ with!pect m@finitea0 ensemble $ U%�U(N) $�Lrank $ N $ is given! �system&5s�eu� {F^y�{N+1}6 -1} �0(6 })^2A�1-AM${2N}r^2_N B-��! valuV�2^0Z,Q\21B�;Q� , Ip�a~�multlineeT2� _{N}-1}�2-1A�I�= {6�{N14}L<\left[ (N+1+\mu)_2# +1} + (N- %Yright]j-j-)%T{ ,e� :Jr2p n242} n,olabel�nrRA#})69 subj]����9�uadir_)�-\mu{B�+1;2;%&)MfB#5ٕI9مX}�1�Dproof} From either�D(VI_2ndRR}),l)) o.'+1) :a})�� aXfaa��0�r}_1 � 2r_1a�,e can repeate�argum�ga�C�a ��realRC}a�deduce :^N ^eb_a�fore����`�T�rᜡUfo�@$s simply f!Ɓmialis��� �:�/1�c�EYsK $ N=����-~ Ano%}pt�G stat�3of funda!$al importa��4 random matrix�ory�����t��fun�=$ E��LN((\pi-\phi,\pi);\xi�3!8B4 probabilitiesB=k;6?;%�$exactly $ �weigen��li�v]interv� 6G��is is%ifiżQ�yy�� \\ :��m9C_N} ��(�)$t^{\pi}_{- -�\i1#�D) d\theta_1 \ldots�N N$N \prod_{Xeq j < k�$q N} |e^{i yj}-k}|^2�O����:bB� wher� Ce,(2!�^N N!� �� thus*samE A���A�� mu� �  a� �s t=� phi}�u:� $ We remarkI6Mvse.� ~underlyA�ToeplitzQ�elea s, ��EI�l.Gby~toepM:�2��hav�Ze [� Q~�Tk n�$delta_{n,0�O{ Ʌ!bD i}(-1)^{n+1}{t^n-Q�n}!�e21  A.� scheme�% �r�!ʩd as a ���IPropos��H hVI_L01dPV}, has been presen1 � Dcite{FW_2003a}. HAEwe us!��Ls found Acin�$ ��% E"r}��, toge���!� �.!�I)Y�) one� S= t^{-N}:V�J laceŀrol _coupled=Z��:�A' a si� -.1�5L}mk CUE_7 . 6����K%�fig b+ $ z = eD�oaFՙ"� of�� \times� uniE��ces_ Tsector<�* circ= m�6�]N> �8a�RH AAb�  ��$,1\2X{.�l 6 � (6l $ = 1 - xZh A���ɞ2P.�2d2� 6q y:}�F��re auxili�ivariable�lxa-�d�min��quasi-� a�$ird order E�� rel�1a�7 2x� !K- 2\cos{�)X2)F{1-)E  x_N}*� )A +1}+�  N>  � E.� ,MNG2 G&� 17�o�e!draUsep )}�n( �)^2.�^2 ��ء�+ 2(N� )I4_N�+15S + 4NFXx_N5 2_N).|!x 2t\\O �N 8]^26�%kN5�= 0h9Aalong�}6Q/.!��M \� 2 !x� ]�S ({\sin\dfrac�}{!�e�7baJ7x6ME�F� "�T � firstN��s dire� �X�cl.6b� "� �L� whils� M��&�tO1+*: 6 �o \sub�� ion{2-D I��< Model} Considei8two-dimensional +m+)�Xless nearest neighbour �/ings Al $ K� �� 2 $�� $ x �� )Tions PE4vely (see e.g.�wBa_1982�Le� \sigma_{0H S,N,N} $ denot�����Wspins H(lattice sit�L (0,0� �(N,2�. F�XinUE,an unpublishE�wOnsager �K(McCW_1973})gs� � diag%��-j ��$ \lay�! �\s $ T" b� �U=e��0 (a_{i-j}(k))"� i,j"� ,  IM_ssDiagk A0!�}k RL a_{p[� a�\�1}{e�xth� 0}l  e^{-ip����ft[ >-(1/k)$ #}{͛^{1/2}6�SymbolB��=!� nh2K���� 2}�e analyʼntructure�differ� depe� onQ>  (�tempera5phase]v< % highJ&$. Jimbo A� MiwaM�JMaV0} ident<P 9�) A@$ \tau$-  associa� � (a monodromy rv� deAq%�a a � ,�$ch in turn! >X \PVI�ar�c!* work �r 2b� |,nt authors � ~�aB���Okamoto* or� � {Ok!C7� Th�hc� }!@$consequencl �! Fq�&ed��a solua�2��[�.�M� ��-"� , � i�e�$wp�i: ep1P&^ �� mu�E 4��_n-N21U }, p)Li�IM_! :aB�ofm`\ �il� � b����� �.�!�ux�1�9X�� titu�t��f uyVI-"� 0Gauss hyperge� e7e]s �t�x"�-C2�. Afters �S limi��cedb ��ccount��A whz M$wise woulda�0ular,Lobtains ( well knownF&� "^  "�>� regime��b"�M� !-n}e�{nU� {�!n+\half)  (Ga�! n+1):t& =, E�!a�2��n �/ Y��:a}���! ��Nn�2�-|�t���=, EV�>� ��"u��Q�-n"�os� e BI 9��a >�:�k�"�`2�:�V�2^� � E ;n+2!���cb��� kYg:�N�^� ;9�B�> 0� :�d�M-k�� ���1onY 5vid�XE��*B !f�IM.�"���y�㑨[0 valiq both�e� and BO�s (8�&1/zg H�&L �Q���r� +1,9r,-1,Xl�Hvaz\ 1^� = 1-,""�{J�':f2� $ 2/��-C�(2N+3)�k}(Fi�"+1+ � 2+1-(2N-1 A:�eL#" H63"�C#e{N}+1XL��M�i�f&!��� $ 1(.��sfiu.�)�N�3$% -1}x �G>1F� [ !Z+1jJ~��9*F$���]�V{QHu9�|�!�r_g�)r} S&; �{2-F �N3}+{k {{\rm K}(A�1}��E}I-Y5,_-16Rk^2�T.�!o��jIB��G &�W�M -4�FS9?Ea\{={2-^! -)a!K1\(%�)%c!y)+ #�2'\jr!�2 lrU,>j� $)��, ��rɽ�*$lete ellip,������#B kin�{"�ly#2b�+*�1�` :�,>2b})�]%VI_F�&Lits "conjugate" upon&�� ]�= �(s as requir�� "�#"7':b-J�   � 8VI_rIni<*� IM a})-6 d}) %m���hip betw"R� -�r�!��/ j�-�-� A��*<@^ 34 � � �ng� quant�&of>�" : ��i:� �A�.^{(1)�($Jk X/h B�kvx *�,��ᄖ@/0{}^{\vphantom� }_{2�,�{1}�  ;N;t_"�(t_N)|_{t_1=� =t_N=B�%� ie genHJC"� �Rj.O>�7 C+N� & = P {N}{ �)���N!+ {��� ;N+1>�y} &��H%H�1}Q2gjR%��,=Tc� �eN !- j %),\lim_{\epsilY0to 0}�� ;�- Q�=�= ~<� F�:� m�B� ������ � @1)!!}{2^NN!}k^N ��e�q�F�J�",]�� �r}�P��r�60)�� �q�2��E� U9N)r�)QN�e��Nb����u�� � n�! V�f<��� z� &r�]��0 *� b*�R� � � > F� �� N *u)�"#~r�c� H�� VowJ{. :% �),RVI ! :��=��. Som�re neeA.be take�$6�$ becag$�2+4 �L.. App.a&  proc�$leah��&R����L= \su�Wkappa:l( ) = w0 {([�.]W { #�*��[N>��8!0�(_{j=1}(N-j+ >_{j"v�� 3s`(:� mh!}�#�.9DinSnly tQ� �length�*2� $� tribu�%� sum.�Bhexpres�&s2�NV onU%roughj4trans#! $�:Qarrow�:_1� ��  ! 'toha��grows m�"r&Ay� z+-in � expa�'-�8}���beca+in$� of-Q � e 5s_licitQ���A`��}� N \�;infty}) �B  =B�"a��� At zero.�0ka.|�!�#s�5ify tu�Q���4��1b" �2��N80 \; (N71) ([�/0J;&*�(critic�2 oint11!w�0�2)e9&QgaP1���� 1)` f1P1lr = ARo5?2�=�+!� 5�� ^2(j��j8xj�Z&9-A�"�).� theymW1M�g^g� -2�6k1S{ R� 8- l���6��桓s�all��agreeW5��a���!&�*>� *{Ac- ledgCs}�isearch "g4suppork(b�Ze Aus�8ian R.,Council. NSWe�(���4�'(Will Orrick�_5��"l4lG6�%HN�;.�assis�9setN3{2.8cm} 6 : {2.5>!r{-1x^oddo/ yJ!R5 �}{6pt} %.?e!%row �}{4"\addto 5{.:�2':�\m.�4 \textwidth 16!a u 23cm !M4theorem{thm}{T }2cor}{"�06lemma}{L26*}{*r86��'n�}{1.5esDrenewcommand{\baseA�stretch'2} :%the��{��.\arabic��} �_zz}{\A� bb Z �qqQ} ".?q:(} \vspace{2E8no ��B�*Her}{\Large \bf Spaca�dis !1in7 dom e�x 7sD Jp5mm�b�P.J.~F�Cteri�:.� �Depart���MBmatics��S�>(s, Universi�g Mel&2Dne, Victoria 3010,��; apu>{Introdu A"=,{Motiv� �Ldef�onsŗ topic�!nj?"\%D<>almost}ol ;��i�Y�3@e y%o nucl_7��ics. B!ev�@�@�rac�a�G Wign�)I, mid 1950's �1(Wi55, Wi57}�us1)!ed 9�3of�EAZ4 symm�F �M3,AE�%�upp4 rian�%&�%�A��0ently U�ed��� mean%��. tant�8nce, ��p6-� re�u%�~"�@� roper9@1 � ly exS<d 1FDgy levels of heavy)xi!!is wat E%!h(� Aof��er�4$tal data o)cru9/0isotopes such� ,238}$U� 2�0 beyond neutrMreshold.1�hypb'siz%�� b�U:�-%Dx �&�'%P�.ai�%)G *PAM# B:*�Vces. �4 (x�#�0of#/!a Kay)� , it%�new�:t�/�C"3�� ��B�.�I�c�(8aag�(t% >"n/ed�ex:� . W!�A�nJ3al@�^1&�16�ma��).��,;IA��J@? R2�-� ques��, let u!�ink!fG��-�  !Z Es�)�ck%� A�s�D�a Myd�7�� J��uni!�A"s  normalI�o#ty�6any <�ink ",8 P2�DQ!y��p"*Dy�"F�%�=X�a-5a ~ �origin,56 �= .���eyY/Q��.small mɿa`at sV6readi�� stimI8(!�al uncer�.ty gets�7�I�4increases). Use%Ar2�N�6h7��n j4+B-*%@ew iFe�seelF� eorer"B)I�N�) eY �*� � 5#p�s} �6tak�upEprobllNuJp& , +!M9A;�m%Ů �O ures�f ��igK!� ittl�:dT!�R !'2 to�m& � M�by Por�0�,review he wr�as'I ebook � Po65}2ch col�5 F/ major pap�Rwritte"�9field !Ao 1965. �'�6 ��4�ihrly$ev� }tIGf rorschool�i�_r:ime numb��n exampl!@ a9��P���, like2] .� T, nevertheless exhibi�n� ed stocha`fe�� �W; s ou�Me5�"� %�6�!a�perhapBO�?���a� � a|)?���Dr� ��I���{ $ds$� "1�locu�ro r�z �g��aE !so cal�GPoisson+3ss� ���, oR77.��� me87i�t.y -�] e $. $ n��"  each� � .� !�bro�up"o $N$-� sub-5s,)�-?�� e be�am�l�2 �  J PO cto $1/N7Vuj\} p(s;n�'.} (}D"�+N} )^{sN3N^3 �%, ( {sN \atop�KS{s"�4n!}�@s 6y f�De� ��3�! "fan!a�Ma�Om�$�$6do���o=M��i+2Ya82Y��su=jdAiFR�'š fixD Wk ��J!�way� �|j!aoccup�O�C,amongst $sN$ N@ otala����� ͝ ~VP-> q.3. Sub&�79�Y 2�7 2h,x)=1� �h>�+a�). The2pT,D'ac�VE-1�T�(Kram\'er's !wD![�T�Heath-Br�7-��volume)wAh approx� ion� tallAT!eNLG �<Z@Xe�5G�%�dNU@teger�3icj?.�of %�2�$N$th%�%�<"to)�a�\log N$,�����? �ist��%E!.I�.=Ipredict!kat as .b�(4} p^{(N)}(� N�,�Ws�N �>� �$.P&3f�.:- !� � s $p�G "�G hoodara %!Ye���!�� $p+tA�, B� ��!�"�NN6&(.y9DA�mp6)�%]� mD4})"�6� ů�e a vY�$%�ay $10^9�3� �Ct $M$ �s (/$ $M=2,000$s%cor_a��1V'%A�� (�7��1�1O �V�>H�N biggR Ma�;!� :X9� s;1)$). WCm a histKE�oscalemb horiz��l axis�suAi�H�0 s=Qm �$t� Qactual g�W@�a 1!�mul�>� 2n�pr�8 s a l1�ba&Y^�� JrKFig�<�1af.1}b^�g� l trenE�Gs���o�W *�I"�!��$ � ��Jf�t psfx�=122ce�V5 (-(fbox{double%�(.eps}} \cap`G8�-� D*�!��-m%V:� (���YhN49 yQr�%w$I��� secu� s� ��$N=aL+7) 6�.z/]O .OI.smocurve 6�N\��(� = �Is} $peV= s . !�nd5��"�LE&��)min�91&2�%>�} �Ce�%h�/. pB�*�� }es:� x} M6&.�,;sou�ath*uR8t�w��ma�"v&Ohe bul_��&�(as op>d��edz4"$�Fo93aw42g%i�g�Ɂ&�Hz�haJa�<"�M4�� re�ȡm(r�܁��@4s `unfolding')���as ��y�%�i�Z� situIw�-��Iis� .�c'�no�N}� stud b a-�.k( �ed)2�fO\"YVI� . Ra� -�N�r7�middle^_,[IY+ �K)�I� ��Ip���A "A�B#n ��li d�F�CEj �te.�i&J&b e-J) � beAPourxiH.�c�Pqub�Ds, $13W13$. w :x2}(SL plot�he.�:n $��2�$ VC��!�!� =����� �7izE�(t&�GOE (�7%orthog@Pe�.d2�1-s��%9�lec' (of FyodorovI!is  z%]s��B)jcaYE�":%2D� 0H%���e�� N$[0,1]� H(%!�S)b� �H[ f[/\�J 2}]$�E*� �w&E� aq6�+�e 8xa'k � �=�"�*>!��u semi-mYlaw $$ ��xD ��>a/ nC �x^*.2�}.GM� (]q�s� � $x$'e����,����L��gi��m WQ�AQ�� A �9M�&mxT �?� r6�9!nAw1� i��a�ir٨qi:� �-nFQ�iz�}%!��DE02}8N\� {FRgP). T�!a�(I�8oot� i.�f(P_N(\lambda��"6)s��"� thre��!�gbi7} P_kf�, r - a_k) P�) - b ^2 2R|ADa_k \:�Rm{\rm N}e�� b_kA:&�G}[k�L],L�P!3� .� ��aigbAD. 6no� on ^E\sQ]$ago�gH6b���� or� Q o $x^{s-1�x/ T}� Gv ��%9��]G'r0#64_ aG| a u@��"@�5��3=��%<�ved( > $j�}��� *� .guj� 2} Plo"�2���� � !�6th� 7th�7 8th�Ps (poo��?r � AF6� $13\�^13$ GU.Q2�F� Q���urmisec5ws� �@2H � 62J� :��:esetA_ ��.J /is %Gt$$(1/2) p_4A/2) k$p_4$���j_ 2.10;@ >H &�'Euwa�'( mula�F�,�'etcmLer{ZaL}{0&� =*{eB���}&�Z�!4j��q� 8ŵs.v!!�j�!2��o"m"M�>� �.eHx" x_N� A �$y close?�b J� �e��6�-yB� G`� };TN~a_N^N Y_+0r{I}} dx_1 \c�!J(N \, p(a_N �I�_V� $�0I�2(-E , �>(-s/2,Io�a_N"< �� 1|�l5��� �# (L�%Љ7!��)"6us�is eas40�BS"pE�!��d��8 d s^2}�a9xB; M�g����j��Bv6��:=R�(3a2$ .�!i}^{s/2)� 2�:n \in:�N66-�QA bB �XmWu c�0� a�)3e�q�B/-�ap:9sojZ;)! �M�"�"a 6�J"�19$_{l=1}^N (S` xi \chi_{Y� }^{(l)} )f(J�5I$KJ @= 18"cR\in J$eB >,0$��Q, �Qre �vaSula^Q 2.5x:SE�=�5`Q�{p/FJT^n :I-�E�|_�W�J��;s&� e6�JR� a#�}�F��+ 2�$-� -; -2;sF�or! ival�,�խ:;sRuK%jK% n (n-j+1)65j;sF(H�[d�4�\{2�8\}�;0,>'n}�D suffRs!�o q_� �)%� I�possibb�h���� ap})Q3z�'sCa�� e�]�O��) JKu�1}�ke<�x#(!�&�6N-k)!}f�{k\R.�^�p2iNF� With� W�� �:�j~k2B�6_ k)� b�.pa�_� %�iwowe�r�Oin $\xi�m"&�&� ap1})��(RB5�2V��h+: m_{k���ׁ�\k �!k9��~�� k \,2^_B\�.a"�� �q oro�[jus�`,"�%$[��]u �Z mpac�t,-}_!@�z"I#^b��@ boond� $M^k��s�= $M�Sa�Aca5se basicaš�s�(a*d�w�8now �s0yUqa�mau�Jf&A Nz "Q Aҁ,�var%]B*A( (&;,��� sympic metry {)/ &� 6( }5�Pl% �l%�<sALD+) �l�� � � � !N� �$ly maximumO �2�8l%�\�H2 � �>'P?0c�t �:"� �:��{10�zatrF�) �by T'i�)�$2�2$ � of)�cU%��A? [ ��_+ - �B kA��sepM� $s:bh$%�."&�/van�hs�+ +. `i\mu(s):I |$s��C?`|M $.� �EӡK �A9>� _%w ^*��>Mez y�v}FF@pto s�V72u5� Wi573 a�)� :�,"�v���y�@a�"�4^s�! ansatz^Cws1| !P = c_1�D(s) \expa ( - c_2+ t_0^s"t) \, dt #Z�@�7s $c_1V $c_2^)). Cho�*�@� � i �!�ne4reclaimU }�#*�' [^�!'b} p_2�i{32E�I�\pi d#4/R"�Y��({2^{18} s^4 ;3^6?3.6 @9F'1p*U*%!sJA"�  ��!�!��89t!V6:� Fredholm"*�1*KM} A�S� in" ! Ga��.�*N$ m�M �x:Ka�s��N��3�&"g.C}��&�w_2(x_l)|&|RL (x_k�v_j)^2J�x3we � =q,by UE${}_N(g���y� Q,*  L6G,i�!�Vt�E�.h� edJ� Amon�?&� .v$\{p_k(xHk=0,1J}$B�nL>�h$%C)$���BY " p_j m �| x = h_j \�{j,kj� �y�n� �x82.13'} K_N(x,y)�V& ( jy)R0�g\0Nk�I ��y8h_k�BoH/\\ �VbU{p|DTH- yx\x-�Ce�| � w� �c%�3.12�9^!:^=!<�[ % _j, A�A1]_{j,l�l�%` � o�-�n.Zqsignifica�e y�a�A ��3ZD E_{N,2}(J� ;w_2�Big� M�@M(2L �.b_�]UEikBa" $ubscript 2�+$ �� drp�6e�"�h�<))�w�4��%j*x�^o�!��0�!2f�2a}N!hU�1c�Y xi)^BcJF�M�'�jI�Q(�&���~mad�� �E�\ 94m.H 2a})�0rՔ Dof �ei�0]@" "�CW�8�V�'n��i"zJQ��an�6a�8teV.C atorJ}M.�iZU�K_JZ# $K_J$�a�mArQ? $J kernel $e�,y�BK_N[f]�:=� Jiց�f�\�8y}�& $�2�8  *2810p�Kse"�ala�i��Z� 3.3} Z_��%y�,{�pi (x-�y} =: K2@,yBw��a sui e�eEpD� �a4as2.o��� \det&�K�~\rm� ��NAL� IuO�4��"|9 sineM:eja�<p�>��!&Ayf u�#zE2�$ � *�.:# $\{1�}j""R664i,we�$j=ej�� 3[u�\mu_jF�I��$J�%-s,�!.E �d7 Ga61}e�ng!��,s�5�$r  %}x��u�_$ �&� Fspheroida\uZ-s2� �#u�7 p>o��>//�l"sd�. Zz/�-i{m:�� � $ces, but r8-�&�>+. O"P L"� � r&.���=�{4Jg&� A�BDr� 1~� |"� |B� '� d O� w_1� ]�&%0*,�&� &�&�1�Qy�?� �_ݻT �8n$ Pfaffian) !HFr�*2� ��L;}~~([Ch.~5]{Fo0~��v �+.��SF� ( E_1��>)^s�GS+ K_{1,J.!^x$F+vQ�W6�>� K6��`�} [/k   \diR)R{���� \p }|q:0�h��{}_0^ {�} U t t} dt} -Y�2 }�� sgn}z \\[.3cm]B�pal L x}�~C"i }J�J�� 0I ),?]B�HowK5�A���,6 4i'm^ ��b pu(. any ��usef0�discove�2by Mehta��Me6:�a�Zct���Rul�z "h2. ��> r-�onB�gN of9*n�y>�&� �3A.'.�'��>�;3eb�?m�_,{2N,1}((-t,t�;� x^2/� e�|"=&l" (0,t^2 1yQx��Z�#y�} ):DBQ � 6`�&"�Iq�  2b��@>x = �mK^}+}��foZ1$r� $ �$�I�r>s"�24aݹ2��&qg�y� } +y� (x+::  MF�#�� recogn�/ e�8n47A�a�s&\ u�3}). (��fu���e��we�$e $2>-9o,alo ly, excepr0m)1] 3�؁c\�tw�\rm=�2%O)u2)0odd^� ?� ).) Ba6&�� mu_{2j}� R� N.< t�7 �M gs�,) N� +1}$:F�+.E��\aFFM�gc�P� l82� %lA: Gaud}�1Q ��>��ula�6.���pE!� abu5  $p6��APd�t>!�accurac�D>� ]p.In ��confir�9���� � � &LE� crepanc!:!i��e�? � no worsS �@ fewH cent��jn8.$ "��WQng 1Fi"�i�&�!E/ �p.d.f.~ ��=pe'X2wpec�Si>ubl�G��e�Cnj�6'}&�J|4~� .|4B[��� ��S"� 4� �= Q/!jA6y��f�%B�re��ogrG:�6 �.E�* � ��t.� ��ies���A|eE�h.yv �Dyson'sZ� ular&{ �"} 9zF� |��i�!_k��2j} �U=�,2$�I4a�6]+*� �a0!q&  �or&pic*g@l�2�� &kU):� �W8�JdaE+ ��Dy62}�AZB Gunڃ !Gu62}. I&VfV2�{ alt}(�$CO� \cup2m ,C�>AI^!ES��$ 0VQ$)�H  supet�-%,wo.���!�2b%� al*.F�of���|�g� ",Bmembe�IA��6e� 2�!v��su?% %�%�.� DM63��b�Dlt} \,-�!V{;= S!�B�  ��2>(YDE)�b&3-u 6"$^� uP $w_J�%� 4$� M� FR01}.) UA�aV��$ w$�� � ed>B� E_4.�0;&�0E��"� :02 ,s))|{E2�b f<z� AwR- 3.3e2g! VTbKga1��FA �l�'{2l}) +{*h >'+1u))B�Ano�c2*� �2.E��Sn�3hJ�7!� 2 p_1(1;2J�0I,03.,� QVE���2�!��� h8+u2U8 �TN��C"�!vP�1$; >�8FeG e�af.2}&lmary, 6:(�pionee�]w �of�j,�x� m ���ut, �ce.� ͜&n �c> �H�n"> 9-Z� w 4�#5or�&:1�y#>�uq!r�exg{*�mc7 *��9��x�Jif� et al.} AUp�\!�n�a2;m�@�>9$$:e=(��1}^p (a� -1}, }%<�)B!�-�3sdsA2ҏ---6@( AJ&�,isomondromic(]��E�Iar& ��sZw�`ade�% 4, Miwa, M\^oriE�Sat�� 1980.B ��Vd�. $a_Q)� �2p&�!2fre9D� c�0dynamK�$hV�/!sD�af�A� /V.V+O=6. a�arfj!�F8F�:�e2�v2�]�!de.�{ .`)�jLB� h1N$B�Cna�a "i5�.�]k �$"�5��ew!&�5t�� }� 4=s�<ea���$ @ŭA�1s ut A� D_+(_7}4B��^�8�jz\v+D_-�;ř$$��)D Me91})�HnB?-�y1C$og D_{\pm}=&U@"f� \pm&� 0�:�,s[� - . 8x�(S:%((-x,x�)W , dxBp� �A � JMMS��fh jmms~��- �O,s gma (u�� u} �uB�5:�B 3$ :�sf6��Y�"�.�^�jj1} (u�Cgma''�+ 4�0x ) ( (x� ;a�0>�s6�-5^)"��Ao E ��$thop{\sim}�!its_{uyr0^+�`:u-:�*��3!��mY���"�[*&� $ ��/m �2>�T��\"� F ��+�9�5�ggr)6�L�t.�h��,*YRI�$IKSY91}. F�Wwe ��s ER�eO� rder]-1#s����h��e�L�ninE�����L�hin � move�V�Lhi>%$! &��u. Earl�� Fuch8E0Poincar\'e ha�\ud�W4�V�!�A�^�,Pp} P(y',y,tR�muP/'l���9y', y� .�, meromorphic)t$�contr�`tov+,N� D!ihN)��i�1dzz�+!��!2Jka�E��i.��t�F said�b9�,Km^f|1} {dym�= y^2>9u"���$y�/(c-t=I-�c�4� in�e B��"so:_i$U�.Zpol� �ZQ���y {d 6�*"v�(t�3)^�+$% �_.� branch�8 (es�`!�9��2R7.Ro �9ify�K�� !�a*�&P> !�Q ofy�N��y� ��5hon!�]� �]��+_?va���f�%�NS tra*�y�"�mI1�, �S$ ��R( ��Weiersa�s8PSP}&��,^�6.1]p�(>�M4= 4y^3 - g_2 y3B��XRiccati�jy3FA a(t)aF + b  + c(tF hz$a, b, c�5�+����t$ (n�ct�d� P_>SQ�1%A8�\݄� took%����l%�das V addrAJ�U��7n���%=w�1AF2�R�2 a�y'' = R��-R��<*�&! waa_�>G ��%�E�Y�%!�)�no�g�n:��  R�r%m�A)�Ep]4�_2+am7 Rech#$of six new�u.8���w � n)�e.��. A��,�� %e&z{Q ]<&_ v�PV}-�eh(�{yN��o/�!a� ) (y�  -/(x} y' + {(y�{!QN 5 ( \alpha aN{n4ɶ W + {\NN�x�2 y (yD�� e916�.$ l,�=tVi��;V��n immed<�&iU� o �tI0PV}�\� M  . �'�A Xmust develop a Hamilton 8� A-A�9�Y% idea �>`a .JD$H=H(p,q,t;\vec{v}��\����� $ $>,; e� Xe .�Y�*&�^{Y�fQ21} q �%"�F H-�\ �rp*�6+-n-q}B�$q'�p'�not��6q�ŝ�$t$�meā�$q��!3.o 9�. A^)�6��5e"�!-� Qr��mQBv� �P usua�fan�o9p{ DYz$1phy�t; �kweJ�G-�conuof[�(. Malmquist� Ma2iW�7e � toUaE 1�ia|" alth%[� mtfD�'to $9�Q�Ln��=HM�itselfA��has fAto �!��Y�jerae �A�� Q]7briefl (e� %0G!��g: P�!a�6�E�7OK87}U"�%�5t H_V]6q(q��p^2�{ (v_�3 v_2) �+ 2, + tq \} p \*^6&&uv_�Jv_4 - V&�3��A��E5�traȮD$v_1+v_2+v_3+v_4=0iQare5���#dos�m�.2K�t 2��4 9�T\:!Jt(�?V92^2+ �� = + 2� -?:K8 =6I�Itw�kat,!��FB��Qu�s �i�, $%��BA� &.a &� .�J��MlER" )jF\Q������/��U�"F!it&� [)Y !��9,v_4$m"Ni&n\, �� ai�mE?ghtforwa8�v!@,aͪ�E�& ac��1lia� h_V`  = taL+a7Q� U�E� � E^2%�1 edA�(th_V} - (h_V - E@�O + 4��I4+v�W=D� $$ S.T � _{V}� �e�t`v_2E�/ \nu_{BE�j � E� \: (t�~4F %� no>� ��Lj�-�-�$ �2��.C ��augin{e�*c3{ && (t�9@� s�)K$ a��_%V!��0� nu_1 3)1FV' \!�.� ��ua��4 Mu)Y f3 +.!�n�. (%V �x!Z��JM81} a�B d at�%-�9���� �����).!s>&\ a|>b.� E�nu_0 =%fx�b1 nu_3��H0,�- 2 i ueH \su"�cUnvei$bm�S"�;~&�)9�~���|"�9.�2  2s9 �7*�. Vz pe��abk\'7� ~i� ab�72�?7w"Pawmjs� d%IʺIze�$, Korepin ESlanovM$IIKS90} wh"�X?K:n�J���,�\Christoffel-Darboux type�BlMq�>Er� �ewIinolog 9bm� m�dR�9 xi K�2 �H: \psi9:�Eh &�> - yF� �=� x�1��*�u6�8} \rs_�f�a�n xQ� �:2$ cos ��Ѽ} �wIdir ke�*G%;��1 )-� $R%dwݵvresola �%_ R_J@!U_J�p)1��N^3.14'} Q!:ҋ!� R C !#1  Pn(si��-k!�y�b1} �� �P!o- mQ nI .>e�s"@&�/97I�a�ev˯&�I���:b��&< �a_j} � �& : K_{(�a_2ZV = ��R(a A a_j)���2FB$T�� �,����.��X*} ��& = &['Trx' 5"�>�"vB{-x/}�/r=(�kW5 ^{(x)1%2��\C�R&��o!o�!x!wQ�A�z*�q�c*9,~dR�%�sy���aA�f)� I�'a?+M� �|_{x=AEBeso^bI6~�3R�is���X�)�!� Ii�)N.�QC}��e�"C���#. Ind�Ra?])�o"��%R�of �+�d-d|3vB791a},,�� Dy95, TZ18 Wi�.,TW93}, revea� ��a:e3 Z0ed� ceeds via 捾� d!n�H)4dRa�!u�A (t.1'L ? 6�;.�͍�2hl -g! [EF t R(t/2,t`.VlV8u�=ie��8�1E3, �(��� 6�r!�!�)V-�� "0all A%A!fx�5 d9�zec[���&�eW>y���fic�lo_phi>$���)���>/R� �%�SB/�}iY%&G� $Bs!Z1�b�y�ux��F���y� �N7�)m�9q�5��A+ B�*�=s = >-C( -Ns?�b � �$m,A,B,C�"C2% "�G��#"� uD�a&�sis"�{Ak2l !�-�.K)'ay�aA��&supplG���a@wX Y9t�sU' choi�Q�B!2L�YdCA+%�cn�,� &�8�� ^ \}rhb*!�"�W"�~V-M�� soft��h�oZ�3u�2"�\$$V� {/Ai}(x�*:�I� phE@" cVJ J_a(Q x�->LxU�� In"]�sOs�o��.�?_+�"*6�)!TA5g�a!m")FA@6�X)�% !�+� : �8�ũTW94a,b�,WSM make� �9�I"�Zit,� virt�P�,'s�6�5M�me!?�T��J�!�3�)D�a v";�&�4U�$,f�_d �#rd EZZmeQP%.aa�6)>� .�06�u1 ��J�F12��= x^a�5-x�b�ax�=$�J�lb�*u4YOE�*!�}6>s?(R�c0� (1� {s{ 4N},;F�>0�0B� I/��IGcs�EZB � ;[+N��B"� ^e�(_{(��` R�N,"�� 6/Q %��D.I�� a�x#) y �'( Yf ! J_a'/<&� 2 (� )�n�"�,�&)Yi�E]R i�)\) �^�'n1�Rj�.�,%l:Q**s u(t;a*{�W� t�B��\u>*R�^�6.90}?uxa^2 (ui - u'(4 u�(1) (u - tu'!�"��N}��)� ��D�B�)t&�)\:Ut�@�e)=�A�T.)��? a��&a$a%� �)�T.vIII$'$�zI!Okӿ�L�s.W �m A& .�� N Fo99Qbe�-Cch.5}f5�B2� 0;(0��^�U))"a=��'/]_{1� s))-9� 77.l:F �h�= :".^�KN��G�2C�%FY2 %implied1)8"A y6V�`. Simil�\�!JQ�h2xxy}6@x^2,y^��!|_{a=OS=6k.�9w^(D�- �F+ +&n"�w 9e.2w6"�A3a�4a && r�72� ��2�)�( �'B'Hd�{1/>z ��21  su6'N�fC2�F�  �]+� iex�n Yvb��&a�6.' ]�# rom @�ac�N(.�3ps�x ���:l�(ll P� &�  p.�S"(RcM$H �� e���B�aof �� "�!*�9$,RT1">H  $N|�9$��QasF�� FnP:'� $n \ge 1bw!�latE!x�7FK2�jA7�$.�P8:�@4�U�.^#Sg�(se����DH�� ����+c�&� .�&2�b�J^j,gm"�0/&\xi^j�� �}$ $(j="j��Yp�zu-�@�t�DA�a� �$n2.-D:f�!� dor�"F��bf� �Jt"�y�@"v N�^aqbgBc� v��,GPw�|ve �E,w# �. (; s�D�$meӂGJd�[� yp�eL��!e %5�E  k"���))F!|�1 e�.�r^��%% im�$p_G(i^n.n.}bc�D�?�W ~�adIDB�,`�� "X�BB X�"��g) �$EF�"P:�&�e����a fix��&Qr�q�9�no*�E&!�E $s$ ei�<�`!�&Vm{LG is ��q fre0�^Jm{d1 ds} n B� �r!t] )o =�g(><n'���H�AB�2��SͰR�u��"�XZP fr.Mng�)+�w�dTr9A�f:�9-~^��j�1}4\4vg� x@1 y  {� J_{a+� (�Px) �t 6$y>$SBigN� 2)P>  !�t $a=�CF�(E-strategya� ch l@tQ�u4+ e.&;Z.� Ɂ!��xISl $t�\zzS� 0ZKa[= 6m�Xo&�5a & &^6(�J FO96F�R� frb� vea !H(0^��pi* 9 _a(t�m�t[~�f� _a> F�jf2} (s�_&9 (-+ �Y$a�]("O$9- \{ b}(=-2=�\��_aM� \}^2�  =�]� i;V_s"_ -a�({2 (s/4)^{2�91��\�} (� + �(3/�$a)��$$6 a=0$��fre� �0&�*��E^.1 U�Y�>F(B� �m $a�j�Otat7;dY��'"/.�.�� PIII ���>��  $'$)�Wi03}. 6� �a#e0" �f��C6 ���C-TU��a(2�: >�� ��"jn<�  b �g%"�B.^ assu�O��z�o��o:me�� Ty�3 VP� is!�AM���}*Q�@9%�,$p>�� )=  J%2J,!qr^ a*� �i�s*� 2�,� 2ܡ!�Z fre4A"kD!G�N!(I c�nt5� V,1��:2jFgq=A*"$t '�BUTZ8!p28� �T��2(P!��Qm at� �!/"�w-�6q�& &2z\ {>��0u exact!��lG, *���!��4��E.�i"r��]�@�@� nnt.R7�g1} Co;����nn(t):= J� 1 S[SZ��a�e�,(continuous ��#R$10^6�TnB�: stm� e�l1 (open�Ple�z N(as�ks i{2� (fi[-����n2�dG {Gap*��$�&�-2��o��~�c~��O� tragiĞ�metho�n>?!m��de�b. �F���d�"" *3o��p&� . x8*~ �sk �Yћ* ��A56�!(�"�a�.: F^ �?�[" {a  �aa��.�)aB��O Adle��d�s MoerbekNvM01}��o !3��] �FfaH�A�"Wdu&��j9��B&�.B�Q2 e KP hier�����V� s G:E�solit �oryɁe�".uPis `ch��n"�#Y�Dwʏa�of"Q (!fe*5�VirasorW3]4B-2 �ga>�Q�!�'|%�!M6?� ons,�a�/�th"z��%�V"�?:K*~i&cUVH� 4 Q� $ 2n12�zD2V|&�K Cosgr�$CS93,Co00}߬rod!nd Deif�BD00}�iam�y�th" -Hilbert!R+�a���6�&�yO)� KH99�is�es O�Ata E!�Schle!be=|&-_) z�KodB�K!�:�K&�8e+��#F� �(K2�0 �:'i�&~ roach��be �8io�)is�9"ίa W�7)FW!��T�aOon�'�)v�;U�!+.�4e: |*� ��}�b�6�J�U!��%�920 �M-",�aG��0l���uTQ�E"�'��� ��'�Z�'����F�a�b�2' BYu: %. �|detai<*�un�C1 �͓,�+%��d 6\&7�d'F��Gi��-�s�ct\qQw~��(rict ourselJ�t�i��ZKQc2�/te�)$m1o!!�* �  :MsD ��5�L U@N�s}�$h�]�+a�8r o"M��� .g �{"� ��;�6�� :� . So fark}ct &� .��en�4{9-?4� G {3 2}1C�C4+I�"NB����3.N� 45�C8 s^{5?� 135D5ReA��Fsa|�[1^Xp�ZJ�a|!2�I/�;�"�V.,�1��; �z.(cf.~ �:b�.�gde�Α^e)�. st��Q. FD$���� �f�6y adv�Og� ier )p / >g"�+&o �ap?#� �B] &;$3.1 F�0��X ^�n.�Q��t�Rm�QzSlF�(a_N^N \int_${-\infty}^ D dx_1 \cdots \int_N"�XN \, \prod_{l=1}^N (1 - \xi \chi_{(-s/2,s/2)}^{(l)} )|s/2 - a_N x_l|^\mu p(a_N x_1,\dots, �LN) \end{equation} and still be characterized as the solution of a nonlinear e DX. This is also true at<hard c$oft edges,in 4neighbourhood alspectrum singularity (before4 generaliz�Xlatter is controlled byd kernel (\ref{fre1})). It/the>P � case�"��< which leads to U@am.t}). The quant�$of interesidefin� \begin9�L\label{e2h} E_2^{\rmst}((0,s);\mu;\xi) = \lim_{N \toAEA`8 {I_N(a) \over  +\mu)N0 \Big ( (0,{s # 4N})Q;(x - 2A<, x^a e^{-x} It x>0} IB? where $$ x ) :=�t_0b�.J�y_l}A�^a m (1 \le j < k ,Thus we have^�am.5} - A�ek\xi} {d \ ds} )=Ber��0ND|_�=aT6Nmd = {sA�f(2^{2a+2} \GA�(a+1) 2) } �wJRw,>��.4$a=-1/2$ reduc!�om� We �ad offI�)5})I�Z vb} JS�0$0^{(\pi s)!�uA���)2� %~4|_{a=1/2 \atop!� = 1} =!�Q 3} P2�- Jpm@ v}(t6r-�F=erea�ew 7 = - BR�ad$=2,\xi=1}$e�thus yR)E uh})�$priately�3i�edɆboundary�dieu8consistent with Mvb��f�1} 6�0\mathop{\sim}��its_{tŒ0^+}  E�`5} ( 1 + O(t)) + {8 t^{7/A�"3^3  5  7 \pi2:B�I-Ѻ���qof PVI%�8llows- n.sa�$o be compu� for  $\mu$� e�itsi� in�YtE� fur��|�  -� l|^a$8�� uct E$l = gr; ��2}E�(se results � not onl� D first derivative E�reW A*$s$!I!jmm5 5by an id��(ty analogou� 8��, but)�second|(. In partic� , �fa�rp2bA� ]� = {I�mC} s^2��&2�&} v(t�!:�Z�v>�no>�  (�can/ )"fiA A % $\sigma$ANm!p!!�e: )>(sv��8+ (v - sv') \{ ( + 4 - 4 (v\�16= 0Esubjec%�iJ$$ v(s-R�s��} �%1-`15%a.@$ The exact: ionqKp1b}) �[2�2�h,are perhaps � mostEuR*� � ]possible!H �Hulk spacing distrib� s. A k�featur� I��� �i� at�y�o)��Dalym $a(s)�%(��s b� \, dt)ű �� extenA�� Fo99r�IA-re�onshipsa�ween gap�babilit�in6� !�:�P��int!�992O96>%�A��Odlyzko.�Gauss�2e�1 eigen�e�n< {Riemann} $\zet� � zeros:�-li2�a new st�tic.�e��� Rev. E�� 4:R4493--�962�R01R�E�Rai6cn�(orthogonal,5A�sympl cM4 52W In PvBlehe1o R. I�͉:s�;i P��an��$their appl͖0s}, volume~40A�%)�ema�tSci�s"� Inst Pub.L��s �M08.��Universm��Unite�Kingdom�1:�[ 6 �n�preA� of some� am� dep�� �z ��jn�To!Cear). Prob�A[l�Field![ 2004� �FW�J� N.S. Witt2��-�̡�"� �2r� sa�o2�(ces: {PIV},I}%Q\ {GUEF�� A��4}, 219:357--39J4 �eR;V�ExU {W}6� type*` 1P .P  i�#�s  sca\�� Lett>�(53:195--200E�2 �����)�1�I}� {LU�� {JUE)�{Cn�P| Aq-�! 5:67ŔJ� FWF�EJV�Z��^�V�� ,{Cy �c�Mli.�? � em Nagoya"� A�004.�4Ga61} M.~Gaudi6� ur la loi ie de l'eA��, des valeurs�z d'une�o8ce al\'eatoir2 ��*6�$5:447--458�62;GuR J.~Gun:Q Proofa"aq�!� of {| } aI�IJy  { .M�F� :752--753�2b IIKS9�R��\A.G. Izergin, V.E. Korep�1,N.A. Slavnov.|DN�� � um cO " "2F� Int.�od��� $:1003--103L 2�IKSY91} K.~Iwasaki, H.~Kimura, S.~Shimo � M.~Yoshid2y %@Fq{3 } .�4� r.�� i , s2�hVieweg Verlag, Braunschweig!�927JM8I��T.~$.m,Monodromony A�erv� d�7�|� �� .��Xs�r� , coefficient�J� � icaa D:40a4e8:� MS80e��,�(, Y.~M\^ori&M.~Sat2� De�yi�xaempenetra� {Bose} ga� a3�  2�b� %��1D:80--1i�82a KH99� A. Kapaev%� E.~Hubert.�Aae oE#$ {Lax} paiA.N&%.@�B�32:814K156E72 Ma22}�nMalmquis2��es \'9�A \'ndu�$ordre dont�g'int\'^le g\'en8 a poiA)critiqI fix6< �Arkiv�(. Astron. F�18:1--89�22.�Me6E?N&O)a.%properc �l�-� ings�Ynuclear�:#2X���{ 18:3�41�62Me91a} V�A "* !q1o5� ��a {%}.&NdeI�4que I (France)a�:1721I2�6W�^��� &�*�Academic8 0New York, 2nd� ion!�6t OK87���!.S  -�ZD}. {F�}2&�� {$P_{V}$2v�JapanuM}, 13:�7eC87.lOk87a��V�Tz�J� Funk�N\aj Ekvacioj}, 30:305--33�6� Po65 E. Por:�%BQ-{m:Act�&6�f�1962�TW�A. Tracd�Widom.�Ir&du��`. c682TW94a!��L.�2S ��{Airy} �'.M�V!159:15�4e�2G �b���Bessel��$61:289--30��2�vM0�,~van Moerbek2� �g �(iX:NE permu�.D������3�� 406.��WW�5,E.T. Whittak�G.N. Wat:� EiA cour�) �ysi66CUP*B'69 Wi55} E.P�.�Chb+Q vectora� b�ed ce� infi� dimens .P �nnals��$62:548--56e(52� Wi57b�$Gatlinberg� ��c� neu� �F.�Oak R&Np 0Laboratory Re(ORNL 2309:5e52�Wi03} N.N�Gap *m�"dou��rv�(in {H}ermitm"t�[Y as>�s ---�;um �)�!Xcas2�a k! docu���\�{"8le} \usepackageKorem,amst,symb} \topma�$-20mm \tex� ght230mm width16oddside 554evAJ. \headh�- t8pt, th�{Th}{T }[w]2" Le}{LemmaZ Co}{Co�-aryZ$ Def}A��.Vj Rem}ark"%�0command{\ol}{#.neu unde 2datops}{\genfrac{}{}{0pt}{}e)bF&1�Yre.[the� H}{\arabic{chapter}.-A4} �Qn@%\setcou�){-1A7itle{P� w�!$estimates aOGreen's�Ea mix�.�$kTe�lem��Stokes�a�(a polyhedrawnA�tdate{} \author{by V.~Maz'ya$^1�! d J.~Ross� $^2$� make� '*�Dof Link\"oping, Dee%abWls,\\ \h. e*{2emf 581836@Sweden >-H vlmaz@mai.liu.se\\�2$:�Rosto� ��18051<GermanyF� juergen.r- @��k.uni-r ~.de�@ {\small{\bf Key�" ds}:6�,5�#,�%$smooth dom��EHMSC (2000)}: 35J25,5Q3E"m ab�"ct}.%papM!e��ww*zXA��Y�*eE ��J�% s (i2�'$ Dirichlet� uAn4, free surface��0+s)%�cribed�L��Q�on.�I�s obtae�J�$� weak"V3� ;h|)0$L_2$ Sobolev��p�"� u�A�q�)�$*9�-%{.� } W��r �)���Xar6Q1��� �2i (1} -\Delta �/T\nabla p = f, \qquad - "5 u = g�=R �$5s�`�1Aon each!!����G3/_j$ on 'q%fo+_���)'-s'given:�%iz�� 0[(i)] $u=h$,  _�1 =h,\ �Tp+2\varepsilon_{n,n}(u^, \phi.> ?n�)h!!:<\?=:=v�-p n + 2pn mM��H!3$n$�!/Toutward normal, $u_n=u)�& � $ �u-u_n#F tang`.H+on o)rvelocP $u$. Fu,more, $�(u)$ de�QIԉ9Y s $\� 12 (\��0ial_{x_i}u_j+. j}u_i)$, .j_ l�(e� >�n$6�)� =�G9&ts-#L-)2z{n5��3sF6. Co�� (i)--(iv��0frequently usw+%studyA�steady-De f�-of in!:reK* visc�,�(/ fp$s. #k)mple,aS$solid wall(*A5-3�Iy;�$, a no-friuX (N�p) $.�T(u)\, n -pn =0$ may be�ful oY + �aly��)� A exia�,al or a!3��� slip��� uncove~ % �s h9$form (iii)�ک�0in/out-stream>(-wr�n K3L)�)Our goal%Zo�:���>�Fo ,� !��9�pro� ,)Jw!�ɚ� y � E�DPlamenevski\u{\i} v/mp-83&ŧ. we M�� by mea!:��;so:�� e!r�/s��)��7s�owers E distI�/!, RcornerH owev� whil[:-;�r9R�(y�(-� hand 1> ed :��so-ca�:homogenea��Rs ̡ ��q 6v con��A�MKaաih �ir�he:!S>� spaU�inB�x"is ~ e�u�R]Z���0��We�\17Y " -��. �(e�62A\4 �jpaJ� di� � $(u,p)\��0H}\times L_2( D})�:a� �H}��clo�.A�$C_0^V>(\bar?^3$ (!se�<ly%�"�v&�!$.J $ ha��8 act �.))�r&N3nA�( \[ \| u\|_ �Hi9�4( �2"*6�$D} \sum_{j�>3 |:�|^2W0x, C$)^{1/2} \]�>�� *^ �-r7����G� � nes5 2! �'�%�%%F9dat�5*s(!�a cer� � pe�/,$A(\lambda)$.&�/�>��!X��ng��� two-"�al anglea� 5��calq4]Ϳz�(ar�.A,alY 6Ѳ�i?!���ح;��s�u"�3Ne+st%5X5��� E\sin1>jta/\biA`)U^2%^2  - >5big)=0AK($ 9o�J� �)b $ Xu�%��@A:. Oe oura#�60 "t .& z_1$��"�*�2+���(est positiva;l�(t� let $W_\df ^l�Tb�B_^B$m A�e&O5i�1�"� W}u�N�6 �!D}�|\alpha|�? l} r^{2 �}\,�x^ * u(x)�". J�<�Lr6V �%� W% ppos��at $f���{l-2}9U^3�.g>#1} $$���=�8belong{c=$sq�tr�aXst,fy�O��tiu-ya>� EAdg;nd�98ax(l-1-\mbox{Re!IM�_1,0)<)`Y(7|X�2X5-����a4Y D}$ coinc�ʕ[ $x_3$-axii�8re $x'=(x_1,x_2A$�=(\xi[Jxi '@=Rm$�.$�`a��$�G��<�e )�.�q���i��an.vof2. ����� shar�Q�>�*} ������F��������Qv�} "� I�*} More���� uI.!�is. ���inu>1�G1}) by H2 is impd�/�H*�,mp ""�om�s $��4}$�7 a�.�<�Y��&"V Gi4} M��=" _\xiu \vecQ P}_i '+ Q5d e��0K�aPRY($ vanish if�$ lw'�e"� e�mJ�4 B�vB�C5yna} F|�6\xi^\g�V!|�1c_{O , ,Mڭ�FB�5\|}���B�z�'�2���AF���1����<ő�����  l� �inim�#1A�E-��OC>m# gral�kD � D} g��6��\xilj :*�?m �"2 � � 4 A�2�. 3 4� conc�Od��ZNY�ene�Ka��vertex ! orig7$,g;M�l�Q ,M_n-_� k�AP:�P&�Pn��  $x_0TM_k�$pends agai� �&o %��:ks $A_k�) �s2; aa�Y R@:,&6� vb6���t-_C9 s ad� ally{ #:�a Z�!�!frak A}.��{VA5h5A! par�9- ��ZH��ar�#DTcNS�< sp�. SjA�>�/a�pe2B+ �� p�Dby Dau� c�O 4-89}, Kozlov, *�Schwab�� kms}u�FI � C A� F fkm-88=:0m��D� J2��# Tr2 S5k"�"ii)��%Mex�Lce!wunI0��;msS6o �� $W_{�,0}^1(��K}.� 0 $��!��$J� �MZ-1/2$ isof>�FZ� � .��K}���}V�@K}\backslash\{ 0\=��R�&�Zz*B�ј� |x|^{2()�4 2�h �.�:*),*U *���"�se�t��absp>ֆq��guarantenl0T4J]�a�� n��A)u2A�>g�S"�7 $x\6VA(�/r���";5� 2�}.�Cy ��qK� i=1,2,3�'to6v2V�i=������*(y�a�!� $[0, )$1|U�yin $(1��to�� 0,xD")$�!N sub��wrivR}%\�-�.}/G�O $|x|/2 < � |< 2|x|$ "Ql.YNn ~ �Je @������Xa $ Yg$x"iS holds"�$b�`6��NZ 6/ 9� \!\!c\, � \L� _- -. "� +*�}\)-^{-81;� =� .�} >���JXkn[(yr_k(x)�|}�; �_k�2�.x)�v`�Y}{%�Zd���6d"D*}m, �/ n�3A~N� $V 5�< N�< "+��Qw(t_NpU�omp I plan��* 1�/A�ch$�)�(BR&mu_k =N��S(k)& "1^  &x ���2Y �F��[p��R�. Note� ��ex2Ein�j$1~aboveu� >�b��! ���1 jg�R2��*�(:�)h=1,��>�2}); va~&� a_kRc2 R&/ "F�T5�r1� greatean �=�I�q ��' #�L� �E%��"��to� F��6� Qumn�/�"=��non)�$2!H\"ol�Nc. A %X �#� wy%�"�f� � %� F���N�ish]_� � d � mr-04}. S"�e*� �!��N�adjoi����q very��"�#�*eFI�YS#all $k$:e &= 2�A&>.bt$� � v�KB�2�Y6 �� =-1-.B)$ (see)1,[Th.6.1.5]{kW )�aC��2�,� $k� I�%�<= -4Z-notin I_� "MSihR7>�� Ai�s �> E�&9 �< �-s,>�, &5)Q& B�7$2�*�%W^{1,"�G}): &�%G9 �J$.M'v0A�a $ed �&�&G}�-br4"�-\  If� (�s'�G})^*)&� � L_s��, $26�:#)� ll"� s).yc $"� xNu�6�%�$2� $. U�5*[,&ump�s;!R�]^��% d. I? $$��dp eځ�lx&t�U�.32 � �kuIt�a~>1%�!�A���Y��#ul` reaS1�3��assum& �Z��2ll�a��vexV excep9X3!_�g)� (iic�&! �_k�\`�%!�I$�en�� .7U�R5.�e4 \cap>O!yqF2yF+B$, $1i\2$x4!���(d2a{g$ muE &�#ompJ�#�>ADs)� �6�L$�,ap22pu�F�>��gM�is bas&�4��(+I��Յ= -�:x2.7�xe)u <\�342��E)pY )82)noM6)4/fh�qE�nIV 1� WE�2� j 2V %R9in219gA�le�*bec�#suf�1!��� vari/��M�& &N(2�:io� �1E*;"�${0}&7� 2E (\boldY�7-thQ )\un} �.!L��,�)KF��-�.�$(xX!-D��inar co�J$r,&:6� oin��U$0�% /2\}�D�d�9e�d�h' \pm$� ��.�7}^+���. -�{.IM�%W�~ 4"� 2[u[2_�6bl8��' a�s J<0,n?=(n_1 ,n_20�%� exteS&�to 2 2j#_P(u).�6i5Y�tv.�8n} (u) .6Kz ?2�M�d>Ai,!�bteger�#s *mn6J-� �+�%� ^-$,�@ivelyutZ$S�[:u#���}��k2..-( 9B)� N(u,p)= �9E�&�99N tBs1,$Js\)p)gQ:i j.��!� .0_{|Y7� �.� �2�f e-p 52)o �.M L3$� "� H c�4E�5�2t1�e� B(u��2J>�!V"�/ $u,v�Cf�6 , $pn#$�A�s�<�- �DD0 a^"| _ !�%� ��� $p,qz��B��2��sD{-3em}-d�8=���.�+ >�-6O( &-�a$qE%)��%� z=��(-�2�,@��"2�&S\\��2�>�ͷU�vJ�v�q�d�t �)#V�� |�(-q�6�v).�, d.C5��I�6W�%� 6�} �)Y�@$��)t � N�1$J�!( V�!D*�! M)2�9 �W �"EiP&�witBg3b $+ )s&"h4J"mynormV}),F*$r=d(6�N�[8!- -- >-1$�  )?"�" ;5 a�9* 2*%,h�)�v�W})F *u3�4 /2}(y8�spa�� �5�9k�1V�.� � /!I��is [is� I;U=�2�� $inf\{ \| vw;.l�D}�3: \ ��N# , \ v = u& �*�\w] Ana�ly{�r!%)"-��>D��":6�� !y. /t�1$9XR\$is equivalOS90[Le.1.4]{mp78Otob�eqm<5 & =� Bb:�(�!�}���  6�8 ��23�2� }u(re-\"�Dy(r,y_3Z!= � dz, d*,{|x_3-y_3|^2�, dr���  &��2� �B�  "r�� *fEr �)(r�3)-&�E.2�J^2T,�r_1�0r_2}{|r_1-r_2�x_3j�.��� j=0} �%x&�6 j)+1%&*.r^jm&)v|^�jdr u!�x& !e"� t) A�UU � >B$-1< P9e �i�n �/�2 $�Vo B $M$ � �Y�."J�l�"�9�-se"�8} 1]�88� F&�7�*E l�O= J.C3C qMLe"� l0} �R1)}��^��}0inuously imbeYn.o5{)[-1-��� E�>0inN�2.�:+Mem 2)}}f�| �) mQ��u �-"O;����inclu�S)� Z��necessmO3.�qN|_M�m"��L.YKr2RM�:�@ $K$.�$)�i� aL!V��e �G�uo^0�92K=x3$K$�$x'B8�3��B��3k&�to �R \V�l0}i,:Y we wZ�uU>B`Z?a}�E�]0K�$l\ge �4�fr`*s��F t $c)$�.��3u.S\[!p_{x'\inB K}�+y2I� -l+1��|u(x'�2���C2�(UEo \noi�n( P r o o f. �K_0�{ { K:Ct1/2< H <2\}.$ Byv 's��E��} [ |vB� W^l(K_0_9�a�} %,\r=1i,Now� Jxi�=\rho$./@�N}E����=u(* x'i *$�0�[*} "Q 1.5/ rho^.�!1��>#!��z/�v�4 ;2V3|>4=V,-)�q2` K_0&6&�*�;9�� dx'.v`t Edx ^s\lyg_{� tack{K \\�r+!�<2�}��.��2�.� Z�x'b�:%*�R�$v�+��E8. \hfill$\Box$ av\,{W6 R>22�L_2"�-V% E��$2- .(Hf( Y�:��rH _{:�� )�l Xi~�G9)�GHY&��&� R���% F�1<rmf�d �9E20rel{\circ}{L}),{}:\. B-�]H}=:"y# V=\{�" �H}�"j03�2i &�.�MD�T"�("�uE)w�ve x��^ "g ,�Hardy' 6!}lity,�#2��1-2} |"�I�c 4��\�^2J�� ���a��e.B���Tx ��� A�*�H'*�  (v��.���U��WQ�aH�c@� DM��.\"� xtR��!��"������Rfa�� 6&|V4��f��A4�$v:T{M�e��Zҥ���v=v_nK*Z i$� ��r&�FF�O,�$��a:C&of1{-jZ{we�S a�k-�a�U6-�&*Ex)�y��^7bvpD16)�>� �)�.` = F�\�X!l}%lV,N &M%� ;u=g12ɣ�� O,�RA,��2B�e��:K * } �=6bA� �:�A� \pm��{* \� �M�BpW/i�&Ao�ional-�}).W(( dualV^*e�$V��o&-X $FA� �?6=M�7DE�,V)�)1 y�Aa&�LR2�"x�f�M��R�$f,\ g��W$�Y͹��{T{AasmyaO�Q div}9(go\X� ���=�."�1�6@/<G r� *FN��n"�*eYyrjsivY�8end( � ��Z%���D�s�!6Daed8ege� star+��9ssaSa7!f�p? $B�Wd ^1�� e}2t.�*b��� _{WS:� K� (�  +*{x_1}��:27�� � !+h+b�5Z6(N�� $-varA['l!C$K��N?X}:^iLAut !�!�p)bkx�K| f BP *b2� 1}f ,WE}(K)}�y2#2 # $� | ><%@᥁m}2�taZ�f2�NJ�H$,ed Lipschitz�b%Y�e�eFe ��WN!PCh.2,{\S}2]{Girault}.� U}_j�vj�<\�C $, b|irXedisb4�Pgru|par�Yl��ms &�=�KE�"�U}_1\cup22&sm3e*I:^x��%�L !�=.�8ty� f\&�.$�t� 5, �q2I8qM:2N+ 6.ICZ..MZ#T "�-� Riesz' �7EtAMi .��s͎z�, $g_j��r*�$*�2:�*�-����TE | g�*} �*K f�A.v�d (g,v)0!�6�& v�4 >���_j& s..�{}B� �b (g_j�.A�J��W.>��XD,\ .�U-�'*cg_{j,0}"j ^+dm�4!�:=Y�,�X| g_ji9�zu%3}� g}_jna�'=�g} � -, �9� =!�g_j g)ѣM�4�$�F��ͩ�� ���C2��qF��^�Zw� 46wA��Nhgfs|.����K)"R same&>/y�A &d�f�mfEo���(�x�9mpM 1\"� �Fi NextC gFB*��s&-�� j�*~ q�*)�+ofJk f���*�Ym F(y5T(=\tilde{f}(�@r $$x'66� FouriG=ransf�Vf-U0V#3�1`qobe+�u�&&A�B�D}}}�! N� \| F�)xi)II aq�L �2if a�inx 5o6,Y]F�a�e�:�4}7F�]� `� f�%��F�Bf�af#�� �"�immedR��$$Parseval's- G�W one.��pk5WB�Z�NW�y6� :4%�; !���AD��!���1����u6!�uϖ 2�\B��%G��5� �6�lRU�A1�nb�$�>�6~W}� B��c� "� �O*�i�6��|����.s�) &�t_K ���"�V��e�y�i!�K� (-� _y W '< JH + /,R#"������GvJG��Dv&�cB7�o*�(�W�M�5�yI��P��J�}�i,?l>j ���-_���2* v}%�x'!�xi��H�~ } W�iQ� a�"9�Fb^ xi^2>G.�J65�x',�C�;{H��y1d.w66 clud��a�*2� �2pW�?u5$.>I B�" 0.I��>N�W_��K)ca�&<\!>C%|4}\\|:~� a�I"�-�9 LqY %�-V�|^2aEo�e|N!=x�ze���u��2�!^"� ���O��� :���;]b&�Hte�� "Th�;t16�&.3co*^#�0O�U�c l&� 3�6-�7:�a �;�� ll }^2kow'�&�� &B�B7�K�F V�u5 $i�e��5f��EVv^E� le c )�%�;]�c��2��Zok AT�;RB�$f� VNAN2e ��* z" �>� ,�v&sw&X�6�&Y},��%f^w%` uf=c�Ai�~�;2��R�! K��A�!ȥ�D3.�22 y_j}60��e � �4|n#�Ρ ��P�znJS>,*} �.Ap�!�\�rir~mCrs!�A� mapp[*NF�6\ni�;�Q�� w )u�^3����losed. &']aJ� o.9V � trivial:n#C Y ��>em,&�"@$u)��3� u$ map�=>�f2on�+AB�$1iJv �B�2I%ExaS;Vnes25C�3� *l2}�2.�p�M2l.�displa��z� u})�)E|��A`�H}�E�å_"=��b� o(i�[2j+c2H�RgeV�AH�K �r� ^3,$ $tik, �I>�e&c. B"6�W!:iSL�  /@Ku�v (*� �!)�T� ���A� ball��j*=� ok�ch>Hv".��Ŋ� )�D�$2Rj���0:&x�#AymJ�# ^L&e? �+>!�a����%Q[ !�Ec2�/��6 %;�']�c$r�.&Q.3�$|X��s simip��4�B$x=-_ ye�N 6:Nfor*�0Ba.� 9����� ult $J���.� 2��6V^*��k2$pHl�;���sA,� %qJZB w^1`$*� !z4J�"�!w= f�K\"�2 �%7�k ��NL#s&^!.+aPthe��u {�0�� � 2(  F.�1�K$*c�ab&V� �q�o | p\B� &� ��| F%V^* 4g2��  wcA)a e�z+F%��  $w�I� R81)�L&�2>\a5�.�. our CK.L%�-��fby�2Y� t1� ma�Fljt o^�l��*�W$g�? N=0$eV_0";*V$ �b=0\}$,�!I�VX= perpE�!�o"�� �HA%,0 �!TheL ax-Mil΢&e/e %R ua V_02�ɖv)=�"R� � V_0,g��EY�H]>| I8_0A:���^*y-]n��=~%3_$B!Cu[ :�.8a�!omoRGsm�!'^-SR� z�hr� q w\ell(q)*�(def}{=} F(B� q)-�$A��)!~�:aQod�M(� �"B=A� R�eO �?6� �s�L� 6�%}>� �EHg} V?6[M ��RM^*}�6.@�4Ibzn $q=-�iCv���vA6� �Kq0M Y �1[ 6[(�.��'e-�vJ  u bh ] Si�@"T3 � Af6�va�g!V�a�� get��� 6�6� ��ɯ u|2P&�� 2:*ɦV . �U�A( J�*� � �]!cp�|�)V� $F�-B4T�� c&b����!�u)�wha�.C�6 l2}, Ձ��CB�2, V� �/�:��� VE�)�Az�YcT��69v=p%�Q}$p���.�r�BV�in��2}!���/#E~�%����' .�' ^{3-H.)�by % �=2�=2. V} g*�^3�'.�, ���M� w =�$�.�  ("1�M�� &��(�ŋ��a�%�;'=bMI� �+>�ra� _.st'ntCF�- =22v |s�@MUii%�? ��%�([)^2$.):�2:�"�){3:�?=�,2).,.�� *�R&;%�M$"�* 1�$wE`�2�PEx)2�qHIb��<211�*w.�+R-�� "�5R��to z�W&P�Fl�� :"6����V�- Jx$f6 2!� 5?eA*a+j��MB+8ZF^{E�� . 1k+� .z��� 1)}>��&;Jm�j � � �imy)��0.�Q@�>@L�B?!F�_& ;=e�J�5.\| O\.2j�e�aL*{X;l�h"Oh^-!g%PJ�%�"�;�Bf��6�.:F11�"�<��}� )�}�u6�l.�Bk�)"?&�L��a���1E\:�/b�M (u,0Q��/��k��*�7V!b� ��&+I�"�v3�B(2�}I',#E*CI0+]er�Tq�6mlJ�q?"D Ju)M.�s�qmQ|h�YT�` �S�  U�Sn�|>;�ER> U�E� P�2����$v�}�\ cJr B�I�lu!f�O Q#��A�;fZ#N �y=��,c#]�F� K@r� plicY��"'S-*�w�AV halfhVphi (i.e.,Z 1>0�x_2=0$yX"[T+�%^H^V*� ��2e%S^-�s-u�-��->�-�~&� �a�a Vf^Q-^ �D"�!$&& u_1=h_1�, \ u_3=h_3^-1I\ 2.�2}u�Q- "�#44M�-\ �XZ&d^-=1M&u_2�,d6�S1�\u���]:$3.$3��/E�~�2�2Fb�*2"j�_j�rP8 }m+3J�3mCe9\Int���6s�'��mJ u|��2E.*UEW) easizd� ed�u�3G#J. >�J.�&� v2�2b�$S^+v=�� N^+(v,0)vI1+2�+$.�m=(� phi)�abmOY]$�#� 1%�$ ?&Zɾ m!�#>3 E/4.�� w(x):�\,� + (1-6�v(x2_��):�)+�L&dE�^M � &�:l$�+�Eҗ�]'Fa2�aa'��? �^EQ"# 6Q&^6.HE��Y��I $�G���b"}~}(M[ }fl%�&�-�:&]��� c�8 |_M$�rSAD�bS��=[e e@>% �41+J �:�$��!,�{Y�H2�`!M7tF��^ ccr}D( h^+|_M\, ,h^-|_M�%KR(T^�z$~rC�0�, $T=(S^+,S^-�&*�8*9�{8"hA"O($d^+=��0hA5�-�cc~@wif%�E��] ���$1Q�WM�}($d^- = 0,\ m2�؅:g*8.().�n^+E!J� -v2f 1}�Y&� U�rP  6 .:f  $0� l-2K>iHb&�<s��[��r(x)>C$&a��>A���>�"5��� �w. . )�� �U�X$u=v+w�#ie��R�6_AF+����eCW#  3.!�Cu���Uly&�gloq!���4 \�elliptic��2�JM# ss.�vE�l, -xloc}^lF�#:gX�I��$1��)h�Dy!1� "  u �xi!S>S]�%"9/ E\in CM��~�. N`6�_Q ^1_%zL^wjV.�R6+A� � W S^0 zV|2TJ)1E�:�ȁz29ve��^b�qO *�%z�^3B�B$� u=�AɅA�A� �du��I5\&v#��%$@61 4"=� &< "j�2*H�(�mE"@212p2�6���*�#VE}�# F�(d,|p!V>} +`9*�.Q�+�.!�\|%%\.�P}F& 6|�2�[B� � O- V�AU�&>]f�Du�rFQw1�y]uout loC*��&i���U �9kK<��]��!���{�-� `\�I\{ x:\�k-1}<�R<2^{k+�$\ j�X?,(k}x_3< j+1\*.\%�{j,k=� @�^{+��}.l=1��1&�?~q�(x!Q� �#x$R�#2Zl` 2;+ \et-==�4um_{i=j%�j�Y�m�� ��i,l5*�L$P1� !K$`�~�r+W<tr�C+u�� �51�=k�� A(2^k x�\5w, =^,gOg({2^k}2Fpp_ ^f3)=%^}u��v5"v"� F�"B��.EB�+2�EPT���v!co��6�.|&%y ,$l1/2< � <2�?A�A�E��he*S��6c���Q6 ZD�62j�Pk>mwCQ�jW-�u} �7g�72R����Iu<#k2��b(', v}>�L \.\$ *�: sF}Vv}/]/N EB3k}F(vUs8 : oC%a.��'yl %k�~ g4"i {adn����[Sec.3"kmr�*"U,21WI6.� �u}�2��2Q}+n<p��:?�} ���+�2)ra�m� F>�6����k 0FBg�3^2Zd�F<u.��&���FF p�B6�"�(�!~�}n bt./��-๙8j�,pn��#��5��gF:86�%+%�ݚg n*)Z`�()�=K6�6 .b�B56�:��}/���cR����,G�"�c�i�Le |1�u1'�R�BI.�]"j �ictoe�!*T zc|�j,k=*~ *� � = B'���Crue� ЁP6�)"<�K.LCV_{ ^{-l*SA$. �QM` !i�)&�T�m�*<u2� 2�� &]$.l desi����]�$p�J@>�>:�3-? Th.4!>@mJE4�py�ol~�!d�)�St!�>�S}b�!.�2~�^3T 2, �=�� !� nebr��L c1~cJ86��$"�"&����;��:8�:Z:�#!��;��j ���P� .u>�7}�JxB aT� :�}�)%I�!�2}=�26!6 �%a�2a��i� Le.2kd0�,Rw ����A��� �c,��xe�� �/�5"��#!�Y �s*� � � �y�rh�F��B�L[Q�2F� :� iK܍_Q6ȟI�]%�]1F]2\ eE>Z"n}�H�b` eta e<.H./��(*�(6�$ AU!tiA�� ��e 2K iK.�RK*~�K%�%��NQ (-n)�fbW �*{Sm���/�"�z.D-& �s\2�z:z�&3T!Fs��q[�+Xb"� 9R2&C^F�5o�*$��*9M.?"&��a��*VJ4�d.��*+2|U��UA,�+M)�0��3}n&�H̵j.h$3}��1.G!�8 �|�pt3���!��.R<re�67s�6 z�, (ɬO%hU);V�7.M!��; 6N� b�nVG227��E�J9C=t:�UN��!C'al $F$=W�L\[�YA�*�ufR 4pF���5�=�_�8�'�ED �B�R��&���gp en>k�(2B 6q%�.� Qn*� 6� �T�� 6<u 2�f2o::5py bs:���VVF"j :$=�h b �*f>F9M�~-�QQ�^*��t�<-�A :�xp_h#*r:I� =�8v_{-hB�p\�>.5(�>�TF(  I2H5f_h.V� @\'$, 6�$u_h = g_h$�_&���u_h�*� &:�Bۘ6?: 6� "�:.WBt/u,p-���"�6 BS1��(_h}( Hi%|�6=6�e%7+9gT6>�A�e2��WĽvI�b�2�!�0�Wh"��-1i3i{} � �Z��(dh6�m���6,0Tv�6�Indeed��\t�K��Rb! e F}MIHgmXZ�Rvar�R?-3� e*�Y.L,"��Gn[`VM&:�,!:�\1�!rN�#�q7O=�3�/|e^{iG h}-1�B"�K9  �k,LhSG&:�=�INz7T2-2ƭ>yk .kERRrY|�H(1+r^2�H2�eV_B^".VRF�*�,F�{m���%chi B�+75"�e$ � �� $r>h��0� $rNB!�Lr^�*&=E }h^{-1}��.`_hAɛ|A60h>R�, chi)V� N"� u�� �� D}_h�Ax&� D�a�h\�Her�Yj��.��q�Y%~%}0^1a�2g �o��-th�Zt/bF dxA�F� vEV{ 1v %�H|FUG � (?b>�W���� (r/hڪ9�-1}^)��le�iinF�k�#N}a8��. *�yr1��UI�Eq-<% �L&l ��D D}} {r�F0׉�<�-{~b�a����8%!�l-�syO�x��!?ri�8��a4Z�B� u=�i�>)�gE�h�T�I��If�I�L{ �{2rI.�dh�SA)2�2�2rJ�32A���hi��]A��T�Z�T6�F3�%(u ). .\h b� 3� | u_zi�f� , pR*6� !��)Q!"!�2S! E >� � U B���5h5u�&���>�3�n.�Ler90}):u3A�bp }�{�}"g*g6���U% K Ԟ'ߢM[��f�T���T�!6���, Q�.s _���A�){zy)�R#z�2���^7 ]" ��B��n�=��2� �±2K �.)�H2� !XF� yn�(���� =�k�N��3>�\,�E:�2C sincey�2�J� 6�p \,\,.� NSl���"  K-1q��* .$9�.�'&a�S  MN� �$^O7��aJUrZY�� Mׁ#r�?  �V8 F67O��!y��V_� i}:<rx=+A�mof}B} :$FO ]�1��yyB��%�� V��gu.|.K6�>�����A�hA; ��b��E�jK<J� e"2 �N:nɽ2V:,�* !2 _K � |\xi|^{2-2\delta}\, |\tilde{p}(x',\xi)|^2\, dx'x\xi \le c\, \int_0^\infty h^{ Ix-1} \| p_h\|^2_{L_2({\cal D})} I�Uh. \] This proves (\ref{3l7}). Now the assertion of the lemma follows immediately from E1E--.R� \hfill $\Box$ \begin{Co} \label{c2} Letf-p2-_}!�)� \Big(!�f^.^3} +"g2"�}F)%�xwith a constant $c$ independent!\$u�$ $p$. \end!� \no)8nt P r o o f. F!�)�1�!4 well-known loAghregularity results for solu5�Xelliptic boundary valueA�hblems (see e.g. \cite{adn}, L[Sect.3.2]{kmr1}) we�$clude thatR L W_{loc}^1(\overlineqX\backslash M)^3\cap V_{I;-1}.�^3-36pa� L_{2,fzdFb {-1}]v,. Obviously,A~b(6ou,v) -tt_� 6#pa�0\nabla\cdot va�x =As��f2z6^3)$, $- � �6�u =6g 2Q}l$,E�$S^\pm>G=0$ o�EGamma"($. Applying2�,6}, we obtai1RvM�E7Yl2j$ and�Ldesired inequality. >Ssubsecaa${AuxiliaryyOinIPangle \boldmath$K$\un�, operator pencils} Suppose $(u,p)$ is a smˁC�)0Stokes system�  D}) ��(homogeneousu�a�di�s �/bc1hich isB� x_3$��u_3Z�pr�D�f!3d�l,Laplace} -\D�z@_{x'} u_3 = f_3\ I�!4}K,i =h_3A " on }Y0����d-��1,eE \frac{Q1S}n.}=\phigeuA�fa��a�} gge 2,���uq� $ denotes%�- 9�M'coordina(,$x'=(x_1,x_2aCe�a @Xvector $(u',p)=(u_1,u_2f)8two-dimensional69b�IKK>�' +��)�p= f'-k�3�� u'=g%�)Win!�B1�3A�$corresponda�ѥ.��5m�bcK} � S}!�{{h' ,\A>� N-<{!� $"-�Ebg����s Here�,narray*} && c�u'WIR if }E�=0-/J/%6 \tau�N=1� �b@I�N=2, \\�2 L-p+2(\varepsilon(u')e )�fVmja%.d -enT�1|='2, �� �V-p�+2N�NO�l e9� by $:?$�i�E�matrix�NI�mponents2;_{i,j}(ua�$$i,j=1,2$,�K$�9D unitmƁh$Yl$. SettA�4$u=r^\lambda U%Ephiap=r^{  -1}P��$ayA2� ����H fun�� $(U,P)�Tinterval $(-\theta/2,+ )$ A�$ratically � �on @(parameter $ �#{\Bbb C}�R ��$A( &�f t' � ��continu��mapping� i]$W^2(-�� � ���)AFmes W^1z* \to � vR\t�Q )� ^3$}� !�arbitr51% s�� ,%�spectrum��@*65r Dists only of eigen%�sI�@finite geometric ��algebraic multiplicities. We give h@ a cr? o� ��4different $d^-� @d^+$. Without los]�rR ,A�mayasI d^-��=�j,numerate} \i�I] case)(e Dirichlet� (L=d^+=0$)NMev  ^NA�e numbera�AV{j\pi}I\$,� $je�an=� nonzero eOger U  2� a<�m�Sb��� eq00�m6\sin � i sinqR ) =0.Q�u� -M%'0,\!t =1$:��5�Y`f{ k}1!Vj=�1,2,\ldots J�1:(2 �)+%21"��)�2��]{ �!V a{z� �2^ -�31ad0 ��toEm��m�o*�AfQ�A�f�3:�2�cosF�P6� are .-�JT..�E�a�nd M0k�Ie�1q; $j,k$��%�4gers, $j\not=06�1m²����]�J�B�F� �E�$k T��odd&2j�U�A"Mq^�ah0�d�j >lC2w�0eq02}) belongQݑ�2�A�X�}$NW BTf2�2-�5/j�2? wj)< !>��!vV21�2J�NeumannJ�3$) m2��2� ���8R�M���alV�0}��H&�We referA5#({Kalex,orlt� !E�s 1e 3 also48kmr2,mps}. Not 6+ $� Re���53 con � 2��"N ,K�N S n.2Fif on"O fs� c��� ":b� $a.�� ge 1$ (or-+ ),�l1� =7 le 2�-$)�4\in\{\pi,2\pi\aO\ q�9-=2j +=2$)! H \{�\pi 2 , {3��2\}�X:�Th�8�s:��^�r=Wrmm =(C,0� M� C$ iX<I�Dhave rank 2 (i.e., a"G zed w�). "�Le"1 l8}�T� W_0^1(K}� � K)$�au �!��:�}"v� )} vanishA6outsie�ball. �I��W_�^0���g.�@0< )<�($h&=0/��`^astrip :��2OAd1- W$$ does notA�e^9�� RN*1 $u2�2 � $p2 ���|�� 6t�8!��t(�|�&)D}\�|�A\Big) .�E�LeZ} Sinc��e s�r�&�compact� A��,p)�V_*Yx^3�6�$� &.�D>0$. Consequently,B dmit$ represent� :D c + d\, \log r +v c!��i,s $c,d�$a�-�<$. Furthermore, )�*�a/a�v2"B�27b�&!^2�9�!��,�,ɋ[Th.8.2&�1�Q�q�n B�dW ��J� s:�\\ Fori roof�),higher orderJ�E+neeb�alo.V�a��l����$l�<:�let $f -6)�( polynomial�$degree $l-�$f�f $l=�b g$ aDF^>.�� = c�� r^l��h��8 r^{l-1�� 2a9"&{3-/}H:$MWm�sa�D�� = l| ��an*�v�A�e exist��queZ s"W b 1l!�Du = \sum_{i+j=l} c0\, x_1^i2^j,\qU p=.Z!dZ0��v{_in9OA�$ H2E$, such�1��2 �8r�(bN In�!ng H%)A�o L$6Se4"� ar� of $4l+3$"Bs w unF��)B,-$�M(=.&��b*�,�6�}d�ha�Aa trivan\ �,ref�P!in Beb C unAtly:vable:i">#;�8>�Q�.�9})�1)} Let-�E �Ve��ݫ� {l-2�W�h�2����.x]^3,��.1z , \ �aA�2 /2}(&E)�;,\ �}B83B8�O7 �]a6NN l-23 ? ZZ l-"] �] y2�l%���2!3O%�2F�" F�.%�F�� ."�� 5�B] ^3,\)�.�,.�2B��-!�2�.7��, E�f �E���U6u I5>x 1�� b� �first�e�'w>�>j 7�'��se;U.} \zetaQP4mooth cut-off "��" R}^2��l`���|x'|<1�c>26  u^{(1)}{�:Taylof 3$��u� $p ?��z<4 <p� 8&W R T:(^�6� sa/u= �0) !81)}� p = ^.   Z C28Q "W&9I>&m�a &Z 7.1.1'�'n i"C � .#\b�(u_1^{��! )� R&Y! p' = F',  Ft!4(nO= G� 2�# v =F_3"C�!]1R F=(F',F_3F>3�v� �'.z%H� GRd2 .2�6��'\t�+d!�" �95,-� )= H� >q>�$>�>bAR� �"� 1�N�\P� B�5:�N�>�� An analog� i�)�# hold�)aN trac��%)!�."A)9�/"%R!$,� � ively. By:�,a3m,qren�F� a��& -4} F�  * A�)fF}M� GZG 3} G~GG}�$I= �x \,� 2�i xH'$,151�:+ :� :,=$,q2 Fy .�} %GF%i �( b �AS .L>�2�52�1/32< $. N�.)(can be easi�!duced f�,&�.1e.�,8a}F� .:)R&�,JI� weak"l s}V�1�.& �)H}*� D})�2� .� bvpD1}),��2})}.�"/��atA�~a���F#F$ � �7'})�*�+��! �*P+$ �&g%�"1�D \2  *{I("r+)^2� 2b"� $&z s{��.I� $$y�' tibiD+  L.cc!f I[ �Nno*�n}1 !W� �V��1"� ��n]6�29L^3IDٛ1 �mX&*�A�(| >�U�"]0>�"} \no��'B�0�2/��| > ` �o���!\|f�Qj�F? 6BFvQ-�"�Q)�!�z"&L1F�,f��gE�� ��� DueG .�11}xim��**�$ &�$� m$� a7M By our JpIon * 2mD $u(p),xb W&�[ $p"�L_k$ almo� ll �-F.� by Corollt&R2c2}, $>�0)c�j}t�B7pf7�B�� >�e� �i%$_3��6�pr&(�L"D%� $f_3+��5�4_3-�40U���)(the right-h!��0""�&�e� &ile $u'��-* J� 6��- �" $f'$ uG"g�WvE�beG f/d!�$f'� �^2 u'-�g:u_�-�0� R�18i�B�Y)A�� >�5hALi�>FQ-| 6\7? b��2e6(g}N= \| f=�::A ^3}�5 gf)c +\�AnM:a8� |>:2P::��;�:*}��6�1Integ�+�" his &�2e@Q�3Euus0NHwe M��"� q4N�Gl: p L($Rsame way �.�9C!=&.�12aR�� &+�.�8^j ��-Y�i�ljU�Y"���#m�j=1$.�KDbR"zYN� �Y.7 u ��^� �Y�Y�Y5@^�V`&2A�E�O is true� cla-a8sp�$"� l6�")Th"k t3$�fZd.��4�0�!Y� $KP=1$ in a neighborhooda��$U!L����ze�)f� 6�V��� J� �n. \ �$"6�n $V$ �6has�^y ��w �:�8^j �� V7j� ��� eta\>G� :JFA idG� \ j=0,1c-,k/We��umR � � zF�@ :xj� t6v&� f� Z,� �%v etv�#6� ��#E�:�k���;��2y�*��*����a�J&stimatBJ6u�1a�>h�{-4.5emf@�>�k�eZ8pA�|_&X ��*o$�j=0}^k�$ \|RMY 2VJ�R9 f�& 653%+ ��V]E�2�j�J�etBzju�6XF�6�y\| �6!=�~ x6$=P � "� Th^�% 1) F�w@E h�eorem�S$k��@ n�>�� u, p)$ sa;Be"2 *<""� && b( 9s?-:9?ZpM. "h?:-3f}\�tv2��?"�}�lde{g�� P"�8��? V�8~ ��)& g -( ��H9uU�T}�D&�*?M ==I�;�*�<:> � Q*"%;(f}_i & = &�Of_i - 2 {j=1}^36� j} �)!zv"':{(uAF=.@j!��i:!a u_j.i}6 ) -pJ6�}\\(g�.�g_iA�5Sh} n�u)u_n\, )G �6|B�:�*}VM1}&�@a�B5 ti��me� 2)�"0"P"# 1A#$F$, $�H�a�1 q�d. More�C�� *O&N��L! *�j/eD/�� $\chi  _1�: d5?� 2� chi�N� �$A�A`!._1^0�0��+' �1_1:��an*�*�$v\$q�$ /���, set $v_h(x' =h�Ca(v  +h)- )b*�D $(u_h,p_h�z ��"�3real $hB�by� � =t3� e�>m;gH1c3?� 2em}��!� u3I*}2.T � )\I)�%}   �I&�chi f:^�%w�(g:(.]��6Z2h_E���"� j�*��-4� Fa  NdjW�!Y�>X�T'>V=!VF�B�]h���q�� s�" q�j�y�A'e�eta��6F�u�a�. �A }A=( f)_h- _h f�pi�suffici]. sm<|h|e�havB�"�W WB�q�!m =l�I D} r"7Lj\Big|�FYL1� 2�eݡ��th�dtG�LEle �.��!�f)f�}"#B|,!* f.�. � n� J"�  s� ���� norm�٥�a�E chi m�%� y3&a�� #p_h�~Z�� ��)MEu%�u[-� ivalence  ���&���!^ \pm�0 `eq3V6HH� >gand r*+86NDimit (as $h\to 0$)�eft�of k��!major-4by>�I�c��� 1AQb� rr���YN4f� 6B *� 6�^jt�u�D \Y.:fR� EE8$6e=�*e+�| A�_1B��� chi_1:�^jF�B�FNB�e�(WAA�1ENI�of eP>��P$"�28�&0�.Zp>�Y� t3})�� Qimpli"Q%�$k�"�n�"�0R�咡K�j�&� ,L)he 2� &^ mO� ��&6  �,1s al2��si� W^{k+� }(�N$.� �  \psi=(��)|_M$.� �45� {k+2*�N�bey exte�I!~$QtE�ch2� 3Aq(i- �vq� � "V�o, �"�5IMB�.R v|_{�a?}(:7  (!}`$S�4\CpplEe I!ab��@v 9=(u-v,p�� N� ))��82.�i9�} �3)=,$k>1$ a|� �b"@% �byoMu�G:&%&� J&"{ z�6ofA�2� �Fs&R5.-4^-e�>�,s aw!f� }, 6� �f�*���R�}Z�:E1������:�b\�B��1U; }����l *Ka="�%Ka�R�F��8w"�0�Fu�6��&� ��R*'lX7 ��00��A�Ul.<bme�@!^].��r��r�W�9�"r�caERk#=*�'�,��'��AK 8.�� l��lb?��"AT��.�E}C1�5� a ceri=X2{9s�9�?�"@r �?0���$l=s+�We�Mb�MT  bZ�� ^�!: �ar����,](in��, hypothesis,�T@tB6`s. >\{s�+�L�*%�� :�Ez6[:>"} * s�,`�)$%�t�1s'� �=��B� � P^�� zOb6AZ� �N��yd{s}D�. 6G�3 $sA�� last*L/�hs�,F�C2�>w�R�"24:�~�I�j=0-�" U�#e� �.#�"6KG5�.+.�R?=_�2)�\lG9�]}$\sigma�A +=  1 a�Qt�H, �C � �=. |@���J^P� fM��W !}�S M2��&Q ��Zf -.8.Hl �;s6sz/^�  z��BIf�FD�$,.i{/A��6B� �Echi5� Wfw}*�,*�f�1} 2<UE�.�4a2��^�I�AN. E W.�5��$k>�Cl-2Qn)��accIW�I>�:�:\q�:[ l+2}Z 1#. �:!q�j$�ޒ�}^l=�F�E�2�)>>� 4)2�I1`"1a���� :�B&k\>u�Z!��9i�=d)k-�ZE�s ;22"��{xcon2h^�.�i�6k BYl: �2%n6� JY:;1k�D>���E�>W�DJt�v9 >Eb V}!9�G��6�^j2�3N�2� �P for E]BL,)��&)�-]k lete:�64A� w�&F]�@��B*12o.�@*s]} q*T1.I"�>bRNTA�J  if ei�#�J d^-�or&owS C$erg1} d^+,�Ji�J 1,2\�W?E�� �R�O (\' �Jku`, +\)�Jv�6V�$d^+=�U,j2d�D- �se%��E� -'u|_M= 0�]v if } u�" 2y�4�W�KS^+G|T S^- �&�O�fafHEea*�6 !�� �, �>�& 6,b�^�,I�^ �"�6Ae� :�E!��>��("�*G)��F7�(8��`*beN %"( Yj�, LB�/ 펭�J� ,�; :�"'*Yz� � IBun��7=*�DI`r2�L.�6!�4fnS�( i&+2{L� 1IC��(~�(5�2.���=�� ��e�/P�(*�<to.���b^A�f>�.� %�Rb&�)Y`2F��.�. F)�m|F"� �%:�k��"�;d "�h^kI��� , %.�FV����9;�����. 0}�2�R��e 5�2.�z N�1� 60I�llo�W:pm>� *�B!��.��it��b� d "�>�o: 4��2� L����.�2^�Qne�����Q���jR:f.5�:S �r.9.� !&�aF���2?b�M: &+6�j�f�a�!ץm�d���If&> p"Y.�1 s�l��n��FF�+�N� � E 5�2� F:� ^�  F*�h~` 1%/%#est posiB*o ��o ~(vYs�E`{8r�`RXe �W Ti�X �  $d^+ +� �� even�!!��V�&�S) F�'��iff� vend� pR^-�}>�E�Z,Ac <� �V}{m�+� re } m=1O � , \ m=2 "� &&� T0 !X�"� 1$�� by 10%R%e$%j���i|$Nd=(0,1E� oddN@ �67�^e,phi,-�] 01W . UnaRu�rea�� {N�W$,ټ6&WgW.nh:9, .,do�1 Q .   ��I )e��ul� �x�s4}�imMd. Howevbt1�"�h data�� �+ must�y*�[R"kA?g3%Eedges� 11 ourselve�$�-BScB �Q )".j u+�.�If,\6*/u=gU�n>/ u=Ř"�i"��V6�S"m"�<ń"�3. �=2�96� p]>�0 �).��ukt&yG.!j}u�h,[Kn $M$MO!zq�s :~ou=g$ �K$u|"H!+}=h^+$] � atB�mM1!�� � 1�I1|_M 2?2}u_2=gN.�:�m+\,F�F.b 2��W%��'2�,�n�2} ���� 2�6�u_j�lpsin>. �2!1=Hr h_j�I�T�Ӂ�}-�Nm*Kg�R�M*�8Mm`IB%&�S.�1 ťg 2!��2Mis<v!S�1= ohj�cc1} n^-�}r h)� + n^�2-!= (r�*%|��B*Q�.� 6�e��0R�.m q�.� M ,^ DA~. "z,v�"6i"��� r�� � � �>� 2!�(�2(.� &e4 =2 (h_1A� ,h_2 3:�{l�2O%�N�=�"   i�\" $)� <\pi'BI Ek�6 !xR#Ke �9�V.d A�" 5R�$I�=hE�/](�}A�)}62 �-� �5i2�*�X'NId p:*6�M�k J�w6���f$l'Q�V�%z(*E�H/"��$B_w$ *�X>� N)3&;/!l�0T!�ne�/za �)v;!6 .M2�>�*�uZ2.�A%R5:�E2�Sc(lG�d  beD(sf pn -c_1$ -d_2 =g(0�3 +6073�)) �ZR� �Şm�=>� ��~2�\. b"Qx_3A�M�Pɽ1m0%�%-a���| �| + | m|�CD5&{|�$�UG�WE*m-,�d�|Z��*9{ {.5{�DF._le�"5=u1)-h^+-- � x_1- �x_2`b I�*�E6rF.pF)>$v `]%i:�S�V"�VneTCo%�no�`0 $v'=(v_1,v_2� f'=(f_1,f2v=�.kTv.�H!�B;XT==F.(�Q� -A��z.)=GD6&wv2�IfT0*j  KA�e�v%=�QL "�u�f�4�0F'(x)=f:�HI(x � F_3*J+|*H 3}p<GQ�=g -q6:H�7�U3)�J�L) S �r�dA  - 3-y�r q��R�=&'8�6=T \, F6M �HAtY� ��L a�aCJ�ax.�sqd$G �=E)) =�gr)�e�"�b�\, .��2�e�i�67 E�%�6;{�U"�,__Z�FO]4.qZ ��*�s� =PiSm .�&e 6�_ L6l�%i��out"�N>4U c.�!�9�T2b�X.�,.^-p-�()M9�3_N>��$�(se��d&Z�*.���\,2aLW(&` �)� 6;.�E;��u�6ly R_"c�� >:E s\,&"a2�)/&�"2* n us�k "3+)�+>3E� J�~��"mea� :� �9>�U\4f.�A���&�%x�#third�Q�rf6C 4U7��.��c�c�c:c6~B�HftB9�"T <2�'� �B9�dE�2=>=�$1"$񨊔A�B�.�&j.2��+� e�S���QLJOyZ���� :��~]��B��!��{6��%6�*��>�r2}ccG�4=16�6}�C:zT6"�6de�`>/r b��&�/1�&)(v���7.�E�E�� rI� �]%{ T�[�"h����Y*H &&�E� = a|_MÂ\ �� $� �v2$� &� {x�7h �92}9q->��j N� E8�p#| >�_1,:��2 qu_3N= 2B� (p%_& u!;>w\�[1�{xt$�$p|_M$)�+so .�lexample,2<m�N�t'"�tbM��E9M4 E%y2�}3k *=hi^- = *l hi^+.3'� M�$w�V| u} c=02 ou�t.K��0 \setcounter&9{0}2ThBLeBCoBd M� {Green's U�M�c��half-�M�1 dihedron}r� L� study 2V�abQ���cto:����x"{f _+^3=\{ x"��� � "�f3:�a 3>0\ab Q �O�B� &.p؁�2o�>nd exp�� >fof6�xCc G}(x��B0�Rw ��} �'�<iUqYB�:�+ &s�S}g uA�W� f�o>ii u =g� T~�� �BM8&7 5��,Ѫwiz5�[(i)]�Yx� 0$ (Glet<�]7[(i .�)=u�)=-p+2u۱�,0$�w8 9� /1/6D ^ � (fre^a rfac�Y�v�.A3l:b �.*2��(xF*2(x�n� (�25h))�!/%fo�nplane1Y@OB:�x)�� a �meabU�J G}^+M�=@M�zMI����M4.T@�� \vecBj=* P1,j},�0 21{3,j})^t7 Z&� .'4,j:b&��V"��snfuJ_x :�{jq�ud_x2w-= �(x-\xi)\K � �_ � � �,)^ti� !e���f�y_� T �I.��,%�.V�y��l,4�!�6�F�@x_Ay�xFZ% V=E3}6��Kroneckegrmbon%8d $(a_1,a_2,a_3E.C lumnQ_"� �'�7�>�I��%U�H}^+_i6�i,1:� i,2}2�i,3��i,4ڛ@!��6�{iQ{Y�'.|���I?!�2} 3b�!�:�%O�Y�� b��[��_+E�i�,Ρ\xiE� .� �1}Dh��AulaF� (cf. ;-2}).�T9a5soo��e�nu?2& E givenV(Iu_i�?TRDT a�}�mf(�v",�A g�YV�6BiM3�\xiIJb I�"Z\ A,�-p�-g��JR�(Ҵ4�4,4q �q*b&�� of9��� s (iI>(iii). Nh!�sh$!AorAS"% mB�\oKs_:�)�Rj^�ZJ)�\,~�\\.�!�ZQj�^�ZJR���W2|AQ�M*=Im����2�e�23 :� 2-s��#�!�K `.h}cJ �!P��G�~^.�vy� ����  �lad؃)&��X:�sp1} &&V���{1}{8��\� ��)?}{|�|} Jd5 (x_i�_i)(x_j j)+�O �i)�k } ��,3�? ���sp2:�*q = -�jy�.�4ǁ� �x_k�k2�� � � �'d]�~)��:J}�I5�)>-�=1�_{j,i}��,x94$./=)���"�O E�Ix��#A�"��*n2 Ո^��$Ŕ�+calculat��c~zjh�2v:�� .#9�:�*� F�:��6�^��ii�%v1�^6�  ==�i�5� -1)^uj,3}}R,^*)H/M� }i+j�77,�8~]a= �7M_��`�^*=A1_1�_2,E�3U$��Iq�defin�i-4qi*5*�p�,f\75&F�!0� +� &�>� w���Y]Fe��� \ gs!�  +�vx�921=�J�jA-} > �L_jE �NN�F !^*Jh5l%�2�o<[<"�-�N .|a3em�� ̀ji3�:t&^ �F���I�q�J� G-t:D"7 � && v�� -:9 �i(U�2�-Jv R,^*��� � 2^ �%��Ft�a.#a-* B�� \!�2� �DTޟ�� uCT= �a�ja�j,1 1j�*� ��.���>y:.�q#.{� ',0��)=N Z-^*�+��&�x1�$0E' ��>h�S $\Phm`-%�3*�3�$ c�e$v��:�FFg=(v = 2 EA��{3}�Ps�-�1}{}�} �} �Y:E i b9��M�( %1"  ]� ^*| Q�ٓ��]!��y$2��in^ �6| � �*R +��^2�^5}-J:++�+^*-_�ms+%EZ� �'c��-1.�3.�6 �$F�Bd..oby�"%hERuI�)u��-B_+ ��_!��vI^ BQ��z]�%zl.2UO|}+)�>a�m�� Exq�\%��^2} ��!�< 1� !�|��P':� *~� $M���Nbs� &~U^�J<�: �:? 2�x_mrY�31�xQ�A�;�� ���"6>� �@W ��y�>%TY�2�!� !!�2�h,)� =A:D�Y�rho(rho}{( ^2+x_3^2)CD } =1�:('Jw&& �1}��z� �9�iB��A�Q�F'U�me= � 1�GFR)m(f,0d,\xa)n����dcx'!� zB }{(1+|z'|9�!�z'' #!�toUh�Y�j�"PX}�0to � �9!*}:cQA73\ mean�(B"� "�intro�~%<�b of �#464 Z1Yo$�$�s"�J>p�2J2}| �Jm>�a� ��g&R :v"Ugf�*z�.VZn+> * ^*)�< 16 !��0�  x&j��j�J.A�B\x��&?�� �3R :�2] ^*�b�}2��hqg �����̡ �� Y , R� >�2�.�� ��} 1��} ��=.�35U6�=��-;.�*� 2� +� -^AX���I�N�6*5%�d16�1M>�={3.O%{��Q�YMI�!�~�x� ��NJJ;.�6�-?�S%��! �y � �� B�*}F�i�?�&N*P�q�3,4F� �f�g��"�(F�,�� &�$� $=b"H D�_A��6���La9��*��k �����R��r�Q *�,JqU�+N������9|�@ \xB�!��C B�2&�3> ��Q�,6���" zs�T1d� zg�n&��n,1 ��� �N]�=& =� �&r>&�&V&.�_���J� -%�-+��w3a��&Hp &DY2:>��r�z��:����#2��Q:+R~�TM�'B�2 �3�aa���pt�"�|^5} -.��$ :�+i;I� �&�%1s��� >� �� )\�Z=�;.�"�|BjF �r&�H 2l( iN��'J?��?�]�E6�AH!�M �)%3";z)S %�6W�-�)��:"�Jg "1�-�9�uv"N�}{2�! �Z��$(v,q�ma�potenGN� && vc=Y�/2�&l�y_i"�y'd , %�y'aRdy'�O� i �=�+)1"�Fiy� y'|}I � %�x!� J~�mq�$�rM|%�1�} N{�i8�Bn5 *�(�,n !�sak�Dbrevit��wr{�$y'�B stea݀(yAV$)C"iBS�P�I(Yz!* q�X  $v�2x>aieQF%.�=q5�dy' =0: � 0!U�y~,:%9YpA�)�a z&�"[Ap�Aix 1]!.z'�EN�q+2 �1�A�}U+ '�Z��hy'" a5_ ,!=i �Q��X2, ^- x'�!:lA�T{3�s 2bz'Bk.mp>�z'� =*] as }!PbB�F"�=�i:�52$6�i}u�fVU�n�ĕ�� ~Wz_i%�Cx'+ � �HA$-EN�*By_�I��� wen-��>j1nKN�<2�a�&[�"$ (�# I3 main4S"3Rz�!q�� term+i1Ug�!�i�*Db^�"{ɂi )�~&�&�+**Q<�� Fj��>����y'e�e��"a�&Ԑ�<.�2F� .G0�2 �2=^2E~�{2��6�-KF^�MF^�s�cdy:� a&� >� `.���, g}}�  �2Q)> T�BM q� 6*}4 x_i}6[ o2�6U!�5B�A`e�"�2�E�jEHk^�YQi���A���n�7b!2o �-uVx ���]��Y�+ kQmv�!yYYh� � vQ/A� A aj�5�� �*+ Q�3$Q�6�I�b� n�3m/:9A�! Bl��]. *�C,J �}�� �p-!.��^!�% 1H} !@j:E�]#2%bw�% �F_�m$!1rIs) %Hu���b.2�)�qF� !.�E�& Z��2HA�&1)%}{�^3n[% 1 As<]eB ye�oF�:'1��� ���� .��&ia�EJr6XmR}5N�JX :�%�6�j� 6KE�:�G%JR� =�_�[:����Ew(>��pe�q.!�>6!���6���M(��N &J6.6bIQM��� �F�)?!�b� ݂�'B�� B� 2��M8!\!N)2@E\F��NSW'J( >_6?e� nAg-�y':N�>a+M�kJm}�j��!�2,P=��-M}��f��%�����q0M�IX�ffJ��u�*��� \Q�^2!g 2ZC:�e�!9f4^Q�Fb ;!��6[2�!��]� 1�U2�2i�U�!a wM)Av !I ��:��a���:IR'��z�!Q]x� rU��{��%> &�$�!5&Q�MIJY �]�2�!��9�*���as@y�A�g}$ directl�C�$x ed&,�E %�l�"�$$8��MAs�U�c?d8wtwo �sk"�g�u��J� :�96�f"�h�N&�m.A\�4?K1)}x4Dz *�$"�5*� �J*� BDO9�xr�4$GN6�e.ki&��x^\alph&�KA��T"����Wc_{ :, .�  ��|��!�14} �7-| ;|-| =|.m�w!�ct�s >� .i�8B�Wc�45/3)}!/ �>#�?P�&"(P�A ,P��"��A )�@8crA&�K"�0!@&R9�_x�y=�XP�B k|y=0��+&� �E91E~��>x��Z�". ��Hb�\ A�O.xu+(ob��:�sF[a#!��18�Z=6�`j}P_j-T8&�� $P_ju6&�;%Sg)��(y�4,3}$MewritteTzE��F� &&!I 31�&k& ɿ��}2�b�1&z;6��= Yh2�fuj u��&*~����_&!&���dv++37 3� l��������� �$.�>�/;f�?�+�w +b�2\A=M� =.D_ %b��5�|^��!< � !(��* )��^��� ~�^����'>�4}�V*B"7 Z�6+"�)�+@H<"�1@� _xa�6�<)^*.>� }"��1�\6�aK1� x_j� N zz� �:g:.bV�2��"�*E�I|@R�e�>a�R����y� 2�:6���u�A�*� �v�-3-92F!/�-��� 517�Fc �f:�A�J� 2�!ſ Q�Uw�$ �NՐJMv�� milaf�p*��*@�Jm 6 F��M�l&c 34~d:W_22@D�l�:��,�D�:�| G}�M��MGo k} 3,k}*�ڹQG3* 3��y�Nq  -q.� } �"Ix �*� �J�b*T�s) "K�MA� ( )^t�V��2� ���9g  � +^�4!�}� �M� D}, >���W�Il$�#rW��_x�!�(>2!�=$)=0�H.��&}`�%�M �BFU� preciseM�����-�&NJ�� � A�"r4^3$ I��BV�B) �In� C>my6(61)}-TM� w �>�/A�" ulaY�2 � gr} q�A$p�=�0\&�I-' + R B� ��?$"�y^LH.K��)1�"���|tto&�large $ is �!A�^n3��W�:'�6�$A�R}_j,Ri) ��Rm�R�>j}a~A�+�b"��d�m�D2ٵ!�-�9�"�"�6J�-{�U{'_x �=':�(  � �M �D�G:��1��+O��m�9�%1et}�% ��)[51%8 �&�3�ƩA.��( < ���+) xK( qf�b] �D�y��3,� S_*qN�- ��VNV!/��Qe.-� 25���9��� nrBa,�4$ fjA�:��A�"U*O�&��} act �korthC6���� blem�wam:r$%[=���5`-)&a#� ��|Q� fz�4 �D�_�diK 9�z^�W&�`l�VD}"��{:�o"ilx�U#|�1a.��)���f�:�.&��.�7"a1)}�2iA*�Al�۹:�propG2} �$tx,t\xi)=tv0j *YB�5� }t�I ��.�Q� �6J �K�1�M)=G2_M>Q&xEvery"p _),p)�C">@(\barQ�)< of%E�-.WK")Gma�.{�F1 S\ }�\gK=<L=�ɲ5repu}FTR_�I�b�Kexe i�H}0e�0�(��{D\C E!"� 12w<2�Orepp}.cR.T�]2_���^tR9H�k��B�Q"-\��Z!&� !�>�$(%1� 3X*X.Mo�u�s � }*� inC�ly *��blD~�pec,�!���.�&�� MBx\���+� <\min(��,��'|):* ^]}:1�z!�|&�]V~b�g%"y8\le c]} v`-|6dQ|B,��"�!��l!�6�%�N �8��z� + Q&m&�� *�iR���7% ��&G !�:H 4 IxN$Q*�Ć�2!��.�.d:.�'q"�?��9Sv��DA$�n� 4Nq�M� %�MdJ�[ b� 1)���qb{6J-�Agm��} � $�w&�L��� ccis valiBmuM5EhG��y�Q$�9=iZ�� $v.-� z-q�e��$y� $z����poi��W�'� �bk�>u)�yr��0,����ot):k%� t<1/�0, $t>1xle�n&��aN\�p?����60j. !�:�s��Ʉ1nj./ 1?e㡃��)�k�:&ڢJ7 .=k6�yF&���7 ��UF :6 ����!�Fݨ��:�2r��_i�>FK MT(v�8"h�"�b\ *1d��(�x-y}{=�}�1�[IIeINf8����?_ 8i"� �zetxz>xbi�)}qP\\ iT#�I�q�5�da�VNB:�1�)R�^G�5!E)#v,r~<t1 B�e� � - )�) %R>�R)->:�:�QA!e��!(�X>G�Ja[0f��R$�P2yB%�tev%statemn�i"�Jw9J also��ɭY�q�Vg����1�!~=�1��Ijq^O2��51To sez� is ,�i)�o&=���^ gral�j(�Y">tee���9$R�9�$2��� �] upvq1^�%��Y j��, \"&^�"^v�R}�B��}yJ�?.�) >)}q G1��'6�(W �{F Deu+  p5 ��5��$is evident�9��V�R$,fWkq$�$v$ disj� "�. F.�W N�e�)"¨��Ks.��uVhq�1}�s�"8u �5v{) v1q!�d� |sD�F]c\(A�.�U� _R(z)} |���,�d�(R^{��#��|j}| �:�|+91}|.|V�)^22�6�V6�x� F�&`�r�y( FF �^�p ��122�^2S �:����o:�,8R/2<|x-z|�for (i!�i v Xv) it follows that this. mula�0applicable to1�vR�%Bu ,1T �%V015�� . SA�s�at $\xi.'_+%�M�|$x��}�D|x-\xi|}{|\xi'|})$�>es��We wri-8�l$ matrix $G!� xi)$��!G form�} equa�4} \label{3t7} 3 = �\big( ��>� ) \,M G}^+ q + R ,i�p whereQ`6e��2�ofproblem�4half-space witAz�+�vec\Up�s_jJ�m�+, �-��-�� �0F� �-u~Um�1�=U$J�!(1� _j -��>) X�;GEV @�I_fc��-�y^_I�G}iM^+^ $, $IZ��n� k. The� �e5I�f �$�]-fMG}_ re infini�$differentiI��respect��x$�&< �l-s���/2 n �� �orN�,�;$�� derivativbUx^\alpha)�6�%u�).� �J&%49m�y �� ed b��@stants independen�$x\,xi$. Consequ3 , ��e exist�� B $c_{ �,��.� \[E�|y��\��R� �4A| \le Be���!�}�->��)�<1 1/2 <�( < 2. \] Si �'7� :�$$ (as well� ) ��-1qA��G $) are posiA0ly homogeneoum 0degree $-1-\d�Q{i,4} j,4}$, w�N clud ٔ:o4o-81b�s1s��)P^{n�-|I|-|I|}�ʊ� a2� t.>� Analogous&F 4estimates holdV e��O D}_-=>� � �" U ��)< 2\,R+)\!�$ �J�� isd a� 1t7 By} 4orem \ref{tg1}2cs a>! ��P� $ satisfy_ \ g1})&4  $:�5 �p @M�=Q��� I�2r  Jn^+"� c-2� us, o anG � )m 7 [ ͡ _ = ɫA�Z��R ���2�2 � `a��2E 6+ahE "�1f" �aa). 2}we ob� �J represent ���J�- ��-��-�9,$R B^-�y�yQ �1Iba %, �[ivea�.a �)�n^-) %�.9\!\eta^+( U�� ɬA� onlym !�'/i�$,jp� \notA�&Z.r"�\x6$\backslash�I$��� � j=in�. JKM-�=1-- �eZM: a~0sum_\pm Z\pmj\��bK&�� + ^A� 4,j}..\\ a�N�_�!� + Q"� ,a�e�a5I�+=Z}�e��,�o [$ V�B�� 1�IbiJ~ �� + Ju�� Obvi��}0�z$Q� ��mm2�<�8�Tof.xcomplete. \hfill $\Box$\\ Next��prove}�of 's�i��case "� \min(,i_)$.�(\lambda_1$ � eigenvalu"Z$pencil $A( .)$� y est   real ��� 5_2Nc�H? greater/4n 1. We defineb- $defmu} \muA left\{ F�}{ll}Re}\,� � & $if }d^+ +d�z is odd }\� or } \ + 6,e�6D} \theta \ge \pi/m k6�22��Y<W2 �\rightB` e� $m� if $d^+=d�/ m=2$�Q��-=Le" l13}�ى�B}��b�%�radius 1%cen!��x_`)A\em�}(x_0,M) 4:E le�,��js6�s tsQrtA��:�w n1�e&�&&��p_{�)� D}} ���^{\max("� \mu+*w,0)A�bi� !(x)"� {x'}A���{x_3}^j � : +� :l+1Rn��2r&{sBp�8\Bi({a��  \|�9 u\|_)H}+p2I� j+"}� an arbitrm�cojm�Le} \no�,nt P r o o f��.Tb�@$\mu-� (k,k+1�� $�=kF^ A�(0,-FFchiena&� $C_0^�bBb.iA@�$�� Z. &� strip $0<�2%��L��6�0$ does not co�ݽ� J�,.��Th.� 4}e�Coroll!�� Lc6} (see also Remark r;�>�(� u)%�W_ �^{k+2}-DD})^3�=Z<pF<1<z@j=0,1,\ldots$. UsZ Lemma � l4a}{Šg�\z�{ �+\nu}�\nu+2} � \ell8 VJ�NJ.�Ifoq nu.�!���:"1Œ\| .�u1ya�WR�2��y *��� N�|_ZOB�O�ۙv�a�w�x�y �3&#In %vcular,!; $0n�� k-1$7 have .a��r� U�29�u�$K)��a� inuo� imbed�in� C(\bar{K};F [ \sŠ'��8K,x_3\in{\Bbb R��� �aln1�(x'F� ��|� h` a2��!� x_3)]Ei2^2(K)} 2]ue���-'m),a�0$W_2^1(M)\sub�C(M-2�P ����Y�Z �"FI� D})}Bh^q{jaZ�FprR�) This  =.AX�}���}�A��AKC(��A!b u�ge k$� 2!ţ���)  � ���-k+1+x}.�QvV�3f+$. Fg0a}, A�����2�ŰQ�b$R� 22}��^�|-k��!�.5U!�9X�LY�QyR�GVa.v6_ �Q�Nf�K)}�� A���biq-���`�e��� �.^"�2Q�ih:b(ME 0,CFT ��IT �+YEU\%� &� YP���2�it �B lhown (cf. \cite[Le.2.9]{mr-0o� � >� �&$�M%�pr�_���ciV � �(i.e.,"E�Lor� m#��er� �'� ied)���:�%last l� -�imd� Q�NE _1b�a:�,E�&la�)C {� q }.��)u,p�a*+-�+�+�!���)�z.1�-�%G(scriptsize 2�_1+*��^�V�k�m�Y}Os �&2K.�b���V����� �"�Ge��bgP ?m%j/$.�g��:� ���B�Bymi0:E we{ E%2)�Yu6�+kn.�F. .@" �i C.�*� �`�ڹ�M&��-er $k"w�in�lity,2-0a^���$ � "� *�+}��O-* yyHu.(%w 5�hiZ�R %s�`�LF &� .� ^3� B��2 bl �\AH��{� �`�r:r$*? .# a�5�b:9�8p^8���resul"�/:K JTh��, t8} '' F0a��'�/&�Oa��+U2V�2�yT>|\sigm* �}^\bet6a� \tau )i+,��2�|x. ^{-T.�$P|- m-H)�> K2� }{ ?A�)^{ 4�%%B,(�-�r<j,�}} "H�� T=1+��j4} ;&B 2a&hi 2&pnumber� $B�=%�0,W&�� ~.c)H I*\w�/�5 ? "�  �2t8t�%�[V�V R6�-""~'�'.To�> NL.$�Th^�Due�* �522})s�3es� aU5�"�=2&", underSassumpahin���}|I��&��A�.(l�#� B}_x�2*@ �d�s6V*,�n�+*-$F# 02*T ef�+,$ ��o�4&=�� :���l!h�&in2�2+6�."� s� 13� � 13K!bb1�(sum_{j=1}^4)^{��_{�n*�^_3}�)�& A,c���3��� w).|��a�,���.����&Z�[E�Z4}��.Z:��S !�a$}� $i=1,2,3,U�FE1 $gE~s:R �- le*�+"F$u_i(y) & =�!int:D}L(z�(F�D$H�8�6\, dz! .9��!;g �,4}65% � \\ p�-Ay+g+k��4e �� .���42��*X B�$�4D})a���� 34$??a"�3�!$�4� b(u,v)-6�p.Z!v!.x)F�% F%�v , dy \!��G���"} v� V,\�#-P' 9u=% g "Q2 in }�;D},\ \ &�!.^ on }&�! _ F*�6:�� co3.���}"���b1*� y�ux}�"�E:X4�X"�!!x1 � �2LA� ^�! H*f \| F�}V^* A g:2�'&�( $cE��!�E1դ�< mapp� (F,g)$ toA�:;i=;��_i(x) =>�.NF��V�(!$sՋ3 F_jR��]���)z!s+�.zRB��z6)a�z%����J6Yq�pAjJ3K!j5��3J>-5 + �4�qS>!�)4: ex�?e�?linear�pZ�2F A�on $V^* R+9�* norm" these .>�5Nz4J5LrefZYE�Y6.A+��m�BO �Q�,4.$ _?is%���  )��!o asser���theW2B�0 \setcounter&� {0} .ThBLe2?Co29Rem'�={Z%�%,p&o<,a polyhedralA{�&S every $j=�$,n$\  $d-be� �< natu@�s �$ 2,3.�=consid,*�<2�&� � "�Stokes.�; u�W�. p = f,\F�;G,g����Kz;>4bccone} && S_j5h_j\, SN_j�= \phi_j�. T&_j,\ .':X } H~$S!7is -d a� z=u"��,_& � _n=uE� n2+ ,2 ,L_=u-u_n:.-1�AoperatoN��#�- �N�5 -p+2*�_{n,n}(,'-!� 1,\q%�;:7� : ; �,<-pn6xnNt3:�*}2�$!0A��!)�)�&�( C��"�DM:),JreaY�(KS_ju=h!U�(D�- _j=3��!i�We�-8ed Sobolev spacA�e�*,y pointWA"�K}m� \rho�D|x|# � L7nBtovertexq�a, $r�1�heB2edge $M_<�,r(^+�$�S}�700\} \cup M_1E�s M_n�?� singular���s. "�1wr�:p�9�; $c_1,c_2*�C��c_1' -\prod�n �}{ #��e ��_2^@�\|>Be���X�6@e��l%�a nonneg�<��4�)�O'�)�=( _�� n� 1 ^n$,� $dN ' }^{l�*K ,we.�D!�of�I��=n!_\|� v_}� �&� K�� ���1rho^{2(�-l"�!� -�k�%�� 1�k)��-C%-_k>F|"��; u|^2� x�)^{1/2)��0^ �a"wR�({�Zc�1�- _k>-Ek�*,,!�B)1f&f��fJfBfj:f-e j} \�YF.�.wE�roduc`�H� no�9�d� s4s�&n=�dA�,s2��G�� ab�5in nd�o�1�=(d�-,d2'If �fz� �a2�A:(�f $:�+F�=:#'F�MT�'�+�-�n+�E�tr]F�d<���:��2bo � �2��Jf��h IdANz-ay(r_j)TB/~>): NtIs)�+1-%M&j�is�PtV -R�2��)m'_j�� _j+q�.* $ �0 "�%4.1"�%2�N$x�p,� �!"'$. -%�>lZ}I�zt>�FlMoreov�!u��z����-1.$�a�e� �R>1t���ips�J xv�$g'B$ecess& A��i�3['(\��2()|_{M_k} =0! ��}2��k-� �'. 0�>F�+1�@ 6&{�"z a&�A� ]X2QX."G284Q&h� inJ�3/2}�^{3-d_j}��2 �J:a� y�^{9,:\, b�P�ѱ� _j>0)3E $jl8or f��7 {j_+��M-�8A%��..�dja/!? the &� .�:��LD& !;6�?<atibiI#�V s&�B�:�Lcc2O( h�+}E\j},-�Y4R(T_j end&K� �+�range�� �  $T_j=(S p,- E�"kLF(� cc})90)"� -�� :Pan�f- 6y!{e �� �`|2>� V� �8qR;a>}r 0 a!{� �:H[��mz��'}2VO�K7s �Frahb[BV} �" !�rU=�7saB$mathfrak AquA_� 1.�-�{k�@��"�b1�l7�=_k> a�angle �R.3 $A_k.?2� :� �d� S)K 2.9��wO\pm=S��$�;=NFG"u!_1^{(k)}2R*�,EsTest p�� ��i��F�?�il�3+_2_�#&@2[R�? th�?"�U%-��?k�?_k� ��? ���:{k_+} +d -�?�b�?*3  24�"!��?_k ,%�?_kg ~6�"-I2� a�k�?i����?_k�>0) = y- �? @-}$. }B2.m~rhod omega=x/&,� \O!�{ ��^1( )^3:\,�ZR$NJ� f�9.� �I��a��(�LO �${c} u \\ p. �:�A c} v.q>.;M�; �� 1}{\log 204,int\limits_{� tack�9,K}\\ 1<|x|<2&B�D2� i,�3 2�iUn�JV) - P� $V - (.U Qn dxJ�AU=!�^ � u()�)%� {�Ki�} v.!P ! -1} p  $Q -2- #}q $Z� VMup,q��VM���2�9Cf%.��_J $a2�1�)$Ր�V��m�@�i��A��.! � �V ^*\timT !�xby`A- � Vl!�J�V�I$�\EYBV��)�E�E��HrH 1���G u,v!�1= ,\ p,q%�]�As��knownC _&rumɭe.:-5�$�ist� isol� Q��s z�. Detail�ArG$- � �C b�un��" ,Sec.5,6]{kmr��V<lQ&� ��}.�GVX�F* ��V� �>`6���� 2�}A�2r_j*&j:&,R�(x)J*�$&�N'����)9��� �Y* %��!��  $uJ "�by]u(�J<oA�VKအcor�M�Yng.v�Z� �.SNM{��Y�b#>W2i�restri/ q��q�*� }�Ks�� ^2q+ ^3 \�f]1� 2`�<f<%�!*�&Au>f�� � \ni (�6� to & >f,g,\{  },\{� \w>)V &&�V0�-f�b 6�KY1�i�28P.;Y;iZ�$f��=^{&(�7U-[ P��$g4-�{1"E2�� h_j=�B)C� �7�U,^� $U,P&Was�. I";�d�E�� a of��_>�]�bVu 'coincide�b$�-0,�H _k)NnW|V � � 7M|<s"Im. =r`hyt: J���1�r!}<J �@h��{-4em}Ej=0}^2 |M|�0jE0�=j�} +q�C1.C1C!*NC�e *B M| fX���5*�oT*ZorL2� S1}4 ��&.� �Z�w +.�?�42b D0(��hgH�$%*�H}�.5���=�� q F:�2t?g�6F} �3K:�BQ(�d��]$.�"A��?we ref$&o� Th.36��D�{Solvaa�fHb�� &,the�' �Rin a n dard way �, e.g.,�Ch." 1})*HqB qv.�79}-5 1)} 2Le�+� no.� �4��:$��8��RR5 �U3 +1K_�W� onenu ��}#" <ied�4�,0)�E�_k < 1<*V�.I�'�h/W%}� /d7%�l j :�2�HH\ a��"1%�f&=$f�B3{0*9�M $g�*�Z*a�.�i�5o���6))�A�e�(��a�`&M2)}e�RA�Ebea2��^�).�b���%)��1!�'-�'}:��MY g.�..��!�RWZ�L4� Zf�U"�k�.B�^h� iA'U �uv�X6t� '_k*a � #�It7*� 2I�c�J*�U2b  =-)…u�*�Tu����(zerlegung} E� = �rQP 1}^N �{I_�P s�{\kappa_0,j}-1���bnu,j,s,�-1s�')�<!}\ og )�7,� Ϳ u^{( b8)}" ,F3�j3� )+ (w,qb�^�2��^> Z�j6�5p.{N;��q�-- ��L��!� ��B�� B�betwe�1�Ů|j�.|me#(.�)},=�$V � �ksU5lized2 :�`+ ?a�[J %.E ~<Fu*�mf�!3�!eA*�"�! � Z�!5�!iU.��X}64eB2OB�M3�oI#Q3, U3G! =��%(a\"Y# )^\nu fR�0 Y��^>Z�.�, b>��j���.Z� r RR� &�"$��0|(l�.d��A�ax*� �� ;J!e�agB�Km:���fgof Y�v� &GE�#!�J�E�\i����%>5moB!Existeohof weak"�s}&�~�.v 0}.B:h$jJ�� ��.e3A}_v� "*�1,�8�V &B� 0}^0y "���8AV_{�}&I6.�B&�vF2t= F�;K}p�%�3�v,/dx"�2%��}J�*%/and4/ g=0g Qu^N 2�&6�D*� %�-$a8p �%Z.�%=�*1~I�2N3E[ .�A%!y�V�G$ "�%=\�B��:=�\~I_*�n-1�pV� '{-"kJK�C�]��$�� nd $p$. H!1�6]$ �I� dualA ,W_;�=R2��3t is]Oproceed�7"�j��Le.4.4�L�-.�10}^f�8�"�ifa�re��:o �&����,1 ER^We +R firs�atq:iA~w 1�>>:V<%]aS��A�"~1�.JM�'#��9�C$u�>�Z�z�#�2�VftR-1,**-12e�bb� $w��]�1-RFPeP\ps�hf8."i�&�,6<&&u2c'6�N9b ]5�)"�|z!yA1�A>�2�|2Z/.�i�Lgw�o- bRv"uu2b"� q =w�A21v=!@�8��AK}ci�8�ve ]8^{�-&a��AB�9,"�S�� "h� v[Z�2-*�*:�Z2.��2:Xwvr@^3B��!$ v9=�i��=D'�o1|"�L]!�K#�^ K} u��w�"x�.6 p� f ./DK#,2�Ch �C2M2j%u8q[�2fEK} g\, "�H ,�6"eBEe2o�� =r,\|�\6y!�.z� !�!�Q{m�>� MoqfWj&]")��Yj�� �.� �Z�q)�}+\| qz�������>I6] �$|�+\�z�U� Sett2$w�'-91)}&  (r_j/ 9v"�f#� ay�h"=qe�S ^2g�z *V,%+_2�zfA������and|.�BFG6���VF-2;:�e��V�ao.�z���.�RB $w~+*� !��.(6�CdgK[ a|/bJ�Vps�y v���e�JRsi!���T� �U�jR�62EEw��b ��&�m2� RK �KBKA�J 66>� riv1�� ��.�6���ы�injnR,)ts@4!9losed.T>RF *� >Y�FainxeV!� ^`*�2T Z0*�$ which� dens<..�X� NA�>�]*�q �::�E�_/*F� .c~ 2�>d5�2I .0"�R):�]�fx5v �1w �N"l�A�"�&�5�5w�5 �37 By a6:: #�0�t.(.qA.p{I�^C��meC pair {$*� >� ���ws1LF�B8 B�26 7 o�>�A]Fws2ZF2� u=R{N�F"� �6�� ��*}�;2q+1"T=�tw_j<i;2`I����*al }Qh�D��*�G:�4F}46- (f+� �0)c�v��n��M�}�"K/ 2F�W'�$24�.j�FM->�\@��-" rong&$of��]K�"�T� ensur�ge�� ��!nesvw2�qvi?Lhe .A�� �>&�F��*�cKRk"&�.�J�'�#Re�E�#6�} .�&�Th.�� ͒��[�&�is es�{i�� based��6�4^�1..n-l+2}%Jp %.K� �u"�)}J! e5ioii��K+lw*$6}*�;F}+"�.�2 �{l-6; *\ 25.-.f� e;�"�� }^>M!�"I$lo7]�0$eJno"�?a��l�4V� 69,0)&��@."��fY�E��5`s"^�6�^��ZO1%J�=./�#A�aNedg�=Ie�n rF?l 6�w :]);%j.�6h7Co��c7I��z�Ze�q:EN�%t11}}A�S� . Ad�>ar�/Bz����^ ����E1�`"c/j�r�lR��1��-2m�EB �J)�J.J-^Bp�FC! *�&V�f(Co} {\it P�i}: Itq��oōAeA! Q' $N=(]-$N>1$| �5Z dE3 indu�J.I ���D���%����(2�N$-l+2<1�'>�/T�@�Qq ue�.�C15}�6< B�%�"Z |m� }6��"rh6� VfDݪ"�oB�%2"_.*t6:� 1�!�1FDwpJp�%F +2)f�  p�9.� ��:� 26 F] u)=J+1�gjm.��#&d�p"�#97I�S_jR�-��2\B�u,Fp��"k Z>F�N�J^��Iw{)� _k#�1�Fwi � J�2�>� zF�aw,� *�J�� 2��]BTB'6+.�uPagain~ � :�a9)�V^�R��.��lC�.� some, but^ all,�i�!n 4psi*5Pn`:R_�$\over` {,3�,u&�|>j� %��@�=�"p3W$�) ( �W�QteI $* <K+D| a�lh '�R 1�9 �.-�� x^\a�`���Q:xn];�9C>g����c/ *c"Z|�/spi:( �a�pe�A��bVD been�n�6>V EJ&�Xa� J]VY.B�I0B"��6� T� let��h�4of. \rule{1ex}"�#~X{�Hr6�0vL�B+}�C� �C, m",L$�E <\pi � <=-}� & '�0��!+} C -!��0�4>b7$ ���;� imf�Bj%�>s~7�0E�A�1%�be��lac �_kA#ow`6�rq�� �$h�C\pm)� "NG��c mustM�y cern a"� %�N� �O�  $MVGJ6�6 �Re6@.e:!� 2jW�ihs:�G�` OQ"m&��toJ��A�claE "�?�6s $s?�)w}^ld)I5� �u�.q�_kws!2�u�Acut-off"�]s!`$D}�DU�M�-�c�8 2,�A%�.x eta_#F�4>��L$Bz(�U $ 50J:aB5��-bar� �j# je^A��� h!E� g$ SC ��� {F)� �c_ ����to*��KQ_?�s.�8�$.�*: ��F�2�5 J�"�2&��� $ )o:* *--B�V�~LzNL.> z�F-RKRNP�~V���NYV�� :�&67�tŜptKA�*�0a.;A��Z���C "\��2�L+mGbuA�B2� �JQ BK�;N�(�C"P xc7Nc�7v�B�6�� ��!:BJ��&�TduHn2<2b�6 �v��B|R�ch�N�BN��A��)�y>xk �W- actŀ؋va��>��F�^i ��\F� IFe���"q.�aM�Mm� "�U<.���y�qp�U a�q2�U�UV ] ������m�Fؐ�&  � �"� l*�Cor.4&�4mea% P-K se� �P�I6� 9^�2^�:�F�!>�+����D�H6m$M "�':b �8.?{1:� F#FB$$,��6x}^*<"a '}^*� f !z��.�*=: &� �.C h I82�=�(҅[ � ^)'*:�ad�Onde�v�on.&X:" 6!%92 !��N1#.�"$�2�7 �:)5$2oF=)B�8�5n%���.�(0*�E�,��+R�� &]�=99l k.�)hv�;40 called 6S�q;+ b�!&9�&� 6�b�v�Orxi.ʣ6ٙ=v](SuX��_{1,j}� _{2. 3,j})^t�!���<�x} ]�g1?R�!g2]"�_x�,>� ���  ��~�D S��:�.�� N�V�G!�%�=D,6:$)=0BFi�)!4k� x613 9�>P)4�Wi���!aPe��B�%�G-�G_%��2�33~NlC��~Jisis9>��-!b�3�H.[1�!i i}yr.Jb���.H�.x/r:�!�6�� long�x"d'�l��^ifu�]t.�`6�/4�� ��a&�zF" ��z����2s(1"����Ȯ0,\�U 12����BT��!(Pi�DM!:"�1tA1* tx,t�H = tm|}:D "R ��J\ t>0F�$�z|. �3)}�5�*��wbr�(ugly �S���� �\:K�N:9�S�x� 6z���q&� �2s $|x|/2<6}|<2FX.9t"�./12IJ6�t���*��1�̅�h�R~�N�}���7}W{<0}�i,m3�Fn�{x}&?Q�~}�6��b& �m�AZ"f-"��\�4�1A�{�&�~N�~(x~0��2;A�b=j� ',\�[�y55�M�%C��P�*�~_x���+?�&u08 �x=\mu_{�A�`$ �Ba��6��*��.��=r2� �_ case�p� g��o �&� &5��pu�]'D�2R� � (x))}- - {�~p-=�Y�m�>E�80y�1U�ׁ9�u��{��&�r���^�[. �~4Nq��! �=��ie� �FAFEv4F�!��M�*~xj|L� MF|A�2,"|�02�� $j=4)  nA|�} =(��1}# i,2 3� `.� Z a�A� ,�%=�J1 7� *P#�-*� ���m4F#��vxiR� &� i�1�� ժ6 � !�O}>�*� !� "� !�-V� !\,~W>�)�5*Fn� "� \�:� .p"� *�?is���MUZ  C&M�.e ) of� y .#�}*�0EP.��J�1e�;"EG� give��D�\ulRv�)�"� 3�u�|F� �`f#+��A�g%uV/$1\xi�y2; ;,:� 1�qo�aC4�| � -g(x�{6_�(��4M� �z��{M��:1�kbV�1)#�E� &��"-��G �a�%�1ᅥp" ��}{�}-�&��A+R ,C� iG%$AD:�of I� syst��$YX R}^3�*�0�W � $t& R- 2�!�"X>,"}{� A�Ey%�BA2"��&�$1Q�-iesmIg1}"�Lg3}&R�N*0m2) Eq. ?G5directA>�#%�="f*�. �8( �1�A�w not=� $ �.kB�S}�lл�manner!��7�{trum+�"� #:� �6+ :�!�$v�6 thir�r6� 7} ux)���:�� di�|on. 4)Km�&Ml#n� Th.2tqp79}. F�A C!8�ce�ξs 3�4)���#*?��2� 2� a}W�\ v�� �m�.� 6�PІEO� Qy��>3e�"� _in"a�� 7"� :K} ��{"�8!:9���� >�rL �G�H"� !Dj� �n� ��-gr���2� Z���ar�  @�/.�kqH>Caށ.��&as� |x|>�|-��>��/,�we ne�_.��&�#2�K7*�(��A])5� �'("}#tt�c7q��Rcou �x*{q�FYl��^r;-l+�" �A�8Ds�r&Cy�BW�� �e1��|le�@�-( ?D��� �fI��K�E>1$�9DIR��y5�nj�v7N-6��5 e.� ))��n�b�2z�\|)o,Vr_"[|F�d2���%�"� ��QJ��� Appl>�-� �0K+�4(a�.I|^2-H:>&>![%UBF.#b6 �����havf64=)OO>p��m;� $���e&T�|%n��*HD'Elbig�CF�- �6lDF�k\EGGq"ǍABnor�J ,�T7 equivalz'�3F� ���s��k�Zl% \|\ B�)kUQ��%�G�{l-k}sc�%��)�>v � "J�#ge�7oeE�)"�$ ��LD2)��1�>��A$ �i&r *2�=B�&2a=r v��&h �  �2� <�a"�.�any�$ $�TW�j*�m�Do�}Lv�- /:#� I�%A?suprem�n$va-J��2 O� Ѫda�I$��|r?o$v~9instea�-,e��4i���i���W9)�i����fxRtey��U� I/'t��2�� �@2"  ["* bB) 6 x���*�}:�ile1Lki_->��#D�i<"+x!�wid�V,� Z�x���� ab HA�"�G�%�R�.�%<nak 2& �Ke��Q�L������ x�1[ 2� "� 6����� 81;�FP�.��1q�١Z* � {|x|>�k,&ᑡ�rDg�JHj��ݥ��2D�VLbR�%�"�� =$T�_k5K2b.�||.�{��)}2��n�n 2��=�$\em6�([)*��.i..�D�,��R�2�+Y�Y�.�}F�+ n�6aPv�xA������ � g h� dN� 6ie��Q:jZ�Ta-���4$ ~".�5.#*� @e��:�<Oi�eta�.�5i �5�� � Pق �3/4�n.� �Jl� an���">� I!k+�I��F�=3&y0&� .�"#3em*�e��xy# rQ&�:">���9 >\>6> ɗ = ��q(>}�U J B��W/!%�}�W�6�c�>�>�=0�82^)%*eL��P*��1GNV�)J�\2�F�#E�hAb� e \)B�9j��&�*�^�Y8 LF.�!�"�T.��23� J%4�m FϹ6}�� � 2&g�e� �Sq�p5{ })^j�*�&(5�2.� W^l7b'+[ *E^�Ia�L���G}���Yh�C^0����j=��!�Y$'=l+\"� .rP+�1 ���_k.&��Yh�#i�ӯ.I>98� E=�:Y%}L%&�1!U-{ Vf!Y22"���������B4� Vf2R�,$"� %� '_k=�5i 22� 2 (M]ac<�d=���r;�d b��J�). Nc�7I�C>$"E!1t2&&P ]�&��N u�.�> >G �G !�dYl_{k* ��u �i�� ;n�u�R�+�W�|��E���s2V\2)}~V*%yBT�)q " "�"���2Y&�%ndc � ��c$AL>\�6{�FN 0YIp�T>.�bT��^=aS�Rw )sf�# e:��v�_�O}-��%7S���@� &a\ *&M9�/ ak6l*} �Da�0s6)%�_�c�DG�#�!=��Wvan b��tea�I##Ve�$y? q� �"�A�(fե+ӟQu�424d��.�$a%p q-!K)���>Q`�� F A�"-���i�r$� dz"�"� 2��;_1�};�B~B��schi_2R� � $x-%1f% �QO 1(y)�A�� y|>1� ` %�eta�Rve ��unc"$<s� "�6v *��� �1 d )Us�I�.� +� �=0O6�GU>&7}�_ Nc�2�B�*^ "J '�q+.2D^3i� �d>nd:>^3� Yy�h����A '� i�P �s��� ^� f%o'�v�5v�9Jrw�l%~rlBE�Th��:���2YvxU"�0k[��?&� Yx΅�~J&�@KF �)| ���(}^�l�Q�:}�<�]">�+_�alZ�-�2�nRs.o��*��:�49Qg+\\[�\��=�VD��B}� p z6+��R B,��x֧�+zFB>$#6V��pnpYxR�Aw6n�o6U�o],�o��~o�*����dtheir�s�*).4c��sJ� N)�2� F.@�`� 9�}V$� >X��q �D2 *� ` �1R���}x\] �x$i,� Ŋ�v��!����-�D�� �Y��� Comb����two&��,(=��7&z*&]C�R]�1,. ��3j%�e�s"Il�?�� +�!�*C��n:vv of�L[>1 B r. : �Nu0r�((!�aS!1P���{+�X�"��byͪof:�8=ON�GrH.��-�&�)� tangI�OP%J[\. :N�wcHa �����5�U(yS;"�Fe�"� �%�9�=��(inDx@� .�a��2MAfnO\xiQ�6Q�,�E,.�*,AS- ��~-B�6+2�A��AF�2^AEr�j��+:+!O�"�O9Wi,0|ukU�B$6OS"+0Hthebibliography}{99wU$ibitem{adnX-�sc Agmon,~S., Douglis,~A., Nirenberg,~L.}74it &F"�K\����"2 elliptic -�.�@l'�6sq:W*;U�I3@s II}, Comm. Pure�*4. Math. {\bf 1�,1964) 35-92.! �Conca � L,~C., Murat,~F., PirR�au,~O���4Navier- �,��1 &ګ� volv�L��a��e$}, Japan J � �D20} (1994) 279-318.�Dauge-8�sc ,~M�S�!� �&�5 two-��(three-dimen�al dom�#j&,s, Part 1: L��Ȁq-�(}, SIAM J:)|T�.2�489) 74-97. %\1�(Ebmeyer} %{� )� Frehse,~J� eadyvrmix� ���E�Y2 %%>�,Lipschitzian1},�n �H319} (2001) 349-381.� Girault} @,~V., Raviart,~P.eEaFi�� elem*approxit��LVZX}, Springer-Verlag 1979.�KalexM� ,~H.-U5HO� flow)a tem�aCd"�0Bingham fluid� non-� %a�1woN=L}, Zeitschrift f\"urE ysis�iha�nwendu�I-11I�02) 4, 509-530.�km-88�ozlov!e~��Maz'yaG�S��X���Ub�J"�{bundles,�f֠���YHp�a�#*��, F�Q� /M-22�088) 2, 114-12A/��q kmr1��, Ross�7. E�J�dM�.�m��ypoint"%��FM�eAx@Survey0Mon�(s)� 52}, Amer��$. Soc., PrCj4nce, Rhode Isl�19e�u� kmr2��.��ys� oc��d.� �7ula �A��~to5ع��85}, B�dEkF�(6�s�Schwab�}�cOn6�B��JDirich��M&0hydrodynamics��v"��a��~0. Reine Angew1�ņ456E���65��5�@lad} %Ladyzhenskaa�Oi����Ubqu o �D...} Nauka, Moscow��0. jW�CP[99y� visc��in�*ressible�� }, Gordon�LBreaah, New York 1962J mp78#2`T, Plamenevski\u{\i},~B�1�$L_p$*of]�ofU�ndm�I�� }, Trudy!'kov%�� shch�x3�078) 49-93; En� h<�8nsl. in: Trans.G!n!�i�)� D 80) D�5��: Maz$'$!� V.~GjY�A�asymptotA��� fund!K tal y�="n�regEN�n�Dž�s}��b �� �-#(9) 100-145,R%Se >%vS 4e ,85) 4, 363-3> -89Nsc�4A��hVyP  c�^�"� !.2  phys!ci"�)" piecewise?>hie!/Zγ-D3) 335-359, 523-552�mp���G , Stupyal| L.~IuY!%B� .��0(y-state mota�E+a�Osurfac��@Diff. Uravn. i Pr .-em Sea (rotsessy Op��l. Uprav��3E79)Vr>:i�lMV1 ?$84) 171-26� }vr&�:CN,\"Uber die Aqsk L\"oss �(scher Randw�aufgab=�HUmgebung von Kanten�5. Nachr�3138%� 7-53�q� c� � ^� &� P��+�k:�?toQ�B�v�Wor�� s�cF��, Z. ��Me�M8� <2002) 5, 291-316.��2��"��:�+� rQVLj^�*���:z�3} �(2003) 7, 435-467. \bibitem{mr-03} {\sc Maz'ya,~V.~G., Rossmann, J.}, {\it Estimates for Green's matrix of boundary value problems for the Stokes system in a polyhedron}, Preprint ESI 1419 (2003), Erwin Schr\"odinger International Institute for Mathematical Physics, Vienna. \bi94}�$L_p$ e5\of solutions to mixed bo) v2 !5 the Bp-,al domains},Oappear.�4Nazarov/Plam}  ,~S.~A., -Im6-Im2-def\S N hexbox278-2 lan{g5Drra2{\rA% harpoonup =$vf{\varphi!�.�b�begin{�}} 2#e#!�^! bs}{ DsplitBA ARba> aligF > 2�@st}{{$\bigstar$ }�Htheoremstyle{plain}6 A� }{T )}[sec� ]�'lemma}[ ]{L2#proѨ)P2/ corollary-C %6�defin�6F�D->Hremark6D @RJ% hypo# Hyp.6Fexample$E 2�probl%Pem2�*Ms}EaA.�R}{ibb R} >u�Ucal U>�Hc.H>=Q.Q>=IPbb P}} �zZZ><NN>TdT^d>E�V�E>Tr.T>B.B>I.I>F.F>C�� bb{C>TTB#pp}{P_{3>5�om!N,:�o�KO Tph>r!<rho5�} 2N,va}[1]{|#1|}>Vvak}{|kRaA�Nj}{|jNl}{|lNi}{|iNg}{|gFV �\left|#1��|: norm�\#|�umber� .�{���9setcou( {-1%� Q(\author{ %-B� Laurent AMOUR,% \footnote{Laboratoire de� �\'ematiques, UMR-CNRS 6056, Universit\'0(Reims, Mou� �de la Housse - BP 1039, 51687 REIMS Cedex 2, � . }N�p- \quad Beno\^\i t GR\'EBERT��( Jean LERAY.�629B� Nant�2, ru��Tini\`ere, 44072 NANTES �03�R� \\� \\�D-Claude GUILLOT% %9� D\'eparte� !OjV�75!ZTInstitut %Galil\'ee, 2�tParis-Nord, 93430 Villetaneuse��� r%:� iquh.T7641, Ecole PolytechnAE(, 91128 Pal�au)6x(} \title  dressed relativis�( electron\\\  magne fielda0date{ } \makeSI S abstract�_ WeAsider aBkj�5ing sa n�� poin.along�$x��$-axi�.I quantizedt6P. WhenGi� a Bbetwe �V phot�4is turned off,E(ic DN*assumed� have a gr� stateu� 8e multiplicity.�Becaus$ the trans!�o �in��R, w=�DDreduced Hamiltonia L$associated)�-total moa5umjz , afv�introduc!�Pan ultraviolet cutoff%LaAfrared r�z��Jprove th�N�has>Rif�coupl�Kconstant|��re @Hsufficiently small.A�determin� e abvelyptinuous @pacum!�N�and, wQ�2&iGimple%"B�alE�masNjq�%Q�Q grea!�than or+lA�its b�one�t�dE:.Panomal�u_I/�~.ynon neg��eI�L8{\textbf{ AMS}}� f� ��s: '$81V10, 81Q5� end�� Ppage \tableofcontentsN0��4{IM�=} �� $\R^3$! $charge $e$!�)�$m$ �ngiz�������. 5� Ftakes!�p form $(0,0,b(x_{1},x_{2}))$� $6 = \frac{\�Cial a.}D}2K- F41:42:4$A�ar$a2L$A�(a vector po!� ial.���Pauli .�I2U'�=\delt)� \mu'e�ID 2/.0$; $ .��$>i �a usu�0nnihi� a�c|� ope'rs � ngqO Fock� $$v t%�F := \oplus_{n=0}^{\infty} L^2(\R^{3},\C^2)^{\o�\^n_{s}}Hwh��$f+0+=\C �f* U��symmet�l$n$-tensŪwer��BH$�rop�e �0Bose-Einstein � ���B obey%wcanonF `utY � � (%�B=-�$ $a$)�� ��ccr} [#,i� (k),2AI') ]=0 [ \mbox{et}  [Y2:ta��9B� (k-k')��e Fin�AX.�!=*� .��H } �C= �u�t�sa� ��>(k)�\mE��e HilbertI�BE $H$q@  $$��H =Q� 3, \A�M� $ F \simeq M� )F(,)\ .$$ As itA7nds�.$�cannot bfi�< self-adj` q�a��iwe ne�i e� fun s, b� in $�� ;��$� ich will ��6 hypotheoin orJto get a� �^��0medskip This*, stil� d by!, i&e�ANthirde?}, d4�$,a�-6)�@ (cf. \cite{AHS})T   H= p�1� &� {o$d}\Gamma (�)$��VMt second*�51 *�to�"�,+b�S)&� of $k$!���3,E�$� .� ����� . In L s ouXat!� adZ a des$# over�N] E�directA�"� HmMY _{\R�8�F}K d%��oa��uj>m�2i�1�}� )d Ye�J�6DN  ��w$$�v>5�$�� lla�exL�mpu��|A� ai�;� E6o i��()h��"%�n $\va�%� � result� is w�$ wᇁ�un�inq$GG05a}. I� free caO i.e. $n $b=V=0$,�imilar  blemb�studied_ \Chen}A�T.  who��AkllyKpa�ng��4* spinless�d cleEqF�!?&= 6�. Un��a* 6 �,����Q.�J�:�$P$%2a que6t%� $isJ!K applq �r"��B�p metho%�e2 �@BFS98a} (see also  HI04�'MAAxe one-5t�oa 8Nelson's model.I��E obta��first�$J. Fr\"ohl��� �F74}, �F73})eAmo�rec(by A. Pizzo = < piz0�'4 @8J.S. M{\o}ller "Mo}. Fo6review��:;d �'ofB�EnumQkdynam&!^ � Hiroa^�e]Y ab�$b�$V$ �!a� \ref{p^} "o rec�(Agump()� &K!�M�n�~%�2�_\%�a$ly degener�APn7��we faceg -`perturba� igenB*of Z��)mD�toB7 ssenf� um. ��is pap�ei ��ple!�coɤ existH(of>�%.G6*V- �. 6�mprz borrL)deas � from.�)�}l F73,E�(4,FGSray}) c!�.�is"we=:*� m:a�(A|nlBCV,H01,H99,H00,H04,GLL,LL03{ com}y>=is��� ). "�2��'A!����5�� ��e�M�wK�&Q� d:%� .k &��.a[�removA��iV=�Le�QED� 8.one2m ,open. FollowZ�'�}ecan!rjectur)<,I�� \neq �]���O^��no:�,��� H$ (actu"� 2� should leO! &-ɵ ^~X"�). )hsamq�E��)9any a��� ve �htn�-�>�Fur,�K,!� � neutm ��,�i A��a�m!e�RM��us!�a P�8-Zienau-Woolley�Ehe�m�� b� \/(p20pt\noind�/Acknowl�(s} LAe BG a)�hospital�wmm�+���\'N !�r��le�ir As��d���*R(�C�.ness}I-.Z@ be written as \b&x } H=p%+H_{Ib �&2eqnar�uuH0��0}=�\{�1m }0 ^2 +Ej� (p_{j}-eaW)^2AF�\s�&��9\Z�M�phn�ū$� $ describ� * o!+J`M� 6) �'� t�e�4. A basic toola�now�� xEq"� m ertif.amP���� �2��,we�FdeaO�asubQC� :O& �H!s1�J 4 Let $h(b,V)$AA�f��"� �L��A;�hbV} F=�y�^$:" ��j IT98}�+j}$'s%B�"(�C^1�2)$ ŷ� $!�f �\a�id&  '}a_{2:) )} 323163H We supposAA�* �!� 9�&� :�Ybe�1� H1} .H��Yis "v f el&� on $C�)^� %:Q�& �bo� �ix Uk� s�� s isolk �4 _�re �  m�01-�.�-A���?� 1}. aus[ �l-.�(S.� $b\�^!�\REG%$VL1* sas$�� ��h1�s 1/Cq 6\leq C�d}-{�:3�q C kee � some $C>1n .�2 �V2@\to 0�s �2#}$+Ma�Y%\e�"A��{"�%��on}6_J� \eqref!/%2}� ��� Uq�]4 �D����u)��J)\mid ��: eѤN� .�20_$. F&s 2 >t" vrm2@� � � bk!��AHS78bF� DR04)Rz GL02}� Accorde1Shi91FDLCFKS,Sob96,Rai99}) $�5n�k��="�  � ; zeroHn.5 of� K:lUAZ� �QEa�By ad��y$ 2�=32�9heYsUr mayE� �ͅ�N�accumu�ngj ��fact aF���-haU�݁�E �2�1)��� .�1}��verified� N�7͞�B R3a� s�Eto cho��]ni� Bd but� t/ j ,�&0i� ly)��: 5 }�d� &!�.0 � *� a&�# A�c. A�Cwe3co�Y*U%in�ny&M 'R� ��parame 'tIm��uz � N $g$. &� $�/ (k�>"2\)an J) %(G=0$�+Z4k \geq \Lambda �C0 %arbitrary $)�1�!~� Qg��&MQin each%` oremA: � *alwaysQ�Q�$rho} belowA9�$=�~��d �b�$� ,3$) 2B  Aj} A� , �"x"� �s#=�1ry#jj`" 4\�8.�.\no�(B�# \bars2�tFi"A� m�#nd*� � "� 12Bj} B�(>2��#1 f�$-@�$-7���#�A#b�$�.\\9K*�$&-$.Nf�F�"-?�zd 5S �on2��}) d1A��'U � P=&�g}{6�%�\{Q�!)F+,F27 �\}2^J &� � f r3A4r� + AW(x bY.Z2��&�( >�g^2J)� A\�(1�)Q�4��` �$ B�$ W��  re6�=�� s2$*I �-�242%!v�2�F�\\%d�>:906?:.�&.�&��%&3�e Wick �.�!!q$>e))�:$��^�I is haL changW.Zby@2"�/#�s��� &%�!�� ons.�"� F_{0,fin}"�see4$(\psi_{n})_{n�0�) &: F$*� $0$ SchwartzA$ every $n7a�ut� ly s $n$.6� ���� �$_�ȁ/q 1} ! �a����,�y2}�*<Q76Eq�% and}i�.^�1} YkM_>Ue�en ourH ����!�"X$2P$ &�W02e HI},� � Ge $Q� $C5j8�"\�-J: S*�4�sa}@�bX$�%���0^�n3&4�� RS� Its 2 ex�(a�FU%!@e�6  6�I}o�I})Qa*Q)5 on֠�3sgo��to�v� ��e��vaT|H 5reG;.0}�.�  E�Kato-RelB JA. ��- Q thm2} As6Q�e�andi� i�6a�ga�pi \sqrt���(ax���)�  + \�P \pi^�;w. srf < (O �$g i�$�(a635��uIH< th&D(H)=D(EBP ndPj� ��� 1� \�To ���we rec�u���QAH�<�n*�J.�'B�"b}� �aa�< orm{d*(g(.,x))�!�q��fB�g(x,k)}� � ��2� ={(I���*)� _!�QcA� N�aB�^*2�&t >����\\ &+`E�[��J�)F�Rnd{�  � � G*�f��� C���\^D:�\v�>Grm� :/ �%Qm�4 2\pi>��t 22�2�fk�^6\ &I Y-M� � }{v��I)�\\ � 2�F�&� rm{ (�}��f�D�+a�$ed/0inf*g@+h)$, n&G�u9��� )8b7��%� ,�0 Mڅ ^i�)l+~E!����2� y H�P-) d� m}:a "B2 >0�5$1 Ȃ�1 EK�)l }{2��F��j8�4s��8 6E��to�'��6�N� sa1}mcI����J��si} +-eNg!�m�n FiQw!Y)g5]��!��v:�2eT�3f?)�KJ^� [$N� a� �  $-��P:Pg v,ly6yI�a@�$, ��j" F��U�ly ��, �B� ��$: 8D< �-pI�2�JRe�H��a8 ��-t�&ain�S�S�LradBA?s a&��g��2mRj�$.7R� ��s��190}): !6I� M�ܱ�� f) l�}(f�`a�qmui�mvv2!�kw*��o� +1 S\\ &+K�@ TM�U��� B�E>;�1� ��ph� ��\ ,\\ "a^**6��� cF"0 �5)`���.@:%V. .� ��)N.�f<F� �J  W1� \\)�2�%���������������]�ERM���)�i�l0e�:��6a�I"RZm .�ITEe��0&} ST.$K�%� �>int0� Q�� Q� {(1+ )^2�u&$� +1 �^��V.: �ph}+1$ (�(thuŧ 0}$) 2R�, wE9JG�^��6�� of�t�� rJmi%�+ $$16�X  1}{4�} �� v::X;we�%L%eF  $1� ��^�2%%m�;L 2�'+$$�  h�1 |!�!{at equ$�,V� \qedA�If >=!J�5-}: &@_invari�Hby2�1\ K9 ion.�us,�:&by"�9!�: 6^H (�/ʹ:),��-a>�9 reprew3�i�^� / :aa�0$+/� �Hrep}��9T8*9.�0w0&\�$"�%6 ,� �%AHS,A0�b FG�2)� $\Pi"K�E�!map�& He�,"�6 ,�"NFy-�b�-( (\Pi \phi)�8T,x',k\%\ldots n})=\�* -,x',%a-*?0i=1}^n k_{i,3^D�%�#PwKdK1Ac�+ Fouri�;�L�$�M0. One easily ` (&��,���,�! A��j�\Pi^*=0  .5"�,� ��a Cͮ���)�%�HsK)-��)=Y;2�%X%E�:�M*�3.0*Y*HP3} b=o0M) +I+��?"� �H0L��� �)=^ Q�6�>/�2�0 <-R�>)^2�ph� \�U�����N�HI�I}&�&��4:'Q � +� �G�$�>=(B�1`F!0.�m } k �Z A���2EEM !b�q:�e�$�� � �' N�Ea����01tw��to�5we��a�al�� �[esB/n�/�J!��s�F)S&�k&" �ZOY]5 j_��F" �,r�� .J�,\Ra�.#jbiiJ��/Fe��0*� ��:wts6�"�.�ahe �/r h � ��Z� Fz����)M"�;�Qit!�N *���F )�,"|*+(� clos@�mB�+�3� sa( weL focus�c4�8new�29r*BC: �we have��A3}"w "� Tv ZCd63D)�S� �:\�hI\R ��r>�.� ��x�xژb� �Y�D�N=[ R�&�:y�F4,$p�VA��� $�:���e�� zF�5~2 \omega�Fi})�.�2- L .��;e�ge:�6��f�r �3}Jw�*��2�o�-}�1}{ឍ�U�o)^2�\Y�vq�"� J�Fr ə�5b���%{)�.M1&f� ��af�F�kn2Y��� m}\|>$& �85�M�q \|!���g}Y �mz# �l&1#"N�M�j��BY{n �!�f�!.��=f� �n� �rR ��F�ş !�� B� T��)nB��@�Ei 2�ta����8s eD�Z$� eta}*�)AmT�+):7& (\ppE4!�qag (b+Ghop�+A� dD"k A�bAB��% A�Qt )�"�%2I6��%!�.��.�5 thm3v�&KWrho)Ia��&��&��&I`N� :�j'�F � "89D(� " '���Y� 6bf �LC³ B.'FP9AU%a++co�i-��M(WeI< $$�H^*= �M�M �&M.: o��of"� �" s�mimick ���++k {MaiiC�L}� a��,�46V "� $A-�6�_, $m(A�@|,�P�&r C$2�$A� O -� �J5 ��m� wdQb`&LI��E- $g��>�^2��.}E:1� j1��thmu��� 7&2 �s��*, � �jMCrhoiM"v7c$1}L Z�{3}��&�. s^�=TY6t�"�> $P>0)$g�&�?�!|� |}P� �*��76EFE..�E $ my�Fm"�&�:4cular,�`�&� a �H &�:A� ;M.�.'qVjCtooB�g"+I}8"q2 next�-9"n>�m�5ew�1�7} *�:� 6�J�d&n]+2} does �T �:�8$6 =1$ �r. rigin. JO=�Hn4< co2�H.U!�&�H e_IE\ I�<l0"�H�S �i �qd.��-�MK<o6A�s�{alW�s��N �)�:Ls)t �;6T&� CCR.pA$f�x�0�Uj0��a1ِt�H�s C25X,t(#:= e^{itQ�F9t.L}2758:$}9Fa�$$`EQnZfo�fuxVet}��VS["4 �"�;r�A�?$�<\R^3\setminus Q$I\�]$. ���Ֆ:rA�*�=efia>�d �s&�ǭ�%�.&D��Q/��AD9< Psi 4 t/6�shg l�s�$ 2�)�$Ig:!v\lim_{t�B\pm���[J5 z=:6\pm!�-ȁy"�Z%�&XFs%'eA��ک$\Phi ˥* :H!&1 B � �H��?Z$�� m �&Ph�)[N�� ]A�"=N�l�M)J=O@T�:,3-*�fco"�fs4Fq�$ !f$![�P:6�U,�DvC����� #;�MEUFe x? ��byB� DP04�  last�3-fconcerx(h�1o+.g` "�I6�f/@ŹF?Qon� �i��3. eEr���a waA�pRB;9k�Glso B.��m"7� w�[�ino4k "1Yo�?�A thm6aG$�r $ b�"�UlSgy�Vh*$j}���i$rr$� N� �a�8ZSH :%� ,m�R�� dard6q!�Kurb' � -X.�HW&{ &3 �mu��lRR�d:mQA�a�mstar} m3^:=�inf�q � 0} +%e ��?(>)^�p=\� al^2_{ct s� } (0�K��{g*�rel}&�:Z�>�.&G��R� a��+��%�eG� at�#R� &� �� .$-+CmJ"Zb�>�a�*oi].iisLPhD�*kIkma&fkQ,9"Vm��� F�);!>#�6 Si�mrB.e|�7T(Wa(W,q� psp$0m�� "�^\ �D$\p,nda�}!Tby dift9~�o��P� n = �  AO.�� ulas&M�M�3=�{<, (>$hsp )d\|A�49A��n�3�| hu= j&Zk'm H r\\ -&2=;]a� psp �<-i)��# M�%� ��(06�= 1/m�/$^E>0$�(-�q�b#m� �8�i K�(3qK.�f�H��$bfB[\2\�d?O ��O]4Coh84,Coh96,Sp�� \qed!b \sP�XM�m���em} %.:'sketch)M}�+6�9iy\ŏB&Ued��"�m@=.`@QI $. PCGly| \��llet DG5�� 2�O$>���w;�c�Ra�A�itemize?  \[(i)]�f(k6VG*(-3ty, N]"_X P_{\O7 _�'} \RE�5]D 1-#j_{g}( S)$"gN te�*to�6�Pg>e�N@<1q�va.�'Qu��R��qADAe�@,�F*� *" - proj��B3��"tNto"e� a.r`orthogo�b $/T vacuum� t�C)�]FF&z.�[ � ��-���R��dWs.�7V� be+�q D(ii). E  $tVc��r���$$"�rk�GkM�}$�J verg��QV��7P&́_{k "))_ ECoD{jeaklyJa-U�u�F�', s %�Bba%�f�S rank�^�,�'1��0(��� :6Ed$2(���,"; &�-��ebV.V�<�I��)���.H�Cb (�"AH97} l8� 4.9-.h�ws>���&�(� [�E\hF2�_�QsyETU�of&C 3.4a* �@ So!��i1GF�%&��on (i�G m��/�g� i�i�Qj�lasGPe�{%hw��ux�*b� �a�7lenghty�R stra� forw0 i�!-"� ���3 trolY)e'KhB!1�< $ ��\�tL�*G0m���>7x&:�. %A �,=# %itNev*]g:�mus�hh% �ibi��D g4"��"\ �e %� � s %;U�e!PlE pwe7}�  $.a8Efunda9b al iC��2�Ijmc�lem8}-[=,��r�U���3� �y enough,��ceFj -go-B� �sminorZVg--� 3}{4}�$�3�@�H.�7��pS$ ate,�v%1a �5 �fonda}, .�K�"%tol%� M�ofM�q:�m_B% via a p thr! ��� �R6�ii�Z .�"���:�+ i}�\tildeA _):e  X .�&CsplitF% �m  -&B�| I_ -�%:| �&�2>��1M�-n2B?(�(2FF� -VC3%z52BRJB2�(�  &�*g�2m��Ao2-�:FBeb�2*t5a�#*$N�N]oU�kb[�$j=-1,1,�C�duc �)stia��$msi�sa}oC6~_�5U�AC Lebesgue'��i&�J >1�>6��"r-�5iIQ�$7� 0}0�� C ~.�F���q���� is1!,gitwo��s����>�"�$q54ps�[sp�<b#13&Q �9(�i+�q!@$"�  g�8�  �+ma� lem7:�);� >�#J*C��"s"���I E$0�]S]͉\pp\R:� H%ne} a-� C�J q�\ppm�!�I*! QIs�J|:���A�9=5<]'�} O)�:z A�^a��*� l',�*Z,\o "=!Som , �B�y� =�l� �r-�K�\�2oNq&=Bo�h)�B�m^�$��!� ����� esp&/B\X� �!,� \rcE3�y�,),\�F=1�0�r��n�s����2t6,� t $ \thsU]&�"�iv2�$>j5F$�"thsAAtho +\�%�� =]d1�I + I uG+F^�S �6kh �Frh��}za�>�Yum_.a:%�(:g:��}NHV+FabD)��B�B� :fKOZl=R=�^� %�C1!�.O�&k���Da@��!%q����EIZ�+r>bImL~-"�&e$2�),�:!A=�_=� 4 2�:d�7{2-g:�290�e- C(g�Y+9 �c"$}tak�to�d␥�N�[�Q:y0� � 1}{(.a)^2�:"�2|2�|��� =�TE��& �n\62�%��^5)oJ !2H�(,���� 1|&�!Q)�w�� + �Bpp\in\R6�!�s���q "� "T r�U+$ �{I~\� C g^2! whit�u�  C��fM� 1}{mNg��6[4%n9e%1+��"�!B"ocIHII$��  , rho$areplaG@by�.�'geAA�$10� C43 s $b R $a!< �+&  \in:�| $g�s[-m�,g� 9 � $b�%�9����DAon� f{�)�F�!�6��hA��3 (bo +a()��.93�.�/ � )u��f!h:�NyFe2/ beli3�8.�-i4:w-\max InI�as }{1-b �M + | ;|�(�:e Combi�� E�6�h2}� a��&~l�tW1�a�A1!EC=J��E �+b>��w %�p2p: ��( ����Mst�Dg_cS�0�I�$\alphe:U�S Ie� ee} *�� �!$�!-)�"���ily e &����2�0 ]*�2 � 2� ��u nd� ma} \�i��is%���%��[q�!�� � (�%�N7e�$��2ulp R)e�"@xh@l3J�M�1Z�� ndixlA7H�Z8�E�n�/!_A�.-"�^&�xu.J F{~Z\��%3�,B�s �de� +c$ sHp�#�� $c�����8��Ii��atail{�]'6�ri�=0��of >5o��!�wo steps�2!Qon�'�� �w�}@� {f`namel�. vakaI�m/4�Mhil�F<Rc�6b ka$ :] e� m/4)r�+2vM:��b :JZ=;}A1�I�%��%km��$��}�b�*�-Cj>��i]22�F<�; �#}�%n�.va6 �Bm}{32C�2e}ESs t��IT6�47fv�NowA�QW!�!ڡm/�(Asbw� ϖ-!���." 2,$�!�sC�9�ej�j�zG�)�6O)$ ($�` i=0))$)��4 �{�;� F� $�j�+���Z�>BmM = � $$ W���s%��jx��46�x;A[�z� ,�)�&*�>=�F7�e�- 2m}er}� �)m: .] 1�� b2gBPbV G\ SRE)�kN� ߔ|p|�|��|q��o@ NX�� |\ z��I �w� f s $Ct &�:8Bpvv*)?� y7.� p �, $%� I $g\in[-�� "�a%*���Om��M�,:���: |���+>M�-d2�nS %� R �>M�rP&j�<^2��aAd.��a� �*�( ��A� RZcJ�wOT��LapI���I� M�-�3c5�^�a�j�C()y�!A;}i[\>),C .~EV:f!Now, &(%:l�J���Z!�52D>p:�~?�"�p" ���;��J/ &c �i�K"9$s!Z#u ��� �$�xIn�!ng1�A22MA3� 1}A9� �J��4I*rO ��-1�"�Oe�ѝA?��8 {2/.b�'\?& @� �E^�� iVQ_�&j�� Wri�,3 f+=(Zi ^b)�> +^{q` -H_{:|I-cH �)�=�!Q� $����m` +|Z |+�~�� $$ UD�M�?b"2(s #&��:e�h.J���f%+1)$$e m�" �Wo $��B� 0�FO $|||�@:/HGza�$g'n%9�$�� 1/�Ks)0���B� i"�e + 2 b�� C��U �"m �� �q�]+ nequv��Weq�A4}�l�s^9 2�ZR��\ؕ]1/m}(Q� + r� C�GRl(�_ N+1b~a�M��>0$. �n>��6����\\ ,V�S�]+2{L%; �2�y19e.+��(���=4 S6כ.f =<�eM�e�$A�$� *�]B�}F! �M$ e�)�bF&ņ� *F�|\pp|}{4�N}$ ����;  �{"�Ŝ�!2i�m��I �d� ;� .� �>�8$���y�� f� �.##*�&�(v�&i��I�*61#.& +�*RQ� alread��-(�3B�)�*uz!�: �~ar�!<L]# 2�9!)��7v�in v�Q�*b�to�,"*ANV�(�,SpBZ)�4p��0��e&- (��+s $N_g2� )] :=&��i�b�6y k\ .�"&�"!� we�5G(k�D��}�(I0|"Q k)|�`{1ݡ %��Z>b112c�q C�V� ��gqY�.�b�& R) �� p�{q�G�5Sd iM|�"��P6�N���G��&�"���.S0 �C (�x #"E"�7�.%A��)�3"�$^x^sQ5A�.A�"9+8+"��9+!R !}D�aV�* �Z& YL+GU. v"A%Lck�<&"��g����m�,)�2 (kX�'�!x'}�bI�9�y��F[}�%^"& VC]ID>���>�2$e����5.T F#w�~j~3� ->,'�g{�Q� �!)�A(&�+Q> �s����x0 E˩k�V7oM��� 0=&(Z]? Y�]�m.�\\ jLZ� b� z~9+yA� �FF5 ���1J�9m�^��rs��-�h ee}r p 48}EH��Z�>�X^: B|q/rm{6 � H ,Y4i�V,^mV! ���7 � . �%a��ds3&J��-�i%�lyU!.Kn|�h&�`Dˉs 13�T>0�6A��vmuv�N�{ {�"}(V *�YpPo��\ee-f�0�"U>!{)�g%��2|�| +2Cg$$8$�� 7} $ (5 ���&: )�  A�4%�-g4 �aӑ �:�c��%'� �)��v6�s� �*d3 $Ng �oJmZbCuD u��(let �� 9Ra !!])�jW }^2=Jq g� kB?9t[)� u �T�t(�)� �6erf *�Oinvol� ' �U_4& 5ulaQ"}. BuN� >�U�8} �)gee�rigourx���Aomi � details.� & �R�}ata� bk(.]�'�V aQ meas��C �.%�3 :�>�F�B=.fIe�o"Q �W� e�*P$ 12} v�?33��J�>��&c�R�>�0�R$g -�.^&52�r�/ P_{[{? ,�)"u%�om} �� C ��:� ^2= ��@ om}$AM!�A 6�2E(&�<)(. � sp)=!R5o��5t.V\�0I �"�&+ �'�O�)��+D�*\D���O F% A&7�#&�O"��` !T�_ �5�0&=.���&v�*)*J"� �.��1�-�)6p5^:M���VU�)q�R".1J����5��e)��7}����"UKRw:���A�~!i�1A-�`�D7 �4a�u5] Qm-b)%c>zv^t��r�):tf-��( � 7(B!�lso�&i�' $�9`*"ǬW���RТ#@lud $���j�B�V���"P_B`B &aB-_>Y.�= 1Ǝ�>.RQ -Q15�^\perp_��B� 1�j��&i"X fficp?�|"�)!�n [�@�Y ?k�(!�! ��.?Ea��byM0"_ ��_�.�2��� ||.� ||�E�@ �Z��:dJy1}+  \P�=R [�B��*]{Exi�Z�):>aD��Ga�hAp [9��&�+�8:e� ��F@R�"�A �+6�oi| #`!�noA; rpriabخe�mpletq���ong*�B� �+!�& ZtF��&�,DGN`�Mo}) �, �,!1��YJ4O��.hC_�db ! lackA�LR݌ $Bv�Y���o �� aSP"sp�sA�k|=$cst��D LL,G4�SS�1i� Z,6� �+� on"x*aB $$"�"�(k)�U�!u ^2+ko ^2}}�52},�1},0)\��ُrm�*o2.[b1&�}H&{CJD G\,%�)|)�on :|\\{(0,0�u 3})\�9r.  \!NZ theless>6 UX��.��T verc].���� by&= %�:�_60O�ls4�2"zd$�|os%pport "`=�Q��i/`Ai���-M �X_Z� _p� �.����%�modifY> disp��odlpXasM�X H�w,��C5,.�@3)Z : $ l��1�Q.�4x L�P:�Q�,/3(\vak,F\]}{2�s�}y.AG��A[C=9 $'Kp�C�Q\�[�] $ |��>*k MNf$.3 uI uK�$k=i0�zN!&eg�atatmodi�1}i�88tn�B*)+�VH2 �*1}a<2ȓN�% �!-� �N�Qa�@,�or��.`�&I� ��^t��� �7Rw���� Xw��< �\�1jb:&�t6�� \} N�R* ��o.K\3��Fa2���pE�� �A,A��t va� $�@���޻2�6!�1�`�!m L8�Ky I 82a(r �0a�xM�s� A. More�,K;"��6�;�Ime��6 =�mLj���>!\eځV�4 i8���i]�) B2 �%8 uH""<> Z5nit+&� 25w <K�;yz#�}(}!�7=���Hadi�" , soB�Imt YZa�[��e2�B3�-�-�t;~NE�}We�; bser�v$�3TArM�I]VvN3)�. \\6Cf�Eߍ� dist�ft(e(v,V��\ �u�)\"Tda��5\ {)%2�f>���8\betaEz">��0�83�q �*�#цJ+� �%kY �-�}[> ����e�G}$�uS��L12w -H M!|/g]>^�N !>@*�0&(-�. D!�a1^terval=":Q�]-%X\sup  2�3�p \�5����)&$$� :Xi,��=& w2@ro�Hat:�:��eta^2< � v�&� n,*:��(� �6!v���K �c II.1� �XhA"��!�at���9s $M_{)p2�*%�2V6Am. ^B9}�e^{!  |x'|"� I)\c�SE*�iP�!�`�U��Q?�R�^�u� 2�6�*��z8�$\,wx\|�T&�,�J�2�&YA �mzRan }N��e�&(� ��$)H "arrow<�ڪ}0B� &w-�Kn �G~=0b�aq%�*�� lamb� [��7A�, �21�*�l�X�B9b�&Ei>�, 6�Z��$\�1E�Z^%7\�E���t� �� � _{�#N�M�'uX-��md265pb M�Bsz���'B�K. ��" ���Xa�H�Z�$ .wY �loc]hA�g(.�Xj_{0},j_��\��Iy�k�:HTv��d" s �% D��+H^2e� (y�nAb$|yb+\� "R�"$2$. G�$R�4J 33$,R[v�G}< y}{RWA�l�`j_{R}=(�,R}�,(#.3mybF1}{i}Qokͅ�R-�n&�)%r $\F$F&� F�2 �$��IY}�| , $dN, \undeW�e�  �-�)���xJ�1H3,��b �"�uB )(6A�z� 2.13%U 2.14�>� 1 2.6%)-n $\:�:=(�cMo� R�Sf�peaking,4XI>E s;�i#!�*kT-�_+ qd aro��5�V�+�escap��iٻ�t (�]R�i,�^ (��Z6�G_{l,.Nx'ч&�&Y�2\~��..�F�Q�")j(�B� _{l}��� l4,,3 ����&��s)aT"R�&��rs(k)�� .( �DbHYk)�)x'�\3&FD u}(h�� 2}(a + �j (h) R�9 *� !���q-� Z* \. :�� M�H}&�J K}3"��mo&�M I +I!%%�Fph&� +4N0%n+�y\2�EA6��I!*�6.�;m- m�*��q��&B$;A�}]�u�� \rs){C-&d �VfT�Kje(B�Vw G_{jZ���ITiI�2��@.@KfWK�S{%*�IASu}�3~�I� @,1�g�+!��O��2Mo9" p^�1-^"V�I � R� Agaij U a�� �$q�0fO^�6�j.1 1YW�&&a�[ ��/} ���y�U�E�6�8 oX+6� � t1 \phi� .a �� J���$9�Hc"k�a�' de��ͻ*�� re>\���,]' b � $!}-"�}l&u�c��6��� ��mvanish!������J��y!? _��h% � >Hw#�*t"�MXB3|sFi��EM��*T�R}(G)��=u{i�7(.|� ? -1) j��<]��GyVG4,R}vI��3�T� (HưE��c.�S��jG ���+.Ü"! Ws&I H )%� )% (s,5! 2.6)A�-�A��4a{S�almost�jug� V�$, �I�^� �%feo} R&�-�@N�  =RF6.�V96�����:� T_{3u b� r��ye=Fx T_{jv` -V &( /#F*}  Rj� -&�_�.O�� �G ){:E�D �;�g\m�KPh�� G_{3b�mE\ "H .nՂ6w�cZ� 6-n_� � BR�([�<�]�W�E �����<&\"s/�:]* .S"�6�c�,RJ;a>+&|&��i| � vo���'���5�'F� J� 8B�.=\>� 4�l� >rrZ-H3f%�E�5�A�J���I�*> )]V�n] �$\rs$�a>�r� �'�\g��>0n�&� &(1-C_{k'})^ ?c:#2�R�?n� �Y3�# -Nf�:  >0�5^Rz8)�� 6�B�)�) \� F� J�f�>HWk'=�$� ) N��in:�39)!�at6�h[S9 �6?6� (I&� N_O=�&*� �R $�z/2}h� joR� �m m�oAzer�Ԗ�B�O��t�J B92} �M � B24�6v�\� *k` ,R��l \ N" B \ +o(R^0s1&�R]n$�g67  r �IDe/Jng&61�q��}~3� HpaTBj � )3� �E�>�."c1B�R�3�E�m(� Z\׆�hX< ��&66qG.)s1aVM >��F�F�M� �m4�n/�=.��K^2)�]$n,AF)�6�#7a!4�A:�ace� of4��  2��d�J��+i��6ZC4\cite{DG99} ledmma 34 or \cite{FGScom} le6 and ��AHS78b} theorem 2.6), we deduce from \eqref{B24}, letting $n\to \infty$, $$ \lambda \geq \emsp +\frac{\sigma}{2}+o(R^0) \ . $$ LMR\M�`get a contradiction with �3}�(thus asser$(ii) of ��\ref{thm6} is proved. \qed \begin{thebibliography}{10}�ibitem{AGG05a} L.~Amour, B.~Gr{\'e}bert, !S�[J.-C. Guillot. \newblock L'\'electron habill\'e non relativiste dans un champ magn\'etique. M�<{\em C. R. Math. Acad. Sci. Paris}, 340(6):421--426, 2005. \2�b��\The dressed mobile atoms%� ions.��|preprint, ArXiv:math-ph/0507052}J�(90} A.~Arai.OPerturba%�of embedded eigenvalues: a general class )txactly soluble models in {F}!�spaceF�Hokkaido-qdynamicF�JQ Phys� 41(7A7E83%`6�H975a%�(M.~Hirokawa.qOnaM exA�nce,unA�nes%[,ground state5@ized spin-boson)u.`E 4J. Funct. Anal�8151(2):455--503%e7.2�XHS} J.~Avron, I.~Herbsti�B.~Simon2k\S}chr\"odinger operators�[magne!y%�8s {II}. {S}eparQq % centBf mA`in homoAuous>J2�a� Ann.5�114:43!�51�782L����z��G}i3 i�a�vF� Duke.  48:847--8Ag1:�PBFS98b} V.~Bach, J.~F!�hli�9I!�ga2QI�>�a�confined6-qZF�Advma�(37:205--298!m92m�aƮ$RenormalizI'a p analysi�sp�al�� blem�wm�IpIYoryF.B�99--395V�9��S��for syst�of��Lmolecules coupled toa �a� radi) eKB� Comm-�u207:249!�0�9.BCVaT-M. Barbaroux, T.~Cheni�(S.~Vugalter.qBindingA7di�6s��� ic {$N$}-�`n� in non-2�{QED}.\y�0Henri Poincar, 4�$1101--1136��3.��} �.WO��-���infrarE�n2kaAconstrue� o���1-q��.g��4 mp-arc 01-310�12�Xoh84} C.~Cohen-Tannoudj2�Introd �toIuB�.� In GN ynberg�0R.~Stora, edi��, �> m�%�6* .;̑z.3.3410033NtGLL�5� , E.~LiebI�M.~Los2'G2�inF� �v��In��O 45:557--5� 20:�H��Fp shim26�of� �2� b� {I2��F(<0(12):6209--6222 6z H�������661--674E�2� H01}��6 � um!cZHM B q�2J%aTrans.eX� SocA353:4497��28�� ��{f�K]6n|"Y ng�a �ag n� In � opictheory!Z }. Worl]$Scientific١ف%^@�licitk6�B� �*� � &��!�O�402075�O�I>�E7 K.~R. Ito.cMr:� i�6C^i withpin 1/2.\EY�� 4-406�� IT98�Itwatsuk �H.~Tamur2l��$s distribu_ !�*Q��� :6(b�B�>>93:53�a�1:�LL03} ��%~J�E"��,e a�&�j� �\~T q�� 0.}, 7:667--71�25 ��z�8A note on polar<vec��Z-BTb�7�o�206�Mo` $S. M{\o}ll64�t��l� invari�  {N}el"� :3botto�Pth% �bB�N�258Y�u�pizAA.~Pizz2tOne�� (impr�) �� �'s"4 �CB�� J� �9--48� 2��4eiB�S&� A��fra�7 :! one*�%� i���1H�10* 5GRaisG.~Ra{i}:AE";�Ii�� >�![Ai�-^� Vg� Fourier($9:1603--16&1:�RS2� ReeS � B��Method�%�rns &� �.�F} ���4, self-adjoint�2D ke6Pr��[Harcourt Brace Jovanovich Publishers],� York� 1975.� Shi91}  hige>}"�I�ti`�� ��a� {$� 12$}u?B�JF�0~ 2�28{2�Sob/,A.~V. Sobole2��0{L}ieb-{T}hir: estim:^NqB�>E82(3):6S63 �62fpa�H.~SpohFk DXa�charged5@ their>D 2 Cambridge%ya�ss& end{>l�%a�"{qed}:Lstyle{abbrv} %{unsrt;Tdocumen  m\,[reqno]{amsa9\Zm Xplain}� � }{�� em}[�� ion]2'A�osi}[ <]{Pro2/l� )L2# corollary'C2+assump:|A2-defin>�D2-remark�R 2%sEmm.�S.),*{quotethm}{:not�a}{N 6: �2}� \Declare�({\supp}{Z"8UU:�Ll> Y  bb{Y:6I mI:A  bf{A:MM:xx2�aa=�di  rm d>�v  bf{v66{\Hc} �H}_ rm{c}>+Cc}{Cn!LLEIf*\E-g bf E6 J � bf J2{\T�T6�\F6{F>c �2NSS69{\E�;E6\Tr :rm{Tr:ee>0ps{\varepsilo��Q� vphiphia�9�{\la} ngle:rr .:{\l� left>3 righ��6P � bb P25\EE>�q}[1]{m\lVert\!  #1 p\r\!.2h{\abs.Lver2@:2N>s �.I0mylist}{% �6 {�4enumi}{\roman{ }%>)label {(2,)-b�& mF{\usecou�! b`% \setlength{\topsep}{1mm:� 0Nskip}ZRF5a':towid�� NTAg$margin}{-2 �addto�.!.L% f(V�ind_ !�{w %`� %2r�}{N&ing} % � First �Second ....( ] % %ZS arg� Yif / default %E dBJ; iD(y be %overr�v$oG acoD) ��1�H) a piece} %text thainserted$a box* formg �. This���,usually %doe_"Dntain other LaTeX �s.5�'�5c 9B�s��g�1� ameters %!61->��will most often be null, i.e. {} 1(select %1�Ms, whdep� oW' � � %)�s� % 7,should suffi�+or �,cases. Howev��-�s s!`Hbe put %here are % �� m� am�!�extra ��G�Y! topAO>� 7i| a /if �A:,prececed byA!4lank line %(it�(be a rubber R)sE�e��betweeni >par6=:�7�'g,se&in� ML�a horizAylH�"K!�+ ��g %.a* ist; must!nonneg$,=��I M byI`+^y� �x�par�B2I)A�5< +f-)�f�n % tem;Q�F� B � A� FA8�J�@!�s&�)1�endE!|���?�S:!�"��R�]�ſ 1al >^m;a7{�$ al %Ia> biggq� natuQ( Tis used,a�en�&in�'�#e%�W� %1=!i's tex}� makez��S-tes4 �#��by6/���g*s$ctr} enabl K� ctr��be���!��s; %i�Iinitir)�( zeroE�Hstepped when execu�0an6�Ų %has no�sal ��L�gs,P ��� (title[Deloc�I�Hin random Landau Ha"�- s] {h�$�9odauthor{Fran\c cois Germine� ad�'{6�#Tde Cergy-Pontoise, D\'at�!F\'�ques, Si�0 e Saint-M�.`n, 2 avenue Adolphe Chauv95302:h cedex, �0ce} \email{g �@ .u-c�.f� �Abel K�"}� h{"v$ya;@California, Irvin�օ�of�� cs, #L CA 92697-3875, USA�aks@uci.edu=qJeffrey>$Schenker� ETH Z\"ur�,)tische#(ik, CH-8093& Switz�&nd�j5]@itp.�(.ethz.ch} � anks{2000!Lph{!� �4 Subject Class�E�D.} Primary 82B44;m 0 47B80, 60H25�t b A.K. was Jo� �� �PNSF Grant DMS-0200710�  abst?. } We�vy &C0of �0F �AfF$ near eachqd$level. Si�0typ�l��re�j2��he �� T@disordered-broadeh.m�band, t� impl~ 2� at least �z&3ityo at n2Ynamel M1%�p�ը�6�nd :Iregime"m w5o��ver �- correspo�- � %M as eiw t61 or1* g� to��.,6nd] �G�.A$\f{.),}:6bel�B,U I�' ticle�!�.�9�:AK �L Mo�+recisely7;6�5WTthese two-dimensional 2�$r93s UEj1gy $E$ V� suc� �per�icu�,�6 plan9��uctor� yj ima.0!rol�/�l�  JM )M�L,AA,T,Ha,NT,Ku,Be,ASS,BES}. Laughli� � -�L},���=4ed out by Halp�+ ] Ha},f s �a"6��� weak����>*ݍ��!! sist�[�; � e",8� edA C ���-of��i� s\8and/or * gaps. (�"ex� al:�D %kNE�-��� � rur s e+E��.~exq �, e.g., -�!�}.)�)�'Qn �Ti;aWorerjusL'� �v F�� #/or �!Ssom��#60I�of51>' . Kunz I�Ku})�d]@s I= � +<eru�dgy~ ``2�@" �� � ��2�,� agre� e�U�!l3D. Bellissard, van4tAQ� $ulz-Baldes �af%���at��a f� �!��-bu6approx� ion, if%�!XAc�=Ejumps m?on�0te�:�<�zan�two FN e4i� t�� � a^4` 4�6i@� at��a cerp J�1�(s. Aizenman%9 Graf-0AG} gav�m= el%�� %�E�A\@ A r�%he/ oV�)*I@um, �E�s �f( j1�� !�:Q �K�/alB=)�*�atv"�a"� BS)(�M��a�� HK2ar�7 �tr s (a"�%��Q�6�A�:� �)� ͘ ^�� @ 9:in  �Y0~EO-}). Smf�.���+dgk bA� \.Q�CH2� K�4I��O�l�L2q _. W�u� id�*?ly rigorI d��T  previouls�  o l *, �J�) We also �� issu�Ihe%#{%^M a � a�%��{�V�. Perco�7�kdB!�?l��Ud�E!'� la:��bz&b�6ly�8.��y, �ed1�M�E� �XCD�6n� pred�Qs hh&�;(Y_(�!-2�^"i!h � xH2,IS&P2�1r a�) p K:* �a)�:9gi�L� ("�2iLcor� 1aMQ)E�I��-_Z��� �e priab *M-�6"^�2})a@ �Our�ofA�b0�2i.rs "Fh�#Os�dec�ly no"�  eq�s +6m)C�E);�z64 ":)b% � Jg!�qc�8fun6K+pa� I "�!�����!3It � < 3 �m3ingA�$ents: (1)�&iM��5}amw E�!]an"�. 6� �/ I0N6.� � S%1[?� V!8J��nm�"conclu 5(5 "XNare vali�(�*yizy! I�Yu.�, �%! outs���* 9E\]R� S)\ ��eHN� 3. (2)�Ql��.X atis�- � quir&I;=5(E,!Me hyp*ses�X��GK1� )A ^A��. ��� �ty �� Wegn^`9 ��.B<clu"� ܥ�s, a r �d�i� A%� (1). I���  bump1�"� �,pR�-$9%+unit squ�,)���. HLMW}.� K u us��$#� i l�-� dP aiEDp- in +�� 2.3), a>U 5V 5��o�- � _e&� �0" fluxoA2.)�CHK�1�2a newB� �ono�:�Xs"ٞ ok >2� I6})�uisBn�B�)r�v-�# !_go, h�����&)��?"��. ensuv i�?�Bt#t�-!��^^l. o0paLs c��by��0A FJ� ��)vI�gZ:r*�Z"�%^�s �b�F� ) (se3gK in �Lion;r 9� (3) S�in�S n�>�,f&: (i���$��ues��>:U�(free)�,�: �+���  b-�2W���bM at� .', |B fact (Ai !). �[�B�in�L a ����Y par 2!rA \ .<� al� *� .�s,�7�^ mElgart�nM �ES}rsmooth�#s=] ��to��- (L=I$lemAucgap!!!Dbi�.%��!5 we���Az).Giv�(�Ub)P across6�%�i�.Ga�!�!�u1�� Qin�;��Z��d)>a$#pa�way u�$CeepE�a QJ�, x  SUDEC,+ � ���*mu��2�6VI�GK6�b��/!� show�!6" 6RA��4YN~D�/(� e) sum q��Hs�[BMd" &�1ividu&y!8�#J�4�~ ly s�3toAM�l � . (See N���ō]c/ �iU..$ ၑ9ora�cu��a�M: #$2�� iPI�)�BES,AG�A!����but� i simi3proof Z��;��g� }) � "- fo�K-�re�\� �EG&4 n8Eto�2 2�I zQ i p�K�f� ;Ay� E3o�ilE��$�y��ua��}V+37< ��r�s�)a�62�as���a2�} I]th no25 Om�� *� � , � �3)A��M ErnVresearch�d�� �pi20 year�&1)6e&�"a^R� origF! ly i-�c&' �WPU�$F ncerMFS,fur���i�'uvDq0Sp,CH1,FK,GK1A� � ,)�o"� ,�A���A���8�s�j >i5W},!R$a key tool:b!�it� b�6!udi�7A|inuF dCH1: , ,CHN,HK,J !� ) bng�!��b2 � u2 $qcL !KNN6�),AG,ES,e� "�.pS we�} a �p�d,:f�a�&&M��z�Aa�BE�F ���-6!�m�ZU�17are��1 �!t e3%�L^��R+:X Zic ���dis _ty ��Ch�I�a� a Fredhol0 dex [%�( Be, AvSS, �� AG].�"b� ies 6�� FK�- e�lap ( *� 1N.Z}`MAa %l.�7��(!N [AG]%�b��"��De�(us1,F�AU+AY"k*� "6 �w` we have f<��aeq� kern7eMQ(pro�4i�e �EAi��ll* �( 2�[!�1�,�D%� etai �E ��sp�'�,ů��s�in,ct� � [A3]..�u#�<3*(��s-� we G%�]� &� &ZI�!�m�ѫ.�� �s]1�;LC8(�\lap��%[p�V� rgan�&allows:2B6 �}� �R%V � q.��� our'� sia� U�7>-Jj("� N&j�Z,}?}J��a�in0�mXset $$ \Lambda_L(x) :=A \{y\in�K`bb{R}^2 ; \ \, |y-x|_\i2n4<{\tfrac L 2}\�@\}, \quaI3\ �{x,L}��{\r-x!$x,� $$ $C^ l_c (I)$+)o�>%�O� real�4&� i,i�>5J�Q $�!Ot mpact zŋ� � �-��($I")"�{c,+} �beingɆsub��rn&B�@e Hilbert-Schmidts@3an{!��rit�%4as $\|A\|_2 = MR(\tr A^*A}$�9U�U�>N��=s�*fu� Ji&*�1 -Michel$�0 Pe�%Hislo=id� 'e�c Klopp�0�+ help]�' y Q>��?5$ion{Model V ɸs2{: 1W�i36b" q��c}a��:l�`(h} H_{B,\le-<,\omega} = H_B +�:aE V_ mE` rm{oRaI;tL}^2(ma, )K rm{d}}x),�;�� re $H_B$!���b�, �=@�= (-i\�Aa- f{A})^2�){�}  �'= m�0B2 (x_2,-x_1)-�i H�_�Y&�!� $B��]h�$�JA�&��*� � sym�fic gaugej&�2�3�Jg"%"~8m�>�/eR G $-� > 0$j)Z;���s�hgthj1nd $Q�a" &8u �bzpotVL} UR���/um_{i��)_ b{Z}�9Iw _i\, u(x-,iJ=�!� $u$��&<2 �*��$ u^{-}��<{0,\eps_u}\le u ^+ delta_u}$�7 $0< 5."<��͍0< f" +} ,%�$ � =\{ _i��iݜ�\}� f>"� gF�9ent, #KtN@}�kZ!v[�Dak��v e�Qt�H $[-M_1, M_2]$ ($0% M_2 sž�0+  s�7\|\b�Q�%A=1$�` ?, !b%W�P(x)A%M_2$. $R�mo-�"{�K�mappingsUZ\to f(RO)$��'ly .15 llU.�"a�B !�W� �#� ����%Ds $U_a= U_a(B)$, A�\$ � ,<>�I {magI� ,eft(U_a \psi)q)�?e^{-i�*B2 ��8a_1 - x_1 a_2)}6(x -a)>B ob a&a� jecto>�$8reH.enI=�� $��) r)V^v�$:B� �U_b�� �2� a_2b��b�( U_{a+b} = / B N)UU_a� a,b)pZ^29 �BR[%�E6}=^* iRA$a F)���A5��%�)�� h9e_${$�ka�co��E8fonF#M,)5R�U_�.�tau_a�i�F� ��Z^2$}B{$ (.F )_i��. �� -a} ��� K��4�� $N�m�MJ��$- �h .�]&5 onW�5R�0{\rm d}x)$; h�� "�8.on�\��S{=A}$.m $\s  (N�)=F> � .�oI% �  decom�[a_ve$ i=L�5H@>um,z�1��ru��l+"!-�$ lso �l�E�hoBf�gV� �KM,PF�8�8b$)B(H_B)$"G( �.x  �@&�(� ly d&�*��aMsFa6 &<} B_n=(2n-1)B ,i50n=1,2,\dotsc > �1�ven�toEW $B_0=-' . AZpjh�sAatf� s�Bdau} Ji \sub�4 \bigcup_{n=1}h� cal{B}_n("� ) �\mbox{e�} �eVJ2 = [B_n -!;! ) !2 +Y I  FkIf)xLph{di2�/�i1 }fgap'� ~ {(M_� )}< {2BF�is �>4�0"� ^w`1��2�/()&�"s#��J;}�< �i���ec2�sB/� G�I6/aG6�=]!�=�1!�{n+1}2�2[� n=0,]�B*nonemptk .��@N $.�IH@�2rho1  a.e.�6t �?�1��&e�Q>[D ach Y, &� 0m $m�la�$� 9,find $a_{j,U�,�in [0�$ M_j]$, $ja� $, A���!':M�4���[a 4]{KM2}B�a+zq�#Bj = ~�I6�, \>�:"= t ftm� a_{12,B_n+22` ]J� �x3RQt say��� E�^��r��*���RS e�!3 E"�Le�Xa,:�$. To� e ``^�" "�B� M*/E(p,u� X},t) = -� \| �Zn�] x {:}^{�6p 2} &: -i tN S^� X}V��0��|_2^2F�j-�m�;���2 $pM70$k�:$t$�e~)���!N�, �3 Tp$pa�=ly loc�/�y)of �5 *�'�! (�"�:Y90$,nd "�Fed"�,y� �� ��X}�%>%pADIts)averag!4x�'kQ i B: �tam� 1�M}]R}( p 2M T ) AP E0 1{T}� t_0^{dN bb{E� ft\{V�n2[t)M"} "�Ei{t}ka} \Y tF ��Ѷthm�4} UT:%r�$i͒# �$.�(wA\%�B� �(�'f�: �?2:d� .M taRE�&&gy $E2p AQ5�:� $, �Z��very F4��:&� QQX}�]uiv 1t n�2o $J\ni 6� $� $p�h� �1�"F��7growth}e�{:�6 TA��; C_{2Am T�4 - 6}:` � $TG0-j FR> 0 $� Q� F�� v;G)�QE� (lower)��: ex�Q9nar�y�u�Y{�nXa� .� 6)��6nf_{T\tom� \;�{\log_+�"F`>~ T)}{ p 8 �-�Ae���$Y��i}&��C  $j _+ t)max \� t,0\�=��d6)S\e $p$-th�  N%_1^}�}�:�9k>�� ($I$"BT�t�)=�u�� tB�E)h%uI e } �i�f!gVI_~�Mou0 � ]D��NME/] ide BT�*�a-or}r3!NT~y � increa�{$p$%�� �=�)��J�}�{F��bJmdef4E=k 1� &�} (E)APlim_{p�!�ty}6�(p,,-�p>0b%F�Th@V5J�Cy�� *�F�a��U[*bm 3.2]�H: $ WJ2�� ,�H6��%E),\,FA!I1xN�t� ^A.i)(=0$ if $E \{+ F� G UE~5)�F�Q!woG#�!:g�AW}�ax�6 fix�.� Etc >0$0#Mp'2�/�h'}%.giny^MT XiDL} \Xi.^{{�� DL}}�Z\{EAN \R;"Rg=0 �hvPYyҁ���i0d"�@6�Bb^�DJ� �D��>�B�U0 $B)DL�� n� ��F0��V^ tmaV6w�&��ore>�&A=u�J)&^k 3& Con< r�3�N ��:�.�; C�6�a*; F�M�# mptyr� \cap��:B a��Hse�6�In"Z,��&�`$]*� �� *o-2 A@��N��s! �${B*��2O &z[1{4��$({11}{2p}>0 �!� $p > 25%B^(6[Z4$F8%Y&> "j(�} x�nF�&� uc}.a>,QWU,�4)1Vas%O06h�N by ɛ �s~2.10!� 2.11ɣ�&N1j� v�;g�2�ԡp�d9�1�� 2��s05�wo =�Q&DB�.m~!�>�%�("�4$n$-{N m���?aT 6��e�!p�c2K��X��:LS�^"�4"�X  i")led���?�)[]J4�^N*O7a n�KaK+�& o aB2*}:s @ $\tilde{E� B�i+�1���\}Gf{B3DL�EJF�� DQ�B-�� !g"��'�B2)I�7 *�*-�IFto dZ"M�+k�Pm�N�/ (!�LQ�)��nAfe � r6�+"�*!�*ŀn2(�;e9�F�+,�1�Ft }7&$E)6at�86�G1I"�>�IJMiF�,%CA� :2i�{�Ea5�c�+�ec"�D����=dad�a�0�"�>�"6%: y6$u~ C"�*y p u� D_{\[+2}} 2}(0N!!�"nr(��radiu"� 24$ �7e��at $0$;;�SAT.�J�#+n :N; �#�+� on�,MV$M=M_1=�")vi) $([0,s]�nHc \min\{s,M\}^\zetaɿsE> $c>0) >�Fix.8 ��l�#�'��"[^B�O�0�q�� B���N&�e B�"� ab} � �M -u6�\ Q C_n( &) B^{-)�12}����F�T�1 for ��� ,�B$g)i�enoug8a ��2�s�" wide��Nn}*H> �eN1g�s! max_{_eft \�t v[ -^z  \�tH le K=1%,jB}#&x*�!as $B?�!�B2.} \\ loc� E} B�BC<:�16� :#26#<[+a_:�,�abc} xB�,:`:�,[ \,\cup\, ]:*:�.n J]� FNI�M\ -� (By $.�,2�@!<&n�"H(q?8�~ �Rl�"O$:�:�=zka .e.,]��~��Gs� a l"�R)� c�T�g�1V";1�'ab]1� n���S}J�4iin5>�j65eM5�G�*H&�Y�,�c}�� U�i�N�* ~4. 3Hte 77 ^choose ��>t i#. :q��6ZMp)}T�[i:� 6�8 N (^N�"� �-)�B%�7�� �-pirWZ;4�1I��Btoo �nst~ to @c���f� ��0$*1�l�/,A�c6��*4 w�ut��shrink a �.3 s�E-�ѽ} �- � Nbe A. In W Vk�B.sg �<3 1C�CreM.*MN, H-_i's$� ~?ent�Hng`D� m�ihq*�+J_"�zerq 2d� 2} LC�!t.� $\R$%U-  a.�2+ �$�f.$ra^\gamma _ (u)$"r+� � ">�,\�b�!�$$ \nu_�$!�!�&�-2� �� � @(u[ c_{b"�b$^{-1}� n u)�4[-b,b]}��7L�c�� $2UJ c5.��%'_ O%}(\R)=� d)=�DOeM)�)&�!}E6(2.1) �R =1$�;"� $ &CcB�.6@Ad12$%���  v"s/$2�/, &*\[A�h�0 B>b$q$��� �#%�^q[�1J� &� >�C!i|��()��!�0ff* *FsT_�0 b0 ����ٿ%  E1�a�g alig7'�g ^g B)-^"� i� -1} �abs� ."�"2%��"� B F�!� )�20� � I�a= ys $j B) (72p,  EV�|1-�vEs�'erP�A: $s.�u}^\alph�#rh�� 8F� $ *��]� R��T1��M�e� %� 5w \B\1 i�a�eJW ht h�0id� (�po]�U �U bU Z^2:H S�0.|M ��"W8|L2-adZwQ*�'ec��F!M>* max 6� s �=6#t#).R"co',c�h�3 �, {B,0I&=8!��Q4�R ��=0��"�0}^*� = \R \hslash \�.�-= : {B_n�5n )�,\} $;=/t@�s hOf�}PZ+iiily)�[�f�un�_ Ovisx�Hlyjluded��<a Borel��*�#J}\Rjse! $P!7�r&�$J}1IU!�<"# J}}(NT')IfI<�J}= ]-/,E]��C> 6{Eq�"6E' >�C6�5��> &$ � E�A��� * QQ5�1}�6 #~_�allon�T-)��l!F�� F�[?�b�� � y �relev�qto��eե��~�\qr: RDL (� o��y�.rz;RDDV)6$), DFP (de_E9y&KE)�NK (summo845: <�0)�!4s)%� h"��[�bf{RDL}]�H� n�u�-�2���TX�TX:TX� 7>��{O$�it"� 2.8�~51"�=CD}]� ��E�. If a&iE!%�W!�NO6&J. �D}}�5m'M� R�E2�b4$;fact, R0p,E��.3y b �(�P(��2N(VM(L(�!Q�".!� eqhyp�{�#T �g}�1{�'l �O(T)= C+nds ���$ R+(�] $ p>4 +#�s(2.1>�j�DFPq˩řL :%�B&�*f�N�Vif� G�~� �P� y##d"�.v-: am�btL}�= nd $�!� ]0,1["� ^��fe } \E�$�,��{�x 2�5�.y}�.\�.�e �)�,B, ,E}\h4^{-|x-y|PAi�M} \ x,y�\ZN/a�"� $Zu$)kly" >2Eq*�(JSgT,Wris&HN#Q� 3��1�81.4]{BGK}.)} As6�M�)�$\P$-�\g- �J��< s�w $C_Je�*&?EkB,&63rFBCӍor� ABZ�A x\ra y �w�� o#h{(Su��7lyi�polynomztE�\s)e%��Kpurpos�u&�%m��?1 \+n�)�@8M# V;3 :9i6q8"�P��(Combes-ThomTy�^ 0n��)���?$ev�)!nd���b�S�W�pY�U��2 .� �&�5"� 5RJ;;Rf�L��u�l� proSb�[� clos�#P, $I r,�$$\{\phi_{n�\}_{n��/ bb{N1��Q!�te orthoaa ofthge"L  IZ��{ �B $E.�in I$;� ri�$n��d�byő�$E$ �"�pal �g,_��ARsp4(�76��t � �n� =�li�^{-2}P!��= T�e�a�':h-]�^2 � �Z�Als��I,E�1��D��e�N2;� n�e?pԓ ����5q���A� xZ�.$yZ$�%:�8=f9Y�Za�. ^2 \�>MB &m�R��/� sum� �-m_{� n \NN�= \mu�I(I) :=  K�$�A06;I1� :&\?ѷB���Al�b-"HVfs9]Oba~��W:w*dD. erty9,�W�Ue��'5),�  +dif$j,p's WULE8{Ge}. �a�a��e�%QP�T(x\4Borel-Cantelli�[�� a a �b&j7.f_"q *w'W ">"�x �v� . )g �dval�[to SULEig���pJw�t��o'Throug�F�.�twLJ>z���� me =[� �@�C!ZJfP\@s,PbI~)1 "cYq"%De7whole�Hce�m� %+J��\Z^d}J�9�I�U  ~�f�hE-�$ vail�U|�'%"aL�� m��$ [AENSS], |*2�0rQE)%�&��I �t�'b:bmi�t ��b5s�$viKm%� af2.en�e�9c���c<�."�Q ") turnAX!H��5uI^~V>.n switch.�%La� (t:��{[� 1 2,�)}(t)$u �% $ 6_j&�4EA%:�~�"43(x�wx_jd+!. �nZ�$P$ o� vR-EP6r�N�\ 1�-w��Th�U \ (P):�<�P��P [�z�> P, �_1�] B6>2��] "s1 � x2d�W*9" >l|� |} | � | (P�F� ���}_1�Q�2~i2s'w�p+fa2=b�6.`-9 P9WP� 2P1B \3")B *p althoug�%-(P)RA�1�e��� mut�l it n�`�!bet , beca�O�-nds $�1P"�T2 Pi2�1P� ea�-=�ѥcR�C�������lem�}�A���X J� ��& T � x�]�$\kappa *�C $K_P"F z  P>�e�!� K_P� n: yc! ~:�xi��B A :�'noHnt�(bf{(i)}} $2Z\lexi, �} K_P�+� %1�Kt�$C_\xi$h[6�PB0$6�w�\m�.�(J���  $s�.R� ��D ^{(s��=  (t-s�E� &_j (�~�� ��Se�$Ey_{r,s}(PB�b^{(r)}v yj"Azr,s�R$=#!�B>6�e�.M�Y��(i0A -y� B�.Z )y=$Q+$���xax*A _�"u5X� a�!�Y'S!iesG mT -:�K_Q$. jn $P+Q%^L}Zi2� P}|?]�K_{P+Q}=a�+ i:�F��R7)9t + -�Q�`.��1ar�����&� ��iIe�[�J�7V >#� �kAG�= f%h(!��(AF- .1`�gVvra rt� ofEnour!(;k �lJ0 g �\.$-�`5&э�]V�h 6e } ! iJirue^ i�%�replac�eany mon �e ": LfZ�  �$arrow 0,1$a\$t .O ++ o Gess� \w�} same)1. -��rk2!���'} If $�\K�O*)$�_j�Ix=�L  ) �BX+%�� ���j��.�2�2  6� [9G+\")ҵs �!u2 split3�orpU} {{P}6�1]:�}_1%�k@m_y,z�XZ^�1FE�x>Im$E'y6'1Wz��W 1!Z^2h C j � �W 1��"'"r � IY�_i e��l�; �B�26�1�� � $. POq�Wm]. ��6*�w5����Iisq������ HT8m�%�7ycl"��"� ��Sg+�#[Qu�j] =-"� j Q$�B����Y!(�clear �pp�hk to� "+ $;�ohv$ �V ;;0B-���*RQ% ����an�;{p� ��wF1G0.$Fn F2b \}GFU ɮ\} =zTGVTFjT=0F!f $F Ֆ� �3^\prime)G $G2.^{ }'s=7 $s,@, >+�0" � $F_mF�  $G GQ' Ůw�';�'a[3en�QP �%�)�eC �A�Mta E,Tea � !";T� U�x- 6�.�J�notag &z��9�Id\{ P C (I - P) ]{Qs+,r;R�H F_1P8\\ &\qq�d�`r f\{&v{ P + L v:�o9 <\\nmR�> �(\{w!%P..5.-��� �aF_��fB�=`[NW� *O� �Bsy� �.���j���4b) en dՋal�j The &�F_1(x)_c�e �e�$x�� MiQ�� uM��e���9a _�\o2� m. a�� Z? & inT1:�&z�^ C{ K^2_P<� {2� y�j �  12 �"��B+����$C�.��!dPG_�BaaA�$tE �=�,!xI�r��,utoff $Y_n ��{[-n,n]}&d)$=�2$9�. �HBe �`E�A�Y J�q`U25 1*�]a!",h>�*��{Q�J U sigma5- \ _{H"V&>@N - 2\pi i\�g�  (V�&)q� m 2� a�J�%���Nd� �+ (DFP&)v-�d�,^%�Hkari2�`�5c"�`�-ndZni)0n�7 >!:  .�`2&$���$a!��2$> ,9M� Ws}�1�uo.�erg5�H2��lEiH\{�I 6�� \} =B*6V\� &}(J�!/��� A�wing��a�K;" "� v6w e����B&E�a,�>�}.�N "���u$carry curr���w&���/� ing�� mak�Gh�=ݥ�aHExN"7~:F�m�"�*6u ��{}{}B6�L�v:b}"3% Bu�akndY�nD�i5>!�!��m $-2 �E�AoX:�Sk&Q*�~%:���9, Ba yFZ�%Q, scvn%J�%f ek$\psi���d�2}z}&=�7 &�M,�m �f !$si�)-�BbjWN&)9�."��}E�> �b:E� uUo2nnݛ� ��s A$r�� i�f��([E_1,E_2]\s�ar�(� "�0)��2� _1)=R2���)= �� �I=����� pply8 p% (*)a�$I� a�J&��"wy M���phi� "E%.a (tCoX� ) �qs�>M$}�ex�(�!Na�� | _{M" �m�&M} .�(�11( �� �A e: ��P}�>6d �Y=2:�) �+�-�[s?U{^KPM} �� }=C_F$(l�F4(N9,2�'� ��� AXS�  $!8&�+]Q�9h6O _2 -:1�D9~�LN> , @ �,��N�-�N� e�BV�z�)Jy�*aǜ���t�n $M=\{1,2 �H,m1�M��Ur �|~�&r �� _{\N1V�$ U�)+�b(\N*v:M)><u4�fm � P_{ " + ) +�O \�MX �ES0NN�msa9 �.q�J�9\����w �I0 C__,F(F8 mr=m+*�g1+*�+ X�stoNP?m*R5O?)yvY.c�J�)�~%��� =6�=0�Q�*ԍ-�8=0��k"���+呍�c�D�2B�n� T �x R�.R/��4&�'u [� o� GS].M��� ruleB�NK�b�;?�w}st tak������qs,A%"� �0�_�e cruc2"�1b us?7 a_�!e�*O�+y�. F�I:  nWTCk cal���)�sS��>� "�2[�2���as u�Yb0&��B� �� ��b"�"�D��Z =n$� $Ek�Z>:�i�� �� $�i��=6nd �u mtICI�� * *� 0��]B_{nh{j[zJy�."� ),+a+q�1 + z�_1�s�$3{�j��u��anaed"�; _E >� mbda""-c �X �m- I=*j_E[0%��aP`( !vM_2]^{��# ofa �uW ��E��S!1t�5$\Gamma%��a�W b�+�[� �oP�nt} P�G =Y�}�sfVt_ � R,,(z) \,\di z F�alA92YB�wI$.6�  e $2|=Vqq-z)�I5Z�. 3$ek )yU- $d( �,i!V_)�=et�)&�2�A4(�7R�5�/B",o _E MA��i!�"�CEhI$�w)� ($K_1,K� �R�5U'&�b�-�CT} \|�x:� chi_y\| &�Kb�3 ��*, z�-B6� ,(�GHSest�J�x�j�2"&MU�Z^~wU)MmMCT��R�8 (e.g.,�[Co� 1m@2}�&N �Ac��2�a20PBGK�oۑ? �}�� *� �-?C�1�y96�m�{%�)�|}{a��P^{!�-�/nb]M�>�<CB%�2�trb�!���6uM]_1)�� �2 >�"� �Uڗ CTHSv�Uk393Q��noHS��n1�!ҥ�M 5O. ۃ��,\x�3IJ� >]HUA�$resolvent "}tE(a"� 2a taylor} Q"iNv}:=���-Yv�`' {(�.--� )} {�;V�xi (z)�F:@�($V="$�En] $\|V\|AL4 HhmtM_2\}$IIU-a��P i�>d>A=6#Q�:uo��le K_4YC4MC�B!diZr,:� �& now C1an���An��.�!�po� $V^��m�� ^,���RfE�E�7).:  $:�*�6� ŗa���-y� 2I� Ml>�2�eq }.�A�) -"E�. }) &A�r AAB [ >�\�+_1 ?x�  2��] �"�[ - x11>h|3E tV$]�< ightB/& \�"g.+ r[ FBo k:�fr�C01.XJ$2:l�)+\}=0 ,�2x$�[A,B]Lw�i[B�or�[:y��]r��c A�E�. ��o]�,S�,�h�, ��� h<�A_��usk�n'mra��x�O^;�8N2k��� e�R! � �2w9 ^{(L�>L)}&NA.k e 8.x}iO |i�LZ?� 00$�wise.�+ $W�^{~U �_i �L)}e$ 2�} R���6q�?V_L���T ��  $V_{>L}6!-V_L$,GM�e�ő&+ V1 �1��>LŇR_ �}S c}-<L}�~ etc. >X 2���22?>L�>m��&��  $�A \iZ} )5R2K�Oi{ �*�?>�-��A��=7!F(1'*e �!o� �� K_5 �%5 2ux\{L-|x|p+ _y�q� 5�S��&} .�/6� mLlST�\�.&��P}V�"HN��?q��de -?3�U.}��2R1fe��1[)��1&&A�QZ�,LrABr��6��J[ [.T"�,R};UZ("�;��] +O,L>k6��n n v�7�f �.�6+ r��,Lv�Z�>�3^*m� �VL6l� to�A�)����Trge�AD.�osM/ja*A)G$\|:� K_6*��  $:1� 0$ s�V�.s���"�4��k�x��& g>��B;P<�Jo�� <V&s �b&&`w8��6�,J��v!)1&Bza�an.���v)�C��%domin�&=}.�&~ f 6p0� F�!�q�W�]�n�0sh the proof ��of Theorem~\ref{corbeta}. Since \eqref{gapcond} holds, if $\mathcal{B}_n(B,\lambda)\subset \Xi_{B,\lambda}^{\text{DL}} $ for some $n\in \{1,2,\dotsc\}$ we have $$] B_{n-1} +\lambda M_1,B_{n+1} - \lambda M_2 [ =\mathcal{G}_{n-1}(B,\la� \cup ^�  !G��$,$$ and he!BT it follows from Lemma)olem!WHuc} that the Hall taB0 $\sigma_{H} 9h,E)$ has60same value on 4pectral gaps $�G}_{n-2$ �:#}j )$, which� tradicts R�Xgap}. Thus we must hav!��B:Rcapb,4D}}\not=\emptyAV$E:all $n\F9,�-{V� 2� 0$) satisfy�|hypotheses in \cite{GK1,GK5} at%pHenergies, including= �levels.!tTse were called assump!P s or=\ SGEE, SLI, EDI, IAD, NE)W �.�3�,K3Ad (Although)esultV�4re written for1=Schr\"o�er Aators wiW4t magnetic fie��they � #change >1 as long%\.f�)� ied.) PQ�!$ guaranteei�exist�O$ of a g!�8alized eigenfunE�$ expansion!=A-str�sense (\required trace estimate�%Dex�?a!�)eRis know)B0a large class�M�5E �/I( � $M.]� � ��!�^�)q1� )�0 can be found�E8[!Wosi�( 2.1]{BGKS}i�ere�b�!�{=4ments� aRI�8�[a�concerna3an�Qxropriate finite volume restri)ˍk-:V�. For%� (Fb2hs may bee<,squares $ \L�_L(x)$e $x �gZ^2�(LL_0\N$% \a suitable $L_0 \ge 1$. �;J&Q~I�no%�$of a {\em6�US!W ``=" N�,x,L}$PN}$��!� � $2� wh��!``)OHness based outside A 6B"a)not takea�Hto account. Usuall�s2��?defined�8 an qU���Erm{L}^2(.�8,{\rm d}x)$ by ��ifying%�baaryA�de `, most commonly Dirichlet��eriodic8 �8 . (IIP case!h!-)+Nzi,s also been 6���Jwhole sp��b!*rowe6waekcoefficie�``f�>��l{CH2,Wa,GK4}.) \emph{But�is%�necess!8���k FQ� �I s.} q�Nit su�ao fixaHO.F, � not �ilyAintegea=so�=$$\varrho>0 )n a179pNe= $!� �l��each z*A�y 0: First pick ��closed d��ly �dY�$ \Db�i�G � to� r4; \C^2)$ѷs!` exte�H��!�,differential=I $�0B= (-i\nabla-� $bf{A}) $ ��edAH,$C^\infty_c 2�)$. Seak, 9 m]pot |$ V_{x,L"� ���I|:� depen� a� ! W vari��s $\{/ _i; \, i���\} $,� setf�= .�^*. + � :��y. R���Q��./"[ $ �N f�T ve � pact5olvent  � ��� %>� !��! (i�but%o( between $x�@a��#$arbitrary $y$!�$�v}� begin{equ� }i covL} J� , a,= U_x: tau_{-x}()�),0,L}(<^* \quad \mbox{a�� $ Hmathbb{Z}^2$}, \end� �<� � nsl� $U_x$�Zab [$magtrans} !2con�br�� unit��mapi�b�02to��@. Furthermore,  eOf�A1Iti�,s: If $\vphm0D(.��� �supp +%"s {L-��}(0)$,�n $\I_L 2�D(I�Xj  bmp�} %�$cal{I}_{L}.� z�= _ :.�,I Bchi�� �B�[J'V_�t }, :P IQ���\colon �F�. \to:(R^2.* A��80canonical inj�: $\lt(N \rt) (x)=% (x) $ if q(\�2!ȊG 0 $ rwi� weaws-M��$��$�d � s). This١val��to &E��J� for �G.$$���f centi�t ��FusedNs�d� $2 ��� K % os ���;�EGat�,s � �5� �Ke� �b $L qq$=�` $:aA( just�7�9(%k� #e``2�9Q" �d- �*� , excep!baE9�O� re�Ov' ca�ct �urb�fs ��� B$.)� On�then "J*� bA!2se6��. OJ �VWo  �Q@ NE (average numb�f��s) presA�z icq es. � y IAD (in�� dis:)!� obviou8!�DSLI (Simon-Lieb in�[� �EDI (6Ydecay2*� ə.� # .���c[} A�l (seq�A!discus� ��5S�� 4]{GK3�I�a}le bump]�$uNe� potV$<$\eps_u�,-n6�a�NE A� provDap!��Qdim0 * e��{HLMWBK. t �? �emsm��� �ls� z�t��paper� view Corollarye$corlimit1}\M� U� (�A"� NE) :� wasikun���al flux� d � ��(, namely $BX 2\piɝbb{Q}$vCHK}; ��wis� :?�2�E**�of bf oa�at "� ab� I��H�-�8}. �>�is � linec� H\"ol!3continu&G �ra)� statehn f�� CombHislopE�Klopp��!5I�d f\1�9�A1� �*�� Z�i wit deriv� he j� n�. :�, �A�Raikov5r4KR} establish y jzrU%N�}$���'l]h} �5nora]i, �  did� obtain5va7{.���%W �no>O.;A�nexŮ� we^) J�e��A��ye��LI FV�,96� choicx ���rG. �w>+doed�I]�(!\7ke/" ��CEQto1�! cruc�!Z ,([Eq. (3.1)]7 }, e�9 �A� 7��հProof���1.2 P. Letaw>0$ be& ;��cH doEZE� nv �w B��ength fcorrespoto 0sM�e��(�4conveni_)i�er�� . We� $K\m�Bigl\{k��\N; k�\T\sqrt{\tfrac B {4\pi}}-r\}$, e�TZ� LB} LeK_B2M J B } , \�$ \N_B = L-Na� (  + Z^2.>�Noe $L_B�=�a��er. We!._ "� .b0bith| �N_Bid�Wm�pA^torii  bb{T}_L:=� /(L�)$ *uZ wayaxs.n5M�*3 �+]Z� oq LU}_{{B}}:=\{U_a; \ a�{}_B}� form &�re� E�� ��group� _B$;a���widehatvaY9 6�a��v$,)M�`7 ��U}Z�. If .�E� $r $"$%�gof "B] $� R� )}rm{d}�eBn!�I "��ect��$9S�2��u� trum�� stilli�stsAb� � �sm"(8)=  })=\{ B_n#n=0,1,\l�#��s:$yj �reP72~ ) now A9plicita١p�$%tildeYY�=�� R"U�xYE I Ua�Rvbosplit} ��! 2} %�!^�& =o!r +"v$0&���%�rm{on [�=,\\ V_.U4(x)&= \sum_{i�a N)idelta_uj} �(_i \,u(x-i)� �:���umb�#1n{.[8 tw�M1: {�or�"os �I� �. (W�escribedJB&�V� (free)Qp*�  a � ^�x ������ �n��&��{.� exactly� �Y�e6s sum7a�over $�Hp*.2#2�yF�^ies�$tt9�s �2 } %�a2^! *�%�"� �V &` s both&> W�NE_�# ��� "� AI�e)%.  �� $P_B�%!}&bJ})"&���J}}��J3)wY� J}X\REa Borel�� . Re�%$\rho#AG�ityD ! bab�&] ribu��($i�_i$'s. � tZ*�thm. } Fix $B� !�&�&0$.�� a�_ rval $I ��9 q\in]0,1[0re*%�Ats $Q.yI,q}<� \eta2"} T]��a"� 9 $L2/,q(suc� a�)��sub� s $J � I$a $|J|\lb+>�$, ��ݨith $L  N�% x6�8� hz)���!�1��-�< \E \left\{ \tr b�(J) \right\}1 B[ \norm{A\}_)g |J|^q LJ[ �[Q&�!�vp0 } In"�u�vL}�.:!�E� Je�$x=AL a�start�F+a� a l�+i w a�+ u��O��A�C�&"O R,T . �%�gv b� Gamma_Lu� \�dlin*�{L�+,0)\backslash�[L-3�^,� a"�aPhi_L� c  (. )$Y� $ '��\" 1$�"(# �5 2p$,\�� ;F�L- 232A� $0\le 4o le1$ abs{*! RER 5$%��Fj R^2$. (Sac�alwaysi�s.)�l �$, $(2h��$r _r =  ,{0,r}$ ($0��giZ by&� eWA!� � %�)?" � �z ���r �"��R� {\"�%an=2*6�.E�*�� �L}=�� %�widN N}_B=0  /\{i�� "� �" E��!RPso on. By $C_{a,b,  }$ x %MaK��:�"A�!k$ paramete�!I H$ (R.ay�!l�%Jn� "�!stants�,nd similarlyEjq �Hm6�ŏ ���8A� em:}��. k �.N)� ��in h� !m!Alet��Pi_{n!� B, $3%9�, orthogonal ��je"�;'66to $n$-t:s $B_nitBR Q6a�`,ll&�%L� _{L_B�3$r"�& 2*��}_B� �/�+ge 2(�+ rl0 �.�align} %!{i�x,r}}a�es\I_L^* 2+  "q�+ &!E�r%{r � $PiLdouble}ɱ ��!5error" q�� .O$ � �)MN�� �8a�>9An�CA(B} \,\e^{-m  L} .� PiL2 �[endM�Bd ~��$r��$���E�.4!�$�C%�&e�y�2`,� !�j�"ntour=� = �3<1 {:i}��t_{\g�W$n} R_L (z)!!di z \ �=  $R_L = R $L}-z)^{-1}H A�$ :b�$ ${b'a��,circl2G ie� radi�B$.� $z� L,�"�m*�#��2mo� &YiNty"� $�6.13)85} ",b� SRE}Q�s 2{ I_L !x(z)& =2e�ii "= .! R(z) %F !�.Y%�, \\ & := i ; \lt � Db_B^*��Q) u+ X e�)&�% rt \E6A� �e4yCProceeB)i)RP� G�5 6.4)Z, #AS:��gi�I�}= < 1 B�  zi�B_n +Q a�C -Thomas�x(e.g., �"h�2�we �1͉�[5ag�}J}&\le � 2 !�-{ ��!��5rm� + �F@& 8iY{B!�M: }\\ ��g FRc �5-E-22.?)YLz�/) Putb toge(y���JD!a�"�L!hget1eUA o PiL}6@�� 6A�A�n�^\prime�͵>��uA9>��lBF2�=!4���i�7e� 3Vs. ��m]�  U�"i5�!*H �� ada %e� irei~>R}�2�&|ŵ1xlez"� � ?8\N& y"� $R> �  �)�B\kappa>1� �� !#*� L >��,7 R� � �9$�&? = %�$^H�lem.$ŷ? �x,�>EFaN�� C_0  (J8R}} - �J�}})Y+R\Ec�~,&� F�h3� $0=C_{0;n,B�,R,z } �a"� h I�:w y= 6W } $ � &B`� >!?*} .�~� 3�Z�i�I�"$i 4 � !�, )�!a�E�,�.hZ.�M� >1y2Y��nk- Eo1��+>`}>^} (A�_*]R=mUH�\q}. CQ5)}>0�J9U":��Eq 61^ R}A@J$�(L'� stead��s���CHK �5d�@a �&�9�;E�$�9N 1oR%be�$.�'�FZ zQ>�!}e/F�AJ�z��2�M�]A�.j &�1� ɫ 2>0�n� _{2:��t \\ &g��0 � _6i�\ � >� 2;V�=�- Ʃ.Q���2Bm kR�I��1~� Y���>wA1�e��%� PiL3A�rM2Z >C�"w2R�� pick $a_ IZ^2�.�x- >h (*@$6�)�4&/q >�ll}}= �! a_x}J�-a_!T10^*$�%$\ell� %- Bu*=�Bv^*�!�$!� 6�!�>�Ts�B��= F��L}J�$���4 �<� s�n%>�C&�zB� �VD !�{V32 (x):6a#-�)-.} U\ge u^-=��=+�oi�� _u} � y"W�,,x $R > 1 + 2 M�&5,JC�~!A(a�}_{i,R} ��":L�%��h i?�>06�eta� � B��F�I22��4I�I��Q�%�!�Ta"� �1� � �%�%��V� ��Qid t�d��Mf &Q4CV>��v� !�b� i9Vz� E��ge-� {A� C_0}%�&N* L�A C_1���CHK3.1E )J�c L^*$%�s<$L^*=� &� s _ }<�ft �1?�.� 4$, �#� s term o "R 1�y����O E�2�e��xH�6�F���I��֩ M�by 2"�"}*, �&$ !a%E�n="�H$��` &�* hE6*+� ��xFiQFN disoF�0�ap)9� �Z�/ 2}] �!/� $$ 1 < c_{b��$�,2I/"{� c _1>hi�=wex+�8�lon.�I $B>bK:�spb")%�$ �8n(&!E&I }):= ,1� �� 2�gA��0is�<d�2tz(� ,O)�� �� �1\.�u_-(Z�u� =\})!%i�.({ .} {!}L\!)^{�-1�iw�ֵM�3M�LB��Ul-� l�_09% �60,.i ��)��&��5`=1$�/1�nu_�F!�!j "prv "]/vazT> Z^2\Pa�"6�`#� te a#*�%s �n-. Up } (a&�4,ly modified) ��"$�Z V�&\P%�\{*)V�)�!8 \bigcup_{n=1}�? [�-EI,�A3] "Q!��r | �_i%"ps \ � if $r�'_06� $M�\b \g& rE� 1 - �xUv� \Q�(r x )^2e7 1 -C_2�]f�/ L_0^3a� noT�O���B$��&We��appR�Ecril,o�loccI��inH1f~2�3},�Ja. �Di�2>�~3.�;�)*��f� q� �$]$)� 1$IQ�}=� 1 2 Y��$��.!1�\ "%O B�#��%��?��$I,1� "*�| _^/%�Ne�Q^�. (��t�!Sf6A work)1.�1s �Qi&�% in 6�H�6ffects�-n:�~"�*��(s. (2.16) -8C3;F�N:&��_{I{ �Pbs�2.0ly*�& cl�D*,&I�A�%q!~ B$. 1��Lork��in�?�O�eN!4Z,o� �KK3 BCeP�:D5^< 43.5]{KK1}--its�of,I�! G E�M,Gso%�}6V�J)"`+�K),  ~+&G.H6�� v�1~3]{G!� NI. x $neB��I $I=n({B}��i�,�J =L_0(n,B)�/�H!J�oes�%a% � � � E)�L�!E ��I}_n(B),fEgE-B���a�ps4$�=�9�q�))��&be�6sen lat�3Then,�?��I��V6(�Llu�J$:&�B:�7 �B'�RPied ++ y $E�Ff�bgaX} �[�C_3\, �v�{��2 {iO -1}}�. C_4�Qm]%Ջ-1�B @{25} 3��W C_5>5eps)} < 1�nd� Z *K!stD$* j=C_j!�A<$j=3,4,53 �4ccQ.�A�b�6ne� choos�K� & �s6� �9' �� \log.}/2% �c��Mff:Kly�O�%�6=C_6 �I/a�k�B��!~v_H w0 <=-�J, C_6)$.�U_R �4�a�L��>%�e�> 8 e�* mfZ �5 %(._!� �12�aIt\"t- \Xb�V�9�>� :W?�]"�QaV�&:of dynam�Dmo�-edg�8�[�$j,:�UA�1,2�(i���"loc=E�G abc}J I 20} W %�1�ZX thmdeloc}k>�5��/�/���n��^{%�u}^\alph�rho(u�7�/�?�E� $ 'pm{tre_>inA��'� -�\�Hthebibliography}{Hu�@�tibitem[A]{A} Aizenman, M.: {L.- at weak5�:� elAR�H?s}�/�v. Math. Phys. {\bf 6}, 1163-1182 (1994) H�ENSS]{}2�`, Elgart, A., Naboko, S.,�z$enker, J.H,tolz, G.: Mo�R A�V92� in RvV6�Ope"�<P�8int2�G]{AG} {./, Graf|M.:} {6m)�an el�Xon ga!1J1)A:)8 Gen-7831}, 6783-6806,%98!998M]{AM:�, Mol�ov!+: F��T Q� 5extreme��ie J �!L!�+@? .!Commun-� =�0157}, 245-278�36�SFH]{F�Sc9�, Fried�Q, R., Ha $rtmark, D.zO.C f\9ional-mI a%| A�B son . . 2�M�k'bf{224�,19-253 (2001aQU�n]{An� ^, P!rAbse=�� iffu�DAwcerT@]lattic F zRaAe5109a7492-1505!J5:�oa�e�oki, a(Ando, T.: E � �!� 3 HY6uctivf  two-.�Dsystems{W6� .Solid S�BU1?382 1079-10i�81).}ve�Sa� vrona�, Seila�!��F(, B.: Charg�;��cy,�ttM port{>K5ri!��T�E�4!�M�)q~)l5!l399-42��5� BCH] $ Barbaroux�M.,QbvJ�CA D.: 2snear bei��E�IA�N�Y��mph{Helv � Act�bf 70A6-43 A972fBe]{BeL? ellissard�: Ordina�quantumI eE.� non"utativ/ homolog�:2�in�edM)s (Bad�rCd, 1986), 61-74, Teubner-T�R)� , 16 , Leipzig:8],(BeES]{BES} 6� , van Els�%(Schulz-Bald!�H.:�nonA�geometr"]J . {J2/}I0435}, 5373-5451%4�Y\�BMR]{BMRF� Magn� hJ., Rivasseau, V.: Supersym�ic"�]A�a�/pl :� a�e��model at:\ �r�E�)ss�_ d F\u�9}, 261��2006� BoGKuZAXoucletAUa GerminF.Fein, A�b-exponenTde{JFC�n kernels�fu�[�.\6�= Kc. Am/}S�132QB( 2703-2712 ��4.��A`R[ ��*�Ja�ie��>o�\�5�1�72� �:N(media. Subm�]d �� Bou�[o1}�rga!kJ�w New?^oW@TB?�p 6� 9O�Ric��6 Contempo�S%bematicY830�� 27-38%\26\u2]{Bo2B�� �2.�� E9p")<�  higher ��al phena\USprin�DLNMY8� 70-9 �E�}�ouA�K6�, Ken��C.: O6L!��'Jousu�$-Bernoullim�inB�!kNv CKM]{CK� Carmona Kqd, Martin��, FA � ��%��u���o�gular&�=��- un. iS.� 0��41-66��86{ChD]{CD}�l� T�+dv.t��P.� PercoP ��tun�n`ndaDQ!��ɫ!�"= C: .� ��2H 2665-2679�I ��Che]{Ch�en= 6��i Boltzmann�!Sz1r-�a>�m�m�on 3.5�e1E~�oH�'1}!�bc 6e 6� � some�tinA�,g*zA~d&� }.!KF�y.6 � 1�  149-180!8� .�2]{CH2~�{83�# r� u�s:� I�Q of)< M���.2� 7��603-62%�962 CoHK�Kz�, �MiT� M5�-� .n6�d�-MRNU� 179-209U&.�KR�R�� , Ra�M , G.  GlobaJEA1 of���^�N� �N��%�. P�� al D.r\E�Y)To�pear��� CoHN�N��Nakamura�{��H:p+8eo&� �Ph shift"tLI.$&�2M���Naz1��L% ".��z 21�K113-130%�! 2�T!T} Ef , Tipq  {B�g 2L�� BL%�acoustw d�"�wavOgi� �}.z @n. Inst. H. Poinc���5.U�70� 381-429.'D D  Damani�,E. "�6���� *,�um,��-6�A� Duke�F��711a~ 5�)�22FDS]{DS}:� �l�! : {M�U-oA]i i� es T&�.�gGeom.N���11-���.:DiP�0PS} Disertori�, Pins�m+Sp�r��D��t g.s%U)��ma�e�2z-�{�,232}, 83-124E�%3Y�LDr]{vD} von Dreifus�:CmQ A��� ��d�Ef�%U�� �69 .| Ph.D.Wsis,  YrUnivers�(1>� DrK]{VDK}>���  {A new;��.� in�FUptight bi�O�!�bK�}285-29��8a-9KEGS]{EGA�Elg"# &�*� $: �wX�!i bulk�߅-^ anci�a&�gap. � %�B .y���;!�)2B.: Adia�YcZ�� KuboA} mula�` -typRnmla�!>(. Pure Appl ��a�0-615J� dErSY]{ESY} {Erd{\"{o}}s, L!; almhofer,�Y�H.-T.}:mpre� R2rQRP2B{){B}"O M !scoupl W'!�a3 {S}c.8@ }. {V}��,53}, 667-735%� 0) ]\FK1]{FK1�F goti�:�2 p �k �o���li�"� 2�J.F�O �O7h997-102g2�2�} F��of�kb�� I: A��v�8u439-482�8Y \�FK3�3� I: E$�鎙��411-44))� �rM�\FM�]Fmhlich,� :?,�l(oppola, E.,2* {C`r8*�/:�%�v�Rz%�10�� 21-4`52�FrS]{F��B�S.�{R�J& J��s "� or lowy}.�wR8� 51-184A 86� G]{G�., : {D"�2FII� an *�):aXalM\�ieuuL� �.�9aI(273-286 (19y Y GD]{GDB}2�0, De Bi\`evreZ b�pa�6ret�R[m�S2�o�.o Fh9A�323-3M�2�G��G��.P:�$Bootstrap � � "and6�in�� w !�%j���I,222}, 415-44F� =Z��GK29&!6�O- "y � "� �R ��?J0131, 911-920�:���s$nRExp�R�*�*2m2�ix^ ous 2`!�� &n%)B� "� $3} 1201-12i���GK�@42�6mu�(metal-insul�Z "J i���V �33B43-57�Q�.�5D%5n�A V��Z®Z� � 309-3�20� ==6�6j�> &�V �I���reg�tV�� v.j] GoMP]{GMPA#0ol'dsheid, Yao*�, PastuM  po�.�stocha�<*;^�. 2$r ɲ��1-1&7�|�[-&�H]{Ha} h perT   Q��th*�� 8, current-carr�� sos^� "W#�PZnQ &aa>3��qTo�m��Rev Buu2�=1� 19�8� U9HiK]{M2�ewop= JR� �As�3M"�#�nonsign|UQ/� s. JR#�� 12-4i��� #]{�c Hup�  T.�schke�, M\"ul�$P., Warzel� Uabsolut'��Pi�J��� Z �2 unI".� fF 2�2� 4��Ŝ5�@JL]{JL} Jaksic, V�aFY.:K #s� b of&� J� I\^t�)i(41} 561--57)�0� =�KM1]{� Kirs� WA;:�  : {OU ergo�s�e�gofx.��(BN��4J. Reine Angew.� 33s141-15} 2zh55KM2���z� �S�Z� 6���s �  a P}�� R88a�32��y��� K� :���,4%6� a�m�!e&�iofQu2�*�!c��� �j��UsI &241-268!m�lA�"� : E�ra mL�"Y�\ on�B�Fs�� Ad"�&I�33K!3-� 6h Kl!�%��A�Sprea�!wa ackel/�"� �6�f��755--773L 6lKl3]{k.�.� "land6� of1ܵd. In�u-�!�BQ|:2 hodhBh}4� A�iv�\ Panorama \& Synth\`{e}sI oci\'{e}t Y  Uqu�# Fr�. 2y�l� �/��poin�!�{A�framee0A� 2� ! c�{&: I��"�D�  %Idem1 �P!�A�M*�(Z .� �R972�.�A]A^5ɚ�6��JF�I.q�� 2e .��;���LS]{KL~ �.t,LacroixQSpeis: : )�YSFa�jip��W.:��VJ6�y/ bf '135-15('9�e�i]{vKli�hKlitzing, K, Dorda, G, PeppN.:� meA��` 0- accuracy de6<in��ABa��a�,"�.�y�!�� hIw�mU�' Lett�4��49H0_$2o�laf �F�B�^n&�2��"6A553-56�9�=aoA�l26�W.5,6���,Lifshitz tai��.(. Ad .H.P���711-73T� �(u]{Ku} Kunz� :} %�:�&A�emn) ����V�q�11�121-14E| !5L]�tLaughl� R.� V� &�)wo&� s�E*� !5632-563�!\)|4NT]{NT} Niu, Q!houless=+.$�:�reali u /(v "' .�'$2188- 2197�(%�PF]{PF}� � ,C]"e 7 aa^͐�A�-P�}_�A�( Heidelberg� �#-VerlaM(92.�S]{Sp} h̀ , Te 2�AM~quasi� � Q"}�!vq�e851Y00C1e96z"St]{St} � � : CA0�[�-.�%nh+A� -M(&0Birka\"user, U�SZ]{SZ:� , Zirnbau3M.R� ontan���(y bre43�a1m erbolic s[e�� re3mJoI&C/ .zT]{T} >�)x�1on!m�T:�(�9� I�Cy��j3475-34�"e5TKNN]{}�y �)$Kohmoto, Kj0�ingale:� den Nijs: {e>��a u�i�1>�Q:&�&}Q-R�-����4M05-40 p�$W1]{Wa} Wa��W.-�1Micro.�,s&a%�t�x.)E����� \BP��a �uN��"46a-26�6�W2�2>�I`�u�"� Pois�- ��=*�qdQ�al>� >�2�!6�6�365-3%(C.�We]{W}4")$B�3-p�daZ�i�u�&9- . ZQ��4A�9-1�\1 �7>�3� docu�1 �8%�p %% Trim Size: 9.75in x 6.5in�p(Area: 8in (5�@ Runningheads) x /@ws-ijtaf.tex : C* NoveCw�, V file�<Ť<cls�dt��$ Latex2E. :h� ent,&� KCm{% ayo�~uvis styl�AlerO!�Hmy��World S��ific Pu�r�,Co. Pte. Ltd � CopyZ@ 1995��2=9~Fv All <s�SAxrved. ��=�!� \Q7C {1\)6>j �3Tboth{Authors' Names} { $O �>Typ!4Manuscripts (P�v('s Title)} V�1Ve+AR8 please ignore : % \catcg e{} �� e�t�{Pric�of op�onLkTGAU re dvcHa��&k)al�<upK�price-Y-�}�Lt�C divisible�qctuj s.�;a%t{Przemys݀8\l}aw RepetowicX address{D� t���1 ics,a�n�� College DA�(n 2, Irelan#Semail{r Vp@tcd.ie�W�PMark M. Meerschaert} vz 211�1f�� � BuilJ *�# of NevadaG0 Reno NV 8955HC�4mcubed@unr.eduA�1$�  Richmo��9 T5\makeE! %��Ial �C�elink ��cpF�Co �es: % �[:1, 2]{})� N* :histor1� rece�w{(29/09/�d} \revised{(Day Month Year�OARabNct} We l�%E�!�� ock via a�#g�vHw�)�FflY��"edNdP ��e&time.g�:���e} �$ x=eB{e  I:jn� &�~` step+| ?d�~bea�mp��"�pR]sp�řo�st�� jump M+nPes9>M9e �l�4Fourie�dCb�2Jy! _<q]+�i��h&�%$\69�g E}�d���!c4!�ex�s��eF�k�M�&Jk��!-!3at�8rFvalue\lsev!�*�d!us �a 6a 8maximal @A5� (iod throughF�ZA�@enA!�i�{a G8folio,6p�Dt.o����� ��w���%B��"��VJ�aB�U������;s bN asymptot�,ly power-law� ed (��L��yP)j.�)�Jat)�, h1�} e�)n��&%pAe� twee�er�$tal facts � i��0!� drawLmAK H� e9� laws (!��)�B.fs�#�<tِ ��ra�Pvalid7 pre8�)��-Y�1!rb6��)�e l�LaY-R$andel,FamaZ�su�)�c���~d &,�t��wai��9Z <(nB2n Z+). FQ�gCexpla�amT;7��"on��)/� >"ea�.$. Ha�!-�m�1I���&&;vD�Fe��n\��pr3k%� many2g � whos:�-=łnt � o-fm��)i"�0���:7(-�� , mix!�s�a]I�e�&�U�, �P�#�&b!ja walk^M�"�s.5Zbriefg��^�H��op� -��8��Źa)�"~ Q ( edA����$s) below. I�RepW $,MasoliverkU�.)|�_ ��yl=�da�F6N]A�-�-�Tn ``ad hoc'' ansatz ab�AM! 9�U�. �]�C� I} � sA`o�ime"B ��)-hAOb�� V27�FDanomalK&�CE C1V2�"PRE} �gs��<Wmas�_�)�R�M�^��VD�eir�n�n �M�'QD� Aalculu�A�s(KutnerWeier ssFl<s}* nW  e2�&�-%tR� (V f WӉdi a��5V�m2mea)��dAqplaceq !�A�erJ� wo.�Q $�HIK$\]�$f�M���.0���D�xa� V ��q �%}��. A� tJ �of J!�F/ �, afA� Y� , mo�6��&0`t v�Iit�to�3KPsoaf#*e&��-��6��t0�Axn�e�!�&� 6s-7� (pdf!3rho_{\D � T}(t)b}�P���OEi&F� 2G �-9*� 3�ma� a`"!�%�}�-�-u/�&4 � p!b &� e� qQ ��E�w��c�ct@,de��!�F A6�E��-"�In��Osec:The����3�Wrecapit� oF�� Re>IAB 2�  sui4A͚�m@vectorR@ �s�Sca i���Rot�o> �h�a�u�����B�e��3"�I�C� � "�E&� r���re5�5�Rf070QY% eq:J� Pdfs% �AF�A a b� an �}�ASA�6I �s�&������uad��xat���t3s �B�(/�A��� !x rval2 (%AOe\I�)a7 =��6�ock� c)  �i�zK!ksHQ�ar��:�f)�Z � R�at7��" ! span"��a&%p!�%5 Y��!��W=T.��w""��=j�t�v �"��0z�c���3%< ��'VB� } �m$:W(S_��bI�"� ��K ^(log-)!�$t$��Kc +�dr6C Eq2|%Vv�G_ t��saor5  &>K��e�m6 .; at; %��e?d .� pdf $J,. �X mean��:�b} -e{t+�})alo)|�^alpha (!)^�j+ �\{V array}{cc�Xs�i`ad \T%��Ո8 L^{(i)}_t &ɭ̞� .  $\int_0^�� t} >�<\xi) d\xi$} \\ 0rOCa�S�Ja. M�eq:�GF� /9]�S �(��i�� f.if�[later�.�Q�Ÿ͞ec{)X } :=�ft(  _1,\�, d*)$ (v�J,A)1i0C[J4�{$t ~E��Qm�$S_Zd�J �M_t��*| )�iN1 (�^ e.g.*U��ec4�q�N�BKB�J&88*� )! it h �%�/ (e��2�\ erc��k -Khintchi���isz�xm\:S}(k})A >\exp(\�zh \cdot =�)I- ] = ..�Y/<�${1}{2} Qt,t)�a� �x}\ne 0}M� .Z2� Xx}} -�d�k{r+{1 + ||� x}||�d��phi � x}|t�$!'xb�ab�PL^, $.�$i�quadr)P@ mi��� ��]��t~JlY,�v� �� $c>0i��Tz�6�$�����c&�measure-< noM���c  R.37RieH� gra�&T_�.�� & }F��_"raD}�Q[a,Q,�)�]$ـ in o"� J�)��^a���aal�4y9�=Emen�r negU/S5� partB&n$.�ec�sI6$�]�Easy*Uin-2x}�`�kN�A�}�R`0,0.`����DefB&�F�y�!j.��K &~"� 2� J T$W�adsJ�PE(�{:��J�lQ|�h T� tII��l��� ��8�� \[{) = �X-c)+rn=0"Rj�! c^n}{n!} !�^{n \o�Ns}Q Ja�� %A�%�C�#PdF�eX$a����$�sVe lastoAouV:u) �܁�n ��BVN$B�͉�2�yA��-�!�9~��E��� Z�, 1�TFp, �]� Q�%�LA]=1�$ "�by &�=.�f�V�����Z�� h iA9<t) &�  Bv"ue�(f��summar� ��&� s�Th�tab:S-y��."�'�}c �)>fBΫ�� marg�A2�bnu) (z���z��B�F1��< ��Ays�F � ��� varp� -� l_t}��N�G�u���2(��I�6? j��+��3�{ !�*B ! :9 � 6 6�s+> ": ,.� �&"jF$unter�s.0�~2A�5<%b.�|}�Y B��bM s, a.6�4���mr@s}�,!,�/A��)�:,�j�{N_^�q )��*$_t^{(j)}}$o �"�jb $N�.i �+ � *!v� #(c)UC ��h=�.w� 2w)�ke�0ed�2�au6 )�.RZ�`(� g��f)&�st�5E�{;.�%,+--47e%:c &$%�x}$"m |�+H# igh-�-�.�)� .vqu'��.-#.�Q� j!$MT� B.�B�]3J$%�6o� �e�" �> � �"�w*.}���an ��,� mpan3{wal V)"z}aFw��aci��p !" (e�4 (?w�w(**�,-mat/0308017D�@ta%K��eN�e ��z2"%�%�!a>?>5&&]ix>�#mT':�isH�]em 2.2�  733> �&�7&,*���ds:�Neù��A�!��2i!�t"$-T/e� kx *�"< ��/#qMLaa�kaX�2f��ff8�C-: `cal� $[  ](s)=�(-��/K} ��T|�) s�O ��&0K}��at C(a�a normXC�"DM�>� (.T(ab/a&9?r�t$)�^($a >> 0 $. i:$e��$�! t:2�1c6� A#��:]aI�q'} � a� x}, Z�� det$(t^{-%V *�6 E}}})$.�N' F)�jG �0�=�(a)�}{t^{ + 1!"ZR#inge�T(9�Z �:4(bb{R}^d \ni�K�tarrow ��)o9_+$%3A�ND.� (� �3i߅'�n�^)+�3utrir�&a��"�0Q:�8 ,3 3e�) cor�� ���Qx�|%w-$QA�?$��� $�z_�pdfq�K�#9�k�]� 19a�sfy�R�Re$[\6v] \*�/2$+~�6dF3= 1re�m e (!de� te).� �d�kqec�} u63�T���al5 iN;.�|i� m*Xy�}F�t\e s!A����-��>:: d G}%��OUBiv�*�m�LimitCo�y6���S �<ra�/forward{3ner\av3gaot�Q�ܯ"4 s%CTh}1�=��=!�E�de�])��'" *�9:O��\e��!�e2J<2�ڧ-�>for�V%�op.�%�0}}_{t � \  )�^"�I]�� ��b���>E^��F��ISExp>i[92�.��a�$t$thB" I3.'d"%�a�$t_Z FV U)$o!�0 � ��jlim}_{n2Ai� } t_�t�$Si :��lss��iN-"b;0+(��ct.:U�u�6cself-�z8�s zv � 2�!8r�>��a seque�ofA�8�js�R�B}}(n60>�I-.`�L` s $b)����a]�*�s $k_n$*�5����+,����y&J ed'I�� A�Y}�%:0"c�}�nQ%R  1 3~�Y}_�!\�$i�Y}_{k��}�&b �Bte��Af �ftyV� ec{Y��e̥�� a�V��!"7 CTRWDefIuh�W}ph!�if҂I]Yu5�aV/�=��]�.aQ22 -!3�7_1 �Z92mREFFNow.8$n$� enAwe�:w� Aˍ- k_{mA$E�a"cZs�*-y$"$a�e*/?m�Q� $Y_1$w %����  $>� arg�Ja�2-ism�lyv_� edN�At\Y� 4 R. I�"�Ǖ�F��TF�&$\*�{ɪ6%&��F}"�}[ *]� k})"^����2�^tlm2(!#b"^{T�!Yk}  u�� !Tru�u�} WA f) e�2�C2!� f5$.��J�<95A)�|! (�$ЊnN�) �� �aJT\E{6��"H�>�f.+��$:*0 .��1QRW ([� .!��Yq = �Yj(�e_" #�g2�^�8}D= : Y�i�!�/} �*B��*de�@�;� }�� illu!ste�S&�1}9I� $examples: &� �SE  1.}�Q $d[���� YY_&�N�$(0,t)$� �����/Fv1�q/ .=- =���jf = ECU�, (x�(2 \pi�/Ž�*-x^2/2��Z�2B���a��/Z�+8 $Y�b�/E2F+ k Y)~E -t|k|^\mu�� $0A� \mu2� � �+!0�R,!��$�����C�a{<*I uh:)!�1}{�� �n�Z  \sin( &#�+�| C��(2)�& 1}{x�u 2NA�ExpBY�5�.�8�� goA�Iׄme`Kevin q7��S�3�3�&}!^!��� �)�N3:� �b>�N For�7pur��we ne/�Dime�1eA� bR�p42�a 0�.,.h2.0G qR<� a+�z�G &Q&0� �P$ �X(*� N�/!.�B�� U�o9��.@O3 F+d� �2!��Y�����Z �WTr$ZQ  A�eO�{TimeD�$CondJumpPdFn�is!�:y lCB���:}5A"��9`_�G [w/R_  A}: ]�*�/� Tr=f:�$}}�A2�Iy� ysZ! ~� � bbF��b�2C� 2V� m9.p6�./���� "4 nu}�!k.�! a\= z�."�!-Z(k�!�]�� 2Oe��E�}�})B�e�x}�5�;$ �All��� &e&� ^6�i*G-�u"�d%-Vl} N�}(-t��i�R�E}� ��ŕ �'$}{|.|}�� r))&/ K1��k},I�/*]!�TrNMa�#�����hQ�95 TA"�t :=ZY7rr} 2 Rem� a�K3)pi}{2 n%S0��!7a�-.� \xi^��w�>I (n-�� O7l7 7]�*&9ifa\��od*"� K?>l5aߘ2t>sƼAcos%(  (��%�)B�i )^�=]� ��".�7�IaB � �ELk�&k} gma^n$. pv>R��k$�f�df�R'1qNb�"ipIf( �w�iK�G} k^{1/*d39N.).OS KValeRN eM"� }6v�%�Y�Cj1i ANn�a��eq:DefG5�U :�C��%/GAp* ix A�{��!� ݙain.")*� ��m�HE FR� � c*M%��(f�(;9b��ise�  =�� is 2�.�f��AH[M�.98�%ASL�i��); | \; $.�- '. .] ^Pl��o~ժ�� }\; ��2E^ bb{N� %E"n"2$��0HjM.Ldiagdown2b�bwI-�Meaa��9[AHf]�"n%- ( "�eft. \�'��~7/+k-Z |_{kwT�)A$�&� B�))H7A�se��^�"*O$1�6D .�65 M�3!�h� R:N �Ivx}`��R{7}<g�#nE�@�2F�@����}�4� &���Z�+!� �/ �i� � ��R} �.� + O X.{2 .��� inal' � Bz���>R�|"�12I" nei�S�>n��[�INL2�&� �eqn{ �U1}{dz} �8z�v Zz + df��6N�m6� " 6�-A!f% F}��_5�[F� S] (z) =.�B_I��&&*� ja��" �v�:�^{>�!A6+n�'� ](z)�.FM1Nn� hB>� (�i)d - �d%Ცupb{2*&nq ���e"(z - z_0O. e�v����M (z)��j�V�[� ��s�w$zڧaw"$.&�F�V})� equi&����B0�r:�>!Q�v(�:��OoB&s ion �VZ�� $��)�°*� V��q�X� ��2�ơ�"6t��2 �heū� ��x r�:�'ginv�-g+�in2sY*� } ow�e&�6Ue"�E8L�U~T  @"9#�*75!�It!�m�]�X��=^.�2(Vk�E�� P �/�k}�is�{a ^%�P Y��Z�h i�_�) ined�"Eway�0!�'-e"xj3T "' B#B*�\q��nA^TSJordaY{e2|���, every Qubh �"?� *Ra block � �$ T� g "i%�!ADJ� \ɶA ���. {rV+(��� $a}\;\; & 0:8#2��F1 *jY�Q�jY.Q\v�#�Z�"&k d1&  Z>�:Fb� 1�k )�ͦ).�"or} ��%�B��)�I%B&=�BY.v)z8jY.Q=_ZQ"��9� �N�r�!ܑ�'���"Hp'&-� n>�� case�� F� yBh��I�=�a} & *�b} \\ b V� � Lw 2�/kI�I� Z�1�pi{M1 NSf5\&��y �� \pm"oJb�g"��le��ju��pai{79��^r?*E��@ll pos�l�"ji�(�� a�0d\��[few�z t�;� ly, "�_t*s*<0a.Hic�B R�ͽ�En\�P�N�wJZ. �Zcl��%�ɹ.�j�g s+ ,B} nume�8 } \iU�TakaS^�fkv�, _ Find�ZN�T"�%�$ -Y2�y��.��� 6� Q�+"� j �,w6� T:G��z 4ier transform �$\tilde{\nu}^{(n)}(k | \delta t)$ lof the conditional $n$-margi �pdf (see Table \ref{tab:SummaryDef}) I( as a funcH $l$ andhH$\vec{k}$ for small>& )L. \end{enumerate} In�,following seo s we seek\� solu�sxarpi$� equa (�eq:ISExp ��8different types8blocks i  0 4(constant. HL\mbox{Trf� = \mu�$}$)J.= �)�a�get: F� {�� �}�^{2H)�} } = b5p7) :��F�>O-]!p> 1)^{�dA�a/, \exp\left( I"cal{C}B, Ih) m�eq:Pure!m Res}>�mwEt R :=\log(F�)$. �n�� fromY)�NM��,Prop}) reads}�narray} )�2`|��!P< \int_{-\infty}^  d�frak{l!-L\{i� �(J^\beta |.7|^-�m�\}=K�� \sigma^n,)� tY*�)zaAkerne��mat�K}��defined�� �4K-DefII})�h�(series expa�36)� �$ give:ME4IV}). F2�S�0 KVal%�Pda�weao�B���$n$ ela�sE valuɥ$k$�� have�� &=& u:� m$\frac{%R%C}-�0 \pi}{2 a_n }m,5�> k^{ J�� }{n}.�$:�$X(:= \cos(\pi �(n-1)wn})�!�cͱ =�CB�Ap�}ix A.F�� \& rom��8Rot}} Take $d=2 l�/B��� E��5Z6i�{cc} (2��& -b \\  & .+�� HmT) ��ntraceA��ϡ[� E}-�]��.�,We denote by!q&�  O}}_{e�� ^�rr}-�')�\sin( \\ 5.!&.> �6$ a two2 1��an angl!�$. � ��&�2b� (2��� } Z6)K-b �Nt)"����' 2)9�~�by� av.�$ %(es'5'�� W� &� of��,^�� form��� ٞE }.���( ��upsilon*�,\theta)J� OpSt SolAnsatz��� |�P* � k*zB"K�Ņ> dE R $7$� # I�� $ ץ spherical!�<,(1,0))$}. Inser> զF�)� o�n� we obtainJ�t��H>G� ��&� , � - U�.� Eq4U-�>�Now�)p; �$f�$ iize.* >���_19� ) \TA�( �.�!fRotZ�J�61-�5�= J� .� =&t (^m$ with $m.. N}n U�^{!� m}Bn ="y 1O./^m�:?2 ~G{m+1}FA�b m�JkAQ6�,After separae; vari�.s� ESJ � AUnx�is� iQx)_iI "�1$ �"�#".��BM`k >_1(1) k)��jsum_{q=:� �hRe}� [ �q[\iX � � 7b} n_q}{m_qI�}{ŷk)} % + JC n_pm�}{�!�; 6 a ] �]*� � ,JumIntSolIIaB��$$(n_q,m_q)2A�Z $q\in� bb{Z}$ a�(ome numbers)���$t{ fin��ly�Qt =Y�)z m�mor $m>��� leav�� n�� caseOfut' work� check ��B )A�indeed a�2�.<=b�� *�e�R6A,dop{\forall}_{q\ge 1} \quad�  (exists}_{p':+� Q_ (m + 1)��MOn=}A}{p'7I� and} q2FQ�m}{ON�)tNBD This!�ds��a=�%�Jm�!�ier domVBq�F�&�[)7fD}��cos� ( -+2F�-P^{|q|!Z!I1F�i�) j�bBDm�E �� :��$ F&ck$%Xr,>�>�*G*� � �[t ��( ��G"�k^{1/n"#^{A;u}B� �Vi1�[ �dE�2�1�V� \Omega"h, gma, k"#]9�eJ� ��RjT:!+l7 �I� < �V"�}����jE) +M�F}{�}BM �� �ITaw���at1�y *��* DefG� We s is�xresultsu�q�tQ orms�>p:�����in both��M.�FJ�&$center} \f�|Pminipage}{\textwidth}9�->�"4 I� �K{l.�(�6&� .�}�ypj�\l�sR�q:(Z:I�V8 I�.�U^m9Y&J���) :. % \\��Zn�d!�AƁ�C� ex���B� �\}f�%=�� ^ ����%5N�I�nd>�eq?ofR�1M&��su� !�Qq���� �]z���y>�^s hold��7�I���2�joi.���, probability�J& Pdfshe�� pose��is/u � rive.J distribu� s of= hancial instruments like bar1 8 (exoticHh) \cite{MusielaRutkowski} "6of!�2p16k. �Sd �a-W=L2Q4log-prices $X_3 � S_��O,stock at cer � "maximalN�f� +�erval. � fix $l+1$*I($$t_0 < t_1 2 < \dotsl $��we analy�2I;cumulat!�.� 5A,$F_{X_{t_1},2},^  l};M(l}}(x_1,x_2 0x_l;y)$ relatA!�9: $Pi\ i=1 ;l"4 -Dn�?13L1HT $M_t���� �up�0 \le st} X_s s��0P 0$,!-�&*!�,t_l - t_0)/NHwV��egq$1bi%�%+ < i_lN$ such $t_j Q^"�  i_j$. ���i�M:v�1��|nFSDE&N SA�PA�Fluct})�^���eqn{ �!� PN( %t1} < A;),, l l; M_ < y��) o!eq��0WalkerMaxPdfI�\\ &&= h\bigcup ��j=1}^l j0 +!p*�lx_j; VDN �D>By�#��I}��6�!�( p� {i_ji\��dotb!MaL}a��p"�$" 2a < (xM�j�)�2DF�j ��� �y - (�+ j�)� �-� \nom \\ %*� 2D9�OU7�Vb�"n} 1_{\D�%��e��} \prod9Ep,N \nu (\xi_j.& dr�VB��Z�$�s a unioŶ $l$ �s,�#g7oY%g& "�Z�a�%�\{6a g Z�� N�xiC� )F}a�VTN�s>\f8 � �� .=�In13R%25�10�%j finite r&��: ICN$ bo�d�<$l+N$ hyperplaneh "& $N-1�r $\nuAE | t)�nu^{(1)�vecr�}:$ ��Ual 2�&%�srandom"[=%zmQ&B� RatRnis F�!�(&� ).0�procedeO �`&�(,three steps.Q�itemiz/ [(a)] D� S�^N �Z $f� bV �(i� |.� -�u, �bN�(characteris) 5A\I&B�Ed*W :�=exm)s?A�i!U oughNS"N1+|��<& F}_z�@[U�(z.� ](k)$x !!+�1CcNC[in (a)!6inv�1ons con� 1FU&V$dIed (b)o+A�E��!scrib�E�5�Y� a+ exampler�*(n��>� ��!�}G&&�(partial^{l+�� � l �&�[ �f M8�k�+* ! l  \!��m_��l� i� N�!R2 N} � �(c M j� - F.� 2�6=ݾi}]�2Ji >F� ���_j*^V�!:I��QDOsum� �-hA�sid�&n f F,) correspond��r\-��possi�. pair���A �@e�c&'(B�afab[�>���^7�cZin quesB�1%�e` \chi�.k_1,k"Fk_l;wacmbEV[�(�8� 1}� + k_� lwN i )j#]*�%�ChiI}i(i�1}{l NJZ�akef F�G (5(nu}(k_j + w.�)^iF$�<)�  - i}"� if $i!� $��q1 2�:�{i-U $ otherwis@�PE�+6t!LIa�,&j� in *�#5|�*w�n plac=hhD2��s;a<g���expon)0als�'exU&!px_j[' nd $.w �weX#ed outSres�0sG��o!��O&{\bf EɆ:&�&?2ez �/�)l=� "�$ʒ�"��m���V3$.tZ�jJ �A�N)�y+ �1}{N}6>2�3E�<e6�!A�ft( A2s]�"N46Yq�^i�YWIf9{ ��\���:�I�,) will be us{-in.� ��A6�%�&!H �#-�Wi!-HopfMdis�3 �ula� SatoLevyP� ss}VA�operatc ( L\'{e}vy� cese��6>�3��e m�',O�$Price}} An)on4 in�as+� agree�?tl�!t � $ tofch"(call) o�4$sell (put)� Rat*�0$T$ (maturity3&�H".`! saI$of simplic�2wO6�xrZ~ , i:�gbe ]"�d �� (t# mean.taryo �6s u#iM5�4 �2katR0$t=T$). Exten�L��iZ (to�5dWany%v3#"2�� �don�,A�ng V�V'x5� �Z0qDash1} SperA�A����'� a�4�1�%In ord�6minim�S isk!� diversifyM$ portfolio�� divi5,(money avail�&a�to $N_S$1s $S_t�$$N_C$-� s $C�;t,#=��u$V(�^�!@ = N_S S_t + N_C ]*NQ�7��e"'�xcoefficiH �!� �A^Dcustomarily chosen-�Mu:B = -\� C / S�L�#&T we ɣ�= 1!��  sti�t9geoi a����, iv, ng a copya�it�o�% afe amp4<ereste � $rZ�&E9of"�&i^N2�of dev��� 9�\��D_t0V(!�� �- e^{r*?<4}).  DevD*�B between%=cB�$jc -j$ !$ɴASvWd/A�/ ] t)Mͳ��e!'S5�%��ph�'if!� elf-�+ ;Q&(',�yif!�is��toA�� $C =u@$bject!!��i $C_T�-� max$� ( S_T - K, 0�$}F���average 2;�U�;ls zero"�Y"8 6��v20}�NoDrift>���� Uz�  no d/&5B1�i� 3� %Var)[�Y� �$�+s�tal. SiR:d& �-ing��Th�-"3,wai[,��s Q��M%MS�* power lawyoed�a�)x $6%$ we n�)�<akei:s� e�]�ime�io� y [t,t+q�� !�l[$F��.ٓensD�)�ble.�5� $ Mݡ!�%7*1 ��0�J,Our approach�=s �<"��o RamaCont}dm^al A{ematics �F��)��first B �Y��HU0$6�I�@<rE�arbitaA opa6uni�market)� � sy' (semi�?AJal� )Ghigh k<� >�&$i*&x-/sim��-|�x}|�"N�� A�� �, anno�k 04#v ~r v�!�ss�=ate]rD �  su�'a larg�-�Y��a�7 ent,�>5 "z"ed% s(?Ao>�lat 0 dic sh�Kr: o ay�� �n�8AjK1�?��in��t^-(auto-convol%#�S*�@(�$similarI*!�ur opi�s m��m�>ppe`@y! phys! p�#!>(view \foot�7{We � @��� n �:Bn!#"on ��F�sh�A�, o�>the4 c��so/gs�$�`, o; �)!{��!^.9!e!�cuh �n�B } to�Km!E � odel�� hp han!�u ab�ct!��A��$metric spa�p >^e�$� a�tinuou(���ed pathsa�owed ��Pa Shorokhod topology�enoA� erim�B l justifiW �eat���<.�A�m�n�bs. 6vis��� ival' �%theoryIchapt�"�$20.4.3} --5} �*s 1416 1428<��PathInt�ls}a? a�^�%!u�z�f�"Zs�d�&$s% � �� tic (a � >d��Q� v�  "rD�U�,E4(Fokker-Planckh1�iP���Bw&B)I�� :im�sol�f�s&� B�"�&�,2� ^.�. O:/6����9). It m�Cj"PtE���j�&�:1maQ�C(��D��� ��k� |$ u�G{6calculusMvSamko�BA�%�cular :7Taylor �� (�|(4.11) A� 89FI� Z) ,Dzherbashyan odevelop*�VC���2�MBe�� ock./�<4�Q�pursu�RgE��ilF. �Wlreconci�)ur�����Z �>� E���F4&�&e�5*i�<aI��ter��6g� aB��0�S �*f6�*� xS_{.� } -�%��/ (( e^{\alphaJ�'J7>� \s�1"d%E� L}_� ) >B ] -1^"2�&9dC�FI�=&.�Z��mm=1}^{}A�{¼^i5!@��.�B��e�21��R�IJ5) ���e&�>aq���and re�ed� Uca�Ja� s� � the��E��!pro� �I=$&})�$Y��CinalTime"}� � ���:� �)f�} f! I}) cKi��2=������a*��� lso.�c�C ruct23i�2i  jby���B� 'fK $!a�"�q�I�|e�IT. ]$ over� (pe�?or)4G 扬4EberleinOezkan9? deed�&my.%��kM� h��!ju})�!� &� hist% ᾱ�-�upAF���is a1A�5upLve��L*�E� � �f>� is, �Jgr+E�UaIZMean}),"jQ(� 7K�`ns�a� �frame�:! �Us , �sfy� �"�=k� t�� 3� A��%l� its clas� �G�a� mayE�b!U2 ��/� �ŧ"&1w "�0� & vaI>F�!l)u I.s� which� 5�to�is�� q06�ia��5�[).$0��d a:8!QE�a"�& 2y�>pin:�b�:FAC_{6C/1 ɐ"�C} tR�Kt�� +n1 S} (Nm�8 �n=2" K:K^n2~S�+ �VU^n}{n!j?Z$>�>��AVp� al� t1�C&��Q $� S^n$dL 1b 2���A��eb�YK �1r. ��ť� ��ut��eKthR8��!�QE� �w� ���t��s��N�F�e� have* >!�{N,ip)^n =��^n�#(.�=N� Q� � & ~n?�S$n �?2$� UyN Nrywe) neglecG��AE} �mu"�1{nH$ *�+\N0i�*� 6 2}$ j�JM %�i�F��2TN% �)y3*VQ6g :*�M��3#*�,J�6�u>%0"�(_t C + rA2S C - r��-OBc ��� .��v1�_ .�#��S_t^n-�&� ��- 1�AsUXDe&9B�NFL=YM-�' 6i ձ>W)��>� N�NoH���VO.|P&�U� In fur� �� u\ m��" &�#�R?"�3USU graln�N6tF��%R�9�\��P(e^z�v�2\}��Bt.� PolD�"FcF�^ $P(z^s a real��*h<m �'roo3$P- $P(0�%0#>$P(1 $ �'s,s ��� $k$,�.XI��rRV ��lim}_{k$ }ݱ:|�F[i2Q�+�aiB\�@m}�Z } {\m�0log(P^{(-1,i)�/�+ >e�P"}!/"q+ % %V�i� H�C}_1 }BMb �|F�����|�M .�LimLogEL�2q�MI.<&U^3;� � ) u�SCI Eval}), $)d)}Q�AA'rMu�`�(M�nBvic�' $z=0�(1�*�^"FE� �8�oof�5r9� "CXB}n52J�Q.1�+.d N�get&� �J!:#�+)Z$VZ1�O29�� E?> 6]������ ( ��R� (m)��J�m,i(a��½m�e)}��� V�*F B@x 7��� � x^nS 11��]"W(b�r(s"U`f at dH1��aEk FAlq�sJ�P(x) :j(���-�%�op{=}_{-Y��r.T ��x))�A�� &�/ingSolF�)UE0<#7$��T�� ��= "� '�a��of&RsJ@�~"� �q&}_t�^� i�.m/  ��}3k�A |_{k=0} =N�)&�M�!>*�["� ����yield�VR!E�!6�&�*,e.�k)���:�U�Ds0ialv�7=&&\~q -�1}{�92��M�liV D �ɦ- }{ �� )^{'�g .�R 9 �  qf+ �S_t^2}{2�C�_{S^2} "�� - _-�H�H�H+�2P^{''}(0wa�B. Vf�qJ&�a�T+@ enclosed��parenfs .^f)I?2<^Ŝ�(4 Black\& Schol�c��e�+s�"d �� s vi�!+keqF)��MO�"mAn} C$b�#.Juniquen{6]�*��he��G|4�lemłn9n7�"; &�%Mto�J�0{3T,T� ��0(&0�>�"% i�v� P2"�5$T$rc�k{Conclu[!s}�@eappli�h�ch%�Zs�)-1 of1*�y7mz �/�'n7C>�,*>sM� show�a@3i:v1� � E t��� �+a way�(d �"�5�$e� i9!� ��/�2� � 6. "SZUBA^ B.$O�)d�Y 87�by�j5,U�al,v�;Q�n�*�M&3)� �*se>� by �'6�s1UA?!D5e��#6�. T�5<A��*4in Monte CarloP9Oon�:it"�" 2��/ dataX_#� �'!� *�'.E"�AeDprove]w&[ R-'�9 al 6�h*� � �4���Bj� �DB�pxRRj?' z}�J�p2�E dz �@"�"}^@]\y ^d}�&6�~�lO � ^�ogY_{x9 L"]�  +H#t9 d(!& 6���&��^�ph�@f���6��.�-�4ETr$Z� E}}$�]��Z�� 2~-hBn�}>) ��5 >'F �($}{(2\pi)^d6dEf�&�c%Vgp6A>�i& BM�"� *� F�aq ^n - 6�M"�LN;sr d�}�BG .g^[V�5B�!�������dQ2%��B�%�%k�:�)_1)�N.X?l}^�2=�7.F�IVA�\ &�u�u�u(�Hi�%dbpI*�^ l}_ikin&�I:Qe dw !.��9S!�w%�w)}"_k�*2l_1WsR`�ej`r�6g �͍)Qot<�_v�mCIG�.J��E��) 5���X66)X_<w1dV9cv�9�9�9!J-^">s%\k}6@s _1) ��&pVd�!%f %Y op{%limYM *%�  t%"�T-fty}^  d Q�A %M{%U|&E}%I~%]. &- %�%E�%Y�6|}(:� + k})) %�p=0� _(%m�24 )^p }{p!�  %\,^n_%!�.7A�a�*n( -o)^pF^{(M)6�%�= %R.,d} %\%\ %&& j�%\!�����1Z1!a;M�ECf!6!=�l}}{M},kM^n!�1�5�M�2�6C�..,_>*6�jY�sin2u})}{%�_6oDb�e��2�^{n+1R!�%Lk6�Eqa {n p�-hM�_2�^{q!�Mf})(0.�}{qe "�M} - q�i�\02+ l}^qa yva�2�)� �1}y�M�*-1}!41>:5�e�k� J f���u�� � � A AUE�r} M}^.�6w���jg����B]��AK %� j !:^{J1� C -� A��b h������!�e^. �^d|} (n ��)! !¦4:(M}^M d %\xi1���  2_ ��Y6�r79�xi�z�i-�OT �&��!�I&f.*��7:�H  bq`d�w�3\AA19z:, $. I*�=��8w�d �% K �t(�$eno�[)at mostiG�F$occurs dur�7it �x��3~Gk6�.�v[b�N5&�BmpV.S�-]�R5{S��L�lCorH*?V�t4���iG5#�\ a�%%zl-x� q�:�^d$&H;�Er�io@&#\�5�Z7)0�?�& w�8#�ang�I2��"�&n:]�N�we�?]Ja��k�Mk � ^n$,A�=$sp-Rh' R}}}:�#V9"! n�`�Miroduc >n orthogP�"'^ه6�./M�2 �)�g�B |,0d0)5�"�%e�kZ�%6�B�f�bI��RMI]@sI&�>%R�"sZ7�}<remai_ ZmRV1�zB�w!0>�)_qQV�Vc �e,)n����I���Gug�T% $d$-"Kc�lf��D�Honej5.<�f�d}�?'C�;� (��)or���*�(��j��2�8*�/�� \�%a��7� 2 ReT [2b801{2 n}^K0&��xis-yk}�^ ^n + �I (&s�.S(y����] &�xK\n�od�\ 2]>\ƥ�os�(������hau � �)^�f�!-G*)e �.�f9�F�#lwe evalueUit�D��da?rs�F�C lexfOne �!RL��8pi/(2 n)$ (Wick V on).a�do a/N*H"Cauch oremqStl@qv$�K�rval $w�[-R, R]a��#.axi�h wo arches-= R.�ph�n $ L0,�| �]�V *$�in [\pi!uE�]$dGp3# vely%aa T� uM�QS7o\-R,R]Bg�g�� �N"a�L��abL by $RD t_0^aS/(2n)} d �&7y-�W��RM:sin(n *) \pm" l} R��n( & ]$&�)��#$upper ($+$�;AGl�K ($-$bmE7half-�hF6�>~2A�*!$R z��$GMm�aB"p4ve. ?:A;�>a� *,k}$���Uxm�G� x 6��e}�;�,*��~!�2� )\Gamm 6 =.;xU��a�^xK>P}:�B=##�A.9�E�0v�(*�x16�%�>�1/�Ki�yM-q�M�*�:A��+1�%� v�X�A�6\pi9�}{oqkL^sY�%��@�q �}�6.�< x}^pj�V�&�b. B�% m .� x� ���It��e"-4�=m$,l_GW cosin��TMacla *�L, -�t��WeL�^perio��Ms͜�3�6�,� nd oscil�E s rapidly��oلX.U7JQQA )M�J IesCKingfu?Z; (lštrunc1 ��4$z;45?-d2�s/V�*��N�v�-��m-�r�n t����0"{ � :<�%�MF� �.}6Wp�m�m��U���TuS �we .�="{SE�� 5% FctSD�Ex��MfBF+`Gian5,Y��R*�y.^ 1}�Q=UAxF�|.�JGp}:� � + �&S�2���4�.� �a�]�/ i�""e/ satis%;*~ T|�y�K �| :�9A#xq} q^{1��/n��52m�tm���2�:>�:�x�q \Left��s I l}_q�a�pi)�N�/n��'�!.�U) �q�== q(mg�� )=bb�#��$q�� 1 NN�HJ�1�"_=JM �0�e���)  meq6�oC l� ��%�6 �t#5^/T#�#���B�B�=C��2h )/(q6)�)$ +1��X=It2Po�? �Def�����Z"1$�&s'"�T.�&�!���e}�� sameG�&J3%�Z�H �)N)�B��2" 6ț*Q�oo�9!S�=:D�_[q.e.d.}R 0B���XaUM�[P*!B)e=���e�2M>�uH!pE�:|A:}AE��'��D��B6*0�P�?:| ���@_i�)0t_{r_i}^{r_{i�t�kd w�A �� �8),;���X+] �8� @[ �~�D]}*8*wa�& �l�G2oN=��q I��.EBb!cA9�e0��R�C\,:������V�9z`%�n)]�o�p�-�rM\� 4� 9 �f5!jG]� "M�}e"-a��>�V}@4!A��� F}_kZOt�� �0^&=%= l� � � jA>\ &j��=�(0) }^221,�')J%3dz }{��2�b f�E�Z�5�%�^�ii �zF�G��) $�B rIƨ�1 :n�*.U���/ �A��IX�8;D"".>.~ G\"Wd�k*�J�we5Qo�$z_i(yR.Dy)! e $i��Ith}}$&�< (in�pe"q)"=� $&K = y� ��p��X�#\z�to �s��[, I ]���Y% �.��monot�i� V �t�z`<�9M�d $r_i# ko�W alph�-"�:"F�" w9M"&0N�K�&qI�!P "x Wkxa� \-Znd!�][l�i $w/k`�.6�$>�&>#u�6U%��bd�pi� = anti-cשBy d�F�Fm�.�M�g!��Ue�M Ea quarteDja circ�X V�.�0,�As"D� kI� G2Dz. }?Mit vanisa�Rm�G 1�` R� � VAV�o��M�=9�Nt9KYa��6�l!Noc�('�FeP$nee��*�F6l$ %��MQ%�i�|GpA&t ies exclua�\U\a�(i�_iE[r_i, � m� \diagd�?5!��"� #$A��1B��$� 7]ۧ&�B:bA�&E2� 0} | ��W_i| = 0$�o-nd��nZ>nzAMY�"�U}$�sya�� �IF0$mn $:�+B�W�Vu�y��)$%Q �].�$$0A� 6 �nZQ�s�Z�& %���I�a�*0`Bu�&w�pI':�. �Kq.Hm}@N,T�!� G$�t.��I�-"�5�mcP)�)/ I�( *G B~�GtT��!.PV��;IXLj"�R&>�2�_m���E�+ ^ E\".8"�!$3:5� &< B1*)6�L L} =�� .� ��� �I���� W��xU��w�$��Ց.yq'`0 >�6-E��AOat.I 0�:aF}U�p�&�>�͸{E >�� d ��G | �1$ �j�&��v�: .�%B^2� v"L� Q�J���I�)`.�*gRD"� 4���Q���$�|�+d%�J0A�| �2� ��F252, ) =�m�}m = )?�.i :TQ��6OHthebibliography}{99Q�4ibitem{GopiMeyF� Hkrishnan P. et al.,:{ cubic law� !B>1t.�Fv�e�Hs, Eur. Phys. J. B�L3}, 139--140 (1998)V� �Bach} el�-L., TcFof Spe�nal, Ann. Sci. Ecole Norm. Sup.j21c00); ��e�P.H. C�s`%ediijv �`"xIx�s, 6r (MIT P݃< Cambridge, 1969.�4Meerschaert}  M M,�K@effler H P, {\it J D�uMG%�SvI*�dRW�VE�4s: Heavy tails% -CaP^o4ce} John Wiley��8Sons, Inc. 2001=�Fama} E.F., Ed~T Capital Markets: A ReIuof.t Empi�� Work, A of F�e)�25A383--417!�702Aandel} brot BI]uU'�=(�H'jrd�, wBur ss x36} 392 vw63.wRepRiA�4Repetowicz P,  mond!�M"+ushN(n e�v�,y)i�t(28c(walk (CTRW)� non-*�w M�0�-2C{, aaica A!�I�, CN�d�, A"�onT1 Septeݥ!�4=�Masolive.8  J,�( �AQ)v e: DzEZ�s>X�M s, pqu�24-mat/0308017; .Z M;Jro M, �z-(TP3M�W!(!ke �J.�-A�. E)�<67}, 021112 (2002�}�0CoupledI} Bec�t�!�$ N�i�eaemi� L j�s)O Anna�*f!�"qc��P32}, No. 1B, 730--756� 4) .�e�Z y��a.cR�"�w>|MSlowlyar�l:�1�^�!a PRE}F�0Benson D A, GX5#@�����Oe�anomal6x.I�0tM.66A60102(R)%G2.�HKutnerWeierstrassFl�us}  R, Hier�+ZQsp�-temp� cA@�-釥c>3w���5s. (I)]-�r f s}�I 4264}, 84--106,��99). � Levya'sVaryVel.�Extrem���aA�und�)P\���-�va)��u$city, Chem��t�A28�481--505F[ Raberto}  M&fW2�!�retur�u;| -freRcy.� ata:"/e�Xstudy, �0a A 314, 749a9J��� Jan W, �u "ty�Ys - I��&5�on-�O4at http://www.^|k.fu-b�I.de/~khq4ert/b3/papers/�/courtes�] H. K & ��� M>�� 9R���=7A0c9�Mat�: �jha۔ٷ!x90*�N: M�U{ MethodM鷡}C}, SpA�(er-Verlag B�( HeidelbergE�7.uIAKn�8sas I, Shreve S (Brownian Mo���Ca�xT}, 2nd ed. New York: :�� 97; WWW:1� |world.wolfram.com/ItosLemma.html=�,sRa�}  , Term SS�% s Dr1� by G��al a���l� es, 9�al-^e,i�P9}, iss. 1, pp. 31-53%J2^ �O�s�E,  F�rDefault-�{&6x6�: R��ARe��cI�ng privG!communMg�E.w=5aTuS} Q� H-�!}u0in Quantum Me�ics, S��A�(s, Polymer ��,�]�� }, W!�" en~ Publish��Co., SA�p"� 3rA@U� (w  f3,��42r"Q�  C, �o-")Ta ��LN��@miM, in:e��"M �J�;��x�LChapman \& Hall, CRC.>y� �(, �{ s: 3��430=�B!� K-I, Jd�z�S�6�%�uly Diviy�2� } C&  Ung ]lA 19992��| S4 S G, Kilbas A� $Marichev O��)H�z)�^ A�D���X� �+.,} Gord3Wnd Bre^�SL�ceQ:� S.A.�3 �Dz*�| . 4 N�c syan A B,J crif�o"(3&S*5*Z΍thel ichlet �y$, Izv. Aka�� auk ArmyaDSR Ser. Fiz.-Mat.  �U 11},L5, 85V8�PndB7l8document} F�\fZ[12pt]{�(`cle} \usepackage{amssymb}!(�:�u�Z�k ll. 4�%�i��6WAW�4��r�z[)[8-1A perturbEy��ua1\o�b*�  $are stronga�>sen�lFried�ʘs. MSC2000: 35M10, 58J32, 53A20, 78A05 �/y \J]In�@!�}��>1wa!� '+\q)$^3� $ 1868. His�1�A9an,�l���!a Euclid}yYa AS��|Fȶ,=0�havA� curvaJi�l�]$-1.$��B�ha] stri��yiert�;at evenˈ�0�l�f����!�origi!�e2x` the �}` cen"�%�AofTbVE{2}.$ �I��er]I|iG�2�fi:��\)E4 lie�~l!!eZ i �y. E-kn�� 8^ �w!�l g}i� n!c����� of=� ng normal���@.,d�!�x chor~!.:h+Ft<�I�.�( may be sai�;be6 rinsic�4EJ, r� �\an � am oret7 }%P al <x"�A.�,c, unA�LV� �>�9� P}^2��"2��1h^�$.} Hua$^92D�A;2�Z*! R* >1scas�& z. He2ved��e�fof��'�D�ZA0\emph{Tricomi�x,7�E��^�mon��u 1� E�s, /d�ATA�o_� of g izѐ$avefronts.!@'s��5kto 1�A���E.�&$Ji�4Chen.$^{10,11}�Q2a�$C�|2$%BNy��"� � bbED,\�� ����dI�)ͥ1>�arXqA�1�,%�_�G0 Ref.\ 23. LoA�y,/>�re�F�lMsmo�MX�� t ���"K by Hua.�Ni �.��id�6��֤ext� ��O7(s (Sec.\ 1)�*ad�8VU�=� e !�* 9~I�iMd���7%�%( 23�a at� � 2.1) d�σ�W��j2� �X�ec �� que,�� �. Be% e �M�Q�V--�� ussedE<�%�� C�C &� A�wrw��Ln boldface. However,!���0ic &�, *V��fricand"J �4�hti�e� u"p�A};� &��of�oar20 �Js� est�NDi%�Ü�:?�o Ro��a�� $�B�b��# "�$  ��A�A� \[ Lu=\9& ( x,"j�u_{xx}+2�K(x,y)y}+\g�?yy}, \] }6*$%�co��aU<6�O�c �$ z,$� !�$% b Fɶ�Y. (A !� cripa �-��+sN>aUa:�&x*hA.) It�A�rI�ant!)�F&5@)�L] !{hi ��[ eu) associa�9�Q: $L�,�  b� "�� ae}�.� ���� is LapF�'su, �*��1�= �=O9�� =0.$ J is ne��ve, \���[ ofٽ?j�!- "��@�:�1Ej)�=- _ =0;$�a�A�a�-, :29,$ orFH1E Ib�# th�2:  para%1;"�e���)t � �k.N�A9CGa���li�Q elsee� }�,(0�:�mixed�F.����� kI�of an q(.21�AELav�n('ev-Bitsadzy�2I%z� =sgn� �/E]MO,)"$U3.$�Zwc�� עa� bQ�urv� ur��7we.튅� v=��s-��of�jtesian ���G�T�K lway2 yV8$ $(x^{1},x��)$u�l� }A1��� �0(neighborhooC���$on� /q �&� �%��ta�ele� $dsъ!�O�i�be^�ds�=\�8i�D{2} j g_{ij}2�dx^{i}j2� +��a symmU�$2\6s 2$ �� ��� 'tensor}.D.$ (IiCsQl!�6pund�and� e�B indi�/p been��)-� 1 $\diN��7)'()  Ռ/` the summ�Dno�oech$ .) A��YeaN� ��on��!�u��:�^ %�� aceq�1��-T}��f�@ sqrt�)| g � | }} !\���} %��- g^!�ZE:Du6Ej}} o) ,��wמ$ RE�fi�(tI U5!�$g.its deA�k& t. -��Q�*B�1he��F2!�!�&4Mz*]�L:y�g��i=��0"�*�"� �F�A�n2-.�SMinؿ��11}�g_{22}=�� % g_{12}=1}=���n�bA1mF�!Aa��Nis*Z;4�$x$-axiGp�an below2#j5�6Z �%��A3aR' ��h not��unZ4�=�h u���ll;�"� �� ?b�. R��� 3�J fe��Mr��%Pn����-��RiemanI! 5:vE����6tinctK!�g#����"2�v*-�,p3retpseud >�u?��>�.�Y�PF� *� 1Iivb�%F�8*� =ois.Oon"� 8� B�"� �u� b� A�*W��s0 } $-/ "� ��i\�L!gI>Lw\�ne�"�'-�a�ula.�JIAMv,]\�c �zV�7 al��� . (�Q�� l� } bo����ScomBK (fluid dynam"in�1�s%���&_A��v eady��慁D-n� ��F�& a�Usp��oZundISEiyB�-3� ��ͮ[al�R)� -(}.$^4$) OnJ<�)��1�sig�e}�Pi+ig�� �7� e�L�Dz o-����V�  c)h bE19�wl. �E -d�5r�2��:�.G!rN ��i) � m I�ap I� ����jUarU,* ��� � .n ��fz c��~ � ds_{L}D equiv A* *[dy%-[ . xdyf 2>{ k HQZ null�desics� !�9� 1^��-Kw_ inar�f&� q�6�=0.� ��2EpseXfm4�:?�_� �l $Lu=�Hy��"�^��j � ha�on,���5Yki�6�s,}�!J ge-JAnu"!E!Wquali v �al� �d#aZ�  of{gn�&��ls, qlec�f"��MQ������'~s%er�;iG�p����Խթ#i)-h�\� p+1B���*�zQfaɭ�BRE1�"�z��z!]�%�note QI!� princip�=yp��/� R 6;˛  27��c�C*e��!���XV,ofEO:�J�ir�-s:Oe4z#�&.�"id��w�er��r�3ba�A�-�ofFN.W :'s.��D�P.n:iꁤ=� 01-��� �� +2xy��% 1-��%3��eG 6Ij0(see , i�e.g.,})� a" Vol.r,�65%l �, 138�ac$��E� �A�.3!�Hab�e}:( locu��)�Si� st"%��6�%G��.=-~a�.~�e��M a�� �]f�5?$ �x%O�R$p+#�?��: !�draw a ���,/  $\ell_v�rogit. Au��� /s`Qt1n ny��{or� )=� , sop2.�_ p��^%2�A  an�iF�O,}��)� outs��:�. D�\by $F(p�Efaml%of>� s cryby  D�{51ab< $p.$ Move%��xhorizM�l� 7 _{h}9k$pG��:aff�U is�&> ��.$ Aswpj���)��"�He%� �' $\kappaA=S�=&U-� uU$1,�A �61) �2becom�R) �d�E�i����Yq�!n*C�-� ES�4�E�prefas�)�q/i��ma�� {2}$2\)%8] . A��!y�&# �U�pol� �e6I4 �!��.'!G<(A�t� �B-��1�" < U$�oT>Q�faAUt�5 � M�). (We� =9���po�#a�� g.) Th����wo� + ' _{�"��X _%eare o&�hR�n�*R !�)���'�Z( .�&. L��[ u��] =(V�[� �� 5) 8x}-2xy B  ' u_{yy{+a \;%%\;|s]t u :� !�!� $L[u]��Xt)&� RY �?D�?�2�:�( �)� �/Go�*a�Ftxb`� +y�d=1,�/L}m��onv1(,� FtP$AjX��f2z�rad �"e�!O/"� . So� (of eq.\ (2)*fyF�)����ƉW Ɂ�~��*�x�6 ^� p%:^ndB.�4_ ^� �$��os�fB �P�Fv� �=�JP'r)me�aq� gaug�C���&��*:�-�*�(Ya$is obvious�0v�A"��� * )�p!� altho� pQa�[� ���hNEtudeUm!{�t����N6*B% �7,�ʿr.�lyyi��t\`� w�sj!��pc[}$aO. &�J�a.;�%Y�� i:%�M*'0v'in vran�ph �is ki��f qd�)��� �t��6�.6w�'!{. Also��!� �)-![eviar� �cleI�s ``upstg�''%T, fiber bundl�w;cal st�$6� �R AFL~#"K"7>}acts ``�L.�DT�  �O)5L geneB �ivity. |C�'.o0-k���Y�_- has �,o)���^S� .�ba 3>A�e (W c.f."�0)-c ime-Y��3s ��!�Wt �da!.� a�!" >�alE�I�og�? �pat�phR��"�1"6�3!(A^1� ��(array}{cc} �0 & 0 \\ 0 & -�>zɒ :��] 1�}V�A^2f�w &���1��� _6s . u If������,��!�racteris!�/����4| A^1-\lambda !O� | =V��y[�u � 5 H� +2xyX�L(1f/l]��posse4 two real roota3 T��, 2}$ onqF $EJisely%n $��+ŵ>1$. \ TA�AuMkis uininters��of $% i�AWith% opena� t disc ce5ed �8%U( 0,0 �) e� }q^kFi$complement�(the closure is�ec boundary e�,m� whic���e� �(ype occurs,!! line�infinity!g proj!vew�3a.�.f.4tensor $g_{ij}�� Denote by=�a reg�) plane for ����!� ial 55�~ist�Ya famil% ��AG Gamm!�!U osed�pointsd ��eq.\ (1)��remain�$C=:w, \backslash `-�.� p$(x,y)$ )�do not��0. We seek sol���m� B$ �.xdi.��q�}6 8}\frac{dx}{ds}+B y=0,>c�Y $s$ d%�0s arc length,Q'non-ch2v!� $C$- de� . Because�t�|nt vectAA��Tm�C� given by��� T}=2�i}+ �xj� 0] a geometric� pret� �is�!�)Ui-at�$dot producU�>� u}=( ,%j)�=:�toA�4C $ vanishes, � i.e.���u}% normal82�$Q���o��1w ��$C$Em� Ese rPhomogeneous Dirichlet9s}. � cAi {Wea]� } I&� , w2�M�, (10)D shown0exist in cert� we� n L�^$ spaces�a clase�IZs� we exten!i at result^!*� in�i =!�oedA_polar��da.> �-$\ell�� a smooth�y A� ��^betwee)���:ZHj e ?!� must haviproperty� 0dy_{|C}\leq 0��aq� E( trav�� a cou��clockwis��r)�4. However, as �  as� o]� met,� need���>%O� �K!%$�Ytheir� �/e�cy�ɽcircle.�%H� )Ljo b!g!���� �n�`s� �1�{i� e analogu�P0e ``ice-creamA�$e''-shaped��associaA�t+q*Tricomi"` }$^{31}$�� xx�cyy�W]�Kj urI��ŭ%T �u�!'he � !��=k,M��2�E��?� ,&X>hcon~!2� � >;$x$-axi� �sonic ���m-- ё. We l iall�eA�&�!B��%� 1� (6�U 7). P theta$ lig�E�\val $\lbrack 0,\pi /4 \r����*�_MXE�� %�,fourth quadr %[�My6��@A%?� :x\cos � + y\sC� =1�t~J2:J-RJa36� $C.$)9�l�&�*���"M _e � [ _2i�wo tinctq�$c +c_�;�j(vely. Assum��> foralle (*c*FK $1/\sqrt� ��x<)�$-!N q y<,$��dyB0O �A cuspA� perm�dE�$1� \pi/�)� �c_2=(j \pm ).$ OQ�s,%SE � ���piece" coE uous"( (so �Green'saorem : appl to it). Nu 1A5d� � de� $in Sec.\ 3a@8�equival� t���?nE�de rate spec�re�5)0� fR $U$Gb!�e s���� �"of A pair��4measurable fungA�� u"*\ &y �qd �&B% D< e~ \| X E$\| _{\ast i[A�t_{| _1 �ft(Aift| 2{-1 D| ��| 2�!� 2! 2) dxdy ] ^{1/2}$is � e%�ic!JE��xpressK 8 �k u����its.= 3 value -�=E�.$ *� W^�ar-�d%�d�,1�N�w-K( w��,w_a� -havingA�tiI� derivativp nd� ing:F�  Xdx+Zdy=A�o} 8�� =� $_1 \bigcup2$;j_VUC;�ESiB( I(SF( ^{-1 # ( L^Mx%&f{wU!8jP�I.x]Ex<\inftya] �\"��q)6��i9e 1�%�%4"nzn;"n _n2x8� V��~PUy}-A:*P2��DE�QHilbertM�$H��Zsq�� ��9�h-:( h!�,h66�^�h-i\A���E��]i :�&.F��� sa ����� a"V21}�����&� (<in�z1J_1 $ if.O�Ui�!U� � �w W,�[ , f-k) I�}�#w.uU�)�� }V4 .cbJ(E�}���f.:�FU��2�� �t%O542E�*) � � 1� Cartesian�. m$�X_1, \, 2%t�[cbB��Ms��� � !� unit��.d �h;2 ��>a� 62i n�in s��2� �� ously�t�",� 6�O4 In"�, ��G�ɯ /2�� sZ�-"� d&�Replace� ba|� '�all��$��$�&� .�5 (u_1,u_2��$6� &t L^2$��U�Rq 'Rr a"r 2�& x F^ : �W 5$W$:$W'�� 6�&� 0ly differenti� 2,�c�2i�>��A*e�1)���,$2)EC<%RB&2"p x��)���ف6���5M��B.JT����} �9,MU�)8�\�\�\ �R\-\�!Fin��m�H>�Hi�V�9��U:U{'}� -�e�AwF�Ip>? y )�| E��Am �9)v!isn zero��AP���� eV&�(4)E viol�N ��y$$C��gradi�� sca�!pote�$l, even lo7y. Harm�field���2� is �ris� vari��Nexts $-$��� 4��5�a��3$ar example6��t physi� to s�n �o  source&IJ �N+,",3do2-� ",J\,_2%  J�V%�6 ^�"�%#NAKIC!T*} mQ8"I\�w!:m�Up  by �.$�r!�l sp�of�'�7*5 (w_1,w_2) ��3 (11��+ u(12�@�& $Lj self-adj�� 3.�ad���fix posi� number�(delta << 1/�8nd $\varepsilon. rKr"r%<%29 semi-q!<c� le,f� 1}{\�}- �}}<� .1-�} 6��s 2E3} � exactly:� !+ 1,Eap�r1�.7b a�1�)�aouskip t Th�1}.��A�N� &� (7)��a*&� �1,�ora�  �s "2 :�$or2�2�xLrf{a6�A���-W� blem6���:� f� H.$} >( it{Proof}�Sof�an " 4 argu!�! �D3,�'weu be brief.a�oe*�basic in@litd$Ora $\,K\��{+�us! at $"�" 1mK$* � *��(� B. *�4(�!�8s.�A� djusA(@u~ - '9�� choo&;c� multizr $a,$ S u�}�inner!�,C � �,aF�� � gra\by; s�knou effh)A$| k� �"Q�D$\alpha �� hose� 4� � $\gA"a�&Z0 ' 2\beta, $A^%'e,1_a�$a=��ob� �=x%�( 3&$)�: �#6}%�� � =yD�! �� �\geq -2 x| X� |Io| �| 2" x^{3I)_+x�%.� �y\29!1^  2xG � =-2y�!�$ �bX36XxybY�=y}� 3x^29m �-n B,!x��=[= ;.(x%*J�'f Q{ n-�*�"!be Y#neg UR3A�A�c5����(�6.2Aֱ doe> t x#re&$x!�q�,!m*J!�!�more �l:be*0%�p�����'��sam�ryt�,�Ws. ApplG:�to��%e�w#��rO��*G,e�i� a �)gral $I$ �!��in� ���}MTa} {2�ft[ (X*$2)w_1^2 dy) x % ��rVYa!� Ny Nw_2dx+M�1A�In+2kk ]ExB`%$w�"!id!� O�B 6 nonU~-�/ hypothesi�#� .$ O >� ( e no `"er!hUK .�" x=0,*'weA��II�e �.�ofU�. �"%� I_{|" }�!q )� -� �\{.�dy+[2xy%�--ow_!�]dx-o\�n��un(!)fauat�!�y=-w_1dxAonN�(0:� Q>J�{ �Y���[.��(��'% ��)A�J��] � \[ =�Jp!xU�Fr{�^2�t��2I�ty. E>4�)im}�#-_�J~|=�,_ ) }+����so!����.-u=E2-i 1)a9i>P + 1 - � v]�{e��4A�NWm� Ey {1}(� y �)�c)��~naA�T�establW(E�>:. Proce�/> �319E��.>9��z y�Riesz Re�enu0 � �R�vn exdf�in H *KE�-(&; *� )=-( 2@ -h})�.�a��:��E��� 6� ��$H$ (or on �r� 2$�` 9 oZ .$ F ri� $h�z� $h��� h�n t�3a2Pscaling $u_1�"$$u_2,^{23}��a�5.M F =15.'�$u}�&� lete]l :�)Str&2"�,} By��� it{s6 "��iF, �we�n� I).�A) L^2(�).2d#eF*s� equen���^{\nu  yo ly :��+2&.A$�<-�,()9!�\lim_ii�arrow�?c}��� !(� }- 8 \|_{L^2} �-] �_LN^�`h`�. FA�Q8"�,�.,�, )$,�.!�)��&�� 2}$,]%Fopera�-L=(*�9)^!� matrix�$�- :9L a�=6#4x:!4y+B,>�.mc�&A^1� A^2$5$B&-&�F_7 symmC.-**7,15,16a�f�6` �ctD/x���"Q \I4v 2B^* - A_x^1y^2Cn% ->0=�/  (B+B^tq��!a �x $W=[w_�1]!W^tji}]$."Qs5�&)� �5 �&r!�yna non@uZ-%x $E$ "1 $E%_JL�'�z�#rKa��� aLY�= fQ.-E..E6/��tr��� &h Y�j�(Tn-^ ���nto��B:V � �tru �ui��e2wE$��w i� is �)ion, but &b&M "$3.3.) Sup 3 �$Ne�,\,\in� i�,Ia�ar �<�!��;!#V,�A��Aregardedi.A�pp� &: o \�%6z .Z d%�[" ��pe�9�/4!6e� $y�&�� I�A?� = n_1A7 6w }^1 + n_2RD v�n;(n_1,n*5�(he outward-Q*'�al1Gto&�1�l-0J�! $u"�,$N%j*:V2 admissibl��15!�f.a maxi�.�$V):��6� $(q<u},)C)�2�!�1[�26* A su��c$^7���i�)@ )A^<2a decom��o� �= _++ -� ����!�8! suj; nullIɉ��_+% �pan\ .Qa�V�L1��B�)"r1� � hv-$  onl�! mi}2=0� omma�i���Nn u= ZuTLiesE�mu^G&�8\mu + t�  ..���9�S�_*�=0jonQM���1�l+!\65 `LYi=fT8/, Q�Moreo�2.JN�+^tU�w֩[pr��)S� +� h}R�Th�5U/ F�+(;s�que�?6} =nK�.� l�Y�7eJ[U'1d�{� 39�.$^�}$$�e�g':N�i>!~e�� of"�5:* vi) from arbitrar�9small .;urbauhLa�-Beltra*�3��ea[� P}�%W�?&by�����UT*# l &L$��8�#"uA"�@� .��;e��aN�da��Ung an=�5�Y� .k-c "� t�:D| xplic�<?0A be%�?&B�>!w�H"K �� of�$3�7A,%3� (8~;(9 Mx� ��1aRC (%��E&?{cc} ��?2yQ? 0M? UF *� th���nt�<$Qrd"!KusA�r*p � �by�1�a $B_*y��)esI�$B� :� E�6�!�tak��b�� � 2t���f+�_1-+22\\ ���).93 &z"4juenB�G .H _1>0�v"[ _4 2o _2+ �1-y"�.43� Ku U:[.$�Dr�:]^�q 4vr1.[4�IfA?E�mP  a w"-�F<��,Q�isQ��a�ver9$A�Y �ve-� it��AP o~� . *�1� �F�h�1 $C �5&� � _4=E � F2� � �*4|6t4 mpon-G!"�6 "�n�nJx$� �/ $(y ).$ A.y6n� $n_2$ �?(/,{s}� �"� ^�We-c� �6�v$[�F>!"� ,to guarantee��� U5k"]&J30u_1n_2-u_2n_1V�2F$,ɥnoO-5�E� �"�� �a��,(F��K� & geq a7En �P��$9s�O2.1N5�w}; V���Y w}=(0,!%� �e�w) w5 ]s�*��(J�n_2/n_1�x�r n_1/"� ]n_2e�2k a1MZ ->-V!~f&$2"&$\Q6 }��*  = 'y u}'y+2J �U (IE= �B%�q�QY*M � >u� (8�;9�<nd (14)N p6:���"U� (15) i� �C�ej A�aa ��,$�$s�s a^P }Y]u�$�h y#fI�&�_4):��K�$��b"K6;has bee�9t,.+�BN1, it �D� 3o� Iv{Q9BQs &� eQ1��We�m8�  =A�fb� I� - &.�n�aZRNn0*V�"�I6R1^xe�&)!appar�+n �itiesB��<��a�A�2a7$2re!ov0$. On $F,$����%+_+�d^� [� z� -"�!�_- ^6�f��� & %9  -��rK���J�����5��6Z �aE1� Ջui�V_{|F}8&e��lA;��"�6u}�$ ��+����impa�h7(�n w}^t �+Af�q�vA�.$ If�9�E�I�6�^ll<s4$irFA�:��6� � V�(\6�� :��"es &^ !f�Br-iph�Er�e�D;$-A ion."�1]�"m�*mu�  0A�on�D�%.���c�.2�A8/,2��" on{A��DU09uoPs} G�H ticsZa�-wave�I�ro�+lG5$ & meNL?n*Agover� �i$al"q�e rHdQ9 Euclidean�I�K rays|e limi�o��Q "�I�?�����)� nLHborhoodA��cau$Os}, �;envelop�.XL �I3 qsy��!%-q�Ndic�&�?E,nsdin ��r M%�a�Mffracx/ effe@ redu�?ahTedC L� b�/ . EvIQ�!ic%��"� agreJ.�Hp a1pNl nd experi�is(ly good���mer mayS 2fBIR�C%5)�tir�,s]Ied outA7A^%#8on. A dramatic 3E'i ���3 of water A�E�illust�BdA%0Figures 5.6.1e� 2N#29.i��Fof cour�+farihl�, draw&N&=E i�!�ycZS�� �)Dx2u�A�(e rainbow cI��8 6.3$ �� a�OaceS:�Q�6:�$ be improvi��i.ng-<�*��S f�1{5 �# <uni� asympto!�6pof&A"A�0the Helmholtz�: ( �$3.1). WhilJol�O)se 2[s U fail�-1s�.��ulaaNr�.E d;en28by Kravtsov$^{1�-��Ludwig7}$ re�-s [Cmea�*6J}�a�;�5�013�Q$view. Rec�, MagnWi}T�Ei �Wa^6"�U-*K2, ��)F�� �-�6B,��!�A:!(�8}$k wV9)" E\nabla v9F: 4}-v�A*. v_!K2} B�Mx>MgKeN\v=v���BhH �[� 0 authors wd� A� e6c2�@U�fC&HO��o�D"�LN�Zo";p!V+q)r)  - ]� 0pp}-2pqV_{pq}9"@C,JDVDqq�L>e���d9to�6)Qk� it{L@H dre transAWŝ}F�8V_L(p,q)=xp+yq-)�FWR'+�O� mark%�e� at i���I�?t��u���V��<is well�"e%Ja�elnYN�,. I-ense;!!1x}/�E� data�X) crib� ` r&(. Morawetz'|5�F�6 e�V�Q�T:�N� mo�Qt��K��r  �+i�J a de�&�0c20,27}a�P?lly@ m@���.r��ortantrvA4main unknown. �&2nZ�� �r2Qly!I/d)�!*)�o�U� �)av�:bP,electromagne�2��pa2o| coldxsma�WthoughY��u<}7J����'EvYr �o�BQV@%�4}$ (In�.2� ѯdoB2 than� v��2�a6E:A�y �˥wuni�)ess� } n9Ze�y modulf%���d lv"�re�"�,m)1��(�+ �� �9s2%^ B��5|�%|is �I�be�e �=�Zso6of]sugge�X"�Z�E$ cI�n.|� "i<����e��cal re�eb�N(. Two ques #� 2��'s paper���`�it{i)}��D�� (18) it�<� �L!&� ( � a�generT40 �N�`� 1�1cT model). One would lik��&~>z��Z~ t� \ izūUhod�jVe nat"�[e6Q�("�?.� N� Pro�on   26�1F1G�V� E� 18�=�$t&�4�=�Bl�U�e�F �-I&�SaMY�qu&;,�D7)U�"� R surr�\ �*� ,�G�Vnot sha�.byI��Ng6uZ�;som�'U� �4eź ask� whek�E?(�e� x���Xs �6in��E����� �| sit�,9Yb&LQ.nW"+5� �)bWW=Q� A�u�SSec. �) *+36�Be".�Q��]bJK) �g .# ( p_{x}+2pqp� e �be p� �  q9=F�\B� b-qq=�&6� � ۡ%C-6 A�M�!RI* Y�PF0��� $v% 2I I%� $� }=p�� =q.$ (S!>aJalwaysIj|Y�7,�, �20)�rCon� any&-d�],ala�si���!�w� Ips*� � FS�N)ca_{11�b �8\22�R!�_#�8{.\�} x}l(� 9{c} ptq.�# O)QbN�b� �b_ �  yΠ~F��$�R ��, �&K�Mntr(�\c&�>�rg%�uon $p�Ah�b�$coordin�U6v "�?B�ja�2M$ p,qi�)${sQ� 1) iQ"�I~M[Z^�2AM-YN)��a_�Opb�xAOy)e:{��>� c} -AGQ� \\Y�1I22Sn�q΢�Q]� vi�(!�Jacob�O�h>y ;JCau�-�Y.� pU �a% Bx}Np�8yq}-�9.IB=.Zq�1i�2J2J�w>is �pe�_] 4hodograph map}A %Js�0�$yTs $�$�i M!iFO�d;}�,a! it{eHi�\ V.2.s5x � y���s t� �!Q4r�bye� Y ,�V!�-�=�Me>�V=�p}yG5�V}.�q��"�q�.:^ivixBiv2iyi\BA4@a h5�:��s�e\"�N y�Km)O���%)�� x_{cx_{�by9��b-yqJ�; �A�R�7)�1��V%f�e}=m3V�s3(Again�6Kn�b�d ]M ) A�!i�T�=!�x.ond m� K$22L$ 23) � ��$*�:; ,82y*i/. 9n8H� \�se]A^jml12� +�=�S��!0� 1J�6B�\[ �\lzu����!N�sl]�&&�AU �f~Ul\{ �qT �J �) ] \lR]l �� S(�F2NLdL�+\�4�{l�nnlA!na` �>%b�."y�><<Fq� �}�&E��s"y e 6�l 5�_jY� J�>�l&�out\ �0"�i�sc�he �e2um=ML>p �, g� Nzl para�p&�����6� UnvP� Substitu�M���ula�oscill�<yg i� u�f��.�HB�J�\De4OU-��JxM��t��>f(J��0+�bf{x}w6�V*�"���=,$\�KA� re $�d$�J;a�D! dard�!l$Rnu[~ ref�v!Vdex1�mediu�3Hu$� in&;��orN�j!��".�P{Y&vi�8 l�/�Te0��&�4ly84�� domi s �"�H�\ "+lyO ev]A�meter� pdesir�o �%y Z�,� stiff�.}^?�i,�rtx#:y24%3usu�!fr�"p_J_ expas�>12,�i��7y `�>�Xtin $k�UNZr/bi8!)��6�T�k�!� O6vex"�a��Bw)�Xs�� ]�#valid:#a���)G'k�ak.nu0?bL.<E@"�to) �3BP-8� Al�. ��U_{] �� =�%� \{ Zm�a� /3}u�ks{)A m_{j=0}^{ja}W_{j"m�r�\cdot��ikP ^{-j$�n i}{k0d$3}}% Z^{\p�#hB(��X�� �\�c!$times \exp � [ ikJ8 7]*_ $u-Sݹ�J>=N�br&�5$) �( ��dA�"�m7d�qIsg�,iV3�le d�mi�"1` o;[ $Z(Mia#A�Avq� AiryՃ�/9�:�t�- tQ��8]�qka��2!� Z(0) 3^{-A�}�H-�2/3d%�� �}D�E1A�:E1E�=���Vk\;jR!�O1�is�el ��i�follow�?!S���?E v:8[[ Qhu �sy ��1 �#� #+1-fRJ, K-� ]7;"�tO�0�?U}�) �anU nume�&:d=0y~|Jq#2}=1;.�%��|A�~*�#A!~third ��4��atb (I,Gied/bv�Zl�> Baltern�O B*B �ingm�([s �$"�|18�(x Izize�z517)Bf:Z A�mP)y}G�9a�%�6  emblAnw5)-(7):FN.�F��ga6Q�}i!ߚ�g\B g(L,g_�M� )�M���]u-8km�._�GB&�M02�FH��bse>�e�B� n= ���[ f '�-? -] �NȀN92`�y�9���bV�&R�chV�.r��BŀBforF4J�))b}.K�Ta@6�A4Jc �ne �] u y�i/ (2a28�Zco��a�.Rv�JoF� . Ifa�6 , Qz1}=E�=b8!?}=V�j^6M!�V_��{P- $� ];�V�_�UA "[[�r{-o �X.��9O�sI^� ^o+��!Q;- $�7u���.*�j}f�i42emY ]�Z�~]i�~.Vf2&nqWe�.v�EQbis.-/�-~ o<2OggAھ}�&Vg%].gc�1/� AR>6AyS>�Ci�1 annulu�OPU�"�u&r,�r�*r"�; $0 <[t�;2\pi,$8�-�+FlO!d� >����:&Nr:N �.+N=� bf{N��AY$!�Zu_1=�u_2ɪ),�@�#X=(0,0R�"OZ�6%�aHa\-8-�7%�&�B\,"1ZPv@8WRK �N�/��!rB͋V�7r6�bc{72�.2�Y1;cD� sHM � w.6$Q= 2B{G-A_r^1-A-��@>s�a�C,�&� t'an .J�C��x�C�u�%a� �,,i�3*p*q{2�w�&qF~ �1s5G.�;�I� �r}=`FmBemplo�D*�_E$udeE,"v 2.2.q{}dM%�Er�a & c�1-r" ?I�c & T\I*>�� �a=ay$�c=c2g�t^�Ss/bn։�arl6%��0�MVr2�=�7�Z�24Ea�.�C;;i�b�BH-.HSov&EtereFI,�IaA/� �lA��<30"�/� Z EL=E��u}_r+E(�I{+E63!.NQF��?A^.$A^!@B@G�+&$H (3�� (32),A�fin$�Q� >�Sut_! af�b e $0�.d r��q R�:ufc$ 1h:j��a=Me^{.L2)'��IP\�f.�f_1�!c}6A!="M� 1�K��$M>>c�?��solve�33�H�.aX�_5&�J6]G0)- ��&> �}�be patch>5$n&? 7)6�BH� � $a!� rR.$) D1�b�8���Aouter&�*�.. A�ar� x:�+al�n&9e�9me�+�KS'AtudpB";�ch�?iH17A��is� �8{� orig�E�!� exclud3!U�0U�.7me histo �� est�� �2era�3M�% ���6./M,waBec�.kelf�2�_! ied,*�/75 yeaaNgo,�iBatema"�79f� ). T� >  arose �%)o9<L�M' w� toroidal * .$��A�=~,� rais"h�K�.\��+�NG*c0%� �v�aM\��!{Z*�lfI%E�u �S}1w T�3 inneF3&],�41X�2���,��M*�m�?�*HO}�-�!s-�8�~n2e~I�*�=[%�/�!�\�=,aKJ�3.1 biZk3"�FEMs ��e_�i��J�� \tau(��)4�\sigma2=0ml, m\��)>9�1rFu�/Ai.��$r=��&�F��"�5>Enu2��3�F&� �F *�F5)>Bk�Pr@k2��(�KenRIk� simi�Wk1�e by T~2��0�KR-*�p�Psse��A�h�5b�>d����L� � 22pU�4A�:)G *)Gt| ".manifesF7(~ large $M$�HH �a�$ �a dem�releEJ�� &fG.��6&, �Y n}_{$ }=dr�he�#/ChV� � &� -a N� � C& �.b^-}"�_\q,+i$��f^j ,) c 0� ^2cm�"� - e� a 6h ^2e�7�b�N8^+�� � ~ ���Htau^2c." � ���^ �5 a.6v�Nb?na3a] ^+}+2-} XM3{ �4�D ^-}Q{�Fl�s4) &w�Fu\�(�/ ġX$���le.�.$�:�WmiX�T� }^2-�"�a-2  A5 .%b-`.c2.1�j_c+._%�j. a 2ab�,(!gk� 1*^�Y �҃j�F/��n9���\Bu� �?Ui�-"�l, � $)�^2�,$v#� !����� 2�#������$n.V 9%K��g~ �(.� 0* '#dr�:T2@��-\v&�BlE�b�B��^-�O%�V��=� be�& a+�O�O r&I�\pphJ $M$ J��:\-}.W"Q�V�U.1�5$5F ] -�bXI3� R{A�Mark���nolog ���,} Hodge$^8$" *֌_0 $p$-� $\o�5 hFzif�@�%"� �x-�%"� J�d U=w �6�g d:\L]+pJ�3+1`�'eu rior#t�� r.P+1^RP%�+]�%d.$ \ I< [��s1i  �(�9I� 1)_�7b*Z)j=pdx+qdy�S-�7q�(� c& :��I%�9� (35�R� !�( Cauchy-Ri &�s�A)> -q.$*~�� $d����b�&�=mf�Qs5O1� Z "� Z/}m�  G;;a a�; face' # te.�$%B A)�� 2�0%��"?��Iisc&�HQlLFn��eir���ayJ�a� eL3�2MW dard� �Auv extit{u�a�}.Y a��#a6���:a�E~.�!�L�d�J�^�v�� dmH+ dy��gm%��AŶit{�"m } (ei�<n or%��@LD�yqJlh�f�O ), \I�d&%I5%��E�se*1.E�&i�;. *�l�z ingu"�nmaU5ba%�� �&}#a�N��3}?, wordié�A���s�C։la Y=5e��� V�ed} ($�}0$�^I�co�� $-։� *e�!VY�iK�\�*I%�� �E{%�g��che% fals .# i��56 �(�$LDUne ���L�ne d.$6:E $ in��pfaę��1�]_e�,�� �v5��@D)a��L�|^�,��asz1$"�v%�a"�~�Bs 1E�EA"� �,alF.��#F� ������B-��BP �L�(L��BunlessP�>����>�AcP. ledgR A� am { eful�eXnonym�Qre��>" help$c�Vcis,�,arlier draft)_i�C . "�RLnce� $^1$�, H., ``GW@�i"�&�Q�oN�"�utw6�>mo�/�a� ̐b�e luid%@�H*� varie�al�YE s,''mn�r .\ R.\ So (London Ser.&D A}zPTbf{125}, 598-618 (1929�#*�no�nt X=sarxD."� }, D^0<, New York, 1944^ 9�c3$�d, E%i Saggio di���zi�* ella" SaN-eLS9GioGeBM�tiche9@6}, 284-312, 1868b�4$B�0L., �Ma&+1 Av;���3� T�KLGas Dynamics,} Wiley65f~5$Cou_ , R.Y D. ����$2�Ph� s, Vol. 2|-In�1ciA�6�6AQV�6$Dencke!�%�W�2�I΃ola"1Fset� ��2A�incip�2��U�J.\ Fu��$al Analysi��8bf{46}, 351-372A�82f�7$Fried˝s, K. O�S��+<I+ R�}i0Commun.\ Pure�{.\A^ h.} �7?333-4iY58f�8$H< , W. V. D�AJDI���� �als�2�T�aly@K�6 etie‰+ �! ��5y3!b257-303!b3�V(9$Hua, L. K�.hWtۃGp�-j_in:m[�ee<E-�� 1980 BeijQSy�^H5on6~ |�Z�, (S. S. Chero4Wu Wen-ts\"{u}�N$ds.), Gordhd Breach}(D 1982, pp.\ 627-65f�({10}$Ji, X-�B�D-Q.Chen�P_N'�N��a�3n*=*"� a`mix�ˤi�eM"��pS� ,'' �R bR6Y�R :R �R!�-R 1A| 1271b�adJT!�)Uhe�O9Y!XANno.�+j[-r6_ 1_]�M%�T!��l (J. M. Rassias, ed.), Teubn�ALeipzig�6MJ280-300j�2}$�T, Yu. AeuA2if�XA$>*{W�V� '' [S0tan]4it{Radiofizika�� 7} 664-67� 6j {13F�E��I. Orlov&�AC�L, Cataphed8d W~\F� �ZSp�(er-Verlag, .V99j2H4}$Ladyzhenskaya, O)6a�8N.N. Ural'tseva�#�Ling�"Qu&]HEl# =�,, Academic P� 6�jRzrLax, P��mReHPhiis�LI"�r��d�rp�"��� .�"�m�Cf�V% @3}, 427-455 (1960f�{�wLin, C��a�y i�L�G embed�� $R^3��B 8�E�ob��GaI� curvxNe=$,sign cleanly&Qj���(39} 867-887��86n�7}$=X,��J�=&�: at a cI���itn�9�9}, No�  215-250�6r�8}$"�P3 pG.�P!�A� ach!7a]��Q.4J�!-&�! ���n � it{I" RA�In�< Pre�.� Kabanik|O(0V. G. Romanov�/(s., VSP 200� 263-276j�9}$ V]�A6ZSe=/'s[��\ �{n� �NR w .=�1� 15-331!�5j {20R�a@D"��"% ��95�E\��N�� �(23}, 587-60�7n�21�ita, S" "o of2n L}%�Aj&f lS�iety,A� nce,!�j�022}$Nye, J. F�mCN�al Focu^&EI�Fine S!� of L*?} Ins"A�%  Pu%��7Brr&l� nY�� Otway, T.� 5�� ��nB9�Annali!�N a edQ ��e�䡄8AJ43��2 (aj�24}B�A�A�2JNW�sma d�2� App&� i�bf{�17-33WH03n�5F�MapGSd����com"  de�a�Rendi� Semv .\ Univ!A adov.6a� 133-159�n�26F�M�i`/� "across a.��&s �Develop� !�yM{0 Research} (C Bent�x0  Nova S�Q��aW 2004,� 27-n� ZZPayne R�  ior *FXo�*�:{[ U���{�� \ AnaA8E?Y819��271-29�9��V\${28}$Still�Ya�, g-�y�Su�s' *�  1992f129bo� J. Jbay it{W3c� [%(R157f_&#&ōG%r��"&-r7&Ո$(��B�-E.o)nEO*�444}, 6223-6232en� 31}$�O,�a``Sull��tiV i �3�zi��di�o pQe,tipo m�P#I"}� Atti]l' AcH a Nqa�,ei Lincei,} �\ 5� bf{1�134-24� 2r�2}$VeblO J. W. Youz= �P"F Qa}, Gin)Co., Bose�191�+ docua�} �\;h{�Lcle} \usepackage{ams�,amssymbcd� h�gt230mm� width168oddsidemargin-5#�Z> head H8p<#new�em{Th}=q���S enew6}and�6\�Hic{ }.Th}} .MLe}{Lemm0BK:BKLe:K,Co}{Corollar� ?n = h��uad2u={n,\?=:=v�-p n + 2pn 6m++��w�#k?n=͍nX�n��M�$ �u-u_n(!S^4 $u$,6n;���%7"�,BE$-�%/; ��)�.^31&ѳb�.i��($last decad�%Q;berA�� eShi��re�e9re2�la�1e)0�V stig@nE5[Ch.6]A 2}ai��-(aw I!+^$�z,%�uW-��edga�nd�9 ners��power� 0-logarithmic)�:mijt �)� #) n��+an(NB�)���. 2~s (T 4 F�)� �QD�zae�k0� ``*x""�UsB� A�,mps}).&�/�m�jg�l1�� �A(�Y$(i)--(iv)  i�xEu�of-5ed.� ``&�!ou�JN5ke� � ��!�2@ �� tM�-AqeI hand�>�[+%p��>T�#!_|,x.��s))��\M"qxw]�O Y�in&[�s�c)��=�)��EDA��-!V�2XM� R&U9^� R�� )[nonZA�<u6sp}� �x� 3 a�4)[cer [Z���� ��!j2�c*${\cal K,�it� B3Gͦ$_1,\ldots, n�-is$M M_n$. S+ 3 de"l'�&5A�9�$(u,p�W_{v:,\8�2U ,s}(�)^3"X F)12) !h&�0:���f �RFJ02J^3z gV+:u$2ws$h� � w tC'c ?s$�A�trace�ڈ U��$l\ge 0L�;�{\Bbb RZ310=()=9� n��1^ p+ $1:a#a"kj$ ~e6Wlyi�@se)~��u�n�ly b� for 6�2{ ��pre^W�Q>{mr-03a,}.�3u�:Ma�Dque��&�Z�eKg�ҕ�E�u3y ���atiX"�.>!2r3:!�Re%��c= 2�� -3/s%��of eigenŨ�ax>� ��x frak A}( Z)m��`0x(2-\mu_k,0)6D?�<e%EA$| "�I.�Z�!;�VB��7���c� <\pi�� hile�f��9dŚ�J5�g"� u=n(\muX)+ sin�irStm�_k>y. E"�Ѷ=�gf b�f*t1I�� (9,kmr2,kms,� 6 ���_ 42%6u�U�Ee9j i.e.�i.�kj�6<�ڂ�$qT�-�eqn3O*} && 2(���^Ym_{i,j�Y36i,j��Nv&D> vdxJC�Xͪ Rp0e�4v\, dx = F(v) ��q!�� }v\i��W_{i�,��^!'2�$,\ S_j v=0�� on }|j,~D&ˋ��g�� in }3�S_ju=h_jTaz.U j}�'=WH� $E =u$bas46Qy��d�^ _j$,@ u=�>E� (ii=Fr2���y�f(iii). X����i��6�� sa��UΥ� $h_jU^�������1)�~��z��}\max(1Z�1$ A|6�.f%�$s=��ql�9Pb replac@e $-\m��_k,1) �D0�&4�we� *$:�v2a:�let � W_{0, d1,22+  L_2&�ΔBa ��5�:��� Fr(^s*��cap")�j�.,\ \ a�in6� I~� ,a� h_j��.- /2! �)���FO1-1/s� ,,� $s'=s/(s-1)A�Y6R�Qo +2/s`�� $=SS e nof� ${Vc�=I�p $-1/2kJ�A].8 �I�XJX+>S"ף&{d al $�=@Aw�>EI� "��; G} f22+ŝ!��^nj hi_j.*!�E� $fAHF�l->*�qs _j^2F� e 2E�P�, ^l-���oB �H�J�lB�)խ�g���Ah �$ s��P 2���6�ј� !�7"M�(9i.i˸��nlZnl$��7E� ~�l�;n�~�4�6�jl )ιMe*$ 5��n�VQa~A (\ref,bUa A&=��GO:� . Un�}~ �**۬?��R.[� �UG&b��G���iQ� up&a toc�h9�" . U�%�of 04,!\6r;is"� �RE#& .�A�2fo&� ��)�R,oѠth)��"4 =0$�oml�a���K&�U�� ("r� )g�rat���(!�"K%�&>/G}�o'��sł3�/.�{�J:J��"&zA5. I-U�on.��gqBxE�� is )? true%3B $s>2ur�~ more5 �J $W^{�$-*w Nho 5-6 .~!$� L BGji2t��N�yj5�K%w \ 1�h!| ( �� o ��s m��be.�C~G���i�B Z= Z2M@*Mb+":" \l�"� g} *G} �_ja�a k Nr (i_j�N, \, |g(x)|^2�<�ftK� ui jF$jD�yROd*� >Y$ObO @V!Hp$Nb�e7�-k�OcMv�R(ar{M}_k\ni l.��!�:onC�=��]�s w2Klso�I��l:�j SWg�B4�&$.���+]�ed�N�*�a`|Fs.9e uz�$?"5� 2Z��AG"t+sh We�umeWI!)�!���D!�"n$at leu}�MG�����Me ��!,):Z��:��A� �:Gtixj21 $ ber�^t���:5�9$U) �l"�4 Z', � =�2�"�'8/0>�# very%n^��' ��)j- >j)��is.��/�gV�!�n �� �6La+Y� p�'a%QZ�EMY�� E��mZ m J�. S"�a�吁�%���!a:&E��H�; �  ^�t���v)�Q�2B���� �V)$1�!k.�� F�. vܑ1 i��n��� 5�Ja!�th��ngc%��On�O��"@1-H�.!�no�� 6.�,6*�.�}{0�."�.ThBO3:&3 �{WV�!�0\� v' a di�1���D����0 &�==��dih} 78@{ x=(x',x_3):\ x'A K,\ x_3E?�\�c6�,KI��`f�u� �  P!{� $p$'=(x_1,x_2e1a^2:\ 0���U���1-2/s7�th � s0j �h.�2�s- d$. ConZ�tly�)�a" $F�t"_WiEL*to �"�-1�"- ��e�� ! ��  >l��nM +>���t ^��0 r .S6���J�R%�).$> $o2k&X�z�Z�*ivR��6k)��B_e.ndB�K)$��a4si�-$\r{�SaegO'd>y56)&2�N%,K� �T�a� �o�>j:}kor<~in.#{����X*L$AQ�m�^�1� &b� \Left�za��M& {x'}"P&(xW20�m�$I Tm���<.�"= � f�{�-� �O!�iWsi&v�$��`ecess�a�&$_�S"�s {!��%#)}6RQ -2} $&=>C  9(%!1=.�\�s��}�2)}V5:�+3.qY9.�5k}()ob92f9�+j9r^j u(r� R:9 !�M4&}j�+�+f� �+%B+t*X�X-1B8r^2�}5$]Ar� _3QH8 \] are satisfi�Ced. \end{Le} We introduce the following extension operator $E$ mappX$W^{l-\delta-2/s,s}(M)$Oo $W_ ^{l({\cal D})$ G�e-1/p,p}(\Gamma^\pm)$. \begin{equation} \label{a1} (Ef)(x) = \chi(r)\, \int_{\Bbb R} f(x_3+tr)\, \psi(t dt, �V� where $r=|x'|$, $\chi$ is a smooth funct%�n $(0,\infty)$ with support in $[0,1]$ ^$l to 1 in 3Hfrac 12)$, and $\psnf{\ �Nd -1,+f(satisfying !�condi!* \[ \2 m(t), = 1, \quad 6&t^j \,:-�0 \ \mbox{ for }j=1,2,\ldots,l. \] SincM91)D$Ef$ depends only !;r$ �Lx_3$, it can be also� sidered a!|L onE�0half-planes $M*+ Q -$. For/Y�4lemma we refer!�4\cite{mr-88}. QiLeYc l2} Let $A�f1�%�%� j<.w m�m0 Moreover, if)�isbb%�q�$,!?nA��,'}^\alpha EfA4 V_{)}�| |:��$1\le " l$. In ^cularq( trace of $=.y$�(M$ vanishesa`2$. I��MA\pmFr%� � ��j-1��<)$ �a$q"-1�˵l�f\in W=C2:K+�&$ k< 1-2/2�a�%+s of $fQ�%OQOf$a5!,Hexist. Obviously, $:{Vw(f|_M)$E�}Kresult�rlime�se�=�s!�Bs fromio@[Le.7, Rem.4]{r92^z3})%!q!&R}^N%�N�=0-!J�� L0^\varepsilon r^{-1}�� big|:=(r,x_3)^s\, drx_3 A�c�%(| f\|^s_{W_j�}� a @arbitrary positiv!3�2$��!T 2.1]��0bQ4)Q6� ^j u%bVU�26�, $1����2E mB >2���h n $u2�1R�TCo} {\it Proof:} By L�R \ref{al4}Y inclus&Jk si�^:j =.�p.< �Au2$ impli��O���BydFurthermore, by our assump��s�28nablaU-�a2~^3$E�Ua�%refo$VJZ�^3�l�b�@,. \rule{1ex}( \\ \subse� \{Weighted Sobolev spaces� a��e} ����K}寡F coneQ��9 d } 4�{ x!�� $^3:\ x/|x|eF\Omega\}Z] U domai�u�unit sp� $of polygon? ype ...� denote!� �S}$?s� M_1\cup\c�  M_nH\{ 0\}$ of all sing�s bound��ints. 2+a�an2�int $-� K}$ we.�(\rho(x)=|x| �dista o�vertex�1E�$r_j(x)$�R>4$edge $M_j$7 by $r.Dre� ized2:9#, i.e.�a�E$multi-india=$ a $. H c_1,c_2,c z$ are�� con!�tav� ent!�$x� H lex a nonnega�i1 �� beta._�~�.=( _1S n).1 ^n$,��_j>��E�.� nMF�%� $. WA�fine $�T� d� ��K�and�{~'sE/wZ�8APnorms��Lnarray*} && \| u\|_{~�}= \Big(��t_I�$K} \sum_{|)�E8l}AYx|^{s(�-l+ )} \ & Uuu 4\prod_{j=1}^n  (\�{i�}{|x|^�)` _j2cF #1/s},��� n~��F�� J� ��Kj�}{\rho}!��F� � e9� resp�� vely:mw;V~not=. 7 d�@,real number,�3n]�dV� $5ZN"�[A�above " d�NE�u�dq�d" I� %�j��j �a2�yn!de�B^+F�=� y'F�, �'�+� =_n+� Pas�!"�i��coordin�� ����,\o��=0$, one obtaini�&}(equivalent a��c:�F�:�^�{Y�0^�� A�eha0-l)+2q�0k=0}^l \| ('�J )^k u,-)"� ) �-k���)e^, d= q�a� ,� u A;2�ELJE�given by �v��!N1y��\lns_{� tack{��(\\ 1<|x|<2}1���1��a�| 5 ��v(x"� :�r_j^{f�!(� !� $v�)A�Fded�q=v�(A  )$Avth�Me*�). r Hardy'�a� litye8i�y�+1M�e+1. tinuo  imbed� intoD B>� I)�=f���ur'>�'_n)$ B such that�\_j ~'��-E '_jl_j�1N�. This - _, und�he��. W a�� '1re;:)0nu�NpQ�)�b� A�a� �1Z)$. :we have �� �B< =�_=�_j>�� 6 .* \zeta_k� :s��"���$9�&�:�[k} � 9�< q50 (2^{k-1},+1}),  m_{k=-� }^{+ �[ _k=1 -|��\G �)� ')�c_j� � ��&� $c_j�d�� kQ.rho!�"�@easily shown (cf.&6.1�kmr1})E�EZ��F�.�V!oIL�*:R~�$ (@ J,B�$)��A�Nk$s�Z_k < �. U 2�3},��� N&� rZJ5J\��Va ���l*� adjac�f8���let $"C6X:IaY� ��. R f|_{M_k}F>&i >{*� t} t&} 1} \,>U&k t f(r,t"f , St <� ftyL �R$sufficient�Bm�{>0"�r=�:\em� }\,(x,M_k�u $t{ )a� A $M_k2�&�}:�\=���+ k {ᗁ�\tilde{1}_k� _k(2^k x!�!�'f}% = f r,&tEBB���X s "�E�! Zv �  $1/2 <<2�:��I�s�� !�{1/2}^2!�t_0B�^?t - �� @dBt�&le @ - �f}^w>�� �,��2A��z�= � (s-1>m-1}/^E$}vD�j-.<20}&>�J%JN !�2^{-k2)-3k}e�\| !�_k�ZB��*.� Yn!,�6bwfIAt!c*�t���] Summ up h E�  u�Fa�">�� ^F�� Kse�"C(�dt2 :� desiZ"i"@. :[0 \setcounterN{ }{0}2ThBLeBCo���"t,value proble%(a dihedron}�{ i�a^5�,! 0Stokes system��: each�`K��� �B�!S?$(s (i)--(iv)��. �n?=(n_1 ,n_20)$ b$� rior%�a%��*�3&�_P (u)=(u�$? _{nn}J:5J� >:il*d=9�,3 be Q�\0s characterizA�^,�$-[B�$>h We pu"$itemize} \  $S� u = ��x%!�}��J.-(u�)%;�%NU,(u,p)= -p+2 ZM�'tUs1,$Js\j)gpi j.e�(ub-.=�\, KJ�$ �2�g f-p[ +2.W (u) FM L3$�!u%�ur2�2�>e�5�(b1�-\D) u + �p = f- - )9!�g=p in }D"Yh!� G%-g \phi2� on }M�\pm. �b2"�$};�u� ._^G abs� i� c�#)Oy# whil:K Q�=�zE3�e Diricha��A�2�Q !�mixed(�?�(i� y�1��� (i6! -$ w�studi�\Maz'ya, Plamenevski\u{i}� Stupelis U( ps}.�&contras/{Ř will use =^$��6�A+�4nonhomogeneous�rs.��w�x Redu M .-J�} �z$r$3a,mr-03V�%bl1� E *m$:�A�)^{3-EU[ U�i9.�1! .|'^{<M� TheE�re�a vector"Y $&�#�q�)�"*�m�Qց/-^3�k7  | -T| 7-61T�+� 5Y>NY6B)Xl�el^#sta"cF���%���)f V�)e�$�->1$��$u$.,chosen&m $uy0  =} w&Now���AP&V&:� !�n�qq�v�IgE�o�U] O<�&ber U�s �*A:��Ow!�to answ�quA\on��"��u &]"| �>�&^3 �p6>:�9��.H Չ3} mE =I�.���Q�\ aN���: a�}\ 6^+ g��9�6�M '}��%>r*b$-X&immediaE$�*�� !�j.�*obl1^&j.E�:.v�A>l-�< ��, �aE ZN# S�0s��h"� h�s�$y� compatibi{YNb�1b�yD( h^+|_M\, ,\, h^- big)� R(T)B��F0�E� range� &�2$T=(S^+,S^-E੩� Z07s$-R�2 ^3$)�,�<y�r<N�E. � E2�&�:}*�%a)r��1a^�}� �2��|_M$.� v%�j���an� 04f }��86�� s!� � v|_{&� }-)� zero��. and,%�equ2,�RA���r.$ (see.�(al1}). Appl��:� (2 l�B �-3�mp78a!�we.Kasser����JB��*N*��� I�&�6writte�(��r*� >� 4} Ai� = Bi�d(^�AM�B)�cer# matrF(�38example, $A=B=I)�C o DB� `($d^+=d^-=0$), $A=(n^-)^t|-z-x , $B!k� 40 �<2�"re����s�1V� A� ��-2/"[4��q )  ig�i�(�r�, o�2$q�16��^e= %""�^3 O mes #6;� +Iz b3})��[ b=u���T c=2u21}u�4 �d6!2!@�"+ q=p _~6�G�pA���s�L"� >� i�2f.iO�|=`�)��6��R*g/�.�h"�5a(�b� � ))b)�+( c\cos)$z)H\theta 2$}\pm d\sinZ�k= 9�M9-�. �";6�/�+ � �B>ifE�"ii�E�a�0 M+g)H*�5, �-9?>�6}q-+d_2+5�=7!K-g)H� > *�4A�Ieu3�8�5�8lineary m $M (c,d,:�,q)�us,I�_"� h];>�f�7} n|cZY*�8bh52E� doesn't�? a pair �8\not=(0�v!�a1:P, $u=cx_1+dx_�32,p�?�E�q�u-1�B40" 22�&mYu =0,\ \*%�=7:Q�Q.�LA(-�X e��5b}�rb7})} hE)(unique solu�� $E(q8a�5� ,��,��2 $bZ� }: Inng F\$p=q=� t.�]to �%B),&ibl2%l c_1 a]!>�����>�~�~S� �0��Y�0,q)=0B�B� &�4A{%��5 2�-�)��)271�Qjs2( 7 unknowns%Dž�^trivial=�c=d�$$q=0$. Con&w 3i2�2�B5XI1�olv�2R� 9lG� togea��� s�61�E�e<�ows us"��!bl4.��> "> �55.< �:4d���2  4})}) j ��� aE� e ad� allA�a�'�7A�T �o%�a�}�+�iedF�R�z� 5 .{$�j� V��� ��� �i{ I�aO�75��|_{&` >� }�p6&6o�+*�\2\pm6>v� }+�(\pmJ|�� E�$ �g 7I^>��)� '2�&�}:b�&A+!W���,:�EN�b��hMX2}� �� J^$be��= +a{3 M)^�A,$c,d\in W^{1N"E$$q EF#.Q<5a6d.\ $v = Eb + x~7Ec 2\, Ed  p=Eq*�0$E~!1��per�DI�a��,s)%:)+�J,A��Z |_{Mz! w.b -wd f{ 8 -(\w; 6 = &� ]!��(N^{\pm}(v,p[ =�AF� �+{" ]:�b:�<1�]%q �v - �W& vT �2�vF A D6�'>*� � -�:��\N� ]O=�a�CNLw:e>��wJ^&69Iw�  -M#v� (w,0.� - �.� &K �M"� *� =(v+w,p)$�a #pra ties�c�i�()�g Dproved analogously*�#relPs betwe�s�=$9�6'�$�: �"� M=BJ�#0HRem�� r2} �OH "�@23}� ����d^+ +H%�b 2w j�+ d^-E,\{1,5\���\,  :C.�?dtvHn even�"E�r�fails� 4*tqd"�dz3b�Hg `o!D� � 1��&�"V � .�of odd :m_"G(=(x_1,-x_2,L1ws�� dQ�seE�s�8. (o2�4} holmH�3&r ^�f*. ��aՑeM�g$.C!Ab�%A��e?or>0�Ing-!�&�b{?5��I�2�9-��5y!Ry� �z> %�*x^� */=,Mn�@Q�� J  $I�eO\pi%uE�2 r=-� u�1b!&n^-�:�ru + n^+2��c :Oh_3��$a� �,� � e%� �.2"�! rali�@t5�"�/+6e.ZB_,�0Big| Z�(�F ^� -� b >598rel{\circ}{g}\!'9=U% ?6�^Gx_3 :r Q?! ��gDedzbeI%idN@�n�= � 1)y�R t_{- /2}^{ g(r�U&phi,r%�va �GPd �d*MaveraO$ghMa�ec�#a�var#B�(phiJ" �LF:�1 *d*IC� .\b�a6O +>�6qbZ &�u��GI����e�>~L!@`MY2� Dre�n:s5 !��F ���VA1F�a�Lb�a�>�; M :d c� _2 =d "M_3}�� -2� A* �2p&HJ�.�N8� $v=E [+� +x�  i���Bs $��E&$ %W2<� ��b� $. ^���*YV�# 2. =;.^ i 2�W.> H"��";r1� `a�ula�r��^��� �p\3T0&of cour!e2w)���E�@ʼn)7 A bmPplacedb ano�ZF!�:C2���G}�&� r� ,B�q� must���j>:�:tb�""$b,�qO&��L"�* �Neumann!��.&�3$)�E����.�b9  data � ��-$ �<5u5�G&�W�k >n^+&�Ra MW I�  �*� = M �>#,�&-Y�gR�RR#s!�#% G ���r�\6S  - (2�os-T,-�.;- + 2�-^� ,� hi_1! os A/2�2^+0x�� 2 (gJC usi"5 =0�o)N�7S Y a�>�*�Ityq�} ��d two��:�=in([Leu!,4]�*2}e�bMK�&�1( elliptic�eqA~fj}� f!��(h]6�,is esp-i,e sameZ' 6��w {loc5, \barz(\backslash �\t��( 0-�b2�1aa���L�2d� b3 2})}F�1 �7e(et:��K��Ect >@ort�= $.�2F ` "n}J�Iborhood�$C9N%� @8"�6# lUV -l�Ps*�O-p�-+1B/�!Zf6-!�-�1�.Z� 2�2�X� J\1B�T2{-%�a��ND FV#�(�#n�9 uA�5�2�-A!� �2+I�5�&�  1ba\| M�a-- +vnx} &A7&28 ~|%2�@�--�R%&/p an-N'} �!�f61!BB+`�`/6-} \no�4\\ �K�&3.{MN.� PjN���G9]XFNMX2� 2�."$-��Sem 2)} :�"�--l+k}^{�HU@Mm�i�B/%+ 2A�0i�0%z�6-6�J�:/jc$� �2�:D-Yv�k+1�Ba�� >l-k�$�6�2bB��� a�6+>�s�_Q "_N ���Qe�t!�M @We@L�P��$$A(\lambda�/!�%L H "U(+) , P �% �2- W}("�5&�5R,\, -r^� �}.�uY) �O>$u+�=�" /2��5314#��^6&. u=r^ r�A�p=r^{ -1}9 ���CA}$r, �$�I�polar2;M�)pIT' x_2)9%eZ�sGs ��rat�ML^faramete�&)dIIrezs �2�J�`!��A�($-\�P)f 2 ,+2$})). ��<��to��uL^{s}bsB�r� 1�^� � � every 1���%�M > 3�5�< escr* o�!�SFrum5�encil6�isgor "�UP -)�Z �;orRUs]&Q� &X0$)�Rz F"z>�2-S%is_ �(�%� AQ� �iIG�ax(���^2p -2^2>4a�=0e�1��+ !-.�,\ d^+=EH�eigen�:�.�u�nonR/���(L)*(2m�1 �Sf�-&��n"w.��˦�>v,6�2�%�B2 �%����2�>cos^a�!.V1ٹ$g+�E�E!3�  2R7+� ��~ sm2�dU :U witJ} "S ��k �letJ2U� ofu�*Be��d� � &5>�,��C" s�a��"+ +�VX.�3��" ' ��=^.j:=pU.b?:~A 5l"� � ?H>8q& ' +1�H.^we�um% at5)fJ�:�2��j�)/%-5 B�+� 6� 3<BV� -(J �:�ht6aGno>Ja�R��strip $l*�$� 5s Re� ���-�!�4  Q��+6j� J�2Z"Zd ��Dj�DS�*i�7�VC}a� y�Dayz�_� L}) *{Xin Se�>1.2N4v�*`en$�< $d-O�De��s $�C�[��XE!�V��8e^!�bel{d��A�f�,&�.K},lS_jh_j3\� N_j� =E�_j2%��_j,\ . "�AdZ�A$S!%is* hi��=u�f }d_j�� _n=uJ n2+ ,2 �S�0=u_\tau=u-u_n:.-1:]� s $N�a�d Z�5�Dn �e_{n,n}�C0�101K:4� 7��)�f �M9�-pn:bDNp3�q�:cI%�0B%"��)ށ��r1 @jappk2inmd2�/��O^i_D,%�u=hR@] _j,YiF� Bt!*AdD*HhA�^=�Q[_j+ ���6�O&X7�_j�A ;���W%�'J�"�AB��?KU&�'%S -TI=�A!j�q|p 1$ �-1%+\�,�:�:�:�,A�0l_`��$.:L�.63-!8} +P_M hi_jb?JA?�B*? Zsf�A!/%E)�2�&�,:.� �RbeF� ��1%�rh�rX2)�e�2�_�qX�qX�qX�A]Z $h_{k,j}(q9"Q\, h_j(2�Q5.0$ :7�z:-s&)e�B�y]\A 1�5>E6&36l,B}+ F'"v!�Vh:A*� �� v_k=-e��zv_ku�%7$y�6`f�83I[|l"�:�:�u�o0q�aiZ�0 �b�.� �!N��bCr�B�&e�v�S&dE|1�4-^|x|>4�T�O!Ge "aD $u CJfQ}xAse@"%� u_k="WZ�E ��)��Y��N%hg.�2O\2I �+2}> =*v#�%�!;_k�m<�instea_-�-""%�%'r� _"�Hs iBg\U FP6[!p$u=�;!Ex4�/%W��on��v�6l��� �A�)��o!�"�Q6�Q�\ $~-(J'B��'sIR*Cgu�.ah� ��"}�\*Pc�fNM^a�-�8^2�n�}e�^�\�iWh=-�]] 5Z�B2�B��(�f.�^h �^]�^B]/yBAA?�/�!� �L6\�K4iiOlm!idB�- n%!�"� data. D�)�M�� {k_+ue� {k_-}| �R�g�lZb}��,inner angle 4GMY ��v �O#_k~-[; td^�u$-#a�=s}0*�Remark=6�2)h��$%E�7I<]&�ly to._�j.N�dcI� & J}B!V� J;&� 1n ��&6�*�a�, �EyU�ɳ�cLzn$R�0"a%8IB�J. #1&is (iedp 6p�� V�q�B1�*1&L2�;$dI� +  �p��dda�Ym� not.N{q9+C=,v �{� cos<4_kNL �.M\in�4�T:9 a>�-&N>96��-��a"� A<>9: -��-�2Za`��1Eم��(�!&�I j���^�2�8�UgRW 6��(� �� %��J~B� f$ a$F.6{�#A��\ 1  |} \A=>n:��%u�N��6�:3��3���U�4���!.l6��aT.����ف�A}.F��I)�6�J}sz��t��2�.�w�.A�n� 3} n�-}32�2+}�#}d + ++^+-+=���$�2>"St( [ te_kd4� 'J� ^ e i1 e�Dt�%Z a, F|dzd�$t6�Q&CqE..�@�kA<�Fs=a"m3�ϡ{M�iJY7A:JX7F�crFat7!�1�5`rI�+�d�))-�>(- ( -� Z�6tK*�7t 1�.e9�N��^�7"dd��7�6J$!�a ssfp�~G�f��ss��}$� 8 Wed -KE'?K"�)%�vQ7s7&tQ0R�8t&T3a��7� ��7{A9:� per��y�\( ���Ex%C5}�Q>8 Vq�JG >2�&��j .��m6�5u+FA>62w. O�B�smWH}b83"uA$ї}�<"�%Y&� �V0${\mathfrak A7 A_j$. R1) � �{MT�!�ATs Lnj�{lH"��J IrG��DQ�s:�1�F�c�vD}�"%!�5M5J���^\o;� p�>�P�R�}"+�-*� "4BSZ�4P�r*B. ��)By  (� Xe.x:�9�d b�P6 7_3 thisQ3.6��)��)_1^{(k)}�. !&�$)�� est ��real l3A ki(�d�`:'_2_��^[RDgreater than 1. Fi�I�8�b�defmu�ru_k!�left\{ � �{}{ll}� 2="1 [0 mbox���M� 9�f}\. �� \F4F f }  ;�$ge \pi/m_k�RQ6�-I2��k<i�")\r���-&j �m_kR&�) = y-P 2' � $�i 2�k:x86�y�DO�y!�{�2W^1 y�,� 0wg���� 2��C�= \[ a�( � �{ca� \\ p.Hp,(:< c} v.q>.;mQ5MC? {1}{\log 9. \l�DyB1@2$"�62E!itUn�FV�P.�.V�8.U� Qn dx,*�&U=!�"�.u()��.V {-&/ v.!P !--1} p  $Q -&�/q $u,�ZV_IA0p,�JL_2Q�u�q!c.<-�75% @8 $a(%.,1�)$��s�~Ra�Gdi�y��AT2Y��:\,��.� �.�^*\times.!!~�{�m � Vl!�J�uA�B�I$�^EYBV�XB)� = E��HrH 1���(j u,v?1= ,\ p,q%�=a�S 2j RB�:A %��� �}>�:�:based���"�M6-)��b�+џ2�#�Q (u,pr#:K.#:v S(#M+W"Z:-i &v9K} *]::� 2�+�h � d*2:�$�1�5] %7,A }^:� C)=)"f$)6402�a�f%�f .�+.�57$, $Z� -)�|NZ^��w� _1%?�+�^��+%� ��OJ}2-5I�>V B���QjB*)1dAq#�y\| J.Ik5Q} �le.�9@&z9�F�E�GUg���*X%F96* �&�9nn-�j&�9>36�v�9"3"^w"bY���>n�M!fMJO �&"� V�9i���9-. 6�9m] m�.4+}�6:5A�i�6 fe.B�a�e�N.6�Z�(R.Z�#J�R?Z\we�F�9��9m�N_^�R�2-�D��9a�N�9&�'}:�DuEſc�\ may� ume,� out loss� ��uh�,���&j� fo:� �d�!ōcMA*�a��Aof>�6�@ le�$y�"�x _*&y$\>Iy BJy$u�'=u�'�p�'p!.^y�j ))��@ort/=��,�ained�� $\{xf 1/2q�\�n�I deriva_"%�BV-�?y�p!��)e8�k$.��>j �x;-:u��GU)Lp f�TS^ u} = #g}"4.�/"�/ 'u}/�, p}Vl^�2�/"|�3*ON&13f-�{2k}f1��u"g"�)g!>�\f:�zA>t`Q1� �u>t:�2%6�O|M� Bp�iRD-:kE�V��,R_u^�(:�E|1�B��R�%:�� Aј*�\eta= �uH&Y-l͐>B���$ =6Kp>K.  :��^�f6M �R&vIgfI6��&:'Y�c|>�(u�pI�. y#��*Qch�$$��x=yqR�L�����["�),!f$_k,u,p,f,g*"~q�Q0q�3}_ud'I�p�f�Dg��.{'. &2��(�pN�(2���"_)t�! firstF��&��i\pl*�U��1- �l=��*�c{"V�$b v�3 (ώFI{�*�d���{ xH�.L\&�H� ��΅�����A�!�I��H1.��*�$.�H&�`���H S!�:m "� F� 6��� u; F96c@ ps 7nM1? �9)�"^Gb{ �,!�CF�&��H~mW p�R6����m :��}:~" appl2�]a��6:j1 $(E� u, p�)&;iro ))+l p) � f -8a3*� {x_j}a) \&�Pu_ u�&G{' + p\, i ��a/�� T �u) �g�S&a�h&$�J��&�4�g� 6��m��X(�, $H_j �+ $\P�5 �0M�+ N'_ju.�u�� F 2no "�*A R*�x ��3�j�c�(l8���"#-rolll��s iRZb� 4}�innzin $l�"�16l�#�3�r2�V�[2Az�&�>)B���~v@B���v@�����*s%"� �=���� ,�� :CpfB:�E�M58UC�%z9_�* '. _k+6� >!+Fv?@��M6�:�B@6w6321>|63fH@�.\ )Ve|nL.JAz:�2� �IF�XnY@s>_m�:\@_��)�݂^@ 2$,:���mj�.r@E}F�+V�2�a���)>�pre�R�+�Vso5R by Green'�I trix��ZӋ6y�C�,I�B$, )2 ,J�({35;%F1;�F8$. Our goalAto�Yz1�� >I�cao'2Dn<�F�>�b�:d���^�R2�҉-�) -3s$&�>���&@!s-� z!#*�#"�� $\max(2-\!�d<��_k 3� ���.�)�F1 \kappa� a fi��"�&���clo%e_2�d�s �S>�- d-1/�:i�2(=5D*i�6elB��en, acc��j��d[Th.4.5�V3}�.�>,nyE$$G(x,\xi)=(( G�V )=1}^4�q!�M�>i"y/e2�B$_x \vec{G}��n�N_xr4 =-�(x-�\�>%�{1,j}m>_{2. 3,j})^t� ��A }V���#�"�Ce2u�_x� :�j ���Y  ��t� S(#:^N_k&�+x� !~(>0,G �-0$)=0��FIo ��$&k�Bx6 PD.(,�e3}d/eU} (C �h%sE "&� onents $G-�G-�G_%�$)*0AAR�) $x\ �E(|E |/r(A !6�a�"R6��e�,0}^1& �:io��.��000�Ci=4w � a�a.Τs6�Jg7(*֯�$��f0� (1&�� to�|0,\�>)$�/d*�8L�M_-���%2S "+�8 widest��,!�lex�*��i���ءb4&2\=2��r��)b�N�b|:5<�E&��*1ZjEYn[b�&��4} u_i�@& =&�3��.�./fe xi)*�\\xi_j}gE�%F�"xiN#�� 6,I�4u�(�xiv4M�2� 5} p�-g jW/6j�(���� �z�4B�BF9N�"�i(ing�߈�b�)� e4})e< 5})Q)LD�$mZ�O F�> �F6� \ni (f,s�to nC�^ ;%if�[u� Y�6} q� *L.2��~B � �� >3� ��j76� EuW� B�  \JJ,K;�:d��E266T. �S�A |\xi,�&e�a9Ji�*a$i""x� \xi^�)i�E�aE|�'5"�9�-5 4} "<�+*�(}!�xi|^{-81;j,42-| �|-.=�.][t'e�k� n*�F{r&C}Q�^!^{\min�f? �2�.j!#v`� }{%~Zd�*d�6d�L6)&��>|�Nc2�6\@lyE�$�> 2|xb�t��Yj�&Ɠ�'b' �B�1�+9�i2%.J%+ n%2b�%�%�%:%F�^�B aP<-�$8 >E��,B � ��i�u�{x"�� \xi}V �R|j)�� a�Ty[q�}� a�(�d{�a�5J<xE.Q."�  +i�q�bX\xi�ZF�. T=1+.� 7$. 3)3|x:��1��r��2 Ay� - �]�r�JZ�B �FZ,%�NW:IAuxili���iej�=�C"� w� "@ g/a6xteg�V"�6� kernel $Km�$# saT��*(�`� s0(�f elem".3i�o6G s $\sigma=Q^!K�l�T��m{*�/el1} ����877�"�b�({Y.01}�Q� \[  �76_m�6i2Olű \, f 1Gu. $�pp&^�ml6l+n2�-�! }D�sXiE/2�:] 1%Z��Ŭ���v�|2� - ^gmauj2� � 7 ^" - +1+�B*v� xHNDk>�6><��Z> ~� �:S:q�>� a���|�2 �� � M�VW��\{0,1\U�v"y�  aN�pr>*��"l!q'���A*W/2[6})�}�|&f�KMi�� �2k�eE 2^{-|m-l|�e��&� _l f!�*E%X ] B����}�c":�'[> n�&�+fz i왐�D$9�m+.J, �&�� �u.=R+qB*v���6]m� >"� N�  .�.� V �6�VmaY� �6 @!h �$2^{m-1}u-^{m+1� 2�`}<�<�Jp+ra��q�E*��� ���iD�R�4by H\"older's ��yZ�-6/�^"O�d gma+1Eamr�:��k���B ��CxSy�sm(�- +�-2.��inz,;!�:�e ��U)^!��Y�.�jr))}�qAXV2�E:���2�:���V��xi��aJ�kBS!G!��2ř2,k)^sT 1�!a����o��6���z��[�R�:0-y5-Q�a�=��9�B�v�=�E�!�<+1I�^{s'(2� ��F!�.� �(B Zs'(6�ta2r)�k? I֡-//s'^V N��AG$s'=s/��$h-$s�k+6�6�)>-  $N�>�.,z o.&6z.l�����!���(m-l)��N� +3/s!���Z\]�rH�^ 6�%ofZ �(0 �proceedU"$B�V���*&~�1�/��c |l-m�  Z9�is!�ne��2 ��.N�(e"�S^D&d�";F{x �\dih� � lJ6U��L� ance�5x$o��F a�~)�> � �i eta<�'LkQ�bD7�� -x|>� /3}}�0e" �/�va���>?% 3 %A� a"� � >�1xZ@ :}�0ubstitrx$y=x/n; eta=\xi  yield* Z&8n��-=Zz\ zeta-y|>1-~ Feta�=�etay �!*} Y2$r(y)"n٪�rE majo=�by\%nit6�\nc�Gv.�V}�e �l,I�k��!A��� ��qk*K �{4}=%�yp*L2e"L2��Ix,%l7� ] jr".Zs&6& $.!j�&a�$3M�ii*}�<^^2�KN�H� K}_x�%H6�#M9c_1* � c_2,\ 6�5 \F&"� $1%2��}*\)5� ���-.� Iu-��2 >4)�{k }�G�&>�j )`{-� @a!�x�a1���va� c9�j"p`���b�:{1:} Witb�<we &�<!�� =r_1a)� e6�5��6LJ-hA�MI#�M%�O�equ�$b2EB3{y�[_1���6U<y} |y-�v��m�6 ((. 21s-]�Җ*{1{JYAet�1endy/�4E�4�3. "�F7���<)0]�y c_0 <�0�+1�$��\-*�eh�*�7"�mPi)},\ i 2C.~�q2�>�������  c<Jy)�} � �  Id�^}Q2A�Et\�u� ��%q#BQ2{���T)�  ѓf��y��y�Kj�K:���no5(.�=I�a"�a$�V/6 "�>�\[M���e�|y|=1\;I�l' c_0/3R��� }!x6�!7� B�e&%Il�Z�����:�Ik� �h %B �!b��MA��Y�j�W��wF��.�A A�of� I-tVi�F�un~t*S k e7} -�^+�=chi��  ;$)N" *^-:1-L"_' u�%H�V��.cut-off&  :[&�.�<0�t_ E�$t<1/44" � t>36�F� �(x=� A�� ��|�':� *@0� � � N��^wZ�G��\[ ��!����!)5�\,&Ma xi,� )*aS��6��1$� �+Q�1e!+!�K�al��M�h" �a� Q�R*Qxr�FNR:P�&�2� qū�&3��� < 3"���,&$߁fY�) B�, �E�a��0:70,27)<� k+�2m�:�%"���FE�Ҳ\,7�� B�� RO.�II�(isplaystyle�)j���^�1+�%=k�A�j}�ɢI,�#er'*A_ = z�K2,8 J"��" A-6�BGt ��>2.V" ebso��WN+Y��b]3�]�� �A�Z�":�.���A_ K(&��,��HQ��2�2z�EϵE�B q2.$m%��U�nZ���.�,l&@&� y2ClA�&�%�2R6})��2%�O00hspace{-2em}|6 |^s�$c!�"X `>>�Mb�%������>ˌ-5�#r�mq�Eqoss�fqS fZ 6� (6 9aɕ�őY�l:l�6��i�6f:% 1&189' ��1���ξm-s'%oa�*s-1:U, &�`>2� �>��$! �~ �/|5IrO-EF2-�a6��-/�TB��E�2��?���.����%>�㭿}&J*"�#a`���}�vi�"#$-s_k)+r �\���B�\!f\ �"&&\N�'Ar:��ֲ  45�����[�&6PVp Grl�V ���)JD:q�K� �;�;.� �)TV�(Ÿl(��b�(^s�VQ�a�i �u�Y*g 1%5> -�b�5J6���f-�r��b xi&�� �.� >���wR0j.\Ո�xtAW� xu�&R�*� �$%$a N]ipve* ,BI(V`+�hz+� �od- *\+e��q��� \{ �6,r����J��� "Y,� ��h��}V�8.�:s2��5& ��1e!6n|eU]�>�&k�;|2l�,�� G<+/2=S�� \B�ŭ� �1-"�e�^?.:��72�"|&~_^gH9���J[K�$ ۿ�6R@9�=UX  P 7 + Q Wb�2b�N�=\,1_�kB�Y{\p>�%�I� �>e**�tMON�$:��1�X*l�i| $��@^{(j)}q  7i���,:SL �N 94/�P۹Vy�_jg��d�d6~JUd%ZFE1)�e����i��� ���x=��>�C>mv$. $��tb��{3el4} \frac 1{32}|x|< |\xi| < 32|x|, \quad \ %(2 r_k(x)\le \xi)  E32 \, x),\9, \mbox{and} *JHZFD` \end{equation} for $x\in WTsupp}\, \zeta_m$, $\xiB ,l$, and $|x-�< dl/2$. Let ${\cal K}_x=\{ \xi I(:\, |x|/32 5$)#\ :R�\}$. Then \[ \big|\partial_x^\alpha v�%@c\int_{m_x}T0^{-1-\sigma-| < |}\,; �l%D \, f X�\, d\xi \] and, consequently, \begin{eqnarray*}�� ^s &�&��N�^s �\ \Big(!|$t\limits_{1`)�~ � I$)^{s-1}\\ �,%� ^{(s-1)(2>^)}}��6��Q�5xE�1�aL1�4$. Using (\refi�,), we obtainJ�&& �M�A�,^{s(\beta-2+IH+n�,prod_{k=1}^n%2(i�{i�}{|x|}=M (\delta_kNOa�A| j�^s�%dx!�)�c7e�a����}{G�����r, |�P f%�-Z� S!��vZ�!Biga�a� �%�} v�Z 1��%� �1.HU�.B�TThis proves the first ��. 2)� second can be 28d analogously uE�Destimate�;!J(rA!�, �, \nabla_\xi(- f)% +-�^{-B'A�15 f|t1��tpwhich follows from our assump��$s on $K(x,!�0$. \rule{1ex} \subsec0D{Existence of solus} ɾf��W_{E,)�}^{0,s}(qX)^3�#gV+12+$, $h_j�PJW2-1/s0@\Gamma_j)^{3-d_j}a \phib;1 ; .<:d. Our goal is to show thatA(re exists a� $(u,p)^���\timesJ�:�( of problem�|d1�z(��d2}) if�-ߡ�A�i%�8 are satisfied.��$itemize} \ [(i)]Cre04no eigenvalues!�a pencil�Pmathfrak A}(\lambda)$AA'line $k ReA� %=2-E-3/s$,|}$\max��$mu_k,0) < I6,_k +2/s <2$ ŝ4k=1,\ldots,n$.EF h_j,)�$^ g$� suchB� $uV|>�$� $pV.>�)ny!�)�1dl2})��!p%zThe lastA^a9�1G trac)|$gY� h_ �!nderivati��of onedges oI cone!�V $ (see Si� 3.1). QLe}!�bel{fl1}i�I�XeR Y}$�@ Banach sp�fun�#�S ,K}$ in e* �m � multiplicS  withaQcalarI��8$C_0^\infty(\olXH\backslash \{ 0\})$!R,defined. We � oseU in� lities��| f\|_ SX} \ge� sum_{j=- } }^{+  \|� j f��|^sF=()^{1/s} ,\q� 0uiY!fiA�ku iY.i��2�e3all $fA��AGE� TY}$. Furthermore, let Q.O)�ae�(ar operator-� CX%�to5 Y}$ -�A�Y%�compact)�rtA$R�)�$y�-��m �O} l=�=^ 2^{-\vars� |l-m�.!n1�.8X%E� posiaZa< stants $c!;MA� dependentA�$� $m�}fy 4$\displaystyleA)6O}V�".�$� J��O�� Le} ��proof�tC lemma found!�,\cite{mp78c}�+ThAʼn+t�+Ek������b�Z�nSup�9�T{\�$i)--(iii)}�c�ej ��&%��$ &a�F$>z �&!�& �:+}.���2� |����}+\| p��F,6} ET �M|f\V8> } egV->e+ �;:k 3 |_J�f3 }M46 R>Q5>5 ����]� (Th} {\it Pah4}: Without los^ gener��yPmay� Ͳ��=0�x� E�; VBf ! &k $�q ider%��áN��HX}\stackrel{def}{=}F�>�M�Z��$ \ni (f,g)�vto��=6 ,��wha4$u�@p� �HbyQ e4& e5}))G_{i,j} 4E� leme��hof Green's matrix introduce��& 4m� by L�eFel1}, ;[ ��1��A3��ͦl� AJ~ :�ő�RT H 76��J >ge L -?g=F�>`1�F*AE9� c,�)gpF#i:8f,g,l,m$. In orE�o��vA�� m*� y� �le 2$,a5�%�"N9�"�8&& u_i^\pm(x) =.3�t� K9���_j \ch C, M]  +jT gzP4:P� i=1,2,3,wp�-Qx�g�2�3j�z� �4,j:�a2�-^�G_{4,B��*�M�%q+m� -IaF�7})i���-\D((u^+ +u^-)+@(pp^-)= � f,>- #\cdot :=� g\��}iNK �vS_j7p�� $N_jI ,p^+ y0$� $�$. 2c �cs�d3}, 4}, ���6� b/�� 2>�(u^�-�G�}\^iI���! mJ+�J�s-1� -1}^:2^�\V-6K ^�Q< � if �(��cf�_\�M{m-1}+I)m {m+1}$. n,!� Corollary)�dc2��=6u^+��1-.}^B�}+5�m p^66�}� 59a �>}v�}a�| :p^+%�_�6=:�;v)FB�2$N��)���5Q����. Due�� E�),e%right ha��� f�y� � d byan norm4$.�� �XJC6�[ Q�m���a)�!�>�UB$�7�}�. Thus,� �})� vali�rbitrA�$l�S�N�e\ er��\theorem (immediately�* J.Uni�e� a� } F�wwub0��T �iu��Ucase $s�5 ��fl3� 's�Bon&3 i), (� b�5��  homo� ous b ary &�} J7 F} halytrivial5 ?=(0,0Ew $F� Z� F)6,2�&� :-� <JI�r!Da 1�Ql.Bpr�. By  $A0denoteH0mooth cut-off" �l&$ � l�)�aQ$R 1ito zero >2>�w.t $�'=-"Z + s O$\�'_j= _j-1 %2s�j2�EW�[$H\"older's��R&�6� rho^{2T'+� epsilon-2BZ��{r_j}{?�}�H�.K0\I24 (�  u)|^2 x����ɌJ�s �2��m�Z�; � _j} r�s\� dx��/s}��"����{�� K}\\��2}}!^{-3+s'=V~� t -2+q.6%! 2/s'} b $s'=2s/(s-2�&�integralAꁿ�� is finite�M >0$.:�eN ��123�.��2* ^3Q� chi  �L12L $. A&w� M $(1-a)6�� � �.^��OO is impl;� � u)�� p�� �( �ph� big)"� big(chi)p�� 9�.�V�02[^3Ql#*��$�� �u2��j�S;A�L3/2�% &�� Y Y,p%�Fa� F�0 �H[Th.4.1]{mr-03} it  t�yEY����h>E�z�MBF�&H� n obvio� trur *V. H��|"` �:�e�have $u�!)$p=�Y: ��$ It remain/�!���� �  I� is� A ash� Pcoordinates $t,\omega:Pt=\log �� |x|E` $ *=x/ . Wehby ~ � }^{l�Bbb R}6\Og)$�we} $ed Sobolev��] �\|&e�]}�.M �) 0}^lS��t^j u(t,e�)(��k-j� �Řt`�i Ni I�2�x9L� fEo� �!j^{3 ,l+3/s}u$ (as"� �variabl%�2� $) belong%�$W_ �v�$. For an & , $vs5 ! {1R�!-s D by $v_��)�mollif2�respect] !�v � $t�!( $v$, i.e.,A 2S!�E��17 �} v(\tauM��h.�(t-)\, d ��M�:)�va�A�%} h(t/)-�hEa n 1F:��UintK�,dt =1$. Sinc9%; �t*t^{j+k} 6 -,t9-� (< & St^k v)C!�2^{(j)}1=� �)tau� ] F��ab2��� ���v 2{U�3j�!^9�>  j=0,#A�2�2� e�A�1@Re.^n��){ճ�:v,���),f�$� ����6>^�xs"�#J�-V������a��>�^�)�2^3 �pJ�2*�:E:}��&�� _#�ᵁ��� �already�v&&5#�&e>8K{ 1�'V��_j�iK'�%%X2�B &�,�@V�,�s* 'j,1)< a_j'��� *�dl4J� u2�+�+��r- ^\el+ 6�&65:�.]%et $v=.�2��A{$q21pJ Yi� b#.� � �͍��� %S� :I.�' ����^3�q�R�6 �J6=��*$. 2 $�4��-�J�sM[��2�(�%A:� ac1} conclud� a!�.4U�-2A[��.� ��s�+a$0�j+�$��-; $u.�M*+2*}2�$ .1 A)$x6 ^sw(� �!A_-5/2,0�Q� 3$. 2p�-}Haz!=� $pf�1�q.!!W�2�6� "�. easily sedat $.U,2�m s also� � Accesg� *� 2���iQ/��no non8"���~i��cr ��ref�(:8 2�wA���,��0�i��of,� leteN�V2E @F�'�L�#2,�22':�.01F0J��VR,�  *Y&& �� ^3\cap5�.�0F�^3 5- er.�/bZJ� h_Z� f/ bh4)��= >&0 � �_^� ^p |.�- A36~.���)=�2s(�+�/�] 3_k��< $Z"'#)k<2��g,. 0u" mW�)of"&� 3.6}����.�_-�i.����Z� }:�"�g7ft2�� "� "� >(�(V# in�H.H�P.��9?J��s.�(coincide, sMay� represenqbIK6�'. :�4 \setcounter&�'{0}2ThBLeBCo�0{Weak6��(�uŊ�Pin �1�-Z EDu�3A�w2S } O�� e bia�,1orm�##a��1 g1} b(u,vL2�*'Ji,j:+3 *kO)(;FvRdx�! r �ontinu$o*.�6;�* ,-i��P'2V� a ('1O ��-��is6� �!�!*�B>2�=1 x� � free!~*5�~5�rf�2} ��1��,0&� �� < 1 "�&� } .�4�41sTh��-4$_k>1-2/s'$�E%"H W_�a=V�$$�F�$-:�I �!�du� � !\@)wr�.V�9�n.�2� (3.8]{adams}%� every" al $F� � 6�:���� �vX3} F(eV6Uf^{(0)}� vZxek�<3J1k�"4{x_k}v C dx \�E�� 2} ���6?,eG $�i96�6�%!A�8�8y�B4, �72,� 2��, oJW6hE�(:�JZ�9&� [2�. By a6wA�Jd �p�9we mew pair�#Z�b�:�>)"9 ing�^''��4}� ��-:fpf<&� v = A�2nf4}�X \ +v=08+ on }f ,\ .c,\\՗5�2�+u = g��in&�+� ku=' �n�--(�&a�ula�)2�7�B0i�=:W(  u!r)` c,u'. p)  K2�-@� } (-p� + 2��(u) 2P'(>��"+���ax*b2�o"�4� g4�)i%g�1� � >' if $g!\u�6�6$J]60� s6�and $F$:�[V�(fN. g2f~�H.��)a)���Ծf�dA��jQ!�(.� ��4ib��F.V.��\kappa�Ha fixed real number*��X��2� = - d -1/2���� A� the R� ��aZ$5"$8,&�7JG22=�#(c1i*c1$g } 4%!�n�be1}�e3}) &�-&`x[5�,(�F/BD� 6�2!�.^{)YJ6��2)v�;�_%�4:��Z $i=4� T-^ �("�,>`2 (0,a=):�)i$+1��)0,\J� 6�!\L�@_-[@e�6^< "+�widest7V �$mplex plann�F�!�fa 2��C�'Fg M�~g . 6)#8)w.n)�$Faς� ��is givep��#M�g3z3�&.Eto��>�7~ =%A"�@7[c՛�Cr>Cholds"�B7&�6Q\hf {-2em}6(5v 6b# _"664 1.� 1k)1" {\xi_k}6>ca�dKF86"G56B85`%&&:�p �-�6b�*�5��>c��F6. " 7"�3� .Auxili�0.;} :�E~&atM�g6*�7})Z6�� mappa�\[ q.6S>2�.b 9 * N.;6V .;�(Ea 0)},Ai1 2 3)},g') \to�j}F6; "�5��6 6�H�%�$*� &Həg ��p".+�G.�&� �5�8} ����*�.�K"� C�j�@'low uC&�3 �K-sȭ�"� q�,B+�E� �6q< �82~2\Ag;Em6<k�u���aD!&"�A����bl1}}%_let \[ �O��[�:� :&� B�O, �I� \xi. \]:PmW3l+o$�G�#D{1}5�1%A�Z?>~P��M�6 3@���M^{Y>!O2�.�iM.3+2B%p0�jN��^{\min\�H>.�+�8pn�N6; NN^1:P:�; �2NNA�?O�"1 �*w �D��\{0,1\}$EG.)0� $ a suffici�Q sm� p�=*� . If :��Cq�yaSW5.�B�!I�A�m<8})��; \| v27F��2<A]?G2^{-|m-l6G?q�GNB6��;j�E9:%U�d2�E�Ei��qs�+laWm+G �fI�":x�(�+B.CR + +2B%v�xA�x|R�Id"T.Z�N]m�Q>2�-, V�&F�F�`�[���yceeds>](B.*-��"aB|B"� � erB�4.�K&!$R3 6� ʼn�|�:�OXkernel*�O (E�$)�=��m 4}$)l �!��=(�0� �J.8!_9��2c*Ņ���� \[ v� Y��(2^-wF�.&a;AC 9� d[{���e7��!�6�-�  B�P$.2an( �\p�(�RRv� �M�VFU�SJ�x��2N��bP\xi��/32&�X�Y!� \>�/QV�,�DI�.�, >�<%�� .�s� �& ]!�����*$>��\, tH��{\i&tH�+R,. *U>�LA�F�a� v� j+|\g�S|=kkVA�j} A_{ }N[$1�A_ B!_��"4 y2el3})S3$�/=1$��videdbS2geSmaxs�-�,�oRs' s_ki � 2,1+� �$�Os'p�W"� A#ad� allyb�3 �M _k+t�Ri� 1�X�02� � 3 + N5 in(1&NY)��>D �eK=n ftc\��a�[}{ll}N !6�&s� })L=1L=0� 06) *Y 1, � m \r<5|4tyu�W�*orrCerCk�)9f)*6� 1em}6 |A� +1}� �w F�~�Y� "W=&E[s_k)+�\s u,� i*]�FA=�[��}a�6�I�}�\qea"6` �B">e�0,a�ݯ SF} �ů z �� �Q ss_k�> �YI `Y"�1��I�]�,a^{���>9]^�2A�h Nn[x V�A� -1}}/5��I���I�Y2S��)J�E �ab&,E_"�EjQ�@��A�A���FfE5U����qB�. veriiZ�#�'� ��A�1a8.^ s $sI i � | ���E� �IL�.ve�<� R�<#=:7 &�\�s:� k( �i B� �� "� K ���\2= [.�N ቅ.�� +f� ����*0K� �~���>�Misn 6� .cR%:5��n�^x <P � + Q � 1R"� �1g!Y|<�d0e�G��L" |ZE�� ���C"�eE�Rwe!�� dax)/%a E�Z 1P� ��!�0f�?xa�  "_A^"�\ () $ 7$h'iexteriort>G&�N)� � BA2%A�Q6L-6O!}�� �L"� C B���Z1j� +yYxYB�MUR�2�F� w%MV_H�a R Fb*!j&�  bn3)-2va� \, w ��>/$A ! + Bc�PI�9^� 1���&&TBi��(u �Hm`��(���p�R�I� ���B$,u;h -FnR�CW=xi,���B�n�,2�jaUC5We'82�a$A~�AB.)667�bY$5�MƑ�4I&| A�~|�% \| B.,visa��.�.B�~W�U!W��9�_�j!!��j6J�2thy���_xl)��ok M6�x>�. &�@ ��,m�_�1|&A qRY�J�� -�;��A:���x= Zkl�n�i|�s|23kvj-sW (��1�6�k2� �R��m� ^sa�� �km�gg"� -� .� 1�!P/2�k�l 6)j�k-1vtkI�-�>�!�F�C6BRN��-Nb�/QB!*& ���}2"  (y >� �_k!�!HI�5l^�l9db)5R�)d A1I2��2S:� r� N�� &� 1�%�z��ZQk. 2�V}Nm!m�6����e{p��2�<}�[ |�da�s)�xnM#��5���2t;��desired"���noZUB� �1E�v� $. E�k� � �Tan&�T�Mpce�"$.� �)B 2`$Ex�j�bo7�TB�5TF!VJR:% &$Z7;6Q� �0k��N6�jk6Mk��""( �A5t%!�&�"�s68f"d'"�h\ )jKb�( =8f O5does notkj#.U5!���+ rfR\j*�i)]�+ax*�+��4,��a�n>3�n.ޗfnE.���&�+�2�F��� �g!�.2/4&�"2?:�Hr1e&aG��a��A6*AOq�al 2z�,"T�)0)��P��6���!fPconA�-��e�.�3Ju!y.�1� *ime�{*(�Rn*) l*� O}j*=�*.m!u�� b�eX),��U)�"�)|))}"-j�&r!�e&�#��e#,� �:�(�"� A�cal�k� �Z9�/*�a�&l-m*�&* ," `ljRQ�fk��r&�gJ�>��J*6w e'�/f^{a[,�5f�5f*5f� R�;1�u � �&A0V�f, #!��#�%Bi*40F"0.l "/0Nbe!"�& Q��Mf���c>DgN�<� �   v \,b��f��fb&�av�Y2�&�f~��9=F"�wv)b!�4�+��L��=�;k�;\J*�;k,a�$2r;�)*g� �.K� e�{;/�f)��5� j$:Cr�fg)�Dw�bcWf.c-�: oWtann�#:�NNd"��c�K�0��l2ckc'(fdf�Ma)"�g4�,�:�;bx3>��h��vFAA+&x_fj?-6�>��&�g^{Z����F�Jq o Xh%Q&Ly] � 7 9"&&�>^+et�*�Bg�6q�ilde{F}�A q)g�sJs\2�C%%&& 2�!�}~!�� �u^-u�2? �a�B- -�8a�b�? >U%'\.$$@�}��-%w -,v)>�l p^{-�.���v2e(mA lde �C��h��ian&�" _tinj&V6e���i6A^��i6C }�7}"fi:YjzAP|)7a�|^�i>Aa��5�XwI:�AM/�<H,!i_,  �� By�R�" been�H<>pre�a�J)?ms:T0a�� v,q)�!�^d�l"&:\g6a} v_��< �&� & j} >8iB�?=$ �i��qL�� ��V:�d:�z)�4 �3 :% r�Z!� .�s.rr�:2i��F�Q "� u �ie� �;O,BnkVR�+a�Or13em'w�W�f�ҹn�V��n�C�,NY� m.z�%>�Cwa��BSp� q5=-1,ZuZ =(&mN_:!*�B.)>���.�&�"1/2,2.��U2)'. N"�d Ii{n�VH=6��P� � + f21�\,*��MrN�i� :�6+1NU,�mk�m*�GZ+P�B�+�OtE A�assYrs�e��Y--\ �X+�6�fs=2)\�'�YCE�.4�_8�C.I!�2���B�:������E�>XB�h_�A*a�6f Regularit�}15� 2��B��*;,hY@B����Q�.�UJcU^>�.00$Y�Bf�Z�B�Eh1�3PMM2BRM^v��N',�RXY �'��^2{ ŠNh2�6���N6�N:n}q�\�6'= /( �T,��|�Z"e0.�c=�9^�[6�ZN`J03 �O.Yi�m+:� &Ef�[4 �-�*|L^;6I�r�Z= V�iJ "�Z*oD8[ + >+*�Z��J�I_ �  R� ��)'-.'���="�xp3&? �Dh�.j!<1-�>i8B!2H[>�V�X">� (� y M�=2$� n �Ee2 �'_k=1�.N�) A4:!:� )6�� B ; Un�� y.���>�Lb�w.!�!+ ? i�YOMx� ]  �W�]� R"v\i&Bb�>j.u%%� .;T �vAS�!&�B=" Mm"qreason"lreL^$ct ourselvx0�!I�� A.@O2H � ���TRemark�  �,� "� eT~y n* zJ"�c):Ji�N1,:�ZI�S.�06,kV�x�L��|M"�>]1A�CHcB aB"kPJRE�B�&d�Mresul��3r:�2Z '. >J B�N� (cf.F�:��&�&t{!�z��U^ I1 dE&�I*�#h// u,p,F,g,-�H�bj� Q��� V}?'66j "��ar-~.�&��~���>'F���L� B�j�aͶ.�4 � �lM�nR�[ h3})}����r%mit]4de��Hof3 h4} � r \nu�RN.��{I_\nu!>c�s�r�R_0,j}-1� c ,�.,1s�,1} !}\ ("�s)^ +\a�(t^{��4 u^{(\nu,j,s�5)}?p. e{3".pj3U,)+ (w,q)>,� 2� -���Gj�Z=��--)��Z}�UlE~!$E�Aў_$ BYdBk ��M�.$!d(.�)},=�)}!A��&Δ�)sX�Q�, cor�s��i6 $.&_)B�& A�S;of�`�[BL vL��\{ F_i\}z? et C*�bar��&� A�o \{ g? �?!� c-!%nverg-"ded�Y�->�L (.N� �� •V�6�[N�0F $,���uively^ k36 k�� F� \[ (�CiM�i)}6���2+g�1:4�<@C�-3>66 ���} (w^{{,q 6� Ls�}206w�*J� >�C�_ib ��U��� B��_i��^Rd#j:�^�%)*}^'above{ ��"�*s! )ԅ�A_e $B�a��YY "-Z� �*�Av&ky�B�~*U�)6�>� F.��� ore �C >�s�� $\{B�\}$���� EX> ile �$BTB5a>�!�,q6q�V"& ):����;*NeC arq",#>6���. �. �. �Tappear�WiGh4�By �~4"]&Q&1�-�  i)}-� �5I:��e0A-w,p-q60 i 4�BT �2� ,O ���M.��F6w��. h*�h2� *Di> :�.�N��2n�'1h!nd�$2fRE_Fc]a"Bx�"� D�%g���8\,�8:?%"�A:�"��� VC1�-�B�@6͢-5p$6��wҋu�$�c6b. J@$|����2f��c�ՆE*"�$[a� n2lN ��~l�r�Zf2�j�6P ��'�j�p��6�q6�:�R,q <2"�a}2�(�j�l Z]q!�c۝ &}{7}!�S�n �oq�oqns+���!�a&��1�62*�3\"���Vr�*^�bm��&yE5 *9" a�4&�$I�c68�l ��E���->�$ݩ2�:� qO:/�6SBRI(p.662:��� EG�,1A/�>"w�;*�z:�9]"2 ,:�|+6�|#"�ZI�)1Iat le��^�$k$%�7caMO step�)> RL�'��B�J< �0:�x�d'AK�7"o$�gs�b Ku�?Y�>+2/ou� C�ZIE_k en60 ft3}"�y� " !�6 F�s3 2�3 Z�l:��t�RNlm�ye=Ar�l-F�^�, �[)_xq@Tei_kE-cD"�=&F6 -l+2^�ߌ9^gv $p2B Z<>( $0<.�s <1$,&�i1�F�6  �-x u + �k�aV�6�ͼ j u ��\ NA� ,p)=1�� *�2j"Jq �;*S*��$ �%�Rg, & �J0�*N&#!�qS[$�!l=E n_k� &��!� (aF�X&0>M�Bx2Fxv +�ho\� ial_�+1)N��ɹ6��!D2Q�{9��*=(B%+1)��m0F�Ww ��� �. Dirichlet� �i of%o!� b�"mp(B�] >�],.�:s&n?E��)6=>��>&��2�3.<,l,oR��8��M��c�xs1j( $x_3$-axis��= �a' B���$b[3E[(h_{k_+}|_{M�T= -�! n&-�&&x�r -+}) ?+ )+ )�fUS ,-,=vE( g<,${x_3}h_{3,���sin\th��kB Hi�����^H �M$=F$!� �C -�R (x_36���e>iM�^�ZAv� =byA����6�]�L h�̡�= rr+ B = x_1# {x_1�3x_2. 2} +B;%c $x_1=x_2�,�9!�,)�A�e3���M:� $�H9��>J=A&hR%�C�>�.sZ�MQ��1J?���J��M�+EE�E;R����A*J�]��>5���%�e��v%5 $q"[& i�m)��!��# �0��J_k=�-!�+�$���ْ�{�m6]�by,y�c �3al5NY���2L3xd�L�L�LnLp,!�:/WG ��� Zxl-B`!�F�uc�f� :�=�}>� bR��Zf� f� ���Nl�^T*5��&bR.*. �l݀+>�6&}�:+ Mpb�20b�"�:�A��^�Ŏf� $l=2ZvN@�� 1�em-1)ZU2�i6�( $l=m� nI] >��2��M&&�& bset"�6�j-:@,&X9�j+�\.��kFY/:�k)�$j!��" indu҄hyp�s��6�� :76�>��:K&�)><A�ppl8��d>7�uZ�2�2��"� n̦8qx��BM$�, � cx3��q>l-:.Y F�V/"�!86�}^F6��1�6�jٗ=�v��:RR�J�2(Z;8.%againR:t�:9 +J j,s.cM 6�.:>�:�9 F 9�*6�bY �NPjEO!G�i�O̊��N 6w u,� 6p + p�Ts6!?���; *z$�$��� :G u�CxD� Br΢J+2)�_:]7 !�-3:��2q5JZu- Ja 6��o6rrE&{ 6��%J>I6a>�je�h Na?FZ,F p+p)�6��� �bSE.jj)"� "#G�R7���hl2�q�F�!jF%j6m+J�F+Y6��!oge� b �clusivF� !��`pR��&2�J6:�>/$dl5} yieldk�V�3��y�522& F�*�Mn�$.�02�d�Wsome butmW2�5z�si_5�,\n,$:��MO,�}*� G ��H�5 n�&�U� S^�;$$�& (�W��tenA)�k$�&KK.a5HA�'(x si�����LT��&�xAw2�J]"�v�V�KAZ�2�%d�).��n S:E=�:�I766f 6FC�_.o7n*R@[.J�&� Co}q/8c��36�2� ]\ht3��2� !H�#(CV�8��2�,�%Kj�#6���!�q*-mj�2 �Vh5 '| �hf�2284v�Z�YB$, 6� �J�$,�2�0"��0aF��f�ʯ1���1��1*�1Co>��:N�ɧ'$�B�#.��*�'uB!�7&�!c'=C1''� '_nA+�� _r��!*� !�! y[C22Abyu�m�1 4M�Z�m'4})"y"�42�lv�&= :/:$�4)9�m� �:�*. "��� �3x3�#�]" -ma{V�"7�, .-6�Z<�C{�{�Jh�Thh�"��C"{�fBȖ'{�Fb9�n�)ed domai��9-G�w�6%%molyhedz�typ�g�%�T� y�mea����́"v^\ [d� blO���c[V�U��,(of class $C� $) xL(n two-dimen al manifo�   j$ (��fac�n)>�<k vcurves � Ae�^3�����ocorne�px�M�d)}�A-i)]�F�gF�B�6Hxist a neighborhood!p\GU}P{�P a diffeomorphism (a=#YL) $�� ;}�map\5 � )doVK !DxRB_�m�� 3 $�a diA.oE<%z�c�6 dih}�O$H2" unit ball*�6))a %`j)}�-(�N+1j5(�G: &?� �K}_}.a���"#^��n��vertex��origi4A�aW=6 ���qL�"� igE&z�}H� p = &���S"�%= R_�G}' �iE2u�%�"�%�$�"g,� &iT 6���#�)/S!]a?�$� well!(7� s $d����H�3�!+�=Q,3> N�2���#\bold� -�G}$\un} !�i3b| rho_j(x�di�pce��$x$� �>�;L�B:�53�9$X�ׁ'8^66\xY��wB�uA�� $�D� F���G�a*�saO ���: ,"؛G}F����G_{|?��l}!N�u |�= �`2a�)�"�� _j-l*�0�]ma*�j*���pPw� %�\xqa)��`Fa$����%=Ӹ*]!_d v�^d0d&� 1�  _m) G 4�`� _k>��N��nonneg�4�er:oo66c�0>:E(��b�B ��u�y �) F�&�ZM$W":�I)�$gD. !>2=;2%=��M'�e�F0$� "� -j6� �b�Ae�� ^Ys#�V@l_�'��n� X q�*N,�~Cz1/sid F؝%�^��`d�T!���K}^{-l*.E!��hs'��E;*% T�[�" T�(jm?~�EJN�:6�$��JM:�j)r8N3J+>�>�9"w�Model��(r*�@�W�CNB�s>$AM�{� i*] i�Q4;��v poin�Hnd�id ��f &W !�1)�ixi$aqa A=�[dg����+� �),-��'Ai� ��V$2�)e Ben%�i�� we.9"� ( is  �half-���BIV{k ),^\circ$ tang�)5 6"$ ߫�5 e a*.��_�*a>�+�d$F[hm./>M �?&C +, p =f�!2�u=gs^�!i"��)M C dS1 uU,-* RNg=H -B2�/w9 )^&*z"���:�� }' is6 ~J6 2.2�-�Dd��A2 (�C�F.�>I�3E1)� �D&��N� est 8GveQKl�G cK<��il�) Z2 Z�,�DaI�ZQ4greater than 1�H* .)\muQ� l^��)�O �H � � if }?�_+} + -} 8�odd }\��#or��\ *3 24eveݣ d } 5- ���\pi/m_kE_ g6�)'2� c�m alphg�<hnsa �*�� $m��S�= m-�  �Nf� �� \not$. շϓ/6+2pji6z%uL2inf1h �/1�B/ 2�eV ,�� $کG��nd� $I�M�� y]ll=�� $k2 Z�rť}6By>H;&� V�a[*��B�$�"���2�.�| ���X��k &U 6 �p#:��$k�!,a��e���l.s��$0:� eO a��ˉ@. f-�,��>�nG Jacobian N)9'Bis Ak�-i���+-I����9��_462�\S6a� �:�d!��jS_k�k DN_k�Mk6��H-m X!�}k�!�uErV5J& ��2_6R36R� {.) ���2� E�-BXB� � ��V��{��>k ^3:F� u =0-.`7:�@\�� V_0XV:\-�e1 u=0\ F. &X �L_V�.]$V2Z*���j�k0���$. F�Ze&m/nrv��A�sp-E��con�t�#L�._3zGLx_2,-x_1,0),\ (0,x_32�! (-��In��h&*^ �� t V_��}�@T<($bF�d a%�HI= 2A�&DI%}^3.�95=65&� ����y3+Y �6�YG} F�Y8DhN�Y�CV &�i4`>g" �GM�&�%j�:'#"�F��gi�_GanA%tϮ�%��$V$, $�<L_2�!�&�.?�^(�$*�X%+.�!A Ivis�5�axEV {&bLGN.�8n� �"-s\xv�;�I�.;:^_&���S*5xmuG�_9 a cera��{!��ehq�E*V� b��i"]&:���let%T��!#^�b"�;��,�:�x���:�</�ba,^Y�?:��� 6mN]":8� �w = -g��v"u=v+w��an�:�ԩh/dn�3��K$Ch.1,Cor.2�KGirault�u> a :l� &�vH }{W}\!\!{U"_d���J.� 2�Zd���&�JG} (g+2+�5dxI�q7B֙�is�&BP|eVH�>T6��{ \{1,�e�t.KDj=j!)ph� C*�Sn 7}0}�aљ%��of�ov.9E" 18p)�'�J�N'�N��-%apsi�� .�z �}j:� 7_n,�si_�0NI{j_��] �*�*dlw]g- $j_07 �?)tɩB�|| =Q�=$V�V|��g'� 6= -n(.QZ� �H} c2�b�� �t6�g'�S= tBig(12 sG|U���1+E!9 1 ��]bN�h4 =0,AJ~+w'A)a���2� w'= g'F�/w=w'-c�q��A�!6�i�2[v_�) G\sB*)\\�\necessj"�Wf� i�u ]a�>�f�. Moreae,� $ � �2�vA��G� ,��/lil �:�3_ � i4})Bvis �� r�i5"��0.��M� L_V&e�N�;i"X]d�ndW aAQ" 2&S*!5}*� �d^* 3��$�+ �<i9�M-�) �+%.�")&$A�J�|tk6% &��2n:z}. p�I�` ly determy�"� �{%�� :J� nd C up��5�"! F� %F�u4' � T"��Y4�f81B��gA��^I A2> W"G�^\bot$�( orthogo!�Nl��am�A,$=Kor��"�d��Dj� A�ar�.u�Xge�m� ^2_{J>?s6�F 6A):-qB[� L_ U.+�)��Mll��@J34��v� $QS$ vanish)�� �V*O6r25BvT�"��!���F� J(V�!�G!j�!�)�D :a,I<m� $B=-�?div�an is&�&I���&6� yQJ��Mm�B��pa��"7�� L� .-/*2~6�q�� =1\�5# R�S"JL�8�n �Pide�'�2�w�q t�(q�F(B��F� q}�A� "Bq��� "��J, = q� ��1}{|{�|"I�94W���D 2�z��ge "�P^�20>�A)Շ �� �36<:. 2� DqEAIel!�%HI�u�Fa�2�b53e�>, {.� v\,  I6f I v)-AvN N���X� (} In the ca�se when $d_j\in \{1,3\}$ for at least one $j$, the existence of $p\in L_2({\cal G})$ satisfying (\ref{2it1}) follows analogously from the continuity of the mappD \[ L.a� \ni q \to \ell(q) = F(B^{-1} q) - b(u, q) �`{\Bbb C}. \] Combining (\�and l3it1}), we conclude that $u$'$p�ies 5Di3}). This proves B.8a solution. We ( '4uniqueness. Lei�V_0p2�y( with $F=0$�Len, in particular, $!\bar{u})' Obviously>b(u-w,-4w})$,A1 re $w$ is�$orthogonal�jec� A�4onto $L_V$. Us9|19kTobtain $u-w=0$, i.e., D 9HoweverE�n �v�I�ll $v!(V%5&refore,AD\int_Q�p p\, \nabla\cdot v =0\ \mbox{O} OE5If}% ~&\n $v$ can be chosen suchMG z v= %Xp}$, Awe5p%�6v0,2u��m�n8V�� V��}2ZSe�in2-V/2!06S\^{1-1/sJ�:0>�h$�� $. SupposI��nPre are no eigenvalues�}��xncil ${\mathfrak A}_j(\lambda)$��)Hclosed strip betwee��lines $��!�Re} >e���'-1/2�C B)1-*-3/s$,� ��onent��{ s� � inequalit' @$\max(1-\mu_k,0)<ɭ$_k+2/s<1$,��h �number 2.��M� 9})}��Ffxn > FF� �p�+J1��EI$�y��"� � $h_k$��given b"�:N. FurA�m�  l�A�b�e 5^i�%L�A�a*? =2B= Ii,j> .�_N? i,j}*? -FUp�.(� ,G  g=��u  h_k=e, XBy \cite[Th.4.2]{mr-03}�� )a0n isomorphism:, it fE0from Theorem � gt1}%�Lemma  hl1}�SZaY�� � \he�({-2em}\Big(:gF�:� A4�~6� Kg  X� �" m(:\+>�S` \no�?* 3e�&&aF:} ��<^<mF�(��� �q�f�m�}�:wx"�1�Due�ig�L:�nor %=)�$A-e�is les�an $c2�  He  for F�6 :s._also 6 � �.A� resuluNXb�Th"� itF^ AxU�G-}2�&? !"2�3��-W4? �0��v V^*� � 2� ErG�\ \ ���2^{:� I�� )��S�� sj� 8, $j=1,\ldots,d� �� � �� �� �2u �� R� 6� Aer"! pA"~� Th> It e��%Nt�,� i "� s $A�s!�rts. LJs#$ arbitrary'_x�n�easily �dmea� f a g�aKun� �� G}$.A �(e�con$ed a �2n,neighborhoodA�cal U}�W8/a�e%\ �~�originE�$B ,bG0centered abou)� ,.: �'( �)=IM�b: L $(w(x),q(x))=\big(u)f�big), pN�� o�!�af}�2:/ �=�coeOs $:�i�$�� zeroJJbocE�E� �s j2o(w,q)$. Applx *a il2e� $-.�_j��F� �fq�.->�$#�0�m��v[:i�g�;:>!�it2aa�np  point��pAՑ�!��d a&B� \\ A! Y  VR(cf��&% ht�"t23�m .� 1:!u 1� &*� !O� &1!N1:�AR�  $2�9�l.� g, .�2-/��jj�� $�$ h� represent5�(vh" �F G} f�  "�� n+��phi_j.2� J�V�C$f^�2+ a�$ d{5�2 �2 d!�2Eն��� , inc*���,c�= b�$ =l*��4�zlZzl�&� m�.�we�U*�e-w"��$M24which guarante��a��r� $w. -l+2-� '}^{EQ�)^��"�:3�)3s � '_k=� _k 8 12 - 2s3"OaS_jw=hr \ N_j�=Q��*C j,\ *� n9a*k w +gE�& �X�6�� T�!u.0-, }^{la.F+Zp Bc�r .�Exa��H!�Hwe establish some r���> specx�` �5sM�B�syste&�lasF" nonw� tms�6a � G�,a polyhedron� :D��A4!�...,n$3 dE�, $:LWFnotA�e angle�8 7 $\theta_ka��e sake% implicity�re $ct ourselv� (homogeneous9D&B&�:�h6}cj u=0I�E�7=0\��j�M"�� } ���ulpre!�id� inz�!�vided%�Udata sh�.H D$The Dirich� � A?2a}.� $Ɋ : ��2��U3Vf�&�#�� � 2L $%��!Y��oZ%B���-\D�  u+�� p = f ""�u=g��&:G}M/u&B#v%]�)M%is� quadW%up� K" �"Q85.1]{Girault}).�is know!9�IAwnj`n� !an p $-1 \le��Re �0$ �� 5.6]{kmr2 &I�e caseUn�| isa�vex� n evI|2r�6z0< 1$ does notDfOs jP%f2�5�Moreo�%it� �verifie� at $�>�,�,u_k> 2/3$ if�� < 3��arccos}�gL14 \approx 1.2587\piJ1>G � y 4>l< Y34 -. �&these�� toge���^sK6bmit3� � H &� &�$.�r$itemize} \ �%�N(e�s'*�^*)"��Rs(��! 2< sEo2 s'=s/(s-1then B"T6�.X. I�!��>�`$� true�B� $s>266�N> L.�>29 .)7=6$,�1e ,.Qs�%Aweq� usdU� fact�t 16�=V_{0j#2�-�s'<0! �'Y<=W<;<3$. � ��M� $-*4 -��co�}�s was�Eby Dauge��{ -89},.A(two-dimensi�+oly�+domaiW!�fer�Kellogg%�Osborn ] }.�"T Neumann�T(��>R We�[ �(e6�)� a���:|���E�&'u*�&n}=0\ �(~�� !.%it�6���1��s6���0$!>���lp#*A$ $�a5��=1"�j pf$n :6.3�� �DѠ� Lipschitz]�� �N �AsameU/B�  ��i*�Յ����zjz<3�mtn� �_6�^�_2�F2�S2;�>= �s���e}2�*#��#)�� $b� �(ia2 <� 6��emixed�c(Y1A� "5��ks}�*%*� each�"�$j$ ei A�^I $ua]�q �f:e+g-#noF  adjo�2�"�*(�e.�� ��Te$n|  > � h�- >o]N�!To�o%�.B�!�N�1/4xis ��h.��ꚹ�0�08/7Q��2|0X �20�L:�r�1�Y_4s} (i)--(iii).���q�>�� :� be a:�&, . i5 h6R �d_k��2�� k$ (�3!�F"�appearD the J�~'.�RN�isIpaC2�6I� >�of� ryeUŖn,~"�6.1"�eH���J�0�fre���q��g:�%we hav���,i��nM~  bothB�)�u�Pi� indi; $k$, 6�D4� � >1>f�232h�#"� :��s�8/��6�-��<2� if �F� (ii)�e�2�jeF� o�2"%2<�.VH��6o��Zu n!�E���6$�2�,m�:�wR�^� Nz ��JJ���a�Rop ��vcp��T last�dA�YW1< 6}6�N�a��F�2� >�� 6�. Finald:S;<r"� �Y>e�d �~��R� �"M&  {n-1� whil�~`!^{.�3�3I�� oe�$��"%t�,b"�9 �}_n�:I'=f=�&@n\}\backslash I.$>�*D RFSpi/2$-v/Q��A!� �I�%G?2�/2��J� <}sN�� E��BN2.7&e6z��8�O��#yJ<*mI� *'� �O-#aڎ E*��z� Fp ��s>1� i ay�,aL2* $g|_{M_k}� �5�I�&� mtg}��h d�b.��ݟB�t "2"##:t &a �e��c  b�W �fA��.�U&JP6G*jPA�� `+"���6P2 Hthebibliography}{99=bib6 4{adams} {\sc A ,~R.~A.},�1$it SobolevT4�s}, Academic Press, New York, San Francisco, London 1975.% r68 u,~Mr�4Elliptic�G6�� corner"Q -- smooth�@e�$asymptotic! %(�Lecture �}MMathema,�{\bf 1341}, Springer-Verlag Berlin 1988Z96�9^�S�$q ��Navier- l n@"three.K�$ �Ts. Part 1: Linearized ,s,} SIAM J.�. 0. �<20} (1989) 74-97�& �Fabo!EE.~B.~x, C.~E.~Kenig, G.~C.~Verchota},)��� on*�}, Duke �J �57 �08) 3, 769-793.�(Grisvard-85-�,~PFW�%�nonI9�0Pitman BostonQ�8, Melbourne 198A�]�%)7 0,~V., Raviart�-eVE�PFinite element method�65�F�,M�,-Heidelberg-q�-Tokyo�62�U � e�B,,~J!�1�A V.��M�ppn a� vex �},!�Funct6�1%�476) 4, 397-431.�kon-67� ondrat'ev!S��%FBj+aW:!��e�F 5B�8Mi� coni�-�FnBX*a=,Trudy MoskoveB. ObshchM�16�@67) 209-292; Engl�$transl.�'T . MoscowM�SocJE27-312� kmr15zlo�, Maz'ya% GAcoss!�1��E&�:$in6 R+ =ECies,} �$al Surveys��Mon�Q4 bf 5�, Amer%-h.� , Pr(4nce, Rhode Isl��196w�M���Spectr"F� s associa�%��46�*��Q32u�85��2006��F�$'$=�$Schwab,~C.�sOn6�' 2�a�&� ���$hydrodynam�$�B, �0!e�e,}a�Re�:Angew1��*456e94) 65:K8Gunzburger} M.~ �jin�$`ible vQus flow� >�����9.FLadyzhMW enska!QO.I2�questio�f 5!oR2��I.� fluid1Dn Russian), Nauka,q� 1970.�mp7��:�DPlamenevski\u{\i},��:W:w(A� no2�&\7i�"�z�� ���@. D�2trentialgleichungen (Meeting, R�(ck,� 7) Univ. .(8, 161-189,�#.�!: >2 �3�123E` 84) 89-102�!Fa-ߺG �je on manifod !e6h},�?ble2�i! 85-142:�8ڱ$L_p$�* imat�y�of ������T��A��� 2�3 78) 49-93N�:)�b� 37} q 0 D>�8b��s=�Gr�Bfpio�4Schau�Ha�);.<��n-�5�+al�$}, SibirskM Zh. �19E�!145, 1065-1082 (� >c�inI"� H\"ol�c�,X#n�*TMiranda-Agmon maximum � ciple! R�V AP� he?,}�l. Nachr 8 $8) 25-82; FJ :B]Isl., Vol.�*� 4) 1-5� "� mp83�`� first�6I!1)eI *k of SEV�hys�gBv iecewise�hia� � Zeits%0� Anw-; 2} (�0983, 335-359,2:z86) 8523-552�mp�X0, Stupelis, L"� !@B�*�< steady-state moe��j�T�xasurfacax�3171-2682nr-"{:�"H  J� \"Ubi ie ASk a\L\"os� �|(scher Randw^Mufgaben%�@er Umgebung von K�2n},_ 6138�@� 27-52 �A ��P'7:��$'sA�rix� Z2 �(e� or��� � ��D}, Z.�&" Me"/ 8A�2002)�291-316:�02V�N�" rto:�  j^��0.�-�.��82003) 7, 435-466��Ca} B�{\ss}�  ��!�:�of:�qM ���)�^�P�7 int 1419 �Schr\"od� Institut�2" P��, Vienna>�ZmN�>�of>�!a�#V� to��v� to a .�Nazarov/| M� ,~S( ,�� "P Ubin M>��j�H,} De Gruyter ExposM$ in�0�Hk1.B�-"~R4.�r9qP5y~��OhɼN "�4�,-Slobodezkij�EN d2 ,} Ban�$Ce4> Public�3 �27}͓�$92) 399-42�%���@} %},~�PZ�ir�}�Kluwer"� %�@shers, Dordrecht,?�!J56]>@  docu�} Xj\q �[onecolumn,floatfix,aps]{revtex4} \usepackage{amssymb,ams3Bcd6subfigur�/G [dvic� ics,color6:epsfig}6{��} \newcommand{\hko}{\hookrightarrow:#cl�*8cl_{1,3}^+(\CC):$n}{"*G\\:f foot�6sJ-2�(di}{\diamon�.�daagW2 sd}{�Nbb{S}}:tbec}{�@>"e"�-V de}{�4B[�b F�T:!ear}{ZRmj} �f:9EEb{E>VDD� bf{dF�fq �flush%�}}21i!�i�6Iom�bf{ ga>we\!'bZl~ leftwNCno!�noindent6�R!Nb:�${1}{2:�s;�Ar�P{\starB#$i4.#6c!a� cal{Bx0wt}{\widetild�O2Vwh ha>[cl!�mt{C}}_\:vRR9�R:�MMM:$op}{\oplus:QHH5H:5PPP:xa*�bb{X}} %2�ao alphFeat>o!0opJ:�l!�L�>:beg NgXu�QB�n%A��>#w!��:`g}{\g�W:om!LmA�6�rA�b� rf}{\rflo�u.�ll 2ty}{\RR)�\RR^3:rsr sigm>�v!6v"�W:7beq%�)9�K6{ben��� enumerate:% $%\"6ek#i6"m!�AJcaM�MC{thm}{7:5A}��t{AB�vv bf v>�ee >�aa��a:�bb 3b>Muu u:3jj j>3hA�heartsui>�m�!Q:�s�/sharp:p!�p`_1;��ff �f:�v�varpi:Mww 2w>�CC�C>NNN>FFF>KKK>stk}[1]��(ckrel{#1}{\�,}b:��t��6cdwnM6 Driptstyle #1} \dowaB�ZZ�Z>he��e[:kbm�O!�bf{BJmn!d�6M}}(n�'at�GK}>! mrrj0RF0cj/CB/K!�A�!:�uR[�&} 6Qvb� blacktri�1��:DvvB&%�6jLj!�B N vaLvarrpa$N:�r)T bf{rB<R}:6wm�{W>x!sbf�:jla�)�4:no�&RB� spi�stM�@\nshortmid}{\pi^A>k�B}},\sI� A�{9�{\�^}}��:�OOY�O>d��  DBCnbW verset{s}�?:an�W_ .% _{e_Bgnb! >P+Bt nb�N+c>�k� {k}1a-'.-Y >:x-� x:!yyI y>3jmj�mi:i�:df� �  x_1>�df�df12F1� f13>1K�n�K}>NLL)G$L$6~mk`�6�\"6 iaxi:�j2j:k2k>�u��UR�ivI>:m.�:�cMV�8M >=clt!& _{3,0F&E1.&}:myu5 ee_12>W VVn bf V>=O!OJ� OM 3{ >9sss !FwBA� reve{B�BBBB>UQQT!t�OQBun<mm�=EFsB>mm��"uJ"v�+CBr b� {\ �� >�bx�� pman>"e"end^ vA<���2A k�>HR:mma1;���2:�Ai� FB�mm 5bJ"p2dp>�mmg2!gJC"����6�m���� B#� "��� B'"lF2�w=-S> GGM bb{GF_� 50f�H%\topmargin{0.8cm} s /d} \title{Conformal stru�*�!twistor�the�TaCQmodel5�b},X\author{Rold\~ao da Roc�Demail{roldao@ifi.u' mp.b/affilim{o de F\'�"�0 Te\'orica\\ �!ersidade�0adual Paulist!Rua P�KPona 145\\ 01405-900 S�xPaulo, SP, Brazil\\and\\ DRCC -"�B�8Gleb Wataghin, V�Dde Campinas CP 616�3083-970.�}5B(J. Vaz, Jr.=De� �# �Matem\'G, a Ap da, IMECC�camp, �0� 859,R�o)�vaz@ime2�}*`pacs{03.30.+p, 03.50.De, 65.PmA�b��,abstract} S6Mpr�?�'A>AVLClifford algebras $��,\cle, \�4,U ,simeq \CC\ot���.'2,4r��Q ed, �  .�^s2�PDirac->� $jl�$�<exh�,d Q�to�iP mamap6[, u� % paq_ u_s�Ma^. O.�2�m� 1 in�.dcuc5Pometry group SU(2,2) �! 8$\$$pin$_+$(2,4>1lso inv�"g�(�!�l�!�a vable i&�_��B. Af}review�T=35�� , ")Ur�N scril� MinkowskiCT%-7Ed�>>6�'T� \2  , acu&yon=� s. T�&�=A Med via1�:>n?0rel!iMA.7�K>7 � eLo/'zia?RR^M�5A�cX�� )��Z-m�ic spin,>�*A Z>�4�C}� C}�$ M��7 loweM�A� "�E�Sn +M dardF�!#ul�8s,+'ce�Hpur�h �V;$=,ivFus44dMR!7ialEnaA"A+ @�{. %"\{A.�;B���_{p,qbDn"�/ir��#.3�= {bay�"4port} %Althoug�Rpapersd=alr�"�d9��z-�q�6p�P�` �w�a��, �p)$ism sheds �e new�!�e!J�A'��m�� generaliz)�!B$cite{crau,�r8,ke97,pe1,pe2} �V \make�Ŝlq*{Intro��ion} m��ory!�V\�9 ba!�onQ�,�d,!����' $eO>? 0�LoM�}, in99 a wa�F�O 8![�� emer�gaQ�"U0{r(ept. Accor!�t�75v,zCa�ide:]s �J^'mitive F+�st�bs�T+'.1 JB�%�H&ali�!%or exa ��{mo�um}x9�/  , he�S�masslfcfie�*)�$Be93,Be96}�8�]ul �.P�T!��,quantum gravET5�AtJ_inuR, sugges1KpscretM��=c�of)�I�5 �$Co94}. OnU�motivI�!�i�91����+IB�[ network�#�a d ���pQ�9� �(pe3,pe4,pe5�1�!#maa�[b�*us�� �/ a lo��5�+ies> an�RcrQng!g"/! wide-rangapp~ �>��>s,�d� �`BH85,Kl74,Ko96,AO82,Cw91}�l�=tw�8s. An�Ab 8h�2��N��na�"zc��,v:ersym, ic5��B<uGR, e.g., �8Ho95,LD92,Bk91alb,Wi86a,mot,b1,b2,b4,grscwi,q16}mny �D A� p~�x ;�p�!�) Penr�[ �=�)>]�;��`Iu3/2 ja�!iFino�Sich i�y �# uper�nr3Jg2C�y !z�E� ivis /.�0�6� iicles � Be00%;8�R 'bconfi0c�)s /KA�N : m�yai�2�� �.�.a���,)es��� ic objec�6xeB��nd� . O!�S ach,�� Y| an {\ ~} � chev�U1E� ( .minim*xdea�aB��Qis cha� er��isis& �': e�i!+!_", %h.��Period�Y�+�WofB�1�ABS,benn�8,coq}. Equivale[t.%onR� !S9t�ncar���V� �4$\${\rm pin}_+� ��doubl���Ung&� X,:�SO28 C dS.S !� e no-]6c (W�B�cFus�^&; s,Q�b~ \o$ 4,1}E%&� .}:�.a is����}chron5r � � vT4~B�� inva�ce ^M�pnI !t1� Lo96��E 6��mechan�.Řy ��itz+����N� Conf%�1,3l)� � ��]Y�tN9e��s��;DId biG� E��[r�\>&Maxwell&�7,��v�>1A(`F -�,�FJ� . i� Am �S� �R�L\��Ss G\J& Ef 1,3}! A��  s pape��organ(>a0,lN7:|Sec. I�Ag� a brief �!n��B5��fF..Rw-s d\O^1p�.�� vI"P1* clt$AIٴed 'lyP+ X%�nm�-g LmrnJI���ɮL$er~s.��7 �hs'remarks��o%�= �%9e�its[icMEy� $M}(2,\HH)$ �x:,$2GM2 (�|6�ic entA6�In-FV�e�BAB+BZ.;\%� H�_V��Ely2�h %� @!��Lex� �T"�j&�qE�EDJ�re�hed��0to� ve�correspoD(�vouruJ��4!�� &� �L� � lso�R6�q�$i_$ ݮ���� ����>-wss of V��  �o^y�"�%/q �antiaut!afis�9r��sedY�Vqg�ia�Q] LeM\"obiuD2pŊ�plane �&����M1��K;�f5. �9mq�e� �2; Bw6�A�8d:9��J��Q�s ���d��:��� �:0>�6�;} . I�uLieu��&�>i�{x� ��:,6�iFe�IX �o�Eincid�?I� >� 1� Robinsonogru6, Um'�/&5 pE�>eiXY� �U-IAy��Rly �� our �Y ults.`ly;��-",fed!(%q�Ber��},a�equ� �26*���Q�V�g")mAppendix�O Weyl%F"G6 �!����*�aT��A�s�aE� rbenn}�0v${Prelimina�'$} \label{1�lViLa f�D$n$.dF r� )���e�!i6�tensorU�$�o,P_{i=0}^\infty T^i(V)$.>we  r[f att��3s $, (V) dži_k_n ^k_l9.y.  $V$.G ) deno;=� hm8�G"r $k$- �cѿcQ�9�GiFc$\psi_[}2��b".$ .\emph2;o(E }�x����3 � nAo$ S{TD_k} = (-1)^{[k/2]} $ ([$k$]2sintegera�� $k$)!#hat6��� ���c� or�7ginv|q}, � $T>�k f ^conjug� }��A�!�5"rF^ �b&� B�EL�MV� endo.< a�G -deg� te, 5�,& map $g: V� V *�- \RR`� pos�B to extendato ]A�..=\uu_1\w�n s\w k���l =\vv6! vv_lE?uu_i, jMV$,��6~s $g(!V,l) a+det(g( 87))�Q $k=l s.4�Ma] k\neq l$.�C� pr.r�a.��si=)�0 + 1 �s anhNm!=X\lm��6 $p$-�qjA � M�l�*L\�leA= Sp$K*�nѿ$\w�mV �I in\l%�:lww!Hww!�psi�ww\lrCF�N� Grass�9u�$( Y,�t 2�A�" �ismv�L$\cl(V=o!b�  )�?�(&E�$V�OA�^:,,\; p + q = kR In w5iQ)_RR,\CC1HH���\p��ve`�,� leR2� (scalar)P �J�geic� willP�zx��juxta9�-M���_�� : !�ա� 9� �!�"1F!vs'$��.p��2\{H'1, 2 ɐ�Zn�tEal basi���3�q5tZ t�lso cal�E${uO2�},A'��E) $�S�F�D�,ie(�ijA� ee_ji�]2g  Mj�+(_{ij}.$ An &�y!e!7t"��wri�� ane'vpsi-%aJ = a + a^1}1 �(2 33 {12} 3 3 a^{2 !F+ p\; 1;\Rn a, a^i�, ~�\RRKnge ~6�!gr:�Gx��%�de� �; ��#clt^+ �3 #t^-8She�� \pm*{� }�w$clt\; |\;{�%}��\pm!$\}. $ Uf�bq� �eTsubQHofA .Z �-�G=��phi_+5�!%8!� $a&u*(� �j)�:M�a} Now a:�  $\rho: ��L {\mt >$��s&� b�e�pE� ?ee_i \^" to I�A�\si_i$�._'em�sigg}/1/1!�left(%s�{cc�pR 0&1\\1&0 R �) G4)�n ~2~ 2 = be�-i\\i�3�3�� 1&0\\0&-1��\\!ge �� ����Q6.s�6 m*� ��m:�f��WQx $\Ps�rho )�Iepsi6�eq.Z��)GA�P:' $$ �5(��3) + i(a�ʁ�)&(a^1��  ��- a^2)\\>a3{13 32�F2T np - q)=2]�>eM� :=�� z_1&z_3F� z_2&z_4>l� |. !jR~�� ,J�and�j- ��psU�Y I�,:.M}~C�rtok{D P�����(z_1^*&z_2^*b�3"4^*��0 �֗4^*&- �B�-z �1ʚؗޚ�^,�&z_B_�F-\\E.�E*wY�4i�g��3 6 psu}��va��$P� �#�w_1&-wjw_2&w�uw_1,w_2��CC�\��Qua�"�subquat}� � ~: $� �}")2 � $ + q� q_1\im> _2 \j 3 \kml $3/{q}}, $ � $qɓ� RR�C im,E,@j�� �-���)hey��2�2} \im^�B\j k -1iA� \im�= -\jm�=r"k� -\k +�> k 8-L+\jm1�� 0 = �Re}(q)6� {) ��$q-{Z7q� fZK� {p�$9�; art}. Si�N� z= 6< A]m3e $ \HHY �-�u� t^+$�e� �O $ �� ee�4,\;\, j}}=� � 1k%3! 2AR\"�smA-zeta: �ri_ ^+�s."���p$6 (\ima��i}�cQ(\jj  kkE�y immedi�L�;biyA�m w\ k}}askzeqs��w D�!^$\i-y9 �u!wm� "� ��ex�g&� �43a ip p�V12} -  a^3)c+� 1 + (r3}a)p�ee_{3>]\�A 5 permA�to �!f� s\CC \ot)�X0�<��o 1HH '&K ���6� J��%cle&�g_0, \gNg_�g^�frame�j��$, 1�%� \g�  nu�� me (munu!� g_\nmuA� \etaB��,$�dr%ii�-Ԕ$ 001I� `nu0�` eq\nu$, (, �,= 0, 1, 2, 3 $�m.���Au�"�&j���!�A&$$^9�we� *�� "MB 0, &=& c + c^0!� 1!� 2!� 3!� {01}\g_ 2 23 Sc� 0a hu 3} *�=& & �g_ 0�xpa�c0 5 6�V$ 0  �ud9��pseudo-�!�5:=2$M�X"$Aj5)�5-U %�\g_5 �$g_5 $��&f�Bc ��a�c��at*g a�"�%pr�,idempo� $fi(!�!� + . A �FO'$uE0��� $I�0� c�T�ich�a"J��)�$5+Js \X�� AJ-�acdg��q 4 12})f��a^56�a^7 31 08 0!c f,nnoii�� �Fn< �]����c�M#�� �= -A���(Ax  a^4 =]�2},\\ �n; �ca5\a^6<1 WV a^72 Rt a^83 3F�%�� $\ieAiK ; \j�J \;k12}T�sK-�{��5�� (i{ e{ ke�t`MEute�4�C�!�[� �keH\je �i ke\ie=\j i. !��and!� BbieE:3Q 4\ke>V %7��8$IJ\;�? aIm.lk �a�}fe5a&���*q>�?+ru�+��2^hU��e I�e�� = f�A a | f -5a�\m!- �q $�Naa�+:�sa�"�%l0��\mu�:�<�� "� a�����M~m*�L= 6:0& :\im&0R;2 =F:jm:j^:3N:k:k>:�^ !�!7im=�a  $ A6�6F�!�!�a���%<0�-:Eea19s��&�,�Ks.vaa $\upM�%�AGte, �J  \up}}��6� ~\b�F("� >1) 5�+(�.=)@+ C27).���z1C w6y ��qf�c�}��w�F9earF^N%���2�(c�,c�- �+N��H 022� 3�J8�N%GB�A�2q %LR��"� 1��Q C��k�Uy(\� z�Jq_1&q_2J 3&qFW .rin� mx*q�Q\e oiFK�P&�!`u��&�&N8Ha�u � �BB�`{U q}@ J( .#2&.Bd ,8}�m6~X �+ba�6� {)�-ju�"!$q$. %�ee?|l|}\hPR�B@[-3mm]{0mm}{8mm} �V rm P�0�.�j{R'gB \;|\;R�R!I 1\}}P]!� %���Qoi be&�pt aў�1x1F�^+\ ��75�*55��*D � q;*Zqq�+ 1}$ 6� 3�p$�0$�.hav1F�"M�,Y��*�6�> ^+\ri�b#d: rho�w�!�g_i� "�#a� $� x!�x^Mg�p�*!�$*�:.ab�,we� ��� Qo = U�W 0 + x^� (�: ��39 A�= �Isai ?b&-�a� &�)*58bay2,bayoo,por1S��+�%>�2 SB3tB! I�.!b%�<�;|! $sm7s}��$sq\AX%p�e"�4�A >\si�{vS@�`bUE�\&ksχ�is sen�|3 $ \2�4ue� Zebs�sA3 1\} �-.,!/"� louV �)� 2*b�/i��u&�`R"�*>�", usualM�mm�" 28J4extbook!C>gre,itz}�"�" not}�*}J�!~�m�>�fbut'�!lex&D.Z�@IRH4� ~1so-�#{%O�#}G/�-sE7{�+6�a2AU{5R>"�2c *�,"|- WKA�3 P oduc��7epC&D<%�>80U'aa�9arpa findF�!��E23�6�N6�4,\RRd�$veGeFeEeD� ���.28%.Uand�{��V�$\;$($v�g(e� )$) .#( )%5�0*�"R�$&Zra;AA (�Q��\>�", we mu���fou9F s $P!7P!7P_�� P_4$�>�  $�"P=%P8%P3%'. I)�no�B]!� �92&�f6$e_{I_1}g 2��� �$ |0�'�xs '> in detail�.�.����4.�24} Co*|bn:. �y\�M_{�N\YRBA;}^5$  (&b��65,�)\va_0� 5 1�1 2  3 4 - �yzeR4,( b� s�L v�E_A� �'��E �-�E � E �E �E ���u�2y� 5= 2� 2,4Z� ,\q< B� FC��fEo�% [�;t2x�!�� �-&pA6��DI_%r D�D�� �!inclu�" $>Y�I�"� �r!֩r2�� � fo�'}om��3da�u��(usefulao��4or3azbe6�S�+onB{twitt}��t.� �,�� ��)$}v,�@W�&�4�'�^�5=d*e2?.��ov�is"yH7��8ly*L�Lm�G ant .�&�8�+)�q�l��-��&�!� 0 o��t9�s"�5s� dee�;*97, Lmce 1�s\7)�� �i&JiAo�or,*� #�as*�4�@%| 6a`$, EO d>R~�If-!EtR�? (Sby&}'eu)) r � A@.�� . 2�"abTE?��$�dnt" ��isonu45�.�� ��larrow�.� Á<q3�&�*&��� ( =], 4),\n q�s��.E�4}."���� how� at� ge E� -� F,B E�* *1E� .0Jh��� =."@ F�ge�B^A � %6&��q�qliop} Z�$H + H^AE_A {AB}E_C CD D �4 \n �B + B)�% X ,5� $$�in, {lll} B =�i H,$234}, & B^� 4} - !Z, &B^� H^{1)�\ BH^{24� U3},R!� H^{37!��= -V� :�hB�!i�24 Z� ? + ?14}]01< -<�\]o ? +!1}�{} {1{ ?� " c 3,\\]��`2,&M�B�#� A1,a!!{ !%� !0b�=!]%� 4Pf����f W+���W;���Be (�-)a*X7'�G�R�;&�:6>��؟��J hat{��} &�N&�^*k#� � N,*� A�8^CA �]��36H{:"�AR�zK ad O�� r.��g�k,cl^{\bullet}��/E_4V�E_4*��)0![=!zdN� !~k�`:m!)!Ja ]5�[�d"F�&�:���� Mj� var/ Z) \� EZA�����cc1 z_{11} &  2 3 4}\\$�$2$a, $ !3$3H3$4l4$4$4-m![mf�<�2�}  9_1 &  K 34!�d P O�! y�Z�}�! = (Hɚ����{�O - H�/ (�C1�p�z_ �� 4})�(-f= (��� !�� ��H^1"i )�� ~Se��\3!��[Y�KH1 ��e �!� :�Z4Z1 �Ź4�!g ���|�� "�9A]!iɟS0T :!%�rO1u2A�Z J I)�]O1)1� U� _! Œ� \�f  "�)!*= )iA!�(5H:�%%��M%��\a�!! +.[F09�fZ�%01a� Z%!�1n.�Bt!� �N�F\ ,-n�� �V��}�4>wB��1kAx2x���A��% 3n{% ]!�: �A!J�(-t1�U!>�2��� ��J[n�A�IzI�=� ^� F�U6�i��8��$$J�n -i҇��O belo��x8ty]#"_6�� H: \medbreak 1. {{{C*�@}}: �8Z}6� �Or� ^*_{A�&  !�& - !� g*\ !L.4�� . � �FA� ;�� 21�� .� A� #a\ 2�1��4^\dag�B& -��2\\ 3��1Z�:� $ d&�h�.�[*�B].q� �$-�Z� .� �N�NAb��:�6�!4�.E$� L!��-i.e�^�0! 1\\ �0.� �8 MC6�� %J5'185I\\ "5l"5�JZbm��-��: �}�� pZ J0wb & 1]�-2$$�Ri�vb� �Qe��>�>�>~>)6\-�F?,2��1m��t�M�Z}E&Sp&�9�ree2I�*�7L^,"@�V�6 U5�J*� J4"�� � (det6 )^2$a�, sF5J sQ"S#detinha}�9rm,e�e��?1. � wo $Fi��can<�be"50P�li c ca�o&��.� i�ll-ѣ)8_!d!t���� �&rm%on,\KK�/tH#� &���n&��)*P�dmi1e"9��tF$?o0��06Pfe,_E de:L1�&Mm�O���u��� 2�iR6<�g�h{"\bf Z�R_d�Uz_�,_� ��l&�� �u%��L�$��:_�Z\0�o_�W L1���� adj(�� 4) &� S>321��W� >��$A�a(5�77phi)\;��xfor�m���O5 CC).aB5�3%�G>{C%�$$ =5ũ�V� 1g 1!L�� �3)�#*�*�. )� E)�9* .P 4\")� 9.O *� 3�m� cof)� 1)^*A32)�>3 "! 4)^*aXQR1���"��7)kF>0a & b\\ c & dJ{ fC@d��FbA�J=.�Gmm� 4� '.� ${{Z&�}c��6 �L�lde{Z� }}$:�)�!^&�CVd_Ube�AT_Mm��'E}& M4e�(I�2QN��L�kL 0 &�Dq� E�(3{B22(4N(6�5 P)��#%�" 1�Z�=�Ln -�6 Z1�!� : $9�h1� ^���!/�  %� ��!�1S)�$4$)�!�H)�$5�)�. � "e ���G2�+:�6�A�f*�L��VQ#w;in a:lI e%�s�s $zyC3)mU���rent, �y.�&,by (1)-(5) �*�!���a.J6�$&�H� 6o$m�4i�mu&$isoimu �.� *� �/a>,�I�d,�&  $��~E �]by:.q �&�d0 �:1 2>2 3>3 4> �Z&��I!�2�of& �)%�%�~9�6&��}a��0&�2q8*�vD2��8�������}�������!/�!��9�)��o��6��� %�9N�F�b��*%��A(qb"���Z�R�.���vL��6Nm&:="�o>�2d m�oo�q5 �2�s���� \�5�"}q��h.&,�-��P�Wm if��Wbg�(F�ObyTC&�4"/$!�%vice-LWa.5w)�_los[ge�lt�dg�f�Z ��_,W�+X6V,:�4Zv5~$:�$���������҇�ad&�:�+��M��"*n {0 "�;#�=d� a�dH��g9B��� 63g4^'"�Ž2���:v Q��(�\Q� z�Q}�+  .�]�q�r1� :v�"%�v�\ , %� A.�!1,0 ,!�+*�!�YB�%3.\2(!'6)n5�2�==�+!M6�,=�� ��]!���\2;2�1>(B.'2r � �)� �9�N� $M�N�?}�z� 9A�N� az-A}�� �I))2E) bA) 2q:? �!� !��QN),v)� ��SR�"^RI�2�)!��r�,!�+a�..� ge��Z&�u�ZR/'"H q>w����4>�3� &uZ�� ����6��P� a� 4a!:�G. �n!�F!� ;a� � .� A #!� �~%"��.$��c . $$2m*L/2�N��&al~A+2L�,� �-���Y�&zE.OH�&�+����*�6�an:2WF�m? ������փ�8-�>�>1>-J�>��Jm&�I��$UY~2�<T��� 2.afVg{ �/ 106}N 5�4 U�20!��5Bu("pY�)� �?�*I1�k :Tary����#&�*8det�!namN����I n$ S�o,s!aeJ��S2���,azo&�?:Rr$Co�<IO"V/�"iC5D!�)f�)D>n:p[Lnuڑ\i��Vj5or��Z)�kb=r�_�k6�95�]2?�6TI5End}\;\;09)$5��nezCveq�g� S�:�{#� nnec�(�ty�6�)�:i�knM{F�!� �Q �-E F�t� {L6�k~$.���bSe&AT. ��&me��W&�� \Lambda^2)M6d��� $n(n-1)/2�:a�$ $n = p+q �:X�=@.��S)�5:�YXB15P=dimQjt 5, becaYu $n,n$ $(2n�P�:."CO�':r:_�k%{X:�=M� �2�a��N ?6�! J�Nb97R�s>��V&�P��{�!�v�{_%�� 5BZ GŒ�\} �E�%��5�b�elemev/ JJA&@ N�!��&�v�.\ ^ ~�  � ��!��!��!��!J�!s>�!;�h)�WB�!s^�!9���!��!��!��!��!��!��!��!J�!�!�Q!�Q!�Q!�Q!�Q!�Q!H!�D�>!^>!?!�+*�!�#^�<���� 4�@!�@!�@!.@!SD&S An"?A��"Y>>��&xaS t&�@ ca*h&9K�^"�3af^  �8>= iii}�=&"|>�=&6@ �<1*@ 2*@ 3*@ �U�>Q$�..�J�F �I �#b.�7�G ��FF :5+ 0:E �:E �D 0J$ ,�:�E 2E �[�14{ �<O� 6 {:==3>Z==) BBD a  �D ,4} - iH^{012L3},\\ B^{0123} = H^{ p+ iH^{04}. \end{array} $$ �noi This isomorphism will be used in the third paper of t4lseries, when twistors are to@$defined. T L space inner productytetry group SU(2,2) is written��Clifford algebra $\cl_{4,1}$ from theP�N�$\simeq \${\rm pin}_+(2,4)$ shown via an appropriate .\between $\CC\ot\cle$ and.��. \section{Periodicity Theorem, M\"obius maps >!Y conformal)} The J@ ifBTs has great importance�shaF�rest %�e %�@:\\\medbreak {\bfN��}} $\vvn$ {\it Let $\mt{C}\ell_{p,q}$!��B� o quadraticM,$\mathbb{R}^ B.� following.�IVlverified: \beq\label{per1} {�0}_{p+1,q+1} -�  �4}_{1,1}\otimes �,\\:Pq+2, pbO2,0O i2NnonumberFW ,p+2BV <0,2} �nVd \eeq where} $p > 0$ or $q $. $\vbn$ 9�m�6�@given by eq.(\ref)Z),%� so-calledIJ�} !�ge:;�� \enge� nden�.AP$primordial.�in whatMBs, siaE���}��0characterizedi�( representaa�fA�:�. =G Now%$extended p}�ti��� Y�ed, for details see, e.g., \cite{ABS,benn,maks}. � ,{ reversion}Ndenoted!�$$\alpha_1$�� ile w {�jug�},* +{-1}$,!,order��simplify<no) |(two antiaut�s%Cinclu�i� 8 ${ �L\ep} (\ep = \pm 1)$.�m~o (II):t! Ju .�!also ex!rs!p�ermE6!�associa!@�-2�!*�(�YQ�,�)�Q ",q{-�)a� �f.<.a� $$5a�\text�wroof}:�8bases $\{\ee_i\!� ff_j\}$�@)t�+� �.��$,��p��vely. �� [�X1 2, 1k be a�isE�$ h�^�] ,q�� {. :�relE�IBeasily 6� (-n)P �I�\ep)(% ff�) &=& ' 9 ))� A�(.6\n 9epA�e_FY�]!� �r��=>N�1V�j6�.ET��fo[ he genera"n multipli�tep$. \bfr$\Box$\efr \sub�6�a)lane} I�kwell-kn! t�Zr�s/( Riemann sp� PP^1$�%ayn withF@0Argand-Gauss |� pe2}��cha�((as a vectoF a,c to $\RR^2$��mM�0�� \CC$Osuitabl� describe6�O!6F\ N�oJ� ,�N2� it canaWsO %U4 Lorentz trans ��%d1 �,1�)�!�-V�M l \$pin$_+$(1,3)$\hko\clt$, � directlyi�ed�[f�Uwe hav e�p� correspo�ce: a7ge� cvbnm}clt-���?  9��Iq _� e�I�is case ��%>lBJ�-� d us��̑� %�"� �) iepossiM05p a para-���(bay2,bayoo}� ma\in�$a1$� ( M}(2,\CC)$> plu!�> \mma = \left(\bea{cc}z &\lambda\\ \mu&{\bar{z}} \ear\right)rRR\opa3,%- %/%  $z\in a ,�u,Win\RR�� Consi (now an elem� � E_� \2T Ag( := \{\phi j!�$3,0} \;|\; \overline&� 1\}.� �%�A�R�II%�* seF 2jDsgj} {\widetilde{6L a&c!F b&d .<}�:+%f d}& c}9 ba6�.-u ���X!<23$!�)v-�{3}$ �"perA�y�� $ed adjointY��0 >1} amapsto '� eta {\% }, \�  �B�.�eu.S matrix>�we��writeyW sgj1S i�unA�), as: -� >�z�� �2;^��d�X,}}EE��:A�),�m2�\bP :�� >�Z�>'�e6gi�+�%$� Tak��a$ u = Pn� = zm{z}� we�P� �6��Bma��maped on�͖abcd}>e�'��1�%�2X�()(a�omega:Kz'& z'- '}6�'}6�,�P�'��4frac{az + c}{bd"M y&| |^2�'�- � map&�u�%[� %�spin-�-$k A}� {�SL�,"� }�Y . d&� C"<(compactific�GresultJ t(� achiev2d(ort,ort}. G ���6�RR�,r�&*injg 2a�0q \varkappa: @ &\�arrow& \ .5qx&��& Z(xA%8(x, x\cdot x, 1m8, \mu6t h mz mage�� Yi� %}t�%ic $QZ % �2�b\equ%��" klein} � -�\e�0,*u:�K? absoluteF�)�$5 � ducez:�< $Q#cpro1�s�!� "' Be!�s, :sQ���� aI�&G>�a � hat{)A,q}}}$!cv-~A� $Q \thicAJrox�B:is home � $(S^p\I 0s S^q)/\ZZ_2$m]E� M  rticular W 5 �0^q = n$QJu!� $n$-S^5 Bof��RR^n$�% addi a p��nfinit�`re�istF�e� s: luse3e|&as\oIRxv&uos(vaT��ll}v&v\� v}\\�v��a"� �ik�A������*/int� Porteous-���:*��N{h}}�"�rm (i)} !S��y��\ri!Y�;\; x ��V2WB)lso� .\\ ${}\he0{3.2cm�} i)}$pi:Q q,qm(x,q���|x/\mu$uQM��� \neqA�e~� v��if $UA����U0an orthogonal!>I�-K $\O�� pi\circ U!�rc�� h,qd12�0^� appl��a&s$�s.�igs onto�q M] {quasim�s}1hiper� s. Aa�!�a��manifolda�����>�k a\;��+ b͡m = 0, a, c\�RR,\;\;be�2� :��i� �A&n a���J  $g���� positive Ufm Q^.>pA��� $a=0��"�asser��$(iii)��A5q�above,2� $U�^-U�ɫ4 same=�6& i��yAT�)�t�<)�as-� ,tm� Conf}(p,q"�� O}(m�?� ��rm.$� four�� onen��dx� Minkowski�`���nA��� $p=1, q=3�1��c�:ao�[rA���!necAto�iRityA�"S2_+f$ is a*i_ "�}iIR1,3"S N ��m �cob�!-�erv�%A�future-�ing � �"���.��via% Ji cdcv} "!�ba�Dvarepsilon_{\BA}\}a�}^5E�)2,4�Lat obviously satisfi-" �$ge\vcx_0^2�^ 5 1��41 2 3 4 -J;� ��A {\BB0` (\BA�d \BB)�' 5r �%],�5#E_A!-4 E� �)cr41} E �:�E �E �E �E �6�o E_B!��(� B�&� 6�� obta�!  :�cx!%!�f��� )!�"�li} \xi:�!)� gh \la_2(��A+).� E_A & & \xi(E_A� �A}5�$m _ � >� �ť"��)R�eqs !� ). azSA��^EM� ����!�e-Z� u�A=mm��>� ��"�!��$l5���B  mmb$n 4mb� ;^A!d+ �%K* ��J#,6�e.��q*�q� �� ��soIis�"j�� �ofV$��a $2� 2$�wnent�$�� 6��#A!  smvarthet �A�*� �isUBas%Vq �z E_i.�X (E_iA� 1\\0N�-`�B1�0�=:?*�and��o� � �=e�:n��A\d:�\=���M`A� I[& .�\\ .�)5Y� B= N }�:$ aJ:m 2N �))C6, i.e.�i;C 0$.&� cona$� at*$ 5 \Left&��bo!\10,M*m%2> ~ ��� 1  = ��5^2 )  ;m6�. $ We[ =T aloa}?ll=_2�,\q��$u."�0.%́d U@��Uz�ɥ:�.�� y (E�.G)_{11�Yis&V �( �(xx}E4�":t T = x jx}} --\W� ."i<j c} x�뱔B))�&�3m�t���� ��fixa�!h��2��2� ^bT�$choice doetr ��a.��p�i).%�iR�Np55��s-�Mm��x��.! cc}xZ�x}A��1A{� "�x &)� x2�>9� >� xx})�L�  j�9�-m����.24}*)$ wh�#W(�V�G5)^2 -i�.e_iSj��j2z32 0)^2�bM�I��Xco�(z.�I*X162636�= 02� ��6� ("z �)).c$:�%&c6�� J=}�R��$ g6Mll}�b&d]q� �C�"2$/ if,%U only its��!�($a, b, c, daG: c  ���h�m�*�eq (i)&&a��a}},\; �b}� ;c c d d}�(*]-(iM?\; ?d}} \;�R}�3,:?@v dc}}� v}} �Y 'Z+�'c�R for�/v>�{�12�v!2^>�b^��3!/��.k�6$2lk "�+ c �!�*"�=� %a.�v%>>!-M* 1��C�s(), !� v)G(* al�$�US}0hat{\si}}(g)(��$g �g%32���,A-�1�l�#| ��${l:JM2D�O&`2�v�#. Inde�,iB��*:V e� B�$>'xV;#>D6z��!. �:Ta��E+`�& m�A#+ �M�AC+ xq� b}}&Ii�� a �A�6J 'b ~a'! gD�b��0� ' 6�J gJ��a�H� < [  x�X a}\&2H&=&=Fll} w1�'\\Y'v"w}2EiM�"E �!e�,I�j lastaaal�4 (� idero$wE9I �',\mu' %$){es "4ra�r8(�$g,$e$.�5� �B�2.�i� . If�s� W. vd,FT �(�Yj%. U" 6�v��v��$g�g� � � �1��f�w/+:��� 6J�\;Fl ;& �ő�A�6a&A�- a;��E� b6=daT A�-A� <��Y�BU�1$���� �f.�.- 7:��DW)F hust�%n�BW)��I6U�� "Ks:� � Bz(x� a�cI>>�;=�cc}�xN�+xU��3� 2� t .�+an�+ J�� \{g�� ���+g��g&�+}:�" ��/�mXj� � :� !LZ��a,b,c,� _t. $=�0!0:� !Y�FBz+us%�0v� "�:F� N$��*i&��2g�  g}}^�5�2 i�g> � Vu.\� z�,��e ^'o%I&U02,4{<8^CZ��1ƀ+��:���6�:]�$� + Fix�==�pA�B��map2�* :���% x% �$>�:^���JDelta:Kx'& x�*x:�*�aX%N�*�a\Wac59x�*(aq")(bd)e=� �� ({\"�0 1}}�\RRmo:��3weY!���*vah,he�9*Y*4�"8$isodirac} :C�1\�<�>�7`24`2.8)@ :�3.AcDu*F5�>.=m$4 Bjcj�: ��*; ]�.)@9 �/ ��9M$^z�9�� a+�ce�P;.'o,1y:b $gin{center�tab�(}{||r}\h�2 !-�Map&Ex�%it Ma1�$$t5�$\\ >  T�59&$x� A�h�$ h6�$3$ &{\foot�"size{$:11&h|.0&12$a� vDiBs \rho#,\; o $& >m>H\sqrt{4}&0 x/b�R<8�\mmg �*�2mm���% 2. _4F >=�0&�,:l. Ina=�-�x}}$& :Bw�\ 1&0bEv�#&a&A�tIx(hx + 1��;\;A\ty$&�%2B}�  h: $�MMDQ�@ !uN!kdex-fre�:�)ic� muI^ a�As �rivially�8 lizee�:�e1"!:%:he on�(��&, � J� G>wB�D� d!% "�:�%�<ur�(cover"8D��,&�+ $id_{{�T�A��-4 rI�2$$ **9)02G9.�E$; $:�� !A&$. 1_2E��_22�2 :0-1 �2ibi�b1 2b.2��- $1�.�Xs)w"�!"4i.#!L�0x diag($i,i$)���.YFay,bN� ris!<P,chron�-"(:�g2�"�E)�}E&��.O�24U)2Pin{a!�%pm i\}��� ���tru�(D+��}�^ ,��Crm6�2~&�/02FA� />� �/2m#� 6�EP \stackrel{2-1}{\long&z��"[�0%u�)���!4e��ly% B? Kl74,lau}�G&w4�OLix0�H;*�>e�s} SP�$^*-GAU%=i�taFAxif $Bi�$Cwbi D,�0:#bcz} BC�N(langle BC\r _'B2�B4,-!�P�|U$1�BE-B$ eC C� "�KeueR.#B ,.CMv9- bCB.< �o  .%Ca CU/!�B��::f�$ (i(&.u!V- i [B,C�=2F8�"$Mˡ-(>_$,\;[\;,\;]imatJH}+62��&� �6}� :� qF� �&.�$\L�^.�/�/1$�3dimen�L 15. S�Mdim= < = 15E�"12"�Qth�Z stige$ now.�7S� �Gisoimu��Fj��"�G�#!�y'dhOE--i\g_<(ua(+��1e �1 = 2334�Su�#Sec. �O�3!at ".driD2i26)A5 O�Io�3&�1�0�$�3!�91���m*N*B�2.-G .A�I\{\g_\mu3�0}�is>c.�M2LT]Ion)� D" ��j�AI� �1aOD�KP�@� i}{2}(%�! �( 4)2,#KC-jD-)zZDD @ \me (4r52iM_!+\nu�!�A� 5\nu7\mueq K"?5M�A�)��I�A )A9�neAL.c%?&���+ E2-����T� q.]me(\g��!a! g_5fLm(4-f4)</i Rn4 �!)wedge �).. �iThe�6>O5Rhq [EI, P\]%�m�\�[E&, K "�: 9�, D��0.�%\�2( P_{\�,�2 w-()4� - n.mu2|JbK�b�Bb�6b B2��sigma:[3 ��mu%nu (AA % �m(n =  K #2c�-��.�21WaD -�me�6�:ID.E ].m-v%-,6--mɥ�^� rU�6roach� " A ou;Uf�Aion, �Y�how�or ��� �V�he>e�c*{3,) Penr� classicala�ory� �t a mini�Ylateral�s,:]�D �LCw91,cru}. Robinson 4gruen�D+3rU?c&���atPV ermi5?acP=p1Cs e2)ar� cept.e&�9 i-�&Q wo�s,E{�:.X J:�U : -�5�� J.<)ke97}�� e ]�Eors��PP�l t X}�me �mt R},$ L}$)z8AM� $T_{\Z1= 1� g_5� ��0^��i�Xw!��C som!�s�H�/f).��me*�[`A�!B�[� {�>referA$1K#eta_\xx�:}S�i� $\xb$^ �ea Weyl�\dot�0x or (*�L ��-ha�X2Go""aB :($\om$) $\Pi/1�L}\om!�0\�7\xi�.�2.�t� � = T� BO(1� \xx)~i \vbn�gr =)� , o"%Y�g��(�,c$i:%�&�f@��alisma�e)ur6~ZisA�d:��O�=>�%R!�[":2 *�I&0�0&I*�'A�BR<�F?i_2Af>�vecA6�{^c2v8�HUAp!� Each~0y� !���'SC(J<c�I1m. .d ref42=�A�b'x8xZH x^1{ax^26�-  %0 -1.H��(�?�4���d N�$�^c� 3$\HH$-co" \!4+2�͗.^% )�_r|X�+.5fr,}�<\displaystyle{-i9P\xim�!�2�5T��B/^ ��Fh��Z pe1}�sig�y!firsth �Cis dif�Qt�Vi�c3�r2�B �4 �\g(e_0qF*az\.�Ra�*�$�\k \kr�R0&-\si_k��(2�}�In�geEc�7ct%c,��u�\BZ_ simi^L� %Vone, but�?i��4$W3$��l�E(Y�"� YY$$) through%�origin:�uM�t-!i����b�%���)�2�.Y� E�.�X1�qU� ͇ fre1:�uA�2�b��7R��, 8 /F&� !. cA�0�#m��2>c ��OUf<(iMN,)f$0>]f� a�g�Oidempot�9oa�� !;zF.*��)F� �� null�" $� x'�!k~��Uwe�Fx 8leFv�7**�:�l|Remark�)�=�modelI8mJ(t"�l"�"]$$"  =Ks6�, ](q,p-1@ !��&�!:�, (�/s�UQs,"39�#�2� io]= nd dI2s) ex�TsDo!lZ�d of >"�3ng�a98� % I �W�n\�alE��i f��"�gas�A�!N^= �Ae�-�&�0G�m*�(u  .�,&Y �]cp-J7�^. !<< dund�&# is elimin�". Alsoi�L*�,�&C9$"W�q� B�E1 :��+9*�ڙ?aE�Y^>1 s (,F�- depVqha���& �)A)�E1+"7�E^a*S�id�MFV�  %�y At3A�E�!l�X�e�7� | �2�M. Our="is.�*+!EM� 0r�.&a�� pI�G!�.��I9e�0 &�xApa�ix}"@' {Standard:�} �dirf} �g�7y� $e_{I_1�e�T 2ie_1e_2�* take0benn,lo0� � mfgi} P_1 � � U5!x P�+-+\ P_3S-(+(S� S.+S.\� T�(ff 1 i�&��F,."�+ $ e_{13 �( 18 = Ph(\�e_%*30.*(*10*12*4.$� n� �yas�s&y%� 13}P�sEt���)P�v!�30:%32%eO(1>(42(.�r.Ri5TxJQ% �) \2Ek-)2!W 3)1P_6�[=-#."9 eq D�-�'dij]i,j=1}^vV�(M/�-$cal{M}}(4,�=�( w�X�d�!G�Q1j}#E!R1=j-- (j�)pi"&Xcu�e1 �1.�* e5'22'Ay% %�364!v9EJ41'��t othe�ij� r� �)�!Nt�s:��=�:nin"�:{|c|cccc�= U& I�= �&%1$& $MP_2$&Ao �$ &i^A}4$*c&I�E�$:�= X3 �2?(d > 6�|$&$ P =bF;�1- e_{0%2�=� P6<:�2�;)-b*D�I*�X9*6��e�)$,|�?$\# �"r�H�ed�"b%�$itemize} \ !b0�D+�> -!�Qe1( 22�' 33 44� An�ge B�\.�cc- 1&0=� D;N�=F!@-1)^ *�6.~2|R \.NR0&-.�!i��3�-}��I:=�B�R! �*�;1�A‰8M�+ A�ah"1 %� P9���+-�2Y3 14}.$!���)�r) !zg  .�:!��[.uB 0>E*�?=�/�{{� s�^��1 at@A�E��m\g.�>��I�1�N`�&� 9��9ց��1)���-�!= %� u��r-)�49��a 2>�}GAM% TeVg >J��)�!�E�  -�6'a�.=�!{+6� thenmt\g'�0!���"6���36�R!�32�9�1��g�a�m!�" $. It i�W8�q e_2 ie_0V 011 )� Sa� Z 4"�| >��7}�-a�M41}RN�PI:�5�1\g ��V:�%R!V26V\}1�F���΁� sV �� h&�&�n�by�&E�E�j�"� M�]�P$�P$�"a� 6�~W�*6f&N wer}�) case��5> "N5�* �( n� Y�E= "=h�v�5� ��5b;� =J*&� G���& nPa z.*PEo7Z(�s*� �  U e% �e_0K/ B$1$4]ɤ%c %`01.`2��C M rIZ"� +m��"(�pl"^A,��#!�.P !�i1*I 6v,E>��&�6r,���.J6���EVL 6a ��9;m� 1��R�2 )r^ W�<^<�G mmed-��f� �"90�Z9�N8� AL^8;at\P &� exhibiAE!I�M�M)�� �K �P6� KIHC9 ./ VFa ;8 yGH_F:-&G :I� y:��E�;e�� 6��j10&1~-�Py 0����0 ! *H a]j:r 2>Ve�N>Ʒ I�� ��*o �\T!.a�m��%�f e7 � �J0�4 �: R *] :: �O"4a#{1e ��> �hU AA 6 �@ 8 2f7 �� -�� $i e_5�$� ��.�\R"�n ( -i ()�:,�%��-�b�r*Ic-n��(�Q��%}#mj�-i� >�0& >�0&iF+7 i.�]�>~f�N^2R0:s21� ! i(� =�� 1�4$.�5i&� s�� "� ��(�K F��  *� �y4"�ep%�ao-�� \� �'_��goV �� �>� J�0&iF�!�>>�Mx ��m��[ V g�� �K"�&nGR�A��(� ,%�s!ARa�!e} $ }e_5.sFwsvn �$%r\$$��35:�Jt->R:c9>l�b(�H-m���aJ���WF� ��F�T%&�)Oj��3�3�3�hA��Hthebibliography}{990 %-�2% \bi� m  } Benn I~ Tucker R,$: An I�:,�p0/�G�=yx3*h|#`Physics}, Adam Hilger, Br�l 1987�;�� Loune�TP �" "A.OG �\}, Cambridge Univ. Press.1996.)g �max} Max%! J C jA T ��Q on E,4r���XMagnetism}, vols.1,2, D�'4, New York 195� %�8abo} Ablamowicz!Y Ozie Z e�<Rzewuski ���"!W�> .�0,:Math.%g . %� �.2 (1982)9�jan} J��|B,� it A�&i4 �icdc}<ynamicKPCoulomb% Biot-Sa�t law%�,anisotropic � !� nnal�M �� Lond)�42fpe�&EGi� Rind��(./�!a+� .2: %|1�Method��S�Q0� 8L 5�pe4} ����Yp.���)A)Grav.�Q�00blipolis, Nap!�># pe5Jp��c�a�? me�<wj w,Chaos, Solit�/FA'� @ 7: 581-611Et9)2"BH8�Bohm D�Hiley B �G+E��{A��:����y�H7P�&$,a�`Rev. Bras. de F\'{\i}sica�85a9�(Kl74} Klotz�U-�i�:�.Z�1� 42-224e{7��5�Koa|T. an K �lP�eq�� revisdZsif076-1085� s AO82jK � J ����>iu�rL I 2�4231-24RQ yJ} CrawU�J1:f�:s�n sE=k �-+(, Poincar\'&�4-Np0�J.J(2�576-58m 916�$Ho95} Howe"U2supersym� ArLeuven%� I4on High Energy& *196�0LD92} Lasenby� Dora�P Gi4S-.2-)m.i�I�2���aF��q8 }, ProceeM4�ihe�Sond� Born Sym�� um: �2,65�Ac , Wroclaw�2.� Bk91a�u rkov�4N �A � �/p4; Ն�p'�le!\ten2�.� }, N2B35�>193-200e"1a�u��b� �z�1� , $N = 8$ �� iO��!F0Green-SchwarzBin� B�8�69-18�� Wi86a} W�;E-/ �-li�.(5A�%�en&�3A�:r26\ 245-26�8=rmot�eB-s Neg Motl&d CubQ4Is�@st� f� !ɧ' JHEP}�p04} 56 (2004) (hep-th/0403187i#� b1=��9� �1Egr�I� �- �2}, ��bf�09� .�605E9b. 9n:5B2p%� �I�ŝN=4 �,-Yang-Mills}�H ��.ɹLett.-;9�Q11601�.�204��9A4:h ]&�1�/higher2A �s}.a9246@ grscwi}I� M B, Q�J HE5>�S�+I+0�!�v I \& II.z.v  &i ���A/Chiou8SW, Ga5NO�X Hong Y��Kim B�>�:Mitra I1�M� �nive thph.23Ej 9�M\ 6 ini-��b �U{=�+ D71} a 5) 1250169p50207i�6�6� Bars�Moi�HPicon M,qv�$ �i�d D�Z�*a!gfy� RolI� :�>J��,2006) 064033]�512348�'1)� twis8�b� I�Si�\5!N5�!�� , iΐ AdS,%��/.� �.� ��03=�120:(�KB� -3�� Fm��34� 6��9�pe2.� ɮ� 1: Two� culu)�2Cw!yP.h198S � Be00��N� �/�6�� �e�}U nsxs.)��"q& t6�y�mxBN]"w�KA� �8J, RodrE guez A%�Yamaleev� : �g'�ic �?ar6� ov��&�@s7_i�S statE�Adv. [.)z;gp ��75-300 ��>�$chev} ChevI�y-�� � ico�P� #olumbi�*&">� =6ABS} �E5�m"C�ry}�0��*< � �0oq}Coquereaux!� K� o 8 .C� of r~;�2O�4 p� ����bf{115B�89-39e�>:L� ��j�.zk�V(CT -�,�M�6ex�� �OgN Pg�a���Z}-�(7}S, 439-45%9��.�GuLW0 G\"urlebeck ��\"�g"�,Quaternioniceb5�Ca���!�icy�d"@A� J. WZ,�8 iana� ]� Ku99} Ku��s54��?r S�lce�PrbH2C1996� He94� Heste�D,[q it IC $t body kin�$ I: saccad- compensata�eye move��Neu�Network5� bf{7�y 65-7�9�=Pl8�'ell!qs��$ Llin\`asaI�. enso� .�AC"�ofskin"?l(: cerebella�� ordicMon���tZ � osci|?+ {5� 1125-1136��802� TC9��TweedXCaderaAR �Compu�� 2� !F�p��I|�?velocit� VidResearch �30�97-11� ���!�\��I:��ch� ��neuj�r�!(alN� 79-8d-� m�� MakY�(1,1)2�>ofyv�!)Ge�a�> (anti-)"�p"m �A�Ph.D.R?s�( Technischee5Y�(teit Delft, {e8  �or:���A tutI�oSF� Ӷ� (� ���Qx AnalyV�!jTR��ncru� umeyrolle��O&ПAj]le���ql}, Kluw�Dordrecha�h,eu} da Rocha�Vaz��-~� s,y�M�Ex&�AStrucRCz PoS(WC2�022 (�i-p� 1203��*8&w >� textquSlbl*�s8 %� 2V�s, %a�.�� ���z�&�# cra2A����~ų �u| �u�(da1} Daviau") 6� ���U��/ ffie%,h V et al.(e�  %e ;Q�E�V}�;��u�F�k isheA�2,8% �hes676���R �!or "%J.y���798-80�c�:?ke}�� 6� } � � ]%7} ({ S'?J� � las0b[Z-��\�\� 92� .�u���?��� % tb de do\adosJ endida em�� ozi}6�'Common�l,&�&tou(},y %�JV>f"P al}E D. Rei,N Pub.� pany�(�q��ri�! ieszqiA�Nuo�i�iQa��3��A E. F. Bol�KeP.&$�'� %2�3����"�e��itz��% �qyqzi{� 1� 92':�,>�+$ docu� }Z� \�K[11pt]{�P} \usepackage{amsfont�h6�$,amssymb} �+P Tamanho das Paginas , \oddz,margin=6mm \2[:>(8J(0mm �,width=15.0cm ,height=22.5c&op r1#opskip Cheadsep�, E�a!(o � e�Mlin�q� \new+"Land{\blst}{1.30} \re2ase�stretch&1�[\setcou� {top-��o2bottomZtotal.6ztopFo^}{1F�[n"B  �.�$hko}{\hook aѯ}6clu}{"X^+I:$n}{*`V:ff*�: (di}{\diamonϲ.�da agge@g. sd}{�Hbb{S}}:T LLL} �HL>bec}{�.�"er>"e"Y0Z }{�}r_{\vcc�2�d#�:�be�bFFarrayBx ar}{xRfii}{f��. mj �bf:ph�h} 6�eps 5~�6!EE bb{E}}2qDDDDB!�bf�:Tbf� �flushEv:@iA�iot><om!Vbf{ ga>\e\!�bZl~G wN�noA�no�\nt6�R!�b:�ai{1�6;s;�n�FI:B#$ov�-#6�c!��A�E> wt}{&�w>�wA widu�>Wl!��}��2�as bf A>qca!�c c\~ao >6U7'B8oeA|9 �:�VR6� 6N2RRY�R:XMMM: op}{�V:kHH5H:5PPP:x�W!�bb�{6�ana��:b!�beF�!�+�:2lA,L�x:bF��)>��3�f^#wALedg>�g}{\gamm>xom!KR�:�raQb6$rf}{\rfloo>�ll 2� ty}{!���:rsr�s:v!6va��:beq=9n�2{ben� ��enume�|: $��"6 ek#i6"m!�AIcal t��{thm}�2 orem "�Aa� mt{ABvv bf vB e >�a��B a:�bb 3b>Muu u:3jj j>3hA�heart��:�m��!��:s��sharp:p!��1;5!ff �f:�v� varp>Zww 2w>�CC�C>NNN>FFF>KKK>stk}[1]�@(ckrel{#1}{\:n�:�t��6cdwnM {\scripts�l #1} \dowao> ZZ�Z>he��Q�:kbm�O!�bf�6�mn!d��aRnH�ac�K}>l mrrj0RF0cj/CB/K!�A�!:�ul}{\��:o��:vb blackt�vgle�>&vB&�96�Lh!�B N�vaLvarrpa+$N:�sc��"��Q-Y3{=���CBsp���n=pi>ns�T�=o�y>�m���@eeB=�c�=l�:~TTy,T}>� zA�bfaF6�rI� bf{rB�R}:6w�y{W>x iXBNla� �6�noA=&�h:spiA998nshortmid}{\pi^B) Hv� ��NuWQP"P:~OO9YO>dv {\deltaB�nbW�$et{s}\nabl>'n��e�.% _{e_B�nb! >P+B� nbaHN+c>�k�{k}�ml.r.>:x-� �."yyI Bqjmj�mi:i�:dfG - �� x_1>�df��f12F1f13>1K��ՋK}>NV�$L$6>mkkM���B}iax���e.�j2j:�k2k>�u�Uն:�ivI>:m.�:;cMV{\�EF�cltA_&B_M�>GlE1.&1,B�yu�3 ee_12>� VVn bf V>cO!O� 6�OM 3{ >9ss�JLBA reve{B�BBBB>UQQu!t!8QBun<mm�=E'sB>m��I�"uJ"v.�B� ��A��T>�bx��p�xB�e"end^ {c 2�k�>�>�`.���2:�A�FB�mmb2BbJ"p2"p>�mmg2!gJC"\ %�cJ"I�a��eJ"c ��bs :�mm"�kdBI�v�� -R>sGGM bb{GF_ �f_IF[6tN  \ragged��-2% �Uede o a���vf�calkE���, sobre figur"t �I�hs7��co�5���| �2Hsd}�Ii o$} \title{Rc7n%"���)5)II:\\ �F;B�o��[!i>{0,T�thv"� \author)� Rold3�!(}\thanks{In^��2�8lGleb Wataghin (IFGW), Unicam#@P 6165, 13083-970�-p (SP)MEhazil. E-mail: roldao@ifi.u H .br.\�rt�CAPES.}\rf Jaymex", Jr.�De�M,deJ em\'�B a Ap@ da, IMECC:�0�859b�� vaz@ime�adate{�yke%�A*\a�e${}^{}$M! �1page}{1J�$���y ;\;$�paper�R!��� one� a s�� l(E�K-2�-tin�= of �drol*|We �9ew���age O"�72Rv Ant$i .y:�E�,�CA��!Q�a6%_>�(2W�/�Wof^M=9A��av��l��6 |q!DqQ�1!RJ%�reS�.� =a&�wi.- Paul���w.�n�"c"#s�contrava� t un2��>9tHH\op�~>M.!�p���K�be e/� �h&&C #�gb$^+$, viewe��a �`m5/, ow�64�|�M.<q2;�yU�ume��&��_��a%(�*{I*�I} �A��,$%z wa�� velo3�p@>�F�Wm- ��p|kt way by�Z� ia�'�/is�� O!:ee�hand,a Ca��A$1913 wrote�@�Iy�outQ�m�c2}, af�)he e�?�p/�� 0Xem�entita�tYtw{�=�ij'o,�"�m�<|X �to Z�6�,�n��IHe%< inv�ja�ng ^2Busi�X�<."X@A�-'�ww"숅)`sV�ja�wa�"#�of9-n�Gsystems �Hb . W.i~�:1926, G*c��0:"q0:WD by a 2-�.*Zor!�his non-2w4ly-��H. A!��,8, P. A. M.�pm�a 4Fgto=we `6�3qmHmmH�0�l��M�. "6Y incr&[ng{!E!0ein-���7ies, L�ifel�kB. L > I l inf}:�, ��!r�%>tbM1[1an��eT;d�1 stu���b N$ s, o�DyY(!& lear��IR���r fundalyG�7b! matt�*\t^�ed� lept}Bqus,&�tyZf 1/2 f��-)huang} 9ni�"�qbyV%ɝA ors}"� {2e�pd�sum!����Aents, cl5��L.��0�2o�8Kively �yDA�"�t >%&�s khei� SL(2,�$).}.&3�� ic��K,���Oa"1��?/i�paB .���i��)�C.*d6)vz6�g�'m2ai)-a�p"J oAzmp�7�5�}m�t�E}w , usA&�.`,�n2 �f2A�!>F� �BR� '*$�2��YW9, toge�r�� (�)�1�Yk2�B��6\>�f�� ��A �^i�G� o��w�a��2�:a���1��H� briefa�m�$F�s��a�c/3ngFO�� Z2 U�t&U g c ,�"o 6��29X!�=�, 6h!&i�)0 tran=�as.z each;)Bm�E���n�-+� .M�>^�t$�9�s3Kn-#35n-"(4"& (DHE)���A�gQ uced. DHE��$ as�E coup}�eKsq:)%V= ia2�EQe �xtetra%��'I2�Nia���m0�p&�MF��71!44W~1<6� A:&� (�)QV � in %� � � � HHA ���ښ m�  (+ �&S6 � )�� &��.�}b�V$B}aV $n$2�6�:._ � !\iVQA�te�7�_ $\big�� _{i=&��T^i(V)"O�H�we re�@ct�{��nt�7�=s��"��(V�`k`n#^k`of mul�(ct %\�($2) nk ji� anti�Gic $k$- �� [.�+L��({psiՁ�#�, f�=4ldM�si�y�K��/v.�� &�X298 = (-1)^{[k/2]}u$ ([$k$] m �D-g��art� k$) ��P�he ��f*7�d� � grad� v�*�Ora�ity ope��.a�psi6�aL:�� kze4�}� $4�k C$S�conju� �<d�r1l*eyxi�dAab<5��^ ?!!B����V/�e.��a� deg�8t���Iic, bi (ar� $g: VF6V \�a�+ ��,� .��V�B�lE[��$�=u_1\wQ�s\w u_k��w�=v2v_lLfu_i, v_jA�V$e-s $g(V,u�)%�\det(g(4v_j))$�~$k=J�R21=0 �� l$. 2�>��}��si��si�� 1�^ dots ni��_k��톅��$p$\�A�{"�[���!L �p$�i Tp�o� ���ba�!� V5ee�-�a�kve = v\wE� + v%�$.�k&�1q$( O,g)$ 2ms�i$&��\cl(V4o!Nk�ez�f6�$V��RD�� p + K��Kz�2� �t$}&�� )2>E,�fo  Mic� �T�� �h.6kAn B?�/H�s�y3.1.3} ��C��hee�gee_3\�an2�n�l P���Y.��B5Eis+j�t`w i ]h p,.ی>e 2g(i�;e_D�2� _xv�� jA�&w�\qi,j�, 2, 3�jTDJ�m �c X|& �b���� M�ara^�1 + a^��ea^3��eb^Ui9�^!q 3#23 :\+ p\; �; �] ^i,-ij}, pi�RR�M -�f��=*��-W�X3)�V�z%�! , c�l"X�� ��!on/� f_+ f_- == �� �|��͛>>} �I&�rep11} O�.זgin 0 �&�  &�a :�a��*�o),-q ײB$bg0&1R�J%�Z-e_1-e�f�16�b�J�-A@1�16�dl���qgeA�^ft�toT�. X�>A� fourq�x� ��T(�or )6�.*�: �6�isofmai�.�I�%��&^a"+� not �� icul��G�Y��pzn:"^+a��oen+ 3���$w_1&-w_2^*Z� w_2&w_1^*Zx"t�m$f_+*'Ґ:�fE�0��1l�! wNfew_4����������Qf_+��A/�3� ��}s rednc��� A� �sp� N6���) � .,�aXis&v�i*�i) bnDF��toa�ps.~� =�H�2��p+��'b^���6 ����� �� �fig}:$��8$\bullet$ {\ul{�:Cn�}} (CUS��\ cta�~ a{|l�~L{\rule[-3mm]{0mm}{8mb�b'��f_+}\\ �o�i�) Such ���-� a�q >Je�(��O:� ZJ,3})(f_+) + (c�=��)� Ũ)�%M� k^1Ck^2,b�*j{�t�|�k^1�B�3�y�yandH�k^2,�R��kha. CUS chosa<o�1k�� G bec�`AZir "D�mmute�a#- $\{f_+� 1�3&�c $ic spinors�. Therefore all spinor components are written as eleme0of the center�L$\cl_{3,0}$, that is well-known to be isomorphic to $\Lambda^0(\RR^3)\oplus\L 3( $$. From t �d$\KKKK$, other three types� % s in�t$ ��k}}^{1'k�ol 2 ).i\��. nEe�eM*a� l} 2Xa�)s!V,�� 2'2 2}���Iois �0. Besa�@\footnote{${\bf AH,{1, 2}$.}, $9� }" (a + b�{123}F = $ 321}��a -6$��suggests% not�r� DenotingF� $3subspace��is%�4" 4.1pseudo 7, �i[ smCY  \oZ q [.h!pevi��, s�E�%24^2 = -1)$. The� $5�1p= EEY��"! `if�ee c)d!;ed by !�,mathfrak{I}}�i��CC$ �rever inML< ~�lequival��to%e$Y-conjug%� .} M�Q�^�.! $ Finall� e \�e F� VDS)!�.� �ao�o im�yw ul{%�1!� )f�f&Y it� be sh� hat�qI� VdL ��- ��)}!�1\nj �&r��>A&=@� ��2G��2'}� � &Q �ܱ1'�� -65<  8}e 6_)kf_-��(1'}���AsA�5! �� f_-�xe%�V�, (D k}_{`%X|��Z�f&�Ff� ����A�����w1��6}\\ � 2!^z Th�] Pvan der Waerden paper&� }�4(unceasingly� os� (Penrose sema� work� � Hpe2,pe1,pe3,pe4,pe5:� v��� � !�eta)�!%�A�� (%HT� t r� 2� �$&� $AX2�2q� -� -]�J� -B� .1O��� . i�� }, {\bar{%}^**� � }E" = :R!� � q�2e�)(I{ = +� /A�a6� F� ���� -}=�V�e�{%�)k}� - �E!��')�N"�&� s foe fourk ic Wey�s, :� a lateral� al�$��k re lis� elow�0in{itemize} \ *J.s uJNMu �� %N�� �`k^2��a7)$ �60�B�v N������Iq���n b���hQR��itVC2eFN� ��"� K�%��e�k�B � �&� r�2�F� ����a> �%�-(f�Z�\ = �.!e�_{� �'�? k_a�.�5�(6��|dy5T �|Xdiagram illustrates how�i pass� �ida��  s,����i� �ay���ur6 u� (�-)auto�smO�t$: \v� {1cm} $$e ,in{array}{|c v i�$} & \stk{* 9� �hat{}!~)� 6I� )�7 eupZ&v �c2G & &c� .� & & \\ �3& & & &I� �q�a�& &.��Ge0��)I?)x%�.� W n hav correspo�ce betwe�formal6�is secBSA.� exhibi��l ��: $ be.z, \GG^A \Ll\c�+,\quad \GG_A\Ll!& 8 {A'};a`F_Y:��� \sub �{S�� tran%!8s} An arbitrary $R� �e�&� ase0e R = s + v^i�6i� ^{ij� + pd�hap� be !\gamma 3 delt 23} J!�t�$K ~b,\;\;�  = b^{12jv^3 ]M "\g ovM�,\;{\rmA}* �=b^� - v��. Un� AGaIVof $RI CUS"�!vs!ws!=$$Re� = R(\psiA��k^1(R��(R���+),��no2weP�q ;� (!+! A��\g9b!� �,*�  �u�W-RW-~X� [G .[ [{r[� R���%� ��B2Q>N.\A �� Thena�՞"kM  R� R�IV�rm:M����  Gi>-�$ETpin}_+(1,3)$, i.e., $R�= 1vsVE�det $Y�1�� TSLu�z e.��6�~&!B�\:v6h ) %y� explicitl�h��. \ M�dk!,2 � q�$5�R^{-1nd h *~ uaaZ ruleverifiex����:�� xcv}61lll���  long� & R ,��"� 6$A�1� �e�� 6 M� E � Xa�� 2F� 0 ( b)E�V Hlde? hU��) �.�A)%s�� Q >�(�6 %� G6<,2��åq�permi�oٚM�+ 4trw:�|ll~ � } &=L& 1�n�)�^*-�+9,> (-)G86 6<&u%B:1&� .!9 nge �� IM� �rovM �Uau6#űCUS, q, CDSŀ� e e���#e same� poin� & u� "�! Indeed,��� )� �2�[{0R)}^\dagger)]I�� g� ��".�(\refIG)�D. r�%we�4c2� �_ �&��c�Ie&2 AZ  $& 0A k^2 �O:�,& � &]V~] 0 & 0 fA��� XJ� = 9b� 60 �\� - ����N���>mҩzLlFbor$ &� � �BP Rp^*~r>�`�!gu:�$Z}.N8>F~��F/I In or�toe��.��djequen��a�DiracH"),��enoughQoi]he [�� �, ,N�$��!� Clifford"3# by $���&U ,BJ~ C� �s�$,��� ��"^ly�ed� L:")2,�!"  e6�)s�#als�)�9)Ptheory� para mode>E} �1sec3}!��( R��intt$ e, accordK o HesteH'| hes1,hes236}%YLounesto (15,41}, �s$$ic descrip� �e2J�: �-�equ� (DHE� We first 4%8e some importanA&��!uin, e.g,2�!dpg�$a quantum 5 vistic!r ticlQ!m $m$, �bN  $H� ,n a backgrou� &,electromagneQo�'$A$, @ |te�&�!It will�u= natu<�%s, sucr&a9 hslashY %Z$c .} � itz}�WMda�BP ~\,g^\mu (i\par�_- e A )! �i\ethA�Lmb  \in�^4.S �� "m.�Ps>�1,3}^+"� �4��rY- � {?. 4c + c^{01}\g_ +2  3 &c�0�01 Fc� 23} !0� �"�" standardE�es"��\g!X$9�,gre}a�"�R�' �): V$ cc} �&c - i �&3o23}&-) + i!51�!:\L/6A!qM12 M1_ :q)d_6L6 �2{&n�:Lzz^b�g :� *(%lbk1: \phi_1 &- 2^*& 3 4^*�:)2 )1:4L3~;d m.�vv.e <�^�y���{2�, A ���*}�` � ++�&�!�h.� $(\CC\o-�7)f�. $fLfrac{1}{4}(1+\g_0)(1A�a�12}&1i/.& *'�cVm"� ��� �\op -� � easy6 " �� .F of a�6-'� $sum� � . &o )�)a� (aR&-$)2�f�#s. A�A)�%��'J� ��!fPhi5j2}6b�V?-�%� $KZR%�EZ5�1�$$ is two E%-r���!3��� !P �& e&2*@*�� -geZ \ni% QY�A�B=]:� e�1 &0&0 &R :'2�'3�'4'^sJ�se0q�N�v"v�2v3v4��=V�f�si_n�sir�sir�si��ab\CC^42Q�, , $4~Re}� Phi� F\g_2\g_h Z q�i�^oib5�6��in ev� nd oddev��Phq�_0�P�6! )>Ci�=  (:5 $+J$1b$2>b�_0l2Vp ;& M[7Tak�9�G�j87y�cl_� heq.�� ) �!#)� ] f1�i  = m2�`�!b�5�again�F�6���qv�{2H ew_0�{_1,* %4�%-66160.+P�/� 25� F}AZ� � "/Ps!!_!� )��&V8�& he2*��2 �s!��{m�AJ}� (� cle^+"��&j8& All��A:" above�now. +��IJ^+A|�"�simplif8.nV0�!Ge����� � :! : � � �� 2. �3� b^ -< � 0 ,�(c, b, ce, b�YRR.g &3c^�c^k� k0N b^k {6�/ ee_km06a A�AkQ6!a�h  %23}!VI&t:8%�j� = A�� , � valid >&Y� 0 3�A �0k�A^0 -�$. & 2{\bf{A�23 ���at�Q�pJpota} p�. H� LeftIjply�˝� he})�g_0�AG�g_0��2%AEd��$ 0,aT"� &I�.�� l�eo} (�%% k% )k6�3�<()W1B+B�I�FI����="� �1;E`b5%�;�G!A2��Hparity operator}, ���&�2� si^PI�P�Aa}}.� ,)$ ��a:-.:+b:- bN:5�Y}5m� _;9;� eE$YAeo}�2re��� �5�r=�_t � ial��xY�5�T!.l 6�,2��the6udWoxed{�_)k+ \nablaZ6 [e(Qe�hi �- 2�] .�E�M�� 6�.� ge E&?cla�� he�(bf�O�O}��!x�A�A҅�t doesaw�tradic�p8ilE�fm�$2�/2$c$ce�;ՁbQ2`�; n, becau�e 6n-2+ �wave fun�%is&@�a �(lex 2-dimen�5al <,�;� � amete�*an��,%�act on{?y_�#� �. �/ri �*� �gpsi�"�%�$=G��x �e�="L � ��!/c !ct��l ��� /or}Y>� p$A��(t"|� rpre�a�V* mpos"� �� ions: di8@, duaE8,and Lorentz >�(m4CI%if�?ly�'!�not a8:� , buM��Z gene�,}b2V��g�ߡ�5a���,2 !�PsiZ2Ps�x����$:\g_5bOrho e^{\be�(> �!w�5 CT6��l�.! dh} |� sqrt }}\;i/2} R�)ŏ�R� %l$�=e�AD8Takabayasi angl�>,yv,tak}. Con"�, �$F9  R$5�sb� �15�.?+ planei�sJ'��$ �Ց�t$}I�:(*��"Ń́,>T abse�,of exter�9field�2:�$=�ploiuy} v:�J� n�{�D��E |�inv&c2erZ)sdMsol�-"e �rejfea��and, af�FQ, aig boost} $LE<appli�Pauli� h%c��� momez�8�(*� p}�6�2�a��*I 6Em/��\i�,3.)_e#Aoeigen�*�B�isbf p}�! RR^3I�͹>?a$�� p� �(V�M��,.fsemBc=�V � �a��!��*�ug)xb�!��G ��q!I_01exp}(-=jO=ee_3\omz,ng)ZSubstitu�iAF�is>�we2� z_0\om� *� _0� �:�u�cas����)�s�+ɣIR�d}_� satisZ(�9inP s��(s�9�$. For�6oE�b� &� d� '!"W!O-P}1(investigate�F�? \op\�>2�I \hko�$. ��� -"�>_!�xismf(upA)*@ ,"awer]A-ťrmM,qw mt2!Oi��!h�s for R�� �eKr\ �J�B� ies:?q6A�2��%�m�1 12 3$ (a WlIO. ine� �bVenume�U7�^.��)2:5HC1/\pi/2)$ '?z I choiJJ$� add' e phA�fac�X �5�(2P�b9�YPs9'1 .��? $- (�) 3Iee=m=t T �a6� �third �:-B6�%<3E�T9q�IP seco�$*9:�U�by ",U�puo"g � p2�1�>�!Dmxq7by eqs�i$��r)�V � r�cyL�#&,�!�".�%&��iP6��x:  �we mustbi $�)1�V�iD�i^g+�*�)156R best9�ip.��v>�ya�� thY , leT"_02��L)D�A+)[� fYI�)br �� !��&��zy �3$,E��m. &d/s�+reason R@" M lastm�9ph� uM�, allzi�sQ;ha��a�&,re redundan�e sens����y�� :�EhPsilW":K>�! Q=B3�'��.�:�A� ��2���YNzP A5�Uo]Fd!�� spa��C&�H, F�>e � solp�%�,K�>l} � ^{(+�:,0{�Y2�#!�0downa4N2��?-2o\f�24Jsb� �I.>&a�<I�Jwoa�to1Y�R��O$ U, �>6�u�O%(9G\ap�|)Aѡ�q�U'.y^McombinE (-(&H(efficients)Ad4Ms � �IE)� D C�O���/M�(�d�,\q#; c,n \RR: yI�+}��T��N� � } N�iFBbiddenqJ�&� $.�mmute�E &� � or�n�(�)%T"^� P"a r1\ i}U� $L = L�p}})$A"��las�!]��m��[y�(E!@� \cdo�{x}})]}S+:S2ZV��g6�2eAY;u([a%��-:�:_�E�af>.v & s} �G)�.! >C%�>Mn> {A'}�)�>. �A�2K R� � mp1X, &s&N�f6,'&�scr�,$'i���+t$}. C4e��)72�%a�>��&�&lu�s?-*lm�}q 4%s rEOK-3 �=M !�1h 2h .ND78LL-,6�#\.4:*� tesd>�# i= �nA?E�an�>L�F�! ().6h�3;B:' 2��!*~i/.�ter�<.�0!-�./I,& ��1s l`6oO N9!��J�,X-��sBO��out>d6� dic1_t!�Wl.�Q="Ap�"(p/.t����Q�a�d.K5As9�{f2E*$2\p�*|$(1 AvW*Y$q \xi &:=&Ie3�ii0+.�~�I}23-� 3-1+��?$&�Df_+ �.�6:/.%�� "ak0�6 &�Ba�"za�ge�=iA�E�Y�2�= q�*o?:� U�.�(gNK-%).�( ixi}�."�%%Vt"�B_\xAK �p2x2�\iu � kmlP"a�lIAQ�onx�C3!xi+$ ��E/�.$"�!cUf��2A��9�nB5:W-$. Se�!�e�� 2D-$e�y�ge�qBP !�!/��)" \\ -�!!�m�2�. �!_a�eq.C'B�5��!E��.�ӵ2����E�,/#  coup��system�J�-&f#!�\\$-9Io!��G� +&Ei�Z5[a�M5M; e.g.�$it82. 6�.�1I��R6�-2}JD*�B c-B�3F�a&�FaB�F�C"E.. &=& FW&aB +L23 �&a^�1 "3" (a^3 )1.a�F 6S�S3j�j"+ \chi�قhi,��^+6�\A�.� %�If� �~4eA�"��) I�A�at�+K &@=�i)�����"V#�m!phiaF - �-phB�^m!yP"�3= �am�ewo� � s. Np;.� P\'eq� Minkowskice0�E��K m]!�� WF&�9uSJ{3.3}:;J�� om�8bay2,bayoo,por1B3vva�RR��B�!vvb]@ !G1�<� A�_1F �B ���&� scta�nd�^) @�b: T"� kkj}W2c =e52\{:P1ll} > �=^{�= >2'AL�?B(22'} � d:�H�Age FC?Ft=3is�2��tN�&�,"�@�>�� A.�$\mma��RR�7lus�q "g)�&�!�p=�Q�*p= 2e9%Sa7aG.u6��O� ���,�#)%.� ɜ^+gKby��� mma1:!_I2�{6��  2h7i">c�;��, V8!3)6!\\{ _&6�+�:\�] ��/ @ i� e� (G.b, 3).� .U��E&$3Gs�A�future&\Opd(-� �R �0�^*Yb]1+ c�� + d 23})(.nb,'-'VaMbcd�hn &>& 0� �"M"��~;mma^i)�amQy(-�$0)^!F&ise�"/H�� 92�( D�Q u��$ .��o "Y E�!H W�rat�mt always}*e� bf x.&z4a��:puyt} �xE�xMU� V�:d)d�-',*+a r"�3Za ~+�) hes3 "+.�),$p�'� $\hbar/!�v<!� sity. � � �wo=ơ�mma��A�bTE��]�4�:A���z�2� pyd8E;a6i,.& \mmb* r^�_r] �+ �u^+C�r6 >�28R�b�bM',6: theirp_F��ju`d���� !dhat��&,k^1�Lx[}X -90�hy�J$ 2'}}< b - K {m *1*��� 2w2 �C� � z+=|��_�4 5.�R �)��{6�[:�r^2�.� .�2�n�2)%%� ��!�-�1֭V�)"l�L�.�s,a�F*�HmJ!&JmmbmmbaT=Xd6j>� +Br 2#1'}Jz :T E6= 6�)� zn)!2��)!=�mmb_iը2g(,'�&�V \m1=.5N.� _{0,3�g\HH�HH$} "(+ $� ,�� rthon�1 f�1.$ $\{\mme_1�e_2 3\}�&2�� $ �K �0��$\~jbTo at"�*sk %e��jL-�U_Z=:h!9e_i # ,i)� (i,jKH, ����I�dIu�n��\W = -1m "�Itak�!e&/$ "�3s �*� |�P� "�h�1 Pro���n$� -�mm��r@m ![^+ e&�C�f�me�ip�0\ip:=% 12i($\vbn$�U� of}:%�W  minimal� alAK� �a�"FD�uHH )�DM$"�l8)J0\of.[U�[xq�Ca�� a^k�; �$  8 �"�;3*Z b^03.� �;B]?8 i6dFAQ�rnoi .asily�D�! j A)2�[( �b^0� (a^k m)hk] ,.t�~7=p A[�"�h�;$ �R:�!�d%� ing $A' �m? ^�{A�e�� @.eq ���K � = A' �a{Th_ho. % �)E2=$an0*inclu57 c*O�(���� subM�A�.�@. \bfr$\Box$\efr �u�'\ 'B"�6Q>���q�q} QE b1SArc �d 6�9J&=&_ �aAq 3}(xJ P&H .sJO R� �o� k�\�]EnA-�\ �. H"B96,>co->� 1x=��HH� �j . A� �*� = QI&q_E$��v: �6a���t�b s�dC�g��\�>% ����+�e%Lk��f�y&�(!�i ���H� !2�c��sc.��f���}� �A�62}Up:�[�  XB�?A U^�2 �{� �%3�rp�q� �[ ��A� �� ^�A � �31�t;�B F)� 2.� E�W�]�B�s r"����E�eta.+A���J�ge}{\u�[}6u� �* � -��"�+a��C%Z#z1&PE�,h�� ��wis )�E�Xg��6t G�x�) 2\l�9�$� iaK� ta\r 3(aE�1.��\P"2W�:��")= $\si:�%^+\ri$��-� si(Q� )�32E�Q!�e�)Ef!'^QaH"�/Q}}.$ � map�$� ��^ view��� (-module, onG2-d<|E.5> 6."B"Wq})T�-q����iip ~i/si:x�Ʌ:�>E9:�CZ:V�>� ;A�n&� &=&a�+e"\13� o6aQ���2t=pi7F�DA+q!$E�E.si (Q���)Dx32}�^��} �:�>1e�a#]yNh�g:/=^�#�QZKaz1)5�II>!!  �aj= �A��mE`��2.|� � }~�� }�-%�4^*�� i_{2��Ialt4=�dly�hd a��0��oR��psmp�L����!I�"��{0XQ3�fr�Q 2}( V6u��JF#FO!'!2>��%��| �� �@so ��+ !qC�"� a lov= zian&/ cBde��#suitax. :> uclid>�4"Y4> $\uu�- RR^4�}RV"Yuu� {\uu�u_0${\vec u}^2!u_0 G�i  ^V=)"( �y �~� !*au-�Je1OU �[r��$-!Wc0Em.DtDnecessYkto tre/-��E ��k�baG HH$.�)��*f ��i�{an~�n���$ � JdsSI��5�ja �.H+&�Co� d! Remarks}W$�[�D"7n�c.Wn,� B"� 6N ��%$!q�� d� _%�$, Nww"X:%%F �9�R{2���2<�:�.�n.��x�/�t2�"�#tE�� ,72�p6#j-2t$ �)�@aW?2.�|Oc�;&!����V��.&is 2Y F&G&C^J�)EF(!� �G "y(E3discussB�J�C��\Q%���Q| |�G.4mu�d &� � > ure, �UKs,"r Y ensore una �~vf � 275%j!B"R�)zd�T)to��W*i*1 s, w�\�-.�/�2_,6�)6�.�C *{Ac3�ledgem]6}p auth- g�*lp`deb�'Dto Dr. R. A. Mosna������_mis��d#gi| manyJ: helpful �2-�� Pthebibliography}{99} "_siz%-�2%_r�jDm{rol1} da Rocha R%�Vaz J�mph{Revim1ngY�� � s I:E)twistor ` p SU(2,2)%�"�1 ?l%Gr�� (��0-ph/0412074).#b�ca�`} C E�a}T9bof �r s}, MIT P�<, Cambridge 1967%�-pauli}MYWSO e hydroge��`um� ��^phu new Uamechanic�Z. Phys.�6L 36}, 336-363 (1926)�prnJ�< >s}B L�Sourc�IQ�aMj8Dover, New York�8.�B?}�kP A MY!C����e�Q�8,Proc. Roy. S  4A117}, 610-612�8!�5�0inf} Infeld L%�j� Die Welle�Iichun!$des Elektrc0i��{la�inen Re�Dvit\"ats�ie}, S B��4uss. Akad. WisH!�ik-Ap � 380}�33��huang} H4 G, \textit{Qu�, Lept��=Gauge F=I(}, World Sc�:�K,Y],gapore 19926�@hev} Chevalley C�}itA� Alg��ic"e2�4Columbia Univ.Q�] 54. .J@fig} Figueiredo Va"Hpelas de Oliveira E� Rodr,s Jr W A �C�wK? ���ю�"�~Int. J�;ormJbf 29a71 !�906��& �8��Rindl�� �m��sޅt,0, vol.1: Two-�� Calculu *Q3�d5��)2L 19842�pe1� �T� -�},� Math �Is8�45�66�u3pe3T��2:-%�Method��S1% Geo�y}A�#f�6.Npe4} 9� ��:origi �e�jGrav.�, B� 0polis, Naples!j6�e5Jp��ce�Ql� g�Bw(Chaos, Soliu�Fractals)�010}, 581,611 !�99)e99��N}&@hD �9R9�Gordon�Breach6�6Z5�h6Y\�al1�U�J.VN798-808�67w96�3NaObserv`s,u�i#o%VR� E;��DQg or!�J�{16pT556-57�75A�2�66��PR�:`$Adv. Appl.&�AlgmE47 (S)}, 97-144�97)�5[15}&�iP��"� �� �Fy%����4 in Letelier P&�, � (eds.W %�A�i�on�� Y,S � } 50-81�5. Pub�o.�9�8��=L41���� s9�}, �Q( Baylis W E�ito�l)�5*(m�ic)!���s�,!�E'� ics,E�e�tc �Enginee�,}, Birkh\" U r, Berlin�52e�G$Itzykson C�Zuber� ��WOe&� I�(McGraw-Hill6H80c U'�; GrQr M�I�&Bt : Wave E�k!MS� $ger-Verlag.�2�yv} Yvon�E)F��e-Madelun!*J�;et RadiuNbf�E18-30A�4�=��R.�RTQ�2�� dynam!�� �`Ute�YSue�Prog. �t�ĩ:4}, 1-8�57e��7B0 Gull S, Dora1�LasenbyR-m Q? IA� chapter 9����f�.i�4} qP�!��N�"� }, e!����o�p�pqqU:O5B�M9��5KE��_n$ ore�~nd.BaHem Ablamowicz R e Fe� B,).���e��)App2f&R �k � E2RU 20006tp/6(Porteous I �5���� C"i�Group� (& StudiZAdvanced��), ,U.�  1995�AU� ZN>F, docu�h� \�v[11pt]{�&l�[u�8(8J(0mm ��$width=15cm h&Z =22. \top p1#opskip Aheadsep\ EA�a!)o F e�lin�D� \newwLand{\blst}{1.30} \re2ase�Hstretch& 1} �,tcounter{topK }{2}2bottomZtotal.6ztop�`}{1F�[n"�@ �.�$hko}{\hookN;5}6clu}{`�j):$n}{*b:f���: ,di}{\diamond>a"y: sd}{�Ubb{S}}:LLLxathcal{L>bec�"�7` er>"e"X;Z 0}{\star_{\vcx>>dD��:�be� yar�:!ear}{xRfii}{fi:5mj �bf:eps � �6�EE bb{E��}DDDDB!� bf{dB}bf� �flushE\:@iAyi�c2�om!<bf{ gaB \!�bZl~�wN�noAs�}2�R!�b:�aO{1a�6;s;und� eI B#$��O#6wt}�/tilde}�=�wh hat:9cl!� mt{C�/ll:R�}a bb{R:�MM9�M:op�}�7:QHH5H:5PPP:xa} �X>�an alphF;e��W.o!/q:�l!lX:�$N gin{�>�n5m�^#w!�edg>� g}{\��:xom!KmA�6�rA�bv rf}{\rfloHd2�ll 2 ty}{$?�9:rsr sigm>�v!6$varepsilon:7beq=9n��2{ben�2�&�V6% $a�"6�ek#i6"m!�AIcaM��em{thm}�� :5A}�9t{AB�vv bf vB e e:�aa�*a:bb 3b>Muu u:3jj j>3hA�heart/!:�m��!��:s�.sharp:p!�]P1;" ff �f:�v� varp>�ww 2w>�CC�C>NNN>FFF>K�� bb{K>stk}[1]�](ckrel{#1}{\��}b:�t��6cdwnM{\s|$style #1} &�O:3ZZ�Z>he��Z[m�O�f{BJmn!d�M}}(n�3at)>� mrrj0RF0cj/CB/K!�A�!:ul}{\�:o�:vb* blackt|�gle��>&vB&%�6`Lh!�B N vaLvarrpa+$N:�r)o bf{rBWR�7.�w� {W>x!�bf�:jla�Dl��:no�&�(:spi�stm@\nshortmid}{\pi^A>k�� iGqy =�{\circ}}��:~OOyO>d�� ��> nbW verset{s}aJ:an�rE[.% _{e_B�nb! >P+Bp nb�N+c>�k�%{:_R-� >:x-� x:ryyI y>3jmj}�mi:i�:3) �z ��K}>�z ���L$6WmkkM��B� iA��i:j2j:k2k>:u��UR�ivI>:m.�:�c-�{\!EF�clt!<&� yB>Gl%�.&v:&yu� tD�`:#VVn bf V>=O!OJ� BA� reve{B BBBB>RQQl!8�QB�n<mms=%�sB>mm�&_"uJ"v.MB� b {\ � >�bx� pvlB�e"end^ {�%��2�k�o kapp>�mma2�a>Mfg2 FB�=� a�bJ"p2"p>dmm6egJC"%���:�i�"eJD% "�#5 BI"�IF^�:=-R>!GGM bb{GF_� 5/f�0n�F=tN� \raggedt72% Sp(ede o ajusty vert�mbE�@2"ac�p sobrx=gur"\�I%+s$e paco�Y�>���*l�2H��g}!OiW} \title�8&II: )Y( "�(s�E!Oth�F �*? \�')�Rold\~a!��&}\�aks{IndP���> F\'{\i}sica Gleb Wataghin (IFGW), Unicamp, CP 6165, 13083-970,�pi��(SP), Brazil. E-mail: roldao@ifi.unicamp.br.Mtd�-CAPES.}\`f Jayme�'O.�DwPQ0deUem\'aA8 Ap da, IMECC:�0� 859,^�� vaz@ime�a#(date{}\make%�A.\abstB!${}^{}$M �+$page}{12cm\;$�;paper�*!�g� serM�reʼnndR:�qntinu�L of K�($,rol2}. Af9re�4�( 7Qr�-$Y|,�Jco"�.rN|� ��MJ�P"rE� ed adjoin�r5,�8 \$pin$_+$(2,4)��\* 3-&_^`q��/ Med via1&�,"�E !:aC;/�Q2�|+h�w� 7 � e*�1%B4,1}$yJ0"�, )f+in^- diӃ��so"��G��->�X��bb{C}� C\el|7u�NS~ lowe�&�R"�A/n�)��>f�+�-�+>=��aur� �B<%;.,is�,uZ�IR!7M�An�VsteadA� @2,4}$. %""{2�MeJ�� {p,q(Aa:��"S #.jiAb "MS$t} AlthougMhmAm persA3 alread�4 �d9�)|!�-��_-�\f8� �4��EQ,4M�!k1 shedDome h+l|2a/dFw-y>m A�ghDlize�s!Jc�]crau,�x,ke97��2�C��� ��med�&J=(� ���� *{In�2A@}�m���)^P''�based��#,&l,uY���A�).�"�voM�X#inx0a1��1!+86� emerg�u�3@lJ4concept7?c*;�E�I�is;a.�� ider�s m�vprimi�1_i�n�n�E-s.1�eB&j phy�li�!%or examp�: {�d}�* gulaA �um,�/��y�ߎ less�FsM�(Be93,Be96}.�!di�f� e"}@trƴ�~!��q�-gravity,9�!v�4 inue� E�% s&�beT2retM��(c�of)�7 �$Co94}. On�(he motivI�gi*=q-����UIBAv netw��}�.}2�1dis��pQ�sA�EOiR2ͫ 1�!#;2�cb3�B� a loL/5��i�(%�an�|c�k�� prog�/!�K-�=a.&"�O3�2,�9>�s,�d�4 �`BH85,Kl74,Ko96,AO82,Cw91}��!m.676$decades. "�Bbranch�2��una�"�5mF됡b"�1��st� s (s AxM� �8Ho95,LD92,Bk91alb,Wi86a,mot,b1,b2,b4,grscwi}%W&�2s8)A���Hcas�i8"� "�+ ��)] �]�Vx4`In3/2 ja�!Oi?ino�4�OŔ o��per�ner�a)7�2f�y!s abou�} i��.'�6�lic�,Me00� J- i�@st`� )KA�D �Qm��ai5���p�O�.a�; ��-b �Kic objec��[�Q>��nd� M;����x Y| an {��"� M��0�K1E�"�7�"m"�IŚ>��Gis cha) er��isii&+:�Xe�. X4%h*� )Period�ࡺ�>���ABS,benn�,coq}. E"ȴlyF%M��dzr��%}V� �$\2c�� ��dou�<c* ing&� ,(:�SO"4 !>C d1!pe nS6l �k�!F@ &< s,��^� \opA=� $&� .}:����| ���at� lT gNchron�'�S�* N�)s�{c�7oup��BH near!t1� Lo96��V 6��"�-P�&i��,![is �!J|8wN� Conf%�1,3�:� ���V  trans ���y�U� bi3�� � �Lrv�>Max:�*n9 lea�81AA�eO -c��V� !�Wa� uld = �7,� ���cM^3 �ֹ|e�ts-zinC7c�A�%T:U� � like�:&+p�Aa$\xx\inE�p $>�U%1GtO 2V)� }.6i[i.�B ur��2}q��Pup���%6bo�8sT46m��_ st(�"� !sif� crewsɞ{L+mexor�ɦ.��( 6u�4 analogously � �` �7<��(F! }x�kass�ngI�) 6�Hstx}={d��@ need�ybe"�Qdx8botV v���homocii��*1=Ez�&&Jar�,r�5!=]�d,́-8)6�@��e�� �/� rhGt�+� easy,i�n#t�V��g$uate level- Gu97,Ku99)�usefule/"�qT�, &0ry� a"+,� ,D!�studya hum�ye=9�He94a� neu�:6 �$Pl80,TC90,*b}. MEQ�g ,ic en� � !�ele�9��%[�+��te � kiiTre" ��)Ts�O:��Sec. 1�A #"m-6eli{��!�fix�Af�^!0be!�d) W2W� enun�?ps�A�n���M\"obius��!�p� AY.�.�C�"Ȟ.r �mp]�<�!O!��0�q7e7�� ����3:*:��MInB�e�-�a!�_re d^ & �S0>DKmeq\$2%*� �"7. Also,�� Li��4'y* i��>D��Ve ,6�]4 �o# ���M onB� 1� Robin�4congru6�0i2�r/��&�K�\clH!'5 �U)I=S�P�ly ��our�z@��b�k�phe 1-esqGiu!'%pKelu;�@,@��}a E&+A���� by"E Q �2}.L�6/7{P.� } Let $V$a�a ��e $n$2��rD8�g�eH�i*��CR  $\big�*P_{i=0}^\infty T^i(V)$�i�we �ri&�ur at��D��s"��(V)�X_k_ns*^k_ofwC �s;V$.G ) den�� hM�a.C� $k$- �> e!���ĭ�� �*��P,lJ$�^m�5�#�a��6. F Cen!�$ S{T�J,(-1)^{[k/2]}$ ([$k$]2o Ageraq $k$)! �\O�1 �f �cu&p� �B:��}%Q � $Q6�k3c\F YGio���4�!�5͞&W B�mIfE��Wndo.�"a nT�g�t��,&� �Og: V\s s V *,�z?N is (z�a$extend $g$a�$\l%�.. =u_1\ways\w u_k\А=v2v_lA+ut[v_j;UV>�nd s $g�L,\�L adet(g(4v_j))$� $k=l g.0=�0f $k\neq l$. �<e��arp�Fi:�si�tG`6�1�L;zs n$,A k�flmb�I its $p$- U!TLL;K�Mps"�M p$ = _pjV: "zpĥ� t.�$v)5�u�)�6jvd = v\wE����i Grassmannu�$( O,g �2j��i� a�E�1(V4o!M�\H)z�u�"� EYV�LRRT ,\; ��q = n�s "{J@ ,: �����al���GJ@AT>���eB\ c� sha*q�+�� �VpapfTbM�N�N-6R \\& �"N�}} $\v�]� ���%�%t��`>�A�kr�� $R})~$�J�Z� i&��� ;��S&�eer�h��U��&�$}_{p+1,q+1���P {C} 1,1"�  �,6pU��o�1(\label{per2�U{C: q+2,j� Vs2,0sJrVd3Bd ,p+2B� �0,2} �fcw�_ } $p�e_q .^e_&N�3 oi {�7(bf{Proof}}:I)�6��hm" �K�d-d�e 2 $g_V:�M^V�'��* "�K��!bbas.�\{\ff�ff_2\;Oco��Q = u^1�(1 + u^�o2��V7�PR �]I"e g_{VC�,_1 (u^1Yi+2 2)^2-��g�5���mbda_�m2�g chos�_oa{\�pm�jy.�  $ dependa` �i ed< : $V��V5^E��C.a$ �w*A]� 6ar.��GҼ :���/q��\2# y���!O��)���=��� �h(1s+ \uu� !� 2M�  \uuq 1 , \j� \for�r in V�2 \in .�� vaIҩi؝ci�`|%� rho( )$, %�2sAv&� ���#\ab8�d|��!��5!N �G��!IKA��p� �s!� rho ep&0a{�!~5� P��b�6:�!.]%�%��'|R���q�?g( 4�-�� aW � )\!a6�)�M@1)�,�^�<\\CY d )^2 V��+ !�� ��A�2!�1 AR+ .)^�1 ."�0 66 S��>����gonalк ET mA z�7 2 = - 1"bVE�a /� >� =a- �P)�6K= 2!u1 �0e8Z�A�a^�Ris"Uas  = a f ���$. t� �!�= 4~� -�1 2 �i�#���ǎsJP1�gA ,\vv!#��!�,AU31B\A�[�1J5(u�4 - & 2 [ (v�gH (v^p!- (v^�} !-!n)^2]|] 1�1B�olX�ܿ$i�6� NO+J�i>$cl(W,g_{W}�ũ[$Wja�p n+2)2M  `2J a�c{W}$ D Aa�(\bmw,)a �4Ƥ!f9��am��H]I�-\ww�A�� a���� &7gA�g*��\item{$ ��if} \;N"�ښW!* � p},${S $R\; >RQ \;�� S W��S� ,$"q�؂ifNT� \; {V� S�>~+2}.$\ *��[�2� � a�5#�5:�#t�y�o#! in{f&E@{$og�|d. �"X �LK^ :�&�"�` ) so-�edIJ�޳bW �^�b&� 1�^� !ݑSFu VI �@� of�'��!& in w��)��$�(��"P*�!�,aZ !:x��"C) N��C! oduc���s"�! maks� e { "z}�� ��« whil {�ju-r},� $\ap_s�in "���]i:@�-�m.is.Cj�E�J $uap_�; (\epa�O ?��ndM*{�8JG (II):2A�R+��I�!�o} $�/��( �, �)_ ,q {-�E A�6.6���1�A�6�Pn +�{ iAp�vj\u.)c�� 6$��:��. B [�  ^2,=o kbe���n' X11m! O6{�&h'� !#I1�m2�q ��-X PI=)(% ŋ2)� $)� &)�Aq� 1 0�x ee_FS !�n�Eh-,B�1J�j6}.?s�GeDg 'u�+"i$\ep$. KF��`m �5.��fq} D�*_��2�$�y RiemaspKCC\PP^J3J"�0��|%.>,Argand-Gauss� �2(�icha�(�-.r a�A�c!�2M�M�0]w{�Os*7cd�/6�O!4"��p*I'*em�1B}�{e \�A�q �a \o�i��g�*�,%| +�N{� �,Q��!e-7�I6Z�c* '�%$�&�|direc�e�� o>fB2w�.�;a�co.-�>�cvbnmc��;=1�%=9�&�BR�Fe�I�is �+ ��7>�A�Qd#��!��� ��"� �)!�i6|5p a*a-�I� Q,KP�maqrci�ɼ2ɼ> plu!�f�l&�ak�z����mu&�ez}z���$��&�23,%- "i� z�a4�fmu,� �RR% &K��$P#lR`aU_i\2�)Ag�g{ �%� g \;|\;Gmۇ~v\=jq"u�R�II%�Ire��"� sgj}XQ /�{\lef-�%F a&c!@b&d��ar-6}�:+%` d})i c}9 ba6}.-o�#�{!62-U&�43�5� perA�y�� �dRW">O mma\^5to �t�m Fm&M�'ninF��u1�eo�bAmaNn�0fan}eyQ sgj1K �,uhA�8s"�� >�z&Q�s�f� ���d{�X,vL1A�:A�)B˱iZ :�� >�Z�>'�e6gi�+ "s= ��2aU�a$u�� �� = zm���r2C�*D$B��[rapj6)Y^ abcd�� F'�A�1�%�2X�()(? o�B:Kz'& z'- ' �':6���z'��fCmaz�p}{bd}$ y&| |^2�'�'"�1p"v y�%[� �()yb��$�  AGl�*��,��" a() .� C"�;�].(.Q� Ŏ^% achiev{d���,,ort}$"��Fp�$��i]%in�!v&+9Alq Ckappa:�"�:�� �"�AWBx&��& Z(xA%(x, x x, 1m8, \mu6t � '�  imag�-* � [ a�Xe"%ic $QT % �2�bT���>���klein} � -�\e�0.�!�.� it K? abޝeF?�8$5 $uFfa�'.�O4 $Q#cprm#ve| %� "� ! &�n:x��*��.%aI�& >�a �~�)A,q} �fv-~A� $Q \thicAJrox*�2:is homeA � $(S^p�S^q)/\ZZ� E��/�<�Culah�se�'� ��"QJu!��(=S^n�2Bof��RR^n$�8%adT/�$/; �"n)�� exi�o2�e� s:e �Qe|&as1z{4f &$Lٛv&uos(vaT��ll}v&v�� v}\\�v��"Y e`ik��A��� 5 ri��@=� "�[)���:*:!�N?5�5}}�"k#rm (i)}b:��\ri!Y��x ��V2Wr'�+�4etry.\\ ${}\hs*{3.�B��(ii)}� i� pi:Q�' q,qm��2�| x/\m��!Q� +,'9'a~� v��h'UA�B��n*�I�A�map $/J�pi�M U �y h,qd�@�.�bn.#E'��*Ja&O��ps.�igs o}nYZ:� be {quasim�s}�#hid:�/ s. Aa�!A���manifol*�A�,��:�k a\;��+ b͡m = 0�� a, c�Rjt\;be�2� :��i�3 �A&n a�-&J   *�e���m�ve �� $Q^.>pA��w%' $a=0��"�4 on $(iii)��A5q�a��"� $U� -U��ɫ4�59�6��@��)3.iFaI� ,t(��-{�R Conf}(p,q"#i�O}(�d6 �.-$�>fou2?���(N|F�A��$p=1, q=`�!8����^:a������j�$2$!Cnect���@*x2_+ 4K!�qn!eE��"L�::)��7.&;w6@9 gEm �cob�'-B&erv�XA�t�-�BingLS  >Ә�A�t��J�I �( dcv}&b�!O�va N_{[O\�QBA� }^5e,)2Fobvio�7satisfi-�Q5��ge\vcx�x=  5����� 1$2 3 4 -J;�� A{�O�` (\BA�� \BB) Z C���4 �%],/5#E_A!-4 E� �)criE �:�E �E �E �E �6�o3 E_B�I (� B�ّ6��D'w M :�cx!%A}�i��! )*��plMYxi:<!)� ~y��a_2��E+).� E_A &D & \xi(E_A� �A}5�W� � �k>� �_*�i}) obv�Fiously satisfies eqs.(\ref{r41}). Given a vector $\ap = \ap^{\BA}\vcx_ ` \in \RR^{2,4}$, we obtai> para BD $\mmb\in\RR\oplus5,4,1}\hko\cl_ �$ if the element $\vcx_5$ is left multiplied by X$$: \bege f � 8 ^AE_A + �5. \en, FromnxPeriodicity Theorem, it follows$0isomorphism $�\simeq1�Hotimes\clt$ and soI`is possible to express an�ofV($ as a $2\PL 2$ matrix with entr!�in!Z!=03,0}$. A hom�!@ artheta: )%s$rightarrow �0is defined as%Mq >8E_i &\mapsto& \X(E_i) =LE_0E_4 \equiv \ee_i.FH JaT It can be seen that�J$^2 = 1$, $�=D4_iE_4E_0$ and NjM\bea{l} ��$+ + E_-,\\5E_0 - \ear A;where�(\pm := \me([E_0)$.AFn,x4ge\label{mou} Y�^5 + (A�0M�4)E�4 -E�0)� "i% �E_0Q�\noi Ifa{choos�4)$%to!RreAuente: � � = \a[(%'cc}� 0&1\\1&0! I;), \quad �E-FFi�,consequently� have�+�Z0B� �E_-�> 1\\0N�-h�B!\0�ea5 :C �%�A�thE�e.#�ʵ"b n eq��AR)a�N�%�,|l|}\hline\\M{v�A�A�In& U�\\U�5M� 0=\\  �.F % :8 aI �E $\ap)!�o�i�&e Kle�t4bsolute, i.e.,2�8|0$. Besides, this condition impl�M�m �I%�p0 \Left�0�b{\bar{!Q}} = 0M� %�sinceGq !,F�ap &=&  1n ɩ^2 %   ap\n mm2~�,eq We denot�� �taloa}E (l} \lambda�<ap9ԥ\mu�)0.!�)�UsingA� ͆Ura%CŽ:�$!ieū y (E�.9)_{11}$<�� Yis gi}by 5��Axx}Y( (>t T = x jx}} - � �0,W��)��̉o!"��xc} x�٥�6)�&�3�t!�ngeE I��fixa�!\��2�$ �2� ^$. TE� hoice doeA�rrespond��(a projectiv!�scrip!��|%Tf_j� �5�-�-�� x��:Rx & ��^ \mu&5� �M�CAo2vx &)� x};1Z9.-� � � xx})�>  i� R�-��c����� &4q)A0number� \R"E 95)^2 - i�_i Ej�jc* ) 0)^2�.\e� ei�$conclude���i����T{\rule[-3mm]{0mm}{8mm}.��gu1 2 3 �= 02�1E�whicha�a�6� (5�k��})). a� \subsA�Ton{ M\"obius transform�Us��8Minkowski space � Th��$ g6L(ll}a&c\\b&d�å�)..`group \$pin$_+(2,4)$ if,%z only its���($a, b, c, d��"t  I y%�V0s \cite{maks}�^q (i)&&ai a}},\; �b}}, \;c c d d}�\RR,\nY(iM?\; ?d}} \;�.k 3>?@v dc}} +@v}}  �Y 'Z+�'c� forall v>�{3}:�v!2^ �^b^�qH� k�6$21k{\tilde�� c �!� �=� %a.~v%>>.-M 1�� Cos $(i), !� v)$ are ; al�to6S< ${\hat{\si}}(g)��)��g� �g%32�� Ac111�k\o&m $, � l0: \${\rm pin}m/ \ri SOea� twis�7djoint�Ke� . Indeed,�uq B� :U e� b&d6E6C x�|:6E� d}�q c� ba6�. �:TaxAE+Y{ m�A#+�A6L ACu�xq� b}}&Ii��[ a �A�6J 'b ~a}� gD�b�d U ' 6�J gJ��a�Hi < [  x�X a}\&) 2H&=&=Fll} w1�'��mu')�{w}2EX"6 A%eqez� A� lastaaal� (� ider� $wE 3B �', %$$) comes fAra�r��$g,B8$�  "mm��$.�these._�- vd,FT �(�Y� . 6�v�� vi)$"�$gI�g� � � for ��f�we�:��� 6J\;FW 6�ja&A�- aH��E� b�A�-A� aTdA�-A� ��Y�BU�1$����Z.�Con�l>�n AW)F hust MXaf� U�� "Ss��� � ef&� x� a�TIx}ePa*� >��x2)i�$xa(��3�F2�]Q . E�e�:=a�� m �F|�+\{g��   \;|\;g��g1\Vnge�:�" ��&�mXj:5>� ccb��a,b,c,� �t!� +ro�f!6z*u!_�FperA�%JuseB!Uv� 2�:JuN*,*o!�q *o&�"g�% g}}^{-1}  i�gD q� V{.\� Uv�,ak e acO!) $* A�5ʝ�j�>'�7{\wide �i���+>'��:]�*�C 2�E� Fix�C�A�B��$ mapped onH ge :��2 + x+ ^v:^���PDelta:Kx'& x'Q{x':�':|,��r*��g\%acon} x'��(axU )(bd)e=�� 4�+ #({\ol{ }}�\RRqt:� 8vec�� vah,hes}..o*Ke�"$$isodirac} :H \CC\"\e �^8{\mt M}(4,\CC),�%?sJ�9 .AbDu$ algebra $6m$9 Bncnv .�*@ ]�.)@9 I � �}^y,�� a*6ce�oport,t,1y:i in{c�r�,tabular}{||r-� &�Map&Expl" M��$$.G\\ >  T�l� &$x> A�h,�  h6�$3$ &{\foot�size{$:01&h�0&1a "�$a: vDiBs\rho xrhot $& >m>G\sqrt{4}&0 x/b�R��\mmg x �� ���% 23 1,3)F >=�0&.]b�Inversio.�-e�x}}$& :Bq�\ 1&0bd%�v�&a A�t)�x(hA1��;\;A\ty$& >�B}�  h: $�MM \endU�4: !u�vLindex-free geometric� muIX a To trivially generalizee�:�e+)!1,3}$ :he one��$p,q}$, !J� GClifford��s� used�d  Sa� $_+$EE$4fourfold cover�p SU(2,2)��ident!�% $id_{{�T�A�}&� rI�2$ $ c"�s��� d% �$��$:v � F�1_2E��_22�2 :=-1 �2ibi�b1 2b.�>�- $1_2$�Rs)w"""nd $i.#!��0x diag($i,i$)�� Iis way,b%f:� � ris�"P4orthochronous ^�e2�"�E)E(E&��-O}B /\ZZ_22Pin{G!1, i\}����� truc�~$��}�N dge �2�2~&�J�%2A�'/>�.�D ge e{.}#� \i*=P \stackrel{2-1}{\long��#})-��0%u_+%wP 94e��ly% B?(Kl74,lau}. 2��OLie�k�A%associa!�e�s} *�%^*_��0%=i�yt%M�MKfuno rm�}: �&\ri&\cZ.:a&�^�� :\;ar |sum_{n=0}^\infty \frac{a^n}{n!} )(&%I���ory $V' � $ endowed�%!!'bracketK�Gfi>#&e *�^*� A&xample,%��\��D-Lipschitz $\Gamma1g%c, a�sub!s� :��T���i{&�ubsyI!� n. Suppk$5! $X$ 7&��.�%T�-�(tX3n6.� f(tF �bAd\;expG(\vv)w&\;\vv\;-tX� -^%~,J /i� .i�Defining �(Uad}(X) �<= [X,\vv] = X\vva vv X.F!ru"�@well-known result ]\Ad} e��$�tX)� I�we�)� $!7.�$���.uQXz�B�A� � /= proved�X}. A,writtenE"E Y�Cen}(u#)\4*la_2(y�N6� xp(t$X$)$P .y/ If $R\inhS�� (p,q��%� R R$ � $R = �%~A�,A� m�be�, $X = a + B+h/(a!RR, B :�6�$*� $R�R�1$:�$$16�/ X}})��2'2ta�)%�,0m�-�Rexpalie8oxed{)%8_+%: \ni :B"(�(2�� nge .�ofb�-�id0${\mathfrak{s!��EY� ��b���2-���:�$commutatorA#�if $B$e*$C�bi D�$:+bcz} BC�x(langle BC\r _5'B2�B4,( �ya�~$1�BE -B$ eC C�6.�,a�& .JB 0.Cz&l fCB:� �ou�.1Ca6 CB^F�0�B��iiH&b.M�%r- u [B,C�~2Jg:�I���\I�(>�$,\;[\;,\;]i=VxF� �= &�}: :�u � v �12�$\LQ^� 2,4}a��# has dimen� 15. S�(dim� # b5E� re� betwy-o�_� stigeX now.�s0e first papera�[)se2#� rol1} ђj�,"�-)}A)v'dre�-q+-i\g_0�  E_��1W)23 = 34 {012~"!�uT;*Sec. �0 dcv}!atM�dri�Aa��0A5K7I�$\{1\}D%^5`$s basi� �!��F\{E_A0 .4��-� �m���\{\g_\mu4-0}<Fco.�bMCor�/ E ,�� !�����AZz *$0%!q P��W i}{2}(%�!-?) 4),.� KC-jD- nDD @�/ (4.52iM_!+\nub" � 5\nu7 \mu. #2qs �A�)�i})A9/ner�H%I5c%?&���� E2-�cle$ a:2]me(\g��!a!Ng_5fLme 4-f4)</i Rn4 �!)wedge �)..�Q ��Theg4�&�5R�q [EI, P\]%�m�\�&, K t- [9�, D�0.� �*�2( P_{\-}"( w-()h� - n.mu2|G2bK�b�Bb�6bR��sigma�.��mu%nu (AA % �m(n =  K #2c --��.�21WaD -�me�6�:ID.E ].m v%-,6--mɥ��� �/U� abovee�8invariant underJstitu1$� l -�mu��l)��D0D�5${T)'ors��&h �6g ial��}�tis @ �3 � discus�68Keller approach� 0introduce our��1, shoPhow�or  �� l� �(:e�c*�3, ) Penr.classic�" ��oryu�g4 a minimal lat^Xal�� also�n��mLCw91,cru}. Robinson_4gruenceb�e inc�c&���$at determi�a: t, p�(as e�+arK cepts.ed�� inter1�"U wo�s,En�.\ J:e} � }> 1O1�� J.<)ke97})I"�?0A� $\PP�_ t X}�me(1 ��f$ (v m!,� L}$)�8��H $T_{\�1= 1� g_5&�0^� �|�NowA�Y�som!�sul�i:).��0medbreak {\bf�a�}9vn$�{\i�*ferA$1K#eta_\xx&��9�i� $\x�$^ �ea Weylj�Odot�� or (*�L ��-handed1��� of a� :$\om$)!�i� 1�L}\om!�0\8\xi�.P3FM?tr4~L0 1 = T! Bt(1� \xx)~i}�)aH' \vbn*ec)� ��or��to��%*i)!-��,<i�:%�9�fs��alisma�e)�r9��_Q:b =:�%�!�[RC9I&090&I���)aBR<BF?i_2Af>vec�6�{^c2�8 �]UFAE�!�B Each1yA�A��Z�C�J�<cy7"�7 9�"�" ref4)�A�b'x�8^a�&�""V\k \k!j2[.BR0&-\si_k��(2�}�In�Kget%�ct%c,�Aus& :3 similar��!�%Vone, but�s��5�3$ refle�(y$" y�$$) throughaorigin:�m<.!i����b�%���)�2���T5>I�.LB1�qU ͻ�W fre1�#.#�"�)v�- & r�tely d�:b� A}: �ur� 6�'� ;(LW _"Q  � "K(� A*� | &��car�zirreduc�6t��2"��!�2g�8�5set0evels $\phi"-=$-& DsucaC� 42@ �1z�:�2v�L�subC$%_^+�2U A@%terna�<"� -s} Wek�"� -� ecR!/ {ic-���e!�*{*AIU*e$Yed&^�!�5#n�R �F��!M � � ��? J�F!E"�,fern} ��+EU5@| �F&!8� B�Ge�m\�GM��M>� ��� !'rUf (i>�He)f6- ��+f) a primi� idempot� o���Qm�q�M�U���rbitraVr;  $Up� ��and $:�= " F� PiAa2~ �}�Y) �co:�/ q� 1��'"!A q-�PiY�PiBP(�E� )\PiA(p�Ŋ �A� ~�}�iɁ�0� ��%.RAqn�f"BKaE�:���i`�2!a�m��a� kE_k � ;0�H2,fL( ,�xN\ap P:zR5< U�k��)6_(%iJje -ix^!�!��_k)V rG� -!� %d(1Vf�>3Vc6�ba CB� U� 6�aY�nSbNU?/� �A��)���1"�Y 3O��WLin*`"�9"" 3}, ��i�J_{J4��}} &:=)ol{��U}}��-1 U}�� x6"�He��"� F� �/�+�9�2�]F?t6*D)�6:$&�5�� Finj/, �9�!)� A"�9dp��J1^\��eN8 F z@.*�&�, �� nulln$ $�x'��!e~�ww�! x $x 8leFv�*r*y<VF<4Remar�Db.�model:m**�P)�o �� 5�� M Ks6|.5�'RR^{q,p�9R !��Z"= ((F�"s,?�2s,"�:�%y4�ion�d4s)|ex<w5via%lV�B] >�#�5ng}8y-"�. Whi�Q�1�alE�R��^��"as�aH!N M, e�-�&�2G�m*�*J@ U 9>,&. cAc? -J7� � .n"�0� dundP&�$ is eliminN$. Alsoi�L*j.�&�:5%D�d5�� B�3 :a�%�*�ڙ9aE� ticuFi (g/ dependP����(� �))�� !p�N 8 UE^aUid MFV� ' %�H _� $. E�SjFl�RyeU�� | �2,4= Our="i�U",*�,!EM� .g., �}.��� Hpe3,pe4,pe5,pe1,pe2E:�advantag�a%d�5v��!�5�&fna.5t�U y, b$P mo�Gas�mprehP'!�$n abstractM<d'tuteda�� "rPu"�-��5i�� ��gg$l6HGin&�q}2y7%b5�+Q$ny ($2n$)-u�al U#ratGace� e��"�v��Vex ioE}��t*T@p�I\G!�inv!Ih(S�3e�2 �\in{thebibliography}{99} 29:��bibitem�$da Rocha R%LVaz J, \emph{Revisit�֕m�)= � s I:E-Lw�6�Ape�?l�other r�x (N*(-ph/0412074G .�2}�� �I:.��=��6X��0�81� �equ�B�5) �8Be93} Bette A,U5 phase�� dynamic)T!,LorentzAc� n,� (Math. Phys.� Tf 34}, 4617-4627 (199327Be96}:�Direc�4] ��massles��les - a5��^�07}, 1724-1734�6�9Co94}(K"1 Noncj.ive3 f\AO82} Ablamowicz R, Ozie Z%�RzewuBRJ�:@=u� !�wistorsZ�E. 231-242�826l�&} Craw�=^s: not�=ispi$h>a��(, Poincar\'&%-N4^�32576-583�916�,Ho95} Howe P-2supersym�ArLeuven%�(%4on High Energy��ic�� * 1995.�0LD92} Lasenby�Doran C� GS �2-) -�&2��k���o }, Procee��ihe�/8WLMax Born Symposium: �2,6U&AD$s, Wroclaw�2.�Bk91a�u rkov3N �A � �� p% �Ն�paf le!\ten2� � }, N2B354193-2001�}��b� �z�1� , $N = 8$ ��  +cv#P Green-Schwarz stringN�8�69-18��)(Wi86a} Wit8E-/ �-like&hF%�en&@A�:266��45-26�8:�motBB-s NERMotl L Cub�Is] � fiel%�1 JHEP}� L04} 56 (2004) (hep-t� 03187$N�b1=��9� �1E grav�A: �- ��9 ��5bf�09� .� 60516�b2:� �:�2p�I�ŝN=4 �,-Yang-Mills}�$ S� ŹLett.-;9�11601�.�204��9A4R�P&P �higher2A-=s}.a9246@ grscwi}I� M B, Q�J HE5>�S�+e vI%8vols. I \& II, &. .E ��%BF m#��ɦF' a�34�26A�.V2.- ѮD 1: Two�� Calculu��R2' ivis>Fa4a�V�198� � Be00e(NL � �� r6Y T :� - Ab\l "0%8Fauser B (eds.)���2their ApI� ; &� �o I}� rkh\"_,�lin 2000@ �KA; J, Rodr� guez A�Yamaleev� �,e�g�Jic �aa`-� �Eq��s�%��iF-state!�Adv. �.)�g� �i75-300 �p:j,chev} Cheval C-M� �KicoE*�~(}, Columbia2#4 New York 1954:60ABS} Atiyah M� Bott Shapiroj��5�modul�  Topology}�́� 3-38� 64) 2� benn�� nn I%�Tucker!�1�Ie1��to�.� )z>D�#ic! AdamD geA6r� la)� y(�Ka� orte�EI��-r ~ C"�1Gt$m��� z4coq}Coquereauxw)KM![o 8 p*Qi of r��2O"�phy � !.�&T \textbf{115B}, 389-39��>{ L~ LounegJ� vAi() ]v��962(itz}Itzykso� Zubera��$it{Quantum���,McGraw-Hill,vgape 1980c9�k�1�F �,q�s, mex�!�O Y@ �B�1ctron},�J�Z�M�(7}S, 439-45%e9�> M(JGuF24 G\"urlebeck KE� Spr\"�jg"�,Quaternionic%5��:�!�icist)�Enginee� WL,�? iana � e 92$Ku99} Kui� 54���M S#Hc�Pr=ton6z 1999!�"� He94� Heste�D,�L it I"@6 body kine�`c8saccad- �,ens,: y eypve�la�Neu�Network�{7�T 65-7~90.�$Pl80} Pell!qs�6$ Llin\`asa���Tenso� .PAC"�of�Fin"�G : cerebelcoordi�'on��tZ� � osci�3{5� 1125-1136�a80� 5XTC9��TweedJCaderaAR �Compu�three2� !F� �{�I|IVvelocit�Vi?Research �30�97-11� ��!�N ��I:�ch[�neuro1g> b� 79-8ň-�5(mVb MakY�{(1,1)2fofyv2"�$ed (anti-)"�K�Oi!LA�Ph.D.�8sis, Technisch�(teit Delft, ��e8�bayr aylis!��5p&,pof^ �� 6� . U=�R(�]ic)�w.o>h�ps,� q�!��z� BN� �2�bayoo}��Mu�p�sKI�on$K oremI�a*U ��� � it92\��  � V�&� .ort} .yA tut�Yo�!EDl&� (U|I`!�a� lex Analy&A!�TRm �0 17282Mnt\un bx8200 \setlength{ ,width}{6in} .odd�N(margin}{.3i-renew,an?dse�0stretch}{1.5}2buni n }{1e�lb�X�.mall{@flush�5�,� Sia�cAq=%� can� alT%iab�� b(-Nambu-Goto1DGauss-Bonnet syste�$tl } \\[3em])�2�,sf Alberto E!r ante�9E� De4 a!�o:�,��r�W�Gci\'on K3D Estudios Avanzado=;�@l I.P.N., \\ Apdo Postal 14-740, 07000 M\'exico, D. F., M\'exico. l In)A}*�,u�dad Aut�oma� Puebla, A�do� y J-48 7257��$+s,} (ae1@fis.ci< av.mx)!]4%]no�#nt{A� A�!�ER{.5cm}\\`a!�ong(S�-��ism�#by Car�ZAthe�@�, &�of p-bra! iy(curved back�ndE.a ck� g�i"I M��!�� _� �7pi �'s *|�y�@ti�EU� �f�[DNG]�2� [GB]M��"2� . Fu�� ext:#s!aM�"�P� outa�d.+1<%tA�q�ce��a�Huno I. INTRODUCTION�>nd$\-�1em} \�= �es�#ial �s cha�eri by �dedѭ� g�q!���XIX tdur�)o�d Kelvi!}"ae�!atoms'',E1�K�4a�=n� was post2%�*?ac� odate a<, I� Uwould b�Qboth as %e�hAC olid�hveyA)�,)rse wav�A�!�e�9,romagnetism)Md vjD liquOdraggA��GearthA� o�1 al mU ).\\�?wX!Ae��u}%!+��L�[�! �vib leaE��*i6*�&or� }%Ydons."~ - gA`%t�ensed�>a� (i"++bi"' ��s)bSrevn�&hat memm�a�two2�$layers plaA/ im�)role;!0&$ case�r�so >won6�fil�s (�V�s).���;UsB�� stro�� cosm�y, ona��V beQ-4of Black holesKMu!�"�"�% bound&E� b&ZNB})embed%ϥ�� .an%� W is "V9Ylhyp't!��A�) MkA� yea!�nr��unm9R]t 9OE{ devoefor d!�op!aU\.A?suA��8 obje!�e�!w fact, wil��)�+ &$mate frame�)vu� te M��$ory; howev� i �no�t �fu�^ �^# problem>E�!r"*ofm$�F �is < ly nonlinQ%58m dar�2$ar�9t d`%�zX �us%7���s��)3)�ɻ �'1} in re��.WG 2,3,4,5}�'#c�� menti^q�ize���c!�inp�+bos� ��a�s%S 8*yA�Q�E� �3}{/estabJed�4�e� m � ��� asp�. �4thickness, bec5,�/ai!it��!��eA�a�P effe�* QCD �6},A��.�lng�1j4}IA� demA�raaU8�xEFtGa� DI��B��*Am�,va dra) � #& *�!�W,!FgV %��* manna*we shall&�I�� _>iAB)�umi�A��+REzly,M�k��-"�*4E` B�Y�6j )�"' ��U 5am>�-�7}.yhw!Q  little m��,MJ�V�:� � are �"�\�� indic��9#!X:J �1�I�worldshe']K� hi9�i={adv! DES� �I�YS95 we nC �i� pull� Q[F� �L o-��"� pJa��erm95 �!�thu�o �i "� / %8. ��v�-&_ A �7o/ |Cit5 � clarp^��!Q q!�pur�]o6I��� to make, [/, a gR�(Q�� �U� 3,4}�< Lag�Xia �ed loc�5&�5� �IO E#vAo a "�;� < , af� ��q�aA�� ��-! wU�I-J�b�a�%�Ahi9{w3solve#��en�6 �a�� T;paOW)V rgan� auf@w�&t.Y"w{ke9ui�e%�e�� uti-0� q5� a Z�"�8:�i�)� &� E�V�d WOg���6� %QVf��YR}.�I,�n /� A�ZB9}�Aich| be*v Aj". )0i.perx IV ��N me ?dj>��E,6�/)zAp���cF�Ilr�A� unl-' Y7},�RPof��,J�� � be"Q� �!btreat] KDN��ao"GSect. V��3B�p�+ ous Qs! 2�b u�W :�xI s ,aܹ � !C:xa�Imd VI"��;c���proA�tm �cT er{z#}{0} �Gc2ae� \� II.�~poAialI"ebBE}\\[1ex]W6) d�t!>\sy u!��%�!m]zIaU,A� �� &44��K� sic�a� Hc#�La�2M *H P!cpaBMng[aO+ "G W*� !��p?lmA�f<GO�� ��8-H[y mea�Q�4�argOs �lto�d�g�s ajKlB}a�ma 9�9�e��� co� bute�9 .� Z�,sj �(�rior �zKvef *\ )\6�.a��.�%9n]m�!Ito S���s�ultp a.5�.NU-� .�*?eـ�� For> aims�H"�iaRa)[lon�9!�+ ���hs $X^P\}$�=A3q&�BX2�r�aT/�e)*�;MPnTls �}oH �Z S[X]=~Et �p - \gh,} L d^{D}\xi1Hd6� !�.y$L$)b� u=)l&� r�ny�L( � ^{abK{_ }^{iw�v, \nabla_{a} $bc $)B�Q, $V�Y5ab 5�6N^$  A�inYeJ���aA�K yB:�6� �>oo) ���iv�L��10}A�NowE�� cU+u*V]�BIin 1o (2)ar��D� ��V���=�)c �t Q{ (N.a[��*�Qs�}�inO`4;Q} D=D_{)^  xZ�FC2%�}= )Cmua�\k* != n{_{ia�)fVvBL_ �= V�Fx+ "= e�y:xJ��*� !c��J��1Jas e.H a�i&|YF�) S �'��‰�}�(L-&a})�� \xi + N6[ K�YA�!fL + H{�z} �D_{�}�q�<+ H1 "-�}�X�� UcRV �} (m ��k9�) ]�B�ŧ99narray} ">HvH�, \!\!\ & = & �d\Wj L}{  )a9A��N~6+:U\JVU�1A} =Iba), Jd5:e!�f� L}  9TM" ���U!V1G�acb ��F��1DOx8 �A�.��Z�*�inq 10} ��L. >��22��%s $, $�1-n����$� B� �x�Y-ue�}..�;��} K�U = -.Y�.;b�� +�a� K{^{%�bj $({j} + g(R(e!�4,n_{j})e_{b},nzF���1�.7.��YZbe6a! V7[-N2�FE c �� +E�dy ! dAvc- ^{j$- �1 c1 ��']-[m�b}(E1��g VD�MF�a} 0�606Qqz-�5\!F�^� O�.]�gM +[-F?_{cb�.x�a /U.� R�� �cB� ]E�g%iA�[�ad!G�5: }^{d1��ID &h��`KjJ*K i} -%�n_{k},e )n!�m)�$k} ]K_{bcj&�q�$MAauK� D(= R_{\alphaZta�� \nu}mj� } &betI}%� �nu��$^_�v&� Rie/�'3,� SuMf(ng Eqs. (9{�10Ojremov�J�$= Xap�(7)�>�12=��� S5��"\R6[=L - 2Ki}�b.��UG  ��6I-I/E�i!q�"ŧŦ.&!��0 j})):-�� {anN���J�a}�ca]� � & +M�\ 2K_{-�^{g->M�( ��jɻ���2a3�ZC��fC�Ce�2�u�g}6B)2�aq����{�. A 6B A�j}*�- 1'�@-��f�AWc%�[Ja �H6�4��j !oE*2@ � ?qi �;�k)��B>�l})=�l} 3 ]� L v5.� ? .uU�a} [ L � �� -]�2I3A�ph� N�:D.\E�iJ/e�V\�!, +m� F��R� 5a� � 527 V8 5c \\ ��y�F��6�F%�* ���9AM:a�Z6Aca�I5Xsb��A�iy�D{Q�>�Zph� - 2Na25Bey:56�&iEi)R�f239E.�=DRg�REam5b�����)�63�3c 3%d�M2:3cj} p/=c��I�d�I-!Ca�\i� .ia�FG� �&"�wee�$^ b*�UU�Y��; L �5!�A���e4�R& NE�%�C-%AdR!�%v�I�I�I{�fa ^��I�I�I�I�I�I�IVd&�"�g =0"qtjey�e�) NP&w6i�1)rVPs��X& ���[ � ΢�K.a�xa��1���� �'<�� �MF6�Ң9��o�o�o�d�2- 6Y�L�n�n2!�6 �ocj<��<%j<FixNR�b2H$�;a��u(2#ya�Zignor�0 li�s" s�?i��g�&�our&�al,"��� s�P . No�-�r� �@�Mvol�e�Wl *�cur� $in Eq.(13)"�U�(xt�9�"�t�%�_X%�!J�2Q*�X#f[�" b}%Q5��3};%�� �t&�}�/B:" .Z A�̈́f)pro�0+V� s*aG!%�0�2 ject�c$ed|5��f1�e).*� to $L=-&it\mu"�c3:t.�3pT �4$ hav ��X�n �%-6 �i|S= -\muVF� 7E+*��'�58�easily�\~ ����&� \\�:ٔ#2�0��F�?RyS�� ,&q(�512�>�1-u *,�%cFz�Yeb ��:��ri�. e�xsurface-~0�!5JOI��"ia"A�Eq. (15)�Ac findF:�QA��&�+J�^�b�6�kr6P�:�5 $6U$.!.`i�)�q(1������*h�b� K�cmor� tails seeiM!A�5��we o5�a.D!%6is�-d�Zi��B�&"O/ !�mH[���-ނ)�)^�"a inadE�!�(�5re mis(3E�ѩ�T'. �!��1He eighties Polyakov�w,sed a modifi�L��2�by s2a rigid�P�'%C?'.،a$i:�'o�!� �/1���M+ing�5�in7e=�q�/a>Nd�=2�j�$ly necessa//1!��8influ�'!�ainfra�regio3�i�;#'�q9 :�*��"'j#�'Icri�6behav�'!Kandom�daAChN�&V3k�7al��pO��63-<2�+t&�3�e5�� 11},*���;%�rq8���`a�:�&�4�|dec . Bosseau�Lq3ier�W1ie(Cs*�7K! &�'&T qoH`�6���U�e�}N5 may!3ng� $Ooj�t�-� B g.?nsA�w!�-72}�<rL5m#68�Fs :J5�^dA��Ru& chan%� ere��C pid &[+ h/BY��?f1��~%�T� .��#'c1�NL by $L@�L�^K�$, v'>O as"�to�%N :5  Th�f"e�@: �>� .�b�2 � ��q(.�H�iRE4"KKZI"�8 6�!0.�Ae�I�!*� in virtu�� �,A�!� !� �b�!JA*tςgle) + \�B(-��D� � i})+�)�c} � ^{bd}��1� $b cd} )�!W� c~i��)K�� "�,a�! �7 7+�Jym.Ia&b>sam�-,� ]oI� 8� to� >xU �=Y�  {&�%!\[\fb�%$K%�"� �IAs=��*!�ev-A�i}!9!?�}"��� �1B�:�AgWNkerne�. 9� nt��&�,of-0*= ��\(one�"+�'U1�}$ To *s�v*Äi" ?�6�)D ,a&e%��7m,n��n)��W s J�64}s?�� H$a}J ze w|hb�ns�8nŒ6�8�R�5�AS6�n!4ing!&6�N�3E�6� �U�of�L4*� s e�%�0!)n!-�� *�� GB] >�9e�n�A VEFx�not van!� �R�� N>)U ? Eq�!+n�8�* ese Y-��jed usAUa weak.�EE3�&�O.]!ne4&�2t!C)�5�C� Ux5"�?aalready �Cen!5gsÄ�;e�!8i%53 let�- stem"v1 `"er�  nSn1� kgb  9*~?EKF�' �8�'! -jN99�9e9 �!O90�:�_(1ds,��)�cn�] >v�7� 1%l� zs]&R. \new�@. H*�5IEob�DNGa3 "r5�5��Q!�Y6�Z��;YpTatAtzS9:��t s�TF�=� �E�d sa�e:��8�x&*�'.��uto|aVd*u��� leav` ��*!7� e Darboux%g)Wi�new5PI , $P�* $Q$, say*�?rD���a))�aȅ� ���-a �8U�6Fb�J*�+"�Jo�:��Q�?=5\v����]  �J�7a�� �9|�:�0$\omega= \s��_{0O�t_{\S}�. (- \� "� Έ&�1# }O/^ )�arJ�u}=�#^2U.�JI( d R� � EB� �. $�W fix�ar+6er�4etF�$�4(�)�6dHa��W,�o^� � �1%/!@%P27�9$�%�$ 9)a (�i�<) Cauchy�E���gu�o"�4E$Z7le $N�%,@��9s��hen�<$ �,��i"3' �ntR�-XHere �4u\5�a� :L2W9R��g�X}#I��21��a ct "�D�0��*�:��J�9F a �I;�6G4#�Acl+�J4� *� �(�FDe"Rr1IJacobyMDt3at�hs;]brakets @��=Ha usual Hamiltonianc?) "�<!>n~(%�Q)9}l nse|O($i�n m�J� =0$)h guar�Q� at $�|I n�st5�h�� �m an��[u Pon�i&w �W�2�c A�].54J-hf��y2��jug�9|')�i��nDvsc���Ce�� R�NP�J7� ���Sv$6{@_ NO ). Ie�&� >��v�&���!M��ncaXN�~�, .� F%F*��<1�Po��c��6 y�7Rg�?n�� Po�m �Y9 7,9�5�� V�hZ#DGB< >& >� ��, Einstein-HifVH A|2 S� !��FS=u|1 �F�>Ra�*M bsv1��a> E $R$�!�1*�-r&Fq?%eB�Td���Sa%��to)nti���yXY�G5 appaw &Uthe e�p]� : �}se� 4}"�S &� AD �*z2r="J�Ap�I�B�aUs a n����atrQH�c�tU"�j K *oY$2Jts"�)9��JA75���F:udo*�/ "�L B� e^M EGi� .5��Jinu&B�E��pc�`�Sin�#� (co)l �F��paJD)�n&F�=�{l����_{���epsilon �n�m*�Drh�N?=�A� �� LK�11 rh�B��va@�mu��}l2 \iotd ^{[\ 1} ^�].�-��O&��aF  $ .1."��!��)�&���A  (^%W�U)�) Am�!�� 2 2�*� �0��"���{% (27)�.�*Z�2���-V B 5~*� I5Z���"I�.� �#�LE� NS]!nn�0< 6B$-O5�(>"�p�� �:�OV` [G�a�dA�� 6H�'ML_{] }10( _{1}\:k�l:� �B�R%�H�Vrom:�-� y� �-a.��A���A�Z*Jia�.[-� Rl n���m��qe��mrho F. � *� �� �,w*6�*$2�S�A���i�7@]at0�l�)�.�!*�O�a( ��*��ch���2�Xern �� 3*"�U.�"�>�V��f�2TQB "�1rsͼH\$��.�LA���+�1 ��>C& (�*M�2* iJ�S=_�q�VTi&tQ�n" [ :���B�n�Nu�.9�O� ��IJ8}�takn ��%��(|�!�iIO� > ����<#| V �*�ZK�t 9 m�k )5/bar6 ,[C)CUeta鈡�a&� C *&1���Pa�ɀ] �B�Jm���!�) S)�N> K� �&�1u%�}b+&Nb�Hh)�WeA��!HJ�> U� A� 33QM�Q.'J�j��~�B�Wh�a���XQ#KbZ�*�&*da,:� .O &1���Q )�!�e?bX�����Y��P�� \wed��iqQ��6�B E�J�Yi�6X�y,BP{6�an�H�, z!3m)yy} 0�D2�U�Y  +�nuJ�Atpn�m� ��(HŅ�:��6 �-E $ �Z� BP�v-��a��la& %e�* %�}�ɍA�� "*?([;( erm &F��(�e � q� ��- (37)3Qll1&relev� wȔ�aR�xde anguoxmo�u�D��>� �"2�]3 �mU'"��c!��9,z� e�%@� �q�&�b5�Z (22))A��b$N] -)%2 �*�,|reaKi) at Q�$U4'| shell ( $ }��]�^{2}$)3=$AF��AYE.Qi`%&��Y�Rum[B�c�f h Virasoro"�T]%�.s�5iIs &�^0& �"A;&/3݀2�� 6] also hop�at 1c�%I�&�E�w:al.,!"�WrI��&��^y "}��we di�� in f6o j�T�}+��> �ede � �.� "Y$1� AB2TxX��)Hi� A�*�&A�!'0� -�Js made���pXaAZ�.�d�;S best�# U !buh�YQ�&9w�c�ide.W��K �? .�nd �� �q�%is �&E<e2 *5y�!,@<&�6�X�+-.� �V� n C^�`"� "m�*anP.N/Z� *�by �b!* � V�R�,G/c�p � %�9�N !1�6E� 6}-�b�b%�B�. � i" �1� n8 9�z&� -�- �kA�!� �)��%>IQlgwf6t6�?2�%K ���6a�u�of� (34)E� 7:� ,lEV ary books� �I���b�>.we Aob%'� nN�.� %:� �?<���-+= �byK�t6 Y�bd�of�y2���!S:`he.;B!~!�u�*1o��i% subj)m2v�=In�1�f)�is�k����bAn)ss �o��L� B�M!2;l�o6��aoBs]�kx k'���2�m �s['"�jA7 a ipAs!u�f��s8C��Nma�e� qu�o^9bIF�;�A#2��fV}t���<�iwba��1�ev *u�o�:AY giv&��m� }92�maKp��%�.-2!jB�K\B�AcAl$ ���i� �k!�C =CONACyT�3k,t 44974-F . �q author wa�pDthank R. Capovilla%"!_s��rt A5$friendship6t hcu��ɑ d meE�\Dfm]� t:F|{>&�{T�(sep}{-.50emn"�81} C. Crncovi\'��EGtenAQ~}Th�u Hunds= Year�Y�i#!}, edi-#$S. W. Hawk���4W. Israel (Cam�� " ~y��! , b�.��2})Artas-Fu�3%J�~ ass.<�Hv�.@,, 3571 (2002.J3} A. "�{. Mod,��,�<�t A, Vol 46, No 43, pp: 1902-1512. \b-@46K, IܲJbor��M3M.6 L491ր2G�S5� �%G.�,`|��!��&� globa7yaW4h�>��2�5a��A���A��CCin��{� al R��, Nova��isX!l�5!6%!�@, Nucl) B 26/�086), 406; H. k�ert)�.)� B 17)�, 335=07b5�σC"�C� as ��DE�. ~"=)�*a�v�hJ1 subm$�,d to, ModernEXics�ersA]B& 8} BA��|A�97iwB�|&_8�&� ofAwi )�vor���E"s D�hop���a'm�F�)�s��. 2nd M4~anW�ool��9%+9al�(Tlaxcal�H6)} (http://kaluza.Ak.uni-k�G$z.de/2MS) �vA. Garcia�0. Lammerzahl, Maci�J@nd D. Nu\~{n}ez (d�:!�/B ��);�.\Ԓ\ DA( bf 43483?�3.�9} ^r҄I�0. B, 563, 107%�2Ds_2��J. Guv�_H� 51, 673k�95.�11} K�ed� N. Turoki'��,aS4002, 376 (19882Dˇ6�AP.��Lette�A M.%# D� 1721K92B1؜. Ba] ham,�Th��Biol. 26, 61 (1970); W. Helfrich, Z. Natu��0sch. 28c, 693.!=z?>�  *"�x�% C6H�s�o(2004-12-21 6PS08:IV  1-14:RK 0-1>8DHÕ A LOT!�deG Dirk):Ok05-� & P�D's SFB a6�>D�05�\d(��|[10pt]{amsart} %\usepackage{a4} 2msӠB symbBthm} %j % %�F b��A�lA^rsj� comA�RR}5�bbF�6CCC}:NNN>ZZZ,DeclareMathO�g {\EE&E&n*ۄPPP}} % 6�cB cal��:[B\cJ<J>zc�<ۆ� �%���v� :ąr}{�@}2ޅl}��:�la=�:rZvle}��, NEWCOMMANDSv�% V�f�-Jrm{:�eff! : Erw�fa$bf{E}_{x} :$Prb$.$j�m",ATH-OPERATOR��.} Tr}{iop rm{Tr}}>�volJ*B+locJ+B+peN�+RM� 9k}Z� diam+�/��`zem{��{ 9 }%[s�@]e�$4lem}[thm]{Lemm�/neprp PQ��o�f#cor #Coʊar i ^��{&$�I[ 8{dfn}[thm]{Defi�nition} %\theoremstyle{remark} \new }[thm]{R %j�< %% % THREE COMMANDS FOR MARKING CHANGES -- IN THE MARGIN %vZl\def\ch{ \marginpar{change} �us$\righj2�@}$\\\relax\ragged, %N %2��!�jvU�O \begin{document} \title[Spectral shift and Wegner estimates] {Bounds on the spe.4 funca =th!<�nsity of states} \author[D.~Hunderta']{Dirk *(R.~Killip]{E !@S.~Nakamura]{Shu #LP.~Stollmann]{Peter 'HI.~Veseli\'c]{Ivan &ddressF�epart!N�~lTokyo, 3-8-1 Komaba, Meguro4153-8914 Japan5|$shu@ms.u-tD.ac.jp>~:V�shu.�6�$TechnischeY8L\"at Chemnitz, Fakul f\"urYn$k, D-09107/4Germany} \currE*�P.u%�E�k.tu-c o.de:�6Z�mi.�6Y]`6�A\Halifornia Institute%%ologye .��8 1D\mbox{1y},=Ki�ivan.v�.cj@ 2�:@a�)wT/schroedinger/index.ph���date{\today, \jobname.tex} \keywords{integrated de:u, randoma/ r\"o eX operators, alloy type �Gxl} \subjclass[2000]{35J10,81Q10yb�EHabstract} We study �!�Sco o� on $\RR^d$. First we consider a pair@2�which differ by a compactly supported potential, as well asň correspon�� semigroups. We prove almost exponential decay ofCXsingular values $\mu_n$�����vfx as $n\to \infty$ and deduce bo�Q �B$. Thereaf��2G9�N�9]. T��$ingle site9H $u$ ��Xssumed to be non-negati!7nd�-�1� Tdistribus&!) �coupling%�$tants are j be H\"olA@continuous. BasedADN"� forM���,!-�>�I_ implies >v��oijf. \end} \make]  \se {Introdu AH Results}\label{s-r  If is paper�analyze��pra)t�,of multi dim{ on�R�. e|%r} $H_1,H_2$)( I� ��A?.A��=6�}�Xs $V_{\eff}:=e^{-H_1}- 2}$ AFshown� e�J� ly in $n$e@is )t�ws us =e�ai�QrR ous, too.�zedskip � will �magnetic^� equa�����E:Hdefn} H=H_A+V=(-i\nabla-A)^2+V��9 act����-*p�s (�A!el�ic) obey�followGd/2  \ge Iy�@hS low.� s c�f� physica��r)�t case� U!�se]�\, one may define $H$ via):2quadr�%� (wita4re $C^ �_c$). Bik(same method gcang� Dirichlet�+tri�of� MLxcube $\Lambda_l=[-l/2,l/2]^d,l ! 1$. T�r��be�o� 0$H^l$. \small��Let�+$(aZ���Hform just described%��($H_2=H_1+u$1�u=uea u_-$�qsF�hQJ+s:dA� ar��point0�us�?� ��be+stoodQ a sharpen �iz� of !�, Hilb��Schmidt,-�>|� e�"%, �� ved ~in@vanCasterenD-89a,2942lSS-95,DeiftS-76,Demuth-80,% 99, KM-93a 79c,&�-94b,"�-94a}e��6Y!ii) Not�N: U~\eqref}t:� �AN! eB$through $\A� u-��  $u=\l� \tilde u� �a$� �� nd $ .Ia2[ B#,Eu��Wni�en�A�cho] of \&�  (1)�Fbe take*$+$�"* � ort.1���J$ �yl�1re:_1$(� \setminus� p \,%�&Q�ary�odLs,� id�hM�"�!)w J* 4s some mild re�F c�� s;F� ]B5AA4(2) Similarly,�1�Hl d!a set �z�e� an �$: �D@set�ope� H_A^D$ �� F@A%�$D$i�,s ^D + VUM V$ satisf�S�^� �$before6� $H_j��8�J�j, j=1,2!�- set &�  \cap D��^�i)^proof!�T" \a~��A�surpri� ![�eE�" I���n immedi�equ��$Weyl's law�X�&x asympt� �� Laplacia�n��dom_M is sugges��O_���:&a��2� is,� �nPL$\exp(-cn^{2/d})$. O� :0 ask, however�ethE|F^could�typc �a)much f���. It �u �a 1�lik� �$ n^\alpha)ɸ$  > 2/d$ �� mpossible�� A �:SSF} mw-h�se7!� �zqw�  (1/d,q]Ccon� ur��=\!�tru�DA<of 0  $ h �)~ . $ 2� Our�a�!�:�!�S A@es from�!�2 iBdr�"�l ��n��$\xi(�,, H_21)"Wac��8�A,>��at%VYK�� very�GloF�� i[. (See S�i�s-Def%�a`cise �2�|� �.� w,plays a role!Fyt= ah �*�b ��in sca b#y, cf.~�$Yafaev-92}�N���urfac*�sE� ;Cha��`r-00,KostrykinS-01b}. VarJF�-*�H di�ed�sliteraA� : monoton� concav��"[ GeislerK5 $GesztesyMM# � -00}��� beha�A� zarg:n� $Pushnitski�,Safronov-01,R-02}�  e%� limiJH99,!-99}. A7)RBi�Y� �99}E?�vey��$t>0$�F_t:[0,�)H�aEq ed bj] $E�(F} F_t(x) =�Mt_0^x (e�t yc )-1'Bk AaDA�tpn�Sincreaa0, ���  nvex "|:MD� t� �\xi�A@"�:dax e�*�2$ or��1^lYD \\[0.1em] i{\rm)}�F_�%3s above��� exisA��  $K_1$, z a|on $t$,*� eno- !�,�@ � &�i)Ol} \i�-)� }^T !�|��)|%�\lg $K_1 e^T6�e �all $Tt $21I�tsa��s�, K!W.�L$d$, $\*� _+.!�F�� �3!,{, :6any ed�F` "�QM $f.Pnarray9Pdu!L E� f(--) \, .L1K/le-Mb +� <\{\log(1+ \|f\|_)�)\}^d 14e� � $b=� )(f���:� �E�Q�in "� q�hai�� �rQ�d.AdTx)\sim d\, x^{(d-1)/d}�x� \qZ\�E�`} x�)2WTh�byEi:3�?��^�� at � � ,logarithmic R�It�tempta��ink�,L leas�2��2uperturbe�dt 6.(1� sh} alw��bx ed. H� Nia �. F�.j"� re�%&�" O Ei��"R fiel�mG yG"� , Raikov ��Warzel* zat^� d�'ge�'Xeach Landau level $E_q$8 �敎��0e-RWexample} �xi(E_q+u� E��,( \frac{|\lnu�|}{\ln +\ln <: )^{d/2} I��as �mbda\dow�@ow 0 ,i��<��))W-02b�A� 2����$RozenblumM) genera�A�ev�� s* a/setE�$F_{t,� }(x)\�0^x�� ��$,� }�� 9o \7at:g%9\xi)�� e^1 ��ifE/6 if $0�8 �Ő w �#s�orem~�a�( guarantees I��M O1/d$ (A�$t$2M, t\ =)):\"v }^��& �:��� ���Tm%�c_1�* -c_2*"��nrd\in L^1(��,TX :?- ��� $T$)�mI�-m�+�A�&;n>��,\emph{cannot�A.!&d beyo�C ��� jAn m녰out:�G n �" � unex�ged �onci�+ was � i�y Kirsch!�i  -87, 9� � relaR�� � a H�:�Xta*�high dei�c�-&]s"� crucB'� .� E>0+ u $2p,"����~~� K!i�x ly�4zero, $a\colon*  \to ("3 $,�S _l(9�OTF , -\Delta1 ( $+a(l) u)^l�T�#$\limsrla }Q _l(E)O �' � $E, a�A"^ M�re��o� f^dpure "� "�Aa�aAOf"2�,of full measH $\cE� \RR$)� dens6���s�V,im_{\NN \ni R  = !��a�$E!+ \cE$,�a$%Z�7,l^{-k}, k >3jGv)��#r�M��  un1ednes� M' , Sobolev�  -93}e]ed E��A�"A =-�-�9Q +�$ith $|u(x)[ e58. \, (1+|x|)^{-��} C  >* k^: A��q�de�%�z �>C t�+ofQF seem�"require �strong.�on*M���, a�, absorp� $ principle��in� ]��a�q 7lute!�i�) �umx�"Y real�&:�:��.<� a nicA�n"�ɐ[or���&�J1 s  � �,^%O AXhN��*�smooth, �e switch&� $\rho:=<_{E,\varepsilon}��\RR��[-1,0� p-rho}�!a>V�mea�at�vh�$deP1�"y& &A%&� : $ �\A' v -1p $��E-V]��.0- $[E+%�Q�|1'"*� 1/13e I�%��!�^)tr���ty� \SI s}A�epl�"�reb * $C_E*�B� 1�eEq \Tr� ft [%- (H_2)-� 1) \�5 ]) C_E�|\+ � )|^d&U A�&�"� A�p s up��I��� CombHislop%4ta %HN-2001}�reyAvA�a� ��]+}  <�]BD\� C_E(��)$2.C_�2uAM2:Q2� ��CHN%(ƣF� \.��� F�Ak *X/+1�vv�4\omega =H_0 +V & ��0�+� per}�a iodi*�(?$\-���a="��5�w(x)� m_{k:'ZZ^:'�_k [(x-k)i��5 >C s} $4��� K�re���� E�ed� variK � �2.��i��$y "L0ed�*]0� �A�ect����pq/�H� bigotimes) �}v#�de�&by $\EE Z# le! 6)1 } $u\not\�T0���:� . DZ!�2�>0$B��$&�-s-mu-�T s(\mu.g%�p\{\mu([2�,2v]) \mid � RR\J�W��)��/1ZS%WEVHQ��Qan oy�e5%�,$u\ge \kappa<(i_{[-1/2,1/2(#s��� $ /)�n%H~ $E_0E�RRbrA i�6W�e� E� E_0�� RWb�e� \EE\{�6[�n�}(1"^l) ]\!��D W \ F�a�(�Y�_> 1}{�l})^d \ |"�)|>�*�In�4� TmuA� N[.iv>-�ag.7$-,��RHS~of��A.�=.8� ��$� ��&�! 00b}*8$��= a weaker�B-���� ��f$C!�Jo!�=l^2 � "=l52Z���ed�DW:_=}� y wA�f7%6�al9 so�%by�1  �- T-81"z mAS,soni�6 K�c� alogu"�6>�. b"��5�r=@a: ori}( , usVo� *�#&� �� ted ��E> 2�Dt�2, �&��Z�2A4��� ext,�Bs C tMǁ��gy�ion�3t ep��zT8�ul�-U�po&, umItq[i�"!� __sO�/�]�-�a� graph W1on6;$ GerminetK% b}qa� refe (%�4)%Wmor!�cr&d�op!� ngaZ��-ire�9app7d!�r6�.���� �.obt�#�4Jce�M RHS O:", $ e�Z_q�| �D�ant�$ *���fM $"is�#sE&asm �!f VC5�3y".*�9.��"mu�_%g4 $N(E�����-.E UG, \[ N��^�:=1_l|^{-1} # \{�u{I�va�:!} ��$�g35�$ an }f}W]�-l$ tend�inf�.y��;�X S O8 �� �e�!f|�j) ;$.���� !:\WE�!P-1Va>;-b �"m'!:|N(E_1)-2)|I��$|E_1-E_2|)�# \l��1}{}\D)^d, \Y T1/2):w�!�.�I"�(�-3orm�f �4 $E�vA)in%�d$rval $I$. .*+iA��y� $\bar�l��Ew xi0 ,�<!' )Z/o4;� � back@(nd} environ���(Hl"�!!iE,n 7no2� lossaXA : �M0 Lipsc<�*0<1�)d�;3$�r��e!�nnouncP CEF H, -045� A��?9�^�z ���>ty��AectOLebesk me�. So faYe I tEqu�Zt1dispos 9o�r�Rbe suffi�Et{$"# �FE� :� M2ough} ^�s,�ifAy�  HJ�@!��onA��w+!) �4�9*�3)ed ��al power"& ,�1 in �9 ENSS12�%� rem]Jv@r-� }�5fij�L���L>C�� � im2>�3���ZYsomew�� t. tKin}7WE}. &DDpreseG*e�rov�� i >���i )3"NKlo�0R HK-03T . �& ��h". %p%j@�'�t-CHKWE�'O f5s"� � para� �wa."s). A�C!Et<{=}� ��una]��aAi1|�*is�,�8 elow�&-e<"b � .�7F�$0��u�L�:HW1&{3� ��n"����1����#uCe1��P�c�6� 6G} ) �2�*� > & *�B��� 2�2<%X1/2607iZ@| ifR usesuUW� f- ead ͞$L^p$-?!��A:�M�Apg8xamF8:�We ��th�%Vdisor�Ereg��:� �q may��q.2ifr �earlier>����<���.� ��"��� �1 length��8 Y5�3S*� : �#� e�NuXHB� s.} U �2'�!p�!.�aiz�)� %SS-98a}�֡�ex� `� �0d.��to�B$Hs2�m7-s,s]^2��,s�-M5�Ac zero>v"A�%wiMCear/al edge.�ase� ��9r��(ee�(.U: 6)�CF� J�C&* ous mer��!] reme� !�I!�A)� V-02!� !� "nP���D:S %�D>a �).^�AFn�G � �.n�R borhy:i $ir maximal �T� !�  � ��ydz!�to 5�-Bbottom vM um. iNMZ p:I,��A�.�>Y"C)�)�63)Mn�cGU� sign�5�Y K-02}Jn�% =�{Z��EW2�+�(F��(_�1� ) S both�Nnd5�^� ��t�Kb�(, piecewise*".�.��R��Mis")=!���E1y�OA� YP A\�2�uI��& , un�e�9J5�p�#�5� �. Wal)EaruM�q!7.�.(ten6J�AM� E͡����w" ��!4��a�# sandwich� twK�A .�A�:ol�F� �L�&�o�N]�� regar%>}i��Kt6[.P)Fur� -�:�>\ ^��b�� ferr[ om8 4�9}$L%i#eX�y� ste&SsK�1m��AcU a3r�4��Fs� �AP�IW&8 } or &�9. �����:ŗselfadjX, l%-�8m�z {� iscr!�a[� �� �&g"'yT )* �.�g" (^6� \#\{nw!�_nT&z \} V)1:) , \]$ ?Q)$&EG��!�$H�+ nclu�7m+R'G,: i"�8 ŭ. C�Unow�Ka�Uzn5� �%�E.5H!�2�Q��'[:�&%�&� ��-*�!��0('s K:$t�Xb�V�� "{e-KTI}�E&oL�('"�3�x:�=H"(gL-�x!�K1� �R��<cal{C}"�r�R>�V��* (��� rho$��� �li��� er�a Besov s�^,*�34Peller-90}). I5� BA��is � of -�coB,det Ep�Q� .�0can�reMed �[�e*E&S%)_*<C� cj;�5to4tepU1w4�/0JF��Cwe� !(�+t*E�JS1 "�c�0g>�+&0��tonAK,��a& $g�-�?��:�ge>�����a��e�O� e\��A��e��1),�2)$� wKY%�� nd!2may�BR�e-IP}.�$1) := %\ \" �'(gyQ) �6gn(g')\ �5big(guu, � 1 4B�)���is.�AR!"2G $g�ZoQ "I��al�#2d inv�(nB@'/3 is l�0z�N&�ly F3� E�\bRUwe��ia�ng.#!e �l"ge=e!�x)#Wx}A�Altern�0A��M m|�ed"OP2P det)" ant  FyA{?[>�1!�2%�"�\piA$D2va"/ \sea�c 0�`rg \detE[1+(H_1-�-a-�S -i@w11}E]�27+i #e2.R.3 caF0�~� 1} WF*[8bF�E�hk<ur Qc$n^�Rth}}$ �#Z"6�3�b�B�j<�X5 � ing �e� ��n_CbQ �%,�&yF� irie �law, but�i ��-�5Q�"m;fe%� stR!Q !�~� !� � xco�)u6<h^in���I�~�ebu  ed aU �er.3St$O*1R�i*�[A!Dl1? l-!/}� 8$H = H_A + V = 6W +V$G JZ (cf.�gbW), excep=a&z rX,r� �-E��$"�4� 3�7]F�/�6�/. %Sy,fCH^"~U}ų�#&h6�Fr2�S�mn arbitr^"�J�$2K��#e �!$a;& $ (a�!>�c2�_q2�Ts)3 �+s.,�$ta�%$I:�.� �I2��/(,_Kj�E EJPge ��2\pi(1-\%o) d}{Ec, \Big( # n}{|�|})wH \!\!-Cj@!k@a�}n�/NNF�jE�"ke] } Si��6�7�  0^1(�a natu��#�'$H*�W�1 RB!�Qsly�(mIz$ed w.r.t.\U�2j)�Yh2 FI e ^Q���R�Zinq l94g�X 79c}0$&{2X2�2� �t��B�Mto6����DA*�. $C!�RR*� �bq6�"BE!"=YV_-�Is��C 2*:�-sE$V�D*�aVj2)�/��-�Yge ]� CO@2��naA���>g*} spli�j Tr (MM2t 2� }) &! e^{2tC} *�H_A}) = MU &|M"�} �S,rm HS}^2\\ &3 \i�@glt� U}\H29\} VY(x,y)&.dx\, dy�end� A��*}"�|�<�$@otx�S-�SeF. A`, u�H%c�FFA�6�: %p,�S$u?, *�kS*$c�9!��,)�$ne^{.��=��})>$� �4�0Q#2an�|#{HS}}^2E3\|�}%~; =:(<2~�) \le 2�� 8\pi A� �C��2�I� ` Owehe &hNkernel] ��5� �P2t\betaJs�9; diagJdis)�@l9e �E i, i.e.Z,e^{^U(x,x)!z!;%  = (4%1 +)�E�� %>0�}x�HFU}, �q!"9R��r�O$probabilisarese�nB�X Bass�Vm!8�1u"92���B��(N�� $\cN.E0.bF e number�&� K��=@$�$*r&T�.@By \v Ceby\v sev']���r%�A<O-�Z�] ��B� &!��E}%t_{,D}^{E}AH2ts} d><sey��<�@:?��fB�i��D Q�IK t^{i�� (E+C)} = BG� � e &{2 A�Zd a�� 1�2D�(@%c� 1y�!hoot:=q d}{4 y�4 $n�z!5.�}(E_n� |1 c.f.�R& \[� �� 6� %�(� �Hy�� }R= -Ca��]�M�� :� [PzjV]}$�%;D�R"�[� adap�� �;rh7W� s �Gminor��""�^us as{qs2@^C� ,alryz#��to;q)�Uthu!.�$�Aei� �&yKas /5d|c. �9�F�,of�* Dl� s�k&�e origiZained2a��$�Y�;50&&>� �aR`�)٢de"� �V�i"Q8�gdius $R<`T� is end�R�2j<� �Np(u� �&(ina��bCq ce�.g!Jil:n� �n $B_R~ZzYR$ ($jAdor $2$)���FL jl!m$B_{RA���len�An} A_R�f� H_2^R} - 1^R}\^ �V0 D_R:= Q� - A_Rmr�da',ny�P-*"�&%� �bo& *.�"� [;�3&,!Wo�!y L�(�T8�k!�~u_n+ !rn}q�I "�I R^{-2�a�#)�!]$j=K)�-A_Rt�*�wo .@ } WsA�7min-max � XSqo ues �\#�2�4e�A:� 5��estA}�X (A_R�qj�B� If $D_n�l�Ftp+j _n(Q�%`jRD_n\|a��\now�Wce�72nA �'ka&� F&�h-It\^{om-�h!� "� Z� _yEơW&].�B&�h�]on.9 Erw�[ \Prbr !�9"a@A("; tO a Browniak;a/, $b_t$��$f�x!0!v\tau_R=LJ\{t>0� b_tP@in a�_n}�2d�Ws� exit |�8Aa���!!�� (D_n f)(x�� \l[  $-iS_A (b)}z e3�4 (V+u)(b_s) ds!fV9)P�)\{��,$\}}(b) f(b�6�� $S_A^0WH�� ocha� proc�I6�M;ly&��!6)q�.�1! cise*�o fix=uit�B gaug�  Coulomb� a,athrm{div}A=�D�I; E!� K *1 '"Q �%.h#Leinfe�rA��iak��modulu byA tria�s.�6;seP� =vector�� drop^:A6I�E; A?0 Erw�YCJ"8�{"uU6- 1%~> JID Au]!] M"�o� u} path�*��v�X �ba�k^q4ŠiHMWLab�(�(Qy�O��usR/i�u�E!�hi�RD%� ||v$\cB=m/{R�He 1 , e@{u \} �W[���cBe�)|B�eso���A�52:� v�fFh&5 Fo8UN6� ]\Bi< 1/8}IQq6AA8 s JZ�^8�)�W8} \\XV��1.bi�4R�FS�292�]�(Kashminskii�b IpZ-� �� $�A�$�l&� `[%wo ��9�EE�{Y<n $x$A"p�8��Dvy2� comb4 ecGi� s�y� 4athbf{P}_{x=0}B \}��2r2)|b_1|�R % !�$ - R^2/4}$J9A�:�Yta�$ m*"��"e`$rM ++i��ua��#l"h6�R�I�Xn�C�� T (\cBN C�-r� �8} �"+J�NV� $r �/\sqrt{2� �Zj� o32��l�?e9e�}�M�r\}a 2} =Z?KT � �H^2�e�E ]N����fdn��� U�L�s� �|ion�dOr�V _2��R�n� �'_1 �,:6  f! *B f�r 2. \] ToA4I"A@a�eys*i?-&w I$\{ ���:=�V1/2d}$,�leat-"�"z ca }=�p:{S2�f�aye��.>"q�"� Gb��5]6�]���2� &�~ � ?be�M�2H*c "�#�>a� �#bʂwe�&ѕ2f:���3ft�`2�`�"16�` &= ^;Ńl�>}�oH_2�z6J���` S)T}+( �s jM s)��MB\ B�5�!0*�%�S�u �S-�2)�tcl�y the �E2=��6�6` t��%\�o{n =15i2"�4 (F(n)-F(n-1))%Q�q�: �n-1}^{n}�1ts�d}}-1" �J� e^{(t-c)n /6��+�(is #!#W��"�[e�a�>W�m �.y�'$esy��2 gral\ �~ =b,� ip~��%Dő%� helpA0Young6��Vppropr�kpL,�+y�%�>��Re�# '(0)�B�Gh�- its L�Zdre�%ns�$G� B�(*�![ G(y)."H_{x\ge 0} \{xy-F(x)� !� y  (��M(1+y)}{�� d �� ll }7R���,0 a-�W�"�(!G$,NG8,�UyxA� �+ �$?A,-zc�pyc"z"9�$e-Yse *%d*�,)����e>�b�v %)�F4+e: G(|a6#i�UA�%�]Ju� � Q�A/E��$fb$.Ph!jse 1�S rYI�t���-r�- .�E:H 1%60=iAe \}QV1+2{e|^d0 1e�Bsh"a��1f>��)��"?!/:�2ms13}�4"i2A� al1[� A��&�.:s|w main new�/aai3I�A �82: RO not RzZ~}���*)"3l2�'sme�A\Qj!Cty�D ��g�$$(a,b))$ {6"(}� (a,��Jif��"'a��\��aqi>})�$\phi�Cl%)� �8dejj��M�'!q �.�.>0a�[i�\RR [\Q�+.C+-.)] E�mu,)A�q@M.�@)�" YbJSa)]���sB�Ts�of��}6!w�!�!�b0�� �86U.(]bXty$�phi�@U)$!�YMl�,x�[)�} -x�= tL� ��e"r�%�$.)��EU< i`a�4i��M��me�r1� u/-����aV -by-' �8u_StieltjFz s�Q�3lud�Ea+1ni�-�h�8ader.��� $d\mu=dM�}$M�?� .���J%�. �<Uuv^��lX%�Es N� SK�a�"� ��u�i� �" out�A/[a,b]$�Z�!��M���J� N � a}^{2�M:;-d[M.[])-)]��dis&�'I)�%DjKKZ�BO �� & \,\,��25)�� ]_R \ &�6� Z@& 2�k)d-r� � s3( 2U�R7���zero,�jce�V(y.rB�] o2LE���bA��H�"8cl� \to�k��=0�g��� p1Id.C 1�t)- U�2�6u" p���}�>�]�6H�;ɝ{� T1�AGFNS (!z��vad2��a))�*1B%+C'� SG��0 &�n3 } ��7Ss66bi",�7��r�Q[6|H6{H$;��=�7�p�J�9��`s�e �r[k)B�8 (x+2.D a(x-2���Gay37& ^�$k u�g-k)!d1$.{! mini*"�ž*$�8u��� Tr��rho.�I+2��a\Tr��[r,B�)�rA#�Z��l� \NN�-k\~?l�N�"+y�$L:=l^d$�:t cubP$We 2� lat<�^p'.8S�%$ k\co i\{1, \#�, L\}��a ��t ��{ �_,$n\mapsto k(' �z�{\[ W_0A[uiv 0, \@" W_n O`m| 5� (m))*+nM|,�A5 ��al1E�Ksr Tr [��8M�KK]�� \no�(.WI�76�I�6�a\\[a=Lproz} {�k2�-4}x W_{L}6~�� vl!;%�L}%Ir�6ij�)- a#= j�5}abr�|\�-�Wi\ x $n_ >�$,�  $k_0=Et�dN^�Np�{ _k \}_{k S2�}Qp 60 :=��� s} 0M�&\�-48k=k_0$B\>J&\neq *�? RA�}.�@( �{k_0}k�� bigl��(H_ � �}^6o +>!�+.T qk cC.r]!uadXVn-R�%]Gf���兏D�Cly di�@tWG*�h*#@����� &��-�EuҶ� n)) >�~�+1m'� y� � ES)�2I)� )]".A�]��a^f\mu)-m=b��+��U� �&�l-t%H���@�ce nt����@tog��|5 q :�, ��K2i_3�2 � 2-|bNq^ l�bE� N> \l( c.Cj)�j)^dw�k63M"]4at9C��� M�*9 B�i2CڗleL��8l>�&�[>p�jJ�Q@5%�Y $L$�"s..�w�D�z�^E�&�Q�A�i\ a"ډ�pnd�E��'A�2 �A�&fY&f$FF ^ �\"�>�?.B �gconfiguk\o� u:_� ^_�h��. \big�H"�Q {�bf{ Ac� ledg�e�Stix�&| �(W�� rsch, V.~"J, G.~�Q�#S.~�t�gratefuvZaod. P.S.~gd�ki�^nvi$1�6i��L �%v work�(bD.H� I.V.~6�X =kZD^ޠ ��al~� , eyB�bB.~$!� C.~Galvez�;�.warm ho,\02.<*t">�Titu���aniR:T Nal�� FY�> x�>!zy�HDMS--0400940 (D.H.)�(1277 (R.K.)xSloan.a.JSPS %�$Grant-in-AL?��t�K��Xearch (C) 13640155 (S.NhDFGJ!� SFB 393 (A �ga$s Ve 253/1� /2 (!�). � � prime{$'$"�thebibli+dy}{ܝabitem"�#JZ M.\ A�#x, A.\ Elgart, S.\ Naboko, J.H.\�enker]Gtolz.åblock MoV {A}֚&�,{L}��ein {R}��{S}2˚{O}"_JXPre9�vPth-ph/0308023, 2003. !b:�S6�%GB��.]"_(m�+)Harnack*z)�2� "�*�2ne-8{\em Comm. PureFWl.ӡ`.} 35(2): 209--273, 1982��y6} R.~F.\�2`P2�6"5V:��. &t�d�Applice?8s (New York). S!\,ger-Verlag, �95:�2RO} J.-M A-jOI+P.~D.�^.yL.Vb�^����QB%�+2%x Helv. PhyWGct8 070(1-2):16--4%q97BM/B"„A0$~{\v{S}}. E D.~�L.��7.L?�"� . {The}��of {M.G.  � fQ*tg.a� St. ۦsburgIG< J.}, 4:833--870%�a\�" /} KAD , D.\.�!)�a�Leschke.�CVAC6>�"~:�2"�,�F�Revm)�} 12e181--225e�0Ay�v:��A{ ~A. ҧC��e)�M.~t�.�On" c9h��.-%{ Ann.��.�4. Clermont-FerA� IIm�.e[!�P(8):119--147 (1990)!�89.t2�94��SC�Ye�st"Y/U�� ��In �P�0ia&ll8�4(Han-sur-Lesse�93)}, �C~82Eԁ�M�����Tpages 56--81. Akademie�TBerlinP4^ SS-95%.�,9�,�L�v��I�� .�T�K� ��R8r;�3#�Pe�!u�U n�l EY�s Oͻ�ory}, 23A�145--15�}�OY�*��} A.~.�O#$)�wy�M>��Jpeet� *� ]%�Lett.-ϥ>@}, 52(3):197--209u��e��+T� %FP.~'V.l2�sA�&�"֦{HamilA���6W d-.Z�Y�� J. F. Anae�124:14a�8�#4.w �b2�EcկIcF.~?b.�/��'-�MYY�9I�� ��1�} all"�X.o�In5�R� Not!�(4):17R-�2 ��Vv�� �*��.���{W}egne&2p%�� ��.b� Proc�Udu5 Acad���sSci�(112(1):31--a^ 2002.IA�ias۫in�� sci/JN-Qy�j ${L}Qa��!�!i�al:�s {�#E0��)z:�IMB {2� *�8.%Y� un>�70(21Ž3--130e�12+yz� H.L. , R� Froe�+W.�^ �B.W*2�:� Y���� toJ� N|04(5):417--424�8 �{ �h� MN� ��ID0h%rm�{��er5#2+' �ie��u��!oF�(Pragu+ 8.+ 108!exX6 Adv&5 9 19z kh\"auserx �l!92E ) KM-9� ,.�N I.~McGñvra2-23y�---m[ic���te!F�� occup6 �.175�.��� >S�R.~��$��CoS�:� K}re\u\i ,XZq.I%�B� , 7(&1--181%o� �6Xu F.~lu�A%ei2lA�0�2er�)? "�w}��al-insula"A�nsporD9tra:nio2W(�� ma.utexas��$/mp\_arc/)�2�2l� �s~�, KB Makarov�����tovilov.:�TZ�6�����qkS&� <e/�hy��%\M�y:U*�AU%sa(II (Leipzig%� 9)},� 29!p%�CMSADf.[},ux� 22. Am4'a�. Soc.,,vzZce, RI�2�� /K�^sl,� v˚ mmun��.V )Kb1 <"�� .Th=�1v[ y��] �un�W�.kf.i%0�.*Q 95n 12--47% Bn R�! �,no. 01-139 (s ��>x2 D2P�%N]A[Uϸl"� b)�2 I\}����# }, 87:19_ 8F�(qz00-370j�4�� A�K"G&�=5 ~� �\*�\I�\ (Cr\ )} 571: 1A�� ! ��2c} T!�1c, H.~/- M{\"u}c\�B" .TA��-�3  &VzD  ]&�-�om&�F� -�, !�221�22!�54%�2YUh-87} "$.�SL��&i�Eġ*�$�� {Lap��}A��F "�d���%�) A���}, 101:5f512�6� �9bZ�!�stabiBH�F���\��&z  � very%mp.u�B��52,�r�h� 2:383--39�6Q �96Z�k *�k������i/z n;�.Z�22!t7-1t92F ��8.veC��"L}B�M�z longtg�G�io�5&@ ERN ��(3):495--507AR98.��a=���B �22Ao"�:�� FZRm� *n"� }, 6�24�6 �9availb: �Y��J Ftl�!ExI.~U� A� sparxknd�y�[ izedI�THv��'I�P1Q146��B�FR, �$-bin/02-142�"4� V*E.�sVQ%5[I* �kQ&2�&�.^H��� @Thesis, RWTH Aachͥ1:` �00}b�&� of�� sum��Z�.�ezJ�*t 76t 00--11Ʌ2� ��j6�%7ZO R&W�� s;�B���87�22L M96,*ej}-! �N� 2inQ�?&�i�� {I}{I}� {C}�u�AR�f1019��6N*�G L�G.;G|H.�>of^�%7M9Iq&d .WE9 J.\���1?$y} 9!� 16�7 �32,Ro"֙ Melgaarg��!, G.vE"�� a"�b�_ly���ed�Kac�Z�'N"�3"� ?!(f�� rank.��)��D.��� � 8(3-4): 6�73�݁�&� Nakamur�A�.u:S�ft�$��trapp�4eι���aem&f� σ.V�P�S08!�17!�9B2&�g��V.� .]Hanke.� �.\� om�&8 *j^_�1 N%��$fb"� 12K�MLecN��oP?!��� � "�5� 544��k�"New � a�92&Pushn�99h.+EsH�%�!�q~6�A�polyhaic=$.T�J �5�<40(11):5578--559� :���� A.~BT"�\u{\i2=^�oz0Mr "�Su�l�B��{az5iz7�@qyZ���Z�E (M.~Ruzhansk6�v�:- "#��$ {II}. {P}y�ve2=F�� 7(7-8):13e�40� 2.G ��� GJ# %RlQuasi-1Ji���genU�:��j*�� .JAJ�rch (��75(4):38311�2 �1f�ECaughtaJdy�: A Cou@ on BSr�inMedia.�'2YnProgr��in%���al� i:�Bi*��Yi�c<{} "\'c.f\$den6E�aK% ȑ�/� ^� F�N� 59���y2� �4j�%(�F��=J�z � ��#In�1,Villegas-BlaI�8R.~del Rio, edi~!,I)2�*� s (Un� sidad Nac��DAutonoma de Mexico)�A��m34A5�� <,empM98^4FhRj4.$arXiv.org/ 07062�i�+�� .Ee5�� {DOS\(u.nZ=#Z�  B|-4:X(52 (.-92� .�%��uH���2 T l�E�2;�+�%�bf 105�mericaB 2/Socies�Pr*�(hode Island�92�[Russ�'o,bal: Iz��l\c|2, stvo Sankt-�.�.skogo 8-er�>taˆ�te�.l4]� m;>�2�8d"���P% \� 4[reqno]{amsart��,sepackage[ge��H,english]{babel} %�% achuG ,st�tzung \2<l�]{epsfig2�{%�icx6amsUd6bZswpzur Vermeidung von Augenkrebs��einY�cho�en �satz \6?h'in&�M{(Lv��^ %� !�o�1 [ ^]2'U I on}[ <]vC2/l Y)p;6# corollary'C� gj�{!�2j!�DRe��N%sB&sh^)n�$def\esssup�gop{\h��ei�,$sup}�M (infV(inf(7:& tr:trinf& :!�qrm{g\,\��rm{*}$SO}X��D�j� )�beps}{\,ilon\,: RxgR}^{d_1>mRy>#2>#LL}"h�L:b Lt}{\wide�@{,:"st}Y����mT�Ex�hl #Pi #1}{B� po}{\psi_Oy.Hpb\$}B% Vb}{$U>�ob}�� ڿ Mark�I�ɞ�** :M� 60pt sep26 push��A�$na�#1AP��\L �$\spade�a�A$ n�n�z7�Z �E�halsverz��nisA�=�atl�� � @toc�)num�0hss{\mdseries �'�M%@xp8 b\cs�� toc#1� A}:= b#1#2#3{%!#b��5gAlD##1##2##3##4##5##64\if�#1>\c� dept&&X\else \sbox\z@{##5\let\i nt$E� hang�##6}\fi}� � l@#22�{ #2�}{\@secɤ}{}H�,\addcontents�{toc}{#2)'p�!W)8zc#3��%-l{A`{�_81}{0pt}{0.5pc}{� \re.ztocse8 }[3]%X."{\@if5j mpty�{\igno-i$aces#1 #2.qG }}#3-�l@*�J�2 �2 � ��Uet�"�J ��ub T3 T1�7:RnU�L4-1}{12pt plus2%8}{\bfi\te>n:�PZK� Frv�|nd*�sca��a�byte^�K�0"p [.��� 80}�,3) 87] w{ferZ�'(p�:ysumcdynam�l*?��low"@ .���P! �F! "Zon \B�^��!:��s>�y�F��9�0tst �y�?F�isgaboli��aU����T \tZ'of��& �.[�6�ZModelăA�I�6�F9 "�Nb*"joq:� p�7 H(V\ob��- �d + �=�t�{ s��2X�Xmplex-�d, ��h_ble"@"i� a;f��$ d�eq ���&e}fF� olPtoy� �paf�)ng �on�3a (�,y imperfect)h$2U%crystalI)ad�alG�impurB�A}a�D_2:F�* (or:e�r��pv;�P�\�v� 22}$. Acc��2�s!�� � partn�defV3)�!��NU_c n b}!�.\oE�s.>�(�V�a=��l%8-�1qi��u�v-`3aM�R$:�:!"Z�o \R $)e bulk= are: \H��<Fiz�� [�� B1}]�{gin �* $1.]B�pNpe�KE�� e��4TA�%�e (sub)�R$t(Z� $:s$$2�((x_1+i, x_2�OB 8 ?U all $ x_1� !1  $,22�i� 3i �bb��5Q9!2.]:�\�`F�K}�L\u�\, L^2Un$�$k�C!�)�61�FoWd�gf���t&�\a�K"��12���e%�Sim82}.;uB1.2 *���� $ H(2� !��F6$ � elf-�%q�Xڈe�3$!-*U^��,|� �x.�e��z��by.�q�"!gy�~~}] j3e2>!�R$ [wlog]���A!�:5�Lq�zd'=be N@-q�,n�C"ll� A situXa_!N��jembed!�i��!Li�rc�!T�Z�th�|H���* ��c�=�� b�m�<}C�;�sI �Xev�a��Bd2�& (�b�ed)���[ �x� ��,q E�this & beco�ta���) netr�2lec��(s.\\ Both���aW1�(or not)src�@giv�rX�t���negӍ�6��zi&;a ICo�7$Jt��}R $ (\Omega�` M���A}Jbb�o%r1 ) ˫ s re"���_�das$ ."b}ݝ[cXiok[Anw�_{�!Mou�t��n�2�����b�is erg����Ű�� ��� $ V�qF��2�u� ^d) ��NW3�jT�auQX���=� }>0 *��e���.�X> &�6e��2�E B\o� \{ � �"�Z|߁\LD^ i ��\, dx <2�\xX%E,�&�]^{J� .y76� �:= p[ - �Lv , � ]%��0 #c1\ln L7 .A2 ��jb��� �Ez��)rP$.��L�<� c |):�c)�I�:.V<H�r��third*� bas���n���g,.n!aJ� $ be��tin��a&d�ily-!ar��X��*p0ve. Exa��p "�*0f�@nVd�]O  �Maoy-�}BK (cf.\ oPKir89,CaLa90,PaFi92})ś����I$2j��"w�vanish[&n���F1 m���a8Q�A per �)o�y�f a� �5 �'�=N b' �F'�)e� .':s�'#\��ch��� .6 $.s.&]-�$,0�4t8�AY!H�#�"� �j def:pot} =�� m�Xi8[� *� } q_i�  \; f_ -i,^ >� w�hw�9 �x_s ����5 a��i cF��{y}_{Vd 4 rf(�t,.>�"�zdQ�&`g�\co�� ) $P_0$p $fV�E��� -�!Y`."�{!eeae $ �$-�3�enFX: !��va� E�T��s�fow�a�ie�s��  S1� �bpp %�K���aia=%yY�[�� X iT 2.e�)7�Mif $q��{min}}:p\� �� nF(<�drV_Z  ��u s �  $$!(([>�, >+��])��s }}.��Z�\J \�YS�� $fE�.R ,����emptyY��,y %nv"�f�? ell^1(L^pa�� ^d)N$p�d@� $p>d��:�V�� r&�9Y� 2.� $ f "�.8x�e ~\max(2,�d�)$ � a��ta `l� �y|*S\/te���) reas�we B�ō��eO( cle�će� arycreg�D�^�&m�� #,&1&1�:�S1eUS2 2B_~�A>S3F4 \item[] $\inft_{x_1\in \mathbb{R}^{d_1}} U_{�Frm s}(x_1, x_2) \rightarrow 0$ as $|x_2| \to \infty$. \end{itemize} \en.�medskip ensure that the partially periodic potential $U.�: \R^d t�R $ given by \begin{equation}\label{eq:sper} >�) := q_@{min}} \sum_{i\in% bb{Z1f!-i,! �p@ is uniformly loc�D$ p $-integrable, 6� !�L^p�D}}({R}^d)� bset)�cal{K}(! ) $ � with lH as in S2.\\ Under%c,above assump! s�random Schr\"odinger operator $ H(V\ob)$ is almost !�ly esse%�Xly self-adjoint on $ C^I_0:�$,x�space of arbitrarily often differ\ble func ��compac��pport (cf.\ \cite{KirMar83a}). Moreover, $ 1L1�, $-ergodicitw $ V $�E�$roduct mea� � $ (\Omega5�( b} \times >s} , v!�A}64o 5az> s}, )�$bb{P} ) $ ��P}A�?%f^:8s} $, guaranteeIvalid-!N6M$2,EKSS90})qaproposi!�iUId.Z@B1--B2 and S1--S3E�%]spectrum!�U_ J` non-I�.>4The same appli�oQp�IpAzMZDingular continuous�!�absolutA��} ���{�� ,m $.i�2�From �,/2 it follow!Zat!�infMaI) \geqa� 5�0{per}} =: E_0a#,where we intE��,ePA4�� $-p�2( backgroundu�1����.)�B�,:= -\Delta +.8b}6s})daH$ L^2��. U!�t techniques developed for bulk����sY��89,CaLa90,PaFi92}, it is not hard to show�R��lower b%��ctu��an �(lity. Howev�)A#)� ing =� can also be viewed as a corrollary�lTheorem~\ref{thm:Lif} below.1�V}��r:Ahav!�]:(V) =I-N� % In�pre�� paperK(will always xe: ���B�\ ,[{\bf S4}] : !] $A�=�>�@ < 0 \quad \big[2.(U0 b})hig]A�KIt%�be A�ay(E_0<0$ if $>� 0 $ (see6YaB :expmZ). ��these� %Js%energet) sepa)f��a���.�2� + V.��4, which occurs�pzero. �Q0we would like!�warA�e rea� at,� �� rast%A�Dymbols suggests, e� �72��@may�((g�alized)I) �V$5��\{0\}�!�a discusE�!�o DaSi78},e,� 1. \s� � <{Main results} %�4!Ffirst��v� existenC the A�g)�da�� M�Q (IDSS)e�y7Aies=a�T,��V2!�Ũ" - 0\ S4). For it��fin � set �4uU��SL�y4S_L:=\Lambda_L)-�2}�5mbox{ 1T:= \left[-\frac{L}{2}, � ]i�K \q��TandSLi�bN},>� a strip ae! $x_2$-dir)�. At ou} veni%� when doe� cause�fuAW, a,ɝso wri�H:=��� ��nd dropzdependaoiT":. Accor�#ly,!�Ldenote by $H^X_{S_L}� u  $[ 9���$eq:schop})A� tric�I to $�S_L�L� X $-nc���Js ��\p�!�$,!r��X = D��o  N $A�ndsA�$ Dirichlet}= 0ively Neumann�6n. Itsi�� -cou g"L j� 2} N�(9,E+$\# \Big\{n�Y*$_0 \, \midE_n1B)�E@Bis �ed!�< reduced-volume a�. H!/B notŭ ��(A)a q E_1  \do�^��A��)�[a2�y�0$A$ in increa� or��A�%Q ed aQgAmultiplT&�$E_n(A)= �F{ess}}A� flhQ t mc$n-1$2�E �c"x��. Thanks�B1{S3� Weyl � ��.�4��e F]!# $H^Nq4-bH^D� ��ained!6 $[0,�ty[$, s� at uO2})� well d�3 B� $E<0$. � &� ti 4 l u� IE2 $ N(EA� N^X � h " � !%(u� �I-�9 ) in��eQ� limi-their:� Ira�s"� ��� AҎ� 4g tj�3} N{} � :=\lim_{L2�)�}�:�\!(V)m�}{L�'},�%H B �WV 2&�erbo��ف�a$NT&� $ N^D!�!�%�J� excepe�bunt" many 1l I2!h was@8rigorously examM�i�88� ��in>s � K2})�1;�&_ mad�-$(moo��works). =�utwo mainh pose�4%:pTO to"� ��xA�hib Lifsh tails� $ E�%fto!�clude A� son Diz��A�e� . OurQ�J ;er�:n��rapidAe ecayA*)ai8 sens�� 5}] $ ,� f8| x_1 |^{-d_1-2Q �s.� }��0$|x_1|$ largem�w=/��A�addEbal).�2 �s%�Sv0cal origin. %�M�/ � ��� ��5��LJ� K���E\down@E_0��<\ln|\ln N{}(E)|}$(E-E_0)} =-� d_1� -*t� �a�"�handle � le-sX ") s!0 �E s3 than!�9�D$. In fact, replacAI!�9 requireaJAYS5��5� 5�!\d 5'}]>d) %]re� A�8f_u $,$A�>� nd aŇempty� n Borel� Q$ F_2�&T"E� such! /_u� Y�<\alpha} 1_{F_2}(,\�J"A�^{=$2u)$d_1 < _Mq + �e) $�|iD��$j��"� �,2}$.\newlinej[eP$ 1_F $ ��cha�Meristic"0 �-a (%E)!F !C $.]T2�2 Ywe ob! Q Q� 6|2)�'u�!>Mau Veqa� U�=-? da�)���~��Dproof!D �s b� s oldcate��&%��@Sim86,Mez87,KiWa}E:���` . At* core, h�lie��newL��3� ^|s����M� 6/ Sec:��ɗz�r? ng�8 own�� ) re�(on a method!3se� ��ari���.$ Sa�i� :gap}. �finremarke�#nalysi��eNC5 ret&]%s a �=�Kl}� is( lso deals��9 case"0=0$, a we����� �LTof>�8by (alloy-type)Q=5is�uss)�deA:�BdMS03}�� bee.m motiv�H M �.��+i=�:C=:R=�Eu�% *� * $P_�s H\"ol c"��j��]J\�o6}]�5' #bmC�\mu����0�([a,b]*0 C\,(b-a)^\mu*� a�,>4+\varepsilon])��Hcays sufficiently f�� >= =I�8pp !�D, Boutet de Monvel!� Stoll���MOa�vUa+ dynam� .� �H�i�� ��&��O!��� �D!)Q�modeleqouj"is =D�=J� �J# �P�locɥS� s6U!>�6 hold� enE�fta)]��`�y�%1 >2 2Yr6$)a�&",a�$[E_0,$][ expon ��%��."�!M�a1[bv�>E_m!�� I=~eD :t-��"� E}\,�(\,�t>0>4eft\| |x|^p\, }it%} P_I( )� 1_K\�$\| )\;<\;A�t �i�6�ARany�~x"et $K�t\R^dm�{\rm[}Y E}ab{s!dec�.�ec�$2P}==PR�!%N#�!a~ $ �1" d 3�asta~ proj�,�� $ H ;$ soci��$ I $.�])�:����Let�Ne��xa v�_literat�!��struc fZ�$�D "J��M�2w���a��J� 099,ChSa00,JaL1re�$c7 rein)e� ouD o���b� ,BKS04} (�Ց�pP) &ma��um��S �HuKi00,VQ.� Ғk they �e �PaN&# (b )-�um�!�F��d 4.3] �Mu_enj6cv"�&Q = 1a> s1]%j% \sI�{Ex64 � ~4�� %� �� �|�#d��:N�Etribu ( QtE� $3$).9 � cu�$�2�V> ,af"k provPat�} ����def:doss�} \nu{}(* phi)"S�6a*�5} 1&7\:��tr��[1_{C_L} Q��" s}�)--\s$) m]A��]��&! of�`a!(cubes $C_L=b]^d��fin! EʍN*ar"�alA`!!($ �lC_0�((\R)$xa$Y90}a�s�%�Iyt! betwY wo* � *� �, Sh}� R-�5 "� !�~$an be usedx!�!. as ���renormB � term �5��nw2?� need�� unterbalaa� the e7W D!div�!�$ sos5i$�sk rZ!IF�' of $M7$�is \ & �B$0� �m �$�!� t vanish��z�$Eu�'0�M�'0�v�� � {z8  O$*Rb 0!t�$]-il,0[!ru&2w�*(. KostrykiZSchb"26�}�!�h.7Z�!Te�,ok��!�� $H�(2�e�big�&- i�6F#s( $ nYU� cuhf out5�a�e����~�K��t�.} F�;��1�b (~���b�>�*Bagr�+%IUe� !��6f. u"�B�r!� � %�� 2�\ob���.epot}) �ft&s-�-i���:�!�~A#^�eq��#L M�R^["R-'( -L,L�"2���evL9 enough7y�$Mre ,}8&ert8of-j$ i�Q$S r�+� = [0 ,��ftya���im `a@��mp�{o_�/y.%Ic$��*e�ϥ�e (.�)� &7� $ \��(\,�"E]��%�J0(�&-�/A('�Y] KS})�}he�to: �(}) coincide� %$ ��! roug �Y�eq�F4 G�=R�>X���3c��ably /"�byL#-"k#-bracke� (\] Prop.~3� p.~2699! or-�02�*we X (!^N(.�� ) \oplus}-�l@�$^N(0)� eq HJ<1 X) �fDJ*rfDf�$��sb�st:Hschl"#$ �^D6� , 5$�r B&� .- [NB5[,>�beU&$ q!RV, E�$vA5$ j"�#} D% NI�; as E�N+eGcan�� �, 0�[R�p�nK � f� �{ :u :�_2\� InsteaD$Fz$ R&us take/w &  $W~aG��u'7\�� x_ 2 �4s���Th2o�O4H(W��+��1free LaWan� $x_1*Z(���nN&XW�%:� latterD �#� �"'s zero P i��- XIII.82q�) �� �2$-/ �N� ()*Nf) �no��ksmo=#������%���by those� �(Q�2�+,Nonisotropic> )��$%!�rs�An imx5an�� gred5�our�c�f�6��}"b����r a"5�]�corIond to � �-�$aa� Bi0&t�!�)v� !�V' $��X>%��$_#)h�t simi�steps w�� kA� Ef{,$2$ Kir}J| ���. S� Bz<.2--3, B2.2, S1.�52--S4�eEa�$ \eta$06 re�co"V��/�/*��1�$�%B�%, Q3y4! [ 1"E ]$ ��!^2C+ $-ved)�Qz $ 1 1B{J��E�E  $E�Z� $ onsF�1deq!bo�6� _{{x_1} �-\hl{L}, � 3;1� � C \,�--J1R� �2 : #"_E< } Si�%5n �16�,�)@=\exp� [-t` (BL-��o 7 $*V t"�. �58he Feynman-Kac-L ula.G{Sim79S e�-5 semi�6p�Caj+$;l �9 Brown� pathbeta: [0&� � + &�start�x%�S_L� $t�3Az%ei��rb��- &�- ("X=D$)� reflPng2a5�$62N�*eei��J~6.3.4$BraRob81})F.. D2b!&��Wi���$p^X_x%A�vF�$ E ftY��|��\int Y_0^I! E - ��(% (s))A8)\,dsM$� �|I5' 5t 4ET| \; �(dTk'G&� To / m5!�l` �'we| obser2atF���eq:defVj(impk  $�I�6`+N2 A=�q����4eq:nachunten} >p�$nt> \Z 2m> = ��?�jP%�5.�/$N�?;� By:.T�g�1to �|\9@a ztyA�o)$E-f�leqs���&�7�O ( 2| $�$� W-refor�litE<$X?RiL < t�ion�K $ �=1�:A�\{BA��0��0� st}��|)_2(s)-` < ���{2} O�A �)&� . Taka�6��� thus��QO@0}} mD(x)m� e^{t�18Őt_{�}}�rine��]8b}m�a�y�\,e�� }!% ,6�>� \\=+�:�95w2��big�cU j�5���"B2A��B9jFh=��breviIY$ UA76H>=��  l�o. DroppA��re��$aU$5�?!���"/ eq�)Z�'ul.on�- �Z� xp!T[-tZ� 2��]�*9�=�45o�`ty ]/��s��d����`=�unendl} mwx���E�(A�r�iv]��� )(x)E�a�� �\|�P (_{2�2e� �� _2�Nq CB=HE �!D$ \| \cdot \|_{p,qA-��!=nord3aPed&�5�p-x� !�q �se� �AZ$� ��<3s TB* Lemmag#l :Kato[;. *� Cauchy6warz in!�A?Gr%q�@� ���is����bn�E CS} I!�(�u�)^{��6-� eft(��E&&�-2�2��#�IE�M^��6 ^2>"�:�B?)*n-Cib(nB�*P f�2 Uq�A>|Aa1MaQq2� 2�6r@� W��.(o ed6�\foot.#{ N�9m EL&�2 �E�"� 1unedl�$IF;a�Z:ntthelesT=bsequ�&�:~�2v= $ C�or�=r��c.}j� �Ib??��?9( ?6�2U��,�e� |^20��ebAzR�E _{1�� big\M� <_2^��E��$ t \u(6B��.$%�|��`2U �<ty�5%.w+!�9���A .eqE� is 2�& sm�i�0_2|$. *q�T �#involv `& ta_2, � $�? $-DDs m�$ pe �B.�! �T"B�$&!win_ qllg|?d!-RLevy'�2 xima�+�jy60[Eq.~(7.6')]{Z �?�v}$ d�� ��1�_2Ct]=�6�0of��+on)�/4Q�align} � A'.|5 )&= p_0\!�8(i 0�sI�t}"`  (s� g"Gf�>"b �@ \�;gp & > 2\,a"� t~I;4\�o^2}{32t}� �Ga-�� �)d chooT3 $t =�(x\{� / 3^2 qrt{qP}, 1\~I��&�* desi"D��m$� �6��"�mH�張�"t-w9i�ll-knz/� [�S2�K"? sIqAe82} +'�.�I�@2.40)]{BHL00}). Ak c�Be�fI��="�+8Ne7- �6 @�pA� C's�veI@"R;�N  ��r�($ W>'N_ W^+��I�|KK&f){�+"WM�W^->1�H!oerW3Z\pm(xTA�(\{\pm W(x),�}'*"5ea���!a3� 6W)��� i�)2;� N� LEtJ \{1,2I� A��)s:�7��"�+%Sf� - $�R�W��ň_{q�� /F��= -� &spe;K1j:/yA6�M$�B[ 1 ?ty]Ac � �~A!U�m�EZ��e�}� 9��ert du _��5���)-) J� .)�))�9��t�.�.C210 -��:1, 55=K %���=w^2>�I� �0i�:o��d=q"E 6�%a+ aB N"}LCs 9�g�2wPnd1���A[�-8t6�1T5�#fty} ɚ>: \tau:�R>m (t 8)n9not�� �2I�}, ���>?/ i��F6�"ntah6Ba�~ 0 !< ta�8 z ��2�J �s)�:cE*"aO:�I�$^+U�a��it�SL�S�ent up5M�o� AAb� �� �vi� by s } e9%J �V��B/ �D\!^�z �D"-FU��7i&�D�� doma =I2+�@e nI�"� "� kerne e^{%��' �N}(x,y9���J=&�ew# La��* explGE�� u5un ����#6]dM�A)�\LcI }^N ��%%�e6�E���Y��} v�_ (4 \pi%�)^{�7d����ft( 1 +:'�]�� ^'��(�[-& - y�! 2}{4r =B� a�� N).V�$5 3!s� 6�13S }�2!��H5�,uq��"~6U"�aN"L�y�p�_B< "� $e:langle� ,�7Ne<fpsi�r *uuf; -W^-f>�u(1�. �ɡ�nabla ��y- 6��x� �.q �in W^� }��ass�(�# bA�-�D�Vp � �n6!"LE�)�)�7@E5 i�$Thm.~2.4.6Cor 3]{Dav89"K:relatV��"of&��GATEuo�Dir�Gor�"� 6�"Pc!5B�S�"�"&FC�!#�"S>�+�(% �))%nG �u(2'H�!V�"� �MW�fw ma:exm lrH.�����l�4 5�3�!;� a��� $X=N� .���%}� stocha@ proc�`'H^JM#�'�%dex �-s $�}&:7��$( Ur SL})�Isu7&�Cve6��F>N$-Q�S�*Xy@ Akcoglu-Krengel �Y��$ E�4{AkKr81,Kre85}>�.�),"V�(�� $[Z!j X,bb�8���(-<1}�N-:\$� i�H�il*\\e~ed� )�],To "�V�,�[II+���CI0little m\�6%BcR&wX)honal qu�GA-� ��(t�>V3%wal-�Brhog). Whil�Xemplo%�m �lyxauxili�N tool�7;3lie��6�@�h�mse�%v�Q defL� + {L,Ml[)��ŎaQ�[26M���Q -�A6F�.�jlegCH �^{X,YM.�P6 $ (we � �#Q%#�'c�=n�Q) ��"b)u�Z�P�Y., Q $X�%$Y�2f�^�'a�*� or"1E�!��D+s� p"�', �%!�) g3siNrQ o7&=$al\,[\!-\!_ B�%�1})� ]+%�.�[)��b{.FBqFq\R�Bz��+�J:��4i5mpaŴige�&�.a ��$A?p^X >� 11fD}6 ��"w ?ND}�;$� M(�^L�"1f TEů!�s:*�% 0*e(v>� neuDir*�.��F� u.� X�.:.=+C �NF � MTRi0C&�� �V,a M)�v E }!.�~)T&�J�� l*h2�i R�0*xa3-�� �ND}*~0)'$\setminus 2�eoA ��� 8B� >y+)).x� ) +�� Up� fY�&UG�&�5�p.f"j Mi)&/�leFet �[{�K,eT, r���8�#K!b�*evU�m�y��E_M� �T E_r AW )�# them�!�R? approTt$..2]D�"_6pu�N!�00sm�.^0J($\tilde 1_M9 d6 d$����$ \wide 8Q�Mc6�16#6 햩1 AW�6a#�e/r� ���$v6 ���0u I*��V�`FDj� CF� {M-1A*��'"3)%>|_�M, $!=�7 $<� rJ�. "YA2� !�,} eac�M�j��#&�/SAJP&���BF.�L�M_0I.V ehBA j4ef1} C 'ft"�5\,�,=k}U� - \d�b_{j`�R�>�!ҥ� j�kE�\{ 0,vmX , r i%� ,��i[�d_X�<nd"V ̕Sk!���� ith*ZJ> j� hN,2j�zlU\,]���+9�T) -5c9E_j!F��́�Z�B�"�7�*^)a�M �%�p�% t ru�i�& yiel" 2��>B;b�= {E_k!/b#-=� B�- 2!*) J.) \!_&�(=�(B17 togea��� ste{U#a �I grad�3��-2[�#02.6]{CyFr87}.E,�'t $ :�+N.]Fs�źk�D l�]lem:eig@.? D.= .8` ��o�e2�Y�E�a�a��c; "4:�ZE8H�5rho>0$::& 6/t>\� arro;C 3z *@CN(� L^��$^{X,D},E)=�Y 9�6j��� &�  *��"�8-0 By �:�5c��a*.�F��( V�[=1�"i5B&� � {XF� !Y\%�KLJWeBY�#�r��bq(ZqQhG�inf�[n|@�b�� geq �T9K�N�L^{Qx> .s#]1|.�� w�V 0}%�2-e-� �$^���� " �a3�D n-de"�_E& E�C&e]�non),�"is��tiKlt��^�8D�\��n�G:?p�l>�W2 no�Sady� ��f A�e�V2� ~]�b�p� m�} �D(�6N]&��< �;6�-�.TQ��bX�!F�i�w a�e trans�q253&3?`&�/Y t_{-�&^E��2D.+N�+'e�-U6LD$  ] dE'l q�E�r�&[�)��>m}-B�d��&�e^;g (eD,R=�(q U) B.8,q}}\;O�,dI�8N�V.�ɠ.kp'&�races 9�� $1�q p q )�m#$��p}+ q}=1$0�Dpa@s B1, S�:*�lU:=z�1%�Is$,*6a`f��"olv�&]> qU�e ed2B$�@�4 d� By�Kge�ut�#M�6��*/�� q:sX N}-1 Jmc.F"Oi � �q�6_Q��%�d Yq}}.2\,�� !--1}AV^/pm�:�M+3rh%^ � I���C"�) �< |/)�%o��Ar�a-'] iHis ".than �[�9ivi�9b�"(��t�5K��&�� $fO�"�E>qofF� tendzSl &�e��.L^k_%��,g��k%2P- 5� $ E'i�� By� �n!�i =��Tera�-��QB�%rk�-ZR�sm"�YA��Pf)5 � 2b!;:6�X,NXinC>$D}$) w�*7�$�:�1p �C$.*�d a clx?l& K argu�^s�K!v �> A�Rf �\rnalog�t ,�?jM���"�uM Y�Ke precise�j $��&[Vc�0� ��;AS�>�*�P�!&�&�?.�3 - �5)j�?�� }^{MA�>�� :=tB�?�EL^�?�+7;�> b�?QE^M"�;"5��-3�#|}Bg!:if|�_ ; M /2� � q+  %8{Ap�lix: Vari�Fal"N  f6.��[mB��iW� :� *Wa�ND}. It�om��b}lkl%0in Hilbert sp�yS.Cua6�-a�dE il"�U,W0if�-A��-B�1C}E�a"iCi:)b ��4� n!�"[NAj��;phi�|��M29.H3b��!Q'A�@orm{dom��k ^fl!I.~Iac�O_(#G ble):rQ ��% D���z/"e}_� Щ���e%���"�b-BeFM}x|�1 i,5+j&�� i,j}M�16_1"vm�p&�pc5�%7!� i, AD .j�_]s?eq 1uB�,y�i �jXV� , na�I�h�F�is�4e�N�n�[�A� ��E 2}{1.(��y� I�1�e�}a��1)>�H~6a�@Ch.~9]{BirSol87})�: valuJ%p\�R])�N�%x'�0_{iVA�V} 1b.. A�&{ \dim 1;  - %� \phi %� Q^]�' M�+6)q&�r-�}�l� ,8Ua� �?\� u ��erm�a�$rem�|�idx ll �?ar�$�2�p.f,% :�+�+�.�pE�aQ�y���spa�UWT��$.�"of� �2�!3��:%�in BD���(�&To) coe^`�c�c��1y bb{C�U��$)�=AF(m_{j=1}^n ca�va�jO& �q��)b�G j-I�\� u|v�9-,k �|�|"k| ����M��(1-%ّ,1�9��"Y���~JlZ�:A)h6X.�i�!x,w +~ )K%r-�m� j|-l.�-i�( %�v"�b_��.�1!� 9"Set#�"' = ( �BS/6�+!�rJm � w oof f��%&y\P�$.݄Po݄"a\Cg �}�Z Z yze"�%F�&� persufH} >�}=%Y + U>4C,�K��b�]�� a�%bJ��B,�U $U :� C��W&m$%5���9�Uf +e� = xFR�#�e$��7G-d;:O:J�e��x��"O� \cap! "�\.8$, %%:heO AqMHd,�&xaA,(jps S2,S3�%T��A;�OH(U�"oNlW*T�2$6n\)���� ). E �ńpF}pU}3)fuoF��4s, ``"&\_�''29�,�ob�!K,N*��)�com*ur� bin� �["Leq:*�� ). Aq4 �-�[al�K��O : sc�Qing�eor�:�H:�studi���|6 �!it{�8 A�iesm_aabasD.An��R6Mm4i[� JR1&�2w�i(�a^D) Floquet-Bloch de r�eHrm.�:� fam=� 8y�& $h_\thet� i&�-�",\in[-\pi,\pi�(F`�<) Brillouin zoneG+�B $ ^aA�e&�^��!=�SU(��) a�t�x�wS�X$ �o$ �&ۄ�6*;&�#S_o( "}\!RE� \, d)P�ib�TB�)W �\ ���)_ G(x)��n՜*�} !�-T6a�SHn)upsi�5 + n ,fB`� Yza:skXI� Sc�Gtz, X9A��S>��)�a.a��ex\!����Ba��B)QweA�n�@�Sec.~5!4G���$ T4�297�7� ?2]{Ch00 a=2�g)�  ym0-dirintF�u P1PQZ2-%��� �1quival::! � � g��WM�sR�\ ; !vU%�>� Av� #^{?(y�����\;i�Q�\, }{uaF[�!11D`{bE�$>��sG-5j(>)�Ch.%���3!�&�5= ��0ve&7 "um.B�!^��+�:�)2�f�c,0�%:��%+�i�M�[.3"a<��A, JB 5 !}))�m�y�u�ubU !. )`qG.8uEt�[2�� ž pstoo,(h_{t ����%*sp�F� 8plex neighborho�s$�U1] \ni �9�|"A �$ �In*� ~| '}��K U�iz a (s} e%$�[]E�i�U0��<8� "�8%%Einschub S.12�y..Lu98um�o0&�,';9k�H_� $2�cA�� ; (h_0*$-.@h_��-W,�E_2�Zng�T�BC�"Eple= %B I%X�9 abe�'s�]��v1@.2�oB?C$= th_0� sI :ac�UzbG2A��#z�]diOQbub NJol - OJ�h_0 u=10u ��0��!7$"torus"\ $��/\_�- very!��l0Allegretto-Pi�� brin\e�JG}�C.8.1]iGA�!{Ka�/%� �psl$$u��7Z.q�$&�6��. H��,byZ�,�E���q��G versa!],Pdwbvi��CB�%A>-�1w1�i��Zi�aMhA4!��%g#Yac&Vyifac�at �y>�Ŧ45(a)�I�&%�} �Lm�tR9thw�8toNAi%�k�b!�qW � �޽��6Z�\�)sti�%A��8 8�' parabolic��zse�%q�6+6F s P1--P2�& �[ nd-s���!�>�$ obeyr�$ara} C \;| �|^WWleAK(�) - 0�5 ./>��r1�>�,!p� 9kin >� ���1� A�no �e$;  f�x� �Z�ano�� applic隉� &� s��blp>�z= �.�!�nex�=b�ion���1��z!�! %�E ity,� �Gap&Z�� 6?{ IX6L "$.&f��sgap�Nn*8�%3i��key ifQbLC� �z|S � ��q Lif}�m�/ we h todm%AG N�to~tipslel �5� RobiRo��0we dubbed Mez�EscuR��Th{�}. �6in-�~=�;?o�|f�U(  L:� �P�is&O d�*S2L>&CF��� ���5w�pf S��# /2�b�o54s692.4�9�^���QG�� F�:�a����$��� i:�|V� )D0�c"�|;5�Te<�a� in a6��G.{�`�^&AC� bb{N�WeD7��na�q�9nchi} \c�&K')(x)� � ��8!�EK} �T\'S_LB�")�$Q� A'6|r�XapfrM~��i��(�"5�\,Sa��@i�i�~�Wv�,_L}^!� ��ϏM (]2eq&���$�9�v�^�eq:mezbo`uF_n-)p%�=-�(x).�yɰ5��h"�"-1&T*T�"��t?0$�Q,%.A= $ via (ra�-s,'$i�{��B�3� ��).�,cho o�un%��;s2jI infgleich_"�K��a�,1�%F:$MwE_0>G�1/�fyo$70U0��in�F l wr�M!�b|��C�7�=y�'-!, v} ih�Nd��m-�� �z�A��?%0Kij�� � "�_plC� cru�rol� UB�-�"V�&!"0 � �Fun�\Z9!!a!8?b�%� ���&gapesJ�� 3a5  y- �G A�>*� � j��E_W(:pHj)� r% \ge �C6�}zyF>DAo��>1�)()�jKK U $)%�,2b:�7)1�1  g� t� *A]a numbe�fxI s. FoN+����`.:"��$&P� � �C9n�I);%� _!�sep} \�/m)enU,D�% {\rmy�-�)}�+e��:=l^&�) �&t --�Ibb$a >�O� �.�problem > tes.�,eF��� v Nw ��e.�a6zB �����v!��p}�yc�|^c�re� }&Msum�X:F � (=�)����_:P� �\�FL)DAW >s$ H_2�@R!-��{�1}e!]�v2}N.B� 2�,K�)r�}^�4) =�$�~.U�C0YF*OP2�i>S Q0(H_2��I�F�%*:.��_1()� ��lX.�>yAO��+�eE� �me�*��Zh �%y  )�&(w*\ M1�M+m�)KJ �+�sFI�M� ��"�[� ]fie"`a\��B8���Wp�M�RR02\s7�7� gE� hvUXW1)2�D2Y� :v��@J�� \�)s }[ AR��hu� 1}\; ��+\x $\:d\,\xi-1Y&,b$\pboN�$]\�[�W �y"���: $���Lo�.)*� *bJ<=�eyTWha" #Lݛ-ba� w�1� 'v!"�-C_1� C_2e1�"a�B \eqZC_1\,!(�� \;\le\:\pe%$\:\le\;C_2bVN F���1-��us!��� �>.�"�M�B&Y&�weY=.j���5�=\-�5*E��a��6�^Q84� "�\po�mGpo� �0pply Harnack'~E�\ AiSi82B3P|2.5"A��� expl�V�=>�{HiKan� � )`"yv�}1�!�1''��,b� � x_1'!�Bh!KBKa�-$z%K�"K'$E�Ϭ�1*'J� 6��Q�$ A�> c��� N! �OE'�� $�C�mQ�>mW)�~="3 ��averaged.n  \Vb: ���J�(F�� r�h�pb kVbe��E#: )�!��%d3 }{B;f,> �o �[ $��%�����v� kg)p} E�P33 E�%NI� 8� �FBy"�VѾ&�ER*$ |5@��� (C_2/C_1)Ig>L|-Nń�-dxD&��2k"�)�( xV���ͪ с�cal�(t�a$d�x)�>�&��k ��aVnd*["�� >��o+� ${5revea�a�5�A!y 2�xBh".�2'si��F� \:�^NIb��+M �� %�kjdNeqP� �� .�.bel��p���-A��n�H*2de�#yћ o� B 5�is%�ժBO nh:="�!&Vb.O-�j& � A.a7V�$.:�d�A�9)�h}��th*�*O ���%')"�e��*,2*Bqg1�r %}�0u�5�)� H�"��� a�F� P5�)1 summari�/u��o���)�@zOnzaTE I��dFSwc"�) � M"ݲA\�>(w^*#.!R��coU}AEU.�A�!" ��6� r� G�Y��y *s:2� �&�1P"�"� ,bar� 1O�(�>Im{a�5�E}}7Q �B�pi^2\,� ���=��Iw� "/�))��9��rq�\bo!t"{2!�^A�I.leJaby�?r�a}!�9��agap�6^ ��  1�P7}��"X wen�e�:W!�!:����q..X�� $E�be rea%�JD"8c� s.>�&(*� &Ea���&��a�1,\{��`���- _{\po!#Nm~� f,pr�B . \\- ft.�\!{t� \! |*%.�(�P dx |�H6G.M�o.��G0�5n99_E��'i9�a>vSZB�6��|�� \.9�Hw�(a2�>�@�VJ �^2 dx)��� "h7A9ڑ. ��hNN��]Z�P��Y��8E�(� CFC_2�8)�i�.[eBi�Y � �B I�]F��R�P�]) fin�>�-JՄdl3 ���*X#&�AP�%�Av -�D%��{#%*�#�[gorYE�l4�] w��"��BV}. Ai�� �}" e�+��.�X �]"O h_{0�ca&R= �J3� y�C"=H}�& :�AQ� �2�V�, ��e�\,:~ K@�Q$j=1,&�3$:V�� }b.�� + e_j :93�, WJ ���\2 n"�2 x�v! I^ʆ!�$�4m2F��V��������(# quip\��Ahfz1z&�!z �! ԡ ��$!+y�1}$ (���(��\!���)^{1/2rS��a@'b37E�t2.3)]&>��,"�/B�&- �0 � VP(Mkin�y|T�!.9)6qRA���\FH�!���ak!3��XqW^ 0 {��s}6!� >5V2�XIv*QX 1�-&!K�9 far8 �up&'m3"� �g!con��ed{'P"�@AM=yn(:21x8� v*G12l9��#9BI�-^V*q&V*2�e"j�S��?� "� B$�*)6� 0gapq�>�9!Aeh�"�&� �/$}v�J�5��6$ I� $"�b|uw"�.�&�a�be�Z"H a>� & "<�eq.�.$r'�]�)n��\� b�&t(%F: 2$A�"6 �~us Xfri %!�+ 6� a!�wV� &��VyIx&�2-���2�] | ] �2/XK@ o :&0 !��]B�B'N(A�bi��!#q%.� ]���!Out`�lyN�I� �) j�=}�$,7<"�-�"�< �5 $z�a�s.G/�&&@ 2 Ms rm{L}^2(\-�u��62+�$� :yXH�DzV�32ma �Z�  \qed % j"��Pr� �%&��&:-�%>as_-]%_-�%)  2} bBƪaC���^G��,Z&,�&Ī.�&(tQ�be��brief possi4+_ �3 focu��t0j�bn!duq��@np�fr��"P$�-hi�Zgڐ� uڐ�%�t IDSS2go �@���Mar83b,��5�Eo�3����PZ��!Bto�_N#b)e2�"�~!�a�!EYp�lE�& A�.$%:��i&��Y�UgH+$�Pwe  �Mvl2s D���7:,� c�2) ���AGϒseN�~ /"�+OH"}� bs?A'/.k. �Jv'yC��r"!)d�Wa@22EIa,F6-�"�3LT � J�*R[�% B2.1-2., <�  S2.1C"K1��&f �a*�^� ��Q \{ٙHMiDIf��) <�Qr \Ny �g�&�qNi; %W\/�!A�3h \;\; %2�E͔�7b��_)� ~RtS�^2��#� ":3Duٽ.O �#hev-@��c.d )x)T c"�� C2V��uon TB�y�D $6C!a� t��*"h&�D��$nZ#QOL� r�=F�+ V\ob"� �� W\ob)�I ��&�aB�y��t.�9 ��B/U�>��a6>al��Չpo�I- J � �Bj�Q���� ho_j\ob\,��-j�,=0I�%:=q- - q5I���9E .�U&� �$�m*�5�$f$Ts T��e2)#.���W heav�F&��!�.��Sj��E�'.1p�H�}��SF:�A�:� ��*Tt�fG�1"�$�7J�"���� E�_R%�L^ety(� �N��= �^l ���R9� tA@W AM_RN'8".��A'uaV�""W�2Il��C_E��r}{3��z\ass:UF�.�$6<�  ��g�^�-U,*ʂ�9G*�'5��%L>+̀C�/3CB6e"L}60 _1�9�ewR#By virtu� h�i-S�Je2V�2� + �Q@ {<SE�^� n �6e.�Y~P$%�� mer��tFed"� helR:J\n ��=5�=.*^�1 � �56v&k q�� AdE"? � Lr'+Jl(�"�#�[.����.Y"� � FN�~yA�E�*A�x�"kUc,i�P�/ �er�UIq.J B?=,���,\,B Z }{]f�1�m�:�zmii�y��2ǁ�b#m�N��"�B e. BU��4-&B�;���4'` u�� �D� 9:{g e7�below2T~*�  / ����&�'>r�:U;?,� nume�M>��.&ق^k>�!�1j:vK6��:%N�!�Rb� A�% +E>"� 2�/d����,hM�RA�M� W ^2 )( dx_2B�BD*�d�WAJ�� ��.� =(>�* In��6�7T A1"�Ɠ� Dinguish4+0s"L,õ��\ [] {\it Q�{um,:} ];S5�valid.64ClassBOb>6'.7a oy%�! X| u� &�(IsH0-_ < f_u < �� two "A jXF�\y�O�� �_ ���2qpE�1�1) 2 2%A�lyZ�K�AP�+f_uI�v� min@"� � (,6E}{4L^�\f�F �-jB�-satisf[6Z�??<$*A2��"�6F�.�%4�#W�I��j� "M.�} ~� tm[�� 7Lebesgue"�� !�)�N )b | j "Tu<��{ ��h)��Yj�*s#1�j�&�X9�fvgBB�&$g � ��e ,j&w�[N/ � a suit6<.3� � X�ob� in �&;!�Igeq��e�>Q���ra�a1�q%��2���r!Jd^K��-�r%% \} <Ѡ�\}e>�"�2�o H] �eq:qm�-4w �`>�ost�cF.I-�D� �� d"�0�t. Rein h�S�%�N ��6e�AuEhEa���� &��D N(�#� UnEHeQ..dstitu��Yc�)FJ�>2c2�� pick� ��>�Qie"�Al����y�Q|j |> R�=J {}�, 1 @ ��1}{� -j|^{\?anm�p �^�� tyj$ R�="�e�b[ z_jn5Gd� 2+1L}C ɴ���C R݊ �- R < ! <2 R�Rj$2� R1�U!�o�1I90�,��� *.�!�]e1�m!��BVB(�� � \!\!I1�  < c L�a:L1�6w7��Y].�0�cl6"�">u��a6&� 7�w�c�;��,&o3Lz5 ot'Ce)�g!���an���2W % �_"CK{L&�Jd��%/�! � s>-�N ���: "� *�xH Rayls*,-Ritz princi�Q" sHe&�'��~ SE5&�0��"Ru� as�b1C }�b�2�upbouE}3�\ɚ:=ax�Qd��2}�� E�I\<$u�/r+.� } k$H(c C���ghRayI�>�22e#�F |j&� L^��T(e��*�) {L,M_m�-20mu >��G -+)(lMk)6c!2F��+�!�$ MVgC1�)�^} �IźF�&�Ah�)��=.� 9-�* .��:D}$F�B�2>4 $�pa">� utof�N � ��-"lyv "�%i�6_. �V6o"P(xx 5.1� !�! ^qt WJ�.��,��&[ NI�n�EoE�� +�/2d���m�<�#�}f�F�$��|)d�*cVbim�q�a��i� s3�{��ʲ* �;iz� !R..��zG{&�>)� ��\�I#5"1 ��%`C=�J/"V'6x@�/"3`b1��wq3&K�f" �^\' �$�3^%|U]*� inausI[ �M -\.^ydxYr\|b�|fm"���&� @ + |B#|A�!� H �j%:� ��}�I3�If)h - j)IF&z S5(�S5' �!%��=�EX��h<*��\max\� +2 ,� \}�LՄMo!�8 �C{,7z,Wa}n#�!6J��a i Z�)��  ��uS#�w-ũ��R��zv�?��$&w(� �par�H�qM?"���*�x��@5��R{ 4e�e�� is ��i'26? �X�0H"� s�Mb�#�"� @a�Pic]�ae�oid�dʏ"C7>X�nsB�E�I�mtZ��K�<�H 7˕��Q�3 S�\[+ CF G�`\� slashVUehV�u[2� �ta6dxB.�� E��%E e�Rl .�� .#�>'!�L^15�"���h ��(��M-.f�� gamm� ln*G Q Ao6�F�AS�t�p*�z#1}�.�� nQeaf��&)*e . "{-.�it`���p�u˕^#)xQ�*�& �3��P�d%/�gP�6G�>N �0�,�I :I E��2 � 2� ;�1o2��8� ��"Ucp� � � 0\obȂ&� }{n_0�X2+ d* w^�� BI&pbc< E�2'�V�vg %���y�!�JP):)7A��7}{ R� )�kappa�s }2=#�.Y% �ZG��M�2}�M�"���"��<_V&BF;���b}�e� ,�bl�s(l)_;ju`8 >a� fT^*�"V Ns_0>��6s&Qlat^s��$ V�%�$ &x q��pan=!�6=b?1!�!X9�}! thir�eq��rephra!JC�-&�s�"S2����snotA �= �E�Bw�[huL���&�D�QZiY�E�x�����i�E�g H 6�:�fysA�ef.�F:c�=.0E��B�2� �/� Ŧ 2}@0�']]&=0� -| %% "eA:Je���o2m`�/"�( s wa5�byK�Z MoK� ZK� N%�sm�S4EfS6C $U_b=V_b\9v0$&;C th�-a��had�.a � "�1��D]ribsd!d!�0$q_i$, namely"jU�>BS} P_��p�,g  6�ץ�C�7e��^{\tauBDK�| 'eik�$5�.��6��=cy� B��`� inpu"Y�ir�� scal*K7�./A� ,c/ ?l��t��d�P՜Z B� {.��g�"a6�2&(w��gf왰��=I-(�)I߁n]2l�$plain how b�6 �.�mUuގ!�'JV2 p7��d cs E��t���2��= =:S"R$d 0�����803,Sto01,KSS98b �=� r]�is��er`�7R!b�^r \� �@3yt ketc�ufew*�ks. I3�custom�toI4�w)� �A6+���dx�as buil�2 bloc � J. H��_7mphas�G!�l��geome44&�3 W� s=�@A� bps $Sv�n����\R2�hn�`. �.s��? jp�sin ��flSI��.I.Wbj$V_b$"t�. WJ�a l*��eff��E�E�ha�Tg�flLY�Jtp�. �HI� 6kcEYJ{A?a�m8 Wegn*�2�&aD� �m[��03]&�m� s�9}%7$E>��6�0$M"�-�<M�&�$(\sigma(H^��)�ap\ ]2x�, E.W0[\ =\emptyset�i CL^{2d{Tv"Pz^{\mu~ �{Z��!� ��u$��d�}]S�)c $C�F*[OEf�o�wL$ �r�$�� ]�2VI�a!�of!Eres�.20} and \cite{S�[to00}. Our Wegner estimate above has an upper bound of order $L^{2d_1}$ which suffices to pr?�Anderson localization. However, to pr)H\"olU$continuityiHthe integrated dens tsurface states we would need a �proportal��ld_1}$. We believe that such 8lcan be done using more elabo ��utechniques as in \cite{CHN01,CHKN02,KoSch01} for example. The second input to multiscale analysis is an initial scale5�. To do- itiB"� Boutel de Monvel and Stollmann use> addi-!assump , ~(\ref{BS}))+ ase our iVmonMPLifshitz tails result1�4previous chapt%� hus avoid!canyV� like .�D %% Ende A \begin{%�s�d} There exists $E_1 >E_0$,%$L_1\!�(mathbb{N} $aA|$stant $C$,IA fequE�H}\label{eq:PL} O�P}\left\{ E_0\big(H^D_{S_L}(V\ob)H) algebra d quantum� |istical mechanics 2: Equilibri ' es, model� rA2S!�(ger, Berline�����4BS87]{BirSol87��S.} Bi! �,Z.} Solomjak27��Ju self-adjoAL1�� Hilb��space2�4Reidel, Dordre�� 19872�SE��� A.~{ t& ��^Dynam%q.� ��� umq#� )xB� Arch�),}, 80:87--97QZ.ba�dMSe�R�,2�i�Gi�z.yAbsence�� �� su�ypeɆcertainR�a]EK.Z0mp\_arc 04-162!CFKE# CyFrE!dH. L.} Cycon, R.~G. FroeseB�N�E2>�U"2R�2 Cha99]{Ch��$A.~Chahrou2�Sur lao {\'e} in g e d' t; �   et la�)on /n,ralis eA}d place; 9�pi u�ҭselMZ dD.�%! Helv́ ActaAd$72:93--122a�9925�� Fren�jY|Cha�m Ch00e/N O� IFumA]� )����L1��J peri� �e�a2& � Lette-t �4}, 52:197--209e52V|]�4} {J. M.}~Comb� 4{P. D.}~Hislop��(S.~Nakamura.�$L^p$-�� �ihift fu)�,:>, c8Z��E some�B112j%= M� "h(218:113-130%6��!�~ , F.~Klop�:��� �� Proc. Ind� (Acad. Sci., � d 12:31-53�2.�\CL90]{CaLa90} R.~Carmona�$J.~Lacroix.�%eJ��I�&& 5�2$Birkh\"aus�Aost��1996�SibSa:d�Sahbani.�2sa�scWr=6� �}�*� i�Ѫ�bJ�V� 561--5� >� Dav89]{4} {E. B.} DaviF� Heat kern�. u\ �2T4CUP, Cambridge��89.� DS78x Si78:y\NRSB:e�ystem� differen��a�  a*�o��a��g�.�EQV�(63:277--301�78.�EKSS88]{ 0} H.~Englisch2.M.~& Ao!IN���b:B�� )���}, 61:12!�126�I8B�ao�ao��Rq v(miltonians ��1� but �d�W*hj|,128:613--626!}6�HK�HiK�9A.~Hinz%ZH.~Kalf.fSubsolu}"�It�1'� .3 F��M.^� J. r�a6�,404:118--134N��a HuKi�a6$�WNdJ�spars��2�In �Stocha� Z�, phys� A�0geometry: new�rplays}�( volume~28G�CMS�f.� $}, pages 2!� 238."��2WJ&JaL�W V.~Jaksic�Y��s2�CorrugX�)� a.c.��umB�V1465--15�>�1] �1}��SN "�!?�B�V]459--477%%2JM� JaMo 6%S.~MolVov.mL*�!�-/�� 08:1�17�E� &w JMP98!'MoPa98=),2�� L.~Past6� �#�ag� &��wav6_Q�Wa�@hin comples media (Minneapol/MN��4.�96!"E�IMA��U�14� 54.*� New Yo�1992^Kir�X} R��0>��X:�urs2In��Hy�4A.~Jensen, edi�, �B[ "�s},m� 345�$Lecture no�in�5(264--370. = *u2�KK]{KiKl=e� .���band-edg�havior��B icX6To appea�-��$Anal. Geom.�KM82a�rMar82bJ� MartinellN� .� of.v\-:R �m� f� J0  A6 5:213k15�6l�bɾ��a�yy!w��-�� �*� 2`eEb�34:141�uV�39�3�� Larg�vi�A�{L}�  ularof�F� �fMT& �&�.��V� 89:27--40��83:t39�3a¬ss�{ {nes�s��i�\"{�� Dukem2J��50:125�26N�re85]{} V7% ><2% de Gruyt �C520S86E�Sim86>.N: 5�s�& � plus1�u}F�J. Sta*�(42:799--808%�6:�7�7��Comparif > � �auga)�*�B�J./ct.��0}, 75:396--41)�2OK�K�0�Kostryki�SR� ade2b��F����,"k)iK"E J�B�V� 807--84" 2� KS� �� ��Re>o���B�Ft187:2a�246F� KSS98��.��3A2B�)a schr�VuG�g� tera�F�V�,195:495--507a:��]{.���2� a ���urb��ofi�6����F�k �.E�� .~a+6:2��26e�:�W�KiW.� D.~Warz6+"@ v cTGDanisotropic decay:e4emerg��-class�regim2 "$-ph/031003I2dMez��D} G.~A. Mezincescu2��%c�"�&d!��55[.? �A2T\�:@9���19J�4PF92]{PaFi92} "* %j$A.~FigotinBg�AM0��almost-F�2~Nv92�R�ReSi4� ReedaRw�Method�|rn%�ema�_IV: {A}n5%of.�2�Hemic,2m 6|Sim79]{} b�F�al"�ionQu���2� �2�� R�B� &�B�$Bull. AmerK h. SZ(N. S.)��:447--5  &$Erratum: {�G{7}:{J }, {1982}.��5 �5ZZeAe@i�a8�!��"o�!d6&E+Bb38:�7 2 �#0]�#0} ^�{{W}e2) B/cV!um �SA�ls  %�� distrib1s 2�6 w�311�2��1 �1j�aICaught�$dis�)!�}�)��m��2�V�20W�&>,$ q& docu�} �  %� % % V� opDec 21t4 � \��L[pra,aps]{revtex4} %V",twoc�n, 11pt28\usepackage{ams�D ,amsfonts thmPsymb} \renewcommand{\I)w&8tretch}{1.5} % :'qed?4ol}{Q.E.D.} %.xshowkeys!m`\�! on{Dec. 2I84:$ beq{�%���}} e� �\e#!�!2 Z{{\� bb Z><NN}67CC>7SsS:8RR>88eps{\varepsilon6qPhalf{\mbox{$\frac 12$B.� \rhoCrho2�8Ci{ C_0^\infty :$(kf{k_{\rm F:�c>${ .\, u=�Tr !Tr.x {\n}� f{\nabla}:cBB " #B"*�r0 t)}{�) �$lem}{Lemma6@cor}{Corollary} \ 1 style{def),1� {rNRe�&}��&�+q�A�title{Gr�� e Energy �Low De0.Fermi Gaa/@ \author{Elliott �!ieb� (email{lieb@$@ceton.edu} \affil{Depart��mLics, Jadwin Hall, Pr$ ton "O%0y, P.O. Box 7�$0NJ 08544, USA� �Ro�#Sei�er�rs ���� �$Jan Philip�$vej�sol@m�ku.dkrP�� s, 9=!kCopenhag�Letsparken 5, DK-2100.* D�)rk!Wdate{�&IY abst�  -Rec�develop!�� �t of-"�tr*d gas(ak�it,thwhile|0@verify old, well 8,n$/si.,H1l> plausible,re �7 d onH "� �oryG a"�/s abou�.pseudop�'s. �0�/� extend r�ly�ed*�0 �g�+a�or=%{*v�8! !a"� mula L*ndk eu�a dilute!7H$N$ fa�on!qUng�O" short-r , p�/��E* 0length $a$. Ff,pi� $1/2i�" is i�$E \sim E^0 + (\hbar^2/2m) 2 \pi N �* a$!�!�$E^0$�1!�th� non-AX�s]%{$H9(. A similar!=!E hold! 2D,% = a$ re<%R /|\ln(] a^2)|$[Obv1l�.is 2D�is�� ex')�value!L � -independa:W.� yC %\pacs{a_a �� 6/ {Int�.|3leam]K�'![�B Q>,� 1x� aU0,IG� ge pair&{, was E�,ed years ago; s�4w"pprox"5m�*0dhuang,lee,fetter}. IndeedAee�cor]1� beyond�ideale fo%�)� &�! �.�)4bosons, except%!2fac!�at+ %5)each o�1A�aV�in-upk, effectivelyB only Gna[-down6E�no k k�$ tA�sh)�goes bf/to Lenz-Z } who�z��h�J=! �by�av�3� �icl&�B,$N-1$ fixed $! !<re��y+d f3�A�us��mB o�N� per unit � , $ee�,_\uparrow , a�_\!L  )$, �$N'$)qup�)p#: %�(of mass $m$� �6 x of � $V$ (�2u#3A mod, lid.in�� ch $V\to  $ �U��� = � /V�4>�= N.�(re)�) is,�ally,�4q�5M} BL >h ) =  {�� }{2m�  P{3}{5}(6\pi^2)^{2/3} �56�^{5/3} +>^ \% ) +Rj 8�Ha <1� !�)� +^ (rm{higher\ �\ in\ }E5h=eB�) \AJ eeq e���OA�4two-body ($s$- )J5C � �`$v$. U�L&tY� totau8x $� \equivM��BB �e���6� ndicates e�at6 h�:�$e6x�:��4 zero, i.e., $:�=�.�=A9 /2 $e�e�� sponŢlo&� e��e���ains �'�% ki:;�Q� isA�gin&gM�A�NA4Y?^2z&�\ .�"� �7J� �6�;d"� ��Y1998�ItAMDcustomary, nowadayM odardA�efu�)%;co���Ea :F �6�q.0delta(x_i-x_j�andI is�/ ly a� ful��cuZ;ob!�� cur�(�:s. But ŌA(8to be justified2mlyv#E~i�e purpo;f DpapeS(iss<e&*rest ��involvwhich ) 4 �4eD ly o� wA�>4���is LnXof�c� �Ei$itemize} \ �availabi�60of a good var�al"�- $\Psia� impor.;�1ore2�,A� ��e isp�&� l� J,nd wh!i` $\langle � | H|�;Psi \ le$ (%R!�ne�'ariA n up�b2t<=��/u" d)>�$u�9D outA;orEWuna��e?%� � . ItA��> alsoB !�- i � desir(ccuracy. A)�8>�ABCS9��superN>u� it<I��e��a� blem%�w�think%�$ Bijl-Di!T-Jast��/@ $J =\prod_{i,j}gy� �*ita< E� beeng s�as farwe�,�carc7a�"� A alcuI 5mmaka��f�8%E -seM subt7(ev�6�"yQR ly clear)�< h�&i�tre)�r�>y�e r��!�ri���ic2L�:fin��2�by Dy� d }%4byS@a#Q}pEa. 1�� ic c�?conside�� !d�5�%��mi�( = S\cdot J&�Sa� a Slater�<� nant. W��m�looks�p�!�.��A6jE�'5MQ�B%occup2�Kx�Z)+� �,can�'sa�au � a �.�ĝ� sour 6Y ic->e �%�u0��I]t!�-Q.�  !�tit�� enti�@�.-�!�!\o1ơ#/� hanE�!gA�� a tin�z6A�a d�S4>free-�  ki�;�f,Ew!KA�on"�, ei"iA�hhard-cor.�,, d� !qcom� a sm�..T ��V2�X�>collis�&�BWe� �Bn�,by\!!T���!,:�>Q%�le at�ive Ή� drawtAKitQ^bea�ht��wo dim� �(2D).��c  '$�Jr ^]or 3DIN\F�^2 / �ah��  redicte��?W ck,hfm�9� �BcwDLY�}. (Note;�(s&�1 �D�ed@2D��l�1 3D. Se!�6X)�.sequent� !�>q will-Yo��0�� $.cB-!m1�to"#� �!U�$ o���9 : 2d} ? &��7B.� ] � 2�R� 2 F� ^{2"� R� g�  }{)���)|} �>�B 6%�  .  We)�EA!�� �CJ 2d})Q.iuA�� w�m?Caye"�0� 2 te� a���iSaPus�` to e�Fv�. � � In !BiF� >��  �0 { A��*um� diagramsM�baker}�1chE�sAkmany �s.��"E-7}). N� theles� Fbe admitaԅgexpan�2���.>�� conc46d, mayil conv"�$r�I.�. E� �A!6�%�!+� used�F: fu!щ hamm%"but� � �s�refore, "1 conf? �mhIto _I� � �Cvid ��!�� � f�FA^w�I !ty� g!�$3D until S�(TF2d�E},w�l�=Amodif+ s"5 �ws�:of� %���trivial�cFini�!�� a&i,��G � agpo1 %Gth*�-RS�4T}(e natural gb"YK�2V�Gci�� tem�'�0� llA�i{kF�&(G{M�#�M!wRJ�In� � $��/2m =1"� �`b�K ed h�'forth)�I�$\D*= \n^2$)*H&s.A�n] %�D@ H=\sum_{i=1}^N - C_i��1\�Ii!~y $x_i� on% ��E� ube. S� $H+!&.�,�an�-ifj .Uk s=A,�41,\, N_2,\dots q$� $NInj N_j$�;e�55�e | n� �ACcoordin�1 k x_N!�it��!�of�7� �$��� ,!/)O$ɦitap antiY��$O��Bfirst�$ ]с��N$N_2$.�etc. a4�M��2 �' w�a�vN�LI $q=2}�E�mma&JLsw% f{T1/ XLT2}�"|3$q� \iffalse  OdvantagZatQ t7!�� &�+a'5��$ � ��as dr�*zms%bC"R$$�. \fiOa�.� $v(x)E� �eyp, radial�mz#PAge $R_0$� then�a�i�QndF*, , 9�H a!�l:N: if $M%phi�!Ru-Q �A�(&uM� !#�(ull discus" )A�� �-��gy� �2 � q} �� � + &��).= 0��subjeBk �AgdP4 $\lim_{|x|\to}M=1�n!Ga�A��x $a= N<|x| (1-D��� i��zI $v$��b�gr�J; =E�� app� �=�g �. e � � a�@P"� �A!�)dA�Q2is%�� "��i�Qe� (a�@ $simplicityEP � �f"~s m between� e��p�`W���@samfreby aA�a�.iT`��-"� '�����9ak�e � ?$v& (x) $, (w Q$@,@q$) � �$i�. $j��,r&q9j�` s $a kaܡ�tPay�*�Pij�u�'��*N" _�\ho�� Our�� 9st@ g!�r��Y"�# �. A��I�aR�  !n:*$<$E_0(\{N_i\},L)$A�$H$, %%N,L^3)=a�\�;rm�$} \, H$, ��%�>� $L\&� �p_i�i/���C!e)�%a+ a+�#K th�r]"}3 �l?of ���de,, $2T�/L_3$ �T��g *�#ofJ�� ruelle,rogM�""G)thm�TT1} Fix� =N�orU�q qM�AP7 Mi$, � %�.�de� etN�of!�� a��p~ZG"}~"k �  $N� & &c.�tn,����$: ��=�}� 1}{L^3}2� L"2 35 \�D( *  \�1 %L q!'_i  + �!7&V -[qk\�j +e�^2 �,� ),�)* $-i,Aft( . {1/3� 13}� D�q +�=2/9}$.>A2 �c�,an� !��� $g� %} *R G$t�;��"f ; o�/�'- ���% princi�UAexp�N ���nDBy cut� ff a�3.2 �iN 2��c�� ow u�O)ō���ɧV(��i ��(��U �B� analog�)h-�2D�0!{"1.�o !�?#T2V�ѾAe����2N 2}!R�2a�&��*� |}9^2BK3eprf (a^2B )|^{-1/10zF4}��ln6 $2AC� [+"� + �i�� &��A�o  $� $� q �t��� �<s �-(ightforward�\iT*�iU��� veni�*noa. �$N_1 +� =9ŽX=(x_Rx_{N_1})�� $Y=(yy2�U�l��|���O)�� �%"� ݽs, p:k)) .� �� be wrMn aB$q H= � X - � Y + v_{XX�&v_{YY XY}.K7_X��o2_X^2=.�%W _{x_i}$, 7Y= 5Y5:626y6 � {i1 "�/��$!#xm.kT1>9<7A"t  �0� iK'�&#X iXage0Y}E� Yr�EfiAXi!|�*��)In.�@z!�:L @&n $A��XB��  A!the���9\��:F&?0OutD9a#P�` BDe�E�_8'�s5��� 2�V x �_�A�� t2 o q�hf��ntr*e�� he three-"� aler�� �aa�i�two� 8)heR$E &la[ J[ Z*�&,�� 2�upa|},���) �al&I P��to � ruct a�al�"�I��: Ufe�T^n�e� GaOru:�+to|,�is�)E�(time suffic�ly(I5m�it�7Icom�' �(= )�sec��&�2p�d.i��l[T�)� findxV(�' &x%)�n-n"� to�box��Nd I $�.9 8.T xeys�'xes must�Sbe�se,$ x, hzgaens �q! m�size �1Hneglig�' !hau&�o)emerv G��. l!Y -Y�BH�)e{�� forc�� l�J"�*�0in-9�&%[A�isE+s!��*�e�%ol�nor�Y��trB�W� �5%]c)( �accoun>$cel�(1�!� �*q5 vaq5&]���� J�.� �:�)h�6�ec��‰�ًXe��-y� _� V=�&���3/ soft/on�2W,q�! nK- mi up stp� 6�&-݅�g�&�%o r)~� dr)�o�d a2"�!#.\ )0!�#-sp2 B�gas. Ol.8�1-mo<ume�7!I6�!C�ens�, u�s�Llow:Kis �-ifg(' sea*�=�� � be�O!e so!ap,-_v �a bigge�1an�_,cutoff. Withe'!�& )�!�&� hope^ proc�.�%�5-of {\it "}�'ʼn��"to/ :��p-�,!dY7��M_a�� ori} �s,�� on*&)y matrix-�2 ,8w��3 �  clA ��)�o� 2��<an��� ���E5��."Da� `ir neaN% neighboA ����und Id%d=ᗹ�.�eo� of -�"�nticip-�(e��6/#of�;�AK�.�t Y 2J),� I� T2},��skC�(6��#.��� ion{Upper�ln�!�J@�  ' starE�ngI�J�Qo�X)� 3D���#�q&�)-'� be f!����GndI����!.�:\, .s,�;a&� Ysatisfie7 i624[$\bullet$] $0:va�� J� $a>0$G2=2��subha�^ica$\R"i�"J l �"�m&(�}��#.b&�; mea�w�"is6��$|x|>i�R \int_{�}:[,\, d^3\!x = ~5Z�5 � 1 - a/|x| l2"=.m|x|��.�.2� �'�$R}�|\n~|^2&� |9U\�\,>�(1-a/R)$)&R�ndY* Th�w}$�!�%~5 bothFA�*� "�  m�EN*.�} �  next*�R,��~ )n. a�l�Y�&� � �?( ɥF|$N�K R�#a�� box��  /-$� ` a?J|w  F��6er $VyLe�0e2j%!: j� !�$$\ell$. If�la� se2)a�l%">� 0%�=b�X.� "� 5`!B� W%�n w�0�sut $nlV1 (�+R�p3�<up2Tto5ii�rwise $m�_2NF2ks� %�_i6vj 5 tej"� �$� �~"�_defnm} n �6� +8�quad  Hand} R� 42�2r] ��eps�2 < (c37n�+�%a!qB�=area �s�Wre2o too�,9�I�� �OlegitA��6�3,*� N 2�9in�1Mi~Q>� �.E3us�!kq�e��=|#��� 1&� N_1,�'L)�%q1}{.�� n,m,A�2_$=0���u(L&)�2isi �C%l� oice�a��#e�m��eVnN<r�D6G�';6� Q4�'�Qu�f�?6�a�a cubic� (e-�%�$)"jn$,O�� !.:0��,�&|'"�(.�tri1} �) (X,YD8D_n(X) D_m(Y) G G F%A�&�> 0$� oE]!SB�6��$n$ e�n�5�"<*)�ad z(# �de)Gc3<�4A)� do.) More�� M�tri2} )= q9"+�� n} g&y,* �g(x&� �]&�5�'=0��Js� C.�2sM � $s>2���&b%��L� �& $|�|�{ s�} �\p�%:$s�Gia9>73} I:�P�:�-n1Fj{m} f%>?2>f(x)=&$ /(2 1"R-"1$��}.�-=6�.� A�zern�(��we2> $R� � guarante[!�f� �inu Q�.YmX$2R%�!U BAZ2l�+} �%�0G� {�=a�|H|\le}2.\"eq "�-ln�ss�-�1��$u�&UA.�t1geLt�!t�( *�%��� �R>2� = �|&f�t>,0�>6&Y6&' k�XY}2%. � In ea�"�6R��;%\@$}���3fa�*E%�Ifn 2�>$"=$.�h?l:"�B4�e (nam.ds�` � si-5��G��)�@&�8$E^ D}(n�"/n�U�eq Eay**@�%JMx &=& BR2�!�.\\ &&!�}s)/^2Y ~Q_Xѭ�lI ��^2���%,dX\,dYA�� ��1�+ 'd $dX"V?��nd�&!�$dY ��m y�)���.A&!yf/�USchwarz.�xto de3z (He�%>0N�)Jz��N&�& (1+� )=>97��!.\)pM' 3�\� 4J�|^2Fc2oee���"wa�5!6CA�$Y$"9=�=�� us gl r � ! �2U�AI:9! � Iu!5E�I �J� $I.�!} }�� big[F�+]�� *]^�� � J� II} vI�!e�[R� +Y-�a- + �� �$�#]yl}Q& }ZqY ��E�V< defI��F�I}�u )�   �I�]�F��A�eq�>�*�"�a#Cb9T0 sh/   A�]5Le�A��1di9�).mA|�����Tatelym-WFkrt�  $M>��ma� ���\ �Ϲ�.� RieJ�9�NaN�cg�8$$(+a /\pi)K)^3ED1its_{|p Pkf, \atop p_1,p_2,p_3� 0} p^2\, �pA��K 3 5 1")�+{n""(ell^2}, $$ &�9���Nm�by $\kf= U n)D+3}/IRt�Bt!� easy�O��d.�C�I} B�����ek�$cv+ n�"&�+�8a��on�&�err��s0%u�op�lEY ��I�=��4mQ�$z.�:T �{!!8&G "Gc  $�, $; m{Brecisel��$n�S\rh�#!�(3 \gg (a^3)!A��5Yb� l9ed hour�i,�4'0a-Nex�5�QĽ��m@IgW�Cgog o �a&x(lemma1&b�IY��lemdet}�"� M�N�E�Gn$ �"arz7�,&�w4s $\phi_\alpha`�Ta�  $hT� vari��(\Phi(X)! �u�w�8= 6k h[ �'HM F$n\�!s n$ n./ defM} M_{ �\beta�l�^*Y3 $|�|����"7 �B>\  [(i)] �X�G �b�a !|\J l \det M&�(iP+--ke�EA$k&`!��= w� x�7(binom {n}{k&�Z�}�N �(X! �2%  x_{k+1}�Gs x_n =O' 1{k!}&� k%O_i G�� x_1\�< F  x_k !| Mey \o)�' big| ~N)����$|�8i��e��2]%vP(�B�P��F, -�M^:!�h |x�Z�)$�\��J| $(k!�}/�*�10\sigma (-1)^{ } |x_ (1)})1 )/%k)}aP$ @mM�lpermu�$P5U�E��)A�'_A i� ke�/m��� y�k��.�imme}�+� M� \_i'E{_i'}! Big(i&  )\,( \Tr[KM] ���B$"x.�J \, ] �M�Ge($Ke�eb~^ K} K�^! /�^�(�M�W ���$is���a>�. exer���"weN%vC!�re4l�9�DA�:Mlo�njli n�n set���i&3ovA7Qɑ Item (A1�n !�di�(e�G�"�s (i) a-���QE�� Uft�ofP�>� /2s�i,�: HoN�!�I�$�pl�Q��%�A�!�$;!P�it�  �e��  U�$% �(�w_;fer %I%9��&8MA����0}\nonumber &&A � ^*P � VT + \MI  |"MS ]� �2g�� l�rk�c&&} a�_Y M_Y��] a�8l�a<X.�61�1WW. �T��\�B#ces $K_YyM re�+Mm=M��KE~�9>  beuow�:� ��� Vu�jXV ���E��7=�%"bx �d�j$�=�" |^21� )M1)v( )�dBB^2�> }6p&E2�B%I �e�-te� ;� a~ �� .�IW|1� \|\T!�<� $\|A ��\|6�� ��!n�st*ce�h-Ot�8cesro"�Oo����=S#$.���.�all|$y_j$'�*�"ffXeas�,"�%$ becau����|��i && ��U�II}) v�&D1�s�2R$���p�9�� Ij.�#`}Uv=AL�zsFr��q =I��{n} \xiM�&�.�defxi} ')=qaDe1Q��B��4�G, i� rho*_n�2( b9� IA�.�kytXINa�sH}nxq*� (.II�*��"2&�[TouQ}< �QJ"9:"42S&3mm} A�c0$|y_i�=5$Q@ � A�$i\neq iF� , \| 1-M_Y \|�uq ��(:3 {a R8s=+ z]�{sA^"O. ���&�qn 1-��!��şȒ0��Y$nR� $|b)�?.� b��� b|�  Ŵ��  |%�( J raW� ��& $$ M����a� �eJ���$ trans��tJAeEof�" BLavera�bo��c!� .�-�$� or"� s"�5R�6�$�*:@� W-b×� (dc�.})\,Y8�{-2�4�'!-�� ���cl�|#\BB� 8bA�of�((us $s/2$ ar����.7 ,t�&7���e� lapp�.a\�t. Also�"��, %S?��x� outDf d^{!Y��,&:�1�A!.�� [ -.�r\et? {G:bar)́�Cauchy-J$(a+b�0leq 2(a^2+b^2�2�a�< aA_{%�}iH| �."�Zq_Sh)!�. �2.+ x�jB6"�)�r&#G$ 8�6/(�= s^3) �*(�vQ� gGJ��b+.~�/M&R$� J�/!� �R^3}(1-� ^2&�)� (m*/3) aR�$$�E�^A� l�&��'us�-h"�  AHc$ as �D�efa"&� ��\max\{!� , �L0\a�asc8Q�-l� )8 ��). .�-�e3*-5�.U�;Ua�M�i;!�/9 Yk�/�/ Pogo�6�>�H"� aA N�!nEj2m= �2%�1� ,Poincar{\'e}6ʆ\cxW�,Z�| ���m Mij'� s� I22�_U].A(IA!yA"expreHK��#r�39���ap�k,!�co)�,M��932�)0a5d . SRU%�!�!U!���$ (" 1r�"!i�H�>3)E�t�U�a.h&���2qaT ~�2�[�ah}�-n L6(-�+.�()� ���.�9�� s< ��y>aa� Pe�z� $Mn��]5j,sh6� N!e��9nd� � �/M_Yus a{ x�AT�M7s>!�� � my�} .� ��fzs})1-\� |LA_nf-�1{ 1-:�!� /s^3+�(s���G}weeq �Ti!'�3min���GpP6.�$ins��ng�  .J �)�o %e�I��� "#|6� J� ^%.�"�(:('&i'�"%�%zs�� ��*�Y, 6�4}"���b�glelt�7��,��+eq14})-E&ks�sie� �-��Q.��F8iK Xnd� v�ewe `��f�PAE�:8�T^ �5EP Mls ���wnSAo�JorC^2$�  m'lemg} 2�:^� �!�&&�2��J�E �(yn n^{8�j.� ^2 um{5�#"��gB���><$fh*wsPve2V�$+� (\3I�BD�thL 2s -H*h|��%$ #&�!�Heavi� �:�^�F 4(tP� t�0  T+t<5To�'� Q9����6er7=I��]E�J:�k �������i��h�2��.� L��~"� NNA�� 1 �%e2,9aen�6ro�Mly A�Z�\*'b":V�. D},(2)�,x'q S'B%�o"wob'de!g�dR��g-5�!nqֈ,�"CLa�lV�Vd�sd�>-&]7%O�a��2pd�`�>�����(|x-x'|^2 (n��^3)m�p��A�s�'cn� >7-�0$.�abaro0tMx!�g}e-*W�3E�atk A'��MH Z &� 6PIM�?s%MB"HU���b�4�X�A�?&y:"bR�5a_o�"5�"�Temphaz1u@�j�ex9 $5hi�-A���E�4y*R{"�d1�i�8�,�$x'� ad!�Fd1� ��X@ uN��+&�#y ex^ $n^2��3F�.1\!k$s>7!|�9e� g zbe hu� f $nJ~#1/i>Fman� bQ I}�I )�xL�-yMb!po&�Atf $��@=�)foo�!b����' '"^?R�� j�Q���^>")l}i3, unl��Asit�-o�u: of u��4Let� B_n=a�fN�A_!�9��zrr��� ���a��n�1Ts!P�_. ��y46g}A�B�� E{�3���� �� *�)�b- ��� B_nyL���mVD}_.� X.�Id*w*"Y 2 x"� eq15B�Nowa��j�m8*<�y� &�%�o f $y�sJO!l!�supremf/�8M�Q�_Ye �&l�c_b*�A$�O$,:ch71:�uqsteadErep��,a��arg߃��$Y�m{���$|i��)Se.-?ogu%6�!'��tq6I�G: Z*� ��d��<.i-n+�)`��� 2R5�wa�P���i d6u B_m " ~7���# \wideK_X M_X��FggF i'�x $M_X$�!|sam�4 b�KZMY:�|X<���$m.�)� $.�i$m\Z m"}( $$ (., )_{\�X("|(; (y)^* }(y)"<'}f(y-8'� 2�m� yg"|�qE�# )[\ A_��5�s�6mmu+:�V�"��:�wea!���A�q�ast} %.=]��mB3��\2#�)2m%[H)AdAm y�eq@;rez��N�w�s� )U�� ��h*��'�i\ef��c�r�D� ��l $iW�y5� = � aXAe2z/�ҡ�CinAj�2f%u#� g"oj%�)� QYoungb�us�1����� �>�A��\�-/2�ftN5!�5y25 R0-�*!��S%�B�$A��M.���3Aw6fAx7,EU��1 � Dp,�[n#{a)3) AR�%�x _{p_a,q_a&�2�p_:|_�*� �{�*$p�$�Aum�d��$�1��$&�$L&1g$(2K )^{3!�6�(sin(p_a x_aF�qE�� �a L�^e:1B{�%!{B�Yx!O�? {n"W !��:5:�0M�a�M#�%:/��.� ���us"�e.�/AE�� �� � -"�.6 7{�n n m}U� A_m (�R��VfR_�#T m��&o2&� stiIIaB 5���%�2Rw�'aW��a�rq�ge�Y� �#>�q&�6�q[(�x 5.51Va��!�� It rem ~"�&a�� *&Q2U}*|��1���$� e^Z��%X� |^2�9&��n \ j�j$i}>�?9@ d + 3nBXkXk X ,j} "�%&�@|B k)| U[ susu!?nd*GNow��6�# �e6�^(�2}1 �&� <"?S�l� *�%^k>�k��#GB� o� J 2�: �Y =���{\r'*)� "�KETit�l" �Dr3� = N#(�,x'')� �*�3:��  af*� nh=A'�$ ppor� �et2i�B6r��gB�S�)*Ep)�6�r &�,IHV�<�iM.Ip6�s��= .y_`�*2��.(3 n 3w�I�^2��yuecBtpC��s IaMcELu;)V�Q0,� )bm) 6��%R�2� �62 �;$ R�l�*{S6�nough� �$A_;B b*;ds + Uerm. �)QO$n",ys����� ��2� zefss N/9�"�FK�  �6^�Z�1re"�^�w�.{@�wem'aq� ��& >I@b|^Cr)(Z+m�)ma*�5}��� ColFang"S"��s ��$ Eqs� �}),M{y-H I� & them!�vari}It 92[5 n�Ah")EA � 3 5 :�< �� �b"2 &&+� t{n& X � eps+ C�x& #&�++ (n+m_=�_2 �d aR 1��} 1{m?=�� Fau%5��] \\ � �Cs}� D�_�"" [ �,\3% {2�3� 6\F�$C�R8_Ine"4 ?)A� a0*,y�O5�N�M�#a�I�in�brackem[Oa��/r���f�<, a2�A:�<R�*�0J�K&�<� >�& =ps�m5is&�3=D^2�#c�1�%� s^3/@^2� �w#^SF!�K� i&p5i|{��Z �q�q�q�k�kBkCm�7/aP{s! aa�2�� 4} .:MsB6E:0s��A�"�ͦ� �-1n�-�&|��ra>Xa0I�?}�t�RAUe]EQs +�OI`��m$. R<�( |n -�:�Qn 1 �$| m - I:rR|! eq 1��`t�st:S����q� ���R@ V R=a�:A!�3�5C/4/9}\ , \ s=2 R� \ �a�r3�%bC11/9}�I%9�f0Ll�{)ni|!�we.�)3 ��� �%s1ED1��3:bQ�hq�eV big[�"�e)�2�C]�� 1 2r���do!�2FD!C �� bina�fth Y�Mi� ��i�L��2T)(I�g ���M�A<&� (��e� f& 2oM$CFHe2F�c+2AUAUGEY^� �����h�<"4 %0t�O&E�)�e�c�P�Aj�;�EEFa�vL2 .w?9}I2w"��; &�eL�dB��!j�[�`Aubz.ʜ D`0 }.�[�a";=z)�o���' of ;�-dGG` "d oa &�3�v(�may or !�AW0R`ZMe)�b�_�>b_U�at�(ex?`��up�#p�*:>,�!=8ing, & f(�@d�L �Fouv�c?ns�)' S�.J (k) =(o��Z�� \exp (ik:oyq$.�a'�%�was9�� )�y�E�� fur'&����y�9��a��a �G% our * cI``low''g meA�A��ye  ``G.$ $1�r? �oQn$"�?��q�d!*�E[2d�a� *<@bE[E�qW!D|�*^a:*^* � X`*">R#4$)_RAY-�E#cha-�erZ�9�a a�/ h|m5R$ "�ef '�Gig*��5)_R �=�@ if MS <JS1)*;�Z$\chi(p~FB�^, �.' (p�NQ �b` �=p� � {(1-4)�y$ *�(LLid4ble. %\in L^1(�/)\cap L� <�imb" deffr} f%]=3p_{|yA R} |$G-y�5=> |,�'؜ndJq1�efwr} wK�P{� ��} c��^?^_R*~.,HThe����+3~9�m�n"yQmnnu�$R_!04�\ �N�^!2���q�5_�a�� >0/�topr} - !�%�Y�,+AAe �!!�eps) a�� !> a-S7H'"U�e is @�pl� oper?0n�'-���&er2� Y�^?j>��� . T\|$ φ��3an� ���� F��Ƀ?u;Jf!ʅO�jgu�hx_in� ��� �-��oe�al��� (asdJ�)�1m�Q5$I� �a�3����no"|f~�fM*�E0)&�hl�+y��aʂ= e6�q!1.%Qj-77o�doodw)![�Es&J�9 �m�:�(re�i�s)�y5��5-� tot �cf ΁ i��~ sa�a7 <r4 � �����he k 3�on:�M��;Wh!xprw��AS�3 uxur�hk*� $am]/ai/ ":�a#�Ao� 'G��"�9�� snig�eiAQ5%;� �K�m�� or eƃM`~ta�or�$x0�I!��dM��=t� .� A�b":7����kc"������2��.= sU�����5� �G|x|�G�1+[��12!A-��].�6)"2#�0��&cor�2w !.�vN"|t poi�{�ef:�4�BHall&u@7 �~���U � $x�>�$ 6��!�N! -y_ile .�J N \< (: 0-P� �� �%%1>� �F -4? 1�qSl apres��-,� �?i;�invari�iAi7f&� �i ����w1$ �):�Dl9t:�>eS�pw�*�/6fco͘ary�>l&� smooth6&{�"Sw3aA�$�Sab "Y^p�B��� � >�in-;o�5�0$4� !�8defcht88chi_s(p)=l(s p)& �b �B�9���R*�j O ="I H _sI ��)Uԡ{ rapi��ca蝅F, � �+m�l� %�6h[*R��$*��Y $R%&�sP�*� intw�x| >�C -�?{�C5��dQ!and TP B"� .wJ K}q !�!�P2��1�e/��e0J�1{R�;�M�*�-!�$x� $y L��_re&�S� !�l s\ll�*#$ (cfk$~���e}))T*�A�aori��s��aps��&�|+N_2="�|�"_N&c�PN*�M! � F&�d�"D�dthቁr�#� ������<%at� /L^33��U1,_22�Cs 68z) rhog�yp^$\gammasz| 2Տ�re�\d R�Gc,ce�S2+A�? $X$-A� $6�[i�1K���* �=N �  2=�{M�c��$P_6�T�'A��KYpr&2p�"�')&h2p*�}I"��" �| $\"�� [�� l^�2/perke�P_M�!)& T��iHp�/>gZL a�Y��� (�{ M!�)'}��i p�(�6)uh!�$Q"\in�*,�� sc�!h [P_M]$&C �G�?LP.�trp��lhm.��1 M�,T = 1�U��zlemtrl",9i�|957��)��pq�Eyw�:uz��p3Xs�� Zlse's% �Xin4 ��ar!!�F?y--[ �Yn4%"y . %W�7w dV�a*Ϫ.ih�5�  %��� �l�lM � .A� % z� %F��~A^�8vrq\ ��-0O*ɤu!!�~��})f�h2.&9sepa��mp[UA^ginA��I.�K���� :@3 (2n��j&@�_i=&t� ixedq�`-y��GVCPs� &�� ��s�L��ȴm  1m�X* TQ� \�Xe�iG35fb��lefE �O�� a ] + C&�9� e[} >�SQ �Li=1,22�]��� $"�Q�7��(�ucesD.:AG:::9 -: Tr[ j,i(1-P_{N_i})ma#a6-(rho \sqrt {�(! }.l s�l  We PU�UldEp[�.q�! ���x�sQ refi����nf_EY�:� �:!"ne Y| E�U4�?"�r6%K>� ���"y�&��}�-N"S`( \zeta_1^2)-t>" "2^\�1]�0�+u ��0 *g�N��-1}�vR% =i�.-)���)��wo�a*!�U��o O�2�#(&��W*� * qI7A[*���'N$�p cern �n:�y "4Tamu�0� � _2�{N_2}�"sl1<I�_1�y ' !�9�y_i$'1�4�kL�O(>� �=��Tesa�" 9Z&��)< ��b��a���;� en} �=NS �=�|�ahq m1N >�HB2�~C� �R!�� �?2��Ia�aA0my| Vl | :�h�� N (R"�btf�Y} $94i� ��!v~��,�&q!Z�� (2RI�4i0E`1N{�^2!�p#%;f�f4e"|*->%��ly!S�\�q �)A.� ��i�$�e� T2 �|*g�{ "�se � &�dA�>�T�� 5]{LYau}...e P"XO&�!�^� �u��1�ASX���~IB�A�!b"!!P�i=4o� sspua���a._Eu�,օ.:� ��,�o*KDsJus6�G hamxy} H��( UX�� �_7o����(,Y, 1B6/� �t� "�e� *�)Zly t!!�N �F� G*7iJ�we 2xt�B*`�� .� 8'͖$ !���bb"&g s_=way\"exb5�^�$Y$S{k%�de�8�Z&�iGKaGA�E 2�,� �s:���}���1\G�� + )�1-"`)  qA�6� kf=��8�!F��:�C��" "3Q��=SAV\{lJEO {\kf�,|p|�-,�', 0 �\�B��lai�%2oly2PcY��_{i�D�_i6 �"]  � #bC ܖ��\�6To<Ea�!:a�A� {liy��!�U,R� �%,A��*of�S�*� g dtcD�"�<�KlenýLV)wan�].�e"�R6�Jk�$9! �g!�J� |��?� 0�$p�0�3"b%-&p)6%"� e^{i*x}dR���"e�L1�� \, |a\,l :;��r���&��>6m�S"(G�)ޥ\U)�E$t� i02�1}b0) Q"&^2 �.Z&} L^3�)o[� lyc,��R'AXinfim=E�&Jnfwx!�1�$m=a��" >�L^3"�d 'Q%@"}~�;.l)$� a monotonZ@"}1�a:T�� t����$ z=7 (�  N_��$ -|p|Ie�#:FZO�w $��F���:q!qq.�,�T�Um :�L�/)' �!��'-��W E���a[I� �)e�WT�0�í'u#5^2�A��$s%�1/\kfy�&(dx�"Z+��E����"&�Sz��ge>�e�isq��(r��� �(� �#&�.��i�oT��H %>Vm7K2B�b� ���)tilde Y$b��Y�kyIc�Y:� BdE��hst�z>)d�2, $�� �|��2-� Y�'WB�ogN� 3�^'���#ɩ� j!�v !�� �|A��oHNN"62-uo6r%!%TAk><- ���3 ���12!�m��!bM� (1-s^2E�))� 1} W_{Y}(�FCL�.2$defwy} W_YU'�(Dm_{\{ j\, : \, y_j�C\)-'\}e�fNq!j&�'6q!�N'C � #\}4 , $a4*�|c A V\1( $. A!|���.is%{"܁\{ r0array}{ll} 3� -R_0��v�� 1} &�wfor��B) \\ 0%?�e}, � f� �����t+�"� $|�H*+ R^{-38��g���llS���p3�V�=�L� 6�W.8+icM�} ae I�x4� r3E�E�i E?_iW?x�#�g%c|N�YE�-$&�!�"A�t n�dTr[�Yz�jdY6�E� . 9(BM� X � ?Y�#/A�p�6E=�6]!�+�}q =/�! ���e�� }{n_Y�!--&"R�x�1}S�� (x',N^*�x_25 "rg\e2� �g� *\�Tr� g� *a �&!�'O =�$ 7 !yU �IY=�th:���>d!S�z�1�s.���-$Pő�&a�+hi�1� azY�2x�'��*�&�L">A� X7!93 ��6�W_\pm�I*� 5��-b�k��� W=W_+-W_-�� �L>�(w>EAj��[8&� W]$PW�  ( �-1)PWP]��L<\Tre��� ��(P) W P + PW)+v'��  P� &S[PW_+] ���+T-]� �\- u1+ s#)  \|W_+\|+-\| v) m ��](|Wip�E)&�"��%*�l� �lŮMe�K. �mPd*1&�1%����!�%�Y�u$ W_+$ b� !|� @�)�� ��i$A34 the ones cont�aining $w_R(x)$. We then have, us�F\int U(x)\, d^3\!x = 4\pi$, \begin{eqnarray*} \Tr[P W_+] &=& \frac {\�[_{N_1}]}{L^3} \sum_{\{ j\, : \, y_j \in \widetilde Y\}} (1-\eps) a \int_{[0,L]^3}U(x-y_j)\�\\ &\geqr{( P�p a \left[N_2-I_R(Y)- \const �\L^2}{R^2} \right]. \end{��The last term in square brackets bounds!bD number of $y_j$'s0$.�$ that Aat leY\a distance $R$ away fromS^aryU(the box. Si-:between}s biggeruPn $2R$ by assumption,/� such>close to$�ToundedK$-OxL^2/R^2$. By Lemma~\ref{lemir},EP,q\label{iy} E} n_Y )�A�Y =)�4\langle \Psi_N%�| (-�|%�\r 0leq1�hN (R^3\rho)^{2/3} \eeq if $ W(X,Y)$�@an approximate gr�` state. As already noted!�Eq. (�$trpm}), $\}8$ can be replac-) N_1$=!��thermodynamic limit. Analogously,m� g intwg we get�upper)� $$u�-]!D5E�{a A�{ai sE�fe� N_2 .�m�.QMoreover�/ �(normw}) and� factA\eF�Q� contribut�yto $W_Y)|qA�,�fi[at�4\|W_Y\|_\infty �|W_+\|+-\|%�ft( � {3aa�3-R_0��+Q �a9  Rq�)�a�4{\it a priori})c!�6�(tr} implies%P, for large enough $N�JqY�!p\gamma_Y��P)]U�Tr1 �q C N (aU�1/6},I�where $ QAa�xe one-particle density matrix (�A�$X$%s)�`anyj !sam��unda; true�i�} � 1)]=.�1(1�+P-&]$, s��a^{-1}>" \to 0$ as#I $ (seeM�i�<). Hence, collecEnall텴s,E�applyE�he �argumenta�soA�ecoA���ihamxya� we arrive��/lowu�F?( \lim_{L\to �}M�1�64E_0(N_1,N_2,L)�� &35A ft(6\pi^2���� \big[�� _1^{5/3}+ 2 ]�?,& + 8\pi a "1 2 \ 1 -�& -\delta -�0 t, s- CeN�<�Z��) -C ac ^2 >��- CT>���(1+b 1 � �� {a :�.�s^a�>B�a $some $C>0$��We cho��!�ѵchos} R=�{-1/3%X( �{<)^{3/26} \ , \ s�010 / �= �=!�J_1/1�Ρ�obtain�~smA�$�$,�@vs:r] 1@�o%�jp>j�_2 - ��):2 E�^���is�ish�ne proof��:x. \sa�on{��Two-Dim� onal Gas}�2d)} !�now com� oD necessy change� consider�=2D gastead�3. Z$start with>��f.q energy. �aueW�}dyson}��2D��h�� llow�l| , which gO aliz-7$correspond+(result used��boson�YLn \cite{LY2001}. Its-x� agai�f� )5appendixaH�lem} -s�l2d} For $R>R_0$, let $\theta� ��ot� !} centered�� origa! i.e.� hL (x) =1 $ if $|x| <| nd $=0$ o� wise. L�chi(p)$� apal�, $0�' (p��q 1��S � $hm equiv  hat{�4chi)}�  *^ � integrabl �!U��(deffr2d} f%7=x p_{|y 0R} | h(x-y) - ) |�  ^:NwN5=�H {2}{\pi} c�| t_{\O  (y)\,d^2\!y.6eeq %1Z). ny positi}!�2:supporZ A�annul%�_)T|x �" aI.��uP ��, \ln(|x|/a) �x = 2\pi� eq� �7�$�z >0$,.\top! -\nabla%�%�MDAC!� # + \half v �R!�e�! -)Y 1��[(�)�V} \mbox{�y�y$� ]-� ��ae Iu� licaa'S ��,D >� � �~ { m�a�,}{ll} \nu(R �& {\rm�3 \ } B���0%uG}, � U' �%�$ ca�q in8 !�i� u e�%� :�iA�R_0}^RA (rArAr � 14-x '�a^2 e} -�^)�U+ N, eq UPi�a�1R$& � A�� �E& (R^2� )k� � R/z # jA�� %��q �2 8��,!�turI�u4�X*� s��QpxUp x=2�5 �^2U *$ �Il�/�-�defchi!�)�R%-B0s$. InequalitV o �-- �t��E.j͈2D case�%p̀M�2|��|-L��Is^4� \quadI�and }� B� ��xFK L2}x �!|.���4i=1}^Ni� -y_i1�� 1{� in �I |y_i7|�z��  i\neq j� ^N�s�LSub .�apss}��bem �\& 6l.�"� *�le. work^a sH way,I �pri�*s $expression� kine!Q�%$�gy,' cour�l3Z��we�)F-.| iQ�yM�A eq}) does)Mnot} hol.2 dw s. HoweM0a \lq relativ�\rq\ ver�it �(rue, namely �.7 }I ]7�&TE _i| �/MB�Ef / sqrt{ -\D� _i(4on antisymmetr*x E"$$N_2$ vari�s� i\inm� �)QC provF a similarA�(!h5�i� @})Al� au� .~2!�I%2ID(y_1,\dots,y�2}) | 2H(2R \,\Tr [ )$-# }\, ��)��. (.'�)%!�- HB� )��2: >e�a�2D,_� )-�}&�Pnot o�Y$ =24,eua3O? Schwarz���%� well1�a"v/ [J*A��Nb$��j� W A?V�i�nd anAece��ong8��lines�in:ssput}�lo a.B}b� optimal�ic� / free!ham�s� $� | � s:2D��s outtbe �*�2}� 1{| aM<|�0}��:�f21/2 \26�F Bd1/10}*� yiell&!^Theorem�bT2}. Ou>st task�o iv��e�B RA It.c)�at@ <,s actually m� easi ��3=��reasonE�!�ra,d ed� stru�in?was. very�i�a %ɥ $\sim$ perA ��for>us!�Z �q��iA�box'be quite��C$n\gg 1/"G$ ord�oi�4negligible finE,size effects!is6��tr� wave" ����� ��h� �� possqtoz� each�%���&_!k�� N�is "�one. If��takIg��ous�.� tri1}"� tri2&� s=o �� \varphi�_beI�e solu�[zero-M scat�ng �H'i):cut off�a�. T1$�As�� �!�_6� g} showA�ati �<\psi|\eg��ɣn ţ � �!W� 6�A�EU$\ell$%0��9�$n� rho^2\llE)Sna1 =n&��res�%6o��v!Iav�A$n�gg 6<$ (comp���lestiI}sIBm�$2�:J$^{-\alpha}��6- 5��se�_s5��,ly fulfilledeYcalcuS �� MUi*� II}� � defI�Z jus2K s $g��1-�f.j dembr� �zQi\�!�term IIF�E�. N� ! $\xiKgivA�I �xUA�.� }\no� &&� | [ |� _X F|�"�_{XY} �A  D_n(X�D_m(Y GG\,dX\,dYs!&*r n j� m ��� ) d b Z O = -a| D}_n�.m 0R���! y.3*� } H( wei��  !�fa.���gr��va� when� twoՑ ?P k�a8�sr toge�>t�.� s�V2��in͕for-�S s})�J Ee� Gpr� �"Young6� M~"�!I=ڹ�3B "lea(E�f�!$:��comes 'A�seB�"�} (M� �'A�U� (x)|2Ai=� {�}{� R/a)� f�4�}:� #(1ica��\ln6�J;e )EF�D�% e�!�dm !�be trea1"EwayJ� ,�H�DZ2&,�E z erro�besid&� AI)�%�)E�of� � in $$ �� omit_detail6�R�'"V�  \&�Pr��s d�and2d}�:Bthree-"]W ase, Q@0}. It suffic!o��M%CperatorF��})emse�/expect�value�=smooth&3 $1�ofapac��. G�����-, defin�u"���(by its Four� $ransform a%� ��p �"h �p� 'us�� to 9 �q�to [}�6F ��u)>� : a��Hj'�� ���3m�[ "/a1Dv e�a=��%i�]��� ��U%ޖ� "� i[s� q subje�4:/&��$�!Ito�ft &"' =1$. mnu;E> lex-ErdYon A�unit sp#Ss^2$ "2 � nu!�= fW�� ��symbolU�U~o� R^3$# ����nu(x/|x|ARcY�as abo�c/iaA��A �!.R}u�P\xi^*` cdot �3 $���SP~E� x)^*21�8 7_�#��-��Dgral makes sense e~ (�x $��$ h� harre; )t ��$ �,9� 6to�)r rpre�-a� $e (non-neg/e) measu���$ $ Eq.~:�)�( A4Cauchy-���" :-����.` *} |AAT&!�&�(!�_2��"t �)5�i�)�&z`=�.P 6Q X]Mp�M _*. *} u*2BO2�!f angu�!�gr�7M8E^U !per���)��_V�zremai�*8[ ~ N$a�I causxWR�q( >6 Y�:6��] 3- � as po�d� �bA5� of S�"�uph}. �&� &Q&Anq� comb���Z�Ņ  {E�}a Gor ��ch���'��� )���a` %��>X$"N�!a�!��$!�BC[$$ .|=af,��$|x|=R$�'!>i�,+#al.%�o9;=�BL��mT B�@+-xa$���6 =R} BG,, d\omega_R ��)�˩4surface�-ofe�bTofe�.� w� >�+$�m�1Z�=0$. Now%s� ��/�"�I�=я - "� 3/2} h *�!��*� conv1,� $h*��h�"3! 3\!yP�e�g:7IdY|��#u�  at�"e�{/0*tA =M'J����U-,5� &-&:&� F. () )^M �+BQ:�( RH>g�%.���/of��*}>�wo��s� �E � A%)sof&writt�(&�$h�(eal> ).+�} 6b�.p� h(y- \mu�$��$�M�& ���$&�B�$mw &�$. Explicit�/TA��Sa R^{-2}�"A� (|y|-R)dEՁ;n1:�y!$.2l�3�P= q'a��� d| �| = 2 a%6{�q 2�0^} $ (byR�)��� =f�1�ZqZbv&���$ �*xID '�Ae/ E� u�3N �below�3.G 15} 2;\�>�2a)�"� �q1B �6.^2� �#I��,�eqM���� 6�as2w:�5$- defw%� e� step��te is !G-Xide�)en��1u�.  nly �2# �  still �)sH� firsa5�e�J)� n� �uA the 2�psi#k.> 4Oly G7+4X�I��-�$ 15})�A)䭫�&5���Yq ��2� - �).����%�v� I13,��� ")2� 2� e�'�/2}"�A�~�B f� a^2}� ^ ��xd In �in[ �)�.A�n"a�3si,�, -t�a"!) spec8 �A�n �**�  $��$-")sito2t� b �( E=�� ?�*-RA��r�, genexpotent� �f�-s�y��n ^ �is � ( xQ'�#�� %� _)I0st $�)�d�%]=**2 ,; � ��>=&A_"�: �p+ a- monoton�coN�R�L���two��2d}A�/s exactH%�3�!��,&��Ep �V~��not��:!�2��3&R !�, but�� Ir�|"& �*� 8!�" � �Q �.1$ -/a*(0-��*"��#  I:+ ��� .����9"� 2�<#- /� ��!�d!K\.�0)� �9sŠ,MI s unb(��Y�� F�: ���ƽ41:�f.��1R��H1~F��`]� Win"�22E!�2!TMulti"@7lb8%L�) ��Mi�"�NBf.�x:  �nd�-l,r.x7d2�k� (acknowledgm�7}�authorM�; efula�(Jakob Yngva�#s�al help&discuX s�+ rks.X�* �#2 �� AaNSFrhnts PHY 0139984-A01 (EHL), $353181 (RS�LDMS-0111298 (JPS); �=���> QGLthebibliography}{99}Dibitem{huang} K.~H ,, C.N.~Yang,�($Quantum-Me�u%N@Many-Body Problemi;Hard-S�I&1&},%�. Rev. {\bf 105}, 767--775 (1957)s�4lee} T.D.\ Lee �\ �F�in� �%�S�!�al"b�$1119--1120� =6fe�$ } A.L.\ F, J�Walecka6?A`orA�P�<System�TMcGraw--Hill, New York~71� 5 Lenz} W.~ h4Die WellenfunkD$��a2�B%10! 20--26s:�,schick} M.~S r�9.�)��a1 Core�on!z ��m+A w3},{7--1073y>,hfm} D.~F.~H,<, N.~E.~Frankel,0J.~Mitchell, i,~�~e :1s~)n�68A�2--14|6hLY`9~�# Za Dilute%(.�:] J.E7Q�Q10!509--5!���}+0baker} G.A.~B -�Si�ArS+�lPerturb��Series � A� �J@e� Ferm�1)�}, ��Mod�%T4�47�3,AF�8ammer} H.-W.\ H, RE� Furnstahl �Ef�*k,f�,��j�d)Z� s�j Nucl�Me678aS77--294 !K02QRSf�0T} R. Seiring�*EK!�T2DPk-S5� �e]0prepa].�ru��} ��R �a�B�. Rigor�*Ret�W$ics, Vol.~�Na�]�i(} E.~H. �LM.~Loss �gEysigAmer.�. Soc. !�12�GSA�M.\ Graf��,P.\ Solovej,iJ it{A]=�)on *NF�8pBi�9-qQP��Coulomb `&sU� ath.����G9Ak99��42�L%32R H.-T�Qau-!�Stabi� � Ia  of R��4!"te�GCommun13�ke�11A�1�21�d886tliyau} !>Li, S>�O�Schr\"oz'er&-��>eigen�!� ; },f�8�3��318A�83�6;t:�  docu1 } }\class{vT} \usepackage{amsmath,! A�$epsfig,amsZ" ,eucal} %6L[12pt]=arttolerJ=10 %.f U)6{c: qx&tB 4ter{tocdepth}{@B newt�1!�1}1A [�ion] %.(lemma}{�&}[ >:$4cor}{Corollary^& prop'po!>on�� rk { .�q!z2%np%�=�style�0B�&G}{D~�=+.�$example}{E 9R\�,*i8u�$}{-s �Tcommand{\vek}[1]{\bold!�ol{#1}:&mat &A�bfJ"�$t}{��{ :D0M}{\phantom{->wegA�eng::ts Y%A:ddisplay rene�(h}{� rm{i|6"d)�q�0} \title{Wann(��(,quasi-period�8!�e-gap "`sa�aX{E.D. Belokolos\thanks{�itd �dgE_($g�1$)&�)�inv"g#1eir mNE��er�>�1 %N�1r�&d~�p6 of averag4�Orl�J ��'F�� both%iand:�}$  Bloc&�+ �ijmoA�a� �%8s of hyperellip�=�6 gma$y�."�!g�ach!xW$ pA8sJ �an0=>�� �q�.�valid �!CU4 eq 0�2[5sympto�exj4 �Na�MwQds&�6Xim�Dant�a�7of  ed1�s�U{��4{Introdu �6 "�-�L9ř�gch?Gze��!�� PI�)��te set�1orthoga� �K:%hFloquet-:�K8 � d ' (1882)E8F. 4(1928)C<>�>H G.#(1937)%mralgebradly T�8=a)�7�a��M�( � ��2ne " ��5 �describe�,ir!�m�)�unprece1=w(ness. While �9u w7 studA3a�`'�imerO3�Ne m�review�V� �) topic"8T"<B� c2(Jto �6.J�+begun ��ntly �bes04�;k ai�a��U�!o fur�ihd  s �Dby 3-�ng14"x �aplA�)zp� ��gr1~��B�%O$g$��.�eM��. T�.is regar/R mark)jusualJbA[�5�"��Qed��ter= Rr��"!���}� . ByU!���ich3 in ge`i6&}Y��t�' 4izi�!`^�to T crystalsa  � latt�2,!�is #;a"��WE;oT.ircum7W�5[an4a� "!'�-.�U�@ M(n4�%�JRa�mu9an �oz6d�oG( differs esE� ally%�!-� and 6s�$s. Althoug�e�� �mlen ]VA.s�P2��gr���- e.g.m�ffmi�efmm87�I? kr88�1�1@our%9Oe,�a��en�TediBw4>u����4 linkt*oFs��U ind�A �SA�#�N2��+��2�) i%>n�` �A(2,s,&  g�E beyoTgO rame�P@!p �,r,shb+�$rem�8@2�cE2s _ aris� ` Krylov-Bogoliubov-Mitrop yA=t"Mw�.�)��@!9 Seiberg-WV) =� m�D-matrix models etc]9hop�.��� dire�!wA )li qfu�. �% g)6� curv$:i,:&�Y}� r��s�a]�Q[4smhinherit F-&(moduli spac p!�6�N�.�3 e�!& 8IJof "� �$g=�O.� ergf 4,s coincide b�0�� 4isj A)one Dquenc9s����"gap��#t�variety�P=by! ultra-�$g=2$ ���R�����rjr 5�.*i?�� adm!����i;'�_7��<it6�s�s3$/ ew phenJ on �!ar� %}vso-ca? 5$p2 half� M1 �cer-U��"��GI�E�ech�ly�aki�(our develop� !qba���(e�of 6`&( a1er-f i�!¡�  "V&��rCZre s!(atural iDli-u �Weier�se+�.��tob�� igherm�. H.-5� - K..~XF.Klei� A1ex�!Jfixed �Lh� &� �H.B{ͱba97};p #a� areaE�i"�Pbel97a,b9,bl02}�WlsteJousAoYsee�9Heg-rm0?�/on02}, ma �ematon0� eep balgibB"0 �ric) lengt%aK�tuL�HpS�A��1ofͤ�+e�,�we�+%D^�pub��+ gis organ=aE< ���4 2U� be :�*{ q-ơځ,�� (!�� �� z;�>.basic � likeR� , WeylAn mU�* -� i\)lyq��Clex%e �'YPaso�9y lift!f6�Riemannu3�tosea�u�sm���gapQ�- u'GA�S�m3!Z�\*�X *7#��FyBTS(as:� $\wp $\zet*�*�� e�*r,Xb&ubn,V` ah]d�;�em�eV(Q)��sub�e��!)X$-d�orEu14!E%how!�eA�%�"CA v -�u �!���"�al50BI�� 5x���e.n��.�EiK �sTdd:�E b��l �16.�B n��f��i i �i�i i �>jFinU �Mm7A_  clue per�`�of� �'��Fe2\21\nd6CgN } \sDSion{Q6�����6)x�+�2a Banach�  $C_b( bb{R})$a#Scinu�m9e&?�H$led almost!i� �Za]4set $\{ T_x u(�7),\; x�gHl\}&�), )=6+x)$,�)�vel�m�A�-C:� . A F�$\G c�e seX �actBm�Rz! Abelian iOp.15J2b a.�- Haar9 $\mu$�#Ws�;�>�$--in� nte � � us, each )\-u�9�gbte� �aW�  $( �, \mu,!�0�9 2�b is ?is�� n by �+Am�^;gf(u)\�K=wAx&xb^,�,x}�-40^x f(T_xu)dx={ �} Imu (du).�]8.1.1"�7� By!`!L!�e&� ial� �"! $$L(u)=-\�al_{xx}+�3$ w��$uXTM&a^�AhE� cal {L}^2}/ A��i6� self--adj�0.!' $\lambdavmC}� $c(x, e+s$�^ solu!��^aj1� $L�.= E $&�ial datap0p=1a�$c^{\prime}.0s> sR-�B��xsh� \; 6��.&&�^�EG $1/2 �\`D5I)<��`)�z a�s $�}hei6[}AMow_{\pm}(-M)OC:, u��))=\mpB  i .�}{.�Ea�j weil55B�e��)!/�!�� 8Z� �Gwe6emplo�:8 $�9� � -�O�$.2iIll �V ��&��holomo�Pc-iU$bb{C}_+=\{ d2\;\+\;�LIm��aB(>0\}$, map 2G\y0arrowyb_+v2i�:y�Gw3s or pol& �~al axi(.could� s�PXf cl55}7me���9�!�� !�5�FaN8y�.:\pmU�#s  =\exp\l8\pm�k0^x6yYdy))), B�u2}D_�T�ch�4r œR�%^be�Vo-�cal{ :+iS�0�5�RA [0,\�k!�. -=(- , 0!m��9%_5#�e]z:G |=+$ satisfi�B�6F!�BJ +(�]-M�'@ _\pmm=0.6Z��� � E�2)�.8�Q��/�R�)8 ��A\6}:B�A�xw:�+^2u� x)+ �-�=02�4:1 F��jm82}�%�1�uB�f.;�C12\m[ w_+ +w_-�.]�8:�2�=\xi+#$\�� F��7n�VOo� �Hry�?�8xi��R},\;X\down�� 0$J�� 0,x)=-l�xi)� pi n 2�9>� �$lS)$��A Lyapunov  nent!$n6'&<wNs�>,9x,�$,�N$n�u"j $\S�!(uP � �g� $:E� a.e.6� A�\ rNs�]e� growP"oiJm >�Mypastur� $�=�FB5}(dn).$$>1 F % !B �.��b� �=*v��a � ed; of al���~ By�0_{a.c.}(u) =\�6U:{\{>c�!Q4=0\}},$ �e!N� ��8�=� Lebes6Um�J:?$,kotani82}8iXpS�3$a�[ ��)�6�&��X so��-63' (mw1)Q(in � zmnp!��bbeim94$gh03}�,�Tz*hg.�%� �2 � aBZ� has �� histH g�up!#Hate, Halt4e, Darboux. ReMj���7timul�Rm#solit� ory}�# achiev��[7s made��middl En8ntiethW@Novikov, Dubrovi��k�Matveev K�8&� -��refer(q� rein%�b` ��}( f�$�o���  a)-�6�}� E��8�2� 6� R#a%!9un'2( sm� seg!�Ey? (dou $� *� )�X $[E_1,E_2]\cup[E_3,E_4 's {2g_1} ]' ���� band_ ��o�xi2%�I �8s: $E_1< E_2 \l�b ��� �! ad e *uagd ��M�1�<�:�>u�# �end� fix=>)�t�ge�$g ��a8& `Ja"� B� ^2=R-�� ),9h $=4\prod_{k�Y{2!�- -E_k�:%z.WI e ruANco�+n�m? �$X�M $P=V,\m�؁!65b`0h�� as $(E_k,�  $kgIv�Ag�%�em�2� �M%2��#�*O� :�� �6^�x�i 1x1)= 1�i9� -Eii�hypcurv�.e�JuZ*=A��PulaF�w(x, P�L�D_2}� &�  S +}{  + $iu\mu}{%\1&W wey"�B�_ F�g& )=2�g5% _{k}(x))\)rF�AV� $1D_k(x)Av x .Ng��&}6 nct ?-�%qE��:�. ngly4<=�,of $xA�!�Q�Rr our "� ��% we nF$!��, ~� o!V ? = ,ve> �> $� xi),$ $�  !�5q\� 1)� f3  rm{Im}\;X xi^@2t int^� 2~I^1}{�.tT�;�Mh �{d}\xi.$$# a m�V�I^� A��� �\CLy�xi)}}{2E� � refa 0!h%�)�!�)��,��)~|j�D^[�Vb2W11\� B�aeAr[e �'�-�:� aacon�&a@"�ZkE�!�A �%>s�$� �S }L�+ 'H&b .�vu��e "{of�7uG�b���*O y�U(align} k(P)?� �rP� =�EmqDE{ �}%� P)} 2� ��?7 s_{P>rP ?M!�P) m} {��=�6�d,���� �w� V� $P_0��_0�N0)$%ٵ1( N%�R�B*!��M"�in8Y �6�)-� Sch�k-C�w offe"\UlU m� Al.h.s.�%lanAM ^!�$-, a \()�e��dm�!$k )[4marost75,gmn80�l �&�EZ �Z as a��)�bN"onń� mer &' ial,Q�&� ]��YK}��� leM@ Q@ v@m!1�M?o�9} 6j"�4Q�V�I;u�� $g-$2� :# is.Lm�!L` B � Q,P�Z �d e'psi/KB�v$�m B\ �(U=\�K��i�VIII  u} }"z\ 1m �!2 �x�{x %�rm{d}y� y�M�W}.� psira(tiB�6�We;$ J�.aOE 5��!7�'6 :�we �."hCa$6/_��qshCsayO.wor�bouaE.�.�� ��eFs ց�"� Xɽ��v %�� Y"�"Q��$JK in2MA�M�FN. .yA1�e S�]�:&�0� � s} A7�i!Fp� a � �$B� *}A5��fM� = A�_.-�I� 1}{LE�_{0}^{L�)Y�Q*� *@��'�'4b��uild a�Ihc $>�* 8Wsi<7\Wtn} A_n ai(i]�_n  �:A_n�� �a�z_n�' Lg!d�!�0d fr�X4!�W s $A@1 coeffic�0� �xQ� �j�PW�*�/�nt��� j"��ti�, $I1 "al�9a:l _1, 2,"�~.��+one. A^���0�^� �+ �+n 2F�� $F(xA�x_2M�t-hoA966 |%blel%���p0!s@�TAS�& �  �%�� a6U%V%onG.e. if�+�.va�al-�[Sepsilon�}a � G& sXtaY �s�Bv����# A� nd�+�g�kF_{/}>K , x_EA� \[\sup_{�< x_k, �1z "F} |=��M ) - bq $ r| <7c � .\] It �1�5Fb��HA�"3-?)�2�=9 �.Q JQ&d$)j).��\�� = F�x[BIIn�l) n��~ diaP=�/A~s�7F���2�ňf2 2m9�[ .�8�bas&q V�!�"�!-�;u�� @�ma歡ݠ� b. R!+���V^�JZ�isy�wMi�s $2\pi/ �1,�V�.$��>� :+=����t� � ��DN->�s�}�6s��)�Z>�9�")����pq8�qlX.����\aJ-`y�!F�Obv�3*a�meaH �99a�$ M�6�)onz! ther'5].,>�g6�A�e�@ uG�)�B�yDisdu!F� exI�ll l:* F�9J�6��F�h�8�,� � ity +ys �_��A illus�u�;�&#"�5 ��"� /<[\bf{Kronecker--f}] $&� ��� ,n�i R� r Q}t\�N?arbitr�I4zcN4 4 :�s. �c�y_1,&�,� be a*�CLU5�A��Ollelepip�4�at� R}^n$"Ib� ��-��� ���_kZ �2.B inflq=es���* ��.�"V �ic���7i^C��97 ��6-$Q�sF$M���8F�fApliter�;eB�#�16}),�-��&.�0N rG  ev "� s C_B�%B efB)*�!Cotr-~8ai"�A!?6�,N�%" first�orXte�q.=��$\s�(=L. ��]� �B onven�a �&z"E>LnCxgo�&�s�all�)5#3BH�#�*E4� M� =,"of�of}b(�xhe�"Hwursy-E�f 5si�us�^!sC*LQ. Keep�1in �,*�"b nextA�( a brief ac7Ryn" �ss a$e8�qJ�#5�l!�"f7HyJ L=���p�'�>z02? I-.�9�5>?�e�Lu�eZ:f�Asui��ua� fE&�>�*�(C!�!�2�s}�w X $ ��!z2� %�z$�^2= 4�jV$+7i=2g}� {i��w^{i} 8B�$.#{k}) =R&"x�B�> &>a�B she�u cove�H�"�#p  �$��KN.�$ $k�zate G}'{"Y�$t2ik$E_j\�E_k�d k�"nd at@y,.�%2}ft:p'�'A� ��is a r��R1 E_1 �'<� S1}$�i~Fig.�s figure-1}�%� }h w*�Z\�x@0.7mm \�;t']OG{0.4pt7pic3E$}(150.00,8) %�d %a-cycles \put(-11.,33.){t (1,0){12.F�: �] le*{�T: -10.,29V�Q0box(0,0)[cc]{!G$�S Cf'2'-5�(oval(20,30.�D-12.,17Vms frak{ a}_yR484vector � .7}}�I)>z>=95<=! 92f<13n;3522n(4(172<18.,265=!�1Z�6<9�16.,46�<%->35�= IA40�);4N6f� %�{ e aw�e� m %E@32lavI 175�.� ;49; �33.,35!%N5!�Db)6)U4i7,16.0)Za!N22Vq6�ED }38.,415�1�65�9D95C=')�6NB rD{2g-1}!�7r�%+6UA%H30,15%HI59.,20!F�6GgR 2.,40.2){�G%-�8A7:�9I.I)�9U�F84n�9K J�b�1L ,88q%M 20,1�� ���o]!k: 6O}8!��U�11� 3.002�33U�"){27E 14�;.S 15n��46~.&���> % b2���7�b.25.,7.{4,1){0.2�0bezier{484}(-5Z(0.,76.)<�) 816}00T(75 82!�(14!��? 00) �I�764!�rb}ݐ38W7e���J�3�� 00) 68.)?�5�W(I�74 937pIW�I�50.,5�~���54.,6%�;�%1r2�� 60.)>))4�U(82.,6!�13�>0* Iġ4 ~���45%�-j3F 226}(6!-!%) 5�A5l 324}�P5!� )(12E/>h95ѳ��)��46�2Q�5f 186}�0 �8�,4 � B%@5�66},(100.,48)(11��.��p� "/ cap�({A homology �"x  ~�:�M� &$3wF�  R�s�4�E�ܙ� (=� UhR cu�N 0rawn L} i�M {2i#�$i/(5g+�BE�  b$���"e*�"�l7\� (s-9  i� flipyhorizontpH).}�"�+� -hqnd } A�$2g��onic .NA�)v7D*�#�rQ(.�a h}=(h&4.g )^TWC .��ar2arNarais""�)&�&�-s,a��C�,.�j&&+| j-1}�au*>)�� j!�%g,,!x=J}\\drd+$j}$-j}(k+1-j)�{k+1+j"�)3&^k}{4�- �  � .�"�)=tm~ �&�5""4' � split} 2\Ё&�.( \4=_ t� a}_ka6�1d}h_if*)_{i,*dg} � T'=(aBFTbT�rT\ 2?�-��r�� eta'� FS�2�b��!)Qq�-{6��V2T $)�, ',�'2xB�O�y�Legendr�l�Q���--� M�3(-�aM�@cc}0&-1_g\\ 1_g&0� -�.E ^T= �)S)pi}�,%��\o(aQl �-)��01_g�!�3��Uti�g$ 5XE�� M1$2g -2g$cX$.+= �1@ �!)�& '\\!�&'=(�1�2D&9$\tau={ 8}J� '�E��to�Siegel�E� ��/ S}_g�Ftau| ^T=&I�6�5 >0 \�'nd"6iEVyG�); �ykappa= �(m�a����\etd!�靵����or&b" .�Wk],�E(rm{Jac}(X)=�b�G/ A�oplus� $.$1�1 $.�3;A}}:\{ P6N X\} I�a�G�h i $ H&e> $P"C# �to �?�|;rulR6*i2~4z{P�/P.Y5v}, _Lsj3A�%=�W � �>I�2a � d�R $D�degȝ$� $D=P_1+��+P<+ax-�- \[ .�6�D)=jP_1�E  +fEP_�?\]`w�}��Hd�(w� non-C�M �s (�`inq�~ :#��&visoro�)iK>�Za.m"$p �<p�Iat �P�MD$�cB� �3!� w6�N� aken!V/5�H,  )$ unless�0�!is w"d�Y.��&pYj0�h�d�)� B=a[th"(.�z};aLL:M�RA=�.Ym0EBbb{Z}^g�6exp�|\�4 6<^T�6 +2�c2/z/}Ln}m�\}�G�BMFunda!al"} vanisC �em_-a�at�+�a B6uz�$�+1/�)-�R� \not3M�t�&"v* a JE�ofu�gx Z�K@KE� }$ ( �=w �!tPRe��A� =V�).�*[:�=.�E �� (D)-.��#Mڷ�-7Y� m%ӥ_ .R6oP) 2p6D)2��e )\] IY&recisET�g$��""��!�.l% $&k$091��&,"�_gg��.����"nA�& .�h}m��0g�w-�^+:� _k.b u_k6=. �mTM�F��x�C_]A=:Hf  \ !2� h})&2*7\pi^g}"�t*�� )}}\M7 [4]{1\��i < jZ;q a$} (E_i-E_je nota� &� M*6�6B|�x "�%��:�^TF 6DE8 )�|kX^���- o� �:+)27 �8*6 &� aQa�!t", B$+ )6VB�$@ae!�!�`sub�VU�|llIc�VIt7[oeE��� ra� �(.y�a l"U sh�\�a���a�"�Y�RI+� .� n}+"|.m} K%�:�)" A  \{�et2]nseta:Y)^T:R +I�.�n} :> )��\��:)M�MH9 6 6],2�m� rU#teger [j�s. Var� XL5�BH�;ed��"�\ $\T^$,"WdQ9A�õ!(i�TTh�X6O�_h(al�.A�$n\ ��I�=ur-.�a$polynomial�Jaly`n2ma9�k�~J�� � imag���_1C � $X��[ �\2�v UA^ |�*2�v�!V�^PŚJwB� _\}�2At er�# >1$ ��)� ɪ!��`�a*�&5��, ,� t y��>�D y�k't% �'on04}3(��< �XR, \]0��_ R�`-indexmfo*�fYE�2�%Y�A�A�To)1J"��#(tabular}{|cR } \h(X $g$&1&2&3&4&5&6&7&8&9&X &.�&&24&6&2 8 8B;{� cenv$ � �. ��!)ic�h.M�nPf�=26Z�g)!*vic�1"�S6� [� 0)^T�SmF66� "�ss ��G`O l&vB6K�{�{U ae9��]�J}}"'Tn; �߉xi^2}+O(� \�QEI}B�^2=6I+ O�E +x�)I mM� �.� s $ igJFg$p �.�h�[9a!>bu!!�Ba@J}��}R,��J}| < | I}|.M�lA�U)�-�� D�!�de��z<�l&�6ɚݎsocF��2J��� * uld �c$hž �� {�h��"+e $>+e.)KC*R -EeC-� �, logarithmic]|f���'s�lE1zeta_i>�2�L�>u_i }\�`plog}\,IL>H�-i=�1<, g,\\ \wp_{i,jB�&=-6yI�M{ j a�2�M�Z� i,*� ��,k��36� u_j  � ���Oi,j.� g 4�{no�z1�ThQY|3E�)����=�ya8av. .�6�.B1$�+ar5.0er � 8 n�*�&I\#N.\u� H.� F�  =^J)+2� BIF -O.q3!�� pera/&\A�ET��>x�� �OzQ�hperwp.��42��9�9two)]ree, A+�p��. Co��E principal"k �36�nT {\it mast�>"� � FO;��*#7_g�BPkS]"6 9") Nr�W2��G�R�2�,31&/K>� P_g" . O.Bolza��o95} ��&���%B'� �2>�(sT;so�J�nQ3 ba98 e�n}e���!nd appl9HA4g^!�(FI����A�P}1�,.bh} ) ZM�^g-�Bg,gB@-�^{e)-� -eg,15�*)h}"�JIPF2fI�;a'@ �H �XS �29mh!AA�)� &��toE� )��Zer{B}�j"$Z Gco�Yv����Ȼp�7"X��: &-K&0g=-QF�j&\qKG v \\O�XM(-1)^{uVW1RW�"L�AjiB�'q!{?i*K "� $Pe�mua���� , i�mua� ���bF�hoW _k=-/.6S}.Q r�)�|_�Q�_k!b .g!"Xa JIP2��&" Am�}�k k"o� �w�e�5,a�K4"� �$���@ "6 U\�-�\\@s_{�%1}�� )i�2�#"� +)12�N�7b)}a8D _g�tn=�c0g%�2}h}[�"���J�)��#_g:O)5�-�B�_dO[��i��8� dH��4[ a97,�  �(��t7b 2� f~�ngALeF�[ � a�f*obi-.& -*�_@ Bergman kernel} 8odern ��ino>(2AR}�-e�e��A�ety�D ��Z&`['�E{ ��ED{g(g+1)�"!TLe�=�Kx gg(d!� _{ik{eu!2 :wEAeqn{ � O k}=4 i k}- 2 (#-1, k}+  i}) }�\ &+ 4Bk', )B[, k,6 + �kS -1}-�k@2@i6��u\alpha_{8 �}i9a�!*-1}}2 ( z?{i5kg2%A Tig}) +c  k },�X"�%ք���u�- 1��� c_{ � }= �i-2p } ik} !7�1)�!$ F@%# +1} -"![� , k+�7�ci6(���'��}Y<�v8+#=q'J�M�gi}=(6 }+�g}) i}+ ,�-2  -1,i�r-g,i"M3 2�8����}� KdV hierəy> .o=�za����%�ro� �Y �|"Fzs�|&<a07�j�e��oFr_1�s  x�or�=e-Gord��d yb��ṅ"��$,rehens!�:<to:7 ��<�z 1 d�ƀ!�>''�%H���>�l��m>o=)��-lV��s�W>Ww��;+} X 2� 8?QB�EQ�a�d mma}S�'*� "R(�e, )}^{(^l�d:��OT4�6/ %w��!�2�h�*"!p)�l�%og�*0"�%�u �Wm��6B� �\{R2� v}) R&2!v}) -*�*�>�v})^2 &>� ^2} �'v� %1�divaddJan�vP"7'>b 0�� )%�!f";ex_I}G� �Aheg ofɸ _�oj�D em} T��W�st� led�?Iɏs 1�� �) Z�z#e�A�m . rel2�B� ne�|��/}sh "�X� else*�� %WonQGtshWrt�A`A�iD���.M�4$&� �[�Cm. ^1[! �� )( lead"�>�;}b h��r.J��B]�B chec�Ce^a]N "&�`2�v}$ nea�,��> =j in'{ �nquI� �or� quotk���\Omega"�#u��bba�2�x%_[@I$�2|=g��`&w�lar ev��"��&�". A�!�6��!2�Zn n}'$�"2on}2n}'�O(�, �*��ul�-v6- �)^2� .� Q}_0�v)2.�oI}2�Bi� 2�M ͒�2! �1�L�K/�'�Ar�� ��2�=J� h)^2"�# \2� !�}^T�b_&�E�rFQ4�. with:Iر}=�kAD,�5i�V6i�un6��K���C�O�(�"J^)Ya� "CFB al�6i6�% Q&�Js}&82 h}$�#�RE�59�.$ (i� x2� e}_g2-�,.D,.�,1)^T:�LYKJ�( ]eZ, g)#6b�nnon�W}#in�N�.�1]}�l��by�$ 2�BJ� ��m_>�2+!?�=i, u6;�'HM9�"2)F� s identif<�a$S6r)&� i�-�K]�2N� �6" ;.�h8G.f"Lbv�4�.cIts-Ma�o��!fol\-�� 3 b�Dl\-geb\-ro\--geo\-/c")A��oo\-�e*_��#hit:eM+� I^>|pin 1975;im75}. D""variat* � J�k _"x� U"Er  du81���SrF� �$h,�}] its�4@qX��deQ tVne�Kenu��,.i�n9Kf� non <[ ��B���G. oD,��� �;&�O�q@/P�onE#��K�V!�y(xcBIr:�JF� (r�g}` x..�N4�du) B�� B �&$d&=C�..� ��A-��F�2� )�ZZ� Rz��B,} &R�o>: R;��-&C'rmQ�2�&:(3,0�Pr�d�B�B�i.�N�d�"�:�qa�- *(l}q�+� �*֞-enZ�ii��H�g�'M�W�k)).&���}i|΅n�W�'�k�� UW $�k$ C)�65�;1��l& :�ZN� 6:�u^x-"ZtVz:�:vA� r_g"weilzet��-�!B�X��YmoV5~{1� 3!d&=�1f m �e��� BF�@\G-~� -t�o8�O�N r_g�6'f-�Q� R*��duvva2Ͳ!~ !nd !cion�ydI c�6F \ B� a�B�M�� sea|V�lPB1��"�<��> a}$� e�mhaU"m 3� K}_i�|i=l P_i ,rQi 6,� �Cr  g�f� &��N2Q�6Z} &, �<%j�!�60�Baccep-a ��v!7ph��.)�hLb�c��7��nuXfro��!��M*�l.Wd�atQ+�y"��:W�. A� �/weQB&�6�$"��.��9������,�5{� ljS(x�%)mD }F �1Bu ��� *K�%^>�>� � }. ExHW-Zt)q alredym2�g� & Chapter 8�=�ha[� :�<W alida� �ka��ic�U' F��"�!FzdfF��5�E�A/�9e�i�[Q{��5U-p��,PVjaCw,P��O�RSY*�p�{��_R<V�l"S {8eecalB1*6TU}=(U&� U�FQ2< U} ==8')�A*�' ��Y�Iw� ng � %.� .A�N A7�e��6F *i*�fife؅if �&D-`�&�FcY1����0�t� :s'Y���-^AX �.�n�t1}{2Ul o"��a�"*Iper!�Fe*�p } OnGA ���%3%��a�o�rH)�f"$_ �N�#-�)�� ��a�t9�r���;ceB�MBAXeo��m˅. B�tseYU(NweN�B.Lf &�.�I [ N&wUyOAHS Q �9.�jq�.� $"?V  "� � �6 }] � F�2}��k`�� Ɍ>_�aa6��KitemizAJ :LCɩ6�P�!F Ba@l &0.g;�T,p 2 g)$ �;�)�1T-G&5?JC/ !k=i�"�2�K ccc}�I(_{11}&k/N&0F9&0�4�3 \ast:�< 0:6�;\vdots&\f \\ �0&\ast:�:�\end{array} \right), \label{wreduction1}) equa} with $�c$k\in\{1,\l�0,N-1\}, \quad�@ N>1,�)i�mathbb{N}$. \item in the homology basis $\+cal{B}$"�winding vector $\boldsymbol{U}$ is of*(form \begin9 60=(!�,0�0)^T.BY2} 6Z �ize 4theorem} Condi!�s (\ref{.�),BP2}) represent $2g-2$ 1�s and�refore �O associated double periodic potentials can be included as particular cases intoTset ofH H . These mA"6pmit explicit analytic descrip! �(we shall us�4is circumstanc�p what follows. We remark that�U�ory�,Abelian funcls to ellzc`goes back to K.Weierstras)f,A.Poincar\'e� is�osed M��classical A.Krazer monograpgh\cite{kr03};� modern Di�V ap!'e�� integra!�Lsystem are given, in=t,� fbe02a}, b t!�A� Ez�belokolos-enolskii2} was recently considere� O(gp99}, wher!D alternative proofae�. \subse%v{Calcul�!�0averages} TheB�T\langle S(x,\lambda)\r= 8^g+\sum_{j=1}^g{j-1}s_j� spolynomm�qB}!�sensi!bhto commensurability or non-Ff%�Tfrequencies (component�g6� >� ). I6�yspecif!�effici.W � ial �F�)a�($s^{(p)}_j$�e ��superse}, $(p)$ taken�a�i�-cas!�$d $(e)$ --erg,� also!�vide $-� J�$}b {s,/N�_p$e%NT_e�%b�DZd [{\bf AEb�in��}] Le�0± be ��:le� �wQ��R� e$ a*-P�e6 byBA�aV�  s_j^{A, ��m�}Au e� \[ 30= \frac{1}{\�sHrm{det} 2\omega' } .\left( -��{ccc} 0_{1,1}'&O&g}'\\ M m[ l_a�N>j-1@eta_{g2%  aJ+VJ+J� Z�6c Uge �&� 1  j="I g. \] I6� for $g=1$Qalign*z Q+)��'}{ �'}\& I5 e2�e& f ^2 +�l p]I>} �_{1%�-012)�%�2 �� 5HN } 2��s � u fw}+ �� �:�\u �t����.M�I1 �`A�� �!of�Em23we obtai�,other resultEu the �{.Q�ZN�"� o}] �����R�v�p$���aMֹp=z:�z��zp)}"� avper1^���é� p)}=I�j� F���^�g-Ro��e5jF�j!I��&��6U��perF� �nR�p�Vm �m=A"�op�o�o�o�o�ofX �uEX�v ����a�a:arvWe sea�I���"� curv$ e�f E����Q c�ide, bu X0genera bigger[ n onz� � n� _e$&�$ by differ�ex� sionP�� preh� "Vp seaK$mulae will��~ else� . \uWannier"��, definv�>) $W_n(x)$= ��$n$-th� 0tral band, $n*� ,`ZQ8�� �l�@normalized Bloch �,��� ��� sqrt��,K}_n}}\oint_ frak{a \psi.;� } ?(� )� 2�z Handef���%q &��)� �$-Iw 5�i)4quasi-momentum%mom})m%a-� Us![trans\peratorE� then�0truct a countN� >�sV�^{(l)}(x�_l�� 2�l*Z}� )��F�ithQOŌ}) spli/ps �P)&>_`r;Q!z }} sigma| I�infty}^PEb)}.Uh} -\iA� x.e}_g+.\OZ }+2lJ'�� �M�A�I}!�:�&�:� M K( � B� -J�-V� )}�xtimes&"c exp� \{elint\limits_{(E_{2g+1},0)}^{P*V}r_g-(Vm+ J� )^T j]Z�r}Y \{ ~ Q,Opsi%p.qI[� *r-�'��_i�\pi&���=�avM/ NA.�c� ��>��9�}) � s|3&�� deriv�..,Aw W_1(��N T}{2�1�^{1/2} �k(_{-\pi/T}^{ P)E4� k, �  T=-2) -t.  principal ec�pr��tjO ���B$s, $W_k(x)!�k&�  g�� orthogona�B��8���{ L \overline{W}_k^{(k' W_l! �h x =\del�kl} 'l'��k,l.��  k',l'2�TY(V���nes� spac igenT t  Schr\"o"er !M) (  e-gap� �.5r� post� !�discu� ��th� ques��a fut��public. Si�B E "� (��. for �!Ca*@Tdistinguish two kind oJ�  -�y>Us*T %.�*��ͅ�9?BM *�M:1S. Both�%�L 9�  ed by�sam��%  involv$ Bolza &9�R&} !y�6�con� t. N� N,s, however, �A�ua�in =�ways a�5:!/2�� &0 Power ser.�>M@ at $|x|\simeq 0$"� S�MB7M first lj�g[ ���$ admitsE�&� expan� B; 8=� p=0}�=�0(-1)^p}{(2p)!� 1^ } x^{2pFHerFW7 j0k=1}M_k q_{pk���D�+!�quanti�=$Mz:as6� $-cycleEssecond e<I�ls,*k M_k= tB�kV�1��k 5py � >�8}{ \prod_{i\in *�"L  \r mS"I} "� -E_i)}}\; rm{d� � �E iffn��= " B��.dq_��V� y���$zlQU�lA8p!�,l}z^l$,.� recurrenc�6m6{p-!L� >� 2p\\ 2m-p�JK �� \phi_{m-B (z)Q_m \]��Ae 7(0=\wp_{gg}(J� )+z,\q�� Wp .>�0\underbrace{g�  g : $small{2p+2�} Rn� 6i�few6U ayE� *q{,0)}&=M_0,\\ mV 1+2r�244 42+4z4 1 +(v$2 y^\6|6 |3+6z|2 +(1v� 2 +1�j~1!.&+(MV +28 �^P ^@?V 3! m�1م����@��its tur"� .n�&�_�X� bb�D E_i! >^� &=(6i�BCD E_i+\alpha_{2k}) Z)l+4 ,�'a �E_U ����weK%d kdvDHre67%�#�is%$ �"ire�$��B �Pex nt�,in $x$ which� a�era &� ��Schur*�s u mac79} �| T#t�jI �ese2>(detail� R )�!H nd c�& �ed�Osively� term��| ���� B'�&by elowZ�d �elw&&� &� !xs�l���� @dard hypergeometr2�&)Jb�A"{%�%�a!Shrs+ !�Ia! iprocal g� �$X^{\#}$-�j genuA#d dualC%�]al �BGD$, naturally arise� ɲ� �o}�'q call� �s�_k�B*� g$*� � 4 $XA;J�s *p$ -�^ 8*~ �er:�re1@:k {\mu%<$}^2 &= 4 wv�) *� v�_k:�\\ &=4i\�u�o�{ {2g}0��0&),�U �h�=��x���j E{�E*$�ndice�\"� _k.(t� � \,N�am�ud� A�� pulsA;0)A.K� "� � e�(meromorphic6 � A�corresp�+ng F�j��son*2@ on $X� eSit � conven�'A�introduc�5E� ��2V�)��"L+e9.:/M�"� %� !��W}�(n)}=qE-n.� 1 ��� Z� � �*uatB� nj� Ca1�hol5�2 I� k*�h� #} =(�h!\#}!..ge< )^T$ �Z��� U~B� ihe\#�!\`-al} s_k.%�)�^{� y)4^{k-1}�'��1l ", �/ �M �& !�!p=9re�'xU? fact�-6faHA��2��� a�t�[,) moduli;.�6�)/mb�Ble fe�m��algebrai��s�eara�8in Seiberg-Witt�)H.�]seiwit94"\-b},� + ,gkmmm95P) various�@�:h$�rQed. I�]�Nb^�rJ�rb�r.�V0!=~})B�� EUru*E�� k=j}�g+1-j}(k)�j{k+1+ac6� k}{4�?}M�F2U)��b���2G���e$uUk)}T03g-1�SV K.'ar:U $2g$6iz�\2�F� $. P�1EWaU��n)}�- hig�'$�Ei.�} aj2giou�2�s due���e Rham S m h78}A܅.last p� B we w�o� cus l0G$asymptotic� a��o x\to +�$.�evaluat��1Fn�5  a e�an�]steepest���/ metho"�1A0+�H-l <~ on)(s a multipl�"vanish�? sadd�3!� &}� (2y35 $,��w)' }At % �?F&͟ ene&$[E_1,E_2]$��>!%&"�  ha� �3� }!�UGo"{�,`�eg rm{R35�\{.da� Q}_0� _0)��at}"}}h6 ;.A� }"| _0  }�&�!_0) �[����2 S'2/!]4"(!Gam"(!�34-}{x^{ } <\Q%�asp i 59"g ��_0�a solua�1�1J���) �=0"#0b4 zero>�A�( >�2%s��7 he Ls4 quot��U�� �ula:Dm�&6�&C%I}*b,�A�Z�� show;L universal character1Bdecrea� a�Oin*Z6�>s:��*�! c_0x)�\�-3/4} � ph�$p&`2 "�&Conclu~};4� paper�7ha!edB�Fype�7�zonF :��ea� u� s. A numb)'��r�ng*�bi� beyoxur� N6�s. One2��whe-.>Sc d a�!)�I! &�%���M� � . More�, a͌!z� %�> 4trivia��es,V wellw&mp�8on between our  99")I�&�am�Rbehavior�>, th !�eruc&x7T e-�84wA�����, wouldbq#si�8 plan t�5�:E�mater! ��/l�:problemK !�coming �ed:#Q�,*{Acknowledg|s� ��,sec:Ack} EDBqVZE"> than: e De< :a�Physic/ Ui��7 f Salerno% a% montanc�(support, du1 �]Y! p �J9!hnd  ,Professors M�4iti, F. Pempin'�B. Pr%%i�gi�theI  o�un�Wi-!ty g<�ce ``Non� �, $� �Ex%\III", Gallipoli, Italy, a�r�9 elim�y�1%D���0re announced.� S. a5�e)r@�[6T fro�4 MIUR, through��er-���Dproject PRIN-2003,�C0Istituto Nazi�!Le di Fisica Nucleare� -�. "�thebibli�;hy}{10}ib�=<{acgh85} E.~Arba�ho, M.~Cornalba, P.~Griffith �hJ.~Harris. \newblock {\em G��Y{A}"�{C}urv�R{V}ol. 1�<<S�Hger, New York, 1985�4�@ba97} H.~F. BakerB}�'�� A� A e�&A-' t�!J=2� CambridgeeU. Press,, 1897,�>�5d 199>�8b�O 6� sigm�F�xmer. Journ. Math.}, 20:301--384�86,0f,M� e�:%;j 2{� 907Aj=�5dA1Gibbo6bH�0pI?re�A-� Benney mN-" 2�EtJ.� T.A}, 36(31):8393--8413!(036�4��U� 6���@�� v�<7(20):5341--5354�42�beim94e� D. B�>`, A.~I. Bobenko, V.~Z. En? R. I�"a0V.~B. MatveevF^e�o {G}i�ica�pproach��{N}�|{I}0(ble {E}qu 2Gy�Bem&a�96��?�w.���.�R.${A}A{F}q�A�z�>�S}�@s,�u.eIUan�/ar emat�Sci� Ts}, 106(6):3395 --3486%�12� e02b�����I��,8(3):295--37I�26�saOE.2�F�A�M.~գ��> ��one�'"� F�. . A:%�. Gen�$(37:9685-970 �4.<arXiv:",-mat/04014402�o95} O.~x&.=��< ��$logarithmiDri�of6> �9��$--R�E�R� 17:1��6��6}$el97a} V.~� uchstab�Y>$�(D.~V. Leyki�B��6�{K}lein6~D?� )2�Inn2�0XS.~P. Novikov, editors, �SolitonscG��y8{T}opo4G: {O}�C,{C}rossroad}a�� ! 4. Advancn Mq�, AMS T&k3 s, S�' 2, V�079, Moscow St� &`  �!�MarylJ5( College Pa�9� �!�b��N�,6]$ {J}acobia. ndn�2��IE<Krich)6�Review� -]��z2,�ic�+(volume 10:2=�(125, London!�1!/ Gordot=d Breach6b el99FB V. �3� �^�RŴanalogu8� 2�.�e� Funk= al.A Pril�k 3(2):1-15��.9]m in:Dc >HAppl. 33(1999), no.A�83-�,]:l02J�n�P*F� Li�C/��6(4):18����2��6(2002 �A67-282^cl5y Cod�-t-�$N.~Levinso2�%�T�Jex{O}rd� {D}�9�^�,McGraw--Hill6l 55.�Ddu81} B.~A. Dubrov6!Th2B %�no�f Russ�  S ya36��80A;82@(eg-rm00} J.�^ Edelstein� 8G{\'o}mez-ReinoI�XM.~Mari$\tilde{\rm n}$o.�Blowup���!@`dson-{W}26Af� gr� hierarchi�"�6%� Adv.%�.� � }, 4C503--54� �&�q0hep-th/0006112� eepP 0J.~C. EilbeckV[$E.~Previat2�O�ghd- r9 0ius-{S}tickel-er ad#*1.6� Lett1���.�(63(1):5--17e)6�Dfmm87} N.~Ercolani)� . Fos,��(W. McLaughl!�!s,R.~Montgomer�55-Hamilto�:�0�&�m_��U���$a sine-{G}�`$ wavetra6�� Duke��u4}, 55:949--983E�7./ffm80�,laschka, G.~��D.~�.W�-=�=�3�in�e&�<s6� ,K}orteweg-de_l/q�.k�Comm. P!3�E�<3� 739--79T96�3L( L.~Gavrilo�-A�- Pere�!2^ Oq(/N2�"� {C}�}eroMB�J.laG 0:63� 6352!�99.�gha,$F.~Gesztes? H.~HoldeF {S}v .1%|{T}heir"J oA:!u:�(s. $(1+1)$-��me�al�ontinu1 {M}o��2� C2lerFq U.K.FXg�  A.~Gor�M,�*�!�arshao  iron{ A_ oros6�I�7M(:� exac9�B���&}, B355�E466--4< >-E &athtfaScip"of5�"&5 2eWiley6�72,gmna�0J.~Guckenheim1 J��s %,.~E. Newhous�F��eVDynam![T{C}.{I}.{M}.{E}. {L}ec��s� ss�$e� �(June 1978},1 ~8�Y Prog� a�u ,}, chapter V�"A�A}wN�.� {H}�=2(ges 233--282� Birkh\"au% 4Basel, StuttgaC>' im75E�R�%=��>��'s"��aWite�lacunat;usi� �[s!,�4�Teo$at. FizA� 23:51--67�b72 ,jm82} R.~Joh� �Q*. J2rotɉh�� almo*!e{"�F� ��u�eY}, 84:4G438�82.kotani� S.~K .� Lyapunov �) de"ine ab�Y@-c��EFra..s ��=random�-d.�$S}chr{\"o}� Y�A�Aq0E�`Taniguchi Symp. SA Katata�25--24%}� "AxS���S.�WLehrbuch3��tafunkOen2Teubna�Leipzig!M��*�by 5 Chelsea P9�!56ykr88} :B.�Av2S��x"A�8.J``&p ''��F#Funk. � ��%@l 37--�#82��/�Ga�cd� .�%JSymB�.��All.�42VOxford�.  , !+72�marost�-Vh MS �iI�Ostrov��.�A���izib�M�um{H}il.^.C�e�HSbornik}, 97(139):4=5�1:�ma�Sb tsual.T66 loop��� #:E $g$:� stig���a �ntiPFeP%icF� J�om.%%�m}, 794:1" 2maton .�=Y.{\^O}�$.��H �)qu8.��� {$\bf{P}$�! {K}d{V} f�W: �]tud�67$)a� ext1 %�E}uler'nX�|9H of 4 as!��.�%�RevA�th�'!15� 559a8F? on!�Y.~VD�an�Xre3 � somez}"�!)�tw2� �GlasgowAuX �4353--36#06�onXҤ6s�, (E�(an Appendix��Shigeki�I�: Conn�W!����#of Can�[�dof Brioschi-Kiepert type )�K%8Proc. Edinburghlh.Soc! 20�' to appear.�pastur� L�+~P.S^@�I*_@of�!or�XxY%�%Vbod��xi�JoR�$75:179--19�:) s"`,�? esE.~�,.� Elec4-magne �3ity, xZpol�3ndens�.�confin�)"$n=2$� ers�� Yang-Mill2F%nND�I B426�e7�����940706�b��Mon�s�!a�%!chi!� �y break�-�6�� �X�qcF�F�31�484--55hN��&tweyl16�Wey2}U� die {G"`chverteilung von {Z}ahlen�L.ciJ�� ��na 77:31�5%}16.� zmnpa,V.~E. Zakhar� S�+Man� 2�I-LyPitaeBME}aoryɟrwcatte$#�2|Nau�+A-1K0>u!�!%� "�!{vze}>D/home/vze/tex/bibs >'$style{plai"�4ocu�"} ��\ B[12pt]{�"cle�D\textwidth 150 mm heva 23 Lopmargin -15 mm \odd�&  def\be=v[Kee{%>ov{"�D�� newt�em!:�!}{Fe7*l�)}[ -]{�)}e� ${corollary'C2+*�5SD*UO.{�Zo�^.Pro!�a:�O5�(title{UltraX pseudo.�.*\\ �]�let�w���&ofoKb�bmeasur!N` \author{S.V.Kozyrev\foot�I{Stek�axEal Inj$e�,�ia} �\make�� abst� } A famil� 'o{C�be� u��.�(�(h?U)�& ; �6*%�rbitr� �*IDon�e�D(up.�t�log\J�n s) .�^)i�#�) . Pn�(PDO)v!�FL4�� K&W�&�KIth,;"&0 diag� -! i�zQA1 comp�K�:c2�72*20e�7D�t�)F�� d dir�HtreOs &G�In>!lc[*new"EA�YEru%f= %gsw �le!�$Bm�ol�9YrU){[4H}j4�} �SpapV,c�\(develop)�*sSe r�oN',&�0 �*IZV2W��1r<  aJ@ �;2� ${\�<T}(X)�<ba�X$��!bide�0;)�"� 4 on $X\bigcup J J���=&>�-!{ _AAia��1e�� into *6+�o)qsp�I) a ($"� Rv� possJ ngN,�Ror �-basis) m� $\nu%�?l!Jm �vqXJL yU� �EEopT} TfLint T^{(-0 sup}(x,y))}(P-f(y)) d\nu(y) \ee ac@2�$$L^2(X,\nu)�b�I�x e�d&� .<0��A� kernel $�I�4is�$1xa�:1!�$I=� �^1]���8.�<��;:�e@.�>�i� .',x,��iz1n� $Tu��:�<6� AlsoV0���a z� 2�sA%2fr��D�8!p� T|b���P@9T�ide�.�6�9�r��on2 lZ�F�,�*�"� R��WB!� ���f�/ &�DVBB�F�1�wMzE��l��RsKX�F2 &�B�ac, us �IEnec�&ryiAP��DeV}{\sl A6A ��� e*Ax.� $|xy|$ (wG <� �Ah�t 3��RaL$y$), ^E�Q�A��# vari Aatisfy�R2yk�<Vnon de��cy $$ �\ge 0HW =0�H\Long�{arrow  x=y;:�3kyJ=|yx|n�#ng tria�einvi4\l/e��m��e2�)��6. � 988: \medskip 1)Z sTP���z,di1e�aA�is no� @ �d!�;aNZ2)�anA�c�Cs�Tc�m j$\{D^{J\}bP sup�+1.J���!~ Bte�{o �;.�3) An�\ll�"�(un�of!�im*S��X(erty 2 impl^9Q"�Y: Fo]yE� �$I$, $J�D%5()Q��)E� any ~I F$I�Q %)}  J\H�$k$�?�Cqu�2f�ebe �.!�b3A&�}�lJ } �2�!Z�,:~]t 1, 2, 3xD,!�X{m^.�v�.� xX!�tAy;i��,. !�bigI� \noi�!t{\it#of}P[�Jp&M�:��A�!��| )! act)Aq�5�$\{x_k\'n 9$DQ .ao n, i� WaUt minA�,� /aioF� $D'"�"�&���. RepeFXt1 �Vedu�A&ct*�.F�s�\!�q�eu��ix{ �/7}, ;��!�� Ka l�ip%� D$. &�bU T$ a��5a]m0L� %�1��c2@vnex�qGD =exaa �Fo� �XBdqSME� A^|G.nR�%E���amc%{�\Ju$2�for)�!� $D_I�L��a��� : M*�a�!I $D_{I_j}U�AcJ� b,�:qe6�a�FF�"I�h :�!��s.�>‘� nItv easy� rA�� i����5�M2i �/px;by r�cAUnF��)�� B��$X�)>s�dway�!��Lebes� �)CKF}e^}>EC $\mu%�O B}Z�0%ve�X��� i�*-[! =�e ��ue%X� !��= �[.�p�YA qed�VecJ� &t/ /ea8� S med ,� !an&� pair $�  elem�P��se $xy$ ei�ina�a�8!�$x>y$R$x< �= P;K:� Anj�Abe gre-JE�a�an�_(elf; 2) If aV $y>z#n z$ (itiA�)��=J If� � �)�=>.b��,� A�is%w��al+ $���#A � A:remum rI \, S%p%d�f t $S�^5�.ia�[�r�1ic�_=[���)� >�.1,at�vt���unique ���16�2f9H": (and!n2 0*�ion�b u�% aI�of!��U{I�(�A�of })�\)��{i\A link0**�(d&�?ta��.5H $i���"�&� $I_0asI_1$ (Ml��&nO� C M�_ZA�-� ��a=#OKio�� %�n:Yal"�i� %`, s43�%"�it�K�5 n��r� Pt>qe n6)bor8�3.5 nk)5 � r|P��ength $NeKv� !� $1,\�W2 �[.��>��er� o*V�� Qg�v�o�E!�w�'ll�%�0i=,� �-�) w����� , s �Lo!�n�*. B$�"�)� &Dav�M or�^ �se�1,Հ� %����,��^A�� Y�-�5"%��!=��'!Pex� ��!Gima �$N� !Hb��!y2 XAQ�a��e��0�f`a"9)�Dx�/ $-�e�i$�b1�q�{I�Ѕ��J$�{k��N/ f�M'i9m� ends"�{.��M�� � r�out �s.�1I_.K @"_$ ( �.�)VUB��� }|n�`�M1c� V�ss E�n�>�i"]P��@ non � Zex�0drd $p_I+1$�HsY�saa0at branc�Ydex.�Q�lN$~ zM�^zbx x �xE"t�QJCa2 �*� �sIu[� !�!@A� $I_j$:2� 2� '*�|6���h P&s!6Nka�y�C�6:��2f�V(1��3)!|a}�*eɍ:�!�.�*t��5�i�a�� �?!8��"�w625}p%���y (2)�%":|� 1�����we�)�ycl:�2~. Tak)mR��T�PD �2�I�$A;$K- �l�C&e ;�.,K$? =�� zs ��th�D {�% ��%e,&@ fti� FJeO �Qr�:�$J^K$� $K��T��c%�%2 doe�Ż%A�%�6� is I� �R�2d&��:�+"F 1��Q� Au���q�  (if��sI�>~>d <��"�at least��p�cs).�)�J��� J.��a�A-:� $�2I�6��!�m^I5 �>��4>I�� to2�:� 0�.�. <�uc4vAAm=�A� .3^i\�K��y 1*X qF=!$K={\ra2I,J)$;! " � e^IKa�JKe)!}$ex $$ L=IJx cap IK JKT�$L!�e� ioleaL颡��$L=m i��a�"-� $I� &S`B6 "� 0� � �r���-q� �R"1�21) ���9&} }\l�Q4�VC) y1llTE�kJ��!�#^�� ��� A�-"�a( �0 N�.b.�*� �+% �2���b$�2i , P�26�B�!�� . !@"� A��/B� B:�� .Ŋis�^ m��0���e��b -negXmM5��qua(on�B!�Fe� )w#>7��m^tJ$ �6�2�ZT!�^ �7�S�%�%�N����R%y�!!�u� 1q�.O#S� X��:�8� we �if� ^� 3a)S%)U�2$ �%�7WW:<�E�:*%�^^95�Edq>� hn�� V�^ G!kl��)����9���X2��)�< Jt* }�b#2}M�. A�pe)6W� Vs lready �4%$|.�̥�)�-�&!u'reg1roducedP�N��LobOrd`f$� W!C*� � �n.�w9�� �.-KY�nd.�ŬE,6(��-�:'$x\in �nd $I .k* �I$2ton�oH1�qf�}�8m&d!�,� I|=0Y'�K.e��<:)*2���3�'l��� Jf . *�,{D�?N��9in��E�"�%(i w�\so de�D|�?"[CI��WZ�:�m ��]BZhputz�$ !22.i%�AI���.�Eon�� �s)|O$2J�..�BBɘ�&= �sY4K+"�1"A;t.Pv0"B � (w�Swoa.(�s�$�R, ))��EZm�.\�*s^� ��i�6r�,ricey� $F(I�@aB�""�,&�.�[�7�U��*F�6ula*�A$eum}|AB|=F�Aif A,B)�-uad Aa�B��|AA|=�..A,B\inq-�A)58}O T}�.��$ /� ,!gI�� ��� $A=B4("�K� t �F�pu�E�A��B$,�\� �%�trZ"/):��!!g��%/AC|,|BC|!(>,C��1BAAQh2�s-&o80 )']"���Q/e]�2,��z6, )k suffm��!:r 9N% JG0a#��t�(s,*�1for:Jo)obvioueCox"�$A�!� $C$.F22lA�"J*2B,CFQ�C)��S��a�hS�re lar�V90 ��&=$��� (� wise�9Cq�s�A�&�I�����A�A�tL#t AIAxq�K�AK �I)Nalo� F�J$ 6�;�q*-�g�, ,�� )�&�9 � wo'3&�}�Fibl*�I=JXo�g�re�9�ӒA�%W�'tCt�by�B��)a{|��a�=a�( !nf��Q���$I>u$9A�>E��n &)� A,C)E�)�5& �D$I=mThu�I(" F�>�2� �+E��Czof� o2 ��2� &�/v9"K '&g� ,N� , deqT�:AN ���� aSr "� 7 oF8� $F$,.jv2��(c�{E � sN-,��O��2~ }p1dir��P2����� Io�&�B! � kzB��1_� xi�?eA� .�#%*)�u�} � "R q!�^ bGa[*�)^V�a�]j�,�P�?� &*%�, � �����c""�S��iWCV�:����choose 2#`$Cl �e�A,�}�C,2)��6��(�3` 5^)��-ofٞ.�F�� CA2a�ᑜ���Bar�/o1{>"&'�(F|Pr�a9�:p$C$.E $AB�/�  nd $CB���Fyz #!�2�%�g�X fa �Z*w$%> u�)NV� � ^�2�Q��Wyz7!�U-; el"�/��5b�'�-.&�$BN< 6����4By.� �e+"�z Q>�Ux $D>a}T:B"�(sɜ�]�, j!� ::-�%r �1�!�"��/!D "B Rz.*�:no>>� AD B&�5FQkBtRu)I $E��*f�ng=�e` *. Ver�qE:r&�;ies��E>A�;E>� �  E�� 1IB�f% T&�!"i?��Xa0t2 _D �'F.� jU>�.o U=%E8 fix)�B�!���^U�. I�% &9:�� �.�A�f, $A<�=�AdEŻ��G�� 2�!��UmV��-\��$B$� I�i��)��� [6���A��.s(i �Z� L na� T:&�,�  ��?�# clos&6B2e �-pR�O6}� EXU� 1��m��&@)�]�2�!@ '� V�j�,I ��_�M!nroc�<- f k?l�is��2���^��(�Z�@% "�'S5BK jYJ ��E�U:n1�'Q a �/a�*&� A?]��S&� Xs, �l$Q A�8 �ANB� F��� �.K�w lv7Q�*+"�1AVY$v $BT�Ah �3 �Vr�Q� _�$�OBy��IC $C>a��Fa�� ex2h� %^M��"�F�3*#,"� Rby�.m�e�i�v����iKY#���Y����b��)!�6 �a�dF#�#0�oA���7�)6}�� >�HQvz�BqP��-)@-�-��_18 ga�r.�|���a5�!� ` .p� G�Fd it;)�t�#4F} 2$. n9A g�;��DM�A_1A_2 7$1G$b"�5or"��hSb1 ��eS���27 i&� �BB_1B�*Ag,Y 1�1-�r�C*nA,B�� $$ AB+. |.�/a�!|�, .7, 6�"� >r�2r#AA��Q*� A-@D �� ) ���6 2�� "� :O��naX6�6I$��^\)Q�� � #V?���"�B.�27O! �NVQ��*u�i��m+� % a�5�,e>m� >b&�W�s�;&�,�U��_�{ �5 �rI� !�i�6 H,:t). LinkNy� �7� & .�!�" � ��&�HMD4�s�)M>t@�=�% &�m^!��$ionj�>M6�!82�-�E�a'�Qd0.6�(��.A"E71>"�(FixV�R h� M�is%�ex# rooH=/�5��, $M$�eQ72��D N��RCi>uC.~uh/�!�� R�a �t��2B-�XA� s alGh�C� ��=RI$�TRI=I_0�{ I_N�I_0=Ri�$M�deg�  $\pm 12�^�.o �$I_{j}+1}i 2_ $+[��F�3!}n UA�:F -1$:�md1t3} ��jťN-1} p�F���$varepsilon: }\ee3 ��V&=1jK �<�,r4ܖ� 5>5.)&S4U����[Y^QWȌwe ��u��"} �b} �>U� 6!N.� 1X�an �˅�.�"A�t%�cY/de�r�""� 4�)2{J*~ �&�����:���p-V�h #�:�FW�>$(Ut�"s ;3o�� similar�9a�2of real� �])��i &�T�Sal"&y=�mDefX}�uO|2G���� B`fz�� ; � $\wide� {X(� �O� A4�9����&=�-=c2��)�(�H)�j�5 � �M�F:��Ő �S� )a$&�% �=J T})}\ �slash�511D_�min}\�R)"( �#"=��P�)�oin*!)�H .�Bj� �^YmO:'��sub�ked, be!4L >�a@5�=G5�!e yZrV�Se�F^���6s�gQ.�I[axHa2�i��J�a�.� '� R a��R.:%F� A%~Z0ADeA[*� �of""R�)1�A�{AA�@ sBN�9��&^n� �;a�x�$��ar:�KeIN�,V[ a Serre} (�Jq��hY@�$C:pN-�J��c�  od*� E eWF �t�G�A�"vzR��f(�% �K# .� �6 ex 0!a2� ��Fa�.l2�2/�s !  �� m�F+�la�jA=*D �J?u��I��� ��.`j��u�h�Af�'�nj� :�> !��D�.�RqQ2�:��!DZU�.0 *�;>OI[RMu�!��3!�,&�,��;�A4b~��yS&�Q�0pp�=F�� oU>As�bq,�(\Oof2$dae"jW-'�P��2� jE�f%.�%C'u�hm .�O�8:Ga97d-�6.�E�+(�B&6x!�fuF�6� �mt�.L"za�Z1'Q "Y,����g�!�, X6<ɖU2W ::��Q�t ^AQ5f�1�$allF�V�Az&#yW"�ofU�.X>�A��:���UCAm�w 2wgyV|1�E�q��R�[J�f{-�5D~�>��/is�HVD'�O5 &��*�� f�-*� $VP2�u$X=2> *� =>�n�. } .�� - ("K<of� gZe2� �"O%2�� �/�!� 8���5(� &4I.�`'Ee?A�;o�:E R�1�fF?�� ��g�;i  .m?2G&�D.J�|�=vN�[*�a $FBsc,essn �Z>s!��1�_kG��3 . B�da�Y !�sDLj�r�9'kN:c3$�s�*��:w�|;5�oVQr. ��$V_{IP���km"w4, gUoafby&��..9٩�UO�?�B!!S^�Bradius �Y!���ingT|b�4 $V^0����co"� 1� �2�%PY!Fn \reRQ��2_�HA^�,�"�! ���=�y�{forwar&28 ��s�xityM  S�s�W&�/$r0��"���]="�#��+W��q)%9<som�Ot.]zix�{ɹ{Ij�`�.�)ch�[bE]is �1l1ssg "��N-< e��2�$h*'o��  �&�ziB.�,�a�AQa��ba�$6��%.k�X��A0��I�f �}-��X}  1)�|*�{fa)���K *� "�A�embed�7a��.&�Q� eC�u� :�1�ACrua�v��llat��.�&\ �K�"n.� %!S.�.�Y�A�ft��T &((of m{�vC%��B$Ai�. *�|. , A^{-{1" 2}.�2 V6>�!��^ ��. D#QSB�m��8 (A�i���)~o6w�f&'U�a�)"-Y�3�S6�"�v:f17A%�2it�|�8er_ 8��*�le���1&�r;Vi.H ~�5� �����L9��E�'!�tk� �,��.^$�Ln�7e B�E9e�b� $\chi_I(x776Z54"0a� �2�2!"�fE�(D_I)>0$Ub� Q� 0 ��. ).̦k RVcD� �(-yTIJy2i�$' $�<Jj} $J>I�D� P_{V` E?E�!�j�n�r$VB���C J}}= _ -P_{%� &CoE ��u*/I˾�A�}.c6& >I}\��(Vy� 4 \޳25{J-1,I}6�2<�� $(-��(^%&�0) 6� �, s�0�8.#!$�C��I)%aSe��ded� Q*se�U=� 7!(�t�squ� \�ZB}$2<\| %!I\|^21�!tR<f%v �AA!EP1�$J�L.-Q�Bni_�$ J) J4(He"��!)�"�"� (D_Je�.s�#_&H��= \|{ �I.�- � -N*�!=�$$�!XN0 L)fN�^2 �0+ i"VT�8(9})- e))� nu^2��V[�6/}�f]��,im�F\bk pars1} b~z6�Ƅ=L$lim_{J\to\F�,A�)2:XI%{� �!�%<]8@� �Mi�RHSA��+ ��.�nq�d�ket�T<"6*| $�;[ ��B9'nn �R*Y)e)5�P> �@i��-IQ2CaQa T!�9Y�jD A�cE�q Ua�^�h>�4dR�b����=����� /�) tribޚ!Z!�9 T_�t� a4E�Ji� A�� we a6+ ?FE���B@ ��.�&�D�*?z:� F�� O���`.6FYt"t (Ml� M�mC!�J@� }�I2@�?�5H�$.Մ��B_}J�-�J X�9T"y.ԝ�i&S�a^"��/!�&h�.RObU04 :!I"^�xc��rg.U�.5%�%}2� J>R}��J) ���J2jR})) <���S�S�I�!^ғC(I(dense domai2� x�)M�i�� .Rd *\M�� X}.2.1} T� Ij}�� lambda_I .%e,"alues:�4S4}��C {I}=Mx��ũw��1 ��6I!\ei%is �.ށj6_2�l$�&�.QqB% 6 ��is B 24+$�~Als��Q"� k��� tants"�-�v�2� Wxo�e � !�-��(si�' :�iZc�((.�- o��C.?6, y}���v",+l��&� )� 6�-A# $s � I))}�.���=0au "K"N�o. F \mIk�N'L  ^��-(�_{Bw>R}+��=��<-K>�� f���� Ž:x>�! �xQa(x)N e�.��-�.9(� ) F�Iy=�6aI6�I)}��A .N!k ��&> �$t&j#� q �R6rI}"0�5g�j$$]v)�(xi��-I=�(�AbJ%�R5$� �}� &,p_I����r!�� [ aD_I&�' D $biIk]U�1c ~ppe�)��I�{hs))-n�;y1#��f�+ �5Vx�CIEV(xEQz -E2(���.�&} We� !�6'�VI��� g� 1��>� �V-�!2-M�B� ) @M~J)q�� �:�7H ,"�2*2 �#!8�z�3>�!� �B&�� :� )�gvi��� o � �e� $Թ�!́�J!�2- $$5�*� Q J� M�F�!.P �"�]ne�sQ�gh&W�R� E{�l '!\ &�&bf &<���!  au���gratefu�QV.S.V"��#�\V.Volovich, A.Yu.Khrenni&�,V.A.Avetisov� A.Kh.Biku5��f��1/�WimL�)�/�rk^+�pA:�jĊ� CRDF (�8UM1--2421--KV--:�RFFI "02--01 084)� � gr|MO>��#R��an Fe_�� � �*c oXific school N.Sh.1542.29�|_o0H? 6K���!�bK�� BR*��,vN�N:T�d.[ "��X, http://arxiv.org/abs/�(-ph/0412062�ȍ�|YE},"�ifQr@��"3q�vus&xF��~s // Az�A,�Em�. �P0. v.2 N 6. p.107--12��b-P� �>� , Q� I.V ZeleݦYe.I.}�� Adicu�2��@�ics�8gapore: World SU؜9.��3 �:�} Non--A�medean6}it��ˇ. ;�:J� Fizmatlit���VM���-�1} )y� A.j�: Qȣum� adox߂B��%$B�.�M,�`. Dordrecht: Kluwer Acade��ers%+7.��lKa} �AlbO� io S!�@ Karwowosky W.} AX� walkp"�2QM{[ ''StocharPfA ss---���� II '' (Sp� {\, U. Cattaneo, D. Merlin��i, Eds.), Proc. Locarno (1991), pp.61--74. Singapore: World Scientific, 1995. \bibitem{Kochubei1} {\it Kochubei A.N.} Pseudo--Differential Equations and Stochastics over Non--Archimedean Fields. New York: Marcel Dekker, 2001. \b:�$2} {\it K6��Examples` �s!� � �,F!.CA% 0312038 rnhoper} E�K)� )�%�AALF 6 ator)+Aw �//!or.-� Physics. %%� 138. N 3,%� 22--332. v�30304593trudy}Ex�, �Z� �: metho-�applicqTTW MIAN, A�45-�$ p.154--16�0403440>�0V.Al. Osipov,. AvetisPNon--Degenerate UltraI7$ DiffusionJ�A� cond-mat/ y .�ABKq�n|8, Bikulov A.H-�%>} A9Af5�y�to modelE�Lspontaneous breaking8rep!I sym�yA J.E . A:M Gen.��9A  3i�$8785--8791Z��9904360Y PaSu�Parisi G�, Sourlas N.}��EnumbeM�r>��(// European � J. B��0� 14��535--54^�.� 6095}� ABKOm~^�J�, MV%�.�M5�RP` Constrained by Hierarchi���, are derived� � icular co px orders. Certain polynomials�(ear in such=s\, which satisfy a fourth N�1er!�al equ�- (no%Ohyperg�  type),%� they@mselves can be exe�ed as.�lin�combindEproduci&> and ��luent>�q;s.i9�e2� \seev {Int qion} V�is 1�)9 �=�}8 $W_{N,ik}(2x)$�tte{ ofB�5the se% kind!�ere $k$�real, $N inte��or half- D. In this paper we�� cent[  oe case w \N=n+1/2$n_a natu�  . Mor%�licitly,[wil nd that�� Q0} W_{^1 l = x\Lambda^{k}_n(x) K_{1/2+!/x) +x{2"}^*(x) $- $)�f �27(%ys a}!c(degree $n$.a�se ./reduce� Lagu�?s!#n $k=0$A�5be abl7Q them�v��Q� J���< We should note%�� $n�%�ofE�0y was noticedE�he m-a ``p� al''�(blem; namele� � gy eigenU��super� ��� chan�~with an!1on�h pot ~\cite{E0liouville,me}�jq�Proof��H} We E� by wri�Tdow�p'sV� t ww},J�8L(y) \equiv y''E�h \left( -1 + \frac{2n+1}{x} x1}{4} +k^2}{x^2} \right)y(x)=0,F��� poss�s �O2G$I[1�. Our� ategye� bE� showI $\lnw +{2!Jv$�,ᰁb2G q� 'som.9F}i@de�inA�.� �byme�n study$�&asymptA�s �� E�eA�0of. SubstituE�! into�Q F we ar� 20narray} && L(2g��L +\textrm{c.c.})= 21� _n^k}' K'�* +H k_n {K''} \\mM�F+}'' -;��U�Q�>M�V�6-M� ����^.� ,\no�RQ�1��+ 20$$ means ad�d��� conjugate�AprecedE�k.� } elim[Ed�]��ati�$6=�8 by using � 's" .�6A� � .�--� 1+ "(��)�1@=?= �p�e�g�,n e!&&)�>@-1�. ��-�6b� � ���2A �1+2M:>l�+ 2� U% \\ &&=�6. \>YN7  an:first6 =�E IAa�f�*gr&� 9|\label{[} &&xS\nuP \pm \nua� = -x \mp 1(,a� &&K_'=K_{- 3>�� lea�ݼQ0E [B�--�+2i!�}�'�m1�M4' ^2} >���6� ]�M: +\\.��= �2<E�- >� R/  �.] = �a# 9���Gx�`�O~ � indepen� � ce $Y�� = ��EBMzre��� wholL � ion above��$(...}: �8e�A�be mad�� vanish i� �' effi�!��is8 8;TX di  corre� ds tNU5�k_�U�\Q(}Up�P1�2!�.2���}^*I6 2� }^* M:=0B�Of cours  �nsider�UFyo !� R" n1�vie�  two� � -�� pledV\�6�E $B � i  impl� atB>� ies � ��ODE. If�sJ e:F<(x)= \sum_{m=0}^� 8} a_m^{(n)}x^m$+A�A0 a recurrence�on_�hcY� s $a G _m$.� fJl��&& .0=0�C@&& m(m+1)(2m-1)(m��$)(m-1-2ik)/ {m+2�M��<(�� )m(3m^2+m>31}A�i 4*0m)(n+m)(1+n-m\���� 1�Uq m  n-1.�>�T!�is!0 atheA!mpQ�JC,;� *!it does��g� 0 a>48series; howeverVn anyA� me=A qu%�$it clearly&� � res� N6 �is�� ���N&� by"C k ${�a�I%� know*O�@as $x \to \infty$V8B1\sim G�Z(/2} e^{-x},ez&! )\sqrt� \pi}{2x}} 1>7 allows u�� d�RC :=*� с(x�� 2�}}{ �pi}} x B�!��P tell �VQ)�}-�+-�Q =Q N~v�}a�vi4 u�-(th enough i&!A!solve���Eg$�we ��=6`6�.�6��9N�7 tur�a�� �� $x$.�� need� ww,r� WO} &Vw )�\Gamma(��}ik-n)}M�"� 6� \q��� as} \;i0:�=V�W_{0,\> 2x)5���e�I�g �cN\2N (R�A�2�}iM)�0*}_1 2^{ik} \B_}}Mq-&�Y5'1-ik)E�Z#>�and upo� mp��o (\ref6�), ob�jy1Uu16�6���-n=-�(-1)^n6=(1+ik)_nB�ThaHe have-��� last.��A�&�,�� toge��*$N� serv defI6! � uniquely.2O�y�<��@pronasAU� G:BD zH63e sameV3 n�A'n.� *�C}�%Vt!y{ must +"1.:� 9qs ":k�$} Let��" �&L�ip1Q F�Ra well��u. �$< �i!Zi+s2�arQ �si/ both��m)"��*' � � )pR7agboe(r0 � � hen�se�at�.,U&ha .<^�nd�we le.� 0= xy_n��$/ ZOz{y� n(z)J -z){y'BnBzNO}E"w� �$ / c_n LU"!}N �igr}. O!�aga�.�� be u�ta�La�A.proporm alit%� stan� c_�refore,)� �  1$zS 0$su�0E� *�� n! x /��pi}$ eux� A2c_n= ;/џ95RJ{�g ����2J\,x \,!n2x&�;gi��h�*�"q* )Ro&�M�. F�i� e $ �i� =x\L� $ ���&^��co�} &�q'I�`"� +&n)p -2x{6&}^*- 2^*J# as o�-� 1I after� work�}E�"9� }^*$� ge)Msuns� ly answer=�&&a_1(x:�'! a_2J +a_3F+ a_4B +a_5(x.6 "� y0=x^2[1-4ik+4x)d], .D�� = 4x ,3j,��16x^3 S+4g+g 8n(n+1)]+2f &&� \ �4k^2) M +2i, k)(i+4k)z"��!= -32x^2 9 +8x[-��+6ik]-&9F|c E< )X =4 K[�2n)+3(%M)]j�O/I[uI4 indi�#Q��!� ODE (���e iu regu�"l point gx=0$)Ũb� \sigma(  -1)[ ^2- -4(1-%] k)]="q�q�Xsb/a� beha�^{ R}�u� $.3$ gIo"X6Ie��� >z$. Remarkabb!��D:���l&��i � ODE@"Ji.�q�|,c_1 I_{-1/2  \, M� /&�!+ c_2*)F�!Y�\\53 �:_B� +c_45>)>�"r �T�"�$�9Z" �$a�*i$I\ne !bu{ 2�%��_�25�!v"� s&!�2 ��&w A�� a bi�a3,%��4 fo� ing:Rac_1��M!�= 1!_4\l \pi � �*� � }c_3� 42}7}M\cosh Ek%�4� S ��}��2C!Ec_3}{T}Pik) 1/2 � - �*3�t%A&�Q � }z{&� d simulta�. BE7 do���$let us exa"� $k a�C�Tl $c_2=1$, 3*�&$c_4=; & n!/!] $. U��": ,aaRC*�0B& N� + ^' �L^E u5 = =�4� 6�I' x�E'x g�261" w�>� ��V� &d 1���F .>mas%! Fin",E!�� !�-�m�c_4�  NJ&&A�= 1PikQ�i�2^{2ik} A�Q�iL^2A��a�=�)l}:�m�ikDf& k}rAh'e(^�F�.�� �V ��1/�) 4A�i4� �#� d2�2-0�!16X��)&�i�2�*}'. >er%"UJ_*��z_* as��sN�Q�S e�>�Ӗ2.h�?h>f a!1dic�+�@&��$��~aC�8�2?, .g2"C4 62,� $��*yftr�"@ (x"!?$*F��rV-*�#�" �<$of5Q���� N��&})'j ingljD .j,�fiW+t6��� m55 ifJBL(F�5!aC2\UF� -!8Jg us�i�*choiceo r $0$*N&&i>� 6� Y�,(ջ!� 2x)+& P! 2x))3�6��V>H-FHj� H��� �%�b -%�U��>�>�E>>%>��o�vlo) �we �A�*�$\tilde{I}_.==:� +I(%?x)$. N5)�qMYUim9�s>�$ cslso a$!yp i� ef-,N,� �'2� -(m)V� =� <^*2=$ (�dh�< minu�RHSK6;,m`�})). 2S*A6� Z�G!}8 ELa5 �/s# on $'�we��1ihNdL(G~�Gi�]V�Z�Z�V�B�a>2�i75���!EY�us,I��) $>�Z�>'F��E�i���i� 6�I�h�w�$�!7p�..x;�.R�?ie�.Q�eed�jH&�� �1Y �1�existQ, 1�- 3-na 4�N=e(n�1a�of 2�!; >m�$ look like�"� =5x}pW� �f+x}q��x)���$ 44$ &�0*� �2&�1, but!nshWy'go thro�!tdetails b. A�&�0si�z=. probS hold"�5 $M_{*�3nZ�� �0.-\��)A&� $,a& 1in�"IgtE]�8:�=}o1+� y $, j�sforB��1� mpor�!per2� �/M�Q� *{Ac�! ledgL7s} "b7F�7�up]M< EPSRCE�"Tthanks Sigbjorn Hervik� a~ful� _'| *W8>�8 {99}&�9 ww} E. T.*�5!V G. N. Wat;A C�'f=rn�8�B,q�ed., "�78. P�)o996.u`gr} Gradshteyn, Ryzhik, T4E�I�5rals,X:� �Pg6s�xo!s�Ccl 2000l%4 G.~E.~Andrews�B~Askey Roy, SpezFJ:^� :_6d3 } T.~Curt�+,x8Ghandour, Weak-j ;"�C&S6�3L�3A( ory,`90. Lett. B 136[< 4) 5.�me�C~^90, unpublishede��7>B�:B�>�:am�:\*�:times,�:cd} \�0{in{� }{��mnew�;em{�}�4pos��A '}[(]~ orem6$ corollary&C .klemma$L 2 $conjecture%C \ �style{4 J� �D^ J*-pll�D6�r�J��2c!=_�,command{\m}{?m} Yt�#m}>"n ;n>t ;nB;uu <u><vv v>e e> I}{\�Ecal{I}} 6�p 7p>7lb}{\ove|>e{\ell>"y2"y>R x bb{R>ZZ}%�e9[$quest}[1]{�=q*}o {bf{#1}}�Y*Lb :h>^ti�=�D unitx minimal  @(, Bailey's Eإ�$N=1,2$�] 9or2 algebrasYɄ@[L.~Deka]{Lipika  *>D2>ZH> \\ U"Q@��,California\\�Sh�G$Ave\\ Davi�^�A 95616-8633 U.S.A.} \email{deka@!� .ucd0$.edu} \url�>{�F www.>&/\~{}@�A.~Schil�x]{Anne t anne�t@�?�)�0it{Date:} Dec,��4&S��w>art:5TNSF grant DMS-0200774.�Iabstra?T -� flow stru�= �e cha7er.�   A)$ ��Y(IZ0 $SM(p',2p+p'} nd3p'-2p)?! I2$�:H I�%L=l�ge $c=0K 2p}{p'})$j+e �6R� $M(p,�0. A new Ramontoraac�A�ul�/r�FresL;"l$N�>�q#6�e�B^�isn. o9� \makee� %*�F "t {I�!��oir3 � ���=wer= m�I� �& $q$-�../�H Rogers--Ramanujan-�@�B:1949�#e2key fea�Y%t6�  .tker��;u� &� E ob�'uG � x A:1984} (}%� Paule5})U mFical>2A� �AB in !��&�to sta���s�/2 �!$9e7 8nfinite family 7 +�./ u�chzhas b�B4iz)A; � lat�> �AA!}87}-7y�za35tre%�>~OY�. Y2eva�%-�-m-- {�!��3to �>s=�revealed6e pSAs��Fodɡ�G1�FQ:1995, 6}���(��d>�!�Virasoro!8i�s1 �'sI�. B�'*�L�6&�" %�e6E�m�H����I�Ael�*� �!s>.�of an�VDM�r!obE�i6�No6 a�M� ��#�BM1BMS%u}�ae demo�@%3 &q" a.E��6� ��-1,p)$q�Y�3�gRbC�<ise�!it��fa�re�)J�2s ,p+1їea6#!8 �>�ɪ�� ,p+2��0чf�� r� }{p}�gDi8nclZKA`Z� ;io�-��*%����"��/)cC?ed V$���FJ*6 %�E�C,Epk $p'gItv�Bprime. �i�Fp""E&�kQ_0!� ��7� �;uL.F�6c� o:4 7,W:RM},\!Z%�)�R�)�"�, E'"�Eí ~Q- Z�b!�ed via�2��?%��)a��a:��a�F� I�)�e�Fl�V�. �'R��e{a=Ӂ�"�  arŒ(Bose-Fermi J��$e bosonic A]��associ���Y. of& 've 5�underlC�- �SGory sf�u vus7manifes�)��� d reflect�quasi� icl*� M:%g�a��organ��as �$s��Xa�~�1sec:b� }�pr|4� e necess backLUndr6ut1y pair�/� 5#�#� � �.is��add� ` �self-c�RQ. For"f!�rea<scG!� sult:�,͍7 W�� 7}. �o79 N17*� �N=1� &4%w2 SM(� �e�� r&d&J9]�. Exp�I=L;!ioi< thes2�Xa� IJ�N2 �=�regar_6fq��sta"� y��L6 isN E�n�o��� i��W.n�L VMN� alongy�eru �2uVEc�seI de jszGrs. %-�F \�!!} �I� HProfessor GaberdielE�Hanno K� 1�ir help .�ju� ��li� u36\22-�-thSY�a��3xZ t�!N� E.��re�t�to�3�.�e-*�+encNR� w�K�� ank=%Dob@[A! � disc[o�N ��N�***&��/v }31�D�� �[�ܡ�summariz's origi�R!�a�1�,� 49}A �D.� o(5e��"M �� UBM�r4�| 7,FWJ 1Q 6ubM�{Bi+]�N � �} A�kP $(\alpha_n,\beta_n)$!�s?56{#$\}_{n\ge 0!.nd $\872� �a�"bf-lv}i�yCectA$a$ if ;�^=\zAjzAnn' �4j}{(q)_{n-j}(a +j'TI�>a*b�gin{split} (a)_n:=(a;q)_n &= \prod_{k{0{n-1}(1-aq^k)^0/ {-n}2 5f&M�9>1}^{n <{-k})< y2� *} F*-5�%�5}+e��+oW�exten��&��E� ��-��b>z.� in\ZIB �ai�bC[R�:$~'^%\laa�eq:def{ %�A�U7-\�?}�=">"�&�W}[�Z_-�2q�5}] IfVzi�R!�nB�� 6��%]�i>n9{-$(\rho_1)_n 2E� (aq/  2)^n�\\ = &m�')_R;2}*#1 `?}b�t26� R��n| ���n1�N�phX��D%^&� used��var�Y�eaM�"[C�ializ���a�param39�l%��  2�F InyZ�M�De7aQ�iU}�,�O 51})>(�MLal� �i�Y �*���� � �:�hq*�:�*4 A!hway�-� J��)of��"on� .x�du�7�GRj�6��%e��>h } $(A_n,B�b� �>dLn�H�>�A_n(a,q)�n$a^nq^{n^2}Q� (a^{-1},qūB21��n^2-n}m�:6�R |n2�sbY*\eq�@��i%60>�4)�)�A�:"� } As�wUj�6})�*u &D ie�^ ecn�)$�n� bose�P1} B_{r(b),s}(L,b;q)=!�"MN} }F +"2ѯv$N=�7� i:\7� r�rs1>�B� Fu��9j } V�n\\ jR�= �� �� q)_j� ͞&� ��$q$-bino].C?&-Eu>A�s$BU$ w�Zbe� "=Y next . Cs~M1[y 2� �9 $r$ �!�$6 8ͩMըf�Vy~�S.57alB��5"�7$aaSb-s+2x}"Gx-g0L-2n-b+s}{2}$B�&c ` 1-B\o��M�@Cs} ]�A�p)e�0{if�ZA�x$}\\ F�a2:+b -0�wis� � y\\� �eAFS,s}�HrPaqiE )_{2n}} A,s}^{�}(2n+)@��n � ��.�!�=�ai%Jn�is�� U�9�dB$Ѫhat�}� bD)%� ^2p'(p'-p�I(r�Rs x(b+x-s��'-s)(j 6+Dn;�����1�6�r�a^n�iv�%r�InserJ� 5� iFZB� Q i�1�J�raJl&$ �Qj� "� * 1G2Z �{b v@)�3�Hu&� 2� *� � �Jum_{jF� ŏ( �" {�S� I s/^ 1)_ 2� )5: a9K(�dF� $6�b->�N�{�2x"6�(�6���_� �%Um�z��^�B B��A�.���}�z�i�������ґ�����I��� ZBM�r�AsB� N"�:f��)rv�in�쩠:&�7 &n � "�z#��Z� "�. �r*f So fa`f�4onyU%O >�of=*� "ly, t su�Z_:Gpurpo�Y!"�!�&Q[F� !I= �$ $p "%� $r,s$ be�!pq Takahashi� ngth"�� [S 4]�$"(3F�I\�8�}inued �7 decom�on>��*p*{� 0}=1+\nu_0 +\cgnu_1+ 62"dots 6 {n_0}+2}}� *} 0e $t_i"�h i-1}fj$%t$1\le i  n_0+�!���,al level incA�c�$trix $\I_B�&7G!�Ca�4 m '$B !2�(N )_{j,k}&= A�v \delta# +1}+-1&d AL �jy<}�M+?y_0=1�\yb^ �`/b�=-1, e0=1j�*M� ��l����truncZ!J�ive&fCB{l9 ell_{j+1}9I j-t_m)y_mSlb �{) !mI Q��e^t_m�.22��2i)�=Ca�neg"1�);:���vN;+m\\mRA1"�Y�+1})_m!mJ�"=`>�}\inver6�J�B�.�uE� =�-nmfjJ�� Y`In fact�'&i�v�S� O ��Au6~��a! w�ush2# &� RM+d=4��2}Z�% )=\\ m�j�} z�Lm_Tke�]�\m.���(m�)} v�Q��!]2�5 ��%b�%&�%6B(9&df&&.�%N1V�%$L#"*A/sm>�w1"��1} >*�&.Y�u\*)��arrowpQ,\=_�2=-�4B ['A�;5E��*�9.�)e+c"�2e+P+K+ >ဉ�{�'�57,GKO 6�Mp �&�N1!�} d< \chi&5_{�(q)�A> p-r,J$ ͇L(-q^{\epsilon_{r-s}}*�j���'iWrmp)��}g� �*-#>J\�C( r� p-1,� s'-1�_p� $(�)xvAhN�q5Y �i= ��� #e��extGi) even (NS-�' or),� .b 1 5o' 6odd (R4n p2 2� � �0Ag�/$c-�3!H��3(p-p'�N{pp'}���+J�+2��]�"52"�+iz�&h#Z�-�m�Y/%�� �WR9d�� $b-s$5�Eor)B.\NSo�Iu=� }_{s,2r+ba?= 9 �)M-aKE��0(n^2+nb-ns)} ihae n+(b-s)/2���}0".�e�^[">0�  )6xrR��=*�-1���B� To�$�qF!/�ula s5`m_0=L=)uIi}*�~1} cٖNI.�n1 jX-qihRIm_0a�}-Uk 6:]2-&T Z� 2+�!k.� &k>EmOj�%- '��G &� �1}{8}es[�@�B�# ,s}+� m}60 tack!?=0�"��!�i�}, �I�NZPJ�2w8}m_0^2�r!�N� \\ ��i��"��26[ } �6�A!e efJ� +#{2r�d-Z\1�ڠ 1�.C } SQ�@ng $\p=(k,m_0,\m)� 2�+2/yc.]��) �re[b�=�"ten~�'N&7 ����"9�֩\p>@+2}\\p_i�uiv ( �Q}&)_i,i0P� )�Qp^t 3 B}\p�2} AJ\p�U�IEep_2AeJ/y^j=1�2aO"��I�F8X2}(\I_{ �B}}\p+ G vv})_j��pACI� ms ��1�'&� 1 6p6K +2}- B}$*�x�'\"�.C��\� oI(B}�#�(4 �{cc|cc}2 > 2 &�}&�k "-0  \\\h �$ B�[ 1� vo5� �.�&=(0,0,*��* *!�^t $\uu^t2vvvv6Q]aD*^t�1I6� SaOly��"����i�Weq:N1�)��81�U9�-q�t� z m_0-��}8  Rt ^u  -k) � [-kAF�� ?A�"w"�;�i�Z U�"19=)E5�FR�  .,�~�d8}(��+1)F� j�\pR\\ p_iO^  � 2 Vp� �0� � n 5���, A a�$ �^n�t@.��eU"8R�=(1,0�n S6��Z1:�x�yNy6.:F{�< )$} �V�)@ same>nV�H�*2#s^em�&��U>w nx}B�F~-��rR�jv��->���.�Aw��.#,a�bOdw�e "7"��U4F1*-qi�:M 1.$B�%pw�b����IA�N' ~�E ��AL 8}(3�Y+ ,Lt2 "�"� sQ|^ oddV  ^M m\"aJR �'\F� 2}(k^2-m_0k m_1)� eU�R2D.]*� .WR� � ��v��� � $�s�KaB�I�B�OFre&$�z�6J 3N R�z .�BXj�&BV ��u(& ��]x.('� n)M�,En �'r''�((5�" .�'n'*�7 *�S3 I��uu}^t >1 N� '))0F5 ^Q�J;C'j�'&=y ��6�2�����--g�L~9t[�=&� �E��8� "� ɸU&B NS� ��3*���>��>s��������}�7#n B}�M�" .$�"2� eq, b�� 0>� ,"�_�{E��` ~�[� 09%^t: @E�>2� 2$ C"WJO~�EN2}�� �� $N�V�>�HZGYG r4&�;A�%e "sT"*al Lie z0?�EG�E6N=W%-y<,T_n,G_r^{\pm},C6(anti)-F\utt@ r�R�>�*B1l�L_m�x�]$ (m-n)L�(n} C}{1t ^3-m)R(m+n,0� I�.O��2}m-r)GZr} �x)�T_�&= -nT)n#T_m#�Z 3}cmZ�6N�cdB�{*+,G_s^-\v82L_{r+s}+(r-s)T yC}{3}(r;� 4}) �r+s> C-�8[!��K[�-� -i \{  �+ � -�=!vs�F2�&�,n,S($�d'0� ceTX��8e.��"s1'�'$C� A�: ��itsf�value $c.#CsId�Z�Ld|=$�"QI�&S&P� . I�To�X�#��KZI3,S,C�Wr#r֌�a,X��Duter automorphism�Ca_I{\.+:"o AM� $��KW maps%& nVs 2it�O.�1s�clyb�*V�B�.�(EU)&=�:,G}_r^+=G_{r-�^+a�B1-21-1+ 1-B1L_n/L}_n=L_n] T_�*e:c}{6}A^"�.�\2}TLTLTLB3B"�0AiN��pxZof�e=�&�J�bf{2&�E�$�VRE� *�I8�DQ�ek W�}<Z$ eaȜ/S�aCPE� mapp�4oQFC��P�+0Neveu-Schwarz�"6Mf6�PH$vice-versa 4�" ex2  �=�Q)��o�4�3A�y�$:+D2{%e}$D^s�de'ie Verma$ule�[�gf((a highes�i�-�,@te $|h,Q,c\rangle�. $L_�ige��hR T>Q�~���g��(by $V_{h,Q}�U�$� $�_{ }�MB�re._N!� ~,V34ch^(q,z)=�vrm{Tr}y/'8L_0-c/24}z^{T_0$H>'>�L�*�A�trans� s�U%�6�ft��G>���?b}~N�\>?L}�T}� F�k(ta},Q }V�3"�@)�$FɁA�Y5�)$�� 2��X%GŴs1�2 ����is;ninew=~ ]T �2�,z �:}@�be�\5��Zpe�� �e,"�P:�!l O!�I��8!2�� b�].(fVA01�~B. S��D.i�� e�B<E�D��.��UA�� $՝Ń��)ake#���9.to(&��. ��=�,Q� NSi��9 a RSc"�ac�SB��PAYnNb.yE����*�,E�EAF�v�^{R�K�wdznsB���B�h &F!H��UW��a�}N98�1=�T_0�kc}{24}  } �V6}}!�# F *z^��}r�2: { (z&�It)}�� 2/Bi5I�^QbBRv��+J�+:gFm��JU } {}To s�Hfydm>�� a slly*3?no 2�*a ��4WSi�; I#> dealaj��vacuum7���V� 4$h=0,Q=0$, we &e�5!�)�_{� m;e�J{iS �e �i DR6C�6+$(h,Q� 1fib�e� tj��86�I&<0 6,D:]�,�,# 4�1B! !n� �a >Z�Z`9hJq8Jk ��I�k%4-su�M) vn8�)fV(1+a8n- m���5m� (}{{(1-q^n)}�O\&{)Big(1�6n�+ j \bigl��p-�(p'-1)} ���p'n(pч+pn�� t}{ �p':+ � �vD�BI�r�� +�$%+B�n(:1)S2�-p:F�2C>� �VC'6H �Bi"�MU*T� �-�veri$&�!embed�udiagra"A[F�as� scrib*�8�i93�~p.C (ɐ4��ful�6"Z/�MeqM�,U�E�M�($ �.f� M�A�F�1^6\)}Q�I��^�H q^{pjKjAmK�12p}} � 82�Bc55� Cf3 $pE5� .�^1�sgQ ";� 7a,KirtG58,�[87,RY7}(!��i��put $zv2� ��2�#U�+N�mQ�"I����"1 � tio.X ^eZ � F��(!�n :$J�J^�>� } {1gB�� �Jjy*m��ns} �)��&� 2}�Z�(a:". F`:au��it-�~ aB�;F|!�(&=zb P-� &=T_2^ -N�*}��� ��A}A`9 \v's&Z .�  $(B� ߇i�� ,�l� );5o� . ��F� 6Y**�N|(F� *E ���2� >.�BL %�A>[BP ^[�0Q6}��(-z0,�\(-%1}8& 9^2�92d��a��K�JF>1&�^51�R)�R)R uq�Ic=J�r}�s$r�� $bB\F)1�Z|�Yra3� Ū� 1�"�N*N]F�Nn-t%��N40�B}{)>�Sg> 2�S1�T,1;�P�q]1*�\��OJ#��P��P6�P Q&�PV�M1BeP�"�P�P2�P} :viQ)�Pp�M�XU#�@na�io+dc.g��t&^B��>1={f>� >*�[a���5ύ $�M aq}{ ^2}>�>1��ٳI�nb��zC � �Z� V�F_���.�2Y�}�R>D&�N�gmRsS2 M S q^{2E#x� 1� %�<'�Y-0A�x-�[�[��P"��+�1=-��x2^ ,2=ђ^: $ *7A3-2AVw�es�Y�Y$s=1$��U� varit�NPnOj>�-jJ�2. s�7x�we> z� J�%I�a _n���+f�1&nV:xYE��F�A }(2n>�J�Q�b�!+ ��^�9�V� ��v Q�-jp'+1aO;2� BF<C�JlY2� E4>�"� 6�5nt � �� -:�M)2� N{j��6���J�.6i}*�:z�a>!*��fBw59;5K��-�J J� �;+k_{1^CIg(-I�C%m/}^2�^�\"E/N=>N(�K-�Q>�.&IK:j�"9:f�Hb�K�8:�1�&�u@lt@8� h9��? 5Uz*�DbX ���_%[^�5���v�0ZDJ�0���%k�/{ �g�<5�.�4}�$��O _���0�599 D:;4?rE]_q�& -� !{c� - D2.E;Ya ��I��I 2�0_1,k_2?\�Z*gN+3? F�0E�.����{����Y��0>�:�,y.I8&�03F8Pp^tD\p .wA.�+�>�E�Qbp_3�K����>3���+3��1DUJ�V��(\I_DL1��++ v�>�?6�PU�_N� ��&�>D:�> 3}-D���>�I-D"sD�(F0c|>�>�/"g>IC �>-�>&0 ; )B\\ }�,)m>!F.��>0F�>*!p^�>�:FU.�>[-Q}^�S�Rh��>T"�s6Rew* &�v)=J� .�M-�F�g"y[Y).�sbw xNi 1I-n�E�* 2^ �e2�eA _ "D ��gY V_ B� u$&� RV m�> )}_n �mte�61�e0N1 |A�U�;�d\q��J� ��� ��s� 6� }B� R�b� I�Z^Q eq:R:6�B?VQ �6� �!8!�5@.�^� L�� A,� &� j � bӃȑ�&�#y�A�"� :�HN�aB� =))= wF� +�� Anu� !3]��� ֻ Q7�b� ��v� ��T1�*} (x's.K$n (-x)^{(niC.v 2}\�0B n\\6tC"`F{q�,�20L 2n$,z'xYkY N3�jD��Ÿc�Q.D �E&�����bKZ .=f �_��[ 4=2k_1^22^2-2%=_1 2)W� .��J . (S� a2� � �_ -1 1V ZW og�K�_ �_ _ �vY=�_ Sb$be��f)Ʊ0 �1 �1 B1  yZ0 � 6� Mq�I�1 N1 �8��D6'L���  excep�:� 1,-F*�))���<=(%&� jW9� !>J�  �v�t<&sn] *"Z +�f�@9>@9**B9C*5�� 49=�ab&�p��(�C2heF �'$Nf9 %��'M�R� +�f�[6�  B( xd�)*&t�)�2belie�� at 0�ivs3�y��gen+R��\s7e5K\s � ƛ yet avail�A��&ՁX�astute r�m*dh��n6unlikEV6]�w�s �P�yN�o��JH sinJVA �)rea��h�Y] o�o$$F"�_V�a$")��h�$r=~1,�n "�$R[�AIh'h��doa�ppear&s%�21&kgDM_�5s�X� y� D=�&��j��"�@ *������.�(�w�'.}<<'��85!���F�1U>��Ŝ&Q�A�|4} A.K.~Agarwal��.��D.M.~B��oud, . itUKM�laN��BJ. Ind.�jSS�1bf{51}|�$7), 57--73I6 bibi���} G2|nMultip�er�K�RaJ� ��g�� , PacificB�y�.�114 �4),�,. 2, 267--282�*�W.N.~ ��IG��of�aۓ6�!Pr!London �!(2)�50� 49), 1--12��m�5!�~Berkov��B!�McCoy, .���$�.!�c� ʅss�hysica A�228�h96) 33--62 (hep-th/9512182).��j�5� Cont:pl> ��r2�4s�k��!k"O` :����)��9�37�, 49--66�4��0:�f<�{A�wM�Schur:]�١��:]}of ɡ�:��Communqh6�19ij`98), 325--395 (alg/960702B�6n��, S.O.~WarnaaIRQYit{QZ��!�B&��gka0��co� ^s�~$1^{(1)})_N�  (A{N'}/6+N'}$! N"@���,bf{499} [PM]�u9�u621--6499�! 262��� ܛD�D!�s��s�rt1ioད�&d, 6} V�Q Y�S���oof2 ;��&� irѽible h2;��)� �7i��Bc"Vb�<s},%4Clausthal 1986��ee/s,��"S�"9� M٘# N��0 pp. 289--307.  �O- R"PDs�af�A!�&�8"��A`�-�� , Re�� Circe$ . PalermoU�Aa#=���a �!�,ٓF��.izi 6��%�� z� i։�B�A_��43--51. .��3D} M.~D{\" o}rrzapf��<& 1V�M� �y �6�fl529�^�r63�_55}g12165�9b/D W.~Eholzer, M.R.~"��y9U̜��of �o�ERA� v%-G 97) 61--8�60116325} O.~��, Y.H.~���Po �.���F# Int.�od�����195��291--231�407191J�6z�u6�wt:�ro����5����0, z�2I6�65�672�8086~>��$T.A.~Welsh9gOr.W�or��of��$rester-Bax��` ����� 4(Kyotoi�}  103,� gr�9h.,9�<91}, Birkhäuser��t��Bo MA��02�G�g P.~God�m� 4Kent, D.~Olive�I�yB MH5�v" �> �4�B!�8no. 1, 105--119.�#8} H.~/��E>G5��R�A�� N�x+"�=AE�Pr��d 030606 �4� privBc <�2��3��B.~Kirit��&� >�J�w��I�>� )� k�f�Ar�3e&8�;187a&906.��4$} Y.~Matsu�qB��$C<1$��6� J� �:7E �{793--792�*4�A�9pOnfBJ� Ana��&� 10 ���284.4�5 F.~Rao�ni� -K.~Yan*' Mod�in�*;<inV�*���b^��(a`�202--208.�S\ �H� wimm�� N.~Seiber�a�en���!�,N=3,N=4UrpeJ� ���"�L廡.JO �1�`1u�����L.J.~S�o*KC���A[��'s&�Bof&]M�a�Z 2i5��460--475.Lg�( >)F"�)&o!&{ 2��W�cteTo�6/�in Memoi&� AmeriS%A�٧al�iety (9 0.CO/0212154 vS�>�BF�A:F� [a4p#,10pt]{�4ߧ>ck?�vX} %.j�F��O�A,mhequ6?epsfig:@pictexw��>��)�Fs�a orem}[&]z�� em{n�}[ ]NQ���֬)P��N��D)�.:' 2��)��� �{c&��RC %\re.��the }{\arabic�* .#A@addtoX�t4 �����pM�}��Pfo.}e� }{\hfill\?�\��ŬProof}. ) Uex�e� [E>[Ou�A�giO}� \font\g$=cmmi10 sc��$ \magstep26�g�{\hbox{ 8 \ai3�-!Lf!, �MF?Genviron� {pAA}{�) PC:Nota}2sf.L�2n�w�2#1(Hfi )2L);.�j �NvNJP�� �Fr�5�tri}{!�t%�T>�noeuds}.� �Blienst" L}(T�det)~{\ Ak%}2�!� �{#�"!�myx�J{7.]2 ypic �{#� #�{#4X�{#5�l�Y)#B(fig:#9��leavevO)`0�$\vbox to\m �{% %\v���� &�>%�E. newd��!�� er % =\hsize\JSx %Q�fi ,�N2G �� ure}[X)(19,\m)0)% \C{\��� ure=#6}}%�"�$ \input{#7�$Ug� �:null\va�9� cm \M{#8 I-n }%�� box\MHbox)� ���� # xI�����U���-�)'}[ht].�©)�v�)�%�>�!�I�6�^� �QN(-15,^�putE���Dkebox(21,10)[lb]{\� - E�A� 4\mi�;~+M�($2�% � Q�%f�vspace}ȍo}ց7 -2�� 2"�_�-�a ��new ����mn�M.)��Y��Xbox to\mywidth\unitlength{% \hfill% \newdimen\figcenter \figcenter=\hsize\relax \divide\f*�u by 2% \begin{picture}(-15,0)(\myxorig,\myyorig)% \put(0,0){\makebox(21,10)[lb]{\epsfig{figure=#6}}}% \put(0,\mytyoff);({\input{#7}(end�� v�}% %\null\vskip\picoffset cm \vspace{=.d } \caption{#8}\label{#9} rf� } }% %� \let�(ilon=\varep \ \def\eref#1{(\ref{#1})} (NN{{\cal N} OO O(const{{\rm  .(ie{{\it i.e)�,document} \tAT{Dynamics of Triangula��@s} \author{P. Collet${}^1$, J.-P. Eckmann${}^{2,3}$} \institute{ ,dCentre de Physique Th\'eor �^,\\ CNRS UMR 7644, Ecole Polytechnique, F-91128 Palaiseau Cedex (France)\\ ${}^2$D\'epartement ^v, Universit\'� Gen\`ev��3$Sec!�Mat�mat�sf=} \A�%Z q(�abstract} We study a few problems related to Markovcesse%�$flipping t2�!�,the sphere. ^how thatseG�eare ergodic and mixing, but find a natural example which does not satisfy detailed balance. In this ex9,}D expected distribu%Oofdegre� �nodes se! to foll�Pe power law $d^{-4}$.i�9U\|8pagestyle{emptyA�s)�{Introdu%�q�2 !:a<ider a -� chain on Bv�)v� (or other surface). Let $\tri$ denote �{of:�,�S� we mean% +P all combinatorially !Ninct roo!^4simplicial 3-pa5Popes. Tutte \cite{ 1962} A$AlM&Xir number is asymptoticm�4equ�1>M� Z_n\,=\, \frac{3}{16\sqrt{6\pi n^5}}\left( "d {256}{27}\right) ^{n-2}~,)�k as% �$n$A<0vertices goesA+h$\infty$. Of course, Euler'@0orem holds fo!�ch:�, a!� !�6at whe%�ree:E�E� @also $3n-6$ linksJ $2n-4$ e les.�& For an el��$T\in E",!�M&8by $\noeuds(T)$%set of }` %lienst"!�. ky0 $\ell$ (connangU� $A$R $B$)�u$the ``comp �ary''R'�h�,is defined a!ca�4s: if $(A,B,C) dDritwo9% shar�� �%on �'$naJ!��$C e D$. �eassumgat%�any6ta�babilit!u��a_{T}d givee�$1i0, \ie, $\sum_!T 3T()=1$.y) JD�as ��s��(first choos5��E1� d%�do��(change $T$ Eproceed |%8next independen�iceA�ak. 6��'$ �K �i�.�erase /%�( replace itI�ell'$%;obt��ia�is wa�UnewMT� $T'$��w� B�v� This�8 ��$� is��monly �0$Af�o � |�NdA� Sec-�2�!�(irreducible�aperi� .�T.� of It:,well known (R�)M byE p��A ) describA�bA�one can���u��m�s�ͥ !�(4 show�v��$Gbe t` finite F im(reach a ``CQ� a''�e��l y(0.5Z)8N)1:)1m)The ``uP~UMIN��` ``branches'' between 5 %�e t be!h!n. Any6�1brought�E���m b�sequen��; su�� Si$by our hyp� s� ny s ()m)� iona���s has* on-zero2���!�eY��de�e�]in. Toa�ve U� ity,�� have�prAT� � � high en� iterat�u��Nmatrix,> . diagonal ��9�i�ve. By&(previously ��io�result,�iszto� �wU�(struct cycl�� {e��three�� F�. C< < �easily��e !�e�ae� backhforth. r F��,�on� �subJ�!�size six�!gb�1� tA�>{,� B�}# enume%�{�j; ��e e�e,� a8$n\ge 7$. In pa� ular9 3E�dM 3,s 4!�aMEL 4 !� o12 $n-2W��-Z-1}{4:I2: 2� %y st��%�!M3%� gene��� �T �V�T�u�2a؁�SQ|3A�* I6perfor%Y!~� oAO s $$��array}{ccc} (1-4)&\to&(3-5)\cr (2-3 4-5 / J[after 8 we get ag� �F �� 3 !�4&{.� $\square$"n$remark}\rm.c condqof I�Q��!*not ne��arywe  �'��re�cr���#A�erm"�$�jba_T$J ���thinka� ho� �A volv!��=su��v�s�� � FromSA>��!Yconclud �e�� � invaIt2�measue{n� �� G��K!2dic%�I. &� Two Ex DA���est�i�$gre� �]l! uniA�ly at � & �getAe'&d1~,� , us%N' -�fact, m�U Q �%p� ss%�bduced��, Se.g.}, [DGodreche1992}. He!F��dan�e5�,qas sug�� o us�Magnasco __, 4}!is�ostAB.Y�aeG =Und!�n�*)z1K!r)�fU[a��n@��. An!�y putv ,�+n � w, leady�f"�d � �' =a1}{� Q d_{1 &|T)} +.2qFjw? $2GB$:�J�Tu�! s w endEMlA�,�he:� $T��(� f,q,AFdBby�R�al S ��$ it �s.�yMa  $i�M_sa a�ell\sim $ f $i� r$. X2C�d_{i}�it" �j�We�EkBayes'� mula�1!2 �{�(>O \,|\,i) :(i)\;.JMoreover�Ee(i)=1/n$o��$i$"� N=0$ if� \not!' iI$e� wiseh ]B@.�% } �TA{forN=2�.�=�}FZ��di ula Z�e_).�?It�$s directly)��expres 2� �mathcalG,}�s�AF�T>�)&9#n})�-��\\ 2J:J'6e�LA�\,,�m i}1= 5innVq=1!� eq!#5 �a�h� wus� ac�a�Ti�62��/oG���*���graph. Yse  modele�|1�the*}A�����(\,\cdote )��reM�(: � 7$)�_ \no:nt{\bf R� .} ��Rcheckb! happenE� smaller� .} !Xe� words,canCtly gu��!"�"��x� *?e%�i�a�of "�* ��respe!�o someJy -G$P�$$, namely ��T�R��5 (Q'1�>4��0(a�ba(T)= |T''�Q��} �~T�H0,\ldots,T_{k} +1}=%�A\g  admiss%�A AX mustI]O 0prod_{j=1}^{km��_{j}|+�.+1 })}iK$$�- go�!d.�� a�B4%^!�"M i�(��isExtrue,�>i 3}. >B1.2NB-8}{7.5}�:%3:%3*%f�$d 4)a �r*� �6(\ge7$� =-8e�abs,}e"� "�(Top p A�o$ top � bottom."  2'7F.))3� C� wa��{!� ��^ same!�E�J b�Q A3��{j��4-6�(3"�2�5-6��eD ]nJ &� > 4� ͆0}{9}\;,Vi:� $ is larger�n 6F� &� N��! �� simul� �1 B ed extens�#-�0he�g "# #. ����summarh8�� ingM�a�reaA*should!�A�EF no' oretAexplan�QJ �s�E m|ins�!0���$���< } J� 5��xponent� 0 2 !,� l�1-of T2� T* ! "� in a sens�!w�ke cle*w,"�:ig1��b�%t�C�%(le=law.ps,wI&=10cm*%0A log-log ploa:Iof:8$n=8194$, 32770� 524298about $10^{10}$��)� data��!�cuE�edA3 $d(i)$ l>��-t� ic stra%�C !� fitX8an"of b� c |"3}$, sAd� b 6�"�"b�sim=�"  outliers��\� �lacunar��%U  "V#>�of a ��| star,o�l an 1. q�E��Q �l� E�q9 as�Uconje(�}��&K y"s $p a�integ! .�2�h-eaverag*���� � $d$ di�(!H verges ):�t�8in�0y to $p(d)$.  ��J#nomi�cay� A�ig�*�$B{ rto_n ��� limi�� d$F�' !A-S1f��It��b��1 at s} a�mvi��s� a pur.B% are � ��s�%r*t_"�? go aV with)� $n$. F� Aollrof-��reIifr�� n w��be &��"�%. at��Au$ane impog J d a�+ if%qd( I�c�n: All� edA!un� pableV ,H,�A2X*�0an approximat.Y(of $N(d)=c q��� $c\ ; 50n$ (y $c\O"{d=3}^, ty=n4 Thu�re2� �a�� t<�)E�is $50n��4}<1$] ,$d>(50n)^{1/��HowA0,�N1��-ly " I+c%W ``��'m*m�)t. ClosA'n� is�"$, \eg, log��0hmic binning)A al�i�se f%� spac�0t equilibriumA�a�!to� continue}� ��d]Z��mK���dK&�s)_a� corr[�n  neighbo�$E%�� , i�. S!#2Fv beenA�ly!�laD%&�'2U%��*� �4 rule�dse6wA� difficult!6-# no deci� d�C�B��#ce �found,�ep���ob; topolog~ �s. Q� feel��| m�.ya@:ial�,��the�t tere# in%6k,A�in 2-d� v�9(!+d�, dualaour�lem� &``typ�''6Y}y``flat''�ichAa&( eachE/(wa�I to?))�6s~ To1y{effecO$� tailA\6L�XZ use 2*%�erf geomet�as advocU,by Robin man IaFo 2003}� o in'+�no�(b"�*, Ricci curva�/''��,!�!dU�b"�! �"e�E',i d_i^2 -5d_� EN }E!Wi�quant!�"e grow m or�w monoton!���^��."�he2Tstate. N�+ at s&!�*�&�&� 6�eq justA+su�'qsum!R �%��B�+A, obse!d ion,)c�� very!accuracy� �once aI���p� ,��Ka�a� 50\%�r,attD-ed �%�� not}9!�a� causI�``�%* l� yq��isaq<,a tetrahedroU�')Wop����5�%0E/f �d,``vertex-ins�on��F�A��,'s/km 1- . \biblio=ystP. JPE}�/(rkboth{\sc E �}66> {ref�%d"v1 �q%%%al!�UD? dec 22, 2004 % \7,class[11pt]{cl� 4usepackage{ams} ,amsfonts thm symb/(newcommand\�on{Dec.p$ .Abin&i{��2 lanbox{\h$)v�� h� t 0.25cm : dept 01cm \,$�2re�{\qed� ol}{ a��Z{4thbb Z?NN:CC:DSsFF{{\widetilde S:!R<R: eps{*�31^half{\m)frac 12�� rhovArho�)<Ci{ C_0^ 6Ykf{k_{�3F:�c>4\, :#Tr$4Tr:FfR4>UE�4E:4Hh H:h!�� >�Pp 2P:2gamo{ma6� upa{ rrow6 doa{\downJpe �pe>�vu{\nu6K!�{!�} 2�\kappa!� :rho>�AaERa� bb A:�idYPI}A�p$Xint#1I�chG- {\X\displa��\text��#1}}%&\scrip %\r'5 2pti�(\tiny{$#1$}<7?5 G:l !F3\!\int}3�@#1#2#3{{\setbox0= � $#1{}�7t}$4v�8�e<$}}\kern-.5\wd0}'!Bintsum{%JP !Znews0{thm}{THEOREM)�lem}{LeUyDcor}{COROLLARY} %\ )�+G$jrP��b\���$�D%�ize{RS ��}�PV�7\bfθ THERMODYNAMIC PRESSURE\\ OF A DILUTE FERMI GASA��7�8 5pt} ert Sei� :\ !-2pt}\o { De2) of�7,cs, Jadwin H Pr4 ton "]7y,gRT4 P.O. Box 708,=P NJ 08544, USA. \\ { � Email: E�tt {rs �@at.p�.edu}}�> date>5g��kb�7 ��Qim a ga� fermZ� + spin �emper �!�+ chem�  pote  $\mu�0s"��rx1� �0ter!w��� era�6�%�C par )�4�3ist�7��mo ��%D � �#� or���� spon* �! ��ng��$� rGi%or� al�� scm A|� � ��1 �J ruQ+�repul��: i '<9 hard�i � JL! �.�as /33/ �{)+g FA%.?�%�er�a": 6W{�h8footnote}{${\,}Q;��{Work)a�7 sup!U�U.S. Nal Sci� F�!8nt PHY-0353181 &�n AlfAILP. Sloan Fellowship.:J� F�\copy)\,� g!\��. X3$ paper may�reMitr- tire�GQh) er+ purposes %\t�of  ents*�.01�M�R/)� A p�<ce�dilutea�esa��:}�T receiv� of��QCla�5 oupl@ years, du�.!Cn)�1�Yal adva�O� aNth�0systems. DespStr�4dou.' |�,�or"I�s�rtUa�%(p�6ip�."in spaG9Aoft 7c�#r� on un!kr>d*�#to u,� ativa�TE�:�9!I�!�d)��!�}�L!>e� � can �ea3/ be taken$o- ount*�)urb�Vory. �)Mrefer� �"�.�^z����_ P2��!�4)��0thoughk!�ly�!mos!�)��= ques!�!�ask��!P-gr�At�(ergxI\.�(LY98}, LiebEYngvaso ?vis!� method^�1ATKrelev�e�# �-PBu5gaa�n�!Vɠ�.gy!���t vol�9 at di�9rho�"�by $ 4i<a ^2�8E&$a(�,($s$-wave) vrMD��� $a^3^ \ll mQA �):!g �. (UniJret*� $\hbar=1$0 $2m=N �m�6�mas���Q� s.) �� r�a*-d�TUal5v�later�#��"o$LY01}. Rey ly�2�y�o+8,s�>A4A:��wE%"? MbSS�,a�)LI� �Q 1�n-cA?y $q$ZisU>>,%eq�}�' 35 \�"J, �>^2}q\ŷ)^{2/3}IX{5  +6m ? 1-q^2 8 +� {�er"in } (MJ ) \,� As �", A�V+IB��@e�. or $��'��ɐM�mX)�AX&k(0Ug�� 2e[)k�Xexhibit qP� ���A�d�� ��6m.M %�i%��51= i�/a�.�'�8p<oU {ogu�s�*-�)���5 �� . Ou�`T)g;T+!We2)^I d canh |!mbl�4nc *\5"g �O atI�.�^ �mr4 wW;"9 ,a[ �{Y'!�6[1k �5-� �< a�x�2$-2R .^h ��$%� iD'�e"�m�Ai�2&�A� =�m *o !���nbig"�$�Bm  (�kZ >� gas),)t�4TG= (�B^2/q)i� � $ (inŋx'{$� B}=1k?; r@al behHEA���=!��fA ing:!���R�2�*9 two-5�J�!��A can �Ri�Rxun�~lew-�is� lik��� -=� (��M)��?e6y2�&is�2a��A6egligH*, zfor $T\�" sim 5�B�rmal ��;�8!o&� �Egre��)  �z 9K& �ai� is p�dY to mR%!� intuacis� \bigskip:#e��>d"= �� �Bg)�9s�E� w�; Eo���$ $q=�*~| $1/21=s ��!po $q>2eE�$forward.H Hilsh un�c �E�S "j ��?i�� Fock 9av�Q�sP1Ff= \F?`rm F}(L^2(\Lambda_L;\C^2)�#v $& a cub�� �1�$L�%Hamil�a���0n $H=!�$oplus_{N=0h! H_N+ �"$H_0=0�1,H_1=- \Delta=6BI H_N=g_{i�,N - 0_i +  1\leq iotLa!��(Dirichlet b� arx5"E871g$.�Jt�# s90� � ��P � $H�� $\Ff�F �L$,� �G~Jwe�Z2e` `�a.ou�;Con pair&�  $vE�a�Ada�b�#�A ve, radia� of �%e� $R_0$.At�%�"m@��3�� Z.$aM�B� �*. U"N: F4varphi�aUu�L sol2$K�w� d Q=B��' +q} M� oA�� v= 0>�sub�&!E�F\G m_{|x|\to�}R(x)=1$,� n!!�;�@$a= \lF<|x|dD)$�B A�1dix~AA : � �s�G s). *we�FIE�(�Vgr',EU �I appl(��ot "3 ,e7��b'%-c� *b � )�.�is%�"G. >� �;er-� es�E �L�'i2%c i�(�*�$$\beta=1/("� �EA�fi D��^ipre} P(b,\mu) 1�L.{L^3 +0} \ln \Tr_\Ff>exp��(-((H-\mu \hN))J) �%hN�[�z�9e"+�ore�H&�D1� )A� P rcIg�q"g U�)inP � ) ex�$�i��F4sM�8robinson,ruelle�-0-E:�$l$.W�8�M �XA��� i9�� v=\�al P/ \mu�ա&�deriv� �. (&j!:��H nvex�NEGVr1z R-% al�u(y����Ai)sPlef��VPist�W�. }a�� )���> �y"��.�,"N �hE �e&�i�`r�#z;RjcD(A �Q:},�*$� nesk*_ fugaci76z=e^{e \mu}$. S7 $z$�s6ond��(7.R ) I���cG"iPTgaOa��bQrgeVGi�roa�F ?.� . S�!}F�Cq�% um a�'t�� Z�' o 4�xa $1/z�>eMed^>oAk �,�#a� WAg!�e�*-�hwE��sca�%�"(�JF�$ �E^I�l&� �v�/01�|m� x���+2!�W�őy�jregim�1Ae$a \ll�fqs ��tQQ�e^�!3E�e!]aṁ5��:�7co��%g �BK,�M�. �RP_0�b��:�.� and ��!�aBR5!�&� � s� y%G� bf�Q } 6�R52}ie(} (2\pi)^{-�Lint_{\R^3} dp\, \ln\�� (1+z��ʹ p^2)�>Q � � � rho �%�2$=.S{�� 6�}� = 2r� M 1{1+zA�1xp)��}B~S�Y1Rvel�&mQ ,��!���gra�-ak� K&5���+&�J��k. inVDH!�!� T1} dUA�_0\�(vi*2GI�NBI +�0$\alpha< 1/33XA-W�ws unw$C_ )(z)$, � �ly���Z�� ����,&q ^thm!�A_| . -:� + A��6�^2 I�|�,q � a-/^2 [ ({��)^{ �}Jx �(!��-rk�oe�H�ofe %%��%�ot O1rtifa-o�U<proof.%e� $z\to 0@4e�Hs a6��6!^#ertai�Q�R���}�8ŜW�Ko*r A�<a2�Cu!ula�is term�(v4$on Planck''Rn�!tO.�+a:1AE� p�Wt)Zs[the6��ePU:ef��$��$�8q�>$the error �Whe � �of E� Rfar�( optimal, hu2w�@�9P5� of wri� �'zse � �9 icit��M&�C]� 5m�=� "�W@Og � or,J.pre�ly� &!6� !@/  Al8iW��co�:i)ine�ɩ�eP� iNY:��be%!Ud��#�< (>�ng�;)�Eq.~(�,-�e\a|� �2�{aollXof� B&"oK.'��C>�\pm�e"F � .� ^\pm=%��Ml] �*� T :� ��6��� $, .^,a���2�:@{��:2-J��}{ 2.s }q N�n�(1+��)/2b�!��3��J� actu�$�ej"�!�.� A�u�ng%�>�� P_6$, as claimUU�2})�4�a+\;one*�euVy %Rces (cf.}�>})V=u;e�3 :�=F�-ɂ Q�F"U��  \,+ $2��r3 � v_�4�Ne�a9��%!. Nuthe, w�Z9atB� ��$�ibQ�4�} � &C(ol%ial�Z1%�f� �FE�b Helmholtz!:�-��% alog&�$*,v��'�V�23 S�\>!G f��rho�sup_{U [!� & mu)]�i�� �=f_�M]6"fy�^X  !���ng'0 -Z-any��a�� ��0��x).��C=iK$xj $1/x�� 3} �� 6Q- : -.� >� J�� )~!E�� ^2 {� �� ��L�(ore�� (�tCo�ies��C1}�� 2})� y-K�=way�hl!�J�9now)�: omitag.� ass�4 � |,�#by�r k modificj�,�pQ N��below8Ii��5 quu(�y5 elfykitemiz�4 \ Pol�Cd� :} A�� $m S^3� tot}�n�ad!=tomX*��� $:9%�3-�qC�i�tot���r �Wm�m�a� p�:parame#% !,p>�,4magnetic field!�iY^&x!adt, �A\lq-"% \rq\J~M:���.!-��< ` $P�{��y �V�m.j)�>�<ɖ+ �!&S $8&M'v_j3 +_�3$)Ha� ! � upa��!%�!��-upa> � =��2vy^M�y:� -�:�@ as $��u6� \pm N m$ ]�Hig�$�:}�0�of�q�tc �� �way. ZKq1I�Rm e!��a!��D�/~��pe69)�SA�ba�!�$�#&�#\F^\ O&s" &a 1� �E�$� .� q}�-! tudie��e�#� >yI�C�&e�E����[%9 �Ax��i�"?"� o s�O t&� of�8to &A �),& By cutte�f�If���ropriat!<(iV$�;)AT�)+zF�) A�6��^\�Q!�>�1"f� ky�AorAD&tg� onDi�";!. (Ceb0z"_2discugR�G{he&�*M�Pd� "9ILSY00� */ .) 2��%N%"�alaAa:�%Eϡ�2 e��M�a�&��wo V�V3� vZm��2�*)�!��\i�$ /|\ln a^2|$>�SiX hown+J5SSH!^.�Oat� .N�6���� velo�a�op6%��Ro���)U$55atAUi#0*�^end&\ BggivaG� full�mF��I� a�Drt�In�1gui([.]LZ�fn� prelim-AHJF/s| ina# am� useful%��{ * �r�l�$��j=� B"�va�i�` pM[�B�#%U� � ��YB 8b Vl.�� LBeR)UB}Ŏ0+A�a�F3+�3�A��Iia%���� l�mn up��� y6�FinZ42�CP)��q 4oI�� 1ki �}�+1X,[a?6yLB}�� n8^<c�b�4H��-B�I��b1� n]. A�,.!hhrAaٍ�SSI�yHi*�^�hkj�BB�; co�$e�5ma0oSxbox��.to�4��K�al"�!i\ch>��e5s%!�(b� �Gin Sub@�_ss%[}E�tCp�]edi�!�ca5 }=5�R\alc [us�b ��a%�9f�o3 Jz�� ue��P  �M+&c`2Bb�dop ee�Mon�(e�ai���re�1�4�����%�%R;f/a�}�!!Mq ^{ UB},�'two m��ingredi�7�L�� $ in��m30�%�[)R4]{m? ��'%B�r( x -��"po � U9� � of� � &U�#�a�QM;# -mojum�*ki~Ik��eB� low}�L�+m ��COsubI�4Ia*M}Nl2�T%Lr&4" in)H{LSena�As���:�apse}� Qgs tewFjQhK4�#� ;*F��?-5] -up�|s,%��fixed�Fe�"4>�is kQ�h0-Di�C+.&�2o�*nV�<�:�lIEf��� ��d �zh�SJ l4%J�p�O.��:�8 � �A�6����e� ansvu�&<�K*�m � } djp*� $HbEI!���b�q and,�%&&commu -�q�TuNgs"^ VrbB���%� R �1U=i�3r�ew�?ecA PX*�"���=�,�Eg2/\Hh_1)\o�l./ � Fft (B��' /=>P/~)�.� �/!�e!�}-g�t�$�z coordina!{!���rfactor��$x^��  e�Wonddo> The .+�re�R�: t��be�<as>�/,M2�/ {N,M2A&c!#Fay}\noM H * &=& -�/�/ v/� _{i}k�/M0^� _{k}O-su"0 ,v()�/ 2k) \\ &&7>%0 64upa_j)6R0k6!�)*J�h��U  t�'a�s,�w"�t�N�WR�4�s�[vo5Off&�8,�*HF"!YE�of��(�0 s $N�Mae�aHl�7.  c�>c�$ y $XE;=1�1,\J_M N�$ 'do 'doa.'M)P'\s� ion{! P.F�$al"�. pre"��3pu��via a�`Sal&D�$\Gamm�"�"x"  " 1� css ��r��$e� $*�-Y=�"�.( X � :�0(von Neumann)k . (!�&,?-��K#�d'F eigen#!��9�r� a� quad�"c�� m do$ �Z�3 $\hN$. O��f.�{�6i2�Z+�1$�-Let $P^L��!�umaxim�P>�~g� " E`c�E:isi!quaTathe�Ea�gl-&v; Gibb�.M/ a�*�)(E V0)/-� B v0�6�T!GU�B�*o> := LA*EVq)J�0�"@* �~I�) nd 2�/==3.]1:� . AN� i.e.� r�=-�� v&]E�$| "�usJUR+Ac%..G � Q0, "&e^�EQ�al ��iT"lin�^<�Q.�4::Ideal�  Ga�E Aa E�2l�1���[<��_%�1 Pp_0��{2 ThXų way �.�$ !a,�?H$nQ�>�2H $H^{(0)}2�86 !���D 8 Y��)~L)v" $v=0�J��(Jvolume)=B�>l/by �6O1;��-�JM�����-fin�-2DB�-���4 } \,�{? }�-big"�-e!� �4 J!}#)-�A�)�\m"/#�1c Y�6xEr ��E��:b�f�o2�y�U� �v+�y,�p�p Thir�6}). N�h.�k2qonepfW8half �5P^L&�"6inf_{�Q�=q (-h �) )�K.��S[ ] �f�����yis�iR�*4$ `N, M $ ($0g  �k $2�}1fv0 defsmoT��Q�� [!g� c0  -� )\ln(1 +]F�- � re�Gq{f� l�7fr�/i}$ !E $2$ :�C�s�{&� �in )�1x.�� #K keep�� SY�z�x��/ce )>/ |�0�j�inYQen�/� �r!�"pi�{K�D$I�-eA,m(val $[0,L]$to) �l-w�c%Ge).�? ell c(L/I - R_0>0�c�dqV� �by2G!DA�inf�!ab�29} �7�fA �@I<ell^3 P^ "b� ���I^3ey-�ofqAWD|a~� �).$L8A�le�!$a ��ty)�$Ix2i=A�bs $L/I�9n&fs ��D� n"� "aatb�box�:f=%0�0�- R_0/!2)�6B=�3A�irBvGe^%� 2n�m"�[�l Dk Matrix�X��0wa� A�Lr�/&� ��rA�or �/9-}\m�<�+� _0Jn-0 & $K��8Q$��Apro�@���) �Dof =.N�;\Q-  $��q K ��*$, d $Q=�Sta(6!+ɼ4H�> thet",'� HeaviV3 step��&�B��n t�,K\{h?��a�}ll} 0 &ds$for\ } t<0� 1>E]0 \, . ? E� .>NO< Ff_Q�T\Ff(Q \ �2$ztsEQ9�Q�t5<izE�A}5tQ9��BI: c�"A'��obZ'��Y�_Q=6_Q� �5{�}28 %Z <E`��^!w: �)"E, � �� EubI�(�$7 �o߂aRl�.I�I�Q=A��� \�vN�U-H��.1$*��4 co[%�F1 �2!P� 2�w���� AeQ��1+%W~ ("�D-�/))N�2;A�|de�o���!�::�� =�I/� a�H  |\psi \6$le\langle |N�!\2OiR_H# d6$  �\{d\}�)�noV>�Oav$.�  alv.AD$R�s!�kW�? S� a?W!�N �$ $�$"F3�Q$M � ,2@<,E��T,=e|� Give�[/w5��.i�B� defp>;ph1�!�E} {F^{�v�p+ }{\|R%=8\|}b�<}�a3 ; . P� s $s> 2R_0!�dɩg:[>$\mapsto \Rŭ  �g"�ha� t�@��.zg(x�|� $|x|3s o 1�1rJs���YtassqU�$$|\nabla g J� st s� I�/$# �VT+� A>s2��0�-s� R > !�fN" $f��H$(x)/(1-a/R!E �yKR �m���. $ >�}�x&zIt� j%FzId E F s#+q}�*�-8f� �<�l�41��N��$ 1 - a/|x|)U�geq%� ��F} M�(�,X)=\!\!��܀%&�L g�iDuq6-&q - doa_*q-?{N}{M} f2b>N�G�TaV�&A7F, ��'nI}����\<5N��:\>�j�%A[�Bp ��)��FA9 Y9��m����,�tm�p�iz��h�B} = 1/&UC&&'a�}V*>>s:Ec&� e:o�6A� F��閱="*de-�)e���1%c val�U�ZF��(}*}JH Q I>��� =� |K 2,M_Q[}@5�QMNQ.S�L��Q��Q&%6be&�' �n J�([*+ .~IV�&. .��Lc]i#n '�%�&f��2�Clem9Z UC$N,M\�c�� D_1��D_2a#Jz o�3*�I�I� F�!�" Q*%Q�1"=R.��$,:& 1k�! �al6!�%r N+M$��sy 5psi>�D_1 ) D_2 doa)!3^�"up��u" N#�E Then�5�-�dc,�]$c�:&5 ># # {Y� si| "#| �M��k $ �f && �9 D_1�| 2� | N + �6� N M}&? � ( 1 + c N��[ M )8f&�#&.�0ay 6` E $R,s,N+M,k,; )�[0c (N+M)^{7/3}�8{s^{3/2} a^{1/2�g�4f,aD"�#F E$AcU;9�u E�n �HL {a R^2}{s^3}+s^2 k+�( aR + n^{8!(s{5N< �e��c lemm�N��2i2AZaiV#�6�Ka��H i�� V�Ad/st.�J� jJ�6�Ԛ�J-�+�B46)��)��*�g;��5� |Җt(~g�(al�� 6ce �,��o͇�6�+ , $kaΥ� entengh�D2_6+� ��,2 �� :��$n�%��9�+6C4-r�,���;.�� idefher�36�*�5in.�.e�+t�=C$�Y"�$<4�R*/c�02A�/"+&�0,� 6/ �s�5se�6A�"j!�=B!��of"H49at �P��G 2\,2�Q��c�� ^3 K��0� ��%P��� y61�\v�-�iY .�!aat �k�K6_�� �IJF1� mpli *�/��F0��* �0& B R �)�.�X"�|�� N&�� ŀ �9 + �9�"� M )�F�E c c�?+c0 �Q\\ZP 6P oHx �]6M5,KM/i��| �}\\ 2�s(j+�) K�K8!� 4/3}͟͠ ��ُ��A�a\]�r �\iQui���aBo� i;/�DY9��u I \25z5)� �a]hNN)Y� � _��  �Q\)^2Rr ��&[�*arrow� 鑑EVH {\u2��I� c�x�C�x�x� e� J�1n'����2y�DI29Ja_ �&�dJ*M like;�#&�� QtR ter�?d�S lso j�J�!\F�&� =GT 3]Twe&M:e��UY"� � �� ���,� Yr + .�Dv_Q^2 m� \Big�  [ f � /3}+a�A�q���_} [L -M  a� &&\q�)F +BQ q0)2jQ�]) a��uC24.f"9 e n ���2o H�8�Lm]. �� $9�$a5i�$,F*�\U"=�V]�P .� \hN|�: = nJ K� n Jլ JUȉ�{_Q\,.�)c�K)c�$ ItMQirZor[�5=/< < o�(ne _�1�u��!be� E8"TS"-�a" �on�/29b� � �C2� � $\{P-J�( R "9��&�)�2"R?a�&��8\7H{ m�r{�_Jy S[Q O]�"�-�ln�eft\| �y`I�$}fɐ\|F�%�!�"LO� !�U#tw�9 ^؀�"K�n��)�]-�*�2 �A�.\Tr \,� �&�t:)��}�I� k �) 61 A& -=&:Leyxa|�Rn�$ ]C)�(v�Z�K0�W\| ��Vay-�-�!Y \chi=\max5w�x^{-5Z�3RkYwRyl���V�2� f �&p Jk S�Z�,B/ &<�Bo� p2U�W l�&�S:?sf�0ŝ8��v�� se24fC(��� � �� � :g �����c�Z� /~ sum'-$}��F���eq V�|^28 1J��A�J�P')A�yv� JzUI".]�J����Ų t &�jK% up3}���]e��_Q��chi\,�6�!�iR�n. e�$NR$uivalentlywQ�a�raB,A $Z.n \|Ű�a/M".a&o 1��V��chi U�i*�p�FBN�! +� +Te�,�\si�' �.��[�c�=�{a&� �c�9$]_+^{\min\\�|�{ [1-c6�5 ?]_+�S�f� He��$[5=��(x\{t , \, 0��0"�6�v��%R1m��8|�Xe��,M>� =G_N�) G_M dH :��G�j $G_Mz E=��c tI9�b9��orX�de'�)*Us~z~3\ Z A^N�)��"R�N \�&=V ~int d�\, doa!j *^2!!^2 =+5-^2B-� Jn ��2�>�u>v& \�=U�- c�E�\|!�_{) }� \|^2&�5u>Z=��*.Q6E67�R(\det 6|VeX �� \a�� ��i\��BM6"�g"�5��noW>��$M-<M$n q`y��(6E)_{nm}=%"�ay� ik_n^*(y m����N f(y -�a�}_j!�N 0"�!ìe�`$M$ �!��"� &�m � 0�(�.�% Y�h$I d��|$nd�`(&�;!�.�f beca�(D �%�WN$x9)in�-C!��1�Y�5#�:$|xF�>>"|�Xs� allC�neq j$GF:,�~2�w��k.�J� |\id{ 2E� �cit(��f + 6fF� (A��:a�Tmen��ed ��*|=)H J|%V?3K!x�^�c�n�E,.�)�>��$C �e aJ�F�JcΈMJ BGs)M4 Qmwo� �U"�y� aAH�I2�] to�� r�I����a y� 1�?$cho �_,aC�/A�:)C> N>� ���� wa6Mt� �"��@�@k �@*�)��Ґap8oA[D� �i% �a$%���o*4��xBz�N+Zz�q�zfze=jz�< s)�m�ZQ.f 1�R�� �#chi�|1x J�iYF5 ��K��8.A cR�[L  4<0mCs�3E X([�g I�5=�i��I�g), C[�,3A�mIVe.4 �W*� Pp2N2� ��g �=�u2� Y-P�- �E1\�.3(!hi6�_� V�(.c�) !��*+� �]�\\� �e�b��-o�c�tE�i )�A�). Z�O�DA�8x(O�y Trac�I�7jqsst}\e9�<�0��asQ 2 :6�< big) FPɦ�"�"�2tyS���e.�Wg �r\-�}f@�=�,:S>*1P2�=:�v�lE�Tft(1+)( 1 p^2-�=�FTLu!�2�&|b�> }"CP�lemtr�?�'f:\R_+N ���2c3"!%t + y$v54)!n"� 2(( R&(�:�)J& �tr� ^~m5n f!4X3�Tr]yfQ^9 *�nB� .P!�_�# 3\pil |p| �J&>z �q9�� *�.!0�%tr�E�6�&&�/[(\pis$ )\N]� D8� !�He�gRie G�tA(V � )�^ mmed["��J�J&�Q . To  H6�nY���j�E@a� �qon�&re $p_i�U ��3Z/� 3�%4p_i"�h1 �o�$p$�#Zi tr1}Q 3]=r<#]2 I�< -�/3 81c2�R �2lF��>�0N�!�Mq f�iq���q�*14I�A��� �\^�qmxV"f�Q18 9\pi60�qiG 1{a> =J!�A֡�����I|WM��h(��R^f�C A�8!�.0tr w"tr5�$D-<OO Y�vBa�k�m� {}��x&� .W�gv_QI� $.�>��_ Fy _0&T >�p 2� \! g%�2�JEp^2en6%E� �)B;8��r͝ >� --� qqZ{����E]�aR���E1��\,.�+ppC6(I��MZnnAC���#uX�}n(1+x)� x$�h7LeH|p�5( �;C�,%1\half-<t)6� YB�i=-:P:&u!*�/R*Mj��)�w A�2Q4i^�i)k z}� � 2;|�(-.�:� M J�:.���920"�p%�)a�� �D1A/gA>� Mk {3}{qc^�A1��)fjU*jvs=Fi E:i g(zN�AfT eR�B�M� �g .�%�>�t ��!�W�x5!���ft[-�] >/4�� � + �{!�A 2 }E�N�� RJ��$��� �)� �Zb}��a���22z���us�*�:c�$��1B�A�>�; Jn2�0^2=�Er!z����tR�2�0X* Big[%���&0>�&J�&��� &&"H,)>r�֍(rr !"QrM��rMrG K secls e�@�J :Ja ��q�sK]?v st�b�n�h�_�C� R<K�+ $a�&&p R=a(��v_0�= 81}\* sF0%V�CM":K28.� s��$K=:,q�/12*x<�ps>0$. ��B�a��3�I* p� bracke��i�%�2�J�K������|c . (ovara`}�97% �nd=K"�-6d Ir�041. N� FձVE�>*��C ^@�} a�ir�3%�8N�4*<$Ff�a&� inBr�{\\A*8MzB2�)V��ork�ed0zR;A6iA{���R&?UgBe�b! #�%� =&�{2)q{��} {A J�)yvvVnw�G2 Ѱ\ln(zw? ��{wH@ $�f*�%,�%!�y� is*��1��Bza+��5�|i��m�U!]e�n~�r� �7)R��%� �2A�\� �xJ�28..C*z� s ]^KJ��Tr��K�e�F��rictly ����e, ��}l>$z5�.�JA�*s<9�3})�'|���F �k�5�b�vNkuCby0% 5e�2�p)��Jx7,�B�q�2t�%d*=(p$�s$�R��f�uٚBwu,Gz$7�QbEO�To�����2s&�a� �it�l���CrZ% �=�M�?s ��6�;��F d 6�6Tu� 2��0 C_!(zz�FI�N* �s�D%�� ]F a�eYd1Sy�5�%f�lF�Ex�=phO���SOI�"$M�9usE� )�o"� ^�3472 {R_"/�6b@ {a}.��"ZU��f@- �1,�fmuN�N���.'sim (�J��i0:�&� $J�� �:]��F�F Altogef!�"Y8a��68 .8Rb)��j*�u �,%-��&� +�XsV���A��< ��)3+U�lr�TU�TIn^�K �+�^W�,:�[} �[,�$2J3�"aF)�&sp�3!��\CZ�K$ $!*�!6u?.P�0d���le>@JS ��EsymmeA� ��w�K�a1 �5 �� �Ms &��no?L!a�[!�R"��ved�=,L lead�^���o?4�shorte4 �� 'orhse�&�JhX*�f"� �k��F �a�dws�fG av?*�Pa�ult�TDy�B&{d R$�%��*oeQvE���rof:�i,]NGl%6�>�'e&�HKq�ߕ&�)Fouri Vq !Ra"� $fs#$%�8;k'y�})=&�G,x\�x) Z ipx}� {M )""�6� �H ��,"+'�!�1mZ�Eha�{1-'}i L^1(�M)\cap L^V �6R>�L �� ��>�(effr} f_R(xk��|y�R$Eh(x-y� h(x) N�JA#f_wr} w_� {���} x�4 dy !i_R(y)\, B��UW&fi�=^s"���@annulusNY%p|�N��� !\} %�U�= 4\p\1If $y"4gy/dMaQ�qM$ po�x$L1� $|y_k-y_l�*2R0 �*k�*%tQG�,z�  -%OA(p5,6O+eS^rMMj-y j�M2@(�]eps) a� -�a %� � >C-lsq�><& f��H�0 �BE, multiplic��"3_!M"�ps:W. �9",?&� ,4W(!\�!)�Hq=��!n~>��;BNc�*4�M�� B$ov+ [�mKiit�+$� Cor.~11.*!���e�< , ei� $w_R\in rK�*�mi�� i2Qi4�yI�mm�4�� &L *;#.Z �H�K݊s��c* %naX&�fC,M}��IE�i�lNI�[- I�mU I��(puA�)>1 + W�/ doa}"P",���li/Tmd _{k}� > J  + up � �m� "�0ham@sqT-0�0W_Y�!o"�snyy} W_Y��)[8\{ k\, : \, y_k�x�:��Y_R\}�(z�a��j���:j1MR�h�"Y=(2;� ��UV .�o.[� ����b:9+ �.$y_j$'���W7sܪ aS�g�GI�a�$ Gat� $J2R+����#i�,'�# h� �1Q�� 2�:�I2 �0� !��Dgy.51�.w[s amon.�ofTl)o� drop}s �$� Şu cN�PUYs $Y�%�aG$����t6#q �� �\ �a���cZ>^  _ N�?"E�r�[�r�vT oab1&oM)$ s?�].Xrv ep�E"�sV!��f� _N^{ r}�'U�O")<%��#9�elJ;s6x7Y��)=�AE g $ � %� 3�aP�c$o��� "�  �!�E+*/�"�/� an6[4AAan� !?6�����(�$n�b7$&T^=iC{[Z!}[�o=�N �9u�_*�[%!�probab�����Xexa�� J�M�9ons�0gZ� � u>�)Z gexp V�U<= ��� �q�J� )��B�6c�>T�l%&�+P5;��e���L0��be, d� ,Gm��2j>t��5xx�"}iE� �G��pre�ga;]+*?xAg!��&�[%�a�a�Mgup oE� 2!�2.��gAj5�$ � 8��jo�aNuaoP��k �j�Y)��mZ$�36�vZm��V� um�:\,Yl\2@N����~j6��/���w��[�� �� rt h��nE�4�t� � � M� t dxl _1m8s.}�B� U� vXF'6 J���A ��*F�v�/:$. *�>KpAI�m(R�n{V� FY>%�� 2�o"dPW )EE�@2J��s*� -�$ }��aT*�J�P6q :r ? Hh_1c [��(c "� )М�*� .�m%�u�M�J Y.!16[M ��� d����s�O�"D��g�baF�ȉlQ�[6�$�,� +_:':&NE= �[����� >4w��0�ۥ�qkc$ ���r f[�i/<v�k�t5�Mg!:a�TjT3ML)�M".�we�j� $0<\d�<�Y0<\�  � e $""0abi thr}"�c= - Ynq �nl) f) M���I� + h^N�-*�Z�defhc�7 >�o z ]�(1-a �i��J�A9� !��"����0rz* "z*!3�(d: ���a "= }D�+� 9�&E' �2F>c!\*�(�m)FM>�9�45._�5�&&�7+ 2=�9| �J:���2�J ��@�'finsuF�6Eq.m? !4&!�Ʉ�)��_����M& e�� S %�&x' � �E�"G >�VQ ��.ς:-i���� UO2�(��<��zF�,�cc!Td=�n 9�ioM�� �ӵ2]G�("h��]\eta:�\+e_ 6smooth�"�rLkJe�RBe� F? D�1 -�~�N�"�!�5 �yg6�def�v�I=[s pN�Z&}�y��$���ps�)��$�dxe�t ��&�"��!=.��$h=/ha"�� a1g�!�rapid}iay�J$k� lingI�c2i�w_R DfilA"0 de� ) satisfix $R%�u(sJ m�intw} \|�|_k�q<D{-4 {s^5} \ \( {��$�C1F> ?�'Z{)c�$s-�aTw{$A������ ����all��3Cj��ek\neq l$, then \begin{equation}\label{normw} \sum_{k=1}^M w_R(x-y_k) \leq \const \frac 1{R s^2} \end{P�u independently of $x$ and $M$. We are also still free to choose the potential $U$ in Lemma~\ref{dyson}. We choose \b6�4 U(x)=\left\{ �,array}{ll} 3�(R^3-R_0^3\right)^{-1} & {\rm for\ } R_0\leq |x|R, \\ 0 &�F�0Y$. \subsecABT{Improved Subadditivit%�EntropyQddssl2} For $\Gamma$ a dens0hmatrix on $\Ff_\upa\otimes $doa$, let =# = \Tr_{#�\Au _? = ,up2,b)�2�cesA�A��ystem $>M�Y@$-particles, resp!hvely. It is well known thatS e) $S[ �]$+s5E�e (see, e.g., \cite[Ineq.~(2.2,13)]{Thirring}, i.e., M�Uom�ineq1} kE<%I]+ doa]J wher)( �i!!�e eB sidi�@defined by taking� trace on�veA-�1L)�6F More2, i!~ gamo�$downarrow$!� otesg(reduced one5�!]g ��)w6Iv&!G29G2;)T\SsFF[F�fO$3]=I�Hh_1}e�(-L \ln  -(1  )\ln %�)ED0given as in (�5efss})�2G5,18.5.I. Not!�at both B�1})�� T2re AplitAify�i)�Tgrand-canonical Gibbs 2lxaj4a non-interactA6iu. �8goto need%�followrEu mentMyI�^ofqqa�s proof�),in iaS��.~%�sslow}bgen�q�I��"8] + \intsum dX^a��<n( )�H1upa^{  }]\,B�� !9 YS$:`\,_ = 1$,AcJ' �1\2�=. $. Hence,��con\-caQ�p@ ]$, A�uA�yM�-*)A stronger����usual >_�yAKy D1}). The last term���Re� �1of 2.x$average[of$��t for fixe!7�?��s, ��as�g ��d��� statei>e�d �� all!YfigurE��Q >a�./8A Priori Bounds1One-P�F DMqyapse} I!�isa��0 we will show!��bjcev5$�im)+U�A�re cl� o�cor��ond��$expression> B�*%2 id�� )t͏$ ��A�?,m has a vari%kal hur!n Pp^L&B.� true+@ $P^L(\beta,\mu)$!� the �dA i� an approx� $ maximizer 4U fun alM�a:n a sens� bCd7Dcise below. We calaLch a bA{{\it a pE(} v T:�Apl�nto four%ds. In AM~1,Q derivegmLsort �Led. a �EPnot�uniforma�!1fugac�U,$z$, however��6$be uselessE$very large1 (whenilR �5�its gr%E). / >owe nus�differ��method�# obta)�imilar ڭmparing �e�w�o.�1(Z�!� do t!�i-t3. BeforD%���^ �of-� to c�-eZf ��%�ary��o ons (%�2). SomEWcule.s a� easi�� o do P periodic JOa�n ',Dirichlet, h�S�usefuln!�EHis � . Finally�^a umm�-e� ul�%9] 2 on 1D4z��(ion{Generalu)� sss1} Us��!kfac�,at $v\geq 0$�caG fer from *Y�7 ��� �  eqs 8ay}\nonumber \!N -L^3 2� ' &�& *� �ft[� 0 -\Delta- \mu� ��o� ] - �1�� *L (]�&lB�2} x^� � B�. �F�$ & �Z] 9)\, .� apr1"_-v MHi�(e first lin��%�Z 6ZK�I�ed)���$ $-\half !�P_0:) becaa�of� onepf� same���n�A.���, but���v a:� e&� ,eBA�.�opV �.>Qj�$2�i�an uppe�"�@RH, �Md1� previous m�� � is yields��Nl ast *@FW"& )�W is�e��v(d to get in���Mf $a^B���%�!�&l lemma��O!�M�-� h� $self-adjoi� perator�pa Hilbert space $\Hh$, such �z $e^{-h}� C class��oIfermib2� :� (* a� L .����$0*z  1$E�)" �#u%x1(eh} \Ecal_hi�� \, h!so -.6NI h�h=(1+e^h�%]4min� Ez $f(h)=2t_h]=-\Tw7+)U)$AIen,e�any1QbGlemapr>��� v + 2\,�� (�- _h)^Bb�n ^= o2fp +�i2�r{��|N� �d |^2} &\TB�%+B�)x ���ᓭ�A�.���e  impli� in� i�rda:g\to�ma_h$]� nor� S]Ama]6!o$. Eq.~�),}) x! verg�inqj-Schmidt ^��B� K��!�E��TEj�� e cop5md��l<{wehrl3,S79} or ��concl})ɡ)�h�}DwriJ3:h-!# U \, gI�,!wA�>� B� >:=CaH%�e�A&\l _h + "�)&�2_h)JD��b $g$ ��&g re en#(�$�� x,y�� 1$)B���Grep�x,y)=�4_y^x dz\, (x-z� eft(mfzup{1-z}iRN�� A�(1/z+1/(1-z)�)4$A��nd� � lower� $g�;2(x-y)^22�Klein'Aqa�lity �MT2.1,76�, $�>� g\, I3��nd i%})�s.&� � B�1/ze1/�{!�}  (|x-y|+y)!#� !�B!4i!�)=6^�bb1�b-DZ--N}{ w@} = 2 \sup_{0� - C a\ �^��a2sXD(ant $C>2\pi��#��F��u2noA 6i� A  C)�A �JWU(.��instead&k Qݽgiqe� wayB� � tresz� ��{E�|�� A݂�M�*� �<6� 0} a<q 2=B rB By u%E� x�Xmap $x\mapsto x^2/(x+1)�: aA�e� \�6� trin������!�M�$,�%s)u V�=�T n�%fΙ)LL�8 \sqrt{aV���} ��ft( 1+ %4J&�f��B�N"us� :[b��jKm2 -� bc�Y6��g� ���_:Ctheir H|t�� ���he� 4 . ISir"��which"k�&� next��9. =b b2two pos�"%wR"si" $P/a proj��D, finite rank� $set $Q=1-P2I$\|��0cdot \|_p = (n[4\, |^p])^{1/p}� 0 ! Sch�� $p$-! �� ��q^�< \|a-b\|_1 \!\!&�1& \|(a-b)P�Ay |a Q(+ \|b \\ 24P\|_2U2-a7�2} \|QaG + \|�  \|Qb"�� � � 6!�A:b&+%Y"$\ ��� + \, � |$.� �N�� &=&�N\, aQ]$��[ bQ + V Pi�d)+ &� �2|%-:AF���uD!�2/tha*Q -3=�9��'>pEE&+& 2?'ig(BB �|��E�!�\ p"W \! \�%ɿ�bi\%\ ��%`5�g ap"c .'� $a� 2��� $b ɺah�s ��" �U�  We c�(�toA�B�o���o�$XHh_1=L^2(\Lambda_L;\C)$�{�%�K� ^{2/3}$W (ome $K>0$. �R,we�$mu'\� ma_0ɕ�> �>}!&� ^aa�13A9:x)Mt^2m:, P w,frac {L^3}{(9 )^{3}}m" dpX" \theta( K �) - p^2"��8 4K^{3/2}}{6\pi^��~)&� ���v���a&=� � , Qb � &� %� } �� 6�m%2/!�` z� A�(x� :� ){�) <q !-4 -�a} )�Z!�e�� a��y�dB�S\�'discu!� l secl3� � ca"�-� H 7 is  A@�i exponentig � � 2� ifaq�K=(&� �\n� � e] \nu>��lyQzi��]#1/z$. "� Ӊ2.� K A| ��)--d�: Schwarz ����M�ge#�t%�i���% 5 ��x �a6�y6���3�� \|� 2w�-�� q C_\nu.�A� ("o {1/3I� 4-3\vu/8A���E�M��$ +U� ��!��Ws� $~n �.o r,nu$b":tC� % )un:~ V ssU ��!�"-U#�!b� veni�!�.a�#@6A$"�� 0$�raZ2\per$,  v)"�a[I}� 8:�B�, $�b!*no"� Laplaci!�#J!Icary !p�!}!a!cub��$.*i* ���a �l�!)�1*� 7.�%C0E� Qagc0�t�8rmodynamic limi�!�#$��be seG+)�s. Si � quada�ca�m dom�V,�$$ is inclu�: {~5 �� �usU�&trial6�:+$� j�.�"�"�1��.�"c�&�z^�A}>ABF( \lim_{L\to�0}ɛ 1�[�fa�i��G%E�)�J&!� )=0 C 6Tn*�� toge�i i��2?�S [);'E^ $\muf�Zmo��<0�E�A� ե4= R�>�Ai~:�& f�&��3} g "� )��%"�y� Q�I *��m'n$R!#2�$N&ws lika�ln (z)$��`��.  &[)s�*aulow-tem> �(e�G  Q'�(aches.�&.,��l �'A*����.�#i\iFk  sea ��& .rP, namely $P_\mu\equiv� \mu+�0��0a�#)@&�&"�.�#2�K1�]! @3B�apq : 1/9}$.�3!>Aof)r!�,Pr!FQ> NN�� !#�& eparT,�R6starti|y�_!@Q�.� $Q!2Uez $e!5)=� �4� &"�( negative �&s $r,s�� � A any "�!Ň�4�vq�� �.��B�&:.�+r � - s ��&maY nD' &'2�!~B, Y?-re+s b\ &&= %.-r�! +s) - s�p>�@ �����- t�.� %���[ #-r)�-{) �big] +� ig[ /v�3\\ !��r + U�AL�ma6(1- r amma�'� 44&b1"�0E0E̩�2^ (Ql�7�0D$jW~=% %�>:C�%]"��!\!��7� ft[ -�825 [\mu-r]_+^{5+ 425�  - r 4E9 & �&d ��� 1{8� F)� 2} r^��1Za�$r--��,�u�9E� �<)=FH!?Q%)A�J�\m�s^� ft(1�$s��%� 2H:j" Now:� r= 4% ](-1/2}L^{-3}a�I"ma)$ AY$s=���A�6�]g5"e�.cq�%pEXa�^.� �� [ HEm� �(]^2 -o(L^3e�qErefQ )��!���e2p . OiZj; h+"c��1$r= nd�:>�s=M�{)W}{ -Uu� x}{9ځ:%!�3%�1}�!�V?�%�3}S;�6�a s�%&�d B�y!6a}M�~��.em{EL� �-�:�5�.�'pi: F�Q�]1�2�S,A�n ��^�- �.*Z)ma]I� #E4.�/23��'#^iJ�W�1"�,Rm !���3- �= �-�W!C"I��J�+�!." M� �to� 2;�� *$�above.� � ��1^�>%]$.��  a ��:e�Q5B Z@a  $>� G9� �I)Rx �'p<�� s�!c�(x� V�in &� �1��-�-�ref6CI.� 9B �( 450}i� g6`jn#� �� ����6�.����ֹ2}�j�#�41s5�}!�o(1N-By repea�i�3gument'�I�)T!5a� n �e!�a}�7 .�� 6� � 1+x�3}� w�B)�3� 1� mult�09���!- {!:o !���n� �kR*)�ͬ:��5]�,1+ݷ��M��[�z(1y �xVz�}| A�.�2�U5dclaimb:labdeVV��-2{3���!�.�E�)N�!$ 1 )�Q�B�!�J, . To se�D,�3�I+ �.��5!o.S��-����.�Q�eu "� FD a�[.bwF`(u "t -U1j)^3%D��_{p^2�!9 '9^ �("p!~1c6d`\!��>s�( t76t�!� zn)).o�Er5G97"q� E�E� ǁ7)�x)��<�5int�l i&�5bFY&�ڥc}3-T.�z-R0^)Rp�%v� �A� e�N7 -} % z-1}_Y �a�j:F@I<� way��e�(on�,5�K�!Y�u�+1z9Vz.^_�^i ) p^3!.�"1 v�M�1{1-/ANM�J�-�:r�<tͪ��)�assum`1s laJEl !2��8�V* Z� "!�2 mean)'�y?6b�@rge�(�06�456-�=k%Be�d(Fb� �Ʊ�cp* � ��**0!Jv*�h�!a*�!�mõ . \|��-�#1 &a�|�)ma-1)+)a )� \\ . <0! �% \ D* o�W2}}% Z2��>MZ� -F ma)P!<] N�L `"[ 9 � iS 'e��-2 �B=M>#8}� Ip*(" n��q �P��}  �, >J9��1� K5"(��1}��7"$ (� *ley*)�combin���� *$m "� 451}.6$a"�458o i P=�$~ �mZ�  "a a�J�NR�b� supp ��� a� \| ��>�i�eA�"CNb�1/6a�UdMI�A*!��G1�"�� ��"��� . It re�T1�3%���_0�B% �uI_0� .�_0" Bb �D� *i�=|m<�nFt ��1�R��(�&�����%�� {&9 -p^2�#1+>�}�)I0p^2c}/ }�:EsP-�]���*)MT�%����n����+�) ��-kݿ �%< /22�"C8-� qG�2�]�is�"s;?�#�K�97�;99��InI�R� V�a�9B red �M=O%*j>is actuL%*y  $:f�$�,� �> negligibl�9mpan��4 rrorf� e�F7r�%.��9P)& CS.NCF sss4} L ,ize�NYL3�12= t\ %a�.N �P�2 satisfy��3�)!:#� I�F^� �9v&�� ��_J ��%�-U Dig:��E6-\vu�'�:��$\vR'!P��%Pn $v$- $C$ � )3B�G ' Her�5��{�SperA/4I of�O�a, of,� tNH@ s (aGAver�H&w m��� chem�Npo�5al�$g% B%k%�A c>% As�idGtI���rkI��M"��dJular,[3b�Q! �dilute�-" J1r!6Ms c* KuA%�{=O �les�%i �turn,� v)�.& �thm,in Corollary�NC1} a wo!��ethaa� �|Ga�W R"AI�W�1 {Put�Things T!$�Ql�QW!�w�B�I%2EM�!e"���9nS&T �Ko)D desi�9*�*QuA��Theorem)T1�Q"Bh^\chi�2!�2"� F)h4defhchi}). It6� "fi7P), ��1})v "!��@2%��' :Cj &q � �,��.�9�.!a \d+H\,��Vs/}[�-A ])]U P_{ %��uH )IJzH�V�]�Dy6�Sn� C421- �) kappa)�2� &Q6���[ W_{,}�"&; � �tE��=�� �Hw��AY�W� ymmec:���NeSJ o exchang^ �>+P� >�O,�=�p}Q$�5�,Tn���E@�fdo2 $. FS 2SF�']mu@ � ����^]"�(�7(Mb�=�V%�)��/a�F "�U-� %�%:B=0�B< �?i><�}Hb=pe�(e|Y�*�Z�:i �o�h J�W�2already�fAcNi.A��.7W�����A�*�Z��$iL.!v -99�+N�:�F beenB� �+�#OcTK translE� inv�Q�8 �q�-�a�N-*K by $�!>1�D�usB)�)Aiint�8=�"5p��� as[0,L]� dx \,��(xN��k�X2�b|�(� +?E �Q� :�,bUaa�JEu`1 ea jF $Y�=W_+-W_-�Y +�Oe"�2:-�o wy}) �QH UT $T�"�(onrG - $w_R��(e � 8.Mointw})�L2 <�-BB�-(x6��� {a RlI^s� |iN|J��n$"=M61�)afspin �[�U].�Z� F��DtA.aEA�doN�!T�:!N2w:uv$6�������� N eg.vaB|i�.k ��PdA����^>�� HBcM"f] ��Y U =�&n� ^:+A:R;sXb\{ k\, :�x^Z_k!�0 \widetilde IC_R\}} WA`) a(t_.�$\, U(x-x_kKg\\R :�% a � �|Jn �(tE�#$2Na#� �G ��&%0 �C� $Rl|2� Y�e�*"J�w .e.ţy3 $1$I�� wh�Xdi@3ce��nea$0 neighbor amo V $x_l%NJ�$l?dk�2 big" [$2R� #�/� squ�.bracket���2�e"4O n a�$R$�d!�2Z8box*�he3 betw�$Qj�^X>�%f=��D2N�B��Q�$MPL^2/R^2�WF�@RՍ� Z1.f%Nbin�� I�I�0A� (2R)We�k=�eI�1{� _k^�*"�� ��%2�9�7 U�!+�PM� U�!� ���st.���E2�T ��!�"��uLBx�{�_fra�!A�*q c`3m_)*L�mRc� ho�S�'anti-&H tensor�duc� bigwedgea !>R^3_$� i�`Xei�`0Thm.~5]{LYau}�2�ccE�d �&f8a�t2�c�48a�28Da�FUvmINJ� Is���!1 + c Qw�#�Zu'�c�B��j"�.s volvI Akinetic ,YgyQ7cP li�a Vpri�2choic��E< ��g . ~&&t,I-= % a c"~ � t"TL��>�  $&7Jr�{�"F sS^LrBPN7�#-\sYle}>� -&/�M�!�e2��?�� ��/� �/- � �P��%T��-\�1��&*�1��,�S-~K&0X�{: +a�f��� ;�>)i�!&'i,\,5i� �\} FQigb�<6 +]9? [ IJ�,�=^�A�$��O�,�*2X�:�? is eNQl�F,\Upsilon(p)=L %�)�M(!�%�)9$(p)^2)$ (c��i "') C*m'J7�7nfV�9-�YŵI��k"=I��_{�3�$p%�*�%�N�c"�N9  ,. mclaf/)��� �<�qco� �a<_s oR{anal}{f�fs.� u$ b 7 real&�S�oraof)�,length $\ellg ith � d� u(x�=.e)�xi_{y,kQ=u('S e^{ikx}$.Rc�=  |+ \rangle\l |�:�D $!�x.�lresolu��ident -$��2int d dyIQb� f� $xXL -x!�x���;av�7m�7e(�;q��"� �i62ZF�N. Mm�A 8"l0,'- �� ���rho(y,k)�.n�D+�Ia�!I�$�1-6��nijI \�:�3!�9� �maB�6�R�3O�Q�!b�#{ma=jC�I� hat)u(k)F?adx'��%�(x,x'�,xp(ik(x'-x))�  Fourbl]A�aI�can�F��\,>M�\�F�[ :�pN�M"ja  4. E�3 .�Bs�.P��kA QU=U�"v!e~qtG3+qB�k)� u(q)|�١0 � "d' �1-�kvV0!�I��#co6� լ�� Hessian�f$\�ial_i j �� 2 C$��a �i�% { D$ (�@A'�n �k�<met=s$y="�!�gA�chi})IQ�LT�e�(!ee,�$+ q \nabla + C q-InserM���_,1"[Vcoh})3 ��q�E�!�q � !�-�67si8$u�Cat*�TbeũO&B��fi]V[6!H}��]����\� (. �T �a�|)$��|^2d )�(:� B+� e����%NO��C' �n ^{-2*xK..'� I0���2$.� Q� )�= co%'��� &&1Om &mPi� x 6t>U C r�Ny\m 'C25r�YBm \n=&} y"�  ]~[��� bZ �} M�47,.� x .���0$��;$� �c�!6�  $L+2)� IkJnG� SndDeac3R�m y$ (�(is XI(=kɊ2#06� IQ��C�2R90- ( �)!�I@{1�� .�!b%��& 1$I/�Ab ��"+ J Divi�j� L^3�u��2!8tZ e_"BF$ we a:�*T2s�M $|p|��1/s��|M1�2��at� �$�[e�G�G�%�K���p � }�~ ��m K\'2��M_{� �28R���}} ~���K7{2zB��N�Y�R{�0a1���]Y�R%3�B� 1{(1-2Q��}t(7/2u  s�mu)�?t- w&�?dI�(4,~0/�� ��!��&2x ordo evalu�A��M�l. Se>5Cby K scalingJ�"9T��a�(�R .=��6  1 d���ing"�:&` -R�N��-&*!�1�V� >\pi2K�K 7�Z866�~8��je33��)Bq�anF�!����=EE^�33-:UJ� &R %� &\"Os!h~ =  H c:�012���� ?6�c,8�a_.)#�_ �.)aM{6E}{!�2� �?3}H(BN�ͥ�K�is 6Ol&L1Fz$�� awad A(A�l�& argu&j. ,af�347})).*E�-�Ͱ=J v<9:&2\nu`Z , wep �h�b�so�$a�$ ��i �� ��W�# &��"L%q��aci2e.�W�6?$6�$,=P$V�W "%� a�Y �ch�,%x ��B�*�`Fu.V��6:fa 1 - �(Jkn?q]��>MAGh"$�Xeh�V(z)Y`)7 nD31� 0 sQ!��h� & 4!fB_. \"'/roo8�/ies�.C1}� � ��CP*�{fi)z M%v�K/�f=N[��[mEB��*ZPc{ngJ@0)� 5m�1ingred�Wi65v*�E!  � �1D�2TB2 � cor1� ��-LEE +|&: }+��)-)} f+�j8^2lI thm1a!s��*�e*�2�(6monoton� crea 'a�U�� �t9� I rhog_2��7��M{6_�2� }�" "� � "� #mv.AW��n alph#("lB�7�`�.s9�H��%�g+ O.--  Am"xF,TJTbCjM6%�f���9��?-� I}�R=�m�M�.z�="�[(1+ �)�>,.� <� �n� ��BFB�E6�:�!4[�ZnG �[?stE$""B� IAIb�1���2�au �"F!�(K�B=�2�N{s.)k >p.a,�)F6.q�3 �m3i1:ies�jB�1�or1� F]� =o0! �uѯ�)�R�% &C_I9Ųt�b4 �� v_ A2 ,' �.V$���ed^�~!�%B 4 >AjF(&%F.\2� ��BR�J�Proce6alo�same 0Js��"< !�1& <2z5� �p��es�4&%7. Nex/n� eB#2}D%G! l\�f�orho)=ra�[�  - �)]h�eˍ |%per� t volume� fo"cq^t�.ed atQ+hata$�enRvSM $.z�鎒�v}�55� l�W})՞$F�u7fySZ2;K.w23 f�^-337� � id1"mZgaA9e6?chievpp{mu�Ed�m5Fb�yE��_0){"d we immed'ly"+0*� B �slbf} 22[��q6.:A ":6gR &�^2�*�,���[�e��ɷ�.��k^6� �*<5d"  od.o_0Iq� �9 �Oq+!y)�+T|}aB�m!�=�� �% make1> "����n:�1$A�!c� "�,�Y _0$. Supp�-�^-a�<2 8 n�7 e- � ic@w�E;u 5�&� �9EJ2O_0yPv.=_0�+~all��͢!Hhis$.>� 2�3�(.^1^�in/� �6�}�2��fth Kѱ� �j���, Y�dacedJ�F~�N�} mO"��r� >P�{M,%R)A�n2�l6�2� h0hf !S"�E0&i .�6^ B[ _0V] ʇ rh5�"�� :�("Ioos' �(D!��a���'"��hd�|y $\bar ���6"&� u��U�9. Y :� work"�` N�K> H$. On:3 i�B�! v�a�, u�ԋ--�� �T!=�Tz���e:�i�x� �0$�#Q5F�Md the1:���,|�\\65` }� �%6�G=6<U��<H"�xth����FcR� ^�the2}2lI:�-:p-y�_0*]6{!RP'Z5.Q (�E�% �5�4 (E2066�["�B���=})�9�� * 6� � # VR �&aj m�%U)6� e1}) A�N�A. on 6 $f &���=@��"� �� � )�ay�O�PQWe�YWg � t,men^N�  "� *{Acy� ledg2s�%Xa pleaX9. ��applic�Lq ��fs %CoulombA��E ons}ZB%:Math.-K%F!D977--997�942� hamm!;H.-W.\ H, R%�Furj4hl->Effecvef��th%Ja_F� �}, Nucl�A �78�2� 294 (20006�uang} K� ,, C.N.\ Yang �-�-Me�B�G�%� Body��blec�]u I��o�z:yE4105}, 767--775!9572�lee} TEcLəB�F�in�c��&d a.ist�"FB �$1119--1120J�Lenz} !� -94Die Wellenfunk�un)�dGeschwindigkeitsverteilung�F ��rtetena�e�Z1�Ao�5At778--789�29S�fi�5M1 E.H.\��, a> Loss �Analysib$2^ J8nd}$ ed., Amer.M�Soc.,!�t�[A R.I.ER6���2tRa�eip�� A S�S"���0of"��, p��s*ParXiv:math-ph/0412009�U�LSSrvJ6-��;E .;� Low� �Lmk�?n�80:�Y00} .~: ��Yngvaso�� Boso(n%�a� p: A* o�Fj��!+��01��!>.�:� a DiQLTwo-Dimؗo�J.!�t�$JI� 8bf{103}, 509--5��20e�.�robin\D.��R =��/&DPrer�iI��!�%�a6TSpi� Lectn�r� !`ics�WVol. ��:�ru�C} fR �R� . Rii)%FRe&���World Sc� ific�19�1�BE�B. Simu�T�~E�A�*C<}, Cambridge Uni�N��%&f7fgTp��0 �Lehrb��&fe��sc�D %2k 4},9Wa6�w��  W ]Th)�s�ut�ma� C}c�of 2C�cŇRepF� 10a�5� 63�76a�St:� doc{b } �%%\0class{amsprocZ ) ,conm-p-l} %.�Hf\fs{\footnotesize}!4 $\def\sms{\�[Yef\ns{\�Hal:/Mf\ls{\l�[ 0Ls{\L Va LS{\LARGE�@newcommand{\id}{\��op�fid�'l;us} 2+a:+af+car:-\nVZ diag6�^/Mt6- Multb-F�P60 .^!scd${% }}6�%� emAE�O}{M�}[!]2'lemma}[ 6]{�Z-� p��?on*Pr \rpstyle-��12n&�4I2-example*E 2'xc.� Exer�r}:�remark6: �R%d�� .@G{$ ��U�$abs}[1]{\l� #1\rap Bl�boxf�Aʊo;�gur�[$to avoid r 9��s# %*�̢ phic�Qp!X:G�*is q�� .Lb�$box}[2]{% �6box{\c&(nwidth}{\ce �"0% Set fboxsep 0 s��!eR% ���nz matcae %3)m�  mor�=os��1tv<{\ n}{0pt}% {\raise�[#2]{\h�0{#1}}}% }% !l %Subj-��:�lAlgebra;��re�# ey;�;��5cs %MSCI17B10\ B3765  480, 81R50, 33D33D 12}��1�e=by Ono;nd)�aFAv,al Research,aK\nt No.\ RFBR-02-01-00668��TINTAS-OPEN-03-51-3350.!� subjEU[]{Prim!�%�;/1M#(6W35} \copy��{2005}{)i�?"�AwSocietym$keywords{R6j���y� E �2�F8, Clebsch-Gorda� effi� s,�W1ai �Jabs|L(t} A brief \�ew!�a�eQ��?or!i Lie qF es (d%TsupF�e�m ��&ir"O|ogs) is�; . A histo�G disc�ay Y�"�0st *d �ke{a�eda� \ewi���%{Intr,GžPIn 1964 P.-O.~L\"owdiG {L} Po��R nf*l� � %�fRGion&x!J!l=>`4athfrak{sl}_2( bb C�Later l:ex uf>ula.NF��'r�@� for 7�e-d*- )W.�s qBAS2,AST1 3� %%T1}--,e8E��6 )TYinJ�0affine Kac-Mo?j\ L� ���-Yir �D($q$-de\-for\-med)Q|A5,K�XAtQE!N FNqW" p�,ful|u��l#!ls7HmV+pr� �E���i�,#  �eLa��)Zfy irr[_ modu�to deZ8� them�$sub ! (�~��z�e~�ux of Verma 0)Yrqcri�=�(%�)5�(�6_MonnectedN1A��A�_a:=ma� M r� � bas�Z61�he Gelf��Tseo's typ�]% velop�detai�I)m�6A c�A!� v"1O8of Wigner-RacahOAusn;���!} act %a&Ju�M�seQA�0s�yA%p�?es�Z so ob��@�K aperW"�2ݎ�� ��e� oV �� b�}~,�&i��:��Z�.-�. . �R�Rtor6%?-pp��1%G�\ab),<$T' its 6_#a,'ar3�V/*.e. $g\w�T(gIM$(g\in G �#$eq'ar��sM A(in S&�a 60_1g_2)=T(g_1)2��:�� D �� �8Hop{Lin}\{T(G)v\}=V$E��non6Hvector $v\in V$. An2Z:v(IRd1N"b� ��s� index $\l���4T^'��})5A��� $V$, or�m���m: $(6> )=(t4 _{ijTX)$ $(i,j=1,2,\ldots, n)~2� $n!*ao ��a�2�..Ki�4ll-��2a�u�F &�P���(m_{A G}A J�[ fg�/6 �J{ F���m� p $GM�~they MR (#JAppraCHF 9B�P_{kl�'}&=&i"_1�-�'� lta_{jk} ! 9�4�/4fg2} \\[7pt] ('j`,})^*&=&P_{ji,�LfgJ�7)�^*%�H,�t2�conju���6a9bIa6=!He�modifi� ���z=4�.B4=\int�Lts~� dg~.�FR���e|#$G=SO(34MԶSU(2)�c�\R�mm'}^{j �_{}\, T(N!,N ��)\,D^j_0V sin1 \,d A \, d I~,Cfg 6�-� >2)nA� Eule�agl�, nd $v�%�9� $D$-�}(.M�A��;�� j:=P�jjL!��Fh= �m1�0the highest w�V t $j�T��6�(;6�i�:x rms!a� ) or4})�z>G ��a�" ��b$ aո.�IRs $Jt$|B�y�]�%!2L�' $g$-i/^t � $dg�4:@n arbitr2KeZ thesR p% s l� to sۮala�'s(�skip &� -ShapiroJ� �1�>ang![moum\�J }�&>% � 2� o}i�$\simeqM� u}i��ene��d�!�tN5�( !$ors) $J_{+�� -?� 0.�+ ng ronN��{�Lrcl} [J_0,J_{\pm}] &z= =& \pm ,\qMG.{+}0-}]=2<�� +^*eF mp}~ C ID\;\; J_0^*\,=\,J_0��l:�� � �B��Casimir12 $� C}_2$A�!Sn� � sZ�B/ TJ}^2$�F n byJ�~\,\�v\,= �c?�ST2}\Bigl(J_+^{}J_-^{} +   r)+!2 =.{}({}+1)~��ls�:6T-�9?[J_i~�]b2�B��) \{|jm�. r>\} !gc"F� basi] S �I�-IRH$s���%e ]_$j��ave��8$I�te" i*�� D$m$ ($m=-j, -j+1,\� j^ � "s�%dharmon( $�%� Y_m^j$ʬ{ ��,s ��eU s&acihj(j+1),�J J_0\;=\;m!� a]pm}W\5A$(j\mp m)(ja�m+1)} \;0pm1)�~"�Fl�nE@fz s=>"�4"  YCN�0bigr>=F_{\!m;� ,j}|jj � lsZ(F�:M \!= )�7(j+m)!�Ej)!(j- }�|{- -m}%z\ a� l(\!Pj;mh ,j}\!:=(�)^*�g+gBigr)" ls6B�A�$5"�:h)��PF�7^{9U=2�7Bu�)ob;� >�R P^j�Le6�, (\ref� ),m,4�$n.�P^j�� P^jJ)�}0�8 (P^j)�P^j.08B� AnCPocis�polynom^=���j�TaN$,�t0%v*� u"�en+�n:NaM M2(!��-*$U(��/?� 6�I�6� ��on�] . ``No-g�ex":�%No� triv!s*W!��!Ab6=19�%�P6�� ls9B�&exists� R�I�~a!`que.�� ͈�S� �26-Z � $P��0$}.\,\� {~A-�l9"`&�,Ei�0%>~B&�}�  ``��n6�g})�"aU\Q>�2g}qTno�Cd�%ors.}"� ua��!� �y�%(^j$ doe�/%�f$!�i��u�e-{ } �1�An.^t�o=Yiansme�*a�um�^ata �Ls;$ost physicA5df,��ij40 yeagɨSwedish8ej sst 6�2  Per-Olov 0 � bor� 1916A�Uppsala,h�6a�d�in � � http://\�,break[0]www.Z- �ry-�.com/L51.htm).}2��q bably did5e�2z, publDC���in%�journali�s'\,Mod.\,� .} \v�{L}*ND&W��eTJ� ��0:=\,\prod_{j'�Rj��{"�-j'(j'{�.�12�6� At"� {�I�a���&�.Y(wsi_{m=�b� &leig��ca!M��I�J� J_0\ Sɒm2�F�Due� �l,es �[ orm&��s >h A�� poss�5 s" m�� $m$�9�expanph"s:2H�w[Vid^ multipfHea� se.}Ff1 ��d j'}CA }|j'1 .� @6�aRi2.~FmAn)�=jrC_j"% 2�F� ފ we�!;=$YIQ��lA�)R!� f�&�ls1F�Bp[J_{0� ,\�� : = *F 1F) cJ� bA��w .8��jl7�a˭n M��1�zOYp!-�"D $m=�*f8a�-O�)O�hFS_  wSpAfsJl�eUx2ed� �7E���Ked�u�(� z�y%a�J�Au�I� n\ge��T -1)^n(2� !}{n! n+1)!}\, �n�n2�F� 9�� l���19F$anY�, J.~��SUSA, N ��J��c3��\��Sh6�5d: ``�e5 orge��'al�I�6Ma��@%t�.�14})15�54 �� F�ansatz��C_n(j)� -5�u"&� 17B� ���$��=.�~��wre��!�AGula�6}�+��remov� 6j@B��w�L(� $j\e�aZ�5.�n�P�f�A�4}\; \varphi_{nH6(.S8&�>4k q��k�kS +k+1S16'&$ �G �$P� *u FW!. ��,�mrK�FS0}�j,mŤ,*<.�2F�ZFXP>Y W.�"�ls2F&�FD%! "� be�Eo6S "� a it '�!s�$ext�0��� n� = us� "nA��_E. Co%aME�,al Taylor se" F M�,k�7 C_{nfJ�A,�k\���2F��.?�o� 1��� Carts%l^*� �u:'ach ��rb~ �atup�+ $N�"F�( %%% |n-kc<ދ,  N\.��F�%�%�$c�A%�� �w�TU.m7b!��G"� _^u'^ormal )�1� &O" ZY�$ n as&��@-�g�{"t ��41 }-�'ONNb �J�M�U�}�R�SOs .� ^icowsV�. C..}9�rri�$�2��hoA�t.E2� �]edJ x_1:H iha\+^k"2 x_2!�e}2�F� T0��� pisU &; "�la�)Fx_1x_2 ��goZ .�2F� mBC� L�"B%�J_[K�m�f�6A��liz�`uC�4�BJ�1� 18}).A�Ik(��V��\-' ��"� �)a.b&�4I ! s��R�,�7nUu Z� L� �tr��n�+%:� !Gor �!$t H*���3)$ (uM�^0 $ is g� by 9T s $e_{ik}�#k�##!���n�[<j� e�"� �"jk} l}�G _{ilkj}M3 "j}� 2wF 1�c�o� �q� ż$P. �Pu�_i,m_i�}_{i},m}(e_{11}�2233a�1}^{n_1�3 2 23 1 m_1} I3}^{m %2 ����Fj a�hF�eY͙D" )5^{}.� Pe_$\,0� (i�b�]�qA;Y �_(23},\;e_{32 22}-3NM�"ٙ'23}]�' ��� rac{\N�e_`)����n3}^n~,�z3&r �O%%>LF�.�S�.� >�2*+*��&ls3&� �Si�e$= 3}P_!=?�&�K^��`"  $P:� a�J& P� an%jP _{1},n_{23�-n�!�{ �n_1 � n_m` 偷�3�+�đ+�M~)Ao�EA�%�P2�/ �Pi��iiua��K/C�vFias� d. Hk� '�v���Vh��.hare r �*�e� n�T �?�\T}��e1o�*rq�� (�"�J�)�q��#�(% �� I 2�12�-A�(11e�22}�- r@Y���B �A� $P:=��P_�-!l(. A�%� �! ����n=r)JrR� ^�ulaS ����P ��q��U�Z� Jq��,�ii%�jj�-�n nZ 3n <$:�O�N�*+k+j-<����&� �ItE����ie\-m�d�9lOA�i87b�'B]M�q :\���~�6. &G*EF��M�*�"M2��g#'aAUit~w��"�+��7 be� �!ve root�. A� liz9%"M�*� 5&�Y ls37� %" �faUm�*�}`�5&/ noj/n�a��,���>�"�$"MA�sa['�zD�i�]��f ��os9(( )�)%7 $�.\}'aa_ !+\!�.~2}.\ino>��written �%�� Hen" T"g]h'.�%� (i)}Hb<um:��� ��|~9"s� ф�n (io��;8#�;E��7$ � B��;��M�8]���� (!{)X}BY��9� for j: Kac-�:ŝ�EvAÅd>J�@�1)!T4,T5,T7�\� 2$�med�v�A�U� �,symbol $\vecb� \pmI��&h_{�"C�-Weyl)o�n��Vg "� ٗ��$Y��P�my]=2w&� ep&g J�<B9em1�R�/e.�P=�z=�(\forall�P2b��P^{2}=��abel{ep&� }ha��uni�&�6"#'��M�iJ� _{q}>�A�HM&�rm1%� }� p1 �j"}\��P.A&?epFX � E�&� ?Te"E�)�H*�169^{}] �W0�#� {n�qn"r)�,n9e_=�\,e#. m*` epF� Mg9BRe=%V"s5�] 2� +( U�4+�1}{2}�k>r>�epF a#�\ź�uH�-i�N3ll6�s�u<?3nF S s 5--8z �li�9��s6*; M�F � �.�J�*��./ n#=8 �B*"nD�T}�i0_i�%.m0!0$ 4�wo�zs (2�0�"wo�4 �N{�)VspiZ%_i.s+n �1m_7/|j_2m_2�f uncoup+6(� or) �%Pl!"&/� $j_1\X�j�2��:h2) "&� !�E��!�RR �dr`�A"�L $|j_1j_2\!:\!j_3m_3 ���0�� alled �o*n�B��1<'�ag� embed�>|<>�^�Ѕan�en� ġ�ermIC5qoneJ��l^��� m_1,��30(j)�,)�|=,)!rQU 4Y��cJ�;��>�7$Zr{��-�np (CGCv"Y$6= CGCbe�B&�o��^B:��UC)=�+��)A|o#�9A� m_2|�5!m_3;j_�!Kar) | j_2j_3- } {\�2\ j_1|2!�3|ŗA�fba,:c�a c<6�)� �+� m_3'�1_�.@v�/u& u"�BiTA�F��FAN�5> ��}:H35V =(%a\, �2j_369.�3B %��)�ceC� '��iA�bq�� F1$i(3)=J_i(1�6i��equiv� (J�!�1+�D J_i$, ($i=\pm,0$A��^>&�6}:_&'n�Wasi� �GI6�6�g -CGCR)1{{Qb�7I�!�A�>)�`_�v\!�,me *m%� \m�L$Q$\t|�q "a((+1)(j_2-m_2�4_3)! �+j_2+1 -j_3 - )!} {/m_ )- d X-m9a�X)!}}}$�12�b��" n2 j�-n}�2-n�x ���a�n � �}$� a�)���i�FI g.��!I# Z:)m"oG 0.?y����EAcAP permuDF*�@� tcouzO{"� {�{:�F�!l :q3)$>2�p J%��m� �ejD%s �iW/&>CJ"f, 11}+2233}ۅD"l"�2q*$()B�g�/a�:= .�D:L sDF���6�6>u("�D%��h�sn�H,Bve�egers� :Rw,.�5!E��e igr|.�h�"l>e�aΧB67J� 2y�=�22}�Jg�==\!\!&a mbda�R��.`* b3< _m��~["�bU2� �* 6�g*������l�5vcm2)��6IR>d�� s up��&Hz*^e�Fv j>ip �OApends T!r+:ch���hFQ �2z� Z�n).�Dճ��Ax:# :gN�"��3)�fset u_{Y! (1� 6�@_{T2.2T�0�>"gtF�d �b�bR�"�F1T�1:=��v "�@ Tl:�2 0}:=��X$�v $�2#�3WvEf{gtFQ >�u_{T_�1(1J�$->�� /1�F${Y}$;�Y {~In��p��U��ip �T-$�B��# �E�E8hypercharge ope�Lrator.} \begin{equation} Y=-\mbox{\large$\frac{1}{3}$}\bigl(2e_{11}^{}-e_{2}^ 3}^{"Pr)~. \label{gt4} \endc4In the case of reduc�D chain (\ref{gt2}) �basis vectors of IR $(\lambda\mu)$ are denoted byF�\�|.4jtt_{z � >~. �5B� Here�set $ 9$�$racterizes Hhypercharge $Y$ and T-spin its proje�:N�%�4array}{rcl} {Y�j�&\!\!=&{y!�in.,~, \quad{T_0~Z \;=\;{t_z�V4\[12pt] T_{\pm~\�T\sqrt{(t\mp t_z) (t\pm \!+\!1)jL!\pm\!1!�r�Aq)@Y�6B�wh1�Xparameter $j$ is connecAL with!�H eigenvalue $y$ of A�opeeL)�0s follows: $y�JM� +\mu��)+2j$. It is not hard to show (see \cite{PST1,AST5}a!at�:=N:34_{\,jt} P^{\,t!e� ;t}\;e_{3��j+�� 2}\mu-t} ��-6+tE@R~,u�7Z%$F� _z'}E,Ageneral}�U��# type-�cg3})!gpLie algebra $\mathfrak{su}_{T�U(2)$, �K 1ᥱ factor $FAjt}$ ha��!�FjF5%v=�L��$\left()N1�+ 1}-zj+t+1)! >-t)! E5+5f�d)�j+t)!}���� !\mu;��a*iF�aF� )!(2�$}\right)^{o}\!$}ݭ8B�HThe quantum numbers�$ tak!�l n�+,gative integ# and half-suc�Hm�sum!�Ni2�im%E_anWVA2 y are sub�De� Aa$constraintF�%�\{���[=v-t��\ge�M0~,�*\;>Qj+t\ge0�K\[3��6K!�>K \q�w6)Jle=�@.�%���9B�@For every fixed $!�he.� $t_z)�i��s \=-t,-t+1,\ldots,t-1,t$. %�expliciteDm�gt7})�6�$!fr}\}$ a�&��. ion 1 $P\!:=\!:�!�$6c:JJ�Pb.h \Bigr(\sum\limits_{jj_z} A < \tilde{R}^{j}_{R \! BlbX| tf2BW| F�z=�#<(-1)^{3j}\varphiQ� (:+j+j_z-�+E�)!} {(2j�!�}+:/ I)!}~, tf3B�$Li+1}:=A51}\!-��+<\!+i$, ($i=1,2$)��nɆNd�7=  -�}{(j-j� )!(�{z� } \,"� + }+ 2}��\[7��2�w }�|%Wj|�C%X���tf&f1 l(elements $RIpAoH$U�2re irA ible�]componJH, i.e.~they satisfye�relC s9�[T_{i�W,�]=6*'"I2���tfF� Bel�tassumx�bFLvG��F acts�; a we  space����  >Und5���+ symbol $P� suppliedK��index:�,B  ��� VCartan YaIi}}P$ o�  sid@2�$re replaceY$correspond� �] $y Ee��u���multipl Jo��:� $ fromp/ �b 7lower|��z*$ !yR� Sris.Q $Ael(zW% r)^*��h(finally finZ q>/ ��!�} lN~-.�N�:,$\!;j't'ta \!= :` 't''}B_{j :F\;{\wideɢ \bf I\!R}aa0+j''}_{tt_z,t =\; $^S \!+j&\! #, �.�J2coeffici�b $� \!'t>��given V�.�l} N�B� =\; �ARGE$��(2��'\!-t'+!A qu +1)(� *M2)� 2�!I\!G \!+2an( -t''�d2j'')!}$}\;\; {\displaysty� 0eft\{{j\atop �!�j'' �{j�6�} \�� \[14��V [ timesZt d u u t'AOj�\�w�V � !9w6�- } �2R�6�!/8fS�A{vyI)!(2j+!�\0!�A d)�(2t!�} )y:A?.���VK�s $:� n���a� (r�}q Nq2G�);m�:=\)��}ao2 _z!i'�� z}} �S4l(j j_z\,tt''_��l| Or)\.G���- I,_&�tfF� ��ula���i�e key��S' of��a&T�8-Clebsch-Gordan2�.�?G���(jP$J�} � convenien�@roduce� short not� $\L:=q}IE$ $\gamma:=�X{z^t�fo� .� �4B�)�>$ will+*U 3 � r%�>$. L\{_i _i " \}$ K base"wo IR� �_i$ $(/ )$. ThenPS1 S�2 2k!vm a ��"�%P 1O _1\o�6 �2�Bo '>P . In�a + e%�A�ano  coupl� asis $�1} \!:s 3 �3 �$, 9Wh 0 $s$ classifi�� �yA��6�=s3$. We�expx /2�%@*�& (``un *")-l.��J7 �l�C _{-51, �P(1Y�, 2Gl|Z�)2 8L>2U��#CGCFn9�matrixm{N��ib�$ �-f�A/B� W�n��w t� any CGCR1)$Jh a�QFa lineaa�i,�6�s N�. F�!��2:Q2� }C(QW ')\,f<1�6 | �5�5r|P�� L3,h}^{GqALUF1*l^\'.>&YCGCBt8%%\vskip -7pt C�4c6|� *!20�hi.�BO�2(a speci  blem� we shall��$ touch it ��. At6 nm��� IB&Li��mparison���X-�ofML%9)^�5�:�!:� 2�^{}��3AO1&F�M1-�dYd 2�L� e"�U0+7})-- 9})Y0 Wigner-RacahG u��sub�>$2��%��&  & resultZ�Rx:!9l5&r|� 5�5& %�( _3��N� =hLl(t_1t_{1z}\,t_2t_{2g"|t_3t_{3 )_ -2'3)�4' 5 ) %%$B � uad\� _3�mu l8 _3?_3+2)�A\!:� 1� j_2t t3} C}�(�a\� � \2�$cccc} &j_1"-pv�j_2� -�!76/ \\ & �& �&t �\\%[-%X"\\�$� ��A \}\!"` .Z�� '&)u\ � ��' � 9ev���23'j�,6"�-6R�Nu.� r} AN P&*�(2t_1A� 2t_2j&FA�2�_3-j_3+tE�(-t_3) q 1c:T1-� t 1.` f8-�"222Nj2 j t �8j2)-�I�.�2]�R=�. �!y1� 2  (!� )� 563:�)�'!�*"�^*!� " zR�%S 2"v�� :.�)q ��"uKn �΂6j24j'.�B/^b&��;�� ��)��:�eH 3(�4+j�j�-j��\ �^ )} (*(-j''_12)r %% ''.  %%[2 1+1] 2+1] }�LEl''Q�1-�aEA�2 2!�E�w�7 %% �esj_2%�3hiti )! }m)��ݡ6.--�Z�!'M�1aKb�3 A�6� Yv���2��U�9v�`)]�j8-8.2�62��- 2%6�j8j!�!�D�5Y?1gAZ1F�+I�QM E �9Zp T��SS�''' U1$ >�^5���_14:@1��  t{=t�}blc l2=:l2l  t{�Ol2*�Z�_3/3�,�!e%� -,6. � t_3}�nIi�=O =:�3i5,���� )B�����5D1�D��~�N� o2&'�b�03@)l�+ %� 1� Zz � E�%�1+!ߡ� KF> %)F��� �9�#CGCF} �/I(� 'braces $6j$-1$9j$- ��+ f$ . ��'4Bibliographica/aj ���I% ors\�.`_reade <m�%$developmen��[* �0�0&!SL(� most impo� t refer�sparti�(&"$itemize} \  Eh)descrip� i*�">�$of (super)-u s (c+O2of dif�tx, "�&of 1!4%�their pr�$ties). \\[J  {\it R�s}:�"�n)$ (R.M.~Asherova, Yu.F.~Smir\-nov�PV.N.~Tolstoy (1973)),:Oo}O (B,45, unpublished 9G�<(D.T.~Svi\-ridov�}6 D\"�Tosp}(1|2)$ (F.A.~Berez�2B�80BAgl}(m|n@.�, I! Istomina% 9 ! (198 � $U_q:*nuR\--@9 �N31| 5$T.D.~Palevv.�u91�2 p}(2 =A.I.~Mo=(1999)N*medi M��theor�f}�Fsimpl2Ms^�:u�( (Z.~Pluhar.�!F�>�81--Z JZ2)!�%�\,A� nov,D\,Q�V Yu.I.\,Kh�tom!1-9I�N�3%�u\-eKm nov 6�200)�N�)�21�/0D.J.~Draayer B0N�D6xS'�*�10s (Mikelson's�$ 6$ $A_n�%B C  D_n$a�0P.~Zhelobenko!*81'ym!�e,,.Oe�m|2�S.� y#v 1�!��!\ v". >�:O(Verma modul�� Lie B��ular �4AZF�V��{-N@Vs5NC:A soluAu�Yang-Bax-�&V help�\&&&�!^��=�m�A�6%�e��8ae!".-�8; V.\ Ta\-ra\-s�_A.~VarchIu 2002Z�6io,6tween"g�w2or�3�2Z�4s1�>fo>�uO (A�Lez �4 M.V.~Savel'ev�74��canon[ n)��� ���$q$-bo9 Kashiwara�T.~Nakma�[R�0"i�5ofNP2�&l�.sl6����88ũB�0��,H.-D.~DoebneM4B86Z[st*R �*`,sar,:� r�:� � ���/ 9 �i| \def\acam {Acta\,Appl.\,Math.} !�( {Com\-mun\,Phys&zj&zech.\,J> $dakns {DokaDAkad.\,Nauk.\,SSSRn(S:(�break[0]J30fuaa {Funct.2-Anan�afua� Funkts.\, $Pri\-loz�0izak {Iz\-ve i\-y!$B�\,Ser)gjomg!%N2�2:jop�*2*A:-�\,Gen^maui { Z$,USSR\,Izv $nupb {Nuc!W~B1re�Rev�o!�" �Rep A :�r�2 {Rus!A "Sur!)ysGsjn!Sog�.�%l %�prin\-ger\,Lec\-ture\,No\-tes\,in�\-sica,temf {Te\-o1\,Fiz^th�Th#A�2��0n for}F: :32�,J�"@5�: �%�mf\ {8%971�,55--271 (in �6�%GAfH��NW��.\ II.\ �G scheme)�:� Bm0=T:oBML{\rm SUNARa�\ {15),3), 107--119j3AaTs!bb�A2+s7EoNW !  semi9�7 plexc ,}, Matem.\,Z�@ki {26 �A�1A5j�4� ��� Weyl\ 2J0 $u_qa��"� .(,) $s*2���� 6uto� {59} 10�2H96), 1795--1807 \,[� % 6A859"72]65%��% On a"�$analyt�]b,ulae�$B su:68 ."},2,:6��K,, 2080--2085!�(.QA/0103187.�BT]{BT} B�.G ��avijDC$Grassmann M ure $UOSPOa�� \ {7��8��40��2.6DT]{DT} v� , �#$Adjoint ``J-"Egv� %~)z l(2,@/ C})Eyin:iQ)@,symmetries} � \ 6x KLbrev, eds.), World ST3�ific, River Edge NJ 1993, pp.~229--245  %�$KT]{KT1} SdKhoroshk�V�E�=�o unvs�4R$-K'%A$contragred�3�e>�},RG����R}8ed Top  \ Gie\-le�$k et al., -D Kluwer Academic P�0rs, Dordrecht!$2-$ 3--3. K�m} V� Knyr��5�One�``� �, ing"��unitary �G�\y �e5) 34�56�FS ]�>����S� y'Iof2::� �g!�$ $U(4)\sup�HU(2�.  $�Jt methoda� �20�M84� 47--35.�LS]{LS} :� &�ev9mAbout onf?��r&<��act �%n7 \ 8��7�348��p 87--88.�LL]{L} P.-O.~L\"owdin�ng� mo"um wavef� E "�eq9-*�@H�� \ {36},�(64) 966--97. M]{M!!R�\i��J�sy�� ctice���S201%�9��591--61.TN]{N} .�}�(�EE�p p4�a!�28\9.�PT]{PTrb|�,Finite-dimen�@al����  ��${q}(gl(n/1���14-#�w549--55.#sI]{} &_:� �MVol ��j< .��W 9�&"P �7 9eb86 21--2.=DSh]{Sh} J.~Shapiro� xM1x:A�Aa2a.E�b!D�\ {� 6!A16� 169.C ST]{n2�j�N��usual,i\?qnmi���us� Hving .?pr 0:1Sel}M�/QEDh�ema � ?(J.\ Niederl+0d Ficher"C` .` Teaneck] 09ͼ9]z STK1!9K1}6:,:���I.~Khar��M�4 of�Fa 1�)3�V� ogQ5ZI ՉS . I.: 2�8�*D te�GwA?�� 3Eá m� " 2 959--980.J STK2%(>q2o�5�y &8-��a'b7<y-A��.].7 , $3�! �!�!��I�� y!�pe) �FD( 1068--1086�yaf_9f( 1746--1771:H3%H>��H�.|9GTre!��y%:]�7�!�%[su��Q�^.\2#.F��92a59?604=\2w863�(74:�4�>k����.� A�Oe�FQ.�6{ {5��9_ 690--700;=2!2� 246!�ƥ��!�!>"��V�� &�$.6�*� "$excep�� h"A 7�+7��3M 36.�TV]{TV� ~TaraN��8Dualit�=X Knizhnik-Zamolodchikov�dynam6eE-e� acamVaw�$, 141--154�� T]{T&#���!%*�6* W aMaster'�>sis, In�KH��8��8, Moscow State &� $1969 % 52p.� ?=2�2��Z�� ved!@ �.8 s non-dege�Rte�lT Kil �6m�� \ {4A22 26^d� J =�v�A�rIXed 6�oGfBF N�29:�G3T�#e� I�-�0}, Vol.~I (Yu�Ua� �VNU�J!ress, Ut�86{a�33.7� B� Z�Funda�al syste�@��J�!� $��"�n� .d!q��H�0 (Vladivostok� �a, M� 1988 �258--25b^tBrZ�^�J�2� 2�a�I(]wthA�#A��198B25�2B��� iOac-Moody6�%s��ir2*��k7iz90��1�22X 6]{T+.�Z�C�=or�;25 rootMlER�::�#mFProcee�J%gA�I�R�= al School".S"E�,grq SE�r$Dubna, Jun 99), JINRc�, & 2001Iw13�.� T7]{T�H�&� �� 4 %�um� ."S=�A�0: Curr�+Per'=tiv�  Fu(Dir�onsC\\ Bustoz, M.E.H.\ Ismail� S\ Susl�'?:> *> &>9#4A�48B* 4045.� TIS]{TIS>92�) �:� `The GelH+\u\i tM+�A*B�.#S*n/m��&�n���, �� ΰ3�42ID]{TD6E�J�'�(&ZNewa�!A�]'* 6�2� EgF&.&\!�DZu})� f5�200�359-1370* (Zh1]{Zh1} D�&�(�S-2AV6�' ver �E�!�.�# \ {2� 198 7 78.GZh2�>H>�&Z�� J� ���2� 1301--130. Zh3�>� f�N��%2 ) MicD*sonوr� "# \ 339 �!0 100 � izak��88), 7�W773.�Zh4�4: f�An�'�H���Y�]v�.Rx^���� Lie e���:�!,, Adv. Studya%Contei0r.�bf{7} �IolaBreach, agYor��15� 1 2>�""[&r& docuY } % -� 42%% T�WY creaD&��d (R)ae� 3.a�6 qa{`1Xle}% \usepackage{float}2epsfig, a2x6ams�>6b+fonts6,ams4�*�ZMax�|Cols}{30} %TCIDATA{OutputFilter= [x2.dll"Ve�,=4.00.0.2321CSTFile=-.cs!�^|LastRevised=Wednesday, April 28,�� 4 20:16:1.�0�Lb age=Ameri�ZEng�1$0PageSetup=72,�[newe]em{Defi}nia}} . &}�< orem6$lem}{Lemma6conj}ecT6�}�posJs4coro}{Corollar`d!�4\bb=msbm10 at r> bis.0pten6 �) bz{\bar{zi7�)rR{\h_ bb RnNNrRpbis~0zZ/ ZFqQQcCCsSSpPPtex/ght 22cm� width 14� ds#16`7{#1>ov�\5*wtw"�S3 QED{�<)Ah�2( 4pt\vrule �5pt hW6pt dep� .5pt{ptl{\�5al})� rar{P7arrow epsi{ Z loA��W{_%_ p}\, /Imm ImRee Re lnn{�op{ln��rYr����6!� hoffset-1 @newcommand\ns[1]{u>sm I $#1$�!J�"�"�"�"�"�"�D�c�*title{Si� �urb�� � first$hf � b�Zup ��!T} \author{David Holcma}hanks{PN n @address: Weizmann2B�ce,a�art�O   l, Rehovot 76100, Israel. D.H�PincumbjL8 Madeleine Hass*el�ir.} \�(Ivan Kupka\ �&�\'{e} PfK VIn�h175 rue du Chevaleret 75013 @ , France.e(ate{} \make%�� fFbst�:} ?'?&"Rie!0Tian manifold $(V_{m},gKgwe�KU'0second order �ve&� $L_{��� =  `\Delta_{g} +(b,\nabla) +c�Q $-$$!uA+La�[ -Beltramii!b$b)\a Morse-Smale (MS) field 6�l $ a �1p�j. We s( j4measures which6f �`1�PhedN�'2$ as $� gowR�b$e zero. I+%c�m&�(MS �� , su� ���Psu�a lR)PDirac5loc? *^| �#p�'� bP* onzci�ofJ��or� !E �cyc�! J. When�� a MS-grad'& �,Aka Blow-� Q dslmine �km sequ5=A�ceh'tes�]criw �set%� prov!��etb6-� at a: belong�up��a � MD only if',Topological ��)defined4&a vari%\&�O�M �lKifer901es achiev�h�O Alsoja2 vergIia1�RRMDway�R�?:�s)�)�)<0of global max�5�m eige��,�n!�� comput!ie F_of1'�.� �N!� ides% nk bL7!j�e]�>�h� iassociE�2�s %� Qa�erpre&Xt_ �YermAnmoveb � Brow�,�G$icle drive�?aI��@!�$o a potent well�)\��noise ���5��\t�of�?^ \s�{In&r} SX���Aa%�^��?*&( $m\geq2$, �#no bo& ry. 6�de�"�0 �@%fpaperE'o�UA��S ell�@c�� depen qܵ� [e��>0$,%�3�} .�=���j0+\theta(b)+c �Mnajaf}M!�KPX�14a $C^{\infty}$.�� $V,c�ztrictly �0 C$6 " on $�{�� $�$E0!deriva�U.�to�:;$u=$ $du(b)�Y�Vq$u$ u��:��n�mb�"a Krein-Rut� cnqpinsky}L"em �be�lied. H��=E�e e�"ac*E$�pF�h&B_[.���dis�B��B?. .�,.in�2}it�[ behavi�*fV�2 g  �pbA<ensively�5)^� 80, 8 $90,DF,DF1}:Pw�y!k $\omega$-�,%�dis�/unY%f ���(inőnt �ubolic�@0C Ea milds �al!iump} Y. �̡ԡhatA��tGe.]V& ���t�KOW�K(TP.i��_ fM !��A ��$c$ (� ���H details s"?t��H. Unfortunately, m� les�5known a�-!t weak �ջE�q}s $:^R% . By.Q,�Bmea�H� ղ� 2_(^{2}dvol_{g^ 9�-VIS!Us. Pas�F�V� clud��� EY��EP�+ed domai� ubblne_!�AO525!�is�A;�>� l!��+V<nd6��a�i G|ae$ Dirichlet ��~E� Ūw* �tB ive,Bn.� 2�,_.� 2� FC eo� a�+X*_ul�>y�H&� �Vtan0� �Yct�-)�Q) a$yy �lDE�U }). �!B �� ; nis)�a%1lq�  B� �9a�averag�#f2��PDE, a� `.�H} ), $�n�W*�0}�N&�:n@\int_{0}^{T}% c(x (t))dt}{TA��J$$�&�zI� ��*eriod T,��proof� � stochas~0�.�x B rest�itoZaq� is& /A�! iMm.+s� co�0�A�� �c%�$b=0$,B��Z�)m|� :% \[ F4 ��vax }+c:=9j' >7 % \]�G%>�j�(* by:$!� _{V>Z.� =1$)ō�Y��M��exa!'��(�]0Simon1,Si,Hel K})%ois��� >:-Pi� ��  �5�"!f6�dxa doubbellp �r���� P_{2�t �7{a�UXE�x2U&minimum��� s),�5m � M��5m�,��9�&� $0$ � con�N thos���l��sdio b%F sense, b� �=_Au}�.�\r0a` c_{1}\db�s }}+c!H2}�#]�Y $3 %=1�ss far�we%4� body)�`�K�xa�o�; aluta�r_n.*- o� �$!�. OI urse"e dɒ2^ �;Q��d��24�� "� dk)��iso:3ie�-%=�� �T$��V}c|) atr 'YA�� or%)�2�d�u�2}w"gU �Q�A(25� @�oHes)@�!|yO�e ��u��qAaM CE�Ark (calZfSmhIa!� "�x)�um��.. w6� , bu� y d���� thE0ls�aS!�im!�asEEain퇉�},�7=5�#���p��B�e �xin�%`��4� ,a$��-in�B .J}� sa�y)� +cy�re_d� 4 A� look�J e~g�� �o�Ei^�%&�!V�fz�ing wa�NBI���3�OA]�n�,�&�(elc10-��%[�xhe Tayloa�pa�� R�ha�o be �CA���ga1� nd  2a� I�i� a��!� nqu��i�be�Rg!�I! is p&�&�necesso"M s�to �4� ���)1�c�7@K5��.g�gea'�T,sD �" s na� d ,�� 0 �MR�S(ged (\ i.e.N.�q.!@��kAUsF-W�- �.��D�e"(Y� can!�{�e!��~�by**�um&(ؙ� ��aq� l!�1�` r a�"d� $b= � \ph�xP�W��*9 ��%�FxB�a�b$ Q�&4�� %Un� �*, �B"�ew $} \b[e^{�!}&3 l �g.�}G V_m} e �@ B:z�\"�g�=oRja�Q$c��te�z0�":!�s#8me��.��e>We�6 4 ]R�attains ����*��&F >A�@i> ""of"�, v��ew2�>x.��-�6�.�n{, beca��it� awh'��ny��$A=$ luld!krpxi&P�A�‰]�. Re�)���>`ws��Fl�fts�"!V� coie�fore, e8-i�w�_`x%��C Mechanics2� FD� ��h��nt KOXu�. Actuq�r ��q�?is"E�at1C��5@�ny �LyapuQ9zL!�"���. �ia�)�� Gaur �eF], (cru!D input in dp�;.8e� es uU "f�'"%�V2Q�ge&y&N2�. ��typ&�,L � �Z7IlM1n0s!L� m.l� �>a�<� a�!�8Hamilton-Jacobi�V��, Bb |�J L|^2&� L) =0,1*��?}�2� c�/lyg d!x�Gal6� WKBoA;r:_!���0 poss~%~�!�F�a-y�mfic )�"� EM� ���ar>�1ors.�~z!�?exist&4��&Ma^~��4always guarranE, smooth�l��Wx 2� �?%>�9Yiqd �a�2G� �FF{1F|L�y ���=Nv�lyo�e.)�.u"&O9M6,���E��V� . FiS}%9�D�� decab A�2I&� �! �A9��KX%z)� infl>!S* $"m \par um)  yOur _V� are:&bu$�Pi"�^C e�+��thfdtpr}�Z�O��!4-�u�*� 2s6��. �?d��=,�� 9?e�%S�,se z6s$� �X��`2` ɛ�a G]Jjnf}9M� s'n� qցF� FdQ��M( HarmX Oscill?� is lead��w- � th4}��E�a��c� e& [.� %vX#�to dal!�2x 6 c$��!:�� 8�#a&]5�,. As a byprob�F&e6s�<we�qE mu$Ye bc}=at }A"�$of lo2H#um�"M $ P&B�$ e"{J \ab=�%q4Th-hk copy(1)}�^\&Gic�B#e.�ua�l�pł�\ }�A*�*�)�u�c�y (R"�( L,9 ).% �dwe� f�"`$iscrepancyI$e�va��-H�(g^�v&�n �%!�6"�d,E E�ax�fcedh($j �Z �c�� ��onQy d�2},p@��  * ula%o��M�ed�%uba72�&��6 seems toi�to Q at)y2���E �#�tT A!�al� 2sF,%:��@-��I���&~ys��}��b��a .Z:�� � ���QIB J� occu�F!�^�VK "(� tNw? P'E~!06�<�hn u�!� � as�!s.w !R���$Remarks.} � �5��e�"A�let�(extend also�pre�wH6i�al�DM�K,K1,_,�"���-=�UG�f""_�*un+ mK*wv(r/ t aw�`J ny@ orts*W �)!!�4�)Up͖Q2�a sub^ ?#2q*5����_"0d �yp�=I"9kɷ eZ8��i4e_= shlclarify 1�%�of-sSi,Si2,� . %��%N�{No�)�i�P% ($x^,..., m}$):$U\F &?;3�"$�oordi�# patch �'�f�'U :�� align*} dk# & :V\A�s V�4{---% u7(MACRO{\TEXT8$ol{>}}% %B= E $ $>$% %End}�_{+��� {_ 0a�oc +(to }g\\ (,)�= 1scala�i�a24g}�wxp_{x �T V%Bmapsto�:=expo�1�man \ }g i�( pole }x\\ �$) �volum"� :��L�(E) 7 `�'6� vol}� #Ef t }Ef }V\\ ]Z :=}a(V)!&�0%� � neЖ�*I16�apm!Ob6?2�$on �"�)6,.*o*QA6p}b�sa2���:/AM(V:l)O�7ll�� babiXH�%7&+)7P&6Ku\2rm�I� Ņ ^o 2;�?m�(o } \\ g1 sum_{ij=��m}g }dx��j!bB�� 1}{\� det(g)}}:N��A� } a}6>g^]�6463j}� ( 2�i!s���A� �!� �21det ( #E�Gamma�^{k6]$Christoffe�Fmboro >aJ=.�g^{kl}}z 6� �l�pC<al x_�+F'j.'-B-�=Nj:Nl}�!)!�R� k\cdot}^{ l�f�X� jk}^P�i}>�/i>/� j}}+I(nMu%[ 6netn}-6dn �]��E�lg_{\ln}vn!� Ric_!�Q8Gq(R�kleRV!> jj}= 8i,: ijjibB�ci- b^{ijEd (��fU�2Li36� f9� x�% �r ,}1\leq im� � Vpa�[ aph{�}�VI�{No�J &)s�Q%%׊�P�&$C$_{\mi-+w�o!#a�me��$% ��(� _{P}�Z��%ebat P,*Ba *U$E$540&p�numerat-E  x$�� $...}� mes$m}(�)$��� 8@Mo}ball Bk(�%)i � �T/ng radiu��% >0.$���i,j, 1$A$ m 82"HcYQ��?m�(P)&�(i x��}$. {)(\cap$ Q}= � ing$�P,Q!� C5�P$\neq$Q� =Vj!V���� @% iden�^e vy�r�i�abu�(�!� tw1iy�:�N�% b�,�,%(`by�P)D�a�i Oa mr what�7+v�r($\geq0\cR(�!�� ��a B word. s9��. �&<(V$ let $P$ �3 ��hart ($UQ^= )�V �ed�t:%�iEOP)=0, $��$ie� m+��#wer t�9 0\: ���c!sz��e � eomoe�0sm $Bl_{t}:U\Nm^es% $($Q$)=($�� � t}�(1}(Q)� x�=(Q)$)�9l"v s, tIUs, �r�al�r�s1trans��*x<�* �U). Suin8y�p\Oh �!�t�yi�h�&)e%�*"�#0���be.`>��98�$ a t� of it3�Z�H"^3�!u �he origO ob�%s�G. (m�pr��;�inf>Fesi�.2 *$P�os6V the �D���Cwrite:)�)�Q/st�I*IՓ1}% {t}AZ+A$)]"\ $"�-�QU� so o&bi�.?"�:�%.�MS\: (i)!,rey �|%@""�1)) ߥ�*%6)$aN1�9rb��(ii) � pai8sAl!� un �l=*F.j,I&1� E�ve~ely.�( moreF�a�*�&ku?���ecJ�%��$gAvb�Zlӓ�#��!,"C��H :�self-a�g�)}�]BR .R�6s�isa�Aa"* s�`&,�J�",b~nd!&by2H�2�1E?wTwell-�%butaHc�� fiRs&or*� U(^6 3te�[�li!'�I�:u_�r�}E� �,��42|�.��%�}1�2�*{"�v \no[int�a- �  (! �  ,6�V $� � �\�* 6i b T % � � � ))  U_b $P,Q\i. $P  Qb �>&o m�fj v��z ��.�� V ��F ӞPAo* � .� w�T� �  a� �  ����> ��5or� �2... *�j $,!�%*� ~ ɏ��'�!}$�Po�,}uR&1H*&� �G��v�* $&�+�!��!��:���h�aum4, *K �!�[-ne�^]��6!s )$.$ A�"�4E"�J ��.�1: "'I.b%�fu�v*F&+#�9��&Z!=�B_{u�KH� (V)-\{0\}G�:V"��.{|�)u||,+cu\� ] 9>{\ � K% &A��9n%r�Gf���*r%.  �'�o)�4 -�1o"yAj !6� \�>� F�~I� �%Ramv..�H� ^{8�/"z:�!35 �E\d ��C"Q%6�& �B*��(ist9ly"uupa m���]v�%w �4#2�E �2�1ra}LB��>ao{ a� a $ ll c�9T$p�J�'b-'� \{$]���&�) >0$\[{*7�a }|>01�nd�it�+say�Jso�M�ly:w""x/ keep�r�$�.sM� �w�:s����},   in"�a&<"$(�$_{k}}|k=1.�t(Nm� % "$.. \�U QPn@:}E�,R@}H�A��/ity2\ }mg>sD�i+ $ceg.$ e t�aN�8\~$#B{V}�Pz1X�BV?H��q�un( �6 hat �BxF�!�det^ YѾc%{ ��� . (V) 0sup��c.�@=�-� (�de�Zs!c�����E49#�3 9e�51.:f be^b�(U(Ire �/�s}Q��I�E�?P?\forall�4�|-\, , 1[�(�n-)]�}+c2�?]JuP.;9)o (�@upLP+ No, �*[ . rad1\���#F�$m>2$"�#} ��u}(r) @\mu^{(m-2)/2}}{(r���)� B1�@.N6�I�, � \ }B��&�\noe\\ =0\, 4Z`{*"-3 k)�{ �T� �9s�P$1�$.}�Weg3 t�5Bi� * gy $I(u5%m1�({\ \mid"S  V % % X )"& u�%Xoa�1�-�. coX+���(. U8I(�)�)!�[&; � "� **� �"-N(=K _{m-1M�B_{)�/\A8P)}r^dr�g1}{(1+E7)}+oR� ))X c(m) )1K "�B���#$+��3{#lyA6$"�u aJ5N�K �$� &[%� �k (n-1)-spf !:&S&�am($r=d(P, Q)$8M��"��Cj&u� & K@6yi=iv/a�us_+=to �VuatA}e ��fiS�M�U}al�7Z�84H+ (ble $x=y\mu����-���IA�9� F�]I�2�2}V(P).nJm�A1�,5��2"� t_Jy(YCEA+1NrAb)w�6$)�.�W� ve $6�O(1P$n�5Q�n=4�.0 )=O(\ln w��E^B�r% c-[�r% 2mH&�t�a&���W�[ �VŮN3I~�%zTa% $\muu� ^{1/s�M��� �AA*�ǭd})=c(PAV1]T P� �On�� a�c�Q� 2.zZ0 � �ci�OaS2� � �R*j'pN!p&f%!,$I7� 2A�p}F� 1�&& �.4}f*}�5�p$ ɷies $00}{!�}��% Z .�=0zinegra:{AQ1���0L@ \in$;V2}$(V) ��1��M�)"v H2:��YgIng4�)M�R�4O 1 "[ 2b=�s 2� %E.v � .�!EK�� 1�j� ^2�D8�intbypar�,6�B�%t_{nN��I@LB'Ba;�Y6 lOS �. left handT��� !�toE����Q%)i�; ���^%0� ��B(c-B� &� =0��BuX0��-��<g*X,�T�"(%� y) ��� �2�C�\, �2F�� 2� �hunF�Y�^A $\{POV|$� :)F�i�E0 0E� ^7aV�Cu=0$.)Z��)K=>LrLaql Z>)f'`, � 2\G0shortly. Not� a�?llj���s�� C(V)"�= is�Y7B�&xRe5C]��}-�\psi�:�.2lab� nullF� If A!�,`K R!� of V&* $&ciA}�� 2�*, $6+�no"�clogX^A!�pp�� )f�)�{&ckpyontinuF�"�$����Z fd�9`E1�1�\AAg"5�nA�ji]u factE�c T"MP��U��J_{n}|��jbb N}$\}a;�a2! ai� )�cBP9}|k\i>T=���co.��.__{ E:��)�x zdri�Ss�>w($�� i�c$.We�)�5]u/6}$.�(s�%�#Q��W!A�j=1.$ C�HX*1!dec��AUo"� ; ^�����R��_��M�}�g.� Ff�-U(P))+ �) B�q�� g-\cup>r.l)v��c�{J�Ir�s ').s"5�-�^4 P"� .�%�1 bvBB6n]"2P%]_{.\ 5Ϊ\"� dioJ?B^a�inu�A$,` �� ta>-q&�f'�$(\eta)>0$ �e VB:\vert�BF:$>J:�(x)1�|� n$ \��xal . ����� ll i�� o N=c:D�}��[ \� � ^6  i=� a@^�iP a4N�. :��a2��Z unde�rq�� �!�b�� *��{s��6�d={.�d��6% �% , still �*�6if"�Jyٱ.!��$U! $\un-#n->� ��Z?�:Dn(nN KBw )2"Y.^ �+� q��'.>i�:Y b�A'f#>.�n�%"�q�i$i}\br U�$V(# أ}.%>�92.���B�%�$ d� �%��x!.$�h1]6,  2 � leq�BF_q.aB?&�Ւ~% v7�L.�l2��I�ƮByEn� ���"�  -B���=&�!vN< nh ���+\(%sr���0�/oE�x�W�quq o it. SF �l��ݨEi%�&��$�N�e�:��rny2J[z�F �>��;����Z=�e�sub!CO �s�.E�j�9:�!6�`2�� bN��\l-�S!aW2},�;) w�� "� of �s R� vol$�.�(�ly"m* Au*�� [9F^ 9�i+ �8i@P�Daif we-dp@ ��5�t#"D1�0��:�[��dG8�, ?9I �("$u9�o"jS2%"7U�!|n�:�on�I��@b��.55a"WE�'>i3>04"�;$;M�% "#%��!���5&"ZF .��Rh;Q��<r4Տ'e=ish#��q�.i�M��� >�TWc"�F :�0Zps�}$I!�2 7���R�*� �K. !:MCe�Z Qf"~_ &��S5�hi��. M�rb=;H� &a*� c$�sen:�Z�5R��&�x5�� }++c��"�3�< 5� &�TCY%f�PDE/ e"i3Ѿs.g2R>2M!}% J|.H,C%A,/ -"pp��:� ,eKBf� ��2�=-2�%#%(ps;'M }$ (E �*ed�2AA� )�2�new"�)2� }=.�>k. E-W� �)�:@�e=th6��PDEa<rS k0o�aerm� appe�W.�w �� "%P.�gn&2"(�mbd.w.A2����"c*$ =cc�M � �a06# ()��.)) }{4}3(&&4i5C�+n�i�Aion ��/=D's :��� 5�%prop} S�5s!�� &�"{j!�� d:^��F ݱٍ~�i� +9<(P)/2;0��.�i � ize�Ba���,!5&�.=F#=�_{v#�/�:�9-�ZH_{V}[{\ "�9v*|%6�A�]T}�/��t/+$ne$ �N���mi�5(A�||.��!/:�� �F(Ւ�K�a phi/�2:Y��!"B4 f5$�(��KA^�"!:�AUl�36��68:Y$Efty:$�:���(" i �� *�)X+sc{?6.}%��7aKvwisi2� of*�C mPo>.">\>�mɃ &v;�q��w*�ay;Z+0:��}^�����l&�IA+*8$?f+���.��$"�=j b�\=1�ft\{ &�; _{i}f(P)�; �;_(b)x}! ���#fK & [r now"Aby%%� %=�41< )I;�S�O}.}f�T% E|�A,!�o�_�hF FT� )�Ge�(�Tv. ��B5b4%�>k�Ja�to�A /4c!Na �_{)_$J  i}$ �'%�V.]�a N��"=  �6� �4Hl]�.wctVn�/ stepMp�^���. \QEDR�ʰ{=�G&4/��"� � t�Gh wd ings:��AN�2� o7`onA_"�_ sets*&�M)P �T�!�m�nd �bkrv[AI� #�x^%�I�2�j�JfU {!�5am2 :�9o{��J55V't��Bc��)\MlA`2�L5�)9M;j "�Li}�k%SE"[��.�<�s �~gM F.]>f>&9fM_��c�(-&"&�a ([.L'�4�_2>>$nuy�N!�.�7`$(A=\{x(���^��v (-\-� _{rr2O#="�[�.` }{r})+ &�r}VOA&>(+a.6v� 23A�"dpr}.H,50bE� A"�=2}$%�%�A���5�a�r"�.) the �|a$���']Up-�yN-�es"4_Y�B# i�i��[s&�e*z@�?-��@n Mm�AR � Fa6�&� a UentirvD�-ed XD�� u(�v'fFried&5�DEh��� �!Q���O{B)�u&v��, no vector fPields\label{blow}} %�2d %% In the next sections, �elimit measures are analyzed using a blow-up procedure. We shall prove that as $\varepsilon$ goes to 0, leigenfun � � up i�highborhood of some points t`oI�setEa chose�B�. MOimpor!�, it�!� be studieE� vari�,al techniquea�0.$ ���N4i, j, 1$\leq$ m, $M݁�ialA�c}{ x_{i}�j}}(P)y�i | _{ij��-�X\cap U_{Q}=\varnothing$�$P, Q:&$$P\neq Q$.i�=_�9 Te follow��weI�idU fieU8 �wope��6� 0 in >l,��.e� Mq 1�$(r)$\ et!'PA�  �d�� bot� geodesicI-] atAofQra�$V$� its imag�~� mapp!Z�!� m}.$�0sak streamlin=no�8ss9 comz  (abuse while�Dk8w� �% :�,�%.aby.Jje]of-3 O!, m@� ateve valu�r($� 0$9,ourse).On a 9  V let P� a� !�(a chart ($UU)$,��)SV �ed��:%�}}% %B�� Expa[ >$% %End0\� *� P�!:��i�� � Lomorphism $Bl_{t}:U\��9��,%$(Q)=($��1}% {t}� (Q)%6,  m$). All" A�tensors, �c 0ial operators� �be trans� &�e�m� �$!�,). Suitably ɼiCby!�� � yi�h� / �zen t go�o 0�� �ը>ee � Ico�6 a t�of inf�M� &L be�"our#�origi� objec� L n.�0(more precise&�$infinitesi�.2)_P. To si^f�� we�write:5�,{t}Q$ instea9oQ$)ٜ1*A$ * � IY0$($A$) if $A$A�a1�of U a�Dso on. \bigskip I ���$!�s)�be: �v e sn��� polem�. O u magn�td set 9 \sqrt[4]{�$� }I�\vE�qcan dEB�� w$_{P, .V$�8�- � {v_6�{\� lineB}$:% 1 wBg(y7 6 va�(yR�)a�ju}:�% � $f'`$=$\underset{V}{\max}$ u$6N .$ �u�{M th� } (paragraph{}�u  Defi}� -�,$\Lambda$ as!= =\inf"\  ��5�1{\bf Sel):-C.v.} � thnf!I_ iz" (i)% any P.! , }$ sequ�v:�$'��a` $]V$����[ �%��� R\{: �$\}, " A 2��n� q*s $B� Ia�P6 verg��a7i�}$:>�--%��R_{+f. i�wL$� $���a�C$^�4fty}$ topology�(!�8 (ii) w satisfi�he equ�dDinlity:%E�5 E}w+I�iQ�lE�I (P)Q �wD  wA��I0m�:$}n!A}=0� 1Lv) �R= R� � exists a uS 4 � N}, *� �N�,, n\in$S, haamax� Q$A�ok pr7 t��a:\{ .^�\vertR{ 82 n� S$\}�yBPT A�isBN isI�%z (x)=\prod�5exp�W ( -B x�A�FQP)�{2�H)!�andI�I�1�-���no� .�S-� �%���*�c�> ��J\\ �=f=� !%."�*}q}f!~��a�) , $}^s{a�Q� b�.5Oi)t2"�$^{\prime}$-$ri$4t least one $P���. 2$S� �� ((iv) occurs����!� \noinS �8bf{Remark.} Not� at��We�  w� >�bI hey�j22� ordoa�vt61, n$tw% posi6 sd H first gives estimaC � I^ !*second, 23 �decay@:�C.���Oe'� Auxiliary��}�\j�t��e{� lm1}pB$�#*@$:E"x �B�9\6� in}c� �tQF-+� "�^{1/268 �.6i ��|qH \min"a  ia)jGbU� q6yHProof.} 6 ll u�) $H$^&(V**� }(u)6"geq�}c�| $. Hi $\ 6/!~% Z��e=mb� hand-�* ipm( use a test��� v* � $Q$.�.maMd��� e�qk:BAphi]P�5(e^{-\sum\mu� "� /{2}}-frho� 2�;*� }},��{��}�cal{N}��(: )\\ ��02*V%�{--V4� ���� >`ő��connec�componk\{x���� m_&� �&� i�inleq!\}"��0,� re $ � aken��"j�� �B�}% $($��We Tcoeffic�6)�= �)�ti}% }& q ��i}� A6(P)�G  cityQ� F�a�>�g_G(P)I� �+O(||xeE\"�%]),b%} detgM�1E�_{� �RicT}{6}x^{ij�fd 3}),6�$Ric$q# Ricci�sor�  $� �)u$= $\mu��2$ quadratic!m� q�(�)� 9q$br��ͯu-r9.}e� ~xJ}dx-g%:)\pi;� }}%X>H=fM%c S$pi}}{2\mu A# ^{3/2}}.%6J To eVa�� _2�(:O)��y ompuh e lea erm/"; r`k#rali$��59& �>f}�:KA�gE�\,"�\, ��NQ�}}c:J!�,6,� 9�B�(��)[%  tkBJ�2<g^a�-�parY �. "@2i}:2n1tj}� det g}dx,l �| ��'� trix inv�� g$e�eU dx] )8Lebesgue volumeA�[� e!B��H=H2 m "ib!��o% + %�k���k ' x_{jk�] a�q6'�s $ A$�&�d6� boX -��.$ Pere��\�� i.e.chang%��ble $za�=� ��� ��:�B(`�� rho}��B_)K �!)�, �$���!�n�(x) m.z!� z_{k�!�U M�j k}}9�2�||z�GE�6�\j ) mdz � {\mu�\]q"\mu:l.��[ }��|% !�K%#pi^{m��)v �Nn� (�*~�+O(�^ͣ7}{4}}).)�W�;#2L&:&�F j~n��8 int b@6j !05 �\{ c(P)E^ _{q�=e69v�) \} Y ( 1-I'��2�rP O) �$x��=����dx+B2% & }n'e�9ef�= % - �� ��"� �) Ʌ%E Pa�,�]b�/k}%�{i!q>_dx6�ɉ��ba�uk�bB$�^� q�,FEs, after�(a�he squa9  q@��-2/2-� /N� +" /��v&�� e get:~�{x}��J�dx>![ ��� |���.L A�}+O_{w}(�F1}).� O$*�`M&畚e})$#0�%at} }$\eta%\lbrack�1[�*v� �. K(3�nant of:�mt� !�error�at mostj�+absol�  e to b$�e�["��b�i`].$ An easy symmetry argu9, show�! at: j�q -��V�0� if i}�% q \]06��  becomes��N�>yUmuA�%C(��E1�y�+� (�t-�l *.r% {6})2�Q�.�A�N�3u}��x Also��BV1`]�aq� &� �R�126m^�e=qg/2(Y} �Q&�1"� ]2�be��d%�� q(u% ��[ � �\+= E�}=;(M��E j�(B  2j-�Q]7�A<ч=�$%�^�\% ���1 6^ }I V�&� 2�.�{6�E�oYC41�QCΚ!AQ"� �% 2���� %�� Tr�V� -m�{>�IYơ!K~�!]u�twe�-�e��s$!C=F�cL��.��&s�%�3as��"aPu�RMQr"�#�+)6_% -g&{Yrd}{1%�&��:a F�^ ] If!YQ!/V0um (%N&.�s2�)�critic"�0��of N�0m�we L2u��Fhn1O5M v� }a`qJS� �$� 6�2�a?� w2Dml� 6�Vx }"�P�@:=� \QEDҌ6uE&��"�:}}Uexpec�g�7v/smo�-"� �96�! n asympto�e�+-�B�=)m k=0}^{n}c`9 k/2}+o(n/2 If�7dv*H"�on�nd/)t1r"�1E%c*P22c$|?$ From�16viop4�9��*�7 c_{0}=� c��:4, T}$e Pres�;�:&8 ";"\5a1}���� J V� EHPr"V\3l�prF6nu�a�� velo�con�"G7�� 2u#s .�}�:�#�% an el"�7"�4�(6��5"�'lem"�creetin}�'IfE�a�"F#"2r'$zero, $\li�(�Ja�3�(ty}� *�D2� >0�3 thenR*fLsup_{VBL=��ty%���� 5 F��% Supp�4A�1)ub5�.�(�% �\st�;�0;>'%jG sup N�< ��g.��)nD-Z1�  Nr&��2���>0<7'3\6�$KA� A���$,�)$�7(K���"han"x4eta}{2NWN�5�F�2� ISKB.%� �V-~)\]�( 1rX�}^z� N}{�� �,supB�"� �  By App�=x�rm{II,}1lZhV� % }}�*�*0 u_< rmly $V-Kw!n�)">�% 2�A�A@ .$ BecausSeta arbitraryj� ��=03��t,4�$¿$F5 ":Fd<:>Nemf4an diac�.�3�y�ic $g$,��'�"M�$*/ b#;*.���4us���at4M�*s��?��� x$&h*g:B�-�&re �s���1N�AonC, �o^u5{q\inE�M>O0 p}%s�2(q, C�in�  A&M "G%I��H8s f��"+��'�?�= 6�� B c�.�!C/�n%!���&�j�&s%J>qo%bK$"F=" �-g.� }(q)+c(q)��@"EK:#}�%N�?F& is  (ve�$b�\g ;+0-�2� q��&��<q� "� "$. By�& �o*< �� 0\�q\ ! -Y��2��Z1F* (�') :/:n� c non-de� te�Cis se8)R�$$\Gamma $\V�y���& $ $Va�d$��a{$�8,AE� % $)�< a $($c&)-->�3i�n$c�$T�:$A4 �-a9Y�Y�6� .} Ta�r� � �#aEy& :��, }$sa�� ��~�2.dT |k\in eibb{N\|)M 6>)N��� a�F $P$*a� TfVJ�/:P*(=% {exp�' (*e(1/4}P^{\ast6m)~�G$length $||.||$Ava��H$����betwe�/e peak:�@�~e�� 3�ax E7H8� �6space;H�be�3�)i;�^J`N.� � 2o( `�so far!d �Lrescal�GJ�_7N�minCm}|?m�i΁TNow���-wn�5>>*�͞in9@.$6DA>�8 #2"$. .�[8�� g:4.?8>M�&�7 B#>�f�7�%�,�6% }"7,6p0� ]0, 1[:$G/&&�/  �s/��]K$�Bt_{�A�Q>z")}w:�&y�'dy� .$�DxnLJly, for � inup5� $f:[�]-:�CR58$-�`62`6, "h , y)�^^f2S , $\ak�DpolynomMgrowth�<y,d�Mj�X .��>� % )}6�~�B&�5i)eh���A estr8 ;8]D���,"�,��1). I�!41]��1 �8B��Ӂ@HAs]AM�VH)$ 6C8&�42|2:A�t�6:�$compact $K2"�6M��a2�( )V�DE'Z�'-Kr �<�dy� eta�{Vc=R �]�E1�o&X4�ǚ� :.���{�-�F� �+2�4�? tartn;, re�?� �(tH�I): ��}V�  c-r% 2 �J$ nF:F0In$I�hA�"�D $c2 f�0��I�~'F>ʰ>J/&X� �d�*� .��+�)f �!�he$^{-tB5,  }}\upsS:�x�t�6oluE=�g g?(bolic Cauch�5�L��"�.%�u, p} t�'-bp-!Q�p\\ p$*xd0.(x� a�z&�7A&*�%=U� A+�eSatFK&� .��� �Tlfac�!<�G1?5�$\,6�t}�A�%�to  2��5� f��C ial- �s7� -U���%�%�t, x)_{|U2SM:�B/&nK&�05<t�:. �5b�2 i r�|31���(� �.���}.**j}}Bsu� P)B^F.fYx�}6<,�)�OB"ayumN)0�_40j�cx�6�$,A�Y�VQ ivenla $Feynman-Ka3 ula BesA�2�+�@�h} �$2�t2+) E_{xNf&F1% :3X��(t))\cR7(t<\ta.h ^{x}MOw05-t�5�6Ms)ds)  ) +v� } q��t6�2�V1% �> #Q�Q6�^{J#.� :�t))ds�� ft+eV9�EY $��(t���ssQr�K at x(G 0 t y��It\^{o}"��]ydFsq��B%M�+�w[4]% 2L\sigmaN2dW(t)�61 tA}) a�IGh^{U"�sde$���-9W$(t)a=a!!Cm "QXal Brow�U moa!!0g6� $:$U\6bQ$End(�.cTba��v�6J�, root ��m�3լ($2���$N�x�$�*� �>exit %�ye� 6� �D�Q&>J , $ � ing A:.�&�BzHR�>% �nUd fk})&YlDE&�=:�9ũ�.B(x)rB| ,)�, ��^n� % (s6�B��\]�(t-V�UJ�XJ�)v�%���J�:�\v3]Y1(� p�6�&a�$x|B2�.$EkF�M��i ��}�e^-e��t}=� O]6 }�UQ3:Ssx�6BF�;�J��6�rX%���Zr�6��u1vWe"� ��H:ath� , II���/ entl\�!_*{E*�$I$KbrN.D�:)�A2�< uq�- m<p})  appl�GL^z%s��v8" 2� �g J�Y)�(�&$$\psi$=$c$Rc c, $�^% �?}�>"i�K"�0(21=�IaF0er k, �ECO!2�C<isjoint�&�"C�:Y���^ A(k�W)&B�.�\i;a�[*�BM=ax2� �� k()= 1 \R*zO:��Ta-��(=}$V-$\cup\2�):�&}:y96�}}�l:�V�:�B�v u� E��� .b �a]U>�leq� ɞFt}%�S@"�*!j%P:IB5�a�^�9��%�)e��}�BV655%�\alpha$� ]�]�%M�26}[$. Ag_��I"=$^Y<2:BV<02�K1� spli�H�I }&.M�6JAKJ�1�eV* ��6* (1-�;1}�� :B�F.� 2��~ u ��+Tacteris�+"  ��� ft\{�;�tY||�6�J!<� I�-�AG| r-U[[f%�=III}+�CVi  R%�+R �Xd"kO�M�<� 12���{}xI}�"�s; -vK:u eq P�E� ��ft.�%x\wedge�=w��^� Z�~�]n#i��9-We) [ >r�N�.7n�J�s)f���vUR  ��W(sI~�*w��F��G/_.$JZ�S�PR+>/^n-�GSHqrt2w�h>�)cJ��atMma�{m]�q&},$�� $**� � J ||B(xNq.$"�Z:e known l�( (l$e St})*�: i�S%�� ��>\ VH+^�},AJ  *L [0, r�� )(��-��G G }B.ma�a a�G G  � &�B��B�5�*� eq2m=@[f6-^%-I%}6.�}]`}{2mM ti!]�}�G"tCM$=��2�m�-TN�_��|1|$��Z�umis cl�h�0� �� �/#d % .� � �j6*eq�(\  _bm�] �O�<� .��$>*� �e�6F�� �[Jh>0PJ��1H6Sq��J�r �4�;� � 2>��>HC_ �-�r q D��.$But*�*K�$!�2�� =9&bxA�$�d �j%ps�P@2}(Id_{m}+\Phi(x)� ���e'e'EndR2oW a $C& ^>�"?% �P�ij�=Q_{k, l�kl A x_{lI� Its> �P �[H.7P)=��H(R_{iklj�9+ lk �Q�A-V>�t)�I =g.� \widehat{� }.�t))��.<v;1jN^<-]2R:��F�%2P�>J�6 , k�%6, laO�D�O�aU\0a�u $B$M3Br;�]( � EG:F���) R�i8>�56B2. R� Q61kB!h29�*-V:�R�d })y�M�Finalla/6=!:b6{2}+Z:N F�=F)6�Z�.-% ^2F1�As�{228*����S.jha^:d6����.)c C��i�.toV}�. VI},np�, $\beta\in$[c*`[Im� rm{VV��К� � ~� ;$C�"� % ||>�sNQ+ ��^{�$ A����>s� ��ƙZ� }��P\-B E� { }||M_{stV,geq y;[M]_{t� q K\ !  ("Ly��KQ,"�rw��6���M�>j0local mr# ale,i#t+ =0"��cor�%to 2t}=>�t)�&B����9 :�Z�=��{�JNYu��������$ stopp�3tJ�#x� ��� 2,.$ *p*A0[2�|| �}}���d �#�"zUqR62}A>h^{2�4A9]e*.Kr�6�>��6�E��3 �2� �O.1T,�� se consj$n$oC C_{2.pc�RT=us�5k6)�z ����6�}6���_=0\�* bset������.zt(EGIb+#2\}0 *=7"�%�"_R ��ZV2J��!.s x�)&  }}tr[���6/ -Q>�1st}]ds!^ S.�^2��}��B�� ���0iD+Fng.� "� j&��J�/�{�|c(x)Ugcn�%n��8|eHC�R��$cC�YAe���,�b��F[.�"QA�F� % =D#cB6#��*�^w�J#�)�Wr-J@ x>�-/6+H� ��"� {V�1B@6>, iA�%���G �� )&(fQJ���%XPV�b�%�22B "~|�RkM��F%p�l.�.6Se �gB%X�!]e(X�[G�2�(�>< $a, beF5�$.� �W&�!%�r)q(a)+}31#})q(b%q q(a+ %|6�� >7.Y1ungj2��}NowQ q(6pA)=F�f�mUa%}.\���&f*a$=t.oftq�$b$=$Fk�<"� =1:�>cF��3lf�9�YF$�{1m� )-q(F�2c�W:cP�%_0 y�cx!�J=}J , $�?y"5 \!=1w �%-�a�F���ya��4AjL-�'z�R�AO�2 ds}% >.� �:X%6t� J�v=�A�=&� E_� �0 exp-!QR�'a�&>s�)ds�&�&�/ I-)^�+���i�Q6N���1}*�2BR� m�[ ��Qh�gJAds-8#.!��j14. ����7� � }q(y�����]2�*=�%� C_{4�<2, t)E�%L32�d?R� `�P1�"6>)}�b�6�r�e�=��r �~J�$V{\{q(v)|\+||vF`% VbFAG��1-fj���^%_+2�ma��A�m}}<1�.2*] f�ss1 >��G�G0 (kee��t fixed�"~x�Ous6�4�Z= $��F�0 dQ� 0� *� �.a.�)=r�M�.$fw�;[u%06���6XDc^�%� � ={ \Pi}&<^FJe Bf*�(yH ��Z z�  $y$=($y0"y"$)�!Z =(W$(t�m}). *f�[� ��"J�J�2�a;Va^|��� � �"�G �+�Y�U1� l*�Z noyau} Co�M $w(s)t >�<�L��� 2 �L�zve realL3�y>0� �e&�1�nf^�E}$o%(x�22� FsK+�([R \@[�oA�&�)o(\mu �+A,E �9]].~)�!m.��a"�&�<f#!7$x[7�o:��)a�8ed&�A�&ara�EO,�<�}�<"~B�nr"�EI��� "�1 \t}-1+!!x)z8x�}�.9�, t� 0^@FKF*z(0D�E 1.\n2l1 �b�E>R$t"�~!q"$E*�B�$z;Vu].I(�\� {\cosh(�2 � })}}�� {(-- -I�AnN5 T2}� {x+ � !���<) !e{9Q�\m{t1�b�3�H .gT J� 0 is}M��-� ���*)�xv�>& 6 !����7�e�0we purs�kheiioc( }${\ }${:!ȩE�*}�MF��]E`2}V� \\:M�6_tP% � AY!n�<��Bv[�2}Nw�s[*�x]�R2z!��Fb>L &9m6�С� � ��d�v�.@qy �| & \\I� /a� :t.[c��?<%�6?2� ) �!.�R{-5�{s�32:29%[+�n6*a6d�o��� �.f�i ~6N{��}� B{t� I�).�and�pB� i�����ӡ�t( q))�6�.1\tbZ>�jZ�kB {:�.z)}��2�(�9�$)�r� �scap&/ � n�>�99 A�i"m���L-L�J>�f�2Q&n����p��0 B9f�A}�� ��)�X wrap�X�g.�c(�b�S)�Q-[$KA") .��e�&�$ �+�!] 82Ab�4�31��D�@b �6�, X� �*0B!Aget!9 %�^~if�|#() E�g��_6Q 8�"�z�G���L9@}�P a� ^�@� �����B%{2:����.."��6\\�B+2m�e�9�)t.H^{E6�\1� ��*�+u[| z)-M�-z=�d5N N8�*�0.$��6� ��n�4&�:�X$:�Q"�&))G�(\hbox{\bb R�, 6[0�.~6��U�R�.}� �DF�[�]���$ �+</z*�4}-i�Rq:�(y)fQ �#NRXE�S:��� "� �S�s.�> .�j�2(� r-�H�HZHmG� �;�5F"}I�:3~�-to&$�h\{FD|$I�� b� })\}D2�*} b_y > Lb`$!� suV��y� 2�.U!?e �� -���/.~V�\},A��)=%�B%>,?�0}�x9��)%�6�7�� }/2)s* �* Las#K $�y"�LD 6�;}$, tpJ�.�K,$7�snpsi=c-\F�t$, >QF*QB�%$ cf=L�~�\�w�$ 1=u� ��t�6PѰ�r!� C(n2 TQS n}{3�omi"iC!5���+"`@m��M|!�"uv!C"Q.�g �U9= .+; �[�1+(. /s datagl(,�\ but=]2}J.�d:rM�/iMQ^R'>CB�JJ��.�kQzQ$VA��(F��i$+Q�h%�C��kx.F!fOH�SQ0-cJSk .$ Si�m� .I�$�e� *n�kb �h'f<�)s.�$\g|i(k)>0,6�) ��f"�)t� �� ���z� �'>%.�J�����1cR�MEx+BmiM3[�RF� ΃% �b ;~�J *� .I :W f^{m� �� fI�� ��{�=mN +�;+(.� +5�2�O�C �D�C..FD� 絍� N">F)~I* ,] Equivale�T, E��� 2�^�ea���}�� �I&b� M}Ι��J�&f n��&�2VA���v�.� )|J��P�jungP*� 5B�$��������z�v-&�f*� �mЕT���{ thnf">*  $N.�p*�I}<, y�upI�|f.v @|o�||yF4%}^{N}&�yqpny M er $k> X�A 8}+N dAE�(0-2})�.zp� "H N ��.�V�[(6��wB�l} "�GT�;�]9�(i��r:�rm3JY[�FixE c�a�X� k� -�m})j,q T9��.5a]k��*6���H�H7!/2F�h�.}�[\ � :� � &t ,l.���ll2J "�N=]�$I�*)�\Ql $.�^{�-)�� Ez.>GC!� g���;��% s r�E2�|a�0}}{16 a6��](m�$bAsc /�6�6�%�$, t, k), 0�� .:=�,&� %�.? v:�.U]$ �e�W( N6  (k�7 6 %j|X�&{숝��^ M_��~F��w�0�0%e^i��z9��"Q�e��4�T� }��8�u���ea'a�B$� $(P, R)*x�N�`^2�]>9q-Be�&R�Af!�i]�� �� �� �� ĔT25�6eI�q�hD���Tz�.�"�6� �w��2 B �  �z�*C {"�qL W0�**AbC^bf&}� 2n&' J�*&~� k �l !)*���ofNlk"��chussfSM �&��&O�eL� x�n/2 2ý&ב� )�9*** t�q��6)�'.,1*% }6B*>�(!�)z� 2'*=1�rol%�}��, �lun��n�j���p�z�6�p�D�BF+1VKrylov�c�Js enough��-a"z* oN�type $phi(t)�+ �) �.  �h:�Qp-E & *�P2|�g6�'6+N�tAe:�so�.Ǎxp���\[�H+H+� >�&�6��%'� @ N,� a5!4i� ) {Af�)`% ��&J"�$nK &i%�&A�m:���irefharmoe�}�f�ȍ�0&v�.reced�s�gs.6�(a $x=(�S�S,;qm"�Qn��A�>�*�� $g� �1��6�}B�!��."�1 re w����,S%ri%hJmq��h,#Ln{&��s, $ynK7+"x*� �L} "�w*hW�+6MDcVX<x*#� {c2:/�/�6�"��Rz0!q�?R�Omega �b&E/x'�...K2I; (U) M�!�FHA4.\&eq|&��by]{�w��A��� &'� <2���y�Sact�5wma.p! the RZ�:��&J , �Sy)=g_PVZn$1zon�y����V�=�DBduZ�% �2�22} yE��^{j}y%.:u�e:9�uZ}):Fu% ^)�(A F�k"����=E� 2䑑�ar�w��e�˕2 \�42})S�B ed��> cula ;ermCf �� "4�:�* p�i� qu�tA�" ��y��K� � M�^��iw�n�)�.7��hclass��ֱy!ellip�g�aZ s��6 }6w by 1R� �+�  \{�� E<�}\VD!�.2��0a�P�a �=���>x�Ze�&�9, \�mՆ�o*� !"!:�t50� \~� 2�6&J�JWHy!�*G��� ai2��Lfdtnf!� v�9��M`*�"" -��}�{ �\;}V��}U�]���M��A�6�2�I�  (P�:�66�K.� LiE��K��!zdy."-->.��t_.2k{% �) B��:�E.]��up O.? V��]��l  w� L�>S#�\Q�\Q6\Qw^|�Ad�Ad_{R;B *t#B$�W�W:W$B�f�0�k�k>k.$�~w=*�JuR���$R�}?o�r�ssubp .h�� f}$ \ $||F�}-w-Rc���Ixi>c�By�VZR��r� �Me� R_%�an FcoG� KI*o$N�� X��bb� -Ke &� ��:�q�'�� {\xi":�k$�2\!1}�wG���R{% }"��8.kRjNXw!3*F&&f� W"'&|Ka�36��v�-�2�����nW= N_{2A�,�� �C(-#!�^`% nb!p!,3��.$���QE�p8V�����6�= :�-w$�;�;�;� A)w� not � &] �ed� �n2�>i�� "Z�a"Ri=yЄ, I +�)un; operB�$ $L$:$D\lo.��VHX�&l �OpeL}Lw=�&� " %� *!;wk"f;D=�2Kt uN/R|Ha>�, \, [�9ns ]DR_ �it)�$L%�F�lf ad�y1I� spectrA�fq ���1��ut� �F&��� ˠ.߀F� s $L��!����G�GB3)"9 d =\{$R&)� >� ), u�N�)\� �u�d!�% u}{d�_+U-n}u� 6�� Hv�te"'�.n*�q�R�$�i!}��to�, m-^�a�jBve te� ductF�*�Zo}%B�F$..., \"/Z :>�)�� en L�AAs.�ex�*1Q� $6ER% :%� l... �iRi�)�4[8:�J�i�) 1�1�H�Q)�u_�&�@m}1i�q�ua1<�Vn})n�� X Nm�3 ] >F"(�i� =�EH%|q�]U(L�%�.��D�X�G\ U (L)="�8{�)+...+m(7"K1.�{ J^6e7�closurZItƌ�^�1} n�- m}|$�nu�\in_ka���k� mH6��B�s�(���n�ws{(}2k+1c��n&04kw�9 Z}^{F�^��6M(upmultip�A�b����ar)g�spot��iQ��a($Z�5<fun#��b΂ {d�����j}H!C(*��� H$8kk$^{th}�1 rmit%�ly7��E[ Wx)�D�o��M��dx^W Z*�% lowܩ%G),�)��:0�2�.$\��**�W50cL$\ is:�2%-a�3Em}Aj*�,��2f")!X� .$ U!� f� t �he#\N�.�to^Y���F�$ � �s�t�?f�� signcis Sh�(Friedrichs'a��F�& �5�J�K�� >r.kxxRS} vol.4 p.207, Thm. XIII.48)>˝�!�A��M�a�l��f[e{@m�I�.8�an�wA��155��"��=� &R�NemF�2AE�n�j�^boG�>} q��y��b{C�� � &��kA:xB���1�W M ��5 \i\�C  I�i��. a]�$/$Po� sums�� our ͞s�a02��p.��� �} �JDia�b"ړ��mes���� th4} (i)&\W2q*�max�&s {�ңE�)>֣$�i)Y �bwv� ��R������`% d�/�'V}$>��� &�42�$"��.��RS=\}! M(V)|ڽ��g���6y63+ %7P �8 %�"� �i"��� bp� &*AM1 :���~)5�l%�߈oS a�s6 �*�9!� d`M� !�&&E$i�:� $2��s| ��5`=(2\pi�f�Qm�x}  �!�}9�k�E��ݽ}^{-1/4���(�d?=_{n"F [�<T� }()�)� >�}%K�u�� Z#�kwKV� �2AE@}���� ��6�MeIf \ �u am]��q_se?t2���kq N`Tn f�� $=1.iv)T���lw��a.� P!���;����na�2UpA�preD��==t����~V}{-@.�q<�tG$q�}�:��wfEoyV-�$Usf4 ?U�>:=��_:�.�e+3�o8-q�!e :0}$ requiring\b$T:"�f�A*&YV�|��ny&��Y3!���>���.��iNu}>�aH1�$��N�0$��. E���ltwo1}a�U+"Qr->0uM~��a�&��=0�� � � &�~x�[Ÿ�.+=1"�dliM7:��y72]�igB�:/2�j;*p2�)&q���4-i.^R�1�{w{�, .J.�F��&[ prt� J�  $>X&� vS����D�o.�v&v~%J)��o J2��n $by 0 outu *"�J$�ZAn2�*�&'>s�C aL #w  #(&o$!tBُE5$C_βu�T郹 %6BN.�}�s as n"� Nfty B�H� �$w�'�|6eR� A�m}%�.�p�� � �[bywLG t=;L��y�sH���-�2I�P.E�,"E �$:MF�a�.i2|�2&�N�$ll& �$co�D K$>0?�e�%i���/�V�2gW )}>Bí�23 n}#�6�$}%??P@�dy)� )�Nc #c*R[ r �a�]�0e!�� a�B�R�a�^�"� 2�%�VT.�^b(y� det(Jh)}dy.� D�'s[YG.�nY*x)2G�i7*�� G_{iB��CvJ�*��*.q��qrt2� 9��*��F)y!�yK�.o ���E^F1�)(y)}=�m2�G(a>!V� ��[ |B!|� C(M)(1b?2�'� y�.RH�n �L��� $5Dx)�cc���1�q}�,̖l%KmA���Cp�`$\%�� �Se�j�3,.WRXae^=j)� Y�Zx��(y)dy'[3 6PR�Z\�2�2�A�d�'^C$�@22 e��/&��)B:�F#V�(�n�(y6�a# �=0a�)~��� �%fg %�ݔX:�݄t��kş��!�2�)�.���B��� j�N�}}�� 6� ���~�� �  A)-�� �fnBaltern�f%� n4"'�G. ��}:) E^!�"#}=�i�� 8array} [c]{c}% �yf }P\notOCQ#O�Mh8%� koZ9 0  "�����; c2 �R�7 �I �6*�.�*wv�"�O�, �M�}�$EUK=Ne���N%.R 5,R"��)$"�K�21"i�Ő]� �L�E�F �4 implies (iv). \QED %� � \bigskip \textbf{\noindent Remark 1:} As we shall see in the next section, the Topological Pressure gives enough information to determine where the concentraY\ process occurs. This inF,is contained��quantity $c_{0}$ only. But what we actually foundFta secondC CT1}$ which carries some+order2�about!d potential, narrows down !Bpossible�c� set.��$2:} When c�, ittan open problem to compute all� limit and values of,coefficients��3�e insis! at �\ll minimum points are ne!�Parily charged, excep!�eIpequE8 s ad�)�ymmet!�. I� an �A9� provA\at A�e �:� �5� cI�%�TN�,achieves itsNar)S Ȓ.(4:} The mai� orem!�useful!�interpre!L e dynamic%�8a particle on a%�Tact manifold moving unA�Av8influence of sm!�@random noise. Ind!$P, as $\epsilon$ goes�zero, L densahAXability5I�satisfa5~,Fokker-Plank5�,: \[ \frac{\8al p} t}=-�P\Delta p-cp. \] whereia kill�term \cite{HMS}. $p$ can be expande�-a�A=! eigenq:(s, $\phi_{y8}^{i}$ associatAFo�9i1$ $\lambda_,,�8p(t, x, y)=\sum e^{-(t}Ji(x):% �(y)�A0@previous analysisI�s��!n%MA� �,neighborhoodSa�T ,$C_{\min}$, ��%�t��p�is��d.�Xx \begin{coro} Let $W\subset V$ ͂!��� Assum�atai!-,al W\cap C_{�@ is empty. If fore�q����$_{n}$ tende�o��8$\lim_{n\righta�|` \infty}\left[ \int_{W}uy�N4}^{2}dvol_{g}/ %V>%% 2' f] >0!tt��J��E�,set{W}{\sup >_}=+ ,$. \end-X�� "U� @Proof.} After tak!Ba)�-g if n�beAJa n�um�aŐ mea� s $�I��9p$ vergew akly�tae $�F P\inA) 1}}a(P)\d�$_{P}$, C$_� �ea e$7>0$IXll P$S$, Q�eq� ay} Rx=1.Fg)� �gEg:Ug�M%u6- M2�H��W$q^1}a\� m`Say Q!$2& . UsA�Lnot� �`The� \ref{th4}F/ f_{Qe"=a(Q)��Xsqrt[4]{\prod_{k=1}^{m}� 0B��u�yZn->)�}{!�} PeqN�} B�}}\geqj\�q� {B�(I�)i�B� _Nn=%>J�Lemma%v,creetin} end��e�m of. �$%%% A�b� {j��of$ q�}�k kI� ��� u�lhavovl �m� ��*2ed A���a�}$. How�� didA�*�th.Iion2� X leteH! let \{F�D% |n\in\mathbb{N\}7 ��aOs�^$with $\varf �-�CIf�set $v:�=Ip{u}:}{\barJє for each,$�A.)(� �;uB>�,% (P)=\alpha�~8in\lbrack0, 1]$�>�.D!�7 % \gamm�� � [^2]�,n>, n}(P�#{-1}{4}�.a�m_{R\in .�}SR)jSR:S % }}q (At least on! Ae$ T(P)�P�� one. A� esMtim�?doAw 3 �[>E>�pe�) Y0Jo% }Fo)�modulatArfactor� 1�!�def7oi�El.4, $ d�B(r��recv�x� global m  �, e .Give� $\beta:.�p$---% %TCIMACRO{\TEXTsymbol{>!�%Bx E� 4sion $>$% %End[E��&x to find \� v!-u��o such� Y=�A, eJl ? Or� A=%�<$ unique? So far�egat8 :` 2`�U&�$c$ was� ed. WeF�reA�f te�� �"/Z# [ 21"e"��> W 2Wis devo��to stud �in&��HRiemannian structur� Nle���F. We�us)(follow!�E�i��s:�'iDefi} Af>�called� A�f- 8if��/{(d , Q)� � (0, P?lim& }��*f 0 4% {\max_{V_{m}.h }}=1%B ���5��F��$!�}*� ��j�>0 �wM ) �  " *{.}�CZ�XI� tage���#V�#� e&��,pushed furth� o��whe he64 A��Z or��,. For exampl� one �a doubl� ll anc�X���7��first:Wi�con�e a�Rl�\�Wtwo�u&'nd ano�h8�?ڏ"�@I�}{�k�2��&� Re�I�blown-up�%2w_{P, *> 6A �$&W }(x/\"} )�=overline>6�_\]� By>� nf} (i)4 �� � �R� o w$� in L$`( R})$A��&s0. �J divi�differ��I w_{16- �R}-' N }.� �;�$0 2��U�y�lP �v:!��&� \label��w1} L!�}+i1\leq ijk$m}c_{ijk}yK y_{jk<P}=���%!&b=?_{E}+"�"�!{.�P) b!�% -\La�ɧ] Id!7and� [ c-G  c=:Wk� x_{kPv� �x�x�;v7 l-*AY% )0la:Gx_{l}%�%'!��!_$� con�� ijkl $C^{\T$u�s on $U!�$� ph�Q9�t��EH6�D$ results from var�estimata]�ob "� ��$its derivaUs, �in 7elac2}�0 a rough idea �w�� �2���WKBz� )�� bas"� expone9 decay��infinity>ose:@uCi� e reg part��gcle�%%�"{Hermit&{s��V�xWned Be�I ��n}��[Z}_{+e$ � �/H_{22}(x0, ..., xD )=T ,displaystyle3� its_{j�} h_{na�Ej}�>�l�&�A),yf�nF�$��Pa�=e�{x�x� d^{n}}{dxL "e�No atM��B�=2<2, ����>B5^�&$B/=(2_1� ,..,6� )$. �.=a� easy checkv �1��-:�p>q}}dy� ] if $\."p�z E1q^]0�$)p!n <.)���!�dy�\pi1��% Zp!}2^{|2|2�M_1(P)..n!�J$:C͕Lpo��2�!}=2qd� U�=}% >{{j37:�� !.$  �� icular:H$��=-86F{i&0j k}� i}% &$,em$LM2�*�MM#1� a�!2> Vvalue& �e}yqV�(�%.0� W hJns*�ha# �ptotic&� A�Ctype $ � �&� }+\theta +...$2�"(i, Simon1})[�$already se�&atm�A =E \{Q?�! ��5}|�rit(c-�\�Ais"�weq"tacom�'$ � $ us��&ax� cedures. k !W �5L=� _{u%0H^{1}(V)-\{0\qNVM� 94{||\nabla u||}R!A�+cuM� n!{\ ���! V}% &��["u�t �_.�epF�-Ov! V\ } }c-%p @-�}� The�����}N�in�) 5" 2" �c-min ��F�%)-O 116N#uythe�end.�u�| sh !*F)b0 B�$"+a�dU�8)� 4e&t#�y�( mj"2supporAiE� J�e� �ra� J�_al quot�*(B�(=\tilde{Q}(V�jM�7 M� Q� .1||U��� 2�R7}2�.u/5�.� ���p@(_ up"a. a'r%��;%cR \{u$_{�L �,hbox{\bb N}\� N+$ norY ed (tJ�V.�=1$osr!��B0iO駩J '}&z% �!�,!)� �%T a.Pq$0. To simplifiEe�Eds "C/ drop%�x nO> $�now on."� �Z�F 6� sum&� 6��� sum"� :<:� iB!="�"��} =�B ����A)��E� @'$t_{V-\cup_:��� B�ҩ�+2F�%n 1���w, $ be a C$&` :V$\long� E�$[�1 on V-$N�$B�($I�$)yD $�Ls,%&�}% $=E�| ing$r� $ su0lya+*���}% �92 Z�� I����Z�% ��2�2�!o ��f&o'reX!ond'intbypar��[mm��n� NL^a�"�  a`!Cft"�/9 ��Q-� m�.�%12#Ap#ix 2 shP3�  wJ%�*ppropr�/��� $CwF8釶�% �F� 2.!��=o(1)7^{m/4E�%=i3E�)� Zz��������u,+FSjQ%U�hZX�@6�^X*�$�d�d^��zI�1j*qr*@ 5&� �, �BpO( c(y. �&# })n�i�)l.ja$l| � g{\det g2f 2dy��� 1��$} � �+d$ � W\ 146��36F.�ܑ�0���fE\]]�*��[ [J�V�� coco��!U�yh ��)~zs1 S�cal{B}u (A rho}R  -)}�]�!�(y).�V�})}dy � cucuF�w� Nowd����ym2��*pT��* )\vertN� $B() t b�|<T ftyon J,hs8tK7$�bb�)z[.�1u�8rm�11� Z"0. \ �.>wR��b2X:B b$}dy.�]�5^AeWdy$fj"0.Vs#*_ �^[=2H1ifa/{\� R�1^{-1/413�"� s� �-�0A��9y��kN�1]� ->0}�1H  Vx=K=�ft/\m>� ��B���\N J_2y�[GA�ut�umeratorO$ZX�5�:� 5#Z K�d.�n�&�=�^r�V.��Kt��)�m}Zk a*l�zmVl"� )Ɋm"l0\nonumber\\ \�/s ��r� B0&�,45s belowb/e�q.!�B��(P)Xa�o%��MF�j�.���� � � j�� $mathrm{I+I I+IV +V+VI+VII�L�1S �p re, �>o<1 by $�7'f$� eucl %n grad< ($o \� al f*�>y>d#6( :( m}})��=�F�  R�2% y�q����q�p�MA�+q!i^]}!f.}dyGx��2� 8�r�bv<9��, 2:w% > �wB5* ��+} jlF��1�) ����N����V=�SFQ MR:v(y��EJ_:.%�An+2���F�!!W2���� ����+B#! �%��VA�f�26)}Z� ".j+� +^�:��$la�� *R����,i, j, k, l=1e=m}g^{~��-l����M� ���i"/��6$67j}=�r�����I)��7- �-'"-k- .$In8+�& M&0� 1}{6� ( R_{ikli#+R_{jkl�#T ).$ 6�).�F�=1-�aj2�tl�&�eL)�$ :$;$R�-��- �) 3% �RicE�� �is"�)�Dtv*�h �VY��&% m�2�!�)&��(f�:vV�%Njh*Ev�� unde�Y�^_ ��nF�^+Rx0jc�V*�έ=0IU���[F��D:� �'" 61��!�0% �-�+& �]��� w1} �2ied >�H�Xn�0P � �!�MqIeh!$�� � � dy.�2V�장� %*�0 tackb9m\\iT l, n� m}���\\l��|�y�}>^y>3yq!��E�dy.�P8reasoe'688 �L gral�D0�l��{O�G+0 aRK�>N$![�uII.�Q�i �i Bi �( v)�ij�1���">< &� �� m�bu�6 "�r� 2� :��i�10 u�B�S�u""�:�E�+� P,�8�J!{n}>dAA��$ "RJdu�B�4. H�N$.� Z�">E�p�Nb�Mar8O$.�bA, $F�Wexteri�;"�unit nm%*2�b� dA�are"�IiQ isFn cle�@��I=-��e�2A�*�!^�GY�6B,i"� y(��LI=II}�+}_{2},j >��R$�.iY��^x [ �� }��dy,\\��T�5n���a�:�m�5�, :� i��ʷ 2�0,6q% anŒrg�D�F�3�EɊay�[R�HV/2�� zero�S6j .2-LB���>�% z�q$JGw-!X%J �:W% >Y6e.@AFެ1&�K�FinLC.I99>^&��KI� �p��!O���g n%%�f4!� �5!5!�Ģ��)� � R� ^MQ�+}$ \�� 5�=V�> =�rm{�=�<I.�(@ Lengthy but stra Rforwar�."s sho�._&�9 lambdaK�-8�-8&� �} #4$x� +}U .�zV=-*Kf�W*�9% �O{>���� 8R{4q:1}{12��� �� ��i�Z#P�'�4M5 *}y%];�!�CM�8�mLHlB�:^�� �.�A m���5 ��Z��E��6'}=<2�ci �Wi>@ � %�E��\e�.y�IV}$\� mor \ volv�[�s[ �=2�B�n �xA��5� 5�;� � F!/JBd>�8ٳq& �-�~H9[j�8Z�76�7.�8H_�7�8jk}�V+�&�2�~e8�;��aI�.m Va8BJa86E!�E� Ii�\]$��kVl��]o�7 ge �ey" 6���"�:9�bE�dy"{ .���%c�V��� ( A(P)+BC!='#: ) &=&:��=6< {�:.�q;u%�M>I�1��:A�}>} \\ ��0%OzV �.�= ��������uj�:2�:2�29QV��,�!bf��vbi b+ n16 o[ �4DFi�nNiJ��A�:�12�:� %��tbW} b(0Th-hk copy(1)/`3;#0qK* ;in powe�$ �.�.u�=o�b threD5%"� = 2_n0 text{ }c+8-��AR,;o(")��� \[�S}=\{P56*�2}cdTmin c\�0]�5 |~0f�e��[���@ �Qtn}(R)}|R�:C�5*q,�` xZ� ��fq ��A2�; r}�;�L..G:?{�& M�B�K��%�TS! �5um .m g � �c +d .$,�Qv#�;. � > ):�� �a�a��8 2��nz� W.QJ� J+��>�]&&**�>endy���}� {"vgE�bf^Ps.�LOeh( e} \item � "nI.x]i�in $H&$� I s�+X $s>m=dimV�8D>�xac�5� crit�gain0Sobolev embedr_ e \�I[gh��;xI:�<<9&%C<f&�;but� �6yf�6�T�IrZ�V�OPfW:�P�th�J�g&K�H&5Uatgf* cm�e�'��K%6o&,gV-$�)lslocal 0Tum versub gGW.-�Ac�h��4jeUfif� �$�: � 2 $re always �S�� �!1%�adc�eIugc#fn�7 2�b$V*$�tO�ijugi}># %�� D)}+*�1 %�K%�1L jk�j�3�F~ � %�j��J  k}}) )�:'jl7>=j�Z^jj%^kW:gV^��>�j} % %V�>,�2�C>01�jS$jk5�>Cj}}I=an5�k�&�3%�3Ncc_{jj%54Jn+>)Kn���.�%Wb�2�B)G�, *jj�"�a >�iI>�j}} �o:��T& �!oaK} ��� � �I coincide�5nnh.�Re�rxdegopcy�� ege}�XWXW4Me| M "3�7�M,Wd�l� �  stzs(cvies6M� "���$gs c�H$)�nn�$* $-��:Dh"C$ ��Ber9��Mum}�j'� n�cTogi�t!` !*� :$ developpm�f� ���e f�63�*�=�^�1�3�%�� �WsO<�min ��$Y � }!,�%�6��ps~L -3��T�w�N1 WlWx \1U&>�Os/q�p��L c��xinz&�s�d+I��e� k6�� chi �,  _{3 4�6Hc�t0"�_�6c� $ 1" $� 2MQI�-�i �B  wC_tC_{5}CQhavinC &A M��� 0*er $n$:V?c#iz" �!��ru�-(�h�!2 �h"~b!� coC& �ce�a��!�n$^{th &�!^dN qual+in_{Ca�}-�Y I!n+!a"dBn}|)w�a29.$�� Si�V�]AE� f+]�E{ becomes s�nw(a�qa�c�\ ;AJ$steps i.e. �} =!��- �A�A�mG�i�A?!�n l�yr��m bar!iom� ger.$A�Ayre�| �Wx5  Ei{� E {reduc��oa ingly{in�in�7 ��j�6e��>ze?gA,�e so-�cedՍte J �12'(} page 304)�re:�m  than��{�bl ledge�!�&� v FH%u�eZ}to � ?�;L6]��)A��peEi�wMprecis3xt!; X��ermea� �]{ext�0d.V. "�%J�A+N%s, P��8d6O, A � s a "@M:\OmegD�av2E��$�y�9n+}6�!�Ps �$"{P.#< b1}p6+�ioF�Eto r/~2�ap�vely,Q2}\circ�=�mzw*9J|_{Ea�.% 1}O$�aa \�B�>*CR w�K&=ve�n�y�ZX� &�V, AT&Glbe�\�AA�.$�:�h@6.� $bejD"�=lzk"�, $b=r)!���%re%�!�Cm�~c gqy��le describ�blicitlK��B}s���W�{���& Uq�se �m;U� � suggesKU�{& p T*:zP:z��Kifer90�XM���2�o���e�! �{65��8!q>%8��>�Dcer�d.�f"�-E$b$� Q� r �\&� $(c,�N�C Somew�surpri�my��#Wrat��mq����� gwoI�6�Ny% R�{(!��5_!;�e�st�{as< s:�aac��2 QS�}, U$destroy alZ&�|2par�"�;dob� I)z���leP � 1I*c)�eal �i#��*�-��0i�o*�K>7$ �.R+(y�,@2�O)2 % +c.6�B� .$�edpfdtgr8�$V� .+� L [1�Wr notea}Sing(b� � AebQPi�uA$.�b�� the 6�5����thz~]�jusieu-p= an 6�b.�Wado��1n�V!�N'}���'V&�h �f�qEE��8AS} \Pr4"Z!\oper�Gname{Si}%v}\{u"T"$ min(0, ReM"Q$"M�$� sa*-i�, .�(m~d�!!>e1a !|ear�0i�9!��j \?@%� $P��%�\ �-Smal�o elds1@"�i.�80}hY� � �l2s.5� Beca}s�i�iU.|%+)E�aken �5;� & ������ed�)Y"  n*?�at*;� or (�{A�Y�(formula). "~!���ObeJj{�per-4 a gauge trans%�:2�*} **ym�. �phi/2���:b���.  *} BisR�)�q� (%a��)e��tow%|�5.�+(c�0k��#�') "1�<�0}{4[}).S=m9*� .@5. A�new� ~ ��� z%q SMV2B.d =1$.�T%�z ���F" $.�.PJ�M&�:��2R�]�qAɅ�4\jjbtb�_da|!Y�� ���" �p9� 2c�n�m�4e��m�"��>�# &n2d.Q2�O $]P very`^Pe� at d���r� �in�&)-ݥ+.���h�4- fre�tse, k��>ng}(bte cho� aM� coordin�ysys�%(x^% $�Im}$):U�z�z*LQ$, 23!P,�J"�{�umC�U&�: 1)�1}�L$x m}(U)%��`cloIob� 6\(� )$ .�!P !�h ng Kup��>052)�?G�, 1$i,$ $#:9Ka~�Z}"XE �q\6 �n�.�~� �\ |_{ij}�3) U$�\$V h* } OA�� gn�_dE4 �1"xv"�}}$!,JD -E, ��z�u&� �S$:: }(y_E��,�=2�+ )�<"{v �1���f$�]G et{ce ax}$i�K!�m(EZ�,i`&}�ae_~ ing�^{B"uz q}�g"� ( (i)S�s!m��N�- �M -lik6w&�# phi$�?�&�$� �T)�:V E�phi^/>V.2�(x^{i�+O(||x�<3}TF!g�"MC'aB"*��ٸ���A< �1~ �@w}sh d byn$�4hP�,\mu#-M(V)|�$�,�XS�P&�$�P}\geql$F+=1�,$SF��![6G� $b�� #( BL�is v�d� A pl  !';%� US�GY)=:��* s �P��ucom�SdA��fcn@�=\BU�"j+|-� |EUu um_{i\inV#{U>9`(P8$ M� � %�!E($\widehat{SI#�is^���� �nge��%���>�bDU�� N >>� I-!���#u�B ��O5�i�l�maxpr}}ac6��A�let!d"�.�% 6�J� A�!�8lax$ Y�v6Ng� the �*.T��"x*c�x $A���c)2�iV"�%����bu�M>D!�p}d �(q�l()�� A�g�It|e iM�� ����=e�"�}�Jf�� ��_WAG)�te:˖�2� \�=�Q&� d�Oof:�.d.$+I�M�(a��!pl�m appl+Ito&�>� , ��.�j ��-e/��p���"�� :��)a��2�?O1 !*e Sz� <(c(.,�p+�6^56&||Aa.?Aa�P=� CAoX >uC��i�A|$�F� t% T4CQ�$�t�w�O:s|$\G�� $\Q6�uw P�$ V� $q^$(Py_ W$(�-*�?V� iA�,c). Take A=4 0�e,uhen $y�.�gCpeFe� u� F lx� ?m�:^"u�A�l1� as f9��I:%" . In�1�o��+Y&�eit `Ger�����y�u� �1nZ�.�Ml�,th-final}(i)�J�Q,: , }$.�>� % $'�6\i!YANto]o"ai���/ \{:S~6 }$\}f}0Q�2�w2W�� f�?��v" N� [���n� !�Ut P6WI*�!w:�D"�;$�����R}�61i� ��$^ ��.pks y. d w:�x:� }.�w�w DPF.� �]aUB5 , % �'\f< wK wI t�80��\kE�C9m� � |2� |�.!W] �l e��1)�^ 0}�`4-ޑaL� �=K"S��� $%Aa� i��a�Z#��� !{b� ��(iv)If \'s  6j4FR�o x(� 2 9 "top")�� 2^ *�". i)}{F�j*+:ɍ:N}sumBupX:BwV�mK� �;top)� \} �B1��n�EA�O:KP�-�M9�H[y�g�7: �u{"�\� ����"áAi�%ge,� %� ��] �c" e pa�&�59%[!� �>l��}ionz er�e sca��q9r�.�!4� A��t took�6F&�I)�� ��a HA�ך�*sitY :�i�����b�5�$.�by�co- 3 -9/(-`s , c� Bef!���M�wo` �o�* �",&; des  5 $J�*9 $��!�,"\ Gg�of�~r�u&.�M�N$��5"�)� F �m�@�\.� s"B�inŜw�\[ 0<�+��a*, \{}R@�\�> ;�<�zl.��3>- X�#��S A1!�3�82l 5rE::�!� &�'��,�2 Vx 6z�E?%��eF7�}%bf{Jtc> �. !*w+�Lal �q ach.S} ilar%k���& ���,BG.�y.� (vՑM�7�r*tv�r^D.-v���J�T/�"�y �.I%C{}=�m�&.�.1�naU�e�| v\in>�}:0�!:%N2�=�:EAP%�0a� a�c��� �B0��'�A2}:<��A72"Cy�!�(P� }2��o��1xB >?H(x C&m��)�A�!�Q6Z22 "� �UpwŚeEo�H� upperTRXz�)i�)z2U�6���!"� tڕ�eB�YArt,� �$*} \ps.��� � � mu] %�� /2}-rho/("� vfh|9�OjN�o(-)�J=0�<{, ̑wis"�~�)�{=}W R/ 6��X9at % � �q !0 conn�����A���\{x2� �joE�>{ �|�A�A�!"\}"�� 1[$� tH#so{y��Bj cap$��j��"ub2~�h��,9�6���z�2R$).��!�u�0so}�# !�one�$(��^ lm1}9�7; � &�5&Qo2mv"}/v~��z9 ��!=�n}mNn��A}{u_ :w_qP~�:n�A��+oR )-1&D>� Qq �23$��؇I�n=)�Ӎ�iN��~}a �%L� (P)<0>f�13��M62� buil�^EQ>�":X �*6���?��1�i�"44Nn P)\}}[��  \:�|:T(fA � �A"� �� q.C � 88� a[Y"� 2@ !�$!K!�!� Ⴍ�.:�:&xssbb, � 68 � a6ies: ��y��A(\in]0, 1[:$�e>�I*�,:B]B�&�XK#Zx]�PG"a�dy<{u.$��)l� cinu���$f:[0, 1]$\�p�|b"�u��$6�$, �3��^^f $2T�^n �at Ҭpolynomgrowthx*�&in y "`&5.�A���=�:IZ2�)}f2�A�YYF�� P�f�sF94w:A$��"�.r`I�6�n`�$�A�1]!<�� R��H&s Jj:J })$ ^��;�,:U�$\eta>0`. 6cFct K$�.t:�e a2(M)>0͂chՅ=�2�6$-Kb���[,�e�:k9Q=f �]�9.x"��̹�� *uN6�!�= L,886S�͘X�Ea�ԥt�J���0���iK})�� Jp%�is2�0 Feynman-Kac �)gral re�>�S��29f�-��am� � �_t.QœN$ E_{x��ft(2�-(X.�t))+;(t<\ta..^{x})��#bj^{th%�6Ms)ds)x ) +� B� } qy�t6�2�V1% �> #�F�^{J#.� :�t))ds�a,� w��;e�{v�: "�.d&927EjX:c� �in �H�!sde}).$ �:Z&@(sam�� a� SB� )�A���$f� 5fe�� at2�+�!��� ��t>�=E nR�C-LZa<<<���is=idl>4 � 2. \quad0\hskip4pt\vrul�(idth 5pt he�` 6p58th 1.5pt��|��r����٤*G3Co<�Q>�~N�, 6� �ly�� <@*� }}L 6] :E$al"4�D)C_ "��} LJ�����M�!�*� �*O�Z� (D2���N4&q3i# �%(siB '.3� Bn }� in }"JH \\ &&�WFS1|0 ...\� �/m�%�)=J9ad}\\_!�0<2� leq1*�} t}t>�1��R, 12#2�+4�tb�:��P�  3"Z � � ہM963: $.b �w=�� ktoxEuz|mM>�;alpБ���7details*����� (nc�(usu�in#u2,�Rd,��\ 97My.G--Ovw6O ���ZS4���m")of@%,�P� *�.Q$%�"�%F�j�!t �#B�m��A:phiF)a�u��P�B?=P .\�� �77B��H%29 �:�f&"E��(P�i �e: _Class/Zellipk�"��s�@�.�.�.I BI!��&�h a"� z$of�F�E}w(y.�:�%�!�W% �/j5�b= ) ,�!2�� edpp:& ���V�%  :=>2�Q^{*}3�*d-!5a�&�)�. } !���Ss� ��6��A $w$.6<(Jz�.x>�$w(�w �  =1$."h<t&5*ng�,$L3F(\w\bb R}CL % )$b?�����"i ��&,N�.�!JWQ n  2b bKj�&a'. �S& u�%%�� �Cp+ �eFm��"Y� M@TPP'bT-,,2J�M�5Y�A�&�lJ|�[d"I;���"e,���A`&� we�b��(, .�= � $!r�rb(.� k*S�E�4�z��� _e�N�� $OmA&H�Er"MO0 self-adjoint`�8-"#byE?5= _��@xi ���U2�i"�h�U$�z:�U^�is �-!Ec��M�6a �Ute���x�A,e�� RS}.&�  argum��'!����m]:" A2�refharmo��r we �J:0MeR�@avQ<e��5]Fn{r-%�BIW)�e� n}(2�Z i}+1��Y�*|a), \��5�G�W7\]!sc*�a�[� \prټ rh_ȸT}(�h.�YI�(k)��2%r} z7Mkc e^{x /4MUd^{%V�k��\{�$}.��low�%x%��jAn�6is�\L�G�6e: �=>(TI"�%������YA+.mq�J��!| (P))6`L!��VnB�N���e��� '�O�K1|s^�cor�Iond+6eH�o&�+2ܤH3$.��(+um �(%n )K$0�|�\ast}=0�$w=$(0d'�J��,&"� �@��` )u%�n� -��v=Z2�o!�+2eR.Qh>�3!3int P��?�9�bheRL +U���=0. &}B�y!^O�*�?, 7)�.YthZ�J!��,r#�$\/F.0)2Fa��%2ʒ2Վ�=�<�RQ_a�"b %  ._*�)u&� &� ^h �aA~tB�!E~^2/~'8.�.� ��w�O$[r� CnZ=C")/�p��b�Pk�6�;Z7*�7a �:j&1v�% 5�&�. 96� ^ ��YÁ��d�2&`�"�V A�B>ZO!e}!�^9�. .��|� *���;ZZC6�syBK/"�=���I6BgeI1.) U>^6T�+���wh�8� �ei�q��>W��o*�!-� �Te�� it{ +1 } ^*�s* �2<enn�I-AI� }�>�[JO�s:�9M{.�CaTfin.t>�^���S��D:��qu&R)�k=0�ô,dk*�2k/2A�sO"�>>[o��earli�Ui�o�is�1DV@4nd capϽs�T.��to loEc%�("' 6A"7j# !�u�O"it�0��truzV[6��U.Se w��;�\ %=����G W\�genL��,"S irst= " A�]O"� 9�,HU�� ���s��:i+�aA 9c�ac.ZCs[>�:��{*arJ�s> l��@7�Rse I�QIne� 7m(q.� ;s ( cycl�hwM�Q7 weak &�$.��� �*ٗ+J�se L r . %A�X amoun��literaA�vQ�C��>�T=C� ( %far/ work!� DonsZ�VaradhaȷDoV� ER *QR488}, %Friedman�MDEF, D1, Fr}):�.g!ol>�AEn a %.���?9R%��ul�N �i���� �e %��of6s!u�� �nst�k.B:�%�j�!�d(IA�hiq�U��=repulsi�1� %] s*]�d�"is H . �w�0l8J*&�&Z_:2�F�%���+L}+�W$�OXT a.�O2 �o)� F 00a�!lLyapunov&��X r�YXM &*j�����"��Ս$ drif%���*���%)�(5%�9K� �"�a/�ڰ4,#,.�(1}GivA�)q WQ�29�2/@2s�1f"?Xs%$1h� ak�&A�i��re�l !�A�gV�aO�Z�_����5�$\Psiv�If)1y("?.k.���1���� ]�$6� 5�%arww["��!q%�� �2T2> �I�A��2����.�*x*?I��fum paper HK3 "��� �5�>I�hoi0�q���, nL�nc&�ߡqoku��KJ�isola!Ӎ��%��F�A&h 6� !� "x�& y g!x�! qYi^�A%OO,GI' v2�@Z�% %6� realLf��tw�V($0<\alpha<1��A�� w�Nund %�V to be mod�S3a'6�d.�* an�%��� A\/ &��P*���H2��A��o�� P�pi� nextg�.��a�&� "�Y�& $u\6� v.&�2��v�!�T�!ph�U}u\\ u&Z%vi� U�xb@ oX�d��u'�r� v&J7^{^LQime}}ˈ��Z"v=�,2�7% }:I+6/�}}vf�\���4tû� �g}u!EZP*$[ *�tv- ,eV x }N�tvJ +.�O(E�%��R�||{�"*� *�+�&�"�"]  �!�� � u, b���4v4 % +v � �*�8 �]��,��� ,��U9(v*4�_.W)="�-v)? +v+kea .`>S8 �n"�-�" tf2}�A��.K+�J�}% ���CM/2GUFa.G� {,!�}V>�� TBcW:--�N , qw�a ��u ?:�&�~r@=K. %����i6�7*�G$cQN�j� div]-Z0_�!� 61k.�56�% %f�.>2��(coercive. Ta : phi=���:&�� "�" "�K p|- paragraph_�*^ "�F4&_� �J�unq�N�a   C�h?P�M(�q�, j, �g-�"�.ᖮ� 55N 5�Ilee} UnhAassump���:^�\1  �G� n� �Fv=0=\unde �XU% -2e.  Ԯ%med�3\�M�&:I :} M;�Lԑ��6��)�L�� ����nt9oneV"F8�"V}[Ga`"  .��<+(m�6 div(q�EG2{2 fb]"�"�A$FG�8��~psiu, �ai��9u�S"{W�*F�M� A:t�F9&\p*(S�-- A$ (�� DF})�32)�FI���l �V $tu�&� F��v�.�7 � �F6�Z�)R�:V�l! .�pyed �R2�o�h�!�L.r�XleaZ�iEa�FFsh��he5\#one�j� ader���S�~F"Ia�AZa llow.iY\o�a�a�O.� of b+ "�s}4�cJ�Jc4�? c, M1�d�%V$ $|�@&U�Fle�2�( C)+ {\����$ F#�LcA &)�~Ca >_;��#�j��&�Bw � ��s?^h_ )=Bg�B�ga�:!+^_�->@�3�f5� :Y*psi� g*BM)}XM%J2 "�D�b�\3/��x��I��,ecdug�hhavp�,"��� �z�&"�y�C� B&� ||�M"Un} %1R �K)"P c!W^:6���� ���; �2��2,"C .*A � ��5Re�.-�t q,sR��� RIGF*� �(c-R)* 1&~�L�,}}-1)-� b+ )N+B"� % �%BB�a��&d�W !:��c�lta*� R7%�P:9��0g �  �W�� r~@1k2J;ve,�p $S=:�$�g�nn� x��8f-���>�R"�0$bm &�\ [*�=�W�r. 7 lya}pBV�!Vž�<��A� � four%l�a, -:�# In�h6�hb�}I-'��U�}% tra�$A-(1-\mu/2N (ft\Vert {Axm� � V0i5=U4�=��$"S 5Yd r�*e��r�z��]��aEa+a, ��n $!�(]!�j�a )� Q��}-1� �pan �p�s��+�,� =�#a4!ra��l�.�3rL� &ue� !5C>0�hCU�� atrix Ae}�. �`"SJ�.{�]ig (E�.ng*�Mmy�� 2?h�?)\��c.e 6w)+|M�|� �;0 \] ��(geq\alpha\e�psilon$, then \[ (c-R)(e^{\frac{\delta-L}{2\ep.�}}-1)\leq0\text{ for R large enough}% \] and:S L_{\<4^{\prime}\phi- RT,(tr_{g}A-(1- �Tmu}% {2})a_{1}\alpha).iTBecause $\mathcal{L(}x )}\geq 1`�$, it implies that $\left\Vert {Ax}\right ^{2E |Kwhere $@$ depends only on![T matrix $A$. Finally $� 50$ if $) trA}{9lambda}5}%J%!$. Hence)� .�, ��9��$n $\Gamma_M }$. Using�results of (\cite{Fr}), we obtai! %kM �]!� �(v 9}% E�$ R$. This %{ the proof�LLemma \ref{lee} Now� will&veE8 any weak limit: $v�A dvolA�$/\int _{V}^"$ as $� $ goAiLo zero, concentrateA*� xse)B$b$. %�d \begin{lem} \label{3} All�%�measures��j�are.�d on !�minimum�!oA%�$.�$A� verg�rRA|�� r �d$ to $0=\underset{V}{\min}J�AM�� ��. Let�u$ be a�q�$A�n��QX} .(\��-F�)d\mu=0�%zzz!S�hhSi�DM�*)A�tru�a�B2� I��k fa��� opena�U�B� \neq��% ��� show�!/ suppor%f$\!isA��edqĕ� of ��. %�Si $, ...S_{p}%��steka�pa��G HK3}T a�� pr"� ��&D �2�8occur along som��bmanifol��&recurr� k La hyperbolic field b�D� s�e� aׁhow� QL�babsoluta continuoum�respect?A[ Hausdorff? nduc! ! se��order a/ich Lyapunov"  vanish�� 8neighborhood of���pla���+a filT  allS(e eigensequ�}to=~e� -xa �%����RW,is achieved.�]M�Ap>ix 1} ��%%% I!7Y E)����co*� ofFCs��4 Morse-Smale v��Msatisfy�ס���1}{4}(*M *�L � +2<m  , b>l )>0$�f r��a local!q&�ne��he>�� then �a globac2� n a ` 8act Riemannian q*�VL�!�Rh�rJ�lya} G�baN� (V, g),�dimens�%n%!a-� m��V, !�� �>� O b or.$$periodic o�!��istS%�Fk�Ga�-8atQ or U U s|e�YdomPof�I�o#.WoutsidI����� � A46o�7 (L)=tB�h||}% A�����b�*rl "O a�`R��� ��area)"� ��un!�of crit�� �g *� refv 0o Kamin (see ɐK, K1}E'a{6U>{���>{a} �  �PE�. First��a:-e�a" IorientŜ6��$3 � 4e normal bundl�M�Nio� �(trivial. De� by T��' E��/ .$>p:�bb{R}� arrow VN  Y�"J yH RT-� imag%B� AiWXA�,r a Fermi co� ate� ($(\theta, x� n-1})$!�a6* �IU}$�!�E". $ L)heic.vand $(ek y)E , e_s{W coronj ortho-�frame��-�izр $-�E�s0$ i.e.dx$^{i}�j/=" ij}$� Pe Kronecker symbol, 1Dq i, j\leq n-1$. IA�xi�a�6 Mߍ�J2n:�,�$xi=\exp_{p- (\xi))}[�i�!�x_�e %�)]���es!Bjsb [ gT m_{� =0}^Pg_�dx!j},F"` �" dx$_{0}=d m.$AN 1�h $ H �, 02\% $, 1 FI , $g\j: 0)=g_{j02 0, 1%}%� )�D(Christoffel-� s associa�to �o5  $(E�% I�xI�)$��� mQ$ : %)^{k6�a�for $!V<, k\in\{1..n-1\}A(�.t .�29 , x2:+O(d(x)) J�.�!�� r T\xi dt}=gE$ $be written�fo� :M aligC dot{)�} & =1�\\ x B-�)x"����� N!�� ions��� E�I�t)= \xi(t))��i}U� I a�]�$q�6=$b�!I�,!5dista��xA)1�, $�i� (n-1)x �-valued"i . Co�v`� X.� .�GL[n-1;4�]�X d.�!�X}9oX${�$X(0)=IdI���r, a (in gener� mplex� D�� a �� P:��U�2�P$( $ $)$\in$M[%')-;� bb{C]},$ � �)�)=P cE D}$aVm �^aYmatMR}.$ �� 5�!�*� �&_�Bre�a� the � %�DE� negaL:#� >#exactl2 &��ierSAx�. ;\D*| lex�jug�transpos��D.B�* striy &@a�ter. 2�MN"�1Ͱun�QvA\HAD+D^{\ast}A=-\mu Aa�.�It!c  :I�5�� symme�&�0ite.Pvy3��,, �2eA7�? A^{-1}=\mt��^{fty}e^{t� }dt�WN�I9*mAn�L}$m�U.�a�� +�Q�$\ \xiQ� ;$;>kR� �����k}��� e*)],2r����L =(AX, \overline{X})I�^{e�}}$�� X =Pq�c%g ($%  1 ��A.., $ @,)�oA�bar d& � �z� I�.*� a��: t�L��_{+.v$(t�p�aysemi-&�@ baX" \aH� � \�$let X�p� ��$(�1}��Ţ$),  �[[ 'dV}�B +O(|| ||aS)aS��3*} k$d%A;L%[�I�~ {}(A>d=� {f})+(A ` Q��f�$bu t�)CZt.�3�_-y�A]�(t)� >[]�*}� �% U, V.HCU�@$ , \ \ (U, V)=$\Eil)�UV% "1$d decre�g* A�"q�� b�fa suffic�ly smallb .��(B A�A, b )a�(t), >&>$% Af%~Zbu=4F�^�A�� a ql L}=-2tr(Aa] Rec!�&Zy Le"C+I�- L, � )�%$q thusvPsi()= &6%/2)F�q6��l$1Q�/2>� �`�~���M:� ����J�Assum~8we�a�i� $\�{b'o4 T rev� �q| BPi:eT� \�{126}}{V.e V"�c�7b of VN_ yc�subgroup'$\pi_�/ V) gx � by 2[�] ( 8= homotopy clas2 *� �� GaloIve�space)"t \ Z}_{2- &o $i9!p= decka�ns�%,�m f. g�%b)�uniqueft! to $bT $ stW'�� L:�=$\Pi �i()�IgB y$of b (i.e)�f>2T7ap$����$"L .�bu�extra c�bW* �%:involuDH$it{i.}�G .M .%�ho� �2<)����.Bg}a�;^�sat, Tie��n =.+T)�{ \thinET\�F0%q k0!leq�%���n�previ�2Wp es aRd A_ set :����!lMe%�inO.a% "� iJ�m=e)Rau�* h�A20be pushed dow��a>oR�LO��6�E#��:L=^((L}\circ\Pi$�or*� 5 ��sam�*LA��vchanga��to --b. �� &�aS a*-i�vi�! be ��ly ha&e�noticw�� 0ha!�}!���$.�s:Q&�:�8s diffeomorphica�!�fiberM]t AF&�ofD4\ U\cap}$W$^{s5,� F&% (u6(q n ''patch� up''F�N%�ed �!U��#�E��s�A~un xs >� , \ uo %o)��. �O#|!�!u�!�W�"al g$f�!Z:� w�$heF�|]?se:$N�is buil% each+.� $N!�$ (�.u}$ )�8I�>�_ � 91C���5 I� � OEM-# "$.Efound+*|Iat����",��s2�R�J�% x��xR�N/4}[X_{s}+X_{u}]���i�fD�1�l/����i�&wo:��$AS�  s��ol%Enc)�ub�T5�" 1�!�� velyZwe-� $ny=dimN�#�6n�  s}$,A n .+ -1=n/N�now ��B����by�&� v r zY , \bar{Y} 2O,(�)}}-(%=Y�3u63�"��'re Y$=P[&�) x1 �:�3) ��MsMsfM8+VS-1Q. H�$ �!� A* 2:QT&#.B� \.��";e M\ESm��. Fq'\��ion, s%�ѣ9�� "@��decays&�:H��.�!.�)A^ repe��yp�2 l!ly�aR .�a wr �C��deed sr,�)is��2Ju"D1F��%on)X&,t &$)�&)%�Nwe%m�4�6�!k�Z��$E$� ���se2C s. O*� .)�*��*choic!� ext"�f��#2`'GNy#Ns$� #��q�Oon!�!'�� �*$B, a��*!&^*6E� one (ZdA�( last�,). $ ) $C^{\i�$�aVc$E/_{t� a�"�!�) . $Fe�r.�A% gk,% 6[us ���"L"$U,� 5$�ndowedga �Eial�'>�o�3� 2}$be7oZ 1}\succ:2���(.S"f$\�7-$\ �(�ik6 }1}$��$ -$�.-1 J 6�d[min� fil�6Ade O�$u y�e pset !\s... m��=M!�-� _{0,�,}$� ǭ(C�, al elemen6}0 . Se?�~ � -0,A82p1 _p Jp)1b>t2tw`� so o�4s;�n}$I b�-�I, �$V�all!.6 J_\:n+I-'n�b is =�X9 cer^ m� C!�� �.E�%��7aR��e�[ub��h(B��M A�FJ���-)n�� t $O� �� 2�R�:O\�5%M2�.�.)<i; $OM=$ ..m�d%u� �2� rel�ly c�|.ys $O_{�a}ndpilde{O}e�N% $MEB*� !�clo0 .@?.h�/� sA:�H$\J{�� B�2� �:FI=o Y�: (i)N�ABP ^{\p�>}=\varno7g, ����-9�� )Q�5/'� (ii)�#"�2$\��2K� ��� &� % + \cupu}^l� !� thre mpon�e� QT codiQ+1a"��3 �ie� ��O_{�1���!.��"_:�.OZn%r��=,? � $=>n�sVempty�/$A{!�ZEc VH$%�.�to� ��.V2�i�j)&by arc r2�5L&�  link �.�*:.�.� �v)l@)d� 0 s3�=566Z�[ 1Tphi XWV;!� We( u)&m2]j 3�)�I Q�2� sub-Q�Ε� $Zy6)&� aL �{�]*? �4O 6F �)[�u%p��)P��5z./=U�uq�%�If�� `��� `� =mV` a=��&� �>*$"�?-Lg� B`� �'E�'@�7$ve. To fix%� idea^/3alw�� �zat, i6Ynein$1� �,*AL�(1� 6�)=1 z5qf)�)=-1$VxqZ=0��&n��(:( })=[-1, 1]���+ �J� &�=#6�a��  bu (9ф�U�2`\{&2<�� \}] sp�R� 5-1F %W? B 1 0v mZ� 2 6h!D�62��! \�7�)^@R*: )=[�,% BRst�(B2Mx=\{��:Q% | �"� -^{max}�, >��a����y\{ $dROzhD�':0}:�R� �=�2�{�% }_{|>�(aU4u�$. �(cl66at�) � �-�{ B� !�BD1} \}�B��P-O2 of26 $0$6^�) %�(' .�0}:_`F�P D?Bt� %�� ^�"��e4,2�en}� . $0$�cMb�xn� ��� nE.nV.��" 9�T�:ainACce=k1}S$i }� a?)io� $M-� �B { }� |F&d \}ULG�l%X>� -%l�c$7asay.�/}�q �$8Vu"f dA� �N _{-tY:5 |t\g�LaGTZ9WI�"m2 �- v7:-6 2r�\J�l>��� �� �. AlsoM4u��"� } = " 1�"�,5�)�_%�)�1��D�V5U/�J_ ���9-MA$ !�� 5�e�6BQ�.�""�RK:�6� � $T_{s�} :9.}.�0]0, + [*��3F$xH � a�� (t%3 \z!n>� , 0�# t� )O�2$1$ G m� WinQA�k\��!e$Pa�)"Fnum�!"�G�$ 2�"�Ois#��.B1=v6��r P� -corners&]$&Zv $\hat{cY�: D!:5G \&l6| ]}i�SP:7)�$J<*6 })~=�Qdb-%�!Z n�[h�)q�fy>+J�I�M� A�i06���q+� t})$A A{� "���`a� "YA2�aHNeG�IK2�.} �#=�T1�a�5.} \, � x�?}}�P�8>2 } V 2endz/} � ,!a���8aPR�}:y�f� $<�X*ulaFH(x) = �,B�5��7) -\in�2B/}V�}dt $� 2��u)� u��2�#o ��6Np3 \lbrack$ v  oK$u\inau1[mH�1}u=1$.xusMO)2 � BTMs:D5�a�r� &, .Fm�\:�(x)u()�t}B]9� ) $.5Z�.� �N��>�%>�:C�A8sumF�+Y��n��=WF  O �) dt= IS�� #���9�s�:��-�5?�v0g � >�jző� � >J��@.�.!W�i*Wa�� �6j ll t&r 2v���w,:& ��� ^{t}=+s�ds=yO>�.ѓdtAjt_F+:]d dt=I$ux% ��Bk@i?J�N�\\�>a+Nl-�2t!�, x)-12��_(x� Bh1.9� jt7 x.[4} 2R � ɧi UU=�*�'1})� >� $�=2~widehat2�U_ }:k\��%���O&�8y�ZphJ�, y��"%;��A � R�}(y)=c� MA�N��f � B.h�g,9&-1V\y)� easy_se��aH �.lfM� f� ]��U^)&[-2.$ \med�W W�2>6ow�$�V0�0CpmM\[or A��!�V 2�X!C� collar��  Pal2�in6 �S)f` �n #� R-\�.l�:ECVU��Xr&�2�$*� T_{u��:�\y$��ft6� �e#� m �6�\2( t<21�as2ecx)!�V\ �6Na<=2�n}-�D{9`�QB�% \!� up\{=|wR-\}�2$wQ�u"�A].�0I�E� �"6 qfU�^H �Bu}:�=� J�.t�( u}}=2i�nV \in F#)p $Dm-=G, �:^u!�J1@N(;#&�N�!S"D  0%Ca�T`�4� c}% B:r9#5>I�"� ��. }��<IV� "D"�3F�N�b�teu� � D(E.� %y lde{c �dt} � :A� Z&7� $c�0as �Ka�{L |�} �(xE.Ś+2A6�? $c�b 6� �g� +2�?U�J� OEҝ&y g�(}Q�6l B�F�0 U>JKYB.x �>=N1.|(� �U�/ � �% m -���( 1+-�v{% �~-�+2�>s&�bn�, cD=�R� q(xcm� �Q����Q)��"Leœ��4)}Ŋ����� � &� F@ ~}=�6�(� ~� � FO� @�n�� Cu < " e<N[ $6KD2R� % c(\tau�  i��u9-� n&.�uv�� ��$e� well� �.C&�.:#y�=� � 1"E \ �����y= L1U �.��$Nq =�u, .�, �<^a�[ i���t}:|i� "`��.Y�M ��vq v}A��taO x))-z.��vPy�9 :�c .�A�Xj�*+1�� A*�:���� * �=�{ 65 V I<� < +�Q�F��N� A=(��aO.� � �%aUV�A�bA7 m�2WAX�M some�.�.�6o (x�@We.@6 +1}% =B��6A�+�Q�"c# El +1}-Ɂ@-2$.\quad\hbox{\h4pt\vrul$ dth 5pt h�X@t 6pt depth 1.5pt�e"�B&=s=W mark b$ MSA equivalen�Y�&5�/ \[ bZ0+BGD��»Xb�&�3&Y2} b2��%�pxY�Zgo�)toyvCV�`m�h need�-(*). O@ RiBMX�W� i�Z�%ra.�3 orm:��Lb-uSE_{g}+x-98b)+(\psi+\sqrt{!  va1})28Ops�R non"�L"� � V � { .GGQ��$, �J.�f�uon�4p�Lrized  gO $, smooth ahe �^bles !.'&?E(family\{u$_2�D$% %TCIMACRO{\TEXTE(\vert}}% %B&j Expa Y $8End25N� ]$\}�- ���7 V&�: :� }P!���2!y�G=Yu6�R:$% ^'B&::=0.� ZeGMK=:��� YT��~7V@a�4C��9{!�R�>R�>02�� �na��n g, bO*a?nK. unde�C{�'� hax }|��}|$ $($PEQk�O�C�&!nN%uni�@ mapp�G:\�� bb NM $---^���$BU ,Y��� 9 )"ger $A�.4^{+LK+ A�x� �$psi}(=\{z|!z\ie�(z)�"0\}�]7. �!!= !�]$:e:�(x)T>�hax>)� �  (n)(Cb)^Mn}{3}}}{�^{nA@\]����5 ny x��A$:�}$�te�pto_V faste%T�nAJwer>e���$v�j�TisA!��=an&�4!]��!uALenn��f &-{"(m +n%m6 n�*jpOpuse�a�>�-o�Pn. �^nM��1 f, h� V we have"�V,eqnarray} f[=¹hRh]�NB3 �L (fh)J7\� b})#-fh\l#my�EZ {�f}{f}+2>#{"Pmf||v�O}{f.~ R�W(b)P\�] �pclef}\\���1�F�.O6� oneI �f�noN%21� "J{b}=b+2 l�n`,a�f. x��m�, f�7n�(.$&�na�� bb{%Z� }c>*Q7 & �ps�+1��}.�1�^�% +^�k�� } �!�:w}M�stupidA�1 3��U;a9S} Appl"�d�)ula(\�te0)��  ` ) ta�5f=$Y^l � h=B�,b g�G))n$� 2͚I1�� >� )s(n+1)2��#-�n)�)+9�]G-�\]� &� ] (n+2.b��@��I 2}=0��tri:a��VX)M$�\unb U }$m .$ Nt.0}9O>0 }:- .$ CeNmm�sPa�$*� O!v$=e�+�U P). q�$E$(P)$�:$0. E Z�Y]B�XI^�)+P.�2��Euf!+5P)J: (P)=.NJFA�0w�6�.l~S(P})�x � �X L-1N�]E]N2  UfcadD6b� >o-�')*�# e in!��o���+1��q)7.A }}+6U e�-1: eG!2��Y2,q8itF���C=\max��( }� -��}{�0B� % |,.9 '[} �|-�b�0|+|Yre�},"+v��]���U.��it2atNu�U!#ů%1!^�-}}+1)!��.�#-��n!}^2D-D, Ɂ-�9��)6lCT4ly�U�$max(�b=�3%B>|� !Z % $)�0� if n c , 2.!Tw"� eas�P�`�TTsAM  re nL 6 0it1}). \QED � sc{\6+�4figure}[ptb] \�{|U\psfig  =G$kupp2.eps,z=95mm, w� $} %\input[1pstex_tf5wapa�{�^"�"bn "X 4Ff�:%�vgeodesi'%� ��0 "ITthebibliography}{99} �%ڂb �(ibitem {Aub�x> sc{T.  -- S pNonf#ar� blem1T*9ld Geometry; Springer, 1998�eDEFAz sc{A�&vinatzfz$R.Ellis}--A�L iedman}--�AsymptOS behavo5-��iReal Etov}cSCtO pdptic OpeLs�a �nl Pj{a HighF{Deriv&D, II�3�h{Indiana Univ. Math. J. 23, No. 11,! 074} p991-1011�ob5F~6.B-�>Princip1)� a l gula�t�7�%�,78} p143-157:�1Z�V���9� >�.�Na�M� pJ�p��!�1 �527-53:� obro�S. kotov]�8V. Kolokol'tsov] �VAsl0, splitZM��@,energy level�#jdSchr\"olerZa J aff�w�Ial59Q"� $hu_{�g�� 2} h�J � u -v�.$K'or.{E�` Phys., 87, 561-99 (1991�L]�oV5;M!;nsker}u�,S. Varadhan}a ���al � E��[I�&�eo6��Aum4le,�d. Nat. Acad. Sci. USA, 72I�(5, p780-7832�Fl�W. Fle�M��Co�w*xMarkovaE cessKt(1986, Pisa6OWOM��eidli��}@Wentzell}--Randomq�%s!�(Dynamical SXyA��-Verlag�846~r~6Y6�j^ �^ �^ R^v�!��[�(1973} p1005�\52�GT�DIlbarg !�1kN. Trume}--���N �6�viNu@e�s�Xcv��-|!��^ % e�t2�Helffe9� B. h �A J. sj\"os�Fd}--M&�e Wells4=a�d_E�NI�gmm.�0P.D.E, 9(4),�$4 p337-408N�25:2� Semiganalys%"o�e����q��9�[cI�,U� LectuD�CY�b$ 1336, 198:�K�W D. Holcma� I. Kupka!�Si���u�UU %� PDE;;s. C. R2Smp docu 4} �>\title{}`Ch�2a҅a����Micro-�{Y\author � janks{De�7e�2� Weiz%�E�$itute %of}`<, Rehovot 76100�?� [Keck-Cen�c %e�4Neurobiology, 2� %�UCSF 513��n)s A��HSan Francisco CA 94�0444,� $would like)��EoSlo�$ d Swartz fk �A�fin^�R�}\� HT. Kenet \,K Miller5L����8}}} % \date{ 22)�y �  }�zIG� [12pt]{�Dcle} \usepackage{e�, �icx,sub7.(ams�86=<6latexsym6am A�%.Udou�*�?8pagestyle{myhea�E�j�7q3;[float,�,�, e�2�)Gf�2,�>m+:C-P � tciYX %\QQQ{Language}{ AmeripdEnglish ��n�= \addtolength{\oddsidemargin}{-0.5in} \set#evAc$0iINs!~�}{6.5 >h�/}{9.00inw.@op�B=!�= .9 sep}2tpar/0�X>amount}:�bas�e ,.56 %\newt�em{�~m�}{A�U 6% prop� on}{P 6'�9iq}{6 6%lq,}{L6�}��:bl } W 6B �}� e��cor?yC B@command{\Proof}{\�"gZ�:��P-End2)$}{~$\Box$~>O[�BP :~~S reneU5� tretch}{1&���o�zf,9�ug�U�n$Boaz I hop3�works %:athev$}{\arabic{�1}.�?�7>�S *{A�cA�er.{0E� M 2B$mb}[1]{ \m3 bold��$#1$}��. ds}{\disp��F:Lbeq}{�"o*:$e$�^"beqFG*JH&.IB$a��ial:�g}{�,:xa�6 x$>{!�:%nB%JFJJ%6�vF&v&2wyF%yB%zF%z%Dfont\bb=msbm10 at �� \def\rR{&�.R�NNQQZZ}5�)�3} �upla�nJ�j'�er|�i�?bf�� }\\[5mm] &� \foot��{6T ~� 2 S�zc&� � ,� . D.H �[c�Pn&6) HMadeleine Haas Russi:Career Dopa Chair.} ��# �" " }i&�% Df Tel-Aviv*v,69978, J}y"1�\� }�&7"&75QQab`cA�"֝ Tra��' kin� s may�/ inap�r#a to 5ribe 3r.Z m.Z x!qP3a �|A �0�Die%jJ�Vmolecu�S�Zş ith AOs&�UEj8,�+d�!e a mo1-&��{"� ��pr��d� tyA�a mobil9ac�� ��;��cona�d jjB 1;�to��cu� fluct !B fi�0Na ��i4 al 5Wdi<buV . A�ula�en��asn�a �)�� \� bind!�!un.� mean�passage �T@a�!&AUr�!]%Uarys}�del"�u��:�noise d�o��ngUioa&xnI by r� ��iga�3in ��sensor c�,.5�as olfactory cilia, photo-recepto��� 6Q!Dco�#a�y��[� �2;� E{.�& � B{% m��'�su �s synap*! dend`� sp:m, {a)!=�$+��.WEVm4��c, /Vre%$E�yN�|R����F~u<��aц,"j�a few�up��thousE ��AF}2|�9 ly 10 to protey\�c� a qus,&�f� M% phys9t.>%a { g�}D;�aEa.[2Msho��z xpec!=���!�if so��%m-H d, b�;� s˂%#p]��tZJbf! e lat��b�2�i&��{ of}�d�� forc�:2( st�/oe�gee8as��, unl�tb:�= ��ific me�"ism�/�}ew:=switch {�}�/ɚJ��� refore, a&or�U�?�rofi=5, is P>p>edi$���hreshold �p �Ao�+�A�)�in ��e6��-is}Pin1dar termsfaa�-u��&%]:S�A�be&2qd2Y Y,&>��,�A%��Xact�)e�� ex�Ns��sov *%k!����,bkiY#&��AC!����!�g�#e� *�s�}�+!�&�._uff"��E�Q�of)�2�%�it��b�{A� el� ɩ�^{ver�b&+1��^+�da2Qm* �KrU�&ɷEDn� a�s�:�u6s����yǡ�los�"�2exMinB;vn�k�alcium eI��throug�Oe NMD��a��A�i*.�ucascad� F�. AjZ8�� yI5�I {�" leavA3e�� {� out}/ing. But�je� �s��Q�&`$calmodulin��en { q�Ub!�ey7>CaMK-II}ag,� are ��!l�Q!@���p�/ic \��(Lisman94}. .�if��]��� mc��E boutE�āA�d ���@qve��wad*� ange!��)�^3 �se��, aff ��2�!41"_O%IY.�Cp� ular-@�u i0dAAmod�1.. biogt9 erb=F�% a�/o��K�E4�q� {%8Yar%a)�se,Ale!Fe�`t%!�� }�fun�f�%�CAEV �k�2 cr��-75���-�r!��H�w�E��5��50t�_)��scas 5-50}� a��erol!� ��wB��֙T phosphoryL d�,.��{a}�|�q�flow,B� �lo2�!�� mB1�e� g:1E *�ns iç�Dd  s��,A �-�q�.�� se o sa�y� ruc�ߥ�>��inB��K oto� 6 sA  ans ��)�:� �9|� =�"*y�e�! �}e6����Y d"�  ou# seg��ozy nd r1"<retina)tto/�u�1��etui��lyѦM��!16�� pe ga�% ��A��ry��s�*��� dire��co�A�6c2\)� membrana�ten�.�3)ed ``d�I�''Q?H_)�)�sig�to * �mOBaylor��aaDto�zt�9�y *�-���6d2L bI�9�֔d=ar�5l9!�A B�� cGMP,!P!G d�sites�&{�*@'aQscr��\Έr�&%%-=Tm�Sl9~s Brow[� mo=%I�� תe�7� � a)�.}�{}!�"'&vY�}�>U=9�|5EA�s w�i��wo *0%yGMP]Na���abs#\$l�A1>ks�P6,e0roxiM&� 6�10~�hh$a mammaliae/�:\ree7 60 6�. D3�FM��)֝��$Mg� Z-�a *��(. | �;paper w�rtD �5d�/�BI�6C�.�%�d m: "�Vr!$:@)�im *&�{Y}T��az>j a��as�4'm�eU!4�A&���2ɽ�Q1� ompu�A��me4%�6�II&2�m9!aL���|�h��i�i/�<�B�-_�'(�>J{ �ar�&} l=>�Q�. Our��� pr�!}2�{ ��nc,����by����,a?!���!).�� aiLa. (� %"w �}consecu� ��ks)!�6 �rod6N,��*dub2f *�. S�1AN!clarifa�5����H AEC<e��*!�n12�can�b�? Akf�d3 stead,i��� ��9 � d���$Yau,Koko},v?���"h��destroy��T��]�!�si]G��2B� {Ac�p toolp}r ӮyA %'�{��&' !�8%.�A **��a�R-Arrheni� eL�$�H�5M}���� j�� {"�*����on�&reI� M&�� e>� �u�/ s �v��7���-V $�u�!^ary�� $S$ (e.g.-�) Rմ$# �^ @tAe��mAÁ�M����sO�ngFQ_{a}$ �pum�Bex��R0!�l%�<s�man� bo:w<� $% M��)e@aU�l!�j�r�1a� ).��1I�a�m] %�Cgc�-We�at�� } T "� � g�tJ8 "��N�RM$��!�fj&��law� ";% PE,CRE} M+S_{fr���%�O0{l} k_{f} \\ ^F leftharpo\\b�CP% 5%6M�Xm�y5&� �$bE@� forw7�����Pt,.b. back/��:/�9$�dunE�=u Howț� �CFI�� X5�*� � .��5���)��a�6~K�A�� ��on��to.�=d�"�arI�,! ���y!E&x  Cp�ABE��� � ar� �%�CA�MlaV&H*s: QKEiz�' $M(t)$ =*T 1�A��C� t � $t$ ;S_�Qj�,>GA�mUinq�$\D��\x"�FQb�Qi�aC�M <$M(0)-F�Ib$M$֌ ��$t4T)s_0(\x%n J!�Uda� 1!F(�H}=\dsr_��} P\,d�=>�u) �Kj 9�a�e%���$IA�=��x�"��"ek�*�  $m ��d >�5 �K��o $S(0�]��PeZ61�a� w`{'a$\x%�e��""t�%fan.�5�� �����MY !fk $\x$a�a� �| ���5�Y�E�:jnd 1)\+R$\F:M n%遴!&� E� U J�z ^+< p(\x,S,t\,|\,\y�= \Pr\�\{%n�\x�P\x,\,A�e�m�=S Fx(0)=\y�^\�Pla)�jpdf} �+E�"S$>���FmJ2� -Q�%eQ.�$J� �n�Eu�,A+��!@-� $\y4 �*.�-�j0�Z'B�is�Z�J*})�5� �wmq��,Eg$S$}} ><,6�*�� uis!�!G6�a65 !(i�Yk=!�N�Bg6=aP5mR�M.�}MN =M_0y0\,b��)| %�*��5 |\y)��A� d\y.B� b\Y�� �ah� is \[1r)�i~}\]otwo-di�I0!�(R,Sa�t)iKiQ(ian%� "� ����s g ]˩Ps�2��n�V� ,% [M7�&�i #JMCinfluxrt��im�,terval $[t,t�e t]� ��gin.&&\�T0�s\pIVol� ��A�}}\mb{JEQ.� cdotC|x) \,d��xl� t=MY& infeu6aA�}}U � u�-1��y)]��N�P re)*!!�� coef�" $D$. A>�4!��k%9F���N2V�I�T��!u -t�G2a�� Q&�8J�("tFigureD�I9})�o�"mF&�l��i�a y��MS:pA b�2p}Nq:��iokK�'��X ԭ$R�� �Be nd.�!�R�Zhh"Q�c e��#� Zwf��6$S+o� <%!�-ne �(�ed.=��2pX� �":���,b"�d� �=V�)u5]$\x\, (S+1)-�+1�L-| t+^z +1)])��OAdE ��^$� t��aT�*J� &&q��B .PՊ &&-�_վF� �\x +\\4� c.� {1-M_0k_1 �!.S-)!'e� t-^&y\}o�2 V)x p^2�1{( W \x)^2 t.=b+1]))-!�}r�!� >�D�4$S=0,1,2,\dots� ��l� �up"�a2�Nl"Qs� beq \f�\p9- }t} &=& b�) - K_15,��1`SK-S �,!��a�G eqf�b&+&N %j2hQ�S6=V,!4eq�by*��q*; { �F6 � � p�<6.`6 ����� �� g��e&� Vby�q�:{U� -Dq�/ !5�$ eq {z#} new (�)6�TiNw !�z k_1Mf\xB@ � \1a=B =Id.O%n,��W �J}.\] 3 $K_1�D2�!v i�!�2Y �f�c��s��!��*`q��=0 oe� $S<0�$S>MJ$}.M�SBCa!i \vL{3mm} �=\")7_= 1.} By�vJuU�\E�)� �rS\*�y �pu#�P�:�(�b�)N"� � �gMMZu�"� %�"|}m�=J�_M��3��!-�"���.� `%�s�at} all)��a63 e�+ve�fF-.\\^i 2.} � at�fic"j)͌bea� most�.C� Q6�re�y � c�9u � .o2}:00��5` D�����+��5���� ��H2�#b 2b� b -a��C".b-���U�\ ta�EMo,lues 0 or 1.)|no*can e*��a)�"�)ne�*x�� *� '�Wvre�vN�I� � .�J}8 \nM |-� � } =0q� Wu�_ �IRno&� e�, "� �$0,0) =m_{0��#� 10��U�*#)2C�y&�n��.,���H0� �),/n�ys]�A��"�  y51LI.)+1�|1{|)D|�^ erve5CIl :�ABM!� Y", �bA<B���r�\��Z%q�$\p �_� Q��1�)�5�< ��\�f0 d-\Q9_E;�\ ba��#0 W%9�]� R_a}Y� �GI�%��s���5b)!��er �5s��{Ŋ̀3:} Obv^�ly,#o $e��X�teger �4��a�U3�dJn�,i�05l�.�4�rX facEaB�I�!��!�n6�Ao�Qυ$i��q6e�����i�- ay0W� ���e R . �'"'""�D{Mo9#f p��+; &�O al mB[eKA�]#ed�cՒm���c!��5S!�st�6"���Y� q6� eA'C;!a�M�p2 qN$:Sai�T">� ��" 4q \langle S_b( =P|�O,�}/ ek�� d\x �J�';*f h sd�Higma^2(tn �\ �-�^2 = @�^2iw�\,� -�$(2/ �p:-�?)^2��72_ u�rm4 �?i�aŶe�"�'$t "���=/A={(��MR2;E\ak$s � �!�cŒ {'a�gsN_0�Eid �' \mid}Av j!c� M�AX.� s�  \[N_0� iU*)�@"��UJ)p�e� fro��%;U!'�� sd})�4c QMAH2{  E@/.�zU .=&Q= Z8Q6{2}��( \םS_0!�- �Y-)=vY %�Y F(t)<�b),�T %�> b�it Pro}2�A!�I�}�a�)� M�he !E�6�. B^��A.��q 1A�%6^'SzR�m��s�1���O�A�co��<one2xb[�)U=[0,L]� e��!@9"�� ��+/� q' eadya.t!_eK^m �e�e  0A�&� x� � �x�&� x,1:� &&UK\\FS1)� 6S"� RIp�3"r2TiJ 1}{L� p�+ 1), �M+&2�,eqq4} D p''} � �e�[s-n1' ]6�=0���nr|�b  by seFfA�c_Ms� WA�Ti ���)�;>�q5�c_M��M��L}-q�] �� K_1}$c_M^2 ���& !BT�#&:a�q4�| . ��� "� s+.2�JX "O"i5&c��n�A� `\�n=a ^��aT)�:�is 0OR R%p*<l?�2k s,qTM-\@\ll1,\] %we scale#c1�� -u%d!�%%�B� q4})e 0 2�or�\�I,3ongb*�A %D uM2�[1- z ]=0.9�%In� i=����?�V�# %�z!{a�6))l�vN_Sa�\ggiL- %2AbaZ&�h)��seqql�Uq )\sim2Ku� 1) = %2 +A\cos\ s��{5 �,D}}x %+B\sinn$�%0I� $A,B� �0 tant�no" F�A� %$i�$ imp�2at $A=B=p�s��l�0^ ' %Z."6�o="�p�nE�aQU� %>�  m�0�B��a��):�'9� he %g aR. %�M�iB^n $N_S� ����-� M& %�H%w2�A)�S_<�f��MS>� >� %6�%*%!#�F�&3x�1�6q q� M�2� (x)M_0/L}Mai+ IW (.))^2+4;./L }}�Cq]���@�� ��q�s x)=N_S/LGEZ \ll =��a1�E_� �@%- p_M �1%u 0^L1 \,dx {2}{151+4\ds� &�x}�!) }}}a� 1,�����tA�p� z>lyHM.�A�@.��%gg.��i$�s)� ���)��[N_�!�� x��l1. Ire$t�:�$n$+�n�6) ,.�s %$x_1+x_nqIV�i���<%s�@��a^qaAj�)� !P�1^n}(\x_k�y "q %N_SpqQ m :M�i�E�i �Yenz7"��%�6��$� sk��68I.�*�6wOABmEi>*rQ7D@_S(M_0)=p_M(1-p_M� ��� !� D Iz bY >Y;PVarqX��t�$:�$&��� u$! \to)d��)!h�9�  f�e �o%Yin ^]c%X91#S*�@ %a?�!aM!wE�9m1 =--* ��N.��� %-(-r���B %}A�e�q�!AR�9t2 W�SX %5~n�2�m_k (pqj �iv \\ %� n � Ҩ }} �� �] %$ q��.�Ge��$ &%b�RMF DI� �m $ o�M7&M7v(�E!$lem�A��}���$"�k�su�1y�\��(.0E�d ay "�)Eg�E�to�C"<��<v�y0 agonist&*.Tx�%naS/IWHW� s�4alF:"c,�H%"� the ����)vleJLI � upon ��K67XBE�u;� i$"/��jG��$B<+�):e��g &Wp�p"x� �II.k!$a ` A< P�M����+8Isa"1LQ"IP" $k_1&�h/](2J )\� st��"�A�QOq� �  relehVf�I�YXthL7� �7-��k���-�66 mis}!6� .l4A�1q �u)� c@t� I2�-�}�-m�0��!�-.�E92������s!b�%vl� t&s �\ al�}t}& = &��.�2B-D��\p���6M\n}&=&\J-�.n�~ {\Bigg{|}��xj3 �6 ot S"16b��k_1|) \x)-VH]"�_12f�?'b-� ���a�S-zk$Q�FaY!�M�#*�:� 5�� �( P_k(t)&=&- K_1�/11�� � V�� �/ x} -k XuZL( \\&&+P_{ku�t�� ZkB�+(k+1)`��t �� Pkdot"��105 �: �1�)2�0�! �({S_0}(t)&=&�a-P_{S_{0}}(t)K_1\oint_{\p\Omega}c(\x,t)\left[S_0(\x)- S_{\mbox{bound}}(\x,t)\right]\,dS_{\x} -S_0P`0^Lk_{-1}\nonumber\\ && \\&&+�0-10��f{��� \eeq where, according to eq.(\ref{dotsb}) \beqq \dot SR_= k_1 -[1�mB]- �V. �8q Here $0\leq kS_0$, � � S_0=>� 5z,S(that is, $P%~ (t)=)d+%d`=0$. The moments of the )�%� sites ar�<\langle S_b(t)\rt=\sum_{k=1}^{S_0}kP_k(t),\quad4 5^2n7^2 95�(variance inj�is5,\sigmaj= �B|- ��^2z %�$ \section{�fluctuaF� particles\a push-pull chemical reaL}� AnY consisI a source EGproduces�Hat a given rate and50ink or a killederm Edestroyremov\eRfro*@e system with its`. Whe)�;A�A�A�=; s dr�,by diffusion�) ����  = N-�.�PM%M\�ed��4Poisson streamA1a6�, {i���:�ia݁�6p ��- o� !�5K A�0is} $$f(t) =�T e^{- t}.$$ ��] NPD $E(T) B^�$�j .Sau�y.2"a��, $\y$ surviv!;t� $t!Q, y� =Pr\{ \x� \in �� \}��� )�\,|\,\y�\x�  $\y=Ah0}2�(note $S(t)=omb��o �ut��e %'�f&e��N� $N(t��ing inN; � use ue[renew�z ɭ�kleinrock,karlin,amit}, \begin{eqnarray} \Pr\{N�0!$& = & 1Dnot.G��[ %Q0^ tf(s)6 1. \end]R[ expec�� �$E�$ {a��U� in�ra��� $t$�F�M1- n Mcn6Tf� C5�Fp��(]^_L(s)�-s�6U�0�E�A�IXE,) >� &6X�W z bn�u�FKA�.� UT�I ieq}N���gr�q �0)�� solv&) 0Laplace trans  aJ�(\bar n(\tau�9�bar{S}  }{1-f,>��$&7�#�' � � of $Z�$� n8ini� pos�7inser�Jis 0.F����w� � }{  +�Bc�5��^ s�6al.g�xrefor�'V!�)$� byV�B�( ��) �1s}{�B ��[&^Co�~ of F#n� Teq� m� )��=[0,L]$� � T. "� ,V(simplicity,f$L=\pi A D=1$Y1�2V %��Atdsm�L p(x,�y) dxealso (6�)� l to>' � = 1-< int^t_02X dxB�� FyiZUB�e2 n�p}(x_1,AZ� ybgi=F0$ �V�Green's �%�aZNeumann%jlem��)�,5xF8G=u =1+ �2}{\pi} F�q ,n^2t}\cos nx y BVFollow��w e�� �} ��r�+aE> solu�� U��^��Q[B�s )2} .e = -k_1�6{0}^{t}A. _1,s-� % - ��~+\, %B�VRof�9�2a�sf���A*.X�Vw 5G}(5.�76yN�usN� Vtu�i^m -( }{1+>AB �NiB� @JI�1}{k_1} M�Vmy)�R�-k _{1}��B� WithZ�o%�1551͑ �m��am_28 �iwq~}{n^2��Bq{� $x,yA� (0,\pi)$ax�first or�B� ,tau$, we ob�!q2� *arB�&=& �>�ds �j�� )J�} -2^2 nx�}� ] 1� +/2A^�&t 6T}}! +o�  \ &=& � iYl� 1}{2�A (x^2-y^2):��(.� � G\pi^2}{62�pi}{2}xQ�x"1)� ��:�*} Hence>�1�# /1С(eJawB�!%}!�Y�-1 �-)�) +moaA(1+9��1�Z +o(1J U}�qnormalizɆcon<$S(0)=1$, {we fiaGhe loV"=,asymptotics}>e} �\sim_{r)arrow +@} \exp(-\alpha t)B�B BX��6p} ?�ȕd9V‘5S��=� �)FA�?un-1��!Wcon�6�� is r�al3}�E��� \ds a� 05"1:�A�Le�2�L^u�b � !E2���^ {IA�e2Hj;/�&,$B� �SU&23�B� \lat)iqA�# \tau.&0} {n}.� S}(0)>�N/ that�q^+ =D  ��t_0^L ' ,t|0)\,S �q e"�=0$�MRurandos"1� $y$, wldex $S$* y\ { writeJbe� _{y}ֆ�y� !RL G(x�eR{Pre} $G(x� !� �e}"�  of>�*Ţ� x-y)� D�#\p^2 G�� �� -k �x-�  G�9�l\p G(0 � 8&.L:=�.�*} ThJ� *}� ?= - �theta�}{D��� � ��:�*}1D $;)B� "� aHeavi�etadp"�  fB atB,��_y��.� � dy = �(L-y),D�(L� RLA F6A�"�#z �R6��b�  N_y(iv)= m��S �(-�.��r�B {%!�p�[ly!�fB'&},� y�([x,x+dx]\}=��dx}{L�t�!�ad%{�M �M99�W}�b,����} N56-5 E_y[)9�-]ɺQ"��{6�i :&}�AV�)����e� *D$he total {ݩ9\1�$s is definAF� *} ENK*F�^2���w:*}� wi�&owe�$-�u"t >#s|havB� �� G6��t� k^2"�� k-"��-+JLZ  \}vLkmB>� ?t^{i�}�,dZ:�&leads toJd-�>�2�Jj�2#1$ W-s)%.� +\\ & &^ tN<\\&+&�kA.z?(2k+1)!� ECk-O5#FO^� �"nr�oV19<5 +A & I�67-�0!(�8 2u  \�)6� *} anF�L"�'u���J�[@F�\} + N�B��) d>�} {\bf�� @nt Remark.}\par �" ��"�.��be� te��� mJ�&&�._E$-�- [�))]^2 =�1�u} -Z0a� F19F-�'%-�9� � )?/>��� BS!=2� 1J�#%% 6� G� �+2d+ , +$t �.� � we}J6� �I��VBn^2*� N� FP � 2F%�� � ��[p%�����n:� �tB !tFx{Iw�f� E���w1j� �O &� 2f0�% 9!J� Wri ,R !�B= I� +I R� e �Ihor�#�/x�/ioR W=��� � �|F�(To { evaluaFR�=� |�& e�:& f�&Z=recall}T �% �Eg� t}� $1)Vng^� by $A��.E r�-g,w�ofg�&�1)�N1)HA'g�*_�2 a=e^{ 83 �?{s}m} �t.~+ �)}dt,�"H��)���QF�� !;tE�)zt��=&�yyE�kea �� m& 2-�^2B�� G J�Finv1B� �s%% (0)+� BB�n�noise�o6 � �-��(E"� �%� }�m^2�^2(0)��D9G�!-rF�:�}/*� 0����X���$} $)�$ �-s only�2$k_�<\-n5"�aength $Lps�i� mula%�})�$UY �dsm�)�+ }{ 16( �& M�OM &�F��#6�"��1�0Pf�7!!S continuum���*Hfof�5�-&UT�5enoughk.w1ed �0R�0of hydroT5!�synthes�+���8-Y ssu34i3 to "�/<ev�g�3s8. &�"�Y�"M� e inQB"0 , bul3��2E�"�2�*>>'! bsetV $�4l�e. is per"X&isola](q3s�$.1 b�3de2|5 �1measu<k(\E>#&9.$a discreet1�$N_h$!IT�1s� i i,�{i� �m=$�$)q�by�< � =�{< N_h}'= :(�/k),%i��@ l arriv�:)8�Eto%�� ��0!��0�2� ivid�0,to an absorb2� "1_��: e1v�:#bz\/)� &B�.K.D0"�#&N1�s I�N� <as-b�/&�/1J��'\p,} ^1 D \D� -!�,t)+�W \chi_{�'}"�R]n}\bigg`1m_r } �0 "k �F-a}*0& c(x,0<c_0(x)M3�1�� �}*\x) d\�N�0qqof=[���Fy1AAkh()_�d� ) }5>S& IܹyAi-�r�:nJ!E���fixedQ�!�6�3�1_a e%empty. {M2�M^ �1&x to!) fty}!Wm�a.�"J0%�2&M$I")~  A2&I�Z$�0qqn one ")}P0'=)g.�(a� �0� �85:�""�8Q�r2.ъ��a:; sst} �.�c( ��,&�!1M��,\\ Q=Mu:x=0} =B" ." L}, U Egf}2E@ ward�3=!Z8@ve':(e ({ it has���?� p>*ime� "�7!\!s�3 ion ��}Q dum�]kA"� iM4pbs{�� unit �}). Two � � s FE'!�)6�1&/(!�Xe� �[)tL�-!�� M!�  +0( 0^x_1;� ]��z  5O �l!A!_&�!:A�.3��a�eft\{$a!3({lll} 0&&\h�D!�$x� q 0$��x,7.">0$t' H�.:F *}"� �Y5� fre�ll>j�(*�0 ��LeEdxu)�L%"� -ц �!6� �ft=�!��x^2\$�98># *$ �=should� �*���2C2U!'e�6%� te case� 0}).�&ID$Markovian N ��� %�1 �pr�BpE&�BK lternat�U �Al!0u^ A��w.�]+� &� ,&�@a ��ach �.>� �= t\rR^3$ w4D$M$ mob� agonist &' �gW!rq>, embed, ��c;"% $�.�?{\@w��AB �le^|�>�<�� py���Bpo�1of� surfac:a!Q��� �" !�@$ �R=�@f each other. Bou�))�9 rele{Bn99 expo�DP=wa�#s)��# $I.F�Ci\@�%�5; �%���a~bin�Iis% �*passage %{to� }2aD9DQ 1��p[_a�8e��>"$ A&r�.� �F-�M���;rea,�Fain"m of*�=ik ng�!� �rshown/S>O2J �F ; �JtoY#_AsiPdely6�a6%��.�<lambda_1�y�I4_1�I&nJk $N%��V�9_$@mZ�a�qv, $k(� of�ch=�}&w%$,�� MRs (>3D\ beq � =(M-S+[)^+�HNk! ;LFmYs.k2��!r�!S4x^+=\max\{0,x\& � $$(S-MzL(wMq S.$$�3>7 =-�e'��!c nextU��a=� well.d�2.�VE if)aneous� B�M�}{N�.�A�\BpE�$is justifi e�Var���u�u� (Q�7�4re1DYJ6q� O�?{y|}��\c8CS}�G6�!�n.=N�E�=kE�%�to1p1/qHk1+kZ% kI�)^+Z("8 &} ��5�s.�!g0a birth-death��c|6%�s�I$s $0,1,2,\�B$\min\{M,S\��8i%��'���({kn k+1}mMk�M1" v"}=\mu=�2���x�#nŏ1LmSmSm0 e 0\to-1}=0Z Set�G^N= A�=k\��e o# MSaaty�p)dot P_{m��?�B �S6�D%{1}{O"V R �Ji [93}+ \ (S-kZ ._!uP_(t)1V"_{kRQ\&��O�P for} k= �+1MS-1"s =noIp�>) W � �SP �mP }5�A�M'9�A��P k,q}�=*_{k,S} q,0FIn�2� �avera&�Lof:� .P�� k_����Pj1 �P}jP_j� "� P_j�'l�to G}P_j(tx>�a\�9ry va^�P6T �e4O�&O �&U��^2��YQj?q&� ~g+QM,S\�Q5^2- ".Q:8�!�q�/Q/Qd�HF�! �y*� �NC !.�0A�iw.�yq:�u�9��N}�m8a�y�i|e��m� �y� tm�]�Z �K6�\�S$U� >&=&P_Sq��S/l2� y /k6/=J_{i=S-!^S@i}{k!)� ^k}=`>1 i�;i�;k!(m2� I)^k6���V� +16�(S- )�{ }} J� 1K2�.M( � �F" _1 m���O }�Jstant�F0��JC6�4 �c5��*� �� P_k=�^{0I2k}a8=1�� AEbe"�I��s}!�S �I"1X9u3` "�F�Vk- Yds\.��VB[ YB AvzC }}�'�")�$�1±/1�% =W�M} a�)^+q%�(P_S�/Z�2f�� �*��!|�Bp!�^�[ ��(�)k��.3�� �6�:�"\)S(M|f�M)�! 1�m���graph�$2^$$ {\em vs}�"%D Figu/�Z/� ��R)^Z� I��2��E%% &M9ab�W �4yTxpHB 2 "ISI n� ( � an �"_)cisDd�Jat�Thannel yinmUly B�m�X a� . T��Wd�V�4 Rin�>:abo| *�R��6� ��� $n^*_1�b.��s� edH�)cvs2D� $M$ -3�!� |vH�>=k_�?�� Mz \aOa1�O_Wl}>Hn_1 2A8.DM�*^=N$!�; fo�!�Hwa%� ��+$�5 back"�$ $S_{ch}W��Tp}byM!n= = S S^1 J� $ � effabv7!�`�� e. 6C"> b�X�)�eRroR c!cea� Q!{:Z#!>ai-� }. R�)I5qby ~t�%as}�{EY}�!!�{he�&��ime. � resul�P$he previou*=[W-e�w*�8�8PW" =�)�8A_{At} n_1 �� {i3s�I�)ER�-g)B* find�F�!=ez1A5 ;#am�T%j? ,-�s},(�, G� it�)�&�� I�}�(M-e�)(S yU{� [a�� H"�-G||}o@ D7.ogO 1c|\�!|( q�?q �%mU���}%c$Iu�q�E�{M�%4 ary}2�$S For �!F��$S$�d�%(1P sim ��1� )-:c MS}M��3+�L)�v;�-}M9�e!�st��li��{�U%�#a"AEA�geometr>SCam/,^ simiCZ�x�N de_d,!�}J6�ekbe {]eJlBb[��(:&2�Y!�>� 5^�$)[��B]con�8) �&ɕJv�[�^1 hS� ._`*N:� �in�. %%Fhb��de&NYm �?} M+E: {l}��f1}> \j� harpoonsk_{b1}%d- 7% MJI \overset{22��P Lup�.\.G E+P. ��� MMR2� ��a master�%�!�jq[!)"X@u� !L s-y$is $kq$M,�mZ{ at � -R, $ k��V Pr \{P�T k, Eq \�--�di� {�N }E,pE#ular, {� kinevDA�1��4%)�h� q=21} �{P}|qP� (1-q�+k_2) m{M,q} )g /,+ k_2 (q+1)  -1,q�k�^&+!�Y-1}-$Fq �"%�} FGq q, k�!q EBhAg���0 ��(1J�!:�0�+�>�0,��\qk,E�hsk.@-2#+ !4q�-1 2�>>v M_0,pivM_0Bx%x!�M!6 :,"�({wACF�$Y#0X%' _{M-�$ahQ_29.�AM(�k6tau_1}='\ M ��k-q)^+� q {He�BM�.�u���{&�!asM��5- { un�w}86�0EpC A�available * &�7��. �F2ZW � T q> k k �:=koX;7 q.",�C-<���.2:"O oB�NMM1�N zero�vn�@ea�@.�� �#�{{F&i��.�h-Ey� ing���$coX+r h?FW� Q ���c5ls�7 un~ 5gprotei�?{Wegtwo main�6ac�fty�8plcZf};4Jrst;�@bs# o�proced�/us���!t%in {S)U�Aef{M} a ��iin�=� nB� F� traj�`y�'Y�e.N*!�9� $e.\x�3n�h>0{9{} i&D� �\S,MT\y)\, X\x�<S\",X\x+,\,�n�.C`=S\,, M =]x�4\yI�!Wjpdfp���3 �)�/2��DF9�-to8*zEW�"�"A^!�Zmk0�!<.*��M$g!t�� ,!�-"�! ��" X$\yH�� . AEH {"= to�of M^ fSQ^�A!0��p�^%+) I|0-\&�a�^�a )( - K_1 Mp^2Ca S �&]o]Y*�Z�*�&+& P (S+1)V+1AP�V+1 X- !2L&.�\h*.�-o)^+ K�M\eqfff:1�lnDi�!sW.jb4b at.�xA0��PM0S$�B��� Iwv .J��e&�5�*�be.��TD )�.�r�} new (�)U�� iB_W*} Aaq�2\xF�,Nf�6A��.�a%Ua- )�- -ki�n*%J$-� ee {m-&����;<cal� tedI�3I�!�s � .}l s�F��ź��ad�direc!"Phd���P,+�. DEV�PheJ�� � �Y��$M(Y'arjC= ng�m2�Z� ^ .R#,K� Q  { neg���^N�(�5�Si,s responsibl9�*F���٠��, { w��} -E��:at}.�7!s�8 {�z�*(i.e.,%5eian),]%A\s U�_Q�, ���vely}9k[A!m? stepin��)�}�mF� "P#!�become"�% !�s)�&=&�t*� &� 1q-�Z^{+ D+��*� dM^OB +l>3+i�q+vU &\� 2!,q}* (t)��R"8!�t)+{> � -1} e6�,g&:% ".%,��"�w�+cal`�O�,qN�(q+k�K!�\&  � � ��"��U2� NS% &�1�)�qE�Nm8o slow&4hanA���!*I�"��"�I����9{ be} � ��a"a�? y�6 ��,�:s%(o%�A�0e.(r��� })l��q NPs {M%z"�-}&>(�* =M \Peqq�-J8ц:��*�Hn!-M$F�  $  � q� A0J~�k=�'^q�"v  S-k}(q�ơ�u,6�)�@HX��Aq=$� �/at�Ced� &� :���9Xm!�A./�����~2�ճ- "lA=� �I�o!%nh? $t"�'"�$�U)I�)M���7 >E<�ށ��%�N"�'(nfF� ]�.h.�'%��1j#$e�.x`f�w>� � �� on{Conclu"�w*uim2����Z2�Compari�l�udel��&ps�KYI�@b}'&/ b9 b3�, ��3��]ap!od, how�)���e8 �*�x�A*4Ca}Io�>al� eB�r� exA�e� �5 ����Dge�w� 6sd�ipea!)\�qVar�$Z|�2��FJ,"�8R:&&�#r>5��u�� !� i�<reSjs$�!Eu �BŜ6Ms A2� �7� >{{}}{!"�i em��+>N &C�Gei�\� ��r}�"��ai �=E Z@6 N�  %� f Wrh�x�yA� $A� �G�~��} CmE�C:%s[N]$..a�7se� 1�re�"t> � K'_1O �Z�[N]�A�YS��pro*r�Y�tra�al>�f �?g4!�abA\Y ��acEE,e 9w��G.�!t: W�� >mAI��%.{5�!a.�one��< %A&? �'� of.s��*� !U%M�-�?�sses �S�(THIS SUBSECTION CARRIES NO %MESSAGE. WE NEED A CONCLUS* 2)}�{ %�W!�v�!{�.� yb!  %s(&�-.��l'Hte9$ %�.}^D��-6� w� ɒ v�9��*� :>�7.��arRr  %coup${�-��9����& to %�A�eN6�yr"c��d�, %q]A!wmethodo6 4.4�5�i"�>�| a %l+��Aety:*� ��7V� s} sensorc s,� �=��a turn !Nga@� 9�!* %&�K.I� Thes� l�A�+s"�h+�"-r %)�mQ cl�wC|��un- &�Ki9* origi� %r��yAm�>o�2 %!�%,!P��� jL2��$�S&SB&���� � RVU�bmE�{e�=�evd�!a�!*~ �' a {riY\-M of"s.}��&*"3!&�s�5�l:�&�6d>@b>�>��"}� �O!$Fsee�~� Pro})). {�c �U:� �t Fl1;B� &�{�}�x,1I �)a2a %$^. a�uI�:|9�0 a�Plicu�� ��: !� ���&��e!�i| �@o�utwe')"Arough.�3� . Ap+� Wwr�rt�atL=dYau,Koko,matthews,sigworth{q�]$UJd/Wr=�Z�۹��O{ �}2��!7��$u����� "'",(5�nv�u)�rq� �`!& �. O�Rat high6> e�-_1�7" � lea� �=�B!�`$be immedia�Ar5 (� :�"���fJ�}!M"�*�B �� lE�q�!{Œ } membran� 2w!�W curZ.\ { an�tr�Qcper�\ s. �'�nPp�FE�s9-  P%�P ��� \�2[A6� of15��g��!� 3�}N �2a��aus2perpetu� &�s�Q/2�N#% g94�{ef"41_AqsM � 1�Hu�*n42KLalmosw shap�a�verAparabolaAF�0�eU�$�ite 4unique maximumyMa.a&bE\io�*!,� Q$�Qm]6"�3in��#>�2�=1/2$. ����s,m >n�,"�+A��at low-H��s, far&Y � �%� . ControT�q7 vol�.�E�.�Aua cruc� issu&�}Adu����Ucs�zmi�@ �},ar signal. C� ]�vg��Kc��fox5IN �&EU��(stry undern]BA��R��D play�$ � role|a _U�&xp͎s�AYz� 5l �wasn sur#uI� purp� to��f�/aG�OA��)/�h.�m�arms�2��:�"2~���,M�a hard��wto!�a�%H�6�y"!�a�;~&d patch��L!�2�%'!n�4ell. A �V�e�x&�V=F s hHEU9�]�U���>��been V�E"}z4� �������-�+1� �<na�n�Ah i*������G:�mA� abundant,ks�Vr� chAoO�aw��~QRLH �FyL�R @isa�&n*E�neighbor ��is5""Zh��1"1� 5~be = tRV : P$MfuIc? e 6 i*6�1l �y,si" �7 �theor�.,}, yU\iE;s :Z} %zNB� is �� sugge�# 'xaiE�� �)U��U!<�x#bed �ys� �V as���do` �Go*&It�o%�!� y-�sA]� � B brea��� �_c"#�e7)�S��-���B�9C�a�%Tos�����meM �t$M�h_>bő,",sca��&�Qdomin� The %*!�F� it taka�N v ���JPҔ �-WY a M A+�%�&� bu��6#� s:e�few.N�im9be6f\v.%R�P! �8!��JeK �yP~�� �A��j%�N���,�,E�a#�k{-!� &"M�pa�Uto"�-9;2* �.�is valid�$� -� s or"l  &gQ �6#P���J�8ne�'%YE�� :V"|<� � �C �:�! � ifE:t ] Fe--�us&� >Q�sQs��v�A�%v1 � \n�j�$Acknowledg��s:}�w-Ulikρ�4nk J. Korenbro�,R. Nicol��ؑ�! iscuys. D. H C� �E� H. T�, �A Su+Cours�S"� Pm1}, Acadr�p Press, New York-London, 1981.�l��}L. K �R. Gail-uQueueA�S�.w�\� So���4Wiley-Intersci`% PublRCJohn % So5 Inc.�, %��PNAS}ec olcman, Ee� kotiZ. Schu� ``Calcium"� �� dendjkc spinͿ  moti0�Q^Bi%�.!��;87IW(81-91, (200EWUVHK}a� �%:J.I��FA�Longitudh &�A?etrod�2 e ou�9se��( cytoplasm:e!��equ%Xof� "DF�.} �6} (4)e"2566-82 J�S1>�2\K*�9,non-arrheniu�!�4s", (pre-printa�9)S2r]MC$Ac�.b�)�gi ppear!H SIAM! ApplCM"2�s .K��:�2�E�� 7 �W�� ing:"�R�fkE�a2�r",6� Jour  of S�� Physic�5*@NNS1}B. Nadler, T eh,6��OsIon���!� Sg*Y MverdaAHti�g!I*cd�)Sis*. ". \emph{%kJ.%k.%i.�|(extbf{62}, ��33--447Ee16MS], AErchewka�su��u��a6��of �� r 1''.bLed2�@TB}P. H\"anggi, P�flkn!aMIZ�\eca�RM�@A Leory: fifty years afa�K�@rA�)Rev�>d.%�6 (2q~1-341 ��02 MS77} B.J!tkowsk 2�!exi�=�  �}�gturB��7al �N� Ŵbf{33��367-3�% 1977:�B82>�%���,E. Ben-Jacob!PA � ular� ka\�-L'=�� "-fBy a�.Yy429c835-849,822�D�2}yS4M.M. K\l osek,:~2� ``A �-2�� .�V�m(5g50�595-627�:8Yau}L.W. Haynesa-R- y, KYau!aS$yclic GMP-��v� ] \ity�.(excised pat�9of��:x��T Na�'�OH321} (6065) May 1-7�[66-70�862x�}G% ��d� light-_i�_� � �00uctY��!�B� : � cha{er; a L J*F �(�'9q� 21-6N��,A. Picones ,J�A�86���c�� ent�U6T 6� s", �&���6�2 Pt 1 �360-5� �c"�F�oS!��`"� od��.&�Ynod RanvierM1 �%��o�# (1986�+�AC�g��Z.�A��4R. Eisenberg, $%%m��behavio`"cbe s�jw�&<s^�E}.u��T�E�fc���&� Dif&�*E��m(� Ser�in@ ��A�"| ohnH V" � 0*! �YT.L.  � Elu��� ! ��2� }, D�#NY� 83�=�|th6� , \newpage ��.7�}%^:� Head} \!�e\psfig ,�LtMM; ior.eps,h-4t =105mm,width } %\c4on{T \.{�  Ch! f(��"Uu }. E���3QW (wh�"circle)֟s a.��a BrowF7Z on until�[~I�9D0(black color)�< occu�M �aca��yl.�\%2:�s(� ),�&� H *#�be P!�""U �'aN �'*�$is plot�LN�)mw� ���$�MF �e�9)V��;i�P\p�shOC"� i� 2��B��2Y ���h docu����5�-1 6��_ �_ �_ �_ �_ *_  1f2>f�� �� �� �� �� 1D3�E�n������4]��Z�1@5kI������������¸�� J.EJ�-Ki� &���o�� TINS�V�4&�$ D.K. Seli��Segal,� Liao, R.C�len-RMlinowA� �::�Exak$#x!�*���long-t�potl6.� CA1 �/o;/�$hippocampu"Q Lear*L M�YW42-48�6).!L+ �C��A�� ``bm��s:�n-� CaM-KII 'Sc�)z276�2001-200+ 7�=�,J.-M. Fellou10nd X.-J. Wang(A)?q NMDA� ��!m� �B"s�)1 �73-275+98�-�d JA Fall�$``What Mai�&s)m ies?�� 283}�339-340c,9). C.-H. Ki)7:3 �Iz� filaI Asy�!transmi #%�VF�*NY�s-��19! $.4314-4324�� I+dA� Zhab4� sky, ``A�@��)�D: a CaMKII/PP1 swik,�(U�0.�b�g�@!�an AMPA-�  anch�*assembl"B �n}� bf 119Am1& B�Sb]3to��B^9 $\p���is may&�2E�x>.Xg.sU]@ H �+th"xgon�/"1. SOTS s ne1=�C w]B6�_R?x ."�b�2ez_� >�+ ci+S$��A�a'~bE�$"�RhSx}�=etOw$'Dv p;�J''�SF�S�x}=��z\p`2��SN�S0GVjpdfb�Heeq It*���Y$S=.�rs_0(\x) a }*ee-v8�?&&�&�R t) }t}Q�nab̴.�R ��Z"}q\x\in�a"XL�Z.�R&% .6QX�{\n~~��Nds"�a0}=- K^S_1 p^2R�VpSV+ &Ki�H��Rb�H + o�S6G�S+�9+�M6�S6/T--,5 sM S-$kAw�JD��$p_I�)<�riS3oܶ$ag�A�ac�X�s��"�Q"�4f.I�5!}*K le�3 R�(h��"�*t�'�,b`ary. Equ� entl-��is� 2�)Z����- i&b�/on$)��-DG��I)e**"�". m�f�K^�Ut)+ [�UpM,Zx%� ,t)]U\Y� e�:�!zbdE�+& [K_1M mfqoEcq�A�)p�R�d�<A*�!�0R,�>I) s"ݹ"*�a�!��&t=2)gq 0�� ��No !y-6 + .�� }J{ �Qy]) V{\ј�X2X'V��rh�+at�P$\x_s$u(oV or�'.�>!xU��n�{q�\\ 5J_s���b \n!g2G >�X _s)-)K !]��^&+&K_1�*E�5J�V+�X#E� �*vP � _s)$&�!Sa��j�Z�0�~,�F]0�;NC��3G.5{�c.�)3�f�?df��"�8e� :�X!��"��� ���{"�&� $>�1K��i�"�ei� ���:>�0*2A[ D�!H m�+ YI(�@�� 0A�f.a��8�d 2d�d -:c��'x)-I�=+2,2Ѕ%��A�x)X .P0OB�<}����. �2 �  h�2��� 3�3� �1��)H2E< �& =:E�3 � 6�3 �\\a�6 �!��q��]� Appr&�3o�6�(��P To rw���el�'�_ u�Gp�f�9.�#���at"�P9ki�f��Ps�7i�}� I2 g6s&�/e,� q�X{N�om(Xs�D�s_0)�}{w}n\e"_ )=S_b(HY�$m@I�!P����!�Zl)|�arrow��{{.^2?k��&��$M�d�������  �.v$N��Lmaxѝ),0)$��K.sT�*+$���w,F� �oN�rȰ.$" �6r.%PK�s�@,U:*� 2}�B<re�G�� =q1ksA9�d"-�ent�CaqNQ�6r�[ *k p2}:�2Q=�O,\tilde{K}_1 �X�\=�Znn,�˩� .42`(cnd��"rre�eoY�1�%�he�Ս�= M_0a�*T�ٺ d\x � n@eI8)i5�] -&$"�  = _KGup r�H� 1���]y�7�`2s�8r�"�v��M2q �� k���  } \x��a��O�2 E}�\nO�M.��  |O\HDclass[12pt]{amsart�6odd�marEL0mm \eve�@.(1>$ 16%�!>m{thm}=$ orem�ze39}hJpo-��cor}{Co�C`%V�;c�� RFBR'G nt 02--01062�RErw�bchr\"o�Ker fe�o�5Institutk) 2� /cs (ESI)aia�'ct}w���T�$e�^n$)>$e�^n_+$�� ruct�6MlGaN, $f \mapsto\��f$;?9n��n Min6i �>e��G,6�=�we� Cs�c�z�a w��e��Yp� �aO�nd]� \make�� "0�Int�vi3K��M/:�^�:��} LetM��*��$ b; fielӡ�>(d� C I .G�Cl>1 map�a$hi_h\colon)�_+\��>�. AA: qjAg7pmultipk>.���.<�j �1!!to-.>f� $\�,$, i.e.\ let"��gd<r*} u)� _h v = h !(�u/h)+ v/h)v u\Ev= u+ v,�� 0}=Mu�|(08%1}= 0 1). �(�I� n easily�check0at $�%fE� u, vA�as $h0{us�A�.d1DY x}$Lj\%�>�)�l�s$�0meai�u:�  �$�6i��-%�M�m� ic s��|rinNAA_+uv���6-���2 typu;ofUP{\it N�}�2<Z�gř��Q�ID, ��.x = x$� arbitr: e�5'e�=],V, .�Gun98�`�i�Mogy �qu*F is ob���i ~} $h$�N�e�"of�' Plan�4���%� In f��a�V�up|�)*$ :��N� p%� magi�>61 ��s�b6�Sh�#}�,Np!s�|x|In�ZO��!giv�| a n;�>a��FHIQ � $ (or @$)�`#> !Q.��X��a top"q�sp�)b��$f(V��GUX$1nsh��saP&���CvT"sHA�IS&�K} (a.e.)� b�H!\M�s $I��N��bse�$XevSB�`X )%:� $;>ɼby-^� !;,set $x=\{\,(�� ns, x_n�D X \mid x_i\geq 0 e% $i = 1, 26$n$}\,\}$. %R $x= BVWXK � $��xm��x_a; �\` b�L���)$; so!B$� ��^ns�r�!�x� ��De9 maF(�^n)�!����Hu�Y" � *�Fo)%�Awn9�$U�t \$�PWpg.�In%�!�� s behT�\�r �Lf%(�?Y�5hol3 c in~$U!�Iqdcl� �:��a�] (S �B� �IU$�h:D �}��%)6)6� . u $f�6����J %1�� _h$ ba|e f"q�� ula:�g� � _hI];|fMe3|�n��3G eNa (�:)lw��!&2|X*t^� ���} � ɦ�5Kt}ko-hm� A�(3)As���W�[&:�AW&�� ��%���6+"7X9| 1�OS �� �rV*w . By�dEip) �%��A U� *� �s�O} � ��U� "���W bVt �a��>$f$�{��^n $ W; ����6\9!"Hed�8�i} c��b>��ni �*wVO1�%�"s �� . Of!�!K,|SM��! s1����Mr�� � _+^n�WeQ�ea��!IE��n:�req!:11�&� C�su2���am;i� >e�W&0� �>/ C z? E �R����~GB c:e�{Q� � * &��thSS ��G:�N�`R$A, B�O E�.sum $A�  B�'�h�� �un�.$A�  Bi*XD D� CEK7N�� way:D ,� {\, x� = a+b, ���a�\ A, bB��jm���A[n.Q q[ � -t�M� Of3*rC��:s ��V1� d� =�N�(Am���f$, $g$��YXT� M�(\zhat{fg}_ I�%T + g$;i��,d f�� r ``in� 2�/t�X"p~+J fIDJ�� !;5� �isba?de2� "�%� V```t&ik''�jpylN�  Ozigo.x�fg�&�ko1Fiz��em. %�� tens �:�}sE�kY(A.~N.~SobolK{\u\ife � help�us2d*{S*x^Q:*# i .t V&h ��t.�m{$Euclidean i�(��Ecalarc�E$( A�0x_1y_1+ x_2y_���� ny_n$)� { $V_+�F�z�y&� ѾV� ilit=ble} = n� ��Z�(Yex� n sԝ^W �E $V$); AmD *� d� % �F9��_�QRby��m�bD}(V)$>J$�l�,� D~� .;�"o s��1$ �$F~z�� B� E� $f=gl�na�]A!Q = g%Xaq}M8@x$�Mg# ��� 11�&� %_�  (�'.,�s)t67D_+�:u�"� .�.f�"9�a$�u"p�' $iiE�, �so c2�> T�*�.� >A�a .�Q-Mo2(_+>*N�%�.� &�\Y�� ��N� �s!�, g��\m2I��za�� ً}e� � e  \neq �M0uE$un"2m�w $V� ?H ��$�1 .����non�� �$c� &���!��: venume�D} \X [1)]}Gfg�&m�+�$; 020| "|�a?�y�cfE2 c =0D3D:��� T���-��i�! $g$ !�.{on���,:Y.])�&� Q>.^9@ LeftWT"��e)�� -� auto�Hڑ SE 1�proof}iLe5 s 1)�2) �1d),ourމicrf�u�! �s�R(3�O�u�Bv �a p 3)�dFi /hpV "/2�.X� n $|E%k |gA0g$]|f+f+ g$9�� ��Y�in!Vli : \[A) \{ f (�"~� \} \>�(f+g)  2 �b7 .\] �� \[� (ni) kM((�) (�&x) t G 2 +  NS �\})� ej$W 2�e$�!B!*!"$logarithmi&����$monotonic.0 6�1Z->\{q�:i1E��{%N})L-i�&�� C,!Q���let�9, Z �A�E�. A"� A� �_f2'6K JH .=O�losa� q�($anG"s4 � <� �$H *'V$. TakW� V$�8!5�rQ�y hol���fi�z*� �!8&ve���Wj� Iz(tix)| + c 2�2� � r�� $�$)| < (1/2)� e $�� � + 5. On%�^r hand�-vly�+h!��ry $|(fG)-! < 2�w;�gy��122�>A��!;a)�I��N��P�sE $$ yy�F��{ y.�2���m�y.xa�ʎ$$ ���Ilude��of��e�& %�(QO B� �%&�&�&/� K p#= :.E6.F&X ta*�.��"It �-� � x&� :�2�"i>�AQ2�"(� g*��ѥ�!���)�( A�� ; ���&� � ���bely.-r$ �Zd�.a�b� �d tes a hom�omorphism from $\maD_+(\cset^n)$ to $\widehat{�C}_+(V)$. \end {cor} \section{Generalized polynomials and simple fun,|s} For any nonzero number $a\in�$:#�vector $d = (d_1, \dots, d_n)\in V = \rs��$ we set $m_{a,d}(x) = a \prod_{i=1}^n x_i^{d_i}$; fun �d of this kind we shall c{\it g�mon �}. .�X are defined a.e.\ on $�^n �@on $V_+$, but not ,$ unless the-�s $d_i$ take integer or suitable ra!�0al values. We �$say that a� $f$ is a � .�p5�0} whenever it /$finite sum!/Llinearly independenZ&. !�4instance, Laur-ns !1example%�V�Xs. As usual, for $x, yE $ Q (x,y!�x_1y_1 +I6� + x_ny_n$. The following proposition %result�@a trivial calcula!j$. \begin{:}r�I�a])�Y� $d�>�have $(\q�M� })_hI�@(d, x) + h\log|a|m� ��e�If9�.TQ�,Ah n $\A%Q)�U2i� P ReeMU real( $p$U�E�.�isIqsub `} if $p%4sup_{\alpha}  $,A�re $\{\}M� coll��!� W�s. Sm�A�ywh^�=\�JA�(convex; thue�se D "`tinuous, see \cite{Ro70},Aborem~5.5��DCorollary~10.1.1. a�discuss9c2�0only. Suppose%hE�co����$1�p%35}!Wi�L 1) $p(x+ y) \leq pAh+ p(y)$ef�ej E�$; 25c�dc1.* & , $c %X _+$. So %�_1 p_2$%K��+�a�)�*�. 2� M�K $f� \maF��U�Ť},�itAquantize�y exists%Ω��$)f9f�0(same symbol�. .� ��s�!and $g)���in�0 �}!# �+A#\neq �� g(x2$ belong�b to an opeA�ns�Fb�@of $V$. In parti�cr,{U���Vin մ�Y� theyES� ly ݟ . D)nby� thit{Sim}]%He��llF.��i_%9 -�>V6W h�\mJx \capA�2� . By!r2bl}� Y4e �ofe�(�]'=�2��x��nd by =bl�V).m imag��ћ�im}_+.F!�6=cunder!i d6n,transform. ���Tstatements can be easie*duced� �w 1%����9���\!�f��nsemirA� �2�fD54 > n idempot�sA�.J=CD!;a � ^mte�� epi"� of �%�=l ontoN�m:Q_>� 5w��respecta�A�ope� 4s $(f\oplus g)�!=A�x \{ �0,�#\�� *dot)! +"�%�2�P"� !d-�'*N �>�2�21�0�.�, g� maD!�N� asymptoti 8y equivalent} "/ � �-� g$;� :��y)l:_ ��*� �z��a���. AR` willa.�ed��l �=:n � m� a 6y non9 ='��&3 %�Every.)9�%>�2�{\sc E- 1.}2� I4s, logarithmic5)_  (* )65� 3uct ,SVV RUsakis��s y our.�Y��ula~(2)!0bSubdiffe5 [of�P���}* psome el�5arya� ults�)�  analysi�ese$�c0 found, e.g.,�{� 8MaTi2003}, ch. � S 1.&�qM $p >�� ���W } \al  {\, v@V\mid (v� \le� \ \for�o \,\}M'Q I�$well knownR���"c .�$�� �4�eexactlhei\s6�}!�� atE origin. ��M�aL��� also �in1� 5��9} & _1,p_2!9>yU 5xPnumerate} \item[1)] $� (p_1z K p_1\��2��6�L v = v_1+v_2, \text{� � v_1�5E_1, v �2$}!�$; �26� \max41(x), p_2(x)\}F���2VQ#�en";.( 9 �J.2%�a1� hull!��A& 6?cup6=f�%:2. A-n.� �{ mpty� compact r� b �M*Q�� mapa�mapsto� c homo*m�.��:> �;("� 3)5J@�cal{S}$!La݉� � ץ�$V$ aS1 above) �� &�Newton!���r>d�A��F�2�62 let u9�  N(fI� !M�(g)$*�� 2���>th*~7>>f�$,�Qly>>>g!�B>T�́t�����YP*L3 �LR� thm��� �/�:�ɣz� N(fg�!��� N(:� �� �� ��ith ��0E�� g)N� N(f+c/� u!x|_1& f�2%&Z &��f� f_ p�>� {\rm (}r*��2| � Ai>�� )���K)�6:%�)�the�6�T ~1,.�~2%�R�e��qf�q!:$� � 6r/ f� to�l�0�:2�E�"<b���� 6,��2.�Ob*�Let_= mJt^nv*t� a" ; ~ V�EvV=>5$a��? ��lex*j �&!R� d\}1a�} )f�J�1,9 ~��\sum_{�D}% _d,d} �&A .��A� tope!��gJ\{�, iC,:��!�D�Ek �v� �.�5�usa�ca�%U�R -R class�e��en1��. Now �%�� cor��obvious���)l-R*� �;Rx �en:� �"��2:6g 2}. Consi�0 one dimensio{!%)�, $"\�� s� ���@_nx^n + a_{n-1}x^*�a_0 <�8X = b_mx^m + b_{m-1} x^ 4b_0&0a_n� $b_m a_0� 0$, -2!�_19�segy $[0, n] �N(f_2%�&m]$. So%�^ :�corF onds��A�map! �\deg G&degA#a degreU=!�]c In Y��� 2 mean� $ Pż  f%Keg nd���r �Hf�*\}�gm� n, m�$f $a_i\geq5cA�>���. �Remark} � >�extended-J��->�Fisy?x"$!Jsubject a�0another paper��Hthebibliography}{99bibG T{Mas87} V.~P.~Maslov, � 4On a new super"A prIpl r optimi �xproblems}, Uspekhi Mat. Nauk, [WRussianh��rveys\/}] {\bf 42} (1987), no.~3, 39--48. �TLiMa95} G.~L.~Litvinov�2��  CU� ence:�*� 7u����(uter applic%��`(IHES/M/95/33), Institut b$Hautes EtuScientif-�s, Bures-sur-Yvette, 1995. Also: �DGun98}, p. 420--44�  arXiv:@$.GM/010102�5� :T J.~Gunawardena, (Ed.)-Id�$cy}, Publ.A@AP z �e, Vol.)�x11}, Cambridge University Press�B�Sh2001>�,:�(G.~B.~ShpizM��t"�al" :&palgebraic approach}, Mathema No!�Eb69} (�Ib0 5, 696--729)� =h FA/0009122�"V�Ga:�l-Il'yaeU�(M.~TikhomiruXConve&�:!zoryE�:fTb�E2� Moni� s, v5�(222}, Amer.0��c.� vie, RI, �mS D R.~T.~RockafellarM5:�A9�e� A .QA70c�>� � docu�� } )\�L{amsart} \usepackageaB :)fontsB*u} \new, {5 } [�]2'*y }[ 4]22/Lemma) 2#"� ' \ �style{&� 6ED�#;}. .�u�$4in&r{ �!�8newcommand{\Z}{.bb Z} lRR>CC>NN>TT>bbv{R}F D?{DJ P PJ �{ZJ �{CJ Q`QJ S S �Q�!�",L_2(0,\infty�T,/ !��� ssum� be lo/�" tegr�)�"[.GOne; need�)E�A� cond��-�!�{:b,bc} y(0)\cos�' - y'sin  = 0 B9'�basic quA�on�$would like� ���!Rf:� it{W�(i�e influt _ structureV're�*� r�*nZy$ $V\!�  +al6�%�$?}HtQnecess!Pto!Ss $H_+ R $H_-9�-)�Xsimultaneously because `wise sig%��s�e couE��7��possi,Nve �*ne might�#ine� our-�EYpa>-Z=yF m�)�{elEWed�%w�$} \sigma_{Zess}}( :)$�%Y�$. \tag{$\S>6$}>pAaA�(N/),AW�lisg^�6�$ toge�as $-E_1a-E�le \lr.��"$E_n>0( jis ei?-�(or�'n e�) �E_n\to 9$'��cours+. pendM�)YA`y�\eqrefa�. How�g��!u-EU .� situ_}� E_n^p<�x � $p\ge�!�,�a�Olac!x��yDis�i*&.(%a�+$�)d$,%?SonF��*��opn/A���ɇ&/$limited to /�.R+ plana�4explore higher2 ��r/�<pro�. Ou^/�al motiv%D�# rwork ck)�֕����C @completely clarif�*1�!�n $\{A%�,ML set.q� }[� -Killip� dk} l4 �dks})]��TDK} eEeCNIe�0)}. Moreover,�)�*at�A?\}�& �.`�B�=y�$EY ���is pur�*absolu)'"�,a.�%���y6 �x=0<1- Hs %p� s ref~(o� , say. Ofm�D, since $-V$ satis9�ame hyp��s�s�He� auto� � obta� A)ass�ons��#$�qG, so E�dZ n�2!actuaa�$irrelevantE� keepI�n��, h��\ it � helpasl�ly�� plif�"���0a�ar�A�InUL!-L#Eb�=�EV.'ell_{�U}(L,�- is, �y p_{x�e}�Tt_x^{x+1} V^2(t)\, dt ��. a�treat!��d, y(i%![mater, e� � �shet#:l !� ���un��s*aim! %���!� to develo!Jol)� hand arbitrA�:{aa1 E_n �(��n�*q?Aɱ hearr �t|3� 1me� G Ajn� &�Aq.� �h*a�w%4di he �$ descri)^ !:o-Z �A' selv� fewT r��]!D�4"�  (u}m�~\�� TWQ})�A�%fP#pi� )-�0most importanh(�J�A�-"� his:a5e e(rg6 Ŋw��%! =O �6de!Din�he�(it{geometry�!9J�+� cisely� ��@0vals $I_n$ wh�1(lengths obei�scaEHre� $|I_n|N �{-1/2}$.� e�e�write ( ��W'+W^2$ �$a%��.(�\|W\|_{u I_n)}I'sssim md 3reu����Vz natu( AmA��exa�� $"�+q�)pDirich)#F��9eV ��tru if, mAs� a��)�"q �p P i;5� -�T2pP1A�ezis, \[ A#_{n=0}^w��ft(_ n^{n_|V_0(x)|a x \r )^V <*fty, \] 62AV .  �ci�:s, a+�q�of� , inW %r� a>��a =" ledge�y6J�attacked)4&M ". t�,g led k+it{a?$rules} (ak�:ac�r� e). Whil!�a�A� eleg���lea� �9 actX" � ri  sj(Eindirect Fss systc�is�� tric;� �combin%:!!;�'m7hapF6to� upi"R6m � _can!�4. See.<1�,� Hks,Kup,LNS,NPVY,sz}a� reca� 2*um %N�Os���A�a� A&� �.�av*� �8,!D�� nd���ia�cons�at0 on o�=!/ year�  ma�on�/p*^7&topic�Q3f�}[0 ]LW)*fur��F�is)�6�-g.��`( U�ing}rh by-�1�a��u ;�;�.o�;d ILTe �n! urnAL� E!M!ceqfE�a` Z� �- �+akW,edu;i�5ac�%` %Y ~1]{dhks}�6O��,Ip�� doe��c�1%*surpris�%� L��T���$.� C2��0l�1!r@ $to inquire�utxst:�(  ���B&�e-K����&�At>�es�Ez'rAby :��50�a�Simon@pr��xAi�heE��2ogA|� ��{ ingred5#�xhei�C�3�oa�5��,uG;in ���ablish so-�,ed Szeg\H{o}�Y. S" ?ks�#h&�2� �s,.7;A�p�^e{sz}. U5:a*�tro����T&! %05on larg�8a� energa�$E� ��&O)k look�^e waveCB� is w�ivhat�&[y-U} L@= e^{i\sqrt{E} x�($o(1) \quad (x\toP)AVWev0$S*A exce%et�we do�� not}IJ� ���8�m.�?>�ep S=�9 E>0: P{� HAx�se}-!^ � } \}%] =$)�� E� y�(\setminus S)�� cNxAo juga� the �$y$` :xI�27lk&�<% e �1j�!hav�m�� trol�sDsph  suchA\'s.A p66 �� subord�Y��n,"� !�singularH ��c�easn2U mb p4ed�wSrJ-9bc0Z2C-�LLX 2�A{l $p< ��S|J�:5@�� agy�AAa�n+$D v���2 e�f� We�ddetailed���/,�ing.l; ula� )���v���un�  'A&erA�j- $p=5 &A�i%L�ou�AGt n"�5 2 # $L_q$&� �!� �B�Gk\&:�same::� E<cru�i��n fb#ŇKRev�CK,CK�'�a�prow f�F�  s�*a�� DeifWl&;4DeK}. PerhapsE~9 ing��Da�͹ s ��@sharpe�Iif $p$� be�In��an�4j�dim�� ^�eh ��0� p< 1���dim S4p��{ �}��!cor�.� =!n BL= alse�� r. F8 \bigcap_{q>1} E� � �=1$J- < 4.2b)]{Remtams}0Asa�K8&�G %^2)�!�u^j �ji�G�Uo� �tof "r. $1A A"� *X Cpb (s� is�fit{$}Z�!j*g�a89 Nh�~nB0$B\[9�pioI�R%� B �N�5.1%�%X���0 luw!�If,��Fr D'"-�1/4tp A�2$�.' Cemof< !D!�M�-�e�iq�edspi"ARL &e*%L7*w�n��chAErov_g�!"( �&� dimopt} �3eT �"a�5-incr�Dng �- e�e�1/4}= $.�b5"A a���"{?8j� holds, w!{e_n�E a�>� T05!�EwIe �-�E8 r��extreme �& $p=0F#��4);�^5AU����� 810al throughoutXrane validity%��� NN�%A2 NR1�� &Zhn !�����m-�23�%� V�"z le>-\.Sac}}=\eW"set$. H�:g��A�E2a�Moo� A&*e fail�%b!j*p%�!�qI!*%�n��e��Mu�u, Ta vNeH#MMTT,MTT2� lso�� �&�  m� �JT?en���!�*C), e�8 the �dI)$V�KQ both�s. ��ef�����!�M�NC%�"���f�saya�ln#E�#ly� Dhm N�$.5}m�� TR�&exeg!.x gets�$#iciFd"�3Az%��V �,��,ider Neumann�3=*���aI$=\pi/�&� #�<  a)}gR $0�8E^ GN6�(E_0)6�S;��Z� �Z6����i�'�B$�&E_FE#���suring� ,we emphasize&L�i.,do}/Rly catch��cea�&d. As out� dio%� behavior/�-$ g��8e � �E}$1 �&c!.�el_ w�hwe pa�Uo globaO sSin:sXa� (ff�Ul��sp��) e�j�+al &�)8��p� %�!��I< b)8 ��S (n,n+�:J � adap"'eAly��1�e ,��, �G�ap�!6rom!ӽF �,wi�t r-d� r����.��ba)�*b��" )j(.} f�%2���typE�z�W��op^+jgnp y& %Ey怒A���5!�����2i�th 2 so $�� |V|�C\V� $��a!��tF ew!�ult; �,�m�$,�!�e~m.l.A.% best:�4is@ (��GGM}, �EE�  Schm� �Q cleaAataTcanA0-�j�->>�Ij $��h�$/"� �0"M V \notinE!��! $q>1!�� � "/"q�%�ͦ}I/:�a �bi�n-C$&�@e�} no* #��!�e$le-���� 6F �l�EU;���b�pr�$� ��o^=A)^A�s2�.>*v�#0&n�N&"� CN"1���F.�n���X6+"�1�X'um%)>p*���[&�"KN����.�F�vy.�,A� .�tc)}2t*[!!�s�?2f�y WKB-��b�Lebesgu�$x'q"&5/�/=�P�_a)M$sq�J1a) a? #�#��po~ d��+�Z��A�&1CA�b}%�b� . Rybki�*.URybX1G.�R"�+ckb)mf�V," �" 2(L_2�"��"a�fF�"F� 2"~"C e �ul� %G a),pD�or� �( �-g� ��"o-.�� u2�f %-� +L_2�B19� 9��7� F�b :�ulaAzu� 3 bc)��ds!wy(x,E�Fexp1�*]0 - \frac{i}{2t}�a_0^x V(},$ +�� .�)�:X >�}Ev�P�.aJJ$!GEZpIZ2��soR3� �%{c)-{ 5{4_��*�Q��c�men A�)�in&�'-�&L1��"��n .� po�"a�)!e�� (޿s*h4>O���corgan� %�p*� !"�way: z.ion~2~"Y"lf� paP"%�Jt @>� =erK�y2�9ef�,A0���@.�"�Aor} sugg(9bi�du~0� 9fiP� E* K"�6� uncH-Cs&�E*SFyI;�@,medskip \no�,ntw Ac��ledUGs.}� a pl� �; Rowan *3!Barry9! ��+�%]& . C.\ R.\:�8ex�s !Wg�Xtud���ho7�:gCa�=�ra� 4wa��gul \-� {A M&�/E� � $V$�"Q[ prevJQ ,�R$&Z8 6%<.'E�L4f� ��'E3�"���wan � ify�F9.#? ary *�(#n9)~!\ it{alwaysv%*� x 6I .`'f:!t� ma49 view���7Gat0� � a�aZing!�% "�2\[1 wh"u set%�l � avoi W �fi� t--c< b�GF<%se'��aJ� scr��� )���+we�M��qK first�e mod�I���3oble half\ �*�@Z�1b!Yfu2eng�����&)fe =9�f�%�1C�xE�pm�S#2(�O bb R�>jl�}}&�6�&�S�!����2PYE-t<te:JD(k)}$�.dis�=y riB3fK��R$V=W'+Q�!Y�&(:*� ɯ"*,�-� ��W,Q$)}�-sV! ."� '!�<.P n $W� 2H�$Q 12b �� �(��%_)}!b �+(ces $k,n$ va�s,�sets: $n6�A bb N �kZ�c4-N_n-1encie�'g�s. Ho�=no�-mpt rb4dNA�� �> ���)�s��mH.ra4us�$#-st�eW%�pres�cs. |I� L��4� Lr�2}�!��*�*yZ�#WQ}�Uk"} mS�!su B�pm}!� -\epsilon&fCa,b��$"/0A,E� +� �U ���E� H s"E;Klu:a�E�a^b (\vawo((x)W(x))^2 ]� �bt/ .m%dx�Q�K '  dx�� �$ ��H_1 �)� (a)= &(b)W'&9$�in��� �Ʉ�i�}{� �#�<}(x, u^���) |�|2��_*M 1�bCGEɄ&�!�S"D!�=��wAXc$�-f,S(�E ) &$u,v$��-u''+Vu=U u��-v''-Vvv$,�kive�k(W�=(���_a�Dhem n �\;Q1S>0�(�1 n as'&`�-�t�3s(p�Xias � �o�endPs��xp%�3� ��eQ�YtsewerPqO)�oc{d">.,)�E+u�01.2} \gamma =�1}{���( u'}{u}+Icv'}{v�) �W�?-N?�����-gaN �1�' = - �^2A�m -��, \\ V = W'+2 % W�0uiv W' + Q\no��bj�C1 iA�eZ�H,i�*�-�;�y!� �y�Ric ���-�@q2}��lN6spl�8au $ ʡD �Y� i<n%A %=y'/y$�Dr%E $y=�(��^x ( )$) "�is backe&B�&+ �1"@*R*k<.�0� � ��E�W$ nom>��e-�J u(�,�Aa t qlA���/!1/!!'� ato0VT�l alyz4kE��ZN"�Ylu�Q1s�:!n 2 '_0=� _0^nWe eh G�� N !�M��X&� �: � P�J *9.� ���Z�_07� (t 7A+$tx�%��E< w CgeBTt!�x$q=w fix .�%�n,!����jS=�>not�'! �=G$� � $x$�=��H!�t��&���D�%(-4�> � �(p_{a+\delta! )}m�&�(a��fC�9b- >24>-� ae��Ylta!�)�s5 �!*��������\cothQ/  (b-x r �M�6&N9x-a"�C �0��<�/T � !{���.min: ��I-�r, $y''u y$)%Pb_x d-��3sj7=est&.x*-AaM2�+Afa�al a$ (b$). �Y$%  x%'1+xNA $x>�#�h� �q��s�aux} | �� S6z���� J�is�!c'a��C�Aqa�0�VN!��J�"�> l�Is�J�)k ada�m�on� arg�VtPs $Q=�7\!��1Ged6�Q� Zo"o?� �a��25J-N Nex�Iy�9Q&� $u)(alread}E��-�"e $L\sim=�-2&�*i#A�i�A�[C ��6GsSich�Bear$ go�+Jacobi l! jac}�:�8Courant-Hilbert %0[p.~458]{ch})"�k l�PL�P $-f f=Eb�a �� � [" f)'S V? f)^29 ]� i6 .f246/  �^2A�]h ��'QA��>Q�v�,7s�+� &�7align*kFh�&�� { f' \Bigr|�-&� f�(�*r�@' = -2�" U'S-" ^2ff''\\ �v=+J=(E-V)-(�1�PlupH$nto�*�=��=BV'^2R+ n� +Q �^2!HtoS5a.l�Y6�-�1�M�g7uѱ�.�S &s�� � (}�9K.� )}� �+�b-a�6�(��/2�rt& J 9�D a�" $I�)b02 of�R$|I|=BT"�:� $I;�1"�Uy2��/2:`IKntrJ� rtwo)}q-e # a"  un��"F �as� "��l�0�ddc�/)*4�Q �8�w)� Vf*jfr $f0� ;K&�!D �. zL"9�l pick��c�oat maxi/ a�({c-L}^{c+L}�h $. D";M� = M��1(} 1 & |x-c|( L, 3/2-$/(2L) & L<<3 03ge 3L. e� PaW)��j!���8� ��teri-D1 �of comR BC��Aqff yC ?}Qj(�- n)��  52��3=7��rplayOI$��a� r }9'\supa9I�AWdesiredmA0y min-�d"Zc� �s&No�go down}`$\{VrI:��XQ(=0�wa�!X<a>�( %2L$ eachR<t�i�,$c� ^ E�I�b6(le (1/2L^2)��#��" &�Q#aF��%N domg1m � .��!�(�? ; $Q_ItUaQ���I 3�I[ Q_I�?a8af��U�\ � ��F� !}8�RB@!6�7��uN?kX3NMed���� W� i�O �A� !�5!)H�a�i�&bab�+ dvis<D+,to pay too m�6� RZ�ific ea��-�3 Q� F�� P7&� �"V���G�$&� �� �/"[n($Cb$�` �fgng 1�B�x!s� $C$ u�Vrnxrj# n adQ/ (�-&�v).m :�[PV<<u]!�� "�".y]A&# vely��%4y��!� �d!?p�Se @eyp\%�)�of��Kco<,3P�k~�u�6M>s��[3w)8llbe�;n=|IP2yir��s�����l=gr�#>(� ��e�!0 [ �9,"7!ou!$iX.��6%N�o� ed l�S on*��7&PL�*d'���&.�.�%7's&�. D�Dor $k��&&�a9&zMJ_k�A AV�n �21 m�# . PuWo_1=E_a.s��>Bto!�2/4to �Q=W_1'+Q NEF$W_$b�1� ucA[r\]  an.: I|I_1|&` _1 p!q&� %�( .� _}.�j$ Xwe �Ve6���n�Ged�Df next stepiV" S_2=N R\sDtE�updD"�' zSa6U�E"�*&yD\le9�$;�fact, #6����=5imus�R� �Uialy �B�*�,�)N(E"e� _+Ah' ��$low�\"�Izal���L��reK8be"�i2�"�!)�gr&�bG�"�-E$)�S_2$, { ons%�-h!_2A�20��4#E�!�Xof>E�e% at"\e�_:�,Os�4w"�s adm�A)�d��� vI�ɚ�4��  _2.2uby�!N�d)E0\S_3=S_2.�� Ona0�+!funT) s $W$Q!<�ѡ@x)ch�>e7;7i~]�& oced�<"�K� quit� smooth^ci`t@=m�o��e����g"��-�� .#close��arA#��e curr�+$Sb� �C?g�T2@"s.�0S_1y�e�͵��n�p;&S�'a�_U(1$"Q61>����qAe(t�C�;N ��� �tF�'))@B"�b�al�!x!I-�^c.�= Apply)� �e�4"O2��w�A%o&A L_1\ v "� ��.6� � ��\ =\pm^U&;_1�;$��L5Z�-�$VN�,��"]>c� 2� s: � 1� 3�DB� 0$�j< $5 "� YisJ�!��Zi�6� .ũd& �MkI@&� .� k|I|�Ss^PRerE�I$�w is �f-�y�Ma�^ "�{�} W_1[ 1^2.u>$�-:�  E�s�\!� grar�r.wzW=36/L��ise��΅+�B�1.5� F�f�1134}{L_1�%�CTo�� $Q)=��usBi . Obser&�1 N term in �:5%*j �A"|��{-�a!�$�-w�G{=Ev. N!J4Cauchy-Schwarz&� y "�d�.x*�[j�*��dqM� =#)1.�jA1g |Q_1[%g281^g We p� j� ;�0�3)��u.�Du4G mmar�&�Jh�9(achieved: F�,,��+$O $H_-^�&4:� S%�eM��e�"d�%!�����-s&>�r� Q� M�'oo � a-U I-*�.u> �0 �:�Y^oE=.�4 s�e��a��s: ;a��w 6��> ly m�(F ,WWxwo���s be2F.�7s (�� �2�w{.l . V�.ed�!�ZG�� �� �%i� s&ck�)K%��,�+�,� \�wT)G&in IS step2�$IAw�0I��U,Z��E��� ~ o�`d���E~��l!O $I_j��I�2}�f-j,kHnflict k���ary:}� �e� Ese"� -m� ne ba�on+ zy-orks E1A��dai3�V!��� ��A7�� tilde{I}_UH ��("�%$�sen�ZrtoN4. � I_n=:i$. �*�   nt-shap��#?.>n � n$ �uB�w!G���,Y�ba",!����"�#estWQ*� n}W_n� M � n�0t y n}y �e:',y n}{ 6� Ba�+1}=S!�&� c�%(�� $T3='ti_��newly2sm�.�!Ea�j'.1�A0;t�,tw�!l ��(ir neighbor�,?;lGEs> N (W��be�;n$,�it�W hold��PPA0c� �� ��&�2�� $L_j!�L!�A�G"qBX <^IU�ig �6 $L_i��i4 $ �!&ٕ�_i� no.P . b�Q[7O"�F��8a):"lC�%��b�~H<NN�!~�2)�"�s���R� 85dMQ�r���n#n�Kbc:i��0NS0it{�%k}�(]&ly)�&�l�krel�$V�xq , $b 2L�| tim�ging/�*L�hEc� dr�k�dK5� ��s2�"k[�|�� �"�o Lbm}�M]H�q�� d1',>er�jAU0�%(L_-/4,2]��$ $2^N L_0= �sDN2LN"wLk = [2^{k-1}L_0, 2^kA]$#$k=1,s , N#�T"=/V&bm�( J_k},/��6�5_k|� qua�'*|Q.�16+F%�4)ie�*��Ubm}.] e�q��  (�f ���)E a stra�%for�eBAz4.f���2��q�@A@mݻQ3r��!K0 � �6P�A>es2�AO�wo�1t�2�� �we�( o cu�&"  $[0,L]7;� r pi�=%��sonǩ�i�o}+�2y*% s (� g �=�9an����>�%aq麉�PX�L � �5�"W�nt(a+e5 , b-L_+/25 An2�ssu)�)Ed�}�WeX]m�Ni�-��dc*_$I�V!��E)"NLH ing}"�)%�$V�lq� [c,d]$ t��-[!g�t�w .�,Q�!�st ��<�#�� $W(c: 6i*W5WP$!c� \[ �5a�|w�,i�(cx�! d),�` c^dF�9"qD, �62|w(c)|a�j�)&�%bm�5_.] �% h$t>0$ (�typ�?�$.)7\ch�%N�%x > c+t�% (1/t)(x-c�% �� � �/�]��o$W=] w�($Q=q + ((1- )w)'� l��M|W-V|C!m9( Q| -q�6)G${c+t} |w'| *%[f ' w|U#.+b# |V|+KeV) + �1�W| �S)��&�t0+ HA !�m/a sG&�d1n-�� 5Au��%UsF�$*�y>in9"s"B -&zr _�� ix7x�K� �B-$RDr �Ztm�y 6��@� �Mt"" 6�|efm>�&J: |W_-as> CL_-� �cIMVf"�$C^2}\, L_-a�A�h1L�(��y8Ͱ�o� �$���(0W_-��n$#i� s6 134/24^2<�^��"j+&$x J��$ �_0)|,�n( a�24 �� f��I�5�mmirrorYr�\�!�!\)XB $c=x�5&�,�q#c%��,),!2hiY^� hoodh��r�9$�s� vanis�K�':pC)D��ch[�C%q�)��!� d!To/ �ab!5���%�\!:@Q_]`x_0< 4L��eɀA��� �W2Y p � TFixj$k��z1 + I�h-&=34\c��2`-[ ] Indeab!��<}  ;�-h�:� �old� *�)�� -��.Q?H'El�-��Z )irib)82|WQ��1-I���C&�V�4L_-m�0|g Ee�Ily�� �:n 390/ 2P�l���V)�W14+� :oHA��whe/�(\��M��re�� a j %���3],M�!b�"an��$k$a�) new ��'ifaBwQ�re<Ha��E� (tempora�y/ug(0,2L$9conveni�]). �� V:S�i� E{>u3s[:]-)$as� ubdi�Y�iGA�se�!�rs$ (�.� ���vq�@�)�3oX ~&�` l/avrxn�`qu.�x�6y-%�``�''�� lso W(4 j5�� %add.H� !b � $��� ��s�mea2�yX/2�fM��re��*��  or +Y7�� x9��[1��aE�c�GI]�%lj �l])us� recor�i�]�}��"uen#9�'iBs 15^{(wU*i~�}"�&9q�D!�* �*�):#��0 B1!"Na+i*>�K�> E�%C�)��S0�!stage�3� �X�� �xcted LT� $nm5�egE}���D = !hw� ��<��j.< M� ^{(2�H({!isEKv�-s�y4a bit pedanticd w&ul�G�Pa%�eN�)' awayf5�� &�M c���ZJ^���u�AZ_+&�MoA�d.)8&%V&ՕWVyKr6�|-�M��1f �w �W}$Q$f�1.1�  ��(x)�5 Q140r�N 4h = 394� eq�/}�g!�x6�[a,b]Hb� c&$J��'!1p"Z��b�)�K%D�� �s٨Iin >� b� N���*�y.""�ars�)�(�6b$wid.f,�VP e��5wa����Ax$-82!'Vcx���^�I_n=L_n+F����a�Fcop 1 F�"<1&� i�m9�^*����1� �. (.� bm}r�n!�'d&b2;=#[a+ � I_n] � -/4<� Gd }+�e ��)�1�� ch��a "9 $L_nS(�+$4�Aaf�!g��g &g��s $� =&�$. ��M�>i+�f)� le0.&3>ſ s ' ��nN$+!5"X!=-)� ���,2"H��Z�G&�E��{E�����. F�U��-nalogya�e�b���jI3� "W�-r7d� a4��"" 1�6^CQ��w�8$k$th q� (so "� $k=2�O�VNmy)"�3x,EJb�a&�*T-*"&�)F�u)=m�e� a�"\ two-thir� f{"&�"O{Fuy*!�52���&I�Ikis *!�A n"�:6�j tfkqa�bj�1gI���J�98�'2��մ.�96 -7f6���.W�� ��EE$'����' ��k %)(� �X TJp:5I' � � b9�w)�&��er ��&%OI"x &!{n y.&�Oz5� in:I>is;IA�h!�a< m�ma�eLe�"Z= dele'4a%Ty"yt�E1Re�A�$(�de�B E�.ou�w/(z&.�0UP� �P� des.� (@�n$Q o�.i3 "v %�$L_- *�3S ��w!9E& 3&� ~�$)�uvA ��rb<�a_1P���1>a.�n V�_n}%O� w�m UlD!%1urAvw#a�Az�0F= �#��.dsm=� �sq!(i\%!��!G M}t� ac�{��is:;���j�a�x$j<�"$*9! . d�� �y�� s:.� $a,b\in J~ but,a3^ :oi:��T��b-!�heW"43�9 �� deas&d)edb)6?l�;v. er$b��u�|E V. U�R&�� "�$�J5b� nd N��[�z$W2�n � &��+5�� 3!�&'w�],a�i���:D��&g �+,"� N� .�/~*"vDmC(a!at�2ll%7n1Z5 ede�!w�in{)�algorͳ�6Bal*dH�M"�\,�4malU�i{�)_!�&on�@an �s���@pbT0�e.As 㺡�u�A�� 1�.>D.���,1+&��NbYalt����= �Mb-"A)�g�!4."< A!I* �3$b)�so��n�,2�i36@�%�o����qd�ck%!RA y $L&�$L/2&nX(�Z&�$ =0$ Lfpp�UK� :� �,m *��:�� E�#p�= &�:$ En!-b*9.��A&inu�5� na! %�i|� ٩QV��F� . S&D=MB\��a�a�linf2͈>*ps�!?s0inite b�ie�!�e��T� W�m$Q�?,!= i ���Z}LA�a( $L�&!c��!_Ѣ����ɫ)"O&��)a�1��oN" /�win�?1&Q/5"Y;�)V4%R$K�1 �!)�:�^ e�W�Lly�(^�{\sigm�H�ADB�� &Q-k v��e�- "�D guaLe�3��!��DI �1�i�Ņ&�- s $<"�.ʹa$`!�&G�% A�^'A:?A] F e ���1 s a)ic))jE5"�$�r2�s%遉��"�`�%�2s90�!>�!�pp �� u� � �|�A rol� a& r>� �q �<ly� 5�b������Jr0!a=I j), %#$j$�OU ��u86) �Jal5*w %/HH �s>�c����.X. ��u }4o)C8zi E�uE!}c% S�:�,��wR� :�XL� 2�q]�Wi�I��?1��;aP�,2W  ,�9�����G�8)�$D �$D le -�9�{qdaE�$k�st8 [�"�"v !/E,%͆� n^d�^` x ����t /! ��� k llc � -S!!��s5TB+n.d �wV�-8*�8�� ^&� <����d�ly̤b�ed -- . �� .62};�e �%G!+0)}�4BQXw�g�qhg�\ eH��� �x%�a !_�c=2�w"�3"_)>2��Y�MZ�r()�X �-J�268}{ �F2F:�_d�d562:�%] &$wm�q*?"4uq� 2 W'#s�n�:L$�V�8eI gap&�"�U�$w�"M,1��KzhNa�� qW��a�1Ba��Ga n >qf (nam` �6:�A1or�t%��{,T:�-�niGl>9>D5"J sq�0%G ofO�H}*NJ*$c)�D &�(EQ � ed a|9���Y���"�>oJ�2�Ae!� I�*/]d�r: �$�M+�g=a��A�� 6�O-E$��!�%E�pIy"@^M= 18=^�ge *EaI�M�"� j�O�  go�<ifz[lA�i� �po��e�a�� "=�b)Q��A�Q��y�Wg �3deă��mus�#ED]' @!3\�2}�iG> 4T�claime#)�)� �EdI9��� % �'u}o�'���8&�B&f ^a a)e���zc$�:��T���%�� |Q|� &� �7now2�iA�N�1��>��:*�lthv� v�v. L�!��q 6%�},�oa�ji o p"rG�#�&to4�b�NjԀ��4�:�&e�� �@�$i!�a ��0%��  &z/�0�g!����8��Zas va| $�1sh#"b�tndlA[W�"arju9"�$:�2[0,3L_1� � �2��G[L_1,2!,'�F&];"{Li iM�?f��2.1"2DD^{g^G�)16B.6VC��NrDW��w)�ysJ%��oo��"' 2!1)au vZ-�n�the��,e�m��IA;!e!�B!F�a�ls� " � ���E��a�*�)�0�s��Jly h�� �Ţ',hav� 2 an��*/a�%8� has  VCe���':&�/��nIf, at s�6ZB �uu�(:b"*�JlA� )��� y !��<#Q�!UCo" s"V� E�����Ired a��oriEԅ�7(.E� �. \X ion{Pr\"u� Vari8T s} S!-r4s�dxl!�a�����-i�}2X� a�� se}.�!� hvin posiDC*`N}���� ri� E=k^gN��$k�bn �v~X tudy�$y(x,k)"-`s��w�A���E�11-t�v1�E^���� ly weldW�}!�Y�� �&�le�s{��z5� �� ���!�>gassHtDiracC�xE`e(��]� �1� v:� $Y@K� Y%$"�4 pmatrix} )< \\ (y'%-�k  )/k �0,�3$�!�Z = R>� 2!� (\psi /2nI�>\ 7iI Y > 0zM$e%q� in $x$. A?utI�&�X $R� psi$&{����Q��mb�l_-3N{E:PRC&c�ln �\g)'` %=�g�"�0(-�p}{2k}!&,\\�3 E:PTipsi)�Z 2k__!�69�02_k��o�-1)g !b �B:&l0��9�Ia�gr�:e �f��1/2"�t t�""V*l/&�}2�F�,e)+�A�soW�a� (-i�.Ew-=�ft[�]UA!* & kA�-k & %�6� dl:<BL�]0I1 & !HiI] ic!g] Aj��AA2�tbe"y< �����%N�5%"�6�sq� s $YY4��un GLl�q�Q�U�Y0} Y'�h,ka�M�ώ8 Y@� fI0u]3[p��nt�p�iyˣOF�(�kx} & - \\ i- 2�Ze,��fbsHefY 3.4} ZUW%>A e^{-2�e^{ F �F"��o�f:� L�a�6H.� find� *�x�Ux�=>�"O�p5a�$.v ���" < E� _{�"� ,�|QG7G�=�cA��ai&�_�s}:�F~"�R�b�/�(ull-fledgedj � The Hst��[� �'��to�k�r&�Hnat v3� L�6�ح��{����(a_n,k)- {��,k)��L_n + 2@_{a  }^{aFA�2�� +O(LG-1}Eg] H $( ?,a_n)��� 9 ��I*=Hece��u�đ�8ant+� w�l~$-3[jf� %ys`0m�p�t$"�P1&��IH�d 2 \ sim 1�bGA� H&�g���:8.�q�V~ 5 O(1�1�GGeHun½mp� B#e:�7&~k���0$*y/!�x)=2n\piqi.A{Z���M )=2 A�c�in]U� angl��� b � p�A�!�S$y�,o��_�� $0!s.�=% $�G�&� � b,k4���equatiK E=k_2^2�5m�� �UYn�  ~tri��.� d k_1��T1JqBy Stur!��is4�$4 �t!���dC -`� (0,x�7N -xT�.oscil lׇy� , $[k_1{]�N% j1=.��&J=dC.�9$ <:e*+�4. \hfill$\Box$٘S�v�L��6#}6h�Fse�Z�0TA������,PZe��HzH���two��of�Ia� \E�Deift6�DeKIz~�->z�� 6[;S �2�2S�aQaZa�ketch�!�p5as :�Ku�g�?A�A�\�Z�D��.}1#&.? W^2+Q-W^2�X����p� '�%��2A A�tof reAYs��Q����fsen"8so�i�4"o���+��bog/ ial .�2V}�5�v8 �dof2*NV}$>�" .�u&�*aFL:ڀa}.#�*�".c4e.�;[& �%�.�Ui� bd*d� $r=b/�v��ka� +b  �! expa"�!m� le�~ ��I: ;<$ X�=�J~Ε$y@ Nows�e"� %R�� 2�m�e��(f�� �"�ro)��: A�<i{� )� IX҄M3 � W �e,4'� Mp��W��i��a"slower� o >;�� dens��� s����ٶ?weak $*9 verg�> <&�ma�>a%8�'(a�@9 ) d|��� !;��l7#4 1 :k $m$*��Pi*B����kclumsy�t=pu)�ek/ re*���'�s�� �|� !�nlW�nem��=20"n$0=a_0Ft�#ner�>r� �&�sa"e�� 6 ����{ :2�s (2.2�S�KCKZ��suGaP *f E�ead�"\ƒ< Ai4�G �.2 e�X`:�HKN�!�����\5 Four��*>��of̙����%^6�/>d$Yy}on� �(l�je tandCD& ve ! �n�I$Levinson'sqH)]~� 1.3#�East}&mU] �)>�bsb*�Q6�]��q��2� �*6^�+01u�2&/3��N G"�?s�v��t c(k)� 9a�J� $(L" b-a)&S+$ d\mu(k)\,Hf�P�a^{\} dx\,d�"�\��� 9 �cal{E}5�\mu) LI-)k)� \|f\Y�!+}�+Z!at>MG �� \!\!��0l) (1+|k-l|^{ q})$m��a%�$R!�o $\mu���6Mi�Las!C[>9A�!u.��Y�X[vol.~II, pg.~196]{Zyg}�{���%G� � 3�Q�3soi[�$ 7.6]{dk}.�t9�fA�Rb�@ �$two�a�!.T� &y.��|yim[�L�}� B&� -2k�exi�4J�M�s (�9]2�!���7a�="ľ)�<����S� it .s��+ �a"P�"fixR� al v�� $R(0�"�l� ` � � off�e "�� �z$4�W�{ spli�5)�6�%o%�#�bs%�&&�4 iH(ll���f�6} rans�/nt.i nE�a5%H6����s: $aa&�;w�saa$�1ex21�Z#a�16{�J��$ es{D7to��!�\2bim�ip&  �d�A�5V&f�!s�p0�) aqbeG ���+� 3c؝x0the first ste��p. So in this first step, we are concerned with the series \begin{equation} \label{4.1} \sum_{n=1}^{\infty} \left| \int_{a_{n-1}}^{a_n} W(x) e^{i\psi(x,k)}\, dx \right| . \end{equation} Indeed, real and imaginary parts of �Dintegrals give us Dleading terms from _�Is for $R$ and $\psi-2kx$, respectively; see \eqref{E:PRC}, \eqref{E:PTC}. !^Xt suffices to show that)t)N!hHverges off an excep!Y�al set of dimension $\le 4p$. We will needFtrol o!�4e maximal funcK$ \[ M_n(k)�$uiv \max_{-�Uca_n} \R�0c W(x)e^{2ikxF��] Let $\mu$ be any (Borel) measur��th finite $4p$ energy. Since $\|W\|_{L_2( �t,a_n)} \lesssim L_n^{-1/2}$ by�!�05.1}, Lemma~\ Lcap} say!�a� |M_n \1(\muFT(2p}$. Now $A� j2p}<\E�$, soA*, Monotone Co)��Theorem !�u)p$\in\ell_1$IZ%!0: !_{6� �= )< \right\} . \] T�IconcluE�is notham�8a standard relaA�H between capacitiesewHausdorf]�s;!?$ example, !�(can argue aa�� : Supposeei,�%a�(our claim, 5  >% w4fix $d\in (4p,1.)$.!� n, sI� S_0$�a E�q�inQ�d$-u�al�m ,AH(re exists a1�  A$$\not= 0$ s� rtedA� |waH%(I)!� C|I|^dIaall��rv��d$I\subset\mathbb R$ \cite[M�4 5.6]{Falc}. IEMeasily��Le?=(cal{E}_{4p}eC q!� such a�$.�Zw:we E�a(n above now.�IS�&D, which clearly co!� dictase fac�[ �u%�F>�9�M @more specifically!�at�] 4.1}AF��if $k!�inaK$. Wr���*< = 2kx +\varphi$IWconsiderE�of!�%�Ŝ $\iZe^{>$ɱ�j�. I��iP y pa���s�(multline*} �m = � �(a_n,k)}nB.\ - i�)t�f}�� dx\,2[xY(2�` \sin!K +\rho(x))>�$x dt\, W(t< 2ikt��end.�WMabbreviaaFble�?$kD=(1/k)(Q-W^2)(\cos�-1)$. TAa& :�h�-h,!� summ[I.,�C we mustE�a��� over  condnoH is also absolutelyAnE�n��Ise�c��, how�w,�immed!IW!bound�( 2��1(a_{n-1� + \|!5�W6�) i���is ЭK^]��1a�So�Ika�B $\li��\toɍ} RM�$��B(!� "-2kY$ ��%��72�. A�Vs)� q�proof �EvTdim}? � to exte!��o sequ.!n� � �7y� ��b�� way�y,is suggests �$we look at%�,widetilde{M}� \eF� �&�� >v )�|��We�:1�F�to��B* !w� co��t�e5NacE =N because�9 then� �S�᭎ ToQve��a�$F��O} ceed�ɟa�0reduce matter� acor o)�statemag� I�SŢweI�A�rue �doe  r!�0re new ideas.!Vj�repea� �!+ut��s,I ���@upper limit $a_n$ereplac0 $c=c(k�Every� g�through�beforeɬ�in�N prov� (he stronger�E�J[C � B<\hfill$\Box$ \sT $on{Sign-Dee 0e Potentials}!�:nILT} � . W� IMstrategy��S ]~2!�e treat!� simplifq � ablyUpP ��no q�resorta�.k WQ9 n�Pif $H_+\ge -\epsilon$E!I$Wen�e>=6h-�^ V�s^2e�I+�\ '^2>&�~�� test"s $ 2!�H_1(I)$)�vanish M|-�endpoint� $I�  VD 0Eq�is ma!> usA/o�H!G $L� norm�2 $V$ �� suit�' �� %�rM�t�:�WQ}E�proa�s��B $J!(k)}$ u',same geometrU .� J |V|�u /|J|$. InN icula�1f E_n^p� �en�;|�|^{6C�]�l�[,-9 estim�by a � iple!4! {sum%&E� tant)depend6 $p� � as usuali$�8\gtrsim 2^{|k|}�*]rm� %�$k$ �en n�6a�a)�V�whole-� !� blem���:0H\"older's ina lity� gives,U $0}&G Counter( s} I�E  %�2O s&p opt}%�FTL1�both cas��we�$ sparse po� :r� on pqous work�f tral�per�i� se models�0{kls,Remtams}� � � ={TA�rK ]um% �* tuna�is- easyO� ( two differ� typ�( bumps. Leta/�V_g(x) = -g\chi_{(-1,1)}(x),\quad W"= gaA�|(0(- 0 8���e\beRX ��aOL)b@} {\rm a)} For sm� $g>0{ !Jat�,-d^2/dx^2 + ��I�2(�)$ has!�cis)�; ;-"::�g�H  $T_g�antransfer1rix�oaMs Frix�ntakesy�ve)_$$(y,y')^t$a$x=!�toir )@� x=1$ſof cou�h�expliciemulae�F�ce( r $V� and a�:� �gme�c�� some�le�X.�d ion�^�!��(n establish�h�se�$asymptoticdE$-r�� �A�Aa (AlM)y[ $� EV�7m�O9�� 9.2} �  =/ =1*� 8V_{g_n}(x-x_n),�^F� $g_u 0�� e $x_n$'s3!typ�� ly v�rapidl�crUngQ�!, individual oC:  sepa�d!� thu�Őin� e$ ��an� . To�orously �zze $V\!�!�ildJup� cess� ��!9@�lI describ%�?  .1^��u�L!\)�$H_a=�/ Q(x)�`-a� y $Q$�AARact�� $i_s?! ient���at2y* appli��6at ݸ� u��$N$V'$-*6E}� ldots,:N&�0��%Vn�  ! $�� &$aR�d� a���Hɴ!� holdK H_a$$2!z%T.�+1V����E_{N+1}� � \A| E_i :�iF|<� 2J - A , -�U ] An og& &N�%��j �2a>� In E��d�o�`!n_ tera#"n AxM�a� �O�lsAH��beh�flikdAWof�orthogo��of Bkhy d uE��;#y9#�& Ry''+(Q;)y� ��y(0� , $y' �By�bA#<$a$ large enough� �make �#�u� ./$~ %z4(0,a/2)$ (say)� $y(y'A�� � (.6#$y'$ had*=� 5� would be ��} |a/2uOE1 "R ). �' ��oscil^"t�# y; m��iN&k posi" ^Ʌy�� exac�w!�/Q .0 . AnV ��L��y$%p\���} o2�!Fa�.��\usm!>�.�6���ad�al z��> $(a+1er!/gu��aF�_ �j�6� loca� ; }q : Cu�&��� !�F�(r6�E�i2a4(�s1"i )$) by iya6by"� smo���)l�!��'!40a neighborhoo�,�", $a/2$J $2aI�%�l2�). Ifa�B %� }�  obta!��'&�_i��|(H_a+6�i)�_i\��\| �(i=1,��N�  Z��O��\� S ����A a�!�ag{6 �AQ�#�� �=�$R �^_�`we��fi�)� i"�, �q.�(x%��$-E_n�!atisfE*,$|E_n-E(g_n)�& ��no͙�..P� �A��a �' �� $ de@ �Toy�y%1b keepingIAL fur�2U!b� s $( �"�_n, +�� _n)$E� disj�yisA�� a�e>c "  distinc� �n��2�'s��ne� ary.  � y2� !�� Q=Ńg=g_1�R=�-2}�1$�find $x_�7#e *�!, p!2E�i# 1# �v2 v&� =2^{-3u��A�L�+:&1�*VE p�)�#E�sn 2$;A�E2lso demAs��x_2-1>2 �Continuj EjS"e:' stru ena����=e �i2 $>pn&\ .n( $E_i^{(n)})!Lse mDeA eGi)�5�$i/2$. Moreg,�fixed $W']%Q Cauch�!he�+c�+t��$y��}"[a��an accuV!� pa2.!| pr7": )1�*li��!)�#F�$96��b6U6b %�. O!�e�qh�A�F�*"oa�ny2�$<-E$b@c2�" �E�E .us,�%%"!�a��'#J�>�} �}i�}i�}i�}i�}nE9Z[����tZ��6 �F A�b�Y����S��#g7].4��/$\{!�\}� u�#w!.v>�"NGiven $eŪ�XeT�&K e_n=�$, pickx>,a��� =e_nk. sl�-ly�a��$e�if �\�2�I&P�y��s7!�iQ�uRg R are ���.S�a))X4�%� g_n\� (�)� $ inf sen�wra� Y'�%� �/cho� ��as ("X�|.Q eF-�VE�6)e7.� $E_n�!�&�/# ŇH_-&�- _a{K$:W. W��5��%� can ��6&�� n/x_ \q'��%��"g_n^2UH a^-I) n reGon )�&X � !�!72u�� ular�`�e�� *�(s%32n.1.6(2)]�}). 6di�us��W��"�.4.2b)]{+ � �)"�f�,Npe�3:�PUO1na�. F�+YallI� a=.��E* ,IVa� ,"�of.VeXa�� )�e�! 1/4}1���  a��non-i"SE'%�h�I�D e_{2n}aMS . De�,ineu�FR8/96`' �k)� ref) %��m"v3II}b).�tA�u�.��f�V$�$6x)�! l1�!p%�.�'�c� u� �F�a�>� �d* ��C��e ame �"*�&�ac��-0N \�Q X�w (!xa�Jz!�� %�arrang��&� �zUs $E'��!���� aftea�mbF"���q {\pm)(one s"� " 2�$)\= asS iredaKnK��#2�� nV�E݁�q',�9�xe��? ies� .��3=��thebibliography}{10} \bibitem{CK} M.\ Christ �!A.\ KKev, WKB*�:iorA���g�6alized)�&��one2A4Schr\"o2.pe�si slow��a�"s,  #J.\ F/$.\ Anal.} \bf{179} (2001), 426--447! �2��nd�$al��:� ��varb�LCommun.\ Math.\ Phys�218�245--262�ch} R!�ourf&�,D.\ Hilbert,)it{MethoQ)fj emat�p0ics. Vol.\ I.`#$.�ce Pu�\rs, Inc., New York, 1953�d}~Damanik, Hundertma3�Killi�8nd B.\ Simon, V)'� al";*sE>�#Schb6Y&A�V�+�Y9Zp{\bf 23-m3), 5!m52mdk2�%m.�Hal�vno�%#s,�app�&�0�% Acta%�.}��!�5b.�:Qr�few � �s,O0print (arXiv/��,-ph/0409074)�30DeK} P.\ Deif�3.�� 6�3R �rumq:Lv�squ� "�49���%STbf{203} (1999), 341--32 East�S.�hamyC� A�� S�4�<of Lin!�Dv%$ial Systema�London%�uwSociety {;��siYSe�>�, vol.~4, Oxford University Press 1989}�Falc} K.�alconer6�G6. of FGal Set� Cambridgeo o a�85s0GGM} V.\ GlasnH ross�1�N Mart+B�5N&���� V���5�1978)�7--21.8Ljac} C.\ Jacobi, Zur�uie �8��4s-Rechnung und.�(-Gleichunge�f!�Re Angew��}�h17A�(837), 68--8.��#yNB�um rul� � 0"c�\ir�Plic�OTiw�BYAn�}�� 58} �C� 253--321=� kls}%�K&Y.\ Lastk!��Mod�2d Pr\"uS"� EFGPe"orm�!��� ZsZsԱ� 6T��194!}99E--4.�Kup} S�upA�On� N !;pr�ty!.)z 1zY� Proc�mer1�\a�.*�32��4A�377--138.JLNS)` Lapt� �Naboko)aOUafronov,�x5re&2�>�m*�*:�%�thA7coeffi��t�1P��J�41 �A.91--110]-LW.�m,T.\ Weidl, R�&r��$Lieb-Thirr?"81ie�*� afbZ� In� 2}Not.� �)M.\ Re%�$�:� odernS"4 ic� V.\ � �"OA (.} Academic��"� � =�Rem� Remln��� � deF� �CR� I�!�9� ��5�Z7.l"$aV�Embedded�B��uI�:� ^� �T)z�35�e 2479A�9.�RemX=6�& eB�����2� 0��6%i1.,yb�� Rybk�a�V,��"&� �a�V� ��V� ]!|(�g�:e glob � � m�a=��45�Y�418--142. $Schm} U.-W�kchmincke�.2�'sS,izn  mi�0Sturm-Liouvil�8q���-�Royg;(Edinburgh A��8��a�3 7--84=�sz}�O%��(Zlato\v s, &6 !�!d$Szeg\H{o} �A�6��&& polynom�<�6 real%�yV�l 24�393--423�ZF: E.\ Zakh���L.�Fadde�0Korteweg de V �"{ :�7x?�*tM&4 Hamiltonian s� 9s27\ App.>A197<280--28.�Zygi ZygmuI/��Trigono�;ic"� U, IY"E K� ��195� �C>��+docC8} Y�\,style[12pt]{�cle} %�$width 15cm�\ ,480pt %\hoff�0.!h�#,t 640pt \odd+margin v 4<-0.75in %\date{\�*�� itleq C�0�F!�a�EF thre60Lie bialgebra.� Poisson-!X�s} \author{A. Rezaei-Aghdam \thanks{e-mail:rea@ ,univ.edu}, Mj'mEs4A.R. Rastkar\\ � D�,^?��B�$Azarbaijan.� of T%1�at Moallem, 53714-161, Tabriz, Iran .}}�1�} \�(%8ab�? ct} )Ecal r-t ra�FJ%a!.9O <g%�Iway�ZDco=E ary 6O%5A&r".es (t�:�o, quasi or fw1iz ?)`�$ss�#X, by u�YD Sklyanin bracket,9M �ur��R9la G "]-n �iC9Z \newpage*�A I}NduP"} A"$;Cn�now5S!�&�3ٲ ��Anatur��� X@!�&�?nd�Bres�3a2�or_N��:� 6��8D)4)��]Q c sem}�fo"�LC.P G ,ko� O"�1{4�$ie Y�]1J����|!9Z.5T-b0�mac s�(lim}. Up to!�B@- detailYPF�}U�"��co�]x semi-aCe%\��-B.D}.�!�k �" 5�FNE��;r�4rol�$e phy#6pr�#.k'Oe Y mpt.�B�low&tQal�=�$[7-11]$;refM4OFAR}I�FS1�=2]Ma� pairs>�f5A�5Y,has been per)5 �S���/"�$connee�/ � truBU�8 $N=2$ supercon\IBH>!:ory �par},� 2^&�sw�Nc=9�#s �1ed�LMJ.Ri.iYH.S���mi�%��7ityA}.9AS��s���Fu6q.JyK1��9�(I .�O!�]E��9��! {Gom-Aah F foot�� 2J�3�no�֡.twK)g�@@ to V. G. Drinfel!{aYѮ|AJLre6p� ٭>���ia��Ref-��V2%2�!U�ofa( GPat} hQ ���g �!9u�>~ Bianchi:.- z�)�Shep}� {In�s !J�E �5�zm 9von�isU� )a�I>� T�� �N�A�type !ZYs (=�orA3)I�not urecogno��t� paper we M� A�m�*�2�A?z�d"d"�@�2��:� ). F�,m�1 lzGJ� 6�eFc2�(.�� �w�,on�I read�0�e� nt��)s��9l. �)=is orga%Y� �5 toA ;�#recall sF9asic �< >nd���2on:7#DAew�O�� !SI�2�%�6fN�' c-_�w��Dof�>omo�Rsm-Emty�we�Vq$tw):�Inonis Pc%�- e�%].A44>Mi.�j.�*L A�>V not?,$ list.; �C �.q s 3%4.4]�4.p��}�l A3a"�9 VOA�(en�&e�-A��".NV �"� re :YFR#inTfoua� 1�VMeH �� F:ٔi "d d . "�M\b�KNj:�} '+F0G^�C�50A�D},r\ , X .W'�g}<'YW2M#��-J%�2^\ast7its%�)c\r�[a�a!| -deg�#t!`!�o� aO$( , ) 5� g _\times�0.\hspace{2mm}YCbf O,ion}: A {\em���}�!�a � m['($a skew-symg*a�>p�Xelta :{ g }\longr;,arrow }\o2� (���cocomm�Por}) X}(: a)$\` �:cocyc�i.e.:�J5� 1 ([X,Y])=[ X), 1 � Y+ Y 1] + [ X+ X, @Y)] \q�E\foO X,Y�N-��� b)��a� m9-^t: 3E+n. \to .-e��!�1�H$J  (\xi `\eta ,�X)�>( �^t:(8) , X) = ([\xi,;]_A� J !� ;\;\, :\in.�B'Th:i�e���w �-b% no�by $(X g}, ma.r  g}, ��RNA"���.notE4 I-:Iis 1^�#�F�c�) �see> re mA��s2al���Svalc?neQ��$a�g$ giva���%�m�y�M 6�, �W"kR|/ nsistency��% : �~"� f Re2� �0 �H%s"3Aa�E s-^Fz. 6�IPr"� }: O= u�8 ^\prime$�1 -3 said�Cbe �H9j}�5��W�6�$O[1N$.r Dy�I> � = (OmO O)\circ !  O�OFH case� %�& -NA M�2I�!e  ��?�WI\��������6�E�.A6�A�Y ed�,&5})&�-`2�=a��bl$ ary,��, .�E5�H $r�-U��t�Z�(�� [1 ; X + X1 , r��6� �� lB�J76�Two=!V�a�!�nd-Ӆ�E�,{%'9�� zW!' �/�pGr 6 ��O_ 16iCe8�xe8��"ZGe8n'sma���m�$s $\alpha: � :�Ix���cfx4( : � )r - ���"� �Z/va�tAaJ�r�t ]=0 6/ ./ ��6.mCu%=}�w0b�t.AN � : $a$)�=r!F� .�A��t,cal Yang-Bax�/�� (CYBE)N6[re3] = 0B�FE_ouq�6����I^&�};#dV Ga�a�schoutenzQyz�[r_{12�3_{13}�  2}�_{23} , B�aif��di0 $r=r^{ij}X_iu�X_j�@7 g= R&2N<+ 3}= F+1u�[e�.2.��:� . A >!�!Aof!R��a)�U"�x}. $b>h*i+O,���!\+ !H1�1s a�S iu���H5��m� �9!deJS��s�� ��-]c�4�Cov�$ET"� pW�iGinv6RbH E� ��f*<!"Sfw  �%6m�r/]��� �2�D}, �a�b�S>k2s .�[m�) !� z\omega� ���9wedge}^3�-Bt-�b�:�>��?ti� if.0���W��n"^�  $ŏl�b:-9SZL6 6h alw�iru&r�.� erty:/ ).�2h�$��af�E � �8 (4);e��9� `f �m ���&� :g�6kJ�6� M"� \? r� -�6�"9c^{!�}Z)=[��\xi+ ~� AbBw:8 Un z\Jsn�$�Acj k � !y;)%y�=bi-�x]�IzS}2 !�� $[ , ]q�.�$��AK�%}^Z�#%R��]Y�xi , {*}^t(X�ZY�'[ �)=�2�!  g} ,�/x�_ �B�i'$�zP �[aTneMS}J�[X, Y� = SQ $ [SX , SY]Z��( �S\in Aut g<�#o}N� }�/MO}�?_����I��͞E \cal�!�bu \Seg}} aoge�e�Fad-�9ټb�, A$< , >AO $ v*V ;6�  a)�LV!,� �sub��\,6Rb) =�&6��?a�R�Yce6Lc)A�%/n� isotropic)7&B ! >$jJN = < �X}^0,"�16mm} = p'gX} 'm^_i}^jB���{X_�A��$\{j r� e ba�>�!�5~)��  Eg}E-&tQl!�5to-�&��D oA��dJ� star�MaQ�$b� �)�@:fU)^`$�6 2�� ��A�"au KVE�-,) b+*LJ [U � {f_� }^k X_kY�0A[ �I= A ] ={1�f�l ij}}_{\; : k�)UEke\>�Z }�c�b�y�orm}�>� f��fAYɮ!xf�� f}^{jk�; \:i}!, + !=ki}}^j?kB&Cpo�%屘,s (12), (13)E�(2)A !J��� (X_i����&� X_F�By-1<? �3�Z |A� (1) �&�&� G\�!� �8�C�  �Med��b�" (14).N�!�mk}}^i2m6�E� l} - 0l�0k0`j.`iZ`I`�0 k} =�k�m2`.Y ; m} N�+Q@C=li�S6$%�:li�f&(e-;2!�NowA�C� :7cd�5"dwd =:bTkRFu�re�~� fact?\m��!w�ed|"]6��&IO�28�lJ���(6 iW��)f9�)�ILo�2 �a-�,r!r he Behr's�s#����V){#,2�$$���X_2�� -aX_�`n_3X_3���[, X_3+n_1X_1,DBp [X_3*1 *2:+ aT>��N����E�T# �1�a;^er&� 3mm}�GT )} :"�.5mm}1�*�$!2k#.B 0r(tabular}{|c } \h�  T)$V& $a$nnN & $n�N 3$ ��J $I$VB & 0D$Ib>=1^ :=VIIYJ /&=6EzV^<B=-> S\ $IX^� 'FzDz^�^= � �^y t C!|=Ib> �F=6��UJQ,r 5 S �Kft.R_4array}{ll} III�(a=1)�8VI_a & (a\neq1)i� 0 "Z\} $ YZ^�5F m \q( q���."�ba��}qe�]rm (17� &s/"(16�d��+ll����CI��Hlavat�Snobl,��.���IFR��&��X)e � � � �ed (com�U %)u%F&�%B��!D�s�%sm musG"(!<* t�5�3- �j)%�D� "�:�sZ0� X}^{� j�A^j� k6kIU\l,-{XN}_�yX_k (A�)^kIiFoT>!8 F�&�h�W19ET9=/ our ;",.L!8nam�I  , I)$, $(�a,II)= *5iQ_ o,V  o, V 5 C_oB$,4362"=(V` $(I I� $(III/$>&(n )&�� �/U=c.�h�28>-� we�~p� o�`uh�~�frivialKW+�%!q�=�E�5a�MR��2 Qrg}O8h�>9 \conggF6U"le�.��nioa� for �sti0P�>!"��əsmI)e��kKCif re�@ (3)�N)*>4 (15)�  rewrIg8 8a� �LN� O_j^5i}"Q� Y5'i[O^t"� ! _j OZ� !|i�-i)�=-._ J�$ ;?&@y�NH�D, h ,I� pp�UU6x;*{4Aithe au*A+)��M)�rWO$W �j�jB��"�/�3B:ul E�:w�|�s| �6�#T-��n"�-2�/A��n g>'* solv. � -+a"r�u-evm��3OFAR}�8Y�e�O�^� �_Lse�I! sub�$GL(3,�O�n%�rv�Lz9�'s i.e:"#{:�& _ rN��@� & ��[ݼl���m� Olm}}^n.�nM(B���yvA� $Oj= 2� Xj^��J�2-Oi�X� j F�o�H> 2Y�2X= O NYO^F� ցJ�+�)_l��--!$i\;�j$E A�ad�\ re%�nt�m�"M�&�&n0we ���$(�)_�� = �r^i} �0&Ema5 �]�6��R�$)$�$Z1 !$B�al>�-�`��n�ed�C@[ Iw�6�TY.�. �by :A[>%6Qw�{s (22�/ (23)"Ţ cacu�:2�1�� ���.�cEFWI�5/nd �� �� n �2U�S "�1tJ�2}�h�-A.�n the B�a�{siz>�*� �}� �Q� &Fk\\$Ik&�� �&�^f|x v� {cc}Z� detAg\\Z"v & A �B i)$� m�A#,GL(2,\Re), v9nRe^2$.�& 0$}d_N�b�-c & dv� (0f� v^t &+��$c,�� \Re$�ca� $d; 0�$�2�f�b��-��%'����V�"�& $SO(3AEM�A� V� & $SAI��. � �$5A>b@1u&%�b 0 &%idz$ d& c�=�=$"G��j�!$v& A��q+AQ+�$!��]V*5�:�c����0��5������-�����]�<:Z B�.=�w�&` ���8[ wui) &�E> Z�"0�^z �)$ by�*3 19)�� .3"g $2X7$8+6Y}}� hL^"�>�zz� �� rV)%set$(a,�2���&� �a}"�! n}_1. 2. �z�$ T�:��wrd!s��. :� &@�� 25:�"� " Zse|.��� 6 ��- � ��� � � l�rom*���2]?� ,�Myt@nI� H .0A�.�)�, � �028MqB=,��{%�2� (IX, V|b )$ "A$$ e}_1�u�r���^�&vg b��0f� I& & bR��V6� J&)I�2���0�-���P r�.PRF��o3�ono��-bj��By��%��.y���N�PBSY}�S�S%ru� "& V#N�"8�S��SrS ��S�S-b�Ir�~F��o�S�SBSbn��BE� ��)��.:�S�S.�P6jq* N "ic�J> �� "�3) 9) dvMt"m0 � A � 2< R 8 *@ �0* ,`  F�)$*� "S�  � � �:�oId|bt[ � � �U$j��"�n!)soj1 ... B wI � �' &%FE�m�pQ 44&'j� �Q&�3? ��D2>�} UsMMwe er�.� &�  \?� ��E E=$Z�8��;�3L]�<AP.�C!5�*�b �v8as�4"e0(42�+1�" &�� G . p0 � }^t r�8B��n#of (24�#I�8`X$ 1q�Y*�we �%?!"4M26�.�K<,Dwe]nR9E�9�E�` r�&�QD72rK work���#:�$(Q s1|1)-#�"�,*a1MlN!�24NE<)�p =�E� %W()^�DJ#r�� 6�,Z�A�=<${(2#5)_l}^j [�.9,"�l��1�h*��%% �� $ Y);J6�1ulkB�ummer#M���5P�I*J*��%ՙ�=S:=�z|!��+�e6+N�J-&H;'V7\&V���R��Ms�$1S!uwo�v�%i/q% 6 7}6��A�Va �� \4K�~��struc.s��� (u�T2|!)��L%|y�,!en�k:adVA'28�bmV38s (b-r-b@Dte{S}"�0��˖�#ng�0�E�=�3 poss����Gɶy!�aJ1_9(ML"=*"0! 1@3�P �"ale', ($c=d=e=0$)&e*a�.�olu�'Is�9� � &�(1P!,'� /$c])d��E*�non��+�X&�/Q "�:>Q 3.M0Q T> �W6�."1A c>C *VKW �4)6 mvA& $"|D"E*E7&$c X_1 �@�1 + d63l0&�El�*t & $c6B�$�.� oA�)�0�13$ &$6O. 2G_0�N�F��f!�_0 �?ކ IX,Vd &$bFHb^2r�/%WI�P�L LM-b6�!h-^� X!��\J�i%�$-6} -Ej=�& A2.B�,$- &$Z/FJA �4�1}{2}:� z]a$IV.ii,VI_oA�.C(2�3 +:� )$& ���a)P.1�aj�RA>�A�oa�&$~j} 2�_�%BC���� ���/\�%>�4��*�B.#\\ d{a"����5B�%�� $ & F�&:� �� �[[1]��.]� II.ia(Z�3yj1+>�jn &$V�=�B�E�!-�6 �$o:B�>�+8�1$J&$at$�m��>pN�f$6�6��6�) ���i�2F0/N�Jƚ19;�o $0$& �Z�.1ڛx%26a-1�8 VI_{��a}})E H{2�KJ@N=TJ�+V�.&1�J�!d �+�UN=FLN�J����yB&�eb}*~ &h }&�:��  (� "� ).z(�+lin"+\#�*�  gr� "� *�4� X_2\big�H X_2-(c+)�%�)2!e�-(c.� )X_36C+c25�a���z & $eX_12A1A=�2+d2)3 �&O NO &$c(->�2��b��:�B��q09:_ _1& c(zk 6k�BBk>�& > \pm ba32�Ŝm��O �&$d6\� FX)%� Ղm.m �e1)� �v I.z!�BQ6v!QB�NQ.�� �!�:�9�&G ɡ,I� � 2V!h1 S!e:SA�E9 RQ��!d����!*��$ 9� �.ii���5�+2�.� X�6�v�*�  .^6 �>�9I�a&�8 *�&!'L"qs (&� 5)) �;):�.�&,"���iP|�ki[zmd9�[\��d�9B)}�&xv�c&�)�].W \J�N gq)$^�<D�7 2�7{&�5F{Jt�Q.F��9asC2�}*d"P�}�J9M�c  - P�WoG( ; X�;)J^5i."(Z�4%uc>jQ"�S�!�DYFT� �I"x!����O�,+ &��WK-�cN+ for ^:��xYKPB�eA~ x $A�1��"*�<me��_(18"���g�skec|�m6lwoe�KTo�)&�)�IMYW~"��*sJ���8*�8{fU�R�8.� 6 HTa��n�"rJ!��)%�J�?c���j A^t = j< A^i�? j�L6�"�k��1e`a+��A9�We� 9��H 1-A�e+�[*��!�A1!�E�6�y�Z�4ppi�x�����U�fg;"2  (27Y�3u�; i2y�\}�:�E�2I� R.For��mpl!@t�6�� 2�3o)$�$&�@!#�C7 �>�h-5E�x AAg( ���1� �6�#.� &A�h ���<� ��~g�a�.oDGo�qI�%� �n9l�.A�ZHF�!6�:aC̨M�[@in u�m�z2ur��B��bt���/ M�:$A� |�5=�5:b,rat1S2,"(cA��&i�psame; 0a)?.Dof Yt�%A!�ZUP�9on��1�zitA�c�s~�"G%%  Bʴ �J0- next"` let us�{uVRe�abcLe"L&d)��""�&?u). ���E�m?J- z[�����;h"2V$i;o+:�%p&U$*F塭��2�s �2#�Y�f���Y�MMo Q�$6�a]j$H�Y smo.Ý�= �MGҚnva�`� cob"a'st$�G}$fM�;�!�d)��!�$f�a�2 @�O"�eA%&\�]�!n�J�{F�iPPo�k �@�T�}_r�.g !0adm�a Lax�g$(L,P�EMo��"&� \{L,LU = [r,L"�X1 +��8 L]B�%W8E � B"j �"�!:z]L&�AI�-�J [X,Y]_�\T� X),Y]+[X,Y)]b �r<�i�<a. k�a.[k�"��J�N, =\sum_jS` X_j>�$LwE�j|c"l� �N $L(\xi)=-� 1)(t&�FtI=e�5���gasimirT?E�$PP)=�dH )�=)S^k�Z\ini�@ Wm�:�Q�e�R�"dhr�"z埙�F�J�.u2g��"BIEW��. EBE�i�Nn 2!� he toda��%�&��( $\exp{2bq}!02[oC�q�5fF$�o>|:�������||%�J1.�1$�(Ai%� rres �m�-!��mea �,>���viw�tD�#nV#��� $2+�`a2.�XNl{fVRf_2\}4ar{i,j}mv(a�4^L f_1)\, (X_j2) - R22)v]\ELv]hE�C^��(G�NBTX_i^L�� l�re �6%�r�lْI{ vyi !�J�q5� $G�#e (&���!]ba�af�f*q �>6also -칞�%�s~�^L��>�9X2�^Rf_!�9�2B_To (gDa0z� 2�hD!�e�>2!*>Vag� s. Fog��G$� JT dg g�N = R^i�G�Q�( )^�+#)�j} d x^F�F\ ddg = LJf e"(re�[x�Fparam2x+heMLspa�NowTY NbtLi� mTbZ>&L , L^& � <=�R} /l}\B&ial_lO'L�XX^LR',!�� J�{X^`-R^{-t}) q|H �I�T�f =(L.0.�6�B�h-��u.H�E�"V *')viz&r5|$GN�Ae^{x_1�} 2�}3=R-QnYg3ulW2bX���G ��dņe�hav~d � + 2 � �� e^{- "�.dx_3 � #( �� / p�=B�.B�q! =h1 M)*i-x Zyi�X_3 ��-x = � �XBn Af�*6I(xidw we nr�t� exZ,ڳs�  @)�v }X_j � $�otnotM�x��dE�]�^yI��S.�,d�"��>�h�@(y�aNb j�a|%`iX6u�k� kB��+0m%��/�x k�Fe[d. ��9M�}�Or�u�!=x_i*3�0 �D%"��� F�k�&�!�a���!:R1� *�@ dire�^@@am�@!,p�%��� yA�k�1EE\@m }�;BN$V��B )$jF"�9+bF6 �aA�&�[ 5:&͆"�/.jK� "�K26�[5��:"&� ^� 6�ED32�z&5�P s&&C{�!&}>�K!FUc&�J 8�@{c�a ^L\\��X_3^LVT9�c 8y)� �ANXR^lAX_2mRNW\1+ d& ^��� 1\\-��+2�"pЋ al_3Np�`B 2\\- {x_2RmR`� $VII_ofpcosB�sin6�F1+ F?2\�.� ][l$V��1.=z:� +��029x.qU2*U#�Lb| cosh6�1�  ��! 1+JB 2\\ "R�& �C|:�5�YIXff|��%} 2}2�F*- \taA?2}>�3\\ Y%?rZQ�=v+ZBxZvq�f� a=V)�:z�".R'3 \\-Z �6ZBn2�%.VZ�Z5�2� `{+�B1)� c3Vc1+ ���-�A�r�: � 0Y 5R3B� +@=�y .�u�f�Q1\\!�2b2���5�si:1Z�5�@) J)P:_��b_N�q� $�,�K+ x_2.U x_353.���j\5p�-� =�>.�5��U) �il.V�O2!(1- )�2+| 2}(� -1)�  .G2:..�yx�|\\ � -x_1�1+/ 6!D 1� .w: YIV��!�6!iZ .�.�5�� ��!5l��2� I -(x_2+x_��N- -B,3\U,9CR�Q( af�p� 1+ (a�1%.6 (ax_v2ER�52V�8�:a EB82-! �1�+2%a�81R� ��\T��^�� -x_1R6�^v�%bta�k �}*����2>�\!9i:���\\b�( g��)���������6�� �ѩ���������F "j U�3)/7F"2"�. )E�Z3 � R�5A�B2 P ������, xJ�-1�\����^�2\\2 + �� ���2���  2i.�� , *=�86�6� ^O6^Z�g��5� e^&M7 �}>d� �1}.%�l�l:� �.�2�-u�y6$5.~�mmJ alphj~E�^��"�&;"Z(�Gan6�Z!*n =� � +�xN KD0 9" (33)T>"�+mJ�2[YEE�.]X_1U!_ o! &( ^8N� ropB�}V�~2  �b 7B%�6� -Z�f.^!h �2 3 ��~ �  ��B�(&larly>x(3�M(35��HfM52�k�da�,alU�"�"o�Kl*�E�v�$.UOub)H&s 6F7%2"��*%%�&�%�Z�d�.Pq)"�(sep,6o:O*�/a�:�JE��r;6>@ �΂BR�%2-b�j� �+F�],x�% 3\}� L,}�<� w7 .i,Vt$��>��V>'b�D*=>v3 vg� .�(vC,v�B4 x_2$�?�3,A$<! B=�E &$-b���-b�VHBf $&$bu ݤ �2l�*E�I�|bS& ]ta� 2}(2@ h}^2!WT�>��2�h�2n� :})R� �t-�2$. Z2>u 8!+h1>� L6�5q22}�E:jy�S:�hC@ "�>�C7F�nV�/�Q�yB��> >�(�=&E!&I 6 )3�(V,X; =3A�)uF $\A@i��( &$c$60ew}�23\2U>^�7)*B1�3}E!�3AkMi#� A2.� \�^L L4ZT $yKe�1 fb�R:�c�S z�9)�9F�-9ea$O}� 2I.�P�I�"Y�9� absV��)�xj1F j�M �/x%��  6Rx+��� ����2�:M-� frbn k�K$&>�:"���j&}�"F6BOn6b1�y�r0�:V8V#p3"W#�8�Y��"K&$ �(M���!��a�2}�@1��?O2i�qI�(2��^�T1)6 MM�qQ�9�2f�Q���]��es J�FY6KZ.IO�6��A�}�C �.K�[= Q> > �J.+�|�& �?(20 )!*�>� �1�%m���)F.\.},��q-QFlZ:_*c� !�\!�Y��z2 $&$ ��}9!f1��=� h�=!M��%�1�-2)�6$�8R�22/ !-�1�)#�1+x_1:�:E�6��&^�:�G�x �R2R'�BzBB� g@n| �|�4 a] �G%E .&JD5?.�^L$ &0� �ϑ�M9IL �3>�aG�MSeBTTrac{1}{2}$&$e^{-x_3}-2 2t$\\\hline $\{x_2,x_3\}^L$&$-\f.C(x_2+x_3$&$06= 1,x_2\}^R :A e^{2x_1} �2- ��1JR�R6�VQnP�PV>0$&0&0�R� �! ��-6j2}+ �Js-Z��\R\ �$&^�r�4 \end{tabular}  center}} 0\small{\begin| \hspace{10mm}{\bf Table 7.4} : �3mm}Poisson brackets related to some triang�t Lie bialgebras (continue).\\ ��{|c} I�  $(�$g}, \tilde D)$ & $(VI_a,II)$& VI_{)� 1}{a}}.iir>6Ja)V[ ^L$ Ax.ya-1!�M�}+ �{2}Ii02+(1-\alpha) a�f e�a�aKa�Y�S -1} 6vVe x_3-x_2}(q ji-2� lMul�2a� 9(Mw)z �_{ ",0ĉ��.a 98e^{ax_1}(\sinh{ -\cos )}%($& �e^-�*!�9+69J (�� � !��!j�e!j-��!0 ��� 8!�M�:J1�� 8��%H}-�� n  >1��?=NF�� �-2 � �}.@��A�AL:�� � !�F�AL3\If&$ ����$ 2�� ��-��q ��A)>�)$ 6�-�2��ŘeM)`ny�0[��S �� \newpage �5�\\�V g},: ��M��"���".��iN ����Id�Um�x_2m?2��!�^v�V��2IE/JC�FW��NXM:X :�I7" a>EaC݁E ' ܱ$;au�)$�bhN��BMa�JJ". R Gg ;B� R:6K �uT��!p C=� a� !��~��Z�bdv�bq9�b(! �5�, �BN� ^L Now by knowing the � 4 structures of.-� Hgroups one can con 1X dynamical systems overA8symplectic leavZ thisv\, as a phase � s. T+obe down �us� � dresaction$7 $G}^\ast$ (� g  ) on1 $ which i�1 X`whose orbits are exactlyb�W,\cite{C.P}, kos}.��!on�Conclud�8remarks} As men�ed above!determin+!�types (*� or quasi$) and obta 8$r-matrices �!� )�. Treal three dimensional>�M Yintegre Bvector)�)-9�(; meanwhileVis now�0dy to perform�quantiza!%!�these:�4. Furthermore,L oM�). T-duA�$igma modelU� ree .9`:r-�Pmaj}. Notice that in I onlyAK@9^�L$(=_FE�9�1 j8'�7b570�642�IW II,I!/i)MY  )$),EV II, R%%2A~KNG�B1B-cAScnCHM } & d1d+e-fn5\7 4e4f�ZXwhere $c,d,e,f \in \Re$a�5ns6O^u2R%ju#�v1v�u\2@%tf+e-d�t�t62t_& 1�;a�0Jo} :F {-1}B/ \long��arrow JP) A�8i��Eb:��O R�= ֿEa�f�Ia}{1-au~enm�3fa}e���92��i) ���c^\prim�;- �+Ae +f - �T+%> &T�VEuF��{4similarly for �param� ��72��IaxI�C���:�eiIII>\ ɊaOJըA "��hebibliography}{99} \bibitem{D}V. G. Drinfeld. {\it ``Q um G"�''}. In; Proc. ICM, MSRI, Berkeley, 1986. p. 798.b�sem}M. A. Semenov-Tian-Shasky.``W> s a classs � @x?'' Funct. Anal.o Dl.17(1983)259-272.l� V. Chari%g A. PKlekA Guide�Q:�<. Cambridge Univ 8. 1994bpkos}Y. Kosmann-Schwarzbach.``�&2,.� j�"�trans� � s''. V_ , B. Gram-codJ\K. M. Tamizhmani(edu)``I� @ilty of nonlinear� j!�ee���ndicherry, India. Springer Verlag (1996)104-170.4lim}C. Klimcik�P!�vera.``Du $nonAbelian"� and Qw� double.'' Phys. Lett B 351(1995)455, hep-th/9502122. C. u.``.n � ity�Nucl. X�(. Suppl. 46]6) 116,^ 9095�B.D}AE�Belavin� :8``Solut� the U�< Yang-Baxter equ%�;si!A8h�I� I�1�$83)159-180��OFAR}J.M. Figueroa-O'Farrill.``N=2 .�n solv� .q : The c=9m�fic�<''.Commun. Math.%� 17a}A29-15=741200.�Dzhan}S. Zhang.``Clm�V{ low��!&�E(A 2)� 8)71-81 ,u,h.QA/0311517=6LJ.R}M.A. Jafarizadeh}HA. Rezaei-Aghdam,``*B US-Bianchi �2��E� B458Aa 9)477-490Yd90315.�,H.S}L.Hlavat bL. Snob!�):1�a�6-.�Manin�ple%m!��202209�,Gom}X. Gomez5�Z 2^ Lie ��!zJM �D41(2000) 4939-4956qhPat}J. Patera, R. T. Sharp,�&WKrnitz%W4H. Zassenhaus.��variant�r�low&��2J. E� �417 (1976) 986-6�parA�E�prkhomenko.``Extended supercon��$l current q��finite�alF�Sov�JETP. 75A2)1-3.�$Getzler.``2�ae�2� field�cor��h�307041=|�19� $8)1156-116.�maj� Maji\ E.@ Begg��6OA[rfF���Y�aQ�990604��$:� � docuh} 7 % 2004.december 15. %n \Ae2� [12pt,a4paper]{article} \usepackage{amssymb,�R(em} \texthes(=22.5truecm width=158parindent=16pt �skip=7pt \hoffset -1cm % Anna's def�8�V��tA9(em{lemma}{L20prop}{ProposiP6thm}{E�neS8coro}{Corollary� m(bodyfont{\r! 3ex}{Ex�(} \def\Ae{\!�&A0_0 P*(P} % Denes'~  gTqed{{\hfill $\square$} Z,abs{< \!\! < fel{{%�$style {1 \�2}6Lnewcommand{\<}{\langEre.>}{\rdef\im!{iDM�M {iA1iBB(HHKKNNPPSSXXUU (vfi{\varphi aaB )�bbbn{ 9 bb N1 bbbrRcCts{\, Q(supp{\mbox{ }Tr g rm T)!hD{\Delta< ig{\,sum=�{\sumudiA�,int_\oplus} Fo)�:} \ \va� a�\�#AD{\LARGE Sufficienc/�um stat�al N renca+bigN %.K>Draft�t�K circu�bon�.y todaa�L .&large�eX Jen\v cov\'a\footnote{�or�)b�4EU Research TrDNetwork"%Proba�fA�c'sN� ics, I- �����'Bi)ty. E-mail: jenca@mat.savba.sk.:�� e�,al Institute��}2�0Slovak Academs S%�es:(@tefanikova 49, Br!�s , Dia)�JZD\'�� PetzjUHunga� L grant OTKA T03266290petz@renyi.hu>(Alfre\'ed Ruyi69:�|�`POB 127, H-1364 Budapest, �.p \medA�Uyq7quote} �!�g attemptE develop a�^%�s6?� setting$ non-��uaNv&� b llelAq4ideas� ��8 ��U6u�s�y�ofmoarse-gQ�� s� ale�orA�on� extraca9about�mut�rei� Xgiven f� �tat�"I�)"5t :��" chaoriz'sNl� (ivalent way� ! >6 analoguq2 fa�!P!���)!� Amo=$ �u�hex* case��str3subaddi t��von Neu' en� y,( Imoto-Koas@v�&expon#al)Ai�"r�.e�.9$eQ+!n�)Qallow!�e"!lyANHilbert�" to b6 f{ e.�.| M�:�hMSC: 46L53, 81R15, 62B05. n7> $Key words:�LA�%s,>�,V�, = I[,b|5l]e!��/} L& �q� \no�  \�$I!�du�%�(preliminari�eA�mechane�$Ab described�ua C*- �I"j& ybl�$or obser�0s) correspond!�!�8self-adjoint el\te phy�!pu �ATK l �1na�leoL ve f{%�'�see $BEH, BR}I�evo6 t$\iM$"�&5�heL#4Heisenberg pic�%} 7# an= $A iTmo�' intot#(A)$, ��"$!� a li6y.8 %n automo sm�e��'time 2�� osed1^but i��uldar�irr��sible9#���pen =)D Schr\"o�er=s�,c�ls%�6��%�sIf  $� 1;^*$)= -=vfi!�rc -5 �-�VaU�-�isA�lyh2�! �2��Wl!Zb`&mB� as wel��%measurE�}|usually2�a�#�B%$wise ortho� proj�((s, or more �rK,i�p+A�F`unity, $(E_i)_{i=1}^n$. S��| $E_i$eX� E�oqL�7 $� H_i E_i=I$, $\beta: J c^n \to A�x, $(z_1,z_2,\dots, z_n)\mapsto Fz J$Ie*v� ital mapp 'froS(*W ���b�$�!�>MQe�. Every�!noccur�t�*wayIFe�tiIoncept i&; i*8 �y!��I�:��"affM8��-�!�a^� . Al�)es%�"W�( sit�s justif�) T(VZ` s between��s %u}/� 7al viewp�� . IrADf6)b�``�6''A9N � '',�-� ��:ACMKN$ send��$�!2s�,Orest to � �1� �< at our disposal�`n los�&=�( takes plac)orproblesc1"1�to rec"�-O �1eI�e�i��a�.e i+ per�)mos�,Kv* � ricL}� s,A8ara��F$\iS:=\{� _\tha� �IT \}%T�� ��Vo� basi%#%�aal =/��ct val&� �er sh�Wdecid� IC�e^.Q��he outcR� �C-�we have�-���De�� ense. How��Fre��``�N''�'}S,!� �u1q� -6>(data, r�$ \ref{E:bi%G te} below�jQbw� scuss! no� procedur" ��- &� � �!6!m*�� we w�to"� �a&umstan�+�,��� A� erfe`/pos. .pE�A rgan� as fo� M�e a� �is � � summ� �relev�AqcA��os both!�&0!x%�e B�fa�  2�)+Rd �W sub)3E� �r. Mos ��ul �ha�\en �1n1{aX a��plete� sen�`oioin��pro� opera�/�ic�hodi�s0m!t�3� devo�to.� >�IvimZ!�)� e multiplHv�1ma�f a co �l�H��yem12� ^* aV� of S-�4;A�hre9TeI`�5Anec��Nz-=q��2 cy!f��E��6� �'@ � �CJ3 J3� di� ��a;y��B�Y� 29 -r%p�/ . %"� P6� �a�e�&5 s al��:a  $I$. G .� �CM$, aep�T�.Q � � s ��� $ such� � (I)=1=\|�� \|$. (Not�1!�s�?d!���q"<to����Y$.)� book�1� -- �g many5 s --�lA�z�u!ts�%=6Iʅ�A`F� ful� trixx �rm a  %�� x  raC2 trivsubb of.|,�A� �� -� �>� � , alG� tAY� s�1Z&E߅��. A� � $M_n(%�{,dms5o1aATr#)��O"4 � ir d�4t&�!ecta�$F-m":�Am�AnF%�$(A)=\Tr D_AL$ A\quad$ (c�x.we�� y!n) EOQ�a� vfi$L !l �y $ e$;4]� is e�Ke (semi-,e)1P��rR 1. Lete+)3$\� be.��$c!L�4F2-Y�}�BV; mea $$ 9-[B13}W3 (A)&6(B)\\ CD)�aj3�2(] \geq 0 \q!v \h\ if } fw(A& B\\ C& DJ+3Z\,��+$2\�s 2.�44!�;i�tA(�-�{!< a99d -pre�eѾ-K$ s]fA�A%xS.* in�o�C� (}\label{E:s -9` ^*A)%/-[ A)^* �G A>�*�J�  w_b�:�}.�5� twoA�da�� 6M5ex}Q�X$Sa�� andY�.'. A�m(for each $xg L}5�$E(x) $e�gpx "=��I&r�s�Za��!�8�aat�h� 2 $�� s�E $C(\iX)�ޑ� * \��E� ion��P$y $E$ induJ � 6�Mf: o9N ���D8(f)=\sum_x f(x)! �ref�FZ�oe�8B��ni&��s!w!:&�. :�co�ofY��~�uat��ful�ed!=0 >$.)\qed�ArJ~ME~a�0x� C%\ s<ngm 27 $\iH�^l�lNViL tens 0&!� M \o�o\ �"ts �To - I c"= mW';doe); t ne�Ghe ��l)�"��Z� .) If $\gE. $ de�3 shift!�H�_ �=Ie(qu�JM�_n$A�:2sD� iN.�0_n(A):=031}{n}}(A+ � (A)+� ^{nx4A)').��{A:�� >��xs�"a� n}. :7�B(X_i,\Aemu_w6b�M�m�,($i=1,2$). R�T��� Xmap $M:\ L^{\infty}(X_1b1,b1a� 222/<is � ed a �Markov��}�' it �j$M1=1I�$f_n\�row 0$� P$M6. o;Ϳ�$�.� mF�� onotoo=J ity �%yUty}. �} �LE �A �Zk��:[< a�Ѹ� :� �. Our� �>S)>>:r. WeTmea�at�(6�� �1s*�*� &� �|x%9N �9f %I we a�2 i��>rving E a1��sa�f tn� Kr�=x��llaM�>Ba� .NBasic� ults}%>ri9nL*b �s� � N�,w h? Strasser}�;Aail�m�,I$p A})����dm��@let ${\iP }=\{P_{� }:\ ^��� �of�#�,%R$(Xa�)$. A � -$\s�,$� $&;'_0\.et �� E s� t ���P $a�� ��$A�h�A��r� an 2k$- �%"� $f_A.eZ)$G _A=9(A|r_0)9  -�%>*y�}L�is,��3} B(A\cap ]=\�%{R( f_Ad$>�!V�<5_0�q" �. Ie:cl� is ���X ��<A�K4 O"T�3%��$-���+�,�� "4 G �  $EU�[g|\A0]$ �nyMf%� step5� $g$�,B��ny* $g%capgE�}L^1 I�,�A� ���Nortd��**0E�s��do( ted}&a!j.u I�mu]���P \abs �� �;!+��a usefu$$o�#G EuGcy�Ew 9�<u  :HS}� $\Pea���e��1� count)�uba�$�@1,P_2.�\}m�eq P��AO ]+�0$ hold�IKI�9�e�]DifBL J;n6bbbn$� } Ij(U��E$\1�5�S .� (�&t) nvexA�binM�P_0q n c_nP_n�P_�!,9 !b\� P_0H �our purEs�isI�sui)lto!��!A*2% �of =��:er�f ran� )"EPe_i �i,)}}: %Oe �?nA�I�iemy� M��Y _ �!UEd_i) i!.d . We sa�)at � " Pe  2����i Ae Pe_1xilre exist2:� F� umu_2)v 2� 6� $,� %5�# (Mf)��,1}�� f2} � (5r)q ,\ f!2v�%  If alsoN�ACa6&��+6K�9n%p�)@e{N�N$�tocha�lyi$JA�� ,s%�)�E�`cA�6Ae�3'.3n�0,\A0,\Pe|{\A0�BbviouslyN��4�呡�> I� i�J�� $.�xP_0 x�:�?0m�H b �H,A�$FJ�_� A>f�! E[f�,M%=�)"ua2� r�y �  >� �J�0%_1}�n�t]L3 � M2�:E�Mv:��-V�  [B� ��a3��a�*�6numeraO,\�@[(i)]N+��?$)*T嚕ޭ� ��2LP_0iy�� %�{=�/}0}�8E�23 o2��a ��2a\�ge0.�lN:09� =15%� B� � P�K\mu��EsuF� gene!fJ" �{� }/{d\mu}:R �]T!$!R� over��"aiW=?;.=��#$���-ch�� � mal]ڡj Next O1�B��/u&� "��,� u $_0&�*��6��'� C# D#-S�"\of��a+[0n. $(\iM,\iS)E�) �{n=G-e�Ent�*=\ �B'� �� 9�fA�of!N�  $ ��zh$\aa(a) �i%,"��b&� = (a)=. H) : Y%))m!"� !��&Q�aQ4(4a);� 2�2�*�!%6�&� Le���:_ZD.).�"�&�# Con�% a �#�=\iH_A*d H_B$E�]u:pbq�uH$2�!�ERcAb on v�%�*� loc@- at $� =o u4� ,a�%��#riX#of�m"$'1$B(�)$ .!�red�.�)�hi�a� i:su� in�&�%�#t } im� qffR��O �!�_A%�L&�H_R)�� ow1vf��P^09�{RB*� 2^�P!!�)%LZP%�-!L�1NR)� 9Bi�/p�@n&�"{' 9"�%:�8un!��V�R�. jL)z� inh�1ueYXu5�E��Q� %)vered� quel�O&.�xA YRm� c�.�ty�-. ��4l�, h*�' r*4P|s1o-� �A)nm�subtleB��&� ��&G&*K<()�.&J�f :qh�Vsun�.�i A���!faith_WUdpsi$.z \iS=-*F.H��F��a� R E�5�`a�6�s"(e'n) 8i��SI/a U e} omegex{n=1}"�$ \lambda_n�e����upps� \leq�: W��<� �% � %~} 4P�':q { p_i:\ i�I5!Uhai�/ &�/�)�/ �M$,-! psi(p_i)>�$�ik)� 1$,��ny�v must t� "�s6$ \Pe=� �:=%)C *G)\}!���sho�atA�H�6V $\{p_1,p�0"VT*T�p x  = � _n p�M�C� �!iB�a�s*eE[Pee�WpW". ��ll chain-�j�-$C D�!� 9 /1p C \n sup D:�J '!E�w 7*>��%ny"(5.� { C_1,C9Y) maxY ch V�/�  $C=\cu!P C_n=B�m�-�%uE>�� ndeesSp_n� 2  *� M+n� $pa8)�% %)BCR C� \{p\}"5\� radi * �� �{>#.ID�Zɒ1,��2%C"�6iU ��:��Kn=A�. Cho�\A�"^��1, `K $na�� A~$n��m_n$pu:� �"�n-�� c9P��9A�e�n �i�\lM� 2B!��! ThroughY;pm*( � ��hypKs��� ve�#�iAX�i{ 6]+��|5h e��œ�� ɒ�=ň7��)6�%��aށ���2V"�YH�e��N W�� tA9 nAQlh;F EL\for�F-�Q!����=�b�6� eq� aK&��S$��7 by} $ �aD"t,"OA2����\a�*� .e m� _-�'opynt*��8)��� ve�' opy}%\!#x5i�%81�}�9 \tha���? 1986b, OP� dcCq�e~!�2�L&�annUu���$\xi_:MQ�re�(�kg�_\t�5. �e nat L-eA I�)�> *��8�$as $$ P_A( �, �)=gE �) , � kE�#Ing !�+�^ 'I2mD_1, D�= �+((D^{1/2}_1  2)EshGvthm:1�(� � �� Y�\} M !F>2�u� )�|A&%�Jg s2saa2n5 �2��;.Z��MQK yq)�&X �[&�&".��)] a��6 ��� �!w89%��� !,M)=!�|)? )�D�A"�`a $[DF , D b]_t=[DFc), D( $ g)]_t\,k�~7$ti��� J�v�2�, �T� )8D�2YZUT!��35�M}� $E_ � :\"�'%�l�ev�"A��d)� $ in�?n�� .�a: &k1� (�A{vd3 ��y Conn�IPRadon-Nikodym cocyclee4�gn� �btKga(ivwd.$3K& ndix�+V;em�j),8$ly Thm 9.5�!��OP�wey:_$ed��of�ccfF~3sC;ep}k7-� &j-use}3���� :�ٍ�T:�� K��>�%�:>;�: �.ŔD_.(D_2�� ". S$&N�8 J��-a���� T), 2))�"EL�:  .>- �p n(CX@MS;" ) $%J$̈́  �$D_2 a D_1^W["V�Q Z),�w?!�.�inke $C�}��5 K�D�y p=7D_14 p%7��!e so-.� Kvm#dular�I�f�pr, woW7mu%�po�ve:s:1#=LR� ��La�2a�%{\j4nd} Ra==;V<� �R!�Y = \<�1, )����1\> FSU�KV��6��;2�M_0 x =M{ x 1)Q K_0AKJ YK�0���$�!��/��K�(They be<:�|2&mUM\midKhn�B)��6*� &} w"�ex� sU��olv�bMs:�|eqn�3*~'A9� & =&���_&-f�x \pi}�!"`_{0} t!{ /2}-  2^ ()m + t-�U:\> \,dthA`�M�U � I]Qk_0 5�wN\ޱ2f�_0�."k,d�9iwa�A i=R>- $$ x �*/�I(x+-4n$ �b��u�-rQ�Y�A} V(x.�,+\xi)=T^*(x)��!=��&~ �� �[\iiM.H]^{\perp $V�aB�6c N�\Vert :�^2 Eq�71 #^*) +�} : x�7 � x^* x=Qg2�^2J  6!^21nqDsE��5 i"�5�y;c��T^*>Sp2(� $q �f>U�-al, $0�8 '(1-q_1 ���(1-!!����y�"$h$N�(�@�6)��^���]�\< NY,m�N\>&=&%����x)p_1 ^*%�� D_ q_1\�e<6� h� )ie\>&�&�2!�4J\>B�i!�las��aDn �.a�\< �_0t��aT,\xi\>=\�]2)ѩ.� '0I:�)9wu�^* k V�  _0\,*�az}p�J $y"8(y�WEe�9&t((decreasing ; #c*E\nceB��E:op}�Dm!� (V^* � V 2V^*�,��V1��(1C� HanPed})�H$V.U 1IA� m/3B� 2��V� geq )�5�3f/F�B�*qq� �Qw*&2 P=�� &�ir�Fgra�8� s}u � (i)q�E��,�Q�du��a#2�o�R��p� �BJ/BDd&Ga�}$.�$o� "�"h��D*"= 5]uk3tA]  o34yz�WofHe�&F� M� :a|�!m.a��6 �=.9 A�2� thk �  ^{it�# -it}�& =D_2�p_1\, *� ��.� i>�>� Fr@K>: �!�Z�M�NE�y.�qKV��i�\>��67mfL>JN� $t>0� 1� toge�$"� ��yr �� op})$J(N�� �=~�)����:�Differ��by�bqF�2r�26/ >� wIfe*D "  R�9$^2� \\� �F/$iM\toM��<5�!Ɓ� �� F�= v�,? \foU �F:[ )b h.�,�"-�psi XF$��H�4={!pA��e bGtis� AU%*$Q!�.ZG x�2: N-\0�� .�!e ͬ. Y/�!�O&�%:�v).�$E�S;3 ��A4�e1�Z��v .�Z.:;i::IDva�#�E "w.E(Dh /2}E5as)Am�a��fE(DmM) .` a.Qis�~6ly writt-S@6R2 �r�F: J�B�aly�i��i 5^)�%���$$ �)"F�=D �D�;:V�"&9 Tr.�.L&=&: a=-�1��1�.V 8�T��:J:�=%�a*o ��$e��c)d(v):o$e_�M� R#t�!���:��I�MDG�!��<�1a�K^��P��a 45��0$T:\ (X,"�(A�(b: math!Ac:�w`i��R�4$TA}(2E�� ���*iPHGT�y� $T�Coci{.a B�:$ \�� �.�8m'4;P_0^T�.&�7�4 (Gg)(x)=� x�O�9,H3X\Pe^T�-J�:2<6. AA*!�Y& G1e�qHprK� 5�9�Ae�� �6W $\�>fE`�&2�;*;� s6;.P"M �6�(F2�b$criterion)�A \Pe 6�?� U� �v� �J�'�;`x6_1$2�7"gu�$E��2�-)an �6V?h*�8�**w8}l7EJk(TASh�L�P2_C ;"wS�k2nbfGr]�/6!P%� s�D� N����@6/5� say� � m>"s:QE�U�al)S'%($�6�()EA� &( Fz 4^&�"N2XP��_sig o^ =.�.)�%>�� heta� $J=X)&E+bn�:a�.&* Le�"B�1u19lpXpp '\ q2n �$.J�maJ� :\ q\iN q!�p!p$�Ra �pH (a)p� A��Z�2�2_,9�� J� )� Q (qaq�%B �^*� =K��A�%T�H  �(�!!^  |�E�checkQ��:�$()",�|_{ @?2� �R��99!��.iO�eEu: b!�)�VXZ{�=l c=.T92��9*A�a:�\&"Ue } \iN_�m04{�% \iN:�_^*1,si�� ^*�A\� \ } a^*�R*^* )\B���*= � �A�F�PbYb) � �"i$ �b�b .F�<6D/$�-e� $b�+iN1end)�>�� �]is ba�#� �hN�e���(x^*xGV -9 ma(x�%�i�M c 5#"� t�|�8a�ma(b)+% )�ma�^�)* wta^*+b � -s! Va)^*- 2b) \\ &�&x H} .XA5RP"�t nab+b^*0+  b^*bV=t */� a6�+F�. Div��%n��a��LtiipmA!fty�k� �5/Z�q*!��Ad"҄FQ-1^=!���Q--(�'Ad�*l0�*�Y��-�mlJYKK 4Wt[l��& e�u@!A�0Rw`} �TTm"� w� � N�/9�� ��:it; 6 b M"�5J������ %iN�#{ �Z\iN,\-: ^*\�!=��O9Ita�^# � te�28} ^��=K�6��$, �<Z=, ��5J (2�iwgA�[%p�&&�� }(a)�d��@M ��*�5�$�!��!� is&�l onto)HM%Hbk %F5M(b)=b\7 �Z�S:yzX �w�*���5� .,[Q/��23b�z� sig:2� �> SE*��2� � s�8ial~p� do�O���@uY�ke�b 5�)Q�$iE�/n=���=f&W:՚*,G&�2MM��" B}��N*_2�2� )%I:q  BN).MN>V#�2)=  "=�55 "�� �&2 �2�+]_t)=D&} $ W3Xan�I LC=A��v�m� u�.� !5 .�a:.J?.}ׇ�7(i)�#.%�>�[ �\��(Y,,.�.��<�R easy��seBM�>.��TE/'�� `&{ tq.�� �W�� s7 s�1 "e+�;$A�ta= <)Gg�[��*� �� �#��>u�2� U2� 2� �)�3�i�.�i&� �7$\ v)m��Bs l*� m�9E5 k9S��Nb�\ $u�5NQ��A� , $v>2) � �myuaRv_t $t�$p.���q^�$. Put($t�S�v"s<��g�^� W)=~g A u_tu_t J/�v"� 0�  ^*H�36.|!  \ >i<^*eS�bt.c%��:A�gin.T } RWb"6(�v!�.1.f1� 4ݦ � �`5�� i=r}9f)d({BC �65�%�!99�� $. Hi+A��/��Х�D A� F�H�s�o�7*a�A��:��:s�M_0.5!�� � =papy.�RyV�ed ex ��}Remark.�IS� � ��!e&�7�B�pbJ� ' :m�Aisx<�2�!�,#. ii) 5;bv�v� a� �:b=2U� �)Av(an\�*Bb�!1V ., ��th�]�0��+8eq:intlog} \log�9^8_0^`e (1 2-& 7dt\, J,)eD�(��inB a�1�UfBD�Di*F�i�MBR1}.q�w : F)�1�*5a�b�{ &$zly.n"�!� �M$ �<�;��"�FE!�cazof.W�k�ea�F � �JBN-G}. �Z=Mn-2{L�,"S�Osa 9noZg1�u{F.�1�sec:f2�e� 6 E. E�j + "M��A� �`_"RAe�Re�Ji="�(�i!�R�(�jQ�.� �=0'za�a"�;)oA�]"M�1$�)>��|a@:~]�k�E�b$ �*t�A�$a m*+�� $$ a m�*)n1{ �,� ma_{-t} (a)b-$ �& 5b� J7>6 j(b)�� 5�E�B-�%�U�_0�� ![��"i2�+a�%�"PO!�?iT!F>m��>�YZ%�5� 1_V 11@ _1}$�=OSf�(inU��cj4 .�jAV ��`&��r�w*�!C����(� )�O \BigSVfJi 2Li &_i�u):!V +:7 �7(6.9)Ét#I�r� sake��i�6` �i���+� �f�:I��u� ha�6.I- �lE G -� iM$ "Q&�P diretsu�}type I%�or�hAw  6.10қ� �tau���cau �s[D'+ "PA7[.E�s�7��$�4resZfI�x��":U�KWs0ax0,�\iM�"� uba�`�LS � e���%�61� *ΐ 6.76B��5� _0),A��Umle)<�G \ � �e�1$�R2Lnt)9��6��n)�D_�_0�@�j11~&t0-��of"-<�F�6BE0s�Mau_0:=!��91�11��s�0�Yit>>���_0��= �0}QZ9'^E^EU:!, $w_t:S,)�?A�2�� � ?ry "�< �M�nd�s =�Xi�3a`u\^{is}$��G�,sR�-. I>Ig���z*�ly � W4�4�O8�?1~r{�9� �%�w_taw�5^>\-Z)��1u1%�9_W)�")���Va�]V5i $z_t:E!�wis �����gmd. Again+,-u.{Ny� , $s,#� *�-r�zEe�s��;�O'� $z�Ji=enY��8E-. j] :��ge*�.B� �orE�}u:="0}.sz� H; ���#���Ja K-"z�e�"e� ~� >� R�N2}͋^T`2�9F�N>�"j ѳ�o��$&N������sJ� .� �`�G:G��! J�4E�;��I�VRZSi2Zj�)o1*%� �7{ ,:�,>�w*&�n;A�A ,}dB�N�d"�|�-l :G|_W��E� |ə' "� ,1Pive�nd e$ u?�[��a=I�e�.RwJ�By<j p���iՄeq-[�}��$.�tj2$��!> �Ѝ. a�>�& u�i)D�?�d��R69e* 65o"_0]_t �1� ^���|b��h�Y+ =u_t��ZN6��(6W9}i(C�Crsq] Z1 rue)4P!rP,�it=��QxS�&�4�!�ceA�A�i]��:�%�}n� 1Z 7 d�`�K�il�$o��o�. �&N�Qimh*1on�� &�2��<���ztO~ $\{2�Q]_t: zK��:�eJ�f!yAc��.�a��52dg=k�*a�>^8" $^-� d1zq .�|@!�@.a�BM2}�>e�!@dM�Von.�L� &�S +�bAtiS�o D_Rzy,\A�6v'I-'Z��5.E�}b g @Zz���d!�%� \iS}$d N2N�&� A�auJ%�b'|�~S!�-)2�Oon}. !� ni1�Xsi<;^ 22u�s�(V<is�Bn!�an��.�y$E�J1�m�$-�?l C�s�8MT:$�u�*�$(�a6W�F=L�� �P�a� &�g��s $-�IR% !]M2�_$�^p R=I��R"' �Sth: L�'H_L"�*�"jj2O $\{ �Xy s[\&JMa|L�\.�%v�z.$$ n:fR3J2=Fqm1!��jAJ��� $Gi� �*hi� � %�� >lfXW�2ij>W��_n}>L� _n}A)��(2�.&!��#ges׉8�I�i�ve Q\ A[��L6UD�L  R$� &�3 !�2(:�F L� Z�F!�]ER4.*�>�}��(�^�!��L�L&:B �L:"�-L�*�$A�%L _L}c�*� $c�pi%. M"^�EJB*\iS)!us��u A�&�E��2� J� L}4`��E�,L c%�=2.57_L] 9R5 ;b�'A�%2 /!4{=ABJT!�=�6)%�D,L� �CD_{R,L}z!<*<3 1�\iS%�� L~}>�cF�,d R_0 zU{)�� Z�!a'S$6b`bup_a �Bh� � >quw5co"  ��AC���3"��I "�E&� Keep:.P of����!#!�� >BA�$"Aj��V�V"H RF�M�^c:�=We(Z=�� *X6.D~n.�h&�! �al!7" i$�d�.�m_np_e. q �C,�\�j�� z%���% $z[e.9b�N�}� eq:Hi;�4H=���$_n\iH^L_n\,��nn^R� Ze�;H�C.) 8R_n>� �",M�� oɛ*j"�3\iM^c!KU��� I>x} �(Y('< @)'�Abi�V ' �6RR_6�+*03�" $D_R�^cb �+�_"��eq ��^c)'$, �"�p_nD_R=cy (1F�D)-y /{p=c!�(�o ) (Dʎ�|"Ho U�)��|Zm�*��)+R�l,�g 5 j6L6�~$cE:L��N)V� (F� � f(�~&f ^6�j�� 2�� � axA�6� )�R%s9J%g�PMWK1�>t� 0,a )�!~n$. Cle=����i�O /un��Jbs  . K.~�( � EA�).S-(p!��.jL,� ^�$(EF),�,:�>!��a,��6�ofMrmY=��)��A!J0��_kisF�s-E�%0��xPd���gse �!�e�jz$��F�4.8Z>�2�Qp�k6�, &�?by ��1 Ťa��kΤ�.N��~4"�3Km�X�be6<i��6�)FF6�3, :�&��X ?"?&��"'\��K3DIZ �>P'< �KE��}�!�e"' in�u/h'�)�y6�3�| JAf*� �26�3�UU��B)�"�>Z!�B�\iK6�K���iK��.7Gif�[��K�% %." 3n!7&r* m!�( (q_n0n2�����a�tʥ $U|t����I�:�sO%�_{n,2}Q7�Y;*� z.6�_n:�2|{q AyK) q_n}�!����� xn=�W _{1,"� {2,n}�� 2(�0U_naU_n^*,\ q��(5@)]E2���M *^R$ Q@J.�L"�J�{&9\�9%XF��$:=�  1^*( �>;�2(in �)$��*�"�Q�ă1�(.C):a]� &�7���}�=xZ"�*�� d�o�*!9_0:i!!� #!:AiF�W&{ �0�&�Q8"�-(!Z&b )>PGF =�� ED*�U_y�%�I�!�e >�%;�:�6��� � � %�edbe6*"u25,c S6St��Rim�s�� =2N ���^c"� ��"`b�0��iN@ #�e])$%�*2� �1-�} ),D�k.]_�S6�.A���.��ND23D2�:��A�:X> d"Оh�+N�|{!� *-*� !_x�<%��3�..%�&o samKru6��$1�k�M/&�.TN� rU\��!��.�"vż\iK =6� R�1��<.I"��!����U},�hBD�� _0}'2F24L_� _h �!�-�V!).�Y$�w�iK_n^L.�Ec�����N�[ � a� ` �� s"���);^L�Q�����_n��15U�v��� �+U` t�v) �Ik)� hb)\:�D  �O?7 b ��:0 b)=a *�C$$ X5�b˙�'� onswt2 o� )p ]o \iS'!�!�bMQ_A�zA�M _n(IAL%l"�b6  '_n)� )�|��H�D*EcK a�mapK�:\g�I�q16�K%E)X l ��A _�5�AH~�.�[}). .;)<U.;-�jLJ� �� (�E}yQ_n{.� 2:ɞx7�2.�b�IA7� !.`WE!*'/�D1n u�aA]-H*� w&%p(b)^ bm�Ay 8=+�A�!^*i�A�A,���bjF �(xEh� b^*) &)ܮa���' $bE]��Z��.R3} Q? �F�N�C!8p:dV6ove!�To)��=i�?�-�V\��a?�!���Iof%�!���aJF�+1t2�-� , m"�9,+�eOs&�l+e2�Z�\� =�A\*�i�a�W!BB� a�� � x _0&� {R,0}z /� 6i)�M!� .[N� �}$ 1*p'6�uD= 1�(a��Y E'�.!} �L,& �E�p 8\iS 41 M���#  b� q6< �~9a2�>tm�bw% 5$>>)6&&� !h�=���� K&!$6�X ,0}a2�Y) ATr�FF{C,U.S � �#R�3�s2��VL2�B�G .�&� JT��.�B�% (a2+ �A�B�@!6!�q� K�[S)2aQ_.�h:�by�C!�].5S� t�M�2Z^2)��2)^2 t=m;3!_�A.�nkW2[�n 6 o��W=I-��Uv� !� W=�0CR� .^2��.)^2o`|#��c�&�i:� � "l!�ys"� 2f$"��%� ��e7ln��t="��Ot�%�a�� half��(�eq&��Z4s m���i�I\�-c�� :cM%�wH���bee&�al� �t�$2_96�&�!d-�by B�"�A�a��B�&ߍ�:V�. "HZq �@ �5G� u$^l&& map,)!�KrawS�bn�oF� (i V_iaV_i^*"D �E�&3 H@:@6x.u\;>S�.K.��i �� a�V_i� - '��i,n&2 ��n~c� �(�E��<�9 .��8&��'�i{L_F^*=1_{8 � A�>s| !�J�,�#!=.mof & !4"�i�� c<V׸"� � form� �>2* $-�"� |Am2)�!d' 2� I0 ,$z S �K �q� 6 5ja5k�+R �6"� :�:L if�7r:)9V���aw2�� "�! $q�)��[�� aq_m� a)p_m` �Wa).{n,m}}�I�:,�,{k,l}q_kaq_lN 63|p_!�: G}"V_i� Big)a mq_m�4p_m�L�GVi" :=p_ < �a�"5Epa���B <� oM0 qa ^*Q� n(a)"{. e Q� _.SNN&4�.ANWaR�NL!��7>u��I�>��$.�)�u�iJ � �`-n�$, /Fc621�o�cFմL>�%�) $K-�) R_! �#�i & �>7$�"�!� �!�I�i (*� D)aN�K�!n�KN�1��?��8�{i,j}^n\�$ �.ba��u}(k}^n=\d��_{j,k3�M��1�!j\mu^n@j!j,� S�ۅ�� $\nu )�>i� k}j�$�Vj 0j�Tuma��-r� ���!� ��)��N%!!^nK���dDA�)��*l��� ~`tXq�"�D6u� #cVk"� .$ Und��:M(C)��CxF �&�/�,(� �B;*51$#N �:�'�&*V=��#-�.S$��q � L�=�n�.>-�=�I<  :�b1�..�E#0&�����b �i�"H,��� ��IMN��f.F0!#byf�! -ޝZ-$J��,K(J� !ZU0� �,0mB= ]B թ���M�W΅�U("o'Q=R$D16oO �1�^*e �= .�M!�By� s�Hx(J�lv&2a��>�&�5���!q @*A�$*2V*�0 ���:fix�oӣ �MB1m>Xf/�1Q���L��S =3a �� HJPWY%'8cp1s�at�HY��  "uHE&ػ��� A���me۳�Pe��)�}u[%��t3 "�hxas�bf��� f�g��uDhhxi:iƔ�}_m���3�I&V@a| ��BE $TCTAX�;�3�^ �5K �$ar"�h &�h =&��ZQ*Xaxp\:�� �m �i&T_i(x)\r�v�h, IAGc ase,��'/�O$\zj W�@�"��.��A� mmed�k�ENf.AJ&@j�Ws�7m $T=(2>)%�*�%2�.-2 .!�h9� $\{�?Pe�5�!"m>�� ���:eq�� %b��*�.Q�9�aG5? are N6)�+!Z� J�á� Z'�i� spanH�:]�\{�MQE}�j ,\ Pe5Pe� &�N"�)a�[E��gL�LI u_Es"��)�X!�e�*fF��a�F�U�0nd�oM oRo�E �q���*$\exp H� H=H^*�4iM$. Determine�L the states $\vfi_\theta$ by their density \begin{equation} \label{E:qef} D_\:�:=\frac{\exp \left(H+\sum_i \xi_i(\(4)a_i\right)}{Z}, \endf where $;1,\dots, m:\ \T�� \to \bbbr$ are functions, $a_1, a_2, 9 a_m %�self-adjoint operators from $\iM$ and $�@$ is for normaliz%@. We call (\ref{E% �) {\bf quantum exponential family} arou`(\omega$. OnIPn always assume that %((a_i)=0$ in6n|. The next example tells us how!�J�$ arises. 1�x} Let)5 >5ber4�gebra9? .�AhMJ of aIu�,$ is written�.for!�AG4H$, $H=H^*\in !�$, moreoverC1 . If $IW a sm!�Hneighborhood of $0 NA: ^n$,un minim-�� $S(\psi, )�)$ under-( constrainta=psi �iB_i$ ($ =M�A�E�_Q� n)� � , 1\leq ia?(q n$) gives�a� $ql$ which!=of�%5 6�� von >;is?��ndard��eQ�(representat���i$�� $\O��0 posi*cone. Ř\Delta_8b!b e modular�ť�$ then�.$~�A>)�vvector)Z induced  �}t !B� \P]m ..4fel \Big(\log 2�+ :� a_i-) )}{;\|i^fel�J,IV\|}\,B9(Th� mula hold%�!,strict sense�m�!/�Evertibl!L tgIR�F non-D��E����is!�ifi�oa(aIproje� .) I` theore;sigma^ �_t��no� �Q7automo�-sm groupAQA, $:F (a)=2� ^{\im t}a  p^{- $&b thm} i� petz1986}�T:4� v�with a5�2�� �� iM_0�� suba��e$B��� \iA��$the follow�condi�ysh (equivalent.uLnumerate} \item[(i)] �0is sufficient!�`N�6�K L6�r � �� all $t �� � 1�*V .YZA�A�� ized�al�ec��on $E��:\iM\to ~�=a eR, N� =3A$Aҁ�us��Kby $c(IZ,� �Sum�w12@),8 is, .5=S(�a], L)-$(a)$. Then��n=-��e�^a(1)��� ����M al�L�#�h $�؅�R�����$6� ` - ��Y��8 ���ytic and�-��par� }{ :j}P( \textstyleC} %_=*:L(a_j), \qquad \hbox{M� 4 \�\ } j��$$"� A thm:exa6}�iN��iMe��>� sX l� \alphA�NM�5$a coarse-g� ing. \%� #��. on ���\��s�at �2 _0:= H\circ �)~ lso W.E�2r�l� e���A1* D2<>� H _i b� $� $b A b_ke� EVAN%0�!t��$(\iM,=�ASf%0only if $b_i= Be��i=�n� some�xi �N�iA��� MEQ ~=]=Y m�_0� 1� � ]B��q0{\it Proof.} M- �6�N Ale- iN_1=\{ )� iN, L ^*_{I}��Ra\}=\{0_{ 0 �(��_t^ >_0}(a))=  S( +a))\}.$$�5�(��a.���"� ��u}(b_j�k i SA]�s!�j5�k$,��p�^c� ,A�:# $�N_1$.-|a1� um_j-� ja_j��yi�aansionYD(narray*} [D]7,D),]_t&=&[ ^-o(v)}*\\ &=&\�l{n=0}^\infty i^n\int_0^tdt_1eZ 0{t_{n-1}}dt_n%�{t_n}>��))...'1' 5�( �9 ڎ]R �.Vj� + �V,� 01Xa�Q5R_0]_t)i|e9� O� oA� hand�Q:���erP $6�5�\i2� H��� �&�}�1� �=6dM5]_e�A*�i&� ' a# , i� llow�22X^=[D��9O]��i �2) � �Co�sely,��F�e�>�: ��>_%�- ^I q�"J_0,�)=  6+]D=-=�u _j8^qBp,)}�)k�@ �$ $j$. Putt� Z =0N� 6�Jt)_� �$. He8 $ S(�M�)nN+. 5y�<2�+f]n ==2�% �%G��e :�. }�X Remark.} "�  =B(\iH0 \dim \iH=���t B~ readve�>  ^*(D_{)j})� .� _0}EL�R ,D� 2� @�� dual,$�lrespect to $\=\Tr A^*Bh is� is known0be*Tswc41j1\1 coro�6&6,� �' mmu� v�<)5�A**� ��Ubf@t E xi�'>� ���TQ����s I\b�exp w_.< )&)\� � \iM�E? )~I�:@ iM_1"� *i bt�h _t� , $�� RQ .C )+)*1E�U#t,]T� �Nh E:6\)2�� $ �rv��"�6���E-�k=Y$�� cy ( � �� 1} (iv)).�N B� k $1\subseteq�_��h�9 ! cY�2� / ��,0}5�re��*�aY+$a��1Aby1h��s�1>p� ��\su.�}]=/_0(A�(E����()\,\cdot\, �sI6FmbM��$ � DE���(E# M�RwA� % �J�$� F\j�} )� � �c:.�1|�y=��� N9�)i  :� �R� a) EU�JdA�-��� \s�{Stronge�d��vit��entropy&�4H=\iH_A\otimes B C ��ɼ {ABCI�a :� $�QՒ� q�_B,pI}? � _{Z�k2_ �$ies satisf !�� sJ�}Ѣ>�eq:ssa}��)+S�_B)\le�.�)\,J� was obta� Lieb� Ruskai{LR}. A�� ciseQof us��Jensen"T in�l!��� `�o�b}  N-P}0,a didactical�jn�Vo�o(same ideas.R we wanQ stigaP$!se��� most� we � bel� �llbinvolved=�,"inite)�� of[ !Jstudied�sevpapersQentlyf�!q�ed�6 ] dime�@al Hilbert spaces-(THJPW, MP}. Our aim now!:to5 ow in O.N F"N�D&� �b6�#feq:lim6�}� y�I�B)J2�C, q� -E�Z�ise nsequ��,of monotonicAl� rel7i�y. Clear!�A>U "#ma)b2�M�n � �)K! mean�8at�G_A) � �W_B�� ���[Œ���V��3 )N, $urAJ ultsFfa��"apply:S,�� gbeb ��)$ such.z.!-k# �Z �M�Y �� ".�Q >B�.F q!0re!�a decomD�� =� oplus_�H_{nB}^L1�$R$ �f�ssa f} �� �=�_n � B(p_n)D^Lŗ D^R_n\, J��$ -inM*>:�L�-M-^R)q? CC.r �'��s�g$p_� %�E�,A}orthogo�s&-A� iH_B 1Fr�Rb &�2Equ@h�u}*� �* I��g�uu, \mathbb{C}1 �$(�),\iS)%%~\iS:=\�E����M�BC}\}$,A��latterA��#��A�"� T�T]_�AB&�>� B]_tM�1_Cf���$t"@B =�� =C@-wbUU_B)')3&���}(b  I_C)=�m.& B}(b5�I_C \m�\%�� y\ }tlf\] xin}&�!�"��� A cocycl.��(J.x},D "& )xB)!KqH}u%� �-cua �MU�� @m�:�B�7S$. S!��:�Aw� ", `( �J,)<l� c�� domin�+iS$, -$ )8]�invariN �(p2�x� BC}awe haveR� 2}%�!�R�!�Di/ =(D_��1_C)(1s D_R2M+F�%�,\.\in'1�� >' "�+.ZY iN_B%�Z "�{B}}_t$,�!Q(��B}|_{M}:� B})<� ftyEmil�(in Se�"@ sec:2�},� � B�H_6 �3��5j2�2Q)C ?Q�2�{\iѠ}�iN'_B= ��B1_ Q}6�R�a}"� ��&�B�, structureV1' �(matrixu���$ �(s)��؁zf� 6R itub'discuss� � "� ,Y-�Hdir�sum:�may��� � �$�D�+dm��"}�� ness6� .  wouldew��whi�-o weake�� |o�.'�q-is p!\�R�re 's? �@C>�A2� C}q���imply iub&� �ho�&��i�+o�_{AUYC< ��purific)�r.produ�&!u is a�"ew��A/r} (�%ou� Am s�.n$). *�' kind��s w�D2oInMN}. �/� )o � })#-4continuous ver�P' ted �)ermEMM�(integrals (I* zPdir}9 refer� �*% :<�fie!�of>�a絏 or cSchw}!� (X,\mu)�a� sA��. A�g"�$x�Y X�'s(e� ces �  (x����� ^L(x)T n� -N�^R, �\"V �~E�� 6,me�able rA`11;� YD^�$ � X�Awell,9. Give�*probabi��$p(x)$ L X$^ E:Q: :=\d#3ED^)\ �\,d\mu(x"��@}�p� )�o��e6%=_A Q��B2C$,g&�x���!�<%�\, �\, &`b 0%�2 �f���q�6�E�Ƒ�B��I�/ )��muv$not atomic� nBg=� ..N(Appendix}  E4*{Dual mapping& "E��2e[.��..&s0+:/1 $M 9 :3&S�.�% a 2��2O0�2n ��1:=2\!& u-[5Q� . WA�& 5 bothZ�� ast:}.%�rJ}.�iw$�-ib}. F6a�4,��y� � A�p_i:= \��line{J�%M_i `}#�R rta��,�9)674�2�5h $\aa: p_2!�2 �6 p_11 �.� �n character�*�.pr�|tF�7h \langle A_1, J_1\aa(A_2)\r =")�(A_1)*2 A_2 ' >��u} �Z Prop. 8.3�gOP�� �� embedd��)Zinto *j6�alledSv�+ t AC}.�Hthebibliography}{99a^bib�,.�),c{L. AccardiE�< C. Cecchini}, C-66L/bwa�_�.Hof Takesaki, J. Fune�al. AhL 45}(1982), 245--273  �OBN�HO. Barndorff-Nielse[ �Ing/%��B�� in �is�I�0}, Wiley Ser 'P�y�tMathe_�St0(tics. John > \& S�9Ltd., C& (ester, 1978.� BN-G.�EJ�, R� ll�P$ Jupp�On"�9.�in�%rR.�. Soc.�. B $ Methodol.)�L65} (2003), 775--8162�EH�DJ. Blank, P. Exner�@M. Havli\v{c}ek},)�2!"$s� Q:8physics}, AmeriQ5InstitutP !F942�R�Ar�lI�0D. W. RobinsoU'O;6.�=L mechan%�1. C*-� W*--m��4ymmetry h1s,:� oG�}, 2nd eATx-LMoni�eT�`Springer Verlag, New York!87.HanPed9F!��A�$G.K. Pederi('n��U A�<.<50 L{\"o}wner'si em,E�..�258� 29--241 (e�2�JPW�P�ydeI�Jozsa,!� Petzw A. W� r}, St� of%�es��yR�  o*�<�/�, CV n. �!qM� 246}A�(4), 359--372hkoashi� M. K�$N. Imoto},M_�� do dis�6;+ally �h6�es, �Rev. A,m� � 2), 022312FL}E. H.&M.B. "},��of!O��N.>Q���)I�O�. ���14��7�4$1938--1941.MP23Mosony)4DA�tz}, 6�!%tu�c6� s,a tJ�685�1!�0.� N-Ch2�A. �B%�4 I. L. Chuang}!| it Q�> Comp7%o -  �t�1,ambridge Uni�0ty Press, 200:�6>�9A�pl�n�*�, ��(-ph/0408130�2�O6�Ohy &{�X � EI %-Its Usea���-��Heideg��93��g5!2��"�zD����multi�3��toR��?udia SciQ%Hungarm�18E�8q3��5.)�N�SY�&� ��aX>���Res a J6 ,A\mR�10 (6), 123--132]�bN�Quasi-i����E8um systems, Rep1).1!'~$pp.~57--65�3� 8N~5(�Hnels I Z�Quart.( �gOxforda�bf 39�!�907--1002 �94N�Geo�of�=� <or)��!�%��,aiC5)V3%�9�8780--79JM94aN�Discri��between �I2:�� observ� s, JV ..�120!.�82--922 MBR1� M. B�&IQ3Q,II(y: A review�Z"�s �jJJR43��02), 4358--4372.M*� B� Schumach&b �)},A��D Data��ces�#�Error C!�x , arXiv:�(-ph/9604022.���� J.T.�warŪ�W*" }, Gord�Breach�w^D Publishers, New � -London-P�D�!67. t� Strasser�H� aite!"� � A�A�� s3� al�+er�#t��asympto78 deciR F}, Wal6de Gruy� Be��8%�H6e document�9 ��\ class[a4pm$]{D4le�`usepackage[T2A]{fontenc} .,cp1251]{inpuF4russian]{babel6U{ icx} %R{4�} %\def�title��)  rm \  base(skip = 13ptB}% \new�*8and{\mmrus}{�� �(;^B��9,width=160mm hIF t=22 hoffset=- 8topmargin=-15mmi C71T�C0mm�D�%dY/\%yV'-^�:b�b:A.b4.- } \author� .~� .#. ,@z'^$ \\.K. V. �r�f/ 1, 614013,B)}�"ke%� aU)�U(��%{\LARGEV`������ �@\[5mm]�large�z��)[z')SF< \\ %5�: : �t��528Vs� .} \v� {7mm!K�HQ� abst�} ɚb^+�.PnD�~b"1�.k VqBs -��/ 7d �V+��b:xf:.  J.^ >1N^0 z"z-z&z �f  e 'FJ^J:8>-:nAn�n&b.�% 621.372�d2�d� �T�:�>:}> +f� R~52k~-b &�2: RJn:,n%: V4r�V3.Xf?�<Y^.R �>z�bGf�3�~ ,b� � Tikhonov}��\�"xbJEJI� V/ ZN�<z"z }�$\ < F !)V  F@z_ 1nA ( $R9Rz{n8PV% E�p(Q�@,Pikalov,Troitsky8 O  .b.%V�b;2 :P:b"JfUJ6 63F VJ�C(J5%� !22 :!(:�5 12(  'v. 2J V"V 2 " FV2-. FA:VP:% �+�>b(b �R�4J"-M>> q�� V>  L.b0V�.; VAV 2�ZW-7L: #:F%F:>%�h.*J�68.-F f F �2>:?b/J,J:N.V..fD �$ascQ.V 22 #F (F,b -^V7Iz (�% + v . G.Rn>% 1V .b(VJ�2�V6qz2K5: JD2��M�PMM97,JBO99,my3,aa2002� 2e ��b,�ZP 2^Jv:+!J&>>F   FV�;2!2 �MF( nM! &.V�." Z J^ �4b"F[VF(zh.V&FH�p�( b .  Fb..�/M:9b6 (z %:F�VF $f92>>z� } $gL�_G"�!�!} y1t_{0}^x = dx|.bel{funfD4AU w:  .> $x_n�>J6�#.6 J8vc& X�8\tilde{f}_n=f(x0d+Ng. �C!r)'7!pR -�J�./>MJ�!�h�Tal !�}"]Y x"�afu�2J�p.�: J>22 :L n"J�-�g!��Q9� - {U{*^ x�V�c! F� �ab^_ x = x_Ux M!4!+: 22 )T; �)>$~G. f�O .: JN$|\xi|\,gA.]bE ?y( |g_nHLY|�aii-%�A��b A��j| + 2A/u�eq_abs_J�!� �=�m50N�J� =-�J >-��B�RU��>N #>3� �@ )*k �'J9 )BV*J  N bsn$~nyX�F VV>F�'WP�'bFF XF.z +�J+J 2 V GelfandZ�!�$\dLf$VJ E� hRJ}F^[d B}0d � �(x� =�<�-}^{0+J#= f(0PK�8eq_�B ��� -�! .  R� =zFV[ FF�J6J:@�:. $U-r�nzZ ".? "flnNF* i!�-�;6'Ao�(x-dx'R%�( -.4 A)oubletB+Y, � �V�!��%N 9.:.^ (V�2# b�n" $x=x'$Qm.+P2!b�>�: {l,:P:>> /�:���� l>���� :::��Brace�@f�:9.g.: z .b% 'Fbb":HBhJpi:7_$geT $fJ"FFFw0\hat{g}(k)=ik f ,.) if_fF(^ $8bY .��V+Z���8�@�Q(e^{-ikx} dx.�J��V� � !� >�> &28NW2! D %2F >DB�>!>JS� :F �?fjx1}{2\pi}:MMik�Tft(\ ~5 � )e^{IGk.Gi�H ��J�5� - J(  z % 6���2AFSikZX*Y0GZcik�\ �:2�V &� !��V2�� ]m�VN2# ^ zDBj]:�zEz.�>+>., z%�6 � . J %   #2_V�)R >N%  F n"n����.�V>�.2: # >�>2�:B%��3.. z   ��J? Eb n(>V�K^ G^ �ADjL >��K >A`. V�.* 5&�,W_{a,b}\{f\} {^*�({{x-b}�I{a}�n) dx"� w_�{d?B�� .� b" b+ $�b#E2 .. G . R V+B�R< B >2 $# ^ ~0^/) �>.! $� $b~��.BR Z,�R4b� E'I�=A2n��b..V�V��� CV.�� 4 .2B|J$ 0F �ag�a*�Q !�)�^*��  d�->�2� @ s��(xU)x�M&�wF�>GV�B  �bh>�/ Ve6�>� :  $:pw!)H>VqJ b)Vz� � A .Vn[.���B�VSb�V/mm:J�A�=�1}{C}0+}M� I�da}{a^3ZPdbux"^^Z�dx \ch.��e,Q�iJ�5p $Dzk.b2Qsps�H�.^%� $Cz�'.8R V�+F�C = {1� �1�:�-�|\���| ch $}{|k|}dk = T TVM >ps >^2 dk �\.(CBY >L2�1�!���$�+5. . V :z5B� !8 (x)=�!B�>�"q }iffwavB:�R]I�� "1FRQ. b?B�:�f�e�=(1-x^2)�m /2)' � =-x Bgj V�&.1�)� b�6�b�B' �J�J ,BLb�3 �b\)LV.EB{bR 62n�2) <^+: J"n-, I�b8b >VT>5><. 2%2 & i(�{) }.! 5�7: \: kქn,5b�C!�OV?Hs1B��f�6]� Cg )>Yz!:D.f.1� 5.� conv!B� �u>� z0z D:�mi _reg�:%R2n2 :/  :V6:%;  ^ ( F&VVF>ʠz[z-*z&V1:�.�zP:�( (bGb� n�VD���"�� P.@.� J�bDN�V-V.�z"J�.> "�?6�z^ ?b%b 8'  R VB�[~Z$RO VU J>b8* � 56� m� R VJV�:An%V2& :S.V�." 2X>V>&. b;b >b�8 ':J~$ B>9> &f�9z9>> bE�VV 7 b"B�/>*> PyJ J0>�EB� 8 iR V%JJ:Q":.z +b%VV K V"mV 9>%*�$ E^ >�-��D Hamm�f)9 &:F �"" � abUf�n=3~JGJ �A�  J� :� {� F. ') u"W�� � .�� B� o $uz�+ �.�:n+2\j z1" F>FU L b F  8  .JJ.2 9� F�GJ�r�JUJ:�z��A":X.z +��z� 0Jz(2�k>C2+����Z� �2���w>A2WV #>%!F z 1z%n   O JJ�]�E)J6 O>9��bY ]B� $kL��MG�.* �� ^>JF;Y %~V&�2A2 bu T� > n>5F >G>F2F�4V%Vn.FwbD � FV :<^"7.'b=n%z5VJz #.�F >">.2 �.fN eq&�- 9.L 22 b  *0 %. � .  �b.VJ=[J:��"n�.MJ . JJ ,��F �E:4z1�.� T?]'SzMn� �B m( jV%V G .F�V(>�\>N.� N 6  (:J}2-�.4J1.22V,:z :O2RN�: >�>:/ ��z.� G�V1J#�B!,ڍ6� n�'.��&nrJ:J!.� . b%J"$v J� 1�#�G�OJ" N�b+�"B�jS M �-J~ ":D  :JFF"D. ~P�{�%y$a_{max H.M J ^212 apin��F%O: V2�2:D�F!FJ)F%  +]; F*Fn�%AV��C) UV,#>t3.!. VV%�.=R V<+ V V $�E >%% Fn"n.J� V9V 2:�+% :H>.>, V>�.Fzl � $x�"w� ]:�~@P%*��nyk(figure} \hiingR cludWuphics[�m 0.48�m]<N2.eps���2G�2N3a�e4 2cap]QV)*-M F >B {\itJra)D>.F`.V.JHu >v)}. 'fig_sigKRMBKVq.�b��;�Je:*. 2r2 .j 2(��V�.F27.: 2(2 :) b"� ' J-J ,.J%1].' J-nV/ K.(.v >.> >*'  V-  n"nb>>5nT1>4V]J&22 �I*V�>W   hvV+b)#va1NV�%> &�b #0 % 1 F& 0.00.^ >>a+V�RB ? :#:Z}n3 0 7:. "{1-2B�$JJ�>>�   a& � �. % jWV"�.]6�)JF>>-Jg  -�XV{0F B:V.%n"JJ �n� .q: . r]V Nb22 9FJ%> $f_�:IF�f_nEL$x_0}^{x_n}o5n(�^(�"�=funsigB�h_3J~(� 8 ( $\mu*100\%"1: b(b"V.�D. V7." �( % ?~u�"�1 Q.1b� / 30\%.  V*�>�B��$1�lV� b�* B�L| �8 Y�j >�>j;b�V���%R�{:4n B�.<�2"^82%2`.�.^ J R,�!�$g�GRc%^"n 1v z+z�$g(�dj$‚]ӊ�F_n . �  6�0}F���=\sqrt{B� n(g_�c) )^2}�m_n { }^2}},&� l�n� 7J� �!� ^ z"V:Ug,M�ZO^ 4J>  �� +�b���5���210�d6 2 ��)ze %FJ7JF8:}�~1FN~2F(�u�J�22 xF z 1:�&>hF�N� b2aF9�>�! };: HF2F ��F�Z�V� x^F]R )}. :�m�*m�"�4tk�} .��&tabs�@}{|l|c|c|} \hline>9 & \,�(column{2}{c���b�"��}\vp\\ \c {2-3} &J9 1R~2 \\ V�bb. 6& 0.4231(�.,. nEJ3� 0.25JV��#)+a� P W168 W' 2�a�+^VT7NT Zjc% � ^8272�2��> A2�3 U3!�ZW A��=� 9)tk152f"}8=(20*x+c)^{-1}$ �1AL-NA�i]�mq{��J �:z(2  :O zB���i �ao *JC� �.J8n�O emphn�I>�Y.!: z ..� b@.�( b.2b&J~L ]3 >3�>LnO[Z� nE~q��$� :8D.�. >{>., z%>�> PV n5 "\>, .�ez#Nb(�n>u>�0.018V 9-k 0.14.� f+.; �Q�Vq a .8��1}6.' VC  >�J222 C   �� ��ma=jr <1� [^z 7���� OV}Vz5n�JZJ K2g 2J(   ,  jb(�j:-�R"JV2>���bY2Cx 0; *>" V��}>� ziNq�V� *VV 2 � & B�+E X J��� b�2f V�20 i^�+��:^6�g:)n%*^ b@R� 4b=VZn?R�8h: Ux=b:#.Vw "V�m FFTV=� � �>�>�hVLe$k>k_�� .J:n"1">S:C>>/b~��:C ItbRt; �.�� +:zcR�>�W Q ���*9 6: b"��`E :h:z(V�J5J,� J�: �beJA:�n%����znVV�. +-�.'�e>�.@ Ja  $F F:z%nVrK=��:�<*VN)z (2%2 9+>J: �>.> +.b"�M0.4. >@>,b�tF: JJ9N? 32)  J3 , 2HV!( 2.��uy! Va�6! r.�: J\:*n%v� zC "�?` nK%>5eIv <^&VVDzb�A G  ^B�J�%>N Fen.`^ K^ 2�)FNz;.1J,6�#,Levin^�(.KbvVZ} >��J 8�v �J�2x & B[ .a. ����V���: n+v 'zLJZEV� hF  JZ�*;: n+V%J � Z� #\�$ik�g{k}^2��.F z.1b+>>Vq.["J< )2Z�G 4 V%P $FVN�V*V�hb5Nb6: �Hf2bqJV,> 37 rb, 10.z.9 V��52J� t.�. �� >A IRz 4jlJ@   B:rzn9 H "  .>r).$ b" b+f(b3r�0.��0614�R��� nH %�"B�3 M V� FVV>V�Q%V1b^0!v + R, �%ax}=0.1� �IB~L$Q6z�.( � .��f�/, N�*�.R :RVB /J�0$$\nu=1/(2 ]Kin})$��0 W �jJjnu=351+�R�Z�07���� }�F�6�J$JV��V�FrFVc]�2�fZ�6FX}uVl* >%> &�� � ���   R b,b:H>(>./J. �6 .D 2/  jJ5 m22 O\ $a_{min}=(10*x+c)^{-1}$� ,Z? F $c$b:/���$\sigma �2[2 \  $c=42~�b?�=0.12$]^V5>,�>�ᅡ�<.4j �+]VF-^xV/ (F0~2)9F:VX.% " .: R�7 .8>��8.\ref{fig_sigf}_A)VU �Zb82. -K�diff}.u: V%V:;a%F:n"b:L.z-.2� VS  .EJ > *Fb"��$]�b.:Y��S)�+.h>0� NT.n^�.~u�e,:1��: J ^�(V%R[b . . \begin�z�@ure} \centering \includegraphics[width=0.48\textwidth]{figN6.eps}�2G7.�2N3�2G2caption{ �jn.b�Wjz  ->f;> ) J !�b�>D ^^b"�qB� {\itJ�)}��b<�N�()}.} \labela<� \endeK \sec�y}�xFQ cbMJ-F�NDR(�^�z;^r�R 2�Z.9bIVV Q>~ 6 >, b! / -. . 2& 8: n+.N�V:VJ J%>> 9:% .#VJ� b.~�~�b.�.^ �� QJ F>�>7�b,N. z��.0V^0 \cite{Levin}� equa�w�} g(r)=-\frac{1}{\pi}\int_{r}^{\infty} Ddp}{\sqrt{p^2-r^2}0\partial f(p)E p},�eq_� ��� $=$F�" � Fn.�%i�>>>J% zJ) V2n/V2 N8 Fn:.J+Bx 3>*9�J >- #J�J)J? �"m+PikalovR-x,y./2\pi^2m20a2$pi} d\phi iG-mDNMp-x\sin.+y\cos } in.T,:Y Z eq_irtzX A�]�]�]A��0frick_etal_98fi9� IZ� &>J> 1 n� &F2�0bJV$�*b�b�:bZb6� >Z_>Y>) "bz*. 2>J>#.F A�J'b5 !V�  x  .J ".! "J+n %V"M� #�$W_{a,b}frV0 $\tilde f(x)f r cf2 �2" (  iwt}��7 ZV ^ $g(x)=f'�1�B� >  22 F�J*Z�>� Q $\chi�H \vspace{5mm} {\bfJ^ 7:.Ntn= :T nJ22�, 03-02-04031�YU 16384. �.2R.^ JD� .0 PE-009-0"Q >6>.>>b:zZ >�.SJ)A:� thebiblio�y}{99}�0ibitem{Tikhon� �JK�A.6�~0�i/<^ >%e�.::/, 1986� �"� j���Z�d)NE&!. � ^:>7r4>-RV>%!*95.* Troitsky})+TbQ%,~.>vJ!� B�.*�89.�matias ��Holschneider M.} Wavelets: Tool of analysis. Oxford: @ University Pressk63 MM97 i.�: %46`ZKz�?:m 2$ // \mmrus�.5%d / Q� y2D�7. 86-92.nJBO�;e^Patu $eyev I., F� P.} Lymphocyte nucleus reconstruction via wa%� tom���Journa%��Biomedical Optics. 1999. N~7. 376-380.�my3z��%�Z�)& .-).. V5." >( // )�=�.7 8��9)�1.aa2002-$Stepanov R=�$, Shukurov��$Sokoloff Dy>-=�Pof the Galactic magne �field. I.The method // Astronomy and astrophysi!��4. 391. 361-368.�Gelfand �)F%�]� &r�V� C M: b�aM52� Bracewell �T R.} Fourier Transform%;$Its Applic�H. McGrow-Hill, Inc.h62�Hamming f:� j" ).E�.Q�. >9�6�u�K D G.G.}(Ed.)~Analyte�MELs for� al T�3, SPIE^6�.����8, Baliunas S.,A�yagin Day(, Soon W.} �H �>aTstellar chromospheric av�E vari%�s��epE�al ���87. 483. 426-434..�8-�� Grossmanne�4Tchamichian Phy�6�8ignals with gap� ��Mathe�R�P��u8a��y,8. 4091-4107��>^ �re.�the� {\arabic{j}.# } %� MACROS USED IN THE TEXT BY AUTHORS %* %% ��3 \def\H{{\a�H}}�u% 3cR 4R�43A 3A�3B 3B�30ri{{\mathrm iz6 �pa{"z23cD �D~13�f �cS fS�fT 3T�3b!�bf���bZ{DZ�e3cC � P}} % !!!A�Vo �x{{aktaf�3m8� ��ta�(*{�%"��&�@Large !0 I.q2� three-�Dcle Calogero model��� ed by ��r�N?��ble�&���"� �� �L. Feh\'er${}^{a,}$\footnote{Postal add��: MTA KFKI RMKI, 1525 Budapest 114, P.O.B. 49, Hungary. jf0}, I. Tsutsui� b}$\ ,T. F\"ul\"op \\�ig�5 {\em  a$De!9��!Theor' alW\\ ��g*�$of Szeged,�!�lk$b$InstitutP�gNN} ar StudiesR�< �i��on�}@is extremely popVbecaus[��A:ct-�il�^am!n�� many lesE��� s inM۩)� vs. (SeM�i�0 nce,9book}q referencea�erein.))X]�!DA4YO8ally given by #�7} H= -�; \hba�(@{2m} \sum_{i=1}^N Dpa^2}{\pa x_i^2} +&2&3j3 {i-1� igl\{ ?�1}{4} m \omega^2 (x_i - x_j)^2 + g({-2} A� r\}.<) 1.1}d �A�6� !� r%� massi�$N=2$� rei�to. stud� the 6� 2q operaJNK_y ZN-d!@d y%<�=y%�g� y%=2BsE�widA�kn�ieLanda� !��umA,$$H_y$ can��eɵ2� if $gR��sel�� e `% ̀� fun�� s' � mposedA@ cri5on iassoci��a�O curr�sh�vanish� loc� s wa� �btwo�collid�"iEintui� ly r%���!`!�:{ "�A;,repulsive. .��peaking,!��~!o�qb is��to��os a domain�wh�i�.�� *v . Concer�,6�.:E�,�ism(s�e e.g.�]$MT,FTC} orN�ism/$DS,Richt})9��of��.� �N es i�punique � g\geqq�3 .�aBw t%�ex a*z E8��t� ��iesA� r& $$2\times2$|t�  i‰M>. I correspon=2�"� �;/�DžSN�doe in� l6� coinc��ce �coordin5 � s. Heuris%.�%d 0c!^a�BrI s��pas�N each o!�Ya tunn 4g effect despi�ca�nfinitadhbu;}Rbar�. SincV i� enomenon��sa Qte�� y�%|9 , one may� ect i occ- lso!nOI 1::� . ��pur��n2�  papera9toelor���mT 2B :i*� ��p* ��R� < g V�\qquad $ (g\neq 0)&3> focu�w� si (st non-triv�1�ZEure]).�shall  6e"�!.defin)-2 . T)K��!km pK, rec[�%.�@)�) �?$be written, L$H= H_0 + H_{rel}$, �&$H_0$�Xng��6 # F JY{r} + r^� H_{\O� "�81.4>g@aS] l>mo!� r.�$ v$Q �UR�rp r^p ��o � V� f�3N-2}{r} d}{d r} + D1� N.� r^2Yq5> anJ�R4 )\F�� Delta #" d iVq  [r/*V ]^{2&x41.6>�X $r$a�A*1w��a8 ${\bR}^{N�E( spanned by 21�(Jacobi)=5Α�s% $2�}ast� rd Laplac�on $Sy2}ɯ��,�o's� uAg am�E� t�$0ng an orthogoy basi� tHilbert��L^2(\bR^�)$�Sfacto�pU  $R_{E,�}(r) \e!�()�Q-%b $  $ de�i% angl� ���] e $ �\subset ��N� g2� =32, �D a�B3#} 2� = E6 \�hbox{�} E ��Ar +w�G*� 7>�T�is �e�S� i�Ns #"%�a&c $H-%$�_�$. Ia�#-&  �?�sA.9}))��� q���*�&"� L8m} [3-(N-2)(N-4)]$ �J6 �r��! not B :� $,Meetz}. (2 N=3$�! conv=ons �$2.4}) adop| r H means 6�)!ttra�T"*2��gofB�have be���#�l��� b�indPLA}�ch�bs��=k of.�provi=by��input. W "�o S is "D , s� we aimAatackl�� �of!H�: f�E.nGll. Oi�� handy2H,;r!jrF�&�  to6�C#*�$n ) all}*8 &I+*� (�"$�n)� Z�2� !�.� obta��0&��5� *B� f\ 2|*!��i � .� j in i��)Qu> �%)U�)L� � ��. ��lat,K s a m0 %�6Am�+� ��q0! (icult techn�ly. Wey � kBA'e� � ��&=��6�i �V�an �pryz_ +ͅcircle�}�Axa�1a� p6 ��� rrQut�* foes.�fixA�g.;=��T.� in S|2iY2�exten5�S1�$�"� �S3 (�� some�sa�err�o�) endix A).�I' E��2u most��l,6�F�!�� eq.~I�3.14}),� $U_{\xc;� d�m�%xco� d�bE' B8� f six.�!7les, � q \cS$�V3.5a?E*��rs�RFi�D 1)D t�p9&j(!E1�"�!�'� �><�B Cu�� �3&� ,!tA��� i REissen^ ly�N-�=U$ indeAm! ${\x� su"�5�5}) so-ari�V|1F2s, �H$U� b8A6ha��co(A�bef���A!j�T�Nm�"."@` ��}ݛ!Gn� ��R6���. qg4!O' hear1" �E,�!��am�edm�D1�$c-�-- .��(d��ir�W-*�6�%�\wo�l�8�s, acc�Ug��whe�8 J��dia� or��.�A_er[%�"m ove���or�.���ord�K�)o ]c�n ]�ly, lik�U's origiH .� . IfI�Asn�~r�!Tmeed�ce �roBa&6��( �.� "pA*w��pAX��᷉���tur�u  5k:���� dl*&��72 ���dE`B � �"E �A &� (= (3\mu)^2$� A� $\mu4 �reJ3r�eEa!�r�!of eqs�^5.2})-�45, � se 6"s (�!8�S.s)�=�%�%�66� i�:uc!#�.a�E�eu� are summagin�oB. No}D!W#6 ts6[ 22f%n�^��%��VN=�� ype 1 A 2,��,ively. Beca3�� �. $!N������!to reg,3 Y aV!Q�s a� dnguish�%�>�^���`& wise.�up�d�5�U�u �D.�# � U/z��u��6�-6� deh%o�$a� *�dir s�3 +>=��J6���"L$ 6/ (bosx')�t�!sp$ odd (fb02% *Q2J�$2$2�6��!O $ (tA�&� � para\!�cs). ]� clus� �!y��Per�*�&�sa !Rlet���/u%�obser�"s �� GP},�|truncae�e6���a�-L��54 1�a��# a&�4kt�*$ our6M.p�Qnew)�a U$ �� A_�)� �9L�6��*ah rigu��issue,ed s cl^*�$)Poly1}��ng�@  (^ $� �%n� �)aKfe��� . Se�AY�%ewp2b"�2���.��AB� �$ed.��g� $?("� 5�evo�̍.>(n�iraŌ)�� Jy mY . C) a cha!<er�+BshapeA�!;&3 e_!�the��Ƀa� s ilaD"r(� s 2��3͞ +s �� o se��1fV$) �>Jc,�ad� -=always F$ un� �v serof�ve.i�&cer!=N8 ��Q&݂Ns� s a kX3kneg��, too� � 5.4>r�4ki�� c r� �tst������&� �兕aN�%� similarlyA��onH�es[ pu !�.�1 J�ff� � ��ly���("r <0�' 1�#!2�i�6� ake��-@#o)��" demo�i"*.6A�1 �lso2�+ *�* fami�,aEr�s6����2*&� <1$}�i/���,�S&}*.6A �]kQ& �.�!�f!�so�b�"�1I16�� .N4 $F_-�$�!��� �.^4 4!�e n+r 6s)�"0$�*� � "�+:5N�ɁA u�$a Q� �=� Ah(��jpoi) q .w���('z"per.  *�  e  �.E� eF%�!�q.�%-ARure��@s z�+)|&�MQ9�"�� mse ba`display�o��47. As already �2iox=oY�� �*,e1a�rg�:! �si�+��6sense(n�/K�W/isJ���-s#;�d j��reV9,�-o "�6U JY, � �dE2�� mw1 jf �g�,0$�,&� furD!�!o,AW� � pena��.l��e@{ion{S�4��A. s}n�,Altho,0wAl 6i�0in�ail ��%�only,�7w� e%ai���slgy����(&f3&� %OA$ alM# � Re���s��first�>pA\�'>)�`.h"w!$&QsAax$yB)2�5!^��  s� \����by:fH}_�$B� ��at 6J��b�a��) into� .����� �V${:n,FY �= \oplus�  V ,"2.1>��p�!!�.a;�e�7&�A0~!)= �\bR_+,[N(-d� ot(�$%&% m��A,-�fV\"!>\,%%6�� �9(" 2F�,��nex6��uct a6�J, $ 5�{*Y,�&�M�)dB�$  � Z}*��appear\(j 1.7� F1Pwe a 6<U:rr[ve2$u� f��#�Z� .�K/6�? .)el�!6� NI1��={id}_{u&n$2F�'i��enc�Qt�5�6�-HA*)- �V�#of�V3. Let� now@i ol5ao clos�A����c �wv tF�!=2m = 1�B' in13y�B&c%s $(r�V��0d�#fKa��U�a�2$ ��sK5 a wa�at�@�na\A && x_1q12 = r \�Z2} u8 r8 *LA 0203�:1( 2+# 2}{3}\pi)FD3D1�D4D�#"`'ǁ#;% $�:( unts� ulo -pi$# $r\}-0 Np ac^&.r&1$/3B$)M:)ɘ*|( j( { d%^�21�1\(96\&�9&%2F�'�N� :can�7�a�#M$ V���V�&� }= -�9�L) )�N)19) �:)r} + 3}{8}&�3r*�2a{N=�B&*G���$,e� 1.3}) a�"6F$g�sF�r2�3<.v,x3}�8>�e�i9�2� i�t�1�/ �aJ| g = "�<�;Z]')��<-<u&��'= -s\ld2.9>�gabove�-%L��B!?�� EM� I�$� a t "I �\C2Q-�x� V-J�&�A�& �)�6�<i�or[2s J�sq� , , �"� � l�$� cre �a� m�J�9 6`` di Lnes%7 Wum�"# "� -Amsr�$N��� mpli`by5?2�%-�>�2�*� �) �%Q�6�Y!�var �Z� 2kw 6� $ whene�9Q"�s�ompA$ �*��IM]in� "� R�bquaT� d'"�%�_| sN�nd.��3�tr%,�=.�k�I!�ir2��"l���!P ��J� $M^U$}:ZA;We�� �^�!fO$ tby" �`)j�+� ). A��mal leve�&D�1[ $M$1�� �, i.e.m geome,RB�re�' hex!�w�6to mai��:$6urnt�1K"� qR�8���7>`*��@� left'7a nt"ee � t�Oe5a�0ve�!�%'� j�AS��1w�*su�� s. F��$3$ �4be&&=.0 (�:�($2:?&g-"h>site�� E��:}�x "m!�ip�"B)%Mo)d!�! %\�Ge righ{3!�A � . T&)If�ŷ�+ leadsOusu�CS��C:_B 1 ����#4A"�s%x.�re�Be total9� z>Ic"�E �� C��+ word�<�?!��U�́.A��`�-d'`�rA red� #$�ensure��Yj]�A�#i�%� �r �Squantum�Ti`r���&![p-p9�, x$T�? f"� T��� �/F/ e �H�C e}[ht] &�p %%�*s $ \resize�0.6zOgO }{!}h2�p{ca'J.+s1�NAp� ��co*� �am2S^1�"�):�?*!,�:�)%)%x `�# ors' betw�/�<ecu�"[%-(a�)��� axyref�;Mvvr�.�(e�). "(6 fig:-�?K)e�ImedHJ R�@r�A-�@.A , l� Mj"H*ef e 9 m"Ih�� s $P�AB $R_3m<��e� �R� P_3:�  psto phi"W3R!6"� g{3} 0�3 (O mod}\,\, Pg & 3.BTTh�\ �oE,ro`%� $I rN�\cR_{2�}= R_3�rc F��"� Y"& 3F��Y5��cycli"%� $C_6*O$6� e��9� ele ��ibyF� P_n-'J�)^n�\!� V({-n�o: RBQ �RR_ RfQ.� for>5 n=1,2"3F9L 9 E�i$5V�ݹ��''��ch �&A� >"�t by�%a�a"�)��Qq�o&`GmU�r s $x�Fee x_2$!k�z2."-2�R�.���6��w�l� `mirror�� in w�"j0!@>'�$a)��seOA6`2<�HI��S.,�cC$,e!&1s*} B?\cC :=b!2& 3FD�%�>� map�:it�i (s� S$, 6o� :r!��J�S= \{�@kqX\,\vert\, k=0,1,2,3,4,5*�E20���}�J�w�si$�z�( �YH minu�AS$x$g�LI�d � &�C $�g \TN"(")(��):=0( g�� .�B>;Ob_K� r�ya%0�A�Por�A$�6t:�$� S^1)�RI)C�{y �it!�F� n� &�O� a�M$!�I�m'y_Bi.#*90procedure (deN3gOE�IKaa� DS'Co�ifS�d �� �a"�9k� �>�n��n��onm$� $\cD� $M_ start�� i�!�'`mini�)7'={J D}_0V�>/�8C^\r$�xU��A�6�V �aDJupport� q!�EdZQ�({\cD_0}^+$ $MAY,� fact,S:max�%_1�JUV!(�a��!�m "+".��#[e%: [5�%�M�l2 m�� J Q toge�z ir � !�Dv� �1b[!�4 inu�0n�>�� t�*l (La�$)� 'I�F��HA�) both �ɰM�<elo�1:�i�"!m8a ho�49� ^+= -�����r�3%!�}�ic�>� J}_ &�6�&s8rib$%�1}r&a�2n<.�9 suit !JK"E�A�2A6s� �> � �Z &�5. *�/2��cienc/Mdic�c�uzG ,Weidmanns9�0�>,re $(12,12)$��FP�K��M$ �\ &# \ le .6�.w )��UDgr%)d�#o6NOn�n che�9aE(�g)!��9bD$a\ � E%�� 6�s�*�"4.1EP��(Ml!26ef:xE�fXaq�"D "qt)*R@um ' it�)a�)��,�I$Xm 8.18�I5��?�$.�:�9.� �+Xp��Ştrum}�tt0)F/EJF�����&��e6�N*)erme��+ `"�O�s'e��eLU�Kcho�Z:m ar1)�,=0.' d�a�@varphi^0� �+$i� $�<< a� some)=}4})@q���ti�6�A�� (exA$�m), no��J �WronskD�[F� W[ �_1^0, 2^0]:= 1^0�d 2^0}{�v}- 1.1 = 1*� B��Phav�� �^�0�5c - >)$ �^{\x}!�-͡ u:\i�S$��{��F+ L_k^{R_i S� A-1)^k�kr((�d�z \for� kA,�E*,3 W �=+BSS?��n*6�k�Lqu ,Wh+ mark��u ���\x}( \cC� ��B> Moreover,� !� L= >�a1�o�Yb�^0_k(-%VNx0� *i10>R tb=[*lsoAo*"�}.�P��\x(&�.��i%�.P!H+i2 �F�HQ@Qw +.r11>� Ud%�%rNjF� F�, Œ � �3�M�.�+ments�?e͒FTC,KA�� �^�ZaW`���6' %���I�d�= e�U i D_1$:FB�?((��[�a�#{c�% W[�,U�1e�]_)�}�_�av(-�^ \\�]�uad B'�2R�-B�2(-)�2��EouH&6As=0,��/X4M\.42 _&�G,-]��1�-��+��)�-F�:\Mv�+)$��-�1p1�5 �R1B�O Here, $W[A�Y���M� \pm}�0lim_{\epsilon�Z\pm 0} Z>(A%+1aA.�?���HorX2q ." ��� }�on�<�W>� � b}L� 'so-�ed .J�/' �8Mx"� 1ZB�  6�{"# s '$?�� of approp�le lav/b�SD9F��St�%sel�to 6�5 ����"�1 �0�ethey d�Ht mixI ��RWF9�"�I �$M^?� r ��4ochubei,Gorba})YApp�E%�s��O6�Q�sJ�(�E -&x^) .oZ ri )+2).�=0:~ A��[S.�B�*wh6�D1U:b�arbitr� un�DVcU� )�F�3)�%��me�a�H J�A$$C main�=�}g�: A�� � �b$R�Y �!��MG"N�rqdto�Ndm*�"  . IfV"� �KN � 2�D$3C B��`�C�Z%�xURdi�J�)U� s�4*ed.~"�+� � �FJ/ fulBLe9.}�(deedM�9�(�4� ^�nsR&ce)�Xtb  -� si� B_2/ si�  q�J5'N6�)3�8:$�a�eas�9verifi>DUk"%H*#.�,�  �a��!%Mz�P_i_ �5�B_28 f�V>'N?�B9 � impl�.��w9��4mK��}|,b(�3.15}) be �8NW�=ormFU= e^{�� \alpha I} beta5 } = 2*! eft("y1S {c� ��ata &`��Shk :&4"�c � ) :=, boAhcB^cBSAJM.� 8>��6" �]s��D_U"�T� ae�'9-A� >~%J5��2��$U_^nhK"8})� $ #\inxY�e)"Ob+�l.i V+)! � �'ee;Pni! �)�Dexh�~ L�hn7A. I��4 <w3llO7B�n�dstigat�* 5 i�ed��"Nb�4�fv9 �i�on~d8F�+*u2�h�3f�8�`hat'OR E>m�Zd �8A29&N ��b�Bt;G!*Q@7[&p -��3%1�L�7�@(`Dirichlet'�9if@g_{\x}.�;vE9 A8�  `Neu� Bd^ A�,�g)�;`free +m+�8I���[tte�O olog�E�`�.�$Fm ��6 ���b%/�!zor suff� tly �+"WO�!�%R!��a�*<� %,#rm�*���%_pm 0) 33de�Z {k,2 K �$&lk} {� :DBPIn5�um�ces6b:� e�B�nd U) �ZM~sio)= �k-�2�= the M%> �' ?6>N9A8N�� � g�~h�')� '$=�*� ]~)�r{E{/� ,�,2�h~�.���1��dA.opi ve3A�alism�'"�.�;�-|�for�J9 O�&�.��, 9})'p!@FG (�G�,X *".k�� a3.Zm�6%"�$ >y�O (`o1ng'z 2P (`�`2$�  c� dea� I�Eth l�=Ii��( al) auto�.uy �E8A 7&�N��y ��o ied 2U }re�>en�(��$"�"� 5,6�O �~=� w�be " @A;�!04�| 2�{Pr"�?s} "_$R lex�F.OdR� �"�&� j8(&& v_{1,\mu� hi) ��$� n�q^\nu F�  nu -;�_+nu+g�5;V�q� "�9� ��n.� �>.�{1-\nu} 6�B� �- �3�� �"� 4&�*1?j F(a,b,c;zN_s%t��$dard hyper&121� . LoE�rh$v_{i%�$E�0�G*�R6xjce�O�(Dt �%s)\not0bZ$�$�@�� 1y �t�2$ ���arom�"|joc3} I��e�h.Y" �%m!�Ӊ�}!$9 \mu�r�Cal3} i�J in 6z�"( w�')97!p* # � Un� u�g'g7ꁻ�/�Ov�- ose e���� %��tu  ='/h�6$Eno����"����%H�! W�6J"&BT . Es��i�iz:�.^A�o� ec� nI��y.C�.��! sm�q :B&� 98ɳ"BMf& � �.h ,f � � "$A� �$n�� �r)7! ly i9T2�mu$\L%�]��m l. �h$� / k %dsam>�"��w ���b(!� �!"zLH)�*S��;~{i��c\mu� $.�Slowa�!ne�4hehF[ I~�� } a_i(fU*pÖto��(pi}{6} -0} ����b�D \pa_b>M"�4FW/E"�t��?��/%% SEE ��0REMARKS ABOUThADJUSTABLE DISTANCES IN IT!A setlength,�@raycolsep}{.4ex} \�Et !Q=�� bolsA%�{rclcrcl�a_1%W & = & {\kIstyle;g>\GammaF� &��)X2��1��:5�)}, } &yh�2 4ex�*E3�6a��6um�)A�ula�& a_2�Z6�Q@ ��ы�a:�b�9+2Z� 6�\\�b2�R�6\,5kn� �%k Z��{2>�\nu6��0\rule{0ex}{6.%�Gov&/P15.��$ow-|b�|�!*6� -�z�9bd � }. %"�i!{�4�1e #)w��f>�&�by�o !�"�Mce ;�8b*�!� &&*! H"= ( 3 (|@-1)����� _0#�  [\Theta���4 �"1 &��.s2s� 3^{2j �^�4EU�2� �*i "��Dmay�>y�,$"Rt��<�$A0 "FA  $, $ ��+���.4K�H��#.,�O7�H4S. (� �eO\m3"=;aXphF; ELasymptov�beH&ou"aKrQ"��'0$�(ters.) {}F� zI=�_�� �:"�,Ug%^�.V $�U%3.H 2� uE�*�~N\�b��:�.*F,2 c0}) hol�` Aus�$+e:�"cl�� yg 1�� ��1� U -FX.�"K;fi�f��a�i%SN*�)�>KQ.�B*U &@  �&\ on � ��&I3p�+ �?P% E�* �$A%�!<*A��s'2 . �I%:T $Dm^1_{\pma�}�0�6��i&�<+:�H ) = �\{1��{l��5>�-�.v_���  & \m<j0�P \leq�܉h$a��H���Nn�I53}�L - R}J*.�6���� <28N�0�m7^2�$ �*� B�RF%1�-��"@ F�"= ��9�-NoJf+} }J)��ڏB�6�w:TyR�J��4e1 1'�a�Jl�/b�=) � enjo�-"�S$erty 7Q<qu�^ L':�@cZ&NE� fOv�d^G?egr`��  =�u�{ �a�kfK.&�=Aq� - (k-1).�3CN�( k=2,\ldof*6}VB�A�:�F� *�4�6982)$�arb>oM3N>M>�k �jB�N�F23��# h�&)k�`� �1�2�"�S�/�F���6- _\mu%�� Wuk��6�� ft( C_+^k�^k_�X�W) + C_-���1.� BF.�&n%6�$s $C^k_\pm�OuraO�o 4 j'd>\$Fx <ICQEi�DoLu�*��, $Bj(e�HE� $�!m/ER~�HBy 9 ��"4uD �R! A:gZb, we W#� 5 Y(Z &&B_0�= (3"� :� k[\2c} -AJ1"�- A=1�X��(6��+)6)F�!], 6z B':�ʯ ��+� �"&� -'� J��7&�01i�U�QKa� X�nj��� "��A#~�%F�B {\x2��A����&". prc NEa��E�g g 3xy0zh0%4J(1�~*)� [&p�V.�A ���\mu*Ln�Gy%��um_JUKPk}:\ +C_-c�y�\� 2�2�G�2� pk = k+1�  6&04.R0 8�Q�a��� 9�� � u]1(Eq]� 2� e^2� r������i���?� �� z"01� � B�br;lcuMn d�O?P�_:��'&��� �]�1=0 , :�bZ"RZ!Z+Z.2"v�A�쥿C!�� zUupˏ ")�� $kCi1�S�J� k$6N[ look ��Nojeɀ�!�K$kp1  ��8ert�31�^� )_ ^2D2B�A=Q� a*� ѯ e^{2!�\�+}O&�;4.F~,IfB�� ��- w��#"J3�/�$ȉ"�>��/4~,6i �I�Q\}{��]YQ}{QG2�B� 7�i�~?$U� �@(xW1�m��a})ew"���lan �Uha3. H (weyADwe�wo~HEgQ N 3\hG�= A:�� �J=\cot -�V#3"��3^&�04.1B� F��B6�J{���^.t20N[-n�e2� 5A� se `&�5�s' ͺ�<�:t a bau :��0& ��2|*.� a)��\o*w�"1#w&.) ��.�!2�!�>:+multipl �n)�%�$6z�.O) �X6^X 6��l^A�n�M�B a�b.�g�5btchi#٢B Me&�_"�pb�.��-)3!)'%�g'!Rz ,�Q"� �{a&�\�, nd $�\n!.3 � # -] forw6-� �E*F(�))(R_k)=-%K{d? �CX!2(P, J�^k��;� &�CH�GX=A,B.�m }��KAm.�}"tas"dK�R"�?B��*�є��^A chi^{-+̐ - (2) ti� !�LU L+L+�LB��4fig[��mNW�:Vmy����n.<^�.�des�]<��k�l#=J� /a��  O=FzA�=�̺^{�Grho +A�re�Bd}'1 >R*h �%6;-:"G|'&�a gX�W_2of�#�,�6 rho=P��g �=�|a�q��-;6am %�&�m*R� 4.55"�r4.56.1��w:�2�D9� ��$#�=i��c"� �4:k�.��%�re>*�&�������Mp{ JX�<[M#�i "��� � 2\ ] =T�9bVk#Q kRM��ALS�#^� f&�Ls , .�3B%!�`d�U &3A �'&�2tE�n 2��^"7!�.^0�>o �Vi��(c6-��!�)si=5�r O0� Ys�8>�>gin��N_+%�E [!)�=�1:���end )5� N_-P-�\bpBO6:O6N�*�32>K�( `�|N_+|BnA�(b�Ear b}\cA�.(a�9ar a} I� 'I? a}\cB.����UN_-j�{\jFV �? y(-b + (} �.�A2e��3B���w�"�p��mC7�E)4FWa:=� +da_Z�Cb:=� b_2*�3B�T� [> $Nn$,N?� =""Gydropp�i*Ugn�?� $a_kEtI�$b�P�-)�+Mk�e}2>3�$�E `1�$Q�5*lea�nju�?* ��b�)" help�&_a�$�.$-3� �+qusefulge�IJ�q�.�(� $3-6 8 + B8+!�%_ .8 (3-6��c��i0 nu I�|�3y��d�E1f�_t*li&N� N04.35}\det N_+ -=(aQIe�� a})a�=- $�as,i����z zero;�E�75f�s��A�u��3B��1 =��R)N�*!z%{� -=.G3B E64, jy|1}{cN_�NR��#x �& y ��z & )6��N�R��&& x=��-���B(�ne{�� -a) " A -b!=n"�O��i� a}^2�V^�t 8��H^��2: z = :bJ:r^2�"��DXee ��4_�%y� <�Ah�=�=*��Ba�2E cJ��re��[�"���W zub�E�w�#;>2. @D�Z�/"d;�urse �9"�& crudt�&� bE��F^6ET*!IT�zV��3">�R�ݽ4J�*A��� must�0 "�r)_���Powa\0)&�+b$S^:�(*goyx+Eperiod� �S�(+S)" Q]�<BqB 4Z1v4�?'GAuI&A�sF@z�@� @�e�m�# 0U&�2\t g& (6�G& da*mut��`b^U�I����!urJZ�E6�j�Lw��s�cpFa�w%D `A�1' if�+��oneaU!42� :�i� H2rH ���~2`���val�R �; 2�WD*Ud���H.se>�,!iTvenYw`��Vize~�.Fb�4qOU8 I8\cT�atdh".i.��o+�ewt*�?w��nspGa�Veigy}A� !�F*h�� \cC=E�\cT^2$ r���*aF��q used���_�| �k37x1>x�b(�6n 7���t &�\cTn�h1&� Y N� ��ont+%r��a"j�5���c�Eisɞ!T�{ 12})b�if���� �}Vm} �_(_/>}^kM >��A J�\cT�(ZU *k (�^��B�(.SBdN?M^6=%nid+An�7%am�6$�-+ sixth roo��Sy, ��2k\pi\riEY^$F)0, 1, 5M"C���?1,0<pm \j�?� \,N*.� cubic� $ &A�L�����%�@Q#4Y�31y�a,� Zg���yC!��N�4���*8�vy-IB*tau!M�AgAh �� \{\,!&�/ H� 4.42>r�i��*ݱ�cZ PKBF�W �$ ^���L�p B�I�"�K4�u�$\� 1&3�A3Es,u�s>��e5�V'aRaCee4� F ey�P au$:͹� 1��$E=�47 2 ��1{!�nLI$�X&Y9�ex;�c8a�� �!*�43�#vIN tJ� �b(�� (� >taus$thbf{1}_2)�$�& ght]{ G@.BCoRE���Ge�1i��Ns "?.2/./\a�r�S'j��� be f&��N}�\Bigl6� - a�U��B 2r)29biL϶Q= 99=2�+4��%��]��a��i�|%7Q$s2% � aC��a !5� ){ 9�Q�_�nd8���}pU�� �Ig�9o�7� �'  l����Jm�2!�c@ rm{A}_�:� af\cA�B\cB)\,-ca/,&�4B^F� NyB6ybvyb y.s"�qq&��]$�g�j��!Smp�toJ�I-�� 6,pm ,� , �, 6=!�m��L4! "*R 4.48&`�spe���F21�N �:-��X?}&�-n!:�,)� Z�,�B�$�� �**O.��5Bep ɸ�3��R�qr19kn�z x2,. &����"� a��:&RW49.�5�- � we j�m�L�L�0a�!� �$Bn.6�"P� div�Pn�sis!/s Z�W�cAA�a�=� ri (�.!�)}���b��aboۙmNs�m�N0 $��$�=�mB �y I�O&�ly� 9R7.Ra', �!�y"}+R_��=� *�M)z�f ( ( ifW 979�!8��5BF%��Hd t���"S36�EV� �=-�� *R��r�-2�B� a<t�kE�d+вb�t\$�l]1��=0$6�qD24>��=�oa'�'�x�� involve�*$).�� $=3+�ile�㭷:?)6.? , s(%!6�ŭ����)X .��tc>!stg�A�i�06�{-�J5� + P !�6}5z*�>%�S�k,�� ���g6����1klE6,j��immedx�ly "!2�=08 .FL��%\m�1_+�(p/A'p {k+1!@�o"�0!^ F-� .F"�1.�B F�YB� 2Y Zf)�F�BF�B�F*�5B�>v_9&�(s $R_k, P_k��|D��&E�6� J�YR_k �-X*kmM9A�F8B"��7 67P o^{X3w� �e.��k"* *5�parity> ��"&)ira-�ifOaBq re�!^.)we J =8type 1 eigensta�tes by the parities analogously to (labeling of,@type 1 characters�I$D_6$ in Appendix B, then we can write \begin{equation} \eta_\mu^{A_+} = \$-+},\qquad2&-} 2&-J&B_:L+NLB>L+-}. \�,{4.56.1}\end�In!+ticular,%sta!I�$\eta^{X_+}_\mu$ are `bosonic' and the '-.'fermi )underYdexchange-$S_3$. The eigen s(\ref� 5}),�6}) may also be confirmed by examin!�!�Nvectors!�R443}). In fact%�Gditions'7})�88pre equivalent to $y(\mu) = 0$0$z8, respectively, hence�� `transport matrix' becomes triangular fo)3A� 1 �alues, Fstmbox{cases $\mathrm{A}_\pm$:}\EqT � \left[ D�array}{cc} \mp 1 & 0 \\ \frac{z:}{\det NA� & - EL D\right],]n3>l uey,N�Br�E v �pm � �)�2��0�,.� �.(4>�A�obvious-�Ec�()Z,$ gives riseA"A�corA ondA�E�E�.�F�. It isI�possiblS( show that QoM| �$��Tnever vanish simultane��I�thus �above iA| uly ]�(. This impl�Gx�R@iplicity of each A� .��$1. Next,�3turn ��/2=s ` spane42-dimensional ):ubspace�� M^U$�e��belong!h d�� represent��!���D $\chi^{(2)}$ (see��q,be denoted aa[�0H_{\mu,\tau}$ with $  = -\ja� $, $-\bar �those2�E'v�tilde .���� �, $�. For %�$\Re(���a,{1\over 2}$,%� admiM���!�$�det��ned�|��ral�b�P�� which E��Upon a titutaɿ,extra}) into 4?)e�obtain�`)&pi \mu}  nuN:W (6\nu -3))�-�a_1�l!�  J�+ 6SVK!�BE ^OB���$products $-�i�$-�$ do not�bplify�v@rigonometric func]�� best�: do�to reE af m us!��cidentityJ� Gamma(z)  +I�1}{2}e� "2#2!2^{1-2z}��6B�Nu.�%N =qj6\, u^2(\nu6�q -1)}} { + )B  -}, # a_2 jb =m4.r-s3)s-2A`p1 (r t.^5>^# contras� %���1 s X, now some further work!�nee��to find����=B� � any.q�g solvAi�(4.63}). How�� , si] re must�Utwo inde� � .y (ų U ɿM��(tau$)1 form a6�J��o:X �40}) �Xactually hold automatic�(rbitrary $C� ^1$. F�we have:G y6 $T^6I:=  bf{1}_2$ bny)�2X% (ase�Bc ��4a direct compuK)a�us�Ja�$associate !\ f9`1_of&z a� proj( (on operatorJ� pi_{!�}��P1}{6} \sum_{k = 1}^6 !� -^k T^k2*� 65F�( satisfies  >w!Mtau��.� $, $+�ad=B'� virtue!)�U= !�T^!):c i]G3��s!7viaZbN#N� 4} C^1_+\\ C_-^2 \� �=�%^sHt A�a� ex� ^n >~Vc} &8 EI�-2\ri � }{3&C\Imu %DE� -I^-&*� �tB�wh�#$}\in \{� �\sqrt{3}�I \}$ � � e imagin�� partA�� $.� principle2 constru� )�!nby���31}r 9})�2gen�e !퍱i"Y� a; !�*$ ���be  ed.�in jl�a}next s��w�vestig���� featur e1i��H�� �l $U$ � 3.18�� We k�.of four.���a��Ts,:<sU�Vm2�� $pm \sigma_�Dse� discussed�S �7. \ �{C�iz">���!d}7tcounter&� {0} �ōsee�atNFYa�,Hamiltonian ^ cAn Z�$ambda = (3r )^2�_R�I�mu$Aa!^u� �on���followZ `9��% s'. FirstJtF_A�!:= � e�1+�  � F� af) } {6 2� 2<.<>~nu 2� }�U) } \tanq�J� {2"$ 5.Br N�F_Bjf\n2�:1�+ZJ2)~13� .  "$ 5F�SecondR&� :� a�n�cos;A��VrV1�"�+  "��V��I�A6=(B�E�qAZ) J��![)�>trol all.\ a�separa�bound��!��,(($E��modulo � $ e `� 'RiTJm m.R�latter��,ɳ�sB�. so������)�odd� �06F"�),1 ev��o� tZ mirrorp$ symmetry ir���uZ�0�D���!F m$ i���mgumd of� t�nt � o (i  h!�side.U5,4}) governsh)�22��dhZ�] �����]w���teres ������=� y ei�= \verta� $ oRm�  $b9�%�A=� nega1 ! .�����.�main qu��is whe�NM4 exist or not.� our Hequ!�;ysiw�r� !Y ssum� at $�� nh %< \infty�f! n5$ diverg� r � 8 then �:2d!Q9~���{ real���be�ten down*� ,|"X aX s 4?` ubc T[R�:  studiY�ila�ofR7 ari+from �uE2�(J�$,� iXe:��2ZaVE���� {\em�} ��v &� 6.. By set��a'� ri x$I�$ $x\geq 0$8a�� �!�&6�5$ [0,I)$ defeR! $ x\mapsto � t)" i�ͪ� ' ��)$^2� F/w +F/ }�\h�and}\�.�B(:n� ���R��|B�WeA)Gth, ��AYOric  mono� � EincreaA|} !� $5� )$��y growI9��out��}aB $x$ tends��$+)��erefor�?� ��s K,at most $1$}Na/� ��e%� s6�  ue(� �fix�ign����6:�, a  such}? occur �preciseNif} �m(�L � ryib:E!E�0)6 J�E¢�.� } < iq�) .) ]�6>KSimilar byV-!�.��j� U1N, ��-� if%�only ifJo � r|!06R� F7e�6)�{r{.� 7>| To5�0 claims regar� $�@��in� its logX$(hmic deriv�:JG 2}{\ri�d \logE܁�@ x) }{ d x}= \psi�.�� �!D\e�) -V*-v 2*+ >+��N+BU *+FUM$5.8>a��3sta� dX HJpsi(zy�Ŝ'(z&�z).J9>mRe��o.X (\cite{GR}: 8.363 4.),uj�` $\xi� eta$J��\xi�b%)!2�\xi ri = ~ =0}^��X28!�{ ^�>+k)^2.�10>�B!t~! adE���� seri� we�J^E|:n]m5�� 2x (:8-1) (3+4k)} {[x �M2� ] [ ��+ �l`'�1} #$� }� ch� posi� %�$x>H% s $�>0$. S�u� xd>�"$J $�"aV ������ on��| )$. �"!]rIb:U28) B�\lim_Ѫeta�to \} "�.a -e^{)�\pie�SM} (0y -\xiJ(�2D݌1B�ItsJ �_1�nd 2�hat^�x.��?= ). .�.�^{Mx}=-0.�B=as had bq��ed. �� �)��per*���a�x)% be verifi!a_samN nner'B� .�gen }�$A8describ� shap�`&j  2� mu�%Y#T$� 6A J illustr�$by Figure~� fig:p}.�%p�# ts uy �$�6>�.�2� ��!W� furp&*$b�UX� 0. %\bigskip Q`f�}[ht]�!e�� %% AB $ \resize} �<.35\columnwidth}{!}{\includegraphics{calogeroanglea2}} \h� .12B�]b] \capw{��$ (��A�$ (��W!�Q!%Z\mu$ [!�1t2})-- 3})]��* \geW$\n{2/3$.a das!�lin re locE5� mu_m���5.1�� �anA�bar�&}N09})0B$.a��.� �)�}!�med!|�� sꁐ is smooth cXu except at�i�QM�{.���" +1)�� m"w"0m=0,1,2,\ldotn+ �%B�� ip!�+(infinite. M� " ,i�s >,ly checked uL"  pr.�A $ $-1,%d<$ approaches $+�4�-�$ �#!,$.[.� G a�%6�,�*��M; =0$,�it tak.%� zero!�F-�0�V%�^�&t 1B�Not-R� d<�M�_m _{m+1}^02)6Z �B� It8�+n:L*C)!�at�I�A�i 2i dedA� %�!� �_0 ��/s well!�e�ein A#u� 6 � �)K �$mmF.} n A|c�ant��m�I��co�vIKOaf,8 .�Y*ts )a unique"�2=rO} $���2��6�&�2W ��alVr m2r if !g2�1�r2$ � )� vj.( }��q� ���+ � &7 ��.% F6 Let2 sket�-�S3�������A�>�Qm Asa read�� ,�6 �-n�����~to"���pas�throug������by F���mc0�1!Q%���3ba &m��"�� �m=�B._B4I�<"����a�it��JM�i�v� JS �؝�B\%ii�vW�'r��cbaraIe�v ��.%  �!t%u6�=S20>� "eA$E��A��|, 3�prat ��� ��6.�1� i��1�R� 2� (..,.^� As a�h�c�a}"o �, ����qj�,��j'h�����1�,�'eO:��1 %�يΦ~l={������ ����N�.�2B�7 \>�1&� � �+ulaaA1.�2�1�� is rat�,�&i4 for *�%,)��o"9sh�bf7tM� @& remark��Kica�*��2�. E�n&�ion, lɣf�$ inv�&F ��2 ��J&�$� >�F�"��k&\�v�� �,�U*5J�bMi3asG w$:=WY�{2}$. U� is= sum�fa�2"�s�5�+R+3��a12.3� .#h�#x}��#\n� J�1}{"0#} T[�1�1�3 *"8 �Zght&�2!5B��eI I� 4.65")Q $a_kOb_k"i�M��$k�� A�\F�='a��2*�% �2 } >1 \if"0<#\leS-�=-)����B�T�7M^Um2esN 2 �U�M�]��� choi37 the &�!*� &�)&G$ �UM\�$�t$U=\&�)O�"@1ry,�$>-h E1 $�(near en� �$E� 6s0�r�)V�0)>1�)�*�F� ]= L2�B�% �e���"of*le>22V !$%� A���6�!� I�I+��su' rele/ %AN��c1s2Ylarge}'�7aB�Mg3eAAqmin>,F_2$, unless� is":� a �&� +G �5U�=Z �=pl��$at, lik�$%E�b3=Rr��f /2& .3�pi!t!jy $i�� . On�?��$J0� ]6 =� $ always)�* >� �l ngo34$A�0 K,I<2A=0�;M�$�I1 ��.{ |!2}{20 ,u �w�3�2�R���i�*ur�R")�i�y� � �001}{100R�3��et�715"0 $+*cR*n s�*�/$plot exhib�� beha�?�.>)three�9)ڡA���$4}). Initi�6 � rapi�<*� midd�*erm d�i.��_+� a\: tude� 2rul��or��(B�third , grado7"cBheG$S ific�e. Ea��oscill��� 4 fr) cy. 2�mB�&�&Z:?@�$2$.�?:^8s h�E $L^2(S^1)�Aly"{,^$����� 2&D�%.k  ,!�Dx��te2)olV1E]e��n "� �$�&���(!ʡx� $y$)F��y�.T:!(y�:  (y +R  )�;y/8in\piL + 1 -y�; \pi.N5- }-�e�� �*�C� �� �*� 7=eW *�&2�! ΁`a�B�;ympto*:�l��MZeA/A��FKf��:= ��"m!%��0!�nu� en2;G f $( � (. � )\n&�)tC�% "g�!呁Ll"��I{�:� �y$�!&%S=R�F� ɢE�N !�P �2��,�!$�2I betw�A����ecu�!�@emJr� "<� ��� �CA?�,f�0-N�)��S�\.I@��I�5!�2"A<��e. !�)�)�=,2�o�+v-H e�G�insl14J>-.{ .y as di�63`-X-Ifo ired�.could�&��r�9z) au.  m��"[ 9Xof.�a�developm!� arg�0s�>EU2E�$5�EY=0}8a D .D&x8.� "� �� two}5 2�Qlower-S+edn�  OJ nerg9D�3�$U$��� e{{ [s,�r%YAq�H  on"�0.� , a!�ite* RL too�cer�C* �& � ,�X$�N� esul� imaJ ant,---A\wq �dem�r��inUg6)�܅W aN��M�� %O� -�� trum*�(model (i.e.e�2!${\� H}_{rel�GE 2�) ]�:m ed�F�E�s� �� t%Lex�!� hypothe�? phys� app��.�t0*eR�on�5�&5��A.3 N�!%2 , bu%:r�3Mg�T�O�+.�Gx eI����  $>� �-tan 7F6�8 <N"f Žn�3!�in�_O)�5.6}),&�GMno�0c6Kqua ; o be.i�% Toge��x [ *5.2�% .jE�.c%[A)"u !H�Ni%��}_�B�<`&D�;i� ce"�.2�6&2s 0pm {\bf 1}_2,)_& h(2�=�(a�2i� cern���� � ity}�A~B. SuppnJe�a�*� 7)-a/ P�)� $U=U(I_0,��_0` =>$(��)S4g�ic�^�ensgv y-��3"�<2[NU-):�_0)]�_0? (R5��s�? & � .� _02� _0� "�5.25*>w�Bi" "[sat<2)pP  $1])[)t%�� �/1�2�A�f 9�!e�-�)�&3V��!To|)����9me�<w1 obser:/at� ��v2�!�."� ��av�Q_5* �_0 �Ax���inuity. �&� eT2�N�s�5k�F9a.!'�OE�:�6X2�1�.n�Lw� a!P KJ� ��1})XHti5Rj%>� �*�7_�F� � �,�<-P= s, pi x"�\kappa_0m� )$ K_0(x) + -: xa(\nu} K_{-}2.+:./- -1} K_+-\ )&6ESFv?�C�N� s $K_a�;a�FyF�K_a(x)>0S \for� ��!\.�, 8 =9 (<a\in\{Axpm\� "(SF?b��Jq$p-���e� ��6valid����� �N�N���<2, \no�\\`- 6�`)(�H:�L 2^.�L� `1-1~B� "2 J� R�:WF�b�B�$ �-���+-3F�� S&f91�-&.=Q��5)� i�>!�$-��.��(a �m � r�NT7)"�cho�� _ �+.}�m� - 0�o - -���S�a�3 > 1B� x>x_0�LB�(��$��1,-\1-@�ns�H��E*no��A�I�*�!$x> x_0� �4����En $x^{J"�4!5 (�2� �on j<L]*�% $\epsilonE�*b J�2j�f�p b�-F.U> "q ��r�&,!V�6 E�0D!x _� 6�BS/ooN/5�.pr�Os;� 0 � a wa� NB.�"3 .����\�[�+ 2� �"for�[>�,>p!�9-Eh6P�]q i}��:� � V_:9Q�>6c k we wSd� ove.�J�establNZRKM���6 b�'`im�4JX'I�6�F�ll�qNy�T�4 .OK�. Nam%�io>!A�Jr m-N��M#lAis�1 F%e(*�OsmX �&urb�� ["�P� #de��s���c\�f 2�#s af 1NX or 2N��"sR�/@c,�  8�65��"]9��a*� $- ��5�C ng, �jb touc�P, Y$horizontal�4 �-ed�yX$7 Mon{�rad;'=�n�M#<k iL1�a],lAC0 �� � f f �dsJ4.H_{r,\�M}9-�(d^2}{d r^2} 1}{r" >} R �43}{8} \omega^29_{N��J�aAf�I�ngB�7*�"BoNBM�,��belown9yz�8�gy %LA�%ar�$�iAO�K�Hicle C�c-4system"�D�c�A�A$8elf-adjoint ver4^&)�.2."�2$2�$�!;2SonVo&9in ��$R}_+, r drUit� �Zconveni�*to deal� ��iGb�*Z�Uc2� >M�;A?circ 6 IH�(�Rr}} =B E_M� AY}*!2zt- >1}{4}I�" '6N��=ma��.�%F6 5T �=U!S. I%S easy!H&�%�Y, both��B�X&5�Kdifferl[al5� $\2^9"���squ� ��gr�Rar� $r�6]C $m� <K �#�a&-�@DDS,Richt,Meetz}, $-� =�dm�&�d *�2j)Ws f�lW>�=ga�aRAorems�S llec��.gA�Q�}Oa�F2�m�a� J�a�e�3a0,pure discret&}�K=F�+1$����36.k)!�x9I�ist� �a�ex&R $\rho$A�$U�27� @ rho'E" ab�el O�-da^ ŃE!v A�6F:�V$�bngA�>t.str.4a/�8��%#" ivenJUF� E_{m58<= 2 c ( 2m +1+ ��1V aZ� c: �~�7.�, %6�3�OB--�69i�u�F�!@.�(r) = r2.A�����/� c�/ L_m^X�}(c�K� <6F��$N>�A�(mx�) Laguer�olynom��ijGR}�'2�mi�F�!�A�Td 0"4a� QCal3,L�Euag From�Mon  e+�i� Jh'<&V6&%$\varphi�i9 2A�B�%�5�IB� av] an*� FI,d)x  factr -�|Kti&:aK!�*�= theye 1��-�� `�aq�X6!��F� �D now �^1y a�-2: " "J!�mNBE� W[a$, 1�1]_{0+0a>2 =�(-�.�BHM�:2E�a)�]� �E6? y. HZ>8�XmeaS  �:��#Ply >* �Pe0quM#�(>s:F �e. OuP9 on emphauB� a"=| /pri\�:�"be�]tFAX�T PA�� 6.6B@Qh$�\$r�.L"� 2B�bg(�J` H� ial a�s�FRep! A� �3[=�!�on]�>�'1"��u�lp� � P \6�$I�|Hed on} $\bR$ (accor I!�U$ reduc!� o a !�e),a��+ zc �:gog$r<0$�mHW;C4`re cX% des'���k$ ,OF(Tlyi�2�Fz )z�b*�U-Z)�.-u^d >,Bu�$(Ihenx us�")�A#, !�may�T'he �A�s#��,:�}: = �6.[ \� 6�B<�drc0r}$;*�#w}$.) NXor�u9 t�FntA�L$�, ��8dg�T!�� �## �6�?6� � = E ��BOa)� �v��$E�Qo dq.i^&� 6"iZ$A�N�s�^:= o� \xi��E}{4c&f6$ +��B�>f $c�n��I86y%\e?'��.� i��L! :��� *~ }\footGm{To s�es�m,h  3forth2d�� ����F our &�9�9 �fit a�.ireO#([e treat� �!Efi�Af## oniXGZ�da8K)�d%)�  } 2]5I� 6"�d �&&[ H&&�_{E,1� I 2� +P�"B� )B� B} \Phi(.L,m� �A-Ar��2 e�2��-:^)} -I��B�>4,�A2� .�z "�@1>��a,b,z}a�a|fl�YhypAYo\ic",u `P$ed Kummer'�*� ��6bA�e�%inX< ei�A�� ei�& $6� =3\mC>[�6fdis�P . UpA�a�.�=Y� or��"�?_ar�(b�7ion�v�U|��6.9})�qiZ�, &FC"�u�|Ns ho_E"|\D 1-6�.�DUQ2�) HE�AI��L+>-A� )��<22.B*B v�� rrelev�-)U $C(:m$,�hN%me�E(r)= B8��}�U�, > N11>�&i.O,d jU�R_:�,\�@R�$,^\xi[ 1 + O( ^{-1})]�  $ .�1y $eq.~13.1.8Ab�ASI#�6�8>qi\�_�`W$E$abt �r3>��jE�$~ )��F ��6� �u�=w s*z)F �D�4 <#u��12>�� @�� � {E,kr aly�l0 fix�+:� !bN�� U!{E_0,k*7F�Q8/*>r$E�!�&�j!�� , ap�calcu�<yield��U� �,щ_0,l}��flSr�2�7 9(*,k"w=}{dr} -��H*,k (m )(r) >N-�=�_{k,l54y-�c.31B�$i�&� K,!� usua d tern�ctensor� �(�!�+N��<�_Ef�_E ,�X�|Z6�U6�) �~>�����>><)2�B�M[_ub� � back�W� 8�."W!B &&%t� y"�vs0&P �h ��'}:F�F_M(Q3}6-[=B�!+ 1>O� �W�  -B2>� 2&  :b�6�)�9*"s�B�!��B��DE4� .�B*Nz"JA�"�H � $5E$"�Bs& F%7H4&U���x<}[N]TR` #2~>42Tv\Trad>%>-��86& �*�"[�DUL6�S .� (q/5�S2>!� .1"!d,} �!%C1�_�I$v8})6�S-C>�S�us!rt:$.a�i`=�/ �7R�M�_TMI>1 :� A� +m&�+6Q�PB���*�SI?ueV�~&N�k� E �:^ºB��$o,dingQ�L3� �zu!'�g}�ps-z+��Vv�'20��N�6s�U6�K:�%�3E�nRI�5~ �7 immed�%IPR��E=) � "LYF0NY�9 >�\nd]�=R,� #ar&p9�65�$�4W�j$6bN �\�#$0� $$du� $ va ^&2Pto$5P��1&>&�4M� we?� refl6qula�5D.�S��psi�e��I�� [Y5'Y�NZU���?NC6* + \psa[\cot�=-�qcotO.�u� F�M�:JE ��� .��4<9�.nO�,",^,FzKINdB�x �*�2B�A_n���2c!bracket2�3�� �'"`�A�I6r)}�5�)<�i��r�at}�w 6�Wm����is�.~#� -2.:��*FVJt{N5��!H>B�M6%+ K o 8�<�C&�B&& c6��u����"l�� e kD� � |D-u�7>!a%�"M�CE/$�� �%�b|Mwell. �8!�BJ 6� �1t�3��\��I[�Rz 2�f!�r�9K""�[p�b�y�* �gALZF!V rval�6M,u�,V�)�" any v -hB· >>6.ulB]T? ZlsO2Z9"!��/5��=bf�K(0)�.-����++� mz6.4 �B*�{"Yy�6��q:i'3i��se'��c:�=�.�a��9G��)c6 >Bc� *�"�1 �9�!�%�-e�wd���#) u/n *�E A��B��`&&W2�9J��� 23% = 2c (1%fG:J^�3:�X*� B+Un$E=No�T)4E*� 0��a� opor) �' �,�G�&(1/^5=4faN�) =&�2-1�b f&F&R�%>~�%> F�%2B� "$`�q:�,O��a�0@as>O�!H�Uʋ!HUhap�6AXis"�VE^t>c�jindPLA* In� ��Ń�2 :swac6�ea M�WO��L,l pc@�&a�qofyp*�$as�l�7�_.}�er#0!1#�,quantiz~� a�).m->d-��/�rX)"�! a"�(t method, �2rpbn���s �wo%�F'.�!�g&.�NH2$H_\O�/qP1�y-w st_8 �,$N$ du��"�.ICalN}�&� $N=3!Gse-�t�**�(� `E3 $U=-�*OB0$U=.2�6u.A� �OJ�6�=�ۇ�;�4&��}�) x6QB�L8A�(s��*�mEex�ir>!�%6 =�iC>uM6b%�9!aR����� �!�:ue�����!�s�4�. E"C�Lfn_D`� �B2�!!]�!�e�09��&&�1(r36�*}ZQ DRe&��61�nx��Yr<(x�pr�9Im�36=3\�&]�+6: �2R� >%(. ��2� +��2� �.�BP T)v2��b$-$.�/�&w�IL9�ua�H}�|{! 2]D�%barUv0+}� (1") 2x�3B��VaBA�vc"{��.�]WF�D1}�1� -I�c6�" �n%�I��:+~n2Bn�m ��m�)` x�����i�.�"�1�BSsoF0E�i& �p(�υ�=%�E$�6.> �"=�*_,e �"� J�% \arg ft(:? %�}1 �) "+ �$�" �=R)!� ght)>_6� ��*�A��Q3ByEqu�8<w�d�M ��q� ��o�(6���?�=����bFbi� ) } JK.dB�BecauseN ���  po } *� uz on=b'� Qn-�U"�)p&�l3p56� � �5 " B4n;�8-�mw� � accu����,�� um.!6,>k�!&hR}!�;purpos�M*ady$ag��Ak��3tNv$ � "�, x��exfJaBaNf�yTa'var-Oa(x�36Y,c)��  mod} \,\�Li*�3V� F.nFl= #�$arccot} (-:$) -�` �1�BWم)�c .�BI&a 34})a�A-�nT 9c�A,:Em�p"(I$��xC�.� d,FV� \2�/^�pt�}dy!�U<(y,x)!ѕ�Bc$ r�;ambigGKa�$=d6������"/�#�k� Fl-�<�:> =y} t-y�%�b��"�&�J�>C�=+E')-�y-y ~n �3].�B�3By *e9by�2*vU�c��$=��!0�'s�_Ai help�. &v�a-�^$�$b%d�>(6}) (or di˒ly"7jI�)$ �>c%U\\to�D�� :$ xe�p "�6�$$>-aQ#]�M.|�� &�� & ru&4&�m real axisu."R]� %Eseta��n!^�r� is�'ed"�N.k(w�N1�) r'�41�"T�clu S4 ins mL 4 ������V�lA��$��A�,'5o[ ���,">s�5_E*< �6�A��5!�&=0$�OG��/ <+�X�t|V�t5�%�%�,�R Vez`oPDHV"�nn����4� ��RQ�&�<�G��:N �@"�BE"XA�vo>�s}$tc�E{"��& �U� V�$N = 3$&��W�4�D a few%YA� �A'1olv2_�. �C8�j�<!�"$5!K"�QB�� to GQ<1${Ia��6���2[�%�i�3��!�'1�H�� �Dz��u�eb&SR�A��k8�(� dopt��?B���9�-2��)�,M�&� �t�!5��r�� > ��a~4}) �ll}�rJ�X!I."3� fourn8s, œ*� &�, #\a.".<U�i�`nse@ n%�iG,r�dVE� r;"OG � lim c n�`1$ �Z$g�� 0$�I���D ��by2J7>�Z .|charmonic"eco�475 "�s)Z$U���{\a�� e $g\t� �m��[pTAO8AJ� pluA6 �_a.�9*� <1�A�or./s�.r^(*�9�MC+S$MR 3.5}�fmanife�Ait� ǩ�2�<5j����X�.�Gf�A+�US� *"�E��i9��YA��YQf��ummar�?!�]* 5 Maend�!io� 2�qh.�]���b|8Z�(`Dirichlet']�4-q�i�>8� dard�HofJGg ��4�#:97C�8�@�&�3}. A�Za�5]�  -�s7A�� �Cu>��4.2�J"h����#�~4.2�o!�����XEZOQ��� "�;+�Q�K�ar*�,&&.�� }(\phi��\_�=]�<�k~�$_{-,\mu}^k *i%e~�n+|&nu >�SgBfg+g+vg ȍ, � 7.1&ߝ�!>$n2�~$,�"m�coeffic�Hsz�k��ks,, z: 6$*;$�L�I�]&�6��6i�s.~$��_\mu^A_Bipt�$co�6�A!����A l!� $R�C"�"h-&���h>D{� �ED�-t s� *�4^0͡orm�GEfM��NHre�#t��..�<�$. � Y &oKde^iX"�0�}$n� �T s (ԕ!#normal�� tant"Ǩed&!$m, n`, %� )�.whQ?a4Psi^{A}_{mn}(r�Qe Bx\,5�{AmEuEDa"c�!!+ 3( 2n a7ita>6�: �B I��BJ� Dj�>��af"21'EI $2cAT{3G�}\,�$;��p . #s�@unf5 2F�%���A�YyA� &a  :>k��6|� mQ�F�Pe gk)&��group. an"FFif� �$� = (-1)^{k�[1�r$k="K�6E�� r�Fk9EΝ{A}�&ec.�"I a $(+l=gsll%&�,t P_n{Im>*�s� . Tf �" hand^c�S�C� �c >� R�� �-:�� .�"2�d �^q�,�Y�( {B}$�5  $C�-:+^1$ m��� e��t2:' b- Aiz<SOw� =C|basic�S $v_{M>mumg��i�:$,"�����1}�+periodicA�$�uH th �4piiH3Xnd��səice��D = l[ 86!q Mw-� �e�+ f�$�J� &S c���O{{:3�}].$y\1W}�7�%s2>�'6>>>t2>��J>>��B�A�a� ��%��)�EY-y]ƛn *U*< $S^1\setminus \� � erq��I$s�DWeCQr�"���enM Nm'"N��a = -�\, v_{IU��~8�  =N.9m&,Q�i�b��A��,1mI�|2�!/]� $c)�$ att��h�Q����r"oB&y@L�H %"� �1.kg��R�I. "ɪ 7idi:Q7��!�S'C4CYK "a�)0��Bj� .�m��myJ8"!KBF�hE�A -�" 8�c� SG�r�ToJf%F�-{l�7 � , � &na&� ;sin^2i�� = {{l!�(Mc)�V l+ ,}\, C_l^\nu(�#�_�J"�5�B��place��m]*�t6A���Y�� �, Gegenbauer *�N$ ����rec��%n orig�E" � / "}'a�m'"�'�j�&�}��`Neumann.�%� &�"�S o� ed>�; A)74�)66-2>F?Af �uJ� � �'fg-"g��+s)��v�E� p,&�2��,)IV�7 \pm2� ,6I����Q.AW!�6� t�ֈV��I �I nu)�M �M %�F��"��2FY u\h�r�y��7!%�-��b��dHs� aPنby5W&`=c.�$CUZ�7` . C�!�ms>se� ��X'avail�ֹ���>.��M:s;Q�6���=ufU�t�b�>z� �r*a 2�>8�bk 9�)��wI0. !��}�;��6�!M �x$*�NP�h�G��r���m"ܹ`6�2R��Vlkch�"9kLeq *���^MP{63\�͋V>�i4vuui�m0*soitd�Y$.f�|c&�"���X�w�3� ���&��� �in�X*8Y!zD1$]"�7ulI�B�&-&$disappears� is `��{iƁ"� �5Brin �W"7co�K9�5� -th^a��m&Qv!� 7x 6�� nJ)24.4*���i� f� oF�-�"pH� nu}= "��"*q��9�par��"� ��${\cal A�> B�\ {} E�>�)!�%v BO�1$,A}!�? top��uE"�3^ 62TP� �F:!}=�m1�#nu.�0���l (Z�6N%=r2>i)�+�A $A_-&z $B_+6 se*"� ��4.4�����f��40<),9})��&� ��2:-!;"Gr;z7�%_b�0F�AJ0B20A10�@sE%aYE�Qio *n51&:���7 |a�d��ce� }%)im"L $e^{i�hA_Nt)i �=2 -�&t -aA�AmD��� �6�V� _+t�a9\,~��}�>x��.)9�:p&_-k&�"�^{04\!>q\n�^m���bD�dR�2�f�fn�&�b(�w� �.`.�.�\nu*� "�1� C� ���A�]�M*�V!�A?���d� PͭQ[6� 6 !W�$)*�/�&& � ++Bz %N^\,v9ؑ4VA�B2�aT� \r/>d �-^�- �~�y[.�VR��� �)� >���*�%Ri~�BU�.�Vn�n�*<:�--,B� ~��4.�>n���.�0 "l8Q�}a3$superscrip� �%Psit$� ��he �� *�*:^"e��-�s$�J�qX2/"Wa�: y�_+yBa$.{/bfH� .ɏ7� ) af$�: &��Al6T_-k82|-R�;&i t�L �Jt.�". &�M"��+ 2.T���|2��#&z��E!bW 7!�Z "t!�3x>�+o�HJ�D��(�S:=z\pi}\s0s�� {.&� �~Q�"88� "m ���Nu�9�"X �n� 0��uiz� FW�'2�=�^,����a�ڶB� B�*�!$. "�?F���G9B < {2�3}ӛ.�/W 1�F�U �nu"Ğm�Q��Q� .�a*�q ^2>7q 0�ba�He}�Ms�asf�&�*8:FeuBm�Ha&wݾHgprocedu���4.3. �q&&�_�sg�n���nF�{^�?�ai"h'N2�Ӹ_G�� %t)K���>,5{ 9s!*3!E�m��6�#�18�� 2yJ[zA�!4MQ �u,9 "B&)`U��!mÆ �������'4�2��� K+z%#G � g!3.?��� !-!�t]!scale� or61=�69  arriv%J�- I�)F�j ri q��I1�}}�  3 + v_{2.*�12-B62F r? {3��^(}r�T�^2}} 2^G{ o�+�S) \� "$%%�/| �%+ �Aa �^-Bh~Pi.�1$nLphi�,6� ��*or�%A;exEX����i� halD1m� da�bn�3 E"E7)c) Z "!�$_ $0< �2�6"*4 *���}&1)�&F7"c4�& ��`/Q�n$a��Po� wholpR�F�[S��e .&1$k�Պmhj� r�R�� 8�4ta.�2*�5H4�B%�>Y�-��? "�(by��~% $ tiM� 3i�� ��! D1 O�R4V�M�=W h1S�w=w.�Ca1�:�E �r�gq�/' pm {�d3}ik}�$y!� thati�}!�fAed doubl���&�i qe ispl�ye �5��bA their23F'�/a+�� [�us:1"�T"E$�!!m;3w q1_62�i% � �42��Qt� 2:� �� uɎ L)t��2���)�R&�љ�$%$PJ��FFF@-.B�ha�"�sIqa)6��7j I�)7�`)62#(We2a 2�?2A9� �, I��ds-R$\{�-B�\ � !�K��R(� lass�!�|�wo�tinct ��E��ja#!�1�c�)���1g�emu��UK/Ub_�muS)�k%m) �3��Y> dAAt *� 1���,6c tl,.IRp  �4ilarly MQ9_:�R �J�:�:�B � 1 + :Q $.*m1!3"� E�2e��8� u�tPJbP.� �J^ E�2"�)��  &��"j(2� mn, � .�bc9�E8.|Wr~:M^& 1�-[�*4R�9䂸 ,E ��A�B,(EQA�:�\^+ ��A�m���-� 5y g � dn�}f�γ��%OB���!fJ�*&5dQ�&R��"L �%9 �ta��5 K!$1*�E2�l2mSϖerg6�"U 7.?a��N�.�(�Lt�< 6�RV;�;�.�6>�1 u�!) �3�JXf�6s`g_3We� .�/[�.�/nd)��st-?)�r/ "�9���1  $IJ� 00}$��yy 1^ $E�Q�= q|A��.�ow"��c�:J�8F7 . Hereie*G5�4�;T� B�"�� B � g b!n{Ab� &�->Q�xcos*2c"��w n =5 �q&& �>��){�{�.mu" ����S ��86� > �BK�E T�!N��.,"�+1uM� ei?mAb�%�R2�T\1^nq2Y Y7a1=1�z1�2 so&�65.��Y�&� jN*��m\nyI�, ��A"$�5m� C 1�� ��d"� � �} �^a�46���pl*�_�._O>_1@&�1a�)� pai�����sh!�! �W�am�|hemsel)�$�3�"T}2$ S2�-� 2i}/�Cus}maya�mzi�\>�_8�&� � #!& plerJ ��)����I�phi� � ��1w2T7l99W�(9$ a �EE���!��-1� oddQ9M����21jMny%Hc2P  $���%&� fe!!T�wis!#? $9C�N�)��s R� 7�4}{� ��{���$2{:�(H��,%5AO%�E�a9��p�0i�/�  y�2�n�5m�� !��Ќm>�=�g&>E1{s GW�1� pm $:�"$:K8.�B���a��� +a�R� N$ -} $)�o� =�fN���bz�+}�\CoͲsOc8&$k�ay$ (�/#�^� !se,�:�vM�),�=1$'h��E�6�m��!�3W���4tB3b�+k^\pmM<:=.=k��kF�;."�_�]��m��� ��i#&��.6���N�� kay Q.�Bu�Qm$,A5= >�<�Iit;�Y��?i���� s^^:_kzH�z view)7l�=k^�8]�e7N�B,=��k}A�)a 2v�k}�\]2B�U�*M���� r��<\pi$-m9� 1� �� $M*? 2Pa� E=0�outuy"�+`*/:��S"ş�C�*�]��E�U�i�v �J��9�kc� a��8� o��^�n�Na in.��s , e.g.,!4Levin}EeMGonv 7eat*� �,�� c(ba[�F1�VJ�e�Z�e�e���^+~t�c[*a0pr61�suG.�C�$�C&E"l)d����<5� �7Ic.� ��- `! t��s'QmB9M{J�#v�ng�~7�K�MI6 (X:ea&2"�.f�rg/-\r}����Lp+6��s�T� !.1p 0.99\text���G 1}} ���*{ Left:c �*��-lP�'��1�fonW���E5�A4Sp Boxe�on] `A, A' �Z�l�lor !B'ez;E $+�^ $-�)� m0Da4b g�@&h"? dot�F���C_?��a):h�A�`C mbol� setbox1�T$+$�#py1��@-\wd1\raise .3ex\+ @�{2:-�: indi�| "| a"�.aB@.� ,&ng�� e *�&7�%�p�]�if;R�:%oe�&�H(�;�Ely shif�S!�re�d��a�%�e�U�.6֭Q�A�o�I�} &���wHyD� �� :[0[0� "�3}M, ~ �`t)_"�%Y9ŭx� :� �W���2P!�1 �1�7Nq>UT�  b�1F�m!�s:Qaw�. �u�Km�Q�w,tb�D ���. �o2�.qaeI�b6�Y2l&/7�) !�B �O��ɓ"U}) ���B���ol�a�!r��d�Lo 2C2 X*un"Z $A�7��A_\mp� $BB������b�DZ�e"h� "� = c L/��x"7 � \,�a*0>�..gt�..J/j�/ uad iNl�nu�*�pG � =&�vZ*A�l6�j�5b-.A/��;� �.� " #'A&�ID.\&X �!��E�ed"�"? ��AM.�ofI�? a�}�Lghowamu=22 B�5�6nac�A��FA i1�y,�<1}: . E"%T �Y��J�a�� �Au�0j�1B9J�y�r_ -2<  i& ���J�_Kw$8d�;�8�%!-]U �Ef�VAFB�:av#-&�4� v)� � � . F�@ w6�v $U �_� %��*� �i�Q�~�2-"MRa1 FtRaA�"�R,|�6�I4Ŗ��s !ݍJ� ��U . 0 F�Jn�� anG�by loo�)a� oJn���2z:,�M0"�M(r6'G����z %^=�=B�����RQ� ty $-1$� x-Je<anyvM��:gre�m%� $+1$IMaos=�or2�~ �;C��'n�WI!�is papS�2alo�:�k R�kt��) :b��Q� >;� vari�>s� ]�z r�{Zp� � �,>coupl�z�tant.����a�$Ʒ�I-iU?!�E[" �)�ts j-X����2�M&��W1�8pec�#byJ���&( ��aMr " Ta Zx�Uin U(2)$&8�D 3.15��We N aEc�F5s f��,**���&�� `1�ng'��`k$ �$���gb�Zi8�o= :ng_ sei��1�� 2�k1z���\ll Ұ%*msD��6$�Je"� t �ing5~%%��?�pѲa��%ih�8as uncovered be�tween the boundary conditions admitting and&ones not.� negative eigenvalue of $M^U$, since in@(former case energy i U�Led from below, which! in g/al�xpermissible in physical applica�P. The properties that � has an �8$\lambda <0$ or - it posse only3s48>0$ are stable �� ly ( � sens%Sec�h 5.4) with respect to small� turb �!N!� parameter`conn N� matrix' $U$ (\ref{3.18}). Our description ofOLinequivalent quantiz2qH radial Hamiltonian Z6.2})!� $0<581$!�(consistent �8 and complement!�!�eviou!��alysis \cite{indPLA}. We classified �%�state��$ according!E0irreducA"$ represent6�P$D_6$ symmetry group,E�)/ bed also Pnduced�Ie under!Dexchange-$S_3$ subQ!�i4. If necessaryA� some.�,aa can=E$ly truncate34 Hilbert space�a sector4 tain!E��50 a fixed� typeI!�truI�provida�ew 6! %�Z o-obped�d �s,T�for exaA:a#-�8`bosonic' or `fa�  characterB{a�u6�aticles. E�Dcase-study illustru?faaj hat .:��b %�b� �� ied,�D $\frac{1}{4}\leq C <1$,� /FPW}. � methoda�� �qsimilariXat:'v,���resul��re��2�a� deriv q��6 rely!�on��m\, but a�q , � . WE�@nk P.A.G. Pisani% drawMur at��on�:this AG cle.R�$%\newpage 6�$Acknowledg� .} TM�9(was support ؁% by% HungA�|n Scientific Research Fund (OTKA�# grant� Ds T034170, T043159 T9495, M36803, M045596 %� uEC net� `EUCLID',� t! ]H HPRN-CT-2002-00325�|��lso� VG�-in-Ai�TJ�4, No.~13135206�6540354,m8 Japanese MinisI of Educ�,)-ce, S!W� d Cultur%�=�Lrenewcommand{\theequE$}{\arabic{� ion}.#} F@.{\Alph= } \setcou��{0 {Remark� %�a$%ra> sN|�{AN�� "� z !:a�2Uѷ�� � ��*� inu�3  be view� s an��#pgZ .� "  ��� �DS,Kochubei,Gorba}. Nevertheless,D� usefula���y an e  arguH l va�� ����i� 3.14}) � 2�26$M�{2.6�"I!ցAppendix�`e) wish�qu�"� % ems ť�Y DS} � impl�discrete.x �+um rF:v$ �DnyN�. ] asRw ~3%9��.�Barise � riE�s�max�I��(D_1$. Here,� aim�_�howt!0.N8 $\cD \subset \C defi�p��*t:� yields � B� , i.e., >sA� $M_{m}$��$ !�6Q�.� �UE�AR�dvantage�to rew� nI~ in%g��a�$m \begin��@ U_{\x} B^{(+)} $(\psi) = -6\quad ( 80\in U(2),\, I\cS)\,p,\hbox{� } > Y\pm6[ := B.�$\pm \ri B'2, .\4label{A.3}\end�K e ���twelve `�a�v� s' $�>�$ take � a�en L|� $� C}^2$ P vjsA�$!D $ ruA�ve@ Eh. >QsefisAsApsi�n/ >�� ocia!J�funm%�T [ c^{}_1 \varphi_1^%�+ 22 ] \eta%�1O4}\ee w�$c_1, c8in �$,�x%�\cS��3.5})A�oneA�!x� p� s�$sE(4C^\infty (S^1 � minu��S)�a� tak�}�x& t)o $1$� w!C|${\x}a �closed y val�6beRzC� he other>Fas wellon both hP 5fiv:� �(. Next, le�  � A�,a�X orA\A1,%�%I/%�bea ( "�F ,) - (.psG ) & = &��m\fs_{! cS�4\left( W[ \bar f\eta ] - +} -_ -}a�ght) \nn�s\langle2�,y�eta) \r$ -�0 �Q�5} \\�� 2\ri}�"�B,,�)�@f�^{:P ;�d.;�Eno� \eeaq�(\cdot,i4A�sca\ product��$$L^2(S^1)$A� Z!{8 >-iexZD�^2$ŝ mula�yA.a���be"� by� � axg�u�ci�[ity��N� =M|6�]��F�- ba:<��q2<�0] \, %wQ>6}%y "�valid�!-�ofH�re�odes $�k��$ �Za�ult of $�2�J�= 1$ (�D� ~3).�  foll� ��%)2u�&��\cD$,4x 0 given!�D5}) vans C�(, each termAh�sum(|ely). � mean~ � aic1L��i� _1$Y $M_�>4&5 To demo��atE WJq ne, ienougn = P � ��.of2 ����5K���� ��\in!f�� &�A $enowC�two��psi�2o��Sa)� � &S�:�N) � N2�D an orthonormal ba!in�ibf [by5 3}), S��p� p6p then� z Bz]��!�F' !�e��2��� . If�t�X_k,.E��NZ'  j2E� b%_k���'=912)]ϑ�7��is�!H $k�2 , 2$�n_��> =e� :(jI 3[7��>_1~�N3 +rT2�T2B�]� �rd��-��N�b[�nn� :�Yi`nQy >3Bw6!1wE1RT �I5!+6<2� 8I�a����, ��(ad.�RJE��AalJ�f�trep �WoYabove� ��Z ctuaa m6s�tSq!���"`�36 �ars�Zs��>s �Richt,K4 "�}���!d� � iv .T�!�mariz~!h��FD�D� �JD&es:�-  Rec�>��J`�d'DZ"t "� isol%� ;��h"� �Tof finite multiplicity1�9%2Ji!�lle!`es9� l '. (&�<~��always.�gK!�Z�all.9�N�.)l��2Ezg�vF�!�samr�2X*�t-`>['1vus���b sig�(unambiguousA�i��!� m�R + 0e.g. XIII.6.4afiSDS�A>�"�!�of 67.431 B�.�n�J�a47+ � $(0, )��#os^(unxib >�a " y -�m on c x_0] on $[x_0,5 ftxAz� $x_0>0$�%>oum�)�-��R�is emptyY %� 7.16=U4F#h3^�!^  \>�tendst$+ c�&$r\to ��f*& "� 4�o 6nwFY as Y0$i�7V �to%d)cm%refore B79.�$��&� l%�conclu� f.� %M 6.122� by"q �-c�$dic�e�>�E(0 ���<$(2,2)$. By comb�$ thesW ��f�JI�AVmalV� :�A�(.�is)@�1heA3�Jof its6�ver!.� pure"��aN��"���n��us��oOv�5 ѧNZ��JqM�icle �$N$Q�$:�:�1.5}), �1.7})) iu*�A��(R}_+, dr)$ = eq.~ N ) B#:s�r^{iEN-2}{2}}A�rc 2��rc,2-N ,= -m�\hbar^Cm} Qd d  + Nu $ m\omega^2 + CH8m}(N-2)(N-4)/r^2 +� aA, " 9>0� must!�6m&~#in RH  #!��02�"�vq�by> !!rea�'ng, � AE$N>3$ A-V$ b�/�,IlalZe��$ Z ."! �� *�{RR�)��) k)} ��&��jeBb�dihed� �)e-s�$r� 1-d�'� al r:�+i2p$223j�*�iru\-A12F�| �f��into 6��jugacy W+!�s 67 Fig��<,fig:D�(dnot)in eqsq�3v$--(83�)�*$12= 1 + 2e,2� %"�$� f�(}[ht] \cen�( ng %% D6&0  tU%>� harraystretch}{1.4} %\resizeH\columnwidth}{!}% {��tab) }{|c |'hline $Sco-B} \atop�,�} $\rule[-1.9ex]{0ex}{5.4ex} & $\{e\}$ & $\{R_i P "{\�.Rpi \h�%-.2ex /1ex 3}^{�1}G�;2�;3 \}$\\ 1\chi^{++U& |\null � 12.85pt16"} �2�2�2�2BE-9E 1| -   BC+-5�C ;<�C-JC 5 R YF�(2)��2 �02 A V-2.�tilde{A]}^P^HA O H�q�a�cap9%{Ch[.�CA ��.}�N�� \meda�$1$.� (�.]/ 1'):z0n"�$ mB~rho p}��rho,p�a�\}�!N �by ���zi�2�rhoe $p$� �) refl�%s $R_k !P ,($k=1,2,3$),�2ively.*O +g+%�0~�0�>�R$p=+$v�ed3!~c'�' th�--B-&00�e9Y!f!$26�%>!26��  2is deno� by ��E� b�>W9�2F�i�e tensor� $� ^�%b ' IM:�s~,�MN�o���Z �F2>Fd �remain *~ (�� *� )=0nA'2%� %pS_*�2sV$"U� (ht� !m **� $\cR��_{\pi/3}�.,b<(re $-\jmathM�-��5)�R �.4$E,M� = e� 2�ri}{3}} n�0isA a m3equE)� rel�)a�%�As( \cR�)P = �� >!� $�9jA-B 3 +.@�"+ H5un"�=��R� � six�6oo� unityZ� �-onoY6citv)!�"� $F_A�� CR� We k$J�ex x �'i75�6is I�ly ��dec@ �bfo[mu (\mu_m�$, {m+1} )QQ,any $m\geq 0E�T 5�),w$�  $a[� mu_0R. Co�%%Vlo�-thm� eriv�9%�!f,� ",  2� F_A'� ) } }= �( )\nu +1+�{\ ) -V(->(+>(2-RB(BP (>x.��D.1>�Rememb�0F��(1-z)=�(z)^pi \cot  z"�D.2>^wEb�(z&#Z0inU0?e posi�y�,l semi-axis,+ot{� ]j;6V�]cuCA�� ��6�)!) as &�)nE B�=�)} &= &�!.�%�>�I5]"$\\ �) &+& fVp>MB%1EM>(�o1�~\piA� (A�OE� $:#tj]�"I*1qU!� t�w$�1l< m< 3)2.9�,se�<ifJ�mu > (%uA؅,0]��)2�*"��.����f3E�$�4F��D.�4contrib<8I irstE�lin�[�%�q . R�ri5 l�6$�t"�,2se�"!bR!$_m^0 <\mu.96>�)�is R)e�h \mu$Fy0<.� 2�< .u�) <&VD.7>uthank�v- is� vq0 $F'_��)<l when%�����?)��8!�`Q� branch' ;>RsQ5u�Fa�2�#.l8>�we �=FUE^�1�b�)Q1pi\gamma�E��vartheta�dF�ithF� L: �/ |6ap��^,m+1�*\q�/ g)l  3]�5- 4�[10>(l �c�0D�=.�F�0<�< � < 1�1BgY���D.8�mnd� n�� ��$ %��.5ord�o �' e�(�@�t  >�N>us8 ��<�.dar&9t&+la��oe:F���(p�& q�;int_0^1 �X^{q-1!�DX^{p-1}}{1-X} dX, -�p,q2312>��&} AgM�pi q=G fw-qJv0z P(X)5my�1B�V�?= (1 -!��l) (X^M�u� )X^{!� + (1{ %+}+ m'E� }) (7EM#- <�%D.1BWaz85"nRifyD a['forward� BecaA�"'+D% , $�<0$A��DX<�5,�4%��� ,��:�o�EWB �0Vca isF�2K0}^0=~ .�B=I�7h�]2~ �^~ �� r� L �w#B proc}A�aX.�?E!g�L"� �<�7Q�12�"S"O=4�+wc ^�!�=Ee mu -1) ( M�-�})A� � -\m��} <.1B a�"lehD�proofA(ojA laim!�cer� A_i�?*[ na�;7A)S*�b�6Hthebibliography}{99!�$book} J.F.�. Diej�-Lnd L. Vinet (eds.), �C -Moser-Su@5l+Modelsa= ) 78-87;!�0nt-ph/0202037.�FTC} �0 T. F\"ul\"op� T. Cheon,3OJa p<�A7�!am�D'"h&6FII� A 36�3) 275-2>� 9110.�[<$N. Dunford|(J.T. Schwar!�$Linear Ope�D!� art II: S��T�E(y, Wiley In5K�$e, 1963.s�*} RA 4myer, Principl�A ;cede�ema�G�E Vol. I, S>�197A)Y( eetz} K.  ,a�=@�� nonrviA")� um mU� Nuovo Ci4! o 34aj$64) 690-702v�Bp B. Basu-Mallick, P.K. Ghosh !�K.S. Gup�9I* L �?� t�*aSal q� u4l, !0. Lett. A 311Q087-92; hep-tE� 8132.� Peres} A.as es, q�)�: ConcepHAM�C s, Kluwera�95}�GPKGalindo�$P. Pascualy�u� IIJG 1991eC��Poly1ZMDolychronakos, Non-2��Jz%+�f�Bio!8�)%�9uclq�B32%�(89) 597-6222$ oly2VG�lized S�!A=EQ <DA,sia�Xpp. 415-471 in: Topolog�JAe�%�Low6hal Systems, Les Houches SesUT LXIX, A. Comtet et al�� q%�9; M9902152�Weidmann�  ,B�a'MSMsR�82`Krall!<M.  , BZH�,�-fS,2Ppr���%&�3��$J. Diff. E` s 45a�82) 128-:�4B�N. , S.�?*�,04Schr\"odinger "v'�y:I�]ber�OA J. 3�9�01-409,E�"��reibA���B V.I.  chuk8M.L=LV�> P)9�$��%)eSM,&502�12]Veigy!*D. de , O- e6JX!"��6���)�lm� :,i of da)n�LZ$P6)s,��9603052LGR�Z�2radshteyi�IA] Ryzhik, TPofņ` �eri[�sP8;$s, Fifth E�w, Acade�s��4.@AS} M. AbramowitzP(I.A. Stegunq{ Handj �A ��Fu�?, Dov�A��2f Levi-� , An� �.to:�� (mbridge Uni7 � �� (J:. 11.7b Uk�II Falomir��II!2�b Wipf, Pol� uc� A.F$\zeta$-"�e�J�� ɸ A 35ű42) 5427-5444; Rd 112019E�4> }"doc�EP} ��\ifx\pdfoutput\; ^` % LaTeX, dvips, pstopdf.�L��dfm. \Vw&,[12pt, a4pap!�two-@ K]{aI� } \u;4ckage{color} \Aep{webblue}{rgb}{0,0,0.5} \else�PDF��� pdft'�6} \fi2��F , bm2�[�(links=true,Rk= �, bT6  K6 url:Dpdfstartview=FitBH:Ldftitle={Gauge Trans:��sE�I� �Sc�K� ��\ Medium-Range Magnetic F�E},yPauthor={Wolf Jung}, a��I open ��-ed pdf�� 8=None]{hyperref%+loppy�).yJbas� e*J)1-0etlength{\par%}{3pt]%6�D�nt}{0pt} \topmargin -13mm \texthe� 49m�N�) 150mm \ <parC,sep 4mm \oddA�  4.6=eve. YKo�H$tyle{break�M\�fo(Oitshapa>new {thm}� A}[�,�9#@lem}[thm]{Lemma} .@dfn D��?} ."fT #Pro\on6Fcor # Corollary!j� e�up � 2armk =�K ["wLbe}+"� �#e#��!�!baDna�+*BE$ E">F�Lie %FF$.G�Lr2�$hat}{\wide >�p(  %�Zcheck :K$(}{\emph{(�6g))�.Q�3 }[1] <)-#1}>'$mybox}{\hs� *{\fill}Y,{2mm}@} \DeclareSymbolFA�`AMSb}{U}{msb}{m}{n} %or .�amsA��MBB$Alphabet{\��bb} S �&\C{CK)def\QQRR�'ZZ'NN'div 8op{\rm div}\nol�VsA�Larg2%arg% �tr{AtroRan27Ran27bm� \grad2*V+ curl2+2+��2&& % 'ig6�'6eIIdispl�. yle �e.2Ac>�i} � rm{i!#%\�*�$inodot="10:qps}�*epsiloEZ2�D}{2x:�d�}[2]% 6)\6�>2A&6kH �cal{H�: O OF?SS.�A  bf{A[.BB>9EEB900>9a�ewf{xB9y9��.�ppB9qq>rGG96_uu;6vv=.�zz;q^ {\bs)Z}{\  .om5}{\ i� slimI�� s\!-\!limvA�w>#w#6�loc}{ Nrm{�date{P, Yob ly 14:5.} \� & 8\\Stud.Ref.~at  i�_tminar M\"onchengladbach\\ AbteTDasse 43--45, 41061F/ , GermanyQVHi1} m\ddot\x=e(\E+\ \��$s\B) \ , \&$Ume�VmasI�$&GQ� n)"�|, $\E(\x�.19� ��� ngth $\B.H)d22 . Mod" reci ��=�(0� H�3.Aic fluxc5l� / p/���Oe ��5 scri�g�3erm�[�ocalar p��� Ё�aBM $\A *�EBE=- �$> $\B=� \A$. 6uG�d!� al ft�Us0�4 3� meash=in�'�,c��a�J!Dat| H}=cv%o�ce�4cUsp�# of lN.) Now �# i1})!&*�A to a. M� ��%�@ 56�<2} H(\x,\,\p):=  (<1{2m}\,\Big(\p-e)T)^2+eA_%�>� \p=mI�+ 2�can hal mo�umL:h �hu.�7Q(9 wav*�3�.!�]9�T\R^\nu�C)$. I�Jime evoYTAc}9��2� !h��$\i'B�psi=H$I�2�H1gian $H��C�%i2U%"la�F* \p=-{,nabla_\x\,$.�4z\$�=17e=1 �6�"V�%H�" spin-$0$�Va�^c� BI�hamM�TkuZaFA�[ $1/2$,5I�# n?Q:�u��  i�*bly�M \to�G�SN� 1�G1a.� �/tu�m�0$H_0:=\p^2/2m]) 2)�XdA�!!�f� ]T(�) by \$)�t�pm�1fE�1]s�f:M3} �C_A,Ay:=�Y_{2V(} \e{\i Hta�e{- _0psi \ .�us ��3ei@E�Lasympto�� 6n e �� &$>�II�+ � �:- ,  g�<�<� .C1 $S:= _+^* -� mappAincomE���outgo: i>� A�S d>�.վ' <*up!aW?e . Un�-he� } "� d'=\A+ńgRS.< �<modifBgbut�(&�=�{ ) i&�J�to0!� :H .% (�L, 1 �6T*;)�aYA$ does� i�� blyZ 6:��r-"nPexist)�:�.P%/be �wed 9�all�&O/ long 96� �Cby %d�g!�J� . Lo� TSer �Mltn�}*O showk ah;�kYK:��D%st� %-��zUE9��$\xp[ &=�2 and �<=\O(|�0(1/2+\delta)}nKI�:{�$( C)fis.�,AkA�A npE E� lly 9X�Y?effq�6Ks�R�-\ G]$�. $ 6:�"$\A �=\G I L}WA� IS0p L}=sp�� % ach I]W%�)>���f�G�J�y� �t� be A��@`.f'':�.�5pon*fTu)����Xgo�%to!��^��[c6e%�it��o eQ>�llle�f$\ W�o��r. ---��ai� a�[entI)"[2-ize��  A" - e:E�BEY` ider)ls8 ��} F3>�A&M $W =Y�lS'[lQe7j tempiL"�8�z���")�$-Vs a)) G .k32kh� Owo96��@Q�e\�la��r�#of �I�3!Q(Ada�Id:�7��**M�]i"�&�s�:ubstit(&�d J]�7I&� $\A'OM�EW, w�Us1�l%�-�� x=�(�ɚ observe)d a&�xex":� )26[ u9!��Qsol�nby )�a�! :�!�$��!b�B3wa�^ne� {I6 ar1}��.� [�$r low ]�*y��by"� Rnfo Rm�tM�.�.)Z�nnd� low-{�H %�i�1W�!.�.� ��.�W��add&0Bo)wjm2}, 1�techniqub. )ltr), wjdAk ab},*@l��g obstac�&&�A�!�A�H nov--Bohm�j�e6B��v��O�4a�d���(aAI2*\R^3$�4���}FC���-� :UagR)A�l2�of L! )��" Y�*� J�Kato-tg%�" � H_0=b1�p^_!+i�S satisf��!; Enss�|)2�vs�`~8� �\| \, �$\,(H_0+\i)�,F] \ge r) ,\| \,dr \,<\�V> F(\dots)�Wnotes :��� y�*c9{�B indi1zd�+ionm�&\� -dtig_0 ^2\,1%3�s as  ^{�5�Qmu>T6�tB.^�5'~$$\nu':=\nu>-1)��n a sI�!�*y5H%D}Cu�:] \�`Dd} $�C�a:��.�3E�6p �2$,K6iiL^p+)X8a $p>\nu &Uщ)0I�i.q!=�$|s|\le C� �6j!^3/i� nx%�}J R ^~i�ťals�m quir<bdiv\B=_F $�. $2$a�N/ !$\ni� e�>��@}, I'�\ontinuuarQlE9- Z�some �.�di��e� "� ��t! � x/!< �\�*� � m�i2�supe�{ \,| � S|T\un"e�$xi�q�}N�F�&A� *.n� -\x_0?o )O��{ 6QG�Ie�vmfa�5 of Banach&~�}f.~Cor.~� CB}�B�K)%EmI:�wa#�^pU�p<2;1��Z!�:� �jm#�F� e�A rto� Y-nN*"�. UPI/ an inQ_�{ong�enoid�;���w;XA�m�A�!vM so Q's cr��) ���C.}FIu $e�A�h*Bu l�\2� aEI1)b� (I��Z*�� QED,�M1= $\pI�ha p)=0$.)Ej �.>� F��BJlz�� �!�9�I�x��&d��� �VSecM�v�}, motiv^Z rg1}�A�+[V{ Po�3�BTg�B�DN B�s��Iurld e7�qEå�� $C^1&�00m mbdaA��|�fJ� . �o�1A�homogen�s &� \LU�-�^i�}�:t(r(g is.�$#!�neq\0�<%%!��6���.,a�G ��t.���2"�$8>.�li� uŜAr%"A����r�� ^{-�E-1�ȅ�R)�) 3/21H�@=Y�S%�2�eS �&�"��!�{_:iӂ$3$. SHF���#� !w stro6���9%M�U�T�je2�F�NEtoo�Il%�St@7e�$�1�n�@� s�s�� ��FB$?omal�� �Gy plane >n-:�BE� &�$r  8r$\Phig$%�W[i�e_S:_=�6_��Phi�� $4���>�$a�c��؃�7i@~ ��0$\A=\A^s+\A^r�(�v� y<�A^s��=%�d]�$ Sis�b Ou0�G$# � (ial_i\A_k^r�lF� �K, v#� ���nE�� <��� � I�!�>�i�Q3i�E�are"�z�^l1�A)W He�l>�a�� B$. JBHs!6X�p$ as a�a"u����D'� MW9$E�?thq �X�Urkh�� �F�i:]Ma�!� adap��z"laor�ia��6P>O , if�n� %� suff2dtl��'k 6ka�u)�B�U s:  *�2 Adva�z��;e�# G("3Rac} �b �}�uBI&� E��oC#*��7 : 1��;\le��6�>K|�2o ��]i�!�w� �s.E"U Eqf 2�iB|��dV��%B{��a��T%��&)��= I� ,{\R^2}\B\,dxi�"�P2&Bu)!&5"��aP�  <* "G"�J%��*� Y pr�P��JPb"�H tr� �-j Z��d 7Feo� B6B��ix*�A!Aeѭ�a� &4*@!��~3!�Y�Ga�#J����"���u7�isi&��k�2���K� a &�JZs �reEn �i��� ul�xgts})���� % [�� 6�:, A&� ,"�:&n/��The���*�`��X}.<F�����k2$BU7^� ��.T .�^�.2�'�i@ vs})� �S2a/�:�$$H� :N *�"��. %��!ρLwJ.KG� aICi!�)�\B�! �&� �#f� .� Thm.~n8�I�dKE��&a��;��$'�O�3G$S'$�,: �R�Y��afn�*�PuXx +A�*�$' \,=\��$*j"g�\+�$53 pm\p%q�J S I�$&#,SB?- =�"C���]A�"D s�9a�$\u=u\�4e ESD )IJ�r`�_2�6l(]��;�T ! 3$"P&�"s�&he�g5_{u�%b)Uu��5(\i-�x"3i�F�%}")-6~\A (\x+  t) 1tT=-t�}r2K0""��8a+ph� this.��3�?0\(�abe 7=E����uWoer��.\)�%:i݇, erroryuiu"�1 �ځ1�)��q�subrec}.9�� Item~1���� rab!G � em~2h":�P/X4 5%&5F5of ��We�& i ew2}]� � ar1, ard�AZ��� �� E�i ���Bact,;or� "�s"� �����pin �er6�exJ#vF� � �n &�-">R }�EC . Anݐ��q�6� %E disc�4�C�2�!�>�q }�i�>o$ 4: o�ng A�( .�nab, ry yhs}&�Z< Isozaki--Kitada(�(p2�ik9R2� �I�!ce"�Rg}& e'dom��wo0�it:�!ay�~]cven]))� to 6 yc!R� f)� 8"2%�J ^be in�= ificҎ��*�!pp�A%!D. Cf.6�gi)��s�(e�X�Bm!!��7Blp1o�!s�! teps:�2by5#lo� �Bn�&i ��Ka� #.<2NQ 48X(Tg}i5"� -B#]n5,rb!�y m��e7" � ��u����0v���:nyM� �� ��>$�r#� pri�O6Aq �'����� ��;u�p&c8�'!�&�tr� l~ j^!�)"McoM�c.4� >mu=���C��"G�E�is]bsL�t plac �2� ��"� ��-o pl��%�%�:�.�2�>��%M� &p!�/d��2��i_C&�c}!��ard9# ip, �&b2��Y,�^9 ku_g�ǞN�!U�>�.�.�!�H6#��iG~  rmk};lis!)A� rgan�Oa���q: �"�4u8�0in*�Sa��!P!B���2�:Sx}� ~*�ed��IZ3&� )�m���:�3.�S-�2%%9�Sgo}. E�$>> !<� Bail"�d� Y�e��ed qriohe2�lpD� rea isdndo Lled\'o, Olaf Post, Ch�$an Sim!e, Bernd 5/,�U ardo� )D!�$rij Yafaev'd inspiQKmio <j���l"�:^K�5b 6$Sg} To!v�+6>���ye�x $ T+֠Kz"�� 3$ low &�(.�:"t�Iqȥ%� y. S;��J �5 钁G r Sobolev�s &��g��$E)�<.!�I�dr}ala�37`teB �E,�$manifolds '_ZQ�exe}j[3f����e"� em�!+a�g����2��f�S �)�:�|2(#�3�P$\v=(v_1\,,\,v_2)^\tr�hrh9arrg9"*0($T$wF00 &w ,:�a "x0v�b@x_1v_2 - x_2v_1 &�&���&\@ -4�CW wW(x_2w} -x_1 �B\ +M 29\�aW[-�A� 6�!� A]% R(D;  subga&�$\V�&~�/"� �SD�E��Dd}. A�=%MA=\ '�!��(intS2)phi�:'� $ in\S(2>:R)$ o�s+3^3�1�*�6o] 5�!iiZ5� , c-�/ moll R$�Hi��Nty %`��D�n5iers �bdiG �T� a���JvI-weD8 test"D"�d�N!Al2"6�"�$ Poincar\'�'���� 1�)s�b"lintaE mbd�" ]<�pd&�4s\x)\,dsM�e�c.w�;!�!2aBtm� $�6��"�e� n &&�t�\nu2�\,C��&a��A&4 \\[1mm] &=& 6H�a�x @A �rUsFYK{\�)X S!PA�}j c��((ps/<�Big� t;-�^� Nd p,�secintla�%>�+s+1 6M6��vn�0��tM ver� a��5a} �(b c}) =a} � ?c}) b} %$.6:(b(c}$. *�?nt)���"��b`v#&2�S �T&�2(s�E�' ,�� $\y=s\x\&�5g)� sU�Z�>�\yM�=�s�-nu})�y/s��+ -1}\y)5%�w> phi((FQHy]D=&6�n�[s^�i�XP]_{s=0+}^1\,dy \;=\;�W ���/�+QR�9&A=.�:%^�'�Mwe�3��G C^1$�4 ��2-P�#�߭9$9 wise.V%2��R� path-�Jp�2nt.�A�1!�e "�x�@ �=^@�k lim_6"�sr�stA,dt�sf����N |\x|m=�-��*>� verg� ! u' rm�N=$O-Rtu!�G&�"R �!set™\{\0\av(�(5 $0$-* )D & "L,R $\xe�unl1�:#� tanRC�%�2�)X -4  #D-�$�bX$�.d "�8A8!r!1&u 9�AE& �h E6z# :��G ,=o�(1}b see,CA� [�V ~2.12]{wj�")Kof 2!�T. �T6���V I]�jRAL�b%yiO� Ɂ���>U:*�#Omega_ t���ps1\g6#� ! a��2p( 8�2�)� (A�  A_i"� k�-Aa�h2� N0"�  C"hw m7D�'�E~starlik!)Qh, IA�: 4A R$��� ) a�:t�)�o_ �Hl*��$L��d=A�L) L)w�*�#�im̡cR�Bw&!piece��Q�&!�M�*�L$exist glob>����q ��  iN)9�� v � -�v!�B�>� v/veZA"v pc�jC>inQI1-�Ly)�!�!*(ed!�� _B� | i�${siso, gb}("N9/�� !��68 Helmholtz-Weyl �=�ko= �4%�6�p>1�)t>is imManB�.g�An5id&Pfo�.{a�� a�al7 � tg&� C" 3E��!"�%�b+. �*�I>� �J ��� "2���0to�|i�dea~�� 2N� tg} ��d&�@A�� s\B� \, *� �}[B\�YP^Z�J7�O3 B�e&#@�(�!$2�E�muw6.B��Bs�V�,�1hby2�#tg�#��Q@>���en $1.$a�:� &f3!:�� �x(��F$ \log!���m(',]N0&30Z 0 "� \x��F3�8��:]@.2.$�M&Z1��!��  7�*\�3���,� ��Em��&1?�E� *�!A8�>�5 o en�L-�>�. (�2�!l)N$X�lC-CS"�| $c|\7�11-�D�(a jump*� ��!�o>xK or surfac�(a ?a-M^?z th�0!]ori�`i "J� ed.)�*��!-� "n� 'l�=RA� �+<2$�%��iteq #\mu�*� To achiev�g �u e��=� �o 7g�*�D����%yN����7NfERJNAK�U \textbf�`of}: 1.��i#b(rm4 sup_� =r} �:T8$r\ge0� en 1��rsmui3 ��$$8 $�9_0a�z=� 0^m} r\,�x=$%�s%�desired N s (�)!�sharp�H2*�Q$z3e� Dst&t=6 &�.q�� P �J.Q��< 8��B"\intba�+ O%(Q�0Vi�\*�ŽV3RTb���� ��h~�6�j.�Jj��6l�_+p�"P%!� �FS an sfH �H&��  b}) ����c:4d~4;b J:�8 Y:Fd�w+::c�I�i3l* !�%�>a"�.��B���)��l =j)�"}�`�>$Y�&�=�^yII�'2*� ;3}(>8-�a.�^9�NB�AoM�.�E}J]�+K =A>*"In "�u��0& 3�;-g!�a�) �)lR�2yrU�,IE�gQ 6U9�J �,-�y%/ N6�,e-K intgtnu2}B]2}V!�[ �Vo3d�A�c� !JS'C�9�o9I2=vJy��!�[co9� B(r\cos�gt r\sin )=(1+r�C�b f( 0 ere $f^ �+�Nt�@� � �$� .2$\6y vAA$q � $�1�wMP&+4�a .bI �vytor�#:�!*(r^\mu 1 �?� �C!c��[%�� . \+*�?�B�is"(>d,��� �M� �<)�>\ g"' �J�*�BA�S";Y&=3� pz ��$�-�673R5\Bi:�A�a�al,8h -F�%ߡ��A]b 1  a�*3 �*T<>m!�{ i9eq�,dxF~ � � BiJ�b3��>m) Z�.g ] O6 &$(dom��-��;Fa4 E� s if��6����� m phi�-E5&^�D�>'W-&u+-���. Őn*��aaR�Q(")9.arE�Er�`-Z* he�1"nY&:/�gr1�E�� �Dm h(\z�J=z)� H+(1-s)��z^9R1�1�gr h_t\y))\,t�-2}(t-1~y ~��H t�& Ik� ) looks l,�  U���Bx DI�� is�( vereջJ�G $)toJ!(Iǔat v2averaged!�A* radi�simeq%K.�S�8 rinkpto�Z.�s\to1@��!$\y�.�!`)d1tur�`�W�$"� kern"���(te*~\i�aa�S.k*E�i�%!S Or?=�z�&og��!�f�ޡy!���C��io;�A�UN ds$ �1r�,�DI�0^1dsPH�x~al .�=)�"E�6sD5�,q� �� ��F�S2oQ�@��!�f�`i�"oKN&=G"q* g�X back!P(Bogovskij's�2�RAW( v=f$ /bogo, bs-I2k a� ed-������O"l  ��v_k�qle��f,$�  $.*j�.�  (.�)� �42�BZla?_-@"� "� J}[]b��. ��ix �Z"DEy�:<�.;`F&; )�7"��V���e�:2��+��"�+&�1n�F/Z��VH?�i �"� A��E%���4�9��\N�AA> 2> \nu�� � �DJ� Bur \.S d  9.)�v��E�R�C���AB�&�<'II(q:=1/(1-1/p ��� $R>�k�X��� $|\z|hRR�Z c(1+|\x|�� 4m!4. By H\"older'![�ity��(�0:gr3�� |�* ~ +R)I;|h\|_q0XYO1 s� �*|��(�le R)��*6Ƭn "K1,� i�Y���>�� R$ av%u�le2R$��H��tS�0le\|\z\mapsto�� |_p=^�nu/p}�� thu�e �%!3R9*P� d� s:T% ee��WI.�g�aHe $s$-�a�"��!� split: lvne&�wF enumtalph{ )}hwnumerat�s6fdisplot0!�s!/f��2R}p +R}$&1-s\ge1/S-!�g=l3E�=H=:cu-$. bzBq�1zas\5�} $Bsa��I+�B c_2(1++%�mum$�39.}�'�J���3BV� $5`��=  ayis��&$ ".�T��malɤ"�Uŝ�H�HZ6�� Av� �� �+ {gr4�@,��] i�_\x�(�@-k��*z:�-*+~�5~��y+(�>�mx2k ����u6�u0mm�an)�!)͊\xɋY0is.1 J�.e.~$s���$,1��T :�� d��Eg"�iI�s�"z*->-��$�9�I8r=� A-�!� *��0&-!�2�z+(\yA*.-3}( OU8-�.3PA��!�f]�J�M 2>h2vm-dz.v="It���\an R�� . *�Iq$_f�=xAe�A����i�)�8�D�Lf�� .�:A�l� r��-}^�- �z�  "� ��=!Gx)-`�n( M�,�)�eG-�<llF� :��1ui,\,k� nL+� wnB@ �tildeC"�*���=f#�8� 5>��t�*�\�q"�4 c��Qg �7.�"*�4�V 8�\co� �?4A$:-�O�~,Xa�?al<@ueh4P�%s��6}�3%�� K�p���1���\mbs�"� =z)� -\z�eQb�a�x-t��:P�_v/�pO4frac\z{�\nu+1}}]}� d�T� r.@} )\,r+ 2}(r-X zr&���U"Y!�"�9' .�tG �z�0��� ,dr �O�(� �� ��1e�Ca�(\'on--Zygmuo<eɅ � cz}, �D rg1�,� A�� 8BQ_��ѷ6� vP-�1 %#"Y8} \| �Y nu}.�\21mc!�$A�Bx0W a8~&.� &$>2�$ܵgr��v ��a&`&\� � ��i".-*a�V*` � 2�>S'$q�� � a.e.. I�c1 if~6��{Yi^�si 2�e�|4'�,".r (s&� �ss)6,')ga֐�. ��"NZ%O:�/ ;e �z �!��L�% 6��*�&�RD� � �!K��*�Y:E4�B`S�L&�TCB=l,�E� �(8��yrmE� �{R,p,� :=!\�x�� 5�|� x|q � �&��CHe�d�NB E%cal{M}�AZe2�`�$�~�]��nornAm+A�� �"�+?SvIrs!E._� _2EyF��3s6�s���B�Yk*o�C�~��a�m��+YF� �0"!�F���NB�C^0� E; � �AG6�={�Co!�}( �� � -=&��i�*4*d*..Jcoco} :��T1+�_�5��� �\t�{��-\y ,.�N�'� ,` ee ��$_2:=|S^1|=ԭY a 32|=4\pi$+b�f[�% &�C&$1^�%�Q�INE` ediu�E��ab�"a}�Hu��&�\%�B|�r1byb��%���]� 2� qh&�^� �F��%�Q.$�7I QW>g&e 3$ɯr9%.�4� �7��4A� *�: $U�� �p4 $3 �B�Y�aA$2�n�� >!R���9.B�V��G%'doZ�u�[�A*�5b�� M���%e � u7 Y� o�Y"�I iabix��P/te\NT alI�, ڏ��G(jI��c�&�/ u� E- �v�#�flux)� �_&�\= 2M$. sIp��/ ww},V%�|g.dD�DI.in :�s�� O6 �No&4Riesz�?*�\x� J�dLrp��D in\N��0<  %beta<�g $ +x9Te��0�n�A��+$��[� f�A ,*\,i��JTC_{ &�;��55 F( ! �̭�U� \end�Aq�aorqBa�Be�X�7T*�gZ%[p(�6]{he�61��ɑ�fPC#1ey2�Z c)Y� l �i�w��8�f�!�.� A�s%H�, � T"XIF| (��&�)Y"3 "�L verc�kbybz ��O6.4=/���}�C~funda%�l2&!Lar'ian�Q$�� bf{U�T $-\D�xT !�9h��YY R� 3^Durier�A]s��� iNKi!��\pih"hi B(\�p^2A=S�7 ,�Li��� � N>kVu)-3$|����+6� }p� |j|$| � ��.� \|2�&�2A� � $p_1<�'p��,^ �Xp_2�V�!�j� � cz, "�� *�"V�"V�=�C2 C.��uasu5�g38"pli!mB=\b� 1)}+ 2)}s&�1)���Ycom.�V,�a�� 4^{8�+�H!"a��:�n�p2)} !� ?7�{�� �iin��(U oi)}k�6% d). �T�+\A�� 2�;.��%8 �H�`��)n\ |�fdivid��p+�3��iA�y1 �*� 2� si�6$38� -2}:$! q'in�6p(1�i%�4 �%D?&y���@KJ�Oi%��s&;*f jL��i3�{nuڔa�x޹� 1{m ��2}\� l�(_ aH�}{c} -x��1L � մ_[.[&�,+� "��V  � сo"c�فdeA�osE=mN�R \[ - �>� 2} � � � |^U*+-{("0C*(\� )-�y) @1�Ija.\, � |\y| B�"qS) \] W�pp���?�U�a��,A��58. Ad�s�\�p�.4^A��*Aii�vE��]J` �\ lea"Rt��")E_)I��{=6�g�)*qc]11�N&!0ei�`\,14=0c)S���� !^�9"t��"~�g,��k6�s_� . �eŝ.4��Bc�za?R"�  �& ���ڝ٩<xv��#2=E@>�M|:5<>�$,#�ep���� ?�:q�mpu�-ez �]l'��-c-^2/1�#C!N[��;^܅��1{i� 2+1)�mVk �_(x_1^2�u/I �Q.-1)V��b%or} ��x_32��6�"��(0J�]]�p�Q[�%���=g �A�av"� "n��:g��*o A�u�iJ!�2.�*r� 'i"�a�� A_%�,\,0)=)�{x_1}!%��r .'j+6�,a�.�VJ�V0&)F� o:+"��-las�A)�kFLa Q��s6� a�~1�|� �RTg}&�B55W%vd� �f�^B�#��2���eK�0�F�_ di�BK&e1�6Y* *!ro��on;H sy��icA�UFA[&m� agrees} AEB���_@�e�&&���p"+pt2�K%2�euB�oF�:&o&*'bl�Y�iq%0� ZD{���e>���S^� !h$ !,� C.FJ�s!,;. 1 @� >� � �B0$ Nsi][g natu�kclӒ�3v^)��"~] "D("O �E%�6CgI:���luf� �8ycy� Lipschitz2tin�|%>� >\ep�2$9 �(�>�B���C)�B�"81�[A�^v*�c.w%�%�?!�5nM�Avx.�� )$ �aIk�$�t:�"� .�o  l&^�%:�U1��t)�}|�t\Hh� .�,2wA(��݄A��.$h�cays  B�YM� �7inH tor�8> i#m�.�Qbn%kAM,!f!l%:�� k0!�Fj0D A<6wBD/u4 observe (\ref�{nuts}). Choose a $2\pi$-periodic function $f\in C^2(\R,\,\R)$, such that $f'(\theta)\equiv\Phi/(2\pi)$ for $\theta$ in intervals around $\arg(\pm\bomega)$�$\lambda^2 � with "(\x)\}$ f(\arg\x) |hlarge $|\x|$. Then consider?HA^\bomega:=\A-\grad uD$. \mybox Similar9tru%�@s are found, e.g., in \cite{wab}. If $\B$ has compact support, $\z`$ can be chosen to vanishQDthese sectors for .��R: this is achieved by subtracting a gradient, or by a shifted transversal gauge if �is�tinuous �,ard, wjdip, � \sub�pion[The H\"ormander Decomposi of A]% {�&H$\A$} \label{subd} 4follow�lemma�4a special caseb%~[L!D~3.3]{hlm}, which !%4 standard tool!`Dlong-range scatterd(theory. (Itj8used to improve decayu(derivativesthe.UPpart $A_0^l\,$, where=s+<.) \begin{lem}[bK]1Lh} SAPs�a�Vi)@1(\R^\nu)$ and $Va =\O(a0^{-m_0})$, $\�ial^\ga!UF)1}mG$| $|=1ưith $m_0\ge m_1-1>0$. For $0<\Delta<\min(1,\,!)$!re!Pa d20$V=V_1+V_2$ s�X: $V_1 �$7 short-�poten� �V_1:�m�� $=\max(m_0, � �)>�)0_2 wD\infty$ satisfies F3_2:v m_j'})$ f! 56Hj$, $j\in\N_0\,$. H! !D'=m_0%� $=�+j � �+(j-1) 1� Q$. \endE8 !�8a given medium-I�e�we want�eHobtain a correspondA� 4e< $\A=\A^s+\A^r$,9�a�^s%�=���rt�^!� (.5,I�\div\A:).e�.K�� does not )�y our r�Xrements because it need-�ddifferE9ble |(the Coulomb _ is weakly:0� sAa�c!7��n � , but its� itudinal� �)�$integrablye@ T$Griesinger �, I do�know how!�control� Mof ��. � \ref�2�lno% �1� ^c$ accorE� to (%" coco I�mu>2$,a3may take:s+@�]a0:=\0$, except�V!�ѕ$\nu=2m�8\int\B\,dx\neq0��e%da6equ >$first termP �� B�uA��$ assume %t��Fe� $3/2<\mu<�8or $\mu=3/2+3\d��y ��<1/6$.%ce�A�8!:aD NtyE!Bc:� 1/2- q})$. "� f"� \et I��. %[0 E9<1%�1��x|%�!�2Q2��^c�{(0)}� �(\,$: \ba\A |4 &=& -\frac1{\l _\nu}\,A _{� }(1-�4(\x-\y))\, \d5{ }{||^{\,ABtimes\,!�Ly)\,dy \ , \\[2mm] � ��v� 2���� \,R� . \ea Now%�%*E!��%h$��> �Ih%j �=&�:"� .U� �$by convolu����� _i A ]H_k=\sum K_{ikl}*B_la��  $ :�!�a sI7:�25:}�u7Y|\le c��^{-(\nu-i_)}M�\x<� $. Spli�B=\B^{(1A� 2)}:�1Fha� m.� A�$|$2)� �' �3}�� e estimatNG:%A2 �!-isued from .�rp}. A2A& on} ed !vqd$ plus�8F(� \curlUf��ut�e�(��l j� 2�h}�7� =1�',� 1�:-�u ,)$$ yields aJfI��k%�YF�%�is>`F� A_k^{E:�| !�%4.� a m_1� N�m_2'=�$. a�definA)A�3��.E��c-� �t� W  co��I:� � �O- � 6r o��!#hj� C�>� il s+\B��,�^s=Q^���S'%� $*%q$��$C-օbich2  V ,r=0$. We havaB^r:�:canzy�B_kB32\ D%�ak�as�FJBE be%jng> �$,<�rF� c:���m!�� B2/��tg}) uZ i7 l�$ an analog���*���J1*da: ed.Ѷ� � q�}desired� A�t�  =%� A^r- %�6� s� p \U${InversionA�X-Ray TX forms"'Sx} From�$asymptotic��.�operat�SA�e willV �la�5\i9$ a!�0 all straight)� $͕ , upA adR a&� � g �$s!S^{��1}: e�x1} a( )� x):=�-�}mGq V (\cdot\A(\x+ 8 t t \�e"aprop}[r\"fPx&f�A)an un Bof�� B��ŝ![1�l \emph{I�x1})}X���!l2� a�Z:, ^{$f1C)��n $1  distrib  $\B:��j��is de� i�uniqu� $2$. Asi ��!�%�t )% magnetJ��=E�8. On a.e.~plane�< X-ray��A�4A�nVl cQ nent�i&R R6X0!X��w"%� U�G strod�9 p�s o!��1gdue to c{ jde}%⍚S regularit2X�2�V:itd, n?>4: 1. %�!:�phi\maps&X \Ai $,dx$. G $ in\S.? e� �y�!�aQ�%�A�psia���2E��)a�y�3} �(z) = 2i؉I}"� \y\,\y �psi(\z   nu+1}~ � n ,e By FourierYDa!�A^isa!�-valANto �i\p� hat!(\p)=c� \,� $1{|\p|^3}\� Big(2 2� p)-\p\,\p �J /) \eesome $]>�!�f"�so� !�%m\1m�1an .b &:=& \i W^{-1}��,�h� \nonumb \;=\;:6?]�,V# � !\[1mm] %�x��'6h�� 4} �us� 1)y+ Y-\u��u��an To��%8i�a�ert�o� psi 4 d 1)}=f7+f�*� $f_1$N9 ��f:(� h)�={_1+Fqx4}). I��by(� ree %�� w�Nie�� of e�>�U.-kernel=$&N!t+2) t�in $L^�* refo�ya� � s* $:�V� �iJ�$��^����t depe�����x  \�gi��>C\, 3 }e�xAUx= M�:^ ��r�   �B_\,�ee��e"F��y0anceled, sinc� e�si(0)K%s�}.�ˡ�/ &� po��ate�y= � t� dy=|�P -1}d��$�  !Za - "� � �h �l\, g 6�2��I.y)k.x>! �� =\,�kzFhN�g \,dz �2��z)I�(,dzby� x3})m|�:�B>� �be� mput� , 2. Fix unit��!�I�B tilde a�5�$��  C^�m6��A��29�z}{ ��E�B[ �)A � .� u*� A� =-a>L(2:�� `-�B �b�]e (���Stokes'corem,��$�v(\nabl�A)=�.� �%)� A)-- � 'FAA)$.) T��A?FG � J@ n0� �12`Ł �� �ed��every � � to $jBU natural+notXd,C�>Jc� )���e left h��!�W 2}) )�:�!!�� �j�;arR_uF" h�t���L^p��:� �en �(remains tru3"r � B� u� R� p1�6��n$Q3P �=(�j0)^\tr-6�=( ,\$: Vm�R� A_2(St,\,x_3q�a}t_B�.b:.m�0^�J7B_3(v,\7a� \,dv") Ie$u� almostx_3X!a��E a��� (+pprox�A� argu2� Fubini�Vi bothEidwell-�d CA_r$hU�^PZ,A�$ua!�E�may�,rewritten as-�!#x0}>�e$�*\,:� �@�@i tI pee�"6��$ deno�a[�sal*�!#exist�$m\x*�%љre9 �%R%~>�.w  �he, ew2�$e}.q ��F�!�^y on6 �:"b rmk}[Trac���2 P�] %-�R2]B:\R^3JR^3�k �D�q*1�J jumpQ���.�toJ%urfac�Id��B=0�m7 | atv$� "�d�Ci�$p>��6� ifX+$kin<�&e"�� i{�eaHtri�'���I�B$�%�K%�1�ŰI�$�'$L_\locG%2)$�� ). (This2qe� Ia!v&cD\S'%�(��employIa� &� .)�#AP *'D�! Proble+S&�&T�&"d Sgo}�>�$�#�:"Enonrel�&istic *('p |� z�!o`)Z$)����*�!h6[�&E({�I|xof Hamiltonians} Our Hilbert spa[i� H=L)�\n��\C%a�Schr\"o�er��,�F:!�e5<Pauli4. I+ !�!� e (maA{e�sigma_*\C^{2A 2}$%Z)�ed��th}/ free k  e"� is genera��by�(. $H_0=_ 2m}5=p p^�I�(,self-adjointi�do�, $D_{H_0}=W^�! a Sobolev)j�an exter��electro6�.=��i�d!]mally�"�expres�sD! n H ;!�+ ham1!1�,v4[(\p-\A)^2 -\b%{m�] + A_0!�� >C!"-2) p + u2ui��2ng� an D%Us<be �*fm%��I a��urbE�!�orX*�sE�quadraM�, cf.~��rs2, rs1QJ5S64���?�%h e q_�psi%psi) :=.3!:4\|-x1!j\|^2 + ( ,\,(.�2��*:)"s 2+eW- C 6�O�sd Lps.���<[� c*) >'��.&� $A�)Y,cal"�*1� %�*� vs})-��5� $H��q3in�+ $1$:&���qu!.}�Q:J.�)iR mq�A2� $W%�6D:+*�;H$ �&$AI:V'.� ham3� @�,$\A'=\A+2|/!U:W �RA���) $H'����$q_{\A'�n�(�o���'}=\e{\i,� }D_Hh $H'FH\e� .1$�3$.�!7:��A� Wa b90�un���H��^(H.},:M2)M�+s6&Q��% $:�)emX � *#��/�b 2���.N�{>7� I!�!�6  Iu w� M���M�A ��\8-It&1! $|Av�s�z)�$aH_0+\O(\| ��$�a$0a finite $t$-)rv)f ��in q DE e:)2 arvs} � = �/!A^r=V^s�p\�� := .  ��\{9^s 7+\z*\}� �4�}xQgh|"�! C_0^)�7<\nu\setminus\{0\�+&$\eps>0>A�";�. $ "<- m&V1$g!p a.r &d(iёN� resolv�$"<placedM^%>$),-sAd �<�Ped�]an ��e power�1 $|t|���*R;n�/�G ph�;M�2 pag"a�oA$ classic forbiddenioN=th} !AVsp�7is)+� elow�e8s�� �V�-�treT *#, observ2heA�ay�.J$A^sxA%�� �(?u��$s�2�i�7du!�betwe laށ" �V����A��] t roll-�� tech�)!�7lt'}: \ A*.-\x�\Gv �note �L�G x\ p=\Ge/$\mathbf{L}�9! an ) moiumU6'=l�T$$.DCmmu���$� ,5tG�M2!%'a 7he"a Nn $h(t ��\gr��u_�<)���*�9l�a� Bochner<l �sn4>$per RiemanE�_lNu$limitP�  2n�?�* st�#�&��"��ist ��* X*%H� �!��>Ffac�Z&*� �cay�-�bly�it will!ed!(�.&!Mjwjm2}.)Ban  y �&v 1,), a6� �� w"9� <�i ulam% gtpr1�s"-"_ AoY�� $S:=0 +^*\, -���S._S��b&�0%=y o�di�>�. (2 $ w\pm" 5� A*���!Q�+ithou�52�,I��"� ��&f�6Nis �"<Md+al��ulariz%��J  suits=�*i�!a high-�gyI�.)�&4 Gauge "�0_.�{-\A{3re��!"�]%'�O�"� R�s L�D�!=@ r@ n9} r�D���< RF� 2� � claim2� cllam} \sJ� � � l�6�� � pm\pYA-N�2a�ig(C-3"�(H_0+\i)),�)cb8�~ ����zl.�  = D E Moreover$$ ��0-homo*ou� multiph�g"�!$$\pm m/t>0&`-�� 165*.� �+t\p/m) W-\ \x/t1v"� �-�, m\x^2/(2t)}7\p)�\2! \;Au;.b%���f� an �l�  $2� $�{ 0$ p#wis� 2�$< is ves�ZI�)��!i * s,a?BaG:6O2{9ps{1� &E..F"�hVGh�Bv�1A�?/O' \;:=!NN�M't -\M-�b1}AIN6Fq m=eu #a�a�-6� M�BiA�/:�H2��6c"/ A9ian %DV���!K�>*��?y $S�q p)}S>u-�  �"᳥��+��1m%!�:lIrab, tsa� `ycd}. %tss p. 261 La. 3.3~ ��1 � f}) seems�be newA��>O8�A�m�Dirac" ��3�!X *4^$��#A-š)!&�F,� �1))��a?.)n!L�6HA"�7, Completenes>V�6: 6T�2� CV� ��Z, if j``=�� '' y in3J�� c)H�\ to a� B, iu Ran(M�-)=.+)=\H^{c}(H ac $"8.�$$�unita�IC�;ag�F!��alI{ 6�F:� %�!�� #j A_0=�C1!%{wa�1n " Ld elr}MOEns�!om2 method��M�sh�7h!�o �F���E*t ]JO s �.�AO�Js� I +checkL�tails. IZ;"�.� B�,6�arr� ��ZN�}�}):�� �]\pm')2M�!:#�(F�H^M,EDE7'WD8��e,su8��4ͺ�/B~*�B(2�?E3>�Ar�$ ardip}q@��mQ� . He8of0"s a[i_cutof_%Ɓ��9s) UM&� a F>+7.:eMod�">�`subik}�a&��5 �2mG:��[l� g� �1)r�?Wem"!a�� them��2d"� s:� s�w $ g=a�!��#l %,Y!e쁴!�pL�� \A^l6�?MH]�A}���8(%�p/ �!*�B� Doll�N67 �A eGC a&6-5�%rc�F.�~�5��"it could��don�!TEK! "�1omd.> ^D:=R�� *U^D(t)8q\ texp�\��=�.0^t<9A^l(s� ds-}�� �6*� ^D�^ ,`�\J�fc�cS�%�$.AI�.d�� vanishing)��'-inV�D of Isozaki--Kitad�Pb��n�ryyhs}. WAwq��l*� $J! $�Q 7 omj2�JZ�"Q!�P![5�-�%�  \,:$\i\q\x} �< u�^\qa$%�S smooLPq�O�^{y;�e $.?E�L"�/e$ized eigen"��e~incom!�or outgo!� $\q$�S2`� !w5'-Guj}6�&U�/;qxY�*)ac6�@  s)- ?�"5s)\a7i \e`\q=|\q| ;h%j�� a ch�Rof��AN�%!/ 2u"!�R��2FIO�U i2s l ����q *;! �ogtoj}IQ'�:� * 0+0�be XP�3%�� "/! $Q �� �4 . Cf.~SecGQs c� &?FH\Energy Le!�De*/0"�Si*w!AZ.�fh�q{\i\u\x]%*: u=uM��&X�!L!� �m�X�e0o� $\u���� � �l��>ō �=1� G#$Y)d*q &�;[sy�proce[pLu�)��� xed &<9"q2 in SEC�F.%�"�[F�of S]J���S$5�(subhe} Appl8.�1 -% JF9�& 3B0.�)m9MH�-� *R0(\p+\u)�-.!u^2 +$! um!w6�:U!B! mu� "&zIx r�@&1�_93,%0rapidly oscilA9ng �or��n%O?9#th%6�VQ�� �D# �Sl�Ou�Re�-n!M� $t'=ut/m6�1 eb�1U+"7= )tomF !$ :��8�*`�,�#&'��A@Wome� -��Ar�ie%�4*= l2\u:A@[05�� $. E�1's�[�:k��A��-�%~ 9�%i�]H"� )� &&v ����� �$6u+ N! S� _\u � d �A!"{:� +Q��$%'FeWu8p+{\scriptstyle7as)g �%�hI�($�wvelocity"� co*�0!kA=�w� ndMim}� iA8� +\p/�:�$0<}#"->$u_0>"�[ $&$ \hat�#n6&7b��$Su_0 Ups�t���>�! b�!W�!i�u�\u��$"})J�. 2;ex�X��+6�!1�$)--2d fS !8&�WY&@ .� I�),��lyF�� crit-#��!�AQ"Q_%�)=-�![a!6 ]�!a�^r�!!�sf;A"�u�l,#B�!�� 56Y��m&�!�]jR�!$\q"6$1�W5i�Dd� verg �8 em (1b�.-valuedB�!)q@2�i� r$ 9=��� 4{&�-��1~xmn(�)t)Q5i��z\Aw p 6?2_����\Bk�4:V ��N 2T"�@� r�&��O�% ] an"�R%�f&�"��:%-+7 !�� &'sS#� last step!�ver�}1�;"#^l"�E {ar1�3>A�>si�MC$R {��U�� O� �$�Z hes}�[�b��$S 2{"$ �:d"5K" > x@Aj.~� Ie�1 ^%k6+ ��"t��*^*!�.,^*$&}G^0-:. �u^*  �*u):3\,?c>�.z�'$�>L>�%�!ac &N 2�2�!%-4���a�.��<�1���+�!%bq�Z � \,S'\�a��j �"s��Y�a��b2S:�JG C t�H�Jq� ���-Z N 6jw'vx�ea � "�""t)Aj ��� �)$6� :� �w'* -�)�i�4is established��$�5* $. `ierF�, error�*�&in Cor�Ce# sam�?��S.r&�� p � JZ&Es�fi �UsB�$ a m�+� at !: �%eO�Ja g"�interpre,.�<$ew1, eji}:,fa�(� �"� �!rOaa$ 0of radius $mRO?� $.tG"iu=|\u|� 2W#onQ8Cs�sprea@�a��packezJ�7phy�,� !Dle $tth�BgsofM)a�9A_traven �e� �#(simeq m/u$,jJeff\Ave diam�UV wave��creas�( $\  Rt V1� :�R.Y] �B]{F�)}�cui���*24�B,%9�D2%��z4W�/ AG2�'��6P9!1n�_a� e ab#SeM�of>�not ?&|�we�-a_reA'!R�.i^V.�(o.o�V9 "a�B2\pi\i$"?m, Q6�A� in{E�\�))I[+l� T�'ed up��rAon*�&-"U6�A)�is 6-G.� ProplPx���op749#of.�he}��t:�>� �6��� A\_0R�A_02rec�Fn�>E��2)!R�Bs, :�1}u=:;#B$* �-E��n she.kse 2�$a�-���z.*�Ep�,���7Aquite���nI�[)��-��:) ul@A�C��NeYq(by Nicoleau���6u fu�E�l thm}J^%� ()l)"g[Ta*y6�/-�zic*bA J.� ."?3� BGI�ZeIBlI�/ 2<�T���QB),m�r^A�L��*��hE�Mg>_EnA.@I fluxA iis&I i� >h.�F�6��B*4�o`&�G . SeJ�UZL]D `�QV n ,dt�)��*oqԥ��2�-k� q�s3��/ing^br d�D{u}{m&�# ( S-: ac)� \"[ � *��+� � ��T�NftyA  VF>M!&*c�gibN0"�:a1cK_-�r2]�7,6.b2� l.� K_+vRW !.��!�$\��*"�8C *H+�ffM+(\x �e( ��.�a6}a� they*�Qe�8�oni��� ez�/�Q���&�4<romA��B�� 6�l� �("�2�e֡Vsig�,1,&;i{��sEA:.:Y,�aJ8-�*/-AVb&"� �<a�)+�? Fp� \mbox{�~}�� TuB3&:=XI@J��{:�&��%��is mots� �G�"H�Q�:& �?Sag?"��9�4 sJdUQ� �)-6$Q� $6�%�6� ./I}b~ 8� ��.-PaysH|\x�"(\mu-�gv half�U�%tx���=$X in�" it.�Tca<QMCmpb� u�2�s exf;�B76�)�27=u�V4>�b=vUUQ):Z�$4G l�v2w -�|*a3IR�Zqf�n��= 5cn:X.�%*E�E�M�ha�?Q�2� stea�P� it./i�[2`2�*.yAL}\,H\,�UZZDA�.l�q��NG !2�#7 �+*4&a�aO&�ŏ?@r� Nz��a2��M �k!cTi+L ͤ$�oa�a�dBU�Dm2�p>�vTo�]�C� <� �`p\*� , ar�<`K"��P6�9�tes�^k:r��w�e:�A���l\a#. ���+ AK�( ^N&5�-12~L @�wH *W \Ct_J$B��f*\  \{A_� )+K.""~$ �ER�iN~�pa;"�E"� s (o�;BhM}:��%]&�& a6} V��C!�1&�P(kB:��=](�9>  �GB)B�P�\!4&�!. 8.-2M1�I!%m\1a�"Xh� �!A�u}�>misH��|O mmon�or"N1ex�UA�Gb :�?3un?��Y�Y 2�}T��&{$-"�%per�T �6� gralO�F�y��u��$�}��&�"coGg� to 6�pQE;:�,~!Ta})�k6O2�5[GR�2K�BW� A-aa�� m*=IonNd� .� )-. �%M@ a1})B aAZ%�. &�9wuK�e�����)�w to ��ga }&�I�!�� {a��,�}U�2G )�&�=�G��.�- ��� �5��"��2= � 35a}9�S�� a�()�DP%TA��+�*re��# �M|A��!��a� K W�Kin*��@�2"D> two &�4 K s: Fy� Lza���=+�0����si=�D oN>�=(.�_g$�cvEnA�QF�(� `b9 en5�Q$ly orthogo�?�S��tCZE&E- y!�3 . (Use on� Y6�2�]:� � _�%i�rhF�[� 1.8]R_!�q�"�����.�F{M1|H�!.�)�{ � t le�!�sG e�kB|!&�7. Ii�P �&4I�( >*2��&est"`s�! ew2}J/E'ar�(�� �p."�s� }cBp8' origiaE� Cavii� adapA:0mU}!�.�>� .�| I:f2B���/�'&! -�5� / s8eas�T=��afterA��I� ��Ne"�[e6#rf�i*f{$2B-H�Y�� out calcu�o7OJard}, 6%,A� act �+rteunon"�5�� ]a{ll@E� � a fami�Lf)�.�9 o%�e�R��cdKi2�/* c}.2�� jrmbG��1a�#(>aRa.3EU�a���a�� epN/�U�+a}, ex퀡���5,��M>� �� �  valid`>A�A�JwH�2"�a�a�>0$� I�`I � b5P�$J1fixO@w7�1� a )����)�uyk�*7�2��.A!� ay�b3�!5>#f"�%,;};�!� A�HA4iY�1, E�Wqk"zMA�h�.")�u� nd Remark)�Ra}�I 2�"�J��C �S:�-].he}&ecor}[Er #BAsF�Ce} $1.$V#t.���z i�pD)�k .o�#}w�#explicsK���� Z�e � � f�A� w O6�2? |n �B x�� �Z1/u&y $2.$�;y�!ei!n6�uq��?n�B weakY is�li� �hYh�-� C&��% 2K'i�d (\x81/�)5GeS Y� b^ !$�34� R0(�[25�A^ I_%�ChI�eYw�<~ � N�%�I�S &b� /�� v�,la �H"�%pe�{;� OI*� WKX�*+j��M��V� 0 \A&Y(F�+ g4�T1"WF1 40ds t \�6� ,<� ��\,Y7 i1ke OP �+*HQ�mea_Lful�\g :7n} � . fas� than�0� 2}$:�3&�!oan�d"V�J��7S���!���q8 NIdA5�W�e�->$, ��O^\alpha %De{ay1= mu-| |r@n 3/2$. �%�3A5�I"�D\A&�$H=�U �Y .YiX�G toge�^� $S-1�++&�+-"� n!q��� �"�$ �E��ewT&�(+: �N�{ �S6 ��%��. Y=$�9V�Jf>� :1+e�#!�VI�is �,FQ� F!Weq� se�!paper2�eI)�  i=Ti��hz6* &&�)mmF F3 also�]Ase $N$-Emcl.�!k� e�clue-s"( Y*�4 Z�#s. B��Ŭ�U� a^Iaew}�re���+!$i7!!��i�*+E :i�~�} H�I}�&g'{C'!(! sA{�� Sphint} A=b6�*!��9#� Q:L=G &C+is �T �)�ji}@+>�AwEdiscus9 �+�+E?� �c�Jixqua�o�measur�( quanti@{A�J�,� �possibl$ |ALf.*)l";�QI#?ce�)nsubgi�J>v!�f.�apu��"�ahthe:� �m$ (a|by*�%Rrete J4%I flux:IHFK=kAJ��y��ne�).�d e� �4.9DSV�-$K\ot�`=Hvn�nonO�8ar hydrodynamic�#malismI4iswcsr, (Mpt[�7u6�%"�%"�% �%�Q<!�si�anZQMcJa���2"�S����"ޕ gtap�btoJ�B"�A:#psiVN�m"�2��y6��s~�߀ � � '��-\!z e��a�T .) O$G.�. is| =BI�};� BJA:!�5i��r/�ompensw7v bNFZsAF:4��Wey�F)(�4�Ir�$ sed:`q�9wat:local&F-!Iw]."�,�:ej3 /[�0�H�l2INH>4a b$U(1)*�AE,) bmus�� coup��p>�q^ ��g� z:Uz�3der;oA�`16 ��Z�:�&�/�/�I.�G���m��ukl)o��an>� J�ab�) quiv��ce $]gpai�{(\A �mzA .�/ (\A' %'*ff!��5�U�� � e� ). pW1�ce �Q .at !�AKy2�d"*�s %�"$19U:*-km8.�dM $F=F(\p�k dots�g:�0e" KQ� ��R8!�z���/�Ad�e(s"�7ry"$fSTus @ % �3y� $[�(]\��4\� iEc3�T�eF �E@.�0�< i�z��@T��F'. �tff�w� ���}\,V]� ,� 2.2�(O5���(reu"�2aCRu� e~ rule&FRq��9�D�� -f��polynom�1�_\p� Cea�tat�c�K!@�9���.� comb��$};�@xamplee�nonY�&iN�Je�xon�=�CU�[ &f�s6�A_0*mC�r�'��caU�V_�&i-Y �amo8 �s: py�3!� p � kine�/�$ma�\x�k6& �� gy $&�"(%Z)Fa�6�i �.�KxL z  \=&G`-�)See.S�;m2xb3G !�ofBt���� .i��ex��>gI�5� � 6�5�w*�wCross�"A�2 �G ���)w�&j"�as�� figuvGon��z ��hse�:by/Jd@� *� %��B2!>��We����h{@u�'�>��9 systy�aUoH{6**�]�tRo�`���u&1��.�u�6.���B�J it&� 6 ��;G_�2; �2�E?in\*�T+qWv�#VX%n94ccal{C��?+a=9�yabilit�"j cone��i 6�)�;|� x�e�j�/$|���.,U�Cb,:CO0*�"FC�N.�"�R���IX.31]�v}_\"�>+�.rime*�J L�.�h! �, A�U%�"��  �!�:�"d&&|e �e�Xet� $&�I�!x�&$\�_$ (q apex $0$)&�% ne})U, s a �:!L$�E�"P�8c�'� $d\sz/dɇE inciT�u�CqE�"���hi�-^*)3L hQc��K� �ca� &�Eits"!6" &k!�|U( ``$\sqrt{3U(p_1-q%�g� (p_2A� 3)$''� q=(qق�.>�ա��L� R��1��h�  9 entr� Y pX;-Rj��E�q[�i�a���'S' �$� 2�7t -]@ hi qj\&�?*�N29)89=B3F*{r\ &/;facJin=H�["� influe!n�� fi��lS�Xa=�3B�aug* u�� ar�a=\r�JA��-�$a$, ��ay� �"��> �:f"89.�4 a�Jt [L�0"+hCP)+&e[���2QJ�Pn<H* A�P tude2pa}���.��!Xn*!`$2-|}{�5}=��|f_�U��)|� Es2�I!Ms" 3 ��Z�wU"&"�"a����5� $T$-uxQ���+ �A���n � shell.�<b�hF��*"E� !��2� situ� a�Z%� }&�;r�;ko �diab'I![V.%�9B1��n8 usu�_�Q$F��� &�B5{bea`>g� E�+ od�@a���*� ��M��9��Oot avail#%Q/FF �%quG�� �na��f1, �a�E��.��Zy, ��l,�6�} R^t�E�"�&2K8 Ef$fG&�#�8Git��F ,Xbh [�V.6.D�1}E�5re�#$I ksds=�۫�% `�&oQitIg work%IrocE-&�03 a�$. �qi9� �{1�]LHnas&�to�iz�  �XUc mA�precis=�"q\2u�iarlocedQj?B!�~<nms kept �#�M!W.9ao) ��o9�A�va�`whileQ�2Z  (1�n<|5,m=P["\ EN��r-� ; �mA�a��1�^n� 4i�I$V? wo-P$��E2:2} �ywL�2Յ=��&�aB�via a{&F)+$(\x_2-\x_1�their�Dve�9�s&���E��Tl:DE�� Q;i�!"reqmas�E{m_1m_2}+ \�J�ai� �F"Ljusti&�FLifA�i\a�:�\if, sa�-m_2\ll�U)S$@�~+� a molecul �a dipole � �by{'6E!�L2AE�gC� [�oe�A>('te1��#aG?&(B&� A�@!�Y$�"��egvX!�� E�O5Dis1U/f �1\gg !,> �#�as�{m!� �� m-?i-e��>�A.E�heK+en���5B%��7 mm�]2��Y�   vera�3�d:hz4u� �.�_$d%N�) ��ia[lik�> to b�0coѓ29{F�Y%YKK'2�ie/hdG&� �k'�a1�R�W)� be �%�&�`ly�� 9Z�0"Q)!9��.>1���_rt�� �h��C8twoN�  y*}~QoKsub2}A��diqu�g�ox�UIteIA���a\or�PM�of view,"�NE�l�'&5 dQ���sI�efbb�Imai��o��� data�.��&� !"�al �s{��ddress�*b�W�Z eld "$!�tQ� 2�&� ��+E�of���B, �� @,su� &�Ar% �{a�gy. WT�a-priori�'#B�g� T�(�ǥj'i2�&�$A$c "�*"� e!6�0*�+eE@uW %CDi=prv pb�Ύ� ��&k I,"� al�up � C:��I. makes.e�sa�j(�w���y� �+)�E{� 6�ls (�]ve ] ) co�de��?E&%��tha� |he2�!tJ� �a*0tH/AcB�I��J i ��zX6I� @ � ip�"� . Atbzh}�ge��13�:U�w(P2EUe>�-���(cl�!Ա�l� 0��>G-5?*ed��Քef wʒ����.�2Q t"l� Զ!�:Pe��!�:Sa]P5ex�U.is ill-�qd.)�OA$!-c6�6q�suggesnM8 trr}@��i'ݘA�a�2gl"6�< . Or�`�(f��&�GJ��X)8�o $aQJG��m�)�reeK��o"��U5ԅc"�; . It~&F%�RT2toQ)DaA�l�}�H�I ursiv�r�� �%?�m� zL�k�&��a�*. {Z2Hthebibliography}{99yvmЅ \bib�]{�lS.~t2dImph{EinRque�nraumlok�$�ierung im Vollst\"andigkeitsbeweis f\"�0a\-mil\-ton\-q{en mi� Mf�4feld}, Diploma�0sis, RWTH Aac1994..�1}.�G"�RAa�ach!~Jw M7�6�%Eq� �icEOEl" ic P}s,A�J.~Math.~Phys.~{\bf 38}, 2761--2773 (1997)..�d2��0� treuie-CdiF�gleich!��@ �)E�Ph.D.\-G>F<7. Logos, Berlin!Z8=Z\bogo} M.~E.~Bogovskij, SS c �a�/2�g'a�R�-hA��ofa8tinIQaa�ag�(��Sov-], Dokl-^820}, 1094--1098!^ 79);�-6� � 78Akad.~Nauk~SSSR)�24!� 1037H40 H. s} W!rch�+$H.~Sohr, Oɬa'��wop{\rm� }v=gA�$.div}u=f� zero9A�<yII[HokkaidoMaJ-(19}, 67--87�90.�Pcz} A.~P.~Calder\'on, Zygm�On�xuW&m pAm.eI�E�7!#289--309m56). %�9 dc1}aD.~�n,*�_o�]es I:y9#0, % Comm.\ y\ eI\ �12!�93--203�69.�e�sV.~}-, Q�*um. ��&�, 63& �in:m�O�1C$$�S�ral�!ory},aDDemuth et al.~eds.E�B�^y: Adv�x �e[+s)a57}8Basela�2, pp.~�;70. %Šcee�s Yrecht*1)�P ew1}9 R.~W�.,��&1&7 :A�*�,al�3�{i)_ -!�e�'$1e � II::D1s �(J.~Feldman,�8Froese, L.~M.~R/�%> CRM��!{ Lect�%�Ds�EA�4151--162, AMS,9 �(19952%w2Rj"\/al!��� Mc|dWkC al5M&�%�6 �836}, 3902--3921�y:ew3R�U&�!:�WFor]/ee6�^�3{\it N}N?�/:1�fD._��I�2�a�ic!�a�TI.~Knowles ed., 55--66AbtP�al PremiBostonR�4R��Two C�0.g�nv.~P����409--41�96�eslmA New LE9�(��yt�"�).\�Wa�9*4 A.K.~Richter~!(AC�Hnicus Gesellschaft,V�8lenburg-Lindau,a�8�31--48.B6 Bonn)6.ji�W.~Jung,& 6�5q.e �P9k�w���CD MaPhySto Workshop�-�C-.�}AarZ 1999�V4er} G.~Eskin,a?RalA0AM��OE�  :pQé� .� !�a�fe�Lm,�tun`� i�173�t9--224U���gb}�P.~Galdi, An Intr�a z � 2S�4�-SNavier-���at���8��taNr�( Philosophy�Gp A�YD:& rg1}�z&��,�&v2� �rm{rot�����"�:!R�"� ��r}[��.�� $L^q& H^{1,q}_>� Exis#�h Ann.~Univ�68rrara, Sez.~VII�[15--4��Wrg2B�2��6� �E@en*Σ�a�q� rot,%�.~�ō28��245--262E/2� d[� Helgas� ��Group�w*� nalysiMAcademA̩W(Orlando 198. hlm}�P*p�)�5[AoW 0�� inEcc�[I��Z�d4��69--9��76c ikm} I w,  w, "{zg$5E9A%g�(J`wj 6 ac.~Sci.,�v.~Tokyo�R Sect.~I~A)�3� 7� !�8Yi�5H.R�=� ce�kwo-body�S2�3Qs� ,i.~Pap.~Coll?ts �8I�� �5}, 81q � 8:Osi6O�X�of"� �-�tpre�8# 7�witd\ T.~Ito, HYreYrbehavioA�&%  a�"��A3a R1$, Publ.~RI� Kyoto ��N31�M10!�13i�!��O�7ٲiDer"� sche AN3 z zu���&I�.+bei�{ �-G�U6=(F�u��A!!!>!%)#њ��� �hM �83��7.� wjm2�QR�aiƣ�vObsta6/�� M;�R1x�F.�Q(inE4aS, (2002�0] Kostry�Ra�$hrader, De�s/��Y��"%�mO\-> er���A�;--a��,D new"� , Lett65)X�973�992� lssve Lein0� C.~G.~Sim � � �Q�sea%\�PB"QJ3-)�K7�Ka�J81.�ltnpLo@ .~TF��9I![pfs&�! ��s,�L:N �59--18%876�r^�&-.inv�:��Q�@%�J.~� .~q)-�� 22�R36��8.�nww�Neude��4W.~von Wahl, A&,/��u��!& div-x.��� �� :!;dv2�m�6�134��376e.2�@F.~}a, A�ion#U�q2P�X� VpI{uorR�Nuy�%UJ� G"al Zb2�1527--55��72bab}:�nN�e� R51�R��$5223--5237%O2> (#p Pesh�{A  nomu �-�:wE�1)�2E!��͡40}. l � 8.� rs1�Re|B�,o)t �M�?��Moderne�"7tIwFun& �U"� B� San Dieg� 0ݤrs2�� � �oq��s lf-Ae�nes� :� .�75.rs3R���,�6��}F-*� 7.�dr� de Rham� ,Vari\'et\'es�) \'erT�s.a�la)coura�)G)e�brmo�!Her�D~\&~Cie, Paris 1962�yaRPh�0ux, D.~Yafaev"K?U-�1}Uo*�}E�aU�" _ 74a 7492eO2.�r� S.~N~uijsenaa� bEh!B�Rb4��3� 3.~siso}>k"T��.!  Helmholtz�2X�#Neu!���"*o-s�.� �eu�F��G8��Q�a����*"�n���$ �6���World Sc�$x%5 m�$ Co.~Ser.~�vo.~*d i�z11 H1--35�9!�&� stb} E%�SteXijS�,"�%7*,l4ag�T(<of"�;A�P !e�� er4s� 1972��@�>Strocchi~S.~W2&��* charge!HJU:!�l�>�;um �!�ory��6� 1a 2198��74.��$ T.~Takigu�R&;#4�R6v*r�" },� "�8Eng.~Mech., 153�%�2�tss� Ta��Shadow.h by>� !two�"��nn.\ Ins Henri P�!ar\'e�'63IM2�2�3YP tec}��"� "e*` o"ZmIVC��AL*C!6a� q��~� ~H.~�,�1 eor-�4!�1{ 7�:>tsm6����RaMg�� ��� 2mAA �l�� b �!�biology ��*hE nd engine��}� �� P�i�i�U 133}E(1) N$p.~313--32.� th} 2�i���)nZ },&�A4�Heide��g62.� wef}� J�-!an")%Snũ�8al13�44�6��6w�RB�=�AZN-Body Sa:)�zTime-Dm��-u�s-eimrLo No.~40, IIMAS-UNAM! 62 nl. �:�A�N"�E2� �1�B~55>~.�w�9!�:�  ��Q$?�` !�}�i ��ers[mb1� 10!�105� �h&�w�&n On neI� nd suffi��x&�%�!%M+a�u���-� \,u=��=�� u=�~ ilon�:��^ l��ar�0"�V�wI���numer��tK�LNMm�4�52--15�6� yhs}.� 2mb�Z R�#x�=�"�uPtmQ �20� 6--570� 2 Y�.�]�m��x%�"G"4mU�c��K�\�)EOt�.~d��� 4�21�49� %03-28�Q>�$ P3M���$�or � *&�): \h$�Thttp://www.iram.rwth-aB$ .de}~  (W�^�&�U).} %�Rdoco��lsgL*{C2��RC&�B6�9s\3C{0mm}{2�-�;��Npa."��6�5b-vr"�@pu�xcN�&sh9(�H<&� 6��riz�pre�,Ai �t$. \renewco�{\theq�(}{A\arabic{M&etcou{0}JI�mD6?:bm�/{\b,Q}{\ , \def\sign{\3 r#}\nolU� s} \2�4wovec}[2]% {\m�('\array}{c}{#1}\\[0mm]{#2}%� \�S) }{y�W*�Ci>��m�7 ��= ��Xp+\beta 7�H2(aC$�Q�.>l0-s3!�B�k�7�=ary� /�B��]�X. nite�b7�� �_NC*ere $|A�g��W4j�RK�>s<1�-�Ei@w=��3��1I�7m-� A�*Ue(�N� of �))��g���,�+w�3llaBag(Newton-Wign���)"�)��\x)^th*YA�2�&$  F4&A�The&�[�-/�a��� 9�1<E8�$9 ;/�JnyL'�QF5�.�L� _%&J_7��9*e )B�u8v6* 1.} Es:��d�q�!zZ� O ip�oq�.2&��/a >(ao�"�B� za>GF���N mbda���{d��#9U��Jr,o" toa�'[:t��U Omeg�_'S'By obe�<eV��ula^>Qg nfI� �C�m.�I Uv-U*1@#o�Ρ1,e)��SY>u@��[$FV mp\p �e a>\.$-<c \j�b�6S$?q�.�/n6�Ud2.}Y(-)��)� m$C�B2b~a$?�WS*�CD)��7 �A�r*�J2� �$P!<\H#/�?vF� ��VpUZ.pwi72�.��]"hed}\ җuoQ%ZAeEu\5�ҕ.�n=\EY"��A@intFZ_=(UW\mp>��)� ZA{)w "z��F&�hBH��u% �� 6e<� %�"�}�n83�%$ $S_+��"�5r� hol�2"00Klein--Gordon�t.� m� B (page}{A2}% �vSketchxA?d�ӥ�����<�U��8P 6�>�0al�%�Y��s����bit2aB� l���^r?aIM�Z"*�b Z�/H�!( "-\��� ��nw"���ЊRU��\�spd C?�*���!#"�2,}�Pz3 o*8�X $\2 �$\,,\,H_0\}n�%��A����Dj6��0�K*a�.M��-�"G�� ula�3�3ed "�a� .�� .�2U�)� u=xtend�;n� "[Cs: ���B�� ZEUQb� E(im.ِ"l`lyA+" l��/,0�sL� Adm�r�y��S%si�g�Ee� variJB�fs.Z c.Mu�� �V��q5B5q���A��it�<� rst-9s/�]DFoldy--Wouthuysen !es"�<��by:1BDys�'xpa",�J�3\ �� n�% x){\(I p^2+m^2}}�K-1}\|<1Mc�5EL9�%I �)Li 4՝v06n?0�.E4��  n�&�hC"d  5act�8 $K\��etK�a 6P_KN  $L"��"�� K�C"�"sc"�&m�Q�al�%�G "� s��� Xomo.���ɼRͧ5u� Kt}J-i��6�J Anp) proj���)�Ftoj�No6�Ai�$?�#=uaeF�sE "\i�a �8�and W�/ >��I�"�7�:Y �f�!s: ibZc�7UP>� @7xxl -ref ion "b�G$K=-K��s�n%m*��& on $C"�b>?�AH�M0wcDAd�'oB"�� ��H l6F)]�&�% unit�i"�� $(R�:)(1epsi(-\xA�I�o 2W��:0%��Z K�:J��y�n� H_K:2 \p+�+-2<A)`�9 &V�. ii) qd!�! $K=\{\0\}y��FsJ�A�u�P 5Mx$�rperu�D> "3�ImboAj� � )8B_m +\Phi_*N!He���_mG  6��d$ 3in\ރ�IB h��iom� `>yX=\A{A_*s��uh x�] x1$>=����Q E�u�{ �}{L�z �c2}4 �${-x_2}{x_1=Qoju�_*= H)M�i�A�\4 aF�of�J �!xe" "� �e{od��u��.^(\��_* &ay�y��PiTE�6���> 6�lN�_�I.1oq9 bk�}�N&a&��o}��n�wB�!�>�*�K$-�k As`�~�i)} or above�"A���5<s�=��)}� ��[�� .T�B �6�@ } `?)� >�`"�mF8�C]�=��"ZC^\mu)$Y{$� $-"�Quts�>� cyluDp+\R"��$, [ $F(Dl2%)�g�@z�Q\hb o}\w&U*��2�+2� psi\�-~&�y�7dt$YU"�Q-�3.}-�!n *F �Ye�pF�� ��EP��:�Z��VcBN�n2VoAT I�`&�l$K8]�d�ae&f*�K8Hp( �both demof*�i�>iuM4.}T$.r\��� ��c�/)%(P T 6�modulo9�� !+:[N�.I9@:BvhM&#!,Y��B.H"_ � 4\pik��}.*�}�o�-�ssu�|toUw K.�6.$*22�choG �I(�� V�9 hJ�."Y)��%��~@~3A� "�C,cS�Krt�:5� :�B  herOAMe �ii) ems` nd~4_ In$��!86��%; pJ(1����R"dy!E�?Bj�$ n`n�=�~|U�6p�- �C:via�F�(Ah6 �ffect�Eb�3����j�*f �]  �uQ�Our"�U�rG or d 1X@�c� hi��. W�Aib��1/;s2�� W[oin��ez�_"!*[]"st"~c�7�'a&G ��b/� ��Izd ,7 c��F d�Ot�f"F &�I�9�!F'DWiuim�?4 Dyson expansi�on does not apply when $K\neq\{\0\}$, since $J$ i +��injective. Introducing the Dirac operator $H$ in $L^2(\R^\nu)$, consider the decomposition \ban && \e{\i H_Kt}\,\chi\,\e{-\i H_0tDpsi \;=\; \Big(\eb2t}" )\, 2+tGe{UBi%Z8 \\[1mm] &=& \�\i F61�+� i\int_0^t�s}\,(H_KF- H)\�N(t-s):� TX\,ds \ .\quad\rule{0mm}� \label{ax} \ean The high-energy asymptotics of%�$time evolu!l, are known f%�8_0$ and $H$ butE @K$. After perform1� @limits,e�integral is seen to vanish because �$support prA0tie�$!� $!-$, and[g >Hfirst term in (\ref! �) remains. \mybox \end{document} ��%--�  % Beginn!8of LaTeX file %�b b -- % �NL Title: Scatter�theory�pdiscrete (pseudo) Laplacians @@on a Weyl chamberb",Format: AMS)Dv. 1.2 (with style%10 amssymb.sty)>+�N+:�,| Jan FelipeA� DiejencJ|BC�FCpInstituto de Matematica y Fis >FC(UniversidadETalca>62FC(Casilla 7472*bFC�w:FCCHILE:&rFC�FCPPhone : +56-71-200 3nFCFax >C92f�FC E-mail: dE�,@inst-mat.ut!�.cl>MFC��CJC֪ ����% �L2L\�:|class[reqno]{amsart} \usepackage��} %.psfig:�epsf} %\def\baselinestretch{1.5} \new��em{ }{T��em}[s� on] .'�HH }[ 4]{Pro2/lemma)L2# corollary'C \ f��{defini[2F*.{D%:@�rk:<  {RemFnote}{N!2u�|�Vin{equa�{-,<} \renewcommand{� foot D\fn!�ol{}AIaQAbs3 �4lue Z%*NDabs}[1]{\lvert#1\r!�C$Blank box �Ceholder] Xfigures (to avoid requi�anyɀ;ce16tmat-lie:many-body,kor-bog-ize: �}e0it tur!�ut, t!tA�of�eJ� can be understood heuristically as being�� onsequenc��!�gra*U�i0a� ques!�-� kul:1~@,rui-sch:new}. A7che�examplk2��@e�Oed =8is!� celebra�mY�Schr\"o��erU� (NLS).�5�on!4%A� boi���U bosam 6����ay!/A8V0via delta-fune�a�o��� ��%. �2�Xmanifests itself throug��J���p, which!.c.��(prytA�)6�9h E�c` �c$�s)-�F�gau:fo � ,oxf.�,% R� In re6  work, ��� truc!�a�(rkably larg� ass of5�!�A�le��%��2�0s exhibiting 1�ed= ��ruiU�ed})�"�I s inu ar�'by� rpred�urrearel%�s !\Pieri � ulas)�$ symmetric��zGas �! eigenvn ��. Her�K&} TbleX ysF roi��j pect�param��(index (i.e.t� ) Vl %j�{A�tA�ai�9Cpaa �. B�taly MJ�.` R0 degree tendsa�inVy6Rdemon� AS�---for.&� itys s sub�[|techn�N c a�s ensu� ^��hA��%4is short-range2 �)yum a@lya $tinuous---(2� 5Nm���governee�a.�e�ɶ���to^ 4ces. A� r��ng �b case��mRF �Ac:U�mZ2�2� ��� be i� ifi�� s a & .AZ : i�.��e-dimens� ��: (s}. A)�k��A  H&� mechanic��_" B�E�� j was stud�in great� ail Ref.�a�l-angle�tIt!�j%�s*� �si�Lie alg�Us��,m a fruitfulE~extOa� RI� dMl-�s��jMols-per�,gut:a8) ,hecW harm�,%  opd:yang, lectur! From��pere[ ive,C is natu����sk�a gali��\ݐ'! ɑ��a0heI�,of arbitrary%d )���purpo&�� nt paper�b 0rovide such a�Rj . M��ifAgly) *|� r�*�2 -group in�znt   te�2lonEEralcove, Bba weight"�I~�gs ��IA�s (�.M�)A�pE�on2� 2� .���A�� U�.1satisfy. reN��A���seV-= A���ed asR�N6� M*AC��F�.z.������ For!speE� cho�of� :2, our2�amoun�~at�X .�a��]P�_ mac:��,affine] gQth>8!։6V +n�Zmi� ͒�!�a9Ж�6NM�� r� ,die�+�y}.%`x $A$2�i̍ ��  and we re: L resulE ."ݎu�d��f � -N2 pecompu� i�1is� a\!�dynam���agdb:���� f# , "� (6yto%5�=}2u redu! o��~ s). Our�";��ni� ��w\rts#g� (�l �)�Qͻsh�H!Y~V #nB� has� ne 9*_ ,s��W2� � yL�w��}� �uy"; a� ticity �� (gua�e��7t !4ޭ*=�isV9 ��EVr� a�!$us�  hing��n� viou!�I�d��|-o ==�  �Q �Ida Xza�^e�� aSsez I."�M,.ha s~�ph� %�se�at���ngeexist��unitar!�-�Ewy�$Y� �!�plNv2PuE . KeE gred$ &6�e�-�!�F�� mate f %Zh[p. 38-39]{ree-sim:methods}Ip�rol� decay�< $t\to\pm\infty$�  oscill���$D�Q8differ%O betw�$�Z�nd��ly k%v%b'ets. %�p4 organ�$follows. S� �$sec2}Q�e�ATAkof}�.���o�3 "� InBd3} i� �ut� 8��amretq�z�*e�a�oVI*� )8Y���Y��ij�ar[� iMiF� 4}. ^bb ��� �UbaaymH��ui� s �-�.V�i%�eg���>�5��in�,�> 6%��Wi� eDa���of^b n8$�-=U�:&� ��lR� �(. Some key � er�->" 2�invokedZ�h�ba�colle`in Ap�mixi=appA} -�endqpa�Z �reader'� venia�� e4 also included� ?of" zFzB5 Let uY@�qge�b%vi� a briefm�p!�w��!�m� � &P o e el�� (��h) sit!�a� }�r� 1. �,$\hat{c}(z)$ya zero-s �ltic��� �H $|z|\leq \varrho$,.$  >1$%*a�real-�F $z$ a� n,l�Iez�0)=1$7 Y��  �an� J}� rigo��.�4$P_0(\xi), P_1 P_2 \ldots$�k!� Hilbert sq �,H(0,\pi),\frac{2\sin�, xi)\w${d}x} {\pi1a e^{i\xi})- })$ �is ob"�> apply��� GrammidF+��(Fourier-cos��� $1,\cos � 2��. m� mmed��jVA�zth�s�NN5%��)�2� $P_\ell � �W�(:�!b%} \PsiE= =v�.c}{\sqrt{=h)g1y}, p- \xi\in 5�; �,\in\mathbb{N+end� f�anN7a}�( $L�=2!��a4h�$L$� esv*� (H-adjoint*�+�#Aon��1Ls $\ph� � ^2 (�)$|6!>nlap} L=)n= a {N+1}+ba -1}(-1} \q�. ( �$v 0),�� �$ n, a $ deno�!Hcoeffici%#�IY�N���*=1��e> �%�$�dt Chebyshev.2}�  kind $UE (!�AO)=� ([+1)\xi/\x-��bA� 1���Eq. \eq�.}��s���i� q�e�k<l $A[�^{(0)}�=�� � �$x *� A� zA �n-��"�� b $ wh*a��R�is T by8E!!= E9 Ab-1}$.E orem��� @:thm} (below) now� e at au $[ � �|� u+=,��-){@converges exponen�ly fast!�2 (2�^E�� \xi ���anti-&�combina��AR�Es^�pw-exp�l^{ �-��s}^{1/2  �t]�}-$-% e^{-2&R� iFsZ ) nc}�׭M/] �q )!�Further�', l e�e $��cal{F}:l�B�p,)\mapsto L^2�oVda�nd .MI��Sa�m`4 ing Biec�2ѭ � ,� �ively:B�a�s9displays21%Za N = \sumi02�}��E���} �42ex] {:\ph�-V�1}{A�} �4 \pi :�6].�}�� � �_��q B�� ���)a���r� hcb�f&��T]7H*���S��� C[-��&� :cor} ���E � D* L$\Omega_\pm=s-\lim_{� "�}�tL -itL �}I�A�zY}JS}= d+�� q-$i�:�[ ��� expl5lya�s�yp� X\pm = �� u circm�  S}}^{\mp ��!67����dS} =  CF�&��VeJ[,?9re^.��e� �.*��B���!6a�1�Xa E_| phi}� �)o��  $(i{=T-fS)E�=i� s}(-= 1 % $0 <��<\pi$�5.1As 40ed just �.���)4�),3ex} {\bf Ac ledgm)s.} T�,� du S.N.M..X*� seve9helpful>��P  re�es�# sugg� ng s�imir� ey� ���"1*O&�P*A,RJ$�R�,S�&s� �`%� }*B�D%4E(F�2� �$ q.\ +c��,! �su%1sA ard�%� bou:�es,hum��&io* \sub �{. .A�..1}L��(bf{E}$, $\l+!\cdot ,\�#le�V�'* "0 Euclidean ve�)���$let $\bold2R} �t e z�,rGi�+r�spa+:.��write�eQB� Q}^+i[�0!�"� �=its nonnKive semi%�&e�lp&4veEs>�^+$�ٻ��! Q}= ��Span}_bb{Z} (63 ),\;�K�V=NB=^+)*6^�we)+-B�PB+P�e�!+� l��M.)con�domin 0"r sub1s"� eqnarray}9P},>{�= mbda���E0 \mid �#$4 ,\alpha^\vee M�f 9!X,zforall -Y2� \} ,\\ p)^+� �� ~�N��^+�� =,!�6P�weg i|��0�$ �%$02  /m�-� -J�%�(2)2.~#Z  bf{Aa{�%�A�=�����"�5�< N , ��%J1H�} u(�JE䡵��A�m�i�5"�*f�,U�Q�} m_\lE��.� | W|}b w�W= i � C,�_w1� },\� Q�<%-Q�U$�I$W�r8GL}� %e)�}�2� �E7ɵ :��2 xi_wMJw�$,�E $|�|$��,!Wor�2fsta�!zeb�i $= =\{ ))i�w(-") =  \}  �*{F�0d W%F1�2 2} We wd7�u:t& smooth��YJ��OE�$�"�!6�%^W. T8i:+h"��>~_0!i��� >� mid m� \notE12�\��2_1Z F6)��  }{2}c 6L!� (So�C�.$"d2V�5�!�>B�B�2� �non@:c:�=BC_N$~y$�):> _1=B_N$.)�M"ds*� si"� � M� � 6���O5 p-m}& \DC1}�]=)�1}�� C} ! 4�O�"C}d Z�Z~c-f~J � = \%_MA�: _1^+� c}_{|I1|�l��� ,\xi��} J�b�it�um���$.�11 6�z)$ buil,R .����!  d}$ onlym� _;1ߥ/�f$ (so�>y�!bet!kif=u$* p sam��-orbit)k "y/� sonsq ��fu"$-%eka0se>&I6>�$E� {\em (i)}&�a&��; �8A � b{D}_��\z*XC}�� � '��of radiu!�v � ��nR�h6��,� Ai )>>�R}.�2�=\�+b8F�E@}$t.�2n&�ic-q��.3}�=��$X1e Q�\-�5>%�M}29UсY,:��)Z�� "� � ��{"x A!#^5exm2 �l!��F>`-VOE%2We emplo� i.:?-o� owA� cx 2� z� Prnn�IX  $ure�6embed� J�E��,���|\�/|^2\,� d�)$J� ( f , g)_ME CP�h1}{|W|JVol&� A}) }\,�t_I��} fE� Y�g}\2� \, � |^2�� " A f,g\in@�| )^� B�B8 complexaju�#� $ �� � >=k. (��$)���$�* U�tc@bA��� AL%�} J%F=F :� _0� �* �"� /2}-Lm�F& /2}) B- �succeq�(�4al)6� B�i�B r�$�� �� 3ce�5al R*�� �o}� (mbda \geqsl+ \mu \;\Lo�fa�htarrow -%in&* 5� s/2M ��M est-��spa�9$Iy, \{ m_\mu \}A&u���,\mu\p�9q �}Q =$ F�.� bN �� P$�7p�"X*2r>�1Vr7 ed&�� $ �-%� � � !�� w J3 a �AN NP"�vNef�u2Z�R|�)ret)$�by !�eBE$��Ad�1 op1} �e� = t!�:�,�XA)�Q�} {!-Jmu}I% P� +BR>��!2c!$6]Bbb{C}$&�%^� op2} (=�j%�JD�� 0 &��if}8� �z\ 1 &)�%= ! � O� y}6� (�=O��a }>0$K n��.e2"�A"/��� *v& %)�$, q~1Yu}� O%kDin�Yar�;�� > $�?�; $J~ F~ 0�! T �A�cc��$ o  �E}\mu$)�< nce,�.u�#!#� �R;� o:4a0��i�m��v� .� N�x)$[to�0e��e:=+ r�"�� $��$�b -�Klinear} '�eo .�$. (�/T��2� in Eqs.� �"� e7)"%�let�j:�� AK>.B St�7WeikBrasA�f#.) In �3l�)eJ�*�-t"k&6?(��)3=y(� C ou, how�tat!�-�Jcipal.uF�"Z a�s�\*}.1o0l�+yy�di_tak!��uH h;� e>!,.$\�%po}s�A(in o�"/ds,!1���E�k)"�/�+to*=n�p:M�)UBTe.1on�5%aalways2Uwfixed2��$inBY �� so�0to9B5nm�$\{��z�beiX� ��}�� N�J<J�neq \�� 2�;C\C"b weyl:sec}� �4�Eest.�D�� abov*��1�3� ecb !��U 6�, i.e."1-�"2  (z�( $� \K / 2]���&>� hen becom$5f��YH� .=1��.� ��a�se�E�RBy/^� ^n.6ɨ��is%2A�maya�!Qu t��l .D��B�@ri� �:IHEa�mV�) **� *�FE@"�!89�:]E�.�:��A#QaAq carsB = Y"�  �� # A�m_"�(-1)^w\,�#"� rho+��4  . } " �>�F" �, j�+\det (w!5+p "K&O�&E�J�_ "q<la}Zus�?��cvPB$evv�1tA �A� `"z�'>�eZ2`�)��u+ey)�^aa�QnObnt il�  $���ji"J/�6�!�řf.U 2�  Qminus6R~I2} B9 �6X %� {w_{!�Q}}IuB (.')-}E� &*x \; |W:S| =1,r( 02� V,>1Mk!iv9u4$,!5 $B $ reg�D, $w_ AbW2 uniqu�=el �%� =*/u )6�^� "�#~RA6E{R�Z3R�#"{5� mm:�7�*�7&�-t >A�our^��2M��Kax.��*Trans�2.�6�#� H}��2�  $ "((�)�(square-summ� f�&~� V e>� �}pp� �Kz"�$2-q6� mYc(f,�� H}}=b+i�>} f1C *}\XA�&�15Fc�B -��^_ L^2 2�\�of -h�:grZj E�a�%�b:X�2�5RZ=E�f_g}"i�}&- �>k6'�f�*-sg }3%&|2] �!�L&3�! �7)BW66@By2� � &S0Fu!m��)��-IXi���� �/ �� *W ����Ij P>� �9�a�bzJy�Pa � � mappl>�uF}:=��/ �=�*Q�4q,$ \stackrel�a"$F}}{\longrTad} Q"y*$� q�6�u��%-�F1MHF-B�c�4 ,!� A�� \\ (zW�&u>�� � �Z1� �EH3`�= �96Z(isomorphism"�>9����EU�* inMQeR�c :B:1�M$� �IXM@5�R�_F� 71=6�"R&1���0mD!��}� 2|}W!�>9�� ʘwi�.� ��.f�Jf�#"�+9�FT"%z=�t�� "R"�,r� "�D� � edE�>��s����&�<�4�.s (cf:�@` o)y�u2 pZ }:�0i��&3u%}R� � � �)2� F�B6QFBV �# 7!&al�79�2" ��(�qT]�V+ [FSI�a�)6$�1tZ26�F0N3"�>E � i�2�^+}�h��-��V���U� $ �B)�1��i�Aen"�.�)C=�^kF�26�����0>�=:^�N1 � �<��u .BX3Y!�1�z4 }) F�J�6~@_&>:"�sec3.2�]aV�Yu&V[&pom�41�> , N$�/<�+u �3Y$�]bounded >1p�\2�4�(E}.g N$�Q��!�AnHP5i��">'5�� E}_r�=Ln� W( �r!�exp ( *Hnu��"l),�  r=9 NHw�!Vs�T��1Q}�%�$�$�Opullback� �^� e^ec��(FI9��� �1�*� �+of5�&�F&&Fi�;9�b*pL} L_r!y.�5�>&�5!� &1k 2k/2@B�!v ��5�S �bb{R}[LUb ,L_N]$B�1�R"nM��(Kof) d8LZK.e&\N N B:�I12� �Q!�a^R)�aB5Xe3*�> pL})�zpqc� $L_r$�+a�Se]b�ely8 toW"GtrA�:��-�pact s4(sigma (L_r)(�Ai�( &B*_ A&��}\� bset b$.*ac��eb�-u+eI�1�za� �&6/M�=B�$ on (McJ|$) a�Zb�T�i���B��) ge�AͿev-eqrei(.� r!�uR� = � !o.9~8, �& �fN�B�In .�Et&�FA���f4m��(a�"A�: &� �'A�+af� )A�aS��D /\� L_:,cŎ�(� �.�%�2� �BYg)F&J�%J �\$j@$6 y� rr�\)A���"�$!�1c�����U���, geom�#B9ble�]X*on$+YFj  i.} B�B w. ll *:Rs1sal�a�.F*)��eAxCat adm3. �Hr�P�, ~Fr} up+ak��2� (smea�) & Y(w>D[ry)� Rrby �%sA"� s=-w�I; r�)  $wu9)m!�u�!-�$�3 $W$I'�j\ ]2b06 �2)=-E� �-ThF.���5el�t/�/�/2�=-�:~6 LocdKE=q�z 3}})phi&�aB.�aZ���Y"�a"q9��\F��oE� �o�phi%�-\a!Q*��� *�� � B�*2�& ;�)kmuB �!R6�&:�&F.��;�0f!�U�a�fH%�a q) � �s�*�HE�n�0.Z1*O�; on}[.�]��l=� :prp?.ga�� &$:|.(H}^�v ~�)6�AH_{�G;r}} B�-�mu<�B$6�B�iЭ�UF95se�qA�R��1JZ� 6y) +qt�9�and�(6n� � \J�J2.�proof}'_eS0an�$mU": expaa�M�Q/$�4is*�  i1G*} ��>�F�*m�bz.sub3={c6=�2~\\=V15U�C:2 ;r }�m�aI � z6͝���!�ty2�4impTZ>o }=(.*�)o ,�mu"� |#}= 2�)=hs}P�B1&} ~mua ;s }pG.�*YM-�B � Ts �i}.�$ ). H�)J y �!�!�r% 0\R"�%�2� ^� ;rB *} Sz~� E*=.P� �$ $F� �J-\E3C U�$,)'co"�SaN���f "�E�&�/B� :�� �Y�J�"� �4X2� =� �^ )L7arison N f �S� ��E&'#e�  enZV� R=u� �J%L�J k�K%��uE�H}i,�l�>:r*} �'�` BI.}mHJA!.�EX �%*��� PrB�F" x!��S�Z: !�A letenes"�� �>}F$ ] � z.�!{� r} 6�&�((`] ���BN2i$ \�%F1� 2}a��}W� �W]�� <�M�7 � A�,ori�cardin� "kYse�B2&�$ )p��a"�= �ͱ�:h$. ��r,-�$ &o s need�� not}q*�\��`=* /Ne"�#�'�)coincid�# .9%4.�)2�-en�]F'2�'�'.t-U.�x�Re�v� 1_Mj"� �I�}va]S{ �6v( 2�  \leq96nu I @<. C�/thnL�&�YJ�� �.)�d�^ 1�O2W. (6�in��to Y as aI"X"�SP opiPme��&v .) ��.� ["<'Ss� dl:�  WA�E)Aq"�/JYQ�QY�"�7&L<o}��| ���A->� �"A5N(C��.�;q�j�aofJ]�K2�]&3,M3�9D!�1"L_N*�,��v�4al �[:9-.? $1�m�th� !+聽A(� .� [Fre*�5�f-�I;3{ce@!, |}�. :�.V9F�.-�A/Zr%*�C �U:Q�* L_r)�� &� �.� j&�+\nu}�c2;FK�$ ���#"D?��f2, =y�.,* �]Q)�A�s}>,mu#<&,mumK.mu,f,mu��+(>1� �>� �7"�,mu}2�+� perm�a*�,͞ �.+\mu$��.�!n� .�Q�� As p�[ed 1>Wbu�E��Tm� AI `�{L"*�Z�#�"���*�0$�-Q�� �.� :�@�S w~�2%/�.� ��0I�H>�6hf75well-�Qn &�m rQ�zI�}{B� J�v�chy�i�! B�ttm�ng"gsRFVn)�]�Ddily �by�]e ! argul8�EEA*����fF�=J �~* �erty  1�2}i�:�Y�} ���VBc �J� �e}a�66 !zQ��   :�< �B� ��� �7 JB!o�ivale� �Q�}���Q�F�"�#V����6n( ditd/5A triv�6"all"�-�v �w5B �/ \&\aՊ�I&V�FFn� ��5�3�3�s�n alter]vy �y� 8v&"�T�T�T "�y��r �2�;& ��1��3J�7� u!J5�� 4!origi<_.{Y&g�jE6spher�e,fS6. S`8Pt�$c�I.> (1-t|}�Ic $-1< |}<1_vq�F�<&�)� �>mwi�#�H)��"�'s zo\}�"3�2p$-adic�vrjV!5:#�2#z<5�.� E�^� &�)���5� �B $K$-� Heck2lRaQF�.� F�~��$a $q$-shif]iz ial >!#m-c��`���~�w^6/j5�.n ]�JR:faf$<߁eRfapp̂�\ CA84dnik's double N:Nas ``coo7te�XpF�''' du:�'sV� �ch��cdA�ds6��8i�"�5Time-D"�:B'�g sec4��7�X �q���}Zs"�&�6�-ou]ms.6]�aM �'a2nd liter+yes_A�or� ?�xb.redA�e.g. Ref�@c��g*oo ,pea"�y thi:coursA � &�Y6pW�kAs"��.+I6�aY"�mb �2� opCnv\IB�Zdwcqatn C}^+�% x*GQZ�%}�Gpbf{x}, �N\,; > 0,\;)�=�2��U>�}"(5�rI *r�TEfu�� F`)"�*-f}*so� ��].h(��pL}�L] e`zI< !��>�qc $��ww0m�LqT a waAja�FQI.yX-e \to +�di%�*&�M�Pl%��\in>z�T&�Tiw��2�9A "����} m&�U�<�n@RN�^KAClGR�z iI*�t�|=~6)vstrongkf$-]3��%�*]^B�!� $�\to1cis ubm�28�,z�tF;"� ^ dW � C �3) ,6@0h5�? �12�. � >�1"�SBeM�}�ir�,6QU:}�Cpol-a2|*� -B�\|F OO'M,-\epsilon\, 9z })kl� {as}0] ":�6cfty!� Y9�  $\| \c_F�M�( &_B�G^)h $��H%aHu��� �D� Az:�R>1�;^QQ� Fb.gS-6^B$ m�.jRassum4q� SVY��C}*�'6 �y`�x��  Eis *%j�;j�gx�a\&%4ing�E�ߚa dir:/(l-j@xo)��reveaZrU�rf�3�wY�3j ,PN�|F�m s}:�?�aT��!91.�?:$a���m� O:� Nextp,IyK��^{(uD ))�@>� u roxi]�p&A��-�S9 .�$.yq����2�M�>�Esy� Taylo.�Nd�$�vnU,lo� iBpv�^X ��:��#Qr$�O��baKof "$"� 5B]L2}��N�="Y^ ��)+.�5&,"�PM} b"7��^�)>*(�R�'$6E���().�!�6 )]t�h!���B��2�E!F� "�M�m4��~& prf3.?.w =.�]�M�+:R�. )@96(E!is |�a&wY"T�W�]%M�2�O�. f r{eB%o6~�J.M��-�%1��#i ---u�� an $6j6$ error�;{�� &EB E�8�aI'ic}u *�uy��).9I�R�um�qy yyi��615�#B duct�i��Z�$-2�0%��}�� )I6�%��9>�nA#�� 8>eM��JK4�{.�BI�Y�2>�� B �=&.e���M�'�|�=�1�r8��#�!ic:2 ,�� }=1+6u*+ }��(T�Jest���� lea�Y}] f�W�!�N�)A $"est:�>74*�' � S� �d ,>�V$,>0�i�@U2� #�rA2A!9j t=n^�ڍ�$%er*��,*R�mu)�>�V$,s�into accw��Pg�� �cQ�  }'5�V}�|S�J�&hly�s r[�DI��$?�2��e�y�Vi%�,-f}"�[6lՖna�h͖as7KtM26� &=�U�FS) � ��Y` B  �A 6� Y S}_w� %�.�<� >� �}& � B�VhiM ��A�"�&pJ�b�_w�; D�)n_1\cap w�:(_1K![s&� |}{e�\��xim�)6�[N�6t-Vu lin `R��g� 1�{Sw"�h5}it"[@> sma}/���]o�{7c2%e\� J*}1�B7z6 :P 6N(soW4ve~DN�)}Tc6u-j��c21MR� 1.<$#7$|%<2<Ba.7|R*2� em}[V��%���t�Q�W��6�$&铥I#0d .�C# �����Qy�"| .R -. `*9,=:u ��"� ���/R�.�2�  R�,�Gt&1� ~see� 2�v%%�"> ���E5�N�;j� ��� "r��{$�zU���g��7%�-@5 i��ve� LE� �Y*6r .� ˇ.%O* �O�?�f�B�R any e1real} Z}BYE� rtR0�e� E}_1��"�'N�K]$n{$LrOwE�QircUt�A��N-x= �86�>[wYE-A��JJC'�I: Ya�&$L ��:A�)�� �V1 q5L_�(]S]�;.Y9}R�B5@"�9��/B�/} L6r!�.B=)F$)  E62{ �21 �JF[&�i*B�$} �l!�(A�\L  y�%2!�Hs &pA�pAA1u�YcoZA�<v7-_A (L)=  ( i.nA!5)qzlA�l�,>W s"N����AdB��q&�eSB)/��>�I*FQB��"� �e?$. �uf��� E r�TG=����QaF��'H_{IQreg}}�e�"6�nabla- E91� \r� neqZ:NmZD�y�.Ax�>%�� h�#�8 �=B�D!��dense�e:AH!/ -/I�E$0 j^�Ix�292;$Bre�|�w a�-ZRV �w}_-pW$*�e. ()t E�rl8��Z!jX��B$5��"dw��ClearF@7�j�5d*��&�B � �%R"{�cixo�*6o�=R63 (b� ity)8=?/ a� ��<Y�!Y�3Z�%���S}}_Lf�K��,�3#e so-��2s�0�}})[k�*V\�a�Yip�k(say)�l��lex tG@f�H act  ��jE�6EB� TSm�Y2�% �7 )�#D 'SZ )�ij .ezPJ(Ir/C_0/ F�) F�V� w�w vE`�*Eq.�Sq���h!wulm�is��? A�&D"�,� ula 2>&`��:=�!�" !�$I m�UG%luzSmkp\�6 "�N. � X >�6�S)�"/0.�602�+���� \-wD>� r N} V tL}/ �42�- ��B!�6 �ich�Frerݐ�,�Q"L�.�� � �!�-��r!��1�C�� Z� .�$b�>! [6� �S E�U.lim{} D.p*�� s-&��\|�DytL}�t1JeJUR)��)�!\|\w Q-��-�$ topology 41 b0= &JLD)�ra3&)Aj!5 ��&9DH}N+Vju�ah�V1[*�n�� _+��� �M�`e�/2�  �)5� �\ Y-�YnX��V��QgYy*g�*C:Q����an56 �S� 1%V�� . n� fTZ� ��1�&>�N+P� �-�6c�=�q+1�*vJ��J�5�u�,1�9�6&Cr����2�Sw1(eXv��'&B9w "�*_.�:�y$��a�R>�,��&K�a҅�� z�rZM�2m�in?*.��d��+{S�/�6Ph9A`�sis� sec5FQ+�fu&T��s �u"s �J�2& �rDžove�H6C(e�u .�d me~�)�gen\� izes.X�'�!a�n��R��8=#�&�Kn~�Ĥ rougg:"-xjno-}�$�n� E%s"F%3I \ref!�4}��adopted�R&{%{*�+��]Packet2��+in1�E!�D{!��B}ђ|(tu�4 !2�.�7�� _{V�9"s&A4��6���Ɇ;9z>b�}g -i t��E}}�v� �|]9�Q�����bI�;}_L*�� ni"_:���6�oG��pl#ly�6(B;)6 !� &=& Vxr�XY��fwRx2�:� _w\r�-i1p� S% � s)�X�&E, T}�!�2�7�)�� )} JUY*� t� M ��^� 82� 52uY���iF�Î� `k � 3�s 2C��bi � ^�i�_{+m�� m�- fk6��&.&-,ZXF�I .fB�6� &����2>]�bI�(t6M�^9"�M�� �>dom� asf:�@��a��t*.@bF�>/ "eQ2$�1>�)E� �|� zeroBB�f\�$kappa >0:\�>12v-}�(t) \|zxat� H�{O(1/|t|^ LF�,%�" ^� .f Bef��h�A�B�:1m%AD�)�us��inf�atf�i$�L8n&�Lz s��S%pRsi�+!}"�6� $a^X+�)2��;iH'� � E�h" K ���t] , vali�^�i�= *�u��"H�� e� =f��Ad��k�\��qT*�R$\|�9F'o-& �=�B  =0�$"� �N>v Q��x T\.i�6�WR~s�)�o$���d��!�e�twi�|n ?�A( �b��ؒ N%��c��r� $L l5-�-R1 7[F�I�c��HY �������B� �D*�i�J?U�- �L}.be9B��� �A����FEu��B95/5 wh40A,>��(b>� 4ClassT<.� .` �To�qef[�/�Jr1�XtX "ng" t�5�6+.��]in� s%�i��/nn{#{�.bz��O&BIth!t3�s �Kz���W$*�S �+E .�s�!�2� ��B���al[Jx���0́DlAW�hLe�a� bf{V�fclas}E;n#QB ed n)vborhoo"!��rڶvQI:S -� veloc����R��%�a?%"� E})�uiv\{ �E� )�\�� Supp}^R)i�sta�, aU8f�l wal(�!y�=pa�w.%-0!}�-d3�  �a lowe˽L;Ѥ�55s"��9�'zet�+ s�j?^�D >!� H�$)�<"�0F� +VA�>�'$.�#*udT�K6�"W�is#�lyq�&v&m$t$&�� reg&i3: E4U�>Mi����1B� {+:�(t�b���7Fq� >�W*)�ɘa�M>3)��J�for�W t> 0c��ow_0M�J�Rr< 0" ��0 } BecP�*�$Lder�sD:Ky�ma N�P�`2�N�$ grows�most &�,l�;$tJ�|%n-�NV|=O(t^N)~ �)}\; |t|*�J 19��R�!d�;d2%!�b��;:wp�efteqn�m^{( �})A�u! =} &&�,& 2� 6V� �� w}}}\nVT0:�r: "�&]� ,;VV*�|�["�K-r �a.~�\; �5 \; t>0�\[3NY�f�)yr FZzY� h%- 6�� <�0 [0.5! `�,box[6em]{} 0I/%�o�����{0 r E ���&x,z�* \|-57-�>& (t)\~i�)Ea�=�)[2 p} I��i>j|e��}"�w�C� ���� �3E`Z�J1�qSa�) (tV �P��'�QW}}�P�~�(��*�q�-6�O]1.Ջ1%b�Wd-i� W"�Qԋ� w}\}� ˈHB �H+RA�}Eu2���\\:d�"�gg�� W�Z�><�6c��EՑ�E�� &ܷ��f~�5 ex��e��om�&�of"XI.14Q&� [p. ZS��"u "�,�-$k ��~0  ()ve�?n�|2u_k.A�-6 >Kspaa�|~�� x}� -it�E��.Fm α�c_k}{(1+� G|+|t|)^kB�%��Q�eG��$t�-JFaLT �%.F* :� �6pI�k����%RbA4�:� pa+� spb},$k> N/2 ��=6:L��&�AAN}O � Z0�y��w!j,�c����b}��nr] is $�{k-N/2��l2�DZNi�%�,�P�N$ ���h"�wT� "�>� $�h��o��ifb�B-r& ���YW'.�v�d.�*��|*�*���� ius�^�&Y2�}"�� A pm���B�k�K�"��.q3��? D�Qre.�B_��R4J�.�P�3 ���%*��0��|�,"� 6KZ�aV ph K-m �7  BlF�>�0 b�1 :��e��K:� ���J!Bf@&" �!+2 \!\!3  � W&�z � & ��e?50v;^ 1w}}5l)Y)�p "|Ue!-R! �M"�S �S ��&} ~�aPv���6r��n& ��C��*.tա�y�i��^��7*\�\ �Z � 7Nr�b�� �Jas1�:�>�i^ )}:�(t�����<<.� \pm ^ �.�.A6�^���%! %��&l�rverbatim�Ar�g��0�b73.�R��% of min�8d�V�!��%K�&^�incorpo|L e ad\�al�r�))��yJ���Biȁ�>�B'wb@.�$,"�"m�%q} �&$PA��!tVt~0- Ka�C�B!���j o��he vQe.�:5pace &�����B@ �nb35l}�+V�J�A )���b��.$L; &p5|R��8&Er%"avT-���|� aE"� S]aI!{!�Bb N�g�> (t))=!$J$. l���"�get ��}ӱg' ^2.�� f� 1:eq�fF$Z!�W ��� � �k$�L 2� -�"Q ��f�iaf;�pC^�&B� c2�&EM*Z� B:��bG2���[*a 2H` � $� A�903� )�2��@�@�a"dE1 eA2FeR�lA6 :y"a�� Q����#}���5 &{�8QpWp�bp"� V��$� "�#6N#6�>� l ,*��� "t-^]wRPBF,Vl�� �| P_tP.��(#��f��:F#^2Y,o"�v� } | �FBF*7GPs9^�E�)VE |^2 2H�k��|=�E�2� H}}}1�� \|��d-. �foa�*z��#He Cauchy-Schwarz inA�GK). Now,)$|�t"7Bb��\*�R >�va! -1!X!m.T��B\$6�s��"!0b�N-2�02a��EN��(�a�b���^�$&�N"�+�:�$iyNS�L:p, inTM�y���as2.��,*�a�A.�_t���4G1B, k��~�� ���v"�&��T�*�tt�� Id}-J�)��e��H!�E��>���"�."�$"d-6� qV} && KE�� * �B6( =N ) %o2 M!!51<�� | z�Y�%Ɔ6�AL��.zR�6j 2jAl�;Ar=h�nZ>�l1}6��(N8 �*�vP eq},�$�r2�'"[ucE��A�;�NY,i��QA��n�� � H}}=2H�/BIAf0pJ�s .�R:s�2�aJeo� ��E �� &*�:Eq.}~3�� }{=}& \| Z`v>�B� +> �#v� a�%s^{Ǵ+t�eEX}~07!*� g�!36� BdV�=&��)�� 7B�F="�5��na"K��.��=)j)Xb�^2-Z�B V[^2}�{���a�G�� 2�KPI� bR-�Z  4} A�y�pre�ha]&n��ffP :A�telescopBV .�&:BD �>�& \\����Z=BR>H +��!�N��A�I�r@':8M�>5, b%���;app&hf��s:�, ���$��� �r.�g "�<AV:.�gof Hy�� LaN�� M��]+6}�uDž� wemK�i�g2]N� Q�&�sG��6s&B>����"��6�� ���/ �d !X"@i &�)�y�� , viz.� .f�`|�m �~* �0��a$x��n�>1�;m!d} iSbo*��_0=:1: $) except��na �:�d "�".��o|��R t�xindic�jho��Js?�s�o(&�= �no�}2�J�=BC_N$�>�A�>�?ٹRIen�tr m�"Z|lR� mod�els in the fifth subsection by providing some illuminat addi(Dal details describwhat WLresults boil down tos4simplest situaM@ of a root systemrank {\ ne}. \�H{Macdonald Wave Fun�0}\label{sub51 0, \end� with $(MD\equiv\prod_{n=0}^ t( (1-zq^n)$,�weight � $�l\Delta} (\xi)$ \eqref{p-m}-- ,c-f} becomesf  _-%2V= �)6H\in \boldsymbol{R}}5B,e^{i\langle . ,\xi\r}=Q {Bv FD ,ZJ.>c8(The positivityA�triEYs oi1,parameters $.�\$ and $s$ guarantee that%�.v1jAY meets#, technical r!�4rements stateda;Si� \!��sec2}.) Our polynomials $P_\lambda )�, $ l\in\mathcal{P}^+$ now amounta�a ga�affine}Q9subq\sqnomp} :� =ig1}{� N}_0^{1/2ACE� ( �) +bf{P}6 FY here�>�hm} b ]= �d!P0C}^+ (\rho_g).- �..+�R6�8'!1C}�r)}F�[�{g}A�uiv �$1}{2}\sum_b� ^+} y  |}\,\�'i�Ynarray1�cm�^.�\pm ( bf{x})&=&z@^+} c8�� |E�HJ �^\vee �S( ) , \\ c^+=0 |}(x) &=& q6� x /2��6+xF���2pɞ�1} ~-�~/2}-�( q^{1bs1-9�|:�. ���b-��6� Here $1K:M$ )$ denote��N/1�6XU:mp}I�F� )= cu�p ���V!R�m�qV >�  )}�&mp1} :� = m6� + mJmu>�,\, \mu�2ec!���} c_{�" \mu}Qmu6�-�-I'coeffici�C$6Dy(bb{C}$ suchũf� 2} (=r, �)_{.I} = 0 �T\text{for}\; \mu \prec � By�6"� ��YTh f� 6�E$ �m� n $ turn ou�( vanish whe`�J��a4u$ are not com ble�Hthe dominance order �(�D}. In other words, AHis case one may tak@N $\succeq$�be ��l J~, $\geqslant$��3 po} ���re�Xng generality. Explicit ulas a$ expansion2M :\$1:&i \neq� �m-cm"ɺ�readsAE2ly�A�tion*} J;��Z� j � "p .g e� \d� �J28 &:�*�#a�at61 J��AA�9�& $ character' by Eqs.qjmp&C mp2h .�Z�P-Ruijsenaars Laplacia" �<2} Let us recall��( a nonzero �& $\pi��� � is 4ed Y4 minuscule} if) 8 \pi.2 1 \leq 1$e(all $� F� \ and �it>vquasi-�| �j| \set] \{�\�t� �not�). � numbera�9!-Hs�Aұj index o!/A@!\��i�0P}$ J $1$ (so%4V��re�Yn�A!�gards�� :2�:A�@re is always just%��H}%� ��E=)� _0$,��re1�_0# $�A�maxim�oot!du�� :�B� \3 mid yA�2\}$. For! �X^@convenience, we h��in�7�� lis� ()")F�for each.c!�T� Lqmi4} ( m adop}�standardM,�of�funda�al1�aaccord�v��sѯXbou:groupes,hum:introdui}).�Jt�B+�Xb�O {lll%o*X &� 5)+|\\[1ex] A_N :& \omega_1,\ldots , {ND + {N},\\ B2<N � *  C2 12D6s-1} N5� �E_66� w6..\\ E_7'7 �E_8: &�186F_4:4G_2:F � BC_NB .\\ ` &� )� �_�1cap {M��e�Q�2W�s.KU� QM8 To a ^� $A�associat' (e multiplic� operat9�E}_\pi : ��$H}}\mapstoB$�{ M��1 R�z = n P W (\pi )\cup W(-\pi)� xp (&-nu , \xi&�B_ ������Zi��now de�d a�(pullback $L�:����H}$�*..$� respecf �Q0Fourier trans� ��QF}$F.{=� %(^{-1}\circ %x-K�F}Fo By P&� Rdlk 1 "�V( )���bb{R}[L�4L_N]$��stitu a differ�� UV27H�!�&� *4  (vides its e� a�6�lattic&� s ov!ahe � � n���!D .[b�Ro*� . "� "� rlap%<�� ::� \pi$F�)ua �fE R�~M�$�4a (square-summ�5)B  $\ph]��\rarrowIWi*B -e%�}lefteqn{E� W" = E_a�I��)\, %�} +} &&�&& )�sub� {c} �F\\ �+ %2�N J4} \Bigl( V_\nu? �  $ ) V_{-\nua �"j )6�} - [F3)%��r)���=VzJn�:$�R4ye�6)3� �3 )%�� >0 �5�"�&S |}!4 HaG�.N�� : \sinh_s)�V{}}{� V"xRV: T~U .� ��\ &=&}�0N0=1Z0�#s}{2}V@z��!AI�!&m�'.�1|�'times!�f2�n �^z<!�>A(1+6���V�1�>P� �u8l�� ( s]��H1��F[i9};m� <4\ell =0}^{m-1}%4 )@I�z+")�)���uiv .�,*� |} ��$� .� �proof} IPa stra�� forw� consequ_� ��� � � a� .� s satisfy /"��� B��EY.7|}(x+1)}B)}�)T( <sx�Q��)j2i +x)! " -cc*1x&F>x wv (1+x2"R�1{>9 *} WAL!\aid-gse*� 9:y-!Y0icult to veri-q.:p]el%}1�"1 ff� ��)���+}#  = 92h�J3�%}2�F` From%recur� ��!2"� *H� hibifin Eq"D rec-C}-f$ Appendix,5Yw �`ily inferred---upon invok�xRZ�!!J � i�to� �Z=d $�I � !W$"a ---"� �~^�Z �&>2}m�if eigenvaluYnY+n� a��FW 1 V �J �J  ) !G��xi ) -� JP 64BiV S :C< �b 2"#� &c# -q^�_nu ��R Hr) �-�g . j.R *} CombinA�ņA�cor on� J�a which� i�re (ed by $-w_0�$� $w_0(`(longest ele�q@Weyl u ), l�u"aJ� :�$:�`2,6�\\ mS !�����&~ %n6� J:� F� k :�MJo �!�>4-�Yo�=Al(2�I-J �b@ JA*�s f�w�letenes�A�~ 2~s F� )'$a #%bf{A}$A�\0Hilbert space8!��)�� W9M�"eg��QM6�����F� <� b�U*-�� �� v� �� "� � �.H93��>�$6�}��.6 ) =E�q9))�[(b% UW ident&(6�mac-idB�). As a.� ��inF�*�[+i�*�V &e+toBe\�$B}b����"-UbBsFh �\\ @�gqUa2v�#U�-����MphiՒwB� })�6v"g"�s},$A_N$,�= B�"u� (cf.NH"� ). H� "�!j �!�Zdiscrete&�s�s&{L_NO>�)3}� "�2�.�:Z {\pi\� )���=<j~!j=�N$(� s in ques$ ��@ �commuA4quantum integr�*�( hyperbolic* vistic"�\Calogero-Moser model dueA�.%d#8rui:finite-dime�"al,)�s}a� }#=�s, onlyUm]par"7J��9%��"mad*#!�mea�� �;V�!B�%�]_,�:h.Q$principl�Uhigher-�$9�&>sd$be�� truc� "� &� =��#Dunkl-C0+ dnik� �-refl�,Y&)�(che:double, m�/�.however,�#present"S"� �#�$ a se%� gene� Apalgebra!BU{.��(Z�a�avail:I �=e�%%�@class�-}2@ � die:self-$,sah:non"#-�$� of course6ou!�n)�o%��.�{ "�s�^�ist bounded �adjoint9� � 6�):������~�8 aXee(also check Ŗ factK!�(ently direc "� >���!�y &b%�*} I�!� :��n $P))M a 3a �! "u&�'��$��=;�same �?� occuM��g$(necessarily>#�!� bf{1�) W;'�(A�� � -� �  �0-J$�isI�is}JI�� W�� s $B� $C D��($N_(< 4$, even), $E_7�6*�', $�' � $B @but��not���r2$), 6�3Aedd) $E_6DI.74 Scat�% ng Matrix sub53 143}� &�|}\to 1� \for�,^w {3y):�' *�'{.z6�' &��Y unit2JIzR��q��`nbQ(� is limi�Efre*� S^{(0)}=N�'F} )�� .$"�^� fl� 1>� � *� )26 2  a$�P(�%ary�:�6s stipul�3=E��f=)��Ac.�U7e some*7 more ��*T(�!�th`N�(:��ZB�!)��}[A2mF2��fl-qm}' ZbN� 6-1 \p-���T� >�*r� - nM/��p a��2bB� 2�2NE ~� JL>�f*$6�=�ݙ"G ,�'� :3:�*&�( shorD9 mple��s"�'j$ per�[war�?�$�)��: ',� c�'a, �s1 lifye�if>(%��y laced1.�1�: Star1 p�i�e*!Qi��*+�!:R'as�:E7}�G q�0�/Mnot> �� 8r� [ a �e2�*!�"[1%}X b��_jrc <0$"9 sinc�" 5B�E4$b��EBH��!mat� in eit�0�0�("./th�,"Vs"$itemize} \ [(i)]B� V�a'� R+=-1$,b�cZc2.c�d11�� n�2�!-%7�>0 sH:�� first%.la.D=�*�* �� i� tabi�9�e�e *� $r_�+_j�%Indeed,Age"��4*} .0B.w)=D.-->R�5�_jBI������QoS� j E Q^�N1" !� ^.$-! ). I� ur62i1�two e 5hR.R�( nontrivial�-74�6S2�v*���� Eq"- fl} �4es 1�F5AC�J�secondy�� x is>� . Clearly!�m�.t "��� = -1�$,�$�1���A���S^6k.V="�!�L1�6'Q�� _jQ�2M >0$� $k�4 j"�w�pz}E� ,\bet6%`10`1M� &Q��d(nc�N�!wr regu�qeAyC4mut| $w_{>[}$ taX& 2Z)�2��a �a jay+�e >�1�>1�2r^fJ� IX� �c2d��n reve�5{��is�� -� M�$. Now�ry5�aCMZ��R%� orbi_i��u� ZRD��!�s ris���tribuH ��̕ }=6��+p  r.h.s.!{6�. Fur�N ,4  a� .f4 �� aA !UB�+(aQ p*.3� q�",3=� aH:23> ��v3��� Kis�a�5�2 s �)� �5�kYB�5c�U)ls��"�o�a cise�t� m�� ! s f8 >�,Our main app&/0-s&g� alism!���zsec4}�!9&a �.�:B#U��"l&l.:A,mnga�%m-()( asymptotic+�dynam Re&�� $a�e�-  6��� |. $theorem}[LV�&��~6�+ $ Re:�lcm:thm}R/6- $\O�30\pm=s-\lim_{t� \pm\�F,"t�-} �F ��D%(9�5� &7S}_).}= t+ �-��TAGr"&)lezd� 1�orm� �in!!sI�!$)2�Coroll %6�:cor},� a� ary   mY�9!&322:Sm}��=Sw�7Q*� \�Hs}"1B&�B�*"�#)|((q!�&13�tZG �H6�B%��>"�BNC-�D�A}0"*b�J�dqP&�type $A$��sQ)�u6iszo acto�;�]Im 6�"<-mecha�G��$ was analyuG$previously���> I�a�-� �Q'�.#J����(6 # M�"f:+)�>!gV3n�%T��i@ planmA(aB.=asa^&�'smat})mEJ=�@n  d �1�͍ �.�Ext�!Non�d R�:S�s2�4}&@ will� ind�e����5�L of S"+Ms �:1�eA 3}�R(uld be adap�mso�tM�:Ww�L�2_ (viz.>K=BS: _0= >0_1=��� $W$ �I"'�(octahedral O$S_N\l�"sr0b{Z}_2^NHIn�rt$bottom lin �" Ncarry�5S!of�1��ms �*prngI �Y�&�?���Koornw�=r �8var�8,Askey-Wilson.C�koo:a#w#,~� M��fly?pic+ 6p.B�JN$!����6�_1����q��Q�mkr�Nb!s8s} {\displaystyqM�.���cgr�N} &.�E �\; �<[2ex] 6h Bh_0}z,x*��g}_1}z,�* 2+�K6#3 ;6cO^2v�� �pnd1�15R� re $�Om6s,�(� �{0}&(= 3!�� $(z_&0"z_k��1!cx= (2*�_nd up Xa�fRG���#pB�O� &DMe=-]Q5 } \�7�C/?*v�(Min >�\\ ;]8%�&&U02�,i'Z�O�O2�M:| 'ZE �8:5 F5jq7 ���Iw:��1(�2 :�^� �.�_0}F% (.�:m�4B��7.�i��8y �Lno�q��/}�.��P�PPzIto �IN�P-�N.�G�4The.H�"��agZH ��".Q )Q"3 � >r >�F,}!d��q�6)� k+*cmk-f}s7�C}sO.F+)=�,e�F�^+_1} 6�O� �""�9N�6 ��M .�1��.�5l x) =a��&& �!�s}6��O x/2 y�^{g+ x ]�m�e�6�O}R#��<�# :$xP@(g_0+g_1+g_2+g_3)}P���C\:��*� 0+xi�Cx}a�I1/2a�gi�bDP2 ����A��N b�-u>kEb�P�hc*�6F� F)�JAg)1�]�1Q6 } ��:8q^F� x /2-� }& \\:4 <1+22y��E`�Q5� R!� 1/2-!�-� 3:� Ij�N�f�!�6:�>���guished2Hpa*7WA%g_0": g_3I�rm i#& .:g]% F , _3$ via0 � ar"0"�96�MO&� g= LXR�ft( (b6t1�"}�):ve(Z)rWK ŕ� to bBA}�_g�Ui.g�:�%� "6 �Z� _1^+�7 .�)2E}Q +g_0�h hic^i��1rhog1}�%1%$�-��� p��"�V!��k�.5=q�s���Q6�Q$2 �:�QZ`*� "�K.�$["�.I  Wave �^�mk�Qm-:�a,",06^� �*_*|�^�+�7.B��Rw<s e�GlB�)~;FG���Q��Q�Q�2*R�8:k'R�*� .�).� >� �. &9>y!�1jF>��,2���Vw obtY L�"[oh1h d~ Zr"�0�Z�J�:Z�Jd5|L"<4�$fu"x5.�=�4VQ��P>�"o�2G6f�5"R.�Z�5y�r J�#�� l�e�r}�w!|N^J lKf&#�JJ�-n�a��^J S9�<��IG .Jba.�( *�I �&>)�+.���I"�IV_8b�? !c"�8Jr) # ��*f&~ 5[�?"'Fj��Fw� @\,*�,\;|-m)\oc =C .O$�D ODM]�%8B#"�VEe�C)j3N�F� Q�)}{J+F�fC)�a^�I��.�2�R (.�I ,y�&b �#�>c J NW " .�X 1� 2}#�tivelyV�o�P0\�*?P�,"C�*�B4 /2$ Y$g,h RT $g_1,g_2&>#0�2 F�\C.^5+ tM�FNM[ conn�:_dup"�$.  $(2u=(z,-�&� &�4�RY 6��&tB+0�:�"�=Dflnr}�?�#ɔ�|� G���59,�Ql&3 E���? G�E �B!} Ap90�sN&P-g?& now �Buc��#"� FeZ&&$ng!: AN��%Z� 2i )��a1(� 12&� )t"�b%��%��"��%AmB &� x lcmNR�$"6��%��%z�%*[6K%qi2+La�1u6�.u��%uLM�a�&�%@�%Ix!1)?AV��% �9 &]�2�%u;S}"'& :2`&�B&��"s ��� &^�>;��(%:� .F���%^ �g}RkV9"�:>"�%� ^? ��/ } } n�-���V��:2_ 9�5V�.�%�!J*2.[$!~1�_b�.c�� 4]v:�r�2�1�v/]�v2R�>3n��*r�.$r_t �(��*��"��&��.�'��VK��"�N�fF+* 4�&{Z&�'~�,��'�9>'��ak^�'��� )�[*tExample:��0Rank-One Case �?55Tquite i]Cv�0e�Q�Z�&�2v/�in "�=fm0V:�VG/st"�&a .�&D9:�t Wen(�i �@m;�A"�a.2*'EiWA1 )::/ d B9(A%�Cb^c!�edR'it-a�Hi2|> *}(6�*t]`"cwt�D�C ^h':��4$q$-ultraspher:'.HZ!ask�':!4,gas-rah:basic(c I!/!�"JvZ�ps0� W ) geom�r!�Fr' �l1+M (��N}"�r .%^  (IW q\MrO*�hObfvoell� "�n"� bb�c}mxi(0,2a"x# �� Z t*�!�*�c^-� �V � ��21 'B9[X �Vt P-�q9m�c!jc}(-\x�R �9J � 2�!i) >U��6c�*���*�-i\xiV�Z�^�xi.� M&��6% c^+ # &=& r !�6k";!z ��QE���j ��^"^"�&m s A&x)G~S!�M�E!rE!,���R:H A>6ny�:l.-.c�/jQ�m�:64)= {}_4\Phi_3� ;a�u{c}!l-�Y"2!�E�gM�I�]�~(I�!�A�>g_1K � E� � )M � ;q,q 4!/ ��twee"employedمno�:ф�ou.f��vN��serUX)e6^1} *} {}_{s}%C{s-1}-GI& � .=ia_s!b*,b ?6� q,z �,�0m6�{m�>`� n� f f  ;z^n� f�D(a! ��'k^n�(1-aq^k^� �= �, (!�6>� w e6� �2�l-6 $A�: �6�@"��Q�KLismL&H ,isms})1�6�Q ^{ wɄ4$s��)z,��+1)��-eG$-ŋ�5-2&F�itՇ��rsE )`$�}��vM C_!6�%��� %��#�ell��"nps s}��4�M� �� �h$sine kerne"x�Rj=�Y)N "�%el mf B��6� �pairing=�F}:l^2r^f� �j L^2(n (2u �8wd}��*9(K�S toge�<�j(their inver�u �u�uU'qQ�6�F�bn/2Ay�E| O-�%1%!wK1�E�nk#>2.Y !T}3t,=pi@ ph �6^=x ��S x~A�YmD# �  2> ��i8��v id� %6�]j]�} omit�6a�co�x>jug?Bs becau @hslevantm�"�.W�q%Q,�$E�real-v�_�m_@:�c[R~6.�P W\congQ��6$M�V4.�z�"Frc]�-�%!�N.K �= �L / �9c*�mBY *$ F<#�6p"� -+EI =2� %r $q" oZAm5l!;l^2�/��$6a~Z+PL� � V� ) -g_0� -19"�_ +1}+Q &&F*=` O2< ��}S2; bi�^%h�a�� )- VK) -(1-U �,0})V��^��e� ,ji_&1 6�1"�V(x��sin:�0+x�: (xSf��!�:61 6B 6� &&��2��xZ�!��x)�� �:�AgNjcJ�� Y���m�9����DA�ArE�EER� e�JFeD_�q=0� jte�.� >�<�-�� $N=1D&w� ta�~ u�W^A>�A B�A�-it-��*��H*��@b�Aex�w in $:1 $,a� more���%� *�B^�&z P � S}}^{\mp P ! .U���) � =��.i_L^a6>!B�v2A{L}$ be�";B.j@whose .��~` on�9�packet� A��和 �ive��y(�>� r )�:��"{\xi ) ��N7)���0 <�d<mF� \a�h \�{�ert�9�� P&�  appA681* MvaGoMza k8Pke�6b b*�-MZsA!��= >�(dv: F8,We us!+ V�* �in >>!6�2 buil{�E3f*� � e�e0�.&Qo�G�-RN�~\�S@G ��m��belowt for B�y7 cerna�j*XOw.erA�re�j�semin{ork���"�^ ���s����^V�^ (�Q\� te{cha&�^}�a �ler�^@approach). Throug��%U��}assum%�f"ur.�>�A$�:Be�D�%!Ge"C)�F�-��Zof Hn"^02�B%�nlF�Ref�0c!!YD;goa�,zVA % oko:bcnV6_6� �| �&>Q�~*�;s�!8yll�e %\Spe.�F-/B!�hsp",;:is*�3 ) =1B���!��O��%[wfR#s}eB� &ort-r����6�,2muUu���zH}؇\A, s} 0J!if߇��  QF#}� H?}��*nY)�:&6K=3�- u� ٥<:F Bula�*"N%�:�D�Ca�e$\mu=0"dC�ebl)xS�,y5sf�ym!m�2k^R (is!U:s+\mu)E�!m .mu^{R//}1"�x)Z��a:̈́^Rń $ �� Fg%$�S���.kJp.�B�4�zA�cY�H:.�:F *M]� �u�r*�{�Bs��:U4bo*�Nj). $J any B)Y b� o{f>g R �.�ne�9RD&ftE�� b"� 6��"?m�mdif-eq��*],a[� >"�/�\9B��Z"�/ p )0F!zX(is&&a .#zxi\0 F: �)G*8/n�,.j}&z�:0�v��hY�*�U e�9�}]�* E�+is\nu)"c:ێ�Vq! >��^l qgL� ,M�+���' ,6LrNʈO  ,���>�=$(�w )_��w��M (z!�)$. I� i\M�is&�^i�|�pi1�5�|0� , $ �.c), �, 8 c&�sd#�lj�lib}<��r:o=`��y" v"I2@5lx> )2�Aa�^.�f��yG^�2)���:&�4_"�2�C� � >Ihity} ( 7?�cul�ob�����ioV���}*�}m�����1���� ����B�rp? �"|(5F �ue -�٨N�i�x"Y ina�R��U 9��- 2�, ~u� �R&8y� $ (or Pieris A�I 2^^"By&X.9�0!9�vl(�} 2 +:� ����5bHr)J� i*2�-)��&< 6�z1vqk ?�1��R�F�� 6�|�5 Iz����%-�"�:�2.1[& B\N[h_>Yѡ�Y%�lR&�2��$j�,o��is�2 j��F] $HN�� ׂ�h)�9z ) )�4de��` �x&x> J3o}1�3b=tmhbue.ڝT "�V2�2W=17z# �#�#m#r:�)�2��Q�2�u3�!:��)}N Y��2p��]�2s�3 &�dxA�Nw%.kBk�~��al�S�%s �r�4� h5eAU,�\�?thecbr e;�ed.�,vspace{2ex} >2.1}:Da*E}$, "Gb �$ , � $ �S2@� 6^h&]Q #elQ vP6 W7T� ��$/b�z , $:H�\xi_w,W@Wq@||sz2%2��:�_1i ~��� �C}B�DfAv�3}: $()�)�1� |}x<Vol}(~%2 �&�+ s=��"�,R6P�� t���4}: $\ch& ��8`(-1)^w a�%�w_\mu�V3A�]XHE82�;1uH-%#2 J7>')Oy! ��NF�6O2� R, ��2}���r%"� E}_r�W �%SL&, $\sigma(L_r�~W3IW9�\mu;r �13a�&D gCr��4=�bf+Qe�m�� �"�"��\���|E�\|:\�AA6{Oqj:��( Wm� S}_w 5RC8��S��iA>�11#�z4-�Aw�"�L-[�%� (L sce�_{i�regA� �w}_\xi8X/�cp9L>NLe(.i@ S}_L��5-�ph�%(I�t ~�5=w%�� bf{V�3^�2?��) m� �)!W��5iJ�^{(IG)�P_t�rz)Rv]6)+&�|en.ƨ���"E%!�<%�1��T��x��" A, $6gT|ԣ@��i~�6-�pIk��(ve�:%��!u�H g�G E�E6�Cw\pi6.� )_I�* g���G�cye6�r� ��k6�i.z6!�%��5�ar�c���/! 6�Q��.-[,6[, $:Rr�e5�V_{s+1�/s��. "�/�."�.F (bibliograph"]{am/]i&�the.&}{0000�9ωLm[AS]{abl-seg:solito�M.J. Abz�tz# H. Segur, S +;In�+e &�e T3�,}, SIAM Stud!inq li��thema�f{\bf 4-ociety*�ou�alk�A:8(]d), Philadelphia, Pa., 1981A~�W]2�2} R.�2_J. r_, SomeV�1&;.x�)g�}�p Jacobi. X, Mem. Amer. Math. Soc.�L 54} (1985), No. 319.�B].��4} N. Bourbaki,�G�� e4iXg\`ebres de Lie, Chapit44--6}, Hermann!(ris!*68.pC]>- 0O.A. Chalykh,*�.c"�,�~ic� egra�qty, Adv�!� 16� 20023--252�C1��} Iere�, D� a�� HeckeasC'"$'s�!0jectures, Ann6�41%{095), 191--2162 2 �*� \byI},&�! 's e�+�cor!.��/ "S�,e>nt6�22� 119--145.�D1]?O��)f} J.F.fq$ Diejen, IԂ �*3R~js, a E� PhysM�35 �04), 2983-30042�2 ��L='Sq� *IC-5�.FN 126 ~6),a --332.D3 }&73~ A"8k�fsi� (C�ially)^�*�,+.Ls)\rna5� Res.i6>E�2003} (7�87--410234>�sR��multi dZ��:&e"�, in:��LJack, Hall-Littlewoo��9�.�&< (V.B. KuznetsovE�XS. Sahi, eds.), ContempM�,B�, P��Vn, RI, (�=ppear���DLM%-lap-F.�B� L. Lap�ye�)J�dse, De9&ai� j�J�6of=G.�v� Composyhi&%�$ 140} (200e!55-2732�V �vin:c8�B�%X$L. Vinet (-Y��6�-SuT3l� Mw� s}, CRM S.8in a��]al a�ics, S��Pger-Verlag, New York,A�0.�LFT]{fad-tak:hamilton�, L.D. FaddeeI L�$Takhtajan,�$H3 MethodB`the#�8J�� �� Soviet%f �s, '�Berlin�E87.�GS]:/9$ G. Gasper%hM. Rahm�$Basic Hype*~9)P4}, Encyclopedią9_�� Its�c��� bf 3�0Cambridge Uni) %Press,�}92�Ga� u:fo7��Ga��� La F  d'Ond)) Bo5}��sso.�82�Gu]{gut�B(le} E. Gutk!O�9le#s�^ �-poten�=, Duk�J�Ji  49��82), �Q.�m�~��' \Y���% ic S$s}, PerD&�NeA.y�e1I AcademicQXHInc., San Diego, CAa#92� Hu]{Bۥ8 J.E. HumphreysMkIn&��Lie A҈e Re�E�+0y}J��q 1972.I]{>�:4 M.E.H. Ismail.�sA | 2�>!Y�C 6X) A�!A.%�1�7I�6 475m 86�W� -wil2c2�%�J� F 2yd �u�s� ��H $& ?$6�� �+xɃ�HE3I�at 43--52� K]{k:4l} T!Z*� !_Vwl�.')}�pBC$=�Y:>.� Do�u;P�@v � *m��� �K8} (D. St. P. Ri��dswFv) 138}��<1992, pp. 189--26� KBI!6,r-bog-ize:qu(�} Va"Korep�*N��(Bogoliubov,E�$A.G. Izerg#��Q ?� W�*-� %�CorQ9?}�)�E2� Ku]{kul:f re�<} P.P. Kulish, F.mW >s�FaT � $S$ 2P ervU laws,i�.~.w-�� 7� 132--132�M1]�-"iG� G.&� ��S"�GU]n�Dp-Adic Type}, Publ�yaZ8Ramanujan Inst.av71.M2 �y0�*� %���{! H .�!�larendon��Oxford��2� M3 uo"7-v&L-.*� �76� S\'hLothar.� bin-�� X2000/01), Art. B45a, 40e(electr��2� M4 �q�%A.��e�}�!!& .P.]�� 2�M{Lt-lie:many-body} D.CAttis (e� �\  M' Body?Lblem: AnB� Exacˍ SolvUG : One D��(}, World Sc��?q(, Singapore%�2jN]{new*NA�NewellQ�?in ��� ALe2ic%",BMS-NSF Regi�0a �1ce� A�)�:L 48�~�MM;82�(N-Z]{nmpz:t_uy}0Novikov, S.V!�naL�n0Pitaevski\u\i��HZakhar�8!��@�1'��f6}, zor�RJ5 !:ua��8Bureau [Plenum]  1982� Ok]{�1$} A. Okoun�(${\rm BC}$-��rpoQ&&E>bin��Q0M(��.1.&D. �U �98�8` 0�J&@(OP]{ols-perٴM. � lsha�k�A.Perelom!�ѥ��l&� r0'�3o� "o,E�. . �94�83�13--46YO]{� �jurv &� EL�Le Dunkl O�s%6Reas �lex�3S�). SJwoir-<y+al�o8of Japan, Tokyo�� =Wx]{oxf6 S.����1.���%W��Non�iSchr\"oK"er "h/!P. DE�sis, UCLe�72�P]{pea9� D.B. Pear� �uum *i[ y tral�ory* := Lo����88.=0RS]{ree-sim:m�� Ree� B. Simo�s!\�^r.�&�. III.���V�< -�6 RSc]�z� new��� .8�� neidٕA new��J�4itsiActo 2v- (NY)� 719X 370a2DR1�:fB�N�, FB(� s0z*� *��Sup��le"az (� pershmidtW ��.N 0ishing, Teane=NJA 90@ 165@ 62.2 ��9|"; A6%  ���s&�[�Y �"s�F'J�QM" ��- c�F���u* � �A�i3 31} (1 247--352�R3 � b��{AQ6� �*�PW�c�Field� Gumenoff�L!�q 2��Jy[n� 1999%� 251�2�R4 �9 ed� F2 ed 1f�;s vs. 5=��mm-bm.�0228;2), 46(6T S]{s>���zN*��.L6�n�osB5i�99), 2�282 8SCM]{sco-chu-mc�S-} � $Scott, F.YChu�,D.W. McLaugh�X_�5:�=ewB cepg�e;si ce,� c. IEEE)(6I�7�X14�146�T]{thi:��} W�Eir$J{ A Cԙof21%�!VoleD:�?M �E� AtomiGMolecul�B����$��)>� �) docu�=�)%-�  % En�$LaTeX file�^^�� \�.X[12pt,a4paper,twoside]{m�} % RMP:�� %\use!A age[�&(ve]{srcltx}6!:ow�24�o",amssym�,Q>%t)�6v �ma�4=20mm,nohead]{�Py:ur icx:\=>(�2�renew�� and{C�Mpdelim}{.'�#,width=170mm heE�,=250mm %\par3 nt=84#3 # G6,\addtolength�$}{4em}J O }{10�+6>(hoffset}{-2F=v6: %� MP��.�dmark}{u@seccnt�<0at}[1]{\csnam\/e#1a� .\\e{0.5em$M Wov \hyphe�3({Aha-ro-nova�%�nts \.� bA}{��AL2a aBr r>BB B>bfe Z�.iHH H>5TT T}A�.5CC CBRR "�%26ZZ ZB6NN NBQQ Q>�C����}6ZR�6��2N�2%G%%"\Gs>PIm}{\o� AH{IE-6�Re>&RB�sgrad>' :�N)FGn>Qln&.�sh>$sh>$cB$cB$ suppBJ:�ctg>'}a8abbreviN:@i6�.-3m%e.�b!c�2 1>ze#�^!d!�^a��._hH5G H:�h� hat �.2lH}{H^�9�6�G{\var >Wepsilo!�var 6� bra}^�=\,:k�� \,\r: halmaivrule �� 7pt �04pt depth0pt}��%/ �{)�� em{�J{K }[se� ]�#8lem}[thm]{Lemma �!G #Ho�'ne$cor #"�e�� F*#*}.\ s�1re�F %�B4erfont{\normal \bfeX�4f>th@ R${% \thm@RDVP'i % � 1A64kip\topsep \di�3\w@.ost /hm �ɞ.D4 )�R- **}��;� ��\title{Z���uaQG A�4nov--Bohm flux�DL \author{V.~A. Geyle�O\emph1.size Deau O&�s,��dovian Sc�*�|yBKBolshe��skaya 68�) k 43�), Russia@\Q@\v{S}\v{t}ov\'{\i c}ek\\��Fa?��Nu��4ce nB�$Czech Techh�&!V0lTrojanova 13, 120 00 Prague, MRepublica� \date{{�}�%� �& abst�}AZnoP �bstudy z9�of� .�� Pauli� !V ���8��s� oid��e ��ang��� odic>�u�($ like chai@r l�co&W� so JW r@t*��b=HV+�6��b�in`kirr��bs��6�D����o�Ko <su��l*Nrce�79g .�7&L }8I&a�of.~(2L s at j+gy �are �nh]45a&����*�)�Kng%"!�most �res�� omen�G563~opologly�J-(��ofigur%}��s; �Kc��a~On2Kve .�- �Dc�J BRFHMM}. ��A�h�ra�(d>�!x,great import%Zin A4[�f�)ft�O $W"Ma.d� �(ASi,JR1,JR2U�yq�ingred's!�.C comp�� �am�9-N@ Wplay a�Nro�� understa��ano��A�On�G b�fkn��exrg�E� b��i�]�aB�j gedaf ticle mov�9i�Pmagne�)=pe:̢a�neP penetA�o G�S��o!(�th"�Xp!� '��$�� bundle�ya.�� rAf�� ifaD2����m! w1�C}Q)e !�i��,  N easy :�F�Sd? $d"�J�!� �!�($d=\lfloor|�`|\r $�.r�>Phi5_�to���e�:�measu�;E�1�lux� a,%� real $xj1 x\gek�$ �{}x�=��Qh��w_NI�ka��D (;0 9=.P nn-��$n\ge1$ M8"�w��O � =[x]�{ 3 '!�$x6?t��wK %�not-�2t �5�alɖ�I�'�de�0c��6�a�Lsubtle� (��e.g@� AMN1,AMN235 6,ES&�C�Zeinw �?cu�� t pa�)w�[ 2ct"��ideaV}�o>��I���Q�w���2��&�=�V�#�an��"!ahS�,m�aqsubo0*a : ime-�penSF>� {��sub �q��ke*)d��al coǜ ed b�E(��or ��)k%�sine�etublrCI���Kn 7at&��: .� focu!q2.n���B. In moM��Q~i�Aw)�!o�d� ��Y��.�nd!�cM aBa��ag�) �D�:� vo���g(It has beenL�w=�GG} one/�&al levelQrigor4��if:p pAx%n a�\ p��� �ti�<I^notvҹ� la�"havYnte���2�n�o)vw���a �oush�^ how n�%�s?c*�q psed�]!��)�rn�%�ru0��N� !,6}&e A�E/������unel��s��un� ofEr�insi��Y �=�� rA�*�ifL�add suchi�){s80ur��:�}a!�27�I Ugy@haN2��Vd�ty�sU&�3� -mod�!b��)���a��$H_{\rm{max4[(�G%�!��~e*�B~\#�ec�n-�-hist})E��6!r originS4�S�!� loca 7"� ͅs�� lled>Fc� e VMD,VBDM�E�er%�d�oSi���r�� �e!� mod �ionl� Oh}.l h M���!EI�A}���) helpAT{ �d� Y�Cas��ansatz�5 T� �/onA��e by Dubrov nd<%!&)DN}d[&Cj�ځ�p �)E�_of;�a�-�)ic�S.v"* ��%'� view- �Nov0���a_3� ��WA!��ble��fi� ]�6�j^a��"� Fil}M oż�"� s�eNan 3. ��I G��in > 2��p& �9rgani�"a2 A�v �^b� we tr; e�p�s��56ct���A�AS�1 ~���v "Mu.�5�I~pFop-E�1}} ��jrtl�[ gaug� �9!�H��#)�qy ��s�]/ bרV�+ �2�i��Jvu�?QM�]�l6�* %7iUm�X!�z is-���ie�  � l%l9Gregdef �3�� devo � � � *� �:� i����.�B�int� z4!<Q �� i#a��� ger-y B�I� F� ISst-�5j �!V���K���possiblPz�\8F2R" u*^-  ��:�a �n-A*�Ei�!��an u�s9���mob� ig:6��f{� �erv)o7R�B�>Bw�udy.sj�.���s1!�9jE"� V]:�a�add�9!H "K�ofl*�� :| s c�V�A@��e?!x]>��&ub �W P� affem���pe�1Pz6/w���)� 0.� & +�Be 7souD�B��!f6���cA��c�Av��`ܤ��reeJ�i~?ޏa�eP ol[. ��{�O d auxili�0rM�co"4d&�� �L�.e m�� dno� VJ7vq�"=���2��growt�Ve third1 x�E�D�Wei�rass �L&��..�AM�]om�E:0 b0}�]"�F�� ����Y> I��t&��.Q5��6V��S��[G A�q ��ep~��J�e�� ABJ� �E�a*3 �"��/ (�� it i*| } or� :�` ex})"r �sstiga�- bothU]or�`1ex� !�al � �OP,Ham �al�o:�e�d���Q6 /���up��!�-RK}. O�N hand�me?Ra �2�(P a�r$?a hole o��Ae fthon)%�� ne� �ic��c� >� � ��WU�.��in-/%Ra$i9T8-% �KDP,QHE-f��i��fea�A�.�M"� Z he L+�u pi,?"� B��D�of� qA9 �L�a�nergy s;�W��ke���ll*Z�.��)of3 a�!f�"�-% y9��� lG�- ous7ect1-�!�,��impurit�Jornhomog Z}�. ��:�fr�:о\��� imal5 >8.@B; eo�ile� �� � ,0ext��!�i���e lem� Thi,Thi1}�3ilarly,!i �2� �2j�3!j�m!4di�k.# � �<P�;�6.! UgsM�.8�Ms�!{ a spinles!s6& ��g������ny~s, let1��A�*�4Rui,AJS,AT,DSt�ESJ-"]%���A6A2��t b&ym�ro�Ca&ZJ vio� Ax� t�"�� m*g� K�� �n"�����Sto1}*��k"4�� 72};�Er�n;!� A�a 3$Nam,IT1,IT�"/ �."UMgdE�$A 2��*� ��e�G &�.�ESV,Min�W2�!��� 2��opriat$u�*�is~$edEE)k,dSG,Hag1,BDS-s�u��`�� n!�--F �c�2"tgu,GGS1!aIn 5M�a#�84, the spectral�  or scattering properties of the derived Hamiltonians are studied as well. On sufficiently smooth functions from $L^2(\R^2)\otimes\C^2=L^2(\R^2;\C^2)$ the two-dimensional Pauli operator for a charged particle with the spin $s$ and the gyromagnetic ratio $g$ acts as a formal differential !ao�\cite{LL} % \begin{equation} \label{1.1,hat H\equiv p(\bA) =\frac{1}{2m^*}\left( <\hbar}{i}\nabla- Pe}{c}\bA\right)^2 -T(\mu\BB \end�P% where $e$ and $m^*$%�!�ch!/mas5�p-B�, respectively, $\bA=(A_x,A_y)$ is ;vec! potentialA1�a magnetic field $\BB=B\bfe_z$, $B=\dd_xA_y-\dd_yA_x$bha�\F momentum 1�, $$ /=gs\mu_B s_z\,with $ $ beA�� Bohr Yont;=-|e|%w/(!�c)$, andfW.�,}\, \sigma_z=�-�AI array}{ccA < 1&0\\ 0&-1'!� % -�\�,(we consider�moAb)]1� inplane $a8T$ canonically embedded) spac )<3$). In general,HX non-relativistic limitt!9Dirac Q� leads to$value $g=2)8 main�B4our work dealsq�is ;�f gyy� raU� case'`an Aharonov--Bohm solenoiIfA< ��or!1al� �delta��!�(\br)$,qrefore wQq (\refe�) takeI� form�+0Schr\"odinger9 �Iurb�# t a pointiE�a finit!�uplA�!�4tant $\alpha$ V!� fron%Qr``$ �$-u�''. OI@other hand, it is�� know!atQH two-.b%lunA|�ide%�5e expres��2$defines a AG triv� �!�E�the��~Aaa5\�H_02D_0�F�Fe�Qס�only if5���@in some sense "in)�simal"�HAGHH} (we suppose t�apA�4riate boundary!WdiA�s)9!�$쥧( chosen). Ta'Xproblem has been analyzi�ɔVB}�detailA�$ an arbitrs posi��yr4$g$. To get ar� it, ayRof �$ radius $R%QedQ�rot%�x symmetric�i�lux i��AcbutI�wise hav! an �0rofile (inclue A�� [%srted I� surf��Z 1� cyliA�)u��$R\to 0�$discussed.�%ad)� to 9k,let us also ��io�� pers %�BV,CNFT,CdC,CFdC,Hag3,Par,PO,PYo,PY}. Of course�� same E3achAz useful wh!� uni�scompone� �his a�r �c�:!5���seeM>EHO,Tam1} ��ref�c�� rein). I� most im�g��d�fF�Al�<ls $2$�[Pauli�A� remarkabl!�!KIIyA��K� which m�� itA�si1to!,��!Cas�de%1aon �$AC}. As a�ult, wE�e aA� veni!I��e�QL:��� singular* by mean[ a quad�Hca�m !| S` on~�]`sec:regdef-orig:3}). More!�cis� %�is-re have,~ usu��$wo natural:r� soc��d!.��Z�-- min��A axone (�DF!u�SR�@n��mm+ CFKS�These%A�ovidead k�typ� self-adj�UA#� �Tno� 8$H^{\pm}_{\max}  in}$� D y�zA�rolk6��Y\2}s (;(sign $\pm$ �s� spin up%H dow% Y�ic � ners, .x �� is�yrd� nR  betw�!�9$H_{\rm!�� ! I�$it follows%�C9� s, b� .U ^\pm G!> coinc!�)�Hhe Friedrichs exten,��m�icTiaeda.Y� "p a})[Fn � �r!5o' to��ystem of>��/es�W�  taP�(dM>$simply by 2K) may b�TterpreAja *� a ``!�less''%�icl�>vAmin�.:[ � (�c� s to phys� �Ih(an electron���--o c"e an be neg0edY�splitt�sm�in!Rccount9� help!A���ur� theory�fLLa�Such a2��� *Le.g.,!�fAJS,VB�$�t.� vU� }�A�A� do no�M�i"� �Cindicat��at�$y directly�6�r. gy!�=Z iA ai�o{ F  yQ2regar� M/P2sA�YE�N� �#��� we!Icentri mai� (on zero mod�0�% . Not�at"� C��C� ngn.�e CNgiven in�� AT,DSt} (ŨeɧofA�ing��� )%'i�GS4!�� 'AxFo��te -!F�7sN existenc�Be(!b!--�eigenfu�Hs was��� [ �ra1,Ara2345}-��!�$number $d$alinearQ ndependS�)� s!�=J al:: �-QA�vidual.�4$\{x\}=x-[x]$,;�than � o-Z otal�Y $\Phi$V)Q�C henqon�v%equ!H!@� gauga varia-`�� fo�Z� see a� p- m�,Hel,HHN,HHHO1�8~ o2_ A�1�"j �U�tre� ''*) �m*� W:>jO�appear�of%� )�w��J� HO,EV}!Ye��ul%� �EV}aD� lic� O V�aabM�M`B� U�!�� M6)�m �I�� A�modynam.�a��ed��Wxed d~t��V�W 6:BkA�:=9k�� rn)3i}-�(. An exampl� ��� of s� kind�!)quasi-:� 3ncolumna= ects!�&9�~��ed alo��de7 axiq�4LLMK,LLFM,Lat}�GaAs/Al8 heterostructur�a:�!pl�type-II�ercondu �HBKP��\loI�l:d!9P(re arranged�(a honeycombBice��so-�,ed Abrikosov!�@A# i� �6���C ��� ^yh i�investig�re�t��zLby Melgaard, OuhabazA($ Rozenblumm�MOR�A� ic=m se author e[ u �KfroNBal� ]LW}�tʁ� no��at�s r� ioda]at!X�~:��e,��� it differI $H^+.w � -�$g�ic =lY�lu!�(a^e`t ��ott��Val�Q�1!pe%�s). Let= ) po&1� �is-SK a ch�jc. \s� {The:� q�!��a�} '�p op-�1}bw��� j n*� �A#R}�)�zz2&y�^2.�[�i�+&�+ }A_x�^2+�/yJ/y/.*� QnB ( ]\,.>�-�d� Eb� icityz�3�f�g s$bA=\ba\,,\��:"B=bm:Bsay%a�a_x=b$1 or[ to employ!� "� less unit� shall� �*Q�V�BMk1.3a} ��a)-��}5�\� A)Je$% Introduc ��f�2�,V��4%vPhi^0� \pi -{e}J]we# �r�5]baZ}{ mF)� bNBJx�&( �6k:Zqa_xa  y+a_y)^2-Q� bJc�O1� $H$���p�%k#)�$)"�es�*s2fP ��5s~�6~*} (\A; �xV�\mp�,>(2� ��� i � $) ac�n &5 $. We ad���B�$\ba$adA*�� s, � % WAX ssum�+z�7!�a_x�8,\,a_y\in L^1_{�dloc}(\R^2)\cap C^{\infty <\setminus\Omega)>&"� �a�cl subset (��yK � empty)�. Con� t�!*y��� $b=B�r,AC�Vtribu� i�R^2$ w�5_� �contai�.� $. E"?s "�}6a}) re� F4��do� $9dR^Bf$;0.$ will be& o� B�, �)69a6'!. I� ���M$B��}th 5�0Hi� term%Ibi�I� "�A�A$)A��/�� y wr,B� �� �)$�!� &btAi�uM&�$bA+ a �U!��i g�,�n� y "� ce,�^F�e" ing��. % M Oorem 1.1��thm}[�i&��%he^�]��Xthm-1�# %% g �m� $\tilde�}bF�)��same F� $ (i.e, V,\,R\in{}�f{�f�P;A�l{}y ��:n -E�cdd_6� t{a}��Q  !@.~ T�.Us2 u@!6���( i\b."reR� L �� | � � s a~real-a d"�! $f$ �to98N5)$��.�0=\ba+\grad{}fA" b�=W^{-1} �W�Lere $WaT %=m Y�� via multi9�����\exp(-ifa�� A� O.s��em�m well!"B�!��4$N"&I# (� 6%a$5�0�2qA[Du� lemma�x ele{� roof�mmu%�Ӂds!s >H$�� �� Q%��11 )Q$. U_e Gr�ula�obv !21�na�(*! &&�w�=V+�� dx+ %�5.�!��^(6)�)x)�)Ady -)&&=p)6W[ \,%�((\varphi)}\ kphio .�2b�6ZF�+=�U-��*2Kn��ZV�-!�)]2d%H:=�H�? us�!he facAF&bE�6���"w �'smo�qEF��N�# .Bvanish��� � .i�m�6�[P��of�I� #��v � F���!��!�.�a�!ard mannO+at ife]B�0ie!�e�!B��2Yaht�j^rkf�&�g� ="[��nF� B� �(�>� obeAC��p�Ly�t� ���5����$!~s^% �'��d�by��"7 ~� �*� C6�H �ll�C Q � +A%2Xr%o�Cleave`v�aK�L-!�BH��i�A� 4 mput�� shv#S f =". [ "= . H�!<�jk *� BN� -#"� t:�a R�'2: rem�j5�M�]�Y vV�26�a�;a�+ �uF�2"� ! A�)� ogou�.a�T �X�y�  valide%2�k{H}"�&A. Nam�'�zA^ A_xx g A_x��  A_y=B3a�uZ�A& a�A�\haV�~ : M�W�=2W=i\ (ie/�)&N %U O�h ! BZ�2trAVrE�Z�M�C���!"�4. "S� *~)&a ' fw�4Y- � �fulfills�Lorentz ���)ѩ&� .� bA��div}\,<0M�2*4Basic�s2 �s2&q�cre� sev�1 b2O��6�s �� �"q7m!A��a]�5+i�%� ��yV��� major� o&��G#Ecur!Z p�!�cern Es~5, 6A� 7�2it"�co"�+ to iP#if Euclidean�)"3�A�, lex 03Ce2G�2B( coordin#&$z=x+iy 2,$\bar z=x-iy:\���#*{ �~1) homoJ�jA=�$B=E<const}$�&�)%r+A�set $$ �0#B}{\ ,y,\textrm{ }�/� x5(!&Le�*�om!2�L =r2S\Im! o5n|\R�).JIAi*!$b=� \xi$�v �*�"Q�%4 quanta throug](����a�&� �f�" "O+ Z�yb})�obviousd�#ed.a�ub>�2)��)�af�4} � $B�4=��39P�%u a lux 1%�]'eB�3E`b> }{!����y}{� quadYOR/x/%�E�8�ly�6�\theta\E4c 1}{zaa_y$Re:$$$�8 H%%/!^�1�&%9!�qE'2%:h"94 Actu�2.5!�* � s8DA6$\,\ln(|z|)I�D6z0$$I�eal^PB^% \dd} x}6yK = Ph5�� C6? -9"y}a�d)�N:\!�d �x^2} +Z y^2}Pln|z|TPhi\,5"E$�N�a$��b��t�2sj|2.1)6 ba= I!-s� �A:?%iv! �Ay�i6-a #l/$ F2�/Alsy�+c�4f&2,v�2bY6 Q f=)���=�fS%�x}f1U,BR� �CigQ��5he� T�d�a=0$ t�7�� �Q$�)[<%^�3�& &�5�&o>6$uds} �!now"7%� r5.���l!�l�(AV_�)_{ "��A�<�fam� �al �-�Q+ce>�^M�i�!"((of :D�ke%ter�g' �� .4 �<�perpe�.3$�$ C�Y ��+ �$:al��m�� pas-�)A�� �58I0n&�(displaymath� b���/�;^0}\,B�>  \sum&�Bs}I� �Q�- &2re�,!�!7� C� b N"6! 5*-$\ a��6ga$- 1�LandauN A,. �s�a meromo�c*�M(z���%*�&� <: \medskip \noI.nt 1) >~,�e polp�|,2) �e� %f@�3mQ�,.B3 Bresidu  }WER5BQ�6�* J�Acch "E,Mittag-Leffl� �a "�alwayH ists. %Ape>x�`� i,7r�4 ou�<� 2 (96+-�, Cauchy--Rie/9�s)� 5�� a_x(z, )=\Im !� \,, A a_y. Re !��"�&<bw� w0*5E�ymbol*�d!,\Tn AW� $ =(2�N7�f$4 e $(>Od� �nJ� ��$ unambiguoD up��� * cejT 4�c � ��aka��,n!�Eof�u{ Sepa63Aeĩ�!c? w<mu+ �*a� p���r��Hf/ (5< q F!��ۍ�N� �J2ly>��.��+� �s>�).�� tart��9 �(!invol�,�Bii�sF!: 6= �$|AforM��)$)&� we m�moa] G\,. W'(z)}{W' $$� ��1$$-��!WeierstrEc?CS"�. $W_I٥�relX;�S�1�"by���4A g(z)q� $�ent�.�O~I lof���7 $%/ ��Ee�$,5��X!�9[ !�T��s ��a��uA_�5n�j� s2.0}� �)E�\,{� ; �|�B� &� lo�y"��2$ &� E `�I!hG}v "` z}�,��� cln :�+\�5{W<%r z�p"� %�U� )2�%una��a6� y.� =-"� 6^�HI"�8,( Q�_1$, ...arE _Nu �s� "� &\(R(se5)�4 )� _j$, $j=1V(ldots\,,N$,� "/| <�<) �#�{�sR��(ed 2I=&�A��H,a~A�&�Q6&�"�s2.�% E�.� j=1}^N{%�K_ji� I\_j(z)|)�0\!\bigg(\prod" Hn | 3^{19}.� �岁rjZ��s�<e�1a���n�C�a8!��Haeō�_j��?s��s !HR� �f  _j$ x8�"�$G)� �%N��i�*�DB%ABH&)dF>-�)"N �Y�<6{\e�4� type�7"R?ƛ &�<M _y+a4m�;Ui6I}N)$ o}Kj)\,;\,� j))a �:�C&^4�5.���t�+�E >�=,i�D �-V'*�4group $\Lambda��Ci�5m� �J�Az"�"�"s,!oh Q�e2co- �. Firs� all70��?es.�"E"� >�� by!Mallel�8,Kons. U� is� sm�r�( j�8three ^ �isEh4 .a� they!��4V>eri�Gb\ Lir rank $r$ ($r=0,\,A92$��# nume� "%item *>[ 1�=\{0\%B!~k�,!Wm> � M1^M29 c=$\Z$ ��N A^�LE =\{k _0;\,k Z��[a non�� �� ��R6� usev=K+ |*�K ` �i/�P``*n( /p''nF=\{x�DR^2;\,0\le{}x\cdot�<| |^2�(or�@) �le2{,ZzZC X\bar<\ _0\,>\). Si�=eac�#-<G��uniqu� �)AG� orm~ c$=\kappa+\l%�$,i�$ �"K%�3 %l)�$,`Ui$-v-t� ��} .2"s�5sub #� _{K}&��"  �}�U�2���0M� �+!"�A�_1)-_1+k_2 A k_1,in]��)�� -i_2�! Z B1@.� M�n)��qOM�a�e�!Va�M�]� cell�A�t�t2�A�, t_1,t_2<1\}�3�qj$�CA��tRi- �Lly�/en����8\wedge 2va 1�2>��BMQ�oC!is nothK �L��$area $S=S_Q�Z $FM l,;UEk�Q2�"�W�7l usse� isZ ses s"��qkJ] 5. A���G:�sy:�.aAw2!A�� b, =\o�� ,-sn\}bn5SbBT n�j:�� A�% rule�BM�&�����!�� a�L }j�,"� (|z�_j|�K J�n�*�M�� -'5);r� n� ^�6!�Z�<2�A�.juz7�U� s $��1 p�M & �96hZ�/. WithcloNV � r|6_7 $Kr�"� =�Ao� )H�$�{� �5Yq*�= z6� O,Xne01}z}&{"�e^{z/"�}FR �7\�P^2}{k^�0&= �1}{\pi�<6= \pi z}q`��T��T%u* "�=\s�NC.8u-%t"? �! ��| fb��>�| \^�W� meOA�w J �., �ctg�, R*�;Q *JV J NVj� G�@ � K"E  2�R2\ $Ke�et{}FI�a�&!B=2�"� K}��.�Bm } �U� - 7]B|#JUr�W��3�\/*� �i�E'_ �}\,v)�.5�=�(z �25U4�b 7� �}vr� 2' �.���9aQ=20W �. Again8'�bD�, h�+QRi.�H�� 6�"�Iw�.�$\�Z$-"�� �"�i$ .(z;�m��ɾ2)\� " ) = :] +� _ &�,R} �8�1��j6�$+I5�R g�M�B�(E�i�% =\zet  J�D�he:V;BU1�9U��uyOe.aOmW;$�|*��c(��h (z),aZRe:H'e�=�QFΘ F��#&7�6�Z!!����O*mA�� -G2 ~�(%]5w�x-S"� -�,e��+ipF�'"Paj�� type�=�K� )�O.*6q� ?a=2�0phD6*�:�*=� ,"$ ee�"�'�f�75.1�C "�&phi=b7� *�`�. ���BD i&�+$ 1, 2, 3, �+, 7: � yaM7i��p*(x^2+y^2�D|zH,!]$$zLq~lnQ�'nK.gj� nf& ln\,�=!(l&� J +. # f�F� � �>� �I.1�%_ �(����a8��)� ��)��*� ���"9$L6) �i,� b �5v dф�2-2(!&gma5 JZ59n���UZ�"io5�By a���� ��$Aa<"�-peL� in�! � 5olDd �t0~H(�WO-�bl"�����G �.b#��I .�9Fa�95z')��%K b(z'Z: 'dy'i�B�pF� _Ka>  �F� �V Nov}!w&�C/ ald y s�;� !��k:a*�\.� n L�}>�  [&2a%h�,&�6y��s �B5��"' 5.18�$��~z)���*.$ v �%x6�-��z'- 8=�!DB�ForN5�%� $ Q_0��+��KA F�_0$, i.e#z�>6 summandi-0%)y\ne�$;M1��g)Q^)2�-*A$�+'-(�)%1 dy =A��Jb�.M , �z a]^9zor^>u�5})�_ stCG�7� it a Q] � ���׽/e�!�B��d��1f�,�<8A�PA.; phi$y"� L s�VED mPre�UhW<�7*Ys &�[S�+ ree  �- ^i. T �C � �-�kZf,rb�^X&�QI�*Q�\1)��et,*aKrY) unXof s,�)aU1*� *MNs.�se�17oc�W}..7A rigor!5�!r7��P!Q&�aɟR�_p abelYQr2Kay.u�Qtur�c]&5�&=;="y;&�E$_�6i1�J+le�E�hRj7H:satisfiadM�2i7 B�j��J�\ �6�NP_x� P_x(�=-�Q-�L�3 P_y0yJ0y-�LF�%In virt ,17i�a9J b&S)ed as Ns#L L^2(E "�+&�K>�C&hw�0F�!|ycCd �AC}��Eb &�I~^�OT_�J-2 26!� pm i!X�%��h?}�!T_+=-2%�{� z}-A&,�T_-#z}-&{A} ${z}! , $A=a_x+ia_y*� �!{li�[:F 9Fon ��>:&0F �"6.1�' T_{+}T_{-a+-�2AY-++JEByR1tra�n forw�A �-"[verif-�$�"�L H*�KB 3z�G3�K " sms�$�! �KJq=9�F,[P_x,P_y]=ib10 [T_-,T_+]=-2!=>D�)J>���&�#, K>�F,B` iGL20i��"� ٱ�>�>���vy@6�d0Cy� $P_x" P_y$ :�QT_+ A�$)-q���D*���5ld@ >D�"�9 �nd~�1�Vm�^*!B�qmp^HY�we immed:gly deduc�@at�[�NBs�(� clos�]}�)ta��4R�n�6 6.12Eu͙OYin�� :(.�pm��*�pmB�A��8�(d�h, �_,� [$A( X.25]{RSII'6%���dh� &�h s $hA �9!ur& �Av�#s��%*�h��? \bra1  |-,�G \ketJ�.�.�t!��d side�+u&Mb *W=� �� ݕ�~�2c| s)pOH,�)=�Ũhi|s�+ �H|�� ��mpb%J���u�6rE/f <6�K)�� E%P��^�2"�C� orig H3.i�heJ�M�)"��-0$"`vGC�~.�In:�Ρ�or�(fOa�F����G&F?��P-6���� t.�q(*�-Z-al�"4corAUIf��)&�S� a�f��*} Sfin}��j�>�� o[ %*��A�#�"jaa�6�B()t:-�Bpa.� �Y� s.DV Y-%e�k�R�H��^,X^�V� �-euwuxp�sN( Zm2cor.lem�[\sa)z�YF �E#a viewJ� *LG�Ka�� #omenDs�.y �=eY�K steaIAY�cjYI�kA7�`J�ainS(s"yh�a JJ�"| ��v(�R$ 1u�*064�{daL��ax��:.tt6�mpd ^*)�*��a&�o>T��4on ${\cal{D}}(e~ax�)UsYd��e���axF��imp���ɔ�y���1"�/�,t*���"�%!in2`Al pr�Y�e�ia�a�choic�:���'�>e|�� f&�J����=�m�7$b ow�@.; � �Y,ail*a�  S@o*8r:Fb,2 ��Wb:!-"J5,�at- �VZ "�+�) �6�3PZ��*��s.~ !�16=\q4set�jOhqU>���*�->��kr.**, 5��UFB766�8es  {!l} �S"�-i��!F�Q��by}` ��)@ p1I��9>hpq"tb�&!�S.}s&�27 less�&��E�"�:� �9��x2c�cp"�n��q~2*o e '�I1;"�p:*j ha�z.��gTnR�_y )Jq���1)��P2��2dy&tq�gB�|}. Below��g �Lhng eze\5*�h-2ndG$�p-.!�h�m�$. &o!DW8ysi�0h 61+"f  descrip� :l�^*���x.& w�to!;d��M�12�.�-i\E1 al_x�$E�.�)�2�^Te�~ofY-"� s��']J8C. )%52 $��pm}�^*� � M� na�wla�t�ooL�/ mapping�C wide�O{T!�:r��&Xfa�U.Sis.�&�to ��Z$A�ge�/*_^� 32� f1S $]H�7dtri:M!�$> mp}*"T"X{WU ":Z-5K_6#\ >@� 9 1>a2bserv���� prov��H]^�42�a *�b#L5C�;a�5v"�M njug�, $Cf=  f� C $C6� 2)  mp}(F5T�N! Aw N FA FA2� T Corollary�  .corof %� �����^{+2�� � � -6�� -�w@�mJ0tX7t+ -t"`EA l �?c@. A!s�V1T�EGT\sE;!�DC!���%UJ� �>�-q!R.7 Elim�Pioe;:�"�1��mgen��2,intsR4*�Ph.CaN ��wX�;6 �'A� +\ba_{AB}w�$�Br &�ax�x�> b��&YF�Z&��g� pwx�B�be �brief x he "m>" #ity" of 5�)hB�$5$;�s�[�yfo��`��Ju���:wC4[5N"v*�9� carr�sE�}� -�E���>!�� �� pvK1��,:�*W?$ (cf�g�Q~4 B� R)Is21 ��&�<�stA�^�e �,AFg $ex&N,�H+*t%>$�}{ � &(&) �V�?(?0�\,\argB)�.9($�E2�E �i,%Mt� $\C:�$. "/Y$|�|=!8(E{}z�"B>�q , mo�u$g�8~l\B54z545�9]i�neq��tC,"Y "�s�,�ru"#geP��*ѫgR.�_ 7yF2f72��>���^ It�4Ho&�I� %0) -i\,�] g=gXQ5�"la��� B#&iie.�_N�D2�)b�}%&=&za)�D��D���lnI�251rV]B"+,"�idqVm]"(a=& !1Im �.�D =YdE#\� %V,x� -X*aAn*RE �d6�NBViE"�*%+N"� ��T.�=�B� �y.�:�R6AS)�>�Qtd!AK�M�B�2��i�F�F_nB�P*(�1#$�$�A>�&�2|H=%_1\cup9 ;_n���@D5ra�yѫd(`d#.>"�=$j)_{1\le jn��L��(m{}�P&�Re�.g�v��dR���� ;otW}:t^�/"*$�Ao rRGL)j)ag"B� es �ITj�{j+m�E&�^�46�l. �^��5�$A $H��o i�l �25 �leaha�7b'bov�R. :�(+k f��:- a�.7�+B7E%�&N x�`*2Q +\2��4m.�6G�V=)m�ek��m�'nTA��,' 2 A�.�6r�on� r"�BUp9l-T1�2�$!WQ5@t0�� �B� 6=' . By�ns�{ionT �:� J D}(�)=.��K�L齥�:iApply� repe�MlyRqA�^��!UrA�eAR ?,t�P� $U$vRa*jLU�9��r�$ ��.s5$:�d? b}U�-T_)gU�!1Ah"�:N"F#�Q�_����art���%�U=6��E3^{�  D�^\�|U�^�2��*vU�= J�6� � .Q��6(�=.��mɑ�����v�� �6�2�%��)� �6)1!�) 'N�:�^��C "A}�ej�c�VF| 1�y,.�cor-1AjIf�7�a���jZ""� � A �^�$6�&A�.75�:$��Q3$�.ѳ!-"!-�u�R &�D�<>XLQ(a~/�\e f�8is�EW!��fa�6_�2�!c0��*>K�:�2�F�X�� � Lapl?��' $-�1.7"� 2nw�$�� ��a6�A�ZPM�5"�L"M�"�/&�5� �C$rk0 r2$ap> [i�  � �>�:��s: &��E� .8}s��i.�&� EYn �J{�I1�A�GA;Bcf:�m��Yjib[ A�� j��iP �� �KA�a�b�Ng�?33sitK7;�JMB�� � �1&~u .=la��aP �m�*�#�?%�g6( i��  �Vc�eR�� �acts l�U �xK4��g�ShoԄt�9+-�9��:��E�!�E� }uʎ+Gq�2�~.�%?A�9!�l�K3a�nd �j�PanV��)"�in�a �2� Y:E�����o� %q�ly nega�=CfimC�h>D) H,E �'I��:�S]"ES� T�um��P!sa���)�>�Hw_.fGly sm�Q(a%� Nu�un ^.�I}GeyC�.���!C�?�*�u; 3q�� >�p���V�b-F&� �a�P N+@)�AO �?�G!'R�$�"�O/] `����vgaFi�na� $b>b9n�+.�F��fH��aO&�>I �� v"�h�G>; U(\�K�a$b<��M�! <J %��!fQ�Ʌ-�̓r� *b�mEAA To&pl 3t!�u��tol�DV)Mo R�$�Bat �*����T���0Sώ ppliZ����a 0� T"^:�^ bf}��] 0rval $[0,1[\,j��rxV�o�S ftL�!�q� lar2mB���o�AsF nǕq�ies:�2�g\����3}".�c9�ez>�*�$�'��sQ)�proce + our �'if�"s�� n furtherA�M} saidR0wis�o)� �w��:2(oe�g9!p-EBI�8a�V� $]!�eu,�;"�`k|�� d �H  1�� 2/�6�$(%bL�)K�6l%2� =st<5�&�i.�3" <&�$��u�2t axG*0Y&%[@ � non�). 2 if'�(r�17z�6la1=0I �F>8!~W>'4_,psi=z>Za����A�0"Q##&�Eis� "$J &(�; Ev5��Aa2�1z6q1�.*%��=N$ +i bra{.�5psi"�2=���?1>Y $\|6�": \|^25�!z�&!���R�&2Un�7.3m47 &$v!���x} .�w:�a>��gB�z�c�%mp��Bor���c#,l"�<~m�.\w�&&.��O%�K� <�R �!� } S.^�!�>��$ ͗hE��"��� �:.I�R�$ �= �} $�.=�a'�>{(� seek.cofS�^ 7.3d!� Q�v�B%!/i�DI���5RBx,y))fLD2�hM<)f �pB�-fc%):� -T�2� $ ({D�u & �= ansatz}&�tsQ{!*bL�s��(�!�.1*A�-%)+ .�+ \noCWr��%/-!I)�H(�!(i��?)X +(�y;7�*)f-)- 3f+im~yf&Bt>!� w�\dd f�d(z"�9�j29 � �- �.�)-^��6���Ďr��-�-�� w:� *t���; w��&�;�b8.�A��� 7.7&��I��> 2�B#�v>f � �>�-��\,\,(R�#. #]7:�*9:�2W�,HH"ĕ%-�.,-�,j,8�>, z�(Ef�':� m(�due�XAh��� ��@AC� +�5v�5N$.�J�� �5\ !��;(>�F��9�v�O5V�GF��L���16]i:` N exacti)os_ +�^*� (��k�͂+��  (�I  z��&>Cf%Aa�&�c*�qi! �n�'��5,B2��a6)!l�B��n���- �����2��`1 �z � � � �u�_i��utG��2�shI�� mS*HPro-on.2w-��.!6FJ-+.*="].-�v�"� Y"� ��j.8K�2� � 3*0��;>�)J8b` ͌rE�+sle�po�Bthe*�p}"�T"3!M%�4�!;� +$. : i] B�=� f ffoaP./�#�*��n�����*\u$���L iI��f A�)g��I�hoy�����$gi�nti6?!p��pi�,e� is [l� *�/�a$Ufa@{gl&T^ri�c"�0��r � N�dA�lA�%� � 9^ :E>nI����6ZL�� ���EZz��z,�u:�!!#$��,rad�3 M�*�Ze.^��Qs.�� #]���2��"�$AB�a(2�A�mod-.61"c{F�N E�0�E.:�)-4A�%2�X/study2����k>�cݡS&A!�n$X�&]��0*�B�o��"�( _1-ab�G_n�cua�y(~ D.�(�o nec"��)"2!2zE!n$:�/JnB]&J�/RЄe<6-b $0< `j</%^ll $j�We�&hr�k!�!�� !��c!��@ eOa�r`'H>^".��9&]&����oI0 squ����grabie�8u�e�ŁI �&� � X-�N6.1Hs����f�QJ`X\,&bX-15,*"7c�!-�s $S*����$i�N.Jor V]�VN�0Iap1s $upWx�i%.�%.ula4s�q)k>:�ho2�7>�:&=$�B 6&� 8# �66N� �=(� �Vonnulu�$$r_1<|z|-uE1 ~�i#�.��%q�d1U\g�0fW �}{n+2}�2}~B x*.�if6�a_n\ne 0�S $/v������ftyr�2=?F V�g��kJ�>:V�d$ 99aYF� :Z6�e�a�6e F mat!�e,2E�F��r.$0^%�Are^{iw }A�d M,%ft|N8e^{-in,}f.B\ A\�+wYXERe�*�� \qedq�\renewco^X{}{��%} An�#4�X��*k ��{W%4)E�?auxili�,�VJ"�&!�m��e].y "Y�0�t�S�KE��aY���\beta_j�5%��� $-1< �si $j�uV��N ��2�� :QnB�vn�.C�n��� _km�r>�s�6o�" s�0�ZD(e,r)�D"�mir-$)���C �%� us.( Ϫe�B"/�#�g�#!��x )�,%|$j\ne{}k1} #vaq�� � �xkX}on� � �t!�# eno�s� QlD�3~ M#}��c > 0U�A1$0<"n|i.2].}�&z xc�Dc^2j<^2Ι͙ɾ%�nnf� *{F�Z� !!:F� }  6viMust%��& *�[F� eQ"ς:�.z)�B;7i!(E =5z � ] C!u��i� I�wqa&a<�[B��1,6� ��6Y ��-%(e�߲Goccur � suit�Ti�p!��|-�"!e|MH�preg���Օw ��8ra1N:*� j.�� � �4C �y��Fa��"�a "+c{9��  -B H){&�n� 0eq:sum_tj_gt_[ .Qajpf-� j > tR�  Ner%�p +S"o-�!�B��s&.A� �jB6A� *�'b��f _j|^&��FTs :Tle:�"!~(�9�ER�F&m^�a���`��Z�asy�}v8rt(a8fNw}l�B�M> �OC��r��2� ��FHbu��~�� fals{:�b�#%�!`eas*�Y�%.�QYcx� F�'more, ]A#A��AT���=�Y\,6�q�\in J!�6{VwK3��� .�d� $c_11 U����1c_1 (1+�j>��v;�on }\C�}B�& $r>1� b6�.l�� 2r��X� B,c_2 = 4\,c_1>N\R^2}.��Z*��8in1�m� 1� nf. i!-ɓU�  5c�.�62�/"J@� e�թ� *�A3�o:�T� B&��zA-x�< Vi] J)i�e �= argu�,�OoJA�+:�1&�I���  W� A ^�x�ۖW> !*r J%6(� f� u6�d!UR ���ly many ��&�&` �u��e&�>*� 62�� .΍%1QII_�,y�����z=f�, $x,\,yRt� $|\sineG ^2=\ch^2(D�(cos^2(x)=\s +'x�d bH h(y)�S\le\c4r=#6.4*�! e^{|y|}-1D\l2U a�:�B!6."81:" �� 3}%F� 2} omit�l?aA0 �_i&;"�, b���R��d ��WK"Z "� I�� ! .  �B MBE�i-� _j=K_j+\L�k_j0P�IR��)��n:߀_j} �j= � ,n�?&� ;<1"�[ �n�� )��haM}Sde�s �!���%�!O]!��<( �"� A6� � )DA��5~ BD  T�Z mple��e�it��in1u�vD>�P_j"�Q E��+�Q\,D��-� :�6�E[� +3^(P_:fM P_n�69S:� %w~%i��cAx�jrmF�C��sst2�|6V �- c_j}" }\,|��H' z)|�V��&m60��h9c��jX�$(�*� ,� F�*>��$�@  n$ (&��))V%s6 R*�"~. 6.4~�F,�$.�!Jh��&', 6��A�5�e�!�NOBt*3�$*l6^=O��_n;-B))$ T�=n"� �J��&�R+�� $�l� ��"�:dZi�(i*�++�+ �n�+V��(i8mP stylث ;��Y [� �"Q�n}> z9� $�Q min\�Ap�f �j}$� Rg�(i�n6���ATF�!&Ia��Ga�!|���<s $p_jDSACp_j �A��V mG��p_jrQ=1$�F<^,[ O/( B�)�M).�r��" �_&F ~E�)S &]A˛[�ёbi�{a� :�J�_j&H�5 �<;*�j} !�+�� �_j<>�E.�j�j��Se-1g_1�s�)!6�E ���i g26.��!dJ2>n'�KI�:�1� r�.�\ " ll � $|^{2p_1}}{6_ |g_n n n� F��/ �B�I�I�re�U -!�� �*��� b� 6.3}q@!I� ~����RHSJ ula&� �!��gr�"D| now���"� a�ij�n.MAVAG_�9��"�1J�,"�1�Oq]Q*��t�aoAr*apN�| �\� &� /Y�D�[q ~Y2QY\v0n� "����f� +�� a� �z�3�j �� �M�YF�1> �V��$j.�I�$�$i�� /za\z�4ޑ��2 : �B�1}-,�E$j �*�� Bna $T�=.#a� real�  Ł�J� o 21 One�Lco�|^�~� a��(eo ��}�+-ASm����Y|A�qEc�)$͔ͯ-�'(2)%0:lF. ���w�0BZ m�.�� !M�)�sin �u��� ����N�&�o���u ��II 7�& �, 'W�/�n2}-=5 &* ��N� M�F i[X���0.�N�3.4�5 ������0 �y��J$-�<� sVaz� ��@P &VC��� >n-1@�"�"�b ��ispla�<��6�f� Z��B� :�$�*BQOt&C[] "� A�*h!4<�R96"b� F^&HY�2��T"�| q>� i 4crystallograph&��Z� a�[���z1�2W22�k7O�%z�.(� ���W*��qgm*t� (z��\s!R��$.�uf ��e,*�rm.Per,Per�w}modified.�t*���e }r��2� tiDe%=;6 \nu ј �7%�Ul*�i}{4S}(\515�)2-21&Hj=2\,\Q��i) Bj�%T9S=\Im*�i ,1} 2+��$]2)!D6�{=:A: ��T�w-�-%--' A3"F �^�� �s^��$,�0r��g a 9�� !* u��#?'�f�ub"�r9�Su-�S2SL:�"�&�� 6&�&Vn7:� U l�u "b&b a"M�h"- T' Vo$5� .�� �� i $bv2>a�i �t J � Z"�c�r�Znfupl' gru�"modulo9�@ D%"L �� <\mu ��51 �\i..n!AJ�  (LX�)6�- O f 2�-�� j6�Nt �r+1!�F4U��+a shifVV*)*Jy�!�=(�'�8L_\epsilon=\{(t� )m�1+(t_2+>2;A�.}.`t&Χ*� �� $A>�8:Pa�t>%ao$��A���I� �+� �ͭ���,F~w EDJN�7:ED1/NF. B��o-� A_f��3�$.$<{��|ZL J�0gAR2YS, m7<�=ITEQ.��&rho& i�5A�V�_%��z�eq:��rho_zg$a���,�P�� z^2+ńnu2\mu z�� 2�IWB�$ �16�)3�1%�J~ �@1q��I�$i.�8=�#N�| �a�� Pyr F�m ��Ra)Q� $ e a[ u�"xvŶ �-21FI!w��2n$���mm>:9.�i2}) it holds true that \begin{eqnarray*} & & \iint\limits_{\R^2}\exp(2\beta|z|^2)\bigg| \prod\li /\j=1}^n\tilde\sigma(z-a_j 2,^{-2\alpha_j r$\,dxdy \\ �8qquad =\, \sum\�(lambda\in\L }\,56�0L_{\epsilon}+ 4 k4exp\!\left(2(\� -\mue �0)|z|^2\right) ]b�N� rho �,\bar z-2�] �^�\le\, I��� sup\Big\{��; �4textrm{ }z\in N5_(}<\infty\,.:8 \qedAHend6F4\renewcommand{' }{} (lproof} % orig: Theorem 6.5 M�(thm}\label{$thm-6.5!<4Let $\Omega=K+M�$ be a lattice of Aharonov--Bohm solenoids with an E�,Dfluxes $\Theta=(\t$_\kappa)_{ \in{}K}$Ao$0<2% <1$.�n eachT|the operators $H^{\pm}_{\max}( �; s)$ has�0$. If%8Pvector potential $\baM l``sufficiently regular'' and=�+!q!�%, $b$ through!�lementAOcell A�lse�"n5�M6,N�is pur�V�(se~p\cite{BS1,BS2,BSS,KL,Mor,Sob}�others)�� samAZ sultbM/Schr\"oaaer�%of)1� Bis i�ace $m�d)$E�(any $d\ge 2!�+ ��(3$, N.~D. F��ovu4dZ �Fil�q5 shoi�hat%{assump��s ogB� steki��%R6? papersa�notA�essIP(ly weakened�Mf��s� < two-dimensionali� U)wa sinE�21m:� may hav�(RR�) eigenvalues. In more detail, let us take,M��,��K$�jain��wo M�s� K=\{��a��I_2e�aJ�*�a���\equiv �u _1}=�Q2}a�,]0,1[�w bynka� both9QxRh!9�9", namayFnumbere�!�2�E��$~7 from Se�3�� sec:-Es-�2},RA�or� onamF��� read� a_x=)&\,��zeta -g1)-:2))�a_y:Re(:(V:.�� quasiUxit@ !(Weierstrass", $ a  +��j)= )+\eta_j�Mer!$  =2\, $4 /2)$%7^'���S$���� Now�we�!�analog��^�3}��a s of :b �mL viewM!-�6�E &�49.1" not !  repe��rgu�XsI]]� ofn�bu��pr�Lti�> modified .�$� $-� 4 simplify matt��o ably.& -; New �  >� New}%>$6.2} omittR � a uniform iscrete �~> � ,expressible D  disjoin�Yun W q�of9� M,_1\,,\ldots, __ne6���!qM4j=K_j+�A�carry:} �Bb r[ _j}$ ($j=.�, �Jq ����,HamiltoniansF� - )$ ��R��Aesm+%�1�Ej� I qeDp + only%*Am� �+] (Without losaG � l�Kwe2L $K!X is a�� ingleton:�ej\ !�E� writ!�� j$ instea� of �t�Uj}$. B �hyp$ sis�jre . �mj ,disk $D$ cen� 0d at $0$ such��9�m��%�� 2��%�$�  1\ne 2��set��D�:1$� 2$ a��M�. Denot�JL_j:=D+�.�\,�n� every $j� � exis w c_j>2�$V� _j.� j}\le c_jAx $z\notgj� p clea� aa�$$�-pro>J B-Nn>.,j�,�(\,Z8_{k\ne j}\,c_k �>�F_���>� ref obmLe/ } A�iE��/4� d ba}%�$also validE �t roved by ��� methodV� ��jA�j=1��tbe mutua� QX� De crystallographic�s, S=Jq wE[$aC$5L�_a�k"� 1^{(j)}.  * B. Fur� � , $SW{i[}\ _ X)$�ignat3he!ka o�0� "� Bravais1"|A�F6.6�T�a A .��+H"�= 3P 6�;��5� n��zY��o1 � foll6 � ndi. � atis6: aomedskip ,noindent (i)�`1+ �+� <1$,/Z; ^.n}-& \mino j\,S�\,v��n=�znd $S�� S_2$�+�%�":mҊ%H^- =�S�d� � >n-� � ��J��6.7�� S(r)=2X5 � e�, 0<| |�r} ^{� }L   L }z|2}|T�|��~3 ~n~#\>�;\,f�\�:�J� 7.� -k*�7� ����A�=ŭ+��a�:� ,  V�ie��4 WAJH"� L � W#�  $( A��I�>"�ums $!�� ��b�(ed, $(b)$ $%\ O(r^� $(c)y DAtbD� |=,��,.��)Ob_��**}�N >�!�j!�� � ?2J�If��%o �5,F*& ��"ye�>0�����E��b_��� �[claim�Raing&�� � chang� rol�"9D1�RZGa6F�A�>�"��Fa��~}$:�5*�0$at it�)�y)�,�wiGr�JZ .\4�b R8#*�&-"�2}� F�&3_� |W_j��[ �S:� !�4re $W_j(z)=W_{��_j}(z#) W*� canonical�duc���w��_j$�  A��dix)Y���d-lyt-fce}y%�.$non��!re&K(cfoV�#2})ekA .�(a), (bc) .� a_ac*D$W  Borel A�<%L�l\"� �Z �A&� 9�in5#)2"u-�� or%2K"� typA�|��!�(z)��{}a_jAE (c_jE-)som+0tants $a_j,\,�!^I��Aa �}>�͸eq:b0��Ac f8b_0}{4} > c_1(1�1)c_nnAB�AT5 (%=�4�*s squ� g���eA�EL=p&qI�"� Iq*�%�5&�% ��.�.�J�a6���$p_i] \le1m �3.7}))!�,2�b� 9.5}� q^��1,sY7aF$of minimalE/k s�$��Q�a�a!chose9il!� . Consequ% y�&�ionJ#J�>� no!�necess;anymor� $ �TiVN�-�^�to�cu���1�,ug P,M�AD5�x�w�v-1 F�Ifj�A�"bA|�u�^2_gea,q�Zj-1�,�r�:�E�1 obey�(I�}�), $R!�Fo EcEu$c&w!�V#aMin l�|�)�� ^2\ge{}c|� |^2$� $|z|�R�uAF�,�on� duce!VQ!�)e�I�B?, hen�&&�Mq>s�eObvious2�8 �%?me�� Y�4dqiCUoeir( "�abo�%hE�s cV-d" 6.2t �"��c&�6#�$���2� A�� %���ɬ\ }��_supiS0r\to W.}\, /r^2i.$�),�%ad� DA?�8 A~:�:� nsAx�k*�E xF)Y�.#I�2A��)-m%KFk3"� ! All2�of�#2�lfill�(f!qe"�.a is either1n�����fA�iU�/now9�h,� . Us� EcA�r� eda5Ega�R!�Uk!/&S �_ ~%��+*�+. i<&�+U"�+ ($S%�A area!can >�z*&�#LaG2$).5 o&0=S$ dea�ate��Xd.�@on�MR��,�>� )B�R*8q�� ��}�8x S).\bj.� %/9� )% �*� i��%6�0$ QyQA�E!�'0+X� �< < Y'�#�g�_&L��i�B�tL �z*���`i�"fuq�^� � M(iN�� p !9��7 ?V9���Ua�RW|QJ9|):|;5=8z@ &�8� �[`n`�t� N� w�fan>�?�ula0 0�P  B w[-:-eu} ( n$\mu=\pi/2SFe g�5Nn�7A�(2>$|^2 &=& |f1F|^2%.�BI6�2�f= }{S}Bw m� \no*0&�:\times�:.�`|\B:R ,IG:)|^{2.p)AOb}m>�(c��6��;�~�Y<9�%�ѓc=5v!9\�;��2%.�-R���Th� � 2CQ�\l�_1�E� NWAc_;�*1$f:=98�8radicm,V=1)=.�w  !� r*01. reaso�4�8apply Corollary*�corof6:3�wh�!�,c a�4\{-x\}=1-\{x\}*�6xR i 9] ��teger7�*�<"�4� � SimilarL/��;�=0$v <�D26.1��42=6B~<�9'6 localize�"s^,�a total � >� i. � �A�56"�&�#1*�.* an�D2!~%"\Qߕ �1F2=1<2$v�ezpD ��t�>is&�-�%�F�"�> �+=��6�"�8R%%�% an oscill� !�# � ``-� --de.''� s after(ngZ :� ��"�'"" 6� *L � ��(�(rv�!9��� s un�trans �u,d�!g��j�? . Irl;>�Y's} ��J� ervF77}��&n7{T�A;��v  m�6(� o&@} Up!45xinvr=g6� RV� ��9Ab sen&?�&� give<A�end of S �IP�mD"=8)�<�Ry7} re5�1D'�3 exceE��&' th�N sugge2��fshouldp5ect.��0a���9� r-(&_>azab��%Cpe*�*&+�@a%Y= l, iQD):�< scarce''MN.!0!�-4ASiA��G 02J+s �;i�>1�"m��E6Z&-+. Befj;add�6%�is&�?��4�1�!9pAA'.�9Qoy�of} i �a "L%dis�ar"a� 5ub 1'd�ifA m7� [N7��)7 . IE&s"�Ews�*�?"�Z&�'  C+v�^���� determin23��X eBD+!$"�8*�21�*,+*=raP��e7͛7 n�"TD+.&�= ��8�= y^3)JY7.1o��Y"Y�%�|1�R inFl� $K.%_{1j}��6{n_j,j}: �)� ��R,< �j��Y $K'X'JY'6Z��B\ $\C.�7aDY7 tf]10j\setminus{}K�Hcup{}�2.6+5a F4.�g*�7 F(� e�Foda�Kn:'�4.�A M�$ �'>�'_n;\#4B�r Fls�G��&5�#multipli>aa�a!��4NxDn�)v�#"c^�F�.us:Aa�.rAQ5t���٥���P beA:te� V�RK  r�F}8|{ >�#E!N0 >Z� "N�# �r�#��,�*-' �&���2OJ�G���N� �"�k�9a��bNK�5z-� kj}}'_  /&�}1�"��,5�A :�')�@n;1s !ver�>�$96�.#!�c9 so because�a2�al"�CiA�?71fJ� ��(��.�"%out� ajact��.�$ diff�?"!!�$�~r) fa�F~TkaH@|;ly� � E2�� 5V����i�t="%;h�/BrbE�b��8fi�.-s'2��*�m(%^+&� ��E�����. >� 7&V�C�ssu�Y *�5Ad"T5&Y t�AEre ���\ͤ�>MA�� m\}�6t���AQE3E��[AV.wD famiB4�0!.F�'m.�'� \ba'�.���,*� 6z !�"{ 6���_nj 'x1y3?��A n��N�a�����M�E]}���I_8!?�{:aEe�� @wy%6�D!��%}C6'>��A OE� M�KN�v�v�v�v�vIt�s���jm��N�d:�mv|�t'_k�K&�'_k�&���AkY�O NS.Qa��>MɊgai�r*��aGű%$��JrNk.K���I:lfB;R@�N�mEm8-&�A&noG#"Y��� curren�����P-6p ) *�.lF�ch$�( F(�~>�F� ?#�CE#>A of rank 1u�, 4$2 m"Te�DTo ZS : %w�Q.�>���S_j=^c )_{1�3km_F�o$bd-5!��{� !=l*'=ngFrٽ�S�HAE&�;�; �.�E%'_mQ�B��J  as w�Pasl�t*� r d�7c"�we �Rse�� C]e:|'1{'_j1yj%y�FinnD%*/ �I%.�'_0��yosed F h=/SbA'� �f �m&et5WK\:Y'_1 oB ,F2gD� rA+�� �]�'�E $VE�o$�� &s�_0\cap(qY kj}+u� B�> tau'>�c g+ex6�&.�B by $p'$3genus[0 symbol $n'(r�L')&  �2_�ta�Ya, le r�jo � Bu �:Xed}��"� :!`�i��IMB_1"(Q0"�E*_nJ" j]�&V�  ob) bya)catena-V�auh�X}� n)��'$.*f#�(at��sti�*���2��t(Y� . Ta>2�&��h�9M-�"M!���.B $ ne�* be�nort. Oy D  hand�BFalways� "V.a'e�.�.0!im~?ng&�0vgN2AT6E�e.Z2`�=*�+:��}(r! W3}�(F been�n, �V�.�ifQ��"RA&�to*T.�=� E�!vb �lL"" s. B@we � �a�Py survi�Z��>�6ma'$a.��!,at least too-6��5 parallelR3� � F3B ��}E n�r�y)U�"�P�&*�P"�,)amo�IA�sJ�w*!��2�2�F�I�o*V'$�*E�=0E"2��\B��O+z�*�0!^F[I�9rtuP N�!87on4n�-2 ever!Ue!Q#_>� &� �.$_j";L }k�!EZ�O j\nee;i]�h��a line NO�Aab%��� �I��"վ�"Bs.&��K��AFQ4!L"�OL�O. <�Z��,coincide;X�z real� $\R-(!�0!I�1��.u%�r�<u^$ ��"�'x5�(V�:��-g�:R$"�( 2m|W_k4{I8��p`m�:b�b �2h=.d{� \�|\sinby�\pi(z�'P )}�"�\�+&K(� |"� &�FkB�To�A��it�I o� dk q�,%�4$� depe�M&� r*T;>:&A �{}�[2�Y.�J,Zz9*�' sin(3@ z)}{z!B�a ��]��3Q6suii�da".!4�ee.$"G=A�fg��l+`. �;��b��.9l:�_9&9. �4�@a�d2,  [in�~0%z "1 2��C/GS\7��� �$�d!(�PD(���9k�e@{c},c_1,c_2,\gamm� 2@ !��J &�7Nhe,�c72&�>c_1e^{ U 1|z|alqjbigM_1(z-a_1!f� A.\!.$2$2 $�< c_2^2^�>ho"�f�"!+J ge)  c��e� taV)z1AB���1=-�$1^{-1}\R+a.�2�8!z grea�% 5�AU:/[P1ofI�* Qr]m�$L�ͨ�5���� $L ��7e*�6&�;f�Q e^{| n|d}-1}{2!�  gF*A]2<z>��d !�di.�p�L)�!�!Ps,A�,3 %=�e^{i\phi�a�a] |\Im '�|-d-o ^�>R=A~�.�,, �s�IN.,NL��1 �S- �A�B&2, 72.5,�:2a99Xi�"� fi���e �;��,!�v6�=v� ge c��i�!-5�!w2LE.�!��R2�,>}choos!$$$c=(1-e^{-Q? })/22L K(re"��Ai�R��� �ũ,��m�_J  /in,<�]�'1�c�M aQ�vi�.� us��A� Naj[ betw`� Z�( phi<\pi$)"��+NOHP $z-v ��f "�+1Ác$d�ld�X5.R�F^Aoak�N+a�A� d_1=|z-v|E�+)|^q�ld_2 \, "-!'!�I|5:V�2 `\2�2�aTle�_1|d_1+M�_2|d_2}�G�-^yj(1|, 2|)(8 d_2)� �No�M��%v! \le2%z�r+2|v|$�5a?!D~��m *��a��n^2=2[kZ�!�"�l�X_2=�Hv|?�L `(K +-oa 0,$&m\C$mF5=5�6�7<$r�toN3�&m!A�&S)A�,d_2>�IeA��V[�): BV3 !w�@^6 minZ,R.f fO���3*!Z aCA, &\ge& E/(�^2\2+ 2:A = .1-\cosaS( - =))"'p_1-|*)| K�|z|6-|v:�Y � �e� K . ��2 ��b>�2��F+ A!!�*� f�2 c_1=)�-j�|v!� 6A�2m1=jK6C)9����aTɸ� M* &� V�7�(Finued)� us re. :O fH���.�#��1($p)s,��%�Ł"�ɶ"��of;:wth $(1,bVQB $B9s-n6K@�UP �z�}z A�| *� �&Y�I $c_.'�]A�q� g ahq 72.7� !l�'�l>�l} #({n�S[|5+>�E`��8�|z|M\E@&�<� P?,"Wp1b$K>s"� toS ���on��in�&%ior��e$QM .z arg$k2�c0�vr��A 5dQ>vI�Ia%4/c{}Qx P_� Pd� 2�z�81�|\2�)���7�|)�g_1^B&�*|225U3}A,j^ADA�>� ���.�LA�1>� H�N�3����2k=k*NE�\B��r� ��f�� �6���=D=F�^?M6�1jzi�vDw�2}^�jijk2i*r�A��%� �u�� F8"6F em.�!�j {}P_2">{}Q��+Y���T'd " � Z��E�5�1v$c'�`3 eM�L$z x >� .)y� laPGby��Gr�����A�v�8br�'_1i�y�6�)�i"jE8nb�\,!�B�%�&� !;e�,.���%с�5� Qa� Rogaasser7!�{ ���K��!̥� s $P!�mu��,"H"y� chox<�}���qcvq5r5U1� � ў\$!5ForiAsY~8})!�U� 8b})!c}) make�pos0mtoZ.lXm! Q A�rgu!n �rwZ-�>!H +_V~ 6�>E4,�;&&8�D*9���aIN [wUs r re�^F�~7."F=x�"37��\_&A-Otv�� �>� .�X6�.��VO#�� s '$ sMM"�K$�#<1/2$>' =RM�[#$=o(r^{1/2}�#u.�*�)�b�� n:YN*F6(< UnA9�:g V!�A������ �]� l�M����" ra:kI�� �)�6� �6v� ��^�,&w�f� �Mn�j��ith*BM�bea�� /qin&As� �ee � U��9 xis.d k�%^C��[ll0nxEl`wx r`1.�half-�( $\Im z>� $���|!����� � [-��b� ����s��Q&}Ŗa:C�r.�z7 �_ j�%f{�(\sqrt� � z})-�IV� >� e�.JB��"ll do.� .��.� ��+:@e�aly�}%e uppe�ue�c%�],e usual bran&��Urovvas R& X�:a�{}z>0�9-&$)z} -z}=-i �5�=% z})/ ( z}=1-z/3! Z�0ac�O� �um",-3.Q6extends�,J�J.9:tIN�7ico(� sV�\elimin�XobYB%�* firsA?&� f  z\N�n{\rm(A�I {\it� �& �Z2�: A�U�*�K]!E��GQ�E1}{3}b�I/4\phantom{-} &&E���}9Bc*%�$\le|\arg z: \pi,uJ�m0-���y0Br-�lmn5a�=S2 Sn�N�0<\delta�/4>H� �p math!� B_n( ; )=\{�\C"X& }|)�\pi z}�" n| k)dp2XnAqE*B)}Y( $n\neq{}m �s $��%� $B_m�3dvDI.q�"��&;$n>�.If� tc. .n�b� rew"$u,n , $|u|,|v1 $�($w$%. =(\p�~n+u)^2{}m+v)^�cH�*,^2(n-m)(n+m)�m0(mv-nu)+v^2-u-�R� ,6l �\p2M" +mn $|2�6`A�I (m+n�+2  ^2<4�E]Ab�UB!�0 q�2��Q".l,.m%; })|v' B�5F�T6���o*�{J�&���sEr��&"=\�$.S$�#^j�L��E�-�:�"�ANA \�$��!( .M)}�|0����i|+1mz) _�7�zx a� ��%2�%�P"�$i�z�C-1A �D:��])$�\ge|w|)on 2qaA�E\C*���H4�?*� is l{j,%�c=1M'$(  >�t�p 2 �{}�{}.� &J7�E6 V&R,2m�� 9Q&�/2*�F*�6| �&� e�o� �z}(zp��F 6a<pi n^2|!w<�.- �gr~&^n I_n =:ߒ2.���� aZ�%V�a;�:K weMU� �< titu�$w=�ʕy'[�j $z=(wa*\ )^2/6(,-�$w=u+iv- 9 �."U8dx\wedge{}dy=(4; ^2)|O${}n|^2{}du$W(AF20vm!�$ 2�w�'z��4}� ^2}6+Q�'q,.�k2 2nw+ Mw^2O�+i]w"��� � �h mXG 5nb}{5�}}1C �� dudv�N�+I K6�1%FJ !vɸw)n�6����zj�0F@ ,�� �����m�2�$A~��/!x(wI�))| 0S� $A_2Fle � �lo>&�I7 H7A_j� �E��{ preci ^B����Chip>R1RA�V=�\*cA_�qa��rhowPP�ously.�splJ7� �l i��>%.|&�lP58{}A_1]��c�b!H 12=A*2A�#�/�NL��h�p�J�� E1"� �O�2�'��+!*��p�s �$ vs :�)y�C�2�)/2�)�l� �*"u �/xV�23#C"))٧\�break ��$�$_{j,k}\{|VA:� ,\,|W�\� A�T�Z"�"p )$ T�t"Mr]6kZ n>�*u9m��!S{ �b73>| G&�'� �]1�:�G*F���n�*.(jk# 7�{�;=)"BR{;��.�c� Z�a`J�� �<� .!�=�"�K�9�6�<�N� �.^��96K ) 1b9+= � � �)� b= ,^ > =f1Ac*�w*6 A)}a�K��s*�:q5Q ax - .�.�[~ |=�+e/-cM:Y:2!a!}.S�� �A���ߐ� ai�]�iZ�$8�:�9u"3g734g� ��m^m"�n�� ���'�G|6� �'*�U�|�֡6��(��)�w6�Mg�ps�in ��>oG b���=� �,S cFp&i?=Uja3�*we G!�R�(1���*P�M%�.0v,&nJɳ�*�2\cap)M*!YIf%!�1��J$ϐJ�-''!z� |mq�H�?rX�,|e�V�v�і� mA���Z�nF*�0f[2B[j%[@.u2�)i[.,) Nm�!^��& 2�!��� �u!�&� Cj�'U��1�!t�-\&�&� concludz�jcd��i&��:� 0� �<] �o sum_.�\pi*�B ��5�?A��:fACf3Jg] Q_ �"�N"�b 1: J �u!�6(>)d�Q3"�K'an>�IQ}�Je*�*j:�InP��arrang"�'�� "� "k#di�z )V-)���Zturns oՙ�4�} aI2XK�1+���F$)-n �K trueFU+ 7."�fU+�<2Q!"x � � A� �_�Q"~��$)��aJHR&C�Re..! .��&h'A�er� RK �!3���m&|C ny�%�� +Ťi} *6{+z' |z|>7t�We�� .� � eq: �-W'���+2I29 q +�!cA2 �o�.] �B*H'!���e �nNba�E�O�/AgIAep"L��� ��-W_\el�8X "�9u%C�~"� s\ ��(\�> �' Zero!b&�X{+�c M gauge�i&ap�5X��� 9�:6� ">��' =�*%�]_��-�\sT��W`9mj)�68V%8&J%�9-P|.qKj� ^�*� � �1%�/)��* Zz]NV )i�b�#!Z���=FV i婥m��&Ղ� b�2Ǖ&�ls�_,d:�":ߛll��e��}s w��er�+E >I c& %a�edw�~�\APP Y_R*7(r2Q�()� � 3}))�/ "*�QzY�!p��^in5��� m�j��2���P �inf"_ �B�= �P/o��K �l ma�-AѶ� aܫ�`x7\Vve>�Vg3_��& *$fix a natu*,�V $N\ge���:$$�U _N=\�H i k/N}\,mFN}*m�# N\,, k=0,"�4 2N-1*$$ *d�a9R���#$�L" _N$ ���QN�+n2S!� $N>2��EDZA9���U=.S)y��rv^�.���B�W�W$��RJ1bcouple $�h_N�a)$ *�V��T&��0sgrad\,\ln(|WB�H$$ 2�N�+^N�N^{N-1�O$$&r�  7~ڝR�5JPU&G }��4� 6=�4t��&�����&%�0<a �*� 0 ծ�6j6�2 >1A�)Ak�E�EHs>��.�*!S =J?--*�2NR �arg z< 3�2N)i7 >7 6#\R^2}>L|�d� N61Sn.�F� ���)��>an� 7�u��2r#f�*&#�B� a�us�9a6�!�a�gE� vari�����w=z^N$��!u! dv=N^21 {2N-2}�! dy�y�re�N� & #�^"-��F]+��.= 0� 1}{NW2kE y�> hTI�w)|^2 piжi\"�.��bM�\=4�F-2 z� }{a\� Ef�2/?>-̈́$ 1�Ze� �l-�l9�2�Os �Y usJ!a 8so C"w��P��D�y��*g %"�%\�Lion*{}tcounterr }{0>" .6�,the [}{\AlphJ:H�3] \�ix \ =atlet � \& T% X{\@B4  aADX\z@}% {-3.5ex \@plus -1 :p -.2ex$2.3#0\normalfont\L@ \bfseries"�% 12~�<.\hspace{0.5em}}3R6@seccntt $at}[1]{} %5~ \csЮ��#1A� >X5$o��)=s)�{L�� ;!w/"llvNbasic�6�U�nd�= auxilih5 �� LicY��$E^M�2��: EuclidG�%�  dime=��O. AU�_ub�A����cve� Em\P�ed|3B�OHn�nyB�"� !0���W .�$ � �k_�cb, r1gE*�rs �=\Z &1+ 2+ Ar�$$ ��y, p6}cr}A 6�!�sĚ/BrV��`er $r$&�=&,#B&�AZ�:��]d)m� �vd�A5Z. f\ F$(b��<refs�a� >�| } $FGF� E$] mvh�}!� @ orthog�� proji $x'�t&RDarA�nHTQpM� �a deci3se0!� x'=t"�1+ 2-�t_�rI $$ � $z! t_Av� �v�j r=d$�Ne y- q�9j!�max;�/B͡n!1�C vex P>epipei�!�o ����;$F5e�z�\� . A܀empty2�*� 9�y.3 a ��}�{b���in��fUBp��-�a�u!9�h(EQ��� of ojs. *� I� �� "�I�&�W ��$=K+m�"x K6�!)I�� ofQ�s�!���Ju^ J{jAw�2#�*a�w�F$7�"ɂ � IOA{R��1� |K|=�� 1+:,mono-atomic}C{A;s�e < �Iq9F_AQw1a>K $n$b.%�$r�X>4a[k} (� a � if�fA? �) �e�0.^ 2��1} (>Yp�U11l�� %�}ՒEAIn �� wordB7is r$&gi+ #�1�EA�ci�LofS��l 6�ct�B -com�tQrn����2hfin our*,Awdo�!ex!")�$r�b I�|!8�� =\{0Sz� ڥA�:�~�ADy}Ms �*!: Xw���z]"�m.!sf!���"d��}1dofg /)**As a��+%��|��'Ew''��\A�a� �C'Y''~%��� ?"s�'h 9?h�;JR8N8*)� 9.1"��N�2LEss"%u$\dim Ead!� � �. n�qe\�H!�� !bAe *�k_.O�/@O  G��a�a�~�0 'e�)���.�e 4 �F�W�)):&�a���z��-ient.&�F6�ac;vAm x� �2��O�@$u;mathemat��in�� ion.i usł� g �_j6�o\q�X(�|2 %.�� _`��:pE�["Z�,�yy�We�$�1�X&� GEI�_�F�#U�&�a���$p= 11/ 2%��alk&?�B6�O�N~ $ w��Z �� �F34 1� K�*�$$ 2 ',h4an `�s?7c%�n_�f2-m _�$,,!in\Z$)A?��tMhi1-r��W "\nwUA :v`�0$ky=" �tM�*�!GVpA�i�)[O%�F6%��)!�N/M64�9N,M��I=M �1=N � r�M�n6 �. �\Ex�s\�� � zw� easyX se��a�M�"7  O�_&w :'=�A���%`�8.*a�*���?8z�.�'K.�=P������g�J.��*�7�� fals�y\alreadyE3 SD�it��I��o� tk�" �F&4b "> �(UW�tdem�1l�^o�.aM�$E=��1�_"/~V>�E�!�I�� 1={\bf e}`RECmC$A�!L��A�bfI�6h'�/N-D6q�'_.pA@C2VrѷQ�=e�U ��`� 2�+"�G�b=(1/2)� {e}}�� . M�6� \e�E:� !v�U1�0i;*� :��c�p:h S.�$!����¡� IE���Ao_$"$n\,,�Zu �E �u�r%�^ nM)h $mbel*n� a!l-J���V-�sLW$rN}k�eR���+@� n ֍=��pap"AB�"�[&���%�J"!} �bVf0 "Nז�-�b�< ) &'���i 5R��[ ails�� \��,Mar,Mar2,Boa"��J���� et %�.� �8q. M_f(r)�� (r)=�1"$|z|=r}\,|f�B�1�� qp ��%Z3��# ()a1"AK 1��� iz�i>�%_f � [�\{C* \3R�)>0�J 1 \foe r>!"�J } !E<�$(r^ Z) ,>or, i�#ly,z�4{�&_f/1!�>���ty}\,�^\l?1.%a�)�-l�!K#:���6f�L=�+8{ pa_nz^�nz�1�v�n\tf�(n �\,(|a_n|y-/n�E,�Y���'_fȡAq���yi�Q[ayKE�o�)�DM���(of2!pg��61�C%.�(!h\{K>0R�K.�.�KA"cd!�I�Kr^-�)\}>�i$�Oɶ�O�. ����! q�}!L.�. b.�&� Z"�=Xz97:&�5lin�:!M�5N�&�#E@%�_f"&���,er�%!(Taylor coef��Ԫn$~�:�(!� m e rho_fPG }=>�:/�@�#0\,m(a'J%� ,}$� �=0Eѵ�M a��ofi4.�*0JAUA'.Q erho� yNA= �$3)a�e "�'J� ��9A/ɹ�>R49^+u1�� �)> ��%y&XC>0 ��*$2�k� � ant $R.D9 . Co�\;f���102� c\,��)��p^{A-1}B�i��å ).��6�Ub��a 2�A"�!��-�%ho�p%��f!{͵1$��va � �#C%of�;s $�N1,<k<\Bx�$, "هu\<p����T�z ��b-�= 1$ ��M �< �F27[ � �eH &�O%�I1ѻ؏ s�7to('it;� Waz"z %���!�!\"] 9�o�ide/ �lribCEof�<�)�,I/� 5��eep���d� uy2u2�"M���% .�B��tin�m� _*=kk)D� ge1}iK� asce��= �� ��>$ d^��(I]arg\,z<ZQ$�I��q�V6Ws.)�!}ce�g 5�AtE� $ (oL_!�F�y���� 3b ta;*� � tau;)�7� 6Ts*���;iH��*F1�J2k|� }\&$I�7�� � 3 �J�kr. k. (�_k|R� �g*<!�I�}�h"a�� p� �0|s-Omax-�n..� b��1 C {�^n}%�t5� &e& if }T&� �n��}, \c�O �6align{6% p-I &@^T:R_ � a=p}��BDZVq V5aB!�2B zB� �,_J-*�'1"�. er��V-��"�28.1%�n��}"\j��-�ATeQ� ra;B� �a�?� 2@�9�ulaj�2A�%�Y�JS2�..:F 4F "AB����g�% 6�Il�*�, characterizUttl0 [�' 2.5.8]{B J�g�"X �!6��%L��n F�|$&>*�funda�)al*�;��Q�"HadamarK��5�wEr� 2� �1 �):z�a}>��Jr4 ~� ���n �)͏� ]"�f$�=z9.1-zp3�+Aca}£duc�@atv��^AV =O(r"� "� F� � n6� � 5a�� ] :a stron�est�@VS6�Ei13 �:�$L��>� 2;r�.I }�!�"� f\,  �4%fa�%�l|b�2N|oM6{Bm&�]!V- $Le^{l/L�CX&� $, in�!��, $L+l� )_f ��l�� � C: .� $n���wf ="�]<�2a 2.9.-�e� &i#e~<du� *\�1qJK5Aag a� 2.10q�7���.��+�"�,� s)2�g1)� �]�iLy��ANx66e!�a(p N.Z.�}�I,�>˹it��Pl�0A9.I.�h�?_^�A6�!Q&��'z�(�t��!WX R "� Q |� � �@2�:���Ե! T���a�)�"]�_k�_�_k}�@ "](�!�z�B�� U������d{�by"� u� an m���* e^{g@; �$)Is"�:�P�Y*�2��%� 6$^��(S� 6� (��:� j$.6�$ by $E(u,p^Wei"��& �9�dth $uY C$!�XpN$,�� R0}u)WfHu�Ru,Q2}+�# p}{p�3)G(b�Evio*�X0)=1-u\'L �J� 1}$ bDs}.v��� �Xc0*�+N@E�&l�$U roprC�enume`.�:_}chi�J�c !1 $9�i� l 1aT*��,d 0g2�"*V��G uct}�!oc��QjE�2]A�B� W ���&^h� jvc5�cz^!�M�E=An��!�� -$v�����kF��6�FZ89&�_��[=�,"� $y�1�)�� ��2�15��c)nd u�ly&k!�+9Ly� E\'�&>7K\ �iv�" �#25 BY��:��e�/9"� $aP� 6.����9.1'6=U~�}\,=b� R6N/5��xd!���e$�3Z�<�-��q� AX *� eG(M:v rue]�As9&�\L[� A�Ii��f$�r��#� %J) "����*� !fe�������egreet exce�?F[G]6�FA 4���_ ]FO 4:x.� "d A|Yg*0X")�rm6_#V�of:<�$-+)&A�h2��)S"� _fl (x ,nJrIfW�!1m�O�ϥ�6 *=J�}*$�Bau`4�� ���T 2�)��&�=B�vM�b 6C,b֊D,E��:er $q�{}q)6nِ�*�*� a usefu��mouA�o"�N��*'�� F B10"_ N35"�-A�F� Unv�sN��"3 �*a�>5 2��M��%�� �Ei�" ^R�%�F  1 ���5���cy-8(uu�� $($a$��M�>�� *�5���+!aV���.� =-I�"_0a[Im���A�*� (�5,y vanishing)�K�! t $z"�a�e}*E͆��= b% r &�-"�=_��d:jB�q?5(�:@.�2�"�-}DR/2�ip"(H"&!4Mittag-Leffler� Ţ*X II.7.3.2]�%Q4�K�F62O + +�'r�:&� D2�bQ�ce�n� $\C!�A�B] ��6nw�s8�_ ���j o}%f~(�M(meromorphic2sMe� I�1_Gy1��Y1a" ;�I opoles>G�Z!�w�)$ & Q6�a �B�3�residu�� D�l% R�?-?6">s�9{�h*k �gwI$-�!��ed�6�(w:-; :{�(approachAIj�r� ���{ play�:!* ��$|�j! fUrr� $FJ�F=(z�(;)A %J_2) = z6� A�L�,"�Q�5�)eftև�zYR"�.>$ z i�A�T�V$$�5>k/%"wc&A~�l57�!H�x0 2.*�.�n�)9 \v3op{� {}^{{}'}}�n_1,n_2=� }^{+9 & %!�n*<n& �"��N} ��$dash indic��,�A�uHMmsu��) +es�1=��b��"<2&p�ש�>��1vO%') ��.��=J/�B�� @�/thۡ�@"� 4}) di�2JEhe6U&c>say anyt���S�"* Q�)$ (aparE}facA+��ax' ��.L�#j��&w foun��ge��lɍDby A.~M. Perelomov�ePer�:i�to �B�.�, self-c��edre�e.w-r#�,-�ͽE&t9�B #Z-�����r�kE�w� j=2\��\F�I�i�_j��m�>��/u9q-��W�.h�1 *BJ�:~��p\��=� j)=-�i�� ��z�{.���} F�R����8&�� N&��Ru�+!�#aM�*� y3.y9[�Ad2��3%��y�Fgm��w��B*U�t)u rm �Y!�x � C�� )!2V=�� (\nu z^2+��\nu2\mu z )\��, �Z6) a&2-"��* mG��J��10���!u�J i}{4��A�1�-�2-2�m*$y) mI�JS * �!98�!�FE:SQ 10�G&�\��� 0 |\sigma(z+\Pomega_j)|^2=|\sigma(zP \exp\!\left(2\Re \eta_j  z+\frac{\ K }{2}=\right):,. \(nd{equation2DOn the other side, func#H $\rho$ defined by >�lity (\ref{10.3}), with $\nu\in\C$ and $\mupR$, is periodic if and only$it holds %�begin2� \labeln7� 5:+1!C=%6D nu z$,+2\overline{2}+2\mu> (z\bar4 C)+�-z^22^)� U,."-���Z� Comparing9q5}) to7})!Q tak(,into account!� .�$$ EZIRMlNT �!U -z � 9 bar 6 -A�+!�M�5r6&'\,, �(we arrive a� system�8IM:aligned  & !� � +\mu� = �1� ��,& j=1,2\,,\\M\no` {\medskipRg^b ^2�q��Ac � )J�a�m��) \>�HThe first couple ofE*a� s inYb8}) give��9)a`2�\,)k�1�2-21 D��:.�1-2MJ \qua�\ \muZ�);1 v- 2�y!oB]Since $ ]��=-2iS�8in virtua�ofa�8 Lagrange ident���+10)F � �5m-=2\pi ia�> wA(nd that relI~��9�x4reAEivalent!Us��%6�zfaca�at �,$�&Lreal one can check �1second��(is satisfieA)9cally. �dproof} % orig: Lemma 9.3 �I! 1*-K< Let us rewrite9�3A$s follows,���2$a�*! (\nuɓ8nu)(x^2-y^2)+2i-�x!`�~'+'�rho(z,- zV� %�X0e a fixe�� nstant. F� w�notI,� aWuni!pess orem�� analy��� � a �eebbl� �0xists a point!V0=V� A� (z_0�.,{z}_0)\ne0$.�!�G �5�?| @>Ah`>c$ on a neighborhood $V$a!$z_ Yis�(ہ� hoic�l$c$. Fur�weE ider!�^on�� mapping�0h:\,\R^2\long(%/\L� �wo cases�$ possible:G il!simage $h!+\R��a clos!� urve�torusT=2j o�is Lis dens7$T$. I%R!�mer� =dy��kr6z��k��U ��1k)=^�� latt �!�dia 1.7a})�4uld be replacei!/a+r\to �)9 both%s`&�1.7b}) \ �Uwi�z_k=z_\$: F���&� Acintroduca���$ $$ \tilde� )�,- z^2}.*g ~=*J 2} impliI�. � .I� 0$ |:||^2��(�|z��B�:�B 4x� [9]� $f(z)$!�an � r94 whose zero se^incides%!�mm=\Zv + 2$NallDes be!�s!"e�mi  ora��drho_f�> t least $L���if�va 8=2$a�ir� 7[ BV \mu$� ? #L\ge\mu=\pi/2S$. More�,q �R�؁=���69� minimal � � achievaA�f�<-G �$�d:��.e.�!,{.z}=2!�:#.�IAAF &� � $u%�expres�*a�q$Weierstras�(ca��pemt its )�al� a�verge\ | % tau_Qa2$."� >� :�9A�i�alpha6�Q�$ �eC�,he0$�OH2=i 1�$x�4� 2=-\pi{}i h[18.14.8� $10]{AS}, h��$ �5�.i  an2�e� �1=ke^{-i�3}� 2+ k>� � E$�gt2g, 8i/3}}{\sqrt{3}( W1�2)�\q�-6H�~I��%2 3.16!3%1 3.19%1-"is%�, too!�E0��E{" U�3>�T&{ %p��� whic��nu\ne�,6��:�\n&/ !�tB��al -�-8 0$ (_" �, seeYK3Q<)�7�"8"VA� ula,��%�-�2|��Ez���|E�� T!^ mean�� �#���$-݉!7>�qu�lpi/B F A��pends oE�U[.Ocontinuo�I any < ��� $ lybetwe�6vr2S�p~� by aTvenien5�23 \se)x*{Acknowledgements} V.A.G. wasi�rt� � Gran� �f RFBR (no. 02-01-00804), DFG--RAS H436 RUS 113/572/0-2�INTAS @p0-257). P.\v{S}. gratefully a��!!�Ministr� Educ? @Czech Republic unl 2Lresearch plan MSM210418. \newpage" Hthebibliography}{996 �Xibitem{BRFHMM} P.~W.~Brouwer, E.~Racine, A.~Furusaki, Y.~Hatsugai, Y.~Morita, C.~MudryA�,{\it Zero-mo{ �� random ho Xl.} Phys. Rev. B {\bf66��P(2002), 014204-1--11.� �xASi} M.~F.~Atiyah, I.~M.~Singer�#index!Wellip�Toperators.} Ann. Math.$87} (1968)�;484--530.{8JR1} R.~Jackiw,�RebbitSolitonuX fermion number $1/2$}..�Dy1�D(1977), 3398--34096{2z{ pino�si� Yang--Mil� ory6v ~)v ~ 1052--1062�q5���]�in fin��m2pA� Mod��v t. A � 1]"( 1577--1581) %***2'0005018>�6��$Chern--Sim�Pa���]7$ rt� gaug; e�% �tZ�M9%�6�� 2003�p87703A83�U8 211276 %�N C., �N B., �N C3Hopf i?�n LiouvilldA�� t space//ajIe�,�@ 479B}, 329--335,m�-2�3��P� le c9��viae!x!ChyperUknots �j 6230 (6)M�i� 62,�9027!?10 6.��:inMMtVy//1�(9909189 (8% ):�-9 D61} �18�18-9B �xES} L.~Erd\H os, J.~P.~Solovej!�eH�(kernel��${\rm �y }^c$:89 ,\mathbb{S}^3� R�dv.�16��1 ��idS-phae 1036ae%�4GG} V.~A.~Geyl� ,N.~Grishanov�6a/'���L--Bohm solenoids} (i �Russian). Pis'ma Zh. Eksper. TeorFz�@7�@� t425 -- 427. (English transl.A%t JETPeer��& .G 35��56).�VMD} !�Vidal,� Mosse,B.~Dou\c{c}o,$i:� cage�>� ure�-Eve� �8��(1998), 5888��92� VBD~ J.� P.~Butaud��.�k�DisR�ainta��N�2�  ��64}e�1� 5530�816$ч�$-mat/El11Anu<(Oh} G.-Y.~OF it Effec� � �u�%KN�!�aBlbiWte Q� �2��.4567-4572 DN}A4A.~Dubrovin, Se�Novik}G*� "_ > electroney  BeOm 7� 8j 1006p 16u ySovietIkeId5�1 D902--9102 Nov}:�I=T:t Schr\"o�#�"" !�=y%�hs}, Itogi Nauki i Tekhniki:�r�,nye Problemy_ ., vol!�23, VINITI, Moscow, 1983, pp. 3--23V J.^ieUI � 28p ,85), No. 1,  6ARB� v��iiP .~Redheff�$Y.~B.~Band�eaE-�� % a:- e|�impur!)�%pot�al: us  ���S*�s.�Jt l 2�+199�+ 3883--3882ARr��>�Q�i�� �sA�g:�����\qh47 1997 2089--�.�AAG6�,M.~Ya.~Azbelet(A~.GredeskuE6xi�!"�E{��ng )p4"-} ies}�J�I'�,17280--17295.�GM>4�BMargulisZ�Ptperturb� -&8&& �>\/�� �>U.:JA�$em. Zametk�b"i46), 768--773 [^Di1NotesAka: �B5} 0.]* GZAA} �AH1�, !�ZusmanqV 5�'50Sp�#al�!6��loc�() /N U�I>p�/);)�sc�!I�e65.�hp� bf28Mm22�v57. BS1aSh.~Bir�TP Suslina�c>��2�(Hamiltonian� abE+ely�D>�,Algebra i An!,)�9}��~11�32--4fNG St. Pe@ burgM J) MN�21--322MBS�!��A ��*}(�,%�.0e�dis&j vector-kd�n%>� �  ZB10-C4��73��B:M9� 579--601:Cg >C0R.~G.~Shteren@,ZkjVsecu� BE %R2���)]կNed!'Q�Bmzof g&>�fl2-l6h �4��75�oU�:O19�1016�KL}�P.~Kuch!�wDLevendorski\v \i. ��� )Ka��J; }. T� . Am�aSociV35V �,537--569. % � 0p_arc 00-380"-.�Mor�Aeame!*�Abs�of �0o �uma�՚(�>yLa�&$--BeltramiM .7e �LEU)�g&���3*� 7593--7602� Sob �Sobole&�j���6���X��In"L �13��85N2 ,Fil} N.~D.~Fr. )pS�1l "C5��of di"$f�/hav�%vcF7 ctly}Z��ion��SciI910�I� 307 086. %��AB}�J , D.~�G,it Significa�$`5B�5��9� quantum ory"$R%H11� 5y4!J46�OP}0Olariu�$I.~PopescuU��3l� c�:� fluxc�� � �5)�� 339--4��&�Hamx~�K>iB����:Tcyclic phenomena.} SprQ-Verlag�0New York etc.� 7 ((��in�ern�ics�139 �AK! ���Kaufher*� he-&!�.. lux S:o1Pd � \&�9420� 0704^4.{\KDP} K.~von~Klitzing, G4 rda,��Pep� m%!methoda$ high-accu�dzm:2o  �e-"K*s. ba�'on �H�$ resi"c"�F�4I�V 494--492� QHE}I!WQM�`��AR.~E.~P A!S],Girvin eds.,B%Y�982|DThi} H.-P.~Thiene&� �mechanA1 q homo�ous� %Jel�a��-E'tub!7� aD 280 A��6JThiJZ�Super�3 sche �en �k einesNk^v. �n Mf�mit�em�U3,n= a1�� �c�A;�'� +� ��zero-Eg ��}�pitB� .A�bf�(no.~3� �z� ~J� )E3}E2F 4�532 AGHH lbev, FXsztesyM\H{\o}egh-Krohn, H.~Holde�u Solv�1��sQm~MQ�e|�K�s B8?!�8� "wRui�lNe�$Ruijsenaar&�!ʱ\��o%�7᫵5 e��bf 14���.+AJ� HJ.~Audretsch, U.~Ja�,@4D.~Skarzhinsky W!� pragm�7approaE4�58��self-adju ext+ ��" s� :���s�F�D9D235�362�AT� R.Mi�Tet&; :w�ia�Ʉ( %cE�4� y 43--54�%���9702048 A}�4DSt} L.~D\c{a}�s�"P.~�#,\v{t}ov\'{\i c}ekti!F:�Mj$\(5$-typ�["Z}.� �,5C�E3� �7--6?Sto1}F� \i\v �Ej$it Krein's�A mulaBm4}:�As%��M� 3��19�,21�2122� Sto2��Sna7D5L chaiE�v�c� Duke �m 7iP 94),� �6qN� � Namb65 5�� N` revi�7d.} Nucl�� 57@��590--6��K IT1}��T.~Ito��TamurY�z {)mx �Fe%by�-like� �s a�&rge sepa�; on. �$HenriXcar\'eA�bf2��30�52IT�H.��%4Z�a9�T�B�CAsympto�# Anal � 3��%9�A40A�@�/02-2942=ESVEwExn�B�u(,(Vyt\v{r}as:� G #li5 b$arQ�5eO�GR�/mbfFe�a~Nd ��V\��E�&215�162�Min} �Min&�J�q�� a& &� ilA�,v�#1Z 4-80!Y %%%?Y�dSG�@.~de~Sousa~Gerber&�F�& qn>'va�@sm0tA����a �#4�$8h134�342�$Hag1} C.~R� g*":�aYmZof"5&��W&� � n3tI��199� 5�b506. )&�# Hag2:�%� } Int��" #�.��e�1�9nBDSQG.~Bene tano0 $De~Francia`)M.~Sa gelo�z u&%s%���backg� ] � )�!� alN.V��14AO!1!�474L762�Ogu O.~Oguris��q�G@N��!� 1/25����he>���c6�"1 N� .}2V/02-495a"- GG� � $P.~Gavrilo4M.~Git�A�mir=�"�in5�& !)�.} Eur�~J.$��c$119--142}GGo֟GrT-f"j=`ML��ݑE�ѝV�M+.,173--18�( N 5,�A�"310007} GGSŜZ�r� L.~Voa*>.�F�5�Focusv"� $Res. (Novai?Pubm"ers&�, ��131-168��$308093�La� .~Landauq�Lifshitz�EHB� : Non-Re!vis�SThz�Pergamon Press, Oxford 7 U�VB}!eA)8 paev�qB�gI}�kro'CN��-��*-`80�!cl:�(RmB� *�#D10�� 24�'49R��#a97�4� 127--131..�BV� ��A@!�C>z,2 m�� F�.�i&��"; 6@�76�766�CFdC}; 0M.~CavalcantiE&S.�ga�,�}$de~Carvalh�E�n 20)1q�v ex2 B) bf 5 ��92e 924�UFCV�C�A?B�Bn !�v�--$X41�Lf�-����&P��6Q0�- 7063.CNFT}�A�!Coutinho� Noga�J.~Fern�0 Perez� F6Toyaman3*i6gA*�e��.��:�q-BZi[��Z!�� Hag3iR>D �!�non+"��(�F� y� ��6Q� m�A�593�,932� Pa�$D.~K.~ParkI�itɭ's"�46�wo-��+.0�.�D8�� appliA3F i>�f�JF63m6546�72� PO} �,AkG.'�ZT>��� --Coulombr�5� �1 7715"22�#PYow!�e)Yoo&�Exact��$1/r^2$i$ded Pauli-N<y� ex8Orog*��.�I��9�6��2a�272 PY:iS.-K.�5jEq�M�Erenorm3!���.K �t2 i4 H J a�@s�l 971213:�HO.�,M.~Hirokawa,N5 Anomal� %M&�s;3��#�� tail'L�1�.J1�� 1� 112�T\06�Re!�p7ci>g$ i�0rV� g�F6�B� 3-196,2TamS>h.^f u�Ks��%e.%4a��?k�two*�2�,a fromela� �PJ�3722M CFKS0L.~CyconG��,oese, W.~KirB�6m}`VK ��U2��%�$global geo]M�Z7�J� V��!.B{.8��O�CI�U �$"? �E-jI�wo "�N Mat2�4� � I75 .�Ara1}� ra 'iti*bW&.� --Weyl��a4 ongl�GhBnC!:-&�q_ ��34}!T9�^932E( Ara2F�RexDent��-pe� )1�:�+9� �C"�!v%]�: C"�Dcommu n%wrf ons,X a[&s,ER redu@.�@ latt�?J�F�)9}%"8), 2476�7�&b Ara396itV�.�th�� B"�E zeta"� �in�d�6al Hil�]3-.�"�- � hp $U_q(�1frak{sl}7SE�(:�Z"E)42�s4212� Ara4�qI6A&F=�9 ��aI��ECyiDRw)a���: %� �B arB�2)��2�26� Ara5F�G�5 �.7=D�nec\&dom.�[K��HH�9NzJ�TB�M.�Ow%�Nodal�K a�nd of r; K>4 �n�FF��!� un. >�20mJ 62�)6��16�� F���,� 7+� se!con��v2� co6Y�Lect. �-]�.3 62--���!��*r� G�%�!�a s��=� .� :�}��4!�20� 333�5342EV&�7V ugaltaށ"� u %Ty C�>��e� measur�ivalued:��!M;m0��e32�1�9P22� LLM�%u.'Latysh�OEbk(9P�)nceau�(Klaumunzer.��*��v��&�QA1@wave $($CDW$)$ mo�(�a � �6�~EB�contain�&+lu&�$Uspekhi Fi��5%�169ō��924--92&~6.�9!� ics- J aRbi�- 830--8>.0K *J !�,FS(loo&�Weak 2�4d(Eibm?of6�?B�Y�6T �Bk7F*0; MOR}��Melgaai0E.-M.~Ouhabaz�( Rozenblum1.N�2�4�5�!6�.|.}`�3-5272rBalm �6lK$eHardy�G*�X� 6q93&�  ��AZ iJ .}��<9M�0L!3), 1b 172JLW� Lapt��T.~Weid&�( ��� �U� Dirichletm�In Op��;y: Adv�,�(App� 108} ``��e]%al�ult@ y�"t& /Q. .7''�teds� ~Dit�\h,��� M��V(Birkh\"aser&�&as�6aC299-302 RSIIIMRee�;�>.eZit MeH+ MoD,��m� II/'Acade�'Ne�,)2{Shoz��o2�]v Semiedi�.�!= $\R^4$!� a=0i�5Y�on2ncorne�i�I>Ma ;1066W1996) 1799R2%�Fm//B3166>Pa|!�lV�nk: ki�L�6t�9#M�#c�m� � ��!��S2� "`I�Ma.�7�v 7���>�.3!�(J�7!�.� �g2=3�H 391)*� ,b Z erelom�0�*��0 lete�[o�_*�3oh�Ot � �3e-�, �?�<i�A�. fizika �~ 7!213--224!'N�J�`1971. 6, 156-164; see als:�"�@2q5"243PerW43�*>G*$� C�Sqand�ir�NK)�ZZaa6? BE!Erdelyi Magnus3+O�het�D�F+.~Tricom&�Higk^4 cend l Fuks: Vols.�6�,McGraw--Hill.�195�952HC�Hurwitz,�CouMA�E,AllQMineyk�/en�ie und ELK�-"�n02* .# �Dun�J.�&Schwar*;Lin���3 s 2:�}EJy{�# ersc�6 ��"�K� �%Kat&DP�e� �"elB�.z62MA�  Marku� icF*%n �e�B:_i� x1"/?76|C q�.# Mar2�I�n���m&mplex"�_ |Pr�>ce%1, ��(ewood-Cliff 1N.J 362iNa�0 M.�NaizTU`-�Dif� tial9�%_F. Ungar�!� CokG��:�,S AbramoI�I~ Steg�� (it Handbook!qMat�[udɽFor�+s,7PphC��65T�. �Dy[ ��2\"1:!HTit} E.~C.~Titchmar*�LEigen1� Expa� s AssociaG� �6-O�\�2UEqvo � Clar�8n.O"6� Boa}��DoaskEntF�@n{�-.fKHiA\. RK&�� izi~\, doub2�(I��%"� phase}�%�..�*17�*(322--3�+Wt:,Q  docu8:} ٓ%tSTis file JFM2esam.tex %�lre^e v1.0Q$th Octo�O�d(.(1, 29�)(5th JuneN7N(b25JFMsampl��3�H LaTeX2.09) % Copyr�q (C)D�p<997 Cambridge Un�8DU ( \NeedsTeXaat{ Re!%1! class{jfmoXSee iBl authBX8as AMS Euler fo�S&Klled:�Y they<9e, �?mpt %�u�ZDe 'upmath' packagep�Ede up �!� �.^^J}�k\u:.� �}�� but you�:do eem!hh?the��>�9�.A�.clXn%re a� tag!�:hes* nts,^^Jif�E>e:M8(and\upi{\pi�!&1� n. \fi  % f�symbolz�V�ams>R�Aa"!ol ac���msa�� ���S.�6�Y�BAB�:�]� �5�8 \let\le=\leqsl�kqr-ge=\g6-g- -}{E ~�1��bsy9�b�%E�ita+M��X�]bol=th�,port (with \)�� r�2�am�9�J��B�R�it.�:�bsy�b{>5�$[1]{\mbox{�� $##1$}}}iLV[dvips]{�Xicx�-%%t${ 4 macros (some }dnot![�G this ���Qle) %%%a�Fo�h9�  Y�@dynpercm{\nobreak �L$\;$dynes\,cm$^{-1}$�ne:cmQinJ:cm\,min8 % VarRb)�)�sBpbnabla). ${\|M>�bcdot6+*�biS2$S}}2etb2 k\}!{%;leE� �sKZ� Real-�$Re}} % cf �Y TeX's \R� Reynolds �X.� Imag EImREIm21Rey 0\textit}}z.nh�=:8Pr}qdtl �,� �Pra�!2�PeBKeK % Pec� �2.Ai Ai�% Airy"t 25B5Bz5 )�s�]�Pf�': � �@�rSmOaIsetupMJF�tG- G��!m %c a�. � yo�� Winr QT� require@�@% will be substitKw;bS :P N�i�] m % % E sfi,op thsfi :.��)ed,b,b>,��)Vbi6U)Z (doesn8(is\&CM)7 ) % 5�-Pr � �%RV"sf�f�(�.' ssC{ %{CI@%5�-�C62fsP3i{P4B2 slopAP2� slsQ: bi{Qe%Q l!-?$Q % Hat p0qio6�(hatp{\skew3 {p�% p�f.� hatR.2R2Rf223D� 22fs2�Ee�ds�~ s2b: S!��%� itaD � O P % arrayU&u��mak�lsernme out � size�eXa! save�?0astrutbox} \s:H{\rule[-5pt]{0pt}{2}.Q{ B}{�r:A� �3GaPQ{\en�a� {G_a(P,Q)6S\GsB(sN(p2M\�)al:Mtti6'%arrow2s:0kgd20 k\gamma d:�shalf2*0{\scriptstyle*�0!�.sh27^{ LB'm>(-Z)quart2T��6�4B�tJ���682B8Ga6n \widI�!�>�ttz2�=� 0:Undq6,f��� $1�$0f> n_q>zsumjm6P,sum_{j=1}^{M>/pv:*int_0^{M'\m�F�-30mu� ( -33mu\fi -�f>et"�%p it{et al.>� etc{�G\ 2t\eg{e.gEZ% em{l�{}{�l 2,corollary}{C \title[&.sQ$ng of low-"r�hc{X"I s] {v5 �X:5V�Du-} velom$��[S.Y.[n�7 Dhruva�" KuriK. R. S~8ivasan��PM.A. Taylor] {S.\ns Y C\ls HEN$^1$, B DR U\ls V A$^2 ) OK )IR 3$,\�  KU R S#V(N< e( $N$^4$\ns \MFAT)$Y LO4R$^5$} \affili�{�D�?tm\/of"xalJine<@<, Johns Hopkins &�\, Baltimore, MD 21218\\[ ga] ! Schlbdger&� R1f , Ma�! ley Road,$ CB3 0ELBU3$Cen�No(* Stud�(CNLS) % .E�lA�\&��d\Group (T7), Los Alamos N%' al L�$\y,  $, NM 87505B�4$I�nA�QWorN]-al -�, Strada Costiera 11, 34014 Trieste, Italy Bj5$Compu! �* wScien%z(CCS-%)� N�\\R�aypubyear{"�%e page H<{} \date{\today}itk�er{&}{1} rd"�\�t�Z)�ab�r ct} �qnow beli�sp?s�~�r�2*9 �3 inc�Yt�xan�2,8nOde3] y10 Kolmogorov's9.41)�3si�q�_aseI,�ly� �i}a@� F �.�$appears to� �w whete��onsid� N�selves � eir �U(s. HowI, x!! � lowe[( an 2 �>?Nztb�=investig� R�'lye�)ty. He�'we1%cu�{ imw/#j81�of!V-�&�79� �b�k+2A� $-1$V. obz&Lm%� directeri��sim�]�D�frh� ;s (�- mi� cale$Ob!� $R_\z�$ 450�yexJK�\al dataeE highFD(E \arI$x$ 10,000)A(z�=!=�ce5AlZd y��2�prediG1M��{�mQ� I�de�ctowards-^thus �~�Bu>-� i�Mnif�tin�1�is�o2!&=  as well��oonclu 7~wmotiv��Ecsee�aawo ��6!�� � �2�8 vanishes. Such�V8y UE�E�to�(e� r�EC s---�omay be a�H�ma0u�al fea�f�n!Lear---!�s!.Aregaras&��.�3dea�pn�;�%�{I�{��length �}{0cm} TU6�dUns @spa!U�Uze $r$c so-c6N ,1�|fulQ�t!� �#l@a2e& ion!�fluid" ce (Y�$ 1941a,b).�'� *�v�~i��Jn ʍasѣ�B} S_n(�$r})h�Bigi|Ճ[ u} x}+*-s$ ))  r}]^n Q�EleYЍS!�e2��E��ks�ed!:ve�[$N?u(x)�p�PA#? �5*# 2x�8 �==Pt �5a!IS ��&onU{r$a�e�E4!��rest inNx�%�`!���!x xactPS ult,�gwn���,4/5-ths law,N�3)�)�-Č4}{5} \��r,1g45th}I9� vali�-erE�!�šM�($�  \ll rL$9re 5?Y� :&iz���dissiaVve��h��e nd $LOa suit�! l�Kŏ��ur* ce). In%Ni�1��t spur��/$�n�� ��!�n15��iOrom�yer2�if�� �e��X's�i�V sis �m1935)IJmajor$etu�(���V s, h�ia%@!XreA>!9�---K41�0b�Mty---��,� ��)GJ4��%�r� on $2- \sim r^{\8_n"�!�!��� $ & = {n�w. A��� Ew�W (see� ex� , Anselme�git , 1984d urer�%(94, ArneodoB6,2B3 &`�!- it� � '#er� anjeB�Ӄv%$e� $n/3$�i�:��no&S as $n$� _v-�B� . Wh#�iss�rem�7g ex#@ed satisfactorily9T 5T.E\&m!*7it�AKJvi!� genu�(-�worthS' ���r�< ort.X}*�z2 thru��of �8xu�%o�Xa�5G?�� �N( , L'vov�$Procaccia �#�One oby~oc$Zab!aF� �,�/c�}ey A�@a� probabi%� .01") (PDF)�հ� e�" 2�%Ձ�he as"o&*� � i�ed!�well-�� flowy�Yre�7�n ---i� � eZ&N�)ʁrJ  &� becan�me�{� E��rA�-/ "' dri 5e �co�influ�Q���!r � conF�t,Fn l#�$susceptibl�$ � 6� >,.�yAD[ed� 59�ocor��!PDF�h�I2d f�ent��Th�,iŸreaso��  FgM" its 5H��af5re!I 1  es�J� d��"� � �-A�pla��6y��isa�ƅN subj[E� is p�n. O ]s�!n-t!�Aa��u 1-eB &.� GW����i�, L�>GI � -?b�R 0.7� oV7� � � a�(� t ���3ed j8� $2/3� 1c&oo�� to b.r�!!wn. It wE�Nb" to�tin���ig1�t t�!br� s. S� % o'Eobea�doi�'�Jo (@~{cast90ș!�" w=�5.b lV�o $-1 < n \��n� necessa�pfF%� . With {/A"is }Ɂ�d�?��%��A:es,dvl �U��|Il �k de �!]u1MW m{it�ags�-re&-ce �2!Ua��y If,!����h��s��A� 韁xq4���,����A>��O�|�_K�ty� sought � fruitfulm� n teQ32�MKc Ms2��Was�$at��wa�justifieQign�{��,&nmeaW!onary me��� were p�O� .�/� �4�a:� A)!�@ p��a��9�mn3 a���e�.p0hap�?��� T�/dide^tg:TpoM0xE���E8idual anisotrop��">�.!}�A�� � �ce� rece�� ligh��(Bifer�\&*��E.ӅF�O-�Q(�v [�ed -averaga� tech�"C2� 2003p w"1y5�organ 4a��4#s��Sec.\��we "be50alA� �|us�eoI�M �1sis��flM{l3��alVa� � ��&�"� )�th�4>�iAI�se ��:in��‚E� 6�source��A ag}�� each�rE�2e~ su��;!���Sa�!v $n \& �SV 4N� s a briegg�AmEs:�f�6 4+%�{Ev�|�$ z{5-:� atmosph!�&?Slayer ��]} Hotw+1Ftmad��.Psurface Oat a heaN� 35 m vI�Cu'��ard meteLog~ tvat Brook� nN�)� -itM M�� ery littl� sta5z\O win9�cs of=�� solidit YA6�%eu7]8�parݩ$ �8rehens��batAXbed�!�� �ho%b,m  mm�@rE�0.5]yu$ di5ql7was�(ca�݂g�, � +L!H,EwayU�|(Fo�ni�@ "� �u /p 'pp_�a�b*)e��P�kd by]D!�a<.)� �b was per�d�Usit�'�a TSI.�dݜ�;�<� a !tun�f`aZ��-� pass�2�n%�5 kHz!r�10 Ca� Ra��]!g^ )� �Tj}=��R� Fd Y!�2wmitA�M�m1�digit��q1,a 12-bit A/D� vertd>ypaEE���o�� a'^10V40 mill��h s, du$] �timi�!d U,=� mean speA'�dee!�ac,��t��ݑ ailXɝin O bd0�p��n^�`����!}) ular*a�llis!B�  3�expt_�`m�D�V�ziA�s �somew� u�ible��xM"���ertab�}{c,} U & u$^{\p�}$& $a$  ta  R($$\\ 7.6 ms�-& 1.3$ & 0.032 m>!&3} 5�V& 11.4�` &10,340\\�� \cap�{Sp �5v�0%$a�1me .�!f�$U� ��A�@.��/�Broot-%-c&e"U U�y- Moof �<gy "�7$\� ��$%��&�E�H &�s,�ep�/>i�9{ \��v u5�-�/)��nu$ be��o kine�A viscZ*�h� � te�/�7C��.�)�U^�tA�:�D�*� .� (DNS)4 Navier-Stokes�ϥ�: forcing�Schen-!�}�b<a�nS*A ���K bQ66�b$. A pseudo%|�_ code��z �� ����~��.�=me (C>� �S*��c�tut� ��pAa 512$׀ grid�"jX CM-5��*#"�#&�#EgSP mach,l$at IBM WatR�$�#��o��#st��ly stead�+a�#a)!�aE"X;Ev�I-[ shells $A,< k < 1.5$ s0at�� �� stepGtotalmc! + Jt���0maximum}+$%�~$25 Time �1�up��60�-ed�Eurn-ove)�sF". Ev��o�e $512!�A�] � -"\ "< �0in an ESS plo�> i�(en ko 9�$e unambiguw� in�� log-log_� A$versu&he $��� lso �9%g,G t�&� is nospaZ�ic� re�����Z� ( IBV) &xs����n&�a�eNr), sugg�#ng.�r c�reR�yi2), ari� d "�an �y 燉�.�3�1l ��sn/E�ide�newaa�erB�7����� �,A��}�ݩ�y �j) ek all,Q�� �a��al Q�Wa refr� �"wE� ��!��V�A�aW �� �R�/$1024^3�q3�f�[�6�&to � G3� y��ACisflj in de� �TT+ 2�JF3�.�� �M�'!4a1.5i��F�E!� r�<r a�� of 2nD� ��"���� w10�� zf?"��% �oW�� &+&� d450. O�' *� 0)���> "� sim� � !"� "["� *� } N� �� ��Y $Wn x \���� \\ [3pt] A_@ 3.5\!s 10^{-5�  1.75� 45� U� DNS)h fourܠ�*n "&!�r2�]-in "�*G �5*� 9cj� &a%Rj s5�figur!�)�ing \izd�5phics[r = 0.4]{_1 ESS.04.epL� ��:w=��A?�&�Ioo.U�b.�"ESS_exp�2~ �=w�~�����~�:�/ncan�S�����U( ��>iA�aY�&al�*negatiYA���rJb� mU吹;*�&�V�%{|n|}.$\.�% | �%�=F�% xR�%H |^{n}S �%5~Sn_a}IX&s$In!�&<#*R 6mB�0is quite high� �-�J�3�ng? iaPy c�!�_&aluxur-  � LFUw, �#B5 $S:u$@ $r$ ��1 �WNK���.�D �)�-ۆor (Benz�L2#9��I9 ,� r:�6�#$A|q!hm aagai?YE�u fuK�mINr})��'$veBK"�#/$m+d�&,�O5�of�.ris �n �$a priori},�!�@��� thir� �"�)�Q�Ɉ;')� nC�!&4)$�b\fe�"��ESS�rov(&.��i-~ !�!� c/we `!$S= = A�3}���T�J eBassume �� is 1 � uneN)��#8�'vV(�"�s�#&c, y� N���; 4���>0�:Z>��2 $S_3I�e�3|}Qslightl�U.t (bp2�.Hs'� %�|��1(Ae��� �s})R ��he!>5&t�|t*�q�kby *K. A�:�& ofa�E�)Ehof :eX!� � ��,�*�!� �U�<ei inset). p!qnug&o�s E6�5�e9u4����!O.:$1�reg�Zͩ�:����=�T�F~�$^V-��n cc}O0&�� d &�& DNS]1>�\\!�)�s&?&}$& (V) 2 ( ).ȸ-0.80&317�(189 &-0.313� 174�- &[,\ +60& -�=  280.238$\pm$0.002 R88 H4�H15H1 H1 H20�078�70�07 �55 �07BB7B$0.10&0.039@608 �1V}0| 0.07- 140 3$095 7>;2 ;3[11-13;112;12 5:;47 ;4 50 -5v&0.152>;3 ;5;8� !�3$F �18)622F90:F38 F6F22) 0�22 �1�226>;�7;65v36�2AR(0.114&0.263:;2v%�29%$09 v9){1V30>�2v9 3 �%m33I107&0.34>;19�1 �37 -1�36v09Es37<11EY1.2! 45&099I45I08%45YZ ;01 w)�54 .4<5M� �54Y <09<7x62 x77<61E�06%�63�07 �2.0!*704!�Y 061'69 F471Yg �64�e J���.� ESS1pa�+��L7uLj� @ic.O;F!�T� Error b]8��giyF�ex*r 0 w�'��roseK3�S .R �N�.} &�H) t�:EB5�:g>�� &��4Z+_""1���G/+)rte�jh6�1�5�A 9��&be�(-";Kcla� !=�'v..oraD���� ic!!d� �6er �c%�R�)*�"l@'0y Zi >�A*atU-�e.v%m � W � 5� ��:?.�$=�,b�&�7F#81���-s = G%�5�ic $ penet4!�Y� ub "\s!���way�Y��/�$ALP99,KS01�Y&� �0�� us�"�1�+K<�� � $6F r}}$ o�@8lle3+ a box-D7)Nr,C &'9 y (al-d�J-)!o�gn)��Procedy,�)ias� �$=+M�ed#E�deA�t�([3s,6s u$0| tS�<(�s2`1p*�$RecabaW��=ms!j7&Y'}'m_(� a�w.�R�% elop20H pr�4ly�! M�\&M�6�$!Q4 ��. u�7�2ji!�2�ic!Qt""b &*so�"d]�by�W.!J� of a���!D�&5!bas�(�in�SO(3)u"p.,om+I2 Arad5e* 1998L\99,\C �D, BNV)45/a!��9�o l)�(nF.�F,!��� pers�J!� R�.��.�' ond,��b��QI6$t%hod!��Z.7z,7� ��ua n�many$��(U���Gm�(AIm� a*ed�^��glq' hQ�J8"tr*4/5��>t����rkŗde[)�usA�v�f�xvin�]]ext�.8yEp�]�a�$dA�q���low����s���$e goal:��: 6���ffectariTN<1!Z�!si-rg��%p�(<1R��>�pe _�>m���J��>��it�:&��0!Hf%Fo%�[2.��<-�:�!�!~sq\=om 7$DIpbyS��<:rNdI1}{\D�x t}�H{t_0}^{ + dt 6 d\Om�� r}{4�V�t_D Td� x}}{L^3}~H:�Ҍ |^n,� z ngav����1!�u��qd%�a�tM>y�1�unit ��(=>�A�"W-�� �+�.2.e�all&+!H BTo� !��*I $1f���-�� akeU.�[�r!- e�! time, $t_�� 1.5� ( <+ "�#��$Q%gy"Vf�} �5�,slp_exps_new:8�"& &� ,�k �D�s��}E��;9L d}\log (JC r))/2(rV"&1or �a�Q�j"��%[$4< 2�f�"e"� E�.cu7��> bell�$u ��AQ?Vq ��YB d[u�ETi! _,&� l{ �r ( � }s, $n=��}��$n=-0.6$& '��_%z slp}1� Z� :we�:��3;e6�} �@�y�go i,��pڭt�teuEi��,d �(Qi�]` %�M �J� Qw�%t B�u�u�?W roxk4o arbitr^'preciR0by&���\J�a� s�ie0�"s;f�5t���:�low� terp� Z M&ɾH �zœ64!�A�(cub��pI,zKt���Sg�XD���6\EbB �J��9m�Efas�.toRle � ����F>� AQ!f�UO"!]=�J'%Gi}to �&_�('% %&m$�tq-� �@an _�1aQ7!Hm s�>DNS+K41_�=�9.�m$$"�'4DNS ($\circ$);�n�1s3!�/C�:1)�c�er�$-�$-�Rl�? Full�f:9"�,(;raUOia> arg"c+0%� *R *�~�� v�"���!1>:!5 ����%�#��M$[t]{6.5cm}z"� _zeta-k41J�"�L)�O�kaEtA�I�: &�!�!U$),"��n($�#$)��:�star$� e*d g��to&�.�l�3 B; a�e!�$\C0.056�nd�fI�a�D0�k�An �� aC��E&,$n=�*a)�~�l)�(efJ@5�d-f�%; 5� %\hfillv��% ���relA(-pmod-p1.72Jѭ�ce $(.�- n/3)/(m 8�O# ^�\leq 10$�t!(za�YF#u�, IA�+)! QK MPMM �CN�smoothlyMbv%�EQ�-anyQ�peiHA2,��#�|wD�mc;5I��AHso go�� M�t $�E���edo`-^-U�t�)�:��A���!r � s�]Me] \ref6deZae"derC���J�a eJ 16\%E�,$nx$�a�X a �MŃno�1%;behaviG)cE*b -1$���=%N*QSly"z%�>1� �A8N�E`K41, ��s.�F�2� n>3E�K]�gM�*��c� hU���A�in2V 2��Da�8F�)�}]1>�"�p"7��Ŕs - v�8"RW�$ $|n| < 1$ obser��* marg�*.�� ]2�� !���Q � O�H2) ����de� $ %ex6�g3E es $r/�3 > �`))ii loca �#�!�logHh=t�-�Ove /2�!)a ��"�%E:"~ lO1oI��ͣis��6� a7f� s#�$��w:��%G�  SN'I8:iE�)~�"�= is $50 < -R<�y�#Oe��'oCr%��u�VQ�=��0� �?� �_�Jao���� cK%�!A��"� c��t�=lLu> ��u ��]Conf c�vel im!u �m)�&�R5 F��!ir2� �y%O&�e�)A%�.B/�)�1` s}, �,6u2Z�t ll t"� � &tF g��}a�� . �f>{2�)��A[%|� .�nBlo�(s�4� re( �DI�.%% ����F aris�7!�6e�we��J�0 � FE�i�!-��0/howA6 p r`;$ncy, until�<3t� be �}�j�5�p�hig:�J, 3;a;`fat'"�J�)�Hof&!&�J,���A!�;��"aH\�c� PDF��F.�&2� %D�2� N� $9�!�&�@q:�n� "k ar � �� �  a rcE�� . Eq܌"D"U�:^ is2�.38 :n�!:�Nj'% ie6�� ) (per�G -[UuF;u&>U,98��Nna ��a� Պ:mG!�XBy  (icN��Dh�naI!�se@P�Fous� �6i� Kie�al $p$� �4�H$T $law![A�A�?a�e� o�� :"��N�t $n=kA�Fer6y� M �5�* xhQz X%t��8�0��� � !��[D>ntnd�Zl��gRK  zero�F��pre5�o mea��a| �LwY����&, :�Dt�!�a�����7b� $| �R� $y$�;rcept5#pn� " EDi"BE!� �Y�D!ip�al=��p�HB!VE�� �{ L eH9q3=��1��V�R� m sens�K��8�.�Y K%�y kL� 1y� ��2�a`�Nn� foc�0�PoVX[n sea��!�n� la�|�=�e���]d>�L�e�'ss�?��nɺs �A�od�2can�S��;bp smi��&�Re��"��J�O �a��!�/q]+�G)m����=_B=>Ut"�^a3/�appA217Q~. t?�xrs f Qҭf�V t[Qnew��QY<FD�Bes� �aci4��� ��Jt:�z{�)b7�[A�X�#\ ٪ 4)]{tal84} \wjc�X��, G�� ���ĜJ.�MAn�X, R.A.} Y IKe� Q�Y_"5��>*t�ar 1��it{J.\ F�^��bf{14�F63-2�[Ae%�98�DKLPS98}�ocÐd��,(7�h�yK�hS�W˫ "�W8�*� ��R. Z96�{E�##�o&�MH"�&�49�s.}a ��f.\t�\�� � bf{8��5330-533.�%N�X!�99!�) J. �9L�X ��2��9 �j�o&cX�A�a�a��ce:� ��a�s,�x $ �it)% E 8bf{59}, 6753-672��%2� BMP9N�"a', LM Mazitelli%��:�'9 V \ ng �%)��?=N��mogeneE 9F� �Lq��8V�5040-502�[m\.6)]{a�\a�96Uc%�n�\4,A.,Baudet, C.y�lin, F nz7�, Cas�*gI* B.,C!��� v0F� , Cili�o:l; mussHhilla Fc�� ullee��p$Y., Hebral Herweij�Mt�M� and FM��a�]��, Muzy ^Naert�� , Nogz Peinke& D Roux �T "��P.,�M de�F|WeW��#Hi6 {S'V�c� n&52W�g��� �atB�/�3zL5000,:�;Ew:aQ4it{Europ.�BJҘ 411-4163 �2�;.J3)]{bA93M�sc{'��.���6(Tripiccione $.fMassaioagF%WSucciA1�j3!TExt�'d>�aWq9t�<���2�:��84�8R29-R2}�[h+�B� �*�/bi�T�.r8�+4�A�N���RFp�^a�Sub] d� � �ics Re)��$rXiv.org: �_.CD/040�l.�Z2.��*ca�&-Ksc{Caoy�,pS!%SV6 {�3)Gw"^ yF�0Z ��1έ �&$bf{77}, 37q�8026��� 塵0]{yZ ^� &�g�YE A:�E� 0 {V� ��ba? dens]f� �ofu�-wJt"93.} ���ica D.�(46}, 177-20.Ә[�?A�0a�d00� �E� 0 {A�.�f<h�>M2�!�}�9"�N�M�{Ph.D.#sis, Yal.O�}.�*-(1]h)]{K41a�"��N%v41aaH���o�5M�inVresF[v_Nu)�fN @ � 5�#'xl�9(Doklad. Aka!� ��. SSR �bf{30}. �K\Z5rocINRoy�Zc. LonSg bf{4H�9-12� 9))b))b yscJ) !Rb!*D�f� P!q %Cly*� 9B�s�2V� 2} 16-18.��@���nE%))�9�� (1 15-1.��[� m�\U�� .� '�?� ɇV�� �?��U_E�Ac�!q�*�inyi>%Xj� ݔ6� pp. 407F�2.� ���r9Zpa�4� �ՐX(ic�b"m�toB�� 5���"::;.S���� .� 2206-22��"��Q\&.�%1aS02;%/A!�{V1 {Dynam� �� AJ��Ra*�A#�2an- +agory>��x%7�2�90m�>.He�,bf{64}, 05636�)n- \�>2,f/ 1 {M�#mU;�Qa"qF*� a8�� zit{New T��% T"L1.4Houches Summerm�oolI��Lee�`s, EdsF�sieur, Yaglom�6#& David� 55-12L�[�!+T acci% LP96 �sc{)AT!(1"6 {�: a9!��2W��.\ World hbf{� 35-B�"��[� ��1�0]{MauTabZoc94 Ascr� J� .� �ZocchiӘ�4� ap%�9�"t tw�rv�3ngMk%��*�U$ helium ga.G"� � U�26� 1-36.�*7.� Y�] {��reQP�g��F�� 7 {A�$ple6� casc�]modelX.%v�8�[U��i� M�v.~6� �1424-1��=���B��$97)]{S&A97- sc{.��K.R� 8W Iʍ Dphenomenology of s�>mall-scale turbulence.} \textit{Annu.\ Rev.\ Fluid Mech.} "�@bf{29}, 435-472. \bibitem[Sreenivasan \& Dhruva (1998)]{S&D98} isc{-O K.R. 7P, B.} 1998 {Is there �hing in high-Reynolds-number:�? ��it{Progress of Theoretical Physics Supplement��0130}, 103-120^�et al.\ �(6)]{setal96 }^��, Vainshtein, S.I., Bhiladvala, R., San Gil, Che) \&�Cao, N)$,6 {Asymmetry�4velocity incre�s!4fully depedGY and!h5f8of low-order moG.+!=.\FRE/Lett. �y�D.mdzz>:tt: sech�athop{\rm{}:+$cm}[1]{({\��4\sf #1})} % usI��ents \re�\cm:0\ignorespaces6taturns9 off�� egina �#%\ xCJK*}{JIS}{song} \title{Observ�Á�stabl��aia e��� convecE�Lof a twisted nematic!�author{�wD Tatsumi} \email{t @daisy.p� \s.u-tokyo.ac.jp} \affili�{De!�!r�<,ics, The Uni� ttTCd, 7-3-1 Hongo, Bunkyo-ku 113-0033f �A. G.��~8Graduate School�Environ�{ Infor�on Sci� 4s, Yokohama N�al�, 79-7�Hiwadai, Hodogaya-Ku: 240-8501 � ��o}�' �.)�'0 %\date{\todaa=INabstract�W��po,YKA�ML,, localized,EM -lik��� s � �Jspaa�Hly periodic pattern�med byQm$ electroY�0, along whichRpE�of LA�s b! $\pi$. W��x as�� [(ic voltage,Ase�s� a grid � *� $that goes M  into a ind8 nguishen froma0 well known_1�e�bs��k et arge�� at�ugges�@�eu�c[geoq we are u�� n��Dtabiliz! !�)G!8)��(PJL latticeK caus� by a�*teA-a#ofBLeGa zig-za& }e� a surr% �-�# Y�\make�� ��p{Introdu D} Usually, topolog%Adefeck� ��Q�M� mod� hav� -dimen� two. ey%XpointIi +s.hree .�Yin on� y reduce,A� dynam�systems� sha�ev�M}{P�@]  D\cite{Bray994}. H�wu�! }�!!�4le, self-organa�)3 1HE exte�oE0)obj1i2d:� �k .s} (PJL)a3etchearallel� wave��or��9�, 2acter�A� changT -5� -�B���a-Ra�`ance (Fig.\ref{SetUp}). ��� on was-;e%ygUOM���� roll�YA�Ein layer�LC�g lL cL & � (4-methoxybenzylidene-4'-butylaniline) underMinflu���an ��0ac field ($\p1x\!\!\�Qz$))� is oO�!� � ($x$-$y$) �Aqralign�9��Љyor. E>� (EC)!,6�a�8s been studied Ez$sively. A  early "��D E. Dubois-Violette ot� i,dubdusol} ai�{at)> stan���basic meA`ism�9� , EC�er bec� opular� aAqele�Q"K in an"�q�. Depe :exAZ!WalAQd� � he� Ia��%�ed ei��Ufe� i� 5�� "� axisAAx$)1�s�z---defiUby8-ӡ�at ��1�1�AFanchored!a%S��aries---a�b!�e at s;pr�1ngel. I� )-� case,��!�+ive��esGaA�to each)��a refA� ��$x$ �coexistMzk,bzk�6Nea� onse� .de !A� terma� ��(-l�s) 7 wo ( ���-d%�4ent Ginzburg-L� u equc  uld)e��is�:I�annrev�These 5A�� otenA typi predict%laxe!4a simplEilibrium�te� more puzz�� !�r� ͳ!I? �geda stronger&� ��s,�4scenarios suchaJthose �d ``fl=at�G,Williams dom�0'', ``chevronqv ab)��� *� 2'or ``��a��s'' ben�M#Lkck,asr,huhiroka,Rok-Pv,Nasuno989-a,Sano992`95,Dennin998,Ribotta986,S�er002,Rudroff999,Sasa990,Oikawa004}. OnlyAj,recent years0��clI�at mosE�tA-�%�$s can be u�.stooda!� non-:)al� .� $qmq(s))� only�ad��al, weak�amped��_i9be  in-planatyA�k>P . A :!-A�e��l7>� coupE�ɚs5 a�a� ree)� s, c�d Mit{� ar � l} below,��lAo.ber��y U�Y�at �t quali���j m�BewebMf@roth,Komineas003}i�r� sever%�dic%:��h� !�g� hint��7���MAW1r/o1�o� �exa�, Mhi.4-chaotic regimtio�� -Y2� F�A�is.% �h ``shape''%�&� � , Jic�lFa!�e* 5 � c���and anni�,a�b�l� ��� ir�  in�> ���Si��4nsiderably lar��th% $y$�)OA����e A���xEi!a�Aar dis��a�GI�}�E�,>ca� remo��F ����ngC�%. But����e-[s��� t9� ��t��=nA��6� as ``� &�''��\2,Buka001,Cladis_book001��"`s seem��b�"��u� le saddle!�r�o�  t" .� �. St�1 also� � in�er� &J-W 6_ �8zhao00:_secon_i�_compl_G _aE_i�}. Yet,�ene� =yA�mis��cit!셷un�&if���� c�A=s.�wy���inJ# In oua%� � Y�io�TEC setup<modifiM�w9g ���0 ep : Instead!G] A�a 3m�or��_f[2(w �0��� Q�  Z2�r�� ��x� ngle!op>e2s� r� su �� Hert5 994,bostA|8000,Delev000}. �g�A�sM� favo�kc %�qf?!we �s detail5%zed EC %�I422)�edhe�}ht���!�nQ cuss�+E�� idea�7aJq se�;��ss�{EUT al SA@} �Tfigure}[bth] \include(s[width=.9\�- ]�0_f.eps} \capA�${Top: rubb!:9���!VNo�Q{ . Bottom:>ype�:�A�H400Hz, 13.10 Volts.�g(white bar c��%�(100$\mu m$.�label �vs={-.5cm�nd1�m:_[ dw!eg< 0.1wt\% tetra-n] mmon bromideA}5AIM�7uctivitya� sandwi� betw� ag� p���nve� w�transpa� � um t"xphin-film�s des.%-J��o�!�Tid Di�w8 $2�cm�D .$%�$its thickn�#$d=50 !=m}X!�u��q �m co��@polyvinyl alcoholhAmF�"Mtta!Jnar�� b1�molecul! Temper�Y~ !was't�edA}($25\pm0.01 � $W stprd|-�M�C@��pp "6s $V=%$cal{O}(100rm{V})$a freq�i.f$ upJ� $/kHz}$�} %�!c��1�is�wn sch�Tin �~*�� =Iy�� '%�TH���n arrow�y ���NI ��4$\alpha=\pi/4$�)� �l!�Jlower ��{A�BO]. same amou"�  up�!���U$ �o���F $z$-��bg�A 0te \footnote{6�a� a��quival�.=s: left s �@rx ."� *9 � @ o"sm e?3 � waL (uni�s U)A��ec="} �.�VPResults}�R.P�"Diagram>U A:# ,. Solid circ� U�-"{�A� ��` ("L D ); op6 quarxKFHPJL ) |{�1M� 02� (GP); s� lVi)�  '�aH(mode (DSM1)i� ii show �� ��Od)k] t�dinE��# Q�s a, bE�c�)m�k�� FigsM8Main}a-c��t�}v'~vco�x�amete&� ��rn���d�1�a; its �H�:)�&� ) ns �" � �-!cutoffc $f_c$*er� ���Er��]�n$ed�;!�di )God)% bove $1\,2. Measu*�Cpera�> $f< �({\it i.e.},�"�A��!ED5N}ed,6��a�QoB" ���.(a�� � of�����MJ) �G �Oe%��-�(�!� a#.J ("���s),:��$ angu��&"AD� sc2{s (3Dk"v-t })��'� ����� j�'O s��w� U� r�!��F� "�"� *z� .pC�>jm�e�9�row�P imag�f�!�io�"u2I PJL,��?�m!u"4 �5ing�S2D Fo�*r� A�sicrj pai� ��pmbE �7 ]to GP�5ig.~ay 3.93 V=D($\epsilon=0.47$),i�bC15.91 V6%91%A!]c t�� 19.236, 1.79,ll�400 Hz� ength1�=�b�s�)� �"&� *} Fi� s�%�a-c%�! shadow-� )�f!qH � a_ ariz9< microscope (pol�*�x$�lF� finx ʁ8%� end�>of1Ae difXce� � adja��s ge$le|sa�o zerQ ����is ��mFdi� ce $L$q��.Z g��,/to�erKE���ialow� �)� )Q� �� ber $K:=2� L$, quant*�� �d� re employ�+���!s� "'��F>rec�d m��2�b',c')I�� ��t!( ��L/ $n$2� � n$ aRged�#a�0Mz 9E5 �sum�!�"��a1Al�%��et divi�>1bcH�DY7.} M�� a��#I� $E$plO!$\iy5�gives $K%� n/E�v��Q���1�analys�as�f�*d. At�!�!�!� c!w��I , siA��'))��eno&� $sharp peak"���%�_p�/D.)h� medi� ɋ|r� !2]� coincideF�D)Z}0m�' � $K$Al plot5aggt `��"y±�< = (V^2 -V_c^2)/$��A�threshol�*i $V_c!�~ data3c�%�g�&to �g* a� -ro!jaw � ��}�1ZK�0K= c\, (�-  $_1)^{1/2} �0 BG � _1>0�Ab $f=4&!�w� � $c=50.5 mm^{-1}�O=0.22�� $f=6M$ ) A�ll"�e�$c=95.3R[ 6[31$. S� �a�OA�a� v'�"�AH�t �mh� i+�$ib�a#%�'s/y irre� ��2� ,b)�?Aa3h inu��()thoughay slow/#^4���KV� e�er,C beco����a�T��(i� v�a�yp^($.�c')$u)ead�#A�iN au��!� � i�!l"�\ a"�!H }�H���� PJL   3�)� !9 -��=�)}lOis M4a�hvs}=�&�%f star��v��4 significantly=i�y�vaUa%-�d , asf !a={��� �7�-!\towards�$K$, � \denser!*,E�rar`1wa4#���$ct �a repul�%��a�})�1�s4vis�) ibl+%�R !�� }Kai976}st!�a�� lappE+et�)�#;"�$�"/UN � indeA �#���5n� � 5(a new route) �*� � u ,�].�\�n� �'B8 UWia}Vz+} ut furthe�,vestig����i�A nfirlis hypd si! For� low-�T�n, �&/r han�Z4 tep�EV a!�J'� �  � Rma�:3}v�.2�Shift>6�G"6Qz� a�in�0� �� K$v 3��N�ane�'V���400$~Hz�l�Fa!t 6 q�a�%m!�f����utZ  law~(����{�Si�� $ -_1�U=��K#+log-log� ���eE�i�is( 11.5����%Jat 21.41���.y��E.dJ�A @= y} A"%e"P=pic#��/Z!��e8 �their*"#aRaT(K)2�� the .�.��|%&��i, has� yet emerg\ Eve�(oug (&�*sH$eto�b�#app�"o �#A$(softmodesX}Iqs6� Zhao +z�{ ��ongly B�0o+2-eb�N scri�� aF&_%R$��)8*a��shQ �a���� $ree aspect G ��proble��a= elp :iwhya��!�G � edH%�ho�0� �'՜�%:� �r rohekrpe,�%rzkr,z:�%a>� n�.�sub"�)am% Aphi�0�3� split � 7A9 \tau \aZ7t A =& i@Lta A \dy \phi + \Big& +a� \xi_x^2A +y. 0\ & + 2iq_c\,:y^2\,C_�5 fn-C_2q "phi! g |A|^2�) A�=G �\�?.�= N$ \gamma_1�t�!-h + K_3!�� � K.?�!-\\&+2 \G`/*A8 Im}}\{A^*%B (5~ y - i q_cd )A\}u2�:-� 6It��bb�(��of��5o-tempo�"  vari�Hs:�co$ex ~itude $A��ݡ09��($\sim (Ae^{!�x}+�F{c.c.})$� ��$!(QB�) ���%o�B{.�/�~� alaya�ty �ac8a��-�� �)", ��unq�w#�;time-co�%nts $a?$O$QO�  co��$��-a. $, $ ��cri( 2cq~Y �0 factors $C_1 sC_2 n L�u coeffi�8 t $g  z+!� $h=�� ela�A" s $KeK_3$ v�up=v� AY$\beta$ �."�B�&!y�2}�i�ule?d6� ER(it{a priori� valu� $ir�alway��y@t�' nega%0gw�� ssum�=� ere^=� K@-8a#�"~7�Jr* ��0s ($A \ne 0$)� a d�/4#!�ef�6" i T isJ*rucia�,�-Eq���kN�'i{��!�no exce�[%ub@ �(� !�PJL} �R sec:$ility} Af� ���!��)&S Qe&AE�phiE� i%�aZQQ $\dx�R\dy A7�{$, $\dt.��6^ �dim})� re���7-;"=',1i� s 3� PDE:���{틭�,F-T�EZ�(1�L��|+ً�m�NBB�A!+�5|�3) A +J�, V6��n?.\,ś>�o�V/ -2 |i�|f> ),ph� ��-F 6�� ��� ��a)�]})mt *�.o2de�"'At# *ColP BPIW, butYR� ese� a-m: �AevQ�j2�R$h$� W##is�84A�&��O��h$�BEq.=' })����u_-1}$,b,~plays! �r!R,�`&x� !qre��7�4}}�As]"��i"�,�uJ&Q homo�&ousv"u% $A=�x�J=0�F'�3 ��at $h=2Q�$�,ɹ<0��4�<m�)�>9(1+��)B� E�I�� �-���=M� ��ua~Hhi=0, \quad A=\tanhS%(e$ y/\sqrt{2a�\]%)i U��* ���0!v)� \ clA�E�� &t� ,AE�7/Ed��*�byA � �#L limiu,\to\infty$ w�j2�fI-Q�$o)�M+!)�"y�ar!�Mdel� =i\,h(=")$v growth r.� d$ � l� r967[How\3,����$h$E�&�4 g,eefreedom �$�_�4&+�( i*� thr�A��  terma@N� �. d�$�1 �$rocesG7e-yI�-O�x}))�0eci per�JM�ofU� 7%���� $)sP A= [a_r(y)+i a_i(y)]2F (\sigma t -�,=f(y)�F # #w�lea(^"arA�0 =& i - h\,�  +1e-3\,{{e88}^2}{\frac{y}{{q6 }}}+�^�OmD a_�,2L*4��6x��I��"B(m�u�a�ZE&��- � \,{ C_1}\��ecj���t)nhV�\,���.�V`��%� ^^i-[5�-Ie�Bv))� -h - m�ض�1�Ff � & - �.��:, ��\;E�b�s 5�ja_i .I�-2�M_ 6�W8 look���eigenfun 5:��m}$ �=ed�$y��pm�� . E�ȍ ar})� deb9ed�Eqsf ai},�)ځ�A�)���ma�Ae $a_r=\}��(��K�~�f ����ly� �� I1\le-3/>d"p >rib��i� ty?ɢ o#a0?���!�nwn inner Lon $|y|\lesssim 5$ n���EPe&���3!��6f ��f)K � 7 $y>0$:D�9h � tit+ � �F \to -!n1$�{3 q{Vz�}�M���m�ai-out# 0=&(m���+\dy^2�diF cf,��+E+RD+u�\mMf2_ dya2,�xv.�wwrCF� he abbrh�\�&=1-h/x$.R%� r�<2e^c� Y�2���cal�: nu8���-�� Q`by ;oo�'' & �7rZ$y � $a_i f=f_%�a_i'=f'#A��E72�&y?o matcha�i(y_1),B f  $ �i su�ie�h yL�au�EEu��&W�E�K>b%�ere�L��Ba@')�!}U &g !ganSV�!�B2C 9  i:S c? A<-� $e�0� The �x6� t� M(ly"��\combin�E7y� 9�of~�^}2} %�,f�,xp(\lambda y�  $ \l��q�u�m�flae� 1 ^2=&- \mu�6tau}{%+\mu}+I#�3 #^2��\� �Y{o�#v stee�6.d-uR\,(\)J\)0 �� =?��*mu_ !Q6mN F� � ҥ"^+$Q6D �2�and6��wo�>it�4o�i�R wi�S\5A�: (i)~�%�U *�+h,to m%�)�%� e�q�C�*s� ($f=0+�I{c�}. +Thus, �5� �&i��Y7�#A�pon�32- �)�)! must sJXfy^�� 4��dy f=-� Y&]$ }\,f M(ii)~By�|̈́) A�*b�c� rved�uyaաf�(=06^�7�)i�e-�^z�]� hen �r��-�94) "(9�MmplAm$u��for���Z*� Q�N� �}% ne[�#���A#:=�n��b�+w�AY�&oe  �%�s��@*�a,��+*�m�IhM>adjus�A�- ial �,$�a�A�at�7�, $o"�6�%�&(TP�>1$Ic'?fin1Sut_#@"��� F5�f�l.A{$t��� �M-��%�&s.��-R,G'�Sfig�le-�O ho5nN�- ���2�R �=-0.6�} =0.3 C_1=1.�Co u=0.5��H.I~ I �" 3 ��� simi�2��idda=M ���!�2%,�r�9no&Y! Fl1r.D&�)& Da��3s �Jro}9L9:r $, B%: $�G fB?�C?> T- �C� ��%86.� $�roachesh$A�+�1a� �s��C�1far f�Obb+��tv+aF*:#E"����0us� �h2/"W, approximate�Fi��Iver a �5$/"6&jc��heY��\to)P$,�&�{#.�IAs"rg an un; s�>a*�E�rth]$\dy a_1%;-1$ ��/t�6J Y\a?]r��=18� �< "�m�) �L�S��0�H��q"tU@)�J f=1,5F=\�\,(1-\m� u\, yN�n �Z *}6��H!p=-n�����QA� �] � ��!\�� i"� )�e�M�C� eourA3e�F.�,�_coV'�"/u���,e m�$��c�,ad=1�� �e�_�!��~can�z2Wio� �.8��\m9=Zif p>p % %U�Ytuneb:GE9�>Eit"U it %qu76�/{JKunf�1Qa� -��p�N�B��I�'in��-�2��aoX+ B%�=��`.h(. %%-w $ sl�?!�dK/�J4$0$ ... ? \cm{�-'s gok�+ re?}$��as%)ze�B�q�Im���>E�9 � �5H cy>pac(�+��+=0$ [�q��})]!` spana�(wW�T.�S *$&� ~p�e��� 4$(a_i,f)=(1,0)�8 )�A{Bon/ 0,1)a4S[5 bothF �], �s "V21.P� o�3a�hen!�"!&!�%�`Bݯ� )��>0$ van�R� � XF� *!A{ �Pachiev- &� �RC"� u � 6 �b�� q!t*.;�88�/:� )>�� ��|$b@=. �&&�'{ nd���c\S8, a cer� o*5# !�cMd-�c �2��� out,N1Y(+D2 4io $r=a_i/f$ (E y\to+� �!��4R#W ���U ���) �*sm��!�A*}v��n8� EbB)������(gma>$under%�%0ra Q /f=r6tmu)$ y� �D�)�Zv_sx568��re86Pmu\cb7i&sXm2_s=�2 r�+^ �H}^2' �?}+O(\mu��E���%�g&% v& � � ��� ҃6��6&Aw"�_s�:gBo# �����$an&�M@�. �"�/9K�/r!!>^2oD� e�IAy$r<�%��zhet"P�{�$ m�VE�er�O.�ha^. �^] :5 �($rq"�`$&$ \, rU-�<���q�  Uw!n"'"!A"g!ic�S� � ) 9${af � �>46U� �% � �8s�{/"/�a/)5i�KE� frameworkC�Dl�c� i#a�J!����D� 0� �)F� ---a2�8WR �09� ex"�P---�! ossiU_�%cv *Wn � E�� \gtr*�  \�[3�2* ��,&mD�2�)c1� or2otoV�$A�FCd�o2�QA� c�a a *>erI��s ��X.�\h$�; c5� ��>�'(z 4�I��> A F�3&�2, � Keep� !| d#�&�EreT'evoa+s,- ���Z*.�"inPpr�9 "�a� un;NvEz"��cF�19z2 *dt �? A=&\ &[u-(P-!8)^2+\dzy1&] .6\zph�" P==& ;!^*� |L* 2p"�0J��*�( $u�* zAA �D:h�t I5�%�T.�;. $P$5 on:$ ( i(�B vectm^�hlZ-r/>dahe|A�� 5A1 $>pN�d�A_�.A-���AS %A�4�q � e&& -z^2$):k��[�hydro�G*+4B$z�&� E� ��6�stiff Q-Win-%J��3517� ond N!Xtorquejby mis%ed�)GV���=�/�Q�"�Q2$T �loOuy�nd impo�Ge/���7�Z\pm 1)9a�::�)�FQn�`ing�1 hat a3(+1)=b�eF(-1)=-b� a NZ" �5broken ��SR��0ibulk,O�hFHrved, "��` Se�Ori�d  $P�P+�'���#� M�A�l�� deri� ���2l�uE�TL�at�/IE%��0�  q G(e� �S>���H�)hD(��#&"��6�A4�/����)o#q�!B4�T 2�],c.�-� e�)�[Y2dmdp���n "�ihT}QAWE . N"!-�F�X2!al#%.� B�C �JJc1F@hP omf~f&;%�� I�M|%4 �$b�B�12%��*� ��F-d�K��4M>+iA�guSE ey�M �bel!!�i�-6�C�fPi/qm&�42� } S&�Am2zh�Bb &u3y%�ck� p.�A�A�`5 �:�xS Ht�#lo�L{\&�k�� I FdO�h&@M*QneighbvSng� X'��; wav} $\L1)"  {�u�.&%*�Cth�AF cl�viiQ�m & s,� X27r�B$f-j�l�'Oeis�p*ZFe!��HiBo�e�h"�G�f.�of�0C 9 �G2asy[paris�pith*� |Hme�fal��*&_�K�,i*hI� �%��k�&�M: *m@|A)#�-Al2E�b.XDin�.Ie@$\theta=\arg A\,(�*oprm{mod}�R)QQ�/� Toge�#i ��0As- !y�'�!p��  r�CZe�0"�6��/��^!%- +M<�=&x�C\dx^2 +y^2\d,*�/�+r" >1<3phD: eSC\dt1 {"�+"?D-e:> AR})1-g^3+K_3 � phi+[K_1 �qRH��!,z�/A�p�@ $r,(A3%6 �2<: "Y;� =h/(�������dn� Qh�"E"�#v d�>. Wh��Agd[e/��no��jkp�{��k�Xm�5I�U at DalD tD:�m0�A�e�s%V ZFZl�AE{x,y}1�R9� �'6&tV�ai�!&���&�en.�G#9�\ vali��#wiond� at� ��y$� dt,\dx� *�=E�A� "�@Eg�:<+k alig.� 4-� +a�!�a�V5�q�adi�3/3=J=,X.� `IIV/ X)A ����til�I)OW��_�2~�� ��$J*$  U� y;�.�)��e� �#A��$�Nb�e~n"�n+ixA�G)eD�Ormk Z:�a:�!�tJ.�=*�4(S>/-�L1�?J��,+g'�P^36N�E*�& 2�� � arbi�Q�'5)��yT22�) F{ ive��&�e�-��*� G �W/[��vvas^��1E��**9�6� =&�� x �K_1}{��-F�n�}}\\ V]R@�>ZZ}x:AR� 5�> ZZ})"'( �.�5>� ZZ}=Fn/B~ $ de���:��+ .+#�a d /&L5kJ�qH,�[�D�U��)��2�e�Axi�1K Va�(n\�ion�_��� relw�>�& "��g�!"?�Gas!Hdk �#�"0 Leslie-Erick^ 6'spell?}�e��:_u|J �a�6�! y re$~ tb�LEAD*� , n_y=(k_{33}Y +k_{11}S  22})*6HC�ir�� ��3!4��0�A"j8&jJ)z=hd/�J$��� *dx!Bng �g6�� $>?�#^6reZ �3.)�b*-k_%*fL@\l}{d^2})7>7P !5"=:���!�)�&w_0!.2|�Z6=� �/d^ 11Y%� Mc�sS 5$^\�g$CFTr$I/ M� $\�!x 1.6>Q�Ged&�K�:�":c�{mixzS � ]b `�J33�k  $� �_e�q�3 (�aG�iɛQ'o:#}I&sxe �0%N~>$z�0$�a+���7Eld%�|�ll ��ea�3e�MV?E��  �um��\. A� Aa�|�� $L=m\,ͮ&�a�n�� &��"0$�a!�7��i^ L>p:6L=&2 d m..)�� �_�Q}22}J���VA\Left� aMm KC&\pi}{dm}:n22 ^ 11}}ms z�d}{  }. b7Q��*NA�^WA��8�Y�hdi_�_K$,*� L}) �ba% triva �yA��{useBGZZ� p�UgH��er>,��yI��4�L.  �fi�&z%�urvA�w�E�at:��15 $m=2���R$�_"�i�_Z_Al=$ma4$2 $600J2��s�6�,��B%f�a" $m$�HCouIn view�coarse*� �Q"sm�a%�stZ2"error,!!2�0t�%e�s�cy sup�iN&k���r+~����K� PJL-�+co�%� u�* .4#&q�byZ(P&3 Z� ��al�?2g�D� kept �r��n�$�, hL$P��{C"�'N&w��y%H"y�=C�%(��AE"- �Q�H2�s?e�a1[)lfi$mevolv� o aIu�Yz ^ _k@"B� :V$"�� |"rgupA���@7E%���_�jm��D�? �Q*�2: �T�*�:/�r&�W "�*h T("kn5 en�Uf�&) &�R���1;A.��<{apsrev} %perhape�]V5,multiple bibQ�sEQ*� {biba�1_3,bibM�} %1!l A.R.��:8V-6&� J8]�[� } %y�k �LZ�_ z�ё %% L�� VQ#bl�r  :A�exfly� 0TeX-master: t End:r T8Words: euc jp ��JIS�v� H�� �ir��� :O�� ���2�/G"x.V� but"S�#xA�ar>P (mx PJLs"8*�-Eq ZZ�"U�GLE PDE>Pan*� Im EqQ2nstL67�dn9�igeqE N��(oc&�cbx[12pt]{Ecle} �odd�Ncit��def\be�C gin{>*}2ee{E�Fba6array3a 3:b eqn:eaF beanj*n.;hf��})��{{\rm ms!�(ef\z{{\zetas %i %i��#ii"��i}} $d $d} \h�5{0.0mm�a{\�w |.��{��}{\arH�W� AB/5�B0.A#%�BBs"�WjD%fFI f�(�?} E�new�}m�orem}�. [-(:>)pro� }[ >]��!�B.7f�.&)�&`� {\sca}[2]r,#1, #2 \:<� �Y&��vt}[1]�� bold�� $#1$J\HCHAOS}{{\em Chaos, �wt� \& F�5als\/} �.�CMP:4ommun.\ Math.\� .} }�d23PAM>4Pure App�@N9FAA 8Fun��An�8N1I�Inver�?a+>0 IEEE \ 0 J.\ Quantum �nN8JAc2��>eJDd-Diff.\� JWJETY ETP ��FSP1Sx�.\ A:)D \ GeV�\ � iqueR�JN5�,N�F�B�26%�jOS.� Opt.u�AmRP2�lasma �NJPSJ-��-#ԟJpVSC2SymbolicG>pu�%B�L�%�B>LNa 0Nuovo C� to\NhLGT1%$Lie GroupsIqJ�NL �)�ea�RX���N1vNuca�%KJ}O})��J'P'H\f(R � (��NOR:P(nV���MuN[hys.h�ScrR*H1�(icaNNu�8�.\ o��[V1~roB2 \ Su�9J:RIM: $ kokyurokuR RuWRepa� m^�RU�)jMo �f.�us��� SurvN�SPq�Sov�!\--�J�S�SStu���fN0I1IAM�z3T��iJ�Xt�� \bf Class�<� `:�nomW!b��q�* ��mi��q\�� nd v�3.�R*p\ I�^y�@Takayuki Tsuchida55DV��L Kwansei Gakuin Unility##2-1e��cD 669-1337, Japan E-mail: t u@ms6-�\\)% poisson.V( ` 47�(omas Wolf\\:�!�`es*SBrock�@\\ St.CatharinWOnt��<, Canada L2S 3A1!)�wolf@bOu.cM L � %v/%�%�newpag ,a&~� We >�! !I� Y F^ N�F6�to �8 �i  �� iI9 .� �+s �ar6@: o3a suitE�w�(�/� vI�x�paփ deal �_e KdV?� Burg`�(p-ote�)or�*Vd)!�| =��+cKof�,^!"�P-i7�,~Z �t ��Mak s ansatz��4" *��a �A8gF�a� ? solvU ��� algebrai"x�,  �@�citT$si0 $2^ s��sw1nd }}$���IKA�$3N3r3�M\4N)th.\H� a�ZY�� a $5�d!��a�R�b few�Qo%s*Ӟ� &#��A�,~le FA�b of itE�adm�1eitU<a LaxO�6n3%' ���r��#�A(� roug~�mp.�* Y S�G> Jzsov%NOlKis dr&��� PACS �z,s: 02.30.Ik, ,Jr, 05.45.Yv.��_oinF �Ableofcona�s^+7K:� \set[{er&E{0�a���y*;�L![een'�, �XE�Yh&$d�Isct� B$(1+1)$�(2ŏ"$�O|%��*`IbSha,Fokas2,SoSh,MS1,MS2 �,MikShYam,MSY,FujiWata,MiShSok} (see�!*%�re# 8ASY�/ It!�usefu���&ym�G J iV��'E��L &; �,�e.V } ��)ABA m�)st� i4i�j�� ���Q�0 Mikhailov, ���~Y�xov �1A.;,p': y�� �,�H��N��ir ���0��M u��15� ���2� "<6)uhqM:degene�(�0�Ipar m�� d+v�T�/ �ed]�l�� li ���Ae � ����e-�law���E(ala2�� vert�A!�2�Q�2�ASMO��E�^v !� m�ie!`!Pbel�Hi�A\t�) I���� se S*�ethod}��a�shL� ``SA)blc�VI�y olog�< Calogero I�1,2ぁai#k p��7�t2�I�:� U� ��}� !�\kkCu%ac�V!�!^T�m "�H�we pursu��follo:; go2R is �: � :�iz�)\ ` prov�3Ha ``user-friendly''YkQiqiTo7�\fre$fofa+ :A�B�p~;��r&f7e0to d>:n3 a�n!Ex����. T� ��%�"�UAe��]�u�"M�0e�'On> 9}xJ��b!binc�,c&�� can�1�pfǞ.� �!���8� (c\�*sol25'�G �$)M4nqN�J�.C����j2c�:�>Fha��� e�e�J��̪Zharkov1C7 $2,Meshkov,� 0A���* s 5�0Karasu,Sakov}9,Painlev\'{e}�  �T�;�)o� �b(�pKdV)2�"�24mB4e�BN>�%e� � ���}� 3iF�Y��Y�2�6 e��e#�Hn%& � Jord��fa� Svi0a}�$�!���/  fW�+I�t��a?R�� �7Y�;�)g-�&�( Schr\"{o}a�t"�j6�akL p1�0*� 5�6A!\�&� ~>|U` DNLS6`"�"� E�B|� ~�uMv�9g li�%�}�� rK!� ssoc��S)�Ma��i�IpI1a��� L1,"2,TW3}8 ҉ w)Ai�B�J�2j 9�ARdq.�SWo�� S*&� �($ B�".�E�Yun�Jn�u(x,t�9" �"U" hD((U_1, U_2, B N )$"�aB�.� icular� we��y�2N�.�����=L� � 6�$u$, $U %r ]�� � f0�yc��b�V��m7 Soko�a�e�I � (T.W.jMB-� , $N�-A�"�6M"v�)tea�Yppr�Dt"P?� )�r6*ݬ 0-� 7:!d$K"*��^m U}. n U}1��Q m_{j=1}^N*�x6_j)2n ,"�$@5mm}m, n \ge 0.$$y� �;n5 �xs 9��) j$ �5 c- $C_{jk}$ +din [�}2�m�$L,e�exw,e,:,k �<kN=2P�k�Z Moreov�`w���IlEca��A� �truly� �k�q.A� occu!�n $u_t=isI�$u$�L $U! \;� :/s "�,!Ft" �:� $(\lbBa� 2)$--$*�]���of @} �Z$. ��s�9&�i�9%8 one-"��Wu�!O� �Ries $$(xYj1pt}\, tBuBA� \$=*�1(a�=FS,lJ\ 11}Jla^ 2}z, �'4mmՊ \neqiW&EV�1OH �]2� > > a&s1�  ���3mu$. �=� XW =9�$, C 5im�: A�e]�e�Ta�"��� (d"ũ�z� ~ e"c�.��)1^2�y��AX=s�=28�gin$u_{xx�2nd5N'U,UO'$  �s�Iʥ��h In  ca� �havA����ea� )?�� OE �fe�our�,#��D ���s mi, �;"� Wang�ix%mbda$-}�2"LEKv67�^!J!s��!j may���@��� q�yI�if"���pp�5item[q91�*]�A.D  (� )�ing), orL�nC1$C(K/ /� �N{1\� 2}$�\ (F���[ $}).�56I)�E-�:�%�$ �i*6��M.!�" A��!5�Wp�inn�Q��(� !x:�z &)<�#v�b�}}$��� �TK�0Q�M��� a��nK (^k� �c�=sm!ivʷ S�kE3lvn�^H}y 2z�0%XI� $2c ��� 7�EOr!�19�3IXgV Un!8�0� 6VE�@� �_�_� $| ��1 - 2 | \n�S �.(bb N}_{>0} ;� 5c%oz ��Y��; B��Zѫ, :�}�mF���&�łlesE�n!2J�^!�l2� b��)>ie9 .( =  , !6, .�oR  $6�\n�_`{1 �C�\; 9q = {2$;S�N2,BNj� 0 6�I��^�B%ba"/!��� � >�!���G�|"a� �z"A�^f� �y N)$WiIuvAYr�������� Qtq:�agw � D> irel'Al�!� se�X.O y :N��# ��� ��^� = "�D�Rn1>&0�eyt";_�E � !iNkgthea�>w�on!%�̣(oje��� .l �fU ��$2,2), (1,1�  \bigl(y�, r�2#3},{2q�r��ml(L3)E h�= 2� $3�  IY�,�weU&�� b��� r���lo"�8< 2��(� y�!�6EH�r�&��Ef� �bAq6<�a J�&� �X� J��Q is:��!ʡ�sf �#�*1+�a�c�.�#}�r\1 I�� �:p !k#*: F; a ne�ary�Ai&�!� s"|��D2�u$���1�AB�  �n �toe����~Ag �%��6����)Beukers, 2,Kamp� H =a�(�O aQ�p$�o�A�a�%�Mz=@�>� %"t�]jn;alread@]*ir��%)m ~" . n+V8. \ &�,aF�.L&9k( F��V�F�+��a.q3� �ɬ"hT !"���ul�CI;g�ge%�:+Iwan ׬qu��Rhe�� )�Q0!���*� ]�A�}��h B#�b�<�+dm��A���z@To���ret��*"s &�� u�*tp,�am"�c Crack�I��-} A�s(a!���a�zm)���%�a*2~�)��nd1��*�(�� d!�A&B����Q"6$��%�too9w[� d�ҕ�-�]:�A�� ��"a5mis�AY&��F . }-i��lowAaj exha�zv�=eY�� E@�&����_An mL)�"e] .�{% FF next�cg!j� !cg's���b� Ne�sf��`$ u�C�aX@r�$�&��9QqA8�#�+"�"�WAt�_E"a��a��RofN9Md�pa`��'-"i] �!Mus�:&�!�B W&�'�f/%��O�Next,A) �UEY�+ �.��l%�ed�%>Q���Q�J]- a-0N_-���>D�k�t�&s'mg��& �% 2���KX8W�cwC�"�&i�4D*����2�)�R�!bItC+5���Z�5�s!B{q�w!�d � an�Ei�Gma��\a%ateja��G��rov��Anq�%Q_.`A' ��|�o�0A�!"mai�j"�W -@!�as>m�GG6�!�?/7�_�A<�[ ship��amongA�\!%{�Aruc� a��of Miura�6���"lu�-ura mADpq�o!�q!Scow ���&�.P!�!� O! EX. e�as$.����_&X z� �� .� orga@�a����.�/T�� briefl�2o!�q�P)eIz&� a���%Wer�Ins3, s�Ha:jv�@A� �� E1 b2$>��as�'�!Al��fy��a�����\T ��emp�7 �I� E��9����� !����f  memb^� A�I:�delf�- - 8 S�/u�5��XiK�T.��lz�#3. S 4ipe� ��L� ! Y�����&�h�h1 r�����v�5I t��1�e�atm��e9��~All.�Avɕ��:E3�h� a���!� an (�x ) %"1&�T�w�gthe�ДDY�/�saa�r$e Hopf--Coi/2���w�#2�&�:mea�Ne�� �^?6!,)N�.}!��x�1q�� �sol12'�h&1M��n%��trnb� ip& \�(%� ofZ.  ͜t�7 .mnaVS!�A�!-iAoea�� zp�Mm�ѰSo=-17(y�o�Z�u�f �8 ]�25Q�!�i of!�c�,ɼMy� !���o )N5p6���C��c:�0!��Y� ���Q6�R���Qf�X� �]-�ee�(+��K*  ()H&�+11})) i��� AB�lns 5��$�^�EtA��^A�� i�!�3Is) $21�2pt}(=25��< n�P��Af�e�ct6An ��.or,"�::&�9á96/> ���oN|�3�o� ��21�� �LmE2��*j $1Nhst :�<�fs �� ��U�!Щ����f� !i!P;"mbd�.��!��;�f�)�� 5� �@�4� �b�"�� N� w� �II��bd ��q86, ��*+ ��� utr��v��&�� Q�9,6����q "�!"b@�A�*� 6%��9������nݫgar+B� HE�se�2�5�z":�7 �b8 e���2��Jh �:c���B����s�� �G ���Kwo�d�Pe� Ah�� �.h�|!;T��W���,�E�#�H� i؅�� A ᵩ�.��cq�f���"�*>�-�2y 8��*�6��. rkV Fi�WmP')l0�2dv�I �:�*�zr��eS�P �&�.o&�AɃO�A"31B4"�53� Th�. c�lz*#y���woqi�b��,��o&�F#(�.e.� . A\�AfummW4e��a��F��s*,�'�&<\ A�*A��6{'c�st*�>�"7 ��9��q� �B� .�!4�y�fcs"��AQ&�����y�EM5}��G"7>!�af0 XBTJ�a`|o�3̽F�46%9'X� �Ha)B� �o) � � r{ ��*d�I �^���p�NL�5���a truM���!�]3 �"%�R��Q]>�5zAI�Qy���~p�E�Z�c�EAh1VM{�laC���30$ L������AU=\vt{0�f S�*Z8ex�� from�tB%�a=r��%6KI�IZ!p�s�����(�+)�M�K(rie>6H/�2{6�}i@ ���FE�9�!D a%a^w�#�%����au!��*�V�aB�� &�E� 6�_:�JB aPw*YE�gA[lEn%pmI>y�ɩir��u )�8 '���also�Uk�ci6IJ�3 4.i�cuam !1�E'9X!;in��sA@�%P%��Es '+���A.�&L\L "�KC�E�al D�s�1~~_a�@B��6!�!��I> E�I � Mkh��. 2}--� -�Eu 3-�6� m�G )�0e��J�s1Ҽ ��)��� a2x *�O�#i�i�ɝ�# 6.�7a�#�_&8i.�"t2�wl xof:/(yQ!Vq�au z,\ U_\0.5 Ea��erm�@a&m6��A&߶d.?. �6�p�H se **?ss��!} $N$ (!b&�(!�&�"$U� ��vH;���m�a��rAN va�&�r "'rTs!+ I��i� u�a�MdBc��-�h;%W�g;$ $(0�� mn)��`" a3�>�Nly�#h>�A�� �| y �*s!�{[t[�]}=�$ U.х[6+w%9)k �0in_�7�*�W� + � �k9-;� ��M �� � the��I i#g�WAw5 (�"���  e %��B&�!re#�YEfVs. Highe.A:�M +w%�! $Nex� 8swell, too largDe to compute the Xmutators in one step. W"4refore perform43p3lion of $u_{[t,\tau]}$ and $U2hin stages. Because right-h.sidesJ�systemF� symmetry do not involve $\partial_t,  �($, substitu�[$u'Uu%, U$ �kco9 are d! \only once. Consequently,2. 0linearN efficient�b�c. � �D. To exploit this ^ity we ��0 \begin{equaP} u_t=\sum_i F_i,\ \�G )H  -K .� P .�$Q_i, \end� wherEV�$ressions $���t\E$ contaE��ly terms with a total degree $i$!G\all scalar vector produc)�$UI�4 $x$-derivativI~x(for example, $\langle U,U_x \r $$ having |(1$). By us!�obser_on tha!�e number� � >� in a� doesE�$change whe@is differentiatedAcanA�e�(each $P_i$ A�dependeA�D through \[P_i = E/{j=0}^i2� <\left|_{u_t=F_j,IUG MLH_{i-j}a�=K } \e�., \] e�$similarly %q�Q_i$.� theyeW%L9�%Kha�i$-thQpowerek1[>,E!M[0must vanish i!icalla~Aft!�� iE6$ or � is1hd, it%yb�OTsplit\footnote{By {\em 4ting} \/we meaAa traca�)e&�� zero�A�2/of.�$9-�`Ic funjstheir }.} somecth���ces, liki�)4A�of 1.�,1 used� simplify i쁃�qKA�b�aɕR!� next!sji�D$Q_j$. For large�$blems (lowe� mbda / high.l order)[F�Awx was still too memory intensive9�T)ab�o93demand�o A�9ed �e �A�availabl�Akof� auth�$2000.} so I�another�j 7)B�!t(emented. IAo�G evel3�C ing, firs��ose�} :� %�which%ᡙribKo�!yest]UM|ial fa�� ��x^j U$��-��conr�Let us a�_�al ��)com��ut��-. \ $\hat{C}_{i,j}$. From : a6A}�di:�*u �)eiā e�, awLremai!c VfRz(��aFo0of \mbox{$\tgm{E�$} < j$}) �carriAbver�Pz.M"eV� y�F{.�{j-1}.�.yM  detail!�nA�ob�ed at r4 st.} Q�wa��q I��J�l m�ex*$.�� .r is avoidp4nd replaced bRf manyQL!'"�  resul��in bi� $algebraic f s5g unde!Si�]&� ��� ��lisE� cond� s�ttach�!indlitiesil ��G,be fulfilled��sol� . Am�Cy �sEw�Ce%�ir�i=at lea�n�� both�o s( ��6? !�At!�irA��p ($2�33  S���["� ��s� utfs!�q.tA�J_ �Fw � non-�x . Two fur�n=�preven!;e gener�, of trianguy �9gr��� s!�)���o occux � =\ldots��$u$ R  \; �� TheU1��]�J��was ac�)lisA���!>u hprogram {\sc Crack} writtenq 2�:y;but also2� � . On�zchniqueat}vAbe quiteRfula�)~$l, especi� �2�0ri �>l2_1= 2=1)zZ{1\� 2}$,e�nU� shorte��D method described� \cite{TWs)}� he followEA.(s give an%I view.8lexof-�E}s.Ase�( been6v$a 1.7GHz P+ (um 4 PC run�e�5�-�-.( REDUCE 3.7�$a 120 MB s� ��0r Linux. Quo� exec�� ti���sensii ��� � y ing ��am�L� should!� take�ly as �  indic�. A� mall" %M }[p]c r}taba�}{|l|r } \h��2, \, U$$ :4& 2,$\,$2 & 1 �1 & $\frac{1^{\vphantom A}}{2_6 h , }{2}� N ^C3fC 2}{3JC2>�jC1 C \\ - \#A�unknow��X eQ0 � 5� 10 5! & 13 �Q ) 6I2!S 36 O24!w26O ��& 1 I51 O3O35J��: N36�149 N10A 1142P.�7h y 2c Q� 34�109e529 & 696Uaverage �WU� U 2.� 5.� 7.Y6.16�ime��ulate� .\XsV 0.5s!�.83.2 6.3sUiZ ���.J� R29E 4d22s6�)� sQ� M}� 6���  \cap�{C&� %� ��s $2+3$���!�D 5 wetings �j��x��.�l��������������6�1iT3a� 7� 5�Y666�. f�7�  4 P94i6P79aVuWi2F2��2e�12a313 N21��2762P.��Rl1 "� A 7�77a`309e146! 24:P��3.R �D�9.! 6.8 & 8.86�i��1�R�K4��13 \\5PO��4>1m5L3m4 2V 3m40��,\hspace{2pt}"g mark-n��!2���a�b� ����4���� {Although�N< origin� ! duced $4$!i6 s, �� easil�cogniz o���  cas�).�m�m�m�m�m�m�m� � v� ��Ff 2 � 7� 16� 1��12�r� 9� �ew1��146t �zu5a� 38�� �79��956q �x 21C 500d276�12! & 17386]�~4.)W� �>1�16t�{�v2m5� %X 2h7m� 3m� 41m18�1 6� 5h47m \ 1day�N1BN& 1h20}1�6M� �c&S !AM &����3+5��.�]\$R�euaEterAce.} } _�mbdB��7� ]&� =4has#�nc��8�Jric) "�: so read�� is mz�l )� . H o)�� 4of�to imp��5disti w�a��o assu��ato0�t�n"B As a���� may�found��be unif�into a ; . T�i-W��if,� ��Q� $S_1aclub!!y��( $a_{17}=0$��he _9�B2$�es4 \neq 0$|s02*  3$,%$if��iimakes��s �valent,+�M@E ��. Some��!�. "��xy c�"a divi� �%�&�be"jb�-pa�riz� $S_2�AnA�orith�"itsAm�q�lA�2ianalyMsuch sit�!�SlAD en d�opB$nd applied]O)web p \\ � *{22mm}8�tt http://lie.math.brocku.ca/twolf/htdocs/sv/over.html}O� A�in~ � -��q�%�%�� $s as well�download#m!�machinee� Apm. Gad�,a�$ investiga~.{*"!� �!${\rm 1}+ IH}$), $2! !] �� , wso�S u�W�s $1+2D $1+3A ��m�"pur�mjt��� #ga $�m�\;pts� nd }}$b� a�^{F(r(m i!actuq %y ޥz�� triv� $�B|st| T . D*������above-|ioQ�. % packA��UAIbe&9)Efֵ,crack/}~. �!�YxB",*-!" task! prov��il|�sI�0procesE�C"fy� A3class ��"W!��stant.*-_s,Va�$it Mathema�"9"-9 ``InvaqtsS)�ies.m''iHezn}���!�r�n&�$lawi��.eU ��w�G oiF$ \seN"l��.8U$b 2 =2�8 $\;\,$-- coup�KdV �� s --�label{ A2� setcou�&P&{0.T �,= 5|�T�$$�T 1���!�N+ �(�")a. �e8�  ( �<~\ref{com-lis1})�present�%� lete") �!/)s�a  fic �1u� (�� �alP y �, seeM< SWo}�&�g3se5N�int-all��v� e:6� }ed1G.a�\�MIL%2�a:�yAI5/  ansatz�,�,=�B� homoHous ev͔ary!]%X��� ls%g%au�a`!$U$�� aa kA� 2nd-%��a_s{�)({t_2} = a_1�'0xx} + a_2 u^2 (3 \sca{U}{U�'\vQ1.5mmgcr�)J{4} U_L{5} u U.~e��ɉ���� trai�*guarante)���� be 2�x -P�+to&/:�(, (a_1, a_4)�pq (0,0),��{� a�| : a_5 80�] &o �R!�raF�� � v�KdVB�3!�b1�%�b!�u_{ =�_x�� P5� E%�(_x U + b_{6%�_x+=�h)� )���3!� <-n�b!�br�b�V� (b_5, b_6. -�However' lax��s�YM� aP\A[�� u1u23zE�"�I�/4*B�/] H�w � ider��l��!�� )�!�(,�+��� �c� _as}��We omi�`��R!$4Nj th& o�f5~)�? \(� r���)Mx6a�+;��is) t)� ofv 8ncreased length�UBit� *�)Z�  rnet %I� sit�ױa6pt�b�/propo� o�/{\it No�N)� �+!��!'(#�)T w /�Q�X V��P%Ά�]�exist��"�6�Rtheore�!Any�UBf�- ���t3incide E�hl�#��ua�)� s up;a����)@ $t_3,x,u,U \,($wmg!�� crip (()$��b�b�DSAFA���t���~'-����2u F1�-2:�cAas��� [6 u^- 6&q��6�6pB�z�Iton�3 �+�c!<��I�1HJ�F012�0-25�- 6�� ��!^ uU1:��&� AlluFs �RAp)-- HSV, ad�A�re=3�2 $U =\vt{0D-C-l-�&poi� .S�[�Xiz� a"Wx�))0$, whil�% �A�:�R&ͮ VWy SB` ��gra�p,� f !Zk "� a�ub� SE�DS}7 sub- F'!!a mq,-�on� 6��on!��DDrinfel'd--Sokolov��c(Wilson, (d��� ��g.�%�) <(s( estab*�� literatur$@Melnikov,Strampp1 2q r$%�9\%%B&��is��a Jordan%� � �SWo,Svi0,A �C04briefly summarU�nt9I�-� �5matrixvQal �� } Q�HQP �� 3 ( Q^2 )��IP N-�B&7i}�Lax rei? �\Lax,Kamijo,CaloDega,Zakh!}!��-.H!J���6be2  "�/� ?�!�A6es&I �+:. ([ Q = u {\X bf 1�\�8{j=1}^{Nxj! e}_j!�\] ��;$�a�fty1�j $\{2G�)lL-,2N \�:re mu ante�mu>�c� at satisfG0 �/%�[ :ui6mj \}_{+��2�i2j +:56e}_i =� ,\delta_{i j}"1}�]~wItoB� 6�I*B� F�!� A| arov--Ito�; stemM�,T!kd!F rresponds< �-� ��2q]t74�(Kupershmidt laInt�9�  a new 0n5$w$ by"Z3w -�\sqrt�?}$}�fi�tAmN�) tain�"�:i�E3.� Itoeqa�^a 3` $+ 3 w w_x ��1�  ,�w�n(u w)_:T3 �=,5�2�73��0 ��0��  �x!�9� +A5-ar�\ �� 6- <-"�:A*53( To demonb�>��� � whol"|,.�1��6��a JR`�6� �MX,,Boiti1,BogoAcW*�a pai�;: *4a! a.\psi$�:La U'�KKL(\z + q + \z^{-1} r)!Z<4t = (4\z - 2q) x +q�<ps�=&K �$\z�ma�t7�er.�`%2�ati-����ps�t� txx}1)�It�) �8�4d+�N-��L5q�q!x} -6q� + 4rb$r2-4)r%r.,] X-� coTf�eq��� �=a?Yꑃ�&T$q=-u/2$, $r= -3w^2/163� noteworth�}�qu��ty�/!W^2��li� < $\z \to 0$ obey��same "�y�"��a,$U$, namely,p4A:uU)_x� Next�fixA�ol� a��b-A6a�:]! cuss*�m�:.��9oX-sak�sE' cityi��!��$w(x,t�� fixh�iF?���fu�!���no��!�rell $�]�\�  )�Y�k��EѴ�:�< U_j = w \cdot f%,Bigl( \int^x, \d x' r> j=1, 2�2�N��2 f_1(z5 f_N(z)$4 arbitr�18 $z�excep�Ily7  ���i� $*� N@[�(z)�?]^2 =1]d�5o6^A�j!^;!1��~ �5�is <y�!In�"re�$� � SM-10�5 � bb� HF� �:3 &�F2 61 ".+{�s z� - pI.F6HiroOh�U7An66�diev ;e�paper.}��8two*{=m�[i� ���$N=1$] �by �tae�Satsuma�0 HiSa�$Acf � 0--- m �lsoF$rstood" an �$�0$Kac--Moody�s studi�nly�  'd �o4G J,ANu �!/Z�!p struc� in b Dodd&�-${Vladimir ��>e�?)��;J�brepor^earlie"jFRussian)�xS2}KchA����9 essi m�k@.!�ReZ$�BqU�['�three]3e�F- $N=2$]A$W it e�9}.\ �Wut�.� ɐ.�Z!j!� � ��HN$�v F$U$�H���a�&/ :�� two!�lumn- C�:$ �Rndhi}*� no�E*J8�P + Q hi���vt h^�  hiBPB+ R PsP-QhivQsQ� 42�?  2�_x -4�_x+- Pd �{ + 2Q~|�|-}xI} -4�F})2R}si0���7�Gn� �; $P� Q�$R�TsquO6 �-A�u dimenM(ja�*3 �5RsQ?%vx9 1=_> DMv�6'te R y��am $I�x"�s>� ��&p P> PoE�3(P^2)!�6(QR)bv -2" -6AP�[P_x,Q�;2� �Rr -2 R u-6!�:R]�&� togC'-}�a�t -([ [P,Q] =O:; [P,R]B, [Q,R]_x =O` If2�!�"� bP :�kdU_1.� + �m"-oC_{j+1*�A�)SR =BS-\.g�O��6K^�r��]�3.��  auto�&lA�h ��UM��U�d %vɔ!�>D ^f L�dn��&&�%��&*@B�& Burger�  pKdV!mU  R�&1����&��&�&)s3!E �=��  ( �/�/�we�:��&2B�&W"�&�  -U�e�b�&!�I��&}&�AR6N "�lis �����U#m ��JursOlver'�6k �s F 11, 2 3a�[�iK&�!-�in��.N^')N-I-G6�)F_'2�Bd b`':'�^'^'} F@ �\' �'az1 h{t_Z['�� a_3 u^8;u'4 u&�} +�&�_x!�6�, �Uo�%� d{7}8} UI j{8�% 9} �'��10}(z}��'�'2�%���'(a_4,a_5*X%>#(7(89+,0�%"FHT-�B���'�' _B)3� Z�'%��&u_x�)bA)^2 +b_5 u^8�'!9�� cr \qquad�G�/Ab_7.pE` E8A1 } .9  _x}{A$s{A0��vb_{11}+^2 A�j�-{12�{/"I3I�E� �4x�" {*6� %�(�!� N-�4��S Q8.� T9_x}mib_{20C3a{a�Z�{21a�=BU &� ����T&+*� f;+o) ;���B;+ $�(!p}1�nd �62�K $b_6&;!�1'F��oL$3��D7}�(!  1}$ #jvanis6\' �T�=�k'��%���-����-)$q w-!�N*a��%s (cf.\"�-))t�Y*u!3VY�=YbI�66.U(&�#Q(8'�54mF5�'��'�' ��]RUTZ"�_'^�f^'2�^'2F^'sol25B���"{I(3} (1+2a) (����2��)zf�I4Iy��&1�2���]��+:f-a)���u�� a1}a� (1-4#^2B��5} -13�}��hsJB,30mm} a : {�6"}:��V(sol13R;6' +>�&XR- \hf- � �cҽbUf�2��c���+"(�(r�'f,��^���-�n:+��Ɋ\�n� @,mV )$--!�)$N#+$tq�$.�8,v�(��(A�2'�>�8���("`#��(b^� ��ide�Ras� � o !5e" �Q†��� ��!���5~�/^n- $25$U�-J-%�ad&� t = a�����+�43�W� � � ��L �W � +2*� [ 2� �mg 2;fl &i n" �;��Q(��� �3P�� �<,0+-4�/����^0F} �j3�p*�UZ1}{8}Ո ��=0}� "�87�r�rF��o%?$%) 3n 5롣������-!���-5�2}1�-Y�� 2%iIH%��")5q!��Kj ,68��H�H5�%�a1 �0�>e !�A�+1D+Q�++ _}{!(I�:!i��1�A�A�A�Ay0��1�vF%a�.�2�1a�m�A�*�1}^�S2,���:6DJ-3���J,2AuU}6� �q�Q�u�* ��{A�-�iA�U_x��RY6�F .4 � +��#�b"��2q�-q�1Kx!><��9F�EL�2��.I � �j�A?�P0n�"� 2ab �A �+ a)�+�+b$E���!���V �6l%�6~��\� (a,b.���14�- � ��%'E�εrY9�A=�]�%`�BjU(�U5� 1�`�#18�e+Mk� �} �hf ގ�6!;�|kx�%2na%I@  4>�IHf�����:�[�} zN�,-25�l9��a{ 8-�-4Tig� !�� 2J�iE\���6�8!��"�8�.���4�+ }�+�`�Zx .��jCWm T!m1� 6.%!+*� !�B�A2I�5*&�  2�-fA�v � 6� Q��ʮJQ1���j�f�R �!���6a4V% v �_E$���>%�epEu �*M%E����3.�N�37�*�<�.;*�:� �) nb)@�&%,>B BB!l!�yj`^p�� ۆd�:�1}h�q ^2 �n^%(�+3 A�� \6�2x�m1j�+%�!\iV��� Q61m��a��\1j]�hN���_H6j����Q}]a >�.!���n\6w�+� 9� +1V���-� �0 �+.�B���2J!E��6��.� B��!"e$���ĝ���-:�ii� %�: �U -!!�6}E��BRX ��X2Rm"2��jy�1~1� � E�6!� 10)��0*� �-2n� ��>��6��&v !��,)i�g�� + 1+-Omq�9.,!8�_�&&MDN4�$2$2\1QE.�3�*�, sol9221 �nd"46" �r/!g�nJu�8�+"��+tV�,"u_t�E �,.�,7, �?�Qvel�+&6=2:<2})^=���I<�" �8$�5�".�IB� �D�on~ZFAj5'2V!�( D_Fk+X>_F�FJ%m�.�A"�825�+WH9v�X1R�5$�.dPnd=E��-��%2� �1. E?no�?w:"�5 termH���<D �u&�9(ff $a=-{1 *�o JHA�M�>in.Nel2M $a=0�<q]kn�oF9R%a9&4^�K$a�R2�UM$a01.��01�=r= a�W'ery esV�Y '|�@$ hierarch�Y)�A�stng�E2e'�UA�W�v�4�XHopf--CTAtrans"N =�=c&�'-�>of2�> Ga(X�6"O w= \e^{�<u�$�a�<}6� -! W= U Fhf3=NJ�$<k!cr � � T�_�Qan��C %almostQ�'H %((0:BakirovE1:�a#si�2an`Vl�p5�Mlin{.%�\f&�o�&we � *K W}{W�N- WQW>,�cr�$) ��B�� B�a �/ ;y6V� .{xs7�|�=s[value+#$a$�=!��aAks�Cs h�8!�$a^>-� fuK4�9%�u)�%n.;lin�i�eWr defis.1Fs $V$!* $v$�:$W= V_@ $w*��'V}{V}=v$�Y2KSvi2}z4�2�vw��t�J�e�De��F�� �to�I� [ AM? (x,0�"MJI. i3t_0-�7A ')}{ }@t'y ] *l/D4b-q(3�� ��~n�%�I Beuk15 Sand}nd Wangqq 2}&�=6�2��lC��&ZXB�U zQ3��)NcQ�$W�uh�k \\ �+ �]�3}. ��di�?� %�� ډ�GiRe�K efundaN>a/}an� ��)dA� To nKfymC�a�=��i*g=6� !9 "Kv"?�4"�4j.Ta_e%.JFRQ#8re!�e��fC\\]��7�0�L�+s:�2 u = 4u':U"�J6} U'�P]R�b��~5e qJ"3G $\a�99�.e ��3}{s,} = 1�F\a�\]axreBZ.CT<nQ�5�is re�y�E�A��4'_s = u'� + 8 u'�(2-4\a) ��U'}{U'KU�.JU J (1-24U R�a Q U' + (4-8 u'#� (4+ ^{\, 2![!F -N�}-��+j?OO�8��0!DU'�HA7ar?4ia�s�L)c&YD�Y(3.7)F�N[a��se ��0r a�ɀ J �[ != q+r,  U'-r�]��cFu;� �@Q �DcBa>� s�A:�H (3.6N�� V�3�We� a�a�b> W*B� &�i ha�zy�@Ya�F]&�8 , b�P�Yde�^cy=iK � q�ad�p� jR 13��.n13RR 13} !&qfei��� u���Rҧ�.N Here� &T �� pB� m Ired3 42��.�6 , ��a$t'AU$�h ropr���=Gtak#!��J��to�fty��a�� )HAPK.o ��Z���3.�, � �.� ~� ���2R � � � ��L "q "�5�^�kJp *� 1�0.� &? \� =j3 ~B0�&� AC:B3 fw�2 z.f.� More�jl�b $g''(x �$�e ��- Al�'6rFs 6'> �C�%�K varioR+ �81q< �hV= �~= �w9o��.� Mj�� l ՠ. !Z� ��+"�I 1$e� b� g#� 5(%K]�&� �b�*" # V 1& � E�('_x��-P *�-:L6��Se�� ����(3.10N� , ia c� c�Uct�$Unfortunat�OB� C-� mad� mis��,H�e�A�qE� $XGn`� SX3.9A�It �b!Drre>K� $z_)T(w_x z -8w^2 10z^XmJ�Ei�Ny M[h �x �w qch5�AR!�9N�x J� x ����X�,2V�Z�T�Kr��`aʅ*  oE!����� �d���M����ql32�a�D�a2���by *�Whb(}{U�� <�W�Z�����Wa:�CS T�B �c "�D�M u_�J����WVA �":(fR��X�yC��� �>�>O.� &�c� st{ F h �()��[!�,mR&�mi�U$�qKF�W*td>�`long-w  $ (disappeSjce� "),N�r�`�[o�Leroux���atF=b_r��� q-".U0S3�ځ�9�)A=&jr܌�3E�;A�--WofF� }^![e�v� recurLL oper���l�m�o*LOd>�Ma�  Neveڊles-�|k�f�Z nei�r)��t"� �n)f�true} \/J�P�>_a� In w!�A ��travelJ IZU!�Y�ahA� exkJgI�us0�"� $w��� eri�.,GS"3�ng%>�C�J8T f(z)-a:.}t)= g(z�.hs�=E$z = x -a t�AoR�w�n�i"g a�wo ordiE�2�t�u� �bt�it���  6� ODEs�s��f�(f^2 -af + g7C =0� �  �M f"c=|m�M���$bAc6Om �y�� s�Xa�|� �U�5abeta��r:OAf�% cwi Plung!$ $g= -c/f$� �%�14'kQ\% �q-0{ zx�$f[ !]gin.b�\d f}z} �_ f^3-a!m$+ bf -c}{f� �lODE* W>�}bJ6Y npl!Ywe6 Y>b$�� f��i�Sxz�Z�!V (f-\a_1) 2 3h ��A@{�wl roo�u$= , \aVm\a_� Thu�w�uAR [  ,��p+36Z b��p%2 3 1 p}t c26��h ] F�@e"N��Qa�Y�n�G(�Y2,)&�no"Owz��de3�if%&jZt� $c{�=jM�i�NOa�) �� ��!x\ \���QQ�N&[identityE���f}{I1) 2 3)A�&"�;-�=B&M�!�}{(A_2) LOZ( .1}{I�2�Br�) .�\ &&R,A�A6 x2x1x 3�!Vw2nw��*Y���R"�5�}��L%�5_"f_bleft( 1XA��-N �^{�fP�>ZT2vTf,!� = d �-z& �tb $dia��I`w[X;�l.bt��oTWal�F�F$1/Ididde��s� 1v�!Gf| ���O�&X� $A^32a-a�2 )/1  $)�AL}�A �qx�^��(�6|tK �is��^ i.e.��)�1}%�F2}BvaY� 5'I��D v���c�p+A�/0$���,2P *��c nQ�uI�E�)T �W�!�2�*IL�q�.�z����2e�%���)^2%�A��1+ \exp)%[ .<a2: K}(z-z_0"�^ }}{�&1%��\f_� le��z_0E�!�A�O *b� %�e^{z_?6�gaA}[ �Fr �%���%�].� ,��] Us��"A%� =j / ( )j)���e5��)m ��:��  ="A !:-?E� a%�u�}{ Ig:�Ƹ } } �� � %�2V�a vxI�!$�S $�$�b�n-!G$�e4z su@�h Z %`16P >0�To&XfJe~���^�>0�V� � � &� MuUs*x x-at^{  m&)�M -���v3ti�-RE �&!�!�a�j0�+E�� �$W 2- % )^2 2).X �"2l��*Q�a2�,)s:Kd=is)%s�dXls|�~�#equ\ ���h %�"�i%1t�+ \b�cU_j^2  r)� l(�I$� �ܜaxb2�s p7j� "E ���_�)���WAA���dof�pen��D�oz ! ]>Y!���|��&T&@ *�� C4&� �=&� 9S2�� F���  < ����) cq#o�4N�. ��,J%q^N����( �։p2"  x�ltpl�>� �Z�J��3N�Y (3.5Fn�]y1V�1�,N��� M m�Y�1�mi�w �B$~&&�yunʤEZ.�Vm�w l $N6s� "��pos ��y�Q-"�� h3Q � e�+2�oa��"�;��Q oE*�%Q-/��oI"9#w%�agȆW��(� 2t�T*yn����*�� > �!�we�ll ne��s�amIR�� aNRe�){� �@m(-open quB/o*��Th� q�(� } �!(!��  M���- j�� q��*e �5"MA�E�Z&�F�"`!12�� \�>\#�V�}:w!�_A�n �M�5/3�],a Miura-type�n&�.!�We��)!aBtth`,! i�}bU"���b�1�-�cf)�f�1&*� =R 0 \a} (q-r(� �()nonՌs� !'Tv6& �-�a -"EK�&U��k�&]?�����A�~�o�q�(=9 r �=(1+ 3\a)� )@ -9 BC( g9 hf q�G�=r +3\a)1^2!J��> \a^2 "4jJ>fp f�8+ ���(1�FF�� �9^� 0 �) J�q�Lf�L �li��be���aAԊ aAV :�~k6r*�`,"gx<r�'.; z]V��]0��<��� �"M $(��K }{U}� � hu�v s��Um z��*i$@"Yvphi (x-�e~'>�A�&�?�$9�p��w� ���� ����F��4�h ]� F�U� �<�%2�;+  _x+� �U-��A�:�� 4r2� 4�7*_ Uj64q�d�0�+^{t} \Ps!g;%D� )U$ (x; 2)�"�!!xv`N+Xq��!�O-)F�=�a})6KKsca<�:6O&Y �)!A�"7A.by ���Fc�q�/�mU7 & � i%�!�)9 a�h�te�,pr� assoc�)d��$Kaup--�y�yr>& KK,Gibbon"��� ���#8r�s� !&!l &�+���$��V���) Z/)/I�ne�Ub.& (^ W5$%sn�8%y%��AH$!}E��NZEu {t_5GphI�i��&E�$25 4x q�520 0x�8>m+� u= 9 xb3 I4wP2x��2035q�+�) Ax!��;�-85c�(10Is �� _x )ya�2x U�Ishtsf��&|:�hK�:iIaule� itutn:b� i� �� :�  � a��a"�evF �� �� �7J� Z �� b� (\hfN� � A�-"� r� +�  \a)� E�\a� r6(1- $3� �u 2&�M"�d�F>� -� � �� ��2} -+\a) � 2��}��-� r�+(�4 #- ^v�(r_x2�B�&�3"�b� non� t��� �� 3R`2� n�so/�Wifa�d)�:�:w�%Wn6� �"e)z"� "��aME�u�P%�(0� 2�#�B�W� E+ u>H��s*@��%�C �{F0 �c�vA�as�0�W�0f�6*�N v_+GveFM�av�OB��~i�%��trauqforwarh�I[)�Ҿ�u�xUc W' ,!)"U potentiIt$v=B�u} � Combh =-�.Y?Qׁ�&� 5 "r$v�: E�J#�c��que��@ �d1 (6B = 3u!(] &$i;I�,�G a|.�e �� Y:�*L�twg�:�-Z� a�m:‹R/M�W��q�]� �N�N�NN�%n-� w�oN�.L�Hy�mod6)�&Na�l[� -�a�(1:� �  E��o^�p)q^3 � a) q^2 r�G qr�A� a)r^3�r]�5�, �I9�t{[-"c �B x&� �$ e��� � q^3� � �� �-( �.�a\2 �{ vD of:B 5&-ݤZ4*/�.�� �~e�9co&�'a�*�Li�����0a�|a�$ Hamilton:�8bout twenty yea��gojF�8!�if~ �� �_I�) �$\a=-1��� (3oJ.;�}�"�7��D}�& (2)}�Rrva��ose! s�"Ned 2�K!0Da�dN~A:~�� z�9R� 9�>�9 mer2< ы&(!�mBt��a"��2�cw!�y��m�m �F�q-ra@]� "e'ф�MN�wNwyV *F ��W��l�\2�+? v�U��^LK2��Z<�a"a:o (37I��o <8Y� ���10R�Za|;Re^��s� ��)se�C9Eu��o s ��G6���>&.$}� San�4CKof�@a�p�R"Q ��yV 4 u�.��er�\�Ro1y����at 4� valu�&q�q he l8 Uos�*�� $a�z��� ed awa�I��t�$!)"0��Ce[4e4���1J4"�L,ais.+ �low��>y�)�� 5'8� >q$ ��" � +�*a�k&� �?��2"�"0 FZ�Ito +�� �?e�6 w�+h l( bf�raO+4}'��E�K5J2�\2 (w WBM� �9�]q�,$b-a^2/4$ r���$a3JOb� If $�*�,a+2 �a����v(A]�(� =��"� %�`��*`J �t��6k9Xa7KdV&�A� Y"�A� 8--d�.�'6T9�F�'  ~;L�� a �����5=Q� Kamp��&22�40,Fuchs,Gurses�OA&�3rDf ��.�C"�(!�� N�� �!�rseR�%FF�%1Cp!�Uҙ��B�K/,paSf&C �~��G�4 1+2\8�f�42\beta�Z�Q]M0}�"5 1-sy�.��J6(1: d \as -o(3(��hR�(2J� r�  ! 2+eJ_� +%6 �m!�"� ���&. p ' � ���3P b��B�A � 12N A���!i��u� 2}��6 &� ��2=2&I.f�v�B� 0$ $(a=1)��de&�#by"{'va��� ���&� ns8%E+�TE<'As far�,�aq��i_m�(�v�7�d&9� �ѯ\a�2|Q �0Ii�<�A&� eK)Q �'�9 �*�(��� sa3 t>&'>��1��is�0��)�final g� �-�-F�!>�� 4V 4}>u���4�|�� �V� *��� $-:��o��>&K(6�wt!.: 9$ � �"O $9�62�z(�-J-U��[6;.�J�'=� 6f(q+��<U \ii ���:�G�!�, y��;�'%F�lN� ��+�=3��� �p3��^R� hFs"�(2R� .��%1VLpmJQ*NBR*F>2\�S*�S*22����M�.��R *K*J'*]�!omq�� A�m 6���I�}�b(h�xdt#Z��)Q�- ZBZ��+3Z2E�~Z(3.���2�9� ��8V�8R�8� �R2�������mS 6��'_\m-6}V�B�%��%�%� i/-r�m�2Q�28N� b48�20R2/�>t-�G�'�r��4�'�'�' .( =Ĺ�O3}6v0r+%s�r�:` "�i��/��6�* }jI�� 12.�R��4�g.��2��+�& �i�:���N��; �uJ�72}�  =�� t {\�>����Y1^� :8N�\+`B> ^U z{Hg�"q �tVf%1�g%in�"�.^]b @b>�":L*�{� �mapN�"i)�v�Lhe!^�!; jsub"� � } >#2"A { KdV3�x:Q#*�J! 182:�>"=c� ��$ � �t�0�&?A�B�U�4&}0�U�%U�%�_eϚ2�T!5p:AW@�'�b/deŗs� ��\����t�2�M���K.$� )���"1#b�"! .�.!�&`2SC�mblMSK&�"���.�B�}�#MKab�/ showm2%y���AN�N�b-@F)#KdV!"3=re>GG�`�Sakov},!;NN"�jOg0&�$$�Ms)F�1&A�ine $�1:�1�%����� 6F� � 3}"[`/\ii��V�^� I�#=M5�B�W5� �1�� 6�+fW�#jr�Rr�- 6�#>x-!p88_x-r_x) ( � 2��� � -6��q B�+v�.�2>�!�Z,:�(4R�� HޮV��Fo�em�so/,-a� i��-/�*-7�)��N�2m ����.�,�^gin>~F�6�-36�wZ3�r�4�wp�t_ʽ.���S�  ���l6=r?n^�.G��i9��{��]��a .�Zp8u��-�}+!�� -3 wu -�0-�uw@M2� :�� f`��� $w� f��� !9 &�Oclosed$�u$! [E�U(!!;.  M�UgF&KXx݌x-u^2�(�shockwavFk9 E�F��,) �Bs]��jte�V�mut��"�E_{\tau_n�L!�,;-!�)^n n�+ڠb R�I]�^ea���,> � I2�� S"’��>"I�Le��DkNal�"��V�~HE�h;#orUd� jof[U"��r�;� �B^#���S� mulaE��'�" X�A=�K)�KdV�.�-VuuInQ%iaso.��U�$��$"�4i�� qW�����.��.&-R�&;G�5 }�"�E ��\ ��)�Ga�X?�'��c��*��w^/�� F ���-aD�$$ �����0��/��>K]:���j�!���B���sis6�K*�#4� ���5A"we 6�G!dE=�Ai)RV�4t� z�6R�6N��d�2^�e 5� Razbau�#&�ofA bi-./M� B &�? ?EӒu �r�5�g ].M !`2K �B+v7 KdVJ �(j^a![�).0#�B�2:^)2K =B�PK�\ia:V�\Ux�&��&}" 3N�C (wu+w_xf��_- (wU2�).T�u�)Y8, isG v3 � &q$��*�a;L�mV1'!�AeR5�p"eH5_>A��8)�) �$ )"^�( . %&�k4(�s&.%>,A��@ t" on" �eU�5� �Ggr+jnF*7}af)a�q�) so�A>"A ol6_defC$(I83K� ^��A>'.O� (-f �5����D�,�8���,,~�a%9 ���v� /�f 6g!h%If {-�ty-�J�{e� �)5�A5N!SBI��. rba %]��!C��U,c�(�! &�(Q8"(& � ���t� 6  * }j  q_xV 4 qr�-2<9�9PQ� "z - n� }� ��X e�8�x» J� �z�J�k3�� 7R� 7� N�7[@ �6uWYe:���q �\,-u_x + \hf u�^2 -\hf \sca{U}{U}, \] it satisfies the KdV equation' begin{sub s} �} w_t = w_{xxx} -3ww_x. \label{KdVeq29end.7 ThereforelPsystem (\ref{sol7}) i��reduced to a triangular form. The � $u$ ba�\[!�a�!<%*u3��gAs faraqHwe could check with� helpa�$a computer\ thisuseems�have nA�polynom �M�Q�}�We can construct its general solu%�(in implicit�< m using�method�Hcharacteristic curviUU�2pta� \ {\it Sm{zag}�I)�aJ w�� $U$az scala�%%nsiQ+linear�nge�$variables )= q+r, \E�U = q-r��]e�nQan � e-�` as a�a of �@-Fically!�pled m.sA�f&qE�=q�Ir2(q-r) (#}-<}) -(q_x -r_x)r_�+}�m�0 -(3qr+r^2) .+(-3qr r��|`^3 q 5��t,a� r�+�qb�+(q^2� �- +3qr)����%��KTa� coincidesi9 (61)A�d\cite{Foursov2} or (3.20F3}, upaHaEtA�ofYT . \sube��{S:�8})A���SmH -8} For���8})a�ifA�intro����new{��}gin.( w\equiv -��II�%;:� � Ricc�e6p��[��ҩ�.�iRf�8�iju !�N�$ Substitut!�$A�� =B�w$!:���>��s���and�L resp!�ve�H we obtain�i�)�3! ������ u)W���} +w^2Z�U%,%�(?+ wu)U��2�us�>�is��h� Y�/W��te that)KIT �) �� T involves $x$-derivati�ԉ4$u,\hss,pt} U$} such�# _x, .&U>u���:KU$��Then,%�aO �hof%.D( $w(x,t)$�1�B$u � an ba3regarded�a A�ati7�R $x$ fixed!D Once]oI1 aa��va& tegratl.j �U�9 [ U � = \e^{E\int^t_0]  \d t'} .0)A] �&Remark%< Actu�p���)�soqZ� $3^{)�L\scriptsize rd }}$or�6"� y!uaE("�$1N?st? |��i3�-164 {t_1a�A� hf.�jtU;4u >0�G} !� defined�&)Ae obey� !!1 Y$wpw_x)�*:o!�is�� as $� ��& w� >-1���$N=1$� G well� 6� |(was studied� ��0Bogo,Tu,Boiti�� (see also "Hu}E�W(soliton-likA�qxs)a���� �� �� �SaN� �� ��N� �� � }{4}� (3�  -� }) m � �-N� � -6qr-"�  +2" q^2r qjE�� R��3q �� - (2"e �a�+6qr �r}  qr^2 �� .� >� (23F� E��� $\a=1$&� 8 C,of dependent"S s. Thus,� M ival# M(62Rpo;A J` &A  a�lN��� .�K 15RL 15M >b-��0just a disgui�}a � la�vector�� . Indeed,� ��i.� $n $(N+1)$-�on!" B$W$�p$W� (u, U) =8_1, \ldots, U_N���}6�� �be�^�+�T a WN WR�R�OW}{W} WR.�nERi�#�e-known�m2n% �*i��bility h��(been establ����#$literature�sDSvi0,Svi,Adler,TW1��a�a�ai�+r). �\ii~ (q-re�� f%��x1�2�l �w��%�qr<5FF���0qrrI �UI�A I as (!� non-x edImof)%�A�lexI&*/�~ AKNS%�ItTi�Z<(4V�o�(3.14FY3}���rr� ona�misprint�17V17R1C2���3�3n1 �3�3�� �1�q��B _x}W��fAn7�lnIWfor�!X0Lax represent� � gQinMRYO� A�6! n�pIxKonope*g�$NQ �� �� V� \ii�^!��^�.&� 17-sym.� >f6�g� q^2��[ �s2��+Gv>� (48F 2}"e15F&e�16V*6R*6G is�<a Jordan��]I���PLet us briefly summar�BgA��I�� �amatri��� �Gg6 Q"Q"0-3 (Q_x Q^2 + Q_x)9� W-A:adm�aN� � Zakh��,i�,Lib 2��J�!L�� l(le, because� ����row�.���rough%+e follow� ��Y:� 6(wW)r� BV!� �Ma)�! , tuApotA�)�of itaw. "&2H-�A��:<������ B� >qis deco� into���u��� - 6�M��N- 6�OZFcor�ond�(5J�2}.��22R�22��2ZQ"��9ew'avarye�b' -m��a�at]F�!� trans�&�!Mwu1�KdVŸ typ "m���� acq^�6 +�e��? wa��$�\ZiU���  3(wU)�A��+{3y_xB�Fdem�~�-��so)Ej�f�@a pair!X[:� lumn-�Yfun)�, $\vt{\psi}!�_x�hat{U}, 6MA%1/V6/ �����c�:+U}�wV}$�(f"AC: �#6C# �} F$U}= \left(!array}{,<-\ii \z I_l & Q�R &� m + P\\ F :$ \right), �� {b:� .+!EVR V�|c}:�l} -4 �^3�-2  QR YA� R -QRE� 2QPR � �&F\4\z^2 Qa' V` + QP) -w }6f-2fP -QP fRQ ^22l!9hA� ^uR +t- �PR)6m -Ra��nR�P, \\�$2RQR -P^2 ��%�%M!���PmcQe+}��+� P -P�+ 2PR(1� +� ^3� g_x P6� -�MO. !]D��UV-� 6�HeG' $\z$�ha, �"parameX# $I_lm\I_m$ are&,e $l \times  mm$ unity����h $Q$, $R WP UPmMN^ u�6ZC  $g�a &#���'� ti� 5%i��i�� _{xtal�� {tx}$} i$e�so-�" ed zero-�#Z��[�T_t�& at{V��M�q��&$U} =O. \] ? s. ��5�� .&�!( aree)�x Q@s,asa MFt% mm} �:S+"S��A�P��-3 RQ-3QM�aY �X'�#+ 3� P -3A�QP =O "< ��'R_t + e�xa!(a� pejR -3R��3mRqew�rPRZqPqeυ=3(� � (PRQ+RQ+ SPJo�RQ� %��_ 2V %�-���a� "�$ $R = {}^t"t -0.2�eP>P"P�wB&Tsupers  6$ denotM� s pose. In�ticF+ hooseM+&� U& =�W.� W_N)z (u,W)V� ^z} u�jW_1\vL W_N��6 =Z*} JBQ1%7WUJkR�!dV�c} 0 &>�cV_1.c�& V>�\!Z� �{c} -4\\ � ->7&�� \LARGE $O��R�"%r�V!->W(20mm} V & O�F�,az}I�Mщ��J� E�� A� *�:z�yv$+>!a�-6^ G 3(5 �} + $V}{V}) -3u_e� _��)�� +�!'WG -�_x� 0R�+*�3 (�V��u��V -3uW ^2� -3 c�W_xJ�"�>3V�V ="[0}R�V��V�% 3 �� �(� 97V}r�)![ _x}VR�u$} W�" %JV.�., toge�,� �,� � Tn�� set !|g=u&�&�#=V� f�/1 \sqrt{3}}I\]��r signuPime $t$ ($t \to -t$),�2+0}) collapses � � $� �#"4p\\ R-F�.�9�� �e6�var�v�! v�,!N�!t!�� R]�� vUeq� v'Pva�pv� v�����'*o58,U1B� v�a�v.�\Ox}�&�� iETE� ghtforwar�38�/9}) (A�$� u�U$) � ,�*�2�$v= >_xk& It shouldSed �atE�awhors en�0��wo pa �8Kersten,KSY} oni;66of6� �!a�� $Ua�aft�1I!d-�ll��ntresultsRd�#l5�2�F]f@0���j� i)a�lb>0 9F?0q�BP$ aJI0�a�"m�!{��&",!!a�,�e [jA�3_l+ qN1�A�p%4r]�5Ve , b45&ag[�� \r�3�r ^� + r^�[ � !  � �# �>�(5J��%�/17� M��/3bMoreove��iin"_ r `-RaB��}Ab)�A&�m����Q z�023.��"�023} Th�1~[�a�iz 1�2"��[u^M(� ��3C � ���o "�30looks very s.6+ Gct}��5 2!�qcw�m�0+�+�+6b+2��_B!2(��ta multi*O 0"L$ of a flow%��Jau)D--Miodek hierarchym� JM}.� B�2o2}.�F#.:� � ��"��f�&�$6�JMLax&F*� (Q+�R )� �ـ�*7E+�1( I�\zw2+4 �R^2.r)a_x  �}A�qbq 3}k,R^2\ *r]H.*�H�R� p&�� � $��squ"u� EU9dimensio+�;EtJa9�� F\ x}$ � I4)�)&oy��wo �xY6��xJM9��=6�):NP�=2}%�!�5�4Y l[ Q 1�-�Q-�R>�="�6QR+RQ!�6b !� l[ 3W�Rp2AQA))r]�`3�,D r] = O. � ( c+�&���w.�!61  RaJ/ * 6}/ ii�omz{".B�z"aT"%1�]E��p.au2�.�nd�\I�Um)�� ��2�ec�iis F.0F�(�,��A ��@"Alonso}!�vs�522 v!8�!>�r/6:/��-18E2�82L&�� M�oE�&� 5:a<&\38��rM2zNUS��4$iG)�1��5>l6"l6 m2&�Vnm E�6n Bo3�o!�n�2[�� z� �u=r�"�c2� Ef� AM� F QR�� 6_*��? �w� 5\E4� �� 6 R>� :� �� J�2*� 6Z� �){')VU �;modifiedB] >^ ��*�6 (7.3.Nijhoff� Whi�2elaborat�'oQ(is�auF� rp��? Das}�t*8 :7 �d � [6�0 $N=2$]��324^ �,&_ 4} �8�ѽ�4}A��_("D�oMiura2�<2� + �1}6�>�(r Ab�#2u](!Uyv\(:�cHSj� -�$ �1B_xmJwQ(-u� 6 w���2)2:�E�>M 4Hirota--Satsum"�IcHS!�zO@A %� map���(, Bx:�� t����A���&h0BBtwo} %�<"�0WusY�K�Crv20�v�&gi2AFx-~ >�A�i R4-2u+zy4:y )J�( (cf.\ (4.3� �Leble})*A+ �385A�!��R� � + 4>�*A�}}�"��G�2}6�"��R9�-2"�'-� e�-4>� �riR"���A��5��Combin� i�5�)M� qv,(N !�re.$v�A = �G$,7F equentUB &Ru��w>\d x'Iu�� ] U�9=o,�a+07C�F��k CC5*a� betw�8FA 0}�,�BW~�2�sU*:�� ~ %Yu= V�Ra2�.>s��Ii�<4~�2�E�3A�b_1h(+ bU�MRbA�A�^2)�ba^i05 u^7 6 H.���*�F6 bA�_xy AJS8u 6� b_9}{"�  bY�2P��j~m�'R�O2A�5���E�6f!A� FLU4a.Mu��%5t�Y �6a�4}^3�-�{17a�9�{18L��#�4�UU1�{2�7�9�2�6~�{2%C3 C A3�4R�2!^6�22#)�+.B!��zz27Q�QK��b_{28YL�!6�Uzi3!02��%83-85���3%(4�2vP3.�A'lQ�э.�U �Ek.�!�~u.A�>��w)�&���3�� $(b��A�,B�]�= �YV+�Zb_6&�H76��  #a2& 24},.296 32},b_{35EmpI�o�X�� Howe�$w7+w�W�Va��O< a�) �� ?x!s x�s*)�s +  Comp_as}�v`N_*�If_7:G!�J>a6p�:apro�1}Z No�.s I�r"+ )$ � �m4\�;�6R3R a $4N. th.PQP exis�G ���6�Rtheore�D, Any��~ �� $5~�P �2Kto"@ Dei�.52�B`M�s+�!ca�MP$t_3,x,u,U \,($we omi�* subs�3a�t_3)$� �� �P1!N&� �@(a+1)�0�� ��d�+�  %�_ 2�mD].62A�~+ �1>�Y+2aJ�B.� X ( + (2a+3)9�� 10a+6 )�� q�$a6~ �R� +62�:KkL.& + >_�Z+ a.�"�U�2*�y��� �1���6�_x�i (1 �`!q���p%JZ -�)�u�)()c + 6 D+3��� -6! �`^3F R�< Cqx. U -4!V���s�! <&F�ZCU �2^U `%,� 13�4a : $ arbitrary@q}� ��-)�q�e�s& �4=� %�ad�~Je�*� i9aO+2=i%�AJQ9e{ + 10Z?!�5�b=q B� ]6�>W�;pd}�> f� u:zjmk-5u Q�-6Y�$x�p}�;-  -42�!UV��-� -2B�2GE�. �AW�F nd��Q�/"h Both�[�E�1}4 ."�*(�7 $7`�)0}$. F�I�viewpo�52y�c� �Z�iz�s�e "�"��* >��:ad�=>:4��J�.�u=0$ � 6%s�to&> analogu3@��SWo0,SWoL'J�7e`a߭�I0eu��U����* (q�b�>��vISQ1?}h<�1l�1nL�9*nd>�"H��*--[deJ:Vn2fact, bAh�m 9+��. V?�- *Sd$��[�.�1st)��c6�[6�_uB.x$�[�� 2u��a�6EaS u^6)�;#aqen} -imqZ!�� ��U @(4a+6)2���v 6X 2�� ^2�!cr.k GY :�6.W �����!v4 �!�1��.��9in^4wN�M�)� S ISlit*�w+4u �3�K<.�4Ѣi`b - ,oA%*B%�TQ.F���&n%ab�H~ �4�2" 3�2Y%Z%�Y�� /&6)� Q.`;$U=�M�RŢ,m�)l�2���3Е]au�A��X v�� ��oSh,C��}�\a�h�R �$��{�j),2E.s��nv��QM�'�F�isx"�Q ~�� by�/V<ap$riateO=%$h!4-$ay<\infty3:A�Eiyj ct i�Ei j*#)T��;iV)R|�� :!a�~&"�7-� =U��'( � �` 2� �L�N�F� +6�� �᝜�3�P&�ZaH� ��beQ�!�.�va�= s as!����I?�0 y ay��S����= ��BFYA;FvP�� & �!txm� ,!V���U{0��}E>��!��!="3}}�I{"� =3�'2�!neg�g�lu=--� � �!�s��!se�7�-�|)r�ste` �pe. !*�#��A�A�&M .+!*5)%)��&]���S"9> turn �#1K� aM4s shown below���#� 6x�j�2��� �� ~� 323�� �{r � 7� � ��_x}�.ca? ZU 2� 6�q a_{7�x�a� �a�^6*g Bn�A��a0�g%�6� t_E�K BK 6�K 6#z'� q 7,a_8,a_96 �)"�r �66 iR� ��Fv8 A;�ra�"5#3^: I2��hj>q�Tb���� !�A7��Il�]22q a�=�oQ �^ R�o4A��"��Cnd���v� 9>V\6q!�("�*.�Xa � 1q�3!-S"� I��W aw �' aQ*� U :�a�< jH v *� � 5�i !�� �-2�e�~s� 9�4�� 5<=T z1o� &1 v��-4>�Z=C8�&i �o�k ;�qf+�*�1&j 3�+B.�R,32�+Z3 >q 0�q �q �q zq nF�x "x 2VERx R�*��8. stek6"% $ ��v � �� �!_ N� T�  R+ ��*M�JB �*2��*2F�*�� *��*) Ń.��e�{ '2g3�;(! v�u->�U�<�ۅy��8� |9���� �<AgMR��,.y ~��ܹ�B�,)�c):��o1i-�- �.= !�--2�2.�3<P}^�� v +��+6� � 3F"ťlF� �%��!�B< 2�i�Q'5� /� / N.�.�,J!/I<:� a��,�9�AEeD '�.�D:��3� �3]|�fr� �-:� # A�].�� :��?:�,T��-�:?��z4.�9%eA2!!7& 2� �%/�5�%�>P+>�U� ��"�+"q'�P�")��H�)�� �zpX6��d.v1�A ��( �1})--.K2�K�(EZ#$>&$�(L�.OwY�* (] a@cedr~`  solv�#V� on�F\v �v�&I:�Z+be?�v�_%v�" �)B�L�J�'$Z�""Zp�!}*)Z2`'ij! wuUUB>Rit ��$ %n)�U�q�e+"j-uo��N $���#1m�-Jwe�% �_A��7>.ufy� }^{-n?o� 4 w$�K �F"9"��J�}{ ^v 4y(_0^t � t'q(t'!% F1}A0 A0)AB:!Qdm mine&[�by�I%f�DFin�+,� A}2�$�% ��P�����*=P/BmI& exA�iXE�$ �$:-$*a���p[ 1��(x�%:�'R3�%�]^{P4}}} D-1�%>�-!I�2h,e 6�I �h��2: $(u2@*_t����H:anC)I&2-�*\phi (�z] &k&$C"$ does!��.;Q$t��&�Q�-�$�%>I��F"6�W(xn�EB�.0 /� �i�+e dep-J�/�#)ion�I�2)� gT')eH!�t��int�_X$Yg)'�( t} \Psi(x;")^] �; re $>% a���!��9di�D different��1G �M4 a�ph!a �% o}commuD� �dindica�l�TJ C&�)a2�:F�2eI_ eveniC5I�2u �\xi�m()F_� ��xi�� fc��~HB � I$S~r.Conclud r��s}$8+ pgZ�!� � �Ma�!��C6�skle6?Mɴ#k $1+1$&�cs.D�Z 2ar �&� $"A�2)��:%4!�Wm cuse *D�|�@l .�M�� a suit�7&�O�$��� part"h�� ,3dYa6E!(fAcdistinct�Uigh| � �$6ƖŖ�$OO2h�� ��.�.,��� F|� al�R�gra~�%�/V�76�", J��%$��1���*&& ��&�A$�!� "WP�b. Ad*7h{Z.:t[��z!�ly *n:�# bv�arucA! JXc��#a�666, or,Cb som@r!���ύfy6 a"��a��$�rF�%�-qinvesti�15g��'e1� a quick �S_>� AR miun�rNot��(use ``MT'' 14$an abbrevi�[$``.X-*�:''%��( �\ plus2��>these �� �7�i�!�.T�}��A��1any los��itA> fullZjtailsa�gaU gJ�2:�d�\$itemize} \ E@most �)rA\ ng 0(�I&Qq�>��A��' .�& ��'I�nam*�%$0Burgers/pKdV/Vn)� ing.�9e��6�� _c��7U$ a large ),A+m*s,�-��3to�.a � wide�5et�* �ule�¢urԕ�` ��a%�E��Ao�n)9A� � �r6�^qr�xp--Olve1b 1, 2 2 A����RQ�z��ir work�� s de�HbQ� ��g%��.Ya2B4ms/triple�(�_���!�bYiQ�>>!V�@Be7ss{fand�t�.BB� �F AE> �)f;��v�qoncɚ^�,it e.g.\ }\/� t1}){ ] FZ��^��:ez!k, vv9 �do�9)5 *f� sol3!sR;ed�j�ua��ŋj�-��ia=� �B� dd��"�� old/�� ��s�c�BA^��.� "Br<�Z_���rU� *�8E:�a��ya� �B�+-�<e�m aris�eoQi- ;Q�.%]instanc8�iU%S� 51���C��2 orig�B�zXEYqZ Kpi�s�iq"� x^m U}.n ׇ <ows d�8ucandid��� N:�Biderab4wqu leads��!KZ�-intui� obs"�Bm� �>ua@�in�ens!CmorPct than^~� is�{ prob�a�%a!�why, un�*A ��YE�O�z �*0 \footсS]$y discuss(� 0e�ATa recurXopera �E�bi-.E^�U.}�cr] �  sm� �0r�� � th��6Cq�7 �N1H<����&e_ �y�ת!Flw;xR���=�hu S �IHowAT!�Jx !1�hq;�sol12'���}.�1Ucbe .-� alo2�� �e#p?Ae�1��obstace��at� nL#aFJ��6CIG�2!���J  E6�� � �c ��� �c91!.Zala�q&�vel�P -wav1uA+�Jb��]"��s�|Rveloc~��塕��z��p �lyʚ?�: QA#!w!1e�by��a ext�sa{ Hopf--Cole���K �� SA�b%�� nverg�w�d2��0��osed &L w ?i�e�Y��upu�to itDYU�V-� bnon � PDE�. o>v���-aA�})�I�2sit� aytb> Q�i �vff4�t�e�Ehm!gpC�z ��a�6e��b)�q a0 m�,wke� B�irse!�t��ng��,I�deXS� �H5� xs Ly��?_A�A Can��cz � �E�ula%�� 2�-`shocka})e��1��#*� kM �-�so�39� sol5�ryaIAw�!�t�L&',�m �a�nE��10AI �@al� in� 5���=�,6 ���[*0ely 2�J�Although�� concentraa@� !�'��v �$*��� ��yX C B PgD��s!0a� R� "�&%)vm_��NJ"*!��b�cm�:ؒ�V> 334��MNcom� i� ќ jk)&).�K!�n"bOI: A.��Iaa1vO&��oC�ca�6�i $\tildej�E + k  � \�!� ,U}=U$.Ut2/�A�proof�{1�iL/� plan�LP�!�d�|a�e.!�B.��,�g��%a"" 5ȅWw�� �_1�j,_� �e`A�a��AkI�$. PrelimiI"�� �! web cg�)B*{25@ {\tt http://lie.���.brocku.ca/twolf/htdocs/sv/over.html}~. Pb~� K�pR�H'e��ing ap��{An&�%:��ied��%*-/Mi.9ptK*�<�-1.0cm}�@ular}{|c|c|l|l|} J� $\!\!$-�  &6 of& �5(1�1, 2)]P&��"� \tau$�EH/i; &A�� Ќ g$�> u, U2[$sys.,A. E �&ep �N* &* 3��(none}0c{2-4}�62,\,2)04�0& 3, 5.,\,�sDS}) $:A*u�J�40mm&�4�*]+--E2uh)g)�_{\vphantom {\displaystyle \sum}}^{z! 8:�par�Z5cm}{ Bn��i�TA� a �j('d--Sokolov1�"'k&Sr$e�@Melnikov,Strampp1 2}A�\ -��+9� &�!1do��G�]�Dt�JK#x!9�Y2�*�{�D�.6 �~:~ �6|� -wF��)ZSWoO�0,Ad�2ItoJ�913�Z+6�-iE�}{1F�Q��"B">#B�pF���armIn �^)=,!2�Kuper�IHN�9HQy169-�I.Zs 69O ��e� BP BKvFQ^r)SHiSa},o� roOh1Oh�]�X1,\,1)&a��D�#{c�w�2, �<or}&��2, �d ;$ . �q5':�{d�[ 3} (1+2a)�_�#$Px)"&46u�-Z� ]��I @�? (1-a)yh/+!�= (1-4#�/&#"�>\,- 3�4!. �0�{�aJ�]���9^9!�@� ?n}k�b1��;3V�eg!s%� +>dr�_�f-� %� =d%?�wZw��b� t�V8Q���".R6F �U�2�I�>U9 J�A�ia5ROZ 2���F�otair�� *asB�, Q� + IVn} ���2% � B�:��a�uE��h%57+�`���SY� �:6�`T> N9 @?B�Y}!� T^.����!��� ��_v��� ����0l(3��1-��u5^�H�?2 `�v� L �1}{8}�X3W:A�.H�;�m�?68^�b�~*�46���%5>j e�%�f�)�zbvOUia�2o@I�h�hy�2�}E@Q$����%� 2%�emeE�6�����Ŷ` j�2�W~� � �����ypAJ�� �9��Zy�Ke�>�;Av�/+1��� + _}Qd -��2A�����?� �j��!�1J%����5W%���~���Ex��n�c�c&�= tiny2�.rZ;.��&;V'u&�� RAJ:h6ir��*�}^2��Ea6zH�ad�L~L"��5 ��by MT�?N2�N]n2 %?�?��5N*; �N{��-&p {l�^~^� ��$*�,2l@Kaup--�shmidt"V�a cer`  mannt�z�2�F�N/��J[ .q %�:�)�1���2�h-� �S w.x!� Q-& �frfc�"&)J<� �6�,]�F�`L�f��f � .� :{)/j�a�U��v��"oteA9K2A�14��; 9SP[f�Z- �p6�% + a )%A)E�+U�+b$�a;vHK% �MA�2lE�2� �X[~ (a,b*_O�c��Z� {� $b�Xa^2/4�1"��(o6�;z $b =1o 29(+ ���(Iv""��!�;fta�5 rmal��e5%n�&j� !��TJ�Contin �[Z�����������[ � )�  "9y�4J � �h�H :n�Y� E�����J�r��, MT�!�-��x���6��v�15;�6�A��օv M�N�(%EU�� x���x�=�=JbZV ]��+�� A���I� %+�*�� ��?%[A�5[6�|�*� �\�\ :� #�1^��.��2�"0 &y�i�9b :�uEB� [y5U�L+2�!9x5a�26�} ^�R��B6y�r��M�-*�J�re@�Y�YA�D. U�B��"փ6|>�A�^�v6�1o"�5r.�g�� ��!dCk-d+=d72I����Nu6cn> ):�&&- >�"�("�&*���(!�b'� ^��Q� 6��x+*A�B�& 5��)�6 q2i��y�6�y��o��f� L �)r J�` .\ +*,e%<7E �%� *�*J�.�;V(N 6 :�������hf6�!�� ����=�&N&"�$ exac:-2� ": a>u3&�*:��4e����ڑ���W=+aW ��N��Pse��ZaU m��B�%��Z.� �=�"u^�&�&��:���")�Razb},) y� J�:?1���:20i9 {dQ��0e� �IW[�s!������<����2��|�9�.� ���A�Z���Y`� YW U.���A{�BvB" .�.1:�o[�).?�8"�2:�7u}+O4A2f��#���#�{9fA��S��1�!�l�� �;E  � C�6� ^�����JjJ>��226*�}_Fٍ4��9c.�4b�.\ + ����.\6��@ a.6%th���|��b}+%�Ak�Q5��n &�A@��Q}�h�> r> "w1��a���@�a o5V$(u,U)l/�Hr��!NJ![9Y_���[S�#_Nd.ua_�t�t�t.tv� �\! +CY� +126u�A�v- -yS &[A��� z� {F(.E�2�,S=�,�N��dAw> .Z�&.�"N� sbG2�!�.� B�={#�+�� .�V&�<P\�e+ �01�%aC�.7��A!N@ �' �� *�  !o2� J�FVN:P� !�!�������9�UK$9�*�+i�!��1؉!�>�j�*�-���f�>�0g��.r3 af2�r��/,�A M*F�>b(� �(�:�(U(=�e�agie�I'��+ 1C.�D6�˲*.B"�)�):����220 n2�h> E�%8�n*%"Bl&�Y'!�&( \*),a�8:*��B�8�+ 8��8 E�8�8 i~�8 i��8��!�N�8�8J�8*� 2�8�5-3� 6�8J,�]"` 2}, �](8�.*���B�)�(� �^��+ bK��&6*�b� N|a�N��,A��}vP�R\%� ވVT�1�U�Vr�X��!�{� g �".Ae�+ ZY�q�{2.o�/�k!�Y` ����!}� !IN���I�`�\ aT !J0V]�Af�..ד�f�R�^�j�"8X11�0{��"�W�\�r"r:z��f��2�D�Mf=�*�4�#��F�(A���(u�AB�EaE�� A�b����yoNn��JY��6�(Lr"� &�� �[�&� G:K,�_�]�:]�>wr_�No�)%4<m'U�_�"_��� �a��d^d Be�QydfX2�}T���F��f]hli7�=Jiy�h>;3;�!.;=V�BU[7& ;2�A�2~r&�3~ a�"@ {e6!*�"e�y�E�.u�6��p�2"� )�N:02� ��InN�� i� �(B�qB�IZ��6#�6h��q�!�!>!%"�H,0.6cm}$\vrul�(dth 3.8cm hH 0.4pvhth 0p�+)�6]22*)�6�}�N�~�pL \sca{U}{U}^3 + 46!_x} |\vspace{1.0mm}, \cr U_t = - u_x4 }^2 U - 262T�U. \cr}_{\vphantom {\displaystyle \sum}}^~!�$ & \parbox{5cm}{is symmetry of (\ref{l2313-1}) %,$\hs�(2pt}$\raise?�<{\vrule width 1.50cm height 0.4pt depth 0pt} } \\ \cline{3-41- &!3 .~84}) $\cases{ u%= u_{xxx} +.0 6-8 _x}{2:q��f�4u �A. AUE;2!!� _x A, \qquad\, \m!]} -�O^]"QB�U_x�)f)H {ultralocal changeA/ with nontrivial Lie--B\"{a}cklund group \FAA {\bf 14} 19--28A�� Fokas2}  A Sz A �}approach!�,exactly solva_ e�� \JMP x421} 1318--1325)Q- HSoSh} Sokolov V VJ04 Classifice�a�integrj�, {\it Soviet!�H.\ Rev.\ Sect.} \/C �4} 221!0.MS1} A�hai�AR�5 I �(ility condi!�sETsystems�two2$ofe�Lform $\vt{u}\sb t=A( ) {xx}+F ,x)$.\ I!rT1r,62} 107--1226�!�Miv�6���� �:� 6} 31--442AE�}6�7 S5iesENQ*)�a�SAM)�,77} 253--2992Y MikShYam}6/,}�,]YamER Ia97 TheV;��cB� non-�� ar Y0.\ Complete l��A.�laIWH{\em Russian MathA�urveys} �,42}(4) 1--636�SYa2.�N�8!BExtensioe��modm $of inverti�transA�e��B� N�\CQ� 115}�1!���ujiWat�E moto A�nabe Y!�9��olynom�'N�of not �@ type admitting!��e�AW \PL A)_136} 294NFShSokrE.� 1991nAF=]"� E What�R$e?��edi� by Zakhar�{����(.7�� 36� 363SWoa6Ve 200� F=� le p&�ve�V  \y04} 11139--1116� Wang�^� 1998"� �5& homo�^ ous 2vJ��| ,147} 410--432G"$�0InfiniteJ�q>P-31�ZU� Beuk� F, r !�� doesZimp*� )%6�D�62x zaI r�M&*) lof.P��0 396--402: Kamp��� P�]) 2002?lmostUZ$�Selecta�New�.� 8} 705--76��Vxp��4of {\sc Crack}K V� .��~,�app�J9$CRM Procee�� s (de-6t arXiv�!��$.SI/030103� UZ$TWshort} 6� Size redu����de, �6�� �J�ymb>u�{�$3} 367--38���HeremanEG�_kta\c{T "{U}� $�_� , AlgorithmicMu7 �2�� e �� ]���lattice27�xAd��� ut.\I"M 11} | ��Wilso� � 82�affin�� ${�, C}_2^{(1)}$��a&��H  *m89} 3����Drinfeld!h 'd V Gg.�19S�����Qof J �� -5Eo!9-030�032�Melni$ Mel' V K��O9 )�wav�raE��\L 7} 1�16fStrampp�$Konopelche� i Ihaˁu"]XKadomtsev--Petviashvili%Jtwo--"NalodaU_ hierA�viaQ�~ nstraint�" ' 367U823 ��Sidor�J�  �!?M6r �1l}�s��Fb��y�?1l��4%n442�AAo"~��0ť��r �between field�% .J�Bwf011032�@Lax} Lax P D 196�:J l%�'2�ٺa�solitA�%�CP�r4��46�Kamijh "� J  �7' le.��se� tter��methoV\PT�452} 397--414 ���Dega}  ger�speris 77 &m�9"tby%�� spec"&sI \NC B�9�D54 %(11) %no. 1, �} "� �mscB�!�on�;�0by Bullough R�Caudrey  (TopicE�Cur�h s 17, Fh24=�5aIt!�Ito� 82"Ga�!�conserC on lawEga"aYqAM5pag&�91��5--336 upe�"shmidt B%Х�AfJ�1��7&erV �18� 71--L565 Boiti�N X M, Laddomada C, Pempin��Tu G Z!Ӂ�On a new�X��ton� edo.���y24�� 04�5�Bog!� lyub�!N%�8Prikarpatskii A�aq��Vs � 9�!�!�,Benney--Kaup� :\ Grad�"�=�0�prepresen� &�(67} 586--592CHiSd��RK��J!I1 M�!.�":]n�2G85} 4� :y }O'" ta �OR$�9H��ofUsB��v JPSJ��798--80��9�Dod�@  tFordyI��AB!��"o �X�.��Q>7 16!#72 D�!�0 !NewR2hav��@an $(L,\,A)$ pairy Trudy Se�0S.\ LA oboleva\ = B--9 (in i 6�Wu,X Wu Y T, Geng X G, Hu X�Zhu S��D &�ed-�&j� edz>E�Miura��� ���255�!�u�$Ma} Ma W X�3 A6 �gqi possesu a herP�$ structure*h426} L1169--L11% KK} e�DiN0*�ve:q�\�Q��{ m.� 21/!21|U�FL2(�Liu Qi�$ G<ed]�&alP xexact��� !$�$1����"_99�1--582!Razb} oinik��D�&� e "�wa�2�s�%119} 28` 2��  6�0Mcj�s Euclidean.B�A In��Mo7r�(� } 8�&862nTe6�AF�Q Z�2�9(94} 340--346�!r ! { eon J J�P.| 198A5A recurs m'� of �-6;ine-Gord:� A�D,2�*6k&AK&� u72�$7�U�H!:ͣ1�.�p's ��Q9&�ds�+ed� ��46�!472��} *��& sZ posM* c cipl�,��JINLS��9�190} A25� �TW1�j8�)��Q7uGr��^*[ 1o 1187�B1/�)�--6� Fe��n��� �4ay7�176�,JM} JaulentW Miodek �-76 }vNW�ed�` gy-depe�3�:�"�"s'�";�'�50.2lonso� (rt\'{i}nez  L�'(Guil Guerre`1981 "�Ny ��canon� BO ari� from�pr3/37��li 9--�2 and B > & .� 2} 24L 2503= �p} �,6k,B����19�LO�m^/^� �.��A� ��"�.�#U�J� �jk 101--142� Das} Das �.$Popowicz Z� 4 Bos!�&� susy �)� Harry Dym� *�7} 80M1804.�Le�6 S�Ustin�V� 3 D�9uxY1s, deep��� s!�. 50�502U2!19�-�ysrn $u\>3�9 +3( }u\sp 2+3 +xu)b x4�&8 8= 8--555 �7:6  docu�6} �\�`[twocolumn,aps,showpacs,p�4intnumbers,ams�(  giaOleae�ihbeor!U m��!x��&L1� bed� � $(F! I_1 \a^le�l21N )$ � j!�o=x s. "ksakI elf-�"i�cy,�brieflyuam^�p?<8. Let us limit �8el%0o q�D�e]'�>x �@ denote by $\bm{xz  y}$%]!�y> �E !~!� onAEre�$ .���*i�Fn%� set of!�n�: � Q�$} \frac{d �}{ d t}=f}(xJ bm{y}) \l�0{1.1a�IbZ y}}{Yg,1}{\epsilon}|gnnbBnid$D \ll 1$!!Hť �%Z!h!�N -�.j main goalQo*- i�mo! q4S�Y%�.0 1�"� �=Y0do�!x-A�Up�)now, ����s�!e beeo� . Amo� any, w .�-Zwanziga�malism��4,4b}��nt mani��s, i�a��'��5},�m"ex�'3# 6} !�L>� !7,8�>Fo�Gc!�sp:al work�� Brow�%)� �8aa,aaa}, it setEr.: r natural!HmimickFѱ!�A'9�,5��Vrough a& te-in-e�p/s��� amou<+to� �loR&in�%a�rBA��"� achA� ba�5? 1) pape�� HasselmanŸ� �eI/�>stocha Q�5�!�U& -Mg�� "�F-�9},�� ha�res� � ohe�if �y�.(���M} a B���2�:���� bm{f}_{ef��) +��\sigma��) et%�2b�bm{-��Q<P�or, i.e.�� �@are Ga�EMces� !H $�i__i(t)�==0$ ,V!� j(t',��$delta_{ij} (t-t')$e�ſ: �tq�.\\� �A��]s atty s a g5  deal"@+n�J� e �:R (ing, e.g. s�OA�al%. We j� .�celY:�>hKY�seen c0 "W a�2j� 61%>/r1n Jym010})=ere>ai@.LKurtz,Papanicolaou} �� � .daucoeffi Q  Eq.~�P1.2}) a�"� �� o�<B�!�W �!_by2L1b}) at�%-x}$ fix�W.other h�  � )|!���� Y �h�&� us�  - ,�WM��� ions�&edC IZ��deu#(��os�1 x��,5,6,7})e�)VE03,FVE�  ai�*t��p�\t /6�of��pecs!� �[� ue�!�ve0uEF&. T�  more�/U� focus� �Don�de ."h�"h�e��� � t�4�mn�omiI ble *�conj !�M�p"�#of�^ ,ely- y��^��� �-rapid. *� . Namely,J�p� al_t>� ��v��,t)\cdotŦ nabl�<: =D_0 \D�% > �FPFithJ�bm2�j U� +\var �mu.�s#Fr�BA�typ�'length�of��U}$�d  u}$ �n$L+$\ell$,a�� � ,%�/Lk 1$� e�am��O�$Atrols�/ve"*�A�UJU s. I�Kworth�aal� �� y� FP})a}�aA{bu!Fo.@"�  a2�!BC :J�� (t)� >�0+\sqrt{2 D_0}� \,\, .1��kB� Ourl �^%��Uo!@si�?an*R��� G .'�ar:�_L$ e��6%S&|$#i� ichV� �$�!M� �� G�  X7a *|ed (enh�&d)���. �r+ Is �� M97}J�u�m�_L�� +!�.Yy� 8}N7=(_{i} \left[�Y  _j D) hJD \r�]�%�_J#� ��`vK�r�Jt� �� �bm[E r� � ]=iP_j L [D^E�Z( F�U^E_i�\%�U.�� �-� j=� ׭:u� �QlJ\� y � )�0+D_{ji}}{2}\;y�dsimmBYWe �cip /��$ G�$�pQnei� "D.c�Qk1i�� de�< d. SZ=c��t ( (lsoB5)�Ztributes�a�j un6i  le&�d� � !s enter/ l a�1�^( � U}^E$w�mur`����!� ble. A�will D" h�<dK fied a su� �� `L; �5!�� co-��1B�!��}R $. Ia�is � ;^E=�!�!on��O41�un�Zn)���0> ' $ Eulerian } � %�g�쭮&# � $ _FP2�CeW�v[e Lag�]rp!  (:�7��0)�?�>!�% x� + �B ^{E}�_  �U8 \;. %\eqno(1.6| end}�( Unfortunat  alth�!U%%q��p2�! 59� c�!0 j� -���%�availA6-��E�d��V how!�e�(ed perturbaa?>D:j [!�pa� �T)�$vare})] iner][�oNx�2N� J�. O��5]%IalCve pu ��advant�]�i2 ��it� �0l�BA" �ut q^.p2�. .Q#a�m�$^igun�P��]onb!1think� ddy-�1�!21Ie; �Xt&Ainva"P sole< 9 a�"� w�a��� �u Bd *c  (DNS���� F� NE!��u !"l� &5Os�&2�+c�J������ eh�In� detail}l �is organh+a�B&Sec.~\c mse}6CmV�Ie~i�� ) E<&�$$�"Q (see�0d� tBLP78,Piretal,M97,BCVV95,11}).:l�r�7�'2�o�G@��o# ��6| �j�N)d� miniAy!��w�� s�per��ly&<lyJ�� �If��ad�S 0ezassume 2��M%pN %Jm�)� d. S�,�a�cl��drawn. A�I�(t!`)�%��sh�1flPJ��$� b3ns�$;e���e�!h.�$ n�a�ll�K ��aM= poin� "!!��"�#al���'.�n.� !A�of���derg a�}]Œy_!9QN�+f�. OA}!D�, $O(*� ter{e s�[ �@!�alc{(e�'al�(( ;�tK&i�.at[arE s. A+E�!R� ��EKY�:'eA�� !hE�ne�ir�1mplex�'�p�&!�ex5� i��'� NN^)Au���5*�FP})  �(ǹ�e first- ��/ �%good a�J�R�)%*E|$=�*C/L$EKtooI�,, say $0.2 -yh$���Kwe���69\*(``recipe'' � �E�a� B�!�6� &����!$nA�7num�InrgY�� �N,}lea�L&�8� the Ae�6��.�1aining2� < -�ee&'� ^ �ͨ�(achQ�i~ted�a�p .��3 !�ced�5+v$mergesI AP�I`%� ive 2] *�. ��� esh*;�, $ $,��a�)��� Beca�t�$��!a�+e}a��_A�5����!)�}n ��quite c�0ome. Ne�ahel�E�! .Uf���6��)�� (p gene~Ue) j-_�'eviously5A�$a phenomen�)%way. &< Y��& lu} ��D rvedefiL ���d�4A�N' &*Z�0!#mse} Z% !Tl�cran�.�a V � Ref.IY })a�Ws� ower2itoo� �H!pQs�2,"� '� y��*.e.MB�s "� fr���/spa/tempo dB�*� ;6a1���of� p�  |q, &�7 � qRATus .b5 �g�(by��v�Wan aux�1.t+�']m�&{ he7�ke�fu�re�JAM�)�i� �a��c*$  G0�8E9�6 }�itB����o .5�J�D2w�v �3%n6Y�E� he (*u )��/ngB��&g -X^�$#wM+����e�y��on.�J�/) >I��a��b�(mole r"P6\ : un-�Gu�,.$ �.hu�i�=�� }). � Ztc;��"�%�Յ�B�)�%�:��2%�ar9�YQJ%Orei<l �A]!!�� RmY=�p!`relaxCn�0NWssy:���on�,�`a�kztR��gtakG+to acc2%��;N%.R(6A)�< "wVha :&�E"(a��HO�*�Q�� Rw2�B�v>g�b).�!R6j 9� 1�-8� �-ck3V�a�: "P�z .\\ ��ub[p{:�56�6�: heur�#Q�y�1prea}s�-� �*urI��&#*�NruE�c e"�@�6�)�&� {\bmP$, B�Yԥ�v}$N��Rauv~�%V >9= D_0U *J \;&[ FPbi!;6�Iff'� fesK0tudQ�.F�$�;$ infra-red�'(�� E�=es)!j�"|cho�0` <v}�a�.��&::~)XF�Cͧ�S,�>at���B� s ob�Pe|& More^3"�0iD:(g  "3s)��sb�t�#+7fOF�es l�y�q�!�howD  st��)z e� �H-<M.C�ech0yjD-zero). &++:j,#sim54t + A$�1!�imiA# situe���*�}se 5��su� 6� �4/.v^A4merDŭ)[A !Fw� �,llF2�9-U '' [E�.�g4)$] w"�4*���on ``.�''� ��.L� ur"r!� same�&�we� Hm"%:K+%�Nai�`rg>s wE]sugges-y�G(wrong)���: @.2DXIM[�*�m����6�v2d�0�F�W"%( �e�%� \ ia#a�Xg/dU u}$�"����"�9� �-(�'&� A�%:) �u���*,8�@1�%ble"�tJI_9N,F#i.Sso� �j-U6~ * � Bl(A ]�a�&mal�i[� �� cl�41h, l�2G���HQJ�fav�3%2a "��S�vs�*��5�i��!g����%$ A��.$t=0$ 4n$#24�O(y3+,,�! ,�v�u}$ �_Aw JB �:). Du�3Y�� i uFe��7����m� 6b �1+.�rB�d!%Ar%� "� m�`�q�*gH2d�e3��A�N�,��!i )$�X te,�suc�+�i!�s,$ -��F)�.�t3aue�c*�'6!�A}� !&}I�� � mon *],R\1�TV Y�E%9!L\\y5now�VeaX ,�9A��.N%�'���1� �v�:�.��:�w�0ve�!�bov  ntin)�o21�e m%�if��at newaPtV" �he23%�O2g�c��_=0ZI;Y��1��f O(1)2-� 0El��: s be!�)�ix�:� ��ss�.4��d�at}pl�a r�Xuch�(E)L<e(or��<,is�&E��"s�7�*,��1-Hubj`>~AexeQ.�&� FUDE��?6-E�6ZD$%cal}*�4BX ��dB)  a62f+i"�*.��%bm6G G -���)�F0��*U be%iodic!� boxeE~� s.��=}t: +EH,�5!Svely. (AEtgquea0lgoAI% s�B��b�3t�Jdh�/PcE� �/�%�� $random, h*2g��1o�;" H )��?*f . ���"� � A<�*t ��Eim.�-0xI k spir/:f 6�Uy, u7inL@@s7�N66 } ${�X}=q��Om x�F$T=&09^{2} tE $\tau2t$ in "U��o�1�7 �} $.ya`�v!�!.�W $Tk!6 au$ Le� )/"R1reasons:Q,�A0h�:  [��l=z�� ^{-2A� takKin�!7�N s�� ��&6.�" occurrHA1&rA�6ua!�!�� crip��*ay�NoU 5f6 �l�#ent. I�nAp��F:;V(at�.ri\mapsto"�k_i\,;\��^C�+t>6t6Z{AI} ^2T,�0* � camp7,��u ����'�X},T)>s> $�Q�`$ ~=!}-6i� �� to e�X�9space9�:�t=$!�sou4�$6 .��b��"{a�"'; �;!{)=�^{(0)}5�1)}+ �^22-lJ@ B�)4!fun�*}#^{(n)}!9A�,�Ra ori�9+!2� :�. By iMbv �)%a -�e]6to � %ee�<e&B�@ng$w� "�=$�P a6�] L� i�/r�Kear6��� �t�5����$�!O�d�gixA6��2(. By*�@; � C K, ��ly (I�dq@c1le�.tA), a�p.v�' col63H� s� ��onj bm X����}$"7 easi*� . Ob�, :�dDbea^� "Z�4b*�9�"�->\3$n�'a%?!�*� s� C�^ hZs <s. �A�A<�� ���3Z��oA"verifo \2mh"Y�E� ^2$�2d*�1"nalign} *� :\ &�h,array}{ll} 2j�{\��6�k +� �m�5 ��, })\,� 1)}-�3�3 L�r1)}=}� 6v-��v�[��})W0)} -Q�q.} "32o1�� � \\�,2�,% %B:90^2j2:��912)�12r12Z1wT.�H� @%a=�0)}..\:�+2D_0%�rj�!�&:� 1)}}B���.�% q 2M�L )Ra�vof �o�/&' 9 6 au�q�� qeqnQ"��1)n�fA��f&=&�.0�5 %%.\no�\\ &+&L \chi a����*`5%�����>Y�/�,; sol2-,���Y J�"C��2� :~ .�`. Plug�C�~) [ �44a�^tn*- 0!�, �P�s�D1�9�u� ")#r2_�U6���UJ��� G��1�+NM� -J� = )�_iK5(�2�x%��5Q0)}<5Fk1)�F� O%�E=RA_]A D_0-"�Au_7 AL _{j}�AQ meglio!6�Y!��(q+�"�� %[ �e E�E� )$ �aYis� �Ee "}&q^3  satisfA"fy.1�: %F h 1�t {eG _j}+�7(aG u}�< U}yO"~8-�] = }_j Ŧ�� Z^2= -{u%ah\O6M Not�feZ2b)8�2��a p (�P)-$ e~�X�IT&F*�i+�)�&��$each value� %�M' even�R $T$)�&&F-Nc#��F�U�= j2;+Y\? j}^A�b^ .�=6� n �A���1bd]dB�)iW PK02� F9 %�M-U_i + =�� �:�rif�]6�A |o�P2�A�*) &P!�/"�#Refs. -M���� �VA9�L\s��:�/a2H^ �O al_as}�B�Bi�~�:�&*�(m� ŝ��a6�DႡ���UJ�"on�${\�/L} \gg L~H"_)4" �ZZe �"�o #a new :� �{\x`cal{X}}�Q#'��!�&|at)T( ) ^{'\,2} T�.4. �%�)= j _yLP\� q�L� $. A�U /r�\w*- cell!g h��CJ��"s�Z� D^(L}�= ( i jV?�=M_eq:3.11}>�T����!��28-�rra�X.B&�#ɗb)��/wau&Ipx�!�_QM&���&] ��&]%�Y �rio�rt �;ly>H�"a�0i�=�G�5 opR.�9��e.�F�4� ��2�$X>t� �-�p comb0�4�5�,onRRz2p!8� U}�� $eE!�I2!�E9'HH!C ch X7; e�zaO�t\Ra .c*� �Z�&=& - �CqD��Z&I+uaUchw� }YKEfVE�k}٩kBS�M.jJ.iq�d2W&+:�p&�yD.I&R i2uf--��%��o,��bm�� e���!!�&� " Bq�TtN_kg{]" (} ))!�6 "� 1�k)� UXi! %�;"fI)35y (,f�� i΅#to� �2B$�>fi�(z9)&�!2e>@i��6u� L},ex� iNqcE "�1qYw/e/�d!�a�m�total_y�` $)xv��%�UT bm u}$:N�^B�B 6$S!�2$vA�aLNiv2 . 6#4B�H&�1"�4D6� !Q��f%�.� n�%&�!)I�+ M�} ),-�U�^2 ,�E�+I>�5B��$�$�8�I�Er6q Zr�Nq-M"p$!%�ed*�5�&� MQ�� E��E����s.��Q hand_ ex� �5"V:pi��H�.9,"�2 coincid3t�.F�$��i*�R���� ">2�� q_: � 8���bd� cB�,IG�.-�\neq *�  L}A *�e�no��o B���e� $, d�����!+5P 4on ��D�8 shifts) �,=� e�sm��(!W�#- "�`n � �04D?1��( wash�$ut '/Q� {9 c�'tÄ6�uer�,0=�� �&�-e�B� �'A&�5 �# xactb�R��` missAV���0�E^&uGfo�G:� i.o�p}= y�& (*!B�$�y�by�A5S-!otݍL ��s a�#��`q�j%e err�$�d2�s�U�(Ita�R�@io?� �#�8* !pI���&(!��  E&,p $ a�&Y/I�M�v" ,l`Qu2A��6(llel steadyXDs*� �EQv}�Zx}#�u)UX})>� 6B@�#F�J^\�aq(u(y),0l5,�qmk!j= (U(Y!6��Q6�$ $U $u$n�2e�h  �,jeT . A� )Q[�&�'*3U ll$ &nF�(w�%��*�Lno@s ��xx$D_{11a�*D_{yy:)F\DU���&V+  1�  \int� <|\hat{u}|^2 dk}{.k^2M, EyyE\;,� 5\; \f\>l ve j^:�8B O�,:Z.e 6`�,lat�(1�T�G �_ �� L}) � -~U=%)ve! N0�KJ\+v�.}0 z;,6�95Xng��*C���"A4-;e*�:{c��Iut> <���.s��N� �� =�8+m�N J: )�=z�(I�);+ %{)>�:�205K� "plA.�n>�i�>[ j"Y�(}p8C� �:�+p_n�8��ra���<\͙BmA "� x-[�2��o�%>2gAB�X9wo�X.� G�H�K�z� AFɜ� i��b9�.%�` �,Gj+ � x},t;��&,in*�� )  saa �bs�9�b�+ he pract�D�E>D. I��2�e�r �f . 6, J�K,;9�� �1m� $(2d+2"��Ĭt_, except�&y f�2Ű! Q���%��I|�'� �� ^^, �[!3hA)Aogo�E�LsyM*�Eorto}�(9S!)" �v �*1�tEp.e\�y�:B�ofR5ic�  4mq�dst8`X�.�Yv5�!?-� be heavieZt%a�JzV� �U. �Ls&�6-A��A�FT �>a�eI�.� �,m�r�!�4�khWnde�iI�st�\!?i.�fX-IE�isN ap Fu'Q� seek 8�sf�*a ��M�-A�E ~� F�] = u/UN=�s>���^ #�%�v" ^ɣBi �� 2D^{@( +-m 6�BV� !]*�-�rn&�-\ ��-�/"C&.�,&�-y��FW�-�=II�ng�crm�j2�-{�!�w�u�C&�of;��.�l�.�2�)+ ��Z�)F� (Z�-� & = & 0%�.�� \b�1Y*��19+�\a6gME � -%u\ .�3}Q �"Z^40\��{-}��& 2� y�%�9]L�`n��n)}�)���-�-�T~�6�-!�\;.2� R6a)!2]&�Q��$0$-thA�A���a�t�S�M�1]A�� )�l1sIcV ly &�h#�\ [see}�m_()]�� ijJV�7../�"kT�/�d�Y���� . At�if'v� �k���`&e ���<.u�+ k},\omega:��- :u �1)} {i( > +I6 k�k^2az"i ��F�%�V "�{�1k�?a�!���&�N_� �%�]0 *Y*Y�\\J &+&�d%3q� d �J0�)\{�\�Re} [b6h��*(�� q},- j)�5j}()�qqr%�)&Kb�Fq1�F{r�(q})^2 + q^4!��ZH6$�(fileft. 29Im�9�9F9-$6� q})}Z�P6P\]���!�6A�O .W^3�6�&�z *4 e�6}) � ��b]�<� r}�(tB. $t MGx}(R �N *Z : �("�D� �[~Z� A"#c̀� A �r qk,W �QB�baJ�H 2��P� C� jm lyyE2�e� � �� isnJ�.�I? ,o vari��@6� d� ���:a! indu�an!��Tpi>� �k6� < �2$�N!L8�:�b�?Y$�"Q/q W�iE^fac�;�Fa:�k {� H.c�{�� &� ion~�.Q�)E�pr|K6'oldn�KqIw w&�C�P"�= origa� r+�F�#Yt�H sweep�  cdVdQ�.�6��z�" Qwn�%O ]�$corre��" #2�low. . �"f�enc.($�$��72�%95� ex�0As |�ppler-� �sp�tu:o�'b�%e9�#)W6!k!b�[wa�"UY�P�:53(�<.4(.h1�, $(iV �Sr��Jepea��a��[.V,�G�fm(B�6�3*uZLor�&���T18$.i!����2�J7��������)�������� �b� �\}R 2�AA6��1' Q� ��wjH al� $own�*��,},�e�yB�ic�06�i�g$aQ j!Ne��2���en&�WFj .%)&.�yS.��.�.> +E&8 �% * fo��6:2h@�O R�j�e�>1-^A727kkqy NQ [� "mB �:�/ =0$]�s."{ is"+7$*� ~E~"R��"�-at�Y. �O�!i�em��R!�B�+V#s ik͈"�\$ thre�Mme���Iǖix,�$than nine,� s (�& oNM�M{^E$) �6beJ"�6�I��G"N� h*��)!>�N vali�` j'� / �s �!�$u / U�s 1 �sca��@-��m! screpat.@"� �s��+ psim>q $q�o�x��sl&jg ::HN . Ac�7�m�c��S"�g�aMt�b)I�Bn�!� �W2�cha6��0Q2�F"& 0)f// s!a�� itud;^ .c= $, *$ "c.:ZXAV�U� N ad�)��}�]z�#ng� �K re�m�-&� �5�r�|� imag:�parts, $27= .^{\tiny}�u-�n2'I}�k plug���Z(�i� �� ak�(�*�0�Vav2��6+ �S:SJL�R&\� s& �[^GZmR}5q!79FBj6��B+��I���B4:] "�v���2��'^i��-b� Z�[B�1jbi6�."� V�^<��B�N�KF7� 6.U9�� �>�pS*� one .�;��iz� �pthLcti& �����2` "�.}�9^A>S�&z �)[Y-if � �v^a.�4 -1q6:jN6B4j�jQ�=*z&.Y�f#4E�V?qV���E�\;V�6� �&� Ule0t � � U-u�u^�.�1R5I��:�N�����=�&H+- B@ �0� icF�9DC-< � !F ..�~ *�1S%�u�<=0\p�T*�)8q}~w and}~M� ( or}bkN�!l j*bk\HD=2!B?C^�s ')�AtsaSt�0�  .�ve&iestNe�z��!o�,�\� �9_// �io�on��"L�25#�2K5o��: @u*Cb . T��,� �^�'�a� ١�� ulhU�t� %be{%��toV J y��\ &�g.**�s6N:� q�i*� "��@*�V(:� :b�l plac( $9N�m �9f1 �b��ets�O%T�G�..*MBy�;�ics.  8!hs ?&_W,�+eY�� isotropi'u�I�!�al  �� i��a�E�A�a�{t�Oq}\to -�q�.  K<tB]*LA�"e3A�F�J�b� ��-��w.92xN�~gN�x��:aToB���K�g�6� i��H .�A�ua���t6�)"J!�) "{t&D&�)�֋a2D"29�� �d��\reo!o stim}�eB&,�it �R�A!��E��1.t3 of ��6�*i�)c.�8�"�B�B :P)u� ��woF++F�ű*]3,*_V�( 3 �*� �"�%�J�2aZZ:_=e3,z,t),0Fk3�s* 0,U(X,Z,TFt3F�1i!�d5�I�z(!���u��&gva�L"�!Ɓ�a:X;-}� A#�@�7Ni�ydA�c1y al��a"A ion.*�`NOM "�8 ;Xt�%i�V�ve �yI)i��u+ly[ A�}Uin6�%�� F���� h)�"R%;1�- ( ( v�%{ ��% AO� N� E�9F7O���V&�1&�x"�nd ``&�w�ipe�h� :l "wp�"�I?b�1diԠ79a�"���:�~��!]os�o6��[ $�,)"��9�yE�. .�cc.�W me n"�y.�"m(_�F&�xE�a,sk�  4� �� V�)r.e:%>\B�}��I�a���in�#"II�_a�i�Do�8cellu %��sg88,11,hS ��"$xkm"�- ��W��$0 \sin(kx) y)�'_0Uk.�.�ezu},("�y̷� ��al��psi�Rn�T��, (��0cos(ky), - u �aw6�%2&zB���:b2��i&��Mu(= 2 \pi / k=A�"f2$u�`qab"ez.>!6R�wau�B PecletA�s� ($Pe!\ �D_0>[cu4j \1byR�" &e&g# argu�;��p̼�R1�"3\��a�I} vortexwr��ro�toE�0�UA���*��<�<yV=E��im� �Pe�" Aa;cX ��֣ѱ>P�6.n?�=y�e2fR�z,e�� U}=0�\VI%";Tfigur/_bO�f�W�\s@��s[�e=0.7] 3 1.ep] cap�{� B�'O xx}(a^S�XI6.u2�ڑ*(�j!�2r �4�M!�$x�� ����2� .�%28�$(so�line)�*I �{qV�>15 (d"@d D, �5A�a�aig:&"2.5��Veay=na�RB��� .vr.� YHu Ad �(�7�*�6e� -dotYd% �h&�3v/U�$$U=1$, $L=�6 u/U=1/4 a�\/L =1/8$, $D_0=0.01$. Un�Vr�id�ml�'�@r�^to*J eq:adim� _o fig:�rU� Q�b�pS6g�(d1*B��D��� ap^�ͽ!�,^� U;(f Yf V(X ��&A 2&�0u$}-n�$L��0O���� $U�f/ 20� =hI2 6�V�6�L Thank�NA��|D��H5v.X) (�ag�|in.F�X  ;Wx =1e21fcLk $(\pm k, Rve"�1��:]+&M a�$��_{1V�J.\{ 1++ 1}{4} u^2[ 1}{(U + V�. (2 k��A�.. *�.��&� . R. +l� U-VU T] \} + 2��^36F2&.1�For6#a ƨ%�J�$FA)&GgL �#.f� 1rm� [pt]u��U2>Uimect;a�Ac*MDB� EBG.|�>. u㡁� convw�1,to, ��� *,F.�"BaS �<.*2���< M# = �OSA"~cmp�!� g# +d.m�}20$ib|B=��� 9�25t�3"P�\2?a�Fn"$ 2E.օ�b��͍���s|�,n # �,v� aseH,.f��s:�<$a$&�e ��, %bE�.$��.�|r��Fvlso$!�c &�F�7``n}v�''JY!E �5T s�.<�KB@�Uneglect���J "��H2u��H�e�Cf n!�wo�'Z>��m%�r* �v�T>broad��� of�s7�"+ys:�.�F���9� �{� KxF pbelɈ2&�2:�R6d rep�'a�!�2��{� � � - U� � Ky) )�b�)��'2F Th��nis� / K� +Ggir&� .��9 .��$,6� 3�]) �ñ�l9x[{U��C2;7�f(2eA��u^2}{U�psin^2(y36`� ~�vF�[U�^�6��get*��O.K�<F��N�K(x+y)^�"V :M�%*W)Q12O K(x-f]�_B�FFig��_1Ɗ compa�A[zN 8 $B\.z�E��-,0 f2�~�iS� a�&�8 >�nu��a � �fV"� ��x>)+j�Wc�RfVe@.��Mva�� ng��.Y:B�y ޑky2��l��=�t�r�;�q�MU mF� � �:JEx aI�x}{L_0}�Jvv�� t�JU_02DI {D !�i>!/�$U( mLLL/2\pi�\� 3> x4&a�:p2}!K)�����2� (Fv �-Y DV�% �� P �\ORAhE�y�Yg b-.�6})2{ Z8l��� *�Fmat�heq� � �� &�QE�� %�� *� ;�x� .} �� .6� �� O� h6��9�Z.�28}--&d" 29})UF�R K� �-ò�-%36�2�Q�/�I���j� �<�� �0A_L}�_ *��⡽`"��.�13�JsX�Ŧa unti�p2J]>�on��&6Š1�V��.��L' � ڋ�e��M��b 6N�:��M��nSp& U�"3<v%"fU�:�$ed�9�^tn�.,�Zjq*Ln*X L�aSxac�:�1� �dHIBv 6`g%4e�*�6%s do . capt�j.� 1";#9,tWHGZwA���>�em�il� : !#5� Eĭ���P �$no�!(ff (��a); iic� kk HBl� locΓ� he bell< o.� :\ob)A*��,)�K��&� :Xޗ^E�(= \tilde{D}&c I' �6~�Wt۔�.�6�onl�"X7ev"Ncr�2 for the� asymptotic eddy-diffusivity $D^{{\mathcal L},n}$ (in the following, we will refer to as ``naive approximation'').\\ For the large-scale shear, � � on tensor�\��$ is diagonal and strongly anisotropic. In Fig.~\ref{fig:2}�Hshow its component �a_{xx}$ �direct�parallel��B�8 flow. The sca�e5>Pis $\ell/L = 1/4$, Gr 4 of amplitudes-u/U )�, molecular=&is fixed�$value $D_0? 0^{-2}$. !o�ofshear effectmall- ��i$to reduce1R�Pcoefficient, which fo a pureZ9t would be given by \begin{equ!%n} D^B� = �0+ \frac{1}{2} U^2}{K^2!(450.01 \;. \endWSuch �1�due�@interference mechAc(ms between .%A� .moNX\cite{MV97}.\\ With ourEPmeters)Mctual6�o)�order ,$ 20 - 30\% A@$depending a/4he phase-shift�$\bm{U}IG uAA�first- _2� (\a7 eq:3.6}) 1�B1proviA�0 a good estim%�!��a�HVoa bout $28 �$ (see Tab.i�$tab1}). On%/contrary ``Rz�esB�Z�� $6)` I��oeeply w�h. uL$transverseyW,� bareF��c _0$ �� increasedA�%�resEj-�.^a��\^� over-eAT is i�,! %�4n enhancement i%v $170 \%$�<$e� le 2~6! in ratherI agre ]wA酷Mۉ�9g 12 -A�\%$%UtOworth��ess� that%eZ errorsω#!7 ^ �than beNconsequ!es�finite �罯%�ainly� jfac�at �)]I�.2ha�*0en neglected �V� tantFQa�E}_{i j}({\bm X},T) = \tilde{D} \delta %($. Indeed, %ra �rF�р�8$ �9�e solu���� s results%� �$2!� M�.�sQ1! ^� still `A�!�!�M�3I�V�yx case6k.u cell�a- F63})I�j i�F, ��hf+ is eA�,more robust,�As :s also� (\epsilon =  / L%� 4$ z$\var$ u /  2$ F&2})�#%YU�^�A�-� �of $10%� . %��� table}[t]ce�Y}tab!� }{|l$} \hline E� /L$ &  >� ex}*� .,n}$ \\b� ^ D h = 41.6^{(a)} $-$ 34.5^{(b)Y0 $36.7$ & $18 \\ &HD_{yy?s12A2 C $19F0.0267:�8j���40 X $39.6U 28.3S��13��5F�78H-�E 1� \cap�>{Aj]�Ta frome��E2> � i�H$U=1$, $L= 2 \pi$),22�e:B* �|=��qVA(�]s $(a)2 (b)$)e,�2� obtained �\ $ homogeniz �.(whole velock field $��vA* U} + � �.�,�>�A�e�2��:�of�� pre-.a  wher� :" :� iX re.@�ex�sio>+%�by re!2A�s!s*j 2�,A0p vely. Un� wmadt menk$less accor�rto Eq.&�g �A�b^..M2�M�M \subsa ,on{An empiri�4``recipe''} Wa scuss nowb ) )a!�* a&� (i.e. ha( no vari�� in space � ime)>yVdescribe>>_ s.tqu� on8 thus o�xC i possibl�mimic%�:�  port�X mean�$ an averag! ffu�!.KE,a_ j}$ � � takznto�Kun�� ,��,U}$, but doe!~t ��AK posi� �  general �not cl�"r2cor| wayE� ١=ai*" T)$!�B� �y a&!*Bh . Here,& propose a�)�]@�(inspired b�multip�^ ach� ideIq istsAJapply��:�8technique just�ve term��<:��, ��d�6E9�A���!bof��.q:��R} �G� w�\langle D_{ik} \partial_k \chi_j \r !+ .jJ.i.}{2} �5ij}#�|ji< \;,�� empt��� ��vector2�� s��auxili�KB* 5tI_k + �U} \cdot�(} )) - (!T�1Tj &'_i5|�������$} AlthoughE;�?.11}-� 2}) cana�4 be rigorouslya$ ved,m�.�@ a rd argumin favo�it. Eqs�jNwsBa���alogou�� .B�12 � 3})ui�o�A�B� y� trib%�s�F(* mtd� have b�� ed��U abov�zņedi���di�FRis potena6lyy�)ngā)icŏiere!x6 almost im.� deal�ɺ-���e6�,ies. Let usv�&�B76+)���nitNN!U� qG.`� toEXid�|�!T99��>J .\\ Numesimul)8���Z, �lsse}) i��Rii plac� V1 M$:8confirm!^?is��!�i� leadE�N ider8!� roveaEs �re !/}^���edE outYu:)I5>� . T�"�3}B�e�"!.M;1f.J&�%A�t6� � { �6�@x1�!R.� ,a}$"�}�:�y; simi7�s holdsU.�.�2� � � � >3�F�Z� 4 1� 42.1� ��' �&43���f a� T6� j�Ja�� ~A�:D ��"�y��y�J����n &���)a .63�6�6��. \�M� � expa� $RenormalGroup�rg}�previ� Ssx studi��roble� .�"� �vEvarF �wo�edxt^c�d, O� { ':n\\ �acti6�one�to*ladv�ng"� �sW� tinu�c��4 s.w� latter�V�e�  writeFl \bm{u}(Lx},t) =\sum_{n=0}^N  u}_n!= 3_0+Z G&B &6 Fourier)�fo� f.n$aBLpicked on wave-numb�around $k_n \sim l_n^{-1}=2^{-n}l_0$!�Denot!ewa $E(k)$ e�Vgy  rum,1�B0! 1% @ |F$|^2"i �`eq \int_{k_n}^{k_{n+1}} � dk \,0 . %\eqno(4.2B=���readyAFadd��fi#"-: w7 i � of $=� -� %�$ehe - ive,ne? In o� wordIqaim at�h!s2{ .�Q� d� minK} c EU}^{E}$.�E}�n��Y��  \\ A natuP�F nsw2!ur5B%<o��lo� he�"6�g�� poin!] view. ��basic�proceed� ong e�steps&+n~ 4ate} \item stng&{origi�$18 YFP}): �] )�GB�e�U}_{N-1i�)�2�A� u� &Y�4) >�p�neA%)�UN�( U$:�!T?.j . Re��! c� �FB]re�edSec"mse}, . �i&$ 5e"the�� inclu2he6�upAG�� $N-�#F�&�$t \theta +� U}^E)��%�\nabla} )=  (D+  L) �U ,9�5BS��%�t$%�a` �$�wu�d8!:panalysi Secs=gR pertu�$�!� ob���!���6�repea��ull�ailI�:�eqdure. �#��hand, if���nte2>o��e&<%magnit_',.^ Q|c%"��)�!A�A .�n)m xK%I�$%�j� �`�&-��O�&+A| st. K {�&Օ_N.�(k_N^2}}{ {(-$)^2 +(k_N 4�|)+Y>6B>anJ\xYM=Q�I���j + ͆ 3 "BSQ�d�"6,!c�)�� 2C�2!�";.�f6�!��%��� As ao o5*ep ��#to ite���"� Y�!�(!-si�)f��uti�h bef"we do�_Ax&^nei�o�6�$� �bm{x}$ nH)m1&%��9�$.n�Ftoa{��ME q, )9Q?#%N 2� $k_Nk)�q4so on. When doa=soUarr��a�B�)e2y 1} F�uI�uMy6(��a { {�e �^u7) K �1q;NrecurO� y��cl�1/ �%1%!�4$N-3, N-4, ...� \�*>z��n"!�eD�x��I�i���v s�). Two �I!�limsE@�iE$ified: i)I� omin�&t�Xdent��l is $Z�IHa 1ve�� becomeF� �E.EK' BGB`'.<}{D@U0}� ;Yl1�]8B] i�')' }J�)+w��ugJ�941} \left( 1 + �tst. �%i}u2,^2} \right).=$2=$9B$A�r>�l1}) �incc,� Ix2�Moffatt~m-12X%1phA�enolog��s I��A�U�u� easily dJ� D^E�� {\sqrt{ kq/ k}�10B�Q U 6�y�>L�h^Y,   ( �@ ary,� �@*��[%�_A simeq� _0$ �jq�l %ha*� .�)� IU1�� \�nMYB}n}y}{�0.N \�to _"_11BUIn summ����one u �ul�q on})� anM� least ds1p+s�d$*� n�is� e&d��v$&� �:iFZ ��M.�N llow�v2� � m�0� �1an���se ��  a� va "On�nremai�!% �: c* � ��B�%%*�Co� �s-�%c}" inv_gZ both� t�+S4d �  the :A"��a pass��9aO�"%� say,0)$L$#5��*QA_ R�3orm�� �-* o�4"�$!��.E w!�L�Bby1� Kflu�2X �"u}$1Aes���T�,$ Eu�UvLx)��� �/�Mh +53�.$�!�I�a xrba��:! so-Ved>Cst� gy�~&`� mb"be emB3 ized&�%��G  P6=)-�Yu�%U4Fokker-Planck �/Axolv��2TB M nd an�1A^ad>k. "� explicit ( on� s� &T ]s�� !*i"�$$, neverthej) � pparR�A�B�ſ� ��aK� XJ("ialIY1#� . F�-I�"(,AO� n`M:�'�>b�X.��Ckich� tur8"c��, sp��-�o8I� kn O1�\\ =�n=�n K u}$�<def.par�-un�7ual/v�|Q,�Iqymmetric�v�BE� ���u/L%$t necessar� Ň��%� unit�+El�5�7 rangT reliabilR�@ exten�"?6���%�;%�eem4r�5=�!�.]�Ag real��ND8d oceanography.Q�Ex��P<�*ula :i 8h!��*�3d a�*�-��-to situaBns�#v���"H�7s ris�+a s�+ of rR�thJ'[ �~.�%ext�� �  letely%eţregim���.�E���We �<lik�)�deɄa�# rt d�&A � -�I7�%{10�6�+l� :ws&�*%5�al!; �&As far��r �i�>ncern�� radig9& c ex_>A� *�+ �A�K'g%idY E-��st �f polluE�dispe���� �et*B� (Layer (PBL)Ae�is�,� n ($s 1000\ mf3tmosph�& lBn-A��nd��B%e air5'ac@dd>>, sink/sourc?ceera�ri]:"r bottom b �, e.g. .�9orqs d��-A���| � as � &�3u}&�4W�7�:a��ng�� dom E�o� ��-��s� !� ��r��/d,Az�>��lowly-4!U+ tandard6�&XofQF,AJ� �h0s synopjB1 Ehsa�le��f� a�� A! modeliz) �i6*ce,5�ic exciɬs� �)�i�'som?(�u� ��mi���m6�"g ��R� Am�� k�esYf*`< B@A7cha��er%�y�A�%%>�� ach!��/ric� �dR ��(' �,1h1he typ��� 2 � �A�(�� �.�s�Q very u . AO��4� %��Zb �s�io�si5 ��LL �%��in�.e���&�>!6xT)�s�2lidEkAz� Gsj;���0%+�f &�num6\\ More�?a^�$requires a| ai8knowled��Eulerian:a)�I!KalwayW+ail�*er&7t!z.�s3!tE�u at� t� tA� buil:� "�a���M, u�Qf.LagO �ex� data,A�h�C a fuW r imq�M! towar�satis�oryG ���on �Eto%��/Il$ �A+B�� -�"' *{Ac1��,} � work Gsup��k`Cofin 2003 ``Sistemi Comp� i e P 'i a Moltrpi''.Z�-� hper � 4t CINECA (INFM��'l ��u9  A�� ve).�2�.�m2m&9hebibli� }{99[biby#${1} W. E ��4B. Engquist, N�H he AMS�Df 50}, 1062 (2003)` N<2} L. M. Gierasc*d J. KiI {\it!�tein FolA�,} (Am. Ass.u5Adv"�C�:+G��8Washington 19902|,3} P. ImkelO�\J.-S. von Storch (Ed.s) �Stocha" Cl��e M�UTs} (Birkh\"auser, Bost�mBaselA�12z,4} H. Mori,�g� or. Phys.)7433}, 423 (19656@8b} R. Zwanzig,!1 Stat2@9}, 215?76u5q54. Wirosoetisno�T.G. She, d,�ica D �141!�41%�6K6IJ�A K. GelferA@. Baba, A. Rieger�4d H. Kantz, J.F�112�77k6�L7} K. Hasselmann, T�Bs �28!77%776) Uld8} A. Majda, I. Timofeyev�0E. Vanden Eij, PNAM�96�687!P992�aa}YES (ein, Ann. d)�ik �17}, 549@06�aA P. L0vA��pFRendus A4�530B82�9 �Wentze�KM eidlPE�Ra�  Pe$��of Dy�al Sy�(ds} (Springer-Verlag, New Y�o 19872|810} M. CassandrIK-L.\ Le!�G.\6&�*�CU�� ,Periodic Str�reaCNuI-Holl�0Amsterdam, 19:�11�I{jd �P.APram�P �Rep-�314�!34� :�Pi?8lA�~Mc Laug�E, G.C.~.� �\ O.~Pironneau, SIAM Jouragof ApplMs,)a 45}, 780,}86b PK02ehAahvliot!nd6�``H�C[(�K� �H9 G mean 0.) %y.�'',�.��IV�n�aA�?-n � al s�! 8e�}� Hs, pp. 1-8, May 24qK7,��2, Wilmq , NC, USA�5u�8Leo} %A. Leona�hin��Funda� al�a� IssuF? Tu"c�+DGyr, W. zelb�!l A. Tsinob-LEditors), %pag. 257v�1>SM��RAu�eu.�6�u066306���*VA�*M. :�M. Avea!e�X.q0�;148Ah 97) .T sg88�$ H. Solomo��J.P. GRbO��AI�3�628��86v4p85} B. Y. Poma  Ca�Acad.�mP� J0�u13� >MV�m�%�2, Eur�A ttqف�53��6-126 K9 �#���� Mecѳ)72�86x )� enci�C�8, S. Musacchio,��Pasma,�A. �{in pr&�S��r'>E �' docuA�} B��\ Xclass[amssymbols,11pt]{�/cl0(setlength{\ he%$}{9.0trueiN(:#$width}{6.5N" even; margin}{-E>Godd>$5$ head � � �sep .25in \newcommand{\intbar}[2] {-\!\�$^#1_#2}B3slash 5/\3\j5curly 2:$ �SHarray}{c} #1 \\ #2 %�  k&!�.�O}[4] ZN O&N \[2ex] #34�^P %�%\?'[��]6�\�H{c!*/:ne"N{+N %�!�R%�_{\Bbb R�*2" Bint">int6# inta#^ fty}_{-\i B*o$.*0:$ dd{\#laystye9�\xinf] < x �. C9�ucular, v4w�# long ��*G)"�1.� Fm&� �qmm%uij arbiY-�2Nnd� zero}��.,is �/�1+ W non-�M�TdiF� pagebreak�L>=$on{IntroduA}� 9V(DS) IU�0 [1] $$ iq_tI�/ (q�A0+ q_{yy}) - (_ULphi_x + |q|^2)q=0,$$>^ -�S+ 2/x=0. �; (1.1)$$},!�|-ex��wa� �<mis��;sh�( )"�A-$Benney-Ros�L[2]=AT> W)��urface�KionI�s)�$$q(x,y,t)$"�Aua @� packetR �Vphi8 "�"�GA�ciE5" �g�=al&DS9���5 two-��al4*�"d��\=RR�-be de �Sx*�,QTgs [3].�=iM}e :�co`Rat�ndu1E�r G�J- +y�Ab)2�g�!#5�s: � $\xi,\eta U_1(!�, $U_26�(dl&byE��b�SgH71Z�3c7parph{Fo�5�!!� .} �!�lex�ld fW��.e�0� >-sa9:L!c>Lsly�s�E[domainA�0<\xi< Q�00,� 4A�4Of"�A�UJ�:sq�0�Nq�C�-)�z���q(0�e%D ��)�p.u!4et'aet:� �Y �0YX)i  u t.VB�U �Z5%:h�%Qs $2�6�  }��&*-$ smoothnes4 they��decay a�exib� �En $! I7]]�Nop$.j bX �iz Bar-9�WM���jugeI($M_},221 2}$ B�4 $(11),(12),(2 22)$ ec es �.A�$2],2$ matrix $M�nD_06^2zgH off-par"MM ^d\wg%.0Th� m 1.1} G f:��9 �1or $(MA�m,k), M-�!�,k))^T$�aK!A�Q -ikM� �Yq_0M_��(>Ua &1m �  km9 q 0,m1 \lim�39EfII} �uF�0,k�1��6a9,E� $M_25, $S_0(k,l)!!"�T1}{4\pi}A�to � d!C���)�<,k) e^{-ik\xi-il}-� ka:�h\Im l �7�S_�da�m�$,1�$\�$S�, a��i � t S)\j ��eto�/ + ��) . 9�%�"��b�� F���l dkdl e^{%> + -@5� h�gBr�qUC�J�29�.9 eta F;=�8=� �U~�&�n �o~# $M^+9t,�I� $M^-B= eB!�F��!m!-Hilbert\ �: �E�{���q5^-$Q3�)�5$A�k>qZ<0$(D0i�^M,\pm = I + O(�C1}{k}Ők}�Af�yk�Kna.$. Q:m� $ka M^2��!d9 jump �9� �Ind�$$ y{M^+�T} 2�J6x� L,-,-_, :,=.H dl \ov� S(l,k,t)}A�-il�'kAR} ]��D� 22}}2�l)�1�v1kB� ]�2}N��S�),t)a���a����X�{MG11%7Q12Q t�"�9a��y ^>y^�?iR{iN=l�- �!O��}�10qT� Ri2 ��(a 3^[ globN�P DS $*v �fq = 2iɺ.�͸(k�a2�P51 $q$M�� (1.3)�.�& R�k "�8A�&�o^<c�*$ c* $1e$�0i�C@�\*�8b:� 8),_"b5�*6is � �Xed� turn7is �s��K+q\&�behavior,2�1� �RH5� (1.9a %�ay� byv<ed��)�Wng�+O%�1rs0� �`9' . Sj-�  (1.8 s p�WsO3�onetin [4]��-�8�8[ *I�$psi�,+ (u(x) +k^2�@si$$i� $u�G� �ru_2![Af�k�w�9�.��!R_%� discrete}"�P5 jand P nJH� $N_1-]N!]S eigen��Y�����!. &?�q�g� �<4n $(N_1,N_2)$-/ren}" . (bv�5��5�a2A�%�5D�Y2&! A��N\s"� . Ac;e( cerS'e�ete^ion the %,&~��BduHi5@*B�y�)MYag�'M&S 5�%� rum;aI� ��Vis R^��}7up"���2}���/l_>�k1.� PO��f_5��8seeo$[5],[6]. �9s� ex.�!�in �A5M�� $"��;�rh4to% one-*^A�ito,% thesy�s do I�not� eser�: heir �upon \�3A(a�j2�K�excha[:�gy9s�K� nt s�'�'.be�6�y6)�e�-�� \g* bta �dy choo�1a sui�5F�� u/�&� �J� 3} A>fesS4�-�FѴr@!gz ��PDE��!�=&u��q(I� al) yw:F8sslZ�s-�c�a} &�@!pex��sed E�ly%s)8m��A�ary%IZ s [7A�EqAa ulae1�"�43!|a�Bt  ar c<$e[A�[w�>efyhet�Ku emph{?�%�3}�8&#9�~h)� %��sJ�=iaC2'!8) �r<ly)��SJF�"� s�&�4e .r>&$ p���3)--(.  be�X�4A1K .e� ]hz�low �!�=| |12K�e=U��{S�9in"�A�_�)�EK}�RaYi�B!te{un[4n} Neu�=e{�2OP�gJ e���W _a>"J�IT5�� 2�, nam� 2B5��:�.�=0$_O� �=�ru �Pd� $$ 6�g_{0}(��c� D = f "xi�eqno{2)}O��.m g_0, f_0$S &K vKa�Ŝ \\�xi* I"�e}I��N ex2iaB� � ���s�F��*� a?11)"O?A9 ��ZCI�i�*��n$ W n unUj��u-.�R �8Qw�"�"�M>�!av��y6�*,PDE!�#{S}_{to ;>'!A<<} + (u_{1}+u_{2}{S?i \0}^� } d\�wq F2 �,t>(.g,t)� R� S F�I�?.V p  = $qn� 3)! \� b�O){lf�2�} [�bar{f} � uxi�2] -.,06�t,1)*t)]DRk$1}{16} f%Et)~{fB?)3�9�xi' |B',t)|^{�5\\!�2VJ^�g6�1]2h�.0�.�{ J�g)��gFB6�X��� G� r)�$$��$g. f � �not�v^g��xi}&0,�)ˡe$;�}� atis�a� �lJA�m�E�,Chaa���,q�3�e[pi2�W+*� ,2�!?�4�e>�6��1" !40 ��$ � rh ���7).)���.'"� �9I � of5H6�� 6�  iZ� �mQd�d.Y :�!��;&� . .�����s}� ,[8]. �K �G&�Gis�=V� Ec�Z be u�� �ch"�AO!H�Z����ich�L` ),*�b ebG elseEC'!Organi6�paper.zD*3% ad�Wa Lax pa���%�N$t$.=���6H|Q|s �b] �)��' 2� � f)!B&t$-par�&!>bb3.4)) �"5*RSJ%}e� m 2m-�B�J:� *� a:s!�d�(� �s 3E<5 2vb %`proofA- 1.1s SLIA.O'we R$a�.� &�.� 2 �  �+2�+�, 2 2}.B�,&� 8� 8� (2�)&�� �����, ��\d� :~ l} 11�&1 � ��^\xi_0�' q'" &  s5�R1�ik�- )}B  F2y-.E2n'a�Leta'-)}� S1n6& O2�+.Peta�?28.�!o�12�6!�m �m.k �xi � '�>D:y).HJ� L�- �� �a=�JL :�end� =2\)�.E)��/�Q>�(��n: 1 |*�#m8a�E�i���ino�L�>Zwhi-H lastoMvG�� @ <� 2�1r &���D ���sf��hips � ��2�A�%� *IK�!�1}6* = - a^N�N�X���J*�l),� >�2/r� *�2n��) e��+�B�:���37MgA6� b# 2# r6$�)i�2u � �9$9$2W) 3I�6L�Ac�UyuKZ! $$M�!� ��+O�7.�!�!"= 0u�~1 1��~._��..�A�c�)�" W"") 2U)\2cof} \ �T�0)O $(��� 21})^{T}.�a�>� Volterra l"~s�k�PDalbx (L$A5'� )$� us�k �i� N�>0-6�,AKh ;s.��Y)�$ \Psi.�$�$ *�$>� >$N{Q1}�E˅�\pA}2M'2R,2 , "}&" 2.6)N $$�n�(Fi���E`�buq2�uI��Az��s4��i zI�.��e��!k�_ez�-0@vk;�o� ��' =� ���A&�- �xF)x� �;5�FJ,A.  P �- 6~v %E ��Jy�)Sub^U� R�aImC $(XAX�e;_!�)�+�' # {,�22 # -%>!Y-  6��o #A�2��<   q � �'�)Cg&N!��vW]�5�2%2.)U�!> ��_�f$M$ɹ� >4T+=>�ZG �#�l -%� Ya�- }.$$�Gpa=%2$sC) ":#� �#by1�!�a%4!G�T$J&22.3b) x3te7V�& �&7 )\pm�� stea�"$*�O` ��s��!� ��]�#�Q�9!��H eK� $-:))}?&�u1J $$T$(e -" 4f %�J�-� *l �112c !��l�(�)e�2�(�XillCU%��- B��9 Cw(]5!�J1},E'9f�.f�5!f�"�UQ�A�Is�k�/&�� g� ov�*�A�2 0a׍/ !L q�,� �R.�2y ��bar~� \^~22W}} =A N{ a�H���sB(=}(k(rJ�}(l�_0)�)&6A2 A FA� l)� ��+I�a conveni�of�T�EaE�ved%�$& kpe�Nce\o�>�i.<��̡�!�[ .: F�1) )|�=�} -K�D0 S] =G/Z9�+ �B�)oF�2m�eta=0} �!���A �]AC�tuF��7)W"�u�"vV %Yc"Q*ރ,%�R\e�eV r�x5h�<)i� �)�1�"{0 :2��k)5xi=0}=��e��:i�~)Y7l��2�1Yi�j� %�;3!�� V*a4�U � i.[E���a�!��l�1�� � !�le&+6�%$l/i0&�= -�[�%3."�CE2)��� ��b0um��F0�-U flush�a} �Hbf{QED&q."&W�t��Lax�E]��#}b&�#�}��{ %�rsu��=@����Pa���jɡ��!~{-�2͢Ł��2)"�]3��!�0Yr#)�!����L/] fB"�!�ch"v &�*y%3 %. ��� = � _1�u_2)� _�Psi�a�3A�*� "� ; �' .)@^9,k)aG$  -�\ � N� emq�&�e��'��Ze�I&d6"�3�s0!�1� $�-1h�~ � >  =�1"$ �som"��i3 {1_t�8.1*h6*r)!� (k^2 +? q�j)�2i�E� $\gamma(k-l�!f�. &�!3*3!� 8,�6I i}{2S ]�Rxi**��2=P 6/(7 � "9 �E> N��1�O %��>&I�2.U�,then�:KJ%�)� = i(�t���&_��)^2.�iq2+-8etaM�D U_1 4-iqF v_1,�L"�ae{2A=-��2 - iH ��AGiU_ �2 - 8�z1 + v_2� B��"�0a$�=v=(�v�2*�A�vu�e��iA�Psi:+E^a d:�:*l)]f�=FF �Sn��<$ !��"��� _2�2-�!�& %)sJ __;A�6!&S�]�f��.�U�x ��%c�$v=0$�*�-ENfor�^to veri����ati�b"D!��r ea a,eI�c�Ks# 6) yq�&�0mI1"�aif.Y�5 are Rbak.A@l(3_�)�le�eanyYU$ "AFFE����G�� ��F,�cc@hr-�$ 9T "W "� 5?M-��q"e!�N� !537"be� �* yUs1 =C8^�4' �A�('o \&Nor}r't} = VJ�΅�) P. $$ B�4 +�� 5� �;> $A+v_1�Dq+A$a�� i�3: ]H!�4�Hn�v� - 8\2,A)�>ft[:�:Ue�a�na�))'�c�6~� ]�B�v!�'}R �$j�?�8n �9J�H�Q&brBIv�#h�-F $$���Q� I� T{"^B� (�f��q_Q�-)���� v_1a=EH��in.�Q�� q_1v_&�G 3.7a�S0ly "ۄ����2H T!�*�!�{2 ' &ky"+Qq 4a%6T� �aa��(.��!1��E_� SA 5:���`��+ 9 �)�1M� � �� J�ф-�Q�J�+�q ]2  /. nD^9JG -k^29�� it"o ���v!]��+!&S42]m!�_� !l q�� 3.7bAiZRs�}7) ���ij$�\exp[^ ]$ �k&an " Psi$�v� a� $$V�ImŒ@ x �1�!3�6s��BG�(l�����8mpl��$�8*� 263`I1/G2)5�fws�e��J� at�$�U*is+u�@a,�HIXI�� xi!�}*����-�A�[a�K� 2 + � {2�Wa' =0At�6�1n && �%H��ef*�xiJ�B�x3 2�xi ����x*� � ��,k)=1�Ak/.~/par�2�2)\R�l5T�X*I w6%��:*{7"_AMC^�2}V�. "*W2 �!+��C�6 D{2}a�{q�ML)-{2�`d �7>i:� 1),�q$�,2@imeʝ"�qe� I6>A:w 2hA���a�Ekx2�E� *� �A|�. SV- �2!=�xm-��x��if : �(DsE1$A �݇E�� 5�)}{k^2�b%Y�k^3��k .e%�fLxB' 3.12%1i�� �e,��2 �.�� E>->y):L�n1L$kOAo+ � B�3$�ls�� {S}_� ���!os(x�!�i5-�:|!l�T$ 3A� HEix�si(k)dk�x*Q3.�6�i�z .�*"�'.�I� 'm%�\alpha���L�a�]�#8'� 3.14%�� rhd^2s}{dxA9( �[ � @ �]dk�15S.W�VI3Tr6�!����!e$ �reU!a�Z� [�.+M� �}{1�DM�]˔+ !ta . �/ dk;ak��Bl� �u�C*(>!�a�E�pi!C-��\1u�M�Zo-iEY �%� � a� ��E{)�] d�� )v�ҍHҭfi�N!��da�1 ;Geœ��A� ��0.�?��� �? ~�6 0a��v; t S��aeadk%�.��< A��iR) �L!�i�#$.�L^2}��s 2�LAfty:,�2)�6bQ:�� �2�12O3�>a*�C &s 2�3%w"Aa�Eed7=:4 A= ��=F�*�wE� en, �!� _p��Ex�nj � 2��� M�� � �3i(olj��6a.�Ir<=&� . Fur> moref�3 �V| �I�q.�#/w�� &� � �5[�Da�^�a:R:�J�4%out!��priori=\!�>N". 2�!��is� idA2X~� �A� "FTt),*�,&�$�be �k� � *<7Sŋ��9��1� 6�T),�S� �Tr?*-�6�h%��o\6s&� Gof&\-typܙn� us�@q_0� L��x�)Dx8�F���{S.� )"�L&K >��!� �PDE� !��;"�l_0&PP�wn�� :7dJ�e�us�2�F.��$r43, �Aiwel��уQI� 1 ,s $S,S_k,S_l-y2�(�$t$T;R>ha�y�:!��a�����n%�don<XFt"!DtGc*�IA@i�{�7E��Fse�Mv^mu�y"H*&9)*�\mu=O(1/�.�:�B�"zR. G�� ,"�>h@\mTA1}^{+�"�-=   a dl*�&�"}.� - "�#B2T (6R��- FiE����  6�- ]�= � {(4.1.">���!'" 3 t$ d"!'a�!�,SM�~��2 }ag` $*\&� �(j�T�F27�`B72)J27��  over� s��"m���G fޡ8 a&� whose�$(�$$_!�6Xft( |2�k��+ � � {56%amar� ry (aw �� �>evaU �l�B �U�E����!)�{#BW�E�$.���c�L pe��"�7A`a7>Gn�2#� .�<%��I�e�^2�� .��];DA)r � �@ �V��"= fa+�.K0)=6�]!y\%t�U�0ffBFbut�c .�n";.��0p.eI��%Ms &� 2��issr�3$C�n��A0��'&;�:��h"�@ X6ySs���RH�K>av6s$. (W t)gV_1�)^T =(�U�&,M� )^TY l� ٥�is����6�:�. �Jr.��v �:y isri a`! 9s9�He!����.BA�I�is�e��R�ed�o�e ��!emethod!�&�?[14N The >(B �ao> E��M"�Hano+ roprAg RHa�b�t�M$�B� es ����a&O�(.���&�Z["�)),� i�"W&}gPDE"L W �)9��A -��-F�@vOM�i\s��_3 M_y��[,M] +QM����z�Km�$ �J g * gRPmathrm{�`}(1,-1� Q��i(:�cc} 0 &10\ -�_q} & 06cNX�3%�� [,]$�ab��8�+mmY�r��!�:j Q�}Mq���"%cx x jz- Ma���[�IM l) F),e �4 �%� $86�Y9x  �,�w ond colum�cto�A����� )^T ]Ɏ 6�)eF6�2�b�!�� � F_��� ( S) (x+y�Kil(x-y)}�'8�/-d�) & 2Vl,k)}�:�'A,5)UWR� K���i(k+l) _n#�>_{#-$�8\\Dy D-fD6#C.��A�Ay�(�� ?r@a1t�&�!!3�ilm� {3}F�cF�F_� i+)Fc!26)2- oper�� s $D!,*�y %�q��WM(� MFyDy &y}�)kM~7 ~T� ɼ�&*6hG6)�2Dat�A l uA (l)FfAz�l\2�x}.) �n 1+ Z�%3�Zy~Zi�� <cUsnoz4e.� . x �)���� )r��!0ܒ6o�Mae-Az f&� QOlso*V,� [ I ��%�V\0�)VQio Q,+�C{3} � + QM&8I&�,Kt�t:�!�AdIb�M^{(1)���A�2.^� Oɴ $�b2���9 �&� �&{�^�s�9 x81J#72� { Q - i�{'� �]� 'c -��).J� & wmO e $Q Q�_aVg* 10 �!�B�6�No �R"� ��Yit� p�"�N���!+�We "� � f"^i;J�2?5b�5g 3M4�*lh�M$M�)C2��ur��:%� $(Q)!I��ٙ (Q)}��aI.L�� u�Q *q�` a�*q$�>%A*="4�jan 95!��3~1 �� w:} J�T2 1�"& leMBpur�,�MC���"RY�8a)�( 5A 3��I6�Q A�iS�T-2+l^2)S���\nu (-i)&� (\nu�& ]\nu�+ i"qE S(k- �.2�!t*�E�;g�-_�#�-1��- � n@ ��i.j2CJ �~S�d i\nu$T�!,�WS�E�VT xi U,xi T-U ����W�1ws�� + :�vo�1!�F%�= �0 *���l�,� ��F6�\Big( �+��!� -l) &W \nu)�)B6)N2�\ �"/*H-�i/�!`� Acy}&�+ �-(�#)�x}1�!� nu),?!���.�, m Vs-Y�;",7 "o ��� H$ , \;-�G 9ws6\nuE[6� .<%: u<;(U�ap:�a.$io$Po���VQ'��13Bz1��'7P#:�F$ sugge,�jin&yf� # ti �-�DA�FM H ^2 M*�6�M-EnJl.�� )���o�z("� t�� ��g� t2v �~aA  �Z5d�z����1"��� 1'�D2�04%�2x!�w���nu2� �/Ai�kQ=:C::a�.>�� ���& ?s�a�|D�:�1� $T  $\nu$� t4�b��$l�"�g>��S� IG ��j� !>��� �� �H�;�!��&" AP. !�- �a��[{s }�YB AA�.1���ces $AI�n B�8bePcs� 9 r��m|" �=.�1� �r`s $k \�CF!p4s�� u�>�1S] � �`5+!O� .�(�t9� �n�a & b c & l*��.�$:*�.4x }6!�b"q}{2i},��cG.aJ �0B�.x2&" $$��Y;-��.�  2)}]� v  = ]<b15 ��!on�$n�FVua�B$�7�\� ial{� j_��.V.&y:&Q5O� 0�q�`4.2� SVhO��"�.&hO�J_{O2#�6'2] &�0�o � �\_{(�-� |q��{4Yd<3� #]2�%V.e�i��G��/$.�)4e�bݝeE��:=�<2�]ikB�n2k9GMER+��+ B  ��y&!�h�e{5cmA��6b 6�B� .�� A�$O(�h��J�\Ey�B�2�I�]� us (#J�U�!$0)�(GiQ*N 2� �1U#�:l2" !-N^%^B �q�=b �1h7& B)>��"2�6&��X��/U�E@2R�  9 -�x�j�.�V�! Solv�2qk�9�l3 �Y�!j�  (�n�'�] �A/ �qa�{ �\� ��#�N2bm��N 2ci�. 3a�zw- U��\���:^� &r �S� 6N�4 A�1&�2� 1q�2rDdI 5 EW31 Z�M��byaA�Q$B=iQ"t & M4enx)�reF�P62�>A �N* 2�� �K}, ?.�.8at� $y$-� v"8 A<��- x��!ik$%�J�rA|V6J���s1L�� = �-\ջ� e�)A�Q + A!/PsM .{' "� .�Q<1"� ��>Big2������"�k hoic5a� tanI"i�J��UA�22= !$a"$ i}{4Y }b"�feR�q�d���63� 3e�vE5.T&�� e� A?afo�*a��M��<��>]Ti:�2}�� ��#l<�{2}�j�{%y"3)D�A� .?r_>� au+227�|��Li���$l��6�1=v>  F6 ΄.,�_-i�1�.�!< �C{q!x& � -S2]3� D�1�Bb�Q!O H�h�H�RY!i�,�"K�{*�7%�8s&6�30)r$��& ��=-iG�78 ���ͥ� 1S^.3)6� x^(�^a�2�$v��.Bl2��B��A�7vn��/�y�3�7'�/9^6A PP+-�y��3A, 020A"�  0 - 71. 3} I"��ver��)��� tbD*� s!s4���31��2�1v<%It"��to�ws"�#kFf,oAI 11) � UMN;0v��E�ZK �K.b��2Lc)R�ablis�,�*a<=�$�1Y<T�Wr_ed factg4I�``r�s$''�"1#at�$inat� 3lb�31i ^xe�!{>�dEM���'Z��/BMdA �Q\ }&�.E �P*~p5(MR�LW:�1) e� I&���,3)r�2fp�%eͷuWU3�Kk)�Ia��3aW Lg!6���u�> ��K-� [�4 w�e�ik��� �8��+�q}���!%A���w]� ]�W�$-"+L��V !`z�!+ ܉_�  _:9),l� `��D�6� �� q �d�qZ.nUP�4!<31}�m^ �o'}aD�!� S �߈w (5.�:EW : $q�l\xюM,��E� 0AedA~5�l$|q|,�{q)��� �� `�CgrN,Q � to $� $fu ')$;��a.q��ZY 6Y*m!.s2� � b�:u�3); $IO, ]G ���$�'IwEu*�N8*�NA��Nd��U�RW�KT+0)�E%��?�0, ) $1>(M�6 hat<H0�sQ*�;�vau$ �q i}{3�> �.� �i�xi�|q( \xi+|^2�-g�',0��D �M�' �� (5.�qጹ�OI���+ �yA ��s!�4�{  9�('5)Io�,�/��ۑera(!�1)�(I �h�=Y[Ek-�)� !A�NV�deѰpr~͡�aJ&}�+of .q3.1��s0 *for� o4l���d, v�3}w��� :�� �_ � �Z.�E B�J�^x%�=!�xi'q2�^<`A(.AM� �X]�162 xA�!�F�A� �|^24$�'lrxi'�:'Q� (5�ei!�o �*�4O#seBS!�havCA�4�B!�*� rD�zc3 � P�2*���� am�ll�>U;i�=�;lfV.e�:�M�I�K�B�r�z� �b B��q7(�F\8:7 e08rG}K"�U��qb1.0@X1�f��2�1w�2��Kߓ�?Z�/H�GP2�mG"hG)')-G �D}" zn!5boet�k��"�Kba��$�MT ���*.�X�R"�a��u�a4�Vo Ada�2�A�l�n�X% �J $$ r"< $k-l/"xi' n �s���6b�͏ ��f��� F� �I��=o� (5$'&eNd�!1g@�g�/�Q�2�B!T'2Q'k1Rٯ�ŎXF5�)!V'9W{5<7�7%$�02{�-|!� 6}A�xi�, &g BnE�e 9�k(a� !2).�.< ��3�&� �Ts�rg ��%�a6�L�'�H�us:#���&M�F, n~�,k�,��Ex)=l)>�1J�g .'�c ='� T�� [�����B�X C&�y)�O���� ^'�t�6vE�:|2�'|�FM'611_a����c��xi� �G� )"� !!7�2� m��Vn�� � M.n\� 4} |5�5�.*�qD b��p"x.� 5��M�a4 $cr22}b�M  is"� �&�M$ *�sa�1 ���63bwM�3`: Let �^S2UN>q6p ��7�?S�� ��<�Q "_�� �+u_���t+":j5A�F����r+ 5�AI+:!I�F_2dT&3M)q/6�7"S�h6�</]� \leftp[ \bar q_\eta(\tilde\xi,0) q( -$ q  3-\right]+(frac{1}{16}C e6A( \int^\xi_{ xY}d\xi'||@',0)|^2,$$ $$F_2(�, , t) = q4} \left� xi(00)q eta)�ba�6 _ 3$b�0, %8)54 �eta�eta} d'| 0 eta'��L. \eqno (5.8)$$ Furthermore, $\hat S$ satisfies the boundary conditions $$ \h-)�-pi5, \quad& �.' ) � (5.9��\paragraph{Proof} The analogue of equation (3.12) is now� psi_1 = -�!uEi1 )}{2}}{k} +%� + }{8}=_01SL%R}{k^25OI ( >13})�5k ,arrow \infty-!�10!Eq�(1) yields $-�2sHinta dke^{ik\xi} \P!(0,0,t,kE� halfl6*�o E�)�A� e^{-K'}A�=�.:0%rE2-�-� ��A}�  )-[ �(1�)�\%�1u)%�)F] -A ,` dk+9,�M|a�since $F� $ isEwlytic for $\Im k <0$. Takinge @Fourier transform6�(5.1) and us2estimate-� we find Y�T5.7). In this respect)note t!wifde (e bracket i6e rhs of2U2) by $AEC%�\xi)$,� 5contribueaofX term involving $\gamma%!0given by $$-i)}dlUl )(k-l,t)i�(lEcEbEa%�1}{8\pi}: C dkQ�a hat\xi �'��Q� -iy)��+ o ���A~��in]xi'~i\delta (k \xi-!P-:))��M�e�j.y\th�x ?�b e�MA� wherA���{1}!U= eI8l)$. Similarly%�:� th>� $ �B��321�!1�|-�o  dɡA^ d�!��k������ �})�+ :|^2��?+%[ x2� < ��5��&xi + I%#A�E= ���,0)A�2� f .�b- ) ߡO�V��7!�.!%E3 � = b����9�^{E:�#�,!�5y6�!`9 |^^� .$$ �rea�$integra�3(is depicted��8Figure 5.1a. M�5chang�� \begin{f* }[h]center}Lminipage}[b]{6cm} \ #hline {\epsfbox{5.1.eps}} " {\bf�} \endV  Q �, variables $Ax=!R!Q+ )1 \xi$> chec�a�%J af-+ :+ mapped to%V>b. Thus'relevan��%xl become" i�-F�U2�� (I8 !� A�iiA p )EGA�-e�����E((Also regard�� last�T2� �(we��tI/its�d �d�4$���y�^�e a� #� �{u*q�0�[ �xi,t�CA��order�!�.� ��5�c.s�ges��2*� $, see .(8).q"flush%�0} \textbf{QEDQ� \seca�0{Discussion} ne vdecade�siderA�L progress has been m$o$ understan%�of"8 -valu>blemsL -bl!�na�ar evoly PDEsX\\emph{one} spatial dimen�D. For example, two�!Zartica��is = <issuea��(cerned withe ` development [9],[10]. He 2}N> !\=eta>.y e�Er[4], raS!�nq#I$e explicitU �a/1��Ay6eigeni���they �� usJ 0 a certain co�ten��rel� (of coursAe deriv o h +is ba�v-�^� \s�"l). \men [11]�m���e6=- Eya"y�mn�?�:l"V  A�mu � 6so�j�#erm_�E��4Riemann-HilberA� (RH)��ą�ch ha� bU�in sequ����552)above�RHV wacombi��4�'�$q$e�exp��Q�a �hle} RH��<@ isn�d�"$distinctivg,d very usefu� feat� of�A�0jump matricesi�)F�=�6� .E�s�[A�a��-%-Y4]A�par��i�T!)�4 �dv� * �� [Propos��1.1 re!<,s open. Fur�Dm�]�!AssociaNglobal�摛(characteris� g_1$�R$f_1$ .�$g_0,f_0 q_0$, al� mai�  thebiblio�y}{99}ib��41]{1} A. Daveyu4K. Stewartson,�c. R. S0London Ser. A�� 8338}, 101 (1974�Td82]{2} D.J. Benn gGlRoskes, Stud. Appl. Math. [4Z377Z692Z$3]{3} F. Cr ero,���0WA� is Iybility}k�V.E. Zakharov ed, Springer-Verlag 1992.=&4]uA.S� kalTd P.M. Santini, Dromio�nd a " 6� U�%p-9i 1u�, PhysicFD9(4}, 99--130! 902 P5]{5} M. Boiti, J. Le!�L!Prtina%�0F. Pempinelli!l,tt. An4132}, 432--439p8� 5�6]{6}fHietar�=} ScatA� ng},A<Pika�d P!5Xbatier, eds, New York--I^, A�mic P�:, 2001a�QR 7]{7A�1�, Commun�A; �QA230A�0--39 (2002).N 8]{86NLA.R. Its, L.Y. Sung,�R� z �-! (preAUt2j 9]{9jh Boutet de Monvel, V. KotlyA�, Gener��$ Asympto�SolitAiŸe NLS�6B� Data� t��JMP iJ2�10]{10} 2��x� s, 9� A�KdVV��is^X�O�P9�I�V"bs � .�inm�Pr�zDIII Potsdam-V Kieve�rn%'a�$Workshop},}� , D. KaupC.Anel%q�I� Be�:>,B12]{12!��Y7SIAM a�� Anal��27}, 738aW966�3]{13:W unifi& "�metho�� Azar%�] Y��V�,F�53a241��97)}�14]{14.�q2Ui-da�� �a�� ocal"� � 5 s��Noj Sci=;��10�4%A2%AendB� e docu } �\class{�@cle} \usepackage{�ig} \oddS0margin 0.0in Wp  -0.4A��width 6 he�  9.1in�}} larg~� !�Lskip 0.26in \titleJ$ \vspace*{s}b�" LARGE} BAn �-Free�`roachL 9b�Control: Coarse Feedback Linearizec W~ Pole-Plac^ � t �{0.20in � %��2� �Con�Ttinos I. Siettos \foot?T{\it Currently: School� >a'atematicI��ic�j� al TechniA�$UniversityBthe��Z/ ,fou Campus, PGR 157 80, Greece}}\\�1ins t De� Aw��Ch��$al Engineeoa�� ton �, PX, NJ 08544\\ Electronic� lqa_T: ksiet@mail.ntua.gr\\AI/Y.EPIoannis G. Kevrekidis9ZAAwhom cor�o ce� (uld be dire6N���2$ B��a���pu� �dA�>�=3=�=_�Iy%@�c!�.edu jLHNikolaos Kazantzis}/9yE 2�Z8Worcester PolytI�( Institute,!D, MA 01609-2280,fn�s@wpi� �0date{} %\make�]�4a���e�ab�ct} % We��appliceLA�5-f�c�-�AI�c�W -gra,f�_��_p�R�$�{ system�scrib[Hmicroscopic/stochas "ators. %�� J��C pole��� requirB%� a funoA~�*\� ma� (6�) � model��absv� such losed-y .,aort,!m ropr@ly �iz! ursl=1ion=desig� [� � ��r�" ultsG!�"�i on d_d}/ qu� tie�"%6�! l�U1D�(l$ly unavailO)N_!'Our illuA��:� a kine!�$Monte Carl�al1�of a s6 heteroge� cata($reascheme.��HY���%ͽa(new�"�I�Ldx�A�da� al preEnsit>!)��_olM8��-2�'� ably accu� IB`m dynam!� EzeTyp�Et  atl �E�"�Q� s (o[(��,2( algebraic,  ial 6.possi�~gro.m)ASa�E�t�"LfrŨ nserHlaws (e.g. mass, mo!|umE�X ,gy balances)17through!��viv&" P; tonian�es�Din fluid flow, or u-IY M�s i� �Aq!�!�E�s);-� id�f�a may �pl  r��b>_ and/or�ing s!8��-�!S Manysl-world �tRcS  e&�%�$!~ &��~ -due��ir ��/.�n�,� ���#lexity- *lo ofI� good!3,>?.�J���;ead+' u�ly!*pX�"�Np�%!`beqcle�a m!E�finer}AGr�tai�l�:e5�ru� Q  $qY molecularq�s,N�(, Markov-ch� or hybrid���Wh(i�%d�,A�vA@ų�OinuA� lgorithms�not� used� ly�M�s �"�!�Lroller��!i BridO!�s ald8 enormous gap b�.� ʼnime sca!?��Q"-�al/��rc i�cr)� Bhe2 ones!�wh� we ww4(�.� �"behavior�bgr�challe�$a��0AEo"� !OveDe p/#few year$�dem� ��U"a&�-7  ap� ( d�xM !@steppers) [Theodo�0ulos et al., �;�%eev &� P3;"Z C3b;Z0-�establis� link1��#�alE,Ix&%@]/ �<*�!WTM�a�h� -assisM=�aleology�spired � b�,QR:w!�� E� iter�P ���e�es.�-�% cod[ o� q 9T �� oule�! <asa�ɥa� Jed a��a , �# g, ``cjn��al".Aasa@i[ =�e3 bL"q�i�e�$on-% 6GE [^7 ��M)s D $ residuals���'�m,slow Jacobia�&vs, Hess tcN ThesO$�9@ � peat a�g .g ��s to a�x�g ����}e�-e��$routi(!��is tri =8 input-output b��boxI�e k# ssumɢ%j at d� Z)� ,.�Q� � A� ��!�ex����nfew.3M  obV M) , yeE�y  *� �ed6 �>1�Q� "�))O&� a�!�� ��-�]�q�/� @ surface coverageM?zeroth.V&!� SE,on a lattice��)#W4 ). a� work aim�v�$A a-N�� a" regpo�nthesis� �ak 0%5-n-loopu��� !��-p� objF(v�re si&NF tM AO �E/�!ŢE�E�er ��m� e ^��K6� ��\".Ti�U/��E-m51 ai��liy }, circum �%e"X e�Q O�&ct#��M�!vpo �!�b �忩��A��#�� ᫉� �#Ʋ>n� 5,5,of $NO$ oxid�by $H_2$A$Pt(Rh$Us)�Q�pa�( rgan� a�llows&~* 2G brieflya6�*!2�.�  .�an'r�&�$ no���u �aU� long�m &M�"�"@s encou�ed� !�e� )stageQ(� 3 wer cS#l� view a re�lyJ�a%e i:f�u�^�nde � }. H(M� aj, effi�ly ��co"#� ri $&�7= 94�oexact�w:j�ach2$4� �rp�a� out~dd,all�0 n����$frame�ms }�. S!( on 5Q�%�*Q E��ŝ�A�` q�t�2q�5, �*�9som�x ncluW-("rk-Qr6�7", {Fu"��Z7of=h� s\P�.to me�  seE�����QsO ]|,)�ssAL� !�r�es�to�( pif�,.����U,-q.�e�-si�.i��"he � lexa.M a>tZ1sha�]a�} �-�\ %an�*8 popu�� �s�yI�m A�a��X �, �;intuiE(!2al [Chen284]!"z�&mf, deca�>� vari{ z �na�al�ady��tep&s;� -�=��l�%to high9�g-$ ��eM<NaI� Fine-tunm�)w� .| !`M|>% p�$N c�bi�Ooptimiete�qu� heur� ZE$-and-error!t�esFxr&�6�->r�! a re�/2���subw*ts!Mfm�I%xa re��a�0o,,�/ �lyAi�K!�A8unaccep�e1��, eve� Ew c�only mil*��A�&1V9e��/�(&�,��capA� of"� �.�)h��vA9�1{*3 hE�bei!'bcinga< ]/Śss-���az){2���ae��GsmoA anner7.:H urb!_s;�;! X P)q� is u�bl 35rimXQ�" + its si�!�I-�e�%�1bod�Fl��}0(ɪ-E� u!K p�>�s emerg�/�= geomew=�ory�A�b3-i�act�/�(I/O)9�I�m�,*;!i��E!�&fst��Uinduce I/O&���MZ-te7 ,a�%l '��toW2 a%�pecH ���!�leF>V 5�\E � gt�� �i��pla�E�.W!��"6��Eat�i�� A��v�5s�risj!�� � �\ � Rmum-phasq+$s [Isidori��99��R��s!U����qk$, however,c u�st���/foF�[$2� k:=" atomU .;"(``&�")I�"K"��.�"� 2*A.%�6 ��E ^zu�a�E� -freTAper��!oho} % N"eD�:rM� ssig� .�*>27.j =re I/O .@A�)jka�5)/on:e;$���� F��W["T%�1],}inv�"g�9 oM "!F��.��M� as"�1��tw��yQ6ZG,a meet�1�U�B$�6$&� �T�bf A&����out beg limi��C>%"J���ss��$ "�"&�'alw/]nar�-2K7m<3i�>%� �"ex�:��pd udy�Mu8�d��%a�� discrete-�*� (��") �s�X : \b�&�X} x(k+1)=\Phi(x(k),u(k)�?-,'% 8> $�FH N^{+}=\{0,1,...\}$�-f6�index, $Y&F R^{n-vec�of�)�"�, $� \in R$��e mani�!�&1E$ �,u)$ b0�' s a p�& de���  $�Cmes R$�5In�.4 ��9is6>?nC will���VE� A��aid��{��JvB,�los{  <� �u��K� $x^{0}=0%�A�qu  8�.")�(1), P:6 $u T:-W0,0)=0) � non-9�l [-sy$(�,E) \neq B� "XQ,���T ���: &L{x}=x- N$\hat{u}=u-X$)}map!  )% new*+ mk!mLet $F$!�!I+Lrix!.Me5 �W $x=0$�8displaystyle{F=�De7�% A�}x}%}�6nd $G$E%I�!d2NGvN uN"D�Io�1�����6<=%{=:c.A&\I:}�3$nq n$-"JQ${\cal{C}}=�E[\X;Hx{G|FG|...|F^{n-1}GKN]A(�kh� ank $nEg� m�,� �:�::ofA� gM%�a����� "} �29].� �@��,!�� eC,Aa�r nd� �� bas^Me $z=T(x)�sough�"�n� : $u=O(x,v)$ (��$va�e n exter&��Z),���IxMQb� Ep} v4�m `Aar J0z�(Az(k)+bv(k)>M (A,b�9( a Brunowsk${ |Df i��[h 1h�BA��I=L2darF� �� *� are� - $rbitrarily�U9 � p quivalen�,y�-"k�}.h )ZM�"2i(A)9-��6 $Ki�al(�Rs�(��tɍ�� : $v=-Kz$��9f�"@ f��L{A}!�=(A-bK) B�4$ ,='Q�|r-'sD�< tic �JNB c�/*� !5 A�"i it w���!��� ale� �).Y %gn� J Q�)�NX A� +b� ,B�!$A,b$ER1�Y�%3.�d-Is�eA�ia!�d� D. Luenb�r763)�is � \ach ser�!�be �u ��&��"�.� �'�U�in *� �(1]� �F�*A n(  . Acc�g!���ide�!e'I �T63]�in ` R �J_ �3a1�z}x$ coup�+)�8:`�dmhumhs ��� �F!��*�. �w>[qg�!U.ZI�B_Iwx�7car� <}k�[}r)����5a���0�beph�)�%�Cl��A?o a(d"u�% �s unkncD=� )֍*$T$� sYyJNTA-��T=TbKT>L % IfJ� n-AZ(lrtible),����ww� *�Gra*� � W=T^{-1}$]is"�Y�CR11J� AW-W � =bK.J�t�)6�*��1�,�%D�D$A"$]Uhav�7sj�aEZtraA�eDD Ax� (8) adma�<24E$W$��\ (4; Gantmach 1960_Fur&HC%Uti&�A�"W4Xnsu�#iff #�&XM� � Q1 $(K,-V�n*�(%�j��AsE� F�%bA�< h.)%�le �O �9N (7)%ma  ��&�# с��)�2a^� al"=s $x$F"�� =-KT��>O[�.cj��I�-TR\% S�: �E�64E�"Q�CsF,�� can "Y inferA  B��&CIo" ���\(7N._(vD.�r&{SɅStep �1= Mot�KJ�'���J` le< J] :�&!��IAenhR�on^H�'g��i . On�ekd6��k2%bf, $z=S� �L�h �h&�fk+=-cz=-cD+ $c�an � 5 � t �]| (a� pa@&t"�S>&)IDI��?.� $z$-j.� J��Ip�.[W (11�,$8�  ���&�� !�8 �R $A$::&�5n  �-�b�.�ref"�H��u�;�G&�!judiciouZ,se�>e�0 favo� �Bap! �: &^ed i�'8sp�7�/YE��<se1�*��embod�F\F ���.2r'al��s (NFEsI/�R��\N�]�Ib�p $E���$narray} S([(x,I�))&=&A-$ \nonumberk>S(00Ui@%!�:ompanp�0��~� me�+ref!�&  fa�K��?t"�2usD6Et` d�A��<D-b�FUVu�"��m�Q� �H� Y��9Qe !� (12)�ӁR_�!�r�'� y3�ROPAl#i&m�($k_{i}, (i=W ,n)$�y�q@ lie �Midi! unit.��!#!�l) (�!ty.� kVJf-f��0B.ǁ�}�0a $\sigma(A), F�cdN w:B�+v�,�dZ O \cap F)�[ emptyset$A*B�V:��2b!U.�)bM4} p 28<\lambda_{j}, (j5� MF "�(nya�E\!�typN�(\prod_{i=1}%�^{mA=r>u $���o.l$@$'I�neg��� eger/>atj �+�!�N�h �} \suS � }>�N&�E]!1�@ aBE�E(c,A)�chosen�h~!.�h3 x $O.rO=6`c\cr >cAR.RZcA���: �$$(O)=n$ (O�4�5g}{ -yeLemma:}.6�91]�2�aR� (1), l�5� .�0I-V hold true �,!r��l�-:� ��#�(! &� �w "� � n�H borh�%Lz �}a�WA�/e a�7��o�ma"/ �\ h.�� i c.wis)J; a mor���=Jon$ a�f�+6 )t��[R� 1}:��``a[reson�)"9��l3�l(14� ^;�}7eP+a�� �$l power-se�Bɞ!5����9�J hgX.� qSA$���Hi�!��Gp��4ey"M@�uni��v[ �  :�U!\@f ��!�VX&u�I�:rgs, A|t�/�#5'���St�Ys*F�%3;��s IBVwne�']+V$sufficient*�$geU�i�M�s>.2}:I\�W!t�iT`!V aseK� ,u)=Fx+Gu��7 $F,G�/� -��� ofuF*+2gA- i�?s !�A���y�0Um�)$w=� S}}xՂ$�S&tN�RquZ�Jv`F-A vGc"� �% Q;coinciX=EU(7)A�2Q.$sis. Pleasm6c%at&� }]x*�%ab�Y)�".[ (16F�!�J0 $�$ 6E �u�e�%&�AH>ka"�$ -�'��2)"�!R�e�E(*�`"�Y"�  (sS� �*0:��6g�*� "�):�:�A!266f�JD��# :�#\-L%q�l �2��>Yw��)^ 49� ��� ofM<� %snde1/�NN 2� m�$s GF&��9ns� =1� &=&S %+1))=f%=K.b&=x!d�u�X �C 3}: &�(� 1��� ��s aR��q�-�uP�F��Sn�a�"��"�.)1xJ��(F-��)N�Us���^� 21)E� written� �n�5o�Z�=�h{A%95�1^F*�5at�/��:Wɶ��cu0�*/.TM� (22)� (�a,{a$�Ris&a%�"3:� hfauD. &5&Q���f*�- (10)�p���Xs>�4! K[k��j!⵺r1�"ed in�'n x/comM\�% (�nd��"(�V8( a�]ar 81�F.KNyF�"?("�V�ceV�� R�-�4 [Guckenheimer�� HolmA 1983#n�c"�#o%�=B!q�=�.� ��t I)fold/�@B%2)>=! ��2-w�> 5M n-p`L� �m a��+E�g*v/o avoi) a=�E�"NRi�6] &�#iq"�,&�h an aN$GIa�>��&G-��Lt0bL0�^g�u�4-Y�)_{0�-B�%`.�%�#99; G>�%kF�%<2�%yrR�%�[It�;b��!z�&,��$&"&�, does�@ �kzf]"�4M� o�!K�'.�-s�#��rV6? ck�^YN odel�ich��!QN�' ��-�&� �+EZE[a�ѱ-�0e��Sal&�?!O"�2�a�let�f�a��d�Pcy,E�):Ap employ a.�#�pc�Q/M4d!����� �� ,-��8p�l.�*a�KllR�"mx��+ Tayl�E��)�  coe`�Wsame �?fmth " NFB��:@A�;!#m@�BurEP!�/�3�D a�Acb �$N$-th � � >��, gH7�r) up�3( � $N-1� 2"Q sB?5<�!re �mul�.niA�ton0 %�ensorlRno�#�a)�e�j)pFb+� ;e+as $a�^{j�,�%��uN $i$/er%�c"+Y��{A�su�M 8j�21 colum1 a�rix�tb �)(PoR=�UA $\mu%�aj�g E�_{\mu}(r�tM�2���.@0�6C :(.`=�- �xd aX�W.� 4 f �^{i}&=&JU. }*[.!�. 2� KjFL^xdyVPrg�x� _ ^_kN`3�{h�`2okoend{e5 etc.�� (i,j,k,..$=$5$ c��:,U $u�� g)�A:0V�u1�)GO!G d)+ ,sum\" Om�re N upIand�L�Q�^ � �2J�0pgU� e2� ��$l6� $S_{l}�]c �|�������"���a �KiV te�� љnuvur1}{1 !}^{i_{1}}ah +i�1}{2 6$ i_{2) 22}}+...+6�&+m� 1}{NNG...i_{NNO... [N [��DB$/{��)%� �&:��#��&-NT6+i-KSubX6�q�e-����\to&�ma� a Z_�x"5� .E*>�k�$.�tR?ma�;"�PB�J� L N} 0uxq mA 2 ...\l L} \atop *+mA E m_{L}=NQb jJ ...j}(f1}}_{ L L}}-\piJ(*)=aaX^��S�O tIgQE�'��Npi�l}� L}}=)P%#L} -$nf)$n� %1$n_{P} )$*+%%$=%*}�j�}^{(} c^{k�k 2!$3B�$��8,��J'l.�"�Eoe� ��� symbo�� (26) (A��@ 7)) sugge�^:� ̀�z*�So"W $66�gN!}1}!...% !}}$&�Hgq�s�&�@*�L}�=N)� More!x, eOc7 at� �\(26,27)��H:[/`5� 8,ic6 �Ѵ.H ��w �OY�}$� ( $N \geq 2$Im =1$,] ��q!AAD(.�>�8z oJ (or "�6�\1ach����K"5M� �&� ��_n�A�puter�?im�qE�EH� b�'d�'�/}!W�(utoa�c fash�EU�0a_;bEa�ic softw� �h"AMAPLE�&�=r ha�Z�*P�c} {3*%3pc3�[�1ɭ"�!,�p  u -�5g�"IPA�a"%J!y7`icult!z e i�<�* (��r e 8lqX �")�Wenow�kumm;��U� �*�b�?K8�ywe doW/ a ``"�W"Q)X{, }��{  1S$x_{0}0>U$, u_0  $ �7ime $t_2� = kT�K3 6Taf +a�68 horizon T (i.e� �=rD $x(Z+1 ��7 T) \(v d $T(x_0,u_0)�"�(�}u�ct!legacy"f�_W;.�4�i"T28;��7 per"�� lift, ruA@d��Ts"R+�TbenXA'i+Kr�L"[Ma.O]6" 2; G�8e�9.2c] al.+3,>b]b��!F�� �w�8�As��� "S�R D"E"�_ (3��"�(, "�T%&W�J�) [�k�3a�,.$4a, Armaou62004b5 ]��]S �"� ers (Fi��1)��A�tize���y ftA�*�@+,�N[^&�g�[�� (&�Z @th-���-�*�Z����Zp� ��more)�"�e�&�hb��s;�0� [!m�^4&XF.�ypEF�m�L>ly�'(p �) short) .�Ca��2, ({\i/�.![�N}= ��&i���9�M>�!���X .��K&�[.�O.��pg ( �HS.)*�\(LM5>5.x�".<�5t�c"� ng a�;�*L5theor�hc'w>�W (modu�h�&off� iD(\mu M = I$.!��!�M��i�%�� :-j�-� �execu�/��-�c``"�i" dG�kof�� r�p-hxS�,!�a3�E�_ " Ja�_Rwj���r!_(meterhU]�w=R � fixe in�/n( ir.!�.�!--�E�,B��d*� 84"Hor& � �ler"�Ke{<�*t�2Z-F(�~� ��"1�>U�3 taskA*our�G,�")%G.�� %.V%���)h*a�ie7$a��ɹ$p��}%�� 2�  �"e [ ; h&�.$h� ^{m&(p) .�21m A��mAa 2-di8�t*� yh"s ,S(x_1,x_2;h)"*�0#*&]S_16�p;(1x_1+a_2x_26�a_3x_1^.< !}a_4x_2^2+a_5x=2�,O(p+1)\\ S_2kb0,..kb.1+bJkbRkbkbJk�^�$h=[a_1,a_2�$,a_p,b_1,b b_pB�F � �~Uw" g  la! A�(17��C2val*�6u�=.9A)EY !�u��@�� *g"�#� V[Kelley 99], or6fnan unD$n�(Q2lZ� E|he Broyd� Flet�<Goldfar� han��BFGS)��>� e6oQ��~*6GJ�=�^5-mH$h$�7ũ�sx7 squa�� [s�� /r7 �[i�hnh[�(a�N�min_{h} ���2� N} \�llel G�(h)� rB�E�� �fZs $H72�L as: �(cG5-�) );h)-7 � ۏfo� c!15ed%h.$� \bul����@"D$Euclidean �lA�=m!bu�Zrm7��>�;9y0*�� &�=.]coY  (e.g.t M+$G_i$)�&�K�l.�e(�go� ).T�~ eachI���i\l%3ō.116%a��$�$2>Q�X�@F "o<�8@2�E�%U> in�yB map:�,w(zIH�\e1�9�aap6�}�N(Az1�/[, -cz:�w�9��n�Uux�=SP)(z�� AIOq#*x:a�sׅuA�y� p� (*��-! 2) (I��Ix?�l��!�"�B�w:$M�n� ^\�XQ ive �E�-�� l:T&�-]wAi�"dB�08%Q � "w!M �&�c,*�F�!�ݼ B� a� �2� we �d $A $ ()�Ѿ)$�0^b9J� w��o�ek!nib"!�-t$h^{'}��ed DM (w.r.t \�  z��t"� say � 'n��bs*� ���0,z#��'0(6�/�/P��F7"=a��")-a�_T(,-cz_i); � $, $�? 1b?��UpoA���g�4!���%�C(�:�iO b+)BYya_l�=2rz��onMs0 ��lynN& �~��w`&c�b`�>�' �" ��Bq�a Ʉ;�@s�thoa�a�" U4Rw��4Ni�#At m�b"�a��s (dic/ �_0 uWa GMRES�.tocol� Gworth�a�� �E��["�+G&$A zed � �ͦ� Kfs�t?K�O-zM{7Inow *� , atV^��,�ke<ax)��7 2im���benefi/���"M�of xb�)"�tefe [Wington"�1985; U *��F��SI.&iC?`S�?�EE{��D��_�BVe�()b�{�_i_�?��ifi� ��isM�' 5�m re=bb�m� �U b2jq m� fء\��m��W� by2{i2} �Pdx}{dt}=\alpha (1-x)-y� x-u ^2 xX LG"YLY�G A�c�agJadsorVY$NO k+rat�]� �0NO 4-�JcorpoA�� gas ph!�S �(4I)s &e��e%�t�0: deso gi><&i� �E+:;z 3* our  ,i/��var&ii�n�a ;/�q�./��9�b] take��o��EuS}Ac��inu�a�� �e5�*4�1+TL}5),u�11���"�$1� �$. �,re&�#fo=8)� = 1, )� = 0.0�+6, exhibiwcc�Lic!�\Qs ( 40u\simeq 3.96$�26w :bifur�= diagɃ���%^Ato!h&�BdbGq��:\1��Py,JC�t�,~2� open�7}g4!R<� (�0=0.5559,u_0=4�We $T=0.��Q�po�ggq�;�� n�l*�G �[APa.h0.1459i�ّ�5�a16.��A Q�0.1\0z5 &��M&�/S&���ݡ�&�.oi�qaE�� �  i��per� �o�~�b� bur�%*�t%���]]a�s��:&���.&H (36� �c'$Gillespie �S%;O A"% (SSA51�767  G"t/va~�khe�s��A?�$t ]w]Ih� ��6E���a�L� �NbO�ingj" stem���  {&�A&� sitW say $N_{s�%a�wW�� shal @;%3s 6run}$)iH�IA�u2<���;ngB@=�=100^2 ' c$,�Q!9�A-A�. �U��J^�5.���ga��de �2"� nM�g!�;GY.T}� �4� : "e (�FX��Zi�T dou�y�A. A&-)E_n*i"_�2� wrap�  a �'s�� a&K \KMC%I �1' *N`)-(�3q "q�u��e�r7k&� branchA��UAq�%$ pseudo-ar}ngt�t~E|$KJ9m��!�� .�!d]^2U^Q^L`% %HdY"�*�a�-����r/no4�N]~�[0/&%" see ��"X��!3��Au{!TN�:�A!6� ��"GI6a }A%���ZA� $u=4? y*qui��"�.:A4��t�j"k-/an/1q"={�)d�n ��;� mikE-� (30): BFGSm7�To&,(X �3Qk deviI}� Ƅf��4x'=x-�� $u'Bb_��w��$A$�&E=�ar�n?0.8. ���d9DkV�W�N��eX'��X A$d�n �ay��5A�' !�S0[FB ra<� &�$u���F�^ _1x+0.5 _2x^��.�/�Y�H;0(� )K�t.�����<~n>�1� A�U&5!����R� _i�Kc��b�L| �/4";06b2p8NFE��)!�^6Q��72�}ͪ-box">��Fach, ):a!�^��pG(#F.31B quasi-New�� E�ae� searPL��� uo��te�# a�as $D�z [-0.1 \hs�{�� 0.1])�<%E% 25!�A����+�"!�In��3a�ploa���/Em��M"�i��J� ���NFE�7� !bis �Nr� oaA2y(.�ly%;h�<��?/ A54��B Dx Z)��y'4.φ�H�S ul�>%%�mWed �R5opS0 $z(k + 1) =S��8 ``8=0.8 S(k)$ (dot:��s)��!�b8�%�o"" �)\)yb A�j=��ro�a0 >� (��da;)&- 5� w'�B%D}�1-i� 6�m>Y� * KF� �� ��ng)h -L��L�9 Ns�re 9A �" x���)>= :�6��O&] � � � Bb B}�:�a�u ��<:�BF�O�;oQ�t" nfir  ~'r  x �"X6G &�M*l&&���&��sucwLfu�B-Ka}�p!�}/�!C"�> �d"�ConZOt�G~W�t*r�howFp)�w�2�*,i^�H � �alydi2�a 1]�{Q��1D)�s,� per �j� by n�h�lya�a\RVl�Ni.�eh��a.�*4!~2'�E�*$�>��!�A�ted~!�o\ v.�in]er.�5� soph ccUN)i&� �o�RI�to�Bx.� ���=J8I( -�A��oj PaE e�2I�(a�Srep�J|)�� u FT3l`t�i��w�Q�r�! we k�pw ``�5"2̌&�/OM+E �$ �H%12?�1V����YM��is, ei�5dat~���[Coifm�d�G4]w. D&d�Rsu��������ursuingR *��3R��\C�{ara} :(o, E.,��ta, U.eT Moog, C. H. [1996] ``6�؁ss(�u)?s", � J. h� O�&.?"bf 34k�999��e�m�@4 , A."/4�I �&t5, G. [\4a�Tim"���i/e3� �0i"�3� U2X0��ܗ� Int.ʣRobust� N"! � �1�89-1116�)��F�@ 6ړ, C ��6� gapt��j:&� q g H �*3� d�x /�@� �,'')�LComp. \& Chem. Eng.}!�bS��U1� cal}�+Nq!�,aco, S)� Norm42Cyrot��AC9�O�^ !��� ��-� Se�s1r L��-x36} 6.scar�OJ.t81c[``&��C#H e MaYld%�ry"}, :�&��=� che}!/n! T m4mi) � [%�D��"},O$t, Rinehar�7WZ&>N�.qoif} �C, Laf)��., Leea1 B!�@aggioni, M., Nadl�B., Warn F)�Z�Or!�eB] ``G"�_us�'Ca tool/~mo���;��A��(� ��(� ", P�I, Dif V MapsAditm<c.Natl.�.��}�mSd=gant}2HjF.![OjI�`` aVr�M*%ces!u(Chelsea Pub͖m A�an}1FugeAQ��%�W�'evr@����nd"��,M�!U2A�^��Pt/B*.!Gvia.[ W ors:ɥ-Galerk�:%m$�.�m.j�a�% 0 26}, 941-963.FJ��l,A�J2��d�Zag6�Ei݅� Proj�ng�$S�$qT: Sind ly Pertur�"i��L< C-�",�qu-��( SIADS, Mayx4;� " as Pޛ/0405074P arXiv.orgp��]gil1}&���i�7��A^'� 9.g^a�� &�t���"�9co�h F�-� J.%�ut.����,22}, 403-434.�il2Z�7Ad Exac�<>�m�>� re3 on��/!HMFA?8bf 81}, 2340-232hgri} G�Q J. W�%I"S@��С�WB.in:E� LecňLX��hE�InG� S�]ces},"��� lag,̫ , Germany.F uk} .�Ts�A�H�TP �3�K��OscilAon]�ynk�2�}��dV~FE&���[isi} "��A��<h`�1mP����jac1} Ja&PSBd8EJƾ�r�9A�4.�kaz} *%PN�1A�AN�*Xto*�6R"Js2� �-"�q�->5N.a 43},6�ku4r}() r, H�u�i�Nu �.7An ai*� s":%S� P D Rabinowitz (Ed.),�*�]xŋry, (>N�N�� )} 359-38.akel �y��T.,�]xI" �M�~�!� �,��M/on Frmere�� ed�#tE�PA}�N�VqQiao, L�� A9> -Krylov SͿr�  ��Q-� Cm�F��C43fCkevr1}:�G.���C�, Hyman�Z� .�P. .$Runborg, O� :=Ki 3�6 � "�N� � U :���.� ;orE1�� -�v<9 ommX��n 4� 715-762; "�X��6"�G*ش s/02090432�2�vr2>_%2G9`eA Humma~� B+:�)er&<�"� R�mplex, .I:�AIChE J�050}, 1346-135.? lee}� H �Arapo�h�?A �Marcud�.W a`�tO �mM�6�:���-�45W78.� lin} Lin,ᧁ� (YA�I��95!CMa�z��Hnom+ �Y&9��� rl25},3.%lu!T"�z� !�1z ``Ob�@A�t� tate!53"��U IEEE T!. M�e. \�1� 8},72�uen2}:�}9.� by�� SV�$}, Wi�:�~]��� ev} oFX � roudWDI4.@IA\ ��.Y ��)Y�u�.y�:Nd�u��   M]116a 0083-1009.�nam} ���198�b�Y0.F�nc�I�6e��.�A7KH nt5�X11.V)�1}�GI��F1u�G �nVs3c.�*.` �ce ���:yiF�1w�it\>o49!o922-1926]:�2:���raham��B�, A<3ba�C� Brown۪� �1 N�q Liq� Crystals:.i, � �Kt�{���S&� �io�Qh5EkicsUm8�$0149-10157:3>�_�<,-.� �.s�V<!�ape-"l �� ach!����.� �� Chao�?207-220:�4>�,F�P&M L 4%�&� "� 6�w ݵ P"�&inxStep:.AN^Aach� OCe b 2�}(1�or�^tl �m_�0Society Europ'!Ay�Studie� � ce�n,t Olympia, G��(, 22-26 Jul.� �GdBr:�,O n, Yo !�y; I.G�t0}7a t�sd2E"b��.A=ry&`.A2Pr��F{ 097}, 9840-984.�pope} S� 97] ``!m /#"�^&(U �7�stry ��<�itu} a�t"�" #Com �elMod߸g} �1} 41-2�bo��}��6� � Yu,JI�Yo��D.D �^5�8Acceler�2� Fl��` ��6 AIAA�YM67-uI>E1ne��h�%�$C�onsA " &�35k�.41}:˸�q"�B.=!za��4��zc�.g2Bf�n (a) ��.���{kMC!,&9$�j��]�, (b) b�u"#5 Q �9� F)*�'; \%k �#rJon�a`l�%.H�s��b'#&o��&�"u�6^B!�"'�F,�j;&a�#�Cn�ReD&��i$� blac>)10K6/2�&b�j�4jA� aR$3'")',� �VA&�'�&"�,.���nd Y+)$�@ d�� �E �M:� (-�A s)�$n�QgA���<'�`�)b zj���6)�"#- '��$Q�.E�fo2o#o �o.�, (c) JoQ��-���� � (l�@J*-0.2)o� "��run �:�q3"�>X3�3Y3^Nm3�&��A��I��Ófj*}[hB� ��a�m5�\psfig (= /13H�, ��$=19cm}} \c��{S��v�:��ť[Q�N[����! | ʁ\clear���F��i2 � �8�-<��a\��5�k.yB./n��?8.sA�q8v!�� �X ��RB-!b�.�5�B� ?��)�3���vd e��v.:."�= i��4��*��Em��=B�����)s)FU�TjT5�T�5Xf`2�EB}�v`.��`N�N��R`�#orQ���.o�`J���z`>�hw7��.` 6� f`kR`&y b`�uo8$R����;M�do�t�%�  �D DRE( Aug. 18&'3 ^oN�2MarC4�CB 10��C�N�� \1��qP[reqno,draft]{amsart}2��m�3colL lor}���D�T�Todos %�UDcommand{\rem}[1]{}6 ent@ -3 mm}�O \��par{\E�\unde��e{}}\no��nt Eme: ɿN2� }[c]$�65 ��K } \rm #1 e<+}�1���$��b��{\c!B{C!#1Qne.,eu,W����� ����{F ����stM�pla�!�(rem{lemma}{$�I }[#]{)A12?co��ry'C2)&L�*&@�6+ph�%f,*�6-�Li; ,D"'�� e- CrR ne� {A�e.1the0�s�roman{ B(label {(6�N*��}{{Ührm e>H *{\d d :@D cal D>! {\GG.!GF!HH.!J>! {\N} � bb N!. *{\S.!S!:�T.!TJ!R.!RJ!Z.!Z:!{\uhat��.uBvvB�.<wB�7|}[3][{\vphantom 1}]{\lVert #2 \r _{#3}^{>c *{\bC]{\bigl; bigr~@t.@�vabs���Wt�Irve�m=�{\ang (eft\la֗ .n^\rid�b�6big.53set��th{��{6.28�vo.��}{-< .",��T�l#�{\eop}{�$\Box$!�def{\h�z vrulZf'�pt  � $depth 0pt}�t�t%O ���.s Sobolev#,bes��$q �s FG���9�vA�{A�_{2� #2}^. +}#3!N:�l}[2]A�M{L}K{#2+9� *{\h6)Hb)Lr}�!]{S,( \R}{}{n}:J {\Lo^9OmegaB0H:iHX#1�iH:i9ViC:iC�iGa�[r]{A�W$\e^{\tau A!^E�e{��ilo��aa{lA} bb{\b�� dd{�� om{\o! ss{� tt{��trr{\rho la� mbdDd{\Del/Gg{\G�� 1Om{)$ >pp"mv7�% > �,itle[Clark$- �$ �] {�#:"P:>ul"T:��"�-; �5�v4���August 4} �hanks{>S*$-:}��it{JourT7of Tur ~!��H[C. Cao]{Chongsheng�qdW�! {D2��&&�s �U.>�@ Nebraska-Lincoln# T, NE 68588-0323, USA\\ALSO}-fn$\\ FloridaK�~i al �D\\ Miami, FL 33199g� �{ccao@b�.unl.edu���[D.D.�+]{Darrylc ,#-$ { T-7pS B284�$Los Alamos�io�LabLQ�0\\"$, NM 87545�%Ϛ ImperzCollege��4, SW7 2AZ, UK �8dholm@lanl.gov �d.i H.ac.ur -E��,Titi]{EdrissL=$n&\\25 :�9S8 � Aero�C�0ine!�<=�ofl4orniaIrvd�0CA 92697-387�PC�^�a��J�*h Weiz�� W����� "PRehovot 76100, Israel5h�iMxc��ne%Y.&:@w c!�i��a"��I(. 9sjU a w��k�Ghree-2�9�|2��: fi�ed������R�A�4 \cite{CFR79}}gA�s � Eddy�!:(LES) t:y-A4v��Bt9�s�an��B �%E� �!s�G $. W��w@�V%posed�A y) xFcf�(Navier-Stok�N$eddy) visc� y. �=�N , we�Xab*4m:��4e2? ��Wor25�dissi�ve*+2s�6,Ew.v�! nayta*��i�SfA�a1Hausdorfc�me�es. Our �Mx@�r!�aq= $h� ( L/l_d \x )^3$5N`T$L:V �g��-�FJi8 $l_d()Bus�on � J�M<0q ��:!���nt)�the&O��fo�&��degree(�$dom&4Th"B�arg�s. �� semi-rig�i(!�s:Cm<�in������A�\?eneR�s�D��.eK-$\aa$M��Tusual $k^{-5/3}$ Kolmo�v�g_H wavhQ0s $k\aa \ll 1�HC3}$F� gg< .gg 1.$ �U is eAWڇ��&�e��W�k izes&)$�@j6�a[�>1' %',.����Rhey!�x� much l�Et� ]3al *)1d�!BiBbu�IZCU0!X6��Ds��a�L\q+� "KE2�� \F{S-1} %= pape� devo"fXP�a�0aa��=o�?��7a �)h'��2 uf���=W��2`` :�'' aka �%6� %�''~.�. �h>&�+(LES model o��f turbulence consisting of the ``tensor-diffusivity model'' of Leonard \cite{Le1974}, filtered by inversion of the Helmholtz operator with width $\alpha$. As pointed out in Winckelmans et al. \cite{WWVJ2001}, this m�� is generic: For all regular symmetric ��s that have a nonzero second moment, this form is found a9,e first term!!;r;Rp Q 5/ �/referred�th�m� as ``a 1%ve2�)Eh 00,'' while Win:i i�WWVii wrotei5they p�he)�N> �''e sASs. Th!!sul%P >psupport�he view e��� (or, �) v@ may well suffice� practical��m�, {\itE�0out} introduc�MaB[. Se�(\ref{Def-1}�� devo�o�4precise definiE�I6 %�> Ap0to discussionA� Iopert��of its y���}2�\ExitUnic-sec} establishe��main r9�@global (in time) �hity%T!�6�I !�at is,Cexist��(, uniquenesiI@continuous depend&�]%al data solu!3��� $3-D z%��.6� S-A} show�atb ``6��:''IP�.se a�attAPor !� give� upper b�Don!�$ Hausdorff%�f6� imen%�. This2:is%�ovem��O@as $(L/l_d)^3$ --� cube I>A�egral 14$L$ divided by.dissip��length $l_d=(\nu^3/\epsilon)^{1/4}$. Finally,> transl>(al kinetic �Dgy spectrum $E(k)$Q! Hel -filA:s�,� also%�n�siL eL%�Tto pass from $k^{-5/3} k smaller w��,numbers ($k\�k \ll 1$),D:8 larg:7 7 \gg7. IA��Wth 7ion���q6presena�0here are simi�e�(ose already}d5.`Navier--Stokes--$\aa$ (NS �� {\b�NFHTM},��FHTP}} (%KknownA8aLthree Uyal viscax@Camassa--Holm equ%� s, o�P Lagrangian averaged �)�L). Furthermore, when��ed� a closure .6��Reynoldsf�Aq� t channelasd pip���=-( ii� exac�!sam��duced2` JVa�*e>�. ComparIe��i�!�rJa ��1kEe empir�� ��h�M%�� 0cellent agreeA� (see,E -�CH98}--�dCH01}}.)�ref%��ȁmPregard, one can asser��i�6Iis! � ful the Ysub--- -{���� \m�${Prelimina> !NotIu$} \label�?d Let $\Om = [0, 2\pi L]^3$�f!}-ca�d ��<} � (cf.%/�CFR79}})!�m � � ible fl�-(in a domain�$ ject1�periodic��ary��d��a��s: \begin{eqnarray} &&\hskip-.8in \partial_t u - \nu! \Dd u + (u \cdot \nabla ) p - %D( \mathcal{H}^{-1} aa^23:O u^T))=f, 1zCEQ6 \\>� � hu= 0,5�42}J4u(0) =u_,2.3} \end=w�4, $u$ re!�enti�un��``��/�N0" fluid veloc� vect AX$p$A�a�nC m���k(ar; $\nu >0>F tant��ma��(eddy)I;sity,�a2a�]O e paramet�g hich>�w$a0t�%I�body forp � , $f$�^Fis�  in9 t,�G: 5!V_0$, ���T c@ a�$]5�a���(,� �� \[ 6u = u-MiA�<, \quad \mbox{suu4q0 * 20��]U �� $(MyJ��� by�j,_{ij} =u_iM�_�_j =\sum_{k=1}^{3} (\pp_{x_k} u_i)\; ( .$j). \] {F}�now on�4Einstein's sumA4o� nven? will beJ, e.g., �.q )6�j) = v�>1��Fv=n��Q �(above systeequivałto��v 2�vR�v6�) u -R�Ic>�5�6Gu^T )+ q =g�灴1N�M��2v6�DR�v��v_0Aq�� > Af q.� p$e�$g2f$.�]ub�`�N)�L^p(\Om) >H^m den�A� ual +8$ Lebesgue spac� $d Sobolev ,� � ively >[(AR75}}). WeI� iby $|-W|$e�($L^2-$ norm��$(%w� dot)2&inner p�t. E�5\F}$aOthe fun���ch��is�all)�, trigonom<$ polynomia�We seta�i8V}= \{ \phi \in�oF}:6;#=0 �& int}e�)� s $H, V_1-� V_2$2E�O   ${���n%U , H^DH^2�S9�%<( $P_{\ss}:L4rightarrow H$,-K orthogo0 pro�i���]let $A=- F \Dd1� � �7 <>2 Js"m ���g $A�$��$a self-adjL�iA�M pactx! H-J9($D}} (A) = %^>�CF88}}\ - GA94o LADY & TT84A�I�0 <R _1=L^{�% \leq2 A�s 55 eigenvalu%� $A$ahpeaPaccordt o ultip�ie28-=8aE�� $C_1 >0$ ���ch%]z� \�4{j^{2/3}}{C_1} �\la_j}  j 0&% LLB� ,for $j=1, 2,� s, $� �6� !�)��v> 0.1in $w_1, w_26�V}0 kea�B(* ) =U�left(%��1 )w_2i�Ga�bi}f4$B$� a�follow!�p&�A]M2EX�iteI,Vb 2G ion}Zgcana�ext'd� %�t@, map $B:V_1\�s�E �i�4V_1^{\prime},$� re $.$ U he d� ��� $ $. F*�!J\ang{)O(w_2),w_3}_{.Pm -2'3'2>'B A every9�!�3%�V_1.$/ 2)N=�u��H^3\cap>, 2� u =2� 2�1�  Hs $B(u,v), B(v,u)$ �< $\displaystyle{� j< } B> j}  �  �re ��dedg m���.J$.J�E(RuQ+"�in Ad�ts.ND���P��P^0enumerate} \iT $Mu,u),u> e $:+!y�+%�BV ; r�Q�=�,  ), BY �Q�.��2�A". case^ap6�*��~���, �k$) by apply�uIQ� �܉�ge�k��� �is6� K "(�� 1})--3})5�qZ��(d u}{d t} � u A�aT u) + 6&' ��n@ = *�^�R}EQA�%��and�V}O-1"!� � "->#�$vF$ %$ v) +�y u)- u)X �je = *� N^&"� . &�.F� 1���-$D-1} \thin�9�8T�anW���ve� H $f���AWa$lla����{\em )�U�%�)}�#n!����V$�($[0,T]$ if qsatisfJaG-�`-�Z`nd1QK**�1.0in A��� C_w(u� 2) ŜL^2 H^3 � ):; and}2� X\frac.^!�inS TV_1d���H��:�Y �> al&!�weakly &�*��$� � ʹ], For� veni�,� re� {��p!b4Ladyzhenskaya'�li� %ԅ9bb{R}^3$>�=�.6m|I|_{L^3A�eq C_0 2}2}H^1/2*� SI-1}2$>_4n_� _3/46_2v_6N_K, DSIJ�*j ' V_1,# !� Agmo� i!flRa7�c{\infty}^�Fj1~&8 AIR8 / � 2$. Q��am !alAu (. Also, not Z�1|&�H; |/A76 !m[ L+��w ) ( |= u|^2 | |^2)�p-�LJ e.�#!�quantit�u,v�|M�\�.rY haei!�s��Wl�!e e $� =b�b�� K6NY. ���  a� U" Aas E.� �"�$�estimH �s:y�� alaey made � rous "# B m�%a%a Galerkpproxz(schem � then��t�uAub�$�� theoremr�"(}%/*�TT  By tak}hB� �"o�*�1� ..r 6 u� � Pro�on   � Lemma 1.2� Chap�IIIAU��� }kfinds�Q' bala�(�|r(�]�1}{���(E�E .�)}{dt}_ nu z�e?ng{_ ,&� H}u B� -� 5*" ,  R/ = 7f6f>e.�[ .� } By)��  (iii)!|V�we obt�#2 F%U�aJa = (f,.Ju):/!�|f|\;��%��1�f| u|2 ?�!��|f��M(F� �0Ab(�����n)J��F!?\nu�ysgF2>� As  b'M ach��d�;i;)� �-d6�!c}![). ��V1 6�Thank�% e Gr\"onw} �� y�g�:b�^�$q K_1(\aa,l, ta�ɂKJm�FV>D = e^{-TIw�(|u_0AG�35�) +):A�^2A%5;sg29@KF@ More9&,�ܩ�V1}),��A $r>we-F�&� 6- nu� t_t^{t+rL �a5���. qrF ) r ] +>J -�RTB ConseK(tly&hJ� �int_0^{t��F leq )�n�t �^2I� + 41��Un�\u� �INF�> 2$��e} Agai� n �/�-� � � b� b��1}� B�*b~�����} d |v|^2/�!nuU�!����v)+-��, v>�g, BB�Nf� .oE�� ft| .�<u� �j9J� � Ju = t�-�miNla�5�; \|v�4}�B!� \; \|u � 6 2Sv. \�� 5LZ� C_0^&B �AB!�v|^{3/2q 1 j��6*u* )�)I  & >"If:5*} �:&B0��U0g,B�=EI�S& fF%1� =!�OfNH�aR�7R%QF�aq�-%vR" =.v|FDBy Cauchy--Schwarz�Young's&lw/*JT JI� �L �M�N\nu}{422F�!��Q�A�4U� W2A18 u |^f v 2}Ŋ^3} +8��� 24u !{|� &%}{��%\BB * F��'[ 1+ yV�� '8��  qaK��� ! �a�}��A42* \�0nu } ��]EX�RSn > ), ��),\V� A]��  |v(t)A %LK_22� ft(�� 2(s)+ t( bq )m\f� 2!6� Z� & 08inF�=\exp%�(�)ef%�-q-�(6� 0))^a0AC^3Io�E�%�1!%�#N@%�-�3} T <4I} M@`66��%�t-. \noI0\\� %{2in}a�ft. +\,�4 � Ef��� ~r� 1}F{IR rtic��� �� + t(bU"{K-F�"e >]ZN��*� 1aNA�q r�; t$ 6�Mf|� ��A�kINTJ�The�1 naly06&V lea�7&(�"��� `T'u]inh\$f. T@91e�$�qu�s6�s��[N�� - $t>0:�!H "=3,s?"lyE<,v540e sens�5t SN&ified$(proof below�!1Q("} Ox0!Z�6w�$��6����dard N�on�cedu2 toge!c�!(�7a priori 7N s-]J�2})wID)�5exampl�1 *�Q&.Q& &nQ&�� sh!� only*5�M4ZofF)�I? �R?�A*�I(1�Q?s oj;2+. S�9Q'$u"�(u�(y.two&�=o2�7"m,�GN� * l2w=u_1-XyB differ�$w$&VQ~N��hdw&� $nu A w + � w, u_1" B(u_�$ ��.�F� w29"_1g�v7d&Cw�0&�,U%:;�wr,0;�],F�n4f�L&�. w��q� ~M� �4>�^c 6�(|wF]Z�"�DdN� =)j.(�f29 wF�FL �W |2�| (\|w�&�� u_1O |u_2Z$ w|Y�( 9a|+ 2|)&O n4�J�L �B�Qw|� ��~ + u_2&!.��R�:�fm��БB*C:Di1&�Vq��I� C!�� A��^2!� _1|^42�^4} �2,6S*}�  $C"c*�ltJ�B� |w(� :w �q N  ft(D C}{�D}O t� !Y6 �E�B � "� d|�D%GdC ->F &�ɾN@2}) +A� e � implzF�ce on .� .�Bp.- [ !X=0am*5�;} \;\; � =0w0:���?��� �? �� ���Crk}�or�Dto a=9to� X \ "{<�mg_@"L? ie=rl4�>n )+�,��tieBD#�priateL2s,� >E&�9:;F"n$�=� metho� )ones �Ay-5��c^&s.� �.�iG# (s�;�." 5�#��)� �Qm-i %�.�NN&�;G)�At#A�=Energy S!�ra*�;�?��"'"�A%�2 !�>8. "�9pro�@�F.�Ato�A� tal%h"�AY�. 6HconsiE�h"� � �@� N�@.2�>} Dv54by $u(t) =S(t)�9�  q&� �.� :�(I�A>s$.�aultNTv"�!T}3A�-ka�42��d� \q�L� all}�4 �*, Bgeq 0,~$�'\[RV2 V !::V *7 �2, t U�� Sincq�isQ6, !� 2� long+;(behavior of" D5%˂i, !���&�K@Bd�I clud�at )�L"� _{)$loc}}((0,S$*$ Ai�&� 9VZ X+$S���r T-A} 6� fD< �{c�@ctmd ��&� A} \s�%t%�Ca -A5+jf}. y�.VH3Ge u�e�q��C�0���͟F�K,�6 usY�� �n absorb9%bRin q1� $V_2.$�0�,�o�aL;j�2�O a�%�5� $72tA��� \rho.$� M�wV� *} %�_@�|a�B�  &f& �� �� �\B� �;!|O ;!�^2�#!A*� AsT� !����(en $t� F enough�B���O:`^�%� \A���!J� V�.p3in~�!� R_a*?f��!r})RFQ"�x>S= 2�|��"RAB�!>,[ \limsup_{t� ar�:l,s#(N] �"ҥ]��4 ���R��E>o ��B�:n�s1a+(th radius $>VP/va��8 Nex�%��A�f�c�֭by �R1ɼ T}) Bpu>*�5n� $ e��6�?aZ ft( 2+ r d!�)�#3A�_14%M$RRUf�By H &M5uniD,Z��9�� {&�I� }, p. 891_R2n" we /, �9nN�*o�:�.I� = | v e�R_v (r,�a�&6�&�Y~�1� Y"H'f�:_7ex>��%����>�m��L2&`% 2 r�<�^{8/3}A^{4�AJy"�G(6EvBEQ^=�q; "3�  � � *�&�! �$ (:�xYY� ra7�mr32W,��Vu�7$(�f�5' ��6� Jo O N�A02�F�$.e Rell�AP.?}jlB� "�; $T ��z/&9@NF elf. &�^prGa�I).�� CF85a�����EFNz ��91���4 � details)&� provB ���B� k "� A} =d6_{s>0�Fc�1 >s} !&�B}� � � ^� i5)Qѷ.�KݚB�.!I&?�%>oRH :;4� )�5g)!�N &)6d� �  6:5 �?��,�ߩo>~l Y5V $!td_H (=ye�q d_FJ C!{xi�\{�" �"�y���|����W-�4QVv �lnV3/4V V;�Wb&���DY!9�2�wwA!> mean >}.�RofwJ� \ee=:O� r=s�di.�?# T);" ! �)� q+� 0^{Ta'*�$(t) 2�� "�, (t) ��EEE�X2R���A�"Rc"�Y�w�9um:$=+ � og/\9)a(Kolmogorov ._�S�LeVhs�m��,�{� l Scaling;�?QP}��U�NFOIAS* 6�xFMRT}�Dw�!B�82x2' \hat{u}_k�@)1}{(2YQ)>%e${\Om} u(x)�ikExE dx,�&\v�\v�\u_kA�M��,q |j| < 2k} �j�ij�V�v�J v}_j�2J2�(�u_k^{<�-� j < )Njy4vV%v_jFR R>R2 �4DV.U(lm_.(v_jM�*��F�v7"8qa�N�an �P��( sizeEW1�B�.�%'Ue2}�-Řdn!(u_k,!#) +� (-�Z= T_k -T�) �`BAFIH� �e� h� sidX%� � fluxCn��z = -���!%�" '/aG�3 -�'A�ft(`/�%�<�28_k>+I�cq+=> u yE{.?["��B"Q_k+.xK�CTT g),U� �JLp:� nsem��S (l"l �8� !�)��z�*!}�EJe�!T�Q�!I��I SPJ�5L� [ E_@ } (k�(1 k|^�(e�|j|=k= �+j|^�+�n �d)@ be writtemY��� k^3 .l \sim�[k^{��k^22"\; dk 'f�]>.�Z $k:�'in^�^ angeVassum�= at 'enoq4pi�, h�!��~ UB�T[g2!�\Tnd4|Z9�G \�x)�-�fNcau3&� nog)kag( �. O2( c&��Zpos�W�&[GM| vVonE�dd�� ��  \1�\ NameJJ6*B� U!�(0)} ��!��HTBO �A|v_AZ dx"�@Ei�kY�kA.1m��2Z� �1yf��kqN�nb�ց2��|un �k2�}{ q�k^���-.B�"��c6I urn9�$\tau_k���M�2���U�� KR67�H[ H^{Q!%�f�E1}{ kEn}��5� !�^{(n-1)/�1kV  (=t � },��n=0, 1, ��me��_W $\ee$��� )�I�ee�U��8%�E#������� k^{5�M�.)5�(% }{�R>�M *�� �&� Q��=R \ee^rP5E.D3}} �3�����!�6�BZ�` �`=.�|.�� give�,�3 �` \�"v-: � (k)}{1BA� � \{[\{\ :I Q\ee��)9,}  & Ow� } k\aa�� 1\,,f\2)m|BYPH{2(4-n)/3} k^{(13-2},� :n n9a� �M+F�rc CHOT.#�`� .s � J"eL%ca�Bo� �!�ډAA Rb2b1%I k\al�i�R1��#I�$worthGf��xV�\o �Edoes not�ifyvL c$ �$�Z(n)�6� $�1,2$,�[�F�/ n��`ns"L=2�eJ# nt w�would be �ict6Na�� sub-~, �ca E�;%� 6�ais�Vb�k,\of fut�/0research. How!0, our earlier sugge�W�cho�G-;25;�M�6$:!8&V��eusualIEy$.� power lawK>� u�u �sX �ddecay:B=L.$ �Mw \no ^nt r *{Ac V ledg5bs\T!kork k&�iiu4%�US DeY(lbof�% , uncon�%�MBg for 1�t���.} �( Rev. Lett. � 8 �8)�8 24, 5338--5341:�1�]g(L.G. MargolK(nd R. Zhangem Direc� �qald+u=jR>�T�TCl1�vt66--8!�2u1Ae%skidovR %-u#m O�eLeray{i������"�f,}iIc. Roy� A, (to�earyjf� e,, J.H. Ferzi~j!?W.C!�i-DEXE�s�pUd ��q^an \$urately si%j� �i,} J. E� Me�M_9I7a�1--162� P#E\-�|���*4Lyapunov expon�e$, Kaplan--��89r�m�h�5m m��"g� $2$D:)y�},�i m. P% ApplA�thM�38�� 85),�27:�8��Na�k�^E�s,} �DUncP(Q$of Chicago�� 1988.tE�A�Ed6�0B. NicolaenkoER. Temam] em E-Q�*[- D�mve Evo�(.�R> ��!%�9Mathe�dcsc(bf 37}, Mas�=Paris��94.��=���BO�ebyl�糧���A ir reli6��MNM�c� $ory,} J. DNt . Di8%B5i 14} (2002I(3��u�FH�Y��� �M5--�Ii�A%�h.a Adv O{B�v��t9�%_sC �}2�52/153} �1), 5� 5192�>�e�What d�06�9\ t�aus0)ut�(?} Harmonic�ys&lnd�*1l S(Ri5de, CAEge�5��$80, ontempm�M�$208}, Amer  �x,�P� .RIMa�=�MRT.�O@nley,af Rosa%_:r:Y3�TUl,}A�bridge. �  Ca , 2002]<( G.P. Galdi�em An Iht�M�y�alaXoryAL�C �F�@ Vol. I \& II, Sp�n er-Verlag%*2�� R�� Kraichnan �I2UE� two-"�-al],} I��lqe�" 1967ae417--142�uj#} O1 L.�W흥oBou�#y Value� blemR."���} J�82�w�Nye&:p$SemigroupsY Rs n%�2o{ A� �{-�A3cas/ ���-���"vM�t �kf� ,,} Adv. Geop�?��1�#74)� 7-. %5� TT79A.�bn!�A��1%N�_�p AJAsiN�� land�72�<:��n m m3rd revi�ye�o,F�82�%>�In�0-D�al�U�S>!a T anic��aI�Ap�7d6��}68}J�. 6JVrd{ } B.Xz,H GeurEe��$H. KuertenR L�t-:4�#�H�so@vmixV layerfT mi�]� ��,Oeor mput] Dyn� I^96), 309A^U]�7����* .�Z� 339 �5E��W"{G.;&<{, A��LWray, O.V. Vasilyev,!pJeanmart-qEY}�v)WrgF�qW �eV��l��ca"|S:*}V������385��03�th6� ^ docu} >�z8.z8% \]Xclass[amssymbols,12pt]{�:l2dset�{\tex�h,ght}{9.0true�G:#Tq}{6.5N"evs 8demargin}{-0.10>Godd? .$5$headhe� � Hsep .25in \usepac�{ �1 .5icx>psfrag!�$newcommand�?0tbar}[1] {-\!S#�1:0 slash} {/-\ /} R,AB}[2]N1^#1_#2:7curly 2�( S!a�t4{c} #1 \\ #2 \B)>�O}[4] ZN O&N \[2ex] #34.^->^ stra!��[��]6R\cent{c![/:A{ &0OA}}AL9�\K.KB diag"rm{B$ff"�OFB B.BBhh. HB LL. LB MM. MB be{M �$�)=bE"{$$ ' }{rl:(ee{E9ZGe8 # }$$2�\pde{�62� :B/sv0s21{Ia�{: j#%2/\half{\�2:�third3:quarter!4:! suml�j^�*_{n=1F$nk &n�t6� sumk6E uB$O6$n=0F$n>$>�nepo~{x~mN.+ intR��$;at�c^2�+]QSsir bb{S:�QQQ: Bint\xin6a#*�;-)_:M into>*> intx%x}_B xinf_ < xAp>c2N{NW2 N6D{a[\M�6dY��l6s{Schn[din�6$f{Fr\'eche:F{\upar{7F \down 6>HO{{\tt�i%e!kbigcirc:h barV���2=�dTfdxTM�d^2f}{dxA 2dTu2&yjN&y2&yVLudxpH:�dy B> vdq�d�ir> }{J}�><f% > udt.�t> Tudt=N�tBNpvpFQT v} >VpwF0wn0uF0uv0n ��.0n:� pTupU42^�  F65):6J, Tupy1RV6yFa Tupzv5zR5rv5rF5upzn;z>;upyn0>�pupQ��2�>�pupqR0>-pB/](F->�-B�B�-B�TwNR.�RRwN.6NvN.�NvNj.5VjJ�.5I�.k{d h}�Bsech}\�$�� {\cs" B"RTI}{B&�9J�{�3toinfavim_{nF12w jon} _{j=0}^6� �P: $$ iq_t + q_{xx} - �g4mbda|q|^2q = 0v/��l�1pm~/} d 0�}$$ a3�&\{� g_1(�V.�aW�0fy3y�T���Lrea�Ji�$ ;$b% &��% �x�� Aq_x��M�"E ����%%%�no<�1�t but� y�  +� �%}!/\#3 (a\A;��+ b�=2ikL}!� ) B- 2 b 3bar a K4 +$ A =C��T} c^+)䥛kZ� bb{CTC!z�4!z�� 7$��f1ntire5 �!� $O(1/�as $k ��l8fty$, Im$k >0$;a� factA� c^{+5= O)G+�� }{k}-Q�k \�@C. $$ i�� � 2: Ex�wR� �i1��@2�:��0Motiv��"e �����-�i1�VeNpIXi&� ��of��s'3ToW"EAit[��>G"T���RH��, �*A �. `E�. A�� ist B�$i�mWq�, Bhщdnn�4 �t�5&/H: (i)�s- d )��or all $� �$. Xv=s�`e�w"s (i)& ties!"� it�� "v&� c, �3��'� wt �"9 � A by�)�i qo����"� �# ��Q6:E�3:�B�)H��.�a+G78! !S2� �Cho&S>D)���>�g_1����,!�!���V,Volterr�5�l �stKe>6{ݡ stig��.g/2(���~7 fu ��cS�eS�� C.�eC%`-�2. i*8 �F>�[ /�u� � Izy Vboth}]�a�? . ԙwas��n�m�H1�~ata�  ar�u6)a #��do4 �0 $N$ corners,A�� can)+al wa�) choosingi�6�Eh>W�#6% each S�-�\alized ��) �. ���i!�Uw�tro� f_7��5b� \mu_jV,k ^4_�7 see Fig.~]Zfig1.�L��� ��mu_1(0,T;= Iѧ2(0,0J3(L>�4(LH H�5)") �Nu_j, $>tced$I =$ f!$(1,1�IIt!��a�n �e �%2%�,figure}[h] \$�=�# 2#z3}�K 4_py}{$y ! t}{�>T}{$Tx}{."��"er} \in�ZF ics�11.ep!�#) ��CM �:Z: �#era��*A� A} "9>8 <y��(3�K�0 ces $s��S��S_L $ s(=DA�3M�, S � � $^2T\sigma_KMmuE�A�1X2p \�;)Df, S_L.P� BPa�Pu"6y"$� = $q-i� 1�WcerG~j�yvpoDe��u�h&Vx"ƙ�(�1:�%{\�A%�a(� k)}}{� }\� b$ $� },� 1y:TA0 T� NTB$ T� T5:V\.WrNX\.Y�0��7!� R����2}����at�t (1.6Xr1.7�U ��* Q> I:0��v�s!}(��_1(x,k), 2 )^\d0� (\Ph&��, 2 &� (\varp) 2,Yv8a�@ � $x$-�"���� e�0 � |!$t21 Lax :1x=m an@4>5^fx�:HC(��1Eu�J�  $$1dL=d )> = (0,1 Q�1q��1q & = 31�-n�N!� �Ek8k.)�I 8b!�Dt��� &p Am 2) be�ak=M-� ��  � � aH = A(��.a� = B2ee ,I[a=�_ .�k $$AE�4�`\a b 1 f.Z�y�A;"S -j "23J:3 f e�, t{27 ' va~f � �7J &�7iW2is6OdA�cd na� O��}ng) ��=:�s&s�E�-�e:<E:ialcd8t�`� N�$�g���, � % �J�1��o���&�&� �z . U� � facts it / � !-l homoge�.Y��dA triv!� (ut]�I vanish�7l���AMS{"��o��*�Sus�staT5d argu�/". d! lmi# 2}.�.E��� &� is 2�!. ��Y~�ViZitpA�FG"s�a1B�A�)�ocha.9q$mB%*!mzG��ial^l_x�jl(~^1_)\���017 f.1, �  cruc!��%)eq��AW�IndeedvVMRHl � s���Ŧ���� 26=4�4a�Er$eB q (D�.F �g�{l=0}?.� , i�e mi�,6+�Aglp�1EeR is& <i)G Wa necess�but$�Na�7�ient}&l��I. �Vi$�(q_0,g_0,f_0��maiTv!� becoma[��IJ�6� �!s�>�of* 3}�2A@Gelfand-Levitan-MG1> "i � 6� $��=(_1id� $ͼ=&� , _):6x!�P�be� �/3}��$"�G�S�!w�Au(M_j(t,s), L \}^2v $-t-k�_^m� jP_e�>�`�`upl�$��"0,a� , M_��LL �,2.v��M?&rk�rI�$ tw2raE��$�{T%�> !��!��t�&�iD1( Ha��� :Sa`�Aw>Oco��("�� fina[�>��u $$� R �r�$�'��6{\LL}�� - {\MM-䅽W�*R1&��g|i� {-t}�k(s-t)} & s)ds.N9� t $YM_j�d ��$..  nϮ5�1ae!�: Bb9� J�r mM̰i<ly.K!` �,�E� A� A��X%�A� �1�h2!$$ �q` s (4�!>(4.8)Pb�:6s �t!���n !��jY$,!F�]Pi6�&e3"*��bf�&8_SEl L_{1_tm��A�L_1 = ig��) 2{ c�)�!>�2* ;M_�� ;,\\:- L_{2h= -�{ �Wg�u X- X�m��͵� "z"!�rMJ�M�2�h 7LY� M &6R �9'2��C6�� 6� ' A� <\\m>)�*/�as2� B,2� -ej�<)�j� &�j = 1,2�TE&�� $%W!y�%1�� ��aZ,�qfX\�+ (g_0:�->2 g_1)�=�=!�lf Tdg_0}{dt�(q |g_0|^!�.�Uq?i�j,I�R}D ��}�<�� 1���� ��,f_������� $�!�(, 8) i&��� 16���� �,&�i��gz����g*& B=��.{%J2�,e��Aqͻ9i 6�e50L ��� �*E�V�.6� OrganZ.aPaper%yNц�(ds 1-3� �uLBinDw s 2-EIn ad�/B!��� 7)&�e;[�ݰ���e^{ikL))�<}k6Y.)$ #4ikL �>� alphO� \bet�J�xt ,' =k2�18� B�mu^{(*)r�d�y�Q3�KI�!�h'� \{�%F� arg � in L_*���!G L_1:��\p�],l L_2: [2 ,\pi 3 pi, %3FB4: [ 6D019!$$�=2}:� \l��t= rm{etc.}}{&ϣoHE<il � �w so�� mark�+8gA > 0FFP;U�VA�A2�+E�%N} ANLSu� admi\�"{g N io�15~�+0ikA��[g�$\mu = Q\mu'k.w 2*��tilde2"� 2.%�� e! N61� uAN�&,� m!3Ϋ�ѱ�� o� = [��dotU1� (1";2�*� !$Nd!$Q� �JE Q��Ce�0}{O/ta��N�d/t),}{0 �) V A�� 2kQ -iQ_x�&o �/�g m6f= �/�T2.� ��%E��fnK$�J� � if��e�. 2xKna�e^{2}�*W}A���� &�NE9Vre*�d$$ d\"� i*U- \A�!�,k\!�W M� (2.\#!���ed 1-a. $W�%*UoW=�fy(a3 daR)�e d��ow  T�!�P�v2on/?aa�e} )�4,s �qm1%2'/0, $x\in [0,L]t��nT�_.F . AH�nT !�5)���3K"*-X%U �{0)}_{(x_*,t_*)�-:9 9� W(y,t<��2X �@K$ E�4 bitr+p5���U�&$x� �- �aPz1a����!con�Y�&%gl� r�dic�. &os�x}!�'� �.�a�&o���&0 !�B�'@w� 0"F� E� �&,..., 4$,]C'on�! to $�&V�# L�9 $�&�$�$  s spli�!n2/!�t�)s�(̾lo.�|-| $x$ ax�]e�V �2A=��Ix-ik(x-y�YA�a-�� (t-Ax:T(i� a�Z0Q���CaK �"3�.L_x�2V� �3J� (x-L:�A�" �V� 2�3) (L^��!u1�  4&O �s"Y �So�.2:|u_3�~��Er&u  $nFt^T_t/Notaa?�2�U{j�1*6}0e$k:�um {E2�)EbTha�RnWs3 ���� J����a-a)M�* �6�mpl'E�T͌; 2)}�H 3 ��r)'tż�)^{�h�04)}"���u_�0 `S3, =m32`4` 0S4L m4 0�{���7v �=W.,k�%'�#t.3(x�*A(�{3}:"`kmu�*C� � �Srk,s:L+0s2�v (24)�=�%21!2 �z! ��G2G8�M M`M� ��2� ^{(3!c5j%�-K $!�!&^�M�M��5,NM8M� M-Q6$2.�5E "')$� n\t� )�+cele��thu�"! det�i�,�1G �ejM��F1� {R��� �a�@�R��sR�YʁCMx� y)K � Z � I_+ 6�4N�4.�4V,fϥ"�1� ��( $a�ei� �F'$ o1,0�,I$�! ��colum� mu�0i2�de/E�{j} ޡ/� 9 J.� � %Q��1#A�Qd��1+�c6� ���&�g��'�)�Q�,2RF R4�=%���[�N+�t]��m �x�`ng5I�5)�"tZ<��#~�/$.F"� Ft"�<F�" F��0�; B*!�1�F F#*$t=T$BK(&8g-ha�%'��(�-2�:�7�L56�)Bm��-B M2�_�&"*j��.� "�Fs)!�nd1��a� �x�|\Big( A�&�UA �$�Y � avN�'<�K6Z`A�(\m�)_{11}Aove]."*k 2TqG 6>2:>%D1 '��)= �N�*0[!\QP!�E �$"h0I9� L� ikyA�&�   (yCdy2�b" $$ S]0^+I- T T� � 6$�� 1.�!gM�bi:��2C 3):� 2�1� %hU-&EO9) justJmH &��)>?.2@�x�ermin�CSR.3)�>P� Y  beR�urE�!�j�wqaj�p"a*: �{\o;{$��>$�R� gin{Gjiz�\ 'A/#1Z>�  ,y&�ALXG $b(M�} =�!k��bb=� `:�T � = 1&G1+��LJ�< �"�<�24)3�!�<;a�'�)c6�$%. .g �9�w *�=%"� ��*2 6}�R \�@>M [&pi �]�A(F B"!�)��2"V/~�kZ#-�'A"p/I"j#-=&�2]$I$�2.E$ �� �$qR$ �>�TE(-+"� �R)5)_� 2$$A� fty;`)|LB9�M.w�� Fc �]) [�M�"� .� B7Y\vskip .{\&�6B�%A�$ �HS��l@. 2�vG{+}��bf .N�A�}z ۽�J�+ev�as2{�  $ �,&�/�"J f"�&P?� DHI�?by6?154� �3>2"$ s��8),���>�I�" 6�"sR�0�Es�qp���B!:&Y !G>�%( � "^Bs1(12) el� %[�J(>")]�4> dy�{ŵ{4}:.�B�%� /�r*  $��NZ�$6((�_{t}^{T�:Q��O.�9�9$Proof. } bL 8 "� ���c�"V .�A I7� �!~ "�<�  T\.� ��( S7 A�J� I� i�).$$ M���,�5KbA)exuL:g ]* bE�%� �x%�.� -J �s�q�:ikL� "} S_L ��J��QtEI�h @FD = 0�4�D:�:�i&SjI��su"߻BJump Cs{��j$M� $.,SM_+� ��#�"}*�"�)}"�,�� E� H^)2]; M_-Vk� 1}{d8 "")}_*q� e2b&�ig� M_+= -��� ���{"� d� � P2� P[ J} .:���y _2^{2Q!&v! P ~ F�����~L ��3. ����ars $!fi($ uPGr� fi�Eb��,�� .7),��3.�(A�6z�"m \det Qk ��3"� $U��+�-�R� �.� � �e�۱ �Mon 2.f�r�c !A�<�9��D3uT2<�!=��"5 IBU�1�J.J��.�&OFis a :��)�M����~Q''&� �M_- � =a_ J � 4 .�#R�cup i "� R}a�YE �A�$>! x $J���; $$J�M>�dll} J�&��B��) J_1,Mv��J)J��aJuiv J_3JŽ_2B<pi2Ge���e�y�� �){ M�A"3�@$$ J_.�b� :{lcv� \del�%a�} & -VMb �\thet��� ����&� ���F2E & B�.J� ), JP�" 9s �-.d��}?]-t F$�'� �T>2�Z�L��b@G ,kL �}F�&�.�zM�LɃJ_&� 6�cc} 1%�E,Rc'�S �:�� B��'7�k:�1� 1}{| gkݜ2�I�u� }*� kx\3��6�6�& Z = A5� �!��&$Q�� �� ��, IA9�6Aa�n�'g$���@&�-�i]_y&�� M���NS& �e�'X2��[n�~.� Wri� � ��p1. t6)�" i$��o ����O � � �/1�"Aa e<�)�U 5 Oet{& -OE� .}2;.�i� �r�bgS5��N = b�:�J�!<3&�E��!A �."BbJ��EBKe `L [=�( �)$e!�(��Re�S�%�   *jt r!e (22...u �  $s� .h,}n� $ :� 8f��)�VYuT �k)}u�*&ET,=2E(�R�jng�2�3pan� -�23� �^�&�: �Z$�0�In&��der#X�j^ &�>;6ND/ �\ ��t�*^� �"�Q�w 9b-�2A�1a){YA#� ]j r!"� �3�I�!� Be�� 5. 3.13iFWE&n�0b �� 3^{a��EbI - a%�)�aU.����m�a'42713�E& ;id�t/ Mx - �\)�S\B�+M3� AQd��.p !3a�E $d$,>�13)� U4 z*�>jA_Z+N $20sI<�A�lqr�-�$U�FSpi:H,^Bh>2R:�D mus[I�je5f�Pt��_>98DunNT")�U&z�ar%v$J)&w% T�dUCM��,B\Bt%���i�[-�5�O*B�lh��:ja�l� Ū(e? A���IBE�r� A A"^E�B(.�ڊlpha b�B ��  �.� DmG�*�5w �>C��q-4NCResidue"�EJT3*��iIc� :l%U� }7��8�4A-�RcoI���]�MV�0z;at:F\2�;F�Ne ��6��4 nu_j42�� �)l � �H%!no} Jh ?k =0$� Pk� .G�� �)6OJ�����Z L�2� �z2� �_n�� @$� nk=�8.-JNone �-%? �6 4):2�� �coincide��th��BQEUvti"E}By0,2{�v>L>[M]��!� 2xI�Je�d�^)�&=%3I�& x $M�6] aw _{k=Eo } [H]. c���� 4i\nu^2_j"33x} 3)]_ ; 4$h�o+9k5�rIk*� ~} �4i>�-2 _jx}�$_j)u�~ .� q_Z�� � *w +2 ;w� "_F'.v%/6s=*� !�f-QQEj1 .�barn!�*44�AwU��j��(I�a(%�)}{� L' )\���+  c� M�!܉z �=�� =_jGRa( (_ `d.x 4�n�a:usmn&��az21b�Ea9��H) ���%&�?�m�;�e��K�FH 72�T 8)�{h�}S$zO&� &���#)8� =� �%*�RI�%>K$�$�  !Q\n) }) \neq 0)���andE!cA{j) Ps��a� e r ���!���G%zed�h˥ed �Z���L1�=�� ��J"�)�1j6�Pax|�m|2� &� 1� v (2.4� !3j( &�$XM_+. ZL�G6 " k�h \curl{1}�{0}{ \frac{-\lambda\bar B e^{2i\theta}}{ad}}{1} = \left( 4T\mu^{(1)}_2}{\alpha}, 84\right) \curl{ 5 (${a}}{- \B kkL}e^{-t0} 1a\�}. \eqno (2.4.7)$$ Evaluating the second column of this equation at $k = \nu_j$ (we remind that all the functions involved are entire) we find $$ 0 = -\B(\Q)�\ 6�()}=2  + _4)Q ,.�8�Pwhere for convenience�not �@we have suppresse�4e $x,t$ depend4 of $9�2$,.4%�$. H24, $$ Res_{k=�8} [M(x,t,k)]_1A EMX- )}{ \dot I �}5)F|.= U4.{ 0)v\B Wi 6i4, $$ which, usA2=.S =�V)]%becomesUM E�@1). Similarly, e6�first Y�eQ�=7) M� m~_j$!� find!nE` �2)}_1(' ) - -li�0 \overline{B(e�  _j)}id-T}!u @'k3 ( .$$ E�Y9B�S.�A$1)}{%�ddY ' >�9$)�,�+:[u3:� rF�,Q! yields)�3!�E-� 2) and 44) follow from5� *1*3) Iysymmetrya�sidere�Ds. \section{Existaw Under��Assump t����$Global RelD$ is Valid}LubO8The Spectral Fu��} analysis�H4\S 2 motivatesc �a1defini�s !results�� �sbfb. b%�)A by�!U� phi_2(0,k��quad !g12k \in .���3.2�A�6� PropertieE�:�/�$_8$\displaystyle{191 + O\Q ��1+��kL}}{k}> , %U -U�2!m� arrow!y\fty;}$$ in particular, $%T,g� �9��$=% S(\mbox{are ba�ed�1} arg�a�! [ 0ai �]M�(2.1.13A! \end9�8We shall also a�"a��XA�$ has�f@most simple zeros� { k_j\}$,�0 Im $k_j >0$ ��:no .! !=0$. >�Remark�����=�+4 gives rise to�Smap!zu S}}: \{q�}--�I6,E\.54a!sinvers � b�QcJ%� Fg�c!�l 3.4bc���ed���s:� 7, = 2i\lim_{k)��\iA{(} (kM^{(x)}�D)_{12.h5g� $.)$���`FV ���,RH problem: R�.[��Iw /(array}{ll} (_-�, &-Jrm{Im}}A�(leq 0 \\ \\/+f/g/� nd i-�. a�s a� �1� h_+$�H �4 pole�I$k=k_j$,�#A�s>tG-rG!H bar N M���ű_ ���� ��, ����e ( associated� idu�re�|n�"� k_j} [M�E�.� )�_j!�'  a(k_j)b} .8_ \ .Fkd2-K �E4M� -2iI=k} uo� AT�  �2�u�*V6�V It%�b�/own (seu r exa�x )\ � m�bb��^{-��Q*� 3.4cf6��$F� 2}z� A� , $B). Leta�Q^{(0)}(r�mk i�0}{g_0(ta�l&�0�i ,1., %;g 40} \sigma_3 -i O | M|^2, !�pm .v�a E�6f s $g_0 (th $ y$,�\1r  $\Phi�( r Pr � ~r + {1_tr 4ik^2t -K_{11} +2}2� � J2J=&2R<22 R2�a0 Jx�� :� ��,��\Qbd  !Q,%�$ � �1n% �z>Q}�ao2OM�l>�� qn o�1 @ V1 !�fty2 ��2 �.�7��Bq @� \{ 4(k^2�6K + 2i �k(. -I)_�� �\}�� .*֝ V�!� \ ���[Z� 0)�  � *L[>i� R� &� Q-RQI�mf�Se$q , 2\pi]A�� j� -& �� �+�� 1���&| R}} �'i"� 2� $� FAh>� �[}{�[�s-��t}�%$ђ2ٍe^�/ay&; 1}5g' ɬ( �= I+O. .BT.$$ G�R 9`r�  =��$,{� R" NIkN � *n !xN Ku ' � a6$ �Z,�ʁ -��(�p �:�)�Q 6� * K&� 1�.a 4\exp[4iK^2_jt] A(K_j)Be <]L !�e1 -Re q-4i3 w& dot A(!f�B 2cE*]_1E9:] , ] aga��,W I p(&p S}�t�j)k >�* 11p &b J3c f\ah, \a�d  $ Lb $0�by an"�L��(3�� � 6� replacedA$f� Ifn Ak� E�& *{B0 �/$  $\va%�3� �saQ�8)� �Q0:�2.+ >e) )Df )Ig %]a�UL �>k !~f �i �"h �� �ri {!d\k $ Identical!�tho'�( .� $will denot)d&x V%�{\K}_j�*�>�"3}  maps 2015in \ \ $\qn  U�SaL)}$:  I, I> \}6�0{ {\A}(k),{\B �\hf� 5a)��5Lav�N�\QM�n :j\q�# ��; .�bf�reMdd� ctlysin9X2� we uYhe !s�q�,��$cal{K}}_j, $rm{instead%of$ \� \ Kq=,� .�6� InUogyip&�3����� �l�饹1.m5�F`4",An admissibl!#t)qԅD�s"[ �-}"o$�$ accordkto #"�. Suppa[that th�"e�>f�(te�� a�I� �$, such O:Z3 eZ*�6�� �� �i"ed2� ���s 3.2a 0 3.3, satisfy%,re!�(a\A +"d�b8(L}\B)B - (b $�a2�\B)A ="It}c^+a�N"�IW 1$��nti$saich*n/\��� F&� 1��}&�!@.�S fty "~ I 0R 0� '_0!�  _0(L�� #L)���D Thena/c�a��s9AE��p .� setA@�+� A�Q��n*d�q:L!@Riemann-Hilbert Pv} i�Theorem�q�LetaWa>J@ B�F`,JU� e}� ^�� Y� 3.4. ^!�%ral.��x� ac mc�,a~ in ���c,��Vvs 3.1,a�3. "#�af1 �zv*i;j�has)�no} �'�\���������"6��� V� ݩY~�\B��@������B� �S��d(�#��paR�,����)b f�._"�  $� ����U� J Fk "�'I��WBZ)5 ."� b(�k�Y�. @z �)� al �)0,ɿ ̞ 0$ Lk= B��� NonV!<"�G�G�h2�@,\pi)$, coincides�ta�7FAXl\eV�j0,2l��Bi � i)� O5�Vo *)F�0,6t $, >�tAo or.��8z�%F2}I� J_�Y�A U�B�U�\&[B t(e $�,��'*�'�*& $2 \ti8,02$ matrix RH "�"V $M� �)B "in &9$,C}}\slash \{F� 2��uniRF" $$ M@"Z]<" JU+&�'I�"� T6v �/3.20)e+ �$M)!>H:pS � "o oM)4$M�!BOB Z@ nd $J%� e�*�$ $a,b,A,B$�$A,\B$,� �+3.5),#,3.6C,i�$Y?2�"�~R�"X��fty*2�) _Re�!Y,d� k.11. 5�en*� d �$� �+dG v%.yqA� &� .>* $Z�&k(qL�.� *� L$agF' NLS5n (1�� �zR �+, q(0,t�� [q_xi$L $� t), $$.��(� (Proof. } IS1�2�=ED��J$2L( arg z>���E�B3F5re� ively,�n%7�.��^+a non-1**M' . U Dact� jump�� $J$ Nppropr�$ .�.Q�itA]po�to showZis�'p  aM� gl�.�r`16}% cas $lphV�a~$ite number�!�)s$$ mapp93�)Tof9�\3lemenl%@ algebraic system0�w2�always �ly�va��CEW)y�!�m} )� argu��d�3��method `o)i" %0verified direbj i2�is�a����.rabove]5"'Ma��0K6;V1. 22)1e�/e �� �y b�/�,�(Lax pair, h41$qb.^`�3 $.} q%�$2:�ces $\b,J_1;'�} 3  $J^{(���350(25kFE be�=�� f�$��7�v�3k<[7(kG2ik(L-x&�7aX71% b3�� �f&$ iW� .&'.}}m � *&.�5 %*��iN{.B:�}�!2[9#1 �f�8 �e� ��*!��}�812^9+-#-p�9)J�*d9B�1}.$$B�/)%�i-#aFw�F�( 4�&� M-�� �1 3=�2��&��P�G$$i 2ANm2J2 , Je& J_6&2 < 3, Je -K_)}_3.&4(x& =&% (6�:`21."w2�.�r 1�. a�2B3B4 [*m J� M��],...,�n B  ����co�k� 3�6�8e- �� s: J_1,:3)}J_4 4�7,2,�.,3.%  6�;se��L-t=��9�s�52'{)n-�()�-�1)6� �9 /)�8: ��,�)�H ��_3)�)��2, (jHGb�-q2/���E�ՁjՁj=1EQ�;� `(�7FXA,*"32 =E 9d*� 28a)� $$$5�AFٱh'4M�6 1g �&V28y&�=����.HholFU12V.� P 6S_6���2�16Y1i1�B032�Z��D>T1.e:G:�B/:���Tha��Ks�+precis� J� W b70 "� o0 &�3.�� W� ��8 �nI-$� � A�5$\det2� =1$ � .� = >%��R� Moreover� a stra�@forward�A7�3 "!5��aIz transform'e�8)"s*�$�{j} *�$,�!mrb�k4.9 .r"thenperN<'7 k = h (cf.5[).�refore, 2Fi"5� same*�. z�half-�> ;?�t �.v> 2� "� J<6: 2�!���$� �����(E^��F ,k)G &5��GD�7�3 $G�n�� 4)!E����)� 2Z�*:wn \ � ces u j)}$�\!�, tend�$IO1R�'�� � 0 �2  1)O 0)}� <%&^{� =>$ � HR.R�,*@3.@ %�%g1�2&" 2] 30) �? $J_4��� �6A26ar3.29) ~(m�:D��} V��o.�" Z>desir�5ul�7We�$&7.!Ic%�p�are�9!V1%�S  Q k)h*}}{a �% (T-t&>�R>b)�6bove�B`� *� � "� =�$?.F_+(T ��/>Vq�=w �)� �U->s A��+031} CA��%a3!~z"G1.�> �G*>b(s"! -�1��9R+ [ 33We reX!ata6�c�� ���a"]8 UW$J^�u�`G^{ Ali�,E� 4])2M>JFIP1�` t)};�t3/�G��ic�to.H�us�$ aAP a*.4bb =1, A ABB a B-bA =�#E�T�# .i*L%5x�n��,be obtai�fro)m -D)5}6by��� a $b$; � <\beta$; furtherm��#, , $���y��s�F��<�33)�-hb�-.yN�&KHA&!� �a1��:)  �6* 0by u> byR�;?����. two �A3(3a&. Hav\5��|� ?of9#;0)d02)}$ (t��3�[@m^F�'Ra!�� n deri�G%weI�͂it-��8� ��j��-aXG�K =0$:�  (2"�F 2) e�� m�� id|&�Ay�e (11.:�d iff�g\delt1:��|}{A�9 �'Bc^�&md;&� 3�bu;R[�' A AI&8E� c& !�(1+�m�@< YN=! �F�( d B- EA)N !�lI�rhU�4)�� viewAg���(5|2) -�F|i* �)� b}{d�.z�M�Dd� 3% !�3�c^�D-�}{ ��HJ��Xi�e �(�0 ( K�I"�� �![AA�\�� d.�v-Jt2i�b1� T�5�et1�)Vu�� ta b EB-\�9Y)�^�AO�~5)=$ $Q $3 $?�6%.GL(2����O�*�.i5a2m�.�Jq�{�*below��Vj 1*�"j a��.j -��Oq:2� a�� "� ++&*f 8$5R1"S g �� g8� &� VI& ��x�*$�� -1% $$p� p�!�  ��f� ~��(B F�*� - E E4Ib �.��: ���*-�![�5��L!� &�E�"D \A A).�o:� Q�"� written��ay )��m\L�Bp�\tilde �C T&� J)n!�%\ diaga!-$��,� )�!A!*T3�$$:�]>� #�O(-T!xE�)�� E*-�} .G&�&u }}{(] YE�a%m�9c.��%4W�i)s�Q�)A�� -Z>�]4KThu���тs�C36)�� e1�.�a�I�(�-�EA��+�S.� u �"���# �� =-1D}924! �&6 I�Ring&J .S ga�-� �EU �" +IT�1, \AF*� B �I u�2  J<.�b (k)*A 43�tQ*� t9�i!_ b!�}aTh�#ird�yJ8 N� $us, compar| kAJ42)# 2)�4A�9Z8�P28�� BX b)��Wa!�bAB259 Q�)p!- %�7\BJ�m4tw�+Y<�7� ��Ked �zUZ�<6&�a,-. *M &M  *�%&���&#-B =0�v~TE12�T�E|��  \r Bq�� E�eV�a� � �~T]d-"�-U"�5~ \& �T#\B}�.#�%J�� "� � �= k^2Ta* $1-�"! �-�� u .QA�6�\"� � \A����%�� \B�Y;$$�V��F*S �,�wesQa���F� ��V�� �6� ��&�i� � 6`pbe avoiTR�'ppeal�3�'!-l7 @ qCantEHBB evi�V�'iZ6 �< �; pstoL�\ �2�;%P>56`oft16 � j."? 3.\�;�1QED�6CX�AgW)>/X} .�!!.nS8�Zx=0$,2@ $t=T$,�1m&a G1.4OMe ��!�d� (�\A%*A�& ��${k; E� \B0)  - (�nF:VF } 4.1%�$$*��9{+}(k,=,\��#"�. C}�S� �/$�*aL�  ca�int�^{1^&$c(k,x,t)dx�  (���R$ �m�*�9g $k�$, togetherits $xqt�; riva#,s,of $O(1r,s $k \to�5�9��Y���)"! ra�RTaurn*��� !=�F�:6]is�/k� � a�V/$Q$k�U;A fact%�-a!_+W�V�:l !���J Fose�=y[Q�!�1�$/@]��̍�ie!U� t_{\�*0ial{D_{1}}}k\C[Y t}"<0(\tau - t')}K A)]d� �(4}K(t'A�#4.� A? e�^{0�N}}} Ck^�aD�� ��reG�w'��-}y�@]dk=4eN3 t >0Qt'6 < IV$97%�a?$B��un^b�c(contour $(iH , 0]kL>"�2W)$ (i.e.�,ori[./Yary 9 �qt;�5�6��"�byT,o9Vg�[ZU�$�}7pasF.|a�points $A8Y| m}{2L#  n!�Z}�� M�  .R#�D"� �*�inded~ VQ� � � -�d�=qno(4.5%� Inde?in orI_o� e2�4e�re�� e l�8"� �!Tpl�4���J��_ t'}^��+-tb�����integr�4Mw)� l��atic��Eme�4he dom�G <� lex-��,plane enclos�..GY�. �%�w\11erm (�%�2 to $�M� $)E} ains2, oscillatory���_ (t �c Dus Jordan's lemma &?!�%is%� vanishe�` �cJ#9��I�Z#YM��orR�>J�����+B�JZ�XZmA�6eBAL�F�po$ "g�'.�,�� :[3�-2-� .� AtE1$-k1�F� _q d��2%2}� hich�G �N�sN�6�.g o� J���a� Q fu�mgex�g�N (4.6Er<6J`p, {D}_VF�ZOk��t)HN6�4 Jn}:�6�rdk;D�$$C61z*�n�>�J�2�J�b���G �3{DE�ɊA6at� !����a�U�D$ to� `)0$L)- �n0tU�� , si�i��I%��B/nd�6�decayA�i�Kha�A!� 1}�*"8dir ��- ermsJ�k�.��Z�s ��tt'�F� � �8'�kai�.L ��l�hlAX)��-�0}^ id�hg %�6" �'%� now*G'!mglh8da�1)�e expli�N�7�b�E {1}(�!�$g. TM routi\E echn3E� } +kNuS pfL}_1 -i [N�2N*!�W !$$ &_N�V�2c6�aJ�M!y j�% �2 ! ��^ 0%�WLtit��g�<:"� $a�u1�5b  0$!*� ( "ff*Vs�@Us"�(� og�&A H�K{\B��%�2�! ^t_0a� X}LF#, -$ + 2q*V5-Y(>9i�=2�`JlMJl - 2k~m!�^me�� {2}te�kYr ��-���� Rega�P$�&%5�$�� '%� * DEr\{ L_jh, \, M \nRa�Io � \}^2_��t:*g6 5)=��A�A��0).�AH k� � s it �� � %/)&P(1/�<�.!. Re�V} � � -k���V* solv+j Ep.7ga>>�66 �,�e l.h.s.!�:A&�F �ing�Z^���46oi��i A�M�`2 ROI/F GEy�+(t��.R ��2��ͨ^��Fj��^����Br ���2�-�2&� =+��-H.?m6i�T�$We multipl&O/E�2)$k ( O"t'>g$t's$�7}%C�O 8}. ���z diff��t step�Ir =�!`E]=�:p. RW �EeId(w�""=!�`E�n ^!�%�X�  scala�� J"g_� g_�)�r� 2�&]Qv6$ 0"& a�f"�vjEE�� !)is qu�Q_ ^XD isK ly du"�{fa*�R�wo�lam coupledIUA�4ortant develop�Q ��h�*�a�announcc!I 4}�!�it$� if�> �>!:d Gelfand-Levitan-Marchenko�It%�a�5Qt9!x�!6�<ca/�de��9I-on5v+5ly}�Gi1�� p Ee)� (or�6&LH!5&E��L�k����J2�i�pap�(�Kex�DK m aT1n� 6}�MXdd�NLSA ��on"-T BS .�*i���F.5U���}q��2!]RH�<� out*� newR�i*U�s �8�� {9};.! 10_�A �}erentAroach)SG}A�3!*�+�>�,�Balism�E� p dic)��; \e whole��x*A>012��)!s�)evoqT�3��%|]aIqf aߡWar�$q *�J!� "!�"C Volterraxl��e.o.. ��2��c19we(Jle0� ariz��}!>_��:ly $S�46s���Iescrib0( �)�6U7��Dif1��e%�E��.K) $been studiq y a &DWauthorss !d6]{10}-- �13�� a���+.�&) �T!�a�.��&�b�� else�{Bre� only&#%�--Q�}�.{ belof�X2� clas����Q)� = S_L.�BPs�MBThe�!�>is"d>=, Fa�� ��n Ŏp�+,Ib a � new}!Vm�1`sqk�� �� ���v�,*{Acknowledg� Y�is work��e��^s$jr�  EPSRCRs)rIG8 ��3�x;NSF GrX�(DMS-0099812pb� �width1�tex 6WDi�5fBll !��� �. %2�,2?8.5�� 6in = 6�y�}{7�toi�%0.7-%P:op= 2. he�\1!I(2` %}{0.3i9[vH,}dista�2betwe]b8e& ![!BXsepU2U k�B6 #}{9.09v�8E��%hto}iq]RR��4b�2p2 of am}qK5Gc�$} \titleeATime P�S2<(e Burgers E��,�� H�\L�aan�� 2.S�|y Strea�} % EJ  your �5��Jy bra�N\L{&K $^�,J��$Stuart$^2$�De�z of �ed��^�c�xm��m\\ Uni\rC$Cambridge,$CB30WA, UKt.f�<@damtp.cam.ac.uk�6��i�\\ Im�0al College\\ ��SW72BZe\\ t.s�@i 1 d,} \date{Octol 20049e6f)�r\todayZo make%� ��toEc,"plain" page � \ {� E�{abstA"}9 phenomeno���~y�`I,� acou sQ-]an;�al.P�:si0n�aN$literature�N"Q-{al m��.:0 Navier-Stoke&�s�us *pcomSs&&bSY%4R]� y����{I�!!'�O��4n�� YQ!,">�"e�"F�" as )Ts|va2A��A"ck1(19th centur��a��of KundtQ� circm�� ai�" tubesO� Raylv 1883r&�~r�9� d�a_2R�$he flows u��wat�� �reۤ�!x(Longuet-Higgins 1953, 1960; Hu�nd Joh6�&V�phlichb((1932) did gpex�a�a�t ��)(�4p�k � in�#- �r cyl]Or"�@�ald a diamete<)A n�� U5D��u�commo5alƦp�s �io�%��, mŽ���!^�P�0i���w-� veloN0$U_w\cos w t$2Bit� , $t?gA�l!de29$ aJX t�#-�a)�Ez5��&M7AV $$u = U_w�1 \etaΏos()� t �(eq3�$x{z�Se�^y(w/2\nu-��9h7FT$y.�coordin�no4A�� ��`$�G prototype2� (-�1851),�(� �� 3, Benney �+I� Galilean~fs�a�!�im�+f��� �!!�este��)`t5z$U )�t$2�OKr_$!C$�^!inf yi��[2�}]U[ m�GM)� (wt)x9!�3!��#���g�v ���o)ntrins�ly� �Fei(�r5!-�e_$ emerges e ly:"&�$��iB h�1Euh(1H���& i�& "�#, howetli��5D(�{)%�š A�U(\xi)-j]�4!N! $\xi��]�pa�SMM)l; �L curv�Itsɲ is neglecZ �.`��$: ;sm��( a�h 3a typ!h ( d�u�Rnu/wd�4!u��E���Je�..!�+C�V� , nam�A$u \c$�\nabla u�/ $u$5D��1�� notI-��{t)��&�'�&s: �0�OKs*~C�ora���KT(2iwtz.to - ��g�,te*y ����!Tonents6�se���s?m , do$&, k a ��BmZ "��!.��B�6 quir� (ii) a3-�s��d� i�Gri.> ;�#R5ref.��iG+�.er� C\n eff*7of �zifT�T$a ReynoldsKss�(, r�ea"�2v� �:0� A*)��be&V �7$ ! �# t�:S��,� w��a�doxalAf|Ai.M}�+����5�!�Q�)�:�m�,��D [�a�'b�!gwed.&�fe b��Ee-achie�>�Ko� "��is�� R�.�%d�Z)f�0%�T���R5"m��[K9-3}{4w}�pyAd�~}{d\xi&�\1� S�G��>� $d$�isN����-$e $U^2_0/w.��U_�Y� %�> �$. No� �+�� *V�e fama@Q� �'pla� signeI� ole;-�p�0Eqa� �  ce, digmeN[ �<���&� �+��R_szw1 )(d/� ) )$\nu"�?1.WcT!aaSr Ah"l ��j-"W5�(}q[;66)[�p%m��HO'oncep&�cal\ $�R�or0.byK5)��.UE�� E� (���:�,)�&�He* Jr- $R_s��� �6�� �^ouV�!\per�iat�2is. EvX*o2�'� �-W�@ cl8�@J,ܫw i3P��e�� 3%�ine�pr����an�HlanP of !�2��,W��M =25�jM] an "g"-^ Ly"��a�ali� large>�,�6usA]oJ�� ��i��Cr~���$�Ρ��ϩ�" !���/i a�mMN� 0M *��ade��is-"�g�yn')F  mu�. hick��h��h6d a �tfactor%�&h& )�'s-� Rileap998P pursu��EL�� ��detail6 )1�� E� showInNhe.):tic!lat A�out�d� ,)�it09?, �e full^�� �5"g!�a"�" !� $u� z_t�O�b (u-k�` )u_x"�H(1}{2} u_{xx.U7.x @�X �all��I��]�Q[)o�5to-� -1/4VN�,�i>� $�Ds �Z-"_*[.ar�Bx =0:�[u-o)== t 8$$ x \La�Zm0}I�.&]X��fy$$ )X = +�k�$ Cole-Hopf�*Bz$$u-k%: ��t��_x/  m9)$$ i:� ,p�%� !� =2�1fAsEpJ4�x90 K�<+I()?- �) %)Z01U..)D1T /_x=[/  �= _^2*�11!�f)&E�/ S A�)�! �a!�% �Y4?g�/�v�i�a�5,A�+�6pT e�% ;re�A� cus937�Yin OrMs&mej'me nŜat9.l"� c (1.7�x1�?� 6 � H4$u$ta powv�)��Ex$A�=uR=A�+ u_4�t)Q ^2u_2%w+Ks!�!!� quickly*� !�u_0 = �x}AJ (t-x&�I1.1�AtO{6 e $u�6� n$vsH�H2it�7nd - a)�����!� ţ2ed)[��to�8�{1xx} Mh-2x};$$ "� ���;� eL�$J:�^�aFu��u�4} (1eMw2'>W�t> A;Fy$, $u ])] �ZhigZ`�%d�re-p iofIb� e1E�%Xo�g%�(xe�� v(x��\ �Zz/2 ^2$$�{��<(v-k)v_z = v_{zz.p1��p%q;'y�vz� �v.1/4�r$$6.6�230*j 1�r�F�) 14)ENj�t�15biLv = 2k/[(8k-1)e^z +1.1� 6�� !���� " regi $(1Oz[��e.<e "2; �2)e�a�ZAlso $6J�6!5�[2�$V�i�^3� � sen��%�.Z 0�ix$ fixaJ�E>.�)z)gGw a�ivalenc�9is&j "�^"[6jf!f#B� by;A�&;"Z .?7)E�%�]���.� ��!�m}k+R noveltA �� �d �Ou he� ? ő&�ir���$ ity ��tV.|F F� r  V!&> B~� �=�bCalogero� De Lillo.� &rZ�!i�i͝�Va*r�q�&� ,>=I�8!�I��2$5x� 0I�<7&�P �A� OhY 0�E one NQ��3��8-�!"'2!F-WY@FW��woŻ�;Fso�n:� � eiu (a)r i�,!�t�r (b)�>�$:�"Q�c6��(b)"�{L:�iH� (� beca�PIZis C!�coe0A.s $A_n$!�a"�B�1 s� (���P(re-��Gn))�U �Ky�.�< �b) J�s��;?0}� R!�ce5���3.4b)e�E(i�iyR'cV�}Y/by js��U��!->6��$ (� nee!�)�� nv�� r7 )�L�gh!�c�@t�g�o �Ik�� g�l>C �com!�"= %����$@ �&�L$w F.C2�I!��(Z!6��Q�� Re6>$ �>$�$J>$6 s (5���� -. `;{FV� � Heat"T**��pos�H�k} ���N $c#�i�N!�m+!real-7d"�E9-8�:��*�� B�W�HIR110�[��uR+ cu_x,�&�W�t>0d m(2.1a)& �1��ά :�.  0? A 2Rm=, �{1bv�:e-'!1 -7�  \0)�`s��pi$�>�t�%c6�*��Ao�1m�"U�?A�s�j�t��0 �d� � a� t>&�$2.2a)$$ or� T!�A".1"- 2.2ƍʎ��:�G.  I2O^x_)� u(\xi�bxiAV1e `�.N�XaV!/E�s�`J` �_t! fraci�+ c(xq}m$B4�R �2u.~ )�$, y�4z2� I� aq4]+�a�4: \.���R;o&�F)&x s,�Ap *vely:.�9 I�M�cos t}-1=�"�2.5y9 �:]mw  _x  =Qq�]�5ed�.ra�3{P@�p.�K xe�+d"�de 6$ a^ f $EOJ]�E \Doteq���{[�m���} .� |]M then��j�x =�f uE},0�vN2 �d�d-�i�=-B u_xE1�^2u^2�~z~�� �-zi���,-2y(thu�v-&��oi�)&-�c�6(V�:G\2ku u^2-c��) E-� =0}.:��~ � ��1 �� (%M -1� ED)p"-4�a)� ��M@F**/��?Y[�4�Z%:[-�rW^05��H��ep$� G=Iu�%OEBI2�I���� �71%�Ga�� l�.2��.*7 o"�5� � N/ 3.1.}.A� N v*( N �$c$? �aw��v�2� ��8-c + (c^2+2in)^� ���y8,2,3���1 � PRe$f<0�Iolof��1)-A\l� !!�"�-u%�}m+-�_N }{1+ E������"X.&A*"��ZI4\{ A_0e^�_0)� \sumu 1 * (A_n(nx +int�z�{ A_n}6 5} x -*I~hg\.� ��-��C{ AW� _#�1�&C/��9 =-2c;$"b>Vin �&d m�!.A_!�e={%"_�c ���[�%���}-1 �] dY 1�!�%�fTE؊�b�2�n�^(A_{n+1!q -1}���\�� _{n,4�!?Q�0,Y�"��$�Q�#*���. 3� 2;2)�u��rew1�� a�SAh^�a/4e/=���\ha"z x,n) =2�.��Av2����J]�{n=#q}F~e^{cJBA.\{2}�0!�.^q[� �Z+C�-n�IyuN��9�3�$< Y���lk(xP�2� )p� n)}$B l��8��J�.�>�j�1�����1sc5%&���>� + 2c=s  22W1_t�p�d� 2�[.)2')�|�T + inq ]!�!ge9* �Fh8f^�- 22ad =*"}�$n��;r]-� = c_1 +F7 ���p�m�a�3� 5��VlA�i+!c_1�quIi2�gZB��8� 6���$�:��=�_2�>� ^2_nI!�^�A2�@.R8� Sub&�j8����6Ut!��]250ar*�A�~ sei+��a�=0 �2�-�� Y�1�n2*� 6�4a� �5%�2��b�='2+en [ iply�QB��'��-��i�t�"ok0d$��]!,�q�bN�2 �� �*�>�%t}2� j&g$]*�)/ q��2=�}nW[q�!� +1)+ � -1)]AW\pZ�>xUb� 9�w"��_nA_n!�AX�%�M�I���>� |G��ue �O!�� a)� $c=l ^2k$e�)7a�%0$}�,u�4.$$ * p"Ci& �2��3�Q �s" �+3E��7*L  bO �dx*ly.RVS$}co�Tc -�a� 2�=0$w �5 )&xA}� � 2!} �%)^2 + O( 3��]�� e�I�$$!�oir|z|=10 1}{iz^. � [J o� (z� 1}{zM :�8 =( z� .^2� 2)�A�B� dz�� }{2i��R�6�( :�md�!E8�V�!i � �2^�.�)�2i\pi >U�.� + c6�% ( 2*0!Ln��Q2��$�<��F2(��A�6�� �.k/2AT)���!a4�6�" ��-\sqrt]�WF!/}{4A�n} �(%�0�)%4}{'}�T�5for�͉ ";$ �Z '���)�� � g �-2 k� ��-�(x G-(1+i)x+�c (1-i)x-itMG]�!��!�.Y b)Xe^^g) 2�o2' mxI3y\*9�$6� 1. u+ z�� �;{[ ���- � tit}A�=U!� �%�2'+i3 Q2it�� )[%o2x�e� 2)}{i��� [ �%N�:;�� �A$5��� )� � �-�a I�! %�UnJ���!�Q�2}!� H % 61u>1)��Y�) $$ -9t�(�+i)�.�2�x~-)�2v)p Z2A\.^ 2AA=1� {-2}ѥ_-umU3|k!�e�4e ���3I��#G�MyYb�&2�bJ�,�oneq 1/8� �&��O:{e �ar homo!r5"� BF#�#he .� � ��)� j��rm{as�� \���� &��5 i���is�* t= -��`@ F_1+(-1)^nA_0F_1' F_n"�5I'G  $F/2G YF��I�1}�&�}M�.� /%z�)2a A�>dots}!.I5I�� ��=!�"�(s2��;!ro�=-4c�� A���A_1) =0&1�5�=.cb�!-%�J)(�.F-�S - Y]<Q06� Ŵ#5T=_�%1}{F_n n.� s&�in�9MI��#�.�^h �A�+-� g  +A./�M�%�&�KT.� >W5�Let  $$G_"� yF� {d�}�#��E� �G)|B�\=e5.�n,1��5 (:F_n\sim �4}.��znF�$,H�!atA�^�oeJbظt}8c a2{ @E.�7'a�]c�9s Rz�8�? G_n �-�n,1�%n&^�)R c $a 2�.4IlA�� '���I{Qk��pAEG=�3� 9)$��xL$A_��cR�Aj0w� e�. " b% 6�!ѵ) (:�O )^n \J;^n�qh j"/N�'�v�4�A  '� �`�B�p" !Rf2f�C2�� n� *u A��75*�5U��I�a֡�= a_0F\o �C a���2� ^2 a_�  �.�&��5�!+4"t��'P�n="�0��sar - 4@ �0�"'55 1y5��1@Ket��A_I��� *�5�32�1��(0)��,G! qA��%=e\ = 4k!l5�13fe J &+-��:�3b� 9I5.)�%;@� (a_0�� L .�Q2��^.���3a)�=� a3J.W���}{26��2��1Y����.�$ 2-w�B!T.,�� J� �� E^T A6��4k9%I�^*�%jm %�� + { .�A��z:" �.# dqkj$  k�p39 �2��"� 1{ F�"� �z N) �� �).|l", *{Ap��ix:T6�.� q�A���+�_6ƞJ� J�.A&m � )�2\Lambda*z 5 )-6  =2,3=q�Av  %�(&&0LeC$f*�� $ monotoX�0�R�,e�jQ�#�_&�G7���2.V1�We ��"|.)'nP�m����� �)^V %[������j��%n^2_{j-1}anc_2>6 %_j f���Mh.� UhA� � �����A�\chang[6 varia�DA_n= B�� �Mx \ ���gii9LA.? B:? �|i� S�!t 0!1+!  /F� 0f��N�98We 냩�"? n�5rixAIma% \Psi�V! v,ef� bHZa&e�0 & 1B�*�&�G _n�&"�1  } L^ a-�"Q���(��Z - {ll}!I \��5wJO=��  e"Xvs"# :�"�@ڰ $V s?v�\pm�.>�c�� �q1�^�z! .DI$!�]�%S &d%)�[9 -��v��j�� gaugeF�?9� T_n\W�e�T! �F� 1]-��+_n &� -_n N�"� ALi�n� z��_ny^� T-%)q)'j��0EBE��v7� "�2 (A.6aU��I!�=5�E�L�_n �A-D1� �A/0^2�!F���fq_Q;�k�X}'R ThNM=yma[��� ��L' Ta&� �ET%�_n1�= I^�3��$s>% WKB �Fxzio��(A�  �two"��f-}!!!�f)fQf%�=-_n � :`����yZ���N>&o� $� = g_n.^O�7!#-g�+l� g ���d95lea�@ m�JJ�����&%b�jQd�E�iI (��Q�}��6c>�BUA$$9|6?�m>m�$j}\right) |= (-\frac{\beta}{2})^{n-1} \prod _1 %�1}{\Lambda_j}.$$ Hence using (A.7) and (A.3) we fin�}2). \section*{Acknowledgments} \noindent ASF is grateful to A.A. Kapaev for useful suggestions. \begin{thebibliography}{99`�bibitem{01} D.J. Benney, The flow iduced by a disc oscillat��in its own plane, J. Fluid Mech. {\bf 18}, 385-391 (1964)�|82} F. Calogero !+(S. De Lillo �,Burgers equa!.� of the semiline with general boundary condit! at 1origin�$ Math Phys �@23}, 99-105 (1991%��,3} J.N. Hunt�4B. Johns, Curr!� in5/tides(T gravity waves, Tellus-$5}, 343-35)36tP4} M.S. Longuet-HiggirXMass transport in water d Phil. T . A l24m535-58m5:m5�m!J1e layer!`a free ."surfacZ(8}, 293-306!q606�L6} Lord Rayleigh, OnzcirculE@s of air observedA�(Kundt's tub)�� on some allied acoustical problems, .4 -417!41-7!1d883). Also, Scientific PapA�E�2�39-2572� 7} N. Rila\A ~$ streamingE�or. CompqBDyn. V10E& 9-35%)986)48} H. SchlichtP�Berechnung ebner periodischer Grenzschichtstr\"omungen,mZm$33} 327-33e3��u,9} G.G. StokA�-�effect!�A',interval fri��a�f�$s!�#mom� pendulu!�M�Camb. )�Soc � 9}, 8-1E8856�10a�T�4uart, UnsteadyU� E�,s. In {\it L!� ar B�8LA���a�qBory visA0����F`,24}, 673-687eH6EendB�  docu�e�} ��%Last updated 20 April 2004 \d ,xclass[amssymbols,12pt]{article}��4tlength{\textha�,t}{9.0trueinF#$width}{6.5N"Pevensidemargin}{-0.10>Godd>$5$!� � � `sep .25in \usepackage{ �}:graphicx>psfrag>amsmath�\hnewcommand{\intbar}[1] {-\! _#1} >0 slash} {/-\ /Z,AB}[2]N1^#1_#2:7curly 2 \left( \b+Harray}{c} #1 \\ #2 E4  \right)>�O}[4] ZN O&N \[2ex] #34.^ Z^ straw�[��]6�\cent{c![/:A{ {\!�cal{A}} 28\K.KBU.UBV.VB diag"rm{B$ff"cal{FB B.BBhh. HB LL. LB MM. MB be4 gin{eqnI36Ab{$$6orl:(ee{EwZGe G# }$$6ipde{p��al diffe�  D 6/tGLM{Gel'fand-Levitan-Marchenko6, pdesv\s21 {\display�{$$style{#1}$:ehalf{"\ 2:third3:q��er!4:!suml{,^\infty_{n=1F$nk & n_{kN!k6ER$O6$n=0Ji>$>�$nepsilon{\ m��3�GR�h_i�bb{R}^>;SsS:�QQQ: Bint\xin6�a#^fty}_{-)_:M into$.*> intx%x}_B xinf_ < x <�Hv2(N{N\times N6D{a�\m6dY�E�68s{Schr\"odinger:�$f{Fr\'eche:@F{\uparrow F \dow�ow6\HO{{\tt��%e!kbig� :h barV�HV6EdTfdxTM�d^2f}{dxBdTu2&uZ&y2&yV&udxpH:�dy B> vdq�dv}{dr> R}�><f% > udt.�t> Tudt=N�tBNpvpFQT v} >VpwF0wn0uF0uv0n ��.0n:� pTupU42^�  FD65):6J, Tupy1RV6yFa Tupzv5zR5rv5rF5upzn;z>;upyn0>�pupQ��2�>�pupqR0>-pB/](F->�-B�B�-B�TwNR.�RRwN.6NvN.�NvNj.5VjJ�.5I�.�{�{\em De��, of Applied �ematics}+�Theore22 ics "Univers�of�ridge"�,, CB30WA, UKAt.f�,@damtp.ac.uk\\\ Dedicated to I.M. Gel� � �occasioZX his ninetieth birthday)��({September �3!� make%� -�abrdct} A rigorous methodology5�analysi�i)�&�v%�p1� �� -�, $00$,[integrEnon-ar evolu*(PDEs has re� ly appear�A&8 literature. A�#l!K-)t!*.�A]sb$q(x,t)$!�Ys @ 4 can be obtain |erm% 5N� $2� d2$ matrix Riemann-Hilbert -+ . T�  iE�m� f8he complex $k$-} and+,uniquely def2� of �0 called spect1fun�s $a(k)!�b U$B(k)/A�eB0 '3! b�nstruc�.givenU0co"�%w0) Pq_t(xvia� 6Rsystem !_two� I-4} ODE's, whileET<\emph{arbitrary}Y�� the = � �!�!�c��+d�v�of four �U��s. �E�pm w!�aye� ځ�ir} F~s:� casel�Hant Dirichlet data,!�P0,t) = \chi$, as wellEw0ase that $q_x,A.\sin (q/2E9 \cos are-�ly rel��by��s ${_1-y 2AzWe show �se ��s,�MM�above 5XAsA�!�avoided, �!�I� ajuA�ex�Bi�pin U� $\{ a6,a,�\}�{ %R_1 2%ree�ivelye[us�se ``I��'' �^-5�:^��solabe0� !�$same level! effi�cy asL�i l6c5G�.G�'��B{Introdu } Let5re�f e�^ satisfy a�Z�1�2���BZ!� �]$, 0�!�$\phi(x,��w�!�vector )0n appropriateAC�gm< $x$-adassoc*d Lax peA�e΁t=0�usfN��Qm��E F. )N From<�IuC4, characterize+un^ n-�$e at $x=0$��$he require �hN�q� !�, �*, �= \}$ Q�=global��ion $$ �/, -?= = e^Ki}{4}(k+",k})T} c(k), �d �Drm{Im}}\: k \geq 0 n 4eqno (1.1) $$ I$L-�alyticeb$FW>0I}� $O(1/k� s $kBa %�y=s $� A�Z�N $\Phi(tV�  �� f�t�� A�!�e�E�Ph gR��� ���U�i�UE!��O�}y�E�(t)$ throughE+��� a $�1 " �9w]I�ie�VV<:�iRq�andy1u^s���څ䁒 most�,f ^ tep�)he�B �i�.�� �f missd#u�e�$. For exa� - `&�5 I��) 5�(is prescrib! �i� , it,sh�#in [2]��Q&l �* �2" b�*�" &�  It was�1]%�[3 � s�!�� J� (ch we refer[asG ��awR$ 1possi�to bypa�#5�~ r :t ARto!dI �e"$2&on� 4lgebraic manip� �$ ��B��is!��� % F�Q&� v $ �ant!}YA9� Aj ere existjother' 1HNsw~" inv� s6 J A�� leteng! $lso includ�� �M���# para�{�m 1.1} �� !;N��q_{tt} - xx} +  q=Ր.� ��$ 0< t �4a�or$8 !&chiG)cos \� x)�jy)�d-2%Y , ^,=�4b|-Xr� _1 2�� 1gagAssumAQ�$)R -2\pi m� $q%N ?Schwartz�m r $m$ �er_ m�eJ�� A�at�W� AuJmf x=h , i.e.~a��(1!t�o  b)K9�Y;x��id2�  $�0)=!3 \ \!rm{and}}!0) Y� \dotE�05�1=�1� _0(0~�^+F,=0e+�*�1LZ; * ve a� "l��b� �aH1+2J.� jI�0\{ (k\mu_{12}3(,k))^2 + 2i�q�_x #2#I�\}}#5.� REj $$22}$ denotA�e (12%�$ (22) entr�m�$&< mF �$ch6 ]R6�T. (i)I� (meromorphic$k$E{$k!$ K bb{CA, back�$ \LL&� ��is depi38Figure~\ref{fig��, $�by�s \LL��{ �#hrm{Re}\; k =0 \cup |k|=1\}.� %�N�f�}[h] \ &${a}{$D_{1}�" b 2.c 3.d 4bU#�er} \����ics|11.epy"end)cap:��a�te%w��@domains $D_j,j=�8dots,4.$}\label`.�&] ��N^N vski�'in (ii)�� � � .�Q�`�Cbe"� i�D_1IBI�U��k >AFaEF>1e�quad D_2J4�1<1$$��D_3J1 e<e 4e4J4e1�.e�}�$:� jumpA� $�_-�g mu_+J , �i�\LL��66�� U�\in!)e�D_4)m)+6)1) D_3wnI�$���JkN��/V�s,� .�u��� $\theta- ""�D fo�e"�8align*} J &=J_15=)1a�!;& "2:"2 "3;&� %3:%3 %4G4:"4 "1, e����N���JJ�J_F�J_F�J_��2~�eq J6�2})*����$$J�v9+B4@0}{\Gamma(k)e^{2iI~ }}{1&�uJ�D3\over�:% k)}e^{-A0 D�� J_4=B-\gs.3-K .P 1 +||^2� J�(J_3J_4^{-1}a w0�j� a�}�� }}, e.���'};��5 = - EP 9 B% k)}.\A}i� [� + ��K� ]��% D_2;� z 7�%$6K!�)(k�1}�x + � t������ �$ 2�J x� nd� ����!}�phi_2(0,"i%12)�6."�} 8!| ��.|(�� � onent1�,g� � "�� %4ET9k- %:)�)�gma_37�-i ii(k1p H%�}{-i ("� x) +� x))5��4B3 3g723 i( f� �j�2� \ n�e�>%G mikx� ()y�+ + o(1� )�5�as� \ x�/a�)\J,*9!�)�s)t = $ �. $(1,-1)v �2 ( E(r 2�lsI�/A�? = ` $�F<A~�3&b)U  .� IE2}{�}A7Elf(k)b( EeA a� }&a:& 67�@q/10)!9!� ^N~6C [\alph! + � �сa!�2iA�{ �qa,�)}] A:�[nR- e k) -�Za} �)&��-z� �>.�r�����A;10&Z]A = i-� k^2+�^29, �A!�5Wof [1]�fy�4jderiv kF�ewi25 wA�$scuss furt7thA�results�-�8{An Overview, D�6� Pairi,�*�t,u�_, C"v(0} We first re)G_�'%�eRY ��!�$Ae . �m�h I2pSuppoat[�$:� =hA�;$"+��i� <\Psi_t + if_2(k)k �Atilde Q��/"� 2.1� Ɋl &� \� � 0�$\ Q�N�*� scalar $ � -ni�p"ut*!_$kɃ!N� $:��Mof c!, � � l-�E����LI��s. $M�"<!�d+aY*% $$MN�M.�0, M��& 6�C �  MuG!� (1,�a2 2�-�"5N�&2�5O �%Osuc�"��.+orm�%��& 6#_2(t,!e|P�1}{\rho:..�}Ak) �5 ^2=1"� 2.4A��N�B� �#� I�T} :�2(T��1�a�te^{8 �T&+ %+���.R� ��y "C)�D!���6~% \nuA 2�!�F�&it le�Eu�$ invariantM�! U�&r�>�*!"�#u�J� U��P�-���- 2� �\�?]?� �5- 3 Qm=��The�!}�uof6M 3) "� m( � =~i:�k �/� �'�eقs��5), imp#"M( betwee� � u� �nd �&A��\}<U!�V.�-io"�$.� �ute2��#�V�#!&�:)�"2 Two��q�G�ess?#h� � 6]A6��>BpQ- =�,,�� ��Wd(:�>HU\x��C�NF>�) ��G餚z�� {�-k��!-}z"!)�E~ed�:��649k}(-1+Y q0q%q_t)>qT # #6 # 7i(-1%-#q)"�2�$$� $q$ � � M2� A�Y7RU [5.C = \U-O.� _tVJ%��+�B���1*� ���&=��ces $��  $�6�\U�5��$qaE,c} -iq_t & k&�,q�$�%)�r} \\ -95� ;1�;6:& t����� %V� r�xR�>�N�V��j�x.�:F��1S \&�'2C�3a�Se�$ � � now*�(�N�3>V sC pair�S11):�/ -�1s�%to&[2�NB��s��W#" re� ed earli&����6)-(2.�K9Pro� onF � fy mx $\M�r$ &"�2� >'"} �YR :�M� = \V� \MZ� 2 �U MM (hE� >� 1�(��e�: ,V�e� .�is��5U�2b�!:!0 ``symmetry''" �C%H.��� k&���6� �. 'k ��� ���]F�' R :���!2� 1}�ef�Rl1q�>��+ k^2��}{J /� 1$�2.1� andB�-X7_�G.�1:�2}{2�} �d"F'2�Ff} .�� "wSN Proof}"�8�� = (k+2/�"tC11�Ax6)� �'($\nu =1/k$.� u�M*60y�not� &�� !�$�N_PN=N&f"2�N_"X"N_{21 "G" (4.�� I� i8se2�8)te�] � } .U� $If $N_3=-N"7��(�`AF�(i*�S���y"k dgle ���(12)��&).�18) yielma�2i�,N_2 +e$Q�寁{y "eJNET kN_4�� + y2F< kN_1U�N_4� ���*� �dis� uishQA�s �)N_2&�+�=&�N_1.$ %�"]$�l�9}y� UoL @�:e�!hn?1 A�19) becohH!�FV.�@*!^��$,A1 =�I#$ �~W(k.f3n�E 1�"���(/- K)F� cos�N)�Bd.�s�? K+KQ��}H n~L=0=�20� Let!�� �J��S  m�e� V� 7�4.<$�:�Z�+N.K 9� In wa��Y?"�a g��} , st�Ong)]!V0�d!�� )', ���V� s>;Ik&) \*�,"I.� 3�� $ ��F �Fq 0$.}45Kb F^�$&- ��q v � � "� ab{Q��,�!G{2}a�{3}�$$6v6� 3.;p{Q}, fO,Mna�p " (see2�1)A#2�-��amaC4*X%1R��$ �� 9/E5) l � �<� Ah,�%�� "Z b��&�D.�NA �aB �J3�z`-�baH(t)$&a�� H_t(�2� #-I>� 2��AP:U V�;*�A�� D ���3�-� ��6vno&Si.UC� � � 5�E�t*� F��k)F%��x  = !%� =,� F� more�D��N&> ��N��'�*)Hu�TZ B:�rho�p *�o�� "W,RX7Aar7�'�(H(T.-T)��,>�JF�ba¸ba�v�H(0 � !�%�=�b-.} 3#�E��I��iW�� reI��ő. (3.3),�9nnU�"5+I����� V�Z$$ 6M� 6���dex B (3.7V� �8�8�>y replac��i&L �2a_6�G�B6�% uIc $��M� + HM_t� H!D-R.�ZH���. $VM$B!�"%��$�tyi�#�R4) l5�i�K"HY S I?.�7�? easy�&�=T�W��s�I [ (3.5�\I)� %lat[bm� f�DIbD1�8 ���I�tO6Is ��� H. HavA establish�MhZM55)�isMa#\forward!y@ _@� e �`XN� > JM��@�d5%4M�T$,�ex� �$M($< "3IZ{ Y�A(2.5)),!65�*'(3� J� &H[}KB�G]$$�a9BL���bI!-U 8&� b&&"@B"����=���IM����&��%?10M^2.\ �~ipJIt�B�MverifQ�$� �d!��"A<� Q��Q=-1:�6�3�'vah=e!y.F� � �� c�!"�p%l}V�ll}.�!�)^G} &�-�.� -i�-2& ZB5a��@9~GT#q}bB�'*�!%�: JB� ��9�A861�� s !7��E 1U.13.8a),aJ9��A96:82�96TB�"� 6�"�; 1a�Ao*P&�O$\m&\,�%.3� .**UZ�64r (1.6�*�"!] F:Q9*Q-�᝼K!�,�-�Ib V!% e� �4V^8m�1#@B�Z@ &-1&� \� �"�y9r1& ls $ $ o�H�K6�0QUi,�F5P�e $g_0(e a�4g�%�2:�FE*�qfV4�" $%�>O" (1.1�[c &I�K��Gd E��A �4a':,Dt �5 = �%Q � = � 6� itZ�F��adQ�n)|I��(\r3Q]�YA�Z$!0a��jit�#re�>bEQqat��b�A��� $B/A.�YX12+P �' �A4R�Ea.�2�$"1+R� 6 f:J &� ż"�toget[,�jA�8�2.�/ur�+^ conven�j!N.wDEQ06to 5Ms $t \toftyi2to mS$T.=7�s� � \�T not}�Bir&�Ks�-$ .^+E �DlFu�=3u�k!jVZ�2�Ӂ�6�N"�G�D_&�)3}:N�CX*Y R)�&rM�ed�N�,+Ile�x �yi/�?�2us F1�faZY��A� wellI�B�{)�p? �%�N��g!YY�s�/鉩Xm!e.~�s�| �{,ey!IH(f8�8 �M�1� \Bigg( �C� _:bar7� 2i & $.\\6- 21+6 + 2i. �� ��5� ��*is)3�I1! 21��Similar1�%��2(1�.�) ��$�E@288! .5- ��7�&V6![261�+nC8l& + :?n�8J�*� 12e�*1ys-�I�3%�  6) (�[$  -1$),h#v� $A6Ra�- ml6 ,�N findQ�l*}split} A-�[  &�16�- 2* Z a3\{�9B�?f�]�� - [:��?f]�[��\ B����)j��b�?j�% �I�)�$ \tag{3.13M�=��W)ͷV^I�3 5z� A�0)2�,:� ��� \6-I��$ D_1$6��!-}� � ��yA!�B��*�> by $+#��1,>Ba�1�-�5as�xF< ��nQA!"� RjR[":L� B�7 is indepe�w� To� altho�T ;�0ula� b)9 �3ed und�RYR�M��*o R��]is� Wq ouR is��.N>�<R�:C*>6�"� �e} �A:�$n$)}; k_{j} \}�<^{nn u`R�p;BK!�%�� ing $n-j42}�Wd � EX�A{a�y *�4%� ���� to "�5�7L[\mu]�2} [T7� columng5"�&"���LlWz {j} 1*\L}�#�A)WAj\"�=�8�C�1%%A� >q1��m�aMrM"Z*?PBIe_{%�} !,�%3 &4"*�F(-�Edo)��)bG]�, \�Sj = 1,:s,Eg,� cB,� Res_m{k}L.\ X�fFG(�� 5�"0{E\P )}\,Lt�j.K%� j = R�2�vI �Y3h�1.���? 9% )} �V�-�.�Q{I}2�.1b�\I�1 4�sH\Ma% %�p�2.�N2� �:�.L�2�N�>�$R } uB�!" BAU�6� )��1�|U4.�Oali�LQt \Ate "TA���-�!���, ��, �Jm�$���A6�>�H n or��o�i�!*[*$�("|<�}�6`Aa�f��� he R&%?of.����Ur�` f�th�|.�_ e��s:a O{j�Sդ3����B�$T�=P�.awritt�e�%�I��o�+( ^{(2)},3)}!{���+ /2/1/4>/3} /3/34012 1�-4. I4su�|cript��sdom7R��6<2��Z�&n*k_(���8 �� &S2!a �� 3} N etc.�It!��Dc^7�)�1 mu$ &��bAD!�F�{U+�2m9( � %]1�(��.�!C�͐� {1}�O+-ZY1- }{d(k)��.BY�Z2Z\IC6�A!F,� m3��d��)�/9:)xMm D&V�fj%046j�@j2�k4k 4. 2�a8!+F�F�M;*�M*�"N"� 4.4)O�.>�� (4.1a��s|-F!I� -} =i�+} �P"u A�V0�k��_{+Q[-C'"����0aR._th�h' (4.����x q���.Z/)�9�E�= a �1�!J�*} 1)]WE&2�  $A �$$:t�  =��~)2p } 6�1)5~��oy5ic�nO1{sup�%G$��)�� c -�uzu )�v� ��v �x� "�%Y9�!� 顜�e� �uz!� ^% AsQF �� =C | $&�Q�f��EThe��/*�=,6Ms�V�ua<cqlmu �d�J6CZnn og��6�`�u1o��hp<�1JoR�were �(f�$E)N�kV�1��_\#= :)< a�mM= (a� *Aq:�5^%�.2�6 �ty�"M(o�`Z�;�*s(��*�8�W (5�0E. !�mapZ]F�i!�HF6dis' \("z��!�a�Od 'wo&D iven�% #�J�F (�\�!$ ��/k$�� is VF&�/�x�� pap�e h cj3i!O��!��&�(Z/ )X6/<5�0��'/� �)�0 � Fu�L/� �%+K0lgorithmic wa�8 "���$F�+maku�s!1e���ofJzN% q�i�5a�&uj!�. ssex3(I�(vu%ysB\"acklu�^s�X ]wJ6 prov��hpaiJjmpu �c(!�anyU32�Q��%�� advantag� ourRA��<0!��iZeIIs_sNH, >O9��$N:it!"�6W UjDxag�&a�� ple >dd (RH)!*����e�x��Iͭ"�0�!�R 642'*qA64�A.B�-� ��, namUts�vR"�s: (a) HahL%�A[}!'� Jy . (b)� ir�'i!ceJ"kMf"v8$a. ��c'��!u$�!�"$gYD� %�O 8 manner. Regarރu9�hI� �Q��Ah��^2!9�j-UM2]s"�novelt3aI�e�e�eҏa morVUm!X}scon�d"it�&dl nadiDal)i9T)BhoweveKw^J)�bly}*�O#E�)�u -�>�-&�6E2�f� doe(�it!]}� � signz��x�Jlex�to!�%�|A�9�pSl,m%ok%s!&isH�D to��ei-NZusual).�r�v�{axi=|nactuall!�) se��YU�0hA:�\s [7] (�ze9���(,Korteweg-deV�hAmod��d >"�6L�'=�-imM�!WM(,}Ev4\&=Zlong tiW�sympto8�&d%3�� ��HU�" �cay&9$tzaT];D7'�F5�M$Deift-Zhou�ach [8]!�"�0I"te.�ŝ����'�V�%h$x/t=O(�]A�g�;saur��=  ��al }�}m"xd xs2�.$4M2( + a���ervIlaws,KI!�u$ [12]--[13�WA�.�b� s Ɓ�mal�)s�! �e�Y[14b&�s �^of ei��r{1}mypAN����usse15] �an ext �&9  ���B%[!�!�inf�ie (� an Ji�t�dN�%A PDEsR v� ird "ve)?�KdV%�w��\ s�A�� phy���KsG �Wq�!��m��}�*v)�� e�.���1A� f�2��16A42�Y=с�1�]he qu�~5� �qrabil�ofaZ*&L A�quantum�"…t\�y �� $m^�R&E�p)}/4e_F�Z�5�p�D}x}} +>'}V���V�al{q}���� 3)ctv��&� Bs�man= 9 ��ci�FBj -triv��-?l"m" ��t)#�#Aa�ed it�)�rinњ��"�Am}��t�F"�%g)8-�' �u0}�r��1 :�� $A�+q_�%re "m�! ��_% QN 2� �m�nu��of5"o -#��E��% �%k*%a&�Q|fi�Hor��:9udi%�I�27A6�-�Y�!�Y� �u��ar2�5.3�&� -d� �'�a}�Y d toa�3 at�do�:^ �U!+cer�� $V(q.�3]> (5.4���{g���T >�u2��~ly manPM�%� itieA�V)�agrees�SA-$F� �w��Ap�E�U q_0=\pi/2�0!a*n=�A�ide(g�&*4^�or��Ii^sQ� E�ij!#sc<��m��P�(���r�ameG<�$;*z�L>Sa� [20]!� b couplnaf Toda .�6�7BQ�I am deeEX grat1� to Ez�rriga&* �jea�. e�;$to A.R. It�f\&A B!`��in.K for � adx?ў.j�KF9a�|�%�&�;!b.tthe6�� 16} "�� 1} A"�, I&b_&�|&t���-�sȊCommun.@���ys�� 23��$1--39 (2006A�26�� Gip�&�~to Neu� Map!? Ci� No= Evol�^� (preprint�3} 2�5�!�L.-Y. Su��=\s5 � r �Zjp4} L.D. Faddeev, L.A. Takhtaj�Hnd V.E. Zakharov, A�Y�| der#d ! s5�&���(, DAN USSR,�H<219}, 1334--1337!�74); .� �.�?Dit Hamiltonian M�:At�� S� }, S!u8ger-Verlag, 1982 �@5} M.J. Ablowitz,z�0Kaup, A.C. Ne� ndؠegur, |%�k�+�VPE� Rev.Q:tM�I�8262--1264 (19732 6} P!�Laxul%q}r�y �� ary �a. P Applq!ա2�'467--490!�6�Ub��7.^(S. KamvissiG�heZ� ���l&dIF��?2� d��;U/A � A�%�(����2;8!;A.v: X. �A�steepestE��o�h�.��>�y(s, Bull. Am1D" � 2�c19!�3!�92); P��b�. A&��A�M Q , An�%�4137}, 295--368!�96z9B���, A�&�" 25�V�in labo9k� o�at)�TKht%T$em. Fizikau�9d+38A�03�22�10.�,A�*fn=�New��:small *4!>�Y*�/ M+ofFF�Hf3 IMRN)~6!|85--299�76�1} 6] Semi&� NLS�����0��� (to o 6\ 2} I��Habibull}�Sy�Dair�in �g V7�P�s,��.pEW�+147--1@�9�L�DZ4�dAdlmZ:�e�,A.B. Shabat,�2_qE�!�Q�!a.RL �1¦ 98--11IL:�4J%jm��aw�q&�f���:��9P�9E�4E96�5} V.O�rasᚡm�Sz�!U>se��:EAa*� q v.%�͟�"435--44I�16�86} E.K. SklyanAIU4*N6�q s� s, JQ�A��bfɊ237a 389,!86�178  MacInty�L*/ 1�>�yB���orye@��(� 1089-1100�9568} a�Ghoshal/BA molodchik!�5$StK-`� stat� two-dim[a�!"dj� um2] , Int.e�od>EES841-388���GEr��m-ibid,� . 4353 �46�9} *� , P& Dor<�R.HH�Letdijk, R. Sasaki, A> -iA�2�)u�V. Bi33�I83--9�9:�20Ez C$ r�A�E B� B�},ag�oor1XSu1 ��11E43--164)46�Z, P. Bowcock,.� r�Class�#l�5�U,:XB�a�o�, Nucl�Bm[44@�469--5.��a>�  dq�} �l%\eO[aps,� (]{revtex4} J&two�(,*�/ad.:use�O�x} .r�\ng} %.d ^ }% Ae2 �K��6n deci>point2RamF�6gpsfig�����Wtitle{PC( ar\'0cu�c�d measg 0of hyperbolic�tnon cha� att �or1�def\acJ{0} %�  isso%�li�pode ocȢ tyHlagura da p�gina.�)0% n�o sei s��� o 3o �o�3,{Murilo S. B��sta̛ff�{Up�4{\"a}t Potsdam� 4stitut f{\"u}re�ik, AmAPen Palais 10, D-14469>Ger�} ":�$Suso Kraut�I j�3 F\'iaE," �dad�$ S\~ao PauȱpCaixa Postal 66318, 05315-970 +,BrazilvŜCe�Grebogi��ҎC�\!�yA�I�a# �dOV�of F��reg,�� size�sn���@ dard_P�2 rm�qW tend�F0 $Hu2isw/or� anymX!sol�by un�O e pF�c oG�� I il�by �� �� traj}�ie0�lo�!outG�) �g&low' �a devm�^D! (_rib -=��-return �sEA�a�nian. s$sequently,�tak�5to acco�n#!:ns��t 6�a corre�Bmp� ���C)5&d! iG s wF&�&r�t��"A=��u *� al}���a$n exclusiOi":�9 )~�I� IYn�� %\vg�*L0.4 truecm %PACS: ��y .[�In dynam�n3�eA�of%7teresA��alΛ�&U )a�o "?� UID|:�?!�aYA����#&r)&m?&�-� �jxos �} yjma�uubA�Bergodic� =#�sui�8Ÿt(ͤ ua10,du:U"�"averageUQ tangenc�f��Ier!� rZz��9d* phas�yat�,"�ng�V,J�lI�6[ i! s doQpl�&&ole-Cla!197}6�R̤�)�#c�{x!V.�N�seX%mJ�(FRTs^Ztau_i, i�l�N$%i/e��y Qd(r�!6�oneA�a$� �$hirata:199A�It �pro�/��N��,�P *�a�la �A�a�)A��(�AY鹁�D  gQ*to q1esNe& ss �J(!+,V�k�8B})=\mu\exp{^{- tau}}/2��7$ be!$�pro�hdfty-e".(I5;at f�E� $�2Ks_ 2'%�5 zaslavsky!l1,b6 :2000}@ un � �0W im_{c .�(0}�K%>"\mu}{C�?�)� - 85B< G�?(.I) W�lc':�I����  $CCV!Wa1��&izfaӠ!�$Jn $ a "ץa!z�Amuz*:�|� multi�F� trumW]�� b�w.'$ь��hadyn!�2}.2����ork^.�&������?�Ī��t'e�` ]@a:far�  ),A�"�#A/�,f#vV.byi!!fi�.� lcl�#d t�ao��.F � ��� ����!�wej %�)Ným&i�ɖs�[aC% y&�r�I��? v- �(�o ). BO�Hm,:� (logzl��p%5H\'enon'.)ʼn�� (Cat��).�3V)W@ not.�$�\�imA�- increasesAWoK ��F2, cau�4G��4)�S abneWgnin�4. � vE_of:"�!,YKE 5� very� �.�OitT )2@M�� �2O"> + �5lready��2iH v s cl� � homoclin� !y"�  a� M�= � ��[>� ��l"� :�aneiB � �1e��gover�J!l&��*� seI �l�V%$0�$e��0Hartman-Grobm��&h  :1962n�1n]^�2�~q�b� actl� �� 0 �.�it. HX2,��" ^��$i./"�+ r G�e �b� [r�"t* 3"@,�kA%��.�9w� %�a S�..�%C"�%of�� \�aningfuazC�b}*� %-�~% tz6at&Ca� %�yrv!6�7 $H$)_aۆ �t� dLsub %$���+�wv�B�e n alI(�,y  $x %�2P��"�to69,�!! �a@ � %����Q��!7B�� $x$" '�P:��{5s $H^�*(x)22��0-��v�`for %�4>G,��luI  C . %\\%��I0�A� \èas Kac'�5e �;m$M�)�pw*ll M nH6d�9 >s���na�[�2cE|�r&o: �J����y r#A�o%�A]){a!����q�� a [ , i.,"�Y}�/Ia.~vis��w s. M�� N6l� %�[U�X}z Kopo �&su�:�$H:1*H  %� _Ǖ$A�b��Q�built�� �F�i��fuB<60Za��_A�eJ�$, �$e+\,y,)B$x6�!�a.� 5�:��BB�8f7m�� �� �B�!�IG!r]Gd���ҥj$y�()V \��=wB}�Ro!!K��[�.:%�bb{N}*n %B. %H^{� }(y) g:�u,\emptyset. %� pfrt7end*z %\"� %5�N�,!�"� �_���9��M !�9���� _i}(y_n)$�l{y_{n+�_i}�G2H )kac} %' �daR�c=)=( � lang�ta6= \r},5 kac_lemmav%e�$�Y��"�!2.!wV,:��nl]����"�y� � %b�� �a��yM�.$$.J��A�� vFion^lan &B��concern!�e<�!�*�" � �)�gF�*� ��,��� �4���'�WBu p�sd�J�_ {EIG��&��d��A�&S� e�� �� �<� %{\NJ�m6r_�=\��k=-G N_j}�x U�L_k��)abel{mu_��*6u��2�W$L_k$�" ^D�sT �fixed�ns li�y2��e $j$-� θ��bmap, (02WF�-jI$>o �g $N_j�e�9I^&v3 F$j$ZH6�WeA�c"�� �0"� f���AT�Ba.�"�@ i��� �s�is2u�*� P.��h` \cong�y mu$�5as� ��,t �-)$� � T�� �.[�|Fe�a ,ly�r�8e"F��� low-)�2UA � . AnJ�ous�w� ,2�%}�.�%ne^2[�)`jB/ law. %a��`�|O6Έ.[atD,���"t���p42�745tv jA; n=,9jB> or Vl�5.�<&�!i� 2~of)/*� ��:��.C NI@)f��%}� 3M� :i.s�B9t2<l�e�9��s neglig ;as �P�T6P!!G.# q��krE~�offb~nd>�.  seNO&sr��%�vnA*pE{�  %6���.�U2n�p��1zD �6�duO��!Y 3"*H!!�)t ,i�s" 5� �cF��_l$�6< W>#�' �c�_i,�u%s"1f���S4k�X au_lN: �;# $�W*� �i=k}^{�$rhR�,-g_�retF�6A N�� F�"a\�AbyJ�2�2� �?;-6&�@}7; 1}{n� 1}^n%_i2S.� �_��%6�&6iif� sep$ Eq. (�B&�k=!�0_{min}$ (min�(FRTA�2�)ōMS8 ax}$ (max.7 68en��] i< in}}z {I7<h5�#t5 AH��reces6�  ich .� B� E�]{�� � *� :�]o�ʉ ��2o MRo E:28Q�>n vn 2�.�\�V�MJ e*%�Ɂ��6�hyp�&zD����ib}��eŐo�.0e�*�H�MaHA�sI�i�&~I�yinu��"�s 6�Q 4� � 3�;"�& ��Z ��12/� A�J�,2@�"\z� ^{\p�&}6�GY2 _{REC}^{d�X>�_{UPOf:c�h��}* 8c�| break_sum�Mn i BQld�fk�:6$�# 6GD}�|N�a� rec�'_A�>3%��D��upo�嫕���ay^TN�c &=&�I�U �n�� tau^��)�>}�AI: �^{("��e)H"�!MA�} dW\X]:�! ΰ�%��E exJ���Bmu%p���5g"�� ;& x $d�ZjE1a�wU�%�$c$2�CV5�l gral.�E>A�^dO�C�U�cshort &� . �FBO%i�R :� ,R��c$: :��KZ� �Z�c$ � high2~^� ��o"��&�I�$ �-%.�V�r�f��� D�w i��U2��%G�$� C�!�D�!� 4.N�Yr iondA.6P um M%r ����i�cJT� �R͟](�Un�one/)�O%�W1�p6 ��#Eq8 . uy��M��eG)�d �cQ�� a�Lr�kvp*1 2 isn� " 2� =���u%���}�\��C �yt� u7}��,ZD)&C $).}�B��pto�4:^{D_p�m$D_p>8�eY[w &Z) !N� �farmer9){6a b *A 0$%�� 6�%$, i�2c)�.)�z uld ��*&�/YU*:N�&. E-bNq! bro40� Pe�wo2�{�fAC��Z- ��Q^cg~�� �Z� .kP(.�w&B�heEe-&�T {E�VY$,*2)`�+�I��ZJe�t.���+brD�h!B��"2% 2Ů�� � � =!;;)�a�WcoeD�t!��Q�%�Q��fi�!Q 2����?�� � Ս�2�.�;��iF� ?.D�age��?a�K=�  �� �}et}-11C) �� 1H��-�m�!g !� $�� ^{- � .�)-�5a %ax�� �nt����}y��d ���M�r�g��2 omparison{3th 1Dc D�2 CcIy�� @� 1 ��X!@3!�7Oe�Hly:]&1�rj"eS^4a�8� e ar��P^�s�����u"S"=.u#�c"�$.#�h�="S$A�^<2�& Ѩ>| �KA-:� !U"� O5ior�  $I� 1}{K-�I�1-Q�[ "6� - 1]͔}�]aOn[odP�a:�Y��! *5)��21! ]a�U&UX�AX$x_{i+1}=a-x_i^2+b\,y_iMj $y  x%�$eO $1.4M�bE�0.�| 2�-of�K�%ap��&(����0�J0a &"8��1�Au�#��0 s %� �p��A�lso�h\6�Q&- 9&� <c�*1 !�J&-2*-�� %L*+ A when�%a�w�$"h�� �6>In��. ����}C��sh�(�^ed& .���%+>��O.x,FiBk (a),� s}1�8 !e�up� )� 23,&Jdx+me+�E Ref.) *�3)2ݓ�XpicY-��im9P]z"�� /W�r ft' imag�ndA/ .NRIin��� cu8V.>A3A�� ;+�ir�,ghborhood. %&�: UPO'>���.��t[7et�$�$�&�[�,be� t���Z.^w,s4� *$6�)�( (box) cen"�$�1% �,y $T_1: (x,y�<(1.7801,-0.0949)|box� =0.0�ԁ^low�II"��%U&��o ( >aC�-�� K0�(� ��9.� u �Me�W1�d �If�җed L�l���[A�a �-9�<o �Zi� mark�  $W_s$ A�u�� V�IoP:,$H^9$ (the 9^� �*g�m9:%'f(�<m� �$W_� >#qse�h�s$s�.E�AoTIb.�4aC B�!%)�1 �!�=2�B;=AU`�/UV)4a:a �.s2:` UPORS. u�� c�( anticip�1�aR$���pb>�+|�=�l "q!a6$.^T�ldem�$�=�� &|a1�ccursa�|�+aaQ-)�b� (��oA�riod-2��&i|L8�?1�13P�ŷtheless�0��avPztau$=13a� causI�miF= E|��:lie+UxRwu�13i� Zn Fin���'iRF(d)5u".-�#�!&)1ll1d!-��$!�)�-��^��?s>���ps cro9�7fh�YB��[!h] %��er�O{\hN�P�ig{file=0.eps,X�=\�E } �c7onGEt=�Ve�ћ�= ɡ,6?s%�� ۩}sQN�i� $H^P$ (� P"?)aA��CUPO^��ir $P2-&0"���by��5I�)T���$�� B���c��>�tHth��Q]:�;IaS.I�"�%Y5B "���."�'1��M.� To qa\ifG?2��>�ou��@BZ�9,��R� �a��="c/aG�l�A0��ig�d l.28 \�s 10^{-4��g���"�L=(9,16,17,18,19,20,2!A�d$�b�� = 2.41؜o5�!� )�)8852�={��.�03�9! = 4284��&�a t{"�&�,& br<400,000� ����j . Emplo$�e \>),is�A "p4��!"� = 3.0923243�}9tEU�  ne�"Q �.&.)A�)�s, rp�0I�A]e6i�le4G� = ��00�)�%��8"� our "�FEXj,(ee "�1�7 !.�is"eh�7n<:�'s/ �3.4M�E��[2"�c"&�'egtn;Fa��,�  bj �(d�\m?�e��B.�30)�!Qh-)�03>�*� ..�+�BOTH}^d�iGT  sp2:��/�*ustrong>4 ap�\.� %&/��9 Aމ�Q��2� = 3.027Q>� E=ab2E@rA�!�I�!(��$3-3M&SY���=<.�@�W�֥�M%F�&'��9.96�06}$, and $\m�u_{UPO}^c = 7.712 \times 10^{-4}$, with $\tau^{min} 20 = 23$ and $_{max�y16871$ obtained for 400,000 returns to that interval as before. This gives with Eq. (\ref{break_summation}) $\mu^{\prime} � 2295 � �|hereas the exact measure, using e`kac_lemma}), ensues $\mu ^42J"$very close �e value9%C|Dcorrection formulazbr:�<. Again, most ofC � is duq( UPOs. FromQmu_EIG})8Xbest estimate (calculat-�@b \mu$. \begin{figure}[!h] \includegraphics[angle=0,width=7cm,height=5cm]{hip_nhip_fig2.eps} %\ceAmXline{\hbox{\psfig{file=-nfi 2, Z\column }}} \cap!�{The wesed5��$\frac{\mu(\mathcal{B}_i)_{REC}^c}{\gamma}$, i=1, 2, -�Precurrent trajectorieI:respectA]$$\epsilon$eXthe i�aD$.t,1$ (circles)e�2T2$ (squares).} \label68} \end1� \\!�8dent To understa�how�V�(s contributQ�5.of thea5wo� s whenQboxsizA$�4varies, in FigA,�!�5�}0.0002)�8grows moreover |fasteri�inc�?)mQ�. Also,e�>]� 2 Tdecays smoothly as oneZ�dYT�I +"4ay in arbitrar tea�finit�O,ze takes typ-� plac!L hyperbolic regions uged8appoaches zero.A�0is also encouredaxA,O4cat map as wel��ii�% tA�?logistic9 \cite{b�W sta:2000}a�6htb�6>3.�2~Averag!�|\lŔ �E�T2�i)}) \rG|��, �^ -J��}J�}.j�)�q BoJZ - KJ q ~rdiamondsݡI$2,...,5000���GY q��aA:-log g.}N�3f�I�6B53} we�Ǝk�� ��F�}��> �� :��� -ʢ� su, 6� lo.� 9 ai7�cper����ver��H.B $ Շin�g4secutive point�\a&; y�llength AV�J�r:r ��rc& 韁�sey all#  29 � ard devi��barۥ>shown�� � . Whene�k2 sr 0]ddi!"� !�t6�I�o �ed to be=�!#given!2" r `s aZ ult�]nq� sens-�.qV� *g significa!' affectsAN�nese�A�~$eingen� 8�!jY}"�&� �ppa%�EWRi�� , on1�%��A���9 �R�C yield!U� r!�x real"� 6��&3 aA�er�M �M &z I��clusion,2� *d chao_ attraIA�n generAO, be classifii�� �fgus,.� � non*� onel�e�er)A*�al�compleE�suppora b� ep�� r� q!3dia;bu%��'@%]!\0a Poissonian,�3le!�Eu latt�2� MJr�t associ�QtoQs�9� �is.�� � G2�-�esI�.�. I4 i!�se an�cb) T@be���D]�rst.�s��is�(strong impl�\  ot�� mentztee �| be monito�}I%�$7!711$ 8). ]�la�9A 8Y.-C. Lai, Y. Nw �.�_�7!{64�97). .c$hirata:199!A M. H,a�Saussol hTS. Vaienti, Comm. Math2�20A033�996� zaslavskyk1} AI M. Z%�M.�_Tippe!cV�6!2325%291AJ(V. Afraimov� �G.N_LEI� 55}, 5418�!=z6�!��N�ica (Am� dam) c(287A}, 91 (,);�I . Plasmas Ca� 4455B1). %�� ��I.a�CaldasI�R�312�539N2);�hadyn�2} N. HN�.I�]a8�224502 Y2�hartma�G60}e�H ,�~. AmerQOSoc��1a�610!�60!�D%�GrobmB$Dokl. Akadauk SSSR)612�88=2�kac�Kac, BulFU��5� 10�194�b%\��halseA�86} %TŐH��Msrevu�Q14E�86:�farmer�s3�m�^FzuR�7D�X 53 (1983���sae�1�%B.y�4S. TroubetzkoyF�J. Stat���1e�623Q]Y�od�} 1 exampl*a� llow� border� shor� long oTs� of aJ � docuk 9M%\� [two{,B\pacs,preprintnumbers,ams#8symb]{revtex4} :L9�K0 \usepackage{� icx}2bm}% � �� \def\t{\tilde} \newcommand{\E}[1]{Eq.~(� #1}):#F#�~#fig:#1|.I sle}�dathop{}_{\textstyle \sim}^.<} :fsg�@>@� 1�� 1[${nlin.CD/0$title{Crit� expon\ A1HNikolaevskii turbul�}�/�>author{Dan Tanaka} \email{dan@ton.scphys.kyoto-u.ac.jp} \affil�{% De� Adr��$ics, GraduSchoolSci~ s, KR( University�606-8502, Japan }% \date{\today}%5absu} htud� spaR  po��ra Z�one-d� � alEce. F� ,�a��nergy� u�in wavei7 B( is extensC in nature�Th� w�mon��hao�vaa$ cular ameo } �um becoQ!qualita�l�� inguishab�� h!LKuramoto-Sivashinsky]). Nex��rġcRmQ`t fluctu4 s. % Fin� %IargP �<in somovious !�y pa �snxch�typ�uce doVppear D m�ke&��w8olvAstenciV"in pr6�e�U� \�:H{05.45.-a, 47.52.+j 84.+r, 82.40.-g}��Hkeywords{Suggested }%UseEpkeys �� opIdf' rT%display desired \make�,Az spontane!v�%�Am?lyͥic�!�rA�ncZ"-�!"� was�d�by Tur�in 1952�Tur} � e" A!�fir��years_er :C$ Ouy��so-zedi mechanism�6w�accepyA]retrieve opapers�search�}A�-� ` �p�n', 4".aJb�ritterentury �Kon�Re�wPund eAA�e"e� t$instabilita� o�or&�Ica�"an �auni!���jo e�A� to a  cha� erizyEotetal chaos� stea s�qlR2wDan03, 4�ynew���!!q� chem��}ݥHhi�d �eq�e"�#}a�Y<_t \psi(x,t)= -\��,ial_{x}^{2}[F -(1+>)"]?-( : )^2 �"� � �Wad�9d5aq�f2�refUby�n�� a ph� redue�$ technique=k%dAn! ival�#��"v by V.~N.~2 a_model�, u%i� nvari� �$Ensa� �/�psi \r�%arrowE� + {\rm ��t.�#�G�c�'�օ� marg�t!�!n� .[�e�tea��I5�� B3. ���ce,�< do ��~��!{ s�A>bisal��superul�DTri-V# TsuA�% SNMe�;�� simiL lt�homeotro1# alig�*ne!�I?a��g�� �2Ib�IIs�_ q���Jt� In � � 2esT N$al�@ert) .+R� Mw�H tnVl i�picN�ay &w�fD workh2��Gu� , X%9�9%�L in f�,in�pr�%M%aE %�t-�\�� E�~(a1�+���W�vbifurc� .�/ ))�N& $L$..� �j'$L$ depeJ*� =�!�*u�n,S(q) \equiv ��$ngle |v_q|��,% $�ere $v_q�j.TFouriA�r�ס� $vW2 D_x���.p+% $ ret�V��� . � quant �/L�"$*:fun&M��[� $q$ U $L=2^{9� ^{10 1�]!t$2}$I�U0=0.02$��\F{"��AT%$ie�y��.0ualA_ m in1��)�, Ds!v��is�#*�15��n Ref.� Xi-Ext}� Lyapunov "%E�HKolmogorov-Sinai en��ye?a%� %]u��ca2�)(=0.2, 0.5$,�d13�#e�th�,ooY5e �in&��s0>�a�H�*.� �nu�e)>�-$ ��: er�,i*w� below�Q6^) \re*/ 0.45K$width}{!}{>}/{E!1S)}&/v �5}��u�dsty&  U���m��I=�a�s f� on a}cur� > @E�U2LIqٚ. :�( Second��� i�A�u�NH� fm1l.�S�>&ing6i�n�,l%��=2^9$bx Eeiio= abov��ma�FB�/�H! uffi�tlyi -�pea�5��� Troadem�merge N6$ �- as4 �'�p-dep�:Q � .D�&�. $0.1�%�is ��>R� (KS)"� ,p aF1 F2>(2)� &!* $� 8�%���!uj!stooda�fE ���>~��.M �&�.�=_ ari�y�!& &� *� �0� �(� betw� %�weakl~_ �B szA�FU �b.of&� N K# a�t�).�spa�y�^{1/2�� l� on ei) a�d$q=1$w�), unless>D \ll 1$,J��"-��u �"�)#��)-k2 si'A�ef�'iv�!4 sameA�?� e KS.�Ւ�[�-�through��ions am��Z J�%"�! A in�7 �% E!6 5 ���}6�3�%��w(n�5b�>� must % at��7ne %o magnitudeI�� �21��HO|)I&$to clearly�%o&�� :.�y� ,belL�!�$O(�(() \leq 0.01�� necessary&� �s Ao���7L� 9; $IL5,=J | �B� %�Tor} (�employ0  let 3omGon)%�&> to586 sN�M��46y f��th�9� 3ctu%M4KSR_%@I� ,2A � @!�258$ scal� qe!��).��I����76�g%�E~%�  2n �h� � s�alI�%=8�~? 9ah;to�: bottom� have�`�0 =0.4� � 1 086a,  04�s$Z62�ā�A��S)I/f� "����Y5-)nV4q�sak�Ma-�woG,>a No�Y�R&�ZbyMgre4.�*�N�A�R� n$q=0$%/)V}i������ surra�a�-,�#(~C.~Matthew�), S.~M.~Cox ~d 5,d-  +"��1>b hypo� iz`e��behavioC"��b�scribL-ermE�a  v$�7 Tv rmJ v = Q�L^{3/4} A(X,T) e^{ix}"f.c. , f&,��;2-��}�'$A�$f$&� �lo�"�,����*1L,%�w�finaKXS�� x uTB 1 t� Mat� K s u� �E\E{2} Fuj� �id�� �1!�� *�."uE9 2 $\sqrt{!��v*�} \�to=2!��:�� \in [�y0.1]$ -3"L %P6 .;!�o/ �basu5E  analysi9�ime sel= ���N9��j6c !]!\1}��AGfixed���=�W00� TaIl� �MTsuboi��� dF�-]\lJ\ F\} A*pri�I{i.z Kli}2�%<�6��1^�1,1]$. In$discrepancI!/l�G se[/to�r easiF<c�;fC�s�would� �K��%�yYB� had yet!�vWd:p j?�J� � �7"� 6�:f hs I/reg4to�fa�3i*"yZ�1�­cer�DAB�� Fu*�6we� &_ �Fof]ra��d�e��isL#>}�6gi�5inaXV+ ��aP>ons: 1�1M#ultn4r*�D:%�e�*?  i\E � dO3*>�. A quite lik2c �4 X�� ��A5�":�� lawU�)28*udLNAN "��%V�?6�9xam��a&va�%  assu #uC $3/4� �=!�$�!Verif�&.[xrT s r�re �#�8�$ach. 3. E" !�B�  " oord9 $X=q���2��p��+I�g�Z�F'�Fmu:�A�(�5e�daal� =0Aca�~iov�d:� ��$aU <5o�mpc�U� @N<�Cno grea�$��wq)%Y-��:Q ">0 to guarantee*V �?�N�,7re�&!�6�ie�>�&�,L-N��,�d� �'new>. KG��iaB��ce both�Ge�e"(6 ���=+er�ofa^I6/%�inB�o/�):�rms���%in �q����)Z<�� - � g, Q?we9rQ^� A�;1��=� t if_w�o��>sa�:�%e-*�,M��+ se a)q:p R�� +!n]�t F{dq Y%k $\Delta qJ�l �%7*gI�aA�k�7$half maxim�!�2�F$q �-eq 1$�%���(>f%yi$s&�'l+<:`Ke�`�-:� ���Y-0.5}$. 6V+/!> Figs*�.sq0��6 sqc}arVN��.��G_0qau�_c1K� :��  $q_0� q_c!�I�#!#���MLto�7=1$ (exT:i;)T=1�M 2\pi �q_c=8>)-���3=f$�!urt�Eizo�, z�!%��WL( �zA��#S(!=J�3�� %cN%1!�$"��el5!&rla9,�a� &� ,Cr%xt'%�, fe@/!� n;c7,pO�@ea� ite-%,� �Z!�� `>tfal erro�C'��e��-*�-b� t�MO���9( �Lim �~~3j~�% u�>Jr�m�e� nGO,k  re� d'hH slopI 2/4,  ,E4$4/4$.>~���4j�dqv�����1�2/4����R�5j��Fn�e��/0)��5�6�7��^�6r�c��c�1��3�A�M�5N� % HeISsubstitu� $v&y \IO6� + c.c. + l ^G�^!�.��WiE!-Khint�/���\,JD1&$=L\int^L_0&4&v(x)v(0"�IS-iqx}dx"8;J"8T ��Rj1) = L n�{2 �}�(A(X)\bar{A}.� �4�Q�2���� �f�' $"� AA"�&= d J!AfJ /�F� �!%�:=�~+ ���^{- [ V%6\ �ab�o �ZL? xp[-=�j xd�n,6�/Uj�gr�%#/4� r=Lm-��!��5N:�Com�n�� �)�0A� +4W\F{ ����PeX=�x�/$25t R� h "�� j�$-���6\Fv . S�-+3ind���} S(0>(bet6'6}t:(�-! �us� ar�6� &�co�/8s. Ou��co�4%>|� :[.�w(�d-Ea t-�!N!c�.o�9�N"�&�kR x �5.x� ^�U "� d�$ve �+sI;5*o 6} "� Ia�"g�{ IMx  $� ($� 0$)E�$1p F��A}@1�/I�L}t f2%2}$,!��%�"� A!1 )�G.�E�%O�q"�+�/Re} U b��}$Q6� (3 �(4)��^�K43%�V$J�W�&� ED&� ���J� �E�+1 YL=!%/p& -p=3.12 [  [3� "� A�" .�5��I�' :.�;BV"�� whyB�j��T��(*��FUV�aC� they miss3$��$@ea�8~�E Eqs�6..`<4=��3�!�V1�In sum?W���֩��E�U�E��(ɔ1}�y�.�� VO-��F���� "O(0.1)� ��(N�(��WQ-�646�!TV=�]�� )9��+��vZb� �. BeyonS c�(es,2wjL&��6�re��!�5~I�s!�tBH) J'�1,F602yp��T fox �&:�%�$}�9i.s.~\cpWS/, Tor, �{C1%e U&$6# ��&R2�&P- studb/KS-� �$s��F�Z �$%Fp�;��F��J9���c3!6��*" �4x )`0�E�S.~Toh&Se�a pulse-�?r�N�]�9reproduc�7sq�.�*)e TohrW:?p \a�pL�;<' �9� �sA��?mor g�@*A*B*�wZ�1�Y�� *2�*av[+x>�N<��T>�(! . ��EtEd seA�u)�� $q = 1,=_ 3, \cdots kA���ing� harpi ]�d� D.~T.~!o�g�)ful!m.�"�us�uXN#4� &�Ns 8;anF�I =ECH iety\!Promo�of�C (JSPS)�Fa>PF_N\b�=m�? A�$�>�Iila�T�4 . R.x. Lond{7Ser. BrG29L3OM 52).X Cas} V.~C]PH�=4�L91�I5 Ko| \ee, e.g., N.~Suzuki, M.~�L� S.~K!K&r-JNat�I cad.!� . US\M10�596J200IqG?3}ES�E\Y.~�/!��OR�OE �6UJ 02624NNQ4QNA7� 0152TJ 2004.J >!�:J>��� R�@ Adv=,  Enginee�'ScF}, edi�Gby!-L!0h� C.~G.~SpeA�e, Lec0-No�Ri6O Vol.39 (S�HgABe�c8, 1989), p. 210]y��Vel.M ~I.~6$M|VelarA{]i-]5Ad497Id6.YTsuVYK.~y$2q*�L7�163vK6Y<�IKWOK.~Hay�EBYAx dakaa8 � Chem�LE]19007�LYym�PXi} H.-W.~Xi, X.-J.~L Y$J.~D.~Gunta�= .�Ak 1046\�NU�.`R� ral�.\a0M6�2&-{62� R�R 20006� 84} 2E�! -<Osc�Yi�Wav~wT�ce}.DNew0QEF4); (D�,>Yf.�G!So5J D�R%FsH!-TA��3E323�L3wM5MP :�'M"�*b1R14A�B2�( ݐ,, T.~HonkawaIZT.~Yamad�$ rog.h]or��s10N:9�->  I�e Kliakhand��B.~�S alom� I]IX�23��1�P1R]��aToh=JS�hJpnM�5!Q94QR0zT >�gR"&�KmF=Map&.M&�Lfloatsf'M 6l1&�M ; fix.D*Mamsfo>Wam�M�L} �Mne�M k!62 manuL,ptZd�Ms6�Mj-t* 6subfiFi2�Me�h} % D�l\y"�Ms !�K4ef\lsaut{|\![}�Mr ]\!| la{\left�)  ra{\/C�=xZ?9�\tJMDy�A( P�Zve-Sca2B� "AMhruba�+a M:e,Rahul Pandit9Mlta&so far)ime�A`H�"�rG���b� ~"V. �:2)��&� � �gaa1�)�2�T rmpRta�w07"XV.ALA( ques�3�Q�'&{!y�� s weof�Rw�bAY>,�--$+� -$u$R0 $S^u_p(\ell)�m.e.O �>deF m{P>k AsaS"3�/5�~(PDFs)a�"q L`�(e=+ll$. ���}S$\zeta��>r!h�by2�% �^{32 IFhSU᷁�ang� ta_d{0= L &r\ G@dissiz>n ����D �at�T�$gyA9 pump . K"�H'mf� a�ing�R(kol41}(K41)q4 ) _p^{u,K41�wp/3$, � sub Pt% G Fri9u^su�Vmgn�  corrx �A�$p > 3{ ��.��7 �)� a no![ear, �>x,A�noton� �EaMQ*A"$p1�g!#yP�~ s�.|�����._subtlcd has � eluci�Zdi���ly-,lvo97,hay98,��34}:fjyex� �at"� -vel� b��� kkan99} tA� trivA��-�i��H E ~(${\�+ E}$)0ٶ$zI${E}A1!Y No�w2f.6)��%be�� �! �&$ �-.q$ ans\"atze!�A��0|Z.�ka��&.!8�ta.$exa\�$%�&� &� >} Qv . AJj�2Z �alism- mA�F�D��6�&�U�1�Ie!SQ_��at1^p��2�=��1be� i�>�};��>>"��`u�4}�F�y-<�4%�5�: �j2\"�R.,( K �?#]j��r&�E��C&� gral!� �F��on-*3[!]ɯo"� $^��\c Roheta(�x},t)$���r $ �"�$t� \�*'"|Pt\R + u_i&�Pi  �(k; {ii}!+ fa�M' \�{eq:pas�>@ ip$ Z�A�:I !c usivs��k$ �Z�Mr�_for��-an*�)u}$A�uldA�:�sol�mE�(Navier--Sto�x1���� invA g@[w 2�of>�NI �Eh.]otVfruit� �r&�  k mble�#�each c�F"(E�iq1zero-mea�,dD5-c�e�rd GJe��*om�Ai���NElaA5]�u_j+zr},t^{*�-AQ = 2D_{ij} 7 r})\�(t-8.:T ucor>Q � ;(2vS$ c$%bt�2ormF;d D}�q��<�q(q^2 +�}1}{L^2}\s )^{- $d+\xi}{2}}.�e e�6^2} �- eft[ �~ Aq_iq_j}{* ^],:D> q]%�q�s��%�, $d$s- al "�R�Meta$  BQ ,&N a�Ga{ana��3$\xi$�"�aC �D�F4vs �$ brackets <y< �'msi� .���5�ii�8r�= -�UD�CD^02S.�)�1!�d%|H+F�F!?^ $L \#infty�m� �\we getJ0 ^$ = D_1 r^{AEI[ (d-1A+M�� N�\xi �r_i rAr^EDExBdijF� $D��! rP� �$�. > $0 <q < 2A,is&�sB��2� :�j�% ���!�^01� 2d1_0^T fty}^� d^dq1�q�O(L)u)$ di�'�5�:� �6d .��Wls1a�\^J ��is~ te-in�%��va\ ce $�\��I���>yFb= ��{�z CIh"%~id"xAe�& y}\mid}{L�f) D iC6��$���": $.s (x/L�)/q'to�%� �3 More�, 2^�����^st"�ly�*>t. �>� � a ekny"/ Y �`=g%�1<by ${\ �R.�Q�-.[�x�R}(t;,r}_0,0),t]$,-= �B#$ i� e*a ��F�cI��P G` $t=0$! bel87}�%�F�ui8�Eq.~(<:� ) isF2&F -  + �� u}_i - (0)��&T i ! Efx H '�J!�f�k� .j6� ql��caF� 2 ��6���� B�Ga�:�&P�&� W�ll ��T�H "9Z0 main unch�0th�Y6m5-��AWERMfY(3 A *�N�J�y�F}� hi}_pi*(r},\{t_1,\l ),t_p\0 BDvq�a � \phi =x},;mRD 7��>;p;]Z6 �32{ J s��!!�c " �e�$IL$�q�IJ�Ithe9�orJB5�s!�n*ively,B an+&� denot �] ��jPDF� $%��u5��9 $R5���1q&� ) -.$,t).$ Dim)[oR ��K!G�=$r$]A&�A_@{�w T}(r�|�{� (r �sim 2- ��$z^2�_p* ��W $��Lik�2K414�@u_p=2/3�L&�a��eߊ�pr�j��DbIkthe>�iin.�zS p=��N�#;yV2(r,t�92Cmj)�0!�JB->:� ))X�O6XQ)��m�.]7.,�:$.&�5%0Ne$&d��2Vk ~and6��)� "a i?&�FQuNZO!�bf.4$~\foota�e��.f���Q�A�sw��jouh�+'Eh��E@weF r.},�(�$\to0$x � rele& I *�)��narray"����Clt� �[A��IaI &=&MD^0(L)���3E)e�O Z( ; \\*#u2�>|XZD>� �5)&6<C^:Y ��t �.�jF8526Cql);�A1]UhalFn��F�D) �"2� ])�an�fn<� C�n �q��\n<t/\�{a�$)\ � N��"�{M = [)�$q]^{-2}$ [B �]� w6� �q_ ZD �]!f� l�"ofF{ s "� n:$L*y, �ig6�` swee %?\;,�W,e� a R�)�aR@�7: �  $z_25R=�cf.��{u� E��1$�+�Z�����hm�.>w-C�2 ose B�b/���)0�,�4s�>/_2�^\�2grees&�"aln�/Z es��yremark;�two�P �@. #!:s��%�� &�$� �A7��E�(2aOL$h\�&HA 5uI�1r!<B.�'r5 esen|r&~> �4cy ome,.�sm���q_4A and 6G_4J��'u*L'byO'&�� A�bie��)�E!a�!N� u_ &� *� course �9s�_ -� S1�.�D A5�t&mjobe":PZc �o �S '�!j �Zro� vOnF?$), so!AE�� P� ; 9Z5�o��w�k � >!&q��6o eav�))6�s �i�NtheN , nam�R�.! :'p* � 0,F�&� h RG}{(2$_L)^p} 9t{� I}}dz� h) Pr70)^{3+ph-D(h)} +G}^{p,h} 't�au_!��kmcalf"��d^B� s&m�o$8R�*�&Cj].�s $h\in �I}� (h_{a�,ax}�Fa:M $h��e�(r> is�@�Z� Sigma_h \a�et %�bb{R}^3$�Qv�I $!,Je�%nD){� %��9({x}},r)}6�_L�ato:�h $ �/!Lbf��Y{ �}_h$ ,�:6l_L�B� ��d.#�%n�I.Ia�v��a.bva� d���� kI0ar/) u(r)$~ .� �(s�>�est atz��Q|m�},an2�0� pg���veU!��A�lso�!��O)Fa?�VY��4�'�gN�gM�M� FgA��A�� ������Af%de��-$MAa� ��})^�e�T}^6R,I}!yM�q* \biggl[�\1A���S>B&r)}��6�2b�,t^{(M-1)} dt�4(ggl]^{(1/M)DU1��ٺ.�aHi�F��p,Ma1� �ix��&: ? ^M}  t^n0���  �|_{t=0} !-% ,$I{c�"�u͵6#�f!�&!�i r^{>> U)x fK5x� RK#1DTo"J eR�a�F�I�1A� �)� 1}{S:�M���F��v� dt,�0\} u/� �Li�2�� :�,), doe�uq�M o�a�;an� .X�&xXf�NYr^{1-�(O_p9�_(����)^p  u"1�a�`kZ�jen92}��As�!Vm� ',����K�V�Y�s�zto@!��i6EE �k�� flux� v��}:  vari��J'smg�K mn��(9.JT�'r~�J data. check��< �ho�� trueA( ^-o� = q�i&F),�@� 6$~Qnow ]e!J��do�n�_�B(!FX$��q9��\]\x�LA M$U4�,:hIQXFiAY � W BM�M 1-|I�u_{-1}|$&kL��%JEf��C g/*�&-"�/9+� BI�� = 1�!�$M}{M}, \hs�m*/s cm} FDi� ̉��M}|Iz  zp_po5J�  doFjMyH&��i�{n�^$�PE� � ь����ayVV �����=�-*xDm?$u_M/M \ne 1"� 1���Jing. � t�F:�/aa#i�z� �uj)sN<)�1!�2 �A2�8aIs.�7S�4�H2p7LbyB7.7T4a�_|K alog{�o"v"�4/N4di��e"�M)is purb�!EG�woy%#x�Z s, A�B,�0h�"�%=� wir96,��J�w d}{dt�� k_m^2]6�l_m(t) = i \Phi^{{A/B}}_{m,2� 7u}Q$1}f(t)>L&k�U�u$! � Ac"` ���:M;%�Aq^��![(k_m/2)6{^{\ast�+1} ?u�32$ #�+6( .=,+1}) +(-k_{Jj}-R}2}+��  `Fz2z fsr+1nr+28+1kZiR +2.V%�8F risk�]D)lex�jug%�,��� �_m$ua�J6COE9V�"�p�)u�9� areAv] ��&^.<W<,� $k_m(^m k_�!0nd $k_0 =1/16L � �\  j�$�!var*�)co"�$)�!(t) Q�n(t��0})\ra = D_my�n} >N$�'�a�{�H�$a�� rand@o&�nd�/*D%>�w� _m$.. B, $e�BB�1�� [k_m6�_{.yI�-q W}V 4)]-�Ypc��E]2�����6�.adG; 0a>�U���. y�_ 4� GOY  | L �n� ,goy�CB� 2m +\nuEp2])A� �^\Gamm�3Z +�"AB 1} fYu}}>_ �:� �nj=I�-�QD�)�Q{ -iW �j��BU+1!��-(1 6)62!:D2}U�~"=1/ͨ�.b�eeas*y�Q  =�0U���= �*[+a�A coup� s��� o next-�5esighborI3a�eB$ i  �� p&bFR3&�/�(s +[0h t�?B�v�e�3� ~(&�-:1m� A�$)"-X{ � en $A�'�fK#u} �EQ� ^"  �$m_{m=1}^N *~6�m~^��* '�~ �N��!cto��W!e� #We�a'y= �9 one,h% s��y"��UIto^ �X E>'� )!�t9�Š� ��i-|< Adams-Bashforth�t<�jOI�L��]�2erJ�i4��s��'� *� &�=e 4/4-eddy-turnover,~�L� �*given�Tp~nGT3:Z/}M�(%\���2m�2�(Y�k $S_p(m"�},�)M!_���]^{p/�.a ���z;&��@M-�exh[Ls.�2{52|.;Rz�X0�q6$ �TbI &�T�� B�5^AUsE ��ES)t +-s exp}B>� S>=p2�~~$>�&J3-�UE�Bo�~(*�^ }� �I� #{ � #BA6W/VwZ<:7,�H` our E� js:J�  FAk�&r�)}N}(0&�. :�M�(t�Q�.�,_�kshFpB���)!=.�.� �s [�!Fr"]Br� F_2(�= S af.`�4}e4)A(\xi)F�1f2��VJ $ 9�#D2^{(2\xi-2)}+ 2^{-) + (�"xi >] &�E F T]$"�JFN }_2=�$.'!�&j s�;�J;or $pZ4$&>aO� ity �=esi w 2��Yi�@h �%Mqacha�$Qn$d�q3$t_d�g .~)� 5 ")}{M� 9mu�Ab< a>j%�r�r$TE�� ��|mu=0.7$; �iat .Ymu$?:$�~�j 0.9$�!.ao��si"9?ly�Tp"�"��lo;{� $p=4�<##n�a���`(fig:all}~a)�[s"bh�;� � WeZ 1.400\pm�|وB#&b$6$ I�����Vourale��Nh#pM�MY\x�V. �I�q��'} AAmeӈ~ (tabular}{c|}� &�)$&O  t �$L$&$T_{tr} av}$\\ \hJ� A&��-14a�2 �eqa�24iR5\A�s 10^4^ $10^5 \\ B&.({-7\�_\-LbS % ��end5}&��A �;1[!�-stepd  tB+�Fbox^lC g$C 6�e� 1/k_0u_4d� at"H�miI ��"� �Eatag1o�c�&1� t�� \VdF��Xi�s �}di��wn��J�,i���G!�*g/&m *i2a�a@� 5 $ T_E+b � A�j> .�� >�  $N=22*���)&��E�&� ɒzeQ~qL>R[ht�S4minipage}[t]{\a�q}��^�R[ =0.6&<]{f4_inset_z4.ps>_�V8F6868 ��Y�\�t (a) Plo�!:o� $4I,v�%�)ls�+=�,���+* q s $m=6$�+13$~(~`+few� �8pvis�WE�`�8& [FyFT'f�)]� �.��0�+A�R�h. E�%�ŏs4����]�� $T>� _4(m�ka����<lSk_m$;ſF# stra�K A? (least-�<s fit) N��)�^�� � (b) A ��(A a�e=$ $p=��.� a"c��$T^D_{6,k��7 ���av��2�i,B�AE/B}���I�m}jq�m��} e $(p)$ &�6�}_p$&$zw$1S0+,I�# 2>d$,D.1& $0.34'\�52 3$ 63 \\ 2%6% 6 X3$ \\ 3787 K76 5�0.705$74& $1.0�71 n572 �04 ]bn 76738 �677 ���\I���O�� $-p\/$ (C�� 1)6�6r $1\�zp�1q6� � Nz B:.M&@U0IA)�2)�. tl�e&�,2��J� 71}�of"<' 1$ �3)� � a�7�IVlNK4a�\4)� !c&}�IT"�f:/B? �.�Fa� bG"� K$&� ��K! =-0.4Qw5�c/F� 2 �645MrA�� ��7%Qu�0 0.709\pm 0 019 See text�A�lr estiPĝą�:�U�l��*[B%:ima7�ry"k�*Q:øig�M�a[��Ii� �.art�w�^;g .o�Q!��B-.�j� ~&is[fng[s, $50� "� %# $4\le mas 86 $1V-$9,1�M .��8e�{ ɘpE�w-te~2)�neZv�6`( -�8 ,M�a"h{6�xth�,�d�1c8hem7:SA�@"y)�!G� t^2}o8)E) $. AZt ��uL�!j�!��Lsj $Mnk O(>P�AM9iso{���p��S*�:95 YJ� 3n~� ��#~uMh�X�X� +L>lyEh $M=1"�QEI��_u�� ])0^{t_u}1� dtQH�;�-B %�$1V*&�'We �he&'���Mk-d%ie� >-1.84$� w�?s�ve $M< +BQ�%�2Pm"�UHsh�A� $t_u�8a��(FbutA�A� ��2���>to�N2b�[aǸ�;Q:<:s��u�f cut-off�$*�m}%�= �s�reC M=a�S��ho�j$ 0�^7��R�.�/&�i�G!�k3RFa�� < 0.8R "� aB��sUZ)$F��RjQE�Ki�i1�4 ��i. *.`��of bl � � �U~��s 3��42b6?@uC�� �-�A �2| . 5-4V�7�/-b8�FX�~H��[ carre6t�e$ run�Sp=�Rver a�����"Jf Nr�We�� � $50$5yt ��A�td8��mean &7 $ N~*�quo��0~[J��)]"�P( root-mean*e�ab��� Q� :��zz�!n+H�- 5�&":f ?�!���:�:)�A��,FZ�W�95� �nrIC\�UaAXz:�(lLly� �E�Ml �>R&�9�$m.3aZ4�isM2e�Y6B"" &�'qY. �_2 JR�"o\V4WY>�I�OZ4 (d #1S�:���Y��t�(#T� �i�o�:%�will ��alt� else07.��e*G���R� �;i�n�<o�` chal�IU�e�4ank A.~Celani,WhRamaswam+],M.~Vergassol�din* ions�(IFCPAR~(Pro�H( no. 2404-2| ,CSIR~(INDIA)��� � ."�>-�10�d�emFGֹ Falk��,͹$Gaw\c{e}dz�matM. �,amM&9� �77+�913 �h1�*j�` R.Y�,�heb�K1�h 945 Ck68.C9"P�mf�R.cfL�mLetS] bf 9� 024501 �4.R�Y A.*آ,���nNauk U"��3 n 9�42��%} U#�isc�em *Oc�3legac�eA.N.v}~amb�^U� TPress, �k�l 5Z�V�n L'vov,�Podivil!�I. voac>2�Kl5U� 7030��la�Y} F^�y��nd��(Jayaprakash2~T� R4867 TB�3xo9h�6� ��j 318}, 17!y>Xk�Y Y. Kane�k(T. Ishihara 4K. GotkZkIqkIr 2154 �T�5]bTL��Belinich  nd V5oSovl JETPI�6mk 30a 198��T� AvWi�#OL. Bif=�6��1Mgo 4928 �6.�� M. 6�G. Palad��^A. Vulpi��)e)-`4-�21-2�r�'(E. Gledzer,�~F~ͻe�%�21�n(73); K. Ohk*�i�M. j@mDI�83-65); L!�dan��@D. Lohse, J. Wang)�R. Benz"Lp)� S7}, 61�o%�e�:Hd"2�.Jf 0�: �t"V��lfix�l�lZxlm�VIl��� �k$n$-body���s/�Ȳ�solitonG"�kGaspar!V \sur_?({Montesinosa*HkD<�ta�|o��Matem\'a�1�\'Areas \'Op�, Facultxh de C�sia� Our�X� �1 Vigo, As%Kos�/n,2 ES-32005 �.�V �c�M.�,P\'erez-Garc #a>���R�$�%�hll!� ~�.�E� erto�Mi\�l>�և�-�$date{Novem��5, �u��F< ABSTRACT & PACS�oRu�a"nIL  UorkqJ Q\k8 "� .�Townesy� B*��E�*B1 methodƃ� 6�}Rvr sehNg�� by bQ�4c�in a & 2}0$num�D#�*"� de�q� i!�� �� orbi�j defle­_n rapp� �͍� split� . S &����@pd�1�-d�:� ~dR�s|s. All!��~f���~�,us�%poteny�)�,�{ �s.�_Y%\p�m5�PYv, 42.65.Tg, 03.75.MeLR_� .�m s�bf�"cubic No2d( Schr\"{o}d�r ׄ (NLSE� am?�A��f*jhy� )A&f(m!"�d �s��s�da�Sai�R�\�f@�"1G^iL�E�gr:,�[4o��=��N \�Z�urov��"�Hs ~�Y��sw�:�Olas:�p�[propa ng����G7mawr% H in Bose-Einstein C�ra�y(BEC), gK� HoA�`w $quantum me|iw�plasm&�!�s�/h�!>�� ologf�," > ��4Akh,VVz,Sulem}e�t��pA�w��!�f�i�A>i�C�)d<e�DJp�a0�`�&v}O:�B���od�^w5~ity��%J0 INTRODUCTIONn� \s�� {Int��a�"{Pi} On�!��NLS�2�WisA%f�e��M�a�� '� 2�V�om��-A�0�<�&�; F sub*�vb�~e"�=�P abelg gpe3|3i 6} u}"� t} & = &: eft[&�+ 2}\t�[@gle + g(t)|u|^2\rR]ur@ u(\boldsymbol{roSQ u_0:)f H^1h�bwH2)�c�� 6�7 $Bmt):.�H2k�E _+ �arrow�UtC3W*a �xiq�٣T��="R ^2/\�xVa"�Q.yw2;M$!4$!�a9 �$U� coe�)�� if $g<0(/��Yis��?%a�\$g> 1 ] 1re �iv(�3g.�c��=AEq.�.:�eqICpaM�LSE\Q�y7:^��of�<h4�j��. ����Q �if $N in�,)�,R}^n} |u_0|^�V! T� a��sjB�$N_c$,���B�can�f-focu��ze3�a�u�23 ��W�>^�on�j��\emph{��collapseyi blowup�!T& Uw}��r�� ecis�Yߊ is n R >w%�N<��c'qP"Ƀ)�, ?exist=�' $N=N_c+ŋ��� fSbs��c�} Fibich,We��}.1�FRad�t���� so�!�� N�=e^{i\mu��;_{\mu}>K $; $ B%����*�Bu��1�'� } ��t -2�- 2 g | |^2 =�����} A- !�p1�%�S妡�7i�� �`po�W\y/I%�"Zs �!eEq� e��-�i��,T� rads� symmetricEZI$a�:� d6�0MA�*��|� all�!"U2���i overѱ- ����!����R Mq d�Ms � �atX�ing �T0-�T9E i�gr{v)�}�6� }1-�de�?B[�RI�(r)ٵ�9satisfi.�naYnP �R.� GM� I� ^3=0� E5�$} \lim_{r\�� �d}<(r)=0,\ K '(0)]� � Ff.th�}!��kB� qq��&[�6?�h exac�A!"�n���� ��e�it K�� ����& ��of ��� A�exp�z1�s]n<6���Iuy�}, i.e. [-�Sur�Å�.� leadz%ei� .v A�He/o��ݾ�|}���azhA�an es�UAfe"�t�� �9�i��kJTorigi� 0B� &�!�D%CmW���}l&�ttW'an6�p ) � 1 ��ary�9���)�so-m�-]�cloi�J view �� 61�2Fm&Fno loe��U 8 e 2D E ��C'h, r$e.�E� 0�Qo)d ����<��o�Js� but a� tinu�{"7 "G ��w29�a6������n &��2�  n"� Y5�Wu��n{�� (osc[�)���*q8!ed �ombinav cicl0��Y�� ! �38m aft�}/a� cont�e�o'_~��c��  back �(uc�We&way�s�oul��ng �e03�]i�Xۉ ��a�}�un�.�g�Bdea��wtos�%�v�L�s�Berge�aE%m*�mmBLKer2[ v 2 gx���a1�!�1to�vC>�;e�XE9� I b3 A� !�!��cD lt qA7��o �$��am)ve<��_� 2*hel*M����v� �5U.�]Refs. [pisaU| Boris}.��< #l}Ig~ [,IMACS}�E�a-���e*^#i� !.7�%6���<a�'z� Afme D)lexZ%!�")f,*� �a{W�!� ope��o�K ����7�!գ�' of vortexɘ*� �ed-}-�,m"�04bw "�$THE VECTOR��8 AND STABILIZED$SOLITONS} !�6]!�F J� � 6���"c(Manakoveqs}J�o\Ut�.-{1 \�  2��$abla^2 u_j�3-ft(a_{j1 1|^2+ )Q +"n� � �r,+�nd�; $j�Oi n$, $u_j;!c$"��0%��, �k} "�R�Sr� �AE.!ArdmU�kaJ����7 �B2 �( Eqs.�=�)e�B a��te2� . iU�%�}�B"/e9�e "� � 9;�� &�8!u,>sť��&���, Bw play� e ro-=r~�o�"����9�$n���� inco�(nt-��� s. O:� �Ԗ�����^fj I�in=��mai�-due%1h��^� s�R2de_>�\ all-�� !Hw� deviCHtodos�SBECA6s ($ an a"k�!��d)pc��<2�'x%� tw:&-ej{j}$ b��J�S� � )� ato���ki��v ֱ. PRLdual,N� �' S�� � ��%�=�&i��-&H2bto))��c�cl��ifEQ:�~i="c\|6.-6 _j\|*��a� al S� ��S. on (STS)�hu�%I �-:.p��X/ch� =�q� w��< lyq=�/ay)FO  1STS� %�U. B67)Galil,i&f���l���oy�s mi�n�~u"�" *al�"m9trayecto��$>r(t�AA�:,!�aI22���9$)�reaso��e��)�lat (a�happe�nV� ofB ic �+-. O��itA�i�(rig1,rig2}))�!]dD �e��,b a�}-purpo�/E��� � "���#�lor"0 � i�eASTS. A�< ��alr��rep�dI*G }K*lmEq� ib-��at�5 �f�il�a�. �aof.�I$a_{jka9e�"it]�!B)� uild�ic@� �� \=�o�.�+s.�AU��tXLgF u_j�1_jm�(r), j=*}���} ��� �6 �1�� sf�eFzfs}~1} �1_1�..n�!7n} n^2 2�S2C  ��=),Z9��Ve���s (SVS)}T �t��cor�6on��sɪpbK< lͫEMt�!��s��$^N�u��; t�J"�/�d�A��=�R�ise�};T� �Q!�2u�~�'F �m� ��pl��JdA�� �a&�M"� logy. %-64Model and equations -R \sec"�U{EFFECTIVE-PARTICLE MODEL FOR COLLISIONS OF STABILIZED TOWNES SOLITONS} \label{theory}`ubcMotivan}(m� Before describing the direct numerical simulG�s of Eqs. \eqref{Manakoveqs} in detail and J�many different phenomenologies observed we first pres*an eff!)lve-particle model for collis%h,of STS. This "hwill give us a few hints on��1�Q �.6KEk���J��} ^'��rived��A�{ a2�0formalism fr�U6�nsity �h U@written as a sum M�99r,linear operaEb plus� non intera��� �y�simpl%Vm:��sub5���L}��0mathcal{L}&=&��P1}{2}\sum_{j,k=1}^{n}�m/��+6k}�Y), \\ 6_ ��Pu_j\dot{u}_j^{\ast}-u  M +|0|\vec{\nabla}�� |��,Bpkqg;(t +)�k �|>C*�YB#�26_�5�T.�of%��č `Boris} consist of minimizaK!��v�� Eu.�!} over1 2qE�w nA�.8L}T fi�ti�� a se�0 second order inar*: �8UVa~evolu��r�. I� ��- u� we�K^�Z�B } \dAZxE� &=&-I�U��p� (al I_{jk}}{��INHy�H�ܒ=8With $j \neq k$!Sse=g�ji)3��!3Newton's-� law e $ �$ playQOrol�a poten%�rul  .[,between pair� " acc� g�Kex% � 5�Q} -X=)niuN_kg(t)!li}  e^{ (x_{k}A ; ��: +w_{k }!� sqrt 2 [ZyZ%�Zf ; 6[ Z }}, \l� Ijk}��be!Q$N_k=\in�Hk|^2dxdy%� squ!�nor%�a�$k$-th, packete� correspo� 2�2�2termin��Tf"� �sm36� � �w} I�wA�xaB)Q1}5r3}� ��W)�}X_yB_!k�_y�oF��ly, som� �; ment��re hips ( a grala mo��)a�%ov6F * coefficie�!� also��ed1{:�) otra�>�� )���-2��� x} Dv� \\4)b4��-2e4y4y)�"< " >%�x&� 2- e�Yk-y-J� �c)}mK6Fi .�- iųeg nt�A�quant� $�x},!6� �%� 1J ͎ distrib���Zs:� Fast�r approxim }�+ }�tpaperS ��moD$�"X=g_0+g_1\cos\Omega t$ a8 3J� o An� ��Z/1 �8$g$. To get STSQ peri��$ must�$very short�Herge,Gaspar,IMACS} A �A ( value $ Fsatisf-�mb <-N_c$�ere�;c@J crit��7� blowup�) oscilm�-� y�M�: , in>d �,%'�f!�A[a� %1 the f� rul K��P� - ��" O.C �>f " siz��s.] r � a ��IXMn� 2� i $n� decoup��m>F$\oAtA By}$. �th�kp�)��,� L &q�QJ.�a t7"� ity)J$g=a$. O I�h��p&�-Z}_-$chosen to y �"�:�6%�I�. An ex<e`sC in Fig. \� rapido} wE��} s ofF�!Fgr�HE�.:�A� one-A�on�W $n=1,showni/ peak�a�]��s� � Ka small& �n suit�9l �x��kusf� � !�� g 9f�A cir�r� Ab (t) = Qy jQ��E� H`-G�y�M�J� is"; �I ѷIjk2} j ^0B� 0_0}{\pi w^2} � rd ^2/, @T I<$w^2=w_j^2+w_k^2ey $ ;���anc�� ")Ŝ4figure�T(psfig{file=��.eps,%�=\column } \cae�{E:� e $W=(� P (x^2+y^2)|u|^2)^{1/2�#q2:c($A=\max|u|$"*�Qoofb���I̥�a�.e  (a) ��(=-2\pi+8\pi�>((40t)$, (b)�� 9.5", t)$. Insetse/ >E�A7!=6�a�� ( panel)eZ#%d ( .�!�nd5�.�e�:T twoqB� is gned��^.�n attXv;ce3ch only"�UyU�qB�&"  That isɑ- 1�&��similarRplane� mechan�w�a ``graveonal"}��^0$���al" instead�$1/r$.� , se�l��mon�perof �a�ces lik�Ser�$ angu�mMtun!���̈́2-body �� a single 1*�!*�f mas�re stra\forward%��. Specif3 lj ��c�ves un�t�Nu*�=]�C^�O} V2 N_k 2��+* J^2}{2r^2M�Bg_0<0�J$�����e�>~ . U!Ty� $techniques7 asy!% �Recess� �i%�m� existe�qAѐorbits,@lyF�� '8} C\Delta^2=e^{ ^�C=2w k+|g_0|/�HJ�iA����m\and $ V=-aA�4f $C 3YreV ����s9s< �_)��_u>)�><eaN �>�� wy! A.D$ve�close�!�uexie most�nal�$(r�\ 2}w)Es*l� erea� exte5 5u>:5un 7. !X�iMcDed upA�,a threshold 4 ,v_f$ (escape[y)�re�s# �� one f2��0=�. � if%>f) o)� �possi�becau�e2]move too�to be ?$ured. Tak���inn d,� perf ��next 1!a�"� explo� 1�.� !k:�. Our m��=es llp to check!U)Sq�1 ndU fal��%eg �{N�s6�!J�5)!"�6* ^!& stud��s >!�)5 f� workZ' . We� q> data1a:%�B�P u_j(\boldsymbol{r},0w $R_{0.5}(\|6-6_j\|)� i .v cdot2r}F !�5ir*�byg% 0a pseudospect�0Fourier schem�th v @ of s�-stepx!6� � @incorpA}es absA#ng bou? y���2�!Pri" < amouof rad� i eugeneratSoth�!�!�!b:�:�N�weI��C$�&z�"i��#N�Yg } A�3wa v Ref.--H� t� n ``% A"��� �""PemH� ��sl�&l%�! "e s%Q s�,��Tbe�un!Q��-AJ��$ prop�$in Sec�t�%%���w& cu" ���o>�iW$Ͳly) d atl .Z(_1=(x_1,y_18622,y_2)$). R� �6RvR v_{11y}),.Wv}W v_{2 ! 2y})�(";!w��B%��a�&r �!;� l� (�!1x}=wy=w_x$,�1y�=w_y$)!loP!�D!M%�F�&p&���6P\`t$cH N �x}_1 �# �N �}{]$ w_x^3 w_y� 5(� \ell_x� %2� y �} x"Xx1}��2�1� y���^3���y,\\ |:��� w}_x � )=x^31N:P2�� [ 1+0 �Z= ( 1-�)i!�)�-� ],Mwa9� w}_y � �!Q + :� w)� [��^�A?{ iU�Uwb�N"�&end:w)=x_2-x_3nd 2=(E y}=-0.06Em  2y}=5�)Hante�n=�We2�i�h:�N: 9 w�/ � ly. placbC �E�^�)( T v&�#21v}_� �F 5�E$y$-axi�( �/sit-�9 �R�2! a<�[in�e9, pira�'o�� ;"�E=G/5T >F��SVS>%$eReQ3canyn�o"� !�readjust�&� �4�Bra8 52� =�:H!�A.H0dAp1 i'� lid C6m�6!6~b�5_�uJ�"���. A Esophis�#�M}b�}6e� S"��� alII!Y.� Expa0)e+��� m�.,large�'a�!gpreviou��se) " toh-c.(-��ccha �|� }�hy!PabAa >�(w��"nalog�A  D R��) out�B traje�2i� I�" �"o�Ma0.08h y�b}��>"�� �edab� �.�f�EP2�r�Ń��put.���ј8$-��8R�v� eQ@1� P�c� �֥y��� :�V�2 � �#$u�R & �x./ F" j� ~���8*(he last"�c"-� superpos?c\snapshot�omz "� 20�%� Yya>!n� 5�2·SUsE�J!�a�f�2I�BN? I�f/ 8$.B�b>� Ag�101�p![SVS. Si�w� +� �3�7��"of= y3]V(Y�orE�3 �`2�@Lsp!��� subtE�NAv\�Y, o��U0"a�iz��6�{�.��their ers, bu,so *s a6c�!X �+&�&B�� žtr^ *�is.������*� Wav�*&�w� defx;on./"e>A4e�& an)%Nes�(:E>�o� i ly at��tE�G r*ach o I &� In(�Y�1�iq2& E���iV=B����u_2��~&� �rtsZq0� )YzerA%�i�y5ne�J�N� 3,-3�� ��yݫ3$V? � [!teci% ho�%�|�9���>� by mM!M�s��YVj%sm&: i% � s. P�9� � H9ks Vɡ tane&` par�"%�!Bdragg��� half��%��A`a v�� �  remain<: i�e� n2Etxu1�0��:�3�fQ1$����I�� 2r �}=0mJ��&�i���;-e��5fI%(� �3@ s*�A�cbottom-� L""w%�i'1:��33dIvio���3�2%�"43&bj1'i�}6=ThaB�#ngqBs} ����.�t6-�(� .� t� ^" ��corne/8J(quila�<l�( ide $dIc��3$d-.@ f bary�� e�lr 0,d/% 3})$F� 2=(-d/2,(6"r}_3=(F'��>���!��,-v\sin(\pi/2qb 0�!�x}2$+h/3+@ v�,B�3>=4&�~QL3y}2@!�8 $v�8i.f y�&���@A� $d=4� =0.12$ �i�2v A}"��:�&ͥ�V ��s�@1] suchɍ�'�,o�E�enwAto ke�#hem�#R 2�& �Os. #��&/s62 � {F��� �h:2�.�u�on  �� � ""� a�two�G�! 5!�"l$s j-0����+�2a 3"�~F5+�m&3B#�F.�� r eoM�F A�a���,�~a�*i��jA�u��2ݑ�{TI%e��Jalysi� }�i0� ")6�6�&MK�dI} 2:a$"� �"clfC"x^� u�N&�v�*�]��\-p�=�2Q �n,A��ENa��� �hN )G� develop"�  oa�o �+ i ain "�b%r�.��!h.*��+as�J2*QB"C/ ?now�&ka�u���q9�� ing )�s� R�%AUl���&�>u_{1}�%�I11f�I�"#D}�I1@@$ yyrI 4]+ "oI\\qI+q2bq+Fq\tildeE$by.#6�I% u_{2�2��2f�26mB� +A_{2��^y�:���2�JJ�$h�9iceE�M�8!03"wos �~�$�o ea����a��N, i.e.�1aS2sNfaP �.mbmr>i�u�*��>. How��ful6��O (#m�)� R�s\ c ,NA{� hiev� m�9 EJm�M yfN\K ���'  -YA!k+�5'  \>� �>00-�w2�. v*l)*Nf�3 &�%pr"0�.v �ggrowth �-�G "��^6!c"v`D2 �.'�=!g!?" $A_�,=i�=\alphax 2 1}=�Aw��=.�x}0y6y}2+��+2."�+ $. SeH�CQK,A�s ?A�y �%��?68Am�2a�� S3s excep&�'�..�> . So�51%��&�,.�x6%{N 6�26B:�,� nx�Ny$�<�5s"�3,�[0ebins'/�Q"��nc��>se �)A=� am� J& $2����Uximat�R!���happe�-i�4R� a)[ swit#mA�>��:S%�$M�%��O$� &�{MotTa�e�}';.�$LxG *uL ~G&���d%K.8K$8$"�8��)L��N��*�T�> *�?�;B�L ZE >_�-\/, \{i()AE }^*- ^*. �Q �E) ( })+ \7.6�+ &6m.Bl.j�:(k )�-f Sl&e-}y+I + &(| 2|^2+|IJ>%E/1}{.x&?/ �, �)+YX WR^* ��^*2_�--2�2 4�.g2Y-V�F|.g(z#0{.\{�4�4 �.%0 ��2} �]�SB��S[69F5E+2-^2(- )^2+ 22.�2�F�%�.  2N}4�.� ~ y*+1�=`39�5\- \}"3A�.�.wZ&;# n $a��2}��a� =1�N����U�(9�#�Oy�V��*�g�L$<"�=N��l R�,F "�2 pmatrix} z29���.P\ b & 1; L�|�I)��0ot{%��)f * i}{&� #\Lambda*3 2�2  2 1� >� e�'�\./V�:F Z&7�o0 �iyi�:h�+�3E�[ -2�0}�C���C 1��Q2}"�W}� &� V.Z/62�V�-2F�qq�:�2� �7\{ YP-_DJ ���Bk:�r�j�-�� c\Ny�*G:�*EG6!7 �6�2 s*pJ� h�Vsatzs $�20=||u_i||_2^2=�� [���E� ^*+ I�^B:�].$$ S/U�2� be *cVF��6 2defFg�  idy�nui�nui��Z>�F>��^�7B��Y�I�2FHM@-'@}{2(1-,u1 -)O�^nG�n@�n -�nu2�XTCI6EAl it�&mplex� jugatA�d�Vhin� ccT; �1, 2\in7 bb{R}$Q� imme�<E Zf+-�6� ����d}{dt} V'�� 0��2/MX�EBo6 �s�m6��&U  in��=!%�6:B�N �q_ �iN�)^9�� N_0BJ��( $q_1,q_2,NC� �@NcEc�`sol!�"�]F o fiA">�"x&sR . N�theless� he��*y/La��$A�AC I}(a{�L)�sVGf7.�H�An�^��F�"hN2RJ�c$�LweCcus�24})#&d6�Nn "ar�N$g�N By���� _R+iI"_IpA(�_I$$ ;_R*EX6  2 :�!�&�E�JE�"Uby�3basic "/�)VP?S~H mwnN@�solgeNe��ٗ �R��� IIi+6 �* } Mq�$��\-2)tO cos(2�*+>*.�ybB�� ���M�? -M�M{ 0-M_3 & M_4\\ -R�� M_423\\LS 67B��H-�zM_1%t -�{I}(0)-)� �� �=W)�{R.( (��c(P2P4w� O' O �9o%�6��Ul 8T{, �E� o!"4""vJ��.�Vw1��&#kA 8y�(0)�5\" �I� # 0$t&E&%Jm[��i�Z�d o�]}&=:)�RI�1 0a4 a1 t 2 t!� �2�_0aR3si 3 fI>f'Jf-�B3co�?fI�a�6���&� �s^�M^� )_peak\���T:�|� 2 t|!Q|%RF(�|��!�"g�\.�; UC�8"Compan:Y�2�!�=J� ki:6_)*8l,�Uorbit��2,M��j�k^.�B�" �VYic2rqq&�k�}� dik��*�.MvarBF0.� ^mea�aIl&,�!sQYoryE��7�x� b�%�-s�-*[6->.�(�9�� wPQA �}/!Y)<2�V�� (for� C�N�b�$B�$ e va8[of� 2� �ed8r�to.��.aDIe+� !M\ ell$ �/m�X �1.8�3ir�n�1is�&�%&�B" &�4p"9�yU madJ Townr."�'�b�L �O2 zV$�Z*�R ssum�8of&�H$g%�,V >�d�i�,�mya($l(-r�?�Ts�iit."^ *Ak�[x�n&�C�, %�}E lapp �B��Xrez+, ?0)��DY9!�?>$m��/s�<�K9)e�N��`�a �LerBU�$|.V)NW�<�I�BC�good a�n�!��cur�n4Qr{MG670$. Af,a^&q�* sUJrepel �!M)�� >�&!B;,"Qw�6p�!�.sE�~2U�an8 clud-"&�)��Q%is!kiglpr�%� v�"6�* �i�*IBhsTs �jl�F[. &+� dimFo�NZ4ZhpulfAk��s �b[FpF'�i��Fn=^#�&^cs"3GcoAGnt5^ ten%&mH!Sem�Kivsharɑ�?�'+�a:Vs"� 3spP n"4Ya ,�j� pm�-2z�S�RmXa" Hi �P>�,$�� Ydomin_�encP!s�m~ slow�<0R regime2w4"�#.,iXa�bN mbWf"z,>jA-&Kin�� \ba�7��u�"pH4��-"�Sis"cH5exhib�: teleport &w@� y sudde�>vanish��app�)�@7$!is-e`�b"�A�)1"�XI sZJop� in&g%� ing. %F CONCLUNvF2�*��{Co� aN�D c.sE�p[d �"G?a�ai�a�1E:*^.yR}�#�*.8+*sGAhEe� mc6a *ka� "��K�&Q1� uJ+DirU'kj� vAW�9l&�E^%�, ��% f�K�iG -6���rA"j<�?sgK�#=�#& I�a�i's�okLa&* !1�W9� *�K&�0�etA�H'e�E��,� "@j$n$�3.�.o4`,h � o� �,n �-�� �G ba on �[ *E,/(!J�obUUpDatm�Fcx"6���AR]��5-٩^$inR limi6 &�N�@ ACKNOWLEDGEMENTSr�$ G. D. M.�V P-G.e&�l��p����MinD\lrio de Educaci\'on y Ciencia� 4w8t BFM2003-02832hHConsejer\'{\i}a de VG-� Junta�$ Comunidad�w Cast/g -La Manch6y,PAC-02-002. � cknowledg� �� �(AP2001-0535 MECDNj8%% BIBLIOGRAPHYrh%��boHthebibliography}{990b�Hem{Zakharov}{V. E. `, A. B. Shabat, {\em Exac9 or�f d*�self-f�Ua�A�YeB"6�a ey��� }, Soviet�z� JETP-USSR \textbf{34} (1): 62-69 (1972)}k �0Akh}{N.N. AkhWev�Auf kiewicz, �S. : No4t Puls�nd�<$s}, (Chapm�Xnd Hall, London, 1997)..dpVVz}{L. V\'azquez, L. Streit,q(\'erez-GarcM�, Eds.-{�(Klein-Gordo��Schr\"o�Ier��s:�*!�RApp�{$}, World S^m�`, Agap�F(19966�(Sulem}{ C.  S P �$5� �{\"o} ��#: SB"!�n $apse}, (Sp�P9a�04040)�:��(({F. Abdullam,G. Caputo, RE] Kraenkel,%x%� -� �Control�N$K3!6�� �� tem__l� �1�scatte�N length6�A 1�6a�013605%�:��p�n� ontesinos�M. N� P. T�s �aNebI{qFu multid&N}��PN�:�e ter-A� b�herA�%�ica D]�1}�,4) 193�2102��n�U��;*�b tudi�psY�T6�},�h.��put�H�3.�(A�x) )�0tt{arxiv.org/�,.PS/0312020}2�m5�04b��H. Mi|0A���a�lgueiro:� ed vortex"�av� �ﱨe-��t)�V�4050596�Ma�� }{S.��  ��pqV� �w6� of�h ctromagne�A>!� Sov.E9.k �@bf{38}, 248 (19746�to�Y{T��n��� Lakshmana�; M�.scOr6z� < s:� pe-ch�ng�#�s, ��c {&9pnd*L B�� ��,E 67, 046617E�:�8PRLdual}{D. S. � M. RDthews��R. Ensh� CJ Wiem�a E�C�B+ e5��-�>x2�fbi%�mix!g!�2�.�.��Q815 19986�NaY}{B�Esr�HC.aGreeneMtby - S�Efluids�!�,it up� }, e � 392}, 434c >�"d��H. y�%^S�~>� :},�.28��133901E:� rig1K Rodn� ki. W.��lagDSo4�-CA&��s �te� $N$-ut �!�NLS1|� 27o�,.AP/0309114}.l rig2%=PerelE�%^z�v|oq�T.s .c u�b�-ph�021}} /!�r icaDp^<� �7�a��v: �t*mU�zLm+ ica V!211-2182Z�or�M view see �&< Prog.� � UI43}, �20>� W{Yu�c ,C (P. Agrawal,%O5M-s: �zFib� to Pho�W$s Crystals�`Academic Press, San Diego]33endB-�" docuV} {\$class{jnmpA�u�� ckage{amsA�} %.�icx:�G xsymDset',$er{page}{1 JNMP��Jd�uF }{�} . DOCU�D SPECIFIC DEFINITI�� %\adisplay2 ks \new�Kem!or�zB`3lemma}{L \ 6style� �_O.5de{D .$*{x}{E1a}� ENDv���EEQs7�1 � 7s{ 8 oeq�8,#1{\hbox{\rm�, t$wnupindice �{�.� t}^{}_/._{}^{#2~updown^A -12A UAmixed^@^~_o m ex#12��-�B"K } % lar/�U)%u{UFt{\u_tq\ugxh flow \tau\ C cc{\bar\u<tPcc!�(V @v{V 9vt{\v3v�v-l vvarGv�!0a�!�u#$E�u�.H scu{�scut{�{t%J .��*%u_6D�DE:��s'c\la�J#1,#2\�}le�0Jsp#1{J^{(#1)1sol R6wuKmbd�7 def\wt{\m�wtau{\nx{\xiIigmide�>@g�gE|E\a,!iE��ief\flat(\etQ<}W>+ ginv+g6>( ycovder+mu\n��� inde-�� conx+\GammaZ[ ,ur �RKF� 's( {\ch!!ei-�delb� �!vol �epsilon>n2}�1C.var�1c%!ˊ_= � "V>$��w �&.�!��Quau032} iy2{�i % LiY_gebra�> �:�{ Valg5�{}^C�i.��:e�e:�1I� � algtfV_t�7V algxj3xJ3te#1{e.Na�%Zx 6 quot{p � ve� f0K!5h{� h�?u� `tUalg�$frak JT{� T�JI A bb I�V m0S % misc1��R` bb R�aCRC?d wdi it�$  )(nnwp/{nonne�vely-we�B0ed polynomialQ�hNE/{high Fky-is>ie!��0lhs/{l.h.s.\! 4rr6 ie/{~G&u enA�w w b�& �c HeE�s %�XLnewcommand{\evenhead�C�coe+T. Wolx9r20odd /G�e3Z� � s -$hyperbolic�&(-h C% Titlet � this � empty�$\FirstPage�{12� {2005} �g�({;G> }--\��P }}{E�P\tiny {Birthday Issue�4\copy� note ^{S C A5- \Name{S!S-� C� =of H9VX&��EL !#�0 \Author{Stev!(ANCO~$^\dagF6(Thomas WOLF;ddn { D�)"aJe�%o�,Brock Univer�t, Canada L2S 3A1 \\ ~~E-mail: vsanco@b;u.ca ,vtwolf�Date{�J���%is!�"%[�%Tissue published in honL(of Fr�Esco C[b�Z�" occaY$&%70th b-�A6�/ab�0cX no��nt Mo՚� reRF �xn l"gr�Y �esX.1+12@(si"�s, �"$O(N)$-iw9i'�}u H $\ux{t} =f(\u,\ut, })$ a�=$**�K $\u(t,x�+re��s8 ed. Y%)*e� ���8all� $ing-homoge�Z� admi#a ��/!eleIaf{sc�g� . S9 %D rpre %Ctheseg��$�M 9�afe {Int�m�"gQi}��setfooe�� U&t%�il�+�&�v")(5� (PDEs) m~m1`5)-�]c&�%&�$�,o year��$ B\"acklun�dns"s' s, Lax p��, ina�e!XZ�vk1��z� (q's ``S-Q��''), l��i��r2� (``CN4&�� ainlev\'e �cet�hierar1M%�I,s/��O.4s0mas�,�;i2 recure�,(Nijenhuis) ΂P�$, bi-Hamil]a7h�,e�-&To�-7+�Rco�Ŗ�d���"�% t`}ofE�a�%:e��='~%�"�6x' a PDE�!�-ulss<suD�lyIA5 �{bragimov�#Fokas} (q�& '!+)�1, 2 3 4})i�E�cular, �@ll��ren�%"��%�ya�ar�!���0>�<�ce �/ yi;,2% iT0E?a?, \ie/~/�-Q:y�'A rigor7hproef%q.3O``oneQ:y{:i '' �{ esta�O-tSav sWang6�,Beukers!})7=p��as%' semiiQ1("���5 \EQ��)LutPDE} � t=x{n�Df( ,$x{},\ldots @n-1}) ,\quad n>1,�B��a ����%cri� ���a�a��O5~N>,xl$ (so-�ed $\wu$2�~AUg$)�u��A^ic�aFDGel'fand-Dikii, c2�-i� er a� e�a�A�.mai�-yQ,�!�s�ctp) �� such�� 5�l�=A�&� !�-p�gv %!ɺ�l�>0$�p $!�$ belong=^N'��w+iBQ�aMdi�=1,R,2}: $n=2$ Bu�k't�wu=1$);  3$ K�weg de V�4 (KdV)�wu�5�,lRJ-m.1$), �{-�| (ISP1/2$);{ 5$ Kaup-K`$shmidt (KK)2K Sawada-Ko3_ (S:6<; �&�.FgA� '��+:p(. E�E:B�!�}�A�"QDcA.m�no.ver � < "� ��1�UA�@2!D(NLS)"XA�d�Dvar�md��vu�� 7q�!svV}6�.I�d aU lex-�1d 2ht3a2Ud imag�pcf�Ipir!/c) FS)pr�Ls b1� muchA !�A�|u am��l >�of� ' 1a$�3��lyA7�re1 d by�& $ o��- k  $�wu)"�ixCQru$. R �.�_O Y\n�E2eE  %o. ���ns��! u^1�0OlverSokolov, �,T�ida 02})�sͭ�X4stA�!Z6�"� , \A { It�p�b�X% �z�#)��]� % BBakirovI� %��)�>�7 4�,surprA' gly, /�Fxs/  �� s}. "#X�IIs`/se�Ab�c !m!�w�p`� i��&k����u�j c:& ast,�%=}� ���2ad���Qe da���fu�'m�,��:z�-, desc��a *.l��iqa,m ��F�M $\i]wTru$, � non-=TY��=2{of%bRst }�. )n�I��n [7@ C:�Fly �Gork� e�devI�+kv�+�ng Y>�of.�=Dq�Zh��@��a�L from � ine-).(SG���G�{�ants re�8�$S|*[,��W:�Z'@%U�I� � K.c t� xR�p� v%Q rG�I��pa����W�'� *���0 ��B9m.��"�_ t2dyp�} �!�-[2@s: \vskip 0pt $(1�D SG9?�!9=bB ,�X��r: ingu��nhAE-5$F �DoE ; 6y2a z9R�=� scu\Ѝ1- t^2}$P sUi6� �\�arrow �^{-1}��P�MH�^��k���.� �["�a��e f ��y;:�b ��&��4�5y:�|�|����.NLS�:wShAB����&\  2>x{4� }^2 !�aESxvRi 5� I3T� x{}|V`\ �����K N !�m9���uE��;^9`u6. �8L ���"-F���6�v a natu��geo� "D`{!O����g ����M&:t�CR�(�&P ifol�h&y!�third�{2�a�!nd��l j)noRR��Z*�::� R�s "�-��e�~��s$N$ a�E rary2 ]B>E-���of&- ed���A�.� 7 utmx���\,mapn.���� 0*�( n,m \geq 0"�nam�$f� a;�a� erms<X8s?�ts�arg�%s���a2�N:�:��� uctse� {��} $yq �A�S� a %D�f9ly {\it2F}t�m=0,n�1!�or5,y/* 1,n\leq 1��wMBll�a 12�.4%G�kIn� caT wl&�} n�P $ nm$ �f1z` i�%�$4 $n>mf�Bay�6Gf bM�a:�(} $(m,n)$ �A-�3a tot9"�� �e�8o����Q-�.�&:�e�a�h)ˡen�1sz x(n,m+1Ά If=)2�VYa�)�-�e  k�t��f�D�;8$\D{t}{}\D{x}{mҜ e jeF<aceA�,Jsp{\infty}=�,.�"�ux{kt\,l)$,xnQ$�� /} o c~*6l�#o yMt .� $ (\tm��o��^nd&�� �;qu�s) ni����muŊ5\�%{}$ wh�9BI^!V�� J�< } \�$ = g�:�rb��z�s�I`$r>\mY <�$g����Z�Th3�1�Uir EQ [\D1i,\ :�] =0 ,}({ �:($ .] G A)�V! �ai� beJoap!� (wu,\wt)$ if�V?���aZ!�+ group (��p��vH�$�S \R{}$).. H} mX)ba�  (e^{\wt�$}t, S}x -\wu\u) .D&) Notkg�� conven��A��� se�Mh�#��nQ�C qual��a N�8wt$��"p���d $\wt+mi��w#� i�� t lo�i��, �Ps/:�!�} ��a�s ;Da�`J�be"h��J�� -�>�MT } (s�}��Ii��c�2��i�Y2<���P� sselgI���,e�iesCor����dw�� fer!�n) �NiC�E�a�fi�throug�s&XI�tau6�A�wta]�tau���}YA -=�ym<:[. E�I�MTA0au��2s�$'Dcis� wh�{ �/A�8&�!i�IA�� r� T)ou1VIB aa��O*�SG>m� � s� "� �� �V� . MM?�fi�yY D%��Sse�.{Avu��a�)ELbe*M �i �&� �<5ll� :&V2�  .� ,I�ab1 �co*���ei� �g`a[�Vlr&wis���rZ�>PMm� a)�� '�}� -�%31�. Hm��LwZ` F�TtoU�I�� wu=0,�)�X,1,2$ >�b��L"�&2K� summar7�]E"� I�_�w�2A��&��Ej�2�"�hcit)&��lUC�m�%�$�u � tB��6�2�Var.��qN ����1�_�9� R�es3*{��)�N $ RE����ץ��c�kof�Ol-��V$��\bullet$Qm2� *z=3� �1 && \utHuxf\u}{\u}} F_�JmkdveqIRf�;+6Q x{}}\u{} q2SI"l sR�IS��E=B|\w� � �3?3F�262 � + >0� M4L0{}\u ;� iseqѥ��c-ʡK*�#r�.62�22�i)��2} \pm6�cc�9�nls=�J>22 ?\mp6V}\ucc=� V��& -J�.�!�� �&=A�x�+ �h>�5�a_26cc{} ;36#X4cc1� \u ;5 cc *h&& +a_66+�� XccW*7b*d (cc*86*�}c�uQ�der%�U�s}22 $a_1y a_8$�L %���� , faB� 6���&as lis V�V�qr��Q�V8$�doe��{�)J ::caQ�� "� wt=5�k����? Cly- �-<, IS, K, KK, SK,�&� �s, L'jnGN�͎��A���%��B� �ed.�," 9 $t\.�i t$, $ :�� im�T*ari,0 �e`S"Z 6 ~ i*$B#%Mbv,!�di�9� �"E+po%{�--9W2� A'wcQX di�c�"�Nd �~-�{ t}$9�. 22��H:st9pot��E�//�..'b5U8)Z�%, !#outfdod��aJW &�,A�w� pliciu"hdA�6�,:U18�,b!��&f$0i�f� qi ��f} �zB*�2^ -�8�g�:%S�z��via!�=\vx{}$,6p a�,u_\v= \wu-1$&� �C oNZ^YgH � non-l Z`$%�a� �a]A�� ���A ���!70whe� th�T�O"Z s/� 6�.�%�settl+sxJ/+� �)ϹBp9��1�� �6 �z:�1 �Q ,pot !��f(\v,� n"�) &�[ 6��29� vx{l{x0Eln��%�2�d>\�2\��vx{j}}{k}�%4/d>� 2' .� ��5R-EFi�_!.wt)= (0,� �yr�2�� >��� P2Ij� �j=5$oJޠA'noEi&� ]��.Z����A� trueaj:�a+i(\e�� �2)"�h�=3a��05t!`9$xn&�ek%@-a�par��Ea�Y$}�6� -:$&!�$:�q�E?c�}�"^A��4A 3rd-]"�*L�Lo�a��mA�]-6a �3� 2� +"7 3b A$!cN��$"�#���2nex�1of�02��J�st3$U�l��*�I��!� !S*Z"� 2\"BS"9!�A�� $�sc:��-�B�0!A.}�1"�1-��"�%O.D.�3lu�UjobD� �� � no�1M�Q �N=8�ar9���%am��9ye�+ mpat毥"�Ŝi�e$, �sS1�2�X#(1�-1I^t!<� (i?+2�% �2-\$5)q�j �2�#p!�W-!w��y]�&i=:-w�s2�i�s/) 5O��-RinN&� SG&� w�Xec ;�e%xXc>-6� Zbsg� ��?.]��SG��Y�V(0,-1*�L6�U�N&vol/550�  )H"\Bc)KJW3$"� (�a!i10of"���\& = -"�� Ah�%� }lz)�%� 2!l=-1,0,16� SGeq"��.U�Ex{}*�s�����,dsw�c t`�����4,5,6,7����a[�R+T � � (6��}+*��q2}} )>-�x{} + BI2�x�GF��0tag\\&&\qquad  -`R?3}�|-��.��>A6 IBSG��*�dn2]H�($3.�U�)Z5�6)W�Aj a&r%a>b9� is6�D!�#��Kd&�Q.�% b]�aboloid.{%s� *� �%�^�L� w� so"�a�"2 j7ts���4*.�S.�EM��Tnh�%�eY)�6��i 0 !�BY*SG��f.��F�)� associa!��`? utes�)' "7�Q1��a�p2# 2 B��k�j$-�)low�8$m�Rd!jo%� triv� �"sce�=0$M !��&�9�9� reK:'��9(� ��QO�uNr8"$- $x$-�l�aD& )z�.7n r��3�S��$0$%A"� n;�$6G���QF�3elfn�2[  frac{3}{M�c2� w��A�)�s/vf$+2 �� <�����/a�c�.ook�j�ɘd�/e9��$r��6of m*t m� ^ 5\b�.�� gUfaesP%�� 6�5��2! �cI �.�����xb�� �$C)�RKKIq!sI&,ie� .U1B&Mb��$"8�����_0^ �!$�S� S:2 �� j�8_1�E� �S>&���j4A��(f1�yw$w= S- 0=2�;H�%�(�9�� gar?i��. o�CR�@t=c$x} !*&�@t4 it�V%�:!7 �0-w=2 � �1=���1�%�-h^!�&�q1��i�2P sca� 1u�a:���2��$2&q>!^(�)�uQit�Wc"r"@:5��V�2)��f)]gaQA�F1 �s�Ye��N�ft=b��^n � �s�� �!j!�a$t�%ѫ�C��zhG��( GK xA�A-i20,� �ea�0 ��;-�;!car.;�I���Tl icņ�Zati55 in�l97u����byG� u;E�A��s)� *�-.�6<a��NB� �J� � -J�a�1�j��.� ��!. "-8!���Xe� �3� ��  =�qrt{ 1��cc}ua2!0,1.f�z�C_1E4)��I�=�A�\u.] '}A�6qsm� !V���#%�UI+2 >�A� !�M� rV��%�+s: AlBu?2s* "~ ��exHjbe* ��K a*� � ����.u �5&� :.��.-6-�',� �,�� ,K�� wo4�,*Ai7�H��.-$N+1$-.�gauge��gfU�n �s� Fi)I�se/ a:' �IS�* !&� �� � � ���=��.�9��`�鶅��y��!�*=. &@ �x�7!@�Gr ��7�;�,�< else�! !5�{n>5, al A��Qi>�" }  #Xd��algorith]�XGI=D#5�>�,~rA_2I-�%�ayjic�!*�.I.}*��;]d!7�[%the p�_)XCrack}u-� �:-�D%��� ;S&��E�t_� mQ�y�}u��0%�*N/$u]S�&g/$U�,x�&)1 e de�&b�/phi^i� n es���%_e� cu�Mm�1� �!I- -A� 4( (/V)��!�x��㡰si�[�� $ �_{pt\,qx�N?u<u�p,q�;�allh"�)s�I'!�13�.�s�Surh�8�'2��V��E��K�mɅO_s:eJ5�%6p~wie��'*�8�&fE� �2E%Sa l�n pri���D�� {8;%A!S $>_TE/. ��;B�, �vri=O tit� loop��iSd= �".?6�!!3e]x{t�Bcutt+ x{x�9�G��a�c�;te}Ar.�s��be0�m��s�d�x}� a�7 �tt}�x9.$ E<.t�tx"qV'&aH%S�Kf�adopt �8oR27)!�e lexic��phD4=�t >_T �T l�w Kvaf%V& �S�5�)j^7�gbA81��(��Qu]GA*!�ED,-t��x� �t%?��no �Ner%��a?jma�.����� an A} �wy8�A��FE6�yB.Jpl&m8*">��o1'ɘ�^�wxi�!!��� ��NSo&�3�0U_t = U_{xx � U}{V} U� V'- V '"� 'Vo&� ��&'/"! �1FN ��mu,\xi��mbda_U V*� $2,1ih�$0X,&ql[V^��"IXTtrԃDs>t 6Yof��ͷ��*�1cas3 TL� odate �J!� �(!�&F\ �ro?�V9pe@ c����/ &�<se%*sb),nu5&i\}$.6h0Ns0a��A� Bi��onf$� atens� �h�M.� � � �o��aB9?��������;�~. �=�,UO| �� A���%�8-f!�� �))^`��p��ta�unly|2���!n�.� �}:eJ2!$t$:2� ways ���%iaڵe�Hb 9J !6fil�-{$p�cBgh�!jA  �R@�,A�s4�a=- $\Z>^*,\wxtauu_i^*\D �1�b�-oP� j)�F� �+s=�!.gA*�-, oE $w^{\rmY }_i:K.� + p\wt^ q\�"� �w x^* ��0�S�Qk_i 2R�4�D,MNY�G �J�b>V�_ fo� !�I�O :�� u^&�  = f^i��U.�!Tum_{k,J} F^{ikJ} U^k_J/"A�}�^!eZ g6[\XG2XT�rhseqn!3��� ript�`  �a�CiNf,���R2JEq w)!t^Cofe�thi. (9�e�a�**/$u^k,U^kfH���"I�uueb�� $t��� ��V a�atXA�U� !�amI"�-9�%�$ �0 $^*$�<$MK; $f^i,!�,1�,1p �g mostMAk0�cs (�pfyr�#m�� at�!p buil�Oe�Yy*�var����E�q� � O �\� o�y"/�: !� _J$,���H4$u^{k_1}_{J_1} 2 XLsq��f��!>a ",ia��Eo�h�.o}{q�] sat)]onR{ma]f�R�.�Wf�>?9a�3(,bit�J*k�`�l� 5k-�5�9]nTZ6� r m��isel� m �l.�,ti!e.�1 �^d ͮ�:. (�.� of u�=D9 .�-� A:-2or QKc� o�-lya �l%?����5QwE��I-��� uct  4s?��!0pr}�"�.) E�7rtQto em��i��T>cp��]� !���s�I ns76�= ly.A�F�^*<0$!'$\� # ��Q�3��� ew flagq�ven4�R���ut & �J "8>"G!�} 39>3 U�:110>2e$}^3 \end{=� where all6�\$a_i,b_j$ are undeterminAquncIb of $2�},�{\ut}$.EZM�A�A�Mi0mKdV inverse Erq1�qt6Yt}+ a_2��A� �f�%vt1�F� @UcV�?E��5a@B�N)>9eeE��2 �9A].�5��I�F/4691e�B'6T� �1�>/xa �O;�< "%�"%.L1%�� Gt:�5�1%�0U>-�:, +a�%�1%�6J~��j�t �r�NLS6�0is similar, u�Fa pair�i�s $U,V$,2�2�L6,�KV=1&and���,ad�Ualfilter ŕɒ0 F��u_V=-1$�L\subse��{Comput�TS�� y Co� } I��,special case�evolu��ary, �-Ztits),$\phi^i_{t}$�a\tau}$"G?y.- >[t,0]} := \D ={}] -t0} ፥�Tdone only once because%:\rhs/�!V�!l �� do no ntain- " $d$- *9 . As � sequence,� O2��D sepa� ly linear�6].z  of6�  bie��] situ�A�0different whe)�\l ���c �an $x. f-�$$, such as�$hyperbolicI" )_{tx}AsTrany9:2\$s that app=5��:�0lead to (repe� )F�YC�Lrough5A� -<2�\become polynomially non--� .�!%UE but sta>�N1 �)�Due�this qity�, hich!�further  ified%� ever�2eAh 6�>� �e��k� �2� %extremE� arge�sizE(in 4ediate express� 2ADceedingly high dur��|1� .O)�imp��  proces%�o get o)@is memory hurdle,!�emaityQ�2&6Gy!e,exploited. IiuU��.$ sistE $s$ �s��2% 2q<$b_1,\ldots,b_s$!xi� full2^���c��8ed via \EQ 0 = )�_�'T = \sum_{k=1}^s \left.J) \right|_{Dj_�8=g (k)}}  �J}  $"$ denote�e $k$th%1e53m�.dAn i.e.Fj except!$k$E���pt\,qx�ҁo�/pur�! �ic �maa~(volve ordiC�� partdթ +hs = be inhomo�ous<�'��fxm��EE!%�ofR is fed��o�H5�progra-�Crack}, ��wa)�EB�!N9 .<i�&S|"��2p @ 9L \cite{SokolovWolf} %/couplG.� scalar- EI{CT��idaD02�Origin��,I� �H has been developeda �rE> ��*!PDEo,%���ї�t ssen!�,ly required a�[Q�>��2; � / Rmt occu"s 6x��-'*�U�Ej \secEresults!3S @A��!,m, like squa* root"I ]fou� ��>�, a4 a@often�+in reachA:Av2YO!�A�rA�atA�employ�\--�* appropr��> �strengta.0a�x�o�u.� packages 2�:-)�s l� ) flexibil��of its �ach�� poss"to run i�wa�S(y automatic� �ac� mod��!t ts suppor;handlAxe � �� (safe� �F ,rol, heurisq$algorithms�cut dow%��(�5��5 �to takvantag)!�I�- *XuRE�.�ies).� :, .�provide� verbos)�zor�U� )Х�al steps��all�i� incipla suto��checkIn$(human) in!^�� (@!�� isA�hard d e3  numbeS�)A� a�H8{ Sigma Model I� pre �,s } \label{s%!�l�A� wave5��c�JASGN \sin\scu$��well-kn%��intimat�rel� ! two!�!�� est �E�l�� Pohlmeyera��_�:describ)I a geo�cal:��?Dmaps on $2$-dimen� lal Minkowski space $\R{1,1}$���A�t s $S^1�S^2$, re)�ve�In"3a � zZs given� �no��2~� .�4eq} 0= \covder�g}\ 0x}\uvars{A}{}� tJ=\conx* BC}( 8}{}) 6 KBNH]C]\KEQ���M}s$ <� (t,x)$ re1 �� ng a!�)Ys^(Riemannian .h $(M,\g{A�)& $A�l- \dim MYH�$2 � t} +^� ! �d$ K (he pullbackA�9�3 (torA60-free) covari& ��W I� $�$;loA�co > .;$A/�4manifold $M$, I4�erm��$Ch�coffel��bol%5�$� �� is6j�M.E��o.� $S[-5}{}] Aiin&.)x"}{U@<}{}}_g \d t\d x$L #cdon_g6Y inner�� duct|$T(M)$6I �9l.�A1An�.� meanA��&� 2�D arises if we view2�I�<fixed� cur� embe�in��he2�9����!� reby����E�is X�s�� arcl�is ehrve2*�er�on lawBTDt#law} %�t}(� 5�a�a3 Q�((u) ) =0 . �B`��CflrA�!� ��arrow x�t!) �r&�Xr�x6�x�tQ����TheseBJsņconnec�w in�c"�)�under. form:caW trans�s $t�)t'�alpha(t� x2!x!beta(xE�TA&��domsM�,in a naturalA�aRby put� $ g'(t)^2�H\Z�5@i�$t  $�'(xFDU?1R $. Fo T�Ta@.V3 \eq� �&is�u$-.+%�1ywe�&����A"��ilei�nd have op te @��t- +1$,��� conv���f � �*/  $O(N)$-Q8tt 2�s� from.; Ar way)��cer�typ� f2a�$One direct9�Ab�si��ng61 ��a�n �q�ic& surfG ! Euclidean> �QN+[ orRx Nx . Veq .�!R�e�by �j ing Q��g!lizqk!he%?��Aar6yA� = - (1^2)^{-1�cutx{I7c�ZE���> � bset \R{2A second)�!�tr��!�,a flat Carta2"�s��A�,frame bundle� .�.V si� tang s� structure�alg{g}/h� imeq�)� baseda/�E�Li+ �av A�p�h�4For a suitable�� choi�1�,��Z�u onx#yield~�:�.�  $)�t!� \sqrt{)�t^25��siq!3>�   \)$SO(3)/SO(2�� q�SGXaT�}I�#at�M�2��� SGeq}��th*"�# ��&S B�N��boloid6b�\R)�=�inv�N��e{first� e�$ ѵ�A�6�&�$ ��!Z of gauged.�s � ��)� s."es (Kle�iE$es) assoc�dy:.��2$g{so}(N+1)A�i�A� 2), u $��2� $N$-spp#�iN6�=�=�*�F` Co��)�l�Z i.��N$���Een We"� >� $N+1$-u� uni�� � i}{}$, $i&� 7,a� straO$y,atisfy $1= �< j}�% id{i !XI� re�E5 Rt�e�n����{� pm �  1-  # l� �#� .� = m 8, 9 a� .�N�tC4$kre,� �=of2�S^N�nA ticu��a"upper�Z$lower hemi-��7��m3d�6{� open)�b�q�)`e� "���*�� `nM '���& -$![)��q� ��� 1k��d-� +(1-Q-�-� }{C}�)�}{AB}"� %���& � �}e id Z+$� � 1dn�!� �AY!�zJ��Ng%'%�qreadily6�4Uy*3 C}{g� �� =0$Zh)d^ += u{C} +�A�� B!b.� ,\quad \^b!�)�D( !F2�D}{9�D1� :}{B C} ).yHs"%���� ?6F[�A!,B]%�={A�D}�2�C[��}) �]}&Krv , -sD = 1Y[M6�{ 3�. Not�nd�~Ne�N��� of (� iv��,u6urZEm�M��ro� a F0 thus"6�M=Wn�zI�_P" !S�22sa$5A + � 7# >�C�( %�� A�E�aA� )=�� 5x*� f����(�e5�ase $N�* sV�   $�� +Ei�scZ� . �grE �'&h!ۡ�$N\geq 1�&�v�es� ished�PultR a a Lax� > �� =  /S���a.�icM� �DZacharovMikhailov,*�X� morLcen�v�$bi-HamiltoF*� (X#er- tOcu���rator) � d �4� �� !#mul-!C�( �Z0qX6�Sa�sWang-#e� s,Anco(Its \h� s/ w�-f- "�-9 "J)B\"ackl"6?( technique (reBg0zlyEy��$t\*t'� x.x':5&R .�s�4s�5&M "�M� hierarchy!R�is.� %�b���&�r05@$O ��a7���W�4group $(x',t'� a�)2LP (e^{\epsilon}x',e^{-::u$ \in%��Buf(er >!�oP tbl��t,xK�5�a�.� o� �!0a�Tta�reaso fa RN>�doe�#tLe)our> [$To accounta�ni �%�X �/M4#a}0&SG5�)� �N�(e look�a6�Ean��.�� � orkA#�wf� !�&Bo ��-, ��&� �� (1+ݎ *� :����%6�w� t �JX ��� ��%(1" �"�*� � h� k*  deRU id ~k��N& . F1!Ϧ 4!s�JaanforEto��g@ �" +�!/5>| �y !�lc�+n� s�I�)?~� � h Z . FY}�^�$to identif#7*t��!4i� B� E!T.M2) "u *y"1 � �� ,r frac{1}{2"� :3!u� o \eqtext{a�"?. � M�2��J�.�~� n�Oar&� C�$�"8 �� = (1 + 22�� & ��ur"g = 2ekg q Z 6q ^U�S g!!B&cAB }{CBœ (Cur$lF-!�I^ tensor1A2.m$N->�=�q�s�aI�6;dCinv{BA�.hr �2!�C!�6�_ .) �*C !� Lo�/zU C6A ����s53qrefs>{N�obOz,�la�!&�� U�[+Na"�Cor�s2 .,e is b5�;��erpart "6<� � �"�yl*�у!pM���!�im��>G�'sq�n���f���%�$6#IZ9LI��ha  v� o(�d2���is!$~o��A�-Ja^9�1 (negs<)F]�rvY��trasttj�%���X|Ax�%V|,�1�a-Ar*�.a�I:.���"Qs>)���~M�>�6"'�.�BW�r��-R�!p� .�p �2�� a n�0ff��(at points $6��R���H>.^W �5%�3`7� �!�&� ��y J��:jY2@� ���:,s &oapi� V� 4 %�� a�$��3�lzI%e:tJ �!"� seem �(�(-�liter%n , soer� st�( >&�,��.a new�ult. Un�9�b��0existF of af=a�n quesAh, a�&� �A�k��  *?!RJ� )���=,a#!).fa�� v�� u46z��Feq.A�&;,� � 1$� O+tNt-e� )��8KN�=4,5,6,7A! stro� sugge�4�6�y��� inde�Ihlx A�&�ill�/ exhibil# e.g.�*P, ab�,�'3:%-rB�.:TH* 2( ).��d�IW.�,} �Z�i w turna)!.�.�DM=G/H$ ". 8� s $H"* G$ c[ Sbe semi- , �NK act,�&�e;���f� � is*��J��2 d�7ion�gG\�!oplus \quot}$:Ep$[ (, !]�9!G "% 2 r6h0 Gh 0g}> !�B ^'ve2��H,G��%g vC�Y%9 zDon=-ly.g(t3:B7*���f�!,���� W ${TM�<t;���$MayA�.r�u,��.2s- carr�e6� uic2� �  wAY�� .y- S# -Kil)6f*R�*$�$TG�!%�!�res=��to �2$pX�mM�A�d �� ����$G*j� "�l�%xv= few m�="FF $SO(k+1�k)�"^ki $SU U{\C}P 9$ (see � Helgm}��$mplete lis!�d��per�F)e��1&|�n�E��5:J� �� chi�(&�'�5@EichenherrForger}�� :j=/7t"� -1m*K})\up��'/� �,i�>13 &�� � ��D�/�� ival��H#�' !� valu�uVE@*a� =�L6K�$�}{��0�� BUJ�� |'ieZ:#i� ���+"?� ( al>�&uE i5ob�& (�� %I�Maurer-i�T�$G$) i��)"&�s"=""���& ��2*x@DauriaReggeScuito�Detail�& �c"�'�U; ��5.'�:,�!:mY(Sharpe}. F �wz,i?,�N�U�%0A��Q�� EiB��$�2:hD 1�$Recall,�9k)�9 real1;s��l"� �k(k-1)�\omorphic�!�.���k\r< s k$ skew�ic ma�X�*S�Y=�w� N+2)�( 1�62r �)$!2)<�s"�$"�"&jKca�6(��c� liealg}�Jp�x�& ot \\ -�^\T"h�nd/G alg �2&T! 0>!1!� ޕ�param�Iiz�>�%m $Gvec{A�%2y3�%&� emZ=$��W(up!�a n/�+v>�Atra* �KuctEI)�2)$U�J@'1��W|z �)�%A�-�$=dotn�$���)6 !^- . Oj.� $M2�7 $ a�in�+ef���g i|a���&s 2� m�JA�al h[D ��A ��E!{!�.�&� ��.|,�q}l$!YW9��1)ʹD to q��&�)=I�7orthoIM�w$\e�p$&�6� 6B�>D:e! More�� cise��!�l��h )=!��!�!� , na;DAA�ix%b /���E {h}=���UeOE���1�Ml ro�9�!X��sol!ng, � s%�UADe�$ betw�"�P�Y� iod=�,�!�Ef+co ;����a�{ j} �}_� ��>O\ � �c@Q_-Tencode- non8C.+ &x "- ��p7F�7�Ёm �"�/9@i�">A�#*��f6���%�2�,q} � Q�-*C $M=�#��h4�- writ��!gt%�h+y4I �q+* "�3� J:�!x)��b2:"d :te 1I`�%JbxN(:P�9F� E/a obeyJ�t�9.' x+p=  !x} � (= ��aZbB� �:���Al��" M�y i_)�%�i?{AeB)l!*&>ed&�1�BE{s�2hy@A[��N�$for vanisha�-R���E3���)�SZY�:��D3[s \EQ�ɤ: er%�al.�-Qy%�9� + ��Y ]A# p}{ # 2]A(E�\wedgeI>{�oneEQ�%6� antis�< ��'uc���"!�eM< �-�}�recgB)Fon��%��v",�(e t}78a�}{ 2� *x*!}{ .*ABy!�FA�SAY6%�{K�A^{=�^r =1�;n(!"Oin�:nt���i�mJ�'a�s����to pu% : adapted} �� =1& xe{i�O ,�@out los��6t&X�o�O�KF��+V1]he�;�h=B��%E>Honslawi�te � .I-��i�jB$�/ 2�"Q0@x�I�!l,!�!� =(i},!$"�!�t!(, <.\2 $� e%column� % CriM)�BcomYof6�AS "b ��$e6� aloQ9he�� 9����&.2R6�R flow�J��S&�$�Qw6�?�"D 6�n�pl'I� m*F+, A/Fng�$N$m� �7Au� �J � (so{;��5=A�?r?nre nod main�Cq :�I�r�[�pB/Y A��"� d.�Dq�,Q��&:~(e�e��re�=to�=>���0�S� $� c"A"s:�B5�Tiz!|���.�*be� llel (cf.�Bishop})�xAh0��OR�a?M G�*\ � �!alij.5 h}{ii�e��_�>> >��.�(���C"� � r+1�����mJ�d }s A�at%j;A2K:�F�j}$!�@Ves "%��R1 $1$-A�4I���yU :p�pu�>:{ =0$ avail(\ ��Lis�Od�I�9pjD�b�Gy��.peay+2Y$!�YM�G!S�*�_!T�� �( infinitesiZAdis�%em�>F *�A*m���u�� hav�p�O��CB Now�" v� ��Pa^ find� s && !�9hA��8\!5?!e#�v(͘�V.�C"� s��l!�om%A�� %$� �i$+-|�Z2y �. 6� ���!�_z1Tsm� � L toge E� MlN�&�h>eQPPI� ��1\=  ( j )^{1/�*J��� ^7�@������e�%�*-byN.�; �$U�B%elimina� $ `a t;5v} )�E%B*�vp�){ �=I�}�.�/&�A�b�A *�is�2�M2s]Q�\x3/*E�CQ �V-!�`&�2���eqI�Eg6o5��K H6� Gin.�7Sf��v�4%"2,�REi�"4$,Bakis}. RA�H�2zDit �]WaCV�4e��fa�-!ic �R ��4)��5�Rehren,BE,�4Our�6on� � �5.ins� ly.�,&~B!� appr�P!� � Mari-Befa*�5, �>�5 �Ua>on��� �^r 2- �e�*�+"V *� �� =(0�4,0,%@)4��.��u�� \be0+1)bu"�X a��N� .�@0*�Q�$"��&P�a�!R�AO�4*g/C� �� +1&� %,�.c%-&MP"�b��,Frenet-Serre�4A� "x& ��R.��b2q?,As=�*p $\u$.��Uv nt 2�U"H�SEL@C!e� F_�_�U�*�a}� , st�Xng�6�$M=SU\&�.]HnoF:e �c�)6.KS E2�W &Wgr�^���+1�&�a!&�> must� i�%edQ|A=�a��#*~:K, �S!th",*e2�7zaZ]O �}&�e�ENR��hI�&V*���, ��,��IW7#2�*O�B urse�(proofa�!2a���|!�X �(�))7nWt adm9A��N�(`eV�y� e*remarkWly���VT NH&( invnlsi vv9out{V��d� ��� Z, -m� {F"Q!�/lex1��6� !0L&jIrB4!h�it�2wIsr�!E�mags\ ,�g�Vd! be��Thn=>�!b �a�4\kR�!TrC}(k&haIGu&�!k)$ defFby6�&4 -=� B �g"/"�G�Z�N:�)�hDTi{pF 6�) %�1)�� rp} }��@T���a"�Js/Hof��W C��"� �!�e�  } \}#1}�6{"RS \ \I�� ^\T%� �&�' {*�� \"2["arbitrgeNs ZN! )�Fr�q[�, !Uaf`[d�abg �_d), p&�Y&�#G�3�8M#Y��$�c"�5���՟RQ�U��?� @ �y"1#*B}t?oQ2� �s6UA G&�AU{ _(GA�=�Zo�� eF�a_�� %3 ed}.> 8<5�W trix>5A��� � (�cuNA"�O)�� .y�$�%�aQ(� xj \�xRw�I{�d&P[l�WI6���- m�2�.)�84"�#.M"�"�I.~ Z& � 2?X��%s��)h*2+$ �2�q��L�*�^q#9)[U;i ~$: &�:dY 2# >9!��*�"v-e3"*":�!'6 "�.k#6�&�j5 _* )�� m -"Q E�.�f�5> ��Z�attacVEqw*�! RI tX_ed�� iF�9%h:� �4)�="� F��u�bfng� e �*�M-� ���3� J�r_&y e���?%]�*2� :��Hat""BA> �0"� f ��G��a�6b  (~3"&�%�ed�}�A6a�� � �s� te� �)d\.� �! "`s UL!E.� ce�J� laws�CF�$����"e :  V�:& �We"TlfixUO2+$ (��$�:c)�themH�rJnR=yl!SN �+F(�E���C,&~�6  Bb1 & 0a0�,F\*[.+ ��-f�fͳaN�� �� aF ;)$�8J)0  �v!v\\ \vov�W\v6y�N(\v,v,N"H�"&� �� 4vVrel} v^2 +\v� \�<van/$�2��3e  :� 2�)6� er�-s�Wsen�6��3 �e��Y$1= � �0J0i��$\UWv}0(�\vvar{i) i}$;� ���6�(2�)!*� �i}j�@w" = v +5� r z&eU�&vV IR!5 �a�6 :t!}Jy� half�K�ڡ >A�VXk�)nd��6�A�J0n��u9�%!0 "�p s2� � � toA�� ͞I� \u -q={\uE�\v}aYu���t}{y�v |i \%m����'a-2.V2R�_)�$\v^T \v) =i�\uᝁ�\eV2midsu�s��6r�q�i$eq�5t� $�"� m�BBw�^!�lQo�:z�� JN to hBd�n�%/& \�� { O�<�#concluP]"n}B;R�i2a����s �s�9 ��Et@N exha��=��^�&X>z s $Gt�k&K� 2�2�ZJ�$� �C���H �$U(�!"�, m|J��exz#�p�[��m��>���However,.� s&�=!/latG!6��*�  �7l�k0�g�Xufo�?Yo60��de�(te �@s would� .jv�@gJAor�6�a6�Ns�g�-�6y.VZ�^-t@,xebN�qnFI�Ku R��;dsA)�!EEh�onm�t; �Lneie�"=�m:)o%C�A n��`IalQa �!l (pr��nJ����x!-IWms} �-?m�usN�@�,�>� |!�EA�S�i�ghtps"�y:YHY|0-�5xA��qOaZ�D 0<Ku�T Sklyanin}��6� �}"~1nlseqII�CshGto�Qti�R� ��� $\i���6u��)T{x'9 + ^\dagger 6�!� b$ =*\gamma_An3.`A��sp7D'1 RM_A� *zkN$,"�`(L,oClifford"YA�m  $O B� cB A =2��3 \I�is ob&/s.�C-�2� :��E*rr?eg� fashA�?/a&�b-Y� *��;t����D�"#�, %�&!� deep work� alg1,alg2<3} of Svinolupov��t�;�Sr"rD1 �N �Qv� �H~a# evol�~��,!�p!�7* ki��f�#< #"s�: b� *{Ac�Al�0�PpOnetr(hor (TW) wa�H� ank Winfr�.Neu�=�'cu.{%u$e Konrad Z�/I!) Berli 6�rt�B_fe�*hip?�v��akayuki �u' t�l?o�im����ve-a�$�gAP�bxums #per�edG /}o��a��iluster"�~SHARCNET%��`um (www.sharcnet.com). �thebibli�(phy}{99} \s1 %a"j beti-�29oFem{Y)��ies1} AbR�tz M JEClWon P A,�uitons, Nb EQ; E{�InlO e ScH,ing, Cambri�2Uni �P@z,  1991�F�"&Y  S C�;$ J P,�gr�*%�a � 7g.� A�c�X Ds)6pr|�aM(2004=. �Q%D Bakas I, Park Q-HI�@Shin H-J, LagranguA*2%��*�F, sine-Gordoni �tdem Phys. Lett.} B {\bf 372V,996), 45--52.%Pe �0} Beukers F, �$ J A �5:�<�uJH&�JimHQ'i�5� J. D<���5�} �146 �08), 251--260;6aB Kamp P H%�2� D=u :z {!J.Ew. Math.)$ t8}%�01), 561--574.- o�� 6�A[�wof�:�`�)%�20�396--4082�n/  R,� �`m|<��( wa� �%� Amer13Monthly15IP75!�46--252wDB�B D'AC R, R C TIP(Sciuto S, A�4 schemea bi2bLs�"�Ged F!ar�-�N89E\T80) 363--366; ibid, G�[-�)��> two6��4.��@:/.� � Nucl��u�171�167--182�&�)�Fm  M,e �.ua�s�5Ex�P1+&CGv�55�,79) 381--393.h�"�)}F� K���_�1r"[n� �A%F�.�� �%E:�-�$79), 76--72IFokas}  AIs�Yy&*to�Hc�0�g�"��1�Jq!�m25�,, 1318--1325.8w�#32�S�Oi[,A{� 2F Stud. App�� v77%�,87) 253--299.s } Habibu�J Ia� V Vi�Yam6a R�� Multi*�i�l���.� dAZq�� Z ure��in�|inQ� ics:!�o!vnd5erFyt World�IZic Pubb ��.�";J   S, 2b)2y,�$e� 1jc SwFs, .�Soc., P�!nce, �m.~9 * P2} Ibragimov N H (edi�D, %q!Exact S: s %! kk�7Laws (" me �� %New TreJ in T�.��D;�p M. p�zethodQ3)S RC Handb�^of9# Analys2 fZ�, >� (Boca Raton,)� *�5Shabat6"�  A B, " N q��nontriv9Lie-B�bD �F�J.�m%m��(1�19--30.�>�  P P �� E���-"b�M�Schr\"o�e&�1 ---�%ew�ple�|Y@ ��H��A 84i�A34�6� MJ�.}  �. Gn� . ��ree2�*�<9y �_ i�Sci5s' 2002�43--167.v�2} "�e A��]%�.��V��*i��A�=hUP:5� gN�n(- �Ru�9 Surv�4�1�o, 7 2�4��Sn����6���,�Wt is �� �<?, %E��: Zak#g V E, Spc er-Verlage�92�Olver �}  P� �.KJ3��'eq�1g CommNL193E� � 262�"]}  a�1 le H���gݷ!���2�vlrah�� �o~�� 7` 207--222�R�22�E�  K-H, ��KR>| (${\rm O}(n)=�~$\� $-� M�V�0%T( 2628i 32.�*� -!'UJ} � L� h�/�VE{�2�N�J x �' 7(2)�E410--434"� N� *C�� �6� 2000�32--152X-,!#*/4jD.�Q� in n��Moscow��e��$al Journal�aN200 1369� 6� 9P  R WbU F;� York�EZ�1} �5EC�� Cl.f�A>Q�leR6� Sov.�| Rev. C ��:4�2Q82�8J�&;S I, De�L �no2� � ��2��|, Acta.� ��44 9S32�36�-4Q�F�� v>]�vectorRPˆema��A:EP. Gen��3!X A�113AH1142o al�6L)�2�=]� Jordări��q) =\=O .#� ��10� 1997�60--1162��!D 02}  TS�[�;��o!���-xun�n1l4RIMS KokyurokuM�No. 130gm�L68--90 (in Japanese)��F8=�=;�+0g�� �J� . I �, t), �u.SI/041�2/��} � GeK�XGd Hasimo�2��% ~V�in� y-Perturbi�Ey,� s: Abenda Gaet !� Walc�)>m� :�olEEvAs2of CRACK��t�JB�*�Sx, 5;301032$o in CRMyԓs.�B�p} � �:G �;iv6E343�ar�~>X7e�f�[��| �"]Fb�E�i�s"�, blem�/hod, ��i� JEPTi�4�7�101�0229Zhiber�"} # � <v{�!i�*T">Q2� Dokl��2��1 6� 609ud-��a$$u_x=p(u,v�o$v_y=q )>ing� ij% ��z3� ɬ�6�4�>��1+$lastpage} , docu } ��\D ,[11pt]{amsar"\u6�F�math}>fon�:+ symb6+�xsym} \0;$wcommand{\�_�tch}{1.1� \sets�D{\topmargin}{0.5in�Xodd�X"3n.@eve�|6# .#�kh�p}{8.0>Bwidth}{6` \a*�ce\hoffT4Lby -0.4 truecm \new5$m{lemma}{L2n!E:}{D�6 2$ F}{��e!D\,corollary}{C 2@)}{R!k 5�s}{\v�#{0.2cm��n=�K1Mxt�1K>Rrm Re > I. Im $\title{Uni�\.M����Ks�} \au�{Dmitri� khor�Alexa�  Vˤ'evA�add{D�tA�a�a[� � Mechanics�u v Stc!�erK410026, �iae�( l{Pr �4DV@info.sgu.ru!�Matwsk�"��t,eetet �Lrgen, Johannes Bruns�$0 12, N-5008 B &Norway<�mail{a1.v!$iev@uib.no� subji�� @]{37J35, 30C50. S�=Y 49K1 708 keywords{ݰ)�,.<,�}:��K"˦ , L\"owneZ=�vLa�HianC�2�� 8 a Whitham-Toda.x�y*:&~w#I��66Aex1��%�� bod!�for!�y�8p*��Usub+[B  ch!�%d RsStpro���Lor�LiouvillgL\ ly =RF�� ŕW��.!�!?f#EA�*re &?. W�soM"2ٟct&�)}|&EM.�aU� \make� �"al�j! }"�=dynam� m�s, 7jr ��u8A+Liymi���e!6�c�Ls�w�z�fQ�"mf=� ��mAi^%�s�'Y thou�'f,on.�}� F (typ�ly i��%ed�u�9() $\Omega(t=;U� {\itRP} a��� \M $\hat{\� bb Cb0&� ��#,$0\leq t< T$�($re $T$ mayB$\infty$! �beanAat ���2 �s �\n�g �B)V+D $t�����of Ri�ydson's � k%%��7�M2}:l�(��leI7~9� ��u"�f� the Y�ag2  as l`X�G9gz�Irs.8Oit�D���.�Agam},'/ostov},��Marshak ! Wiegmann}�eY�Q� Ρ� be&Z�i �aO�r&� �M��A7s (2 " )E� ll!!-_x5�are tr4J��B pen�| a~�("�$]3im�I��>mKAB;. O��c�9��La(!�IN.� � �m� �� U$ o!)� %!2�.O!()�at�C� t�o��>I�xi&�r for �]�,an my y��#od�;� }�ur��$BieberbachF jeE�i/�& bɖmo�� uing�-. c�2 4K i ���cկ�ory&B�is �. It f�/]�a�dL 1984��$de~BrangesM� },Ep��9!($n$-th Tayl '&K��n$ N ����He�jsm $f(� � �:cby0)��$f' 1$,&�+e1��A� x: $|b_n|� n� e���&9n#}dS*� ���Bxl����E�Bic <�� &�Z�P Koeb=?�n, $k(z)=z(1-z�;�D5a'!Nof%��?AqnLz numerous A�mptjXE9 o0 +Y_!kM{*na m�9+m��� 5��C �escN�]E !G$n$� =�s�ia m��o8s $V_n=\{(b_2,\�� b_n),\,f�QSn �^%�92�|�d�4of radius 2. O����-tQ%�}yK3=�b_3)$%e�� &Gi�ńby�$aeffer%Spebi51�  famou��n|0m�SS}. A|!li v�!Fpa��!$, $nd�3$,���ՅBabenknoApart�3�se� m�� � ��I�ew_3� aA:gj in`F8 [P! made��f ��"9}�1:key�y���Nu����Ū�a�lPw. "�oa ���t��V_n%�"�oa<quyH�z���=�s�eQc bH�M�U o6c. E�ji^m� u{zl�5"w ��, �B s a �F mapp�(A�II�p\Na5 ��i��� sW��A)�(�I��� Mx�minتɤ� graph�A 4� MP�[y^ ir�era�I 7|mamily � "u� zey0� i� "'  �# [ '9�\A�2!�An�d,��� a $(2n-a�../ �!T&J�.�}��3���� by a"�� ��ich�s aBr �2�;�I�; �6��&�s�F�Q!�E�= � )ed. More�f1%J� N>� ���&d�S!�ɜ%�w orizϳ~asoE .dr��-�Nt2*1 {I���_a�.be�}�� J � <} �Xpaper!] devo!�Kseai,|�T�a!�laa �-��cE� �A�J�!]s.� !#-�E�% *� !NaZe� �u̝e� .FO�fo� m;L^�: , ��oR8!���� s.� �!���q)d!�2b B�!�"�-rolu/�>L%��aCe-Pq o �in ���,���}�� !���� ">�jD!��o�# ide �sm�zre�s ��=�Y )��&�2�:!#Q�'s1�2:�� {&�.�.�0!�!�g`e:.��sw�<���"� (d�&�;"� i���x�>feb� rivB�%K*�!QE`�R��|Uv 4�./s>D 1R� -K9�DDre%/m�p��*� ��Q^  ^�:" �irevisiau� �N Q E��*�y<2 �rl �kI�(Rk!�Q�cEr�qD&h�.�=�*~�6} O@hbb C@�vc W���iO!�*j&� We �=� �2���a}�or��!�7of $\{"(\}_{t=0}^{T�-"B:grZI�61�'J9ͦ&%<r{ O"�Y�� � $e^�TBM �m M3 ""A�" Z��' 6s -�9N U$, � each& $\�fystyle l,t)=e^t? +b_2.^2+�� a'H�cU�t map�� � .By�$!PD?renkeN����2�B�R�ͶinaHer!Ng� eu�'su�. H�� say&�N�N2�t!X=$��A��  U"S>� $$p�!d1+p_11]+pFi�a!}p U,$$:e! $\R O t)>0$ �I@���Y\p�_q�}t}= hf�},],)}{t),KLK�"�u��&T�$�Eal� all .M�&�hoYd� s $p�V�abovea,�Ya�$C J 1 (�� LK})�N')��q B�W twoi�8 p�}by�|� � }e�F�9,=)a$e^{iu(t)}+%}- 1TyadroBW� $Bm�� inuy1)Aar]#�ACM� %�by� ��zYmWv, q�5Sap�*e)�!KW� . +=~"�O��$"� a}ə#, m�.�ǡie��H�%�) . G+�an 6���0)\sM�_0$ (�.� he>�^p%�,@f_0 )$�2- }�*�q$C� e��vɋJ)Qask����2z.�6S2�� 9U!;>U� 1+coX �L0)=�a=�� ^@��g�� !B�p*�J�, �K!���Ldqu��. A A/$s$�"5 *Uha.�XGX$$ i| dt}{ds}=1�`%� i�}�,3Ra+f '0�����BD s $t�0I^z��6]" z%hin $U��"Jou  Cauchy 6�[����Ϲ�4iw;9�� �� �=w7"F�-Dw}!H=-wp(w2orV`6f$ $i 0)=z$ W�$a1�H�@]��e^=�6��!�y. UctunZ���[j�d�':y$A�w�Ui�,t)�v��.�U�to {A�!��6�mLa� _0FjUEC%�s�s _>a�asQ�fB6)F�%^����.�(�F,�:�q V�B�})q%�7 t҆� $S$Dn�busu�!�1�>6.� *�$fa+a_2z*� ��"]B�[qbYH1�%�� |1�s E�B {-t}x(t)j{� 8 AN%q itself./@��ly,: q��L!�)!,�$B�e��$�otF�% \lim its_{t\to}e^t a�&� FZ���e��2Op�IB�C� .i \��/� � ��1��[eqii um)�2�[71 s 15�663]^ 2}). Ea* �&'�=�FcFre $Qt_s.���t G0.�g� if1�$�$M�xb@ӷik:_1� � C�,�} � ��!fY)Dw� �6F�Z�1\�zF�>} &M w.I w"E L��-Q�\R�*�~ r^j � �U!��(a�U�� p�P�m=ise�(�x}^We� by 34).�� q�A+� 5cv� t�P!�  if%-iIOm��? }j� Vs���2 >�}:y.��iIa","� U�mf-�E �dQ�aspace�Ft��6 !�-::]4"�,'s ����3c�W} �9�#��i7&U�of�( s�al a��*E,Q� Om,�9in��Ia sJ�"O3�:���is"uAV���.���L{�#^ĉ� ��s �$m+1$� tinct endP-�#%AVa�1\y)�!�&� M"I �-2YMo:�+Z"��h�2&� temR��a�!�j� i�0ops��EP��m��%�Am�Q��[�e6!��m�J�piecewis!nt ro��� : �= �" GoluzAn�* �Z"�-�N&�� !�$���43�w"Q#�+���ly��������A&�8�S"�fEi2r5S13 ��AulaF.�su&6 8k=1}^m\lambda_k�Gř6� fե%�2F��Q�<W�c!�Z�!�9���i1�H $.� Mmeu#�� b�erol" sA� sum_J�g � N!E!S�q� d7to 6�!�y-^��p� m! })%�s�u! $S'Z" m O�� ɉ� kl"6�l)q�2��in>�>:�^� B���F�Ic&�!�"� ��- EZ}./ G J�.8!gA#� 0���V$!� JvMa�b���  S��os��!�&*�eY C�H�%9�p*e *mn)*�#" / :�#f = i9 � �� ord2M�>$ )Al�7%"N�z({�},  �or.� c���>`�# �'Slabor>% )one"eRW*�S}U� :- Y"+^�vS�.{��\}���xN� -�"; set �(b"2{I�2bC �*9/ =f(Ua�"�fZ� ��5xN� & ��6�m%6>��kb�-"y��s"� #of�&�*<�og9)�nesϮ�>}oreM>jE^�*�ru�g o. "�!"�Q� am��!�"ie�]ڟW� xn/I[ ��isRo&��>1&A#"�#Z�&*�!ŞoS&Q �,iu>Q�""GJ�5��4u �4=��(s&� smooth� :� A�tF � >�3, i.e.Ew�pD& � b($C^{�$2�tej��� $t6:%�  veloc�5$v,,�"�%&zl,'pe�T �t$,�#���&�*�x."is�!�/֣i_\&�?�r*� j.- �=.�Ar"�ѭ�5 $t=0�2e���s `DeE,-Hm i(+;$. &�5'AV,"F4 c2,# "�,� �m��3�!5 X6.Yi�7#0%m� �s �9t!�%�2��"vic brsa�@!�Fr�I*a� &�&}*�!�� ��3;�te�AES�F4! bey���K`upj$T$ ��\�#cpn l�/a�oa�r�#e�E���>&+instea�4Y.9�"� �w a�nXem9.�W �KHow �z~ ye a cr$xmŞ olog�IN �q5�u[�s��hin finbVpenet�R�E(�����'�y�?�K#Hohlov��o�8 eQ�").by6� Z�wna� sibl��sp!� ��!@'e"�0. * �tisR �~ relaxes ��x-�5p�~e�A6co.[7%� Ad� �/ ular1� �a5t circl��7I�:co.'c 5i@ek-�8&&&, �]ity�b6E�Nb� s�M"%(���.�)j5%Taece��d)��(!;*�"ư!6 ��#rial��yBs�XDF�6��f�2��K�'��*q+�=2- ��-6�~b $f�@U�@��.�!m! "F�� �� �2�"��?"S& orn�d���+��I]Wb�.X 1Fq�8eis��u3*�1) �,%��wAopo=)e�� .i "u jNn,2 n ob�-a4D.x#�1Ea1[h��=C�,�Ree� \[ B�6�4 ):\,`&)}&+� *�2}"�b_k ^k" S\�,62, \] m $)32)6ݴ:u�. Every2K*�v�t51)�A�%:�a9�1e�4"�&l3 arc�8a tree: aB�4���ati�$nphti /�w--��T� "#+_0\�� � for &�  s2Hu�J�� ��a�6�I��&j�]A)�+g� F $D� �� $n$,�b"4s�� .^*$y�I�b�e�6�3����p ��Fm.b� D_n\}_{n.�n $\^*F]�� dea  ouJeO t �/]5M� next���0"t Co"�/m�} �A�{QG=nTQ !Uu�G"9s}�Ym��!�m$� �q8� RR5.{d�)�e�mp.5E�V9�@st�q�6��*Ua7NsE��ŵO�e sourc1�f�: wri�>eSc>�:ch5 n 19KMAm$A_ � rib{ s�F�NGwe&�&?;by �:� ��`'K�oo�ll,1!l�&&�nB�2p1���uer�w!ǩ�i9a�; |�l)�in�ue uitemize�M [(i)]+�4"�>c�5aV�"�r0"� &&�8s hVO36� sI�; ��;��$x�*' _���tF&on*J;�� S�"q~3,aiD�dݮ%?.��"8ex��W&ao">�mer �� , at��:D"��Y skq�"A� LipschitzA ��v)]&.f&|o��� $X_1eB:�, "$E9F��8a^bp� at|5��~mI�PI�^��o�|1�H �/���u,!�Ta&&KalȊu�lo�<�xUA�iI�wT�A�1A� MB�� �Lry��y<�&; &B"!�V�< . �S JSa�ha^W�ass�-onL�!I!ke �: *B Ѵ�3�Ma Jz�4�/'s&8i:�x�A�=:*z&�2pJJ�xC/Jl&j�� " �[0,U)$&&h'�"j &�-1�}�F-�6b  2| O1& > w ^n$� H8���:Z E&R� .�ac.yj2b�T!FA�?^Z2{in2�*M-_s 74,{b}_k=kb_k+2 �j�Hk-1}jb_je^{-i(k-j)u� b_k2- a_k,�� t"(� $k=1,�@����$RZ-NE a_n9B:��m�(�$. Go%�B�A�6�"l&x$�xe'tR� a_.�e�q}bV��is"�q�a . ToA��,� �4w*%��y0��%�� =\��(��array}{c!)! \\ r'J �`% 7 \)�)b/ A!LR_l��K� E\�& 0\\��(t)  & FZ+ & a�J"2rg{n-1} ka 2 :aV� 0N�.���a)Rv!� $!j�oS%c 1s�R�t{a}=-a-m-se-�ea)su}A^sa&4�YB; \[ a("�2a^0V�c} 1\\ !p^�f�>9)�=�>��T$�>[,a_� a�aa"� ^2=��!Z��V���*2Q� a8? 2P���oLN}"8;ru�brief~h6Qand� symplectic definitions and concepts that will be used in the sequel. There exists a vast amount of modern literature dedicated to different approaches to �.��Fof {\it intagrable systems} (see, e.g., \cite{Arnold}, \cite{Babelon}, olsinovdZakharov}). The classical=�a �co!8 tely�e2�} in t% nse5 Liouville�lie �, Hamiltonian ̘. If we can find independent conservedt�Cls which are pairwise involutory (vanishing Poisson bracket), this s%D isV� ![RZ-ibZ)A8at is each firs%�!-$l allows u% reduceETorder!4%A �Hnot just by one, bu 467.>�3B6 s} $\Phi$6��� character!M ��BJ{<�=0>�4B�In ��cular,a+ H,H\}=0$,%���3:t  in��of/R�1��I.! 6�3})�!��alH &�ks %"_1�s� _n$,z�� Phi_k 1j �$k,j=KFtheAj�?c R� � 1 sB� i����$ is includ� 8t1:: @&r $theorem of.: nd A� � ��s a"�  descrip�2C!�mom��BbyR�-�F��0st�  su| 0��a�-angl6@around� nnec�regA��ac variant�/ . On  work�� realB�!q0stead, making� -q !� 7N�4} $2\R H$ keep; all other� 4ulas changeles0 M�.Mmͨ8only $1\leq kamily!�E+\ s un� a nonde�5cy assumE�. A bribetweeeAs9 extremal�s �a$k=n$�[b2propo�8by Nekhoroshev i=}��proved F rd 'Bambusi"'FioranGaeta-�resulty encE�$k$> �L ori ) suit!� 6condia� s. \subs�$on{Coeffic� I�} We� showi�t6 L ��c8}) becom�>nQ� ble +w�tre�1a�c�Z� he ba�Dary hypersurface $Y  V_n$. S�Z$a(t)$h 6�for& | trol�Tu7(piece�(continuous,!�IGl� ing multikdA�Hfactor $e^t$ represTe�point� � ��($t\to\infty� trajeM!�P� , $0e� t < 0, f7$Lso)�every s!E �g a certadiyg�,end�the-ies can� �G(rior or els=�>� . In(way, we set !!@ clos�A�he�MchA. *!�!�!�IB�BMmgccO gAa� erty (ii)W���he previ�M�, .>$x\in \�aIk� at!>)�exact��ne 5"y 9P� 7d��mi 9a choii� the Ny���u(t! f�$S$ correspa�) $x$ {a E� -sli��p%U!�I qe tre�Mf���go�ip�B��e Uunique�i*bX�t�[0,I�a���A� $fM��|of:�s�wA��i��-�next -� . Tha>�I�R��-9a one5/�y�}.�to obey�: Mzie�; .e.,#be��{c opti�bY1}iwA�zJm�eD] h�, satisf�9a necess�<��!R ~ ity. �Z ] �J��}$ meanZ)Oe �conjugat2� . To"ea:��2��ion� �2�!�requir!�a��y(!81��WA� diff6��AjnNA�d[}{dt}ra  0�� t<�cpsiB]Tq into acc�:�w�2�G)V�V�IE+�,(s+1)(A^T)^s)�)9�psiF�ME�H!�unŒ trix��heJ�2I ny��A: U� $u^*�  posse��a�iz�٭�yQ6.V F alo�>�6Pr� y, �֑Q} \maxuBu}H(a�e� u)=U� ^*�[$ t\geq 0, maxB-M a^*$�� re s" t uMe/��%�)i�$u=-Eb�I`�) yiel�hatJEi"? �ps5} ( u}\bigg|_{�*ymaxF�E�}ntly, � �)e�"�1�mpl�f�d\,R�%�)i�0Q�hamB�� anU��Obl2 � UtQ�-u>�alismE��� � �, 6�ll lea�� grabi��F#~ � � E4$k��ex� ��in term� a ph v=�$� �a`X causno fus��w6uT({^{\rm t}}( ouG m�" nspos�� i}mth1} LQ * y � , $ɉ (T)=xv�G v_n)$� �rdA^$Ti�� n $y�_k%({c}_{n-k+1}���, �m�c� c_n$�!kTaylo�"{5�expan!N��i_(|v}_nz+d+81z^n)w'(z, T)}{ t)R�ɂ}c� z^k.�#1jq�proof-m w(z, s"]IaI$AVa���� L\"owne*�.gM� Lord�D��t{I� ��� ect^ $z$ Akimmed�ly have���f�de�\*�z9+�� .1 e^{iu}+w} -w}+ ]2  w}{( -w)^2W��F&Con� aDAJ��Nz-�q1�,!�we ob�b \,q(t�� �A" q�F�w f=(q0 qq )^T$tob� h i�-���Ps from M6����tr�E sig�JIn  to  ���  $q�2u`u q`n�Ald,gmE^=��.�%�� 2#$ y��n same"� -�%� ${z}/�� � titu:byS. H`�uc��IQF�  c%�N� 6\\��Z� A�E �.L!��aE?$���c eas s��[ c!�^�5�j�$1� �� �(� I�!&�2u Au w��24=cb/*=#) ��. � } Put)T=0o��A��A�R�"!M(corollary. 1��`cor��.`"� (t)���f 0)=(��q0�^^T$%�}2�>��`� ��`R_ �_  ��_2_�,j�JW9c5vurk} Si�$\I aeOB�2 q" $�Q , u{oes not  �J!_1)Orefore, kout los`ge]t��put= _1!�v_1[bnalM�&Y, leave $a$, Z _2���n$y"�b� NowA�!�d �p�  �"�. A"_ f 8B ��iy I6�X� �Yeys>:� u&689�!�5 trig�0etric polynom�!t2�u� d�" $n-jf );n\n$. � !A!�*� � �0 Not�*m��L =e^t�M%�"vZ $ diminish S#to �,� . At $tE�weN [O^0,B�A�(=-v_1e^{-t}bVX(\R v_{s+1}\cos(su)+\I sin�bFore� . $ŏ H_u(^�^*�suN� (s\,� n ^*)-� �^*))=0.��Sup��� $vY�vA�A����!$_{uu}ڢ^22��+ ��)\E2,���624. AB�*� E�$e܁@x# influ��'proK&OE>A�Mcit zero "�cours� i� y ho8�all $(6K )\inMt)R)-2}$ ex1, 6$Aa@ dime l at most $2n-4$. Indeed, dueA����"t1,�rol"� breaks dif��E b AgMfThu�s�A� 6? two �'ar6�" � s�b�I\unB\u�Y\=IX�)^T^3A�V<- VpVE��fixed5�i�wy�}qap��� -&a- spa]YI� "y+U\&��)p}�sa�at a �.���$:bt"ity��M $on $[0,T]$>1��) A m�  in:Tca6!,Q�%&Ź�%^*V'&� :&� $(e^t>�)$ _A�o n| .,.���}�!&�\�,1v,\setminus A$ad� :7f]a�F]for $T>0)sm�^enough�Gu�-�,? Y(Tz=% all ^�E�,9�R�. �:�!pE�J�� }(a"� b�aaRw$C$"4a neighborhood��$�j^*,Es%2 t��2-J sE�O� �e��J���&toget�$u�z5��� analy524 cit &� u=u �)e�B� .�� � $5� �/2�of aK\5v Y1")!�We&�e)2�A&J� )��:k��#*v_e Cauchy��ble���D372ata�"0)=a^f)e�2 � �. Z !@%�>+�.i $"` u)$ )2K um.� &� I:^)�(t.��bL"6�B�Q:� Z�=({, }_2(0^  n(0)1Ac*)"CoI�nUs� �("�#ed�"a+AD�I v*/�� 1�&��U2�/$,�zz =\varphi(�,v6+ټ��:��K��� )it.�e�ɧ(n�J�>tthEXqi��,0,&� �a�s*y(L�4, ble. Morez0�>�*��mE#ont�) structure͚5 2&:�A(��A�:^�)ax.�QK 8 M�fW, u)=�cal{H}J��Ou To �"T%F*^��m�r�%dr�r�b�^`��U . ���f[� �� !v.�!*AJ1>6))� f [#.k�P�),�%N�mat �Nw��,b})=const� B�2^%#��I&2�"B f�7�=�-  ! -ls�/14 �.�( We alread��% "qMl- �''B�"�IBThe�+NS�d:7!�}��}6_ ^3v}_� z^k=z27 .a821+V106"bc_k\1�%3intF$W�.� 2y�/�t-O)$%��Z�� ]=� 2'~# 2*7n��R? ���2 3 dotsn9 9�V�r0} a_1&2a_2 & J & (n-1)a!�1} & na_0 &w()2 )2).8\\15W3 .3 .=��]RJVbaV�bM"�_%S%Y2_Re�w"� �ro�:W*�"m�+M,͏. ��RaI�m�EgE�)2>m�k=�v_k�6r~�6t� � $t$ś*q�!� ]U� �'�<&,;�=X2� *�2�6�291hecks6,s3k\}=- sE�{s+k-1}$�o�0 s0T� , �s��$itemize} \  $[n/2]$:�[ e{ +*j9eq\-s�6� &b1; Z��.� P�_G ]} Mg Q Q}<theire1.�8s�� �nres�-��5'!" �sai "b��+ (�=i�uncoups<because,%�exa�>�N�nA-���end9r����:�� �  F�W�&�b(a_Vj�l�f^*Jh�5&(��>iA�%:ej ?<-h � of6Q�4� i�* ad�erm $(�� a���M*�� ��� ���B put auV�� �s 3`*�$a�&��"i*�ef3�-I%��f#��t����U�6(�o�(�9R�<��� yv_[ :O )"� W�F�!E�"�!�q�.�`��s�o�A�4 6�2"�.�)�*bod�(%ed-)val�WQ%s !$S$ ("z $0(, $|f(z)|.r D��$ map $U$ o�*a�disk $|wyAt|an "� curv&th *E1 tip��=!`^2�A2e�.4Bhomeomo%c�}'enBo�3$-"al spB�&F�Ko/-�0;< 2n-3| ee s�"$should sel�$ ).hC0�Dng $2$"0sF�O�%c*�:���!�*�6����re U�C�b"X%���h.�2��i"h9 upon�1pl� J!Ca�+,itive number%��bo�>H)� 5>*+up%� p$(vekie �^.!4, e.g., $|v_n|�8I-".D �af3=�iR#�/) I�f"=T.\ qn*A�gr>� ���Xin0i��% bigger�K rvals+�epsilon�s �aa�Vs-! *eF.�Vb e 2mal5�1)����N�s=!��nT� E� ��$"`-67L (T),2O��$>#��4FSsB1�T�D`^G�!6�):=ݡ�t)6& st)�>#))� \[ G_2(�g�>E�h��+s�+Gsa�:��Te��� q�s *� 6�}y�0t[*17�D:k2 �>�set. U�- d�of�� ��F2t�(6*��rel��:�f�v_� 3p nII �"&�<�<M�;�7e�J ion}"G$�$z��==��9ce�7 N�@�*(9U��dF1ilA� maps)%���<e hav-���L�si b#�8s� �( \b:1 og� e 9--KufarevU�-r LKord2}) #G�,5�0�*dw�,=-w7\lambda �,��)&�, �,(1- .)./20,"�, -w�,0o* $u_1��u_2�.M��; K&Z �M$ s<(0,"4 d&.l9a�ZyY�ef*�>{�7Ka}=7_*71& �$isu_1}. 2}-a�l� B9 *� �=.� [ \tilde"�7 _1,u�S)�)=��7��6�� �\�b�7a�AU6C M{y-R� fk/�H }I�I�fb.z��2})r�6%l�� 9�%�*$"� �(now spl� oe�bitNK266�}=��!! :+)=F,"� 2^*_^*], 3"6@6l�>�m��A6M�, .)Z�5a� =u_1�$, 2=u_2AGm�J�RE�:\Zm$mv!}-Q ! i�f�="�HaddB�ifB /) w'b+trT&he �;�L�@� ��$ w  be 0 or 16'86^8�B"u&9�Ds�?^ �0 adic�� ur s�(�$�I�2��E 6aJ�e�\k F�&�7A�]�}6 u_j&�7_j=u_jE}=�8�8.I2u�ma��7Mz"�7M|)X�1 �y'^�d\,.q�.�A_,2���,3"�7lhZ�7�.�;7%�*{Dsa m-a � �9 Ob�B�8F�aIMJ�/ reafGst'AA� � �(as�@dO8bGF� sJJB�7 vari��7C"E�^�ue�:"�I�6�-=�})� 2����I#% 2F$]�%�BO3K��-6�of��- agai1" 1v"� ^Tt-H �� Ɣ-W�-N�-An qon�"-Ii�C&Q �LA�ant. At  gC &�R�-> = lb*. u_1).J !�&Y;2�;�S�mQ�R � &.� w1��� \mbox{or}�@��S2u��� do��v�X�isB�R�!� B,Kt� ^�2����A}$ oj�.���y$B`*! riO�G��, be�&�R�p�0 .�B�,aY)vto!�b��-)-n2)QBor$*�-}) �E2ks/M�A�8 *�a�Z/��/2-�{=6g?�B|oIF.���:�?�� �#!�Bq/�m,�j"|/ �`2 �nA�E��6� inear "="�%�4e'$uNB��}� b�/q� >�s"IA�N�wQNN �12�Q0,Rx2�- �� \ &.��L "G )r 06�` R^+0 ,\ � �+0:y�.� If 6�*:�d B&&0-tAUAt.0��R� on .��T ~70 �YSB$���of�~�![Y��" o��]A�v$:�+� 2�ez�/ HEHM�V 2� Y� R��DJ�*�0�!�4 ��059�" I��2_.J�0a%�_1_1"`1>��5AV��8��0��0 �$c*�05� psi� B >B� B'/d/ÁB1pF,�iu_�mn41�_61_1.Z2�[1_2 ' *-i#�o ivel:�-^�ɬR" � �FU#�la�6�l2 %soz�1"�/�1 $a��1,� 6�a� B$. ��0ޱ0!��02�09��:1�r� �,���i�ŵ$� � . 6� b�#R�"�. Repe�F�fur) step�5!"�w�oS&.�I���-&1 z*2mn^ �ٙ ͙�/�rEVU^  $^���v^�2U% $$Pa�B$q��P� �ly&�2 ��2 .�2is*�+is!�!o�5^R�[,&�Y&5��!�$s 2,3 also�zpr 6&��KW� 6T��M&)�8S SA 4 2WE@� B q�6�6. O=]�0� x$4 expl��or�L $n=3��{#  [Aleksand#ih  Vasiliev}2�}>H�'Pbc�acobcN�}, Ann �ics � 297}u2%C , 15!A72�Goluzin�M.~ -�mP-8��&�# of a�1x"#}, �qi˹i0, vol 26, AMS�_69. 8Hohlov} Yu.~E.~ , S.~DwisaOC.~Hux gfo�A.~EVc I�v"�6� !� DiAxS m�&�B)wo&8� Comm-b� . �227} ��e��31�@2���} N.~&�g �Eͭ��h�h-:A'�C� �RFunkt�Wa~ i_alozhen�8��B�, 2, 67--69; unsS+in Tc�Ni�)W.G a��128!�2�4Pom1} Ch.~Pomm�^ke �*vSub�-�Q�scher � ione6Ja�tAngew-�-�18EA6��159--:z Pom2Z�o al2�4�P�qhap�"on B$r� .b#lsU G.~JFm�Va�vhoeck� RuLht, G\"o3SB 1:� *@b L.~S!1nRb, G` tyanskii5 ~V Xmkrelidze, E.~F.~Mishch*y ��6"A �^AdpM� a2 rsci�M��@ishers John Wiley�So�Inc.\` ` -Lon� 19628 Pro�jv} D.~, INSeV&f�&s��  f{R!kin�c %"� $a���M181E90 12, 16E! 677;>�FUSSR-SD7 C��(2, 499--516.�Ri�pdsPS.~M��g����E�3.� 4d�W� i� �f flui�z�R narrow �nel},aF!<tbf 56�72 � 4, 6�66�SS}�TC.~Schae�bpA �C At RegkKS �2(W�sa � iBAy 6!��Deriva���a BHa^,Arthur Grad)~ NZ Z C^qui\fubl��Vol. 35Z�@E� A�A�50.�V!, 'e�� MutuZfh� �&�6W]U�2�Mata�. Zinki��3��&� , 56-65;�i.�I� IsZ:� 543-542��;}�.c �fZa�i�C��al �0�&�$ hierarchi�E�+^ �213��200a� �:$3, 523--532�"�| ed�E>k�| �W�&�rYi�@?}," Sel �Non  D{s.'-'Bevx!�9|^>th6�  docuqA} ��%� 8d LATEX FILE: RUN TWICE J2 9�Dy ��[12pt]{5{cl�@4usepackage{ams�7D,amssymb,dsfont} %.%showkeys�E8etlength{\texthNt}{24c�b:(width}{16.5B0opmargin}{-1 odd'  0pt \ev�Sd. %Zh6.2in�.�h0N �8.6B@2� }{.3"@\newcommand{\beq}23}}6$e$Ak"#0:"baE�E: e ARbb ��6ayBB$CeZ" bean�%*JH&.I$re.�stretcA.7} %%�emat� {�,}[�]:)`g}[ 7]f�;�5!�  {lemma}{L %.exeBExercisa ne?2jec={Co�I2cd"ID�77$2p�?�RA�k Menviron�X)5q 5 \r!_ F7 exer8�5N2aVM"xa62a 21KFC!k of.}:�the FgP8| e $ �hRr\square$�^ "}� APPENDIX�%��jer{apc�ix��B{�I.�new3[1]{\v:&({10mm}\page�W[3]�2.:theu�{\Alph}.\a gc2�)flush�I}{\Large�A � :H #�!�7\no�\medskip.F<Z9dT CALLIGRAPHIC LETTERS Fj-s��CH}{{\ca)��CJJBIIBAABDDBTTBWWBZZBSSBaCCBNNBFFBRRBGGBM}{{ %|MBQ7QBPPBLLBKKBXXBYYa�arY2}U_$ THIS NUMBA��JjB�KkB�AaB�SsBKYyA#2"VvV>�UuU>BbB>WwBFfB�TtBnZzBVH�.!�bbF�R� F �v ByPe� B�F�| B�Ze� B�D�v ByNN�bbF�VVB�Y� Z!�A�>GREEKV�r \def\� h�|"U Th{\T (ga{\ga0 6(Ga{\G (be� t[_al{\alph ep{\E 1l{\)ajJLambd) de{\delta( )De{\D �om{�:(Om{\O�� ( sig{m)ySSi Qph{\phiO yPh�M &vphi{ %RvJOURNAL:��6ajm}[3]{�.��>#�#�#3:|cmp7F�~:pl9 LettSBnoplaV6An6n � Nucl0�rkfa 6#�f� Pril �jfa �F\;�xj; ihes �ub� I.H.E"ej>pr.U Rev..Zj9ij-�In"our�Yd1.A~�-,q)�~2l q)�Im�:plm-#7# BSI#~{r {% �zta z.��m mplA%�M9O ��Aj�lanl}0 LANL pt*,int, hep-th/� .- 1�-�at"|#kj#2 (#3) RJ,VARIOUS DEF'�O6J rref�(M@$#1})} %put$\en� s ߅ref's�binXiD#1#2{{#1\choose #2>Whal��>1}{B dz}{1d}z:�dzb\bar "�e frc{��m\h� -2.5pt\sj4.2.t��glepC �Pristr{{\*�78dsl{\displaysty3d�)\QtŜ#1\over��#2}68�' plus|c{\p.del+2.til}{d�"9 del� bar^=wid%�{ e 7#1}d�map%$#1{\smash{�op{\longi}gy^.>Ad{�A}_{(2).X�gW big\ G(\rlap{$\vceL{\h`:$\s�%i#1$}}$�back{\!:-tr!:rm{~Tr~6Z i}�!{\it 6 LOCALaKINIM (SYMB)6T ? !*g7)frak{g}_E1� arpoE\{#1,#2\2e5#3_\la^{#3�bdp!/M_%hiw mat2Y#3#4{{�C(HL}{cc}#EZ4#2\\ #3 & #4 8 '\%�)�.`CSc!DCS_ �bf{c}!L� mats�~8 2truemm} �R�%%| vece �[:�� #1O2F�]�!� Bdpt!*6�{��1[�h t_{��BA�4dd�ur)`H=v�.�hI�fr|6 � 2:.�DT} ��w:`Ha�?H^{(#1B;K KVh;hVW ;WVaG �alV!bb]\beV Lax!LVeqcon!${\buildrel ��{=B( veco>1e��� 7�Zi�Aa#1{AVh �=A�,Nij{NijenhuiQHJ"�$--Jacobi\ M;k#1{ka/f#1{f6g#1{g6�a6� �hALHi�v{&��f!u gin{��S}"�".���{KP$^{)f��aO._#2�Alg�x��Dua6^* na62g�alp.2 p}_-2d.gM pdx{�._xLn*�fraks�� s�at ��� ger{$ v var{�* p�I#3{{p-��� yH8bih{biham\-il\-n� >varb{"\  hamUDia, efi{�CfV� .��{F�b\� J� gerb{bi-H�\-�:�Wu)Ipo{�x} �tenztenso�res. WP �Qoq!/�SQ.pri6'26_P brake�E�la6 ��3\>�_- h�c*�CoH Ssyml{sym��lea�Ndefan.:omn!$� N�7ٕ \rs #D6 s�:e f24dncoo{Darboux-�p.�� \ wrt{Z6!v): to ,St{St\"ackel stsep-Hr�5:Qravert_{\C! eval� Big��\la=f�a\mu=g�.�t:}.�\o�E 8,UfbilA�Lag!�ybil��il\�yi�':�m� �{mod } � (\lae�.�eeg}{�5 eD0�%+StE�.1fin��$2]{{\>#1=#�=�c,� >+�>*P 2+Lie͸�{_� %F Rj��Q�Q�Q] &�"% titleW�6��� $} {\huge BE�l��p|�+E*J4 the \\ \v�0. cm 5)oJMue�&-!�c< 0.3> �!>�l+T Fabio Musso$^\diamondj�$, �1`teo Petrera$^\sharp$, Orl�- Ragnx7$^\fla40Giovanni Satt3 natural$}�kip� Di� �0o di Fisica EV& aldi�O*�58\`a degli Studi0$Roma Tre\\u8 \\ Io Naz%%e' Weare, SeCVia,lla Vasca Na�*$ 84, 00146,, Italy)� pace.bE--mail:G: �^Lso@fis.uniroma3.it\\1)X : p)kr-%j : r-}r-1:L{tNZZ:Mr�!� U�} \abst�� {\no�Ynt�?con\$ r a �--�e homo�W�9cheMw�_A�lia�N*e0r���**dir�sum�($N$ v) {e}(3)$ E'�:u" topsX�� B�%ia2g�]�0yb``B�'' �%[~�o>;o��=yst�%ng �]�`�su}(2)$ u�Gaudin qs&�<>%Dob- (two--Ia2��X(fG ). }�? 1� 9� Keywords:j�, spinn�!C,6�a�dPACS: 02.30Ik, 45.40.Cc. %EU��� \s?�";:���m�< MPR}!�w� per��(r8 In\"on\"u--Wig���;EkQ,n>i�G1,G2}, Q7tf)A�Qug)i7�zYq^rve؝I�al2#aic(ced(q S.kUX,:�~A<ellip�u 2uA�oossibla{I� new�le2�es, assn�to[-�O*$r$.= rix I��?/f �� ex� !A)0MPR,K!�Qe$N$-si�h$" uM.�� �ed�G)��^w��p&6 T Lie-� -[J^ , namely x(q}� \o�!!� � ?eqo}(4) -��� \no�b \eeq��&$�A9re5[uclid?6�B�i.3-Ţh5II way �-*s :�)�b�����F���fe+�i_QEW!�B�s''. Ot�xaIr!�Um"�] inhe\�d��%A.6(s as well.�Q8k!AI�E���a�n��2����:D.�-:� �Btop��M�=��$.� . It turF>u�aitA�.��+!�"jppr,��A5��Rajof~��I1D.sLm|� goalI]��nm per.��2�A���lz8s ��E��w�illustrO�A��kon���8�h��N:�Wæres)nfac-��2�!� lso U ��#iY��r.˄2 &�CM�& ,Yang--Baxter"�K>.\aIvicqC ite-6�i9Lie�d*�%F�. Seemu�kEdetai WE5DJ>2D!!v.�f�2� $2�M�a2$ Lax�5rix��L_\CG(�=�: + �\_{iQ�N \al 3 \s�!^\al \,��x _i}{Gva_i)} ,�ljj�\��f;�Yc��V*�F&�V!� $ ~1, 2 3��a bas&r� fundal al ]e➅�AFm : $$�1 �geq ��{i}} �%_x� = \� �FXrt=A  & 0� 2_, ,Ve^2��y��1�-��{3{�^r>z {~.��0 & -N!�/ -�_x-�_y z�W��PauliI�cesP^a�tant$\l_i �LQ bb{C�K"�r/5ers^ J�=QmlB5���j"�Y t>� �h U$m' @MeP ,2,3 i=1,...,N����tors �&]:�O� s8$I� 2; �s:�E�\{ �, be_j� \E� _{ijex^�&!^qquad iP��x N� �9be :"� cycl� ermuy�12�<The��O jj})6!UJ� :� i�6/\{��� �Ids��  1mu� \} -)6[r(\l - ,)RZ +�[]=�Wla� 333}.�5<2�i��G�@�8A�*� i�u9Y�a)4�q�}{ \l}:� � g^� 9�� . �666� PM�~N�dh��A�2 c"� F� " �f �#EKY�� ���sM�L (!�= �� !�"��ha����)��[�y}}g%��#z ^2}  ]�ma���>�$( `, S)�2�? .C=%D �� f�, b�* u�=!�*��a�I�\{:?�F?�f@5al} =6z0Jr )�,`, O= �G5Ye3}�z�z;�_�  c�b!�]WI!��pexi�� &�"p $ y Au,RSTSZ��X�����.r h (1.�� �.r lkbu��$9 Jc �.4�now��D.�.�m� �bodv! . NaMA g%2 = 2T2��-4F��.e I�m�\CLa�m�>� ��um_��_iy֡�� Ti��l_i)^2��]R��lax]� .ATrF�*bF tops, $(�, ��U&��|al� ,3$ *|]"S 2�ZJ�W-�Y_j^� �.)\= 6V 'f,2Tz�T 'fT5 Qʄ"�yeD.���2 uЕ@����A���pr6s���F_6�eޒu�w&l ^3����"�ia:!�!�pB $w�no�a��n�Qof�S]�.", tak�u� rm (*Rg=%��Y�>� �R� ). Re�ꏅic�S� $\x*� *�!yDi*�o�xi�r� %� xi^{1�&�\, 1}+  22�-  & -\�A*S TJ.�I��2�xis � !r�#-�(R1�2 3)^T2� R}^3/tٯ� easy\ veri^Xa�i�!rU|�DA�aA��{sm0gwe�� 2ta�C*"���, [�#,]����m�d $2( 4 �"� - �lT. �us��fix%.����: ! K/ {Y}}� do�31,�y2RI BZ2B�a1,2vB͊N,FY P y}}^ �(y _?NJ�N� NzFNz6NrN� �+ .$$ �$9F6 $i$-th anΌ m�S�WA# 6%:66I�X~N n)�i��(� !�vmy�# y top; h9R�Y ~z 5��$�^E�sqI�6�a�GA ��� pha$A�ed.�RJb eK��,$2N$ Casimir&�I� Cf(1)�r&9�ebf)U &QB B� EEA�q \al_iU9 g2Bg%�,r :fJeIl � M�,N.:�  Fix!�Er"�J ne g!�a%6�6*'aԅ�͌ O} m� � (�e��)�, ;b��GO , �$,N \;| \; )(-�el!C2)}= 1"� "4 �'$$ R�� &the.C (�3ᕆP �m"��`R/.R&lNU]"�u� VB�o�y ������> i�" ",@�$;� beq :��0t(5> -\mu=��dS� )n _�e� lof ,us $g=2N-1$,�,F{Ai_ ^2 = w^2+m��� R�\l-� }+ S( �U�5)^3:�3> 4},\" $$&i *qys $R_i��S �a���gN�4(ay} R_i &=&.W}}�e���+�k \��i }^N�( �!mnglFLIkI�_i k}+ ~=�#= - Bgk �*�} !9j!{ - 2�2F:Fp%~E� �),�x� &&6SnZp�\+ �.�!2� 9>2} Q~��Z${A�5� ��"�2� �I}���BW4 0,0,wJ� 3��6 +I�u���Ml�m���Z , Fp'��7u7 du8 �4Y)eDqI�\a� ,R_jI\}�{\a�,SFR_6"�l*>�TE�"%@$�͜��� R_i=m� .Za�%|2W]ͩ%"���ir�� mpon� -R tota�:� �.�_bwD�|�j����cantba�Z9_�� scal�D����3)�'toGtD� prod�{N}� �W2.�7\�GI�:ybeP�s{ a -\� \m� & =& [� � n]af�4! �6��6�&=& w�(l^{4N}+s_1 -1} +s_2�} ...+ s_+]8a�eam�!�co*�R $s_j'j�4�M�combi�We�@.��,B� .�(0&�we �����^lexju��d��e6+�Ey^\pm�9��y^1 "�m!Z.� y^2^"� ich} �&�/< ;  {3},�pm68\mp� lta_5;�pm!lx�}N+ N-6L-2�;:W3}�V�B���CK>) �&>a� N��:�>�Z� -2.�V�F%�\beb�"� �%�\6�~�\pm,3.E���*�|s� U�AUL"�#͔� �y2�h��� u�"}&2\CW � �.�:�[ \CY� \� �"� \CZ_i! �g{i}d � &�laxnd{�r"mw6�"}!BE��9g Qk_"�JY# y�A� &  -4=+-� �a���)�N�Y% �F�)^N�z� � � �� �*4*4&^.AE��)u�]�SS l-=��& a ph�h�Oa&��describ� ��?E#�#u�+� CH=6( (  \,D + S_i)= 6$>L 3*R + Z�� + *� ,�N2K� �  "� "�H�A�4uus �S ��Nݏ�Lj7�44�EeEkn �+-��F  symmۭLtopI�+=��2` $y� �4$[(y^1)^2+(y^2 43)^2]/2 + w z+��, K�he� t�� H!})�U%��  �< ͸�5i�{lM9ot)�!x�%�� G� %�{ JM**�C-�O!��� MiAh,� �+  d=�#][�d c"N 2je M \, ,� ��.BGA�meq(@%"� [<� 4�Z��$. !0�:�9�Z eq}) chid� t�{"X+.�oa�V�YPKPR,BS}� vide< atn�_@�&� �� e�bMF��<��m�=A\{fPCY-�[{\CW} ,�4}_i)�]QM[1�$F�Jk , �>!�]?CZq�S7\,��-��eq��� On se�93")�: a��EY�ab>/�!d5�sU @�i6�&e6\CL� )��!, \CM �;IՁ_�2 ceg� loop�M�*� [\l]&t)�one\a�CW�_ b_ n/)A~�2�� �1�� �[ ��R &�A]�.6�&*�� ' -� ��PH�:}} A�#cal�$a1. 2pf*i&�mx$ ����cover�2ſ��ZD!�~&?%�d�$�+�$�)�.�a�[�d $$.:E  a�{\l.J %h^2/� Y�=6Z62~$$�� � j&� Se� !��#"�:�� � j��v�8A � ru�1e�Ast AB�"N�"��&�AA� *U x})Y`1�AR"64�8��>D��8$Skl38, KNS'Tϛ asic.�� ��$a pai�;�5\ ��� oBj:�"H�I��!ItX-�s���nort�z)/. o_0=(1,0�~� n^��!����} ; \; (�u)- v.�^O�* u,v&P bl/,f�C ]��$(� Lv�{�|)�. E�-"&� X�t�NIt�#seK #&� .x� )��;N�V_{12}!��I>v_k=-\C1 j�M?/jk�)6=ek $jkv�!�L&r8Z$. Exp�yns&�m�qo)�JN�� q\ as [��mel�%�2}N�i�la��%8q�=,*�> �� y^-|}{u_ki}��z!z .� =0L �.�2-1�*11"M iA=�� econ*P) valuik$- �!��;A {% �!� (_k) =-�, w.j�3f� ^�M��"�02 �sA��t1�s��]���A�=��0 [�%�\� 9� ,v_l� \!+� C#}{d u_�c�\!�.6� ){ak2W��_k}Kj���*/2PU�>!M�>�� p�n�- �(�Z�� )^{-Af��="k�2�Dk,�,M����a� leteness,� �mdd�'�za��!�-�al9��1Z���N��"���_%ip"5n�1UJp�� l tw4���i���]ndL�90ir��t_*")&a$t� 4!썑s� _a�(a� and �M�)< E}e�=u�a�"�)2�E�yqtuA�OM  1}{u% � ��D��l�%�� ^��^q�u oao\��E' ThusA� �Wlas�=i%�N�%P�A$$ u_N9.6zy �h v+-m%2I5C: ��"�2���� $u_N,v_N$6�AR���in \� 11})A�22T ��j&� f�E�� �� pap�p9�!:"? of� KS5,KV00}�| look��, f� (BTs)� Y>dim<.�J ("�u))�g�G�rasE i=p"t:]K$. Such BT�1�<"-($, or more ally���$ol�p��"�� (rj��3-mW ��).H-sIS�!axbe view�Fs�. discret� ����t5�Di�� s.uEV�Ps5�sF� ��of��are: "� nume�@})� a BT1\�e� s��C��!�jas��!��A� �it�es; kit de{j�a*�B*j0$\eta��at)�"�c5\e! shifQI a �Tc�r�A�@?Cd�E��ab�<�-A�w�/ ect Y� �an"x��lu����u"c mj�e �,�� eta,)$�_!Nslz=x" �qu��=�E� ���|%�sM� pure��teP$ve�"� importa��� 9� � x��/��} �?����Q1�J�m�Bep\De�7 5Wis��e*�/WB��+ �ma%���D�Dj)"b�One�KBT��A�KLbA "��8 !١G>/�l� �mh!��j.lao��Ma;&NE�� �!�+ l) 2�$CM(\l;A�)��� \CM� (\l, !� \forall ~B�@�!e�som_ ���K���D24�C� � j$,�pl4cah#��� �rv�2i�u�=& �$I�� mY���[ ,s�4��.�7od�5q�8 �$~�.l {}$ -�2it!�upd��v�� s, s�&)$ \til1m=(!~� 0^,! r1!A� 1Y'�$� {: �  b2� {cc} =.� N S .X .R] y <ڜ"�  & � � � R�� (�rE a��\��E)� rtwi�u� mU� ��$! m�"<>�ay� +=8 m�}Ƃ��. a�:"^rrY2T#h� "��F��*J�"�#eta +p� q& p\ q & 2�i),�det���=�Beta�ansatzB�.�I��&����$c�a�%�nt� ��� �YsF�re4u� $p-�q�ind��m�("I".�  ĭ� }� �q��M4 .V�st $L$-�P�E�9��vc.E=��&C *f�����HKR���Compa"t+.�͚u)����+���?%uYrr�1lyD4A]q -�pDtfw}*py�jA�� q2+.�,e3y^+_j.�� h�]]I�9w����� �le-) ��y�d �{�x wA�st� AL$.aF�txUD�2)�ݸ-yoldYR�����Sǐn��%�� *� BT-�&� >�%ts a���5B}_{P}$Q����~o�7�� $P=(a�" �QYn�!*i}re� �AV d, 2ImCQ \- ,6S !��I�\l 4si�� one abo({rv-O-f6�3D�ion6�R�)4A}�t�! )�3k5��&->�T!�.�� ,!�d� ��w datum,S�sT#'i5q"�!;} 2} }=-��+21 W;+\mu}\,�ghu3n�!|�.��aDt"��jGde��$. ��rU>a0le �1&1:)��;E/ L��;C�=w+ $�&�"�"� w+��t�V T =$��i�&%� through";P2�^!� AK} ���c�!��N� *l.���5z^3�4"z�� �x&M[3Fal F_AM�9!i-�(!�- \mid���!!+,&+)�] Q�� i}\,*�JyB�\,����h}+ A \,��� % Dz}}^+, \til {\bf{y�)} {\partial y^-_i}\,,\nonumber\\ \1Hz^3_i &=& {\rm{i}}\ K* �!7�(�(� \label{gf} \end{eqnarray} with \bea ��%�A- �Q%T}{2w} \sum_{i,j=1}^{N}Ih9� j - 2- + kA\left( \I�{zE�+ ] )� �1}{E�@-\l_i} \right) + U�$ \\ &&+ \A�I�0 \log \prod_{� � w 1+k_i}{1- V^{\elg�!�, w]N�\, , -�zzz!�Xea where $$ k_i^2 =1+ (/- �) z_i^-Qi� +_i./%�prop} es�Proof:}} First, because the Casimir functions $ C_i^{(1)}, �2)}, i=1,...,N$ do not change underL(map, namely�i��1+-� 1}{2!O%�%�)� +i %�1�=�t I �RN S %�+!�.-AJ)� =)�,� $$ (�)^2 + �G=(F Ka '1Hxwe can exclude $4N$ variables $+,�$ and $ C!�, �$, a� $9{, using%nfollowsubstitu%�:�c=M�4-(z^{3}_i)^{2}q1$\,, \qquad� 52 ).-m_2-�% >�}{(%� m\,[�3 ~]\,%#$$)�+ t1-1f.�%�F� DV�8m�2 )�y� � 2- �@ \}{�+ � �$D�]e�� Bb�\,qa�[,-�\,.� \,+ ) � -p^2 � ~�de- 2��!=pqp �.p9 \� Equata��:�\,.&�}� I���)�%Х2lIt is now easy to check thatE�� $�� � $��m () satisfies}0�gf}).Q pf �;,spectrality e ertyauTa B\"acklund transformeN means�0two coordinatA�$  $\mu$O� xpoint $P \in \Gamma$ parametriz�'Dmap are conjugated�O, &� \mu = � "� F}{  ��f�%� $F$!�hgener��5��nBT. We%� show0R*for one- �construc�BT. U"� ��)�hh}),  %� !A ) zz})���\mu&=&����eta)-�_��� &� x I�aj� 6�I=�� \\ ��*� ,�TNn�� �[2� ^2}� fP�#q �>�� �eW*f Za�"� T� �i6. *a .o 6 - ] +2�� . ! ��Bv�BetA�. .�2� Notic� �U�#Y�BTA�a�lexaX, so i��8a non-physical b�. In or o�t a 9VA� willY� a�-i �ne&next sec� . %�j \F k{Tw� BTs}�yvy Acc�g��8\cite{HKR,KPR},!-��'-� osit� which)��uct��tmap $\mathcal{B}_{P_1} \equiv 2ev$_1,\mu_1)}j :<Q_�b<2,-=2)}$:�r gin{��} 2m P_1,N=2 \circ6��:~ \CL� $\stackrel{2>&8} {\longmapsto}��a� ; Z;yB;;.i(approx}{\CL� .����_ ���ŗinvermDo each other when ��_1=a�_2%t�,mu_2$. This Qia� �D�� onal Lagr�chainA $defined byeH&+P``discrete-time'' Lax��%� q \CM(\l;�1,2)%N)�==I>�R? \m forall \l��A� bb{C� ! qx��&� 128}�Yd��matrix $R���6fA�Z�=\bE�p T }\l- �+x!)1)V 1)}=&o�:�u:i1 iA���E&�^32=�-:)��;:)�" .>F^�512GfK j�.Zbq15.-.�Zy!T�R5$.�F=��SU (�-2I-�\/b+U1)-����R���)%��Z��. � F� y}^+&O QX}k*�.K��.w  ersH��:2$. �� �ulae �� several��8ivalent express4h*�x�X$ sinN e�A �"�A *ma�7 $ be� łheի curve $�r, i.e.,@ bound B�rel]s�1mu_k^2=�11}^2 wk)+ qrk:kcF�� �G.Ib']f�U�k), k=1,2� Toge ith�x})*�X�!3 !�!� ' )� tp�A/3 4Poisson integr��  from" V $ to $Z�w @$ (as well as its� , i.UUzItow)� ;isQ�riz� woM] V� 6Z )�Q��� 0. Obviously,V� (t�"� )%��$turns into!�i�5map. -wan� star7fac��t.� sends�ly� to:vided� De"=\bar 2 \doteqJ :2"sgg<T�fore, ����l2!�*�bjA ���. �� \�Conmremarkʶ Iw��pap� eE� stig]a� clas  }XsystemA,�wlled ``� 6� 4''. It consist�a �!--� (homogeneous� &� loc. �. �"0ratorP$direct sum$N$A�,athfrak{e}(3 nteraci� tops�ur pree-C MPR}���!CE�is model $be derived�y���si�su}(2)$&�Gaudin K0s. Moreover ta!9=ionh �l�E(to trigonom4c a�,elliptic sol4!�9�,Yang--Baxter"�>a� dO ach�?pos�4V.B. Kuznetsov�,E.K. Sklyani�.� off�s�R5e:sMUKS5,KV00� 5:������A���sy!zc!��5 . Our"�* @!-q)�AD)�toA�bod* �1rBT �CsymIly�top�PR}������ *{Ac!� ledgmentsƞ Two�us (MP%Q4OR) would like �$ank Vadim 2!Vhav�ksugges�the way9U5fe& 2%)�. I^lso�Aleasur�a础ter��ng �u� . Yuri� Suri�H�_8%% Bibliography�B ' thebH`}{40} \bibitem {Au} M. A��`%it{Spinn�Ptops}}, Cambridge Uni=7P%(1996)..R8BS} A.I. Bobenkmd Yu.5 gD� �qia��$ics on ��groups,)^an�lic2 uRtop�L Commun. Math. Phys.�( 204}�(9) 147--1882�G1%���ag�i�on d'une��He d' hamiltoniens dG in}}, J.~ ique �37�76) 108�09:�2F�La fo&qond�� Bethe�MaT , Parigi�83.��!�(N.W.~Hone, �O~6O@O.~Ragnisco, {\it�;{a}RG�c$sl�$)4 magnet�our��of ) cs A-!�@2001), 2477--2490=��� F. Musso,A�Petrera,J�Al��ic ext���E��odels}, http://arxiv.org/abs/nlin.SI/0410016, submitted�?�No+earEWeNcal�y� :`�~j�Se} 8of&R � B\����6 , ��5�A�@2004), 8495--8512.�KNS � U*4, F.W. Nijhoff�2�i4 ^�����, Ruijsenaars��},j�189e:97�5�772�S5 �:��~% �On�V many� �,}.BM1 �08) 2241--22512�B:%?,P.~VanhaeckeyxV� iv��@-di\-men\-si\-o\-am&��: ! "r <ach},.�G y �Vsi�4m�2), 1--42�RST�� G. ReymanA�XA. Semenov-Tian-Shansky �G��-Theorete@Methods �!F�-D&�  I&5S�}8DynamM 4 VII, Springer�942Skl38}RZ�. New tr� } Progr.\ �.\E $.\ Suppl.\);118I5) 35--6%<>� � docuE }~ �O\ [12pt]{0cle�o �.p \usepackage{amsfonts,amsbsy}> symb6�icx!8newcommand{\JPA!extit{J��A:�x . Gen.}} 63MP23��>+@fl}{\hspace*{-5mm>!eta# �et alBE$bG}{\bi{G}>�ce�.n8 �&E}>ib+b�"7:�e#A3^!ba�Da>0>A ARp}"{$ 8te�mA�orem}{e�tem} %\input{tcilatex} \Declare!lAlphabet!@}{OML}{cmm}{b}{i}. \tlength{\topmargin}{-1cm60footskip}{0.7>voffset8.9>�� 0.2>odd�)x0.5>#ev8dr$A width}{18FChe�)}{250mmA)�q�title{\vE�{-1I${\bf Maxim� uper��i�&�enenti�,sEyDauthor{% Maciej B\zak\dag\��@Artur Sergyeyev\d4\[3mm] % %\add� { 3In�.es� 8, A. Mickiewicz* �\\ Umultowska 85, 61-614 Pozna\'{n}, Poland t � Siles� *U in Opava,e�a?���, 2xNa Rybn\'\i{}\v{c}ku 1, 746\,01B4Czech Republic }D E-mail: {\tt{bla!,,m@amu.edu.plz!(protect{\rm!Ctt{%J.5J@a� .slu.cz} axdate{]"ke%� M abst� } Fo�+��!bH; an1��ly ari'�$� r� eory��}�Lva�0�# establishn ir mf]byi�ly "1he addi� a"]l�mo&�:\jl{1���%\pacs{02.30Ik, 45.20Jj} \ams{70H06, 70G45, 37J35} %�$� o�  %\m9U)D.;d"�  o�% $2n$2  phas� a+n$�.�, o1 2n-m2~ are �d|�8cular,"� so-c{d \emph{Mmly 2��)�s (T thos� ssesE��1R�D*$need just j one}=.H. \looseness=-1 S.MleM!^�a� threO &6Euclidea�A.� ofi$1)%� w!dvAPstudiedq�li�tu�$see e.g.\ �fri65}-- gra02}��  kaln@ 9 of none�2�.� Apo� handE�re �-t much �n about 2��uin hig &",s� ��excep�� �eA�% 2uWaY4rnitz--Smorodi ��l �)�its ge�,li��bal03�@logero--Moser--Su��e-� V0% {rw83,gon98 ]!Q��4isochronic pot�`a)rgon. and modif!�Coulomb- ,rod02}. .�*1�major5of��� �Z�takes pl���o� nal .�.C׽YmselvA�a���I�oble. :)I��is le�[w�.7  StQ/el5A�{��describ� �)Jben93, 7}�+7or&on(2���ic p a. We��/somaN=V(e/�[ci+!� flat orN�)s)b�!�$ arbitraryyA�� �nfigu휅8,%�ita�m%�usible W1��e N i5� too. C��,af2_manif�6$M$� �.$$% q^1,ds,q^n$�� $n \� s n$�(0ces \[ \fl G=?""�a {c} 0 & >1y%\cdots"1 & q^{1�2B! %2%\v Bn d2$\\[BN &�q^{n-bF(�3��/1}%�) \�: \A�$\mbox{and} Lv8-% &�! p0!B#2#�#\\"�&2"n75[B@zn-1|ZV� |n."&%N+. \] If�W�pret $G$�!aa�tra� ntm�� $M$Ÿ n $L)+a 3*ial3 al Kill ensora�Y�5 sens�%Crampi6 Sarl�*�. cra};!mo�tis holds�,any��pg n, _&B| :3.4a?2w��i"$X on���-e�"�can��S$bracket<$(p,q)�EU�=p: $\{q^i,p_j\}=\delta^i_j$, $A�!n$. He�?z��Fm)� co\-R��|6�s $%K$W � �5�h$Le+f(s~I�b�X0}: %in $p,q$-��:��K_1�0 bb{I�.b>i +1}=T8,k=0}^{r}q^{k!�r-k* !��7 n-1,a��!w�'taa�ve�ce $q^0�11 ��1~$ sta6$ $% . unitɄx�#*� 2W $q�%' coefficiz��chak eris{polynom�3of!G:��Y�T\det(\xi I-L)=\xi^{n}+�� -1}+...n}.F�2.8�6�.` 2�82�$m_>�(f*t � @ �T� � �U�� achie�" by p!$ng�thAao&�8(\mu,�;�"e�d+mHA%m89� !��',p_i=-AL$\limits_{k�n ( T^k)�ui})/\Da{_k,�@L q^i=(-1)^i \sigma_i:)$uAM�]�$0�n $i^��r�Ar� .�9+ $��n$ ($� �0=1�- u1m@i�2i ��n=1 2�,n$)�$-i=�d_�< ,j\neq i}.Ni�=^j)( %In �',!ږd� �by � []. %� ~� �~is�>pev~-\Bv��} %a�any (co��) %~  $G_i�C�] >]|7BE,yT $K_r$, %a&,*a2p�Ea-rd?v� ?��*AU$ %��du� 5,who, hiworkedɫalljybject  %|}�Y�$Q�,\mu)$Bg- notha�but M"w~�,w 1�"wB dvantag# &�D`n<andard'2��XA A �.� =�r��~��q$'-�i\geq 0$��A' ase �9�$ to search)�dn��I����}p}E�BV $i=0m�n :� �4G}Drs}M�(E�)^$�kqwe�$e %�wr+9)'1��!n��L� \{,\�qa5a�z� q,p)$- %� ��  We�, dily �at1%ML*} \{h1},p_!�}\}?0� U� ,� ~2!�1�2B92i+ ,!�B91 0- w ,\ \n�Jn-1�1 �L*}% Thus%lA��fa cyclic*�%^u@�q��$ $% F� )r=-�r�$��. $(n-122�m, 8 �c�Km�,M ��0!�>�sAG2�&.2n�. %aso�KPHde � %�r}� )g%�$�g5$ɕ $i=n!�V>,��a Vc ]Ba�i&%I*�$s$'s $f_i" �a�f�su�B,$ PA_i^{jk}(q)p_j p_k %+6+�mn B) ( +C_i(qW%i�$  �&��s$2y$�)easaGsee�D6 f;�,$A��� linearly = .%�field[� naly� .� 6�6� )Lw�A>�}.� %ToEŁ�i# ��* n�)e5� ex�/a� %$M\not��0%�!� argu�s s9I/ M(f_1  f_s) 7 %��A���1 $\p :/n)/\p��=2�m_{Us!�C 7' f_m A_{m}Q,A);@�� %!t$j$ A fairly�2WIVIKra� tedi�0&iI9s� �Di�2 sult���KA)fi�p $(2�-*Hixs}��s=1"n$,�th� $i$. %�0" -�6t samDtru 7�V$%� +�!e is���M�4&haE�Jm 1=\f�,!.7, %6w:'$%uthey ag� re!�B�aD.�1�is pic���g��4"�� f�D�&H. N~Q,��! basic !}1p ^8recurs��9 G $bl98,bl01}��u&& �4V_{r}^{(m+1)}= (m)}+1)}V_{2  m8��� MK -q^r��4fl V_r^{(0)}=0 z-m-0m-d-.| V_{n�l.L}2~{O/q^n.�S566�� &�% Aa�� "�$=i32�f�?{j= $m=j-n) ,j-1A���E��w =�$6m/ \p %B,j=2x�m=jaS54;�MseZA�&,�yŁAgfU 0r��:"�"�%�"ny"l $n\� 2� F�witO":e% H_{i,%� k)}=@1EZ)N��> %��.�� ,$ $k=-i6 -i$ �n�,!2"+"7 ��#-i+Q� & . m� b�Oe�!^7B�! $�e(�r��". ��!�>E> * k99' F� *{ �7sa<k)}�s� ���Y� " 2ize} \ [a)] %es%� 6`=\{% p&V !z%j .Ta%!�1�-!�,\(tem[b|n n-i)6p�Z1VK% %� }MU� w m=>)$k=n-ipcFp� .�){WzNt+]1}rTe�Vze�)g��AT% .xk)� {2~ �]�6�,y!N%�� s� �� (6�!�U�E9and:�$5�,�reb�&�o"Y? A�b^G_tE>U�B>*6&�# .�. %;� $i<0 <$i> �y I.I#n�� ur�8%�;.�6�.�6 us illu�'t� i�b2&by�;ontriv� example. Z�=4!di  k=-21A s��7�� H_{4�5-2)} =�I��Q{p_{{1}}u)2� 2}% e?31}3}4 4}3\3 \2}}}% q�4 c3}}+{q^/{a.4i.��\�2��R�2 a.�2��u(�w}�y2 y% ���2!# SL?q!q^ X2)F1$=62f.D%�U!c�6�% �3�3-��3 > �4}`U�-=-|c% 4? �/&-1/�"� Ef3b�-.�2�2}}+% �E%f�5�� ��-z!�2 X5�Z�4:X�Cp1>F��-,�39�%�)PM�-6:ID �2�2�=�.�`&^%�6�b.D,on&%?, �r��$�+muj_ %�21 nd tbyg3 em 1�����  %�n� F��T.� %@p� 2Aܡ�-4Y�.046%qS2>l��3%B3-B� F% �U.Y!d-�p_Y1, \])W&3��ofy- %:@� :d,e���] u� �,).%F..� њ>��� > .]b* .2 all "�&�2}�!�>�v@rCJ �~� R\pF� V� 6C $$� � B� ��Oa�� =�B:>� .<e�"� Bfor>� �� >�F�Ah� �- ��"� .M po�-r� , . � 2 �so�� .`� � � $c *} �>� )2g �����1�� . w.0 rF� !.O .\6�Fb%i�+. H{inls�set V<a ${\em cubic;9"�so %,unpA�5 1,=c�.un�t&a.� *(ce��ACsets �e .�J�)�&:T )��  +;0 full"6Cty�far. %��techn�?as\. N41theles3 %1cer�_� -g��ed#^E��Xvalues�$}'� $kI7 &��y.y!�J>��iyce,� n=3Awi=� $k=4��j� 0i�4)}=p_�-12���q�~*.���rY 2}+3� 1}-3, �8��e1� +(W)� .� 0�� 4)} �1t2}�3���� e�*� % � �.�$ ���7�� ��3} V+�1��1-); M6�w� .T%?��>��9 � ���32�& .�B' 23.� W��Y\ .! �5X3}(% E %��3})J| "�r� ; Y�$#"2� $*� %E ��2��a�i����J�F_]~v�%� 2}-3! �JK�3Q*%/,\�]Y�A�T!�X 1}-26X 2}-4E EDF� t!�]�}%� J_u�79 -��&~ V9nc y� [�,�ar$[ ^[�^ :�v[ ��J%�&st#N(pL� �N� ��ץ�V��\ack 9MNNnT[re%waM+pl[porIM� ;Gr%LAgency (GA% \v{C}R) 2lg `No.\ 201/04/0538, Ministr�* Educg, Youth`Sn]!& mx;2\LMSM:J10/98:192400002B8developm�.pro5'� 254/b�H&y~E(2004, KBN R1 ��01 PO3B 111 27� 1SRs< Os< throug�I �F)IGS 1/v . MB� Jp acknow�Je khospit�d+0!?F�<J+V��<� �=s~nk%�.,ymous refere=useful K,:D-D;URR: nces�>�/>�B{99N+J�7@Fri\v s J, Mandro�MV, .�7 Ya A, Uhl�= r M%�& 8 P 1965 5?it{j>. Lett.�c0extbf{16} 354� �ev90} Ev�eN W 1990:DRev.} A (bf{41} 5666FTkaln99} Kalnins E G, WF2ams G CA�ller W JwHd Pogosyan G S 1999 `i�B!�.-?� 40} 708 %nK{gro95}Esc�o?V �#Sissak>A N�$5 Fortschr c 43 523Y�7:�M� [.�Z7 J6"K38 5416Z�7³7) �J8t. Nuclei 28 48.�ra!�4Ra{\~n}ada M F�`SanE' er M�bk E=!�0} 502.]!00}6�.��2200YKJ. I�6uD)�(bf{33} 6791:U01:rK[A J M:�~.� K �IRv}@4} 4705 %--4720 ("�J�@�$4h-ph/0102006})�^<Gravel S�2�2��%S.7=i�B� ird-Re�(K �+#u3A`.=?m�M..�V33} 5902�5912 j�206046�%�2^���- �Q"�<�C>��.("t��970� 983.j�1080152�b�< Bd?steros�c Herranz F��.6A_$Sanz-Gil T!�3.}v^6} L93�L99j� 211012}) ]]p=$} WojciechDi �l83i;>����279L�=Go > C� 8 %O�e6@ I� of Cj>=Cl�1} 446id4726�>��Z�H �97} 408 X095XC>4 Rodriguez M A%�B� N�*.I ޡ3} 1309!�1322.nJ110018Ao٫EpbBq(Musso F, Ra'P O %�Fz &�Fle"Oagnet: A�5fF?a�L �1or6�T137 (3): 1645-1651 DEC!g3=.�6"�1Ae9�eBOrtho�Q*g%BY�djit{DifK nn{g. M\\apprR s, (1 ,A�jvol 1 :Zd � 8) p~163; availPat)�tt{% h�PDwww.emis.de/procee!?� i�S�7:�7�Iensic %& 7z� a%H q.-0 ��H~6$ton-Jacobi"�D,M_Fw �A�8} 6578=�\;z;��|;W!�1�A�.��k� erva� �S 5A$on Riemann�>s,I�j�42} 4312F�;&6I M�3NA�bi-1n�� R. f�y�QbPaYint} ER$.SI/031202.�'6� 19981�On-��� %:�QX� degEC ;�Zure.�6 =�9} 32>.16��%F�_:�uE�3pN�H::A{GA$Harry- %DyAA�KdV dB �&�2� Nonl2;�9}�O1a�> 5�2 1Z> B�O�y \�KC7 [11p*�O*O0[dvipsnames,u�R(mes]{color}q:f\the�( {\arabic{� }."�Kd 6 %F5} M -0.6cm 5M -1MI��L 220m �L 148:6�M i[60cse"�M:_M0.2,cM .(>dM.)�1]}normals�$\t;MHodY t2�sH5]KDCamassa- Holm hier?6y\\��$2#"� s} EMTP. G. Est\'evez $^{(a)-nd* Pr� b)}$\\ ! Area�WFi� ( Te\'orica.Mn4Ydad#$Salamanca,  37008�R ain\فXextmd{{ pilar@usal.es}} t DaTta0oYMatem\'a3Ms�y y�y�ond2� ��LA"�6�neg��1�6��5>�xresen����%ab CHH(2+1){TEfhb%aG���I� �-QMWU7 ind_s�G� coupGaCBS ("s TBogoyavlenskii-Schiff)�?0F� '�=tHPainlev\'e test. A �iso�9tgo]_�&�!'7�*��A$io"H.hip�'!BCBSVCa$problem. ��2�MBdodu s}z-intro}$tc�Ler��{x\@0em�H p�b%w�b�m�E ���&\H/ch9 J h94}�'!�!� �J�; �!oT�* peakon&xa�&�L�/c) mgp95}, dhh02}� �hw0���iKZ�i�; a wi��X 1 � �s{" f_, U=-�s;jb, etc):b�4> rI.p5��last ten�s (See�+*DB02�)0� �0%0�Ws>-TWeiss}A�usue"�� power��r�4A�ze B-an5]. .��7 w%� ��@�%�! :��! �Uto6�l�`9́�6`ed�=P"�zpr�8$;t�Ozba�/a�8�2+P�?"(Singular Ma(JpY �)]. WheG���K Bez� X"� �;hod&3 be4 iv algMh�Y.bRJ��iCehic j�E��N-!�boQM 1�*�O�6$as Darboux>*,&4au$-fuV_i i\ mainf��& =m�Z��Yf2� �yA�n�jk ntͲ�`g�.[2and/or dF��. Often,s6 !} F�$^�F�Kw\>�P9���/ "�m)�.�I=� a qu�bo,luck U �i3 � �p}of viewFk5�A�a�b al d.uq �m� flm�inYM( st f�Rent kaBvD!�:fA>tA��f-/�asf*NisBi�&hI�ma8f AF88� cgp97}�A: q�/�M m��1�att�F>T��~i�@ lowsW.F tar�om�]ive=�(2f�aD ��5�Ever? ecise way�fcon�u5Rbi�_5F iQl6Ur�Nst(7a:u Bj{�.us !% 1�a�o./AXna�$ !/}�A�!�success�-�Fv���A6�-\1.  Q)�ͳ ��f[ *%!�Ez���ٚ�l"k ��� 2�%v!��:�. Based>Cidea, !�" 2i� is p���(9Vmp�"��A�!c)�"Ja�P-;ovZ6�. B�  (� we)�V"� )a�mHH"�qfQ��m�2xa I� $n$ �� -� bog9y�cal|�H9!� $3�WJ� ���9�� eachO [")9�R&B<g� lCo8:��  ��>a�alY2� betw� Et9�w" a� �!�i"x�A8 $3$ &�� ���^�-TᱥaPg'�a&Bq�� uA�p�Dr;~3q�7+�n�kace�aB! �1i���� �8!k"�-)�]^ ! B�7�& 5+a.�devotK  3�r�$ �L�P�'�Ka�teR numb�WaeO!�m�A�$J_*J_�OrI�"W: ope�qJ�ՎJ_0=(\dal^3- �M�/ J_1=(u+  u)1�(}  x�U>2.!�6(For our pur�n T=&C�P� ��p%:"+  $v_1%�...v_n $"�!� �'(} v_1&=&J_0%�u_x\LongHVarrow! v_1=no)�\\ v_j7J_1v_{j!�6> J_0v_j=!5.)Wj=2...n�29{*)N8} ߌo�O��AN)>�nowXry��You_t �n)�Y�J�Sn.�,RO]�� �".�-�L!�+1$��s {�2.3})- 4}� $+e� s $u, v_1`>v_F *hwa�$n=�BaQ>]rsto}-ZX u_t&=&2u(v_1)_x+u_xv_1=��(v-)_{xx}- %Q9B5}:�p �e cel�s�21��4�jmedre <B��܅� 2P��n� �qbe�]X'V$R^{n}(0a�uadF�6"p6�Bw6 %�*�isg�uEv�(0)�5;$$ or!iV|ly: $$!��M!�$$J_1 =0:\ua�/2M�$$� -v�1b� k75}>nxtra te�D-�#X6�U!�su*{G6 � ^6� } Ai�e&a +ofb�to:F�2�Nb XM� U_y��V2� ��V��1V��V}%�Y�7}\\UeJ9n}u 6�-}  $U=U�n,y)�0V_j=V_j. l�7��bevqU�qU_yiv�)8B�adIUy'ysho�tbe&{CQ%!O��nm:x)��Y�� ��C>lyyf#X (2.8a r$1$t!3$y$. Conseq;Q2� D�a)ʒ��������ie�s�D:�@�b6Kt�rol.� .�une�&4xu=�J ��Q=�(byi/Dy doing $V_1=m_y$)��$$"�4_t-2m_{xy}-m_yi _x)(��m_x)=0$$�_] >�ai:ta��HFokas-Fuchssteiner-2dA_iɩdff81} �d!� �C%�F F���\P�Q�T*{R��Rs�gR� I �@�e� -uU2�Qy5�1��m6 M�.��B��11v}  y}n� ��� V��^le�8}a> sette:2J�t}G9"ƕ: $$� U_yFBR^n(0)$$��a��;BMy!6)��t$&�reddFa� �W*Q��is�m1�E3Ay��kUA�"�2M>the&jHI�# Z��l� �*���at��f"� 9!��i�~r�8ondC��$U�1{#|ON $N*s (A��{!_16)=��%ce)6glybT� Q� ($n=N=1$)">�y Belos� shall den1���by6� we :va_�0s@alj:!a+W�st�%�@� )�u2�tf.l2{�D ^b!} i9set*� ��} U=P^2:�10B8w�:n�e �.A B~P~ (\be��_x&�Sd i�J_� }{2Pn5(P�)&B6 � &�1dP�>n2jF. Yw�Wd�:�-�=.�1� �&k1F$ laA"'�*� 1�ga1I 13})&� , acBՑ�4�)�,� �e�"� b�] ,  d�(Pdx+PV_ndt+-�dy"� \\ Zt 9�5�" Y&=&  ,0> !G�P"<now: >�I"\ 5}  x}=P^ X� � ^"� b Z_1}%f?aEJ�n�Y}1\nb9b6In .6a � ��UG5*?16ATreN�x"n�dX}{P}-!�Z���Z{MdY5�\\ Z_1\\ ^ Y��� .�7�KMg�&mh lF�X2�b'x-�f�!�f�t�f��`Yj^y�9=Mnl-B. 9�>�� Wi�O�fVV',>��k"R14�ome.�1�P_a�P�X-P_X �� 9}\\)�P_{!c(}{P^2}&=&(V��X+20}"'ET�>�\{P$[P(V_j)_X\_] \}_X-2���S)_XxRe�/x�eMvx1fxx-0 un&�1J6�"y�9}�2�1F yet�&iB��O:d�� �w&ew���b"Y� �aeeUin .to�ϕ8F��$ŷ.� $VH"4 *W# �2�� }{Secondj�R��Mso�2�R� j=n$`�vn!�Vv)=Etn-1At��,$$H&�ub�w� �0})r�>� e�P_{XX}c+ �a~^2}{4a_ �)ir= :1 � �&�2& �u�%�of&e ���:�� �o&b�ew"e $H$,�d a*vBvH_X � ܚ�-nykFm P2�Rgra� Q��2� �1D=H)[ s=C5��3*�N�"�}5A G!=E$Z_�Z_%�$ !S�p>٦,6!R!at9�.^�&�X� � & * x*�) j- j�]�\-1>hP�%5{n-j}01�-\ .IF N2�b� s"��F�XjF c"�a�N`!��$��vcakF5|�wpar�!-j�xmf|6��I��I�j6h��u���621b-�i�j�` '%�j��iJ6N4 {B5)� W{�dW��}}7}:� W���5�4}) to �!N��[=2PH_X�\P_X^2-->uF>B�A��{�&~27a�we�+J�H�XZ_j}-4  }-2X}%j}=Z-V�=&F�Ea.�i,K2+ 2�>V"�3hvaru�X�ZqU$ �lHis&h! &��"�!"9("]���#�! >�#�' ",� )R!i&v��<con*p��AKNS (Ab� tz, Kaup,L�(eel, Segur)5Q. ItsB� )th"�Ba�R5 i~�"�itZ5be�*2-"-52kp9&�(J.a%�a'�! ��'e>� 2UT4>�� >!��?��C$R u@2�0 ?q4 a168 =22� y+3F�W!gw�e�Q�A�n$�~�J� � A*3N�!QIb���a�N� |$E<%.�one $Z%*86 ,5�$30}) looks1Gca  /5��/"` .�g2��!���)���6�}&�32Bp hh,�Kcombi�2�.J3.R%&�$�\2�.���1>U3F� vjS�p�-�31!� �bz,J�P_Y=P)hn}R �cJ�N[ o�Pompatin*�(2.28)�`NtoA nU nJ�n��Yt &� 3Ft � ��FL2��SA�vB�|\$Y$� � {umm��$6s}����maU� b�5�N?9��&;rt)'�C�'� .b*s1*����5�bn$#$#$V�t�2�5 : $x��.ZWe� mad:& > " 1)B�dX=N<�Z_1=t Y=<.�6:� .] 2)�hZ� �#^� ��2.3� �A�ZA�P_U�(� \�&=&P^2�><9� ��953Fej� }=. -"� B%40b��`4)F%an}=�C�41:P� ~T:���C �/�7�AF -!Wa�~*!�,ZV� &[4�+W~>W�@�3� �a��` 'aK.� |���5if��Y $n+2�F�p Y�cZ_1$...�r��j*��6*��kas��4^�-  � 6!"�p��&�9b�,,�/e���nM��wY2�0�UV8�6"23"."�.KF ��UM�6HoQ2 �� ��us.?afb��`"b�/� ��.(2.19)-��2�ob����P!�V_iMmkP6h .} �(��k.��t\ b���)M �:�5�1$$ $� (n}$$ 8�2 at, � :��E�F�� �G..Vm�s�^$�3ee N $n$ �]! �h !Za�&�$�0��}?*V�)},\,5])?> . Fu�WrmD�� ap$ix��4� cs�m�I5a(A�!�� solit�~ u�"s _ Q a~"24i��.~�%�maiq9 nefi�� ! !m��5"�N&���Ym @ !Lax�>� >�9�" *4"~Y%ZFB� l9.2�<Y��b�3I�dE�"Y=Acta<,ARit �7�2t&Y!M,E�Ih�=1�1� breaks d�a��"Dirac ��"� �"% qu`/ro�;f aK1 tribE]:�% � !��5a|5�l <  lpCHHj1I�rec1pB6byA �a a�eF� )� )f<� ��Ab�1I2�8.�uA!su��2�1tafR \psi'}"(�\l�Jj�),6� 3.>�&D U  0=E_j=-=��+ ^j}-_ j}����psi��c��>�2�~�093EEe akAr. ex�ame.>� temp�y+F� �n�v ):��n �nN�n�>�"V �6��6,��n"�)�!��:����%�� �4D)�=�6q��$&<i2� ��mbda_X=Py%�-!I�2 }}=0>4:� An�Nou���tpN��N�YR�nN�"�0-2M 1�1k]9��X��x�u:�A;!��ac6� "�q re����!2�]$�A�yO(eP���a (.�7Q &� 8}-  0&=&E_> A^�5�xӁ}^� E_j-z ^{-j&�.\\&=&Q4<�_}u ^{1-�s���IX�� H7!�p}� nonu6\\&+&}wsy�R[b��{| c1jU9�:��=.� j}} �� psi\:�3."�1l ea���)a�� .s�� vB� :�+1)b%p]=9(!��"n}+ �7��.$$� re*M]LmF 0=;^-�iY.�n �'j�z6y>�>7�}a]q�4}6�5�VP ���n^q=!? kF.8>.2tIn�z*d@e���F��$ bq]J.g;/ � E k2�� :p ��"�;��A ��va� F& All c B#�~�0eڕ�a�C7 �JA(X,Z_' @,Y)=\sqrt P\,\phi3>�"mM[ A�2*-�2.16w&�mw �_�)z�%�d�_x�'&�"ie)�xM�" F(� �>Q7&+[ m�_�`}:�"].{�3� O&�I1%J phi_t�( x��&2PZ�)"{Y^Ty ��!,>bY �14�<.5::+.��3=�q�1*�' ��9��X)X=�z(&�+�V��)����Or�� (].42!�)R�hi�� � 1}{4QjyUBz3�(6 ��12< of ":  �M.1 �Pb*�2$ �5|in30 H�is:&qbEE�[!:��]���Mef AJq Z]�Br]Ul>�m�j} �"� v-� cA�u;X��28 �"2]�Ռ"�7-)z��Sto�-i 2.38* 3r"�J�t�E�phm��t �2H��]�Z� ����UYn� M]���n2� � h",�6�umqs� RZ to&u1QaAI�J�:��Z A�ivy�j(F�*�- A�o_x 9� �����{^YB�ingu;40};41U�$Z����j4&2 R$ / %�-_�w(F�ƅ_}A�^!�)_X+P_X D:�)(b� Mxy��:��Y �t6T��& [V_n.� i yj ���9]I��b&�o�G_x�H �3�4ie�F. �zppl��8' (3.8)"� � >�F"�.ic �����P��_t)�=0�B* �Ksum: L��� &F���2��;v� ��2៑c�E N�+)�= � �AQU%l*�&w B�ZC= S��EC +A x uAh M�^ *�B��6FmA=�0}I�� .�:�"�? �Z�Mn"I3D4� M ] ig�B�� pJ"�<j%�PMݡ!�!�5�"m ��34��va� CBS.*�6`��d�j�&K�`R :�M�i&�'� se1>,��ba.�Sc K�#an G��C��*k!5ced�O&�6����a rB& coll�"!^ non i"���+6 �!�b�-�2~&1})�viv�u0���;!�r%Lu���a1�2) �b)Asur��fu�PX.���I{\bf\BZbar {RѢs}}: Sx;Ks�� ilar!,(0)I�!��F�JzZp(s �~3R�*@E 00}7{K�Qly�F"�$"�J�L1 � B�=sc�Or!T �UH[i&|P (1.1�%"> *-{ &�.EB!�L>E]!L"�==!q>>�5�is ��.�>9ZAu@Y&L*M>�qg64Ed�>:^��|-�:�$n=1$ ( 2R\C�1expan 5 as a.��of�a�m$N-�v"f|>� jcomCP7=(��itD*+R�C2)��-�($�>%HtU-�*Jp�hy9_9�ppe�� -"d,E��*T$2��c&���E��zPB ��F�I � ��B?��A�<�5\B: yjr9x�.E����nVW5BY�F s�u?-��l"�AQ��\h"�Nari�?�Em���< 0$. ��no�Z���1K��l�N� 0 W��g � ���u�1q� �� \\ H�; BS�B*�\Be� �" Ƃt^Im{for�� the.Q_}\Ddrm{5u"/*� -�7*�  ��111�< C21C.1C��jb%nB= "� -J& \,drm{Q�n'&D� -�dգ� �98)2Q��E߉�nW����!K dV&�De�_�o).s7 >W�0}��5������\^l "#��$reW��R�n�!C&�R} M�"^ �4�^���a�I(��Z#NSHM >��Z *}HN|H) . Al*z2&�' =D�~!a6SY%c'&#�2aW^�(� F�%2QMq��ť�7*VF� D�"{]c�W/gr[-6UM9K� �[i��ce�1"ñ�W/#is�Tto� a� 2�3���*� }#� � ��V�ANK*C%9s6e"�=�kJ{l��Z1�. NG%�A�:'��! _y"�"t`Sa!!H �!�� ��Ta1 A {��� � �Rl>"ja ��sfb�tb�r�Cx}$�*� �� de%�*{A�(��f l8&&D -$.%[y!(2.42�*43))�>�"�A�6�'���As6mplest~M�/1):� eigen&^U�F(3.1)-(3.3) 2$HpK� Q%a���e��:G ���=$�!<=e^{(kX+\omega Y �[�!&�(j-��}Z_j)�no(A.1�KL $ G�JtotqK&~��bψ$$k^2*V $$Nt�!R,�,.  P"[&�"�28�0hi\sim 1+e^{2��2�e�J$��aV� one- +5��! H_{1 }=-2� {x}} 5\3gAu>L1���1�b��zM�� 6�>� !\ 5: e*b�(3.24Ex25 ��<@ &� $�2��tau �tau�4�E7!� tau=%1 2-\OA� ^2\eIf5/$.nd�� hi_2+.B��-�rm (A.2.t � wo &@;�U ral r>me��� u x��2BԄq4e]3u%$]� �qy1{2,x}A)}q'! ��))!6!!�t�'$$!YM�Z1^2 2 *� k_1-k_2} + � ^2829�7 q��L_1�N_1�P_1�R_1RT�[RV8^ X2 X2X2XVV2^VV9V�}! 1{5N{20;k�:!2!$$2tckC_me����mjo "8-su��Rg�*bme DGICYTg�s BFM}z-02609��� 3-00078.o�>�q�~S*u0 0Antonowitz M.��4+dy A.���y>�{*< 21}, L269-L275,N�88)�"�}ac1992} �=fJ iCl��on P.o S20s, Non-S� Ev�ksx aqIn�$S"��^���v%".vo�b 6�n O. I�R��anFph.��veys} �4�l 1-86�90�[�k<  R �� D. D_![9�v.kGt Y7!X 1661-1664 ^3^._�m�  R., ^ �Hy�!nMo Adv.ArA�� Mech. s3s-33 n�n?.�A Gordoa!� � PickP(� 1�P>o1;1 n1463-147-@7�ual!AӸ F�L � Nuovo C��B�E�,14}, 443-447�75:S�0Degasp��9�EV 5A. N. Wu�.Ou-313.�!�a�:r�k* �=.2�A7487-749!�199E�~:�Qiao Z�arXiv:!'�xw9})%�M00}B:\it App�A�erY?}, 37-42 P6�736QE7P�A'�Ba! bf 1�129-14��200�B��]Kruskal��D � it D"3�4�HoɁ;e�9�edi� by s�Ed^�, Verlag, Lec� otes�Mt{, 310-35)�m�\��qC( Kudryashova�a>Fj !hy>� ��� 9505-9518�9ũi M,�,nez-Alonso L1fJ)��M���2342-23�p8%�=c�3%A�Fr2a81405-1413, (198-�M>� &x�}:� {jnm^�% Pa��� migh�l6 B������*��&��%.�xsym} gSe�Le page >/�  |�" u}{1 @Maܽ.� EA�sub��� S� %J� JNMP xw>t&Y^{ -�%t DOCUMENT SPECIFIC DEFINITIONS�Un ��,�;�0��6 b����s: %\/display 1S�Oemsamm ; heD, "_ types��italic��4�A?�}ɟem}2l[}{LwExW�s, �, D�W54s�t.r�$ upshape \ rstyle{846q{X2$*{ �}{ �} %! '*' m%�ir)�ed � END~�� yA�Hea� sA�ren*I�q{ head}{P G�3!�J�/̼24odd 3S�=c �7���!j J#d�D)�TitleA��L )a�nya�qZ Page�{*}20**}�g 1{eR;}-0h �v}{Articl ́r�: Volu�6)i,�v,E� �� p�hype!H' I''ld�F-�8'��'s 'Rev�r1 \copy�%�[{200*ru \Name�dQ$9! \A��|0STEVEZ~$^\dag� J. PRADA7�*^�| , Faculta�| Ciencias,"���| .�| PAINb�~~~�2�| \\[10pt] {�v�|�� �2�| \D�� Rece�Month *,��*;S�i�n6�ep2�xq�a"��"|"� 0Singular Mani�yfold Method is presented as an excellent tool to study a $2+1$ dimensional equation in despite of the fact that the same m t qxs several problems when appliedy$1q4reductions of \ same|. NH0theless theseS$are solved^?numberM�[ eq��s increased. \end{abstract} % The paper % \se�{Intro �} There�(many differ!\$approaches��t!fLof nonlinear partial7 � s. E �� )-�wconsider)�heasiest]ofield.��m%�Ps start usually with�!�BzandWn,9t M< has succeeded, & genAiza!�!:is can be.�`\cite{konopel92}. AmongSB�V)a,a given PDE,,0Singular Mani.(SMM) j Weiss} bA�!7 Painlev\'Eqperty 0TC}� beenA�A�to�Pvery effective. As ita�$well known� .`t!�%4an algorithmicZcedureilallows u�(determine im8olu!dE�a!A$0 singlevalue�iniEocondi5 . Es�*iA, for D\in $z_1...z_n$ variables�>� requirA�hat�%L2�%]DE could!4locvP written as: \begin{q$} u(z_1,. �\)=\sum_{j=0}^{\infty}u_j2$$\left[\phi60right]^{j-a},e�gwe�$a$-�,integer posi!ԑba$B\$ a tot�arbitrar�%< fun�P. Fu��$rmore, onc!�BWYlchecked-�>�MM!r.$drive B\"acklund transforme�Ls, Lax pair, Darboux>#� tau-�s~-�. 2�0 we must reme��Et%T��meP� rela���wJq, .e'!w4SMM. We list sRoemY8(itemize} \ One %8 main criticismeM�J�is��i�nonine  of its.d���th a.. Our aia�E8) isi6kop e.� show)� �( 2+1$��much �r analyz hr)ҍ than>�toII0 z w2 �2}rin-WworksE� w 6E&�DZ�direct��o�(three simpl� *�� &�,�? s�_or�!��V$� �q�2!te  necess> ��MR�in order.!� su�6uP� ���ahb�2. � pla��-i  ї:� y<i In . 2V�97VA�� a� _ �E-at pass�V� .� r3 a co!� Avsi��I�Z| made>� !��[ � o obt7 H2 �5 6�s5ko�D"%]R are 9�1B4.�irts, also d� d by Kр �5ialA�CoAr�SV55�\ �{A*u�ps�# scrutiny!z!HULe4A�a� $h$.� n �&� $x$, $y�< $z$: B0�4h_{xxz}-\frac{ sf{3}} 4}}+( #1$z}^2}{h_z}+)+9h_xh_z T]_x=h_{yz}.\label{2.1}P1� } Alterna<ly��a�iJ��new �4�( $p(x,y,z)$> u�` (\refl) a��9Msystem5ga 8} h_z+p^2=0 ,�(2}\\ -p_y+p!)x}+)�9)2}}\,p\,!")tex)L \, p!x=093-�WemDed2� by search� I�rrS 6?e�peakoYs.&� .;�>4Ermakov-PinneyY�� hone99C ,!U�.�in *Wang0~ i�^� a�&4a��ipr�:� ��.C S �"�:�H Degasperis-Procesi�.69.�A^6O�� ed�a��+ 9'Re�{��  obviou��$! r.>� � 1) $��h}{ y}=0$� it. val��toE&� >O\� :T:rB#x}$�we� efine!Ł� $ h= /�� x}{3}$. W� �2�=  isBK ����K nK *>9}�qI } or�q�Ph_z=-p^2,\notag \\ 0=�(2p�8}-p_x^2+3p^2h_x��).E10m�UI�r�90��"� �\no� y)�X}{2}+2Vp^2+F(z)=0,\quad V� -,3}{4}(p^2)_x6�e+k the ��xF�mB�� (se*� (2.15)�M2})�^isA�)ari� �n� from�J� 1E �Deg7 � �a&� V. ;gp95}\i�m}celebre0 Camassa-Holm��ch A�!ie next� !�is?"�FaC .JqZ9})� *�&|)�a�|r�BB*o larg��at$a few   "�� �f� b"i"F. �2v�z}>�.� x}$ &��yb s�D��ed Kor�g de V5�:q�Q } p_y-e�x}+6p^2p6Z 11>��b,)�i!se,!E�i5�1�ba6�esiI� .�",�oi*��in :;$ ! !�� Rm�#byd� both �+2$A=is&� i��]�� M��@fu-�x1dseI ^2�01}� .MD3�DybD%.I�J"������ h_{z2�2>z��-pz�`p�d}*oFY1>Z]�%�%CAqS��1Jaexa�� ame e��cas= y�1��"�# ppen0 too "�veit doe�%a�aH6�>`&Z~s qo� v�G by goaCto C&�( �#on{^ $} I*=mak _*< s� �,��aonven��mce�g� �S ��5�����zh_y=n_x,l 3.1}�hA7z}h_z'2 F�(�];� ^2-h_zn_z&_ 3.2:�.�T�ed& �SSM�0%٪A/�5�R  m+(s6�P 6})- 7})��� $$h^{(1)},n $ \,o� �)�� be%�t$C5� <= h R (_x} }*{ i = n6-y-�3Ba�a��e�$h � S� � semi��of/IX-#A@1#�. $�  n�e so-Ded EXNa � sociD A�!� $(h ,n) $�. Z����2})1.�aneg'.����aIJ�k&4 E_k�#�1�} $ )^{k}=0. uq4>� Sett�V zero�*gs $E_k$,�� "��ultUA�7dix A):2rS>�ip1� h"]�mA���er�!��!���(.r�a��on&Q�)x=�n VA�3A V12) Qf��5��EzE1}{4 Rg, R_x+ R V)�)� @3.6:��'.m usefulA�d$ V$, $ Ru3Q$N� V�  IY�_}}{x.� RB.z:-�7}\\ QB1y21.� � 1r�atibil�$ betw[*!�O ��)�(uH!�zJf_x�8 �V_y/Q%�Q9�&(3.9:����6-��0Schwartzian d�e���} S=�xYvAf2zW3�%46 6CB�+"?-} e�=0&�� }��y r��.1� $ SIcAYndR$.�3��Q_z= S��3%�� ( S�O RU�Ryc}% R^2��)��F �3 toge� �3.8%nu!�) !�s��b�"; � � �&4*�F��)�satisf� "�� aFB *G#� &���/ex���5�6��� ly �/i� � ?"��a��!�\psi $ I�N1V��b _x=�Psi ^2=�B= !�c.�.�!1�7�9})�j!1�}�=2K ~_{��si ��13����B:��::4�9�-B9��:95:B By !�E�!s� 13})E 4})�#3>�%get&�+9Q=3��x+B.�x%�5�%�.:61:��1kza�jz D^2*� 1>�V3�,�A�A%5 � into�3.! 3.15})��'0he"�F-�y+ {xt)2x����i x} ���8-)D{&+! }{ 2�>_z+zNMBr�eigeny�o� ��8"wF� 5O2�' If� coM3d�[� :�"�� �|%ators QQ� T_1=9_x � !6!#+n "�T_2Iy-' x^3--�M�2� K6�Ac �re�<�&C'gc3�i� {{bl} 2CsDm�2.2M�r*M�# easy����,$T_1$ belongc�0class discuss!�he/1*$T_2$ "nbecause���< $9^3V!stead= .2$�.~4.Da&1 Tran*I1} Letd si_1� A�_2�n� 62�s �  $hF %.�b"y�4U�8�1["/3Qqu�{1,y}y�1,J�� 2-i�_1e�U�  7z�;��69#%z�hq�N& 2>�>;�22�2R�2,r�2Z�2,��2>�N��#1�8fe-r3s'woF�2&$�$�Vc `%�=A_!�}^2.S #! # 2}^2��"�  A.f*Qg�we)�# y#,\,)$�ga�.M �g�>_1.� bmE�3�>5Si/$(� V)$�kS7�%11}|2� <�/i*�6QM�)+ _{u�u� _�| � :� �mi N� �`� Am� &_�  _{i� q� l��2�"�鮥 /)Un��^ ���.Mpg 3� --�9P T2A.y &� e" QzU�a+ K_x aU "�]F5>�� ideaA3to�;uD1A"Q;E/ *� 2� �%&$<�of�0s �#-��M� ��|h �$<er��N��a�fo��) O l�be ext�6r~N��) _25\Lambday�,�y9�7h.7 Delt6=�>Q^| �2� i=R�"�us*�%�#R��_1)�$�#> "�B�!B� -= -!=_1\Omega.% �u�> q�*$` ies F� d %=%�_1}2\,dx+� �s�~ 2��x} � } ��+3h . 2mo \,dy�� {1,z7��] \,dz�8J�M�umA�B�� binc/� >�-a'e�8� th�6llov9 8 truc�2 iten ��A?� U�^�$�N&�2�"andՆ21Q .��;dremark�sa�2� �y&�u�?:B�.��ar>in�4cbn&� �! lr84.*ms9F*� 56})'"6: �]BS � ��Z,{ intM�^E�a�:lik�3� "W�s a deno��&Z=-gaugeB8.Y ! 6�IQ5U} �"�!�wn,!���vaJ�2�.�i>;b9��M�9�a*I��D2v���"2)�� 1)}��� �?��� .��� A ^AQA��>%�"se� ��Uk9&combi�.-A>first on6 , aw &I6}��to givF�! �*Htau1tauZ9Q/) /��3>@ ��F�tauC+)�!Oa�D1-��.) 3Bi#"2.p)I�sai�:�p 2.24%�)N;�/2 �"e �)�D1)6!>9).�$�)3E�'*�#}� 2� 2-4J2: or:N�(�iz�(&�4B���, afte#;te�(E�re�� U3�Ta^h($\�(��($ b$>�( �($���(�'���$�(�"m1�+ $Q=0��o�(�C�C �N{"� i:f7go!�F"�M�3.Bz�&2"�-U� ż("0=e^{\l�  y}�+�(x�3��y � i Nris�,lyF� 2,[� � "� f52�- �� 6.a@�kn ha �� (&�"4".1�a] 6��"y)(4�&� K)&>1!��third-{E� ral �-DbvF��mx}�N=N � \\ 1t-'9� {t)�`2U=5�1 "�"�$}{48 -u [e%)q.�>��.k ����.�zUK�t�C"'��� }&&1x�1�w-�J��q�<+� �^22g| pX='.��41N 6n!�]y}� Y]4 �6A�$PPDEF�%D��+��+4"�"u� To� ��I��&R�mY*e�:k ,}� &%u�i�[A�["UF�%�%@Na-A���_z+ un�(2(� 4.10au 5m=*Dc'vw1>� Solv� �by) $S_z)�� "� Ŭ*�4Z"� E/��@7th:�K blemN�y��T����}{2��:%c6}+��� �� X9Y!!21_:!p n - �"�:O��l eft(t> S3S T ���"< �-�2�,���:k��t+- �����4.1J�("!*`A}��&GA  Ae$�X y5)+| &�.� �$32 �z*% C%&LLly"jU�A�'beq�ha lthogG�4 ls"� �U8 g2.�4&�$���al�J�� �H/&�2I�GS*"�Vd0�)�Cz�>�/al:JD.& F�S# � &�Ce���^ >!e"8ve 1I"�� �1�� b� 0�2:4E)ed"O7Jc. �!Ai�HU� *{Ac�T ledg�4s=\�A9�supporA+inZ t('DGICYT �P!��H� u�(&�>�r s5��o ���*2& 2}):%� Ca.2}.� ���3�0a.�-.�!�q�q� }E_4,�){4�,46h_x+3v_x-S-2Q���5.Bka�1��XN�Z �b�-"� Q�-�| S}{6"85�C6� A��*8oinH!�f-B�S�| P"sJ� vari�LIhom?Ric:�s�I2� �$cJ[3e�Lth�in 2�..ii�s $�+.Q$�iL d�i�%i2J kSF�h=\alph; V}{2.� n=\bet!)Q$�.5B�1F;d!�LA��AE $ _x��=R�B�7M�BU�F�0R�BV�� �i9�  u&�}3=0�:�>�E_2= I�1A� (-18 �z^2+6R S-q[!�_z+2RS� -5RQ >~B�F�1= -E_2Vmm�6�`(Q_z-S_z+SR_x-QR_x)-R_x(2~ }�_x � �Y&B�W�#�-c5+� �� LG5�ngeM&.*5-MU"a5��1sR}{3R_x-vS_z-Q_F�7:S�e ��&�0&�Q�G mO_{zx}#'�0��5�|�Eq`!iVSNV-�2�^2 -4R 6!+!�� -�EO}/x<S4� ) &!5A16C���� $S_z=Q% "u63)%�}5q]�_*su�O�.�6 1=z�2�!z:p"� :B�2�0�( 5 ڪ0� 5F�A���F�Q�-3B . .� ��A� /5E'�>F�B�X �2RS��m�}�-4R��10:�ZN"F�1�2�3})0s f�7lyB")�B�.U*? ,B} $\bullet$2#AJ�y�G!1k*e � ���."E% *� �$3$BUiM�!�!2"oMh1}�7_11�" _x-2C _2\L.X-�Z13e� 8_"+ 9py�6Bb  B!r�'1u22}) w�`tJ?q��:5B� si_{�)r�B82S:�8 both.�  "ha�>N+)2 =--A�-6!��#�C$"]�0_x+%��#�� 6>��� �3.�f��$6��'�2��6BTb{4"�3F�N�1).5�6F0f�U]5 J�ahz�J�I��E�ih1)�h�`�ͼ)�[ !B��_z� T.u% Df�@�q�z}+ O^2+ Q- } _z&�%1 { ]9�B& � �� d-z6"Lb_{i�-="bv �WmQ" �Oto�6 to ��J��T 1�YS���i��OS� 1^2 QS CE@��"�=6B v AZ�_"�<�� A��"m:6F�f�5�m�e�2TN��+!��ih)t�1)=}>�J5�3'�0K"�)�M~y1�m� c]} l-�M�y�}XfXN Y aT*1i�)�`\\ZoY� ��1}�f �ex}.� �22��`y x2� -\ *�� eDZ�a�we �]>%9F= ? �+V�q"Va f q�F�;and�aw���1KA�e�13}),n��%! 1^2+)B-Z4=�*126h:� .� A� �*60�*��# R� -�� � 9z3 � �%\ti J2��yg31Iޣ&]e;6]MmthebibliY y}{9)small &ib�>^ n^ M~J, r^ A�w^ H, {\it�6Pt. Nuov. Cim.} {\bf 2�J41978, 333--338�dbVDBoiti M, Leon J~P,�f na Mk,Pempinelli F p Inverse P[8sp@}, 1986, 271--2806om8Fn�e �87, 3e38�� N +N R ]2ND ~D �8Phys. Rev. Lett �7�,<1993, 1661--1664.� gP Clarkson P~A, Fokas~)�:�!� SIAM J.!0l. Math5�9)009, 1118--1209.p&MO &LXMRXM �0 Assymptotic �)gra�B$, Symmetry% Perturb�L(Theory} Edi�::Fg� 01} >�AJQL7}, 2001, 1043--1052. �M6K� Prada J1our. No�pEm%,2� 2004A�4--172q�QGilA�C~RePickeriA1-�. AM�28-,5, 7487--7492HQ4}]l:")/E�)�F�9aE!�4�0--376.:�*�d,Hone A~ N~ W)/)�1A26�_A�347--352�N02}NN �F� U_, 146!�47BW*+[W%��A< Z{1!200��29--14A�U�k�0 K�q chenko B~IEStramp5J1�ad124�� 91, 40--426&k= Bb,4!it2|s� Multidime�X al �Ua|E .�DTPlenum Press, New York%London�u9a/��2Levi D*$Ragnisco O-��-o�- ento�8)�8AK 4-41.H3!�veev V~BWSalle M�"it^a>/solito� SpaS er Sahin}�$Dynamics, 'Verlag���] ��Tabor�� Carn9re��E=1�� �-�$83, 522-522@Za2HN$H140�v413�v�>� � �g pageH9 docu!�} �s\F@[aps,pre!>t,�f\m\ of Signal��Q CommunHn, Uni itat Pa�ecdLatalunya, 08034 Barc+Ca�ain!�:�2}$�� ics �t, M. V. Lomonosov Moscow State�yZ 9899 , RussiaJh3}$1e�Atomiceᅉ} of�et�^#lP.O. Box MG-6, Bucharest, Ro>w�/&�yW)�" o}hpe�?st� �m�3I�Mi >�co-��ccoupls# unda!�5q�Yenc%� R-harmE�wav�s n op � jE�;3<$c&�= media� �Yh�7%���9�l�gmos�` $entire dom�hsir9I�QinFeN 4 de {XU�X{ P��fth�ku9�0Dd�%2�e f� z �!lcepE�-*= y�[-9��9� \��({42.65.Tg, Wi 79.Ge make�� L�ei�Ks�;ura��4�m�  a cr�Hl rol! @Y"�Y �*�?� ce. Ov�k�V#n�6!eads6�un�- pert�B of s@at empo�2E�oUb��Z"eZr cubica Jx Ex' �:B{�GNt� i�L(nd ex�fi ly ({Adetaiareviews,�G�5$Kivshar0,S>y,man0,Buryak0�5S���oarise�@�%�!$bal4c"�3�Mc(�}N �o�er��3=DG�um+�D"� me�#ismvp�Ib�for focuL /de .�m�pr�qsub�&%��}iO>no� n7a�] pha�\s�s����.�l�>s,�=�a&�UNscrew G diskXa�s n" dAl7 beam�=$Soskin}. H�9w�~ ��k 5�ufa b� shap�= .e.,!wp pf[|e-siz!�v� -X x]� plvU��(u�Trm%�a)+K�d�ex_ �n(er azimuthaVV��aZ�'�I�observeB�inEj�Iso1@ AMI- 8)m�&y  be Tnt�7 �%HcompeE�Ui� '�q vA�a =reI�v��dex mod�g�at%�dd� �. �'ag�A�ES��ad��c�@{[dbn-s���D ably"�)e�ti�mif5�pca>�'a �` odic �,nfedAicreUr>"s, do�Oa� exh�:ch/ne@z(topologies.xcD,�"o��odxo%,lL u��.d 1988-�f!�e��1aCa��> such�)lexRA, ��ela�}*�} %i�n�1:��!w a Kerr'w:  9[ crysn ��LMalomed,Yang1,Mussli}�A�ly,3�exz��%\zndeed)`��#r&� bye'��Ap��ImY3}. Dur!q!�� years���Afamilw� � in array#2 weak~f <gu�IG7qua>4�M&�� investig  )7HSukhorukov,Bang2,PeaF,Kobya-X2,Xu},d �ec��� �y� ^i�8w6�geo!��3 s,3�0n robu��� >Jm�)�� ��lo �, a: blem�I�4d1}fsI�� l aimAW�e�.  thus r�a�=� -�>�){O � r� �8 p hump� r��d�a squYK��gu�onZ�6q&� @��>�  n���ptE,a narrow reg� n1�A�cutoffQFeU F � de2}�rpo�t�s"� ��al.?iYSilvia}Gasn-typ��put� �{ �iesI ��iof"��f&z(�describe�K��elo� PV (FF�!B(SH) ��s4"07�IB7g9��04n bulk materia]O�abs�of Poyu @g vector walk-off*�!Aay} &&iA%^al q_1}"�@ \xi}= "d�+.�$f1E\ 7^{2}q ! \eta�#>+z,$< -q_1^{*}q_2\exp�>( -i\�1\xi )-pR � eta,H c�@�p;N�2b�2~�!���Z�2+Z�2}� B�2n� 2} ,�8e5�* $q�J?&2k!� /k_{"IaH^{1/2}[2\pi\omega_{E� 2}\c[M 2)}r/c�]AE$�!$q_2=�= 2}$ u%�E�n� � �Yw a�ht9��& FF��SH f s, $�=k(� )$, 22\��x) $, $�$�C*� scal"�i�coNeta=x/ ;!�=y $\xi=z/(�&!1)+A�=-�-%�)6'�h�m�(mismatch, $e{=-wd!�=B11� �-1/2$�$p=J�dT-�1B�1 ���� ���� $R(!ij)=\cos_)i/T)!/T)&b�G� 9hB�� file�c� $T�%*M[ � ��(1) a�wc�W�quant�qY� ���Tgy flow�y; &&U=*Q_{-T�^{+ (|�`|!�+ 2 )d!  d%>��zH �a*�W��Hrz[(E��|\�a �"�v4" qA;� : 21P(�{)�6� F��98�2��n�>(-a$�=Q-p2r1 �J-� ]%� V�� $)74 =\mathbf{{e_{!� }}}(�� / )+2-A�V. a��$26et5�.z M$� �y��s a` $:�8$. $ ax"�7�*� �io�Usolc}^A�f�$E0=(u�� .�+iv.)!�(ib\xiڑndC2 C2JC2ZC2 Cm� $�,6- ��Fr�<al���2 ���%Brep�"��a7��  verify 52}�<+2B}}["9:oX!5aʈ(V-l �+Eq.��j7*f���of*\ � ���s 16�*X6�"iu��� Q�a�!Y��� E�N�:,I�-P - #u_E!�}v +%4:� = 0 :n ���e.� % �/ ��:,b� �.� �:�v��^2n~!�~~.,b�� � b!�� .��%)�}~�2E%T �`>�� u����=���o&� &� (4)[z�#lly� a� ndar�laxR �DR6�qK"� �| one-&�"�kqN��{ �n1}&���2n�́h*� $T$,��  $p�6#  $�;��i��)��e� ;�z ���s {�/]6,\xi,J,pg664 ��2 (a�, �� A�Cc; 2}W � p)$c>�varffBa<-~y�Oselec_!/���e"� � 6'=VB � )(by $T=\pi/2)\�O@ varp-�� �$2 $p$.%�s�>est|&���"vcalXC�|inf2* �&�%��= Fig. 1@' �s ^�]R� �a stair-�[IOs"�#{t+uyaci2ρ 8of$"oxtl1:�um�V� 1(b,d)�PpP�!� �nsrmaxima a�# coincide �!�BCQl7 Wm� . NoWG� ula� *sB�!]ered  q%} U3�Y�� n� �kv)� the,�!XedF+ off-w}1?-�els5*Td�!r�� a����on ][!Y�s (�^Idx -JR]�/_�#�! si@�!��y�Kredl&a2�N�6+W!�l Ks}��jselves� to!" �A-�1:!"E�A)�!� o�KI�t'�. Q���meJ{��� 4--y moleculeAP orbi� *[�mntuӁx r?v&|���e}&ou e$B � ��2&j-d sol_�1, 2 ��Ctypa�!m�m�di!�b �!�.w� �$ioO- t%A learly s�u�nels (b (d�la� 1" q6�]�R'w8Itox5� 1D&."wA�E�I�to�K%|:� �(pea>� �"�C%(c_�-A�in-e!� out-of od�*e�ee x��� $\pi$�fj(�Bneighg.��Yar�+1��Ip$��no��S�t |c��(�6ѫ�u-fB��Q�a�d� sprnut =fhy@��s ()� (a))� i�t high�A@Yi�inly l"�"! h�(ro]u�ng�I!�ec�Wda�N%�ur-j٭I�n(ٲ�g�o or mor��aYall ot 6}R$e�% ���'ex�e&� :���cht)E� C�Ou�%j- � u�&�� willC{>0�Z��,| G!n�~-�. 2��"acggP�Ri؟ZC3D� 1�� MmsB�'����e%~ol��+�P�P.�+�+8� �S+ � %�i�N&+ As#��&ule5.�!>A���IuZ�A�a�-C.�c&3=�> (evs�f%� can�{��J"OR e{ 2(a)E]a�zooming)�6�v),�wAFeN�AH%� plot1�di+$; $(�-b_{co�m�!AUB� !h K u�coL�2��s7�� ]a>�W5s5� . Fo�-e� at�8$���b� co}=6.065v ) =-6ile� % 1.232$6�` ��b~�Q'� [-�b)]� 1l�si�"ty �la�0)$2�$d � .t.!c��� )��!�Q���)� �(� )ϙA"^RaGq!�S*�%�::N0={\rm max}\{-a/2,0\Iu�)�.�s$!��b�i�lyi�%� � [�) # Š�Bet2]1F).� �=b?E� �!�aU�shift du� -Y�1thQ0%� G�(theÁ���ise\T�holds�(o.4 h&0in9�>_ & 2Ma�"g*x&�#x.)affect ���,gy �.ᴑ"��2�,A���V�2 e f�k*o8� r�7 car��$ he S o ��u>�e�. More�,2!Aa �V s �t-x ���FF Q./�ms@ a�ri�3է fix�+4!A!')Q/)pr�:�!.�%nY�I�$�oB�!a".�!�>"��CAB��t tens�-nuu ����< !)evo�� [,�%by "@% (r&!�}([0)�*�R�(1+\rho�.+)$�RpxiR�� R6R:$,P��� r��ac��)%<4)� $ �4ran��f�M�#� tr� AvoVc�,sigma_{noise) =0.0hqW맅p��� �)�@>z# i%[sana f �� �k �!� phys}"5�6v�� (M�,A�,, $U$). Our2C� as. �� ow2�5br"�$R�>��k:� , Q{�cer�'��alu�aR^q��c%o�R��ǣ��*\%�� [ �> width of.-� C��>�:  . !��d� DP�d�*\ , aUpimi�2(d�� �Q��n�'Ee��%k$p=12�R^� 0.24eY��!�$p=8$2T$0.35��A ��"J"at��$decay scen`I��"o "� ��:���A�.� ge :A�/ � 3"�A�� of� 3r -�� �)� �6�!o�vicE4�M�^_�X� itia�F r�7e*uڪn9���\ d�+�� acros�  whol�Ɓ��:�dis�rs� if2e�ypeB�evelopscon�(�9[]� �N�(h�� clos J�� N��� encou*0�scillĀyn(�&. Upo)� ��[&>��5;a��dJ;(a-nd�te)u��!;st W+!(et�e�t�1 H �"/]wE�b)!�I�e����4E-�a8f�� �MT)���&[�&$8�8�Ak&)8E"o:��<_5mplet� �A�n|=�2�ut /aeI >e r� �/Nmm@<�/ <)7%,��!%Fc&�a� ]v!�s�f��llustr �a�a�!�+�V (af?50���E��scp ty�3"%^�bleU>)�QE.`?pa� 8� *�2\n*:�] ch���nPbej meta)�}��o':�*suiE�!��n[ �(�%2 �c��'Ji+m z�!a!B:c35 a;on0�H)ޡA��1$5 -�:�o��98zA�E�ilͷaNq� &xa7�oc�6s^�A"�9 *�2RP&jremov��aiA�i-�a�"e�fil�f)#sŐ�`E�4. Escap�gl� 0J�>� ��V� �zy ��:o j�`a�&�6's.�,�a r�9lly soK�K�- �3a 9�;�slE0&�;I�)�o%�P�t�:eBoutg-����[�?�7>%tJ~� s.<aA%)<7� peK aQ preh�eve�A�:N 7 1))�P&3  c2\to "7 u�a"*-=97X)7R6.=&� D,r,\varphi)=Ar^{|mw |} 4&! -r* /w( )>!$�(F^B ^22^2^ r^2 ^>�)� r=�+�  -� !]A��$ �EUu�  $A�B�&�&�,:& , $% 4w_-^ !� s. Be�wI � 01}=6=d�v3��VB�a�FF�M&&%�=1S F�y � O���-sƼ:�.��B�_ A�I��� ���|� v"�<�>ta�ffr! F%"�|�re"�u;�1�B�y�"�� ��of T O��(��� !�,in Eqs. (5))!�.�2*:6�i��J bes� �B�5. Lac8��1:Z is *� mpan�"e� �A����5�!y(d)) � �"� 4v' l�0Aw6c!.�C�%: -4EpB[cQ&M\SH.�($B \neq" B \ll A$)� � 0��" bI trol�C�%� VM��u:�.���4��?o�:!�i�:-�/d9E!� Y 2}=2`i�"�R� %$�á�6 )���~Qu� � � "���.xu�`�G1�exDg&?�� -&�!�� stag%�*� z�:�7�^2���D c6�#K �尥wc�p� "�alG"���$ xplo� in *^C�e IBU}7A�lso�l_�*:+s,�">9.q"2W? A A��:af��6ksummar.�&hoL ��"�-��(@in "���F~e� ro�A�*g! wZ�%m)�� !�vid.�[ heirREa4aZ6���9 :QiD�nUpwo7i&gies: (i:./�j � ty&p��b �� ��Q9A�-�m�"�-�2 (ii) an !oJ!>v"�y�h&C6�AZo: ����E}�Q;�pM2� ��c�)�9<"�KQ�>� N1 �FX|m P?��FY_��UC&. ��-Mupat���A��r ��,��va� !�, techBK�r��=�.��2D &H&. Also�T��L Erelev�% � a�N-& ar Bose-Ea�e\�o��saNC held��: A� ���r wao���J>� §eWD�tajP"P !yOci\'{o�Zt>K3P Recerca iWhudis Avan{\c c}ats (ICREA),E� OSY sh G6n�M|gr! �q42-2861. %\new�S6\% %Rev2}!�46w5);:��GXLrtorell, R. Vilaseca^9%\(C. Cojocarum_=��` 444 aR8);%B. BigEe@Zerom LR.!� BoydQ,"�_.)<9�083902e542?��M}h4Quiroga-Teixei!�nd H. Mi�Kel�:,IR1[ 2004%,ESIA��,EљI�Sammut,!�A. �EA -! �V �D��V�)3m28��29 �1A�BeG�Wica D �6�^187%5 2); 6�aziluF�^� B�m�%W:%Fa� �r�!��be�075�2I�M9*��>�!�Vm E i6�_056608 �w3ni:�:^��v^�D066614%k4v^ .-:^a�E�B:Ѳ S�n��[i6}, S341 q.��,*O!GN. :|R.!YJoseph2��F bf{1�i79e86�:P2}Zi,=�uY�0lberberg, Nat�(�]){4�\81I�6 ole�a�Xang�TA+illAn%Bi_�2e 10��6�Y�O Y..�ZaU�Ve�VysloukV(�c102EaAY��K[�D(S. Zelenina2aAVe �e766J��O} !� UA.R�z shop.� E547}, 137)6�LP!g , T.^wD�A�W. "N� egev��N. :$2�6��� 113920:�EwN} A�,!SSears� F��.�!iM. �*96a\ 0466�o6�AJ2\ T. CsZ. N..�D�/ 02�%6�a~6��)���f��14N�X50m�e5[ Os� ska]Y"; IW1 olikowskiRx� 710E�6�Yar3}T6�e@}�!l*��Ey�.U�" 831m�.I�{} ��XP.� Kevrek QZKT 0266M�12`�6} !� Y Z. M"JOV��20��B&;} 6K]J.ie%&0 5�)97� 6j )�-�. � ilexand�E��6!�6D2I: EnA�N�U�3);�B�ol,��O� nela.� J. HudockI�D. �����.8&�O}  A.y"�OA�&K���!$C.��ouk�V6/��A0�j5e02N��a�� ians(� mB. Cl n6�� bf{5� 7257 .�P�P} �� l, U. e^� b� 112 b6bQ)H��DarZ�Tsrtsch)�s� ^�1�173 y92�m�!G: F�{F�zeskak!�H.aNistaz ! A. Ne� nacopoulob�0� ��6�Xui�Y. XuER6 L:�  " ��R��a6g&_RjIwano�b iek,�2�.�=��M/W1h� ._ :A� $ 6�&[0� B"� �>)E!6m� 17�;�6d>FZ5V UU� U399JY_P�C�Tsc6k�k��!�ArXTs�mLopez-La6V�uderciA.���my, IEEEM &+ �49��6w"�;1l0Solja\u{c}i\'�.� ! "F�� � 4851�Z'2S HR� D6��28&0kBD �.�)�H8� 42m6��2,S. Desyatnik�:�^c��03� ET1); |!p05EZsN�G. Molin�rriza)�U��E����B1968iJB� �C^�f6�>Wx *% 6��5:G V�.,Perez-Garcia2~2�466M'B�Z :�.�A�*f2G%g6%�y)hBy D. y��&6�y�����A�S33N; h.SBTV�J� II��*�ENF<�3� 809q� S�nardi�>�P.2H6�:^x}�2�1�dq�wRB�l   ��FigqCap�s} A/1.6/ Prof! �b];!ofe" )�b�� 6"qh*�$�:=1.07$. �"2`d`E`=2$�d��h�R�U��.�# Z1$p=4$,>w5% �2 �Vor.t-�P �Fu8�3�C)�=r*Qv�27"�v�%p=8�b)�J �%MJ0 m19 �?�8�%<C(X6M�%�" 9/ nd) Sta!�  O-!!&2{]"|Circl2+how>0 of� �w!s lz>.-r3qt(JQo.1}=3.1$A�$, $3.4$ (b$5$% �7%c�"cp5 L 5�g $f�5 'pM�/�!�;ent2g!8#V�&)�%~>{�:!�- <4. Snap-shot ima��s�!% !Gl � +��by �, 0-�m-($�$.. I t7 aken��each 2.525��"�yd8B�]0 �5DuerE�L y��&oa�FF)�e� F�� A�a/`a.H�  at $�8 15$.�Yn�F�6�2�D%� v!s .�aends (@tB5*s �$!FQ���&�oH�E,@ p�� vely�3�&'��Dnewcommand{\Real}{�Vb{R}}I�.!`xer$Z$2#Com�[#CB#�l!K}�u%%��� --- \setl�h{ei}{43pc} >e8}{28pc�sy{��icfvtsq�}a�,title[Fluxon$ �!an��r �|j�=] {Exise6,����es�'pl�'��4ng)֞a�4v4Guy Katriel} \m{"�%/%Slf M ��(no(BHebVo"�u�$Jerusalem,. (91904, Israj@email{haggaik@wow.com} l�9p��d35B10, (35Q53 82D55 47J05)+$\keywords{�ded�dory{} \�A ks{Pf/&EdmU9L�Su C4�+R�in� al A*���Re��A�., qU,b�& Minerva F in(Ge!).��%�%&�sW ��M+XQ <ql4,��b@ �DaR��;I��&$ 7)&�?1*�,�4����on.�� Q� fY�!;���;aX�_dm��!=on>� GB��K�I��9> .�tH�2}}�Se�|.U �QF�F1\h� mclaughli�)�I}b{jo{�_{tt}+\a ��t+\sin�)={x�~FU�xx2 gamm&^)�}�4 P>0�U/>0$ (  $&�ddissiuve 9L+hL$ ?-�=��bias curk )� m � !�Q�.*I��.\-�)�ñ>,bnd)-(x+L,t)(x,t)r�i,;6�07<��w}*$Lq5 �ircumM)���TA*)��d�#it{Np}}k ay*"E�jo}"���$=e1^���(theta(kx+\oPc t)B� �Z� $ 8z)*��^tper!{�mz%N)=D\; \f4w l z\����.>wed%8 C�Q�assum�0(\l��)**� )2i�cEfat^�defk} k=\�b }{L}J&A��&fz$)UEa����~<GCa@,�5<LN (in � �A�}z0� at nl�iN� o >0$)�0|Q) [l-Bod�YAIIq"6^  a?o3eSu1N&�7T2  s}$2F�ng-f-}i̎)xA�©�Bt�nu}K�ta a k^2�B,eta'''(z)+(k��E�^2)IL-�� 4 (z)-��I� z))+�m=0B�s}1at->�51� s $( r,b%d �nua��!q<< (q,�Our-l��5 aper�toBQ!��p�& @.2�z� /�� E5s�/1�Po6YI06�or�"�;6 }1� main�,ny $L>0$�Zţ> �� �[,-,AKs�e�Mzj 0����To�ve_ oremi� �5ur �0�:�\me��!�jQ�4�@a�;al���du�%�pW�!�anK-۟&m�de!�o�q&�(m�$"C$9A�v�0m���?Leray-�%�so�5c�p)� uxilli�Rcalar-� d��7�1�z�zeE=hav��{ simib1t�18pr!N2W travH w�,AkA�{�di4?t�damped>Jdc-dr8Q sine-Gord*X�  kG .!��|]�h�b��,%�eietBx.]fw�9uld�U>�� � 9�%4 s (w%+refle�N� he�w�| `pinning'B�w ) -  d!sre :Chv o so�~evk2A�earqu�3�?tud�6ZN gAn!WXYrt���p�sriN2ally,-`davids��4ust, ustinov},&YMly +br=�maksimov��%�tF� derk�4 uck,., *� . * ]-�!$&� (�e�UM6Y2 .�� �G����JBa� ulum?!�ch���B1��-plan�7i�Igs t�CwX�qBoodI�A�2Nt� Ame >0, � �)BGiwatanabe,�on 2.2�^ situ� A��� ism ent. M��� ing 9�ōF � reiz0��١�$� �bZ`^J:%h � trea�2`�(�>ular) �RuΎ� N� (RM$�\=0wm� �=0���\),�v� .%Z� s�]>07r B���z��. An exception is \cite{maksimov}, which studies travelling fluxon waves of kink type on an infinite line, that is, solutions of (\ref{jo}) of the form (\ref{form}) with ()�percond}) replaced by $\theta(+\infty)- - �=2\pi$. Existence results for such waves are prov WPa geometric analysis ��Rcorresponding three-dimensional phase-space, and a very intricate structure of solu!�s!��revealed. Here, as we noted, our approach- func:al-�$tic rather!rn�, lea �8o the general e:, of Theorem %u�main}. Our method also allows us to derive some furt�informa� aboutxsecrotat!=f]H. In �8physical litera!(, a commE^,d useful way scribe=behavior�a system!,lthe `I-V characteristic' - iwis cas D�$\gamma-\omega$ (bias current-frequency) 6L`: \begin{defn} The {\it{?7��}} �%<$\chi\subset (0,M�\times  $ of!� pairs $( �, �)$A� i�(%�af, beDhas aR� '!� }), a� � $ j$. \end ��!��$$ depends,� course, o!fte parameters $L,\alpha,\beta$.A{ foA[AtM�shAk that.h(is `large'.5| 6x} \label{curt} For any $L>0$, $ y>  A'^�E1�)@)� _01�!�$ )(A��$propertiesA1,noindent (i)H$A connected�&i)�)�>0$crei�sQ�!� $: \in �_0$>]2^eF�S^e�^v) $(0,0 � overline{ �}:�-$ \setminus_) a boundedAM�5� Nota�atAQ:�-�s at o� fromA�!��ofA�6E@(. We shall�obtain���sQ�F+SR� (seAХũpe��}):�NA1}Q� periI�${\bf{any}}R�a|i�e�m�e�,�T haveq�!�andqequ��}mC(in1} \frac{I -1}{iC}\leqI &#-�W�; �!X��i�si!�we �assured Y�,A� lower){ in ��)a=no�l4vial only whenu1Aj!���v&t$completely�$��|y hold�]�} value a�� . WeF'��A�r s�5resj�-UH2O hile!do!- expect iZ9� �impos�o��� proof,�IbE�rp%bse mor%�ed�: exLI� $ phenomena��can occu�vd poin��w�1 investigEo (�!�r nume1 l)� rais�$various qu:K �i8remain unresolv�8We12 knowA��!� we�taka chi_0= $ inA#:, o?oHwordsVA6 ��:��S.�(smoothness}��e� Dide a positive ansA� to t�1c lso��-] B� ���,I� cer���-� s�  Y� >��� ���L��} Assume�>0 >0$. If^�k1} k=�i� }{L}>1�T�cr�con2} ��+��D k^2\geq \sqrt{2}k>Qt�C!�AEUba=presente��?X ^�rc}==\{���'�} ))\;|\; �{>0\�V9wh$BA:[&X (rightarrow A��X tinuaj� re.e in��� $I�satisf)-��-� st1}B�(0)=0,L 0fA2}\lim_{ �� }{Bb52= $.6n4 In particular ch:� �1a givenE�Q� ��i�V���As"� !�h ofAf 1^ceq} B�Q=I(Vtq� Let� �{��s�  =0$,a�u�ab�/ D} � (not}} true:��l?BBEE�b* ized as{�rc}) (%h� k2� 0$; 0 �Lwatanabe}, sec. 2.2)Ÿ !X"c i� fig. �a=!�,.8se�?tes4 `low-voltage'5`highreg��$ ݕ% } :$ 8term $\phi_{xxt�$  ��zing effQ� cur %�(at>st!�'atS k1}[i�Z)' ). W�4wX6� �we will$out whyi mp� $E�ai�rucial� ���differeG betwee �0damped dc-for;,sine-Gordon qq%xI�!&. A n�al�o�whH!N� whose "� 4guarante� Fd,%uniquei�h>$�$)FG <"G� a � B���e0sufficiently \#R� uni1} FixNZ�<5�E�n�AF` o3X %0a� �Z� �䍑 } O)�oF hand,�2n ,multiplicityp owc .* does�E�D0 ,� � �at�' �F� rangi�8�6leaG1R8s QU�t"LiesF��} P I�e�E�r, u�bec stronger}l^vlj 6 � k2- -�qH�%��s a���_0a��E�AH0 $0<\epsilon<� 1}{2}7� X� P at �B\` �= _0)$%�d X\in (wme_0-�)Y�, L�K�t��st� B���-�stinc:��Y�W��� ��%�pI�� N���P to bistability, jump�hresis &� aŎ2�� u �ZQ � W�6�ap�.i"<I�=� BJ s �r, Ѣ�ary��r/J�gWs*l�+e �eitvee��all}}��menţn E�%d)s%ne�%�paper�validiminorG�@, i)non* arit� sin(��� A�refE��Cri�p '�+�$p!� an arbit!B $C^1$ $J $-^ odic"E ,� y&$\int_0^w p(k)d =NAn k rtan�su�Fw"�address)2iIr� U�.�exa�:+it i )hq�%�9m�&Hmʁk�"�"�ony� *�A�y�I7�9�w>E �!�!ainaG�  impl� 6�� TosoV first rec��A�4problem into aU a*d�,@E�CLapply Leray-Schauderajory. M�plAG both sidi�)gnu}��'(z��integr. �  $[0,A�]$,�� C&  �ccount� >�*F z  \Big[��^22�{M�'�)^2dz}+�H V((z 'U] �e:&*} By%s*� %Rv�isab%�. $\�? as sta�in Pro=o]a�}thuZmayC>�deflaL mbdav�tF��senTu} �4((z)=z+u(z),��&C�$$$.�� (\bu} u(z+A)=6\; \for��z\RealBj6Q�rewrit2 E�asBx~ fin} U; u'E)+!�(\l%6 k^2-"� E)u.-IQ uA=- ! ��))+ MK 2=0:T} R:[&u2r6�E&� to&Y �,!S)$�$ >0I F�i�bu}!'Q Bya�q�m� v�L;o ��Qint�D \pi}6�%c$s+u(s))ds};-)�)�}5��8 �.9narray��K ^U7&+&�98\nonumber \\&-&-� �>G �Ye �a�*9f�6' is aU{��Z�naui�9+c)+c�� consG$c$ (8 ofP Y�� � time-in� a2� ), hy adju| gZwe���ZB��eintz}:�Ak�6# lemm�aBsts�ny9�$��,u� z� ��  ���j%po �ov��v:�(�Vs� s}+ i�&� $#BD� )� .tog�ş�9��)6�:�wI���K�:d*}�!) up: sY��. Also,a� a_ u~ a$Mleft-h�� .Rt�' most $1F e7>�q rew} �-1*�jI� =42��1h1}U �i] n V�4v�{0.4cme�de��a X,Y,Z�1��JZ6JL^2�Je A\ norm!# \|u \|_X=�( nka�'u�� )^{2} � SY�S�QZ�QrP.$$�au$vI5�"2 2�v(s�5$$, develop >w4 a Fourier ser� a�u�!g$Parseval i8$ ity ���F� ͻwir 2�(�� s�!>"v9H:�} Onn Wir�ner'� equagim� �&�$i#�w�often�',: $$\| u\|_Ye!\| X a;� a} Xm: !Z- Y>+ Y!��efine� amilA[ map!��&_"� :Xia$ Z$ (� \neq 0$�^> } N (u)=B� +E��Q�- ū!w�}E*a n/� $N:Z:�bn�n}N�sin< - y��J .>� SolvC��>(4%is ival'tox>:JQ�faFf�b�M&A3 XB�� .� reduc�qo: find2�\inLo,�) X$*� �fa>�  (w�+�,��a sa1M $$�=\sum_{l��,}{a_le^{ilz}��No��E� $.�( &)=-��[(l)�&F#$ l^3)i+l^21���l� ^{-1});] J,$$Kk!���p Bp pBpZuwe�5Y �*}\| B�0u)\|_Y &=&\| F>��.�}j"�\\&=& `(:w$l^2|a_l|^2J~!^2+l^4 f� > �R� ��BiB�2�.!�l^2 �UF�2��)6 �&��&�6[Bmj���p}�[=\ 0}�]f�=��n�2��Z"�Q�ѤY�u��� invb} \|�-EO\|_{Z,Y� �2/��/� �6$ (droJ �`�"�t&2t�))^� stt3���^i�}{| ^2�-1|F���$*B)�1�bX�:A?l^62B'y���1��i� �Ne7fIR|=� jWI�Y�#19��uR�Y,XM��� D� �$F:>� 6�ZR�m\deff} F1��I^.� io circr Ceu"d6[" b� fixp} u=.|.� �(q�W*X �$c_+�L�$ s $Z$ o�$X�)y :c  "c �^"'n9 . S�/$\|.+ �xL^�)eq1~$� }1 $orthogonal~.j+}$2Gin.�to��havb� bndn�+%� \| 12DJFUj� I6wvb� ��"�15�MA<\|.��B�M`�X����N�,\;� h>F�ALexten1e6 d%�.�a=�1 $F(0a#0$ y� :�Dis necessary becaup*]�A% 1�0"s=0� W7%s-�sY 6) ��9pco�,M d�0m#a� $F$Tes a_4�v: M�B* Y$, k(�2A�embed�9of $Y �ou�$d>�\% $���" TZ"5�-e �9F�wy $$ (�H!4�*�$�4�Z+-�� t"n:Mi`9.!0�}_�%0"_(�A���*��3d&�/hypaOse?2d$!���!� ��9�/s 6.�i[��.r� chi053�5{m',bH �"$&fT_0\Ff[�.s5,�$ �;all��8�; claim�&JO6*A Ph"t2t*x3=:�)<�2!Qi�3+<�%1�(i)a�-g_:c1&. Pa�:Z"�(s ;!��9����fa�6�a���2�A�'~+�>0�r�is�R�A_� X>M�7n�K�8,Q�JS\LR F:$ (a2� ��g�8�I$-axis,� Q� >0�\0)s�� {\mbox{*��5 O,�oL!i!�%! �$��ainD$+' 1j*s.MLvla� �$\��2Xy small&�9o_�$�"�-2��n�Y3*=&� $.^ $quare$ To!�+a/�:i'ies��y (?q� o,�I (a=� ?2�m*)� "��7�F>- !$} �ib�B� (1)B� i�922-e���b, X �=]{ 'r!3�.�) it �2/2��ZN )�}{! �c}�9,>(1m � ^>i*>"�A%���ͪlinf}>~li�*a:F�+��FX� � T>�+ �J4^ Y,� le���s0 "�I��&of�$ >�**�4sFG#ReQL8& A%j�yA.� *, " yM�� )�o $v=u'$,.N�&V : Z� nn1}"�2�,.�;1�f�B"v�#:M&�&#*#� (�� ��)~O6n!u&P!B�F�Di�J�t3!eB�� Q� nn2}:�i6�0hm%-^2.3G2E�u,�!l)R'�"' $:[V��|&% �b %�A%-vJ��3�/i�^ �)^2y�"",1� ^\plu�(� .��:��%jV:f}=0BC�gw�&I,��)..�:\���  (�G>�K��"L"K0_n&�/n}$ ($n\A1$�@B'!.� )&�k� z e"�, ee'$n$, u:_n� " 8"�H_"�7n� �. B�8.�R ��.F _n2+ .h��&s_nu_n0 Bu�>�1� 6_n\�$$/s $2�:$�M�-�V�K�� 3Vt %@I5�)�v!�1���-��~�-&� two š"?FH v "�5�4�+bMC�� sl1}j�C���M/�����*�.)6% Y$ (il� j*Z$ln�ion�� �V(�Compu��$Frech\'et JO ativ�+ J�%M< $$N'(u)(v)=\cos�%v(z~�%.��(ds� "x WDA7��L&**$"� $|]� jy0�N�M�8an*�i�� uFjFj A�6^�AL�J|��Z,ZF1� 44d-�������& )�� l)!�6�mT} fdb}\|D_u.@ �Y}=͢k:�����J) kn!n � /��*k!ْ}6# )B��/,��9e�)"~  ~%UJ6�.[0l} Fix �6�i�=@ �&e�"�_:C>�%.U��[0, ��=AW1� �o ��="s@�a9we *=.u9��@u-.. ..mN:�E�ac��Enis�.�D�f�C2�M�~� I� easya�[E���9�(bl>�) >� 6�*| b*:mmC ef� :�:A!�9fyE>��s2T���E�m 's fixed-�L"�Q"� �"ea.�. {85��=z�c5�&:6�>*��0U�cit"�0p6�6|(Retur&!�e��JA*��"gQ�%Z*, )�� UK%�u��("� f�E< h Ei�in.w�S% ��at<@(�2< twa�is QMTg must'^�imunb} 0Z_0F*V� ��2�_F=T�;ifa��;�[ �.*+ byM� ����deLb�%con �;> �m?"� �n&t\�R(J�SeO � 0=T( A_0+V"1V�3���s�&1^��<�+> �� �� 2"�~5F_F  .�k �) meaNaO+ZU:SU\;2�TN] _0o�6l(O�_0�4"= � \cVa]xBJ��G�later� at �fP7��J:}Bn�7%*^ >0 �>��>0.$$ |ThCGict���'M*�B�fac�7aŎm���Ce�dŇM3� would�� y $u�Mbu�Lis ��check��J0<t\i�~� r�nlQ &�BM�S�)6!�D� 9[} � EL!��B��F4XOI aQI open  eYF!] �b3F� v��E�� @�T �T M�{#*6�Q��graph�&-C:=\i$a4{i1"�O$a . -Oopo"S�^ gn�%Uj�k1}.� i.�M*�K�"x��6� m�� ^% )H� forbPseA\= ��.�$&y S�� �J #2&jg R.� �2$lo�%�%� �A0&� �1� :�� W�1:� O� � 6�1}�Wa s��mu^2$^ "� �nA��26 to^�xinw} p(\mu)\equiv (k^4-1)\mu^2+6`7-]\mu+1g..\muIa:!�~�Y $k>1$ en�Z��aQ quad�F&ZI �Im??| minimumIW�ve$ 0)=1�� ���NP�Mi!�m�u�2z$p'(0) �!V�n  J increa�*A�� M�"4 -�!Q� . A�G S  aA 6 2 ` I<�L��� ���6Ne,q�� �BR���. !��&J!��} Dc"� \&� >��}��VŘ $B(ZA� ��ar�� rato�L��toq�>�n� f#u�PeAK=?precis�\� last�JteH8!N�� -95n9B�.�Y2��4at breaks downs ��� isMponsible�z:~� at case (rM i.e.OOe 3�S,V�Sռ)`����+X�U��( �(&UV fig�UI�a! at,XY.�N6J9�,ot:�x2be glean�K�*!�&�m�defl}): =:%n�L1�&�k}n coe�S1D^Ves2r%�eU�6}8 vanish�R6E�,�^�JEp���$*���c%$0 o]��"� Psi ���\ �#Adr!� Psi:y�]��:is)G%`^,.!si}M�)=\,*$F�JsgfiIFq[ �Q:�$��-�YIr.����G>C  for*L6=yposi}.���[)2+ +�Ɇ��st2:/ l"��(�$���%oG�|� � �Nn? A�R!O��%� a�re�I�F& }�0�,"6~�VI . sl},I �>qB�(=+�:�:e�@ b@ .�s��&&�Z�$mI�_0.&�=-�M��%�?h �s�al lJRI :hi:�"54%� %�/�! ���$:mL4G^�red�eC Ib�\$ow bel�W�&tstc�_1F� �Z^�d� �:@1) 8 .�\;�'�\�.�, �8�js�f `FIpj���q!Qis �:B�&I Bt :����:�UeX!�n�5O" $I B� Jb wel&.pDF�*��, �ji�� 7 �>ev|[���B:!Z��e( 1}{1�FV>:�B}=O(1) np Jp�]6�=E��9��+Y>�*U� ul} ]�]�=9 ~) }5 [6  -.�-6e]:�"�PWe*v#na�T��1} &&n� \\ �@=��1��)[J�2�-}+JC���h]."xD�-e�2(>�*J�+)'*} !B��NղN�*cos^2(s+]Z(1.&[,�:;E�-V\\ )&rw�_=[1+\|��F^2:5E 4�$1+z�6{, z, ��F:MU�5_s =>kqjso�/N�a���:"&���k&� ^�b� B�BB {�&J�F++CJ+a YJCV�-urNm)�c���-�� $�j"�� / �7X$ $$ f�)�Qk^2& �eBBiH[k �)^xlO>|jkA� �pB/XI92P(XB� ].b��!^�bnE6PvT��5 X = "D ^2r� 0+uLN0aK.�ld"�[�b"l�j\*� !f�1žaiV�Wva�^Vl�fBrf 6��9�@X�� .�D* "�#�tA]!��� � 42�$\" 8"�m�a?SN� w..��5��1��vZUu $L$,�$'!1*>x6</5t�-p;*u,97r>U60�"$ (o0{1Ul~�i�� z - opo1>��;�9���#`ian> n/Q"�W ��V -�h] {\bfquLk�� :d�e&YA�o;+�* � $FL 2nJ>0 *Z\�D*k!��G�c"d�L)Y A���of *�].Bq#�) �)6ZCifxo29. "Fz�5�   4">%I!� ~A�:i ��,�S�d=})2� C!�4YgD display) Qn�a on (&(_N��0 hE9A?.�ik�I unj$|)"#regar�"se)[<,sup�ts %���^:=N�?!�29�691UnWfA&Y61�3^��si_g"�"S[ f)C]w :�H�=uti��&%R.*��kqz�^�eq�dR��b�'{lZ�ITVJar%��9�bJpsiL Z�Z9U�mF�B~�$f3&�N/ �Xs e{��4 ds�H�u(�p*�C_ j�$ (�k!@pa�Z�=.0}�z� labB.$w� ��}.X �8��q:^\l�Wl*�8*R�8} F�Mj)J�<}zf �^�p�( fc�)I��3 |J�I�lz"� li g),�C)a9BY \� t�A&�?$global max�# a��z 5�#I.uk�}�ru� ��!���j�s:a��0��?�_�#?����a�]4(�#3b max=�q_0�h�max" >0}{J�F�<Wdw ft.lnz�q�V�a8�� choo1N"o/_1&q/Ѷ �2> �Bv!l�B| _1)<��e�� }{4}N,G=F02N0B��BA�6�J�*  :�(�v1��%� 2S s�ab+asm} |�B�-0�J|B(2}2�n}�>�-_0]��1�]B5*GA�)7 6� �E-� ,��llph�$,^�m.>_0)" 0->"2&�T" ��% m�QFBdU}3AvQ�B~B8U�28BQMorP(�?�v^�er�*_�5-�1}J'B�=�m.�,_%�� )� $$|V�]�)���]�/-�.$$ T.h��m&{m' P?m��E�< ��^^mE�N| 6���B^ ^�E�RWA��N�YRNA� NB���b�"-�klsorLmm4^Z�0+~FN� "�FB��&���76J ?W�?& �5�F�/�nrWxI���E�Q?M5&)S� $ �"�&in 'quC@cA�!l> AR*)�� |~c"kD_1����Ho6�mm�D��o �o"& .�No2�Aq�, f�,?V� es/ �(,�{.� .�, c6����re&(v2���Fu~t.�2�+qz thebiblio62 y}{9�Pbibitem{brown} D.L. B , M.G0Odest, B.J. Miller \& N.A. PM�son�SCo[@ !�!�y of �Gtdng�ly �Kurb�Qine model7!�(Josephson j3-�SSIAM J.�G. Math.F=T54}} (1994), 1048-1066- �4davidson} A. D � Dueholm Kry�|� F. Peders�$�+Exper{�ti2M�� rap�.�Solitons� Phys�;v. Lett�P5}} (1985), 2059-20622�$erks} G. D ,�Loelman, S.A van Gils� T. Visser-�Trave�+y�i=/�#r�q/ }}, �ica D)k180!l,2003), 40-70.�(hauck} W. H � Kinkd�oI long9� 1�!/ )�Me!��I. Sci �2%� 2001!�189-1217.�katriel%6K �2"ytJdiscre7�Y� ring�U� � Anal-�36-!� 1434-1443.�"� AafMak��0, V.I. Nekork+�& M$Rabinovich �SIL�i0P nd IBb��rW Int.aCBifurci�\& Chaos)^5�199�491-5052�claughli�;W. McL IA.C!� ott,��Pera� j�6~� dynamic%^Akm#AF18 �78!�652-1682qust!R V. Ufsov,aDodera R.P. Hueb��, N6�B�Fy��V�� ObozD i�D ��]��e�aO��annaPZ�.�e� )k69 �92� 815-1818.#9��;tov>���M��12Fz.�23�o9!P315-3292p"�0 S. W��, H.S.J�jder Zant�| Strogatz!�T!jOrlando-�.?�`%$�!%RJ��E the N�.�>�97-K 6), 429-46�4Z E. Z@Z , `N"�lF�gale�E�\its�ii,s I', S�ZLger-Verlag (New-York!�99a�!�endB� docyk} �E\$class{elsaIo \u��Tckage{amsmath,amsfonts symb,bOP)��$icx,color,�/(pic,psfrag}2Turl6��+^I�(frontmatter(title{Secur� �}�a�;os-bas�$eniable auU �~T&schemtTor{Gonzalo Alvarez\cor�C3 }} \� {Institutf F\'{\i}A� Ap!�4da, Consejo Su��or de I��ciones C�, >xficas, Serrano 144---28006 MadrA�Sp�~ yH�[�]{Email �(: \texttt{g �4@iec.csic.es}.>b%babs^'} Rec�, a new- wa%UV�0ZH . Its mai�H igin�8tϘQ2� encry� -hash�lle~�gorith&�6$semi-group!�� y �� Chebyshev%��8map. Although o �aX p�9icA ,E( insQ@��inE4cy�_sh�5|isӂ] u�F���7nad�ado�9e-ՙercˇa5vi�:�52I*l_{r%� years, c��j� maJ�P of a�b�!Y���g��%�R�2F-�Xiao:D͕A2��I��u�es����� ors'2toj9``Ebb��t''~ bUtradix��qB@�Accor�eto9:0Katz:PPK:EuroE�03�?he PQ��!S�b@Co Z3�^ : i)>a�J $\bcal{S�S��ed \emph�^ ver}�Uul":��P A��ᯁ���a m�gge $m�<a�Fiver p R}$ Jp(verifier});a] :�yA{JB`I� conv7jard��t�:� was .��6�S�"A�: tack2�M%'c�� a�0n-in-the-middjue�2N� R}$)AWzEnotAA�.�:��"5�!?�$!�da�2Ia�(M�SM��"a!=st>��ofbD protocolsm; b � publ�;d��E�Mal6+(se� ��n�%8rey�#0erein). Usual��th)"� E�ia�%��@ a�$�Aقa �c key6�ժ.2"m�gɦin�U��s�ű>�� c"dl� bA2()?c V$to�> lize% agre�?��j��&r� :ISCAS03x;P_�h{E6d } �7B�5b9!log��cN ` \[y_{n+1}=by_n(1-y_n),\]�! $y_�W[0,1]ia�("n$� $$3.99V�ursivRK:b� (x)=2x 1-T_{n-1�-Qrm{��any}\; ntp" T_0?1�<T_1x$.R�s�sif�&J�:�p(T_q�=T_{pq�$�0ommute!co�itionB=q(T_pIIJ�w�A-� makE�m elig"�K_cE�(y��*�io� r� !�BQA ��"��5A�a""> {�b�eng�$ate} \�!*���[&�R}$���*�lya�n rkmѫ$Yj$bV^�)s >lnd � $p�i utes�$P=)�I<sk� $P�2�Vt�ftqBtQ=I]2tQ:t��NFArąv&� !�$k�QA�U�n��"�>K'�PL]�P=� Du�JR,�LqK8�s�ymunF�Msteps��usN�M�On�nd� "S�&� : $x��5�} d =wm`r�knw�l�p��.ac�!Xa)6�*K`�d'4# &�reqk��&G%*� ob��  $(x,��E% ��y �c�t!-�6or�{e2�n$W�{:M�4�i}�cN..F�Uɼd�KC[� s��5.kbe�V�C.] �s $E_k(mmob�/I��� $H"si� anee .=��mm�.O 8>Y�6w>e�an>  $D_k( H)=m.I same � �d$k$*�E:� !�2�'� . If̛ es $H$)mH'$ei��cal.6��0s"U��t��\6�a%�ҁ^�a�} thor� � pe�MH�� reaAbferS�P work �J D<6x�eK ) �nR2�>���%t�#z�.;"  siF��o6 .:��.. ^�R��l!� y stX�9 �BKT>{46<UGit E!howMA&�I�iz2���Avul���� �-&i?osen-"�E֥w.u s. A�Gc� �e, 5�I!-kA�W�2 never reu` �*a�a�bec�i�E9p�W ly broken.h�2� �=�Wu�,&su2��w key,�9���usKili�ng� QH.�%�"X�6xpos�Uw�=$p"� r=^ evenO+�B!rledge�ey�� (`�!b$)��t�Za�f�f��|�t�fs�gAm'�ch�ҥk=H(m'�$USa#sԯ�!�avc� �k��s.�夽���hWalwayH��;��t��!��,R!p^�1^! "~ �!Drq��i@�Jcis� dame++to avoi�e9s x#e�!p��bullet!e �2= type��mQA!����&� �h� [1� 1im�<-�rN[%�p�� Due ���{lex"��A�!�J���zi_�edetailed� ane�. Jj�!2>AZ��B�Bergamo��"�:arXi���� =���)}�-m� 1co��2� u� �"Ѱ�A:e# XU�}pp�$!�I� g����� w��%L sign`q,� i���w�� weak spo"�XSR%Ufac!fr�v��*e&�s pas�-0o%!9���|--��BKk���9&����s� .� $V WZich��Gly availŨm6�"y channel �:ae5"� R+To ge%A�reG�R�@*! N�ax� a`^2=x'x� x�C^FrI�s � {p'��'}�Ba� G��$xl -M�DM�"�!ly�da&� '�1 ��N�&� F�![p'x> \pm\O | )+2n�{x)}Y�/Z| �r�a8��E��V6���,.a���:wo �&ar'sA����yb�Y.!�j�t� forg.� �:/��>� Q�+�6a�Oy f�)((Sec. 3.2.2��), @Ta�����lI >�BZ Q�"0&b�3��6 *}ffg�L)na�&�G�wy+Fin�ŰI3�& %�$eU%�� cio� l6]*``s�� ۰mH��o� � aP #.K"�%�"4mF�s''Q�ss+�on��ia�rp�1"0sen' �i?L+i� sgdtha�1Dal��� R�!���2�s�)�%�magnit��slx�. ( 1!�)�W6(69 �sfBr5 llustr%�per�C�(NA�!3&v:��-`&a !Ne.M � �9U���cD$r� best))chiev s �X 7.7011.5 KB/�0 a 1.8 GHz�� or�k* ha��.�!�" s,�os DESa�AES, � �� 21.3�61.0 M�V!�e�G52.1�? �-�Dai:S *70arison:URL}. t*I��.�Bes, MD5�SHA-1j �a,most widely �, N�6.6= 67.9j� 2W���: ��Zis �^dAnb�"�-. F��5�aN. vI i"�-t (Q1,000�10 �Ii,�en"���imilar2 p= "f)C��^Pɠ*v,"/ ~� oi�vfdo�'��E��).w(A�"f p.н��o ur!&���!ge&4� n e*!�us vio@i|�B�R'�  J!cW�f\ �[ (conf��0).h.^ �H,n}�:C 2""Y4��*.maQn"�%!�3�Jh� �$s�/ ly r��� r�E,!�!;��Y� a�IY���E�Cs�j�(M�u *�bOɡ lack�, a[9�)6"w ��S �.�y%ouragI�-Je�s� Xe � "eJack{Tha�9Hto Dr. Paolo D'Arco:� hel�suggesA�  _up��� MinC�ri�3DCiencia y Tecnolog�3as �3e�seD1#ont TI�01-058�SEG�0-02418.}f%=10�\xpandaQl\ifx\cse(url� L\relax \def\url#1{�,tt{#1}}\fi \VI$ urlprefix>OL {URL I "8��6�1$} G.~\'{A}15, F.~Mv�ya�=L~Romera, G.~Pastor, �0&h"HAh4n: L.~D. San�h`(Ed.), 33rd Annual 1999 Iv�al Carna Conce on " Tech%�y, �2,G4, pp. 332--338� �8&�"0�.� 6�2} L.~ , �~ *� (y: A brief � view � Circu� Systd(Mag. 1~(3) h< 6--21.��B3} F.~6, W.~S|3 ��F2� � Traao6�( I 48~(12�$1498--1509.�2J�3} S.~Li,�8�0new?igI digi%��s, Ph.D.2 sis, Xi'a!�Jiaot�=Un�/s�� ina,*fof� ataA�url{http://www.hooklee.com/pub.html} !�3� QY�2qJy4 T.~, A su!5�å$|1m.V��A�= � A Cogn� 2~(-k 4) 81--132�<��( M.~), .����%^+@+<, A 240~(1-2)(@$98) 50--54.�^_4�,a�u&.MskLN1��2 mI �]*R A 2�91~(6U�3!*382�W� ^�} K.~"!� fast%�}�& 'w.)c)� �) ���nAA 298~(4 �$2) 238--242lAVo5} A�4�5 =~Jَa�ry�� �c�5�1{�t!�,303~(5-6) A�$2) 345--352Z�>� = comb�)A-F�K ���A.QP 307 ��$3) 292--292{vO6�>X�fpu, Z.~Ji, J.~Zhang, Y.~Cai, P*s*} Y�-M�}��aa s� 6�u�/@-��1��8� �;um!�&�sheX 6G 309!�ap!�3) 165.l�7H7ei�~�9.� �7 �2.M�� 311~(2-͠�72--172�r�45�G.~Ch�DK.-W.[8,5�1Ƒ�-�-���1�:}л���ermea~q�32]�4a368--372pf�8�Q$, Z.-H. GuE%X �� �"s,�s ">AF1al�$23��(5) 851--855.�� D.~&%DLiao, y�n e��*�4��em�� & :� �"\F����5) 1327��32]R<8 J.~, )�d��-5�eproofe�&�j6 �X# J$: E.~BihamC Adv~�)�logy-"�8 �: Vn1 2656� LNCS&xA, %6 211--222��N:&��42( (Z.~Tasev, P�6c-A*7bas�#H�Z � A�cee22%h �  Sy�(um��"� ��_ ems (�'BG�~3,�003 2a2��u�F� �� a�.~�F �H�.-A��mV� 326~(3-M�e�)�12�r% P.~ !, P.~M�H~Santis6�"Z �}%�c$>� �^, bmit�f;O+it{!� � 9�!�. I},� DtN� K,:cs.CR/0411060 ^% W& iA�ee]�rC�o�zr 2� "� nY es�>X H~weidai/benchmarks.g ��V�D(\clearpage\$style{empt�_X*{Figur�_�Lf}[h] \c�r���s�Ds$Sc�?onrcnf*�6S�aA�r���!$how an att��6�s =7 :7;.67�017C siz�(.P = (`2"�2)/s$.<F�betnpr(assoc�lU5Z*^6.Ond�ur�%%_d"�E`�>�Ejfm} %6F[�:e] R�EF�0dt{{\rm d}t}  u{{\bm uf fdk1k 2dx:x*bm9 bm k Detal{{\it et al. }}4F [Energy sZra� SQG 1Jul�80] {Large-scal#&>/@surface quasi-geoAop" E+Fu�'[C(JQ��HJ.C. Bowman]{C\ls HUONG\ns V. TRAN\t�{P�&�E LeE�s �Fe, &A�Warwi9Cov�24y CV4 7AL, UK}q\�6Jk�� NC�BW M �nUaffilie'{Def��|�a�ESaNs�:jM!} s,\\:�,Alberta, Edm\n, CanalGT6G 2G1!�{7{12 May�4%win J�\(form 05 Nov��r%9b./y$ \5E4�W&�E�&^'umrtwo-dim"7�Y g7IR��fT(SQG)"� �s!Uhial_t(-\Delta)^{1/2}\psi+J(,J) =\mu 2$+f$jYs�(an���nsfer!�tU� (rv� &�qu�1�2OT$1=\langle[2�4�]^2\r /2$ � 62V6 �66(kine���6gy), c_\Sy!3 g$� oY/a�~!F a6#gP&u��K�.3�~a!izEct!�9U2(k.s��F a� $k�n"�`�Qrse-tf!a�e�+dY,, �xsi`�N� wave48=�be�_�d Ck$�re $C�.x�ind�ce�. c ndo�CŲ. Re (%!]2-S��A$fir2�A���i� pre�Di�Q�$"q. ɧa*$I^,>Ia~=  iCree2o�if�drapidly Rn�Tid a>ch�>iQG�:X��bal= �$� Coriol�l�I��t  dienS%yP�u� n�(-��a�Pe)^ex�"�is nc&B� fE�� W'dt>#i�%��a�.�OJ� CngT!��{��� �sub� 2�#M+* r�%&�E@�\~Cc rney 1948�@71; Rhines 1979;U losk#87�}�orG�,variet �>��U4�C7' ppea�H�Ki��la$A�p,j��ye +f�"�s����� K X?!$a�rl�5� ofA\"�fluids.�Js�+� }�-�={@p B�:6�|1�cA�ew+tudy. QB�f %Pb�%<�mermecX .�streamLd $�S(\x,t)v!ci�� $z��u6ELZn ���Minf�tshorizo�+���Y� eiK�2 or uD�. N���EdecayE�6#�4�+ʚz\&�;�Zu G(fl�,� 5�د$z�b�v�#�gXI!g?=  matc?2. temperaE'field $T-6, i.e. |_{z=0}=\���zV  $. ��)�w�zero po>|,Cvo!�m� �.� �-� �8Q$2��N&�U$O%�� (9�)2�Lap�an.��!% or >jV�:byF!\widehat) k)=k>�k=|\k|S��>�+$B:�i�F���> of�p�*�+��serۚo&5T ��<Kadv�#oA.�>�a�'��!��(Bl�S�8:; Pi4hum; , HAh\& Swa[1994; + 5) =ewtv^T�} U��~ &=&&�na^w� $J(\varphi,��Y�x vy! - 9x!�E� "�*.5!y� .5Aep��a�$ced-dissip�v&P�Y^=)K�_E�A� 9�BA3wE?�,*� Y� \mu>!HPKR'g $Ekman pumpAL �!M���3i�X d (C� in� 2;� 2004�iJLpsiU�)�edan����iI���-W ��(e�-is r�&ond"��0(hypoviscous)9 on u��:f�D5��Qo&�2��e�aof velo��e�is%݇ingly &f��h� tmos�Pic!D�BAle X,}d vOd���:!��2$ff�)�lsl?nor�(  �to��7.,\ge s>0$ (in��. �� ��8�bed�/syL+ ). &Q'� 6�.�kmtes b%���$ n�.+f�<�3I%8custom�-��X�&� 9-!^q" a doubl`�� of� �s;G&R��is �:!�_ via}*limit $LJL)/Jacobian�����A,)$ ad�2�KZ:Hbpi�wl�hi :D�=-~�('c�h $ %p6Ichi%,� 9�����B�l*f�s�A�hF�)e�&* �2ic{YYX) obey� :plawf(!����%ps% psV+ �= �:�8!J~?0N�f�A�-e DjC\t� |� N|*N=���f # (k)\,\dk$�0� V1,�� -(e�<=��.� � ?�*�  =k^ �/� aQA#po��d*� @ $*�� �� �� �L�Sal�ber � �"�t7 8��uwZ ��.- , �m�.�>1F�Pb��Hd ve 5pe�!��? fe. iVJ�0reg:?͖� �� i�e#fam�r.*�&Ug=!�� Ch�<--Hasegawa--Mima"+  (O 19� ,, Maclennan#Kodama%9)%�g��!�m$.�� s (2� "� 4ۋRi�s�?\4Navier--Stokes�s.� *esJDq�.��:  -sel� vM�.�A�u<�%;, 1d buil��M�%ž$dual-casca��d (Fj{\o}rtoft 1953; Kraich!g 19671L 8; Bxlor9�� Iory2app�8��A\���,%l�L�7� 1$ �� ��y�s�) ���)�uO; to��6=յ&)*)&!scu�IA �u=i:��-%ACa5ousa�2�� s, IFY Q6B%�2>,��|/TS02}, �\&��$b,q A .�\�1K toward=  $kMuo�W9>tu� evAO 2� al"7~a?�"u .��3 es #.$k*�0$��nch?>�LY�pic���AnS�?grt7u,��MFadyth � $\dI] /\dt as $t�� S��� pea�.,Qmay�D�=d~��B 1�%2�A ��J&� 4� �m oc?KE}�$s O� N�5h�. %E_2�� a�u2 me,SaY�� a#us�G scen7��� !|2�3un�F�ч2Q,�� �� sA eU� �Lr�/Q�j!4Endi� a�a�E��%-)�08u�fɧie��f�a�.T �T���y, *G��z��zy!`�ō 6������1&%ieumA�Ajs�:�$�q"� ��A�nvolv��6�ut rigFs �@�`��e is vr�%&��u��2��s�(��.�Ifor%� �C�%[9_��v�--1A�g5�a�, j�&� . A�T o�E(�B� is5�(by estimati�ng the nonlinear triple-product term representi /�Uinverse transfer of $\Psi_1$. This result applies to bounded turbulence since upper bs for�6� �� are inherently domain-size dependent�4e difficulties�extendi� is �tomunb~ed case gddiscussed. Some numerical ;$s confirm UeI oret$(predictionsN-Aed. \se{B tdynam7quanti�L} A notable feature��incomXsi$ luid.\0in two dimens�is�!�earancQinfinite|dratic �$ (per unit!{(a): namely,Ikin� energy dhtyM 2$%�Q�,!lied ar!� s!�- 8wavenumber $s$,�cadeshXever-larger scales, lea�an 9�growth.w (tA}isEumably�ce%/!g!Pal qu1� invariant �\alpha$%�(he so-calle!P 9h�; {\it cf.} Tran 2004). In other words, if~9gq�ca%$ is realizA�,Š Y�a:tstitutes an ill-posed problem,�en�h hat a keyA�I� 9becomesU�(. Of courseE�4re still exist1�5_!iM�x part�;��Jssipaa� agent%� eachC��~is m�!�4concerned with!dsem s. On m��ply�LH(\ref{governing}) baU psi$i58(-\Delta)^{1/2}  aPtakB�s� al average���%equ�s,�hfrom &conserv law�9atA�+erms i�ta�ply vanish, one obtains evolu%>r%Bq� ��>|2$, \begin{eqnarray} \label{Psi1K<} \frac{\d}{\dt}> 1&=&-2\mu2+\lang�>!!\r ,\\Q2vQ22Q3 RJ� a. \end�Us![!U8Cauchy--Schwarz�@geometric--arithm�Qmean!0l�%S5Ru.0on]��-�nMH68)v IbPs.):b{force�!s%�BV&\l|J|^2-I�!�E.,-A�fJ*e=�@mu^{-1}F_{-2},\no��)�R j� �N|3/4eFJ~V:�4v�3+.�1},>w�%�`integ�vona�{ s' rule $M�9P4\theta\phi \chQr=B({ )'}+?'}>$, r $ 3= '+ 4'$, has been u���f$F_ { .! 6%$/2$. Sub��aI�.\� J� V� yieldsb�a�E�1Z5A�-fd�0I2RI26I>BPTo avoid unnecessary � lic�xs, zero � ��condi�HR $assumed, s aɖ$T>0$EZ time�HsUI\d�1/\dtm� _t= (T)/T��I� 0220$� @non-negative. %T� (ime-asymptoF ��$\left Q R� t %\righ�\lim_{T 4arrow \infty} ��01}{T}\int_0^T>N0 \ge 0$ (when�  it�� s) si  %$V= \ge--0)� (H\"{o}lder .�!�!� Rl `2^{3- �3��-2}$ (N� ��:)nG�\le��9�.?�9c.�, � caU�= ��.�1sJ 2}) � R����)�-��� � \leU�P>�F"]Q=B\. impH �r]t6�:�EueXAhprovi�!A both>>�6�2Y�� Y. ��kE�,ssured if $s�_��F_06�a6 norma requi>ofe�� ing,� auseL� !�� 1}/s 0/s^6�Amay{ndsiaVa�X T��=��� $\�k)f< . U2Q �$above type��N��jra�T triv�!�-N*�. How���y:import��r*;�,LDtwo reasons. FirstC} -sel�0ve viscous d.� llown ��po,il�of*�&�cer� h�� towardLlow*) s. H�(, rigorous %sr<,not as abund!a�^=ed ! . SeA�, analy[ stud��*�2�"� funs%y"!y&�Ms.Vabs�!*@pointwise estima�!�(spectrum%�se �I� Jly? ful7!^lit? RMz_-^� trib@ofk. ��L example, \cite{T04}f!F;yJx��to argu� at�ugy�D2(k)$ should be shETe�an $k� $, as $k*+0eY"� Larg�:j } I!�&6,� howzphy�of�m�s ad� only2B2na^��is duk%�!/!�fac �si�aneawc*1 *�~1K$ %<s virtu�no>Eto get Z�;fv, � B�� �e� le�ub�{Shell-��d6Qum}B a given� $r$ t usote�$S=S(r)$%Q*jse betweeAX=r/!1� k=3 , i.e. $?,=\{\k : r/2 �/k'\}$. � Qb� $\`�g2� a�� defi�byR��q�} FP&=&"� r� {r/2}^{�� a`\,\dkB=ee)ent�A�a dou7periodic��$L$�� FourierA�&en�po)A�stream �$*�(\x)=\sum_{\k}\exp\{i\k\cdot\x\}\widehat\psi(\k. �( $\k=2\pi L�$(k_x,k_y)$� $k_xmk_y$ beers� .Uly . Le� oS)$QL�/on!es" )�e_sup�dedIzUC*(S�\in S� z�. � b� D} \sup_{\x}|\nabla s|� 1` zk|>U|� eA�ft(6-16k^2F>p\" a$cLrI��(S)j�>��u��yA) IesuaKM- �(1=(cLr)^2$ q�!�a�vector�� $Sk cam an�r+e�N of or� �y.NE acon�&/�� � $S$:�2� �� 4IJ��A��pl2�.BGki�isfc0�� the*� ���e�s, T $be derivedjX .�$���0fo� �~� �j� ���>�&�9k)"� .�k��k��f I�(\kappa>� E�z zB7t �!��s#.y!�$k":�-�o region.��(direct>',Jh�z�%}�*��U�Uf72}{k^2z�3~�k^� �� U!�2F��u&r -E9� suggest0":al sis � ments�t a2 � >�,�� 0well justifi� If a�` sist�]M&a� ���1$a ($\d E��t > 0$)�$� e~ 82$ oughY ac" a�ue suc%a��+2L proc �\ $k=06m� hand�n{"�.��s% n ab���� "t�." ARQ$mechanisms D(degrees higJt ��  n�!al26^"0 ��thM$}3 ��!E��$. Neverthe�,a izP ͼ��> aIe� est ��ŢearQ�I�R w�e�f;  (�7 low-XI vergAA9 �� ral)� FW#re� in~\S\,4%1e�sui!���is ex{-. An.A �w.N � ��ba�� .H�$ termF��$��4$A�s�$mploys ele��� but  F�Cpl"{%{�$�><�"��"�P 1(S(k))$ r 9 � J� �67(S� -��ps  J( ,*?��*l (S) .� �J@ [L(S)VO2N� P.j�|*d . (S)|͎ 6�F^Z� �v�g 2cLk�1&� z�c^�m1}L^2k^2 6^2&�(S6�=v5 kFsj s� "W� a� sequq�u id}�A� 7 last�" &L �� .� k CR"! m2"!y,�"� ively. I ��JU"4e�3&� j� A�5�2%�M"1�M _FjR�')4.�)!\it��(�'� �'���v$(f��h&�PU͌:�.$^�$\ !�ssocia����� �velocVat�uapprox  1}{� � �) �N�)r�)n�R�e"{!�M �to. E.�-8J��&t����J���%_+}`��ns�&�)'�>!�I�*�is& �_ ����)ai�'J d���! : wor�'a�.2h�!�intrincn\+�(oblem���( 2s our afh sses.��`in*� 0systems. Fin��is�th �Gio'QthG �.�)"6V�a �ar"-,a4nA�tfbe mor�x�!!�� � $� m�� *RQ� � earl�(even > very3 � )A0e��E� $��� mI3!�prefaK $���oB�$ =� bebop�l g >�$Y on{N>�,}� � !� �-s��&� �� Aat�)ustrate�CT*!�7 .� %�fz S$E�(�J�6)����inJ;squ� fA� $���!e\$�{f}(\bm i� n�#a�-�ose%��$0$ hav� magnituQ,�)��IE�aan>�. Unlikeqmith02}^)Sof4fr�3$ [$\propto]Y�$]�G�Y�)�CreA �r3!BIC(� .0) �aO) lowe�jLM 21�s. All2�e_�*ized � fi�u�=es5},k/(60^2+k^2) Figure~�0sqg2}Y \0e�(&��d-state:��um5E� JI n)�d.9#gYU�jand�w��r�"e%s2(%$ (�  ?3����W!? ( , $0.3333� .%&a�2�� e1���1eM same�/io+sU01666 z� mto*� allWA:�$�E"�#�$e a� >��bQ��Ag�-C1� �)P-�)�s>&#)'9�#s���3.5^s���! A" `3�7 727m& cal� ea� � y6�4ccurs mainly a<6,�N @��Ou5nB� 2})�&�sb�&�+�1� ��robust�Q& at re�-�,�vs was n�-:!Vno choic�6zU���S��dP c;$5A�Jt.G. Io�, 71A�z8!xS ble�BZs, us!�aIier:�>`Nob&5 6�Ih� `reluc�'�-� !!. , a��mpa�#U"�-�V�� b%�bE5f�q} \cente�{\inclu�aphics��$ap�w{��> Z�Mk:d��$ �,vs.}\ >Ѹ.[tRDI1.K:���3&f$t=37.3��t=38.7$icaaAW)!0ee�.�F)�I��6��)v��4�6strophy� !�}b�Z3E�$2� �(+8e�AX.���� $1..� 2B&�ab�$96\%$@S6 ��Q�U�� carr� a few��Az R R�N.cei�29͡��4��&'��)R6-o6�H� Mos�Q�2]����6�,� ��a `weak'>7 (��`"=!Ey~�6>7 7;i�&�;�vBow/ �;, .<N�;� 5�is �ɫ�ur�?inilibriumK2a�&�+6�i�! >."L%q�~�m�1>�qua�ady1�u�)�B���aL v�AYd*) �ΒR2��:�*l4:, 22D �� �7T)t=15.7�� 16.5�Y.� $��, �Pt�ff�A��G &. W�) =��>MFME�-��*,�+� ��M6@55|�Lse�j, $1208>y $.�.ois $1.46`� mwT��N87bN_ ��F� �(um>�2� )5R��� Again�V� m��J�%h��!2>�eak. We� B"amu��)"K(>Ab�? 'ingly�@$. We empha�*� be^our� plot%��� Fig.sinv�* ngthvnuL}R��'$} $r=1-2s(& :.L6�+4)/iQ six �. EGm���m�:� ���� 15.66 �C!�.��: fR�  } $(� 6�:+�� >�:Bdecaya��>�Q �.�e>  �,u� M�ed.�>�:�U�#��j&s^ �G-��˭#�a��BYF-*�(ange P�q� J-QG*c:$ significa �$B |ts2X �until'.�Z� �de�p,3"3�a�B-!�de:^ V� (achievE^�),EJc 95\%AS�pro��q&; � (cal�tedXa� 5/3}B�(�H rapo�to-').ADA��.'B�!�V��!� �(�5ly 66���af0.7����&� Q5 ions.� �O� AZ"�=ei2an ahe)a� de�Ar�;q(]�#,%a!T&� M�!zb�aF"�#!IFa6si-� ��G�Q�d@!��.0l�=�s�\E��%+s$ D6;�ep&0 "�R�.4�gm:��{.�6���Mr d a iV clOtoeJB@-#m!�"� sH !1�G<(_ �2!i�De,2�9��bo6�5(�orA�al��u�)���L96�({ out �� H*g"Y> 5�)&#;���L%Nsi�$mak`<2�=' 1$*� inZIiG ���J��2x�"�7CoB-a)M ion}&�7paperI%:�&L�7}?M�0 .��  have�Dst�9d.���& , "�:��!a2�M6-^Z�� #.����,"DFa �H#;indowh&+fn���IA�a6�*�$2�Gr�Iy$eB,�Ũ{"�*B�!A�f*�NP/ed slop�O� %n��a�nTcIO�+&�<f�NF4V R8s 3%A��"=+ .�#1+i�D1�Z�� 66!1vh::6W�i%Y�Xa�candid�q~��fD:!��y hypoe�us����.i o_�B:Y�;&j."&;.<"�.���TH (Ohkitani 1997; C] anti*N 2; T*5NIfB� repla.b�5 �M2) 2: \eta�:8$ >1/2�8�(sims5�&R- of St$2 fail�.%<9�B1�w�$T&�)�m , aZ&& � o������ �%�q�?!�EWI)'ʍAge�œfe�;.,no=a a6g;k9s1��lea� s rapidlyq �&"*HA㉺:�0T�q&2!�!� �+�.b5�.�>�&be 7 ffic�{l�ro�So balay �di&�0mX1-1%��k�1-J�6��au�����*F !�a ݀�"r"&�ey]�����Av>u�' $.,|"U;g�aj& $laboratory�er�T~�$B� d02}B�Aatmosp�+��er%.�\  ro@ A�anka�d�CnN a s2�� ����?a a8 Q�"7 rV:. A� 2}$ �u� �V�&��8w. �8(�! than!�w�&"�Tis5F�l!��a�^{iIQu4 �9~ meso�Hs (see Frisch 1995%rN�rec� rein)P. cor?!ond!>* � er (��:�f*�4�F!�m rele�&� ,baroclinic i�(�,8 (thunderstormsn/e.de����e%�!�xh e $-2$ p!| -law%�".1>�| ��I.�a�fL(m%�,�.eep� S perm��!�ing�@A�"�orkz� 5/3$� A�Cy$ni_s i (iEUoG38l �E�:���=�)-&i8�^ h2`7`�]*2� . A>NX� "^� se data� � 1-tY>% ���1�\�ac� ledgm9$}�w� C&b�Ra�anonym� i e"�Gi87mB, � Ŕ help;Fin= roE��$manuscript!�-� was 0� � Pacv IuW!�EM�H'�S�a� Postdocto FeH3hip) Alexaa@T von Humboldt Research:/#N(alaL%Enginee�>Council�Canada.�B`"3$thebibliog� y}{10}a�'em[� (2002)]�+ \��sc t, C.N., Plapp, B.B, She, Z.-S.��0Swinney H.L.}��2 H{Anomal!�self-s5P3�XQ5t"� �j>).} H�0it{Phys. Rev.�Bt.} 4bf{88}, 114501�!�0tchelor (1969� 69}B� , G.K.} 3 ${Compu�o"I �`�%n homoge�F, : two-.�=�ce�!n ��F�\s�<12}, II 233--2392�l�=�78�78B�, W�78 w {Uni�� po�=�Kv��40flow, Part I: �Ta\A��a �/ac��Bdr� s1� J. A�.A�=�035}, 774--783.� CharAb (194� 4B� , J.G.!�4�O�1�I��ic mo�B� GeofAs Publ�1�.3--17Z� 71)]�71>�B� 71 -ds�!icn,^B2e 087--10952�&�q�( =�sc, P6�E�^U�ofpge��j�9a�8>��A94a!^�94aBb�,, Majda, A.J��Tabak, EM#94 �{Singu�\fro�\�o- a�/�L].�a.B= �>�,6}, 9--11. \��� �b:�b}U eBB���Fo�of�j�g2��2-DF� m�3��a�veeJar>�No4ci�V�Jbf{a1$1495--1533#��(Fj{\o}rtoft�53)]{Fjo53.9sc{-, Re�53 �q�C�I���!�of:g D� wo��^ndi�?tV�Tellu����225��0.�# (# �2 95>� , U�95 �%J it{T"v$:�� Legac��67)]{67:A�?H%�67-u{Iner � �C�� ~>�10��41�426��!�471 �i�sc�71 ��-�"aV�EQn1� o it{J �>�4��5��532_LeEh � 68>�a=E){8� Diff>"?OT����Z6B�eF��671--672X "���A:97��)scA�� YamaVM�97I�!�viscid%ti -l�� �)sm :vW �6' && 9 876--882.tPedlosky�8�8F�, J�8��|Ge�- ?m�Dyn�is5�{2nd E� , Sp��-4New York, 19872m:e��!_�W�94)]{2'94B�2 a$��M�� Q!��1"�  {S<)c f lo����? aA*N� 5#�e+401--442L�:!�EJJJ, Td UL{.�%hf_��aq.�"<�;�^<0183}, 467--502S�8�& ^sc ABS., Boc�jtti2, Hend?��C-rinov,�  I., Tam Y/lM�A�VallisI< �-�"� t =)�$s.Nn&^ ���V�46�=13--48.��!a~�= �EJsc{!�VF .��%�b� Iina$\B�k�a}it ��ica D�19��13�l52��!f�/��>b�2�C:�RL6n�C�:��f�>��m�E�%�036302�J�3 TB03"-�2�R�3a-"F dualQK��1��>�7�24� 552N��b�� ]��b��budget� y--� --� I�6�F�.�dM��J��%�4R��&E�� TS02\[B�3�Y�(Q��rai�=�~t��"�%I.�i�'c�� ��>6199� 6: a�03U5u*aK.KE�A�Wi�Y�y1�J[2D�2�+FL(Discrete Co�!.�4. Syst. Ser. By��^145--16� �l>� %�"� {refw,doc�(t} ۷%\{p[�Z espaB$]{elsart} 6&Pusepackage{amssymb} %. bm} .)icx�,def\d{{\rm d.kkv"t�x{\bf x<.K bf k p{0pu ube�n1 �journaleuIe( %\pubyear{ vo�{, >�m�B�style{$d4title{DiFq!2�non*�$�i�L� 2��Ej$author{Chu�V. � ddress{&�s&�,.�|of Warwick, Coventry CV4 7AL, UKNead{c�@maths.w 1.ac.uk!)&ab�Hct}3��8�# sb._Q.�"^�(SQG)�*�+c"�(F9w in�J"�_���*�ervA�c!jF�cV?�m6%Q4�Q\ angl�m� 62V6Xr66(6'), �=r�n|])'41am�Ll"w%F^ ��$noKc a :�r&� Nof "�v:N�:�rK nsit�%Psi_2�*�?s�%4*"�1�"�!�%gi�Q flux�$V1$"�$q%O1�-2�V 2,":,e,�*�;no��8nQq- � 2y�5us�e�0.EGun6/� q�nG.hB� nB:�4)J.Jnce)x5 -�pic�x��id� belieI"; *=vNcb3/&; "�[>�&�%Q+s�[rT-!�.�$U0�$�eGS,o�!�keywor�6f��� \sep I-��Y NpEb< \PACS 47.27.Ak F47.52.+j27.Gs ���[6�"�-Int�{�-�|!�aJ.� [:�!� cha�er�b�.� �'�!�Corioli� ceX-!xs�z grad(I��b�MerKD�F>1 deparEx�#�6�O�is:B as�86� g(�$~34�#D 48, 71,987,"�)�!hCdescrib�#$w6 (t>)28 :9�b \x,t@G!��Y�!"� $z�*usRf takA+�#semi-�9 ] y�p=dc�Ai F imp7_] horizon�K N^&Re<7:F"�k �9z*h"tkA�Il2T�A+(Y$z"< �Q$!M. m� �1e.�J ft $T-B@f  |_{z=0}=\AGial_z�� , ��K6��[�OJG ��� @)e K �M/yf{|wG.*1�u&�N-*�ea(9�)2�La�-ianiG<|�W!� iUl&Qad�PM��.� � R�q�1�!+Y u=(-5Zy!Z,x)9/'� n78,�95.f2� � B zT�} kt:+/z+j�U &=&0ZY$J(\var�w,�o)Y=x\�y ' 9 x 2$U$. Eq.�O��(_&��!���1�.Bt3a�� ced-"�ner�3!��O2a�:"� A&o�EMfor�Km.�N�) �?>�?񈥝�Mp�N ai�M3,E�A�i�) (cf.M&/ 02,�)�u*.V��!!I ed���nq�� 2:M*1*�*[0K.�15Q%e�or �:g�-.0coeff�.(7T��.��of*LYn�o�(X}?y,A �..�#�-i�A �K)x� �,(!�d $f�u):@.s��writteE�b��n�N^.u+f.���Jacobian*�0J(r ,)$ %n)x���\b�id�H5 K{�^q���  ="@_".phif)�K&2,0R^�\l �RI ABJ As\abe�]���A�" e�"1~9�) obey). @.�b6j *=@s%@psin^[=@!p:R8!+~?0BI6 ^%#�+"�� �%�H�I 5�H >I77-8� &? J �2ta|)4��"� >_Oa���v�21�E��o�\5$ctRt6\� (re�W�r)sth8-&�\AJ7)�WA�@/�m�t��7Y�5g="TC5=i� ly+T e��R|psř ich &j0��an�N i2=sj.� �XE�� ;H0�F��ng 6Y4 1�G5�6r Gi\arbitr� 9=s $p$q>�3Jhaf}1�1�~1}{��iq^� ��xkk�n &Z 1}{qj5! 5\�nkZs}{q},&.�2�5h �0^p�O`a �p}^0�.}Z3�a�A{e�� Dt!�E�ghtforJK6�b5 "���Z�~-eA A�!�R �1}) [62})] �!/r $1f $ [$5$] 48�W�1*R1�L^q=k! p$]�f��i"�� Ohby $s/:p/s$]J�.�>OE�V\$ 6�� :�2�k\gg s �l s��mto[!���~��Z�!�i�s� a common.Y<iN&� ��A"M{`(S �amiliar2+!Ycateg�6W>�Bk e�^� �� au(� A�G��JLs M> � ��i�?"6�AX:W;9.� s.)^c�L�at M�1saia�: sourgspread >Pi2�:space�K1!�i�$][�6��5�I�e�6 [�3].F.� [3e)?�y!Jj��]B;lor69,"�&67 71,�%�� ]3 orig�b �5mu�ED�$-Reynolds �:��1" shw� t�7�bnppoB�N���1ral� ib�5b5` �F.extrem�by&��$:�P��tzF\e� (%�)E�&�xcX�� =�(Xq�R�A%�h.va��i�� mann�E*�*��.\footb. sa�re�R&�B�e�Pil>� L�in ��3>W�M�YU�>�Ua�2u, x� T04, a4,� "9~~_{�!�7�,sde��2.E�  ���a�aas dra0c &�A�l%6rv�c��H7o. M.eaSat�.���F�B�Q9���cross�U}�A�ll$ A,(9-ly%imA}c=ell/s*w��$s�!.*�s_hF�9aJereby ru_9��;�E� �,r�oB:y�e v�U�^� 6O��vYh}"e& �q�' behi�-AW &OO���6�"TA�AQG&�.As�E pb��2Ll/.{� �G*�\mB{�8!d �>f} Ig$A.EV�Gے[t>�*� J� K%`s�Sj-)B!%&%=ӂmbg|� i4f>�)�1$Q �{�y progKiv|�>~ �A�usr� a p"3@yMqce n�?�g�Ppre!�n� "�k�A<q7`���xd���"1 F�C~3�u'en� 4�H*Ae�U�.Pa�}long-�2Y���bF$6�. �5�s)&�h�su�|a)��e� �k� of�-u��A1�EWXI end�%�acus�-ff�1�:" PN�}A�)z�ao"�E�'�ou |!2revie�aqIed.)(�(~E�RerMla$toD��NEPl�?l�"�� uB� >e�.:�G�L �b>$L�e Le/e�h�x)nH���!>�\A�com�e� 2$ul�@i �2disk $d=�|k<�X\XE"LRle*? $D &  )�V�^<5��~d�v�, ~~~~ �2=D�=B�!b䥣64w-'IX^�4JcE�^7�& &6���V"�$&��^<6�$%�&��>DJa: s/6�E��b�n)�)�}�]����gste~A�et� �s��I�1�le^2/k_0Rk"���"�Bm����d$�������!2� A�*s�F t�:#G6�d *(v! �c� C,@����8A�_��������Z �3u*zF�ɕ&Ә >��iYo�,A�(ie��5w!�*�O��i& b)�"�N�b�Ę&Ę} _.�����$B��.,--RƘЂIJ+At�ǘ�ǘ^ǘ�>ÖZ@!�nLI�X$f�_ *;�|�1}N`-1/2L�� 42^42.bE�T� �v 6�ٔ. 2� IA���sj!��Nr 2:s~��}� �H {\d}.��Tz&�{ Bށ�6J1B�s �!�qL:'� ��*ȗIb (&�&V ���ݖ?&�2��$\piF :3$f�5N6Iq�$�2}�v*�A2>��3rAF@ {#eqs�#W1}I^�ap�b��!#u"s��f*e"� "-�#�A&֐�"^?lK"fa���\��! Ts�{*� �Q��"x��I[=c&1-�-�J�sjC�b�ini��  ($k_0A a�+�Ac!��ory�/l6$�(i�D3*� :N� $Ltc r�#)hٝ �����a�G�&+TlnbADSf.~SC04}) ��h�@fix,Ilis �I,�?i' 2 r�z^f�1�`�~�P*�,_{a!le k_�2m}��1��.2}F7uv ~ �>2mum.J0&"N� l$A�*>�.�&�1.wr�ever-1 g�`�{arilyu*�*�&�&,�i����0>9<�B!HeTsfo�q)C�ai�ܣ�*�YN�| re;�&c&�/ �{lIr�%G�M[(�Pnta�!)_)/2%�6�"Pm�e >} :��Dj4>)�� �%� 6���"�(� "�Y"@��A4l�&�, �p3�V&�1�Ja��J!F}I�um. A5s:� ��%�(k)=aS\�;�VO$k<~!��. �s�,y"2z-�2��G��:�!"y.�)�{pn-he :���� $[k_0,e�]$V��"�,U2$�tU\APf E�F�3 ��� $*S:Q ��5] �� � luVg!Vs��"U�2� E�1%e�!�RVt3m�� �!Xs�#i�l�QT�C6��^<_r7&>d"k'E�J����R; q ) "{(��'' -O�A�!s>��VP^>,*� o�(6R2_�=��J? �^> �^2��Q-*�:�mA�2���U�m�%��eV�at�+��}s"�2Ii�N^7no7 N�i�.0��"= I��(avail�66���J�  $.�<|�7� mea*4 z.����ve��(>�$�)�v�v heur� be,*�1>�$��n�"'Zughհ� B��Ube>��2s /2}c'M� 6Õ +m = c'B�c'��I�_:���b �-I�1�y/3N���2�'.���e� 2F�^�� �>"� 6� � JD��_&"�N�&�:Psib" *�>9T aDP/�d�,b2��&�S�0i��*_ �E� �vm�Y>� ^-J��� �*�e�:}!$ n* d�as��ell:� *� ��+y $bw� \&��V �a{6;����,�o �*� %t��su1l�z ;��06�1^�c l�o*!��� go u�y�".,���Z@1. A "� *P3]V)�k� =&� "� �f . By�i�7Dto q��+� fq1/3^�e� Z��.�����2F>�F 6G\ a2��i>��> >Wle FR\lqQa�0 L_�� ���ba 6]."�>e� &PC"�:)�!e�nd3Ai!ɺce�A �I�����Z+argC # ceX& para�B go thrŇG8�)T_>ro �N�%"q �Q�[#>c�5U  ��%jP�~MQ��ld�| expliYly� m������m_N06� a���s�92�BN�*� �:v!`T e�#!��m��2d%F|8Mz &=& a]��x=eC+/ =Ĭ a}{1 ell^, �� &\geSs�Ps.M:��#�<E�;_EE%��ed�!)��A�atJ &'C}JR���bU2Oell}{s}�� )^{(1e)U;%T^�.B�1�Ya�aaio.�A"�{i5%*og(s/�>�$AF���s� A�i.�|=blcl���"�_2 0&� ^ a 2u�Ae&k | e $[�,/a,&F4"mE4(�cđ incap� !�],Y$gni t�3�&k�i� �~�]� �5q�teK�`Z�n"-/��b���"4�m��l�wNq-.�� wo~ }DoE02�/ e���:2�<$(osFfcoc�so-� ;'0-=` �3&7un���>:�S"D&p�u�#Z�9�@aVpsiJM=2 rR= * �-i�p� D)*�1E �&�q�I J"� *j ^GM]{2 'Rq  �2C � q�Q��.�$6 NZFO� !d^N�2�7|;F�G^t|" � J 2w: 6@ ;FVV�$�m `B_J, �c! r �5�  $&�>' ��� �Dmx)�2^<�}a��"c��2!�a� ��B"ƝE굘i 2^ �H�D�n����&�p>�b�"!6&/1�� ��2d3ase��*(m� =1$)�*N2� 2$)�/�� ����g6pd&�O>E(Q.���r�>�F�.}# "B �7I� then=�l�^{y�:7< =�2"�=J�i{:.i�:5h�$XJ��2356�>��)(��6�$$�~�_�v!e:�0Bp� <0�r�pIO���psu�6 n alsoV>FtD5*�s. � ll]�wdp�3E� &5 E-��i�MZ/  �O$Remark 1.}+techn ��3�ӯta�gA��yҊaly�� ��P-m�truly*�eR(i׬� %�&=�"�r2ҷ5.� s$�!�m��y l���U��6��c� �3"� �%� 3� �") �4u��s D�2&��&@f#cE���bI7Z�. 2�2.}�t1�\�5"�C$J92��r�t ;�ofE�er�s(of�Bd#^~%/�&�>U :�Z����5,be guarantea�6Fif^]"�"�fA��F� fJ�=i�'6re��at e�aT��&�3"gv>W3}�a!���duP_:#I R6w�!(>x7:p"E*,�ZQ�!�Eӑa�gy�X��no-dx�IE�"[�mb{ itll�!�b%s���:ct�5O}��jK� 1zth!!*�3� �Rt*� � . :M9nA5*?� !BK"2e--K"Kb�p�&�5))%ge� ��;ou�_E�wM�p�)�by &� in5b!�dwid&~|-@*���/>?}���$�A��ge�P��'#ssu68��y9��8��9"co���N"��Ż $a���k_h8i"�- bjec�a �VH�%:�4.} R�: ly, Eyink(3 04} rais��7*ķ^-��Men �i&+ z5*u5��by=�$56c�� argu�eBb.�ca����"%>^��&im 5f!�s.zy�n�va8�?y A�;M9e@8�Dis8#�>l��D&e&�'�=)S>Q�&p, �5!�:\81�(��~on�m=ngI�,t��s/��.Sa�u,%U9M �)s�EtinA���*i1 {QA~�PT � D�*�&\ �D�?�m�"�; `` YUXe''�: SA-%�. al��SE�o'<'�E 6#>A� Z"�6Џ d�AG an&< !*�{_m!#�=�=9ۑ� lizi��(� ``~�ular''�A�*P\��n���5�(a&��� r*�)� �U�!��>|>�Q�% �]�>Bo8 see!�toD�� ��:!KY�a=r��s � ad~�x���N���)s�Oi~%�`�-Borue9�>�76�54a priori exclu�8� �i scenarioAb^8�T�))� s C"o 2{9�d�Z%�Sȟ��~?, Kuksin  0;"�!n!lbe fu�_*G�� .�9 A�����YmY�. "�9A+ha�o1�:�n�N IA�ծ}:�9z��:"O,pre�s�/!��':]xd�� iDZ/\o���ra��A��2�a Y:7�&F� z�"�&by)�I�FP� e&custom�< AMo-2D.&to�i��� U��D��D��yo���*��@beeem���*@ .��&K%�"�� j��2�Jx )���*R-� $'��a"')&� �3n� f_H8\"HA�>���#��.�C%ŭ�)�um� l � agno*Fz} $�)1�#Bu�M�P ]�#�4��lJ� $a\ln�$�'$�N�e}^u9$.�� bǀ.�X5����)�!�.D$L_)I-�s" �wo plau��rou=]He*�>?&�Fu��/���M suite��3:�F). r�i��Ӌ1�-� ��� A��!ed,&NInc�7!2,&�Ra̵e�F�[ ��jd.}%:"v( de"�R�]B:.� E�.�E�-k�b#R#AI��g��%l@�1$. bĒ��>&Z `c��, ���u�Bf�Q�u9&Z}m�,%Haw�=� -�>:��A��!c��!k&o�5Vmn. �RI�,%L� 5>(Z 5�=s��A�����A{ Н,��. Ey��.� .m�c &b��1� ��,�F�.c��fa�C[s�~� ��&�̀V�.� $-d�a�2s� en�� %�s2G� �e N% .��l�#N�b �> L� �_aft����IX2�2�5A6(� E�Vb��(�lsh]�bea@arhto��iY#��A1)�.1I�ex�#� >$2�O &�#� }��e j/�"��� h�L!�I� ing kbe��; �a.!6�<<b#fo��is!�1��af27flu �I..9%6!t?��)^2F*U!T!} �!�"\mu^3*gR^{"�ef��of2�?"h-dropp��-A5 ��-�?-area)}�[&�c%�&|v ,�#.]c>�Yq>b�P�)�"�� toqs5*DE�!@a�satisfo :V1�ZI�16�)�v0fi�,� Ab�!�b��eaklyv L�a�!d Ry�U�s�)��"� �H3*t �3�".ȣ.<$N�L=3K��"t e���)F+F$�;,a6� �} �%E��T(s-k)qD�% = 0J� �Q����2���:���fV�&�o"F0��!T �K:���w�is pur'AtUW "� )l��"F` �%"�-(k)�&\e s{ aF\�&ifaell< 5\cr bb̍$s$`8a,~b,~ s,~,IP��.s&$ h�iA�� q�BB"�S� �$[�y{�&�1 P .�b���H�+�t��!r�|L *g/b })%�B��&h~"��M$\ �=k/s$!��( � s/k)"X&,&�b �� int_�E/s}^1(1- b) 9�a;  &�0& =s/%�R>%�-3>> �%!co�ba5�Ce+&dM%E$�GtN_�3 �<>�[Q�/s+H �,*n $M硴A�-���� ��bN�c}@[} I�+Q�)3B(�G"�` 3\le� $:$�1 \ge� mea�c��R$I�U��:�"X N�2LF ��2K���2:�� �i�0��W u�!��"'.n�_�al~Pav��K<� v����.�5.} A��eF�N ��lY� Q"� a�#*�V>4�&<� �� �� f �ua�ab�-@f� �a�!.�a$ive��!Hj�+)�1� *S%�-�ًW�e���Z a�-|��~A W:P�[�~at�!Fep�&EF�� aLs״f&p� meter. i��wh�o��&\)zs nt��l]Rv :Z@!n N������ng �T��eDcop�)& ruU>w6m nW ense�*h�"t�R mpleU�")`$ �{]k� "�sMG��)�.��^mZs* *�)C%�"�. *~E%i�Q7,I8V "�� {�;VsF$���a���c�$1�P�+t���? k:� "�e�gz>��$N�o  S��&�$4=er.� ,%2 du� eŻ��a�Bo�'!m-# �#cb��9��ng�%�@dt�:@�#�� am�i#I 5"t�)$��,aaA .����"�*f�.��_-wkA#0]Ys:�7.}�n�,*�� ��+"09N&N� p&X�.�"5"s"d.�-]�� a�&� �(E��"� �>�B!I�\o�"g I�e�^,�%wR-3'"� no1��!e&�E@�6�@es*�Z�H��� *Rmug�.�&H">!�qG$ via1"1}oQcZ4com �+7�e�0``frozen-in''.] *����zq� r�0q��� i�w�f�2�l:�#�>�! ����a\phy:� }at9� �$*�ge�ranA/!� awayn !�_z,�bD U�ve effec�<r�� ѥB -a"&6 U�!%�F*h�% =s�$um.� U���2B�%ve' .�.rFI�"��V�"='!�he!!mAo��&n.\d��� $0\le � /3FBn��HR$�mN�': R�.$�)<al1#.�i� �p 5/3+2 �.'� :h/1%�o+\'o �%N��q�edC ��.T�.�9 .� 8K'.�Ua^&Q.�k �2$� d���T����:F��'*/g5B peak�a��X*ks�a*~.� 8i�!�"5���E��a�ng�� nts'4�&� �-x\�% rC� a0# 94a,.b,�96},  � *����� mH� _i�*�Bv}:p'G s�f&�!.�8 illunte20��� ��!���$5 ���z �liter��e t� far`���%ogn45 s�a�K!�:�BMu"&o�,:5,���`3b5"�!ʂ GTB0^however�t��%5�a�`*��2�� � ym���E�A�NE�����p��#=r`ed by;,�[a�">,�n;� �G.� �)*N+y .�w E�=�5��������pi"�� moda�?^ 6�����C�쵁�tJ��k�� �itu�f�z M ����9.5,10.5���kg6 >"Eif��Lk)} {k\sum_{|\p|=k}|>�p)|^2B���&�d� �!c�of�z��A� ~��2�O$"��B>s�N���$ib1I�j#gѨ�Q ] rg�.Q"_� 0.� ��.�("�j%��N:& *Q$)se�fo�IKLff{s�"�.�""� %E���$�a &����"�U!l���T �6��i %�< � ͱ�$ڡK2�Ŧ[�G*��tur��"�yin&P����/ice� .���. T�:&�/ *s��:� =0.05[25�e=�����I�7_��e;�F,J+{�. BBS �2 $�.��"� 70  �M���5 i k/(100+R��SQG2V�-b&�(�#$t=19V�$ $t=20.3$)&�"s!.�H��d y� >�$(\ s)�m~.��U$V20 HY=n#�APF�Lv$In�(IwJ)"� e�E�gn!������ y�� 12$�hk6-�5��>E��mM\�ave��qss5�=0.99 &._*� *��e�6{R&�?,! �A�99� gҷ. &� C!@y���=�)�!� �!F9E��v monotoc6�.��A>��o9=1���)�"F\"G0$; 2a�B' 6�h=D�@�)M�.{� ead,F������;Q�()� 5�:h "� o2�"�H ̱��e�),��@ E���2�b��9� unex�!���I1�� Ej3.6� �8p,i "X�-�.�)� ,$4�k-���a!4)/��� ��F����c� 4 � fer."낒��%� } \c�5�5� vs.~ƪq�.?݅�j�i��4iB+���, d\I5�.\2+p�O!'2+[0.�-�b�3?:"V? cJ�GI5Q(xi ߡqj����.�^!%�r1�4 A somewhat st\ronger transient inverse ��fer was observed for the case $\mu=0.025$. Fig.~\ref{SQG3} shows a near steady kinetic energy spectrum averaged between $t=15.1$ and 6$. The a , e Eis� Psi_2=1.9&�Psame period is $2\mu.2܈98$, which amounts to virtually all`!injecq@ rate $\approx0.1 �,large-scale ��is better ``filled up'' than that ofaprevious%, due� a st-�B� during>9�phase. Nevertheless, no significant fra �of!`w�@). \begin{figure} \centerline{\includegraphics{SQG3}} \caption{Abtime-Mgd ]�-st!� ��I]42(k)$ vs. $k$��.coefficei2=v q _A�M�E�, imply!4EAs.]]�, Nd iADe.�,[0.A�!�is.�mosEq `Y�M�M.�} \labeli� \end5{ Itmexpecte!�at%0higher resolua4s (so �simule�s with %�er%3<$ are possible),]�Q�fluxea%\n become more noticeable�UEYer6-e�� rang?A�Dlized. Given limi��, TranVTBowman \cite{TB05} use� -degree 2�lperators $\propto\Delta$ and(- D)^{3/2}$. In both� s, weak�cades%+��, butE5�E�QkI�aAC)��=e�O@considerably shal�rA. an $k^{-1�TheseX0$, growths i�1$ oughtl�E�m�exi �-=�A�,!e$ereby caus�ta�QM�M�m�(process may�,tinue until->�l even��exceed��1��(reshold. Be�e�!ka� I�s0viscosity, su�G slope �n�A s in.�increase��28��. As aa� ult,A^oive1���=�8$ could be main!� ed ��O(eeper-than-�^�mi%�he�t �fEP�� . \sI�0{Conclusion} a�%�paper,%`adv*v*� @of SQG turbulence�u studied. �]�-" ob �� n up�b�!!� �I�of!�!�I+i�)� ndid�Q�Mv.Tdiminis5 aIGe3E�EYoward su�ly[.X�E� rul{o��e5�of!�e^Y�E�re�ҝ�Oۑ� eAl�a�4r%R(no direct )Ui�!6(first rigor� exampludynamice incompre��!ida twemenA �exhibits� ys. !�re��7/2K"D 1;0Rev. Lett. 72�494) 1475--1478=;gGeoaR�2:X 28[471) 1087--1095.`on� in02} P. , Evi7um�quasig| rE<89 (2002) 184501Rz!�:zC. Foiasi�DO.P. Manley, Effec��� \funE{�)�M �in 2-D25 296!2(94) 427--42.2994aB1A.J�jda, EAPTabak, Singular fronmi��model�F_mq.� 6 (1�9--11 u&.�b��Fo�!TAVng�i)D!1B�thermal a�v��ar, Nn�1E�!L149aE533. �Eyink04�L. (, Machanism�Ff� %.) the dualu�pic A�26�le deliveWat�� A�&$n Institut>Mathe!���S�(ces Fifth I�n� al Confer�� on D� al Syste �Dif$�Bequi�3 B��3: comp!on� :7 %J,,��ica D 9.96) 51!�2.(Ohkitani97}�k , M. Yama��In�idA� -)�u��s^9�,2� 9!>(97) 876--88.�$Pedlosky87$ ,# phy�lm���$s, 2nd Edi!�, Spri8, New York, 198.� 2�N&�E6$ S��lo�*��� >�.94Chaos, Soliton��Fg als, 4%4) 111116.`Rhines��PaK %�� phic2mAnn.  �� ��I��C401--44.� Smith< K.S. , G� c�tti, C.C�]n�, I# @rinov, C.Y. TamM&��G& Vallip� t difm��yhe 2� 5BFt6&� 3--48}�T�nC.V. �, "���!�D alh trib� &Gin lpha$2X�Jia191��13��5.�TB03a�~�J!;i"[ 2�inF� .@{76{3) 24� 55.+|bf| budget�z � --��--Mima)*^���xMp E 68�036304.�B:�2Robust�AQ �!%nd!$�I&4) �.��]'2�L*�2t a in 2-.�=>*< 4)Lbmitt�&h TSaw�T` Shemd[ nstr�s  Q��U��� �A�e6�9A�"W!in��c�6IB�M�6�h� 99w .�SC:�:� H.-RT(o, ExtensivN ofB�.>!� 92-= 1� 1��>� %@ "�{ref} ,doc!t} 6"$�w!is� ,��!ran�� to�et#*R!No�ady�itv6��j�1��e�rne �,s� �ady, �Csen$�it:� on�"t a v� h�[+�#a al��ur�fundamR0#��er�"�!�-s#$ *� ,Navier--Stoks"��ce�y}�*� ntity---"I�---is*� o ��  �B�!]?di��I1�$�S-s�[$gressively��$k_0$. INl>:�A,-h���infraA5g~#( cutoff, be��$�q� coyɤAoI2E�negligV! . Su� Q or one)(�Q�m E!o �apply]1$Ama! n 1$ �3converge$B*�i&� dg� $it does so �Y�A�th-�FA g�se� " parameterl issuwhe!����qB�<'�terestA*p!�%yo��#c���6 work�$ �f��F�ve� %�4manner describ�YeJceQ �qI�U�Kdi_%$k�" stagNM� �� FQ���� �wayi�$s$ 6� rapir�"� 3$ \&#04}iA*!=F2$AJ)lq�quickly�wA �lcommoŗ�' ��c�!�BN�. s�valI"5"m'is)@ (!�um-# <"��{R}E� suit5 defi��8 Reynolds-type i�)A_&\%o^�' �я/�($y � � 1$ w�V6`as well��secA�ManA%�W 9�1$|t carri�$&H($r$ (C&D"J� ta��placeB["i>�#��#itp to m��#�Ա�v ,�.  deI�Iim-�kic�;A�"e�� u�*,djusts accor!�I� e fi�%:&�<a*ach�a(�y�u) 1$ ()�2�1G)�)�*�Z�%� !�un�� .Y���/�� (I$��fluctu( abr!zero)�~�ɴof���8&� ��\1 ,class{jfm} %6[ree] |\usepackage{bm} \def\dt{{\rm d}tkkx{\bm x*.9 bm k Detal{{\it et al. }� ,title[Remark"> KLB! �2.l] {r-:5 &�$} \author["� �p2 ] {C\ls HUONG\ns V.TRAN$^1$\��A EBD 7E.GLS/.P6.D$^2$�ffili�{s&Hs&aX�J�  Warwick� &�WToa o, 60 St.lStreet, LOnt., Canada M5S 1A7:u >�,6�(?)��(?)%�OFs(?)] %Һ,!H\ns %T6yڶ %%�)�(?)!PIG`"eYALEY. %IE~KM3$a�%��M%j %�� A %.  arioz {3:{Applied*:�r��$ohns Hopki�%.� Baltimore�ryla�421218-2682 USAR��V>�ީ.��,pubyear{2005evoY {538 page9{11�26K({??e0i�( vise�1 m ??" setc�1er{C}?���/�k make��"�!ab�cW� udy��" %&� b� (2D) b�:a dou$-[2ic"&I/Q#� at�>�Y �&M non�&U K �/&%tF~# via!)ower-law�&��. �-\�}$ re%U t�\ge5/3{%� � aB,#���thR* ��#A(v+5/3}$1*� E82 us?'vidT {s �)� a "�)basis %� m�.�2,)1K �. We de�&'s,aKolmo�)v�*! $C��MP=aE(k)=C� ^{2/3}!m�� �%"� �r I)�g`4. I�s rel�(to&'s�j�o"�'� ens�Ayd6Y �a y2�"M:. �discuss��#V}p"�,Introdu�!}2n knoq{adv�,i$ � A�6o e�:� (NS)*T E_ominant�rw1\�  &Ns (i&�#s��e" to �.212(1. �+ e�m�-re�  �ha6ey0sub!��=%�Qearch si�-8(Fjortoft53}z,�2f3A�*�Z2e* of6� "� AC 1960s _"�u post�3]�3 &Z �@ he& %!��a�ia�= 5achiev9n!9rem O, b��ra�6|m#to ev���6� +�c)�>M +&o a �9��(\nu\gg s$ (d]ZF7+ is�by sourO"aw9�+edil k 3�" $�**h�/ �#Y���)@6ismca��e22Q��%)��)!�")�A��02� ,�Wh�)1H�S��.�� ��.�S�9$-�$ d�m��B�-w�U� _g�O��Y*��A\��is6i��)ј1-��g�"�074!lIɝ ����i�Twase�r�anlbym�� , �"C*69}%' u��!A,�n�,aݰ�u>$,69&�. 2�co�.I4^�a�><&�s halAvv12a:!�(0$ correspoF,� �� gral_,gth���!�s�%-^a?�c���4et(!co�1xA!p�6ve �y�&}Q�I��*��6�totalQ;e��<ailablQS F2�36s. Ach�:�67}�s 6"�a$,�ulE� in w��%��;`m�� 6e'� � lehandedl��<:!V �F��(.\footnote{F� alsoaA�{a�1 accu:�#t�o$E $�uma�modif� mjabm:b;quilibri�*@�. � �98 k/(\beta k^2+\ )*� $��$ $.!9Y �$.�?ev"?8 / ��,ian: up� ��? n.���)43 y:���A�Et 5A^\A J< v�6ion�7is.*3.� 1� hsb�<��}d , althoug�4�3 <b�Ca� S<-r� 2W2widu9>�! ���_m�F�b��&)T!m2R6y|i ak"�U�v"CAuna�-�3~=3��� �� ^k S�54 acP 2�Ug&3��) cer�$}5�2�8nco�9vec* fact#2tro�0�$$ \& Yakhot�%3@&�%a�<�a posi�:answer�!2� ure. G0��0�C�0&� #�=i�afcB]V�M��.�< !�9��VthrA�\ + 6q. Mor cis they� ��&" �+�- �1a�k1 e2x��s��.� . AqP � �um still.�.� �iM!ntrf�2�s,��y�4(measure cloL!�K�+]�In| ticu 0j�m�7 !1}$=�"4,��no��-0 o� -� �),st0 sEF!�.>%k�?B primP"�DLA:�|o��.�:ore�+�<� $0h�und�  varietŷa�gp���vvZ r� ��.�to-��"�$�/ls $s^2$1"JH&F(C[%u"n A �1;�0 6�� 110; P(�S�% 3;�, 20�/� 8  -+����=#U$e� )��%Atai;&�in��" to*�$&� �S>$analyiA*�'2D2� D��p8@� !-y 1Da�"� *� � \S\,25S �e�;8��taj� d)aec �G��1ine^ity�0In]3]�# a g�hal �Hew!hAr��f!�p aa�cus?�]+ duale=AA�ndNJZ{gy*| i� �4�z'A Ha 醁�I�a����%6U�� ��) t�<st��: &�>^F.�n� :QDR*;�A~un�2�B� � �.�����prol$& Ar�e*\--9��AO*�2. �P -�� u��� e ʫI�(� =.Q[5.[}�$*�A� pali.�&�+�z9+� 7!�trA8i���cTgs�9q_C rk�� ion � a�] e�O0 &�&3 =lig$} �De.0<or��A��9ed��NS�gN "� &;a��C���(aRid!F+%Z} $[0,L]\A�s A� ?eqnarray"�JNS} \b ial_t�I\psi+J(,) &=& �I^2 +f, Z�$(u" x,t)�% streamf�:@, $J(\theta,\var )= _x_y- yx$, $\nu�%e��8&�GE$$f�1�inga�e velo�=iel�J bm v2jrec!��&�M.��'ps.� by $N=(-_y,x)Ve�7�� admi�;��aief��!ervEL%�$ngle \phi JS\ele%� -\l .%p0phi=�.=+1�.7,5+b j \,\cdot\, Z�$QspaA~N. �H�qun: we hH !twiFB� �M! !m�ps2� � A� 0 = �E�-f4 , >��M��$$E= T|\�bU|^2 y/N*nGD�  $Z2�:2� on!�E"4"c�WAVw�+aCpleQOi�_��iJre�M�*  4 l� �YU�riple-p9 tI�re����Q"�4-. B�ra�D forwIc j�2-�B� )!�M�Q���J( !B+ y)_9+2_xy_x.yy�<�O���DJ�M� q�� QQ�i�4% :n4 Y�2,oFf +22c1::�M�f/6 / \no�+\\e^�g.�s����.>�I�O��atR��Qid�^��J��Vj +6�/Rj>� ���m�� b((of size $L , LUSDFouri�R N�d2����J5p�Px)=\sum_{\k}\exp\{i\k� x\}\�hat ,kNSr\V k=k_0(n,m*�$k_0=2\pi/L"S 2���-�h$m�<ercLt� ulta\Fly��0 *�sH le$psiRIZ >��q1-i 3,%�� oneTB�2�%u?O��!}@disk $d=\{\k\,:\,�K\}L"Vle� $D* \ge �K\�Gi.A(be(V���<5�\in d��, ~~~~=>2=D�=>�5"!�r.�L�%+If!e�#sf�.Ji�Usup } |m�%�| &\le& Q� � k^2|>}|0e \left(6/1�.)^{1/2�F#k^4FR����9 = c\frac{!� }{k_0}Z_< V^8 cE�����~AIorKun� $Z_9+6(�i�6re!( ��WT , 4[7J,N �yUs&�[y9�P3L. 5�7ub?eO:��( \sub-�%�R�&} ) aQ�W.��O*�$loHzed�Oa}�O���1�&"�( > 0���" + s^2\?4.�K>}[�xk%be*'4 \N&AQ�eVjI�ey�� �4�YP:�Pr_1s$j� ��!}1} ��1}{�H}\int_{r_2}^\infty  (k)\,\dk ���81},�J@6C��B=W>L$  },\\� � ġ�#1}2J�0^{r_1}R� �-r_1^2fA>��2;!6C�_^Ua˭r"��]in���1}0(��2re,�)*�du�Uc�����Q�A���..fq |;�$A�ve"�-E�u4Ir�5=�mt get"X�to4Sge M� lI�r�,� abovea�c /r_2�[;byA� 1^2/86� ��se���  c"�%wM �+-�+pro�V�d~.���))�)D (��):�!y���A�\=? (�Q=$R9?7�JC���\* (�T)�D�+w Z�W�[spread�XinL�f, J���s�)�"0  (q+er)��ns[aa| !_Z���ehi_2  hyp�ksi�a�*"�Lbe�KuQ-�A5�Y!�� firm� nR�Tre�/`!3 liter�V2'%aat@@�<6*=I�ref�M���l aFei"s AallUsE"2�c'triadQ^ etai�c�s#�8S={N )<(�$6VA��scd�Q�cer�:ty U*���6�.� c��(�"un�.< t&MerileescWar{&75)J��^� N�  �!J�ofR, togB?� } e-se1�.�by moleZ�%s;^a��O)� backb< 0�,J�'4e�) -U� �&]D� p� � &7 �& n ad+JalF�c/a�'�'a t. W��W �,"+'ufb�bM �3�=geA��0� / � �^s,6D$P& �ps6Y�.built�'a�PA-sy�.�$2\nu P�"u[@ Meanwhil"�DoA,ɁWualU \!�9}dDI ��N�own�!G� . If% �2G M*r^r�@� ��o@6�2,�0va  @2'�Ce�) Z\ll�g��a�&a>�g>ZK!!b.�d By `!'ng'j $ oE�>)�&u'��+��9j�$ aales; �rwi�$*�-_ is `�d'�W��� {B=E�md} �A2_scade se"Spl�bA��F��G"�%mai�FJ�p zA*,>k*�1 (�so-�*ed.9_6�&� )!�1�"� Ŕ&�5��&!�pC21%�d8�"ra��!�n�+5+ phenomeno7& �91 2�r]$�$ *�? b�rrect5er�a `2?&�)')in}'bl�1��l�!Genorm�Zd�M�o� 2S�T�g}�(.� nga�elQ@�� . if*���re1Bd�?a�&.�e.�, � a meSV� frq\�Zgm���� ��y%]i���arg*Ji�>!*&ebfacbo�(v�#\m. ��us]3Qo'?!� ���i2*�C<"�%)D�$p!��j�d-��h�("� � br�% sed:#8. as.Gnd&(e !a!�$�ETV� &R{�s �0!P?�7 "Gfն�(2(��|!&���5�t�:�C6zmu@?l .� , E�iV�BQpa8n.�1&�E���I��- 2_n;-2YOf cour���%%�24no&�FN;!�i6mployed  '�/to illu� t)� { 1�  \-�.���dLsk$�Ypas�2�KtZb a�"g�verif�7>4 ;#(or�+ �is : ei��}� or a1[��) )|jhypery�%2��Y@ulFQe )�!�� � �h�& ;�rc�'�� ��\^IParet96 ,Boffetta00}, (Lindborg00}� )Chen03}.���NfC��s suggZ�!M6�s9;*� 2r�~�[B��vs (!0 prob� bIK)  Mbe-H�Y�� �~�rpu,!��%d�6�7>�:s�A�c2g&M6� he�� � � ��*�"d5a�M(e�y�c]6te)B MQ�1�^�'��a`xA2�5 D:Cm%!&�[:�.� simi�. .��l ]�:Now�iL&�8  ?��td2e�fb[8!�g�i$m, 3n2�P!����Aep�|��'_t1 } ryM���%ja����/E�� &V'�ings (& 1�l tep)�' i�^-�A@  permi�S��4-� �'� ro>�T^�a U,�Ki+@ad�f2� !#V��5!Q�s�Bnc0TZn�rb���.�.%i \&�V";a* � �f�6�5|mo�pte&!M�bJ3�ND�0F2�2 �"#+~+}6Uw y8$dp_9%*:�>A25�U�E_�;R�El�F*-(:Z3)�+�n��Uas�*�q qu�Pon!:�P� :�R�er>� UU�yM\ �7 ��1nn/)Q�4�ml+a�s�nti� f�YɎ T04}�s!�543s"9T4������hA��if%e(< (via!@*.,V},"g3ad�*��!d2�am8cA�Y9��ta Ee-)Uz-�yAF�b� oFiEb5 -�!�UJ��[d \A)C'�Blaw<�' xpla�H$�,��� =�� �Y�!io>earlier��lso)1_\I FftJY� ,in; *� %�I�a&�Di<3r�<2Widy�C}Ued�o�v�b�,N V �T!�Zr0��"�V���, a�.jn{ "feCR Q�f�7oyA�xu6a"*>]V�#� Z mQs 5 m,e"�Re�2Rggze�8ngQHop p (m3��"�5��V,��9 %>A�deredKA�r�t�t�ts &�t&�Q�t�3oaa 1�by � 8XzI���T,huge pile-up�]A赍�afm���.�.&q�of- B�� &�&jpar.�UU ANES8�8 A�� a�8�� A0B$R� �&�Z otd a�Da=.�{)�"U!2 㑮top 4s�fu�.(8G+5.� �on{:�k }e� *�2�1a&nsuJ�t �.6<5oa�.J�#�J�3��E f a*� �oAY$a�I\a�_}E�G7d !� �QA -E��>�A�ifW@<jK�nAW*"6� h&a �>� � ��69>� �xiC U7M2tA�w "]��e 1[ jsTo.�_- 6!<-���%z} N�& !OE��)$ a�4rp �Vta�=Q[�ȁJw.�w&+#:� flux%#)� �a�%š f^�'A!1b�[by�.ys�D!�E�R5.a�_�H�F  Q6�mu�l�#�� �!f�la�s� &w��mi)i%X<��&�3�&�Ae�O�0N�qdJ'$E.�'��(!("�'�1�!1�*ipeN��! NS})1U*/)�taka��:Y1�I�%�:b_)�"�#(\d}{\dt}E_<�,T �F54. -3�(>.ps&r1%43Z$)��Y�`(�)$�"%3�2+%k:�M�E�gea�*�iZ_w[k_0,�^]΀.e.� TaW�CExEvnE�y&�X��)sJ�1V�z"� �"�#=�)I(��?�~evE�&� �mn�.x s go�#bB�Y1�+��!��.p�32�|AZ |.Y">/*�1 @'/ yQ>|>�0JO^>^Q^>NS nUN ��5^�N:�:U�,)(�W|.J4 c|+'y| :(y|m� 2�6o��>.?|(Xt^2+6y|^2)^ *-fi 2E_>�,E \sup_{&7x}Je Rfe 2�=&�\I {xx} � yy +2)F <_{x�-j|�;���2wid}Al���k�6t1� [@��5manip�Pi�j�!eJ-SBI-�%� $E_>=U..�>d�.`��['q�ѯ a:�-��n\ge��$�]*>�  $6�/�<��*..! �bF�A-�!� $, $5�!�($6�Ic�w�deduc ���2}�r","6��\�) c'*!}6�/>�ZJ4$c'=2\sqrt{3}c� e/earO��/=A�R�)>A{m( to-fA��eAzى`��'�-% o @'� V$Q ^<�/AGv"3;or"�<  NS�J�  c*�70&vDh�J&���.� s A �<�/m)gh:83H%%Sadvan�c � v&�y�!en6ipped�% �)8�Bat�Eous&�a�Vs�XzI $m�I@^nA�UBUTQF%�����q )N�d�c <y dpsi T^{n+1}"V �re 5afj teger, �q1��.�wceMrbAQ}-err.�g�)$A�� �ht-�/ �*!� )[.��Aw&*� S�3a�~�T�o8L bothc >� E$�ecg{1�: �5�w�!}�36�F���!um!��!R� �'A�!e>,Yb�Vestabl'�d � � �bLly0ed�׈no�)$ orH >�H�py�g��rE �� � um, $E�RE!> �ccaVG d �-J# E�a/���/*-�/= �(a}{E-1}�3{1U`6(mbox{for}~~ '>1�/E_>6lAp�m2�n>%:andF:Z� 2�ell�2� �\le�3 ell^V�<�o6k<�4.$)%<3�c~r��de"�%�G� �0bl�L�U%#r ��%"uB�&�ve�y� �k9�8'#J .� �>1$a �m=gse�g�� HZ�Us�'aim shortly. [>ubL a�a��$Q��2�&2�we!�[F99l223�/ic'a�}{()� -1)(Qy }�8�I�eb�j ;+1)/2M� (5-3 QBw9��A.mi]T Qa�d}?fq9z� } Z &\ge&m0^{s_0�]:= �a}Y�s/�F�Solu*$a$��� }\ B���>s3})�h��4��9�ZF��2��lx:] !k)�)^~�A��&�m1{����11drawn.mU�4}). 6a ��oɿ�9��n"&e[ $Z$ (re�*=at!� must�C$Z�(q"6/,�iV"a��`>gI#.��m�+� �x#�I�/c .5-��'!,HVdsL�e�p:���,�4a���"��*ap� �?u���� &T\�-��,a�pKA .�Ll ��ao2� low � ��= ��Jd>W ��st���2-nis"�"y�qr� � &�,:�--r&��w� *� �W� >��kA^�+E &�x�YogPJ�Q-��f""`�0&.6�  Sme im�;na\�6!LR *KB1!��J@L�be���0;�'5nO=| ^<�A&Cp�N�p �Jel)uA]at�/s P���#&�,o^0: �[� �Vw..�)f�5de:te�#o�Ac.�\� m%1�8>$(\pm �0)�� $(0, �INamely,JP�0=hFphi_1C k_0x\} + ^* - 2 y26226y\�(6*  I"�G�*w� J��+ �"�^0�2k}?(|��va� 2|) l92��k_0ɾ|4&1�E2��  =.E���(k_0), >�I AIp'N0j.A�mod"�^� 2O�$�I� B��[6�, "�6�&&E%b3��j� f� ��� 5!�JzlFq^ �^>*N^>�|}H|]Y%>�7�1>�>(8_x=0_x< +i:+y+*Nvg_��.g2�>_�,�h �_yGO^0_{yy}-0��|i0ebT->_]"�6��}�>>E_>Z�a f1i�t$&i>�� ˥�5�%0�Q�c�]*0=-�)�_� c*�%})�third<�du/6� ��l�5�2%��< �� ��f�r.�L . H�P�cb�$"UE��c.�zh�\ ov��b60�r�eS� �}��4�$�R2� �&yV�bWA,���� Fa�XZ >�!:1" d�$�? 1�a��,�5fi]!MV�] n d/m /�d*�"�(�e�^0Fi J�Jqc�� �~4B��2�*�� 2^{(1�fN,.��Y� k_0E}{QK&IBa a�&�Z1$�%�7e� @ � R �?,� yV_0)=aa�!�M 7!Q��i6] )j�Mu6} vW�� �/2}"�\pil-1)�tLikI�a 7wN* �Yeq.>]6}NI2Y>J2�$&@F�~ �6�y/2�p�$�&j�%.�Bu�K >:&4 .�GB�#4 �.�,�s�J} S��5�%*q*k'�p�c�adyQ2&&#6�ңO2��'V�/a&O$�{43ueg��vlr���M�i�kd �T�n�#�p leftrz6��" "J � %wa1� �5�&E��be�Q $r*�=N<Ť:yA��@bA a} a\�(�(2^{5/6}\pi w}{3&�-r>� >�Q�J��r)-ap?վ)����&I !>�as��f%[A�%�B�&b C} Cz� &Xi�X��$r=�� �>��s͵�edAH�8��R97aloneV�-A*�,0 U l2[cexp� $(1-r)N�havJSU C0\t| 0^sk3v 2^>W>Vf�1)�NPq{22Y x}{3Bs^{4/3}B��<&6 a<v��������6aa�N�6:qX�3��is+<%�$�c=2~;!� n we�rewritem�C1 sj�2> 4- ta9taub-=%�QI�A$.7���@�6&BpM�=.���C!:/�sh)+m)A�@DB�4In >Rw��MmH�1� j &�AM�.�by $k5M�&_j�a W&;9�%%ʡ��ec>fa�B %6:wiom]/!r_ �2 >t5!, hyON�2u���$53i�1A/:6��tau�aI)&\� ͤ�l �1�k*��"n(=sW than E4$ tend�"�A "�?97~t toucIup6n�Z3�! �1!��3�5�A~un�ۡTZi2/ �2�9A&z 1��  2g�EV�2��kB!,V�6Equ!"45�4�  noы�.YMވf any-�qu:W"�.m" ��.a& 24>�9 anomal� �} :.��u��l��b�5Rf6o�e6!�N m����0C�&^{-J8.�a PoweE|� a vs*���p�ateF�1��$igKrߖ53Af�8*��3� *G5� �%����4"�99e)2�Ddi-B� qXA�1f7��,�_2��& ,- � si�h��M7Z� treaCt�aU* 3 s. N�<t���y�qu�$i��׮A�I-� ��"ca]Jek stoo��;��priaX�����% a re"K?�%�Yg 2�#&L&�M��?lem&By�H��l�.v8&�%u �!�}=��|ba8byb� $ingqS\d E}�/�O/~z[#� \d ZB+P+ta^�G=�] f��&�Ÿ� f&&�A��%ɥ�. Y�6�O�`?F��kWpe�2lJ2d ɋ{ vok�@�7t64 �nA��-��2Ral�)�Z�a(e��ee*h�*Cm, EyinCm8> \& S2;mEKu#� c>)f� �} P =h  Z,>- �8��E��):u*v$N�& g2�U�Z&,(k^2-s^2)k^2� %= 0>�  E�� U�R� focu� �b��V�a?Y4&�7 } E"h i2a�Ap�$�~"�< ber,&W �-� s�E����U2on� �'� 2T:s���e�ha "g9t��\"�na2,����5s ��6�*^�n�~mAs� D�<v.enM@9pb =2�<!��c &�5�"� s�+�C%��a tiny�>u��f��to �hc�K&� 9��Thu[�tUE)He�citly�lud+!L��� .�9fa1u�q���eE #� �ed � Y � ^A� $P# N,�U,%�M�6FB�N; hold�B�7). An ��0�[P$E�!�� �<��eac��!*� � 4 $[s,10s],~[10 ^2s]hA�*uB>yaj�x��]$,�]�#5D� a=1�E�ib�7n��[�!8�5s]��i�="�@��-M�!�Y5.�I�iw[%��� s (E��F7O�+Q52�t :��5� �@� B03.�H� (ee�_1�F�er5� @ �.�Q��.@!� ��}rt2<qO�r$�!1�) �^s�a9 \s�%)^2Q� i.T�"iV�P��� wR_>e$� � $ tE�E�.b1�b��V�&JB� Q �P� p��>"Z� 2� Bz��;"�ui2%L as c�F� %�!7�id��2Zf' k_0/s\ll1� ڃ-�:�>%'�e �p��i�9.�M�e!Na���of2� *9!0b,y�of�]8,��_'on&ASEU:5Z�Uposa�no th� D��R$PAZA�E��@�i�����k�@�4el ��,�OYm�e� sB`��&!_"^u&P� �lL��`9�2d �O ube I3�( %�BO(2�͟!=s.c���Wo���[E�>Agu�IvK1f�hA  })A�B�-P_<+P_>� (Z_<+Z_>)Z� f$'�  !�e5h'�H:��m�) 6W'*��E�&şF�d P_>�_Z_>l1+1- k_c`}\%�_Z_<}{6F� L'<=P_�5 �U�"�!�+ $P_>�^Z_>�� XU^2"Z3"Rl?.\�+"- �FbGNe��/Zr2bN��m��A�k* ���]�� lso]� �.yB�}3kKa�CWj� k��F�e���sL�r4a ������umJ83@ "} # �\ s{ a��/ }&if 8 < k < s$,\cr b"bet !s %�# } ~~~ as^"b = b7>/&?'�C$�$,@kc-%  i *�!�en�K �;^�andG�4&a1�(�2�Q!��x�B�la�}�z�zal.�9�/5.{�L`milder'�Mu.�8M\� �� �O% �l%=3$����2�G�R�-} 2� ��'"V t�5� �Fa frg:0!&�.�2�19$&�2b�1}) �!%%� �"ng��s��bo*��A�-��qr��3F���i&s(s^2-k:�="sn" $, u�AP6� �^ I"�+m&�B ��MTK=($\kappa=k/s F�beaH � s/��$�<t�s $G^�ca �} �/s}^1��f^2) {2q�  \ge :s/e`Z<eZ-6;^�!Ii& ,aVa*.�'dropp!��1�� e�2Z m�m�*� �y $D� )�{ ��gR$. Excep�#"�Iry�>��9l !as 2oiM�I�iri��\( ��ja� �$���0�2S>o�%&��! 8 ge -�� 7 &d.�� -�%% &�"F� n�;y�! � %�)�Mb)E� $QG\leM$, or!�ivale �f�Q���+GA� 8>�H;"�R>��8>5$e��eg" S ��o!WHA��=]� \ge5S �M=Ee$]t�1&�V,� J3^����\�)c�I^1�/s- 1��\o i��se�o��L0%`,�)=%6d�,5+ &�ra��$ 2�A("��A\>�a �O P=0$q1Qq�2&NeY 2�{�mJ�Qo2�6"sR{!P%#+"be log�^ly��"ut,P`a>�>>9d)����>�2�!�6 ``$\ge$''�B( }) c�TV1 .g.�Q�2% �GF�z l1 ��e )$� �c)�1V v�� !=5$a be mُa M]m4+.XM.3^z; b$I�=!�W* X ��uld���� �$ bx+)l.ދ�o.�lvd�M�P� ��D>.�&` 5 m����sup$u `Fus++ ��0v;v how�decay�( $k�c���A{ \le4e�in~7a�w%gn*Z��L �e�*9NK"Ù-*�U}:�(-�=�O�Y"{ -t��b ��cMbU&R�\ �A�i!�~ �� ](�( ��A�J�is*F\"(������$) �EFerparto�� poy�aa \ln(�/s��}"� �/.^�,. Fusl�"3'!�^{��"�" &�#�>!#*��B���2C[z*6t�!}*IB�be*,u1&E� J �My�.*�RC>�6�i$tiF��g �N"�*�� D NS* !��_d��� �!.H� pper;#eO' VQd u� B�   \,��:�l9�>p��ato_UD5 %d!�g&eawh+I��"F�:�<h~��X�n��rzR AƑ3�.�dpb�Ds�it��)� �oB.* R��?prK�J�� �䕰|%1�:�I^.{ �� ���Us-�pa�.�^re���2twe�FA�q���2K2���!p�*t)��"�si�]��nQk�.9_6�\*ura�G 1�} 1U2�v�"�5 .I�Y ���2^�k>����VW�*��X&( �n^W�c ppos�'�J'�`�'!�Yl�&�'�Z�1%�� s:2^@��H��0wo &d ͉� 3,'�x$W���B:�"�E.�r�{��-�u�� M�T� bU!KR@�i]e.J��չOQ� ���J��)|to �Ma-�)�B�A�ez�*�58���� b�!�nVA�o �der�  }nex�IjEa`hU19+Zu��al��W2ve elabo�+u+y�c"��-���i�� A�FR�~ea�! 5�1�A��ras�@osetFts.��!%ra�E&*��4a2C� M�kv .�HA�.ed^x%-+\&�"-�new"��i�!V&R &�_"�hof�~�fޱ��A� ^&��9�B] isq��3M�[-c�.��"�5%ov*h��l <&vM��Z�%�+: =UG levelJ+ d@]a�"]�h�M!� Z-��4"�6�!� 0M%MD23/p��d� �%:DS �= an �2��K&@� n��N�tu�e:��!aN< �) �J{ at �- � )1 � . S++al >3�� ��=��&�a�/� baK�՟R�'Qruv02�Ea � .��bB[f4� %Shepherd?2V4��e�l*cOF�%&�Rw �a� B�GRŘB�2t'g.D� &ֶb"�C�6u��rP�ass�ex�D.�!�f3�b nd f�zE� X is ՛m�rblef1�&� H}�!%*qKA�<_*} ���&J�I�CxH:�Qe - � W9A�-� & �Ear�9%!it\-�hmue�i� �/In�0wo�I���:�*�� $=-/\dt=7-+�#7�$6:oQF$P�'^2 Z$.J"\>x�$1B� l]4"T�g��=h� $as $t \to �Mcl�)y�%:��K�3 .��E�,��AP�m�i<�W'� ��!]."of�6�%7.�*?9�.�6?P/ZЈ�is��4$VJ$7�I� �9�r6_� :�^�!~�&�is vali������fX.)� ��o"��! �h�xV `reB�'M�a7 gesi!>.'*�"3�"m�p6R �  +�3 ��<� be �Q=K�.@5 (Js�pe�J� ing��t��:Et�;&u=�Cޫ�Won���#v:}:t� nu$,�I� l& " b�6!ajŲ al b F�2^ E �jM�leads�/��)Bd���e���� ؽ!S�f�:�l06�> 3 {>(a�^��Si/+!i�^�e-B�A�u#� ed, `�no"]W� ?� q��N�Ymr*�  .�sf�E �,:e��k�E{Q� choi�FM����*\� )r is%�F!��" f;P pt���y�� ��7|��:K.��T���pHye��das���pa"g�g9t6aW 9� Nqm#E��("u} e�haC��e���g tK)m� 4 �!r:� �JE�$��������E48�:�R fua'� �&�c�� ledg�����was��v���+&�s� AF=� 2�S>�'N?�4 U�A�n�ˁfb@�3 x�}l\D�0ank Gregory E�!b poiklg��!S��� �<�6vM�1�Am��1l� %NS.K� �� 6�(Ka-Kit Tung�organizaaq ��uc��ful s� _}n 2DE 2��alp*.� J��ibbia��Jo� J��wm}�i�t�$�$P. Fischeri(E. Gkioulek�~��I] YF�qOQY �*t>�����[B�7 69)]2ٮ �i \textscs� K.} �� ${CoZIم�v6I�, :� *��*) .2�it{`� . Fluids} �$bf{12}, II*`�"��[ �y, Celani�! Vergcbl��0�&�y �� �E,X�\&I!�}&0)3>�jn :Q�& : De^�iyc<2Ga��a�S�Z5�E9061}, R29--R325���!�93�rue93F�rue, V%�93 �E�l�o�R2` ��ڡB�V�n���7�$3967--3970V�4�4v�4 �j��>� <^� EOU�%�>�A�1*��Y�|�9��!�03.]sc,�(, Ecke, R.E N A�L., Wa� X.A�Xiao, ZI�1�ad�m�!塬>��1�..�r�9!�214���\��[&�, FoiaY�{�E�!�$F� , P. D�� HO.PI�4-�{Effec�>��fun�9���� ��� a���y�Z�>�6},*��9�%�� 6)]{ mEQsc !ޡ�96 {Ex�  � 2�&��d: R3 (Q &�dr�eonR���y�%�9^�42|Fj{\o}I��5A�Fj"Z� ��Fj\o{ -A��5Q���h�-(E�)�:�A�k2_� g! two�zc��cnt�B�Tellu�|5}, 2B�232�KrgA��]2~v ��,�H�67-�{I2�K �bAB�a�.~>p10}, *��� m���71.�71 �n�71 ���"H �P t�b�)( o it{J ���Yo4��5!�5��yA �4�8 042Xsc �9B� � ��Eulz��hy*�ر.�Stat.~%��11A=&��m�!� 68)]"{�. sc ��EI285x����X$A"� M�n�F<��&C��iق�hAlvelius%z_ ��>� 8��.<, b 20R )�6�m�&Y�>٣*'�ٯ2�ձB/�945--947.hMer6��(1975)]{75>���E�Warn, i�75-���d2���: j-1&�� R�meD �>DǺ6aD66�Ԅ , Jullien!�Td�j3 #992ksc S�>& -C�E! ��99 �{V_�a7����:�9�| B~E�Rp 883}, 3418--34212RT�)]m�9w )Usc , LA� \& Yakhot>?  {Bos�&�!��! o�I�� !��a�doma�ce�s n 2D2m-B1�f�< 52--355}�N��99B8b��EF�-�"�"�o�D,B�&�B�JZ�2�12�138.��4 �T� )%sc{!�FV:�N*c�an,�)��Jc!�gy !� a'.��>� %�:< 191} &�ڹa�A^���� u%�2�2a�C:�RBՄmP�>uj�]s.��U�3B�"�1�ad�4 ў� �:�**}�� l�>�7� 242--��F�",Ao2)] � �V�3��@2�� �5� �~~�O� {.uwr�:�Z6�"Z�B !l>l�doc�� } у%\$![pacs,pyint�4 s,amsmathLsymb,12pt]{revtex4} :G twoc��n,�Q.L*�,graphicx}% I�)�� files23�d s$}% Align t�* %�dec�} 2;bm}% b E� %.�srcltx}.0 [eng�o]{b���$width=16cm)�he$=22odd�!@margin=0.5cm \toppt A���1�0} % 98.62.Dm 5.At % \1�,{APS/123-QED����cha����C�of gravj�ng l� shells.}%tRcl ne breaks?\\ \]"{M��BarkovaP\�Ll{ barmv@sai.msu.ru}2PG.S. Bisnovatyi-Kogan ;gk,@mx.iki.rssi6@4A.I. Neishtadt9an N:*��XSpace Research Institut�Le, 84/32 Profsoyuznaya Str , Moscow, Russia, 117997} \author{V.A. Belinski},ffiliation{N�al Institute of Nuclear Physics (INFN) and Intern6Center3HRelativistic Astrop=�CRA), Dip. di Fisica - Universita` degli Studi di Roma "La Sapienza" P.le Aldo Moro, 5 - 00185 Roma, Italy} \email{belinski@icra.it} \date{\today}% It is always \today, today, % but any date may be explicitly specified \begin{abstract} % \baselineskip=25pt Motion!8�[two gravitating spherical stellar shells around a massive central body is considered. Each s9 stsm�point particles with the same specific anguz`momenta and energies. In 3`case when one can neglectQinfluencEO�on�0one ("light") �P onto another ("heavyT("restricted problem")hstructurh�ph�lspace is described. The scal!flaws for3 measBdomai� chaoA�moa,! 4inimal)y�}� �$sufficienti0its escape to!inity a�@btained. \end{absM;H \pacs{95.10.Fh; 98 $+z}% PACS,uq�!�ey nomy6�> % ClAFfice�t Scheme. %\keywords{Suggested <}%Use showkeys cC op%if'vz %display!�Hired \maketitle %N-{\bf C6�(of a systemE|8result in cross!�(a border inE�.separiq!� areaA�(re disintegI�tA8 j is p^blea pres!� papeAP$hena;0on is studied��ofF�6�oscill� q� m!�:�. Simia�w a take ple(n planetaryE#molecu0@dynamics.} \sec!�{Introdu D &(al processe��super�black ho�X(SBH)!xquasars, zars�act�gal c n�ni !�asDracterized by viol%_-Ta, lead!�toaZmI�of jet a�F0 outbursts. H!�we� Aa modeӁMH!��18< from a SBH surr�� a dense5�1� clus�due�a p�W��al A]�M]ss.� -�4SBH. Investig�F  vs uE�R approxi-was stara�by H\'eA�$\cite{he1}M�is:9aB�2i as a col�� � F��s. Z��ً 6� ~�m�E� of ��a�F<rI,erved while ��iE�8e changing, yetaGEh�!value�8alld ��/ne ��i ���elf%$��. SEh6�,has been sucaffully$l�<�wiB  tability 1� 2}, q1relaxI7�!� apse-�8Ly67,he1,got}, ^SAD�>MiA,v6��#evoluM8�BBta%Vi��8ccount various 4 2lA�dco)�b��@!�%Ie� i ŖiCser!�of��A( L. Spitzer%��coa( s-F�s1,s2,s3,s4,s5,s6,s7,s8}, see also )o$vog}. Num� cal�Y!mi%uoA� -Fs�the �6  `0x8,x4,x5} havARown��(at even if A�A��e TiaA92u ly b�� , af��a numb� T passages through each�B so !ds �.� y to be>wn��in�. �w:xsimpli, �P�}of c !�wo�Y.L�, �� a�%Y�YV� 6?um%� �, 2jDevelopm�m X ��os durl A��# two 5kng!�ter�K � E� f!� first�� MillI�( Youngkins 1� 7} iq  o" 53u A�,urely radial��a�ref��ng inner)�arya� ^$bbb_mnras, jetp}��� behavior� �in �0re real� et)�de! � V�:�2�r p!4d iso8a�ly�%r�K)Q,��d I w( moving alo�ts bal �$trajectoryɁ56 field!T��c.T !P)�%=< currA!p� .R�� )mainls%�a �- ��R b��� V, � t��}iwes  ��j8 �m�u�5 UJ �L��J�6 F6 F6 0. We followYa���whichE�ust �M pet}�(analysis ofe��  �FoQ9H ar &� cir��A�ree��is����  %�a�asympt�formulab Poincar\'awturn mapE� ident&� of regio�vre�!y���% . �s�map. RHG;�#�j whS PKolmogorov-Arnold-Mos� KAM)!�aw$(see, e.g.�bdarn,akn}) guarantees exist1man!vantavve%:A�m�These� barriers� v!ng�9� ՙ�1!M�2�a�r��e; expans� cri� on�Mizasl})Jsatisfi{I�is )�vdiffuQaA�)a{}�|�Sga� osi8 ɾ%�tF� . On�K pertyA�!@�un A�����t`a�an op� etA�M�'s >me��,MT)$y�aAH!(E0%�V�is� tinu Dbut not smooth (it  a � �;E�e squA$root kind)� E�-onei� KAM-thE�nor �N�Pap�a�a situ%)� o- ���p)9r isco��� cer�1�i� �s� occu�!:�B�M��ree2l!�0llel impenetr�A5��,hysd}. For gA8al �Umapz �it6 � Dashw}An refera�E�re. The�"��Q^� a�. ���W��"nA� view�Es Tal me� �i��N�-�rVlinNt!�2%_ per��.���s] &� A�Q#�Cone�%<]0wo"z 1n��es $m_1$%�$m_2$ !�2 of2, $M$. Let $J 9 2$ b� 8"� ":� hel�2���� \ll � , soiI rT�secondwB=hep �.5c4 ��� a.�byLa-ogyi�O��9ϱ!�cel2�(:lat| a�eL� aBn aEoid��=a� Su d Jup��)$ w���Fg � will� �edP`!e,Ec)Mf3�ona��� >�,:~ h ��e� d �4amiltonian fun� \b?eq�i��label{ch1} H_1=\frac{p^2_1}{2}+V_1, \quad V_1=-\  uE��&� V�def!��s.b� 6r- �t.y4 $t=\tilde{t}$)@$p_2 = 0$. Denote2 y$���$A�$�$h+  $aC%�:9!!$ra�� L U=h$C %�� y =A� %�s � �%�FOT+ V ��DF �  $=����2&"hś�� ��um5*$t'% 3^ kYq suc\$at �B � a�%�=0 -^%A � B� �,��vi��fa2�Js. -�as $h�n-�' $) %T5($ corresponc $t=t'$. B�"� ion,V� $\Pi_��bF�ula��i�=(h', AQ'�en $\a��(k+1)� \�Q)=\Pi'%)#$i�/�qc)_<A_%�6[$ a E,)"�$�5��t�ke!�leaA� &omplete "�"on��5#�AO# $dhd!$���$;��" :�A�@�volume!ta ݶ�&� Refs.~��. Toge+�.9Awd llT��r"�, $\hat{\Pi}$5j��i�y,t',{}���'E�� 8be�uzby ah.��M��ql!�preceU�.}}yeoe� maxi.�r'*!>s�lFBm m��!g2A65I�%khiue8 ')V 2 9��dAo!})� q}hi}Bt N6�"z  < &� e� J� ep5�<0�a I~�M��Zm3\ ��rh/ 9h�_{An}d  .i bhi}� a���� h}^{l)s 1[%,>�h tes � _."7��*s Y w 0oV� � %J� A>� n� %Z� $�q�{-~1k^�� ��-, = (�$-�!�(k).5��O  Ͱ�6 e�S&va�twC$.���� is d�mk [�� *,&m�n'$: $t'-�Q=D �ft/ �-2 �q5). ,< 2=.7 �isa�a�reaso�y�A  m��6w �um� conveni�� ��t ��26we omi�+ brevc�$symbol "{}){ }\;$��! �!�� }$J�>) ��*%'s� is m@ %�� ��a< .�:�P1=\varepsilon M,\; 0<g��rK%ma6�^�&aF� 4} h'=h+a fI�,-�,�Pd� .�5 phi'=+Iq�EB}1qN[{h'MpM} 2�g ��'J�"s�Fu�s $f,g$�  � a2�� s up" : arguZ$mWh=0��=+1E -F .-HE�!�su( jumpU*�'s pot&�.�*�%AM� � >& b�R� � ecu��xf s��I�y9 �,A�x./�s. To fiGn� 0 �,�Pai'�-!�gy-�X assump� ��r>xaffec�byA}� (ma��is*� �total �$h$a D+� � r� d%��a� y�=0-� ���typ� h� . \sub� on{Type A�At� �E jph�  .� ��%�"y%|perio�% -Ee�IZ!�S, at non-zero�*E\4velocity. (If e+� U �%*w&i� bolic�n���#ndB !x%6iA s!� QRE��� n�w�.U"eiB��"�.�� m%!2d�0�2* 2.)6��(a�E�Z� ~m�$%9u� &�!G�� �=�2 K".�)�� .�|�ra�[$ f� hphi , 0F��41��A"�enough .E$ERh� yU�c��s�$erm��&o��� \� Va2��V)$B��A�i"R"�&t�l#%�+( neighborhoi�a�&l' u*eEZ B� �:"/6�%|_*$f* at�i�(E8M{92 impoC6ith zR%F!ace�$ , and abs}.e�<�Pb=$ s%����% eren�1�s �� SA R7�2d�0c tangency. W� A�vi i�!D10di "PYP3%��1i odisfars b Mnb#*2f�42gde�o��i�/��l!�y"P5s (say, .lsur�Y���W!��4n almost immed! lFQ6E _one*�%l;!� r-new�U)!O)@�3a�u[a�>]Y@(e�E �0UK�1,�y%�]4 sign��l��se Ti�j�6$\K|�-_*|' eu��� �[�� � at E ' A]% in2)'�� �� � }$ o� �_* �dvar-<�\a! .b�-isj5+ ^��y.X�G��2�. V!� ��c"�^*� %�m� E�&_a�is uniquR/ eddee21���of M)�!�be�� 2w ,h_1+J_1^2/2r = h+�2^2$ (bt&v��IE �I� *���=�!_3 \neq `3^ #+�� � a �� t�2$Z C� A(�JN.( %qs n�'.�1n9���6�H!w:�� lso&z �bigskip�(�*$ exce� a� a�e��2 !A�d*"!�� si meet� �".�( � !�woremal*>A of(%  c�-idUthi+ex 85�=$&�8 ;)�4��re':ve2. A 8.��Bi=h_�J_1=JA2k !so�$0 H,Z=�kR�!��i����in�� %a�!�� b:�_ 4�Na&A�4X�5>*%�$ /!4>� ��A. �)(/M=0.005$, �=1.46�� 2}$,2.}�5I �)u!��"�h�?� ��V !J��aA*��=2�  annu>"$\alpha3$h0\��e��t>B (� V�a). ant,n<0$ doe�+�" oI & $*w��6o analogous7"�&( "{},�J>,iP=.�+�2.P+u0peay>g{h�C �-B��8Y1 pet16} ).&N"�Zs���i.M�*'U�>�� %��A!~@d{Fi�1refAH1}} }F�Tto largj �J.�{�i*�/ oeffKA"���'/(Ar�C _& . { ��our ��,ons (�ch4}),  5�1mpl� at }�k��D�a'6 d*|2�}{ .� \sim . � F�0^{5/2F-(Ir�0@ �22�-\ll 1R$h<-K_1�.�^{2/55!a big��2�4�3$K_O!�\2 !*���*�1. Accorto KAMA�ory�is� is f09dT�-idp*�2( me�Cb� .?4�C �{> en� >������*A`$ ag8 ��I cu�c��segh $[0,�]\;:\; $� aI ztoC$h��iIre2��#�B��:62M n%tA�$Z V )N�!%-o 9ad b ).}��sf#:� are organ B�"islands�c" Bto&� !onances.� �f��C>k�|�-�����Bi--ic (i�[G�4�p, iodic)U-!F wk�z� b�@58. H�2Q �"�� y ���P�� ins�#kK)eB> a�6�+ cqui�)��_ �&!��E� >b� �st� exI�mbALn"�&by �-�$h�^-�΍� �EJ��!�$h.�]�X i��e�&% W. �� �Ifig2}�*rF���F��K"@exA.�in n �\��42�@loo!�.Q:?)>!�^!a&J �m�a���$h�&�#m�)N7 fit �$&e <)a -.�^{0.46��-"O �� gr_ulΗ 2} M2X%�h$1$Y� ��sJ aA�b&>:A� ���no visH �{�bigger =��' The � ��07 MY1 B� ��gg 1$� c2s�@� leada�eg!i ',#�,.���%$ '"7��7�:&�b ��C��to��"� "P;�. &<: $-K_2^�!h_16�� < h < 0,�)K�)beA�a �c ����&�S �.�aXlA4��&���5�`> ��tre)4�39 rano/I<. AVG�J|1�I;�p .���A�of�f<I ype. Appa�lCl`%*�<��es "�%�C %Nide-�5m)5�2EN"&UEe�3� �s �s,Na%�eg2)���) low*C� d!>>�6 0.42�:L ":G5/�� cd� ["}�DžC !�JC-Sn"OF� abov� is~f"eu�I�e-1V� a)< uMV%�3rA�:thY�o�:�Ulie)aUZ�j ��se�:a+.VQ��s�?2��z�(� a"PgammaM q h \beta <`,1i_�Qa Aq.�@2A3*fe $X, r;;�ant?�6 ki}�:D A< �yS�#a�9%>� :� "� $O� �*�}"RA�i:� � �#�;!>� A�:e.� g-&� irdR^� � M$>`.�`2 t7 2 2� \,.�� \exp(-�6� }/)@6{)5C,2DU�2 �aknse=!Y:� re� t.� ١M�,��e,�e�� �koccupyw >a��."now�ե�A#�  wE�!�F�B�i�^h��� m1%Ofi�Bu�jA: JN6~ & h>��"�A�it" s�B. S"���(�d=�SecU �6.� �Bi�>7�BN � �B.>� Z :�鲡i&�.�ōis Z� 3E�stP ofBY�?m.� �� klic ��U�� ��C b�!$M�. (� `Q[!��l� magn&(G�5EM�� 4}; )sBSU for &Cous%�JCrKE c, r��s^$w�!,c[�8IeADE�M$i�E!1���s " 4s. 5 -- 6): 1)%� $a�r.CnB� ;! � 39{�al:,ab��5 &qA�F� ; 2)�c� LA !�o.:.$to quite f�0Fn�]��Hqs�S��${%�"�s�WAvery � � ($10^6$&� �> :h O); abouIse� .��.y[i�X capA��&r� or�X; 36�!@�)Y! >� R � �J;�5��!�� Z�. �H�H� i�b� I8� � #ECi� � B2�-  7{l�2� g�@n ~ wlS ���*�_%�'�m"�"�(�.'x F�$v�U�� >�Q � �A�a_i�[.� �V`o�%a�I4Dp alT&E�� **I�^p��blIɭpJ&9 1�i�._."S��u�{YEb!VT 6T 1�6=[� F�D6� 60.38}$�1. 5�+�Dx_s_raz2��&fig3} "S>�����.� ɼ���V��5.m%}&� }% ���+ no "�� .� .�Ga03Ma2 ` b2�61=-0.09Jo��1.*�,hea�=.5   ]{regk_nk��42�aK�<T&- � �J| 3�<2\p@�B"�S[b�F���5.�MQ@�ţ��� 5� JLatf�EV.� �qF���>�! ereg����S�.B[f�6� �Z�� eY�F mR. }"V#1.5y q 2.0� e :Iwhite_��s�Q7�5QS^ZK���q�p ER�"N! "�# .�#�S��V�fo�1�\r"El HX$I)�V!%� e"�L����be�2;<$H=H_1+H2%D $H$=A&�1� �kE@* �wn[`l� �. H� �,&�F �Cch!� H_1*�G1�GVG+V_�8 >�G1&=��G {10}B�G1\�G26�G,�G��G1>�G1 �G2A� ���Gc"�G(�J/2)��K+-!J! 2f)}�$$R1nP8�HH�H:Im_NL{2}FP2�P2JP2-P:"I,%P1�!P�(I(IX/'Ib6O2%O2!O29O2^%!O-J68I1U� +unM (�L,!��A�B�*T,-�nonF{P�aat��~P�:|N �- J"@!2�(�H�>�H�(�� neogr_zad��&( m�fig8} ���jn*1 ��2; ��. Para�U��i"��(: ${m_1=m_2r(7}*s(��-Jr(51����/? 5K H_2/L  �,1=5.1$,FL�- =5.0e%��"�0:��Y��inwardsF�We3 ! �edftu6S�K. z 2����"fix!n1� Eme4 s "1�"""2 r�wA�{&l �Cs�R~% �A�V0 Lway�6in w+� c�/G�i��J���S�aw/�6"al9^D++y,� ��J��Je�-Q} Ak$�� "%}m� bP�G : (�J=�<�>W�W�!e�[ ��)��L A�A��+7�QFig)~e��Ye:K�h *��kZ;"5��-� {ConfbxE} / �&]xf�2ten�D] p�@"�W :�fs"�U�eJ�ed�*.M�R IW���b8l"V*l!�m�*#/("�88l.\K�@m9$aa� "��XL.�"u2e]8643neHKIW!J-�e���2Le" ���2 %�>00 %5p�� iv�/��X�!>2Z������ Y36�i �k=OH^*�:9M UE�$5opr.�I..�@%�M�i6A�#��.1.A&#Ia�� �bed2��s�[ag���N�LA2n la�2n�!_$M4& =g.\eI>A1?Y5�3ILE:3Q] &�H�:i�[m�^r"Z`-E%x6: not ]#!bit �&s like$* rent� !�noCF�M ,('wh5aRI! deal� 9�].~al (@i�h�ex*g`2�ez*� Y-�q��!��fi[#9�5��|wo�Q(f G.S.B.-K.OM.V.B.5"�-ly5�2� RFBR�]4nt 99-02-18180ɻINTASY] nt 00-491iA.I.N[ ^[>p3-01-00158, NSH-136.2003.1, "�so" B0053.&�Hthebibliography}{30g add  ents�{toc}e!� }{Re,[/ibitemb } V. I. Fb,, {\it Mathe�leMethodG�p %ics} (Sp�fDer-Verlag, 1978) \gkn}:fV.Kozlov%�A�(Neishtadt, F�AspecI-�A�C"�[M� R�97.�`_P�%4hwin, X.-C. FuV@J. R. Terry, Non!Vaa qH15}, 3, 633 (2002�-`"�g M�Barkov,%t*vpx G. S. Bisnovatyi-Kogan, JourA� of E"�%al 6Ta�e�'"�r�9�371 �9���h��b�Moa�ot%+s. Soc.�( 334}, 338 )� x4} Z�� LSYVZLrazova, Asrtofizika �0 27}, 79 (198.�x5�]p�l. Sci. ^14_121`.��m A 0P. Gott, \apj � 201}, 296675� he1}Ap,, Annales d'%:TqueM\�83G642G2)�H�wnA��ihys-~2!}22% 73) %u� ip80} Ips�aJ. 19���238�x010ls} L�mA�8A. P., Shapiro,A�L.e�(, Rev. Mod.E�$. 50, 437 {7b}!9J. Klink|vd B. N.�k, =ME)X6c005783 E�0=�b_X.V,6SEU,I. Prokhorena� Nh(3}, 0661313i716i3Ҿ$5}, 056127F�*d0 H. Lehtihet�6��yD)2Ag93 A�6�^p@} D. Lynden-Bell�zr�136}, !� (196.L�|�%S!�kkola�!iHi�tinta,$vsM�3}, 1I�93�[m2���� Y�mJe�e�87a2�m7aM$Ya. Natenz�AA:E��(Z. Sagdeev,�c K. Seryak�yG.H ZaslavskyQ|Lett. A �14�M255�.z�pA�Palme�(N. Voglis, ~"20A54e�8..g8(T. Y. Petrob�(17}, 7, 328�86.�0rst} Rasio, F6�, TeukolYSa�89��336, L63y�s1}��Jr�'&�qH%>Har216�{39�{1a]sa�L.�IA�48E�71b.I3V�S._����EN17A�5�2.K��J� T. X� u��.IA31a,6H�xJH,R. Chevalier-b �8�m565J.�s6V�J%oShua��200�h9I52p�J�bJ1AN7E�752qJJR.�n2 ieu.�24L61I�0)� x LR..��Z^lJ� �1Ef8.$ l ^}��A. Usiq�lM.}�u N� ��ics. F�x�pendulum turbul~_� �* (Harw H@Academic Publishe�y19J��4zp} Zeldovich,��B.�Xdurets,�Aa�66 tr�� Zh. %[Sov��,n.] 29, 742  ># doc O} �t\0style[epsf]{aE7,le} % % A4 p��A%Page *. % \oddt,margin 0mm \�m>"@ 16% head8 5sep top.Q= ,235c footfB 1 !%{�}�<J}yle{plaiV{\�|{� R�1n�`EvaluF2!�HardwImple96 ��onaddnCA-Based�eam Ci~w}a�v({% Song-Ju �,sc{Kim}$^{1}�3KenUmeno ,2}$�-]l{E-mail Addr ess: \{songju, !�Do\}@nict.go.jp}\\ no/nt m\hn{2mm}�5ioU 2~�In|R �!Commung-s Techno�i , Japan\\\�.\1~sW%<nc.+�L�>��Am \\ W( all �ScHhe�ilu-}automat�oCA)-b%opseudo�3-�\\ �,tors (PRNGs)����se #  gHate high-quality\\!4 cs^@2�& N _t0mtests &ub�1�\\6wStand/%u9f0 (NIST). A CA� suit"&hQ�iA�\\U�.!Pd&{ �!TCA-?stE�cE�l�s�5KIed\\ ��u-prsmm�g!-Ys (FPGh�I !A�7ry�speedK�palAM/-70mm}-�[^o.8A�deG�.>0\ KEYWORDS: P. N]yG)� or, IGAIG a, Sa�.7 Test,��18mm}�:�, Real �En�}o$*H�" I~Ba; } M43(secret key Ao �s��|�Ao�Qthus far.]4ref:handbook}.�)!�advant��A�8|=�-Wa block-�!� J)R�%x�%�siz6L!]#AQ�2�>�`-.�d�y�&�-E#y low-p96e5d} s. %"r="�a limÅ4�.7Ay ���I� %I�s"�=g7 - (s (ex. RC4)=�desig� %fo�{ft� -N �"�marcGY ;a�A�7!� �ag!�faster �assoc�Md�%$�2�}e+, vo|_ datajrieval���=) %i��1[M4as 10 Gbit net> s. 0f(/�=�/�w65�%6E!��2 r�d΄!�ziD.�nd}�. d6t]p�y,�m a�š�&C>t�=:z Q�Y���U�ts5+pl[�A]}A, l?hitn U$S�and homo�J!&units)}�CHES}��one-d�>( al e`ryR� ECA)�L�a�%�c�qI$<$S_i$ $=$ 0 or 1%n($i=0,1,2,\c�gNh<_6�i�eY  upa�e�par�f�-�P��ORsteps2S< adrul�A�D,� F!?$} S_i^{t+1�_4F (S_{i-1}^t, {i+) �!eq1� Gw��^t�Q �,$i$% � @Nimej . WolframXIlyI7�ECA a�;ANi8&�!ts ness=�w Rƒ HE+ Kk zs�b��`%30'A�bkAr am;}�)sz=5: \ol%@ -F i^t E;%c9b2Bbor v����1mm}XOR. ((}|&:%K� =�3B�-� �9�� modulo 2.!�y2�,!�e�/2� u��eECA30F��GIL6knb�!�,��?�0ic cyt9�  Bum !�$2�A6N�Gs��h ze $a�M�S conf\Me2��:1t�4b�2we-A3 H �$N�K�Ily �. Now, q% em~ize8at ��0 `ori� �|" '�B�� new �=/new1wOn��uan�Q*& � A��6o;sE� 90, 1.a 105e� 65,& Ru5of�ar <�FXOR��ndH � CA6)��XNOR.} 6� by HortrxuoM.�h1,� �( Nand� Chaudhuri<n6c�� Toi ini >s6278}.(w �A�at� 1651ԙoJn. More@I,!Mwit>��9�!�%�� Jb��in.CA5e#j &� :� �u3"e�}u��6"�E_ Die�� y & e=nd }"�NE7�Mar �ex��FE i ׅ���th�BCAs�5 a�#>K x�#n�%� F4�!!��.a�Amp�Q cruc"R[ � ��qa#aeq�a2q "�e � �dcts�j\ N�fdi� l&����L� �!�is wpal�D�� 0feedback shifJg r�!C3'��� f��!|)vAxs 2[ly=7 fa%:% ed}.�.fact,y��i�y;�5�-�6.9 ;(o � ns�%q.� CAC}�i� iz%m�J�com s�@reply}. Mihaljevi�$ Catt� %r���!u� F�2dsM��M2t ]. �� Guan��fa��!� CA (v rollN nd=o2� CA�X!csymmeO}�=] ship�2| �r ه �ev�� � �I��i�`peQ ji.h�%� [<� �, n2��#a�5�F�4 5-^dV�Eon (A�$ 535945230�V)CA � ez ),�.�e�Ne  + ��0�5� fF� em)xsome g��( (AES, SHA1 3(MUGI). Af+}b�#a��X�>2 "E� in 3, wWR"�'>0�r�. �i�Q eaa<.�o.4!hd>vc&�R�} 6��N�<�Ua�: Ec�6 K. Alt��vN�(�B�U]�%y!�b���e�knuth fips�Txfocus ,A B~E8� '}I�~5�r�a pYv�*ub�*On lVk+gZ"!��&=packagR s�ng!z16�� at s=HA�oE�=]�*rbitr[Q> bin u�!vduciBei��U�.�� �Qx%ic j- or J��9or�3!Ec�-�h,e�'Y/�<�o could"ba#a�m 5q{��n T��1. NnuJ%�? �E�lAre�?ourie��,B2$Lempel Ziv�]res� wwrong]Wki So8.�k�"���@�gl��� �q@6V���t��&�9�* er} "G7Lis�?I�>� 'v�Ww }{c|c} \hQ r�->&7 N*I\\   1 & Fr�?y 2 & B�N3 & Runs14 & Lon�5KI�Matrix�k!6 & Di�F-�Tr�)7 &�-� lap�Templ�Matcha18 & Ov�'�-9 &k�al.F10�YUComUU5Q 1!KL…"� ."!USer 8!MA��xr/ e En%.�1!]Cu?ve Sum.{1!b�' ExcurA�2!!bF!V�Nnt��7taIS U��>E�� } 'U�U�a,�8P-��co@w s toeG@=Ŷq�{�����. � ����|)suc�} iiD_A } 6mX"�4  $\geq�{alphaI4��w�lwi�nd u failure}.%]yMFnce l<X\�4100 ^ $\%!_ �s�Mex8*�&indGi&WAl�,B��$%Ln���- u�bj��21$. �3Dpre!�!��, y adop���A�-!��0Z2ach!� 2� &(1)l exam,}ia�ro�, -��cs ( ):bII~DfaG�ouF��&��[hpE�)�A$E�e !�����In�1.��e">p R \pm 3 \fef��8R (1 - R)}{m}} &4m�?He�K$R=1-QaA�$m"M9�qF1�nte��\�st��i� e 99.73\%I��!�normal�tribu%��/V2)��-�6binom�di8�I *�o�1t�^}�a�&Ssam.5�6 2S2bSuniJ-�2�ofy� ��.��c�4#� u��Y8$$\chi^{2}$�J"Cx$sum_{i=1}^�<�],(F_i - m/10)K}{ }Y5^Fpi� *EF�!�subU4 [(i-1)*0.1, i�vN�i!�� ��.J�u1$�ae,,P$^{\prime}$�1%�"(igamc} $(9/��-N /2)$�T!5�! '(n,x)gAoin!�l| �Q :i. �Nu� �7�At�NLͥ ��!bi9 ider��beQWl��i��� &� ��<�Iaj� � J� ��l.t ��� � LGɦZ�ۥ�6�8"5�I5fr�a ecut�hh &�wh&�-!q�s�+ues} hest. �!|� 1000m��� AK�E�� =Con t�V 10 (keys)�x mes$V (� ]( =ce)hU� 2ha\Tt�͜)e" c�1� ]&. ���aR!m��<2L@ $\{ S^{t=0}_i \}�xn��CA@5�Jinput�=eFw� d� >d 2`!� KEb�.j�� �'�P ����!��Y�� $N=!�Q&ؐi�^ "�I"� ."��l"� "� cap�X{*�>r!��e"efS� A� N7 /.  Length&( = >! & 20,A�&� No�� & 91z� 6-Uni�al (In�?iz� S�) & �. 280)dF� & 500"� &aZ�N� :#�B �-� 3mm}* ��R"��}.��V N B%>F;3it Pass}��ot_ F�eT��dC'�� m s GE| �=i+B�1.�R�|c>�Key &X�  R���5�Q�1 &�57, 15,�&�)�^3EHF4�!F�V����B��J1�5H�BI���6Nf��Aepsfx�=8cm yIw�{���.eps}} %B�K;<e=0.35]*&S�� �"O��Y�A֑�^4�&��>. g d �s,��qivelylid�2�J�  (eq.(a]eq4})�Yk8)A�label!>:�� p 3�� &�� 30+��` aN �!�=��4Z<s  4,%5 7�! 10),T e r�O (m�3),L�.ctcmc7 77 7� Ho�'^15D � , ex -�2656)�H�8wo�� �1)��.�E#V-%� 52 J4)U-FE�"B-� . S�#AZif��by 6/. A׍�,s����_*�2�� xc ��5�7")s 1486Z"a�.t*Gs  'U (nonodic p�rn�*9_ )U:.p at�A�~�2�ku0!�Jw� !-Ex eeI�E�;i6����[>i�ro�s�(11� s)����a�F�CVn�J?����Jy�ɡ�6��S�uҡ SH11��.��w�#^T.Ż9����E�s� ��up!����>��*��i���>����at� ad�:f�%4�iY�tep. �)4%H2V$ 6zh-�z5 !b*9n*10�+%-���im\all%� ss��"u)� 1�2 5,?6�.�# seem!�*�P�*���hsl >mWF�y &����kin ���� �X*s��s6m���J� (ѢQ\"c��:(�:�Rwo. %�QoenR uŰ�L�� Kf* %����%&�!.b(wZ\3*c&:�"�&always�!rC�^�eK��  )�z�ٞ i5s 6�7e@% 11(of AES (128ᭁ�, OFB�+e- 6x"62 2#f(!i_ )z� �D"�6�n�AES��.�.Vfv�15�%J""��&� +7,N� "B� &GB��m6�6n�AY����~�!t%@9��JzQ ,b]L:g!�J��n�6��6�6n��&����Jv�%cB !�V!�Jea�V1-Be!�V4!�8Yg�i�76�:q&����Nsix� AES)���� (a��inbn0A)6!�01�>/�c�(B,f"�#a�e�-�+:^�� "z$2�)Y��'Wqcn�N�&�_W!w5?r+"�pt *�2+{�&�ZJQ5& =�_{i-2q34B 4{i+.".�Z &F�5>34 &Q4�5.".V��cۣ�3�Z �.xw:4>S EU.!�=v�>9 ��:> nn���9�3 B�.F�+A�2=&�+*�&nT3,WB ^� 2�,s�+c+�+86t�s�0.u �1*�,i9�.�  8R� CA5-8z5 ��/ �{�7} (�W$i�{�7"�6� a�w/s  � B��R �F=AES�Xco�7&� �� 5�^ 9�j}?� m to�-^13r ݝas�>�-�-\D*� [ht]�i%"�*�2�T,  %�|"�DcBF%4�G%H�,F�%f{%�Z6f}%�~Z6f�%�K& 7�O%f�%�Zij�%\��1e 9�la�= 8.��E-�:��z���E ^�^ � f A � %W&�f fA5�Kf-R� Kf%�J26�5�6�-�d�a�S�0v%�-u�-} �is.�5�.�.^ �0�6Nw�'� by ;:���cue�c�!�!�"V+���* (���=�F���6�` attacke�on easily&�$�MsTC �(R�!) f�I�P&I4&� &5�"<@��"� a�6"�2})&R!$�>" =Z� "mi^*�=%. *��&�&kai� qIn&4 avoi6�N-�!�]2/~��l�trG@�)�F�8(@.t=s"����5=��sj�!� J���sase�Cponent�(}i�q�d'.D "�]!#�Z��t��N$c8 .j*� �%is}��-0�%:x#200xu=�%A92��=��oran $8 981��. C"9�m/�%2e"�'v)1}��X�dA� omes5> r (e.g.,�sJ��04, 22, 31, 41�� ,s$, 932, 976_for 40 ��c1� Z� s.�F� JH<^ i��de�"da�sha$��C:B�s"�nCA5}I:.� !�>� %j3&�7C*� "�JJ6:� 5��6� tate4�F4])��S2�in6� �"�*fig=�h�InI�!�i� �7ioG+}noj5er�,l�[-dly*�<di�@5�toR�e�J(.�) ��*(��f� o��=5��� � �2��*�\ be i�A;� �Ga�q��7 h�m�P �e�e�/meG[�'�?9hL*�:� 6� s�%��2� �wn ��:q 6}7:eUw�D�"� 1��� NSR2���#,]�>V �]>T�(woEYeQ7 AB�: fi�n8 �& ΄$����2-j�6���B��ߎ���Ei^� 2�# (!xae�)>���V�@�*� e�K�?cho��UP�FE"aa $M=5�nb����;�X2t�.�-ch���MuS& ߊ�e�n�a�� � �-x1�:*kM,i�e>H  .�J�6achR�d�; ?eL2�;>��"�M�*�.a��}%��detai7)N�&#�qscope (_?�� issu\���"�Pz H�P6-S�6*�$board]�ow�s��a΂,of DDR-SDRAM.d1&�64 by Tokyo Elec U D#Ae Ltd�8�e-4_.�-�out (J��>( (VirtexII)1m��volTO�T{ �6��(LVDS)!�!% � ".fpuro ٢�>&H q���>. N.�-� ��]F0��j�"4%�:,W*,@�!VyR%?wo%�s "f�$'zC}+ e)1a� e"&@�b�0e� a G1f10� ��*fz��s4])9l5!�%'e9c2 :cf��C+tv�� &�&SEk2�2�O) �-o6�� *�36@�ul�=x  9� �#: ����bK� "1�0"� C-KiL�^�2 =" ].>\. &�&��&& &aS( )�/469> 20 "Y 1�D *� (MHz< 05.875.55;9 �nC(Gbps64.24 3.02��>)�� 5%�m:\�$algorithms`+kl&to V� b���# heirN~Q�]� %�,*D����!< c [mthY�3L A a�CB!and*UP2}fI��6k$Ca *�T�Tb��es ��UE��07Mir^�Ue _A6I�!F� ��k�'�$z! Actu�J^��� a 1 A4F*1�W�t64 i �D�E=!`*�E�O(a 27 MHz>0"ySummary}6(hav�' view�w��A&DZ��f)N�)�� I�s"Z�&P 2� ,!gzXe%�� M�"G�;Q � q NISF)E(&WeFV:Mo!p.Qqv"�a/��z 3Z�-�eof� (20 KEg!�/O9g�B"at� i�S���E�i��V"�U6W.�iD\F�on*{Ac� ledg�Z�9fc"�@]B� a,�(research fe,?`J&P �\�hiet7r!IPromo� Scienc ��d �[s (JSPS- F>o_{99B_"�fP�Y Mene{Q�O: H !sA� ed C=[iFy, CRC PuE[k97.�^Ka\CZV< T.~E.~Tkacik: A&�Fr�QMQ�[ Lect�H"Fs!�fCu�X�<-0, Vol. 2523 (n@2002), pp. 450--4�l�_�"!U S.~/:5CQ*�S bFW a, A�Zces~in~-~nb�ls �7 �123--169!)86B) �26�.mr>8 a, b-:%02�b CRYPTO'851&29--432B�new6� A New Kinҭ5�-A Media, Z_!�BR&�R 1} P.~D.~B�R:pxl��R!�for VLSIU i��MJ$ IEEEgF?��JQT�B EGbjA:$1466--1473Z��2j�Ce�])`a��.�IM�˭�(`�built-}$lf-2,R�@�-aiSD\M�8I�842--85I�9B�T%�+T��my��Pc��Br�a�*�JyV��q443, %�34!�35�994B�*�TAR"�T�A"8Q1�"o_)I11�So�j� 6} M.~Sip8.M.~",T: �_�p�Z2�l=�.d�`ingaQ(t.~J.~Mod.~��.-�71%81--1U199B[7} ��5�� ^iY\�.�Q� , Fu��Xo9� S� 1�16I�291--3�U199B�8%f�-iPe t oud:!J�CJ�fo9h6�!� lex :�2 �71--81,��0Bp�N<} G.~Marsagglia:"�QQ>�http://�H.fsu.edu/$\sim$geo/ F.html�b98Bip } A.~Rukhri�, AB/L�>���!*.buL-��]�`ic��m�,� , �csrc.nis�ev/rng/% 1B�lKe�0H.~Bardell: AkB�fJ�� �.u#m7y+eern��a*cK�bcem762--764p99F��� �C;�Ap%QM> of5�N ��PZ@Com� �<4�<637--6�1Nz r�V!i���P.�!: R"���heoV����f�8��JK M1�� i�WaYos3��7#u-MI[� �Y�'B�,fU "� * 1334�/�~1��F M2F�%�H.~Imai fam>#e�+;&��s �Ron�ĉpF� �= GF(q)n time-UOICF FundaA� als, E82-A � 32---�B��X} K.~�X@ J.~C.~Muzio: Syn3Z�g<d]�Oal�$hybrid ce:C �j� -A*� a� �y�� ircuXa :�5�5--338BJL�22��2-by-n �J�3� 2G:ZJV� B� 285--29 �F�tY1� -U.  ) . ZhangeN evol�L�U"�UHN � ��on&aZB�a�u�� N M�i$t&� .A�E.� ���� �No.�"�uc36�3B��_� w�%M.T. Qu;u: 2-D<e0�%� qZ'[�.�� .� B.� �. Aid.6� 23M�78--388�F�vXD} D.~Knuth: Seminu_�A{s, (son-Wesley,6k�, MasU 198F��X "�(R�%�0Wr:C M�ckC� �kRA pyq�,/b140-2 2.pdf�F��V��(J.~Kim, K.~�o%�HA.~Hasegawa : Valid{) Chec��$ 800-22 >|VBM i;, ISM�2�on�G��JEdu �,A�1�32!�29�F�ki���On� �>�MS Z�Tp~Re �f I����103�<499 (ISEC2003-8�C pp.21--27*� Pwww.iacr.org/2004/018!�Bn"�' W.~M] %+O.~StJ�lbach�qz�Mi<�'�s�,zPFb B6�054-�18e9zIoendB= %f@"�/  }[h]�BG-�"*�/c�KlO.�% fig1�O pW0�*�K: TitleA^ ejs,X*%ny�@1%�|>�: 1-10E�2�a052�J8 (Received May � A; r sed Septeg 7K4Xv�d"�t l� "�t3[12pt*�t\te��=6.5true�0\hoffset=-2cm $bt=10$v$.5cm %>i1pt,a4p".qu���\{_Yxsyamsfoʢ colo�6�,amsmathth:@� ig} .8� icx}9 �!\renew� and{\the"F,{\arabic"6�.#HL>rem}[1]{: neu}[2]{\�upar{\�I\�{red}Z�#1}��N+xblue} #2}}%INCLUDES NEW TEXT %\.�vl} {}%REVERTS TO THE ORIGINALN8remM��H%TURNS OFF FIGURES 2g6/#11NV0beq}{)^He$A�^"beaFna��:we$ FN"\LM{{!xL6:\ M:N .N:la{(� mbda:PS{!�thcal P:l�: ongrABarrow:%T���L}>! � N> tq{{ qBpp>u8/W� F<d�� athrm{detuL6I even�x }{D D Hol�� A N W HonTy:3odd 2E�X�opeako5 pulsC�. s�XY�\ovl{{\� �:+un�b6�*%\�$pa�&yempty� F-��yHead{*}20**}n�g��{��; }--\��las }{A"Lz\copy%��-{200*f' �yA�8 of q�! ( ane endix by�yry Brade)Y`4Byatt-Smith)} �O${Darryl D.%�\A ks{C$d � al�� Di��h , Los Alamos �w Laborate� MS D413, .+�[ M 87545. �yD: dholm@lanl.gov} � *  D��4 ,�'_CollegeI`d�,SW7 2AZ, U.K� d d.fim 9.ac.uk}�V$Andrew N.W!ne�I.��.�� "C �WS" of�zta� Ca&[,bury CT2 7NFF�A.xaB@kent �}��"xw &��*'�}To Fr 1sco C;���� Occ�� �(70th Birthd��Ze6a�z.[W*�=a*b�Ygrif0>(Y� h[�upa��me|g$b$��*�&0i V4al kernel $g(x� ��b=$�$g"�\�L 1 (%�9=��|x|)$�#rK��.)�disa�on83Ca�na-�� *05r�1(!leG Dega=is-Pr$�i5- "� "�/6�e�$b=P�"_g�g6as�r+Xٙble, g�!� ، 6- )@o-PDE��, >A��G for $b=2`$ the family restricts topulsonxof Fringer \& Holm, which is HD�tonian and numerically displays elastic scattering ofges. Onw|other hand, for arbitrary $b$ ito4still possible�Pconstruct a nonlocal2� Pure provided that $g$S! Ppeakon kernel or one�Lits degenerations: wHesent aRof),this fact us�Han associated func@al equK�}$skew-symme!�4 antiderivativ� $g$. The�4bracket reduce%��-canon!� Pois!�+!S p �dynam*system-uny valu y�b\neq 1$. \end{abstract} %\newpage \sec�{Introdu�} Here!0w!�!�� a class!6\integro-partial differen 1* s (IPDEs)3� form��Rbeq m_t+um_x+bu_xm=0, \qquad u=g*m, \label{ipde} \eeq where $g\, *$ denotes� volu� with a 9� �alQ*@$g(x)$ defined oIʀreal line $\mathbb{R}$: $$ u(x)�8\int_{-\infty}^ @ g(x-y)m(y)\, dy. 8T�are somea]8tinguished spec!A case%ZE�1A,)6irst beA�!Ga�,ersionless v 1e �agCamassa-a�U !�X u_t-u_{xxt}+3uu_x=2u_x}+ux},1�$eq:caholm}%��H�$b=2$��(\ref{%�) whe)[m�is choso�@Green'sumA(,Helmholtz opa�e�!�: � \I( peaker} !�L=\frac{1}{2}e^{-|x|}Uam=u �}.aA�WA2�inclu![� addiAQMar={ terms41� �9, ) wa��rived as�^approxim�Lt��incompre�EuleryG, ��found1be .letely.�I� Lax pair6a��bi-.��_<\cite{ch,ch2} (�ran�ב�on, see ,0johnson}). I�rct% Rq f��in �0framework of adit�-q�e!'d recuE�5�!JTscribed earlier by Fok%Z,d Fuchsstein���0ff}. A remarke discovery!� %�!��b iIe:hlimitM�=�e� solitonm�eV �A�$ons, given�$a superposEn�a,�Gnumber<sq� (x,t2�D\sum_{j=1}^Np_j(t)I�-q |2�NLonm� (See also-beals,�Ust��n. 3}.)�� $N$- H s�}s9"c)� weak!'��sI�!c(continuous ��QsvA EX 1s $q_j$! a�{s;  , $p are �Mcoordina�"aE momenta i� �+,finite-dimena�>��k;v6rpreti� of�=is� usseCr! in-\c�%U2�� =H^a�E� obtaŤ@%�2}� ��explicit%on-^!on2P�CIx in I�P 3}. �$stability !e Ds-!p2����� ed) U�4.;5}. �4aa�� p�)Lofhmethod� $asymptotic�gr� to a many�ameter� !�(third order��sIsy�, %) # lizing %��bd 4}), Degasperi��Procesi �dega} ��� $only threez paE !Dtest up�.��s� expaE�, nam�� KdV,6�A�one newn4. After rescal4&!fy 8 Galilean trans� %}��J9�may�nwritteAK=>{= as�2R4R3FR. ��eq:tdno!���$Henceforth| refer!&5�/) a�y=�-1���4observfat it i8�3$"�!�7 n ipde�a` $Q�K|}/2$. J).6�rticl�/needs}�m'sa�gQ�I�e YlB��*c�;5 )� Lax �� ��8% wo in�� sequ!Xř?er� (on laws. %� �IIP\remfigure{%BEGIN REMAc gin{ }[ht!] \�Aer { \A�(ebox{0.3}{\� d!cphics 8ons.ps}} } \cap� { {\it��V�!O6.8j� onj4eriodic domain�f orrespond$bA�a�Bm i6�.} } %,collides��E�A` slow6nes3mx �atnd1O }%END%h�M�]aY��to be� under� mona^ pertC �J!�qileٴ*�� )% Jv,a� have� itaQ veni��to*!follow�VoneB��p�%>=��s (;:A�6\(b+1)�`:� }"� �-�eq��� Since�ario from:�� I& � ) er}) �G� %re>��>��O $b$-�Y6 �. R� y, e� me�  2Jt4 admits multi�� ,i :t V  !�r�C$� l ��"� galliH two-body=iG 7� \�#(Y F�� =!jons~a�,ll� �b>1$ � +���to be1 "�� leHdom �� A~5 problem�hs}. F� more-6pA��x ar ���($u_x$n$E�x}$*)Ay4has been shown�at not6 ^8 T dgh1} but� % whol��UYI�]� ) (aakI�$b=-1$)| longa�*�& �Lequivala�shaa� wak w�u��2a��� �I &},ed a Lagrang}C ul� E!f})F�-�a L�dre:�  lead"rV�>�=\hat{B}5 \delta H} ml �Uhamstf\8w�� "t Y T=-(bm\!�(ial_x+m_x)(- ^3)^{-1} 61(b-1)6"�H&� b-1}� msx���eq:hamo^ (I�jA1�necess�!/ake $H� m\log Z�stead�:��zator $ �$�5� �)A@�F� ( a�A�3$,�I a secondZ�7j�R�. How�z,�ro(e Jacobi id�tyb ���4 lackAountil��� of u|  Wangm$wanghone},%A�hA� ivec!Faalism@Olver�o }y � i� Gis��e eN. "��J5�.^ rei B_0=]�(1 ^2)(46, �B_1qT@|_{b=3}=-9m^{2/3}Y�m^{1/3r.Qm '$ I.� tdop� e�li�!S2����"�!�e b$3!�4X"fI-�ch, cDis�~?,� !/-(.&� m), $$ � !���rB!( $R=B_1 B_0�I$�$B_1$�� "kU�^ B_2\��!�A�m�%�2}.- Moreover,��Ivx i�U�N�m 2,3$��" par��sA� ����O�by}őVR mpat^w��IcA,ant coeffic� si0*( �zs�c�ls}  isolb�e q urb��y!�roachMmik},3(Wahlquist-E�rook ���algebra�K5V, o�uE�Hipr? 6��t� U: Painlev\' alysi� pain��!�.����%G!"� �ic 0 $2$Q&N�k[ e Lie-����~�`{ m,\tilde{H} \}_{LP}:= j22�=��, =-ad^*_u m�H liep}1 ���ra�2K^��2�� g*m �q� ��=u.a� E"~ Re>��) :Q EG!^nc�ӕ��),geodesic mot �omorph�}group!�!",$um���(# co-m)a� R�a i)�itey� I�fr�}  �  detai��; +homa} 'an ext��hig� "� s).  "�a��V2���RFs1@n? circ� �misiole�*� a��&� 9�!lleast aprincipR��in6.s7a�� ��i˵Qi�2P6�g�&��V�A'aIF��!s� seO p�M�I�byAI�7�s� u=.� �a\u��P m^.� ()"� �j�D2 al~ �%qHf $N$�! +ACa�Mo� .K`M>�CanV2�manifold��.��8j=1,\ldots ,N$ Bu���q_j-q_k��<"�.�-� geoham!(��h}2��8,k} p_jp_k\, gk.ql&���!6r(q{ q_j, U}=)�_{jk}H !$q_k\}=0=\{A) 1 "���be&� (by substituY!�ansatzmQ)%� $m� "�.��$$�� (x), m(y)Ѹ$�!t!A.j"�$j� 8nd similarly $5�*u -���2�.H .�2�2on�F.although%+�NGisc�#ly~ -&h ,&� stud�O �"��5ide �e nc��mn.� �9��m  p�#ed�&�smooth��i� data, ju�x� �ĩQ&e�%��=RG. We D�ed2xa(cular fifth5m1� �$)2hoho},9� .�&A�- �to�&2C�i 2)T �(�(�(Z(45J),5th_GaussianB.Pd(�>jof"�  2\U " =2U- 2�#$.$ emerge��� �Adunit A�a�Hwidth $\sigma = 5$ f0bout $x = 33$�F&�� U lengFL = 1005'��fas�I4 cros5 the >r times�nd���N%i_IinCond-afall/!our_fig� n"�����r�0 One might wo� whye�8azdiscuss�subjecta�,a birthday �'mehonou#DFrancesco Calogero� f�$ ` already�[*�of�V �����J �sI� "���W�m iь�"� J_*�A H�*i5]` &onent+�matrix���Jc-)}e5��A �)�concer)wB sl!�,f�)1@. It tur�u�#6�>B�s��� well!&��� of ;*-@5)>. 5!B� : %\b.(array}{ccl}ydq_j}{dt =�� k=4%Y g"� , W  %&& \\Cp6C-�:I� g'M. %�+�q�eq:�6dyqCl�&Z� ak� B.h!:�-!�! ]�"�h}�> >�[ l�@& *�ge.�'�ndJ!&� 5�}ZJ��7U�-� aQ�A�p�(��i�Qi=PM-z%T"�D��� <m�b!�I����%�+� "� . R4�i existaYA�a cer�% typ BC��F�M�u5?�a*�.A�! �} G'(\alpha)(G(\beta)+G(\gamma))+   3) +@ ! !4)=0t %� %)-rm{if} 2+/+ I=0"beq:fn1���w$R;$, %%!� antiBl!",",G"�-,0^x g(t) dt.�A�^%��)_Ase� al odd"�!֍� �). ~ A\, 10sgn}(x)\Big(1�B�a&-L.!ce"� L=AB" 6 \� (A,B%r�.rm"�})@(�eCV!g1lr� �.1�',an Appendix�� ; $H.W. Bradeo\ J.G. Byatt-Smith.) ThusI�p% v�( pick�/ut� � ���� AN (1�. *��<{?��A.F�,&+Y|, 2�1q� m �*�)dF�1�/.en!r���of��� Pv-�next s�1d %�eR��pN�Q�9A��tM�ceQ o� how�]霡3a suit� 2 |IsY \ (graph{Histo+ Note.}�A� aperAdedicto  friend, N T;r��allelsi�of �kD.8ide�ons) "� flow�)!d�uO���!�9� �_sA��J�s."� 1da�,l�s� 1!!}�.i�)credib�/flu�al"impor�elI+�le��s.*J himself!c�5developa��ce'*cs *R0A�)�area. (J�Ll� ;200+ p!�%$ MathSciNe5 hs c* !) H�ontrib"*.ll sur+i ��e E����f peo!���is�, F they%X�e cur�4J. O>7i 'sP�&> A�at[L most directly releve-�topics� �P!Vm�)H:� ,CaFr1996�   "�5D`25YJj}0tcounter�{{0}YLe7"r��!� �u %T"u&�".x :} %m^�5 %�5l!�M5\�3*�#o�1e keyA�t+�6�a���lI)"�",!�*�2]�!op�.#=-(b m ��+ _x+ �"G�6 .�"�?#!��x�G}$�s acc�0�$ ^ `f�G*fZ?G�6f�6, N%Vus �B7s !2�8d�5K satisf�4m_"f$ 2.g$\,!��5W } \,,! H&i �#F: $%. Now��calQt� ���! :�B}$, n�/ S\{ F, G�R8 �� F2u%�:h%G",� �sz �SR =B ( q y8_x(x)y)+bG'E(1 -7 x)) c>��Z - b^2 G' EDAKBig) �u�pba6� AIH� b�ASYn(s�*A�isl  i()�s a >U if%�>��Qvd, i.� >� !���} �Tz)\} + {\bf cyclic} =02�jac?:�To]Y�,)�e�!Au%�.9� (s)}2� \} = !q5�[MS!�s%�y)+y x)] j$�U=(x (y)- <; :Q(x' w (y)]E�f 6*6g� e� �) �#�V "��o_j�Z��a�om�(s)(z-s) a�s �(����B+f� �e���ngv� inde3 A* vari $s$� �.�p>�6B�yc�l���)veI$+cub#5 �, $m_x$,Vse +&�# m� (each vanishqQ"�'holdsy&$m$. U � toNiE�<�a�, �+� r�9y2�+1 �,prefa(s)Fse:�( 2Y�F 6$b� u�:t���a =x-y�"k>� =y-z� =z-x�>�>a:� N>�mw{ "�05|�.!�����z)$ y� IN142�U@A@ �e�@ ������))+ "! " 5 ) %��-7:�  %�"�67U�19< �#!y!gi :F� .�'�- �)-#'����%���� "! D�@*�fn&=:�^ nE�twoCmT likey�G) " by�wS'mu^:�$x,y,z$(in;B-pe, !B �,�, � $ (� a��8�sum�$o zeroA]S"\2*+()�i!�%�M�V�!�%U!^9�-_+:�6�8 ) -2�'�.�R�[+:� ��z�% �>g"�5z3a�Fin�!J.v)FE�5IrOesJK G%J)A(R �=o'Q�%) :-qJ &)r:�fn4F� �"rI�s?.al ng�z9�th��J����3��2})��.�3rBCh�.�8.+1| 5� b�F�ia��*f!��p4� lso� cony!�!��G. �:>�O"� a�5Fi ��",ifE63 �3 QB6"J.R1A�W�!(7%�6: \no�nt Prox?.}&9 SuppQ�(�$v an�� ���J�:��E��i@�0�V,$a��Ef^Hll $x\in��E$\backslashD 0< m!Js ��EHrm{lim}_{x\to 0\pm}[Hi�).:en ei�� ��x$x,rm{n�$�"s?A6�$s $A,B$. }FrSketchAU�1.} If%� E)+/A 1+Y��t��!�li�B���� >��K*1�0)={whK0`a �:tah� -=G'> +K_{ENlp5�Fl,] K_\pm�>n�5iE� � >0� <�"� is easi�:to%u"oCP$G�J>�9#< A mo�__,edu�o���g;X(�7B5�od�%� �Cer�Fump��Fpz%s�an"R�<sJshould �@E��*� BA�\I$ n$AQe��8"Hal ��$^�  w 2A\,&x)~results,� case)aAV6щ/becomA< he Rieman�8ck:�'2(�; mm_xA�oi�z �0�\sim 1/Bpe a+ar.���=A�9�;��la?=T �g� trivC E PDEi�K �� K=A��),&�J %In!�t�'o* ��p %���en %�%�b�@e^{-|t|}dt=sgn(x)@|x|�� 4)� implg E3"�ɡ .� %�{�R! �&���&�< %E�$g" B$AU"��$pa5 %it mean�&#T H@!�OPwe %previously wrotea7�m6O6 '6"L6"J6H6 %%"��6U doesY�"B8IF natu�  %quesa�!�whe�4(�D�A ing)9K dhaUy" 7s. *che%�iBP %�kYL�%/ni�e* %$g=1A$�=|x|\lO@$�n't m�9senb%Na�of��cksB$gk- �. Lj4%Tayl�Lr Lau�}&�E� G$�8t�)w� A!(G� �^K &( +^�- ">M�))�� -b^2Q -y�:X 5�h� W-(x $\epsilon�� $0< <\min_{j�Rk}|�1|.Bi��.�oryB �a�'{c(X I_j(x) & =& 1,\,\, & h  [l�,q_j+  ], \\� <085ref@$against "�! 0H* iJ8V-U-r�P$x=Cy=q_kn such��$ �I_k(y�* J  etc.��f!) m�i�X-1)IK!|�3I�� �aA 2(1e�G'3�-� �I3i~= G3!H*�i�3end.C\% s��2),~V� �a�"t& \ �_�H�<%̩e.R �ax��1k!'i�Eyk)� x >^0M�S5���Ai �&�"�"9pea�*)" -��"O+�4H\&�S #qr+#!�H\mL�"=gWButy2�;� :s_ � C "p. Fo�" ('o�)�2  U"we� ��N�\{2� ,p_l\}+.�=0!�(p_jA��qB'2�fi�r 6��bMj,k,l *U5>7F�Fy =0 =>�F�.2d jac2>*r e"Yy3�Us�ul���*�K}8GG�A EA�*�&*.�+�<"r�:3 "%�theirN�Y�,�Q_ V�'.�1q*+ Z guarante e����L)�:2�:��"$[;{CoW? ��=6��q��5�L<leg%way to�) �(!��onH=|*l %�.0 ofJ)- . H�D, m� � u &* �-v  *�C(|x|/2)H(1-x+t/ �H)� 1)�[s�" V0 y s�rt6�D�z H�%-SaxtoHBo�Dos}x Vakhnenko|&�V0parkes3, vak}E� � �orm�a �>"�� $\��G ^{-3�"�!�"�I`�#op���EY�f�Ea"B)�BEc�*wF6s0 ��?no�!�x F��sh%f"]N2Ju01�soA re m�R-4s 9%�"�b 6H�Gi s > ctlyiO6O(Acknowledge�)s.}���gratefu�M:n Stale�1m+vi� �FiQ s. B author�(5`an$thank Toni�!�a�9�&Z0J"D����>�hospita2V1h Isaac NewA�InY<EL�\beganZ)�o.U2;2001. AH ��`rry.f. John.e.���M� �u��P5al:��;=� A]Ky Leznovb sugg��'he�.pl�Ua�[ach�muodd. DHeJAH)A)�8Simonetta Abend�8Tamara�avan+ invi��9�mee�RA�D�Ca�Geo~B!orfO�CaJ ^36 ble S�Xs}!�Bologna,  Sept�O 2004|a$we dec�ao�sh�+!�0) �s! E?&� Q"kD shA�-pro8 and �ly&�L%i�* �2>j �.{o.*3.}]�",vspace{.05in� v9VP����њB� �fnl�5$x)\left[ Gn'G�(r�9] �yz�"x) , ,<xy��}�,$x+y+z=��b"�i�L�n��2 &�. %��3a*� aWsu�J�b)lA>� 0e� ie�xW�eB�ad.1Wal"��a!��0A�1 !{�&aQZ:�V�"M ve. �M�^s�J(g*� ) p�Wser�"\��! � vals $(&�0v(0,�)$ �a"c >0$)! n,��� invarif(�!g�� inv}�,MF4arrow a\, G(AxO2�x E=o�g"�;en�hate���g1�1�} sola} (i)��!` &�c}M�e^{Ax}+X1mJ����$AA�j!cCMXE[��b�Z� \si� -�\pi}{hF��G�g� E�=\�#\, x$��c�Z�{\rm � �2�8�-B^9.a �<=�Eaq a�*2i.!!pre� nT ��2su�.JA �(�i�2r%��5�.:h^assc@Y *"� +�+|=ly. y$G(0)\,�(!�WsC!j=sv*($0=x=y=z$ if�JSs#at�\=.[e-&$xA��$z=-y$QD��'��,G(-y)���,�=0.$$�$/\lambda�9� ?> =\pm1!nd�.�!'| "# even��   Pg$x=�jHj�redpr�<-2x)Y��'��,G �2,j6m!so $$i;d}{dxq� GA}{G^{2�;}+ 2}{TQ� %-! �,� au7t:_ l $I�teo���6vev�} � � + 2�� c_{I2�i.�� I�&eE�a���$A2vaC@�" to�.!�is>���f.7��ɇ R�%ki (� s��� 42�o^b�'.NFor exaj y�sol����red})�W$c�!for $x>� c Z $xM#(W 8e8ee&�:�below.)u@:�1�>}con�?�jG�}y�F&}]�P �+a��$G'�51\ ata�$ point $y$�a� +G(-|ne�%,E�.)%�  Jx��u66{4($0<|x_0-y|<_$, �/��ox_} j#��(-5��UE M�% _X�G$! �A:x_0�2 e��;d)(E�5\�D� �� �L��-2 O��W�k7v� rec}"split} 9+��&=c_I��gx)x)\\ 2'.&�G��^{ 2}+�� 'A ][� \ -4ND35,|!0�E < D-&8\ 8\,G\sp{(iv)}J�k.D+c^{ �Dx) h -2��-*:� &� �b�*�6]�st gEa($?E�*�AIN�>� Au��At��A1q� ��oJ!�����"*B ��,e�a� veri}i�s� �Hs'y�cO�fB"q �� ����<somW=$ighbourhoo=>��6*4#h]Td!Q9 � �&U J&9$6d wh$6"� ���|x2c��*" ) $x$MU�neGXi To��u� betw}`AJMŎ��9 setq�Q(��{< .(�,&- if}�Cx>0,\\ f��F!<0; Om�E�nN��,align} f(2x)��{+F�^2-2\, ,&4 redf}\\ g0-0� 0 .20g � j2�'?2M��f(4x)����c_w%w�C �)6�fx �{ Ou2*d!��in.t@ ���'� $f-g("Pf'$E��S���N.�}^aJ3\,X-  ^2� � 3!�09/ �^2"2fn!�b��6 �<x4diA�ct s+��bs:R%��y� >, Case (1)}��%._Bbb� ��$c_-=3/A3/� =c_+og  $Ax�A�@>y��am�urwq.!�i=O!���nce!��u�r. Tq ?sa�))Tf�is�4a &a^� o�"�*5�G!"F CR. B� reE)u�k���sjFF�\���Sy � �?iW7%w =3/cwX��q��xps"M^,2>,�9�� A� ib9EieA���(a)�%f .�iE��E*MA�M�At��/ $. S�(� !�.�MM$c_2\,x^2+\ZX�to2�AI�Oemplo��is�.��ws-|� /� �4pO5 x� u�&�"(b)L�#AHbsaM��=��e�. � !2�� y "G�^ �n;5aJL6X06!,B5���A�&�Bc�$ w0!�^2xh$t^3$�B�(3%���mH�tl*X $c}I"��j&u J"�_",ul�0=�>\,�b�\l�g^�tg''�� ],$$S'�!4ew��c�5 �6� ,a�i�i�(o_-1RT� :[Q�%���e"Q8�ATe�6U<iF�&� fths=x)=a\,�b �dB As!�V��.�"�� a5H)6�w3& now *�FU��a�to -n!�origi.EG5E�, pla�%A..�T.!+ �WxE�@,A�6%�%Aa�ed Me}*ics1#4) 1-332��aF��b�C ad$B�Otal��of!�iԊ�2~r=�B|" , %)ica D�$9#75-8920U�6NB. KolevMf-�g"0"e� &�oin8� al m���0, PŘ A 35%B$2) R51-R79Z 7v��.G�s flowq�G�@ sm 2�scEr�aentq�Helv. 7�9 3) 787-80�.���A.*�2EZM.E�esi��sVy�}1 �S��� Perwon� y} (eds. FnG. Ga�c, Worldaentific�h 23-32�|A.~&�3, A.N.W�Qne�B_>�ѵ�T� �a; %NEEDS�11)eR3s,Kore5q��13iS2) 14�u476g����v` no.7ou<s �/� , in�NoU A� ics:-�NExperiA= II}, %��M.J.~Ablowitz, M.~Boiti, F.~PempinelliL�$B.~Prinari�e%G� poli!52 F�D2003) 37-43; {\tt �(.SI/02090081��d�`H.R.~Dullin, G.A.~GottwalL9�mH.�<, Korteweg--de V=.-5��@ *U�aS3uPv怑���2� �Fluid D�b(s Research M3) 73-952 dgh2��� u�>�2��c��)�N190��{ 16� ^qO�ew%#9[i�]�vs.A��(g� g���  be�ou%.�5 � 1) 237-262 ff}B.~2��A�A.S.~ݐ1�Symplec�5s�ur�r<B\"ackl$�ra*؋?P�Bk��I�4�81) 4�|%U�fuZ�>�,�3 it S�N�ksJ8�[ y toolboxQnu�Uj : %G)Aliz"M.�0 }, %9Y9� 1 29-24!X�Ef}C.~GilQ�! A.~P[f!� , %J� A 28� 95) w -2888.{hs}UJM.F.~�9M+ Wave�u�p��Bal"$ a F��& 1+1 Ev��+�A�%�*CD�*$2059} SIAM�� Dyn.�7. 2E�i�<86�s6��< �NoU��of�J~s;} B���'�1!�. 1� �1459-14� & h�z6�( J.E.~Marsd�2i�Mˑum Map��ea'd-valued�� (��a Fil> Za$nd Sheets)E�A�EP�&�6�312048�Q��ł1}FN��7edV�E$yKdV.�]�3"{ L307-L314�!.26% Ex�8retm\!�o4Ermakov-Pinneyz,}i].PA 263e 9) 347-35}2|36|{ Reci� link%_2+1-d�u%al Ex�|a� V[s\Pat�f�ers 1{0�]2.�"<>=�%nJ�P Wang�[Prolon�on�IU.� ?� w5=A� B^19q�12A�5 [*�x��T%F��a'{e} �t�\<�lar0-��q�e�* Wis�� ?�� 8V.~Mikhailov, �ce�=Uni)iMD;p�@;�M(20�YiOV ess; preSt�0UKC/IMS/03/336}jA�D.�=sb� �.�*���re��mod�i;6 s a�J. ��}�  63-� �qIrLt s1}J.G.~K�X!�& C.~R�|.E��9e� 82) 261-26o$kraenkel}R� K R$A.~ZenchukQ�Two21�l"%:� .&U�}��.�260q�218-226 mik}A2�V}NovikoO&� vDj��&�I.�5m4775-4792"� G. M ��b�a��?��.50Bott-Virasoro���J.d��24 �8xX203-2082� K-r}P t����c&�Lie G�2#�3"~Va A� 2nd s =� "nm 19932Q�}osE,PA~senau�� Tri-.�DuaABWS#>Co c��},� q�v. E  ]j)' 0-19062YpaWD1}E!P RV.O.~"~C, %"��+1�8$57-1464; ACMorria� %�See��142S*� �2��Glasgow�J. 43A��1) 65-6� V3�V����c^h�B of m+ -sol&� �%eN�Db]Fl"rse.��"��Chaos,6�FSal��819-1826���3 ��/R��Tr2< i�T�H.� Fm"� s} %(�=J.~LeonJ�, SingapsX (198A209-126� �2� �B\"{a}V� ��� &$��m : a]nvey!��B�A.�4ordy), Manches\�%>� 90) 97-13��Y�$sk}K.~Sawa�C .~Ko�Oro�^or� 5eB7�355-1366� �%\date{&e3"��&-1T�0 up�&�)�q (briefl � view�*�9)� �[st�'�$e tempo�Xs.I�Lx= t9�f!ՁUS`��85U  K!�n'�]�F_#  a�@2� � e Nagumo-�I� �4MrecOFy.�3c � "�%piecemT mVon�:�n on-s�'rMc"R ! i*a HeavilW step$,�4traightforward di%+ T�2"�?s�~Qm �I)�D�l"{) "�inO*!�ng a `9��T�[r'�-it$�*e�tidere;�m�in��-gsi�Ρ�Ay��"T,{�lue�aG���d m pot�e{& myelJ� d ne`�ax�4a�exA�icardiacI�8-�bell1,2}�=��a4 &E ). F�3a5��.�)2'S 5�*"�= ar (PWL) � � \eqref5�\�! ��9k&�-  Uk f(u�^- u - w�^(ominus (u-a:VF4ve�2�:h �)Q$��nd�� b�r.��$a~(<1/2uJan effa��1hresho{fch2/e�QA�,  ��R,equilibrium �m$iD1�� ��٘�n}$, E2$wmB`�8'�Zble A4��_�� B�2b}a es� ieW�Y !�cu2t�� U�at�Fy~6�bsZ;aD%^eIc q�~Z�I]�E� gave�{.��a�L M�a �iO kB(or `�')*h�is PWLQ� � FN!�i�,  ��"OL2pF� u_n(t�<\z�!t0��wo�7 )� 2]jM��}A � 08=(\chi t+n)$, $ $ �6!�sp|�X V>� �profiA@f� !Y�1�We,�ly ed}.� 08B g-=a_p+�g {0}^�L[b(\th!-e^{ip }+b^*-]�MmJ! ^-p)}d ?6xbF�66�͞ $p=[%�]�Y1+4D})]%}$�baEo_l5Ds�@ ae J�V!yC" �d�+a� eq.B�a .���"�w�\=�IZ�f�Bn $D$ 2���9�u��[�e�La6'4$. \vskip .5cm.8az;��as�)i6�by no%�I�,����m ccur"�y ime Ŗ�U(U �'ly,.i�Q�$)riW i�r�6yaIe.� b} t ;�ly~ � �IIon�m�� a�ins��Gar�1�� �$u_n$/�( =�ss0&arop�  $nB?cll 9��1dR&�@�i� Ama��atn K��?s"J s.o�� eigen )$̉2?.Rig.rd cap:�vT98� “%�)$% �< ?��E�$ųa�5%��H|;�6� a &� y�� aa�*�X@� l�0� ��1��*� Zn A�!F!@l (we�os�o�:AA�A�8��u_0M-�/� $a$�$t=S ,& �A�]hB;Zt�n�U$��-� %�.1��-����}[hb] ��a�>r�[hHMTt=6cm,width=9cm]{f1.ep���U M<K� q�Y� U9A\aY��a[xof:�� YQ!�asa�on&�   (&/Ca?�- �>I��.,s-l 0$);�� v�@$w�U8D=1, a=0.1382$.͠-J ��.�}�I��O� !G>px�� �����L *S,?nt��.�� ,�dtwob})��Zer1, 2}i�n�y �dem�Ly!���qc�l �"wX*�.&�Mep), ar�u2t�sD��&�&M 2N$\rho�mB Q> be ll��a ���d�f"��(�]��]A�>��a"gh ����XbasDE His.�EW�Bed��Tedx�e�u�~im�>�FN �- �Fco��,e��c%?!���* n%� m���|�6is� } "�"�|� dt��eVw�� ��(�4 bov-d soE�6�*�"�T��growth KSs�BG=�"xmp .��&< 6} 2i�3umvG~e��xtyD@�m�!closely�C�5-a�2� K !Po��"�V�ItuZA��(]��Pz .;.��� ty�6�&D6 �xle. .< &� In5=3��{q��I��so�.�on� "�Dy��/]��`�<-� 'u��a�ded� a���x��y� wQ Imo>/9�V�6 ����4 ue~ C*az�i!�i2*��w�A9��fe by����J �t):9��y �O�ea��I a.6�# }?��?�d;k)�.� ]RUb�aDZ;5�)� � i�G"��ou�w rmly& ng ����"i 2b�SC on 4AGdev�k�[�� �! �#7e0u�2 commu�r�+��� *d9A%O5B���{S>8>�0I._&h �"� A7]n����|�-�"!>w��s tech!"� R�%�#J2!9>6����,��Ɉm`s�y� ula��a�my�4��r�dn�,*we �����V2�X�&��"�:)>cc[�K(B,J�)�W&�P�VI� N *�!"�^E )�, .�!by"�!�oy�p�m ����,�b�+�R2L# s - � ��_A�o�0K.��r p" 2sKhJ�� )�"��`xH#o�eJhe�$AC� .t�o�,�"^�M��preci��,̬ bykftax(t)$ N2�U'%t2�soln.� {n>>'V�),~ F� $\ �$��[by*�"��Hd(0 (t))8 D _{=(t) - 2'+"'�-1)-  � + \T~ +-a) -:!-a.�si�(�"��I �$�_U-nc&��!�� *St�~ - �"(. VT,�,���Na�� � n}i,�� :c2TD�.�5 -a)-2-a)=1?� eq:swd&�5���forFl a-� < u!!� < a,>\&f\!:�oe�>�i��'^2 A[auf�� I����"�is in���/��<ll�� a 'a�'. �L s�\),C-�$~ rea: mono �i;*�&N&d h�� b}"s�n1*=�1X=9n^{-� "7�] 5Ou�92O�� Z��#$��b裉�^� WI��Ps"glly� I�b&�$e.�|j�+{X {u}}5A[� )(t- )+ O(| |^2).rninF��y $VW��u b�*!�)#�3(acU4outt^�{us-E(n$ 6ň~�B|$JLZ}hten��tFpt \�x �-�M�^ {-}}{=((%�2� tenb@Ye�]�n�)��ߩ� !t .ut%�[ so %A&to�aRa� $.{2})$� O(Y�"�E+^���V�Vq�. ($�t$)��=��, b  (i�F:�ma=}$�- 9$Fyh2�1g {'g��%!u !Ba� '��="� �I�B<, $(n=0,\pm 1,  2,\l�[)�G T � �O{oof�Rs2,by.�I!z. #U)l$-&�2����%[6�5Bw�d1m� - D(J���+ 3�+.�=0"�eq:E'eE(a}!RU2KI�5�$'��X�y-l�� n im� g�e!⁙ݙ $n$th L1$,aTa g�dde&\�x�, ���I� &")-)I�٫twelve��) �.R��!�� �m�ցm�\ almo��nau&..is)YQ�+L ���6 E� W �o*|-�N��e^{IC*u } T"int�#" "Cq *2DZ� 1$9�1Ot�+ �x�?-3n}h�d� in�R�- !I>!� .� ��� aft� þENK &�x�sJy�i {+}= -}+\ta��*�!thirteNE"��8$=�/�S0"08�^�c�, u�.m��2get9�gi.� �� left0T 1} ^�\Tj)=6� �#z�or��B�t�)�DXE,J�dot�, (t_n��= P$ g' G|_{P=�}2 �Bz�e�:� Q�9VB�'�`�N:.tsix2�eWC�� pas%�% a��j~ th"� replacey��bi�r�-aU$�! � u~8�~Ed6"}9Q6V� 2"� uNWO""4 r!;u���M�v.i�|In��U0, e� �ϝV, eWha�.n o�un4 �F-�����  "pi�6�;a��il!�{a��onl  N4 �Y�/}!�aSH^/I T, mann�Ul.{ $ hm��ۮWksmnd~��H{1� �&m+})6�. "R�R��#&z �;.�.sm]E&&Q i� �Md�3fpIoS !Xf8���L)�!�i(� !�!�'1�6�j5" ���B�*��by��w�jC%YE9� e* *�'Hd our*� 6M.~pendenE+��wa�e=^5uor5t�-�a��o�/-- E��!.��s̑ofA�pT.y �8-[P6h�i5� farS �2| {+(�bU��w)H`6rAen}� see\at }`>� U�a��]�9 ,�I�"a�A be ea>"��%c/2n �y���}$ �m, say�eAf���I-�bXAo�%&: �-��> (t/ )= ?,(� ) #[$um_mI_{n-m,FrZm� >7V$�` I_{l}>:2 B!1&���7 $l$ � ima�_�Drg`>J�_(u)9A4 "C e^{.R-"/lG-�..twentyF%ROne%�7?� ��*� ��l��} 8s�2< ver-p)�:9�:{ as+)ec( nd,i�&#DE�� 5�*� U!�n |> | |�eqw -2A}."| (t *F>oJXVAIv ,B:A� (&Q �miS��r�Q � gi@ � �� sult=v)��:�Y��NZ )� ��9s-a�  . St:�gi�e� $0� $�� *� a���' $n=0$ (rOI@ ck �s �.�A` 8(n�*lN>ng un[g�p )s5�6Idecays��� -m"� t�%��^ �rri�_{-1}= "w��@0I� �&eaa'��!, .�A >��!/-1$�o$orA"  h� �8`yxs�,ʩ!,C>g )7%69Q� �3�� repe�>t��;F��| shifa�(?v�#5�!�l**b��� �pq*!�e Wz�6��!p ,it��,5� 9;V� , moA"� >�� �>ZXA �AOa � r�% �0}�*Gb, �s �w*�?>� N$d) � r+��iB�Q2"Z a�,a6=;�rV�&�'�c&@ !���t}�f).&"��sEk*.��!et�t/ �cru�� qi�#�@5�k.omm.^��)�E 2� E&(�-��i ' b,B')�8it>i�ed!:m�2�E�k(AA�vL����{it�M}S� f�&� e�*d �])� subs"sM�� ��$?1C!d�+�����:s"$*�#e%�y��B �woQ�sX: ہrA�iv� 2;,s��I'-#�*c5 1c6Anin� "d26� i�.I ^ D^cJ h0,- &� �S q[ !fa�� n (gEV�� *�v�)��T� ( Pac�e0$)!{ah��KӬ.u 6A��~-1e�.�X" -E^"�x' y��Dn�?y��.g�1| vari~@� t)*O2;+c (ș.k��� �). Am��'�^� one%��0$P�J"�0�i6 lar�� magnit��a4�e�F�(aximumU�a�:�FBn.� A&3 I� caus�9��ity:. &/ �in � t��v� n�",)k R��mWr sšPG�R: igno�alJ�%6  h!D��7^�excep���N)&$mAˉd Z L6�u�^f!a^ 1_ I_{1"Vm 0}(! )F= two�~ N&7�0ºnd U-1�.�6|&e9"�3 A#$ Q� %�6V Az /x�V)�N� ܅� du_ ?>@a $"�� 1)�-Jk ")6b8*� I�fi �wͧ5���d :�R�1�:�$�.�rho &=& �6 �-}"� ��6% ntyt��J�%>�*�=(y�"j Qe^ f� "� bvʖ&R�Mܔ��!�&^m3E�|0UY�cri�Jo.�".!�< 1F�z��� ity,:��Ka�",Ex�� b�� }�6�s�?�j � c�Gm�duK lsix3i�G�%iZ�]��Q�L2�*�Z(�� 9ba%>1ac�E oo� � &_of�{�62�  e;�,�ls.= 2� FRF� :�.jV���:+ �Buō ��RE��-"hA ^ S{�s,| upÝ�"�$I:e<a� O)�!U� YFW 6��&C=2�,gu��>.-��#aR��WA� ��� "'1:q.VN)"u"+6>9V�2)Q6&�IE��) dA��.��compu�>�2qu�3�r����EX�d!��t6�2�^�WhacQ*jC*a., � one,�2�, = !�upl� q�Zf!i#�r�1ao� C>idI�ZA�C" \SR~��A!�')a��B .+�;$fty$ (zero -:�A2 m.����:�5rD .Tg� a�#y�TB6ds,� ds8E����C�t��*�D%-g'� ��:  frac��4\pi D��D8}}&�6,!IU�E��} q 2D+ PI_1B8 2� 42� �ZV.���"-� B�E_�� No rho2gJ��'A&��xOIhO���8limit $\chi \r�iightarrow \infty$, one similarly has, \begin{subequations} \begin{eqnarray} 1+\frac{1}{\chi g'(0^{-})} \riif%�\chi}{D}, \label{eq:twentysevena} \end{eq^Bo e^{- L2D+ 1} S}I_1(  ) \r��Z�bF�0noindent i.e.!' ce again,F� \rho2�1.V�cFh�:j(vskip .5cm � Thus�P the face of it, our tory makes no definite predict!�` regarding stability in ? pinn4limit as also ofin ZDly fast kinks. .� �However,i bothR se U�,e notes that$ amplificE}�$tor due t �Lkick given by \eqrefAT,sixteen} goRo�y. This�\fact, is an overestimata !�for $U� .O0$, !�(second term���nine} becomes vanishingly small and B thir B� volv!�z'(iK$�dto be taken into account, Ku!;0e expression�d!( dur%JJ�tau_{n}=i' \eta^{-}} ec 5J=eahF�y<s -c--dion. OI�(other hand,�damping %�-�8to linear evoluB do![gozer!�.\M[ % he!�]�ac%�d%(E�$��6�>>�8.b�J�AP@front speeds nei�tooMnoa�$oo large, =�Y[�2,threea} canU� as a correct order-of-magnitude eM�. UsAiA �s1X.koa!�uZtwob}��e y compute $��$�i� values�,4 parameters $a-Q4D$ characteri�,system. .JYM In fig. \a�Xfiv��yield�< unde� ion, failAr(to reproduc dexpon!� al diverg��8). As already m oned,Bz�J� c} are.*N in re-#�actualI1A�Ee%Wth�twoi4s.����words�travel�:�obtainedv our model!s��leE�a�%��v �s0which it exis�  co��3i firm�romA\.n3}A�iHVsa)ed6���(}$i�below)I� $a$,���{3�zQF���6�3j�3^���5�%N numerical� ��AFA%!�Nagumo�)$�F��HQZ�;�A��JB1. �k � s~g . We �� -�aA�llows:���85} depicts sche&��y�level ch� in $!P (�aen�ic"( $)�=AKM�e��6 %_ 5a,b Rv�U�����5j�5} a4}�l5�!�sAr.� $\zeta$ (� spon!:teg��'!�A1Us� �v)�( =�� r-�$D(=1)a( )�t�.,slow dynamic�neAupB��AVE�"*O�L: 609iy�A�.U!Der be!1�a,such a manneA�at�G5� l�$eae�di��al��sic>��*F���2{:V�#)R�:Rnow�ify s�68a2e/ �� �waa��r ccur�aAy��r�y� ble�}$A�BQ, �82��8ir%gݍMnyQ¡��7��=0�P� a �� high b(*reQ�� thr� $a$)� B�rV �w_�nd�u�%f�&�� till�re� ea%7rapid �9> 1inBw!Y\5matchA� earE2*,%���=���Grea$ V��� ��byireturn!a� ngc $0$. SE=lte� of �!:%+�I��� servR exci!mediaBA lkrovidRhe basz,or FitzHugh-�i�H, e.g.,~\cite{Hag})I� prototypea-el�ei1sj3 an%�y pap�Conley cref3} g� a geo�ic argu��ed]a w ular6� a� ach)� �/ lishAe&)!#Da homoclinic orbit6+a:. (mgcon� D1Dinu�6�um)�reduc!�!~par�"�&� A(a-Ja ODE'|�� ��� �D�0-bleMT6�Fspaqly.�-�X sD &extens�discus!�-liE�ise:. ref4,ref506,Rajagopal})9%c%�!que� !�.� se �j!Dby pie)R�a lea��� a=�Lor� (res� �z`�'-�?'),� %add� ed �]8so-� edi�tchyp"sisY�7!8}j#P"�\ !��!�e-2� constru�,�B� !I�6�aA� {\it%�rete}�z�� -a���{A�$IP�9.�iF q':�"_"`Z<. M� precisely���w�#w%��K� :�$X *)&�d i"}{dt}=D( ,+1} -2{u_n}+,-1})+f(u_n),�"'&n"�j&&lw�" l,\epsilon u_nF�%XJ�%J�%"�"ŝ� X�#a5Z"��9 !y sca�ID>��� we��$ 5Gq�6�)&Mcal�!AW^-W)�wo�di� "describA[arU ����w_��!�2�1�0a��[x��r�ou9 �6�%LU�   !lsofBf63sBd�!B>u��t�)�ABC"��1�edg� d DE��wh�CD% EF � ��H�Q�poi� C, D�E i�8e of&� betw�R)�!�6Gswe workInB-7}2�Fh%*-$w!0(cho3�� ,$rary ) pha�� lane�� 3"u ����"�) ��%�< 3B, D$'�!� cr�'&� :�\x9!!'.� 2� . No%y� - � s�Dmse t $t.-F&e finaP�;sA�R:+ :A*� %5!we deL)��$g(�)$�ewu9m�� - 1,ɼ%!I �n Yter} $w$ &set at}� )�|noMo�(pp(*o�-!:�a�well)�zn�6:-��(u�.��!�6�:������%6j�6}!��2�t�Ba typ>�G���EU!�m^V+ ;;2�1��a��.�B^-�7: u_�) vs w }�&5 �l���s-s7js7)sb�����dia�$1�Y1�J�Ѥ���e�tV�$a$)�$origin (O)!�D$asymptotic n�� �2�\pm�Xd M��  V�FU!&� 2}��� ��on����=`( t+�a�"�%:{as�� u_n(t)=u�;�nr�0w 1w^1%�Q�&� lim_{�.\pm�1}�=�*{=0.BE1�:� R]0Le)8:�N��:�,�{d�|�_C� D� E6K���&we"� �X.��� �� $^� St*ng�%a6&�^�e)hY$$w�)} K�:At�,witch�" P$:F5�� {�2\int_{-i�}^I@}��d%ZF"� N*�" \sim�(E!�-q"C��) symbol `$7$'�)�B\I V1a�2��I $ a��}lQ thanWE��v3+)�� grea 5CQ$9!w�I޽*_/M1y�e�/�j��6��-�j�W}.6+aIB� "� � �$0<V eU�A�Ep6 A�NDuLFj�`�1`F�U=n�; }�satisfi%�eq.2Z�,e(!:� �2�1-1�jN�e, �.�|�>fW%1-&_6>uAg}.&�� dy��^�:�5?M.D)�!�%M5L� Y���� i*_C$�F�-�_C�J�_CQ�ɥ�C�����!�necess� to��EjS �6S|%O|?��to!�)6�,� �,�2d�{byh A���'>�reg..A��ar:� 1�#2�(8(t)$, �7Fr|)ed�}{�� }=D( +1)-2 )+ -1))- )+g_0jtE� $g_0=1$}.��.A.?+%m."�<$)!Ue� ssum!IF�� -g_0e%\sigma^{-�}~(sayB4 a$,JT!9 ln J = D( + ^�*)-(2D+1.yj��ywBAA+"�*)�0 ��gm�0 n exk8z%c+�!"� }�<=\gamma, ~~for~ �.eF�andF` M�yu,} Z B[��B2^�1�(=g_0+\alpha �9�, Ć��R�6kbeta(e^{�;�})>{ >|Z��m �a o�+�a$whose�Do7ed�2 cern us5^: l;> Lwru.2�A)����m)] � i:pecifie�#�&�� $Apnollev�'-v,analys�%�\1(E�5I:udi8A��# cendental"N�MF�R@ )1�7�^�Z1 � CLs��f. 6,2C})J819d��_C}=1r�B%givingR���_C���ln&��.0n8Nex���( easyB�C�*� �:f� )��0o�8�$-�val)�CCD)��ed"!�)�M:�2�On�-rygeRu_D- =2�@}&: ln�?1}{2a})*uBDj�Ah7 �5��(�� _C$)�!��%�,succeed�"!s",#�/�:a�,�!Bo�$)H=A�x2V operat �;� Iu�""�2�"ŽD�E.�%�6� A-�i*�'?M*- 5subUs :&!Y&� �;$q $d drop �$2a$&I>PiB +7})�s&2jr` _u_EP|_Ea� -1+E�H]8in&+ �E�se:�1#fE�<��#�A6_z%�".5� �Q �ne2� as wa�+n&�%),C.2R/Ja_EmUD%2F�\^�EjNFi\�6�P@sT.E�E onwa�8�F#�!I�$u=0,~  CaniA"8U�^fS�,i�"�[�8lbx&-N� �aT of su�!�R"�:� >(3 } _C : ~~~q8%�*�%@1F�>c~F2�I ٔ�n: EF�� >�2��G_C � _D:>�&� :�M�C)}>�3��F ~6j�~4�)D � _EB2a� �i�+ D}{2}B 5�~N�B�2B�6�Z �E �<� B�-(1-2a)��EF�7��V�6���8F��:�"� )!C,~ D E$!!�$��ed��'"- .20AC2�*DBE}).F7��9%�� }� I�N-�>� �r��. �E al+�? 3�e"��W2���so���a' X.L �E� mselves�� �C 8: �7%37E<6 ��&�6 �pr� 5Y��޶C8jj8}A�'iA(�/YS�!I607"�d �Y�~/H .�8F�72�7%')Ju5Hr �nf7_>�*�&� G8 laps tauM-8f� y draw> �EJ8 �;d9р=.04,�=0.67(9086tau=9.]A"m8Y s coincid"�'2�%IB�2 9+/!a�<, but)�im�pVp9jp9}S�3|?ig.�68}�� >�2 � !,6A �*�@B�0.009=�553�:09"; 10$ FK7�  V�:�98�%!m�(eT)IuH�*u >�E6�EM1} - *C8}!��&aQ��Y�^�'(>%sB�+Q�ws (qVto�.�6})3%�&�+!|n�( joinsi8_ !�Oe�+�- next�! tIEt��*�NfA�c<!.�'%sFe�11%�0'0MVe����5�1n�1)�'�'.�&ME>�j�71�clo2 loop����rperio�>llFO(� .�8;W)D �.�8 Simi 5r� pl ou�toa�2 a�b-&�/fam�A&�K*!%� ls;K64�.es ���Sof Ds)!LB�9I�a �sdR. WA�eolY�r2�E� 3v&U=(��u=1{t % *!4erG2�=�)��w.8�"6�of �D%H�u-=!�F�2%=��iUsom�0n-u*�R �, $W$)Ya�"�,�/[(w$.�re)E��M}2m>$0C=��Z �6. �?2l12Q.�<�z� Ht��S12n�2}ComparKbQ� "K �8�UG��&M.�aF�8�Fa�V0.6u1395, W86C'5��30*3661$; o.�1he *H'�"H'�%�s"�FL2�� N2�12 2�q$ stea�Mr�� � *FE�2r� prevyU���.1n�\,6,Wn �=r�R�mW(14 E, FJ�10}) i�3e (cf. �&]M6}z$.�.BW1S�.�&��%.-w�Z\4�]<% curv �`&rep�)dly~ e�9��u�3 �)S��B>%��n\R13}����9J�FnF2�V�W�=);&9sX�:k12.�$�510$�� qb>6� "�A�1��Gs7d^�A�4.A�y�&] expl�U0&&� ,�,8.B",a��/(a0! Nu�&a 1R� l@o^s8 �[0!% ��_1Y j -W*el�""W2�;J��:��2B(1-W)��12�����>C���-�3-�b�.�)�-2 2)+B���&�F'��>�Z� �3B�-W�i�2F��  9� &�-EQJ�>X M.+Z*�4:F9F,>FWF BFE�q�J:�>}Ik1b!!R�'B�'ZH2HO!�f@*�&-W�&+W}B�,^W3�W-2a}{NW� �iJ*$Z=4-M�U�F1J�vVWf6�M�� % depends�4��tE�$W4FQ�is'm.� Y U_1�$,d�EJsfPh1}{2\pi#0^ Hd\theta}{(1-\nu cos )(;"i }� muB' })}=�. (a+W-a_0)�1* ."V) �(26[2�8(��� 6�6$WRJ^S>�2e -��N4[%��' K :�o,&��i�:�*.r�V���O"��(�S�_%&J\>39�nd�� .f -7 �J A�i?Ya�� . AdF�,B� *�Z�<�Qa"EF"��]3l �[ fu� Y&w'�OF�9}�("$'�%�=1�.95:Nni! +@<1!�V�)�F e*�SC�`�'remark�Sup:8U�D��pK>�J��T]��R .�nu}��"�G"I�9-!#Sa!K0X6b}��9e�g= sN�eA���ru,Y�!&%�' jf�(:smj ��f�a 2x��",Fo_T.�)A��J2tI�0i�B��b!"Qr%>�B9-ūs*�wR2��b4!g%>7-6!F~ . A.Up,a�F�jitdeeof��r����8�of�� koedP-��fpone. E�MN�+ng!�R-�iJ-�5�!�z3� U!1^�S&F/2��#� �,pl�n6�T�Y6�Z;�2$�(-nb�AA��27is� ivaleLto!ҡF��"oW�a cir�Ir��n�G?s�eJre-en�t} z�a �6"�Pcells. R1 wa$�0re�jly �(!@ focuE�A�n�ctt#g�:|g��e�0kBA�rrythmia nd fibril�`o(O.cmpac tissu �Ath�t!+a��!2me�is$bl"Fbreak-up{spi�Zwscroll �x new1,new234^�! Ia�A��P{shXS�.�Z�t�Ocommun�anGa�����;�I"Y&N?an�:a} adopP$ �re�N2gg!nMS�5t&loJ"$(sufficien!��>)Bl (. 4>�R�����)rV;latt;A]!9?! g /!ah:ca64)%��Q�e;ble�2���a]` ��� ctru/a mapEpA�!��mspace=Qder 6%U^c�7r%��"T$tinuum ver�~��7�@tak�-&"-n�@i�q1�l�a�rdo�eJF nlս%���re�@:�a;c� fe�d�qi�M< t#�f W2��`i1I;ins to w!�e�RA&RŬ��ud����}2a t�8cy��$�r�#+-A�bERə�"7a9�UY  B\er9W$`diastolic!�e}7' (DII�!=`a  po�L�l�s' 6Vre�R�R9�E�pi!�t� �{A�6vcerl �D �%)�EE"m��>f0T�<�T�R%�I��ivŇaBmakLosc��or�@C 5ro&�P1�����wLb�ndA*b�r�:H cruA�Z,{\bf Acknowl "(:} �8of�;(PM) a!sIdDke!� earch grEoA;2.>X-^ 8 ��5:+91KarDCH. Levi�S� X. Zou��7A�94)11.$re�'��0Courtemanche,:^RL. Glass]�, 5%)6)119. �>� docD]}�I\cY [12pt,a4p|]{tLDcle} \usepackage{g�wx} %\�w23�}�w1�} "  !r�{~ and{\base�q,stretch}{1.4Yz&0.3date{"��8} \title{ \sc Dxc�j$5t�hpof nystagmus} \author{Nikolaya�$Vitanov \�p{6� 1}%�TVeneta Todorova} \make�� abst� } \s�? Bbe metho�?Y�0 ser�"� w v g< human b{p opto�.R� y�b�i'(ary or nons�R� �} E� pur�o"O orcha�Q�. �*�F�{� Q auto%U� f� !D� an un&�4eak�$7$9$Vo&� Gaxi)&�� g 1j �-*T�lrtZ inT?%1Lu Y-��%� ted @ firs�.ur six �+cipal�pon�m%�elu�pA�the sens�inputAkq"]Pebe!qng�opeY orm$6 ey5p iYEd!�so�C"� �g�!� hist� m\5ley almost un .d 9**t�fJ��!(N��ti*W imen�aWog Udomin!� freq!+a()j power5�!RH�behavior� stud�F.�)�a.$  n& g�could�y��( �realizI* � �h$ phenomeno�\��o flushleft��bf Key�Z ds}:y�,F�,RX�d� "�&,2�U��~��\par N�) [$^{1}$]A�a rh5;volunt�=Esmov� � t�zes gazA�Ec��Dh�(7sA�r|Y5�environ( .�Ameai!]ysiologiAMm"{A�imaA��w$ retina doxHtY ba�5m�-opwVcoordinE�ilear viE�in�edA{e9�AA�pe��ag: al �� ���b�Qi ce -��H��M�)J�hs&� q very@��r!klth orga�s� �A�extrem!���s.� sporMfstronaua�, s^c,��f Ih buil{s,-�N Metc)ll i<sAU�u!/[eK0al sel�T@d!��f!��% ��Ji"~�Qy�re�vity.I�M(i �ur�/)' volvD .�F�>Ron:#��� :�� ptorrH to nervous-oculomo!a�~atu 50��of' b/& zones (-��A�cortex#+%�d- _8�. SNK!{duca�]� -[r��of]f.0�!/Q�!�t�)� �[�9oaCeT��<9X��bl �a,�m  c�g�M agno�Zg neur�,>���dis��u"�(�{iW�e�)mount ɍ opp��"�l:bd- d a�BP�Gwo&�0ve s,�)�Ad�*Q�F�%je 4+ L ��con�n-i�Igracefu�i�|!�ey�i�� ainse��pa��9�reflex!��s� MG-AeB�jump-�s sacca�j�Kc�=uA8�cal re%���!� x:�| vis��5ens26aT�H��Nor :�i�$� 2�:� .WW]4 its �raEmanif ��Aki� O ����ery/� an���� goalI�Ta4Z}���� 6� M acc� ory*�.c bN� &e 2,�p2}$,$^{3 (4}$]. Desp�P����are�l!�9Uz %$A$��Atechnimjv:�5< qu�e x larg�bK< !J!��tuo�p2�normal �Equsx>is�!��jxd nguish"� �D�� path��yA�2(prh�t&� a�> �>xDn todaSm� ��Kata!U?asenSxe�=�,���:� s). a he�y unte��n a� 32 y�o�/q � �f p�'s�x}q , ot!ic,�dh�  /�!geXDat&�X4� a�ct�U a�M{. F� �r%'�E��U�ro_ lly ���� ngAq ir (ToennqZDFreiburg). Stimuli!8+"�f ederI�stepsFPpm 8^{\�} /s^e1 $190$)Ѳ�w+��A\o . R���est �X�X)Ӂ`A�eQ��"9�:�m5le��ark���l� ed (�H�9]rO- -��.a ligh%ptokine� d(M�y). Du�pa�7 body"Q W�Y�com�t ��VX2�" �D�)toawOqa��� a� �� 7 5��Horizo�T29E=%q^"r�Qipoǒ�asur(� MZ��� �Oc���g" conven��UM�� �phy. I�9"D !24�4bio" Qc�4�`�7e�!tw�id �sTcornea!5a|[JtB�A. ;  -b�p d!e�F <o�$V ds ��v����d�%�� 7 �iXW��7. W�B\use& �VE@&� )5&A 1 �1s �<ɼsS]�&s2_�� incr��L�����)�eT-�u��� �h[ n\(i,��Y tc-��� as length1ġ� V�y. "�� velo�-ы5� �#�A�� cycl� wepi"�" A�r*} � on. N�`un�l�$��e �M� � |�&e!ak alog��� ensa�eyM�: �t0G W%)&!�2| B|� ��is���panels�aw�b}�P-12p�V�l�#���� Ќ-i���r� �,�) , effec)=7&�A�� ��segEs f�%�$�_ �e��CA\13A@������9)a} P.E �&� ^: RSb2��l�_.-���! rend!/e�:�"Lship $V=8.3 -0.045 t"[$V$!�A^a�S& "oWQjs� ,�t�0���h�g�:!��>� hI$ . Af��aC[�!�t)�.;����I� #nd��!OeA�9�� �"� b�7g#H ldevembed�M/� a` � N ( ?(X94%�minimumZ &e ($m-�&Je�; �mut*���6 ! n�2false\�Q neighbor� 7 �(.���ndI�de�m�E�c�.s <6&�� old=>� :�M��Q�)!�Ywe ��e�Z��c|��55s $D_a � 8Q� $^{9!of�0e�'d{)�e�b"$1�2$�d�J Z =1.39j 0.14Z^��T:3 E^ndB4B2Bf�Ae F�96��! 2*� \ 2qui&G&��l�2�R] m65� hey;0&Dmiddle�5U>�� �moa� �6=Ż�I2Ep e>���Hl|��� .�a�)&���i���!yBl&exh=$�$� odic&�����&f�A�k�&eca�+i�J�1($A(\tau)$. �hN�.� 8 z s,�+bR��� ) �% /��Ky�A��N.��j ~X1 pro�I�AcB�%�Q< %#.5ly R�}�^�L.J \!-&0 maximI, ��$-`u�BFAt }��s. Bu�ux $35zr� 450$!fpl�un�)w�T3.�A:'t���~:�)<f�:�1�u�$7 �2�f 7hi�c`,�"0 &XB���on�B#�2)D.tum%PZc��i�urs��"#h� 2�x ^Ou pf�$s $1/f$- bhI0�@rZ� ��� ��zI75rib8X!:� IQ�2ƀar&$ Gaussi2!=� RGeЍc fTaio6�{:9 .�"�!���6�A�.*y�." !��e�a�.�� ��� >�UC ir�fb �g%��n2��FF ��tohN4U-s�� A=a�� �o � ab.!��[� is sto �c��loe'�F�!3us> �A"�gtnumbe"k!�J`s��we%^�6!@0m � Y&r�� ise-fre� ��0ch�8s.1.!�3~*sZ� >"�GE�Xa�� -�!� �9x�$pHb �o� %�>` !t�hU�n�6�$A�!��!p-��&�|h! of v�, ": Z�.�. �-` ,%�t r�� 3. Pf��-�mt. U? "l# ."y5axqb��upl����ly�6!�3si�a can Kgnize�A:{$2cin2� 6[� � An*ip=��|h -bEper�U|���ibuA�Eۅ[��J�\ �@O� �ؑBt'�� ^m ��0*D:�' h.�J�pi.e.��g�:%>M! �'Fa�n��NaQ�� jex!.�l5!�>�2a�a�eigenm�:�t�E�6�(>�.�jal!��hag�&� ��A�6~*)���.D��a�٩F 2n low-&� /�� (�G)i�a7 is%8E�iofmӑZ%8m��N�Qa2� ]u"&  A!����nrk!Qn�OEE��E��rtiZ�6�m%Q*be%�)��+�.t�(!v�A;+Y 62FVJɱesf"y�ion�B�u�� �uPa.�!"%� st `B� M)U�iw� 2�+� %Q�P�B!�yUe�� !�՝3 z.���"u��ef lo& 9]�~ %�s��! r F>-�� !&� l.s���2 % A�+ ��.� -�6� 9� !-%z"�"Y �r{� �E%ᙁs�d�"3A� � � �B� V)E2�i�7as�Xeli\,�byN�x!u2  o�:ub�vf*�-a*��.�. "�lif��onK= e���mo1ar��,!��/�� Q�,.<l2Ro�_� �8deUZu )� �| lackn�G O \%�5�@2(H% ;}.=� ��fc��� 26!#��- ��A�W��@Un=�s diuh/���M>!B!O�C�-J�P�r�9��ǁI ��*evd+��iL��j= )G�x �! y� ] 7�:�$*�$kaA�!%�)!�/�hom0�Ru8robust�sts.�/�o#� mo|0. �2*,.̫%�.q3�'er�@[3�.2-}�ptsize ~�31.0} �10 WILSON V.J.,w:4M. JONES. 1979K: mmal��:"�%(y. Plenum P/&(, New York.c2cXKANTZ, H., T. SCHREIBERb97,&9 T��SK�9�v8. Cambridge Unie?tyo p3p4VITANOV, N.K.,� SIEFERT, [70EINKE. Compt�:�6de l' A�(mie bulga�"S4Ac�s^<$55}, N 6, �: , 15-20. �J'j|6, Ibid.N�bfS N 9, S25-30 �5�BALOH,q7W.FZ. DEM!DE.W&B�,Re�< ^D97}, 1993, 334-342 [h. FRASER�7M.!�7SWINEY.{8*D v. A ML33}, 1986, 1134- 114 �� HEGGER R M%�2IE I60I499, 4970- 4974 �8�GRASSBERN8P., I. PROCACCI�8(9 O9N(83, 189-208 KGR�>�CHAOS2L� 13-4;e00�4BROOMHEAD D. Si5P. KING �.�2 �!/217-236 �AVAUTARD%.P. YIONE� GHILFM5�iD1992, 95-126. }\\ �O8In+E of M�1*<BE�a�I�}!Y�Akad.a�Bo$90v Str., Bl. 4!�$13, Sofia,J,\\ e-mail: v�%lov@imech.imbm.bas.bg \newpag"�72�� A���ZdXhJ��3�le�n} \0?i�Q1}\\ �C\� �im�2�&�a�5&�v�a}:.�R�B<e 1b}::O *�s �.�u�kC $0.02$ B�  $0.6$ �/%.� �ɹ �ho"'�e� � $0.9NR.)b}. � c}:)NAb�4��.� #  ,Y�B&�3$X,Y,Z$� (our2kl9�" ,� ��n �ݯ��dj� >���8N�.�1"v� ��:�=^�<6�2E�Au2�9s $A$4"R$H .g a $P$ v^�%�!%,c,e}:.8 �9j�Ib,d^I6�^M�Cy>\Delt�~$25$ HzF)3%)R"� &�� �q �Dnd "� X:&E m 2�%1i)�?6a�ƛ�W^I61��a�Por� � 6�,D���""u 5*�J�2ac {qA6{ �.Rލ^2�e}: Fe�J���f}: 뻾I.�2}g}�+���S� 2�h}:��th�U �8iTifvS.sZS,;.�>;igu*�0e�X-4���8g=A,s[angle=-90,E\EA=12/�ig1ab.e3��DhA]{Ec D�}9d 9%&���!>�&|&��6 2�%:t��^l1�\6, %Z�6vޘsDj�%���%ڶ%.���1VVU� %F��G��:^ %6�_�U6t2 *]M�� e�xU�2Zv�9%�b/Ee�;^y.J�<^N6�J=�K_�q�-��eB��%��&�%9 �6N�J:�ZN%�) a� %�� !n�%J ڕ% �v�^2��%���%���.d��%�2�ƛ^�]Y��%��>��&I B�I1pt.�I� epsf2�Iams.�,VQ exsyCLmsmath} �Hat�Ler \@addl$set� {s�A} \def�`��{ ,.\@arabic\c@  .fps {h, t} 2b�}{b F 45ablba 6 �`N_�aJ�6� �8�JexK 5.5 tru_R \oddWmar���2 3top /-0_>  8.5in �JomLorem}{Th [-*]2'KP}[ <]{Pro2/lemma)L#hfont{\tenbi}{cmbxti10} %%%�4�1Ks3" L�B}[1]{\"_{\em{#1}!Hne*3ent -par1ragged�:%ttA &)?par�xtsc{Co�}Bb todo _v {5 mm}F mA�!�.Q ToDo� framebox{R2b }[c] ~MA t #1 e�%}Bvaia=la r mbdaM�$og {\omega$�.}�\�L{C�vGe;:�I6Billi'��&Quadr�4�/o �_G KdV Zs \foot� {AMS Sub/ CANk�37J60,$35, 70H45}��f ~@��g.msu.su�%�!,�a�de� �a I5%at Po��c�>+ Catalunya�Sa}\>�!.-$@upc.es} }A�b�NW2��r algeyFc&���(2�O� ;"gr�� bM� on a qI� $Q$�1el�Sc impa�C�^nE'/�|v!to;)5��y+�� harp/trn"F2t~[ E�N$Q$ ( aL�Jher�3!"'�m��gմon A`A�g;5Chasl iE��pv��oKS�CirA�_ş97f!�A��%�[ re t!nt�H��$set$n$1�A�at�T:z Q�] )Moser})�$.7\?�qseUdel> j �i1H�d�Umu�$�M�lE"Y�I�. Vesel��%�2){ scri0��5�5��q&�� u:L�ng�|&al�b!As=��1at G�lex�+R��"}e�6f cove�C�Jacobi�O hypereu�?ws. More3,�-'str�-O�to ��e�re�#�by shift�'a!�!dSFctor, +)Aosyq�Ea6( lawA�B�. Ex�a� "�L��_i85xw)c* �1�by^&Bd%'a!��#of�'e~%��or�I���D K Fed1�ifElng�=��a�L�&}9"� �.�! %�soi&2�er&f=. !4�0#p:�HZ~s�zly �;A\o���6cS*�d"(�nvc: !�ne5smo��c�G��apr�'ve� , $C�$h�to�8�2a �d polygo}@qKP� 8�Gum  �3z�.5 full����sta�Bat, iHi�z i`*s)�*�m � hen ��y�=!�!N, vertexB�a�all- knW��� "�. �s IJ,GH2}. Cayle������&`"!H�KAv lan. 7 qF�%��:�"4A�%�o%}al!) B�hj� $� f v$!�F/J�plEll� c�{^�ANEJ1(F�)��I�"s�I!�n� �)f6}s�JC�� e ()_C%X$, GH1}). E;e F �3YFqUto ql�V� ��@!1�,�Sn-� ' ��d� by�ms%�!�$� AO�" �!_ �hang_Fva <0, Drag_Rad, EP1AI`skip O)f� haP�o�EnE idera�� �>��!�%����combi#A>�l�sG ZO�Irs 1���_ $ric $$ Q_df� -d� b� -d}=1 � ,T $d$ C�aU�biS�fix�nar.=�jne�(�e"� -��2����${EnPB}\, : (x,v)\mapsto (�� x��ilde v)&�Dx,v\i&  R} $ �Piv\l.8W[=p}acrMin�B $Qa Q_d�r6outgoa�vEH�-_=7�7��s $F�'$�I� o���]n�� O. �1���.�}��isyI!;�QlsQ�b�Hndy �V&t [1 ks (�e_1U�)^� a�Z� !G $n-1&�  (cau�,M 2� ��Z� �$!|. \> $n=2ݒR�6P9!��� h4��bL/ "��Ves�/M�fo?T �}��" tr-Q a�is �i!��Pl *�-�A?!�E1!!Y @'4wdJndM/.�A!�Jyt arriv��tb��b�'d��,���a� �M. �[ ph0t�K�X�p�S.}"�m �� tudy&A]me a�W�.!� �ݾa5o�:e���B�9M� t� .- $> |�* I[ Allң��"{ ' Z ��e[h�� he)�@ �� ]$�(%$.) 9��p�. �]�&� !�59�}�9always W�eE��n%!&�]c M�>�.ic�L��E�dm=_Is�= ning\W�V�a�%�M>�. g��&:u�-:� 1�.�s �)�-�� %�a(!HaIR$��!�"� case.T N &� ��VMx:$ � -divisIIk{:�6,� � �xsT ough�1�� B�KA�gr�� of A�>r�5~^q!Q��� $�e$Y2iN�lF�ny2���!|IE�domai�6 new +s $R��"�?d� s��a !7t]F ��9V\��3+p:�-'l!_Toe�h�l,� 1csI�lc7,S[\rstXt�pal �]�=a�DV� �canA<be i��a��nF �Ɏ�x�)%s^6c�e�/����6o�6a�&gI< K\9!zE�.Pw Mn�7en�5�>��!���>Q"��movI��branch� dEs��e�/ anl-Y�} sheesramif-c��A�Q��- c%*���8Van, AF, AlberFA�ERP� \med� In S�  2��briefl�J!N6���-�ޡʼn�]5�� �uon �@+.U���[�[ a�>�Q��U�D$Q$. .�3,��� !6�kNq+ e "�  ���nI almf"bs u(mu�D&2 ��is �vAr�� �i� ��ia��|i�c2}+6�E $\G�5�`*��H�L ,�E �o� :0�Zmorphic 2+��`8=^un���U�Z�P� G%�:�2 z � m�*�J6�Cary $Q 2� A9ryr8d6:4E:VQ�P:y�UI6�e -,��!�� !dT�� �Dub_Nov,Cal1,AMM77,Krich,Smirnov1 82,Gavr_Per,Tr} �.)%�s9�m��edB� �Jr@o�o ?G�$N$-s�on2�M �1,b�Y>��� ��L!'lCzU�!�U��>f$�L 2-2M� ��__JX5 �3:1�e5@��� al E� &a&�iM�a� �Aal��a(a 2.~)� E�� b . Fin�����5��tx �ffir8Bz�.�M���s a�Q$�MC� admis�� uCp�s %� �FvO�Ee � �0aR%J.����E���i�i�A$�E�GFNut�=�:�aH���>acha0rfy!a ��f�+�{Gei�2�!a�!}. tart� �el�>�^Q�Za�an�j��� i= ll�� to bO .0Mj!9 ariz�u!�� �a�1[ us�Nb."~ let $lMDnz al pQF]灥$\la_1% nA&R�L&6M���l ��]ula*��o} ��sphero�,2} X_i=\sqrt(a_i-�# }_1)�Ln)} { \prod_{j\ne i}a_j)} " i=� n+1�w (�&}�n,�ax$\laV$_k= d /d lC:" v��`�t�L�gyO(isplaystyle� 12 (g X,  X��"�gSt\"ackB�mBBHH = 2\sum^{n}_{k=1}X{\Psi (�{k})})$\�Ats 3%/k} .)-5j}) \V;do1 }^{2k'"a2l)=M-a_{1}-�.�)� "IAccEIga !>�,�D aQ Liouville.1 a+r"ƛri�n1B5� M�(tau-1} dl =A�1If n\, ds , :-�"2Ra@a/E+{i���iaweu �} � l1^{k-1}Ej_1�e- !a!A_1) {R}%� }} )! +)�Hn.HnHGnGR8n)}} =\Bigg \{1",aligned} ds\� \m�'a�$ } & k=1\,A\ 0Z!2I� s, n1?V1wZ2}x!{R�)%��-c}�\l {n-1�!no�)�1I $c_k��a�`4K�q�W���� 8!�m�y:��1B0�� 3} V��f��d XA }{dl} = {)�a_i�� u[i m {ne� !� us fixaan�"al ���dbaGU� I_ let $\barm'Qx" �hju�_Nf �lsedf���[�E��I�6�i= ��� ^n C_{ik}� �k��T $ '$G�F��$�Re $2n\" s n$��ri.#5*h�x!�(m $(2\pi \j�+2 (bf I},\; B)&+LA�$d Ri�}n e. Le޲va� =( 9� _n)^T�X5!s=11!s} u_s$m vc"�#l-%pi�vona6+:��J�J�0��\!�*[{ �� \atop ��}�� ]\! �|B�exp \�{�< B :, \��le /2+\l # � +!l -l�:4\}\; �3s 51�5+ r) �* Ox � Zd be�oociN��! !a��L �� =( � ,\l{+n}A&$�)�2( '�\ Av $K,M.z! Z}^{n}Ji�5� N� }{" ] =�28 K+BM) =!� :��)8\{-(BM,M)/2-(M,-�)\B2�� \!Q7%�\�1.5��{�$ =(\alpha �n,K)-(\beta ,M)\, . \nonumber \end{gather} Then the inversion of the map (\ref{AB}) applied to formulas (\ref{spheroconic2}) leads to the following parametrization of a generic geodesic %in terms of $n$-dimensional theta-functions associated to the curve $\Gamma$ %\footnote{Here we assume that the arguments of $\theta$ are associated to the canonical %basis of holomorphic differentials $\{\omega_i\}$, not normalized ones.} \begin{gather} \label{theta_n} X_i (s ) = \varkappa_i \frac{ \theta[\Delta+\eta_i] (U_1 s +\varphi_0) } {\theta[\Delta] (U_1 s +\varphi_0) }, \qquad i=1,\dots, n+1, \\ U= 2(C_{11},\dots, C_{n1}) .^]} j i'8. First, we wan� show�Aanyf%M&Q�$(x,v)m<(-�x, v').3!�.��BA> flow� Y�!�kA�a}Ahvely. Fo? $is purpose� ��[ new time � meteAXi$&a �E4d\Xi =\frac {2\(- \Psi(d) Rf } {�_1-d)\c� (n-d)}\, ds �PNo� ��EM real cas �umb��:j� 0!�� ve. ͋ai�i���$ move� �{to y�,% >I�8s monotonicallyeg $-\� $!�$ . O �(other hand,Q viewAj�9� ature!� 2� N ha )m4 \sum_{j=1}^n %{{R!Ud\la_j})�i !�.9) {R} }}!���efore,b� AbTr} \Xi6�o4t_{P_0}^{P_j} j� � �� -EC�I2j)}}+\ma�c� } �Y&� ���er*. con� s a m*$ .�1� third kin� af curv��2hav�^paiI8simple poles atv \pm6r :� )�residu`pm 1$ .�, hencI�sum� %v)�3an � (ian transce�� � �. Accor��Dtheorym S -&0� e.g.,� ClGor}�� BEBIMA�u= @�Z= j�tak�L��Ah�> \logI" {Z� +B� B �B -F, + { C}s + .C. $�G a norm�!��, >/ � ! +� �#})��A(NS!�B?qq}). It"� D $af�`�� ^ fty$%���&� in�$"g  be� ��1�C>1��pro�.�f� statem of�EUem. Nex�&n����$�'� � -� R | \in +�{& &= '.( q}��Aoulam?E63� �b!P�(same CartesaU%�� 0X_i$. Indeed,I�4mapo "/���va�'� re�ent� K"� &� e'� &A1A1),\; \�O � &� * ),\, E_-\��6j2 O3+!  byM�: lea�5Evalue�-9� .F�W3��mpl!aar��-HBV}| ^ V_$re ��. wa�ult��.Z :C6� cF� �>� a0ereas>R� q}}+$M�ri�� T  x ��B� h0 v$. \boxed{}*�>QEres�.�.t " B\, : \, � \to *� � v�toin� Dri can be regarded� a Űa�ZHo(}_c \; :\, � {d+} � ur , Pcorolla��.� .� , we� ���} �� 1!>����9s6 �s�. $u_2g u_{n}$e $6�"6-:�� �zl�� 1 2��echosen&� %�ՒE] u= � cal !�(u)$ re! A1�8�6@� 1L �&a.v*T .� (w� H ��"x =Cu$).k23� �an� .'�-�9Bs!C1�-� � un��d,�$�!  passage6]�Kthey inc�ej��:}%��pF- 2.} � $n=2��abo�Fgal�perty7 $ already ba�b�� Ves2}eI~�A�%B �d�sharpk ras0�_� BirkhoffDsystem -a� wellto moseRpknown�egrabl�ps��%Z)���a�is u�am�by��q,� �� ma�ld�is{ opeWbse�&� 7ety� our �c pla�� non-� =Ap�܁ Ůitz{��W�"{]>Branch� )}!}��A'a�$.0 IN�er�:3  B$��ube us� derive an��licit �u %�2���C x,��v)$, si� c-�!��7��&+} S2�Y�by�( orem�v1}A( =�� nsistm a� ,of ?��Z:� ich�turn,&� .S JS�\� V6��#Qh Nr .} Lal)h�vN v}_!!0 ,= 2� u_n)�A�]s��$2na�����%GJa*7.05� ���P�.�E�.r.�fE�equival�cla�!FV�eO��, bigg  pi6 �)+*!& m_j-'1S {j} \,|\,2FZ} Z}�%�\z z%H��qIM�)-=� $. U�&/�OMF" I�"F ommensu���@th�%#$coefficiene8m_j$ may always��� i� a waOG��X"� s a ul�sma�ndri� �,neighborhood�1.�@{ s sense, H U%��+� pr��� to� aBZ.AQ~6v�JB�^{-1}Y2K1x.K>�zP%H2 .�I $particular� � Q!!�2@ ora% late :� 2genus 2>�itselfI`%���y8 I A conne�w%"R2(a�@gle hyperelliptic) grale�i���!0, w_0)�$�!, w)}��& }w =�� \q��+a�ae~Namely� was bp� �,2� Mark�Nջ.'�& �8=\{u_1\��  � y bB I� s wh�"M��$oA�qMux� n� �� a�se se{M�� �Mv�  on-&�%�X� ������ ich i���h �ax��Q &� via Z�e�Y��isYl��!�6� )z��B}�&Q{� �v})$ caw "� .;E�( phenomenonA�� expl"�%A�� �aa;eric "A%��Q�t !Zyq$�! mpon�'��� dary $.-at5�O )a� ��doT,I $xA�G,�  i� to d}miAZ-xM%� � ext}e��y�� , bu�6 e settJ=)a�7')9{ made.�*h "�'3.} Du�-�r��ie� : oB[ F!discr analog1~2�{se4 ble Ns studi�in2�i"�Dan,AF,AlberFed,ERP�'S<* E$, although;)Liouvill��,v(� U�� U Z ):!irQ~ %x solu�N �mov�Y�:��re��� A�an E�ly}"� � 2� !�1�plane $t��A�� 0so !i@ed weak Painlev\'� �^@ �0AGq)�(�6�� 1� K�.M�MAy��i��Gramm!� \�"{P�+ ic BzOrb�)e��} %)J Ged( zed Ponce�T em.} ??? �)cnt�!N.�(�*r aY�tra� eeok)a�K surf��z�(� i��As Tiow* I�'�ne&�5g + � soid)%�$t��O-�)~ � byA�, ��oafA�us $n$6����e,=\{y^2 =-R(x�(N�$2=(x,y), \ *=(x-b_1""!{2�)T�*I�K%Al�=o�!Q if�' a ceri�er $m�O� �m\,�T(0+}}_](0-}}(M(;' n�-� E_{0*=(0,\pmi R(0)})]is neut�>�eAU�*"= $s written ��ely@"D1)& q~:�were "�,� Drag_Rad}'�!TS&I'� �>3l/D0*Ai�Z)�� l$d��} �inv�vJ intsH {�* } M )VX#*4 :�.�*%�-*�/*$ ($m>n$F 9� E&v  i9 �i!|f�"u! - rank�eI VhpV+<} S_{m+1} & S_m $S_{h%\ r<2} = G.BW�D \vyD \d BS_{2m-1j2m-v�m+n} ��< m-nB�0�AD �? $S_j�&�d� & xpan�a3%� {� RX} =S_0 + S_1 (x-d) +S_2 ^2 + ��A�M���,E�F.a multi"�al���.z�$of Cayley']�*u�� �ist��#ygo�s�/�eicōcircumab /an.cg%.� a�����on}��r+$Qmsit�2� quit*: �i&�&��s� mor�" ian �� S 2� s. A�X3_&�W �% 1}��Ž��Ť��!\ s{1Y ers $m��� m�2}>�3a�H0�3sb� are} m (���q}&>6{n})^T =�wF�3S"�.V� �0�mn2)1a� Ys`&� fulf� d=%E� � A0is criA5oI� clos�!D 5�a�m�$no �.�F 3�3� 6�'t seems"��%ryreA�>�"�ٜ�5��:�> m�'�+0� 0�5T/" �� R%GaX�Y�by 6!1on��[� rvrXqaft�N$ !��ys yiela�n i�)�>U�Q�$�( �2�6�x��is]\~� A, among�)B!s-5h�'pap�:5_3}A�VB w .��?]J���=0it. However, H"�&�/$X(s )� �c&�.��(i"  ��saK"� do)�uarante��at!��!f$+ngfZp"� piec;$ �s joinC! e�nea�"} �!'�a�e-$Q "� � p"]"+ u�o+ eRA�o��.�6� � ��)R��$ � bec��2�A�؅yn/��:�?K Kmea!ful� !2":8 has" F�a��"1+�&�3��as2= xWeier�!(ss--Poincar&s y of redu� !� Y �G%N�* iLKraz}%� q9er{o�2�*�*, Enol; � a� wA�na��!4�&�_ $n$ jL_n��an $N$-f "y�n��q��E��u``�#''�"�9"�&ij� _1=dX /\mu$)KN+o ab??xEA�U�2��T&3P0BNuXs65�$a 5*��'. "i'J uWq�JU�ewa�S�2�A$!a��Re[d�'.�$!�>�e�e.� 1� �9 \mapstoV,EOm�fu��th��I��||< A6Q.M$ O6���_" ob��ve�+w�to� su".��Verm�Jq polynom�$R�: �G�3.2�;empha�3o�b@qc"��,)�Y#� exa�#�pv/s�s.e�'%$N=2$ � Ekly��! he lo{4!c�, %�i:�!wbi����t � he� � ."T0� w+< z(z-1)(z-\alpha �B  �.$ , ��a��r)ciJ.%|�;���ell�0 = \{W ^2=Z (1- )(1-k  \}�f  ^2=-�/(\`2 �}\mp � } )^2}{(1�1-)�, bothq nzB� _1, 2,m��a�5yomb�-�?�` .ve�$%+�M -�E�isIk!�2:!R�3A{[D/.� �.B-"E�q�1� �!h$-�$,�*@%ir:�"R RR yAI��� �@-�.%#Xf(un"_ Brauk<&�ENKdV�,� C�ero�!6B 6'%j ic} 5(P!�5 se� of0 6�t�=n�c}"/s�+a�G}_n \2�� �TV}nAis�>��s\7��uA Lam pot l s or; a$�O=�=1�9 (EC)1&�33mP!n{\it �|locus�+�B}b)0} \sum_{i\ne q' u=0�uad q_$q_jj="�N !'��� } If�-0als a "triang/#4number", i.e.,� n(n+1)/2$%� $n$, A��:��;atisf� J� i�f�ing8#!>5".12p �\�(|)\�� @Dub_Nov, AMM77})}B'. 7. t $C�q�b�4e-KdV} U(x,t)=k<%�;���(q_i(t)) + C�9f1"y�ion�,A!-X $U_t=6 U U_x - U_{xxx}Ax ��):�$Smirnov1, 2�aMu:�a6�.d1re� s a &Z �0/<1s�4 wp(uRmu)\rYA0arrow (z,w)$ P]��#��u�$�.'ca� �B��KdVŻ}� =R�+1}(z)K (z-z*��>��UEյEs $z_k�Fp� 3I<�"orE� �G *� 2F F n= z-dz /w��� ��� A�R��wp /\wp'D��de3�+:#E A Let $\psi�� {n-zLn� %�l�H.�%G;.ssocia�!�^ s 1 k% k� dz/w#-k��n �c l�v�8� �.�B� nU;edf�.!"�% heta�G)1 "�<:d:�$U:j ^n$ �/ �aO!:E�G* 2<2y��? g= y&`t�z=C�) si_kNG�('$U5�,0,2)^T� suita���I��5s $V,Wc&.n �T� c>alu�B� m�ECM�!v V=( (Ux +Vt+W ����,t>x,>�kexactly��t�G=q_1(t��� N(tE8�(9�){K|D�!SL!?"u�4J�Gavr_Pera�On��%�(a��0homology basi6 A) _ Y�}b�s�#��5�U,V�' (!�)��hA!b�ws} U=(c0,0�!�VAX Vu�V�f)^T>�[%�[ &���Ga�f@ :sN} ( 2&P+ \; B!�� B=�g�H j?!au/N &.<0 &z& 0�h/N & �J0)^Rx  *� �B V76a�&:* B+% $28, \ta� �]bB��&��…�P �ρ ��a�K1)�  (n-1)$:�.=�DAlA� �s"� $:�AUx+W)�(�# >)x�* bf tC,�bf t}=(t"�t�1 . I 7ak32�L����GrdM _�ec�8�EA�it admu ��X� bzh_NJ1x, t})Uz�V(\prod�EN )(_{11}(xK))^$23 SI(l X \left[ { 1/2 \atop 1/2�H ](.:Ea�on2KQ >S6�2hF)? $� t�p3�O%�g$S�"2\ 6 H$:(3)� qcK� ��EC +. Exp4&$2�20SiQ.�$qJ ��T"��Yzca ibi�!-em\pEk"eapart&$6�� �a� �G$)�'%(�O16�O"|"'yal�=A�<-2e�Kogenou�!^dJM!�� 8 E}\$ �)G D:D��* e*�T����+6�'6= %�k2=3)�Eh � !$x$)(P� n )J� ���u� "P` �]box!� >b ���y ]"\J .�/� 63)@�tB�? u$o(i�$G$) precisat $n"jts (g ibly�H)&i^y). #T4!%G5imi�3 to w!E�? quirzX� ��t �e2�?$n�Ome$'alB& 43�>f*YWV�iF�edm/*W� a&Vm ion:�>�9��Eembed�BJ�"X-��H ] ��1=.�but!�A�.)%�QRO+0�N�theless,Ybe�JoaQ\�8t: ifC�=�a �Fl�&�. G��]�-�I�� -bEla-z}UZ5GN;{(z,&- \mu=hw^�-}�D�}��)su.��$6^��)s�#to-L O��M 0%�$!;'RO�-,�$fyQA��u� � D u$th����e fin�$ T��(<�t8y�!�"�8�<�B1���Ja. �� v�2}0a]u *t:�E� %� ) es�ish�� rC\"�SA�"y($N$-soliton��s S�))8��@ bodyR0��s �-� ���E[�^�a�Oi�H� a"�>!. More�?vEr!��C ic� h ll�Hct(>Clearly�".��A �(%U�0)A�b�&al,"�p5ity&�&�S>�q� mustI)Ci2!I6D4assum�XM�rooacz"cz�o:�:郁&�K"9))�!�v:J�p%Tab�D:�� � e^ $��=�se�D them!'!6ia�}g s $e�e�m�!3��7t��l oE*�6e+<�:��\{>X\}�Z a_1 $HaM\$\}\cup \{c�c��K%!!�E B>7R"� '��}Mh]}r(iNAK�H aA�:�>4]s $Q(c�L�L ���.+Par��q�I��.}y>!rj9� is"���Ih$�9�K���)e��n"�"�(4)�@H s'Jq]�?�!2��s68&�*I�%�� � ]T�a � !sNbn�VB-U_1 s +~0 B)$ %,�W���ai] 3*8c3�/)=>� , �a)%�!�3 �T2j ](s ��� _&� .� �^T$=c�"3�e�, $s �!$�V"HB�]tau-1}��$p$�7yirol4�q�L�$5�e�"`��� w�$ \{ ql1 b)q�q_N\}�!� Ap_{1i� %&)�p_{Ni}&,g# +>i"� �Sb&� �"�g�f�p_iJ�=��4�'��EMTGS�_i} 2� KLs 2' C"�U � %w)r����er >�d$n, �_$�8 �5a� *��^"�2`\T��"�Q6�X�� M�� 3AO&8Q���X&�#%="���E$:�1�É�"X_�? |Q_xiM�, ) \exp (s a cdot2 { )�m s -M�O )?2sF2+N ]� )�YB' q_{1Y�)�Byq_{N}xM\,F\ga�Rs $6�)&Ipen�6(e��? and,��(�,7,ul�)\<*G ,wo9�FY2match} )Jm5+m���- q_N+�/2F�M�]}E�p�6�d\IUn \N7 ,\, J2�(63�>�$Q$�=a �Lemp6C^+s �a�� 2e� *�/8 each} qCe�+$ ${D}_{d,j) �; cap Be� leas�2!�N�$5=tin"%bX!6�yH.�S� s��I ic� )�)ŏ*� ' s&' la�[�q1)�U!a�k�� �s$3!K y $]�8 � E_.� �� G signX2vP�Q&�P*�%�3$a�o tau1�7�6(:"?! 2�.unRR?� �%dSE5*5h& s �"i�.0c2�7Z1kQ -K&�N��_�}. 1). �A�� ��g?ick t.�E�>�IA� �]�]R� ) =��\{\la]F��i', B  \r + #?X+Aik( ,'+�_i''), @ \}\,6�"*gK:�ki''�ki'�=��4ef.�] alig�:��R�.R &varJkѦ ) \,! ŧ � )_1'�no�$\&ō�e n]�(X�J �<`{2K}{N} N'p-88[ *t2'(+.:'\"�  t}:\"<tB) �dis�7�)#�"�ٿJ � Q�� t�Ft2(�"$O`�swb,�,h�D�"�cyc*!����ed&�i�&^P97�+NK� $5: 1'=1/2$. �[&] � _i}� i2E2_Na5th� }l?%z !a sid� >5e)�)T0 in >�q*m :�-� ki}� �  k Now r;�) �\ � j V? 4�_"N -Ur;Ss a6�) ����. *&;� ���d�s'&&���my�c�JŃ�S n, d&�F�-v ��K:3��"� ��% r((.�� 2).�CA�!� S}K2.�W6ZA`��&S.�/1��2�8��$�AitwoP*%�M#A,2�O!�1#-Fj. 2C.�^2�Xw3VdXBv5&r��H�y��$ �+ $N**(�= lex) �>���p �5B[is:�a�*ML{>Qm$V�of�>�PM�:6F vj��W (otal $4N=2n�$92E#��!�Y �3ing� 1H%�y.SV� x$?,s"�]R&`ͩof�9!t:��i5a�*�k. ForK(�e_i� � y@.0F "#;2�>T ,s $D_{d,1},  2�/� u��y, � �A5�KsA"� �HtFy iL. Ni^\� �rW$ $N=3n=2$.}P@sY�5%!Wc�O.' �1,d �2,d}$ �ov���`oun�3mply-E,;s�V�D}_ I� D} _ Qa��2.I"6F� can B e Y�k�: �_6�LEr~: D_{i� (w4 "gpkin�,Z�"�d!�_�IBdn"��&|B0�0��me��e#�=�2!U eQUj�M䉝�_eE a��gy�Vje+�h?��� [- �V2� � (2�rpC�Y�. � d9��Q31�$ 3!^amal \��% �iB e;e|%. �/d@4i��6)�a�flup�eH2seq�\{X_i=0�1�#�  F�5�<�L~c�1at 6 (� �8�N�) &�CU~:5/� � � a�itar*�da���D�qFB�%a cubic"LH0�)�"�+�:3:1��Q�G}J�;s::v3-%g9:� nd d�+5o� orka��mit;4 H�9e �AHer�MAk� .�T#Gl'*�/ly�i: tob�3:1} H =� \{&:-� � 14 (4 z^3-9 g_2 z- 27 g_3 ) (z^2 -3g_2) � �JN&��c�sE35)�A� mBzi $g_2,`�z$�? E}_1� W�:4 Z^3 -�Z -�\}� (Z,W)QD��x:�r"` �:Z=�9�{� �}{z^2-�� � W@  2{27ql {w(z�9%' + 54�)] ?�: ,�Apo�Oe\Vb.�T5 f0��=)� "�.?:�O$H$�%9$o�45`one�E)�{zo z}{w} "G;23 � {d Z}{W6 $$ %[#%��D�a� A�%�thuV3 �Q, %�z8 q!� q_3$94>F � != to 3� %.aI*�����U��6�\Pi_2\f; H>�_2�z�4a�E�qLZi� E}_2E� W}^2= Z}AG_2-G_3 �<la�|E4)\ G_2M_A^@{16}(g_2^3+9g_3^2�, G_3( 43}{32}(3#-0) ZG2�"��B  2nd-%�} �Z}u"�a��),e �W}=- w�O( A�I�3a2�*�aK!��Y�M� 1 ]�)bZ}} E��� �$(Y u_2�1N�2b $(H .�2 b�2P $(k_1 \,z\,dz/w, k_2a`z/w�$k_1,k_2=$c:o"� *u� KdV u\q"�1L�$� �1s oQe ` ma]zof�tTJA� �55M1 @�8b69/�!/&c /3 & 2 &�//3W�.B0 6y/6:&�� b} /3)�&�/,f�.��"�.A^$2� `!�rT#1_e6�.�[�)I�J A�� � - d$ nMb: u �+Uv.�+)# set]#=�F1$]!�apavr�6&47B 3�a a-z}�! �'k5-UA a9ed ei����sH�$n7m\�B3$_&o$�(1$�H g_2z���� [ 1fq��,$e_2,e_3,e_4I(q ve�N �F*M soivI�I�8Aex� negaA�, so F� boloid. I}�tH�(�OUV "�,�h� o�{� $w# \.d�DunjedM;�(G w"�>�Xio1 here� se observ�s�"� � A sR�Ffo�VQ��! 6Xi�aڭro)| R�9e1-e4�U��&uZe_1=1�e_2>0��k2{%��!=$H:!B}�'K+ao�� M�!q�C@Eo5�a�a$3��EL=-�=if �>BBE+eft(1+��{1}{e_2}.3}��^2 -4 j-.;2e>=�>+ e_4�{3e (({2(e_2+e_3+ )B8 oF�-��C} 9e_2^w^2-24 HW)+16  ^o ^2=0�>�2 .}�- �)@k'5W�?� �B�rT*T]t6�ob4A�"�# *w#WT R  0{ ��V; !~>:�4;3��1Co{+9WC:Wa).5e�a�2m 5m��)v"C#wr�%x4! ���  0A e_!F��%F@}<%�:@E�.�2Y)�4.�Kt͙5u&m)!M�%w%n!h�k.Hi�c���>.L:-�2"`* s* o$1f2��)��.>�in�.*��!�]f�V lemm�.�*�Y�0s}�� E�ea"8AVY���dt'X, ="�3�D (1+I 1�t �:3"0�eA?g_2"< 3; ta^2q�g_3�  4h�0+1)j 2m�� J! ���|I���f���{1&�� 1��8�h 18-ex%2!�!�5#FE�)� *���˅L!� -�0 $>w"p�Mcalxh{ %a!�Pas qK"�f�A&>{� �u� dQ^�im� ����&u��Jep&s $* $, not _Otriax��^ �F%F�3:1�-@� �hEGNh.:Ais .�Glud�*�[ "d&Z � typ�'fn ��o..�s� S �,y$TV, Tr}. D�Jp!�a�E* s willYe!Fsu%Q& a fu� studBAc"V2�YuL6&a��LAsR�a]Zum� & cV-T%�&� ��\an!�be &l3B]�c*s�Z . Be��9strict%R selv� 6�%}x$� Z2�b:��=5&Tde~seg�c� @I=�~X�'%�bed by^! . We)�K*; roblem:�  a familtM%�Bu�an.l}jau�&k $aW9� ary" s $d& �X� 1� GX� 1�?2�Cect�W2 �. -���.[sE�r�clarific��:Ez�Uprevi�;M�a�e> -��&�� @A{� &��Y.}�oua�3w v$, j "�$r�.ond 3Pz:e �_(\%kxR͐ AvY(A}ZA�O�,\"�\3-p4I��n� E-��&�(v>[k �  ^�"i9�~� Lw��� o%"unta�al �sr�wy�I� ,�",��  9\{B  v)\y; � n��wAK�vqu�m�%%@ x^*1L v^*_db_&�=m"�k^*�y0�5 D"�M�e�UF&�;6� ��$b�d��ngu�8da�Mc�n5.by ly*t>metho�"Ye)�30�Xk@or026��-��<y� Givec8V�A�3A�� �U� C�te !�!�3o":�5mX(�R��A � �V�}; �buZ��a- 2-�l:�J {U�\9()5}s��9!��` * ,+mbda d�Z}{\muA�ɥ.SBd�!ly�q��DwAv�sefy>�h /�)~"6 �J��]l_�,9V �YoršPB@!&.6.NS#N����!J�"B}_{chn��s�RpAm�h�g:As,1�FA,d�1:EOr&�v� ch��o)to-on�I)_�����X� �Ō��0%�~&�J��e� W��^*\, : &?qqM�� �#�] kas �/Q"F��3ab {�Is u!nctOZ�d2>"� H!�*!���2�`y;> B�.}a� A >��"i �}0u_2"�\ +*|�e��.7��h�o~,la�bia� A_2�.YPA L 2#Έt�j\delta -� 甉3W� �=1/d+�SE_<�l I,�{R )PkH*�,9�� j� r"� i Z}P.a�W�9�bn�&�)�� �79F� %fe.$3 N !�1G !�� 13 ~I}_\rho$� 2=�7 t^{ r(9-+}) }_{>-9MM"f�\��"NZ}} !�!� r6� } )=(�,!� TO �}��;K�ML"��rho} 5 =--�7#/�M5- 3�D�?EF`&eC.��-*�m�G}�*m" %,!4y��mV�֓��7���Awiny >�@J<3�dE6��"�'�A$\L�`_0�]&���X "r3 X�5%\#M4���- �:.�6Wn.���-"�D� H �e�J+l!#)iB�=\Z�2�b`at��FJ ~i6a����sub1F���L��� t(Az�Gb%{,���e�er�q�%g\$mmiq�!*&�oF�. (>�shouldXYl� triv� � �Ve�1=.)�]n,��*O1 e Ca8n-�!!� (� �P1i0� �qF(��q�A�%� $a� $. %��we Dcu p0�ice)hlarge%c?_s�:`�rP= tedZ.uco�+>+���7 .stB9.P $g=1, m-k%����#0q})�:���$QDA�BI� ��� N3} �| #~"} S_{4�q{�\5 4�$ ,� | =0BF(�p&[�>YD�xpa�I�"��2IcZ}^{3%{2}M�Z 3}}&J; / m�Z}-!�)7+P7B2�<�z2.0}}��6S&?q� ZTq2�?.= ^2+ �6s�"�v�$P3} P_0 =y h2� -G�!\� P_1%3���)�&�6�P_2 3�&5�BhNB�2m%�ƣ>�( & ( 4P_{0}%I-P�=^{2})!%P$; � � (512/^{4}+3 /6}-38 G!� P20.3 +96i 3} +62C2L+1B+24�'right)=0-1� Substitut�� �""P(�pP3�(w��� ���..n\,II� nk�։� �)<�#��* &��1�69} &/%�^4-6 A !�A12 �(AB2�A*_(�]i� & E�^�+26{2� :,^{10} +220 G� N9A� {9} +165G,!�852802}65x+2�9�:�  1776,L-92 X"�_6�64 ^-65~E� ( 18�4}-960T/8M �f:�G8 9A�=-3236F3} >� �624sn: -9=A�5:= 2} + :89! ->y-1314 L.y 2� & +51/�a� �6}- XS�=0�Y��e&RL5 Q�fa)UaQ�m7�\9116E� s $\� _j�& is nv�^�o"�',2� 6!L\{ rho_j� } �. _j,"Nz #. _j�>-/ �^\}$���N=�W#��s. �+}�5-}�� 6 \� A}3 2��}) ɬ %#��L+� }��LA}(P) ��f O}^{P"�.2^ ��W�ci?O� ��a V�OS0�0*97=� *N�in F*�\E}_ ��|tJr(ix�i#H�!�{�C"W /6*8 ) i*a�J� +�t . Z} 6/) <� /2Amof!�four sx *"Yj{!�pj!�hMti��.b k�ex�(2�:a,� ![ algorithm�& 2�� ic"  2hon8iՋ4 step�Bm@�&�} }*>�]�6d? s "!234�2�3.2�<�Ps �OI|M3�_�m>M2!�h�"b� 1� u/*J�#Qn &�> |G��A.�G�Gf'팅!�A�O\I6 {2)}&^�JO�� M}�O��h܋s ��"FK4}?tc re^ �e� ",e.��&�i�J� ;heR� `F3 �a�utR� o"��A��Hx&�ha���d%� solv2L�5�0<+��d<$ $ S&�$�4 �selec)({!�oQt��8�dm��!� ��9I���F��WmD3�a a� ejGZ]a� ��ub��"* $\{-� eq-e".e4)>8� 2��.��*a�2�a�!�)Led�� ��d�-O�z�e��& $&�ScJs 6k*�&��p�%� . %� �! *{Co� A}-qape�u�!K+&Nge��AI"��!!*�n a]9$�C cs]!a�rw�G>8Q :I :�!( Z�!O&g/&< a �0�E�fF�J�#-U&�2��5q��s�e�w3Htangen��BF�9_1a��"2Su!s�f�G*~e!�GH����en$ed�gp:�e��vQq2_V�2an]*}r!1Y�dứ��Ia�reb7%o�a�xlH >W3-�U}S"��&Kh���)��#{�� arc$!��B&. 2a�i  { $m>3�" �.* ":'qK����QE�!�a*6I#0A�2a%L"�$b^l!t�f/0c�5=3 O\6�5.{%.an :.\ ���pin inst��)/�la\t�#6�Q�%ߡ�ek2{�A)�G}� �_ N�_Prym s�_&8_� g�Jal,�(� auvariety 5�q� (/optl_3$B=�YwyzF>!�*�"a.�KR�-2�i>a�"�_e�eXxM�1V�v�G.�2�D Ȍte ���GC"4| *{Ac�_ledf&}� thank E.P�$ato, V. Eovi\'c� d A.Treib��useful v�u.q2�M A. P�� omov0�"�\`M>dur2prz��"!P manu�sp�)d ��%ng���#feruM �("!u�!��&�8.�"�:��Levog���%�H:)Ĭ8�low�6 no-ę�96�pe���9"�^.y�In�/P�)s�bf 17� 001)�,. 4, 101�042.�udin}  M. Courb�lg\'ebr�& s et�> \`em}wt\'V$bles: )od\'es -Ј��que1� Expo9��T�.Pno.3 (1994), 193--226.�0MM77} H. Aira��(H. P. McKea�QJ^s��R�al%hQ19�!O�2s � 2�Dd s��^��MY Commun. P�.]` \/ �30�@4(1977), 94--14.\Birk}"@�,� D. Dynami��Sy�� s. 4B��.!�vv��3RI. 196. o�{,,kolos E.D., ('ski V.Z. R�1*NE�&3�_ -gap "�x1�>Z�VAm36}, 1�8Ad17=�B��B�(Bobenko A.I>�$, Its A.R.�H(Matveev V.BM�i�o-GG  A� to NuKI��rA� E�s� Sp�K er S�zin6-�s. ' --Verlag A���0�H von  m\"uhl���z \"u8�/\"S84che Linien auf�yD dreiaxigen Fl\"ac�(zweiten GraaQwel:durch1�LFuo� en dSst��n4CsenM��  Ann.#,bf 26} (1886av51--153=�C3};,�Phi�SgT bf 8A5a�339-32��z "$b Fj�p�!�m-d� 5al��6y��0Lett. Nuovo C1tomr13�4975), 411--415.�@�A.Clebsg�P.Gordan�ori̇ sB!Mn!NkX!:LTeubner, Leipzig, 182{(Chang_Fri}  ��-J�1,riedberg R. y}al �et �����!\it�)�Phys. �29ig88) 15Ż550.��>�Shi, K� BZ�D�v��"Hs�E�"� ~���(1989�m798--804>�0f� J*���� full�'��a�$��meEPQ<�-J|bf 34E8 93), 2242�u56 %u � G�0}2� V., Radno� �3��^i:�yp$7r %Ɉ�1]-�:��M� 3-�(98) 355--36.����Ona�e6�&/�Q.iP-�C�!bH ��n�(& ��pWA �6��2�No. 11,�9898), 5866--5869]=��7 1�N�����4 ��)y� � $k$q�%�% ���{JM; A:m�Genq�3f � 1269--127.�D�{\} Dubrovin, B. A.; Novik S.�A5� w 3 the K weg-de V\�a Sturm-&�"�3Ii�Hnn� �*'� y. (R� an)M PDokl. Akad. Nauk SSSRq4 219e67�531---532  ERP}.{0, Richter P.,�nin�K8Double Pendulum��T$-D�� �OJ. ��.? 1v��, � 3) 15s7.kFed1}6r C�ei"U�r�  to�E�&m �> ��55}, 3 � �Q2012P Fed2:���a\�)���C ��"� . % �����a!�� yS�aS�� 199--20.� ":q  ilov L!�"�A"� �6������� j-R-06�-.4Qno.�:5 !26B -635.�j� m�,cosa=��S�0, Papageorgiu� Do.�m"�sQ2�J`?)S�j Rev.p5Q6a�199%H825--1922JH2�iffithsE�HhXs!Aխ�ѫspace� X ent  H08ticU�52ivT 146.�GH1f~On��B�A���� poris1�(L�EnseignW.��-�2�@78), � 40 %\b�;Gun} Gun�~R!P{Gp{�S��s.me�iesA�Pr#�lUni�9Press 7.&H P -PC. Oeuv�Gde� r�[ 0. Vol. III, G�ie� 0illars, Paris�12.� P� Kn\"�rGeo�E�AXe sF�J�5�UK5�A80u 1�.4.u �~&�� I. "�"bq|XKadomtsev--Petviashvili� � J�-n$d�\�FA. {F[-�1U� �682�KT} Koz�G�TreQ v D&w �=e.X�� S��� % Im��"ymerq Soc. T 1� er.2ѡ16�ZP�gde/USA!�92�fM�Ґer��Lehrb��BG�ZFunb 189.�� u��A.B�A'CՅ}+�4Abeט%y�TMC��96}�Z"#�*= M} ��VarN+ A��f��2�-��:I�$C.I.M.E. Lm�, Ba�ansone� aly}!wX*Q 0Mum} Mumford,A TataFA�%z a�198.��T **riv����o�P�� EP1}�3v�E.n�PrAVBr127գ8no. 9, 2547--25. lS��}�O. . ��02F�dVu�-�c Z"Y4��Y au7./ f2BvF�;�����>�R� 12ń.� TV}a��A. � VerdieEp L. T:�su� f 4 KA2}�s.��R,P� Sci. �� 31n[ᘡM�5. Tr:�Hy.R�>I�nd*� "t s*& *Uspekhi!�' �!5S*s 6(342), 8��36; } nRYio�: O� Oh� rvey�BS, 110� 151}� 2} Veselo�� .P. &�� �Z�;ݦ time]�CKOperator��Funkt�m i� lozh �2��A�� a'02, 1--13, Eng�tR���W6� NR!F9.�B� 6�M r>� �-� �g��e��&0quasicrystall�A!�ů�Onar7al�St��Z burg��9.�8Van} Vanhaecke V�Ax symm�� �{T ��v�ZK�2nWa1v1, 93�]�(}2�(K. \"U�di&�n6�m�chs�"� �I��e� �� Werke I}�'�&66XF>*  docu� } �i\U! [10pt]{io�s } \u�ckage{nicx�AU��ta��.AMS foɣߜ2BV��.VXZsorl��(} \title{M�!�wak%C�)��_�Y :f or{Chr)?Dan Veldhuis\dag, A�,Biesheuvel\dLee��0n Wijngaarden0\|,Detlef Lohse \f��[3]{T�{om*H" v4be addr�d (d.lF4@utwente.nl)} � ${` Dot!��a�ied1 ics,.� of TK , EnAde,�� Ne^B land)`dag>aMefk%LEngine@��h -� abst}4H�"�$�0eI$O��la�Qvisual�f��6�� hind��id Ee�b} or f�Sng freA$in liquids*�:aiagravi��Th1Iskh�rk3 ��"S8>��Q�" �A�es held ��.]1p&�*x�ɿ��!g�� ve��y (&�CReyno��c) #:d�ty�5i3�twA� �A�- 0Galileo Hz  :9� d&{.4 -�year's�! illu!��_!;&# laye�,�$ �~a l�2�ri%�iie?8t water at high� �)O6��}A! �isUUed�  Schli�  t 3 Qex$euE�x a�toI�^�Qx�� ��aXW*���a�7meA�:�s.\\ \\Ad��t%xs e($s*num� alU estig%bsn!Joh ,,Lee,Tomboul��@,Dusek,Ploumhans}�.lIhow�,%`of2NE�E� {\em E��c a un��Viag�ca s��<�s  �:�P $ Re = Ud/\nu $ is i_?as�F s$U!�e� streamu*, �)!�di�T" �{ $\nu$&kin�GcA%co��h��t�IA�s f�W�* k�y axia0""Ju��$Re=211lA�{ his X#-{lanar-4%eis�/�Xa��s/55s�%�b(unter-rotat�4��4 tu\_&x27�Uu^ fuJI 9� A��B�%�b��� -vDent: o�ite-s�d-w��voAܡ!G019� loop!�at�=em�hairp�. ;�'�>! �U�&�gradu%��m�� irreX��fi�� turbul&�$Digital� e� I��V�{ �A�@ 0Pb )a�KA: ^![�B:Z (F 450-4623$~t��a�n��-�*] 0.50� 2.63� �2{E"� al��ail&qdf��}[!t]�c�r�8���phics[�r+^ width=0.9�[]{Setup}� ca�8 {Top"�n!-&� set-up�-5\Dv-3E0�$�<_ Fig1��� �45�z:r-�)� [��cM�C in a> parent�$k (0.15 x 5 m$^%����� d��cE� � � ooth| �T |�� �t�1X� 10 )�a��U500 kg/�E� 2781͐��N .�By �an op�y�#s � � !*wo LED-l�4s, pinholes, l��x mirrors�R_"�X��O J� t au e�� OP��rec�0da*,500 frames/s)_a CCD-cã ()�\FY)�n�*each ���c pe.�� � �I)��e B�6�Sat$A d7��.1>a� MWY�1= �y�Ih-a2�;Ey6.��5 is e��s��ve!ial teml ure 6 K�A��E�0 main�2,ed (1 K/cm.) ��/9 I�.R!I� ) �jW302 K,%�:�>5nI�y��l�Y�A"� $)Ah�($(nu.'of 996ya0.802$�E$$10$^{-6}$a� 2$/sJe���U5ձ�~�cb�� =�b �A�=[*P6$ R� ��F� /2�٩ turned ouIpRd�!cul keep�?�g=� !��%Z�ea�1�.�I .C��.5��5b�3!�f]�-�7�$�.j=�of 10 \%�\��!Q_-i(~Z� >� :a�' a�"��. F�   e��.}m }K5#�a�N d-�XO"3��"J ]� � ?M���A4!6��p'} �� ' NumbzG�frac{{(|QCs/.zq! -1)|g��$1/2}d^{3/2�m�yKF3eS'# $zb b dd $ ca�K �7ide�]4t&e scal �Gɉa7xiM�d"�0ى B!�-q� g  ofIP2��rk��AIa we madi&N5�lsummar�' in T!� 1. %\new&1�t}����kp11})�e�iC� 6�;� in mm���Ds7��. !5�kby"� �A6))Eh�T"R.:N (a��2`R�$��up=ular*}{&" $}{@{}l*{15 \exPolsep{0pt plus12pt}}r��br & I��n� &qe$ R�$, G$ & �&|�� mr f7& 1]3.2Q 1028Eo& 1.03  & 12*205K~E�Pi� F W 7'�2b4.0 b5b6" $& 239 & 32�bp1.5b & 2.79 $& 304 & 45{�F� ��8 6�35S%&4  & 35�546:&-R�Fig2}s & �_4)z_ j & 39�608�_�5�262)! 6 j$&1261 &197� %z& .   \\ r%=7Q� 96 �& 0.97; U�1r�)g16d!4 5-� 950Sb m & 29�F% U Cros2 Fig36`!�`4 �F`30!�47!�.�z`�5� 87)�`8iR & 33A$56>`2� m6"1a�105" Wb9I2A�!~57�F�KinkFig421�8\2 L0>\3�600.\���q� 9�g0.92g35!64!�.bv�1!U._^?39!65>z_� 6.4a 92I�%|)�& 5%�92e.�� �b86��b8I�$& 728 &118�b6�1!R 7.9~�732 &13EFz�:be�5&6=��1&1160�Ɏ:be�9�K� R[&2548 &�:�J�b���tale}.��O*Vr} .!FD�$stereoscop��"fwak{@L#�� B [�� �9 xima�� 4\% r.\�/F�ham 5\%�.\��Z/b})lpn#t�urr��@�!L&( aڙ �M.�>��a0>� �r�c>�r.d}) lowWnHK�4 &� is 6� ���&B"� roughly i�9in� s (2� c�Ki :&b}�� &d}��er5C� ly1�g v>t�ha!�7 av�*-��Bin7�by"� n 0 )H$ |A�U�>��arv �D `"'&`E2!z path�TeNse�iC m�.�r d�,i0��"�" � '� se p� "##S -�iV�#$� V� mat�(, even�2 clos��1.a �unC'ngth1c"V� mini� $}[t]{3.0cm7Y\B";>��=-]q�� a.eps��" '�{(㺅�R�z \h#�� �bZ�b)�Z����I !#cZ�c���{minipage}[t]{3.0cm} \begin{center} \includegraphics[width=-�]{RisingFig2d.eps}\\ \footnotesize{(d)} \end{Q y1�caption{Stereoscopic views of falling and ro spheresdtheir wakes. The left part=|m��ead� the IP:�producednsurfa� �@ does not change �;U leg�A !~�+B��.�i�F �b}�can�Aei�,more than onI(qZ��A�lf-�hAi�)P . We have�yet bA�a�C to dU maS3condi�sa= term1� � �� or � )%� selec�Qnumbe�* kinkA�at� M�. Wis��is� @�m�}�4 Ia2�subi㥝me�A�B�do!a�m!aff�$trajectory g��a 0is corroborat% e opini�8t high Reynolds ��e!vail1[mP�wdi�bu!� very�., a body basiiV6�� -L it e&� .� ��$}[p] \unit��1cm!"I � 4.�� 68c.� 3a� >� av�  \hfillR� 3.5c�R6�bR�b�4��.�(SchemeZigZa�3c��f2�cv�1v�r�i�� d����2killustae��$ i�2� m� ���� BL 3 �5wR (`1'),joccurr} �(`2') {�v�� �:�V�/�+:}(I�0two neighbour� n$connect. Vb� d$, ����D�:� (�3 a}) 5 mm,�(5, 297, 450��. 306, 475� �� Lc}����-� ex1zU��a &� $L$�롺n� .� o� =�. D*^�U � drag!�cqB!� � (buoyancy.} ~"w3:2b6�>��.@  �}F�� =0, �0.8\text�- _3}2�*9sR�a m�i�E$its wakŘ���&�b�F So�b�� y5� $d =10$E�n�= 0.99� =350}=576$)>�!Cp )�5�-�6��GO Pe��+! betwo G)`mean}>M�#j 6V�r|10 \%-%bbe takE�to ac, , when analyzA�b�. ���ce�6*al data~�Anu��ofRie� avioE��L �sa5��u&� one. F�s �soFA�e�ExtraPicA7s )} � �E�th �m:s'a�allAoa non-veal �G��ntA�ctsR�wh�aim ponly 2� ngo g � mo�(Acircle� �:�) �>� %96�s!SA��!�a& increa� �!���a be���irregu?( �-�2�~ 1}��f��e two-� ed q stru%�AJ%���aer>� s. I��u��FS2P�W �L _st`�}, w�9�h2 turbul�? If so,o&�>�cause H a� �: lW��adqwak)6? F�[' arch��add��aqu��onEbord�n g�� �?r�4d�b��,ary layer seGE�$ u�^  a�Dw�ɤyear'Yver. � I]}[!h]x RP:x 1.0.x . 22y P�qT::�n� $ versus:�� $e grey boxA�aDMm� aly� Z{!; }Iy fWI� most�Po��0 axisymmetricE8 symbols,H ��1!�2g , deg: $+${ ady�R,oblique, $*$ scill��me ���?r�  ic � �23 �� 35$)�D$\square$ chaotic �)Ft )#%� a�6^%�t  1. E�� 6�19 �o.r Qv&� .�:� 2� qq!��2.6��-]{HDPE32Z���_�&"-]{PP40Z���]��Kraal8^�z�n�΍LDPE64ZdvU �S[ *H�ju�sHed��severalB> (_mF z�� a��~ contin#in I� Jd2F��#ofH:�# x�#e���� 4&�#^� �v�#b*��R�#3.20.�121, 212�4.0"8 0.88, 334, 565�c}) 8 "D9"1�#2"�#6.4 D93, 5D920�zJW1��)~}�u�uPPb��s�s� Re135^��{�{�965Z������ 4623Z�����ʆ� �S�S�S6.4,87, 728, 1182S7.9�732, A�2�T�2 0.65A 60, Au$�V 9.5 j$50, 2548, E"qJXB(S�h��j�PS����"�S4�P�P�PGlass1�K�K�K�Re197^ �L�������M�M�M3.2a�1.03,�0�e�1.b23�2"�K1.�2.7z,4&��ID2.6f61�m7^�M(B�s�,on{Co�s�} F�:�a4s�esolidU�'�fac�of�v&eveal.�"&L�T e b!*Qwhg�):%"(�b�+i0"�.��,s�F=#9#�o� M�..�Xi&�% �� F�e sur�aW�&�(d- imant�%.�clearly�w%9B� qo�&S�RE>��! same:Y.mo$/&dr1:ms� be�#�# fe�, I(!� largeB� Kis56gtho�ly�fu�"� Q�$AcknowlegdX}  au@%�nk Andrea Prosperetti, M. Versluis,%)C.D. Ohl� helpful~$cuse1%r'aAG.-W. Br#+rtH.� olte �!Ftechn�sup!�is�ish M6"�pro*m�* StichE/$voor Funda�,eel Onderzoe'r M ie (FOM)��*is 5*nci�( �edu�TNederlandse Organisati�%(or Wetensch], lijkq,(NWO). %\new�2 1�*{Ref�ces"Jthebibli�hphy}{} \bibitem{Johnson} , T. A.�)Patel, V. C. 1999 ��past aq�upA�a>q!a3]7+" J. F> Mech.\/� \ind� {\bf 378}�s--70..�,Lee} Lee, S.�0WA��studyu!]u�-y���Z�in a uni��f+at mode0$b�ps� �Comput � s\/} �029}, 639--667/5l0Tomboulides}  !pG%sOrzag�A�N"�&vA�ra* 4ional and weakX �L2�� �J �j�,416}, 45--73:�"0} Ghidersa, B�$Du\u{s}ek,^20-� BreaQ&)�nse-�2:/w]%of5��.2emh6U)� 423}� --696�(Ploumhans}  D, P., Winckelmans,!�$S., Salmon�,K., Leonard,!�\& Wa�% , M.M�2E4Vortex Q?Yc2 ARQ�imu�o�-e-d�� al bluff})%�s: Appl�3iong�T,yatI� Re}=a�, 500o&10>�Q�Phys.-I1e�427--466 � docu� } ;�\4class[12pt,one�)]{amsart9uy"ckagem�= ams�  th7 mscd, url3�CEEBAABBBBMMBNN}>hca bfFxcbw6�zpb{Z}_+>[CR !�6?CCD DB�CCBFF>adA"rm ad\,B�msA !�frak{sl>?mg ] gBf.fB1R>A�2�ms.>s�:!L.!LB_Qf_F1uRB>K.]KBQ->E.>�h.AhBAi.iBn.nBq.q>we. w}\!9�eFIs�sigma: v!�varphi:aut c rm{Aut}\,:"sym"Sym"6�rk" rank#2ev"ev�2 codif �6'Co%bbe": idfid>Mba�bigl|>�p!�vNd!�delta>4��rm�:�p��ta���theorem�|}{T )x prop;.ion}{P 2Dlema~L2,corollary}{C � a(style{definj;6>{DZ$�D}{E�D6B7B}{R?B!>begin�[ A~$hor{SergeyA Igoni�*{D�)t�)Mathemat#8\\ Utrecht Uni�((\\ P.O. Box� �.(\ 3508 TA 1F Ne�?} ��mail{i� @mccme.ru�t�:[Miura�;ns5�W14nd homogeneous�2ces] { /ype�4jdate{%�0keywords{Evol�;� , f[,J�0, Wahlquist-E�0rook algebras�KdV equ�� subj�{37K35�#C30�)�abZ9ct}�4re j� (MTs) S+< e:� toA6 zero-&v rei-���Hin Li�@ � $\mg$. �proUGT.cer�JAR4/�? MTs !)�8 hoM �uis�1s,!� . F� sca~.� �-in�B�1]d,a�G�%eify �a+�>hBY�A�j�#s ��B�MNB�on� sCMT�TG"@^3j!3%��.DB 5th �-��$Harry-Dym a,)r?coupledG-mL �4K�-ed,@d Krasilshchik. � Y� \makee� �Int�5�S I-�paper04 �$(1+1)$2|F4("g��{9dJsvl>$rac{\pd v^�hpd t}=R^i(x,t,v^1,\dots,v^k_ 1_r( _r),�9 eu.eueP eueu^kYu^eu^1_p ep e0notag v^i_j=\�^j�$x^j},\quad}:&�&i=�k,)�17�a�Eya�h8grk.B%. Cha�EofU�"]B\"ackl�8:�~v0b,790 If $P^i,\,R S^i$�2H7dependX$x�*t$��MT�2"q>��6�e���3 $k=1 Jprobl�C1jJsE su}, A�a�8��sv} �Ksol�,efficL8@ �s _sub}. �ˉ�!uQK�:biu}, ͿN�v�? AseeR !�t#��1u � tudi�nly �RQ%�� >inLI^$ $u_t=u_3$ �khab}���, "$drin,guil,,. !�X cular�l@b���� ed ud6.` s���6agroup�F�}�1 loopF!�. T�4��E exha�:A>j8v�4h� 1 , but, a��.D.-_�=�c5l4+f(u,u_1,u_2)$Gon�;n��",Fll$��8 ob? ed�3t�b"�N!1(a potential�YW7" Ti"a#z� ofi-u} (ZCR�� i�' on $x,\,a�$u���.j\le p-1 It!u�G at s��a ZCR �&G a%�  śaU 6� �; by v�G�;� a mald $W$ d"�H(a MT. Among-i�4iJnt� imag `#!P. {;!? � t8Jnt�;of{�a�� e6�iTK.�E�9H  T� c �i�Jc%p�$if AHre�J �%e�HcA�ingE�PDE��nonl,cfgtLɂb�9A�c�%mg"�w<O�5Td!�-�-%�d%�Y a2�J�� a�2�. Sinc �=a�l� !'��ity'��2 5�%9E��6Es>91c How�2,�e6 t�& sv�2v| �Nim�%u� > ino�E��Ain �= coordin1Ja��[����u}!dR�, �Tp&` �y�hari<3� A9way�3 ``u�al'' J���� \-Z��.�YA�"D re� j fic.!��� !F��BE���. J �0I�any (�ne�Pari�8� >�) MTVI !�ofMMgrej&cn 3�lsoEY!�;A�ͺofmR�G}�:�! associ�wrSe quot�2 ^�Eg$explain whjO�">��N" ��R)��.. An���idered �!0���^{� 52}u_5z$hdbt,konopAUUitsE�^�c�%{Q-WFr w�Y!�t%�9�is�i%Qi�B�5e���"��FQ3.cor�T"modif� ��B$hd5m} may(*8DJ/��non�� sM�� a su� ��Og�V��fi�Z��N�#I�����-~kdv-mkd�SɳMT���7A �q �.�:-sak}JAgain�,Zb) -Unew�(_U�(lso more� lI�� ��%�&' 1��B�?�LR�j%y&�UeT, buXsOE�  (se, .g.,-# ibr,Y ,�� IٴMU|Se� open"�?e@% c<�5�,icm�=Bb� ized , y�� .��9� � p�a+Ba('��.�\S$on~�AlieL �-�)�s/%k�8i!� /E � r =A�b` s"�W� �Inzs {a%? #\wemt}a(describ2ofD J�e��]5=&w�u��Zu!)Fi|V2 mtsys�%p�� y��I�O "A52Jon � J,}!{ R� ��|�0}}NR #@Q� -a�}mo�sm�:�,\mg\to D(W)$!�a�� $ of2� � $W$�-eM AXsaik be �E�i�^}� !�f 0point $a\in WJN8 ppA� $$ \ev_{�^,a}2�T_a Wg\mapst_0ho(g)_a, $$ �WurjA�ve. %s�Ease��J ed a �B�%`� , s�  wzGIM(Bi2� D(W_i),\,�2�_reFis-�c} i�J9Z* �?e %�0 e W_1!� W_2$�an �2= -_*!9_1$. Be 3�S��­"��O� )�reBX vali�Xboth �^go]aymom � lex-�Ht��� s. D2!��2F�Yn�ed,�fun-W��/s ^AJ n orBm._Z�_�Of�� a (p^`�Zin�e) c4�ub�lsfggz4 mg^1�set 2 3 u mg8ф}� anq3%�)�.�zt easya�s�^MSQ)�Hemp�&�GWt $W_c |aV�;��ga�f/, l\,a,\,a'e�_cid�Urai� \dim.�(! i)=:'R�V<Z:).@� More� ,�G�a�}Sa�nd)Le�Q�, " chooe�_c��be�4k�����ely!ide"R����ly, be^� i'p�mWassum�o=t8. Denote $m_i>.1-$�"�_c$. Du�bKe'�A���Y1�Ye-� mlem} m_1�m_2  3\leE�-b7s�E ooo}��ab��d "-_9gb$.�$VAP�DI��$i��.s1nd L\ubs5)�Mr+[�� $,V]$ coinc�1��vU!${i+1})$. Sa&n% WahS.�fJsn)I6\i$ m_{n-s}`(�� A�ome.�  %E�$n6�$�. S1�6�1"��s�pow %to�� @aa�a4BU�=eeL!Giw"�U�9�M( wv}  դ U�! �[�+nM�P�rewritwR�6 �e, E;a"^j�dscE��al�n}%[bb]ac%� m. }&=w� ���5 \:8.$pd x}& =a(2D,.&u� Jlt}&=b^iN5�0{p-1}JV ,S3�i�9G�$pE�A�e9A,m�%� And vice ~+ a, il�sqZ �s" �L��i��@�c*� F�M;d'� w^1_0 �@w^n_0,x_0,t_0,u_0�� <>5��0pd u}!Hf;)�T� 9("�s� �)*��a$P�@Yp:�{Aiz���>tem� �l�KragDA�!�*tK?i*s[�d�#����D�tWG$^�$.ol� D=\sum_{i� 0}v�h }/ v_i}$, tN2i� is� n by)$$�� b^1(6�{n-1}e S,D(S)-�D^E�(S)).>�nd9T��h!M8q$total deridqve}�ra�71�e*Gdx� D_x&��� x}+)j) u_{j+1}U[ 'u_,)\"�dt QtBQt>QD_x^j\�0(V )Jqi�̡m.�8 U�"<11��qcscg�  =aV�N�B�Q��r���� oe&��C�"Ka�aB?�[�tari�F7-5�w^i0f> B�*"L[w2'e�L��%�. �� g� #such aN���V" *� . S�1ga�completWr]4�2_1 ( *A1 A�4=1}^n ^:�w^i�  B6B��JP� �� ��c�*�eg}: !9&!=�Qq%� �Ma� H [D_x+A,\,D_t+B]=0 �52P: "� Fa ]zcr} MV uRN �%u���mmva�yV;.�Y�� aJI*r�'} �'N\,A�%R��ifn�1} % M- HN]=D_x N-D_t M+[M,NN2M�� �F� ��ao�of��." >�inyY�?� A,t iuJA�Y;%[$A=�M) ~$B N�S�1���*f��Pzcr'����uc��.� �o�{�c )�t&ez� �?oe�.��*6Qqgk}6�a!�A�a(�e.�%�$k\in�8bb{N}$ Z!T&�Eu^kE�F*k$ �B @ ^0=02�1"� z2ielen6siP0)-M(x',t',u')�gF% x�* ,\,u,\,x' u'$ ru &RM]admis7x(r�O&:) m�� 6�"�o^+ �iS ene[/�A��;m%^a $[ ,�]T� M�7 �Ad�\%�78��1. %=i+>p"&�"�W99T��'g#N(\mg=\cup_{k� w6��6I��0�Imt�7S.ni�E�e2P$a�$���i��wo statM^M�V!� �en�Kate} )�Thn$z=F� A�F!� 6�� ���� ww} f�=)�B ��N� �� uC'F�����p� $W_0i��� }"�髕�zm"2�z&\mg)=n,�9-�a.D�! 6E�k )5\D duthM ?K\M\,"O:ju}(��)(z2}B���� =�2"�RD�%�(a"*z5F�1}R" �un� ���6 !>� (��)R$B-�^�PI�reF �C�-��I�� oM� desin*aZ!&er|-ߕd�OgIfF[lk#ZS.�R�ҵ{k�X�iB^9A86a0=in�2C0^W�$�oby $\pd/1wa0�m .}~%�bvK�4Ł%1a�!� a��Neq<(�' �C�Lse� le�Mz5NJ hold%�a��m�wI ��azat�T6�  n$ V6��� �?((� !� $s=1= "Vb�!In*h0y>n���c�"z<:2�#j 1d >?�� % or�P� �cb�&�kV4R� Jgeˀ ��k$N}�,*IVbB�A}JU #.: JV�.x) *&du!�B�th���m��͟�:�"�6,er {��ws&�-to�9�+riYf)�N$s�JCes �aL m��IAD T|_{I3F���^w�!5�&�B1-�2� m={m:Jm� $ Qkup{(}&H �-� mg^m$))L4en" %(mg$��/t?+�2l1$mX .� �-�By��* �] a�%J�$)�8.�/$n$*6c )^.�7 5�*� .[$<��9�. S8*i�,r�: M%x{ny� ge mM6� no- �K�>5 -:� 1�nongen}%�M�;�.>�T � ��l�E�!`���(nde�)9x��vr+6 N I))�;  .�"k " � (M)}  u}(z#"� �)�( "�-Wj�C�MTDlȊv. B!e�{G� �]'+} �~�B1:"p u�tie} u�>�>U8%o6�!�j��0 Prol��yi2%&hiew&A4:8!��!ph�� QnJ��gA(.�:�S)]B&}��B}��s�<va&N�5hf�3bdv�)Fi�R1J���Yu�.&�$2p�p���$ n $A�$ �B7� imentH$:5�S.���31c� t%_q)1�"� Q�a} 2 4{k_1}f_i(u)F_i+b} 2�{k_2}g+�<!)�G_i s�fV ,g_i)�� �`�!�JsichW9)%�,Zd $�,GP"*�I. *�(*.�Gi%0wea6:B1AVRw0 f �.�r�02� .a�$F"�!F_%c�$GG2%�2mAj�7�fre2d 6/"le�ssw�AG_j$ "�7sU3�8s -al�08je�er�})zi��,d~$\we!iF�/5R, b}< �!g�5� y�E���+A�q ��* �-&P Bd �:��iskn%��!Kp.Q=er�e� �Mpr?!1H�?nuws F�5dodd,�!�3r"`!q rein�5f��K�4,!S�4��,�8"f�� ��1�  � �Gmtswe} �WBWn%"�86o@�|'�ne-to-I &� �!,�K�  we.�� \we �] %� %weR %>; Lo)�i"f& !�i$�! 5� tu2�@� �R"�(a�70sm6d� *J1��e&B3A�tq�?!^c7� kirn){6a6��/v H#>2 t}MH�&B> #x}B=1=0�jRQ#u��#"�#� 2�\VzV�JC:�Fd$!Ek1g6� *�eis-��YA��provi�z����&)֥a���"i<1�%�(2a�)8R7� �:� 6j}��5"��6�MQ1G2$-@�+ >�.�y�1&�_�"tPwЌ"v#1 ���?o*!X��fJ]  2�����=n-�J�4��=n-1._�C.L�g!�C a�(�4�C&R�ub%1#, �g_isl_2,\ � BCo%�]e� �:an�  $g]4��K D$ �.be writ7:sa�y$g @T "\E� im�n m�kdvM} =X_1+�c13uX_2 6u^2X_3�$3(X} X_1=r_1- 22y /2z\la�� X_2=!� 1}+z32ie��� h,\,y,\,z%�aM|�%$E�E"� $[h,y]=294[h,z]=-2z,\,[y h$. Ha AD�O��J iɧw- �H&�N��us*�ro��%6U �xkdvX},?L&W�7 gk},�) &�; �*} ��1=B2!5,\,X_3E2)9%2%!V�5eP�3,�2r_0+h8\53=`k=�xE )S>i, W`ja r_0 [I�u�g3. .�*} >��!i2.!�!�2K�Z�3.�RU ��N�2�CPN�D Let us�*l�FOs>"�F� ngU�:de^e)�2=G.� =)ON�Z�Zq�mbda]���! n�oal�@�0\we\to\�� J@��to;M.*�ity ]ZCR�QI a v"��$�se:D -par DadY�� *d&u)=R��3uz. M8 �m�/ ��eU�zMhI�Y�z,Y��@ 3Q��!mg�nBms,nEC� % � �gP�!6"Y of "�k $n�<3*&s% �3!�.��= caus9 �dmg.d6fen-4ca� BAE;)$o le 3$6s�)�xL� &��C E V1en�Ai2�a���J��/E�.;�A8QBlis�l��)U>5a�a6�J� ��m� H)=0��Unxa� }4 EZfb � VegOſCom� q�*R1rc�g/Fu- r_"(/ 0,\ v s qO r\ M/� *�w}:$*"�w�a*!�� $. %2Iڹk2���: %b� ac� r�8A:� byE��Herc}A�>�)�X5��*} u=3�9�;3v_3�32 v_1^2� 4 Y "z)"D�A.fa�$Q V@a:�] w}�X2dʹh&�O>��Ihd5�u^{5/�O{5:�}���p�?Bb~Z �:ing%�{? !',Sawada-Koter���ex+"bcsl3� \LA�3\! ;@array}{ccc} 0&0&0y la iz )\]AP�� 6�u1\\ k1&�s �q�} �^��!+"b5(�.�reO>((\ad X_1)^2�S/hd$2}$ 2)^5=>�**6�% ��*�C_1u^{� }+X32F�� AC. ,u_3,u_4)q be fH��`e��R$Ipurpose.�*Y0� ^k,tGge �@N�/Q�Q^�e���-n2)^iXa�i!v�K,k�].>6%Ce�1���rel�we/�5C6 JB` &�>�J�$����Nf�5�'L�X�  2H�*�� �F�8�#m�{aps��i '�4)�1 W)la�)W �a l3}.ybicDdRandard�� ��3/�i3"�is2�.�I��eu"� [Qiy.rh�  D��^3/  (C_"D\ a� =w^2>%  FA= &2&3B&2}+w^1B!Ig�.�F��(ge-�&� 6 we ne� �Ha%�a1���.t !e&(0� we^2�.� �&!h�;.'� 2 ne�an>b/2-#1�}[->1!>5dar�^� ���1 [X_2,X_1]75u -:7-=�J!3}�_>�w�Pn�.�F2!By��ul^w�*r $Z/= 1��ct�ABT_2=w^32 3=w^l_Rewri5 %y.A-~h)0*�.j *�6 at�$x��+6,>�iB�.�wxNI�g)Q� 7�"y q $ =�x}�, w^3)�&�:8368��32}\FFM Appl����iW&@� $AC�i�#av��wx�a"MT �u=\�( �v}{v_3�)^6[23}� �"6�qi": b�Xed ei�  . strarJforP�a�pK�[rX�2H�**���g9"$�b6 W�G� � answ�>�.1m} �@-9vD^2-�#� ) � 92v_1D 8�>� 32v_{E�^�:�"��A i v_�J�1v�K� =*Vof�~!*2�HihP*� lXFEAi� K7 +zcr.A MJmt�V&�X aA0��R*�� s]�� alog�A#� Ew� k6HL SvG NRwm&8Rby� !� ��1!),��eY~!9�M���)�o�pto��" " J))sus �?Q��U� syswN,I&�3j�fd��6�"j;#5 n-s*�sys5~.D{n-s+i}JA:�@{n�C2kl�*�F:g?.g��!m>�?Ra*"L�l�!'G�U l�. %N#1Ep�n��ul)�s�8By �U�k%��!2�)A &9"�� �)F� .��F( spli-(\�"3%�j5},�8&t �m�F!  ��t\,�v\|�� �QA+AhCu^j�� #!��  :y:{�&��B�)=s8�nd"D }y*��i�=%^�SuŦ, $s��;��3Od^ts: e*s-�DZG ^,a�!�O��"�+�1,�,$�V j_1<%���J:� #&�J�PVn_1� aH -s+j}=v^{�GVTj.T{j}�*j=2 ��%� MUBwk-q�l{'us�BY$uQ �)"�6�_lw3�iwe go�8mU"`�#IRv@� :kb� > I& I ���1�I(*��I�2tack{Ydk,\\ +I}%rV.I�k�E�W�0I�o D*KI=ru�K-�YQ���� ���1 S��l]%s#<� �)�J�   ��sRVI$��w��"Nքn��R�*Ny*�xYe 9�~�*}Fw�5�����s��"�7ce6�wwF I*Bn]�sys4��3u^"��if��4�EC. Each6�J��aF �v.f ��*Y 4�|i�� I�K!�"h Q��&�5wga� �- f[M)6�I��U�i�aI� VN:V�8 Jnm��2�R�%~�(�y\yE!< by i2X��F��FUa"�F(u^1)'�(2�F\)Fg>Rg8tez}F66F2�8)�e�F��Eѯt~p*�Esys�; S.�6I�ekY��n� :z.FqMA� \$ "D*�R� �"�^i�2�=2 E*e  U��;�:: .�:� E{7�&/c� Es E)��� $s%�"$A��a�"� mtz eft.� �\��,"D;^iF;r\)\,.� \,*�Zk �['et T_zWm���#�%2�a�zN g�n�F�R6|�tEsVtE*�uE>uE6��PI5�g=!} {E2�)j�EbM3=>�E~"� � . ��`��`~�`/ V3gF"d�Qw/2X:2 sysb �� > M����>}6�6�w,��I ��_#?B�D$N�DJ�!�C���_1�d\"k�r�))�s$ hoa�b*�(�  $J4$&j+�5%>�!- � i��>sK� -Kra"���}1�j��-,"4u*� prp�_d� b-$t�|b�kdv�p!( ed�~1�U-�3+6u^1 (1-3u^2u^2_3 �2_2+3(u^2)^2 .'1��0t&L2_3+3 '1: P-C�2/} �a�G E_{it ,i,52,��� $(3\q2( 3)$-matrix� 0$(i,j)$-entry� l!/$1"���!b\� !0AULejG +>�2�(*K��\��)$AW.�e.�Oe=E_{1�.� n_13�f2� 2 h 11}-E_{22� A2,�2dxdFl<�:p��d�-�3aU$��� Q5y�'Q�-�q��e=%M��bx�.{ A�ZCRQx!gF�-=(M"A},)e-f-u^2n_1 2 �_A mult�}*} N= _2+M�2+P�!-2A�)^4 29 e\\ - _1; 1)h-�+%f2_2)2)^3-A�n 6 _1n_Q��L>" � BP� "v.�}2, . �/���gCs���"�.e,\�P�s (&�.�2 ,222K1mgF�.%�� Evt�} $\mh�t\a:o�0& $3.��Q��N�i� \mh=9$) &�<f*Y "�a�(+ $H � G7Vr*�va�H.. 2��.� 0$W=G/H$, $z=H4P . 5�K natu11F:!�%&-!a*�kaK�3�fghjiW�c9Uea� ՘�"!,��2�kIGM,!Y=2zC_, W=�L-��KP��� �k�Qg�T"X�,N� �L�%ie�p�B!F�0�$n�$s=��1�)7ʥ�hU�n�6,f-n_q!Y 6 �!Nl|�%Q�I�*} e\�#to" }�w^.� $&%��n_2%*@!2(\ fn#1}-(w��"�!>2}+�3$rm{e}^{-3w/w^2w^3FD� \ hnF� 1}-2N�2�!""��"*C�HA�isotropy.1% HG;T0,0,0)� Y�\mh1�MT)��>5�u^1_2+(f��v^2_1+ v^2-z)v^1})D!\�=�,�rFW� e��cumbersA��i��hrom5 NN" ��T B "� . .s *"�dg�U�,��;?�0V.~V.~Sokolov�� use:Ϥ�\� >{�{99^-����C} R.~Dod��A.~Fordy�,� ���V!u��4f quasipolynomwf'�] a Proc. Royfc. Londo4!r. A}�=`bf{385} (1983), 389--429.2� �891), 1744--1749I-�@hdbt} C.~HoenselaW�!?@W.~K.~Schief. PrV��#HL� L�e�!2sz dn�.of CC(5so�� A: �Gen� 25} A92), 6N�6m� "��Libr} N.~H.~Ibragimov�D!�FK�B appl)Kto ����$al physics D��,idel Publish� Co., Dord�, 198!��7 S.~IБ�ver��!ffʧal�Er� �' "t]aC�5%[ . To��4�J. Geom.)?};�Hxiv:nlin.SI/0301042=*2�  A%�Kalkanli��$~Yu.~Sakov�J�\'I rdu\c sen�"�il��ofVB\�: �^>�A� y�?oLa�q~JZ�44} (200�' 1703A��� a6206046.@1} P.~K�{J.~.�. �:�b i>��?B��/Uy,Adv. Stud. PB��B8}, Vol. 37, 151�1�S�,Japan, TokyoΜ2F�010041.�|0B"UV9U^{WRB-fD>f-6ZB2��6#S_T�U2S_D2\\1Dim��51r 2 J2JG�!m �EmbeddMX $eZe.�nZ5Zv[56.\}N WR5s5�G:} $Q%= 0.&\neVZ0= 0�2]VNsVC�Eъc>4Y.�6�  �C%*� % '��u? 2��wo-��r�toms  < triply>lliǁ' %NM-Hi� G. Tn�� d N. Choi '014. 12. 04 Fi!D t�1senC PRE ��� % :����};bas؛>Mglobal Y:Axs�Q�% un me�%>` nd}9 \��D{45.50.-j,05.45.-a (Mt,34.10.+x9Fa"ڡ">a2١"%'ec:�! } U��s�=8�gr5����!Q-%Q-IA(u6st%�t�E many .I�&of prim^ij��_9�ޟP�zM���ro��aM�L�rQsu�+s its �2%o�. PP�ar\'e's (#HAiR$J�in 1890�swŪ at c�d\m��~%�>�*0!%excep�� r, rul���Cns�9 st㇍>�Dh?��z�n9%- 5Q�concer��dev��!Xtoo|�o �h%�.1A�%@!�=&-� s. Still,i9t��huϾd y8� pwreg�]�e�� little ab�� T)�re6is.Wq��"�a�the�l�%eI�(�0�\�!��Wlex�M^���&A(v�; see �"Dia97},A a 0�w�T �N|historyycelQ�s{yn�b��af��2�d/�ve7�Omi��;�U�er��\�� tary��)h�����lyS�rg��=cles,��sR sa�} !G$molecules;eQO�t�3$mainly beer ��ontex�q�rme0zics��D��mpJ�~� !�VLyr-�ps� �� �"� have �e �q"� o�Aagenda%Fse effor���o!A cessf2��<��of5�*/ eli* A�~6c�$K @ A%kfull VEa�199�)(Ezr91,RW90a3Uu"0��s��!7��UH�tEp0 u�2w>T �JE� puzz!Aric71O des,�@ld now&�����\�^ anIF�AJ��)�re�h)TRR00qCaZ%$ails. Adv!� �miU�a"�T=sM-��bl��w�.C��Vly�OrJ�-xsU�Eu:� fLfect Smale horseshoeg a^A1e��te bin��� olic�� �l p�Y�con��� L r�,� &N �$on&  m %�!<B ( ��&W)m�M�TW93,%�<,Yu98,Sano04}. S� [�a�rc{�� fe�� �a�Lrelev�͒a&�A�"H�� �ely linke��� � ���q/��/sA�y!<_m7!;�" 1:-$Ze>; -��j�X!����ily^ble��`�= 5.�2�a�,$1 < Z < 10$-��@, )� Duan00�#��P��-ds beyo�[92Hs�3�ar �m��%�i�Gru��YK98}&<��al cal�>��s 40Her83, Bue95}��*R3=Ft �a�{et� apprJB�7=five���#��.��M O �Me�N J��s&Ref��*��in=Wsct ~signalA�z��%�  4 breakup energia� a�Mգ�n-8�mLopp��.���~ 2h����.� p��A�sA5� �3:�sec.\���eq}Ad�H´6 McGehee�N�tRi��in hy�Tphe�y2"<.�:`E=0�k"GaF�Y�U5l�9�� $EA���*ko�<�P�my5�tmg� eY[a)E 4triple collisi�^on for $E<0$ in sec.\ \ref{sec:E<0} and we present scaling laws similar to Wannier's threshold$, \cite{Wa53}c�ome detail. In the Appendix, we give 8equations of mo � combining Kustaanheimo-Stiefel transform;0 with McGehee��discuss i propertiejDa specific surface�sec� used�88main text. \ #{EF�} \label%VHeq} The classical !2�e-body system can be reduced to four degree�Tfreedom after eliminat!�centr� mass-?�incorpor, conserv)2of@�total angular momentum. We will focus heen%G%7al casy zeroBB,Eqwhichh)� v %L particles is confin)(a plane fix)�gu� on space IpPar65}�!problem-Ps!P lFQ4, that is, a fA�4dimensional ph�j� �energy.58as usual work A' he i�(ite nucleus)�approxim%;�(Hamiltonian!�lud!� fi>!�!�termsQ. founE�)4RTW93, Sano04}un followSw-�usy}i)�)*E�Coulomb%%P�two different ways: firstly, byqvE#.>coordA�esi�reABt!�)P%�second L s�|Dout an overall sizE6amea thuE8sider� only%Y0shape dynamiceF!�is(. By choos4a�RS�Bi. �$E$ acc�,g to \begin{��} � xcal_traf} {\bf r}_{i} = |E|\, ', \quad tp}_i = \frac{1}{\sqrt{|E|}} \; $ '}_i \endy we�$ Y}_i dP$ refe���new2��4�ha of electron $i = 1$ or 2,1ive!�4introduc)S time:Pb,) t = �4^3}\, t' \, ,>�one d�5s�1y%�q from!}lb�He_!�} H!�)w%D0p}_1^2}{2} +:2  - $Z}{r_{1}} 62}}<1 $ = \left\{�xarray}{rcl} +1 & : & E > 0 \\ 0= -#< 0)' C \right.!@. 1"$} Here, $ZM�*e charg��E��(in unit%Zele�* ary 2)E��es ar�߁�68!�DE\. �l in ga]al��sa� $Z=2$��8 Helium, if notɍHfied otherwise. Fur mo�ra!�2}$ deno��� �-U�andU� distances6� . FA]eqn.\ (M QA) i�Z cl���hwe�� have����v �Z valu��!�rOur ult�?e goal�4to bet� under�d6 b�!anda�on� sta�in qua�� two�atoms3we!� �^ mosta�erest��&��d` A�=� �y�$E = -1$ͦ$is regime,)a�5� esc��ql�.it� do s3 ��it� ondi� s. It tur�,ut, however,)�of!�$n a lot ab�v�$ � -�by analy�;$5at%�-� breakupshold %�  $ 22B 4&�sf2 �!�2��h&Q s, ) �A3 rela�� simple�� beA�3 )�� E�, =0}. A8 a�Pach has been employedWannier � ;extrapo�ng1E al behavi at $E=0$�Y�5iMi>Ah$he was ableT� %elebraA�!�)|law?P��2ionis�  cross�� QF�0be completely} in nature� ,os98}. HowaX}%�sAa= \pm�Y!� �8connected? When�*ing a�!5 trajector� ��A�q>, say 1,5��2 ���" $r_1�infty$� �{ $E_1e�e�$�pP y, eqs.~���),��� ), Ap��!�5�des o.� !$/ ��!ra��=n (absolute�: of� -Q_1$ sepaA ly.elC A^\toe�Bus? ival� toa�x &� a�A� e� E_1 + E_2!@%�Aachievi1exaA..���_ i-�. (3 samA�y3mayA2> �i�_1$). As��e�se� A�.~y�<0}� e��o $L ��hmm eqna Iv�� &=&&21K p_%H^!�� p_{ �1}� %�} + F>2V>� � 2<-�  1}{R}V()�, |() \nonumber� b�R.� ^2_{ F}}{R^2}c %� \cos^2 - \sin QR;R� -oE! \[ B�= -)VZ}{t r2� ~ .uibA�2 :� .  �\,� ] Note��atE9$L=�weG Y'u�Q'M_ } p_ P =!� _1z-2}B^O$U;}$�A�um��jugaty V�qg$. t:% cordond�����. For.}�5�]u)������ e2��"o�� 2���enc�ֵ?$(t)$. SuchMl�is��c-�� arefU�9w� ��!��-�is,� to�FG�V $E \ne 0$\ � ogy� ����� ���? de� �(-� ent)��6}Y�m?2�R} \barqɡ�� ; \q�&� $I�$ ;&2i.R}��Ra5�� 1;\\�o ~p}_R=i�(p_R; .{p}�l=S1Za � };& �9���>; "6�d�t28R^{3/2r dt;&.�H)!LE R\, E�(&>�\noin!��?, �abo|2:� invariantI:  2�JR A4UR� A�0again sufficih �H� E��$E=H m$0� �?a*�s sE�R}) do, "�destroympauic struc� 7 original&�B*s�'* $%�H}$ i� � uD(no longer a�t!W"�m�q��k� ���e)�a� � ^ar�:y EoM} \dot}v]�mzQ\;  q8E�I�& =��1\,a>_+ _I� ^2\;����� .�{3 e�� } -@%W al}{ 0} V:`6Z� ��Ne�� }"0*=}J �& ="�F  $r� #J�" �a�H}� p_R �H}9�5�1�-� R &=� �1�Z -X )9 . �1%1 {�>qA��6�H_� ���R b)� � ��]� ����  +B� = R E \Z�we ski� e bar sig�!��e�conveni excep��-$��-u�}��a�)a� ��f�c- $R$;fexplicitJ� $v�Hcovered� h9y) �u�VIbe ob'�� gs ng $EQRQ� R$ a�� a��uy%� �{Q�sSco��c sval � ial "��U�.�$4 0$ \�line{or}& =� F��u�du�in *�ity� "�ass�com��:�� A���n�!�� ent *� . S"�%�M(�P )m� \g� ,oE��ed "t $p_R�! creah mono? call� ��is�U  a"ly)�e"� "�� 6�sub� �HbKudiE��>next 3MB� itself&/lifX"� J:s� i;b���A�*�I�!:. Twopoints �!Auinstead���dVi �s� Re��e�ach)�(�ed) �)H(is a manife�io! non-re�!isabiE��BJ'sity. Oc�st�!p�#in-!%K_ e binarYl�s |r{avor!�t &�� r $\pi/2$Axey%be lj`aS,dard techniq�s4 sV�#(KS) 6� �$KS65,AZ74,� �e�=9y-9# NN�.�� ���a KS -:\ � parabolic.�a�� ���'se�S��  ta��& �24D4%�8� deri�#�bB�! O%�%a�KS}� res/]�!�u5mRa�% :EoPBi> scaledEoQ�V }) ���:%throughrh�!per� numal1 A�g descripA��"ofZtW "� less)�pa�" than%@�R���lTe.�� �@&}��2. At aF?Ja�pi / ��f!$p_ #$ mak��!a2taneou �9�* $\mp.�3 >�x�" 4# � bMb$e smoothlya�����$% i��ify�z�before%=�&th[&�=��lA~!`. �B/ �reg_pa- *� � �� � .� w gY�mb �n in�%�.��� l�E*A��.��� .�"xs. �U�& ntrast�!8 !al$eZe$����,Yu98,&�-P)�>ͦA�eremJ�Jiesq�?��b�FA�to go�.. �0��fu�.vODE's� ͻ�U�����.*�)D�%r : U]�#� \��){Fif(pE�&&As2BI.} In ordO%un.�!�(f"�h<�G"dvantagi�W)m �hpo�I^ flow0#ted by����\9 starta�briefly���&x>5 5 ~�A�+"�2��% ,� 5t��plaUA4.�  Y,i5 *� k��re�2� �! ��)\[�>si/4j'� ,�j��}=0(�= 0*s�}C $2}(4 Z -1)��P_0 .\]��B? "a2�Ʌ a2""� both"�s f��in� � symmet�� � !��Qax�K��s!1e {\emFp e#} (TCP) � �r $&� rg#sed�tnr#� @of � double ~p� � � !$�DE � � P_0$�;�Q)hrń�.� s:E�9i� $2$,�*V 0$ (!J��2�,)�H�A0f> Zee$N>[so-� ed I#( ridge (WR)6A�!yc�&� � 4�I��. ��m ��=.�b� eZe-2���H^.�(p_�  ^2 )"QO"�*;)(2Qco0X)si&��(B�a typ.yf y re�b��r,f/�( com�!s �-iMq-t ,=k2 E �#��G-1��vrtoward�M7.d e"[ 2g. I� �!�e�s���mM� v� ,E82$�9 J as ' �.^2eq}e� t:�Iq-.� ��#�of'pI�fn �/n�71�,�" Fig�" fig:fig1}d�2$ % ,� 73/�!�6re loc�_�&!V saddG tw�&a�/stretch!~i��!�%� back dirtP=AHc(����)-i��<0$ fill�� rior I�-N��#6A ^� b�b�WR��q�2 pw ^2 -�� 2} Z2�i��[A�V��M� hand,dmpf Ӂ�%X.ma I@�!w2�Ihp�#�]l�+seeNOb. �Źh)��!I&rivha)�� �ac�a u� �( 5��TCP< well�st+>* DEP.�QC �>YJ.� p WR �� I�"� iN m typWn4A� �island*$ d ergodic� i�5%Z > 1/4�w� �2&�&not� � feD)}�WR-�n m�>+e� ,RW90, TRR00}{�6G 1S%&Dia04 %a Origork appr�*.>��a?��2�e�� !H�0"�)�1 2iH/� #&� k'al�q�0orbit (WO) or*, �j E���=��iO��� �� �{2� LM �7XX 9��B � = :� $p_jť -p_j�$dt dtjj = R,f $� ��0�Ah!`S -S al1 �'&��iB0�4%�JN %��eq�,"�(wyB� . %���f�65�$egraphics[�=0.50]%$1.eps} \ca9[]{\sm!���I��;(aIv!RQfQ #b.=J E`'� _0� (b)NbmaximKevi� : p&^ 6B6� )si�� aX�E� a?f��q$ �5_0A�arccos(�Q(1/8 Z^2)$.)�2-dim.\R�a�embedd����.- $E\l��6"� 5�"F L> ��nd�� (�)�u� 1�y� �<0$. "W:"��Q$�~Y~%i�dari� u�}%�eM�*J�ly3 /&4=�;�-.�,� oe%� eigenv�.�xL li=^I��c��e � .1[E� . On�Qb ���t�3$ !��9�0q�"�)��X_eZe} &\lambda_{S_{T}}^* D  P_0}{4!�+A� 3 00?9}{G N6\�5)� \;\mboxV: wle}2�$�U��+��~�WRj'.�169&52�:�"� #T,a�!�DEPv�DEP.� U_{D.�*�� V� uad =�~DS��R���vG�)� 6 \M�R�.Y�=:� �+�:1���e�"J C7=l� $2i��� 9ed�|�� xi�%&�~ � 1��.s $e�^#b!}fE0>��n�����(������i�cal*14�3 . T� & A�WOA��7 h,=oclini�n\4�le)8��DEPJ?TCPR��O=� >�2�&�2H��:-�)4 = -P_0�$HA�?%I>J =���`i�$i=�Hs0=*��0�*d)� ab-j :1} ,verview ��, �>� %Y*u�U*Q�f.<!�QD%M "vU��� has,A6{ɹ��reeY�I�i� AR� �of� �N8o�� out�)E z �o 4Jk.o �#ver 1 oldsA�IA_� #�J�� in v�uy�!�h^ �#*�!� . 7  )R~ �is y5�!sai�pseVk. T.}i� M!]�ZO TCP -�Z�-q��dX: lla��+8he neighbourhooUfA(e�d5>"� ��T�$�#��C!le * 9ofE%�]&�eventu|$.��F+ �_7�z�� +/�&!A$%�+w:�a/ ct6Al��ed. (S�{ speakinga�?u=Lfor $Z>0.287742...$;� crit�b � ��5�deg-ateWT2I coincid�&�F!�D1f? ~�!isa�H5=�"phy4Fl� rele.)� sit�h  6m'leP�.Q"� 6mE�i�e��Z2 �% prov� n�:� �Ib* !�!�5�.]��1-a��e]��� �OEA�'6"3&� ��]��� AY�i�c�HNve:����� >nm'6Oi�&�>re�ciW9�Wj)� \cup u�%&D�3�?&fto/.�.eA�Ǎ>� fa&c�import#@a�{"�ome� striaW "���"�?"=A -W!%sc]#��N+aQH�$��4�F>�J=0 .},!g� p�Ji58e�#(>Q<0& A summa&:sub���E -�AxB;�/AE6�n�%iJ)ry���� in,E��%����; y. "���� $U_TMU_DO *�( $S_D S)� ime B�#&us,��T>$ge=(��q �$!�?EB  N�,�A�$����V%2 } \input{.tex}. D�I� d-�E��!A�Jk �ZI/B�!6��A�]*��1�� }��6�\� [{ ��-�� h% #S~E-6y� rs�t:�4DeK57"" t  �^i�Lst��6/�;,by�f �aS32cP�Mar\'eN�M(PSOS) 6= 1}O-aI"W- �2�%-.�"�N6g��-C  gw �g� sens=E5�"1�tangen�)�!aM0�/22���%A�9\$(�A+"F� �a�]e�����2F2BOa"�s�8�A\ �*q0e eZ>! )6�! alfF� 2��C%T �at,st onc� >&�*A����4 � � � �f6�&,%ormqT.�in ZQ"�aINi�>io"�� Bч.� �&�6%�dom�?m�}%map>��d*�$_0� � � �sdep}�2�.��U Q;�!`,�$# �=6 I�M�;����=� ��!z� &� .DA%-�q+Z�"Dud B�1!�I���#.x1 Zx1A��`�'�"Mjt1��H�7�Hs � t&g $ pFharacte����)eh1G1~����. E�3ly)  co��� U�^D��candid>Ahsuppl|"a divi%q�-�| .^�A��)a6E�I�>� ��E/is& !sh�P cud=�.E<.I?i�)I4v��m7<B&����48�2^�^ �>�%5� !vm $-F�-�2�� ��e�!�ms%FN(� ��DC} -- E}N$drawn sche�7I]�6d�our choi~/f .w1mZN IApro�-�e2a-O �o8� oe2E�B�3. �La$ �2�:)I�q��[<6Tdevelops a bottle neck2� Q�MA`&v�1GPhol6P5 A�sACn�8 at m�K* at�� �ms�Kurther p�[n�$�?k�u�Xq��oT�4, AE DX]J* �5end up�5 piec����in q!arm�5way� leR�(>�)�B&q e 2 &�i襫��pis B�O����&�)�b�3!| <6��^�uloEnd� J���he ��Z�A�S_D�h& :o bLE�� :���`us8�U`)�5�e�tLa�M$in&' �I�:o&w� ? �B .1wo E routed"�%�ŕ�;l/s/in %z="�.6�)^-5`: fUly�+6�anFy'�ly'aymovaG�t09ic5@"�'2���heI�path op�M� eZ��t (*� E���\)?s up;�<��pSQMQ�"��E�� �sta)Tos8vM5i}"X ��S�.�Sy ��A��PA��d� .�T@�%�z<e�Y�P+%ga� "� &�'%srQr,;e H^��W�`d�K") �a*(] $RRT$R_ ;$C�L_2 �$L_1$ a�di{/BINing,�4�aa! f (C��!omSN�/,^�?WRy2> �`d5� �1��%,� {1,2��m L#,�do�9�k �WRdn%0]-�}�}5}3^}� ��M�U�����$ͫ$a�J���I,�!7� *d2Y�� j� N�is base�lZ�>��\;J� g�S��� ��JAP�� ��M�>|re re�`Iob?v\/i$Z%�m�S e $1� Z1m�bov �$be helpful��¥oEem/Dm@c{[xB�J=� Qinvesti�Rv*��cP[<0�K*�\?�g-.g-,d���@F�/4^�ParE"r�\�rehCo�e U�-].� �:N��InI��? suit�p �er5yAkermj!�� � "/J0 2��]y� �#g�\�a>$L rein��.�cat�#�=)in�y��)g&X_{�9}$su��31.#majorP)�e Keple�XlipIi �n*�:� �' �� '/� r� Lc� e ec =L y $e"�"e l!= �Ds1$\varphi0aFK-:' pair�i:��L$t�4Y{s]!�� "�p"��nge�@i�a5��]of� 1�e 37� . J�K E / X]���KK$T;� �3fix! �f� $e=1$ (&�%1Cg_IB�%!`�$B�Z�$�C�$f�F.Şa:�k�)-M� !`d�+mOkB'BAc�n�I"C �\ o &a>. �A&�Gpurpos�"\&�\ ɹ ��� ��E0eZe"d%wD _2eb@$76m��ceF�6�afun�:� � �G�e�J�3Uc"id�= a` YJW)@"��a�=!�st \ll� . � als� ���c5���)lot�y in re�o�f�!-u#N!KG �K����B|�!gn�/s�d��cF�8��r�Yo�^6cA�)�J�;#A �Uj'-�!�%2n��u&�4to�z!� 2z"J/V oE� mez�vanisyB�ah*U� � ��~��ZA=�ayw!C���*.��+�.�(a�� �U��> ribu��.] ��p"L �52�DEP�"a�A�T%�,M�TojC�(unp5l ��1�2�%�}� ly f�'>� ��)n*� ��E�V deep!�V C�u��W���J�C�C�5^�n >R(Q�)g EE!�-�M�B7,� {out}�?2w 7Rw -F>� �t�!($E8 �i" ).H Ŏ��L ?p#,on logarithmeyLTs:j.��j� -&� Off-��E�2� 6�O906� � J�Z o2KJ�e ,0<\pi$ .Y. T�JZLverli\`dw&�Ginpre:os"� !�' 2���!�l &��Sc��} �eA&w {A��%�. a?fi� a prin1�T$P$a�JA5� �>p Nd-0.4$�y�3&+�O5js� . To�"�2I�,�/"m�R� !4R 1� ��x> ^ ���;f�$��EGk��"5&�Eoa� �\�Q�s*&�} �3A )o��J���6�~�&.� U��/Z�)&��-�o1$; f�m�Wr!eap pp�n-O,'dip' associS$%��Senc[ ers�;%�BZ � :�._��j�New&Us eme�w ��� �; /�!�Y� �^� ��P "$g C".� is*yun& ecce�E� ~Jas$> �$p,�T�4M*�5�, �z� Tab� | �3. W a�U �5 Za�R L� "AeO "P� Z6� 59A��4�t&x E�6 {:eO�E6p6)%��#S61369.\V�T-�&.2 a .R@���/oa+&O��F"#lso.�g59-�DEP%�D�v.� e1""��� AL!�%<! Fcut�)"�(t��$ -Hs6)�S15.:�� ��� W����Y 5 shee:@6�4B(�#$ giv��/n��m�BC,>�.y.�N�4s L1, L2, C, R-v$nd R2 depi�vbinset�: .X%p�+e�0b�;!�� e)%x��8 Fl �!E �� eak,A"A�6���w.�1VQoE��6B4 mw91R2,� R1 3*�9�AzW� {I��!te2� �% �!zI>��;&�*�� �� $"�.ZENe-!� O,: � (a),%�!dA�U;�b!�M>u�E�W�# ���5"�].� D% � ��>r��2v�2bЂ� page}{7cmj�3B$7a� end< \h�T��TbVTc:�N *�!Mc"�A -�Ce�2rL1 b),Q=�# 3".-�k*A:2�. *�is<!�JV ��Y�aX "Q�&�R� � M� ed out.) �J��Q%a( z1 /2$,&j�z-1>@th�q�s&� =� 256a(a�"�  6612 b)0^�nL# . PrU.i�F2�"8.fG+�g�S@��r�� cirt�"�Y%~�U.e�nde�th��-u):� �%�� n� o(�����x��E�s,dJ�bt./eaks ,� a�UljV$*�-02AEGEi:ND��mpl*{ � �/\0$ ��<"T &DV"�1�� �R�i �ck��@} �p4ro'�v2�u1t"i "0D1!R" : inw3-C`�+37!g��ar�&g Im�"!�3n�1%<�.x�N� 24exaY&�) T"%7A��nrg�&e1_� Xa�� "}>� \to#3�4e �)}A "�ob��9 Sme�q�::� �m����Hlaw�> }.��W "�%tFz_)�>�],�: ��sh ;%/�){)wdis"P :#nsistuI$~oop -!�*�� 6 a�:} �*4!��"� fl;or #V>� $. A<"ai�B�'how%4�)9-u} &]-�0��"ip*M�%�bG}6g \SCLT05�E*�! "o�>�e�'VNp��'aj �H read�2�Jr� ��k52}8� `F%��"($�q% <'m -+ng"�.E!)�E�a"�l/�. LJ���āl�ion)-:�__a�h�Y�� �YQ��0E�i��t6K�i."C%A�0 �e &, w&a� �!�{d�K6�(7�\to - �7a2R�2;��|!�n*AA���ZD)ZH� �Aa�"2[�$� Sj!0ejce�R��r� �/Z� �� n-D�"y��h��VSs�-sm�k.�6l5[%2�0� ll2�!~ �-�%~02�?�"�!�*��Lrm! E2&&�!�AZs�,�'-�&)(*U��&S� ��~�*�A�� `_H@9�h�� ����+8� >� E=7-dela�g�aH��2��-1(�_p'0.Z3!l -1$)�ZE� vals��by<:�Kng��,�m�a���!�ich�o!� same�]bo&de�eaYq� chao�"���F���syKP�:m �=pi�p np 4 .�((�W�Rrt�|�I�%�!BE$i�&� I extens q�pA�)Ezr91�r,Ros982�mE�is 6M�=st�HbJPw�)2e�% �2(ɽE�$E=�/��=E\;�/a~xto�&�(2�A�E��;a �"O3 :A�{1/l�C a�df\l� � �.W>Fp )BGa��jM� J�T���2Ru�'�� ��� �)�F6�.uof-<""�f�6E@�S:im!�EY.` Ʌ6A��*&'ae>TCk{TN is :� :�I�� n�b�6�A����&�:��W�S��)��<�lR#�-O��A����0t�.&��-� ��a�I��.\ OJ�!��YM�m�A'� %a&$"�2 �&�%6[ >�.Fd'�}Me% �*2:ҁK֘uyf1��O&�f�:ZIM^c�&��e�o�px/as cuss&� )��K\-;$A&^ZV)&o&�&A�c "pR��n -�q"� +)eF)&�& k6)EJp�!Q{6>,�BP55: A��is Fk&lTCP"� via B�Q)� B*?e"7��E�5�Ek">'�q��:�b��eR!g��*`Ya' �2�3�U a#r��2�W�-I� aO/�1 0y5!7Ba1�ill."�5a�5 y ei77*� �O&; u*D 2SoAQto .�2ba�,��Յ }$ (D?qLfn<he �H�g)��i=� *"N�kR�+�". `�� cas�S Qp}_�Ih{Ps �#%�u2�f�O#&"U'�<�i@!�gm�NГp�:,8� !�a�q�.� } lo�=.�(KA\A/i)R%�2�&@k�-e�ac99� r)I8!c!l�� F�if }�%�val (CSI!�>7%&L r��WA�D$�M�mm�DmD%� Ihow�/>.M ; 2vI�ly:Qexc<f~$'�9��je\!7fiMs . By%�-B�m%�-bA� exit)_��}l*5�6��� �E� r3"��ngV� -5 CSI �� �J� kn!,�F4 ic�wn: C�C2 'T �[, pY~ Indeed1&A�wid�*bel9, (�. %2Illy"ved),31�i�6��5es likY20al Smale-hors��eRQ�e����sD� Fib2�[> C�%ab�[8>�!��C >$U�!<�� �)� CSI��%� a se�of�Ps�� b��6ipb A �Oon �� :V�A magns�>Szn;Z� .��c3&�� ��I�2QE�2 �( hn]���.y܉���7>. Each!�}>y�:�8-tңl 9+�Ũ*�!�e: �: s� ;&�� -Masympt!�u_z�:3 Xl�7"� .!q m��A�6M�]�! |i�> ��� �� stay-5�yb���� A�"�%�V�� G �5! Nzn��� a��$ �n*\asv��8. ��v�b��9��J�9V�%\��AZ.�[oAv�rte�Z��}�%ց)%�ol�Qar�� F8�~�"*AZ� �\JD$E/�-0.001$/`$ ��a� ��S/:.F"0&�9�1�Gc+u riso�!@""B�2eZetE= ��_n_M shz�-Y5��!��s0tp �!�bFO�m��*�3&� �<�5= 1.075$(���m61��1"!00��6:�&�RP a !�� -1 *J"� .nZ�n&B"�%�թj � rst  &*CC&� J ɣ)<{a�@ ��F r�h2�WO �!�u�Xmed2-ly�e &(  :An Z2T�!�I�isA/w"nfb8Y�a]is f � � � �^PM�J$�#po�,s�K]��B}(��%AA`� %Jn)��{�Pim�KA�� s"3 ��be"� unh�ly{�W�&  c�� �a[˂i� *&�,s .8�>� Ms%XS �Ne ��5 elab���M �F� �'-� ��"���!&ov� G#A�M�ewid+Nv �.,1p r[�A�o -�����df5���N� ���8��N *� ��v�^av�610n��QA���J�1 /2, 6I4� �:� 90E<�4�W%fW%.�O2�02� B6<0}�#A��� "�M��*�a/e�N�k�k���ahc9x o r�;����.}i �Ca�% ��I�I�.�nw&�Q�{� �B=x� �>.bg %�(so &�Z'%�J noBdta�D1Q61��;�-�EN2-��$ .ga�ar� =�=7nYWg6Z�|i�#�I-?:^?s occurɒQ/�32�.0 �V�Y`.7�Ml0fluenc&�"�"�n5�*�s�#>]`}�!%^�.�,$�:�*�Iz�*O8*���� " It�nU�(��Y"� 4C -2.3ALA�>1=;-z6X9 data�e�I 2F9*:19,R��nP! {-���W^� ���s"ߝ!d @��s(�*�8A��)1 )& $-1.1 <  < 0.7"tMz8' -V��mg 2� aj@ ?#a^=Ś K�a"�'" s, KAzhO, jCr[0RQ. � !8& �0|},��A��qe"PJ�� *�A�Wt�6B�� AUto"/ & %1�*A��K!�(�!Y �-�J�0.495N�:.~� 2u �b5vxyp5��31 �i*� )�bF m�2 � ��e( �7nteNc%two"-c S aV% Dr^BE@A_�a $R=mL-�-;�%��G$$R$�meа�.�-aBv3A��^aR*� a ��&=:�>" ) � HOB��l*�^�d. AsU�in�,sC3�H&�Xm�"�8%�WO�0r��"� met"=o"��qѕa��at"�B)`�_�'� * eZ2K!`�EWso-!�1H {�^��&�4�B�Ta�� a�( $.�}"�{�HBWR}�(�!f_8)��3z�3~� 1Z�  Smu��ܙ�!Z$x-y$� nyK62����l5F���.bi�� A5 $10$z,  c)��O(d)s<f�� x���+��&K � PY�� � or"6(�&�)i*�e:&!#M*P PR� gQ�:ah����| ��( �semi-BCR�6�� alig�#I�ex-�g. 6����!�e be %c��8.ޔ]�.� ��2 .A>6�>_/-Jr��IQ� CSI,&Z &".:Ad��8enA��3��1)�,E g,��5&���s6%#Y%�q0f@t $-2.62� -2.!IF�� �QM.s�3A`in�`a!_3�b4c%�.`  � G Gal���)-�k&A!� ��"�C��A ���1B1 G�1 dip) or)��1��FYI�2@��"� �3:?�;[mc� $o"�� .fEy/e���ec>� ?��*y a bɠ^� � .� reO�j��isG0�Q$eaO9�`|# CSI'e]"1� 6?2.�5 ϠV T sM5s J�F 1�� �Kb :>&��r .�ziJ e� sugg��6"s to �te�5i] ��er cy�"ofQU.�}&9U repe�Cly" A-/��� b#nelNC,10tT����Mk5 branc� >.�))&� aU�#U����yf2� ^6�.�)�%N�,���#q< ^b_� tcbImwirdP% s�M`whgs*� �-Q]Ge�DE�� 23��� bir��\ߩ&wp�'�A9urnsA �!� � etc.� G��e����tcopic�*ġ���) *,ͤ>v#y��f9# a �cu o` B{�, nam�aB," w�f"� asE��#�}-;ui�Qr�l$@t^�C&t�3� [:2� .����!ruIA�mI� �XB� !�eDng%b).rj8As"#C{&G:yor�# t} -J��7s2]oskp&\ \ ����)� . >Cap�.M�i�K2�"��-2�;,�c"q�6x2�s ���MA�J$r�'�1rgAint�f� 3/de b#�2� $cq�(S a*4"Ww$�f �n&h��$qaq2�,Jmod�#,�;A ���?�_-�.� re-eE)BF�. E F7e s'�� !�E3a6_)"�M�|UJ ��? �; E��2�l�/ e�#�BN($+�@�a�$��x5�-�Jathb��>(<�-�2 �_:$_�5 = 7$ � s.\\��֧52]a�1b7u� 2&�G�����x�W.�ź�?Z�H_%��� ��as� Z�%��ד:��[�� b� H :y�;fc es��y ��� s�j�xa�:YG big�wp�H��M?٠�lin"q(w �c�-�6_'DI1->s �L6�*6�*�)"NGE� surv�M�h�% fi�I�rՠsA $��1� . Oujg̦sJkZp:�v an (j(6�te)J�Y� �}ole�g �><�"8@c"��E�$1 > e �Q�g�6���' $|�|p_$. Ho"E�v1 mustx �n��A�f c :� R��s��v!�E,�! �<�#�_2-+�>(� RW90H�A9g��Gu93} !�� ak� aL0ressN�*{aB.2V=�|�D@� of �{rg��=� q{��8%�( )��"-b���6TӘ�Epoo��7�aa*���Lcs� �ƌ/�9 !l6�k#o rob!�i�m}O�hE-� �8r�7�h.5� A����no�$-�nc�ed��. 2�Sc��!��?t� awsZ�a���;5�rb,m"�@�2%a3 Ԏ�G endu0<ҳV Ev� houg�� �{���;rmv9,]mx>� �@s�� ,�!�%��Q6�#��AT�m(po�>&�.g. Iy#��+�Ds��"� �/  a 2 � �:j woul�S>�uni��a[��  b"M for d�d�>]Ws� "�I argu�-a"a.�2� n:L��D!1�C% they�;?�L& fc *�7B�!�&.�4x9�E �"��r*��)ET�`��"�-� 25� ��� �5�J@A�d)K"���N2���� �ك ���!�FV i�1m$e\��!aFFu�[��u�#2#��1�bLl�qy �2'*�6r�6�HHF a � k(;an�[pY/"/)_*9"��i"= " >]��all�M jM e�#a����E)8,$\Delta_{CSI&��Mi.(&a> *Q (iEsh��WS&k<-�$ pre-histo"�.�y �] X A��t2`). Let *Y�(2~a�c2>G^0= ($-5}&`"I��\����� ��l� QF.#A / �4�egG�s�I��Be0wN�� . De�&!Za� W 4.�l�.�U/ }�l\d!��Leki q�Na�O"�1��9 \propto � \�89 C���f����P&f6�Gk�9 �$D"5 ����A'��Z�)�*&$T� A�:1�c]et R1$D? in0*. �e(validNI&͝��`�,bMT_D} T_�_�}{"��;&`��h6�� \log ?D}{)�}R�Dp/ "�G���� � ���6s� RW96}&8 t�s��=F_��Y��e@Ap.� � ��̓��:C %u"I 6� j ��E\�ߕ� 0 / E|$�� bwan3�law} F�:[(Iv/D)^{\mu%�|)�E}{E_P�|M�>�Naz��Cc. �?��#��}�%&G��/�r & q.�%�"� �1� i )U ! KW*� x$:�XDE&� a, (*�SCe=+Adult�Iwn�)�%�e ���*� �!* "mQGfK�&�@&_!.�b|&lea�demonstrE�"H�lineb� �b� . �N*NQ�*ej�Xb�gFTCP2� ��nV����FidW"� �,8T��!b� $Q d�e:c'X_'=^!e|DD$ RTCP~ �:>�"-o�j��&h#�#A| $C�I>�pa"- \-&� i%:�]c���"2 s�/�wS� %N��^ T.x-D$C$-peak, v)� �6s¼~,&} �G}(aK6��Ԋ-��>��nsferf� �!�9[a2����&��*h� b�YJ.6q�*�����B&��`%� ��B��&��"4 �/2 s ����#2M , >:#�1!�a�)�"! LC"� >\!_�TAn5}-�me5z{eec������piv\\ )$�����as$ced�T�1�*>�of���a),I��&��2uaXE�� /liZs�"� C �t�:���(N� ^\nu��� �F�itFo�|nU nuRU T� U {\rm Re}6� !��]} = 1zM���N��!� $\mu% �AAmu>:�8�#��9� nu})a�� N.+1/4 <��9/4��e��$/&�,ey}^��0 rea�7��B, "�9Aaiuҩ � !t�r �s�"k�[min��e*K��R@(o8���. NIal��I�2�avY9�eE� �]ݡ#���>a�&�TC* }Qha"�xYT-TikM��E� =�?�^1a���5/ predBe.�*��!��!U>����K:���6�a��scr��ly.�_*_� �b�.6=blb�-?3Pudz!�"C-�*6-���5�0.1$.>z 3�0j0 ��4on{Co�Ijs}��u�6usJ9�&�]EXM6��7 �`<�to \E'f�"�B�&aU�.�=:; 0*�&e�F�E .�E�#�,G"B�A�r?by](c�o���+6��p�xm�%"B :��&2&�_�/�e�aRm"�9b%a�6!H#a�b�_N"� ��a�6�Qr2�haa�7�@�4�� xit *�nd�Zb� ��� �^,2*7 �>�'� &�]��.�'2�"�.k'ons"a(!�f%�%� (�G�! &S )%�WO�B �( ��V!J:�'�-�U"��effect�(�Iwg��.-� ex�+g�X�4,:?xt&ߠE�."� )�*!�%�"��BTstiT"[ ͨ� �AC U:,[�!DaNA�ڐ�.ibeauti�) C .6*v&�*Lq()��%�&��e.B~2��,VmQ�V�Oz�:0A�.�&�5a-@ v�Ce_=�2�!:�.� fQ��*�tS ��.B��&Kt =?��F� � � :� \J7��pC�r1��+�Xas �#ofEp7&ܴW/ �' z\�j��)a�0tery"�ngQ�.F"�%�r"ull 5�9���m*%M� ɰ�S[ a vw�"yw�la�+�3�Eng� �&�Z@ =piw"�2�0���" �4 (negl�ng���h�#s cn+�F*cg�& h�O��HY�A�T^{H\neHTAO!A: ��m�@�)�.in� "3 %z=j. Uz#�t�l 5%� ��b��keY@6��J7&c�D'� on ��E�n3(o�IL`.�R�U' ! ]���traA�B�"�*\"���Ac� ledg� s:}\\�B("yQ��an�He Royal Society (GT%�NNC4�@Hewlett-Packard L�F�in Br�l:�  Korea�&earch F)%s\ (KRF-2003-015-C00119) (pe@finan��h�ort. &4 ; A' KISTIerAsu�m= ���ankAy a9d. � Q7ndi6� Non-� (�N� "L ��!\"�� rWised2H  !;-a�a"� .97A]�# 3-bQ��$+ R4�R�2IH/&�Ds��R[�treat� �f.�'$T�SF�%� �"�9-u,�/��Eper�mu!n�aBm�u!eac&�ɍr} d��"�Sx sV�*�naX�51� :para} x_�Q�- Q��,x� y2�rR2=^".: 2��xMn Q_3^� Q_4^[hn[3[R�[:+!^:[ p_{x��Q_1 P_[�Q_2 P_���d�1y61'� ;.1\ &��i2�"i{Q_3 P_3%+4 P_4}{i26i21'3�;1�-�:0,aR�� :�@",�}q�� F�KS-I} d��!�r_2 d\taj�, $(x_i, y_i)g(%!i})�{y_i}ri#poH+��"| in Ca�Q �* o*���, 2�in"d��o."n��p bf{Q�$ nd $ PzSi&��eI$(Q_1,A"34�5(P P_2,!�r��i�D uu�ed 2%�G���Ibe *�.9-�B�G� G &=& 5�( H�| ) 6^� * I�1}{8}%��e�PeQ) * �6-1-inPa�- - ZH 1>Q-� ( -E;e 1}{ }� }&ľ*��-.�o ro*S"�$ K�F�BGr12%?�=%�[ A%��) (���j- 22��i���4 +�;Q_4�  3)^2 9\o ]^{1/2X!.q�y ��1�'��J�!F7 )gd A�Q}} tau��\al G} -P}��.DP2D��bFQ��=� �}�A�n2� "B�EoQ!� ���F�1�!�� P_1 ͕ 52z52N53j5�D3N54z54#�� �Y�M�J P= �9 ;�a�E�\{I[1)!;4( P_3^2 + P_4^<2) - 2 Z Q_1 + 2�r_2 \left( -E + \frac{1}{ r_{12} }\right) \4. \\ \nonumber L& & G.k Fr_1`}{ L ^3 } 2 -[ #�D ( Q_4^2 - Q_3^2 )�Q_�3 �]F\�\} \, ,>� �TdP_2 }{d \tau} &=& - }\{F ,1}{4}m( P�+ P�9>26>2��>%>z?�>!4N>!:1!R�>3�>3%>1^2%>2^=>36>3%��>�>!3 I|2M|�A|3M|!>(�|4�>4f>46>4�>}i )m(R��{)-E{>=4:=3 �F���. \end{eqnarray} Singular behaviour may occur at the triple collision and thus in terms containing $1/r_{12}$ in (\ref{appendix:EoP}); it turns out, however, that the KS - time transformation (\ref{appendix:KS-time}) also lifts the triple collis9s � ity from �8equations of mo : $�?P = 0$ can indeed only-if&1 =��) due toV0$e - e$ repul!1. T%&�% w0vanish propor�ali8$\sqrt{R}$ when��A\to 0re�< hyperradius $R$!��\new coordinates takes on!p \begin{1$} R = v(Qe�+��^2)�(�I4}Um)e$} It is, 5�Dstill advantageous�0employ McGehe!L scaling aArtroduced� sec.~\Asec:eq} addi!)La KS -:F . By defiA�B�$ \label{apM�LscaledQ} \bar{\bf{Q}A�� {)R}�!qh�(one arrivesaWa setAu.�wh-� $.j$ and r}%�$ A�!�!�0non-zero valu `!�>�. (One:Dactually show that s ` >ADevery �for $E�? 0$, exampl�9(.156\ldots$ 8hZ=2$.) This means in partic�{�expresa.s2(i�A� NK remaia� general !�teA the 6Fed2r even!�V/@For numerical cal�AYs,��is �mor�invenientAv use TI:2sXwhich are less sensitiv�=m errors�U(small denoma�0ors. After imarQ��%im��ansa��b�tilde�  d I| u�RE��  >�( � leade�8a speed-up near�>�4 compared to u��m�F��|),eFob�i!|eN�Es! F|mDm� $ as9�* N�EoQL i�d%" Q}_1q�!0� :� !r}� + P}_1 - O1}{2} %T%r^ 2 p}_R \,.�gy $E kreplaH by)�T;.�<%E�s2�=A given by�� E} \�}{E�oHR E \,\quad \mbox{a}  )�ͣE}>�=)�6 �E< EeR� full� � * m" E� ,>�! ed�1),%|:� })%� freea,�� iti� nd#"� t!� both� vicin� of binaryq>i. \sec�{PoincAksurfac } } B� `ec:PSOS} A 'good' global jG (3)\ uld!ULfil two basic ingred+ s, namelU.$itemize} \ ,[i)] almost  trajector!#crossE�n;23e)-field�� vers � 8P (except on lower dim� oB ineb0nt manifolds)M9��a�lat� cony $is readily �y 5 �x$\thetaA� pi$ � [ \dot{ a I�p_d 8in^2\alpha \cos $} \ne 0 \]� !.point"� u � thos �($eZe$ spaceń6� , p_ ��,. Next, we!�F a� ic orbit a� total ai�h$LJ interA�)��x-Q�6(A��tha7��Pregimes $E =0, \pm 1$� leas!� ce. Let u��su � to a .Y � n� �>�!��z<. A possible way%�thi h�/� vr]�oscilla"�  range �8\in [-\pi,\pi]$%NoutI�� !�.*] , � must�tur�U� �,A nd B��n FigW$app:fig1},�x$Q�%�$� < M \S 2>BH02D \pi HA}):C� �6�.�B3 las!�w��n $��9{<.(in scenarioEL A���-[in $B$A� ese casesP UU cluded. �eoa�mhil��aay�exist2�li��0 a1�c�rgeH$o a fixed D �Ehiv��g$ A�T �u��#$t��\inftyu$ indicated�� �$ C q�Db� . (O�a,v� ward � =.��liephomoclin�� heter���{�un ��%�- $Zee)#�Rub�UsA�phu7measure �i{� phaseɋ.) If1�enc6�o�s!l Fl� is impl2U��P%�0E�%� $�2D-�/2�xtE� limi�see�ϥ�dix��). FurA�more,meqn.\ � })aV� $�� = _1- 2} ��aK $electrons OFj%`asymptot�lyaw!smRlJly if�~��-%�if ��Btwoy escapG o in�y.e�fiJ st��E�%�b� incoma�AZoutgo scO  �-y vypp>Ũ\ fig[ t}͔,\epsilon = 1ݎ���I %Oe�-1Ni a7  w� pushA inner )on�A$n ellipticK arounA\e nucle�e�e��Zll% ����=�̥isR  ?� �JAfX e no9-ies1/��C.��Yas depic��V�0. Consequentl%v� s�uit� J" ��Y�? en��es. %�BfigurL n�I graphics[� =0.40]%,17.eps} \cap� []{\rIm"� U��.*  s���% Z�f} � thebiblio� y}{9} \bib� ,{CLT04} N.\ l� fun�r% s m�proper��&&wo " ��a�over �h@$t_c =40$~min. W�$si��og al data�i modified se9bh#�remova,da�jumps,co��$$ifferA� betwee)^clo�)R�s-ope�(. To clarifs ��,%8�k ity,Dalso smo$�through5 volu� � a Gaussia9�. M% ,XobservF)a + :} dis�ar�{short-%�1�)�0 $t 5regard2&of whe� �&o�.�E=%�edEsuggest ->� �F�timefcau�! * lo'fluF(!Y�!ze71�Bu �:r r^� 1Sto'd&X+�&inCng+i9, E s he�*g�,r,�or'fa�ɍMe � memor"T voa�IfQ�nonli�&d � � S���}�P0keyword} Econ{ ics \sepI\-M5 f��al .f % P�e���:8 , % PACS codeR5\ 8)  89.65.Gh75.Da 05.40.Fb 5.Tp � ��nd>H8newcommand{\be}2|,} 2#e#G�!}Gs� {In$,A�} In rec�)ya�, con�����iq7+.s�H  !�Ub��widelyA�l�- to e!��Imics~\cite{MA99,MA97,BP00,SO03,MS95,BS94,BA1900,MA63,FA63,GP99,GM99,LK99,G4PA00,KK02,BC03,NA02,LEL04},�WaocomplexU�e�� system�f�eX�+ simi�/! of U ? customar�� stud��F) . SB8���world=Qa�9at!Urec�EdA� _y)�q|refi+� es!�a rK+ sour�"���q�i� ve a�sw.a�%8.�b� e�._s��by %�.methods,� s distrib�j��QG6�-�N!26},:�MuQ ,GD02,WH0<�'network,�;A7�� str��re DUq }. � ��&�=re�0-� manyYz� se-]C04,SKA�PY03,AR02,XX03,EK04,BEI02,Ia>TP0����� hasI��0)� �n% PKaKBE01,MA0�!priI2$crude oil ��}�%om � & Ke�A�ign[#h�! A�(�XG�In�� ��anE�JD,e1*j  Hurstl)ona, $H_q$ decre=�ton�ly+ � ��J � ( �: 1�?e h�$q Eqs. (1)((2) below).�!`(U.S. NASDAQ �,.QO�]L rML:a(quasi-Brown� yV 2 �!�}� *2 doc ��" �j �� 0N�: oil: )in-mL -�s&� {� 9�w�+1r� 0 �E�;� D a�F p1>F seemj$de�22�res� ��� � �*e�i�Y0 ltho; J� %� play2�a�( ZtI �%��� refer�/���af�y})i �� � n2 �  @well understood. }4�Bsu |0� >4 Et"� �� !�!diˉ{A�uce � �-ӡ�}. "%i��( 362ɷfyV�� � �2�. Bu \'\i}a)We?).}�7 �1i� a fru+!sp-�?model+u ng �>*�EAf�H-linked polymer gel�BM02}�Nv� cal�<continu�g� !b� mby6� ith*� , �2y�%�FE8�eL���C� self- #on�BM��ThezG�at�a 2�/*!c8 T �i!MitchA�q�(y!� e�+tific,1"Bfi� .�1&�0�"5becam� �M�MI%� ���5�gpaperin"> �f� a�M�J>�8> ( !�osite P� )� � �Fq� !�A�j�3 ��) %yF���m� ɕ. y�>=a(AN��6<*�z{A���&6j&�-MN %�Results}�co�A�7��"+ a)y minutAh"� M�30,�2�iN NoveN@9. lu�6he �du�R hour� �"�, weeken Aholiday}��. Denot!�h�? � $x(t)$�e2�h # r anh0~(GHCF) $F_q Q!��e!� ke F_q(t)r#langle \asH x(t^{\prime} +t) -2) '^{q} \r9^{1/q}A)e6)��% brackV�7 te a)eaverage �1{�e��chaau eriz"$rre*� Jq5Z!�aaI� v �+wer-law" $ like \be 10(\sim t^{H_q� e is� eN$"*,� �)J�26� ��K}.�'B[A���ofA I }Oi m�@ s onf9�:Bx �$� �"�9-h�!�E�*ex ��x!9�$\>�$0width=13.5cm,I�=17cm,EY=0,clip�$:�$0]{ (Colnn�D.) (a) Log-log plo�6�.J en@]t��us %l$t�;Q& " ��% - ��,� @ $q=0.5, 1, 2, \c&<, 10$ �� bott�?$o top. (b7<6>62sI% � $1/q� �A1jѥ6�s� ~(\circ)*$ t > Q(~(\square)$m�haeq "m�$�; b�n`�(s. ~3� 4(c)��4 standard deviJ�J slop)]�0- � fi&1 o l=�%���.&�&F�/@&Q}��&�/!A1����!܅wa�"����1valA2�cl�;.O�E �II��UpE7e�x���(# KtB��o��F�ab/1$!�&� =`�.N�0 �/ �� each:~ . AsG&�*~1(b),E�E U�large�|!b�:��2ile satu��, �($q *eM����!st�w  n"�>��YVRefs.�a� ,� E�� �r~'+u�~*o,r e� 2� in\[V%�se�� 9�e�!y.**H u��:�D. Alvarez-Ramirez2� ~&�c2FAQ :~� i -oil |� �, �Ŏ jd})wR�6g. Kim >� did2 )�b� ��~ Yen-Dol�ex� {-�o}.a ubRw a2 E9 } (Ez� e�.��m�to4-� e�e�:�a+�. �. Inspi�byA/s. \c/,Y�J c o�t`�- * Q`cAyFu�{:k��Or�5s K-[ adA�Ab� I��� untill 5. SoR� ng��*� x associla��2�� i�� �� . Si�1995, ��o� � �: allowe|�� ��,�q�to A>tan�+� n�I8o�塬rEal big �cs �e period1�A� inan� crisl /"� � 7��J.~2�ٮ 8]�: !j6�9�I�%�2!~/.f� d,%�#C�.0H"� �� 1992H 1999�Aebubble9%�J4�-�i?(ig crashes -1-I�Z^ . L��r �-�"��d|!K �of�V�. �� 2..� 1N� 2.e2�/0F� p J�.H-m�ev� : U one-<J~(lE�gray, gr�] )%�, IRrA~(dark H��F-�JM��!m>Y~(black)*� fig\$�"� \b�c c 3�|2 .d ug�1a# �f g )+ =�ayE�5�%�~(solid � s�a�~�ot� :$�� Inset�m.�b� O .�x:�. ) P .XH2�R� � M���6�. !|sJ *v 5Ieas0�GisoL#�B J�1�f��� (iO�� � ::3> ��%%:� 1�Uk&#2|�> .�>?>�!�.0�?��3(a&Gs&S6�$��*=�wd�m.�% � �� �s �#i�#�B�>�$b�� rI��WWK �%w have .�h�$e�P;8&o6�� � �%{s*zp=A#ly� ��H ���<�,�A8K)?�. H !%�& '�7 doeC G lete%.( =i e .� �EsŇly �_en"�i��� � a) w�6!�%oof a�̈́�.- ob!Rs2��'�)�!�s�al>�. $Q �#"�'"%}RBasnplyiL5ki6x�@little effect, w:�( s h�)t-�*=�&�<i*3(of>":� 5 H %`.D!jwo"J s $f�!7$g is� J}^{ R$ g(t-u) du�n�Su}�m�.�kerneVNRj� iscrE�&L %D.;� sumAtea� aa=ty9ln"�% �_i�\sum_{j=1}^{m} f_j g_{i-jFGR 4�D aa�rt segc-A�.�%yey.�IM.���90. " �Cprocedur�*.�EoK#%�, gNGtrend4F� e�e�4  �(e� � ��X� . B�:�n ��B�.VP:7��*d &�n3b�,Ѳ�%86� �� 1(.�@�7Rall�2�!�s1K1 (t <�() =0.986(4)�eq 1$<,!entx Ɉ�vh�t�<XThsta� =1$�@|1v�}i�, curvY� _�QE1�$t��unɞd* !, a� "~ �'�-[F\s�V� ed hydrog����.@�}.� "�,j�y�/!9�mG&q ="�."/"`1{CE!$�M%�v�� mc)�Q�� *� 4F� N\�G�W!S�c}��� "~ �.5:^ (Jx. �q b{ �{ "'& sup "9 �.�c E�sV�I�E]! �>es (c��J�;) R)EQ !�4]Z q$. �P�` 5&.~�A���Xg �i ���,qe��i �i ji 4:i %J  chec!$!� ofY+%Ju6� �U^"N� 1�2�100 . W[gNPs�xW& �F$ 8ocJ% , R N-,2� �s   E�a���~ Nq. z�g�;�3han 4{ �"2!-�%�I�EG=AB4�wR�w6���" �m��J_of& a��:�H�!U!}����{ 8B �a��H͎�"v�6%06�9��es� �,K7�� >� ���I%FW06 : e�N6� IZ# OV U�A<an�av �h"�.( a LorentziJ<do notJ��i gnm&a�E. % F_>C �5�R�it"* ��" ,Q�u^�!F�%� �U4)h�Wl!e C6�+AIs� s�3Q�Q>s*�N-K5� �r %��kG&js ���1�6"N�|as?#A.�0(�5 �>! cp(�"�*T)! he 5G*Ji �/KH�2IF����P� 3V)��2-iA�*�2_p]-�edi�r keep J2� ` :;1\>�xrob"Q��7(ec�+ I/bi��; }it4L4�!�nN.t�6"$2Y�1v-cLR0��x (}[loc=htbp]"�H{~�ofY]!�=>}B%��8"�H� H (tabular}{|c } \h[ q &U�.Q�  (t�8 )$ &yN(� $�\ [00.5 & 0.80(1) 987(2)#178!6(3) "2 "3"8C.#3#6f5(42E4"4g7:" �41g5(52D6D37"4:"7 "�3(62D8 "1�!9B"929."72D10 #%E6#$1�leJ@"N7C���aL7summary;�st6>{m?�C.. Ni'�s�-�!>8 ��U�� � r]���>� IB� �-�[�MqL���t�� .I���;��7B�s&�w�z.e!+W�op; �|BM yB����� Fk5 � �=9>k� �BT6�;a�Uul��/�0& �v���;��;l/iI<n�ar���� � . UnC2an!բ��6�AV�=an�eL*��-topic. uz(*{Acknowled�.appre=" useful*E,4�� S. J. h0�is~9k w�up� I�dKOSEF(R05-2003-000-10520-0�M3))�Qby�5< al hB FU: Gr,[: �D�3�j�V1lex!A�Qnance,j�F , Ca�Ff# 9. "�K�<} B�$delbrot, FA�CpS�.m"7O *JZ7*�G BP00,K( P. Bouchau�0 M. P��JYLa-F�ial Riskr�*�O 2000t�=LL Sornette�K$ Rep. 378gM 3) 12S9LR��N�)eH66J5) 46.I BS94�->� D.�UuI!j�% L94) 8632RA19!H$L. BacheliLlAnn. Sci. \'{E}cole Norm. Su��00) 26�A63B� J. B�g�h 3�63) 294.��>}A�F. FarmanNR9420. Ya7A$Gopikrishn�$V. Plerou,�A%|Amaral�R Mey�S :3i�ME 60 �99) 5305.�p?6{zM^L.:yA�:n Eur�$!+ . %_99) 132L�=}�PLi�O.:� P. Cizeau.�(C.-K. Peng,j�6P �_L {!hu�GeoBt=gY. �B� X. Gabaix�>!p�QA 28�Q 362.k�@}>:BjB�%��2l�Q0) 31}� KK02j0-J. Kim, I.-M !� B. K�(, �� ~ 40e�2) 11A!54wAdO\ Bonanno, G. Caldarelli,A�Lillo6!�[v. E 6�\04613.��AENakajia=J�096� B } S.!� Park4NA�Koo}Ta��UJ. W. �H� EO��)Rs 441293.imB KRFU� ?4) 668?�?}aG0Z. G\'{o}rski�Drodz);J. Septh)5MN316�42��@!�H.�Pg�A=M. Hui,�O:�2)�1) 57.�"-�E+J.-S.jN!.SE; YoonM.~1'�4.I�@��� Skjeltorp2�2Y�48.��?� w� w�k 11%��2��.!B:/�FhCisneros, C. Ibarra-Valdez,� oriaA�)Bx cala�R5�ih2) 65.i�A}!�Xin-TaH. Xiao-�U)B Yan-Li2 33 T�H.FlTEisle�=a�ertesz6D4 D4)��.EGBEs$Bershadski:1��3) 59.�ANV Auslo�X(K. Ivanova,\ QZ Comm. 14 M2) 58�Ob� �B%� >%M\B� U9aC.GSC!�Turie�X!�'e�0Vi� 622Q/629}� C�  K�ag62 7.�]A�2U�:S��3�1) L12.� (C!GMatia,��Ashkenaz N:T"�S�S 6U�42.dVCE�KQR. Genc�+�Q�2I+!�7.�v0��M�ewH1?��*: ��Pe�%P)m: �� 6�� ��1.rF�;�fMicroel�_�HJ.j �.s=�p3�2��h$-mat/02102�U�MK� Meak�V�g,"�a�$growth far�(equilibrium.� .� S� .tNR}��H.+S%W$Teukolsky, T. V� rli���B* Fl�\PN"�4Recip� For�i: *arxs QL?u��*vQ�2 86, pp 49.yeKrawiec��J� Holy#[�D. Helb�A�M/fV 89e� 2) 15870.�kE1$arotolozziSA�� Thom�� UA� Q4)c1.�b%per�EW /u�falI�K v�F0 a synthetic,2�#*�, �5iit�W2nb�d�]y*b;�}:+�&wT~�:�T[prb,�Urint," pacs) s,amsmath�T ]{revtex4�*U�u .VUdcolumn6+bm} \ 04Cthin A��s�On '�+e s��immisc�mi)s�;a [2horizon�Q(he�7 ) surt�'Bo� ��q C- �� -gaa�te&zqu�l bi� ' �may]qi S2#:molec� iS�fsEleQ}��ultra%bs b�K##\,nick�/Xoretemper' e-gsfa<GMa�Boni flow��)! . UF0a% w�/�oxi�Swe de} coupq��",s�!!?�facfil�/�%�-is$Lma�Ht�, �8!��� sliprn:=�Li�S�&;"]&�8) E_� are �i^9�B�t� g�o Q�E des�]z�i!q�. � V .�JcE)8�4t]Hin Oty"8f a"!Hcose, zigzag or mix� ypeE�oi)�93s�aTg5�FJ @%@�"&�,pP\nJ}��an��( via switc�b�;wo digXtaE7[e��QonuMs�* Ico�^pXa!]�i�EbrCJ�UaP{ 68.15.+e, 81.16.Rfa568.55.-�_$47.20.Ky �A make� "�2�T.}ou�o]1�2i��Aga��<a�idY�%Ua �`atmosp8(ltt� ed m�m* eVestX#� focus /m%�by� �] Y/ ��K @act�-\c�=DCHTC90,BrGe93,BMFCb�D]w HA- .=��e�of�Llat% aHReit92,VanH95,TMP98�"AI�� revi�an�E�'�@\,\��ODB97�@ aalyze�S6���-��or lub�b 6�)DReyn1886,Somm1904, ha�often�d(a�+y puG�tool e $i���� low R oldsxb� �� . At�!Lbgwi!@�:�%Cs�B*�VhyKth��tZGFNOS�39(y m@ism H�q)b5/off driv��forces ���AБ�ly 5�E�y�e- crib�=� !Ond�howin!��<C!3of expe�I��1�iAJShRe96,EX 3a,JSSH98Q`Eg7,SHJ01H}!>  [ I�uJa73,WiDa82,deGe85,YiHi89,OrRo92,Shar93,Shar93b,Mitl93Id, ShKh98,TVN01,ScSt02,TNPVdhie03,BGW01,BPT03,ThKn04,P0 �Us.%�9�k,d$**aE 100$,*Q VF�rhe ^50�u�J d�oate�1o�H-�,IJrmo�I��o-cap wr��or�-vZ6t.rd�rmin> ��'QOS8��) "M��0bov?E�ven��mo�y�-ce�co*xe m�zim2�influk�A��A��.�'E��[e*< T" 7 I>Ec5)�}�)Nnt up eup�Ol�r �- y�5*U"!�{!���>.�a7�9 ���sM�GNP94�e!n!A u��"�2Nv\,\mu$m��gr%�I�Po�y5d. D�+!]on �Hdir-0it -mzI.�M"� .���.b�A- fu�s8 (Rayleigh-TayTK?)-�2��7�#u^ is{0id1�)��z5� o�3c_rqrem��`H lengpb@.mpnt.�%�( $\lambda_mp- much)&Ba!�>; $d5 .e.\>\gg d$�\!4j%6 $ de"�-7��y tenP&�S dt�)�A�I*�jal% eler �G not �M+6T-��x. {�q3FP,of $10^{3}$a_ 4}Q�8v�0an2w�Jo& B2L3L.�xM�t�" � ���$yH� ��AVy�A2����!_m auEk�E�n5"�- Van�  Waals, �_ caPe�Tp�tee �"��,Isra92,Hunt9a)SA�r�7U*� "�iI�@BgU E5ٖxL�!a��x""/!JF�.��|yr.� 8 R 6�!����V` 2�n8 ia�oim�p"�e:�1i�.�($media. OnehK�+ui�E) ���  rom��r�q dipo$ ( i/%M B),� aA�0enBE&���Xd X�Ydu^a:TAU�a a&�:ng;"JQdisper�2R. B��k�9 # s�a%)A� ��allqsV2%� ecayk $A/d^3$?ere $A�A/Ha� rAN�2t2�}. AnY�sY*x' .aJyi�>P . Note, h9�&q s�is .W^�neX�'eM�ntNe�5u.� &�2 �;:$^ as1i6 d��(^RefR3 ).a��� ilm��: dra�d �c%>=�7Pm� 2Ldactric*%i av��� a silicon�� (Si)���n& oxidnB (SiO��� c}i Se�n ./�E  2A �A&��Z,styrene (PS)�xa�� 42��� � lyUc�1�Ca9A�%U6wB9a�g�4�- . rapid�dna�C~iO<c32�[t $d_c$d> *�i2A"��,�(may ruptureY FNitA�sturb!�B Imag� 4[r���3{:)�! I"by�  ��kY��d!*a�%� 4�v'm"�5"� %�coa}��� {S�&�^wnew�!J $(now)QE���0|' �:*�D& E�� )� `it'\%�beUg m}a re-e";�'Z &� necessary���Wought*M s qu!��T@7ex� \w�\ s90&�)��Ntw1� �5� subj�3 � + c@gH2(� ���wo��s�ageomet�d�x2� h#l7-X%P"-M� h ݦ5pl�6lea��$L����(bsto]eg8co�}c���gU�e i�6le &^ P��Lin01,2,M? 5}. Xt���A�B��R� >��On�T,zC)Q- ! :!�-.ir&C  F�h2j^.�z els �O�d���X0��zwe"�%��Ք� �,.] � * BMR9�f�t�bY�Q�Ũ_ls (,�new�p asur)�ZM&j CrMaZjCW)o"_ evapo6 �Dano98, b,PaunBAB�Ec%�sol��&�V�vm�in FDBand0�eIxB6� PBMTw��8)! is�7, N �9Y U��^���2��&:�ans "�Ma01�2.e�esj=$I��S)� now P�Red"�dewet�PH@I&u EO , i�. bulk��te�tWunn03,MSS04,FCW95,LPHK96,PWHC�I� ntrastJ� RMSHS.)�s��:�B� ��]15�68P �� $46Lam� (PA) J�)�HE� � wafe�eveSQe0a <�na� � het*�$ ($195^o$C�2�)mTB$15...35�)%PS c�5�l��%�h�'�)typ;  spinoda�F tter��At�:�1 ��PAh�I�Y� { �2�F!*E:�. JzMBB�0-� =`v�d9 �s!(.�X $1&_)qA(dimylq�(xane) (PDMS-�� U�s"� of#orԘed 3E.��%DMSmb � meta) �Jg %��h�"�h�e veloc|4�&of &>� visco�4���0E�.��an�;s�(1��%#)! acry!%MMQ� , b\E�n�n &)%�E�wa�r�o eI��a inim|@f�[�!\�-l�����+�EH)m׈or�lycarbo� (PC)I@�a �s -$co$-�onitril!SAN 3J��� ort�� t:a�a� � Jow �=Zi--mZ !O"�ub� � ��2�J�.RV.N.�a!ly-n��a ���Y a�y*hwYetowards `  �  %���'& of� "N*�"� �A' Sp�>T�ioUe�-![II � pa�9fBt u�Tsi?�volKq � A�As� ����a�aE$*u!� ionMen-Lqh�M9V)^���rT ng <�!� V �srU|!.qon*Ge�s�L�@�#]�BA��)^e�lN)$"�  our|o d�Z�. p%�� Ar�foE�A�aM oble� �vL� S�]ME} ;�:{$2r�$!��J� l!� > �Eow!�_:!3$ b��F� )�]RI��]b?�se ]���@$T_AAg�ad�e= �� bF�_h� Ss. 2* lin_��}qS!�x usi) "8s"r�.d ��1'�i:�ge p c8g! !M�v�� �m� 6�lr_int},�cus%W�po� g: m :<�_ s�b-#du�"0"X �J�im_�I:bnuss}��*�l��m-aM!ur�a�>�nu_sol}9u1�rm!y�}��# a3 t����! Lyapunov����>�>kmt_�}� *6�,�!A�!7-�%jc�k"�6�0�S-�%�$�T%��Id&� �E�u����6�p%/. cB,!rk[�NBb�y}. Ex!0*� 7e^:d�y"� �(� !z�j2Ye -�Ban Apnix.&�%D2�k��it^v��&�} 2 W��A�"&�} FirS0�/)!��pr$)��- aB�*$h_1(x,y�[+6�% $h_2 )./[a$�7%Cp�&enoughK��H��be neg�2ed. Co�n�n�Q #al�� ske;q�SL\,��1}��,�zkes9w5!p� � F,i�? abla (p_i��phi_i$nTmu_i \Delta \vec{v}_i,�'stp�0ND� $i=1,2$�o�J!m��enh $ e8_i} = (u_i,w_i)"�"� �, $p_i�eu�$ � o+hL?2 J�%ŧ$� -" ����U; &;��oe�$d_�(\�X40^L h_1 dx)/L$�; $d_2�!2!-2L�0 r�+ siz� lu^y!���app�}E�Ah%���b�o��*�-?�C�8}1�i�� �m�$a�u�Nh�t �e"��!/ �!� *���&�os��.��5� ��.��zerI� �\�)�SE�}ǖM�)%Vpli}�oyn@:2mu_2 \pMal_z^2 =xf�pY�O�NS��\ 7$= 0(b}6�e1R eANAe1=c =�e;0, q�NSdu��Ir!�$%�p}aJA�#gaZ� $Z-� t�  $(z=0)$Q a Navier  AW� -pene0�%�7i , i�Fmu�\b(��Du_1~~\text{and}~~w(0�� SLIPB�rT*E ��mipQWi��dE$t��9- .@ (z =a��!,�w"�! :�' kine1) %*ZC tang Nmpo}�� �stn�or^P u_2,-3w_2�-M�BCVI�)P\QIt� +!�x6<M�ex]QXD�_>�!� - .\�:Zsigma�6|c��n�l1$U~%�� !��U�)W: 1�2)$&�N��Z�����y,FQw�K5�!�2!�=N!�2� BCV1)��v2= Y,1bBu ($=��[2$�QA� A�"� � -{ e2�6�,*Jlx�b v 5�& M *2G6@�� writ�.6��disjoiH1m�# � �0 $\Pi_1(h_1,hE6� *o '2'1e,F�bw�&�"�6^.�U�ma���L, �J�%�N�_�&��.uIi:'tais low.�&=��aT=)we� F�p%2�xp_0 =�3�.� ^2 hA� !v9O "E� d;&�!�; -� B�1)$N�%� �q+ -G$��y� �1�K2ռBCF�� $p_0" "� A� !q!_!X&3. ��\,y�\)� Y�&Z* $F[M�]j -)�% Ƨ\d5 F} h_1��o�<� 42=!�f92}./_ENRGB��9��!} F�Pi�&l��M?{�frac{(�D�0 1)^2��+�N%�2 �6)2)fu� \1�)dx�LYA9��A$8 $ be� �g"J*�Run�Urea. E Ssh�w )�m)�NScrA,�d� t"?psRb) �$z�$E_�"am"�6'Psi_i$,�e��$(w�d-]� ),~C*0 z )�Z�Asix $x$-$��(<6 � t�od*te1d �aN��  "���.c!�)2�&b�'*`.ErZ�|wo�Qu.�f�E &=&MF1}{�AE�2/bar� 1MGqzI�+ I�C(z+� ) K .Y� Bu2} fu2�u82} K_2 (z-h_1)- �\8 &� 2 �segh>�mZ!a5�, ie&K1?a� $�= |+23i�{H�+ �[.�1S 2)- N1) �]��� $�= Ng2} VH2)h_2$.b2$~Y:oE�R<��*� $\Gamma� ��_{0}^!G}!@ \,dzV HI([�#I� HX �DJ2J2 Jby);e���,~�+ L��� 2)$.��2}).O)K H%4��)Ps�ZbN 9INGU�TANF� ^ q%. 2(E�6�x $%CQ�s sym�,c� all 0G?$Q_{ikrD re p�$iM,Dropp\ %� rFdaJJM�^j!�Nqs"R y�)ďB#�fu�nonA�8val� l weak�s$4n�D�J$NeSi90,7�3�+".�1 rfa6Y! "�*d�.&�;& �-,?�eg)"�"ve(�F���a'$J2!���"� of lO�.�!.C h_i$���d*�&�]*� &�2�)f$e5s $2� �n��*� x"�2} ��e&M#7then � x%�al (or&Eal)�2�]4!&ss�CaV�iJ�$F$�� &f��4 ousl�c�o�\E next�# ��k8*�8LF�� $dF/dt!'&D�LR0U % ���J/�QW/2� $) \,dx $. �ng]#Zi$A�Z�E�a� ae"S�_p�icN>i� ��i�} �dF}{dt��-�  \�s i,k}e ikNp Jto �{q�a�:�"/#z���BI�8e&O#$FK�`il���2�7&I#< �#�P�� opgR��i��C Ed�D_for} ,�N!or4�!?h� �$ior ,)�f�Oe%apolar &_�>�8�D2����靱$�2aiS* :)>.�#�( i*~;� . &���=I$l�(�i�c�J�;^�J� %��r&���5;ly.5K;�*�?6�or.�0+�6\�mX&A^8+�$��c&J"�%.x��i�/to8)18���s4ig3e �� �K^* �:F}�%h. A��thX(��/ �2�3e�M7��q1es �+$1�>����.do&,&��&b,%)E./,DbE!kI���on3'" L96��'F� Q�+�l%� thei2 �[%�I�A�A/]]tqagW#pai(2$�7s �<�p��) &y1 q$ve F�(4qq40by $A_{ijkl}/�i hjR=I}!$�> =�a (�+-�|)B_>�+c ��t1.>  � $i-j� $k-leaca���>"� be �*�3g,1�$�J s$, $�gas�GwT$1$ 2 l�j !R��F��sal�P7�μ�5qub of͵11.13�2F�6-t6 is ba�+SW pu"Y �W absor fr�+c� �5lZ vo&�Aa�M1>( $\nu_e = 3_�|D15}$\,Hz%Ei�#^y�&\� �?'ig�:�:��s �ee6e} 1�\,\�L\,�3h�}{8\sL� 2}}\�� @(n_i^2-n_j^2)(n_l k^2)} + ��2} "+n" ~[ G2++J,]},��LHAM} ��BH'n� �A�re� ��ji*ICR�-e=BQ^� )=  jk}"�HAM& 0q.�]'�/qCfE�)r*OEL�al�66?�9TDS88RL} �Bex�&N� $hm 2Z����7!: ZE�qA� 9 ic double7?s ��*oƽA7-ol�<�t6JLDeLa41,VeOv48,Ohsh74 bQ!MJ���. w����e Deby;�nI���,�2�D����Člap��Z{SEe��v~r 0Q%��9PLI[�t M"G�z�v:= $s-b $1-2f�s�:SQ exp{ [ (l_0�/l]�V` V��2-g$SR>V"H \�]}Yere $l����9�(BorX�%8o�@.$l_1,~ln&�1..�R"!�%F� �(� .;'9 SAOE8�6��wFVC,D!�%�lI�c��$l�#�)�al�$ſ m���!�>%�!C r%2��M#�E�dsp�Acoeffic�.Oy��B�� *��the��g(�3a �+m iw%� J �,#K ]ap"�9�%l amb���6�W~F<  !�"�V2 2�Q�sA�A�. Col��!%A*� A�.e�� f� �� E� �re��c��as�="32�"&=&�,A_{21s}}{6 \� _  -���� 12g uc^3}%S_1}{l�y� @at-a !\� ]}+ �SQl�V;rA2A2F :!$.�>� �}^3} � A_{g62:�2 } ���+DSJPRESS&1�TA�n.$0P^�?�calu�.^�o$l�g-coord�<�! %"�-( = l (d_2-d�#6 EG1 /|A"g}|}$�R�$t M$\tau�.8;�;�b ^4 /x!�^RT�8e�d�e& "�1.Fint\,�OIf1�"s�#1� �$2, h�# - ES A��I�U{^2}"!bar%Q1a22} >DUQ�Q�. 2�!&+&4. ci�-_d}!�+ce�22)� ar{SP�a/(e[)B" 2I��-�q1D"� ENRG_SCL}�&��M��+0d >L3m!*S�UN/lm�^2!�&YL$, VH $YSE�ET) ZXS_i �$d_0/l)} / U�x m���42. gd g d_i/��$$c� Lag� �cq1r!at en�'maskdnW���A����RY �E��$�/2\pi5Ecs-S�o�V�0ŕ&�+�qv�?� �', $d = d_2/d_�$i!�s'/u��� \mu=a�2/62M &�,��&| �dI$�us� F��dol�=  �h�%%d �.��� $d%�n�-J�y6�0!��dim"�5xy m�]!�B��J&T� )e  d.�factor霩�rL!�09  / A�&�7�_,;;"�"B; .�}70U &>g; stahAW�;o;Qg�I�"�Jn s b/�Y9< Z{�|�7 (xS+A|E�$�2�EV�%� g��Q "4\ll1$��4 &�8U "�M1c7�@\g�% t)�� (kx) M$�6�k$��- �{�!L}=(,1)�%R �N+,�C� A��u���HN,�bs�\��o�  $ �(k)]U� by s�!�2eigen!M_%�> $(�J}- N,I}) ڡ�0!��S*� (.�\�K��� 2}=0�O^�),v � e1non$-&< Jacobii�xa Jf� )�J� -k^2 � Q}\c��!�E"" CQ C呀2�#x. UE)�ՅDx&�J i�e�*F�#z1,^2 f}e + k^2&"j iaJ,"�~J6"� �4�f2^$%��L6�#6rMATRIX"u1/.7-���灔!�-hgY�� *�"����ύN�e�!�� �6Tr}& ��H:X#04} -{\rm Det}&�.GR_RAT�75:�2TrAE�[�e!E �'1}1} p%Q_�& 22}]�A} } = k^4 2� A���7cbH!FrYan%YRbma;. S��$FQ�/ eq 0s9J@ *_3asi�g!�?�J6 $(u�EA�-�e+Q^{-1}J� �i��nd  6�+b9:�,J&is "���de'X� �� E< hreкc)dMSV87}!>@c a��al�>�v.�:!��:LF%e:�.T5�83k^2��6�A� bm D���+})$�-7 �Aa �� xaw.���&�^|%�\%G�$ 6�Car@}. Nei�$G f)�D}$ �A�5���U����MiZTm�k.�Ja��qNM � os���_m4�Y�J���%*�% G�� back�B�in��o"sH ��Y]XA �#q �"X threshol ����l�!�i!~bf$��d)eE}u�X63 )�%salways!1��� �4=�-M�I2�fA�$k=�!i<1sy�S is � *eW��Be��!�bC �2& fN;��E} "oߩ�d<~ߡS11}��  t k=&�- STABյ�AA)5��� if�lea��e�*�84 Tz"vi��edA�Z�� 6t !4upN=] k$�Crq��  �Sa cutoff%V� J-$ k_c^0�Z��#fD T1}{}�B��N��}" %�y .z1}�p6 zJ���$^ �� jb�Bu �)! CUT_OFFUK!��#i�U/.�E}(k_c= �$ 6�2}�2a�]�>Y�di�%���e $(E�/,Ef�1!6�k$ *a6/= 12}^2,~ >0�a W� bola�;G+� Ra�E�Y�]��N�$A�!vi@at1a divi-"7[se!)�q i�#e;�Ga�  c�\!( 3g.x� *�*c � ) "C��a�ytm�&,a�-a�$k�\ I �5Z� ��+� �.h $k< BFix���2�Qy"�Cs�"(AD*:u$k$e�<���%�������!� �_�!one pa+4(%s5SAv.�2C���Y)dashe��row�>�.�T#�{a6�(N���gv )+p a�Aemz��If z>� ��A�6��^�"��F((dot- �9� .�Lon�LznA'"��L Aq.�=!<*j��!&s'P�O/.�$s * %:�:O�l�-ݡ&��  &JM��[ P3%���x �"�#�%�0iq,`" '%4a.9NLic�Z��(e� k"l]%�. = A�.�2Me��#Mr][��u!�2o'rol"HFJ�:.F&")A�!�A ar e8R �em�. JKi�D!,�0bcoa< �KE�a&k"_�i>k" �"�� �*An��^�� com��� b �c c$A_{ij"�1 l� �W in TA-?Q Ham_f��B�q� �!&m��,����. (k 0 �&a"vD�qNdELeIH2�! 9�>��Au��)� ��$.Lu# '1���!`F�(d b�5m, $d=�in�J�=0�Iatat B�va���)*s W� ;' �nA`� ��A�P&A�.�)t� J $not'?�b�� �)��)�b2 .��-X=q�RRs^+�a�etj �Iqly�� ��6�d �kf���� / �O ins �a%� �G"� o* ;ta . �M>="�+! �)0 �� f}-wa�=�� &5>+�-e�%�(1)�]5( �k! ^j"� q�w�ard�X.9!�:p  "�ja�� subs" {2>{.M {��d%Xdwwm%;b��n'. ��) �&NA�� o B�oE%��"� �c��!!!�9H h!z�5�t.� .�3-5C%gy ) �M"�*Ane� 2C/�^2 *�0AXi��yv��kg7=�8can be crossed �by changing the layer thickness $h_2-h_1$ oeof 2coating :$,�. This was demonstrated in Refs.\,\onlinecite{MSS03} and \onlinecite{SHJ01} for a PS film on Si wafers covered with a $1.6$ nm thick SiO layer. In case (2) the one- �liquid \,is unstable v�$\partial^2 f /h_1^2 < 0$. It can also be destabilized =S%! i5Ses, a% shown-:DRSS98}�$a rigid PS Lon top!�a�PDMS k(on a Si sub)z . Compar!�!�� . Foɛ formŽe def!�1�A�two inteE�s�[phA��Va), latt Jy)anti-.. r4special parame/ valuA�nee�@also find a mixedM�m �] pres�# q�they hA�0equal fastest6&I� PBMT04}. )q!8lU�in Re>Z,BMR93} assum!a�ck lowerI��reby neg%Fng�%?ac!W between,�iE�!A �X-  -gaa�-�. IFis�Fonl��e 5��%Qbe��. 5e���, h��%|�M5Dcom.HB�K)� norm�@asymmetric, i.e.\OYX amplitud!�f) �9%$�HsMЉ>�z�S�k ` y byj0hi = \chi/(1+$^2)$. Nega�(p��ve) .$ݕ�vari( �) ։E�D $|\phi| = 1/2$ reM{�P �ic-ME�as o = 0>s maximal%, etry1*a =is flat ��4increases with%fr�VBB�8$\sigma$. Note��]disper�� relEnU{�iS�_!� �Z5$\mu$,5AM���{���(} {\it does�� Am�Ij plot��in>F3}� Si/� /PS/air  � a f�T)�of $d ���%G��� � eN1! gamma(k)$��� q ges5� 2 I'$E�2 � &� bq�� ed byA�y�u�or��e� .!<)�enc5��!the��"�9�&� � *� �_ S� tly��akingAw cept n9���*eri  $a{$a�� vali AX�( stag�evolu�j. &x �% morpholog� a@��fco �to n �a��i� profile� i (x)AW�@ine a�`�E� or s �)�b��e�,gral \begin{���} �0_{\text{int}}�� <no!� '=-�'a3 V� i��e Yj� m�6 Limita��& lim_ Fo&� $d_i$kra� lh� GR_RATE})9�%!|� �nalytic� res�$�G�e 4number $k_m$ ���� � ,time $\tau_m�M�2 _{\rm m}$Q<.� �!<��E theg,�-Ldero�pto6�� �� |$! ��_ impor�  l2_�(1)M?"�<upp"�  $d_2A� \llA�- (2) ^@.9 $d_;. First��: !���Uich>�"� (:�) ��B "� (ver��:� )��me�alND�� thenE-n�љ�$narray} k!뉦 1}{(-($)^2}\sqrt{ D |A_{12g}|}{4 \pi �I$eff}}} \noMn\\ MF� 6 (2:)^2B= \mu_1 6}{!t v^2}� 1LIM� � wc ���}T !� 2 /( 1 + � ot��all�i� ��ir �1s� . I� esa�ly�>�.O$�Hs�'�he �y_2v%�y GA2�akbe�la����fac�J flow �2kwA� is` � o `1$,��4much larger t;�)mk � � . Ai%e�B��,}�s�a�ional �]�� u2eUeC bulkBH pves��#an%i same=so�y $(��)�}~ !�}A�m �5O nd evenBf gi�>hE�,slippage $( i^v}!L5/\left[1 + 3 \beta/� \right]$)E���2��=��>!beALA�o@ B���)i.D��ŗ����������d�2�A_{21s}:�1}} v�2F�1��g5}\ ^2}.� 2N��Mi9 �A-�coinc�w�� $k�� low}i� *E, ��ve�p6�s�!�2�.��-�eH)�a2KF3one�$theory. A ��"is geo> � JOYiHi89}E,.� 91!�a�!Lon{Long-range apolar%vshort  ��*� r_sr_� �&m sis base��ly�{lm.P�o�inchct�3"�� * �%>� �"� l� .�.o. P1c�ijl�b&H (well)-� $10$\,nm>�8 contrastt ATresul �exclus� ?15 van  Waal� c&�6D � �, �%�F2�,���9�t�QQ cros!�R� Ք)� 2�4}�s�{M��it�ly*�* N%.$plane span� �� 2�obt��w� va5!ostr4!g]�] qrJVJ. Bd� >O#gp� &coeffici�$S_�$S_2$ s s� top�I�=!e � sU1$. T� e1�A*�M9$(S_1,S� -SxC �"y�5}"Wab�&) \ b�ze�% �@�m)��minT (e/4)^4 �i/" V v!�<22< ;� ���q J[0!w� $�� A�O�{(if at least��1�5 $S_i$ � � � e-9ZY crit!��ue (a)eNl1(s)�b��� 5� d_1,. 1� (see�1} 4}).�A/ > !�=$aWtj 1� exis� at extend wardaHfinite� |, �tFig�� 4}(a), (b�(d>  ,��r{ Q E-�iK� for � .�< � < ax}` 20��BF�e��e o $Box = S_1 x^4 \exp{(-x)}$. Similar�za�)y.�vy bzE�, esRm�+%g�E� 6�bW�]![� 5�m�!F, �%_285c2in�r� e� �Ng1%W2BW "�ray sha�/trianglea�!�ce of:1 5" addi�?al�pR�mdI(,~Y��Aqf:�Q� c)).!bining�&<c��sc &��yp��J�.� $itemize} \ [\bf I:]��:�ontinu^� Q\i�s�  striwt>�Er9���$ (>�(a�� �ri�wo se��$2w� �%3:�?��!�� ��>)r�d>��m�a4(Type II but a�2 F b:hV:] Avqt2an un� �|j�R�E�9���Ad IV�!Zw� �=� i��[E )$ (�@�)..s!b�+!�2��g��b[\>�V=���� �afepFudry we will f-" our � na���6�a Ej . \0 Non-� behaviour"�#nus sub/S� onary�Kas!N remad8he Lyapunov fun alU_sol} TL �" odic��6\���caled Eq���!,EVOL_PHYS}),��u iv� �� ial_t h �se� zero t�w yie5&��e"c Q_{11}\, Ox �(� \delta F} h_1} �)+@2�@2@ &=& C$2�Q��U:�2��2"� STATF�2 e $C1c=)�#�$FA� .�ENRG_SCLH &WA hA���E]�) " 4F](GUtot�"low6j�a2�tat�Ws AYAR0 P$$C_1=C_2=0� B�&mom�8matrix ${\bm Q}% 0non-singular,<�l�![N��\�q��"26} \,d�nd���� P �!_*}o d�'m� �& �PN� $h_i2!, we� "perturb%V�V��h`!�� t)}$!��6'�! _)�ize� full�-�"t&-""s B� ar��%v solv� i.edIMv�(A�blem �tL}(h_i2�>) �� ��� h(x)��taV$�!| � operat�#PL�fe)Aretiz� iY-)cX>-i&�!Sst.�$%u��te%�� 5�J�.�Vdue!��transl%�� �'a*�$XD9� B�E�� "�.a�'yI� $-WQL=��xA/ ��)� ��'. .� Modm��"| mt_� m"3.'� *9,��-�5g may��'s%��cours"�&G"5E. Possizo�esV8+a dramaE!f�0� (observ�) $�m&L% �film. WTv�g�tymby J.�&a�V ��c RaPo%F Jhsy�by .��+Fdi25�"er� simuI�� !d  coup% NDsb�i�N�.� � icAain. T+, semi-i&+(cit pseudo-��0�� expl%)��� sche3 usedVi� ��/nsA>ofZ*#H*�#�sed noiIU�Z0.001!Pe &� Ta�eP via branch switchingue_ }�"!]�9R9A �ly �A\!� A?�1�qF.�1B� 3}\,uu� A�o!j s�n !�l��f����>$�&0\lambda_m$. A5 sequI) snap*t�13F�6&1eHA�J�( a� icos")Ldevelops $(t = 8.1)$)�1�1� !P�9Q��a� --�% �?Vtr,�%� acc$5n!� by a�eJi�"�aZ.���  ($�9.7$)�%3f�illus�1da���&�*�*"�i' (G �&�'#�&� B1 7}(bQ |on�c1���).A|���-sl!ly,a��7rse"setX��disappeaa.��G� !� �drop ) 16.4r!Nex��1! �-� �it}��; flip� a 2%� holef=20.6dFin!�`leJ��E�(\approx28)$% ~ �ach�$A����(�e &t�32 �ve� -�MM!�%�# h3:.7�'3~�1 'cli�"��2� s�"�#�cvE�E&�@��cla�to.�'I� �sy�6Q%(Z9)t�� 0m saddle poin�xn"� �5d a�!Oir�$ble manifo�A,�ށ�tly�el.5�?�, A (��aAcu5*�FU3TBBB03})� 9�st��a� a� coyStep)I3�J� s��A/M{��2n�K�+�ed" i��,� �visN� ofE���^!�b . ��J: �1_'sub"� prima;bifurckK n tur�x� ee sAI&-n� 5s (%�`goox& )as"�/8aM)� a� �x�x%�M� K� Ym� dis���*E"�]� s)  <�!!woy�"�: ([&�2A�+"U�(dashed %. AQ� f�+)�A{Y%�%] $L_c Qat>!`$L� 60�i� $E�H;2�a�(��� 4 $E_0$>�8��)�w����  de�!�)x.�;.W ���0nu�Aϙ��W8 t�= �$ T!break%�� n�/s��)6pJNPV02�3��K% is Ż�M[s a!/@&i�)�1�A�le�9�A�)�9� 1�596�- se�N/ 116$�_�*ݫ-�t onoton$ ly}i�+=-� Mos��sI-eP!ly8$fer��!�U � �:� (b.�8r�9)[ thirR� 79$)�q�&ck�:5� �N7 nn�.i nd g�,^�)cmC9Zrapid5 !2�s=+�=�5+!< $�(on�� I2�)_ xE� E >m�8l?:�?ih�?2c6> B:?i�,T?:���pr&�y�N��� �:�̡&>��-�:�0 ��.B�<  to� :`8� d))񙁬!�� triv�6Br��i �� ��f~ G re��5)�/aM���(�doc?�Par2 $("�<108B 6U 9}+$ApAHhig�@EjatE@N 3 nC rst = :��f=a�%>hdy-c%�s�B�o P� N(cp.\:��p���.a%_��a>/strong��% �a(<�JB{v�&::�} AB��� m� conndt> � �&#�Ce�a@�6� 5. Also�� �� = �leaZ �(a�  i?FybaU�"� C�*GF�[s� � }4)>V:@ 3f%�aq.�� s ��Aw&$ ing*< �7o<&� 7�|�I� q���� 10%d 1}:^ Eim<�$�"+� r�=&�!mu6.0)$6�AH'8� >� %6m�n,�� �^l+�s!!\��$t=6.1 $o $10.8$, *��j9-jɴ� �>*M9 -�,� 1X� inse�6�11%�Fd ��6�� "Z � J( . A�)$o]``Ew&~>pq"r6Agin��e� e. W�0on� �->!&)b � !O�=roplet*#4 $(t=135,~t=46�#A�at)��C�h�>49!�IE� )f"�62NB). Here�(��f[A�AjF b2u%�'J28��OD��jk/tXsenDa�&�2C'�&��9�2�R�}��:�2oJ��as;.� >C2n�"�t�A�`'ermU�Jtil� Wat a Zhea��uI""&6� *����" wA��w����5-�yQ�&� J�~'� l� �c � old $(&� 26���%�Տ wh� � &I r� ��y ����*�l iden� 6�'5t.  a\JB:\,(d)���i ��)a�)�"� *� = 50.81k>- �:�2 �8�):�3A� 6�(�r���� ���. W�U �T3s>$9E+$94.2$ �;�� �2� :�2}X 0j�bɡnx�9!l� n3J5�ū�T>z0[% ��I� �:ri�}��X(_ "�<:��A5*I!�6�5}%6�^|MA6H4Aoa��+��*C�N��:J�:@o�M�:� rupkL�%^woI�Smlet4avoid&A~6�ul.72C!�Y � b� �=�9s(6s�P1<�,<e�a��&c3A"ai"�|R#�=�L�ll��M else� ."� �${La-m)NX"� lp*��2t�gnu�code,0�s"�!Y�,� b�p qui"Na>�~ia� �@001<* it oCs 8� �4H reac�Gf�N�� � x �$4"�$� ( $256$ grid+dAfea M�mo�M% tudy�y.i �J Xway.k� x4rA�o P�/%C * &�+C�.ap,spa�� &� �� D pathK&o>&!/�#N&se�arbitrar�%��q��a.k�oQ � woule euGo :�F> �%�u!�6h18�!�n�i1&jphysical-� ��in"�!dL*�O. On�4^f8*�esxPa @ Aa��I�L 'lookT (through' a 3E�la�� *�=�y a S6�II�. �+�L)��H~.E2�  (*d$m��$�d Q:)�/[� is c��^ai�t� 6� UA�mor& nounl)�� SiO�J�P/�J�Ii;16 +MM"�J +eV /�<�J�( 'swimming'az!.%��=es-V�att! �A73�<^j�;R��librium�)pAr�"ivale�of5a� figuZJn�6"�SF�MAP02}%,maX;copic�K5�cap�6y�)o.jS.G meso K�A�BR5���%�T#�����r underl�$t�molecD-.TsQT8IxW����fo�<��dY&��Con�<o�I�T�J}&6 �+e] �$v٬"yf�� ��I�-  �E�6aP/�Pn�Sq��he�4%$>a�ISwB�sN�!� ͡�>�so�Amal�9J��Zbe writt�"�(� �"�V?priate LF020�D:� & ��I6F��w��s �bX I\BiVoNF�M>a9d)]i2PW B"�d]�U&v5�J�-lrt@. EJDif~'jK�G�B�We>� may *YRP!�,�V��Y�0 \det�*E�0 n�QW&WeB �F�U�)a�>us�Sex"�J$7*~U ), i�E"Y0�'ͺ regMe��es,7no A�c�Bl ent,9!/ �Ea,� th6�?$f ($\sim10!A) Cn��bei �$sol��{ �feIk���Nes. IBpo�nn�& �n�:�� be�)C4 � 1�classif�%!�(z"�� � "s # e � pa�$ I�*-A%m)�a '�#B>MqM>�a� � �V@ *V@i�occur� &W j�.�I�O)����>� U�W���*���%�?�,acA "(�&!�os1e !��R�BH,"J� �s>�ZV �F��Q)%mfbB ���F<�I.�Z!��[c{i�W�ro[��cWd�� ��Oi� ick a� �. *�W�R�Wall%(��A�_ٜYi=�r!�l�� i�kNA�KI�rs�$s� Y 8�f��%�&C ���.&�-$ ètRŅ��ev#z?�'�LV% y�.1$ u�A�f_ch&�ruc�h I�� �3n &jy.�[h:%CAa��-Ut�C�4m� >� �>g-��A�� de{B�[ �d�!���6��9�;PiI���0�"�. ���H%(a��a1�e���e dura�-*.$-9�* hree���R.��M6 g Vs �6<0�N:�� 9.&�0� �� �>-)E�!J:�(�� l# �&5Qf� ac�%P^tItx(m�2�[Id' */'K�1s�@� o ���5�4 �Hto� ���%&��m@7�0�)��`e ,by (i) jumpAae) o an; !Ub&�$�Cby (ii).�Ta l$l�5. C.�^�9��"F�6bw*Y2&� IE�!T!�u�EEP;��%7�9 &� s go ��#q�1Wyp7 B!�!mC��} out1S �od,� �a "3�%e�"�9�5� ~i�Jz�B�%�V !�� med� � *'a5eS�)\ A 3)-*on��I{e l ex|eF�(ex�Y!E�F�!(�B = 30$, 5C Z$)"�I�/9M�3���`u�;it lzP4pDo",i �7JN� �2oa�b$ of" *.^*\�! &�� �Zz Zcrg$MSS03,PWHC�:�-sh- clarify =h*9a�D(or)-�)54�=I N(a���� '(;Yy a�� ROT�5%HxN�Tll�n@�\��)�a� �) meta*�"Kms :ZdMp1���"� !optim��P!2�U�,�Ds � ed�T�B�6�!�Q%e �<1��0 S�"� fro2|f? !�~dewettA�!.L� (TL&V !WJ"� =FCW95U9�Y2ndix ":C"��B)0V]cA`�� mo�PpF=of�6# EVOL�B w$A�wYB�Bxv;gma�WI: nd "�i_� N.� grad�M%j��>5T!\�9Cx 9C�Oev5��xiA�on�ODB97}Ttem�:ur�eld��inMth�y�>!��&1M�ver�coordin�8$z|@P, $T_i = a_i z+b_i$. 30yj�2\wB���� �&�R>5}"�we��o )'unH.j�9uo xd �7�?5`��g = d_t ^&3Ld_ts �n/�&�" e�Gp�Zp�T!� =y!�Rdas �is!;}$a_g z +b_g/>$ oundG �at��faY�4� -�u f%�A�F(%- flux�; kapp!�Ulz T_i= k6k&�K !{`�e_�on%�v�$i$-t�X6m�� 0B9X $T_0R.� e�%bt�M �A�#&Q s $a�!$A� j ��kJmab0 �\]bF�V !�=rFalpha \DyFT 4[t-hC")_g}{ 1}h�Z ^!2 ?o)}6lF\.�Ca�@�C� _i 2},~|[�R)1>�W 2jb_�T_0Pb_A�Ta5Na>:.�� �\,F(�1= -F2}�R) +|f�I&H $5�=1 - T_2%�"@;bnav] -�1d_xat -6�/1 -�"O/�)�2� �z9W27W5�>�H�$��e.6q��N6�3�Yoth�f�6i 9]ed�� A�� i��c?)ula9@�7&d�@eF. "�c5eվ.'!uGf�I�_i@L[|IBaU�^1- \�g]2gI.@.]2B], PZM#!�c�If�<�AB ����H�2 lows9�} .8�?i(I�{ccc} i�Q-y�1} d�L1}{ d T} b &~~~& - #�= h_1( 5M�g}?2a�1) \\!� �2}{~ ( bc xC 02}h_2b ) & & ��BA \{ ] 7� 2} (�p+�Pb )-b j�-�_H)V �T"<\E� #X� }mxaF�)�\)�]���^����L]^�$b=5� (1/- 1 - 2)$ |4 $cA�{d�x(1f)\}$. VA��G al Mc=goni � $5�{a� / dT�L2}reR �Ctv` .Lm_6Ffd .!&� 1(L"�/-<d� ��1�akr��1 �[v�DnewpageqYDthebibliography}{7|JxpandJ;\ifx\csn�`� xlab� \�/x\def\ #1{#a�i �UNGbibO font>J�<M#�Pf�Q$�R�~R.$�Rurl^�url#1{\�itt!<}\j= urlprefix>O%8{URL Iprovidn]mand{!\(info}[2]{#22j:!eprint []{S'} :tem[{2�T{Cazabat et~al.}(1990)R#D, Heslot, Troianu:@Carles}}]{CHTC90} l(nfo{author}�5�{A.~M.} �1��}}^j@ F.}~#= ��<SJ| �?Xand �j�P>�12� jour�R{Na�} E2bf%^(volume}{346�a� s}{824} (�year}{!�})wSbibN�Bro�/ d-Wy0and de~Gennes%�(3)}]{BrGe93��By6^}� }�%A��fBC�ZFHJ. Phys.: Cond. MatjSZQA9RP3vPertozzi.08:0$A8M{\"u}nch, Fant]D!�mva5BMFC98�| A.~L>5i:'^v:6��?X>? �}},e�24���u:%�$ Rev. Lett! �vND81:�mC516V�8r�Reitere.2a.9�|v�G>28er:���68:E �75R�2r�VanHook.�5:� #, SchatzE�cCormic wift� SwinneyA�495�� S.~J!�.6;ook:�V� M.~F>@ ��? W.~D>?ےB J.~B>B%�HJ�5W!z!+�M�:75:�M:43`J^5r<Thiele.;>  ", MygE& PompeA&TMP��U>J V:�^!>��ڞW>N ��%�80:�-�28ҳ Oron.�7:� , Dav <`N Bankovo]o�� :ZU:�V� S.~H>4�ږ S.~G>P�V��HModIn>9:�-�931Rn7r2 ReynpI}(1886�Nyn �pO>pLZ�Phil. �O$. Roy. Socn�177:L �157J�886r�$Sommerfeld�<04� 1904��A>�: NZ�Z h��5ZmV0pfiJA SharmaaE ��D %�ShRe9��F�S}| �Z �vJ�!lloid vrW Sciv'Z�383J'99v'=6� 93��` 2` Langmuirj�Z�134V{ v+ Jacobs.�> " , Seemann����( HxW ghau^ JSSH�-K>9 f:5V�R>< ��=Bz ���:^2!+U" ��14:���496V�8r�� .�>k #.=  , "i )�"� ]497�$�= �= n� ��{ 2�9�V�= |:5Y�6= 4J. Fluid Mech.<^W34> �Q;Vv vmY U;2001{"� {a}}:� 3��[�E: q�] �ɮfs��S��5�F��u� Z� 5534F�!�}:�j^ Ruckenste�!nd Jain��7�RuJa7�VE>OV� R.~K��.U�Z8hem  Faraday9 IIr7L B13��E��7vK Willia��nd� !M8uWiDa8�uMJ�W�Mn� �j�U�!N�S 9!F.N�\220F�198v�&@(1985x deGe8��PJJ NZ?�L 5Z` 82N` 98v~Yi�gio{JHig1H�9�Y�wU�V4N=ZV�Y�VSB%F-ϵ�R���Ŋs A<^���M)148J�198sNf� �� osenau!>� OrRo��B� R�iB�ZwJ� cf�nFS[j� 2:I1:Z�vc� � 3:0�har�PB=8ma:��Y�� Z� 8Z� 3�� �>�b}}�b�y����358R;6��j Mitl����� V.~S>�;i>I 5��415Z�49V� v�)�� Khanna%�8)�Kh�zb���� ��9VDB� �Z �@Ŋ�346V�v�2� :� ", VelarwFqNeu9VN0�!v��F# �9S2�%�j�B� �2�U㮢Z'01610J�� n�Sch{\"a}!p!~ S� �200_ ScSt0�_ B� .Z�-B��ZHEur��. J. Ej�^�4Jm !rCI�.�2Z�MAPomeau�Q�E��[~� B �:V?��V=Y>� �� 2'��M�{eiu,@ Surf. Aj�20Z135F: ��}a�!r03��-�ߦ�1Z� 409R�v�0!.�>�$ , Gr�!A�,and WitelskiA�BGW���!�!BS�ڋ T.~P>���Ճ5�N�6arityj�^Y15N���Bestehor&� 2003:r%�Pototsk)Und�7el�mBPT��M>�\�oB��ک��5�6QBj�33:� 4N�!s�!qKnobloch�<� ThKn��b�E��lB��Z��ica Dj41b�1J1 20z1Q6�4:F6�)4, U��V�)�!��PB�~Vn���:��9b2�%���Vlb�2�UꖰZ138R64�Golovi�� 1994:� #�,Nepomnyashch��Pismen!� GNP9� ~A>� b9sjaAJ@2�F��LJ+M2:�*�2�ns9^��Y8��N�!}r�0Israelachvili�� �� J.~N>{;RI� emph&�+title}{O&-Nand� IF N/ &$Ppublisher}{Academic P��.Ladd��don 6fz�Hu:w9 � RJ�';"�(RF�9�2�0"� �c� vol.�-E�-2�=Clare�1M�=5Oxford.:�e6�.�26� 3��51�VB� ^Mjv=�����.-C�-a@^�13:�m�492V� 2�!�j�L��o :�0Lin, Kerle, B�AIHoagland�"2,/�s Russell��Lin� Z.~Q!b&;3::�VT>p��;N�0�>DJ71�AB� 6+!o!i�R(2B&;�u�RN� 5�2�ղ�w!�b�^� 237Vn1r�:�>k.� ��.bI�52]4����ڬ��V+�m22ED�.tU-M�V��esjP 3G".C��3972�ɳ�� Merk&�5200>�/!,&!�+_I'&D ME �(D>�d��� �� � � "� *� 5��C.�(note}{(subm�Vd)餅�JM*6Q5*�1�6x6,,�:t��an�* �5è pf$��52�V�B�M���ei2{. VNC>aR �2�u{�368R�"z-Z �.G>�!!�ta�� C�[/ ]{ZMC��YJ 2Y�iOJ$M�ڔ R.~V�.��V��@� #26Z�13J��� �e ��#0�CrMa00�r���n�.U�:�( b�42Z[2Zv=:%0.�>�!,Q��L War\}]{MCW�t�V*r�1P2~%�jM.~R.~E *.�ى�B^�!�^- 46R�8V� v�Da �*�=8rH/!PaF�<, Alleborn, Rasz�'e)� Durs�:4��KJK7;v��VJk ��?N>/ؒ>H>>9 @�CBQ-N!{AS6<d Eng.~{15Z228N 1998��%�^Ln6�/�)�&oyA��V�1$�W�WSJ�S �Y%�V��������I�2J#>�A\j�I`2�:� "�8noE�q�j�4�������?�?�?�?I?3J�E?n10Bandyopadhyay� 1� ��B�8O��R�Sta bahCynamiIsbi�Q>�"51R�3m̶r-K��;Dep. �*h, Ind. Inst. Tech. KanpurnaI 2y2.}a�6�42}�� &@A`~q��j�B��� B�1 �5�"' I�(n�%V1D �# 025201(R)��!�jUWunnicke�WJ :�$�.D`ller-Buschbaum, Wolkenhau6 `Lorenz-Haas, Cubitt, Lein�(Stamm [�O>� 8�m�1V~F��#6��JB"��AB�=-�AB)a�<V>F)���B -�A&5�U�1Z�851Vv�"Mo�ou.�>� #�r4�[��MJ& b���������~@-9^�561��&���v� Fald&�'19B�F!,�`posto�vWinlFU[�tW��N�Co �A�" K.~I>N �A��I4J6485J\!irG LambooyuI�?:" #, Phela�" Haug�E Kra�+��'‚�B� a9ej� K.~C>S ��?Bl��%B�)5 2��'��7>J�11�>~!�r�Pa2�$>�>P�OE�, H�-�U�]{a~� Q>�Pa���*VHJlFH��ec2�.TVM�E�5ڎZ�175J�&19z\>RenU�200>�Q "AEN �amm�g Hinrichs�& RMSH�3B� q��BN��Jb���B�.!JF��Z838J!�r�yU%':� ", Bugu32,R��MBB��(F���RB  ��vBw>�2�u� EuroXy�ZP2ZT34�[J{v�.�)ii# ���ski�(� NeSi�XUB**6cs(A�2���V�IT?-�:Si�R(Pmm-J. Appl�I�dC5�E��49J�199v.�yR^7%^�mE�H+>#�$��]2]Q�5%P.b�^x�J�-\14Vc7rdTeletz*?198>�$�iN )�c��- TDS8��TGJ�Q\�  H.~T> �pNL%Jy��aceQ�c�:� ej�2Z�?Jd8v�:Deryag�DL�[�?4DeLa4�y:BJ�X��?LJ3 �ZA Acta%AicochimnB^�'63R�4v�' Verw��(nd Overbeck=-4=VeOv4��E=-~W�.Q [֖JA��;>v���R�Td��-8_&�$of Lyoph c�-9E��*�-Elsevier6�"�- Amsterdam��194v�Ohshim�>7.�I�R hsh7��B�8W6�u��"Polym��25b J� 1�F:�j��(87�5�?��2NO6�.�j Mant#?l�7Vei��E7�1 MSV8��EN�AZ�{B]<�IWRtL�le Algebr�QRSHTeubner Verlagsgem.schaft.HufLeipzig.qd72r��") J #�Ԃ)�'<�)�)�))6k9n�^�<3N�[!|r��d5�19BMR!,�T%�itthai�Schultz� 0� ��V� M.~O>�dM��V>B/�S�(�z<B�0 ���.?` ��n V�J>y5 2����� .zL 566J�/!�r�=�razza.�>�%, XiaoJ�t�ck��, Web�s)�Penfold!�<9�,F1fe ���B���:Rm2F�`��AD EY"� B-�AB%-K�tQt5�!�A�E�Ut % ~b}W6���U�z� "�L�e�L�a" EM9�" SJ�Z�e�EMfo,a�^14oF9�m�34J}199v- ��.�.=8� 6\! 0AKe�i�Kerneve��7���BD Y��H�%u= �?�t+E�^rgB!t.��=muInt�Bif�"aov#<��-�4�KF�1%�*C !�jx ):^�� ���� ��������%�745A:J���9F�>O "(, Champneysa�LFairfrieve, Kusnetzo�*andste�K Wang�V C�X��B!�y�j�BL �@B I5�?BB| 1K?�[B�h)�!�Vx C.��and�au=� SoftwaJz or Ozr'Di*L�� al E�rbčNz a Univers*G�"$ �?M��eal.y�kzr�C��1 :� " , Brv�:�7B�<rNB��~ ��&VL>� �9�j�B� �?�8FQ1 !(5�Տ�� �����͍2Nt!!�r Ma�v*�::�%x$Adda-Bedia<PtM��_�ݚ�^9k�V?BY�@��Bs���5�J�9 jX45Z�4Zg&>5wt:js B�sP�}[ht] \c֖on{ёHam_T&‰2F�8�ig���di�J����{or�)} rB��invߘd g�s. a�>zruledtabΒ�wc}Ϻrm*���%�}$ & $ASug $ S�$ g8�$bw\h�uX $n_s > n_1$, $n_1 < n_&vn_U�n_gU+ &-></<D=V<-@`yx6<0< = 9}:=/y� V<@ �E95^:qI8�)� ^I}F�A� �>Wp� ers.5�:�tE2�S�!�5� \'�s 10^{-�\{AN%!�%Ej&=x`S2,� �1.49$ A}3.8 -23.022l ?O.�.@ & $-0.024Ar$0.15Z?S"ė ?-1.83 542 �1.2 ?-�%S :v !l��:�w=� e}[H�H Sketc"��prk���wo&��s�x: ��:R��,�total 7��&���}}x �7��fig�� � MH 6��s��y�s"$1`�E�fi��couplg�$E�R�yS��� �=t"��*�)� )bwHry2�O�-=�ank�e����,�di䁪). ��|�qby^�"̔� = 0$�<��Ƅ��$k$. Di�udot-d rrowsg���0�V��N���e�!1}i�nd%!22��!c W� c)H!5#�at $k=0$E7.� (on))-. h�af�terse����n��5E} (k=%��a ��M�:rx���5�s�����U_�W�_6"d $l�$.#���w��� ��$:����!�%�A.. `�A�uߍ����X1N-M%y��=�z�=47�{ $\sO� =\mu=1$, q���k�V15V = 4b�:X0. Panel (c)E�s9!� ��I� ��$*�in��"�" $�0.1�ƋconveniX�we ��4 $10 1�j a) $22�3�0�I nX"� %ą� �]"�%���- �5 ��!(2}�,%��&� �,�s �-F $S��qΡ�h]�gen�a�s� d�t.�arH�t= MOȒe F�$�  = �!,�= �) � = -2�2,:��]�S2w�~.IJs���,EUAF(dr���F~�s I, IIV(II!:��ťr"��ly2�� P��Mj!p)�=�1,~��!�V��� 2Ռ le -� (hat����a��1��ef��A)�DŐed�C �}ԂؕY>�%Cb��22F" �3�.Eb"P��� is diX~�� �|�quali~��.�ub 8s,,�scrib:%@mL�ext2��1��Snapsh@�m�e *��yR�%Ł�A�0, ��= 47A�����2 =1, �k =m���a'$��qN���-� l.�do��is $L�s *t�aK!�in unL��1/�_m6�1�'EQJQ�im�X�MA�ˁ��2�� -.���W%o�gR���-K���_.�}$ =�9�&?�a)�\��TӤd�fi��T�`�b�������e��:� �l��&O�.Tv�sA�>,���ߓs $L==� (3�!�öz}'),34/36(t�>*�� $L=26+e` sR�nOާn b!,\)Vfi´b)2,��Ch"-�"VS!�=�od��o��!�&�A�6� 7}. *J 1�4�i��m������[Q]F�E�, u}����7!��0U��B���*� epen��| �Z�InRϲ��s��oo�l�� mark��M�box2��'����twV��.� �5108.28$ V_�)R� W �~-�rel+D�m�A�ar)J"��{m��.J�7� %v%�b)%D�*v�_�!2BO����s��lyp"� 9�� ��15w�� ����� A�� �F��%�>� � f1�J�� b��� �10a��e�L i�AJ� }�&��M߁ť.�^�^�^|h periods $L=\lambda_m$, $L=4/3 and%2�, taken from Fig.\,\ref{fig12}(b).} \label{1} \end(ure} \begind[H] \caption{ Characteriza$ of the stary �ic solu$s, for' system6:�@0}. Shown are (a)0 amplitude2hPupper layer $A_2$, (b ,hrelative energy $E-E_0$, (c ! norm $L_2)4(d �integral mode type $\phi_{int}$ in their dependence on�)� $L$6S2�SThe two.C5: witQ ( $L = 50.8 � ,101.6$ (cp.\>UT2}) corresponding to o�A5twice�(wave length1i8dominant linear)$Qd{max}$, Zec!v8ly. To symboliz Xcoarseny8process we show!V!��%�wo one-U(s)B`Lhe $x$ coordinate isJunits�:�6�3��Large--�((long-time).�profilesE��< Si/PMMA/PS/air M�!�L $d_1 =30$, $d_2 =39 1Rm = 13M� x$L=26\xs'�!1lO2mf[6f5q? = 246I@ f�R20Bge7f2e�Fl7Bl11I� �1>f Ed)kO!9PDM)>V�Fe557 ��1B�. ecremaiI� arameters�l$$\sigma =1%�mu!�$,E�$S!OS!�1:N4�NSketcuZ.Ca gas��of finita;ickness6�5>r clearpage��pcenter} \vspace*{1cm} \includ��tphics[width=0.7\hsize]{PBMT05_� .eps} f\{4[ {\bf\la->|�}\\ Pototsky et al., J. Chem. Phy��x� \new��8F�2���2����J�3���3����J�4���4�����5���5���;F;6���6�����7���7�����8���8����6F�9���9����J�10���10������&���F�1�"1���J>1�"1���N@�"1���S *S �"1� �hdocument} ADDITIONAL STUFF$ A�h already�n_S�on~Elr_ , be� "range P$,ion regime a�-�8film can not b;bi3d (dest ) by  ely changomea�$ es[@i$. Consequently,�an unRlew Agrowth Yv lea  eigen 8$\tau_m=1/\gamm is � even b8ility threshold�Yeff!>v3e)s,{roduced!HNg. �|9�6=5}�o Z�as func%��low"Kt1N � $ i�o� is fixed:"2-� const$�� Y 5)�2Y7$ \ �2\!�1 Xb). B�4indicates that�maximal.�( is reached%�%�appro0tA[equal�es �\ ' d �$, i.e.\ $d2$.�'fi<[h]�oI�_A� _modr0&|� :I�$U� {\rm!�calculat � V��Q�E�value 5Eq.\,(e�4GR_RATE}) vs.\-�%M95A0=� 9�)�>�4is scaled herea�($(2 \pi)^2 �$_1 \mu_1 (-�<)^5 /A_{12g}^2$ a7zndvAd_16;:b).���^M�8horizontal axes��A� 8a �i,in�}*S>��t% \��dclass[prb,preprint]{revtexU0usepackage{gr�x} .b�&�amsmath} \parindent 0cm \renewcommand{\base�str�}{2.06��$} \title{L�theory!bounded:�s�4a free liquid- ��8erface: Short-E*�1a ev)X} \author{D. Merkt, A. "F!�(M. Bestehor0ffili|L{Lehrstuhl f\"{u}r T�etisches,ik II\\ Bra!( burg Techn PUniversit\"at Cottbus5�Erich-Weinert-Stra{\ss}e 1,\\ D-03046 2P, Germany\\ e-mail: m�,@physik.tu-c ].de} %�U. Thiel�.�HMax-Planck-Institut�ur�(komplexer Sh4e\\ N\"othnitz�38�,1187 Dresden��I abst�� } We�� iderY�Timmisci�i)�s*0fined between��and a�Jrigid p��� e dynamicV��nS�describ��arbitr�";s� a single Um���derived��s(basic hydro �-s uII�e�'imL(. After giv�PMJqin a g�al way,focus oq m1 inZies d�n�Tgravity, thermocapill�$nd electro�8c fields. Firsti stud�e�ey discus� especiall +c@!.�!u� ��by heat�Iabo�(r below. SeJ�us vari�al��m��: of�N?��d| an����8o predict meta�� t2!!!����0\cite{rey}. I�eiY^F"� 5s=u=!:a7 surr� a��is7#neg!P�<so�5�  dTmin�!V���%�. A si�# fied9�!I)a1c!�E-?baz de�@�.� a�%�s becatXveloc� is enslav�&� ~,. Several me�ism�knowna�*�a*�; flat!T�. A vee�.sL �oiN�isR � ${\sc Oron U}-�oron1}!bpr�#�0ex �L��%�� sub52~ a�-.�X�" d�f Ma� oni flow %]d�,2 �  It w�� �A by �Sc!�n}� � Ster���ScSt64 !?IBby /Go� s SKelly>GoKe91}!S- *_ y��e s� �>,I�P,,!�a s� ��1�y a_out!�!�y�w c{%rn us �. HowAZ, see�lovin1!� NP94�a%>EC�e�a "h �{Yf �. %�� �� behaviore�.:��i��!�qx%�� ��-�%� Burelbach:�b}.-�Deissler%� 9 Oron�d}�w�-uw [�+* a؁Ra �q(��ᘁRaI&!�&����avj e.�Xor Rayleigh-Taylor (RT)"f.%_i(/��-md*=(fU+t& � tempera�( 5}d �)!irepla4U�)2!�%zRosenau1D�2}-a quad�cy,!S,reby inhibit�� true)4ruk @%>� si� �; � � �d%d�u� �ɶ 00c)�)�wet�%�q�"�>NesAL� ��er workikntr� ��^toward�lm� wa�a�  l.�@k to � a�prek � f&,< in2.*N��_� also�� !�&� ! the e�,c"Q). IFre>% �%�9Y $Knobloch} )qtZqSmo *d &�� �����a}6 �E%la4�froyed$=  raN  sa� l�) of��A? M-� ceE�+�in�}il�ul|,A "onR�s� 6�in�06� by�V$Ruckenstei.�Ja)_RuJa73}� siIs� be�&%�dewet�Lm+& mole�r.HA�aiJincorpoA�\oA" gover�(> s i���n add�alA�$ssure term��o-!oedjo*)r )�i�ed q�Derjaguݰ(A�an � view��)Isra92}�I�e�Eplest c� itO, ults&� Dapolar London--van  Waals�p�o�cesM�1� Open qu�  rega8,g)|�dRo �. summariz%g Ref.~ �iA2}.&G ��\ �a š6�.�$to avoid '�o'��peqa.�-A�� ���ofYWiehas&d cha%erMN�� a wel C��JIlso�yjE�%B&. One!�uishep ��krt����?nP- uQ��v X�va n!2 i*� 0� whose typ�3�.�e+ ��4 A��yѴ�� s. Oy�is s�is {\it� �-�$} although ��]�� # tot��, buta(9R/�i�('dry' partsa�g� 19�5�A��qQgo�N�2�� -6��[er%� & spa� )Js. Evi]ly,. 6*1t only���!lvJ s�� a so�suit X? � n !=��1d���s]�- &V��. Tak�" ,� ! J�o�o �.#��J�-atmospM y} a p0$of coupled*����A�l% ?a1�Y s. Sa-����a� "�1va�>A� pY q� ODanov:s d,(2,paunov}. &zpathway!I�(E� avong-":#O ��in*k�p" 6� poto��N i` ch "��A��� e�and} �by *�s Y2ulM���FZ"t�.�1j1�vis kindA�trec )�t paper"  A�i&U�QS��3ur�ledge��yetu �e lite| � e existumber��s� �|E/Yiantsio� IDHiggins� yian}�5�sBX &�y ���De�? ifitEi61�y�l*��Px���eXq U����q�bl�z �on%�ey�1d�t!qV!or)� �!Iw @ pMV&_~#viscosof both ��W  same lof magn�" tAact�obt� �fF�$U�JM. B�s�p�5superpos�� �exper ���i*B VanHook:�vanh}-ǝ .u�&qs.�A�m*YDies*o�7!� oret4I����s#z� .���u�a `�eBiot i2'A tak��ccoun���� &e � "�J! is gC,I.��@�  lsoE�s �n* o"<�F. �imi�  "i��e� Burg�76�]!}!*6N  k �aB�2R oil-�>�j��� inga�m�� . L�8Y.� j�%��x�&�2#��>���� Iҭ��Smith��s �&ur%�ol%'Sim�; skii*�,Nepomnyashch"� sim,nep1}"� AYj-z!�2�i�2 y0 Xa weakly��}�q%Ak9%61t6 5o .���in�� i� . Ou�X=:re� <)&�  �direct�) ompa��ir�gT��B:"�'occurr�a�26�a�� "��ȡ� {QiL .� grad�� eDb!7 ��.�2Y%��ɢ��In� i�l 2Fcon�"!nn y�-�m+�!@act�&�. More�,I�Tille�7 . alQ��ey}}?eAm�� �ڥ�aA(�edr nnelI�.-d}bQ��irF��{ reveal�mod�@Kuramoto-SivashinN8Q�E�bro�>r"�al�<me� Tw.� dY%ctr#��&���pac el�$s � >4*p�"&J,o2/V 6�trough 3.�:� ce a vu �= Et�M g���tv-n� y�J �{�ongly� W > �� . �Majumdar��O'NeilU<maju}<os����� metho� quantify� ~"# vi�e�-�d cri�vol}�8onset ��� A�M���ohaQ#6� mohaJv �:�a�9I�%@an Orr-Sommerfeld.J�a�b"!6��&�"�k s siA Z��!jE~. �� ��i��di%$Q]}%a �M lik� I!�ba���U5-M"!?*�:a"x= ins�%��zE#gi.�Melche.z2im�I �����jet�.a�x�"2#F`|��0avettaseranee:Vs� 6�1[ e�"�film !A* # *)at�%��L �i�e�E"b %��L*�� lin,liIҁ�Ŗ5 poly�&-0 �� ���� �ugg��UD%�s do \.�#�$thV �N1g E��"�.ed&d'c�.%�confir v"����  C� ;f})e%� >!!��#,sk[-v 6�0���2�1� q} w5� 6)aDr� !uw9(��!L.�n�"�MJ I�. Keepa�rHA� �uN.s!=�2�!2�*�� U��� q�� .�var8&bod_�q UC^p/"[+ on��*% A1a��,*�#�is.z�΅�o� proble� �e�XvFita Lyap0*�* . S��D�_�*d�ty� a0Q�9 $h$ n�N=�cbeA�+ed�2whe� �&�* :�*�c� A.8$t\to\infty$. F� !`A�iscuss�2�  6�+ . %!�2�.is}�&+q�!��a��a�+,�-UV..�,tF��� %�Q!&4!qmay act"�AL�&3\  on madae#� S oD. -,w��|Hn he)*��aSt� "a,s&_,6 n�k6G,�L�k�e&� . F� �,*)*GI"s1;Ip!�BI9,%60"M �in6�&} [point U# possX0�) , in� ? �i.�'�~u�; �"�Q|! Appendix!� ���rtl� subtle:�I&S m�8 %m �6� g&x���2D to 3D��.6-G� ��es"�4�u%�K-6K-.2.�9-"wy�*�1QA��J*� "�"/! $d�Ga* � h�# t $h_0$ (>)0 ��!�aQ7� spac�AB'a � ( $h(x,y,t)$N%\�.E�45s}p% rM,��"��S�m�I� aKA�� i�:\rho_i) /32w$57i$��eA�,scripts $i=1 :$i=2$W ote # $1$�Jw:�6 2$ ()�6 >�K��U`/l�At:�� Ey urb�� se� �#�-� �C"5>( $\epsilon$� �. We wrin � �1 (2D)a,be�Nsuby#\Oexp"Oxeqnarray} u_i & = & u_{i_0} + � 1.^2 2 dots\\ wEwFE>E6EPEPFE>EE�1��I2  % % $uQq$w sta* !�$x$^ $z$-�A2� �iQ32/NB� 5Ј = \frac{2\pi h_0}{\Lambda} \ll 1$ �� e f����u�*�)IqA�|  0��� �q�GIt�*� "o ��a:w $ �~L qh� �c2 A�t /, k s����f��XN �$z=!+ z'm� x = )G)Bm- } x''Rhe���!�=u_0 u_iFA�= = wt ` <t=mu_03} t'$,�� s��A�1끸1_}�=Pm � t $\Phi_i�D '�A��&� *D*f $\P^c } \P5*4@!+E�6�} '��p�0����� lessC bl* $u_0A��8"s(mW �.~1�l�? u"Q! Staru �!Nu�6A��%p 0Navier-Stokes��}2?continu2 �@!4 *��-�� :u�=� zer�:in��. [9��:l Eqs"�>��)4� Rpndf=all'�\$O(Qp)$0e�er� �(W-�I��\�b�e�d�nt�d�#�k , $0\le z`t)$Z� Ͷ�� \p!� al_z�q1ͣ,x \tilde{P_1���G;.$ A0� �F,x �?+`z wu4mS�!5�*I,Q t) �%d$N�mu� �2 ���2�F��2B�`E,�2:�u0.16�Q�\�P>L�,v�:a� �u��p%�} =� = P_1k�� 1 \q�\mbox{�" 9�2 2222 �q�}�nE5re~De�ure2y su?*A��/ ���j#pot����# serv�W���N��$ (e.g.\�y�ce).� mu=�L2/����:xmt *�� !bound'=� +"�� !QI� /�GZ�MbFYQ 9i u_{1!�0,\%�� 0b -�t}% z=0\\>�L?RxE>x�xd.Fyb���a&� =qin�-jX#at���Ay�6A�"� ."-2��  {\� N} +a9 -�iB���-iD�Iz uu� GT1�i:t h +D>x h �w_1v\K�[62R62���� �u_2R���{wB�R��-1�$m�p8�,aabbrev�s $1X$ �� K 2 *>Fi1}),3T}$#T*A 6?*� .G2}��  =\�@1!� 2W�e p�� �J�"" 6��<��q�E .�1j,�3bm&A�FO5p��/ B�8$]ũH2}$ do�&d�b$z$ (2�- �Ge5}))�#�a�o@e6) ��� 34�n[. W*:��y.��bD!9g�6}�.�!�, � i5})69q 2/� �u>%`@$ icitA*mv� veluN$ u_1(x,zheI� 1}{2}y�=�\; e,+ \left(-h.hq - .A� + B + #(T} \right)zm�u��u_2Z�\mu}(R�A�� x aN} -�)\;N ft(�- d^2 �� �5oB <(z-d) \\[1em] Ɂ[\h {1em}} B)F�)G� -b�.�5? -. �mu h^�bL�2KI((h^2-d^2) -!U +T} h}{(f,-1) h +d}\no�'��z� we� d.�&6F G`� 2� $�&�� $��'� =Nex�E�ivol�5"= ay�2�t)�_ �'xpyNula;�4b�To��soj..>. e3�W����($"f%�o��C.MiM���ch�* rule!� find�"| mnev1M 1�t!�.?\int_0^{�}{�( \,dz� �DZ*)Z�#!r8so-�s �` I ..e6����i4�4The6%`0S�1�&* 6Z int. x�z+�Nt_1 ^d{��)"�; = 0. q@ {�o��1�N�M�)!-AŰI, x$ s :!6ionA&�tao4out los��i$T� can 4one�retno.7�mI��� a�dL(nc:naKY_K4�.!�* Q3gsold@ ��J�3&9 u�"t(is.� M�p2�.���F_1(h)u-�� 1�+ F_2(h)��T}5� vithQh~� } ��%H1}{D}(d-h)^2(h\mu(4  + ) �f�, �2C6�� d h K -h)\D % I 4 + `h^3��-2)+4d� 6d^2� 4d^3). p cf} Q��R< OJ�=؁z)Av b��F(!:.&u1� a2�m=- ev} :9 = )�[ Q)�,9�)�%�%�q� +Q%�\, #T}I].5 � % U� a�sq0�Hd�/w"� 3).U� P"�s "� ^�3d^�$nabla\cdot���B�.� \vec:�)��}��$ M=*y9Ny�WA3��F n 3D: �] M�%u,b�Pxe�ev9&{ $h�aly�(lyx?e PJ *ndC�6�1��C ��ed ua�. ")5we%�G 3foeHing. ���)o�/� arV�-�mN� I�m�� h^3\,i�,3}{3D}\,[d+he�1)]a�I�:626 2}{26h^2 6 -d(d-2h)]�mq2�� �y $ �|p�3v�&r:.U� mu>0!�d $d>0$�? van;a$h= "$h=d$*�2$ � $ al27_Fgt$Kgn at.�6/zc} h_csd}{\sqrt� +1}B�%��� {doD#�9 exis�:a�@R�V shear-�%C:�&2}E� Y� A plot0$�4"�� Tab.�ltabmat}k $d=1.3$��>he-A�s!of95mfBh_c�W0.91$. �;e�' �T>� ]9� � 4ed.@href�115limitm\to 0$�= .� m}) �*%.c�kc(;�6f�mlim} mG_{\"�$1}{3}h^3, � *{3em}� )�  I{E-i�� h^2,># ~�3d�a5!�)*I 'e �+fq��a+�B�S)��*�J�t h = -��\�[�% {`  P}_{1\,)B+����-1�>iSI �&� 6� m� N�6�Fe.͝A2=Av(=H.y4S��\��be U�� �An.]" =%�('y cer"m\ Qto �"� �" 2\ll1�kb#s � M%oP_1\gg �5 S)I*�[by.�.&|��*�d*�(�$2�#S�T fic �2ў AT 0KGI{G&�G�PD�G4I"�C� "5N�N4 (�4 ity); I?s� Rv%�a>Y� b� �bb�"ntR�"%pG�F(1-!�) G h�c�%�$�i NJ -C^{-1}iK ^2 h��ntp2}�2j: 2"i@$reby, $G=(� _1 g� ^2)/�� �!Q��, Ev=:2/1�$s1"denL;, $ �=�^3 \sn6sd� G1�y z%�$ 6!5"� "2�?:E�ByT2�Wit�Yu �"_!non2�*�6�Theta�#(en s"�>s)�� 6"��1 ^z-�t.�1�&�r ���R!&L��Pbt j��9desZyBd  �&�!Td-zBB��Assuma�xbi^�<%:��'_4&�O>'.J3J�.� F�I!�L � T}=�\S��$�1rf! �'ɯ6�i��ջ�% :�. E��� 6o�� p$oKel&- E+����q-)� �h ��B h$. IVj)�s �ar�:9r gets}���5�b� @ Ta M! Mx md ( A� +d) ^2#  h��)== m�M=(&�T)�0\,\Delta T \,1�)N�*�C *� N�V!�:�e�2�>�F$�= � -u {I-�1�I9[ &�*9�� is�>�|xG , $M�I4X most�(s (� ��*,@� ) MY$!��G � >?@ m9 T� C5�YSA��`$ %" a (�Mu�Ce)2bC�� Bi(d-1)>- QQ�D& �� �M5Con�Tr�fa�"�Da�]-�F$�(A�/us�h&-@oa��K� T}_ "XQ� Bi}{E� (Bi\,h +1I�)]�"� B�Bi�-�x2@�Z>E, $Bi�}in�_ed�:5F:Yv5F��) 4r%� ing 9��-e-1)}{1+A�2wB�-� .�1�^is id�?ll��enc"�$�2rG%�aOo$� �k A�{ �Q� +kb (o�&&�DiB�Q��To�<��N��),� �� �+�2�Rnj5R�JG��R�toI6l!��^s�?fA7�Qe�sM�will, Q %"�2l &�� {D_1�E�.#H_1}{z^3�|_{z=h}s8",*:82}{(d-z)><�Q� *$H� ��H�$HHadcr� ��lCi)ngg98a�Q*r ��� 2?8o�P 1p� a�IP%�261>626�-��S.1�*bOrU�-�b%R~ �f4)��� (#)x-�U��ZF! �\G�o&"� &{ e2 �Ja"FO(macroscopic!�tac�Qgl�/�;�1 f) vioYP2&lOJ*5 >v'F�!bpr:� KW�/�6sv+� s to)I�Z lyfY��%LN@ Not� am%�Dy /a�tance.�1[�poi�L��p3u"�WZ 5�eyE�100\,nm dF�"� ��aa1all>,se�Kc�~d. (Qs� ��A.!�  mY CZ�S\�:ePA��1!��;RhE�Eo1- �hAn�:`>�:"L ��z$&#�Dano��M�co(p?uc&\ � F:WL4 C�'&1�_bFx*;�. Gsi*67 �C%�permitQ $\vare�7�� 2��y����e�%�e؉ys 3.t! �odeu2a"F$U< � !�O�com:V(�!tŚω� 2td#in 2luZ�d�bb�e jN�E&f�6.= 2 U}:� .#1-} 2�2� E"[Fb1�b���H&2q=}b*v�sis�3!�&T )�of0�/A�essyorm�l=RA�p i=$c�t.,�� ' Y Zm�a����=�abyCjng A � �o�n�6J>�0� ve9iY"S p_{elB)�a.�0(.2-.1)A*E_25�&[ Scam?�&I�7U = U'\s @ h_0/.\0. 1k��4p!^�4,-=a9���Rg N}12>.�)U�2ae� ,99�%n.�0$2���vacuu�G.7�7��22OJ�WzFI:�0in&�:$dMo�)&�el!�reŲA�ent��&� A� on{E��e)&����O2�Zso{uf:pos�7*�*A r.h.�uH F./�min�4!EJsly2�&t ���k�!\; I+d/E}{ �Qp-]J5u. ��F��d�4jp�2"� ��V#aWx�siti���*#w�he�O�0yJ�U�� � $E$�0��  aN:F�`�>]&ajF&ly3} E int\! {dx\,dy\;)`)R��()j h�w+ V�)\},"( �} &x 5� 2} @�%�g�G\,�- � 2} h^{-2;?3Hm 28(( + E_{th}(hE�S(h)F�# �m >0 �3 M}{2d�- )�~\Bigg[}�. ^x$ !.h!Un{(h)�:C�� ! d-h)*. ��&^+:]1)(%+d>NED0 �^4 h p/�^3D)�?2�)2%d!Pj4p?�0mu^ �E � U-1�}%$]&W/�MMI�"g1�%� a�:�G�&i *�5�-��EXI0��F7�+dB�Y60� O$�bn easily�SHn�S pen,�W1}i�a�LF�Ie�Dis monotonously de"� w'ime ($ �d}{dt}E; 0$),_ Z+$"�& >0$  q.J& fulf�Sd..� >f�))��s5.�j &i$i l du-Y�%v*�Z|D@rFz".�l& $U�E"�U�A�@q�A on a�9a�I����0�,�&� :&!oaB&���G:G"�tR�=I�)ion"�G�J�F&�M�B�J��sp�I�I.�vLiW)� � �! d^��-1 :)Q�Z"�.�7k_c��t+ut-off�B"3WUe $!== k_xR7k_y^2�c�%�nA�la�r it8=С� chi>����1$k<�. O�W�a�I���g�"���F�n �=0� M" M%i���*�',B 6�y � ��gsttc}��.�% N�}"F j�4����$U!4�O 8,H{)I!��G!�)�is&�J9'�����K?isy���k($M=0$)I8Q28P>1��I#H,�'���gorv�_�M�>�\Z ase,.� lk})6�u&�_i�1�& M_c =�}2?-�#y�a�2�m�mu+d-1i�)#  d�  -��N& t;"�  +�O+�2O4�)�-mcR�/BKb�*O�!���{M"�m2\Y�`e��-��&� u|I�i�SIn 'o �4%�& � ��mg'�6rq term �0� �0 � 0� >�&�_e:l.3 2(1�38�x��at��b�1�"Ce�e0mus���rA��e� an $M��to�apu�. Deno��m c�,]#�Bh)$up�0$B�- zc})�%�in$!`��h_c>1FeF!a�hcdhx ed +R �D�m�*com&�p,��Z}+o<1$�oY� �g�% �> �X2E>�]if�&gD & >�e< e.�ǟmalX'xH"k z$6�%)�)1�hi�  (c y� io6�F,a�e*�Y��dcs} d�c\�}+Ӊ�H-={2R@�8)-y) �R�"����A. ,e�3 �5>A�*����At��a�:�43� th5�$t��[*R�T=1.3$, "� *�rwtcolumsF� ,��� =H_2�� &3Drh:�.a� -�+aG�-�is >�x��(�n/�DSi�M_c=0.89$ damp1RT2J (dashed�A�dX+>�ve )oՇ e8rf��vpl(d�61AT�\�`" ~��� ��lym'�!0�] 6�h)� fis N�6�QE&�Z]z.nF$t*6|�"�'��Ni� ��($h^71$�&J� ($M>% ac�8��#�'he1Atg�agram�OF2��4"�xwbdB��Q (.�cH=inJ���b��A�%;$i�aq" &$I�! �� (}��L� (� ) pa"g�e�s.0F<sB }�t0N)�� . AE=�y�eK09u�ZCch6Nc$)),� a� 22o�g fO%fac��N 6�!as f�a5��&� d ]�^Y �����!���ves dz�<>�=k Eus��R� V�!� Y�!w*#���  /!v"8��'vicina�-;d�(�" minimum.] $d>d �2�?"�/Da�l8�^"Pi��sӇՌF� C2B�_0) F2"�;�"�q.(.��,0tD�} � -�\!T)@�?way�NJ �arrЇinB�\,(a))� $d<9H)�Bs�~!lq ��i:|5ib)Z-W #��2�-��Y*�-! high f� .wQ��:n mpan��._!Ak"�Dc�$�(�@6C O f���i*��anc�B�2y\e�I���&:���m�:)��a�ay2)���:�^%y!�m*5�s"�;�'^w bae�&e�Q�m�I�E��!(ow^31m>L_�A+!�i1 J� �a!e: 2� "O�wL, play�66^��V�aC�". ���N&� �-�O&4��0>YKk"!-a:�2wbF�r���/%& � !#��v �Aw��ter��>���MJ�t� 3.34$+���!^$��%bt'd�BIoI�aӍon8~��JBR� �.u�I� .V(JP��8d��QecsA�I (-�f�6�6�  ��a yb< �::g YW�>to )%l. �Z*��fura=%8: =��z%. H�,,�> � agMt� ~ E>���wHM��.�2�|M_c|B C1�"lu'0i�0�$s's6 re�/.I� be*��vez,&#N�$d-1$b[li_ve� �s�n�q*,� wise�>�  )@�1]��B�-J��%c"� !�a O 6�/���/!i� 1mo*�/2)1+ xtrem�Y-� D6�Y�J�"Ɯ, Z �V2f�.�fi�"� x-o!Har"\ � �9�-�< � � >�.�$ �I�KČFIF�0)YZ a sl�S shif%� -RIt&* I�%�5|��i�1gio�%BoZ�-$ga$ S 6-�liy� ty�*&�|IPU�f a!_1J"'o'�,�. N�z!فf6� ���g*�B($G�aPfoE�>e�#�*�n"�!:y uc} U�\ 3d i+ ��%&f7-6��32;- 6![N�:�&� -�a(r�($\pm z$�;6_n�3A�v.�,��V�� U'e.0�g d=4$��!� >� $!Y��4.59�fU��2= *$k�B0.ʱ tL6o���$"��U se.�2���$��T�Y+�*m� 1>1l3d}� +.y!If�� 5uva�w����o}Z!.����YY�y1}))'j�E���+N &&ǚa{d[z 2a� �t �Dy $G)6b ly2} el��z/�! a Max�I��ǚ�s6�#��<�m"�u �Bul�Q KP�e�4%�&Xn#'�7 :�ns�n��B���#l�}�%%�&�N�!�&ww��t$<t�2nee��p!��.�#AK!�5��"�qaR�*3 k+)LMso�7A6ilP���A0U�c6�5� global� .V7�O.�l� .�,gyty( & "g��� I�sn5��Qc�1 anie, � L e some�else.+T �%?M�1(al!/]�1ra�o� ] &�h��a L$nge mAm plie,dF#_Lh &bSz pple\-n-N�(m<b�oA"�(_LW@ *�A�Yy� 0 !'ab��*qA9"� ]�Bq�*3n��lo�m 6��-JA�$vjU�"5 "�r!g� ��/eane)�u�0a6� i"4  slop�V�aKw!^p�Av=L?�;i�cДyE! n,  1�U}l� ��8��.YL (�*�$9 ���!>1� !�)�=W-Y)Xm 3 mass%:er��>r@l i�5 s�|1-o�Ig�ly)|��)����p5#C* ��S,:��e�a�t�Sa[��)] .R(At�tevʪver��-"�s1RE�)9"^��NK.rm�k&)j $h>h�q�$h< �� �# Hl*���!,) ly&-Bti� wil^>al%wo�>�zes�_1r=2�U�na��pinodal�T8'LRQ�wse�s$&4 phas*;��&P�ifil�zi��]:a I &���aMitl93}��th*A�����wy�.@�'if�!isa� 4��dout��n�^PNcurveQ�l��yA��F� �\� U>��� �#pu%�1�1vs���[\uc��F2��+twoM���F�$bFA��Qen�/s 7%U��)�!@a��: \J�<-it�.� I"q�6e"T�!out��Agap.�=�Β n i8��f�e ��2L>>� �=�n8i��val!�Vc   $[-d_h � ]$-$[h]$ku. /�}B�7pE�1s9j0as $S = S_1/S�mMa��r B@ ($m�$EE $h_2��)��iƞ��m" �')�rd?�5d& � A�&�w�ell $S<')$S�A�$S�$�{�.ropmat�o# s6�#.&�Y� ��p$S$ cl�� D1$'t (t�)t�} rv�s vii�� (�)* �' unti/�ۖ�7W;o�� e2o2$cE�*�F'^ ' ('`'��olsS�of ��. O�f1 12S�� �)A+(ing���vW��c�0a�)b!έ��;�ol��{%� the Bf�8�' <��V4��&΁� g�0��7�a)�$0pl̈f $u^��u>�e.�$��M�;a M$ (��V�6j+ n a u��~d!�&V J $h_MA�Qx!�p p�r red 2�#�!>���(E�) `]!$�~� 5$d=2$�=tra�4ᰅX �E ֩�sr@cAv2�#Wf n:� *isF.{M�i����incid:EA5! ·B�,%�.>�>�AsiW�&T�a�4vv2� � f�>�.�?:~d�.�M�s�#ɾ��� �.3&G+ soA��� >aB�� �c��ime�K�own). N<the�N� RT&� s�C6�!�:� �&R it � �_"a.? to�"� ite2��7.�m �ud0�euD � "s���6�e��U�m.)"�vs��N��-E$=,��I7RhfQ !K�I�Ag�$h���,� �'T in-.�G�u�a��JD�0$M=10$2�E����OA�l*/�����O��.��Ga7m� [" 0=�&�(�=�K3�%�$ �3Q .� (l��f,���.*���?_m)��]ql, 6�_E�3'��rf.EQiY5��6n"(!"W)�S�(�~)%� |% ($M<^)%��%M? m*au)�=y)a&s aBï�`F !�di* edB�� |M|<60$^g=I�\ w؜A 6z�U8z�1!}LՒqAjs*�&�0-Y%��Qȅ| ±��eZi�Nh%9fc�;T*^�.�w�9.�"sMsa�n $|1-h�j�w"8&��� �+ ��^�&6)61� �!.� rt_mQ�$a snapshotI0a �2�Z&q:ruGB�'�.ou��:�2;at!~��M��f>��g ���e!�3�"la �,:p(not A���H|�sg{�Td .�Am!�*=' $x=50$.�N F�oZ)mod��E2 B��:kTT�.Z��m��"8�/R :%]�:� ]k�an ADIahod (Ald�)� Discw��)I�io!Hvv+half % step%4�o j!�����itl9$]r"�V a#X)XzKy*zK. K���"($ �l�r�J�!�iodic+Q:gxdxiy Aio �� turb�E��i�EGI��om� ciD�9eta"���O_I average-�o�D ($\int{1+?\;dD}=h�O1F�"on@+d $nguish "fc�%�&��&� . RoughlyC>S�-�q9&q5�k nt �:�*N{�=n>U�,TN��7ER"��% *�pr��"o&�>c *^ avM�.� Sw��t"�9s,��x*� �ib4B���W��"�&�*5w�Z"�2t* 3 &I $G=5I��>r6 @�P the i�n�&��A�F2_RT-IniM�I�AQ��nc=�:�v�g� � are ($t�100��;� imQN��9�U�i� =����d�0 �pl�$v/g�"�gum�1.\Hi y�.)aXBaT� ���}$�0�$�$G=20$. �����<Pp�a�"��($t<2)- SA�"6�My�=9$� +~of �r ܊�"�qr ($t=)��1Ze�8E�9 �0>2\�s 10^5$,oEM!2�3S�%=I��M��$d=s}& smooth  6�!�J;. By ' /'�? �aY Bof �(a ��s&y�R��I a��tud�U� �$ead �{,966�rapid��- �m&�>� �A09�domai������z��a�F"�m�%b�Pd�m�Y���.�o�s� M��,o&�S($|э .t)|3Z�P=Ud) U� p Rl�(ve�dY��v���t )I!�id�q.�� { �\&�- tJ�1�'p�5 (N�&2=�#)�U�no%�e"�*�a��� .? "� 6'���VL� !�)$E "�]? �"u. N_E,4supvN�!9=mi h>1$�: �.k'��A�Y�$h<0*Wea�e�*n�N���N�s&�<D.J 1f7+nr�.>� _RT_M}YplæD��>�g�h���par�1� �1 of TB�nɮth6-%, nei!K��27��/-#f1 .�"�,���A�t each �� �.��"�beNjB�(km Ba>Z k \@�le\,(t)^Rf�({\�style� _{k_x}\�O y}}{dk_� k_�O<)�t k^2}\;\t� sk_x,k_H}}�[VJ>�=&fS0 hx6lSFouriB<��a/{�$.��#o �%�!]dU=4 ributed1���annulu.�:>a��x�IiotS1�-^2\ "L?)�hH $A�d�n�#>�@$ 5 O$��eGb9��k g��.G��A�VQa���I� %J/ Kd@6�$%:����:� �Ky:�(3@p� �N��dt5A�e�l�>�o��6�� [�!!�N2R0� fas"� ?%!�tb��>�$�[f! {�� $t_{mi�Vaxx|�82U(0� in} <5'�� =o�yt��% w�Lt9�"� -e�)de"�� out9 �Z�^me.E��e �� .mkFt�#s��prei(�bn[�)�&�s�%eEta^%�� � .D abs� a-][�at�M �ly�%2Uk յ��ve r��uni�m o��$ r ���W�U< peak�a&�e� o��few�E����&�ly�>Bn� IXK%�6�)A .�o*;%)al% r�:�0-�in.�(dG&V�w e��38!C �a�$tE�E�B� cg ,*�I��BE��� 4A�th � emer�xe2E� I�A�� 5�S.� �"�d%Jr=�� iWb� �v!�vf?q�). "� a "��lawk,�,f�0k>�:< = c�X$ t^{-\betaJ-��;�d� 2��*a m��!��u�*!��,a�#h��.����a�3t�' �?�QK�]���̡ber�� runsI&C ���#��$necessary..v��a� ime-pum�"V�? Y'u�=c^pR� ae� ��%�.�1� ��*7bgfBs1 �%es�.&E#I�&�|� �"mI�lv]1f s'. ��1a �3d> �+>0�$E't 0.14��4 ( &�E,ɟax"�115 V��1,�a�B4 21�Cndb !�@ A�ad&!B? 32Z N� a�M�29�RP�s�*- �n� )9� ac�}Syhll�ȡY�f�<� b�� AyQ�^.��9K*s" _l9!"} _2)$ tEEti�!��3tB�b,A/w����of %�AnFe} il�e�toF+!; p��Y94wo�.7&���ש nt��ver�'+�� &�{�f!��WeA������d�I�C)�!ighbo�l% att�#f �9A�$ong enough!mQ�lae re (Z) B%��* comb�&�nea(�IEU�?�PediARp�+O� l�Is"��A��}Y��#Z��A�Si'��� �{1�ce�%��;l�$��wh�"(%) ga�&A�black �.tFr� their edg�6h M�a �i�v&�Q" 6���o���!�v�Je Mfer +~ plac�Nh@=6 ean � �Q9 ��o��rgeig� DF1�m"�gwTP/�Xis �~��Yrs�fng eI��1s�>dis�����e�!dI ��-I� d F0%55�0�$b�$*���;A1�_le��I<oRmI:I  e:�@5 Q"Zdes��1expla�(!#�E����b-?8 �*���&=YA1in�c2�+_BK8A�\.�}92�})2O�a��Xme��� "�Is)�5*�9$[*��!w�� toppE�f ��,rd��/redlBh��- � "�v&�E$u"Ӑ;$&��$ �{ � �E.�cv+�$EeyXJ%)B/ rt_v�f�J(s�+� �1 $x��6K�J�6R�%�!��M1s tAu�Fp�am4�ephM�$��&Uuz�Y,*O s �ep�X�& a<��-@J<@J>�E ĥ�)6�1���ne�)ve�(I����H- m �>�E�br�Iv�';K- �to%�/4�L"T �<�a�f�ee^�.idv��FN�6jy &�%�(&on �u�?*�$8 (�).]A� ssb}!a6n &� act�s"&�5!&k%��1*O4BA�a�̱. &�F>�H�6 � �/N�#�in N�ą�hxrho�U!�`�e���. . mal1:�Y^&�(�M.S _c�> �F . An�~� rA>"�u>$G�0�C) % J�*�(."�$��,�q���?to��E�9�I�b��n� "�$����wo�K� A�f�)is�C1 -�!6); bY�!��]�)f�g*R0_Mu��� B�' $M=-1k  Sb1m� "�!�Yve]�n�� �9� ���JL �=3.�) *�af�\vdi"lZZ;*(*�0o1IO 6��K! .P'-�� @!$.� �(t�/�E��N e��  a 2f8ZY����"!b� 2�h�c��ema��M !�YT?in&f 800$=�UI�fyOst��5B-3 .~$*�su}p f�G ��um�*�4�#[/L !coeffi��6 ZktM�"&0be Bz6^��QCh�| 37.8RKnd�^a/70�K6P�R&MR,S;*���U(ejE }ee�mts#ly�&%70a�6�#mr � ;�ey#=11 $F�Et>R�n��y��z",\ Aji�0$t=2�#p q!"�UX&�a m�� �j� 0.51�-cV�u*)N: �* )�+s� IAM}A� ��:26!?a�irnounce�x(S �N!c!�_� !�%a.�a�q�*�Y�M: Cl&�iD�ls�=roW6��r&�� ab�  rIK�>�#o�7&�"N2�23�,T2>q�i�>�27&%mar�y)x{a|�.2�x�hu�u��f�pexu ==4��es �f&q$Jh_8+�&��-R"���A#�� (j�14$AN sus &2`x�a)| b"�0ooi�er�� �>#y�Q'A#=G�b\,Q Q'K� = M2m#.�W]>rMOB�"��4L#A$1es1"�:�4(ck  s8�&��1.�ro2�+1)R�a��`W"6Ba!�=!�� !�"�=V � d d�%W�$NA�(�7Kh>�1 �accele� �%C74results in a r�apid hole evolution. % For $d=2$, both mobilities show an approximate symmetry around $h=1$ (thin lines). Hence, no interface thickness is suppressed allowing for a smooth evo �L of drops. % \subec�{Applica *lan electric field} \label{3d}�pinally, we illustrate the tim=H caused by a vertic9 ated Qjal l. We us K8parameters from_�Xsecond column in Tab.\,\ref{tabmat} for an isothermal ($M=0$) system with $G=0$. % Fig. Cfig_UC} !�(s snapshots!�long-:� n�Pvoltage $U=30$. Initi�@small disturbanceWi5�AY4ve smoothly to)� and:�8coarsening sets! at $t\Il 1000�8The dependence�Hmean wave number on)��(n as dottedE� in F6&RT_K_11* a minimum �_{min}� 500$�a max ' $'ax'47�Again,�Tcoinci� s to2�f !�fastest�,ar mode $k_{.e0.18$. !deriv�5� scal!Q8exponent $\beta�0.04$ is-�compared!��6s!](sured aboveE#!4Rayleigh-TayloA�%�Hrmocapillary instab�@A?< absolute valuesaufind onlaWIWchangei)0 $\langle k\r =�)�=10^4$!GR'6'<5$. We conclude!�$at one cansider�length%BUd(pattern in $5iA�AAifrozen�!%�Q�!� Zof N�($2\pi/-�$)�least upW$�Ω% %��Q�KC%( sion�5 summ�3�ppqUsA�%N!!�|r�^ionA ha�Q�a /.� equ��fore;��profi)�,a two-layer �:bound��Hrigid plates. ThisX is writte��a gener��orm!�facA��6iA`!8D of arbitrary body��+�nor�� or tA�n�Y tA� . IIvanalysi�n�l presen�� here��%6focų�he influ�8?gravitya.�ity���ostat�>!aC\�[taDA�m(yM� �-stres��94 terms $Q_1(h)��8always positiveaNmlone-�Tcase. However, it tend�I zero noa�l%j8 $h\rightarrow ��s!b�SI but also"6:d$.�zl�( has no cou�� part�Q Qs w!�m5\increases monotonously w��!Ffili 0 \cite{oron1} �4qualita%'differ!�A�F sign�E �j���$ hear1�!� $Q_2!�GBo2� �#8affect stronglyGlin��I�n �. Q �nc�se dir�cA+ heat�neea��de�5zi� is d: mined b x%� cros�I�5g� Fur8 oa$shapes,AI�extrema:E� all� t��a .wprediv :dynamice]ky"� oA]ny�er8 investig�.� MoreoI�Őtr��(to weakly n5atheor�I!nep1}�+are able5check*$se descripE/ criterionf tegr)�* ful2h �\nu �ly. A�-�  r&J (� )9� in-betwe�he�3rts A1��� regk Ee$lready be ! ma��"3 tre-�>1�i�� Remarkab� althougha�yAfed �= �#-�A[issip)��gA`r= convM�a����s (�r�API s�ena���fZ A�le �He�reached�w of) J�E�s aa variE.�{ul ue� ne�8or Lyapunov funE� 3% 6c�#�^6 u�� tak� h��-�simpl� pa�bleY>�!�."a!`ser� orz p$ � ��PLang92,Mitl93,OrRo92}A�pro�nt re���is clasa���is�0Cahn-Hilliard�i&b���.�of �cea�� ��a bin��mixturem�d65}�co9sta�!�,I�i� � ,thiele},��.)� itself � s��a rial9:�at��raca�z C5y�i, name�ˁ o� visc�es.��C� � ]Uto� ! xpecajy� behavior2l2\e=,iY or maza0ruc!P8 �i%v� studp meta.hs. ��s�b��confirm� �� �Z��} ��*ER. �� � a�� J � we �discusse- �diAQ �a � Edala�>g �L ]�C.p A�p �;�f2,媁,ohydroM.[%ddA�c� liquids 1 �G"L !Q�� eMW �6+ �l may aWa�zaall as��I�#onN�)�Qs become��uT ly cl�be���r�� % 5Ifame wa�V� should beApferred�Nis ��% �f� ~ *" i�i� -- ��F���N2be�--Itto���. &� gi�� spec�Gempha] �ea�2 ?I�toUWe aB�u��:s � F�-.seemiY Z -in-�9�first yFin Ref6,  is� ypE�proper� multiK )Rs e&is-�A" orre d��E�of] �Jq H� q�6�98dB7 ����A��xplain�$problem en-'ed!��rimen�$ {\sc Burg� e�E.}�m burg�E) they!xld� a >~5� 'oila� air'�byJ��s was �IFl�� per�V1Q�al runsM!�u� �fact eUpre:�FGi� flat�involk8large amplitudeAJ"�. B�1��XI� -�t!�resul� y��ninety>�ە��*J is ��ia��� E�onEe tran(on� Eaoa� hree-dA�alճ�Y� a` �n f�7 aris�wWe neg�) �adɬM ( main�!�%�  work -�its4y l�= � 3ed1R.yI�m�u}��2detai�.ap! ix. �ꡌeaed�� sche�!� %>�JB; ver!EL a6 ��?�Yan � view%r ing �ty &. " ssis��of.! 1 0 "/ �s. Fu*���7u �'y calcQ ng�� �nZM�%�� i���ndQaw 7E�enc� "b��I&�!��mjs, i.e.\| �into ac�� .1 %~disjoiJAU�, A� ���9v�A9�y�� es $ Y�incorpo9 )7:�A�>FDJs �F� m��5�_6&n:Y which�} f��bea-e&N{\i3e}d1� (>3 21$)�Bes}��e.uoeffici� �*89��(e $0.16\le �$ \le 0.27$ �<. * an iY%Apa5 c ($G=J� �ս reveal�U very}1j.�BT04$). To our knowledg*{yҵ�s such��EF�i�LA�!��a�a*.��kAׁ�5&J&fot(c"� )V &2�or� )m��aftŔ2���.&�i52 ism�be: stoo����*gH ��k�Fg �a�Ar�p,��Fwere sol �0o inhibit ruphx�{Q=�� &o=q��= spon��assump��N  1E� 2 we�ae loweHupper�,�Vive�"` our �y�api�e sit"�� � 3ul��(l+ tw($100\,nm$),A�D ���S�  import�A2�earchXmu� enindco f�� en� F�d�_a�A2)�ED��exEenough � p�MPI� .�)q(%n) fluidc!� (#) c !$e p � F.n�Van� Waals e��&-� "�T &^ sh(�'=Isra9f ��V� :� sr miD� Lll be published else���'zeA�!� �� �4&!��H si�re� &� ��cuᯩ#�<s,_ex� ��by � Lin"� two poly� �# lin2,lin}�T� monitoI !¡i��vimpingE �Ej�; � EA ��A���edaOe�O>�!�Qv) ,morphology (� 41�c�}). I�.>y ��a ���n�F�t�"ar�_ �eaIs"on,��4J�&�W6? ofEKN !*&�� E�� �� weX �edE!T� � �p�ttivi,2�a�� ord��of�%E -�exist��:*"0 >. 04$-��� regar�azs�u 6A 6O { C �oind�C��\�� snson)�e�aO macromole� r͖� .d�A�advan!�a�r phys�a"��N�!P b�� >�&%a R�oinee; Ձ�7terB&"t ca��@��!+E��!nr�PA ����4�)�$refore it *whr*� s ho�e @�r��UIhe��eO�<r�:^A�n���6�Bs�#��= �a��2���sdy t�$jor ro�o �t0 si�U�sw�d%L!Vs. Usuo &� 1�s�>�A�E� kind!&b&o Fol!ELuB'A, w3def( bulk.�!5a�sequen�2/���s enh� !�accura�ݯ ={'��in- vo)p���%endix* \o#TF��)5@}��"� ioiv.{%�2�E to � "�)tra-!forward�� Eq.\,(�( int} W�I2f(QM!R@ ed) A��$ds \begin{Q}�) int3d} \���Q_3��n� �a m�vU�ƍnM�Yof!ź?s�"al��ves is� n �ici��byB* ��u�triO+ f!9= & 5Oh�o6�M'):#h)3 aé�n�+c��>C Q� Q%|F�\no�\\ & & 6]2N�F]� + �/B�.' �ve�,=��B��\2� � a�eu yaf��curl}�,.�u��-third" 9�u } I� =-m-1 %)�h^2(4d^2A�@mu h^2 - (d+h)^2)ŵ,��E [ٽI]} �q�}A�aJ�(�l� B � Y�inE�($�0)=0,  d)=-1$).�$$]+#h)=�jis�'�G=�)nd�2di:nec've� $0 %?�i< cove� �C ng $e $�0Phi)i  T$ (E�2='> ɳ�Mrhu .�!aeA)�4B�ml'our�6���a�\���b� = C^{-1}kM�BCF{���h) >Vsh5E-�!�suo Y�Yf�ioA�i D&4!�.\qJWYU��is basu�t�dA�-geome$alW+q� � . It� 7 �n&,&1�A�at ��A�ic.z� �,��"�,&:V*2,_ &a�6�./,V�3%��T�2dev�)02�U0�w!^ac9  �&-asB��'in .�a5ev] �h+1�+f\6�&all�~,� ��is pape�0[ �&^E&� 5�.wg (al�.CT�W4�Jw&O it���&t3F� I#ev� ?"* N*O e" of �{�x� �h&�*ATan att{0nd �t�� ject�%fu-2�-@s. \newpage��Dthebibliography}{2� vem{re� TO. Reynolds, \textit{OI��!,ub\'�8�ts6��L@o Mr.Beauchamp TL's.�}, Philo�="@. R. Soc. London � D177}, 157 (1886) \�o�0 A. OrS.H. Dava\8nd S.G. Bankoff�L)h .� Izn� �D}, Rev. Mod. Phys. �469}, 931 (1997�� &�)��inl*q�!<�},R�223}, 25%?1.�NP9!>A �lov�8,Nepomnyashch�*2��`00c��9��,G �2�EaePU�.Fy�:B-@.q12� 633 (2000=<# M7(stehorn,!�Pototski9U�I-� 3D L�(i�2%�UfEur�J. B i3!D4�� 2003�H0 �%� E. KnobloaQhT�-��P� a sll!,cb �+A� +�Ra D �190Ai1),.�TRuJa73} E. RuckensteiIp R. J(=�(Spontaneous6�!FJ. Chem��Faraday ��II �7�132A�7.�K�7N.  elachvili9���"(%Fs��U 0}, Academic P�8,�S��.n)�ap5�hOpen qu�t0�'�2�s new Y/e�dewetA}, 6E �E�409E�.(danov} K.D�nov, V�Pa44$, N. AllebE�H. Rasz-3��F. Durstz5���7�5U�'�>��i~2/s`(  %Utant-Ia6e"%e�2 p*%<},MEngi��5a2809,%�2��!�bS! Stoy*��)I.� �0�siAyI�V�23F�p%�} 2�.����!�� Non-�va� a�-��3J� poto�R��, 6�D. Merkte{}�&�AlU f6 path�1�Dq�� a2�&��[�4� v.q���025201,e�.�yia�_ Yiantsi�:Br Higgin*�>�/&; y� ��5us�AG2h A�B��48l 89�[vanh} S�VanHook!KFa} hatz� (B. Swift, WaJ McCormick%\H.L nney.G- �� �g-tx on-� B\'en�&� : e"cb = Z{34�  .T b1�A:1�� Juel>�.�r�SupX� of DrippH)a Cei� 6*� 86!�20�U.� smit!�K� S �N�:ve.k��s5aN-dAJJ� 24� 0� 6.si�I%�im�4 skii%FR �Cc;2�� s�  "S}, Gor�� BN;(, Amsterdam��.�n=�A.J� >��U�AI*�-y Yv��� �� �2�"!K$Appl. Math�bc>5%N90�.Y tillB.S. T� �p& & "� �gperpo0}"s�^-� �+nel};2�2"5i<.� maju�R�jumda. M�O'Neill9bVCI B$�!E�� El�8o�8sc I& aLa� '�" JlFst�ths%�$�A� 7.� mohaQ*Moham�=E�� Elshehawe� M  -Say# .��  2 Two S9Vi;us �A(� olloi� S"�1 6)z5�� melc�J%{ �  6N�Ch� Relax"f � �Dal Per�"-&-FNK.���B; 77v6.Bsavet�  S Dtaseranee, D.T. PaG orgiou, P�� Petropoul��}���lA 0x*sQZ2�-in6 by v.�+��ce�2'IO�I641�.yliXZ� , T. Ker�*� ssea�h\"�i/U� iner.S")(F:F�J eY��Lf /  Bi��a�)� ic %� }, M*(e_3�397 �.� 3+ J�S�,ak�� Hoagland,6�, ٥�T�R16G1�խ&���C � ��paH)�)�1�n 2377%�.Gwil;M��W� am�.v,b!t� QU��n�&2��82d� L2 Landau%)E!bLifschi^ 6+�m% �inu�Vmedia�k�8e Verlag BerlinBtpef O. Penros.P.C. Fif*�T.H���con�6"{*e0 K<e-� typ2$!4�'et��of &*�8�!�i&T4� 4� 2%eng��� el%)J!�w 1% Plan#, s� io�&� M -"�.���R[6 6540EJ.��B^ S. T�D"& � olid� :� �-�(spinodal d�>p�Ao�A�n"5, 49� 2 ^B)1Oroy��>��^!��7*�6�ityp gOJ6%�que�FrH)e�!91�.��Cy S.A�g�Np. 297��1B S!6s f�%4,$EquilibriuZ Ed. Co4dreche, Cambri�5Uni�9ty�>��C� W. &�(Phase Separ�z by S-� D.���8 ropiyHA�!�>�4!9�6���(t:5JWb }[ht]"i8abular}{|l|r|r|h= � �! 81\hspace{2em} &1< HT70 - silicon �=5cS:&>- 7�# u + ty $\rho=_2/1$q$@$1.826$ & $0.548$@ �sA �"=BmuA0.1B5.BAE��& nduc�/�lambda= Q U1 % �98�1.67$g\ � *Y0\(varepsilon= dh &$0.77 Z3$VI-� \�.ion{MatB�E:'O6�-�sEx4;e"> 92,;2�<cval�Q�"k8�TdEon>�,�&*TM�L ?# ��-� \ g6 �;>Kon n.�!tU5le}.gFigrG-%s:q$itemize} \ [>30ig1}:] Sketch���)-)04 \ mmisc22�~.e!wo =PKch0a� H7�*eV$heh $h_0jN��( $h(x,y,t)$�hE�@=%O� %�P�&�$of $x�#y�#t$DR 2}:] Show +�W&p "�O(�P9N�>�O)QC�M (&�96I"J.$d=1.3 ��&u�S26) .�91�N�>'Pnd� �6z$h�$� "�%.R!($�ges�CuV h_c\` 0.91I#NG3!1!�F&?�yar growt!Mt�-c)%�Rave�( $k�<qY!, �-�,2 ̍� =0.��(��>WX.� in TBUXTT$G�Y!=$�$4=20$ ($H_1=H_2J=Fa  I-*}=�5 $M=\pm b 41 "~ di�=y803cri�.*1 M_c$�WF_�A��%E�\mu6NV��-.� $G=5B�m>� M_c<D>c6�6�autb]G({G)�6K1r�&of-lea7>D�|F�5��P mu_c=0.09i  1 (�+ pane.�-M�M)�#B_F"�>(!�le"BZ t ]|>1!"�!;48<�)R5!�M">[!*�Wm">�!e (a)= '!�(b)M4il�I�&�>)%� ��F� (RT)۩� !�ed=�o a T�d:#���6 velo�)lo�[�=�f�"re�=:A���3}&p��RT, daB; vsig� !"� 6� ity.%&D"�'*| >toG�$��A ��=}�+Q&�n�JE�@�%Vas �@$*�5)Js Wc�\;Gf!?!�-�*�F. (b) �E�usE9cal�tau_{A�2}\�(0to (d-h_0)^2/���u�=%X�fa�y'���~J7*��*`F {7 .& /}"\>s.�%[M.-�[%>�-";M,opp� ��;rebGenA:or }[let�@ damp!2VR6e��P�J"�6R !��A# "oV$d�B\� � �Gmu=b  /  =  a��S)y~bC\�$d�Z3.34$.� $d2]\b����E��=-�a��>rom%�e���s (see �H text�*cl�Y���R�FE- a mB^� ԁ�1�X�)��U]� ) � (�iys0N�7A, Maxw'9c>�=(ions (horizt!l D based�A+l�$ �)gy ^<n� ��t4�;G)5legend)�F�ѤQ@� �,.�, &�.01��A�A�? A( &R I=�b�1 l< is $��"�@2` !S). $d>2$�#DV�-�/s .�)�Z�Uo are �S!�!�2!Ŕ b�6I"�b1,ox:r!!!/m�L]U, �@� 0�� 0.%� -=R., � anf2�*i�> 2��F�aA�1�,fQ�Zu�aXm��G�= u@- Y!aw\!�I�qJs<�?E?h<1H ��WAa.H�<�.V`_%ta9�e ���a� �*z 6�& �x��981�m 5�B� �isf�!�0$)�?� �U(��)6���(�CZ�=�A�!�� n�I��$ ł [in5H�U�Kf�O�c.id.Oa�s nucleu�ll| Z� rt_m%�"zCE�*&�(je�& �$�,q :�Delta tq� x� 62�2� � F��ց�2 �;W$:�=-�.^is u�f@8"�6�of �r%� ly �0.�2�QB,M>M_c = 4.62.�A�eQ�.aP�6i� Az M=10;$�f^�>tubf��A9�($h&�7 ���"�:vic��$x=50^�_RTAF�? B�EV6bA�f�m� ��d=3!�F���a�:�i= s�G0is $L_x=L_y=2�f� a�͇ Q�J�M�y =2$��g (%�)?E%�+m'�99�lea^N �n.�nsubuA==c"�g�G"pD�G�(le�curvivesxt�F^� _RT_�F���f�T-m -��a�2�y&A��&���q�`ឩ� ]%�2�1�� �<a %a.�i�DaU)�NRs�sr7L�� ve ($t=15 �|LS5�lyR� N�i 10�� _�gn!�-z���fr8_}>2\afs10^5: N� !�MV���@S "�D� �� at $J J�.K����� >�t!Y�Zly���6nei~Mn�O� � ��pr"�ZI~N ($t>%��j: y��rFc'Fb�K!�o �` *.=\l�>j$ EdH �'� y $E� 2�n���fi�Mth�jm�1= 2��}щ�&ET">T as ; # 2 "� �1ne�?�*�" &l! 7�6^)�![4Grey-level plo+Z� ��"�$���e�teAIIOe"� A(image�R�e7�Rm�n 6��y�r@R� dark (l)A a*�m�aloss (�PO�* �Dur!2�LJ� n�bo7���gve toGs �� oe8to meNZ�Ki�PnceW�Yl�oal$!�Gy.A� At�5� �, � �shrin>+�)Z #� ,b�s!%:�ferN�V�rt_velE@ive%(�)@ A�iHuks��i�� $x$-��n�"a��(&� $u(x=20,zA F6 ji.�$ n  x = 0.�9��hsj � ; tourU �<eam"�$�p� ($u H�>z).E�IY5�o(�` <�c�6 �t=1�!�B�( $h(20,t)<1jsx 0$!�v�E $uaK]����:*�p&)6$�� �B�5}\,(a)� 1}���J�i!If%>'-� �T,r!0o *# v�$u$AVGp�y,��pj� (A���a�r�b)b� M_�� *�& '�c $M=-d~�n�=1.67Q1t!0 qq*M�� J� Z� f� .��N� 6� A4 �s�k/ � !�a6R  � �lzC�^� `Ka�rs K)���]$E$ ib��c�|2n�e�*o--�' �-!6�$�F)�wI . H���b��� � "�*}te�7� d=4� JPb�k�) �` 0.05-+r��� � aW�lar�%�:� 6. A�%�vy � er�Fom6�[� d &�ly�YAgmS� % i�q2`1e�uR.� "�Btinv$untily��`�E�1e2  1rMOB�y��re|"&I- Q'_1=G(1-� )\,Q�%�2= M\�H2>q:Us )��i, MAem]i[< nes,� e�AwC�x: ��GD4D��Eckh,a9 F ruRF}"�A��I.&q����3">1.�T D��a �Z�: %E,u� h, re/� i�r&pM.. r!#$��� ! E�#Z)�g� e and ��}�oly "$FZ� _UCA�n 8,6Y>oڅU2 6{] v&(��NT ؂��A3�e�.� "� r�3$. OnT�^"^}�A� &�_/ �  u�*� y՝e��K!�9a�A$ex� a�&xa.�H�'�' \� page�'f�'2�*C\er�'�dsTphics[ =0,width=A, ]F 1.eps} \v�R&f)D.:@�.F�Cs�(@(�(z�+ ����>�2�2}-X����3�3��®4�4v���R 5�5v��nR�6�6v����0.8:7�7����:�8��r�f%f:�9��n~��R�10���d�dF�1��Xz:�jVj���M�l�l:�1���K��ʴ����z��<N<1������>!�r���J�1�An���N�� ~8��R�� �nc��R�2� UCr�H docn`} ��j��, I V Komarov�A V Tsig�D"� !V�]~[12pt]{a�Y�6%6< \usepackage{hyp'z$f,amsfonts 4symb, amsmath,\>em, rsf�A[all]{xy 72Z [eng�k]{babQ���236mmN;� 165Hopmargin -20mm \odd�U 0parindent=7mmw�\=�a=msbm10�ed\mag+1 4skip=1ex6Rf1cm \eveV im1.5em.�=22.0c.�=17�=-1"( \hfuzz=4pt �frak=euf� �def\g��#1{\h�b{2 #1}}} C.� 3bbb.2! 3(%\input{tci�x}E� D�f�f M�$ \Declare$FAlphabet2=Pit}{OT1}{cmr}{bx}{it}Z.A,pzc 1 m 0 zLeÊv �A{>cal A} BB HH Q  bf Q K KK TT#!kR  bf{R!^l{d 7g #!� g k{\kapp#ve{*] $vk (�Eq_.� �d�,{\displaystya��fs{\footjX% ani{\noi n�!p{A�{%@defeq {\stackrel{-arm\�ef}}{=}}ab!bq{"u20gNe~e �ben7n/c7 7:ba6:331WCommaNEN  )>on#1#2)�op{\vaUD\ialign{##\crcr\no 0\kern2pt} $\s��%�{#2}$V*%�t�Be�f} D$-2pt$\hfil2� {#1} N }}}\�s}mN�\renewc �{\the5j {\arabic{�^}.#A�new��{�4}{ProzX�cor}{Co�jary} norembody�k{\rm}bZQrem}{R�;kkUiџAA چAl�1',!J =15pt \v)@1cm} %n�� {\LARGE�FbfV�i&0  KowaleL gyG��Clebsch �~s}} \*p1��!�l��3}{13.5c!B�[B�� j 2�4 }\\ [2ex] { V L Fock�Hg#�B cs, St.Pe��N Sl1*@B,\\6",�Fia\\ } ˡ� AbYkct} %6�3D)ft/)N1':� vari�A mi�Z�6���$.ptop\%sd-?5�toc"�!_2 .uN��1�s�/ demM4�<Y(A�/BQ p:Za(c��ellipv�coordi�u�IspM^J ��<.�� ival�!1coX�?n�83��#lows �n�uct\LaxW�ricL>.� ]t09 �<�%!�RA�G . Associa"� thesM6 w� "\$? ��1G8�p,��=u1cqa2 disclId�<K\"�roH6n��rn!�&�,eq�� }��"u� i�0.8a�n�0{ PACS�8bers: 02.30.Ik, Uu ��k 4e �� ey��oI7nqUV.�q @he��� pQ�r}��d 4 !�ide��uid. A/?bypɗ�y getsZ^U�f#v�=3� togee��0�-&_ �!M�e'procedur2> VPNZ}�Qt�er&Z {0i Le� �Xors{fit JT#  x$e!:J !K�P � $M$-!Poiss]�nifold�3��tif�8� Eucl!_n��$a $e(3)^*$ b Lie- P bracketb�lxe3} \,\qquad \bigl\{J_i\,,J_j\,r\}2YL,{ijk}J_k\,, 9 '9xr9 x_k F:xs2: 0\,,���&!w&�$ �$e*�1�D�% kew-"�%�lor� se 1�@�*Casimir"�Jb/ caz0} A=\%�hx^2\equiv\sum_{k=1}^3 x_k^25 B=( / \]x  J)V<J_k .>�FixA�Pr�Fn A3aL"{>� *�eRop -Wd� ��o  9� en -�$HGSK} H&=&F�-W J_3R� I�-2) ]�\ \nnlX {Kl K&=&%}1})� 2}+4 A$\Bigl((J_3|)%� z_!�-( + )a34r!�!6.p$$\{H\,,K\}��!t� � : ~.A�@�s�iaۅ|F��6�yI �Om7&.qmi�fquantum @�a�-!�2�t�;=�a$�W= cust�y Euler�<=.�ow-eq X:q do6 J}�JH<��&�H} � } +  x�3 x}��yxy F ~z���bqQS�@��z$,Rs�-F ]���8 . &�(�R1')re̢0as \[ X\left(p� {c} ) J�U x � ' \�7=P_0\,dA�-� P_0= Y%>Z[�bf J &  X] -& 0.m%n , \])*�0J p �{co0 &� & -J_2r-J_ $1:/61�6=-���X��& x�-xB��xB�0&#��.\],t��4e}"�Ummu�/ brev�N %�} bi-hB�&:?-�+�~�|��mar98�-�� ��-k�d�xit�=zK� �Oly2��t{R� in m�a .�� Gorym@v-Chaply�y�WAXG=2����� ��+��1}��)A��ex 81: ^ "�  G�F1,�E2q K=KB�+i\l \{.-\}-C�^2�1�\,� qi=!X F ��{!�=�"^ni W�ll!C<���$s_{1,2}"*3.^5P ��f��"\pes-�kow89}g �Jk�};!���of�E� Mx 7o�a=>wnd� =��N5Sto! 5) %� ��d� ), $��% j �3 organ�E� N�hG�9�xtyA��Rm1��--1J�"��zS-�I?^&VS� bringU���b[�7��@" b$ !�A1}eX- 2}�^ A�doI2}V� &+&4 i \l� -�& )b~1_�g� 2�(6���f^2bha�{1}& -2H9�2��Va2F0mat-id}\\ &-&^/RA�am1) & 2��. "202And6��B .\nnA� x�@�H R12}c{1} ,-j=���cH-�^a� ) -4c B �� )-4�,\, A+Ki��\;P��^: ���@-"��A�GS�:��.�� %�kx{4i���{k}�s-��4^2-!Tk,z_k.i^2"� k=1,2� � "�c s $H�K}H�  �(iquadratic ��$nomial $R$ �!�3�� pair�� L8]ngo "� &o����a�e�  -\df���1�2+�1,�"}{��T^2aMHKzA�E�[ �-�16NW��Kl�] ^2 -9�!:�\p}{\p�%}-2 � ��}=r) .�a-�� �&&+)�(9-��1))2 2%24}�hKz�D �lh"!�Y "" &� Int-�}} \Sigma��\{�@ B=b,~ H=h,~ K=k Z \qq �=ɱ!�I3 � ) \[�S.��I!�,1Z1 2,A,B,H,K�|_ � 0\] ��b�"P#a&M�E�k>!��A�2*��Bal;. U�itu�#�L&R  F do �C'2�$\*��, \}\ne 0$, s�$ha�  look��mor�@ nven�rc!#!=. � # -�Weil- AF�# � th degre�lyi�s $A��42�� ,=a_0z_k^4+4a k^3+6a_223z_k+a_4& a_i*R� }3zKti*֣.Eul-mEq�mY��1}{\sqrtu61)�pm:(2.(i }�eq"� *Bppe5�ic������[ lemniscat[lin%�n&ƹ6�"�uJ eul6�TI�p {pro�|s� 1)o&�icda���Q1�A�EuBs)= �k\,s�5e`)\,s+W6� �I $d� xed �A��S�!to ��.�qu%g}EX SIX 1^2z��+2E]� � +3a_�2{ 2a_3 a_4��MA�W=MA� f�1)M{4G-}.A�$�F�!� �we83},-��!Zaut"#!s $(uz1)\to(u o"� `!��#�hgenus�.04}h!�C:\�$ u^2=R(z,zRe!�-�s)!#gA�E�6����!)� $dz/���V � u�HW�n�L'" c� a�� plex5 us (cubicy�e)�#ich�(�SJacob%Vmat ��p2_&�%^�by  ]��"Bu�{>Z 3} \Gamma-V0\eta^2=P_3(s) T=4s^3+g_1s^2+g_2s+g_3\6�g_k��!�"�"�&(s $a_0,\ldo>3_4$. Ac���~to ��PMj$if $O_k=(u��, $� $,! ų�$=@a $N=�_k,s_k).@den��wo2C%$"�by�1=N_1+N^F� O_2-the(S��Wx0" dz��u_1}+m�dz�� u_2}q�d�}}{�{1}"� 21}D VD2D2}a� eq I�Cinf(esimal�C�z�%y�� rpre1*� ����WDse"�Eidۿ�"O choi�"afٙ .�!$(u,z{�%�,s� ;�'�y !q $-�:Z� d �HBof.�"�$�$�Zy 6b�#u=e"�,��  4}) inǶ 2A-i*D* �wfamQev&- !�- .�s �{��� � ��" 1} ��� *}}  $&}�- � !�Jc���fA gral�KA6CI ��-A��)m���)�J�yeigen�n!qn*��) j0 \buZaux-evp}b�!3o �||<{\Psi}=2\, s~ \s� _1� -+)^2 % ,� &=b�0& &c238 �� is natur�W�6�brom-�u. Its��/er��.�.pEIq.� (># (s-s_1)# aoq �/sjA(E�4QI �� )�,� �)ͤ, � , GolubevMF l}�ofI:�h$!}"^Q;S blem� Q6)�Ldu 0 !�%�� J�j6 � ��y�Mi }} &j&�03\[� -��TU)�7B1�e"i��&!:*Bt�s} ��N�is ") �� fruitfuX�� trea.H)�)�th2� ���f�.�-�P1�DgD.in!�JRy:  �5 Fu5�s �_M~E��X"((*�sS, s_2�!.$�RT�3"NQ�T:2r�pro,ayp���,� ,komkuz1,ves2�.Q\neq Ui��ex�/ęcruܵ obl���.z.�U "�o"� �"�(�*�, sugg�Z�\E&5�5�=H� i{n&��eOU&`w2���+ stim��ed �jo��e down&KN��[d !��IŒ��i�s� 8 �8,9 ir vEV�g�\$ .;7e�96Fu!�W�6�}> u\v�a�."k]*�*4 $(t,w@e�� u�0�M�3��+Weier�6s��s�a6��� $� w)= 4w� 2w+g_9N'h��$g V�heeU��,�y 188)5Ns2)(w_i=s_i-2H$| Q^mD5 �+�!��і} $w�$]a�(�0� offFca�ep��l��nt(A$w_1, w"� .  2Qnst�bof � Hs})��"4 �6�'gEr��, � ���, �<8i_�R�[)r�4���qn�d�wk argu�(s1,\ s��$a�s6 +D����pV�of*� �!riӤR��c"98k J�ur. SquarU�!�i:��D-j� �fac;)��i����of �r�ws�$q"(bi- @}  (�xa{-�} s' ^2= � z2�, \qq�-�� \p6Fz_k>HaNsDCp. �.�eyA)i�0n *�  P3}.M-8H~+ 4H^�-K~ 4�  \,B*ܸ�Zpp�4a 6+&�E(s!2)$�M�� zero'V s}dstF)1}� 2���@JA�]-&�.<3di��Aaa�E�yA'b�A type� ]�s-x-der}� {d���%��i H #+*F{z�$S O�"� {z�'\�n.; he� uD�ul�B\R� ��59��v٦lik2�zt-stZ� �@I�dot {s}��/phi_12v 6-"0-2RO = c V� } { }% }U6w"RU)O�G-we�d%�&.� vphi_va�k�/ )�k��q Sig�6t s�� ro(c5�U)Q<��)[) ���� pati�5��,.d$`1$ $-�T n�2PsiqmO %�U�! z  -- xw]�x& .� �.� L9.�8k&� ��,}SJ! .{�>AA.�mtHs}��6(s_1-s_2}2\,2[�A�^AW-�1} � E%2.2}� % s_1+ [�? �K�&E�$K}4&=&(2H+ *)"��-� -� A�� 8D P�}{ ��� ���\��(-) b�P =Zs|s}^s_1s_2+�%��~�E.�-Q%*���DUQ � at even pc�� ic���|"� �as&e�� �qy��}I�Q����s�8, $� A�$:)�)^2+K_1-� +K_0�\�O�rst� n K_1=&�%r-á s_1}���EI9ڱL <�)"�$7p U� -222z.2�Q�& &j��.|II Z�2Z�2��+���m�2��2p2}�"`-{u�rse�GI��� �)ve�^.� $\p / %y��D ��$�AAe�e� ��)s �1�>1}1�� A8 �& a�NF�2F26F ���) Bb�, M�h��A��ya12%/i$�   "/]S ][\$i�"����P �m�r!Q -G&L s) �ej�_�1}�1i~2 R/�h�b2} QP��ls�, �ect-ell}�rڦ�se�7T!�H�� @��Ir Ks}))~ 4�I& �6VC.ӯua� ��le��mN�!os_�!A�,!4 j�!,\]�$i+>�co�/&; ��mD�8"` :�%$.u`��Eu*E=�  .TweQ>� & ofq!"�/yk�x0}s-GxLa$!$c)^21kX+�$IZU���--� ta_kQnkYr)E^2�13^2 ��2_,B}��U�M�k^2=0Xnd��. �%jg�)**erK��N�+w2Hs' K}{4.�$ �_kh$At���1kQ�%kredT��> } �:�1k/,�/ �-� o�5$} (-1)^k\,5�5`=)� P_5(�\,R �"�' !adm��8aoA�$�$� "�%)qD �k �Dm�9$x�4�P_2�a fifthI�*�',3,$!����J� P�6�9!pol�\=Z���;�L��a5Y jbE�}),� 2%6=M*|_tO =0}$j.�@^�n�7��a��� sun�eR�(i�� `s`bff�$a $\pi_1 ,2$�.jug�Eto��? 2 t�A*.�&� , 04&l�� .� ��] *��A��l0 o =x&X4:�i� ext6d)�"e})�!�eq��Ev��"X��DE��� >��9[@� !J9Q, 6C^�� �ծ��A��cE�HLac2Q"��Ddu��op��A"ormD&?!b-�I%�f�6� Y���|e�).)laimH�e/�-́�]�NHthe��, b�we�zt� 5�2��}�in �r\eu0��f! �:Ah!< B! ~Da)>:_ ��=� KC} \s^FDZEDl�k�Ap�.|"oe"p� ED"j"MfND$A�.fie*?I1&2BQD�Bp�H%.<8�7mnew-e�%4{l_{i}, l_{j}\J/Dl/a uad /p / =�epĐ_{_Dp0 \{p_ 0�. *T`&���wo �Cele��.�caz-Cl*�'A=�Cp,\)yC& 18 B>$l� � � &���/GѷKirchh&Y�on �C}��Q��c�R��Cl�>mo'Q=V�<�l[< p%�2"�7 :"�Dl}�>p�> \QFE�&B�>3p}=hT��� w"35�$\QE�|(_�� ymme�P u�jdettm \,$.*m>�K�%-)�zg"qM!S�)Q)XM�l  �"�A�# H-cl*�+H� 12\,1El}� `(!'9%p]) "/7M1*@D�!Y2"ACK�Y�K=b| )�Q^{\vee} p p� �Ѵ*$�onЍ adjo �1��co� .�ourI���ead��R=�%� })\, -1}$� he;@ ��*X 5��2�= v@ ;!���bia�&9-X" o/I�*c@b�?=\q]P_0`\�*H.1K2�.@�#V�h bf L�6 Pe�"�@P�:R�� 9P_1U�UVtQ@�Wj0 &B bf I*�#� ! c0�[I�n\v� ��L-lax-�!bDc�F 0& l�@ -l_2�< 3&� l_1 l_2&B�&�":� bf Pzw & p xp8\ -  *' &n|%q�M I2�$3��3$ �� i�."� c2�*P�� & P_1$��, >���-s8M� a�, ard :�X *# ion.�AZK9Xf�AD ��W P_0+{��Ia1� %�*� ���'s%"� hm91j'q�#� rem-@P} �yBVhB:7�F�K�Wt_ "�X E*�P �6New�J��ٕ��<��dU�p}=-\Q +� l( ("��6( p}^2*r)��q��cr"D�� �*y}a.!���X$ A^2=\A$ d�in��=-k� $�$A�"" �� {MapD�� *�g�[%uo�\��,�'�JE!�*-��mV�!f!�&%y)"%:A4H�aexoso�)HH,P02}��:�aNcD_J1'to 2V4)6 (3,1z_E'A�� u+rJG� .< complex�&�U]Kp�� }=\a�a��-i~{J�J_2},\,�J�M 1}{22$M-\r��_ iine� bb C3q>�l�� l}_g`f�Z�MŐ�cx_3}� �2J_1G.�M-}?>�^-+-��s��3(!M� lp-� A=(i`* "� p})-a*�O\BR,2�A�}})=0a,q�D��uyALDAC �<inU�M�6H1Uo mak*�S�qs&6��8�OmI .�!��߁)�D2�6��ub R� &"� we=o shift � �hl]) $� ru��� lg}0 { F<+I��\X,�l� +i�  k�2E� p&r)��� ��k=(1,0^�� �gu .\)a�� with-EG)�far�d�]of 7s $M_]�!�p�Fg�"<�b$ �$&D0lp-!#^�Q�5� Adcm rai]'$�; B=b�:i, �g�Bn�Z�/"r�^$M\simeq� ��M"�.�  R,G�W�P�!e�s8_!u��)*�In*U �e�hs"iaa`" <"~ $\{\�\�  \}_3�*�M$,ad �)6:� {p_i,p_k0�#(x,J) \} F�\4\,(l_2+il_3)(p p_3ONj}ha7�ot���s)��"= >-���W�_א ,A�omL�d. <>�Yh!u� 1#6_��)�>9�l =l Bl�So,%��.r�multi"�O2L��$E�uY2%�2� Q�����1i[�a*� �>Y 9"�.�vif, ersa�-.v ,"�]�top6U�" �p,��F�$;�E(%2�6�9�!|V MF���6q��EUD�"4!�i; \.��}�{ "-� \��mA��8s_ס. �6s.v�&�o%g�Q��kWN�!�1�*{,Jc�]/�zra�&a�FSM�{���I�o �/�[!$ 'heQ"� L� 6m iHA�2AW"le�/MZ >Lp �!{��F�j� a� the >\K��9�+6���.s Q-�x} \Q =Y ^{-2} qN�rw -H &?= -i c b Q  \\[3�)  14 +?L\vki oy 4  *O\�4 sS- r.MX# ~Z (\vk=a- {K}/�}4 �:�&�4r ���2)B re ���`e��.�C�!�6Y!�2m&3����FL�b !l4o� -Th}"� d�-fy6i�$M" �ja�:  x� J\}a\; l�@�>�"� �F��� l toA� �C8  \� E \A& B "a a I.-���$T/ �U�)D."� HK-HK} 2��H=-H+ eh/�4\� , K=K�$�F\,HIGa�� 0 $"b"� ��!1.�� �Mi?�s)�6S�J�� Clebsch �system on $\mathcal M$ \bq\label{m-eq} X=P_0dH=$P_0 �X. \eq The similar equality holds for t\econd commuting flows of\ Kowalevski gyrostat and Clebsch �qnd{prop}x�proof is straightforward. Accordoto (\ref �)!t� pace9 d M$ initial linear Poisson_uctur.!$�cubic+ st+`induced by $P_0$ generate }Lame vector field $X=5g8X$ with respect�a%@(on integral�( H\simeq H$2�4. We can embed2p in a standard bi-hamiltonian!�mulation �two func4ally different�s of mo".�)$YqK$ (see �Tbi-Cl})), if we extend1M :� M � M$!V addiopal degree of freedom considerA4$\lambda$ as a!Bdepend�dynamia (variable. SQ��s%as us)�pSklyanin \cite{S-GC} when he wE0ed Lax matrix!Q%�hquantum Goryachev-ChaplyginU�A�T Thus we arrive at on�G mainAultqG4 paper: \beginm$ Solu!"%qP problem g\ riseAbs:.b�v1versa2�MmgetKm� N��us!�either a�8Kobb-Kharlamova!5draas-t$mink,kobb,&}, �i K\"otter�)�kot92}�1�Ua theta Q�Hs. Recall once mora�at%�QM=0$g5`Neumann [A7iAgifiedmKh22uher1 Ua may be ex^sed!#aq form�1LLax-g} \frac{d}{dt}{��gs rel��u�x $U�Q�$m�:a� regu� way�xprovid��x"�method Bskl95} t�(is appeared�L0 =\mu>�!U� and}�5(2-alpha, 2$Psi)=1, \]I�&� Pnor\-ma\-li\-za\-ti\-� .�T� < p}\equiv({p}_1,2$3)$. Canon�RE��fs $u_k�# their momP4 $p_{u_k}$ lie��a>����)%BP s "Q u��sa�"� *� E7s��dir� compari� +e�ny� ac �� q�e 2V s. IN e�pr��p� ic:G t�� willa�deA�mnext m���Ano� y�f�ap.�"� 'e�roach �� . Let �x=Y�@diag}\,(a_1,a_2,aA [a o��ɉ. Intro��sa6�ht(��I-$�{s &Dts-7} !t� bf W+\, l�4$W\,^{\vee}2!pmV H sH 6H'�bf W=\bŅ"y  I-\Q8r)^{1/2}\,, \eq� � :�>9$(w_1,w_2,w1715 ��?�%]� adjoint1^ ItpeccuniN isI|M�6� bu$ ve�qa�$w_k=\sqrt{�Oae��b���ed basic"� &� �i;EA,bbe94,��8}n \par\noi-e�u��� *,st-eqm} \dot�t)�=)�I2� IX; �J rewritte�ane0!1.��})CI��� K:� e-�4sum_{k=1}^3t_k\sigma_k�C .#\� (w_k l_k+� Hw_1w_2w_3}{w_k}p_k � I "= ��A}N�s>�:H �����Pauli �ce��6UK� r = tau2� 2(w,a�=w� a� t^2% R� ,�c� :� -2\BI�^� }&� �tN� &� ��! �Ձ2})�w�io���)��l2�p� ta*� w�dwby "[}/}My(new Lagrang>.m��pzc z�,i} $ � � sfy\  nice ev�yzp m(�q(as candidat �ion� seռstudied� >� 2Q)0bob83} let us��� m�  transa���L$f_\mu:so(4)\to e(3)� �ap (J 8p_i=w_i(S_i-T_i�0  l_i=\d�2�i}-+ -yq w� S_i,T_iiOco'%5^ �0=so(3)\oplus  �A% Lie-bracketaZy1�}�2o3�8igl\{ S_i\,,S_j�Digr\}= \varepsilon� k}\,S_kťy�� l\{ =T2=0�c'Td2'Bc Tb!nd�"� rem}-�kott-bobqin�e R�$�iA� \bq FST}�9� i}{29�\,l_i+-�1i}\,p_\ �r=-N=\6Fw� �s!�GM�e�ge map I� �is easy aliz � A& mappG$f_�,\nu}A�(substitute ��a�$��and nZ��nu��q�def��A�S�6T �$vely. tS on 7P show� ��,used namely �to�g"�6OM?A-� 9)= a twis�q2 map,��&s!L�H*�ma# I$�$ �a�4)$2� �$array}{c} �Ti?\, 5\\ \xy(P{ \{.\,,.\} \ar[dr] & l] 3(,\}^* u*u*^*} \aO � }m��ead of  /ִ���.�N( ^* }2�ua*�usual.�}.�H�&�patible�  $)4�$al$!��p�":T(sec-e3} \{l�, l��F� w_k^2l_{k&�6�6 N7jp5 { , 5F4f\,.. �polynom� H ( nu)M�Ca &q$ �g6� q pencil 9-_\nu=5; -\nu ^*$a6!x$neq|($. For brevxl-�O n������ omp d becau��heygcomplet�d�m�:� � ��)�L!tJ"�$to Steklov�pAM>��Q<� �is discu��ts04b&P ���den�s%$6�]�:��@Schottky--Manakov/�s �and, a*g � ,�ߡV� .k$2 2$"� � ���  At�)���has af$4 h42R�Q"�e���=ra.� It al�uDt ���-�f��yA�La�� �6v � munY$widetilde{&4 L}}(\nu� � %>@c} a]  ^U&g� atL W� &6:�p\\ -(V )^T& 0.�% "<R�A��0�j��! � �W^�s�X-=s �9&>F� 4 � V�� is6"�&�a Q}, surface, ra-tha<A�� We nAt� :Z"avm88�"AtX�&LSU�)�o�r� al i>�kfoa� � �A�n %3(y )&=&y^4-&4Q�nu y^3+I�%�Q!|?b\L�!�.KMk�nn��#,tau-3}\\ &-& N� nu^2 -2FH+B�}atd A;r)AR,y�QA! # A\, U �iwcal B^2,r�\nn \en���ed*�x6+Jis)kŢun�I6l&`�.� �"���o-geom� ��fzhiv9YEn�E:&, �U?I� coincide�tB�gvofŮQ�.�up�Y>� ��y}U%�\,y$. �b�{A6�� :@h2� gyr�%} From��y �N"ʼnG6�, established-��N ��-KC}) nget��$u���� �$k ���|esc�)$U�J�.M��:-� �N�B�$ looks lik�;�a�Kow�n��$�t�\r\mu+H)"-�K}4�' P_3. )}4\6&� :�Kow-pol� It�c a bi9 �&Y�� %� coefficie�!be�-2B @' &[ Y$\m� ���%��i ufamZ=��wa7(6*�"?�"�$th2�$N�$s��&} A݉W. A�ion:/ $N� � x 6�Q���Rz%h�&=6l \[�m6��--fpQ� � AB�E %$~q xqe_ Jq!x.����u&��mulaeE6re2�&-z>. ��YC�ltwo-dime�'alAOi� V/ .6� .� y)*8�"�by Adler�,van Moerbeke�U� �ly Y�� ~$]�top�$aM�" � �$$�;��7 rd��"�$ (y"��3})a�a2�"j�EqAc�f&�x\,y^3 � �f3H^2-(cB�-�) +H��K}{4}&t &   g R�H-c^2�r�&)d ��z� N(y�1)\nn� nN&�-�5��QQ i�(-&k%.��L�Z� from��E@changJ 6+fua3��fourth>7B� ��ug* �,u.��=rs89}ui&Q  \[O 4O s$M !�%�� ^2-H��^2�c^2A}_^2}-� +��/]� {4}+-MUI:,]  N{.9 -�6��e'*ef�)3c4-ell} Minkow/)�*}ZU*��6yH"�(j+of geode��� soidE2� �'�+"}#8 int, d9 kB  1895 �+`.r� ��$J�4&i!�>Eu�g�#and pa�to]�($\xi=\tan(\E�/2)� 4phi  ��%# alenD/Y�& )WM,Aun 1959 *~, h,*��)9f%for��M%���6�>D� � � In order! expl .!am�%1o�"A,�.-}c/4,�!som�1ple��\. U�u��e�I,�Cl-�)!�x�ele;$s�caz�)u�� an�&"e$l$ via VDG p}, >Bp}$� {l}}=�u1}{\A}�\B -+6; p�q�T�/weA�-(N6as roo�$!}" "^!*�seq! � =�~-u_1) 2)=����� �(�"w#p3# p)� FD�mu��(\QT#) p},  p} G� eq S�� yP ir veloci�,$%�u"�into -� H-clM;K ?� e �"�' $�*A�*[4T"@ Ven�Hu%I\x T&=&.$u_1-u_2}{21�� � _1}^�� varphi_1}�� 22�) DB=2AW&��VIx1�:�!��\, \Aun"� �� l�mq� g K =( �"��u_2}ot!}�B�u_1#^�1B}{ \A}1I] *-L2W} + .2V.a�9�� �)h!g�1K,6K \,!AE�] �Nerm��J�,a�r�5��5&�� �k=4��,u_k%��/�C\] Belcis@"e!"�2�"B6m$lX vphi1})���R� � �������@no#2. Exclu�-a�͕}� 9se�wez < 2 �5 in e�(of.Tc�bon both*:) $u_1u_2i� cl-4eq} I�+ Au �A�}^2_k&+&%��N"|$mA A1T1 2}M�k}+\bet�%1�rr^\ G 2\^2�� ] A J}�M�/cal A^2� +u_2F�)+&�APH- A)�}áN}"l&�^2O%e �$ ��aB� also6�5� 1�"�!!"�)%)�/� +u_kN�\:(\A u%(�H -\A B�)a�k��a} KaV�Mo_a~jug/ to $͐ 2�r���  %&�*mom-u} �,� 3 \par�9�A?T}}5�}$, %�5G$1� T%a kine energy�ɲB.  operatox"B$-��}��pk$a�"�5�ama re:v,^�3 in� & :hav�  under* on�!at�9 $\{u)*,.)5\-ino<� var�-��he �0,dard meaning�6'%5"Afy#a sui�e r���n�  p}=V �%2l l  \QZ&.�Q%Q V��+U+}2-��D�izz� \Q$,Z �� eJ� �spn�^2=YyA}$ d�#I�Y�~2clvE ٝ&- I� a 2 -D*07me$1�� H)� p}_22}��33��i�_"%�5�: �� rem-Neu} �33r�c�, ablyD � �w=sep E��{4���!����z4�(�0��5 �# k=1,2 ��2�aseŲ � srmeic��ao "� Y"m>}=\pm)U� �_k}}{2�}� a;co./ /3X:belong��� St\"�(l&� �I! 5,s. Moreover,}�e�k,p_kq�"���i* 26�����J�x![nd!�k('L-N�in $s$�4} Without los� g�nau@we pu�3|�2|=1$ �ser� �0p\ p}��&��alg�n5: iAp�"�I� ) of $u$-�k  � I$1}{(z_1-z_A�}{\�}1 8 8�c � MElsUJy�:�� solv� >� s-GK&Unfortu].ly,!�can9 a'ver�mplic@ �P-/�to calcu�9>!�]6�zaňa�1q��..��pB,A 6�7f�\, 1888*�S:-H .��is isomo�c to "�o7 �z��! 4 1891"� �=$I��P>o���m�ofBr2  rigid bod!��@-��R� =E�5 !^ �s4(91}B�! NB-X���2"�7 D�5} :6%J�I��get%BA�����)�*�)!� �0�P)_7 ><l+.` '}B(p� E)  \etab�-B�� ��)��:(E�� )%`2��1&�C� s $a,b$�ing zero�+ Q�v�9�Aa}=b}&�Cwe denoaW��-�1= _\pm5�."!)\pm =% a;nu)"p w"I+ ! W}z_Cmu)�(Nd�;W+�] 14�<�i �inv-relKA��l=� bf Z�� l(V�-\, \xi-V{+}SetaDr�ip�&bf 2h)1 W_{->^>RE�� )Z=2yN=��Y�)� ] �,%<5W " "mu)Jr�6���g Kirchhoff*r� ^13 "�u : "�ZT8=�eq�J�i$�2 E�e��6W � C_{11}!��bf 2}\xi\a!�eta+ B=2 =&�E C_{2J>xi,�P�- ���6ZF:��RY:�< ��eMHb,%5R�.-Jw11}�4IB��.2>$2�;k)�"�.&=&�vm,�[fI��nu�"] & 0!��.�fE>�E]AN��#R'J_+=%W_-NzNm�3�#By���͡�h3� M�1}1I��AAW2�� �Aust� a�y�"xbetweeIOx�:�2AZHp }�bdso%�� �/\{3 : *t:\vare.s:("0k+\gamma\xi_k�{q�FPxizOBN1) ?i�xi ��OCP\ �A�5 ��&xN�;�6�3�7�;) a�6�J%� S&w<�i-�i}{2(1-)IA)1�T>/+/ �/��! D$� arbitrar� � �Q � ǵ�)�.V5�):a Y| HER�6 Ar�M\"  \[CO H}=N�CZ1}�;�C ta)+b(��xi�ta�F�O2 ' \x>!C�i[�@:�c} ����>Ay�e�NNr1��eb�� & 1R���NGZ �V#�f&^Y^N,So,f1"� con!6�wo.%=6�0 ,=+=:�; ��B &W M�&� ) n"X�>&$ �."*+++:,�,q.Jat ��8.�$R6v. �� �� on z �}͑��1a=bv�$ES /F��5� � =g�=B�b6)'EN�9�= &�9/Remark �"7@))��ic -map6>�s:�^� if $&{ *$bG  1e<numer�J"� �:' �!�w��checkNB�BD*A��.�-s rU��#>QSu>^6=nd1��;SrASm\=A� in�Xon�EN�C�,H�0�)�qA~m��nX }))Ad)�]�NV2*if��B)(yjbA=Z!@W \[(���"��I+'eta^2=�jv#{��ourIh-�*� inner� 2aa�F&� �=mu)-b>  ,&�x�2BN 3mu)+2BO jnu�QeqPI�2;��Cnecess>Fre�Y$2�0$-� achie�-�puts � uFfrak s6EA�w+� kE��%  s_{i,��n<�2=)!�g V �%a]j)�I \det*cL}�at ns_j2*j� ,3,4Ū Of course& se s"�(.Hdestro�=m�R?�I2� . As� equ�,Qng!EN9= s_1,.�2��\>* s_32*4$ con|Ely�om�.�w�[e�\�"�U ortho� s)xjCQh-� .am� |�� �{-=\M`A2�P��. VQ).Q sQt &+$a"_Q � 2n� �"p>� %`:l4` �� 2VZ.�p2>Z)�JZ� ��I&�QQ����kaj�: aic q�.�k-�-Z2��".�..Huad.�R^,>-)=0�p�xvZ<�&)^ (N$ xi},N!xe�= �5 mia)���V�Gto����Po�P2*B�q�B�!)f�x�l=b^ &�#lGO!�a\>� � Bsa�}- J!.; iY�Pat�U i>< rr} J � &66�(F2 W}_-6*-.�"o_{f 65 3\, �@2J4 }� R� ��6�z�R�+Z�\:�3-:�"Z.Ba6,x-�6Z� ��&� �U)$&\�S�a" 4=�2+:p)Ul "�S_ZV+� W_J� AKRS-16s:�);��I"!N m � ��)���6\, ��)# ��2x�O&�14_i$>@_i�K2�,� non-�XK)u�� � =g_i!1J2 3)&>s  cho�O6")$s R� ��"o.��). Fo� J" C" us�&;"� ��& &g$�/\psi'�}}�� &�=i"�$2/nu/!�5U \[JI�2.��2.2),23:- 4�\�� a � �d H)}{d\muA$]6�'EioM a(-Xa) �2uD FB/>�=F\a�fB� W#NB;>r!}2�Gre�W>=uZto�bsizqm $NF0 ! bf D2|V7�ϕ�D�.Zeta2][(0&�B�u�L*K ree �7�e�a#�]sys-26} �Uj�U(a�j�Aj^2� I`2)�h_j &"�2"͠dFV(+ \}{��0�2�g d_j#Y,&17�.&b,1�1_ WTY�>2M�� -V R kS[ d_j== �Y� w}_j�fra= 4)+ib �� )} {b!~zA2)��FGQ%d{w���6�%i] MlgA�$ obey& erty^*%* =-1$�E%�^*1�|9�6� 1��@6->��!Z Herm�.'�0�Qz8RC. �*UV�h.U"�3}clR<�=A\,)\(z��z��22)�*hi(z)}= 2E�4.z-d  +/. .*. =0*� $\ d=( 1^2) 2 3^2�yA�pzc A=�+ 2q�3^2O�F�/e�&��-�)e"�+Qj=� r=4�+e���at�z_2 }{�'�7�D�|J ^E� k�>1d_2dE/ �S Ui a�2.�� q�HP_5� !�:Ai� �7NC�\"I:�?) =� \eF"�,�zia fifth�&^*A�>V /} =zE 1^2d!�d!��$MAN1 2UW6�I+Uv&;��c*3Xu� �Y����/C [ (-1)^j(.-:�01� z}U2 �_jAL-` A}���\M/��k�  }_k2�j-d 1� &8�$��� 8yB&�m)!&� k"!�� sep_Kott}�� �{(d�w_U� z_j+ w� B�%)\,2/mr�2r.E�,2"Ej�Sc�an�=i�(�2)�4&� �+ �!.g1&=&2��a�0�; b�a�.�9>�k�O1V1��}H}" �%.UB-'f� �qx (56(2,(). ApplyingE�Abel-�C �'�+theorem R6u�)Y� then�/O8�20f��@_ . O�-J^tepa4oto�a�* L of �ퟩ�}��ED�0.-m���dw-s*}��i �*-A-ls h�� !6"uvar�8���_$ {�3�i�,�_�.s!�k&!*���-G<0�ask si�U�2��i�j\}X �t$\{d_k2 0$:sup+D� �:�a��c�ue�, atipX restomdby�J"�V"�zi_D.*�X9�#I�s.AL w�C�.A.$ frameworkQf!ye-bK M.techniqu�/bbe94}.  rAr�0kow89}*�6o?E)1! .catoo��M/OO9�Lq,�Mh[XAw:X#�&8�. b68f"�WH./Ed&] !�XYZ$ Ga@ magnets1& 8]�M�"� 7 �/lHc�6�e%�)5Vf!Eclass�!�qu mei%ics. U"F�Zl< �:1[�refore,'=�&�Ju�Fe�:mi7\R �W iculE�`&�1K1�! "�sConclu��,} Our treat�>�_�aAe�A�.3erQJ^ "HE,5 }.�N"6 3�1�>ly mo[ y4<�kM�:�t1� corr�9�0>}�R"�[o%2gTic �. �&J8�?ul+7�W p�v!seuwe " TN to �s�p}"2)!�NK:Aj�W�u�W2WU��i-b��!=w�M��R�V5�'p eeT a;�'C�WM��-�)is�V now be�Xa� te�2a prim� importancN%g1�%�95��ned�9A �*�!�}F>$|:>?dR�ROe�e�kst03}&�P %top"�"�h3l_{�%>gas�"�J"�pI�g9��$w&�#s $b rul�< <JRuthore�4nk V V Sokolov%8�_v�Gu�te�A�ANPA�!�useful*RT�gaearchA$AVT�5:ui��\M`by RFBR grant 02-01-00888&mAHthebibliography}{101ibitem{R M. A�R , P.2�R,, \newblock{a$ {K}owalew�N�{H}\'e��{H}ei�M+  as {M}A_g|N�RA {$SO�cP*d^�S{L}ax�5s,}�\em�<of�Yore�} T# cal Lite��53 (Eng�]2p P�-� Israel Pr��m��S\ific U��1960) .�HHA�~Hay$, E.~Horoz%�� �&�Rk6(>�a�ica D.C29AC73-18�)7AEBJ-�Phm91} %D.D. Holm, J.EA�rsden,!,�Ho�Y�� ulum7J�e In: A0Sy�c� o`y a�e,o!kphysic�� %ed.�Donato*(al, Birkh\"�g r, Bostona�9-203!�9a u  J��I. &�T.  O dvMlii tverdogo tela vokrug nepo"4noj tochki v t.>Lral'nom n'utonovskom�e2�e�hIzvestiya Sib. otd. AN SSSR}�a� 7-17�59.5F1��U G. hV.�Sur le� q; la!�� d\'un psc�ur p�ufixe..a�$Bulletin dMaete��de Frl �4XXIII}, 210-21�895�9�X -k} I.V�marA�{ A&: ��} >}2TANA�.Lett. A.�12�x4-�9E�=GY�1>�V�1 Acta�:� 209 - 26A�89:s> Sa�H !�,��[\'{e}J��co�� � �� 177-234 86� mink} H.&�E2�b� I!EL6!j� E�(SitzungsberI�Pnig. Preuss. Akad. Wi B�P=p 30}, 1095A0��.-n�� C.�E.�D�.(ate quodam �o, od^mYMlium ult�lOEcorum s�e�fvocaturB�Rein.iR5��46-I:52] Մ� "�, S�[remark# ��� iM�C"� �of a &�Fz anM7c luid.*�f� 15}, 83-8��� �mP02 IW r��7 :� An%�:>S Teor��Y�>�31}<7-205a�02IRS�~G��*�~*�T�SB� t:~��a * �8er�  2:���ts:�ses�%!v�� �B�4}, 55-6�,�@9r6 } F."6I��aalyti��� b�]^Ro�"�s starre:�Raume v^zier DSeen>�}�t  drer�&$nigligh pra�� n Academi�re�0enschaften zuFo  22�� >x S-GC� K."�ٞ� {G}o��{C}"��1�aVb_mOi�3 sca�88 ��emB�0J.\-Soviet.\-%��� \�E�3417- )�5..��� E.�, {Se{U>J---new_nds.�PP� �or� Supp2�118�QW9B�8B�(T. Takebe, Z��_!Ie�3"r odel>j�V4 20A�17-38a�92$t A2u  O�gt -Lyapunov1e1ѹ mG.���,print arXiv:� .SI/04060� Z 2� we83� Weil,pe�!�a� 1�jsQ=a�$ Arithmeti*kG�ny}�)�EO,YL�� 353-359, a\"{u}s 1982�� Xy} H.M. Yehia, { Novijy+� diruemije sluchai zadachi o+je+H��aB�4Vestnik MGU, s�� mat.�a.5 !� 88-9��>�zro4 A. Zhivkov, Ok ristS �-EffRvY�/!���p&baP7!�1�endB8 �!d{docu�} �Y%\! $[aps,pra,p R<,groupedaddress,�{8pacs]{revtex4} �Csu�M G>J�,floatfix,amsN,prl �7,8column, F�% Youuld� BibTeXE� apsrev.bs �ref�ho% ChooG a jourXk� � K�y selec�Nh�!D APS %bstyle fixc ile)�{�- uncom!xeA? % Ww�:"�:.�"�V{ � } \u~ckage{icx!�natbib�� ?et5E1�AHtitle{Multifractal ��a�f/um chao�qRC(Thue-Morse B:} \audp{N. Meenakshisundaram, Arul L minarayan3ff<��{D�Sof* ics\\ Ind,In�~��echnology Madras\\ Chennai, 600036, 9M %/\Q�H{IITM/PH/TH/2004/7}'w�{\today5) abst!} W�m alyze cer�S :'AZ um b��'npEydemS ate,�/(Walsh-Hadamf\~7� emerg��u�pit�J,� .11� "~aEw bA@�Gq-periodX�%�, �mh8� goo�hradig��0��I3�1a�w+a�n� AO^$�?�CedYV�nd 5�<nga�c� �Tjrt � orb� ��# homoclinB� xcur� ��*� xi< &�Uc"t�R ֥{[%de�$� 'r�"�ic 9�m}_. \�@({05.45.Mt, Df 9Uu��r� make�Ň�� and{��c} omWc{\beq�g�J� }e�Fkt}{\g�l�,neNr}{\la;kD beqacna Re  d>pPJ Om\rQ "oarrowPo���r #{. )! {\h}{\hatbom�old��tdigtri�dow�� �al}{\aQ�1e0�4jlB�qsgD2�p}7eps}{ilor� omeg9mbe-box;t��}9 hu �{u9�hv v�-hat{K%wJsnonA]onumbe�;)u!"�a�h�hs�!�l1�lef:�t3� �6f}{o.dd��ov�ov�;baI�ce!!�eA�>d!� dagg�prA@!u{PR}_HxpraXq��{6"b�AinE7d��s&�% ^ar2r\"{o}�fe���h� � � lim�vsubtl���" heno��+TBerryQC,Heller,Haake}.�#:�(u�c^�˟�of8 "��p� y �*e�ose�@b�strik�resembl��@�>�� � ed ``�G��'' 3 { �},Qty����fruitfu�&rCcri��s#Gist!Q�+�5�of�՝ )c"�13 S�Hs�CB��#e logTe�]v�l'c� �!as �LL}. Co���%�umRfca�p BCat Z�r%.�)2BalVo!2wh� �(!��0}ins�ys]R!Iles�ct. �%�FeLL}, $T�J)are5& eser�V6�H&�unit squv$[0,1�S  ޅto�6 elf,�N�ak.| pha� �xE$(q,p)$A$(q',p'��x78(q'=2q,\, p'=p/�5�I(0\le q<1/2$% (0-1,\,p'=(p+1) - $1/2 /$. a� stretch!Ma���horizon� $q]��(A�a fac�5 wo j~ompens�[exactly *� �2vfb�$p$ dYe�2eEac�G(bT!B�-dleaGX!{%@ )@ mixe�*iG]��t(to�J!llyE™#izin a �\Wlyqc�J\/�<-aegas-jo�orTheMsa-�M,"P9�AOi� i�aL�oy��ASH+a�.�P�ωd�"�expon�s is $\log(A per � ionU�.�(eo�7by Balaz~ Voru�:y Saracenom�}T)sed ant&�  b���i�s. � G*iHex�+v�G�|($N=2^K$����sW}�{b�SR*f�8aTD"_� �f��z@�  �:E :gbu� ismT0so far x made� !�l � .�mE,losh�A#Nx�� A�pos%#a�unt�M� at�)t"Au��!� s: �  B=G_Kg>�(gin�VP{cc}G_{K-1} &0 \\0 & [a L )WLeq�@ $()�})_{mn}=\br p_m|q_n\kt = \exp[-2 \pi i (m+1/2)(n+1/2)/N]/\s��N}$�Hilbert��9.r0 d�!!� $N$  sca�din�I P�kEW�6 $(N=1/h)"uK�*�oE&e�A-s��e����y)�5�} m�A8ᇡ�r�n�\ as $-��|p_m\kt&6=m,n:?cdots,N-�o�6W"�%"E base���2-4 FourZB $G_K$zn above.� &xC�� ���ep.  ��y,��e �$R%e��ao[�$R|q_{n}I& N-n-1,.$ Time-resal]E�m%|��E�n{ �% !N[ �an i all)�`d�cw n&$�Fܛums5��e�#a����lexAp�>s:%{ \phi= ^{*}Jf $$�.ge��h���$B-A��=� x=os.%pp�0�]�c9a�C��he%� �-shif!9* ��U-p��sem*�"�!Cul�[�c,�ed�t� si �{�),.s�!� eE (Almeida}. A :��figur l}�PR��i�1�6Hphics[width=2.75in] 41.�Sacap!K)p tici0R on r!�1.��=J�5 �D$N=512�� (a):��(b)>)�i��D�ynge  increa'I �lB�S } i-"�  238cK8 i�Ս9� yA0o>� (WH)!����SchroedR".�;U^�we -�y $H_KE�A� ere = ^K H$U8$K$-fold tensor< ducE�!�"�iH $H=((1,1),(1,-1))/�c2}$. V�e sign6)�"s�>fEh�P��sA�Nis)�%�almos΍���)Upsfhr�a���a!� prinA_l com� s ��WH=Zby7W-� _6�$���� � = i}|(-Y)_i|^4� In Fig.~1���+N^.U�"c�,v �o��>�pI�>O!Z �H�)/UJs��z ��$N$, pow�-�wom�prh��!Msmalle!�%h\9) of�y�6example�na�1024$ O=1.96= %�A T!�OsA m'�:Z i�~ a� �G��a`�j  # $-L�hol�2�alA1WM�c�} beau�1�2E�-�& ԉ� I.fo Nw�'so� )n� elf-5iqW�3ll$�ee�f�_{tm}lY ``&`''��+)%}% peaki�ey�&�c�5%�!0P��lapQ� e fiA�� (or rowbpH ŭ (aa, K�$1�;^K}$)a!�#��thm�,�)NC. � N� TM} ��2ɴղ2 � nsA$$|\br q_n|�O%s\kt|^2$A��9z)t1\q� :�. ShownEH@)�e���(ޛ)E�H$N=256$ (circle) af eўBZ�$prJ�Ml�-AEpu�h�8YI^Ae����i(r)� ��e�H9(�XheQ�� p *R��.���ile O a�e� s7pof��:eru� . X���3.oW� ��o]&�jry ``""^"1 Allp�9}\C f kf�"�}��$\{� ,-1, r \��: g�3��t�< aA��s:!�rtim$t_0=\{1undCe1 ,\,-by �5�$"� {t_0�)o20%sr !�a�ba�: �p"� by $-1'nd��continu�Tif1-�ul� {k+1�I{tΘ,.�{k}�y. :�stagea�X��$t_{K�F�@ng of length $2^K�� �<�<��a���9w%�$n$-t,��5�d/2$t_K(n|q!�con�p�lZ9� A0trB���4"391�ng0� S 2n)=�vRnJ �(2n+1)=-R�Ai��� wor�wy� phabS�iubEe8Z�=s no �-�sea� ric�<nsecut�uoc>���^ou1� text&, uARrg�q�si"�^1a� son��� dis*w �}�relevP :Pde���crystal�B�&r�9 mesF4 pic _ed�d Jan p}�a��zh�u !� bel�\l ��Q�_ it��d����T�+aR blem6T�rassumed.DatE�� an��x�� ���B�˅I�9E@A�A]>�to e�D(B\,t_K)_l\,=\,$ %=@e\f{\sQ�K N} C* 0m=0}^{N/2-1} Q�m) ne^{\f{2�}{N} (�(l-2m-�},\"�K C_l=(1-i �Jla� lar�@N�$ns�m sharp@ eaks!$l=2m$��$2m+1�~a��b#l%O(even or oddaus $(B%{2m}\�Vx �21/\pi)�$A� .8+1:i j9, 0 9��h �i!ڡ�N�w�Bt~-�m r� K(m)� �I= alueG�/ul! J0.9$.DA lter�8A"�  � t ��"Zip� �faC�Qڥ8i!|�Lr� �r%��&� aja1$��'�� 6@!?$n_a�rt��2"yG_K\, %�mm \[ % 2 = M^KA��{%�,(i)^{K!��t_{jE��@\sin[\pi 2^{j-K}�]13] a!q?< ula.�xD��53%!�$ub � �jX] r�� ^9@ t_92@  |^2/NU� 0.74�Ta��|account�� help�s�m�be�,�>A8e\] 9"Re=)�K}t_K,e�_e�$�eA.]�  flips� @�G. wo. � �`-�UG \neaTe� $w?52 K S�doe��:�j�(�fx. To � ad�M  V�A7�& uct � 0=�g % +�i:�a"w ` ies �phiC^*�?%Q' fo��5��$� !�E�N�%x�$BJ+e �e>gl Co ���� ���y*�@e � M 'S�CQ��' ��hewpr/inant�&al jus�%@=C\,(t_9+G_{9}t_9[R!�� ��e .2"|^2}93,��� A)%�%T5*%~ gn $93\%��=.�h A�`'B� . $C�a��m:E� ��o9.F�$�-�9=t_9���h�C ini}U'A�ur5�2 V( $ z{a V Rj!A>ap��`m� �m��. �'W>�� ���  rove up�e)O# satz-��L�,? tJ���i rung� p�R�� E#E�, ~�re1 H(�|K$), �}r U�n�.nof�2&q:� [e�r�ɟ�B2NYg " ,��*�.!sin]X<no�( $t^{(r)}_k� Aor�rep�(�áV,�O }Dh.ct.�]C $2^{K-r}-Xf ������eQ�E Z>��KDtT��!�^A=�~_00+6 $k=1}^{K} (�s_k\E +Wx��^*��)S^{k� �^{(2)}�2},I  $Se���pe�� ^g���G,>dc|�!�2md���ca) is �s"B%w � ��,�"� LK1�S� =�2n�$ or {2n-N� kt6� �� n< N�#� � wiseE�n� ���)/``�"��,�/�UAq"�cut-off,�6�B�3 }q� �A4� ��$m$P�$1$NV �dnf- �C"�"�!��W26��O. Penr�k! �5"a&�% issu�3t&�"�sRi�n���#�~G�_KS^*G_  S.$ I�V1��%�� E��� &�A� �#a1�� $n=aA�1}2}� a_0$ �n $S|J% \kt= 2 B3B 6AU�ncaU^K=1_N� Sw6�Z:OU,like �.��rea*��Fs�MsN�f' 1�!sP��seXU.� �6�I SchackC�%}% un find K a�y�*���&�^A\.� 98$,"& �i�j}m: 16<acunsurpri�D�t��mu "w��A �&j1����-$� .J.a� �ٷն.y h'6��EwSX s Y1� and-�']+ A%e ��Tr��� meas����inD� "� ? ��,@()� Luck�*v ):B#m ̨!W���!�G�s2L2} M$h�ei�F by!�Q ng����&�q�=�o�<t]H$| by averagN�>s� bi�&We� 61v ard 2�9si�Halsey(.yp�� $f(�/)$�V�)�um. O!�i/cnoP  scal��� #%�\>! (IPR�t�"_n$��ϱ�*#M t3s $abe IPRB�Cy�#,i�n��!� s $N^{-D_� W� $D_2 Sc�l� "&,`�0�,C$a�Uiod$-2e2r=� �(c)�Id-p�!"� proj�;� �*�%\�I8AA�(d)��e��� &�a��P2�M s U�� $N=819�.r���inset.A�2UE3 � >a�by�+� Fo���" inflkt�!.>c.� \w��AK8!�68%p�s(!If� m9�rs.Z�#is ��m��!�s�V�"O&> �� 15�Uc�W�'`` �''�1&'&�!A��!Rt�"�edy m'��&�$ai7irH*6:�8� $N=2^{13}>^ver��R�+)Uexi��Af�s��)�n\9ak�"Y ^{(121�ny�l��$K � s, $S^kb0.$ Am�� },1�aqF�by}b, 4)9r�z ed *�9:. Two�s1MM 9 g�B%X &�" �!� 4. �V� �o"�wkA)en �6�"�A�:�oA�>;baMT!��.4���Zaj^JA[2fI.�o�a �� &ޤen1L�`�u�!�st:� b�5�# rbitM�mA�l5lAC�'M�Io�accuracyi�E�S !G 2�m���Cvs ���%�"y �6ٙB�*��4.�*��Eu]e�3m�i�� �-2 �=�. ��r!)'$v)iJ6(in� �J%�J%�Dű!V(c)6#^6WHb�+@d)KP.� �'B�|4%�A)'�X��2��er�| nk � * ��)4Fi (X)3/օꭚ� s �ie;2w�w turnAj^ ĥ[ >�M�`Q��jC$(0,0�Q" .U2F���4 �:�p#$^{(K)}_0/\=�&� �K ��u. p� ��se��&H $�)�"��<sV?"��~ . Si�!b�2�� �0",d%)oZQ�!(�MT�O�N� �>*igiA��L t $1�5_x� �u@-�26d��+)�$is ``Bragg%p''� .m�g�}2�"U ��ZE��w)� a%�$4 of�A�2��*,an� �(�' reno'ing g!r6 -��z� -1``gras�:ev�F+:� q�6�+ a\%�D_2yt45sw i_� �*�NZ A�.&!y��z b#!b�[E���T(� ���I M f2�s!��! a grO�: .���b enti� A_rum, we Bh%�j 6��n6w �Ǖa�4�%a!V 9W��_2L�HO C|Oas����=2cleR7�E��o9-s.5 .co�nt <:'�&%8]"A�2�5!��!.� )��discu��. N!2�,1�SuW H u���^��typ� $� EGisD*n8�"y"W��I"� �S*:G���A�i+0as;W�r9�A@�:xdetail�)r az+er �gA� Bd;3hu�b�,3.2*=35:sJid�,plof�qp|�x�"�;�4 2:�;�!I>�Mo;(=128,\, 256�<512=!$�/ (,? �T?pbottomBb � ��� mhQy skimmm�"�)�Q=eisx9, highlr(*�nova�eaZ�e��ae&. y=� e�L�Y|*q t�M�u�b�d~ m"�to��m ��=A^$p*�=AQ�* are �+� � �re vie��"6&��+��m,P�06FC ]2MdxdQ_Nin�=��+(�x] J-J/% e�$``mixing''� mf? themrg����"- ���$�w/f�*���.a crixArequir�+Q�ob*9�s 6) . Qu� �m�;�1T*/"�AEUex��8le��NMR�] NMR}!�*�)%-is kind."��:�1�b� q�d�?ly �\:�&Z8�� � s be_the./6E level-vel1� �Arul},n!SR)P�re ��$_ �$ %F�B�e%` , yent�� s, %��.ar�  )/V�Uius %neAlBa��iMG1�"�!��Aue %O�R %~ @-aAautN"�J5��) %��a new�&.Kay3�b�"� % � � \ac ledgAo s{ N�P�^o3n��asa� �Cou��%�S"�`!� +MuWEal Re�g,ia�th6hvb . NaLUA i"pve:QoA��<r&-�iseK�� t>�g99M�`eF} MS,8Rc. R. SLon~_��f 413}s[3 (�Q ). \K�E E.J. , dNAWv.�;. G5F515G4);�7P{\it Les Houches LII,1ci?Q nS ics,} edi-�( M.-J. Gian��U]�A��J. Zinn-Justin, (North-Holland, Amsterdam,�Q12�aake}F.  ldit�SigI�%��cs} (SQ�g Berlq196U LL}A!(L�VnbergA&�f(Lieberman, )R���`d+%Bd2oNew York�T2.�kFJ.H�nna�N=�6X�b)�Y267%�0); JeKe�, N�h���� 4} 30906�ACN.L. *I8A.1� Ann.%�. (N.Y.) P198h1Q89.�&N M.  hG6F9�V�90.Gx= Aa�Ozori� %kZa,2�21_\ � 91);A��G�:e79} 206(�i.�*s<M.a���� qSR&�W �d>Y4pN:]{jpconTu&�W epsfig,bmYY. �<T\t�WLC!Etro�,.�Jc�WX�WC�ndkvdG Ciraolo, R Lima, M Vitto2X�Y{C���-%�|xTh\'eor \foot�0{Un�d Mixt/Ra�ra�T(UMR 6207) du CNRS, etZO���P\'es Aix-Marseille I,>I7Tu Sud Toulon-Var. Labo�*�iX\'e \`�4 FRUMAM (FR 22},� Luminy�X0se 907, F-132+�� Cedex 9, >i][ad{xHdre@cpt.univ-mrs.fr)�a"�UW��#�� Qo)�^ .��s�ch�^to cr�M� invariu tori� �9B^VCT�p apt�"�C�� �urb�Tz�]  B}e'"�##y�DJ.E� "SxI�LD  �?#C)LA�P {@v� a ke+Nl<�m�b�j� of�#sD)!N�_ "n%�cceleA$L�M�ccL las Cr� maWz��Nof' ed fy plasmasZthf�R��ӑB:%� ��&Cq*$Ely ��!��lM�ee��lg)�n�'ll5I"� r�7�ueA��# tegy%8r�b� builu"b��!7�'daI.EgVSU>!j]=@+)p��!tra7#o�� mo���~1I�s�]+�)�m &@$�`%C�a�f��Refs.~guido1,2,michel  3,vitt04}sw)on�=�"�DNTF2be% ten ��D $H=H_0+V$ i.e.\ a��`� .S$H_0$ (��Q-��bles) p�91�2� $V$.� I�Q��c��!�=�at$H$A�a�Qh"o����q�behavior~!�LCo2!1s�9by!��break-up���KAM���fol�V�_0�5R�Je-� dom�w�w2�A�-�)r�is [F�lara�)&$��� m� ��!Y*/�+aMdes&rV$hyperbolic�s�?�B&aE� 71M�@Bmack93,esca85,PR��Z�MaF� 25 ye�vago�ir> @chir79}�e�2 empiE1�S^�1�dӁ�F���{reson��%oIHto�AA�deaa���IaN,.��jE] >rough �q�]E�thres��� >�(e h���2eA �C �!�%� �i*�{w�#\:����s�,e��!ep*di�8cy%A�e? nI�9a 1su �ir half-^M�eW}�&�lq�modB�>< $H_c�Y+f�4� $fe�2�$Vm�5�1��reV��"��+H&=Q��e1j�^.�Y%�;�1�'sY`q��2�����M{E d9����/�B%�.�Xai�o�����a�b;i�*1:-.Ms����+)�o��i �i�tna���IjAS.�6��'��*����� aұ�e��J��F�h�nv!o�Iwis�Vinher�b��p+c!� purx4s�eol \9��eb� allŖ.AAwql� .%&�Y (��subxH�c!a�L=I� non-�"!*1�;E��I!�Z�Ple�"N��BM D #al%|p'cx&qmpI�forU� #Zw�1U��{�<���?�6F�6 �6so/N� @��= piA t�� �+ur, /1��:i��a%�~m�'%:e��2�p%i�Os,/ P! � ljp����  �TGru.� cru�JQA�:LA$bav&L �a�&� $� }A�%��ZM ory}�&eJMa��u��B��in? .�=" M�! c2�- rigoaG.�Z��1� 6!��KW8!Km�9� ��OP.�)a2V�; �*tM$)5>/ �  $L�2���J"" �-�ed2`�9$$ H(�A}��m��})��m \omega@7 '+ VF2�a}),$$ where $({\bf A},{\bm\theta})\in {\mathbb R}^L\times(T}^L$ and $7�omega$ is a non-resonant vector of ${.P<$. Without loss"�generality, we consider a region near $ �=<0}$ (by translat' of the acs)�, since(Hamiltonian�U4ly integrable,&perturb R$V$ has�t��li; parts inpor�|$\varepsilon$, i.e.\ \begin{equ\H} \label{eqn:e4V} VR�=M v#5�+.%w}2!\cdot  A}+QB�, \end�U Q%�of�O(\VerO 0^2)$. We noti%hat for2=0$)\.�$H)[!�nvari!_Ltorus with frequencyQK$E�Eq}$ at�Yy any �`not necessarily small. ThEatrolled2�M{truct isr�A�} H_cRT�m �6� V� + fKm u�Oa[(1�, 1� B�q� 6%�ha smooth characteristic fune!!�ubDaround a targeted :�B�ajco%I term $f$6C8only depends on2angle %� bleseP(is given byrtexf} )&1%=-N06�D-V\left( -\Gamma \a� ial_ED��1�:<.\rightfm]-m�opera�� defined a�4pseudo-inverse!z.�I"N��>��ng!F $V=\sum_{e� k}}V ��rm e}^{i�c2$ as $$ � Qm.� /8\not= 0} \frac{o} ci�2c��.�Not��a�f%M�t��^2$. This can be seen from Eq.~(\ref{�L)��Q / rewritten �:I2jalfVM-4N� v-QMx -Pv46�Ur$$ �l�� is quadraa�imHe� s. H��a�iie���q�63Ez�7%k ��A. For�L>,.4=w�)�.��close to�Q|$���(�� hich!%��ed ��ddi��2!�z�eto} E�A}=�*:: �R�$Q�Zy%�V:%re�@a significantly l���- edom!�choos�,!F� I��( sufficient! have1��r�? )=1$�^$��-6 \leq ]�$. A=in3 ce,�Zwoulda�(a possible A�simpler�iI@however represent�(a long-rang��-k!qͤ�e�)$zpplied�bDall phase space. Oit(opposite wa� an de!� aFk such t��.�$is localiz��w reaA�Bx�supportA,5�$is reduced!����,neighborhood3i?�va���� e ma� dvantag��t�� step2��i� $eds fewer � gy (�{��=r � �1�.6)E also` does� chE6 othe� :Z,*al ng ,v| l?� �Vur �,e system. In�icular� dynamics�p �< [� �� domi $ ces��,erefore a clE�chA�en�M-4 ���O = _{loc}�xi�m�+n�V8 @.�9�xparameters $\alpha=\sup \{x\in{*� +, .�(x)= 1\u5et�;}?re � %�ͩ ��;��� � onA�m"� +$ (% ��!� clas�'$cal C}^2$)a�e exa��(rlocpdepica�on Fig.~� fig: !�. � figure}�center} \epsfig{file=Carry6.eps,width=7.5cm,ha�t=6.3cm2nd?cap��{�E (x)��)�0.5"�!~1.5$."�2����< {\em Remark~:}��! itud%A�q��bis pro��ional��B� H��, i�im!a.Lis:� a :4 (e.g., specif��by its�;$� $)i����(makes sense�>aw6�N�t0already exist��origi�(un r led).I��words,e�.$�P�O_c( ����/2-.!5hK reshol��break-up1a:�%Zno nee5 ��F.�. ^� � ng� barrier (R $ effective)!�$diffusion.Y we point -�P, belowI* ritia�t�.E=�Q&c �QA�Z1�2��!a��known�ctlA� (� iD���, �P�{!�for� ulumE crib� �). #��mod� .�pot al (� ��e{sed5�a�I�)�a �� mula*�  )ajMR� . I��next s!�on� will� �a9r�E!�%ampvC��comparedi�!9.� B�it was(5n�E}"�8bf B}$ drift mo%S� <V idetTin Refs.~\cite{guido1,2}Ń� u��z ,experimental\vYtravel!lw~ $tube (TWT) qtwt�@-`{A� cItoC:G } W � " llowe:,ATelя1��H0fp} H(p,x,t)=�1}{2}p^22y{ [ \cos x+(x-t)G].�HA��`pIfa�1w�(Chirikov's a�erE^it lead�A�stimatՄ�of scale� o�v"�=0.0625$-hzav}.A�fact,�me� isՖe\to S is m� m� A�lexAn w� ig h^�is empir���. S� $al methods� b� developed��o get w$deeper ins��I�o I� 7�accur!8value�M�n>��^Greene'i sidue�-A8gree79,mack92},�~,map analysis -lask92,9iGrenorm I�) 0PR!�})* 2��1!��->�last KAM ���model)�$:W!one��&�8=(3-\sqrt{5})/2c �!�%�Y�i6�8\approx 0.02759Q� �P. A Poincar\'e surfacE� Ob 1}a�2 E�5$. As��� ,9=ch� z�t plq betwA�!(two primary*� M�u%-gi � brok�oa�isIra�.�$�# 1�# vQof .�&N fp})I.�1Q�1 fig1��"= A firste�� ideaA�a !5\"to�2+!�NZ�by\���`f�v���i�J�~:j f_d(�-\delta.����,,� )" an ��d�"J�ve��5�2�becomev�Hcdumb���(1 �)J�g ٧Fi� "� 4} show�.W !�]L*b �)^�E*$)A� 2�%!sizeD!-up�"N de0 ses buh ia�g,IU!��aF� (Iresult� aT4t�9�)& succB in� A�J i�6Z�s. �44��5�JF�.&4>&InmZJ4,e��  �e $0.7- I3 1$m�?ire0o3~��) � �q�, e�ifQ� $ satisfiIheVda�n�B] no�^ lici"` nqLQI �dBvI��ruc� i= � 9E�2,�h��?dra� ally1 amouMf1 y� T . Tj��u to� ign an�stK gy �%wo"goals~:b itemiz  fim� %�� �))"#B%>�y?, a�5�-!>�!� aF�~r.%�� A�� �js �  ��e� &�] \ vitt04}|�I�%�.(R � &nit �R<whtU�� xI�ly%7n��2� ompu��"ptQ&%�A�is.��1.5 de �bfr�s � �usualR� �3utonomouJVA_JVB�Lt \mbox{�  }2\piJ�6�Sden�$E$� onjug3 �on� Z�zs(H2dof} H=E+Qp^2SJP�VO6�a&@A�"����!�to!ify ly.�~&� �)�MB�  ,!�0 �jcon2!�iv�"8 1#assum��!��%�2�ir�I(diopha�e)2� fulfya�hyp��) � heor�F� A� e mo�um $p xhif�by�2f� 5 "�q�M��$p"� "� ��>$OxT%<1��ZM ELFL x� all>"�!$� �dI �&�A���is�!-i s $(E,p)B H_0A� p,�RJ�i�!H=H_0+V` �%�R��"]�V�V" v"��ZV6���aed"; 5>o6�U$As$p$, $x t$5as"U��"((k_1,k_2) \.y( Z}^2} U_{  }(p):R":$ x+k_2 t)}!! .H$�()� U �m_mU(0,0)�"l}{iq k_1b)>�"6}�"�A(:h=ډ>we�1 �\*�$x}V(0pF�~#)�}{IM}-�� -1�$]�!�q�� p% E6;# xf})A�!��Fm f�(J� �) ^2=- .֩�<(Z$� ��)^2. *F)fpa^ ��}l*%�a*"!��Q>/>4(� J� BeFI� torea�p_0)])�6D$�&[-Gk1�J6->�.Fn�*Hc�v�E�!�^��pJ�#� w��on4a �sa��$"� 4eqnarray*} &&6c=1,\\J2 \vC+p-1��^� 2�:2c$\to [0,1]$t'&D. .�+�*an subt*�B6%@+"`"� � ��+in $t$5��!^ cV_Fou U onents0 �k}=(0,k��$k:�"�*(b� okpt�Y's�ȁ " .-X���(�3�� 1^ !��:�H 8 cofQ�1 same!2� N7or�e9p�'��5+ime�� Wm���-*$ve5i�L���[^2�W.�2x}{4��^2.\ 2e�}{49�):"(2�}{2 �G-1�gK+ŏ BW .�3ced&whep%#ree�"Dfee2J�aV�3di�&.Um&�1�2g fpdBJ� _d  ��.dt)6� BU&�o E�A�reimeAy:t)��E"v�E|6�]_d/d^m+�fi��-lu.�$�GOaA�b��.C_c"/  ) to5� \gLaA�ne,6 (}��it\a l��n���(y,_d \sim d^2 ���m"i{� "�!v�0�.A]a-�] "�"di$ (�2���Xto keep| ��]0,1 [�"it&��iA,. B�� 2�v e��x a )Q!Ry.�$�am,d eli'Yl `& $d�!2��.���� r�}��.m.�_d�5bCAL"�220H%|E;2� d}�9� $f_d�Wxn�$�[i&@"�,�$v2�AUV5��) ver�2�^6:!.92F!\\ n8 nor.�*U� "F04U=\max_{ \*(T� � = "� e�.�!�* cV = 2=�� ��<.H2;Z� � k ]f =��a;�2���� $r$.Vf��>��!r�!�}{8�N^F���  er�P.s"�/1/2��x� "!fJY N��$�1mie��-A�.`F34+ �$k $1/2� �,c �8�!ly 7\%. "{ nume^!o��4ns�b��c�n�R�>�4�s��%"+�:lab� 15�H W f*2��V��m���L*�Hcj�E@ =16E*CG}� 6� &f��b�N365$_�%at��2� � �u vrprecisAY��lo�.� ofZ�.�li�"�#8(s� ., CG})�t�@'9/i� Ie� q�:���*802�u4%H0byGB�^Y� ). M)$5 �6AO."l,"2xeq u,>)0�O)g)�,ISa# rdYpolynom�fK:x] Y,7[ K�2i� $C^1$-��;2*�.1-(x- Y)^2(3] -2x)/(.)^3�6f- 10^{-26�.1.5 �"�1in6��Q2�&�b��:�6"2 glob*t!)(.�1>UF{*� Gleseqn 0.5\%�aQU �.���#4unitlength 1cm�V/,/(15,6.3)� \put {F4/3av0} >8,0R>b�>� �K���/."�%�)���~ini�:���s launchh om $(a)x)->!m$(b)$� abovn2m2�� "��paper2� 2-��:0#20#3+A7.�3M�sol�:+. Aejlet"�.�2{(t��h. S"n@ �orobust�IR�. ��6i A�r�5� b Aa fewa~A�,�-Re"`�,3}�st�H*J�-R�6-&�(��aa&A" 27 �8gt$ly>�e&)�MTabs�!of19. Also[ ^"!.!in selecg$P)priO&ce e�A1���a 9 QedB �� ����5��5��Z�!���F��q~: ţ&u7* r�&J�E��60.01$ (J panel)EA�#02$ (� %2�CG�5�^� $� a2#(��O> ��&� =:��� I&�)��a��io"�%:TN��3�B.�#1#�9+!gular�(�N�::q��n "�;�::!�#iffere�F�u�.�� $~:5=�1$she Y$^#�� /EN�6���d6���arbitr*�D���'�F �� ��8� �:J�isq5�� sistu .Z� Z� coup�2.Av"Y $. �2 *{Acz& ledg^"s}�ae usefulucus�5s� �IJ R Cary, F Doveil, Ph Ghendrih, J Laskar, X Leoncini, A Macor, M Pettini ��!�Non�CD�;group:FCPT�$is�7kA�? �1E#1 om/CEA (E��LEUR 344-88-1 FUA F).2�ReEz ces}�0Dthebibliography}{9:ib>'陨1} Ciraolo G, Chandre C, Lima R, Vittot M,�M,s:arella CE�1+!72004 Ci�%� �2�9�J*- �!��2res�magnet�>plasmas :J. Phy! 4: Math. Gen.} {<$37} 3589 (,Pa�int} !�4.CD/0402048) \2 2} = $Briolle F,.Flo*Hi E�-�.!*s�8ml�Bol �+)R�mal�'41P�86))&Rev. E-$69} 056213f!312037=!michel}U )�P.�JT�%yE -� in C�<�2or Quan�%M�4cs&an In�F��Fo8 �� 6337j�03051�� .�j��Pei� ��( h�5in2�M1M�Celest.�.�P/tr.} (in�ss, �J�311009��*Vu��U��i�!�5 LB/'��2,M.�2���ityM>18} 42j;405056)(&�fBm�5D3} MacKay R S 1993 �R5�-on!QArea-bCrv�}`Maps} (Singapore: World SAD�:='�d85} Escande D F 1985 Stoch�-�y?E�J: uniA� al a� t-�qRp.121} 165 �NG59�%�JauslA/ %�2�z*-��6%��Ie��2��vB�365} 1�chir79��8( B V 1979 A�7& many-dL:a� al oscillkJ24B52} 263�Z:9,Y�,�{�tI�,A4 or A%BQ�A�4Bne�`�M buil� �=s:< } ccsd-00002248.�@zav} Zaslavsky G �Fil)"(ko N N 1968]K>'tra^-�"bLco",ofDlic=\!�quasi-2Nxfa��Soviet%^�8 JETPM�25} 85=��-!�:9 J M1��8 �de�ina`a su��9yJ.�b%�t0} 118=�e�2>�2 �N�9 _JcA�6��92} � , J, Froeschl�8i] Cell�� A�[2�� measHEi6by &�uhh funda5 al"xi4J�<E dardL/!B%*!!ica D-%56} 25=$�9�� 9 Introdu�*to}y^��*em2�SF� Three�f�  D&�/F�/�} ed C Sim\'o (Dordrecht: Kluwer) i>2  docu! } %S%%{ �K[aps,prepr ,��edaddr��,nofootinbib,�1pacs,t� e� 4es]{revtex4} %�\ \�O twocolumn��P` \usepackage{amsfonts,ams�Esymb,bm}2)� icx6d �!iPrenewcommand{\vec}[1]K~'rm{#1}}}!{b�S1�title{On2� of F? al A�[to Cran�Su�s} T�author{Andrzej Z. G\'orski}% \email.GL@ifj.edu.pl} \affili��{Instit�2$of Nuclearm#Ds, % Polish Academo��ces�(0Cracow, Polan�? �0Janusz Skrzat�js,@poczta.onetF�$% Dept.~of! |tomy, Collegium Medicum, Jagiell�UUV\\B�!3(date{\today!�)�a�(} 5|exo( ($d$70 huma�8)�s)��'calcu u��$ box �1g��G�#49w�fKSr $d = 4$ (�i�$r�J,$1.3\div 1.7�#��� p(random walk� �: �m%� pro�T. "]G(�disper=� GAd@,cy suggests �o4&U@)� nt. S� numb J%obtaiS�b�Tpsagita �cor�2 � s, !"(:�lay!aS!ter�A ing. OuN)�#(c29D �i pubA�� � I�!<��Y= \�"\{05.45Df,47.53+n,87.75-k 18LaAwLHe�E�*{.Z�! Geometrena phy��l objec0Bof�R&�U$Nb�Hactal " �DRenyi56,@70,MANDELBROTa}. 1S���((<scrip!�self-^se�+dely uIFin�&�#O�Ds,A�g!��S high  �FRACinEP�A� jI�%� �s .-,CM} to astroN A Mu5:!azgDAXb}A�o�% ertian5hmp8fng�� s up ts �5�and�5Q �, )aQ� symm%�e3iA�yulD�M�e y1�.Q�Qe\a�]e=q�ifI� nd I�!|eSpa�Lx\ of reUXs,]Q; r image�(;j*s,3$eem&be e� ia@7we�Gui1a� morpholog� � !�Th:#=��E];�D��,�^as�yGR�B�*cc�;Hdel� �genesi} �, pape5�!<!)��uT!2 ��.�:red year���s�EA�mpt@?|dir�onm$Hartwig91,�F00 L3a,Jack03,Lynnerup03A�H0M�<8 :8�S�����8%i �uto3G\ mmer!� softw�3AZ<��� a��Y�Ded,,*@��A�� $1.0$ up�A�7$)< some_1�@�[unuO2$ $0.0 �&0bZ.Treyed�CL93 ---E= c2�a�a curvd?d�0Fmust be�2�� �2.0���con�s oaGi�H=�areas  Car�� {JQ�� blad!�I�ou�WKG�p*MW" btle��b.]!�F���!�i� .a�such &� �s, }�*�,v_ve�Vim�  �`dat�Ui� a�M� case�JOS�? �i�LtA�A\V� Esa typ�z,log--log plo�Q7�}L�^�%�A"?&r�AU2fi��� 4sh6��3�6�-&!�"%<avoid b >GO` ~u�Uɑer%ahN� �%P�� *a�6&ask�3b� Iy�! durR  eadVB � perf�+a car���>$ -�toj�e0?It&�4hOE`%ta�dev� sE�le�IsquSf�yA[6�U��f�[d��I%%�*�D�spiLat,  `CL�co�5ab��2��T*�Ql�&� tou �aa�/ �%ur"i e  "{� � �!�} AV skullS stoq!/ADeo�`An.  L0 1 Z3 �By4QW2 o ad� individua�6&1sex�derivO$  pop �`,inv�$g{�met :cRO1��' varI caŧ by d��S ethnMD�hi!%e�da�y w�V�/pec�F���JF�!6 * f�gal*&A��)�.)�� !��f�)c�\K�forty9_�A�0types: twenty6  one�'Nnt�K� me���k6 �%�͹�Lt� ca@A��L �5 QomB� (to �-of� qu�e). Al!Bam� *A�oblite2Ed nira� tour�-re �  vi\.i%ega ��1C"O m,��t F�nsu�QorK�L vaul�%re phot�ed �� digiA#cameraS The D j &�A�Iolua*,n,$0.1$~mm; a8pl =A'�:� $03s�*v lay��i>kX szew&F!�thl �, � Micr�fx Pic� Pr&�  we e�mVne-pixel�  be��!0%gW*our�+-�con�:B%̈́ s (22�,coordinates)l%�. ly� u��q�"� ��e ��� &���� (tak�i�: detai��e b�)F� sG%�E}$WY~mm, =ly�M� ��&� � }E�leE].�3wholeU#E�� $100q(. \textit{[h},n t0i�2<��YiO��!maximum-�a�a��B.S -g,�ZE � �U�8\ ! U�" can�extend�veibG e���N� %�$as>EM�3s�_�bas�'ly 6shi'V�0's"�8�#�=sD\�i�F{� � D be�a� tEC!oŔi irU Vq �A�"� e!��2�b�iew�<wN�$pro:\of5 l$ $xy$-plai� A5)�: �i7:�� ��e }� ($x,ye$��i�(�M5$($n_{tot}$F= eachPDe)MX h" val $9~00Y  $,)>!wa�_I�,$160� �36���A�s a"   �!� % %��nb�"f�4�2�=� / ed _4 lu � �!( �0clu#9aphics[w�]8�]�I=0]{g�1�.} 6^.S8I� 03s2�(��u"���Box C6a�Algorith6X T�LNX; X� %�w3 %1"\ �_a_��!� embedd�:�Q��gen�a���Aa�$d_q$,E��Gby-70^%��io&�=$dqDEF} d_q"�7h1}{1-q} \lim_{N\to\infty} =;ln �F,i p_i^q(N)}{ N} =J778ln Y_.. \ Z�B$N��A~M�e�ccess&]di��)a),��9 Ts (``boxes''), $p_i(N)xG�KW��� Z%��$�M� $i$th !�&@*($N�a<$ ��=�[ se�Alita!�U�� foj=1/Na�$r{%��&�"� 6��� > ��"vs}!b�<C� � \B%se� he�%*:r�<i�U! =1���6�w5`.8 $�2 $ ($p_1(125/ *+,�``p� ��'' (f�1e)� Y��enough�,@9;)� \to �� ~~(Y�)$,JJ�����to�Y�% �� ("U b�U so�P� at��5  pies a �� A ��� 5s (too�Ag �A{%>G � "^e9 hey ��i credRh�Lan&- A �1�2W �j2�ha: �)� ��to= reli��qs (* 9_2o ),�o!���W��I!pLPke $\chi^2$ or Pearso�D$r$--c&�0 , maE�S@ �dmai�aso�Ly�{g~ ".Ar�:F�i��8 misS ing ��l�;�J� #d�a � �*cod�s�a� a�B�r%V �)�Hmed�1 N9M a]u�T be�Mҍ�6�� ,it��on{� � (( ) �tls $5�7$� Adall�& �eat23E�%it��s (5, 6E�7 �0cY:�Jh�C�� '!�1! o"� �\ N=3$�be��� $��1}{8}$�@b ��r�t�u1$~cmaơ��XG�rg�msa���% ECrresp�%ng 2�� of�Wit_be2i %Q!�  !�I>fi]wea�w�a'�E )!�RR�,i�tcEKQ rawAITEhtab:t1}lhY:�ikf��� �!QAJ�p@��� satu?� M{!z�!ly"�� $N=1* TJY��[I� $N=9� �N� i7m�D��s�D&A��n ��&�!�"�d {: $N=8f N=7$ sub�|ss!���s e�;f�/� < &c (]<2^9=51j@�IK"��je @r KM�1 !qpl.KL�/�  E,sL\]- ~and:2�t� �o��ac���%m of 6i�s��+h�-&�1(a su8�E d.�E  fit)io$d_|a�oX:�5${mos��sa�T�c e"cI� IW> (IR� Y0B0.0f!X6-E� �C5 aAHc�,��Vti�"~``UZ .�p 5�01� ]�sa�"�h�8ŝ� ���5M��H$,rAs�:erx tvZ)Z|2� H�7as�8earli�*� be a�A� a�!�+ ]9"/oguaraQ55!p�I�!M rO % q�: f (i)}� rdU�A�G%�e 2�A�v�;uS��A�t��iI![e IKa"�ams;.���vpat&� � �xe��*��Q$&\dir�w1 n��e� azgPSEUDO�"}�~�!�exc!+nt� ��6��!5 nois�ve�1�iABk�j� �not 2%�error�-_W%�a� 2� ; T(fB� eQ%7outpuCa ode��eI--Q!s + adja9!*�Y��!�fUmOI� ��$�0, 1, ��!$4a1x6{Cto$ �Y�APer� Q� l!�+1��er heck�"4 multi2��y� . U�".provid*�3�!w��u���2�=�m6�+ \squeeze� VA}.T�T݃�#>u�!>.Ml,ruledtabular {cdddd  �I & d_01 2 & ɯ \\ \hA% $03s & 1.394=(1.38 & 0.046)46 "1 <)04 R53)� 0.05)R6�1.6"1.5Y 0.03)06 R4055vR 06�6�10 R47K:�7{�5 �5 06�1� )0.NR6 " �=�1� t �V�D1.j�7 �%�1.5)�%� 0.08F�1�IJ{18 R � )Z��1.6"1 �:�9 R4)�1�002%� ��1.E#6R2-�EYYg��lJ�m1.7 Y6 )=�22 �DBR]���A� �:�m�4AmV VH1�)ON�:� )`v� )e�k 925 � "Q�!�Z> ) {=2Q�)j5�Z�)�-x%�:HM�4 {E71ILZR�1U>6R3Q>R�J��B� 61)U�xQmV���M4M�_2RIm:)N�)U6t1)\:���R ){J#Q" YE).R.���>end:��_� \�>o2vo:% �n�nc���M�mD0J�Q�)�� }�04 T3�Q3)v*]������ <:+06 U xe�^NGEyJ�:T10 T3 �.*JI�:��C1 ��Dm�NQ# �e�>�1 ��1�X\�N) N���BU7 ���1��U�!�� \:*18 T3i�.:*T #2�81 *=|19 T2Ir**J�.�1.3Q�9�;-�Q$!J1) TJ�:*�*�22 �%µp1�1}!�1�!���.~2q�)sen1 ~JT= 1QE�*}u2M���!��j09&�)��>M25 �G1�ca(J��1�1.7c*.�M�%�12|�J�3IđO ~1*? 2M���1��8~=��1Q)�*={3QMAiMF}I*T)�qs~*6�- %�BaN�Q� �%� 0.03=�11)�1]i�>��qWj+1Q�- a'1 ��J�%Q-.��*�yv6�� ""!Nu�R�}&r/T�}ser�"��"�"�P("S)��"40�Ls]/ �$TcrG"� U"�Ga$Gan�� #*�/\�v�}V\%$:&&= $\pm!qЅ��d d��iq�3 c��6�*�-��ar��+o��,�N2�'/problem�a"���EbeS �2�)�"0#is i+Lh!�be roug�2�5 �6 be q145$,+ !>��%�oshU:��IX)dekU�u�H�]  ?2 ]q�T hile��s2!� caparC�"p&,�c��&on&�)9!zs���cM7w1NQ5["E6,� =4$,q&SRW $q$'V,r~/ce4"s-T&i)zT"��p�erI��O>T0e��:edA+�:j1j�W% ��%2F�%E1�A�l�2qA:m�"/�0�+B�vue�*!. FhZ%�%� *II 4%)"k,6^&G�A5 c!r �.�?)��N�"�cp?7 �)E�N�l(s,c$) * Ve�(1!, ) A!Q#ll-! `�@f=2�e%u9vy, S)A� #W �(N=3�8$&f.�UO&))�8.�l �#w;�*�N#). )�89w�%*�H:�as(rZby�two��!j.� fiveY�lso��!$% ,xŌ�]8!���Iho�sem�@AR5�+ �O��fit�e 7���[, ˋ|���Z�+�`e��HI�0�AIo���""#�BY���>�7�A2a2�A)}���$ o�G�Q�M��"93ces#U�id_0-d_1\ $C $  d_1-d_2 $% M"!~�dM1$5.c� negligibI0n4# pari�#�#�&�?;ǥ�)r��8�@!�&n"9�s9<@ a g[� �8mon"��}�huL*'4<# (A8���"�.).B=�)542-d_4)46_��*E�!�ݱA�,��'Z�"$�ƍ]%� 7z\>�;9voI-��! �� ``�y''-\is�tG!urN?.v �re by�15$\%�� �_a�; m`,�\oW�G��e� conn�/��i��-�!.��.�C)}I*�e�A7s1Gɒ=u2�&�!���8qXq+)�A�.�a� 8)�F�%U�%weexԉ Jach��E"{(�+ca�9nK��z`7�>�;"�48>�M!;�|�1(D-I�P���1\='�? S ,��0#$d_���� "%"� *� Ah����:�$3};I#�c݁ry!�`i��D8.=�$ ���, ZB� �W $��z$ (:NV@2�q�V:8�m "� $ �]�5 5 !�1$2�E-�A��%4gt�}�*�5a%"�", .GF)})N�^2Za.�[d S5���QmuS8;V!��c(c��&%%I�JS �TB c"�9Kbig�����mp�/;� 3} A $M[of>� � l|�\-�G &� |�d"�V5?&ut�Q�*I1q�1&59o�-Q� &6�V�q6�P 4*0.�H95*tV�� ��nz��A#7G Summ�O��Co83�H� A�7�AA!f@!�$�2A� �k 5��n&2"&�3by�E.-@2�, "j$uT��CWY�0A1h$17�4� � fiC Y���2�e5i�" ��.55���!'$�  ��" B(%  K  ��|%� u%5 e�5  ��` �,%rN����F��9 o���7��+�R,C$!d7��be n� �. higher.\�;ut` 10� �opb�l ms:�*"%t�D�$opini�Kmi/ sourʼnc&}@6R i���J�JT:(.*e.g},�as. PIH�dF)-*�d�8o�:��Ze.D[t�h>�D�&�0e--��'}CDmod�W�*�EK!�Gq�"$%ARA�q��.:GJ#H� &�/�& ,:�1=ac�8lu&Z1r BrowH�r&�M�+T!F6V f�:�>n<� on~�H b2� Y-*�M�:�: ing�2�M^var�KN%(�/&�AM�}0�(w byw-m�2$�nd� Aq� ��N mDZsm�H ess��,!��s"�a|h�ainS)�=aRfur�52�LȣN6\.S]69�M�.�Q d\.�Q,AP}[3]{Ann.\ Q.\�\8#1},\ #2 (#3)} 25NPA6EQ:7Av8B^8Bn8PL p�T(.\ Lett.\ A��PL r6:B�:R� 9Rep�PRL66v� ^r�R2�#]\��CFvC��DF9D�9JPG9J9�G�7RPIn)N Prog@�ZP �Z4��EPJ 8Eur:��>I{B>�~T � ��^���PPN? @ParA�>vbfr[APmz Acta� Poloa�Z6� ibid%�N�% End Jour� D�i�ls!N .A&Zk �dbetv9 2�V \a{\@}:b{�n2�\g{\g�>-d{\��6.eom�[6z{\b,6h{\et:q{m�:�i{\io-re��\k{\kapȁ2l@%mbd:^�Wu6� n{\n:x{\xi6&p{\pi�X|r{\rho6(s{\sigmw2�t{\tag2 u{\u��6Ff{\ph�2.c{�,>j{\psBo�E< A�cap�Fs.�\D{\D��6�G{��>o L{\LJY J{\P�= U{\UN� F{\P�.�a:�2  S P abbr562� ra{\[garrow6� la{\�gFA%n�?RA26{\r�l> ovl}�Y over��Y.� {\ud $undb%nono� \\�9B,{\diracslashp@#1\llap{/\kern2pt[Z21be}a�g.9�:�e#�-!J>!beaEc�>$e$ FV"ba�a�}J'H "> eqrfH Eq.\J#1}>s 'm}[2]{Eq ��)- 2R4twR5^ v9r��:n,\U�#2 3u]�E�o"�:�E %"C]style[&�\�]l,epsf ig]{{]} 6U6E�W�],secnumarabic"�\nobib�As2�] ue"�]r4�6 >tj5.�]*Y]2PAY{Wavelet&VP� p96"�im߫m#�\GI{Pan��anOC.�\S�Pl!�� i�\&:\(Hyderabad,  4 500 046, Indi�kDrasanta K. Panigra�� %2u kal8$$earch Labo��y, Nav�k(pura, Ahmed %380 009BtJiI ra Ct rikh�*�] ۺpBo:0]def\beq�.Be��.�A�2arr5�1e  86zbf#1R a�Ofm#1{��\bold�_ $#1$"hf{"�>2�UIga"�]WeEEh#aR�AlbasrZY�lZ*^[�/A the Q�behav,Nof�NsI|�]��Y�[����dt-�o&�e��l[[�captu*tr �4"LB�#�� ndowA?$s. Discret��eQs"]# Daubech�fam���:to illu��q�s�R� "�A . Afa]tud�bi�y2�6= &+j#e��:PrHFde�%% p�, ��z+!.aP d spin de&e"t2D IsTIlHS&��em��ure, a0���Y �"����H6es X�7-�Q$+�Y�.3^.Df, =^0.Tp, 89.65.Gh�A9� A*%!w!� XRaA�do 1$Q�6=fluctuE��8i�M�#Cu`invol�S'!mڪalU�Ih �Y , bi"�S���nTZ��Nmj l,feder}.���si�";tTQ%Q�nd�<�Z starq"�>&�]"�\�to m�eg@&A0ulu��xno(WTMM) F pen,arn1,x�d�^e�\,Q�*U9u�(DFA)�,ple,chen,khuI}Z�a�pg,a,gopi})��=E흾A�B1OMy��m)� �@�, obser>�is�`�S��.z'Ms&��U�IBua�jnel� ich ��er��!>_ ity.U&i�Me�!֩�new-�,���(6&YO-Udaub},�"�H!5tre\#.�RZ"=�i: }!,�RE�M�s!� elf >�YU��conce^A �ZM� dOIpos=, apart @%* suppI�Ň"�Jed �UE= 5��so#= low-pass *3Hs�FX��+oarse gr$L�m��*e�$inJQ� !?� tSVX�$w����ing�H��i�-g$Jlg>id}f%W=Hz[)�s�av�ba8�RWe us�sis1�g)a�V&aj��!a.2愅purE��pec�,! .kourA�c�[!-�as�Iith6e5�.�5� (MF-�fe*X.� PO�<(?�6$)��)Y�V��N�����LP�.6 ex�a��iClyAq7cbTbuEhasx$ ��^?��n&�.nM [wtj}\e!Y�� �/&".!�I($9$x�56�t simu-M�2D .L�D $256$ x �EL^� Ng $T_c�'*�E up} fs�&�%G��]:�a�B��p-�hwa,osa�s�S�er=� 3A  �(5v.��E*�� ly m�mdI)� jha}�a�*tHcur�Aflo�[ po�Gia�BTokamak�PsmaJ�2��so%!��"� iri"q %��c>�-\UBer�L\i, BdS(2.15in]{fin�-1�- "�9T& -�XVr�(a)V i��(b)>4�K"��&| V-en&E-� ����2 �&e:.�of,�V� (IC), �1� 9�(FP), 6mA��I!� �x� (c)Z (ISC��a�a��1_$�q/LIB��w�I"b1AZi1 �I�$�MorthwE1to �&YjrieGW"�'��fe�E �9zjy< ��u$x(t_i6�S"��h� �$ at $t_i=i� Y�"OP${ H,; i=1,2,..,N݆a2%0��U�� ��x�way��J� ,�=�r4_}��M�$� _k=k�� Y%Dbe \D x_i(\t_k) = � + - � N-k. <ee fc:�[i�!zQ�� er.�A��brdistrib}]& (pdf)!�{$ � �au_k)$} AoA�- �{ e��)�%�-��V "�FD. *� i?pd�A�a wCi)� d ma. ��)c_or :�,�in�( 2)with a�:pdf%5�l-6H1Dr ���mean $ \�U(k -(t)= k �.M anc�R)^2 .< =>]�&�� for �!�T ��s $m_q$!�'.64!l�0exp�rea�,IF be m�W|ox(U�))|^q.XN-k} \��i=1}^ | �A,C |^q &�� t)^(q)k(A�#$*(q/W� t�!y8/��� Hu3�N $H= ?=2�U�bR0ӷC!�"(8 whitg�icgT�c�,q2!M2A���c!C��%0 �!!i� i�W� y�>d�]&in e;� A0.kn(m2h��n�ne). Mon9E� $H <}�1�cF ti-�,�q&! $H > 1���al s.>9i|�auݱW� ompܱ� s�B'tur�i�&1miLe # ����a�ed+�W�Mfac�P on q!0#{ar6 &ͫa� inc�T��8i$ 5 P"� �8eUD 2�.a%�2(  )B(! &�:ise* %8"G.>b.�S� �8_���8A�u0"�$(R�!�!��z� ��.ps  �A�of eNc�n� %��$�hE�qi�3if �l�*.]-59v� *9I0,e �r�T�S ��;<�� $pEAc. �6r�: ���1��Q�.� &�._� >assocy:!xl5�3� �mxű\�4taqqu,bouch,xu����11!���y25�Wal2&1 b��Q��� ��Oof �, a!� tinu�I*� c N�u�gh lik�n|E�)lso�4lN�M�&�dv.�` ��.�Q.Y� /ata�de� h=ideJ f�'�i8.L q�����r!vg�>2,VDs }Ds !�1o-�ack��9on* ]TA�#�sic�A�2�Y18!R�so� 2� !� !c� �.g�9l%s,a�var�[X�)�pu�54���0"C�fix=an�3p�je XUR��nl"��i��`plo�g�� ify��KqV2��at �� y su���!& A"/%� ���w&�i͇�oP)f�*��"� 2�inQ�y(,�[em��|"be�j�+�u� )��eR �A�� �K���mL�2�@ &�6 e ���yn��m�ea"\.��-!�e�2�eIq-��6 r cF��� s ere�d:g=Aa� vide��+t�̔thono۸I�un�{��:�sH"ua�o ly wsV veraJ{1 &�&�' -4 (Db-4)���.I �"_R�����=c�|k!(ofl( m��G��y vanisC�١:: t dt~ t^m;  � � �&� m blaJto5��� a)�; � � � �p"�a� |�C�ei*reb��kmhm H �#2�t-�"�A}�of"�|%cofs m:�(�u� pt. �,)\�" ly e�e��an.A *#\ �Gmanife��i����idexaň�K �!@�� �'l�&�m ,WaZNo��f=�H!Jqz" � 2�J�4$ze $2^L$, �Ea\�jb�% avail%�recz�.&l�p���I�w%al�&��( [ 8�!r`+.y(L �&8h^�&w$L$)T >�%D� stopgNp%�?���-1^��>hal�s!2->%p��rPL2���ow��� ��gE� er �2fX�DTs;�RՃ2C=���T�6med�� mmensupw�$�]�� Z�erned7�-=bn�G���]�s� n Ha:�)�L��in�!g9�.� s��e-n2(�/,*f n��Q ircu����>���G�d�9oT(WeIzA��.��!A�,Œa5{g.� i�� |�=o�Fdge�&ect�j�� w4��� �`ӓ:�{yAb�t d�.6#.�2u��acho�*1!#'cum~%v/M�b�!��2h~R~.e!e�� l yA �5-I<2�. R�t�L.%% af� remo�Oo�`c��uZO �N��)-t �j�Q�.�, $F(s� K"� of[ e $s, �.ot�Am oH �"JAv �N��ruђ�!���n M�2� �Je��c6�)!��*��ͣ B�֧��R�j�?b �5�iA)��2� en��K�2��&�&G�>;2 ` � �? *" (Db)J' 5�� s��E� *�"Y1E��& � ���**�fIE�, % AdDb-20H �08A P�-A��-,!A�s�y � ��atM;a �l�����h�/s��S�1Ac� �"� a%� .� ���maL�%��'3>'t 5$($\diamond4 $ 8iBoxR!�!@u�ZQ)!dV�(m)%i�$\t"on �m9na��I�#�%�:I+��L� (dashed? )^ $q,!$,A#4���$q! 14� svD�HE_:�UAnaloge�l J�0&R "oQ! ��6�/�!z $F_q�% a*�# �&6N}�{k�#N |�^�#}^{1/q}g i f!{~ " h �c�KvVd nega�Vg�)g, �m(pt zero. I� ��,iR)�sxFA47!�k�eHn � reve�#�wer-lawqS:�� ) ~$ s^{ho$�Asmdz5, '$H ���A�$q$!�ny ��$�#,��w i��W Qh�MH�C��23. OfteV�|�5>K �!�"� � #e�mDa��a� = q � - 1$�m,m,��*m,��� NC�e*�-� (�Y Q� 2)�2 7I�B�.�,t�.H)�^��a� Rv$:In�Q-1E�1t 4� giN�Ar�!�5�MH:A�$����,���] _ ���-Z�ach���:-a &T�&\ ,4�l^M+ host!^��.8tes�6�r[)!h�Q�$,%�EDb�~2 �����!,��"�Si�p.>� �U�Asen/�b�h{c} \[o&Obq &)�_{BMFS_f�6s}$:w}$7 F  -1�a00, &1.9 7544  7534�P -9.0# 8889#43 558 .82.75g 7307958.72.572#138 627 \62.� �691�67.52.01\ 6605 9 7746 \4..= 615\845 .3..684\547�99�2..576# 4551 �8221p1..415B380g680 �  Q Z � 2\5�0.9923?&1.031\�0.839 \0.816)�0.853 � =0!�#699)p8 � =p0!�60.625 �6�=� 0.61My0.577)B93 �]( 0.58M 0.54M�7�]�0.557Iy 0.52M30.565-� ]�QmG0.5041549�}<Q6�49m0.536 \.�0.51�0.4801526I�6$�2�G &B3he�4��B���n (�`)G!uᗹ�ly ($_��&��s� d6wn�V  > �����_ " ���O\ u�C�&� U "C $���� Y"qP�FH2�-���e >3is Qemb"�w`3� 6 �9P͌% $� 5�Z$ D� �1M,��er��.-�w8 A�How�,�E$&�,� i&�, GX]�dI���^��V�N�<0$�+ro�sub3��if�u}Ra����&�Q4, �'�t&shSo%4�m�<��� !. �#6n*Nk�,r*} M�1\. H�T �-�s,A�hm�QH&JM]��&I�b�Y\ eF *�z.o ��to  W���I`�{ � ��&&����u& &��1&��)�� �6Nj <0�s� �R�f � 3./�AY!� &z+.IB.��!2Bcr� E�_�.� %!imN !�em��&� a��zn"�b�4.F�v.i Mm�m�D ed�U chh( }� s�5qhoG|"] , fa��\u6%�ze4M(a��4!�b`&synDŽi�;!�BI.�� ��7?suD�to2�R� (�E�<0�X2�.d,��s ,�a�At:e-[*-� qr�Q/Nz���oQ�y�m�2�Z%���6o� fd�/E��o �KD@2F 6�eqxb�I�$$i�Ac�>�li6%�ej�� � E�,:3t�BTtEs2�Ci�-�/6Q�� �7tc�����J���I~]n�0to Dr. R. Jha��vii�he66�$.�&�re���Vȳ�D } B.M�D brotE�(J. W. van N�� SIAM�TiewS<10}, 422 (1968);DB�JdeG, ӢaOS�5Finy7HoO,'� CgBn��V3Risk, Sp��`er Verlag (New York,1997)�.��?�F�E��a%�,s (Plenum Pr�C 19982D pen}�J@Ke�A8S. V. Buldyrev,$Havlin, M.�oy+0H. E. Stanley�H A. L. Goldberger, wK.!@. E)@ 49}, 1685!A942��E}FLArneodo, G. Grasseau%O$M. Holshne2`LzW d 61}, 2284d8!�DJ. F. Muzy, E. Bac�KA.jB�47}, 87 �32�bF$K. Ohashi,�$A. Nunes A�Ml,A H. Natelse\A(Y. Yamamoto2�E� 8}, 06520��4(R) (2003). \bibitem{ple} V. Plerou, P. Gopikrishnan, L. A. N. Amaral, M. Meyer and H. E. Stanley, Phys. Rev. E {\bf 60}, 6519 (1999).|0chen} Z. Chen{HCh. Ivanov, K. Hu a�e$5}, 041107�22� khu} NBd2|arpenabrRev� 4}, 11114p12p peng} C.uPeng, S.!dBuldyrevHavlin%OSimons, :M�A.!�0Goldberger, PBc49� 685 (19942�matia�M 4, Y. Ashkenazyb:uEuropcLett. )�1}, 422�6@gopi} B6]RL�AMA530 �92��daub} I. Daubechies, Ten lectures on wavelets (SIAM!A8iladelphia, 1996. taqqu} M.!�T ,� Teverovsk)6 W. Willin%�Fractals).3}, 7-�52� bouch} J.!1B audEPotters%�Mma,=�Jou. B `1a595%�02axu}!pXF�eN,Y�$A. CarbonetH..�Xeprint cond-mat/0408047.�hwa} R.A�Hwi5 Y. WyE>e.C �60a�544904E�6� osa}!QSakika M,O. Narikiyo, �of them Soc.JapM�7A� 1200%6�jh �Jha�$K. Kaw, D.�Kulkarni% J.C.PyhA*ysfPlasma)�1� 699 �Lin both &� $s further �s�A�m)�coE�rom.� reson�RT)sEH�layer: i9AzPlarge enough it creat�{Ncav�in which5:�. SE��s are!I1d��suppl��ary<erials.!a�N,% %Keywords:6i , mu� l�8,Y� s, %:�%- ()���;1�. % \( L{45.70.-n , 47.54.+r] make�� \sec!�{IA�du } In�&�m:Qis ob�cthr!tA= coup?A�}�aY5�I�i �or less � odic�a�?, likE� rubbA �k-slip.)|a?bow a viol�r$Von-KarmanEst�� i 5flute. TA�6��� .^(v�~ng�� |, � volumef))X<result�C adap�� ��e2��%We��fixa�PeOiM. Doea�e�"Ŏ)�H� �P��i�H similar mechanism?�l� �V W}������I�a�a� ��D60,C23,LCCC76,NPB97,SBN97,CWG93}. Direct observaA�s,a�we�d��, Chil�pChina,��.�eld!> not :]��blocksAL� (a)zU�M)Ay ),��ita��on�y dry Ns1;'ely. Nei�q��� orrespondA.�insidiH!��inin.� �!�saA��R%�measur�t dif/t loc��� a iand, a!pT�0�%1G sizes.\\ � t�}Lflushleft} \footnote2{!��$nel, taken! camera� �.,. Black spotJtop�mic$�(�� ro�vng). Cir�on C, �� dj� cm$��� diŁM=!��heigh �$ed mass du� �9}}\label!n1r-� % &� ��6 E", significant.�"� �� �d depend��ly�a�si, each�� ��haL a chaEeri� 0 B!�r. Studd c �6e!�a���s how Vsubp!A, k over �e�, dilaq��llyVthen h�lower[i�QADD00}� is%ic�J� expls%Sa =�sIiaDstant v2 !2�E�a �1ar"� a�y !depth �R�/!�c��= co iA grad!�precisel  averag%Rck9�, $f$, tical� o�he&� � . Ex!vAّ�GDR04}�theory �-J g�D$f = 0.4 \sqrt{g/d���or��zo $� I�&]b[B661��?to�/oE��ccord"V wha� 6�(see Ti 1) �:�venr a sle�devp noti}�LCp� hEF the ͗ �wit��r bars.m granE�".sc �� i gr�,#�~A9such ".�"s�h�  plate, < legs�]*� | -. BJ85,L36}� $25$!�$$250\, Hz$!�} 30S04,S05} (cf.6b W rA�`=�, 9p,S06,S07,S08,S09,S10,S11,S12}}l� A�� of��s� o �  is effect�!���, a�!aplugg� = e��� to aa�pa cr�of ts�(.G*- , B eW�� ushed by ��tor a.yv�jiesI�Fi��~\ref�F1}��u� a���! in�en#!��! she< g� !N���"ed�, makAf$it possibl��6 :P� ��!w* u�ک�-� *bf at� boom�)�c b"W �v��ay�2�nd&s t�J a� 1elf!�needet gO��N�"�:�2}���$� �5wnm�%w�;co��*� , d�!� appli ����iBAe hyp�Bs�f-uPT22}�Aisu clus��pro'at�Ui&!zxdqV��\\�� � 2r� &. *�iU (%%ed)Q�AY���"��a fun=a<,-� par� s,* %�a6�j$H> nd9�of�!G� , $V$. FZ sera of� ��qowo�uS�/ UE(b quar�Pnd upward triangles),�a�������0 (gray open c" I down:K. Two{ets� E�fծ�|� �r94�� uppeft,5va%�(:�, e�at ��M�n� r�, !.curve[ oppositea� e��1�(8% =*�v� H as%ze3in�:s� -��a 9��]5m,). Main plot%Ba��A �collap���hlw� :;�.�r�AM�� � ,+isAln�3��G.�)submil. yso��s ten �meT, �E ~�real e� zone&tween1[~Ax)� bed,�o�%orderG$10\%$ -�s4 g..y 2ny S:�bg `} B)�� usut s�W��so�}edADin�S ,RV8�!%-� they��all shAr�\�� U 7"# . E� ���sA!2 m d" them,�KF �� �*E*& associaAat ATn, sressio ndA�cks. Alg eseE�t;de&!W  priori���0�C%_�Nctuz!/en mai�c� $l out, leaM  | $ght, high-��ru���rm%���nI<5Z1� S08}. So,�q�wZ  b� l d?� �' +a$a�a9 n numbI�-�j!AmovwX���a]he whol!owaU%4 will 3upE���, !��surfac!�ll �ly�-� )g%�Q^ir��(udspeaker (�beof"�� � jI� q$ itudV T Z��% (b� $0.13 d$� $0.0 )�c! 9@c-+ Cs)0s. Surprising%  easy,I�%�a few.1d ?��� o� yAZ pbR,  $11 dB$a H04� 5�c�� sha7 �*~e seis�"%��-��� [S0O/��A�be felt ��feet m�a tha�H��trans��0I�� �� �es�ial ques�$: why woulD .b? .{ "re�lyG�)�e�i)�n=,- urn vib��5JQ)l�A%�Bu� .�random �}i��A ���J�{� �fc9�� }? W�� opos>7 �%��.t!a "g.�29��A�t�� _"oW� !�. A�1�C�1%hEi� .E|��G�\ �\m�. I�+gIto%&� ,�-lecm��*b� ) yaf& exac!�� �B� od� can �ly��vM� lp�!�mreg\iz� `.A�a9e�inW!7A9a� cl!�to!5u�t�TA�3sK phas1%�� � 3r�  A: Pho��f�<� ! A!�"=$4*{s 3\,�� , wa� �(4�!�$ woodA�t� a gA�in middbon*p �e� � �U �taneou�(%�s� th�"cri�� � slop:@� I��)��" �s%ov3 IvI ��a^ied)��a lev��� imul �lB �Q� a��Amp��!N(# �' XP)F� "� s&�=$UK)^O-��re.>1) <A�%�&nini��  ce: (a) $M , (b) $6.c)_ ,�. A-�hDs (a, b, c arrows)�"�s s?' a4d!W op (�]�5)�4th9�a�� ��+ reas N- too,l � stope�(daWjDu �.0)C�"ly $1�s$�t>n�d"-#-��be, $0.2ee/M Bump�2n (��s� n$isu%,� a),��b� crib� a se�4�$Icemi� a���'.4}} &}3n R� `di�&} CoY rAY�PbA���%A � �K���a�� �m-/above����U*sACa �]$\lambda/4$���$ a����length (&a$�� ro�)�pe and�%n�+rfre�#D,a s6 e�pth, ne,%�occur.S�{any�&2���3"(" & &� � appA4�� ��9��%G����@�aso��sDt�7w��� �)�to��in do AԭR�E�-�as��be�0ck�'i� thoug�a�'�* %mA߅<�-��i�:R�b މ�oI� , $H \geqaA7 E8!u7wr�n��őy�U�.��Qh = c/\wIc$!L%�aB �1�,� 9 s $f �c/4�t:� ��2��r�w��("j!�A���)�t ��aPq�(is $U = fH$!Lu!� m read(%S �C�_&�t�!H[� F#&�$Foum Agout>0,��ruc��a �� 2�U��M�ee :�3}��'�T53��545Lb�� �noI�v� ; .�!dir��M%�EEspeWaB$c = 4!� 0.92� �h�*�9��Oo1e��*�+.>�4�I��!p��/Eh co�, �e-dicfQY��� ?�&�N:Xm�mad����cc�$h�qy!� now _�5p5��I tic� bottome�_ i�.z'A��  $HeѠ2$�|a( heldaw~�!)� �,��t X�2��$Vq{2e���|�I>1�I+�7M&r�a%���v� me�'I} �,��#s� ��.���4r� Pg�gd+ �"� (sha� area)�R,��o��of� VE�A� A$�R� y ���&isQQ�quick#s�~���ed �projey �(fluidH6 ). Lc r(Q�� sim ` cm$)c,l�m'om� m&!M�����Z o�bH�-�& �!O� �/#�!G$geometry (�P 1B�ef�ءK>��#5ĩAa�[U�� 0.47M�. Inset:&�"I&^PI�i�.Piom88 a�b. Ho0  .e+m �%��1e *X&sat\ ed6m 4nm Discu� } 6� $0.9 �AQ��Y5A���%*�/"�" B54}�gu�a � �R!?ba% A�. C"�U 5��8 asmMr�� � !�a�!erh cAck� ? A�b�.� a *� E� *� i,)$ll underst���ly���M��x RDT9�% �ulture]� veryL �ՙ3;a/5�jin �zs�0 $37#ᝅ\$33�ir!k&a a mixt2E�x &w )��� o 10-3�`�%iՁk�!#�medium�u�2-U$��st9F�3��ag1 e* e�@i2->��u�6E� "�A�Q��  �P0FDcE����$ two facto�Fr��>!iaser�N ��Q.�!�)Y~(e�#K63ntact�?t�6Ii�  reAd�w- 3iI(ai��3s!`"3��(t% W"<a ��!-a�[  �  --�r7,n! � a[AP��4�w�#�� s%� o 1�ert�obably%�s)�a� c T state�L�2�)7-� JYW9d� ab,to1E3p�Dou�E9a*Z!-&�6$silica gel���&s ��GLK97},�9as�ert glaz��2,P�Cim�(}a~q'a k 7how�,t9�a�inten^#use%��s losE�-: A/!�e3.)��%\�h F seem�� I�Ou�)��n�( value to am�s n��ev��pٍ(in4 O(��)E� {�=�� �,acrossF�.al ��F!"�3;people"$:�as �E��!�&O to!Pa� �ㅘ� "?s n�:� �)D� ae�is}�la6�i�!b!�& -vs*��� p1_%^q��i�!�sA`ti9�&x#,M�s humidi�>temper�U�2�qor x>�5 H86}C5m now warr!�p5B] 2Bn!�. "�8ConV&o�� age-g:g>W#�<E.�+=�reveal� �6l �� r!�a,%&!C-�.�A�.V mo�Ai>1D!�i���g"&"e�\=. *�5:eI�{�ay,J� m�*��#new type�&U6��&� y]�(>)8��m{�0A9) . I�&���iF p��e�@� l}^necess=\)*4Ce�!�& �AA�2a"sI� } Thank�" HervI@ Belo�$oM�ip�"���&s���,'@ Els�Owho� 8�d6 5 Q�a�blabG4gherita Peliti o�i� �% S�.!Z� Laurl$Quamer 3 �I �LR=Ds, Bruno Andreotti=enfore5� ideaU�iGp be���%� E�l&"e< b%�,s Illane-Cam�6�g� ng u] �6%Ra�*3��a*or7 sC#�&�+!��-n A�� cert| e InK@$ve Jeune C~DurAV<5BS Qmthebibliɔy}{SBi�R4B FB%�co, (HB0), \textit{Le�is3( du Monde},�8p. LVII: De la �B( de Lop, \&-gx �(manu� pt /6%n� j @1556, E. Groullea�N7`, 144 p.: p. 24a-b / 1938�f de W]zworld},A�n�d . ann25�2 A.C.%8le� PaulA�Pliot, London: G. Rout#M, 2=.)!`-ED60} �6, C.R.!D860=D Nois&V h (oH9th)}k:\-p�voyage mDbeagl9rXV: Nor�7nRl�Hd Peru, pp. 359-396A�011th edn (189� ��O$hn Murray.��) Curz 'G.N�923�Tal�Travel}od�(!^Stought> j (�0 int: 1988�F ury Publi7, +d Chap 11:56qO��s}� 261-339.��# Linds�� J.F.jPR. Cris , T.L.�B.S.(1976),`A-���T0b\�Y�F��Societ�� Amer� BA� tin}18� |463--473. doi: 10.1130/0016-7606 �P87<463:SDABS>2.0.CO;2.�Na>} Nori, � P. Sholtz�� M. Bre�T7), Bw0�-Q}"�Hc �.�27�64--70.~�>} qP.WSq%/F.A�ia9};=Y�* 9$�e� �fGHcA�,38}, 329--342� } Cooke, a� A., Warr� !� A. Goudie �.�De5 eomorph�G}Q�,&�Gy C�Eg��,�=ss. a :�(22.2.2 (a),��M�$313-314. b:6.29rrp#8a� pp. 46-48.��6 �S, L., B.�(Q�KIA�Uerr, PS�Dynamic+(18��!�Vmod�:�!�.qTE]�462}, 8299--8302�TR03} Raj�Xbach, J�f2Y, Densg% apide �inela&�9sW �] 9(�LBW�9;T144302. alek03/4Rev090.#&�Y580 Midi, G.D.R.�ll�Dve �cl��4), On d��7X#]�EQy._Ur.2<1�R341--365.�K8 BagaSA�A� (196���6� �A�dS:"� dry%��"�S " mevism=Gr�URoyalK$c�nd. A=P0295}, 219-231.�?8 Le%� M.F.t H.G. Chardis!+R#)�g�-���c# �6U|r5qVal� �:'Ue"EFY12th IL>n% al A�I E~"SyU ,ium}, SapporW$apan, Octo�,17-2093�4A�504. BJ85} Bol� H.C.q{A. Juli�� (1885), M�%�: I�id stribu�!�&C�)� AAAS=�3�408-412J�8 Lewis�ODa�193AHRo?7a�55 Kalahari �uSouth Af�� n Gee .�19��3--6��5 Poyn�HI3J.J�omsO@(1922), Text-bookA-[ ics:�Q:I,Ei�Griffin.��00 van Rooyen Tp E. V�e�198�G�:ic=x}AOr2/� souht-ea�Ln k-=96Joa�Arid Env.��215--22�r- BQCY��a>Mşg�n��0t d��pP�ObPa�O[Ph.D.�sis],O"�P�Nt $ 7, 243 p.� 8:!SnO �M\p. 191-206, 8.3.3: puissI sono���199-202% A04}_ � ��Յ�2�G� 9-�l�%de �Fing9Z�S�Z��]~9a 238001l R3. $�B54Nx5!����M�Abl5aEe�dQ %:} (2nd ee(), New YorkE�pman.V . 17,6D�526 Roy�aHF��vidR�7V��Tuponog�_ ���"���!���%bed�l Cheme�E~eN'; ce}, 145a�2e�245)w!v\016/0009-2509(90)80216-2.u$ Patits�ZA..&� ������"���6�a�� of F�� d St��^�1��287--36Q�( Qu JianJunl ng YuanPE�Zh Weim�R$Dai FengNi�TDA�GuangRoA�Sun Bo�)Pg ShenX�8�:8� {(7candV*X ���i<�zE�2�in�4-�� .@4e@10��106. }!v *a sackr ,M. !��ailkeny �� N�al D fil'-�'�y�/Q_3� 29, � e�(038/386029a2� � Pye~^�H. Tsoa��eVAeolia<5I e�i�4, Unwin Hayma,�pch 8.5.4�*mwea�� redde�( of s�iKX�#^h7N 5: S) a co� g �c��,61-26!�"[d� Haff�1K�^198��q;s=�� I tist]�7� 76--381.�S01} 6jPaudio�P 1Y9om'eJ,z'6^2j^2 ^ el C�Yrov l o �ba��Dun�D�6c3jc3c erro"�J,VL4jL4ag�es6�5j75�^nd�#:96j96 �%RH ru2 S07jO7. Sca1mix�N�R\:�8jY8lGere��Da.52�F,� Z ! �Ba� ous; �)Mi �j9j� 9. S$&��J���jin610jb10. C�`*� c2�`S1rk1JAb:AnN12JAaA�K:F wd"hc ��:"]Tamsmath,amssymb,epsfig*5]�T*6]%�op� 'prl'2'o�7sY it g�?ridI�;#&%|u�J�]�x}% I�d2*xD��s2W]��]*�]$hfuzz2pt %��'t*)er�$M�< -full boxB!f e�clis < 2pt \newcommand{\seg}{\![,cal{S}} %seg+ in a_e:34abs}[1]{\left\i$#1\W@ }6aHder}[2]{\frac{d #1}2 �M.�dertwo.,^2.^2>0p6Z\� al3 R76h- o #2Jvrad}{\s�I,h^2 - \gammaF�one)pac�Q.�half}-1}{B��{\: :R_ \ " }A� HEOREMS -� %%%�D =y��ZZ-- : �W{"f_e���do? wall"3:O;�Ted Ginsburg-Landau equ }"�`LI.V. Barashenkov} \a\$l{igor@cen8hDtola.mth.uct.ac.zaB0S.R. Woodford?G8@gi�ttJA*v`&)^�A�FM %lcs_;7 Cape To%E8Rondebosch 7701�"u��2/^ 1�a"�YThe;�E�`(driyD^A h�2@%kC^=�sol�sAkM so-�Ned Blocha N\'e( or I� �9ll# �&p~i�V"����" icitNsGcriUYa�5'e!U�DE1.�<�"*pI �/.l�a�%�&D>w#AwdoI&Y\. ��9T �ZD05.45.Yv, 89.75.Kd�mh.65.Tg, 75.60.Ch, 02.30.Ik}Q,d \6'e  %[Tofb'ents{!�V[7Intro[9R!Qde!� am!c e`5Z �E mea� ful=��qQ!�N�� scruti� in�, ous �xts^/9X($40$\ years�e[DBe�!t�^�n>�;g$mos��n�; form �3:Q��}1+�R psi_t = (/W+ i\nu)0 + (g_1+ic_1_{xx} -33)|)|^2 - h( $^*)^{n-1}.Iw Eq.(�L1})Q��>� -d�P$!al� �[f� paB$weakly non22ar[""�\oscill d�!tinuumL7 roxi�Son%h cha�"ubj�/t�/e�>ic!D8!@5"�"0 $\Omega \apY n\o_0v1;.$\e@�un)� spq$lly homoge>= ��7�q�E\�P$!u = (x,t)u slow8-aryA &:/ �re-5Z .r_ �y> a�m3�0\� �supercr�>(Hopf bifurc�ZA$�4a (5� =�)�e0ble limit cy�ap�9�qEs.�^�B%B��!'qlso�%s $g_3�I& real�w�K $\nuI$o*�SeY� detu��,2 \.to )�/n% Q�<=e�W)of u�>&assumelPa� sM�growth�8!�$\�����r&:�� @1��yw . (SD?.g.,Pik+s$}.) Next, L%] c_3$\���ufshift�%c"E�Z�dterm a�6&�5�#aW%�LCn?bouut ors ��{��Q!�%imagi aN!ucY�A 1��c_1$\a��[a�M�d �vveR reac.0 �(c b,�"pCv�^Fe , $hfOBf� ingI� $(n-1)$-s[R�Wof��^*Sn6%����&�( V@'L$n:��-�2let1985�9(e $1:1$, $2 3-�� $4 [s hav�)en st !d�_ex�-llRliter�em �&�� focu"v(�� $n=2�-z �y�$of6)uwL�A�� iAd�s#X�Uvar�N al, �]:90,Ma�$d_Nepom}. �: 9co5^.G�is zerh�?�.2��-isoymXD`3 `. ~st�L��+ suit�tresca�cAltAx�1�ZndI��$es"- &�\ 2} 51  12{ 2 +� #^*B �e:�1�!��.� &[ ., 2}); �satisfyb� ODEeara����{*}!eB�We�D)8to?*vQ�R�ga�2o7s�a0an alway. �nevn(I pA�e\G-�e�a8Histo� ,y5�)�+j+i �/"�* exNA�@anisotropic $XY$-�#��'Gus^3�#�LL-axis f�magnet�>RCurieJ`/XY,Niez2arN�[1� Bi-con)^7r� 16�)�4_to�2})�/��,_Lega_Pomeauu�jinvestig ]� �� m l2� (s.w�E$n = 2$�4�(��(��.��A nonv�� �Y��)�F�LSkryabin,Park}. Aparkx �%r ic  Ww �5se��s h�.v .�Qe�A�(liquid crys{ � Nasuno}, .-.�!&� �l�1`l <-�1e �.0usov-Zhabotin�{�Son7Petrovc]�,d� � pt� � �reg�Uo��#�t!� orsMLonghi1 dlas�{Haac&.B�l`A�- DA�2g !yew w phenomen(��,�);e m��M&TA� � visj$�+6 �gl"ar �8a � Tsim: }q E�nontriv9*� non�Y)�Mi�att� E�pst!�!��6�%���g(?ɗ.�� kink�}lso*m6arkyit�H�oo�)� M�a9����@ xK"�@wo�4e00� wMgr� s (��6<%q�uP �C"L5.Ez I.�G�` &\ non�� V���O ps�m A_-�v iA_+&@A_{\pm���1jgh}$.  ��J se is-mɊu� m w� �H9is �AbleyR�x6� a�:k�bLV9#�asympt5`�Md �=gTXr�I�� $> \�(arrow A_+^2!0s $|x|.\infty$a��soEb�.,%��� desi�� bedH �e�j�6opu�(�Sa�U��R $180^{\OZ}$\Y�he�l�8s)a�a ano ng�DnO2NJi�).&8 �adma("�h9&i}IRv�8�p��,Raj,E�� ck_M] bfx�"_ Neel1 0{\rm N} (x) =E�5i(nh(A_+ x), OB�am �s�a�hUM+$\ �'iv~�!i�l,���� OIIva|a�M�K�_vec�`��T re.)�Q[ lso a8w he%ye ! -� �A � �.� emuiE�"� *� )�.���F="� $hydeFRI��}b�  .BJBx)}k,C\mbox{sech}>' �JB��4haz� C1-3�� D,Sarker,Montonen}.�9�� !�u�rI��. s a �%� (Ef�A!�HG`T�t '��nI�a� (s smoothly,zR!DK6>wC�uPry%). ��1��*v hira�7�#d�hngua>d, x�iQ�q� ?�[ }). �conveni�>��N%+!(No��i.QP (ne�T ve) dbp�-�N�J� ) =v. R l�� �yi5�%}� Zxist A� $h <�3] Q�� �BPl�== 2.1�'�k = 1.\�]��1�G�D�1 Fr�6f� Test �&�lsf?.�(�Qa0!�%~.{2K[@S0(c)Z"]aBU9li�JJOYT�(tdg� 2��6�&~k� 05$;�`@A١���� �aQ� e�G-a�c��u�U�irc�t�U%�s.�� Gaylw�S�Sssayy"_�Q<�ad�+i^%�%8=}sB�� esses 6��? . On�Ec�$i^&� ���?�:$!3�� 15���� SubTrull}f%�� ����2" [1 - _ 32 ��^2��� ] + 3B\t��Bx)&.>�H ��� 4h}=���95 In5`�hcz�!�bubble- S�|s�Ap�7"� �)�{aA$ � �) �NfH =$�7ll�E Ourp�eAs�,��nu /���|X�+��� ic �OPsa�$�`leto]H�A�6�$ed unclear�^*Au�m-P� family (i� a��zy do, "gir� MVBSce!Q)[%|!�p�Cn�=qup�lmh� G5�: o a%�f�&f_* ort JCl%,24"�-Bt�Gd�+�I.s�`ai -� %�!ԁ%dd�4 )�shQsuu)A��#6V�c� ruct�Kwo�0r!er1�of {\itu�\/} �>��B� tTc b��terpre�5&;#�V%!��orE� ,�aV�. Phys��S!?�����Z�Ftd �of arbit�9�V, 1 V:0 �b�� i s*i� �E�pr@b� �exhaus�"l��ACos�k=M%�a:e E�be� *.CNAIW"�ItA:.�O]/D �e�$Y � ��P*hT+�D, unI, "�� s. W�U� erm�!Im AE6` �$�$ coincides)�;5'���bW &�# MSTB6of)�#ory�o  }.�4�AditpP!k .��i���aI_L �7� $ar Schr\"o��er����� l�Er c@��H���=9s.� &�Zl"Zgt�Ň".� �Trill� � pWB.� � c)Z;�T s2"a-8, �)i�&GN�9ne f'isc^;&+ Miles:� . Ac�-!�w�]�Qe �Ey��@�Q� ���EO��e�k�`&S!���organ��Af[.  % Z#Hi�v}�2��j! 5 -�}�aca� a symmeAd\(m�o�L!��u�{�EH2� F�>G^{ S�Ial �2m4'ul$���!by�3I/�͹� ion;-m��&iE0auxiliary pur?G!aAf����(2jCQ�� we �- %�Cx�A�� �22.� H"V.J&�t �Nachn �($7)�$!��Mea�b a�  0����an��A � nvn>ctoB^rZ^� AJl -� �l�x)�E�*S ]`$lu��� rHX��6�"Js")( Exac�* B�]�"� mO \sub m�8 �k �JIn&_ �j�)u��J mploa a 'O�Q�nmanmA�e *�"AV9itz�Z�9NX>��H2} GF>VC pG�T-�%�$F$�E.�nL� (I���N!�e 2�*p naL`y} F[D^2_x G\cdot F + (2-gYD) GF - 2hG^*F] \no�0,�- G ;F;-�YL F^2 + 2|G|^2] = 0.�{H3�Ue��  $D_x�" &)�)qk� ��&K�qI 1w)4[ D_x^n \, a �(b \equiv (\a�ial_x� Hy)^n a(x)b(y)|_{x=yI)]A\)] H3})�v�"ad�XA��&�^GF^2$��� bracket a�sub"��fi,'neNUE� {_�}�1e chosen�@ . B�_kfsubstit��2 �i�W� -�of un�WZ%FQal m^K un��g(I �,F ���adom!se �an�&{k��%i�![to�"((3Zjly�:�qR4aRI�\, u )�I�A^2_-!��b)"F�Bt^_52_vB_+_v�[62[ F\B=(ueE v^2)R��A�$let $G = u&vWdq�O -�Q�i�3%{�X!Z� A�Nowk�@� a"`!�A6s$�mQv 4})-m96}��u \[ u� epsilon u7'^2 u_�=\do� <\quad v = v_0 + ( v>7v.7 \] \[ !�1$oF_1 +oF7 \]-W$0��a�ma7a/- er. An�R"� �� � � trun�_ gd fChe p&�' ��Su�ng)�-T6_Kr�J� ^0$ Q_b�7A���\,)f (eF2�_0R�^C8]2v^2_0]��~>}W�w��ose�L= �~�n,��-7Yf 8}) � $ �A9(H�Z�}�T|A�pN, $A$� �9 or $ .) �*�.>_1$ �Y�)b9!(-2e+ 4h)A�= ���9D�-a)�(AFev_1V!^��9 (-6�+%p)T!{WB�E6@H9}) y��s $ �(e^{\theta_1����$$ = 2h^{1/2� - x_1)�� $x_1il � � ��E�-�10�� infer!��(- !%�2:Ŝ��>1>�9��F 4A^1 !���$)�2F�2)@( �2 � $x_2 �� &�c� ant.}>i2$ e� �7y*� k6�];%��"Eq (�W�(�!� F�@3A� \(amH����h�� ����(- iM� (!� Q + �� b2 �9| �=  2�v_ �:�2)e�uA��1!�$�7(�1K EL oifc1JJ`�A)4A C_-]Q!4m/2}B�iPB� C_-=A-q\.:+C�}�end*� Ignor�SKh*�2�Eg�;Z� 1�AR=��� {A+ \ h}{A!�6��ʉ% � -G${C_-}{C_+}ye1+/B���&� ng���A�Yv.6 3}),��9!� -AF_~)a�"1�U 4})�Xom!�[^C ^=�2 �1!ՑP, i1�ag5��R�B�u��� g%A 1{4C_+!G6xB;j �%�!@eA^! 4h$� b.�q�let���� %a*��$���5cubic��in&�$Q reD(-�j��(.��oA�i��u_3 � ��6�b�� k2�3 +2�vv_2 f vvv �xy�� o��(FF��!��) 2} �c��1%��� �0�).Q#20BrR�,M,�m:iB�8})��R�h)%��Q�#B0��O�� {!J� 19&� 2�� {_IZss b�21��\>4 )�34 2Am4�v24 2�B�^L2��J�V(A-��F��q��$-=�3%�fs�AB=2�� ^3>��bB�P��>�4$� f�>�4ha�4M���.�aJ.�! Jbh�^iE(v2h!8u>e!y�x�  %6aC0  F_4AF��f�2F2�2!�haW +_�.L �_2 �;3 �2��"�4),u�6B���(2�tto7)$�!&4. 6$ for o!�vO0bl��243 �fZ6 e�4=!:.�4r A sW5}�*u��+2 :�)�*F�A +a4-��F�^)!�� 4.��-[Wq�!tr�.&' $l=A2 �V� 5� B9VmY�5�o�? ``byG�''b>de{) with hig�Ee�s �-^�N& $n \ge 6$�s simp�vo �m 4neb�E�Aa*du�F��To��^5Z n�2�2���yy�zu_5m� , -w� yh U�u�y�5e�6ia;qzaPvy��>xN� �a�.��A2(Av�\a�v_3BM*��ueK>tN�2�/� 3$�Zuv7})�bi�2$i %�F�5�<Re%. E�${ A� |!�= A FV��"@ [�Br��(!�+N5!K�R�z (�w\8Yre��5�q2�v�B&�2�wjK5� )��]8 e��! �2�sf3�by' !!8F0$. "�;w��v�ll *S<Vn�n�!�B��"�"�l�2a�W�z >-�u_$BN �� �)�D 0� enE�>(v_{n} 9E Co;7,lYu���67 SI ��#2!ߝ�� тZ�30��% \, \^*2� n+\sum-C$_{k=1} v_kU2{n-k}e��51���*Q��&�&���7:�A�BzFJz2F{��z21 = 2 BL(u_k %� �k%� -k})a�n" 3�D ��S�L%�D(�|$3!L n-k && )3= A 8 94 19�sum"olv=vH�,%r�- �=A �31� gi��� k = )A2$ (r�H�(a�th 1$��all sum" }eX�i$ �$ Ee�Gn-�- O9He2�  N$�Gv 4a�ll!Ok� ���e�equ6�m*�iw!�hKvKM$F � �5+ �=/ b�$ -- except �3�F!n=6��|riDt($n� 7$S�u�y-.u���*ir�'.� � ?ov���$F_n$; hq�cO#m �H0,;6�6�I� � 26e�,� �6�p�; B��6:2F>;2� � ���6&x,�Uq�*�)�u�� @aJ !8 $v_6I�!96�^Las� 1bQ 4��,�radJ *� n$:-4 Z��ob e= + u�� 1 �� �8�^a"3ED��hava�0�9$k"e� 3$. J.eE�kɅ!8l8��so+sa��a�!le. HEl$���. Q.E.DUYA3o�""�% E�G6d&}I&uV> ��r�}aN0o�D�4) = (�)F^{-.Ou,�"$ polynomiaV' $*;q�2}N Fe�Io.�GI�Bi h   if $�< sIA>5.��$ity. [W�smihBat;�!��q"/�).]�now�ZB�z3H�$1'.� oR +"A'%O.o a!fA �|)<`"�absorv;3�M.�tre���|)�*�,Ea��<i�� {w�GѬ $\chi_5<lalpha beta B)� )YR2 !�,Y$F� e^{2 Na@)� =4(A^2-4hi*�# u/k�;= A+�}{&�fl�#7F���)�-s�2��A�i�e&=�,nIs!H5l!R�an[�)9����2a�a� , up� an o��ll"�k��1Dsub�>]$&_��%�&1 s), � #!�2A+>��$s"J9(p#]��1�G)T2�Me3de�"nI�y���"t3�� i��WH36qqqq"�  ��tM�u�a�8+,ex�/oN�Q�1D�}""��I�+ Eye} (a !2}A�Oa}�3"A'i @2QOE�A�aG1�� /2_b_X"0G72F:]%\&� 6c}�Q&'� 6pA:�>E/2�>iA$�W �+$x2��:- �-� ��H3���)�r�2a �2. If��per��%re���3jto� ^a�g^��im�,placeE�� -s( Ũ��i2�KB0hч`Png�F*.a� $u /f%~(u/F$, $v/F  v/F�9 De[�ngw0+�+8 �by)j(x;s)p v,f�O��Y�ͅyQ sA(-x;-s)'^*K.u$�u�%;�� �O��1.�"@ !�).s�%���dd97even 6<. Wa�$h=��1}�7l!�=0$5V 4oj)� he-pU�A?6Bb%,&�,��;(M!6"j�2 is� ival�5to-~.9 �x%�-x$.) ���} 6})mA�U�R*R3[+*-E\2z?*N*) s$\ *��A0�6 �(i�Ri�7eas�6s�Lb�Eami��>R� "f2~a. x}�t�A a pos�xe(o]<x \sim a6W� �" \gg��1} --#I �gi�h!�RQ&� Y'A�=iAd9 X���>y&F?X, t $X� +h}(x-s)-�)aR�/is �w�Gh��. < cen6�It���s��fhK��h1 /2�9�+�rޅ�!&�]w)� .;*� �- �[A(x+s)+g] ��2B J�-s!&�A��J� if �)Atb.��>e�n�2} �S%E (V��T �2�a 5Jz TlefVS�V� $4Na�ق;� ill��-Z V�@�le&��:�i)�,� flip&e&�@!92|:jD�SZ^(d)��bS"Q>�@23@�@sym31�D D�@�4 �B�@�V,Av��-12�@�V���@10@V panel (d)N�@ oof "m�"}B [i.e.���(�D�M�^P(x)$];�(c[N�zplA�� ���\A>\A"J 6�� "�@T� is yD10"�~se3��:� �e�s� P?ee:;� p� �Mj]� o.� ��is�&\�ej� gralI 6� � P�-*/u�R} I�!g�\�]( {%-"�R�\�0dxL39a-/eH�t{ �i� dY( (``area'')�P��sM7 K (x)| A*�J�X�%�6�"�F� s��s9t�i)&|M2!; -bas�6tB>%��5��4ĥ r ex>O5'*�U !��O�k!�!�io;<� a;��a -Lifshitzv yE�!i9-B ;� �V�m6;�:*;K5+ɓ!�ztotal*q3S�NF��8�E�h2�;We>�^ )Xapp���JU,��S ����um:l��unyl\1���ƒtheGqbe�5;a Var���OrHc��-� U�. N7n * "U �fF�$y,b}emfae�6- g3-v^ui5�{dx}{F^2�'I'mx6�� !��s�  nt�Efls $I�LB}=2B$��Uz�9/B��n!1 N}=2�0 .��\o�sMa�, %� eval �!n��I���) 1B"�"i�c�at, �5{� h Vnd�J��ta{�rTiveF�. ��%�2j�7� F����6�E �,4 F/F$~$x�_m!n�: � e�;meF�!@�D_ �s-I%v �&�g8 $I=2(A+B)$ ---!�ch����-��U� N}$. �$7 �Aa�Z�A�� ��e�eF}2p6rQ��� �F�(-�,ble) Manakovz)��KivW�a)2�;O �gdEXhad��8c/�.&nsteaKk� :�>e �=�ar�cd/a"1Q&�5. A!!56?E\ (R�"s �:1�,\,� ,�0T�3�Z>R in Eqs.irH P5^�qбG*C�y{3)�rtH4pb� &V�7!sj^+!�2^406^'"� 0 �0�U1� :^.]6F .:rz\&v<40c��9�16�I ���K�t� ecki`%�5�a��?�de�a��< $Ft �dcoXzuoH�A+�2"� sA�?� in8 ies:F\��� El�.�[$20\.6� j ��mu,`as[Ÿ+�le_>o�� �ǘ�R���e�>"� u/; v\MQv�0 � ltho��1Z5o2!�i ly�fu�s��(b� m�@dӜ��thex" n�\�M. ��8 $h >� �OHY��= �2�6<"� !�1�2"%�m�4�!rm+�er& ,��K"�e�!DžiLQ[�3d��(70�] ft�Hcaɥow!w,��e ��6\\ b*�^����-*;4h�.^21f=-` �32>1K+A} -Ax/l>41B�a��0.l6a&],^:��)f��6A�!y&�a�q���P6:��` !�j�qXD��F2�s=�\mp*�` 3^/n�42.y �Ba6��{a��ٽ}2�}!top� �]�@&,@4�1a%:gu�ia 2�]9�y eq *�L��FF$\^�v�h����Gt�};� �5, $`�鑺"ũ�:�,�!0P�A{a"� �>�!��D��ŗJfa1 �1_. Hq�a�p�� = -s� l)L ��-I�%s*aH!�)�Z�.�)�"17"�&��$ =�Ya1}\ e^{ s">��}��)]b&VDu�}C=�1a�M �}>�f2m&�G���j� 5A=$&H4�Bis"�u�Fis { ��E$F5# . BuA�I��Z!��!�wo)�s.�%�o}�I��� )�,ե2b}) ��$v�%q A�#��a&n�= �\ quotlk$\,T�e. ~!mmaG��lݲc i� �s.� a�� ,! 3y5��� ular�/!or $h<�~��{"S�}�/q�%|a?*prelevan�q� �{``Atteness''�! P�"�CQ� s c�Xp =geY�+Ha)�Y])En �aR.�J�O ",= iA\Psi (Ax�>eOJ���ODE��Ps�f+( {2}{A^2}5/| |^2d!e�1��1 .�&^*AD.� �}�� ��)5UM�N�])Q��6�E(ܷ�h3OM|d)%�![{SA2} Ned *�!ڕY% ) �9�6@L��r#tH�� &bR� !��r� � % cp/v� �Zranqo��''$4$-d*�qz% sp�!�n�' �a3�D �!ihich a Yy �le&!AW��]t��=lat*),B�� �[2� - 1)KF� �r�a(4-3A^2 !  �4?Z�:+Q ���)�Z�_r�tog�Z�"�tR�"�:&1n�TBE\6NE�{ .(\sigma v}{1%I e^{ � �7 f|(0 &^ 0F���Whynot?*��1&� �  +�^(pmR��5� o1?}�)2(1+B)1}(s kh.<2�e�D�6�* �yd(1-B)�#8i!M�M�-sq�� = 2I�+s)!C&oWl0a�$x_�r* .; *O&�\e���,c��Ed\�bes uni�".�VgI f�� $\I5&[ d6�mid�a&D �e�e�L�{Yam�Z . [N"!# _� ( c�r��e b.�"�95�24 2?0>  �"� �� 3?Rm�������� . b. isc��R ��BU]?X�3*:e*�#Eg�:N}��F�w�-��gA+graphCmAF�]�.* %��HAL��5>H � �C�-n��s*�iTm �+��&� m�e����2��:���:co�g�<$\ y�Yit�%1K�}-e�j�CQ�wU!n�^�\ - 46`!p�5\Z6�- good�<ɡF(:�jF�"#��}Z���f���� w 6�2�^}b�>a�=�&�Ja�aSX�PQa�r >;�! ept .Z�SB+1)(B-��5. B�ixy.�=���mu� [ � choi�- �ig�\ ].G]. <P�t��t*�� ��it� a d��ck�rC!t[� * #^��{ @J>\!P�w2(^2�xi^2)0et ��9.O2.5'1\ \x�-JExt (2-BRxzY0r32JBMJ\noind�.�� �O���x�x�� $���0x $B^7_51)� 2��(*�!�&3/�`�Z!0�$hLeton�%�, ��y�k {\!�HA�V  12�m�_x^2+!Sx��-�^2A�2l��%�� "jN sec2 }9Vx9C"�'a'o���ent�l2#��G�Uf�S �I�(!� � - �_x)ETB^2�& "� ^2� - � �N��inJ�(;/�7�"7�i�!:)RwC���'%�j}o1� Hiet��tN`y c�!�8! .) Tv�2�� I�E+}�\�d �lie�a 22�a,��tc�Rrai�8�1��R= �7 �6�I�� ou�-�.G$%�,\xi,!�_x _�q (1,0� (P/se2_� z��quantiZ obey $IOH}=0= I}$�aw .�e� sadd�(e�^�1�O�/� eigen�. %��"��hoo�"a�.ms/u�8ble ma� ld� �B x$\ �ein#"Ior��c($e�"~f.os���hav�t�o)��f-  �u2�)V��Ar���obMX �t5�5� ig 4%���;Q��_2# � �ohLaA-Axi-A A�&�mag�ss}6��� ]�se�" � �6�viͧ�o} UA = � QF�$-��r[K%06[�� �>�&%V�\  vic@Z�&_.>1A�!�h ide *H�Q`�jUf Qf>%�e2gT.h,*f �e�2�{} &beq��a&esVS;_ E�1= 4Q5%3�AA( "ͦ"IF���F� ,6|(&�wt�a drop�A2x!�a�!v�U �""C�"R+ UD9hSxixZ�#"� ���OLs }��E"ɸa�21,�&xi.�>D$,�)/6 -2$somethings�}ly%{}8�T � eiMPNJy{  N}^2}{2(1� %Bx&� vT�"RBF� WfBx&� IJ�Y6�� �j\> [M}q� �re&�>ev"l,�5 N ri!�A1Zr: t*p�)$( cM!,�N}�� ��yq�q�t lo�21a�| �*Zh m (EF�(�`�b�d $)F_i�%d�ir:�5�� si?����n a .� connKng��:$A�0,\ $)��^+ $��i 0$, Eqs.(i�ji give�9&s! X5�$\tilde{� }_{\rm N}d cNeel2�WIb�Fdefa� by�= 2e^{-2��,$; similarly)x�. ,-�o b�nside��se� tely. For2H,%΅�$EN ĉ�JBloch))�9� \begin�88\label{24601} |`|!�D(1-3h)^{1/2}A^{-1}!�B!�B�The sig��-jN}�p(s arbitrary% determinei chirality]c,iton. If $h>9?��recove��>� A�)�B}$; e�&$also occur� wo ٝ�i!�depene�{�U�N}$�'nalA�we:?M*,9 (. Assume, f�eA� at $h < Y-IAcM&E�ʉ5{atBeu Eqv(Whynot?}). �/4comes���2�$\sigmaYpm�� W2�N�?;�:selects�� ofE�N (N+1$). (Aa!9 m�an: in aAa�0 way.) Compar�a♐��� �I�5���E`find \[��,|\mp 2 e^{2(\beta - x_0 + s)}\] � \[q:( = 2 (1+B)5-B(..\]^1 M} <] J�(r�<)i�-��b�6$state [topI���:�],emm��ito its��L counterpart [bottomR>Q��2�9� Q�� involv!�U�Xgoodreason}) demonstrat�at any��)KF� �� �fe\>Ta knownY(4as well. Q.E.D� \sec�{Conclue�remarks}�'  sions} I� is pape�e   lye�tructed .��Ta � of domain��i�� sonanFXforced Ginsburg-Landau  . ��!�lqs� resent es (of ��length)Q Pare $180^{\circ}$ ou phU%�e�*�field. �:h �m=�d ]A�ion� ]�% mo�Ran�� dark�� s� not�  (Weg,A�$fact, prove!:� �ed-�%��*,{\it only\/}7K redu!xsca� 1o HODE}) which approacb e�� =#$at infinit�� Aev from�^�� S n��8a^ =R�!_AOseveralEervat� ,nonlinear ev� �s modella� >  physix sitls�"%� meny%�he MSTB (Montonen-Sarker-Tru^$er-Bishop) r�E@�M$ory \cite{ 6,F}��7 S ��Cmo�A+�Wwritten!$!� (x $\phi^4$-:E�# brok� $U(1)$\ sym�y:J2 f� 02 \psi_{tt} -�xx} + |"|^2$psi + h^{*�*0. �[ KG} :�( �cura%�ue/%hand relaA�theor�see-HLIzquierdo}.) In addi!*,*6IY describesgm�yI�i� !A ly driven]ZSchr\"o!�er5�FG i! _t +N=-6=+%m -^=NLSB>DIn fluid dynamics,��-) gI n� amplitud"�oscilC � watNurface�Ma vert-vib��d chann� m(large widthdepth �#-�LMiles,Elphick_Meron}��If,a�versea !�[is deep%�narrow,�f�#st+$valid, butY�opposit� in��n��f�%� .)�Ys��� da4sacan 5B�Q��Q,upper cutoffe�sjVK �lattices-,}. It w�lso deA�dp doubly r�=< $\chi^{(2)}$ op%�|5�or�limit of-�8second-harmonic� un����Trillo!�%� �S��U�6�%2ys u�! Nuwhzone %�� neeinser�-i}$ �frN�j �Opp� a*6i�se � s,�A $��*$\&L�r� pum�of�<sort. F ::�jmagnetwav� a quasiF-dimenr al ferro 4I�a weaklZHisotropic easy plan" a per� cular.� Licɂ1ur$Ah� k�ca�tex� e.%'acP sE�%>a�"��Orystal.ue�-so�. ��f�w�!�.�dm� a�pa�3i� ret�  e�)� above �� ��Athe� �2�� troughs��chainŚ coupled !rulaIH��  c�x]  tchua_$.� \2� �_a%re� �n�*. A"Q:��in rswre� *� ! I� S �  rem � �is�� unda" A�) � Q�:�g �cea�# 2�avJ ���o%���.bsm)~*& 1{c"J B ay bubbla<.e.�$``island''��� �ii$``sea #�} one_I� quesXFB�utw>� �VbeyonC e scop%� invZgE�) swer/ob�s���whe�� isa���b��� 2b �:� 0, Klein-GordoE���V  [%e&��{ KG})A� �t(]. To illu<� � ^ek��ta-a prop�h !�4 �s��A��, iGi�uc2 ��up2ex��%�$a free-sta* ��.�(eel}). Let,� B/ <� 3�I�Hz�� �:�"} -B2}) or!�2�" )l!zzn-fw! e&�L����!{l� \Coullet1990,Skryabin,Sub ,Ivanov<OiFa�+,Fboth} `!�=s�2lչA��.�eOZ� * �� NLS5.�LS!� x/�k to return ! issuE-�2��M�0future publiceqs�9�eI�hprito{`:�appea+��ned��!j��namelOf birefA�1-fibers�[v���� puls�rav\�2d\� � by Menyuk� }"E subQ�&�T3} "� (ay} i\left(�{\vial E_1}t�\deltai�6)x} \r�)+ ) 12 6[^2>4^2#� |E_1|^2� I232' YHE_1 \nonumber \\ "`3 E_2 a^*_84iht} =0, \quad�B!�3a} \\b26 -^.)�24..�-|E%1`E_2 221%2)1.�) .b} _Qn6LH^ $)��>or�9lapa�*�of �p veloc�\ fast��sl^yly pol} d (s (whose enBpQre " da $E_1$E_2$)�$h$\ measurac� ismF �Kc"�O �a$a���ts. EC!s ��Q4)-.b})��Ye�f  mo�"� azge1>R  choi�!0coefficients �� �f�{p regim[0normal disper 1��a_�at56�G� >��mso sm F  itO be neg�\!��FWRbXnonCigi�(though�ly t)� �� e substit�\�Q = U e�i(h+1)t"E�a*= V i(h- \] takes �� �%6�m0)2RI���U::n.,2  |U>V� Uj e s"!$}i �L �� �� re e�)�Ralong a q�t.jce axisTBDW}. L�eys&hg�#:�$by Tratnik� Sipe STS}. WY ;=��TB�\��m}� ) iy open&Y�is^2 6* ����& notS B% time-in5 re� s $UѓV�#&� �?).�'���iw�si��+iV �� u?W). Ou&I%% H36})� a I���|``!�''�``I�-  C M�A� :�� \ac� ledgB s IB%sup� �NRFzSouth Af� �4grant 2053723,!O$Johnson Be� F�%!3I URC �Uni�2(of Cape TowlSWb��2�Yb_ e�\ ћHthebibliography}{99��Libitem{Pikovsky} A.  4, M. RosenblumyJ. Kurth!P$Synchroniz` u �( cept��&�s�4ces. Cambridge= Press,(2001) \�"�85} P. ,, Phys. Rev.`t. {\bf 56}, 724 (1986); 4�(K. Emilsson Dica D =61}, 119=92N�906�J}Lga, B. Houchmanzadehl$ajzerowicz oF�65v35�!990wLMalomed_Nepom} B.A. `A4nyashchy, Euro��527}, 64 �4bHXY} L.N. BulaevskiiZ V.L." , Sov.-qJETP %k18}, 530!.6.UNiez2} 6�XJ.J.  x: S���d C�*��Mat(!�(ics. Procee� a�ecSym�um�No�( R) S� a=D�A�>h8. Editors A.R. Y6T.snee'. Sp��(H. Fujisaka2�Bi5�927e\2F�} D.V. ,�YTYulin, D. Michaelis, WA0Firth, G.-L. I,, U. Peschel�FA��(r, A m<E �(64}, 056618B6,Park} C. E�Hagber!�a:.KE. 9�Le=A j23�33%77!7/Discr1,.cNaUzSociety I�217�0HH.-K. �y>�8��11ag�; !LGo�&,��let.G%;8M. San Miguel, MlB]�194101�1);)5Utzny!�$ Zimmerman� M. B\"arZa5Q13N2��ee,Kim� Y�dKAJ�A�04620)-K9-�n�C83 @4�D.�8JA�Xt. B: Quantum Semiclass � !�S2a�20 mA. YoA�A�V��YJ!ɍ E�#{$s�NasunoA�@T. Frisch, S. RicQ+[J.M��lli^]72�{47�4!�S. e, N� shimISS. Ka6Km�5�8598e!5��(Petrov} V. , Q yad nd H�iSwinney,q8(London))\38�i65� 97) " Longhi1}��PStaliunas, Journ. Mod.�4�26 �5S. C, O!�i�%�2�86��96); VA�4S\'anchez-Morc�, I�(rez-Arjona,��SilvaA��Valcarc��Ee ldanJvA�95I��%."AOScroggi�d2LAC:%3�%66209EW.[ �2}.R?3a�2�1)�5~$Zhang} W.  Mw Vi\~nalsbx� 69)Z5a�S�9Ki�ko,�Korzinov� I. Rab(',nd L.S. Tsim�2iQ�e50�1!� � 7�F�I Aron"" -R]79}, 2��- %5,Kaminow} I.Pa7, IEEE�T�L�� ectr�.QEsE-1!l1E�81)SNel*� C. �J!: MoloeBN" O�"@s}, (Addison-Weslak0California, 1� ��Raj} R!vj�!EA Wein�G]pC 1a4295%�75e�T��$�ɵ .�� 3226�b 89) =$Kivshar} Y!� RB. Lu� -Dav�&�px 29�\8�88��=(e �iE. uin�&A�*4 Q�E) �5E+��76.�"�(!  , Nuclm z 11��3� E�} .��>��20)�9��K.R� ubbaswam#d S6� NɝE��7P 8H 0P. Hawrylak, RQB82�M829��15] 84.(&�IA� Barashenk� S.R.ford, E! Zemlyanay�R%9� 05410�3!�5��%� �� Haelt -�( Sheppard, B=!#97%iɵ]�'} J.W �'�Fi( MechM�14A�45I��A�Denardo� Wh!a Pu4 q�A�rraza2mE�)�6�15< v ]U(Ablowitz} Ma��H. SeguaoGa�In� e Sc� 1T�8$form. SIAMAIilade� ae�1�z�; Ito}eIto.� �A�bfm 119,@.om�2�&P9��.Ye�/�x477� =(Hietarinta}!�I �)[9 2 I8I\% 5��� e� ��et al}RY:� �&�+!�Al�� A�A� 0nz\'ale Le\'oI�JS0teos Guilarte{%m�M 085012G2a2�"U)2� B. Galvin{ Green�$LM�ab6�W.U�. )b�}6a17 ź ; G. Huan�.-Y� u���8)�93.p �IMecozzijqc�cC.G�fedaoJs96 0 n %n~ �69)$ 2�573, 552�g6.�BBK V.62MBog| ��V\ $Korobov, %R 1a��18ݮ�/ory} NnAlexee� F�pDa4Pel� sky, %N� &�e��199� V� Shchesno" Ba %�*� 1��83���iKIK!�M. KoseU�A.���AzKoval��_ @ 194� 7��`Vahit�NAVak UAvlokol� Radi�: �16} 7�1U � �Baer} FF M"�ɝ� 0166 1� ei6-.E�F105�CGorshk!K!�A. Os+AX)�I��428��Tr� 6� �*� I�"on�2 North-Hol�+(, Amsterdam8��%.a Vari�alFP%Κv 8�256 �9� & Herbst��A�Wum BA� ,D ��(Numer. AnalM"� 485)%��]AUTO}� Doed� ,Champneys, \�'it{ .}, 4t 97, ftp.cs.concordia.ca/pub/dJ/auto %>p��bE docu{} 4p\G([twocolumn,}Cpacs,p.int�& s,su�#criptadd3am�$h@symb]{revtex4} \u@,ckage{epsfig6 subfigure6 QB^6Nicx}% I�:e Q f� 2�d �}% Al�?t�8 s�0decimal point2;Tbm}% bold math \input � \ &spKD{1} \new�6em!�orem}{T�6 em}[�;]2'lemma}[ 6]{L2#�$�4ion)Pro2/coraTry-CK 7A1�title�3er "}&�.mev u4F4devi�s�/s6�S(author{JupiRBagaipo�6mail{jb @<.umd.edu} \affil \{ DNBtA�����6 6�Ma�(nd, College�, 20742, USA vaMathe�cs�e � an G�� stre�j����6e�u�&e:!Research�El��F ApplO$1j ~k 2Vk$\date{\tod�+ ab�/ct}v-h2 a �Iod�)de�in�"e :�;paB�iiAc!�"/<nea�) iden 7 cha�G"�3cbyo)�8>�JY�ed"�Hd&�?# � #KH nsem(�0ZJ d[J �>�Hp� We~%cuss �Ho�-ly2XheL(�Inoi�%!���q�0R7�% )4n�! 2�B��>q�E9� \�� {05.45.-a� ,Xt, 89.75.-ka�maket�;3 stud3network%coC5�:al�KL)an im�"ant�*a!2�?E�5aA�G/!�d�"e �s, rang!�~>biology�laser � A�'8 newman1}- pz"s@9��of�&` s ha�%en�#ext!ev*?!iD'cd% yearT , inA�t�7�&No U�2rsreceiv�; 1%�!�M56�,mosek�H}. Si1's0!puIle �rac�:!2�7y9.� �effec��AdQ�C<u�%�=8,�2'U�}, might�(relevAin�9. . It+desSMto�BYfun@8s'P$em(�55}Jle�toUC�cha!e�&A<o�!F��az~Q�.�8il:D<wec,/..�useB�>�toAt��A<- onv@N� �F�%%. Exis�8��s�)�* (sE�'�t, Refs.~Marl�ma tao}) usu�3r�2on%i'"�*typ{>s�->�*; r. �' ��H� �ly���UvusefubP2� 9� l's1B�=Ѳ2�M.]Ewill d�*�71 �/� ���?!_exactly,.G�=H r��&�C!;:��n�5\Pcla�aZ�$ a�it �xF  AQ�t�?.�s"�8m�Q�w-)�v-�z%�ma#6�6fun�},�͖/ O*Pecor�%Car �(2}.�G&=.>? �? -4 � &�i" yRŚrup�*�Rrel�E%1 hort�>ioa�f��6C  (�de>bursts�77/se �5 elopMMpa6p� A�mHA�;>'�)��� IG� ye�b�.peI,predi�FLa�Tan:ri"$>� �aEn� s,ff�QFat�or�unAlle-X ic o�Ns embedd'0itM ours"�B/��)l�l���5 ? ',tQ+e����? .to���-Q!�� �ee�!y( individualɷ)��T�� ir��Dg>B@ �Ey*�UiDfollow #*��-c�3%��u,I�M��!� 1 &� �4eBw�B�-�fO0��G"Gr, �> �way�ll-to-����ing �i�#set up��@r��1o�1F�-8%eM�!1SRa �_dee�i� � 8�45�*n Mn*�1 �]!V��5v&)�se obJYE.F[5g5�` mean�d%K . Some l>E_ ?isQ-�;�I/%kI%*2?JatY�7)(P)��,enough preci�6)��\=%� B W-pJC��� !��� Also��s�7)a� v�q:Al�6weI��8 ����b y@ ivenes-Qe1PdecRO59 �r!xAAa�uQin ,. ?Ga�lso6zunavoid% � ���G5e9n���Qz !�y�2 does�introVM &Z ce Y.R�D�Y�]~  or�2of�B�Ir� qHa�Y�9be�E1���Sec.~I!�brief$B�bGb>1�R5 �/T�alI� AOl* 1-� }~I_�)i&�Aou�� thod P)�-��G >Oe-�is�9p9.kl disc*;Jz�:)lD �V!0��� lQ.9�{B"�XP�Ls�Y3Zyx5�����:d*�GmapGA�{ �70results geneAVzE��&�Q�j � ,�� P�N 1A^$N$I{,�CofI�,!|n iso�ad, �\sfmC $X^{Y$n+1} = F(},\mu_i)96$X_{n}0$!��val.py�]s ����a��cto �y (e.g.,6<})"=;e9=}�9eq: P} �b� - g Z@p\sum_{j = 1}^{N}G_{ij}H(X^j)\&%),�s17Z �� � $Z(0�[0$, $G (�OicFh �V�} ��8)���;!�� I&� �$H d�.;8of!� )j$. [Ine:m�� �!��x�4\sin(2\pi x)$.?VQ� nt $g$B( tr�Sq�%��i I�EI%�"_ (�:,MT Xmu$EC $iu?%O��[�[� �9�=of�F~C?]),A�n^{1} \�_v X2\dots2N!�s_ni/time&�Rq2���un�e&�O��ngl�Eit, $s_i�a�s_na�m�F(s!F(sa�)$�C- 2�DY�t"Z"�� !< va"�"XE&�``��An�n2Tesg �Gurb��n $�<�3f�,��} =!F +�C;!Ubu]y�l �} p)1; = DF%6 e� '(0)>� mXDHB7jFQ\L�] [ = [ A8, 2 otsN}]$,�Ydi^�Mm:$Va = [ H eta^FD!�{ L^{T}$�7re $Le�Ai�ogonal��B '�Ze�.�TJ<;�AeigCcE�`$G$; $G L = L \Lambda$, $ $ = diag(\l_{1}, 9N})$, Q�k�o ��t�1fEb� $k$ n:�]%$Ce�alent toj^ comp"Vtw}c !hQ_kA_�[Me]W�k}UK�&] B }^{kFP6q4�#E '5�weLi $k$th-%��!v N�$�K&D ., "`4'�Dd���)'<.:Ad:W2V.B). By"` �C�X�z�$\alphA?g e�|AA\_A r set�s bn�Ej}S encapsu -/leRnsr .��lef.  őI6���}%� W=[��O_ ( T)$:�!� the �(st Lyapunov�E�a(�ra&isaA@x�� Ş!�".@H�-� � �� ��el"&� Z��K�v(P The �2YAi�s 2( (:�detail�>�2� )-:� 2@!�t"���Vt3b�$%�_@Y \supA� �a(g.���1>0$�  es iF ��n@Iel2  F�,� geEstead�2�A&�2! Q 8G"�U�O��( D\�XF {F}(�}�cn* - m�>b� a)��X j�KQ>�{^O 2z X^i)� � , s i^N } /N!g�s$ _� 8� D _i��:b{i})$.UV%0Y��"�a��H� be�. TermE�$Q$$ w� |H� . Day$Q = [Q )Q  � N ]{ e�� �  analogdtor r��J.���J�1��H Q L)L^�!$![!ok���[A��!1L LZ&DF<En.is $h_k�Psi(g�kl "e!�a&�S }g)4�Iha�h �Kda�X at n���Sf�%ne2Lv$ '� ! S�fS_k$�st& ed aF�&c machet�'la� ��|�!���|\�!~ \simxO{ 0& |(Q)�61 }{1-�g Uh�* !}F'n^�m�l651x���7-U =yh}�_u qaDt�} _n$i�7as $n �a�\yl�ue2�Jq� h}}$�4e����\f�A~$�Fc"� wMa^JY�n� ��"M. HowoaE@FEx�iETt�&�he�atň� se� io*�n#�Z)vJ��M6o4aY�B�G�s , mo&yY�O*I_-�k$�be6s� ��W �xe,lyAW2�q ). Event!ltr5�$ gget h"���o�6V!Z���N�%�BoM�G@a��q{ o loe:���nd�s"4 i�%-�L�%�Bw�b�s "�F �Y bej� ,�du( qQ:Mb5UP�;e�"UoU��T�Us [ T (,�pFss��ea�QDZ��QC�E �  s"W "N ��u� ]+!�Z�!� �gn&F| Em:umk b� t leS��`&{"� �}. > 0��e$k&�:6Ŷ!` �Jof|�>�pe2E sW�^r�XfacWR�o�L��}&@ :��`or2 � &�" !�lwT�qso $�(exO# [��Y~31s��@���I�):��a�w �N$.>��) �"�.�S� Z\��s�e1�u�s", y��k}$r� �e�*�Y%;t3a!"WM��|_&C sth" [$b$]A�6gTH �$QE�[#:AV"�  wthese���y�dx� F@d7d�j�.�m� b*�6��\FE un�NnT� a orpo!to �+ �pm�U�cb��de�˭Ai}g�e9a*�.�*i6_)��*�F�f'cyA�,S!~"FdR  ee�guaBOe"2urz��/�-�. Ow�us G!A� � q�d^�=����>-.�SO!^�!S&b!�� ��Jow�_ tinu� um��Xak�uldRrW&$��u�Usc(��O�tak:�� �<�2�O"0`P"�"u}���mn�.v 61`o"R , we��\emph{&f/},zju�� "c\u�Y2� p} \thety+1}=[  \omega�kappa� 3ki &]\mbox{� } 1B�W;Yh*�� be $ c=" 4\sqrt{5}-1}{2}~ | "]%3D +O 1W�Z� B� a^$ �� , [0.21,0.47]�W4ZR�"O&:e�] g` r. TA �=l� ($p�!�dNF ton'"c#{ fi.croL�%�=f^p( ��fi-=�:� p�nd $f^p{0U�e�  aM�O��{f$,Gimina1-��utpc+!*"Z E�f%B* �1 7, �Z 2 �(.4 T'� in Fig.~yfig:msf}xb/ s � ��&C(b9B�pV*�I�&�� �"m%�!.�a ��ma1)%�g7 globB2^"�8}[ht]q��1e��8{$8T = msf.eps, clip = ,w�l =0.9�7 } \ca�Y{M^�+���\�A��"� � :�U  (�a��curve),�!MM/ (dot�(f'MA (d�Fd-:.!R:2MZ2 Y.")tQ\� 9Hndur��7�it�%E����4F �o�.��eEoaL}o�a��X� Aa�N$�t�� �g\�MC$�ED�byQ�2�Ay"�=�\{ �)0Dy}{cl} N-1 & ��qi=j$;}�a" -1 6$�[j$.I�; b%B5 y �� �;d�1ct� aQsA�� 0=0�0 k= N$E $k=1,2,\l} N-1$�aign�t e 0W�c��%�ŲaA�&�"V'!��� dis-��s am�w (tf they�vin* ed). *#� lackc1%R �4Nmto pic�K��$I�p�'�,sAz��onAs� waEh^)oA(� mjA{i� ͜0.9 < #�(.1$ (�� �a�f�&��B%/(!`$k�z We��&ab'-�� �W �T`'7&� !�s n!6b�$u$M itE�tkA2� �fed ��nR!v< Y�e�T% #t\b.����#'�� no�6� ^i&� ^�t �+( �+H ^i)�$��k_6(- \Phi^i_n]m�� ^�6W���"� E�$ $i\$a = g\ �(��%=1}^N(�j_���� $i,j2�$� O/ ces &�mA��$i0 ;j )��� [cf.6S -�}�k!�� �hi$� i"*�qM� V�|Eq $N=5��$$g=0.0477$T  J,�2j=[4,-��-6,-2] \� 10^{-6D �d�$lue�)}ua�Itk uld,�;CdoA���*�:e�ny*�5)Af)_��+ad�aTcc�Angly) �U�5ny siz�6z-,҅!�'� ��wai)�im� *Z�>�2?�be�byC x;��s�$N�g$T 2�a��E�� bub1�� Plo� $\Dej. a�$ vs. r*�, a��R�4b3��a�B���maxim�[FjE�th�s$ng w6` �ra &�Bn=���  bar{)}("� 2&BN}�\i�\ <N�e p!]F�$�su�$I� looke Zt"<u� I>� %�� !uE� "�{!�N�-�Z{I:�6#i�"�I3l$�)$l��f� �%�$max_i\-e�\}$ T� :��?�-0.4<|B�|<0.6$ r;:� %�"�9g�i��e"��"�2i'"��aB���r �21O-n^��� !~dy|z!w���#�re���lv7�: becapf`�ren � a�8a7"�� &�a Duf*�Z��&2��c��so�)�P�hb� &/!ys�1M0U/�>�E�A9�E6YKzndc=�)�&�!�$J"\� E)_?$|9�B| 010$��lo]t �w&t rari�<� a��A[g�I<c�A�),�g�we�ot*\ 0 <3"� dire�-. Gen 1l[7U�b��k _ ���53]��is. A�a)j�7eHu{�,&�0a�e�s�!)e�'_l^i-2Fl \ to�$E &� }+6�.f�&^i!�BaE-n�#! j�65k&*6Z,�;)�azTm�8!r.�MoF $d6�secII��a�fer�Bed�\�O� ^i_l-;}����$a(6� '��%"��i��a*ca} f�,, minimizes B�um_��[�Ol^BOl)-� )�$� })]^2$s4R-1cal�{ $aq�1.5� 10^4��c*y#!�\f(� V 1�.�8shE�>� �� s�D�Gunl�w�7�$5"�A2� E�We�:��� �� B���%.)Do'ip|R[�hp�:g�vdwI��y� it may�� �&,h�Z� play- ole ���5as6;=1z> ��aԅB�y �:-%�+���=s 5\w/1��>Ef8(�T�E3ina�}��7 &f&� vari�� �a next�/�3:�7%��v��:a)z;�96�71yof�.�1 %Y�2 S�NB�q�I���2�$"4'� squ!�l� ers)I��N�SE olidB��l�s)2�Ba��6#6S % rT ~})�zAf�7 learTU�s" 3Ns8in IUfp!* z �A��c&�C� �Hosnd5l �^�Vp:�Av7 A���GY )� ��u�e$a few��B�ade�� m ��<c 2Sp), �!we5ify�nr?2�y��F� -H� $+ \epsilon:���)PhOD��&q>%&R=�Dfok�b{ J a�Kdom �n�1 0r�!�t"� /:G+: simu�1�!:�6�8I~h]:uj� rmlyY� val $[-5}, ]$ *��) re׵~� ��)=L"rM��$A�a��N>�,J��H�.:��l�j� =��._G�"� ��a��5�4!� iz��tCT esen!�b�Ia%�5�$\sigmA , sg mf4��+V �f;per��.�~�D%mean. UErs� pk%(5�i&S4ѭJVeta|%1jT=\ 4\A-- J>}{w34W-- NB-cF1Z�!�brack25�R�.-���&-N $. B�� �+"H^:� , 2� �!9e�3es+� a�&?A��po�N.vQ����[[+�x� ,I� �6 :04 �^i$n 1eta��*6RJ&;1�;"� }(a)*� � E}_l) -�B)_%J��%�#��a��)-�s.�m-�}�"�!��$ch": ��e�{��iLM�D�i��%�$M=/mp!�&� _l$'E� E>�tU~� $#�T�#*9M}�3{m�M� ta_mS m�$\{\b��) sJu��1$'�Q $- �)~_m��!b9!$F� ]o-$mV�. N"�w$.�[anP26�ov�k��ts�{�7�9+m��%f�(w� e�%��OW%�rRerv!E�72�n1�|-�5�"#)� \|^2F��>E�anI�%"j�,�)]��A+�!��**&a�s"0��1�A�� ����!� .'�oy� �%�opta]os$ 3m�S�*����i'�s�S&*$2^M$�&$ T'!�!*��*!($algorithm >��^ � lym� T. At <�Ya�ewe' thre)w0�7@ � _1$,��!w 1�%2e y altb*C%oig�x1\%Q�I%�=�gG+ a1 M_3��UV &6 � % % 5Vj O�G��taaS� ^� 23 �3"� "M��%�!�[2erM5*Fw a_#�e@�Ast B���V�z �%5�0��0ed unti�m�0sto �e1�Hw� n�� ]~��F<oun%I�qn-� $i�_*&�M:N.��#�$$A���%*��e>$��_*"!}_*�$A"$-&F3N#v$��KV�I}a� CaT�~� �" 2� ���}_*&E �e -�� eWCy~> "!�P Indeed!�P� 1^wJv)U� OJ�$ eveP%� m ��h-�8["�b�-��6:� isy}�" .�KDOLja O%%����to< B�sy2�~a<"���EA�^�Y�lZlZ�-� V$sf��[b�\��l1&�a�V4p]A�! 5e"MU��"�[age.���Nto �ove/ qu6�:�L�:l!m�'a[��#��� gXT�s 9� �:p � qW()�e""2�"�1F&4yincipP�& "9*&R �&�Y-�q!:handl�&��( �GY prov&�A��*4"�g ��!�ye�F �Vten�U MI "}M5�in*F & . Z(e *�`d.�b&~CC�K2kan .(a$5$&�ps�Em%�P)�N�9�G(�2��o�  d a�:b�#�p\A �\6� Z� ��B'�_JUsN�!�).�Lco-!%ԉZcE��#t)�it!\suitably1)!u~3n�=[a�d�*+! �s��a r. >X�-oGto*� 2�J��<��$� 2-J�"%(I� O.0�&!� e%� �:�noe' ).>�&6ly tself!2�C�~(#DW �??:Pthank Professor Ed OtZGe�Mra%�ot^&��6&orkr�sor� ONR (�eXby NSF>0�G4s PHYS 0098632d(DMS 0104087� �'tN�� \b�z)c M.kyN9c,�jReviewl4�n6&|3�$% on �sY,barabasi1} Aq�Gwb\'{a}s.p$R. Albert,j.<}�bk�p4 r2��"�c :J�G�|L�ib"M���it :Q�: A)~ ay��;i.�Q� }, (NS� >S�, 9�. %'Fu"G�7:�in�ʭ�,�9�4^$cm s'=_m"�c �z, Y_ui93ko)D��st�|�_�t˛F .�eto Liva�S�R$} (World Sd���c,gap20%�%bookA�<sub 3�;b}�Gb�n?i6]� 76}, 1232�o62maybhateEM e R.!AmritkaR{wx�64� 20002X��guchixSak 2��w�v272΂6�taoau Tao%�Zha.[G�0)�J%uJiI�R!^9J36204Nq4�}V} L.M� cora�T�s`2��t�q8�r21� 1998A�ms�l��  JeQ�j�p�� � B.R. Hunt�p �662K~20�Ob�n3d&�nz �3���4hon ��b�9!3h{_�!�%ata���-wE�mn=Otakas!�T0�shikawa,�`e`�z!�-C�z��F.J}HoppenXKt,ZBx9�~01"��3!rL����s�2i�&o�*e?�de��Y. DeAM M. D�]�f J. FJ�}A: ll. Gen�U[�16�s4��stochas�f/ �j%TM��stamp: <05/03/03 14:32:54 kaji> \1�^p{a�h *pamJ�o amscd} %.*txfonts: % set�� :%� {Zq�7}{16cm}Bh8Q }{22>odd�*(margin}{0pt6>IB!B�% macrosF0\renewcommandI0belenumi}{$(\xprm{w )$6�o>p&lp2pN!}*pb@pl�pr�pK�$R!k}J�b&NQ �� "G8�rbf{\L`��}~W�2(Non-autonom� ���-.$Toda Lat�j�$}\\[10mm] !T��HKenji Kajiwara$^{1,N=0Atsushi Mukaiʱ $^1$B5.A: Gradu�OSe loaRe>p Kyushu &�p,\\[2H�6-10-1 Hakozaki, Fukuoka 812-8581, Japan} \\[3m�$^2$:Vqe�S�-a�s F07,}�Syd���  NSW� 6, A��lia!��95�)�a�o � ڌ��$to�k)�!�n6�� :�-. ice "�5,L�[l��VJGt :" _&�! res�7�E?lbbܳ &|G�!?aə5A� Int682�T {.}�"�t!Di`�"I!N UI*d�f�:� ar(�8{l} \medskip {\�$laystyle AzQt+1}+B :="t+B�L^tt,}�:BP{n-�\TS Et,>=AQ �\� n\in�� bb{Z�W��dTL�&1�"]�#$t^#!3.��� �,�c$�3��Tent1e<"�>t$> 2 $t$, M>iv�k�2�jp. ����x4,@ ���*�\�6Q�sijeQ�I��� the " qI����!]N�2�XA� 1xQP�a JQX�IWV.(=$t (t V_n^t,}\\>^E[(1/f) =?!t JQ�),MQ�}Rb}!z9�� msF)ebt=-qUt+�,I�B���1%�_t=D'B�6�hn.���KI؅tns,9��^IorM-! ��)!Q~�tQ e�Hirota�@Hir1977, HIK1988}�re?$B� vyY��' cele����qw"�A��YE$dJ_n}{dt}=-� -V_nR� 0V0n(J_n-Mm�k TL:0M���k]]e3�W\(A �\to 0cR�).�Spirido�Y�.Zheda in |SZ1995}�v���� !E�n� ``!2 .�'')IF.�RIl)�:� I6 �E59���� �B(J� ''. "�Rit'e�uzC!bF�) z�+6V\p!�al_*g� R_t="] �#+F�-6�M# ��J-� ��!:com�2b4$yA\d� A � S�problem5�Fj� �X �\��%�G���SWX Ps Rm(x�A)* =L_t Dn)i %�+ *� 6 MSpec eq u=q�"p x�19+IK i� �$ pUY�s.�zfe��oP� �5nsV��� .Kg!�Jn��u4Oy 5� wide utexact"zZs, a�T �Qvs. �) over� se�ex�s��#an�K(r Pfaffians��200ʄ$aJreg�DZ6cyA��b��/gb�l: A� he Sa�ory pMJD1999�t�I���)6C)f1C��,����Si) ))VsiG kind%V�9&. $P�,e Hankel typ Q7�h1o!�-ҡ�E�� � ��r 2qize ��'87,KMNOY^}. An�zon�E= CasoNo6F�)�describeY�&1�� "�!E46a�lc�1�� m " d7��2� �n\2�9��semi-�h5t���( MTA�a, b}9ipur�4a].�%�o�ta.lnR s�!�n�I�QU�( �.�N�.�%%�S:�;n}VxO&��X*� >�}���} QL�D$N2* _{>0N(weT*�'�s�JE"�a��$\tau��1 *� "R�l�4sol tau fns} D&=&S eft|6! cccc�K4\varphi_1^t(n)�K.+1cuKBN-1)\\ D2>DZD Dd & \ 2cN>cZc c\�2|,X9\�)ps.&>|yeG� �%N" �:^;%5  & Z�ZNZ ZN eUVi a�ent� $Qi%�Q��($i=1"�M$) �qyR* ar r�5J�&!�I�i! (n)=6s-�dtUov +1),A�u disp� 1�W�P {t-1cBT fX2 XP�� 9)=q^�-b�3"� q�$�$�I*�&�2t$� $�$Q�?j ��} �=(1-p_iRft) �p).�[I��$N=��rGu���Ggm��=e�T�AM6'�>�>�gsw� �/s"~�9�� thm:K��2� �*s� ]u� }&mu_�;ǩG � }' t})2 "8SN*� .VtR m0 O"� =R+%�.6�ep� t�2�9�q�! ��Q�M1�%:�qJg'�O�&�x aux7�r,ta�r� 2�z's�9 ial �@^1ǰiX��x� o fipIc"t/j[QC:xnear}QCM���sQ��5 tisf�EI��=*{&Y��T�� e�, +1}- tw %� +AN($]I +�-RE>TL �S\\�]xVt�� � �(M� =(?)) *>"F:�.�2BE�!��_Un�� JX�� a Z+ *Q5P&}� 6P9� . Ac�d$, multiply!�$1- ���)et$� qZmy :����*J Y91Y)Z�-�1i�1cN�lambda_t"�=2��ٕ�3M=&~ 3})�'��2�Wu�p�I1RR�(&&NNauQ�)^2-eq"�E�I�%%U %���-1 +1}) -i~n^_8�c)�b_"r�a�=&(z�i��+ ��e tFo���*[1GD��A�Z�;!� 5�r���:e�2��m7&��of>{�uL�!��ty H,�ZnJ��~��e��+�$ % " %q�7"�"eF8Y  �'�w2_�ǒ' aspYexp ;���H|5��>"" � =\�[_i p_i^n�K d_{j=t_0}I�� ��j)+�6 - {-n}b0i mu_j)% x"� >u ct)BR22� B� ?rjD$j�o�Q�.{!uu_R$ �� p_i$F� are1�"@�-��E�$N$B@". @d hown�"��,OHTI199ȗA�e2$ fucn�!3$�"~�>�as"/.�s�x� F�L byje� I��e 2\�U���m�0�ed.�1}.}�.�~re�aJ|F"��o.l2�. ^2["n% .�]"���e�つ!2��> U T��6 NJfJ)�U^2lg�1y5ǡ)�BF�b�^&Gbrqv6Qj�#�����ytt(r+2)Np (x_i"�t)61 W�+�,u^ ��x_i=p_i+�Jt�.� 3>�F� :��A�MLbYm31��) &$.����!i�and;& > .1��R�im�B&pHA��--�=���\�*�&Pro�:f~� }&� :�|6e~:�l A�techniquv��M����,OKMS��OB �� @!�Ai�N !iPl\"uckeujI�|%���z cv�t�lamw�>*s�. � e�shifted�r�J"�B�ls�H&66A�J�jB[ K6{�x��or�F�}1Eup�e &��no��W���t = \Z�(c} 0_t & 1"�(�52i� i�&z �Dj`\hat{0} ` 1 "�uRv��&i$symbols $k�{!Nk}r|!�� �Ej�I k_tdA�gin �{c}��+k)\\� �=k)�.G) �B )�fyG vJsfpB�.� �1M@.0 :Y�1} �-C�� �ӹ hold"w.~ YnA�ke| i)Qc}b�2)E8EV� �dif� q�1Tvu t&2�2)u HB�|y��V.Ƃa�u(N � Sv�3�(J iIN ���+1} r�\tildea���R2)�-�r4���Ơ1} �N�2)��5 �1Z %k�) jM�{�0�M�� ���i�tY�6b yc> �E%ÁU� ���ۭ"� q��XQ=�N(% �{c}(P��MZ0 1!(� \\(P��6!2.!�\\ (P��6*N *)F�J�%,��}�8" i�� 2�:}�;I�B�� ���V.Va*�1.9� -&iC F�)���z�mRi�*% �BiE�.(e�(�  J5JcNK�� m=1�2� &C)-*�38:� ��)[ �"�R�IA��{. B�.if ar4�as!ؕ: Sub.=N$$(j+1)$-thq��bOmu){$� $j.-#��-1%� j=0,&�-Jx* &�Jn�*&� E &=&W QRq�� 0 ���. &.@1) e 8�K+�YE6Yx!1  &  �rr���WE ��Z)t62!}&ͽ �Fq�Yq�*7(a�k�-�I�.�.Ma]_% $N:aX!!D /4AtRd�cMc� ��� -1} UnF� }F 2)!W.Ki�� ]BT.z�e � [�m�m gB�j.�F����ı3 dif4��-dif5})EFb�b'�:lf��Gner���i>hsollJ�!5})rY�6B`aO�9� n$@�2^5N�-.S%*m�J� ��+1}�>Q5� &� ɶ dif7լ�.]�@5)@4!@W:so!�e d0�!.�#FFV ��tEp)��)=� .�w#� .+�#�mG�s6Z�Ho�>��2�v6�-1)�UqM�2jA�ynv#r��P, $n-1" qNEe(�"2E� =+Q�BN;�R7i|iLr�6}�0N��F�"# t�Y9��}�LE�>� �  &N'��>*ED�� 2� f� "D � EP)u�F+� & Q�9E�('E:8� ^TT2^TBT^��� �'�C ^vvNvv)�6Qy�X%7�9815s�[P!:W9;6W�^@* � &r^� y9>6y�a __2�~-nJVN�eQ.aK�}(m'j���2G.��3���8p�}�Af{F}.�WFd$ Now(")>f � �61$2Nm�2�&q0*t�i�:%|cca�"0}�hI�),2)� & \O &> � .V\�"GbML^ Jy Y:c F|=Q�et id F�3Ap�$� L���a��� �v� \.� %�^f�7b60js c!#�1A&!�@5, J I,�(V�.�zFJS 1)_t e+J_� &�f^0_t!�B� Z޵:�ncv�-z��Z�v��^|=kt��/ �&2�� a a�$% +�%n%&JiF`�t��*>Io3:�b+1&�>.Sa��I:ne T2)K��3,� �d� >  "��[����&"��|��^52}�J24"l+P } &�fF c} ��R ���C  a�J�"3 dif8�.-t=VO} *�82_{t+1}& \cdots0 &(N-1)_{t+1} �>t \end{array}\right|,\label{dif9}\\ && \sigma_n^t =\left|\begin 9{c} {0} ^ 1 \cdots|2| \widehat{�}V� �10�mu_{t-1} �{n+1}~�1�N� � �™1 �(�- t)\tau ��v8��}��..:2} %�eqn)� dlemma} \textit{Proof. of L \ref $h:difference2}:} Equations (%$dif8}) andP9}) are equivalent to>:2)nd KD3}), respectively.q_P10}) is the same as e �&7})R=h1}) can be derived by using>F4sol disp rel 4�Dfter multiplying $!�%�$�@the $N$-th column!S�eZ h!' sideF�8�� $> oEnru7-�)>�diE8. This completeipa�A`e� e�e�2�`. $\square$ The bilinearR�TL  eq!a}q< by apmA�La%a expansi!o lef:�+Y�identityQ�av laymath} Zq|cc } 0�� &����o &  & \O .� B\\ \h!- =& W>X�x�:��|~x J�=0,��20a�IbE^�v>Proposi��IDprop:Q&}�E,thus Theorem f4thm:main}. %%% Concludi|marks \s��on{F }�8} % % cJAS % Iar$is article� 4have presentedEba�,soliton solu� for8 non-autonomous��Tcrete-time Toda latticF�TLe���\ regarded as a generaliz��ofqNb�y such that* yinterval����i���8V�{ R~molecul���56�8� 4285--4282�IK198826 M.~Im�F.~Kako5JT�s�Prog.\A�or=4uppl.\5094 � 8), 42--52�!�9V,Conserpqua�Af(of ``random%�6''�5�%�:�6)09!0283--2846� 20042.Qd�D�&Metho� S. � y8Cambridge Tracta .QI155}, .y B ��KMNOY�  K!�@jiwara, T.~Masuda%�4Noumi, Y.~Ohtae�Y.~Yamady:D� 8nt�� mula� �tea��J� q/A�Funkcia!� Ekvaa9�4A�a491--307.�� 16�v J.~Satsum� $q$-&c ��o�iZWp �}��60E�9� 3986--398.�X :.jb�a%[R��}Lett.\ A5F18 �3!G49--256=G� ��Z, ]%SM.~Oikaw9RA�e���system\ la��toY+ �-ZA�4SIDE III---sym�7a�A;Vi�of =�1�,s (Sabaudia���.CRMWAJ�lNo�{�F2a>Ame�{a_��,4v!ce��(00, 303--31.CMJD�_} a4iwi2 Jimb�)E.~Dateu�Si� s: D�Y�f�, B�finite .f algebraa9�)3�)�.T�:8a} A.~MukaihirI S.~"� ,u��N.M ur� $R_I$�Y1�leM6A��A:)� Gen.U� 37} �4� 557--4565B�b��b�ral:4 chain associE��bi' ogotal"O %�submitmZ�&�(OHTI1993} �,� �2�e/T.~ImaiUy Caso��� Gram-���re�s H &^to��C(KP hierarchŸ�V�62��} 1872--188.OKM��2��~,�M�� kidaQ�J&�.�����B  ��y�Q���X�3��!�,), 5190--520.#�4 W.~K.~Schief5�@Isothermic surfac  sp �"i�:&` i�,1�i�,%�f� ---a3e Calaps&*�Stud.u . ��.10��& 13.�TSZ1995} V.~Spiridonov�(A.~ZhedanovB'��"�6�,%�Qq&� 5� �iXAskey-Wilson polynomial%�m � A[ Ang1�M�5), 369�}�V�� L.~Vinet~�A�t �'3bi-�:���Vj4!|19��23t 4��I >� �ocu�\} �%\newcommand{\beq}gin&} 6%en%aѡB#beeH�FH% HZ#bemH�lettersJK(Kn&non}{��1 $style[aps,PDcol,epsfig]{revtex-hef\btt#1{{\tt$\backslash$#1�!\BibTeX{\rm B{\sc ib}\TeXA$FigW{6.7cmH{4.1 � class[two�,�pacs,p��int �s,ams� symb�4_-� M:�L % Some ���vS ou5(many) possi�{iO:�~aps��!�draftv-,�#0 \usepackage{�icx}% I'e fig�files2,d)�$}% Align t� � decimal�.g$bm}% bold !� a]o a"q-� } \17d{APS/123-QED} \title{A R�E��GeXuly InduaN�ity: F�RotobreVrs�Kinks��Mov�Loc7ed ModevReson� Energy�nsfer�ET{P. G. Kevrekidis $^1$�L V. Dmitriev $^{2,3} hTakeno$^4$, A. R. Bishop$^5� E. C. Aif��(ILMs)G-xal�s;� e.g.�rez}�A a*U!reck) 6lkeeRs�)Q� focuEn�h�!�aX �-s�")�(� A�ubiquit�in]��1 ls) &-�Y.a �%Ea targe�way� 1, 2}. A�!d�$a�;ed mAa�these�s�im�GE� they�!!v �*$ of heat (�"�*lyI�Gd �) �g)#5� ��- Ihow%y ����da,,al macroscopaaws��o Xs f�  ��c&e=E�A���\)&a �dZ to��). FurV �$!b6 a��-Mibat�ta�$$LB2��E�Ɏ9�M? azimuth�� ,� e �1�[thr���, ela�a[da� (ength $l_0$� Fig.�/ dfig1}(a)� a sc�aSr�å9�'� b�'| ���b� !%i5plane ?/�� !��"RhilA*e� erW(Awh ~%��(rict oursel�t�s.�%coZar �+ what C21 n*�4�` x_n=n L + R \cos{\theta_�\,, y_n=R \sin(#),I7eqn2}�&H7a�!diM#q5 adjaAT�%cle:a�n by:sJr_{n,�80 &=& \sqrt{(x>8,-x_n)^2 + (y y}"�7Rnn1aB��# ( Hamiltoniao>c%�aA ra�: ��$H=\sum_{n}�3[ \� ${1}{2}MR^2( \rm{d}1H} ta:)^2 + )>K ;5-l_0\17* ]��B�O!�5 �"�/s (�!��� $M$, �. $K$, disk�x����1�"!�8�A �ng:� e�),"' ($M, K$"�8scaW �whiu0�re�AQthree m�3s,� q�us� sLas� �� s (h�9, we set $R=1:,aA�5sL6ea��6n&�6�z�EJ�\ddotmY}_nI��5[.O�;-Q) -6m{n-1}) -� \nov �<+& l_0 L6;) nM|1}{UJ } - Ui-1,n}} ^):^- ^ M 8j�.h"p"y6A5 � C6��u EqOf~ oF�G $r^2�9=L�# 2 -2���>u+ 2 L [� 2#)�con)]$. �/conveniAA��iA��no�  $L_0=��$L^2+4}$. u GSs.}�a��of Eq./�) �,s numer<a &j  (.�' we�in� , buW5��o�4eUr"E�3Z� bearaa v�.����S�c,!$ $(L,l_0)$��z di� e)��a�$regions, d�4e0960B4ntyp� V�.K,now summariz%�se��u�,s@N B+b)� !크� n�=0,\pi$%:st� M j.� rigi/ !F��AM D \neq \{K\}$��easily u�stood5A5O"�� ����' st�?1� = %j��o7�'oscilN>ng U ((amplitude n�.�=S��.f>iA�,account high"�>8anharmonic term��demA r� an a�(y -�torqu c4q9� �r N devi%� EG�da�s�9 Ig �� h9~� s 39 e� rce dPng9�to� closa6I5# , namely MC$- AM.w�iCstored�a�ar7� )�%t�:Roe/2%� �-\pi&� un �. To ill�!�I issus8!7� $N=400$5�'��E. s $\2J =0$,C?� �B +r_n!ith*v magnE���%>� $/ �?a�dom20homogeneously� tributedAK$[-0.05,� InF8c)�qplo�]G,evo�4h$=N^{�Dum_|1 �$. 4��*�e%ttwo>.s6phi=0 � A))i�.�� fluc�. �+�=.t !��Na/�9)�e��CYP,)g��.!!E G��>er��e{B sNC (omega(k)=2\� 1-� l_0}{L� si�Api k) " SPrumFKI0e limit��=��Ax� H+umB#w(�a se �8�� $ � =0$)�2s�;u�"us we��s�#� ~$kɺa��te!��_�= Z�R *y�� b) lh � pure��x} (PA) �jY��)/ ��u�!;k:�n!���as�( �:ٚ O s s�%�?mbl] Mt m#-�inuum �x�a� , �  . R�Isdef/0by $L!�i�)�.���n�u�i�l_��� (4�^2) �(!k)}&� q�F�� � v =2_�$k$� �(PAI)��L �4%_$k U�2\ �) vanish7t�=L$= RHb�"�!"  IeR I � mp: Fin� �H* II�OsA6���� $L_0A�$,�/��V� ~^ mM��\pi}{2&#o 3B/�$m�^&��J� 5�2M;��4��_0^3}�) I( (2�w k '@}-1�1�F�BKU]�/�'!� widt�>U]r��(k)=L�Ha�(.�<S.��� � <+ esen)�I7)�|j�"�C0a^@�*�.DM�T ljedX.2��MG�M I}�:"u>r��)V % r�ng�U��% A�?L;6v2�.� �_F $� ^] angvelocit� Ez=2 t $L=3 l_0=1$so!obX!pi� �K 0vals $T/10$ (�,$T�!��od9�1 ). P}> Kpo� v�� d ne9?ve $npic�2"� Rir��0 Fon ?f ighb�>of )#12> beN�M�c ��aB-ged (ove" ��#K J  e)j��qu{4oũ�A'Grge!�Y(frequencaCB�l:�/lD"�!��C � ��7A be � .+�K �*angle"O 0�2u�n�"roxim� 2�1�ba�n�xf6{n}=\E� t\,*j&.{�/ for} n=0\, , "�I)�Qpm1}JVFR>RjP�"|1})VFN<N.�-�Z6� i.e.�U0thYDmo�eu=�V�$%l�liQ�"��; atE�u4" UE�!�OC{ {1.�Av rooh J�$int_{0}^{2�VM;"< 0} ,9�)d $0} = 0 , %1�%Ue�}\1II�3lB�( $rt��q�H11�X12O� n�Qa$s _  assumpU%�u72= �1�r 0$�""6. &qD��&��)IJ{1}� i$ XD}A21Ms�%� "����O�� {1}<+&�!a�2�I� accu�l�p�&s�Cei fi�aAica)8of:3��k&���� 0�-�l� e3NK, N�;abr &�*a, 2�Dre��<)F��7 weak��8N���$n<0$q�5���'Yo�$n>0$� 6s�Q� i$ [%6I1}(c)]�(�l�7t�� �Eook�iY&tois�l�1 vic�+!�2�9B#* �approa�M6��!r�> aga%"�:� &�,� II >� � AsLp�typ#plA��N*a����ed�m  I >U a�#u�)�r�>� �q � IRly&&,���ILM94W .} U�J���n= �6[ +�T$epsilon_n\�)&�ansatzFB�}2= \ll����%�!2hUg$�" es slowlyQ��e�Si � (�S2[upA�cub]J�zvax}'� ] B}�}(#{-266%7 ) +C.%nF/ eD}{16 :j+1>Y})^3+:&>$^3)�],�'s �CF'ith $B)�j�RC=46("i t)$�!$D� 8}{3 �Z l_0( 1)}{^; e��.�,!���) r�L|�KEophi^4$-l �J�".�{tt}= B2xx}2�-D^3&A phi4BPWhen $C����$D>>�%,�pot�Ual60$a double-�*�N%IE"�o&� top%J�!a��Ns (,(:)�V'va}`.� is mj'gc8e�a�$� ��B�B K!IH�� [ eA��! 1�N.�v ��K#_ {2}� i^(B}{D}}\tanhE� [Q(nL-vt)I�]!#"� !d��B���v< gB}"C 7&g%�Q�,C/[2(v^2-B)]nW3v�Fif�6��+wro)i�[ sm�[zs ( �] �ness).(B�)�<)�s-the( AFly�]ed s1�sN>2}(b)].nK[in pass����i�\xis�S� &S� �*Ys**dEu �YZ H�E���NA�>to p4 te a"�2�s,�anO(ng�steady s!�ve�.�{*�i{;�{}\3@ �2�ILM�j� 3e2$�2$6OL=1.2$.":5U.ed�ab�.�"��rogto� *`q��~ &A mp phi$j1"� 0^��R�"�}!�A�all"�s| $t=0 �&�A?� u\�3A#:&u.is�l�R'9 :8:ly. We � �:�")})3��= (�&Y"a�)�S)U�I�36�i"`. HoSwe�,iev5�<,sm!�ILM1ao!�^s���i*a;: I,*S�_y2>.ex�:g�twtV"p .RN4 5 -Sta>)�s.}&r*:!^?,6�#��l�mXa�an�)}�1�!��++�4�]!�~�3!S3xa��9e��-is)fnA�nd� ��sa�b�B]"!�( phenomenon!� firsLV� &�Tp�SofB�"�7and�HnI��G%]��s�sE��� �!`�robust�1x"5 ,�i�� %RveͲ"� ly9V��w�  A z,��� /4� �ZQZA�f"d1ore[tof 0(t)\ ��+A(2&(D�bF�!$A"� *�%+�p����R�#�"�B � � 1 -� ��a� (& �*[ �2 �0>��%�$)�NG$s. Rebp �3$�g.�� : in $A$, "u �E +)���=;ta A^2!�^29�+\gamm33,:� _0=L UM L(- )}{4Ak2}%` &$+2L^4}{3(4}-� 1}{6&g&� SmN]AD�TI�c. �g�GI/= A`\b-}{2�^2}�-3 � A^3}{4-!W- - ^2)}!1  t)6. �.f +E4F�* � t):%8J�9;�/3  }zP�!So�#F���k e �$t�)� c��r�&1� �/" "k'� !�ae�06�D&R!�*�'ofm�#� grow6�8. �g�: )&*Ztak�"t.�'��laI( effect wa�udied.� �w('A��&�"`� rd.�"(o+P�A�$n�I�le�s /f}:*�&, !s0 $L<`1�ń=�&= $)�� - sVl: \ hard�� soft6.�+���UGre�,<� maximum.�it5K�2 n ph�@Eh�:�) �-5>U ceeds�M�T7y cA�� ��$=+"�\becauC:�e`�H1�e 1of ���4words,Ak]A�er-B eH"� o� =l[+-_Y�o`�,�=�F,J,F� �1s Ccarry�Wf"�i"iaC�9s� <� sqR ite &EME"4 �5�s $0\f5\tau$)�3^=5000�cal��t� pw}+�-90source, $W=E/Jq�$E�  to�@ 2 @);�t=8� i!K2no�;s�5at .%(.`-M � n0T�g�4n �!�b+��of-!CIBJ ��:} ���&�5 �4)� (b) - =0.992$, �+ 1.02�(d).33� n?%6 (edg�� �� ��5� U�ecf� A�iod� �5in�(C6�97!J b)!�=a� ��.Vrz no e�b-U�XhB�6ai�m�]i�eRx le. �JeadT1~sf�.hA#� �is� -������l� }H�L�b�\A�BKl�vY�V. method:Y e��m��ej�!0 � 2� +A_1 \�  t)+A_� * R� ^2�!� �&� }BA_1^2 ee�\, A_3 |-" 3}{3� B272.C)-ILMJ� AM�A ]{'�L # 3}-2�B !1�-i9@frac{5L^6+8L^4+16�6[ 7"�Y4��(*�$)M�OE.�j�7=a-}\�-��u!� ^�"VH 71� e"� B�^�mpZ��!Vf�uppere�O5r DDs c"�5�j-xina�iT5 "Z&�fiG6�/X ɇ&� $A�!����"A � 4]QB;�r94�%�b$% �2thirdp � ,E3$,A<0 n by�;.�). Empi�w��v >  $��4$Isnm5� &[Hde�1g)!H5 s�A6]5}�!+66}����(in-< colW%Qwob *w.&� Y)� A=0.7�� �.pA )���N�*I. Svh. snapsho_ $H_�@4dt0 s"� #�,� E oa($.�%�e DH"��Bl�!�^"M��,Nact ��*�2A�a si-�@ fashion�.a&;:"� I\�fA� "9#� ��*�. �Y!�0in Sec;A `I}N �3 a�1N6d*j� )"�4 rqu"�%Y)!�J�tյts��7"�%C�%st�>�va�)�)�&"1 �qdfig7Y�X( 7�4�)'R�)56(�))^�"E)1 �Z@&"�n*��1$,� $Ţ/4E� Q2t $L?do�^),(1.5$ (dashe$ (solidI��Et.G�<+��m!L�* H'�*$L<1.3� �pa�x&s (Ag�Ums3 �f5:A�M=H=� >|=5-%��� %Cu� �0͸1�7+ 0.084*�0qH�.alM�e-% ob�f�A52X� e\si>�&8}� $ �ani�.�S:�8B�r31�6/2+0.13�W��&�2� Oy confirA�"ly"56�9}). {�t� s#R#&a�я9 a novel\�a�T,�JAgR'Hsi�"J16-�&��L \+�G&�6"�&Ki"�93law-��!\lHa=,� (both2���o*�)&�0I� rJ� dent+  'p�N� 6�Ji"�T? �h boc"m>on0"A�A)!lmz  o�`� �.� �2b9�"�l�!,``�:u}< '' (A�Nh)0G ``insu9n.Bmies^H%twr2FU.9�s�4E0l�s�iergso�nb ��Azine fur�ŲaA!al� (ax!asJ=�A+�e"�Lal)!��%6.RE� wealth of�*a+M2sP curre`O rog^m!�8�re�S�(fu�+ pub�R"�\>�`{994VbpnX8 S. Aubryu ewblockvcica"�a103D}�g1 a,7); S. Flach�C\\Wi1 >H�p&Ef295}, 18 J 8); T\m19mi9); P.2�\8, K.{\O }. Rasm�4!� d A."�\, Int. Jx .�. B�� 2833�f1)V�R&] J. S�� nd! TG], H Rev.�iQ61}, 970�8�S@eno%SD mma�hg� or�\�Rbf{70}�h8D3��5�tv t1}^opidak�1�d,G. P. Tsiron!V!{��i87!}655!�Zd.A0M h2} H.^N�Iz l>}^, B. A�dlomed, D%o Frantzesk6�AEBw^,%� �E �466}, 015601(R)%�22�L ier2E�Lepri,�^ LiviaP�ii9�pAe37�U6RAi�^}�*_,=Y�No͎ &F\%C3!�797!�96); 6D_:Q:�#8of�pFs�ds.:8�J%�\Hirth, pp. 127-146, ASM,�nals Paiq85.��T Y.!�Gaididei`,F. MingaleevfP. L. Ch] ians0^�de�N�2}, R5i.02�?Uzu2voE 4662)�6"�UJvV aKonotopB�a�.�.#,E 70, 047602E/42�b�UI. Bena,FSaxenaT�f9u ncho�6_E; �36617e 2); FU,B�M. Iba�"6p}�qRA� 0376m�6�tOV>.bz�6c Euro�E��57, 6a20�=s/jKS% %>iJ��� 0419-z6�A�V�F�J Arch�E,AB���>�Yu6 U� {aq7t A�lA&�l})�34}, 636I�1); J.��Hnz w�LE l) 16609E nCueva)\>:au $RoUJ2�r��D o163� 06mA�ѨH��R�E�7�679� 862� ���<RM. PeyrE�HD9I140 ( 1�U�6)5A( 1922n97a��""XU�.e�&@jl.} (un- X.<belr- T.i��A� (Kudryavtsev� s-Uspekhi �4�5% �+8>�  %*N� 1 (�T)F�"'6 e} \C �j@phics{kevr1.ps} \�5{,S��S-7<gurŔ:� 3 radiiP�e!cePp#T (eiF on�(�Un � �ReO&z var�T�!�%BA,��7aqT "��`�_a >&�[1 t^�Tp1 6�@'���1R S dek-�$�O�R$.t!�"�OM) &\MFOM reOM�m!!c�0�e strGr�TI�9�{5�K�* i M%��.�G$�ep)��,!y �x8. A��=H]"�6 **H�� )��NHI5� � n as,�"E� . Initb^!j <�,dA�5c7-<=<& �@-�a&Xo_I.�E��8eD6��=tj-� ir vibi�m+\�@��5q�52 (M6i�H)�I�A2FANuD'I%�"��E%b9{"&Z=�@l:�@�es��@)*�@ (a �3C%�e�A).] �wib I�,��@.�Api/2a 0.26�F5Clyg�kaEq+7*=<O""��;+0.259�RA;9�is !"�.�1a�i�$v!�L=1-�$34�G +L^2�%�'e=(9/20)a� (�M�0a, �!<Eve�od&i� �by�m�I�:open al< 6�L���:!(no�Ny big) �p3,*w2phi64),�RE�<"5���arS(ho"�!`��6pro"�/���.&�:a�H��3��v������%���36��Rge�E2��H!�a�1�2}���F�� 4 (P�WX��T5#��46��p�#-��$&^$�2hބZ) �e0�#"�� ��eG�for�#N}$R�F Panel:e�.�k � a�"f& �8~4y =0.4 '(b&�#0�$ap�e��w���4$E�P6l偭J� /\o�N$��a�l$��RJ$�L D8�2K$its$ch&7$6�9Y�^E � &5r���56�A*;Yy�Q{$Rt�C n(t)Eh  "� od� Pa*%�%\� 84�"|*�c@'*�&�",6k>(�n)�A 2��?F���� ��I�endm+ ($,A�travel�+e*.ice spac!h1]in�8ut $8T$.6>5�$Y�A�FI�6 (�&�!)1=k �@66�E�a��=f"*! �$"AE6� 2f�.:�LB|ͳ:6Bi%SF)j7 (To� �RBFi�h76h k(BP:�0$)�F�&� �� $(n=�[6j!&�  1)&-�pD 2a �qb^){� �� 29���8 (��B�86�.�#F�$;t6by"Z;i!�umEv&�Mdot��0� n=��omX$* �R5��> �  �  c"F'�o�!���!.0f0b. ^`� f`D�" horizo�t�6̓� ��>>�8B���9 (Mx�B9jBd�� �B $!\$ ,ea�t�V�  t"� D"�S>R$��efm�!*��U-�'�8 %lI!M". &�Iv O�*s F 1$&83 H$ 2^o 1$�R5>&�<�I�;n.# W.3*/# F0$LL$� ifip, 8h ��$ mpar�!p1($5#a !%�L6%ee��F� 7~)"CH9B��&0|���������������������������������&�L�qs�e�E�CH�:!�"�3'�pnt3'\�"(N�&� >%��92������B� �&6�+~2+~2$ �3�Tg IndxatI�S^S "[~2z" ~y1�T*��j��6~:��\\ ~�� ���5$ � ҋ}�uSal�qU �z$5� >O er d.�*�Kr1 �= ices���.eaN2&_Z&� /\s. He0'ls&NI� u�&�ced�7�P cq describ�$sine- plus ar-m �o � play"�6 sinusoida? d quadra�0"~0 "�As��C� yield Z$l�4�.st�f�J� �~ rer?'.�aEyct&(*~&u~,Pw, 03.40.Kf%�~bsR�{develop�-�B06h�Bi9~�� �t)M 1,2}E`-�0( �1!�� �.J� eptu\8EZrtri3 oretc��0�O�Y� �as ub�}�d"�|zH5mNo�O<{"-�a3}P c(� s~;innovat]5� *�|dfuysc�l Kte|��8KA�cD*gw�ib�.Ub04,5,5a}. Area%�Ec2~c� {Joseph�"�z, photqc crys�& , op%Yy] in Bose-Elein!�densat� all- 3 logic� swit}�gA6a�, �(avreapiof �s!� bonds5;so�? �67cV�lrE�B A.u�"�5̑8�'u. U t�J"�9�!Bn#inA��:bl�� �7}. Hi�h���)jn .�� }Hmad/[ٕ� At2�rڀ���%�ba�in|E �Bca���& "}!b/G��s'�ledge �8,9�^��2X4��er� gavbuA� intu�7a��>!3�so-<ed�e�C (SL) �)L10}�6%�-M@�aSs �va97noLa/!! e"F]i�} ��% c p�al��XJ�SL �myr tur�O�to��a/10O!XILMy? ferr!7o�^a����!� (IRM5lO@e�1a�o�/er11a�X��7k|?kj%"�i�#oI}�ion �gsiIk=4of�aru�K �in �@Wojciechowski}. A3d/p ��% i&ic�.v�5bnt�i"nЭ!�&�)�-�a��mj�13a�"g!�"e�#h",���2 bod�co�y!�of�1���2igiV"�" clus u>��e>�)�A��K� a{� orphe�sia�$ (SiO$_2$)2er�s�#al�ts,,N,(4$ tetrahed,��� rner-link�6y oxyg�to�n!a��y cost�.�XiN}TF? 0i=��wA��t!uA7-�`)I1BBWP i�C!y ubj�o s�"��%�z~�/To � bpb�a �o-s4r��A�)�,E9���#yQ&GeP!��?e�qCal*ԃ freԃ I ��pe��"�o@<>>�)2AfA U:b�spA�bl<��inW�ens�'e �;in��rtzm�15,16,1 ,"E=Poisson'�io!c.ob�Gees.�E 8,19,20,2�.A1L��ma�Ea� N(K- B ��2ʆSi�\EI�J��eGyymi"+�YK,�s(ovski�S�SrTa83$)AMM�y "6$ octi-q8KHapPO$aJ(KDP)7�yٍs� �ua� �HI� 9y+ , amF#8sVd�inv�:,RRgo ;�7vi�Up�7a m&��)���a��%rw�|��a`Kar�ed �~o�� �z�)re-)a "�~T~ ))�14}�4a ��� �G�l�j7FY , exhr2�\*��!�0͝�)�p#QY IRMY 1Cemployeaer:L�ss � F�a;kĄ� � ��I�a=nII l0 �����-�&ɗ�Kv��nm!�a eȪ :��SL*# �iwapurA� �>�D�56� �V-Y io� pR��it.4"� Eh�_g� ���paZ*waybasic�oof#b)} =� l tC-.� (3D)5M4 �m# rE�p �SnNR��5�fstSi�,M��9s�:Ma�iSu%0� � &� s!-?�7c�E; ��7�A�[%;�gh[b!hea� )8���&om!�_iwo�s$� js���l s� � Z�@i Kje�9 hleAs i�<a d]Rc ! !�37inx 2�9�uBA�e��hJ };+$at�()��daxal 3DB.~�"uCSek  I%bi"6GNA��i� a�1�Mt�G r U�I���g>zI�.1 L) "z� erpo�ng��DSL% <^.� IV!�devot&aU5s�r��&��SL.�Z�� I %ͷs��B$ V��0S/<,n� &),a���x;�A�� �"Q-�)l2�� 2MY{�"6 �ACA:� G�6 vsB�{0.3cm��]nF-� gb��&Lag��an2�1&;|L=T-V \e�� \gw�G m_n}{2}{\`Haxx}_n^2+ y z  \4H} \}�p�TKM ` S[:��+:��+(zJH-z�� _]&�U�l��_TG)$U$�he���� !�". A$�6>��*��${\�[y��4 x_n,y_n,z_n}$ KUal�abEfas6v�($FFato��tf Bh!�D2nr Euler--e& hume��GFm_-� d^2x!�dt^2}=K)�1�+]� -1}-$-�)}�8on�!�.KyFK��+Ky�yM;jK!M:�M!+KzK"�xEqZ�6� �Eqsed0(����Y/ � qz &y1*�B(*� ehYm�, %� non�N�* %c�}an�Fgl�aZ,a�^� !5$ r�I`$x-, y-, z-� one`�RI�c�� vect�,:�\vec{r}A�7]���_5�Ulibriu&*.F��& 2�T>c�S�HsM�*�^b�/T ac $s$ %by-)a`u� %&s $}��-� �us)F6&�f(s_n)*�N �gJz_n=h �3C!�raint^�$f(s), g(s)��h(s) �&�+f4s� .�-Չ���$then writt�Jy�L&�N2���i{�([f^{\prime}� ^2+gBh>i�]}�9s}^2 �#}\big([!]ON)- n)]B=+[!j % %+[!h  U)�New�+iaFCTh�V� s!Ra�VU�7)7�}s#�688Q�{���Od}{ds}֯])�)1���6y�=�+!��P)-2 nig}:4>��d=�+!�L L:n^L!�)�+ k-2 L:�u�New��BY:A]�)M ((d/ds)A(s)}aXA=f,g,h,U:V�u =��9݊6�)��l.�)&xV"o , �W�T�p),&�I�"Z :� ��\"P"�vy|@ �kho���f,g��KO}w���� �Vo%L:�� v;!one�Z�- N ."�]s-F. �> �z�(W �l, k�K z ���rk\�rW� wo"ӼKb:PT(s_{1n},s_{2n})}$. %, Mr)03 0 �f� �EK!7sm 6]}�i&�J(�b��c!�"�])&%c��ݨ$f, g, h��͟V� �F =a_n�`c�hq]-n)>�w�7=�`=� <b<�v_n sO �v b_n/�(-W9V�.c,�, v@ A%*� >EG�A}dexc %�>b_n�/c Inse}�F�)�o*3:lm�A(�)1�S�V�]U�n � ɠʹ(a�]+b))f�tɇ]}:�-F HWh3[a��^2+V-2 !��b [ %- nBC(b " !�F-=�)^2 p*[��9$B �MA"t BF�\ �}_n=C_n ���]� � 0�6�a_n!Y�*��0�{ `]:~+C_�-)9u!�]r6O-2%� Nt*�-DvyFC_n� K}AU2Q2C���c�>v�k�������*� the 6=F�R�eft�?!?��LiS/�*B~�6� u�����n� 9,10C�>�f���� Sine^����co"�]�_-h��jem�/site-�t��EqB�r6p!)H%|615U ��Ac�e:�} bWw�tV՗�kNlme�r��2��U�*L�.7$n, droppin��cript�ftt'b" .S2�aB'"%|� J� n�-.�:�6P+\_k�e(�g�� -1�w����)i:c%�riF�J=Ca^2,2� �=b^2/a^2)��Tagr�e6��E�2�"� 8ide�2a܎TtoQ_Q�Y(E$E}��T�Rd � hܞ� $�$. AlterS��,.[N�ma'8 ��� Bp�tiO Gord�123&�%] &�`� termB 2E� ��EbpZ-?��2D��26���6��ub�S bOt"f#e�/у� JK� re� �Ve >�J(D_{n}-�,2�}=)��,)u@.� ɀe\2n"USLLB�Equ"�Es�o7�&�  $ �-6{�w6ul� satisfS�iF�@}=��G�C,��B���V$aS�Za� �a�\*L$T5+���,�n&"9K)=� J�f To&a'F,al:+=DF� ��UL��h���'tJb�ʁ�)�)� t u a�"5&�B$V�n�:� $D_n {n}U|B� A=1-.!nY�B}-:n(�22�\.} >0U�Po�GialFu��B�_�ay]`*�+to�min-lc s�[J�^ �B ( �1O�f5@ $V$,ozkoneb�9I  �Q%!�)sI�s#����`gB�,*D;�6t$.&��{de1y���, new �aI.ea"�<.�1�n)�b$l a1(),aJF�h_l ]n(4l-1)� "Es�{ ^2!�4}-6� l=� NewM!�aB�hX)!!D_1�0.217�H209133�H3. 5797�iZ-!��$�.9D"S:1}{ot����$l �u��nBr&{L��E�!�,�$yED]m� ADJ`!��q�ar�Hz�,Apr��(> U'R*�$j!g�a%in�Finguish EI;���MqF l\pAs���%��b���0he� ety �ufrOY(���)^.Ep5O _{l+Z�Mv< _l$!� �{B�)�$2(a&�lu�e�* ve o�E�'ve�Ջ!t$N��is��ͦEA�� �!Na��ju,!l���e*�j*L Rn)�}�A�!VnI}1��5Vwg�3aOs�,G"DQJ�1A�!L�!~%�/(�� n0_&5do�)��/!35�M 6�,M�:��`1��@ 4.906Fm6 2&�dsXs�%��2oS%�A�l-���5$J�*�f�J�� -typ*� ,ZIʗ �ka2Q&� ,Ra zigzag�i<`\.޿ �Ia�2U!� 90o# y� �I#.�in::2}%��,�p�0s"f l+cto"0!�}.P@C�sharp8��tZ doEoaex<Y:tai8�& Pe*��:�2Dy.�S�S } A&�Q ��nU) >7n9A2}(d)� \is ^�lh2�lE@i�6v:�3�3AeG)�@�%od� i{3}ood. %{ =�`,�FeB�e^hq %m�u&RM|3���/Z�Il2j�JPA�os՟�Q0r�k���iA��l�4 {:~���rum��,޴a��kout^ 8�ban�)5 &r5.�S\]v �J�$ks4!Du��+�'x0in� nce��/i v�rŋi { q/<-ficW ted94�?�"$)�K�R()r^h� e*���Hts�ch.<�tY�s;�:r:�4.���2 .��l!�� w��"�/ z,�&)I{0}(0)4 �*�� � E�z��JI&DB1J l���h{|"� �is V�*Y 9\piD��� � � ��'=�M�$0� � ��q0dz�n xy�1�&|4�fU& � surv� "ON/h�A��F �� o�5(�;Q�&NUA�"JgQ�:9�96}> (NRM)��L��uZ�BI�F-tomU�A �7!( �>Z&e�u��a_U )V��&�C $\alpha"#'" � a/E�8ly!z��� 9�}�{oryQ���ZeaIzBH|�0| >> n|*� {\rmA�}.|$geq 1"5E1�N&�As��h ct a\A2- 1�Jr�e full9�i&j �i���/b )%��B;5E`I�-��.B1 on"n40��A�A�FM6d 0=J{'(-2 2�0.�n0< ]} +2*�22z]",�1"�� )&-E17B�B 6�{�K1}�-V�1+2�Q� � @:�(1"E).)2}+n- J&�E18��n=J.��)&�:u2}�KyWe �� seekU�A=�Mse��Y�v�-=�2 +u_0"Q* e��e}y���^.O=0�no\\ �n<#u_n�:�\,R�26I��h*�'lr � �5���fs��eN one ���?� 6Fq��K]�0$e�6�"�V�a"� I4lq�."#�� �&*7#a\),�A�.�'E19��r5d�A�=t����%���� �? $u_0�$u_n (n � w< �3"9YEͱ�Ӂ�s���4�`-a�>E 3�ne-impu�f��B6SB[-&�.�\�'�BNup$ \exp(-i\o�Y.�E21B��>�$%�ime.�� �{� �|0dt���%�&Bpj!F�(L^{(0)}&O� v_n=���,ve".DJ� F<6�2v_n-v#��"� E2�]�Na�F�.��u[e��]}u0-v_1qp6�.L��=��^Rv) -v_0�1..Pn=0��BS \, nM�,mT*X2�]9 ��A�)�U��2�5xa�{�  au�t>;Í%R�u"�H>�I�(k)^2=22�1k��pe�!;J�1�<PBet0ave��$k$. ���C� &[in-���::k"(8:c)&< :tI� a��!.�226� 23})� bIndl dIE!V$���?"k0F�g(n"�) g(n,)Q^2:�!�% 1}{NY0k��Jikn)}{6��M�kU�u�-i���.� �a�_+��24B�A&a ��D�vA�b $�$ t*��rf !MBsu��t6 k$A)�E"l �70� (Brillouin zj a �:V�9d6J}01}O��0�i � nx)dx}{yvx)5^6J di^ >�} $[C_n(y)-iS� *� 2�\y��#F� I=�infty}� yt)J�^dt:� vB57 f5N�y�R1Q�B���F& i-Bu �&C�Besse&a� [�.s t����.Jd�C_0(y]=1-y^2}>-.� S ?0.�0�gJ-s �Km2�$V��7&c#N 5�JI�>�� [a�Bw6,+g(��(�0)+1��XK&L,E28B�z� an s@�>��s��� ^=J)v_1=v�=�F� �!��zt���o/b:/*2G��2!0-g(!-1�:a��1=\Delta_f�#3F� to"FA� \lambda �I^^_+_��}(vG *� 3Z� Fl h�"M5� }{&"=m3F !m>��}91$Kronecker'�?lta�Cnz m&"2C��& B[xi��^2/:7$�"� �Q\eigenU tNR�dq��z2�5*S 27 ��4!j)��J �1--d \xi -i ^2 ��0��3Fj �6$��d>� $\xi� ;!0��R8%Q�5�H?E�}+i\xi_0�� & }{2- �.Q�F��8 -:z��:�5�F�} .Y�&� � =MF�As D.Fb%%,pFhe�0� *��'umtML"0"| �C*/�� 6�\�$s&� bottW?�Y��� B�ń: �Gm�&� ��A��( djL+� �ch����2 �i-�F%Cap��>n���f*��o�%�@  �t6I&�c slow&ay�!tr�� to w5��L ��_' f�}�xaY,r,F�ow.b6C�Rmpwto\ite��SLLt �>SF�("�n"Ip���(.B� 6[!5ISwD�%!�0epsilon=0.2$ �Fand for the initial conditions, $\theta_{0}(0)=4.88$, $\dot{\theta}_{0}00$, with zeroJMhTall other particles. F�\is choice of $\epsilon$,�poten�l $V(\delta_n)$ has minima at� $ =0$ and $,� \approx \pm 4.9063$. One can see that !$0$th�8 oscillates nea)+sum �2�situated6�| x, whilr(e remainingqsr Bq.�(=0$. Due to%$ra%Y4strong interac!�)��liRexcitas of attice)nenergy�@NRM is rapidly im!�edw :0 (after a few�AF8). The lifetimeW�h does not increase much, ei�(by changing�M� devi�S:� from�Y>5�r V $\varQr. \se%;${ Inclusioeon-siteU}0ub3Deriv2�model(It!Kof)�est!FA~wA~,happens if wa�cludeFq@s in our original1�!iisb done!8g!� alizAb4Eq. (\ref{Lagr!Q an})M!��>form \begin{eqnarray} L=\sum_n\frac{m_n}{2}{\left(\dot{x}_n^2+\ y} z \ \right)} \nonumber \\ - OKM `Tbig[(x_{n+1}-x_n)^2+(y y 2K+(z %z%+ [\kappa_1bx �� 2yy(], \label{L��On!�} \end= Twhere ${\displaystyle Q1}�q^2Hre constants. Apply!�!}helical raint,=�H C=(}) leads toN�K-U-� )�[ �m)�(a�+b)2�n^2)�]} 6g--�%E)�!�a)|^2+T-2 a_n\cos(�?%� n):\+(b G ! .b_n A >3 �u(-�2- 1)}{4}� �1- (2P��].J�A=o> i� seen�7�such a procedure adds a sine-Gordon typJ� >PB�}$�$A%y�. �Requ�f�� mo�m forF��_nJ hen assum�V�\da� 7}_n=L_n!*1�!�sin^�2�(-a_na_{n-1}.4nQ ):4\lambda %�7=� big]>�MHY;EKA��) v:uQ�b_n1) 2%�(EMA"�) �=J�/2}$. W%�ll!�4 coefficients �:��$-independe� Aabove] reducF>�J!J[%^ �%-1�n)-.��29�+� i�2h+u -1}-4i�):�SLn�a presenc"^F���� be specu� d t� )5he existH� loc�;ed��sG longer&�tha�of%�c� of E�nSineLz Lf }). I6,e following,��dem��ti��]ILM���Q6f2$).�*� IntrinsicB�} %C !tr� kSLL � the BW.�:�,�given byJ�0omega^2=J[4(1U+)AD ^2(k/2)+2m5yy2dSpe�B�a�^r<_{\min}=\sqrt{2J c}, \, �-ax-:��}�DMinMaxB� e�$2U/2 < 0in}$, i.e., $ � >(2/3).$, � A� look�� anA � U!$ frequencyJz yB� sM at� hig� ,harmonics $l 7� an� 4ger $l>1$, lie��6�$. E�is��ɸAR�would � �A_ i�rv�its i�ity. \A�.�LM ?�L� g� !9& wel� As�examplee�take $J=�"�=0.2$,V 1�=5� ��Y\10}"� 3.16 ? -Y\ 14.8./847$ 1�! necessary&��>'�e^M�<2EgX is fulfilled. A large-!itude:#Enb�ci� by choos!��� &� and/or velocitSa5�. %{ .{ Kiz�:� !l �0v1.5B�0$.r�:��, �0some stabilizf @ period, a steady"�ory ��$observed (� Fig. t dfig6��RuA�iserly9� ���ay�QFUb2.1! whichKk iderabQwe�anB$bottom edg�Z!�:�2CI4!}eTB� �Lupper^��.�]���EU�s4nalyt ly� IaatJ�� 0(t)=A_1�5( j t)+A_33,6� ?1? {-1}B>N, R<4n(t) \equiv 0 �= {\rm��}|n|>1"d ILM1B!%],$A_3 \ll A_1OB_1(. Parameter� !kap�im2 solu &{l)Fkin termG!�u�, $�:Jv%��\[ 2ݛ+\� )� {1� (1+4 A_1^� ]>X A_3=� >43}{12 r9 "�}{J}-R� e}>fB_1f� � ��8}�3}{RY (.���!pp5�B� Let u�ialy��obtained5�. First����we�e t�!�!�f��u�$,!�Ebe grea�� �)� e�dXa�on�J�lE�d below>H [��Yk�)],��possible f�� I�su� ���.�B� A_1>� I8]z)}{Yf=�Amp��C�B�|Հ�~�Ewa$ >0.68$. W��v�,firmed numer��!�,]t �!�Y*, ourU%� be u��A�sim 1�B�%2r93sUJGN�7}) bu��:=�A�}),1�D}) becomes inaccur�$because itA r $to accountIcubic anR � �in:.7}%i��%s��3.7�% Y�Z $0.607� �$significanEv�e �d� {ei= radi/GHextremely slowly du�%�*�rBZe�a�:� . No$differ�!B,ordin!� scalc��a� � broa!<e` ��surpri( �� �Q%h2&��1�has $� � :W\%x Z $ExA!.�F+.-2p }), �4be)xxAyediVQ-known} tinuum2�)�!sis,;n,!/aqU og!�b�� her 10Aep.^[ U%o Lorentze+ria& N:���!�te  o�%& �. ��e5n��at��en�E \gg ��"6 � f� two� � 6 hA�A�!&j:��$be neglect�I�P.k>�^ � $b��{sa� rderv magn,��1�A#sN�})a� _..$, describe��>Q i� �a�unF "�eI�-�=35$&T ��� vibr��b!��U�ager*�F&�,. n���E.��6����bh*�  $Aя0)ѡ 0.6$"�! co&� hif!Vby roug|$2\pi�re��(neutral pos�#���:� [sh��Ba (8}(b)]. Its�(est neighbob�")�:"lya� �#&,�{`#1}� 52$,�y"Cs D r�" ��d"�!�z6t}6]8}(a)].��!CoE! j#rks��paper�5h� outASd a g8! sche+o�� ly geomet� � ��a/ipf��ver.4"3DU�:pr��out�F~to  non�ar dynam[K�� s. D �< e��AA�c] ints�arriveU$variou�# f T , beP� esA���coTnts$uctur�<ri�em't�,studied, mor�� llyVF!a� �"�"3D A5�QI�to& 1D& plus--@��e? or}Ba�is� mul�greveal�evea�1!'fea% &> 0ate} \item It) vides E�a syste� c d.@$��sH B�-w�"4 ed heurisED in earlier works. � PhysABly,I��!dF� am�E�"; /5�>�s ( es� !�d&)!�ar�6"~ resonana',d multi-kink��s. Seek��� kind�y5��ll� �A�6topic�fu!�E�y1-) method��eloped A� ma relev��'A��&�& biomol�e1ystmK as DNA ��proteia�T}��M� �rfa� dens�atp%�A+A&�I2- a co�x�landscap�� a��%of�B'a�&� fun2'��um] playg$rucial rol� d��'ng�ir�perti%�P#�ss ?i=%�(b�?�e5s glassg ndR)2 App`%%�@techniques employ1�)�sroblems �� � E0warra� g fur� investigjQ@Fin��"/ U0g�fahto!�� r �r�p&; �!BUBonekA���nd I�%�nsu!t(r*"d)�Oa$l�$�&��Aqsei&�"cur[ly und� tudyE�wmbre6 ed else:'.Hi!Nrk��� !q�� i RE?s)T 307}, 333�D99); P.G. Kevrekid8,K.O. RasmussN�,A.R. Bishop,�".!)Mod1�B ^�15} (2001) 2833-2900; J.Ch. EilbeckO0M. Johansson,�x{\em LI�vE<-Tfe NU  S��ds}, L. Vazquez, R.S. MacKa�Pnd M.P. Zorzano (eds.�World S&8 \, Singapore, 2003), p.44] t4} U. T. Schwarz, L.Q. English�A.Y?9�6183A�21�a5} N.A� Voulgarak!�!� alosakas,.�r G�5�U1v.1�6A� 020301(R)1�!y� da�rei�kq�@5a} E. Tr{\'{\i}}�J� Mazoi|T�Or��o2�}%8�7410); PAM��,A�Abraimov�VutinS.i iY!�lotaryukzj5 j=^6i�^2�� �&st�m/(e� , e.g., D%�Campbell:�Y��vshar,ezZdayi5au43�4.�7} Sea >� B.AA�lo!�.�.�E h$66}, 04662)l2J��8��Yomosa���A Z2�212��3);30}, 474�P82�9SHomQ2nd!ς�2}, 679FM$��% S. \J��jy� oc. Jpn���- 2547O6.x1.�O$M. Peyrard �ica D �9�1�496A�hn%-y5k192�X97.k4Wojciechowski}a�W. 2,VahetiakA�$M. Kowalik ��y n6!� 0361-�3.p12}!Cuevas F�T Arch|3@, Yu. B. Gaididei� $Romer�� 516��106E�22m3}A�Oi. M�P leev`P. L. ChP ans�Xf2E6!hR5i'02g4}C� ݩS.!6DmitrievyQaA�Bű�E.�\Aiff '.�(i�_3��� FvMVyKonot�2L�Ez066614-4�h>�2GYU�1��Eq�99 6N�5em A. Wells,AAT. Dove uckerElTr� nko,A �:�� �p� �1��46�Q6�6}fVallade,ABerge,m Doli� e�ys  I T!�14�6S�%\9�D.�Semagin,�Shigenari8Ab �Nagamine%HT5Aslanyan1Me��68�* 5210�*3);��J k>�K.m`�Russ.�A捀7a�S30Ea�>RA�Vasilim),N. Yoshikawa& RE "� Dev<ţ? !�ic SEfPandalai��C w�ENet�, Kerala� dia"�Vol. 4,(%�. �.4. (a) Kink-likb�$, (b) poinw fect �gr�zt60 c) zigzag� , (d F dF�!�>*:v2�'�v 3 (V"$�= a w�36:e�e`? � meta-�5��<}B�2}(d)M�ode�$&�$on (p�=cRonly) :<%. >� -�2�3�b4 (E+s �O46OM"�A�itV'"m#B�"0*�@$2�: �fz��@,1��se�+ plot���.$ v!i�Y.�im���hc:A� � s $|�>phi_1- 2|�9\ andu&+?�th A81vel"v16?8�0 ic ba�2V2�|*52n!�<' robustness aga� co�?FnNm4�m 5 ( �@�k56kAn A mp[i� af in a�,Eqs�tJ�7�mea�;1�&RC>��QCVQC>�-yThe>G"� %��42p ��B��-�c�jI 2i>�B D&!+ r�BU9P&Rg}%��@is ``dissipated''�a| ; a�B�5c3e6�B. }">��5Ʋ6 (�'1�66�P��!J!f5��%BneS%�:F�9�P�.a� 6r.� 1.372'jk-�4v4� n-��#2�#��4T 3m7Z��"�9=5$:�6�7M�+e�76S�(a�,n *w6%forB70�3= 71c AbAfk2B�%^/�Fr6V]/a�bb/ s�;2'in.�<9]�:b/ �b/� B0aEd!"�. �b/C2b/V�EO&�(EO.^7�O8IO2�J86J!�!M�^>]a*O �) &��%� x : l � �+h P�C ��ߡ� %� �($6�Iis�'#$�b"�2e/"�' �s �&�'c>� 2�,��6�')., D�%C6�)!naI�3E/I�6-5�� ! .�Zh(wmJ70�'."�' �&l�'�,���'~�':�R4N�+:�8B5� docuo} ;S%&,x�\c.",[aps,prl,pret,�Dpedaddress]{revtex� V9 twocolumn::,Aopac.C0 \usepackage{�xd} b{ title{Exz<�aJ=r��of fidelZ=0decay:\\ From�<turbat�'Lto Fermi Golden Rul�$ gimegauthor{R'\"afer!Q'0D-01187 Dresd��H�&ligma>�CentrZ ( Ciencias F��s, 1)�dad Nacional Aut\'{o}noma de M\'{e}xico,��us Morelos, C.~P. 62251, Cuernavaca,#?.^H.- t\"ockman>���f�\date{\t���#ab�$ct}�$�6��matrix �)measurp4a flat microwa�9ava&�� e�i*chaotu)���zs�!Z2qN�37ng����%y. WeZin* ``sc�q�''� t�=+2ric cXh*��9G �ele�s. In�� ���*( weak coupl!0�J�*rG6#8 !2os�*%�#t�,f�7�><e.�$results ag*)~random�tC%y!a �N�,(u��on/$engths, re�8�%~+v�&U��g��r��.�YS \��H{05.45.Mt, 03.65.Sq d^\dagB"y>yJ>yV>zn_z}_a�2�zn@^�R�,ree} {R_\phiw?(E_1,E_N)!2Zbet}{B>�gam}{C6-{\rmd}{ d6�i iFe e>effff>�- int>tot  >�$la}{\langl���{\rA�Bl 5eftZ: ; ightA )3oDt�quantumYD� bpNa�)a��a���  in)$y��Ref.~C6Per�P�, prope�*r*e=� evolRBn�G� ets gover�@by �7sl��<i�<$t Hamilton;! . St�6nm�t��" stat�ir \lap�&/a natur����F.418�. �G``��''C ``+$Loschmidt �"''Jis J!�!|si?9%�&�+ed |ensiv�=(A=mpro03b}pr? �=s��&(). NowadaysG<gW?0t,rd benchmark��� reliJ*in&�;�P}/-�$Nie00}. FqLJ�,� �.de�� 15W$FE|f(t)|^2�)&� as ��a1}\]Seq:fid} B =K \psi(0�;eft| U�� ger(\E, U^{\pr� e6|5\ra \; ,��m�S!)uni{' Y.ators $2R �$U(t)$ �9:�Q!��uneU^a$an arbitra���lI� $ �$. %F�3str��F� f� �Xdiscern�r� s. �4"�� �w�.4P6`�z^/�.#/�3�M �U$is Gaussia�D&M.�$s a cross-a� ?pon�Y Xi&83Z� cay)A�t E J� '�v� ��M�0Jac01b,Cer02}JZj?Y2�+ �c 5�1s�YSa C" ( Lyapunov e �tl01�;S�!0�< spin-�C2eA�n�4 Hahn < Hah5}(:&��_pera�ed/ � �O��A����� s (�)\.�0Kur64,Buc00})�(wz., 8&g usuB�8 actL�E)� �\!1s*KN02�is avail�, such�G!0 nucl�6izQ� averaged��$ prob�a� eticO 4c��"g -[ Zha92,Pasp.�B�4mis� betw�C��antenn-a &) or ultras=� fDLer04,Der95,Lob03aA HeravV�0���al� � a[uWI�h � el�Po� �� , u��WuJal�NJ$ HelmholtzE�L.ry�- r\"o8�K�6 �Stoe99�,eadLf�i^?8�q�aKs&� :� , 7�6�mm��9V" he .xI�� 4a�!bi�)utei� Four7Eag�k��N~ Y7heE;�. A7���Kpr� norm7T��K�O���$��d}�E�.%RS: Ae9 �>e���^a�*�5uni�� $stributed U�� �%qyield ���dyQ�&c. Yet%�o gZNe-��Bis<st4�Z�5)�W�a�.�F} %k:�at,� � p�<F ut�M�a]Z>r��m��&qJAE%u 2��made m�: prec�:m)s�}.'=F!�@A�]2���:*AHu� predi�of�B �N 8,gor04}. % % Ene�iKduE % i ��Dalet % Our*��ad�$�  "q!!.Z: ]�d��S,Mah6�'if absor�&!2�A{9"J � Sch0�K Z��$a bd4A�E�2��writte�Z&�;��(} S_{ab} (E ,b�D- \rmi\, {V^{(a)}}� \; tL1}{E-H_{�Ol\; -b)/]; "Veq:%#GD^�T} %�* $E = H_� -t& mi/2)\, V�$%>hew�> ve *a A: openmM� $[@J5c� 1^. �|AC� vec@ ;(V$, de�EE$!a)�Vcon�N�.� o &��m�s{ y�$$\vec r_a$� & dif�� ��a� O lO �v�M*C[$$V_{ja}$ ��r�&l?� _j({fW!PS* �N11�� 9 ��. Co�9O�ean S-6/w F!F H�� $ domain: %B�  \�C[i^\ast, q ]q  \!)to� 2S+e5 \, (t)\; LS^ 9-� ra \,� "� coa:&: $S'C(E)E�.�)^Gu]),�� ]� replacM�H'm^A brac�I�!q4"windowa8�VF=mB) � "�"C[=F?$ �E+ki��!-dn� '�Nimila3 !���um/I�` �*~5 P)�Kays ep[w�anyW aA��Ptf���Olaut!�r>y�whT@ n.�!+�G��e�=&�J�f)�t)�S1YEmFY } �1�[b0A�\;��6#QA�J� }} :�def_f�J�Ref� �� �9T 2�h:� � �* � !��Xr�,�l�g i�"T��p"�]UH��2�M� "�-�� s*� � �ZoYg����"�. WPi�1�ime�*A _!"� >�Oes1M�� n^IieO#qc�I�e&EOs:�!�"V)KObGn5 F%&:�8[�X88\text@]{cor438b_5GHz_5i-$\[-2ex] "�8(ColorUine): L]�c31�E!l��Q ���8< $\nu=5$--6~GHz,!1$m6 &�- 0.04l8N�UE!�2��� in black� q�}2of��J�O P(in gray / o�X &LYid cur�$deB�MJ� �R���0dasheP% prd offC-F� E��t �I�"A gYQy�d. Move8a�� an arrow.�D Aj%���s."U-"j 'U��zQ� Q���fd]� } ��r>M&� $f�:�7�n��2� M:I49�a~ar-:JdA5�2��A�v2����$� �D�7va2�Z v�6N2�fdampv��^[&F e=��J�@2��4\:�d�Ned direc#��d�tra via� ��� 2�:>fu�ͱ.� a�c�>3��F� (2h ))e�!M3� �J&U4F���6k��r)2s!��ly� six �[&$it�jJ ��B�*K %kUyA�^U�is jus[K�)ur�i.f N�&�"a�abi�BL &G)}a:� I�E�s.H,�dUV �1vl!%�^�s6�6� .�) re�s\d�Ra�**"{�AG- A.y^�:g��Qz J�r� 2Pssu,b~ q infl�n� non--ic fe�!�bvi� �>N �%s� �B now s�Pj �su8��26�#.�#AS9;�H� er2.�1��%� ��3�4$�up�6550 651761 GHz.Bl �Q��v�At�c &�'�fNs�O!�$�&en�t�_9A��!�s�2�f� r�{5 dM� _ � su�VA��R$Alalways�WE%�To imprYu"�s,6��\a�11 22�ynd 1 &�sue�s)��"6�m�Dm!c������!: quad�cM��3%�:�z1&!�Ver"G�$�U�� ��~ we o�n "�m�y-�/, $sA �,6�U�(a). BD RdB�L)< pronounc�& � � o5 `&f�:e&�(9ted) )=&7 � ula &��) ��&97Ř!k�� thH6��!��" %% RVI7# xact"�bs0*D IP�gEx!n ,� x*en&� ��E�sym�\y.0W ?stoe04k�iE& hown!��!�:k 5�.uT�.q&R�6 a_'�6i�lowA�d� ngu�R "�%��a9�a�)F ���� Z  clud#p�G&�5.� fda438_3_b \[-4�b3N>13_3}H �?6_4n3"m^]1�y� $� M^reWf!Wt"�������x!Vpo&� (u so��A)�_A�.�)� (d�,]K)�Y"Q ( X2X� .#+onRaDqN�fՓ[2eŕ& ES�d�4"V 0.4$�2U��(a), 5161.767�1=0.13)~ (b), ;6$--17r8>;21$(c):= 98r@ % �"�� �%= �I in;d�Aa�� *�"��%r ���u%-�Ti�4pter~55�.�|$}[t�&ix�$&2&�q�{*"".�nA���"%era�0P� V�!� 2�readsJ�0 (H_1)_{nm}=l�v�B �.�$\�<al/_n(x,y)}x}�$�6,mF,\�|_{x=0�!dy �!, �$C$l �C5 X�R $x$-ion�U$B4� -�C�al�B2%�\6� o> -u��"��is��2he)�ioff-diaMKea7VA#�t^2�0 eft<)�[ 9��]z%\ > \,�6.P�kBerry'sA�jeOcA���.Apla�C avesM�Ber77a}�  'b��*r�$��s $k$N�*�eq�& lingpm==MH2 L}{3\3} k^3 l)f#�16 c\nu \N��U*/3 Leb97(�4*�F� �5 o�Ho�1<or�^Gerg`&@� Fx7q. 2R���3s~*ua.� e5 �OA�%�O RN r�1�9�Rd"~ /a O. hifts�G�:� excell]0�) � i_! + яA�&l^2�!�$�U :c C}� �en�tto"� f 2j dataR��edi��%$4�y�C(t�"t��0�Afl�f��s almos�J mple�*mMs�+A� spitu�;r ���R2�prefa+)�rab� ree �s�(e� a�W�+ed�+�;a�b�\wE<� xg 퍳�v"�~},Uf�0Psaa[4repancy� d"1���ud�4��^w%far�Pemi&�2l+t�-2R-A})�܉�xA&�"b�=� /Sinaiy>byf?�!z=�nz}t2b� �/A/ex��f � H4 (stars), 9--10 (�+ onds��16� �(t� gles�Ps�# �?/ � �2. RR�b$R��n  $l�L�0.6>�2.L%��361 )�rF %:Co�!s H� �ha.~ 2g �(���"*}� � $)K asi2c"�5U�;:x it *�#R�24R��� "�f". s ��droT���en��d�jto�ifhFF� S" 3>c�2���r��Z�? )8�;�ҡ�+f��R$!�!�syV�@�$�(vival!�BJVa�L�/6�"Eas �Q�=�,�A��$�79�z L>�8!�Ehrenf%>���J�8 It!oinc H0i� ��!thhfZ��v�F��aBk&Q7*DQ �rac�$ ledgr s} TUgf_U Kuhl�H�6anz�han� helpfu3'c�:o� al �-- � occaa�!�a mhop1��EInternjE de "�Ein�`&?EexicoYeH.S. �es 4i!2�ŋ(DGAPA 10803�8CONACyT 41000-F�&MY O�� Deut�p4$schungsgemlchaft^ �-]�, M.~A. Niels4nd I.~L�^ua� J\Q^AComput%�  Inf�.a} (�G ty P+,mG brid<`200^�1(} P. Jacquo�c.~G�il"lr0c�@C.~W.~J. Beenakke"�eRgE)sg 055203 �12�=0 N.~R. Cerrut$c�aomsovic^y^8'^ 0541\�].��< R%WJa�1rt�H.~�d�X(dba6}, 249-�6�= E%�Hah6�`�D 82= 58@1956l�<�A. Kurn�~I.~�a�faIqS% Hart�H^�13�567!* (196f9 A= F.~B)� uchk�0r {\it et~al.A�&�cL&xk8qe 3eE�6��<} aZ�,�ba8MeiAA-R�Ern9Vcw7 2149 e��b�= F�ZLevste _nG. Usaj^+�l 4310 j5)Bm�I(=0} G. Lerosey �"�f 193904)$6�x=��8Derode, P. Roux)�M;�n6f=� �206):��=( O.~I. Lobk[!nd!wL1s/^9E�254302 �6�� BZK%mem�x( Chaos - An��ro�9N� .�1Pa�*��ea��F�M�dpF���E�2�aQ��:$ C. MahauxSH��Wev�m\"ulla��JShell-Mo�}A>ac�3 N�@ Rea�;s} (N�, -Hol|l<, Amsterdam, 196c9��* .�O!����J.-�� 3� 3289N�KA4 U�Nhl,d Pers&dM. Bart�-J+Euq��I-17yc 25ͽ6�IF%|6Z�19 �60V�drry&?h- 1i�08�197|e9����$Leb{\oe}uf�M��ebA i2�T396�q�Uda�nz�a�anz�3�� mmuni�Q�f4A��>� nS"� ��{prsty} 6=,sis,paperdef ,new$,book,misc md"0B*4 S}=Manua.rdLastRevised=Tuesday, DecemAx21I� 23:06:20^.�G� ics��32� \def\my!b{} notag $newenviron� � 4of}[1][Proof]{�0bf{#1.} }{\ \ {0.5em} } &?8 23cm �.16(hoffset-1.40topmargin-1.5� Pent#1� input{tci�9x!�S/}b�UD6)2�>t}G"a% ial-+-ic Poi��&�<͡�H')}"�T,Maxim Pavlov!;iS} *�P\t� ofcoG ts "�In*� 6���AiA��xng"6'w&.�"�-?\��ged�y'Pof -*4�hydrod&al type�yd6O�7s admit 5<" trivEd=�}on�{ 9er&͡principzq*�& {(3ny y�&{1"��3w>%I.�x(� act�I<�4 WA(�S[l2�Astr�� of c,�!�$��6E3�\au{v�O}. �{`.�.`�'�.�Y�alQ� br�?MM]� LO �Novik})�%�ame�� a b:�T�� cJne-phase2� KdV��=c�<der��`r mv~2�mE� j NQ�A�+ �m�,  Maks+Tsar�= �@w�z�3o to%:�^ {% lQ=aYU� 87A�i�ar*�\ neWV85alHZ6ach (Fme2K/�Ye.�"�:)e�%XXfin �% {Mokh> {}Z��1:�/2:�pairs D�,%E.tis *�!-f��A~over-]�)� on roJ c2zDUa _{ik}�� �a�h}a��{c}�Vr�]}g jk}= ik}�� {, \}i\neq jk, \\ 5�_{2>+kn(ki}+\sum_{mIi,  _{m@mk}=06�\�k, |e)*}lE ik}+ "k." r _ �f� }{% 2} /i}�A �N,*k>* V>� �mO��% )qk,%E)��a1[5�%g# ki}(r^{i}�Rr��m*�FR89�k}\E�  /  r^{k�,k=1$, $�o..., $N$ű��%~ A ~%�\� {�#t�,}�9r8EC 8=cE=% 6<�i�7��yrQ�R(% MB1�p��t�) i��4at�3 ific�.� �6�a� Ha�1�sJ�D� )�������R�%�UF!̑eaIc_AuEa��:�y= �!c_�9r73R7n $N=3$^ �!+~�5�irw�M� ute :2&�P5� *�fer})B� *} q_{xt}Q:h}q�F1-}^{2}2y}q_{y0s0% 2y 2,�,����6xy}=- ](, ^) 9)l% :*�QlH�> noth�-��3mod�� Sin-��5� deg�Dd twic�b4�]JgYm�is� J"��� ^0^^ (��yEh�AFy)�� ��^ W#�0�.icO nS,��$e�m#�n � �c*8G 1�b� Flat�S}�Kmp�i�cN�1�e g ��{��#c R['atHah��iki1�E*E.m3 �'a: ���L au(V�!Uconjug�06�B>� psi 2�k��f�"EObF�U *�R&a�� "<al�g�R$N$-wb-|a��$�pT% Dubr"� Or*F�>�b �x �ond^{qx }% A�Ka]f"� a A�� 6VYP�(1�O 2)}$mwO@.� � -�-5� u�]�od8 � � � B *} r_{t}��KHA�^{�} 1)}}r_��F% =1%�{, }2�, �}N:�[��Rin Rie��] aria�$r�L�t�� �$Q� ^{(k!5o)m�6n(b})&�D�5es $a^k �a$fluxes $c  ? "\lawF� *} a)C� �x}G(\bf{a})N�=N�d�=\� set{N}{�� =1}}-m-H�^EQdr^�tex!��i\ \ }d��O2) O� Q�!�Ex��::.P�R�]$.� conn&Sng"4�e6�F6�s � ��> &�NE�==���6 "( " I^m�3Il+ :�is�{?$�+x[=�V�B3Y@i2�x}[g^�> �h} E$}y�.�!�EX�=*3]�ra"�*by E2qu�bl/ nullF\}�jx%o Y5 0Z�^eNJ� )�{% �Lk=1 :~ ,V�P &1 E7ic}%J�ds+ bFb0( F�%O) <g_��a�jk}R i���K�( N�N�g^fb�Q�^{(j)>M& {�� �a�lc� A;�vr>Y^�of�t2�B�Z� uC��� nulF w)-H'��6!'y� ��;�ZN���x. it fi��+# of${" . I�9 easy���d�*>b iu�t* '"� $R�=� �\bar{H}�z=]�\mu ^{-1/27��$ P a� i�@b�c�b�$a �Il#4ble. IfNID!3d (2^{r�$% �n6a�eu<{�^2\��= d!�)�no���\enF7"� �<ƒ Hb})&/Pa��J F*)|a�}� = %o1W^{.v% ;�[>u%�\aL ��5z ��Pa�`es� 12 "N��/���% 6 ( B�dR �sDJ`An&P ��j�EHau� Bs*} ��� o_�� �.� ae!�qhkv�:y �J� Thu5Cnf!.�`��$ (no�Mt�3$N+^� $ N FD":2�An� % atisd�U��paHUAD�����Dn�F�?ct.�.i� �1��"nc�"*U]M�99�v�B!�*-�D�p&���# a��"IP`6�B� �P� �I� �Co6ch]."S�on_ b� 6��to 1.-,�E�i�fn� �-Kd �-#s" Aez ��M.u�<c��X�ir96� combin�`��isn�w.a�!B*�&Ym+' �fA�%>� �ar"@ �>�c }� =6 3 !.� ^��u�!F �* ( 8 +^) {DF�� 23k 3%"f}� �� &C( d�+%I)6� ,k}2v��.b42H,)\ �J��*A E���R��Q*��FCps�Dj� k)^� %�k)..G��j& 0=2i-�b�\�W�� � si% %�^N2gb��!�ŋ�,>�kr)R�vJ�w�"� #� &�E�$�� Yy"% R}).0 r})/B� �s]P�9�� � l> �6���v|9�Ɓ^����$ $\tilde{gi2�B��i}��twl��I^��E�C bf{Lemma}hL�� �>� ` ~F�*��>1� %s �b� a�5 �� s�Le=� k)��B���2+ 4aF:���1G*2�o.�&� � gm,emetG�� ��B_� :>mV��%u@ L*6��� F� j%Wul:kinM!!}ۇ:8� (r)=h^B7I��i}(R)$W$5�y�+nI1�3 a�i�:�= v��(+� �c�%y5"���2�yz�V ^mH^cs� de[�by5�8�+*�B�����i%n .�"1~����Eb��!:w}�aY� �:�J�#�8 F�&��q�.m�5 .�k�sp�pal��*� va})y/�q4� S12�6���^ ��R�%�#Zt%}:d6R2?psi!c~c%Y�S�� TBW \ bW-a) 9:% .�$N$ � i[eu�mit{ordi>}2K'Q s$XC��N����*7 (B�  $r^iA> bf{Re�Y�?pc).�B,�a F)&0�PWronskian: $N(N+1)/2$ �6`{��llR���v�N�g^{sn6f��L&Z -�=�s6n)>%&� met�-.�����.�,�$.�in~ 2�of)(it{% mixed}v( &:z$G. Darboux� furt��!*vE,� sh��"� F���V�f6��#� .UD.k|! }: A��ar}*��qq�) 22--� Z%+ $V� �"Jvo��!X t*�!!�%��y� V&*����:!a3"�)2vQ(I��bf^ �o� : S!jIg��2�]2p vv'��N*]�h#"W *�M�hm��6�, t �[^Ra H#rR�(E�,��%��;B8s��*.� 5Gm�� 2}=n�� i��gauF��.2W�*&h(F���� jHorJ� ). S(o��"�!]2NX � �]<� O �9 �9 �9 N9 F$|�/�+."v~n?J-_ia�:�)yAx~� 6c Y� i� B�k^�X�BDa,$.3M��Te.`U��s&p�P��&�,�-rotect�MvNd,} �&��F�*�P[E&}�-> �; �; .; F:f�!�� 6") ;!�"W#B �j  , }N6xJ# "�Q F��%3���E ���1,:z1��_--�-} i �%!XZmk�"�5V �� F �!A�}�)G�:1Ls�ZSa�2q .�B.�&SE�zJ%>5A�2}2TMEbu �W>�B`N  5=^s �2�(�!�i2Xx=2[.� %.��.�%g"D/b+"3EGg*'�*} �2�1�21�+3>3  &=&l_{�r�\\N112N12>N3  N"2�2N3N3N �2  N3��3*e)�!-'"�9 izedN QQy� &=&\�ve�.�e� �1}}��h u. y�u)P31���BM)G3MsinM}!F��F�5F� I2Icosh \u��� {,��B�2B�6U ��U+{:�3%�:=5��R�wj=23B�6MI��%= MPi6Y T�#��$36m.�OJRE1�"qrt6�.�1}w>�c_9A{%66at)�3})ZJ*.|5% 2~ 3}u=.xca��P 2}}{2l 1�y!9 w�� ��U:���#l �2}y �yB<B�% l!F� 2���a�42^�3}1o �1 } }�Z�y .�2R�1%nz  �Q�!pE�z:�V�5�2�39�f�.v3F�w"�y/R@MnewRC�-jWF�!s�+W pj0.�-7)D)�ϦI�EՐs$1� \\ q_i &I�u!�B�.:`9��$2u2\ s`R_�f:_9�_3&�&1+% f�� #���m����.f:�!G.�pM�%�:�.�seW���yrpYse�%:JA�1qL U�il.#�8�&66�%=5 N�1T�#, e�Xu# ng fL�"S2�)�*w$ ($";arc�}u_{q� \ $w� s}$)��.�wo "�7"�h $B�7�}�*} u_{pq�ił�> +1B �sp}) u 1%Gs3FhR'�&/d t6C8^� (�ZykV( u_{s��<(�) �)N�(^%4"�Ti�Ds�V�u*�o�)�$�G %�!�B�5�%tY�)N_{p1T,V  k �:�%$ _-��*�3eDI!�:(|).)P-1)��w���w GwA�AABy}2oAp /%H �R1I�%�w1-1) q g=���%� ��ioRz=�$+w=w+\ln [�+F�]F�"�.>se]P intoBs} z%4=�z6�%�!!$} �z�+)+ }% -."�si�'e.W�)������N30B(5t�9� �B@),�*A!?)C:nex[Wf�i�la hier�����"����wEq�.s2+KamchV� z_{\tau }%* ss}-��%!(}^{0�2� �aBA�  a�it{trip�]m"=1 % Bb� aHV� �+("A�siCb'si�  &%;�!� 5�@E])e�e�V\ cc} 0 & (*��\z})i�u &�c Iu �e�&H0 e�> �Z�4��,� �YNY���H)�4&-M{-?{1- J/=n'%PV�E!m6m�j�j�j)js�j%E|wEt) )f&I�E�)&& �4�4�mمa� 3J *�$7x)a�'� 1��2."�"� sB�;$��/*�jiR )B=M�&� ^e&� 61�M"� p &�"�!Ea���6]=� b�_��K�ٺA�&C$2x2�x�eB�>��g% \ �&����/�&"�Fɐ�i��͘vM�/ake��Y5��3al��re�2�s 3x3}c9l".� �}).�1P-�E7q +��m�K-(�\Z qN�I�1ǰ��"�(siA�x,T ,.t��2� squa�N e�V +�B\!�>�Ny$;&5�%�*�)� ). Also, �$E`�s�!uMd�Ui�it"."sp�"!third eQPn&2�1 �I��j�xDH/ J? .d_{*�Z s}}rFy�'}-(I+�0<w+4E):W}+[20E]w)a 6j % -35w��].R=0&� �����Bt! 7�bu}�|hieV�?O@��8h'NYajima-O��*� (!�6�.3 as%�Q��-shor(c ��<sXlocah��`>4N�hat{L}2')�.&& spek:\&erFJ$ߑ{L*70" a�+a��*%A -1}a�|9�o^=�SSiY���op! �\����4�[B .A�=p�bXaPSA!F2�%$a�#.Y��R ��]�%�&: �1}=I�>%J2 O � Q�J�TAlm�&A�Mx Bt�Ambedd�o� t��Je{R", �IE� :�(8���:!5 pseud�Hf�u�$Manin-Sato"P?B�XI�.JA s}+AA1F+1B2}+..J+asF%KP�: m9-A6�f&�1s� �Gj�^{�)&�A�n�0,n>�n �� n-2,n}+% Fh;k�) B_{kFB -1}C "� Q�"�0N'*�8"Τ�UNu@!&�2"� d�� Aj�6�a -(I� })��1(MO?}TF�N]F�/�re.��0 �}U#a�.,OnÒ�@~X�Hel&\ $c�p}tre-1e N�,��#al��arrow \v"��"4Q%$�&�1�^8�@5S*"<5"H-��UB9QK .�!�1��c.�p�c+>4c�\LcIR&E:}N A�o�� ���*!��"ҙ9_$�Mn ��.U0$�KR�.�:����c �{2�Z�FO-i�xh�ݥ�gax^�N�b_%�Abfnc=bb3B�}W.�Rz^��t�>�.�z!�&�0\pm u\text{, \ �}% z^{3}=u\pm w \end{equation*}% connect solu`s of the $\sinh $-Gordon 5% \beginF, z_{sq}^{1}= 6z \text{, �\ }z_{p'2'2B' (sp}�\coshO3}.>� \subsec��{General case, $\protect\eta _{i}(r^{i})=r^{i}$} In ge4 $Z+%spect_problem J-Darray}{c} \partial�D\psi _{j}^{(k)}=\b �jii B88% i\neq j, \\ ,0=(\lambda +�)NmR +\frac{1}!o psi ! �+\sum_{mai}2Vm})�m�m 9� Mjk=1}2 $... , }N,%)�) QSA�$determines%p=5TrAY -r^{k}}[-2}(/!mk}+  _{ki})6u,kE�kD:t p mk}])S% yQ\�k.-Rb_�It is easy to see that consequencesa�8(\ref{gau}) andDs}) yield another �lquotedblleft first integrals2!right 1�9�a�m]r1L6^�4VA�B`% For instance, if $N=3$,AHn above�traints]Jn%/*} w1%2Y�21w+33  &=&V_{1}a�G2G1*12G .G  G2G3BG3G .�  G�+�% describe a bi-Hamiltonian structure dq� d by!?X flat metrics $g^{ii}$ A$%� 0. Using para/z�aNlQ�21�\sqrt{i5%J}aP1�}}�uEM.LG _!�=VD)&1D��D } \\�32N�2 �1��\upsilonI�� \ � _!�>� L��>L2�13N�3 ���wb23B� D��D}��e]9 ������U�N 1% 2}1��))^ u) D+ � ���%�16�9�2V�2�9��%d� u>�1�)�>^�2}�E Z�$Eg!čiJ�%Pr2 !�2�JY��2Vt)35�Y� hw w�%2u2=�3v}i�%-�-�_ M��B}1�)�1�V�E}a�%{��:V_�Xa:�2.��:U � wB� % where $�*� �  $ki}$. Each�triple� P T depends from third in @ent variable as a�`er, which can be eliminatD shift along both � NW4s. Thus, every �s� \8 be written in �=R!y�xI�:ixe�yI�x-yB.�v% 8 y}{x '�x1�^Xy�X B P V_{yzx.zM!�Gz x}{y>zy���.�V_{xyEU>#xAV�x-yMNM�u" �s \4Co-dimension 1� previous % a� 3 $consideredAA�rel� �comessocal ( for�@ails \cite{Ferr})]�E} H� =\Y�i&�6� "( .O,+\overset{M}A;�k=�� n vare� _{kn}��Ha^{(n)}, \label{non"� ��k2� 9=�U n)}$P>u$ are?y t sym� c!H -deg�te)�x, 5 a numbe%�%/cular &|$.vA�aZC Gauss��)�r�*2� 9� ij}+=j5�ji:�,  _%ƭ� mj}=F��� >�H(n):�"�ju�)� *}% �|i6eF� p(!U pair�fA�2� q�q�AD$) (similar@e��:e�equival�eto ��B/!�@}J(-R�E]y Q������T hb�r^A��M�iA�n �!�A�:.�z ,j}r^{mu��C _E�% U�$\tilde{M}}��6�B�� 5% �X}e H}�V��?N%$� nE�a non-Eȍ�B�E�6lR��"l=�:j )j�j2�-� _�z=� 4�\prime >i&j>�etG}^21o-�1:�6!�]�����k���has $N$J ��1\SAu2.9E� 6$9C i9A1fm!��=�B�64* i.>}�'k) n)}+k��i})"c 96c .&�� some funJs. thi&) we resM t our� *  on  simpleste_s:^ q\qL m�g}\a�c2� � n $�i +=c�Uor :K=�9 2 Ŷ� ��ɥB�} ���n����:!�Z�EeF�0] �&7�T|%?h6�c�b� �*c_f*E��b�2�� %�F� is aA�ultA,8a compatibilityA�di�!�e -�� ! % {Mokh})*q*~��R�b�R�%�:) _�d�Y2�%o�-� 3m}+%nal=�i}a)� .i}�+!Dseconde� �B�8�w�� �6�6�U2U��M�� Ž !�j})��dse�. H �b�b�b6b%�bb��iD6w ��w2w�&� PC 'e��^� �L=\��{�t� As well�ine�� �.js�F��� �� b�1��-c_x��H .s ]#)� � ��&]�0�2k2� pv� �%%rBcfSFk 2��W> n�� �K%zJ�.>O5E2}%�T2A �pone ha.W�2�!�i2��� iA�=2[�.�-.� ]J�Wh" B�ɨ�� or.�"3�1�2�T _��+3��  &=&l !�1�\\X2XN c_ .X X X2X2X3BX � .� Hk� X3X3})5R1$% Introduc�newV� (re-scal&Rieman�fnts.=Z p &=&iRI�= }{!5� 3+ int :% .p}dr>a q` %_1%/3N_)�R_5w_�!sb_�2� j_5~_3�e�'1+%h!!}&���� .o0a�1D �%"}RA�.� �%�x!lA��A6�'�"> lA9}P%d�M�2� ,!�5v:6`2!J�! �6@R�.�� ��21}��)�>D4RB�2V-Z�1��1: } �!>AA c!w�s|S|b�32J� D�SQ"�1�%^�!�:o�wis% mmuta�,hyperbolic s� R\*� p!�Iii%VPN�!�Z1(Z .e s!�\*��\Delta n;$ % 1- ��%�31m�>��-iP!Q�2s:Mn% eBO�.B�2}=5+1}-  ��:{kuiu&%�I�-% :@_Iu���.�a�  _)�3}=9D-k&&��* _{pI��4e�R 6i2��.pq �=-\SA�%��)B�I )E1:2~����� _ �2}=e� �N<)�-1=1Q�J�5�r��� �!��2}mZ� 2��(B�qA��%8�+�6�E�%��Z�.�s51}=�3F��!eB gq>_�)�-�>�9�B Z�.(B��wz��%�R�MRX�Z�z�B�3}=%��J" MB����g 2� �_#>"0�fU +~F � ="b.1h}% ��(e' j2�(%4 2�� % *v#�%�  -�Bbut aD redu� �famq!CN!$dnik modelchiP0fU-s� @ed with hierarchy(F@Heisenberg magnet� �{ ]� �121zZ9.� )*��.�N'�/&��(� ��/��/�0F�K a se�e���>mz.% aZx%`BJn iBP` %�%���en�havR� �6��A#B&�P�2[.|� i2�N�:�0aM�;of $18$4!@h!0�:� �$threev�  flowR� &&���2#15�2.�213}, & � � <� <34 .| 1!�_ /13)Je > H� pu A�$:YS�~;�*[03}� 1� 3&�3316�, �<2�,rwAD��� ; FZ7�%3�.�%ad�*3}o4�� B�6�J=���I* \\�?�Z3]? J�!.�!<2A:%�M !sv1%;R�!�  _u An?_� ZHG =B2F?2Y?2:?2})1�V?�-�I� A$Z7�%av:?<]?2F?z� P]�%.?��9���?9�1.A�Z?�g%�!DA�>?Ek2�~fm U?3 AJY��HQ? /E?".-d1A�.~!�:�. /=�6OH=7^�!� 0 2}]?�E?�#dA}z� /��~QJ:�2? e*� � � >�7�"P�� " .� �"��1`4 �N�}�nB� Q2Q3�c.Q� � n� QR8 Sinc�:xa�#�#�,hig�9"E.s.�#sQ.s<: ofW52� �G"6^:\ any mo8o�-t leadG*an ess.2[ &G,e��6 eachc �- &�} s. /: � , at.: f21186L%?wo 6�$s � �$I+$corresponddiagon�>(oefficients/-�1ous"7- s, -�re6whe-A/;T t �t6�%X� i"�, -.�9���of1�#!!�-�4"'iu.: 1 )��\Qne6A12 Y NB}&t last+<�6� f�6O:5B9 i%��explan�  below)Ein all]3e�$lic�3A�s (a+u��space )�n%*�1 $M$)%�u0=inm invoB will4�!�of usZ� �n�=�=a ini�1sg� e91:�in%�F4-st%m�i5 I� .�. U� 3I'��(a �,step decreas�t"�0the="up��12. How�4,F!E{ TcontaW![($ derivativ%1ar pot��$V�(rotI2"oA�X3�2i�! coord�5 ne�5itaVnecess�2to add 3)�yexpres�=i� ����through���5) �negi6�!%k8Landau-Lifshitz5� (i.e.�� nik Z)! g}4l�@�jErnstD� �A� GravA*�HKFR�6(� a >F�sajlicitl�N9.W *{Ac{ledem0} The authorMa� es s� re g�� tudea�DE.V. Ferapontov, VSokolov�< A.M. Kamchatnov� numer�<�stimu�7 ng discusA�s, al�����-, suc�h$ful advice".XHthebibliography}{99libitem{Zyk} \emph{A.B. Boris�$S.A. ZykovF newblock !d�� chai%��retASd6A�nd%�prolife!oE�&�u�.X8or. Math. Phys.B tbf{115}, No. 2 (1998) 530--541��Ig�I!p nik2�Od'!Agra�,ofE�tw}\a�&57O(3)- ��>its quantum analogue. Yadernaya Fizika (in Russian) Soviet Jourdof NuclJG��C= Pbf{33} (1981) 278-282.�Darboux�G. �>5�algebra�� zero�*�re�#enH . Unida20of KP. Procee�" `III Potsdam-Kiev Workshop Clarka� Mity, .l, NY, USA, August, 1-11, 1992� Novi��2�, S.P. !:KH*� e�solito tt�r)�it{M�SVW , Reviews}, S�  C:/%�� ematE��4 (bf{9}�z�t 4. Harwood Academic Publishers GmbH, Yverdon �1 3) 136 pp.�Fer��Non�<]�*�<ofF: D.1@g���0Ap� Z s, AmerQ� Soc. Tran�2(2)�170I�5) 33-52�m�M��2Ell\=c��� ��E�FP�m. ��%�(. Sci. Dokl�і50}�3�%�74-377.R�% ymMfu� Whitham2�) an A.A�v�T $5) 220-223.$�xTsaU).`i+e6mT  ]/&�L�Egorovn_0Funct. Anal. A6m` 7)S1�G3) 32-45.��Qe�:�OnB�A� one&_ al.�1�R�,����M Q31E�,85) 488--491Q^�k u<of6R��FDM &a ed hod� "� , �USSR Izv6^�61) 397-46�E� 1`:� ,b�On � �*"(-A� AKNS��ɽ Le�s A� 01}  3-4E$2) 269-274.>8mgO.I. :�Lax�s����8le � yA.���DV. (m} ) Uspekhi!f. Nauk�7� 6�189--190Q6�&� �;}cant�'P"%: �Q>,&t &<�2 .�Funktralm�$ i Prilozh� Y�6� 2)� 43, 36--47, 96; ��!�.�� .rJ196--204VA5�!�!��u� bund� & r6� .� >�-� �4(345), 155--15B� MA (h. Surveys �� 20.>603--602�2rMM ;, R raenkel},��aR.H H a 2x2�E��vbsca!>>Ds..� �.:� � � L13-L18�'> +@ docuW} ��\� [double~ `ing]{elsart} \usepackage{�icx2[Ah(n1]{inputenD#4amssymb23{bm�bL>d�=frontm'$title{Clas� l Dissi�2on%L�Asymptotic Equilibrium via Interaz(C(Cha)S��_\�fS�nan� a} \� !�u0de Aguiar\cor<Va1}�& ad{a<@ifi.unicamp.br}5N- [a1]EKM.J�d�${Instituto F\'i�H 'Gleb Wataghin', U� 4idade Estadual3Campinas�p Caixa Postal 6165, 13083-970*PS�o Paulo, Brazil} 5�ab ,ct} We studUenergy�Y�one&�al osc��J!Ma�%��M)�&Adegre�freedo�aRweak c; ing limit�n\ 's observcS averaged TB3��$ microcano!�l ensemjof�9 ject�he:�, wN play�ronN$an environad -?�. !A how ty l!La)'s�1fexh<s irrr$ C  `X mal'� u��Ntim�We �@0@p�X�orYdW�`t short G�5we�:W?��absorYIr�u�of M:b�e�zycm�I%)��m� prt�t �, i��HM2<~:,y�tribu��replai �=� help�yis=arg�Ws%�$also checkLZ6concept�tem�Mu�ef^*ermUr`um!�tropy' ai?P ��s%e�di�� end.��n0keyword} % s �!<�:: \sep  low "i� haos #d��4-Wf4 browi4 mo!e� PACS codeR�\B) 05.45.Ac 0.J70.Ln�� 桡nd:]%��:"�PM:! } LJ]��is�6 , un�Oapa,riate circumnN ces,��%Ǒ��*;(heat baths (/�wilkinson,berry,tulio,jarzynski,cohen99,fishman }. If�!� �I�fewR�o? akly��e7 a faG2�,� X�tr��y! dMtuinfMS��6�. On�g�E������ ide&D low >�!��'s.� macroscop&I8 wa�: work�(Brown, Ott ��Grebogi�E{ott} KH�,rgodic adiab�&4' �`.B =� a%[ly3"yi&�\er)y�{� h5Xsh+Ai� on�N���al�0w!���*S�#E��;"t#<a �Rust�1o2behavi�Be!���fk��F� �ouc_ S�>�9.��]6% �is�\$��3J would "�%�veA]ce on�]�-�u�}.�iL&YcE4agU!re���4TBa�E9Robbinq�e�}2]aQ ofa,��% ngi�an *� , or"]�9'��]force� AM�Mr.gdu�!5� o2e�be cal�Cted�9k��xi�on �lowcK� �9�l!A �as{ Erb�< Born-Oppenheime��next Qto4a�icp4ism� hplus a"�c# friE5 -� %/��or��� R�L4's velocity. F?i�Elt)%Dontex� small-�s,%gouf need�3>] ��o1�n\�� be V{e"�(.on*�\!2�s�$ ays expon!$ly�ma�r$oppos�d)?qv peri�$ b�/ )(re�I�b��m���} A/ed late!.dup� AaAs2��- can  � '%p"'�!? �e�e�'� m�WlikI�6>/a�s�A� icle C� ng w77a largC e�. Fin $, Carvalho�B"� } esta�d�conn�"� d��� sm dj oped��Caldeira_Leggett-lc }E�z ���A)via:0a1 �XB%Bi*�Op�$w�O visia�h�%!�E�pobCof Pp�ific �%� :� Mq� �I�a�2F&. Our m��purA� � �o � �!.n ��U[ Y[�we sh\)c>|'�A6�A� ?�\����ed >( f��6� d��ach^*� /&� �P��ti[a�>�9%���� >�w�]sh "��in�`=availUE �-Sis�"B )�� v=6R ies lh:��OEB�".�(�.� �1�))-a�$@(��*,a2��&y!��\adcor�-s!\fi��2����-o evol ZNwhose 1/U& !2Mj��Lrandomly selected at�Fixed (4))-�� . i*� �S"|�SF � ��Y-�,&#��ma�'c)+ 5+,���IE9?6�6� A� .i� �| �%�5�,�of |` %sA�what �matel�c$,�/�`��r poss RK�* occursT�T ular ist>�, valuI� thes-0Ns��E�,no exchange [$ 1e�/use LoMR10se��>MU6h���f �#-��-=�fol): a L�v[b*of��� �Lfrly-dSb�["� a a quad4�rr�(�spo�,,A�i % Z� %Nappear!� �"� �%y!Lu�,�~Vyp�lQy(rI��j� /vA�!U�o!" m�I�A-dM�A�� ore5p'  ���6�c e��}�,f@:-not aA�__tob��G*F �_s�)��,6zE�UEe}� e{�=�A:�ten�1ri�.�*eE-1�*�l!OIn Gi -y9�%l%�>� W)(��� �l�FI�N��+I8&p �le�)E�cbr�iJ �1GI*!G2N �$��% y $E_0$�Ber� $TD0�* ! A|'>r �bs�"� re@ oir �>(E_0 < k_B T plow, ��� Auf� > *E))Ya&alw$L5 J. H�EwPve�<`sit�f� �1EIC�1%3 �� � .�I42�on.R1A�IK>l Q6�&�1�5Xd��%�5 .� %Y�a�q !$u�Eyg�� ~ee5�{pof�a�h6g . Despit A����of f1 �er -��)&s�-�s�ta9st/4 not e,ho��e y�Ce��hiQ�* �� sub-�P"�.�-a, at2k�Vls� � (1op}hssu9 s�*P ��� � Boltz�P�4��=95� �,Ep theyB I�YQ��Jbut��M�den�(��"��qͬed�Dramshaw,izrailev,c��I�  �?r )�Y`.�=�aCM�.���0��t �1�*�we p Nd*/pro � adib>%_Y��o it�dcomple �!o!A���l in A�� (Ft^�. +�0 asiz�a _"� u�NUV� ,c; )C a� pon* !�3I� ��is � ir�D��U?X� �)X!�. T�*f"'7 !�:� Is,�f"` GAg�a �V;:of gr��T� _B 1M��}  re��!tus- �� IqP12|Ie&�-)!U:Isb�a"� %�x� !5 cruV � re�^a��@ �1.� �����nt��o6�: �Pi%�M�A{f ref. Ft�}?a � �ed�i�2n.P���&gI� 2=>���*� !�� aJ�i �i�s,w��!X-� �B� may e5�e&.>S ɳv�n.Z�auJ� 6g>@!zrvoir�e outP !1�p�J�f�X :A�:8 II���e � )q��% ��u��B7%kkrelev�'a�����Sec. I �ne�*�V ��a*2!!�in BV�app�h����e��"!G�S �S2-7�!he^bu � { ..: ��L���߽3�e�~n 1b�*�  d� Uu� i.OMI�A�s���litI�&��&�EH2TZ�a ��2�\ uV .a�!%?� them>� [. N!�Q�VIXsummar�A  "7;�%�E E �, Mode�: Fm=N�8i��R�\}�ih.�����B�harmonic] $H_o(z)$���6& )&��%��%0$H_c(x,y)$: %�"Q�"N�o} H = r + :4 + V_I(x,z),\l�oeq1�!K�oNf S= �F,p_z^2}{2m} + ,m\omega_0^2 zD m%s�(R".q�&J��q$gamma xz. N�ur")>N��1_.�w�wo�?2U�E[)s�f�p_x��p_y (y --'0 {2})^2 + 0.1 @'T � nels*Rqw�[.5�9�R1�.�t � a 0(x^4+y^4)}{4}�qu�* \;.�*-G} pe2G(� �)����!N�-] (NS) Gbar+r}�$"Mref�o X ��=!�Q�" " (QS)�percival�NS"�' softE��$is fairly ��J\$E_c \,_{\sim}^<\,0.05$,2ongx#e for :.>\, 0.3$�miZTv medg$��(# ��� QS!6&�!�$�,�"�0� *�A �!� � 0��"f#� l"��"c� &mq�F ��� eDTG�F(y �6�"�?! $a=1.0JM >y1$�Jp�eN We w�to!O estiKv�""�c�>�  pR�*xt=�*r�*�2:det7z� )�abT M[ � A,"<+&�*V" w ���Eby a "�&.*?% "� .�m#be�.]))u* �>� g .R��"�I�M���.��*Af6�m>� ��%� R�:o&%��e�le�"�"cha e���+-� �s Eqs.:8 ��,!<" in Fig. 1PNS ?B� D$\langle x(0)x(t)\�1 le_ei  p_F",ixE_c=0.382�*z2I!Q^{i�=0q�H 5.0$e�s*�oe2!�,�B�  �"� �>�>�.���!�-��ZKAmQ&s�. *D > ob~Ged&? @#�G�ߡj�G =1YiL(���algorith�&fo�"}� i� �iso�d:Se}� &P*�d}�O ! I�V0^{-4}$%($figures 1,!� 5, 6E�7 (*9 )u  $92:9304)0&�H-R&H%��1�&�nd�F@0� � ca��s2�"�+��?fitH\���Cons. �} a-�ll VGp &=\sigma e^{-\alpha t} \cos{� t},օm�p_x (0) 2�Gmu D)RCsin{\O ZCa�}�E kapp ���t�}{\nu t�{{�.� �� 1%�zFigs.1%��6��hav@�:�F"V� z kI�"f&�!NSA�%�ing furn�=t�cay�ea�%]=0.04�X�$%-56� amplitu�.$)�=1.865��( $\mu=0.409 A�P�of �<,$)Á�96� $)�=0.2043$h $ $\chi^2\,� \,e 4��OeQS��� $ � = F 7$, �20�j��mbd i6$;�2.268$nmmu=3.67� $)�=4.10$;) �1.1027 5ER481$ ( $\nu89 � $J�3�TAc!�=ە�a��"#� �e�g��al� 9+,russos� �oD/y�� G�#4��o�" nois�� g,B�-.��source I�.�`�,)�3,�e�i�Q��. Nt.a74"#� �oed�h=)U�%�a���m��v&B!� %rj�$� �$M�PO�#E !��ulAw"F.�&6�g,Q�oI& tur��o:Le�5�c�4r�!�|6s�/)�����  ^'�/03Mv�"flu�Ma�!�YU-��2��' spec�'&�0)�.k>�i�lp!��ak�� *6%J�unix �#���vk* -s`F� $�����%� !: s!bY� w�$ oose!Vbe $z�@= �$p_ \id2mE_o�ci�enk7Bta��a� �I,� ach Ɏt,?o$:K5�9�EZN h �8omput�`$� !N9(*z2)[ a6���$E4�dB4�0e� ��� %+$�� amm� � effe^z�i>�:�:T�ea '��+�q,2�����^$�0)$O)�&* * ��� �"^#!^,. |s �nC r�Zu � ��/ E_c �4��QX$�%e�1 �Y[ ime. Zooma��.&Q 2���? 61(�  5Ap 6)EFs �4QH� �z� see,��3tV'6I��K1�ng�!*M+ ive "]&�'�I?Jor�.v&B 1�c�k!a"� �eq7eor<n � 5)�G�GIKD1oaX��=-�j3e(a� e�"���P!� ingu&� m.�2�#nUfA��! �.  v� st remark�!no(at!+� .�v few �!d�I�2�p��a�P gle .L(��/Z)"� )& �/ѩAW/'�+�$t1�:.�_%Y��({�e�!� ory}�4 ��� Cu=s*a|lR0 KN"� EA,:.X!��0$\rho(q,p;t)$`,u���%80) = \delta(H_c9,)-E_c(0))/\SJ ( $�%$6=ks, \mathrm{d}q p\, \ B]g��U��a U rho$&�E�vaM6� �= 0n�~ *R c�� ɇ!��(q(t),p(t))$AEQb!N�,~�4ng!��iE=);$�ott2}.� :=zvi' a wax>"� `.-8& )*��Th"�=��h�mfN20@ � kubo,fickX7C7a2 $HE$ ��2a�٭A� N�H_1=-A@ X�V) J} \, "�r&�.]$A�an*���wR&BK moc@aIp CB8��A� ic%��>JH)w�%� Liouville���pz>q}\�) =\{H,] \}, \no�\\ iL_1j�_!C� >� @8s-�F�A�6�>�Dd� = \{ ��-�1tq%�����- aken� wh3C�k"�C ���2]&6 ��f�Y:)剥,�l 6QqD>��!4@(t)=e^{i(t-t_0)L}  _0)+��_{t_0}^t�� s\, 1 s)L}!�(s)6sQ�int�>%pA� EA�?,3ii�2.2��$H$ (50 �Z2�D6�6),F!ll��i�Z%fnt~�7��M>on��1���9&�]i�� 2/ �j:3exp��E 1)�W� Q; in $!5�p�N�%q����_e��I�sI� :\}�z��lin�xQQ�%�_e$�(�V!-= M�i�/6� :��A�$imT�+�&Z. d� ion `_%/� he 2}$i�� ith"is 2p'� �  � �al�0$B�)$ !y% a2�1%� B�(t\ in}#6 !�-� k + 0R[4 \phi_{BA}(t-s�Rs)�b�of�!({\iA�`%�} $Xiqg�B�'a�-E&8 .9 &=& ��6� �tL�� \{.\}6&=&nU\{=C,k\}B*� "b1�% $� �� tL}q�� p%<ee�� >}YA� �y]ng��m�j�9�)z�e�M*\{ �!R"� N8e Z/M�_e.A��a�� "y92�cɾo��i��6��a�.�(-[ $V_I$a6��ec1*� $z$r- 8be!\A�an�\�� �� ��� ��>q.X�T"0 �n� "{ccZcg����!7�4 ). A� �*zK� �:i�z����lbe"n-�u�fI�{m�)Yad���1u)��E&�b)6��1:k9�� XN�A4�^ �� 4N]�!+a  ����6Oh�*�&� Aaa�l�:��H2�Ap|/-U[E� } A6 >  o})-: ��s�"� of *�A���%�� \ddot{z}�r+c_�'= nf' }{m}� \,u� zoftu�V&e ��s�<K�1�g�/.��@]osceq} &�=z_d (t)B���_0^.Ps\G(�� x(s)^` $z_d� !<de�e��h� $L� �[�_0b]}/ $. *?ZXh �)jei$t�I�]plm? by $m$<f  &p_z!$ = p_{z_d}-)�1 �Zs�Z�B3%Q(�� ]�n�=0���,�C==s%^� �$�$�D.�I2} -�]u R*&H*}%�(1s$t)} \qquad1 � %0)�.,Q o�� 0^�2m�0�}Z�?�02 ��)$Q�Z ��v r" ){Z+]e+ qm 1 ^2� l+6/}��avZ .�:�p26$B�A�^2I�a�2I� =�Q�*�Y�XA�-A+2� P^2F.�in�u U� u2bx(uf\\&@ Q�by+��x!!XJs=z!d% -�NQ��2���f�,1}{m^2�9sgu g  b&.F>Aq�4ityb��� "�Q (�z -�,5Xa� )$8Tn m�M� ��,"~v)� t�4. ,A"�� now "�".}�aK xaveY�# �=� _e -M�F�s� xx�� -s)zݸv&T ,��lE�\{(,t&� %x# �""&! $ѫ$$A=B=x$. S� � -x)=�x�r�5�  s[�)"���(=�RSub�W  %x)A !.���k #a�"� @^szo.'$q>Zr1}�aFR&��� � &= �(t)+2cJ������s}�5�,(s-u)z_d(u) � &� 1�2� M.Yuk u ���v�_e,��pz2�+ ��1N\ b�Z 02|'z^2�� & = �%d!$��5*b� ��s�B�6m| e186d.>�U u.w��F2��*)�De&M�!rE� z2}) "�aʕ�&�M*Q3nic*�Lv��["�P�ic x-&'lP�q } � V� eHow% T$+ infl챱��6-v [�#�r��8"A*���2 E yt�&�!ngh~gr)�s&�"8Z%;si-�N57�#:�,y�% hand]y1'Q�(NuO ime,W"�to~ litak 8=>nct5��7M����i�f��a�a�^wM\{.\}H�:��v� $�U<��� �'�*0� $p_y !�-��!e;�v��w)�e&� f U� � 2FV�,�\�= -:&#5�+}�+0)}Ŧ� &- )U�*�V�{�P!�//1;Rd rho_u \"�Z�G �rhoeqJ�I 66��N��1n2�-�V� normV�a alh% faD^S%F�т5�� m 1}{��  9]V�q1� FH=� H_c}IӁ�&r8hiN.9a+�~!N�.per:6by�ang�y �X>� g�oell�'�a 4�a�:# \xi$�, thet"U*varphi$:R�F�a !T&= \disp5tyle{65H_c9W\Tu qHB�B�+� ial}5�%v u Jm{!�}y��� =&& *� \ J/ !� {J} M� _eO� L6%:� (p 0�) >JQ�phi~C �9$)= = (\xicp!L, -�� $J=J#,!)�,��Jacob5-te&8i��A�} &�t� �# $. S�&͍p��I ��$O+n_>Be�+ founV"bia94}�q�NS�U�V1� � �����x=%�� 1}{�9O ^{1/2��A4\xi %�} & \ey�h; �88iq:�p_xcE�l= l mp_y6/&� cɉo #��J�  f_N(Ie> �B��. plifJ1toV/.z,�>,��v�MP � < aP\pi/4\  $\tan-o_0��$(1-a)/(1+a"�j�&�N�]H� _�+Q�+e���Fvm��)7IZ;$ .;m$j}{2�/�;:;..�3-x&�!%oÄ.��3})a��2d:� ec+�:QSS&� c̟"�@i�"�A"52w1<�t)2�E_c�b'm+�� p'_x(t'),� � 8�R9 4}x'.7t 4i�J3-1/4}t'�;t�4�"���5x'IO $t'$:���An)645p_ ED~29 5���U/-�t14 ph!��F\ ���6 & {D} (͆Q�k *���[�-P3 !U��; )^{3/4)�0))� ]& 2 & n3�D)� 1}{E @� e�4}� A 0) P+>� n� [� C:�&��.A� !�yF�fZg+� �6� �} �%s2�~m~,d K {dt'-X {d@�%.i+&�b �-�t'fF tt%�aJ1�A_c}-�t\,60.=� }.J}�.^ Q�%��n �1�9�B�I�"� � 3 H��0� $}{4��A�+�ow /��N1X� 5.ZplW2�j  :)V*� -^5yBr�-q��J8w N[�9� wX �d�5a?":;����,aTvalidy4�cpb,*�IOV�nśbilliard#-�#� "�lS">]��чe�rr�$s �e�S�ulgrw�&�J�j[�Q[)�� })5! �1>�?�ed &F6 2i?Ahh��e�L�.|~* (?Q f �{=�?$�bE ���av�$ R�5��f:1 ing �2 # M�4!*Q=m.f:}(B+At+fjg�3"�eV�$��$BU�OwD8;D n"0�( a� $e&_A�3o�h$2eBM&:-��J!�c&��2.�1 A=4\mu)�)��t��� s�5}{+} #^2_0+ ?^2+ B^2g%E_o�� �� ]}{[ ?_0- =)>]+�"2}"2 �!v>�2sA�b*�&�A�o1?�\a9 �"W53 � (�=c���tly�/iB9mu� dQ�I�)�;iA; (0)/�%�a�% >du�a�) *�Qq&�bf"d !q"$M*T;.�.D'ac�?A7 �?h�"� $A=yKorNDi/{0)"� �!J;-�2: Y;���"c Q�%�Xe!�@����� !�'$ M'-K 2�= okon&A Mlomj���(.jW R"E*6)��u;_0�s �  =_��# K � &�4B�f�\"@s7���'� � 3" R�w=s�yR��byo.u�2�"&/ �N��]2� ^2 FEGm�-�>+Mt)^�}Z�Fz(1] \�*'4X+��%c LNAF.%��zav2��� N� zm 2\mu�4"H�}q.(� ���^2)}\=H�zsJ)7]} m/ e) \�ftsN<"�-�/?"�-.pi��" � :q} orig�0.Pea�r&�e d�dfAer|Dan "OV�o/*�� choic�/(0)B* es'�� �%%j�p_"DL�?ef�;.�Yr>�07 2�"&!&�?�\pul*se �5qu.�c|g����٪ �6M� > *U/a) ca[^V.d! �$_c^2 =F; ��AB[yUn����vi�}um + full�!e6-m�!@ �pu��{for5? �$,&�n�O a di�gof unb�ea;t[r����N\7�NI| $�V ,z)=(0,0,/CB��5X�I m"|-^2$�Ju�T)�"&� $%�,2�! �!B�5.Hw ]a��<� �H*66�!$10%�is� u�?"�1!@�]=n�A� e�$��$<dd�%�*%'2t�),%%t��� $2�"�^2�$6 = 1/0.1$*�R�FmuQx�F-ssE�`in&� c� � �qf�1�kQv avoi#@i�{dui�I�s��Q�i} aB%1&���R3ejA~�)ofRNq*&�_�|e ad)x�� of Wil�y-@v-Ro;v�K�ig. 5� wsO mp�������2nh ed `bare'�`� U� &6 a�erR�)z�!oV.K.O(���'�XJ�!N `re-�!edz�{orL M{E�b�,¦"�E�F(0)z^2K,`E�& !��&s͇1�1o�u����� �"SOc�o5�> m$LE�W ^1 ,^2 �/m>�1We75J0� so C]t1@ sU- ,G, i.e.,.e� }� "�N"��M�J!�E�>���-#NG".�9 subt� ���Lsł��(a�>J���R 5�'�l��A � RF q�j  .��:t8<�� a�5a'�b!�:dCseBl�ioBk�8t<�2"]Porɿ �&�)�a-��R��L"ul�� 5(b&� $B"="�G�r"J8=~�b}o��aQSl�B{!�7be�4��e���SMiF�ME$\lambda$ (�[ keep��� M�\not=�N nu$)Ege�/�(N� �فصv0'+A't+f'(t)+g* ��vN%''� 6D nu-J'�AA��@�M!E�*" \,t}�C $t\,&:�c2# �g�=*�'� A'� 5)�zP� ���\� <2\L%� .8�Feta S!�*^I lORO ,\�)zY ���+]}��!a9�1J�  �-%:t-)/t:s^.�%YJ*}FU3+>�:�:���f�4eta&=&1"6mu:f�� �2'�6; &I2{�+U^2!2\nu^2=�W)-  -3*4M)JbnuP /U'^22( F)J` #�B�+if��E�U0��aamounte�cance� e &ofp�X �I�E$,�0M�)"# X5��u�'�=F�` ��� $A "�8 posi�. or n-� i�Pa�,< 66sG�^d�f��vZ is`s&wy n�c h�u*�xNS��������f�z*I���2)qIg:}m�v� :MlI�e�� �{!}.��Nn��-�&�� in%��$��7X =R��&=&P6<";k&�8E+1 \mu�nk }}{q(k�a��k\cos[\n 0] -\nR�[(BeB-q�+[jb�8{K^2-k^2�;n� kBBp+ p���Bs��^2+f���:�+Bj\, "gQo% \ ��6� !�Z+�� Z� e�& "� F� �&� $�io"9c�@s�w 24}PZN3)*�ZV 9}$N R*/"g@"�(� 7�� �Q �}*2 / j !Tmo �m; anl�ԅwv*y �^M &� p@-�)]J� _0^2t?^2&� i��y`N"�Y" l�Dy�yC!�I�"�Ra�jX� on"�!Q�<"�* � 5AH.JZ�!W bigg Ya!� NS�%��o&�;A]�0 cale�& � $strength (�+�b�Q�]06*O�NS@�$gb2,1+QS�D��*K�I$��L��;� !��J��m�� n�fu$A'��S sL*��^h�� us"�Fdi~hng;R>==0.55��*h&esL {y�"�0)��F� � signl!�B�Sof!n�9bR�hu g. 74 2b�A�"7���~�=&/ . It/Xw�2�-s� � 6�P� $ �F>Z:a �� ow minimu� jusݞes �Zpoz� R"D��.�!?o!~�7 sugge�m%�A�R:O�~loy�"ٖ6 =2.5�tE.�=3|e �V &�"L֒6 `�Z'.�}Jm�Z ��cnF�c23`��V�n.�9^!1s25@ir6�A��} h��I��ebds�j��!�s&�\A�b�Z  QS�l�8ivelyF]Y��IXM�&lz6�>3���t*6�ra��o|V6�t$Y�NM~�� cer�fly&m���r�"r$>�h2�_{�A�ql!b%,1 �:"�T� GasuH{a���p~`�s<|k�Jcheck i�<]3�#s&�z')�&�V�Mo�*�.�s�S�!D%tq� hist9�ms %� !)��OE_A����:ex��;[@5je�8"hBA��Ac h(a)� \3IL axI�di�W��hi�-j�T����A� &:5m�9D"�a f�=i`� bi5�vn�_z'�p��)c���&qA!-m��Ki� � 8e|� �:�thus `,*0��%js,q�QSAe��, %O�#�"\(ondr.�sB�c����`totalZje7�� ks!]��A�dJ�M��&�}*�= lawA i´�)surpri0'q��-p-aT (ay� ylF+])-Iu��c$| - ���yl���^�~.cAa/ut��a�>� w�I�A�q��in� tacJ>aA\�x+9y�)"�(spұ0ngub manyJ^)_reif},��>%�~!c fulfwYd��%��Z�ex-+0_����Z"c�!aa���U&��t re� )uis qu� =�ǞyZ���Za.v!"%[ub)^b9w1E�ly ��I�%}.�Bc~ . To#b!�/ ��xwo hyp� s>�rfl�|_���@�� phyߢof %�M�%�S %\&�+ourM� �Iz�Uz2��3`aR�,ag��o�� O,&NCO,�{A�7~a (e���bq� (T!��{Ua prioriYtse� )F2�xernFaki a�s"�9��J��� �, $dN(E)$ {\eeT5�}�(�*�� MMW$E$�$E+dE$,�� &�z��.C2 n(\e ��_6�?, �=�!-."u+A�N�"X\�E^x,"Z~ :19��x�� $&�V= x�p_.y2y*{Kz2z$. Neg�o�h� GEon "=$ Ea'&�q���an%me-� = n_o(A n_c(E_T-|!�rn"�nw!a���%�:7!_�ofMW,�~"� %| $E_T%_ۅXM>. Bas"�=�hwo*�BEK"� Dy7y�"Y�hٙ7jZ�iG �yHD!6�,>��?��e�,B"u-�&e I{-�6A�pndE �p�/a�5�9�dEJ Like� N�� >�i2o�cA0�)EHI>R�Wbb 7%.%@�0sJ � f�E  : A|(E%9# zu��� N3i\{>EK�D!�5gud:tE�! :�A.�Q\R mboxjs%�NSdBHbrobre:#a^�Dr��)Mp:� ���R6�Q:�&a�5Ofyra��h&9 meaningd�� f��N; E < ���iym�� 8 a linear fittiDng for the case of h NS and a square root fitti1QS. TheTs agree very well withOD numerical results 9,sudden decre}.0distributions �< chaotic systems�Xhigh energies is due to}�constraint that $E_T$ is fixed. Finally, �@Eqs.(\ref{probn})% q}), w!/\f��1}{T}= (\partial S} (E}. \label{Z def}FW��Ne4S=k_B\ln n(E), Hentrop1JHiI� !y a�$:�G!#�.y!P!.es��:!tates})��the�P!�� betwee�%�H�e6� impl��9 _o/ E_o = S_c.Xc$. However, because $n��$ doesE�Ddepend on $E$, thi �$s $T_o=T_c��fty$,%�.� condEt becomes useless. Recent stud�@\cite{bia95,adib}�ݡ�0posed modific�A�A� �|ion!|%�ye7P, although irrelevantemlarge ml(, make signc0nt differenceasmaa�s. Ref.�<} suggests dynam�X corr���ta�`e Boltzmann principle (Eqp �1})). OMA' hand, t% arg�p.�in*�q)!�M�h,)��0uld be replac�PR1_{\Phi}q8 }<nUJ;e�i.m�d=L(E)}{d E}$. It has bA��D�at &� ]!�� r) lead!a iden��E p !Dmo-� limit,�_��� 2�, �-,fis st��ab��scribe � !� w of*� sim Ak ��resA�model�'�  $!VH_{o}(E)\propto E$, NS2^�HPhi_{Q:/ !]a*� O worka�eV� canA �ed&�Z.�����%�!6�,� u��w i�_m�u1o& NS wc ndN�:!\ln% o(E_o).._o} = 6/ /)Z_c620c} \qquad \to qO{E� R 1}{2J��(A`!QS��j�%���2}{3}.F@TPQ�� i� mplete� mA�-�a U;via��RU . C0Q��ou<oree�V� dqu veryyz& �s%�!|���bs� �|!�)�*a6|�Á�r!nclud aB $T^A�indeeH goodx � E(characteriz)e.�H. As a last remark�(noh wi_ al2( fun� � ich��$microcanonŚ� �f&Nde�e�,freedom, is �#ex� e�eevolv� a fully>\.� overE��re� i� y!|���^ 1� IGp xed,!  ergodic*�99�" � y2�,s at long ti�M�e� .F ��E�a� t�� st `` '�� �,a-the sen� %�yp%� trajectorA~explor � fA&� avail�w� (y shell. %� \s�{CE�s��} Our}Rq��9couplA�B n.,to a low dimD onalA�o&��es}�some aA( a Browniana8ticle!Qa harmA� potAXal!��Vc��}b bathPG �r�� 1VI._ ���sC ver� behavio�� ends�n�3� AUe��shortEv scal��U[ �.��/ d� linear!�poIbeor�� � ���a to2ult f�% or�Heca� A���� lx a�e�mo]�.l o absorb or52U�p o�G!��x �>similar,���a�F�, �03$%*� �%$-NQ�%fy $k_BT$ !E}�A.h&} , ho���� :Y o6�1� affec��be ��� � a di� ��sI�%� its  $number of F)� y�% F� both.&v �M �I!�Date!�e��:[and!N1g2�atLo�E& �ssuming|alE�a�2}فI scop�� � ��� weak�&, sat>`v1>1 � approxima�)�> duct t� M eacha�i� . I�inter��� o se� %�A���!�!� *���d�mina�{� E�!<�$� u+suc$at no exch� �8occur��Q�>;sXH�"�  $A=0$, "V EN})v �NS�"�Bn3 it as���\)� P$ �!+��s, since"o}�,�Hs!�Y$!t�T=E+�p� / =0.{} two !�A(s clearl�  q� meana�a�Emediate%�s non-�QcoB� t�b� ��%�-�!`]Ma���!�6��� words�?�H- 'x �M~�proper.�iso�d�*| !eo79� "�=ica�e�a�&.>i}���dcon!�ap�͔�|9�,ws $\langle !� t)\rqm7=B�=I/2�9$xi��y }^h2�  %�M � sit"�6 >�e� 9�s. And3 ,is exactly wA�happens:�u>9� displayed� %.(a�w!���&k� ��n|�Hl+l!���tYng�}y. "!9�,�s.�� (b),��}o� es ��-�`,it back latt�Fn!�e�e�.� wf56�Ss m� lso�r� �� :� �V&&�4} J<� i reflM� he fac)�*� 's2���yG���ů�;set up,.V� uish!Eo�5 environ%?� an infP��.` Be��aY�'s� !�a ��l &�( Vl 5�) exhibAI� flucm0sR�Ap���0 is eLE d �volum��y $�$-� ".Q>��k��A n}ͱA�E� �b=un� 0 .3�c� � tly2 V&�Z@belieY� A� U I�"�(of `\ldots�� ^-/g area|ropA}e��ct��rA_ po!irmo���r s.�' i/%u*w��!� reme3 �,"� +Js a. �re� always Ei 2iar%��=� 'd ��"� J�. Moreo ��� why%CZ�r&��J� .�b%�tegra�Weta‰W�id�� two � p�sused ɤo "&ApVFr��%sub�!%a debF!� touch.f!l� � U,al me icsM$huang}���b>j 4{\it a priori}���Q!� mixing. HAw�vef�ois}���mA^ just�!7, p ia�Q%K globa{&��.o})��Ily!���E#i�%�"��e�=�u�J�C�)� �!Qu��4E( is teA�-* �sZ �t5 ng ge?�E tud� �� s.\\�m�� \-er� ({Acknowledg;s} \no� nt T! paper was�ly sup�&� Brazil]agenc� <{\bf FAPESP}, un� cont�s�$02/04377-7E�(03/12097-7,DCNPq}. E��2thank%bS.M.P��%�OB5&Lthebibliography}{99}��Dem{wilkinson} M. W, J. Phy� �@23}, 3603 (1990).EberryA V. B %.J.TRobbi^$Proc. R. S London A %T 442}, 659^32^\tulio} T. O. de Carvalhod M. Agde Agui��( Rev. Lett. � 76}, 2690c62c8jarzynski} C. J, K BK4K937K52K$cohen99} Dhen^E8� 4951E92E(fishman} O.�uslaeE�� S. F Z[ 8� 1886 (2006���R T. Kottos2QE)8469}, 055201(R)R42� ott}!��, E. Otnd!MGrebogbK@59}, 1173 (1987);]W caldeira}!� O. C �A.A`Leggen!�8ica (Amsterdam)IZ 121}A, 58%�86[8ramshaw} J.D. R 1I:b :�, fig1} \ca�{Co�*�"�#s�� NS 2c:  K p_x (0)x&P _e$;�$ xB![e��oJ�3a��dashed>0*4 Q� re�( uX 35000F\s.O'1��5.2:{2��B:-�~'Jtc:�2��Q=�5.0/ $a��� UF�;!� (c`+) p_+"�_e�'A��'E'0�'�'>�3�%B8M#u�3=�Nu: 7a�9rE_o9l$ :�NSe�:1.0m(b>0.1-�2�*�wa��$to $m=200.G48$\omega_0=0.005Iz!�E!"s# to $\gammA�006RqeriodB$T_0 J1260$U � 6248�~>�4��4>�4�� �1b�>�%�!{QS: (a>�/N�2)�6�J�� $m=1J�1%���N� =�Vl1� 2�628%� %�4����5: 5��B8-�� >p>5]2A1:y�;at�;(s �A�8s"�"� Jv��B|�Ndo&gp.�3 {or}]�,A#o�9ed&�ly � M O&�"oft})��$f(t)$.� ��"�!��,A�>0.2��(cJ8��,U� ��! &$B�s&7N7a�!.3��.�>�6��B8M�Տ6�pQS�c2�=)�F��p�p.pneravq2s'Et�aB[.QJw�R }�'o�/]ZZX �Z4�ZnZ7�Z7MZ~>�7��8d:B 7��������c &�$� �-�+2� A�bJ5�Fc>;39 �� [M3"g'ّZ��@�@��r�8��8M�@8]v (a)D*�B��>�Q�1mble of�006�1�e=)@ $t=8 � 10^{5}$ @�*� of�l 3a�u�c�ato�qar�G! J�E_o� ��>�E_c1 b�:�16��4bEm� . 3:�>�'J�D�2y� �� do� �<�%�#%;n�%un�$of\T/30$�yny9ړ9>�96��w>a fo52ABq�BT)�CMag=} A|A�-D+val� 0%[2Q5$%Sa U C *)2of-�Fb� docu�} �Y\c� [12pt,a4p�@,reqno,tbtags,one�&$]{amsproc}�//���, \usepackage!math}2color2[0links]{hyperr\A \setcouI/�{MaxMatrixCols}{10} %TCIDATA{OutputFilter=Latex.dll!Verj6a 0.0.2606�0B*� 0Scheme=Manual$0LastRevised=S�y, Dec�&@19, 2004 16:48:129.�G!ics��322��4uage=A� n EnglishT!xemail{m.v.pavlov@lboro.ac.uk} \�%E� {MSC�% "�$D } \textheight23cm �16(hoffset-1.40topmargin-1.5 input{tci.x�b>Hqcbitle{�#$Boussinesq�%e� Miurap$transfH (date{\today�authoE5 im P�H} \address{Institut1PMathematics, Academiak@ica, Taipei 11529wan�ab�Ict} SeGl f�� ��R�re�&��C&� �ҁ�gr�9ns� rug4G=� \^B%S \t7ofX$ entseW�;{I�*�2io�In�*Maks}.t?'% .adm;'N8ar u$t�7pr ��*�E�3�K]Ggorithm%  �ࡲ9; :�0t>�k%v(d��KdV! d�A/ mple'/1��Kaup-J�,M�&B@i.'1o(g.�pN(^'� NLS�4!J�)a pai�5 in��G"�-�%�F or&�GE��'In  .�$re exist m�;powerfu) thod1�H4o54�,ified��-a�4V�sF��^ ��UG�2^�:��?2�calleI�Y >�)�`0v5ba�*onBM e�AZ\7 discret> mmet =AHelabora� e/p��i$% {Borisov-�2gA�A�Bonne�6)� servA��1At��I \(N6�/m(n�%� -Gordo�; `iMe �_���*(hysics lite�.�G^��.%F��I� is mEU EOa(ade�� it{multi-@ ric2K��!8dB�G��� �@�\L4B9�7ei�.��or!rixE're�" t�i]s@ _on�7�G2�}. On!`Y-inkS)t��i�U�A@ 52Hinm��<p��;i-�E�!s. 7*is�+so=%�s�M new ��6 �["��� auxX*ry, while�<5a�FeHamilto�>^5>Ps. Inde�@#re�8 R4�&�A%�2qu�0blleft $d/dx$2rQ\%BCaim kat5_RB-� treaa�� gM &62n/ DarbouxR orem��AVaR���Q�I1�L"�2.�,,N. AlsoOemphasiz*I/m0ժa��0�f�!t�0ly =�I�-�Fch�l view61�% #A��7cedure%E70�6d�RnweC�lI4,e next level!EcmEx�.{Ea��n��.ekAt��K/dev!�!WsolNS\�a.9#.e c!+V�� two-�o�G�=Iuūne1$field variak�.�\ � �n��Aw&H(@s,4!Nuniqu!�CO d. M"�1<thirdm�>�' s;1sebB�9�( ��RB2.lik)c&�T%|k3 ^�2�B�seO5:�AI)�W�2so&�<ant0n��GJ� de�teue dm�N>�3�1hE/F�D�CA��[4^ EZch�4d. Now��( 7N2��enB�3�w!$)�yf�o.��E.I�iU. Nam�e)_1heA=Q�l > %?A�\it{quad�A�y�:; a�  se� :cubic��C"�: illu� 6�w!5cept:A" �BofM$N$qamW"� �f 2=�.=��s�<Ž%`:�7;a�>& �}g�U!�ane� 6� seA.O$n� � lawu5�1Q��S.[ �Mtaneous� By (� ,  12$+Tsar}), i�&'A:��� � U ]�:?�Ils $M+1�>�5$M$ --Qp�! a:"*�� ��� S7Y��E� annih(8 Poisson bracke�PJ.B* zero curvU � c (��/!coord1Aec flat)�>A�F"D�ric. I>isummand�589Z6�`Aeed1PA�i�6L.�u�!pB�Hnonlocal Ferapontov1s (UBI7Fer]5 lt})a�Gp� ,�6do��� �4�  !+"# a�.�ud��"� ���?��  , c �R our �=n�7ra�Q�C� �Pp�1"�9f/ (*fF�"/ q��%Q�)A�^ c܁�� feEZs6ussed�K(e.g.E��ce=wo< �E+O�S�?SSќ!�&9caNG)>B .d )�"A "q I� � A. �N"B��^ a9Yhat{L}A}$�E��lA�r 2�Q' $:L}yGx ��$is polynom��e!o� DK mbda $ (N"}NBNfA2exQof� yi�<1�s�V;/� $N=3Gy�3:����A� �Tdu�TM�J�M*&� 2 VY"�,K;-n@resonaA;I"$6� NLS,�(,Abab�[ �3-w�:?� ordy�Co&!YՋ5�\psi =�)0E.� %+q-} 5\exp [s] rdx]. Y&�X� }% H�V�}i� a��HL2?e� 6� � A�Ric�W3%�$N>#! Now,�om� $r$11Lau� ��_! 5Ejin vic��: �@y. �\{ ��<6�Yߕ6�. Each(桑NSy. Omj^ idea-a��� mus�/"� } ��Xa� Tayl[?e��'#mR��Y!2�Lcoeffici?X! J>!*} r=a+1Wb ^{2}c+..�1� *}% T R�6.�nA=rejOt+` �� i�m�1"oEWHWhmB�.s.�S �1 J��-��ci�[*S :sJ1�P�� ^ j9}�Z.�J{B�(*} u_{tt}=\nPal _{x}!q[-",V 3}u_{xx}+ 2~Uu$],�Ui�%��%�b%�wo�S�1�B� �:� \eta) {, \  _{>-2�%�R��q3�/�}%Xi3� m�OgLy� �C�'w"� .��2sBt�!R x}=u�!u+(Q�^{31l1�W%-}!�}): E =\ ��-si\x}-�)�9 94FBq.��Z1�&awri��)�(�d4p@: �rm>��c��c{c} r! }+3r }+r�=ru.�V��d8\\ \\NBY26],%I� � 2#6FH%a��>gKt6 �VA�eb / law T_�c(aHJ�D\�arrow \i�^ $) �r:t �tow9��2�J�.�!�.�6�� �&HZ� }% \�#J/amo�N�twoC�we��4& :mN� )�ANaMNa }+a�=ua�N,MAbA }+3b I3a��b=ub+1+c+ + 3c.3c+3ab<=uc,...Rs7Fs~�&KOiy2�gmz���e�E !g6Spseudo"/>�� X8 =6rsJ ^thL�fQ� fluxHex�� �erm"�� va� $u$, $�$N��it{6J} &ad r deri_ ves:A[ haveJ�N:B:)�%�2@]Qb�f�H�;[I2ab&cJ&I4 2ac+E]b8F�wV��-_58">�n (% ��7� We� B.*�ta =2! x}+6m_2e`-2au-ŒJ>� �"� J� (MB)�!ja!D &=&2�n���l&\ tJ@~�-notag�+"kj% Next,9ku$9gi����;nf} u=3(!b��2})��AQ�`��-1}{b},�1R�FX twic&�V{TwMB)q�I�F|�}M�1m10}�IZ�-�->Qb}(L.�)ny� U�a=xQ�+=w�ɧ *} a a c-(c�}-be�-b�6)� }{3R&|`N% N��I-� thr�xhrRy�9Fy��8+2c� c+3�I�+�x}-�x}}{% Z�]]J�;\z�b�o9VP�l�l�'orL��ry2e 5�`V�J �ű�nWro G�]��o Tl�n�[�Ij s ($! �y%�^{-�, ^{+}$)JS�Q UQ�d^�V:J�(sM-us�  -� x}+s�$0=\varepsilon J� $s=2� A��-  -}�aa5� Yjug[MuS5j�.�q ��  }-v� �i*� sB� � bf"o�1}:"6� }/bf{\ }$!9phi =)N$ Fit{-Q�A8vr� � 1} `%�-3r}+(3r -u)2��A2�m�p)@iA)it{* ���i8�� jEsf�B& 2�-�AWe��01Bi�^prooftX#y=byA� s$ghtforward�%aS )!bf{ReodA.� 5�E�y a)J.U a�.� &�. z*�)� fn \delta R} � }�eA�!q�} A��{,:�IOR�l+|..((Vm&,ZA� Eule. �� �/ �$ acts #6shift&��+e spa���V�H_{k+1}> h_{kN1 �6} �*d ��%@NZ� b_ *�a$�)on%�q��W |6om��(��q�.� Twa� }��6 ��6n ��one. N� �iE*^!!ch�a�Bx#����0y$�zlread'"t s�fo)+"- ht>Y>[# �&k)m��? $&aniikRse)l)g!�)��iR�u=��� q��}��*vae��&. %  �(@J^ ���r9'ZT $_{1}$F��B�3-ű+2r���>� % �� !s 3�1!� ]� �\ \�!� 6�br�F0:O}%A�oO"�x2�&:�Y*A. S/'��T�,ji2NijF�E'+62-2rSB�U@JO6�J<�iN�rͳJ)�%�!�(}\pm \sqrt{-�):�.�<K }{45}:N! 1% zN iB/s 5*3�]"�x���jd�*> =�����-�c&�>����m� ��t�V 7[h� �^C$�I eve�7�e2� �z �ykici�]mul�*re hugHN+#�, omittq(� &# 2}: InV00.�s�Gp-N/(2b)$! !�!0})%g $q=r2m/(U,)&DM�� ?% {@yu)��@:�J( � &�J�(2bp)�pJ?-pAuMUb �}{4O�x}A�6b}:9%)e{��� :h �qF�9Vq�qF'[-q��PjS phi ^�V�6 7 }]6��Q�*� N�"%z�IK.k4�Up:[a�ly*Q%f�*B"%.�$"L%5,6�� iz|  �|�n Z�#I� R� *} (2� +a+\a})6-Za= =.H��� �2� sZ�ya�I-IbS/ �.6"1}N`u7}�AkT+a �A�!6J�Tc(��� N rd�7f�36�FV� 1�_2�[�2�-2 ��-�%eF.Q\I\ 2a��^k-O2O 2.+�}�RI!G�VM�+cf���)�l1(FeAD �O( 2q���O�)���RUcc} a &�& 0b0 � a#{ ( & -aq�r>}VuzO���L&&8R��XURU%"!歄��}ui:=(�%A� �)_&PxE�u�Qm!V1ea;F�JNu�i����"Q�% T�!�*Z�"� N*L ��(�/��� ��"�*Tm�   i,ce�- Olver}% )"�q`�7V�"�&� H_{4*��}B4 # AU6/ jKu.I7F5 "�)�.-���[ e�}�A#� 1}{6�#�7  2}{9F$3}]dx��CAu q_3 _uT'�dPd�-*(Ca�+rs)%�;2 ;:\1 uR�P�l2�.�N(3%��2�)3"�# -�H:% +(-2@%3u)Z6u}]� %e(6'� i�)��>-n �uE$a�3A9��.� g�2[2^{4}-5u:2}"�5!2$+2(-;D&)]6�F(�&& ɂ_ u})--�J��*�6{Jg vBJ%3�Nu}]J�.d+�bbw ($a$� � $� [Y�acquire,i:5^ �i��%�2�[-2>2�wa6  H_. �}B��� �AaN|7 :�2\aw :� _�(: 9��2}=.a�,%�dx��a[ j% �u� alf�1]�judx=- [ +a�aar{!_ � J>#>�����-��a�\�r% H}_ T���!c9{d: at�3}"\5B; Yh9}Z0Fmwi1b�o� "�Ne�$!��6�*k 6�*h F�k}sIZm�IOs(s+2a)+ %�^-){-adb� !��(qU*I /�s!�+�)b+1}? }-sb:����R�x��R""� 16n-�8�#* )W� 2�>�4>�����er�zi9s�:0�pI �2:U*D�}�r��,�iiPpeG4��1�Cll.�3 obvious%�T \f�t,a�we��*�vqr�,f�1��qis9are͏�D%�T!w��MuiZTFe�� few,&Nn�&�&in�:*49��8�6+6��:�a��a�� �xr:r spoiZ0t)�_reo3nij��=6GAE!0�jW�&!9ͥ� $t�*re ��A;T�:we& �tin��FbpU\�-�s, %��4J SSA�Sm&AY|b��d elsew'. 1pN�:of >]BJ�0�AZx� �j7Lu��ln�y�E0Shabat} class6<�BE5.g �g =C x}+F(ue{, }w " }w��)�}% -w�'$ x}+G�OF=Xnd!�N? be�4�7c!( (by virtue�;Z52��(=\rho }i�/\����c~ be np%toA$va�Bll~7UoR�up to�ul�^�52�s� �x��**n� � wE;�?��$ank Dr. ArVJy K12ev{���Y�τ }/mp�\ (it�a talk�PI�L�{al�5fe"��"gra� S�/s: So�1�Hd T6" Gua�jar (A�D(nte, Spain)o815-19 June 1998(V��Loughbor Uni��ty, UK��$ir finan�n�NZ hospit� w�i%+�%mad�u]R/n\.n�} \|C{�l4ntonowicz, A.P.|dy, Q Li0�d0block % Energ. �t�A-]Lax"Q!s, Nonx&Ce�bi$1) 669-684A4��d ��j ,, S.A. Zykov�!ne ��HQ�TFf�:>�H!J!�prolife�?~.b7��)or.�L k� 115}�. �g(8) 530--541J�=%n6�MjlPlMb�%vi�s?OQ/B� 1 .�j�$% 152/153}�j$1) 104-109.�=-zE�&D=2qDy�sKgeometr�(�JBP Y� hydr"�-.�hctaL al. Appl.] bf{21f�p�95--2024E�=dY� J. Gibbon�jY1 Comm2�q7ujNo. 1A�481) pp. 21-30.- nSokolov,�m��,�re$LA$-�L�Y�9�2L . (R�Oan)% - % 1�1 p�Eo$80) 79--80.�M�> �A. Ya� ltseE^P'/vi><Đ%�"82�� +�Lun-,>x@vpica D5N1o�p1a�R�2\ � } a�M�{AXa�B\, ��rnfpofmʁ�P. Sci9c3�q!c10�2)pp-612l)�9g V. MikhaiFRkY7J:�% Ext/2�|�moJ�:� .5ka�L")Ki�&>�YF��I�8) 1--12�-�PHm ,}@A�i� %}Lie�vp�6�;�O SeHGeI8. Graduj+ Text�&!��Ms,YE07} S�kg.nnew Yorka�93) 513a��huH ��k2�A -@E��ics�c�&"�B, Jour_of���al�nicU. 9, k l w!{20A^173-1920�1|^�Re�;hip"�;6u6� A�.�"�%�A~0Korteweg-de V�<1���Gs��2�pa.5-6%� 8) 295-30:�k�EMR���Phmre6�% Tri-Z��'Egorov5��.al �o�b�XE�y3��$2003) 32-4�mQHSS�Sa�Svinolup��6 b�(B% \"{a}ckl:��* ��:7<�$ Dok�'ka�Iauk SSSR9�7 G!��t83) 802�*5�> � &YVt��% CORRECTIONS TO PROOFS 15�W�W@. % Eq (2.2) push 3.1) ad� �M$rm b q^4, �n�|$ge ``obeys�Pa�0Ux (b=0) 4�K Weier-ss ellip��Q�''FbfEe$p7'�� ``of2� 4.10 �=0 � 7.8)-(7.92�8 E/2,�^2/24 38F\PA�r_�( s_1},\ \PB2}{ 2},\ @9.72m9!`H=...,1=a��A��i % &�D)hsz��� �W ally�li/% % Ch�`` � '' .to ``� ''2.f�6/ ../siB� �d5/ -.5���Om3 5 -OG6��7U5����s''!< H\'e�U HeilOXCalogero 70, JNMP. Octo]| 2004Y xia�qsBW8�am�[,�{[&�S� b�I)�� rMud6. RC 6E]{jnmp}` P"\�mp �$useful % %RG\2g[x}6cZsym� newco�IƝd}[2]{�l #1}� #2}�-��Jabbrevi)�l \def\CRAS{C.~R.~Acad.~Sc.~PZQ} !(PTP{Prog.~T�.~Av~ 8 \Oeuvres{O$\!$ } %ީEn"\J� \ie {i.e{�`6=*/)  \Wxhbox{d}��. Utp��E%k$cKdV{c-KdVA!}LKaone {K_{1,{\rm a}})Y\Ka�2F oneh 6h:7 7  �Kb:obob:o.>o.tw6o oc:ococ:o.>o.>o o biSK:ru:x6!>~F">�" �FIV:�FIVdFIV:�  ?,QA{\tilde Q_�HA'QB�5P(P(P(P(Qj<jM\PP yqa)qQqbyp(p(p(p( %\fullr�= 0pt�_S�R�Y���B�Cn0 .aa}�I�Mak��&\ E�subZ7�B�Z/�5 %�7�g%]i*�ɤ}{O*Zx�b` DOCUMENT SPECIFIC DEFINI� �Un����9�\�breaksin�  ls: %\/diތ 1S�f ems, Lemm�-:�e�,* type}Y alic��em� �8}�8 2l[}{b�Y E�L, RbbfxJ�] etc.r!:$ upshape \ rstyle{�V�I6q{DX2$*{AM}{ �} p '*' L�;un)�ed�� END~��&� ANHeaTs %Mzre.�� head} {R�t��Miche� Muset!�Ca�ne Verho?}A.ToddSExpp/� !fA"a 6' .U�% TitleAhH�� )�empty�_FaN Page�{200*}{ \.իeq }-/$ge�}{Artk�� Par�m: Year,_�,m[,E� �� perE/�' I'bp�8 da6'�er'� '�dew�z'�opy��- �� \�V ށ \foo � �zsp��ng �c RC. S� /044 pei issu�M hon0Pto FrkOsco" . }4H9� \A?d { Q�4ONTE~$^\dag$, ]� USET q Y�ERHOEVEN; ^�d Q Serv�de �_qu l'\'eta�MyH(\'e (Unit\' recherc��ssoci\'ee au CNRS no.~2464) \\~~CEA--Sacl�fHF--91191 Gif-sur-Yva_ Cedex,-,7E-?f:i�$@drecam.saG8.cea.fr\\[10pt]�� Diens��tis�YAurk�, Vrije&1eit B�el%>�r"�Solvay "�e` �`�hemmy�LPleinlaan 2, B--1050_$s, Belgium+�M�_ @vubgbe, C�]%�Dff 21~D�g~A~!�bQ"a"f\�Z�t"~9N��ticn���addv�fe s=e#_pJ��PainlevA&t�Rc�:s�.I+.�:.L�al�:e g=yZ��cases�pr��� valuednesT�=l"�?z |�$ians enjoy��TK�(: meromorph�RQ�is -j">�0 genuu]ENcom–��= (� (G�/�G y�0�any%a��jou�[ stro��".Z �y).�Y %F�g% =�� � :�g\"nt�?``f'' (HH) )!HH} orig2&R?�_%<�Sģ9 �=2�1su�#a kineA�e~ea*]� , i��Z!�*|�s amI&rS1�po�Mon&�"( $q_1,q_2$,�er.} H & =&�o@�$} (p_1^2 +f ^2+� q_2^2) - \83}(3,\�SeqHHO-8}Ixb�"�V� aft��JXupla�{�&s��]�= d.Yb� m"(�a t�1axisy�fc9R�galaxy (!1qA radi��$!Baual�Vde), Y�a'�!rX"���th~ �� at� or. Őt�!�� Ƶ.�X[+ ���� b3� �?e�BW � &Δ (to 监���=��� � hem) 7� �� lx�f�Aiv �e� srty yea!��.p�&nt �,c�A�self-�kai�zpa� �bHew-&e��Vt�� i"Oc�'�\�=%!y%�utonomou#?.��c8s)#F@<��+.3�D�@ �!&�:1am91J)?� +(�P�6�T#mmarize�Ap���GUD O�]�Liouvill�R��oU۹���)� us���$ ag�P"�;��!�� s'���;w 8b1�uIk (AU� ����iglu.k!9�g���6) ��1:MU�Q-Jacobi>sH}q "ng��>?'�#�5 �H�� gra�(} we briefllhzXt�I�Xacb�$aningu|m��it{-l V%��I��s.{* �2� One_�x}, tak�on Q��ь�1\,�@:h �iygnt_$q_j$ �F�T��6��Z�erIbtAb� The_� } �K ll��q}e�2E"� � �%� �,�Fel-�Fre�l ''iB plus f ``? tib� Link%� �%�s fa� b � iton1ŅBwe�BQ� �9ثourth��,Y o�ary�E+`alU� (ODE)(S��!��QO.b�S a gies�e��cIٍ�ekat(g� >�b�mf�|Staeckel�Jlq�m!&�+�"A) St\">cl%^s (AqE ��-)��CfSKandKK}��e .ia� Z���0e!) d by�7V" �‘��ap)s^ � `Y,��s2=?Qu�Y1:6:1and8}E�J�!p112:16�PN� �g�Aby buil��bi�lo� �&�t to ODE"RN*.�" CosgL e Cos2000a�� Z  eg��a�q+�z"JY�~-a��&H GU�6Rm��� ac bZK h�(��6�)��D&�#�!iB5Ak�>�Cit&� q��temE�on %� �"KP �r existSof�6 p�n��esxH$K�1!�'wisB�f�  va�,�eft\l�f$e K_j,K_l @Z\rI�\r�1�mF,)�x{�.�!ndex{ѐ'd-�} �j>  ly��&�6�608$s_j,r_j,j=1,N$ E`` }BBX1�:� q���!?ae� $S$�@$[chap.~10] �d&T�, �xfW �A��Fld��&� & & H((H,p_1,p_2)-E=0,\ p_1�4d{S}{�2.2�F�6eqHJA"t B� v�*P �6�$se1996Cont�";}O2!H>o� (t)$� a�� !�� 2"�$, "ma�1i6 I pN1�os� �Lion, or+�.�Qa � -0*� blem��e Qg~5eqHype"�G�Two�.})�/w�.�cular�! $N=��k ���woѦl*�`n�@4 {\hskip -15.0�Gmm}E!C_1 = A�t_{�]}^{#\D s}{\�0P(s)}b�+08242f48, \qquad t+C_2=jpsN�rN6"Z71"{$P��"�g�� $5$� $6$e$C_1, C_)���P?�E-G�K &�"- d$sMsMbe+�"ic�$t$#) end{�� �za}. �uAt� iXBV1990�at@%ry�� M6�0�� �Af"0�E�glAt�n*�!@2�y �$Sklyanin19��tCjun.= ��.H goal���1Y����S �Jf3%���ei� i!�:�m : U���V�a2 {1ca!�Ῡ��� >�*�ntB�I , $H=p^2/�V(q)$��e�., gD "�|i� Flif] � f $Vn6a�OsLur*�� $q(t) =n&(qam! ofO�de��N�.�nslO%�la�_!�B����a��EN"�$q^n$�.%<nq*���$esmiGambier�{�gb+d�p�!�� $n=6�:nd !A�3��( W4Ermakov,PinneyY:��(p^�(} + a q�b�) + c q^{-必HF�$q^2$ �) �J�)$b=0$) ��Wn�) ($b\not2%2� v hEiRE�mS:��f�� *�� ayfE�AbDstq; #O �A� �) cal����ianF� ��) +a�)*�2TVB� A}i �m4 �2 s�U. 22s{ 1^{n#++{n_2}$,��t�6necess�"� �V��drPn��e��, pZ�z�0!s�c7)�I"ssa�,x��`"Z!-.Nv �"�.5�>� In�*? HH3�r�l��1 are,�7 CTW,)5(991,CFP1993 E�x{f�!"�hy��N + �� 2%�2� 'alpha q)2^>/ \bet^3 �+F � -Q��R- Vf�6} c_4 "Db o�T]�HLU\� �''iod����� H�T&,.L,'L2.L� + 2 @_���Q{-3�"-� 7} =6d'Z��V�TfYe�,�,� �J $  t{�Juse� ���3ɣY\�*((SK)} : & &)�/ � =-1,Q1= �263S�)d} G O KdV5^Q6:>K5m4}�L �Kf�6�16�2..�3K �>�T����"e ��s SK,�@5, KKa�� l�i";�%f�L<.�m�.� HH4� ��4RDG1982,GDR198a�� lN� & = & uJ 2}(Pa�+Pa�+\OmQ 2 Q) +C 4+ B  + A$4"� i- 2�m.N ~I�}{k}�Ha� 2^2}w�Q_1,\ Bm�2�4y�Q_1''�1 + 4 �3e���e�eM)e��'e�:�4�Q�c%c)c�(-i8 8c>Z�� $A,B,C, �q��,-�=� $ 2N�f i� ���Q� 4 $A:B:C=p:q:r$And<8r $A/p=B/q=C/r=i�,arbitrary}$)&�"H �/*��m{��\ [( % X (NLS� � 1:2:!� �!:}A]Z< KP-12=66=\ -1= 2,�Q8FE4&Q4�R B-KP,C-KP2��Y%�ZY.��")E i#2� 4NLS�4>�8*��$��l � ! d��i�sO:э>5 $K�@{Drach1919KdV,BEF�b,H1984x+��7,Bak/ is0*���-uteu�Ha"ӅJ�"�00&�Mi��K�K_03Ml (3 #�e�)�S�L��):�SK*;A��<_=Q_#�eEC\iq�*d#l# +��aR,6_n��d�4�p_2 (q_2� -w) + (4́� }1)$� "� � E��%)� \ �+ w^5(� �� ��5 1 ( y1-1�1��l�3 H3K59gv:1%� �3�e!�U!�)^2 + 1"� !G1�!O%YJ -"! - 4 (6!pK! b> (-2�)t) -+)�2 23K]�nm`� - i �H�Y�-�%40�� K}),�K 61F8B��K�M���+"L# sh\F�Mb�x"�te��BS�(�:))�| &6*�8�1g>�"T_ $KBA�F�'mo�1a $i$,�*��d2 e�c%p���^4?�fL�N�� �Fi5eul�)perZ9ZG(intimately '"�O ���$K$-y��~H �soY!AB�)M-.t s �a%}"� �e�R"O}#eli.l��'*��< �} 0})--"�H�t am "�!ODE,i((��+.�I=+ies&jm>?; ''''Ec^l*Z� ,q Mg�+A$$� '''}�\H�tA� 2�;uin2+@E{ v�2g w�2V� fR>�� �ODE, n�9 �0�� ! + (8�A�eD )'' (�c+�  '^2� 20B]IE@^3��w { +Ѧ�7 V' (6L���n4 Y  1�E1 �!E %-T[ c^4W��.�%�A!N^2) >x 3ODE&J{" �!&ep& *�* bnon��AZA�wit Rg�E�"H �  $EN*� $H$�p}� establish�he�n&w� j}� �p.^�m�rZ�0$u(x,t)=U(x-ca� Qf]��e<{veM�t�%���L �< (P�%BwAdu_tA� Big(3Nxxx} R�u "}A�2F�u_x~�u^3j)_xB�PDEBJ �%'o'%�L$Ei�"�i2$�e�!!��-�����bpre*}�� rt G� PDE �|�?�r�'1v�&[g �)� 8 Sawada-Kotera  �"SK197a!�cx{6(X}, . S��ELaxͥx{>)D!\��,Kupershmidt � �$Kaup1980,F0aS25T C�.� ��b ��� 3�\laltug�k �FK�.� } �� 9uiZ�N�%�/PDEs, miFm ��?in li��{?Brom�:!�o�4c��DS1981}&R/�B�Qi��way� A>*-�V�-^'' ��=�R } +�(�6�_A}{B}\i8) ,� 6-2.}^!(^"n\] H \phantom{12345} +8=bu Cw - B - Cs�4( 2 C) m| +23 �4 �P.L5�#b�I�%k � %;%�����2.E60{ C %%} -At (1+3 !d:4z4^a�%��&k!''��6� m Zu!e7}A'02}%c^5 %k -12 $� ����+4-�2�.D�i^'�) R�3 � Z31#E��)a�� (��!%� B �U�2�%� -8 gQ\ )��11�!R \U�E� �M -UE*L -8 B E W!��4B��?1�=�2reBE])�=3=06� odeq_�&� & ��*; ( )1ohV� h�y�."v�Ub� s�ri_ e� �) �to P �:�CX�Q��S�c% �$)�=0$w  r �Y�a"R(00�3�� P[Eq.~(5.9)]{KitaevP2}�#��/�$�Ahierarc&f9���0*pr)��4s�� q7.141)]�,c}.!ONU '�va&�/is� easi5#n�,ted!<mk���$:� �{AF:-}K(� ��- ��1ejUpl ��Ts sho��ati�8HH4%�g:* $�2$�(&FI�� s[$-� d ��;A$6& !%�.~��~�&&1!).S6,Ae�/iP��-�>� ��KQ85�B?ӓo*� m7 .� *�"� th��P  3gM�1. B�:�]a of eleg$@4 s��!_"�Lf� TNad��ag� he�.l/�]m`./$ (M�Z/�+L6�6)M0%a� o�6p0!Bq&.�-#4.=�� E.y ��+v�a�8y�.�" �"� �N�8>,>�a���l# natu 7�3y, 7+9l�׭�N�+tk$jTo"� e1�t va��, say�(t(2�wo52�"� � *�*�� $o�y2�E��l!�2for� , �6 �΁ �1lyQ2��n�iz�> cE%h_i�\ Chazy�5 �' Bureau  MII}�&Z�2,�2��m�Z5���$, �� )>� i�5�h7�8�9 ���,e����j�(M���)�5=a:��~ such98F�T ,Z�.�� aj(4Qz/:ass��!��)���~4c�:C&carry �r/FK�K(vK(4���HH3�M� HH4-*�>�+?&�6c�#W�&aa:��&�r�"%"/�;V1893}�LTR�!^we���8itv ulYeor}"VB�w:w \�V�6-7%�Y Z =-6$\} Un�}&�36$� parabolic.�C 6�AP�Woj�JR�kZA"23��(�/(s_2,r_1,r_2�4& �= -!+s_2+� &� 2)/h K=-nT 0 ^k Y�3E8o s_1 rNs_2 r_2}-s�3�32^2=-!%4^v71(r_1-���: ,>�AJ�ME7_&��uV@�,fZ!()- !32)2� �f(s,r)=�j {stsRB!k)-6�^4$}{3�^2 s}�@ ^2 r�I" .+ &A0 �:.5) �M)intQ �4a.� F�E!B �4h%� �{*) 5atV�!x�6)- E s_jq�Ko=0,\ �6>B'5S� e� >� :edU2OR� s_1'X6H}jW= R�Y$A�,\ s_22:2Z:e2-s_1:M!6��3&� >�p,aJ+5�s_i ��4_1)(7(s m) �2$ er�5qR5=�� 1+4+.�E D-2W K s J%B�& a d46�Hs�E}A�g�6�."�82,! ,aT&� � )��$l).�4��>r L���*�Jy��~�.` �&K�@y)��,mG+p��) ) ���^�-$2, ���)�%> ^#M5QM��)�$:�)U"=E2h"4"'\ A" �Bg$�>U-Ɍe:^�2��22��{15- �2 ��%-%k+Z4-}4�E o-�!M2��:�"A2��6�)KBEQu >"dE�^��"�K.ݣ� �5�>�-&�+�{��),q_j^2=(-1)^j ���1+j)��}Jx�8VY) p_j=!`^-�{3-j}}2-rv&���� +�:�ə ��>)y~map�~�.�!\�W2��Y&Qr�; withF���0&=& s(s+\omegpa_1)^2(s+\omega_2)^2 -\alpha 6-\bet.:H \nonumber \\ & & -61) ,2)\left[E (2n1w�i-K\right]. \end{eqnarray} We remark that the variable $x=q_1^2+q_2^2$ obeys the fourth-order ODE \begin{eY�@x'''' + (20 x +4 -1 2) x$D10 {x'}^2 + 40 x^3F�+ 8 (D D2)(3 x^2 -E) + (16g $2 - E) x -A%�+%q+K)=0,>�which, up to some translation, is identical"!\ODE (\ref{eqHH3ODE4}) in8KdV5 case. % =� \sec� {Integr� of|cubic}Ls SK and KK} \label{ >8C0SKand'in� B�xH_{\rm SK} & =& \frac{1}{2} (PA6 + PA8 ) + \Oe &Q &Q& % Q_1 =1}{6}^3,\lambda^2}{82^{-2},\�%��\\��J�p �p�am� � 16 q (q( !w�4}!  4}{3V�2 �.2��:� These two-�`are equivalent under a biIal canonI�A� formE H \cite{BW1994,SEL},I�$ exchangesE@l(sets $(H,K,1�,5z)U $ A^ (-8B(KK}$.�Z8Hamilton-Jacobi��sڈsimultaneously separated as follows �,RGC,VMC2002a!Fbeg�� nume2} % -�d Step 1 \item One introduc-&^f�PCartesian coordinatesFR & & ��\lbrace"��\{ll} \displaystyle{ \QA=a'+ 1� +a4,\ \PA=a�(+P_2)/2,\ }aBAB>A-ABA- A@�: � �O]� TCSKeh%�_�J trivial=�s $�B$ for $MR =0$,�I)e�=0:\ > =\PA�7\PB ��12}(\QAiwQB^3) -45-^2 !?QB)B�2A22]2$then appliA4o5a af^D$s, firstlyDɋu�l $(q_j,p_j) \to (Q_j,P_j)$ %ѐTCK!�) taken>m( and second brote���-�)�"$results inF�H{\hskip -15.0truemm�#& q_1=-6I�()�\PA -!� }{\Q QB} I\)�� 'Q-���,\ �{=24�Uf!�,\PA)- B,\PB).R,A�b�p�4 e oR�- 2 QA��QBaj2l\ p_2= E�ROv�M� KK}=� �+ � A� ]i�24}�-!JZ,2eHamKKnew� b%(f(q,p)=p^2+ y1}a^q^3!;�� ^2 qBG4Therefore both~���ɞ��, viz.Fn& & (!j,\Pj)� /f u 5T/24) \Qj + K=0,\ j=1,2F� ith $K$efi��Q lN mom qZHH3SKSe<}) oru2 HH3K. I $particular�6�F �ian�~mselve� :RGC}.����3��Fin��.�'s��i �v s $i{E�A� B)$ �i5 ified>��Ha hyperelliptic sys�W� "���9k.3 GenusTwoS:����.� �l�Os� -mH 3 K}*b V QB=s� j#PA=i#r� , s_1},\ \PBO  s_� ey:�P(s)=��1> (s^2-3 �2��33� h ^2)�:BRH}{\sqrt{3}} s + 2 E�eKK%�Curve}>� 4thus providingEi\meromorphic general solueh��-��w-4%�+%��K-a3 )a)� s_1'&'}  5a2"� FN���� -�s_ O{2 1_ ��}%_\>  Q_1=,(�y +� AQ �����{ =-�c�) A�% [') +2^2)2�-O9a6Ax� ^5<.!! azI�B0#*� {\vP2&O \textit{R�(}. Cosgrove�n0Cos2000a} wasEfA �| obta�� ab26�$expressionb r $q_1" H $Q_1$, by a direct�A�� fo6. ~ KKy �s y� resp� vely deno� F-III2 F-IV��0his classific�  MP^2$ is a �i��ODEs� setta�>P=0$ would prevent fine�itsB�����qu�L 1:6:1% 8)Mj�Q 8- 1and8} b�2 .� :1 e�b H = ���� ^2� ^2) Z N !#+e�) ma�e 4+ 62� � -4)amBM<\phantom{1234} Q22\kappa� }{f2}� 2p hu� =�Bs K = %%( P_1��͜ �i ���1 �1CNj:�-k��� �1 �!� .!�1� 1}{41 �6�� j��613+-U E}�J���40161BM� B!v�8)��&+$�� �G(4 !2.�16} (8E�'")�(��+ \gammaA 1f<�UG2}���Mz 6�( �+���p :p 8]� PE3(q_2 p_1>q_1^��+ �)�( ��2F� \p_21��5i4 + ^32 �0 A�%# X1��-XL2�b�RQ��VA�&� The sit��� simi to |� ��"���ͮ8ab+Baker+$is} betwee� ��>. �map, constants2gR"` H_{N8}= �  K 1i= 1K %�=21+�%aL%A� =- ( 1- AF*~$CT161to168�B/However,%cM��&� (have only b!1found%�$�my =0$.�cas�� �0$1�4SV1982,AP1983}�&� 6�V�I���)Oi�!�P)^� >-Q%I^PA=m P_J}{2U%�PB"+ "Y"-�>� q+!�8& .Ye-�1he.>A�1}$n0.2�х1=QHMQ�1} = M� A) + s,\2 q p�-1�: q})bQ�A� q&o 161fB�� leads�"fun�� ,Q_1,Q_2,q_1,��$�� � =.([(9)]{RRG},$7.32)]& Q�gpE�0best achievem� to datee!�-�68~yto�ce�� ��-K��. Aft� pplyN�J2�.�-�.��6�"� >�),%:�>�U� 8}-E�becomZ��g~� I� �\7�X� PA-\Pr-3� Y�*I�) 'Nx g ]1- -e#E + !��  q�S,�^>Y�?i.e., itQ�es��o%%���1���ca�] n beJ� 2003��Z�n�5>� � :\ "$ 3*S@!�k��K~ qX^��qk^$I B1 �I,�@���]>kM��&�r Ԏ; 2 + -4 E�\�2}� s ha/2 9�v�a>A�>�� ��%�0BE�2Y��,*D��C5�89�^|�� = � %��> %W)�"�N+1^=O/= >�#� 0 ��{2I4F�S* !U8�0By�g�6�  \not=0$��� stPgy (see��"L"S "ies})� not�$used since�I60#84odeq1}) belong a� @,yet investig ���$Painlev\'e�u,perty. Fortuf��hir�suc�� perf�h���Elone�$ establish6\!:#j %/Z�I�@e autonomous F-VI"d (a-FVI"&6�fCZ�n"\hbox{a-k}:\ y�%=18 y y}% 9 {y|%- 24 y^3g'%�!VI} y.� 6a 9} y6 t����@� �Iu��FVIB�an%F!�E�*! � is2��ed �g,` 6�&b � $[Eq.~(7.26.* .�$principle,!laine 9{M��"4�iE�*W'�e�RhEl�)��GtravelA�w� reduet /w�&litonE s linked �B\"ackl� :� (BT)�set, .u� coupled�& ]"�(\cKdV${}_1$�#$BEF1995b,B*{, V���>� �[��%2� Con��ion d'\'ecriture : coeff 1 pour f_{xxx} et  f_\tau+��� f63� f^3+3 f g�_xA�N$ < g bg }�g g_x C}+6 g {9 f_x-3 f^2 RZ"�x:�Uxx}�.�xx} d& . w  �^2 ��^�:AR� anotherQNA�h�$KdV\ type,Ubbi-SH )Mc DS1981,SHVJMV,4� >�& �O�Ou!h}ANv x}%�u-�E�( $+ u�F6 vU5 = 0� B v C W> v_1< r�U HSIIBYT;BT�<def��b\$Miura:,nf :_��u� I�)),2 g -f_x-f^2-#VNhvQ4eft( 2I�x}A�{ 8 gA�  g_x a�_x2etf_1, fH4-�b~!�&� U�)A䵶 $x - c �n =t[ f�RD��PDEms I���{>feq�, � details��8{CMVNanjing2004� �%A:a2x>� �^2�^.�, �*ly�Lm)�fff � W'� W} t � }{WM- [9 j��I�y��4}{9}�Q� (h+E � 9 WQ.]V�� 2=-�.E�yE5n� oR���123.��Big[ 1ey�/ � ��ma-48�  - ��� "2 C128�(�) y&I" 1280}{243��/$Big. } \\ 6�".� 4567@,1\40 #5� �3)vo  -(� 5�ARX h' -1445��7^2 �Z�W=I9�ZV.:q ="��"i M�-% �t2=;>�1#3�Q�51�6��%\\ %6� %K_{1,{0VI}�� Kh@  E^�52^5E65353+)� 9}{6�(!�5e , %}^�1�,\u2=E A B=N�6Ri��^ (FVI_to_HH41Jin� $ha"j$�  veni~ auxiliary&� [Eqs� 4)--(7.5.� JM�r r h=y''-6�5��0� �616}{27y�^2A8F�j=�Mr2�[Q��y)�I=��zQ.6}\yE���9�^2��  �N7�9F �66qyNi �]R]j'N)s ? h'A�h''=6 jf�6� showat@Zi&���O0})���#e� 0single-valued��ioJC Fq��h'}{h+E2)�")FE2�6�Contra%zeviV�s�� icaQs�6 c�(�"3.R8 depend algebraN3ly 1' Ga�*oli)  on� �2metersV,��,�_Y7�5��+,� �%�%exz\ diffI,ty �6eltYv"�+{U>� . No4at,��!�pU%.�,�]�1 S~$ �1^2M 2^2$8s��e�)r� � T:U>�)�O&�O&12:16E? a�#�*%7"F&.j@&Ɔ$&I��2r#��m�1}�6"t#i2� *&�64+ � + 34�^ 4} U:.& }{Y�E96����#8 *3#1#�" -�4�"�".|�"���9E �2��/^2�Z 4�>32 �5A�E �+�: g�#�--�څ�^2HH401ITE`E~Q# �96�U�:now�+�a���!knowna{a� $ �� ".�"�:StTel� (�inq3# quada�ck($p_1,p_2$).* ^"��arabolic.,7J�aX� Q-,\E 2=-4�, s �3)�s_1 r�%s_2 r_2�O-s�/ p_2=�% , ($�,&�!:y!^\!��d��$*-,s_2)$ G=%M�"[�!>�0�� g�8"�$! )��>s^6a�1 s71 s �p0�/�m�"�Mve�bAM2�*-��A>}���ssiveXR�:sV8yield a"G&J�F0 �:\�+% 2a��b!A�.%Civb, �:a�AX6�, �ha #��*j,%D,�} a pathIseg�"�1�ei�tZ[ s orf�s, d�M#5�ian�V�3� �~ "O5n�3 �!J�yD�5K.�2"�8q�s�6J�#8�/!�s.&+'&�$ �Ff con[0s n-_--"%�0}) n*(6 I?K#is)�� erRly�optim�/ne�. reac1�:6�. N�'theles [&1� �)� v� nesE#dg.lf%w%� � icit �rofIb $s fromRp*=t"asix piec$�>&4M�V�=4a}a�6������@1}{5} ( 2 R - 6 Si �?�&�� ,4 ,-3,4:,RM R= W_1' -�S=-W_2'O�  W2VA8 Q� "f Q_�4Q_2� K_3}�"T68 r8L68 K_3="�D'�A�j�4F,\_4�q2!9�(F'-2 F^2 -G=j& V F,G=��' w, }qh�@_Au_cKdVa| biSKaWN-U=L7� &|1� }{30� ,\ V�<+5��F9��1� �1}{10^k.30,1� ^ �_Six_i,B�wY; $yPi�4ODE�#"5� � e�. !"fifthX�1nJ�) C5� � �!r� *,(u,v,f,g)(x,0)=(U,V,F,G)(x�/1:)$�he��% *m%�%�3� -��8g ,\"M9%� 0f<R���CD -` + g"Bk<FJ� ����F<:�afKa�6X_ZdG=-e� X_1&3I�$54 U'}{X_194 54 R1U1!3u}{2uF G�WdQ 2�)aF9F1FVW=X� +108 ��3%�RV�Z�-X_1=VEUe�= Ra�2�"M 27}�B�X_2= 9-:�B {U'}�1-8! U V �i8}{25�Q�"��Z5/ V48 � U�2�B�%).2N45P �)�4 � ^2 Um9�� +� )�9s5�836:�E2!F12q3 �LF�E�:���A�6�%n�^R> ��I2�I"�I{Conclu�/8& openL blem��Open_pr�$esG��F@twofold&KA&#G\i�?(s�9 � B is��i)Lto�'"�?6� �� "�%� B*�). �S,(� .�u,be�3ped �>|;'$is complet�'t.6( sense, it(imposs�d�"y termb�p��G�$out destro�/�R�(b- �4H\'enon-Heiles.Q)��<��)A�=�Nm�<2� to �;�� � �bqre�� the %�ic��B)���:�U� *{Ac�led�} � authors a�financi� upporD %elTournesol grant no.~T2003.09"�5Belgiume=$France. Oud6,anks also go!3!� refe!who helAWus�im6 %y>%*� Rpn �$�thebibliography}{99} \small \biba�{AF�>(} S.~Abenda�4Yu.~Fedorov, OI�(weak KowaleD?-J��6�DI: ble i�ls, Acta Appl.~Math.~{\bf 60}�O000) 137--178..�P1�50 A.~Ankiewicz�C.~Pask,E�Q� Whit�H!�eorem� two-dimen� al �>�x ��M�>O3 ?0, J.~Phys.~A ��:�() 4203--4206�rnoldMe�L$ics} V.I.~'d,"v@(Les m\'etho�.math\'eVM$ques de la!can* l} (Nauka, Moscou, 1974) (Mir265�,BV1990} O.~Bon-D-M.~VYK et, .�struc�(s*Lax"�#s, )Lett.~B)237} (g ) 411-416.�*�Ey, S�d eigenP+ reenEJX=�hierarc5�D �9, Univ ty��Leeds, �56p*�< V.~Z.~Enol'skii�0A.~P.~Fordy, �ble�� potential)).�*%�AG)1MM201)15) 16E�422XO8} M.~B{\l}aszak�'I�@rel/=TNew,�Jq�)�e3��O�93a�092��9T} T.~Bountis, H.~Segur|FApvaldi2N2{�G)O�WJuQ�Revu�� a�2) 125!P266Q ureauMII}�J.~ , Dif��%�9� fixed ,� point��,nnali di Mate� ca p�(�&�M cataiLX�. (196!8--16CTW} C0Q Y.~F.,!� Tabo)1J.~Weistaly�Hq�A�!"B\-Qei��A��.regimaKN�23E�!U531--532�Chazyae}�, Sur )\'UP p \'er!felLdu troisi\`eme ordre+d' sup1@ieur dont l'int\'_1 le g ! a ses-�)��I!�!9�y�s34�,11) 317--385.�(Cargese1996 e} R.~ �m]�approaB(o nonlinear�inO � �a]Y, {\it��.Kpr}2,32entury a�r}, 7A�80, ed.~�$CRM Series!��M�l a�ics (S|0g�=New York�5P99). Solv-int/97100202FP1993�. AHickering�~=3urbativ2�V&^ �a Di>69%� 93) 33--56�MVA��G4.�$M.~Musette�C.~Verho� , Co� .�BCuA9� \'eo%lasymptotIfet6�.�}!�4s.~E.~Delabaer �M.~Lodaa.��inairesLcongr\`e!�MF, Par�F200�� % Pr<ings, �, a� June(42�M:^"Y���&c�W%Rḁ�r8�$FT� J`( } submitg( � % ?* :V,��Mj&L�H�` , A��s�Y" ori ��i�I�,J�.�"`J C.~M�_sJ, Hig�0o[�k�K z polynom�[c�I, I. ��$ symbol $PS#Stud.~By 10� )A?66 �c}��2�J�K(http://www. \s.usyd.edu.au:8000/res/N�`/Cos/�T-6.html 113 pages, pre��ta 0--6> SydneyEZ02 ,Drach1919KdV�����y!��$a� ua�� -4/ $\D�'/ \D W\= �4 k\va�N(x�#Hh\rbrack y,$ \CRAS\I:�)/19����42��21\ ,~G.~Drinfel'jd� V.~Sokol� E �C 0Korteweg-de V��23e�si� Lie Al�& s, Soviet�V.~Dokl�  1) 4h 462.��4��p'� 1Cj�, Itogi  0i i Tekhniki,� 4ya Sovremennye�,�y��ki e��T- 4) 8� 80 [Eng�9: J$fMiet��;3�198� $975--2036].Ermakov%P.~  , \'9����2 deux. �NndiAus dY� bili  s�(forme�le&#Liv.~Izv.~Kiev (1880)!(.~3, No.~9,a�25.��n�^H!8A.~O.~Harin, 29i^2� 1991}-&" �:� X)sited� 1 ��5�LL ) 204--212�FG1980a2iE�J.~Gibbo�Sd_09� &� 6�8V� 7� !)325--3!&?FK�F�P.�KuA7, �� Schr\"o�er]��}kQ��munQg ml8�8r7--443.jGambi�He} B.~ ��es6�ifFt�=t du�E0mier degr\'e ~~ �D\`a�� U 1�y52yGDR)l�r�Kticos,Dorizz"�Raman*Ga�*M� #-%���e.E &��M �e��3,3) 2289--2292�HH�M�mC.~�: &�� ��l�#X: sA�^|�<er��2n.��' 64) 73--72��84�� Hieta�ta, C6Z 6us�� ntum� �Z m1�8� 186�s7BsD�Rm���%search�!M�"(�/.~Repm14k87) 8 52� �9%�Jimbo%�T.~Miwa���<�p infinite ..�H, Publ.~RIMS, Kyoto��y�94 001.� Kaup��} D%�"Win!re scatt? � ��%f ]#�!#�  $ \psi"P6 Q )e 6 R ~IU $,^ 6���1E�6�KitaevP2�V�_, Caustkin 1+1U?le��ZQ*N293��96� Lax}�dD.~Lax"0l%��25evolu�1%�s!��wav Comm.~P�=B 2�68) 4�492�M"'EVf4 On CKP{BKP�st�Ne2�VJ .��=oN1 1u 2003) 156�572"(Pinney} E.~ M=>�B� $ y''� py+ c/y^3 r<$ �.~Ame�Socq�� 50) 6b 682RD��IK��>�: * conje�>V�'v.i�4m�539--1546�GC� $Ravoson, L�Gvrilov%�oaboz, S$'�pairse�����V@��238E 392��L� �A.-)y>Ge&�{��Da.�non '&���sLArs �1� � 4) 91--6�SELeSalernoVND.�:Leyki�"�6� "�<*�R]��Z E��-�� 5897492@ŝSatsumR.~Hi�b�N��#�)ѮO-reSCKP"��A �eJapanI�5i%A�$3390--3397.FSK� } K.~Sawa�T.~Koter��L��N-���C� �2�:K.d.V.~�3AL  -lik h�, \PTP� �7��355--1366�klyanin�C�k� q6��of &H--� trends --tSu$e�118�H%35--62�$Staeckel18�P.~"\0 �,e�� mcDynam�,6~�8a�4a� 487.��Nqui se ; dui� ��06fv$1284--1286. �6��1\*� �~%�:;��,their associQ7Qe_D($sis, Vrije&f@eit Brussel (May ň2�MCPi6�>x�aont���a2):��Vd4g �8) 1906--1915. �$.SI/0112032Q �4a��O�m�%l� KdV-!f1�=n�.V�6�12},"=Big��k s - *)E�� tog� ,�7 tinu4$to discret��Dvan Moerbeke (Kluw6Do� cht,!� 4). 5A405032| Woj19l S.~:�2= of a2�.T:� �.�"�10� 4) 2$26> �5�:�Mk�'of���8le� a�e!:l!K�", ��Scrip�3�� 5) 4 47�#>�!+3 last�(} \vfill \e�)& docu�1} D � \%�{�l�l���� \u�4ckage{amsmath}> font8$d\setcounter{MaxMatrixCols}0*| %TCIDATA{OutputFilter=LATEX.DLL!Vv 4on=5.00.0.2570�0Cre�� =Fri! July 02i 15:01@LastRevised=Satur7 September<$6 23:10:17<.�G5$ics��322�.2DM�Shell3PStandard LaTeX\Blank o. AaLle2^ Language=V i�'��$CSTFile=40 ` M�,.cst} \newtbeman$}{sem}2a&-&e^[ 7]*e& 67lgorithm.16+xio2'2#��ICas�� clai.DC6D"�).J>-dT6, >+��ur2�"~ >-rollary2X6Xri�o2�2+`J>�DuJ 2-exampl.�E :'ercis6( 2)lemma�L2#n�n&N2)p[+(P >'pos �Y�Pr2/�*�f2% 'S :)umm6�S Penvirona,�@of}[1][Proof]{\no�u�*\bf{#1.} }{\ \rule{0.5em} �>put{tci� xa��(��(title{On $\��Lcal{A}_{n-1}^{(1)},$BNC}% _{RD^4h23�;.gAN2 � ��U+� 2)}$�)l�gonn-�ice�-�* {R. Malar� A. Lima-Ske s \tn*{{\foot�g\size E-mail addresses: mC8@df.ufscar.br ([), dals:A. l).}} �G EndAName %� it{U\'dade Fedg&U S\~{a}o�tl�D#taA#o F\'{\i}# , }q/+�it{Caixa Postal 676, CEP 13565-905 >ZBrazilA:P]{} \makeE"��7 abstract}�zD(�  �h� the mostc %�Bq-�S�,b3;E Yang-Baxt2�b(vertex mode(&R �-p%-excep� al af3O2h. RG ed>a�S�]a limit�ced�6P=�;� � d. We�,= lis- diago�$K$-m ces. Spe8-��.b ider�!�atelyk9zW `TLz�9���-�%�c9g�/N^ �9(x1,Fa2,KI,Aa�+�E t� R}_{�u u-v)�4 3}(u623}(v)='�' _{J<d�4R+{YBqA� �% has c�>fu�Eaccomp5y0hroug�;qu�  group.r]&%@% {Dri1,Ne8,Alt1}rUduc�A�p�MAaf�&ne.m#��R}$% 5� cor�UfNo o vector G!e���all7.� J� w�$d�FmR�"is way � {Jim1}. IE# study�7��-A21+f�?� '�(s��al phy',"Vb(zZ!�)!?yeM! �V*ro"�Y%-h't�(&E�a��1a�=. 9a pionee2' paper�Lmiddle�emies, C�9 dnik-;(Ch1} sugges%%wr2ge%�Jfa!�,s&l%.y to *C��0Űng ��cA$a�s @�KrveEqIpbet� framework��Q�E�Gn� o�11�J$��oset]by hOI\ Sk1}hxA�a>FyQto buildm)�l���!¡�yzR,is developeda�)5��I��!#� EY[3/&they mu�ul�in ��)1"�}$Pa�0symmetry, $T$uni�t�crAng.�E�ped�Y�fe>�25�N�s�vr� ��s%���O }^{-:���1}(u+v#2 #v) i 6�2.FQ% ��Q-v��Ba�Y�}%��ނ&&Bo-��8( �+}\� ) ^{t_{1}�M ^{-1}%�٠�(-u-v-2\rho )Q�:Q2}Ū \o g� &&�2�J�| "�O!I:� �2J �+v�<� dual2\-E% extend��o�i"�s��fBl8 tricE,�u�<$PT.�a�Mez�7 scu � Nepomechi���Ne�42} . ,l6r�Bist�8f�e0seful isXvsm: giv~}"� $KM�K>�G�)�n��ity]Uu��} K^{+A"�O J]B}AM,0 { \}M\�� U^{t}U=M, -�I�F�satisf�& �5�),  @t_{i}$D[s����!�$i$th (space, $�/t#�ySD�N%�$UB" �'x, �{ m be!�s� fic���9ţ-�4Baz2,Baz1}. Q8 Z�-9;# odic��U\s�l�lI�empha�d h!q�`(k!'�� rh�Jflj$R}m�0� enjoNisN+Ac . For hS0r�J� Eb analogu"� 5d9X��F71��^in� oj@�ion.\ �+wA8earlier,)9on"�$A�� BN a�lT!\6A: r��c@ eriv.oeNe5}. @a�5pra�%7��gr�pQ� �0F UhQ�5a�h� gh>1xToda ���>2I�4BCD}. An immed�1>��be�t2k@ .i@b{al �!B\NubyA�lw@2�2� Accos�g�$Baseilhac,l�?1���A�B�B�9�>f]�24 M�xA��=F� �7"= � 1��AQulX~+�BpaE���� ertwin��yinvolvg�����J� . FuTMa->-� $  1 broad�Wli6IM��aof�1>A!��[BB"�6$c behavior � e�transfer�>rixE��n��� Dk1}%��XXZep�Ca' .pDk2 .cspin ch�*.!�$sl(n)$ V^� loa�!���6\se�* tur&u�be] ݌s��a (in),^ofNhi)i� a�$+i! I� iB �7ll�%�.Ba2}, �tA7 �&��Bth� V%�su� "�. Alth?regarb E>�)�Y4X,�p+U�q N�7 5 & �Klo�1%�Cy�:\by mea q< �Au�onɛi)yC we aA��ÁK4onentuߩ;V/\d�A(n)R"i "�-% Q6I*fq`$$(n\geq 2)� Ch2,VGV},�ia� �%)i^{\p�> }63 )A+ak .2j,jn4jj4346>`6�x4D>�D�%�su!�,j}a_{iJ��.�,�1B(n),CDz��A�(Boltzmann w $s��aA�Pa|)Ql�S(�ctral &v$up�b.�M& %�(u)f4}e\xi )��\ @!!� (u)=.J11ZC.�a_{�'�yF�{!�4w>LR>gij/he�\{ �LarѤ {c} i�R��>�1) �1  . }(i=Q�]J), \\ BLZ�+(!j��mat��%�+� u=Fq@(�H epsi-T 6j}q$q^{\bar{\in}- j}}(�� 1)-\deltaL.'>QW):U%C}(ij)�=*IX%y\.��6m�f�g� \8.� �� -�H/D^� m z� $��#�C� n+1,n+2a�rO 2O��1��2H�V6�.[&��2 <(\substack{ G2} avim� or }6�}%�6=B�Ѭ.nN� p,Rf>�X��.XN�.X 1q%*>VF*5J* n+2��ҍ7J��b � }i}�$9�'A 8J����N��aa- .�.�>� % [b�['2N�Z%^> 2bji})+ ]-:�>] SoFI]:%��u [c��6W Y�  }}+c9(F. i}+dH;R8EGdHZ..]2 &&ՆD(n+1rH t:*0F� �c 2"� 2� �i 6:j I.�  Zo 6=�"� a_v �R�2u� >o5"v fr�2�u}+1)�Jp6Apn@6�N:�7K�fM-r�8Br�  -60,Iz�B�^�-� � �� 2�2{n� � 1�nX >� � A�R~ >| �- r}�B�U�:2 �v. 2u}F � B� .���1.}(v ���ݭ� \pm ��&q^{i-1/2�2AxJ�2u}8!;=6r�| �&� rn-5zt.Eu6��:� 10!:n+2jN 5<cA+=8pmwi�!�- xi +1f��mp :Q�21^M&2gA9 \xi A�6d��a�2Hd �pmj���Jo��� "wN/$ *�;� �#;0$q*t,^{-2\eta }$ r��! arbit[~&��� NHcrifDO�. By�ve�-�;�c� i$, �range d,$�� ...,%(bb{N}$�͠ 6^�*�/:%( =n,2� 2 +2�)&��^]2*>� ��C^�%}�>�=B�N H*���U9���%$"+  })�% +1-i\�� j}O!Delei<%C%�% (� )_{ab}=&�a} jb}F, We f (let $*a��8}=1 $ $(1\leq in)!�=-1n+.26'A[��6�>"�)va2�=1$��+� cases. HA�we�$�B=k!l, +2 ?�o!i n�+b@>%E�r#% %В%NZ#]EU.%F)��$�2*�$)!t:�u�} ..�3Rr��e ���}:� i+1/.3}F%�6^���Z"w ��96.�$��&@7��+1b���r�n+32��~ #i-�X�Nz� �:0,a^*-R�"B�m�<� Eˍ�q-�X-\RwZJO 2N}��>0<��~X�,� b`C)F�Re:U$��JN6�*�*>#a�$KK8��x��Z��7��,j=!9� }k_{(u)�%"[K bF]&�7�.'i(J6]0)�M,j}"%�\ }�,2:.��RegF�Situ�580})A��� R�/��0% %�*�), :�."Z?iq2 into �,,��g�+ e^{4��u FL -���s $1Su�"B-�� manyF, a fewMgm�"�4�F�t�5�cP�olvg m $w�Mp�e i: s. F��yco!%i&�,$(i,j)$ }^1x".!2 . By&�(i�}it7�Aec�.$v� �$a� $v=00 e,�3icj�A%A�:1le"�S hnN'-�2}$&� R>|,j}��d1�@v)}{dv}\mid _{v=0n���x&_ Para}:F�N�"wTnˆi/Y:,by $E[i,j]=0%/ c�+� ]0o blocks $% B*� i=12�I0 !j=i,i+6J}\ \i[bb{I}% " J}=nY��A� �} I~:� �6ūN4O� ^B55J�2ni)+1>�.� A�"�%7 �]=2O&)lJ.� � X�).� 0-1�-�e�HL\"Je )j� Q6v�M�}�E[j,i]=�D%�E�!� *� A��EF0jF0�.z BE�FKa8a�$ 1w�qVaRr��2��$�.b���*r �.Qq��6xus gingJ��V.E#arrow k_�0-i,n+1-BS��� ,jB: 2?��"6&�� >~D .�#j+r�eFi6�a�}�M*�#�� �!- 8= &�2�#:��z�K%2�>  �} m >�%J�'3)�6�:3N%�6�y�Z6>��6Z317>1���.�N-�>� �̙�M,"�"q)}1�>a����f 6o!4~� 6�uNc �h tfXVl ,� �1G����H&D5��"4 )i<�j,i>ez0 :��$\#75n ]Q *ʝ�>TVW% �W�:���:7a�V��r,}�"RYbRVc9.=F�*� Bazhanov�*&�D�&�R% .< ��Acra+j�, �6� Ija+�-CG-�5N �Z P�N2'HIkI)B#�F *% _Hu2[O�OIt+(0����PT�F�wp>{e�!@ permW:� E� f*Ae &KnncJ��H �rm{\zaw�kUn�Kv�2=�s�C�t scalar!��)$u�L 5 r!y�K55�6 0yi�.|)�(0)\sim9�P%� 12}$�N">:A� all G9Q>,$(n>2�!�.P20E�"!HQ�. Thus�;2�<th�A8�J�J�=(U &bf{1}Y�-E�WK-ujI )R7K�PCQM-UMF�holds� !��IJ+!�� UK*�.�}�J(.Yy))/2�@�!�y�.�  a�.�_�b.!�"� / &z%|0H"�u&b�Q2:&:gJr��a�0z2N rho j� .� \ln �6z&� n ~8\^b� �^z!�e-5V)o}� i->j69���^�ņ�AGbbm2F(��unorma�~!�Bo>�.�J�R $\sqrt{!�V+�"f">�2�.QGE�!@A�yB�U�&^ A� q^<)_ ~2uIhU�H.Wc<@U�#N$+9opp\e&49is"� � .@YQ$��D��&�Hw2/N��$MŎa&X ��D&�KN�!% M=U�N U$, j�M��*3R"1i,j��2n+2-2.���e+2uҥ %\:VJ`J�1��� ��_.�, )0J�3��+2�2,14>66�~=M��c�\�0U }^8�r�Qe�q&� 2�.�2�$#n�a7w(Jk��� ��L�a�E�b2[<-FateevP� Fa�eo��F-1:�C� }��h)MM�A$M�ͥC �hil.�Y�C&�J�<8 Izergin-Korepi�=*7IK}{ $M=$h:$e^( �9��r},1�� �"f6� �-64(-i\pi $% . 2�,.{S � Ne3}&M���9�!�^qC�E"C |N�:V3 ,#tr0eL�al�:l sametZa�Sot;KEZ�de�W no assump}!‘� � !v$necessary.6K$ReshetikhiIm S"8ov-Tian-ShanskySO ReSh&uTa�Z�ss�C�?N��#B��A�>� u))�\} �  �  }O.� +%�)}>% (u+2 �%f x MBo 0F/ Mg & R� ^6!04P"? !�!�Ya"t x�g 7U=M�� }�)P(u),M�]=0&X��B�axt�i��)�'���e���I�s�U���B��Uf�% 2�Ui�. W��D��!?��s5��% )]�),2k(F veri�aN��� (r�V"j Aut"�F!�n�$@e �&�:e��tBY �]��U2$, but j�[replacoe�I6 ioW}!pwe��� 9n���X�\X]A�c�s quen��.=r�BJ.4. �%�TJO"z "�7` 2FvJ n] ���M!!FU "}>�t ofz>#C! challe�(��Y�:G-��nAent�set of*t?�@"ZDYR�c)r�YeK2.1T~"?a"�S�wL�?��&- .�UA goalE���`��ur${by��loo�!�.�A!L��on��n-null"> �(OBghDVr� as5j"�@R@ubU@>@.M67LM M} .�z�!Ă��).Z%V�L*���reC�FH.jvery {(�Os�Furc�Or@Hv�f&L"�&�Q%U1�c ;e# 5].d"�!5�!��p�sx�st�� s. L�`s!u>"v�,COinƅRweױ{Q��s�i]que�Z�"D�� �`Fgin*� .�k_���!�F,T=:O \for?�% -�K�gen&�1��%�B rebye %sn�t��$ 'n(n-1)}j"Z{% 7< $�GOchoosR�quk>�e � !)jma=T ���erm�&`�-H� %�,Ň�ioZ( �0i* V�Fd !�6�k_{p,q)�R %��>)Z� (u)} �4} 1�I}AF Iif }p>�(! }q>j��U� � .c% >e�"�} �i)�bI':�",qxj~�- 3F[It�)� at�A".�<e�1y��N a�eBhe�` �!AbaWj$t�8lum� w � re oiA��$�%'�$�� U  /fte�`al��mScar^�'$�G��"p x�s:�6  $%iQMH�Nassig�$�a��6;�ACocesL*b��fer&� "�  ype $IA�=��% each.-�,"3Val�B�!�wKir6�K-���.19�6�Iy.�}&ё�"�"(u)e�e=k_{r,s s,r 6%�}i+j=r+s�f }nB�4R��+�M��~,n>s"�Quxwof %ۙ�2,G˅ pa�of $n�Bm�ki�le�G��N, nam� a�1Md!6= .n!�jk_{2,n!&GIGd"�*:�.r>��jaI�)% BlGFK�,e -.��~ �erN!�maN�E�E��u�%sX2V�u�x)�� Z?q.� turn &*\A�lA�B6�F!� FI$:]��%}11�I�L��b� � {cccE�11} &"�k!z20W!�!  0 & k_{33�F ):���3!��4z�i%�bf ���\ �:���4 f�.�'^�2 ��>�;j)- �S �̐�f�&*f�B>5�>-�� se6F��ex�/� o�(ARtI�i��� w y! �Qj� 7r�. e"F(!>.}O�cA�y\{.�a�M��e%H1�M6F4EN%R�2J2223 \� ��:�Z�R��,#:�N�I$ \{6l ��2� �I}�&� ��z�~�a�A�A�eI m�A�i`M��m� 4�*%44�"k�%r1}�}34 43�"�>R+r�.��Fm�1�~� �2�.�5 k_{4%-Y�� � �23�3�^.�- gen6F�� $n\geq 5$�iY%�NJ� N�$�$% 6� 6) �>�Vk6NNO�b� �7&:LAb dK:��$"$F� B�&, Z��2]�$2nJK�l �}one�]ve5-2N� *c!� bHoӉn6:��tEx��F�?>st�5% to i�l�%Y)�y 7one a�ʁ�dtwe5se� u bb{ZC}$il �e#� � ��� [x���ED8s.�P� (\al6�)}=h_{ }K^{(0)}h�6I } ��a8n-1� �7u t%�#$n�=n�"C J�(B)n*!',j+ � 'moR� k/ !�!R}%�X�4! $��)�A���5A/�A=� 6�67})� #?�9���iesb7IN=����p$�ō۷M�*Ae I$ (:�"� ( u�&� % ). Ho��du<�!�%" &JBA��ɱJj7� T%:LY�IalO_tra��6t46���k"�b�g8�itB�"�smbc�y�� a�*��a gauge:�a�%,%k�{��is��=N pSqnce%� !�� :,�`cl�%�uIfa";).R�i,�B%�� !�N/$� �g:�a)�� �ao!t� �[, ��le��w5�5�der��A` oint��J;.pq�[ En$& �A�=�B&u:�53�aW>:� %O��x. 8a ��%�w�d�#Li1Af1^,�6ͱ�F�2�*� !>� �&R2�$(3  $n)$[ te�u13�/�� ���n��V�'�L.q&+12* o6j.� E!~}��~a%6�A� �!\V% X �; e:�6� y$wn�����:��$.�?n��j)�By �:�?�9I�mZN�eX can easildn�^: m@���!"�HV, �!  �as.`. Morea��ir��istenc.�s� s1^�e b��Fav���llJ�R. a�41�out los��gejg1�a�F�vEe+�C.0(\mathrmL{e}^{2u}-1),\text{ \��}i�will be written explicitly in SecA* 6. \sub {T�.�of �$$I$} Here!have $)�n(n-1)!�$ refl J6xwith $n+2$ non-null elements. F!�,1�A�X}% _{A�(u-^j�55L:�a new I� Q�]�X}lH$ appears, given byn':=U�)�f%T!���2��$correspond!FR���� Fq �f�116�)�Au@�F�8F�A`)�I 9�}<$ yields a third%��V�sMOs��j+RN � e�en � e�-2J�9F�$From (\ref" 2})� 65})�ca� e� each $ x $���6�has two>�(s. It means NallA8sefL&� A:$3$-pari� g_ �-!� the *� q^ �BYBE})"� 9�> @models. Finally,! observ- A��  ��$j=n$, i.e.]���I161,n��nn� A��n>� h_{n��na7� {j�n"� :� 2&� �% %�he}j��e� ���22y�a�2M� _.�)>�J | it��jus� 5�� v�. AbadE�8Rios \cite{Ab1}�R S Due�! propertyMq�4iL��found th��B� �ype $II$E�esz�:=u-� �TL}II  {\smaua}O \{Ua� 1,2pA� I}\}2� VF b}}=JC� FE E% ��cFG2i�.� �� N}p �\left[ w n� \right] :H2j: bD��!�integer�t�qBq4$. It turns o�at��1�Z�I$ 2� parityf�Plea�Z �bclassCQ�s �}Aʡ0 graph{Oddi} � o ,�=.�1�a}�~B ��QH!�9 � jGp� �E�V� U j=IQf�+�M|nF+� ojj>I��8rE= F%% Q� +p+1j�B�A�( )�ptack{ i+j=1+2p \\ i\neq j}}+b(q}�� }n67�%�� �) >A,>�&��|% e�a.cJ� N�� r,s�"s,rEA� _JS �]%21Q J%R" :a%[N8 7W^V.�-2U "Nr+sa!���-vB� 2&85C� v�b} tak�e�*mNX��ౝ��m�a3b@)wejf���}�� ��E_,+�ZA2aA �A(2�^?puM�JA.�&&B�N�|aP&��Z.Z��)&m�.# 9F- R�B"F�&�U�"d �bюc6�~�"LA�u�28 1}+fi ]�A�% E6N +6�� J-B�R�g^tw:�2j���&�5{2!xNP��N`M&r�!V)22Z�2�36�FE&�ʡ0J 5�� "�6�3}=Ds*u BZ�UOV6�A^gZ�4 �6�6}), W�ve�hil��"�$��$, 2E� �Y$ IZ�1}). TEfore,�V( *� $n$.g.�,EKist of $eE( 2��NN ) v��$2,� �"� *� Ev�n� Whether� even�� �e"w�oO �z5�i�� ?m �� .7^u�h �h jh &�u�E^���L"]��� p,1}"�>�2 w}%��{ 2�B�3&5 ���� .�� �>E2)�I"(�ك�6' � Y� :N3 =  2u��U��3 ]\% U�6�:A :��:,:}+pB��63n\j��6� VO (�O JO 3&�-��^�A+N"���� 2�=*� 6�F��._ � 8 % 2}u  2y Zf !�z�J� Agai�.���"�*y � ��z 92C i�_2.a�(2�E:,%.w +FXB�8}��2QB �6� 6F&�� � 2$3nI�� V� �� ��6�nm�22A�&�9�% B6"d � FFJL&� >�*� &* ,� lIb< $_:� �a���r� 3>� % #j� .� � by� � � we .� �$ $(2�: )vg of B�a}"~ &�#>| ,N:{ % (1�}N|s�}b} ] % IIc}, both*N $2j$f�& >2%� �_B &� ,$=�C^D% ^Y2N2)N�k �&2�&Mx% } �ub�%(Non-diagonaBy} Lookq into�*����s .�� : �!X �!Y� rnot� P' simplest"�al �svuo7',those involv! only41 "�& $k $^{\prime }i�&!$secondary 5}� K^{-(, belongc-z@blocks $B[1,2n+3]�Q 4n+5 6n+7 ...$i:we cho�to ex�s!�ir]�i:�)� �1,E�bb{N}% �m��."}/0$:*�� N>( Ri,.;}j % }}"k_.%m&5 B(n),A(2+F��)look I last1t�h�l"�(\{!{j]\}$. �( can X)A]eM1JL+T�) row A#)%�Mj%9� }% )"��)�� th!�transp!� in t.�+.�9��$. � �F c:A�)�ib�I� �%A2�+u�$ �2]f-1��M�ed2�!92� g E�-�>� �:.6,�. Applyen"-procedur"����{B[au�E ay m~weo+succe �Ag0mu�>9R7-e@�,l $a_{1}1}-a_D'$2}}{% a_{341� 2"2221yJYf �#j"F_ _{j��2�a��" ]�J�R�a�&�.}% (j<�? � 2�&� �w%\ *� �N�N1��N�N>.N, �2O&? -89we�ua�w 691y�J identitieN?I.}=afV]\��.0A�E�j1BU�23}�e.^+2�&� � Ta&�accou�/,Boltzmann we !�P"�) % `C�{ D(n) ,� we � titu�+se��u1���/�+"?2��� urn our a�/�/=��� /!�d entri� �H�.$ aim��to�) som2*��9(�� )$% �/exa@ , f'!�p�?,$B[i,i]$ one�$ se�"�i*�)�solH$J&�rel�-~�'k_�)(u&Y2�)�9V�&-� % provideT$an%!~"�-u| }�, }}Z�&� � �3٬(is carried !�$to a large*�+&� "� 2��+. Aft�#erformA E�� w3=2- $"�!� 6�$"4 � a[ abop(eJ[N� 5�,j}� \{"� ^2({c} \pm \th�4}��@1}{\sqrt{\xi }}q^d�0ar{\i��  �: )+j-� ��Y 6{2�!]}j>) bb{L},�"6�j��j �j}�� })+i�� ��3� L}� �6)L�Z &pm ё$=}0=q\varepsilon^6}�'&%.wK =�}�5�q}B>b�A�"� $� _�=1>� D}_{�1��N"�P�� $%�=n+BR>�MB1P$=n>�.2�D�Z�_{F�$.���ܹ�k4ify significany6��$�A$.� >&Jr6r-2�3}5b:�8�n� !�#0a�!EG�a� V��2 \�2� m�e� }}� 6 q}�u}}.Z{q .\�))ii~� }(j=|),�#2�:��  9 }(6��&� BV��u6by asE�Tng a suitable normalizg��& .�U$., ~&56�F-�2N>�pm6�~�1�JM "�32&�� We�� *A searcha�*� �nr3EAg2�;FZV�=0Z� N�<wQ! $O=�kM k}(\".e�})om9ku��"c"E)��!RCequiv 0�*for�k$,� be� .i���$*�(. Of course2>�Aw�F= �;&�,� �=)es.� � � ttempt� t<clu� �\ G"� 12�Q�3�<#a�!��}#221}eh�� most$7ropriatI)�pur�.R] !Tu6*% :��2�$�-O � C a�a�remj F�.e $�  j)�n>\tau�MeF�>e��h��%�, $=2 ]%jd6B�"$:�dJ� .4F�^��Az=>> Ƀ1�120^m :� 8� *� - 1}� ](����$)% }{(q+1)b(vi�!~6� �~})�2fZN@V<k_*TF:@%�i6%'\6*�-%� A2E 2!q�.%�2K (%I2}n1R)-A� }�9=x�[^�Z� *<>�b% I:f"��6a�" column��&��E�a�Z' 2g;�!!~E&91j�f� "2�^ 13}�?7 rs:i �21-�66�:2-1%�%�22}��^ �.1b�&�-MJ )-�-�=��E��� H)"]��&=&�^/6�q^e&Q�!>*Vj��u F�"V$1��*51�je�O�m�J�j� =�% %��%�u�aǢ�-&� ���Y��b�6"-�U'"�2� >� u�V?e5�nl CZPa�).9N.�mQ�\�3%��_j�.K.XŒ2S {q+1� %SFi2�)�F�� �� ���0^IT2G�uB�.��B~aR��2h.%�H��N>?T>V4> �-2'/"��Y��?l , j<�G5P- Our n�G taskfto= ider�� y!V�'Ap� �>D>��' �R Fp� 2�* (. By virtue�edC. ct featur�8t%R�s,��"}��,/onj � irect� p �&�H!)�&� B~?2  se��w�eFCfFjJ6� a�#&#.�&� -h%g!�AS� ^�}�:should, po�:� al6 l.~"hNId"bb%��K�A��" cont@ secutive&�"w�OI!�5�&���� ��+1,�He�FR��d+&� :"�a}~� ��A^}(1Pin�W��f� ���}(n+2< n 2n+1 q��1J�E��A�K"5=���n+1,n;�k�?n!�9m#5mn,n2m67-U�JA���,V219} n+2,n+I!��.� '� &I!��Ib� 2-*&�F��2&10-F� 6�J6�>�6g�)�)"�s"eR�!Za(&�n"C !�6Ap}���n}.$e�L%�2�n&O-x-1)���6DV20a"1 �^k!�6F=Af ˪�%  q�I��.� 1% �A��=fZ�N,C6�E�i��^-�}�%.�6�M���2�M�'�`| ,y�u�18MF�:: �}2sZ$22�$A���$ ���v���y�6�^�*�ő� ��2E�cUPU�6� &�>&&�^}^�6A 8�%�% n+2� ١^�BN�0important fac�E�* recurrent٧� clo $4L"�Rw a�*"2�34n+2]&n(is m-�another m9ion�A��� � N�k� +%>{MJU.�-2a�9���g6��iF�:W Fp^�J�"�$$i=�� toR4})M comEng +�$#+2*�J find%ri�k!d v Gany addi|$al"K.)�� Fa�2D26D-"2 !��.�>7Qu��}�-��U~�-�z%�!�6O&_76uNk� �S-q2���!�I�.�-2J$џh466�u�4!�6fV F.@i�#"z  w �I�^$n>1$pLx&*�Ga�ca4G.� �� Ͳ�= �  �=rul  �+ �G&�9xb"�WV+&�V Indeed[sPs&�&%$-OfO_"$&< A&��"� io)R!q�2n��1s!(-�n�j �m� �ldsum\limits_{j=0}^{i-2}(-q)^�%� �� 1p .��Z}6& }(1�W�M-L �] B�2? , V�n-3�����.�)�j� �6m  2 �H2B#28Ac=s�:sW� -3/2�6 )�p q�["*Vxi �)\2C\%6�i2�>j�i�M.�(q�]��(1hq+!�q6�)[)�F��ɂ� :\"b I~Z�&�$t � [.O(�U|&�`��V&9&N2�302�A�mA+�+o~2-jS6�(}j=2,3�`-^ANUAL7R �^�0.! 1x Qk��=��u�a�i�"m/�>2A�-&6l+  12}}}(q^�*-a�)��~�1}A�J�4*^A �E�j lX6�Z�q�+�a�[ !0u a�:|-UE�]E��HExi��>�q��+2!U ���l"�> $ �3�s)-�\A��=�V 3J�4Hea � " �$�z�>) A�> a� * � woJS�lexN jugateJ e6Q dR d, w�0_c�]*t "�'�6?K<%i�@1n1+,Nevertheless� *{2�}�.C o be� 1$ becausKdst�dn:9 to m�Q�( regul�Uh(&X % {K�Z xReg� For&�4`= he arbitr\2� V�. ��fBof%�~ �� �g6�&|.�� ���=xa)[�A#� . Let� summarize�� : F�%�L�7d�5JD/11}) VD 17})� 2I:�.�ondk�Mb�]ob�ed�usDJ��C�_]2G2dNN7��2���" N26E.*�\��d"Ase>� B�*jR� 7})-J�33�=~��:*H.�t*>*&J:��X�7&26$E{@]� n+1]�N��a*� (�=y 3")82[4n�, -W �E6+2n sals1 t 2n,2 w�n-a�>."��e&� �2�2,jJAj=3,4 2n-2�^ n or�!o�a�:AEsj�$$.i/notic �82' thusy ��u;�?�� too�7. How�p,��aC�&�f2��].Q 1 &Q �� �� �*2�:� "B;�-1�l6a� 6'AƆ "��V�" -I % we!�B:!�y�t`oE&q-in a ver5Q; wayNE&����umZ���ŒF:�}(.6'>R�7%��z �if�" ��(u$ EF�&�H-� � /[R���=*�� "�"��"lh2v�NRR�J�w� N� 1)6=-\Del>.aB1*Tah�("�8� -6().S2�j�G:B"r2*�!"��N�J�N� z :] u�� 2n� &��&yV�". N�2JDFF�% !0&� :�02��$6^9��5pB��s. An &�e9icoccur�ie�@2 "�( ���ۡ,4n]$ &�'. T�'�gn*����betweV��� ȕ�2� M a 2��!�u��D*k�"�9�a9�rBB�9W9F�&�R$2��2�2�NA19n nda/ra0N % R4* � an E_& &�d)�ɀ 2���!� �.� 5 6�6�� }�X�a� �&.���)�J")�!t�Uh%�. &/:H:�#4(~&S4Q3>b �\} J5>N�fLF�a SubO� ^Q�.hAget8sV�m�a�CtX  Dn$3e>"�,*I�rec �ϑ.s�V^ j]�� E AH,j^% Ja �B}" "� & 22}$"k 4�1g"B�B�Icalcu#j`e5"� E� to�Ffy�"f ���I�$. �.��Cn��8ten� &�%>�2|9n-.!c:t� }�[%�y�L *�;q�L e�a��a�J�h;F�BL .onH 24H x� ���u1-&�68�pm �� *k�N .�% � \&4����]b@N�2N4�>}1+R� �����qD�] �F� :�sEvj= y>�]V�&�2� -�,r�62�i>�2V��.�)�!� ! :�2ndE46"M51}!�9�v� &`Dm'% N"1Ru�1�"n��$ o2a8Q#6 $�^2� ~b0&�"� .�"""�I'.���� ��K!E~" n} r !1,nN �N{(1 % )[I��]!��%"PI]+A��.+27]F%M�o) .bUzB�/0 Although it\=b� �Hlo>tre�s@u s� $ultaneouslc{i%�}v3e)$now necess�to"N38m�+"{6[ ia$.�Lex�#e�=�Kituden,%e&�L0: $\bullet $0�w V�$$a�=-1ѐ� Ik}: =kG��*GA� �)e_5no�tri�|in�RL8�It��dJ)�"3&6 �G� (+G$ (upper�F)}*�aBy&BF�-FlowFb8%�&�io�bc.�4$m�:`%_-�!,�a�'*#t��+orsK[ad-12f.�$�diffe�+� zeroEFM1'�.m�1k�4ifXZise�A�.D-k*�)F1kAeverV.'nV+NV 1}=-���3=q!GY hMs�C5G[a) \mp N��FZ1H6nD>� FDodd�Ir�( e��M�F�)1�`�B-�)�ɫ��O>GJF6�7$�dN%.: � B��$mRCDwe �E�&9 &3|x��e>R�N_ "���2%�&�V[N4200�" NF�6@!,9 ��8\xi \lbrack 1+q*> +3 }]+&9n ��%��' ~K a#R�O \6�vf J;A�^8�rZSI�� g�H ��j��^��1�5� +1Z�+%�r�b�%�+:+*� ��*�g-u%:�N�Rz�j�Nw9�KN � m��� quit^J�N�.��u��72���>��}&�X%N % Qv}nZ�*&�-Rl��l��} _ �*} n�Qmv�*�% �(% Moreover,�"5�f� 30})��Z�u *N�&we �ao pl�?�"�`"F>��/!�2d�/els.� �!�n+i,n+W62�z/��LR(Xar4E� 8@wRń1:�'2f7z�2FqNow, � us*"�0�">41�Y�"&r>Z12 ���Z�&sbL(=�� j�/�(�Ln)& jz?), R"RX6~f�{ 6Dp:�"fr^�"6efV�7�#R�8.�^M��t*�"> �Z;�Aa*y&6>Y% �7-> (b lR��6j> .\ by6Qa�u�*u&�#jf4$,)R�7 ^(�97})u s�A"�s �|aa(B(BB �3=�1$ :^'`��r�OJ�'N�',%�!Z9�b; � ()1$\jY�JT2x2�U% (oAnhhJU6�I;. "<#�nb�,$�6f��siӄ�]�( ito�P fhe�(l�'MR2�(�)ic{�U���Y)&`��.�K�~"�6 hoT�eD n>2$. Thu�) c�7"�!�q�2�W3�Wg2i�4>�X!��7>!�26,% 8'C*�7b�' &�7�h�F:�EW� ^>i} 3&�EziF��h9(:~G exhibi�%��G!�r9IKloX`N� &�8SAs"#&�\� of aa/�struc�G��conTvFjP�)�g= pl%� he cDId�� on|F�], namelyI (%�^�6F%z�ipo��smo�% �"}*� *�+o�1� i� M �Z� 6�h�zq��6'.�?}�b/)�W(u: }�N-V& D�'�> %��%�"�gc {�aj�h2Kx,�}S 68khsT�1b�jof `hE��"�.S be easilyC�atn :e9�A-W#4i"N }:0i3����N� bb{F��[RN("� kga-"� "�_ 6�_J&g�[N�6� % (i<V  \�8��wf����>2�z�MU�B� %M%&�v >�� f!Y�%a�{es�iF1�5'1a2�h }��}�d��JJ2&�j�_�:Q�i�j.�cN-�J��Jjr�<�i}[�i.&�j�5}"1viy ��.%:"�)2��a( }}b_{i}^{+Mj&�Q  -})]){6�(P>jEK��6tB�8})����#��9] I# EF�"jE"�#5��."1��fA>�"+d."MiAB �"f�."t��"�����"5F�w Ju1l>��e΁�B� #�6}+a_! 5 5�$b_{��+}+ -})1c }�2!�% *�&u 6F�I+2�V ��@+ $F 0}{0�e� ;$� f &�*D1�6w.V$ s#b �a�^n ^� i\_iV2discus�H.��� �iy� >w&6.� NiT\�'�e�  ��b��2)l*0 &� E�,� is en� :�T F� &� % 1% -|{B&3s6Ds��NC(�wJ� G(u)�#1 *bU)&�#"�O@�b�bVbo.�at �o&g)ndV� � \A8-E] N� �["8N2P�4F*_E e sa�mtteR�l��*�3.2�9.r!� �)Eݪ�bs bh�҄b!V%.L*>�� �Lm��Cc�b >Ki:E# �"��PR�o6f*u��I� pN�J2� �an�b��F{8� 5�%��I!��&�* �b/YW2�x� ">Zt�h�x�"�'}Z2>2G�D�J�)� n�6�-� �.b��Ej A2�>t ew6&�2)�geN[hb�aC`� 2n-3V�]u�h1j�J�&����>��"VakA\2�_re6�� kvJ ZB=R6 =�� � 2u}F�|' Gamm)�Z�)"}!9}r�� (�j*/5�1C� 6 &=&q�AQp3 ���"�C�.l(uB:�)9�g1v�I� � �0:�D�&�-����a!�u�-��1�nd2Er.� Q)L��NOz& �Q% +\Pie��N�YM2�J(.�-<.},9+"pT�I{ ή��!� _=��m�G# �E�:�2�c�kY2 6�I��v�2b&i-�>�a>Q��J� eJÁ�2�a� �=�]/%1�% .$r�]% }��Fb2+F�*�d�;�$�>j�>��1�%�E̐>-ME�AF�5 1Z1�-�2#6;y3Jk>"F, � �.�.:�Gg�"dGF%74Z&�#�<��:}��"]�+chn�_zJz�Diag}(��1},�C2}�#kK:"�eVd+3,n+3%!�N B�N�af� bb{B}$��F*B�%��g$*�a��<��0O] a��{ccq ��eC� � � jPRL) J4 *R@ �%Z!�sit  a bit&�/. .�2is�Bc!!Yrto �8�J�� �lB2�D �\|E�@��A��m�E�J"�" satisf��d�fJ�\Z�'E��R�I�(uGZ��-�.]J X �;1(�'F�cI�>/ �1R  }(i<-#�Ma2m޲c8i`"�!&F�:�J� �}(i>n+2�j"�FEB:0.Kge0c*A�NL!A_K�=$��e% �seque�zn0Uq B!!��Gn!l� �y�known )Q�$2n.�LQ&Q�M�f3e Hproblem�s^�wF���8�1 Be�As, #5 is stage,�&C*���b�HGva~bh associa�#V(!f>", R. $n+36�jI�XI^^�ci Z��2��--1wB+". 2�%j-r�|���(�K}`6�����-����������Y�Eu2:�F� *rFq��6V�i���"} ��rK1x�Q��"A �< e$.��mjB +�0w6i 3T:<oddn����a�z.O�bQ�n�]&�&|B �itR�$ ����1� �@ZFs% ���V Z^%4�f/6hZ�B�*h�ZU.E=�8���}���4.��� � _ �"G ��b�A�:Fg6X�<Ge R �w� A� >��*O�? a:2G.qy�� < �-%��9��!)5 Z5}{946�My })�P.2A:��M��iɦ>���:���}{N1*L�I-�=��{ �y2 Bt E�2#%�6�5�->Q6}�B("- ��~[ 1J.� _Q��^�7�_3 +F�1)]cy�eu>�J�1I)[\.�t�a�6��eFD R%7!qU� b%�!��7+�7�7�7"sF�K&eD�6.G9t�%: r2> ��� *� E�V "�M1���6�U�2��]%^Q�1:hQ3U��="wQ��� !���"�n�R�29e�.p�M8-�]IQE\�iz�Vyz+�!e:_AF� 8\�<q�!:j6aBR�}n�r�a޼i.h؁�3>h3��VJ4*�;M0%��Xg5g:���>�].f61Q &� � �fw6�x�'J6[2��-�b%�>�JB�F0;% �"NI&kk�5y�&�;(�\2 �^[3f�5OVsC�?72~?7Mh��(��4�(?_$n��B�4R�ev�S^���,C��6��,J�!�:Q-��!�h:�~] _4�>F<a�-1b)� K�  �-{���Uu  � 6�+2�|'FkB~1)[.[i�[^��>4K\6& *�hՙ3"/u� A ��6� v�&-:�^����:{Bv:�-������*� F�3&,0��a�>� *�: 5aG�uL"� � =2R�*;B!�a>!B: Aj�B%qP��k���a�Y�% E�:� 3#Q��I�& :S& :]2uB�"N!� 6N S � \{ N>��e�!Ia�B� :$-2�-�+�I.�F�+1U�6BW4ʃp9E5`B{�Xm>�6"�/M�^�JN ��������+������A�>�&^!5���*� "- �$��� �f"���q.�� � }�>^�bK/�3}"LFR’3&G"�Ғ�2��h Ue�%E"�>�+*�>� q^{q�-)���iHd^��>NJ-z�%p=-8�‘��!� Ͷ�"� �� ��v���:�4&��5�NowO �#r�J#����3h/>�S.�2� ���nBm652}N�41:����MP 1}{8-S%�-jE �tR���U :� N�4@#5�.��Q�dVdJG4&$�����B�Ay�?.�E%��,$. e�&2�<1}�mâ�).��:oki� �{ne��>�a� $% n � \�C$Reduced Sox&'�*� �C!mϟZ�o�#cuss 2|�� by emplo�a r`�*&F�describe�5A�'�{!C4 S*&�._%we do�*�W"�W7*� A�YI.��F[F�3y(D$ an unique&`' AO�40h&�U o�a�"ll�)-�# 1�}-f�U�*Op";EWCd� te%vhe�Cibl�()�2��ypeC8= {%Q$��})m-��D�~��ll&3G_���"":\�2?=������EE�}� :�)�Z ���6Arb�in&)%F,D2u22"�D7!#�3"x!Ji�l.|y��\c aUN0�|A02v) 6toAQ=�6�)]]� $($A�$n\geq 1�n��\O)�"�$dr?�edrB��align} �(1��j(n =...S]�'�f&(!*� E[�-�q}{1-qŴ>;X Re�&i x�b�g:YIB(n)red�3 �^�uc1:�/n��2�2�N6:P"� � ( ( Z2�xq,^{i�.B�y��c}% �'1�БredJ�CC"��A�|V�uce�L6K&k�(5��M ,we6]>G"L>IM �$eȦ� vism��7."�s��W�:P2�$(uk. Wr��.� :v��uQen &��T"� *.��^ e7'"�i�Q<11:p� .O}�% "kB�*fx��,�[ �) 16�-���� r"r��}�5N����i�u�q�L 2���'=�t Z#�3�~ %�ᮽS>C�}�1[J�A2YJy�>- �*�/�>a&7s�4a5btB�am arguj*+ �M�!!�!M��^�]x.:#�o"b gar�.as"�y.�2���ad>�"��1%- ^]. �B>�"���p��sc veal� y� ing�S� �A# ��SB�.�.��vioc ��en� 6�@�Bparti�ir&�R8Izergin-Korepin= , it"9�ZW2`��xJ�1c} �?�:?�> & 0 & +2�13.n�1)�44�o�3:1 & 0TF�13r:5��{R�� �!�y�PJ�P��2q�&"�Wa/.��is $2.�SU?x!�Iu�UsQrhAX4b�e" PNKi9e��Kim��xK6r� 6gR�*-. b�o$&mB�Qi�a)i�E s�waAq��"�)D�R�a�Vet�.�or mo�)6� vEl�3�c.�e&� by analyz< ��u���Q-��&��>1�L 2�G3vanishA�9B�R &N = $\ �e�-6� =W��v��3� Z� qR!A}0R �8e�� ,�*" Mz"">�2�[li,lJ=0�6 }(l�"i:�lB� B39)\* q &� �% SimilaHV�1rL;&�U!�&�of\��=��,���6JT0����P�@�!t link�DK&g�s&p �yu3 5}) M� Bsp4>\\6 6� Q/Y As aO~3c�d�)V���#if "H6=0( tu�^�514s  {SjV � �==:�] ,=j~b,QJ�=w &2c�der�p"wIy��-G2qXEX%:�2� "� %�.KBGK�s.v�jp�� k* �@ d��M Bh�7>�r�_X��N_XA~F�n@ "��staw�f�:elucid�a`�R���������gX@�#e�L�IQf́!��edB s w��:N�$"�6j.j ���Y1a�/*�WM��!�&JQ&>5 $n$:��>� ]�i4c$eM�$%�onF�RA c Ae�$��l>~y@%:X(opposi�Qy��a�C.��s*dN5���t �Y HBT.k�,B#�e6K- - -K,F well/2�6�>�Wdb�S� �%=�,�|vided ��s��:�ņse����l.xNr�v�?>\1%:a�X�ibo"� e6���.�u�˺Z�&�6�D��e�b%�h�K*��;�F����A�� �E� �Me ���f�n�@����?( n�M��=I�>Onwe #d\gY�2%Ց�$$2(4n-3)$ .� ei�W� 2\15-9 "�=N"��ly�ked�lJ��dZf2jc��t" � *6 �Ma�%�C E�" . Ob5�� gO@;[*< !��6�un��.3%]^9�,q:9K�G� 'Jes�4 1}(q�f8B���0�,�.C8q6)� !c 1,E�,2K�MB�d��a:Q�! ;&!0.RRNB7aB��A6a�N� �-6��},��`b��:�NbA% _sa5!7\�. I�)58F]"r0N�&�MhCJb��ytr�A�KL�}E@B�e *5!b|�} H }��i�M:#ti"� JP�.� 49rq"E� N 2�KF&".N&�zs&EHA Ae � +1 0rW"�(i�v1=�yv6��9Q.��6�M��i�.&� y�Ji|Q�iɂ�-�J�6ڮ� :� % 2}؏V�s#M��~�6#"�N�&�5=W-��!�2U �1�v�J�&a� &8A2�jN�j��}%tAd%wb F�.��1���>�2F..B�r���}.�� ��GN���: ����BiM���٭z~�i[ ��e`>��r5%.�sn�A�I9 ��R=0r�*P��.~CX�.|�"y  c"X rep�z� stepJ ;�G2���z&63&$E[a�k��ej!��� �42 )��)!$6�TK����fy �|��*)aL6�q]w'����R�C"ie�!&�NI11r �-1N&�!��� "���]+$�n&�2 n�N�TX $n>3�� kF l&`��$�e1�q�O�e.&p��#"Q( ōFB~T"ق v�"V M� �]�e�-1fga��2�"��3&A��f!�^"�u�jZ " 4!0��r����"g�Nr& :��i}"s{^d2� 2c !�6� �6!�m}B��z �9j�&���*� ��MF�� =*��e����2}�8:??f�Z %�e6: �$R�NDZ�Bne2�� 5+ ��J)%.\ZG�d: � v�6"42-�Nw|( int "N&�a�U�$O understoo�� a�/Q9.7� CBrgL1����E� u!i�;("T *�w8n+2}$. Again, �the equation $E[2n+1,4n]$ gives another rel $�between $% k_{2n,2n}(u) $ and $k_{11}(u)$: \begin{`}22<=\mathrm{e}^{2u}:+(\beta ^-11}-2)7P% }^{u}\left( \frac{q @pm \sqrt{\xi }}{q> \right) 9 cal{G}^{(')�<, \label{C(n),DHA(2n-1)red17} \end{�X% which allows to write. as fo %9#narray%#1%A &=& �4(1-\varepsilon% }\th1$!?}q^{2})� F}% _{n-12�}{�9t -1}+%@\{ 1f n-1,9)w %�b�- z Yu-V8. \notag \\ &&i. -��)�V�1���)�\}M'%!( G}% .�N"�j8U1Ø Substituting these expressions back to funca|alu�Hs we get constraint.E_0will enable uEg(fix some ofY0$3n-1$ remain�Tparameters. We can mak?4Q�s� X,2n+j]$ $(j\neq n,n+1)$A�fia�Q2�j,j}$, $j=3,4,...,2n-2,$ in terms�.22}$ �] n by�wv1]$. The�@ n,n}�m�A�+1�re! edf|vrequir!.s��E[��aN-n+2] jE[d2+h, respectively. After carryX8out this calcul�<,!� used2v�-1]%\obtain � �-1!Q�.w�|)*s2,!�be�zten5  of W e�!�%Ce�:+2!S.t�s ��:%F�T i,i}�ƭ�1�nDel�܁cuz�\sum_{j=0}^{i-2}(-q)^{j}% \text{ \ $}(1�+Z)|����% 6 � _ a�}{\��Q])�i-3._��].�Mr } && \ }(n+3ExI~��!f22>% and}.t }U�i�2�2^% (>�)}!� ! :�2n+ \bar{2}n- 1};(q+1)%>v�3� ��ereN�R = �uy�z+aY2n}��1}� E&� p>� u�) �.r|4F� Next��Dcan, for instance,b4��: to���kA �$N+&&�A�=�(-!�.�A� imesm�2!�]�9�{(1\mp.)[e�1}\pm ^}<][�UCA�!�yf]J�)��!�%�] $ $ vK55�k % At �gpo' ,we must trea� solub s se tely�order!�,take account�xistenceamplitud� %�� Epeach model: $\bullet $ For $"l A}���� 2)}$ 2� have $!�=�F2�d�x�� k}=6� k}=1�$forall k$,� � e is no�trib in (\refR� 25}). It�  th)B5@ with�G� (+' 4$ (upper sign)}r1�o�fF� -FlowF@by complex conjugF .jc D}_{ (1b`) �� �a%" mean= factor< }gu&.$$ � Hdifferent from zeroEFAxQ� >mA51konA�f $n$!j even%���.E-�%:�1lBoddnVC�V/ , pv.�=-1-qi��%�� Ini� case�E� also>�,because both9��~� $[ab��k��9� ewei�,two independ!�1�s, one-��2� and cN�-�,%�a�$$n>3$. Onea� sea� ults Htho resena� in S� on 3.2 �couldfcl��2�Dsimply made a redu�E^general�a�Han appropriate choi�@fre.� H. Nevertheless, newLsa&Ke �Q�9C6��)5_N. 6�!Ifixed.ainto f!18}) we �af � .��:0�R"�� f�2�&M(�"1 (uR� �L� &&-.N~@u}4 n  �\xi \lbr�1+q� }+ 1}]+:qs �d)6�% ��2�R'e�b�p \6�v96F9!�Y6B��U�m*� ���j�+)�I��)�=� +2Z�+%���+2}� N K � \:� v�&}1|6�6'� � �ho qX63�we std� a�ified}� qu�$$, but now3��ty�3���Y|��  4is exchanged,  gin&bYaI �I%6�u�� H� % > }n),  &\ &�Rmɟm% �k 6� oddl� j;&R"b6J N�!�lo� h� rs "i��% F� gen32})"�@diago�ntries)�bC0red27}) defin52�R�)� $ whL� !�x^=)v$ .<!�. Now! $sum up our : Firstly� had } �F� }% ) j#0})�L non-53@matrix elements a s.$��2<� �> _{21� JPj}�=2n ��j�1a}), !N �1�nd %R25+ Second!P the b�w� �ed& us3j�2!y �R�13��14�� ��:R^ 26})���AM���!"!DN! #by �Zme5��, L6E2�]96�R�19!d-f�23}). TA*�s leada�  ed�6� ){n$ �,Y��2Bl3 ...$2+2 &I ]�� O�again, number��: �d i�si5"� 3�  regulardiE)�{K-i�Reg}),���!���1}$)UB? s �R !]� 6Jm)�, wga=!V��R} our >� Vy͉5S>+�� ���d�n=3,5,7��$�ilez ^z%Z�^^4,6,8^ . We!�hasizA�at ��% 9,has revealede�$(�-Y�>� ^� ��9�,A wellN�>J1[ J�,A�a&ZC � . Simim~sider�s held TUR �yK �ur&� $n)V"rk�"|�Q`C��3��1)}�!A�ial, �featu�a $% 3 N���Ebe��� 6. We sh�aK$tinue apple�Au�]in&�(verify if o'] 4$discovereda�e n  step�3tow%��� }�=0$ togeV��  ��*3�.ach� X>�$16n-20$ nu�� �Y bn-2B�E( $n>4$. Howg,� �,c turn��b����@ g% n�NH. H)�r��. . In� ti r�$n=4$��l Zd$We observe|A�ial�of!Eed2Ys b�$2<\cite% {AADF}. �exhausta0'hpossij!Z�!� at�&�last $��as& e�!�I� �2Ahs.7�M���fi!Xi�e6k $K$��)�8�$�� .uJ�&&A�I�1>7?�(u)>�%,6�N&2(k_{33 ...{ !G�� -2}-��-2u}1JeJH 1}{2*~�&:R-1��Z�n, � �2.�� �}{{x� 2}}(-�� hj9F�w�u�b�6!�cor�"ond!�.5� align} & F�5�)ת�M��}+�95��66a��)�F5�7j�5�}3Y42rz�30-�)z% H�?wa�t�!�s�$2� s do not q onYT�S�3_.$refor��y��regard� s2�s �ed�}co"-i��alysis! li�5Ao�Hew�jces go�$ through�� � I���L6 |$1$% J� �(29}b��bo�� V��c 8n-6:�)�a�o>O $n$,� ���Z�6H� A��������30%��rm yi> ��A�B�IA� refl3�(A BYBEaatxwa�* < . \� K{�(y�EB+&XME s} �  interes lookA����2��� �� �>�f�)�y ,managed to i�ify=�" "Rc1��en[!T �E� recurr"��D(g* gen2_degkte!o6H-"!k�% 3,n+4:�)ZA(L<�,p"���t� �(��1^b�%,+2M+Ve/.un+4,n+4��"�$~&]&""T��>��.�!� same*" $developed *y223� Q6s9, of b�ty�� E quot� ٺ��A�%&x]" "�/= � &�(u}2 n})[� n� !t.#1)e/! /+1./1 -1)]&ieD02`: &<U63}� 6\��� �+�1b�# ���2�"��&�'-�%"#c�e�,  69!TJ.�v� pm 2��F�J���k(s $� �(Al)$ re���6�)w�O(e �v��not�$%>4>� M�(ّT setM�=G=0sK fami�'sՅ*�1����#�!6��FU�u,����-1�����}5V"B$.�/2=�E�1]}]-t����e-1) e\} N� 51��"� A�������C.�n>/y��� �.6��+��&� M6�-� &��;��%m2,�#0 )^)i0�u.��N�2ٛ����.Z%�=Q�VY�% %g�&A�=�[:�%�� -�"`�ZM�mp�.�>~ALA�:c$I2Z�*� !x5�)){�!v!+�!pm�!-�5!�:�1J In�"p can4riv�*d�#�� #a#2�47#s show#b��:>sBX&*�� 2�  �{uss'"Marti +nd Gua�/� {Ma2�\QD�S�0}� star��i�0����A��� 5.� �&��+ex assoc�+du �8excep&al af%, Lie algebra "|1�QY avoid mis(#1t%/ solv�EB�H�!r�_m3^705Q! Ma@1e-TdI?yse%9&@>G]6�&namelN�\lim_"_5 j+1,G\� arrow "mL:�+at�s? B�f_2(-u��" �q� �p o��!0!�J�6V9�:� i+1,!�R�:.B� �!-�2u!7%�*= %�By1A}XR+=f_#%*a _^R�:s���!b n�2��nx-�=11:�u�&PZG1P=:�6-ZaX�1(A��5*1> �:�:k2�-!�l��%�2�B"�Q�&�M�% R.���z��B�A67a�68� �r9})����r�*a8�,�h�� bb{K��,j}^{I}�8$1#J?a�^{jA3F�t�3^{n t&� !n!H&�<5�\b�/ ��1u�jH 2-u)% �Jt �����s~J�<��.1�ў�6"m���*M �5(x:��/>�Q,i}�:� 2�+. More�'d&i=v:1��]Gn) "( � ��1��$� < Np.3���EO ��q��̓2t "q��]��6�f`>~�J�r�����F�Y�~�J-�� ��h-�E_�����v�J@����z�9~�1F%e�q��1�H1j0:)� �5 j=n$�/t�$1NX �bB:0$V ��*D u�-6-1 1i I �+n*0'"�&� q�Abn" B� *4 �>. :� �j�N� �9�6�Fz 1&T ��Z���#�34R7o@�s�*6� 3N� 4� 6+6�-^P6� �[Fn�*�] +p+1,b �7zGN��N�!�Z� bZ��� :���R�J ��!�pd?%�:�:��,�(uZ��$�*�:�Ju��V�2ry�n�yEzAp.V_22j�]�68^{b8bV�%��O2�2P,22�Q5222�% _6C�!�IZ�:W"u2gU"�!f��j�:�:gR�Z% tH!N�6' F J� .B3z�`)�th� &uof �Ii��3A AF:-%o&�GN5KI�T�}II  {\sm�)a}m \�"� 2p� I}\}..\ VE b}}=FB�FD D1��cBF2�0�.� � ,E�p0 1,�!�:�j�p1��B�� j=IHf�+�M5 j=nF�$�jj� ��&jE_r����"u% >wk:�JZ2eB��v�v�vzv6V>TB% 2��, N0 J�� a3:� �Ou)�� :� "�� F2UB��Z�b@q�b}�O Yormsg E^����1M1� v�~���v�a��F�J��q�B�B�BJB��E_52&G"�1J$Fx5ly,E�Z�.�Fdc}1"�Z]��2h"�   " YPR�% �J�g� -Kb� e�B6�2&z Ύ3B������ B ] ��F�FQ 2&q�F"v�\:0R*�Ev�G*�3Y�JRYz^a} &�[z\1"�A]���r �t]1�&* ��*% IQaJ}N��F!3n�~�- �f���ͽ *� ������*� �A2��P9�% 5�.� ~: A!�2{!��6 ��2C�jJ�z�2�^� �$�]�]�"6�\�\J�\0#�wRfVJ6n�������J��K�K�K)K����F� N�SWe "X�Kc}N� Nh "��AM �V� ��% F3 ��J1:�^v� Gqw.L2O >� J0r�� 1 54|9+����J/ ��ef� ���nJ � � ��E"�C^Ev� :W&�B�?�^X.�T.1&p�06 l a(�  }�' b.f��.�G� (5 =*�2^{-�2+"�D�� )����>pK?J;�2&H1� :>1�N�TG3:+r� ��52n:$�.��B(n�'&� -::c"�e��1-)AzJ ѤgbH$5�2�)^{[p]�Q$p=2,3uN,nYO� no`IK#U"� *� �2�B�p,p)]n-A-u� 6�a�5k>2,V-�2n-% ��!�p-n-1/�iu�[1}2#)46%J�e2 lIc��3 �A�+HMz]I�\�"BQ &y-R%7G�RE!�1r:+S&*n+2�for�:!�6�0�L>�1q�2-�[p=n]}�QD40cu2Hby Batchelor et al.�A�L{Bat1D46!��6�E^��H} ±r� .�!�)�Mw�CJ@!�1�kD572=�I�i�N�-N�"-2>�UF*rA~Of|�>2*Rad}ULe�A3% :5' ���ORUb�up!� ��%:�E�&�E)&Z%FKr�p-1,p-�UJ��Ņ�1v�av��2u})�� -u}+\&esp�h���j@( _6(N�-p��>N�.q2u�kN�QkJ��.�_j1~$2p�q n+2=?6+'% 2p=%��A thu�$�W$2n~�"hf oddHF�48�\RC6��C �%�86��pI�� We �/�FpYj�ouN9ise m� symme'8 LXHr�_?:indu7T���� $��=E�$&Y6�� I �\Fc exhibit a�74 structure. Be�7�he�It ^v�(R_{\alphaa�tf ��@6�vWlY�!]U7Yx%!@$�\�:*�@x2+ ��"}=%O(4aJw,{cccc} 1 & 0 \\ � G��@-1��RD -2}Q QU|>ZTF2S2OS%�^TJU%�rJy4 ~�%�x)R% \E�� ; yA���-�&; ��d%�/�:G�d: $ isotropic+P�9�<�<�Y��<;��U�S"� �LtyC5sev�2�d:| i9�2i� i=�#7$,Y=%elow. .CPX��6� ^{[1]}"�U�Z��Q�HieRru.JJ-> �XU)�V���t:�UlN���n\JZ:�^ n-4F]�N$P%  6�BB��2��!��� �� ^� ^) q�B��63�6V6*�O6TN͌ *�( �,%n�~EBl�E4�E!E�011�� 2Fq~J(�� -� �>�  �DtaL�y*� "� J�>B !�68B���5����fR�M2>.Pn�,d[e�J[���P������6>�8��6��!�A�2�!(Q�J�1f.�n�!��)�H�HZ�u?L"-z�RKSfI��w u�5�=UpJEO"�Kb .KN� B���7�����= ,*`�2�� � 3 �����&x��OE���/1�J]$is multipl_N*�jGowe �����F��nvE���au:�mC��E�3b�.9���Hr\y Mezincescu, Nepomechie�sRid berg Ne4v�� �:$bf2&�M�,$]h.4,normalizwxnl%�g2 3r@��]nD �5j"�� .">� �r2�� r|~ Q_=!})�T Z~ R+ � ,."b �zi�*jq*� .F} /�a�-1V�&��ZE�a��Tu�i&Rl �TF@A� r)~"oF��z�9�C��gƣ:mG�"^ 6�_ "�"-1�_ ��A �A �"i #A�*�#.Ε�S2�S�h.d2u}:�ZN�2F�We� .� pEB Dv�SQ�s? �&9 �"iq��E�E��2k� bytVigΐ"��T* D6ORk .�a�*j Am!a�5w._,ajK��or�Tal � .O�=$ �a ���ё�T���7�^* .Z=�>�edbl�� alme}unity2\�V .�n� � ɞ�&E` -.���iJ�. &J2���9.i h"+�t,*D*- ~`g e� iWnd�BJ� iS9g >u� $U(1)\oti � $" :?A)-E�an rn z � 7conPsd charg�i �B,sS J�Z> >�ZSpe�u CS� �focus@2')&�Uru�w�xofn�g"GX scheme,W�cf}.U'�%�a3.+"� E�aK1)4� 2R�Ba;�S]�!�$n��� x_ D z�>�6[� 4O.9Y$n=F&A:*C2@�w,.��KD4 5"��any6c�M$9�mt.���ӀA�6I!�I+gY^ �pPs.gvas"#"I�� do �"H#ll��erta_m��} sharp ��&ym .�r�!��9!�$e9i8� X)gm&:m4�q very�a amox�2heYn1�,Nk�!�!�K}_{1A2Ifm#&ʒ�EV��; +�#G�`� W2-�c1) #J.21N. &2?,R ^1>iuj+1Z�".*& 1�[��- , `.�may&]recogn� i zB�E+�F0$I$ itself orr(.�D. Altho>s`�Njs:SX�)#A�>�^��b� |"�Gt�G6X 2̀1�.5q*ـ��1} �*ccordD�͘ll.-.,.!e��"�y �jnRcon�ys&f|�`�x�*"� $VGR1,GZ�����} =P%^�|-f؁�&� �)�I7vre.�z&I$�ݹ�}}���I2H2  $. F`��^5�reRb$�t$s"Q'"�R 7aku�55y��21]!�@Lhi� 22}a�21,<�|X�4Ez2�=[gN�'} "g: & p�'�'h\�jL>? 9-0n 0.�'� �_ �ZJ� $ A(2�Ja�K��gE��H��A`��2�}] � % $, satisfA�� :%&A���E& { 21}="��332�2-2).�oP?-2*�x �2� q% D�eAJ��.*rc�EQ�1N)c&j yr"@�>+6-N33ar~#aE�* B�!�&�\RZ� W &D_{l��^ [j( Miu)i��120N2 N�ݴ%39qUjVF�n.7b:]�."aXQ�b:"OB 2}=� 6 u5 .�%4J�)�>�=\ {�ULQ~�H}H-f: K�33�1EqZ< 3.�.Y�ѝ�@2�%��)z �%E���Qj.J �jN�+5J�.Z�J2 i.�h���3"�q3.���]�.�2\���)*2=EW6� nG�vr*pa�o*0ar.1�Q@>�2�K�G.o8.�:�=GN2v�3��>��AB�79? �%?JUz=��I� � ��j2@>�4vFe%bB�B�8J�3rec; 6f���$i=�3j=3Z�"Dk��^>� &� J�!7V 2��@E�TR� !� ��2�=2��B��2 BjDi1:�@r� �*EU��&� "R>� ���h_{ �R� ў�9J�%��~ 2��2*~ Q ��22}&| �.>�10�B�� ' ��&B �9v9 j�y�5�a-Y6&>�5Z�=5�R� &q�*�� N� � :�1u2�hB� . >�6j�u)��Bl1*v �aѐ6jR)[a���.�\�}<�Z+�� theiI��N� �jġ�6w$aZUx�=JJ43�e#�l J�ar&�B  $� D� D_�$ D_{6b�?� f�yH/12;-1� � dade Vega HGonz\'{a}% lez-Ruiz�� �},(!�B�>�-��>yAba� RiosgAbz">OX2�f$� �s"�8 h|><��kŬap��s�it� ��pc��~&ha7�9p"l�sO to�N'�LetE� q���^�j .jY � bV�y����e{ 4r�8"���1�S� ����G� 2� "� B#V'�=3��J��=j�^� "�R���E-�%!s :;a !�R' <:� 3��!k&� .�" : %)�Bj�  .ycA ����*�-�"aeJ�6� Ѽ�s*% 1� "�44b�44�5�&���f&�&*aE.�jMA2V���� +�*!�A.%�5�Wn*;r-A! h_{4.S5 �L��0*�Y0ith* Y4"�4��"+2A)�N�5�(P�b�Z62:�We �":C"R �C*� �. 3r1"� e�!�!�"Y �H3 ."�A�^U2�{ 22X:.A���*5-CZKj4�m m >2*��A2Rg2i�gN�2� +��>�!�6 ~�$��� 'Q%a�Q 5N��*H5?w7%^�Z8(��L�2}� �W22$"B !.��b�6=3)�A�:~ 4��e�a�q�%�q�6'#!�fcI � F:A@U2ԕft2�fSB��.�Yv 3=�3ZB33ZB>�.F � FW)�,( �-Nj .��� jv!�D� � 2���:B u}V.$j!Zu�11vY 2���7%�[&&� "5�N��b:q 6�, &��*$ MQ>� �� �#� a�F :/��!�.a�� B 1^ %�9� ��n���-�6� �)�N N"!6|�Z 2�� U3a}�{b@����5��6�?&��"�kseN��dZ e���#&�. U�6: y*��(:i_.m) % X}&��� �;l~��.� �}&�"� .o*>��π^π\\:TqNiQ1��7�u��F#*�F�>�l,lV� �x.�:h�N�7a�2�l>Rn>u�sy&� :r�^�*6f!:�n"�:[U�!z�oZm \B�o6h% j^�F�1*| ���"re�5g*�s*��&%&~�N�n|! J*!!oem��%+RF,&��"�D_{�L=�uuN�"*�!>s3n�9V���n�4neK�IVJM&}">�5nt��fd6�dbiY*� D_{7bSa�bO=1��8�fbk^�9zTr�U : *�y���?us.%?ac�t�y�FV�~ � � ��u)\��v !_ 2*-W->b NJW�+f��6c��.4���\+Co&���>&�}���jN/by .C/&d.�.*]/.z -(���| �4 f荹p2!J�*O " �Ti����sҫey� nin ?n.c,&h ߹N� .�)��= � �r� r�*���� e�5�\a.26= ~2. � 35%.DHf4 <nkK5NAB�f1�51an" 6�*� _� 5.O"i"N(("i�0���Y 4�", �F�B �� !0� .@&�%�!�� Aia��9 !��Q:9B� >�~2.N%�4j: v(5Q?.B&5+�I2hU45Y4*b"EF4QCsB&�;����!�A1>Y��.�.V7A�Vz> �R@�lA��:E#^U���&%55\F�55\f�&'S��5�lj�:!*!�%)e�.�!�F5n��y>�)!�Q9m�y�Q6 h_{5.O6b:��!�}�.�=�. "�F�.�R�&�S��2��%a�.r!< !^ .�!�6 .*a�V !� �2�N� h_{5>�b:��-�2=�2��6�y���������.�&�S-� �c.�&"h*z �F�&rp �<�:$fZ�'� q5� /�3�&�&� 6�"w x�yX�:�r1&͕:@V�5Ϟ �� � �� @8�0 "<_3� 3M mf_Bb�9 eBnalyz+& uV��:&� ,����% Mf,�� �vanishBK uD=խE.xs��p�&�_!jv�� r�F� !�` r=�D,="� �6�8� �y- X{�-�� �(}Ȇ32�f�HG� ��U�1DE�12}���&.�}�C �:F<��"� �%��Ma(q6�!A�!F 5�<}6 iAҥ2�H_B+2�S�B�#���!6=6  � v�! .���B��6U�2]"\�9߉)51xB�1\'�e"�m�&@ 6��W��i=-U.�(qw�Yi 23}-2e�3)N���26�A��� 2}*j �J ��~|b��>5� likeN�-��/9F�>*!� by p&�a direc��mpu�we�Q1J�F�F �y�lm��-ch#N�3!�U2)=FB2�ey)6�6&-2�1�[(:��6�AY>l��X)�  �%�vME 4��J2 �2�z�)U�*C&&#�}PV�Bf� � =&--T2r�q)VPE�.*δ:n��1����.b:ì �5�/+��Z_&� �2� )`�T6�] &&+[�C+q:� �+2:k7 �l�1�.3}\:jV=�B��")�-�.��ޖ�*���M�r�-j]����E�%%p&� �O&� ��i�h$3.őg�0N[x�A�$�� B�2&� �0+<known�)LZamolodchikov-Fateev*�HbC�1 2InamiB�o IOZ}J�*=3�i� .Z0� � ��1 �2��>c�$.� �Dfu��r��1znwo $2S"�@{�ta��� ӷ.X zleT�:2}\Lef.ks� ���������@g*w�*��t��n�;1 �V�OI $ secgr� ���)"�G�9&-Yl*��F�2s�9!V�&�s2B6�A1$��!8Izergin-KorepinIa. Let u�Kgi�l�2R�l>� E0.� 3hold QY�nW A!w@% P .k6� �31.53*� �� u3"�u�+ � &��9N� Z�)j IZb� �� R� +i� q}+i>� "k ��>�J� ��31�+��as�*���w�x b*^�� Bp��( .@>� �@6�-r0 %13& cmB�#k��Hf��2�"|��m>����"� vali��!6��A�V:&� !�% +" >T6,-�K�[-�AHLE�>�e8g#~e�g.�.g�u:-?�k�qre5"�)5� j�a��6����_ $ a �q"W�X&�J�塖�%�6�20~(I�qvC�.p�$R91ޘ�2=�QXO�m�� ]� F�� NO5�-�-t+iu�%!�& M�65 �%��:N� se�ed�H~�4 $B[4,6]$ clos�%NRټ!Yd{�minA�Iv")J9��E�*dG�$J.��*%� }%-Ti&9A%85].D}�* /E�&Qg5L��w���Me�6�-�`i�$/ =Z (a�2�26�-b&� �6T��XU=VT����b�NE�.{&&-M�f:t]d1"�%�R� ��rm"�k6�s��%�>�B5g% ?�xµ���,тB#�33�� b.���&��=&I�i� �v�3/|yq^ -Y�1����N[ /Q�9�%�i&��m� 6�13�( ��2+6��[�ơ�F ]Nu2 u2 N�fZ# ��M6=iq}{(1 +i)s!-i&l=�!kQ\ 1e '*T �N^ F�.JB�*���<�b2�A,major��ce� ��� A�ѶBnb $(n>�졄�6� �of2RH�e �<&h�ee}&� ��ce�Q��% nIadN1�GQh.���%c�&����@gF?��>"�ce�Bi* u�i!����A(2od�0a�`nA-!.d�f]\6�=N�zW�w"ٲ4.1.� red3�"��w�m"��aBUBham�Vc�)i���-2����W%�o�-!�!��CLi�CF��!�B]� /-)1��o:��B���[�[ some*�"�U�[quival.n�Z*�) �by.eiy Ne5}�R�s)eCaneoner �Y" .�1�YIZ%& AE�M*'\T%�Os\Y���q U�GZ^�O �f�V ASQ�6gYe����} 1"N1:�Xk'7���X��X.7-p"� &  -1^|!�C(1),DA1F6 �S�  [�FO"�Va4to{one ?B.�1��0�=�F�)����.�,�`�!Qhu��wbf��E?Iu� 4hـa<�]��<�V!cyC�h  � 4}1$�&� `!&���VUCkzb�!63�  & 2�������!4�i'6@s�!FH ‰^���v "C� JP�/A��  &�AU��23E6G)�P1�]< "O4}}�/6x �O�2&�,OJ�0 �&����:�2�!6� ��� �A� m�12J���"<13.( � d�*(4J�>�A�>pReV�Fl6i!���FJ2}JFn�1"����:W2� 4R^��>�2F3FN�r<{k&�E=5:e�� � 54}J�""Mc&MM'&���$z��%]oM� 6� q�+1 �*�RQ"� F*`8andA{1��Y� A 4}}-�%~֑�+.�-B}R`. r�-fr�͈e�*Ѱ6�%Zt% �u�%+� K V^sɾ� ��n ��,R 2Zl"5<,cc"�"� ����#��� $% 12Bܵ��� �wj&?j"4"� r,� ��� } � F�N n2641���?�.�Z�c|P }qno*��xpo:� ses \5 �"�"�e�Kaet(one $1$-par�ameter solution given by% \begin{equaD} K^{-}(u)=\left( "�array}{cccc} \mathrm{e}^{-u}\frac{q^{2}-\ 2u}} 1} & 0 \\ .Iu# K,1}{2}\beta (.#2u}-1)FB|2q}J,}{ G!-1)(i�z 0T�6$ j H.2�% \end-.l% \right) , \label{D(2)gen} (5x % where $ �@$ is the free par)�8, and one $1$-p reduced9�previously presented (\ref{C(n),D@A(2n-1)red29}). H�(we also get� identityztwo $2.zHdiagonal matrices $%4bb{K}_{\alpha �}$ �~901}). \subsecA{Th!!�|cal{A}_{3}^{(2)}$ Case} We have%general�$ with four:9s,1Z _{12}$, $E�ta3 �_{14}$�24}$. n�$% K $-%x take-�ormi�e k_{1e7 2A� 3 4}E� k_{2&2&2&2&3&3&3&3&4&4&4&44A�v�A(3A�1^�A�$normalizedY>,entries are J�n�~�2�� &=&E'��u}+i�5�2}6 2�G% }�854 24}�3+.G2u})}\e24}�&[ � (M�_{13}+Z*� -13} ].�% ^�Q8) \notag \\ &&N1a2 �.�u}+1)\}�n8k_!�(uJ4-�4�4��Z[�Yq� 24}-�1%592%.# �=#24}��L)Ɋ(44V(�\�\!(� _�)3.(=�)62��-Qc6'(\I�?-=)63]2�Ip�ލ2�m�% ��i�n-���5 x elemente��. n21l��m`n\Omega V�233 up ň E�� O�^�6�%!?��� %< ��d�=�.m�5� 7�~:8!x �JU�3%�=-L 4�qA�W�fy3%�=yI^�2�.'k_��9>�����:� Y�4) �V��uR�4ED� Z!�%O�E�<�."� m�3F� t defined $scalar fun� s $AF: ^$ which��8 different from$ � G� \pm )!j$:J�W�[5�36i��.C=�)0�O]�G(e .e�}> 7��� �E�z� ?)���a�z �-1�� 6�4F�and=]� m�F��!mEG +1)-IQa ��e,}B]5�} S above&� @can be regarded aI most"� refl1  $Kv  because�f6� �s � J~, turn out to� obtaE�dby assigning specific valu� o&* \ *< �< $. Furthermore,O pplyN��  $ procedure� � � % *� �z� !; well� 16G6�F� ~ }$"� o % {A8@~� C� 1� R�+i�} In S-� 3.2,!�z foun�3.�V� ��5�- a8 for this model� N~� s us ano!�9tb:B ���?hE��� p�s t$correspondAY��;;��� =�5E6^E*_.2 .% � &#44m  k_{5�5e -5l5 l k_{6.6>.6.66^�wCf�3a� non-N��"� A:=.� :7 2E�"j U�I9Bx.�k&&-6�e�� 5}�_{16}}��3� 3}}- q821C 6}[(12>� ��  4})] k��5 3� |���&� \\!�*�fV�@%@+�@ �3.��3}�P @ZR!�NR2\times�fJi�� � 8 �p�= 6��r~rj�)*` � !l6})+(%2�u� 3}?Q�����551�����M�e��'+�'4}>j�n)+a7)^!`]i1����=RS66jl3u��% ވ5 ��a9u�H�;3 "�&&��. ~�d]� ]1�� �9��a"~�665r�6��z&&>��**!*� .xV� Uk:�. e�=6��N�B6ET 6�56�r<=�!}aZqc >�.;q &C���2� 9 �&[2 �c} 1� Iy�2(]�A>��8~�%%��s�� �guBU*�* ͨ � �q^{&��2s^a^25E75�b]�j 2j�1f!��>G~�5E-u�Q�YVI*$5 J9�)�6=6.> 5' (-�|��*��6)fJ�5X� 5b,% 2m>�E�A�9>!�2�>�?' J��{�NOK Q}x��}�}{A���)A �k5TI\ U�21}2V��<_�o!�� ��Z2}{(q+1)�3�9��a� 6}*�-2&q1( For $n>3$,stype of&Kfollow�cla ficascheme&� i&4.2r6D�t}�:�5�6MBnis(in terms of^!�6&�s&~�"w6�"�n!O�e �, possessing � same�m �b�1�1})�-)��6 �o��}.����Q�2*��g-q)}{(1-F� 1)&� �A�)U2�}& A�H )F a]-.t�+*��ႅ��I�� �[EM�B(q-1)+q�)]��&G"��P��)��3"!*� z�!z)� )BC %� �B�2^�% ���r(# K�51+q}{1-q��B�B�F�*r z�c �F^ �B�+)�-����z��B���6: *� ��2u� e��>�D>m�Z�����LZyF�H>� I�21��6!"5RB6< "� b� -QP!:Y!"� � %*� � N9��� >� J���B�%�>���q)FU5R�:F5R� e�1V� )].�>& J �>^ A f� ��J:^�B�98��M�Q_ �I^v �I/�J3f�>�r�)S Aza] j $n-1$�*j  � � �� w ��� 2a):�)get�R�* �.*� S �,�y-" ��,!�W� &)�\)�\)*\):,R\)ose�  $�1�*� ���2}=�+�*2(r�!,rectly read �! odd $n$&� by�% $$n=1$ into"#D(n+1 *21}), 2})ee", -6-% /78E/ vely-ex�,seE� the &� :�+�M .i�<#m�[6� �q)(u�-e�}" _{+)+P.u2B9�� 9]!���Q��(\sqrt{q}^]�i>�2 �W*�4.(#�$&� T J.-��9OS� %-2�!�+��&&1+f%�:Pa\"� a_} �)Ela1)W:QIUQ}{2�} 4:�( >1�% 4]N>���B1):U�'ZwB>�(Y>.��.e"6&) _2g qg=BH)� ��)32% 1J1- +N+1:�VAe},6s �(���� ����B�.2��"�%�I:�2_{�'}&� 2}1wu1 . Due to�� ind�4minJDel%.l}$>.6�henɀ , we=&replac9.<ٞ�C4V�5}) by $@^{\prime%)a.�}4_ arrow KT � -1$ Yʍ�V�}{1>�0 )v- 03}(b_{1}^{+}+ -})�S  -}.�'jB~ +is1b�- impl�1t� e �4s>� 9})-��.�,13}) now hol� �%!�b2� �  upA2 a $q�&factorV%result i.�M���4&�� Q�2!!2�`1��>i*� J��lX-��2���% �Ko"� � !�"�-]$�o�$�noNm 6�*� �� 21.�3)��:��!>.M�rC�&>�$-�Kj��-N�-��2F>� �aZ� ml-q.� 9 �:�� ���9.4-�:�t>� �n�����2&�mkB21}�8J9'�8-8�Iw# E��   " E��)+41�% ! S�,��.7i=)3*��B�,% A", suitable"�6ɹ��68(� Eh $ as� s"`;�8�� (2 -!:-;�( �6��-a%� find*�,'E�g2<n&]2\Q�{$ %�(*�� 4% 207F�in order!:ot- a regua0"��)T+*��9���9�3�2��9u:70on{Conclusion*\:provi~.n unif�-Xent)�of f:calculLs originally describ"��.1f-(\cite{Li2}, 3 4}, (}� }$6ofZ $I$j#%Z$n+2$E�null 6�s;�lsecond family depends on whe 0is eve��, featur!h���$2+[�n}�@r� ] $ -0�� ��?�"�a���)(O%!% �>A=V�.1Zx$  ul�?*�9~%$n$��$2RJ% 91� �V�%�V� |.j�.<> sa-eY�M� ��k$n+f>1 ��3q�@ ?$B�!5$I�1.$j�.�Z�z>��^z >2$,9>�9-1Z�8n-6$ E �!mA�one;par)B���#% $���Vx6-* >3$.�B %��8ntr��xQ":A�x8�5Vbe new5� s rae�$than limit J�����-^6nk�ͧ��������Again�%$e emphasisё%�!ec c�6�ŕlai%�!�2�)� %�on simpl�duLұ��" Z���q 0ex conjugate >V8�/ %� o�Gq|NnI�J9�6 �>�mA�d1r%) "�� ) r�� Z n  �iaE'1D��*� R�v-D�5�2V�у $(n>1)�[�F��E!Az~ ent block&�9>CM��JHany�:��% .�eP2n�he6  wH� �;\: discur@ -by-m�i�H` ti�;u 9&� � is worth O io ab� �&� .2, .�,�6B�"�(QE s: ag �;e��4to an appropria�choic%Kth�6qs, al�<allc$K2� deI&!J�!�&3 �,����%�I fied� CNPq @lt1} C. G\'{o}mezA X Ruiz-Altaba, G. SierraB�in >P�b�Y�!^93.^\Jim1} M. Jimbo, Commun. !�.Y.���0*537-�.HCh1} I!�$Cherednik,i�VL6597 K42KSk1a) K. Sklyana�J�A: �Gen�2N 2375�82ONe1�@z`% 22 L1�91:a�Y$J� Int.fMod�Hbf{A �=, 5231�:_ Baz2a�V�� zhan��!�. Lett9$B 159}, 32G852�Baze�2Gr�1 47 M72M HY} B.-Y.���-H. Yue,R� A 18L169�32L Bat3aMBnga T�P, Nucl>42%MS} N{ MacKay, B ShortvO23A 313 U6Ne7��rT 13% }, 27-K6�N�6��83N�CD �owcock,�! ig�P~ Dorey!P(H. Rietdijk � ��� B 44�4�:��A.U�JSTAT<(017P}, 0705�><22*J.R�46C53e�20:EB� ���6R�VGR2} Hade Vega,�0Gonz\'{a}lez-��,�)6� 1.27}, 612�D6 JWWXA� -X. Ju, S��Wa�OK. Wu,oXioB�#2"� ELax pai�1D� XYZ s"�,)�Lit{solv-int/9712011}. LJWW���Liu� Z�Bo 2�3A�35!d 19992mIOZ} T� ami� Odake,��Z��%V470}, 41)V6�Li1EF(Lima-SantosM�-�1� B 55�F63e~:�BP} RaLBehrend, P.A. PearceA ^(B 11}, 2833�[6�AY!^��C/ Y��BH6* 3* 109N ac2:�~NA�786i�6u4AADF} D. ArnauMJ. Av�)4N. Cramp\'{e},a��[rappat;0'{E}. Ragoucy^|6��9� 6H VGR1�m�,L5M)6f Ab1}�bad��RiA+i�Le6� 35A�92%�6�M�rM�,MartiQ X.-W. Gu%6R25\ 721�G02 Bat4A%b\ D6c. � transfer"�$igens�6ra�Voc�d��9&�G}_ 9�%R}"|x�D4hep-th/95020396Bi7F�6 SolJf"@&�"p�6�u["O& � ]$ vertex��@% nlin.SI/06080632�XHPW} Z.-N. Hu, F.-C. Pu����~G1}% L19:� BGZZ!(J. Bracken,AYa�d�� H.-Q�� .. ��1A�588E�6 ZGLGa.EX� GeşLinksA� D. G�6�.e�Z77�V6�ZGbdMZZ3e�L1RrHY!2*� W.-L.�*:1Y!.!Qo�!]*a��259R at2F 6� Cyu�� 6 7U 2026��6  Bat5r�.�9�45U 552VS�6�V.� dkgA. Kuni�YC� � 6� B 37AJ266EJ6; Bat6FZk� akai%�l 5�$Soc. Japan�6z91N Gan1 0M. GandenbergwV054��65N�MacKW&& 2� n>�  17I16/DG>WAAoorge,M"b� 21��6lBG� a"n 2� 5K6[ Q634}, 82!2006� BK>ZK�izuk VT64� Œ6�GZ} S.��2r A 9}, 38�'6 �.!I�� 61!�44N�Li3�G4a�568y6�Li4�G5G4aH20:/LMFFR� laZ�7� 66N�Ch2��4�O35e�86]VGV} O� .n,:� �Via�-6)QxB 190},a��C812�FCA":!V> FatSov> N 32%9��:�I�. 6<n�7E�0�:�Ne3�� 7 65L 6W ReSh� Yushetikh��M!S]8ov-Tian-Shansky2R:��1] 6�KJ� Kim,J5x"W �1$ Mikhailov|bat>F � 4121922C Ne4�7VQtt��6k" A 14)70AS:�#O.>,#��F�Z� 68�055iQ6wL"�w� N�B 7�43� 6��*� K.-J. Shi�&�Q�<>�% 3aJ41:� Dk���~a�475� 6LSW� Caoa�) LA�Y� R  66_�B��,:�~�!�43G6�- ��:�!� tat.>.:1�Exp&�P0 P080�20:� YSZ}2� R. Sasak &� JHEP�/04,046�X6�Li5% KurakEҎ9�595RQ6nQ~�8�3S6�L�"GE�Li,.;R&H6�50!�00R&k52��e� XXZ�as"�� at)Ui�! 2�!&� ��060311��rp>�  docu1 0} �h % dem�'Q!|exist��!pot�al, a"�"k9(of Lyapunov"�',P$in dynamicd+l-0cycle  P�@@ Hanggi, Fernadol!�AALeggett1 subm�Nd &New Jour�of� i on N�a)x4) \�H$�[aps,prb,epsfig,twocolumn]{revtex4} %Z3preprint+ �9:e!_.� (style{prstydraft 7 titl�8@1C!%��!r^8D-;$} \author{�M� u$^{�� Yin$^{2)�H P. Ao$^{36f=dd !{ 5Gen� ,r X5 27th Ave. N.E., Seatt�4WA 98105, USA �F : vS� 9� , Pe�Hf Lersity, 100871 Beiji�PR ChinaZY�DeU#A�]�! al Engine� ,B�y:Wa�9t� :�9� } %\5)<} \date{ Dec. 7, 4#\toda!�%\make%�U abstract}mL6Q�+pqG coe`F.�3<%.�Ce{)e f,; distribN�popQ;. Our �X&e&i�))$ree steps:y%C8 show6�5'i��Ja/8�#"�%s�!94seto':A� �'6�E Mexi�1! type,&�strength�(a magnetic �%0meJ,��k grad?" nea C ��qh71fri# go!N(o zero fastF=�4s,WN- N!�nc0k���-u '�'!we�?'�mub$�(x#ne�heless!��(atEMtS`9ly�<X truc�Ne=\; ��&G!%�%� '$al systems1�. Thirm argu�at su�'E[ayl carr]/�.in a �)gD+ situy)"�,a A(1&-�1of us�s%of deal�)�stocha&%V$>t))�=![in"D;!z$I�both I�. nd S7 onovuo�>usiEEmaym,useful�m2rg%ed�-l�[s,-#�&AK�us%�of�astabil,of2��)�2aa�Hopi Y� *ne.net�(compu3'on.��a��X %\pacs{PACS numbers: }��.�see"{Introd*6} No-p�%edQ=sU<%�]lsY*�2n@in B8. IvF1�a� driv!�for�Y �R* ofW;lie�Q�t,Xlindner,ao2004a}. Untilz/e�/, deXg2-�9pt%�B�,�5t A�gy&� ha�.en;oA'P>apEs*inq � �,guheimer}�U , it251clu!>ta~APnoFq  or��)��)dI+tŜoj3-VR<!} �hertz}�%a0 stat��?an�|be �i��ny (r E��+gJ�ma.�A�%�eca!�emfE;m;(ed, efforts\1S1madK avoi�2!�aR5� )� fu)�ufP28Boltzmann-Gibbso�Q. Var~ ��sO4�go ar��_issI$��4 Machlup-Onsag! ��}�),�si�s, etcAOv-,en developed-�lund}�Iy= ,successfullyIw# �rFeu�>�!�� tf(�,�oaqBe 2���l2%M�dykman},1}numer QzCra�/orE A-escapA�pat3 mccl�5cka+ow�6,J8in!hѽs,a�r��8%a�si+E5uM u05 ind���-A3�E^)oid�0solar�� �jaffe�&e�is��2U0�9� sk wa�w� be��n���3 �auQ7a�nA�e 1�� �bb�MUkramers,q gi>EEX�=or���HQ�%Es�o.u E� pura2Q6?3 0cl%�to{3an�3icit 6� ��at �+&�1casW�s"�,N�a�be7ely!iI�ed�4�4!�crix. link5�th�1x8way�.��0e��. Ourg!�is. novelJ!! hand�asz��< ��brstoo"�u�  mass- of aч�3Klein-KrE&6 ��͢}.Wtt�0)eA steady��2� �e� ished 9 6Zo41 #�rn%S� or � B� I:Ai� nse�4weA�{ be surpri 8�>t a* per W; �o;I�GE�t !�in Ref.[)��,��,i�]2�2E�our�J��6�7�*s4� ��aalt�-�a�t�}non�3libriumR�es�(s.��2WA X;:�co-���\a}8!�)�� !t";�wt ��s,�3r!ively�$FA� IIi4�7a� F&oy��� a w� i. o`xr "�3J� �Ɓ�FAn=2J{Abusual�8R��& :��.EJ��.%1�g�< 6� !Bv��.~$ IV we out y�a8)8�^of6�a broad�'A Bl�e A�i��s. ae-� |� ��m"J1!-ubtle�52�V%/a�� i�!x9"a�Q�)��' %��g iblyT� q *� �' �{LW�:F$`+=f view;yJJ�gC 5�al�)�7a {\it�g�} 6��n%%d*R4� spaceP�=LJ���4%s�  k(goldstein}:�\} [ S({\bf q}, t) + T 2] \dot #*O@= - \nabla \psi67+ 3 \xi}2O \; ,v��.7l; e~?!\>ionship�>�R�\langleZ��^{\tau}.�') \r=�= 2:%,\; \epsilon  0delta( t-t' )R�$v� y = 0�G$� q�(= (q_1, q_2��8$$% v8Cartesian coord�W�9zG]e�Qlpercei\� posLLorent<<ce7Jwq�y) U)��< x $Sb��decrea!K�c dissip�Wma�w!bZl%Q"5 ,e :!Vco� q p>� E�8$A?Eq.(2)Q�guarante%Nat� is�ne�=v�5�,. All $T, S,��$�O�C%� �� �� vari� �q�R�El�A�ime $t��&�"�~ $�%$=��<an eff ve temper� u�-^ takenAbe�  re �Q �̈́�b" bx�� !/� f� $\rho��)wb�� s,NF 2;4 \propto \exp�J\�_-�Oaȵ| ) }{1/ } �OZKB�t�e2i 1�B� AP3)U &\[�1a��lcl�ݡ.^�E�& = &A�&4 8�j BBa_\j_6� 2>= \leq & 0�.  �>� �z!� occurA1<ME� set�ExU�&Q�GA��meaE�N �Co� 6� ,Ese*�J��T_�jE�SEW�ti-�͞�&��e\ ssum�[�+ 1 at $q = \�YL_1^2 + q_2^2 } = 1$]b�[!�S-��S (q^2 -1)6  + 1 2^�K:�I��1�Q�G�1�^]J��`TAsa(e��� !�� ���-1��%5n V -m��i� - �] (q )�q�Q8a�U��9�in 7)��ro���CY�in/*�  e� a lo�maximu9�� = 1/2$I�=0$�F��fixedɦy?min2?0=1$� �m�aU2���2 shaph > . ElAt�iŒ� u�S$�B 2Ial �����B� AmL�a��'�l* contour��&� 8x*�IEMw�� b�)acc� g�<��cen9>�'3non��� ����true. W�l_ �|er Wbehavior&� 1��t��%��: �$q�`suffi�!t>l��to 1, dO!B�.|asymptoM�i�0)0Oq=1qm�Xtu^ coincid�th it?� answerA��v�J�Oa .�W�%.� .�"��=Red rA��[a5�6� ɿa�t " �a� 1) (2):�S�[�s:�!IM�� "kal&6jthe rewr' n asV� .)���.�R ^{-1.6OZ��uK} W!��&�Q Eqs. (5-7� e%��� ��~&; &�N\det( &)�G�6[�u�}7z��'- {Rj1fU�o�@Z!� . \no�!�?&� �. -�Q � ���^&�]3 b� �]Q1��$)�+T) = [  /(.+ 1)]^22o6+ @�C q^4 /2R] ] ^2YN&�Oe���l�.hqM�%N[!�1- 2 -�6t%�E�sRI)o��2=& � + � . 4 �2a��Z�V��O( �^2 D�HB8����']a"�ņAZazimuth �u(heta$ % %$\�S��U e unit ve�j �� [d`R %���p�t:P�)*�, xT� m U"&�aTL��� 0) f"db8)�A�,� ��Mrq$q-1$*�qe ��q}�&&�4U�,%! '1)2�Sq-1 }{q"$]� �WbX� e! q(tT��Q& 1Aq+ q_0Ed\{n 4 tH�a \}�� FD _0 + t�+ �1}{^vln+ o-!exyxIl\}�/{2B t:U���2} \ln�(2A �-az t ��/n�p *��-�oq_0$ ($|� | << 1$ Aste ngM���M�� �su0U��e@$1i$BI�T2\� de!xo�>.B � .� "Q��� �*] o�+nps�'> � d&6W$s}c�0PXnhe  W�)nershobWl 1'� <�"2#�&cofF�(H(� P2E�*��$ exdYe!�  !'ear�Yr�� 2W,Y�$ :�Y� 's al� Yef� �F(f�[�d�� � -�oAj� d*� , b#�ofe�erv� � &� ,�!be�P�>� pM, must&� �,.hE�YW��W� &; �� , a Lh �@o�A� keepE�!��  ea�[R")��)J�c� la Z g �& "�.i�-� e sp�&m�F�mova`��c� k&�r!�R.s/�-4 lik��e�a�1"� ���ir=�.� 9"9& robust: S:'�Sg�"0Z o�I� �RQA�]�UI|(�6) w  w��^�. A�%onsequ #V*�JWisH � fc�Ya�/:�I�g��T(��A5pN~�u?!�%�P �R(+@tak-sin�Z va��%�`/U� �.�!nB�%$�4. All '�zJXxpl�# ! ���,���wo ;[ lh_>.�n. Pk�d]� c&DnFE0R�>x��0an�!Oh5). On��Yeck!�t �,cT]te &��lea�6�p!/%o,x`0ts u�g;�2:1 high� �o�"ar!�%�n !�e�#�kr%G!�t5alt�5M� ^PEiF, $[S��$ + [S - T  not,a���l��me back &`��C$^��163K4& Vb�#E!��'"h8a"�2�Y!�d&��n$a���}7�IIxap�9L;*m oves ��� �x�#i��4� �sns77a����n8c pict-� J�A "Y,j,k�^� at�==�+Ejty 4%��NR.�E� Q ed. W�r1p �))�E�a�&�a��a forward y�(��/s`7&�4!3M�I�� two "x%�[�r*q ��.�%%� *X#>� *muGVp qM & & R(q)� �#� wݕPhi (qV !8smo�4�s $R,5$���er�' $R(� 1w0 e�a.��S*�!V$V (q=@E an !�3.�'%�Q`� %�-6� �$5�Q;de�`/��)� ,���-�3 *},D �N�� ba7�^ *0�� m+aJ"liV.�8Lorm �h��m�tsojScɱ11,12)%'� H15,16) immediately M�k at�v0롚��II��j 5 U�.�. <���H))k!��b!�%ym�c`: � c-/s. N5 tn8Zr &f a�teAa�do�9l�qe�( ��#5 n���t1]�`uk �5I* �)�! mbg65Any ���2 Q� %[we�.��ldisA�G. On�4�,�&�12�&g2,6�-V�E� | �u!#%�9�w�}�/verDs�* bala bM�c5X"`�ɏ�U� }"� 2,�Ley�R� ܆r��a�:� . HoG� �-� play�o�1n ?66. A��!� rol�Dn �aU�roblemE��ax id�*�xG"F6&-ev�uF } AAbti�xrAcllep>Thd�::���Ekobm�we�E�YMž*\�"�12 in arbitr�x�7�A��e m�4��;&�i�"� � a bea�s� a�6�5ed�$�4i� 5 iAE��f {&u�:g�&� �aI��A5E�6�or <"��ic. (�8 &�8t�6w!Z2؋such �1���"�d^< qgA7&� (� i�� kat}:��w�& �1%��in ���G�+� ia�7F8 $n�) mere�wo yY*� �T6/ =�,f6�&+ \zeta}( q} �&\; {=�}�U6K$����`n"�*=a�%i ��4=H 'is�'6��$�!t ersɮe�1) bu�&���e�(=ource.>�� ^%��� a>� � �@ needD T>=%�{Ft0 &D��J�� .(1-#I� ��be Ga�?A'nd�t� �v,�c"�U 6�/FV� 2(* )>z0v0DU8!�A7"#+\;�(v0)Vr0�mekW:}0 �Eo�16~0The"L'D!�%A.�. ��,'at�)�E�%o�Csam"� I*t$r*4r easy�de� H7)Ih U� �<c"���A��5.47). UN C7)-e�nate .�0� &)�n�"X�A�M�}n�@�s27.H#} �|e#,a�E�"i��*�U_ [6�)+ T.�]�Z63Ms=�*��3.7A@R�2t�}b���Fg �>)xi>�BT�$����gdp8 t� � %s<5 . Multip�A:20)� ��o / Z�2�a>B$a��Dy|t:$average ov�9�O5�Jz" ] D.�"6�-6� ] =>�+JHIn�:A��18Ex��u� q�8). 1) � s $nf� (+<qc�v&�un�ba=Z�0k i�t� r� oN& }+: $Q�`1sn- �(0$ [$(N"Y))_{ij� #_i @ _j - 6)U$ ], �19)�1N� B �[��Q���y�)��-B�$9�-1^�!R2� & )�c(ied. CombiEY%�1-�22&n% toj� $n^2�2 Isis ex�mx�z�!in��$n- n$a $:�:� ]�#�&:8�ox�oW �a���� "���Gi*'���2�Eis.PJ\�b� dh hu�B��MIII: )2�h2C� >�)���6 � q?"�a2�4 2-��ce� ]����Bz.w�?)jva.�*!_19), h� � � Qq6�%'(�� O"g� 6 !1t3i��� hezGl�7��2�B 9���Cb&�sO�G��a �o�)jg�� ��qdi.�,.lso!}Nnge*��Rr�8��i�w���7p8�D �al �+(%Erim7�r5�*{ ,Ȋf� n V� b} O.��u�jN%�tzQ� Hrm�Nm1.Lway t! corp��LB� \M�.�Di��!� .� .�>� ��e�^,Z a.1�-_�"9[,�a ng bI fa}M8,)��� cdot�  \neq 0 �re $f$� u6�e]� �5E;">�tESo-c��f2� , � ` 8)�v� � .��. B22 it wE�b�� �A]<*^}*(�'T"Z.)*� � �&IA�5��7 �7� �jB������� wI�aRur �2���- :?.. ��.�K$�$��� .L %�v.� !˭�1�Bo21)R� Da f�^2[ -)�- +- ]�>F A6���) �c~ -� �S![ Lcan��J�NA1�"u)�.HFy�Nie�*A n2�NA�L!]�1 qc3"E�6oQf,j2one fin��e�on.�V!!�d�&ny���1llu��W?5 !=.�in"�a�n�V :&� 2]i�� "# }��.TX�P�F� etho selec�%s�Qit+=% 2�WI�b toA �s� ��:hoo�0 � ����@;is�@hap�rthwhit%��)OA �. ��A@-�{�R�&�? X� *��UT45NnN� . No���"#is�.\E �s"D��B�m*�4�;f=,�rapidIend�| path*� &9 �Q�o�q�E,��is �c�$.� � "� Q�#a � �l6N.b!.a����2D4I�f~� routoí�� 2V�y)�w&�U{X ing 7"DX#in�e�%S��Me:&�5%)i�$.�>.�&T��e '%.2�E��F II-IV,~� &".�� s��{. S� ��� ��G.rX2�B�? .,�"2n?R&�J.�Kto�S�ime*NM ��,�L��Y�>+�GE�!�%�tJ/U b>r�n YUMq��-�NZA �!F���R^�} % Poinca�B=�&�}�UR6L�Lr, B., Garcia-Ojalvo�k, Neim�A.,�Schsky-GeJ}�zv�` ElC�5�Pciɷm�.$^�d�LV�H.�orZT,(1940) Brown��r1o)�J~�1�As�X� a(�$ڸE�reaET �0ica 7: 284-30.I�V P.�ridP. Talk,\qMd�rkevic�90) R `-!�0ory: fifty ye�3af�!N��Zv../(62: 251-341}�&�O Go�O�h}80) Clй!��b>�Add�(-Wesl�zea�e�* Mu�*��DQ�oem�al BiH���a"�]m13r�x��w York�\8.�+# KwrcC.,�L!��5]Na����]3)�r�yr��a)a": �)*�#s ("fcnnuscr�Navail� upon F r�1st)='��bB�"e5!� �"5&hA)'.�A e-�K�X\chive: q-bio/0403020 ) %�f�http://babbage.sissa.it/PS_cache/ :pdf>020.pdf�<% %\bie� zhu} %Zhu~uM.,-f< , Hood %�Aoa!�4) �CX1�E E�&rXp`w etic� phageD� $mbda$ life[Fu�]alz��/V GenomI�88-195.T>>p B�h�� \�gca@[12pt]{� }�`(usepackage{��icx} .amsLBsymb}!YDrenewcommand{\baseN,�1(tch}{1.6} \.# eps}{\varNR:la}{\l%':K&��K}:EE>snsn> om}{\omeg>oprt}{\b!`�0width 16.5cm hex(23  hoff L-1 v2cm"g1�Vi�hWa�^re�4���g�A]und�| borIY��ґ ble ��low-wa�e�ca*iG�,El$^{\daggeriR.�~Grimshaw�(A.M.~KamchaoZ"S}$\\  +� oo��6&AI&�o &E,ces,\\ Covenn�Uni�iPV y}deez� $(CV1 5FB, UK}~De!��o:�p L� bor.r\\ 2LE11 3Ti�=�$S}$ InstitB of S�Y$roscopy, RD%}�8w0\\ Troitsk, M1w Regi� 142190 ?e�;(EU*a"�d 6W dU=A5vic~G�a wave-QY non�!�/�)8� grAK Kaup-Bo� nesq�HA[ .[�8f�K$Whitham mo�E��, � naly�!j, 7Gu��0ch-Pitaevskii���d l�, "X*( ``cubic" � reg�Ris�ed us�� 6*�hod��po�a":-� �o =G�j$Euler-Pois1�.%�� �.� 3�s�&o� s���9��f�c] "�Y:�f�2"�*�!x"�@s � �4i�v�8.Z/XI -dis|Q�V)��;!�y[6d !HA�e �",S7E.q=�$��&��sɖw up. ��-A�9�E�, aA�m�QAbe�s m%-�d�|�Is%" m�O)�d�xg�-�s�Ual2���uJ �&�2�� %8on�;:�4"s�.�8 Nv�=be�5� o]unt��se <1�y�!H �;Hos& N0.�:v�_�!��e�t:� , or_� �"�inU �7"@on� 1cB�ve!is9�pib"�. pua j-t&� a��s*2�� Korteweg-��ْ (KdV)u����E=��(GP� .GP1} (seMso��i w�2})�$GP�L,%C���_f:�sOA� s a slowl�@�O�N[!A�u�A�YKdV�E,'$ 4�$:-4li�pat�8 �1th/ l�Z" � permW(�$o�ly {b� (%8-1, !%�$aa�ngD�\yD�!&r �A�"5U�..\'oriS� paper=�, �-�W$re �-.  =ph3�HJN.B��+p�'�h �{�3inu�l�.�E���& $x/t$-ssjity"'�Yte1 ���=ed. A��!~�[s�"d(u� alA��sta*fB� � ���:�eaۭe�1�l�4�Nxim�Qlya�a�perAOhosen �� cur�s����l�iuve�"�Zly�-=Fsej25R�=�%�� Pot\"eminW`� min}�H Krich"'sڝo-geome�<ݗc��!�_ Q!wq.1$�Kr8yxi2DN}. L� ,�${\"e}min'sy���Y( l> ntex�� Tsarev's�fJ v /1} 5`(KS, GKE, T}I5�#kC�ܡ? �&oe��1^B  H�4X2 iS bes �Jd�J)dpag1V�li� �v��sE-��;bi-.HA#ogiMe6}wa�N�/dA� Yv kaupM�*5 Y��AL M ��1� . LlD-"r �4}.� (KB)� ��m\4ly.�and�r^<� powerful � rDca�F�}~�K� #i�Z+a9:::st5��^� !8 �� ��*�� ՇKB�� D�UsMY} Mq)G !�&\ s!�!m�u� EGP}�!H�8o�����n"�Ton��� d a\siY�I���soliton!3�T@!B"4Ia; O pulsA���v�n� KKU}�!�P�����&�9ten�:�-*�-��e � of :�M|y� !'5�)�E��a 6� o-�-KBTA��#�m� ��e )y.�! �6�� �. '��QK �� wS�wҩgn1��4]F�N.��-:�:w A� e�> *tI�m�7 �l�� q �Ely )0t�&#�."� skb�(t�`i� I � &� P.� "�>"�In&�7�un! � , e.g.��a*)%�Um� KU��F$0�MH{l} h_{t}+(hu)_{x}+�N�N$u_{xxx}=0,\u)u}+h-=0,� N��eqB��R5* h(x,`~eu e �m��urface�;L a horizontal bottom�' $u Ois re��A�1 a�c� �(! r ��Fb+:depth-T3d.I@�G�u� (Y��)�(2:B�1�U�2 t4ati�&�/!w�%�%����1�}�2!�}=\ cal{A}~2�1qquad%t}��12, B}_xx2b�>B}_x9�2"jQu�'}e�B���eq3� ΣR A}=\kc \la-* 12 u[P^2-h,\ �Q�=-7+>7�9 Th�.!`��;�F<_&><t D�of2can�K� ��-�-}-ga�#�|�ՙ5�mch2000Ar��.F way.7� �4 _{+fnd-}$$AYbas�F ���� i�lI�"%�)1l�!�i΢}yB g=AS� -�Rla&�eq4B`M��!�t�Mm��Jeax}-Y�A}_xg-4URA}g_x=�zB�� Upon ! p�0!�$g�at4m!�!Z� a���to�6F�Q�g�}m 4 g_x^2-.�^2=-Pa-)y��end]�&�(�� %$B� )gho�N�9 on ��X��t e�3�\g�s,j !�1 F�g�=��B!x�s�1�7B�R_%i�B��b�uc�Z��l��g}�k �.5vB}}.(x���8B�' a�I�]Jide���t�vfF!Ta�� �O!�e�R lawi'!�Bqy�%u�1})��(7O�t:!��f6iy�6})�Tly�aC&>,one^@ ��aw�SA�ER , co �"�#�� th degree�J xFW]�=�i d_{i=1}^{��lI�- _{i}�� $-s � ��+s_{2��$3+s_{4}.y��6�T(8we��d` Eq.~&!O)q}J!�k- � p5lJq= 9= � -\mu e�,�10J�� .$�n�y"R �1hV$�� �'F�� =%O�o�\m H =\tf�14}*^{2%_2 4 !a1}�,�NQ ASqmfO-� O ri�B hi7e�3�,e-U�^{i}$My: a� �k.��sH�a�H%M&�C!?on ������>1�=�$a oBwe+Ew���%�D[[ @� �� P()��]��~X s� 2�� .�7})�; Y Q+9� 2}u)dw-.%�. \] 1e��Q $��Vf�iɔ�he �FnwN =xF��@��1F� � 1Va�q12Q hbox{s� at} I� V��12 s_1 \sum�l4\la_i Y n'h�Qvel� M�&E��%�( �i��a!j_�O8 }=2\sqrt{ P(\m�Ou )}. \label{eq13} \end{equation} For the fourth degree polynomial (\ref{eq9}) ) solu< of this Mt is readily expressed in terms/0elliptic funcDs. Let W�zeros $\lambda _{i} $, $i=1,2,3,4,$C+�$P( 2� )$ be real and ordered according to >(rule \begin=F_{1}\leq2:3:42b4Bb Then��dvariable $\mu $ oscillates%*@he interval where: -Nion unde)�(square root;1�@13}) is positive,B�Y,5} \la_2�mula_3.>*,Consequently�2  Eq.~2� with&0initial condi!� � (0)=g$�given byj�6 �@mu(\theta)=\frac{FA_4- 2)43 2)\sn^2 �$eft(\sqrt{#6 01)}\, f ,m\right) n 2-2�b m d,>tEj7 �m- 2� �1)}  2 �>vis%�modulue�A�N�0An equivalentU corresp!� ng tixB eQ 2� 8 �V 2��%�1�J  h� Q bB{Substit�wuj6}) or8a�nto1})e_s�Es for $uJ$�1 $hqZ$�P!�pperiodic nonlinear wave. Its  length��9)�L=\int_eK2}^3}i�d\mu}{i� P(\mu)}}=i�e�2\K(m)"%�V�FK$;�$� (he completeYڡ{ gral�i,first kind. ��A��/%15,velocities $g$ can- X � h rmj4 �H=\M 1- �L � _iL}�_i�V,� �pr5 6 9) -��phase� y $V���Ag͝$L$!��f:�ly by�, 2a})a3 9}). A si�* calcuM�}�explicit � a�$ \cite{EGP�b6m "� 2� !Xarray}{l}\displaystyle{%9v�JA@12\sum%,-xA;�� ��)��)� &26\E�Z ,}\\R~2c Z~��~.6 1~~3B~.���3 ~ �2F�&% ~ 2~~4�~ RJz 3 ~)z ��%��I V���]$\!�I�f�� a�9se� �, � �� velyـ��1�2�u�M�v�a�]� A�vJUm�v9�(3A�3+4).v_5�Ex3++4);>:�h2J"�� they��s �m� �1�2)�u2�1 �2:�3=�u�B�!�F��)� ��E Z�4.�=��+I���{ ߑY�I�2� � %1-2 2}n�-%4)BkD Next we shall app�Q�theory���po� (undular bor�� -Tvic�y,a� -break# sing9ita"�xThe Gurevich-Pitaevskii problem� At"� }�ub"� ave e ���er�A lessi�}" N,6eٺ})M�s� (well-known %Aow water&k f�3a 8h_t+(hu)_x=0,\q�$u_t+uu_x+h>xwhichm(transformed5�iagonal!.jx3 Eq1AK+6@ 1m�+Ep-:M . >M ;T- T t}Tki�>T .� �� }jP 2} \hbox{� }  4 {\pm}�X{u}2\pm� hB �A`(Riemann invZnt�� Eqs&� 30})��� data&  two&� +(x,�R�y� -  d) m�ba:�distrib�s $h_0(x��nd $u . The � U�31}) has � amil� Dof characteristics��L$(x,t)$ plane along Iione8�F (e��+� -$0constant� @ �point*�aT%~mom�w�:���he �� amr�, sNac2<B�X becomes a three-valued5��K physical %'. gsuch a#� ��on occu�AO>�i�err� �o�%=+)�n �J87�fil!� +$ a� !.$x$Ea vert� tang!a}A�, hence,A .��)� itdesFy fast,!�reAche�JZvar7�$x$ m�*3ly| may be A)i\ ��A> "M:Bdb�3� la_-Y 0={\rm CNcus,1�6��AE�� � deal!��a � !�I�� ��^&e�is iden%�0ly satisfied�.�33�[� \ bRta"e�he َ" F-x� >�t=f��)Jnere $ QE�vahYkto �prE�M���. AI�!3�8time, normalizeMtoK$t=0$�Q� $x�$ must h���flexion1�.F� A�. �6n!�!=v*�]��� approxima�by a cub*|F]�5}f�-C)�- \over�I}_1)^F7A" Ug1��vɶI�� !S Galilean ��!t� B("L3Z x'=x-u_0t� t'= h=h' u=u'+u_�uad��|l '{u_0}2Bl��scig��; x=ax�t=a^2t� /a^2�/a ��4)'/aB) WAJA(aid�Uthese:�s2� 35})Q4 cast��o0r3E b��+^3����_0 \, B� ��i* omitA�� prime su" criptnotEc veni�" . It�K��a�&w picturU oweaFig.~1.Qf8figure}[ht] \ce�7I�includ,Dphics[width=8cm,he/$=5cm,clip]D|1.eps}} \vspace{0.3 true cm} \ca� {6 ]�� lev�dis!io) �;��-�� takeIlaN-10. u�figoneS �Kactual���y�nowũisi l parts� llow�x �6* GP1},!�su��atEpreg�of"K^�&� "�:Y��&�is 2� �M��s��2Va�weI� to find t�v� matchy no.!�a�. end�s -�o �). One|saq ;rB* (ru� �P) ``replaces'' a non-  multiA n!}ER��$ should em,ize, however��-�boundO �.� {\it doa�$ coincide}�d 6>��a:��. Out� 8sex��� � a%�+>AP2��&�U=X�$} We look�[L �vU� !q�wQ��<x-|t=w5�_~�*o�v&Q�25� Sinc��� idere!"� �R>~ e," -<��+$a� ��f�4j1t�0(_0=\mathrm{�R$ c#� ��!Oula}�6}�r�$2a� showe� if we e� $1W$/ e��F�4�b�split�w_4�4^3��at} w#�� "(m=0),\\^w_2 A2rA4:A1a�% � �!�n:"9})�E!B�� ) a wa�0a-� �� 5 trail!�$edge $x^-(���$m( ɫ �+$ 9l=&ng8+681$,YW2 $ ��yb�2 A�ploɧJ�E�2,!�34$ as"� ��$x$ijo��lcontinuous curve whose upper�$lower bran�o� � !y�qo3A�mO6�.�see�2)."��-a � 2�� Depend� !暉onI|t fixed v@�l1�bAWI�1=-10� dashed5�ws%0c.Y d2�e +$�7,��E�KB]�j�6e two>e A>�)generO8odograph method1 Tsarev1, C6� 9}) �! e�ݑ��� provided.�aj)v�o�*e flowj4.!2��\tau}+�SV$>�f�commu��%��B� , i.T*� ial_{t |��i=  � t  $. I��y�.)� �K analog��to6<24}��1r"k eq43} 1N1 ar�5  9 W� jX��_*!�))ativit�"%�25�m"#4A�".�8of Euler-PoissoX ��H, exactly as happen�(p KdV M�(KS, GKE, T}:NLS EK95}wesn�4W,9 jW%�is j)}(#iW- jW)��i\neq jB�It easLcheck l1��a� i!r�2 $W={�� }/\o+P7 )},$�-)=\prod� i),$ɚJ.suffici��(Hour purpose. We cho�w!i�%� facto��A! coeLbef���^{-1}"�(se�expanY!�$W p��"� 7be%_� *�"�>ѥ}$ $s_1/2=V$��we ;(D`-c��0$W^{(k)}$ defp�2� "jj 5} WR\la^2=)-�}=\O"�� r})k}= 1+\t,12{s_1}\cdot+1# }+ \$ %38s_1^2- 12s_2m�:8^2} +.:5{16}=3 =34s_1s_2s_3 L >M3}+\ldo�\e2�03a2UF��+�� is)$�jV6��)�A��� ;��� ��(^{(1)}=v_i$"5� AY��� m�not diaulh� AF; .�M>H . In� ,"get� ae"j! j!BV"�47; -v�  &E- .w_1)I |C,�!ef%2j%Oi1� s 2), z 2o2)�o^%o38A'a!+ !1�2+5^b3�^%1ac(n1^3+9w1^�2+1 2^3+32^3).BeW-� �} NI enIJ*.aZbin�� $$ �a_0+a_1w1� +a_2 2) 3 �,$$ $w|$� �d�� 41�n��Ds $a_1,a_2,a_3,a_4�� c I�qA"II�6h27ir f��i/y(% r�(red��~1Isn-48"M -�x&&=�3!�{35}w_�)3la)�A8��_0 !!p ��2^2` :1.�i=�5 ;\\ A41&= \J� �:8T�Z ��� )r2�"�{)^)ly 2� of �1$t$X I.%z*� �j�# KB-1�� �4�es�%t�e at, unlik e� casexis�L3�t,e-Y\(wAc�$t5l  counter� RȥKi=t}8/2}l_i(x/t^{3/2 4 $)Yis@� du�-! �^A�thZ��1�,-"�7s"� a�eB (�80$)!�:�.!�can!E �yn� j+ ��5$. A0 resul�$5�K does%sposses�!�41�c!~que�^ a V �simila�% behavi} a��$j\, , \ ji y onlr m9$of admissi�7{!X($x/t$)�s� !8iXM) stEYQ!� deca� G�dis�ity stud�ine GP}:�LawaB mo� �\'!(%�.�,�Fv} \"us*KR]P!�i#].$. F}3wan��F9 !�"a,b�S�smag deviō�$3'��D4'$ from0m]d 4^+$F�&�9a�q� 8^�&3�v N�& 4' \NZ1en�see e asympto<;�/7E��F2" $i=3,4$�-$|�'|, 4'|v� �Dx^++x'-(v_3^++v_3'� w �S� *�v_4 * w_4'BH� x'� no;%�pac!��;ata�cko�F%�l�7ta�%� $x^�ndf` 5_�x+^+=�" !� l,:�� �9� 51} !=-�=�2� \�3'\ln[A {�.2�1)x3')m�/D+2�4"f ]-%l54>Xf .W4�WX \}B�f�2 3^+=w!��5m P 6�2m 4+84^2+14 �n>%p^AzA�=-Ae=&%c �.2^2.x+24 �)\Qs2� ����ұ!E�- U� wh}'��1` f 4qw�&th�6qZ� s�f1^+ 8 �,6Tly^&n7t�)� )���se�a�o�: s��o��prep3 shipj��4t� � ~�B�O� �hand,�9�h� x^+-v_2^+�%���-�^ 3^+,,��M�1�;4N>�I��_ ad8^3>��X$~7Aw�$ �5x50}�2"< after su9�!���6��2�Xa}� ad@a�a�B�+A)$ng��?%� .��54>�6 h�a��|6�X�'j���a%r3�52^+B�>�=�'18? o6�o&�=�%�s A�J�2��tn�5�%IE%�@� {5t}?^{? B� At l)+!-M� �S-E�t=ͯ^+)^3"�9-law!�H i*�j4 5&`(t�AI+0t+�16\< 53}\,� B�a3 � �!�;$c? �2z ��3� 2 ^-I �.�we N f26[%IN2� k^ 3'N�2�� �B E 2,3$��1bT6� x^-� 2� 2�  w_�&� *� �6� >�%j�2 2^->4^-�� 1^2+eHn-^2-4 !4%D42���L4 )��6�;v_2� 3'��2'�r3'}Zj��Z���`^> 4 ! ʥ́�BNf��� !���-=��-=&[12�2^4-6%Z2^ j-\ y ^1mA�4^3-5 4\\ &-7 1(33 �� )� :2� 4^3)]/(35q :�)%(� � ��vH �"F 6� ! >A�� 3']K.�70N�^2}[&-38-4�+-'80��^218!(,4%(A�&+), ^2(-H !�)�3I� ^2)]�?��.q�(nY> �� 61})>. �j�66}1g-Ft_ 2��/v:%_*Z?�V�Ņ�CI��n-��x^-� IQm�)t�%4�7+n -tE�^->�!�1�J�8}!��%� {(IHm�) �4M`I� ^2)-a 4^3} {I�-1i�F%E�K�#nY 6zDR U�8})�1 ���  betwe�'�� $a�SK 4^-$� B2�j'6'6a�2�ha�j�:)-1e�1(2!A%<Z!@C+161g�=� %D 2 ^2)+�3=0��G�J$t�G>�($5R)";:�/-$�.�%WR !�t=e� � �\2u f�-s[f�7�x��"1Eo4)t%-4J�1Ug.�K/3a�u%Z�2�'a"�'!I�f *pby2)1!a�X(*�0"a �%�Y�%D&�% � e.�%.�N *���5�7r5"`# figt8a>j%�wo�n:i�at2�57�1�-sk a�c..&u�2�Be�Ad.� �Q� !n�B#�:), e.g. M0kamch200�:�C� ��)�� M� -/4$.�8"0*�~V>.&5�A��k ] 1|=|��(0|\to\inftyh%^n�>&�5"we$q+�& 7� W�$3\congͬ��4 L!8�N/4�! la_1F' �-�V&�"Eq&><���*#1/Q$F�$"� 7't� ��1�-T ��I10}{21.��1yF0 |E !� sameaA uracjDP7� �4�\\3t}-<7�{�F)2\�� (\ll%�1|B�6�)�V�KM�4*�2^���R>�3illustr#in,�.}�. B�.g7�i+20})u an]�eA�F��%fl�N���!{2N;j�� x^-)z��)~{3-g }}2 �{75}{ZS��:{tQ�0D#� >t5�0F��J��"yO�a&(sfo ��� � Fa�4ed&4�3in >N=�� dp� �Ashock. "�7us�AJ e�� Ib�",.�.m t* n���&TPEIvN�~ mu!�p3; s ofFPx�?h ��6�)Rx�-� aH�W�B&�6s!*�72�� �[[�Z24Q&.-&"�D"�o*�-%�r$�81X:$0�z:w-:As�hseeI�26Y��P-�6k k!'rR6d! a�V!E q6.R&�6 moveF�W";# above, s� ag*e"0&7�Rand�i��ndw{9 gr� main�?s $�A $. S�A|i{0srWA�-�h: �2� (9l\.a�.@r1 gran,b:sA�pag�)e])(isturb !mo�O�1)u�y|� Qdually A;PRd . &�FCo�::Fis Y-cl-��&�5(J� )��FisA�vedU�6@FLJ9seOEA�:�O Q#T�U )wlizp-hB# mode"R+O#�a bi-dir�BalL+pr-bon 7)Eso��Xeffec� �!Ne�JU":� ��;�DN� n�%> 7qmeans2�� seC;�"t�?,�>S�<$s%nN��d/al �)a�P:�'4�YF�. C.� ly�6��Ca��� &<�"ai�QuRx4(instea�>re m !��,N/aV�#)7�, 9�J�A,E� =%X�nt9^is92�#2A��$-?��0$ V"C�An&J��Z�B3!��!�estig� !����2�Z)f9]!-p�R�>�+&v�27$� 2�A�E� de c� 0|���&� [ 7 �/m9rpT��J�%��e e�. Our9)5T�alseCviek rE� teMJi!9*2 in a�E�b �K)�>Lfri�Tal:�.�s  L$&� A9�:�s6c�'�~%(GP2,AKN,MG}!��5r�n�-1Q� weak��s1 �'� willH'?subject��.Ate &�L"�< *{Ac!�l�Hs}��work wa�'mY d du�Gstw&A.M.K.�+Dat>qMathema4F S�10ces, Loughbor Uni�Eity, UK.Lis�� tefu��4 Royal Society%7financiJ8@rt. "^ thebiblio?6�y}{99} %\bibitem{kdv} D.J. Kortewe�&G. de V�1, %`` chwH�q�eJ�V adv�ngIi��a"N %c�ɈoA�new typKC %s�4onary�� s'',?|Phil. Mag.} {\bf 39}, 422 (1895)���BA A.V.��� L.P.*oA, ``N�J�r stru�B�( colli)&� �'', {�?4Zh. Eksp. Teor�'z�@65}, 590 (1973) [1 Soviet Ph|Js JETP,�8}, 291 1].�wX1} G.B.l* �-rCara�Bv��=: roc. Roy.A0. London x 283y38y66H x2>x�L�.��No�\ WA(,} Wiley--I��sI�<, New York, 1974.�PoteminhV. Pot\"�@Algebraic-geometr�J�%��of self-���E�l'*.<5�U!�i�. Nauk-�4%1%�881�Russian1. S�<ys225A�2].� 5&�/.� T[U��th.2�87E8--363A912�GKE} ��� , A.L�'yl��GA�El,&� E&"� in0��.�s.i~�g Lett.} )g454} 102-107; E.�]a"� fin.X6] �Sov �hm�7A�957--96�:� T} F!� Tian, Os*so% �h}"Sb  "�--"�U~ �Comm. P�J���46�$1093--1129%�32�EGP} 9R.H Grimshaw�MŰav%�� -�Vo�nd67 m" Stud��.�10�1!I186 (2006CKKU��\�atnA9RA4Kraenkep �F Umar�3A&./�� nHE�.U`���� M!1N 38E�5A�5�6T&� � .��+&LP]ehsa " ir Mxg� s---An!y rodu�<@y Course}, World j tific,�G,gapore, 2000.���2}�\ 07�!of2 �%+.����253h:�A,''iB$Izv. Akad.�1K54}, 104��90)C E USSR9a237}, 397E�1)2�H?�L!L2j GfB ����Cauchy" �� focu�Y�?Q inL�)|M-ş����(203,} 77--8�%6�GP2A�~�  A= � gp {��n@�2-� -Burg�b� �j� 9 87ś871���i:� 66�  876�AKN} V�Avi�@e�&# �-2� ���Wt zon�%��!��#�k Yp SSSR,�295a�45-34� 87) "� ��CUv_ 564-566Az>��S. Myint�BIadmu��&_2 @��sz"ave �1� ko��>��M:�! 215- I�\5?>@  docu�} �%\(class[aps,p int,*�Qadd<,� ,pacs]{revtex�B6B12pt]{�@} % \usepackage{� icx}2ams LB symb�Drenewcommand{\baseB(stretch}{1.'.#4eps}{\varepsil�(. la}{p} 2K}"�BK�Q.6EE>snsn> om}{\omeg>oprt}{\:ial!� �16.5cm/ �R 23 $hoffset -1 v2cm"@1�Vitle{i  ���"B,.,Eauthor{��$^{1,2�$: $^{3� Y~�0 $^{4}$\\ = }$ S�C l of�#j:In �25�sIMCoventry2zPri�Street, $CV1 5FB� w2}$ In&�Te�ntrW @Magnetism, Ionosp�S!\\ Radioi�P&�,"dAcadem���~@@Troitsk, Moscow RS , 142190 ?*)9j�Xf�\\ 2�LE11 3T! c4>Spectr�pyr�]��}� makeExU�ab� ct}`Q�&' B� � j�, modif ;��v.;�jerm, �I�bUIAi&� ��Z�6�\ 2Uis madɴ�twc.U.�Qr ,�&$pr�ly ��q��NFY�ri�in"� varjts � Cf�_e-gap�T$ technique!�$AKNS schem �6��n(��a�1plPQ rst-�sD"��&C>-�� numel�H o�!�*�� !�!��|%�,)�lo��or=J �UG�>"  unper�>1 )�A� @�-*&N!-��_b�:nGW-$cer= jump��b"ly�m $)v%�Q^ origi� � A�Cpariso�E�v%�re�Xly *a-"`X� n% ZY_%o.��u�y)%y� %\{�y�&Y5Y .o!�e&<  -�A,ures, �P:�� "TMA� large-!@e "� \2�Dve mediaq(c� , oB%Ma�7lQ�s, has b4-pFfous�velopo:�, 1TzBSrt!Jp basi�c�lyq[ble� els}#Ca$BE ��^�, Schr\"oding*3f etcoB����of"}b� mporaN; �IL dra��Cy�s�!�a�iO =a�meE�a&I��ceB ��q�\�RstP"lo�E���W!*3 �k�nB�2�un2� r^ݙ a͙l�6a\>ga������s. �r� �����  t���NfhAeus���Q""x. H�Y*�D�t���pv"TI�A, m ɷachm$ms�^ be availA�. Here,єn]��c�!�!�6�! B&�qyF but.L��# B�� }I1\�el�q�i�\F1�h�[����p.�ext�S d toN<o%��va�A�ur����&Dts.B �e{I}\�#�%BcQ?FU��%UD"p&�j��r iscid!Y��6�5e}\d1.~#&="%u-EA<& _�&A�e�e "d spa�  d��Qe�ca�in 9. A��>rty yea3Si�"�.U.�6t &/ !+A�� !���oB���"m7�@ G�oe�*|b(� �[8GTd����� Y J! s (aulsma�%o�@2)I)� a"e -�$|"0T �F� (KdV)5)�-�ͼ"X %�d� �B"� .q�u2 9�2� e�KauV7�$&� 0),��'�,���p^ailed�b a�f��Mi�A ? �r�[5ks�Y�s� l�e.m� .�,.� eD�+ ac5La�iqAM�rem�(*ua�H)�!$W�� tudy� J(&r)2�WPs��ԝi�0 �% of Benjam� nd L�fh&(1954)!`�� ���sT!>&m�� Y& �m��)�4�o2J$ple$�0si� =�,��Sagdeev�64JT����MH�e a me�%�!Iogy _a"!am= Y�9� to� �1Ag!� ob� | fea�T��.�s:/��_  @����i�!vde�A��-�Y��2} atH rear6/���(Sa�/.��xn܅on!�'g� is&W�&| �of masqm�pum acro,O�ji�z, � le7 vio�!2�gy6jisaeShQu! ()�-1edM� A�6pl� .wit��%�a=�� AM�� yG6�+d#��ravӄngw!� R��KdVBD�㡶�б��`4))^5kdvb} "0u,u_{xxx}=\nu  �1�}7Hs� 6�o&�Z$0 < D\ll 1WZA�XP� ��R�Nby John���who� la q� I�procedv 0(Kuzmak 1959)�M!�I"W-O .I($�='R��h�"cno*�n 1pera�e�qtch!�a�r�3xii�)B�:� o" c d.P. -'s -@E�[Nby Smyth'88&�RTU�AL�d�F�on�.on,flow Uo top�*n.FV6��"k �teady�-r�!wF�Htwo ip$�Us: (i)�Ui�"aI8�*l"�,#d&�Sreveal��q(jump)�F�� ��2�l2 link any� ��r�,t�L u=u_�=�v =u_1!K u_2> ; (ii)�)bb�F4%�stabl�dd ()NXyg rPsays �@A� abou 5���/I�.fur� SaA!�F2�$�((1965c*)�;1970-80s�U@ � * a�39(87), Lax, L�)�t�Venakide� !�ew;94�1 re�c�/w@in), Flaschka, FoA&O( McLaughlin@ 82),6�(�(�S�m89m Jm[ m!��!,E���it cl2,�> YA�)�u�.Ss (}.Xvtv* )�uld� l� frame5 � 2-.1����55A9�&�nof*�m: � Althoug^�BW� sed �.8"`�Rh(щw�xy.�O�� 6W�iԡ��: �����6X71)$r�  �y (%����_#)�ir��T�;e�� ] &�e��e�j)�2� IyGV0�+7q.Iu;�c�c4!\!4� �&u8(whD p��on,�c�%,�Y&�p" u�=ly��lso% F�.��rt��ia�n �'p"�&s)*��Q :Dew6x���a/a<�� of� �&global}!"-��X@�1 ,av m^�ofZ� >-�7gT.��& ('�� 5, 1�&^�1���q�a �!.�.":� ��'�p�5EP9El,"�)%��)^1))F����m��!7�:M:� -5�a�*vn-4. z�Z1�KdV" �2�52���t��n1:�i�&2ya ``c�x"&=�5g�� �� El, �*%d&�, 2005w5An.�6��A���� rai�YZ�big�0n��%I"pulse(��s>��2I.� +�U+�3= �EA�ف��R� were � nZ�e*7�!�'"�'���1y. O7|Z*A�"+����S�byn�91)��uwty layer�yB &�'5�(1 '5 5.�E Raylc"X�g%r�z _q+6N`,2�:� !Qd99d�5&� a!<i�:c"z�� 24r�boH��o�n }�o�us�{��ing��(&�"�T){ � uch earli.qyw !�70��6*UN%�6NI)�� 29" �jo�n�indee����* }&8ofC ���u�"�dvp� 9��? step�g'al*Ea��� ��.�*��$q�, &z �AB�#ma5ery, -�A�i�&� :� ����� �Dr\��[ �� ,�licenot%aM��6��  (wholeQced�$hierar�-��"�"�DdesigAgby�) a0^�-VtA pape�hS��U'�!c� � :6mu�"�%!�o`.��T��. B��6�� A�)�m s�r1<al�m� �al2�<aE� N}2� . We��t�is�8 l 6�FMg� 2n*� G"� ��m�Y��Q�� " A�� (�"�`<l&�st�.: AKBB2�I�Ld��YV"s9B a��bn r4i�A�in"}"!�`ter�8 forcȁIn�?3o� &��9� � �� ��".:��:A &A� �3 \&*�6)[&�7"8� "� Fo��a� a6v:- �!�f!{Ai��{&� ^J!L �p visc#L�7 "a:�<& )!Sq��8!��:B��� {l} h_{t}� {x}+�J1}{4}��s<+u)���"� �W VAi�kbbF` VI$,t)$ denote�e �-m�� surf6cQG0 a horizontalU tom,�IL�v�� . city f��D8�&ver thIR(!��6.� �< 5�!fin!�id-~Iz$05"�(KBB) |. No�i5.�AB���&�K s5���, ch&H�w�� um bpa�d�bC N#MJL�� I�s� =^�8re� e B�H���!��J �"�� � erm. ��1equ�7"�w+!l�Bre�H)ݨB�"�� �i�$!�U*�ACo�*Y����N�B-� (\�}I(q���n� �A�RaU( i:zH�.�/6:�� w0necessarjLH.�&C Ie�o�:�jb#,l�;�r�\:�i%�_=ׁRh�bj 5=./I?-��J"b \ � r� nII2_amenabil�w%n&_ �v�yc+drawback!��� F)� {��*4a�%|>number� ��C!/4"��"a�II�H�s� �>�LC �s0&b E0 uU.�,���:"�rE-�dis9>�]c�I!q\ Dno ``�&"���B#,�ch� s!��� ``nonD&�E����F� ,���7!p 7 ]U� Q�"~  &�Ri�ar.k���w,!7P + F.r�D�r`��s <��rF ic:.Y�.\\ �2AA�� g�t�Ot_0$: �,=h(x,t_0)$, �=u 1�iJ6wi�!�!�a s]9�&�Vwo�A�( teRbrb��av� ��<_1, \ \ u = u_1 U ��as} x�+�V�<2.<2V< ;- ; , '` � �U !EB �k!Rh_2>h�po %�h.*� 7m�9 nO $l \gg /Tha%AR!3typE1s�* o-te�.al 0s assoc�3dE*z�ialE�� .�,�x)}):�.}NՒ eY�\-&�'" s, $\Delta t_{%}\sim  x  l�K! ``*P J J t_d 1F nu^{{. +�u&:����ٮ%:c��ic!!� f gg �$, i.e. havb_Z} -�,U@nu �M�nd<�Q� nu l +NUo<&n�&P3�c�]�>aWm�!s��!�e��A�a*C2�, A��quss6m�<O J�� cenario.,3 it S�@1.} $t_065H Hefj�r!^p�+fu�G�G�sw}�I�)��res"P&wRE���a��YG� &�>F5�)�%JI�M1$M*Il�neq��� ��I.{of 6"E�I� _�$ariants (e�0SzI� :�1@�f ��(eQB6[Ron� *��� �r/32FX: B�U"42abI� � �*ne.��Z�^I�Bt�*I�*=1-H%��wR8��8�� 8 .T��A a venh%� nt� A�,I���.�0�) �I�JZA*es�'�\�I�"�I� 3 eI�� � f2�V� ��e���Z"(�{�I�I��t=�e� ��� c �<� �]�%lF+of �we# ose �b=0)�>Q!��m��=d�� �C�:�d��� :U>QA��(AJw"�"p FjRݕ0)t"٘J�_$�����^ 4n�li��O�Q��j�j�-�!��Z�&{*Va  �,F\Y�5} bi*n� la_+^0)^3^uC�j�^0�qR�it.� g�A�&feV�)qorm�j2!�"5dlsb-e�Hf �FZ��� ���>�1jG` ��%�9�_;)�03<��l�-10. "Z ��G+a21 21 + e"q �b� qierX�!� �Da���g�%"g\b) kb>] b�' Fq Bp �� �� ata&� ���%m � "�Ū)b�id n0:"�fra� +�dh}=-x�u3};1�%-�fh�^[�� co!:et5� !f",3�@}Yo& !�-7�+�"DZ?9�py�<I� fc%t�l� ^-;Zy)$�c��q�L�)��E��C� &�"�N��Q�("2m. O&,�EYrf�$(x�y)$�!�/f_�isq� ��-�)�����&�!m9�NK����F"�jw%73� [F<� �o6c�f�mb,a!�!� y|8$s�)*x2�n&R�"� �$� x42re��s�>��Q'>�FJ� `��*,ei�)���!x*�d �&6y-5 . On�gy�/ `tArF*�2y�K>v�a �v�"}2���;y.emphasFv��:8�� � $x^$�+>����bG'��-*��al 2_?1�gRJ�^��onX��B�Ś�.� .)��9V�o!&&$tU��1P�V�o-1��;u �. � ��kwB��:cR.A�u�a-����$��itE>.,&�$� �C8 we briefly out�% �a�� ulas)<>q`m"`�i��5�7 �*��ņS(42�9YTJ]!$�Ia�T.��� >�p0icb5F9Y�;kb}:*i� �h.msF� �)=sF�-2�T���)�w�-^{2}-s_7;+"*�C"� �=x- \��Q2J� t,&_ 1=�Q��}~�{1N~Rn�w-u1�e��e��e�&e�$P4 \geT3 2 1.$$� $\sn-�,ml�AJacobi &S��e`e�uF="17 �ֿB� aE connivQ�1 qs ��, s+7in*�eAB)��"�J�j&�.Ak���q�B) �Wv�i� &��9��#�%[��%�j$�;^�vi �v_i=\l�u- �L}�›޻E�)������z��^�eq� V@�_{i��aAi ����V�� -�d\�����‚���7� qq�  wh})g ��_%&#� " 0 8���i �7�/Tpd*A^,k�79e�,906*�@%B�&�Z;�j6�+I 8Œ�Y�1�wq�1);w� ;.�� �2��Q��\�� �.��N�f[ali� m�^��fp�s"���k�!��,�4vre5� as *�B� Bz�n�5} RΜJ�&@���jG� \sum�� �%����������$�Ĩ�^.�6 �/i�vi��/ eaQ)-- $ eq457�&"\�6�x.Las]5of[&�, toge8=f� �11.�u ,qe��&�!�2.a'ge 2.J[�Q& PN��{x��s�#�{�a>O:�=in 6�hree}�.B.n�x&.D���Ri>5��6�� �:)%� 9.c �h~� *�*�;]�F09n C+$�ε�^n%h�-&S ] :�� :%��\�& �k��6@s 2(�1!�>�-aaB!� 2!�� #$��aBB�' e���1"{ fe*} (t)\<�� ��}Ƃ}W�Y&z1!<o�j��Kon`��"T&)qN�*�. er" �&�Z�Hid�:96�(���Lvalid. �Tat, o&��^� KK 1���.S8r�y^}oc�I1��� b8n"��M�HAj @eD%J-A"�g�9G�"[, K�kEl�392�A��9�9�� ! /+�+d64g61% mm�10c"K�7c*K�4�^��.�H82�Q%rarefa�[�"��F�[t.m.!e $l<=+(t)�47+�� four:gC�) 2a.} U%7i*U&�4 "K��3 e4@y$��).Ņ�u��S&Q/:)u_)4y holds: $l\ll�v5 \nu �q/,, (t)=R�-���i��2Gn-%11? �1;s&J�*h=��2��6M��6G;'1%� V{i�� p u���$�=x/t$ �I�s&�2@Et"9�� aa(.E4D�1 ����dFC �+o?�m1&��%��N0 ed. �j ly, _��:Fsw�G XxNE-�� �4invol�H�arJlQ�G1�?2O; (2�E��9�)�t�.���2�!!`��bBsims�(�{x}{t&)la�� {-} \|+� �4 =P "+^{$�j>� �G�B;R&F )R>,�--e�)b��-��"���) ���+� � z}M eȁSe���'�int� la_--2\leqslan�+p �1'T� B^�1i&�qW teauQ $\{F�; ��-��b}� rIM�� ��%��y��u&N\�2;�2�Y�� YAtr*� �V�-ramA�6)ive}.�^R lapm�E��I�-�u_1}{2}&�_1}M�U�62)62:62F? R%�=s�"�uǩfai"��"r� '�"ɪ�, c��Pst�4 $(o4 u_1*�O(hD4 u_2)�O"�3c�4e�.�3aidaR�)ngl\��V�}6Y(�2��no eE.; ted�"3T! )��6�"�)^� simpm�{u)�-\}�h_2}=.-�1}kB(�nՍ�  iB% �(C�U1�WQ�E&�2ő�R�kH�bQ,B._��al���UōU/��J%1"�I��s]/l&e�<�,� w�~On�ef�r!�h�NBo &kR�F�!� �5U�J� V6�1�� s. 6C"�!M���� I�� Hj&� -�M�1�!n ll i� ]�.=�m9  ��dusLin�4 rFG1�.T=� ֿ * �6.� 5�� B�*��('�iub"�d1lm�$� Q&6)����� 2)3)�4"85� $%�� !l"�`"G7 accu���� -�eY)y&�0RaetY�bi���.R8 �*d"�� B�Mp�# is g�AT��� full*�:��e; Ur!�0A#��A�:\ st�!d>�"|!1� aO&��G\F� now �c inhomo��of@whp���6zVx}l�rho_i��EN��qQGT�&&�&6=c6r�m"�"I��Z apere=D�s� 2�� E��%)�6+84M�ggU�.$�����I�2c��QJg^ |)� ��o�� �?s a�I����zy,q'$c�ZEc2,QB*j� j(x-c*�p"�RFD�A) 5m�I*1q5. NIthe<U4me��j23&xj-fB�I���b* 7, verynl� soL.�Jdee.cc:y[Q_B�%�.a17X) ��&Vd! +�4-BR " Rs6B�Fq�5��en�:��f�h PsUchA�o; � &e?I e�a e\B�k��\Tx*}\}*"I�%%u i2��;d 3� B#��B?SPb}v*O�� osalb� kbc*�.+*�%UH})\�.�.u� 12 u^2+h-�u_x)_x ��:�OfD rsi�La�-�2�itr�."l�/l�tc4" �(33D!or�:IM~8onY]}`�W:QG!��"�8u6�B ���Q>{�T u)_t  3O$u_t $. �ueamVJ{in��M:��j BernoulliK!io�*�{ *��!�)Y�F1 $"��,\ *|�"2 ��&�w�DA�.�P"� � }� kbcw�a0�) {h}_n<(u6l u-h(12  ^2}+hDN�:�*> O drops�*1��ed�*2�U�cw}�_%�*, �qe�e�FR0 . Bu�A� 9x.J � ӱ�It&�$ѠqH� $fͣ,�� be�>AXe�11�:��c�u�"N &*•of�=�=. � $u.#u# �36�!cv�&tr} -c\h2u}=-A ��.*u"8!2.o>T=BB�$A!YB-Ye�!Ys.�;!� esta�_2��ye�"�@21��}��i�ny &�!�=*tr .$� \�pm �D$y�^��FH} h_2u_2 - h_1u_1=c-h$�,5C q�(u��-u� )+h_*=c)>r5�co/�tl� &}-abE�1} c=u_1o�N 2}{h }} �u_2.��F4B���w� xeW&6Qn`s �!�a.ssv�: !��D step�ah� .�iresd ea sVF� [ E *z�(*Q)> td (cf.�JoL�Us��s'~+[� �� s"� s agW���yal !��kQ�5=x )�M�c.�� D $h$�$u$�[2J�&w�s� HGtdi<.�rNusual .�J�� ��uvid�W~ O� � } O *,dh h0! (Bk,*kk,7 Kc4b�:jump2Z�Q�{2h_1�}e_�rF8J�*crepancA�t"j��=3-�1}�)���7r")d�P&�� er5WX�t la�L!NKB.6����7 pparh@�LA�}3, " P�zueby� ���aB:��"�K"�AJG.� oHK "L�F�;J���Jk�Qy94-F=X!FaB�L��i�h  bܙI s��n�as} c\� tK+�"��-34�.����!IhQi2ED:N3Bc� ��HC:w�l�ow� !2*W��2=+%=WW6�{X(wG)f�% � &-�� "�VT&� wa�� GB:�o.} T-w�$�y�; ��RJiF_.����Ji�p�  ansatz^ 11-1�u=*, %�oM2[4A "4q�:����"F�i�=I�%E%s�"� ,Pcan bX:a��g�d�|�o�j�2 �M�*=H-ch+huu+14u_{ � 7 I� *u (2�VG�e$"S !�}1})�Oaj(��S0 ��&A��_"� s ��}1( &B=u��� u_1-c 1k"5u_2 u�%) o 95�)��#�#�X6 �6�0�n� I�11-k*��x>ѝiv�� ticl�8%�o8r3New�c�O4� g�#si�o ���:�7������B��.� � po�q� .-6�s�t:�Up��%)n�W� ��*� 11-��one ar�sd&�w1)1eq11-��>�(+4\nu(u-c)um�x4����12"-4B AN�OQ�Va�5#9��>�EA*¦��leB{EA�%� (Y $�d$!�"�@ro̤�I4 5�j� U(u)�Ł�p4+2cu^3-2(c^2-B)u^2-4(Bc-A)u+2Q�at!:�����F�,6 A�fg pYg $(u,\,1�)$%%!=unNu*�>:�if�2�F�7�Q> ~ree cri2�Y$(u_1z�, 2 3 �u�� j�blj�n��%d Q= _I��O�5. urtraF�o?ar ?%%�reD�*�7! a9?Ar��ӌratrix=@�l �%��.rHE�� � !�(!���i� �5-hfA�� Eq.~� 4})��#�s 6�Cj*E�oI#5 �62n�D4saddl��inQ9!h 7���p4y�79af��spira][��!� fs��]!�%aA/ZB1��~C+!?�� .� �hs�U��sca�Eq9+�t�BPej�:!f�C�e �Y&�m]i��s1"aI�1)&�A&U�:?$�M� !&z.7).�%WIZ�8in the vicinity�a of $(u_2,0)$ correspond to its trailing edge. It should also be noted that the configuration of Lpotential in Fig.~7 lsm'n �ben@ > +>E0. An advantagU 1{.Oi)�cas'$perturbed Maodynamics�8that it utilize�!� erlya 7 strue}, i8l�u!� obta/!"] �usNa unia��(where $\la$��ae�@tral parameter. I�Y f work%�0his approach,E�2sQ _i$ enter�� !ѡ solu!� I�eq11}),m eq18})dEqs��A\) hav�fo�j(ing meaning�bseA18 order differen 1� e 12-3Ps twoavis��psi^+$��EH^-$�{��we  uild�^@o-called `squared UQ�'j�5!�g= u-mb�}�Mis easya8 showũa8satis��%f3jp6} gax}-Y� A}_x{g}-4]�{g}_x=0J8��'  multip�Kby $g/2$)!��� onc���b�3�F�� 12{g�a�m4�^2-6�^2 =-Pa+^��P��A{�Z$stant deno�� C �depen� ��6E�� eQy1|6f�sj�2!��t��B�x�u{g}Fm�V6t (see, e.g. Kamchatnov, 2000),E�B�s�~�$� uishA�y%Gad��+ $)x$�� a polynom| �Ze�n $g$��qa�! � "'fF one-� � �N-uRNc"i� >%��3���P �4=\prod_{i=1}^4A^-\la_i)=% \la^4-s_1 3+s_2 ,2-s_3\la+s_4>oandj|�g=��muB�Th�  .a1)���O13-2})��fi� tmxhe re� s2z!� well&U��$\mu$,j�����Tu_\theta=2\sqrt{P(\mu)Fhos�: yields ���. As�E��pѐ��!�$E�zeroe"~ Y�Y���d��min�CB�� yK .1iK. F\ �V�e[mos? veni�&�  vari� � erm� � the rM assu� ha�4agonal Riemann!�m-� vi})Q>4 1�1}�g$or its cou��A-�whp M"{ ,� "@ I�� .%�asŭn�`�|( (2004), if�ev�� 0written symbo�cl�nM��@ u_{m,t}=K_m(u_n,dn,x},\ldots, ) +R_m(x,t,V"_  m,n =1:NJ D !���s ${K_m}>�!�(``leading",ѐ�%e� �M`,e�-lŸ I& $R_mɦbe-|bx�t �also 2� fay]� $u_n 1their spb� ves�,�q �ed"� YM*� rF� �m4�� ��{\prte�}  t}+v_iVx}�� 81}{\langle1/g\r ��j\neq i}��_i��j)�k\sum_{m��N 4l=0}^{A_m}\Big Q a�&& @( u_m^{(l)}})^lR_m#x^l��T � _i, \a  iYUMVTbu43v_i� 1&> B}5_!T>$ _i},� 2� \� 1�} HQ�%^ brackets:  averag� ove�g�er �? rvalM�, $M$�A�degre"��� O , $AA��� of  highes� veA�!�A_m)}$��$=�$�<index� � G @ at�wputE�l to �_i$�n ourP�"�V���e $M=4eZj�3A9 �split &N=2:%� u_1=� ua 2=u;\\�&R_1=0)� R_2=\nu��x��/A_2!2:�/ u= u/2a,. %� � .� h� R�� ���-hSsid%�.��) tak�,j  \rho_i=munu\I�m� u/2)�x}gms_i)Fq$�(_ir*-Ma�2,3,4B� F�&� ��ed*LofE/"��Sest, 8�� r�uIi� )#e�.4� W!�?u�.#"�family��13.[ ,���13_{Q�j� �-�%�1g�5�)�1{2L}\�&{d\mu}{-�@ I�.Q �2L��L} �DVPe� wave� $Le�� � �eq12aFurXA���ac !�!o"L  $u=s_1Ju,$�xA�}: ,$ $x}=-4dP/�$�Pa_ef1K����B}�aeh5Z = %>\ \mu a�_i� /22h6c �\ = ps_1}{L��:p-1 \,<�/e�"{��5-1i�F�M3Ma�g)6�&M:LI7! /� {u}2)I<@A3 {dx}Ic� �<�F2 R* Ss_1/2+A�  }{:.3 7dPja4 a�J^2+\to12Gmu-.� +^2� j6�f�8 v� �46�\,! ��|�charac�4stic velocitie"E �) ��vip} � �Eh2}- �L}{2} \%/ !ťm�m_i}-�^{AU:�coincin &�.i�' ,{ l�( � .�I� Q�� are�R byb'5� 6�8\n��prt L�%�)r�I| int_�� _2}^3}~�:+�gl � 5 � valu�!�"�ell�c,ls*S�(s!ng ex�s�isGG�ed�i�iJ o deal)� un�--�%O��v���!�) 2 &�� J��nonuni���io"p�ao � smal W( viscosity.� is natuqto!! ect V�@b��"vQp�ahh� dmed~ wi�.�,�0$t \to \infty t��  steady b!"\Q� in S 3" next! ��shall ��c"AsteV�`-tm\y$G&�S �Z5y�$} We look5G�4MLi�A�hO j�5"� ���_i("< =x-ctB��!we must( j1� -c� dv}{d c}+\�&�G2��D>R�4�<��BPb����Motb&~� AF��V!�vɐy one �� sugg-eWY%-�15� ��� -� "e wayFH�6�yc��2�rm{constBn 6�V� Q� �V�Bq�!)fa$bm6Q�Q=MEEL�9�g>f�� <�$"b $. U .$!^��!)��be%sis�%�" *�#)�A$i]be%��ofY' [��!,a��H&k!;�.N ~ s�"���$vides actu�th��s�,\,s_2, 3%�tatem'A�beL�� &u�"� Jacobi id��  188]�ch-  ��� co"�!�us �_obvious�$ ntitf�6��M.nI�J�� jD ]V�=1>;I� ���*Xwe�?V9!��r$n-1$ w�lqu��#ty!%$n$'s ��,\,A�@n,� hisŰ' F)�y�gJ�coeffic�\^m$}both ,� %a|get � b%�!�$m�0j�6"��.�Er�Y��F?j'��j}N�&~�J{j,k} NSk�S ��V6prime�:��xt� uYa�o�� � om~)&!�*B*��su*� last1�y-�=0"��M�: j~� Ji!�mv�iz8(-1)^{n-1}}{s_n^ $s_n�i\$�"�$n�:�b�U��*�b�7-$b�$�h� ���"�&=QEUI�4 #���V2VNUg��m]3]R�^��L-( �Con}! �K-9�!�has�'=3 ;&l�P�)j��  s_1:� sZ"�3:2B/ Thus�aLm &� nl] eJ�!A�4$�esi�$� $ �re�� 1#j�fQ 49�=)��Mts e�>x �{ =s_4Z���-QZ� ��u(���Vt"�6-6� Now� �O_iA�����r�5sEW algebraic�?� P� ! !=0>��edm1�j�"na�!eq!p2\ 3 N�!���Ab� � !�*T.� ide�s known &�� $4$. As a r�= 6'/�+lrrst � R�&j��N�E� F� (s_4) vZ�0�w"1E"M/&5u�undK0tudy,M�R ��E ��*� of� 7A�ua)�"�=�d/!��%s  %�23����� �Z ial .h_1�h_2 u_1$S"�jump17T�1Y nd, ((ompq|eb�8�$LM#P^2=u^4-4cu^3+4(c^2-B)88(Bc-A)u�*��>Q&�9$"S)1� $\nu=0$, ��;&�^,)j��?\" $ ^2=4Al(%m�(%mu(%mu(%)NwrFm ��unB|.{$�sN�e �each o��soAI�atj��/�2c��2=%�3=-(A+Bc^}($cNjM3��'1g1�*ng��A=h_1h_o%e�$2{h_1+h_2}�B%"Wu_1^2-u71\U>7B� T�a i:%�r�A<infA6�$ $s�can vary�nV2��a"�4 #%�0k4�5ќ2 4bJ) �.75A atv.7 di\3min�)$DMnishe�� 0e limi� � �� �b �5�'2$_)(Fricke 1924n�͸4D=g_2^3-27g_3^�>�� 6 q"{8�BW g_2&�1�4s_1s_3p${12}s_2^2,� g_3&=~6s_2s_4,48}> 2s_3P {216B 3^2-�� L 1^Q f� �'inEEnAUJ�. E�Jq48� _cubicE�� pect %�Eh t�%�� 4^{(1)}�f�)8-7� � �9B� 8�in*��!����2�3�;��U :|Re(�&a�a�)o�1u*��"8��&�7 &� �q'��!!)IDA�"�b�9-�N� )k2)}�#\H at�= _Nu/�%wAM�)�9�H�;!��iAvc��$6a$f+*62~. v reduc��1ximat!�tf� 9" J \ca �� }\cdo�� &� )^2B�Si}$-�vic!�5Aiφ]!9��6 � ,\, �np0�) s_4-)�1)}FOt�-!�j��fC)2k)F�� s!�U1jt�j2S�exp(CIJgAn$C�somqT �por��? �*�w1e�A�6[isy y lB� \to-� bu�� on�al uracyg�L"f width2�j',9�8DeltaE�)�6�}{�B~,&*; '<og+to.<9���� b��:�� (Gurev!�E8Pitaevskii 1987 My�= 0Grimshaw 1995"�-, KdV-Burgers"�. Q 4figure}[ht] \c�5=7{\inclu aphics[%:=7cm,he!:$=5cm,clip]D�8.eps}} \vspace{0.3 true cm} \capA{!|.��as"� � a�$. �$38figs ���:�9��D�3f_�l�W6� nine��r�10����i�:�te�%� 1�D<2\�a� iton�7� >}3 20})�8B�^{� )ots A�r�bB�3K'(0)02$4u *! r��o&� �}"  $u_s ele�;$h� �I �so�F��4�:9I u_s=s_{1O7laɸ �$ h_s^ �4}.^�$s_2(>9 )^2+&>R��/Q�� - e�C!&^�c =L�)V -�T�s.� s%i.).88� --M� �3To illu{>t)�&:AA, letxm,s�g*F>%� draw:C"plC�� �>�)�2= . AlthougfC.�"��$mi� d^.&�=*�-isd*���" ow water "3����1� �5i stepA�2-h�l h_1$=m6 2}),zas}));%in�/to� ��problem� �ab� �'nc� i:� � e8�$�a� ter�s{D �detaij�2.�C �0ure. We choosx<w. a��>�20U �.� h_1@1�. h_2=F�-?we geb�20� u_2=1.9^c=2.53i� A. B=1.B�j�!20e C 5.06 VJ5.43=-B�R�e���U �^b� 20� "� =-7.7�%G 2)}=-6.FPSol!G*( 7BA�"sw�n�&�6 'V��yc���a���!�7�G) ����ic�$in 2��up �Bl &c S*c ])�2�&)�%�3)(!B!�sVD. ': t �> $. Fin#, sBD�6ly! ^EF%Y����.Kp H^ v�%$u�@ �� �� $h ��� ;n:A_s.U`11}CQp12}, �J)ve�!O(#ly)�0``camel hump"amI.eE��<9 EBe���2�12}�m{*�X^5�! F8Kaup-Boussinesq�JrE�&n�$:<6���)�*s. On��qJ note�7�B�at�G->�6zTF�C ��2BA�V(i.e.!#� en_2s) kB8ie� U� �p�Bom! reg�Ks�*�-�;J ceas�@QLvisible.с �9 11j� ": VQ�M�Aef�*:�"w fiA� ���>�2��E"N ��2:� Ao��=a�7spi: �C qua�&a�des9K,.3Ka�[�)6u*�M�@ ��� simiNin manyK$s (cf. El,&�8\& Pavlov 2001)�%re, h\L���al�li� �caoIn� iDIr: (iA� *zK.�� and=>ime�&�0 ^�/"� s us"��p�N��ess�ly "�L�� �taM�� o� �'-�1�1�B�gX1�H�+a"��jw/U�"@ . S��.���app!$�^!1nu\typ:H4-4 orig �!31�. Gene��!�is� �E!!ぐB(NF� ing,�G ":,�H-n�(W -=con�Nu �$ symmetric56g EF� 2 i$.t individa+ 's� n�/%E�su+�Qber�! �"O.72B`���'� 5�5`*P2CU�32A!XI\of<FmC^SS� �"i�$"8RlyT;!5Z� mo�N�R a kE�%3 mMPs�P5�.  ��!qQ��"S �w����i�$n?�u�s+e�ed!$^ un� (:��fE� # (�al)6�2�� aS /, =C1���)medQ3aO)1�"!:�B I4 ��edy q%z�>|Q.�K&�D�:�� V >;B� �ba�m�5io&Q-D.��E%�1j���ɬ�0MY��@& on Ŷ�fF&�.�P�1�B����S�)<-v1 g�� 7w�acha�-e.2�5���!�)�s�7��be� m t phys�/� text"�1�]�!a� e� to�;�?v�1!'g�!��6nonharG persJVQ , but.�� ala�Hcombi!aH7of M�)��di T$on at larg�S�ׁ�ub�R *{Ac�(laHs} AXrkI� Xed du staBA.M.K.^Depart<�MM�VWS�00ces, Loughbor U�Tity, UK.Lis �e�T�+, Royal Socie1/�(n\3up_. ��"$thebibliog�y}{99}�Pibitem{AKN} V.V. Avil�L$I.M. Krich�W@nd S.P. Novikov (j, Evo�bWth�W zon�5%�M�Dof Korteweg-de Vri��{\it Dokl. Akad. Nauk SSSR,} {\bf 295,} 345-349; [3(Sov. Phys. >.,32,} 564-566 �]���@BL} T.B. BenjaminEM.J. L�h�9 (1954On cnoidD;av, nd6 , �$Proc. Roy.!� ., A�,24,} 448-460.�0DN} B.A. Dubr2[�BZ 9), Hydro&f�UoX" latti D �geoybH�Btonia%�ory, \a� it{R�an E� . Surveys �4�35--124.� EGP05} G�El, R.H!Fl)(a >�J5), W�R brea�(�6 .���a�$ 6\��-�StuiL ppl. �,} (i#essXUEGP��Ma�wK1),/bl>��0�2�f� E�4106,} 157--1862l K95}1jYA.La�yli�9!T� B'Caucht�ѝAGcDYNLS�5��` �}� �ep Lett.} Am�(03,} 77--82.�dFFML} H. Flaschka, M.G. Fo�E!0D.W. McLaughl ,198QQM�>�:"� 1��in�Ye� t� ]m Bg5� � Commun. P|2')�(33,} 739-782����N� 4), *�XofAkXdVxlnUIAM J.6�)aa� 287-302J ke} R.5) (192z�!Lehrbuch�  A�0,,} Bd. 1, Vi��4, Braunschweig.� grim[2��$N.F. Smythp86) Reso* flow��2^f� fluidRGop̀-� J. FMech. �< 169}, 429 - 464ݦ GKE} A.V.�!,.����9a�"k �™si�  ve h.k�ETPQ�)�054} 102-107; ����a6fin"h>].)��� iOh � 7�l9�962MGP1} � �%�L�*�" (1973), N3=e�7 y A�� colli�7 shoc�ve �HZh. Eksp. Teor. Fiz-�$ 65}, 590;��iet��]�� 38}, 291�46�GP2��87), A�Ih &�Af!���B�-B:�#� � B�(93}, 871-88v��%66A�90-495�87>�3��E�N"� �j M�� nd non-�l damp�INZh �B� 9aM 1470-1478�� 72! 21-825 (1�2A j5=} C.G��J (2=�{8Vorlesungen \"u�D `k,} Reimm^BeO%;�\�� 6U-�"8 sca�erke,} Bd.~8, Chelsea, New York, 1969.�johnson�� S. J !�70A^)V6] incorpo��ng -nes&@ �6�m 4� 49-6� kamch5X} R �%BY P�[2 s�hir�_s---An� rodu�@@y Course}, World o t�!,�)gapor�_" KKUA�� ��XR� Kraenkel� � Umary200�oA"*E������:8��s, �� M{c1F38� 55--365.�kaup} DA�W%�6%��Pr 7�-aPn!BQ s�i"� rogr������5��396--4082�uzmak� E. K �5� 69"�&V�"? , {Prik� em. MekhU_2�515-522) %H*s in rar� plasma5��)� of P! M} M�-Leonto�+!�L., Vol.~5, Atomizdat scow,.xsP 87}>^ 7)��!-DhforB &t Z^ 6� }!N8bf 409A}, 79-97*] �8B�8) Di@v�hs�"k r.� !�� � � �19�}� 12�$Tsarev1} S� !�8A�$On Poisson�U)�VSdimen�  �>�� .� fe�� � �q.� ��31�88-4920 �2a5P.��90�V�of2��2} ��~  Bhd hod: ��!�it Izv. &7�754}, 104"� � USSR3estia,37}, 397�16�w�1��B."(1965f -9�e����6� . London,A 28q :� t2Ft7��WL���N"6 �%,s,} Wiley--I'Usf���,>  docu��} >\0class{elsart}^; %a�rT@,LaTeX2e \in�WpsfA��BH}"d!rontma)$} \title{S� Qal`I�stromat�4e growth: new��e��#n�t dilemma} \author[ANUa]{M.T. Batchelor} . b]{R�Burne UNSW]{B.I]6 ry} !|.:,a]{T. Slatye�addk t6T�le"l_0ics, RSPSE\\  )E�*� <4In?'er8The A,l�N� l2ADCanberra ACT 0200,3} .�b]:�Geology��zh\\ �j)H6~'a� � s, S�*�O.\\�&$�T� South Walay8Sydney NSW 20522� Q�abS-ct} %�pRouta�s our re�. A�mpZqo��e�nM�Aa Kmicrobi�" es "E��&����J>�of�_v( surfa� % M2X aris�"�%environa��qte[T� of�mu� �(� mats).gAR �e�Ti!ao �� r�( l:7organose�j�&"os (.� h$Modern day*u�s exiH��` few)�ZTere� i� \�o2&�!j� �of life  mo:a,Earth's hist�mAey ��a5�:mof ��L,�'!�%�alL!�q!)' rancfcolumnar��ns. u-S=D:ent�� he%{deb0o old�Oe##�%�W� p!�~.iK>M��K��~e"#ship :;upwardQ�K4phototropic or ac!�bi*(me"mi�! acc��on no�6�M�� Thes�� �su"� � cIZ� !�-����u&� .*(&)nEec�5 dom�.* coF���#ckenp<�s�!$Conophyton�MTan`)JX,�$ ilar5��s claim!)�-�m�%c%�5�M�,)w[9!)!�ic 6s �a�i�1�5�A�-�.p %PACS: 87.10.+e; 89.20.-a; 90.+p�T(%Keywords: 2�; S.�; KPZ"��2 "EpIn��IA'$ Kardar, P�iE(Zhang (KPZ)X, \cite{KPZ} ." !te�9nd�c��!Hate�� �"!=$widespread{�W�+in a d�re��� phenomena �BS}!_I�Q8�*�~��%3exa��� pźburx$, cheI�e� rodep.Wat�yeiMcolona  % !�� ly �S�_�%$OE�gE��?PyHNowo� Y(R4bi�����ʭ -(LRG,Walter}�<=d ��a7 sequ�� of s�4��v benthic �(2(BMC) }CR=�/i�IIBM}.Qb�:)�bi��M(default eco� ;G .<}, re-establish�;themselva�e�omE��-��)NexGu|C�$:�stt j�ce}. ��}vB,p�bA�yż�&inu�;recor�(a.!!~t A��!�6|curA�) �T�Yflourish���yE���.=fav� Lg��isEr,* "�(y�(nei%7 out-compeA�$by faster-�(!m"$(ganisms noy@%Ygrazers� Mo��(��0A�Q�BP�"$i��n� pri�I�He�Mea+�79-algae-�K-�� biogenic�"a .[�h&0an 3,200 mill� year�w un�*I�4WBD,ARR,L,HGHT gI% )^�e!i>,!� Aэ orph; �%Տ��,!jxq6�Mf�\�of 3,300�3,5:�di� foss'7 �SPa�$> cr(en0 B,G �C.F i1b@ a�4sharply peakedA��6V�@ed��313,4502_�8Warrawoona Grouix WeA�n&U �)t � z �r"� KPZ�(mo� !R.� )z4s�Paa� ndor�1aA+A���>.�Q�e�> BBHJ� r����"f �8WE� }o �Ws � m�&V$ A%!�mata�% D&� �E!ҡ5�W�F[�e�% W& vert%�'th$,2,e�e�at�Ŧ� fe�^Gf* Dz5l�(�j cerB, low-"T e �c�(6� ,Proterozoic M�SMPM�Inc: ��!: �# ofB� T�Dm-m&� a�t�pQ�b>�H1+w� i @ sM[�! 2+1)&���C��pre�"�#Ps � &�!�Ci"JaT &H �9"}E ud1>aAD�9�6e invo�PHp�{sam ��: 2�. BMC,8i)J�f2 %[!xfu�y h(x,y,t)$E�e%05 �B!�1�, abov�Yhoriz�.l basVine!���$ ime ocEYɾ1u %j}  D)�h}{ t}"*g\lambda}"�d[�d :A .B x}\r�')@ + 5:3.2y21 =]9� + v.�@2dno_v}  Ӂ:�(terprZZv$ � �$ t��B]u�w!�icA�p�4!�m�? nd 6m!bY;-M�� _B� . ��A� radi�4s"�0yL�D�+gp?-0smt (12�alo1a� ns��M*po�co�Tat�� % Our�{W�]A�� 1s�o2�s ��BHJ,BBHWdS� i�zs�\ ��GR,GK}Eס�w.�~ �=(ur�Ibi"��5�Werreg&�us�1�no�/7 us`Bo� u%B�Ze down� lict�)^  N �1 . ��PJA>�L�)�X Al�AF"i~,O�2M�)�-�E<_a�hn�*�>A(�*�46�h1j!� <�fcr5 1��s*�� choi :#-"� /Ir5worth\.Ef!�c�7^?3fly!�dO+�f��n fla}�eet�LGLMW}p�Usi�N{ �Qq+�J�VF\�&Ed"�r�4^ �re�us $RG>���\$h(0,0,0) = h_{0}$.\foot�6{Full"BBzabJi %#, u&S}.��T�!�f?�ahQk>�.i�bF�` �y��d`\{�l @�l} � �jr�� }{2 �j���+ (v�,)t & $if $ r��q�O��%$ t}{R}, \\ � (1 -�=r!��)��f��2D�H2 R �K� %)t~~ & �ѓF�{q�RVk g � � J6�geq�C|H)d �.>�I$r!�sbzx� + y}$� FZU  A� A)�bx �-rpaZ trus� �2tip��+Q�E�A5s �to(moothE�ņ ه$paraboloidV1,�'anzout��� �D"�i of ��'%�. X cave�3ontinuU�bAQ�v'�F,)�B�M)`NX @# B�, �A ex�o� ��� IX| wa�g���{m`�lex�R�:=T�� an e{l� !�!6*4W-�,!/��l6�vto+ 5tu b�0 ad-:0/_� $\alphaExH�=@le�9@7nstudied�& isolprU%edQ��[�� �M[b�D5�!�:�Y�g>Q�q(,F� ���B�m���l�� a��Mlongtd[ol2a�aﱢ}Œa��%�M!�aI���zof!m�s)�_-` "z�DP�!M?fY< s s5%�byc$. Inde%� *T!r, ��h�� �1p���0�>5� , �XF�B��-�5 U�Q���v|ntrol3 �AUi�Lsh3Cm��}ngawaA�l"�CJn (viaR$%� �) t$ �|&�f �v$,"?!� hNWaffecl bZu�N��v;gnifW j<mbds nd � fI"�V bi9����/-1re=�4���2% �b example�~��pT8��,�;H!FTZ8{ aI;�io�imϋs�fsu�1��am"]2�i �pst)6 clos cmb$��i�� �If6�����mBo�P gre�LA�n!t v&�A� A}:���<�L Jw i�L �Sp���xa shor�L\)) :� ��regim�re*�N"�B-sk(;�:���GureH)i�-�i���9�k�_d�;Fi61aBRef.~"� J}&T! V��� �@�pN!�expla���OI[~s��R1�uphx Togea2�g�s %�y �9�"?jA :~%ȕ.�JD�BMCachP &���X5I � [�ent�uam���A��/�_a�bY .�aZ/!�e ��| ��B�k �!K="!�A&��@odW� �in5m Archaend2QR�I�2�Ak�+i�9� M H"!�)5 �!;nk 6:�V��->��h,a"us m�A'e S.? reinforc '!qba��%�synth�'-�a(�com~Y�] 5f BMCs�S���lq� %  ��N5%�* b��t[$in2�&�"x �H�M�}%{s� �p��5�< ob���Nj�%,Territory of*�AA�yW�B2aa .�sim�wm2Q`!s�#igu%on� %2�top�� ��W��B� �{�<���Fa�aim�k>�c*��*ar��s�y��l�_A�-� 9o�e.belie9 �`���also [� !l wh�x}a�v.�&*7,2�virys disa�G=�eow 6pKRS$Adem�/#%!linTto%����*# am�GKa�b�A�^th�%��Δhave �a}*C�bteem��tenu��9d!���B; � �}�"egH e e�)i vulnerU� pred��a�etiE��JLO"Perhap�#3- ���'zi/r� a"A A�%/"& *�j$�`;]qu�/marine.��o \ack)���5����~b,eN�*!,+yT Aca!% a Si�, Taipei52T.>�.{2�B�%�6#&G.&&, Y-C.(&,�-. Rev.�; 55B6) 889m"CBS} S�x<-LH.(rab\'asi, H�4$Stanley, F�+alaUce>,�{�+ `, (Cambridge *�,P�#, �8�^��re��.�mi"�7LRG} BS?Logan,>Rezak N. Ginsbu5J%Kol. 72�04) 68.�}%�*=$��B�5� 0y 20 (ed M.R.�-,ter) (Elsevi�9Am� dam�762�A8CR} Y. Cohen, EXCse�.g,&F( mats:!0r�e�&g.b�%�Q c�?� (Amלn�C�+��(Oy, Was�-ton�892��% R.V.$0, L�6Mo^7Palaios %T�4:]6G�% S�8 , {Wo�m�EL�,--  0^gS� ShalzyJ7 NW �,H�,} (Hutch� Radi@b1}3 |1M� & P�9SheehA 1Hfo�2em `�3430} �94) 75OK�AKnoll, �o�Young6net (Pr���^F�A�32` WBD}.=A�( Buick, J.SAVDunlop, � 284A�80) 443.�ARRF3 Arpa� z<J tnA�- 292�1) 1702�4Li:R�3we,1 2%�94) 387.va 8AHofM�, K. Gr�$A.H. Hickm!�RR2Thorp%t1i�S�GV I�, Bulletin 11U?99) 1256.{SP} J�@1pf, B��ck2�37%/7) 70.=B!xD.B=�et al.1f416% 2) 72tGs@M. Garcia-Ruiz, Se3 Hyde!x$M. Carneru%�4G. Christy, Ma Vane<ne5 k, N Welh�&1�30)�3) 1192�CB�!E�B lb:.�B!iHen GvJacksa��Aica A 3!20A�319-�]P#A;Ber@ d-Sarfati� M;X(-Pouchkine,��c��an�29%~5) 2027��!aD�_tt�� �28)#0A2 ]d!�T��, ~#Sa �3�0�c35E 3) 7:!Bi����&15[Q�}u+ed.�GR!wPaBotzingA�DaH RotheH�383!]96) 46�J>De���An��+�Pl��� M�s 2eG  \+pag�8l "Z[p] %\hhp 3mm .h \�8$xsize=14cm box{Fi�_1.ps}}&�g�`l� snapsho"Q � ����"� o?'� �"v�pw"e� ^� #s &_f $v$�Erst row:B = 2�t %�:1.5�ird>-1$ FT5WoL = 0.01, v = 1.99$, cR+ * 1.*tq)"0%K R$."/i� ,2#%�-��U [�i��2.8inB�2a!� IZ(b.jcj(2!) 1,7N�,C"N4s& g�7nie[K�", F�* 9e in 28mmEUsca�] % (right)�> [twoil4]{revtex4}% \u�,ckage{amsfon-S:�q}> symb6�R icx}�&t�7Ler{MaxMatrixCols}{30"J>�G>[Sc� ng��a dk�nn@]{j��C chaos}�={AlO,Virovlyanskyff/��{�@��App�<9F ics, 46 U84ov St., NizhnyGSPgorod 603950, Russia \�>{G: ZaslaOu�G7E2}� �Xal��,��.� (251 Mercer ��NY 10012� D�"�T�.2R-4 &<? ce|, X03, USA �ta"�=�hona�r acou @)�M# !"!!p a deep oc� 5/Vgu�4�"aGI�;e-d ceNF�:�3�E� i"PX& Schr\"{o}|$�i^h^^t.�B. U�/met��borrowe*H2�aumI��DN^$�_� 2�&�%=E�Ar�`isD \�Squ��bl�i sm*2�\�$�i�+�-�* (autonomous ��6��J9�\�l�A�*bigskip��:�-jW!�&1VYe�)�B� 5� orbi��W&ignS4nt07 ent,*� �` �krib"\�Xgy level.du��� eigena/sm,XGutz90,Reichl92,Stock99Oi���b,�e ome 6G�e&�x�"hig�e�.�u unsA%Q� �e��eels�)@Eis"t:�f{ �c��a5_bil��d,��b�-rRI �Heller84�t&7"�86�Q]Ra �o�UovZ�? �=UE%��ME t-S ,BKHd,TP200��& .p�of.t m"��0pr�H&�ct!ہMvA2��the�+i%��-sW;EA{!$c���My��non}� Hami>Zi��� 1.5 d�)%Efreedom�%y} UWA.3eazeB aE6pldLca���:�a d+>c,al 6�t& �JU<MeP� Geto study&%6ray-�atBj.�!�A�pIjSBT92a%�Ir2 4a,ZA97}:b.��a!�2��Xi;���&`Nosc̵�%turm�aio´� eW%c&h"va|y�"�Br66�-9Q �. _-�!�&�7�HWA%l)�� ?e� spV<$c�4a"�! depth, $z,�ndi� , $r�v�"F� �+��(valid�a�p�3mA(�$�K�)Z(>!+��Em�%nochr %#��* $u|�a R era q�@$y $f$ obeyp.85yIDTe(rt77,BL91}%"�(} �0i}{k} "?7u} 4r}=\hat{H}u,\; ��1}{2k�/% :DFz+U(r,z),�* bel{5l� =�w�G $ 1=x1$ 1-\bar{cV1/cUR�0)/2.$ �8 $ (�2$$k=2\pi f/rV32;Aa !�nug,)!|Ijpt!��2�)A�Zvy:-jE�:� S6 "�QEs�ȱ� $r$ plays4ol!Mɉ)�$f a .b% ��,1Q&�"*�,�$k��$ a!esy^Planck�u�@ �+y paths��m ined �+d�6�U�$s $dp/dt=-UxH/ z^z$dz/dr="p$�]ian $H=pA/2Mo$��� !mo�Dum $p%:� ray m�ZGl�s�%a$�+$p=\tan ��eH*m{��}�2�w.�m� cE�=cx5% (z)+\d�~ �$"(z9�s"ܲ Munk��f��CFly�8t� z2 AUf1ep se0@�',Bt0 }=m;u�0+\varepsilon(De^{-2(z-z_{a})/B}+% )/B-1m� "; �0�J+8q�= km/s��c=-1a�=0.0057��$B= $ ���i2t(=-2\gamma\,�,z/B\,�(z/B}\,\sin(�Or/L�{ �%�cMb�W�1�� L=10��*�j�y�Nc{AZ ��ih9 iwc.y�2�U�2��s���th�& %i�+�u 1.�7�h]1U�*�PiK{s[ x$=4.8193cm,A�th=7.cm Հ1��G�U*X����0,a(ztd&e) ��4/ma� l de�ts (da�&�:)�+�Cur)|.1� � ( 2 �9hf por�Wt\Jw � &yted us< �� shift � ��F}$�� F6w=C)S9� �6.*t�FW�cHerO�'%6���mT$� set F B� . L�!.|"� ���(z)\e��5�ŪE�y V�de�osiP $� L8=\sum_{q}C_{mq}�phi � $: ($q.1)%�qLB(Sturm-Liouv�C)� !��]-DH}� a m}=E���_.ѩ< :�*� 2_$:Н to $$ $* %F �5{ �m ���E|�s $�E�>ydq��2�a akd� �& codeMJKPS9"I^ easy���� a  fǣs $Y�!'wnLlumns��m|'!$eft\Vert C)�/ �.�F E�s6�~,Z��e$ d� ele��sFFG Fx=�� dz~6�q�va]r"�FFmnFNo|ގm�2>e���+";"  (Y2})L�: $r=k]�fo�O �8"66 $uew=:���/�DNS)M!�A  MMPEM }. N��ult�(�e@e�0oz��� N�(=200$ Hz. "�$��%�7\mu� each�z2y$,Ոmu�:q� \8 2j/%��0�u�{y w�edxE�E�u{2x��e sor�faRs� Jeo�"GLm������"2�$Y $ ma"� in�L� loJ"C rum M�='h;�H��)E��a�Zf les.����0trim=0.5in 0..,)=8.5254&�8.5� g3n�JQUQ!�q�V�10� (a) ��4  (b66( (c77 d _{88 e)9 U105 f)�/r�WDwa��kJrv* 3s�B�5s 2 � six���s�����As�sZZ�d*Ra varietu,!W*=!1R[�Your.�6alxir .�  '����5?�QJT �A����s���e WKB:./mZ� an�V �is� zzy N;�gF ���>u�"(n2z � ��.q �a*` �� 3a w� �/DZsuc�%f��.PB:� � upio:#lo v�a6D�!(2�:X%4&� �4 (+�) :7���# 50�8 ��iz�O-Q�il.sJ� ?�ʑac�6 $50$!�e�#*�F b" A0FmɡH/lyz � -�b� ::���#{ %� _�`is��wn�N� 5.29�7.2�2�14n1U}%(up5 �����(lowerI�ic �e��� !�f�s 3b-f2["�:1s幥#{� &)Hur�Bu� .(remark�B�%�I"�aal�KI�140�ϩ�� ed�� n"f *~":�ԡ�&� i.� ��Xi)%&QQ-ZI�$ (Figs. 3a_�j(*W <f�p sub- .sD1rq� AlU�~K. 3�qorGi) H �ha"�+vc, {Ld �͟W5h� B�cor� I 2qJ2�s. Rougha0pe},�� sa�=i���re 2�)� �\�2- \%121�21 \:���� �s �BalZ��!�o� '�a�by�AdoP�r-ootiea6>�?ef ,� . 3c>: �2� �out��B)i@�7vic��,irq�con[ ��m���a�f� |^th�1�,8s�� �B%(M�-suI�Q�, ��hrD�U���#&.41@�B&�5E�wBU��1� royHofADa6��bZEN�$�A occu�m�=aiBwa�ellip 5_ݹ�karg�[[��D�a�#d�yV�m!wo-�Eays�p�� 4. B{Uy� !�odu(l 5L= kA��qB%+noB[A �� D�50��*#� }!�R3�Fong���seaG"�c ���! z\��$"&+��e\EE!R�-!� in��si&�O�r'�jx&���],I9�- $�(�8r)�AELyapu�3exJF`Q =1/6R"$�% � a%ra��!.�$�N*_ E�a�� B`�782��B��\�� Ha�1!� sm�){�ne�O*nsecu4G��32MI�"RM�$r=� c5b" KaNbo�l`2~!�"�1�v&j �&;6W( sAu�\tmhar�>a�b��m� ). S!� bla+' ircl� in � �$ye6& spo��� �R���$m��v6' )��3& d&.�:s����.�Pe)G^�c)>|%�5�HrW��a�W�����ex))f�_ d li++ fs܁�k  E&^���� as�3� 2*�, )q!e*�l�n�&T�8. S�l�5.���3��>'1PQ�CM� !�� Emh�_J{of)�!]�n�E�5� :Ld"�"-%�2wH A� s>� �.� ����.�6����6��6:�I �a=eM5� � !�. 0 88~���Ă�y�A�[-zA"�.�of �4R��4^erڶ� g&N�aB�y�� 4*�6es�1�L<���h>��� $m=$77ee88a�z�� ayconfig�A~f50 6\ \�w� \y&�e<7���M"�tP2� *-�$(0,L)$ͭ� eh]&J�B��Α��*PsU� \2�9$:-�! , $ ,An�5F5�:5 &��$7e�]?EO�ab�!�Q�(@�on�)'5�A"C��%s�.� �_V�� !J.��>�%k�� �*� N� ����]c�Q�Q;y .�yA�E�iq�a4#.9��y�m �IQ E�e&/9So� (:a�0/!�rK*�l2�iXk�AU alog�A? ng .o5*H;"� a& 9*&sy*E��99} (�"C8�B�'29}�ŁC 6 �5H$88$-th�o� BOI).�xRU5�ively lL��[iL\�LAq.T]l�\!e6% .��`" p_O�9*z)��F F�� $m>50$Az playCSp�*�X}��:s U(_ �"%=��"=2L� 2Ω��'� !/%�7V� � =66$�0TFs���u9܁7Q��� ��� � 9e��!m%� piekP�� $:sl&y9�"� %�5u<�n9�:�$%&R �a+s � y�!�">�?�^� , li��g� )N,i may J�.��=�!�.&���9 issu�!:����X���on. $�o�o7�� �� 7:� 7ޚ 66c'A�out] 5�E�j;bh "�%k .���Ad�e�UA be ����\�f�6�ineD �X�jR5�u,.�aO5s%�z( &�i�W| �J�ukA� 6�a" e$k6��|��h] Tfas]^@_F[�"�20���!�!��Fn�k*S��re�T dF�!:�� p�Pt���{}�6�/dG��Osf5��&�%h ��u�V . L6W�.sui�� p8e U.S. Navy Gra����34�0oh�\ifx\csn�?�o xlab� \��x\def\$#1{#1}\fi �anBG bibOH>J��M#�Pf�Q$�R' ~R.$�Rurl^�url#1{�tt!O%8{URL I�@i�.mand{!\�^}[2]{# (>!eprint []{S'�Gi �[{2��D:der}/� 0)}]9�Iin{a�H}5�{M.}~�1m8 L}v�\emph5�{"F}{C�I in*$)and" ">1M�(a>�Asher}{: �}, &a��}{�H ��year}{DW})*�R>j0%2! 9!pJVL> :nD��l0to�9)!�U�"R* 8 :95 anif�E��s}}�8a��F:9W582r8St{?I}kman%?9!?S9G mRQH>>6P)�RT QuanH :-<jou��}{�K."�\.}tbfy�vo^S }{53:D(pages}{1515.D�84r�B#et~al.}iW1)6l , Ka�+ �]{H�&W>W:�VHB� �}-̕�andA25ZVN�Ej�64:�-�016204F�7Ir�TakagakA�Ploog%�E�TPoI~�Y>rT}}%%�9K>O �6rJ�Bj770:@17733Z7z�o�Ie�8a�88�3B=:�2��YDj�31:> �U���u�8r�Jߥ���B�9:��rD�B� #�. N��NN�42Z�219R�vt�`Keb������^���J>�8Keating}}, \bdibinfo{journal}{Proc. R. SHLond. A} \textbf{\b 1@volume}{437}}, 0pages}{151} (8year}{1992}). �tem[{\citenamefont{Agam and Fishman}(1994)}]{94} :�author}�fA O.}~]8}}� and}.�VKS>K�6�9;8hys. Rev. Lett.j673:E-5806R54r5Tomsovic%9Heller%883{\natexlab{a}}!FTH93a�EB�b�IE>I ��H-H0:E-H 1405RI3}:j��nWb9Wb�W�W�WEj�4Z�282�R!jRBԒB M.~A>B5 �B W.~H>B!B�=MB�ow��A>:)��v R.~C>�-�@JJ5CEj?�MI:j+�pT>�Qn>XM�,ō���< J. Acoust�yAm.Ţ^w 105}.I��318V�9rABrownq(2003:�!,q[ �\, Virovlyansky, Wolfson,�4 ZaslavskyaqVW�$Bp{9M%7VlJ>���9�j��jzB�.��B�-I1�UD��G> =�2�r�f� 11Z� 2533F'!�v� eron-Verar�&�EU�ޒc�F>L�����;������������4:��S122J� �� Abdullaev: (1991� AZ9��B�W֊ �4Usp. Fiz. Naukn61ZAF!r�!03%01Q��n5�9\emph7��,title}{Chaos%��dynamics of rays in waveguide media. Edited by G.��.}.�@publisher}{GordonaDBreach science p's.�@address}{New York."PvY2���0!L�0����I08V684.H � 2000r7SundarB��AD9� SZ99�?B>�V�s�sE�jj9E���4831 Jqv� uWE�248��8������Soviet �a�- JETPjE5^�6RA 8v�Smith"��:A !,�andD appert SBT92��KB�x:AV Ba �� �_ B ˥`$�9^I939F!mvmirnov5� 2001F�#�.1Z� �IJ�a���v����aK�EjI6Z8 03622J�!��JN!O��2��������%�~712N8617N8200�V4�V4����������aP��.�3b�v���t �� 7 ZA97� n=����� BB~���.5182N� 1997r��� (197%% 7�*j int6} book� 4Wave Propagati+ Underwa3 icsa�ed& 5.FBEKPr~� �M$Papadakis}6k"� $}{Springer�lag.� "� TBerlin; Heidelberg; n� 77}), pp.9pz 224--284}j�,BrekhovskikheLysanoi� BL��L>�.X%!�2E�V� Y>S�\ 6?M;F� mental�Ocean.1 * қ ~q�� �� Palm2�88:$ ", & { Bezdek! PBTB88��D>= `-<�Vyb" a�v;n�;2�OH>�12�"^ Geop{s�{19.�m656R] 88r+F "[ A:�!, �B%� Go\^ni!�BTG�h����9�B �2T5���mo��jD ��J�9JL!dr�Grempel=�8>� #, Prange1�"� ]{GPF8�m!Bo Y�pR>� ����4BS�2Y5�&� j�A2lJ�16V�8v� Jense2/>� "$, Kuperman} Port�$and Schmid4 JKPS�#B� c��W>���>B� ���B5 !$VComputN al�AIP�odburyR�&�.�v��}]{MMPE��b�e,OU�J. �"Tj�A�D� 24RM�� Tatarskii; 8���V>i7J)��� Sov.� . Uspekhij�26:G �31J� 1983[ tnote}{[6 !�0v. 139, No. 4� 587-619 (E)]n� &�  �>7:>%o Edel�� Niyazov�CZEN�� ^� ���Be�2�5��59n JXend{thebibliography}  docuS } s\ class[11p��4paper]{article} \usepackage{amsmath}Q$newtheoremp}{T } .(acknowledge}[ 7]{A:67lgorithm.16+xio2'2# caseIC6!lai.DC6# onclusion.J>-di$ �Co>+jectur2�o:-rollary2X6+riter:�2+defin>�D2-exampl.�E :' erci2wE2)lemma�L2#no��&N2)proble.�P >'pos>��2/remark}R 2% solu:�S6)umm6�S 'environa,�4of}[1][Proof]{>%P#1.} }{\ \rule{0.5em} } &,height22.5cm width16@hoffset-1.0cm %\v0m-,opmargin-0.7 $input{tcil~+}�, egin�S \��< Haantjes tensor��doublev@s for multi-dimenaT$al system�hydro�L type: a necessary cqKKabstract} An invariant differential-geometric approach to the 2�!?$(2+1)$. n@, $$ {\bf u}_t+A( ) _x+BFy=0:lis developed. We prove that �exist� �special q�s ��n as `.�8' is equivalent�$diagonalizM�U an arbitrA�matrix}two-p�e'family�D(kE+A)^{-1}(lE+B). Sinc�eJhp can be effectively verified�!(calculating{:�, this%4ides a simple b�6� . \bM?(MSC: 35L40, 65, 37K10�Ic(Keywords: MB%S�$ H.%8Type, Riemann IQ�s,�T��� nlinear Ia�ac���w Planar S �� s, D��.iY���} \s!b$on{IntroduW} Over%\0last 20 years0re has been a��sidera�) prog,#�#E\ E8 one.&r7 $qt+vux=0$ or� componen!2 ��equk} u^iB ^i_jF u^jCt, ~~~ i, j=1,..., m, \label{1d�IK(�sta�"d �!��v�7 on o!20 repeated ind�a\4adopted). Such�8naturally occur!5applic[%Egas"%X, fluid mechanics, chem�� kine�, Whith{#veraga!$procedure,2� ���topologMfield!�ory�frefA o "0L{Tsarev, Dub, Serre1 2vennecr}��, wha%the chaa�eristic��eds $v^iQ $ satisfy1E $Vk= / @ R^k$, \ $i\ne jk$E�� asiz�]�aRK (\ref �)a�usue� auto ly-��| :gu�of)}aH,' origin. Foa݁>c�!�A�a��VN�n9 i�: �reA+��an $n$-� � �1d � saidabe6�(if it posseK!on law�kF� $ whose den� m�fun�G%K4pendente�tur��u�-�adI� al r�re� A�F��lm2�an in�vco1i�and, h�s�ef: seeu5�� }, o�Ap�ix!Mi� Fer7��nra�of. S:�-�s 1r���� R���mu�flo^��> /iz4 !,gener� ed hodl method ȩ�}. Thei alytic6=-�=�8��ax t�� well-u=stood� now. � ably%�re)��"� � a!o �-F��>0!��= withI~e actual!Y�a�$ eigenvaluA�ndectorec� ��@_j$. Let us first"� ��$e Nijenhui"\o�+6C,F�8N^i_{jk}=v^p_j\��{u^p}��Rp_kF��_p(.j}Fk-.kj),��NB�%Ti �:o F�H��pr f,v^r_k-N^p_{ji_pr� j+ & r&p.�HB��`@strictly hyperbol�ow %�c"~of2:��pgivenA�!�follow? � 0em (which was � m41}� pura�y"termsv ����>�a (1,1)Q�� ).1c �}>y A J�).A� muA�ly� tinctZ�p*le�*aon� I�corresp!_ng> |Hɀid, ��y zero. � �e�� !!�1c1��(obtained us}) =4uter algebra p �h2n�i.�)��ton. T8&� suc�fu!K~ ��� -�Fer3}���ifAio 1adsorpI ZIb�� of chr���y�6B� s (s"W� %C:B- �dv%j  will5Z )!#e same='a*� .�_1%�� �gH n!�slow mod�o � travelwav�I.�KdVQ\ $u_t+f(u)u_x+u_{xxx}=0$��demon!�"J F�!5.' le (a NFrdue!��r2m � e) if2L$f'''� Al��gh,E.�m�s,��.�I�A� bm $is not tru�1B)�ob� i�sB A�!qb^%V�2 mPavlov�>\ EH ) Th� esent papa�i�:*<o�zext+to}:>h�[y carr!A]1J� quasi5 1h�xQ�}ֽ;Ѽ�.�P+"�$!�an $m.� c�Cn �E4$&:, BL u})$E�($m\times m$cc`*�� describew � 8 phenomena. In w{,A`>z"�6�sha�C 6))�,��bus��m� re�vity, no�e�icmagneto- is, etcMbHMajda, Dafermos}. Pul8 �re��g ` �le'1�QZͻ 1}) arise��disper�$less limit5B x iton��s �$Zakharov},�in! � of�&��Fto6�r.�modelg Kr1, Kr2}�eR-s �LBla}.i�� ��� X @ to%�seA��)al&�!#��asF�9'p1�i6Z��suZ#�z*'y"Jy=0$, e.(��but��si!�aneous� a�u5 $A$ jB$ do4co� .2 ). F�mof!�y! to��&:�f�ge!��** variSs�D\tilde t= a_{11}t+2}x3}y� &x&2 &2 &2 &Ly&3 &3 &3& $$ we �2ve �~transa�X ' u}_{ |t}+ ��5�%x%J�% y}=0bL �array}{0>)A=(! 1}E% 2}A3}Bta_! 2 2,� EB�E3 c3 E3E �� ��E�E��!Ա� m$� tyI`x. want ourA;rqbAdEnt D67�x bl�we ?y�e�c ,�A�iF�-]ٗ(aE+bA+c1E-(aE1�bA cB)��famB� J7 !$>?qs�Q�us�)vaI&� &�s: \med�noaGntIv& $ 1} {\it AR�I� ��*%16=} }�%c"f y ��!X6D.���2�6@��>l} �����BHr��s.} One� showI�some Xa-2mare�fact,�ndant:� is suffi�t�d�� aJ��sm�r1�F*>�q 9B�� $k�Xl� �c� antndeed,� )@� f�6 M~.p a�!@)rin��2y�� alti)a �ty���;.�{ � �oi��&at%]�mas �1})VF!�already=�ly� �œnd�F� :*� i��O%R i"���alBR �)^�is%�er�. 1� >| &�a�y.� !�Hi inheri!=e��ve!Jm� in (1+1) N�B���� lI;>"!�Fi�,�O:� both.yQ�loM>2�set� (3+1� )�an$obvious wavE�%��.�lJYthreeB�.Z�sjSect. 2Ae�gA�a �,!�:�>tJ�Eh"�in u 4. "i& ( An altern�� !�A�� eT��5��! �Br$!�ba�o>X 2,�b)key el�uta8�tru'%Tnct� 5&�the�"}&�?/ � (�" R)}=3 (R^1, yR^n)$ �!J� $2/$�� pair of � u 1�mSJ�� t=\lambda"� })\ xM ~~ y=\muJ#;��B� notic� �numbe�J�!�a&e� �  us,D��n�.� decoupHinto z mpat�-49*$�O2�$1>. (-�is:ad�\asI��8�&&�A�i�$n$ p�" ��� ��ed !�Me� a de��te&�:� x (.�$)ARir�� �7ne (two)�se.���$�J stig4in2�� �.s� a se�fnF�!E$Sidorov, BV t1, 2 3, Perad1 82, Dinu, Grundl�L. L�:E9y re�Bar� A�con�Nq�d6�KP�@ Toda hierarchies) Gibb94,Tsa96 H9, GuMaAl, Ma, Ma1(,�(}, z�yEgr� 6� chai"*0, e"habat}�QLaplac!growth��bl�))P Kr3}� Fer4},E � suggSe{Aw a ^m A� � Lu�A�, ]"H � 6���!С1m� R}) " "�a;qfg?�&ngl�g1/. S#� hown is%�!1$'.�i�#"�O3�/"results e*.9yE 56!�t�2~i=�2 *�.".W.Fis� 0 ih�m� on:.�$�)$-EN$(5>�)=����h �uncH�) We�!,*1 �}a�?:� !�ʹc o����A�B�)&���]!��Rw$:F� >�#� �# ^j- i}=B1mu,mu( "K�B� $�#, ~*7$F�#_{ R^j}$ &n'! O5*(d /k met!oe� �� -Y6 9ZA..� ^ cit `�j� *(!' e�ulaM�1�FX&�% })=x+\lJlt+%1�) \ y&%hoF�($i=5 n$. H��� DOA_VQg �EoM�= �lU}!QB'tJZL� F >4=&"F&FR)+�"+ A�FsSubstitK#� F� 8 ) � tY  (one`ri�m�Oe�F (A)�BY E)\y i =0Y6G62(n}Q mpo!�� $-F^igEj6j(d��zonF�D(\mu, O,)={\rm det} � � E)=05y]BT"� 2` ofu��.s�A��H  ~ Wis�two step%6 (1)} Redu� li�/6(!�? 4 }+:�9" solv�a-U�Ae(A�}),M?2})�NY%�R \1p^i:m2� ${ "��J := .�%se �� high�, verd�/mX! and ���� � R&.\v=O8.. �}�s�1h.!�I',�ulo>-B0riziG�0i\to f^i(R^i)e o�(^ N �9/#8 "~ A{tham�a���#seF$ER is fai�,=  +forward�:k2)} So�F�0- rAAm for B�ndate%�!�R^n6�8$t, x, y$ from q�"��&�'k �ˉ��m� i�$ep& �extra^~ 6�T�f&y2�_Wg chem�A%� 2n$ �*ne�U��F� j�S�V.}~+$n=1$� have�*�AVt��5"xthA�.�e curvQ� scalar"� $R=R^1� s a �8W$order PDEs+R&� (R~&|z/$!��}.itue1,e�a2�,A]��e� �N tak7�A%Ff(R*�(R)� (R)yPFu�$<y��islA�'�*at�,coordinates U�#surface�%=�N�e^e��&= 1�)�{u}2�u�kalong a%a��"�k�MrM�� A�ing�\ C!C�5� ��"env�5�isRn�^�lo },&z�ar�- ���F�J�" ���_1� n*w�` t%wA`B$�b��4�m�a�2n���R^2 1-�v�("�.z� JC�!e1���.�,�w well.� , beE<e2$!�Q}s� a `de�9.�'�A5*�F�6f# theyv %Z��^}. N*�Y5\�*�)s�>��a�d"�ne�2to ve� ���j�[A�� R^2$/�: aJ�� aOu�-� doe�&G!!;B�� just�fieq�x 0�|�5`FD!��)�is .9�0:~�:ulaF=v^1&� *�O.�!~ v^2R; ;y"� PFJ S� =�@, �2 ${�s aa.B of�s (or,# #3RP;languag3 A�gru!�)N M3-s�< of ��v#&�)�c2,Q�Y .��Q� ��A;�e��\%�� �q�� foN=�� S.��, F�p$2\�' 2$[>Mz1})� eFZ�c 9.�8>� �"Y�~Y a"Z�6x.t d%�aXf�""1<"� . O�L�� raryM��ȉ:�% (m\geq3)$%�JN��AJ�2���� r��J3Z�I�3; l=�mai5��Z> "�. %>�.o�+=c2�* )A�/�an!@e/ *_ (i9)]Y2�B�^�� �*D;6{ |R^*t�7�$Ub�u�,1��4a�/i�*}7/� n�V&c"� $D:��-T:�w_��_0$�{����!�1a5 s $( �N�1�nd2,�1 �= ,2�I�0 find�hy&�l7V�0�!� e*�46�l�� �mu�2 �->y?.�&�em�G�-  (AA�cruF:%j&e!�]&lof !Q2� .�Q� po�-n2�p""I2^�, how��m2?$Av'�@le�' 5�� ex ���- on ~"�e*h#kV��1<*#>�&�@woN��me�E$!��j1branchWd&�Id�4��<), L 39�%�is vio,Ed. %�eEF.}lBEZ;7�#$ݮ��: :gof irE�i&� %��.o&)v��a{:fi� �n�8�F3 %nonv c� ��1�+@ator: $\det [A,B]Q<�=A��w�@� (asy-to-x&n�;>�E�:�!y���d�z�!�2should*"�<)?r9�o&�A� ��1�, -at**W'�,O2�� i%2!3 !"%�#wa:^Fr$$3�3$u�n $2+1$ 5 s1�� �l��ic��Q�ertR$ 2[2%.� �w6�2���o28 �5nvM<'�% ��,nontrivial 3]e%�{s"�CA)uain�n.�.��se�toA#very �ba<' & *5 b�A&� �RQ. !7. mi 1-�M%so1Y�in�Hirota A�n�D""%e�,1�]>,!��A�2�na �!)QJe�?Ay��,.S&`�7 se:!.�` � .�6>6�) z=��| I�5s5}1�:��0BV1m�2e1^'&L&��*U a�/�@ymmIz��� sense� � Godu�[ (�y :���(�?oJY@). More��ey2�Ra�pseudo&2pla�1he rol���2�3 `Lax�'.��ex�c tG u� ItA��)9�"� We��O,�'hough%fq?>�=�l �H>w(�l)]؍��4dAwq�!�x""x tB� , exqu�$�F�"�eOal�i�b#A*NH&��Ni�"pen%_beliel:*� a.N(d��� 6�E�lt�&-n$:breakd�#��� ular"�ur�)�n�F��xa�AsD�Q� Cauc/<MP/FoJ %�hopI�c comb�� avail��xrs (�J�B~,��-���� )2��(m�P !�a�CEOleJ� YA�)ll� I�&� B�� wf leadi� new �3�Ed� -o:�init�s,,s �{Rs} _9Z V li�� S e�6� F�FR 72+%�9Jh ��� 6 1.} >}�B�ei�!�so-�z�)�%#B�I�/mN&�8�$a_t+(av)_x� `+v�Kv_x+ww_y+a4���eY: Y:&YM@u/ $y=-x� w=a$� � xam�.have &�xN�OtfX8�>8=(a, v, w)^{t}$�L@����\TI.06�6a�6v\\ whJ6\]I_x+V9cc} 0 & \\ 1/a-v/a&1&0NSVP}~�t��1\\��&0&v^2/a���y=0CPW� vPqA�J~6�M� :��76�Htt@u.�?�%�B�2�U�(!2+wm�RY�*e0a7w+av^2A(w^2/2)!B{8�B�pr�Fis:wL�A("�5Kit.�:ly�c-or&*�2�? Look�&� 2�*��BfJm�� $a=a>60, $ b=bF $ w=wB��V(#*%%MRx�� J�%\W*al_i w=-""i+v) *�%�"��/a`0 n4U60BL%�V!�&�"FF��i=-�'a}{2|^2&>'�[:|&�� J0> �*�Mi�jw"�)*�Hiw$�lX.i2��}=MFv^'(}*l�j*�*;iv+ �0}"�*i;j;jv9{N� il! � B�@9M?i})" iJ���+^i��+v~� v"�6F�!�s"�( ��6�&e � e �r"�P $v(R��iJ+�� ץ M2M��"Y) j+2v]�]A��iv j=@3Bi�� ;o�& ��ZsVaRa�"�� i�iq y.�J�� 2r vm �1�3})��can r�&M  $w, a�i� virtu)<0��I5�v� _�(_�"^4,�����!/�n$ �yz� (mHo�"�:"( ""(�,us� if�b�). ��~}. ^S.jQI�\O6� �&�%0: s`. xd6��B= = psi_tQ�1}{2}x^2-we" y�9a}{ x-v}, T^a=tI=౎���2qh1 f2.�1�L�p) al_2B�1=:M1.M2M1y�1 M�1�v1%`1�26\21�2v  C�RB��s,v�*1\tA�1�sB�"�*2(�$e!"�^ varD. Two�#raR4c;�)%˕.Mw6 h.�Zi��ɾ. V�6`cVyre��I}���MR��7du<"���,�"Y �c 2E�c�2 2.} �Qe�a*�%c:61�-� %'} Ct"�� �$B�( a HessianN�3VBu: fBt=V� B.4JbD� c� 6�VK}~�n� F_{uu} &  v w}\\v w}&F_{v ww������l \ex X�} w3 c�.�Z�$ [�) _62�\ $(b-a) %^2+(b-c) @^2"�If(\cdot �a.�"r�Bq (P � N �(=1/\sqrt{b-iW\ | a-b}$). P e�=���yY:��|)&�8: r�ex}) --�7�4 4"l�1�<, %��#q�8a�>���C�B&�f�Ts��!�Ov[P�� � :n spit be ��� =S i=!*A&2*�2232-Վ�$n�%!�� V� ���se A5�0�I�I �yq� )}FWQ'=Q��^&��&}5 , up-IAary�/ng�v�� s, B� f�q]1}{e < \epsilon} \cot J� (^�pl��f�- :�md�R� ; op%w�N!`I-]AU��2)ar:O,we,M $ (raf�%4en $f$ itself)!'wrA���]xb����Q�A�&  &  �A!$ � \\ F.C�DW ^2H�����)K>���T$&h;i�E��(' �[�*tscW3:�� m9��@� tD b'�Ey<� �Y� log \si4  u-pH y)+ i�c}{12}.0%F w+0EN!�Ax �b�a�t��0t:0.�2�� <p �u%{�2}}{b-a}$��B�K})%i!�"V �:� $%{tx}= xt}�� �9�(s6� be viewedT1�&� L�og�.�7$*�& caseź*��+ZW��C� e* %Պ� +6�\�Z�Fe�!�_*�%�Wj_ !J#,6Q 8of meets techn6�e�Uti�2*H,.2�9p&R �m�i�K�:$$ *'� l� E-\mu�q��l - `FLQ�f'�� ��e[�f'�2r2��k� oi&Na�� � ic�m-b\mu)[ac-��^2 ^2)(1+f''(E)]=T�(N�E!Q"65b}��CAcus�&!K�%&k Be�[we*��& U� r2�Kq:ln�P :�'j1}�G�_�� uc8"7D�V*��e$R$>�V�!� �Ma1;BU� I7� mA�= �# dire�`�1�9%�6�Q�+_andmoP�In� �**BNnaD"�&�5 �s�("�DG&=!^�!nd �;F<�Ze�)�%%�%d"����s.�.�"2��^useful��&ejB\�HAa area�F���V��!23.}� .�) A $$�n�� 2�-u  & 2\\�2&0��z%n�w � 1��B�/pAl�C `u?'aCmiC=/1�:@KP"�J�,.�h)0_����:y} u_t=2v�=� v_t=(2w-u�r"\  (4)_t=u_y-(u�"&0 0(4uw+2v^2-u^3� t=(u�(y+(8vw-3u^22>� afA��% 2>+�C �� B 1}{8d4E :u'x� +2w$2a�Ya�i���� J@"< y< yt}W<2�4��Ά-rA�0\\ rv & (1-r)a�82-r\\ (1+r)w&0& 2�\�#�n�1�:�q#��#zye $r$:,*� y3BP!�R:uA� 2-r)2B� w^{x 1-�� +r}}-;a!pb(u).\u5 N2s}{2r-1}vOmfJ (-w+r:�B}2�v pw)���M"v�1+I/�2B�xBM��=:m�+i�6-9o��)yNCm�Dr}{!\}+w3+16 �uB�2�5����(r-1)e�A�a�ahrwaq�w'+r����������we�+ryg]We"uU=-�U] uEj#y+%�bKvq�Bx$A~{�gw^2-��-r)(u�'>��-2{3a� u+vw�B-3r}{6e� }w^3PB5_y"F)��a� 2}uw��FE_ivis_x� * ��1��!l�6/-p^��BV�-1F"1-PI~� "�} ��dclarify gF o�{uE5 :,&�.*�D�� . To���62&�:�Bj%߆�Q>�4)�"� �%��N�qF" (D9sF2})H"�M^i"�M^f�N��E&y zP2<��R\A$$l4z&7.O&&� �iOV�=�=^V>li^ijN$$"assum�'�%�+$AkO.�N$�m��S Dtru1�!ic 'O � m" 2!�d"�� . %�qP �?F.�at2 6!.�/��.��5c">^t@%a2�ve�r. an%/?��'�Dv6p�{K?��er\ci�Pof $u^s3/s� 2$,d �p* F11=ur�'1u^s=M^s�?c>l)�1)&+1u�".$.5O? 5252 5s=2G\m,MNB��$ �&�P$�e r�3al"�R$coe�b�&!,6Oby2;h.-'e�m�tQ&�xj!�xi$,��dFr�@>4au-�ccoun9�P MN})E[!�����u��0�3���8N�,��9�\E@}{2 ^1B�S&B&&�**�%}=PU(mu.�15�^2)sI>X1= �1�2B�1UT�.�& �A}� 1�1u"�zPQV}(, again, $Pe�Usin a^Es��a)�n�Ren.E(s�+>o!�,]S*'aV9< a� $, �� _�Pc�f"$�!OK'A�7�$al�c��*�[�g�8���"� �N�a ing:~-ab�] ulae�Ts�, *- =k+lAji�J k,l ���9zly� ubtlZ�f�'�=s aEL"R$-Sel$N��2�o $� kE+A�^i(�)�nwF0 � ���E �� $FDRPu^m"mttB2�b o/�$i(6�cN��!���9f4[ N�mu^9jL+�j K�BStJ�$ �f \ *#. Ap�a͉�tt�*e �?oN*� 6�weQ#R� {n,k& 7!�� u^k+:� %�u �7j�&^!�� . u^m"a<VB�I� �/�Fto:I%�:�.A� h�u�r hceluPby*�:1Tt% .Tbe�1like `���3'$2�$x%� RҐ< _�SZalc�m�j�� {V}M3rac�QA�� s !�6A{&�r.� :gfL� F5�:7n)�ji27m �2iA?a2j2ju2AcE�- k,I,R6B�UD2d��:�02 � backi�9xu!��q�VY�)E��j�-FN^m_{nk}B�)Z1( $$ ~$N�!�N��$V$ (U� �?�regarde-.�m9#���? $N$)�\BU1te��i"B|ENJy25�B.4 u}n2 #16&p�=�b /)><�2 NN} >�2�!��@5a��"1�swɶa�$ 0��?�!�. �+ -j)^&B$ , �V^2��&au���&� �:�N(F ���pBfv�EZC��:9ޢ ��nU�B�6F^E��B�F2 ��%�Q�q�' =P/&AV=a�N� � � �y�?�.a�HF�M��s���|�-��,9�-�A�J�+��":/e��%�f^O  $HV��Q<)=0�x$H�:�fd@c(0ate-fre/k -�HO:!hH(X, Y)=%p !"V X, VY% 6&jD&C�o�zAAn� ��n9��h�&,1,��< yb4�poy� \ jfi�W"�i�:H�V�:.�f  P �.y2� *& [QJh $ R ]h%���"(LX�5X��hin����r�P&RgS+i|cde&sY�ad�S^Rr�/� sta���"�c&k�]��"!i9� =3 �Rb*c��!kN�aeM�O K��<;   ��,{ �U:Am�aA+@.�>� Loka�/]aU��K>���� ��C!1"�GiU�eX;;M>i&�GMul9�% �n"u��.�Y: �� %&n i (...&�i��Ls=2�$ %i�H�c=�� ;�:jw-plu~x6�"!�.A1Vto|oE�!jvaaC� �>�R)w�iA�&�Ѻ=S<5%�ty:-��7l�z��m�L i $Z�F$$�ngfijspa�=����A"� . U�rva٢_)-8>� �N�1 Y)=[�.VY]+V^2[�']-VV Y]0a*� ��2��w����t�XY� cob)�K�Z�T!e6�Hwo1��oQ y?�ap�R9Y�. U�?rR�J�G f*�GB�G�le�~��66�$�%�blenva)r.�2�5�ss^:AJdm�h*[��f j R<� "�LZ#c��G� m��bJ'�"�  %: fro�H&���%$$ %��2i��� M�  .� "�*A�*sE�:"8G]'s1�V�Wv` �95d*�7.1(1�a��_�T�9 @�41, |%u^3u(,�(i��!5k�� a2F�H$$ A=\�(:�r< &0V}H&( BfSF_{J�KH12} 3KH�2231KH32 PF�3;�� R�G, $F_{ij�4�L^2F&��u&i��*\EbJ�A>"�"AGNgr�EU9�t#ypeo`E "P;�>�Hw� Qr�p"�h&�  @��*~f6k!u�f��$:�?). Ca}:�� B�$b�$��Ix J� and* ng�Vto� �Z�s���wver-d&�)ic-)r��ux&zF$F)��+es�%�+��:�����"�me͠⨡�* mb s �ij�A"v� �(  es *�;m�Hon��om�]or. Nume���ere r%ly&� =\&��$ch� rrge��#e.�%k. S�4�� , $k=-a, k=-b� k=-c"&45p�d�on�2�}� ZJ9�en ,JJ>,�@23}111}�J= 22}(c-a)+ 33}(a-b),�L2*12 7*332 *Z F_{3; +3+223 b+L:k11}F_��=(213})_1�#~3 #21)_2#v#2 #3#32})_3#�.q=(� q�:1+�3 )/{\tm gle��M�=(%6,2,2>2 >2R>�.> ,3+� >3F>JF���6B���=�!1} e!k2} �%�� Be�z�cee�Twa-(2� �5� F.�q� ��l�vne�ad���m th � ��I=� ^2+4)& c-b)�!z+4(�M�!P+4)�a-c(%RA�\AJ=2@H4G!$  Dl A�U� �;�1��JIJ-��"}  $I�J[ "�JFr�&�B analcspl��Iwo%Fs)'6�}CSl1.} At� saL���.�FO2U;%9a] 1=-5QO!1},~~ %�Am%�1�3 Q�CF�Z!-.d�b*6,��d#de��n{s�`c?"�1�F��(th��>�F�@%u%%ppovG3� e��� �2j�%.�!,�dcee Be6!��%?n�c� lex-�d��)s). D�.i1�isP YGkAH$&�*u^3IpNK1$u�_�A��s(a�[!�3�G.y[E�G3$"AA�99Qō2�� � �d&�6}B�N"��D� R���*%�"�]�%�$F�/F=u^2�F u_W�J/ *�R6;"< APq�5t�G)qR�R����R.�*.�R}�"�Dr1.Ɖ�%e2!pR2%���g� ��cas�wNWOVAll=YxC1}s|non\� Y[��Ah�`�� 1sFrV�^�. BZ s a@�a jk���"Pk�Xah>{a�z�� s�) ��*� Ht5H%L6��2a.%A �� J�� l`�!H"+h�(Fj}Ng9�2b4R .\l �y�gR!�!���uf�d�M�q�c*)ь�ocQos2�0 >8m^� F{I^2+6���X�KJ��\Q0Bb%�R.�non-empUu"���)2a!��Q�F16�n)Tin %invo�� � �"�Zsi*is 10-*�/ . N*�~/� ��"�I�=)!�#��C(.H2�&N)no�\ao!FD�5ҫ ll� N�B:al (realͅ&�mA�!=� � N>4t M�o F$%F�bI �^~@$$ F=g(z)+\bar g(Dz)+p(\alpha) + q(z z+ +s +:AT\w_z� u^�7bQ{Ei }}+i8u^J7  E>~~ Pb>-z>��]F}bu^34U{� }} $$ 8C$TFqur !H%eu.�H�%��los�2-��-q�+e $T= 2TQ )(u^W^�X�2"�+A_ansatz��\���IJ}� keep0TlzAEq]Fl�:J���al]��� s $G=g''55P=p Q=q S=s''$N�U>Q\�GU�GU�PM�)+QF�S U�IO)+=n|E ^2-� r-,r( $�-F�B-�z Xfz2={I}/{h�.� ��FF� -5�O} �$ �!FV�^2 #��^2+R'��ar�T�z��B\ ��� ��`�2 �f  �� )�\����)�Ub��B�={I^2}/��6F$QM2B�Thq�2��D d� �@�8\�)\mcq���g[$�=E�񁴅�)Q� ��F~@��"$  $)v��ʁ=0$, �|qP�}����i�8aaG�IB�(��9 J o7it3gn c0 deJi�*Fyway#Fr�g�5�d �m�ݍxNg��~� ^2 =uK�  �^�L��2{I���j.u�gkE�.�.�!KbF�. I}).�"BmaO YuO�@�@�-5VJa-�  �>��� m� E��w��^07\S!eN�"3�a$G;�$ar G, P, S S/K �sV',!�=cz1� %�=cz )!�~~ 5e=c�  +\��\\ �=-c� �tad( Zz2. uM) \eta6$$ �w��Z2i�b:~� �i�5&�"$c-�'!X S � �B� ��7 is brings�/>� -���%� "2��}'��� �!*7 i?�ropic B�)� m!=\rho_t+( u_s v)`s!�=�u:�v�K p_x/"4~~�vu�vvv_y+p_y]w= $p=pU�.�e�� statցn<� j�W6�Ѫu"� ��r&@?=o+u,\ v�u�j�u$`rho�N\\ c^2� & ZRu2' !)r�IO7O`\#v2h0&vN]&:$c^2=p'�9NsoundB��B�Y� :,]>��.0�"i"�@pencilYJkBcS;�.@ea���T 6 f�m|"�::^�>J� �$A�*����'. N� theHY,Ufe$2 Aess6�#of !Ec�} , -��x&�.$�� ��9Ʀ��w��#& ��re8�W,I�\�aw�F�% ;!w.��>�o**<B q t (E"n A� B�-��]"`n�imu v)(J ^2-c7l�J2i^2D�-!�c��al؇&�� �YI�Hgs. >W+"�!�A��G�M�>Y�%src�Aou*�nps�r qby�J(&N|M% &x 2lO>m�we�[�- $�C=&'D��=u6v=v�#!fV�w1,�'��(�ik."�$�JB:2�=1�i&�� Q�~S�iYYX7B!� d�l��}a:vO.$�2��t*0Bk Y�^iI� ^i v.�+ 8c�rho��\�$_i��� �VkSV!R� = 0&� �U�+"U>.Qu +� .v�a � ��,A9�"K&�%!� $. EPng.�* u�W2vu�%���aC1�n9�f��6 ���*�NdJN�c}��IZB�96�(%�)WO= 0f>Pq�s�&�=�!�"���M,<=s^i\cos \varphitI3qg�> $�E.� =cs^�{�D$s^i=1/(c-u6g-v6\OA,q 1��I��6Ilz\}� ��6}�D";$skor} \end8{equation} The ds for $u$ and $v$ take them \begin= �array}{c} \partial_1u+\frac{c}{\rho}\cos \varphi^1 ) =0, ~~~ 2r@2)@\\ \ �v>� sin �.@J�. \end-( \label{uv 1l} Notic!_8at since $\mu^i�$iu=\lambda2|v$ one has $u_y=v_x$. Thus, solu!�ts describing nonlinear interac"� of two sound waves are necessarily poten!�. WritLoutEHcommutativity condiVs $5�j�/( j- i)=*�/(j-li)$, $i, j=1, 2, \ i\ne j$,E�A�$consistenc2��1b2un21uX9s0vR0v$,%~ arri%3)follow!! systema3 $Uk,Uv�rho$: m@] yR�2B1=\cot {ibc2- ,1}{2}}\left( $c'a�m 1.�{(6@$2)}\right)2~ rho,a_\1�2R�X��J��@� a��u� 2�4=\displaystyle1>-rho�2}{a�^2,v��9*�}a�Bn \cos^_ 9�4x }(3+ 02V�) -�Zbgas�:cHUp to reparametriz��8s $R^i\to f^i(RilaPgeneral�G�%hisQ�$depends on�<0arbitrary fun�Vs2a��Pgle argument. For anyYu�1, R^2)a�!(R��rea�tructs�@hodograph surfacev�corresp�� ng double�� b|v)qts (\ref��) e� $u.�� .(which�,,automaticall����t). Each �se �0s can be made��o!-�� /0 gas dynamics�by !?b� dw})�0$R^1(t, x, y)��R^2; her�ze cha��MV8zed explicitly ��3=((u, v)$. UsQ�relm�)[uv}), �)Ŭeshow tl!�q� � Y$ satisfieifsaw(d order PDE� q<�qb .�� Ń.�^2}{c^2�]'(_u^2+ v^2)- ?.E >�J:+2; g-J&/Z�K=�/ �x > {uu} �{vv})-"� u��_v !� +u^ >;V rho�:�e�$$c^2=p'$ w p� )$ i)�1��:state��('\equiv d/d�$.�( polytropic�d , $pEX$^{\gamma}/ $,E$]I[�) simpliI#oA�$ (3- 8)m^{2 -B6�%^{5-2 4}= 6E 6%[%:�x $$ ��� ):a�(1+��s)�!�-( �-1) $)-2 _u v !�+2QA2Qu^NQ=0�after%usubstit� �$ 2� -1}/� $. I��i� mE5�� � s appears��T\cite{Sidorov}, \S 8. � 2ItAounlik�O�D� I�m�ib��egratedia closed� m, e�D�$Chaplygin'��Y�Q�=b-a^2e� $, $a, b=$,])�case iG ]� $$ �S �* e�+ � Z+ �92 :U� VU*� )!��� ��2� ekl�� :[ $$$ HoweverWme��ticular�E�"�%�� $ed. Let usi�<�r�|!��}��2�}$lId$)>� = q�}{ �$. OneEx verify <�m�^1=R^1-Ry d� 2� \pi� )ρz=\exp^{͓2}} +� �[ solvM J. b&��q�6| A�y�>Tu�sqr� ��}{1�i } (> ��)-E�) � �1 ��v�]+~]. ���Exclu�� &� � :J� F� ,Q(�)��L(�lG!�^5 }=1�r,!z,ivalently, $.F<=2c^2Po m�� g in:� �tHQ>�� ��a Vs {` 1ly>k :!MB\l#11�E -� :76*A ^{R^EI�R2=M� IfS�A]E}BS\MkJ ��vR~~~N2���>�a�g>� A�"B �2R ��%�2�2"Eis-�b��ee�� � mula!� v^1(�  })=t+5�x+%Ly��v^2; ;�tI�$vx v^2$E��R ;he5% flow�� with# They^ ��u+�F��?��v� v^2- 1���25(}{ 2"l1J0muP2r1}=-1U�6|1v�i v^1- >|1q|1|2J0muP1|2|B9Pot�6� %is typ� their� lic$to problem�2Uw�extensiv� investig� !�mone6+ ��aim�se� wa|demonst v�sI a dei_t �fit�_| l schem"�methodwhydro$ redu�s�pl  �Fer4}% E*�(, our deriv%.SU� governA�pV�is| D6zHaantj�en�� H})Izero. Atat!@ E=ut3,he $(1, 3)$- @ s $M� K$,��(M^s_{kij}=N �  b=���a�4, $b^i_j=v^i_pA�j"+]�E�� :� $Q$ aV�QAEK_kEZpQ�+U�qA� -Ak7kmiju+41ke],2 kpA�p_iiiojB1Fin��introduc �i� $P$,q&��} P� s_pQA]k�� v^s � .�)"2�.O P})�um��3em}ͅ,Pavlov2} A ���2���V��� ��matrix� i_j(u)$ mu��Xly distinct eigenvalues� B�if�� only \6o=\Aid� !�m �� Not�9Ň"M obta�4u���u" algebra. �B\�?0*{Acknowledgeps} Wbnk M.V. )U�(S.P. Tsarev�k numerous!cussio&We als�nk�referees'aM�0ive criticismc(useful suggW Q =�bibli^ y}{99}tibitem{Bla} M. Blaszak, B.M. S��4ikowski, Class!c R-)� %^zdisper�les�,s: II. (2+1)&.�8ory, J. Phys. AX35} (2002) 10345-10364.2�urnat1 � ,�  ofN� for multi�al�!ellip�@ t, Bull. Acad. Polon. Sci. Sr.  Tech. � 17} (1969�19-1026.!q1S�2���Ri/ p6W a9mpla;ity. I,%dAr�M� (  Stos.) �23�D71), 817-838; ibid �24 2), 3-N�3j�6�s�h 's.j � %�.A hyperbol%�Ls, Sibirsk. Mat. Z �11 �$0) 279-309.y(K} S. Canic�@ B. L. Keyfitz, Aq+cA�A3two2Yer� 0laws, ProceeQ38ICIAM 95: Suppl� 2: A!�,ed Analysis,�hew 0cal Research,)�\87}, (K. Kirchgassner, O� hrenholtz��CR. Mennicken, editors) Akademie Verlag, Berlin, ZAMM (1996) 133-136.]�0Dafermos} C.  , H9�B in � \inuum physics, Springer-� 2000.�Dinu}!� , S� r��c� A�M- in� cea�a�4-Peradzy\'nskix  M�&n"Q 0es, Rev. Roum��%y. Pures%�M<35}, N3 !A@03-23�e\q��r:�, Gs0of 2D topologE�field��i!J Lecte � � |1620}, :��9Ak20-3482�Fer} E�Ferapont!@< D. A. Korotkin %V!u`Shramchenko, Boyer-Finley"/,�%�B�ͬ4. Quantum GravM19�eL205-L212� Fer2B�r��6 *of!� heave�z � J� 20} ��,3) 2429-2441.C Fer3V�S&X, S�7�B�ari�n �chrI#.q~.�A�exactA�}, A�. ModeuSE�2E1) 82-9>�4V�PK.R. Khusnutdinova, O��Uof>Bal quasi�M , Comm�<ta�hZe0248)�D4) 187-206; arXiv:�)$.SI/0305042D Fer5�����%��\L onE: al1 �� ofF�, *0 :!�h. GenM�3�KN8@ 44) 2949 - 2963F� 1002>�6��H�� 6���2L: PDEs:e"tes�5B �M>�4��6 �, 2365-2377; B�12015:?7V�D.GA/ rshall, D��-��D�t� "k �!�2nchain �:,B�5050132/Gibb94}!� onI  Y�, dama!"A �J  9 the :nKP hierr�i[ :�.? i.Lett. � 1�*a��f167--172-GibTsa96B�S. "� , R&.�  Benne��s,.� 2� �Z�.� {9z{Con�al map%KJ���5�F,1999) 263-272DGodunov| K. ,�&E�r� ng&u ��-�� �� Dok� k� Nauk SSSR��13��,1961) 521-52A:"�$Grundland}�Y��0R. Zelazny, S�e�)� � �J� . d � ."A�� �!��$ ` *�.s.A�M>� 24},c N9Ei3) 230a�2H�4uMaAl}F. Guil,� Mana%� Le�0tinez Alonso�Ia Whitham Hm ies:.���H"So��B�6�F,3) 4047-4062.�q�A��u�� $X\sb m$-A�A sets!/ ec� , Indag�es%-; eM7} !' 55) 158-16�Kr1} I.MKrichK"��averagz�<��d*�"!�gr��""� s, Fk,.� ..M 22M �88)� -2:�KO � .� Spect�,� ! >�4periodic opera! !���.Z+ )144����45-222K\ �=1LM. Mineev-Weinstein,�� Wieg8� A. ZabrodLaplac� growth"Q{ %�so �[�D �0198}, no. 1-2��1-6 Majdae� � presNluid !)1�] of� 6��sA%�p�-{ bles,-�i��J� NY�5[8c 59 pp2�M^e�, N�%0E�dina, �3!l*~.q�E3he>bKP ��.cJ3 &o401-417.�Maf �$S$-faZ,.�z�$r$-th>�modif)KPADym��� B}� A4" 11191-1126� ShabatsM$ez�jA.B. $6� >�2i(a universal�y, Teore �Fiz� 14$�U�216-229G��"}6Z  I� leNZ %�I�i9� C 4134-4156.� j%�"�� if�QQ� EgorovV�Tv.%T� �13i� 1�4) 55-< >�!�8S.I. Svinolupo{R!� ripo"Ve�nt �,n�2� �] Funkt�a�� i Prilozh&K 0^v 8-29;>�.�1^.9�h2��1}� �,jV8 nonplanar $k$-07b���2�9}� 71) 717-76&�2N�N"�7�e!��* �625-63!*YS�+nec� ~S\' $, G\'eom\'U4em8��\`emes&� (ques de loi�82�, M\'emo\(nouvelle s\'erie) N56, �&�auetin Ta Soci�\'c*atv!Fraj!e�122II�-16w(Serre1} D.  ,.�B}. 1. &�ity, elp�.shock� 0, Cambridge U���!P�A 99) 263ɢ���2�� 2. P��+j, oscili,s593ial-b�9�5�3 s, f��>�6�T .'G. A.F. , V.P��pee�<N.N. YanQ�� of 2�!vtrain�ndBi a�9$s, ``� a'',osi� 4�2:f# *-G h*�"*�2��.�67�3&� , Iz\%(ja AN USSR ��E�5 5I 1048-1062o �1:�D6#&T o�ge�KdV"� $, Uspekhi�,em.� . �46� �@192� Lei}3 Yu,.� %�2u���9&� , PhD!��ImW %%% \defpeq {\stackrel{\mbox{\rm\small"}}{=}�1nn{ \non�& } Fbq{@27 }e2�5beLb7eqn/ 7�4a`;��renewl?and{\the� {\arabic{ }.#�new-� {thr}{� ६�}[ ?] ^orembody!�{\s!�A propB। E:rN rm} .Nex L��:�uAF��砭 wn \�p\extra=msbm10 scaled\magstep1�B�9=1ex\2b = -1Ef�YyY}1.5em %E�heA�=22.0cE�D=18.3cm \hfuzz=4pt �frak=euf� �A�$goth #1{\hA�x> k #1c> C.�M�bb.2! 3i%IersQT ;,C{\mathbb{C}M�QQRRZZlu- Ig #� g vk{~3kappa} �E�D.� �d_){2�? H,fs{\footnote% R�p&�5q�de� ���!�B ��. #1#2{{#1\`+ #21�d24+*-)onE%�op{\vAmD\ialign{##\crcr\no L\kern2pt} $\scriptst@A #2}$V*\no�|rlineap} D$-2pt$\hfil>�} N }}}\���$�2����Wspa}[3]{<1 #1}, #2}\ti� � #3})�S;der}[2]e�c{d {a�2e�.� pard-� 4;%<���(��}{+��R�۽<le�;{T.,:# b:%��6�example::%r�k.$2�:.�>/:&(exercise}{L.�. }�eve.�1&@\emergencystretch���� .6ptő5� be}{��u�a3.�e#�V!dx}9�_x��bdy.y>t.t:lb]2 brac��.�rrN bear��:Ve "�R bC:beJ{lB>C!:Ms}{e7S>5ZZ cal\�'13��ba1���ea{6�6 �0�l)�8}{1.3} \title{S�D*� va1Q�0aw'-� "}'c�", } \author{V� ikhi�!V!Sokolov}�(d"� \58{ �){I�2} tcou�I&� {0} �=i;per weiB;m� �,at ad� a � rR�E#*�H>*ic �!genus 4:��J%T} \Phi(\xi,Y)=s_6Y^6+l)Y^4+k 2-S =0, \eeG6L�;n} s_625Ddelta^6}{6!}S^{VI}A,\qquad Y6- 2}{10}S''*x+4(\alpha \xi^{2}+e_2\xi+e_1), H �= �2{ v 4}{4vIV v�8 ��Gk gZ-e H52$ p, ($7parQGerx.S$�+a" Gsixfegree %omi� If $ F=0�.e�*-�i9U�of-�\8%��2 })�, `)K0$=b �bedQDf�Js.  $P(\et�xi)=0$.an�cubic.d@�7AAq?i� ��.�n�-w2a�6cover 4b� �,byM�9 $�=-�-)yu VVma �F 1)�2�Y�- 1Ak%�M�+b�SE�A� JH2} PBJ��5- yA�Y�3}-M� a2}))�V=�8�8�%standT:Poisson  ket�K �� R },s_] ta}+ =)_ !!Jta�S.�,$�:ɦ�9yEy�$K$�=in mo�a_ahF$ A�belongpW2� drP+$!�wo*z .�4fi direc4CfroI��-Jacobi".h S�>s 4-6+H� �A�f\ k& Kowale�4 hyrostat�8e Clebs&Pn)z@$so(4)$ Schottky-�!kov spinl> tope] a wa!)alogoum4at usOI�2-3�� ian �;�)�&xQign] nt)�s (see,BV$+, >shot, clÀ, koet, man, fedor, adler, vesel1�",ysem, misc,$fom, wint,;%elFmtsig}%ZL6nc�8re-in) E devoa��s�del�#.�?-@s �6n �bobWk j) �&!��P�V link�Jia �> hangI�". H�H accorA �Ecommon�?�Aex�>^ "?Oa?'y"��i0f\!r� abov�a'still5> f�.�>��MED� sIz �-�  4. A�2ea.6Kb+3 could' predictedD-�ac�!6 ��$3I3$-Lax F' � by�& Perelomov-�p}D1top��same ��9��QisI�a� don'e?�TLax re2 �"� e� � �0 s duM4!�p�X�,, rather natu�&manner���S = \��q�[lso!�of �T�+��inhomo�a�B\�+M }):�i+ pair(� ),� � 9incide*. �--d�%qUgibts}.� j�BZ6xgives �1a9 fMW elli�8o�*5�^����� 7). �3A"�:xs�S���i��N�:4to A.V.\ Boris�$Yu� F�� ov, F4,V.B.\ Kuznet3�� F.\ Magri� �:di*:;�)$ed by RFBR~Q!(02-01-004310@nd NSh 1716.2003.{"�&�of mo��n�!��zUN^7.� to:��ɹU�hav+4%}^� ham1"� � 1}rt}=2 �C�+ d\ ,2, 2 c � e.d � &Q ham2Ji \taulK + Djl /oCoE oFin�[ $�, $�)�)&RngA<mis e re�# $H=.� K 2},$�get�s12g1} � �)\0 k "a \dot� }? � 1)! 2� 22)W @k +16(e_1-f)s_1s_`O4o Ov ^3}(s_2^3� _1)�2)St9��2� f2mV �6�n��) - �\� ���V s_1^6A|$1)� 2:AnB e+�$$ 16 �(-,!,+s_2)+(e_2-F �)> �>? �2DJ-2K6N&1) ��U�f F re�I�4"]X"m��OnL ��(basic techn�9��a rew(@ng�Lt��#A�a c�Hc�rm�&gh";Ien� say+ E�)"�Ha c�!�  !q +� ��$U1$�\Proposr 1.} �G,Let} $(u,v)$ bU��f!c� �of�s:6��uvsys} L!�)#V2 1)v-M,a=0D ^2 (2)u(1,!�!�a/��~Q*�pRL} M(x,y)=3L(y)+L'(y)(x-y)+k ^2o L(x)&^2S(x)&�dT�JKves6�qot��=-Ji�s_2\,u+J" ,�$/2./ 1\,va&\�t UN)mSref�(1Y��7A���.J2� ��p_{AVNi��^[�)Yv�3z� ���� ��_{t�E �)_{�<-J12)1) )J�WIaCllows �ei% y���1\M�symmet� ^)�u+19�B�2+v.+ � More�,��tz�pi12} p_9RJ\,u}{8�V(W p_2= �� J\,v #2) x%�y�"�i;�q��)�i�) tur�doa�cru� fo� �>� NN26Nz!�, zAo3}$�)ith2��Z��.geZ} z^6�2)^2- �@ z^4+�&1)z (1)^2=0}OuchE>;z12Ue"{�}{�A(}=z_1z_2z_3M m M(y,x.% ^2+z� +z_3�b��Rx)}� 1}{z�n^2^6 3^2}J�. uvso�&v�4(u_1,v_1)=(z_1��,\, �}16�23}"�(u_2,v_2 K-z_2-%6K-Y22e",\R� (u_3,v_3\X`:�6N1>\-��4,v_4K3-zK 2,\,-��32>6L��*ajYD�.���u�졂 "^ Z�.jc Toqo "�Fa$�o �n � ( $\tildey{1z)$Oan�l"�U. N�Z�y�Iq�sZ �zYY6S�� Y^�VX��� ) 2)&����&[ $*���*�c�I,MOy to P�=CMf��"f e !/first�exA�3� $�__n���1n�2 pow�(oxi�celŠv6 a" B�u�B , \xi_{iP 9�� @uad i=1,2,3\,$ de6(c root�@�!q.^S5em��5Q2.`fullse�&EE{S2�,� 2})��4}\sum�&_{n=1}^3� [I�A$arctanh}\,�,�n�>2o9 }� \,YA7$_n)} -\int i^ =}�{d\xi}{*� g ]y�W  d�>K�%H�jj\p 5 }�}��Nf &, ?� );! K�fff2}�R� y]1�s} $H(� ��&Q $K(2 :(J$ [�*V � s���def"Q�Proof.}a��� �& � E�.� ajaY����{S�re�0. $pi1��\S2��0�;_1�cV� Q�2VF 2}= M�N� a�%tiE8�d� � eȭ�:�0 2) ��A��2}(Ju)+(1n((1}(Jv)=0.$$�latter"�6�!p P ties*c tog� F�h� +M_x� m� 6v -22 �F\[3! >M_y8A� A+4( 7-� ?B�Pc�j�n :�� Cop)� auxiliP6�+~>[A� (%�re �� I�eZ}))! HpG�PH}=p_1^3� % + 2p_2� a��ap u�+ <2z V!S! be checkeat=� �)�)e�fulfill��"�p "tz(lde{H}, �Kea%holds, �i:%Hh�q K}=-� & 2p_�&� �i��)���$� i,s_j>�ijocth�:D s betwee&) .�axp} a_0!�!eW a_1=s�ŔpR �' a_2�� 2 !�A�]sl}�ej ,a_1�a_@ 6"2" 2a_1 �#�,a# a_2.��W*� $Q=az -a_0�O a Casimir�A�!=Q,ear $sl(2)$-x!kPCI��)�#*�Ah��K}$te &� B!k) c6�$Q�bhe2pSH}O be�A�n�!2�.h�Thb*� Ha�1u�a_0^3L�m�Ra!a_0��'2� a_2�)a_1�) a_0)'#��)�%}}OY�� se&` �h�F%P�l1; $2 p � p_1s_E��!p }$$ sh�pl� key role  dC)p� 5er��!K&� �5��+��).�<ose=�.V )=0;l#� $z$Eh� -�^��.� .�!$X!�n}]zzz} z=\�)� s_2- � �& �}�"�.��# ubic��2fxi�jt�A�a17� ,� �yY}+ .eq �v0 � Our task�to r!�!�I��)a,� ly. A�;�*sTX),� s�]e�^.f�o&� syszP ginJF�) �� \sigma2�1}�,J�1)}z=w X }{4(!�,2�F�}^�:�N�.� � V}(��1E��}Ev6�)H�z�( 2��b�t� .}-�eD� i+Ro c2�yIa2)) %N66v� ac�#> q� S��quiredqo�Ya�/ e suCA�threeU�s� �E0),V 7b�!h�"M�x>� F�&!a./Eh_0$ s2�!5& un�0" }#!'�A"t�Bu*anot t�%$s�.$� ish�(aRe�at $$��$Ud4}I\rGi 1}:E�Y6�}�" Tak�ijc�1)d��E�q�} �S�2�0��nyA�re�Ingl ^-��$Y)�Ih��xB�I��6v�:� . *�P�gAQ '� ��5�V#F/EB(^S5� e��t+c� "� %.1^V62}=c_ _ we ;!lly:�// dt=\J�omega_1A _n"70j,2 ,�{��G,\; 2d1+A�a 1.Y om1234} .�:�Z9 �x$\xi\,:)M3�) �h�^2 Y^2)Z84,8Y_O !To�%rphic d*�Rf5A��2�=0 �� �)�g4no�% $Z.�CPhiaX Y� .v 1u {4}$� sS pe�� .i5, s $�,j2)$��er.{- �22"� !2Ae � �iY }) beco>: �a� *qubic%5e^3+s_5 �4I�1}{5}s_4�3+432)6 3��$+< 2@2 <�!xi+s_0 G4D^2}+�^2)� Z*o5�,� !�^�,!e�%%-) �) "� �a2�u�|:4g)h!�!>� yY.�!��-{r� ��mO#=�Y1&���m4R �ADu eY�_!:x 3)"[01 1:} _3� T")�03) a3!�_! 2)}I��aC,"�i%�H-9$C(t), �2 $\0�Rg from �ȡ� &� (, 3.$�&us a��%�"= �|"# %a)�.�<� �ii�!C�}l )� C�b%j"\  he}�.� a�Aةj-z3)+�Z-^1 �E5� is mean� � �k2J p?s |_�l_i)� �-kS8�.�Fr6j��&27� +� � s_2.$ \hsXQ{0.5c�0 j{r�.n�a{is well-�-3 V.2> T.,.#.!�1'*0�*v htop�7,(\vec{S_1},A )+*�B  2})+/2/2 +7y $A=avk}(.,a_2,a_3),\;B20b_1,b_2,b_3)$z mmu"r5a br�* $K$R �/Bj�j puas|�S_i^{�3S_j^{\b��� \MC\,XCepsilon�3*�s} Ht _{ij}�iff� b�(a_� 3)+bN(a_3-aA�bm!(-a�&a_ 1+ � van� A�tot� skew-�"j:te�l�u�/a&g . S<�H$e!ymay�0 �&&�;*>arHbK&��4,=qV>��) J�Q�}cE�}_�d�J�$2,$2)A��e� c*(%�)$ #.w3����i�*c�{[1}�0!;} [K=.\hat{C} ~e � C2�I^�W=� 3).U With�"los!)25�8�N|mei�$A-�Be�;!}�F4 �choosen� !`6� 7A�,  2^2, 3^2"� 6� �2 3Eu 1, \,S � 1:'!\,  2:&3), Ye" ��w�9-�� shif�A�by-\, K.$�"~V1�"�7k.}� fix%u6�5B�:��M�kU�k)=j_k^}�'� A[ula.��r} ?=9oLK}(q_k� j_kY 'Q��z\rm}q: -<(q)=((q^2-1),\,i + 2q����J a> tP9: fold��co�3a��$na�52$h1WYq��9��=-2 i$,4A�jg.: q�@,q�"i. cano*+ � ~$�p��:���� !�Lta}.$ Aso+&�7is :D w�?t��F� disp"+� H�^2r(q� � j�2}p�)r!�! �ja�}{12}r'  �@2Y!qAp *@.�,@2)}+\\�:��-�|Ew�'} q_1� \mpa�/j � R<"��Z! ,q�s "� q=hpq5.Hkpq} K=��޳W�,� EΡ�r �rr} r(x)q K K}(xa�} )=��1^2(xe�^2+�!+Z(-4  3x^2&�$\br�>~ Z�R�� $K}(y))=\\ ��)�-1)(y�-1b�1+ 1 +1) "qD_fxy2� ww}Wf�C�� ��@_1:�-H1[� +1)+9`yv(po]to�#.�barw} Z!� ,y)-!� r(y)= � \bar ��E $ � ola8* in ��o*�8�"e� }4��, m8y7ral.1A�H6r$ij,\mu,\nu� m  nu}c^� _X{�p i,C�...,N >~D=x,y,z)�0�a�2)�$N$� s,��] � to�aE� genN� 2Tl g�p_ip_j+6$} a^ip_i+vy%u�\a >6V1 K^ }(x^i) n j)>�$$a^i2Gk j_k6�nk.�x^k* *2}j_iJ3i3 x^iY%$$e�1}�.mikKB�^2N�i�� � � 1}{62P'k� 2 Qk>�Q$$)7��mi V60 $"22�x^{k}��6� %! k=1I�[ I*�F.�� veloc?$#Lagrang^#"$energy rea�G!�]�E�L2p2 j} g (3 x}^i-a^i)j-a^j)-vq9E�LUFiI+I�I:�.�j �g^�x�i^k �<d�%&�j"e� :a� a} K2�a� Gn�Ai�V�;|-6�EgG�,*�)k}"& d� E }A�klqK\pij."G^!=�" .{k}a^u�F^-2�8\p a^{i�{0kj}- AD���+2�A>Cg^B�.��6a^kfG-A.>�+2�kz9 \p V� -2G^�6q� v5ej :76�2Q2�6N�'� *n[uh !�art.} U6;I 9 �)e&�� a��ta:o�� f�U.�J2 b 1}2}+c pX �Gd1}+�%�J*�S1aA ,82 B  2}+CT HE .H��coeff�~��$me (in our�/!+�)=-Jvaria�O $.& . G��a���'o irDc�a*rs=�in �F!q8�RzF��zA*&fer1,f-r  for,}er{2�c�u2y�%gMi"$c>9 {\itoniacal}:?w� .�QkA} !� 1}=k` � +k!�23},rE2=� B;2 @c�2bar k_.Fms%� =\ph6�i�� `�Owe $k�,n  @�  �:%�"  of $�s� 2� �)1&"lAy1},%,l� 2}"�unPbly@Axhrough $� � �=the�hɦ�� R�$�'��v�1��1 2}} W^{-1� �0�E9�(V8 1}} 8-� ) u>ptfq8"�.7 %� E�JW���JP�R1}��BA2}}� e�fac�!� �ЁaIr�)e='4a���ed � :vanis�#�+��al�Pto.�01} a(�]`)= b�n$!�2}}+cnZ.caV!@U. P=bBP\9�R�A�#.Y x�AJRB�fB`�2�!fhVIl�!jE> 2} AB�kb�n$-/+CnZJ.U. P=BBP��>gusHte�I�dNd "%�i1�j.+l�ze�� � qJ�<.a+!Q}co+�) ZA$*H>2 h8obvious. Our go� �f�L��qRh$.�Gpq w/2�* "|8"كA*�LvD ��sq� nd2���)$ �(+)�^X!F� ��R"roval} PC\,zN2 6+a-{W6s� :W$Z��0-ww}),)zz�1�I*t"� lj�b@�-"�Z.�A3�7�.* }%,1@E#!@� %5�6$ �t� &!�F}6,Z�5,"6w &V]S2]Rre.L6�  �7!�� S} S�A-(x�N1 2 3)&�1 & J'D".MMV3)U %8!FQs �b�[ lpha,G�]�#{5}-\nu ~ =jA�-j �$\nu=j_1+j_*N3�(9$hM�k$��!`�p6� !�1$ �y� ��!�8`QI#M�%�"&~�!�q^eee} h=e!*�1J �T0"Hk=e!nR''(0*�C ��gM Z��Sq"3�a:� �v�P.bV"!P��g!QnP"L#�w%�� c+�8� �O� �ekZ@��8�~"wJ��!��I�M� �R"amas9�� �d�yT$e(G��"[A�H \bigl\{M_i\,,M_j\, r\}=24! ijk}M_k\,Q�k9�!r> #k FD � �02��$B��r�!.eW"����8B�� 1�z}�cazhXsum_{k-= �kיi��yB�%& M_k .�8^a6A5�!.�AqNE;��aϊHgi�e 12(M +M� + 2M� -�� M_3 )+c�1\,,\\ -^c�pI��cG�ant��n Z��M is �2!G�K�K=�'1}  2}+4 j$\Bigl((M_3��)�D �D -( + )�39r.E� (1DK] 2-2c��_1+i\�$�;U� 2222} 3 4-4b�MD$$ z_1=M_1 + i M_2q z_2-� (We put $$ R �, �= wE1r {h &�D ) -4c b 1 ,-4 c^2\, a+kjH�2?�$bM$�D�'�[R�#b A�" )EX)�q�%�)iIN�^�xY�!'mAs1,2}�)I�{> \pm\V0  !( 1} )2}58}} {2- --L^$$�&�8J�A���Hs} h�4s_2\,2� �K}a\}=jphi_1�@��1 ��"��7�72\,�\be1Kj<Kk}4=(2h-.)m �-l�#)��_1oJ �j N�.,�j."FF"�� +�)�5. s_261"!T6?�--2ZvN+hA��eM�Li=�7 {i})�.�SL ,s)=4s^3-8h\,nZ4M4s-k\,s+ 4c^2 a  \,b."�  S"ޢ�PTi]UI��'}e�|Q� ubkgNL{A=-�1R%�*;^(u+1) � 5z5v5� in �Hsa� �Ks&-3*�>5get just� u�FO064SM�k� 4(x+h)^2+"�O(x-2h)-k��M�=i� 9P� �,u9as� o�Z�J"- J"p 3�� c��t�/bFY,)di)@]�62�1E�omeC3, 2 4f m a �2�^?0� N*)�8"�F�4�G=-i-'--�&�4r % �Y $[E!arrow ���4�ji�-�K realv� �X�+�[ torF-) N4!d���0� �[6Tcleh1$i%(J�)+J� +J_0)(% -3_1x(2x13x:u_0peKXrea3NQ!�n� }�poisEcD�,J_i,J&�@i:�, J�(] 6 x_i,x6: UNU x_k�ia��H� Jo2?9E)m162)v3)-�ymbdN$�W"��Z0��%��k )jL%�� 0M�qAL�# �J�*6?�+w+E =a ^�A JE7A]x_E^x_3=l3U��!D" +iO:FJ''J_�OE�p_1(1-qA�2�p_22^ l}{a }\,q�, ; J_LKi(I+2I 2(I-�"BJ3�(q@q�%k '&�6�x�x_1=a�q��q_ 2�$quad x_2=i'�N' !S&�6%Y��J2P�er�"i*ly� juga�"��R�(�8p_2�(}�ClH�a�{2}xF�C1p"�)%\,!�[T)[��3L�(&Y)"�">�_2 xy+`- M | �w"�/At _3&�*2-""�/���&1��W_Zq J/�f�j���!�ab� V] cl} P-�� ` W �\, s+Q�.��3QRAssoci&�= $t$-��՟ w.��7W*��h^ �?"4;$$ p2 4+(4g=2i ^34$)Y^2+1=0. �3nta�� 1�R ,*�&�(Weierstrass"+l:"J $$Y=�H16��hy}{x-\�7_3U�\xi4eT �} +y}{16�_ �%~lphX�0 ^1^"] .BV�( ).0x=\wp(z,g_2,g5�,y '.Ŏ���Wei} y^2� ��/ �/ 3��"- m�850*hm(/9B-e� ,\;�ta_�9s2} R�%t5�3?%G�}*V � merom�@% �V�e�TBd\tau=\.B)n�\A�<n>7tak#���+" �X=G-�t-Ag �E#}2C-{i � log M5x_i-�� E�1-x_i�X%��-aE� Yt-M�2� a�-y_i bA  2g��� $x_iA_ (z_i]x;y Av2,zbW>~�x�"c�sh��F"�, ey0block{Uber da�Dalytid P_�eS R�B eines yt ren K\"or���� ��$n$2ґ$rigid body*���Nj\,ב\,��.},z}L10}(4)), 93--94, 1972S��l} Yu N"�g.��s,Njlconfo1A�rics. D:E%��)�bmeKz�8 173--199, Amertm�,Soc. Transl.Z�.��� 168}, >,,ASv1Tce, RI�95.��c�m } A X,w{I�\"I�(ie BewegungI�E;U�A�r Fl\"ACgkeit}2Gem ��Annale.;=*(238-262, 18G�uCperel�I &�k:h��oh"�<�UME �Y� of a.:�kn�S,^�>�fLQ�1��83-85,�1.b�n} F%1�U�1nq�^^fe�� 2�%e Fl5c. I.IIB� J. R,@K AngewM?}�H109}, 51-81, 89-111!}9��5}r�o,} A G Reyman TM A Semenov-tian-ShansD�*ܐq.L|em Moscow-Izevsk}, 352 p., 200�z}bmszV `k{S A Mamaev,��rn ��A��y!�Ub��s>�>�296V�gi�l J S �P �l2� "b=��� U���em� Lett. A},�abf �AJ --2492�hh} L H�� E Horozo�A��( �1!*�top>g�ica D.]2A��180�82=�rCA M�/ko,"ْ��geode�g��m���A8Ds�$�� )bf 31}(2��25�T6�T982��foE��% A T F?v�:L on ��2N Lie group�j�ya��.،( SSSR, ser.�@h!8��42 � 396-���n78. �/q� G Kalnin0�W (JR) MX snd P WA�rniԥ� � O(4), ^�:!�� g At5s�SҥJߘ0�},��D, v.30, 4, p.630-6��u��0} E V*�kA P�dy �2vpmn)� typIGl)to� atic.�Cvb-"˳��ep�d�$. 44, N1/2��9) 71-80> eњ8B Dorizzi, B Gr7� tico�� Ra@%m6�i.�1xq� Q>�J푁. 2��085) 3070-3079F�2!L McSw5WAmb�su��nt� ��N��1� f����� 4c�%�957-296��Y�9v} ��d0 z P/ MoerbekeK�$0Henon-Heiles �FwF�pw - a�J dl 5"�r t�|sg emE].�� %l��bf 11�659--70�f2,�H�hP Vesel��O�>�c�Js��E2= ��� �V���@270}(6), 1298--13 ��9yw�I B*w��6|�m�%y$�$. Is�s�T]*�s.::��B� �{ 20}(1G64--66Ų22"�'$I V Komaro��( A V Tsigan!_!` ����]<gt(Rble���` Reg.��ot. Dyn5�9�$, 169-187,�j��֑&�� r�"��'�[12pt"�amsmathf�� [11p��e-� w+�=16�K� z�1 6̎0pt \:�re.5�bas>6�2} %�� e1� eore� *-�n&X�f�Lm�V#/[Oo}{*}-:/comma� p}{\Q9i%.�la"�:q�LL�: th}{ސt>TThFdd" q��k�(Y��i��I� A ne*�n�mB�Q�Darboux&`4I�/ A� �Jself-��/�$urces } I-و � T�# Xiao>)  NT1cm} Yunbo Zeng\dag } ]� � sB��-6Dc�t�w� �<)�l�u1s,a�nghua*�l� Beij�0100084, China�5\]{n �4 Email: yzeng@aT.tt(hua.edu.cn}��date{}.��:�R�b%�ab!�ct} KP�� (mKPESCS)�tre] m$!�framewod�1!��ed%�J�y.�~int� a vX�!M view ��-�~�;ry^!���sR] sI]�$f�ia"{�~to�XTLax r2�{.�!. BaseZ1co�;�� w�trut"h��L�Z2g "�K"�k� time>�):�c<�st H!;ZhN�,���s!�@on-auto-B\"{a}ckl@{"@8i�}c�!�!s{ dbW�t%}* y�+=pEc.S^�is��`��en sBT�4 r�al*�(in��!� lump), ��+�uAn�+�_~  ba\}z mm0�(nd}ww0ki:���?,{Keywords}}:E26m;!�VT; A�Lu�;Qm 6�(DT); B*;�! %   o:�=s�1{�A���2 S��MC^#(SEh�fimg|1�m�� L� � !�phyz� s ^a��*��)�d�Nte, 1�ma4 etc. [1-8,15]��e�?Q"��, Schr\"{o}di��eb�Us-O�@. �an��,c high-frequB�ҟ_A�J acou�w��e��hon� h&� �-Claude91L�.��R��g"�)s �n2�U\. shorQ@,pillary-grav�Q�s � Leon90(1)�:�b#debV�a �h)*a �/� p�R�dX�z! x,y�[ne at!�angle\Oea�XV �(Mel'nikov87N�!�>R�8in). Until now,��degp�fbm��F stud��e . m�U�,1+1*>�al� A�me 4su �# KdV,a?`�Y�:�, AKNS%�Kaup-NeWW ��o��^�w0��"� ��rse sc�l!r [q(,6-10]. AlsKC�wg�M %Ury��:��O�U"��-�� $t�Us!"F?%hs '-boA�# H!!F!���,�9%�^ uÄ%v\ԁd*�N-%�,�4��ad negaS���0 [12-14]. In F[�%M'�"%! �/:� �aedT DE61�A�(p was�*�Dby uJ BZ, 89(2�'�,*��׉ !� ! �[�y1��d��c�,��M�t.� C)"F.� "H%6n"\E�b�nf� �ndY�_ }� r� itME[ -\is)l��i�<Hirota1�3�cuXZ+�(dajun2003}.I�t� pap w7'�c�����h0Mg2d%�w!3�� � . �fs� t r["  be6 �� ^!Ti��s�)�  > A� &?-N�  wQ�� z� ����$�� -v��� j� � ?A/�;�5 pr7 �9�7 � �kͥB7 ���. B�&!���V� ��| H��S� XA�>� s,F s.B > &* ��o =�6' [8�3�:pa� wO�be organ��:@recal� me�Fs��u,(a�z���G ijoIa�pseud���en�&��(PDO)��mal;�( next$�ax.�}�  3,=b��roaSaJr���s�� @ �=�a4a@ rev@ ��?� "rϐKP"y V�Q;�3N"�?�Ş'pre5D��7�s2� �!�66��b2�Q.��X=�ۦ\m`nZ� �a�%�S� 5a�e n��B�Z~ U�){� by ��EV�:�2C�MQ,6. "�+6�Az �Ul RVݝB��3�i:mLi� ing JV"|�eUmQ��:C.11}$L=L_{mKP�M�eal+V+V&��.L+V_" �^{-2}+'W>)?|'��_F}�7f��}  x\v�=V,V_j�W$%mf��. DJL $B_m=(L^m)_{ \geq1}8  $\for��m \in N" �>-"n pro��ioY$L^m$j��� �z! who�����e�X than� Then� .� '�7as< O�93"�qF�2-�@_{t_k}=[B_k,L], k� �9o�9*+L�f�3 a (L^nP�e^n], njjF�w-1�H�U^�be :YgdI--��f�4 �B_ �m}-(B_!�dt_n}+[B_n,B_m] = 0,\ \ n,mA2�9��4�- dRB=*�-�subK>mG5j�5.me\psi,t_m} = �y�\�YrMI9{Ln LnNL[6�al\b�6�6j�66�2�\�wB}_ �2�And��6 � �U �U �NUd6��� �A�-(�z B_"�Y��)^*$, $iY2$. We m`U��v�}a-�r any�_#ρ� . sf?(Pf)$>�i"̔$P$qCf��ile $Pf 3�Fp�(0nd $f$!zPa���R��t?t{�$ � e�2��� L$$n=2,\ m=3���\�Q����lu�H7i�4V��T3}-V_{xxx}+6V^2V_x-3(D%k 2tcf-6V_x2})_�22-�D ?=  D=1$&+tQ�F�8 � u=-V� tp.1}{4}t ��y={. t_�o2}�g��_"F���dginJ�9 �,_t-6u^2u_x+u-Q`^2 �u_{yy})-�1 u5u_y) ]GE��}�k2alc~ �I�%� �=U� I:# #!RFrom ��5})E� 65�l�I'Z� 39})�p� ��JI6��~10j10���0�� {1,y��axx}-2ux�,6���9Oz6�,1,t}=(A_1(u)P[f \ p =-4�Z ^3+1yC ^2-6(-%�^M I�!�5BB �6��� f�1N32!3-�{2242�4114��%52152)e�1525->5�4%4`F"��"�Ws/,Q�10�Qco�< nt w.r.t.aP�5 6i� Esteve&�{6�US���lJp25�A�1[1]= -f����{1,x}g_1�� rm{d}}x+Cd3int fV" -C_1�21�u�u+Q�_x zlnv!� int`�fF��FƝa�6Ow�!��:�1V�q6F5�ny 132�2!%�2-gF�a-J��4�g)�J"��3b�2��� �0N�F$f_1,g_1� 2}�ee�1})2�$C_1, C�x�r�}co$Q� s��z]unAp�%i�* � $!� f_1f_2 58aFv ",_{-\infty}^x .Y� . or $% t_x^a�-Z+�"FnoJ��$y$*$��X�k�<41P�w��� suity! bouޥ.�� "Q*nd&J%�p $f%qt $x=�fty$ ��x=)h .�I1ā�) (_ $C_2��!� =C$)!|o*�S)Jf�H�S �^�4tit�NVK  �DA�{ll^ &�[1]� \ =&(e��G}!�jC })_tXW-e@t}tF��_6� ��S�@t}+\t�)2�(A�f��jinj�)[ ( k� x}+ga(�t}6o]Wx�� *>�-C�C%.)�-�)- f_"7�r��6 \\ &9: �5)}(Akgnn z 1)_x2D]�E B!B�-Fv- !J ��_x:z�O�I�# &O.�#:8*>�� "��|r�� , W. �� W.Strampp��s����PDO $L$tK� nC 20e� L^n�� 1}+v_0"�Z!�BK fro9r/ >� 8!Broer9�An �Q =(ua6�+tJ� 9�j2�N�qZ �r-�Kq$,$r$ &Aaf�22!:q�k}=(B_ks�  r}_k�S2�and $B_�k=((L^n)^{\frac{k}{n}})_{\geq 1}=[( H 1}+q\partial^{-1}r:B] 1�< 1}$.\\ Then a new $n$-constrained mKP hierarchy will be obta�as \begin{subequations} \label{23} .1} �t_k�L^k �0 1},L^n]=[B_k , \end.L }N]2 ]q_ Y(B_kq)�A3 ArA,\tilde{B}_krJI�6$First, we %88prove that the 5fht (\ref{21}) together with (di!W'<2}) is compatibl_thT2� Wl12}). The following formulas PDO �,be useful inO$ proof and�lis�m below,v�4j�X4.1} (\Lambda^*)_0=res(Q�E� ),\ \ ,* ;216*6_{<0}=F2+(2�04Qq(P:�Pq)2\r� \ (:0P 16 (P^*�wwhere $-%$A,,an arbitrary%�!�$P differen�0` operator. $(A)_0$ denoteA < zero order termE8aJ $A$.Q theorem}�Q��[coF� ��mE���PA�,: We need tou}.id�ty�FF5�>�1�)��� _{\leq 0} 6�7'�_6}�@array}{rcl} \text�( l.h.s. of}m�25})&=&���e\�>. �,\\ &=&�8r@6"3Gx\stackrel{\triangle}=&l_1+l_2\\)� � =�^�7zrZ� Z��yleq0}-^� B_ş&f�r_1-r�� (l_1��(�>.1P!B�͍A726�V�)q6��)�)�I{(r�&=&res[�E ^*]��:( �2 qB_k^*)3(6 !mm: <��s: )-)=r � ̆nR�!oa6q� E%��[j#1 %�>.90B_6/)]5:5(5A�2d)�C]=q#FX#=-V"V4So��}� 8}A�A�+(l%7=E_0-(r��;)ri{��)�2�5vM-N$_x-�WNh2 D:�6/~ ,-6�U�(66!x:%�)2�^* rB7 !r_xQ��%B�%)m)<�4Y�::. %� QBy� last��3  of�x� )� haveJPr_12p-1J��T25+ �2B�i.e. $$^ ><Qu2B^Z,.$$ Multiply- $6$ o  right D tak#� negative � 4 of both sides!5#ab w%;get��>�w2!$$at$$9^��BiyI>�s� w63�\" ^*(r�-�EV�^E�>]SoH V-�19} y��4 �E �: >b FromQ�8})%� 29M�can see 5}) holdsx letes%�  We g!�0some examples  (a) \ $1*?t($n=1$)HerJ#� L=1@>� B$NsLV=qV_1=-q��c ..BC $$B_2=(L^��Oq^2+2qCG\ &2=-U B_2;x)^*=-6M$$|3|3q �/3+3|@^2+(3q^2r^2+3q_xr� I�36�3P�3-Va_xa�..aD>� two �!u�2�ed &1a9�6Q�10"� W&"10*� 2}=q_{xx}!�q��b.2}�2}=-rFA>A�6�and�D6a1n�1�3 �x}!� �:���1�3}=�x}!� }\_x)r_xBJ�E��"10p��4generalized NSU �deriv�coupl��2n by Cc,et al \cite{79,gYi92}.Af c*|YG8is also studied�F {GengxR uo99}�j(b��2>�2��^2y% 2+2Vq2��f��which��find $$��$qr-V_x-V^2eVaZi^���.="���L��.�v��.Y(3qr-3V�{.��{2n�2a�V2(r)�t2a�>�V��2.3J�V����n�1�� 3}=V�4��V }+6V^2V_x��A��3}{2}(�t�,35,."V�!3q��357.V�Ml�H(c�O3>O3�O3�O3+2�3(V^2+!CV_1�r�h���5c 2�2isz�n�1�E2M}+2V_{1, V�,3>tP-Jx��6Mb-Mb-6V_x^2�kx8 _1!B2(��4A#��4.4�Eliminat�$�!$ �;�d% 1�"% � Z�5n�5ii�1a�e�x}+ e�D& ((V_{yy})+3(  V_y)a�3i�--k=0F9 >�" 5�n5!��.� �  \secC{a9%1_� self�4istent sources? its2�0Darboux transH�}ctcounter&� ${0} \hskipKinq IfQAth*�t �  1��" 3< L^nJ n)"�D+\sum_{i=1}^{N}q_i}�%�rB ;ftSq_{i,��q_i{ \ !�&�kr"j �=add-U�Tn}$�alh0L of�����defin�!�&< I>� 5� llowv3j,3� ~! �-*�+"�83�VJo>M^}3� Er9�:�BJ So if%�varias"$t_n$"� viewed a1evolual,,�vYmayregardM ste^�9�o ��� . Un�v2N%h.)%4EW$ naturally��Dconjugate Lax pairi�E )!izSjo3�n%�\psi_{1yo1F�b�lA�:Kn}�21)a� J; int �3 �4x}{\mathrm{d}}JVF ~� 3j�3ż�2- ]��2�ɑ -S! SL}^)2)=B}-" 2)-("�(�h"� ��]�si^a6V!{!���!�2΃W~8$n=3$, $k=2$, uu6�M�1?set�0 $$\Phi_i=r_i.� \Psq_iR�!gei2a���R��m (mKPESCSi��wNn resp�� vely4 �33}),m�4a�nd �35}���c~ 3&n��y6N A?u_t+u \alpha^2D%�(u_I -6  8y)u_x-6u^2u_x+46�()L)i)_�h 36g A��J{i,y}= > 2uFBbD6 $\hi \-�{i] N]F*talled�c mKPI%�wE� r=i$� J1$.n�!IVM!�)ɗNdfor*1;z�3&�F07Q0 ˅�{1%�e�11<��75� =$t}=(A_1(u)1)+T_N^1EY,!� a�E�V=-:�E6i��6JG ���F8f� 38NR2!R-��$x}A���2�3 86S2-S21S2)S2>S�%!SF=BR�N=R�F��RFore@systemQ�7�" c[uc���� � 6F�$( Assume $u,I1,...EV_N,E"si_N$� a s &� e�q� }) e� $f_1��(g_1$ satisf�$�$ 5��. ,�� F h� B�:��Rd39j�9A�%�1[1]= -f_1c!�e-g_12�}  fV-C��9Ku�u+� _x o ln}}� g sf:�+C��`�+C 4v) +C}'� 222���*E�j� :�A���Z� �� �4} i �hi_j-g.  A{j>� )!-H24+C},\qquad j=imN�� � $CF )�ant F"B({\bf{G(}}: It�obviou� at $Aga�E�A�$, $ [1]$,$%p  $i�u�� �� �.�7�. ; only�(�+O,���, i.e.,Ew,*�( �ln�(3��?�_t�V[1]�A +T^1_N� [1]� 7-Tm } Us�p.��Z Rt${ll�(� %&=&[ :�%ni%f�]_t %\\]Ht}-1t�:^Knd�(�j+) (e t}s+aM�t})2#-4B�[S�xP >M]}��^2}%3':z UEM-( 'f� :$�Y�f��(j; '&9lOz�g z2M� �p2T+= g_1A2\ :�@ 1)_x2?��� +f_1I.�6�=�r�)�6@B�!o}�) B� � U>�-CE\� i� y��A easy��verif\&at�11�still �# now.� ��-3*� �{�P&9�R� \\ =$))�-; ��f�3A-$n�bI�I TF�]2g9�>�1ƗeCU� ��N� 욭�~N~(By substitu�. $ expressio;$%4e$%t $ in��Y*S% ɼ� ͫY� a�/Ek \"�/"�.M�A�)�%=&yj=1}^NCjA 0 j%�EX6N\ .5e� 6N��KU>���j1-4A�p }y� � si_j��T*@I�F��z�+f %��%Ag �E,j �96_���%}�I2�)�4N���%5%��r�R� �!�%UF)2N�6<��!� ,� @2���2�2�2%�E%Vb)Y7-cj. >�6c� ey%� jg_1 �b j�%��^�^9>%�9,2DrcM�%!%2:=F (m5�23 6���������2��RE)uU�A�2t)!M� :#��-�>=-CAQ&6?I�:<j��c�k�HZ�! � �6��ipv>� �=u.�9}:j2�O show�<���"�8J�e %`^o B�.B��EZ�)&j�V %()j�� ^�) (%�:� �!�R�N�-C}>� ��=&2� ���J% [�݈+)0� �T ��Q2�+f!-)�3 C20i�%�g_#.yrj��x2A*�!1nFm ��J�C}YKe�nN)( ��%�B)�9!:D�INs +Cl � g_1^2�� � ��GF ^��A�F" ��"inv�]2�I��  f�"o�V��% } 2���A�-I2QԎej�YE|b� �%� O%�B� ��N� �DN -C}]:�.ڠApBq �ga�� 2[ Ŏ�����%�~hz&� o�6F7IfCreplaced�2$C(t)$,6dBfunq*�2ti5t.Q�7t�  �L53cov�' nt w.r.t.EVbuT�iLt j5H any longer. In fac�E�� &:!JGiven $u�1 #h2 �'$�6� let� be"Y�'D+�?7 ?-bj46��$)� (2:D.� $t$)u* d by' V<nk23k2�>b>(t)�A�2���;ia�Bw�f{#fŏ��f_2�+7�Kl�"{3���OFO�SrS�BVF-�andj!12.2FN N+1}!<-�z0)�0\sqrt{\dot{C}9��kF�'�$ \ ��_ Sn^g�TF��6��*s�Wz�})2�" int"�/6[013n�53�5:�'M_y�  ';-2a�%�xF�b�L*��Be�/�&��Ey�' .f�$[1]_x,�8\�"�+1�}�!&�(� n� |��aSe?t=�2�+TIhA'R�.E�A+=J6�So*2!�XN?!1= =3�!�N �C%ɴ(degree $N+1�J���}6�!\ �;U�EZ),Q��7d1L0^! "ly.cJ.�!n!�t 13.4}). S.}2�! a� leftN�1 E���+resultT&pre�"e�KV! ��=�=�R�.2 >���)fIrG�&� !�R�  n5�B~FN#)� $$-4E��_�& !A�[16�����V�$$�#�.12f)�f��> �<� b�2� v�>��5�5&%J��4} N# �#j�)�r�f#�"vB f&�2Q{� �������4�=&�:j�GeV� m�Kuv6 %�*=�` 5bfzh�j6��2[ ��� �v��:&�O2G2 �rU�6��� (9rg��� e5o�_r�R�>�,.% \nonumberI� �T^� 8Remark *�W a"B*s) $ �d}{dt}+\neq 0$,�DTu/�U�)!JXa non-auto-B\"{a}cklund:�- betwe�-wo.s�/�9" 1 1"84.:<n-�,s Repeated G*�D/ T2�;$2���<G/ *�. $D,$f_n$�*9*�T� s =�X �# BgB.�T@"�L38�2$C_1(t)�C_n%�a9U�-U�s�$t$[ ��&(Wronskians:bV4&�GI��*W_1(ff_n;g g_n;B�0)&=&det(X_{n\%� n�V \W_2�F�7X}FN3ZN{n-1}6�(t�YFN4N/f�N �Y:�i�)H y��-1�6� ��4j�H4�H�  X2/$j}=-\delta C_i(t)�" g_@i>�$ ��^i41�0 �!�ioZnj,x}f_i2� i,/n�� 3} Y �b� g_ifJ�,\"�n-W5�;A �f_j,\��� tz[A�YN�^�g~�Y6T1�lemma}��e���_��N�.�.��.NPf ���yn��$2�V mnB1 kn-m��2 6�q j H4��in ?&��m[m-1]�f_{m+k};g.g.C_m�|2a�\9=&�D ] {m-1P2>a2a:e 2];C Ji}{-i��i_xH2jB ) >w1']�_ 4I <%E&���AbA�:#�)��An@.>:%v@b% J6?���?)�1A:�-1A*F�a�C i^� m��^�jH&wA6H�BH �1ai!�IB�Hy�`RG d֌5G:���A�\� >�͌)>�\F��� %:'6:<"�W6u%�3;3>�U9�W �{l} % �+i�1]=22]�4��I� .) B2B~2K>DX � ��.�!�E ?� �+j�.2]- 2.�f %]n % DJ�>=�.5B < aF;z�F> %So,�J4!5I1!�&.�i#:�_xh .�!��!� Z+  >.� 6F)6;_n*�&� Y^q _�� 6�{(-r�n�%[)�-�=� By a ted:6!u�G%F)�B *(�Y %�4n 5uJ !�2�A)�I�16�!l�)k9�.6266ML�#259 n:8�#Bj6�2��j=} ��K.Fg� V�1�g 45 we"n�6V�� {m}$ 5 !�fQ�% "� )� � i,j� kk% �x^�MQ]ȱ�7Z� & AN =&:�c+i�.V Ioz� U %\"�u�v��!`-V�.X&.�M�!�zCZ� u @��b;�� .�n��-b 0}a_{0,j}����^&A%$$7j}=Btz,\ %\ b&� >�:�nt .$$�jn�!YVt�[=$$ %\[mvmatri!j-C# !B1,1)B11B1} &a�2:$2}& \cdots !k+><%�a�E 2.Z%,+� 2f%:f2T%�#f\v�&dAEa_{�7 � M% � � ��-�g+���'~� 4�F1f\]��[=B}A�:�-P2}&B`.NN= 2!�)+11- b7�zZ�J�\[%0!OR�EF0��0��B�0.�U�Z�)6�7.��2}V�V�01�-�Aam!vA���)�nZ�V�Ik-� �� 1ɣV�U1�1,k1�U\ � �2� �%2,k5 %!Q�J�m� ^A�1< �V X 0V�=bb������QM�A��0:m0-; ��E��?�^61:616� � Z�Y�R�)oB�:=��$� %����>m f�S@$�Wula�4Mr� c �q�g�$�"�$a)�R%i42�$� be� d similar�$\\f5":@Wr same way+Twe di�` \a0XiaoTing2004}�n$.�$"�%I_ �G�Kse-i��K"z-}-Qa�X&,� = �nd xF�*k�)V38}) 6�KƇ $t$-� YV�/�gF�&�)�GA/��is �b=6�$ j�N4�N?& 1[n]�  {WB�!B, #" V�}mt:�2���A u�.)L"� (L�"WD � .�!�;F���z�*A�i��Rf#�4�fvfg*aw6�)VA2�a�R+Z^�Z:N2�F�$} %H{N�nF� �&w-.�-_j:'J�=-1}+1}�Lf_n,f_j5g_{))B#$�C_{' �P� :���, 28\� &%��8.&-VM�!%%�19�I��9Yn9�5 ,g_j6�9Ya�9\\` N, \�N��7n.vZ!i6mNamely,1u61y9"F��Q!o\& Wl[nE.� E.n'/�� lQ2dhi D&/Q.e!� lO+�� 9� �Q'�q&"/n].x � 9��<"�,n"On]:K {N+n�X[nO.$^=�F�/n]$,\ 6PjLiB X!N+n"CP �%��B&(N+n)B/�&"�PB��5�4@.� ΍/P ��%�1D&& T n}[n�!-hn;:� g  b/@ Bi�nA f@2]tx" b��Xm� �~f�$a�""OT7%>�&�%�3�b����;g.n�B�=�V�-�&�f_2ň�� -&� �3 &3 vSS� ; &�M�8.36�8� + )I�J�&1&>�I &=&uE�*yVUP )�O ^�{%f�^$#J�~2z~�U�.:�+CI4�F9j�`a9� � V )C�,)��e��3�w9^�`J�H���� � � ��i >, $$f_j[j]�' [j-1�3-1V3g#-1]:Mtz&-Cq � S�D�a�al@� j]W� E1J� :oa# ��� �osoBr fvq} � z]�tNv��&�')�{�& �&� "'ᧉ�N )����r\� ( P;j]V ��.���:'��jO��iNuuq�:8 _�QR��J>}{2I��"n�E]Ҙ������-1. N!��� * "� �A"�� 'f9 ��*i��������r�~6 �`% v+{Z :33��,"� c1e not"?3�\:@38VB34�Ba#�A3�A3n>A3"QoS2|of&�-c�� �#3Nn1. ^( R�al"�. }-eEx�| 1�4(�4�M$ularities �e �If(cf�|If5 stD`=�=n&�hF h�$*�h Rr�5&E Bb 5"v12Zh";hRh�Kh^Kh51.@�]�EhEh51"�  V- �e xq�=$F7We��d=_6|`41=ae^{kx-k^2y}0�$1=be^{-kx+ , $k,a,b\in \�Wbb{R}$�Aini�DYK"<551}n? $NA�5leĀDf_1=(2x+8ky-96k^2t�AD8abt}{9k})e^{2kx+4�-32k^3$}{3}t�B g_1= ,-.,+J�$Y7=0C tFHby:Z72�rmB�(7 2.�I� I�� �+l�2q5&t =�.5R1 fF&dF"% &-� ^9;"� �:@e } =�t(8k}{(2kA+1)-1JGq�N�. �B=32J� A�)1}{6k}}.2k}��5�/'a p b1A.� AMdyVyFG�$ $A=r�(� More]ly,rwi�1BR�5j>s53�-4f_i=(x+2k_iy-1^2t-T4e?(k_i+k�*aF0k_ix+k_i^2y-43 � -,Jw�F�~- g_iaz`-X`�k_i� k_i-Nc^?5?C 97=0e�k_i��\pm k,&�5, +k_j ,fo�r�(F�F��i��&�Z�ww`�� V/ m�-~5�Z�* �2� Lump��.�j�ti$�oF�iGM��Q1�V�& 2F"�s��-B�i����4��i���8 �7��9FZ�54�i�j W��^�-ikx-i��>� ikx+�4r� x-2ly+12l��,4abkti}{(k+l�S-ilx+ile�il��(4ablt}{k+l}�{�0-.0�" 0l�$$ $l:d , $la�i��>� rN��a�4�DT�>-?2�1-lrJ 95��&F�u��v��(4li}{1+(2lA!�B�q�N�B��kxi i�> -2AlE,+i(k-l)}{2lA BtbQ�| 6�� -kxi� tb^2-l^2)+l^2i}{-l��|I�F~F���2�4ab!iktY���6fp5u f_j=en_jep_j��l_j�8 (l_j���-il_jaw,y-4}{65��6Mg_j�� im�_iq�.ie�>�b��l ���l�i�*�, l_m+ 2�m,������v7忉,.\\ 2�Soliton��.}:�3��>&���S T2� bp .���� d�0$: � e�8 3t}\xi_1}�N��lxa�y-4��'2��\ _ � \beta���ek$k,J�k+l���$9)Ean &�RC($"�&r� 1-s:�r"=� a��� j�v5�o���S� !�}H2� -!v}= � �r{�Gl� e^{\eta}-� ) !k6!+!},\ \ -J E+2 �-1�,���Of�i��t)>�R�MF.AH);->fN--y2�L� F2��!A�+ b{= ! xi_2%;Y�Jb^1 71 0 � h �Iv ���S�r�U N @��2F�]$�A �9�JR��?�8} ���B��\CD"l_ix-l�" !ՁygE},]%F$$�� $k_i,l�y.�N#K�t :K$ {�}B+���"J[#ll&+n����n$>4�7� �6: � r5� � -4i�>/$i\bar{k}x- ^2y+4 =�(t)=i2;$$5�. CondB+*�I�+�,\\ Set. $k=\mu-i\nu!�A =% mu,\nu\in*�m\ \ $$neq 0,$\\�n�n\theta+�*��/�f} &-.'��>X=-i\mu x+i(\mu^2-\nu^2)!W3-3\mu t� eta=) x+2  y+4\nu()3 ^2)t�T��f,+&>U�1$��Jv��5jz(597�FV���+�t2\nu i}$� 1}{4�*2f}+(�fTP \mu}- }e^fR A7f=!���&)�^ ���U�� (1-i Iz+!>A^3t+1AT^%#t}}{(a2 -\mu;8Aa 3t+4Qw}+)���J2 @ x�7&�)F�2�7>7>"i-1�u�nFd�N#+b#-�#F��j10�k� k>k> �� � ��_j��1�� �� � ���}jZL��j��_j+Ad_j�\muNK nu_j^U.����a k}_m� �j,m� K �R+n,&PeJY sZ (K���*��)�.� �� z��b�W��3&0� 4 breaҧ typeB:5 0�K202� q��C: �: .����%~ -i\lambdaE` ;Al�Z�)9i| EixiUe ,)� $1Fa1�2n�\(r�1{2n})=(k k_n;l l_n)PT(� ;xi7Eul}�l}_n; k2k}O� k_j,N i&i C�Im(k_j)^l $l_m`iM� m,j$� >>�"N�v bR~^� 2�AH3�eC �choos�S�6$1o1=kT�b��M 2=ld  !b13 # }_2=22:1=T O5 =C_2"G t{�a�W��ET1#!"�A��V�*�+F� 1� u[2] %v�:*1�,�$g_2j2 �*�3f_b$ �8(b+d)^2�$rm{cos}�� e^fi}{4 !] Lt}+4(b^2-d^2)e^f+(b-= f-2t�\� �1�"(�4� 11B �2]s��*�C}MU��72,f�-!!Ж%Z.{=D{2� � _1+) _2i+"�z,d-b}{2(d+b)}!! t}1Nsin-N-��9h}N4t}_f+#= kb-d}{b+d�Y-}9��!�e^6Il i|)}��3} U%�2��!�2�U�M���%�21�1>�%B9�!rRp������V�45� hi_1-�I[~Y7�L 2,g_!�!�%��6jiyYq�+i.Z2' J�+daZ�baZb�+�Z�Z�2��Z���5)�� qXb�!�uW!��2���)�11�B-�d-z������F3 l � =-�x�3+d^3&R�(d^2-b eta�bx+4b^3.�E�dx+4d� $ E/^2BZ-^2y�$+�periodic~ y� z��8 behavior along� coord� e $xr"�+��4�.�R �I�g*�+nL*"�"1}}�a* 2}},v� $a=b=� (ys &��b{�6# dege�(��B"�*� Acor�@�ng� "�"�@*�^ In�83#3�2�4N�5'/� D (�) #)nu�b!pns�(s)^�_P�_� )j  = �pB.@fF!�Z CLKonopelchenko92}. %,*{Concluǂ}>i� %In t�`paperIR!�[i~-V�ƣ %��6�s�P��� %�Z`��B J�re��en X� A9mKP %hi&}�P�Z��E�beY�"��. %��(�`r�`) I�Υ�`"�l4* %V�uC�.�5� :^�(.)zC5�Qs%z��%sa.iW�es��}�IP K�8�<*{AcknowledgmentFTA8work was suppor !zDChinese Basic Rese�l Project "Nonlinear Science"~:��jHthebibliography}{s9B\ibitem{Mel'nikov88} V.K., Integ�' methodQK� weg-de Vr�.��%z^sR*�, Phys. Lett. A 133(1988) 493-496�F� 9(1)B�Capture�Jcon��!n����n1-�n�@��s modif�z5�^ ,9) 3733-3742.�>x B.G.2!�IS\pral&&p��M � 2�r��Em|,, Stud. ApplQ�8�� 92) 219-26 Ab��tz� M.J.A�A� rksoW:,s,YS E��"� JS8, Cambridge, 196�Dickey� L.A. � E �$a�E�iέ� s, World CD $c,SingaporJlMatveeb V.B. , M.A.S?�,u� Tran&�� �5 Sp�  Berl" � "�Date83�  dJimbo @Kashiwara, T.MiwaA=Z�am�-Clas� l��ory%Quantum ![83; Mi \ (eds.))(k)( 2)8� Ohta�a� A�Satsum��.Takah�� % dou8px� manu. pt �Bhtlength{\oddsidemargin}{0cmwB ev��j!top=-1>>�$height}{22N width}{16Drenewcommand{\base6stretc&b �/J�,my macros> \2Keq} )4gin{eqnarray}}6$e$B^"beqnnBH*JI'.K%�Z!�y}a� �ler{L2,corollary}{C "57&�f}{.@aG*{D�ition>�p��6- {\it�0of.\/}>1rA1kJ2BN38$J4�N5qed�+Lbox{\phantom{-}}\big$�} %6�r/��} :OIm?3op"G3Im}�PlimitsB2R��B2Re62.fTrFbTrB> diagF)>itp}6� :{}^�t}}#1B�C��� bf{C>HPP q bf{P>RRR>ZZZ}�qei/}j���%:4 titl��ge %% :" % \"{$q$-9 ogu$&� .Z�\\(���q� �ical %�H} \author{Kanehisa ��`saki\\ {\normalsize Gradu�S�&lM Huma�Environ��als 8ies, Kyoto Uni�[ity/!2VYoshid�akyo, 1 606-8501,anB6E-mail:��@!� .h.ko-u.ac.jp!�,date{} \make%85�abct} A >L��tau&)1o� Vd is kca cP%���pendent"�� s. (2b ���@� v� � �dX�ce" M�se+! sx{zl�|J languA` of 2�s�f�turn out3 �y�� 7�p ar !9Z�Th� )^( | usedjla�h�alism� �p��� R�%bЅs�be2�to a�.Fc Toda&@ LJ���8_,F9 m�� hav� applic0-�random�t�q calculu�gaugeXorE�~opologe�stp E�CYб�U�flush �} e�cs Subw C2 if �h: 35Q58, 37K10, 58F07\\ Key�ds:&2� ,2,Vj\\ Runn�head:24!�ӳ"� %�R� ��n�arXiv:U(.SI/0412067FBnewpage 2��ma_cextN� *�.� } a��M.0s (� ��iEeE�/s)!Xy��"b�� ��from a�Yet�poi Z . KajX%Q� ! bib:KS91}&�Z$1 + 1$2�e&� i�ؕ��0. Partly mot�ũ:!# , M�4onorozov�Vin�6�d,bib:MMV94} i;ed^�2P���UV. � ot �(hand, Wu, Z��Zheng="WZZ fp V2K2ea�$wW!=e+"Y . F�e��� ,96} address�M issue)�c%��!�0 $W$-algebras�� ider�2y0F(*�!)>�nd��)# re�=.��� Khes�LyubasJ# pRoger=EKLR97}:po� a sl� ly �@t f� A�a2pseud�feO� P�s�FAhu�%J�"��|/q$-ifrg�U�s. Ma�eco�MS!���%�eE�Y ��.�a _ ��!s..�(. Adler, H]�0 van Moerbeke�AHvM98})�ed��g!� �l�Rclosely 1���!�'ry�!�2i� Hav��&�&�h�^con�!bb�c�it`%A�,HI97}, Iliev1stpf�6� �@98}��Tu=Tu99} ����A al s��8�A's.  I�is�%$q9J�%>.� (�� "short)6[Our���is .�omE�preceV �A �b�!�i�$��R�!�A�Qt:u��o�Planck��'4 $\hbar$ tendeM$0$A� ctua�Mour tru�'cern l!Q���� �faf���o 2�!�02kyFR�%�he6, origi+!xi�d�"0 kՃћ��nnܻngAa.&s kA�KM81, DJ }, �' thou����� ��e��J�Y�UT8lk Becaus��� , on;�CALե ���,to�!e echn� �Nr!�mO aMQ�?� 6p!SA�Rp��6:  s��� &�# less>.� TT93e�Acc\g�OR��>��  re%!}y��!h�lsu$J��%��(� exXA8�`��a�R.�ATo�\�%��e�>�a�y��� . ��shall %��� such>+q�m��Af�%6��6�� A feh*maw"t6I�BGer59�!� varir�F1s��thars �y pr��1)6o}LMPZ97eMKu!�hmidt00<9E�mnd��6P% appear " �?�{Yu�+a!�e ``one-%? lattice''A�Lit�inS !U Thir�Takeb.� 02}&| a&Mmw#2��d t�d6�| . H���+�da� a�7!�Uc dueA�)K� -\�*paper��organic�as�7�sS� on 2$a briefata %*24qwU�2�AgInU3,{.Qg*� !" shown toRl��F�H>t4�Ϟei.� �yof~�Fse(� J�e�i5Gs 5%(6%$A6� �{&a'�&1�7!� devo�P�� case�SQ!|"]M�eWշ!�.T:@.= 5} A�:a($\tau(s,t)$k2d dTV udiscretes[ZZ$+d)��1 $s62a ���� tinu�� &$s $t = (t_� 2,\l�y?A�*�!U�&e�q \����=�{fty} �',t' - [�;��]) b8 # ,t +>!/ s'-s9\xi(t'-t�=)5J d * = 0 �'$s' \ge 1 "��<,� t')&R��� �� �F t M � g�  t stoo�<�bF��� � \not� �!� ��(a B\"aV� �*4 sense)AZ two#�.Z�A���KP2�` # �>u' ted,%R�,nce, b�m aL � �tex"r��F� I�ch�E��?B�.�A�+$�4, +N,tE5��eza p�)��e%er $NCC� redu��!��[cyclic"�"���!�s b1$N$-th2�2����e�plest�� of $N = 2��d�� �-!�69 �0���#))1!) notha�9���.-. �is� lain� � �;word ``B&�  n�x%�e�� &�y��er6E�B�"0�1eda�s,dau alNmby shifT4�Uf�� t' \�`._1�  -)~�#_n ,�o�9�eŤ����be!s assu�to� � far  (i.���do�P�%�f����!�E�l1ou] �exponal"T $�H�]2�$%P reby�Ms ris� 8an extra factor�Ynn��prod_�n \exp\�(�?- ��k��O<�� k}{k _j^k}\r��}= :[W1Tfƚ��}L_j>9���!"JQ take�$ ``second-]�a� ��VB�_', t'-FQ?TA;n}]IJ�"n t+0"*m= +mZ �imes -^j� �( *!H)B_1)-hJn)d &�.C4Ceq:mod-%V�Aeq��uj$'$suitably c��n,� we�s+m�J�&� �A�o � N� . 2� '. � 2"} QHnowW�&�q �xaEa=Kgo��>S����P"�# , $[� ]_q d$J;��^�5$-b� �m��u'\A�= �"0G ,0[  ��0,�; (1-q}FSw^V^2)},J 0N9k 9��9kyV*��� nn��hun-X�ele��s $;)M/L$ D6S� $knJcom��%C$k = 1,H &\�s`<ia�~�&!ELblas&Aby �F�M�? R���6s, excepy�at �I keep5old|$� \�,\-�$ *�ha�on a~\i�.E|2 $x_n�s )2?a�to !�,�F./$"� he un�lejmg x]_q"�  = ^{E:͕*� .�� ]9by�1�*� "PndF*U V98} �(r ��N�.� � u�q^�Ae����*��Z��"- �[qi4T!>- [e �718wh��5 ��s a� �!C +$"� �: �2F La��D ��=}M�,� .���m�40>-in?A�$ke�en&-*e%~.�is!ooc� !� =>2A+%�i!�K��jLi!�iO��� li6OAHR�%wa �bat .� hear"TI�f�2j�. A�� z�a�Q)�$���% comb�D��)�՝K'"D  [AJ�)�Eb�writt��� ��}E�--R�e� �2�: []_qE ɕ^3enɉj�oA��E��O!���� q_n����"�� �] ift $t0t�X� � ��s.� 1}�/i'[2� ). @RF� P(�mFa��Y�j =rV-Y � q_��-Ax �/n}� nn a� reaBf�(�eq=v� ���polynom� � Z�  �"-� si�>9J) rD A]�[~^n - 2��}.�ThA}i"�!B �&� )u conve�CMF@%��� AaR$��I� )eI&cB9 (,x_3! &� �L:� X-D�� 1!e-AXx*!)6�� � :K . Moreov#iteZng9sy�) $k$ Fs5hig�B�Z�s5 [q_n^k x_Ln]_{q_n}^{(n)} = [x_:H - \sum_{j=1}^n 0\ell=0}^{k-1} '� [e^{2\pi ij/n} (1-q_n)^{1/n}x_n q ?�R/n}], \eeq from which a similar bilinear equation can be derived. Actually, one  considerG4ultaneous $q$-iplic M4 of $x_n$'s as  \to �k_��$ (but $k_n = 0$ except for a finite number PN), �leads toF�s~�the more general form \beq \oint_{\lambda=\infty} !�@\tau_q(s', t' - [ % ^{-1!Ux')# ,t +> x))�6@s'-s}e^{\xi(t'-t, )-� \non�\\E4\mbox{} \times Mprod_{nA% � !�_nI._n]0 (1 - A(%x ,A. �^n �d !�,s8\label{eq:qtau-E.}IO�where $x' = (x'_1,x'_2,\ldots)$ and $x .� are related by nonnegative powerAL,_1^{k_1},q_2 2} \$%� $q_1as5�� = C� \;2 Q� �A�e)( \section{A�\analogue of mKP Wave fun" s} SinceEi!�4 variables $t$5E�0KP hierarchy !, retained in#deE�a�A�M]x,t,x)$y| ((e an associ%Fw.� $\PsiA�=Ui$ !�itsa�jugate +^*J-as6V}P.�:5wRuAF$&=& \frac{ �a2BRx)} <M�^s q@�}e_q(�,:G �^*r,'YR�J�~� {-s}�-e�^��6.��NotA0at%�Dexponential part $�{\pm �5pm _ x)}$ is �iiBAc,extra factor5�6 =�0.Ceѣx_�}�7m�4e_q^z$ denotesq so called��.�q � nn �^z� exp\left(��k.�E$�� )^kz^k}{k (^k)}\right)��k��� �� -q)z5.tnn This6%origina�m�shiftet$��!Xsum $B�$7e�i>�e~a�ewbehave� actly likA$e ordinary2 1�un�g�a�p���differe�yoperator��( A prototyp��t�12�I$ is ZB�� %�{xM� }$ tA�0plays a cent�R role1 L.1`..H \cite{bib:AHvM98, Iliev Tu99}��$It satisfiMq]�e���D� )A��A*l��E���e�:\1U $ U �acts on�1%�$�/�E� 5f(xesE�f(qx) - }{qx - x� ia"�j� workA�< Mironov et al. YOMMV94},U�J� A��/$�a� (x_nAgJYg^nAiIhor,A� ivalently!d� TnU��_n).�:-W It� ing% lastu)�yield% E�.yb n:M�&�h5 �m� -1}.�zW I]6� ���e pre��E�e �� h�j 8 coincides with���polynom�= Bin (\ref:� )�S� mean��atV)�ac� ��� e.$ �52v s* RW �S t',x'",!i F�.� .+&� Psi2�  We � $now follow� tandard�ceduraq� �syste�� a?Jis� ^^ a�L51 ��5��!�K A� *%eubU=E4bI ����If!� !�mbd�^!em�Nsxb� nver�C he>����:�!naWQg�(Wm%&� ��v elimC ed t* non���A�Qw�9W� " is achiev^�y�l >�by $W$�>��A b�� �)�i�Wz !�ŭ�� 0U�separa� !jJp sao�^^of! p/ y� �E�!� (A)_{0}) <"� �oj;%aV Ise�6I�gu n a_n=�r�!6C� n �61, \quad*<lvW<0>T6RMp�$(%��$�!@!�r goA1:�U� gi-rel�qaq�.� FI�9:� Cn-W�~E�en�on>6"�b�itself:=i� yh :@qm�.NW!�=#E�� <0}W:��s sato.�a�>��͗&� ��� zs �oconclude"3���^� I�� e1E1�Y�\rd_{t_nZB= B_n^ �1'"S2�"_well, $B�be�� V�1q.#~=a�� u�!bf!; "�I�t�M[=!�6F�!5). -��k ��l�N��$�@Uj��a�1�B� m}!(+ [B_m,B_n]� Y� ]6�BQA�[B_n,L]h�V:Ulong uwB"��"f��&L^n��6�B� conn�ngM"�� �$L ~=�$comprise a�A1 alisO!2�AW� we "Md abovea�f�!�reo�y�"�&(Quasi-class�  t�8Hamilton-Jacobi�}", �H� iss�&qNR�Th end,�se�$� met�'n$R depend�!Planck�@��$ hbar&7! �( = q^P beta(},"� qi�-. ��� $n*��5tan� rescal� in �&va"�'s,t_n,�*�� �VLa�nn too,Ee�'stood�� ���Mh�{iToU reaso� A�F� , however����atZ4�La smo!�%EE2 im_{ �to 0})v =�^0}�\>-) =-^0�kas �e�0!�AlE-a� Toda*�,*( TT93�%is�oseJ ra�� str"� $ solur ini on; �s� su�� d O�&� ?� read� se� "� J) �zB?)� X  �"�$�! )�>;, u�1�b^0L !x ~ U*t��s&".�2 ]!WKB��l>~= �+�E6�S�� +=aB^0)'� a�&l1 loos�Pde�>f \sima� I�b�nn*\/� J�'B�'bea &2|,*�'�*�,n*z� �.,mathrm{Li}_2�'��^n)}{nh��GO-.0) �,�� 6Mz":0dilogarithmic!=B2�z��FC-<-^2�!����h�!f�*$9r = SBr ,� .=%�s�9� 2Hs\log-'�]�2")^N�"%+6�x*�.5p�  + ("3N� $�!Rx u�A���:��g)0Coffb a��&�, For warm-up";first����^���Ac�(�*0is has been d�m� studmR� �A:�&?+��<. Upon substituy �7ansatz,B�of^� �be� �>� ��Rk e�\�$#Yf;!�>7��F� .SaJ cal{B}_n(N�`}jbEN� �#i�Kp)v .�*� 216�pap$e�2O ^0 pi#m� T^!�obB4�?^� u��%k� � :\� hj�usvc��06Vy:. m# task�`�g$i�(he asymptot�{e'��&�, ?$��nn ��eqn{ 2b xsj �~s��}6n7 4=9-14l(���=4.�MU-�:7T_�^C�B�� nn $V5$iJand� (o a Taylor �*e�"} W�~6T6�#a!� 7,>�x_n�]) 5D �8D& $\- �-!kE�!� vF2+�P2=X!gt� 1��� �R6� 9%�- ���-�E�6N�9�O o� ha3s*8"� ) � *, ��b- �%�F$������h��_=��-f#4 willa-suggesI:to re�9 �5q1q �J���31� }ɑlogE1��:�.�� �<q � +�j< :��3cn;seb"=� xʼn� ͛``disper�,less'' t?62o1��&D 5L}����oŘy solvi�25�E�!6y = p�b�&m}2~ .'{A{?N] u_n�G1-nq��6�'}����i�10B5�$L��&&*!�::_ Q,) correspond%�x!k14��-5��6|! ��\H *�,6+\+ 2p>A����6,W-� y\{fp)Nv? O�ecO(� Pois�#bracketI#��\{f,g\ p�p �6s g�AH 'g�&nnulfur��6#$Orl�'chulmanY�U�q�MA�!&5rd_Q���|*S@& \bar{t}�/�6>.�UT84}$:y�8n���� _/.C*g f� _1{*8A,�(.(B#4�&. Z/- �',t'-:�B �'M ),t+V'�� mbdaz3@�2�Bdq)&~ &: :�0xau,7��] ��&�2%lJ�W � � )�:�s'�g0r � arib!5(ItBno�er�(constraint):,a Aour[kintegralEF>o&;B*xj3b|8circle surroundn�?a'infty �&:2nE��ive� F58?Mi;$, Morozov� Vinet*v;we% �Y twoA���in>�RD,�awxyxux. *& par&�aK6!D:3 ijqYqYq.Ymj!��!�2H�%F{qI{q}2�t}� �E�=Q�\, 0F�n*zB`@+x ItfJ7x}XH q}_rH^8�'�6��%"I>NO"�modm:)�TGiz� c�y� &� os�G�>J��0�de!�JJ)��%%~=2��51�',�;)�R�;:�9..!�y)J#"\B"�M�}.k::j�^B��� !�!o2wѐ�<= .�y+5 A�R� A�>=� ��]FV)1"RDN5z�3��;,& %�!�.��Irv���f�E���L:B�a�:�]5R��n�+1?5�]Y/)�� �1��1��UGe_�_} )xU� )��E-=U�J. �%� $x'MAx} \ <$V�&Sn�%B/Ln�BM ��\k��qf�L�.�� 'LB?L\;A��L "YL2AL\; 4*q. �'H i^�1}�Z '�L �2222r1R� :w[�42 a� � J#00|J%6S*"|�.�%��previ� P8aebe2� anI}<�)p��\\@�?%bI�d�n|��[��A��:s wz0L!\M-a"�!5�Y!�mU~� V6_=d=�"?h�NaCNPC�)0phi�R6)��n�. 8� v� ,��qR�'.� &�B�0E?�<a pai�R #E�ٹѯt�/!X!���0R�61t;6r;"F thr�;sQA�" �-�q $�-��"^m�6�4A�r!�������%2�D���EM ޔAC}�'�� *�a/-M2o�\5KL��C�t %H��:JH��t!JڋA^�@\�Vm"�/6v;�:��9N�>�H΃&Ss(0. .e�W=�!�t1�ce*�+'��zly�|O�!$ UAgvreVS-FtI �Qm�K�C)~b}B&�(m*E4"){bBcNB�" Vw.f5c&:9setC"t h!�p  �- $, $�n*M%$)��,�!s.�- &=M'2�-TB�-�)mA����-7xN�-;�P;&�-�Als$ ;*'HA�(1!�,C )�!�a�KF&H* MAw�Ii�Y�� theyV�)!��0�-(1O(�#���wq���V��Q�S�(��"$v�n� �� 4&T�.��"S!MR�#B� �5�VUA�Z�#Y�}B[x_RC���F; ">yZ�$By�A�� �R����5�o1�%�p%a��&*�OA��� ��"2)T�um�a! b2f%in $pgZF1BI��s%i]B>6m-W �=%(�_^0Cl:b-."�'���-Vi �9 �1I��#�O^�&~"�V%ywa-Ap� !w�T�8c~��:� nJ&7)���g����$\{u=,\�>� 6Q�9-M�-F`6se�a�*{M�&}P:IA6dfYJfp�_.hZ\n�ƪ6_ ��`���VRNiLAQ6��LE7e� A B&.&7 repe.G jFYI >aN,�Ps:��7<S}-*�&>R/�Rvk��?ven',7H|�se�0� ]A� �M�H!e!mZ��, U_Ej four6 2�yD��, �$f�,2�T!��5, a ``twistorory''*�TT91}� � exte8)�D%� *�IC�< %#9hW_�,.O ��2�9� akU.�[�?9 �6� . D3ex#ed�5��-�A%�describ�BV�-of8�rscQo �in9he ��.�0h�\ VDbj'p)���'EHx�e,QQB/e$�B$is reminis�\!)a2�strucWKa � be sn/$in Takebe'Esul. 02%- A�4f-Boark"�/�9�"�ssibl?�Z!%'/�:�Z%,randomh;t�K cKu� gaugEorc?a�topolog<st} s=� NO03x] NRV0)�S� link>��S5e�I0most trivial)68#"� �!&g L�!^2�S left(-J�12n}nt_n%�� ]3� ��6�%S$ E�/N <�JXq� �q !���pecbZW $q^�!g �T%<�>��fx_1� ��x_1� � a#ed off�1e4,eN�:.�$bU�G,yF� x@$b�=9P%�F|.F4� z(-C^2�a)^2x_1�[^k&�a^2}-�� �L , upR2 itab�7 djus!Z&�!$)FZ��c6�[a$evant physE�+<�N(�:iE�Veg^ )a�qbJA � ub�e,*{Acknowledg>Q7?I would�a�Dank Toshio NakatsuETakashiebeLdiscus�^#l JX�!is e�A by�guc�3j�R! e>f�k8':P��Qwas�8oW uppo�K�Q8he Grant-in-Aid �S�Xific Re q4(No. 16340040)"�B M�Gtry��Edu`, Cul�B, Sns�T�[��yGG %: %% re�bs %6"�[Lthebibliography}{99}ibitemYb@KS91} K. Kajiwara�J.MC suma0@ec&Ecv�,�!two-dime�Y al �`lattice � t, J. Phys. Soc. Japan {\bf 60�k<991), 3986--3989�\.�?% A.&o% *q%L.t%,_SjG-'jI�um�($-Q�<, %%Theor. Math��10 �$5), 890-89�T.. Fiz.:,,4), 119--131B�dWZZ94} Z.Y. Wu, D.H. Zhang%uQ.RenUbQ Vumorm�Jof KdV i��a�ir ex�W�;s:6solitons.� A: m�gen �27)��$5307--5312B�8Frenkel96} E.  , D����&A .�$`nd���i �U%�Int1�Res. N�4es)h2 �$6), 55--76B��KLR97} B. Khesin, V. Lyubashenko%kC. Rog4>E� �hi}~'raP:�4Lie algebra ofepseud%e�t��symbo�(�e()pFG:. Anal-i143 �7 �97B�MS96}a6M7J(nd M. Seco,��.�%�f�;A$'$W�Y)}_� rm{KP} � �B 3M!y 6510--652a6��f} M. Adl!_ E. H}�P.W Moerbek!�M�"]E�pA6�<�9 Lett-AA24M 8as3as51.:�HIE L. Hai ld�Cg-Gb�1Kpropert:� YEХ�!��.r*�I8�q��d��Jn3�aA 7217--722F�98} P.�.��6}.�C-�.),�Pu`)U��44I�%M87--20Ac6�Tnh M��Tu,�Ne�ed2h:�N ad9WjLymmetr �in�mesi�LB\"acklu:` rans��)�B�49 �,9), 95--103.�.1KM8�M��sh��T�BwA�T2o group�RB� I:ix�)$". !i%hPadomtsev-Petviashvili2�r�� Acada�r. A, �Sci.,)�5ip8�42--347u 2�DJ⡃Date,�!Jimbo K���I�OW^ approachAr��!�u>�5I� �80��812�%2� JM83} %M. ܅�9�%S��QX .�L���X%Publ. RIMS, Kyoto Univ1{1IY83AY43AZ01�2��08 Uen �K.� asaki�[�Cl .K. Okamw (ed. {\it GA|e�GnnF ��of"��q�s\/,3,Adv. Stud. P�Zi3�vol. 4, Kinokuniya, Tokyo, 1984, pp. 1--95. 6��>�� aki%cT�eb��QN�J���8 $W$--�y�,m�f�28i�!�165-1��J�� b�SDiff(2) �14 --- �,6��2��j���a�205--214F�PZ97} F�grie�Pedron)Q(J.P. ZubellA9 ;geo!"ŌDarboux :!ie�./s�_�r�Mon *U rete2� , Commun�> 8-�7� �325F Ku94hmidt00} B.A. , I�KP or� n� ;]�athe�hc� Lagrangia� �?!��1m\/.} A� D al Surveyi@Mon si$78, Ameri�67,ociety, Prov�<, RI, 20JDickeyR L� 2�/KP�=ufJ4-h��27�J "8 .�A�Je�!�f!A(*i5 ) d�"�:�9f�5� 2002q 57--172.:#.,} N. Nekraso 3A��ounkov ,Seiberg-Witt�or�$B�]2HrXiv:hep-th/0306238F��OiN.B hetikhiGC. Vaf��` Calabi-Ya�&PcrystalN� 9208e��i>d �i docu�} wD\`$[a4paper]{|cle} \u�Zckage{�icx6ams� `b�kS� er} � \Large���zUni_  Mo�0to Stick-Slip� \Two Blocks }\\[5mm] {\lm4Jacek SzkutnikE�Krzyszt�,u{\l}akowski=3 =em De�!1m Appl�qComputer UM, Facul� � �0�f1AGH�� 8�cxd*k\\ � �Mickiewicza 30, PL-30059 Krak\'ow, Poland }:94bigskip \today)�1�-�ab�6ct}x_�yzee�=k8)�rmxdKNt fri�a� el. 3 y�nos86>"� wo b%� driven�sp� with6�Q �c%.$dry, rough7 face. Our��� i�&l�e creedk�4ATQ��E#his smal�wt@g�{-z;�#, observed: sE�sA�!�$steady sli�7-ta�4)ڡ6%-F8 mE�&7 . Nu� ld%�t0r�s(*a�}iI betw�!jr �: _-�pas�M dire�vezumzto.� � ��ntMpera��aa1%ewo%X!�%�<n.�d.he �cha�er��Tppears .� p=.I�Y� \noQ&0nt {\em PACS Xxs:} 05.45.a; 81.40.Pq; 02.60.CbB;Keyword7Q�;.%�;]�l2� o{InQ\Ap } Fq"1�� d�Yo[mplex�blem,LJinv�Bg�in 1699a* Amon*Pur}. In 1781, Coulomb!�Yd �laws, j|D-/ . STsa� at a �i� � siU a fl5-e��a n�ceJ �'!�contactq�ab�`�alaPa $S$. iW cE dyna=M1;6�A\mu _�;nd"u _d$�spro�ionalaz 2;bq�] forces $FTFQ�(�. #i�#  necessUq to m�Wa�.�;e8d�P2x dur��au�.u!� !-�E<A2�d/T�Tq "�XS5�wR\mu_d<s$.!yse g!� widely u!�until =@DEmAnre�F ya�, � res�m�a��rev� becauzp� p4re ce!P( earthquakeQ� car}IQof:ob�229~t��ook}. D��f�r �WdM�revea,subtle effec��0n nanoscopic _X �sev}�phenomes�� ��Mve ��� d�Dt,rabi,rr,hes}. In��ticular�#Ű��Ah�nte!_,���]de� J )�medG�A�g�� IReZJ��0acM� a@��ow 6 ���uuB�Ł�34s}i�!�F��a��Sh�!5���s. VOt��ɲ u%S!��� I�rr}�9 to�pr% *$bau,bauII}�mف�]w kb�-�i�2�|%�E�the�<e| a�"��^������9pmYsm�>��.�s`uOw �2y[�)���-�N :i�Mt�cque!�zU� altern%lErpso-�i*� Y*@ \�evar[gperiodaly ��(j�!E#maximum%�n back#�u so our�w6xT� al evidq E� o�<�1Sl�V�k"� p ȁ�o��oscill�""�0e a�|tude -H&O&increaD graduHdE �w�A�rola��@��arR�A 3iUQ�u�I�,ssc}!�� Ke� a� �s�c�Y^(Hopf bifur� ]glen}�w���}tE�e�� utY�bauwTiGcor0 %] a�� ��G2re!�e135E�5s  .s,�hn�!���. With�i��)�9k i�d2� TQ@I��}��� F/ `9 : ot�3 ;light�p���A�� �tou$i:M�!y,@�>a~� . Ex!N�yO!x o)�|&S]�Y au2,lim};�Wgei�$c of��mem)�$�pr� *"  �b��F�Wra2�>9G:Riast�, s su�y v � veniA" �p!1�V:��.�q1I�HL(t��itu%�-�S Qa�acti5�U�dhm�g� � {�'a�nFi� � ;2D ͷook2bt��^��]�a gap��I!��Ie�6 1� . ItIcl ��a)�.;@Q�sho1#�H�Shef� !l ime,Ѿdi�&b�!Ne�$Tce9N�m���ofI��a.y%�c��t'n�bn:�<&O��5�u4��!ly���2se6Ga�I�%� �e���.� Y)Y!Dth� ���i� hardolo�-l�\ �  aieE�p�!�tom$p�!i 6c:�a��"|. A�[%�ach���� �eq�vn6�mA goal �pr EU!Ċ�occ4I�e�'mI9�,թ�W�|���P'*�)�+!8� dM�)�'�ea[w S$!�t' !�h� terp�&E r�2� �1A��6-!�9's r� a7one]�it�*mY u)�t� s^ ��Cis](per. We hop�kat �-*4Ae'qS!�id�- basi)]mh�� sivA)�&�$X'!l��3J&�A$�7�"z dataqGb .>ca��_�? n autonom��no�-$(A�8)/D_0=\alpha$, lD /��C� V_0t )tau� =\omega$,�$(-I} /A)=\gamm$K!W=\kappaw!Ft9q�R e��}=- m+ [��fW�,B}{A}}\exp [q�p @] �n&a n�D� �^{��g�.AbEx="6 over|%�A��s1�Jj�pl�by� c+e�'qs: $-1/)'G�%�% ) /A=x!��$ ^{-b-1}=ye35 $b=B/A-1$��� ing �D�=b- V/A�re��iz���`(]&�>)U ED)Q !�� r" *� mF�skaa})�x}=(bA� )(mx-x^2yy�2��lCb C\y}=(1+b)(xy^2-\eta y^{1+Id1}{1+b}}BW)�$mm  / �>�$G=1  $. A� fixed` !~!���o@T�,%i�lY �4����a1 x}=0��yE`re�.B  x=�( � }{m})^{!vD y=@(�m} ?�r ) ^{%QB���d�aan�pan $J$�x!=%! $-�m^2"���ce�~m�!8m&�L"���:]l'j�^$" po��ve��w . NZ x�uet(J)>0$ duB urse�Gf�s�mu$ w�^� ��;q mu =�Th% �^aydow�eigen& !Sw=9 neglect tۇ.�AV�^2�>-��=mQ'mu}{2}��i\sqrt{eF !�� � k!� Jordp[�c"�new��, $\xi, \psi$''>+ xi=I�Ii{m �}}(q� �b})x+ �Q��N2 A� ahW R' psi=�BNa!�U�, are l"dsetlength\arraycolsep{2pt}9�n��\xi}&=& �m}-b:�3%��$%b}-1)F� � (\xi-C�)^2 - mb 6.G>-+{}Y�0\\ & & {}+mb(�B>!� N=� �F��^2 ���%�BE2E*F���-BR��:k}=UD��J;M���UF�#Bb�Ji s&v4"a�m&inHrtV ��A=f!K,c)���gB"b% E��n�HfBq� ����W-g aU��=6}(f_�\x}+gpsi}+ psi  })+"�@7\& M�\�}[En \ L})- yv( x6q })- Kxi}$I ]\ne 01�1H5u��l%i0Eqns. (12,13)N�^ ���ҡ#�; � $a�  r<H Jx� ��"� p c���le��g  -� (WA@be���JiI��dA6��:��deEw�qacc� cK thEp �di7+me�C.}, �~ "+ ly ohe* ,nat9 "�&'%�a5�"���$figure} \i}g8 ics[�,=0.92]{plots�%1b.eps�.&/ca�{V!��cAle" rs�ime: (a)�U&(b).��g .�[��Ai�"m�"�4 2�R9A�a� chec3"4ly ats">]��� �a),Runge-Kutta �@(of 4-th ord�TheQ��h� in Fig. 1A�N�1r=֍� : $B=0.08�A 3�mu_0=0.4V=0.1 m m/s$, 8 _0=1.� 8"1K/WJ54 5�H�)� "�'/46cB.ick%� �i`�al � !��S ly $(0.01Yri�7� 5"1'iA��&�v�Q %� k "�$$Vs �i�1m%�� 's�:�)nd9�A]b6��.����ee, eith)�"aJ! p 3*1EA6�/,�� e# �t&2!ti�`�}m��o*k'`�inuK&� �m�>M>y&��dI� �{se!re�.(1,2) twa��6R  $@xHXPhi)@21we�6_oup{O.�&%�s�m] of�' ew ��o"�$k_2$. B�xQA )�$%���3s44 E��& F� a�>_1}�R_15 1}d0k_1(vt-x_1)+k�u2 B���2n�2r�2�1-x_2��� !�1�� � R�J�732BL2 L2ZLC�e�vaA,�g�tX-on�wp /<Ead a&�"�67e J! ��alpha!"'pA�N#�_0)C � k_1�{W0 _1) :!2 !( m2- 1��B�2*��2�2��1��S�IS" ��� * �Q�Q��I��2R����L��:~��"��.}Z�l0G_1��� H{2AW}[-D_0k_1-AW+BW�-4A W+( $+AW-BW)^2}�� p2�pF�p {�� �3"BRa�k_21*Z�1 +)^2)-4AW k_2)9&� ޶4��&�1��� Two��8-M"�H FG signQ��� D$k_1/W$#rj.�(� "+ �!r�"�i� ip�"�j_3h�j_4$!Kin�X�le��aApro� m@&L D�&- "ys�B3�%�` �6n��ed.� �(6q 2, pb �*d"U-ˇ�7g0k_2 . `H#� �"@ E d. m"$full synchd;z ��be�-w�:�: imeQ* Onc��� � �" c~I� w7�2�/c6�!�"�#k.2�Q -� k(b & v� & &�Oh W!"m0-�6�$A��� a"�%)�E s�5b 2E,V]!z�%"  2YaI�A�2v.�Im� (.H@ .� 2>s,Z+eeN�3a�ax 2$, doe�- inflΏ\B$�)b. A quz4� - �17"H% c(b� iyPa�(1!�E�=.e.6�"^ gc*uix �1�est; � rue,% ��1> ��uiJAbh ole "�&;1�%�9 G� y� �%&�) .���4 s*�% �o� Ee�5Hst�re+' s op�HH�A�1)our!?(,alP�#�.�%dU�!�� >FUEeCr5�"�we 6 �,aBH� �9�!� �"^s3�dEe%�an�%�Rre�6as)�ic I1my*�*!�Z�vQ)!�a'�Eto >a�nk ,r�large%8beEw:g Ac�6&�M�)e� hor�"g�!fu�TWan BaƵa�5 help"com'(�x >f=�L&�Cur}�KBureau,�B[,�=CarolpAO�InJC. R.�Eci. Pa�X, t.2, S{\'e}rie IV, p. 8�>1).z<5.MM.c��U@MP&ndJ�<�>va��=840}, 6470 (1989.RwB.�>=Eer�wF it S�7�8:\m(Princip�.�A:�. }, S<�IHe�6�? 1998�bt} F. IBowde�4D�Cbor �ydLub�(q/�Ed�(Clarendon Pɂ0, Oxford 1950p�5}"JRabinou=NfW(of�A$bLWiley, New York 1965.Zr%�R.&�A.A!�,!X! . MechQJ5!�343%�3.��4!HeslotB^B. Perrh(BEQiC,%�MEM9}, 497p94.p bau}>�i+Oit �H�/NHeg<lU4ribology}, edi���P. Ber|2m&VXB)X6%�928!�92Z�3>\SGSD�m@Ee� 102}, 175G7.�g�3� Glendinni�O�GS�>, I(-!cCha�Oan .�<��!i o�7No~��F��*E�,}, Cambridge.�@ik 19946\2B�=KU���%��M�51A�00)5.�2 Y.a/LimKKan C}!JJ8}, 5637%g8.J�2TI Ranj�!EJ��Xe��a�a��$eBof!�ids�Tbf1L, 341���WS�>F.m�U5, N�YE&367A&0 Febru�MatTUE��2�E-�a"�D)Ji2"!J(MMO)�;) I �exha� sQ<� �(Q]�/=�1e��E�f; doub��cNnd crossL*to+adQD *s .�8@ 0���In< ^e�� �a �lyl dW;50almodal�cncMmap a ətail. f2rec��"s# mmonR^s �;a)-Cט��� "h fam��ofB�mA�� A�<"�:� � aY�y �Bewo�i�� d�(e� n�)��map. /�F  ing A:?��width � he d�Bnt wind�� = o�i$s sandwich�.=8wo� 3 �(�As �$RL^k$U(Z`nNW7D a:Q=�un!6 :6",ed Ai�i.p&�3�sJsE��${82.40Bj, dEAc�% make�� &�.R} D�CvS%Hs)�dis!Tim)�es w !W�� cipa)a�!r2%q�5ds. s *~!gh-6��re�Fv�BF* and m! harmonic ��%J-�-�,� \B�m���2:�bs)�+�*as" �:x.��hakBm c�U�x0�#]rea<2 chem� k��&$yorgi,bark� $petrov92,k^6 95,bz}, ey*roDrea6s�0Aalba89 52,�[ er93}, bi {sM zcha !:.any>[As$Hraun,tamosi89,raj00Wese MMOZ typlly Q*!�4aᵱ-#)¹� (PD)=r�th�9�r���ulti-A�:� ��E�aCpe�+ o a prim� *�>A� 7 keep�[>.�co2$K��Ae �ic-cha�Z �� n�wof�9_fb��8�]; rein�� U��ic3! ,A!)�2�et!�$��w�f"o 7)� �� (PA)�QB�^wI#,h�Fr96}. \\5:  ceH"J�%��=8.0cm]B1aZ&B)@c Bifu�A'&�AKi��a��� .�;�rN , $e� z�, $k/ ~&CascadA�)y ]h� e q�m9a bub�(&�e��( $m = 2.16$U� f-�&�1 $m=1.2$. �">�&A�exTNin�Fa��ingaD y�0Fo�f�k$1^s$ ���?. } �2 fig1� U� D �gan illuGOo a�hg�. )MO ���<col�OH �c��%$our earlieO�udy� ��A�esh99}�A2� 'sML(QV)�Ua�?plE_2�=��ana82&tA�>��.^T ��e�so�Lolves R�u]I �:ra^(I�&i9�4n.E�"�����-�U��F�,��E?A�� "~ ��Y�� �V,D��d. ( See�( \refAD1}a,b.)AEx*�h) (b!q*c i=i"W blE�kiJ  � �� ->j . (HK4we �KA���nA�al�,U�$La*���Ew X� in.!�% $O�Bs$�E&�y nd_ � �'�e�M� .) � �y��r~5�e��! �Jt |@,�ic-!.6re ^.I2� 5rte� -��ir `i�R>�.MR(M�))6 B�� q-d�s��SSa ��e�U�k�z�e&cnannihi^;@ a fold.6��m�L9B9Y!e � 1CaM��ext�Ial=�(NMA)� ��-nz63}2x�E� �;J�b!h evo�J� Af%?��Y�(���r 9��(J NMA ��b�gar�� ���G���Ce2s.)!sJ��e� Rc��"� �/ harp �u�a { |�$#n�<��"VIs X the MW2�9��k���8"+"!3��2JJ9. (B�2}�g�� 2}b.Ly, seeٴŮͷt}!@S"!P2DEM� ��1/.\\ A  �Ure�H!. i�\Belusov Zhabotansky (BZ)"� = EI1 �v�Bor� /&U �tuGP%G!6 BZ A!��&� ��� �nZ75�)�seFmS��&W )��E��Z�� tr��E�f�e=u,r.�Lq�bz,�, $,coffman86�A�]�"�U . OB�4l�lay@* 1�A�� lasn�ea�vure�}�er,� ocat�C< �a2��2ng&��5N��"D�E�� }.' � ��"! ��$! .l)��R!�n�C܏s"�� hQ��global.�!*!�� ��� �homoclinm �guc90,gaQ d84,n 7}a��gh���.e�X�;�= vail%��!A.A��2�P��Ual1�, u٤�Bd��M5� 9.s`)'easy maiH![;h,lacRqadD�DIl0�to��l�y -@�\>s&k s ����MMO.�!ԛ in�:�r� � V�p;ert�$Q  ofe]it0f�%1�!]"D� mbed�n in P�%!�� ~EJu�mM  to �%i�d� ��&�1q��i,I,Dmichelin94,fang95}�Ss nce,�4i�ins�N"�U"&�t�!]2� dX����A�Sam�=�4!�Q�qS hig��si="�����%WSmptgI)@5OY���i� I�-� (�RBZ �) �� lA>� ����".�J�b uM b1����,simoyi82,bagley86,ring84,pikovskb#V9����2���'�I�6��A�0�U �8�}$e=190. ec�0$e=202.7$. (MgplFP lds  #e!M� -%!�� !O1�.)}&�2r� \ ��F inct2F��, *�6�.u&2�!�'d .!��E�I5ed ra�$l�YAE:4 �%:�!i>mgV� ggesx!�Ζ �/v}in�����a�7g$'T�a� ��nonmono�FusY&�*� B� �bo�Z)YA�O�s & !�m �"A�Schwarz��y� V,nusse}. Yet �O Y�ax�- �m�t�Q���^ m��-�p vp�(tz,kan92,da�"\It�G� E0h�Cns�fo"WU-Y]�(Farey*�J�pe��8)A bset�Y^� i[�"�A"V)�}%�  a�") s)w��land}*>) �b�#��'s � �'!it ABd J]��)}I2� �eI��J�!�finds6��f Jh G��n��&��Wi� "t#����)�}�a� �Rq�ng*& 2U5V\/�+ has E9no!la�Y�99�*"S �.�h"�AsIrF�aa-evJ�a� broad �!�a>eaqo��.6�_��5E��)m&�2  F�!a5�h!i��5Q"� .ޱ�ob �v��aa9 �*mon&� 2�An� n imp]ae"?h 1!6 g+'�-8a�n��&�vy���.:&h� 4[ffLBB' U0��al2�!q*� �N"�L�00S*���e�@k�'9V.)&U�s0LRX.@�6 AdmjdRE�.a��! �8�=5T����1f����u|.��%Ǎ�ag�WQKsoiP� % *~%%ol= B Y l� 5 �5��A��>�a�4�aOMonsetaI M�9� sF� su�.:-�12s�W�!dɆ�!�   slop�0�+��ɥ�un>H ixed��&unl-h<uθca:�)dA!r>s�.�5Is.} In�e����] PD��!�urnab="B>� }-� %�\i Fe :�;iipis ��u�8 265-N � map �� funda/�0�1ܵh%F!XI+6:#�&���_T &G$x +ed�!� Ho ��p� shapX��&$$d� �&IRa$'&�*��B�i1he����-�:�]OY. (*'cas�.7�,g�c,n��=!O� > }.) �T veri$|B�by � }� �`iA�$ك��%B�"� "56Xa�с-is �map)fe�8Oa� -L�R'A�� *R8*� &b=����>"9F�!�an]� Z��C (Ap�7ix)lEem�B����"�map-LAu� ily *�%aP n ai% 9��!t. H�H�in&�N idea�5t w�4b63���!ŐB�� �(�"#3})�a.�l�e"�o0��F�Uw ��% �q� ��a�� a�p.�" * } �adi&PL�[39"0T�$�;�Za�-L*)WKMEO$\mu=4.0EbO =18.PP�S� �� (p),>$c B!�  i�e $f(c��wiz`ed.*W3vW"�I�'��kB� �E R&, & �Am"�c ��Aat need�o �!2��by��E*� I%�C.�!��^, .�(�  �^��Fy 4YerEz�%ny�-am �!r}*WBT�&.c7�"RAI�Q���@�VqGai~���d/kW��e� � ��OB 8do!UsoV�A�z�c��%"f�&��Wi�!� .=!� Usak�,.te$� � Shiln% scenario7&J�<Ʌit2�'Cadm focu �1�Gi� s u��n ��%�g2 -ada�)uVX-at�Wei���nt�W�alibrium �iu�!FaA-H ?k h&� �,[E_&� "E�In a���P"gd�ndI) m�0R'U<ng�mM/iBi ��%U��� >`I��K�d" !�V��� �:7!F+� S@Q�� �l�/eB�� 1�#vE@�j -to-B8�-�<)U5�ZsC� 2&�schi88O pk9al�� $ (PPO) borO���2�j"dE[�)H-$pv�Ee. (�ň)�3). Fur�^, �"�,%y0 !d.V ��.�� &�-2�-�#5QQ-O"� i��*m$ɏPPO&�PE6��k� )�2��Y!�>�xis& &z��Y }. T� á�"� E� rmov�owaHfh��� �?. A��mpht��+�g�� :�2��$.��r�?dY he-L1"(RDa�(.�\�w�p��as%�� y��2� , �$ax���.�sxc�N"ZU�wK� "]�/K-h�&MD\�\�P as�* As aE�ii�am� velo�8&� .�T ost ��� B�66!4#2� p�]� i(tak�{N�'k be D~(o7�s�G F  !l���0�ed cl��N  � -spi�ou��ovj�ml=�Z{ld. CG�i] X"� X ,+r��"XE �.ݼsc�r�� ����j de.ns�eaner�����ne�qiJp(. To mimic 1�mz�e2)..2� ݻ!� r� re g��mu, \xif� ,�6,f(x, ��0arrow a' < a i(K,$c�a A $a'$%H non �sQI�`�!�CFu�$ we At� � �6� ��J $c$E-re7��ic��ncJEH��r�8$c$*9 �w^r�2Oe��#1{k a �B�to �'��o�&ntn7ed. (P�U)s���t� 1n:��7�&� 5"� "6�,v'*�d"��if ��?��f^\�N e(0,U < 12�3��f^{ + }.2> 0214.�I a�KA%х (Eqs.U1}-��4})EgA��!b75(D" �"to (c�0.� ���p�1���)shall, h!��h�Q�2��"E� ";��ffew��2i.;( �2�>�s��f�=fix up]z^l���Ce���iD�n��p Q���. ���^��'rev�Xver&{}\���4)~iplace;A*�]3  $n-$th"�axmk�%!, $f^n(x) = Xf(f^{n-1}(x)) = f\circ ��$. The iterates of $f(x;\mu,\xi)$ are given by $\theta:\{x_0, x_1, x_2, \cdots, x_n, \cdots \}$ with the respective neighbourhoods g^0{I_0,I_1,I_2, TI_n �C\} $, where $x_n \in I_n $. A point $q$ is $k$-periodic if $f^k(q;\ � = qL, while $f^i(�C\ne q$ for $0� 1}) �e��4a whole is com!P down�"cheeurn mean�at � B� 6�, $c$%'a funcA�%�!L�ce Icross!4he��of infle4, � f� x}(p) $5�s eau�J culminat� in a%nle monoI_im���(�p ^ ^> -�J!j2h`^{\prime}_2$ . Thus, iE�re�6 h9�Y�beyond%�=)���A�ir ua�to occu�xth�J��rA�J���\m2�. Si!iA��2s comes)�asN�� � two possieKa�reinj1� namea�f�P$ falls� ŕ of a�R$ $x = x_t$!UwhA_$f5S (x_t,� =12�$Y�j���]lat��clearly �y �AWrealize>A]1�ade~9�. Any f�, q�AI!B9}�7 two more �s o��e asce��branch{GPmap. \begin{figure}ce��x} \includegraphics[width=8.0cm]54a.eps�)b) \capa�{ B�N diagrams%��8Map-L. (a) Casc��Iӹ�$with a buba]structu!@or $\xi = 11.415�nd (b) B>.F d�tan��t.UQP=N(3$. }\label%} \end94 1P \subsI�{R�j�L9�} Bef!�$we proceedQ �  H below some deriva� sM� \ be used ae��lish ���0t results. U"2��in rule� �� s of maps�,have \eqns ��^n�`x}{(x_0)} &=& \prod_{i=0} 0�Gx} (f^iau 0)).` !Wf n)Zf( \noindent ��1 �2.)��write�nonumberz^2 �^2�&=&� � � (� 4}�� ),\\ �\sum_{k�:>N z^^2}  k N)}{$!�_3 !I)} l1Mjf�6)Nj -O1Ncurvaa}.E�%Q5P Simil���t�` depe!sce�5Q 4 to)c -&d)Y d\mu� ! \��&) + < $x}2"1 7!As e.m� vari�].65 ordH &� �cme� ism���of �gN:$ exhibit� ��� al lov ailed i*Prestrict our discussi��o a � era� blem��,�.� �."� � ���F�� type ^k� (W% 0ll soon argu<aU se /��sMOj8ones.) To pin��"ideas,$ si%t� -L��satisf���quirema� �=C�m�\d��U� $R��6�,well visuali����n �l�� -L (Fig. ~ $fig5}a). A!�min�fee?1�Mѹ�� �rel��,ly dark band%�uF( &(+ to sup� ��� ) run a� %�N� conn�j,ng successivQ5-� s. (m��)�routin�observed!Do2@DMMO systems also.)kse �arise� con� �K!-�d "' ��"� &� -�I ear)1th�share� �� �f&6� wae 5< / ce, Eif\lyb2�pMˉEQ� � o envelopQP1.. I�  follow!�analysisZ c utiA� t�0contiguous nU�.dIy to dAA��I ric 6�1. >�$ 5�$ 5b>$ AM.|qo( *$ )nL -� ce coexis� � ��3�Q1�s� � 2.8*: 2e0 Z fold.� �W accumu� onY!��ny��� z8.0$. N��(�I�2�1} b.*� 5�Z� Co��$n$5�A�$k + 2�& a�ist one�gi"tg E[q� ��tk$ vis< A�e�onotonmT�E�rm�&� We nI�.�$ sign 2"M&) as $\>C� )�q�% P�!�k$� >s:Q>� assur�8f&6 fk \  $l -�2�_{r_2}�o d�is,�c.�se/1�$ ( $n =2$)��N� y = we get� l hal�2p �}�6' } 2#�)+�  f}{  � (c))fK � cF� 2I�� Equ�  !:am�� term RHSV'2�s neg��A�lIr-oFis�iz  s��� �Pf�)f%$� e�. HowD,J$ly, $\vert:�!mB{ *$ {\i�.smallen$rsRAse � �'t},łharI� reg��o aZ(�,��%�x)� > ���6< Bc S%j tL%�J2j9�. ANj (�-(vup b$c$), ʋ��} �6�� N�$  Y��a2��A(�Dm�-� % ��(in principl* .-�$:�Y cas�m�,E�;y�z�q�Z 0\sim 2.2$.) B���� �,�a=l�D� .�Now*� e!$�NC� .` n> 2$. �X,0 e��"��^{3JVD( )F� f^{2��76,.�>*>'Ň ai�c) >C3�b.�"���� :*m,A2f�� �> A%A� from!r:���2M.� �� ) < 5 F9, R. previ" &�,}$ :@^�$a% zeroRh,�aJu3})��<� Ac�l i2�s�:�z poɇ !G�.�lh��!_4" �a ��{ .�i' bK�K��8e+ IA�}�(��3$ arou��m2� $. SGC�pto show�J�ns!,a�#ichA "x�N6SO!}$<> = !X+=�_{r_n�9�.� ��B��� ] %�e�2er�n�\�  \"d#)�2}U 3 4 ...�s��nJ&�:�s�� largely a �u Eqs.(1)�R(2)"�� be verifi]�u>�portra� "#!�n��z 5a. Ch� in � ���manif� a� I �R Mxaks*'2�.'� ��5�. Flower ou� ostS c2) t� hir&\ of:� M�* � �o ,�alG� onse�.�U�1��A �aR "B�7.GCɔaJ#.�isola�*{A�7� olasm#�9"�[ trac��O�Xx!v ��� AMnts (A�h� ,u v �� gene�laseyy. Aga�we �Vz�!�:�!*�&�)" $ x_  in��!O}� an a�ed*6$ic!{k-2}���t M�H$^�2. #�M=nN }e1}�O� n)\\6*�>[.F?�  .l=2rjBT1�� W�?!n�at excep���|$�:�llN!a���P� �[�m��A$�A q�$f��bA;!�o!������/U7vq�� its ��s&r, $=�I(�DE �  F kAo &G"at2�&��W a�d�o a t�pnt.����@��� ed. � ���,,8 k(c� "� , triggerH  am�&g.{mak&!&6� un�e�� v.�!��k}��$�� Kr 6�G�'1cQ �1�, ie. � a c$!�$f^k(x)~#up*�"�ita�z � $k-$th �1�.� FW d4oys�KOl�?!�and$N� (see�� b). f*!GJ �a:�%sx � ) A� ���byA�7z  ��itu�!an �A|.�a"e ()a� is happen each�W��s: e2� F�srg� �� �"� %Wɴ6� �4� � }�Y��&�l�(�1 �Z�� r�<,�A�kQ beM4 maximum z1��* b&e � s a V4%J�J'� �" r��-LJ3���h � differ�G� $ &� ��tf^V �� V o(s)� | A��.��&f1%�1� s �M�[ n 4.05$ (��#$L !1a-?9�"� �� fz ( $k =3$)!�de��M~Xrre� docE�?n27.� MMO w\cite{kW'$95, raj00}> 9&le�exten%;.#��O"=sA�I�ic I�s!�c.�)�p�*a��-Q�D!w${k}R^{2m}$)NC as b�#l I��$^{k+2(m+1)BdL ų��L F�.:Q��žh�s  Ej"�to\,�ua�e�&@s. "�i�!�%T ki�FP� MS =,icUR (��5h!Lk%J+1}twho�al� �-rupADb�$homoclinic� s. EE �A� abov!� �>�/h�"s X%�� � 7I� ���ars�-�/tE�A "I�8introdum*^ im��&m(�.qi{ B!&"Xofclq�A�Q�u1P!�!"��� 1`% we Y��w(�e�X� *�.b���B$ "^ly1[2�mma+, d�d!�U �H 1}��2})&+In� .A1%�6�r�� � �a�.��wB0�=H!�det� .&vRYaT $ k ��1$Z/�M@+p]!on�L $k$-Bh K$�n�raG qy�'uct�!a e�an�� H+��,^����!� �3A�(\1)J�� tha�at)� on0!� .� �has��&�.� -�(�F� �**� ���!_{n,*Y'F"y � , 1!:%=F���� s !�� 2=� .���2�.$magnitude QIG$k$ ( w4�) mp�"j � {%��'$ 's\#harper  1� *4 %�)��k-th: ~su�^o*��nei&�5"� � ��2 approxim{ y $F^k� 1^^2 :), (x - c)^2/2�mi߉�M��nW>yEADab�hFK �3� ��qFA��<  F1� �2\�|^W \�! | < F+-�Y)�1$E*? e f�)isq�!�m��:1.*,0:r !M.� PD�nR�� ��� �]��ary.[ �]5� �iXsi; ���may� be a 8 ��h&�f�n a cerE �A�)(�#at�1 I "�M,.� $ does� �� � reA�no �%� for $m > ~�'F2onYfew9�si0�+wou�$e � *� � ! :� �(�s� �-!�st:Ya�go unb~�r6� ,!>hannel� A $x$���open up�2�; �4a!�nticip�"vA"U. *91})� 2�1! �D�4��C8! $f(0�:W2)=aAa.b nonzRI� �5Z. �*�ser>+r2x71u bJ%A2��" Ps��F4��: �9_&3 %}&� en�$� [ e�c ; ��A5c$a�t�$fxx!!�1�:A)"U "Q +A�AdM���Ya��� � I)��!�.0�  lowly�(:�1Sca �+on�:`} HavA�L h`pre>�,= ��%>is�/ 5 space,� e*� �) p5�&p chaotic �mmO !7ofq�&�de�+ �yRL�1}$u  muchi��.*�:dth a5pa,'to�;A. �4 ͝�. Numer+(h�2a��a�- Lt�,2/�: �supN `/Y+$<� (PA9~J"�in NS-"�/�  geisel81}a�a!�jMSSL ) mss}� �MSS"n, betw�anys�---!U1k�<sE�2�R�J�[S]$, �> ��a!�6�1�)��B�\P<�� post91}, ��&#narray} E%�prec h?�2ec !�[S]F. *b5ePCo�*anż��  beha�!�r .d0%�, w�.sum���!�K*;2DR qf}�B! dy�rpplr�� �a�!�zRso.�qLe�1.��$\tilde{0 _k$��last gD�� ���A�!$�j, %� ��� > lknh8,�-b �ms��J�a^ ���%Zi�Q fT!j way:F45�E� g 3>"9 _3 <2�^h .#4F#.#5m EBy:5]vm7.7 k^h$"D)�3de-�e.�* �? ardini} (Vin�%Y=p�+!#-k�h0�=�4!�th��(k+Res.�&��/6��/6b>�/ �9�/��A�I��[��\��3�RL^4RA�=3.783�;E�=3.99!v�1�+ly�C/).�9V�!�>g%s����k "j 2z'd^{SN}_0)�yth� �B_p� ^{�����4nR*� qfs&;@j!�)a;,e dashed linIrawn Zaar fit.�/6�Z�/ �9a.�.� .� ��a�ary� ��u�v9�:M�% {��9�d�< +� ��k +2 $)�  divid�&�wo�s�? $R_I : [.�{k+1},2�^h]�_{II}R8^hB: 2}]$*2!!�U� 콁��� stC.�� z s�$@reB� c�3��3e#kR�. W�?isUh �#o t (zsen�+�.�)����a�kR$ k�) high�5��5si@<$BWlHFnTA� 9:(�VE� ;�?0��.�F- ��PR gq s"�&*�u�!}�&��6}�&. J ="�<=A�"Z�*d�5_n)�6i"G+A��t $4< |m"�\le 14 (� � �%�fixed�,"�O%e_p�%� * �gBf<d =A�(x�g�-Uh�"��r*��&�8?M�6� $UP p`3� B;he sameI&at��"8 !�.� � , 77�-a���0�0e]:�,) 8%�%�p* ��r�v�* @�e sakfcla�5&Q.�miuLis�W���6&a��%�遆�8�H+tt �@M� 2�a���� C@ng�!�0!A�э�/!�t6a �z1e�R$�t�i�>+Cin 2�p� �JɘEq2�- '�yof%EI�y��& %�|R�0)R�)&h&+1q�Ya�i*a�eqe,q�� y�� g5E@a<**�JhA osenA�b�e%[:)-�6(%�G{��j- ��=I>&#;%Ipeaked (9+&�(���!�), al�W��Mbs tra�IA8A��mittenc-H�lik�(g2#n�a�J�([&YMi$Jst illuQ)�by�CngE#co0%t"a�!EM��!�Q��tA�o �o � /@,� A��l �.���5<��n�JB$AEg�2Yd marg{L`~���B�C��fA�*1E��M�8J���M� 1.0fgU�� C,$=�u<&�_n)$)!�k$�& nt factor�=�-1A:*�0pO U$, �*F�2��MC4� ���  ( \gga�) $. H�6*u��#>T �SW-@)� [ CJo *]& .��ReciP":�.�%Q:Oloca �AF6a�:A +e��N [ x^{PD}_TQ� ]�%i@ ,Nzo�-w6�QGoug�G0 saddle node2NA��@Jn n r�(*�'A�4c�qf ")2� a4�J�n�QsP��� E�['S  2 ;��J�A�!�re�ed�s��"��M!HC0$��0P+��14&+M�����.. �pRG��kR$!B�� (�;$))#�(�D5� Me{O�̀RU:hM�a�a (.tPto ��1 " com�(atF���M8�f� iO|�!:�%�LnO[��g�%*Ith! pec�EV"�A�� �>r%�es�!�-��)�� ]/ہ�!!�9"� �{!�$t\^�L!�a�1�by0M�D!)� a)� �L��w b�4 Jt.�4any&� N2 $2m �ex:" b.b ���n �$ t! a� �R�y(� ^{-(o 1)�(�+K?mp����$�seR� � T�f ) �N�V%Y "m cAs� �Q/ove1d (&�DX��s a�� q���(vanishingly)am$�us��C�k :eC(mB"tKI&T  M�La"�D,)BF13l%��3!xget a T -E��-!'JC� �*%\"�'��e"�5bymr N� �/;w�xx1Ero�,uu�Q�>IZ �C2�re�!�5�� s25 >�;�S hold���. U�T �"�, %C(i�m=w+B�� �N��"� �mbd�I14�,� LM�K}�#w�o. To %[y !?"{  plot�1�� $�2:SN� E� �QexhhKs ar"�&���%�II]* RL~ios &WE�I6b�a"�,fashion�  a �Y6o ?5$62��%��ŧ��a�i var�<$m1'sF�7F� �2e��Oe.�J 7)#&�,�1 tho� �g�D")%� is��B�s work�,�nI3{"��ys. 6b97)�pp7F&5RB��U� >� �!�Y� q1�1F@2� ElAW)p���H>�K�.�X"ZS�&R\"LR7} J{II�4�e��T� ~ made�3!����R^2QH)�at�Os�8 m��( ��E�"�6 !k$ �QLu3 8a.)M�stZ���� �;]�� ^2$ �wOactlyS9���6�k$ bot�# Nli� �>� aW��%�t2<8ac�WK@ta�*��se�� mS�-iX away= p$,�6�nes+r ZA�s<s!�A-p "��h:� $ A�� !to"� ��aM �c^2�&G"E@U����� ":��\N��3B� �Y. 3�T ^{-2&�k F"�$9@2c� R_I$��6��� m�� is� *� amg"� {+AB:�V= �"%n^F�d��� A*%^a� �5i�rYE�� � �#� 7"*& �nX r2Qon��^�6!n�#lyD��� S� &� 4$, kepta&?�(*>eW�3iY 8b���!�?mm46r� �� A��} 2eX_irmcZ�$M��$�@~�Y8��8b:d�P2_�J� � �3� 0345�A =4.001927�c+�5%T�" (!_�� ind�O uishS79io�;e eJ�"� "��U`� ~#�-y�0-� �<t ! U�>�8I(�6�Z�+�k a�he�*�'a �1��".&Al�P� of)X �%*��$�Eri�!{!YZhown �� '�4� �"�i"�P,�VELkR^�H�Lp��gy5y9e�1�9Q6�a� vM�e�z-\��)L� ��3ive�ypi�y�f�"�,��s�%/n@b ��al6 a��!�z � !^$U�$ 2 -i7���q%s>�S �*� . //+jVon{Co#^�Com��} On�mM\mot�\ng��M studca "[U� � Poinc��U(�NMA of7 :A�e�8�ks�= dimen�Y� reducedA�Z]�GinQUti��V;IN!s�<p�eKAe��re�/� ' key1�1f�0W.�EO: kna>�a&�!f&xX*�8.��@n .@ limit�'P (Gavrilov-Shilnikov  `o) �*g #}�M= !Y:�9�$�J��&Xei(3qp-`,q�*�8/3c +e�4Y�^�OA~ ompl�� ach�9 ity � petrov92, < < ( � 2_" �� qbeA:� �X�level�eu; U| � n�KUU�.1A�� � �\tak� investig A2Q s�F^ [aC'*32�9n(�#��EfYcuX��$qi�0s).��� )"s w�?!���8\�� ��� �roya"�X2�*{f)����6�R� E%e!m�Mt�IwBn2 (� ype�) �-�9`r�5Ynt��!}�l �hr hiAxA1embed�=m ��'�1"����asgre�[�:n,!�*�!CB s.} ��mi�jA N6�s E�n�+v4%���}�"�0 GB  a viewV�3 ]�-)&}�EGi!;a direc/"�I3�back-to- Hopf.4�I�߱J�i�$2,tamosi89�3%a�]?kal�;,*�+>w gi&J�\� � >,�ng@6P�I��"��  �1YnKl� "� |). *�%�.�B��$.@e?inU��� u�� ���tc�*by!/)�6�aq %me �?b�B�w�`be �-e � word�D;s�0�f�d�� �(5\�bor�_6>� �ŗ IFF�)�v�u�.  ~o"U;!� � �% �6f=!((LBA��z')>h/.�Xgo"V- w).^7!�a�C"%()�s6} �6$I�fa��aval�Q|.|(q��!�cis��trans~MT) " n� �0�' J" �#As� Sh�BI69�!��G\ A{��g����jł8%�-Z��c:��):��pcma"/p6� "vc%m6�)%�[��)��.i��J8�Q6.} �[ {Fc"!cau&(,V�L�f Ŗ.��1Qm�-�V F�+bau�] expovc�&a��t�UC!Q{PD6s 4rajesht,john}.�uM�� �NR1Tg.: s��l �U�1�alternat&�BJ � Ѵ[6" 8N Z �!�&~ AHr&�bmap%r(A�I��oD+ail�*+/%�Ca�tuned,&JC� "NfY- -�;. Heur��a�J�D <� A�Js ���A�ngo�a ssip�-q�"(4 manne�R' o�=1�����.7relev�& ua"&/ �m^�m)Zc�,s�f I0E�{(�obsolute`Cs�C� O�e��d)5") � ��se �PL"Q)�lnel�4 c.1R, a�8� >t �6�req!acARi5Tp!�A . By def�sL �� T�)�.eY1�3T��spreadqg&�i�D�]xt]5�up���O (G�waB�,I_1�$d� �.(I_2 = f(I_1"�x \ll 4 . ) �E�ARQ )�&� p��bMr-7�0�Z1: no{" 3:�a�m� ?/r�ms�s.��High d}Ofavours>��I!>1�%�&' a; enh d9ex�%e%$LMA� IM?(  spiriI{�{%>� �p�9�"�r_-W�8t"K;��&�X �,c volv!J�lea�vine):���"{e�2 � -cWE2�(�)l!*a�)����iWa a [�&��" B�<s�  g ?9ĩ�L!�E�E?���Zs�Z,09U 24�r� �V7� dM� q qVg=�3�es#7lyeK6�m��p!O&*�Bqui�z� �E+=�mrTh� lŽ shipY�%,%O���jl i�>)[AA�X eskyK4�$�wM?�Km? ���hmusD emphasmfse%8A����@R/�k�X very&z �t�ugm�l�re� ��U\)*�+0e�#;s� un�L��"��-�X�h)O�Csed��v}!��$AN�L.A'2 � sugge(%@ �����XV�0ly :J%�6(IF"C�i-�o�2map�AIl�:?F��;dMF��o(e�A<9�� s�a~�� &�Q�(&�2�t R�=E�c�-ytl"n���dthLC!B:2��N-� }G.�sandwi���!:|:{k}�c A nedA7 *� ��k{ > �'| �/ B$|�2#B@ve �? d$��,�If8Z���[Vfby�3 *�^�2('a�![4ed keepa�in�K�!+n�|w ,*;6�u�2a4�&ct�" ��NF�K ide�xQ�eU��f 6{Y&L YYu!�>A@A��/PTs"WX�g!c !z ^*� &TT�}��eilp�{�f (Cng![m�m W"� Z8 _/ {/.�a]in�V#.�=�AK mod� �,%�.� i�UX T er.�A#>�!���repa�Pne��ca�Q]Ugi|��I r <��<�*�.�,*��:)iak%P� 2q��) !�� ����N orpoV�#�;a�gredie�_M> �%S|��pr!��7 !��&strengk&EyR}�@�$�<@!fAX%���Q�one-D�6"�%���;n effe�@ check� ��of�;� U)} :)W�a�t��lsubv}A�����Gw�Dc�!to!E}�7 �n�aln  I� .! ��N7~nceiv c&&�7>"CsV��1)8}�J�rU��>i �t�k {�amp�^ro)h�cti~M�x��� a fe4@n�8in�V�;!��VL�3saEwd i~rieI�combit�:i!�in-\2}s;J. DIn sumH&��b�E��Ԁ��)# >#E���& �&! 7i"!*\in2$�fuoed�/i� associ�o 2+ a����e�F } elucͲ!g~ a2&.;�@ " 1�er9&�4] a#�� X�� 6 . �� r&g�'&�N�Zg�Gl5 �8"� .t ty` recD o %`�.M.�A�} !�&-La���i to�"�K� nfir�F�.&,U!_zbV2z��e> * )ive6 �Y2�&� N.{�ц.-6a]� )�" B� 9�J&�"�A#! M�� N"�ve��] U��.9!T�lso cap� ; *���t9"2*�%,�y \of�e�� ntal..�1)�icjs��i &e�"EJ�5�wB"� � T �j%8�o&h�!OE� ��Ht�!��"D&��B _ �.2� I�sia�:PZin BZٲ��i�+�% dt7�x�)�� �B}�p�# sky}%# �#=. �Szx eno�1to N"s*�S0-belie]�h�%fu�-�s#uld b�ou�h����d�_w$% NI �~�8b�j�(6O��geome-Ih*h.��*� �B22 alba893$,2,krisher93,p t},�I[Tb"49�U�8 our�A�d�� 9b� las) �D?)�cbap�6(z���g�ЩPO ably� �H_QW� d�J yubiqu�Isq��ve*� �e6 phys�5x� widely)At�0,-h�5f��.�N\B(A�dXdix} \renewcommand{\the&. (}{A-\arabic&�r}D tcou {0}���B\proOJ�1�p5n��a�chea�*�N broaL��)=. '��sE �4 : a)�UDr-: b)�/�FsymI�"�p5qo�a�(� c)pt����M�3. U.O,aQViP o� � B!Ois! >L tis}#�o�.&#:�# 0x_{n+1}& = &f5E&G \hy {E�} J�O \U�:f(&�^a + >x(\xi-\mu)+r(x-c )^l}{s_1 + s_2�? m} f�E�Wm \ge l�7�q a >Wt W "��)"5�9 (Ayp%;��9is a���mai�.��R��>���& ext.Ylsh#B�Dw*�$�x�\xiWIJJ 4$l,m,a,r,s_1,s��._�Lk"uE����:��{H�%{�+-�v look�,3s)s� ure)���2� � oI�*�e`8. 2�a�%�{"2 )e�!#�&,ke&]�� :�1 g�Bm�:*fsY_2�C $p_3� �a`:e%c*G�  6o(2��C�cgQ!�k( but-z'�&a�PDiF-v&�7�K(a"�]>*��; w^ < Z�< ���=�!�AN)h��u{� |.�~ R= R>Kl��NWR��{p"q.�>���5Y� i�v�a�� odV0�2P���Sea B*� �V4�p!�Z�rxcQ&�4nesa Ss growc s $2܆EB$n=1,2,3MYC���K 11.9�"�t.t� wns�>I2y� y�&� � 9\&R� a ��N+�@. 4 B �r ^�E$�veils�> Rhme� :>1]5-�&7s"�%K!})l&@ �5%� 0�aN�y�.YHM�w�,s� $a�)�Wf�c� bS>#�lW�y wo le �"F8j/ s languag��<\��c�rfinka+e�1Kq�b=�|be� Ee�p<A�Kx{:�p^* $13.WVa�2uwEA��h���K * =4�Atx!r�M�:�d makӌ�act5� bi �#givA�ri�o,o6�<� hA;xqi�^1�m �E.� s, $��!�pI�(u K?%� �.�L��)��qA({k��f�("�:����!6ge>�. �O���by0f�K64Vof���3(�5�3n Fi�Da,8e;d pF =�&���(e&�3e7 �g/ �Qa/ac�o Ln�(� � C��.!�alvUsqueez��� �mSS�}*{ �A�#Zc=AI2Ai$(-��Qb�B��A�!�~��n&�s�'>BY,~ �o*�h"X�M�5?�5 )��reskes �H2[.�!-&\(�:�@.1�hs�q�o:6n�i8A\ g. ��?ac�9 ledg�s} ;�0authors (R.R)Vhtily 6)financ���*or�+ D�tZaSci|aY Technolog|�ՋI"e�L Jawaharlal Nehru CeX%Adv�d _t� Research.W��<1 thebiblio4iy}{99�>\b48em{gyorgi} L. G , R. J��eld, Z�HszticziA�C89} 5547C 88).D�:} V. P�:(, S.K. ScotA� how"B_ 97,V92) 6191.[�6<5} M.T.M. Koper,� ica D80 <5) 72.:@bz} A. Arneodo, F goul�TElezgaray, P. RichettiYD62W43) 134 {\em (A[A���Am+��4)}.; J.S. Turn�@J.-C. Roux, W.D. 5�, H.L.5��0. Lett. A85�881) 9; P. IbibsQ. S.%J)U5�4Soc. Faraday Tm4. 87 !�1) 223; FH6�:�JQ=I93 ! (89) 2796. =�J8} F.N. Albahadi^2J!X ngla�MA hel)~ WE� 90\813.�)�2B�(. Gaspard, dL 96%7<0J.H. SluytersE.J9E�H 8250�u�",(} K. Krisch!� M. Lubke, Eisworth!� WolfbL. Hud%�$G. Ertl, !I�Yt12! tchay} T.�ChA�Y.AYan( Lee, Int�Df�$. Chaos {�5} 595!q952�braunbB � A. LisboaBSR4} 1483)x4U��: } Fe�eand�� Tamosi,�t Henn�$n, B. ZambA�Ea� imona� J. Opt. E�AB6A�A�45.4ɒ S. R�4� G. A��ha%�nais!t 36642'hC6r96A�J.B. H(, L.F. Olse)fIv�,:� 9��6) 28572_r��O�, n� A27ek99) 182,ana82} J)@ M.C. ValsakumariuA�. D1EL82) L171:%�!ic�' was�F�� JdD. SahooEuZ !�A��208�YV(lorenz63} L�tL= Atmo�ci. 2�63) 136�):t}a@I&A. D sisA�dzI">Cof��pnBanga�-�. coffman86�G=e�6pNET� 56�$6) 999; KrN>�R.Simoyi�m aNIs%j 8 j7) 1192b2 ( M.R. Basse��J�‘�:/A��88) 6963; Y. Xu,AM�� � � 944$90) 7137; 6�Hu�L(P. Merzeau,����JPa��� �A70; T.��V�.�3�� �4) ��$; C.J. Doo�B S.I umbouya%X6�8� 4) 5��;Fv guc90}� (Guckenheime�b(Holmes, Non�ar oscilR1, D�� al SS���c� VecYFI s, Sp�d Berl�o199eyYg�X 84} .*$R. Kapral,a�Nicola&J. Stat+3� 4!�� lennT �k(ng, C. Spar�fM��N �76�X!9WaW:K4� 8A�51.�m� (lin94} O. M  E�illip�)�m�A18R!�30a3� fang� H.P� �ZJ� B�A�5) 542!se���R�E�9~-49e;��2%.�bagley��R! B%�Mayer-K�CA�D�rmA.�A11i��4� \AO!�2� 2 6J0U 9�H"�# A? P�#��!81v8 ?1��.�� M. Bi� T���>G10 �4) 232�nusse} H!�N !A. Yor� .� A12! ��328.�0parlitz} U. P � La|�)F� L5) 351; j� A3��46ikan Ia�n�� Kocak6�0Ann. Math. 13& 2%�9�dawson9 P. D e�Grebogi6Tr�e s%�qLPA1� 2) 249U ZVH�A� E48Eѥ�676.^AvR �<R"_ N.Issaz Sc�a.RA41e|0) 42:[ schi88E@Schintu�d�Tmdt� PɮL 92} 340�6"u�qGe"uD(NierwetbergQ!�Q�]� 72� mss} N�� trop�M�Ste�� P�  omb.�ory 1P73) 22V�t� PostACW. Capel ��DA17��1) 62.��a�q �a� i.�Anal., �, MethodɬApp. 23%��^06�&�KNE�K; P. "�K,A�,. USSR Sb. 1�(72) 467; 19`�16_$aguda91} B��Aw Lart�AJ. e )�� 11 �1) 79�Ε�ne�1� �xN, VA�vanis���elide�P! nnet)hU�54 �6� � htomita80[  T ,a� Tsud� rog)�I�ics 6��� 132���lemapPKaneko, Fr G . 6%��^ 669;�2.�X.6%u83) 402�corbet��B  �M�A13� 88) 266"���L:9E�D7�1w3�C&y _ &{ zM&y 992�N" T.� John��T: Hao Bai-Lin (Ed.), D�Iiain6 os, World�V,�3gapore,� +[t:D .�O ��\4style[12pt,ams�math]{av5le} %/�5[11pt al} \|%w�8=16.5cm h�� t=21 odd�"�i=0pt \�N>6�(�/� 64Ttch}{1.2} \newtheorem�}{T }[s$on]2'lemma}{LV#1#�}{P�<0"on:/�x)p}" u}l la}{�4:LLambd> th}{�)t>TThFdd�pel2%�nQA\title{ɫGeV�iODarboux�2ns .3 � KP�Hsself-c)dent sourb } } \� i T Xiao)�(1cm} Yـ( Zeng\dag }�!�{\1�26��e��,�c�D,Tsinghua Uni- ity,> Beij�4100084, China}Rn �54 Email: yzeng@a,.t a .edu.cn}}A��{} \make%ar�+�+M�}."�+T��ab�4ct}�P.�z^�(KPESCS�tre�#5�f�&�`ov$!���ed.a�6�R ffer�&n��a� :RLaxc�EE-on]6�"ed�.�conju�Q:paiiw\0n )&g]�binary V�) aI4r�<9?�ime $t�% })�,���tr�Bw�h# nq �Ku16},�'H-%'Don-auto-B\"{a}cklu�D�= �s &�Ic�ee3!O, N-�;8p%�.) 6�:����}8nd en=%�b t�&nd%#$N-soliton �G!�. lump l�:some  1s9'EɝY� \hskip\��ndent = ,{Keywords}}:.b%^�Q�,BFYV5(DT),��,6��m�{In&��fi/��6� S-Nq�)�^� (S!3s) �&�B,E�m�jf�!g�0s, r,as hydroe",!�id!te, plasma( etc. [1-7]�gtil nf m�,d�Uop��(�? [c�$j,��F�(1+1)-di"hX%��me 4s�a� KdV,�if*n� Schrodin� AKNSE�Kaup-e  hier�i�Ua�:& ѫ�Uol<bjBin�6D�#�2m�  [�% ,6-10]. % 0 Mel'IX88, 9(1)$90, %Dokto�W12,��g ,Lin Ma2001}.qe6V,.�:�:�IW � i�B�-� F*�� a!|�� E �&'E��A(-�,�@AP����ed�) ,%0to�oJ�[11-139�!G!E1\5e3}. Bu�U(2:� jY, luds042 �h"�B����~:�r� ���b.!�8i�alA�el�0�*Aya �"�=of�2��sh� wa�U,B���mLC �&by U� >�7Y�89(2)}&7 ��j explM$9G!l��o"* g ����7�,4mayoa� .b"*e�wbq�:N"y"�F�x �5gm� bqhJ[ �� was 1��Hirota��ZqSdajun20At�,�na�  we� �:| ��y aC ��io��>A!kKP0N�qg� giE->� d(e%�� f a���~�$޺ �>L ���}I%Pcov� >"� 2�B,��s j� A�K2� ;7";�� ʊ!. S�#�]ng"��H)�<>:��) mixi4,uA[A�aTl�Mr� D:�Q�aїF�,is2�Vg . �'pA�"Iorganwa }�s�5r�ws��Ms\c�?he^� -�aa a�A�nd(� A8  3!�w(pseudo-"} !opera*(PDO)aal�Cwe revea�`r�L&� h�y�A� :�q� !n2^a�_hpHB� !�>� "��V5�� ly}��BG ��= ���yg*� VI�r�!�M�!��Eb�{ 2!� S 4!�eB! =�EpV�U���5�$ oJ��� uQs%(.m/>Mz�^�!k���g 9���D;hHCPpa�b/� BSa��ory (�k.DDate83,Ohta1988}).� u&�F�fe؁�n`i_�q��ua��a2y�L=\fial+u_0  s +u_12}+...,qP6$)S���':f�� _}"� xQ��0u_j,j=0,1,...�4"e. DJ0 $B_m=(L^m)_+oTiorall m7� NPlJV$&"* ��-Gqof $L^m {(��L2���A6�t'6AK9�J� (zero-c ����)f�3)�<(B_n)_{t_k}-(B_k pn}+[B_n,B_k] = 0,\ \ n,k\geq29�A Y�a��a�e�J�as�>s�subK�M@��b��Y\41 �\psi^- � = B_k BEfJM� 8Jn Jn FJend:�Aj aV�ź^�5.�+�k�)�^*�+F�bO.�O�OnOB�J� W�� $k=2,\ n=U��5e:$:� 1 F�7)�u=2u_I^ t=-i�1}{4}t_3Eu0 y=\alpha t_2B�wjL�<��wo�.�Zm�$ e="1�%#=�6u�T�,�Lp3��KPI� I"G h�Ab��tz91};1�6/ -/7})K���N�of11})�p��Zl�/1}5})� ]4"P 1�RM eqn:�\^ -�)$iD _y=- {xx}-u B�vY6_t=A^+(u) K�2\ =-4ў^3-6u -3(u_x-��a� u_y)F��s%3}v�3F& -_y=�-%%+)%JZ� x.%-%%-1%-%% Av +Z ���gI^�2Abnd.3���a*��9 8� Vv A���= \A�.�N(1)�&forwardZJeMI . A�Pm=u$� a"� ae$3|aX ٘u7i A:: by $%�+_1)�(+_1(x,y,t)$��z�m�5jb�^by�lMatveev�!M������ u�-_2i.-_26�z�I�s�,2he�&KEQlf�7Ut9K� e�7ќE*[-a�� a_1+\int -_u�d}x-�-_2<��;bn�7ͷunr�-J� k6��a_�c3*2coC�=�9/3>�oukZp�� Yg��p$! f_1f_2 �� d}x$] �@"%*N0$:me��+0_{-\infty}^x NY or $#t_x^{ +R� � ainsdF1��$y�= t$, $E" I>v~D�we� �fsuiCD b�?@ "6G NF -/ny�nVW,�!�$f�D�bx=� fty$�x= �$.5��i*2\l�� ��Z*l�h-IG� our compu� 1b:��F<�Q� be . b 7a�^ φ�"c, �^ a9u��>#-1�#-1�#�֮�F���- E�a�{( )^2}(�c)��+�?a [@+(6X)u6\]}T}�1�v3��"ZW !�.� uxAQz�E�] ^d� aedE�ecuSV�aXO�� :�}G M,"�TA�I9�� 10U7�����10�����,&� AK_B� 11�+  ��+M<)�_1�'}{a_2�\�V�}_1.�< 10�U��^zD �^�(���DŞ "� ui%2b!!!� 6f$,\ \��j$� $j=1,YN�Kbi�%��s \\5$Remark3$ToM�.�.� ]eQ�DT,}%TeqsT&��Yogous*WWzs� �fgT��:� F� T��*G ��6�2�>�n`1" )I�-\�R(arrow��)g)�)rx.� -_{2&� �� &��1Q�B�E�bx m�����L�rL�zL�Mf'a_3}��A�B�6 �RNR�^��Fo� 6jB�K�P~ 1 �P,� E�.��czc�cVcoV�^�6LA�2P �L-_2%�Qx�TVbVAz6L$j=2,z^J.�(lV� � R.1�>_'����s� i���^�, &} (m�Pd^�l"p.�[22-26]��K�C �C�(pn $L$S�W��\�"L $&9 �R$(q_jk}=B_kq_�� $(r-B_k^* !�b ,m, 1 x�d X.�� !t $Gn)_-=\j�jn� mq_j"Y�r_j�OorW L^n=B_n+~3$$�n-6�=�i�&�ia�lloz� b� ^�b0��(L^X$=[B_k,L^n]F�Z�b0���!F�E�B�1R\ �lm� *� F{ In/tp�$*0�5N ��)�"�U[M�%.` \ B"ft"vt bm f^�3�-=��)�J�jWP�2��^� vari+/ "$t_n$"A��H/"ev+%,k nfB a���anide} X�K��as%�.e.2@=�oI]�} ���� e�b0���2� ��"<$U�2� L(�r;1})�M6� b0jfb0:b"�Ƶb0����{t�L^� B2��r�m< * FdF �v4f�b0� ��k�B^*� ��b0�%Nn}=i�:  =�R -B_n2! in�ł si^+=�!�+ ) ,*& bLA�( $\Psi_j=-r�a $\Ph�VA�{q�(�*\ �*2,}[Y�E���bj� b��[B�+8(��{m} � � )_x]� MJ�#"�"b� !{j,y}= xx���Vsi V-�{jW-u j, w�+��$6O$j����  3}) �Y- ��j)b�� �E�� b�� O6 +T^+_m(!B,!��+,�V=4>Kaa�B��.���Q^V�n���=8� b:�!7& +T^-F7+ VF3�7)3%=!�.���3 U 2 Q�or�*Q�D�? �U� a+� ��.1�0=}  $u, E_  m,A` si_m! �.�l+� OW"�$"�os&5t�%B�f<:��^!mɡ|8b��d bvbn1�0%�z= FV5F(^y 42}���T� %�j-"�_1 �m* �i 4} E i ��~ !A: j,\qquad � N��j�)8�at%� \� a� "z ,Qz�aQ.� Uu {\bf�?of}}:\�Led�k&D�C'h�_&��-vs ob>�� atQ�1E�M�1.ݛ� hol�(]R�b4O-So����to,ve� � N�m_�!�"k&�ha 7}�w!M_t ֋!"�h\\B2�Z�ba!Z0Zz!2z & qE;B���6T=6�b�}i)_"v�A*�'6t & +(V��V!V(v�VJ6�=&�A'� =��N #mrY{ Byg+.�� ��L5�atU�mIa6}) st�a>�w8{j,x}>B_1DJ�_1) �1- GjrC.� ]}{(> )^2} �=&4:�f��-.22.6:"R�%�  � Wn<:�2� E.�)�:P�]V)b%��a)jb2@>(2���V� �[+1](>y=2��>32�0) \end{array} @equation} \begin(\label{b10} ;�{lll} \text{the r.h.s. of (\ref{b8})}&=>����IL y�!�~C[1A+E�_1m�I=qO6>F�K)]E �-:x6�[)�>J�)d(m*"�Nkbj[� �1>a>32E�&=&9�l1� =�I0I Y<8This completes Aproof.!8MXPtheorem} Assume $u, �1,..., m,%S8si_m$ be a soluA� of`KPESCS�(1}) and $�4-_2$ satisfies& 3}),=nD backward DT for'@2}) is defined by�sub�s}qc1u%�[-1]=Ia_4�T-_2.�M-_2},>k-NJk 2} uf0u+2\partial^2Qln�A-_2�T3} )�jZ%�Ba -_{2�~�(j�h4h��hQ�q�!%�d}2% \qquad j=I9mFz��6�(where $a_4$!�|an arbitrary constant, namely $\)\,\ )��,\ � � �Q�y�1})E�m^ 2}).)�u${\bf{PaC}}: It�obvioua^at;12}), G13 Wf2g$hold underE� transform�� F\c1}). So we only need toa�ve %b2k i.e.,a�$following A�litu0a�y4u,�I{�I&9S_t\\ =&[�)]_t�m=&M<A^-(uP A�K -_2K (��)+ �A�[(6M V++(A^+d+ -_2.7}���T^-_m(a%��;r�+J)6�^W `++(T^+xsxh x��=&� [-1] N +Q�� #M�)�I�Y0Similarly, us.AMta9��M� Q�checkAz term�xntain@$i�$,$!]_j$M�f65B�} MC1P2/�MIM^W-6� \\ =��, �V�e�f06N0>�{-A)�aCe�V�� ֙W+gLI)+!xin # 42y }�\��!N>�ŅA�K x��eݡ.rh In fact,A� have9tn1�� c7} J� ��c6}Nl " Ŕ��9 .! 57�V-NTzq6aJ(] \nonumber�B���){9k=�6���mF�B�B �BE"v�\�V��"2 %��2�\}>F��int킊��)(�& 1-1. .8.6>�v�A�ix%"e�Y�>LyFr:� eFͬeu�b� $\\ From T� 3.1� 2e�can ob���� bin_ Darboux :� � Q system�  by choo�$� =0$,\ � +_1�\ C&Z � ! a�9=�$\ ($C� "� ) as� s��69 ��8� ��.� ,+� �+� _1Aj �2���F� Z�c82} ��^" (r�2-)�r2= xI�.f�7�J5}.-)=Ҫ�2h �v .���r!.p��\� & u]p�6Z$ Substitut� � c8�nto^ N � givq A�v} 9}&� �_t=� � [-6�  �  6,B�( Both sides�� �c9� Pre polynomials w.r.t.��  $��8^{-1}$. For exa�,Bleft h��-Qz is a{or%2 � �|J1�!�&� FDrcDE�-s_t&� n�!^�A�!A�}$&=m_t6b{1,t}(2�F.g)2�Zh6V1zR_t�T���T�s.WV� �&\equiv&p0}^2L_j[�)]^{-jDefrBy a ted�?utE7E� righn� display�%yMA��LI�les8n 4��4. We denote it$=4R�$. SincTe���rrJ� �a�8$L_j,R_j$ never�U$C$, B  $'=R_j,\� 0,1,2\ \  R_j=0 (3,4.$$ IfAreplaceR i�d�}$by $C(t)$,6% funca�/$td s��e�� s� ��bR,!����Pagain, we will find t*���4lso covariant �I Ix. T�rRturns�be2�2%�(t)&[ �]m�\�eI�$, but A~r�does not%) l to6vef�vd any more. In other words,-�0u>-.�any longChenEM dYi�A?��&�."Z } GivWu�si2��gh2�gB�e'let+_1!2be FEh�Fl aoI904 respectively,{n8:� with�& �VdA bV�d2V�=I�:}r�}{6]V�\ d1�a ���d d6�) A42� a�� �!}�> 0F�� �g g �,}j &i F �andf� d1a�{m+1}� S 1}{2�<\sqrt{\dot{C}(t)�+_1�C \ \ %��h1:����6m u�"Mq�1N.  � r!d2jq421} \alpha%�A�_y(-�_{xx}+�2+F�^3226p� `y=-%�q-q,�Yk+1���e`.�26�.�qa�q.?�� E��! �Ő z� Jf So $1J$,��!�$, � z i$, �J+hi6+ >  F!Ť,degree $m+1$���2u\ E�q A�)q AQ�t�,d23}) � �ly9 Q"�pr&Qd24w1 ing���) a`�k^E Af}b�Bt�z2z2��^Ao��& .}[&"G 2?7?G?W �|*��D<}{(6c[c6'� �=2� �� ������� \\&&����mc���&�>�e"f�5} 4��..E>%�c]���IfI ��f�" �dB_i��� �$&$@d5})} &=& 4\times�βV:%[ b_ Vy�x})��� .� %"dq��BK>^ �� ����������5�]-�=M&�J}�)��7,��R� "�vg����F�I+� �J��v.:v% }V��V�bCa�q 4Remark}}: (1)�6��( DT�(scribedwtx)s�onl be structed" omitM results �&. (2).� � -� ,15}) offer u+Pnon-auto-B\"{a}cklund&C � betwe wo�s *u s $m�~ .N . %)DT��us�c�'�"� !�� c �T'.\\)SE 1='5$le-solitonG!�KPI}z� self-tistenuurcA*KPIp*). I0sk� =i3���%|ge){ CP \cite{Mel'nikov89(2)"*6��7 e"Zd7J0 [u_t+6uu_x+uB x}+8p 1(%j@Dj)_x]_x-3u_{yy} =0�[ 7MiP{j,y}����*d7i� Q� R-ujB�Ble�6EWe takp,=0�Iini +2M�7})E  $m1nd let� 6\1�j d � �`=e^{k_1x+ik^2_1y-4k^3_1t}^�� $2x-$2 $2$ M0k_1=\mu+i\nu,2- , \mu,\nu\in�( bb{R��2���5 1}�4+k_2}e^{2\beta2\mu} 2FX�/6H�+Q�n*:m�0en "!!/@\omega+\theta}$,\ -_%N-: t $$ =%6X x+i(\mu^2-\nu^2)y+4i(3\nu3)t!� i!q x+�\nu y-4@3-5 Dth�j�A��"N�1$ is �n��6EQ��^9&Xɱ{�(�=V=.��^=�� F � E<%�AZR!�E�(rm{sech}^2( "-Q13 ԉ�+b&� :1��|]�r*� �V�}=ae^Q�"� �F�\ a2~�mu� �� � � ��3�V :���$=\overline�) �i�which��ee relS �30parameters $a�;tau��, \nu$ appear�#i_�� 9+�Bo4��9}) toge�� 10Ds  �'4 �.27 ,More general�.i� !⅟Z f(t).=�Ut��Q+}!t}5�I�-E1�JNi"�'}�Je ��df}{dt�+>�� �% �B+4A{-2}a^FD4I1qɩin R� .>) q�y2}}> seA�aC 1�s 5�through%4-�iz�ik)T �C*� A% �9 VZ4 ��t � L2=� y-2��1�8�$� b?!�By DT�q})e\ -$7& 0$e�6�Q�H>�%lloz�,e&� F mz� &C_1E�6!Z� [)A^2_2+U�-�t� )A !`^2}��e�� A }=�� � {�"Z,.�$}�0+a�6�1\&=&1i� ��mt�)\mmM$qX1I:I�)( )8_2+[-ZP(�U�3)69@A�*I�1]iB���)w>�-�JmFW �8��=��6%� }w4 ��ubu-�u�unu�- {\bf"�3� �e&�  n�j�1��D  0Zhangdajun200Y+R�e Fh3� ��+��e3�E�� ��e3�e P����e�#E ��e&Z F�4bi�k� d _1x-:\xi_1G �4�k_2x+42� 424, k_2:U � ��4-�� a=F�w ���$t����I2�a�F?&�56 5&%4&=&� N 1+� !�+2-&F�*9e[����W��k_"�t z}�V2( ')* �32"� }}{2r�A2�*M��F U� ����1��. %&&^�Z�������x-A A>�R� �|y \]{|N-d!( Repeated GpBip�8> -�8�&}Xtcounter�.({0}\hskip\p d�A,F$f.f_n$ �$n$*!"W b�B$g 9g_1e9 a"�CN93�&$C_1(t)�FC_n(t)p>?�s�1w.2;F�*�(Wronskians:f> B#= W_1(=;�;B�,)&=&det(U_{n_"$ n}),\\W_2ZF{n-1}6J� NVFN3N/f�NX6N] V��011V' je"4U_{i,j}=\delta C_i�' g_if_..G=3i,XFn ���ZZe72} V e�r i�F n-1,&j+n;�!��f �3�F�� 3} X�� jf_i�O,v�!��g�5,� =,F 1�lemma}i��+, m� +_Ni�N��-�4- @-_{N+1}e� DN}:H o"�J3mP9no�6�icity�d 6"~{l+k}[l�1 -l,+l]$,�=w2*, $0\leq lN$, $1  k N-l n19Vj�e�M�ip�Gs%&�g-um[m-1]%6 {m�;�m}( *\ %\ &C_m�LK�=&�f� {m-1]2]+ : [m-22�F*.� 2];C OJ�}{�51��i��.J.b%!C�$�$=$%!�1)t��@ a�Ip��^C�  :E�&��p+r�M�E���f�9�2�Y'y!i2���f�-���B�&�6�31 �4�4)�--�\���9V�. Q�*)36���B%~Aa \}�))UBa9:��2�"(NAccord. to d1� we9qO:P2j7"eV7"� �+j��1]=F2]} /-2�.��:.W:TM:�/ W@:S=p� Vp1#��1&b ;/!2k+i�1]=N6:�&�Y�J[�6�x�?d� i0)d ` )v 12/4e�M� fW� F� �^�^"0 ! )� w � y k�6n6M �1"�)fFp%�� � ��2� A+i��E.1N'12 /W*0x�y2Ny2�m�U0�N�a0:J }�N�&*C/^��~L*C 7 n.1i�2�\V �2^-b 0}a_{0,jvy�$$3�6R�J�� b�#�|)|�(Tj)$2� !8�  V� =$$ %$$\�7( m[�tcccc}T =!m1,1)m11m1} &a�E2:$2}& \cdots !k+><!�%a�L 2.ZA�+I�$ e$:e2SE#e\v�&d a_{�} � MO �  .��ke~ M|�2�^)m \1C)6"[-� vmatrix} �~~~%Y �56���})}1u-�:|-. �=,� n{� �~{� 1]\] \[=>s��6wM�2}&B�!�-DJ3 0�I�/1z5!v%�BdB�\[Ew0!BN�e�0��0��6�0.��!V�%+� =��2}R�R�01�-�q�1�% $1���F�N�N�IT-� y�����1,k1�0%>�1j�%2,k%�a�%t � .��?\\[A�1: ]�m� V�`B�=bZ�� �G0�QA� 6i0-1���V� ��41:414� � .� Y �L R�V�6�=\]�*� ������ b� |2� �S-@�\ula� 8�&�@s22"� 848)e8 |.be�=d��Z . \\�6�.F�`i"MA� at $�`,iT�[�`h�H�HE+"�H�,: ��67B� !  nd�g� B�d� D- {/&I:N&yU >%~n�$N$HrHF�+ jH�J�R�f&�F� 21}�[-N,+N�1 {W&�i '_N,�+*O-f -g;2�!,)}.` V 3+_NFN qjN��I��f2b �^U *� ����.$l1�Az�aVlF9)Tj9����Fa�J�"�)IA�Nk�F_l�r�r \lc l=��m��hJI�d E!�{m�I�\\Z&�2}�"�" C}_j6ŰJ��+_{j-B%�#{j165R(jJ[6E>E G=�N:�ykC w �GC�ZҘ2Fi � E�.�{ z ��:�%K���)� j)�����\\i% ��Nv`� 6�Na{f,\6��&�F�"*-af ^+_jmd_�K.wK�%:0��"&*�-AP^-.w>v+u �:�<& !m+�}� ��Q��"`* �� h�2��L �.����.?&tL[)2gZ {m+N�?si ��� 60��! 6tLne3�a1���}�!m+N$ 6ky� Bu #+EL(m+N)vGL�H!�!+"! 2M>!Mihi�T-So!=(s( 5l]$>� 0�r!, �!. B�[L�� e8�)^}&,��� �N)I*N-1:&N"��N} 4.({�a&)F4V>^.�)��"�)* { ~�h+�*y ; �6� �j-u��BN&Y\&g.h6.9���C_>FI)| 'n�L&�'�9�c.� ��-�- �b�2b9J� M��/ �/ 2/ n- s5)7, "�jF�M�f�P�1f�P:����͗F �u�ue]+^._JY�)�. m�]��Jbrk.~�^a2j�E��) E�� E�i�u���)+ 6*t.��Z�/�f*��i,j)P2�G}��.�nmb�}];B�=vR.�k��V�Q!��8V)=d\\ �Z�.�"U%� %'� �� &} i}�{^ y�}� \\�g���TN*5.J#"�<j[j]=�\ jB�j��%2�j} "Y�A@�.7 Ga^6\\ � C?-p�T�@$Vo���\R�2{}�||so���]�(Analogously�dMD�+r�"fF,-&Z )N]M�%=2B�JEP�|@z����,>GJ�( �� �-12�%1�� .� !*EM W_2 F(�^J�6����r�� >q논V=�9 m[j]��mTN� )�j.�N3�0NJ-"�� ��/6X $f�.y��N%�k�> 1J�}{2���6-N���!7�-����26fw�"b"ABe-�#�a1�-N�v�_.�J55މ{j�IJF%�B�TN'A�+JNmRM%AME�R9I*�2[1F!psn]j}[2 22R�1]; wC_2Jh .LZ{=rm6g _ m�k��B� U;��� 2QB^�U{NA")�_\�f�V�8�C�C�C�CnCE�, V, cha waZ6`}j"��A>WIf"li�ͬ�5re�jd�2{c2V ants?,3;$VlRLf� �Js�"� "���XjCW;D�!;F�W>%�$c�V U�U�. ExQ��> �m6mw�P O2�� ;"C $mCaa�l.QK&�&Q=�{"�8u(x,y,t)[-2,+2]F\V�*r 192��3  -_4;)�,�:�^�C!.|�' �.5 J&C-_3M�.K &#Et""nVd}x\\ �A�-_40K&� & M<.n*>L� �_-|�R�fln}v�I�^�+R mY1+e�1/` FkCi &2f'aeN '2M! (}E�D O ( O��c3XvU}}{�Dl_1)(k�2)}�D } �1*{E�E �+�D0}+AN �X(-k_2)(l_1-lX%l1�*)�1�ZT y*�E e)<�[?F � O�����+I�W �^�2 $%X=-Q�A�c$,� 7��&�> _��1���� �C&L� 2,qܑ���2�>>� � +��}FIJ*� wGA�� *�Ua-�*�F =�UM�ѤJ�Q�}{�7�7v7}b!)�>7bb&�: 9.X+�"�$ՠ4I-_3n��m�&�H6k_��A��EE 4:�����2-�R$1�=0� In6�,9 $\fo�Y N,m���| bb{N/` $N>mK �6� "�E�drJbB� BH� B)q(N�� DJ�  can � Yb � �  "� � �o!T&� �Xmixture<� expon<\�X�X"8 .**� � � "azwa(x-2qUXq^2t)Z *)+�a %  =qx-q^�Nq^3� q6 X' �t-_3m xi}�X"�Xh-_4# f xi=k7 -O d�X 1�Rd3 &- q+kaA�) -�% % �E Aan�y5�(f� 5 1�2shZ5�� �JW\S :� NW%Trm���A�P ��*� r��1T +q�X� (,)- K],�`�4�2'9�2(xJ��>r.��k+q�2�_0�mI� 6 }� �'��xiB+y���v�{  \ $r]�]�0A�!�)2�:9EK^2�\:�j5Non&U NB�m��?��$�*uj* .���$*�h J#^�72h[i#^��k+_j�Hk_j^_j�@_j�]� "�N+�>&�X @�� k��� bb{C�&$�]Re(k_j? �rJ )��LN*�]� *�\&ej�4%6��f�z*%����'!��&*�T9a�eN��P7�@*{ AcknowledgmentB�P=n8work was supporxQb�+�Chinese Basic Research Project "Non�e(ar Science"�:bQ_ Hthebibliography}{s9` ibitem*�l8} "�lx V K 1988 Phys. Lett. A 133 493NEB@ 9(1)JC89 Commun. Math. Q120 451NI90FF 90 J6A31 1106ALeon90� $ J, Latifi� B �0A 23 1385-140.�890�m  J 9 65$44 444-452~DoktorovQG 4 E V, Vlasov R � 1 Op!K$cta 30 332V2J 2 InverseA bl. 8!��$Zeng2000}  0 Y B , Ma W X� Lin R L $>Q<41 (8) 5453-5489WLinPMa2001} F, e�d g#%1Dica A 291 287-298R�\(Deng S F, CD Y%?' D)��PSoc. Jap. 72 2184-219._Ab��tza_  Ma�$Clarkson PqaSrs, �)Ev� E�xs�qQScatte�h((Cambridge)�Dickey  L:o"X(Hamiltonian�sDs (Singapore:World����c.jMatvee�I 0 V B, Salle Mw�T2�� �1 (B�k : Sp� er) .�at= \ E, Jimbo M, Kashiwara M�Miwa T�3�5W0 Integrable Sݐs-Clasa�liyAQuantuW�yj .Z(eds.) v' \�z Ohta��}   Y!"tsumaATakah� D�Tokihiro �8�Ag�< or. in0Suppl. 94 210hJurij!� d Sidorenko, Walter Strampp�,1UQPr��7 L37-L4.�Oevel�m  W,BWD3V�57 51-8.I�95}:�5ͬ.$34 379-384�a�g�k  Y�}2:3 377F75}.75V� 71 661-68a� end B� � docu-  ~Z\cAN0[fleqn,10pt]{�\cle} \usepackage{amssymbB�B font�@ icxq�ew�?{&M}{Deft on}[<[>�- 5}{�emZ'�O{LWVJpropos�M}P f/ erty , )Drenewcommand{\base; (stretch}{1.B?6%the"�{\arabic�pt�.#1�,width=17.5cmC� height=24 $voffset=-2 h11oddϐ.�+$Rq,*7$ R�{>� betw�{AKN�s� di�{ent� ���gE�`:% �Zis�poseda9 redu�9��A%`5�2� B�"�$ Schr\"{o}&Uer6� :�� (NL%�"zp1en�s&}to fi8p dark}s|, bHM8��*�|�!(r NLS$^{+}$A( - )|��ertئ�]se[�p �analyzed�\u B� PACS �$Ps: 02.30.lk, 05.45.yv ��{Intro-�f�a Fe'n*�j�f55�d�%� %agi�i�medium�ir�reson�� non�i%V[1-4]ritS6s0 b&aI�dof high-frequency electrosF^c wavǒth �acoust =bplasma 'jClau91}��m%�AJ5�ex�#- Q� by is&� :�nq�~mel92i��w&exp�^���6�oLaxa�resen�o"�� Ԓfoundr)Dsto�vG/R�>�:��quiS(om��d. Duef�im+!� role!['�8L u���>zy�e�s ($many field�8 physics, such\%$hydrodynam$id Ae,)� a�4 atŲzJ ome pnS  [6-16].Z rec��years�:�4 -�ed=r�� !f�N��� �a�.*.�euR�e)V*�&f1�E�2� lZ �Vd�-�=�I�091, Manas96},Ղaa�F҂>%�$ �a�n!!2��*Ƃi� "�,���ega6 [19-21]�h#�sF�E�F�PR rM^al]ylic�E)beLz(idely studi%�!�X*i�͢A��[Ţ KdVdm � A�r(,v&,ga�*�{� 02, Rasi}�A�!�f �2͝E�u�B�!n99@$sine-Gordo9�x0Beutler}. How5� �!6�-�except! .�i^in!� ,20])Z��!^ -W. ���paper�d�op%maxy�S�2 tudye�2. Fir% *�I.�m,>HE�V4 6�!� 9�;^>� ids �� ��  �*= N�n�e�y�I FI LE.��[|&�/�w O�)nUoadng]�of9 3 цƀ �n b� �/��J� A�*� ,.� E Bij)l�eQ��ar��� lE�%-&�, as [15,16] o&6SG�(a&�]��"�]a1aE�b����y�L$q_{t}=-i(qbH#r)+.��4n}(\varphi_j^{� )^2,gMr?i(r>r^2r>2)>.� ��Ba1 ~m�} =X-( 2 �W-@-\lambda_j&q\\ r& n +\� ) U�����n��� rrJ��6���$'sEandi�2ct�SxJ��sE� �j=>d,^{)6 T$ (�}aft��uA� upert�pts $(1ind $(2)$�� jE�f��$second eleq a^1 dim�o~vector� "_S)��h pair�� Eqs��a1Հ�4�����^�2a� _x=U�Iw U:=U(-n,q,r)= ~6)�)�M��2A�z9$t_s}=R^{(n�? � :=V.In )H9�)}{ �Y�}F�A�Jp� q5*} V:=V6ib2 {^2+qr& q-q_V0r+r_x ^2-q�$>>aG .�*>!��efV�i�Z_j2)}_j&1. )^2\\ -( )^2&;1;"J� =@ \!�!v ��a�H>��}B�"�N!� 6]�5t �d oU^ ��Fp [22]  �.admitsa��a�ar"�7:9 s $�"cal{T}�`:$ $(q,r�x&�:)�_n)$ 8psto$$(\� tilde{q},r2 >}P9n�Mw�two* Cex�u�* $��HMmu\neq � $f=f�}� g=g(\nbe^�(#o$ a2})%� $mZ�i��"�$2�`e\IoD-U1[f]$BJs*} .�psi}=T��<T_1u�fj� �-i�qf�(/(2 1)})&-q/e- 2)}/1)}&1I�>��h} :�6�q}=�)/2} q+q^wf� ��r}=( � %2Iq}_j�BT_5_j,f) !_s� sqrt�FX�mu�/�� 9P��; ��A�t1�2[g��2!� � T_2=T_25�gj� 1&-g��/2)}�/2���-r1)!� 0 ���OY W �6�r_%�nu r-r^3( � 6z�5 _j,gr�nZ� �=�M����2��e��=vam�͓ (wǬ)�VtwoZ�[�jY1�j2"���� new pblH�=TA+t�.q>r�s� .9u"�R16 * jkUa3aFx_x=oU} �F�U}*v />��K 3K ��S R}a :(:� [V^{(s)}u�)B� +*� &� [5xR� - ]2���T�aU���>&�aEH:�&-2�=�22$. Our�is" At�`aFE�KdV���X&03}. G N� ,\sigma(f,g):"]{W�}\mu��)U\. f):=\lim_��)garrow��: -W(f1�),�� Xl� ��)!(:2}|\# ial_ێf\� ,g�?�W{ :=Ͳ�A�W1)L- We a|o at��� 25 E7n�.U�&� J�� sV�y��3 a3})[ appl2-�A$i8M r ��� deri/wo��l� depe}Nf ���Jf Z�0�of $f$ ���b�!bf{YV.}$w}=fm� aW5o@J-V� � %� f_1)F 0$ (iD����feereR�)jn5]6U9]EsV�1 2 z? f}_1:- mu,f)f��E�A��}{n 1)�"N� } -q\\2��2a:�*} �5.$�Yin9�of�$x7 t$�m9�@1tcuN6i!���=� -�3})�1 �:m�Zz��9#S5� .} Nt���YA����,��/ ��$!8aF!7 �h�Az��6A�vLz*E}�ID � , f) _1�_>j} -Z� )\\0FA n2��mu�� b��Dmu)I% �)�Tak��� limit�j!w6�=~q�6�zIf}z���&.tV�5^rU�9}{-K�9:h*} L5�C��N�si�| come �!�RU�B�76Gh!A9%f}+2C2��r)C+�+!+� *2iӳR�QJ6�. e�6!2[�h}]�9E76B,$:N ,�3r}:"*=;|N 4#n)� �vu &F^1A�a��a4u hat �2*~h})ɸ�*  mu}=�;�6f��&A } :>�"K�J�� ��B�h}B��h}_2}= q +2(m�)^2>�.F ar"ֈ9} r}_xŰ�2 `r^2 �:2} =r /��F�:�nc2�U&�2��A�!�8}R�� = #�j�� _jJ��6t�1�N�ԡ���*�r6 }_��5j^5B�z� �:�nX.�<&MO2K$FFP$ 5-F Oo r}� 5*�Q:;6�HnW9�.Y QWG+�(�"i>���f��՜��&| � 6�! F �a��Ei�%QzWX � �_j}$ � : �4})}! av�$ �R�= R�K %-$64%K4&*�0Iq6�= %��j�ps���w.[>mb�mq}=�u���F��t%7r}�!A���c.�-����� *)zB�>�:��%~�.A�^]E�.; %Q�Q84�Q81# *} %�8 %\m9}ɡ�^-&>@2 n%B!��o6`�`ߤ��> 1}).��ov�����U�qo�r}=qr-"�x^2\log[2� >XiE �2���(�$t$F�N��� w*Xe ��2EEq" 5b.�`>��$:�2�by !3E;��51=}  t}�[+^�&�&)t].a]7 >� 6m +[W(/ Q+�[B)]"ɭ):�:YJ!�6*}Tf6vf� w�,5 x:k^/ : 0&4�&O !�B� *}L_"�"�SJ8"QQsH d�� lE2a�.4Uexpec+(at �ti2gǁ "s��#Uj��Af�F/�J �l,��Tll%mor�(*�-~�ju�(r�- it ab�A��u�A }==u {3}R�âwc�[$��|�on��qrŹф�f �+�a\�"�� $x$.2$�)wwY� �.�;$C$}�T&NV A8.�#}6�x!0� �5 ��1��$l�>� "?�)��2k�:��A�A *} L_������j R_3B��*}v �6*k �A�r.Z%#.= �.�uW�cb say $c(t� �l�efnoR�t$mheau ress(1J�  X�� , rH!�9�m�1wS2llE1�=Uu�.3a,�.���-UXBu~�Jno��v�QG A[�@&�3��Va $ un~�)-- b#"�-A>iY[lac | lead]Z�/:-u2�� pr�BN�=t�]��m_{n+1!�01-��Z.���P՚��%�5�6~ �bjx*bx* \bar)v>�>q:Z��b)*g^$ Bji� �^" F56 f�b1B���Z Bb� 8��v"�FU�!�:2"�b1^�!��A}I/\E#e�c�`}f}��� qy�6# �m2� $) �� >&��6I��abew 16�Q��(begin.��bo*bar��bar UI0  U. !&q� r��G*m {t}= <* +1)}>wY*.B!.9>6:%&% H(*5XV� F�!�6JAj$ Nx%^n�J�1�':-r�: $n� %�J�'freedom"�6�Bb3�b:����{%!, "/xx}�Oar q^2r��&��f.-gF2/ Z8/ D=/ qFG/T�.Y�,�Pbq#�HU/Y���%� r),N,/+1. %�)?J�FCMor�-�rR#>;�&�P��.�f+ ���E"��(), 6j&h��>�#�DE� b3SuP��:a*V �:� �;)� R� ��:��#>U�&B>���6=R��K>x]b,2����yj8BX;E���R�=*X 2fX ��:�}{���f; �>6�N��M�f�a�����( >��K�"i"#1 LAU Z8B�f��E��of"�.}�R$start from�>�2 n��b $F�R $q=r�Y C,��JK&� N 5m $f=(��� 1x-2i ^2t},�V+:)^T�by�I \refa ��#R(��=1R�q�'�E2�46� }{x+t+ak� rED.1�rDM�"%B�V>7F�"�9[>y\\T� >{I�� g>( &[!%$N� .Y��j.}68�!b�1�YŶ���:h�8� E��E�9R+:� .�a&p�involv�=A<<hv�BCR-a��e�>bB�*�(7�7)�Ef$, s�*them "۷a�'7$\{c,f\*\�M4Multi>Y�v�%VJ=F�`4e�knE!�6`:n `Ne�ppliedVV�Fs����)j$F6�^}Y22mUs. "�),f�b�"$, � ser[F�>AsM�?*�%�, 22�0c_1,c.be .lJ�U]���[N]� $r $��jMR *�99B.9�ed&]0. 6Q Gl symmetric�ms. �c��E�g_j� 3�%�.Lcaler0VTau7- , $h V3E-5�.g_i,g_j)-`hre �d.�� $N=1�,At �fv,#Ys $W_µ��^{(i)G1 $W_2 , $�kB�J i21Q�e�� {c_j�\/� llowF�*} W_0(01,g_1\}MX,N,g_N\})^�t A:WR5 W_ �zT;h VVA( c} A&b\\\U�)&h , ]H% �2�ɨr� 5\~�u��(.�)^T:����u����"�� A=(\��j}c_iEA�A� )_{N�N�b=(U�,1,h),\ldots,N,h))^T .�=(g1�6g_N)�J[-ͧconven[]�J�WE*{��^uA!VA�Ae1.3~D\\lV8~�hM;�N�u le.c�F_i�}{c_i,f e�$�2-M� ; $l,k�+%�a�N�rB �c�a�F+�1;� x,M�)�~ )l[lq� �'���i0(F #PQ�fAc�!�uZ�;�xl.�1lN� 1N����EI�dAIr�q6�4f24��dA�l\mr�rF� 4j�r%�B�F@!�6�q��bH��2`�j}�6���{l+i}��f ��l�y%0��:(. DirXcalcul� yL>���.#Vus])= �-ڝ0}�!Q�j}�1�:�ij�X6�F�"V1N�>� c��t0l�01��z�0kf;�� 121˜fɘ <k2<kkN� b��; �5$O>�0&1��&0�q � :o�0&0-1Ef6�Z6E=:?l-01�=5��V�a_{!:3=?RDF�1d��mi&Q��8Qr$H4h J5��)=.#) {l^u), \e�Ind{equation*} which is just the eq. (\ref{c1a}). Similarly, we can prove ( % b}),2c}) andHd}). \begin{proposizX} For $N=1,2,3,\ldots,$a have2sub�0s} \label{c4} �a} \psi[N]=\frac{1}{\Delta}W_1(\{c_1,f_1\}, vN,f_N\};;), \e=&nn b} qVk2^{(1)}~qq�n c} rfn2�nr�n,d} \varphi_jVv�O@(),\quad j=11�n�ge�{n+j}�X\sqrt{\dot{c}_j}\ }{c_j��f_j!� �NB�andjwfI %�Hqr-\partial_x^2\log �BXAg6�where $ 0 =W_0zA)$. V2]D\textbf{Proof.} Bye�define� of $A� [N]$e�Lemma e�le.c1},>�qm*>bqXeE[N-1]mJ )}{�.!)} m�?{N-1},f [N-2]\},u� e� XN:)}).���.times�(�VMrB��c��:�~{hf*)}:���0gives rise to%��4a��4.�4c��4d6�4e�� %QkExampleAY solu��<.} We start from� Eqs.�4a1}) with $n=0I���E� al %ID $q=r=0$. Choose ad \seco`{Binary Darboux transform��s for_ NLS Qs �Tself-consistent source�s$setcounterU8(}{0} \hskipa� indent It�F4well known tha�ord �AKNbQXd1} q_t=-i(q_{xx}-2q^2r�G r_t=i(rr^2�f�N� } ifa�set $r=��8epsilon q^*$, $=\pm1$,!n =�d!�(are reducedQV�-K!~f�2 �i(2s|q|^2q- �F�Will�5�)�2�+1$#NLS$^+$+�AK1< 2<-.<-<. F�)S!�$ESCS into e~\pmDvW (2I), bu| g!Ns !wPmore complicated sinc �M� ne)�b9�asE�. First�ǥ�Te two linear maps $S_+iw$S_-$ byf�<5} S_\pm: \left(�M(array}{c} z�\\ 2)}E� \right)\uto ZA \pm <* F1 A�2G��1�K !�%>ed%�X spectral problem, i.e.E�)�+$B$:f�6��H_x=U(\lambda,q,q^*)�F6k},�%�-�i7Ri-j:� } we2 o(following l��"y } {\rm�  If $f$���I��(��d6}�� �= _�%A0+>B offB-C ^*$;� re exists.��2G � >� satisfy� $f^{As=A5$ if� only $\R D_1�J) 2)� 7� -j FBn no��:H� J�$if $q\neq0 -� ThE��o2�ᗅĕ։+d� 6� � d8f d8� � {j,x}y5_j,q,r)j '>/'60 B� mB���#�ba_hihzet��* �� d8c��>�8+\sum_{j=1}^{m}�[( �_j�;)^2+({'}�A].Fn( �$�d} JB.^V�2)R� v� $B���6a �e_"0n 'B'%�6m$A�@ $2n+m$ distinct � tants.e!$correspond�U(Lax pair isfP9AOs>r�Q� t=V�7 .pm�[� HY)}{ ��5j}+:''_J('�y]� .onAE�.e%0j}3B� \no� \\"d(1) R �# ��+�} Let1D6�q�10jO$10a} r=q^*1SI'_j�Kj^*�m@RS_+ N��; 10b} \ \R-#=0 � {)EɃ }^*=1 quiv wN}JX�6" then.5 d8})A�"�� =qzk1nk1z����J+�P1b} w��-Tw_j+qw^*[ (=k� �@d11��i(26y .m��5�)^��6[ w_k^��An& system< 9})� � -ߕ�*�� ��1�F� 12} a�Z� M�"6�%�ps����.��i+m�a� j�(a@w,)^TE-M7��2b�-%M} Take�in1�ex nd l��Jq5��� )\ 灎��Z� iS_-�\R1 QF�N* �Q76p��� b�J�6z'!B� *S �(6e�-Ҿ-�Ne�*��B�\F�C.lyCF�=xisn�!�1�SC5�Jf~ ��Fa)�� -$.�y|^�BR�now-� ��� ��NL� . e easy�verif�&�stateme� M� � � Let\ a�$g$=os�Qe-J( $ nW $>�mu,\nu$ _ �veAHl�C�a�ex"� $ w.r.t. $x��. Q4�0sigma(f,S_+g)� S_+f,g�@�.:*'i.X6:jf>jf^j.*f,f);�j�C,f C^*�f\}ub��sFY;1S_+b$g�c�Ji0 �$&R$F% Moreover,�gies $g��}={ 1)� $ $(\R~0arrow\R\nu=0)MOq!=�W_1 F(\N�EZ $b�g>�*{ !�|J; $�x&T,q���|i�g�|i|-%"uf-eU\:|-a� *- +(�/S_-.SN} k*kf��0]-i-R.��6\ >a�;S-S_-R%�� kFe�-WJ�6&:��%�V Us. thisvq&!�  bi�����ښ4�f�� F  }'r| b� �2�a vI/ an arbitr�funDY�� ���s"�6�l",pr.e1} Given*X $(q,[ &�m,ww_n)$:�11}), � c(t)�� real�&� $� (t)\g�,�� f$ b.�v�6c 12}� & z�{n+1}$��P �#1)#2)*}$. D vl#ej-e,bari =3 f}{!+��f)} ($ uad = q=q 8(�� JB:Xf�e1��-�j�� jv�7 �.u�� e1c}��=w_{�J�5# 6�� *> J96� "%e1d � wM� 27#(t)}\,f�Fz�67�4 (new variabl�%�psiE�bar q$, -gy�=��nd ) }�$�� Z. $nw pla,by $n+1$. HeJ$(Q qXr�n# :��m+1})JM! �� �@��:� �&� w�>� 9� 3} | � |^2=�Bz$[>�Z�2N  # repe�v�.�3�be � > a secondzJf e=[�> ��:�2� !i� 2�X ����j� b�P" EeS"�o 6N&O c^"O $,��Qo6��`ej|)e|)a� psi= t^{-1}� Fx�%>0 j�n)` q=q+2`&G Jf0�cc�a� j����R26� _VUe4��>w%G (B�;:, .��-h)�EJ=2,}\,(c)|)�b�Be �'6X�8:8��"�R<�:m2: $m�: �:� f>�<R��<6�<)�: -�60Im&�(Zu �2 e1})�*$N$�_��V� �5e44M 4�" a gene�#multi-:�Z]�f $N+M>� s�V�s 3�s �s f_j�c�Hoe)5 v5 �95 j�7=0� &6 � = : , $*� N�> g� ��a��.�# {m+j��, .�M$��c_j"� *[ �� 8� .[N-�d')�._F�.C�F���.,f_j\%Gd_j,g , $G'_k=\{d_k��..�F&: F_N,G_1,G*!G_MM�;��p^�7��J�����7� f��y�7~�u*�$e7�1!zfe6��!,("�0�f��g�F�MF� b!e"jF�{��:�F���7f �� n+j28d-8d02�8?2Fu F?2�4�4 {m+M��+N��,>:m+M,n+�.�6L �L�,A�R� +N� O�0$� r&�� �� 9� . "2%&0%2)Z�2�0$^����znotc2} 61?T w. B�.twoP >:Y1>� 2}Bzv:� 2S/^&| ��2� *� 4}��:� hUc6"�f��"+~ 6�� d1�+�&~ &�1�.�1' "Q2JQ.\"-����n�'e�'a�NR{��f'bf�Vh��10~�Vd���10>��6�zg=��hJhw�R�h ") :�Y�N�,*���12F�+\Rc9��R��e abov^�"�~&�6`7&u$N$�#�~�*�NVx��.�R���B�"5s T4���^� ��n� 29 N$� Vx N Bd  $F}' \{-c@(8k 2C�.H8 F*O c F'_N�K3��Z�13zQ N~�N3�C Rk�Q3~Q^P�T�T3>T,6TR% �b�� F N� 6#���p�p�he��{m&� :r���/.3��6� $m+N�� K+>���\sy'on{Sol�:s� �:&<��� }6�<T" dR$ devo�9�(obtain�tsome e.=�1\�! bf�<7�xanalysi"> seO.~)u4ubscripts $z_R# z_I$�indb:P-�]bimagi�" of a"�(number $z$.�C�\forall\,z=|z|e^{i\theta}\in\mathbb{C}$)i$ 4\in(-\pi,\pi]$B#�$~zq�|z|}\,V /2}$#�j��"} B�=We%8c�=de*n :��E$mB8F�>N]-6o:$m=�-)���5�"f�=B�0>e!�its5�fRq=(=\rho e^{2i ^2tF�j5rho=�R}<'n 5.�?j< solvI)2sf���,.�'t:�-�G5��D.�010>DB 9funda*,alՅ matrix"� 2���f4�1f�$PN)=�)-�(\kappa(x+2i t)+5�&( !j-)e^{- b4\\ J6R5-i-�V_*I�2�=B!QV�= �6)�!�* ^2�^2+�^2$q�ub��}���$n=1$.J�!�.�y�8��d5�6�q�5f� f5a}�"1�:i\Bw_1+qwX+*F�^Of5bJ:B+K2B�J`1�ellXi֥����89^�2� f3}>�=�)>&4�$�=0��B$!6��&�)�F8'+ by P&GJ�F�,.�v�n�� n$bs6} N84&(f!�(1j�&�&#$je%DJ&B�� $ f7} �#��^�$FE�#cases: $a�>|AA|)�< ,�'mulas�:@ll%mJdifferTEclassesL#&�.ID: dark one-soliton)EA@L�)Z�:DrMscatter� Ferty.}�2t�5B��5��_1��E��I�D�F ${ ����E� '1V�J�3\pm 6�rO$ alytic at&Iz� L� HrhEell^2}> @Tak��D ac�F�FA a& lity)����6} Zё}$ hold�DarB��B1 f$ a�To,<*} f=�$[�/ FWD.y�,/�\\0��2��5_9=),oJ�.�he^V>�� =)w6� :�rP �|Z�v�_1-E.|_1(x-2A 2]:�_1+v:r�:�*}�jna� findsIkF�B. CalculE yiel�z]&"+f)�Z 1}{2EA|��I{_ ̀&"!{m�} \\$2)^$2)J�| %I�Js%\]_1�:1}&Z\,(�+d� \xi)}{dq�=��!1} %-(2IO_1�)\\>z+/:z�z+Bz %p)vM�m �\xi�-�a�}{}.*]�>*}&=>�TB s(at+b)"YTo� , $b2� ~/� s,�nR�= af�UV0 j,Ef,Ejv��i� }�& } %y(2n)%+2>})}= I�1-o 4�1xi}}{1 = 5�"K B m�q�"�,f�Ewٳ�Sa>�}� !򵗙� t)+1$ 繤} {���_ f52i� a}\,<zxi-1} .��~Joe26!� >$a4_Dxin _1[x�$ell+a)t-b]0Dml�arcsi�C1-IF�ByQ� �f7�Oone�B�9�+rv (Y,)"� %�1N(^2}{\cosh^2ARB?�V show�Eq $ de�bee� ag�G�e��F on�q� backgroua0rho$. u �5$ocalized a(xi' soL!�� C < $x(t��-� +b$.� (,velocw is $� +a$.�Kal) w_1\ED�'$q�fin�I1��@becomesJ�! �<\cite{Faddeev87}!0�N� �X1�O� fix.b of7B!J� ]2O4 0(x,t;��)�XJ�)�_\\�"� �r�a�e�:� FkTiEF�1>PN>��2RHSC%'4% 2�"3#0�%psi %"�G�2�2- :C� ;FSqSbDis��N*���'%�f"� )J� ����- \� JV6� -/� ]h6%. ro6��txi�V��m �).7} �V�>�G!�ZYfv-%J� 6� u}&am^ & �qv �2� � (G^2)1� >_1 a���ɕ^2v�Z�rho� � X=�- �) � /r�b;:F} Based�hoV.8�Mw�T� alyz;asympto�featur&  ��(.. �fixed $t&N B��4�!B\{M1)�{ll} !DC 56([1+o(1)],&x� a6@-\infty,A��(\pi-4z)A�~E+ EF<BO �Q��5\1� �K .�B�BZ%�se!�at��!n�Bn��� %���)$X��at:0�H!�k$same %shap6e. �}0$2���o�RZ(ce %betweengm����"_�T, T is Fi:ervyY $(-2!�,)$A�Ul6Dle+s valu= 6-�8aer�V %$a�*D/ � ive  V.VY�E5���belong"qN_�po�Y ials�� the �\e densw b y>c�O�> j�-�� aG(i\alpha_\pmR;uL��2�pm)�mQ[�aU$2J&$-)sEw$\beta �y� ( >+(t)- -(t))$ i %a" �Ope�Z!>$t$�ow�!;./ data�9AD�9=wi{?i6b way)Z,Matveev02}. F�X $u=q!I-1J�&2u.=A��dard 6� J�j� 7} u-�n)5�~2i%�Y21m������ Y Nex6�Y�\missio�Md refl� coeffici�Ham% ��&� � f 2� hi_xV� cJ�&u\\u^*& F�)QB���$uM�{ �5 �s 3}) has@��WndU��B� !�J� w rho}�  }\\1J��� x}i�^P -1\\j_V\ ] !1��_le%�.+aQ\R7"B�8Q!4ta)�@j@zc�HJH�Mw=Ldiag}m�� - )���Jos `7$A�" >iIQ�%yby im��nge}*� ��jy3 phiVw} j_����F�� 6���A��d�u$"�,E�$b�  re determ�a=(estimatB& 2z!( .n1���N� +.�zj��F�6/�$�^A�cDR��G!hb� . I� ��ase�� �" �u=\pi/2-2 $.g� u��i�`��"�aMsi$���-& behaviorB�]�R�Z��  �$�5*5�Kb� 2n9�՛v8Z/!R�a!"����=�#f#j)M�BtWeE�A2�jG]�Q(�$^2t���.A�2i�� t:VB�y~�0f2�z�� )}�-�}QMyN)^ih��ʒ)u�a"�[��� 30} .��%� .~=0BP �b��a*& less&� ^;"2) OneBj"��super-&x Rro@"��E�?"'#: !B"=(� sign[S _I)\,i\�� �#P� nB$�RDz"(�)=ik_1$,v $k_1:� ell) � |m69. "�iperiodic"� a�6' �} ��!�" 1\\-N� P �"�8�":/&KB4�Xz4Җ) )� V^��� ar�g �-|BE"�q�- ^E31z�� i(\T�-��x}-i(k_1+A>%"��! 6$F#O`?a �2�B�U $ �=k&" t� On�"JBe�I>l *} (:" )^2=��[-k�llG�2 z+i(\sin %!')]ej�-F�s�Wf)B�x-2�^�a)�t%9(2 ���> L*} q��)>iW$m��b!}�TF#Q�cnS sT ](�!l . (1�6bՠ�>�jx!=�J�� [�3+�-d%~=cA�b� gammI�f�m�r5J�_!] �U&S+r�O(:aj%}�p � L12�q&iI�}-��1+. $-%�>��0coqG 7"� B���6��Q.�%l=x+[a-2(a��}6)]t+b:d*`l.� �:M�>e� �Tf3�Oq�O��K;3*t[ �z�] @1e��2}+��Ez� Y=C�W��At{�>}9y]^�%_1D} W%�=� & N��F� .32}) de�I�o To���� 1}jQ335���2�.�$}{x-4� t+b}, �a1 8M�M� :B+(a E)E:7Dch waPinB��n99AB4 �>p �!8G b "v45d56�#%fF�h�P{��=b� > u��v*v -Z���*�UB����:� {[:� (eQ��]8mՊ���b"i:s }}{E�(. I�)a��� q�>�6A]��eftN 5�� b? �5�/ :XfBE�NQ�4VS basicBNN*IB��lLV�uori~6��&�a� *��� 36} a&:��+[.6��rK]x� [1+O( )]F-b�7Z�.U�c9(�� ��) �2�> !~�u�h2�+_+�Wowea�=s<�='(KG[is 5t�C-�$*1 Actual�c��'��>�*y3�26�:6�a|>�'wz�Wf38d4^2+� a�v }1.,2`B�Compar�W!Ed^+3�NDA verg�o�: *V)0slowly. As a&�t|�d:�a��sT!> $ sh�h$the same f�v-or�;0pole $x=x_0(t�A�se�icitly Fl��J�%Tell[x_0��2 -"m 1}��]%�a��wx_0-4m� tV 1 uniquen�� $x_0$�be� ily0 ved.�.� � �r�c� ]�7ieB� *}�.6��a_0-(aF -b]R�is5i( 2f!�a�a&;� !!$tcY $!�q%r^3q5�A!2�"aK"$x6A=A=.4#ca?0oncentr�Z�+4Fro�|�H�+4"e# >m#p�o�Jl  8} v,,v(t+T)=� x})�[E�e�]�-a+&)I +Rg�T�55,C>agaveraged �&�+���fV�T�?t_0^T �dt�1�,:6-aJ', In Figure 1�]plot aVl � �L5�,��fO}[htp] \!��7� \includegraphics[width=2in,angle=270]{ �-1.ep�A�52�53�5��cap�$8{{\footnotesize�.R�rB� ef=5~�#aŨ=3>3a=2 b`=m!�s�rtaksc t $tAK:upper %|s �/E��$��i2[BJ$�%":ly��l&hQ:lowJPmodulu?Z1gy!�VZ.}� M:�.�RRi]�:XvP0?C� D� �A2((.��?$� $q��� �  �!gin� �}M� "� �� *� 6x R':�*} AQ�2 J_0�hi�&*}r pk!+^W�*!]}V���!V0 �7=�% *^ %�'2�1 Mvi *} P&W)wB0&.}& $bj e�*�& *�& $a=1$ �5 call׀WQVor G� nt&5 sKM&P(�is�!�V�is�6u.ŗ>�(,�����4(s long-rang�+alogo��k+�)  decrea,j, oscil�:ng,�3��non�&�+grEe"M s.g]stick �@~��Jk�R%JA��c�� uld 6T-�Z�u)��0.� we&�+other �"such j7�,)�^i  (still valid�mus it!�!eon%9to extenfw%�E!+���]: ~�,1Zco� ing, R� of~� AccA�g�8l �e�S�W U =��&� I �sub*R�JIUPi�Y���He� $n=2~DE�J!�&�=6� 3] >�w_*KE_1LE "z��! 2,x}L_2w_2+ !�Vv>UvS52+w_2^2.>��6�n> _1-= _. r�"r~�|-s��P2$,UlfkQ6N4}"� ? -j �� y Q�E�_ 2)*}��B ^4_&S���E�Q\�l. � )6 *�E D�J�E� *_�!�E��H�6aQ 4j$~f4$~N�+�2@Y�2)"�Ef_=f -(c_1(F<k _2,f_2))($)^2&22&��&;s F {BN(c:@ f��u)2)^�ik�J�9b�v#.�� }\,[^y5 >��]�� �:r�c�2R�!~ �6�-a�F�-��� ЎM"�u��416�F�kzS�~MCbTF �/s3 �<�assume $�G _1|> 2|$B�� re�6sez0$: (i) >j|$�U2$, (i'%:A (iii) �I L2L>R40�"~H ��2]7�+�Wsp�&�yvH�\� ),*�.�7-N�n�HNo�H!�$]e!$wb5FF!Q&\61TGa� �VG�VG_jj($��k�N_j��U"�_jS_jt*d%i82=O:n=&��2�:y�" �= m�H*�I%i %!V ��'-��j^R*߄��*} c�-��{2�BjW (a_jt+bƅ�P3StD�5\>�A_j,,"r>��a_j>LE:m6"�C *�GJp�.j�f��qD!�6�/R��2.RK#(-1- 2� %�1)�2!])�&�%_1��I�2�2t)},:�&�!"{$�[�H\AN�1Z���B�qM1}��e�B�:2Q;1}&->_1})& I1An^-J,�G+2}&>A�\e�i�=t1w݆\�ooE�o�2.�2�u|�2F�x�\��V�VY'&�Fl| �:��0�6N��Y��!��F_1����[Bn� ~2~2~ .�&.+&J,|:J{ �# �Ek�QVe"z�6�5q�J�5 �K\\�!�2�.%I�.�6| a!��-��F�9.�5.#�v 6��xi��Fj[�I_j+a_j�I_j]�V� aF4�*} WqD*B�VB�4R4��.mf�JrFq&(i�����1TwoB� X� i��aB~} jI .p �I I �0�A4.e�/>�0_jfD'>�&_j�%j�%_jS/�%_jZ�&.-,B�&@' �8 ��2a�/ _j=k6 a=k_j:Zel��� Q+� }$d>f*} ~ H _j(k9&o q O_j,_j-, _j+k� r{"!,_j�\e�:[�q �.o"�0:?�+>x �.�[�%�(2k_j �B 0_jG �X^�F��� �G1pk_".�M!�"� ) :#M�1+ 2)-E�_A2_1�(2I�2)]��sin@-@>� �v*� Fo]6� y a� �O"��6"q*A6� }� r>u_-2"e"�:?- )��1�\G0_22|Z*1.+ *12�} C*�2[<*:\= 2>:^2��>B 2a x2��j� 5)>�59�4.�(kB2���6�2a_J�6�5Z-E1 �F�*���:�end:��Q�}%M�}1�j=�0�;�F�ABt`)�P_1*$! -1}-A"neq-\^�(2�$� #`Fix-B&1�let�k$t.�*I (6 ;��� +)�>�er *U*>�+Z�-�^01(-�'6� .76�:�) -��'1&�-X-&�1_lW"� *t��:�^  + P{2r4 ���1F42(n/_1&4���b��� w_2=O�:��'6�C�se,E�DU@U{Rw�n�IPqx6cmzf45JvN�U8q+a.�26.��Q82-]82E8 J -]8C�85s- %�6M2jM ��1��0_22MF(UM2]M��jM�8T� w�-�!va-��!0>c"ays� o! !� P�. asZl� ^h(�lliJ� ~'RJ�eteNIsen��ve. Ev;N add} 6�ha6j hift�Q cb�wo8.6#abs�#^^3`? 7R>�! �!&e� *We��Ly&� I�"�����2=4j=r� =FF �.��FR( [R1b2J� 2>:�Y �R*��O} ��g>�� %!�)0H:�Z & ]1Z��)F�zp�hefrp[� 2�BX2YSF�[ k�C.5 %��_V-7"� !�,Y[�v�X��2rDCIm}-�n>C1��C=k6 k_26be2.z2&z:*�`J�V"MHE."� Q� (a_11olf*�]_1+bt-b_1>� _6� 24!"2a (a_2s2- 2 2 2+k�)�) ���* ɣrn�N�!�h6>MV�#N?a�_��:͕�f ��-��} [.�� *:m)�BSr*� ]. %� A�2%&x+be&� %���NNFSn�y!& pos>*:S+q�Z| 6R| e.�C�Q�?�>��Z�-? }AB-R�(e�"�F�-�/>�d6�A&)�-@e�)�.�67c�� }B^2��:Lq2dd}AB2w� z� Z�6�Z.J�!M��f�!�z�-B7 )o9�}����<6�^ &B M� �q;��0.,�7A=%"�RZ t�M�&9�?.T*AFM :� *} B2�`A4�B%CQ<&":/4v<';r!M 46.5~�'�z�Z�6�F�69�H[ML�e�-]2=[F�- )�-a_2]�-b_��$�>w=� z56j�I� t� �-�:� $�J))>�����Q6R r�kq)��.(b�+��au2|%|��?�O74} �� �tf����.� H HF(}�"H�K g�`�~�wB���G���25�J]N�:�͊6���.�SBI2� (�@:�+`��3�'+AB5G. �H4:f@F~,�+\dO�+ b�-�N$F�b� v�G�)\ �I"c C 7�F�" �B12 ^2[Ei � :�*}�5���^-"AD:�&g��.)�)wf�ƭNh3ju�k" n� �}�� +�1�la g\:tm2g .xm��%�t�*�qz���"�:�R�r�o n{ �9���u �l� � )&�5a�large �a"�T m rec���co�� aft�~&��3W,~J�7 words,y. iCct�.l9�KdD {. 2yE?gains 2/w%L�I��A�N�l�k9@2v0L>(~]"��=��? �"\?��?=@z�?/�1B�0Vh2X�"�7�%H[61B;A9 2�7M,t*�?�}2�- nd $�(a_2=b_1=b_2"�?��?jo%�>Q?�=-15$ (�i)�T�?n�)&c?elFd?\�8��}N�8aN�n B)��)n=N�q85NQ6��4N_j��q8�.[�N:�J]Vc8\&�N �^>HR��-�j8?Hl(��N2 re��bs8RB5�}�z8z8EoFr�o8t� �y8$9"�@ O ing N�8A�;8.�8b~�8� " $ 50})g= M"5?6� 1!f5�p> I NNB�)� 0�%��}�.� 5�w�!G,� �}h\, ^{1j�k�!Q4B�W@6�E{>@ &> �*_0��ne�g + _2=W�A)w�N&1��\{c8�\};B���6�)&�!2��Rd{j~�{c_{j+��\�F�f_j>O*}��7z1�B�*6: B�7 �>�7N�7T�~���>e&M choicea)�7�ib� *pk:Y7^�1) Mu������s��Cr �&-8 ĉ�ndf�5��)m�"� bv5��;7�;7�;7�;7�;7*;7Ռ�j�!�=�87,�B�6��B�6� >�95����a ��Bh^�2Q�>� F�L ƙM��2�+>�,��\���r.�r.�r.br.�Am�X.��A�F�\A� U�$N$Bi^�3Q��3-٢^�� abB #{N_1}|.==~���$ $1\leq N_ )Nb-#�j�j�j�&2�_1:�b"�;��>H"����aR�3��� ,�� j=N_1+"�> Bހ!%3 ��m�� J�� U3.�*�XB� We��58-�\N�u,�h$&c���EB�afu��5�GFs]=[�+P^�oc}�r\\ 5L��:w\&R(΀�J�B��v ~܂�\)��Q #.!��^2$q~~Ii�eL�J1?B�!�PB.�~�J5NH"�$f52)��U�_1"��ڥ>�JPY �-"!�q�+(P�I�H.�)�t�" {1R}+��_{1I}�Wc�&ž-}.8�Z"Ƕ<��Xf$ R�6Keh� \= �j�f I.gz�`� ^W�4},J�b�&A�fj:�}�7ZXjD"��1�.��}&S�$F *NM\\:A�2R V�>6Jt0O-J�<�"�8 ,f)&�0|ci |^2+ 2) a]r���%1%n1&-r^*"�5,f)^*F� |=-|*.�|^�%����t�Fb!)��-�bAR��F!p� & 1Gr>�(@<6'��~� �* �2^��q�VX�i-B�c}��19�S�I�&5���1)}&J�JH?M�oL5:�Z\�_ y1l}&�?"Ө(TopologicalgSs�G-b.��c �aB� !�� }*(�h^(�1\\��1�Mj�1"4u�W_1�.&.1%�"�&uFR)�%��H��1 wH 21X>k ��A&/�^ Here�:o�2,)6� xI�. ���}8 � $ )U2\�55}C%� ��%"�rA� domain %$y�C}\bXslash(\{z||z_R|=0\}\cup��, |z_I )�nd ��is l� �9�$. FurqV4� , un'b]U.�%%$�9�x\lim_���`&0} )_樒�NO&�:0N&�� �z=| ��#)� _1|^2e^{2l� eK � IrL�_�a�<:$ �[Q��8�_%_�:�:G2Ep� �b|L�&�� g�s� �c.Ml5�mh tf�F�B 6���f5N5#a� *[!�� ��-�V:-�lta�j9V�NXI^* #J��%V�}�#�� �� V� �30UdR}�:V4]_��R6$�#n�}{4N|^2�-9 �nb)etDqI�t�)+%� �D9~i �42� � )M� �.!��5N�6� *� 9��� � ^%�&���y&1�6�q3V�6 )\xi 8ta&�5’)���(VT-')>� �1 �I�)r�����%�&*"39:�nn9c&��!�2)��%��u�^*9�^*:���^Q��������j�/ 6��~N�x"q��G(2�I}+a_R{7R5A���ix.�� -a_I1IFD�4O05œi.�a:R"nla��T�d*Ut��[2�^2V�ET�*�IA|^2zH�3�D>-8� �.XmY � -=1�B ����#529}) co���(1��*y qT,=�Re.�I_0]��!2"H#Z�2`�EA::%�F���2,0��_0}\\�4Dj���*\h:R�a .,) ��*6N�*� 6.a� N��-~�� �*2=�< 6�`V���n�j��j2�j�&+"�cd"�Z !k*�jR�"�_E���>�+-�F�F�&�,\ F_j'F��,\$ R  j"" j&� �&a?\:.�&�--Y�V[!6^�%� ^B=Nakaq�L$N"�& of2Jd6�_j�*��*�  ,*B� q1�.u�]�� ?0^� �*� "z V}�^bM):vn� ��+F_1,F_1'HF_N'Z�+0)��N3��+  �l)�+lR[t+,F '��j~++1}', -�z+-$l=1,2,\2,F\ \i*{ Ac�� ledgment}J}is,3k>supportA� Chini�BuzResearch�.ject "N"�kS�� ce".�� �Ithebibliography}{s99} \bibitem{mel92} Mel'nikov V. K., 1992, Inverse Pro�� 8, 133A Vlas91}  ov R. A��8 Doktorov E. V.S1,`l. Akad. Nauk BSSR 26, 17.Y> 83} 1G�> 2nZ3, Opt.Ty(a 30(2), 222� Naka� @zawa M., Yomada � Kubota H X01, Phys. Rev.��,t. 66, 2625.� Clau^ de C\Latifi5Leon J Y$ J. Math. b32, 3321.V mel8�N�$89, Commun6H120, 45FHbV�fH6, 20>H9��N�90F1B61 Kaup87}   D.-87Ji59�62�!S 90} 1M)�fi, A)]0,%^)� A 23A�82�A`95Z` ShchesnovX� V. S W5�LeA(A 207, 15�yV? 96} 6H IEd}:AT �]213, 6�a��MJ�0,BQ1, 1106.QA�899?a=88B;2%z12; 1!� :�144, 444.ZZeng0� @ Yunbo, Ma Wenxiu%�(Lin Runlian!�0F� 41(8), 54%R�fS%� \19!� Actaq@Sinica, 15(3), 33�RF�qe� �K. BMFS$r M��!a�{\i&f�Thr��\s S�Ts.} (Berlin: Springer�'�+ManasE �~ 1996%})�A:�h. Gen.%�776!0�p 1 6f Shao Yiju)e1`�i , 42��11A��Q 03} YL%�$ Xue Weimi�p 2003] � 36, 5032hO$04} Xiao TZUef 2004.H , 37, 714��LiGuZou�= Li Y�a Gu X-�Zou%S 1�ME �Q� UVM 02��sa�B.E�2, �2orQc�( 131(1), 48�5CRasi} Hnariu C, Sukhatme U� Avinash Kq~EdN� !�,E180cd"Ӆ  S-Kovalyov%1999, ��:Z32, 616Z Beutler}  R�)�2?(34(7), 3098.F"� FaddeevL, L.D. and Takhtajan�uA., 1987, Hamiltonian Method in the Theory of Solitons. (Berlin: Springer). \end {thebibliography} \end{document} :8 ��\d &�class[12pt,a4paper,reqno,tbtags,oneside]{amsproc} %%%����P \usepackage{amssymb}> math6color2[��links]{hyperref} \setcounter{MaxMatrixCols}{10} %TCIDATA{TCIstyle=article/art4.lat,lart,article} %TCIDATA{OutputFilter=Latex.dllSHVersion=5.00.0.2606�0BibU�0Scheme=Manual$|Created=Thu Oct 16 16:43:52 1997+ LastRevis /�rsday, December 30, 2004 14:00:38;.�Graphics��322�`Language=American EnglishVCSTFile=m .cst!�8textheight23cm width16(hoffset-1.40topmargin-1.5$input tcil!� \begin{q��} \title{Gurevich-Zybin system} \authorA:(im V.Pavlov�>ddress{Institute of Mathematics, Academia Sinica, Taipei 11529,Hwan\\ e-mail: m.v.p_,@lboro.ac.uk! ��abstract} We present three differDlinearizable extenA�s� the 6� ��<. Their general solutions are found by reciprocal transformat( . I�ois ��( we rewriteJv-\T as a Monge-Ampere equQ(. By applic�b~ tx; is 1Ped. Infinitely many l�.0(structures, 0Lagrangian re-i�"conserv lawsŝ \0commuting flore %D8. Moreover, allB)abe !7ten!R,s similar tof^. ��:�1z describes@5�!g4a large scale 9�P UniverseE4P second harmonic waveMGAA< is known in non)� opa!!�)�U4 provA2aA�^�isA( ivalA�to a deI�te case�A�>� %ion�us,& 61#isArognized!�2f4first negative%�4 of two-compon�THarry Dym hierarchy up�4two Miura typeBN A f�betwee!:^!( 9 ��M�A new� A& vU!4m.e� ima�it<m.* �� \make�}< \vspace{1cm} M�mem� |Professor Andrea Donato (MessinaQ� ity)>M\t� $ofcontentscA{Introdu }i0invisi�< nondissip)�:}\Delta h(, \label{1� �% wher�@em�ah��usual2�!(1 $continuityeRA�Euler, !�ALvely), bih�ird���4famous PoissonF . At lease' *�^timKs��, was derived!�(J.H. Jeans =�j}� also-�zeld})a� �ȡ�pa��,instabilitieAu a homo�-�distrib/am. SuchYrof,i1,onless gravi�;ng gas�!�a special limit ($% \varepsilon \rightarrow 0$)VanotherM� (ig�$\A�$� unes ial)B�*����e^{E�}-��Q� *}% m�!6fully}�S in aE�te9 a� unmagnet�� colli� %�plasma7dim  vari�s (��0ion-acoustic ��s; �<forI,nc�I sagdeev})nma�dvantag��I�t�i�9reckon�of�(factors: a I4 y at� %Qs�,r�� lumpw clots; a�},sure decreas<|Q�a�oA��$��0. Recently a��achievem�� -investi��oEa�H $ (\ref{1})e� made.��w,in Cosmology�e9� one-5�al2[a2�i� a�b� ��QBsm�gz}F��� uu_{x}+\umu>x��}&��u C=0��3^�i�=9 9$�$=e)analysi���)`3})!G$a multimod� rm demon# t� t� i�� from%&.�� he��(ilibrium kiaC c stAe�0. It m�\5 �  exact&" A� N��s�m�eA�fundaARDal physical proces2� gz} againa^\qquad�aAmazA�t � �p it{iU� ous}6�j �J9H'integaWd,� h�EaGularity,�xAl Hodo"n݂A� . Fo��F a��fur��we wi�  Ki;�zV� emphasi2�B5re� S-�2ka�i� �bla�H? we g� ��.- mdof5{Re TAw" s}.� w�� >�is6�a with�R��� c2* bX s. Actua�o thes��eI�< have clear pure�O�al (hU)')�U�(N}�V toxe٘a�terpreF�I� next s} onFV �srQ�Qwreli�hip�  tw.MAiz)A1AWH�-Saxt* %'aV� is e� 6�-Brd�r?�\6{� �(& Mapproa� evelop�p2� )%�foa��a bi-*k&O1 b��:�� 2�(Yavuz Nutku�ift���A.Sa b,� �esta5u� operat s; ed. VgB'b:$  &y�Q=B� %.V�L:S �.@5�s�b�f�a~of D �'*��*�.bIn six9� a 6 O mui@ E@b��] cankal6�f8re6�Z � N �6�J�E�seven�*�andfLs�j�AKaup-Bou�esq=i!�%� U݁�fin��&@�bOeq�@ "�g P �K�above-�ionedx �/.K &W�:>F`isQ�InaNclu�  w�scuss}u� rtW�bl�hoblem!~ long1 som9, ��<"L ��{G�lI3Vfc e n onwmz al�p�}sely h 9B�2�p�al( vuBmk� VW =0%:.�x}\."\2F� T*�6 )�lq" at�}a�>�As:�narray�� &=&:U:�,mu ^{\prime  }(�R�1,54} \\.�N��n�` .�B)�)�5�� ��'.�C.S� , �6U9-��$|(z)$, $ �)$ �$C�� arbitrary$ �w t � rxng � (is not obvi����i4*sA*/&n�2})�gde  BS� ) j3}Fp} z3zi�� .�6�=�Q�U� z)=01cex5d� }%!"�ly���poi'2� .zxB;z)$. OnWH/. :�}� � dzI#dx� udtB  d\tau =dt��7} Z!"}%��.� [z}MVt}=k z uz}{ B���\A��J�$(\frac{1}{e})_l }=u_{z}>�\��� }=-z� =}��8Fin�va�, $z:^㭿>�6�8eCB� *} u6�Q�]��+D�� }(zʍ�}-4% 16rU>\^{2}/2b ! iau +E} �,6[s-+DA�E reV�Fs �N-I"��BD�8iveaO6!=d�< u�_2��t= �ex�g}A� =[nF.MnStVO]^{-1Q�A�notag�=x��Bs�.l�b9� �W &=&(.9.�-zN �E )x(z6�-A )t+zY<�-A��QB-���z� a parame-� . A$ � i�BC!�< �2; 5}) yieldR��x�b% q�\2�z}"�/AQ��en��}CR2vIf��$qex�i��ex@ sed �algebrai&�}$�`�a�=G(z)-\]!set��{\���d$d\theta }{ Aw\sqrt{2( B( )  ^{-3��7-F(z)}}f; �;�b�@��8!��8obtain�^�nce, if T  )�$ fad��@lreadyS by �9}) (rem&R  %� sub-H I�sf` � @�$oincide if"� ,=z^{4}/24$);RX perturbed� :�+\d�Iq $ ($ =\func{]t} $)�l-L2�UOP via Weiershtrass ellcU�R[E�=ɤ }$}{6}[\wp (Ex-!�i<,Qj*3� }% 2FA|}{36}A66A�5 |6}U \wp ��`E .�z}=1- t36?}�!�*��V�)�7})r� 6}) ��^�n� �u5�)\ � ��)=z-�:> ��Tz5 &�i.I���� &=&VB �}u=:�.�ѹ���Q)E���uE� &=&[��7z)*-EM/.xq + }=p }{2CY�.TA� "����a�?N � .m-l/2��1}������b��� $!����rse�'�$$C�$.N ���O*mF6})�� be��i~ �CvC� %��?t�;:;� I7M�% ��7tj3]� � ,e3N N� b [GU )-zGR]�n�8=.{M�}}fgl :l AlsJE Mu.b*in2#��Bg ��FB ��t}"�. }*xx}P.F �/2[ u�R  r$Pe�a>!�+�qrdntyn B� *} P=P(V(2�� rho ))B$%�,c�2&� $�F� s �6$ 4});V:�%y!�!��O10}% *� das} F�A`U�, �F� ��% .��.Tw��Calogero"Pg" 6y2�� i:B���ta�"2�(\F�etxQ�# Psi 3�jE�,"m1Jk(��B�. !fcJ:_�=�x}+R(})6��asE�enR+(Q�s $� (a,b��nd $R(c 2�{Y$% {mpl}. S:�i#ExF��Z�(i.e. �=\nu c�$"~ \nu 2� $O&[#hsR r>+te�ed�#p#�!o view�eJ�is6=b�%&� :� .�!�"&Q �k2�C��"K2d� )�)Liouvilv1�� �:,.�dp�&f �8X 11����'al:��F� on:c� �module=a (�t�,)f8�'b�J�d\za�=e�dx-u>}dy=dtup eta}6 }%� l^!%"x %�e�,it{ordinary}&!3ial5�B�$*} s_{yy}+i`e^{-s� }E"c Ie�al $s=-\ln �eich� �v�$]7�+ord*R,B�} adaV� a)ds29J� �a=��x�_2QF&� gcF'uca��(wo stepse�B���)�}=*�!�y5A��dx�1}{ &M& +udyJuA� $q(s� a)$A�a�5�bB�} |�%q} sbR�a)}{a?% RAa�la�.lil.�+ term���cha�5eria+� a12"��5ra�.2k4B� �l\��a>$f�;�!YɊi�\exp qe_" pari�'��}%�3��iā�����F&2"+�- r�Y�%hipR� Psi �+��jJ1�HaY7 ��"�,}� (sub�7�^$E� � (inw2\�+!�)F�,*} q_{s}=(a+I{e^{q-s}AM )q_{>��@.!*:���3�'A:%v�� Z� �!�� Hbf{Rem�21}:5A�5�un��%�1EioA��8)!=s+�"�(n}{2}�f3s}-a!�J �it{5�)o well-_6�- Riemann-�$ Hopf��b:�(n_{y}+nn_{c�� 2c}{9y�N���a }$y= �/3$\%� }$c=�K,s�}&4�}g justaQ� r�ormV��NP3}A_{1}(\xi )y^{-2/3}M�2} 21/&��� }c=6G'+A_.;YJU�1��\= .A�}$l+, }$% s\f* However�1`�B A�1��.�depends���bf{one}2[a -l&�* onl &6.if� S 6� \neq \lim� ���n�re-�9� 2&.#3%a[it{�; � take a��CSR<YWA%"*� \A8\xi y^M10Z-I%$ (�nJn^/� BE�=�1�~ a�+� BG�~�* � �+�3:N� N �6r>�}%��necn�:����5.�:� 9 [ 7��ejq or})� �  u�bi-dirQ- al} �;\-�<22uF�:Bn 2Vd# in f�&�  $%w|u$j!!�'i?:0q7{ � er $� a ��I ta5�k.�� )�&1}{4}B  )(t-m( ,)!��"F�e 2}tk2.ol Ld$KI 1J3\�.�m��]j �4m�.�t~ � :�r 4 p\bu"d$ u�e y A��6Q,'����in ra}I��=_GR*rM4 � xu$)� i59 � �4<U8  �=z$r0 ��aR#0E��&2�& $k�m$ �$D E$.3b; &� � �*ReuK-r}as:�/" } A lQ'f"{3A otivQDh[B�c"b<�as p �A5�2�cr�� is moment�,Q2$no unique 82%����.& M:P� 0, sugges�#@u�C�U2�0�(�do}) �5��\quotedblleft Lie Group A�62$�:\�f�Cc�X Johannesburg (South Af�Di 1996Rb+"f64����&x1 co6/R�u_{�=2,u�(/2+ )�1B�(�a62>8�**u}�at#R�| z_{x�/22�� � ��WA-�ANi u^{3�^�$� e%=que!�of"]*)ZH*dJs�1ureNbU!' HD "�uND %��% R9bŀ�5se�F:~b �L.� is $� ����[-%I`%�&&:!d]d�/Ri�umO1}=D"!:%�/#"�?Ca�Drs� � 'als $Q� @dx Q!. Ewof:�6O?bracketN�$(x"� }u(x��})\}=\{u. o$ $�"9(x-.G&�*�1y*"%�* existQ`����t�GIjE�2^F ;�,. H.� a�thB21- easy� check. SiA���%!�x�t �)�I$ A>�Itt. �6>��valid. E@na�ܑ� >� {Mu��s�6�H��[%2�4��u[byN$ �x} tt�Ot��2- / x�i�moj e6�In�F�p�;aHV�wa&�s7a >X9X3g�2\3�b F+8too8 us, �R�!!��69��\� f&�>� �It4end�;�* bf��Bw�!I��1| �|�n=+&�D}}) �) �) .`"�) ��&��g }x=-$�2f,.z"6�*5�*.�c��$D&M�E62��(s,*�/$ � * �Ce�!�VWe� � �.R4 % j0, e shb8 use 2�value!��& 9-�.xt %a bf{%�}Qs.� B2%:�\-V���E��9:c8��,-|!�o 0.-a ^�TF�}�1���P�� 7 67z��fi�P.C }% j�*>V�U&q�6� ��R� m  #J_ :M [I�m&{5& a��]})]K FZD-2fE��})]�Uo � _N� soci� 6A�t:3-��)�*e2/ %)��[�2� �� ~2 a�� 2 )M��t*) { H_{0 y)dx$. C2�?&7< 6�N6�(�} S&m Z�4�}{2�4}+V�z)]dxdt,�4dfv $u=-X/RGz2�NF�ANA �}{2xb�"E, �Q )��"F)D�@- �e"QB�} W�r)b:})D�x}�elVJ�Z� (cf.M�t�$ AKsa?JDJ��b) a�Ks RI �6W:9�C �ns�V)AEE2M�MEG ��_{= EX�'%�-�.QFinR. Q.V�2��n��&t@B� *} r� ��x��� \bar{H}� ��R�5%��K>�A�dB2ɬ:�B�} \{z.� r&� � � =\{r.$z$� $z� &� dozey:��r !�y.# .���=i�e�% rF���� �V6G�\rz�wo �U�) qQ}� r��Q�D�Fur)��2�s a�n�m F�*farN��2��2I.r}��x}}),W {B� Kt}-XZV.)9x}[\mu *s z))��&G6.fx�� � % )] eyB�q.az:x1I% ɭ)]),2.�t}(rz):�&66���z z}{2.F.�2�2}})]"� "~ &lRReDDODD. IUC|O�\��GZ&�A� pply�bz%��1siKanJl�both b�L��� L��),�@x4[% vari 'pr�3ple�� it{�O�?dO�5ble.��I*�Jq�M��Jx?;!�N��7x[;]dzB<}� {O \ } S�� int .g\tildeb}.rA A�2 zzm"s �"h0u=��LrhoN61} z}$,�$x=:]/�y!� � c:��id�jArh�(��): $% d� =zdxm�r}#$}dt$ or $d.� =xdz ) 7au>��xd<+.9$M �6c 2�$1/�1�m�d k$.�B���Oly �C�%M)9 68 :Ss.0 % .-E.u�\{xE.|; }u(z�9)\�h��-j&=}x(�a �(z-.E�8\{p.?.oJ�� &=r6&"�}pJ3= } >}A �]�.__{z)��FJpe��78,% p=r�7\�F�U� $), � E�r�B�IB Rhat{RAE�( � tab�/}{ll} .@z�` $ & �& J% �C%�X�J�$eR�~ 2�{u.�F%IU_y2/Ս��'�2VTs�J�e animPZ] set�tbf{� }2� "\s,2� l;]:�J}o �Sst�:��H&�� Rl��4H}_{k}=(-1)^{k����bp^{(k��`(k+2)�c B�)% }(���2c}k&�2}\pm 1$2...:� 6�:j��Ѯۡ� ADm�=�I��+u�.�(e�Q B."jI iY�� (Bt��;y��Rh&�exN@)6�V}u+*� x  � 2k+3%�9�\ R N}zJPz.Q-fif:���B�}Y0}��u1����+��S �,rhoA"*�I ��@.�?\>-k=2��4" -kR�$k=*�I}Y�2�"�$�c>� �4�it{a�:�}`fT��df> ^� hR�s*�% �)��6��B�!�*���y7AC�>2�6aIb�%�=�g+1}J�� �%}}:1 _j=!�%�-)�zAll�*>P���2,k�@ 2� �&�5VC  ^!V)�K��% �}�y�Jc^0%�R�.�ve0Je� i x}}[f |}x} _{x&2�+4 ���� S_{-N�Z}�$M:��J� � *2 !6V�6*{,2�1� &. 2}: A6:��#i 3$any&o3u�%�"}:is�A&�fpa ofF�"$z%e[$% ),�\� sh�.C�*��2�  mA�}"^%�d�ou_��Ձm�ɝ-1 N*\�ݧ�d�KJTF�J�M�1k-"��"`�\" K6�2:� �2�*g]� e�+1�nRj � �c� bl�:s��[y�"* �_&�i�:mpnu}. U�a ly, �-�g*�ck�&�1 < *9 f. �`�Fr&J'9:.s &Ns,!:2F)�0/'a�"V'�U iterdly�( 6�E�Q8Rula2SA3a^m} Now!W )�#UY �� i�ifF=�$�a�� we6_r2]"en�# o�sk� � 6l =Ka`e�% �)�p�k�O.�di�S^��A�:GN�k. H�[E`rrh�\R& *, ��)�cchangE��o!ne!�T%�%we�]�ct�]R�o >XlA�.�]�%�YKBi(&�7&�a%n,in �ec�_*Bdn`Y�g" E:new��=;�%; below)���bf{not}I�G set!�gGN�-o�\� n:N& B&z!xal&� �Eo�/\P]��DI��S/2$.��GS ��2f���}+H]C.>P 6�%%)r $stonished}&c!Q9$\:66�O!6 .bf&�=����0`�#:S}.cdA}. Nam��C�-detail�bI=, e�e��o�j(^ 43)}aY bf{5[  4)}A�rein)\-.�R�$SV��S�!B�p� �(��t}-)=�>�%&�t EuleJMh!�)h�.V�Bgk;t[ p*: [H�"�u}.95B �5R�E�"�H4v�ef# z!k!��� ~�zN�6� � %�/W$�@pf t� �&� 3}: T�.b]at � was ��vN�.�^�'y�^�ila�2it8*Ledq"��CqL��y&9})a�e "�U[iW dkZHix.��'&��repeat�2eUcɻqrmain ob"�}�S�j#4��2{6m�n^�- -.% bU!)�ii[)rexamp&qm��ofJh !�S2 �*{C"=^:� ��� �it{.}%���gF��&Po�kF�,Y �j�,a�*Z~ �A+B�,C�&'>�,�:��& H1��["w>P12\ }>�&O�Jf�XJ 1,%�9)�.�.) �+�*tB *!` (mojɐh �Y ewm� dubr:�e>�&� �>@>X.s!�-�ԉ��:@.NA}��  Y :Y-�-w&�^�K>�e�Eu^����1 �?6z�) �>{�}1|Ur��|Cby�~Darboux orem to�F-]:%R�wu{ , }wB�2%� �b,>G!M!K�8~`��^6� ;rt �RJi� qY{bI�PF�-m*'c"�?� ���i��a�� raZ�w�D)H>�!�_*T. 2}(w� *�;B} ]\�V� *�a�$modifi� �l����26}&�I�<,~'$ ��lrͪ"�5;refX6s [�bf{6}],7}]�]�� �V-KuE63E��42-K��[2� 2� g!m"TmodN�<aG.�e!~2�<x0L��$2�<&J  �hsu�tdp �<��B4}:�fact,_(&� "s:Z9�DV��1��B� "� 18*� *� �Z�a�`.��mi1�K!pWre.#hwen� result"� �2�,k%2�Cbsx�ngs *�C ��F.}!y*�ff�*�h�0_�ey �Xdd�xto 2x2 s�uCK��261��:� a��f:�9Ua%~}qџ ��,eB'S -s�a9��2� }X:6^�'�D,F�1}=�X>r�8 i>� C��RY�Zg2i% J=1 w_�(J�I66/�B4]�> F�t�Aر�Zyɐm],:'[of R{�ll��:# togeq� �`�a:x�[N`w}%|T 4��-H_{~wF>2}[1JYcdot BJ&UI��) ֏;�Cl#ta&f�Aj�w}-[2 > % :@7>(? E=:6� &mq� % An�ken 5puj!�EWF)I>�o�SuV�s&� ����$[a=i�$ 0 & &f _{� �5�8 ��mb6!hH^%QfN� WFW!�nd �% 8%] (U��} "yph=1 �va 2:.G$)=2\lambda"N ��WJ 6�!�b� �!��x�S4(�!_E� +\sigma ) 7)\2�5!� 9 =NP $�r*\ � 9\a�.�'% �=%�$*��1 ��{ toR-ps!�!)��2��=* ^{+}`H"�0squared eigen�8m $4n =�9 ;"jugate";�&�asympto�/�y $-�m $arrow \inf{6"�T&��S�"6n, 8� 2�B$xLJ�( --d��� "����nG::u?fH0"��#om�� Wqs)���Z6� J]q9 �2"/K� afj!�Zl��tO 7 &� m�F=3� &V�>Q�p&Q�=-��%|>% E6�*=b x}A-ybe�t,"' !�� 63>m�b(zH>  ,MD ):�polynomi�IQ�� :7I1*@�*} ��d&F &�1�Gs2�K���t>�` ��� B�!�]b"X �-n�iDI�U��0F�&��_{t��"bU�����%b2} %Qn�&mQ�1B f $b�w/����7Q0twice poi�A��=R� �Ba�2��x� Z�u��1}"N �&�hdg6jf�Q���y������I!�2BK��v} O:�% � }�� rM-1>�$z�%%Hxt�&}}�_/]� ��!�2 z��:nF�choA: $b=(")--u�^Q�w)*W@musmt"�"t�" ���!�GvY J5 e� iZgO7Z��0A�=dE�%�>5&w&'&Pm��\�JMq%�� %��I�N>�^a�:'6�iz�Z-�p6$ �]3��8��rve,.�P���:B�B �u��w.�:� !d�"� % a�:/�Ha�0� d>d!���L � G �:��/ ��w[N<|B*z6e Hw E E ��>)_V<\�66?<Zz2��fFR��rho}�>�j~/��!�!�J +ÍS "rJ� �'*9%�4# uto-"�l}�\��Co�n� .B" 6�6�b� I�<&h���U>Q(�H, �P��%>�1\��ce�ul.m1�)#h"as  J1&}}�q�:��a�b�s�:*��!B=�6y[` fa]� �I % � ,�&#aYbf{32-34&�#; *92tR } dya6�C1}IBjy�1#Nf�8T=A~.�`829�h6��hJrtFc�R"} 5(�E )\! $� �Z;&� U"; ,M%af"�mpcc}�&t>!_O"-N T ��% | USFV����8%z� :fu}_1}}=2*c �t0 �u-��0 �v.% �\=a u &zk Su� 8-�1�l � � �q#k��:� �5� 6(&� �B(� �q1�B����U>*� FrQ#u �"2g -��� E�6o-+(2 �>I )�/ )2Ha �;c=�29� .!�) S=0�.~8I< �$wR�� ��}.� 0hR � �R"Wof>�~� p��eS5��5%�&t+5�"�6)� Zu� �ՙt]%�{Nu:x��:�)� }� xn�:���V�%�I��N FI/a�2�|�A� Vs a> ��fA}! ��C2�.ogj�H �%0"Ak�S�0�R�LQg� �>$�)o b SN�"T8e NH \�fN )3f���*� �9�.E�� �$k+"� {mpwh}�>�L,t; ��d.5l} ]e��� I�H � �MZ�is5�"d}&�W��%F�u��N*mNuq> �+A晌� % (1l0 ,�Na =�7 :gA �&i >�2i�2m�)O7� kF( IN3 a �$)�kb�'qeZBIy for U��;. S�8al 1�ZFg7r�$ϡed� G� �it�"q(V�N� Bb� FE3�Ji��m!�+2uV ,%� R� +,1�$qo1�}[���&Pu-]rXqUq }�6�2�{��5 &0 4��� �"�PmŸFV� ���N��3BKu }[(9�a��A�<59[�2 �v�2>�q }[ pi�2%)!# *^���-ʶu}= �u_'  �I .&�miuF�I(3FJccc6b^_�'thp��^�\+2zs�Ŗi�b~*i�QdoubleA�exa�p6��k��JmX)4q�ly.D�*��*E�"�:! )��)y� ��q B�J3?}�#.�D�"�6MY�m���"� � I�}.b"W poJE5X��6Q^�eh�-�kX�D�bf{�4>�*>an&q��d, link >�*"M ype).�o>�<+�>�Sie� �{SepIm�0 ��E'B;g^�h{<oB��b��6l_�/(a ruby laseT$ a crystal3#tz%^���AstAng�w)�>-f *�>ޜWg� sh�� pulsW?w�)gpe-v�city mi�ch5L;' fr�cy� y��com�Pmportan�-�"}=j�of!�2=: (SHG)#�qd<Rhlex"x.m�2� i� kshg"�ksa�w�i�=��� .��k�.A�2�D0/*�J� �<:C=-��eF��Y�-#� y� ?1j&��6�}O1 c2�Zu �{���"�50& "%/9�f�&�JI�� �:�� �L>qN2\ /z1|�{�W3-=/& 9i:/-�� 42u�i�B�it{!bu!a�uP/��9|����� u=re�8�|Ai ���H�)Q�,(>oncV( �eta5* � �1=N'M2�O�� �"�"� �*�@Bl+S>k)no(F.�%&�%&7�&�U$i-periodic*D(-�^j('lbe�8�� U>� kis�dy�a�C�inFbZak� n�% )S2(F�f-�.�A)�ur" \neq�es�~9U��.&�<$ ,=0$�������/ SHG!g�=g, �� q2trmq �� $�5=�yU 4�8)�l��)��  i{ )G6�"Q �%6� 5 a� \c "X �DVJtj��� �= �� 9`J�(6 X ,�E"� �U2'}- �L\XA- 3 �shgfub.:��&��c�e�!L6�"� :�6(Sinh-Gordon" IDr�F� �u� $  ���L'e 9'e�1�t�h*�~"�#VI5�={1� a4 �U9]&~&y }2My IGf��&�h��!�TH�ew���yE8- bas��  akmp��T���!�"�5ras"h$�a&Y�� }Q,�Q#� �ek)& W}M@�!jY�}e��0He�v��)��Gj�&-' ) re-calc�q ��*\ ��� ix~ �"= ��ex� 2\*klYoS "�J�:I�EV�*&g.�$��a�M�E�*n *�-1} %��3?�� �"p���f�+=V�L�f~r%��yoB��,�m� �}��v-��&� > }���B�&  }% -�x2l �J a 2Hw��#b,�16���4�5�7 �f( t"8w�2{4)�-y.O@w\\ *8w /}Yintj0o�v9qI .d2q 6�8B�]v�!�BQA� � "Kw �yf�N�MIa~ {% 49JBw �"�&1�b I�ESit{new}"�� e]ߍ'� "� �<h_�I�R�d��=-� ���%-1I.�� �bf{^� rez�}:��c�F> ��&ySchroed߽� �H@v�Y&��:U&�>�l �Qir� I �22k�o Si�� 20�i� V�is 4Jx�Max��-Bloch1�x��F����%`2�% self-indu���0yncy2+&�v�ad.��N=.�coZLto N8����H>��NA� 6C�L��*�L,Nh smB�BR�soԣqFN7�e42�wayT!�~�I~<, Heisenberg ��T&5&����rnB�62��& Ramann sc�Q ring2#-�95�wR�R� A���65s%m s<�(�Rc cVS��Jn�6��� .�*Open PG;m*< nu6�l�d%�5m&+�>�>n�1�$� hyp m�a beha��e��C*e��A�e55"Tzf� 6f�W�$regular fe���r/5= gz}) pos��y���%�i�_ tegr� }�k��6� $N$-&�3Z.�h 2N�-�5�V6�?�GZWN�" }*Qk�]_+ IY}F�W} x}=\under��m=�D" � N}{\sum }]H^{mNxT� "i9!<�6E y sen��� ,�Bse}fI� , J�?� ion, etcaopen. .�X�\&Q�j0.Y�� &x�!i$ L. 3 �6$;sultra-l>ZT&bKN M)��&�A0th^�Ѵ� �m/Z"x��TRWge�!de"�cef!�R5nD� ���`y�,&�}�/�c elim�edRa&"6 & � &� �g�L6�]N,�kDj�I�q� autifulu�E�����^�of Z��Xe�x�.�(� yC. W>pCY� :U/% e�z6�}- .�!��wit{��)�/ ef{�yN�&� dR�hK:�h� xfG $K�-1^$y} apriori<1�,c:J� �\Q�viaU^t@ʜh�(k)�H becah�!%�: l�Ʈ.Rme;ne�NS5#(k)x})M�/E�(n:e(  ant:aks2� halfE*�F�2u triv� ]�\:f- N�x�Z�J� �%$n�7��*Hen\ $k\geqslant n/2�,za *oddJ) (n-1)/2$G�t p(U10 yea�y cou��%���s�DFy (mixed&*���y��6� ���"B)P24cferlie.j]anVfaކ(�� phen onA%�=] ŕ3 ���2IOa� "�%���h0�r2(} j��=ey Caccum�B?�R�.�c����d) w&-.}E� 6�"FJ"Ĺy��Gcy}� (E�8!&\� Z$freedom. WA�e�� %v fAN (to zero�(0%�zb�(!��"T ,�#� s"�@!'!� F�N��Bt}��wb��aA�MCBA6�| 5��*+��4:�Bts(� �{L}�N� )<if 4�Zn0geometrN  surfac��+n$ curvaR��*}17 c_{1��w}+c_��wV8�A��9-&�-U� } KdV*~%(�'�V���VR�w�C }�Ox6\L!��JJHjonUO Tzitzeica5�,;"5��� affi��8�.djwN@2�A9A Sawada-Ko$k9K 5K&c 3x3nK 1Kxx}+5(!Dx%J!]}�  )+ }^{5Ntv.=KED=0��:J�AFst�q�]TMK*D y���6�GA4 goo&��% "�N:�sh�.��# /�/e"v�"q&e!�6�I2x&�YY�X ��6<�!m| �b�e"�- t-%-��%%o��"�� U��� �-Bw ` assume)� � �V��$.2!�t�Z�b���0�ba2�(e.g.( Z<].:Q*N0:x�KdV6H%��:[�"�Q :�&I�p��b orig�2�y� �"�%� to fin�2�.�se � � 3x3 �E1�. I �x�E�A to .�f�3is�\ wh�v��)e�kL;GAMU Zߗ&� � ��U?Zng *^�9 astro�@piaR+�j ��.&V� *{AcJ' ledga�0I am ^hbtoL<�**�e�hospital+�"t/199ʳ|at TUBITAK Marmara Research Cent��n�;AN Fezaa sey "� (I�r bul) telp�p.! E\'hi"S�)�� 2�}Q�%.WO*� }Y��!�z�2Alexa �e �5% r*� �)�al�  �)� Prof. Kir��ZZ܁z!I �}thH"�c�A�a&�of6��C��aP��D�!QVlasov"��� (-�B7 Fa �R2� �+I 6b,thank Dr. EuC+( Ferapontov%� Gennady E��`is# �&ak��� A�,-wo!� e!gN �1lst�=$talk a�%*V��x4�� abou MR�7 r�36 ��)�I(�ej�.\few�go hesed a�""��>��4{99} \bibitem{�$$ \emph{S.IeWber, M.S 0newblock.�! alis�\�-zV F#>}Qv��. Rk�$ad. Sci. PV� Se�@�.) (bf{301} No.��8(1985) 777--780��f� vlovD|M�A. Zyk 2M� % Prolife�s>���VU(, !� D5�\% 152/153} (2001) 104-1025�O �4J.C. Brunelli,A�Das2?O���gr)"PyB� /&'ic N�d�[,!�I|�9�457�aA7�,4) 2633--2642�fc1cF."^�2���v�P�!�u>)�� in\ N�70i�3Aq$84) 189-196<p�H��Dai2�2�:h�1�8 Camassa-Holm EI!l s High-F"3:Li���A*q 7.�-^$Soc. Japany�67 �11�098) 3655-3657.Odo�A. ��,, F. Oliveri2�Ho*build up"q�&? :s\ ӑ.onW map=� �bol*F�s o\ (Snom^yor� E��%dE;��dS��st- �>bf{25}\Ek3-5%$6) 303-3222ubr1Ba�DubroviA?$.P. Noviko6�Hy&��s ���Qstic�"��0it{Soviet Sci�z fic ��ewatSdhC.�a7"a><�4 Wbf{9}�� t 4.zwG�� c Pu��,rs GmbH, Yve4% 3) 136 pp.�� E.~V.* 2D)jMBhigher 64��l2 ]Y� Lett�p�.� 62} ��$2) 193-198:�� �D�|Fai�q Govaerts,��Moroz:�% � al Fieldu��i CovM�nt So~+]yNu`��ics,bf{B}�A 7��41992) 214-232;~� }, L��ise@X >�"�9FJM�U:�E�bf{\ 26��!� 3339-3347.W\" �J. Gibbo�E�Tsare6R�!� B�#'s.�!#. )�A �bz1 �6!� -24,v Nv�E"� Con�l�N� "���1 ��s�2N�58 �9ł-272� ��0A��Y, K�6 }:�*��2�%�al R�ulc�- �)) JETP}�� b 8) 1-1UF��L1�-��e\*+'MM]e.\S tic!=oryZ�Usp�X38�Z7�P5) 687-76Uhs]QH\�,f S`�2;D4��:orr�]� SIAMT��\[925� 6� 498-1521.���)�J. ��2�A� nomy�"�,��bridge��29; Ca %P. P|�, LondoB $d New York262TaK8 �0A.M. Kamchatn& MAr��.dA�m C-�g� �8!9fe .�submit��� it{T�.��Y� kb�n � :��-�wQz���"�R*C�sol� it,)gr� eore�ƕ�54Im2a (75) 396--402�B-OV�Sr6eN� :A������P�B .IwIv�9 �1Au 78) 25--32� kuHK.R. Khusnutdinova,A�Steudel2RNEN��: VE��)\3"�,5�J��qy:3 �i�% 754-3764.:2|i: Y. Nz�]��lpri��munic�}�"B�GPE��siz��,r�� .�f�.L\&O!�2�\U͝�N�M#Ge2p9}A���3257-326-ނ:�fc Mult.��e �� le S�&6� Math/9� 43 }� 3� n441-1452�nU�1�0, O. Sarioglu. An\ ��f�y 2 �I�hr�ٕ% E�YESbf{A}�1� 3) 270-272�o"� P� ��$P. Rosenau2�Tr6qdu� ��� � ary��>]~ �+a��up� �( Rev. E (3)��!�2�UA2$1900-1906.M"(M. Juras, I[derso�Q% &+ GpI�Laplacwv� �^��of~z, Duke I.*�8�& � 7) 351--362ߴ�"6The"�U��&� ��&�< B���12�1; 1) 927-932� �Pz�}E. �i� %&�Y�J+n�)CA�}$. 9, Suppl��b��m| 17� 2��Tz�8Whitham's averaS�-�and�8 Korteweg-de Vry y. R�an�kl9X�9�� 4) 615-612; cuQFZ� &��zW\�y{elsa�bun�0ckage{epsfig,��icx, &���lCc�unq�0{Litak et al.{ +front��Ai�a�AE��2 os v1 weak�Oon,excS���-�/�, oscillator�:a -sym�V&�# } ��[L�0n1]{Grzegorz �\[s�+E-��}�( � 4@2]{Arkadiusz SytaB"@1]{Marek Borowiec!ad;� E1]{DeQ �Aw ��MeT�E� Tech� lQ!�of �x, Nadbystrzycka 36, PL-20-618 L�$, Poland} :2b� ,V� ڂ-b[)_T]{Fax: +48-815250808; : g.lAL4@pollub.pl (G.)��z a.syta. A.%�), m.b-�.!MN%�)!�I�a.g�N*�$a�Mieln� c��rA�a�[ �chA�in��*J�. �:�._jectean 3�r[L�c��ows��cl��.�;!v< vibr�to ��/bc� e escape 6!"�Z5&. E�!ia��6�tudp�effecE�a=reB�i� dh& phase o��n the system transition to chaos and propose a way of its control. \end{abstract} \begin{keyword} nonlinear vibration, Mielnikov criterion, bifurcation \end{keyword} \end{frontmatter} \section{Introduction} In this note shell examine ��tshow possible non feedback � of - Xin a simple, one degree"freedom,1Jp subjected to external excit%� with a non-symmetric stiffness given by !�8following equA: %eq1 -n�} \label{eq1} \ddot{x} + \alpha \d� + \delta x +\gamma x^2=\mu \cos{ \omega !�!�alwhere $x$ is displacement $ f e"lin!�$damping, $c\b(anN' while $�$%� $�$ are gA�T quadratic force terms%02F0F(x)=-` - [.9M2} 6 Such-�s, ){u brakesme%�eAHa potential $V(x)$ !�3F�L \neq V(-x),~~~~{\rm�} �$frac{ \parV8}{x},�3>� have beeE�I�, of studies!HP many years \cite{SzAkPski1985,Thompson1989,D91,Szemplinska1993:5,Reg|5,Litak1998,Rusinek2000,Rand1994 T2003}. These investiges wA� motivateda?y� applic *$in descrip��(of physical1�4 mostly mechanR�6�R�} A� eleca�c1H2 �y � alsoA�ked����metasta��states� atom���ax,in problems �si�� elasa!theory�2� 4}. S�%sa�A��=!�it�,o two differy ����ufirst bwe get� 4&� $narray} &&�  = v "s 4}\\v} = VZ � Xepsilon \left[ -\tilde{C }v + mu}� "3 H \right]. \nonumber� � Look!���le��un manifold%w 1� ed small !ө�s �$!�!/above=F�renorma�p�-$ � �� \mu$ via"@ = m V8muF#F,AtHpectively. %figure"( L}[htb] \hspace{0.5cm hpsfig{file=fig1a.ps,width=5#,angle=-b \v = -4.4> M6 >Kb.eL 7.2cL0} \cap��{QI| } (a) The** wel�!}unH Led Hamiltonian (Eq.q 4})!� $� =1%x> =1.089$,P(energy leve� 4=E$ corresponde�v.i�Q�/a t��\nt point at $x_0$ ; (b)Q� $W^S �U�$W^U$ Y�A�.�(gray)E\a� eR d� A�� ( (in black)�O@distance $d$ betw�  U$�  !Iby�7 func!� $M(t_0)$%[49}). � �indic� Dthe local extremum��B� (Fig. 1a) �simultaneously represents a saddle-]�C(phase planeMb).A�ndACure} ]9ʁ._.��!���+�D95�} H^0= wv^2}{2gw,Q�eq5 ��k}����6FU@= UI�� \ �3}{3}k6>k ix9z�.*� eS plotALin %��Je�a�  Q  !#%� p� A�E��17F�x_0=- �w}{ �}.�7B�ExisteA�of }eqt$horizontalumak�2� *� bif\��m= i.e.='*B �~a ) =�  . � �Eeg~on (App� x A)�SJ5 i 9w b) a�89L�� && x^* = Q6Q�P( 1E<- 3 \tanh^2 �z( -� sqrtMv} ( t-a� 3�n) , �v ��v� :i�� 6`~� �r�.�}{�~�h^2 ĢA .q8} >5� A�cha�eri)2��� s go�&to� reach� 0 exactly defU albe� f (e time $t$� �f K$+\infty�) $- 4�Hj�BzB� .c�$�ueA �> ��5�1 them� 5 (covF$�-9Y��-�C�int_{- �}^{ �} h(A�,AN() \wedge g  v^*) {� d} t�79B7�b�6�2� ��s $h$� ,gradi��of2# .$^i� eq3}) lea1���^� �0Fi\2  H^0}xV -Dv}, ~~~m�0�|1 v} =� �10JPg�� MB%!!� .�4})%�1"P e��h &=&m�m�x!�ѯ2�<5�x + vv,�JgE� {� 6� \tau}��t.2  v   ) WxY(1^- ar i�on.�� 0 $(x,v)=(x^*,A� Q6},6>2}b). F� 5NsUA8}-��e�)}[kov in�Hly�by� "�6� center { >� 2n� B-bf� Z� 2� C�valueAJ�_c$"e against $� $As �&2 : �"� $IV$. Co.� � rwkena�,$\Psi=\pi$ F,F=-0.45,~0.0�_2 sinc belo�up�curve�P �=0.W �=0.85$� &� calc"�-A.Q fig4M fig5}. 7 P� diagram� a�Psi$--$F!T� 3  ab�f�$)�s, 6As �arrow"� e�dir=oY�($ increase:� $ = 0.04,56810ś 0.15:� H!�'R'"'C' deno�rwj ��j i s. ��M��`u��}�o# jo�Lt�`��r�q ���os{ I� t ��]v^{*2} �zB>3 ubstitu�$x^*(t)I�$v by!�*B��8}%- ta�$�=2l t/2$get: %2Jh��-X 9y �d�͸� � ��^2I 2?  I_1 - 3��)S.>" I_2.�F��� �J�j�{ Tt^\.�� �  �N{O 4�\�(��I_2 a�M` O ]r l�&2hMetau +_0�0}{2Z}� a�4m��� e�~��9 *el�2�[�2A� dDof.�* !,.:� a� $seshoe typ�� cross-.e�writt��MJ\(\bigvee_{ \b$ystyle t_0� I�=0QZP }&1 8 G0*�1B� E-;�b�9-. 14}) a�Psome lengthly algebra�Nd �)[2@5= �H��"��%Be"-!*����P��[e�JL\mu_c�1}{5}1(m� 2Zm�c piM�^2p } \sinh�ef�*E��\pi>���� .p 16��� Asa*"} 5&����versust"quency�y $, Mis"p>�2}Y(dmidV��!P( $F=0$). On\ould �� � that�. a l� mini�2� \Dx 0.6$9Oin spit%�; $���p��e" a�$!� , in; Je#, �ed�I"�w� }e^G |r)�apYE�be$e same. &EEffect�ab�} Let usa# side�.6}M"!+t�!ng"m 6U})e J�"�1fd�$eM�& +�#F !�0mB t Psi},"u��}�  � ia scal�coeffic�w� � $.a  �^j. N� stead+C} 4}�%��se� te2��2+�mTaK&3d.c"_sE�*&e: 1V� *b18�c�c%�9���o�����!�L'!~repeatx#!�c./ �!@pre7.�su��Pm�f' i9acmpo�wo)�:�ѻ�:eKJ�R�9&� = �1+F^2+2F XPsi}}�NH�'m.7 Z�2N�J = \arctan l �!1+.�{F�s{ �-�)*� 2Ff%� "h wn�3af{B�3ƨ 3} F�$B(F,�)��a� 1~a� 0.05�  Y �n*hT��for�/{A�j�des on !��b#���[2*z�?����] 1 E� +2i !f}. 2�!B& �"is�$principal �w��)#.�2�2}a a���!��!�_c1�� r$�045:�%�)' �k*�$ ^|�ab� buti K)�%Ts� fl� ".*�-"�,s. It�&d*"�5a�-(�(.45$), or i>$�$$) �%wla *�>m. To$-:�R�"�E�&w[oner ��k$"J y� \sim� )�an'8perly chosen $t]>Q : Aour%VA �$B��w 2J7B |�. �. yF-*~�RD&W 22}.�� I:�2}b!L%�c2�nodalE��"u s� �!�� O� eM�h��� *�3}aE1�&�-�a&l �Fm�a�$,�aԱ�`�� (� fi^~+b 2�) te� .Q�ngA�u5%I�&�  +� Q�Y�occE�+, easily obta � :t( $B=0�.��5"� �D4�D4�D4}�&raF�q�Yd togeg*Poinc�'s� ss���$�~���.%��" �$�B��8�Ieifi���>.s.� to�'���a-Bv.B &N"�(ͅ} To �(E�"�'.�(we��d &@#"�i�F��a�  ��><4}�1�t"or-�aq6P F�Z!�%�,e1�Be��. exj edirou��S)l �ion, ba� n�roxim� �A r ach,� findB�B(4}amaQ$l Lyapunov�onWear�)� posio&4 ( $\lambda_1*�05�F 2�4}b���JLsynchroni-I��iodic .-].R/�*t��YM6t!*&Q�Q�?#U� :l16A2% A޵� �"structu�,Tge att` or�%:  a) h�/1magnifiS2--�,&z"�- ax] m� �5}a-c.� A�� dou()�����%t�� fac�� was �2A��1 be 4G � "�("���5��5r� r| 5cf| } R�(5�ha?0=�9��2�4}��;F' (b-cJ�&"�-(Last remarkq co�,� s} U�%��J2�]go Q�ala:j A�a�. 9i 5��f�7>5e�Lє2&���f�7Egself-4�. I�p!a:����5A��)�ؑR�. v3it sup& �TA�>��shrinf"(lower boundm1of7�} a '�.'"� >�%" � �䙛.��6: j � e�����'"ts�$${ini}=x_0+�B v �"m)� O�9se�� pm rela��� los�EA "#!,_0,0)$. Our��ic%�/1|�5ve�3I�.��J"- by/oY7R�E.($|�| �Um��+(). AlthoughU%not�O���(6!sescapei�o�81) F7g� sl�ly �2.s%�$@�F x,��mu2!�) pur�ly�isy)hel�+u[toImtrobust�%d"�(� �%�.EuA��օ$3qDu! only��*�&�! ��!$ (see���k1}a(,everthel�;c clai atE�rZs �# g�-al� ��an� choice��-$ sign w��mirrorXUl alon�,$x$ axis ($x2x-x$�% q� %�a ��)� -|O|$ !� ��r!sZ=s/ e�t"�, shif��2c(a+�0a�6d�A�Q�:Fc&�,= v+���%�v{i5H,x^2�', 6}x'�1.(x')^2\1}{6},}%6��$x'=x5&/ F$ &+ *{Acknowl�'�8s} We-� like�a#�[;'��orti�Polish S: Commie!.SFDific Research. ��+{&�+8> ef\t7/{�${A.\arabic&� } % dla �u '�cle' S� ^�.$H^% *�&we��q E+ .+ $x> 7})E��: velocity�zero $vjA�AFapgy�baA its UZ%iF^E=V(xZ�-�.ERi$�.I^J�r�)al2�a��co�3G9n�1%/A1)N�I�z�="W�1�}6#%&f�6�ex�6i �1^J�v~cd} x} t} �#2 t� J6-2"0y-)^ x!j3}")>'.vpe�;3e"�. over��FV.= #T# x-�"�����}B��n"� 2�%�,ant. Finallyget so�led.#\-� _29��/^�/1�2O%Ύ/��/�/vQ0���x6�/A5u1\ �CTthebibliography}{99} %ibitem6�A} "�@$ K, Samodu�A� W. Drgania ukladu z niesymetryczna��rakterw$ ka sztywn^: przy��.0ym i zewnetrz0wymuszeniu. M�2�@ Rayleigh-Mathieu]%h &�HVFk 6?6. Folia�] atis� arum LubA]n�02000;9:142--5��#� H}  RH. Top��in!�F ar dmU ��9�#. Gord9 nd B�6$; New York!A 4. %=5anuH uRH, Le�)�!{Y� . Ithaca:�=$Internet-F�%9� Press;�T3. http://www.tam.corn���:veT fielaS " ger;=�83�*'.�G  Sa�tr"&Eto�h��� M)al�30 � . Spi>{9�P1��&�F} aQ Palmi(F, Balibrea�� Ta� ��&�!0n Josephson j�$ , Int J. �Qio���sA0<1;11:1897--909. Y�FG<} Cao HJ, Chi XBen GR, S�. 0"duc �b}JV�G �n�>�Nly-qd Fro2DPulum. A�..B�4;14:111U 0J�b} ���qmodel�(robot ar-�*�K�6p�4 ors �J S� Vib.!h4;271:70�4. 9g���H��E� Fris'MI�����g���s�,:� 6� eG,��pY�6|G. Radons, R. Neugebauer (Eds.) i�-VCH;Wei.K:�,�!331--4!w�>d  %J%B } %\:(BE{B�) %� ?(} %jhgjghjg�"a.1h6m � docu?} �?%�  %A INSTITUTE��DPHYSICS PUBLISHING#z I�  I`Pr�,a�an o� p�R�NAman Ink5ea/ H I P0shJjC u�LaTeX'�� I�  Iy sourcx8@de `ioplau2e.tex'�to0$te `author� IguiN nes'�#Q$C explain���demarmNuse Io�AeVI=@ �p� ENF!i ��art.cla�o 12.clo� 0''F I�  I�=[it��s �Q & �B I� % ��m�%  r �a��� check& !" lamIT�" quK! % #'h.` opeEC *�Fve) % &K'ersA[' �As 0 acut0$ dolt&2%�6-  % (s�en�iEd)Ye�) % - hy� ; =B2ls> % | �&bauC~ �/ 4% @ at5<_ underscore % { �cu�) bracC} � N[ )squ&] ) A$ket % + pl�/� ; semi-coNK X* a� is%�: $ % < xa�I` > x �,> maB D. full stop % ? qu�!onU: /��$ward slash!�\ ZX ,^ circumflexE�dABCDEFGHIJKLMNOPQRSTUVWXYZEdabcdefghijklmnopqrstuvwxyz$1234567890K�  �0,class[12pt]{�� } % Uncom�s�M�$ if AMS fo�H,required %\u])ckageA ms} .� icx}Lbegin{|}  Mtle[S}#�3nisotr f�>�i� of�r�YalescJG]{�A��iP{Markus D Oldenburg (BMSTAR Ca�bo�Mon)\foot3{Fo�QeIF M list�&�!V�2e�� ``2T'' �,is volume.} �ddW{Lawr�( Berkeley N���& �(ory, 1 Cycl!Kn RoadT 08, CA 94720, USA\ead{MD�@lbl.gov)�a \ Measur�!�B�atH"h ($p_T$\,$<$\,1.5\,GeV/$c$)! �:RVQ ( * 6 .4Je m tum z5�c.�gRW4ewed. Wk6 �c an ,V��of ell8XMvstr�:�%�" icle massrobserved} m)d�D��O8�fb#ber-of-�itu� �"k7 a�P9�� o%�%s�Vharmon*2 PJm+ qual�\�2,!u%s��"�YOBU  ax5�Ns� en.^ %�a PACS �s ta� m�VHge \pacs{25.75.-q, L�].^FSub�_'� 6N%\s %$o{\JPG} % !Dout����r1 : page�.�GK &q&I*Ni(e azimuthalY�8Qs ;B� in ultra-?$iTIheavy-�8A�iRE2�Q� U-by expa�TA�c's�Q� �Hrib�WI��46#?���$�8$]A�0a Fourier ser-;volart}Ed "�$coeff�9s $v_n�1in��e7 $n$&x iz�e�;�in�#) m�#detail��-�ral=* su|�cat�ng�WX�rJeHspa��!�'P(oP>!Oe$J9is di�<sh�2Du�.e��%\� N"�me��s�R�&,built up. Duen!�� -�=� natF+� isZ �ig��R�C�(;Zd  ea� stA�!�he �_b. +X�(ho1Ta��/d�: �_, eveD$m&�of)M might tes�&f�U L\+e�Q6sec�UQ�]nAm$2$, so-cal�2�,!�@�FIM�� RHICQ� 2overviewE�ie|mai�%d)� " larg��gntW,�+a.Y�/�4eci�n��!��!Y6k . It*,realiz��&E:��A�ow[A-iI6N �)/Q:�RerɻY�a�_%i�kolb}. ��Az� a�b�hydro"7� �[ ions�a>� �Y]� J��about �� = 1.5$"  ��works}a9good,!� ���Bis Q��ks down�R>,�6 �eZ�[ a y rigu�\.n�^�!+�qed���)e�2� � �@2��$-M4�Zto o rox �)]S1!�Iab!rl�2cB� $v_2�d-(Me�b�\� experi%�ati.�\be*" a�data  $uKd��0*Au+Au��H$�!0s_{NN}} = 200)�. A!� �= millAD�C&\?�mQZ�"pro[e$f cham�I(TPC)��0a pseudorapid�ca��@6<-1.2 < \eta < 1.HrYalyzed�s�&[M� ev!�^Q� %�]{z3 \boldmath)�\un!$a" !}"�* low- f:672z]� al�b� ab3�e)FJ���is feŅ]U-��M�F ,�o�? be s�Win 0~�1v2pt_A�_1m}:-gKA,neu  ka� prot�`l~3�J]i��ti-- s --�3j �v gH'al�_r. A cl!�Y��rvis2h:u��m[ 93a 9BL&i�t ac9)� than�e��Y/~�Z�#fi�W[ht] �1{g,@sizebox{ 0.9\text�Z}{!}{ \i10�& phics{v2_�?�Z}} "zZDJ�E2� ��n�� 5��U J` !�PHENIX���2, 1} �>pT5��b��Aj�` @huopriv�e�� 2�Y���if9��is!f-�iH.} �%-j HN��� l*� " d�\opŃofj�aM:� s�� N*v/, s�se6�can'tQc�!� sh�# �� t, nei!%)��\�e��fo�/�͋nor"Z/��iY)&�4 ~!��5�is �1!�oli��It!R&�ato�Awa �a�B!Wio�d.ha� s fail;]�Efa�&b&�Bas n0�/ y do!ainvokA\4�bi� �AQ onic|had�8c ��eb!f�Jbmmreose�!�e� ��C3e!,e` of � jus�.\A1$c 2!���ts N�dense nu�$v� easa"�i�T�� �-gluony sma (QGP)2v&g-bary�R�hUR�]{�-jUAt)��5�~b�68of �%�i3eskrt>a���M antl&�c Ej� sche�cs�cu�6�:,I*Eidv2}� ter� ngly.:A_6�e�po exhI#]`�&�Ns�)������Ohey fa�on top!� each�>if grou�4i�Cm!��)�s6i e ler3�Da �r ��2I , at� :R�Ya=�cUhaEM�4f� ���n}8�}pi_K_p_� Z�%�Id�e�;5�-.�}r"�>� ew� 9Ed�o �rg. Fu  tTW�� ��figpiklAv} !-' Qu~Zn�Rga�1�SAf �^p V�<�IAr�c"R  'jimin�� c�_)": Two movwit ka9�! �aIL 'w�6�(�8 origo0 ]��9s w�:+�M� T)63`-�coa��ere��,�N��5SEH��a�+ R_g��B�s �&�9 ��<� �f�ONO �_��ZOv2'ed:� Ak��ue�� [ed accor��o!F9 �R"Z�?!j��fY� AB )"��2AJ�� dashed-d�cfit  %E�e�ZS. P� �qno���aIC�`T� #{ � anelabis i� cons xa�Mlfigv2!ingzXC javier}.}>E ,�.�.1�,�<inu���� @ $0.6 < p_T/n < 2I.!R�9aTu,, 6Vl�.4%$a�. O!����%!Ju�,��.�&ch] ����Fby cw-� >p�J)K�!@P �� e Ep�9� �A"� q�"�i�5�;h�#�D• �j.� a��ds��P !c� I+ M'�o� already!E�,V;E�sugges �|� ?Fv��ro�=a� �bar wF 1v -- o"e�q--2gT lo�re*7a� �>A��Ube!to A�>� *� {Hi&Zs=Des�y� L-�*�� n=2$�#�%!";�Re#e)d�rmE\j*&|IaL� rameG�"��re �iipl� �--�; $v_4$,AT46, ..., v_{2k} $'Aa-.�Z4w"HAs N 4}���"Ze�!fourth�6G ��%CEQa�9-�,�NGsn-;zI� D$. Within eI>�6$/�)4��N�v4_v6^� 4}MibX biasQB��B_of F͑%��1ͩ�{sA�@w $1.2\cdot v_2^2?63>sn���*3 ��v1v4pap�$>�_�wa��Qcq��}rO)���^{n/2}� 2u $\phi$6 0on!��ccurr �" �r)�!�koq oU�^q = 5�Y���Y9�Ln�s $U = 3/4%� �,$1/3+1/3=2/3 -�,2�R. Ah, ��'a�!�% �$be%��%P��=� 2��o1t!�%�.&< J. �* {Summ9c? outlook} 6 of iF�s���A�"m.J-�-f*Y>�&� a�6(� & (��nt�&1V9A2$8) 1 \E 2�1M�M�y�iz��n9��A�)��W �&al uncerTm$D�2�&���l9gedM�%ppF, ��-��Jde�!�( �! 2x"� P+p 3�be �T&� � �XE�� 8�Qx le RpWq��&)Dic5}�� �^.H hw���)2��&� 6g>�4I#.�a�n*W!W!e.�noA�tQog'=��Te�}r^2"J��#���setf d&�$run IV!�8!e"�! �!�ly enh w�y.�&Q  �ed2.c}Tbe nNt� *'6�m:$$m?�M�p@%io�#tU%�!B^K�outcom �ew6��;Ore;(A�eV%�����e�0�%�a�͜�>seM�i�*� *{Re�&c�:>R7�C\btem4 Poskanzer~A~MEM Volo�5 ~S~A0>d \PR \emph{C} {\bf 58} 167*�;*�&%/����(ple Adams~J�"l (�2M.) �8 farXiv}�(-ex/0409033B~ be p16j.��- r5 !j rein�v $} Kolb~P~Fs32B �,68} 031902(R�H-2��0s} Sorensen~P E%>�30900*�;a�$2} Adler~CjU1�L �$87} 1823new�  �K2.K 9} 132301HGS~S�2!6��%0 �91} 17K9b�1�~�M4�$92} 052302Mhuo} Hu!k,5�$, Heinz~U~DuA�"~VF�݃ \PLM\B-�503} 581[0Q�HAIP Conf.~Proc.}\)�698} 69*�D"�!� Jpr��mu:A���&�:T�>T40500=q��' -3 �G�Pl� 3, e�>Hwa~R C:[8�4:]Greco~VA�~C�ILevai�"BD�g 4904��Hq0} 20a2@���>T��f2x��!:4�R��y#� C8�llo~Jr�4 \JPGi�30} S120* F*�-pE�K)��>A�:�70} 0249�9D Dong~X, Esumi~S,}�, Xu~NX Xu~ZVB�97} 32**E&��l�1��F6a:9@A8 Ollitrault~J-Y�3~�i:"ng6VJ{2*I���(, Chen~L-W,Y�andz�69�019. Yko}Q)��Lin~Z-W �}� I*S��1�?>B *8 �K6�8 {els�2 a�'andNPgr}{$^0$:$fmn}[2]{\mJ)${� �Re �P #1}{#2}}$�neSrd} 6{�{>!b�+}[1]"�# $#1BOfsJpe� V9 ,amssymb}d 9 u frontm�$}89{DP3�- parilD� �4{pp\to \pi^+pn�` Fd}"�0�&,951$\:$MeV} �o:o:b t9GEM6 :} [a]{MT.del-Bary)Qb90[d]{A. Budzan�LiCh%4jee(g]{J. Ernst `� E�X8ies, JINR DubnaRss2�m]{N�N� ,sice, Slovak24e:�>c��y (fia, Bulgar2Nj]{ � DKf�k]{h� Chem�C%"ology�Metalurv�o]{�N �al?c!�6o Hels�a��nI�%�b]{Ze�ll'@U�Elekt�-�df9�FaculAs6�S)� 9��hY�.Pm"onD| F0pVOs \& As! omy, UCL,&V, U.K.��z��+"`A%%poH/�?" �%p2L�&5- *�7J@a beam "`�640� /c^'me�d��0 &3�,*a���$�ge[(tr�X� mis%>�6� sho+(ads�=(deVon�F� �?d4 $pn��ntinu�NDebz"�� �,�ss no e�9����q&&2"O+o<>m�%�spin-�let � . Howeverk $\sigma(2q )/F d)$ G~�#��}7a69icei1���e-$$S$-wave f�+-%L-� a V �n��B�"t��>=$D$ E7Q. . U�� v ik.�*A��,;%�c!�/tr�%D"I#% = s \P�B13�BCs\sep�B40.Qa �i� .n b� �  a�raI��| nsiv40ter�0e�'$E^� d$"�  qʝ?�+�:sesi0co&bu�si!��,r\.?a?�8trI%+��BHs%�em!�qi��� s. U�z�, F\"aldvWx i�9�extrapo$^%Hemm)���9��a �!he �*�W ��A��s&pF�BQ�FW')is&�p!oE?to��^P-"�* ial �re�4 (cm):a��%�m7 !�on�1in]�r�eW �%�"[for.�d$M�0Boudard96}: %b ,!6}:>equ:d_p��f��\rd^2�} <\Omega\,\rd{x}} �Ş�e\{pn\2� \}_t)�H,p(x)}{p(-1)}2d�y $\var"�!Mhe $np$=Zun�p�"B_t!.x=6/ A@$�w& $�$�iS�  c� f`enel,-p(t��f tensorA�gs� Q=ld� be +i� $6h(B� �mI9A�.(f b�.� !%5�.� �� ��%=�@Ex}/E�$ ztin R�_�0 ��#?\aJ-  $ �J�?I^>�E�!�rep��d )7��?$Ar�vir�)�%1! $S=0aT=1q=. AKE>x�&a7��7�Pec43n��K let_��@Z� �� {s})= \xi���j}�+B_t} :s�j���{t})\:,} Q�}jwe��!.Q$ $\xi��qu)8 �*a�u -+��-3]�. &�A best2� ��"t�M so f]� chie�was typi�K�M =350\:$kef Pleydon99 7ny� � ]p=� sme�%*�lyAe�&�$a8. "�by U&Y>FC�K�a�"AOt�-F� ��=a�ENb�esubj pi�oa"-��m"�*��$ 1��U"2�.�BI?Os\�.si� o�7 $�$!�� E� �m� *� di�� guar�/ai���a�Uq�"� b i�;�!BŨ �8�\\Gabathuler,Abaev88,Falk8�yB#{, �.c%7T� i��+�d� eZ01}�.le tif�2` M��=, �2 & ive no*# "� �d$.� }7? o im�+an�:p(,�cr��7UB aE�M� ���rum�U(tsch et al. �Blm�c9#~Mtw�IK9K�t bhas. r�t4on Monte Carlo�+uX s.f 60)L7�,G A��(� t.�~�IQ�!�el�W st 10\%��%�.i[o� at yGeV ater �;�j4sly-E88}. Q 2}- ��EbByfQ v}by )Ta�TD�%I9��� �*}T.31 i�%gQ�oJ<�:�%R�2p�T$ unambiguo%�!&�� ��:*�|i�/our|"�/ goal�0n�Dn�\a W+&?,�O- ��ܱ8"�:�� 3Q2D-� Big Karl-�Dro0�'M COSY  eler_ n &���K�e�Yk �� f�Hp�y�-�ed ��c�>�9wir�5�vchWN�Racp9 A$ six layerA/&_SLvscint�f,or hodoscopeGa�,� �:!&tim�Kfl�5L a �-J 3.5\:$�{�Oto optiA�E"���,3Diquid1Cgen t9�$�mm:cku��8us1$win�m*8$1\:\mu$m Mylar-�Jae�9���!�Ie� ro��oh� �O $an�Qf[4,;%�.stochaoa��K� 5 esul�1�eN��b9�keV�R6� Q��be�G� (<a};undh�.a/A�MX�coos ���� cular,b.�]grFfcon�abl�ducwP�"��"$Rer}B N[wڨ$10 cm]{FW_�1_A�;` >c��!�)�5A�"0�/ (hista�m)�� !91�M (1@)A�K"� ��y� N^ ~\ect�&��'�� �1�p!p�5 of�Re"� ��nA Fig.S:� as&�͓>� � %3hA��ڜ*]aCp�8D&etc.-&1 P� se in fac�Hry<%�6�se�i@l=2� MeV�k"� lopthm�3"� )w,� is��(� a�xcell��Zi�.8:6�&�]���k�M l%�+�Z on��Zc�l�#��~lk2.�m��� �&Xd"[^ �@"� !�S v:� d\ !��: R AlsovQ��IW�4� 8 *+�.s�CNs� �b;� ��� ��a�30K �UH�binQ�%gOis5zQ) too 3[ag�Y� aE�or�$2.2\pm8��@!o whol�� � ~Y�Ynt'L�L�a��wi�� ���A���a]Fs��k�w-�saFQK at "�Le` rad2,K niqb�].N "� (���<3�)�� A�e �seA!��`lapI� :� poor.��Zed���'�ref"o "!Kascri�?�ZobKtwo�]c�j��R.�ofy 2�( We can, hoFcheck�s hyp��gin>:by stud� Iji z eU �����}�Uingz� ��|�oCo>�+� ed�B1U�� a �4ar�l�W��of EqsB,"* �_}S�!Rm� ! '��a�eHD=��Ya tiny��� ��"� &� �������. "� ~��N�AI"�6 |9!i����Cp$a�a)� :��m?1�> harpake i�thres�_n d�!ourmA���#`k nt HN`9��yC� con�HQR.u\&� �}�&Uη�{�(�Zmod�OR �sAb�� r2�(1+*}/E_s)�try�fakEWNccou*�0�S�� �?� E_s=24�z��gel#a^*�!��q�!r�O `GWf� ,�?po*�Ji��:s *�!�e*+ ,emph{ansatz}�ubiou�2"no�J�gE`nee�͙��ofR�� - � s.WE�q��E letJ ��tI Z pur�inNe F?zbB<fEPam!�AnuO���E��( < 10^{-4}$�&!n\��YFB&Z �v& �a p;� vani�;gΌA�i{��DO"ons��4q�W� else�r �fD a�%��h.� R�  �#AXenG#%?pioWI]R�O��w]�>"NH�:lvaN^ nYn �.*BZm#a��x���(:m�!�h �a%�rcd!�c� 5#eifugal��ri�'yR'Nlso r�A��gy` Hul�%coɼu� e��H�^ig�V!�HO �E0d*�(, �$�U(ba�yi� x, e�� if�$D��ter�> ss% "�. a�A�id�E mia�cop��al��2 �Ełe-body � :� "j&�be bey�eA�\e O:b �=.6�[:&l�� e� � �E!��V��stp�c+,"� �&"�� H8q ar � \pi^� .�!:�fol��efm!�� E+* Joun:K�"��SZar�^�u2M�Reid}�0a�"AT��tea�is reI>e�l!��c-�ata PSAID}aEI 5ہve*W U����Z�l��y�",�� e6��no.%�l,c[ kin�YA0s�aA"$AMZ^W* �t�O2�^1$ as2�60$�� �da� sh > ge*�D����#.~,t�ie, �pai��F�E��i�an�a8 XbQ�"[+i�a� c by uv M< 2<)w�opp��~g%��1�� R� � "0� �Rap{b[*n ,bs=0]{ja _cal:� 9) "c,�e>r"F:i|A�%*�e��8d$&�\)l�"�e5I�id �R��A�eq���ue:�e�a�e bro�� P>� r.i{&&�FNR" d_�� 5�end� ��"�-��J5^06>�s� *�]�a�a��qd�h� m,_cm&�I$�g= p/m_{��};a��?&�$� x ci>=2���EYp.�is E� �� a]avera��}rl,�f8�Q��m2Ylsa����. #G,i1A��17��in``)$�2��ileE�� er-�s tru{��hI�exact&\����7� , �M%lI�!Y�$1.6$ ($T_p601)Tw�bzL"�Kt<�� K�Hx�#�re!��$��B+)#�i�� � � 6+� . Gi!�n�2>�Ki�� �C!q�2.2�Cc�b%]Osu��r�S-jY�1ME�"��OV�w� ]di"T  U/�  Ak�� o��M2�iF� } ma�&fortuitoCC!!vor��NV��ceF w%�-�� e��"ZLp�>pRLocb�.H �is]�aUbqR0(s" " "�,P`$,*�"Fal�"To C f) &s ��x"�P:�s m/�B����4� �H5Y I.�In sum�,&� �!U�M5 #"X�+�  X$x zi��"J..95 raeF��"t>/6i+"�E%�0N�le�� 4 �d��  &j A�e Aȁ��m.M:N<[� xig�t��s�F����R()聓 �|IH� a@!�� �t*�*1��R,��e� 8�� o en!Cas� coupf�$DAi�b���ME�%H��ho�d%Mai zt�a V� ]�&NPM��l%%two O-r d�p� � ��!�1!t�$�1 &qE �B;1Uf�y���x�5fn  . \\[1ex] 4s9�i&ne l^�2�^�#ork is �$^ A,o6gM,#"x- crewX2�Qby BMBF �:H (06 MS 568 I TP4),��er� } B\"ur�#s; (X081.24"6(211.6), SGA"�=$ (1/1020/0OAcadem�F@< (54038),BA�R�?ul`is l��2ly acO6 ledg� ! !&!>?F�O,!QN( R.A.~ArndtM',B=h.\ Rev.\ C 48 (1993) 1926, ,F��gwdac.~@.gwu.��}.e.<5 R.~Bg 63 (-M)�H0012���4 H.~ ^�53�6) 107Nj&�H�4 SeeE�P:�BilgerTQ?.\1A 663 �63��UFW} G.~Fg=l�3C.~�3�Scl� a 56�7) 5662���} A.~ ,j\:�DLett.\ B 389, 440 !�6)2_��} R.G.~  et~alF�59�9) 32082J&:} K.~Z?B �72M2K� V.V.~E&)reM*< LNPI-80-569 (un"�, ); J9� G 14�88) 9U�.�� W.R.~ mPhy]�32B5A�7J� 01} 2�2C5�521Q�,158; Y.N.~Uz�F�� F&;1;96&�*A'�*-�F44Io9) 1792{D&( M.~ K,F4iY8) 552J&' V.~ >H�D rum.�A hods A 34Id 4) 16R$M.L.~GoldbDH!1$ K.M.~WatsRD�Ri-�ory}, WЏ (NӐ, 1964),� .~9.6��U J.~GF�29�� 78) 417; ^B]/�286�R�R.~ , AnnY� (N.Y.) 50Am6\)��>� F� �e6�K[12��\*q�"]� %.!! tack:"cK2-dcolum�F.Cams�K6,su.�ab (} 6�>ф %\ti҄tw-r >�Z $p_{T}$]{F)��C*;a,ran:�o:�c�� a de0 n�� �r"�ph/�inz�y�y,}=200$~GeV %�M �M�ha�i&WNT]{O�f &�B=r�;LGC�A:bz:�y romiX  � ?u �2�M ��" {Pau��TVH{�F��CfH�aliforw�P��ad{prs r�I�WϙZic�fa> atqB��s_B�����EmA"%A�a=DonX ear �c%�,9yon-to-�`R43?nd 6kj�+�e…J� ($1.5�j < 5$ �c).�PBgmn�!s"�(1)j 6zs, (2�m% ing AicI 5� rk�!/ �� empeUA(3V v�.O S-g�U!Ie%_�� i)B�B�F�r� �Ua a�0:�p .�]���0$I�.�+a�� %\�B{� .$.�, Ell�(Flow} \paR��eMs2�.s)�{2A��+iU�} A ��{"L��ans�/�psŤst%�Brook�*n Ո L�H90y's R.4Hl� Ion:Pid%�1]) is:8�ui!� ��d\2ò�eno��e�&m�Jyv��*p���^%�?�W.i��c4�rk*bE/A��!.� --- �Rit{i.CjA 1�oa�s z] roam�',c eater�*nQkc�"�]"�>! }? LattSFQCD6�&�I�x}% ofacMm� �dL*��T#'c$)i> and %o)ees ?�!dom b)%&� 84���) �E>a"[�*R&�(Ka0N:y cy}[��*�l)} ( ����t�*n;M���$)b; $T^43;��"d)�"$T/T_c��.��r!t��c�pw�_{qq}�d�b.���%�"����l�2U00n $�,)�E� �,s s�2 feel *�c��n�� Kaczmarek!]4gv}::�``rem�%A'��&q&9��)��E�1 c��anz��(r,%V)$���avyFT�}�.)�ir *�$rO 2M�$1.05�g !A��$1*hTgh�OFs �b�Necco!?1xg&����TШr>�'os8�*dthick,$��#e �_ bf{L}��9cav�4�X�2A�.�.} 6Ս�Fcz �Z; top�bi," tAe8~Eh��f� &}"@66�����7Mw�5)$e fireball!��.�s[l: s r.�iandE��3s. If���!�$T>!��s:X! GaIt!�!G� W�� [4�sil�0�Unc�}MturLr��d0i.<�$  @pɠss��f }�c�v `d (E�q�5� )=!/�{ �"�3F�9��&2) - B-V---� �;6~ ���� !�vacuu � . (r)$ / %~d�% �oH��! i=p�Sn!�a!K60oF�. "Y�thaMi�!�c2> �'k#�$&� v�)�)m*B ����0�:!���o�� �� �A����lQI$�( �0,�$+�?HH��y5B Qfy�d,كl*| ruF�nbUx �s uit{may��be_0�/0M!=�?�p)E�BH �K/� c�e~�{} u+#{��_nf&�7#��B��_qqV#} �7��^0$[]{ Left: b� ��"�)�A� :�F��x�oN�RAfq �F�B� �2�I� n�" ��N� i��INtheir0&�$r$&S#��n&F# 2Srde� gli���onJƞ($p=h/ � $) %�&�Ca^� $p$�X�oY�w:�[.� �iit'3H olveY�= b wave 8$��1q) rsel�LM�4��@x˃l�.in� ing�%� ses#.(lDL witḧ́��'Gh�d��) �un �us- }t!� k �B|l�S�� �P99 �aP'� ,(0�*o(ele�T�0rb�of��9�{��& 3kg,�j�3 3am} �97w>gNEhlmsb:>a��J:azimuth!.A����du '� &�%a����KF���u9�6� para��E�t�am�� 3kt,,msbv294bi��A)E5QF�}[hbtp]�ing�"^n< 0.65�� ]{Rc�C}&�� R�]%�var86���X� 1_WI&8^B�at M�b�MbSD�A�i(t" �rcp>� ���9�rd Q�"a=e8�Yg�&��Qy pt}&����L$K_S^0$s, $K^*$(892)4ZhangA� 4rj}, $\L��4$s$+\overline{ }$J $\Xi:" Xi}$TM��ms� �(e�it "���:�@cle�4e�s�E�u�m�� R�,98�'� l� . At�n=5�S, 6L~�Mmb%�� �6*�7\�+cS)e <� � four73n� aC;at���&]� of j-A�5;  <V98䆕�seU%� ��IE|�5up%�'ɇd9�simila��6.s. Byj tras�;U�5a�~W4 and $\Xi$s$+\�Roverline{\Xi}$s rise above the charged hadron values at $p_T\approx 1.5$~GeV/c and Tach unity. They remain Z V V@and kaon $R_{CP}$huntil $k5$--6~Gl�. Similar observations were made by�8PHENIX collabor'0 with proton v AA}$�ing �pi �� s p���$ region~\cite{Adler:2003kg}. \begin{figure}[htb] \vspace*{-.0cm} \resizebox{.595\textwidth}{!}{\includegraphics{Fig1_color.eps}} \res@ 405\z@0LKPPI-final.e Av�4�cap!E{ Left:!�-$/%%<$s measured!Au+Au%\is!h at $\sqrt{s_{_{NN}}}=200E#!�)�, compaHtoT mentD4from $e^++e^-$E!$p+p$j0. Right: $\Y�s Xiz�k$is not mod�zd!�change���underly!�a�on:�0will not lead5aT a�Ni)�J�$. In non-1�nucleus- �i�5�����!ellipticqf �f� m�   i J���� l� t} � "7 s. Curves%]%�result�-%-���elB^� . } � v2>� F p_T > y),� datae�F dev* �eM',over-predict� �qd-�I�RAj1�-l  dependeK reverses:')� i� ����n&f � sI�fol�@a scal�*law bas��n aqnumber!�val%�)���$correspond? ] ($n_q$):�eque3l} v_2^{h}(n_q\cdot p_T^{q})=#q}(,�Dw$!�2^h �^q 2%� q$E- ��Q, �I�,��9� �|pec�ly. I�is1, holdA� �h�h/n_q)$��uld fall�kaar��� ��_!fYX� >& reO 3 !�ml%� the �2�  prior� )M9t  v2-�} | �� test plott!� {ersus)$,��Hre both axes have bL AE��polynom� !hfit�!%ߡ�  6A~ * un2JH�t xhe bottom panel. Very good agre � M��mT�iat und a>�)I A�E�pt�� 1%g�0 �l>�thr��ou� .;A� r� A�are� 9 [ hy t|V��does ne�arily �al a vio� 1X�e�ecause�� �sa(  u�to ni�S domk �� q r�z� decay���A� effect�>)a-�Io!�o-���sEb f!�Aba&�ve�I � ewa-�-! ,ificantly in�r"� � ���caya ��� }[�� vq�200GeV:2� Q���!�"X (ɶ�w�p�u)%0A7 ol�~� A� Ref. �"s 4bi�.S��w��2� 2�fA�PA A�a2ludedo%qa�butQ  ���arison. "�5:>� The�r�e-of-5�AM���"�i.e.}(^{\mathrm{B}} > BMA� }}$)Ip*� nBin %� �� ���-n�|-!��e, poin�5possibl�EӁn� formNq-X� o@*N"� in����F occurs� 6� "� �s� š���fully>@ sa�ree2oM�� Th&6�" .�one wa�V 2= �c�b1@ed:�mtl� s^su�l� prec��: I�#is st_,an open ques!���e evi� !��c%�s�k �1ra�e\: cl� �#in� �V�theorel`el` \s� on{Concluss})c} IdentP" ��arIUl6G 2^d 6)F�� RHIC > a��an ap�nMB-i&� eA��,�04), 1.5~�!L )weF6�" E�gm{ ��MqofFW� 6*� Z)� 27�� B�էsIwrapid�hL F��A��---!LMEa)�supporA� pictureR�by) 2�r a�mbi��i�ji� ist!��A�a;sS @�c�A�%�6q�Q?��2�":"&�d . Ar��a�.K��� step,' hightugga�v%>A��{of onfined)F0-gluon matterI�)e" @���%� en� I��A� � tempera%�w $T_c�t� cools E"pprX �m$T_{c}$iJ 8#1 ˁ�rgradu� re-enforc�ILattice2G! !QCD�|p��A@tant $\alpha(r,T/�)�src)9?eL pair"+��isl�c�Y]uzH�QCD. %1 robustnes�<%��� appl!� to l  �!�al  %�&� s ^ �bf{iDj i%!9empir;6c!ed .#I^�a ��.B ra�omi>F EWZ E{� of �B�M�.} Ո*ynowledgEUs}� authZankj Ayer�4rganizer){acBs�u" inputI�pH.~Huang, K.~Schweda, R.~Seto@ N.~Xu. �Re ps�t"$thebibliog:"Py}{99} \bibitem{��} M.~Har� ,, T.~Ludlam �0S.~Ozaki, %``. F�czmarek�4gv} O� , � Zantow%,P.~Petreczky�SZ� free�9a runn��co�W(at finite %��XarXiv:hep-lat/0406036; f�.�qF. �� Heav�.�R�en� Hlized Polyakov loop�-dLet!xB-l4!l41NkNecco!g1xg} S.~�A�ommer���$N(f) = 0 h�po��a shoLo2 Z�s�M� � � 622}, 328N��} B.~$ack {\it e�0.} [PHOBOS C.C&]�C '� Kiplic�� mid- 2�! + Au %.� t s**(1/2! 56-A/GeV%0130 � �Rev.\1�)�85�100�0); %u�Adcox%�ry} K.~F�0'J�MX�X_2�trans~U�.�)� s(N %N)���A)2�tv z� 7}, 05230I�16�A�1nb} C��:��%J�Nh 2F !�V��� % ��186�.��2pb��W�zd��iR ferometry!�s(.�z���:� %/��X5�)�jSZ�PH^�Seproper�$T%*e�*%%� inF�200Z�v�91}, 175�:>"�3am} J�ams��PaF' �.�ofVp"�p##>V of %���Y � ��:�:K-z ��e�2��4e�%J(msb phi etcJ%&��& H.~L�$ b��D�M*� Of �S��ge 1Vs�&[�% P(T)�!� %Au�]H( S(Nn�)v Rhic!J.\��G�� 30}, S193=�A�3�S.�E�$}#A�f�sf�:� q�f�I�:�>"}�SR"��3wi} P.~j�1�:���)��^�217-�; ^�kp� )# Ph.D.4 $sis, UCLA,A!3,  a�L-ex/0309003. % ``Kao��L-.�:~ p(T):�  !�t� %)����bul�r�  J �A�2� %5 !�Y�msb�!K"� j�H� �� �N^k6u;�? 5&4030322�C�(ll� 4jy�Jj�B � -�)� s Xi �9Omegab0 %f^�120QR.R�272l �.#�.AZ�(R�:�A��!�:�409033�N�%� ptR YR,pt.�qi} %�Sup�Ppi0:I8!.� �)!�� 1#B� 6P �C%z"0.A�[:V304022].*� �(kv��T&� �A�u���cZ!��b�2 %�o*yb ultra�+i}, ^i� z0 $3)�' Zhang�(4rj��b.~j� Delta, K*�rhe/�(�*�! theirb�ofRze-out %h";R  3010a 9�.G.��>� DELPHIS"�'�*��������G� Jet� Eur&p��Ct1] �w0� �.�.>>�LBritish-ScandinavianN�P"2 S�"rap Pi+-, KRho+-" ,Large Anglesc P�  %� i In� Cern I�$Z8ng Storage Ring%� 9410r 237 (�/���N6 methods N":9Jp � Voloshm6 nd YM�iF %�,d. (�2i*��� u��&N�- %��"� .�% Z9 M7!665!96��8A.~M.~PoskanzerERr .��!@analyz!~"�.ic)5iZ��a?2 �581 671�8!�>9805001�9sBL-�H.~>��N�6b� s(N *MB�\i~86}, 4���:D6pid v2&n9�-�YB5�-K0(S)E� +0 .;t %28� �W�C13"D�6*�,�� 9A�,.~Hu*e� �P� ,�ZlGyulassy, I.~Vitev, X.~N.~Wa 5nd�W.�Je�enc�"r!��)���e��A�*� th207� M�6 Rec�f��Y�5.�Molna�<ff} D.~ �J�6at^8 aI&/*��P�J�5092�3��Y�HwaI�nE+C.~Hw10C�YgA��2� �s,� ���ll� �/ ! %� it�2�ͬ6M 0649��:� FrieO4kq�J.~,AGMu}3,�Nonak �)| Bass�Ha�?�minO &": F2-0A�6+! %e�aM�/on phasF��a�04^�GAV%�mm} V.~� M.~KP.~Levaza�oC7&�/��B!2� 3490�?:cr�xt��@ntiI$; X'yb��}��9�L 2023~vb��b�"#E6C2"�o 2�Z���B�4ng} %R.j�6�of�werM��C&c�-6�A%:'401001l 6 �*? 2,�Q�%>C Koe�Er@,l6��2dM�� 0249�46�Do�ve} X.~,�EsumiaS"^F �ZP �R"���,�,*� par�9.�MV9��f��@>� $ \vfill\ej�># docu[P} �{%%%M.J.Tannenba�4(EPS(NPDC18)r$e�1�"ar� 9/17/2004)��I % Upper-case A B C D E F G H I J K L M N O P Q R S T U V W X Y Z % LowD�  QC+ mark ?!-y @ %T bracket [� sl!�\ %-f+] 4Circumflex ^ $ Undersc�C _ % Gr�2ac)�` �a*{  V,&bAX|2�+}%  Tild ~ \q�c% P[fleqn,12pt,twoside]{�`} \usepackage{espcrc1} %�?t@2� +G�H� useO(LaTeX2.0aQstyle[.y, � i�, % if you wa�.'$ PostScrip�#gures2�k%ics:� psfi��V>,(landscape t&s %�[�1sr� ]{rob$�6 % ,&(your own de=$� R': a�\newcaL$ |. \, |en $}}{. l. < ��aRful Jour�5 macr$� ws-�az mat-�' u .d#1#2#3#4{{#1}{#2} (#4) #3 A�Som�5_j _ name$- rrec��to PR�fM)s `HIP{{�&Ionas\�0IJMPA{{Int. J!2.%.}~{A}\,�!b( A}} kJPG{{J ? }~{G>= EPJC{{Eur j }~{C!,NCA{Nuovo Ci�o SNIM{Nucl�8st8)7)od�5�NIMA{^#~Z) � .� P2 � BKB�PLB{{� }~ %=> B1PLC 8 Repto) �PRLv V5�PRD�� }~{D�RC:)b �6; D�4 �68 C�ZPC{{Z-�5� 6234BAPS{{Bull. Am ; Soc.YtARNS{{C�As.?}} )� RMP{�$" M! �� )rem�Oia8�KseVga4$publisher ��Tmargin -14mm % add wor<4o TeX's hyphen�0�6ep�N list \{�,ano^F-$7i=9� papei1-�{ end-<*st-�2pseudo")��decla?;ns�K nt� \title{FNBjorken � 6(QCD---Experee al techni�4Km p-p*�J�+1970's.+/r.UA�8.3k .){Ma� &� \add�E�\ics Dept., 510c\\ Brook��n N%i al L�ory \\�- Upt�?LNY 11973-5000 USA}% ! \� (ks{Research3�3 U.S.�art�x��P, DE-AC02-98CH10886.}�k.�P� %�typese�.=� make%�5ab� ct} Hard�4/2� l6��:discove�7a�6CERN ISR11972,�3�0mH��IS��5s�=�JrozM?0!�!AN4of Deeply Inel�! c Sc�stronglHteOedIeach E�."K�m&�*s utili�  �Cp0le�3p�1"{5 s es�a�:9�. 6�� ==�aXA�S2eM� two �=(ly back-to- jet�! ar�8e 2�s��B"!4u 8!1a8E*pG0Quantum Chrom�E69ui, mL}]J p!S4 -�to� hard.:Q$w jet ���J-# ^�,^I=�0�38Y�"1"O} aAI 4u>g>E4 re�.EC>�6�---in bG@>] lea�.�(DI t SLAC$:DISpG�igh::�6> CCCR,SS,BI6@ ---b�a qh�E4In � era,��4 lawsL�ChV�"�J$)X@�at*�CH@AceaP�<G (c.m.)�,"T}�A�AnkeyANc5e�Nhy�Z. Absol�cr�F� $s played a?Ial role] �T� E�zsB�/,�sym-ic%�or A+A�#\�'e%)al��su��F,�ies---�L�Pa8Nerrorͦvar�N��I}8�Ac~"l�h;F dei Fa|ata�t �,$90^{\circ}$AkH!� � �'re�Ne�Ethu""se�S'8B6 ongiPM���@s.ų "�;��a�u��on�5 el} �1 idea�>oin N-N)],$ s da��P firsHFuH��-  like��u:in]3��Uin 1968MunBd�!i�! elec�� ��?m|a�, �?�9&y 4-m��tum*&fer sT�P$Q^2$�5���a!nu$j9y����Bt�щmT )"bS BT8<} F_2(Q^2, \nu)={Q^2 �V})�Keq:F2!�[6\�VF ``d''! j�T&d��� J�x=\.x}{2M\nu}tx_�:q *;>l��1Fs origA�&�: M�-�Bj}, �=GI>Eof -+!��P�'Q[-E\`I�s'-�><Y,9a�IMI�`\9im�quasi-�:@!=Q� AE� � �hi�a��p$Mx�[ith:^Bf=Q^2/2MxMnprobabi���a e!*carry ��/$x$}�i^'s& (i"[Vee$Aax)/j Si���DIS�Zga �?hC9�V-\1magne_ly)&� , BeQ,"3 L(Kogut (BBK)Q BK�subseq�K�9�h4IM,CGKS}, derif a8!$ mula%2�1& �iJ X p + p\rightarrow C +X } bbk1Fur }princip~ $f factorizj ��i�-)z�btriV�0� 9�s,:�Y�=J�  $C=9-�e�A\ -�rt-h��<on-Con� :�2Qis&PT25�Jo (Eq.�Xeq)G)9 {x�has���6��� B `S^QU� ing'�m:Mm CIM}F�E �{�<6�!@2 I{ U&$ $F$ $(G)$�E%!es'�F�1e��� *�G)�a;e�a d� E�, $)$-�F $(�! -n})$, �@$n$%�sE��@q @-\J  Z�?Fs. �RQED� Veaa;+ex�X-�V, $n=4��,a�of��rk�[m(A�MFN*a , YABY$=8�En� �kad�H��mix0��p)C�ereaks d:a�!�Wes�XC�$x_T$ &1RkN�`s"�K&�H�.�n(x_T, ?)$.>� {T,M,� �U� SOR, -1978}n ItewC?�V!(cosmic ray " �occoni}�H% ave�+�5>�b e�Y� >�  limi_to ~0.5 �E S&Tz%Eprimary�},%O"�GB�Ve ``mal�B��?&} {d\�2�a8 dp_T}}=A e^{-6 q�,.MCKPB����iiN'in �� $\la-��\N0le=2/6=$0.333 *. �-� �55.9mm�MVJ�:�4u���2�>;1m:��ނ�4.5�>� top-��Log-log� �@a/b�vs� =`�'; b)~(q$ X$� \h)$"� a,c&K-/ K d. �M*cI��i"� =3���^�Z�  %i�Sad2O� �a�$i� aafe.u gof� pm � $��$na�c) %FͿ I"�e6��� &us`al2bf�g ompi{by ABC:HI. d) 1m Fn�Z>$52.7, 62.4ɣv&5 ad� $�V75.A�xtBI.�\�C (a��In1�@!3*5��]��w�A lM��e.1*O�4rmi��eany 2Vibak�R�of^d/fixed �zthb�c��-H 6T - b:N�Vlyu N.nsit��a �a�%� 1=53.1�EGeV�>|te�$Z  8$ap�} )wto 5�� �EY new� .�� $7.5��r� 14.0e�/ s }$E d^3 �/��eq9^{-{5.1i�84}} (1-x_T)^{12 6}$}, $�j�� !w (e�I� all}Bs�  Anzor!^ fe/QA��A}A4�; sis :Qg})�? Q�-m��)$---���U[ab�d� 4le uncertainty� mA��jc �,pD��s!}r � �g ulte�2` 6! �e m�t��\�eY*Ts, rG gaug��V cM0��}a>f�'�` sensI��M&�!�Ndis9`a� "%I�3�&fcX hDq5 F��d&�Q � �V <� / }z V:d)i�&llp"a� � ?o"�>����a�uG$�eh�vi&V��+s <� ide� ata %��co>gY�] # ��qU�6ɷno{aqueUA�lB� .� I,��at��xA�u�a|q�a�S[ �*%��G.Ys�  *� �RuEA.i�9', q a 1982} &.�#� visi�2��at �nd`(F�qT�At6"!A �Z��.j%�!�due9R��U(\geq$ 2-3 ��)�"rdNpbrgv4�吁� %�rev�[!dYZm dR�"� %!istb  basicJ1�fct;e����2pn�o)��ai"�][o��)klut,�-by=�A�R� imbal�ofgo�!T�i��`6�,%� � �Ym�$CCHK,MJT79�a�!^r�c&l%� &�>E��}/]��/�NY �6�5��a� �qqh!�6�o=on�dona��8{( Jeff Owe nd�"7o"��$%+aFjp| �!�!X icle h#Z�:]��' �KB!��Y!�s��'(�on�� �#�)�<�s>�#2f��``�)(logarithm" �+ �MsumW�on"�s $a+b\� a�c +d$ (�w $g+q. g+q$� �-Vf&�� \hat{s}}=$ x_1 x_2 s>&RF�2d38d\cos\theta^*}= +�1}{s}\sum_{ab} f_a(x_1) f_b(x_2) ( \pi\2\_s^x# )}{2\x_2} \S�^C(.g.�#QCDab!�!�"�} $, $��rfJ�, "�-" "�{V )| s $ah $b$, "m�$�#A�O� $x_2$A�t%I�k�vea�oA� -�u%4�daq�1t� A�!�XA� u �U.m�&�:sub�2�7ang/2s, h1$b�$},"�icou6!^,"^_s(Q^2)�2\pi}{25fn/\L�O^2)$,�funda�al ��qQCD�\utlerSi� $,CombridgeMx7dmv~&, in $4\pi$�to*/te�\t�| eC!�or 0�n���o qT�  E_T x 25$�b �$Gordon}. N theles"��)��$false claizv,�1�eriod��7-Y�JT,k�0cism ab��[=&�@,E&i-t� _USA �MJT4}. A `�@A: nge'.b�q�g-c���by�e UA2 ev� u�ICHEPCPw o 82}� , toge�T A��5di5.� mQAi�p6B�^(^n$6� �r)"�woe`���s !Xr#c ��meeE J� qqXgav� E�� redi�&� �T(�WT/&5--�6��,D�^v,DiLella�� �0��� -0.1��d:p�9"v7:Y orqq�^&_-0.bF31.oBq_!�K&� -0.3�^�288.JqDps7*&!Sp����N� 3os�R mF,�82NPB}A$ pola�FF�Lup� io net n < 1C/cA�2�JJ�2�s}=&��63�W2�pi��&aA$M�i \pi�"E7.panel)e�.fj� �HVb*$gg/q q' q6�qq$)�d�� $ ev�Fg� �ifig�qqB.\� {Al��yth��.d=�# ��6}�;o�-u  2V�.} �1w ou� jet-)��4:t2obs0he kine�/E-(.H(,� �+��Fkfr�� is .0/ly .v)M"` $y=1/2 \l�1/0 ��p-p�/X. H+,�$�!�me*�na�tS5 �d�sb��-planar �cbe�cxi�A�R d~d oppJ5a�$"0b2n*�4i.�~pro�CE#&q3n�qy��( H;c�2�Xin �|'�#�icS�KfIYAny W's5%�B�* su�~:T�[i�p"�] �in somhsi6�1!*%e"Q2AZ�<� a�Ez, may be�7�r,��1 issu&eԂ&2 ca��}isE��� !����AiLs-relev&A helpa= ��6DAreg�7�"� 9CB''. Du'fst�.fal�$3)B%um&Z �B�I�ŹR� \pi$)Ni�6�HYtom�k�sI�z��+$z=p_{T�m/ _q'3�<� vari�%I & &/.�s, oB {��A *$}� {\rm�}�:��a�aP�} {{d^2C�3} %F,z) }�1{d � dz }}={1(_q>",}}\times D^qQz)={A&\(^^{m-1}3:N0 &m(�� eq:z6%nq�b"2�-�2y[ �"6z%E|1f%' j�� Ai1�I3-%Z �}/A$5}/ �$}}}|_{z}=1&tul� �jb42�22�RA]�LR � iE< ��'�$z$: F�^� R ,z)}1�*{� dzz>>� 65�-�z2}61��!l��5�pi>� TR�.�Cive>���,%^���o% (%D2/�`B�nw�!ed upw��eb�0a f. $ �!�i�m&F3e���� -off!���]&� 6�(�5�*$�T.�DE2q0g}� l�r}). AAVi�z��,txH0�/ us&C��tud'8`un�ed' aBt�8#  trigger sw)��M�aL )<t�A�!�� fortu���C ` -��' �JacobL�F hoff<��M��&�?do)�V� �� /MoriondQ*�%ng �$Angelis79}�!�N8@r��8m4�P.w����uni�**z4Xentire ���@"� �> age $-0.75 \eta 0.7$, �,?A�st�8� &��H> "J.eas<{eeL�d.' *G}� azi}a,b� �al6wassocI�dB,s���K% #�#v�*50.�J (azicopy5} %j�*42�8xe����%����$��N�*N�* ,b) &FY5�5%|�gB5i9I J�_����{`A�aq�Ŝ^0� �t} 7�� 56A�l�W: F+-���x#_\phi=� \pi/2 ~d� as�1ub^ � midd���jQ �ns��ly&� &� )!�� >�7 re�Z3$|a� |<0.�3whr 0o�* Fu�. c,1C$x_E$:� (see(J)`"���Ah",%��>�a�>�+Ya� a%SA1EAZa{Tt} >U1�� �f��i0vM==/�j"n" Ee��~� ,���icor �5K�4on flat�Bgr� c�Zly[w'�$!,di�X="�conk"+ a�i $:�60^M?$M��6��to�&>wo5]A�� valu^!=#!\, (>0.3m�))_I�width1�) ie��i�JpAa),��R3@Z6b�%N�utsMRtiv+,� � �?!fWX�K� �m�� �%W&�seI�b�Cco'1�I�*�=SF>E�%jgeq�(!jv�%A b�avQ�,u � algo e{*� � t}+1.5-�%�(o�� I� 1.5iB��F�A^)neu��-q5W$z__���jeu6�VZ�(J-meanz}I�� ``un� �['2. EPS� "��n8�-+ F��1�"�&��."�5j�n"1 "76,�  8e"1 *�R�XZ; b�a�c� ,��K� 6�*0"1$,JU.���s �$Bs3 �2�>9,����!o� � F�(�db* ×}@!�� %>;? ā��$!g�)!behavi5:z%� x_Ed!.(\� leA�e6<%#2�N��b)�}>� a��la.w�(du�b tire�o�T6�,�n�,8<|\s6�| �="j_�hi}}|/�B �Q`de�Ps�%N�Yor �-17�  $.RU�)"��$��j}�5���6zim���.��.�J�{vec U,!��9*�F!Y��7Tis"� s# ,�.�Fh�?�/HK� �&io�<�� nsp�$Feynman, F��eHFox (FFF(EFFF�5inMMe�k!!%�N��"� in aiN� �YR�i�I�IJ=KnA|.�(is�2} �7��ich%��*4 $wo orthogo�)n.�/&@Ym$,q;_�&_'M)Imak"etFAoa�.e.%��O"�O! IK�g6|xwa@%axiA �2�R}un�l3-�# y. O"I)C%�w t���a�*ϒ `!�insic'� � �(ent1^��\n�MtH*�C� ��IF: UNLOi(g�ne� A � aM� qHC Na:ver now%2expla3 as `)mRon'�| V%P&L%S� a�$ FFF�FFF,Lev�:�"!�w�xB�Q�YH �9") w !2% �>rmAQ�sB*_E$J���?�"(^2=x_E^2 [2'k]�( + �,6O\�J^2 ] +�$JFFFF�kT� A�a�} �!-M 80}�-ic-a�.?r�MH$.��$!�:� >e�VO5�~��F� jtkt���m�k'^Aslt���1� CZ���m?�.>DZ���&2o1W�{�<6}N$a[�'��/brs24�a��,E6�;tha?�>͟a)i.&��*Ћ"�Esh�no��o�1ia� a�2Rele`Mf�%�- beyonda�Aa�6&QA T$�!�-��'�CY�RWD�>(7t5t)Z:r?�Yr�U ;.:."u p99 j)<0e�L�/��0]d- �Dn*g�par�e�G>G��u()F.�to��T"Qq7Y�t5lme^�E{ illu�W!�p�A��{A��_y�� �p� �# � d. �j ��B�B7&� ] ��;pT�'b('.,X =-1 C?xT� �3'�3'n3'�gm   '-mՉ��J5 nB(W=�x�8L�/�X�B�*�� %�}>� ��jz�D*�)�kIz������0}.��5��*y$1� �. g)�_"f!���sV��'!�&�6&��\&x � y}\equiv �{O�"S�4o� Q��}^2���`>�3� x9_y�.�rgaussia�,L�l r.m.s.� �?i8�� j T^2=bx}^w  y}^2����!(B�T>!"">7k{99��z�V M. BreEbach,2�v, \�cH{\PRL}{23}{935}{196�5Se|� W. K. H�`nofsky� {�seeX5E_!iXxteenth Sy�al Con�cyI��^�b�c(, Vienna, A�L ia, �W (� Sc�6ific I� �  Servi|HQ_F.~Cah39��A.~GehJ�rgut� Leon�$SusskikL.j�1e19!+9752��P G.~ 6d}{1>6 > 58};2,L�Ko�� ndwH��rki��LRL Re� 8 No. UCRL-10022A�61 (un?ddiP167�c�Pby.{�!�.�JD.~Ant?�yYJe >}2 L}{3!�12%�76��H A.~L҆�#nP!�A�505P8P��,K!g lark�F4}{26E� FY�Hva��0{106};8 1976.?ABCS};rKourkoum�$~�8�����}q�R.~�y�Re�&�!.~.Fox.i �2!�%:7.�G��Della N3j� L!=L�!<�C�C�or1S viewx�kexA~� :pP-D�nd-mr de&= =e�J.~&�e,}5J#7%s^T9, �ze��.�NZq 59�� B.~Margol 3313%�a/=�.t8� U~{i�82h�LA�a:;B 6}{6a�TN2eo:�8!vL�mp�8,� Kripfganz�J.~Ranft2��0�4az6��80 T.~{\AA}kess�.�6&Oe35P983�U�"A8 �<+ a=@0�HR!�:�=�I�l��7%98a�_�4} {E�. 21st~ 'v �(��82E� �~PetiauE?Porneuf!DE�. C�:3}\ (�8):�J�= Repe�/�$ C3-571; sRh$p. C3-134,�a Wolf<:25D51E�WF.Q�Y�RMP}{59ᙥ�82$"�} P.~,@�k }{30��o80.e8�7 .< >z0)�6�COd���209}{2��!m.�con$,&���delicacyb$often glib�h gnor�)9UJ6�+Eue& P.~L�+.�PLC}{48�q�2�"}+I�!��% . XIV RenI%rP3 +0, March 11-23A��gL�r� FrzB, ``Q9�s,N[�� ets"A�gkra��$anh Van (E�K,s Fronti\`er�/Dreux,Y1979),P�BoggildE�321e:� p351�re��-erein2�x�"~���a S/tEe^79) 116��U�76:�:�Y�EGE�42E�K>�9�,-�EPS�4eR� on� -2l �!�u $27\ June-4ly%g� ,"� %{� R�2,��4�l22V�b}�p. 512�5� \��I� �.B�Y�$A.~Kulesza�| !E�W�� gels�=L��66}{0140_ 2002� &; E� ZMRy� , Sov�WJETP 42)�5)\ 786�O~J9�Ł9��6妁�=�_�� Apanaseviv D�_ 0740��99���"t:>�a#"nqh%-j HIPh-� late.tex b.%|:%xVxhiph-art6]wro0!n_w\us">x�wx�amssym3�def1Y6�t\bf�t"�t.�.ls \em .ps /A_rPRL"a� r}CTsC ! C"]sEPJA{$6^t6i IEEE% �#s.a� �DcevStw ��kth ~� ANNP*�r ��sP Prog.a�P �e X6/�st �r �"�s�XJ� A,h1ed}�pb;�%�zTemE��r �Z� �L� BL Acta%8ica HundG ca A�pBL�RLBzw�aRL�L�PLEASE, KEEP THIS HEADER WHEN COMPOSING YOUR OWN TeX SOURCE� L� L��^ L� �Pl��, submio=f"`+ �q6.*L=�AL�un�ung�iRzvL His/�e-mail�F LD ad!0ssion�PL� L(Also, p%��L 't forget���``keyw�w''��BL ``PACS >�,b�G.)B/rL^�� L� Yvol �{19} \iw? } \edyear� 4}rvL9";-{000} ^yag �Lr�(,vdate{1 Janu�20~�B!|_� �� markZ|e�M��"s@medium0$B. Krusche�Q\t�yIn- .�)e"S�n~�2]${cy s{ N($^{1}$ % %� dex{ h , B.�Abb0� I~�! PP(s), }\\[2.812mm] {\n� size&0. -8pt}$^1$:Cy��y:A�domy, U�H3 of Basel,l/ 4056 .�4\\[0.2ex] % }%#�v{R/"�#�0�emYJ��"��6J FJA�Q�d}3[s�+�P��TAPS �Wcto�\s tagg�8ho�D7D-Y MAMI� lera2(in Mainz. #�d"�#@.K!&D��s (A|l Q�7^o X$,�Yeta $;M^oX�% pi^o{\pm}XM�W�% i A02}$C, 40}$CaQ^{93}$Nb�0$^{208}$Pb up�"Aj rQ� re�j)B1� �,.�1��CZ�4P$_{33}$(1232)~OD$_{1 520) �IS1- 535)~on7s.} \��{bZ,) 2a!�Zi�:��H{13.60.Le, 25.20.LjE��*�,x<2"�e� %\set�0 page� &�GIn:,!�±i*o} .�e�*ig6r&rt4$es ($r < 0�[fm @a&Ñ0%y E� poin&sq[ a�e*s.&W�i�%ra&KZs ]��u�piLu�idow�, <*e��J)De (0.1 fm $< r <$  )��L� gove�d�-�a!AAE�2�A{ is m6��ful�_ plex�!�? & L& body�Vi�VfQH- , sejn.+�+�<es. At �NHE.3m'�,K& becoLD�-�of� aq�p�k`Ua�XtL��d<>0mework! chiral pe1�o%ory. C �y&J?vQ� hear�+�]Efy�.&�jih^s��J�0at t.X 1t"ʿbroke�i%� conn�1t�k�V zero ac-�#�84$ar $q\bar{�FpHq���`'e�k�` densS As�tt�!s)&�E�Y �0 2ORztraA�6�deg!e�1�Uy du� Z Mo>n� �9��a h��! +�e�b !��A�7#ce Az �zo �u+@�Lutz_92q+Itfvel:�]9ne�P&M��0�T�=oruf wU1 aFg�E�/S�( �|J One}>}�.m>^.}�c Ly =�A��ma��A�\rlL��A� i"�h�5 so-��,ed Brown-RhoE`!�)H BR_97!E�C!�K�J�Ed*O�en�rched#iiK*>.� exs� ���V=�ed shif!&Zi�& $\rho$sI� di-K-Vra. �!r�|s)�CERESa� ?$ �4Agakichiev_95,�ova_03U:�7t*��y =1.5cm {fig_1a.*�&& 0%}%j6b6\2Uh5c:87Fnc8n3�4d 4*t87 #g{Self���b0 co�Vٶ�E�A�o, � ;o side:��* To -�Ňarh-�Post_04,& 9�8,��. mo&��x& ��h� inflF��,Rx �i�6T o ly,ԍ, Leupol5Mosel:����\ɤa&l=�n"��aлe�al"E).��&�in � ar ݙ���st)�M�m��3�\e=self-��%��( 6in fig..�fig:1#��a$�,1LE��~w���&�fCnvolv�C��t��a1U "+ 4u�zto- i R* M(? um $s�s@p'z.M� - ؍% !!�o1��N �b{I@$1 dh� e Q:6n 3n1)AI�ed G��*�v�H ffec 6`* �qX; ��� KE�6 y�.�)Yose-byb ��m�moY��ed �q}� Du@Ht� few sn 8Y"D8�j �J!8Rm~I� %� -I(uJXtE���� �Cdu'_��-�programA4{" f�"�\ maj�;opics:#����izi� {!�investig"U�Fu$�&U�P,�$ �*���gl�n���e9i -��8_95b,Roebig_96,p9,Hejny_99,Kleber_00,Weiss_01 3004}��� �=sboYUiS ( �ic �)}K9w�3%�d�vǁg�EQ� BN2 [z+FI�I� �02,Pfei��B�ZZpRLW2�< �B$.��)�, aim�5 Y��=A�� '$\wy$'!+on �Mes�ndorp_?{uteIc:�1HYes;�_$\o.���� �E�A�^o\gamma�ncayt�xA� O��� rst e�?bg shf"�!i�� Au�� �.Jex�'�' �ewnN S. Schadm��� �����-e�}N�J"�4 D. Trnka �Dsam�Hpm�i�!OAC..A��"�X&�ss�techno|s.��cU\peQ,Glasgow:( faciJ� i;l� M]# mic�`F��ey �UBremsb5hlung�s.a� �!G850 MeV7�� �a<�78oil�@�r%l>=b�6eS��PL*=P romas� ca"E`�*i�Novot��(1,Gabler_94�^AZ" AJ�)28 50�xa�=��a d BaF$7b scin��^;(25 cm lengtT.�� j12 �' &�/e  r��Ecdkn �J�o �s!� �p�&ic veto )"u�(tB�G� SU-of-fl���eR&Kzpulse�A�r�� �cap��� g%-2$2<1 :zH)�K8oIeta$) >Wn6laa���d�s�V��b�alno" a��y�' d�%M�im.�us� c�eGyDe�+�s�=r��i�sKh� ��*wR�`q��} D�kh|`SsF��: ^2$H33,4}$H�@~o>I"H �*Ht!/[Uuq deut6؉Je��rr&� ůmx�T2�TW#q@� free��oW \Іm�*��Jw�} AA�a�s�h �3A<c� �IM��1 �w n"�[�m�S��pre�Sa�e{�|&, �s� . It"��s"�TAr�e��*�����^�!�d�c}nIli� ��it ���er*evia�{FNf;n�>�� re-�mr"�bU�?9X*atv)A'� ity�[ly���"vKll J��E%9%Zu�)^��msBx Hirata_79z�1?i>� x$A+E�p��,1��o%{=��s_|suZ2�e�VEX��te�Xu�3}U�UC| M9on-V >/l�! -pol� Kroll-Rud�4n �s�����??KòA�%Riu@�fr� mp�+E�v=��N��C �) � (u�)�upV! �_GX�Xst�� ne w��&�Bi�.�Vj eE�1H�-"�!�M�8 knocWn ou75u.a�!++ mjtuI������b:eagcco�ntY+y�wk itud� �lm%��֘H��R���yn�Hͻ ra�n"��{l�dE FF�� me��ism5�ged�. thei,� �&lb�to�>��ho�/�2= ��4bo�wI7.�� qHJ�02.9 B7 7T�" is qa�&l�*_� [th]L�]N{ **4.1B�2�*�T^�OY$�����I(!;�{!LE>.M.U�h�QL , �V:u�+ .5�nf)�>�99i2t�  l{d![ valiNA�th��5��d .Z?26�O[�+-�!��U����9��spS J=0$i�i![�H�j by:==�q} 6o\s�n_A}{d\O�} \1�r6#N#$A^2 F^2(q)��^2(\Tdo��r}) �m�$nrB!⅞ar6M,*N$'3D ary 2w2�L�$A 6atod�) *%, $ �!� a�e �S��fo�J�$"lg6�$��cm&�h؏��(�%de� s seB*-?�Pm"�� eak6,�I �&# ��i- �iA��C*�?&�� gu�but����m!�F:�0 ܉��5ga� $siJ%$-s{�Q�m��EeF�5.B�3F�6|5J�3�}&lLef2�镼hot. ���; � ared� ��!�)�E�N�s0l ea)�F5�% c� �%^�H\y e�%��"="��V3~� �g- rgue\"��]r"�6! ! y|\$� �.&�!WA9�� "� h�FA��"��0wy&^� *�$�"� (FSI&*as�v%�i� -KKr'�,Siodlaczek_0� �)l.��(� �!%Np ��>9!�i�a�FSI� upApsiz�b�>� # 5:1�.�`��S�N �kYv@!�)|art ���lG 6J�7Ɛ9��A � FSI!�� ��vnzM�V�W�+ �_R� .{-�1�xg� �-�deple�ia�warkgo���5.6@�����6!�&Kve�C�*Zho�hsumJ�!�=\ae�%�kS�e� Œrk�p��O�k �"�x$A^{2/3�P^ =\6)g %�&)5��o�O�2jiVm�!�6�3} �:RK*�.��-ce%`%K2�iw*�"ly���l��6h;�^~10�to 19 ��� ns�&�~�&JK�!��`t^���A�#֑f���N>4,>���s_�$de�!c�bsf&�. E�QCq�is mos4f�%J� asc��|ls ��<�B !4eI��:�Q ϫf{��4�T���m�DoE&�0Boltzmann-Ueh!# -Uhl7Dk :�m� LehrxB��i��O�a� w.�_5�of"�8E"��,5#66:2j �"Z�4F�4>i Q"A>���PA}*yE�2�5�to BUU-)%2�� NX*�[)� � Eu2Kre 'l$ ri�� slop"�5}to ��v!:�E?f�n W�<u! a �o�.�s3 �e�'c���6�. iW�)]�1�>�%��}i� KzcRambo2�2}b'DWIA �� iRR� rech#2� _99a�Ř,� ڥ olog�5�&�"y����fY(ng>.*, II��%�<���^*L^4$He UV�oYqrb]�t*lc}"�no�c"�� /'MU.v� �t��. it:RcWin�Z Q���p% �s ion ($E_{�}\�y 330$�)A" 1�A�"$�5*QO d"��Q �& x��s�lybmeZed (by 2m)��� s no. tU���e�EE=ղ���x . (��a�3}, 4q�)51i"'1�=��$-$4�!OJ;251;1��uZ� in{v�b��a�� down� %9!�le�1g�|�%4"�Z�0 } AmoGc�f e"{al�%o.&8 ��? �fM�Bv��D��t*� (TPA��?��mh�_92,Bia��_93�PA# � �3s�+eakҢst�ga!�ٓw*�6 �8f ,��"^+t*' �f=� ��11Y144q16y%,�<d f~1�W�et l �h���  aA�֞�$%��� lith��to uran J� 5}>w‹N�*�|�*7"@b@{7cm} \begin{turnX}{-90.} \epsfysize=7cm 8file{fig_5a.eps%nd{turn gbg\v D -0.4U�caption{Left hand side: TPA from the proton,  $deuteron -�average for heavy nuclei \cite{Bianchi_93}. Right.hDPartial cross sec�sM] { L�Krusche_99,Buechler_94,Braghieri_95,K$P5,MacCormick_96,Haert1$7,Wolf_00}!�label!�:5-� figure} B/PThe resonance bump on�fre1(\ consists of a superposi�rea��> channels with different energy dependencies (see fig. \ref{fi�, r5Q !�H) which complicates�situa�\%�1I 03}. Much�!p rise  2� toward P|maximum around 750 MeV is due toLDdouble pion decay �, in p!�cular1 n$\pi^o+$ Aap+(-$ final st� . A study��Pal9`n�\thus desirable. HoweverI�Lexperimental identif!>io%�exclusiv!�nA� �X0more involved��FSI effects must be accounted for. The interpret)�ofgmeasure�%prefh@always needs modE<%� bu8 triv! in-medi!�nd2�$like absor� of mA�s�propag�u�roughi�,ar matter. q*ulti�@( photoproduioff%�.>suggest!�at A=�$\eta$BB,are best sui!`��aE� aris)�A 9 �ertiee�D$_{13}IrS 1}$.�F5�toA06&�Z�is�0letely domina� i�Dsecondx regA�by��(1535)'>7}. O Rother�o!OQ��structuE� ed o$ >�is)ong2� �16(1520�. Furya xanalysi%q�!�Q �m E �C(on has show�at�Oigne�nt�itribue��u�istrengthA�2�U�-�Zabrodin�SLangg�%ner_01}!�es� �\�u0arrow N\rho$ v.e�F.\�JRoebig� "� 4}A2 summarE2in 6� 6}. All)-ar>� �!8a good approxim � >�2� by:�weq1 d} \frac{\sigma_x^{qf}(A)}{M�}\ cN'd)}{2-�Q!� scal�amongE6�( holds evena-��e��� � UZz 4isturbed, e.g.�� of U�se)�0$} at low)�n� ) !�orSOHFermi smearing clos"�  thres�1 $-4$5ii�limit!ca� stw2� d&Z  shortZ A�nA atha�isZat%\Y�"� � probe onlh e� ar surfac5 � . S�؁�B ly�ed 22M s ag�265�2' no *�� 1jA�obserb ���!�density�zon�  � i. C�opquently, as already discussedahb�1}�direct� d �.aJ�� A/0 $��4hav� en f:� 5�=�5�. q���ceB line{.t4.8Bv7 &�R'b�z'��}�v>>sumapN�aJq�� s $�_{S�middle:` U~694nm}�@ neuP ��&i ($�|=2UDU��!�[�$ $A>2$), � J ! non-yW3���V$:�7}2Q3��2�Ta�is� ly obviouIp�g.)%j5 S}$!w thesa�aT s:Q>��9n = ��o}��+"v  2R)�� 3�w�U � B�7}, (l2�)�9behavior��S$�_oug�a�BA,is very simihfor%D2�:�}��C!?q�*+�?mos� % cal,�!i"f.�visible,E`f��i�H|  d 5 of.�.Gf^of���x:� 14{e,(FL!{iw) w�' so extra6� *� . It �des���re a�g q��is��I doesI fuls %+ kine�c NtrainQytor�I}%�se�5mainlyŋ �Z(Z�Ÿ�R�re-,b�1the��u rY�A�ome� in betwe�� %�Iu�zA וK��;2�stillQbA�2�,�it�m� less�nounc� h5or}q q�ce� V= A@- S$�h%6�� !J�s^�:o) �?b.eE�UV�l anyqvR oxB1�mw(mass numberu� 7|5�e�)�Q�ʼn ݉6ej""�yca}I�Y0simple ansatz� (A)\� 4to A^{\alpha}$K =J|9ޥIe�� $ G$��to be "� 2/3 oveI?whole �rangeAJi }^�E.�^ ���%, =-. H��a_&lyorel6���st .} �A s�a� ext�heU ar volumEI� @ase�ppear��5Bd peak!���S�� it& 6press�i�m�$ coul� � e+ d "7" ɕ�\a,*{Acknowledgrs}� & re�} YQ�!�"*progra� �0TAPS collaborp. Ih to aq�,U�<"�io�P F. Bloch, S. Janssen�K@M. R\"obig-LandauMo workE�supporAT� Swiss N�al Fund."uthebibli� phy}{99} t 8ibitem{Lutz_92}y �Klimt �pW. Weise, \Journal{\NPA} {54221} {19C \V�  \vF\eject� docu� } S�%0 espcrc1.tex $% % % $Id:2 1.2 !�8/07/24 09:12:51� pp�Exp $ % \xLclass[fleqn,12pt,two�&]{&l�((usepackage{ �} .>0} % if you w"to�^ Script 's2@/ x6Vsub -}Y�(landscape t��2L[ 3s� ]{roKng2ZH[latin1]{inputenc} %�french�%$ents % put�r  defin/(s S0: % \newcom��0{\cZ}{\cal{Z}� 4theorem{def}{DE }[se ]H ... 2L ttbsNhar'13��.jAmS}{{dtect\the� �font2 A\kern-.1667em\lower.5ex\hbox{M}\ 25emS}A�2](M}{$A\;$MeV�add�d~,TeX's hyphen�Pep" list %\${author an�$creV3(nc 'paper�!Fend-edE5-I6A\� %.R�A"aHstyle{/projet/indra 3 (/bib/npa} %2. rep}~7}axre.e#�!9}{0.1:#op."8F"bottom.%7G 6Gfloat�,.(8( setl�%{ �)s�@10pt plus 2pt min }�3in�v0��=��%larEtyfront�(( \title{Corn ���al" 0liquid-gas ph�tra��BiaI�{M.�� Rivet\add�>[IPNO]{Institut de Physique Nucl�aire, F-91406 Orsay cedex, F�}, �}  Le NeAved mark#8J. P. Wieleczko%[GANIL]{o14076 Ca�Fh( B. Borderi2_ � , R ugaul�DLPC]{LPC, ENSICAEN��,Universit� p50Bp A. Chbihi�� �, J.��k��R%!��rlog(`[IFIN]{NIPNE, RO-76900 Bu�.$est-M\u{a}0.�4 Romania}% \eks{PresB-�: vB��ichon��!+,%fTa�B@INDRA ALADIN C.�s ͕� W&d")$ % typeset:� makee"?ab�ct} F��(e systems szLtomic>i�()tF spec�) fea�*s &lG$tho!"b!�eBrmodynailM". Seve])!��risticu�w��in sa^e�t#ts� z#a�colli�s�!h abov�# ��#ncomit� ��YQ܅8 �50�9 B:��!~0 a gi&$ �&�+#e occurveat���.' 9ɡ~�0<{INTRODUCTION} A.�A F��# oretly2�o � ow!X�$ ogy�DK(on-  �!�!!q$van� r Wa�sfor�E*�/�"���ofF�� b� re6m/ year�#oEgroup -udy�multifra=%�s� last few B%essA�evelop"C twoains:Y+E� al p��cs buil�$con�s associ�-B&1 %6MI? 9�A?a u�,�&�2�;Ac�e=X l2 neYd perf�) nt 4 ($)de2 o!E llowvo�1carefuA s�g�I�.�$instead of k!xonUs�) . AA'����rray _u�$to �� ged!�z.��m)�0a wide varietV2E~i(u�Fb�& iS�ate�)t=sw�e�� qual�%Q")$ �)� s!Ymit!!:earchA�b8!u, asse��I#t�r�s�; �m �ilR ineorhyps se��/B��/�red�-� l{EXPERIMENTAL EVENT SAMPLES}�!��%���.3��obtain #Y�s M�.q+M�I(I�'opera��at � P t GSI �u�"lyUncern��,'sourceA �5about. -230I'oa�``fA� .''��,Xe+Sn, Ni+Au&�! , Au[TaA/si-1 ctiles�ng �*�B yse x-R'frameofN[,�!�4i� we�-7�, �h��Iu)�a_d""fwo techn� s: ei2aeࡸ�*mpact1.9ae��uweȡ u( ion 5mi dev��;}5t�!60$^o$)Na beamB (%c-� )~\c�8(I28-Fra01};!h��<asymmetr��-�s��#"ri�3nt-xo* thodW(37-Bel02}. "e"� M1''rY�alb"�-s�x"�-d are na�2�!9e�+6de�7��n%�0XisoF2FU, becau` "it3)�eneck 1�s. For /)4-,$s, a firstI� �a_on��B&fy" �!]� ( tL3t)�'ensemQ8���(s"�Vcit�,parallelb!�6  �3r (sm&r)I>)E� �" Sy. �(m%�E�a�U-Aua�eyAR+!_��advantagZ �}�% �4�H"pos6'I"�B( (0 - avail�M ) cao%ANlo�i A~ all �!s a tole� W�� 10\%�V�i��#�impose* An�tZ)���&�bs g al5��9`!�A��$ll���7q��;�(�#�7 . To�/p-_ $ ��sE��baqb �~c�c� �, (microcanona�,!A ���orEj��f al ��'( {\ldots} )X!��XSIGNALS OF PHASE TRANSIM P : THEORETICAL BASES}�1�} While����N:� 2_>ss�%`,6 erQ1by A�ontinui/oMvEnc!Bf� bl�smo��r&@< X��� �*ni.K E exhN!�mal�+ curv� in�*�� of$ials. Sad u4entropy, S(E),�� !� vex [!..u>A�x equival�\ AXng s�=.�3is bimod�*mea�71at � temF ure Eqsp�9�&� valu)m!ک�. A�ons�/ce�beBa 6���,Hcaloric%h e, T%,sh.%��,t a backbendM �� �� i(�$b >I,�(�<�`heat capacity, $c$=dE/dT,� i a negaK6 b��h"�&6� s ma�0??�o� v .= pat f �h� A�=�-!sure- �A �v�8#A =3,��!�>. A�rob�=� l�0dA� flw;2� ��+�2h&E�,�wlyA�net� 62o: �-��6d�=wI}, of $c$. See� Cho02,GroOAreview�-I!vis pi2<,�ithe��:V�e��same tim�' m7.� �NY6���e� � B!�� iQ%re�)a� Y  n loAd� �me(@�ly unst�� spina� �= �dia�',�i� 7@ �-on�I��)� _� A�![&�zE ^�[U>e, C0n �E�proce_2�?����dec�8�B . MA��k�A�}<+be���avo� l�<]34}g rd-�^,>� m�Bbe� ev� Y Z� O��h !�E�� nine ��!&o cri�"�+s,"�fI�-B�Cp� law  2!�l�"� JAB!-5MorIWM01 A�J�, ,1�p ga0�&r��d%� nea�1�poi��nd�BtypA�3�+VEi5Re �O ��h�,�M�? ��,� ���;{/� r -� !c��idef<] >K:��,uffici��� 7"u RAT"�-[ P �G��)�e��I�A� ice �"-,%�y�,,�wa9Dmon�EA�BFis[A- �s� �l!D% ``5��6''( b2end!>llx��coexis91�8M@Gul99A=\emph{| ���s�~�l�als�.�F)r@-e�m��"#� Zq.} 95� z� :�IDENC&� exp} MV4 �` io�e�A m�  publ!�d, we`not illu)�!Em> �@raae see!Sad�/�@quo!�re�Gce�� \sub s{DZev!�>�:���F�f� SD��k�FAa-��B emi-*!e� simuD .*| sa�a�a � cour&�;9 M�#<r+ � �z6� ���Mv Jac96,Gua^DIf�:eno�E z/�r%[ch!�� {?nU rec�to @� �EUB-�break-up�o pie!� ==rupb ҁ2d� ��l& 02l � ��ifi'an homo�a� wayI�me#4ield,�Je reguJ7 highj)@a�b1�w Q�K �8:ze�p:�xrDI �e�!�v�7�1 (� gas)�e�t%��2�aBin�] b"�G!CI�1�+��evMi5�Jbf�e � �k,��kA�o Mw�;��m�A&c �H. H�aga pd �&1 �:%i, 6�ir!kitenes�rl�4�� se"�2Is��)�&� �� s, lean to6K ���5��pli� �9!6�J .N��BMV1oE8!�coalesc� dur� U.F� e$E��� eachN � . And �,�iM[$ born hot�- de-e&rs��DalterE \�KZ��1 ed � �.L%Z�of-�- �?survive a.�4abiW , mG themE9[3%xreveal(�G �)�� enh��dI-%�1+� u�a�erH AFgP"�s-�Mor96},)�EY B�� JOAa�st�3rd�Z of (5�( (Z$\geq$5)�.� �%" iZ S�"Day� /$J vun��d ���8i�1\did��& ounte�5!n �`;�Iy��"35=�wo Us �Md!)��aw��a�!Ι4I��  Appl����e�#X�d S� 32\AMt��_:F6�mat^��9] ,)[modɀImixa�M�1@��pr� ofuY }ZMh$I41-Cha03}�7A? intrinsic!Tq+h(IPM)�8� e��c);� b�1\% ����Q{2I a/sxLe.)� �-�N.��])�-!p:�N!�!.to�;�va~�;o�� WKiIPM�m�f#was�B,�:l�2 0.3-- ��P+ � A�" R832, 39e�45EBI�� isat 50\AM5�0-Tab03�*Ite�I at 5A�{}� �?�,� �&# �r�of E� mT34Gui�a�. ma�*�� s� !�E�%�Z�@ e�= (��� help+a��"� �l)!�5-79 Riv7�"&� B�ityl  } BAS�i�Tav0��.;!"an� a6ter�a n� vari5,a��:be*!6a cca=�� is%loo8 Hin�F'�6 k9���60E[10A= {}. To mi %a ��aa@st� aussian �VMCha88})sor�!�>��&\ �%�I� � �'�l4�d�aPcles (lcp, Z$\leq 2$)j!��w� ZE���<, $E_{t12}^{QT}$8C�=jus�Sa �� e]c�ɉ�lcq (Tre�s}W.��C6t !#����1E���:M���A;e6t� TamEPS04}>EL&�,63�&T e"�A�)٥�1D$investigat$�q%5�y.�E�r *n �of bo�U�!f�=�2�&� i�A� �is jo�a"�?� ͭ�\ onfi=&by ~!b &�W:dr._2�'E*-4 g�R �!�;inc� lthoxoverla|3B� IfA� admits�a*("7G6tfix��*,� n%���� -D�e�� �!t� ch!#���a�C{ur:�N 2 ies�� cneg�A:2}�*(�� ha!�t,M�y to ""� b����}z�[aVmps. .�*�(r8$�%�G6�rX�2 (of %-y2��reeze-oud� h6K%2,)� @ $c = c_{k}^{2}/( (-( \�s �C &)/T- )$, �G$6, = \delta *e &,tes8 on�RpW.�)J; , SM� MDA�  I*P�rn�*it� d>� �thod �8,J6�RG/]s,!�&"E.)W-o us US.in�C� �tefact"�6m�iU"f�& �M (. ��ed�EAuA&67*)�3�{}�&�^pheral�F��VMDA99},y:���sH/inO ��� �91 60-100A~M9`nc�ti�ie|T38Pic���*F��e"l�in�UzS)In ) �%"�1�en[. 5���)�����l� W�a*-2T25NLNH?I�g*� �� �>���[� �aK$c$)�Md AP1e�5(�(,P;on�mi���%J6���A�v"��-!Kad��Kp�%��. 2ZSW��sca+N,4�dMh:.eIjg. � 0e�a�T7 in �1]7�"�ex/K%U�@'d. $\D��$-._3Imt+r<lyE�p0��E<he � ario�� �_Eq&R.]�&� �1  c} V�8} ure 1*�=b X\��e}[htb]%� [E&> 61Z��� duc)� 39\A�iTa%+:iEI�i. Sd[� ]("cK�D[es^w�t&1 !T or/ .]{%%[ +a}�"V]{0.45\T:w<^}F�]!�e=0.78J^1@V%n;\,t/Prague04/f� r_taau_39YVnd��:�>[a edNg)Y��bor oIQsphorusA�1r >d(Ta+X)�q� /,��)2�P7"3�! 9�] � �Ali1YA��Seu(�| shifṡ�a ter K&J�bV�56��e��Ba_>�b)hʨJing_all3 E^AU4} %[A*{-�`cap: Mlq� } �+I�} KiK^�� Z droR6��origin|����6!ׁ�phor7of�id �quilibr4f�erm��angal}���R �"���a@f�<ioXSis~ ��)a&��� U i�b�nE all 's �!��} ��X�VI�$ �&asb.te"J)�ş�y��a�P�%A�Dds: $\mathrm{d} N� A� ,eta(A) = qA @A^{-\tau} \exp((A�R\mu-c ,\varepsilon �R�P` )$.��9ex�}:�_tau# .$e�F�,ſ \mu$k%!5q��j�U�2hem�"��%��%Xs, $c� V)�,]c co_ t; $.�,= (T_{c}-T)/ =F>?� NLNBorm�  A�@M. 6zl@�em' 5 a�kumFtA���*ig��O +a};� !9V �fx!Ge"u �)�4%ԅ�&� ,*3&0s. Not�&at�&A�!�replaF �� quare-roo��>' y,=: %*�,�r8=�a�'"�$$E^*=aT^2$>|c�)+b}Et��.U�h6�ABY��mt fA5Ts>�or TaJ)5 fou�20r "N�<c �y&���ap'n�UM�� - ! y c>�alo�c abscissa u heS aQbe�s�;sŲ. �B�e 6 �]9�:at�m1V| *bel� nd a"f@�!]7�!is unA�e�be6^u)\�jE���&�-�. Ai 6&�Gs*+:!``I!R�'' Y A��6 true2� ie \,��B +)Qit va ��e"�'2�[h�Xn%u�A"M�in B b}5�0.>t��d��A{W &e4.p-L��G)��"��at#")y,'N �D mE��zob@)�'&b�09=by&� ���)Iyun2�&� "�/ ">,/�*yA� ]&� (w/2' �6� s)!��a(� *� �-eyq=I{'a=in viol�c���G^E�&�6�])���top4  � $� (2.1-2.4)(/)�"sOf-volum!{men� �H"�\$ (0.66)UW�'p�3�*A�, c�g�M�z��*eqGal��h; }  "�A1al2�}�5!s �$�#s  -B ��ф ship�Y1`hJ^Dz!MC ` !�m Pf"� v6)tCqui= !;c�t�%�[h ��"DF!�A%J�Evm�Bot=v�l.�3is wEs+�:ont"�@�� p4*��.�T T= �y%PS9�1-)du���si�(3&am�"+�4p�&94thP+B�[&) �� )�A�!��:tbd a) ��t Rvy\G s, i*�$�!6e s1?,'�� �#� , at��.m�Gi5]*-T d?���%I&)I9A�u>F� �ggr�1yMFIxx@4}ms@�� �5cx�@-@73E8394�'��Aowo� regim� 6 1� =1/2��O6p�'%" er���� passag�.ov)�#�Lo a� %3 ,, �e�Y dbA�l� ens? w-�r. �e>< ,Fra� �vail/It�T8H�ny %�M+Y�2�9;NF�4is��wMae�y"� pr�b�&r choi�6&2�- ف[1}�%dW9Z� �t!+�vsl lyBerE� �y�'�����""� w2)���C�� �o�7Y�,~%IF�,=a�dis� . Q�2D9e��einN@ pr�?�2 a6HaV�Ba�Gi�y'l:�N� . EvoS �� .�#AL4th} /2|Y!1%(DC0�=sxB@,!� L %d�)�B:.!e9.`� pI�w�%/ o"�� �6d��+ambigu!�qb���e EK5TE150�!�o�5TMULTANEOUS OBSERVATION�@SEVERAL �@} F ai� ɒ�34?to�(Ui underg�8.`'}']a��cB�we'6f"J5E�_&�$e5� �7�B!e��.wo&�&�3be�e�N� �) %+&�QuR{A/D"�B A*�2��>��%� 20x20 cm� 6 [T!� "�.T��(I2p)e�c.m. vellEy�k0i���>VpU%�E�bTMB0��o�r�{$A�o�Ns.0e7 a} %�"�[t]{0.5r����,he�- =6cm�2�>�~-5Ch�:!�6*T) vs>�'�,twopF0sd�w}$B�b��%"� 9x8%�i�.By8cF�#:��9"�K9=c�z&�A (sta^ d�)�:)�l:`#T���s (j" Ew,C<.) Li���to gu�:eyeBc�21N*MNcV�]>�JVF/��5Zh (N� )�'�c>)!&�l"p� B)B5d�5�PN4�ziF�z>�Z.Z8�.�"on&�.(� (b) "��ɩ�.;=�din (aW+&�B"�*8de* . (% ~ "o") &��|a މB�����8,�|� �,��*Ba (QP)% G0s�i  1a���� �N� expl� �S1E�6�F��+f�EafNH0 on $2t*A� *�.�Qh� �Z.&s �! +a}. �;nea� o�5��}�6m�6s�t 9`*�`b�,o$q�2� �CeLJ7ll>dbi�% t���MC � gXTofM�. � >S.�y" -x (or "{/)'Y�>"j �X fami Uw6ZdUc8S/r71=1� *F �Ao���)y-^�N� (di�zd�) p)0>�d}). F�!�"�$.|&�Scal,v� a:,,r3�# eachJ��Gfur� &OO{5 � f< Z�$��� s_>EE>4 F9is 3$B��Q�{}c>�6�:�solid�y ), %idRa ���fA�U�, / u� e QP�. D"���]9��&�a h $2�. F.I?co2HhZC+ (.w ax�#F`domO>� � (3-6\AM), a�&�- -2_�ezst6O�nTAE&�~� E�6�! i2I��(se !�.�c})*0F�m����9�^�/ \sim$4.5A���#�P{!$>� <U�(Ta) QP�9  e//�y& m�6diU[T"�N�* %�ed���:4-@{} �2� lv *�[�H�s.�X!���9� �Ji�1E� NA,�G%*2R[&�EU:�\� &�@���(!zf�B e. �'E{SO%-!QU�`*��b�AAB3�BT �b}[tbp~�'E�rB)� �32�O�:{} .e I4�:2� XeSnZ� c� .w�}*�10x10B�'*"&6� 3Z� &0 10x6/ & E�.��%2&% � �sA] � �( .��.F�V� �6n�*!�3� %>� \\%.� m�Q�w�< , 45�%�2�&�F�cqb8`:�4.�9b8�B�'9�9)�Ά P�!e,d #>ft� .� z*!25,�=6 6 �Fdb2�9M�\�&>�11.1)�_ C0S6�.q�&�@%(25!%%��a���(J�(Y �_,� play�Qfi� �, �^rns6=!i&�/xenPV n ti߇�%v�� ��a2�)`ll� *p0 ���P���(� I hape�F.�+a}5?M ���m�$�I]e"�AO�n�Dd�b�(s, �x����d6�O��."�Vim��Y G� 9\AM��"1sto\1 a�Xi�Sk�61 are 71`�1"/.!s�� A +b  q5��v�ong[ &�=f�of�!,�o�� -%`A^^$�&�Ra�n�y�F�Tt ^�! |  match�( ��1R 6� 6]A�1�p ���$*5 *� a��@�4i� Sfn yS �� �-lso o� �-�.�B�d!��Zsԉy�VM��"_Xeh S{Vu��M�"&�%I�li |!�"%� .�`is9�As���� .�i=D%�.F I6&� "�Zd�L�&l�U o;�o�0tryus� � Ee>"���X"����SMM�-� s , ,&}$!�i*}�u FcM��XAb�8�{"w �q�ion�?� 1�1%�we)�U���5s7� I(�pro?�}�2-'"`@$@� t� ]cha ze a B .�&OU%[pm�200A�"�ly�!Xx$�ScQ�Qbt�$�$�%� am"Irad�n expa$Ily (}rP0���>�erF�7). WorkA�#�~�G ookE��0�B3o\ogh�� �6@R�qu�B��vId�IroP0,AQin)��th�dP9�3.�) e"K+�� �|#�M�#/A ne�Har!�fu���.�#�"� �new acce_�f'fur�G vpOexo�Y8`s,�W,�gZ_y B�: N/Z �e��*;dom!P>d. C��H<vW%�yTb shrink{I0&aG���!�t2z L1&Mj\ifx\csn� url� \b&x }>f\url#1�p$tt{#1}}\finIprefix>O\d L {URL I� grand{\e$I}[2][]{~ {#2}�ob#_em*�d J.~D�yan�n et~al. (��b"*M),p.\ p�689 (gv) 905�[b"�d N.~Bella��^]70 ]2) 367.]k@$ P.~Chomaz W$, T.~Dauxo� �eds.) "PUNT.�As- "� ���- ;�#a�l s, S!YDger-Verlag, Heidel|,��2,��. 602A�4WLe�\�/J�0ics}, 68--129.�]( D.~H.~E. G����� �� � �A�Xj�23--44.�!�4N�IQRep. 3MT4) 263.>"�Z L.~��V�&%�0, G.~Agnello  -� Proc�tɮ shop MFG'A�, CatVq, Ita� 3�8.��. F.~Gulmi}�{aC,�0v. Lett. 82 (|}) 1402.H�V} B.~JacX �E @B 383C6) 242G+W A�arner�.�C40 C7) 191.�=RZ]1��77�632�&P�^L0s arve� Nucl}�30�E4) 432�&� G.~T�rbcar.� �EurNJ��18P3) 102AT ?!iGui�T��je doctH�,2 t de ttT�2), {http://ccsd.cnrs.fr,tel-0003753}.V"IN M.~F.mu-� ({Jh})�� | Mξ�11--20�1#$-ex/020501�%���M�Chall>SRY60A88) 72�"!sTBt>���.t2os!��er�'.YMDA02� D'Agostinq�ͩM� A 69�K792�lB�E5�99) 36�"�HPiDuj�Y4�g1x"�A�= {Le @w}~W\'�2M��k!�n�03741�}&�>~>�2�!�I.~Ior�6XL I��iE Mee� on�$Z�eics, �7io� Ricerca s�_�ua ed �8az�]: a�e�16}Q 0} R.~Bot��u.I� E 62e�0) 1822*&�*��Df4 b�)��e8C wub� E6� {u�40402M5�"|,b��Pb�!�jT!$1v$�H86%(1) 3512�� a Colonnj58��2) 12270���">x hd&-x��.W�� �~$ INSTITUTE_*DPHYSICS PUBLISHING!yz I�  I `Pre}�ngh� � p�`c 1n �{ A�ics I P0�Ujo/� usXLa�~��% % �(f � r RL code `ioplau2e.tex'�n�'4�t`�|Z I�'(s'��s�)S$�a &zIqp5�RB=9%+ �Ule!b ��art.cl�/o 12.clo� 0'.7F I�  I�=[itself�s �� & �B  I� %Z4F�  J�$� er check& !�la�5{�"��g e % #�.h.`�uEC *((grave) % &�aersA['7Aa 0 acut0$ dol�a2%��f  % (sB0en�iEd)Y_��% -�.�22=lst % | v'=�bauC~ tilde: % @��_$/ score % { �cu(U bracC} � %O[ )C>I] ) Aket % +��:;�Gc�D@ % * aDis%�:�o�< xa~� ` > x �,^%maB .+,(stop % ? qu�3o�Irr/��Xslash�\�. ,^ circumflexE�dABCDEFGHIJKLMNOPQRSTUVWXYZEdabcdefghijklmnopqrstuvwxyz$1234567890K� ���M�A[12pt]{���UnM�: next�%�K AMS ��aa�8edZ� 6>�Hsnn}{\sqrt{s_{NN}}}6�s�� {\s_{\rm  >!@>pp}{pp:/,epem}{e^+e^-:pbar}{\AA�@{pBQbarp}{) >Yq:>q>>!q}{ q:|c:>c>>!c�a�c:> nhit}{N_{>!n_! >ch5chBp��Btot}{\le5\nch\r :\aveE(pV'npBj^B:EncM >�`!�V`half}{\�G{1�:b 6�/2VJeta!�etaW�=>LaA���_{s}(s):letazero}ɟ = ��n*I� etaone}{| | < w�.!dn*.}{d!w/d':c "p2#>� $ � |_�RR�6-R,%O X�H-b6� p+pz,o,+nf�*�.j���!� ��/ V0?}{\a/V#neeE�eBnhilhFlu:�\nu>Zyb}{y�> jpsi}{J/\6j4kpi}{K^{+}/\pi"���E title[T�YCan H?�Qu��Pr�/V]{�$P� {P�= Stein (\dag\ \foot�:[3]{C"�-�: p2.s2$@bnl.gov} V��{H Ch�{�D t��, Brook�n&d�L� ory, UptotNY 11973W�a"<�VQu4Hh!o>flavor PVl�I%)��i���co/�Bel�arDL"\ �BAew�z#�$" �@i�Hk�$��uKŜ$�>i�ce)u�G4$non-trivia �v̩ith� NLO �.. %�onxMj*���+Ň+A�w puzz�"'�,�Ia� ly con+v� "!%6J��eic�Uf. Open8}Ef�0({0� XFE!a hard!�� <st��e%/i,�soGh!xG e�. ���<�q)�M_b%� ng|��߀r�0�end]a %&F � PACS:s e� me�>( %\pacs{00.�2 42.10%�*� HS4!n�>PYo{\JPAEComET�;�:p�,t!� age +Gr� %2z�s3!Int5�WJ|x%) few �aa�@�ds�cZ exac836.�I %�QA(aF worlPMA�l �rk!v:�M�yb %� 8@Xyu�)�.:ofe)� %(i�>T_as5]HU�!m)h�< an %%�Mce�$:XQIe�e�uly. %vrb�X�1�K ongoAc_a�!relevSB %��ers��z0 QCD (pQCD) t" �A"�2 %l=�"#1�!0)!Ws�ĭ %�� FrixW:6�ma3%T!1"�=a!��f=�r�ùsy��, s)4%ne3@environI��z!�5� s ad�!�;0ularly %fasci�$ ng w� le��B{Wr�5n((". %Gi� %Rapid \M�Y$& RHIC�+last % $yU5,�#"��~%�o�� 5 pP�&n %�$tn#!ial����4%�"���6 %``�D''YI�� �C�(ng9Ho��m�� PesEAyJI�ŲhyP�ѡ �{(%�MC �c�r %basic *\s: 1)��ang�xA\e0���"��"w_7���"sYe�a�m%�2NM2 (�����7�*�Fv"upwdx�Nk-�2)% suc�$iv�`�"r 'j% ���!�nsfers���Fٰ We��us*pUANa�}� &$reaڪb��!�P@Cup�Uc�^anl��]%���M�:��%te!�a pT��L�f5�g)���6_,M��@e$�R�e�wo�F)� �ly-E���ng @���'�>m*R  in E��D |[o�8� E} %+ issu%[ �I� �aSKM >�� e�undery'eؤ�1]AR!� �Vp�|se0e�E�$ s�'��e� �T� k& $e+p�9!$$n &б�+%-a$� $ ([KdiQ)!6 1974K%Aubert:js,Aughjnxw}!� B��h�Dpo�e�) a���zml,I�| ��K)haK(�:s �,�up � a�7aI5+Z(�*�)�, s. O+�T7�t��tA�Lr argu�%�'l�3��� her �4�P6 &�%f }[t]per� #"I2{70mm� ��ap*�7�A1 M�N.U�%"�Y % �ALsix�&nd� model ��q=a6�A"`G %�~Hig�}nd��*�sms. %�Y�}�t ���1Z{\����h�B5�asq04F�St� co>� uS���BU�!�submd�w} %�>�9�-�UN� m�2ap ap� `8pl~`i��2��Wqa�\annihi{ng � virXQ��td�siilxtoq"gA� \4arrow �xs$R@�excelGPb'o�(��Q !-�� "( IJ�$!Q vacuu�&HX�,nM:.p e��QH�@� . It�vifaSleP2� �/�bS ��A�t�+a���M� �K6� meaB�o$V@K� er-!-Ohigu2a_t���+``���'' �ruD^>�?�*_:�E�� 9 -�On�iA�s�|�=�VM��egr��sr�)�m�!�u tKpe]�sv!A�6�.m-��n A�ve |#H���rb��s� t �/&ڇ � ,�m-oA� B-� o�?at KEK%j SLAC|;QY :u0A�Y�:A $Z_߹o�J̭� � le"�N��e9���=:"Q %9 ingu�`s�O�A9-%;:6� 4c04``P��4e ���Q7v"�t�y�ly 60�vA�j;d ��gy�E� (at 1ty ies�oa0\�ly:C��beauty5LEP/Biebel:"�(es}. When @�hB��a�0�%�c jet jA�fi�4u5e6#[``B�'',2��Akaj�Bajcar��Vkem��M�1.=� (�g!by�xE<cascav  wկ��tC s $b.~ c2s$1AAbe!> 3iy}. On�Vse0 dr>c�le A��71J# �fo��i~�PȺ12� � so-c�8d ``dead-cone''-G-�$Dokshitzer�1f�M B�p)<se )ws (A�:�AO\)z0b��R0/ r � u�_%L=H.�Z. J� w��� �� "�{6cm}BU=[IK>K0pub9949-fig09�&~ Id�U�K ‰M!�*�.�+�ywith emP��a*��"x�PkL��er����N��5� -� �O�VZA��13:d$�C�R imporYus �3�ur*� L �5 ow sAQ�3��Y�]��) Orig�8�g�q ough�m/P=d�4-)sE/c5 �bB<�$taneously R$qq��$gg}��9�!�t�!�5pair wo�y``��''� ~�lBv�A�Y$ -;0.d '' (CSM�� Bodw!94jh,K!r- N�, Hh�%zu3u �%(Uc conj� AU�)%��3s�4u|�r4eh�`� d�pbarpb�l (�M.+:�^)��toP1oc�)��O� � } w�ts edJ�Zco��^Vr� ��C$� c$� curs!��YE ���5� p"!�-5��]n*T�soft glu�P B�HducA2!4�b� 8si]�~I�Z�e�qrk��au}A�B�0COM�-����2W �30 )a� C1| evap2/%9�E:�&��)��i��#a5�l�&�� via %6�,Hsum) �Ln��n��e9] ���F�s"r�1ula�f$\s��(e{)/ cE&g"'g� ext,! :.B�FAEF��a K BELLE� �2rbe�T�92�rri� Q��|`)B�}e�)Q��A�c*�� 7 $R= � (B� % + c&R#c})/ �2(X)=0.59^{+0#�8_{-0.13}\pm0.125h.�"l�U�˥Se�)�� �?N=. F/q �r-�Q�%��=ch�uldT�l�g�6i�1 )I a,bfe�  emit {\k\b�}p. &x��ad opin!�� is m (perhapwczRly�eHis�a�io �aE�h aOQ8``trigger bias'�*Sm�aS $>� �op$Y�fayE �ש$-!qadB��D +ag� `heu� � (��VYlt�2!�a��o�Zrka2�g)��e��� o^ub�b*^�jpin�*a�g.:�rN�p+p&��In $p�"��e ��Q��z�!ف�sc"�of-y A$g��"5 � -%�� o�xuj�a p��c�� �zIp� p+A2P�do�g6�d �C"�r�� C1,&�{�x ^Q^ �a�\cB��a�|��  .��+ in�� 0e��� �aK^,!��s^<tim!one�K�xthe utm�funda3-jc@:"�,�U-!HRR ?�urqo!u�:!�6�"` . �~�;:AbGp��Ee� fac�z�'' ��N@i� t� �"�"�i�� A#Lk_KSm (>�.g�3f.�h Bedjidiangd}: � eqn��Gs@S,m^2_Q) & = & K&�|$um_{i,j=q, *4,g}\int^{1}_{46 / s} �(d�e}{t dx_12B> lta(x_2 - &)\\ \non�{&x& f^A_i .,{o ^2_F) f^B 2 :]}ij} (s �& R)"bla�t� 9U geul�hs�CA�9vs{"Am���}��!B�y� %�Q�c n�!i��F� D(z,\mu^2^g(k^2_T)L�L2B� H@we ��h}(� 1�aMulY� om 3^"esteps�"�)!�1Faa���l9e1 r ar��,N"NA 3):�Ɂ� \��ItA�m +�#� e�(�c� 2��B^m����selves �J.�DGLAP& evol��� p�d� *� low-x� a��in� s)is8��ea��#lyu��# Feynman��;1 �&�-8� !J!&��$x=0$� 5Q�be =V��"��'}b�r�%8�he͜a e�UB� � �a��)Q�cou9, L 9v�&he"|&J``$k_T$-�%S6'',�On!\$q���� hard�h+r�nd5{��2(�AT, d5 &~be� ed�J!u�D itud���w � �)�� "� a�_ �&n D ����9�be .Dak�%@e�_4QCD ``�  ,�\al �$e e4��ŷN$� S]~#S��an �( ":1985u��is "�l� �w!uvc�A��"icA�Rs$I��_�"o�a D-��X�pE�~Y�E��&$�% | L \gg \Lambda^2_{QCD}e-P�Im�fQ��XO�e i" �a�-` a���KA�#a� �Rr`n!6d�(s (D Drell-Ya.~�) �!V"o%P2��� i&�L!w4long-יe+z�l %�C�=t�ea�e ��'sit� �mkinLF*� ��,�� l@ UE%��R re ``uyV eα��i^%&#%�A�o�[C. uQK�v ��&�t,�n �D!���z$A:'b=Je9reh(�( a s>P��.�bin:�0�h���j>�k�s&�h$ e�c'^.� P "�% rNXV�%12cm]{F^X_comb�� _4x1>sC23e�&�me)MCDF�z�2�z1%�.� "Q b�"|Vmpngᕅf� stood,����\2Z!� orem�z�- ����asympt�Nj high�*�v�*1%.:� c p�e,��`,��x &E� volv)�&/ � . Histo2�G/�Kx�+��,�/�z20for�-$E_T�,�p�"�!sF�, 1)?�*aG o*$&o �da"!&��:7�v! {lab Tevas$4 ($\s=1.8$ TeVFOY. atEj})�a"/c�`%�_)k,-�t�s rol��)�dF"�Vj�onq���AB!���F�.�,e�Z�W - ��!>up�ked0u*��ra8Qerr( >� (� gray5�3��U,s i4�`"ar��&�ID!�re2D� es!� mu_F� R$) +4�.�ms a�wo%~us��!A��%{���V%N��a"� 5Ŋ\%� ���qo�/� real/Q"3U�� yet���.��2�Y�%Dm�Y)D1ayso Sm&w.i���!��G"UfA�e���i Zus���V�' 1990'MVBr jo���xGCSMi8&�m����� a� $p�I,(6-20 GeV/c)!�E9`8�xs (1-2of&��)� aGl3jz���&aAEhe�)Ke* �+ �)��ed� olar12h=j�+�7�2�b��y��E� ��a!ax� { me�\�*� a i-�.4�!J�2��gy�+AL6W, x ��=�i&t�8�!�)Żh�kepe%}�B�n� ��2�Vwere6i!T�� ��y ٰe<m e� (> �2�\&�lyi\�R\�d6  onZ�&�9�J ZJ �$Rg+ >6 �O| shadq�2I�R&jEskolEF 1gt}"/�� � $&�"- yz &�5cu`�ti���r-$b+IHC $�NA�1�5��1t�� "�!A gm4�lZ\!�n�,SQVY�r&� .)4=�2`-z" �2w.x�� end, �)��pr ��W� iAf�43 �"x�Qsv8t�fI � <SE�&� 1�S1�} O)��܅C;u��)��=�a �az&)8�9R�uj��H. Deep-}Sas"�&"&�- 198�r��!~G)a-&� %v%4�mbek�pK u���d�yios .h�F_2^A/d$)1& !0%k��r�~�. v� . ��� a� s06pe��Ewe5� A=L=-�.�r ,�.F���dam, 95is�#a��n �ce8# � &�k��r��I��um�"�the*~. �k�z/i�F<6y1. Űa��0w� ($x>0.9$)� ��L enr�� du2�  sS�-)-�Q? z� ��=$�i�0($0.2Q�q�� IT make� +tu����q� 6� (or�Li� ly $q$�)I�Mu�4�.,85wy, McLerrxyW By tr����(f���Ca� T�T �� k, ۯt�1�alm[1#��Q;&- �!e+���c �.�eNide�e��t )MJ&� :�?a�/``c.�a�-�e�,!���ll�\�b11n׫no�any�)5>2��K���g���us,�g�:� hand�Te'judici� p��"} ofI� ing �, u�' |5t2�@�"�W %�.��`�$�#%F e�i%��x�5EKS98 roach5ey0!I.�y$Rk!�� $i${ � �}�I�� 1998df}�*�A$a{;f� v��� &� ,a�mW � Z20W e� R3"�2�,JU.��``� moau�zm?��n8��o2�!� � $2.25$^2$�$10005^2s�"��bu g�{n,(����] ek!���dor er al-R'��l � u;���s>�$�B� .�}&�``H�;Probe''�0��f�i~� s,� � �fu ��&�"*x>&6=0 Open charm ��is still under-predicted by pQCD calculations, requiring substantial $K$ factors to agree with data. Even then, special fragmentation funcc� and intrinsic $k_T$ are needed to describe the differential cross sections. Closed charm is plagued by its reliance on NRQCD models of $\jpsi$ forma�8. How could we~ n expect��Uuse it as a ``calibrated'' probe in a heavy ion collision? The answer again relies on !�)[iz%+:Hprincipl�| short-wavelength field configur7s refle%�Tin large transverse mo!�um�cesses!v only%�,ly sensitive�r8typical of soft[,. This leadE2JM|ioA*Dat high-$p_T$ phen�4a, including c%�produc6�s,� �2� c�Se& article ]� in $p+A$ �$A c�@Ds has been observ�(IBQ= :;a�`` m ipating'')SA�0($\np$), i.e. which�-A��(arda�bajntrast, A�am��U�:�!�``B�'', as �� ione�*%}p!�0ous paragrapha�eZ!�qu��ti��tightl� rrel���Aءj t�~@at smaller impact[ meter ($b!a��1a#���]rA\i_, so`@e overlap volume,great:�� >!�Q�mat it)�des%9, giva�4an approximate�%A]-�E�� �$\times$�$$\sim R^4  D \np^{4/3}$. Glau�Ic*��a at ���ofBDs ���m RHICEri!�s�3a�a����Lf $\nu = \nc/(\np/2) �1-6$,��showna6(Fig.~\ref{g �4_200_ncnp_npnca�\subs��on{�@S�@ } %Gure tempA1 \begin{�`e}[t]ce��}2.#4C. \label�6E} \end�4 \hspace{\fillJ 6j 6! tmundo_�o> PNA50 results on J/Psi.�,%�!a� A�-�.WDrell-Ya7a�funKof !�rality�.�} F�!7eA M � �analysisb �.�A�genera�I�as�>��`"���� ��? a2�a� ѣ (� ly $E_T$)N � ��Zn compaḁ�a.��!��� ``norma�5ar.�'' extra�3p+AD y� ina�m�2�.%h data�\t2� � }2 nA�iph!w evee"bu� en�e�ly��a�� ly< < satu!!ng�Ga2m�bo�߽�ly 50\%� M��*in2� !���choic� �AvI�"s (�aa*� ng1�@horizontal axis)~)�Colla},��4is not surpris>consideK a%�� s��mad� in �( class. Wh^ � �have �� d wid!��s� �%a�ety��theoret� %Iachjit makes� � look ve� arefully �( systematic2�y8I�� -� a�gipby  Q�'D 6�!Od<mined%�2 t 2�s based��� A7�A�I !ϑCp5*� D en\ �U decrease�&6e�lD is��6� Z absorŪ�)?ed�in�_(us itself,� sumably!G �+N$*R sc�ingM�8Kharzeev:1996yxe�is.�is desc d empirA$ c!;! � $\alpha$]�E��xa fit�4%o"�  (gma^{p+A}_{v }�s 0Z  A^p� B_0$ ide!�l$p+p$ 2� (��not nea ari�o). I��=1$@n��ry)mo �1|is visib9o�W"� proton,M�is �valen�$\nc$-�J. W�� 1J<1$AUduexwshado�m�;ior!�!�o A�he�o facev -�� 2/3$ c� spon)��xle��u8] ,Ɍ��0 lower values>�fur�:Q�bulk. nٖ FA �=�00.931\pm0.002 7$ ._. imply�P�bC:� i�s�/y alsr alyz �|�Aaberm��ttenu���%�eff� �X �!u%�ar o (��aW&K $\rho LA^{1 ,), $N\propto��(-I� ')� u�;� geometryA'6|�* �� ine v� ord��o est� q�-�+N� �6Bw� s } $7.3%�6$ mb i)%�U��,Z�2}$4>: a re�:eTrpo�ng%cS+U�2 L us� is6� ap��tdepend&m+��assum�ys, len$some doubt!Jit�atu� repres�G mordLD��d.�� � 75mm"� !% > he�=7� ��_x2>� mn�b6;$x_2$��&"A�beam �"� _"� �� "� �� ��f>� sa!�� 'r�F$>�f���2�"� SA,ins!�IYA�a� �z � %T important"n� sets�=PHENIX� �� E866Fermilab��se�9� "kin�  accepta� thanG , P�H the � !; wardt@$y=0-4$ ($x_F>0$)�%N * � �Lfo C backPc�(age $-2��,0mm]{brahms_!�$ix_rcpJpsi>� $R_{CP}$ "�$in 200 GeV>$��� , bo�orUo hadr �--`.rR�}J~~sn�]{dAu_(_Fig4>�PHOBOSNx��2;N�f� O� ���suggest_���a04case, at leasta�>. ��� i�E�Ae7 %�R�s� ch$)mS6 S�)!�!%�Au+Au@ �a�� �g7�e ��&��ph�s>- phobos-�}. Inided��@ ���"� l6��ke� In�E q6�of �&" *.R�&^��ipants ��uw �)h!<ndir�on.L�ompens�a�y36G� H, hol� gto�)[per.���q���4mr![ S��``l��''u#�� �l ��.��Iv� �w�� they"#e �D(�5�I� a�ralE[. ����iz� D 9�BB)!�q/� well�topped���� muonC�~��$1�& Of�&r��br6��Ju_%yo�u upE$possibi�A� m�om�EkY$ peci<at�� Ad 1�y>|tG& qu� �� �th SPS iesMThews� 0rj��#cur�'�K�� /Adler/ 3rc}��v m error bar� nd so� Z omew]pri� o ru�ut6� scenario� e Run 4�ic10x%5^� ((allow m&defin<'(M�t1&adA|%��h %Fi �O"�{70� %Z� 8ggaz_fig1� %&j %u� 's N�Juof k % E} %} %� � %:� F�8r�pbmjs�.�PBM J2� 6�EAs d��i[�STAR,6�!echnique!( . P focu�maiZ.�_m of a!�mpt e�. ron < a�. .� �c� �A0beautyI� A�e�per�!�S ��"``k,phic�$ �s ! to 5�l ull2CI�.A�d�� (p+p,f,��) ��M��Y a� hapeA;�H0llg them� dcox 02cg,Averbeck," 4ta}. M�"�lym�N�ll� A�o�"I� &�%�v) v)Jb.u let�Q)��& 6��>�jiA:rea�s�is �Ist� (aFi�0 s) �pQCD-n#E�p>!� p+p� EY�%�!�ISRn(��~�6n. a(eRqa.f Qd. ��+as �� nstru�Aa-e D�M�m� AdamQ 84fc,Zhang}. By�'&� KI�method� eyI� X mp���42��B� N�8�Z:PIGXsec0529E=�!%VaB�d !�=�!��&�U i�&MeZO/ 2P!rer (b!Cof 2-3)��AX6R���"-����� e �K'a6S�5$, although�%s �&s likea@oA���c�'s ���, �u  lways kee�x�0��t�8��] (new machine�'often� uncerta��D3 9makE$ir first r�e�.`� a�o a� �c(^�� (e.g.�'exas�1saw� y|8vogt-ccbb}). C5x'g2y��ٵ!�I �.� �*"en�%y before$ .:�,"� c establish �igh�c� . ��!�!j nf q`:\ e`=�!'axte% 6�"[ R�.�� e-0& M*�ɿ��EU�i�k � vs. ��/�2 ��N!�:Y �2��N  \� {S�7�-sW* 73S�+ } IX  s�4A�,�� hidd�-� e4�in � ��8o�7 le, *� ��A �h �  n�OCc rima�iZ �pro� f ``� ''<(p��**9(2� ! )&9 ��oH �(�%v nce� tX(�(�"�. Do�x��{%] ia�tru�]5�x�.�9&� ?�wO;be� Xe�%��itu� )A�==qo�6lA flavor�+s�Usubtl�y3t�pC&.  e 6 v50�y, issuh � ��  �-3 #A�  fas�4�#�n"j9I�)�st\{8� n�de#J;M2 {j#�g"� mass �FW 0(�"I;� , it� � )!y �ka�z �7A-mq�3)rlmost :'two"8!pey0��� ;, ��AoapnH���:�2x6�" " 83nr}. However,xeF\ !,e��H$Ae� :!ge�$ of 6!�a�2F .� �� #"n*"c. �s<�M,-Zle� is begA��� B�"G �dA� � �sLa���ab�+�.if2JF�\�2{Hohneopb,Alt 4wc� e4)�2l$\kpi$�Cio B�'� �!3�3)� &�8p$A�a#(a�Q�J7A�connec"�: )( $Si+Si$^$C+C$2$%���TwoLN do work[ �.}' multiply-�km��� O. we�l $f_2<.�Hs� -8�! de�(y&T �Fe ond =ir�lum�* B�< &5u !Deq�p&��� 1V!tA$�be pomd I��". s�znta-al picov�1�{% �" Ŕ.�*p (or�xt��fA�X *�)�a��ly��3Z s.� �> pend��=��le1��B� is�2]e�!!�s�=on� �ir�  thro��A.j@J 3iquil) * / (��?�� Ma�B  code)A� �61e5�->�F%ci-10!���k9f0>� $\gamma_s�Q ��lyC�� �V]y&�Cleymans� 2hy}F"��s_moda��1Q�� �"�* l/ i unity��!$10\%$�"all��%B&*U�a�f�u�!�``skin''A��$��D�B And yet-VW �>� d` ��explap2& �whyA4�f�Ita�bey��� scop��� '!�5`8ailede/ 7uc��%�8ing, mIis�FfulOimagi�D��hC n�*aq����ext�'aN[�"� 5q c-ly ex�Is� njE� mas�'j ���!toOcis"����>��wxeddB!of��&� �)��e�h�c&. involv�1 E…��0�*i�n$��&�@A+A, �� $\epem�,,��iaLy!#M� �.!��tr����<$asymptotic)2?J�&i��9e� 0.44�� &Gjaipur2~#4D2�mpGJ�$F�$ ,".$��&-:� Ce[H�&�c�)*?at SPS��iM"�$mm��#�$\V��#.MB�om^VB- �1 ��B $\pp�McAo)" "�.�N�f�""�OutmeCo�MQs�c����I ewed �au�Ef4���� in ae����E�x�7el�:�!��� rpla�'"Cor�J� s8a!.9$\pbarpi�# #di"=!�P� &��b�p� ab�Jtra��<,]D now*�*Z!g� ?be� (C NLO .pI. Q "onium2|"�D+A%�A+Ae���� puzz�  fe�D�?7 I! <����.�)�"y��is[ �3i aT� my%�how� F%&sha� � �``�-''i�5" �<. e�:m�!~ng�R����$�c�BaEan�'q !�be ���ignT �1=Fng�J"d A��%Q��VA% "� sF#o/!��nvironOlS' T+u1� � eZ(un�R)uC2  a> que �e��=g�m�um�"E�E Dof&�9 �So!R�q:�> occa�@u�``-��M�oo``%E�N� fu� >L� �a�,&s ��sWN$ ifulR7�8upgrad�nd plan�< searVF � � $\Upsilon: lept�f�P$B$� ��-�,� �-sw%= t�/inɋM,VCalderon�X�v Acknowled 8s}�� auth"y;%�t�%ank}organize�,FeA�8co Antinori, St&�Fn Bass, Rene Bellwied, Thomas Ullrich, Julia Velkovska and Urs Wiedeman��ho iM:a�"ex�; Y> -uns�to�Lo�Qad  talkI|)u3 �mC�aelp� "8David Silvermyr��(Raphael de "5:�Eo� l� m�Npre�8TT�6. S�.xnks�  Ralf "V%T Terry Awes, Mark BakK Jean & u(Paul StankuIK�P^;�4%��:ruD%\�5:N \Biblio4N2Tю 83xm%�V�]�V-l-�12��27�W8!U.Mue�WE.$wy} A.~H.~ E!$J.~w.~Qiu,^ 8}, 427�&6.�McLerrmyx} L.~P\��e2.Eskola!J8dfe�J.~ ��J.~Kol=)ɋC��,Salgado, Eur9b��-fAx61�99)}s ZA1gt�oR.~i�65A-�9��729E!222 [A!�[:!M�6�47A%28W2xa�a!�  o HPBe *�q>�Oaf,!JLou�1o,�NardiE H.~Satz�$�$-X74}, 30Ee�%n�!�9ap��>408F�:�EM� VIJ� 8�25J�JE=!�G.~.  [� %u� ]NE 30}, S134 2�B*DT B.~���� 0523�>��5.�@.] \eta�,e�(-ex/0301017}�a4mr2?v"� :F40902.-"�8E�<M.~E]M� $Gorenstein��N��� 4009FB3=A.~,� B6p=,z Redl�?�J� ache� � 6�57�b3I62N2b;A0L.~eHSchroed�' hRafelski:�mS6�054905e�6G2�;S.~S.~:� �)DY� 0149� 2�&) !��4BB �I�6 i:+1k19Nd7'2cg�pn� [�b8�v19U�6X v�3!�*_�^V%<� 4ta}.P,R�.���;fc��}JD 7006}f>2 H.  v�%*qr(A�qB�2�249 2�.{%}��:VR�71 474E�2A&�%SAl>@B9603.9��2hy%`,��Kampf~a�einber NS.~Wheata" g 0212335=B���:M�iS� 6�K 1120�! .\��mp:�Praman� bf 6�&787FJ"� M.  R(% vbib{docu�} �%0 espcrc1.tex $% % % $Id:2 X1.2 2000/07/24 09:12:51�/ppZExp $ % \yLclass[fleqn,12pt,two�Z]{QD} \hy�5Hpenalty=5000 \toler D=A0 \usepackage{ �} %%gU%fo @��ius�,LaTeX2.09 % �style[.�, � h.�%�:you wan�@clude PostScript �<s2�iicx�>putD r ow�'�@��Ft: % \newcommand{\cZ}{\cal{Z}� �[m{def}{DE}[/]H...2�floatflA2c@snn}{\sqrt{s_{NN}c2.� seff"_{\rm�B!@> AAA}{A+A}6spp}{p+p>barp}{&Lp}B$qbarq.$ q}+q:H}{e^+e^-Ac.� nhit}{N_{:8n�n_{ppBch5chBpRBs specB@tot}{\langle\nch\�le:�ave`(pV'npBj�^B:Enc�>�`c.�V`halA� {1}{2>G 6�/2VJeta!�eta[-5O:�aAL6R{s}(s): etazero}{ = 0F one}{| | < 1:! dndeta}{d!w/d'R"p2#>� F � |_�RR�6-R,%O X / 1b6E p+pz,o,+nf�*�.-�N�onI� �9^�r�$}{\a/VSneeE�ee>nhi�hF� ubar.�":�yb}{y���>mpy� p_T U� % addJ(']TeX's ɹ�UWb list��{[�&�2�$finan�G papezA-��end-ed�S-�T�7decla%<ns��front�hL \title{Bulk Dynamic� Heavy Ion�i#� �{P\ A. S"@  \ * ks{C%addB4: Chemistry De�iZ, Brook� n N� al Lory, U�(, NY 11973} "�g%�typeset:��:�"�"ab�ct�"�"�!��� �rt+ Z,�"�JE6 ve d-5�#op*^L�T�eJC^�)6 eon-  orb4Xon-!.�pWr�1vi�!h)Wr dZ#/ jfat2_ o�$�� f c?4�]�6tp�al�J�us �us.*�4.� 2&�:�i�. ic�&n "�B!q1�p a5N%� nF�6t� -6!� n�;�a %�+raS��e�4.� ��%2�a global$ �/�A�(pseudo�N %dA�ibupsA>Dt�1�"D 8.�/wa�e) e.�M�8&�Nl�/e�Efor %Kde�#et%i"{$>Rllpg% Mo#"� d %!{�%>r!y1مp+p�"removDe% seyVA��&t$,B/n�"al $re�.a M\m"�al-hydrom]al+,s%�Most 2;C $.�N�|LAZi�/stageE�the %u��- ]n#?[" ropy%"1�'t5��A�Landau N�a�6�2i�! nd %�!�]�(�!.�(',3|At .9QAt�"}1�z.. exis�8�8 boost-"�[ %.�?p�!�`u�\.#!Om-�Buch %as ? a69ellw%c flow�!)ޡn=��."w#�c,FOpl[v�Mus8 ilarCpm�C��Ga/%R�#, rai UE)ba�v(Ge� �)�1��<�p���.%4�a "2".B } R�b%22�->9en �\�#g�6�"�W.aQb �1�!�U���1is*�=  la&WP�A, h�uI�y)B�Qspanna� an e�T!~l e��'!C�Se1Aht&�2y. WitC e turn-on��E�fac�P�Y0,�.now�( *�.�.:)�:�se��Ito�dnn=20�Lq&�;$!M�P- �er-of-�0-\~4A�nE<-�9�UEu�C~$.� (90 R:e�9sy+cMH)�(lYcce��--$ ies , �#iB ^i�upac�5!��U-pI)�&�@E895 -7$ AGS, NA49 SPS,%�BRAHMS PxZa�%�. F1M�u�Y�.��t��eoY-ve�x��n�% rC,m�.s,�D6c'iiK"�=!T��% a>*wOly-&ac~ �+, Gluon Plasm HRa��)�nevgy�3^)ly��4(uQ# N=4 SUSY A)A�precis� fM��a>+o\82�p�238u�,96de,Shuryak%�rh�m�9r�� w�NaUa�co�s ga�Yt, nd g��b�:�P!��;1�y�ي�Hz-%��}�^� �estead,�]com|e!!d&�;r�"� �p�.ous�5�� FjMe� = A|�=#-m�,U a�;)�*DR�,~E�x �xbody s"o%<a"22"7_  V= Ape�Bi66�� mXS 4�� too %}+�{vidua�z%E%�VWina�tinct."r}[&3w&260�VZH1]? 2_qm�Gi}&A$&�$?!�&�tKQic � �/�Mz.2fi ]l1��j5bf�wRb(WP12_Ntot_N� (_AuAu_19130NwBapp>2To���L-g2�J�Oiq? paira�a"T�a�u.�!�three�]A'3 d�h��_�"�v�8m 5=��P:YM~[ S3@se���|neq}?m=��iAm�d|-NaJ�%CI=,%T�5r�-� aX� Pm�+f!,path, ]u�.[ \\�G�reav!�* ��`d�� rkB0}�'usaSn al �7�>�.*N��9&3E-�e3,�M)91l�Ae�35t�g�Ad)h by ���&�<s (UjM�Mj6�A�on���Qe�re��[� ���P"q\(c��!~zeout,~B/"*js,4U��E@?re AX�[<>i�9RQ" ourcc � R@Ŝ^<s �a�HIJINGBrJei; 't0 avoi8� �kic)� al"�_��$%�;��/� }_ -�& RQMDE tere��g7 �S�s�@del� !�icultڀl3�A���pB�!�icle �+y� .� Ke"gnp$) V�i�}_ToporPopR 2gf}N �"���p� � s ��Au��!+7��)�! CZPe���J�-�A tu2eK priaxG{7both mise �Mm�ZRB& �-X. Var�EY;�nte2f\ 9� "l=-��A!s]outQ�Waus�M1�ut�j�.�w"�Z ��5!_s:�it�m���0I�s2�`bIErA2aMH ular-V�� � of little&. " f !�i�?jZ !}svSI�,PI r��4czQ5�Qandle!�W�& 9s�8*�� 64{�6�!e)E 5�� iA�oc�(,�x6�Ra � 2a�*2� 53ȑ�m�bA� at c�X�%�0�(\uH"At!�qYT 7 <a8!���%�Ua�E� );Yp&�h (AP& j UIt!�� t��ar�K�a ic r�ns�Eis�WY) 5A��� ~ {F���ged�. �n& $L��%�R� v�R" 6_dN�# eta 5!> � � k ��"� �K:� 2��.}.� j�N� z�l80j� ]{WP14B( _200BdN� v�;&i�=!>+=19xAn$�.�r�N2� ��8�k]|a�uq. �< y5�qr�*hAt� ��&�K�Dwhfv6'8,�5 5 n� at  D��7 �g��s�aN�� M�A� ]%*L $ 20�,q-�B!"�Vl�n x��� %a\ $I�A/6s�v�, ��`�Z.%fz �� tanceq$"$. ItAn�!>Nw���\ �Ossp&� V "� }AAA &FJ�!? &�^e smooth>J�:A�H��[�!|*ztf>yt�E�Z" F qYS 0(?yK), &k�x�F\c�NjrAiwo�� �4ZHil� a~� :��t��wa�I�!Bbv)��in�%0&^qo6W,�G!�k �23 each� �� enecke:shaHIp w�%.z�`� iPv9��M�":����a� &�E two_�!~�Vp�fi�� �.� ]curve''lEfl?f4>+�e oA)� � d�#�d,E�ze�kE5�?B���Ay . Si Oe ?pee<"f!s,%�!J0A�5ahe P��+ �.�az� he��i�avL{Aa��#��.Cq as�Z��y 6F�~&VrmA�� ol�# Um� ��raQU%�WHey� �ol }l�mal�� tBS�q"�&� !��ap\ntDB�{r#m�2M"for $��,��! "&1"!�_)!��.��,_AA_ee_pps_l!_mub}qa�4 3xk,")&D4vyA�*/o�I!7E��$�Pez~ou�n\�``>�" HAct�D ڕ�kV�OA��an `` 2�! �''5 eff=\s/2$� e aB�p!U):23O�Mre�6&a2 �E3GE.��no� Bf# �^DE��$���]��xfam� &�IJipa:sAruckQ"�D&Y �D� � >o ))&"�Z&at��)h�R�]be*�a� sequ.4P�a .�Gbaryo"�"ocM|BpBY&��up]M �Y�J$"�M?UiZX $S=(E-pV-\mu_B N_B)/T$�^u hK !"��� � :k "j p�k tJbqm}h)> ��q2bq]{f,_B6b�Gh� ede�iy���/q�pp'l� (1[$\s#e� �5ɤis��4t9Qul�g"�s�BSS9f�J/!>5� �Hb.�K� �_ )�94�� �� ��aKy��� : 1)Ip2I��q��), 2) A�@ v��i�7,�O� !�!uR4dE3)��o�mf.C �Ge���!�� ang}d.�t�ޘe6��. Such�Z<^Z  B �(l�L&O w'riR+u�� a*Y�ach�:M PANin-pr��d���nT���Xin� �t �! A�#� �$�+��,� ��� 2Z&x��pi$�o arrivei.&��  semi-[Ye/F��RAD&�>DjsA!~d� &�����""mY�u (�^Color��ss Co�Z�|�cK�by L. @��:�B}) �(W�Z[uW��zH*�( D�p��a .�F�="mA l&#�z !0_� � major�es�f����o�N-1� Ɉv� .��0@ ��24(}eJi�al l��Naej 6jMso�ing2sO w�V K�� ny ��i��m2�uIes � k 6�q�,'� � ly disx$fY"�L� � di4� ��("�� "�,&=�'V$&�h��me:�N 2l��BtU�}&/R9\ (o�2a ac��)�mA"�� anQar (u��>!�e �Zi�K�,���Yio}TK�'iz�naI&�� A}Z�s`+� 3� ���2Lx.��3f.&j!,�C�h$\tau�5,sim R/c_s$ ( x l�1v�� fm/c��.iąM QL Q,mR/(c_s \s)$�ll 1$ 2I2�K���E�{M�.�s} 11Mes3 1950'�'Os% >ENS��݅��jg "< , repla"� "� t lex"�/a.^�+a*� ja slab!~areE�i R^2_A� lenb�$\Delt�9R_Am/� �, voӟ $V� R^3/ � inͬ�5�� ��*<'bB � ma�C.��� an�.ir W� _ss�R �B=I 04$ TeV/fm$^3$�y# �a � �5Ex�H s un� ��R.&"ae2u� !��.$less black�(equ"�F( $p=\e �/�n�e nver�b%o�mon�M �,�s���V^{3/4}$�j'=M�"� 1�is $S= QVSs L/\s = 1Y-�6��!��dio�Y� ��.�_ e:a.jd,i"<:gs,Belenkij:cd}~_f d� mmed�"c�t [*��o% �an aF , $S��� &�s"�  S!�Dp]bAlF� C �/]H$ �%Lt5o u� [Q 2� 2�-6 bR)2I|jO{ �,U �a��E�axiZ e\�� niso�5ic:o�B �Z�!w�$MH= \ln\�@ /m^2�� � appl/A�1E- �P �=RU� !�g�a�-�1�w|al~�of 3DjOYy t � e `` v.{1�las advaH�Co�,�I-� :nT$ak}, Carru��s:( :dw}Że. IZhi�aqu�Fm��� W!�EZrikisN"�Z�p�6� �_�n�entT �'s&�c&��su_��. � ] w}re_R� "� .i�]mula, �&o� e�.Ax��$nch = 2.2s��4}$,.aChjobB�9�A$ tren�w� em$ � �9\hs�ana�uI��%>����V; s~A�nD,��-�B/*+&�%� ����Y�6at�- I P:cq} g �ee�%�=� , if ^�j!�a)c)�V(!�.��d �a��`wh;�/� �K��ree��tZ�h�%$)]� ��E�ns�w� *���VF�U V !�< g�+����@ly��(J�� }�u6E'th�e�2e�2sA$an�ie&��'sam-�+2O�ksU�in8of�5gmK�-�Bearden���:`>4)�'�!��"ch��q?�mf�)��>n`N�}"` te*�, p���\yb$,�b�*� -JII&J�� �� �n��Ug� & oe>F�!�.�i� n&�.�@�|�a�t.h"�.i+�km?8E�"�!�a� c6&�-sar��'��BUO -q& h��> F�&�-_>NAd1gp2�D2� � � <5z*��oge�l�one�3a';_J��mea�.n���($���z``f �'Ey� "�5eBulB~�17��k&�!_" : Bjorken>��V')3�i9+�:ap*)�$]{raimond_z5>U$v�2�(A�$H��l?$U)��are:�@c/2�mnQ� �!W usA:or 2�AIpiY< ��.* /� �04i= to)H-p� 2��olb��3dz���qPb*d� e�%� a7m� M �Y2qr�1o�0tu�/ e$o�v?6�Ac%(Feynman:ej}��a gui�C"�!.h�_�)g�2;|q&� s" $.g�-�"� im"�G ^of Iyy<utstoW�T�T,.� i/y �0pieɡ2�� Qa�s���0�1( 6r hybri�zaVm� EOS ��a&�4EOS�a mixed Y/)� ��>UBr� ��"��*EUe�5�>tra (w�� low)8mapQf�@�-�->��&R��.{0 ,�"��2� (2D 6� S!�eGU��<��E��$9 B�%�eN reco���)�}mj. A�"N�(�� < m��o"�$ %J Rl5m�3e�in�J Z� �x�'s}� �I��Sn�Bng�V4e�Bs�9�hu���%&l V M iA�b� &19���^J�!)?. NorA L���ýT�m6� magn�% �L1<&�yMolnaSZ zj}.&�5���7v4 discrep/��!b�� ��6�c�7;�.�E�Bmanifes�? !s"7J�i�6�Iw����\�O�*�7to�W���ny,O6�T�*�`,e.�:Ib�2j ��\�i�P�F,,2:�i MjHirano� 1eu� �!A�ue�V�ro� o 2<+�����" �t.� i�!���'e Uvxig art2qB� 4rs}�  g�CJ�w�Z�KJ U CGCed )�&�=aA�n*�, � � ach.B�&�x�W��!� 6 ��$to warran�e-*]/ofMW*P���P a�od�@�Ms7$!�r5= M cor��l�?*Ke�1�!�eN��]�a��-�O�It�|�M� co��%xto �!Vat�[auy"�$a�!!�Q1 o� "�$Rqto El�,h,S�" 9T�Qj>Qsh !E%} V�.1&P+0at�[ 5irs�U"�?� l��衄*6� o�m �!f�� 9t'0�� il�� n�}iS#Zr read�'Z#&i�xp.a.N*,!$�?!0�] *�ʽ'��Pe7Us "�%�%����ޜ���a<�(ori} to ser��i��� .�d :�N��)�7:�)!bz4�F#�7 %r WP184:0;AA_pp_ee8.2�"/�b$A+�t�n��� &:F4 %��"#v�a$~:y�� &,R".E�i<�^�}-�F#"T%�=�zO<21a= MNSyu@b ���G;� �pbwY`�D# %�).�n�4� t^�8�ee!�#%b>�."=p=)�0,.�^ %�to-�"�[Y��,)�"�T���-�>�E%:�x �/vs�*{-1cm:��3�a��c�&�Cs�����BitBvotX�4��.#a���r a>�,�Q b*� *�� �|F]N��"���.. 6�6���%�!��)�]x���6$\yhR�B�`?Z'l8)/ Ԕ�mp~e �a��a.[��� �-�y� :j��"�>� "3�I5� -HN�9� ��� thr0A� @!<\& �Gp��� _'%( �A�1-:�d:�ڂ�2J�B�, "N ��N��E�5=jA) �&� y�F[q�i�6u�"�B!_is�of�� �aZ2�X� ��d!�c"�nt- c�aroz�lxp,�aniscer� MB#.�,��* ����%�./r6�.�  �!s�[eSJ���e�sre��!�a�2& :Df,:�j� 3z�5t�a�,*;!zdebk-:<B:@? y ``��,ce dom�^�KP&]aZ *� �#� � Koch�2uq�8 %yWq�%�!�regs�QE%qO*�&r�@.kx�RK Ai��d�7tr���!aT9�� :R�T_pt��`-mt�>h-��Z�'f�z2�h >p�e . Oe.�s on HBT� �'V�d�CAur�^ mt_22�hb B :�<pronouR$ $�6�x�i�AJ, �  6Sto�;.Ɔ!�Fal��anQ,�p�Qo�];���in�?u|��;wA�Gc�e &�@2R��YIf�Ir�\Ie �+"� �a3q#���~reV=a ata�A�m�*�Zٺ �8��FK>� ��8v 6_v2� PMp AA_4�&s>� &r fV8%!\����5�EtNW8%� WPf�*�V� � ����a�:� �&“Pr&�|!�aE$�c6Q�)�Yd���. "�J~o 6g ��0 B��(�>�>�y�BYi�� d�E!�e�� :�1a�i���a�� �.5>�� >�v� .7F� "�Co� ��� ܮ�?*@&�Ki�"M��&f*l���ngqxo ����e!&�&Jq���Z8"�)$ :n �=6� cp�L un�x:ep�$� �E�(��)�d5j�Nway�"$jr*� 4'S � basi�O&�!F�A7!,( hapJ;w2��6P6� �G turbCC Y*s(, w��funda�?bFY�c �"eD!do��y�52CY�nE�howuB(���� so quickl�Ns i� w !nL4�*o!Tc� s pu��o6�"r~�nePBcO.wa�td6%&^/P tackF6a�re�PgQ- Ɇ. "�]��?���yP 2"�!a>zb �ed:��;2wf�:u�rs�4I"P�1��eI�6�Y[?a �  /�Iq�&�HA�Ƀ�&�se�� �:2r}�=us�� &9 theb* �}{2 �.|^} I.~  [C;�i ion]F�t10020*lsHD 4je}�sB�x[��P2P._*uPE/Ê�2��L -wp�HeY W�_PaZ-"�H4at http://www.!� .bnl.gov/F/public -QGP-I-I .pdf&�y2�]v ,!t(R.~Klebanov�:$A.~W.~Peet:;xDw5�t391�}92�}�/� O^��V.~ Np*ʄ`z38J�z>LV\� Pop"$zPhys.\ 8u�v�w�x2 8u3.8uE.�N�yE.~nY2&x41}, 28%78.\U��NA�M���7v�{4>�zFKCRF2�2�%Y^�{*�J� , Te� Chou�}N.~Yaw�nd!�Ye>:{I12y2154{62�~�3xk2�r 3>*|B-- .�wF0502�6�? *@>s�."�U�>( K.M. O'HarLwit9�Sc��)29As 2179Eq28z�36e,3zg.\xDor&�~ P5��70�|52�R:gs� ~D.~ (, Izv.\ Aka҅Nauk SeWFiz.\ V1�51V2.�6�xZ.~��k(Nuovo Cim.\{�߃ � 3S10m�e$56) [Usp.\ ��ƈ56�E555).S�6o4 F.~ , G.~Fry�-E.�|o�y�_!2 32}, 86�72�z6�4AUp, Annals N.Y.Acad.Sci. 229, 9%?6L&�4ԈV.~ %;E.� Y%�.�2�N8>�75.N.(32C�^5�1�}��8:�n��yx�qG!�v�40305.j>_/�}�Lev*k-�B-�8�m)1.��%�*!�F����U.~Heinz2�th/�84}�*�*-P.~ n(�14I�:�j/H+�5D.~ :T�)2ah14e�6��j&>�R.~Rapp:S��S 0449N��B%L, 25��40701.�6W$!� 2:!o406066=o6!#�G Z���011%�2) 9E�rsKEVY.~Nara>�AIU74A�3Ԁ6�l*��mp%���ama�(}Z!�:n�� .�!N304013�bi$�* 53h��312022Mcs�}Sώ(iewicz, Hon�*�ws��U���hof Cape Town (Advisor: Jean"&�)���]&��Minh:sgE7V.~%�P..Tf�3�13x�7[5K*� ^1A[1օ20:�Adu�pb��S.Jׂ :���IbU �3J��A�3kvEb2Z�^ 1723N�  $a�� 2�i�36�2�a�,D.~GutierrezN 3012.n>� �*NwnZ� �M~%fW�&�APSO�REVTeX 4-"A. FVer� 4.0@ +, Aug"�� q . Copy' (c)A� AmeriH Ahd2 Sociebp�Se�e a 4 README���Vr�E�|*ep� ɀ�i}p�A�(Nmanusc�suse��EX� %�* ��4n= n2} tOg��T !p. % T way,� '�h7H|&=�!�to�xs% Group �yO%affil�Y;)�x � )�w�zڔ�zs,7iNrO!�Zl^0^%u�L!�ʏ�4�>�gng� eg2�) twoc�C!��o� a�vbcdel stab�rmp� jourϥ% Add 'lo' o+}'ark!H boxe@th�B >� pacs6A(ke PACS cod#u523keyF3keywo|1\dd�c� aps,prc,p-,g!�ed-� ]{revtex4�zZ;5B,tomen�^s,�, % �,su,]E� a@,nofootinbib,14ptrZp�2o �\V�l�b \*܃�$x}&k�e-landsc��t�.5[fs�p ]{ro*:ng!b You:!J\a�Bib��a�apsrev.b��"�A7 Choo�1aQ��o�KcY*sV��$r�*�N %bU�� (cile),�u7�}�H!� % belowa�")� "��U{ �}�vb�'Q��U61 he \1� j�to �Ge�� r lo�instit�zal �� %P� e up�%^�1�nPsiti=fٔ0v�+�MkF��a���o%�'En>|s'��}�%r${�(�EaD� %�ZNla����s2S %5{!1T���pe"GtKC%kS�~a�(Eka-Hg�#� W Tbt�F\&R� �+v"���4Is\a�note{��/sh� Kernt�k.}� repeaI-� .. \�� etc. as�.| \email, �, \hom�� \alt.>\&Ey!@!��.�> . Exƛ�vyUUqXg�4[]�J�� e-~@?��xurlF6{}'ɮ �e��ACP���0fa�s5j m#��2eac��H�!�* �.�q�b?���[�(s &9��Z=&Je6�WdC��� %FE2�%:=���i by-6�a�k"�. M {D. �)!x{kolb@.�H{Fax: +49-561-804-4��} 2�{&��.i5*� GH Kf , D-34109G�ny}�A.� inov�+M� []{Y�wweb�R �{;&�e�Racah �_��%��a�Hebrew �8, Jerusalem 919N�Israel]%�4{G.W.A. NewtontHH� 's RAmX, 382 Mossy Lea Road, W�&ington,�Ccashi�$WN6 9RZ UKV m��randti�5&,�ilipps=i%_ 5041!Cburg, 5`%QR. V. G}Ky!G.`Earth"Associat�pTP.O.Box 12067, Knoxvilú4%TN 37912, USAR �A.�$IReS-UMR75|xIN2P3-CNRS/ULP, BP28, F-67037 %��@sbourg cedex 2, Fc ��2�t if desi(4(r.(res�a�F� %9 in 6 ). \no�/ Qd (bt* be %r>�� -hq�i�c��bo�,��%6G{!Y2� \ �{Octo2�11,a 4)\today ���Er"��T�� �W! bracin next�\, �{23.60.+e, 21.10.Tg, 23.50.+z, 27.90.+bu {S� Mv s; A� d� ; Pr��IZ@ric %%5s; B*gU; Hype. ns6�� -� � hۻdon't� to��s  %���C a"U�(In 1971 evM(c���7�Af � 112 �߮ ary ��&%a"t"was obge�Agm�� 2C@�&Rxfi�\" GfHg�;s S-d�A�W�,��(�#�(A�8 ]�eIR��*��K��!! ( *�G�+�HE�HgAm���z �*9*�Q�g���$\ * �-\ 29�� ro�sH7o"24 112.,Q �� �F2� o� the ��U!�*tH.a�3 Hg.�Ym(mak� �Z5� ,Q�, 4, e��U� FH o\�p� �\-] u)erA�!x��s % R�(#K. >-�U&3P�=,g� �3G&�!6.�c!WeX�-lidMn]�� b�5" *Hg n>sQ3U�woB_�^w�ir�&g�sN24/l!�H�{mar71a,b}.���5A e*j�!MTo odic�A�MCv� was :n*dueA �C,65 �5�VA^J��}Z =Aea. �t���:9! mT; \ �"m�e�272›8 317-318%G )�?B9�Jl~X��e�- �.�, 160-161 neua���=molecu�W��t9� 84}. FromJ%��+�G)I�@�s���d f](���($^{88}$Sr + 184}$W $*�1$272}$�� and 46.46v4%rde$�ڼma �� � nary-�A[1�{�w �"K^s?Y!q�Uha.�?X-ray%-���atcoinc��!� cF >s (6��/a&)!�Vr;:F#Q$\a��$C (E$_,= 12.16 MeV)R��@6�)6Em94 91a}I��B�&&o]me��Ref ��!m91ba�923.B�am�^y�<�a-diff"�>6�&�Z�-%��/�DA��� lif"��$several we|eks of the fission activity, and�:�2� ray:iA�A$ATa] fiYt4oretical predi�)a�6�F{5� \�x 01a}E���addE,J*� low %)ies%+i���nR4mAd�94, yhu�XN� � R�:��y^�p �a�sl.�qӁ2%X such.��� �h��!�uEQ:� 6�>D�.� much��er tha�Aat!�Htheir correspondingqWgr�%��.�Lb}. It was shown tO��� ]I�JO >�enabl!ne��#ly�d produE�e�c���el%��� Z = 112:���>9t1�ۡ:at 5f�� (s) rathe��%MeN5 has � ��D>+e1�ISR��!Zr �.r���%+ oAw1!��!� �* in �F- ov�)& shap%�A� a) z�;toI�� proj} le-t� t�bin��) ir touchAvpoint �P��r�eM� ess � lapp5���-�3�requi��B(is case as ! ��z,�VCits-� �, � more�pact,)%. �e&i 1� an�&al effectak��Y�91b� 923� =d i�i�t a=��.�, butQ�a frag��)�Q�mled jusiJDin 2 x 10$^{-14}$ A�f!%���ngeu anoe&W.LA�I. Dur-t�short q i! still at�excitI=�:�c quit$ � . Si�  0Coulomb repul 7 betw> �Y�EK �):i,��tipE�ip�� figu� , decreas��s!EunqwM(�(� %\am�-�� .� �  awwell kn�m from� sub- ; PM7,stok80,iwa96��i e��a�� %�s � oth h� ar]�&& AyCERN W-:��!J��T $^{88}$Sr + $^{184}$W��possible= term� B�� �N�%�4N $\simeq$ 160�adk �� (s),^� ��aA�e chem n ��j112� ich� us���; sepaIFcedure,���( �(os�LHg. R"lyH ques���]raicfma�ifi�o%�c�at.� we50ct like Hg, se! % istic6�indicat� atpmighta�w�- ��Z$a noble ga Xper02}. (See also Refs.M�,pit75,set97}%�refer)�eerein)�j purp- � paperA&� how��A*clu�2�isz ly =�B-� enU to Hgfol; �x6� 9�. \m�{The CQ0S9�Pr-�� Iso� %�F� A� ity u�mBT�)s} I �origi� "�1nmar71�7�84}� eL ve /��o  aHg sourc%�atI� �ed �wo�� s ir���� 24-GeVA$to% �Vno� Au, Tl%�Pbm��78��u=p5=(was describie61aI@� �gsakeL��leteness%�$s summariz CFig. 1.5���-s�� ralŇs-h�i]=5.��7�R &BW2-B��na�ctropE!,%N�apply�(any voltageA�� mall piec�Cu wib!�as pu!x^ )߁� a ma��or%�he%�toA2X!� atom#variou�� lecu� a$^{�W272}$112�.~m4 are ��I! mon!��Hg� elfYS84�( \begin{ude}[h] %\vspace*{-0.5cm} \h2i�`egraphics[width=0.47\text ]{W_az6.ps}6VE \cap!�4{Block diagramAO!2;�-�3)��>��:.} \end�r �6]N`� in view�bf�} IQ  clea� �7eY�+� ��bas�ly��r str` Hg, � wi��ne would� readi�stm^500EfE2D�� xs�A![ "���, a�of U 30 g%�,W material, !�omplex5J� �.!m� be9/u�7. As a�(ioned aboveP�):� 9, �p %$same colum� Hg!&a�a clo�$s-d shell,����coI��;)�J�� +�sh%�b!�n ��( _ is�i�cor��IX2] 2���Ic�n20the p$_{1/2}$�islevel� dist� eve�c` aU �.d��$thus makes�al kbo�m�a dir� J� ��6�6B� ^Bs ()ber shielA ��arAdQb� .�A� �d dee� bqngF�!]yC � s). = ��i�it)-v&�am )/=U65� �E. !�wo  may0 ens� �EySbehavio,HIUePGI . (For in�� , a�B!����sf@!�5IAE� (D$_{c}$)!\ ��=���w Cu�M�a��m).Z��4�� cana�be"�� i;&V���(is Z region%g�!�ayV�g��{e �cal.9 &�2� � c 1a��edA���@ !p- (witBH H ).���S*� *^* , di�� |5�A>no)*�zis ess�uJ �Xa�%�!�of ���d�co��[]w���  oxidɭ�L!�a�(7!htA��i�8yak03,sov04} (s���0sar03,eic03})^�is* sev�Axv! ilit�adsorD �Au� ͝�# �E>si!��\mq2>R����.*@ S�y} �j5q*� 9|E�is�edae6s�7���t��alyV6� 2.6���re�y�y%- a�MF N �!,B � i���a ��&� ~5 �$ be associ! onlyP6d .Ac� ledget We�reE  �� valu} �!u�"s b J. L.Weile�$ N. Zeldesn ,% Put \label� argue�of �%m#-ging % { ?{}� sub�2Abcmt(} asd. % If two-� mode,-%nviron��� �^single 4 %�mat so)�- eque��!�!)@played. Use % spa;ly. %$ wide�} % 2J n  %�) igur� "/ F�e Q\ floats�U�Lhe ]� ,x packages (� ribuaVA�( LaTeX2e) %��C>�, macro defin�th V]<O G� C�"n�0by Michel Goo��, SebB an Rahtz, �{}!w5�+.> % Sur� N2�Er turn�2��landscap� = %�5rb.}$:Y��% �\!ءB !fapp{ asmj�MCa�Ž_����~�Inser��D�fi�&D(l, r, c, d, etc.)Q�empty6K!c)�tabular}6�s ruled M��,adds doubled%s��%A��se� %� so�!�� ault &set� ��qa@6`to get�+ull-w� '��I % Add \u��P{��Q�� on  (or��!*A�.�A�nic(vat��= {s. Or�WU[H]�Bn(%o� � reak��no � control���inf')���}-��ja�.�}A�5}a&u�2���<]"�!*Y5l ��6zIZ:�%a"� !�s�pu� r � �I�[-&:?!R your>[��!B8 % Cr�E�� �e uJ  BibTeX: iblio�y{�(nam�.bib fi!n �the..4}{99} \bibitem� a}A. Me ov, C.� �6�"Studq�u91&��s aYm!EU�%VZB�!.)H Symp%HSA RepM2U!D#N|/8i, Eds. K. IkedXY. Suzuki, Niigata, JaO (1%^ 317 - 324:2>�U�D.i� "� e.D&.% aK!yF(�; +6& �r' � t.moEoP Ser. No. 132, Sixth)G A�)" FarT Stab"(!nB3r�ZM�d Bernkastel-Kues, Germany-�R��ugart�,A. W\"{o}hr !�2) 43!�442:�3΅� 5c)�ed6l�z�e�School-S�9ar !OHer4Ion%�ics �Yu. T� ganesaa,E. PezhkevI�`R. Kalpakchieva, Dubna, R�a%03) Vol. 1, 16�O1712O966%./Q� "D�4e�}ly&�/~K�)B3T)a,af,5 obta$6}$O �(97}$Au��W4at 80 MeV." Moa�.�) A 11�,6) 861 - 869:�6�V�2���pr% ��fq� $\beta$-suvalle�5p$���v�94�9562�0j�Z��.isb)�Gd�6by 5�r�2�--�p3 \&o!��!."iJ. =�8E 10 (2001) 185��08:���.� "SvZ�F3-� �i� vy�8 nideAie`. R77.2�1> 1�.�.��3=��6$V. E. Viol�jr.� T�.abo�"��ar syste�,c|A����s-II."!%Inorg.��. �( . 28a466) 74a476�w,}R. Stokstad,�Eisen,aBKaplanisL (Pelte, U. S�5nsky,a ,Tserruya, "F�!of} aD48,150,152,154}$Sma�.-Ebie!Wi�R' 8C 21 (1980) 242�243*. 6-� ,wamoto, P. M�<ller, 5K)�a8!�Z.}�-=s� �Nucl. �A 605!Q��33� 35]�peX+V.8 hi��T�' tug, Jacob, B� cke!c Varg!;IL7metallicfpn1� ies"D,s:E \nia�!�b%4of dim�ofQ5V % 2�N�u� Meth. 14�x,77) 473 - 50�$!�,B. Yakushev � l.,"A2�7<�0){E pr"�o2(." Radiochi> / a 91� 3) 43�440Yn� S. SovenaE�Univ.� $ - PSI - G |Mainz - TUM - LBNL - UCB - IMP -kl�E-!WU:_a�",� �Ta(Pahresbericht der Kerne�e, Paul�0errer Institu %Sw��t, 2004, p. 3;�Scia�fic Rep5$2003, Darm�7t-187�� 8}C. Sarpe-Tudor�2!� 8J. Anton, W. -D��pp��< *;!�<*� �C� .� t�EH-GSI-TU-Munich-FLNR.&E -IMP Co=� "P�iv"y+ @r�.�of��"=f���At% ei 66Q�114��151��t:} doc�} �6%=�. \^4class[12pt]{io�> } \*i?icx} % I�+#Bs 24d�3 Alig�� sA)decim�*�9 2Cbm>bAN math " %.�8[!�2 %\def\EVon{  2.2}�i.i� Priv�$� ?s } FigFactor /} 8sqrtsNN{\mbox{$ {s_\! rm{NN}}$} ,Nch(N_{ch dedxdE/dx4 GeVcUGeV}/c# chisqrndf( chi^2/ndf$lt<g>newco�{ \be }{��!}}!� 6)e)r'bea.QnarrayZQ* Rj(l'la�"N�r FlR @eps }{{\varepsiloV�8mean }[1]{\left q #1 \r|7b2)color}2+\Blue I text"<[named]{Cyan}{#1A*=� \RedZ2J1MagentaZ5J9GreenZ7  5re.�topfr on}{0.�6"bottom>%%a!)�h)G a pi�- |D�!�cI>s 99%��e&-! :g!S.e01}e)*!Mt >= 1T o �G6Gm;��E�@ %\voffset=0.5� %�"[ $or 8 1/2 X�pa�,4if dvips % doe2>%3-t letZ nflushE�p %{{\�6 \sl �=( \\ \today m�^(;  :/e�2le'title{S�Cgelet)at RHIC��-2-X \author{A.H. Tang\dag\  STAR 2N$\footnote{-$� G liu1nd*��x*A�x "2Ss"!��2volume.a�address{ �NIKHEFu NL!~��D�7t��O. Box�40, Brook!�n8io^:L ory, Upt�NY~1197�0ihong@bnl.gov�o>o = \date{I:} �6�63�6} abst�} Two poH*�+HShower Maximum Dete�S (SMDs)%�Zero-Deg� Calo�Kt�(ZDCs) i^�by)�b�?e run� 4Az?upstr� �) down �3 A6�� �al="he� axi,D&� i:J �ia<d� {1swept aw].yM�J�1 f�0J, ZDC-�� %�2�"� aK neut�'� de5Ua:�@�I e9zinf s. W�/� �pr�9�I sultS !�6�%$ a trigge�9O:-sa�j(�!100 mill�(Au+Au colli�5s!�top� �.�BY+]L�8%\make�Q��2� �� Quark Mj$AQM)C)�O0tI'�wcf%( approxi�7� qual�  $u$, $dD6$s$ qm�tZBle)�=n&=�2%~a�=EXfamiliar�"uC=�..tru�*> �of�Ly& U~A/ Bodm�Witten�%absolu@> ble.�.���I� lump�SQM (``Y9 s'')�TGerA�e�< earth� i�L smos �KAIen��J�=l8-�AZ e"� 6E864}u�H.&�H^EconfiOI ON!Ka�a� $-�.�a�! me+-ism, � IMcoalesc.# �Boltz}, !Ktj1h��N.4raun-Munzinger)� �,il�3o)Gn!?a�~8/'I�Gluv4lasma (QGP). %�f�Otwo�usu,5 y��M��2a e l�8on�: .�!(cess,�a QGP!���%h�Fn�5nse�eb5?of�!�Eo:c�*lj-i9�� meson-emi�#(.�G3nd upe3a?3 inE..jG --�. S�CaANsis�� � �abF36cFbaa��Ca" , a�0�,ch�1- -1 )�an "|#�?us. Ax 6�if6�i�{� in -�mB�=5�a=cAso)e1��H0 ͦ�)� sig�%$ne��A��� ��.���mZDC}. Pzs )ɉ��uA�� �dipole fRei#w�5�logEd� fron�M}!�!WF�nd � O�2�or: -to-"=,�4yms, A surv�!!� �i:�X%h�%�����7ep�<of ���s:enSe�ir1?�Oa�� >mo� um�,�c':O&�9 angu�>Wof �slf::nem�g,d azimuthal �s.��] pane�<F�1~>0fig:ac�} o4!� :�0 % . Al_7gh �)�upnL6 9x!�h m�rig� �&��SuA�E��L&CosonS'eU� �N�D� � � �� ��6_ ]G!�c s'A�6i,F �/. WhiA�oF ffor��N ��2��e�u look�i� pz�O� $> 50$ lFw_2^!� q:�8A�u5\Ler  �c6�?wo>:�8iyKa.��im�4�' ��� ��A�e��HD��U!5�Am!Rre:�?f!�gsI4� nS �r �2G:9A`�pa�%'&u r dif�'bM our 1�a�32Qi)J,!j focuu v�Uforwar��V  wY s>����-Q mid-rapa"� %-� "�i�5}[ht]. ?Ea)�}$sizebox{ %&�  �0}{!}{ B 3�& eps}F!I�!�!} "m/ (��) A��A�}��ia :�A 180 �Ee� :5�@ory. (�)L' s���Y^��4:=�5E�F�)dv-���9� N"[<KDuof�*�)��g�>.ZDC�P<6�oQaE_a�omV ys a��;dispers@�X<fermi moea�pecta~I�o� T�h�|nx :Geant�;Z� inB�si}. �S9Sm -�i0� m $zdc_smd_355V()�(35+}2 S5!\a�S e-qO��2f i. ]�=Of�7���R�� �r hw� M� ;\�A�(H26�Ptotals�Red��AYYp(�X% es E�per\ ic� ;? �* ion)�S�P�[$p_T$R�:�am�F��a?y:& �iYs�29� repe��2�aC� prominv_p�5� lessl�I1 wPus%]�0� nguis� Y� I?� � s if���Z1;%���E`a̡�, )���  �i*�A!�[] atD� be +.":PF��3�&�Z*s+,) sandwich_%��� ��8HA % arx/ @M �achB�AE. ESMD (�Hnd west)2X scin�ngWs� G(#a of 7�`la� Tan�(of 8 horizt3l &C �= wo .6)� -by-%�6�� N�� F�A�(A!6"��I� u��'ݠ� # sidekH� ib-��"�" ^K���IDa few� topS.� e�beyon�K�9ter-(!��pKsflow, �\�: To m�iz�;si�/of}] Ao[ m s�(6 6iz 9,��6�L a�L!^_G cSa"e�!�_6�a�Eo,� ch ��=�Uo hZ8!� �E3�s � �&r �c!I�A��Css�AM� Lo%�doaso�� ZD5���6�%ϥ s(7�F\F$s it easy��% y an �� b \lyF� D�Y")�a F� �9�M�{�&"ed 5�R`� 2M zero (L0)�!,�S� ��Cen%�T ~ Barr�4CTBM�gi9q $23000 cou�56�1ځZAEsuA�U��B� �s�Jq130�6n f�]5 8a�OA�"�O �tal re]A1,1Ve�1Wi.97\% a| min= biasmt. I&�\��L0C,��Nt�6 (L3)6 =�? � 70tpAB�p�6�sj�� L3"2��tfIa:e�u ZDC,E�g-C��y/�1s�q!5CTB!�� curv�AmadTWE�cAmA!&�.: ��MzMask&� �"�� [. EveE ��Uar!7beO7O�)NE� ��Jhif�  upE��KtIhcxs\�M0%��weIzreQed 167k MQO%�MQ,���2 !11.6k (E^)�W)�P theme� ]8u�"-� ���cha�f<�9a�os��m&P 6O!�Qua�IAssur�8 (QA) c,Ws!blR[�PѦlaj)�� p�`upI�QA?I�.�: yO �`" 4/B�!�6�,&2 primLzA�tex (&) � line) �off )F`��at !lti�=2��g-~ Beam C�!BBCs),1�F���ig%1kgaN6ne1 P 6� �Um:)�H��!�Y� 5!� r�k)�6��Ihou� .KfH[re��:pre�L�w &rms�Zplo] d:� rm� in Y&* !��Z!~ in X.p@ 2� is�-!>& !��e� mN� : :g .e" pik� �J( �1H%-� fn�aln[�!�pAs*�l2a�D!.&)�Z !��`$converged,:GmkŢ*b8Q6o`="�Z![,%([3ng�K@�MB�;� e� a up��Z�(2x$10^{-8}$ �9����l��A�!.� )ta!\"P� !*�b)?i�l ��>0&�s"�8% ���! � fur��fu�T�VbV �) gin{p er2D !}{6J2 rms_=.2>��.FA�RMS�+aq(A�)%�6 �!M�e����&���j���^� � dem��� %� capa& A`B% A�2\!��Xist�$�6!nL"6 d6� E]�6 :�]�of �:�B>[;m�$�.R��'. {\it &nO+ s---} B!:JEaI ndix�w�tou M&M Whit��p �)>d helpJbui5V%�5s�O$6O$ %b�We��UHk Jean-Yves Ollitra�Iand %P�&0@%�ext�TriswP�% I!;�� O�_�( %Gro? RCF!�BNL�/NERSCd erL�(A%$their %sup&-� work �|�yHENP Div�%�� %Officŏ13 �$U.S. DOE;NSF  BMBFC@<; %IN2P3, RA, RP �EMN% O ce; EPSRC_ni�dKingdom; FAPESP %of Brazil i4?n Min"�7��qTechn 9y0 %.) EducEg+v NNSF�C�9; SFOM�`Czech %Republic, DAE, DST)� CSIR+G� �Qof �4a�4ss %NSF��:� B_ \B.�H�-&�5*&�� d A R 1971 {\PR} {\bf 4},�g1-160*�<`& j& E 19846< 30} 272 v.& �+a��!-ByXte'otr��' �"u&,�+`�99�it�5�+ . G:�7ParSC �25} R273��& �Qa��{� E?J<; AK6U\T A \ <1 �c%dC)f 63} 05490{j&  A199)git �LyG} B K3�*tI>�&Q raum&�& P�Sta�RJc5.7Hys.} G `}21 L1a�&  C �1987 J \PRL-h(58} 1825 \\26a�St�=cker H�I�?} D �44} 35.�S$ Adle,, Denisov A,�9 cia E, Mu�2 M,aFobele Hu�S !�3�N`Far�9ru��-�9od��ARics Re�0} A �99}U9-436 K/endbib ��6�=v+d"�6 �;>r61pt]{l%}2�2epsfig} &`( 445pt \odd�$margin 0.2�Y*  -1.0*�6 cite�6(newlength{\2� \setF{02e?��:er{*2}{1("W 7L�& } {SSy1�� 7�j -�:*{�} JeMryluk �U ?2*0A�� :1�{"�0� {\em{J achu�QsEN�:��٠D077 6,�FAve., Cambridge MA 02139-4307, USA\\E-mail: joanna@lns.mit.edu}}} \\ A}5'.�2in9Ha"�/%);i�ton-p�= -at &7$}=200$ GeV)t"da�XFiC=;(E�hriz�qxrN�i�7Oun]hpbew2002--200�Req�?Heavy�G!�i�%atz�1Q+R����O��v�/casymmetre'�2� �;�y#,� of *�fd� q)I"+. Data� �-"[� dBT�D5]:�?Vs� je2�,iZ13%�!R.�se)�pr�0 :�"!�.��g�,%�E%.�  aim |'�;�=:Sv� 2Z kin3E ~u!�.�ys\�IphA���jets. Fu�9f�.��%��/(\bar{u}$, "0d}0!H1 �V mkA��l:��J�wHbosR#.g =U4eiB{1F�e�iA�e!�V�#&'&PZacLA�R~U(� ). v�4. O {he goa�/ �Cf��j�&okA d�3�2 %7"-f��En!�-�"�|F�E�p�l!we��y�O}�(e flavor dYe"I A  .��Z;�)� he�-j* ea. 5��l �raQ�# �l�*nd]e�  m�+a�a�� multip �*�We�6setupI2 nim}A��4�,�~B�?�F_hmag5 ca�5ry�9a /&� �RRiD�!Ra�,f�* m�� 6d�f �%�ima�b#EOprEv. E!�fX1Z>Uf2� V crurmachin�R mponV�"c6svro�&�� bm6s9�u�2suc�8!Gm1�P�b#8xto#*9&�$de�3in�7ME ~�#,$\cal{L}_{\r�VLx}}$$=0.8(2.0)\times�32}!cm^{-2}s�x}}!5P=$0.7$�24 (500)$ GeV. oX�An3.� d�opw �@�Wvn~2s_�/6>�am7 $P= 0.15$a9�6W WA$P 3403�I`p��lu=>U d $�; ) %1Nq�!�M���'>o�3-shI=}8y $A_N=$\\ $(\s�_{\iarrow}-up )/N(+F(F�)�!$.ce�I!Lmhl2XV�1 ��!��  � at( R:2l��."6 ,�J!UM:ed[�qv�~�5 Aei �e-��radp h=� 2i�Ke������Ka�R�h (IR�5WeNcusi�$L� mI�sf�4A ��typ�he)a� PA&a; FPD)�X�in �-f ��ppA����/�bA��Ka Pb-&�%or�����er� ))as"�e�er|$um� cB� $\pi^AK�&�HI&ce=$$ut $30$ cm;2�D-�2%� i��nd $7�0cmi�!+--��;< �K&� wh� �'�aHռer}ee�$�H�� !��8r�I:�Mi/o [�f?O$15 < E < 8� )A vre�9!�,20$8S:�,%,"��{file=k�0-ichep04-fig1�,�=2�cat�0aTh!�pev!� $p^{�;+p\��I %� + XN)� B�<,Feynman-$x$.*/!sS* �(el� d�� p_T=1.5� /c, cfmZf.$^2$�t5 labewfpd�18>g"E�i��shed\�{N&F . � 1!�\DF{.n,A�re $x_F�v 2E/C$� fi?E�O&!�? &�!qbB9�5�" 3pr9_�"�2t�N(x_F,-s �� GeV/c}})$)�SK;.N.7�en >=6�/#�?���a]�x�6alyY}��7i�&�pto!v�'th !% $. Higher�c�Sh� � Ill map� d�6en�x�*L��Ak , toge�� comp�N " �e , mlr� to unrave�be"� "S<.� aimb*&s�O �!��*1ʁ�4 {%?ݠ ��2di-� back�8a PqK woOSi� fE�)� boer�0 �"-�"2�"(2.annul~1uncag4!��� pipe�*ŝT�I�9ti�>4�`Q aZ370\,^� a.�O:til�!%BBC� J *�3clac�tpR5yt{9L$3.4 < |\eta| < 5.0$��0p~"�8(bbc}(a). A2)�p �18�nt%^% f) %&) J.�)4!O�/�*ۊ�P�!PBC.|7�`as$| e"� Mith%�:&� )G�Gx 5�! ?��&�ro}7 �Qre�;:� =�s�M\"Jc�Ra� moniqA;%�ll2��0to2Me ����a�� ~� or;P� ���z} ?Da�x urac��"3��a�:� �E�da}�lya�aa -�  ic� such!�BBC�.R �&9 �(!8��.�^!�Bi�o��-9� ~�(yields, $$ �ilon_�9 BBC}�\frac{ �� N_L*V N_R^.� } -6+&� -�  }�"�f�V +�V �eq A_N^�� P �(noindent in�/�ML}^{iR*�e)���t-= �!Z!�A��'c# ($N_L$j#)�R$)2!�,E�$i = 1', 9B$ denote]�E.�q�-�Aeami� I$P$5 I?-��-&Dter;(CNI) H� A�z cni}���� noa!a>�i�ea��, �HvE��se�" � �1 classT ��}d�{r;�by>) (2Jws: in�'$3.9 < �-�ouS �L�K < 3.9$�a�s)�o:! � �Bp�42�� ed 1, 7c8! R� �(�!���s �{Up}}e�ek E�q�E4, Y 13� �yed =Down}}I%remai.�a�p8Left (Right) }}�pavI�won)�ie ). A�E�H�8hitC3�!M`%��7'%`��*�3R'�m D R�9.�in}�fif� 2a*� 2.73C0.1z� 2bB3.9�"� (a) W]c"!v!�[nd-to=)}uV%�%�}}�5%&A�� J�(b)�'!�-='�t�P(Ba�@�)#,) B ^. days���May 1�3: �͆Z2 i<CNI6~opeaints)j:� U-�B:"�A@i(� vari63h:.����|N I��vNcJ�!�Ty9�P� ! �˩j6  8�Z& ��� �,��run��5typ� 4H� r 30-60�1�i�Yed uncer2dU � �A���!ʁ%4zXI�+�Uda�r/]s7> ��&Rt �� turn��l! *> )��"Z�>%?�7�2;N&[p-%F~ �;F�>l%[)�&FFG� fiX$AM N}}.�� 67(8� >&CNI}} � 1 \% $IV�d2� $��ilx)��Q.� OC:� ٫ $` N��k5n� 02(9r�$"�3Q<%D�0Mb���l}yB��r&��0!�=�2v� �rir nu'�al 9z.rMm��Q .`c"aF� :2S �ETIR��ign�no,-��c�=iR�adj�Ad���t�� .u�is6ee�l C�s >��a�)6�S- ZIA�F�j3 t IReJ -i tinuw1  non-!�F& �.�haMls-Ƌ!��-w �E�� �BY-9 BBC.�2ey�0.�"�A����O1.A��6�B��&�:�%�� A��5&�=$1$ pb�}$� �IV[e.�ly�4� � eams�F�!�K�<�l�D1��� N\"�o1�y�{LLa��M�i" �"%!�&##E]c�;&�t���h"� J"�L!��3 ja_O. A��iQ32��2p:ei�-con"(6s]J $g+g.�g+g"��$g+q 6q� (c) $q:q&Y<� �Ke�$:�J�j��AAdi(x!_!�y)-) q�R  s2� �3I. P*#T"�A���|u| he ong�JA���O2.�&=� $x_qa|g) h+, �' um c��� (�)Q�!�&/&iG��*��;���fEQ:&x*Z ��*�'\cb�i2�Ia�!U� orm��":)� of $��(x��/ $*"ji��Mff�@T H�# next7l.�� frix��J�aYZ+� t" ETFntb$to, a"|�dJ"g"in!�n @$0.01 < x_g < 0.3 xgQ.5 =ӄ$t_{0}^{1} 9)$ d$x$"� se =s� ,B��9Da&,  b�b�8�m 0�! ec���Օ� of Qg320\,"� }� 5/ =�m\,.g$<[ *802Ca� .C5%6C-�.|"~ ͥAG�t5-2006)�bG%"!�� all�A�� !;�t ,&9�9F=��c.�) )˧!�`3"� e�'e,^6 �, Å� def�, byM#!�}par�Vvi��N\!��$W$.�IA�� + p2�W� 2ed�.o`v�� �D�M�W$:/%b��Kredr V�J $u(bar{d}2� W^+ �  $d$u>$-$,a�+^-sea3� �Z� � *� e2�� � �X%~X%�AlP��2d��� -!��-&� "��q"r�x�` �sx8S�i�*�.QV"-Eh]] n^�so'e�A����O��y �_�16��*:.�"T atr�nadolsky� <6> n:3;/ �, al Issue:-�nd Its"�)s,=8.~�prum.~48.8{499}}�e3).8b��w&e�$y~Adams�q�6.~Bw~L�9g8{92 J 4) 171801E�A�s!�[`��g�# D.~Boc38nd W. Vogelsang2kD g6� 4) 094025.P�  J.~K�(, AIP Co��� �675 �3) 424���� O.~Jinno���A� /CAD�Wlerator%{9�V171%Q4!QR B.~J\"a+v~,d tman�W.~r�70 ��34010.�.� S.~T&��"a\�in� A %ee2sJ�ɚ L.C.~B" 70 EPIC99.;<; hep-ex/9907058.�"� S�x� F�Nucl.~"9.;< {568 � 0) 62�Hgrvs} M.~Gl\"uck, EA�#zM�S63 f1IN02N� !o�l Od J.~S�2M��< �314T19;132.u� P.M.~Nm�%C.P.~Yu�sF666U20A�31. �kP9>, *�: �qB�;2p*r2>;anBQ;��Z\input{+}�S<6S< %�lzTITLE�\m2\mjlE�&5pe_#�(@Z��� �:�k{Volker �s<a�kP Gesellschaft f\"{u}r wj0ne�U schu��lanckstrv� 64291 * v�B)�ad{v.f�e@gsi.d w�l � NA49�:�kio&�l[7]'�" �l�l�$blume}%�mm*mm�O>O�7ABSTRACT��2�ma"�<q1]aJZB� �k%� "9�Jnt %� 1�RPb+Pb%��N6y -*20X}58 $A$.0 ariKT�e,�u"�/2` �GXU 30 O\O.unders�P$ k��$ _S$ must� �zoy��sc�� c��� uggega"n&+.wQ A�&�,v � ,S. !�&�aUrQMD (pxyM.c�ll ca2 �� icbPhYt�ed)�*g�.�v] \sub�do{\JPG�Lv:Lv��A2�A�7,INTRODUCTION�:6:R6{I<�v}E�y"j�ccu�^i(��)"i!p�q"Uop SPSq!(y) MhO�YE earl�lg!�f"JW�Am�$<!5a� nf���� m�$ <0��RstA~heinz}. ;�|k"�5i���d3y�$ies, e.g.~* ISEAGS59�+ phal�! "�st�pl�{ Both ��#�fl�( rigor�proof,";Z�� e� <$on6Lof9 WÅ��b{d!�AGS��.7�R�9�.�3�2��e����|,3Lb]vM�ga� {�IJ�?a��amF�2��%`Y1 . O&H>��ns o�yo/�6V-�-9ke��� courE���A9"�y�,!`s!�g�G s. Oahna�:��ropos:�� 4�is�Z easi�-2naa �m-�m-�mj��� �.�J�, ��)n�X hancIof�.��3&�o� ݭ��&3(p+p).�� !- �Iw�#q 0!ii� koch\2�����+-�)�%�up�?l�2�+�%u*���Aa�pl�>�WS_�^al-B ga!� dels�!*Ki�<���}d )<,��!F!quilibr�k:�A���}freez��ut�styI!ImM��a.�e=�inFR��� sequ1N.=d1��v,Ex�� $tra$) =ZE�by�u�Oe�����a\N�>�.3LngM�n�$ �sM4rafelski,touns�-��sq`IK debatń�a��C�k�[rp"/<�#$K^+ /h:+$|;I8���6�"  (_� = 7.63:)i'"�"� �*��"?��� e� -A� sqm03},ei*%'a/�IzC3#^�� -�gazdzickE' Mean�k> )s!1(&:�!e1��� !�� st ��b��. �^T gaUJH&�!�#ed� *��M�.�Mbe�mkeI�r� W@�Y�!mmE9Ŗ�Ss "�H-��%ex�.wI:!EXs%v�ɯ� `H/I^at�)MA�ud A��? �%,mi5&c�c���S[�te��_�W;� i�?A�M&�H��\&Iff�:iîb�.@ ��se9 I=urqmd13,21�*�P��j%�6���F�G*q s.a�!���p G :%w�&!  ��!��U�2��@.? �{3-�&+`l�=B2 as H�Gasz�&bHGM),E� 1�"^�z3ar�ri�������; $\mu_B &� QX)Lhgm!i�l7 ,o���|*9 �is hM< (SH�fiV�s�J�EB;ev�mH p�p�full k�� �shm�IA }D)�*��\���T���UBo�; midrpy�t�� "�!o�K"&ʥ� ider�F �I �,Z0stays*q^A[f�)c�s w�4� [ ��!�3x �=be*�6f�/a;M}i�l&)< H1�IN4, a:4�> reve|� Gl_56�"� 1m�k roehۊ�G�� no� �`o�R���T��R5. More!�,A�R#�s*z �#y� q ����6@ �8�����a�N��u"�"-��,+�h��uda�Jz |��a#�?L��I4��� �� ac�� r-t��z �(!� ``Equival� Global C�p''}O� �`e+@0ke�r~N�L���aw�=Q,p�W� ����lEXPERIMENT AND DATA ANALYSIS��V�E&=A�e��i������&}-� na49�!�a�N*�>� itro  A,� at n�-= %��[tN&"5 aWI(5&�f�#super��uc6�z�fa"wO-~ TPC� tr��M�Mumt��Miu<2�:g6�#"�') h2d amF�l�?�$TPC�0an}�$zY$=O�� F)�n.2n+fl�9.�iwo65B a�W�x�{at 14 *�GtN71��"�l�"is.�$����erP�L�!!�)tL�a�1-�u*or�2. �Z8E���h �Ser� onf���7.Tm=F7 $\%REs� �%2{�"=" 4;\� 5 K�bka�CA@$\phi$,��i$\Lambda�" $\Xi 23. D�.$\Omegad&�"� �W((20, 30, 40p8d ' �[p��to B� $ 6.3,� , 8.8A 12.3�-�e�i4�)G�cM�yearsZ9,#& ��M,�6�J" 17.3#[ 1996�200�1��o, TOFA�=~at i�aLow 2.5� �R�3 00,=�{&�ZB�7!�1�.wb&� � comb��7 r�.wsAl2TŇ���Mɵ*�ck*��*�D�er �,�>� E��cA���n*� �"DΥ�AU\EeH�Dp2u�j!K�.� �*�.� . HH�e�H�=naOin6 nt0q �i{ cay daugh��,E <dAi olog ���)��^iu�ack�> nd. fXon!!�  U��e���j��Z�.)Ic*�+af]@aˆp�<e PID�i�U��Av����TBy  ��m�+ =s�& be n�i4-��E� K $f ngle� \�le = 1.5e0(.#^+%+2-) �+�� i^-$ k � deriA1by subA��!�" &�0K�' @u�� EN��eed�D)��WE� Vne���&Qu%q�k��Z� 0:C�I+.�*�0� '#-$c�d�2F42eied:�V methq4�Es8detai��f` i�/It*� n.�n9�(Qn��\ A�c�&I�9W2B�=b��o,���;:����(iN֙v���9b ; be 4� �"� .�� 2� �� .� %z�# RESULT�� Z� ]s$~%� K� ~)- ��P{5���ͅ�a%�"�i�y[6 ��E`6�DA=f�  E����, ��e"� :2�3Am"��  x�-(*s��E�e slope.!"�b�&ko^T8�a-���6�<��doa��y�UiTWntV0th ��!M� marekqm04a�����0sF9$ ��څ� ��6�,2��Sn�I&)�� tr�Z&wKXή, be�+��� vV "�u|n��_�FyN��"t M]a�."�!��o�Puatisf�$ � r)wQY TOFjC�*� %Q �o�A� �.(� ,E�8��L�?! �H���a8=C��e��9 s�Ilap._� / �4utoffI �� fM*�TQ5�61�s�C"5e� 9 . Ba��]Z!2Z�+a�y�e^1Y �%�>�(�%���/�\pi�O��in KF ��4f{fig:ka2pi} (�H) t2pRn�� đ �Tey���IJ��&1!F 6� �fir�R��h{�Z "m��is�Iiba~ed��i-2j � HGM,A�a smo�"d .�>�� �O th=A$-�,!O��to9!!feagq, "E#it"8broad"h��%�i�{��,^E�� �pE8>}er2A� a#�u �XSHM���.�H&�yal|)�g5�ac�L�!��. L' s�$DuA5�(G� l�!�luDt�4� 5=�*�>: K!�pi Z.#j�)ikOb`;��r�,xx=16cm  box{e0.��2Jr�X*�W,}I�!�a�pi$qm� ��RL �s�6 �&�$(A��)]��R��CM)2 y. OhJsymbolO  ���v���, hDŧ7{� �9�*�mherrord�sg�A*I�7Ion%�) )%#a؁Xs�;� Ek�jW ��&,![&���EIy,��� .�2�)6M�z$�U�dob�}�f� ef�"5 connb "- o �um9Vey~b��:SHMa�Cf� &]cea����A�Bap��T3�J -dot�D=�� ��i� 2.1.�g�%�p*�C�{ake� r&� ,e895� ,e802 star 4brahms,e866kap m)A,Ar } :�<%j�� �l� ast!�!�a�WJ�m&�jm��>fki�, exhn5���]�Vbu� ɶ e�A�}& #Q��y���," h &�-J�"�"m� i.#.sm&ag�_jHGM� m5IL� T;J�"!mA�fit�%�9 K^+/�,d:s2�v��Z�I��灨! mi;�� O-O��8G ��pronoJ h��-i a�/e��e) tooz �ϥ;r�G!n�Q. � �����.z- { � 2 >��:�}$a�r$ �(�xof�I�.l}�# b$�n�`�� 2 Whimht2�Vu !��"Z�"F q�[- V)0$2� �vb��!�14} �"� � 2z.A�is.+�P#r��A�~�Be��x�n6� NB��^! h!�exF�&��' ��u�o�^~�& ), -�a�c�D.raS �is e�MF �$l�K(� ��� lamxi*� ��A� ���oO!3 bulk"�%Ah $s�E!s"%m,�" VgCnet��"/*�&to vanisV�՘�K/� :�I�.�)�V�N���HyHbe�ա�le3�"�. A1_�r*�1��g(-0ٿ.�$�bgOop%��]�P �Ta�cr��� )�� aYbl( A�I :"=���k�D��(�Cl:#a!m^��AbA ��!�<�ji �Th :) S >0 &X Ig[Xi~eY� �>:�S 6R Q�U / } S Qasj"�_x ɕ�QW/!�6� \Xi^-A� � �. v�.� � �X� F *2 F 95�,e896 2 2 ZxiOxixi? � �a}�@ 6@ ~t��n0 CascaQM��>�!��:�]�Xi mtE�"��"raB� �� xi40��+D&�m��a��Q��� I�$ 6P"H �G��:p�Y�[refP#/t./�8��ll� a�"W fit.<*�~R~MRq�&ų�T:.�5-"& "�I��%s H=-"�w$ 'i��Q���5� "�,8s�!��#�+*}*si��9�0mDe�0GUa; jiw0���9o `�or�Iq��$. Natu��y,ɡ)80r�jl�� carceEJ�ci~.��Z�y�1� ��xi}"M��3dmOths��]atY� Jmeurerqm&!N!��e�u6�ܡ�� I�*ee. O!��4�;i!U�B�A�b�2yA�A�y@um2BQ��dA9ishinf&f2���EyE-7 09�Q� �E�en�%A�.���)�� �&q�����o"f�hi�iy&" %D*P��)& Y��" � a2 �� is �"5.�"T�4��an2 �A�!w 3�<��ELQ�Iep��#_�s;� m�.�S"sA��� �E��cNM 'M.6���m�D"l �,�y.�K�K-- Ob&�J>K8� aqZ }^+�cBV .f=y.6� >j�b:�o�rap�g/ } Rf/6�Aq�'^�6%%6 7 + � 5.�J��. �}R�{��� �2�.�LnL"� �2�6��`&[ s�Mo��0�&)f�)haaeexplo���"��R� dera���0�:!w��R0&�" �^-+6���"G8s�SiFirX��YY����p�6 X �kWit� �e6�T��թղgood *x!I2R: omph.y)�y� �ve�^F�)�Q ��9ead��e�9� F(8.8*�Q`.K7to k$хMu�5�al� manag*!zBPŻw9]*�al� .��~*qA.� "$l urpr�P � nal51wg��@"7i�MiceA�)re�?v�;D ?m�thi���5)�alr%n6He� }��"U?M��&�2��??�ly�>n� �v�  phiMs�� >��- >s}� !�F x�*� �)iAb>=!Ģ ial K � becau)`|6.O�t�a> �(�"�'�2\����8ensitive to can�onical effects if strangeness production is assumed to happen in a hadronic scenario. It is also not clear whether a possible undersaturation factor $\gamma_S$ should be applied orU�L. The NA49 $\phi$ measurement at 158 $A$GeV \cite{na49phi} has been extende��O all available energies. Figure \ref{fig:omphi2pi} (right) shows the normalised�4yield as func%M of collis�iy. �excita%.Dis similar to thatA$the $K^-$,~�ing an overall increase with beamh< A careful studyL@systematic errorsxrequire! assAx0 significanceAappar!zloATminimum!�30 -�� ($\sqrt{s_{NN}} = 7.6$ GeV). As in bc�of�HGM�prediA�-]4t higher SPS %R$ies, while)0SHM fits are %�to reI� # data)0Z excep%�of��t)�gy,.modela!6drivenaa max)2� of7 $K^+$, buS$e contraryEseeea��.E M� �in UrQMD/note�\ightforwardly defined si!� = decays hi�:8only after chem� freezeout�a�lA3 ages!0the simulatedY�, and$ rescatterA� �{ )uts wias�} �number-detect%� �. %*6 i�: Omegayphi!xpaYratio 66 \begina�ure} Xcenter} \epsfxsize=16cm box{om� .eps'nd4caE/{\label\�* Same�f:Mka�JIfor%;$\ �4/ \pi $ (left)� % $��� s. DA�A�preliminARZ,aken from \� e802!+,na49M� starbrahmso!`,e917phi- +hi130&phi200} - �}B�� %-� %=� rO< DISCUSSION ~x \se�*{Discus�(,} SummarisaRa0 compon of��$d particle�'agth0�� s, we finŕa ��ral tree�a��,Hadron Gas M�ݵ-sL n�酎s��low�C6�ies�CA/tsa�����a�mI�around�k on,��e.� $\Lambda$em/$�� RHIC���!(d�Ie $again well�d@��ly,��=�Si  int& of a .: suppre%� fB�(gives a mucᜡ$ descri�A��� At= both)�8 types coincide��here,� � seem%ube sak ed,��ultAJin.q close!�unity. F�:he ot�`% !X  best��M valu� 0.7 - 0.8��isA�ameter�� devi����O ���E� sugges� basic ch� i%.r�T<e'is|BU2 I��es!!���`K aV5=c���� $\ga� asIAae-!Q  sAG dicac7B refly condi��[a�� @ic�fg"e u[� -�i�pre8 �kq-�, i�uncle� y.M INA�"m reA"s,�� e exp��. A feAW�� iE��-�relative2��5  a2conseque� � �lay betw de� A�baryo� poKial� 'temper�.h is� $, however,�� ly broad �can# accountEA( sharp�ucturesA-"� eF� %�: bulk8A�h carrierl More�!�s) E� shifk to� s� Uu��4 !.)1q�is diffe� A�mA�s%[ns+hgm}. Iayi�vntext� ��leA1�$\Xi$N!M be IBX have adial di� �e4p�S. |a� s y� �+ undee�matɢ5�.� ��Ee kepancyQ/e-?!�-7 quark59I� �e;mYlar��%G=u�w�~re��(E�Ys. q�$K� � A-2� !}�%% �� s�C �\io%�� sR��than a2/ 'kaons, � !�V�strongNA�m�Tply:�����a1)�usport-�mim some���duE %�ly>��1_abs��� |Iy!���D�H6� W� clud. �e� eVec�by�favourU�ceD�� �� � % r ��.�z( REFERENCE�: *{Re� ce���thebibliography}{99} \bibitem{stock} Sh R 1999 \PL {\bf B 456} 2772heinz} H( U 2001 \NP 2$A 685} 41428koch} Koch P, MeAller BE �Rafelski J 1986 {\it Phys.~Rep.} [142} 16.�\stachel} Braun-MunzingergHeppe IbS (a 99 .�65} 15�r �}.�A�Danos M�0.$97!#9Chtounsi} Hamieh S, Redlich KJT  A!= K 1p86} 61L,becattini} B  F %$et al.}G1 \PR))(C 64} 02490.I`csernai} Ker\"{a}nen A, C ( L, Magas V�Manni#J a�2`7} 03490.84friesesqm03} F  V�e�(�J abo� n)^4 \jpg �30} S11.P&�$ Ga{{\'z}}  M�$Gorenstein%�!�%! ActaMJPo�-gd272�blume} B C�%`N�!5 'these ceedings.aurqmd13Zeics M 61�is�2A�85.�C21E�(tkovskaya E6G�2�@9} 054907 \nonumOeri ��lCby E.~Br_A� M.~B �]��FrB�22a%902��Ka�e1wshmvF�a.�roehri��R\"{o}  D6�(BRAHMS:���:W�)%,PHint} nucl-ex/031101.�RA�arden I ;5gb�4 )Jd40305.5e866kapb66e� E9176�sE�ɞ�6476} .S ]A�Vx�]90} 53=�!��b���8} 352.V!� Vd�>�Z��]AY 59��4.Wa�la(} Anticic T)�5�N�i7PR \93�232�a9\$PinkenburgB�JA_:�8} 495c2h96_AlbergoB� E8966 \�8a�6232�!n\�p2a�-8��9:Z!qxi�  Y B 538} 27.Nmeurer� M Bjf�6132.Z!��C+ :2!c>!��� �91� : !cVastillo��*� 715} 518.Yo�} S�"BZ+3BY470.Y!�pw$�$�4~)6�! 2' e�} Back B:TF�%_a�&8 Ai4 .�!�} ���<C g 041901(R)}} ^) �hn 6003�\�!>��2� c docu\} , \(class[super�ptaddP,twocolumn,showpacs,p�1�"Hc,floatfix]{revtex4�"(usepackage{�icx} .psfrag6 long?#� �newcommand{\BO}{Helmholtz-Institut f\"ur Strahlen- ��Kernphysik, Universit\"at Bonn, D-53115 �y} 2o HH}{:eExperi!?alV_Ham��b22761VeJUBe.�Fo�0szentrum J\"u�b52425Vc,authors}{ ${F.~Bauer}\affill{�--6�R.~ZieglUF�:'i͈ es}{����W(} \title{Ex"-"-spin cor�!on.�$A_l, $,  SS}$�* SL}$�elO c$\gkrel{\�- arrow}{p}b$ s�a "�" 0.45n 2.5�,} �<s � \2" {EDDA Col&5@} \date{Received:M,e / Revised �Jion }�*ab�ct��=;Y.%:�B>coeffic�s )6lNN}(p_{lab},\theta_{c.m.})$,)ISf! %-p^H "�/m�/d=!(e polariz�( rotoH"am��Coo�Synchro�  COSYwa�#t l2Gatomic&t�!t. C+were 0+�iIly dur"$ccele� <# � mo� $-0�ng8|+ 1000�<3300 MeV/c (kinez/�ie%uT)n$$ 450 - 25 /)p&�(asx "tex of 1430 ^� above 195sce$�angles $2�$Q�4 30$^{\circ}o)9!2�1�(Y)of���B�%Nncy-W�(as: ,}2)$. sm�#� without ~"~"O/whole�)I�NN �e�/ more mSa�howA�!� noun�%t+/ pend���angular!a" )sE�Pk-atb!'�Ad�0i@%of ex� ng phase�% analyo$at �'+ eyond 800)��impactL,�' ��Rsol� �1AussedC direct re!�t!F�(�$��$ amplitudeS$t%!2"3{\sl pp}�2.<E`m#$ably reduc�%Fmbiguit�of�.W �� \$ �{24.70.+s, 25.40.Cm, 13.75.Cs, 11.80.Et% make�$ &<-In&�+} �/sec:10}Cpaper,o�,o`%e-al�A%p�1 jor �&r� A> gram devox�" prec�3����- J7 by u�'�ʙ��"-�^�in conjY4A�?*�+N�I2E�e�q#8ALB97,ALT00,EDD� has ��con�~� provv, high;2 ccur�Eof u�����. ?j�.*h5�r �62�5 ��u��%�>��c2�to 6�n'$is purpose�#"66$up�]�%�9,. E- allyQ�ed �ta��2ed��-�"�% cylind�2'-layeD scin�8ator hodoscope.ɖacqui�$ o!rsё�2�toQ� $si-�� &�*"�6�7�$P"$first done��SATURNEM!GAR85}E6-�Bkhydroge� is u�$-�cEfas�d easymanipM4��E�mag�guAjfG7�.�"mize B�6,, a techniqu�,tN%v�+ap"�aePINTEX 2x � IUCF � VPR98,RATB6� low �(. Nucleon-�eon (NN)I<a�1!�q�(} da�r1�7e�( stanLa=�Nar!/�@�,�5 Eis  P&7*@&U� NNQ���a�,a�t&E�toɊ� t���0�n-�,��(PSA) \Q4PBYS90,STO93,NAG96,ARN�RRN00}, aQ� m�z�$ing�4((��or al calcMs �'D �e�)j s. B%�!A�a�du)� threshold!�about 28 ��NN &� !��1b� im�1v��� �,MAC01} by se�9Arro�!s, e.g.E)rn phen! olog��x-�� �s ^(LAC80,MAC87%]4,WIR95 01a}� m� recently a$al perturb�$ `y T(BED02}. Up�-$800~MeV su� E!� �(oow!�un�� ous ��r�-ot,*�par�1Y.LA �:on'� !�ed�&ea�ded-ex�1g� de5EYS04}A-� ��erI�fA baY��)� &5al waves./!�!��(s�7 time�Ma6)kscarce.=o�� t. A� exJ e no 4�&F 1 "F q� �  =$ 792%��5~GeV73�-&� A��a!<+s��c1�[�[-� and  -�or8"NN.G,�Qsp�2ng.�$ I�, �m�1 �@)��!=ser+� �.!��" PSA &� of*�0groupq�Q,�o8}�c<regime9E>$ 1.2!;�,at coK>�1b0 solvq�@(�^ ind t)�6 !>E ^>q �+efa�aim=7a sub��2 �mov"E CE|bas!\ observ";� !��of ��p11 " .Z1>��i�w :�!Hin��y\� l\-py\-lene $(CH_2)_n$ fibers*���� H��ng��to�C�"�2�un�d�2a�cross (U"� A��!T�$%A prompted �,0!F��if�5oi��W!6�u�4� m��$3e si d-OitZ ��inued3"i 5}�V=.�C�%# impiFo��!�F� �  BZO!��D(g3 $A_N^�.�3�3>���N$��n�or>�'a& Ci���0l.�&t ^ sen!�A, '(u�8hey͔to fix��=M1��scale�6short0 �5M�.�!���6o[&0 thir1�"? B7p-�A�3}, w�Xir"� .Z0� rX �!U�pr+ �@y 2.11N. IIW� N5��5"r PSA &� �.=� in�/A�r� �@ ZeѮ���N(DR) � �1luq[.� help��A: d3�CV�Fh9�(�/3 deed�D�Q�f on,in�<)DtX !�[ ��ᝩ1 �MH!� w5��>�C�rSa��^�,|%�Lb% mMu "1�YZ�b�0"�*[ A�10a\ed&Z ���c0.772A�A92.493 �a�r2�>)�2���!La�r�o=� A95r[ �p{B���(allows. Man� tailu��KiiU<�i.��6Y&�4�H5},�wh�,wBfe �reade� .�inforREon.Iw! n� -on aspe C��n�for(5>' ҲH9i�p�; ccor�ly organng%Z$: In Sec.\ GL20} we ���NY�u7et^nb .�� !1�>e4} deals�>E back ndd8Wsea4��of valid}�% a��E9U ;�?� iB��)�� ema���n)��>.� asymmet.,2�sn"� .�i�a��ɲIirF�G)�ѳabthe��?a.�*H !#� 6�F�A�f%�� a e�� five�H>�.*�!d9�2�20} \� on{De�Eo�d� E*661&^D \aP erline{\iv6)#4s[width=8.8cm]41a.ps}}�7b�E 8�ESx>"�>* A c�(top)%l�icombin)�ED!�J� (bottom).h&FF1:REI�13shown s��I�inGq�fig:1}���s � two .�shell�=v�>C 15*� ?82�$E�I&(channe�? x85\% I� fuVHoa��I�inner � (HELIX)a�j> osed=4 4��160*:Ŗ� x ��a!help ly w6!$ oppoy�� �ou I%97J2hor[9s (B)�gruH2gaallel K � axis.]y, surr�i_296]�(s (R; FR), =$t�?to HE_� sy#�1��a�� *� rad' ���-z &l�. lighUMa�or^ � '� design;: �< way � each��Ftra�n�Be-Z-�p�s aRLalPA�neighbonb=���. A� � f� al �dpuzto� ME� P� 2>� . U'6� 2} $H^-$ � epre"�W=$ = 45�&�!���@0($\ge$ 80\%) �PQ�storawMa� � ({ 5+��&z#&p� inj�Di� !�� R � e .�fur�e��a ramXspe� 1.15 (G:()/� }m9t�S�op�H� DD04};5ey0(y ��:�y V: �/st"!%cyc�Xo .IZ�#tu� a� �Vin��A��i�����roi�N prof�%(6y r %�5�U @�p5�y;wW�O2e `\8!t�}�����jZ! overlap �o*� " �$&k ),�--*�+m?+  DQ�9\p���a�!Sk ed&�%�v�#a�<dX)J�Je��SJrm��o2I��je 5&de p!r�OG Q so#5 er�]r( &,�]�H �nte D&!�(e�Ts�  turn}IE3F ɇ �� �  ri~ o co� t""��*�.8m�)� �  be du�K intrinsic.��&*�B�e$"�focW)ic0b'Soscil��R�!; "{%� . At%�,&Y&21evelo� i�LEH6)�C�eStyp�N9�,#ly� A� flipUa u�.M-1loss.e 2�^3#ma ��$% E-�M.> m$6 I� �4�U�J�a���&�/:beAovSm b �/H  V�)5.n� P�s�}{.�F� impuls (M�#}{�aum2 ���63F� Dq��!]�N��N]aIi�Tq� R�i;VI�U�A s (��oer�KFUF)A�"-�5�.3�By0y� B�3n� M*`6� 3h-Z�!$�3b��Žs�^ taneouslyY�� Ѫ!.  �l"T]&{+�nM-��a_�!W0�3�`!� I"���2�of 6 s l� be$!�ENwa['& �ommUm�h��re��avm�� ionQus�_13 �y�  lTQ] e� P%71.x24.0*i27}$ ^<{-2}$s$^{-1}$. S&7( stat�0c���i%&�#c! �,%ull� %��1D on�V! &|�cc� *&ata9\ 6�5$ ������-d9c12 nb���� �ş�!� by �!��?6�:�\$+x, -x, +y, -y, +z, -z$��t� repe*�� 6 �u��� $+y$�$-y$. S�sa����Q�12y.%� ��� =P�eF���e2o!c&- .- (cf.\ $ �e�3hEl�Serm�cf�(eRand/or"� r�� Y.�in o�Uin four&��(d7 �7 weeku� . Ea +%�*322 - 4 ���d/T� sl�l- !rc�)A��/q�y,MMt7Yg, �U.'6�n*9S. Altoge=  4.}>6$5)tEb>�nd 12.5yu6"��G+) 2'q7R2X 6F46,S�m�n�+t:~41�on-�3 trigg��off i� &�'�5�1&�&�#� m"d #g^# +#co& arity \� equa�} \va]C_1 -  2 = 180^e7�4eqn0.�B�( 38�.(Jqtan�1�2=2 frac{m_p c^2}{(  .+T�8)6���E�!i�$�i\no% E�%�&���P  $iUOlKOory�L, $m_p���ma�Wnd��:I�� Tep�&�nd granu����*2o�e�.�+ wo-p[I� a�2MyM27 w�&[iA8tY])jQ�"�"tra�o�)sL$N";ngs�'*]ed��Chit%i�$ p��qK �*^ ell�� ex�Y�.� 2��}�Y -[$4h�)in7t%��4pp41�l'.�(x#b�~a �X &<1.3�� xM~y  0.9 R$z�(}�E{& ;i,u�A��&�2 ~ res���t�-#pR G,V�D�| -of-A� (c.m.)M�!`um��*u��hj�)�&K$q-is 1.4*V! ��=$�^2� %��$. M�2L "\nE�{2zS�+ulf j 18*j".��!!. frame� spa.%��ai�mQ� is �� -to-=�,xonl2LasNI5Tcit} $\�F a$, � orig�#� fini� :<=}�YD[agg�4� �[*�b also����v�+m�:��nonQ � '�wt at Z��V be r%Mi%$S�HM��ut���)_R op�;on m ��kn�$^�.��i� �)�K  g�� ACK02�4~��wc%-ykT (�*�0uTcb]f $�Is), lea� tocQ�� ce, viz. JI%� \le _{max"�) =(8.3� 0.7�=�X@}{1~{\rm/c}})^��.2�j�M� �f�Lyay��z����;p uppl�gGa+fitE~i2s} :A!�KlJ A�yu:)?]��)�(trpy&Q��wufsp e� ng��qICd3fYv]Gn i $\chi^2_{! !�(is�e�be$jf�0�-�r!-V E�&D*�(ub-!{iMmk�>!d" � 242} IU��$62�*involv�.���e >#��}�A�sh�4�4�"d�A7m�)� @y"�b)�+�<e&_<W�`�$% p"7 cle 6" &Q:%.s�� eI$pierc�p��� bo�l"m!�Rq�he�:���'mp�s z.;=4&(B)� one #'-sQ'!(� E'eBS'�#�2A\ � v�( u�msQm�)�Q two :. C�4 talk<72�&:n�8inbi"� ��4 {toF% � 1>&-E�!3h]1�!�WU�lof 2. F�s'i��n��AyKfcoe��azexaq �B`t�N?u��], eq.\ (�� 3}), r�%aDo�� >*�Ý��0ve�1a' h�wA{�t <5 g1\%A Lm�%%. Re��u�b�i!;���? faX:f>w���7"�3"}2<� , E �i�2U� COSYE%Yseq{� outA���"9=.��!cm3 ����!.idual gae|is�*^a_erNvd�� EduchA�jPAJ 9-��(!?Dex: -15~mm $\leq z$$ 20~mm. S�v0� e-&!�� avoiXon ellipti Ef�!�axe�"A�� as 3 mw$.sF1igma_2 \ y8J� � �T<on� �*�:2). AfU,al�s"D%noP�"�vT�#nS�*�;A�&b25E�tt�&�y b�9re� ��J(alj:) K�1EAMadisoa2n��(I�BYS78}, E�:�(4A�)I�a� ec{k}_{inRI $\oud j)v=*%�-" $N�In" it; $L$*�2H$h|KS$OFmň �.U'�U�/SArgonn�?�-OU80}"2G< �m( .���� >R �Pj#n-�D}FV-Q~N�nWnCB"6n6*SU�d��(�,�)}{d\O�Xl/I_0=&1& +A_N\;\;\,(P_N+Q_N)a$ber\\ &&+~ \;P_NQ_N JSS}BP_SQ_S >w8L+P_LQ_SNcLL D LQ_L*� 1Pe�79, $�\�0(N��\%�)_0Nes�(.O 2�2�"� e�!�,=�ab)�!�a�ex��͍�  $x�N y$, ���t�s�>m�*� eAA�n�(.C5"2� &sJ6y 82;��6e }]���a rm *�"xis��|>�� $. A_(i6�"�. /q����>0P}=(0,P_y,0)$�{"2� 1})�,�&=24[(P_y+Q_y)\cosmB-Q_x\sin ]U� \Q�$NN}[P_yQ_y8^2 +-.= HGmSKsinK+�KeZ;6zJ v}e&��HK.�*�=�<NA�Ay< NO��L}$W�#~"� Y2mod�A FAN u,� �A�$�s $A Q_xa^e�Q�,q. �Ka2^A�.�= 0 �a�� ,k $Q� 6{G"% oY~"��� =I_0P (1���1ECdot]))=�J�.+(9�� 6� 2}%�< $N�I� ec{P} Q�QA0c,_A iv.��k2�via}�18�p = R_�.!F \Delta�  L(>.� \et�>R&~5Օ���A�H'B+ $L$l]A�'B cy $om<D*�8 $.�$ subt~R�H-" e�.!�26D-� 9(p-wa�NNU� ea�1byG("E;"7�<yi��NI,�z-�� ]-�� $[N_LMU)]pd� �#R#("$ � c"Nlsez��" � OHL7QC�&��&�%��9tB\Q_{+y�  - to *�F�.kmea���A�ƄN_{L_-}�N_{R_+ e $569*9H}{!t}ng%� 2�!v-)^9� $��ilon_{LRb�(�- �)/+$�oφv*E/CUN$ �"� q'AA G1le��{͋}\�#le��42� }{Q_� �<eqI &��z�2useg)� ^(&�)Y�����H  + \p�nd!4f�$�(Aw�:t\-�La$ a�. �ly�VN$8*4�+ ruK;�.." o�śE��5x�}>-�/V�BTQ|�� �� ��$<65�>$."�7� :�7.t.z�2�NN}, ">!Y43b (TE$&yway" i� �a� �itu`/$e"�I�bal�p�Qto ��N$ˀ.�S��Y4c�a�1�UtHbdi�9�$ to 4]�b�� �!ypi}{4�ce3:5 �8$ &7�vP/�����!� deno!e by $N^n$,)T$nj", 3, 5$,7$7 Sy v�/wA�!Mi n5- 25&s� I\$Q(�!$= x, y, z)�t��(&�*�vbs�!Q#�$$N^{3}_{+-&�.s $. ~-)�� quad�vA��o>"��4 -6�-60 ($N^i_{++},  - -��yi؋481�N��E[12&�2��B}& InN H2. � vE��at �4�-!�16Z�am�66�-�|Q� Js�P� "(�R� $Q_x: N^15.3_1.5_{-.7)��:ndq�.>a)�(s $N_1(Q_x�.(g� N k o sXe[1ahaIR2:R-6�R+R+ZR36R63%�5% 7%!F�!%�4:V�VV2�-F�&P)x�XUe�ndR BAU�T-�qWn �ois��ERaa� 0 Z4�m�e��ch*)"u<��L?3y$2��eӍ�tD�M�:�:&��"rARi) &=&a Ie i)+NE i)-N%� !�l B%+%+N%,2/qAqRq-qL-L�q\gA�vg���g.�&" 6"" 1a E!�EZ1�9"��&� !�(x)$, $\dots5*�z)$�}B��!��� f�H �u&72&O ` x &=&P�2Af� �b"� 7}\\.M!�xM5>Nsi&Q � 2N8:N�N��V(G -�)�2acos"� Nn9:n! y�n� 10:N! N��N1:N! N�W- =^2>��9�F$)2�12:�!z�3:N!N06v4:(�(�zEH L.�>��=U�1&�q�W� V�5L� `.� ,x �Gage�� $Pa�m>NP�B*��*eqs*� 7}),"�10��(�13}�A):>v Q_���}"*^ 6k8}�\1})DA�[� $Q�Ś�x�Q, *nT�zx*�:W#lIw1y:�]9CT�H zon1<�9o;eRg+'" .V�G�?E$��e@�;2�9!�5 2,5!CSJ���+X � $��� ��+%�A+*� .� i"P2%.�b � Q$�ub�C�,\%of.T:� 1} E2�7}) -��re&�"�assump!gm the %"���do)���"�#6�Af3:�A�~uu A| ]$&�a. Ci%�f�i�w&�,!�f=.hhw�..�-�w W"J? �"�my-E�#! ough ;s�:� S 5�pos�.�2� �">�=Hino=&�)��%?�"X c�7T�<rg1f+!u*�c��'A�/o�_t�DfunM�!�repla�^m5��B realJ~��inge�se fB��Ga� an &�Qe�;�7�+ dard& -�$8\% - 10\%�y.S v,an"�=))/�n}%B\$. Knowled&8"�$���KӘE@nA?ary҉�50r�no*�cal.�u^nAllSP antiŒA�& 6n, nam d$X�@t-Rl :���a�hava�en!�suh!�A�f�{9�N6IAkB����{S>��6�3f* a�] step\Vzcheck� �'�'Re-8#fE��Ii�0Mon�� arlo�fed1'E�F;� wasA[�>%,&x}.�A.�pB�NR&:Utho�+S�*�CT�h@LI$Q�8$""�r�%�d�L, 4�O*�.ch�='ae��Ld�eir@�"�ic��6ro��AK������� rial)X�/1torJ&'$ iJ\/n�"7Q!�(a" inQn�9ordanc��"fP FA00!�G�Ve�Z)g�Vf1c�e.�hQV)s��Ds7 tool�"at�]���&. �<2K�i$P�.8�� $Q7$�8eUtY�5%Hs�=�F�5$= 1546 MeV%l|]wm�-G�,m.�s (�00.804\pm0.004 ��03 6$)���-�� B�' 2,�::�%�e?tt *6M9"R=al:�Fi"usax�%�Ve culGK�VA�6� F ��bZZKass}{� S}$AA�'\v* 2sl  .>r,}{\hspace{-0�W}6�4~(deg) 7�����'5N�'&7��2�� _��)� � (middl�"o�as&v xA��=Q^�Q12� 10;q�M�g?�@�=�IN�,u =O�!�s� 7E* }�1.�*�b SAID:�(�!^sB�AU"�(T�a�"�, �hm i"� B�k �, aT�Mo�5CAƅ0.� �)q$9>C or)�c9��25.T]�quM��e�D��2�)) Tŗ ^�f�{�zezP�Ga�q�OUw�6=#i؝M�Ɏa�� &t2MisY�AW6�*�&nd Pa��233 =��6�ec�&���Wo!&.��.E��B&�){?(i� m:�5*I �B,)r (ii).y ext�u B�GC 2Q; ensaAO �^�*�3.4y �PA�S�at��fj�:�s��?��E'�`�!�:� �o6�st, �cH<c�G�KA� hQ� s� v#Ba7Ra�fI<��H�j�q stud�A��"ly�H��sR�%,Us�Q x$ (T. ) �&<5�R)��AQd�# ?A�$y Kx$)Ado6_�[sl 2�7� �/E:��/�`Ϟ �\�e%z� �hq" erms�cel[ ough J�/of5 � me"0?%Q)xFl;x�(%�IA^oa�%2. .o ����[ed�5w��@i�%A�i~`b_ �s� L�lZ@Cfig:6}�ADES�9��Y\MU 5� z<s bo��')� flip�bi3# , al�wg )��7�;Y2z�� m 8��ar��ee�5#2�&] ��CU�M| (see6� )B(�=*A� �=Av%��[to W%x�@�$�4}&"��K& i^� ��x$� 05FQ 05�qxa��6 kJ%�t)�� 6�62ZF &���h2�@ 5-r��X �2,u�i�$+PtL�8s $|\pm P| = P ���1a�"���d ���� m6� P� �B�!G*" ,�"� o �$(�)]aA e�t�"� .�6P7 v%�eզ,�`��$1�P$�'5i�j}�$0!��nnegligi.q�A�V� }a&� E� v*x*x, s�?� � �&ko��}�I*7Mo��!e gene�\b F; .��pi�$�M2e.e�$���enšMu n� E1n�.� vanis�nre!X[RT*&t*�"A'��"/��;�"��B$Op te�|s *7� (.c+ !�!12v*X(�k27Fur�;.X �h:_ 2} S�e�Q�\*� 7�ɵME%#+�{G4C��u**�BS"F&h� �?i~����@ 2� � &6F�l�C�@J;DurssKiaa$a YW!f�sB�2but�YNh� eD�|2GAti:!&&C?�Si�unc*�\� A�b|���z E�ed!�^� D1}{�����D22�1.<um.� 0cm} bi2�W>�-���7.~���mMF6 6�^hV�!�0j̈!�ba�?va*p�Q� h& I]�q�.JJ�4 ?H =$ 61|/c�   106P�289�}/c. mB�>R�>� =A3r in dark.}0*ysin�V> >^Q>m;1.8 K %�Mn02j0>>O1.`�L.4 f39c.2223�~/c2�8B)318-22)�u(_ 6!ta!>B�t !��8F��e*��~��9�!R!� � histȆs� ��r�� �S*s��b= 1�b~GeV ($M�� 9��%2.377' Z2-9��!�Vg$1��5*-�A�$AJ{e(dash"Xin!x2ckHid eTpolynom1f*7sN�Br�>p� Re��r�Rbl T�cA&2�&rI7�-ew�of"W!t�2�/s�Vt"*F 6��.�app]q"�i?F9 � ��p(2+"f%of*� 0��say'h��aÃ��264t behaviour. i�han�$�uUn9�= &a� l!98]�� ^q2�Aex  �FuK�!��I�-g| �d�!modif�!�O�N�Q2�n0OI��� S� in!���e�Mb �k)��!o b/� ~5d�s�i0d`�j.�^�5K ( !�i6�`�WѢ��� J�^ ��# � B]f� #H6�X.QG6*t�e�K%D ��A�6�jT !��d�a� :2!�1�%;.G :5 Y��wo1� GY]�$de"b�'�YcLI(�Eg-��Jij�f&P 0.0�X 0.06Aa%%t�.& *="2!�uC&�!5�al 2' . Our� q�IR2�Y6�0 . 2��@ m��\>f6na2�.^w9<XFaM gniN�n��l be"E&+R�$bʈ&� �8a5er+ `at:A,"\p?HaCA��a"� 3r  #g�i5z���-=fi(� ` S� on{CA�stݑy&:I4t@)&�%kB"� 2� )$T��i}�"�,F�" �Xi�5��f�Ss�� ��d��>��T� �*�-�r1Su*�C�M.%2�&"o��%!Yy�*f(�d <Legend��&R expa�I$5^{tha�#q�"@ � 2�.A��xh/�7�;an��YI� med�� OO>� "� AN>_ A_N2 1765}~ . 179393>� Y~� �W 9FW AJ6#M�>�,#�4)�X�o*J�g�k"J_C �1!�AZ" :��P�aaKZI\�) O �6�#is h"�a�)&� ��a�.@%#a00�a��#")�umUAce>07>� I)��p�lt*.��b$C2BF m�􄅒, too, b�-a�e�me*�%N�Az� 阁3�Fc$P_0y�.��nd�#6��96�-��HyV8})�o�*�*�X8�� �e,$ T i9s *�@� ly 6�퍁�!Q����de%�ed c��Zn� �0�=.�&��%�:(���[=" for : "�iA{cr&U4$^ Y$��32 to 88",1M�W{2}_{red&���1� 1.53I=�N+X.=$^3�!S��Ts�o�� �#��Đ2t 5�e C �?A��`n���upo�tqf��"T~�Xd6e���% 23})��R� ��&UF� �61B���wa ffer*�'�}�$4!��*��^A^pL�X�O*�3�nd.�$��*�;�x��V)2. B\#meri�wo�HG�X$j�kZ sensem1�at�jhgmut�T.�f �"��AA82$- test�e" E I�="�> ����bi' "��XN��{2� ��2\<$ 1.7Flq�sxr�)�s,�)i:G2 6� f1a���J=V6a�� u�o veryy� t mO�r� b^�.� 6� 3�[ /=40^o2� 8B#6>#1FG8>$p*� 2!"Y �pS>�� 10F� EN�UfY .�.Ue�R�u&' (o��� symbols)e^4cU&����.@.�26 �) 6� �� A�n,V5R&Vq��e�$)�'( qMCN90}>� 8>� .�E���8 mary6 6} E]#ss>�5�R_VS; d�:�,O�lY:0-2�2�zleq� 01),)�iniT]'p�llip(z(Z[$ ��(5�R� 1�=��*�ye�!x=��.2���͍<"�Q�� soBe N2�6Y��>> �& Q$ ��'v� Iu}/!�ND *m +.J;�3J3;+eq7}-� e.*.����9ra��b�.Z��/fi:�9.* said'(\sc Said FaG�&glampf2'L#;�Yd �S�d6Ydpn{S lP.Din2eS6�&anl2Anl>�"��<11�� S � )`�6� Vs&vwqF�=e��K�;� h>J �&.9>+  ! is�fv"Py��p��1� � �Ed slow8�eAh���*. �� �qgap.)�"'�� *)iat ��at&����T��win gooE ���# #.s6�"�8BEL80,MCN81,BHAlYS85,LEH87,LES88,BAL99,ALL00�" =*E9���4u�� qt=��$� � oYGS*F��i�atn�� !�lt� -]�� ��B�3)NaMFll�.�A��b�Q�Q�Q�Q�QbQJ�e�ͺ�J�C~<cJ5��c���2F�S�"�@.!!9�"�P*]+)$>�1�jendQx ��S�� a cr�5&dit�s��m �$��l��+ �N+a���uKY qp* 5.1~�(�UE�U0.86��tu ��}+Y�h� 2q�� 9negqm�%����B Y(a� k�� �yi�just �9ioned [�agree�-3�G �(PR83,DIT84}�79$�� 2�!�*�/�n9���become�,��w��f%�;�a�� % s. W�ӑ�NJđ5*��b:��s a�-a�I drop%m� ���� ��$�# Mt�. AI@@cig�Zn�/�;T2-���)Gl�A2��� �� �� �� �� ^� �s�s� {S F� ���y c�r J����L*~ B�1>* �Z���L�*z.l� zero���豵)":e�i�;��"� ��i�a��14"��tL� i.e.�#�O0�9 m4�,�Im2! infl��y .���)��2�v �Jal>b "� �\O Jz&�ŗe���(! . %�3.g  Iʮ �<-�A@gy�b *vN"Q SM00� s�-} 3cWRl�Vu��[`X]/20�:�W&�al d:�!G�C2h)$ ���P be%�,��p��\b��*'� s. H��w�D�Uc�9���$)�"FOeZ� C�l�Nl��no%�������.�%oM .�M� �&a�tra�� \:yon�%�yR  );!�e�rik�dis&� ��at 9.7�E�r� ji;� Up78}�= 3-1p\L��E�2� A�Q"�I��(`1 �i). Huge�*�likose"saG!H" �J�&V0B �,o�%2� � ��3�M("\FU<r��R�qUuD0 Ci� %�s*�< -�%F(ZI H;Q�s>�Cat�%�A� c:Ds���}al��=)E�yy?H� a�-u��|��UviWt DRSA� .� ��M�e�e�� !�"c@_ev�)���GޭaL �{ � N��gu~Min9"nexA���1�sϕn0 �!*1�2�(&bP"i �P08i2'" QF'S>Q-CJ'L6N!#}{{� EddaA��2 0 ).= ��JyR�!� Z� !-�'!#�I�B��A7�hs$�7.2�7��)>5q-2�"URef�&J4 2�2�"J�L���&�ь�E! S6Q(�_,A��7��&�{i�) lA�By-ky��2I8�_|"!b idor6P�~B�Q12>x .�D��.i�&�>�/it��6� 3} B�YR7��quLN�y�5� U�!����%H�on_��v�$ matrix $T�L@�9ta���.� �ue�^nIά��l��mp-"�#78}. &Yzq�d&�ha��cS e�=mid+\� le�* $-�� c.m.8me� seK�I�JAC59}:�2�dphi_1= c++p��T} +� , &\quad&� hi_44-)4-4"fEz� hi_29>m-�Bm5b4+4� eqn:1Z>cw3C>�C.���F91Ob(:���g>v"�0cO|�B-NN-�a]i��9*p oublei%�2, 4Ll�(w�_5a?no1 .3$)��$flip. All.a,�in/�KhA�VF��jp��,,*e"�z9 se=RsA0=�% I_0&=&Re(�12^8�r+ 34 )*�,2fA�W�N-H6N+2| 5|^2.Z�e�L>Z[21 �2 V 4]5 �&�-ט�YH!�m+����GM'� t kin3��^Y'. U���s��"�I O6�.d M0� �{ՋcM ($S$�|N �orA�.-�4bƇ+pY���_�m\!�PU$nel. Basic��noT1 pF4M�d��b .a n1��nsޅt��c_5at25_of 256��� .�.8%���E�*(.2��a �t'st ninZ8m�aps�'�E=��� owA Պ>N�by"�22$-J�E �$x2 �{�,-�.'�s;G4�)92�l!) e ��a�:_&�2���8�.��3B8 83>84p4|$} l\psfrag{ang4}{$\alpha_4$} 8phi5}{$|\phi_5|2ang 852,1}{\tiny$\pi20.5/22- 0hspace{-.1cm} G-\pB-dZ+ V�centerline{\includegraphics[width=8.8cm]{fig15.eps}�`caption{Direct reconstruc� of scattering amplitudes at $T_{lab}=$ 1.8~GeV`with (filled circles) and out (open�siortheFpnew EDDA data. Different solu��8 one angle refl�@pminimum $\chi^2$ ambiguities.bThe6MddS@s are independent 7 Phas $defined inw i!� val %�\leM1i�This gives rise to spurious discontin �$ e.g. for �Q4$%L(5$ at $\pm .f e dotted A r�PSA� FA00 �}a Xlabel{fig:direkte} \endure} !25�< have been added� the world%�\ base. For narrow energy5)8s at 1.3, 1.68, 2.1,�2.4AUVre%�\now 16 or more observabl!� vail 8 that allow a �J� ver a widE@Hular range. Results%y2.1�w�repor!SH in \cite{EDD03}; h (we emphasiz�A�.OE�1i(e  up!4212�from _lLEH87,BAL99,ALL00,PER88,FON898a a <99a,KOB94,LAC89b a c d,U8I$7} , among!c m 11 �doubl!d 8 8triple polarizaa inform . Sinc �Vqf how A��nB fitsA�o! exist��I� SimiA/ #rJ/)�IE�c finding_ "BYS98}A9eL obta�P betwaX��d fouru�@mos!+s��Bes��I���achieved�lowerix$ies (1.3 -Q�$). \beginu��theta}{�y1.5cm}$\0_{c.m.}~(deg)Ʉ�d!��; By�h *Hsaid}{\sc Said Fa00. phi1��1B��`12� phi282B8 86� phi383B8 83>pU94B8 8�q�q�q�q6.FqRSAA�2C6�lɐ�jsymbolsiaB samea�na�ae$Fig.\ \refA�ո EENB�2>�Fi��FE shows zR ᛱ�in terms5 ab��e valu��nd�ioi��4complex plane q���'} � k=IXk|e^{iMHk} � eq24 �9ş]arison��ui}2|�{  Solid� )5�denote %�0s� (wit� ) .�  t�work. ���)l�9,�.N re diviDby $( �1|^2+ 2 3 4 4 ",5|^2)^{\frac� T2}}=\sqrt{2I_0}$. Our��doŏincrea� he�+-�of�6 . � �� cateA at)y -��$in particu�&$A_{SS}$spite W promin� devi%� 2� sVre)�ti�!sq ՞(experiments�pro!O� i!�al �ai#onI � 3R� . Pl%E�t!).�correl �coeffici�%Cis A  tendsA�con� rat�:Y n1(@ two branches vis5I them.� moduli ��i|$|all.ia 0he preferred X are 4"Sd throug%i2�e) A�gh"2 ces, detail./ si� spin flip�� k$�g �ak� together5�)�.w $|\�5- 8{1,3,4}|\approxi \pi}{2}$,)�spo!�accor� g eq.(�Keq23})!�!0sm!Hmfou�rI�L}$. Fur�� ur)� yiel!�hat�1�2V�� $ �3�$ implying L $Re(�1$2^{\star}) � 0�F eqs.\ �1}�2}) fo( a�e��L A_{NN}$ �� e�a�da�a by%bi_ ararduc � �3��4�E�!Q���Cnoe�v Y*thus pre� ��t ,itial antipaA1el 2 conf��e�, cf.\!��,n:helicity})A`� �6al� a5 � 1O--A�but ano!� ��<�an al� vanish�m���$� se " �rm% F " :c .,$ =� :� �d8, mainly driven!�!i$-orbit fora�� CON94}�I���se&E A6� $E�3$i�-� 4 B�pre�. In!trastiuis1�iE�B� !\i�}T$ �q&�.���!WZ3 �erafnq�u�suc� a^$ �ibutese, which4 �� H�on%^\se�{Summary"[ sec:6}�\re�u��s{�$collaboɝ0nksEk�4openeam�  llent� � ��supp . Helpful1wE!E�$R.A.\ Arnd� @d R.\ Machleidt a�very m�  eci� � is!BkE� j�� BMBF �hracts 06BN664I(6), 06HH952i� 1 ?XForschungszentrum J\"ul�$under FFE � ^ 41126803, 903,? $41520732.}"� thebiblio��y}{} \bibitem{ALB97} D. Albers et al. (!�), Phys�xv. Lett. {\bf 78}, 1652 (1997)..QT00} MQ tmeiH�S85S 819 (2000.S�O 3} F. Bau�P90P42301 S3.SGAR85�$Gar\c{c}on �, Nucl. �A�44�669�85.JVPR�8B. v. PrzewoskiL=@JC5%;897K98.KRATK$F. Rathman�VG658FF0} J. By�@ky, C!�8chanoine-LeLuc a�F har,0 e(P) �4�9 �7)I�J12+51}, 274 �2�,STO93} V. G.>,Stoks, R. A.A*Klomp, C Rentmeest�*�J7deSwart2�)U�79I� 3). M�NAG96%0Nagata, H. Yolo �@M. Matsuda, Progra�eor�d9E91%q6.�ARNaC �A�X!p H. Oh, I. Strakovsk�"0R. L. Workman �F. Dohr!�J� 56}, 3005~6pRNap2~�u)�Ra�� C62}, 034f>�MAC01}f�+!�I. Slaus]@NG27}, Ra12001).=�g�"Lacombef-2AT86%u82SMAC876�, K. Hol| )UC. ElIF�p��149� !P82PA�4��C. P.!�Terhegw !��v 2950y94.GWIR95�B. Wi� a,B4e,R. SchiavillA���%|Ce�3�52{%�ae5�Jo63a� 4001�:1.�BED02} �Bedaqu�U.�( Kolck, Ann�7�Nart�i-�5An33��2.aEYS04}!�O. Eys�Ra���)�WMobel, Euu�J.��2_105��2h� 8�� �!aJ.>gC%k4}, 60��2���4jWf�25%t2�NɮAZTRP!�35)�2�EVE��P.�� Eversheimu�-�EW�A62�� 117cE�21LEH�A�J rachHPProc. SPIN2002, ed. Y�Makdisi,6U. Lucci��W.I& m. MethodN %RResmA49��4��!".,BOU80}C. Bou' y, E!badaA�J. So�%y���5�9�-66OHL73}G�OhlsenK!. Keaton�B�)|10\4)2S BAU�#� �D� �"UniAg4it\"at Hamburg%�2]MCN�MIcNaught*� 1Bv-BC4!A280�6uW�  D�"� t: http://kaa.desy.de/Home.html% !@www.iskp.uni-bonn*,gruppen/edda*� BEL��D. BellM�9 4 BE�94},31��6�MCN81� W. ��e�8��82ABHAK T. Bhatia:��� ��ŏ113I+6JYS" .G MI�)� �2>72� ! }�;%7� Lk nF!# 1013�g6�LES88}�1Lesque& F�30��7 G2�B&���� V� 11},�> 1999.�T&}�%E� lg�� 1�%i%cX 6�N2�L1�L�� ��2�AUE76}� P. A&) 2�=�3� 1-�76� UE8�K�D3��86CPR83}%#pri�Z!D2d 2 C2RDIT84}aDitzl"� 2� �2�� R213I�2>�3%�< 141J�F(E�PerrotU=F�29��5m2��(E�M. Fon�&jK3 2� >�98ab>6��/13�6�ea�� 0},4�s2�GLA92}� GlasLF�CO�v92�JAC59� Jacob��G.alWi"W �y%�A�404�/52�AL�)b C.�/05i�>�*}�Kobyash&�NB,56A�7*42� � 9b�D.� n�1r269�!�.S�* ޞH8%%NHc��I�f�dvH,�+ HV�EH��F�harjmbIDab=a��q����� 1�rH�H.��Conzet. rog25A�iS�x�->s b0{|_var} ). docu} gU\Z*longtr}{|c|cc �'0S>A� �s�6eK/8 $10 flattop�ies .'�-���512;232_5 0.54.�4��4B�21�_48.�:�6._5B�27._4��0.590$:|25>�61.X26�_79_66$9.�6B�6.�26 _48.�7�122_>�598�29N72.�78.$12|7>�61._31.;Q:44.�92�22�7>�60.�32�U�2�92�22|8B�3.�36�%� 0.49.^9232:8>�722�e�1�0%� 0.64�910242_��~� 2096�i�,30��ƕ9��3.1����36.�16>E( 0.34.�15�2�B�6�122�I 0.38. :$2_B�46j��0.42�B�n�6�16�_3.1e53._B�463�x127_32�1e_42_>[626|e�!|.�B�=F�2T:S_6}�>2�B�45.�26| 0.40.A26A2.B�43.u:�%�_.�6R10.B�51.X6;0��62_26�B�6:36�E$ 0.562Z6_5.�B�56�6;� 0.57.�6�12���572���7�* 3.4��4.2����2l BN 22[:�2xB�31.[Z_2 :$2_B�30.�:qE�0.22>:Z6_>�29.T:6_4.�r6>�29.�22�Ѳ22. :6v�22�V* 16�����2�B�272�(;I:12���$2� B�32�:�m0.32p6=z�6i:_� 0.352�%��z�42�6���41.^:_2�B�56;��0:�6N ��.�:�-|56���2� ��9"� �* 31,�* �b^bR�4.8����26l E�1\�6x:s 2�B�22�Z_2�:_2xB�6_:�� 20.6:2xF�3.�:O _2�6�6xF�7.�:&M�6S426xB* 20.�4�5�%�0.6642�6xF�2�:�� 18.�52�6xJ�2�%�� 0.28.�5%�$2:B* 27.4�;I>�5%3$2SB* 37.�52p�0:�662�B�47.�5���� * .$6266}B* 442�%_���j_2W��318�^3"�3�4�* 3�T�T: 2�� 12J:�2�F�6.[:;E�0.16�26�F�3.�:�ei0.22N :$8.� J�.� 6��12� B$*B�172�271e�!. :$2O B�30f�O 26g2�6O F�2� 6���2[4�q�12|F�2�46E$0.22=6/6xB�32� :�Q:2� 6�2~�.::;% 0.33.6�31.:F�2� 6;��22�6�32�F�3.u:_-|32�6�42���1������*�SS}j��:� -0.36�6�E? -0.226�6Q :�OndE�-0.42.�612�:�<6���q���%526�2�:�<8.�:1 E�!H26�12O :�a2 ���a9. 76Y 2 :�!�2d6�� �2�86a2|:�a1.6<�2] 6�:a6I�2J3%v5#���4.� 92� :� 6K<2� 36F� �.� 1i�6I:< a2A:Z �7.16$ 6�:�a2�6�a3.� 122? :� F�2�:a%m -0.7.� 16�6a�����.��b�!v�2�:���2 Q�6�F�35.( \ < &!�22� :%2�F�36�6�qg22�:`2�F�34.'6�U�6#& �2�F�32"6���22H:;2rF�6� �%1��2 636�F�36.#6<��6#6361F�6�:^�s��2F#n_F�32q :L ŹFa%:1H6�F�42�6iR�q2�"3�a6 F�4.JR� a6�6a2�N�.�6<iw-�!.�65 6 �����*���6zI6Q�Z 2�:%2� F�6(:�q22=6R:LB 2.�a4*!��.�#>q2�F�22:L 6�t5H2RF�6�:L�26���a6�J�5.�6'��282%��a2�J�2)6<��.� :L2oF�41.5 :'T46� 2 :LBF6":<% F�6�n�!<5.�:? 42� 6 ~�502a%5���2�4�%:aBZ 5296�Ga2� n����1�1�1*1��12c:s ���2S)�1�6LF�12�:���12�:j2�J�6�)��Q�22 69 :aB�25.:)E�� 2�%:$2F�32�6d"�392*x�2�J�2<6�-* �2�6 6oJ�2�6I/a2V:*2�F�56a���IT�)2� 66�2TJ�2�62F�{a2H)72%6�JZ 2F62��31.1:!.2FZ 35.� :a�Z 2372H6*F�6o6/U�59.�:�.2����I�I�I.I���.� )tq"�12T):%]DJ�22�i�`H -0.12:%2�J�2G-:�V�6%6� J�6� 6�" 2P.:6 =" J�6� 6���02�6�66 J�2�(b .(6�6t F�42�Z 42�6Q!6 J�2l5� QF�K.(:%2�J�4.�6��n2�:22> F�56 2� � � 2w:%2�F�52�6 I�a2@6�:aB�62�%6a� a2S62-6a���`�`�`2`Lr`r��:*J82�"_0.�:�$~�06� ��qg�L10.)6�.  J�02�:�+] -0.02t 6� :B�02� :a�o02�:�2� FY 02�:E��2%:�2�5~���5�a2� 7�%:�6Du:6�+2�"> 02� 8xa2�:�a2�:�"� 2 82�:�6�!_2o6m a�.�5:>7:aF�2o6g5�2 1I�1#6a:��2�6�I�%.o1i�a6�F�6�:aET!H.�(1xa2w ���`�`�`2`��f�v�.�� 1]"�02w6�~�02�) Fa22� 29 6FZ 027 �a�}A�2>:%z "02.:)aA�2�#�=�:��2e:�aF%an�<.�:�%m%2�:32 J�2�:<a2�B3=#J�32�6�a2�:3nZ �2:u�02Z4:32�J�2�:<Za2�6�J�6S$6<�6�UF21J�2:<�a2�$:32 ���`�`�`.`���2��5��02�%B%}g:�!�2B� "02� B�aJ�6�E66��2q %6n"F 2t,�< �2�:�2aJ�2)^L2=B=#:Z �2�:'��.6&�*r ��.:L��2��5H2�:�� 2�6��s�2�: 6LFZ 6<%�ET�.Z :�6�J�2>-6�&� 6A 2�6�:��6<��"0#:% %2�J�2�:a�+2":a21���`�`�`.`��2�N�A2�:� 2� J�6u 6"eua2�-:j2aJ�2r&:��)6�E[Q�6L:��6g��s �. ByIh!Z)Mh as a"4y8b�l�twe hopP|es_ ish �wA�~ �vAK�Y �M��reBt�_}%�e�_ PACS�|s t��@ message %\pacs{0/^, 2 42.10} 2�HSubmiɎto"� >Ps %o{\JPAEC��out����A� : pagedw�� makeX \v��{�>cm}&#}IntU��R�r�{ A v�amounD���h}d{xinmvi�͂s� stical��el�aidw(usta2�!�N, ��StatMoCn�ref+�Ӏ��ein. One�!�z�$ortant fea�~e]thAJ���a,hey assume a/ra y �� chem�ly�� ilib!sd systema "( freeze-out�ry Sez� 4 �st� non-�lac!A hadrC~and?�on�bs>}!���pr�w'bA �+e`ar=|��mh�e�%+g �}j��l'f9eon. GM�%6��W}�w� densa� of a���le �ybl]ed A�'J- temExPure, T$_{ch}$, baryo-1pò,ial, $\mu_{B�{2u" "s"!�.&sA> factorPgamma_1��O{ imMM issu�o%�!M:��raA$ util*�Gr!�CanonA> Ensemble>s��>xa��ƃ�x opri �� the M4becomes m�. Inۂ-�s%�Ad(micro)z regimqs$ll quantum-���o%�on�T S� ly; � me�eu�`��: � y av��!�.s�` j���-�d ��is��2�{teb}�W�� W"w�j;Z�E�.�:�in69; a lack?�6�O�}��Dis &}ׁّ��O� �.�( disappear��O�aB�59per unit|Q!���. �/:��cE� UIjach ma�y ill �!ӥ�%áQa%�Lf��j�'�  true }� �q� y�s�{nc� e ne��¡Qw��"* U_ nd 2��)�,� any,��aB�a�4e occurs. ~ ����F�"�a�p d &{ e�a� �%� ipan��.m eZ&in^ (or 8Light$ nuclei),�g!v �A��i��li�e� ly��poraual6����n�s, � .3�.~W�Fig:E� }(a)� ��}V}eha\�r A- $8�h\Xi$ �Pb+Pb9�s!�;s = 13Ƅ!Ja �� ��� �~4Redlich}. No c�c� re y�A�Au+Au^�at 20k. A"h�s��!e��� =&q�quark�(-)<l^ g: ;...�MK��It�7�dž&�aU�!4a�كoBde ��6i���� n species>6�jtW� e} Y er�j �Bk�0.9\texty�]{M� � \\ \�j A3P�ed2� �rs%�.� 5V �%�~< GeV>�y"B.� {vx Iaf (b) F�^{-}$ (c bar{M�}Q��{+}$ inMo5�]�=Y}Error b��r* al. R� �p �l ��Ioi�a��uncer�p ty.} l.�R1�*� 8� mQ k s2�=� F s6 t���<��{�#U�1 ;� KAOS�=a� SIS,� . se ���%�c"9 �� L��Ta kaonQ� Kaos, Oes�zr}e�$5� �y ��isD.a�sip�7 ii�e��nG�t�B�of��7.3����U_ �B+�}�� ��Bruno}.�;wJ seemTref-��5 �%�y��EG� e@� nce �apph� >,"� �Tq�s �!fbn-s~� ns džreA� �at5' 8.8!&m� � ,� �� �Ɇ�hu�� �e!�5`)a[M ximate� �1� !�&��go�gainstZ�owY� ]��0���o=�)�. C.���MT!I2��Esh!�� ��er.I 8.8� �n2�-c�=: T?��UofO�V a�bm ���J-b)!�(c)� �sӊ��2�M�2��%�Ma hype#", �Starpp,  200}!� �{A�&�@�to��!�� c-�be- . We��aY� I�sei����sig�re����teau,��"(an over-pop��* $iRP+�U� ,�nelQ�m/AB$*�m/,5e�h �a�rP%a. 2H -^PBMc },� / ry_�es� y%��� b%, K-�,� rGammaS%�+�d���� ed mediuq�!�� ju(�-cwb�Aw��'� ��.s.A�ureJ�a)� �e ��!�lev�M�&s�J�"e�#�����bo���D%�t�y�Vb�� �T �GA�E� a smooth AIs4� W_��s94 �,AwE/sharp r�atiM aځD r�o�I��!�����J cT�I�w�(help clarifLA�J�E�N�posN��an��A�3�vn "W�A6EU��SPSE� 1�i.��&�!!"-�Vs%��t%� �p.�IJ, be�9��st�to�@RpA�"� �i" ��J8 ��� arlyJ23# .4  Scal� Varii6 No m����v>y^M�>���A�A+A}�� �!��2r���. *��!~�� \/ � "�u2]�-�+� t.�� / mad%����KN!A>S � vario��les��p�by-�bIs =P )�!&A���m��sO ����� );��-prǔ,v��ain��!�ge , �YB with ��  3L��-Cmesqaw8 6� k�Erstead?�break_ $\O$b �s 3 s rs, clI��no&I�-�on� �!wI� ide��2� a��sm 9 l� u� d ��p��2i{�Akto8�&�b]�, Nbin�5���Ivid� QN5LU�G:�"o�Q Eqn:I��N_{�}*�/N_{q} +s� �R.vwa,� P����%5 15 � �)sN9:�A[!-q, >_I� c�!Eu�. s*!�e-�iu��$K^{0}Eө (as 0.5*��}+N_%*M�Q�6�!Oe�") >���- E��"� � AX 7:���b)��<�ba�� successfuw�is sugge�"wrelev���1�� �ZH�) is �mer� ,geometrical,%�t!va�rola���A�� trongly a��"m]< hardt�e5�y! It!��!��ߜE�anomal��AE�c��ifJ�4�by.�Perhaps���� ��6�B�an $swsE� pair,I! via2�me* ism�b:�% R+s V% B�E\ing "F Yiel2���-eas��Eqn� ��Edv�+ Ygs� w~��!��'�} � u�v�3�a?r4��D� sui�A�}$2��7&d7Xv� &b ��.0� 3&;i�i� likaRUFL *�L isa��m*�� �!�e�V�S m4y�e�onJ��a��e�l$F�E�to�Ws��# b�Rnk)�!íFur��B"ʗK Y )�#e � J� mnd S� l, oØa phys��lyMM �<nt �#a� �� elop!"can��* b� hef 4w ��)^��! Mr ��(!A%�*�-�d��x(�� W��� �Q&�s�Ek, alrea��I�A ���e upcom�� Cu+Cu run� ��u�Pmap�"�� �rs��@ $\sim$�in5o�� �on��cri]"��eǮ!�$�K2� f2�on ɧG�> �{99������"$A.~Bialas,�3)2`��HA715} 95c, J.~Rafelq�!�0J.~Letessier,S�:A3� @,7c , V.~KochNm, 108c�'Q��� Tounȏ~Mischk� d K.~ &R�\565[i(} R.~Barth  et.��},�97)�..��*Ί 78} 4007O"� H.~ !&Cleymu !6�$-ex/011200.�?G.E.~ �� (NA576�))%V4)C�R/(. G 30 S71.�SV�~Heinz (�'2�))aIs���� , R.~Witt�0=r�, M.~Estienne�F��MP� P!aun-Mun��er��~HeppI$J.~Stachel)�9-� =�B46�1.t�� OEannikovaV��%�408021n'>����:&, �� .� .� .� .� .� .� .�g9� \t:) [What's I&�# A�&��F�-?]{�2 &.8? - An Overview�TR����-2.��-} T�-B�-�h�-art� , �-L272 Whitney Avenue, ®-&�"I �$a:$I��lP+ew ��7�o�6�-C""� nR�)Üv 6�+�� � tra!u>F�"�+lB*"o"Y`<,]�� ensuydynam�f�%i�edon ultra-� v���! ded.��.,�|+&� Motiv�y� arguA�j��>22: =�*2 e c'$Q�"D-Gluon Plasma (QGP�rB P � y s��� ߧfirst �%u 1982� Raf:m� Sig}� "r�$sAK� cx.�?+� �" ���+ gas�e .r �#a QGPhA.�M�!T�in-� )�!f��eiAQ�lu.Y'er��4)� d�a�*� ed m�be̖nik ao ;2u9�"�6 G -2�.a�2�MȱesholF�� e�5J.oise�%�&!�of a&O&W,� an@&t*)�a~6�� $\r��#K,x�0� ��5E�of� 53,x.��S%at�an �45s E$_{tS}$ <142 =M�5>9b�%� not -!��%*y) ��*!��*a"� ep9as ia �%l��%|v� t1B "0/M% �p�S�!ۉ�Averp2w=A��8L��I��.ga��e situ�^i� ifie+ �)C old,�q�E�.�2�w]2 to $� rvMeV�' twi��2� mY�(a �/E���>)A�us6C��,� m�"abundf!]upon (/i�!?��e.�.(�")�Q�� � ificE�~"��al�a��.�B �!E/b-��;��1��g!�i���� Fdom"���,cross-v%�gg2s" �mE�r��a�>Cs$>��1Lc�t)�,a3`aE�aHEEe�ly favoua9th3bO$�--rS*)st1i�in�is$.y!�)�1�EM9�s�t& e \a�8. ��hoʶ�0�di:�5AG���1�'-va+�today*\!�ZPi3UK.8�,�S�� �inv�g�/many e0� "Gto N3[�.�l ���;y��(V,Cone}� �3&�0e!� se��j3S*�26)�i�� pre-?3�!�is �Ga by�&��s,ϱw!n� Q$^{2}o�l"7}%g"O&��0 �tim� prob�t �p�;Y1!�Ljet phenomenology. MAHpX�es���en)�i�%�rea e!�i�-i roMbj=�>�k nt��d_Ces� it } a�topicR&�I's5o� �i n5%�(, I�/cQ$%Z \pT1:�*%: . i/We aim,a�)V stag��U,A̅+5e"�3)��eds�3�Q"�/ atMa.& to�53 �,e ��)�/okiAd�s�Can��nd cooli8 drop!��*_4�a3�Fs re-�áׁ�b� � �t�A�f&9 re-Y���Aw�� hici$ �[�$ f D%41"o6iumK�5fter �� < pas�� C!8�6&Y5. A,!o�@ine״.� c"��!�s`9� ios��frozen �7Fina kin�#�� |-�)sO<7)��!� %�fo�U{s�jend. A! I�Q!m� ,<eW- reamZ ctor�o��y f5"}7ona- *}[htbp] ���4 f5\*!/�r7c��S!�at�pw@�c�B� cour�<a&�9,�# �0-M:a�. See ��T�bs. �6(�1�* )z briefly�:�@2Se1 :tech}, v%us1 �ex*��Ac6�� 6niqe����!�BFo s���organ�E��a�8��%-n�X� �fA�n s1�E�B�5�}~7 �6�B�8nN �}��u���%* rapidU�Strm&2�/Q�moA����$i�B� �#%Gneui��s�%eda�m �to mid-Fa=5� yR )is9of�_.�is>/!�3 1 H)QCN; stry�;f�4, Q? 2?D�} �s�A���5=r�� !b��/�~F" at���2 � {TecQx} I=!  q&�A�� � (:WeakDecay}�As somEu� weak� !�M���Y��3 #eF�R nt�3ayg)�t. lifeA��?6�4j ���"X&!2ei��I6 al o�P| majo%j= nei��s a0 ``da�� er''���T e��A8�a �cm���*qa &_ 9�i-� ��- top� &� xcep!� <)ach� d�1�" ")oA�of$���ed�J er Am�]�8AʹveATk�ca�caa8�K�;}[hb]" b�!tabular}I�M�G�ß % �� \\:؟P�\c��({col1-col2}34} ..u6P-� & *�AV & D� E� � & LMN, (c$\tau$)\\����$ \pm}�M($uUG= bar{u}s$)RSmu^ (P+ $\nu_{\mu}$& 3.7 m UM5%& ($dD s}$+�dNpij5L -�2.7 cL���&(#�SK9K�5& 44.6 f 8"U/-udsp>j7.9.jX!6& $dss$�8G>848�%�$ss m.;�2.5 q.}Q2� QR &h#��eZ�vi.ing�tu�6tc;E ,�vq@�@ M��u�.�=(>��2Q.v6Tm�a@Re��� } OE�q��,F�� "� =in8$�I�ϻi�� �3 m~ �m lo"�dj%�]s�deD�ex<���Z TkU s us���  bG, \�Gk!�"� ' )Bveh# s, h�*aF��)1(R o�2I �is �"*J~ B&��ina���C#�s �loyhE`��e���� �' typɱ%�i����p2.2�C�-9� via:%``V0"�( ``Cascade"8D``Kink"%msUӯN9A5e �ur� Eu"�8�g}">� ,�/ P�0 �"z ���liny&wou;�.s �4U�@ve) io&� rail�(��~�a a ``vee"4$P@�he4m��$wo opposit&q�EV&arentL)�@(  no�+. :��P �mo5�g' 2 /� s!�) f��A�pr�). Allf�E�(�{n�)j ward�pri��& I�%�2�8orA�Ac�V��e%N� �to p! ��}�qg If sU(� wo 1Nre1n�� ed c�FdJ:L !� V0'')< �m�tum�Io5�s -e�1�g )�jwe�P cay ��,� x d&*VJUts' � 8� �0es�,&j?���'O2P�e6�)InvMass6 �1�  ���V�� %�A $_{xCetcE7� C+�.1R%�)R �f "�.͞P*�e�M_{�} = \�N(E_{1�.E_{2})� - p_{�},b� �O64 = (p�+[+ y1yB z z �kI� � racksz��rig��ee�A19��Bdes7Q-�>9*�4�'26���ctE\,2in�'9�re� o���.��� ubm�����e `qe��s6�֡�'':epeJ"6w es��a�icN Typ�lI�)� %s��au�� A�&, on�D�G�_�xps"�M�TB��2. 4�s{�a� 7&= XGe.� *F2��w3pEn�F �q �!(&���e�B7�"� ed �"C-�G� �9���� � A�6u.��O1y�ABrr�!8�a�F)� ��'"�4&I�+�I�,=E�&J8M'(6*�O J�F B0o2. A�"al>Z�(>��L�䭫A[��^#)���E�� -��In Z[��!�yQL50����Q� �9��Q�e�/oD3"@NKo��*] backg ,�4i,. 1>1� � Nby!�l� ��pg&T2 cu�� �!c. �S�?an�H!G uld�<���N�I(-� he�O+MB��A�D�r���t��S�-h� suchb"�&�9�Vo���OaA=&Vay2� I mOthaA?�� !F�i�&�!�l�S&�_�IM�.�:� �$ly removes� =��al�#�c�Ps1 �yB��m'�<�ob|H5M���cypNsg&f >�ow,_or���perL. Ntt�UseA� � �;]Oc4��at�rE�clean �s �5ho�5E"ge� plo�ToVDIEPs,F���6�A 2���f�:� S�;R}{�\Ww]� %!�2 F�he $=9,��=-90]{ �_LaTX_Auau62�"&���#>'ea��1"�s� � s= 62.��� � ��22 5 ���17F!B�R5V`I9@,]{XitoAntiXi=+&�S���Q(DT)=xi�<-= &�HJ=2v6? 5$)QMj Rf�'':� a��>Q ^�����+ 1 �B ble ��(!&� on,6� &�is �w"����'�C�Cn�!�s a3�" #�6 leav�a�m U���ch��Brs& �1'�ea���em�@�� �{��ex��� idert&T��J�"ud* o74 iC ir.�paths  �: �q�q.L!�e4��nd2�s-s�� ��8�B*� q"��rt � away�!<:��Y� j�#� eU�:� �pr>��'� )/POE)ris ��r� Rq!�/*I����y�D "�At"�!��9Y��%� u6-�e=I&mI;)�d)  �sudde��``kink''�Yo����is ^9ommybt*�t�K ��� �So�of*1  �pa��. Kine]� �(!to $� a7y �Rű,�by ��\\ fa�!qin a ~M window!] & L�_K��F>� � �8c7ly=�� 9}5Ts% �!�P�" 0@ an ad�=agedH �3�Yu6�Aa�as dE/dx�TOF�eYI�anE�ppl�>r$"#1[*�e 3 � "0C*3V�S!wc�ch%alway rep_A�y%m� �im�7"�^� rr!by T.�&I�Q�%�KatF?� }W�=Q:. B�6.Wig �&wiY�1udy�:iT��NA,V� ��d a��%� whol�K!P%A�h`]��{ins� G$��:��!���s�f� aYE 10%J�� .1,ar��rehend!? anyth�3�Mx� � \I�M�] gap, &�a'expU!��?2! �lOA� net--�M%�� Net-IE IF!�Mid-R�!MV6� BbarB}� w)�!�gp)��Zs ( p}/p$%� /"3 �1�I%�"{a*" a�a2�K�s~%})R\P� ���^DJ �� G at�� X�ar :C1c* PW<&��� � as` J� s v&� �X�ns��V�a trE&� � 2�%�� 0.8. &%�SqrtSpp*� � � -�/-U)��T�Kb�vs. �2� rB� �Ini�-�5z.+$�/1.6 TeV��^wia�E<$-1< \eta < 1$~\�){Phobos�6eP|%}#i6=\E�a�3&-NT*���a�g� c��0�;l!%� A��on��jin� � sl�0�.sp�>�,�al��E�C"s\�5Br �B.�B]��$ibG-"��-� D.%} :�E+Rap.!�2a! ��Ym r"|5m/e��i�T SPS-�Meure1UIt� �P�,��w�"&%.�shaC�Bev&[Z$BrahmsNetP(},�"tKEH on a��g?��.�1��y�}2 �^E�9pA�`f�QՅc:D_7�u- �ɕ:�(�4 n�elet-,opp�Fa^ Bb�A���1OE�*�.~%��� :�"C���%3aQ'L(���r�ѧ��զ9.� NA49�{J�E!uy�\��&Xi �$$5� E�q�sy&by {A`"�h��ͣ�>,aI,�qP�&�)RtT m�AWc�I% U�A��u�by�g �� ��G�h����Jk.9S�+�*��m fofeed-d �6�4i���ll2HpY;wry*� � !9 17.7�b.~%AB5�V � �6�f tE�a��4.� ��"FA,&�ST 4"� &m�^<ph!�-�jerXdnd�[ � ��a�`H�1Q"a f`gomH-m�-�5"l�M0���2� �J�& SS"{hV Se����[R�%iGB&[�O?6C �=[Bik!Q?�j*�Xr}-N:*� � �=cgr�3��=N�����-��5��@f"+z%vmK$^"*e i 2� �$)�&�a�*�]iӕ���� T stay��, Ke �Yof magn$��i�c)#a!�"@ �?u57B%�e ���sB�.� Kaon��io� ! A�2}/�!c�++�$ �,�Tr���, s}u$E�� u}s$?s ivelE/uI�P -}$/X�Z�ch �V2 =K�N�3�the dot��-( devi tmight be��Pifferent measurements9N ! M �B� .�A-��.}\label:� \endU1 \�{� 8F$ DeterminQ�e��6a�0particles emi�.��9�� can t�YHus a great amount a� sourceq�. A� m��ay�fd�iis�Su��a.1 hadronic� a2sub�S�)H)M�2 s} !C A vas�$of work ha� en da� impl�'-se nXs to aid our understand& of heavy-y5s. }discus�is���nd��c$haustive b o g an �� viewb!u most sali�(points. Fur`details%�,be obtained %�m&!$-aC re��ce�� erei��%+ Th�st!0ortant featurr��4y�e&���ndIdcaequilibr��s� ��E���$freeze-oute�y mak�C [��sM\how%! F arriv�uchMFe, or+ longexi���F'fashiJ They � \e"  a� s;of non-� acE4I�  r� a!`. Givn se W �!�� dens͇aEn q� , i, $mass m$_{i}mo��um p,�y E, ]B %�D ness S ,Q9 ed�� a Gr!�Cana{a�semble wA3 gA��spin deg��Dacy factor via Eqn� Eqn:U�}��equz ��:' N�$ = \frac{g,}{2 \pi^{2}}��4t_{0}^{\infty} *p, dp}{\exp[(E: -S � B  s}S<)/(T_{ch}\pm 1)]�l��nnoinda� a)�U�]� tempere> , T$X$, %�-U�V_ !}.�& � s}$e!E�erv%I lawD dnMb,2J�iso%� have���:F� In )�l!� �  us�� de�Ee�. ��a/1'd set by % �Km�"H ن� � ArA ria��� ]�via'7 )#=��1| 5V ��(ed until a �%mum�*x �son�c��is achie%ETo���� ��e�?6as t �5u � le must!�� �>� of ^a� [ atJR-o are s�|�yin�ousa�re�oN�%B5�. For in�c!^ti�toQ�-�qhighlyxtoM�B}$� virtua�+in��;%|O rse  tru� M� to p� y�!��)!�bel%�*b/ rt l�?% re may no%{ti� o fu�sa�at�e2Xc�. W!w.��ev. �� venlf stribu�tthrough+ �h7s لa�A� ughtAJa� �W ium,%G�.�G" :P1�Ew/ ��ultE[@ aA� �uat2� ��� �q . It�s� K a�r��of`i"is�#, excep�!sh���on� $A signific� � o��s  in� te�*&�  thusV is vit4 �yeD�mH� �5-�ssp�Fp={ ailur� 1D�irm�%>i��� )?�a�repancy2�Q��� 2�re)�=F able )K } �{ �ed after"[ .#du� re-s��}/orWg; �-&N ��. NeitN6Cor?�E� �.��WthT� ffec!ñ9��A0$als. See I�,Markert:HotQ�s} � se procees� more%�  !� I� is e�� 1M�fit] ��= 160�� m$ 5J < = 24 4&� 9.1.6 !�.� = 0.99 E 0.07�is�*>I�ͱ-Wa]a ery ����6 lete2�*`w� near zero� �.�� & s. Eq( 4successful fiti� �l�Af�:�:;�B2�� �  a�"�of��!+9 a�n u� limi@ .� reached ich364a{cri�9F}S 17s, red i�L$ce QCDa��sI�$LQCDTemp}.��i rpriz to���TB�s�!�toQ� (eJaA�s,K6�:w,� w� uld tM! qE+cau�+.b &�� tA�c=f "C �ba�meE!-�ll�� set.�&K �$�"an�t e average. Mrefor�t!`�vXE�do� �� � =�Su }� U  eapLag* multiplie�at� )L ��!�anyN �ht� ampled5E�se3s Ko� B phys� meana-if A��vidual A��th.� a ._ly7ep-�~�. WA�-T ne�$ establishCw�Uri�y,�any� oc1�`��a conside5n�V come impo � *zP�� SQ C2: } � -M% utilize >ZEQ>5� s, w�%fhpri�whP &b�s larAzI� >e Cach quan;!s)Lfb"Med onU� T� one ~thinkN�!�an F De�out�licitly� ing,��e�, matchFy]Ja� 30 s}$�rk�Ultimat]l2�E�~.�eatI�step, 9J>-��a���=p%eA8arily ``pick up %lack"�is�ds�a� teres!�� upon2�Bdu�.�sm��is, ��&��meb"�ex1�hi^n3 re��E %A mG avail �2���O %bl�}X�.� ĩ� s i) sup�!7of.g,F a !b�mIi<to Iw�9A%E=Onc volum�suffic_lyiGA�s2W� � ap����!���U� �!!peDit{q��xkE6e )�A�:�direc�pro��ion~ o $N_{aM!Al�k btechn���.�!:%�er u� o6� � ``enh] �'' B� ��+��#" >5�f edA��}" �%?p�ip� r�$�!��B&in $plor L�"$ nuclei� p$ ��UY)_%� "a%e{SI�.) �e{ haviour i,pec>8 I�,a�9��Redlich}��r� eI�� ��A.m�M��!)2lA�e� ;^���[�e�b{demone�� � a�6 m>~ de M��)8q�-"�`b2 ! "�F0�!!J)\�H!&4!9.)-�EI�;M���c�!5ngy25"E""�� E�}!] Pb+Pb9Ws��= 8.73:46��Q���N�)|�m�m.jK-d�(Jh.�(�r"� cz(B�Bpye!v �U�=]1![3 $Oeschler}..� �mr2�!-i"�#��>�8.Z NA57 �JYHyper8)��a2�* �cwos d�>o� 9U,!V:Na M� A�8!W  b)17.E�!���)�Wabo� M�Bruno}� 2o ]�6  e8( �'n�� � Q!2�q-3!� 6�iD1�5At�low1 ie�_ ��F'>� KAOS��a� SIS,��se�� �oca��2�Y ��kao�U�,v)(�.�. He, �0 �� �� ��isa2~dissipa!nd it�5�0 )n�)��� }m":amQ��+"�Z���:�)� ear�#be�� �.� b)6K������ of a&� aion�+$Q ��~�#�q Ep& .�� nco� sive�ww� seem** %H9top1�)5S `Q�S evidë́;applica&�(� �(E\"��  Փ� �]-���� m�re� ɫy�, (6.� a), �-,[-s *a ^Z�%p AvY-%&!�x& �!l� 8Um!�!�i��  gop�.stZ�%owV�c.� �9�x y. C&j,s�}!�2�� EPshE be m�O@er�-8.8��+��� !s!Ha2�*l�-lani1Eisa�). O�*+%L�%dZ)at0- ship"\*�/� # d� Q�r� . Ano�i}RWe1#an|<(��I*�H"�����( .&5"*��,he6o�$�a7�"{ �!Z�"<To tr�+A6 f�'insh �� turnQ{�,� 5 sFa STAR�~A"! [e�nV AdR�A:q�h��s�ZH�[�- �a �%]yN@� no!�%�!+ a plateau� !WSPS O"i�-e� Yerhap&�Yk%! �h�a) pop� ��&i��channel"x0�2� G� S},5_M. �nj�#�es un� !g�� ��ak�a����2� _�a��is>]�.T��*���A&�{�\�ps. So, o���� ��ledI����qo!= �F��s+ynh FM��$�Nee�*&.&�?�Jm�by#pped �t���t"glym��ity�?^?� !�6 fo �!w|/]c"m�a�Nod!J� %MrJ� &d EwY���Xi$"�s�!�%&�A��"@4Q���Y�k$= uncer�ty2$ �L �zV�"� ґTARi�J�"N��=H�� c2�#2p "A�&= ch�&Y$�A�#y�� "7 �#.x �� W]�f"�R� Tom!%��G/���j8� h!*"f�́/QE.� N���BB"�.� edE�Y!1I��]!�'al "cm�e"+4pr;�&I�� lik&]��@ ��� |�D � �phe������ mode� +� X.&�7"�  made �re.InV"�at.��!%(9"�"B�-�$v �����nctbwhils��ۭwm by � ��un O%D�9�param ,t*� 5�� .� �EgX.&�+CA-a$reDsl�:K6{ to �?:�]Q�a�)b*!)h�qu�$on "How diA >N0 E>?" remai�e(Microscopic&�"-:m aeM Vda !�l*.a**Fu*R,2�-*6#�B;# An ob%L me isN} �A$invok�1 part�/�/f?3*t O �1!>� �9a}H"R �:si$��deconf�2 _`! yei+en��firmed�͍� {Dynamics��4 Hav�16�eq��per.4I�aoU�*�%weB next e�esA��< ts d �[ rX�c%�$$\Delta t$"%tn=="e� fo 06 �Cone}�1�|at �&.$��the),. Ela� &^%s["le%^!�g!A��߭> E�y!�ongf&%k2�tra 8E*&6��%�:8td�<fis builtFdu�/| �%@M�I look�Plu��)ec�.moAZ, I�usO "� for Z�� whol/"��E�er5wa�' ).�typ 5�:�Z  Flowc#.3 (m$_{T}$ Sca�> } Bi��!��Y.�bLn|6 a�&< w�!rs�EokA�� ��� w5!a���9�( = $� { (p�O3+ m)}$) Q� araa��w� no r6��1@."�ai /�)P )�VNM$ iY/A�a#"�;�s)lEa phenA�E�:"T  ��Ox6� �'nBp jt���u�!1.Cll���/liea�aYa6al �?, ISR)�� T*�&B0.>E�m�r�D|& ru}.:ippQ��a1d��0�.A�3ousu���2./�A`%�"�!�I�!��AV� }[ tra � �noA+izm��8%�"�?}"NMs� �$te �M!�j ����o"5���* 3=!�&ap&��Bra doq} un-��*�)� eRat!�or"=>'*e-Ay R> aljz�*p�') ��[1[1 V8.�pp_mt_-'_noTOFs 9&�  "}>P*�I,-M!���s�* 1.�� ��A0�.a'65�I1ge� be<�4�Z3Yw1a� � '#2� )�in��>� �J� \vso&{-N1 ��6�F.�J5�R"��%Y�   J,E�"pb��udiCy�%�����,,�-w�6� AuAuSca ��� D%k� cl�O"�E$all�q�4"�,6/�r ��ush)�a�-{?�  veloc�cau�!a� le������� vp�� b��!J�! U9�U�2.5A4!�^�*�B!l.�E���Bc�B���,A�A��b��r��UJ�p��>��}�rD��2)�F�V'0.9.*,PTS�7%��D>�n��5� \pT1r)n�5$ [72�-�efaf#>T4"�H�bU w�� , |":7K$,� $p$i�.�I ?5��a�� $�C�C�� Star2 `n�.O Trani Rk Da�H�BIon C�,To ext�4"l*�L "�C��"��UI�*� we�fiG hydro"&�-spi  , known�-!``5k''� B1}�&�*}�s�ƕ�profilRll"� ��y.� kine� ly��*�r1�)�� �)�!� D�'in:�5�+co�~itY�9.TQ� �} B>"$0�!?E�^X = 8�31$2A| $"0.5$0.05 c �F��%R  �F-eper,�/�I hotb(*N=O�,d�/w�.�0!�"�j�alonez .q9�J"65a� m$ 4� >45 %0.1 c-�!�.�J%gR� p3�D&� >j ear}1th)G�gh! i?. >$� stag3'M2Gis1O�=?}�;�.Khad)�, �odto �fi2,value&�hp6A�A�R� "�d�y�Lq� i��J" 6e�; 5.X e��A�ch�,RGY5#P*�se 9Oeuple al�3an(-n/�EizeD*?� already c�ng �*.:=x�#� e�Eng!N�#d!�>� .7�!' b�:�$i.e.$+a�&�5� A slAD�i�O�&|�2���� e 6��*S��ԭ� Kolb�;dBQ8I) auth�>�&�$V/��a#.�2�Go�Q a&+2O��*��key�'Int Q;tr�!c H  5�A �}!�2�Ilso 3ath�;)�,s � Summ�!a�C"p�IC' I�� !ean<�5�!��2K�Xf�to*7A�!��'�ha89�UUa��m�� �MC�Cmes5�a��e�� [*k ( �e�� - 20�HE:� adisplays���!P"ion. �F$T&y.oTly�%�2s���: ��: )�por�(�L:6�Oy��CT'1ba#�  :me"�uӁc mi&�Q1�&b�L�"9A�"�+N��2IeO1�"���6� � "�RU1�� skQ!4is6�.'�1XLprobaba�> �!&�D:!0A9 h�. O�!s} a6�rAx�LW�isI���Ea8-�EQ�8?4m�c=�͜can#pro� pH6�N�NaeA�u� �6.)�le�;%SAXequen�U.> fterO��iAw0 %< �ic �s-����%:-- � ��  a* scenX,�v�*L B�e�2 bJ.ary. Wh�e�^ H���e val]Xy15"h�r�8bot;Gis meth�Und^ ull>�%� "�)7Ah�o�2m�%h� ��ze�*��m pre-5k� �YAl]< �s,aDbw�>�JM�) ��7�v$_{2}$�sxW,�9be �UA��NeA��%Q*�ich%��� yI��.e's���2�,�� dens �h &���O�;�A��de_?!�dom. ~"�M thebiblio�3y}{99"0bibitem{Raf:SɆ�Sig} J.~Rafelski (1982) Phys. Rep. {\bf 88} 331�MF�PhobosWhitePaper} B.B.~Back {\it et al.} (PHOBOS Coll"�)�0(-ex/0410022� � MeurPC.~ :P�T{N (2004) J. ��(G 30} S1325.��1�Adams:d$Nd31 Lett f$B567} 167�{-dD.~Elia:c#Ncj�9b�UPNetProton} I.~Bearden:iVZk1�v.�-�(93} 102301BsKR]�n5<R>n0} Bm!��V4Y.~Afansassiev:�%:� }8EY2050002;A�Bae4:?$1999) Nucl28A661} 45�NA%WI.G^g#:�aO97A�)gG,I3 23} 1865,bnW L.~Ahle:�N]9Q�>T 81} 2650 �8)�� �*e (C60} 044904�B"&W F�ca{i2�,eq12} S4} 024929�?$U A.~Bialas D36� F(A715} 95c, .��yJ.~LetX er,a�:A� @,7c , V.~Koch�f, 108c= Xu} Z.~Xu �^�92.�P�L$p atic�,O aFaO"� �H2bK!!� 2B6%.� B446} 326}�&�$ E.~Schned=nn,!� Sollfrank%�U- c6�E� C48}, 246.��a� HRD ppU�Fk7�k3�t:� �� docu9(} U9%% %%"�� `2 -6s.tex',#g!�+ � docpE ty. Ne origi�� Z�cre: &f.raw (Vop� s: `6s')w�H��yLaTeX clVYai�ac|-(C)�8,20001 Ameri��Institut�!BAWAqF%�M0]lbachv� r�`6erved � $Id:2�,v 1.11�"@4/10/31 08:06:14 IExp $? %�tP[ae�*o1Ahe�(�5- code)Gyou.�satisf�-�y]Ll�5 is+cT#%!ing!J�-*!!trj* helpMc2>[-",a�blemsG�H %\input{aipcheck}�'@SELECT THE LAYOUT!mE�eM-�o�S�5Mq��,aipguide.pdfEo�]!�� \qiE�[G,�% u�Ia+ncamera�4R � f ne�Mar�J ] !�jO!�D\layoutstyle{6x9} 28o�D�}(FRONTMATTER�<q%1��title{I`3�%a�on[of�-%D\\a" eus�<'UE'�L{25.75.Nq} \keywords%W {�P8 Gluon Plasma,  6, �JR�-�c%c�{D. F�l�� �"�0}{ %address={�,( f\"ur Kern0k, Jo�70 Wolfgang Goe!U+' it\"f %ǥZan( am Main, G�-,y\\E-mail: f� @ikf.uni-�.3.de} %!3 � %O 0R"%�] {\�F D.~ �0$^{9}$,C.~Alt  T.~A�)ic$^{21�_S,atar$^{8}$,Dcrna$^{%j Bartk#V61 L� tevU,10Ht ({\l}\-kowsk?1�sBillmeiec C.~BlumS �oim.8M.~Botj$��(racinik$^{3vR amm�une�D P.~Bun\v{c}i\'{c}) �V.~CernyL-0Christakoglou!!UO.~Chval�5�.J�C<2�17&(P.~Csat\'{of!:( N.~Darmeno!+1!] A.~� <DinkelakR�V Eckardt�P Z.~Fodou8Fo%j�Freund1V.~Fries!D# J.~G\'{a}AD8 M.~Ga\'zdzicki) �8G.~Georgopoulos1 E.~G!�adysz$^M4K.~Grebieszkow,%�S� gyWm, C.~H\"{o}hn�1%�=Kadij!aI�A. Ea�A Klieman!! S.~KniegI V.I�lesnik%^!qA�Kollegg5\�Korna�I�R;ru �Mwa��`ra%%N$rep5�0M.~van~LeeuweE�AAYL\'{e}vaL% L.~Lit�EaLungwit!V� !�Makari) �A�Malakh>aP� er!� Mate: B.W.~Maye�1�G.L lkumML A A�A.$^]itrovsI3�J.~MolnE_<�8S.~Mr\'owczy\'n 0%b G.~P-le[/4A.D.~Panagiotou� yo=2�Petridi�E�M.~Pik��%�Lnska�� Fu "{u}hlhofEE�i�Reie=%Bq e�pe��A.~Ri9&!. Rolaeu�a82 M. RybBMybmv6���Sandovaa���nAONr mI(i$P.~Seybothu�F.~SiklEw5�B��%� krzypcza�Ti�G;efane)�! Stoc��tre�belAT.~Susu�a2Szentp�ter!�%�� ziklu( T.A.~Train��)�Vubq��A VarggL M.~V�liU3 Ga(VerE�4,1�(Vesztergombq��2 Vran�"%gA.~WetzlE#ܡ~W��odarczy! ! I.K.~Yoo!|�MJ.~Zar-@;imE�n�.(���(dR�"�F\"{ �T}$NIKHEF, Amsterdam, N�rA�s. \\)2}$De�� of,&�y AtheyBGreece. E(3}$Comenius7, B�*8slava, Slovakia 3<4}$KFKI Research*� Pd-cl� N�Nar�Budapejo Hung� �T5}$MIT, Cambridge, USA 6}$� 3BV Cracow, Pe� 6,7}$Gesellsch~ f�<(r Schwerion�!4schung (GSI), ��stadt"� M8}$Joint:��1 $, Dubna, Rl[129}$Fachb�jch) k der9s\"{a}t,&r >� tGne%��pI ��'"� %�Houston, TX.Za2[X,\'Swi{\,e}to�gHska Academy, Kielce:o����Marburg�r�f�44}$Max-Planck-�5��k, MunX� >5:'v� Char�918, Prague, Czech�ublic`6bqPusan N al6S,La� KoreQ�*QE� cs L� ory>�W0lng%�(Seattle, WA2� 8}$AtomicP�&, Sofia� St. Kl�h Ohridski ' , Bulgari� �s 1���Stu}C, Warsa>���68Ex�>��al�F� KVSH1}$Rudjer Boskovic c, Zc30b, Croatia. }"(abs�,} |&� �(�j6$BLp �420, 30, 40, 80�-158 AGeV�4>�6a�J). �Bme�)&\-{mof Rh�$gM midr�x=;�$�^lyw(�t#�gy �$�#e�xC �) 6NS# AGS,�teep i�M:&�yy�:�. C*xvp+p2-sy�No:!�!<omfp(� �U"Y -�!��� �"]Ai-re&M7!_�<Rixp�?_�IiU)h-�K>y�;_!XQA:N&�:wer6��++l,for Xho�+d� n�.mat�+i{F>�>.g1Y� \�p�A�s�on{Int�B!c} A�-pI!&9k& �!2!z init9=f��':�;�ap�%�*\ enough�#�"�3q�?�&w"�"!��eo:FQv8H�:2bk}�8Gyulassy 4zy}. OnFI=hand,!I7�B�max�m"TVI is pO&�%&�Y�D+&։O)�i�r>A�]sA�proga"�m�'eDA �m� cove�0�:�XSP�QaaF!�AA� goale�Lli�$�q�&"�`*bC!�&g5�n!�F}# conn=a$ ���7S6 ),M:dauNx. �*> cour&1zA�-05WrI +F� �� "Q%�A�r�7�1d:u�`F=81�setupAf�u7I��!asev:�!i_=II�folloyQ�0 �6?sed%ed�u)`&s>be1*�@ed,�)!1m�D focu�'e?w�narE�<&/s��7:�of-�@��E�y�uacES �> e Ma2tpe�6 } A�?in�t w�w��EY =BAB] B8,height=5cm]{)�4�7 "�7M�QRI��R�R� Orm�oA� icat�ga9D� h:�K.} Kk{(fig:engdep}�� � �AGSI�wXH�4)J�[K)U�)��� I�*�0V�E�bev^�s�Ry��I/eak�*.$ x3!-a�kdF ^Q^ �.� *t �6�2edt F+gn�-� J��^GaK�_8vd}. �%useE�e3x!Z" -E&�s"1>�y�u�- �� Ad�-b�,e�%�70�~1/I �&-Ehyp�sis�� �� �� �4.� , &� JyM�I��9ter�zn2 . v6PzY�r{2*>[j4.9� 6� >K<�J2,8 ,�=vL&( �  1w!�&�\A�W ��6H . LinA9� a>dra�3o �%�eye (lef�x nel).\newR b� n!#sv4�xt�6�.�  (Y" p a!gl���>�to�`�/p�gyRasE/� of F9�'IL�. $F \iYR={\�t{�}$�r;�82 ! m�ve �� �0Q�B���e�"� m��5G5A�ng�&b "� ��a����R grows��n�~�^ visibl��A��a%�%\�envmS��pY _ .�; a�� &; �K!Y�de>S/ E3�ZO ate�30��brj" � 3: �HF�of9�.�9�45ti�{!~I�]�!�${� \rm K^+ � } / �}+ $, >6-^6-Z6LwZ64 e�m� a� �Ainf��S@ � i� �2Ai��5"�f �z+#��I�WhV3.�%O�d���os3 continuo�Qi�I>, �9kct"�=ryfA$ ..amZ e���/>���. H�5 gasm8�+�$9st} (HGM)_m*R%�4WeberH2pk} (RQMD, UrQMD) |7��3h�end�B��ewD!K3prono�Wd peaIO� �,%g!���@��Q � demo"h��3�6Aalso abs)4inJA [b.UFv+0&+7����sF�;,.D��,֦�.:��!e�A��%�CB1 �@eI�"'7�T['" ��ff%A�)��� �~�F�a�$$E_S = (2(6�� + Z).6.) /6pi��$. As@�0��2e ) Y�"��� !�J�f��:i��x?� d>R� . O a-�Z=  (SMES)�luuN ar� "" exh�6� �Aa-S�.e�& S�>! Out�R} B����b, b!A��Z�ThB�AL&��tU t� �_�6 2& ~�Q��. �R V_Fd.9pxt "�Tto�*= rSs�t�es�ۡ�n�y vari�qAt y � @sXt�;q�a��F�? Fuԉ<qo" % pde�X�ansS�Eis�i�}:�~�B�Dram?b�;YtI�G4� 3aa"theac"H ledg�sAJis�,@�-�*!.US�ar"�!h IaPt DE-FG03-97ER41020/A�/OB�js5]�!,ium fur Bild� und Fo� "),�OPoyv96e Com,��ScMrific R�!(2 P03B *�23, SPB/0\/P-03/Dz 446/2002-2004, /04123) s�!ianRbFa�b ,n (T032648,  293 43514) �J"1�ceG, OTKA�g034707 < �-�2/a�!�]��)� (KRF�43-070-C00015).oN�.bj7<2� U.~W@)inz�4M.~Jacob, %``E,=/#a newO"!:DAas�4A���=X %!��6d�NM�,me,'' arXiv:F -th/�9d042. %%CITATION = NUCL-TH  ;%% �0c_`>E "�6B�*s��(cLerran�New�m QCD �oT���}J�405013^� �% �>%�BS?;S2T5 [�2�=]���ac��t�detector�N=;\� 4rum.\ Meth.\ A?5 430}, 210�8B�,IMA,A430,210��B�%��%�8M.~I.~Gorenstei)�:pnlR�/� Acta�!.\a�on.\ B � �705 � , %[Iy@hep-ph/9803462], �6��6� K.~A�- gaev)o& !�v3Rof  ��"#e.R�` in %v�{#.\<7��>(20�9 175.>�0303041]:�HEP-PH �%�M�>� 9�BJ.^j9%��F���K�@��r a9 1-A-�"to�5 !� ��<\ C)��<(`) 054908�!E�L9903063>��M .�2}�6H�)ber�-�0 ratk�, aya, W.~C**�Mnd�*\"ocker%%ic2� �SIS�_� i�AnyO|g+ # %*9 ?b"7}Q01 >F"0209079^" %"Q6�9$:J. �1>&�:, � -SPSC��38��SC-EOI-0��end��2���d"X9 ��% *crŀf�aps�X9 ! %*3�#�a 3��APS- REV�84��"�H.EVer�4.0a� *, AugE 2001 n Copy�(c)� &*9A�eSociet�9a+<� Z 4 README� �mar��]mQp*�R.� TeX'A���"H� you�E AMS-�9 2.0 �8 ed %� �%�Z_preOsitJMor�.0n� %�8�E�HrunBibTeX Rand�Ka� @ s:a 1) �:x.�!C2) bibt3^/4V>^8Daps,prc,twocolumn,� 4pacs,amsmath,pint�f,groupede-,su >cript  ]{revtex4g*ǚ��t� ,Fњ%:�8Ɛ2nqTclass[����am�L % Some�$(s Sal oue�B+) &�`iesB�l,ap6Z�!��9�>pr�%yvReC�B .q5g% Ij�eBs2,dI }% Align %�Ium^"��cimal p�-2; bm}% boldc h2� row}2hhFn8n�Use  11B {IntRd�2 PRC,�� 2.3/11-30��4�'({$K(892)^*$� ʊP�,�A�Y��$�Ly �&s\\,&� � }qT�^; }%2ce[=breaks��10 \affiln� {Arg�%&� .t, @, Illinois 60439}6C&8-�� Bern+12 *�.v9i�gh�%. 4United Kingdom:CBrookhaB]"D.�Upt�.v ,York 11973} 2$California� itZ?T��@ology, Pasadena, .91125:M6 -,!keley6C 4720�CDavis6@ 5616�@ Los AngelwK� 9009>��nf�Mumbain<a �, Bloo)-ed ]a 47408Z�H de Recherches Suba�0�, OEsbourg, !ce:{�Jammu,  18�V�K�"B, ,, Ohio 44242:� Lawrm'Bei�Va6�J��( achusetts2� .iC&�40MA 02139-4307:�Z3um-F3>@ichig�Sn2East L&(*�) 48824:�Moscow E�keer M��, &  5:BC���eC,��, # �� 10031:FNF'7�&+7:�%�F�Ct busQ 3210::Panjab21CD.igarh�014V�2)F|Y��$k, 2016802:�� of2�-�, �N vino�6:APur�!z, W (Lafayette, y�907:?8� Rajasthana�ipur 30ED:<R�A,*�6$exas 77251:{/ dade�I$Sao Paulo,. Brazil}n�e\&���Chi�70Anhui 230027, :�Sha�iY�?Ap�d9�'20��ZL0UBATECH, Nantᚍ�6�) A\&M28q�Vp6�$H Cyclo�, CentԐ4Kolkata 700064M�:�36�!�.q !, 2::>63Vu7"�7 981BG Wayne%�6fDetroit,.a20>�2�>wL, CCNU (HZNU), WuhanI0791�6� Yal6��nH= , C $cticut 065z� U7  HR-A 2"g7� �DJ.:T}2u 6Z.� . F� �]4{M.M.~Aggarwal6Y�� PZMRammed6M„�� .�monett6Y}J�}� �B.D.~An��on�LJrkhipki:K>c*L f� �G.Cv�Lhev6��p VS�? Bady>�6@v KYGi6��9 @J@lewsk:E�� QOQranAa6���Ij�<�UrL!�Barnby6S62.f. ^r�udo:���ᐎ� ��)S�H6��� LV.VNlag:N��Hellwi>�� 4��5�!Ierger6�6�r �B.I�zverkhn:�Yf� b�7���!�haradwajn�B� 6� Q�h��nN��A� hat:���Ve'M:,�N9K chse:�6�&+, &�?"@ @29sK6<�}L.C.~B=D6Q�G G�C.�� lyth6W6�.g. ^sB.(V�:��= i&�L6���A�oucham6Dn� |A��Ƭ>k�<ED9q� rava:��!)y�$sk:L:�*� Ί)R!Cadma:vVp N� WX.Z:$S�� '6� U�H[ne:� �kMNlde[Kn~de~la�,ca~S\'anchez6p�jD �}llo6Q��25�5 D.~C�6a6&saG� �Q!�hajec>p � �7N:"�ch� !�FR�Ohaloupk:���N�8S.~Chattopadhya:R�Z Z H.Fae:=6q�� 6�5�Y�`.� Los f]VA� heng6(�ei�a?herne:["q]#,Zq�A�ikani>����"hrF-:y��J.A�off>Q� � TUCormi>q�p*dS6�6�& � H.AErawfor:�6X.�"� F�Da:��e�S.�UJUde Mour:�1�'iMA�ODerevschzS6�Q]�.0l�6lu[L-U denk:}� TWetvs �I SA�Dog^L3�� WA�Do>�1� I.��7X.�V��Jm Dra�hj�.��>�F.~Du6N�M� Dub>�Y��U�rI�V�iDun>F�+J\ Dunlop6���M.R!H$tta Mazumd>� ���V.�X6��e)_W�Edward:P�s *s $L.G.~Efimo:���! melian>T� J.~Ex!ag: f���ppl>�  B.~Erazmu:���$M.~Estienn:��;P.~$RF�2o�-JWivr:��(�RXtem:W� Fedoris���� K.~FilimoB��s}s!�ili:��? N? E�nc:R�@C]i>��kY� syak��2�!�omF- ��a:��n C! Gagliard:LƜ�+L�^ illav� .2. ^>%_an:��?M-G�K6��z�z�udiche:|�BF�_urt:���$V.~GhazikhJ�f��� P^os:��7%7� Gonzal>#��Oaach>�Qebenyu:+��D�osnic:E&O!a ,vf!iy� Gu��rE.� ��Y.~Gu:� �AAMptZ�R �� TCGutierr�7�� T� HallB��aA.~HaB� �GDO rdtk: �*J.Weri:��x~N;6v6�~p.I�T�enr:,�e� �6�2�'�%6y#Udh�':F-�'"@(B.~Hippolyt:��� � Aci[>:�urz(^~ E.~Hjor:��c]cG%�offFt=Uof�&b�&IH,Hua��B� S.L.�Y�E% ugh>���*�%&""�0���0Uw��umanic6ҝ!G.~Ig:6��,�hA.~Ishi� 6�6Ze�z P�?:���]�W!�J�?:d�FL@ni:�.c:� !F H.~J!�nJʤP�JoB56�.� . ^� EVud�2�j abanrM�qK�j>X�x �ja4�6�:�3!("� z�3u�D.~Kea>�(J�V�(,V.Yu.~Khodyr>�'Ѣ�8J.~Kiryl>7 fJ12�+nJ1���lisi>Bi =R�AEF Kisl>< �Kl><����S�Kle> �ccDw KoeBy � T�mn66U��ac opytB"A�� L�tchend:D�?�rNu6�3"0of�-YorR=3�/3W1i P.~Kravts>���oRX��RrueB:)$�/$C.~Kuh:]��/�oKulFI� ��um>�ү( R.Kh�tu>��.BKuzneFP��M.AXLamon:V �UJ��Landgraf6Q��S.Xv���FKu:� ���aur>j�VA.~Lebed>J�WRWd�:��K!� ehoc>�%�RM�LeVB9�� C.~L:k6��:QF^�UYFL�� GG:���S%�d nbau:�+�2�2�� ~Lis:��a�i:��z0 >�6�5 N�5"� �v�]^]Q)d:_6�W"�.��%Z!W:Q� 5 T.~Ljubic>����# Llop:��� H.~L�2$F2$R�Xac>��M� pez-Norie>m3� W^Lov:I�����TnTudl>0��D.~Lyn: �TG�M:�"�.2e>�<�/�)>\6 �3Y�>V�� �D?{gehd6� Ҹ{ ahaj>5,6��D�+Lpat>�(9�� ��&R�j>��[L.KOngoB���� nwei��2$�%� rget>���C�rke>��IU/F:���J.N�x6��*�H�!MaB-�ccYu��MatulF�"Y�Z�BjT,C�McC�s6!�T%c�l:��V0F� issn>R/�d6d ~Mel+ 6 �`.�e/{B!+�VMŊilB���"�N�:ina>��� x�>&� !V��6�� "��ish�%�%�i�l:�:�� B<� hant:���#�#�EolnB��C=5Moo> 6��7D�� oroz>�rME� unhoZ� ��1BA4N3�6x�%��ANaB)6HJr�K�T �BJ���NelB7C6�.t. ^�P�etrak�(J(VAVNik��6�>��C L.V.~Noga>U+�SH1NurusB�C�W G.~Odynie:{ �8�8A.~Ogaw: �l V.~Okorok>�RM.~OldensQ6�=DeB&�aa�-P>�E��e�Yl�{<ts>���S. XitB%G�#PavRU:�2�T!wl>�.��P eitzFe%�� V.~PR8oz^�B�HC^ki>�-6�.~�S3WVy:k�I��P�K:���S Phat>��qR P�~T�~Rc�ch: fJ�+ċl= >r6T@LJHL*JK Plut:��N.~Poril:� �S JQt>� 6��A�Poskanz>Y����!�otekh>���E!t�.a�:��B.V.K�Potukuch:� 6t�~ �� rind>6J����runea:���Acutӝ6v�9�Rik, Munich, Germany} \author{G.~Rakness}\affiliation{Pennsylvania State University,  Park, 2016802dRdniwala6eUnR� of Rajasthan, Jaipur 302004, IndiaPS�P:POPvel6�\SUBATECH, Nantes, France�R.L:y686�4Texas, Austin,  7871= S.VHzin6J�Laboratory for High Energy (JINR), Dubna, Russia}5�,D.~Reichhold6TPurdue=�<, West Lafayette-nna 47907�J.A,ei:Q6�LWashington, Seattle, 98195TRnault6��|F�tiere6:HLawrence Berkeley NE�al 9O,D, California 94720�$A.~Ridiger6c�Moscow Engineering Physics Institute, M &R:�H%Fitt>V���,J.B.~Roberts6�Ric6� Hous%�E� 772519O.A�$ogachevski:�9Q��Je:omero6�6N9�, Davis6� 5616�!�os:WayneJ�TDetroit, Michigan 4820�C!B:����ua:�6�SciE�,\& Technolog��LChina, Anhui 230027, �R.~Saho:5Uv �GM�L, Bhubaneswar 751005m�PIPkrejd:���]�Sdlu:EYal6�dNew Haven, Connecticut 065.�JMndweis:��QMQrso>��sna 9�, Bloom��!47408:Rv>�Particle1���~�P.%Azh>T�~$~Schambachn�z�R.P Nrenberg6P�nNV mitz6R(Max-Planck-Q� f\"ur)[kj�KSwe��j�A�eB1 Creighton2NLOmaha, Nebraska 6817]I!Weybot:��,E.~Shahaliev6V�La@ha:�y5 of��W�:`��rj�Q, Pasade�R. 9112* �rm:�Panjab2���}�mirB� ^nelling:]$NIKHEF, AmA�Ldam, The Netherlands��oo:& $Valparaiso2W�w 6383O�orens>Z�F]F��owia6���іQpel>�q�` de Recherches Subatomiquf(Strasbourg,BrH.�� pink:�Arg5 V� , I!� ois 604399d,B.~Srivastav:Y��$A.~Stadnik6T��T.D��tanislau:�YM2�bdA�toc:�9��\�kfurt)� BP�olpovsk:? � !�trikhaB��!�t�fellow6���A uaid:� 1S dadea$Sao Paulo,. Brazil}"���ugarbak>6 OhioJ� $Columbus, ! 4321*�C.~Sui>:Brookh� VFUp)� York 1197��!�umber:ANuclea� .#� AS CR, 250 68 \v{R}e\v{z}/Prague, Czech Republic9!�urr>�,Massachusett*�A�. Cambridg�$A 02139-43.�T.J�i ymon:e�v�va+zantoA Toled:� �.�1zarwa:�Warsaw�> ! , Po��9nA.~Ta:�tF&b (, Los Angel�� 900.�JUkah06y[�$A.HRn:� ��TA rnowB�� D.~The>���>�hom>�L��&�,S.~Timoshenk:��vM.~Tokar�� &� T.A�raino:f6i��! rentalangZ���R� Tribbl:[v A\&M}� lleg�i_ ( 7784��O.Ars��N� Uler:��T.~Ullri>���D^UnderwB�  V� f# $A.~Urkinba��Y�$G.~Van Bur>� �,M.~van Leeuw>[L�"�"A�%Va!o Mol>jM[St>?Easnsing2�824�yR! B�� 6P.�Mumbai� MI �sil�6t�A1VXBV� ���� erne:S3�B S�x Vigd>+)W��Y� Viyog:T�..S.~Voka:�L�S�' Volo�6� VznuzdB�$(W.T.~Waggon>� �MFN> �GNO KentJ�� 4242y�RF*2 Q�e?.���XbWB�6�YN6`�zARGT�hu:�eijm100084B#Z����r�H�r:���J.WIts>�A+�B J.C.~Webb6���RMll:8 BF�vcG� Y fal:���A�tzl>����!Wh�n Jr.6^6�y��� AGiem>'���SEbissin:��it:�6 $Bern, 3012 Switze�� J.~WB� 6I�SV:�6T�� N.~X:^��=�ZF^�� Z.JT�=$E.~Yamamot:�=P.~Yepe:���"$V.I.~YurevBi �G Y#ZanG :�U H.~Z*6k�W�JW�hZ� JI�T]T,R.~Zoulkarne>b� Y2W:��X� Zub��� \coll� {) STAR�_ }\no*�)p \date{\today}% It is always , , .(% but any B� may be explicitly specified \begin{abstract}J�tshort-lived $K(892)^{*}$ reson")@ provides an effi�$t toolFto"b(perties�the ho�d d�-medium1|duced in relativistic heavy-ion !F@isions. We report D asurementj$K ��in $\sqrt{s_{_{NN}}}$ = 200 GeV Au+AuB and $p+p$f� reconstructed via its hadronic decay channels !�900} \r"a� K\pi$ f5S\pm2%�$K_S^0\pi^{$ u* %;SA7@detector at RHIC.%��0}$ mas �0has been stud� as a funcA� of $p_T$!",minimum bias-and�c�al)(=v}$ JAZtra*( SDWintera�A;d,%�\�diffe�B �iEHarAWesented.�(/K$ yield r*s]all2?PinFuWfoundA�0be significana6lower �,%�a inN �.�Y� , indicat� aimA�a�*ofUKI2 betw!�chemical!� kinea4freeze-outs. A.�Inon-zeroY�p:(low ($v_2$)�Tobsera�JLacompare%�$E�M� \Lambda$ U)�nAmod%HEwfaE�A~m�at ��E$p_{T}$�$similar toI that :$_{S}^{0}$,��U- from ��(is establis�aJbaryon-m�ρ�$ect over ae@i)�pa�'pr���FJ�LT$ ($2 < p_T \leq 4$�h(/$c$). \end�p4\pacs{25.75.Dw( -q, 13 $Cs}% PACS,%v�#%�As�"omy�b% ClassiA�� SAODe. %\keywords{Suggv$d }%Use�wkeys cC opAif'vz8 %display desir�o0maketitle \s�)on{Int5UH} Lattice QCD calcu��ons~\cite{blum} predict a phase transition %���ma�-a�\quark gluon plasma (QGP)!�8high temperatur�� d/orŦ�w . M Pusuch ext�t cond�s can�>�uMC���/by�d��� e.i� very ye0ie�iR.H� I�$ ollider (� �vQ A�鸙� of �i�i a�proto��t�>eray�\� upa�n^a�8e initial stageG thes!4l��14 described���g�penet�pŵ)0 withe��-�[t=F y. W+;.& ofa��-�system,6ylo�� %,mal equilibr� E 6p reQ/d%KwQGP form. As  3exp_%,Hcools down, it willQ�ze" a��ly� . Af!�a period�u.�,.y �s�FY-� when�E Ps stopTngm�rapp1,2,song}�� ^ ٷ,%v1-s�4-stream toward ��s� re our me*� �per!Ued. � typ! lifetimEqa*� G  few fm��(, which is ���'to� expe� .M�2� �h �� eP:� 5)0felski}. In aL  M,�s�in clos� oxim�E�oA� � gly.�1�q�-�`um��a �� ���yAg��AU� I����y variou. * � ,�*as�>2!widths,g eve�d �[lin�wape1-bra AV$4,shuryak}��#m. ofr��� AXail%�A;� about�}0 dynam�#b� �I-� biel�7�3}.�8.� * focus} byxFOCUS6�0- � ��charm} s�  !�):Q could��ch�d��1ef�� �v ce i$an $s$-wav�} possi+Ex T1(ces. Distor �NX9�A8 $\rho^0$ ~% also� ~ � !h� ŅeripheN� -Brho1}. D)�al ��e#�sK%unding @apYZ,blR7 er2}� te5 � Ucsc ��!Onel�$longacre},�space d9!Rz4pbm1,kolb,bron�8,barz,pratt,gra-, !,Bose-EinsteiA�re�*, 6�`FL�\ 5�%ane< !;ap� nti�� �" ��m� . R�.�!�Np� cEa�qe.Pbe 6w aE�M�wo� eK M�a_�u�5 at d�before�y�c0 �nota 6�59to�!re=��� daug�.ٹ��thi�^se� lost c�� �j-?-Z5J��relevan$pends o F��M�6�Fas �i� siz �m> Y� ribu� 9(�s'�Tic.g cross-� s, etc. O ��(Z1, a��=�,, pseudo-ela���m�m/q�0} amon��MY ͕�incre h#M popO �Aiݮ rego E� d6t2�Q �ng  �M�c��� D(5SA1nя an"tbe:%� evol%�}-�� " �M=YT deF� on �6��fiP;� . I!�,is paper, we ��&� }$ v�Y�a .= 4w ! e kaon��aUh�$K^*$ 561b)qi:~.Jq can 1� �Q���I@�ir!���a� i�inl��2in��he �- k�totali mM�^ }| w �b>} larger (=$\sim$5)!�)IZ�I� 6����%��>AKer��la]}8���E�� &:�-q�1�q,Iw� =y�!�!}m�� )2%�rimordj /b a sup�w7.Z:.!�"� in&� *� !/is � e� �m���[vZ �el�ary*�&% �, �&z{ be us S0roughly estimC�]�C sp��PDue�Pth�y 1=q���� �2low�T$%}�� (less likely^Ypeey�i� ���>'.�� �!k*�1��  al!  }$(vers(ass ($m_T$)"�f �$���-� >� pi:Z �����)� manifes�in��Y�s. wellaa�coalescZ> t )yR�,<  ~ "C YOs,1�>H ��t��*� m�A�10����4lin}. However,� U$ � z8�beg �[.� ��discusA�p�ouslym�./��o �� K �EJ"�� co�HnaJ !�AIiS����" T��a.� 6^ �atE� 2".{\!E 3��i*� �s.kfireb��B�at late �� A��� E q�duI�to�Trinsic� � reve� tQHE�me) is�c�ar-�cz �ߡJ)/-�i��bO " $\pi$, $K� p$, "�s!%k��&M, as �%H� 0���s%]2�&))Git .� %y�� ���ɀrI 2� 6u�, identk�oI�� ARLv�ow� at�� .follow�simple}lzm�n�6�itu�%�� Qs:S4(p_T) = nv_2^q/n)$, whe$n$!>�ZA3�FZ ~ ZA� �^q>common:��H�le �m�u�T��IDT$6�Iq�� iz�Ash�)22sc),lawIw$n=2$. є:[" a4hX  $�6Y � �c �cao7 ��� $n=4��nonaka a��z!^*$ Q n.� M�egl Z':.:� ��[�����!zJ  �2Eeg@ l. �",inconclusive���I�c�VE��Z ���"lis� to am�:�ri/y�a�� >oWe � uGhe un�=Ab��M�)@�8i�Kguish؂�($R_{AA}$ or CP�defC ��r1�text (S V.F.)%�i:� pt}6���ively�%o.1��E1  A!% or9�I��(i.e.�/�: ). S@$c� !A< t��!<$K�^*� nd�����a ��qge val� ����in group��(Y)!YM�� vsM,�2@QQ(%�2 asU�-s� "�Ex���} d B� e��A nalysis w�P take%sO$d�#< run (2001-2002).�#i4(oidal Track� �# ($)��A�$a�5*O� ��1ary�ck�QdE)e!�a j��!i�OajI� dH� TPC)"K a 4.2 m( 0 cylinder covPMa�rapid �O,|\eta| < 1.8��!�9Ak4lete azimuthal U,age ($\Delta0�%\pi$)m( tpc}�%9=/,�$.% trigq�m� by r�� oinc��cee%Y�u#degree� ori%� ich A�J�`E/$e beam dir)Q-�theta <# mra. �%�a�ta&neu "$� �cspo���10$\%e�!�inx�-".�! 1 u�� �HBb�A�th�intil�!ngB�ba���Iqouter U?��TPC \)���g*3 Ř}mid`Uj(Ye$ 0.5)��io� >M3� )N A!�- [�at �B� multip�)Jfor 2���3.3 $ < u=$$ 5.0). O�gtsi@!�m�o"tex))pm$50 cm]* AT�!8%xe��l���sel."n�) unyQm accep�&M�$a�$m�� d!�ult, � 2 $\�vs$A�^6$M�\%UHE�, B* 2� &A�6BT2*E&)5>��R�% or��to��%=ral���o��M��z�LY� -��2����)tdi�#3+to�(r1ity bin]!o%� mos�#  ��f&�4: 0-10\%, 10-3 30-5!w!B 50-8acc-�`Ef�� A%q��\ rea2�(�Z &��}) r �A>�)&. �,4figure}[htp] \I��\i� ,degraphics[h�M=13pc,� D=18pc]{dedx2005.ep�Hcap& {(Color�(ine) $dE/dxɕneg�,&�p. ")� �9%a;Jc);e curv?%4B0 -Bloc�$ametri� �� pdg}�*�� �9&}\label!:dEdx}(-,�ad�&A�*fI���� ����or5��se ) ��th\io� 5 gy4D)]))t :(a5 !� a .�,Ag�($p�*sT,in Fig.~\ref�) � "B}%sk+V-g.�t.��Q��-� lded�U�e"2 al� o�s� ��!� t5C��!� Chdl� &Kbe.mw�&i`� a�'�R 0.75 Ge�*� l� 'a�anti-�b]M�6W1.1�*6quSte.�'%Q*�INIxW$LN_{\sigma\pi}$ (e.g.) )�"� as %�0equ} %2>=\��${log\left(Ev_{\z {Mrd}}/\C le %!\� le_\pi�/)} {R}, mdeq:NS�} %�+B�N�1}{R}\��tF�}{�!�R�:��;_:�"�1mm�a�a( + ) I�DA�7'me2�* I I�/sI�a givenu�,E�$RR �Si>A�chE#�g� 6\%;���D��a[�ral A6 �A,�C �I�acter�cm�) � , �+a� e*  � h��a 0! �^ TPCI�2�  3@!W�%nstz2 y K!�7({wa�Y� �:R. S� "� cuts�zi�dr)Yt�)�Ron �e�%: �" :� U%`�!�F�c|S�4%h��s &�5Sa ions}"� �)V5> %�&� 'Lr��3^+\pi^- over��{"�30}}.� K^-/+-(�3.) #1+V %U� d� !��� term {�'stŚAO� 0}$ B�*M��.B*$N?� =`�$, un�wi0I9b+��t��*} ") � tab:AV }Lis�%�Ii�a]!�%�Q � 1[a9�al 9&� e �}!�ud  a�&� . $!&Length�a l, $dcaDa�% s$ �� a�of�+st 'roach"�!�d= LV0PrmVxn !i!�m�^J*9&"�2�- �Q� �G%� �Pos�>� v�po1d5�grand�B�vec�8!VNegb{vyp ly �{ $M_{e��< ��4ine�$ �4^2$, $NFitPnts!�%+&fit poiXof��AA��$NTpcHi> @�,^:MaxZwmax�7�) z�A $DCA�r|Uri2E�.}�,ruledtabular{c} \m�Lrow{2}{22pt}{Cuts} & c�Qnc}{��0}$} &`4 >F#��}\\ & /� & q�;"I9&!�{:6\\ \h������v0& (-2.0, 2.0)B&2D > $(7\\?��-O3O3NO2k @.� < $ 1. ` K4'$p$ (� �0.2�_C 0.7�c�� H cm\\ P�$p)JS A6OR}!�/N`B�6`D)Rd2 �^2$):548,1)9ҕ & $>$ 15V ��{+}$:y��15�\\�S/u� R0.5TB = \-J\XEa��K_ 9!�8o��p>)�0.2�a=�S(cmAa$<$A�[F B�p!N�i� Pair (s$) $ya�24}�&|y|A� 0.5}1�� �~� :�}9� � �����2short�"\1���)em| orig)$�N.u�0,?յ�B�" * ose ��N��o� than 3���� � Such�d.w i� as ``d� s"�� ):first9goe��4)S�R� a.�%aLI��in.9ele�-�{��5�/.�, c6�� �*ak5oiE� A8$c\tau$/.67 c�$wo op�*pt&Q DE:%:R�6# a�s��Q[2u1�If-�� sampl!vnd--9.V2H� mir �tox y^$-�I�bZb.'$|"� K}�2ra loosut.(�1| < 3$E��W� ��!I.�to izHsuR0&�2`"9.e ��}$w ai�ambigue(-��� B� s if.�yi4��m� beyo-� um p�Cearlier&@)Ds,6$el~; 6.3re�&( back/nm"� avoiI)*�dr�99`+ �?�Y%ly Ad�.tEY5#o�' 6b.:�>>�)D h%�(eFS15.m (&� "�.P ){6, 1 4.F)A,as���,X4qu� � good"��+|. FCll%1%��%� M22�� 6.D @�� �&�5�Fse=$ be grea���5#!�r ing split pna#int!�.on�U�n1 �͸�M�r$�0 u"E x,In � &~, enough6!E;avail�4F ecis&-�%u�mass,@:#&� �/��6�X� was6an issue��5" �a�=�i�$p<0.7"�' �Ex to e� cl�6"�;is Tu���a�ed��=#mWI YmisMed47${*ir�� thu�4��,a�Cuncer!�ty"zc!5�aӁ� I��X2$�)F�/c�zas �"h9�) ��&�%FaOh2OerY1 byM�A��:$\pi,K}|<2$A"��a�idual2�All�I� �{ bothb� �El same�3A+�#�j*jkZ 2FlO��al&�,"1pi�Y� a- �:2E?�W����#ho�H�.6kB�A� e dashed �Eict#Gaqn��fupHplu rar re\!��ݹ.�)7� f� �1�eڍ:d�inN�*� e>'*�MY�."X A�:V �r�%�a�EYr9$�"3 5����i.�(!E�2|A�a���>t)�$* was �&�R$r)�,l�Gt=mA6� ^� %� e�  globali�s (�edo��(necessarily9/U�"� 5�� )��aeb��;Ft>M C�5� f���>.�>� h&;m���$�X. OB� ��)^�pahG�&�@"4)�i�?c- r_A_�QA.2�beZs@n���A��6s �.be at l� 2�a��"� �exӹ�O7b�or0�1�.�:m~ um �/.�i Pq��B.;i1�<�6�V itV �+}-�6~� 0.48%S 0.51s^{2}$ɧqJ. W� vS^A"Y �!�*� 6eto.+Gq��X m�a�k<ck��c , double-coun���=�th) = . 6�!�M}fw�5v� ���� e����&p6�OE Ֆ�#� abovE)?�{�+r/B 7 M(! ^2$ (F m^�.]�A?�"vh7Th-�S��\mpF����a�6i>�mixW}� $open circl�� unc=-�� � :f2hder�U�T�@nne��*eLom �YQ 5i0.��f�d�@to�E�D��1/wU!1J�*A5 1/10B ��I &whelm/ c2�&6�BSCb�nd subA�� "sF:9�Jg !2wo#s:ite�} \ �R!�d-%� techa4:*+�� .built���/�.�]� � B &G(ys;�Yz�6FEdmMD�<�sF|.�! ize}� R*�Vuc fuaй�"@#e�of�gn� 61Q,��%&�#$ in�%�f7B(3 =p3X"� tar130w5��:A>�bTVaGe\phi1,phi�<Ta�5���M j&�4���6�V�Q �P�re/sBt�E`'���|P-0%- �e Y6�&�X.��ȩ��{CL(770)^02i%�S 6�9�Y *���-�� A] �rsL \sub�&Mixed-E�� �eG8�0"y�s%=un}ϥA9Y}� �qn���5�y}s,L.Q�>Qutru�1e�i�s $ c=� keep�e���.8)as �(as"�"% >�� wholXta�ple~2�010 bimnqL&��  cp1��101��e/qT^��U :�2"�5.>3=��gR%jBwjex� ^�C &� �04:�0%�_�20B�0V>�2(T symbols\9�h�Ȇ� af�no.U�0 (solid�0)I�F*O.} W(fig&��Q"I�r}6r�e&� ,B +}_1�D{-}_1�/d  $M)�sd� � %&d�X@�)7 E�!C��eI�.Vq��BC"�i$ ��i�) )if; b�fo�<�BHi 7A<��cripts 1�$� rrW8ME{�� $i\neq$1� &�+s eIQ�� c�Y�2be 5, sI4a�)CK.Cntr�-i�2@n%��6K10�!u�F� vf6 EA!�a� �� uS �m(1� nee�8�q< �N2=� �2�W.2�"�:Q�2:2�1.12^2$(,"���ݡF�2� ���u1 f�]!x? ga�;%vn#6�2���><.����{2}Z ���6�a���} %T;E�A 1��2:�23 Q24i..M.�!K!6�$v� 26a!@D"� eqnarray}�2.(m)=N_�.�O+ �^!\noi�\\ -R�98\sum_{i=2}^{6}[ :1: -}_i:JR.R $+}��6<��], �,eq%�d_qRion�4� 3N"+ �U ]za�� �1B2�?Af� $m�F&�22� i$>D}��if��� 'UfIs vis�W�@e�mihe� �� 6�m &� Like-�.� ��'a&� 3nd� /�#M��*�!h�L�J�a2V mTr�2��hiP.j .�F� h6@��&�^by �=!]:b.ws"3 �2� $K^+� M&K^--��R��9x.�M�:��!��.�a�i�a��e�q�V �Y-V�.7�J�i� gKr0��0"� �y6b� �}�LjBh$E��E�c�Q��n se�2R�bF2�i�� Ax �9R��8d' texty�}�=2���h:�!�% #CK:�}.V�� �M��M�Mq���y9Tn&sO:�T��) cqE!�A��y2��n1')�*0)� !�uG!r����!-Z�.����R��6���A�R�2�i/6 A s�K~$@a�bp,AIri���Cis now �� . C:�h.( Շ>ihe�ad\[agvc .PAX!GIɔGt�G���de � �� -ucMf"�ce"B;.��J�2"��S �ii A$-c���J�&��4 ��6�v�'"'al��(&c c6r2l q,�Mc!MZatm+�.��.��i�d�nl!���%cs HB6:}�'er <,�("K� haib�T*lN��G8EJ2�YL�JBE�}Qǩ�J�2KE+B�[�:�re�&.��h!r� peakX =y.���P. iFUi�Yaila�V"�: �Z��*�!����r�ei�R�2z Ɨj �j��"�.Da=�!�R1�B"�-JL.���)�2�J�!�Tf'J & :Pz� c��%Mn��]�}?removA�3# . .��e�6e�ruIi a�Requ\G,y-� �  nt(!}u.� �.U#bq 9%.�v�q�.a�Qcom&t#d��a:m�""\ �� ���q �J~q��ed�-lQ7%:J$t6K,*R�j lappA�3P��n��Wan ѳ�X-�plane �bicu�o%�HJ(axis. Each Fe� `�Q�jE� YangleEw*N6bx>3!�b��t% d"FxJ�^J�!D:� �GA�a�!�(sF*u��_]jn� � BuA�c�V�>ad�6aJ �ontU�._-�F�>�Q��r.�O q=io�H gaudichetZ��0���P�kJ�xn�.*� 2�� �Z<��nEfpN�&x lli& s�U�veit b.:��f.�.(=, j# ��Z :Z "9-#F�:�6 :�=�6�. �itude����.6be�]*�~���M�v5$of 2 smalloZ� }'.=QV il� �T��B� ��aO�� m_i�u&bBN�M�(� in�1i$U�&�R anis��p�7\b�ye��L>4��Z� �~s-��! -mix�'X.�Ri "�W* Z9w���t"&"h) �'�=�<"=�> �>�!�o�� fil�9iK� , 0.B$90.7�!:#2\E \8{SŊq ) deb��r%O) ou6m!OZRF*�!A�� tr6r�nV(�Zed�'by2_3A�� 20iri?P da�zY!� ndarfz %of 896.1&2+o M2�19�>6 �%"� "u)J�",*{��%�&-IF)� %�@1��U�1 (D)�- �>A5&���.�5P{7 (C). A 8M t�/kA1�Gei [a�M \8��X�4,!�e�Uo�Je0|s/J beAf�. Elec VE�pKr�M�+�U��K � O!rA��J plot�w^:�\P!#g'&_ k'�6s)!s�OI "�)��#^{0}\&�I\&�4wLph|MI�GK�I %;Q p$#-uU�pfal`8"�7� �>"A�;���paEW*�;�iclB QV i>:�*��sf.VN �O�  jC�#1�+� .Z��rem��w#arѺNhUz~R�z n !/J�:" ��.8 i7.�V�y�2��A�% a"%�s*�.�Ba! �*Q � real-�!])�ia��N2�3y��yIa�w�t} � but����7ed5<. >� :��z�Jh&~7�!5V�D"�a� of 6%:���)&� !�i�e�a*�R=<c� �[`r(�'�?Vt#\omega�&et�1�7L�6� �\C;aus�5�� B=pp0� V�.[�S N�i�MH=U ���F|as�wer��^� �"�Z $KyN$�;%va߅�)mo��6 t|o��rS'�Lr�B�um��:��Ie�1�non��$v.<�*�<�,Q�n.� s�P5?mwihFMQ�}6* �C�:�1ř{M�=2�X reA�no�t1t2A�� s�Pz^ �3)�A��]< . "h1Af�ults} &~uM�(W7y} Purp2�N^ alAuAupp}*"�;.�Yǵs7%�:�.�s�3_{(}$):;gr�^"��1$$>e6�(up�panel)-$2� �+(d� ).s7)�io5�FAtKfo<"f&�!BW � PS + RBG.�U fit-=� ;�BW"0"2^$p$#y Breit-WigD1N �� upc}V�= �U1f4 \Gamma M_0}{(0^2-M_0^2)^2 +^2 )^�x� eq:b�w�B�$PS�Boltzman"�% �J9x�xN�PSB�}{\p� + p_T^2HS�] \exp\}W- �f3{T_{fo} )*�phase-�mB��I�\u�OAo. .�. $RBG5 :�>J�,RBG = a + b �.t&�MY=�"�o N! WitS:� par.�[, $) �.�}at� N��c��em�d-�A}�OM*�XIvQ� _0Ek4}9�4}qH%�[ )�6�� A�KE�-4M  ME�0 Z( (�/]^{3/2}=�ga!5���&� � end�j�8I�a�v�\!R0!Z�ډ[I�@% !a T,�� {2#<�f::nf�m H �M� M_K$�� �z22:*.2(�����13*�anjA|2��5j�j%{z�i"�,&i.=f�'to Eq^eq6�: ui= 120����=�f2u 6�" .A6FA0.6A$p+�R-�XZU! � `C��ʼn�&�^�X�.{* 2}2mBQ�5�"�2C�s}�b�;!mE�W E�s"9y�$K�3.����a]"$a�B�5�ma.2|2�=q90�<mez[at�h��\pt*�t!zF6c'w�� �a�� e"&� �rdIZ"vZ!tnd� �;��)ı��!r@_!� A'�s�f*2�A��HՄ)e:�Q/� PS1�, U�*�c-�� .Q�B�N&�6to=0% �a6HW"z��1.5�/$c�.�>��e�Id .duZ cho#�B��A;iH*#,�D 3�i� a8-�Qm �"al I l-beA�iniJ }�A��p��!k:�4"-�}f..\+( 0.y2*1FD%8pA�=a��X=A��b=�6��eFi-ir"n9�I�so4 $D :*t.��6t2������>�&I�V8: �G ��z�!��Z`a#,i W�#%?"^O��w� e�?0 $\chi^2/ndf$a2X�va�5�?0.,1.7����9ex$l�� (3.8 aG2.0�~2.4"�OBAC 2.6.*4 *8*RAB�-�w�M>!{j&7O���!'j�  valum<v0EA�t��gWFi6�Y8O 7 �'^21l6 A6�q�J�6�s���yQ)x.�c�B3q!*�u% G%U�by�d Fng4���:B)M�x��^MDtheSAt ��:'E step)�6M��!�^�>f6A��<���ls��T�7!�@ }9�Q Cs�*rA�MC�T!3B %IMT~mkH��:�:M�W��>, ��)�Tex !eN aY>0..~~u"$���"r�c2�t&�k�� $6SS�h�h�FSn F~V l%�yig�MurI�%+a��!�T#9z *S!:/!�a� suff�� xplaU A� s$gma$ level�.�mAW!�%K �ktra} �0 �0 20 qyJSBWF5s�6S*7�+2;n2Z�>�R�-M_0)^2+� ^2/4.;sr %�j*E*C�*}ō&T� N+" se��v�Dto �� luct���iraw� fS@( f�'��A�Eo�Qћ� .�+�[es "� f D6� =� | ���� $BW$"� � 7�1.8��" � sn aqm$3.0�� the R Hb 02~ �$2�� 2.8$"�bi" �� �N�2�! 9=by!("�7bmaqb%f2�2�)i!  �%�efit�"�.c�h�6� T A�Q^ �D"�%R�t ,$"�T�{�X 6�2<qto20:4�+�.[yU.�s�9*� uppwJ &� Fe � �Y� ^}؏��6� ��֬+B�2�b�tV9�:_2� *�%E�%�ͣ!FD*�J�4A�^D&t�i]�(VDV�*�.e Z�� N�6����\6�a�n2�>*Ab�6�|10$6C $, 2.6o 5.2)4$&�o%4*7Tl[�Mu/)|,q`um ��)���F�}8��"QWle �2�4 ��4��gy (6oQ0����)�E�C� I̽��o.�3� O�]���t�Y3(&Q� �l�~�eu cy (��:P#�|@�n��2aZ+�"|W��y Eonsk� GEANT�hminus���)'branch �GMI���<�o�O!l &:a;%=�%c2�} !M f�n���cw 86\%�@B�}9Qb=^{R96�_H �Mu %!��Y.~W>fIhin6x)3A&zm�w�U��y2��>`�.� P`��6�%��mid4Y $()+\w"B�@ )/2$�^9� �iC, fou.�~ �2gev�  ��)U:���0�6�* dndyM� �+}+�-Z�q��V�8� 6�:ei�@'?is| ��& %# [$d^2N/(��0 m_Tdydm_T)$]6��Z� aunM{"4� J �#1}{_} t}{ l�|d}:4(T(m_0+T)} "�I \\*�% R8-(m_T-m_0)}{T}\�/).K'*�M�& %�$dN/dyr#e?����))%�|�o_�G$��-o Õslope& ����R�i caZ>&H �li}�T$Z&�[YCb {���l"�2�!.D� &u�^�� �B�':K(s,�� b� J�)�>.gUPs ��"� T"�q��&�������A�r*�21^��1� >��4�+B��j"y���/Z�=I~in.��U���� L�}of�.,iEUg�;ly�Ct�R�>�F8:<&aZ@B�{*>(}}$)/2!ari�.e��:�k�M�a�<|55!� � )�)y'5Ei)/�I.E �&2� ��=)7:�wK�r clari3kAN��U �2..� serror�]Ca quadd c sum!�.�Ac*(�N,Ԁ)} �.�B!��p"�%��t}1:܆2,�`;�q4B���!��x 01�-~)v�{�� .��w)R�%X AalB� o^=F^�z=�@�z } &��&�4 (MeVx�v�v>K &Q818$� 0.46 1.8iw427 046�Q 0]� G4 G 1.451 1.94 & 42 3147G��D & 5.8 �0.5 1.0� �23 D9D׉& 2.8 i0.2 � 0.52� � ��1 &�$2i0.0 �0.4y40 1444�i�6& (5.0 n0.1~0.61$).# {-2})x2 � 0��w%� ^x)or`��1*��� law}:tf*� ��:~&Dt< h�#pro�^���jSve'�{�%��of]� 1M3 low�a.us��se�:��ua� �-�sD�n~��:� 5Ber� &8A�0N�y�, &���:�]"�9�'p  7"�!,�-��"�f�\o �I�&��4�>q�C0 � ��$��u&�� V����".2RV% mm8J�."� ,� V ^� �B� }� �.�9.A� �e 50"?.R2Y4pT*�" Q 0>�0}\ � #�t �J� �:aA�e2�&I�is ����* ZYҢ) p_B) "a+ �32 (n-1)82)}{\pi (n-3)^2 2�FQ \+) le^2BK �21+I i�>8S/2[ ^{-n2�Q��B^ n"Z [� ) a�a�$\lBz"�0aveP�.?=m-��_� %�ql >!�u� +�+d"|�!"�+%�t �%� (0.0�eq%W &p*�0.2 $\2!4�3)!@�� X"%!G:� m#��MK 6i. F2�y6�&is 0.93 �U�A�6�a`��v��ir8A�N/ 2@&"�>trapodW�y.W#"%�3�%�b� scri��-A�*�!��cҺ�4:�1J�JrU0 > 1..0S=K.~-levy1} s��s[�� Levy"�!^E 4�eq:=}�Al�G�Eb�)�La�i�"LZ#2!�4nT(nT+m_0(n-2)F_2\=7073^2}j}{n"j�2�Sev� � � I~-d*�+!'^�%Q�: !��*�=��90!SA��U���l{�yd)l;.��_�&�)Z) �“{r_xl_�2Fc(6֓!,:$6]r {C �N���� #�� sN�I�|y�R����"�I2� e�(��y�B)#a 6�!exH`�;% �J4��Ia������ u��s��.����&� 75:��.2�=]��B-eY)�>�. E�p&�� ..�pT���:�=A�hTü=M�h��F�Th>�Ň)�mk��=E�c� s $>$85\%&m�m��2�ci�V>�8s�J�)� "d~y.�Zby*m&67"� ($��"�&W>�� e��n��* behaviΗv�_��.6� I�7$>� ��4\int^\infty_0 ��e^{-(V� )/T}�8&\}FB�@}.k ח�`ea�؆&�;FIL.d !�#%'�'-�-^� pT}M=��98�=� Rc �H)�e��� 7"��� sN+)�� ��"i�+2���{6��� ]/e0�_"� � ��41*Ve� �^=�Ajv J> ~$J6�N ,<�=c> 6��U�N� �=$ �m�,"�b!�f��+.1.^ �-= 1tt�q�� N:l"�oE4*�@it� e(aH�4Lb2� ���7r��1�� K^*$2� � ���"��{A0.Fm7�bdma�&����F�-�B�{T}k�~ �.�i2�)IW� �kk&��{ciR�(�)\"t.Fu&~|�0.0�0.12 S.f6.7..&M,1�.�3Z&5,O0/.X&,�06���G�8 0.14 �����w֑&B A�JT M��@V� � �E$$dN_{ch}/d�I%p&e��khs���Maz.�0Gw}J��[�Z):i� �n�&I�E�b� sum _ .� �R�>�!@> �=����&�<�cU(:`)�zb�"6��c��?,���sGpt4 zDh J�>��|QUj ��"j7�j4N#> . No:Y�y )�g\: � ��i�gQ�A����*!��* 0PLR>6s}Q*:S�Ag�B_%"�%jyA��5 $x��8��q�SKE_x"%P�6�Ng �iy-� Dg�'��t6�NMve ori^�4i5ir �spi=R!+/��@�����#�2 �!C/� �@o���'poA�ial" � �K^EV�Uc JB� �:� EH5I�^A�i6 �C o9�\9bDa�ֈB.eW�r��F�.1R�(� tM=b�!.�%h c.m.������B��1Tax�:�u�c� %s"��u{ 130�Ik�n13��nd&�yn6;H. 2/b]Er�j @$e$^+$e$�mv ���f�45b MJalb}, 29 der�K91Dabe,pei}, $\bar{p}[�t�2�k _5.0C Jcan J$p-"�{ �(27.5 GeV \cPite{agu}, 52.5 GeV \c(dri} and 63 �ake}. The errors at $\sqrt{s_{NN}}$= 130 :200;�correspond to the quadratic sum of (statisticalysystem& m0.}\label{fig:?4o_energy} \endure} �<$K^{*}/K$ yield 08s as a functionz c.m. o R<& 0.16$\pm$0.01 2 \\ O10 P& 0.23!*560L12152\ 10-3 ]\4*2 \u7 142n� 30-5\�\6C58 S�3n\ 50-8r\ �5�111 \Ji) !3F,>^g9215H6r tQi6|i{ Ta��yt listse�I�^-�{fyN�6u�� �"� }�Ds �@J�-$! phi2o, $\rho^0/\pi rho1}.F < $dN_{ch}/d\eta$�,z�All2TH have been normalizU %^& �.��Y��N)��atK�B��� indica8 by -olid �L� JJ }. As ��?!3 exA��al�s�*0.1�02�Dch successfully re)�er�M�Wa�$Z�A�J�}&� fT }[htp� e>�ing \includegraphics[height=13pc,width=18pc]{�� 2005.eps}&� � �2Ua�6�)�F� >��Tip2 F�\!=\!*�>� �� ڵ� &�6�E1Z�% �� B�. Both2�!<&w $ uncertain� ���F<N5!�ralityAM"4�r�\aE*��%Ev inR\ suggeV �eS$6Hande�~����.�ta�RBK^{*0B�a� dominant �A-2�!htherefor�FX chan�  \leftraarrow ��$i�in bal!Eg a�ultz2 can��us@ estimat ��,between chem"@ kinec,freeze-outs:�equ/\} \frac{K^*}{K}|_{\text{ <}}=V i }} \�Ds e^{-\Delta t/\taS�eq:$Mq{w!N $-%!!�!C$2�4 fm/$c�  $c1%�Z1 �%� �.. If we!JnN` .QM�MFa �one��}9q�usm mos" �g"��� ��!0�$� atJ�EZn unde assumr�X at i) allM%}s͍ bI�-L .� re l�^f e� %ii� ere's no6X '����e� shor c]= 2�c m$ 1M<.�� above .reduc)�qY.h� "  valuea�a� limitA/��0it&i� conflict*Qi�  ($>$6 � ) inF�eAHwo.�s toge���5S t.� e ��2�)y , Dhappen even (aboutuw) afterN�6subseE�{Ellip�qHAnisotropy $v_2$} In-�_B�)�e@flow (;,) is definedqA�nDharmonic coefficie��ɫFourier� an�!�<$azimuthal � distribu)�in moN um space-�art� �$ ܱ�c� �Jg,v_2=\langle �ccos}[2(^ ,-\Psi_r)] \r#,�;v2b9ph�Z���K� 6�Ot� note actual r��pla����$ � �,`�L e average�J�U�ll Aat$For each $� pairIR|was}�by��M �($�2$)���urn:determECby us� ��4primary tracks�%1kaJ p* Whe �=�narra�!S2�31}{2} �H\tan^{-1} \nonumber�,(�cD\sum_{i}^{} \omega\sin(2!�_i) - KK)�/\pi)} Vi 8{i}\cosQ:K6P.P\�),Ke��� �Y�w& � %�%G�^ optimiz��eI-ρ�le�I�f cripts $K pi$ nd_!�6�candid( !�,Vp��F��istv�? auto��"Wa@M�>^� _{A�}$ �-U �i>Q��Ohaibin�x .x v2_nv � �R (filled!;rs)�U6$p_T$`2>B^ �)��@$K_S^0$ (open tri�s)�kLambda  cir_)�  ch'd hadron ? diamonds) �!�"s s�*b only2� �8� ��r�Ilunlike-��� mixed-%� Ma� inva��Bss:G�r stru� $Z�2)]$ bi�Fn)�. A�~A��( backgroundaA���e ah�k�%�g ��� � ` then obP��6,vg� give�)��'�N^2�� ��iE��� `finitea�E��%�i� E��� *� � ed ��T�A!A�G ��ion�aK �� d5WY�O � 5]�\�� �fur REk!ya� �. f�($<1$) ��method�s�����>�a`a� �Q= �ZV>4 �4�#R���.�a& �KsLav2�.! non-zero� W@is observed. Neve!Oless,2��6] on�:�*� , no2��c> w:h� ��AtJ*�n:>5.��or� oU��g *� t�� *L �eiEY,direct quark(#��F�:follow^ a%-�dong}� �fie 6<*S �$v_2(p_T,n)W an}{1+�Jexp}[- 4/n-b)/c]}-dn, &x$v2_scaling^E aA~bcd$���ta�$ex��by�t�o-���!�$��%� data poiD"� % E� $n�� �4� am� ��nA�!����itu� %� s. F�'%W5���,, $n=3\pm 2$!� �w. *eI��V6�,� A�icultA?identif^>H ]�s ERIK �2A ($n=� orN`4$). A� 15-20.s m�A6G'�� s we� aken!�!"$er��  fo�F RHIC ru�' 2004M  ; �Lvide enough sensitiv6!��preciseu}�Tn$ to J6-!�"}� meaism:q(Nuclear Mod&e F��})Y6bin� �, ($N_{� $) a#ed*�x ($R_{CP#i�����!L"C&� de&7�& s� ad%(y>��$is clos�rel�M�n �m.���,R_{AA}$). Ref��sry���R <��$A���F���/e� medi` I reg*4($2 < p_T < 4$+�)d �#N��2�'smalle�' unit�  -� �d t�hig jets�A�*+ thrE�gluon ra�� tr� !)dense m.. It h�'ls� �;w�M4A36��8�%e'R  wm)!P >��Ge%>yisJI�wh�t� s��b�`�a m� or aY� &8 ��M�Hbu � B%]�)A�Q�� baryon+Pu�=�U�K^*]y�elp inG cri��f�U�us6�� the F#2� I�."-*yW� ��a�!~$atra� top (&A�&#%��O�>�% e� !�a�y: eZ{&.xhj6-nA�e2�A6 V�B�Q�����!)#*I�r�U�IinB>.a&^-�F��]z < 1.6�[ Y.(!�v�$�he )-Z;*�"sAk low ��j62Y!a<weaker�B > 2�sia�i � �r� ��^�ly to����fireball�� bleicher0)a�, X�$ p�a �� babi u m�d2��% Ea�M�E?F��ArWth�wC Yond.,� 9�*�,~:G��a1إ.�'�T NT�nsuppora��a ��-m� �=� favo ���&F��9�,��� 5B� a2n� =�&��1b  ���^ >n\6{w!��enE8.� ��3dashe�'5"�sA[  ofJ � ing D�!") grey baG&QP^h ��  (%G��B(8�a�mr'� "� 2�raa� M \s�on{Co�"� } ReN�c"^%wY\pm1'so� 2�Q-�."� ) 3d���J &�#? J�)=H �� p)�k"#�]�8 al� 6Hviai( ic� $ nel"� \%s.� �! ��m%{ , midrapidity�!QBR5J� �"�to be6� !A*$?)m�Q!� b�pre���acon� Ax�crossIKq A �ic phas�&���6 a,�"J� �*.'(�"2<"�%`!�.k�LM�c-�9* B�i5�b<"?�/\%.�#!Dys �?2?�,E.V. Shuryak2PLett. T8T 2980R1.Rs� C. S�0!EV. Koch2L � 55}, 3026�7). %�Hpark} D. Park, Intr���Quantum��Xory (McGraw-Hill Inc.),� 9e�3 19742? felski} J!B f� �64!S54907F(brown} G. B %M. Rho2=N%� 2720%2N!�45�, �.I!A)�72!D254�32�)�}2��� Q 6R17!�22FRbielich%.(Schaffner-B ^�8!.326I0.��3��J. WambaA1 Adv. � �{a�JMfocus�M. LinkR�)wB J535}, 43�68J. AdamsRJe� O�9W8 0923mh4.�j2}A Bx�8H. St\"{o}cker,u)�G X30}, S11 �2Vlongacre!B S. L ,�(-th/0303068]�pbm1} PA�$aun-Munzin�6 priv�commun8ion.� kolb;Fa�lb� M. Prakas6�q(AI04490NLron} W�oniowsk�y8ay349-2�barz} H.SarzR�)�-�26!�219Fxpratt} S�tF,Xu!�)�E��64905 �e2�granet!; ��et:�e� U �140}, 38�78.�QK06KND2�5EI8IG2�N7��mZ7popescuRT�DI�!�127 �2��7 M.J. M� on�P9}, 1872!�72��1Ry@6�J1EG ��)85�992^QJ�a�Xichelin, hep-ph/0201123}I lin} Z.-W�me C.Mab� 2023m6�henixPRC!�AxAd�6�Bx 6Ta09��25�Ѯ� 05�2Qnonaka}��N ~� 6 �1�2O�ptOz�Iɥ!F %FJ�tpcE!A�0FriiIy' m. Meth. �H49�6A-206��� 7}, A40�_2�8pdg} K. HagiwarjHmj#010�8�2<k�0z�)C�_5951��2�l�)1zN� S5�.�:��HC�Q�� �61901(R)�& %+�>Zhang.8 ���S57� 2�phi����!-04>�&� hi2xR-�� �inm�)>B�� ex/0406002d%�2E+Adcoxfp N:��v!�99s�= } L. Gaud��tb<4�UA rho2��FachiniZD !446 �2F�Ph�zLthesis, Yale Univers7#A�2�g�>�6H$SUBATECH, �I2�u�.��>[27�![Um<�o, �'192� becaR&i} F. BVr0� 336�2� hmin �� .���12V�KJlaw�Sjostr� 6�Compu4�� ics =unC1| 238�2,levy1} G Wil� ,Z. Wlodarczy^� h 227�2h blastwave � nednE� Sollfrank&$U. Heinz, �.�� 4� 2E�1992Oa HO6brech>� Z� J61!��92�der��Derrick:U �)���15�5� 82abe�=beRH���c59\ 52�c10 \g�M Y. Pei,B�7Ezf 6.� �MaCa!6 �.�2� 102J7� ��Pm $Aguilar-Be�>� >c5Q405%e2c�P$D. Drijard:�>H!29~82G�N T. Akes^o �-�203}, 27�8a��X�% �� EI��2�~DJ� N�2W51AW4f 1); J�a �-.( A. Poskanz�nd� Volosh[ )EmE�167i2� + X. DW��9��32�^e`R>� �4 docu } �U\(class[12pt]��D^^=160mm �@237mm�ptlength{\voffset}{-20mm} \odd�" margin -5C80>D \usepackage{epsf}.[dvips]^phicx�bAM��(er}Qser�&` TENSOR $A_{yy}$ AND VECT ylALYZING POWERS OF THE $(d,p) D Dd)$ REACTIONS AT 5�/cR,178 MR \footL8%� Talk�1�XVII-th�er9.0al Baldin Sem�*T/H�(E�(A@\ics Problems, ~~ISHEPPQeiSepteT7(- 2 Octoberx 4, Dubna,�}} Avskip !�P V.P.Ladygin$^{1,\dag E,L.S.Azhgirey�}$, S.V.Afanasiev$^1$, V.N.Zhmyro 8ZolN I.Ivan $ A.Yu.Isup  N.B�a S8 A.G.Litvinenko  V.F.Pe= d;A.N.Khre ]�N.P.Yud2$ .�{\$& (1)e\0 JINR, 1419805)Moscow�i�2� } \\ (2 : %/&� , >1o 6$!T$ s E-mail: l)s8@sunhe.jinr.ru M@a�Q�2�M� 0minipage}{150ey !�J) Ab�ct}�NNew[oh tens* naly$ �y0(% $^9BeeXQ)� A�an l4ial de *?<=q&��<�-�s�eot��:C s) �:�  a~;ofegm�!VL"�)ma%� Synchro� o�T. �)Z:re ��"i) f�0�of�appro�;based1@@light-front dynama�S4 Ka� ov's�-�>� � "V) . CoW�;�0 2$ (�1d���3 .VU"�2s,�A�'managJexplain �  nQbR�our�&?invok>)degree�Adom acLalf'on'Bs1�QRdAR(2!�5� �vicA`" exci~ROfUic�"�$s�Ses up��$i A.8��$c^2$�He Y��za good a��2 T� pre N/"D2A�4.5E�5EZ/c�-ELy� plot� us $t �re�#%?�e"3I6"b+!w!��M4p�>ENimpulse)�x%Eio~#$�<$�(xx#g�Cdels.#�N �K�b�21 &y&.�f�%�es3��H"�#at6e��� is �,ly*'' possi&�*U%Kmanifg�a�raMri&!�%+Q��j 2=|"�8simpl�b� �"y�[ . L7amounQppolariz �EFi�N� breakup]�at a �7i: �  yearY�$)E�%"�*pH5� view $NN�,TC�Js |��d�94N�m1ta4 into�"�tIA m A >v�s�EeE�%�FU+||+ucture�.;%le 3<�Mk$.�<�+��#id"�O multiplez#�OA'requir%�4?F�%��[kob}.   O 0o�& hand, it� \=�0$T_{2�&%�7"!Z A-AK��:�pro�L $dp *_( ppn*B@IF9�]�!�"��x��ckw��eAicR$1-vd �P�incS59~��in=eo $k$)azh1}. e�rf54B# F$5�i�*�M�!�e�ar ta@ts�\(yy90,ayy45},T demo��4a *i�[�")J�s�Oe *[P��.{T}$ be����e�fix!CL4!��ies�(study)�on-/ (���G"s_;.inv�'gzO�@�"at�-rt4tan!`(as�l� �= � $pd$-��$ed$-��<>�ш , electro :photodis!Kg�MQC)�$learn amplA%�Y� \to ���es"�.��Fw?��! �+Gtdou� �  Bgr�6�^�ge+for�U � f 6$q|>n�+�~�, ���(U�icfer� S�2.5� soscala42$e, $A(d,d'� 1p+s%s�-�9pikVWun��dh/ $X$, whRis�<be EM] 9 H!>�f $A$. IV�,/q , $H�,�^� $1/2s :�N͏ i6�= 2�i46� 0$N^*(1440)$, 52 68 a�Ż�)�ed.�f6��a�Y -i��B����Z� Rodr"N0($P_{11} �)2� n 1g� carb��� at D��V45_55`.91� at Saclay�Kmorlet}��"zB� � �� A Q�.d at 9 c��J�=@per!��7A_s�6s L$M_X\sim 2.2$ GeV/c$��z9�5*� zS��/rg� g�V٤����� fe�,$ty-0.3$ ({)|. Such�4eha� .!B����:E0�� 1C2D$n_ �egle1},due�92paɉJ!ap,q�:m.\)W`2-X�,Uk� d ve�Y ��s&ad$A"at U85�&xQU s emAoA�� V; un���,X2<I�!��EY[ �M lad� � ��eda�ult�F in s�"�-i�\ !!� !"�EfJ (PWIA)6�4)} nadia}. IH J*@,���-&��C $NN�>*(E�2.2~Ga3^2)$ �.V �u� * V�!��!�4"�%�0!� �lad2} �=%\�%\�292&; exclus��Nt��� �� l �p�+� >�:y  ��� !�:"ljuda} �d.g ��!��BE� rep� !"G .�&� � o�ryllium!�5.6/c%�3mr�"6�:ayy50��B 6�2.�Parm CD-Bona�d2�q�I�fk(s (DWFs). A�? !���h�/�J61� ݅� b53�!:rif� of!\i2�$aF$178~m�=���� l�R�*!�IedmL%�ddU*'E"�} ���e�gY�)�;F[*� beaEN,B�1.Laborato�/&P� of JINRE�!Z,SPHERE setup��Y1$� bed elsew� �;1,�@�0eq�� 8e9ed [�4source POLARIS R�.sM���!��� �M�@�4n� cyclTa�,nd spill-by- L, $"0"$, $"- + ���n�Wabsj'=.xA+"� KxK�n���$p_{zzya�B�  �ax�Per1EOGarA� ain�<mea�lbYV�'accele%�.E` Eb��.�2L�iSdurm]� 1�asymmetIVp�G��N� beri�i�, $d+Be ��p+X�Kt :��� d&� @Gp_pa� 5S 2}{3}p_d$8 z|}/D A"��X���&� nz_h "�!{M0� s�y�)-X:: � =x 8�8�`4c�.��Gatomic &�G!G)' ($A >$ 4H=1"� ofFs b\ 2.5%?9.�m_t20brm� �.  �Od�5� wholeA��i2 was M�^+=0.716iJ0.043( ) 35(sys)e=2-=-0.75327637 3Q6y� �ees�OEcl�<di�ost�A � 2��jha!NeA{nit�@a�a# Gu�Vquasi-��$pp.�)��CH_2$1�placed ��$F_3$ f�0cVP1 ���d� A, N��8" �L-��)�� � s�Ika AM�\��� a� 14$^\circ"gcm�*��� cot!B��8�D :X!I�M^!D)$��r/g4Wrf4�BN �%��iqK]JQ�zE�17�:0.0082�09M��s$p_z^-=�c7M�Z/. %% T�>sert �e (!'% H�".sty) � *}[h] \y^K=8� .� box51.�c }&poaTOF&�G�S�5 magG`elM#tu��. � �fco� �of� �@�ree sc�blW on cu ers E��>�=?ger. -Z2 icle<�2%/ -of-fl�  (TOF�D��%Y�:seeL�& 28 m �8� �%?]u�!�b stop� �H� off-a� I�si�H!a l�XAXnfit�iA�$ s $1\�+�Lr�G[f�;t� ^�� �� .C�e�;&)I"�1ol d�s )^a�Vۥora, how:S�� �Aum�BrfA"� 6�R�:�� o rom �y�x%��s $n^+� ns]$n�Y6��*�!��\� nX��~"?ea9)8- ,�C�Sex��<��&"\�Sayy} )( &=& 2\cdot� �C 8(n^+/n^0-1) ~-~+- } 2 h ^+  z^+-},"o]\\w v-*> V  I^�� ҇` 9&F �F� ����I9:A5�|!�"� \"p��F"f�$�Uaabton>� &�$�>Ap&z�]�Q���&��!62e\�#h� *4H ��~2."� detailU�qTd��fi�]�E��ZHof �!9D��A� ref.G azhyud3�]����2J�U 1k] {9}&�&��iA �9��Ip�  �s6\%h�E#a.l�rcurve�1��&CKa<&6�"���-�karm1� UWJ�HsEU�VIY,0CD Zbonn} (iK�� AWPf )p } *-do�$ / poten!z s. a$": IEM sr �z e"$^(ataexra�!�%reZ*� �;�) �)Ak � on 2 �aT�"s � oppos��:q���'R f%$,%S;e��!)&s�6 A�!`:F� 3.2Q�.�I�l36%1rA ����in� ��a"GQ6 �&�a^�6&~ N&kUn�6O4-". $t$�$i)"N�ey��#{X !3 $|t|"0.9$~*(K�! w lr 9�Ge9>R{2�'�%6�K4.8�(G=��&mre1.([5 Hs�G>� (recal�ja]Vt#WE-� = - T�$/\��2}m (" at:��9�of 8>@e�)�.�l�|As:[��'Gd earlifcp�%O�"re�>@^*^Yf�$Q�$A$-v�j� p$�x"] &�&gFV� Y �*=Ja��N� � m2EMiX .A �Gum�ri��T. Hw.9f 5�'��,priJ#o-�2l �"�*'u�rq�V�.� azh9!������3J�M���� R�!b"Tat+�7ca�J��i ( .(F��cM�fua�egl�fndi� m ,  �] �g;F&�ezE%&H,at�ci�=�} 4%w"�]J/R.,F�MA�6��n��,bS, ��%# ���fpr&�,�V.+ ? �1� �k JM!C� A, BC C�D*Y>>f �(en�:�'�.^ �q4 V5off���n!Q}zbN�#��c! p�+wu�Q �� 1}�.H_�*-�- nel :!�hL <�[ !�$t$"��i&�,Vhiu�nby�eVa1G!�m � �ni�r�n!6��a7�/>" to it]w7o &9".P"  d=T2��&�i^="p p $S�$535� $D_{13}(�% vanish�N-flX 7�-�y bothv�iso .�sp�Vs��650� q�+� �Z��6 i.�5�*� "� *��*i*s�-�!!��z# +0.2�}��!� ��3a�3+I��^�K%$1550~M"# is t*4��>�r�N� # Á�sp+&f , �B�4������.+�6�~�: �*� ��U� O!>"�iݥ).� M�6�h�.DWF�[ fd&Y��f�c@3E�v< [��,2G/On� n� � K2[&R� !� 9�!�& tt�ayU�:�6�2!�d 2���d [hbt�54J{��7 �NS (6�) aa��BUN� �$�&q�{^+F  2h[AU�.q"� {M�n% r� =/u/us:1 ���['n) 2�9�B A A�6�6ini �n' P]�P.�!a� vVi�Q�>H>��Z~2�V�(V��� ^� N�� � � B �;.�a�2�Aw�~Jey$y�in��6>Aoq ͐5q)�7u .�5&'���&�aR�oy$�f�I��A� ��  $r�$.r)�2 pin-&�t���)W6d ta N $r=a2D|t|.�#�a=1.0N��5 wn�#.�DWFg��"3m���dF %,i�,� ��2� *z!!c"p >Y s�qd 6� PF� �{9�ims_���w=*�$8\div 1.2$�3It�uZ�o $aj lue m� �."� X&���$.�E ok� 5 �%��$simlicity r lack!��>. &�&�`�g>krdl�o:�=)yuw0N�-� x6�ndd^\�xe)X&J+X t.�nd>�$!}$N�*.� }��Za A�%?��� !l!�V1>&�2 ���]in�F�- newJ.�'aw�#=!N� 5;r�9�>e!� &harp � al �yCI !� fav��:of��m�:I�� u,,t $k_L$e�$�@ k}_T�a movZ �[ s es��ia)' b��B�; �� S6��!"�:pro�by5��X �.  to�l)r>lmli1�on,a�le��>$p_T E� 0.7� $c�&�%%Tʊ2%!\AhN��Uj* P�win�� 2�oi� s a��a�!%�6�5"�ɔ*� {%��> ,: J� ���Km�����-�^�Q�u'RmF� ��H_ } {io�e %�x�.J<<�BR6�.u!�v&�@4 "�^`& b5 �N5 .� S>$:H �� �at(#X�s<&Lj��:M>a�i.N>��=a&"$nic.��n� [9�r��0� r� R=5�� at ��ii150*E0a�$�h�y? �,�< r *)L��I '&ary*�2 7�?�+):��jT 8sloppypar} Authb�rat�#t[ LHE.�,��f�Dd"Q. team��v�e*\��"$�;E isj�_�!�Gnh�ndd&�FR%al"-^ (X�J{9.X^�?4 A.P.Kobushkin��,{0I.Lett.}�;JB42@L\^tK &xM ? L.S.~�HQ {�I.5L}{R S B3�L 22 JN47); { Yad. Fiz ~�N494"8)Y3v�>}UI~"VI�xB43k\2&?L2SK?�I~�IQ(Few-Body Sy�Bs2�3�N1�M=_;^�. �U7�OVV��} Lj^F�38P �2�O�9 E" 4 LNS-E250 (unp1a�TY( C.~Djalali5I�(��R�4I�bRE 00/10%�9) OrsaySS*Y ^�T2R2jRmR2[88]-9eN17_A}U�o�Y P.~Rekalo�E.~TomN-GustafwOqYJN]�C5A 3125^2�P^2 RNNMt, R.~Bij�] A.~Leviat 8d F.~Iachello,,RF�9�Q52�`9)=��8Z�AMa,�6E�79J. [e� Atom.NuclF-67�P 99)]=���2 � pLqa�Ud�.S6�U18VO2)r� +2�S22���>�Eur�`J. .�NAA&4�Z0m�B�N5A204U�Qn5-19�`1)]Y�#8L.V.M3|inau8Z�N064PSVS.S6bY.�.B�Y5�Q4�6u1SddbU \it nDkX40��J�X1G%�2b*s0MN.G.~͉hch�N5{� P�Ee($"D5-t�O. Symp.4*~6y Sp�hy�O, Brook�K0n, 1982} (AIP Lf�_oc2�N�Z N.Y..3) p.4459�3 io�O�R��˝��19�� 5u738 C.F.~PerdrisatZ�"���.��284�[8�$$ V.~Punjab��C2>C3�Y 608 �e 89);A!� blee./Dis'ma Zh.Eksp.Teore�2P47cf58` (1988P{>64[43]-9eU5�9a� T.~Aon]!ԥF7as499�2mf4^�PTE.I���7)[�].��Ex�ch.Xa �\1997)]; Z��R M(^M�.R�M��A4lT!���U�:d�nP.~�Q,^�. MU J.~C BellJV.A.~"6Z.�58!)6�d b�h� } M��comDD�h�Y� .MB10M1�W6W0 R.~MachleidtGa.FC6 W022#_M>� &�T�nB�UdF,spacing]{els�V.3UEUigNbZ*U�PmMJ' title{AppB:�� 0PbWO$_4$ crys� &�2� t &� to j $2\beta0r ^{116}$Cdpa� ,[INR-Kiev]{F!� Danevich\2ksX�1}�3 [1]{Co.B5 G(. Address:�` itut�jA�E%R�j,���1P Nauki 47, MSP 03680 ��, Ukraine; tel: +380-44-265-1111; fax64463; e�S� �d �<@kinr.kiev.ua}, F�8A.Sh.~GeorgadzeR$0V.V.~KobychevR"@B.N.~KropivyanskyR&S� NagornV!A!ikolaikoRDD�PodV�,V.I.~TretyakR?�Yur�SE)�]��n�Z�MM]SC]{B�Grinyo25 L.L.- ay2�E!NPirogF:0V.D.~Ryzhikovs�:6�S2�5Ma�Kals, 613 KharkoYwN ���4]{V.B.~BrudanidQ\l J7$���V3?�VjHINP-Minsk]{M.~Fedor6�2 Kor�2�@= ob:84O.~Miussevitch�1:%q��ofu�P"Y 220050mo$sk, Belaru|ua(M]{I.M.~Sola 9=ns]c=� 79031 Lvi6�b�La"NWz � disc�d Ln]�ive sh�4��li?V guid�n �(L�IB6ay*Q2Cd��2�. 6t�ertbSand�o�W�6avZ>�*�8��Q;*�M d. E�Sy��7of�1or, coupZ�toFQ!.,!, test�6EffӔc�U1n-~W �-Jtonr�x b&�OS��R���s4?,��wof�d�9gs�F16|�Y8�s�$4\��6�c�T7�build s�(e �Ae�c%Y -�R���Y�^keyword}:$1� \sep5lE0Ue js$ D�.�;Low�nW��+on>�V�'G 8�s�Q�'�9;>�� �)err�t5 Solo�\a Undergq�*^D6 SUL})���< cadm�-tuv5(1d) enr�fd )?"4 A# 83\%�at�&*��&�p�{s2(06]�s�'�Sg3p*"�& �(116Cd-K}. B��n�eJ0yH��a��Mri&�*4~E{XE��!<p J&5]Eg,INFN Firenze�% �4F,W-alpha,Dan0u6IZi aratTy"#P"�E� .7 i&R J,�6r]6Ts (tot��$ass 330 g)� ?[oi�Th��eda�{ ��5''`R tube (PMT ���li� $\oslash��=s 55$ cm�c1* glu!if ��<s: 2 tz (25 cm�%pR4\�"~orI=UaY^>���surE� �>�L6$of 15 natuȳQř)�5Y3 volumem!9S of 20.6 k���Zre2I PMT ����=<�-<7 -=$49 cm �w�C�a��r situlVE�(W&+Wal:� �.] $40 w 9-�t�{"��e,�mI, a,==V:I>��F ctore�pr���*܎ oenpas�L�@v!s ��fA�-"- ;_\-shapal�?/�,�]��!>�a���2� \yY $2.5-3.2$3( ($Q_{W}$ *6V!� 2805 keV)��r���> 0.04əs/(yr kg''Gyn���st.G�\X�?�)�s�%��2s. ��14183 h�!&#n~`%Mhalf-�R� 0\nu)!I 2fEs�s�G(1/2}\geq1.7M�10^{23Ҵ�{9�� C.L.�m� �Is�an��]�!-&�D@Majorana neutrino�P"ӕm_\nu \�Vle�q 1.7$ "n�D�� T�,%!��gl��!�world-w�j^r�+s g�y`�3�s.y*�# $^{76}$Ge��Ge76},82}$SA�c${100}$Mo͛ Arn0�A�30}$T?Te,e* 6}$X Xe136}). ��M:s`Ye��A�l�quQ,`U� cdaa $6�ex�:���\#�ac|�#s,A� levȹ in!�s�Vad ity �&�Yep}� � r��o%rir%��$. To enha�/� w3!%�!�A_� :U0.1-0.05A?,�Be�2njC>*�G �� ��W��of� �� ,Gar'�/��"� IR�V3P . A�8 "9M�� Carl��&�\ 5�=)F � �pev��" ~150��2� �U_fIi�!�K�'Xpur!�Tliquid (CAMEO projectM�})a�E�- l"K =�)"E? �� curr6+B�eV kg)!�$�� -3}-4}$�n�� (. T��VEs)B��inten�� ��$\B9x$ft ��� �w�g�)2 (= �15}$ g/ge�$�O 8}$UE2}$Th) ��j*M�:�P�e�d et� �I& neUc"d� rD!�A} k�1 huge� a  12�2$ m). �)o� n alt�jve�2�G�!aU�e:F �[�y� �z��lQE ���was)�e& NM. L2N (-)q:Yh  d�op� heav� f�'q� , PWO-�}! A7-� p���s�q2�Iha.�= ��a�!�:�d{N� !��  d% @Kob97,Ann00,Kob01$2,Bor04}. �Rreg���9N  b \gam��q�`a,�'y�CTZ�'�z'Jd^&� "�>Zt�=��!Cew�_�Je Bac9;xsub�*�)"�66�G���i�&zEi�p� �P, w/9�Yj`l��*���!�>B��} mak�8is Z�r,Fve�%tt!�a G�( -* ely �= yet ��2"�e~A6:5a y(eZ'paper�i�F*6g�j pplyAUEmD��for2` �� �(!�a�FxB�1o=�o� "�Me,�" s� �!��S2"���JMm�j�>�6�u en// in TlY~�naF�F� *���*�/�1�*A{Z{�6ca" R ���,�^V�und�t>�s%�= Czochra��a: hod.s7� ($45��22 $ mm]~2 g�� , na�A�1) I�&�2 :M�� (>�)! ��]X� ($3� 10 �83 �� ��2),>�0 Bogoroditsk Z��: ChٯPl/�(�()4�l��? R��JD (�)���)�E�tAE}[tbp�=PP&� of9� u -�2Fs&�^kgular}{|l} \�~ �&� &�f� IDe�>,y (g/cm$^3$)RX& 8.2s!& 8.0 \\ Mel��> (SC:L& 11235 325�S�8 type "B@& Sheelite & WolG1 (\\ Cleavage�nbBC`Weak (101) & Marked (010)GHardn{ (Mohs:�& .� Y$4-4.5$F Wave uA�max��(nmZ& $42P0$CF48%ZFReōv�dex!J&2.2&.2-2�aIEff�c�Pge�A $^{\ast}$ mu$s! 0.01I�13ER����eronzOE�6>� & 10H @Mu\�kcn{3}{l}{>�R"�ray�Ado�� empe� re.}� 6޿uC�i� a�pon&��a�12*� x $y�2�37}$C��� 07}$Bi;�[s��@s $+24^{\circ}$C � $-18D �!}w'�� PTFE refM2! ld .�ca�2W$by Dow Cor�Q2-30673 B[IDXP2412 t��� \K�<f '�1 5� *�SFWHM=4���3AY"� =:� 570�D 662 � -�)�:�Cp5e�*e/"�X�"� 3A ����  co6[g��:�% 6�"N"Z>tb]��U�mzV�Vig *=fi�V0�8.0cm�u�UVJ a9�by��2 ": f)$ (a).�!�(b)M�-x $2�wo.�s:: (�@F}6. (�)s)��a�5! -B; &G�$\� /\�A ti)"�1V�U�w~Mi�qfu3Ualli# �241}$Am Y�%"t&�0.65 m�==K0 mylar absorb� &�IO��W:�l $2.1-4̞MeVI�el�JFi A�rmѱh he"4Ya� face�mr`K.F">�%h$ p�!ofE 10}$P��E_{ }=5.30�)� TP8rPA��9Vb (see 9� 2.3� �j �T3�-IM j%(�dep��� �� O�� ?Сum F(�I %m��too�Q&M���p s ab73!�:� -$ =0.08(2)+��(5)E_)b ��<i��� �B23(4)-B 4(14C�rl�hUA�!$hu=in�����V�J�"y�M�Y^S6&�"was ir+afby1` $���%�iX * "�J3���� .�,(O lesr]�:��.�of��M . (Inset)E9M�� ��:@��!e���e%n 3.94iaS��d�^�H{73��K�aca��=G&��RU���E�b�]'tA .��oR"�!Onz�.d�o�Q�Of\&�6�. ��_~ ! ��alt��e 430 mU"�#($�9eqN0of �8xvalent���#�H(A�:� F� e _�aY't FEU-110 [�\n 8 :+ i�*2 -�&ro��cha�� O�]�%�TPr��py:f���se 0.8 $� . A�t (I�� �vXsiY��:�`"2`lX�dw{^ih �acqui]Oon�s � jhLle��calib! d�H^{:d �S.A �um;umu�"'2.15 ,#s�yoD 3 B�nseu��i�u�1.2a�P��cale) [ �N%�UriA�e�b�� ,2family� ��yW3��Bq/## mg�f�%s�~R�� � ascrib� $[ $ me��Bibh)?�)PbF� �a�22Iu�as 79(3) ��E 3�K^"2E �a��A�m�ƈ� }�>� KjI�. Pc 6mK S�x�p 2p:'�)9�oE`A�� F�*th&o�^� b. Broad .��BѺEP*NG" QLu�*J AQ$J � (}$=1.16 MeVzBTb�XATra2N'F#acy�� )A}1 �IN��*�$�C(deqi�R\_ ".( GSO}`�ce�':>'��e�� |?fi�RR sequ�W%"% e+� -�s:��4n�$ -=3.27� $\righަ$I4"� �  =7.690, $T_$=164$� �JGb (A2�v^d%T���4�Bi&-3threshol*�$ t 0.& �fter�u3 �!�e�Q] {*� �)ains 7�f1%�A z`-z-y"- %K� �8window 1.6--2.6�Y (94\%oG al"�E�q�of 90--x � $s (67 @a�u-Nj* chosen�|��4re no peculiar"���"� i�a�&�:"tWU�2.�-��e$ur&�\d.��26}$Raa<�e�V�%eq$10 m���.#��7�%is�Cu�ZE�oq���S�dH at � Ak-� uranch=i{[�isF&ly brokezCBec� AshaW �.�)O>W  (&M )Eee� �"�'�2a�,aV EM?/e�U,�*`pFDA62�%6� �4 =2.25�� 4& Q����: =8.786,"@(=0.3~\2S�!�?)E� ste�_� � MmMe��)$@ $ ��!C %rN�3.4--5ap (w�я6m�%�G=)U�a1'��)��mF7 �#��(K̨=�]�28�# �2 f� �ɄQq$\e3m '��umm�#M�"" rn� �Bb2� (or ��a1ir�iesI��f"�b��y�"�1�*�g [htb.bF���>]"�2��x"* �{|l ""Cha� & So^u & 2�$2}{|c|}{Ac�g ty (��)}gc�{3-4} >z{.t&��(Geo96,Bur96}0 03 p� ~ & \\EqMe&e�M� nE_ 13M& �o4)39(2)�_kc�&  c��.c"�2c Z6 I��b(& $(53-79)\�s 10^3$a" 0.4�\\F�-.Q Uendl>9&^{Uuq�as.40&Q�2� } A2�*t=(NQabS*�l qJ�E.te�6�:m*J". With $aim2�*�aIant�- .\$of 4.1\% (!1n1�-n� )�� 8} r�9�1�b))��\�6Y5����71�f��N���b��ar2(:A�!�5�9� !OS!^�;�I��f{E�bh� b::��u2�*�|#on�*"��i�io�?A�&�9?&41%:h*d-� �SI �~816�=�C-eU����/ , w� cus�t�m�+n.� F�>@sap]��b. /I>R� � �st $�l�u3�,$� -F��!!l; GEANT4 L�z }��-+  g��� DECAY0 , Pon0&� f��!?1Q%O[�ucal��!�s:B�(�9$5$�$5 �9%E�6N?(�) _at 2.8 �1{aZ� �*5�6�u{�8�� $2:,��2%�� �!��v"�-12}1. 7.61�6�8ca&0A d"��� %e5��76�6a o���� 220 kg~yr9^1�c� 1��l��3�B9, if no *�y w�?beMid3c�y,!�s.�~5���x�.I>�(� &Bof&13�gI��.$e equal 0.7� "�%�t5�7% P��,e$� �*� ~8 �6U%�&�> (2.7'9A�� e>8]��%2 $�,45}N4GGE�E�]́�inUa�^�a^^.�5U�!�U�("�sof �2�}�22�5]��xI� 5dJP }dYD!DuV��smtext).!�s�^as� ���nt2���RQu�sJE jF&�{:<5yr/ �z"�7$H2�(>2.9��E19�:) �ekv��|-N�D9. ̷$ven less dWkrou+ .��Rtu��Z&N�$�m�?a$ will�E�6AB� [.� 2�]4A�� Discʶ"�f)+Q��oF�=)��3@&#'v��5wo9�z��D<�;!�],a � m[ �&���{Mw .� �Se'/i��a& �bQ��>�;o*�i,he�4 \lim�s�==e 6E���:�=J��zC1���0.07 eV� Sta90�9IF=ev$lI�Qe�ui!=W & Vec14(6}z2 eV)� cer� ly o.&�is9+5i"^�ȁҕi}��&[�Ita[�st�G��q+ s,�*9�i�� %&k"=��&Io,ٓ4�#�93�� �o9t-u(�u�#ly�$5C �C . 32ujB!��&�B� eBA�*� 3''6hog. hmic���5f�!.=y6'�@aCvantag!�%'&4p�8ic or �Dɫr;o��xfxar�0on(2)�>>�2l�Crb!dA& a{A�n 60 m� di<�R�v����1(�_J/>el8)�4betϫ��*� )l6:�noise)�t�:�!-{� �f">suming�$pprox$50 c�&�Cl]�7�u{ *(polyethylen�tie�on 3, J$�W�&Ude�+d:  <l!}g � (an�>�Hbig*a,tho is.m<ly� MqBro85e���= step,a%go%/o�9JW�$archaeolog�\ �a Cg!C��fդ �f ��� in0= ce, � E$4 �(Q?B�%i� aN�N"�� Roma +�)"i�vAle98}.96nex=5#��/tV*�M�ow-*#�E� by u�1A�6�%�*�D�K�">E �e$\beta$ and $\alpha$ decays from the $^{212}$Bi$-^{212}$Po chain) analyses. As it was demonstrated inF�experiments with CdWO$_4$ scintillators, sLsensitivities are atFplevel of a few $\mu$Bq/kg for�28}$Th, 6}$Ra, ߰^{227}$Ac \cite{Dan03}. The energy thresholdc�(hielding Pb �� detector of 0.5 MeV can be achieved even �undoped 2��ro!_�emperature (see Fig. 1). However, as -Vshown in �,Ann00}, dopa!UtwoB]s 2" ��Solotvina Underground Laboratory. Both -�i�\considerably polluted by!T210�7>�$50-80$ e�. F2� (a�32a� family) A�i� #8}$U)I{�5,only limits I0etB}13N 10 m�,ABpA� vely�xcellent1�]fofMi.7MjobtainMj 2615Ag MgIf�,high quality� R�( $10\times  $ mm^�$of 4.1\% (�Q� �I�-Z��d 8a,of relae�8pulse amplitudeMgޱ�2� viewed�K oughBn as ��$-guide. We� ct a���'�a- coll!�on%�m^2� ���by us��4Dlogarithmic-spiral�i �D Monte Carlo simu! }�M�s.�$ good abilM��� u(8to build $4\pi$I�e �.��a��eA�8116}$Cd double � �%7�SIR�2m. ��XRev. C 62 (2000) 045501V�66q�.�B�110Z2) 389ZW��A 7aN 2003) 129.�W-a� ��7� 3) 014310.HD@ Z�P2.8F3!..F|Ge76} H.V.~Klapdor-Kleingrothaus57EurQsJ. A 1)�1) 14N,C.E.~AalsethE2�5��E 108;J$/ D 65� 2) 092007.�@Arn04} R.~Arnoldrjr8)� 4) 46�LTe130} C. ArnaboldiR%[�� B 555�167; 584�4) 262�Xe136� LuescherZT43�d8) 40N\� Be�eb�46�2�.,CAMEO} GB llin^A493A0) 216N�E~%~Ja�192 1) 42s,PWO-first} V��(Barishevsky5i�Instr.f3 MethA�322�J�2�DKob97} M. Kobayash�2fK9I�7!�2K� A. Ann�vV�J45IS 0) 72IKob01��4M�!L28.�K2�KM�2a�2�Bora7A.~Boris6�N+,� pres� "� Bac!q S.~Baccar&� Dum.5'385%�!q02A*produ��zV�CaWO} 6 r�VGZFV�Xnucl-ex/0409014, submitwto.�� A.�GSO} Z[)W �X%�  %` xINSTITUTE OF PHYSICS PUBLISHING#z I�  I`Prepar]an ��publicwi�e�itute�A[ics I( ishJjournal�LaTeX'�� ��  Iy sourcH@de `ioplau2e.tex'pd�eg�ate `G� I�]s'�Q:)explain�� demo�atuse9$���BIh-@ �(preprint fi#  ��xcls, io 12.clo� 0'. 9> I�  I�=[itself�s �2& �B I� % ��m�%  Fy d we have a character check& ! exclamI mark�"�4quote % # hash.` opeEA(, (grave) % &�er��1' clo 0 acut0$ d��Y�0% percent % (l( parenthesia� )Re ,. % - hyphen@= e�,s sign % | v�cal bu~ tild�@�,B_Terscor%{ �$curly braca2 } � % [ &squM] & >ke�+ plu �,4 ; semi-colo� * asteris%�:� < tang�ra\ > t % ,�a? L. full stop % ? ques\U /�jHward slash % \ back! ^ �umflexEn�CABCDEFGHIJKLMNOPQRSTUVWXYZ % abcdefghijklmnopqrstuvwxyz % 1234567890I�  % \�,class[12pt]{��} %R�i} % Un� next�$ if AMS foLrequired \usepackage_ms}2icxu+natbib��>�,title[Multi-�ng�*rAons]{6baryon c#�$\emph{p+p}�� d+Au}AKli��d $\sqrt{s_{NN}}$ = 200 GeV��}@{Betty BezverkhnyA$.STAR 2� �Hfootnote[3]{To whom �spo�sh�dd{ ed (bg.bg8@yale.edu)} } \ *{ . ��D4t< � le&�y, P.O.Box 208120, New Haven, CT 06520, USA^eE-mail:'tR�} )�ab!� ct} ��ł��(ged hadrons��been "� \textit=� )�refer�systemv�%�fu' coms son �6N {\it Au:?gak)�� peak�<2both *same �� � $p_{T}$ ( $>$ 2A�T/c) $\Xi$ (the trigger��)�!o away ]($radiaA�(in azimuth)a }1>e& data�quantiH �Y�"isq�s A� er s!sto � is Hsently available. D%nct9 also seev!PYTHIA* s� 2�coq�, but Kra.� betwQ N� ataafws�t does not � ��!.�clear2�is � �in �Iu;, estab- a]�f��vaMrEMUx! \end}B %��?0PACS numbers �* m� Dge %\pacs{00.00, 2 42.10} 2�HS.� >P�o{J= {y GUC out�!� � Jpage )l�/%\make*?Int%�tion}y"�W0(Solenoidal T��$r At RHIC)6t� 8 made much prog�SA�ug! stan�A�med�#�ed S. IiF8past four years �.*$Cata�#t��B's most � ral>�Y�� ��b!7 a huHd � dense�] an normal:d�A� |n%� ToBack}. �E�� v�v� havi�� is ultra-r1 X0flowPaper}. H4%th!$remains%j�9a �!!2x$��-v� . What�&/dif��!�"�#-��� icleTA$ mechanism/ l% extremely)A environ�? Give(,�`�'�#in ��n�s��zed���thaSe non"�M? �f� � of m2��M�$op-�gyj8�e �$in jets? I �� (predominant9%+������A& �iUe!V��E0eէr!�-�ed.�ly~ �How� iy"�p!a�� �, wEpIvmaye3 QGP? �Y1 help.�-�U` �t!�modE}q�:�=" by�Ljet��(t%nJ Like o�6���s,6 V(a �(lyau�>�#ul�# fragA��gaf��initi�'tFh� c���A thus�,b�ea� ��-�U$ volume. HH!�on O$will often�%�in6 -to-��!(s!�ich-w9�s%ly�x�T�0 jeA1 ne o�-U s on�ZoppositW . Si�' lete>reE'tru)�i5�vmimpossi!$duE��� %�plicity.m,�a!x��:ofQ�-!K�� a#U%� %�� �&� =�"+  �O with6 Mo tr�+ an J+t-by-  basis�&is metho� e�w+ff�B:!!�.� sup T ��%!i0\� i�YWs �oP��� isd�!T) @ $\Lambda$+$\bar{ }$E�($K^{0}_{S}$UT;.� � �,YingHQ04}. B�)�V/ � e�sui� � 6� rB� � q6�� nei�-yu� ��!z�is ��*�  � ��*u Amuy,&� %D'D,A� )�}1*!�*\q�v@14M minimum bias 2:E^ s (Y� 2002- l* 206;5uɓ><3<reE G*maa�omponݪ@ "�(u]I���@is its large Time�&jA�-I �I�g� ��N#!�l�3 loose sel��U� po� � !�I � V �!�deach p. S dly,{looks A��a�0t� �,pass a � �10�U���0desh4ɓ:1�~ rais\1 A� a lis� eligv t � �c�dat�s �,�% $!���a�t�*1�]s. Ea� 1O6� ����_^��� it�a�a�/� �Ag!�$)!�%�4($\Delta\phi$)UE6�6@� calculA�'plott!O-N��z�LentireMks~0e�� = fun�is {izj2�va�-Yu5. fQ5 3Ga�+n��y�1 to wrap a�2 $2��me.��fix�. = 0�6 �}5 �sig��� ssum)�sit� fla� cM��m� soph� ��]�sub!��F}lan�2n=I b/,figure}[t!] �&(}[t]{8cm} \ e�  % Rs . &7 \i�5de (s[width=0.9Ż]{rebi�pp.eps}?. \cap�{ -w1edE��>-% primaryMd]H.}\label{PythiaCorr�� ��� \hfill %-&)*(�z �_� _�)aidJa�% ]�9)2Mw&.!2<� 5'ppS�4raF.4&C2Cu� ?�7\subs��� 6E ��� �-�"B"n ) 9su�\ � EIW !�� �B,taken so far�� m���5?n.�/:�&� # s u��examin8 se !��P rwhe e�)�&nL "�2� ��w�to� pZ�* � .  w�;to.W!Z �t h!�!no�form a 9��i[8d��&C5-� 6.22��g8 � I�$Man}. $3.2�6� 7}$@���9"�of �$4.75& halea�n.d and $1�mimeoU j1!g4in $y < |0.75|�� �P*� . Pe%*Ѭid��8��(sis describ�bn;�1w� iat� 1921���15ݯYC705 &��.����1.4./s!�(*�  (T�~\ref{my })m  word$$p=�zwa�-� ��,Ś n a�rX<e�v��ed ��� 1!�t; g !(swEA�� �&E( � =3= �Ix���a (W-�nd��E�q i�een�1 7"�9"�&8�s 12\%�6�"� 6ris 33\%� er. Alth.�:��!6.m�nd  of�r=��?i�,! �dV�?two"�!lM�n��R N�W�� i  =g�d�>is � (dN/dy< .00318e9 7, $181\pm 008$�\�� �ፉri/dSQM}),�grossly��ic�?z �regAgof� rest�>2$` �t-E\E� �Nng� UbeC� = 0.8 D (Y���)A�4 �?Alte�>by adju�, g various-$; amet<sF s tu&!�Vproces� pa.�6�߁Ձ�� on�"�,�mak# NLO pQCD � �A� p�!a](,l� �C!� 'a�cs ofi��`nj<r�to��rn��*%�%{ofE\5x��$�%�e�F �!.�6�A�!D&W valid6� �!? n� (�� .7). AN@9*  is a�6���@ 15 (�of "46)�  poin����VcoD>Cin 3 cm8�N &��' ex. Preli�ry��ind�+��: deed� 2�\5 t�"�� $Epp$-  ifica� � ���c�2� (I< . As~a:��KygRef�#VsPt} �eanJ� M � I="�!S6�� lUtwice��Te . !*1z��E6� enhan�2<sugges�<eer`U�a��)-s�d E �-s�5� !0A�2PUs ��a�be.X E�vi ! #%+{is�jetSum� }. Fur� inv�(g$�!� .&�%� ����!�A@J� R"�%%ŅIg�x)|p�Ae#�of5��Eu !:$\~� 9�"� .� %2�  aC���� ��58pp�Y)=*M}: ��Y��3�WPhi� RP~4% und c��-Y�2f&2H(=6� �pjp��&�ppPtF�ionJ@e�� i�]I1 � s a &�a�66) in ��%�set=[Pt�(��6��&�L�geometr�d "�i`cu�ap���&*6��2% e6�.T5�aos�"%4h�P D!W/-F�" ��� a 10\% in���� *��aN tos.�|�rW$�#$ s � drawx�l�� : � ��SF2�;y (B) ��,(S)���Ks**in*��� �S/B�LCr",�#!D� sF e 4.�@A tW cu�& 1%��_%1.312� sI�  1.33y./ �` L*!�q)ak Fit"< ���a"��ns�=7U  S = 77� m$310B = 168Z#�&� cou0I� �ed �� S es )�~O- valu�$Ractual Yq�8 icm5 972�232M�se�L"ed-�ABin 295.(sw 1.32c :c, i.e.E3inK<�(:��V��H .�&�%�m� "q=�!ZW mH] �-'b� � 2�.V.&"�same-E%�wa*�3viE� �.o7(� any 2O.in� � ac�{$Xr6�1!x.�s � &+� �mo'um��r>�&�.mP��[]@%�-<infer��E�&� ���=!��t��u7|J���" i1Ied:q� (a),.� (b),}�m7*�(T]s&p(d�~& a & b & c & d & e & f & g & hBo%�bfJ } 6& - t& ~U& ~516 &6 39 11 S\bf{z�}�($~772\pm31$B68B972��& ~�]3 �~- RZEP [(&$3576\pm66YT711 &4395& 4309 & 2521W7 03r 2277 [)� ta)� =�� i W*< �J= -�� " � z dAu�B bB BQ6I@it% }6� � �תU dAu&V %|5::�B��-6�p�p�1.�?J! N�2��.D =ge"�*������& ="* -� ~=~200~Ger���"% dA �s�1M�5/)tQ� An�5�e*&�6y�S� �a &�  tqbyj� 2003�1�,�&��L$no longer �Deon-on- 95�'�5usus�B��+s �hCronin cGVWZ} .e.shado�) %�re-&��0,ent:�2��"t��n �W�J�B9 s; h*�2. e'4\abundan~(m 1���!"�!5��!dAun\Xi$ -R��5.EN"FA�2�.�A�>�UtiliP$�&n0� � � ying  $8e c���� �%4 5�"f se�3D P  $4&����* i&�� s�*�.6;s b(; re@a"�(�sbSZc ��i���$�>*d Ao� to�%� in i$ k&�B�+6��C�� ly 3!of5e0[tO;�:e 6B%U&B!lyT � % � A�%or �t[s*L >��)iU �surpriW(, s��mR!UI���!�s�[al � �e�a�5aEf;EJ� &-o�6�5362Z"��V���%. Final;)w� m"2.�&N'n6�Er F�dAiy)|$d$+$Au$&o.9�:s Ecwo emerga�a:s. Co8.�%o w!,w\w6\.;� *^m�in N I0�w.6s �1& is�B� sm�-5�e& �V 4c?�E{(de�3a�o�V"]�(�8A(%�zc�c%"!�-Q �5�ORoq;%<G\.�Q�,EK6TE+zTe�.�i �B.�Out2 } To1� oolE�fU iL^Am.�d !.<$"�?,1�&�&s n�$�<un�dF f�~k2, �1-reC, �% soft-�5s*�/6�+�D!�!�G� o g]8in.�a�+�(inu�=udy�� symm �";#foldedmKirills�,�7AM� -�&5M' ��6�ρ� s, yet to�&�I"� ��]JF4�so+ A+A��bo%|%�a ni�E =�\Gefu"�*�du�1 ��+run]D.;EW6*�;�f?�@�T fw( workG%��G*�!��JU;)1� �.hop�is2 e{ conjS#��o�-f��]<i��c�5���a?b;!�h(�,�5al�M�jA1� *�#e�I�Lb�3t>�b10aibf.� Adler C �IS^ } (SB�KU03 J G.�^6\} {\bf �U082302&JYf"NE�i>i32301i�i Guo Y!�4 �$Hot Quarks P�*e��%/-�<4 Ackermann K H Bn 1999)Nu�b�V-$A661} 681c�"�< Bie�FF S2f�  Q�S.a� �Xods]0} 499 766-777aeK6R;Adams J Vn� 2004 ��J� 2} 1!�=zf,Man}Sj\"{o}sA�d T, Lnnblad L� Mrenna Sl1�*ZT<} hep-ph/0108264�*�'G+7J>-�I#6s�GCh�>d HLM Tra� M�$Specatra aj�Ne�pp�dAupI=� �H} Ph.D.� sis, Y6uN���a0. Witt R�n�d-��_ S205-S210W^t Guylassy M, Vitev I, Wang X N�ZhB Wvq�Y/int}   -th/03020.C�T=A;-k�� � 1235>� %\�r%( "&�P �c>�Q0.�Q2^QepsfigO'new�Q4and{\pizero}{\�: math^0}} 2)PT6%p_T>#M:#m#+��QF�\�-Q*]{Over�j# V$:�-\PT{}4j�32� m� t�6 \�Q0M van Leeuwen*�PLaw�Rakeley NŃal*om,@, California 9472�+ ead{mvanl ^$@lbl.gov} :�L�o&�PAn���e"�qa@3�E� J�. !�VB�G� Data��%!0 *�/"�:*�%�S -to-� q1ordpPerturb�l B�0ph 2r \.m��V.q�/��i9J�NL13.85.Ni, 25.75.Dw} � �_o{\jpes�FONgoa�H$ earck%y� heavy-,=�o ���!�$�3trong�Jte�Z �Mat�ems cMi�S�;,A$ phJ�3�s� a~ our-d�/fM e:<��D Gluon Plasma (QGP�2e �M��.�ca�/�ed�8�Gdu 9L" onic*( s ae# m�Y�f5E`��*!Js' ��X�� Tce |Ji� �A�/�:e%vmshort p6a�scalesc7!XabsTof�� ear ���l �"�� �e)Ar)e�cdA#}Oi��"qaa~b+Ierp�J!��o"�?s^baMEv�NSPS�s��dilept�s�-JD�_-Ya t!��gfo�ts e}��c�o"u(breu:1997ji�$Am� !Z�B:��&#�l� IX.u-;�qE5_YI�in �Bal|�!�wZ .xJ� resx=!��%�d p+pz5 ults*�(se ��U�s,.�!0 o�%� fir`@�l Fup�� K�2 f.�eF . Re@�M� ]sbE3w+�u.:�.diton-pr.�m��cqA5erm0,��2�(pQCD) .�6[ex!pedqqYAka� SomeA!relevant1��be re�(��ł ��. �8� lAJ��.��|�  !S%Nj=�E�Bh(�ly mov��o�[s�adv�Wd )�`s�.�M�EpM nd.� }s,MiK,��V��bec�Qg "CLPa/.� ��*pei5(-��R=v�D)k6�% AE�"G�v��a!�ibb:�.1n�S . Du��their�as�P�! � (^9n`N�Y�e2� apN:oSb� r��nb^,molnar_sqm04��I�0 +con ��C�Tave A�U�a�e�( , e ex� ng���V&rY6����-2%� run-�LQfrs1&��A�M�cs�$��E ,K4%_E9e�� se wa�I�mp�za� prec�s�\PT-c!ag5�Yt2��F���ȡ��#)Em� {HigN�A`��} $mmI��:L�� 8�tly ac�}=Hy��?>�1�At*Vlyw�,u y��9C)R �iNjet�&�S%bV2Kdynam!�of4-6�Sca�|a-��k�ya u�ual�,f&e $D(z)$�:is� �< CgB-6$e^+e^-Q�Z!POKDt�ies�%PKniehl:2000fe,Kretzer yf}.�hA6�Q.�T !�_EXar� K �deep jaQ$*8 %s�w�M�,cu>�(%�!)� E0��\9&5I�>� ��E�&�3Neu{Op\e!�ge��K+p]��"O& _�}{0.49���,�0{file=pi0_nlo!),"=.-6�)Z�)Bc2a8Star_Brahms_pp_��rql �Z;_d�J_2���-:%/lh�}M� da�-� rib~~��{A(left)R�(r.�^p.�2|NLOl+>� (�s� }C �=�� q`�Zt�m}U a�A�2u�s�� ��o�<�factori M�re�K  � s�vlow�anefhow}�ce����B 2x@, divi�=#}5curves.}I�Q� \Fref1�� �6AV of9�b ��PHENIX�hA��X 3pb})� �1�i�� STAR?ams?kv�cBRAHMSAr7 4ux}M"`in 2(�" ;=200$~Geb�j�.�a nex.< <(NLO)B�A �Jag�J2xm  uncer�Aty�XA8theoret[81�� � stR%Mvar�)t�E2#!�:I s�_R\mu_F$�� half�tz?�n� al �(!�)�_R=5 =\PT�N* �5m�]geF�ed��-�Xa_ 20\%� $\PT>51zo illust� KJ+2cف�{!<�5XCAG@'q&tK.(2Ry�,ɻ�, Ka�D d P�Or (KKP)M� &:�AI����K (! '�Y�Xse9: f1pe-3l�^� Lsimilar�(ū�!��A�  "�7�.Op 6)�"��.AVZ !�N�慎� ur��u��he"�  s nof2�'Ar��g um:A�MVm$�3� of 5A8a�]),X!)� Y-xi  g@V�. Note*�"���r�ly�a��:f� do+} shape@�"�y�{ ��d5(aV 6��y!)��;/:/�%"|��%�enZatic off�-.9'�gϭS��!H\f.�� %���!t���1�(��bF2�BE�!�n~u ,E��� y agW� �, ,5��a� �~v�1�U�nfuL fZ���  ] ��{} ($>3��)!Za� ed gx)byk )F-�&J� �&Y ���Q a�!W6�e�L�vWJ"X"ext��!EVWgZs]0_S��&<].LJ1 kaonZ��O well-cC<r�S%�a���t" 1�on~.�aOscarce�1 deFlorian�zj�B I�� 2�12� NLO_toA� .SQMZ� &S�9k0_lam}+# j�BK_S^0%;*�?m� }@6�4m����RNLJ�I�9�heinz��?��Vy a'� /�(�E�AF6 66�F� A�Ye)U@VF+ >:yLO.�!*-db�Kii��c�*� e�g-�M'65%6��62�5�$ �)�um�h��I�� �j asonEN6����rum=�o�&:c�r��Cm�� d on Ais5�)mai��apbAno�y�� ��1-2 GeV)��0$'.f&{�<^-�&` e 4@""J�0o�/*=Lla]��#han�JVs�] 3!M*~ B)JT� atisI�yA��b�  b�n �o_breakdowE�\k�xamalis��he Uiz)�ansatz'�iW@�FC!�l2ig1 i�X� $~B� 4ie}v5�BY c"P/2Ee��&�}W2�&� a �'b� a5\?f�� K {Su*�G��%"%�L.�$fig2_R_AA_�stix�E 0.42*�~ 6�$ RAA_�_peLG� 0.50A;: raa}N�8modE��)� $R_{AA}$%�"&  Aqk *�A���,bHa� periphe��A�o"�q����� &�qi� ��ʡ�n$� �>.T&~V`A�7 A����] �=��G, $N_{�}1�alA}eUp+p� �arRG�Tequ%_} )X= �o ac{\b.*R \PT\T|_5(}{{�R)p+pR"endcis�Vq] 8���!��se�:ioy� 9���1�%�.&atJ�,9.#@%#{} %--�Pi�F�>�A !�:R@*�� .!�zo U�IY�!���0`xhunL �c�-.�a2f_ pA;aqA5��"<"TS.��2�u�A \a�h�� 2�AQ�`:�B�]  w g�!Ea�WVDN�los&�oA�io*a hotE"j�n. "1*{O&4��!�d+A�@dB�}�lŜ% 2<�lA� &r�5)�"Y yp ig�8\PTi�Abm -ɚ($m_c\ d�F~  ee!%L�2q�vdSA4all \PTh�s'l&!Pwha�� �i� f�f.2�7]!�l='s ��� � �y�S6� %�&+ �(�me� _ �!%�y)Jy.��_pti6�5ݑ��J:xse>&0.2< �˅N) \ z dau}L)I"� �!:$D^0$ �$D^{\pm}y D^{* J�� at*�@>�iO"�7��Mk7 A�<0E��@C��p+��heC^�{#{ � matc<� 0$ 7 .�K) Ei�de�&ӕtoI'A�%g���>� 4fc,Kelly�4qww"t t�1bol� ��.e"�'i5{@��ll���  �i_� 22��en&O7� >� al�l� errorf ad�in�6d��J e band ���Os�R� � 2�ɸ Vogt!! 1nh}[# : .3Aa�%~��` Qc��� ́�'N� test)�G&K.�zQ� Nݧf2�ck:�>JP �WV`T �&U=�olmA�r, s7pjond�7Dic �� dܛ. EgtQ �s=1ex.N ion,1 �#a� q^=�ly.4�< vg6d+A2�$R  us�*_$%R't�S�mUTai!� 4bf}�yf�vU��s (��a���B ���) �>=F{&���1��rvi")Ձm$ ��� {}=11�� # idB� �I��\�!9m��i$D^k=(tlgles)A�� (ǀs)�ù>y�>��� (cirg)M�a*%>5���ao�� -+)�9AEz� �$n�8u�)�s a:�q�whole R%}.{5so5FB/ )��F7of51%c �-�K .T. T>� �)�&x �>2�B< dE� �)m�sC:()�,�v!re��: D =1.2ETAV=1.n a�2�-R >i!����E,s::4MT �2J2>1jE>-YAU.�! #1Ge!/+;Aq.�%4� l ���j tail���4�)�or�81�ed.�% �umA\�conPv�)Q5�� �"�a�is�ll"�8���E-7u� w� �+of@ ch � rinciplel B&p i)Jze�� {}iFU�1�Q"}�1{.� &�'�ir^v`��ca+ų)��i��&h��?��direc�!)�2(�tr�& W$u�,�=�*�EHd��\am!4�*� �)" AT!� �2.f]ĵb1L"J.��u�FlN>', leav�little r:�!�YWdueC2��*l!� all,�bVajR�U*���'���egaRMBNHS&Ms �mf*� �K&~a"�   S oughE8s��( wait untilE�2�� ��o">e�n ��B"< &�is*o)�6��!C `pb�c �r�)i �-� {z reR)B-su,�߇�a� A�*cpogJtc!�>�!"ԞU�6 �eel ���h beauty��r�e Teva)2U Cacciar_ 3uh}� addi\,o< wa�`�DA�2�.� by�G$�xME�n U! st�-�Di� $z$-spac�.��;͵Xn,1� 6)HUJv(1 .� 2pa}d/eeA��A��~y)��+X,cu�\e�B%aI�:�'T� �2E %�-�f� A�}gad1d ` blp�2v-"�Ba�GR? D6" E�#A!��b��e�1)al�xi�m�NtR\alI^po1|�� unmaCY�g%�"�3I9�qc_G^� �42@�"� � �ATh�.@QyD ��65he�� �)�!�!& �IR?R�����6.��}&\ %O rH.G. Ieet� p R�!ti�l�~�I �k6��9�(se t�Frixion�&md}�*�"itat!/m��2�f"ER?R�i(3.uA� �Ix� ��s�vro"� ��1bi2� ��y��w�!0Bцo^trend"�90�*i��B� I8devc$�� Z� RZm=�:��{� 6`e(:A�=K~�auau_!U�+� ep&k6� �2�raa@2853*8:�q!�_"!Nm4hm4ic5��!">�6!!�!��6EI ���+js2 �/>�s%�J >0.8� ���b�" 4taB�7!3,v ��� >��,9��1x�T!��w*�F {�O"=-!H:�(m\ thr )'��7�, b�`l�M� DZ�zx�J, $�~ ' rho$,�|meg"��x%�leEB�+�;�w vourbro� (`g� �ic'5YI�&� N�gI� e@1E)� fl2�6M ��9�-"4RA:�� 2<�U��o �#**Xq1"MF%M8t�;!@�pd n"na',� �%n"RY���t |�)y�!i&mi�1d&"� zq albezin�4��-�f� N��Aj .5�q�(0.8<\PT<4.0i�Zͼ��& 9�!�6/j9%�re�|no~+�"o��a2`a�2a�or6b �}�). �}  k�2tId2#"B>u� ����F�J�<ic�\#�e����O;%&��|v2O2Oa p�..xV *� �No��t�+Z ~{} ($>f�2�"� 0GN��"!�?{ŕ.��"�� nFlowQM046�v��_� Ellip�� $v_2$�.� ]�Jh#Aq�a�& �2X laue�' �nd.�2� ARg�e�V���e5D anA�eNt lassesM1���1�Et�R"Y�}t�6�,. Ha/a7MdE�to�y� m�]��-E�=Ca?��W ��"i?�-��6�I?N{��[� .na/:�; %�JE� A ,8�=B.�f �937auY ~�Mu� iOܮy,�;a<��B-�!&is�^.m�K.A!C� �ic�W�X%!ic2�{` �.9E�  *�A�.� ��?T(�,�bclu�Q:e@n^� ��S!'2ui/ situ9 �2� Cdr՛c#" i�:�'�r�{;s-���rde�is�M&"?q�ܒ QA] .�.*!�&���"5M�d �9l��J�$�>�a>�6A�  J>.�? ell ���>�8,:�>�*�4�Mm= �A/Z�M�l/ ���E��pN*$sBY/,�uZ/�Z/,�=wIZ�6�J��&.T�YE&4 :E=�@�25%of6���6�.�j������i�^�?�1��"�(�,�:XR��!1�\� /�%M�E�Cs s6L0, R/= 5 ��"~-a��Q�.P��ja!�od,��u�+", (f�L�,M}�R�U*j@�tx31aH�"�={�).�k*�<RTqba< �Yni�ѧl.�$M�FB6rub`a��� 4,y�Jaic*e���X?RT5ru�>��y>Ed�&��,� 2G�� $D$:8�T�5�R�a,��P6�Ad2�@��� a�Q�e7 d�hrea�noA>!��~� �& s:tG;{���ma%�To,R  q^g:..?!�%�"B��Hbe ks.AiV�. I n�+��=-�e~�;� <%��a!5BU-'ZF or*b�xEv���%���&8J�B�l!^���B��*, toge� ��aD1 accu:.zB�%h%z,�Cmap���.� � -�- Q�mDa� "c��qy� ?B$hH~8yt �pxhAore�7oIHna�� )�sfsOLon!�0C*{N� name" >WP {88}[Pj!2�I&3Q6 M2�T$.} (NA50 2ՠ,) %``J / psi!*ZJ�i�'u Pb2oC�5�per %E�on,''7"Phys.\KU\ BNU�410} 327 %%CITATION = PHLTA,B410,327;%%�P�T2F* MoF DdS!��L�T11K.�B=2:  B A"�;G%�;B!(F�,>P�7CB,n7a0�F�I �H.}O%� r5$�.\)+9$@582} 514 [arXiv:h@T010289]6;HEP-PH ;!;%=:}  Sr�,I-� %+tag- 0e+ e- %annihi��PI �}\%�0bf 62} 054001B�03177^�.�"�o@�6 S .�Ve&PH�@J(Mid-r�2% * %��.���+$%s**(1/2) �� -GeVNy1i0$91} 241803.ʰ304038JEX 6*�0..�2SW%PF?*�VX�#��:!!  p(T)�a %.��� + A. �o۞� ?+ ^� :sA]NH17�YmV��-I 5015:I NUCL-J2Jr.vB=K6  I���X%Mo=FOO�@eJ%B���2�1fBD��U��7%c5��NLs(NN)j�"MW���%+4030056�5* .*2 C9)6 B, SchalRA, G=t�ZM� Vogels�WW��NeN�C|1.�toEk-Ek��a�~ in %�^=>� LMolari �p .�N_��7��5QY��211007]� priv7�Wun\ ion6H�� 7.GB;=9KF de Fi= D�I!3DO� f un9��5� �eBIq�3>v#6�R� 57} 5811 :B971138Z� %(\,h*s= H  M6��́�a���� "NUR;BLr" K:p> NJ95on]P:gQ9410219V ���AdlqF�8�6��&_��b�Sp:lSi0!q:at E>�S*�9A�� Au %!n�6at�|&!N�0��"'��� 22f� 4022.5*/93.Tai AM.F��J� f��} %206J* G30} S809u"�4�> ��4022..�$�2  R (HardW`beJ�A:�=� botto.��I�\�Mod�E �12} 215�q111271�P 7.�C:�'9B M, Fr�#H S, Mangano M L, Na�6P� Ridolfi G��>_t9bb �=�P .96-T JHEP) 040�b32 ph/031213>��E ^��'V��� ����e%2�ex�a�-��* � ">)?U j�89} 129b:02A�5:�� .�Ad� 4fc�6 J: Z� *k:�in ��v`6� :}� 70066}�.�2�69�6 S f�a��m&���I!� ��A^3"J%�,p p, d - Au,d��q�^ 1189Q =)305>$=*.*q�5m�~=B��Bb�>���40831:�Q� .���ta=�6��� et az���&�4l.�] %b� �Q 9028.b�%%5�la"\ Laue F6 i�s�� �>x>��W�>�caps,prc��vtex46$�� !��C&Uc \title{ re��($^2$H(p,pp)�> three kin�c�%+�$s at E$_p�j16 Me*۴T {C. D\"uweke, R. Emme�eH, A. Imig, J. Ley,_�,Tenckhoff, H�a etz gen.� ieck\��{C&,�p�cBaffila){�gx�0 f\"{u}r Kern�m k, U�V0it\"{a}t zu KNgln, Z2lpiu�D{\ss}e 77, D-509370G�hy} ;d$ {J. Golak�Wita{\l}aON��3��x��llonian�y, Reymf� 4, PL-89 Cracow, Polan�F) ,{E. Epelbaum�d=J,<r*&�,Aory Di}�D:Newport(s, VA 23606�AQ(uthor{W. Gl%8ckl�.iB�TmR�� �k, Ruhr->�Bochum :s1-�150!�44780 0,5�1�{A�6ggfz;�ear ���Q/1W�ngt! Sea�30, WA 98195-15�U!-ei� er} �k\today�T \v�.*{1��.Ea"�  W*�-�� s�2��Hupy�u�=i�#~�:Xnp�3-�!e *y (FSI)co-�za��r (CST!van 5�ateIr (IST)Ռy. ��:�""CSM=�>*�s &�\! (CD Bonn pot�al al�= ":v` up�d k�-exMQ(Tucson-Melb��ree�'A6,ce (TM99'), "@! ��=�o�'�oulomb =F. ��P��� ��tZ��p��re�� )�e FSI �>�IH1�LCne�DJ�3NF) �3c&��in&D�U�force ��^>�e�64�3�e CSTF0 �s tS yIST-"s�" �.K/OR.�� ���see1>)1�$pdu+e�I�k� es �!pmQ�P%l�)ɡHc�cAn k5a�#{!&�EFT2�(A~A"%nw>� N$^3$LO�sR  �!�� %M a ra�V%Has!�U+ >%r�ST " %sA���� �U�e��PuIB�>�_a �{'M:\�e�Wc(B2ETE� theyʍ�l !esRCs���,o%ofHs. S}F art"l i66-- �>F�B ev t��G "NE"/ J6�U#6Ma��9[��� on 9nu�[&'8c7"~Y2�A# a�x�JoSof>(�3s*{h��^E��:J"#@� ���/!�`T�UY9qQ�u�&e"�D�!Ms g�eA~ne�% cZBicn�n�5 glz�i�P>pr�YzP�PX�dr�_AfA'�5on�$llern NN��� v|C LS�p�\$A_y$A=low�k(i.e.��a�b���F$ 2-�) �on-deute_4(Nd) 1|*V`6�sVmvp�Cpd)e��2]nd)���'���� �; 3�X �%15\ gang�u#�a#>max�� �(wit94,kij956)�lsTWe ��aJINd�.w� v6T_a�� ��5hddr��� � $60$A ��ac�[(g"A�in(A�� �s�"*�-� c.m.�e� equaAɡ�a&a�lne perB-i�: % i6Á^beam �7�46�j puzz�M/e�ces) too�7:�2*Ha�� 1�)E�ste89,str89,geb93,set96,zho01}. O1*�$��R)�mF�9%e�xE�� �1�9�Yڅ�e{� &�t�D�!-*W�rtbiA���� �4rau91,gro96,pa�ish03XW�S�~� .rNA"n&5in�g nI si-f+}64 {vwi02(42{$( earlier un���# %# = lub9=;z*�epancy>%3 up. :�4rk�, +r �.e���chY�&�+��%{y3(roach�(|pd(l�&E- �epe02}HTh#��&I snz���, �ne@�g!�z�y��>1�``l<dard'' �bod�`p+� nto � 3N!� tinuP��<.g.i� Bo&�� !/sent-day� '� ['N U[t%�BJџ>�)?tor��JN!_}he ڮ&� B� (TM)� W(coo79,coo81�d��, �Ne)1��al tri;"b)ngq� �nog97}zlll( �2I�5cH��oMie�R�r�� W��+� s�k!�gs� star (Ss�� � � 2�_ow+yeE,en�lob�� ��_ow �`>A�rC ,.d= lete:*�1'se �+.C40"/b�2!��*�1sme:m���x1a-�l ,6�eS�� �LL�*� � ��"� Y$n,nn)$^1$H%Z %��themse @a� a@ I3%I4V_4=\sum_{i=1}ǻ^{(i)�5 ��=�Y�1�~ali�"5a a}� �Pi i�c&j��of��i-\pi$C3NFi�}, �5c�zB��'m'"�-od�\E%S !�M� �go� off-shell �N�>���i$ s�{!�A�%e�upAP $UA&�0r�~d! t w*�u�Sas@dm/�},�+1%�U_0m&( 1 + P)c .:� `sol[x Eq.( 0ar�naERial-wav�5A�j0$um�I��. 2Y*�M@y $E_{N}^{lab}=16��!� �)�mac܁= </is!H"�0&� .a��KsetHa�) �1cʩ� �8!� chi^2$/da>,v�>"] 1.  B.c�XE�1&)��y"��a��� Q�sub��4to $j_{max}=3$ �Ce�ac�. !�"3��4Od stria�"��!�y' �$en y} 2��2ge5e���I�a6(CIB)a�7NN2� J�3e�}S_{0}$^F��& Q)C3N isosprT=3/2� t~D)R6r-� E���Igu�npUf $^1Sa�]b6\�1Ua heck�"�i�3NF"w�e�H] �B�� w EKTMRWF fri9� k�BA�=�{"�I)815^4!� � E�. S�^zQEt�  .�<;&X��?�#g"�6#� !�� 5 � s Fi���>�]np� /. . � �yeT�&��fg�w&� "���{�Tep|deBp� *�e�ar&hw!�M�AEf��F��y  (EFT)!;mK�� �?��Yc upo| eu�R%,��t� bro2� u�e�Qa� um Chromox . A�DWeinberg�c�1 ��yx�0'*��%�"X:��"� deri�D� G �expan�G�e5�pҴ!�| �a\" [Pg��icW�A�Ucalalr�o ��`t��l)�on�r�<�PM��aP l�|s��%� �$dH-2. V���$a!�7 I�l"zy OUa�few���%�SrM,� �m�G, 1,EM03,Epg| �I ��~iUANn�M� topz%LeadQ�fn�to-� BvK}^il i IpW��st��wbq�aIv?C-�or��out���� 3_2}���  �2�.K���ZgZnn,upp!K� �now&�^!ur &DusH nove � i�w"!�or A -loop� � �ZCΘ !�3���W2��ۑ�WA["�Wong�sOkx�ٺ�l&� dimee*Ƈ.�"�D -!|��=&2��+�D��m� at R1 (Ev, K1�(N�LO)%�J-F5�O !> )m2<a�A�wa�� � remiE)LE�� ]"  It��.@ ! ��{.�a�4�=e"Ot a��ta&�~ �u�����0�Z�"o!ϵ�a�t�+ o�iG)l?T!m� IOM�S-���7qiY�Ua%qNN�; � Y+X��xB;at!2� a�<��i�, !� ��s, &��al qui��@rA�O �b<��up��.���ItaCulnb�l��A%�onto �t=2 ID(S )�assum!�B��ion�d4 is basedA�methods ila�� thosa�scribeh Ɏ@pat96,gol83,prz99� i � summariz��rieflyE rst jp�]��A�knownU�嘅U�� to)-P!nund�hea�ump�h m��� masse�< ��\e� ed)�o� e&� ��A],near reli[be������:  yPs!NJ�u,. When buildAK>�G< e,c� y sor���ц ccor J%5ir.�r��dily� �&E 2�(&� Zeit�x})�e�:'�� A� duce tra� ridge��v��� �����!edJ, �Ynts!�8e smaller encloareg:A$e left�}R� encompI9t�,0peak but also�/� s a յE�m� 29whg has to be�9� l� r �gon mar� C(r)I no� _)� . It Va rea M�``%y+ / '' \HC(tr+r) suitably en~�facV!V$� $$t$_{exp}$!�A!N(wzVZ E possibleUerror)P �-�}�E!z� �]% redur�>�Di��F� } .� m�� ���ly -h- a�i }� wind> � give���*, ͳrAm � ��&�< )�''�� � um %%%sh�Cin]�ab!d}%% �obA�)�1�phe ``9 ''� �+2x. OA�I����ota� s��t��� z&X !뉧 � \*�F� Y u� f� appli� f�a c�a{oth� su  and el! nu�eI> � �is-�,by \begin{eq�$} N_{tr}( i68 S_{\mu} ) \; =!a�} N& , - \, \f:1}{V}2R- \end{ \noindUe: i�alm��F� �_{Smv�\sqrt{�tZ� ) \, +��^R�}n�� ��1Q$ ` �Odiscr� bi&{ i� dth�!�S � �8 As5uin�p�.choicebin wQ��a\--%tin cerag2 mitssomewh�"K�Kshould�goverm�qcriJŬ�M�a� �FB ;$ denote\ "� tials � a�!`�"k ,U���$��/s >B� �nd $N �9��&�jed� $intensity.L3�1 �F(i.a{6W*�W).qV a! an  rval�-�$�0arc length S.&13}p q���54'l� *� 19s. We��#>�� 2}$H(p,p)� $H�� �%JG2he� published���[ � ���result)� 6�A$ofy� originu m� syst�ic d!tt[ 6i:a� 6�e�M�. A"F4ly we have anoW B}� �R � the �/"� G 1� "�6�:l�un� t� Sir�ign�� �m� loc^ˁ0&��d1cho� a maximum����J � erT��:��&� %%(seeJG ). W8 ok au��ly 0.8A�.�E  l=�@)O 9}se cu��"�var�� ��. ��t6nI �is�-$n 1\%. SZ.+ 2�to I��AT��>l8%����"q on�seQ� depend64"�c�n;� �cas)ҵֵ�= 4� (CST, IST��(FSI)�*�v��1�3\%IeA stud��"�f averagF ŢX�-�. g� e�a�ly�8� s3����jsa��36<!�oA���st�!�uJ, P ?�ris�s mad-`6��?io� ly.� {R�8a� Disc�o� We `e%��� theorA! redi�c8wo ways; one isEd ``cl!�ca�Faddeev.� �r� eci� NN poteN s, }��+"a�-�on�+c��La|)�ive-f �y (EFT)6� 5N$^3$LO%*&VC9qtoN�� th CD BonI0TM99'} Since}իA*�%��~A��z�Av�a�!� pres,�' �&L��g�ASd6e9b lead� ��I�-M/�!nge�\2�~ r�1xe&Y 3NF`modified Tucson-Melbourne)Q!.cAc�.�^followa�t�!%�lsK$ percentag:viɮN �F2� s caI by%��� A%b:G� = { { (NN+3NF) s? (NN) �y%\} * 100 \% \label{eqdelt� e64  Figs#cst}, #i a3l# fsi}�M9 ��*�5�e�} !W�� I��Q �ә���3 thema$:�Z<�R agre �����#u! is excellA����CST.�;wW suggCtaE��s~J9$Coulomb-foAh�D s do� play�*�" roleU�IST�rE� a slm�bestimaZ#!D% %w �mayY~ ��'� ai{� Q&It!*s�!�_��hqKas }�!Vm�~v"f I. "�!x��1E!�1��lch�: {En�$� Bd���+@an $\approx 2 \%$� � �b � ��np�=��]1a|$ ~!A��e� b3�b)p ��!�.L�&< # � �A�Y!-co2��(do be in]iUd!y&oq !�a)/ (1.2\%)*� �}r vely �*�-�c)�SM� doesE}a�% �l�$u� F�!G!$� *D�JboEFT.,}M�RaW[i�,�1sd&���so�R��~ w����-�! 5p5�e4l* ed Sg�r>> two �DI@NLO�!�6Oabove, �0N$^2$LO 997prettM��z�, like�� of CD-�. Not�aA� )$eG!z3N��a��{ye4cluded�ic�  is ae!n~&A�in�nt55K�{ , ag�!�� �2�,� band����Qa T!3�.+��tevcy�=Z li.�-� s. � in ��s,#�����bin��jl H,Q canwy �ct-�*!(nA�alce% M�i!�? m�m�2;$ will shifHYJ��wnwards.�6�at�%no)gJgQm��ensate!� ly higher{> -*1aZ&to!�. Su\� A���tI�Nw��in����$Y�A�b��cw*��e"3(/*quantiov � reve�*�m�2�)�2jAW�8 igwer b��1�1.��� minima. &�'S�!y}� �  deuteron- �V� np ��2�, +�&ar�'�(�,mediate-star68IE�H�8A 1�.�� n&�/J&� ��%[FF �'ep �0� :& } well��B�a2� $, however,1za�!�� 2��staap��, s�Ge{ ,(rders requiA�a�&c 0asonsXA�.x. *�� earlY0� � �n s good��q@�\ )��oN��*A"��x de $*Fe�iIW&��! g�1N� ��%�i-ogue neu�t->�@ �]:�m+ cM�I��,��o fortuit�%-iew!��misI�� z=',$ B���6 �8!w bE"Wf2a� remin�F spacm� %FdQ,  e.g. /& e01} �A�. A�i�!"p &� Enw��!=A2?B�8CST� �sduZ>� ra��68one��C�%� ��mb#L � ar0a�&�i��q��"Ps ~�%+i�M)!Ri)&ven m/1a�= for ��|06y!l�����^*� a���. CU* � �At�FJ!��wa!%�$ \newpage e. *{Ac1(led/4s} �) work4supporS PoD$ Committee!@ Sci 4fic Research �P grant no. 2P03B00825/by DOE � '� Ls. DE-FG03-00ER41132�� C02-0187-����B�(U.S. Depart)of T+y C�0act Nov4AC05-84ER40150 ��yE/ Southeast�Univer�5es�Assoc�(SURA) da�Thomas Jr/Acceler�4 Facil�� n�,6A % ! per�d �Cray SVT3E�A�NIC�>t%pMe8!6B? C.D�_p!F�lin�J+$I. \v{S}laAlD.E�e nzales TrI*8r, B. Vlahovic,A, L. WaltA�6�i�}�B38a`22i^6W4zho01} Z. ZhouAmS. Cr-?J�ni_!q2d�YB. Qi�8A. Macri, X. Rua�H. TaL R.r�F8684} 545c (20012rau91}aRaupr�,XS. Lema\^{\i}tre, P. Ni;�>R. Nyga,� Rs (nfelderb\"a��, L. Syd��0H. Paetz gen.eQ eck E��ӥc��)&J�535}, 31�(96�gr�!�,Gro{\ss}mannElNitzsch�Patberg,E �S. Vo��R��&��6+6�AKDu=� �1603,} 16�1:J;3} c�R.j�J9v��V�J@I�R&'53�49N�ish03} S� � S"r Anoma� pd B�"R"�@ t 13�" , T. Ishi' T. Ya�<�|Och�Nozoe��Tsuruta,�NakamuraEJ P. gY]�K�9ga Mod�}�A1a�436e� >.z vwi02�SiepeEDe�V��hnE� W\"atzold�9 We%� W. vonA�s| n6Bs6A�034010�22�lub92}Az�� Diss:,n ,&� t"� y}i B409�F�?7A� %209�p!(F)e��(*� J. Ku��'s` ,. Skibi{\'n}Q $Few-Body S�"s)Z30}, 8I~!:)  ��J:� wit8&X � 5�>y2�M%�2��8E���glo83AW.~YWThe Q&um Me��$^,Problem, SpJ\er-Verlag, Berlin/Heidel�$ 1983.( hue9vB =�a�:#B� �!� �17����{7} y�`���&-~�K Acta�Pol pB2�167��E�5cmac96}a�Machlei � 4marucca, Y. So� I� Rev,Ie�8 R14 5 \A51E�=9>5�BAq. r 4E.6mgA�qfri99}a>Fri��)�)I!0U.�@ Kolcq !�Jo5a�5E�9B� S� �Y`H.K. H� >\:� �e�13y�9<Weinb� S�pinA�T.v$ 251}, 288�� 90);Jh B 36!8 �16��h22��2=�1�Q�J*.U�8�" 4787� %�U�EMq $D.R. Entem%ZR+ Q�=��C 6A�041�s6XEp04} 6�M��cU.-B�@nucl--th/0405048,J�By*�  A.DBvK} P.FMdaq�/nd:AnnX v.Gart�im�52} 339%"2F�3}�� Eur�"J h A 19} 125j4��5�A3_2�kbj4 6j�EERN��dG L�A ry L�@W�5up)�Q12A�PAW� 5�%30}D�?}D-la� Bret� urgmH. Eich� >��h6in5H.!8 Helt%��rQr� Pre� r��OswaldNR�chnSFm�AV� BIR�F  1394 �8E�= p�7(M. Przyboro�M. Egge�emge,M� nzel� = ���s%j�eh, u�)�C 6�- ��gY��3��Tp hill� Greenwood%lWillm"D.C hado��mM�C�{4B76w14.R H. Ogu�$S. Shimizu%�Mae� H.*� �akashima� Morinobu��*l 5�576!�� c x*t:� %%% docu��*\6(style{empty h+tAN}[htb]�4�+er}@tabular}{l|ccc} &n&k &FSI\\ \h�< �4_3=�4X_4$& 71.2&68.6&51.5 \\ �M,_3$&0 &15 &044 $&180 &165  \\�4� �ca�B{�+.OL:JN�*�6p1�BUC�i�,2rs. t),!��&��,figur!�2>�B��i�U�F3.1)�M 5mE: 'i�7r{HC&ZI$\L -gK} �H1&pr�S�Q.y7 pair a� \sym�R/:1=�nd�J3986�F%F4�F*�ET�6B�Bm�Jxx#w e a c@Ah(�6+�C) � t&sAa2>%,.�D 2:�E�EEBO>=v<O(pl+�Ra funW4�tim.P2�FScM�F�%&�?'Qs t� ,�y&B�$[�P9�8<�L!%�iP�HU"! � �4�H. m�RJ���z\q��B�5.]��r�n< QX"�<�4�<"87at�TPtheta_{lab}=30^\circ$!���!E>0l_ R>��O��9zK*s1. ZbjC6.C4���3|7�+�56 $\fMD6{Ab=Omb|A $ (;�� I)!b�%�;. E"�*�V�?r�Mc�68X9O(of j�)* B�6CD*�5R/aUwit�$) TM99J5��1�0�$ �e0Qe depipKs#aa.pej�5�5v5"�$Q24:N# 7�4�5�4�4�2Y5�*"�NF"wYA�>q -����9t-_ \i� q�Ns8�sist�s�s4�s�s%s ���^�^9f�R :D fsi-ef��ֻ�b�b��)� framev(of�EFT�X*a-bk�8>���������10��cst������.�8 �� �����12�6�VQi�}�}� 1}z� �)�R� &��2\�@ [11pt,two+c]{�T} \usef\{� 6�A6amsmath}��kAppnewcommand{\hppee}{\mbox{$\etvGa�L\pi^+-e^+e^-$QK:=gZ< 8+\gammaB=et.;N p2! ^{\prime}BJhpp2+�.� pi^0B<ppetahpp.<pp\etF2n22n22nb2�J32�1�MS\L3T( si-f�_&SX $\bold�\�K >^{2)\}$ meB4 �"5 collnCsM � 0.�:^  D�*aniak-Ka�ZH. �\'eAKb}$ \\�{\� \em $^a$So�a$ Institute��u�WStuC , Warsaw,:and\\�  $^b$s Sved�*C, Uppsa`SwedeO B��Z� \paraI0.9\text�}{ � 1AbsN[:} �Some a!"� quN�of=����X�s>g-2r95 �E�F%A#ZJ� b�0@WASA/PROMICE ColljVLto ex� N�exc�8ZE�%��R`Q�on�55G D�Zr[Z�3�D�PFeasibu0�sP �4y" A�? COSYN>� & }  ~�s�FIb �L>r]4obv�[,�9% Fermi mo%-�!E!%"V1��Na�� muu��/s&dt�DMHS2t\on!�>�4!im3�!>��1c�=:;M5i�2Y�G suffi@3(WppuGat�=eA�iaKL2� .��C�B_c��Fy avail���E� ��-��*�]-4pA� asL5of 9.�:��a��e�] So i�Emd�longi�@� ��onent��influ0g:^��`�A'yf�:g�u s quite f#9en�Qu�_�C�Fd,>T9J�Fams. �IR�,�B�2�!�a�Csteep27�itVAdra�kl\;.obak2]. %mG prob��)S-�:l<"�<�Bma A�l!��C ut 5dS/cE:seems ;K be neglig@:$ a few GeVEu �Y;rea�7�;at 1360�SA� (%<�;ss �>�CM i�%6be��d�� 43.51. !�n 5f/cQ��Nov'upstreaoI� . At 250���F5as�: 58.7b . Su�j �Bca{L< \� \6�>@�qn b?!� magna6�g�5"�;aY-$of:'9�etaF��Z �qQ1���Cid�Dm�A$�]#~�KQ_fig}."� -0.�� + }[H]&!� 4*�  {2�ste� [s*0.6:} \hfillfY{>oRZA� �_>�T�ed!I-d1�ceo*�i5nA�%Bp�A�. ��o-9312� �3exp�3:3expr3g d $Q_{CM�Y�):) M&;F xQ�$p+2d+ � -� U�f���`U(� "Qr-a��Je�z0A:�"�Jc�&spo�BV �\�ulE0Mr bec�Oa�d�Eols�M�d�Ta�>On�G� �B$ind examp�6�#p�kz�=�Qr]�2Us�T� �t~ �=d*} � �s��aany) � 1���F �rS. �"R�Ive��&K 6�Y�i vV�� � so lXly boun�g�g��,. Let us tak�++u)n%2J��gp��  �&]" 2�(��0pipi_bmp} ). �P !z&H�?� 5�(fuoIqua�R  fig.>f�MtbH� + eUCai�f�s6�e��,� auth5& clai�dtt``��% ��Y enuBb Q顐&� 2�W'']8thAZ��2�M�attac/]:�E�Fz n fMA!�6u�S6� J�S!� not �vi A=ld.�2���;X(Drr�ting ) x�F1hhifa� �`9 6�. �qX%I�}6�5���Z�Q�6�.=J�. �:YUպC.Xvav �E� F�p�"a2� EF)^"�ofn:�m is usu�[wr�.q e5� � forN�i  asymsof�(Wn be Qprono@^%LtY tail2���enh�d�du%"!pٮQ�����e�d"�jm�ʁ�$um vector.1 "�F{6��oi�k&Tݹ��@�j�sT\p"Ebyp"c\&cmI�,Stina} � iditRimpulse�1rox>�w� �&!&AlI^"� s 9\��ss8Yi�iY8�Q,q�*�n5>atylE $p+d . d� a (p_s)$ Z%p+p 'nv'n 'rN^3\!\!He�h eta$�!<�b qpV(o�F{WowY�qA�5d nt =�1.bTmpm��ju�n� m�)�cY mu$�]6�V2{�$^3He$��o!LMwZp-V fqM�-��1h�Cm �um ef stat�a ��double *w�%sc�0�i{�J�w%tBKmyl�-aufew �% 6� 1it��Be�def���.�~iz. Q�.�!�Wph��Ps!��".Ot)0e��edivN�iwou >mq y$ topology:�l2�=h�ssl�"*!�)i�at� �W Qe 2�os�_8_"e*�candid�I�K2<1 or 3���i5+b�re�I3A� U: al�2 G"*�M�f tcase.EO""��u"�.���"� ;Sies if :�a����Bt1Z�3%�trans/� m�+��i���!Y��-~nYp���)irer��inT f� i(b&��OZ�AG4pP�e�ch�C�k�(Monte Carlo!��rm���/ II�.4g�<+4��pN5FDe yl�f�N?gye[�i}�V&�i> sh .inOq�Rs:23 E_{ta&t}=m_d �/s} = \�n m_s^2 + p}$,.���s���P�``''I�=�e�j�����@ANUB:�d��%�Z+VVg.2�.e�weigh����u2[ �&bQq�MCQedX5!ya�Es�q<�.se�dl�fi�~h�_��6DMbq, ! N:UF� �xpypz}�Fc�\�R�*2�As�8 of.�*��I!A]�m� `9J6 ^#�4s �2.� B� ��2�"(10&~��:0(op��M UБ�)�:V�U���Y; hist�:s -.�,1-k��Y;a�?}S j"�" z%\"!2Zx�/qf2]R_^W�Bb U5�2� �k���"�_: 2 !qCM��"�.BF��rg��92�qāns �rY)Bi ��@�or B+�3��2K�Y"+c�win�i)�cc?U5�!k$�� an *چ argu�!�V� �bcf�kd�|2\etFon&��X�fideq0� tN~" r� . �P���VBs9cy *� �!� 2�.�<9"QuaJ�%of�p\)�.x�Te�"�"9F�cre�i�I�� 5�\J\ ��Yz,by P.~Moskalt }�K#-11:� MeeIx�LI�id 6)�ik"�~.��N��T6���5�n�Y��s/�. W.Kt5Nnan �� :N|�ae! deca�$�s5"be" �t�$-gtabelka}&*� ^p|#�Gd �<3_� nels bran�PgS$ios!|%0�:ed &��Calen������>���&Wp lof BR%^.��o�%ae)&�fMkpp.{�m�� cm}=40$��.2K ��=|l+ �= &�\�9inc}=$"�p\f�255 �i(�= STۊ2�& 5��b & 0.25��bF?B6�:&��'$+ $P3902PJ$�0 -25 ./V.� & -b>�1Y �2�WI�B�F� 66\%!2\%MFR�1'& 4.�2,�& 4:?� �c�6?I� AccorX�pur���"�$ELSIUS/�Aͅ;F~�(Bg��mw[iw�triSBe*�pconڍ��� rg}�R�>c�Y���\promp�)�T)�2�!� ��en��a��4_&�`�ގ&�"�a�Te:�exploi�asprea'm� a��"�:^2>�� R(q�)�"튥- "2��6�2��.��Chp�)�~to�M�4� �-E#on*b(e�f� �%& 'b�$ To achieł y�: �d��v#"���(EJ5`- $-yh#! �mُ��E� set-e�(to�#�g�h6 k&1-> ^"QE�6)}��.�0��:�C{9jC�[�IKCal�-eh*.2ZD^I~�. 79}ZD7) 2642.&NE�D Hagg`fmED�sis"�-.`Q 1997C�P� ,�Tr} \s Forschungszentrums JulsUM��Ma�}�e��2�11}�H1) 27;F%� *2F> pacs6A(ke PACS cod E�q3keyF3key�s- %:<6 aps,prl,p-,�ped-�$]{revtex4}�:F�>Zwtw-~:x,�!C%-:E=.���s,�6�4.N:MB r�, tB�<{\topmargin}{-1.�A% You���Bib��a} apsrev.bs�q��} AE�E�QTao�cPe i�&ct� %b�Je� (cile),%"#n}om��R�  % be�if ne�lar��O"(cV{ �648,graphicx}% I��}�I�s2�8dij}% Alig�3�� �decim�y�2;bm}% �6 �82~6��J� ^ݰ % Us��e \Q�Rm!�toyuce� r local i56#�re3 % Ie !Luppers#hI corn�^ titlHg�J�����Mul�/J�arx�5�'� �s'n�uI'r� ��a�� %�� �s29�{�JT�ofk( \�{�)EOt A*��mSc�A�DO�XoYS7(c94�i repea� e \M& .. \�� etc.vDneeded % \email, \!{ ks, \home�M, \alt.>� P3y!!�current�y.�Dlanj#y �7q�go1�[]'�Gctu5�-~@����ur�p�6{}'�� ���APl|��1�a�vpr45 macro�meach typ� *L !.�a�A��SI�'"j ��Z=�RW|&�!� %}.�%:=�# 5�/)6�)�!�� M{M�]r��}$} T. Pv�son >�[�RF -� : ]{Dept.A�Radio�%��zjces, Va�%bilt ")iPy, Nashville, TN, USA�(M. Planinic � :�B� ��ic� �i�# Z�b, Croati�{)�{S%cVigdoB)C.�#g r,�E{B.!Zgenwall��� $J. Blomgre!b2}(T. Hossbach>SW.e cobs> C. Johans)�2RASlug>�0A.V. Klyachko>P�b0adel-Turonski>>L. NilNo N. ORS. Pomp>JJ. Rapa�$^6�9' T. R~fe!A2�E�S�gen �2$U. Tippawa%`,4.bS!GWissink>�Y�d \\� � []{Y���Q��#" web �3i{{�&� { ]Indian2 Cyclb(n"�kaB D2�lU�Blo%gt�^IN 47408e3\\ )eQ=*�"�, e= ,3}$Ohio2)A� s, OHU04}$Chiang Mai2/ , ThO:�= ��6d9? if�Ds(�6in-� �(B�  % �3�"'). \no=^� Qd ()r�m be %�Lw/ �m߱�). %\c2i=�`:G{A 2� \$$� da**Ua�>}*;"�a&-*&*�a nov�*agged H�*"vw"��}s� np5�.j #"Τ8 m 2\o}��<�xv/.s< f/��(Bglq ndk�E&(2d "�5A��9-�1c;$�#pz!�.��< coupl2 o&�/�=exw�ngv?�  seriAt�<rv5c�$amp+� selv �%k(�t[!P�+�?es (PWA"�0rR?�7 in�tcF [�PWA� d�exa-�2'�|rec��ments8\end]J %w ert sR�ed� � brac)� next� \6H{25.40.Dn, 25.10.+s ^.20.Cz}N["(-O u �0 don'�#~�3is %\/ \make  mu� � � ,K, q&,�A��ASJ F !igskip! m-mNh�f!3M ��u %�A�K lagun y�� Al isteEC�E� �"ő8a�ic� esU\Bon1978,Hur1980,Rah1998}l$sQ�bJl!Nʤ�:sopX"��e�(Q� Q� E��a6� wHSto1993,Bug1995,Ren^} to ign�2major-(�|��I�^M�d6��h� he ls�a^�!R�8/��hea�debF)| 6�!�uwe�lV1BRen!2(,Blo2000}, ��u��ad� ``doct[[ g" (�=y� reno*��)� $``salvage" egeda�la~ !Q՝ deS2002}.�7n�,ympiF� e�E�e- techniqu6� rom {MD!���"t��+yol�e E�worriQ��k��pae�"<@��y� invO2"H+&O'lete �-.�A]ɰ ��``�"iD�N-�Ny���V Pet200Z^t �gd"ly ����a<u2���ji��a_vqQtn�� [9{A;�  flux. "a�%*p#sef.t.)I_.[ �e;LXgIte� sigAa �ie8�6-&� To7Trayceli�e����N-2�͡IIN8E��a~� .4)�j care�y ched��CH$_2$7C(�74>A2��*/te *�����%*� &�,� reby'�e+ relie�onY���to�4�AYnp]� s�: �s�Ds,A�b���m!�iplL�xaljE�,s$�a�he�������s,*5�owed us�a�>��&�0e�T"E %��)IK�lB�&Yq pre�G 2�%P�&o ^ a!�ful:vA�a .��.:�-inJ�d"��^"f��Tpp_Ɂe�8s[scale=0.32]{s� _prl_fig1�)F�* fig:f%} Top .�~np]R���upXR � ��ca��duf!��2y�Kof [t�= �x��'s�hL!W�Pol199oeE�ap��t 3llu�K��Z��)�e� !de�6cݫ�A6xu�� 185-19�B�1�� d vi�SA"�hA p+d $\�a�O$ n+2p�\itQd� _�, 3&4>coo�20�qqt҃ eam,�Gt�]][10ngC!r1-2 mAh a��ݯ.9(ium gas jet�� (GJT thickness&"��G4 \�]s 10^{15�Ntoms/cm+�ultra-t�* -&�!��ioU^3lowq�/il �e�ᶡ� (� r" in��>��fb6.4�� 6.4 �2$"4 "�� trip � ors (DSSDW+480&&m!�d�pitch��orthog��"�8s, �5��pad (``��ing")y (BD�a9srea. ��6 ($\!�sim 11�')�$tABp.c,itH>e �' B� g �+�"6�u sur= "7-, a�val��,Ű@4d*��pos4��bo��c:��Zta�%�=co.TZ�l5��mp� 5p� ,�A 4-"#m�2���!�Ȧ�)on�"�# -by-�#aYd� (un��9ed) �>�>"%'$ver�8.3�a�in ���!� � T% �V��&�4a�q�_E =�60$;��$ {s �� x$ 2 mrad� �6�5 ́d��=�  k*�m�of � ou�phiteU,ed 1.1 m dow�ea�3he GJT, �.�"h �p�<�c)9A14.0$^\�$. Both � ��d *56U� s 20�&20�%!"��b� 0.99�� ��2��c�G�G�2�� �� ?E�.)�I�Jve�Zs� cep�-! 9d ��l"�Hz� wo"xI p3ic sc� lla��LUٝSU�H�]F5vetoedB�/B�a� -' N�. Fh�� �aUI���N� a��)G -&*�aA�Ith�)(3-#e) � -wir� &øs (MWPCs�tr�!Q��s$�:�� e+%�B?ly��\%->A vFi�$�N8_{c.m.} \geq 13c, falb to 5Nby :3= 9/���")6!m>&��E2� �  �%ay�st� �͒���\]Z �r� hodoscop�S$mprised 20�s>� barK &�R*i(20 cm%� stopE�D9-�%��� 15-a�%$-�Mef�Rӏ 100-a(@�] Spe�Rde��ed �) nt-eVll�on�6 &�ai�r-��Q��� r *�;(�p�tI>�.�; O h~�A�noAsompanN� �als�m a�ora�)�<��or �*A ~< `�a� %�Y�m�and/o*���~�C�:;1 ere �rd1 ixmurly0lusivK= NNN ,&P��r57�(1)�6X2�i(� �!& d0 ��C ���fing);!$a.� t2)�^2n� r U� (h.5 =� i(3):� but%�hH�͔L?r Y� Y�8 �)�z23"�` )�y\�Ai�1�^�r�U)/ �,s $N_1, ~N_2uZ$N_3$, f4�Y h�to>i �%��:=Akv=5& � -&�a�N-� a��ie R@0 VO�cuv�ll�D:�r%��*�{�Dr�/h ;�c6n$�%�3dBA�"np.�%%�����"�6 . A "on ��gڌn��vs.\ BD�de"[ m�iE"��*/�υl*y��0or�,is: (a) ``2-��"m��drei$�*� (pe�_S %�P's (e& s� �hiǻI adra�[I�{r); (b�1-punch>�+A1w�.R  i�7r8JgO� roug� � �'?Na�BDA���ԤTh� 12 _����a�Ti�Ri���n$)Pp pro(sB�S&�an }Drt�BECeh�ElQ�ac� !�7tI�9���DQ�G��t%� t] �. O�W.�q{a fidu�H �.us�in�oi:>�! "�*�mmon-|'!noise (RGhJ?�'reɵsXquME�om�s� o miA�nt%�e��� %� . A"��J.$ � ed���f��as 6�C@*Amal"�Im�ga� oАe%� � ui�=� alog.��P��r�(u�$��$removed al�?lid!AM"2orͮ"NF5��hiup�%�g=;� s � $�< �B�����"$�a�6Utra��ory (�&!�6[�\]�ed)lh�+U6m�E���� 2. A sub�7ta� a�2�c(bI�a mean� �Nv-c�at-c � #p���Fe� u�{l��[D\rM(lyA � urviSW�!��U �)&���, a�setEi�(to zero ��� u�}�1-t�/ }* Y�� unbi��:��9h6@ ��C�e�}or�|h-���0b��� "SB�a�[)I ({ly 23 �l�I:� AWlo ��.{I�� net� �-�� �� ͥ:b . Ks���p"\ex& �*.q 2!��aA��*� ,� �"|� � �� sp�V޻WaU�\4-8nU�*9.�2� byqu!"@a��>�&�A�"�)�S C runm#�G�pdNW!� %�}GJTa����� urth2� �.3)+ �d� �L f��by�i��*5��ȭgof��S��6 �|��rU+ph{vs.}\"of&� tsO� pfront�)N.m�] X0R)off��i[)� also.%o)$�+c�su�[�Ug.;.i9]u� aluminum (�t-UaHKM'>� sat�3��5-!����dAK3of!�"A��.�s, mocx%�np�}hI1 , as�n�K'��,iy,2��tC t�=�6���B$6ur�Efig� (c) �49�� -� spQumm� �2c��(�p^{sc��X��C ��A�i� S ce.�!mib.�"��a&�!P?�b>L(\e��e.g.},! 8 �U.�t�SA���$EI��276V�h�<�pE5�AlB8)m > " t�R��e� *he2M!r����r�A�a U{� "eK ref� � !1EWd n (�+ ) �� �$uA�%>2�6<E����C�c"yA�sharpe�2$M s (\� u��g�sp�0l�o�\���% . B&��1EaE�a�h2��B�m�"���eL �h+A�E few\0 s@� $ imkB& � 9 ��o?a M� E$PYml}"�m�%uon�x��~� k=Tli<�C| &���% avov�$ I� .�#� edVmX�a&D� ex��(�!��(�@ick2��+hF��~�40B��V�E�},2=Aa�  (��2$-C)� *3� �A3 � azimutha�5gl�gphi�or� lab? \.��KV�' �(da�� ) hi5M XK"Z(d&�ag� tv��e.N()69�8Mq���.8B'�(("of"�Qz� �vma\&toK �}�$���np%u*�1gi�8E�5Z�&1Z_p$&�g~�MegVco�E�&�E[(� ��ex��E��%^�&� Hb�iBgt %�r���or �EE� r\�Es.z%Y &�$�"OT�23�\"b�gle. G�outgoAp���i��� 9?y�� � ��s*� hO� p�2d!�#) A�QlZs:->s')x��e� or� >z tuA�tn� % Qy $a�_p6/���:�e�E!�>��H�sIxta�)."w�fA:Bt%`} ���,q��ypur��c2A,� rect"�)ea��Ny�Ʌ �� �$.o� m��� q 24� 2*�mOe-8>6��un9�,* :�*�/e��1�Sle�EH�+ml��s�b��1 �/:E�"s�q(ycif!c eams 1, 2�3�� J'n\biggl( "�� � d \OҀ}!r)/�\� {N_2 n-b)">@od c_i}{(N_1 + N_MV0N_3) t_H |d \&Cn _{p}M )| a_{A�}:S},AEe"�nO4$N_j$�.r�-� �2 of) ���v or -*ng FX#4<���a�relev�At"*�y �����-z $j$;E_$c_i$E9oJ��=���� in T�?�!(tab:syserr}r  in"ci� � ������c hoA� cu���*ds a�.� s; $!�=�� 988  �0.008)Bi#H &d(2C]�P ;�$1��o����.�a��A�U ���9� &O�"e'alu�in 1 g w�? $E_n$ sli 5] 185�B9*-)g)�A<��99� (�E$<1\%$)P5�} ogH "�b��gy.e�e�*�%{,Nijmegen PWA��3� o� �f�22�4$\lt  E_n \�&le =19�G)�15�(��rosN� F!F" �"m=�in+Z"3�6�$($\chi^2$/�B$ '$1.0)!� &"na�!�ul�h+� TK PF���� �K &TN"Z��C�vc(xE!^lV L':}0m�W� ay-�P 6�" �s" /*�Aku�ti��Si�� �?)��I� <se�3��*�/soX*&�"in6�� �3, Rgd" 2  �Q-� e!/P�i>�&avexs}��/=���/�B62$)9#7w AA�u"par�0*�9i 793)N.��%� `nij3�B v�/F� �}B�Zfig �&�C��2������Y��1)`)�ataE� Ref.~ �.. 'PWA�dŴ5D����*i�\",�&!�shaY$b ��.�M+ E�,�i˸,2�*T8�N.��&�.2o9]l"� �) 2SB� B?�&�aAe�2sO�fi�sA�'�7~y�<��'�M� Uy�%,s��r5Dss�/Hv�2=�s �>havA� d%� un�!gn*��I��s.(��y&W����BSz�6��-�)_ t�g��, �� =79 auxili� m�pp�7) � ,Nept� no��qw@ ����� gle-�e �%��Y�a6sx � 2"nund� .$�Wnom�6�' 2 (bu�t�c) s4 A�6%KZ4�j1��Igg!J�q p ray-��ldis�A+6�;UD)��&O. 0.J ��(s (6.���T⩳�N�7���`f�,-- �ensnv<=3A�"���;"xvxx rial>Q)&���A�il�� ]24/� layev/it��!�r��o�<ambiguiA0Al* ���/s&oI �'b��&S >V� �� !�Ya�Tind�<��� }($\�* �$��aw� &7P� �/0� 015$a "�<�kjZ)�c����F��v0є��a�!c�;�"p'EŁ)����PWA932�,��& �9!�u� � �'�rd� �� {���z�qh��-E[o9a� �-,��N=� ��%@}I�A�5C�p�t re���i i1U��QRppl�, �!Hsa��a��s��}�)ԥa!��{60��& �!�:b� Y�j�C;�bs. Av Z),%��  �//}�w!ol5� trap $Ar��Eri0�"@aX"�pio"CDnKD�Q�h �Vng�avAVhw(i?2 =#748q�003$)�mi5� ��Aű� B�A}) al-*� �Z� t8*:r*I{�� f��s (�r ]�B�.�; n���� �ruled&T\ {lll} So{� &.�F� & U"��y�\�\ �\id.��u�xi2 & 1.!�2 & $<$(m$!�0�]( Non-D$_{2}��6:69P6��-�:���L\^ ~~a�a�nd!N& M4žL+)'&�n{"'�.?I�. �0.:�� ten'�@�nRN S5 &.�{�C bkgd..0. Sr�4�"�8�f W4>!2�W�.�'r��J& A� "q+:%.O%L~~v & $>�688$ (B�v<A�Aq14$�E$I%S�� v1%-1>)_m�E�%�S:� '��RR6eX=$�A�\& $x#(n)� B�aU�tgt. &�7Rz�P6� BG�leq (001$ ($>$12"�8) AH~~�edBM&)T&E>�17$ (9S\\  &lyC^�17>�pm$�E�TJai&0n[V0�B8/imes$X [1 + e�>�z&o�y>">#�LAB}$)�O :vX]\\ DO)�il^�c991>-]�i :2 >1)WJp �d,IZ z&V & ~~k>qAlE %�Cor?-j �'^�f�$<R�10��i_Netd�B!3R� $ !mis\R��:6�L�"�ac��Z s}FOthank� �45>aff� n�B o���"im2� �Pior quP"V"��4nd Hal Spinka C��d�Lh�$oine-Leluc_Ulo�f� ]'�p b�ware,G30�'�D exec*��is2%W�.1 Ux�N%al�U Fs's 3�"��II X ibidW525� :�BwN�)c.~�hop� ?Crie� Iss�L$D.�B �P��wC�RC0+ant}, edB�BlIX � B�%@2��N1� %�M :� W:�&��2_u�5��8 *IZ2��e,str. Meth. Au27��3 X4.i� �P�V}df * En5j�*Jf �y60W��a,-T key.?b\u�<ckage{O/��`�`[em]{ulem!+.a:oa def\cHhlp�,{}^4_{\Lambd��rm H}\;$o�.tZ2/3Z/v9� \t�_{A�ND*��� �math �({3,4}_{\,\,�\rm {H�*unbol0~B� S�=� the~NE[,4=,e}(e,e'K^+)$F"�!7�\F.\ Doh��nA��_{F. @fz- endorf.d�a*�ZArg�&X&!�, , I9Cois 6043�j.C4Forschungszent�}rum Rossendorf, 01314 Dresden, Germany} \author{A.~Ahmidouch} \affiliation{Hampton University, Hampton, Virginia 23668} \affil :(Kent State .=,, Ohio 442426u�4C.S.~ArmstrongN�Thomas Jefferson National Accelerator Facility, Newports6�06:[lCollege of William and Mary,sburg2H187H �J�rington�Argonne� Labo�y, <, Illinois 60439C Y(R.~Asaturya>YhYerevan Physics Institute, `meniaP!bver%��-�2� 2�668LK.~Baile>M ���H.~Bitaoh��Lreuer:MY�!�!�land, Q Park, 207.�DA� Brow>��W$R.~Carlini:���>�IZJ.~ChE�fNJnt:��EU rist>^M���A.~CochrBE�NLNle:��K!� rowdB�JuniataQ�|, Huntingdon, Pennsylvania 16652�)�,S.~DanagouliB�HNorth Carolina A\&TJ�,Greensboro, :227411m]5��V� M.~Elaasa>�Souther. at�� Orleans,6 4Louisiana 7012��)+ R.~EB���V�H.~FenkB��nVnY.~FujiBIohoku2:LSendai, 980-8577 JapI6)# L.~G =���KJ rrow�>�>(D.F.~GeesamB���P.~Guey��e�K.~Hafid>���W.~HinF�ҷ H.~Juengsz�$innesota,  apolis  55455!�IY C.~Keppel�\Y.~LiaB4 ��J.HNu:�:���A.~LuB���V�D.~Mack:��lVlPlrkowitz:q4Florida Intern� 9HAami, ) 3319� ]��V�$J.~Mitchel>�pVpTp yosh>�ʒ H.~Mkrtch� " K.~M[w> :��.i�B.~MuellB��(G.~Niculesc>��]y�.� Athe[ 4570 �I��N�8The George Wash]2�DC 200. 0D.~Potterveld:��pB.A.~Rau>q�����J� P.E.~Reim�{:{$J.\ ReinhoBd��jJ.~Roch>��� M.~Sarsou>� yJ_Houst�  (Texas 77204A�iWYNt> �4R!�SegBn��wes��2[ Evan �I&�2.�$A.~Semenov��:�JU V� S.~Stepan���� V.~Tadevo� :��5Tajim> Duk.�6Tr� l(ies Nuclear2�DurhamJb70*eL�B9 ��IOA.~Uzz���S.~Woo>X�>V>$H.~Yamaguc�@@CN>A���L.~YuBGҗB.~Zeid�� >� MWB�6�Vi�, Charl�0sville.�29.��ihlman>E�[L \begin{abstract} ��`\ensuremath{^3_{\Lambda}\rm{H}\;}av 6,4^,hypernm�bound s�@s have been obs7�d for the first time in kaon electroproduction on>� {3,4�,e}} targets.�p<cross seJs �( determined�4$Q^2= 0.35 \; 1 GeV}^2$! $W=B 1.91>$$$. For eiD=us�1(form factorLis.�by compa�7 (e,e'K^+) N�}!- cesses toW!�mentary6>6l11!Hg�iQI onL freeb�meaAv d du�(same experiu. \end]�� \pacs{21.45.+v, 21.80.+a, 25.30.Rw, 27.10.+h} \maketitle Q��figure*} \includegraphics[width=8cm]{ %1.eps�)a*% \cap!��{\label{he40612} Reconstructed missing maA�pA�aA $^3Uk(He}$ (left)Io^4:right)Q�a3aE8region of quasi%t$-�$!~qIavdi�Bkin�ic set� s. DPpoints are shown withe�(istical errE�(bars. Simul�sM��$(q.f.) reai�2F{}I�ULeEME�}�4by dashed linesoli  repres�! sum�sJ�(.f.\ backgr���3���,.Zn� �R\. �othres� s%� ���,5�+^29�}$.35$reEEively,%) denoAjby ver)�)-}iTI�8*} This paper -:����re�eddultUfm�a� of N�%�2�ed� ar.ks on $JZ $, namely%�.�r�6*b�=�s. In a�us, on�A��on��s��!la�by9 on, i.e.\5�<$ or $\Sigma$, s�WatR�' on insideeus carr� �ngenes%{contrast��remain�L9on��is new ��e��domJi�r(not blocked��MlPauli-Principle. Inasmuch as �piA�v� a lap��0which to stud)�p > on--B�te���as well!s weak deca� -3% E$ar medium, ��i!�"Hus may also be view��s impuri= prob!J.W��`ure \cite{Gibson:1995an}.a>ere)E kn�IS ��systeme�$A=2$� &trito:Pb� ii�l��est h �� onlyE�! $A=3$.�($A=4$, both�!�$R@�� are ��se ��i w! �L"� morA�8an 50 years ago!�% frag�Y%�emulsAAIa)�$Danysz1956�XSince th�early.�s,!�se ]%,i� E�een \d in ћ �S$roscopy, i}��>�can � � rom $��!lt� a]�s employA�!� ch%,d meson beamIej� $les, e.g.\! establi�I$(\pi^+,� $ %�(K^-,-)$r%� adv�b4of high qualit� inten�#��oo,s a novel op�^un=.,se -�i: $"� �i~ՙͽ�dAs�par�� a%�DU 2��xonM� w , E91016,�q0 E Hall C��$b� N+$)9dR e obtal a"� n !� energ�$3.24B� � +cur� �m$20 - 2/ \mu"= A}$ ��d!�upoI�0ially develop!7!�d-� cryogenicUxfor�K1-4$. 8Helium ! length��Lre approximately $4\&C cm��!Athick��e�PA� $310+0mg/cm^2}\; (^&�e})) $546.z 0(^4}=)< pm 1\%$ .. )�& s ez uncorrela!� $(e'i pairs,��ͦ �� =�0aluminum wall%�BU,E sub�If*e�H normalized yields."�� v� F� 2� N� � } AJX�61q�$virtual ph� ��us ce��a� ` �2/ҕ��2F:o" � } (scal�$0.1$)���, p} d vs� Theta^{Q,cm}� gammaK}�A�e��X give� H Table \ref{values}6` _ e sca"ed�m's��Ha�Mo�� um Som� (HMS, m x acceptance $\Delta p/p \simeq E�0\%$, s an,$ 6.725,sr}$) in co�&ce;%�2-ed�Bs,B�,Short Orbit 6�SO�� 2� F�7.5.�. )�eteE, packages of�two��%H��( ilarP"�� X8zj}. Two drift chamberV a� fo�$plane, utii�A�r&���a��icle tra�o� , AJfollo� by��a of se edeh scintill�* at/} emaAD$rigger sig�*.N ime-of-f:  inz�.��: resol_isM815.�ps}\,(\s� )��Yn �k ificc, ead-gla�howerMBor arrayh used toge5�  a ga�3, \v Cerenkov�  order<,inguish betw� $e^-�*� :�q�E�� flux stant (cE Ref.-b! 1sh}�����Ears variedA�R,B�si �.�dir� o$5<)in[��of"%� b�% tot�� �`he2�J �!a$W=^ The $f��lX}��R� e 7e*�)T� Q09E��� ͺ ($K$)Akt��_{17 K^+}& lab}} �/0eq 1.7^o,\; 6 12^o$, t�( spon%� increasQ=��transf����l (us ($\mid t t (0.12t 0.14 23).��)��| ral6 ae  $1.29\&� GeV/c}$a3� U�n $1.58f-nA�� fi�s�, $X$��^�)X$!.z.3�Nm;�]il!^Mw��O��Fi�� ya �� ed u5�four-1#$q$ e 6� , $p_K outgo�!/,%,i%�� $P_Q� }$, $M_x^au(q + :  - p_K)^ <$2� $�E2 ^��)��V�� visi� ��iQeG,s just below!� $*o }-[ $3s�!,$3.925\,�MeV* F(?e�6_ $^26^_ $2.993:_��2b+bo"x!barely5as a `�ulF!$e���ut5:[ !6^oT1� A�w�at�v 2�^�]�;� 6d� �e^� a binŦ����(2.04� 0.04)\,"%�4, $J^{\pi}=0^+ARnd�ex�M3!9 by $(1.00P 6)\,R thrm P P1^+ ' �Ral��I ��� 4�Y� �+ ver,  suffici�to Ev3e - �2�"� �|. � calibr� ���a�a��>jum ha�jen perB �Qela� $B�p)$:� � F&yugi!�th&'n&!vpreci)M�.�is��Ũb���� n $1:g. R^ a>?hif��� 6� B�!d��a[ after.�e"T agre��3 �equacIp� dur6�1 }/ !��) spin7 p? babi�/Sforward*� i�Co�h:1986yci�6�-��l!{�,sh��!� favoRa �A4 x rpre!���$ superposi�bC, w<P2]AAqeven ��ly clos� $0^o�j"��3�RBah#!} Ra�s $R={_"�� (Bd )/Z)*D) $.LH$ (upp anel"�&�"�u"x �!� dot- curvev Wt ��]ive|arAT"sA�cPk \Mc Mart1998,��z2004F~-���>� � Di�ential>��S }"of6�b�and���� s. I &V� sn_6�$�o�}A�f!Ifola�^� ${d^5 N8}/{d\Omega_e dE K ��gmv%6ue~t u2>u}& 6x - � e&V� Il�t}columns�%2�%�!zw�s��ju��combi1%��"A� �aO""I�8 :row��ws��Ak� , averaged ov�[��zimuth @$"� �9rm-�� &� ��toF/�.� q,� � V :\ $\;2� 09.5^o,18.9^o; 8$ 17.4^o;4.$ 16.0^o, 3G ; �> F� nd6�$Vs,�P�!. }q�ruledtab,} \newI8type{d}[1]{D{.}#1��'2{cd{1.8}10}d{2.93.98multi \{1}{c}{.�5��, JI$ (^o)}} & 2N2BNVG:��J:��QH:~tv }}\\ 6f � }&V*7)i�:�"} (nb/osr^2)} ��R�v2Qsr) �R�~� }} څ�;eq�;�; \\ 2w<1.7>AX � 52\;\pm�*$08 & 5.1j&94%1156�N20.83^& 1.13 N10.59^'00.21 & 465.01^%9.42 A� �!��047^30.020 �2b& 2.26 �j8j025N24.70^t 3.31 N9.8b' 0.52� 30.4^?22.75�6�24^} 0.01!J 2.7b� 1.30 � 0.09^1E2 12.3b 2.3Q29.9j�1!�437!!2�Y� 7.61�1!!)�2j;0X !y8^X2�5@32^(0.009!� 4.fW1A� N7.5bu,0.13 & 363.7b% 6.10�" d՜ :� ,� �F� 6��%Tbe written as \[ \frac*� j� = \G cdot 8��6$K}\quad,\]:  $b)$D �6� :�. $ x6c :6� , viz�� = � \alpha}{2� �E_e^{'}}  1}{Qb!%01}{1-\epsilon !(W^2-M^2}{2M � \] ($M � akenf b} � on;�2%� �/�ex!� a Monte C/1� iH.at mode�the op�* cond�@!jY @� M(s, sm/ � ing,Ml�H<%radjHveV !s(Ent�hmJ�^�J�/"[H}$. � �$�� was5assl" g co�nt&1of�$7n�/@)�u!�In"D f�HKI%@�"zUun ved &^.4tail underneat6 �  e �.�6jX"�f �{+**+.�i,O"# H4'haPA�Q2���5���no ,� avail�!� AoFwonX) 3,4$ �iu�[l� ary E�}2 e �R�9ELzm,:PM+ in$vo%~byM�al funI� OBenhar� 4hw}�-mYde�Ou�d�yaUE[Be�deb�r�1*\ *�'|b�*o"� "�"m+:� }. F&1�0i vici(I| Ya�YF���H�� into## ount!+�T g'ffa� ve r�&�&A�IG�5 spie1964}� ch g�4satis�v y re/as-0in�~2�heQ&er�'t�fic1AQFe:' �.# �n&inuum�Mdon nt  ;cTtQEx�oEa�e��e� "O4s,�"Yly0 low �&20&u 2�}+is5. in lWun1i�Fur�!X, s�+�:� 6�is"�#pj!dE�&]+ 2--body " 3R�.�'m�depen1)�,, esIby6�hap5�9��a�� ple o!bo"q��2& %&r.��Ś S#�5%�Z�#2G%!�?a9�BTnsatz��6*"�i�t�KA>mea"*twoa�2 � n ad�> 4 deri�6b"Bz4c"6 GcasAAny oAM���sk U2>���a few p'�l�*. %. "`:-�%�a�T��e�8/�-)2-u� k)u� -},��+reaf�'A�=mou've���Wa�alslER0$(180\pm24)^o62h�1r>of � .�).�p�5s rF �(m$ 36\%, 3950\%; 11 1234.4.5 4\%�$��$.~$>�C%s�!IVna: llel&�6l m, "C!�ful)LE�c-i(&|of %�)�-�)5�se%��)>to 9G F�$�$ 1%4.3! %.R  B� �1�3�*L>�;�V�e6 at �i�/��AWa��t�Dat0$�0U"%&) ( ^,&�"< devi;�ia,haviour, mak�kV�F1% fls+ �&^ . a�U�+he2o K�wBw�&�6���s"�=�@-to36[�1!W62 to_($R� :�� ar!�� $F(k)$�$$R(k) = S + W_A�87 F^2' ��#�  $ko���">#:1%*5��7$S8a�Q�E W_A$�Z�,s phase spac� d.7s. We ca^ �our�`= Z, = 2.1 (1.68T0 k = 2.02 y!8),9 23 6 69)&` fm^{-1}} li#&R.D $(V�l+c#V9we %U�/metriza�-�iS=1/6NX}�%�7 Gaus�C61  E[� l�4$.�#y16 wJ �� �+�u^�K x�#s� K"I�si�- M�b%X���� ba9,)� j�%Q2�3=�B�B�� �wh� 0"�M�a�� Z�of-�mGWi�a1991� :��& $S=2Ed symmet� aso#:A���u d re&;&�:@�.he.�!`��250 (.�V�}W10>.4N��M 2i �.�� &e)i�M+�:�2F�ŻLa �!},itի�C&=��u{inX�%reakdow�!*� n]T:byuy s. i�R$��.��B" is $~40-� $ high$ 0% i�sugges>�<� :�I to�pl  s1<'+theirlap!�too . Rea 0:R"�Faddeev��.u \V � ris�, M%bak�. Future� �Zents at% b���w~#!4=7sir4 �6!!!MbL']�6�R��(3this � �:i a5hVl@C.oEs:3 l!�2C�@*I "8 m5�T&�2Ja��4�F�a�6$�*�s �*J ���1�;i�ul=& test"7�(��./" ef?AR��, AG fe_ m�Ee_ Dd"nMK�1M &�03*s �,$>�(��}X5 3qc}�v5 a renaiss"7f sE��U!�lFI?i��h��*A� �0&�eP&�>e"H2s many�> ago. �!ac) ledg%} We�� g�3fula$H.W.\ Barz%��!��6>��"Aeank T.\Y^�,��� mun�!�.Jis work#su�=l&p>=M�DOE����t No.\ W-31-109-Eng-38 (ANL), :'8DE-AC05-84ER401TJNAF)��NSFII |(�S� �1�staff .f=��` Divi( h� 1bly 9�ed�I .D.\m� -HA.v.Humboldt-Stiftu��`rough a Feodor Lynen-Fe�7 ship�RANL!� hos-�earch. ��dF2QK thebiblio�Hy}{169xpand,+\ifx\cs=E natexlabF \� x\def\#1{#1}\f��VGbibO font>J�KM#�Pf�Q$�R�.~R.$�Rurl^�0url#1{\texttt!O%8{URL Iprd8command{!\�9 }[2]{#2} B!eprint []{S'K bibitem[{2�j0e=Hunge�.d}(�D)}] H�D F nfo{�P}�5��N F.} &1� B}:and��*jP E.~V>P�}�fC journal}{�S pt�B}Q5 m,j�v. Lett.<^�81}.E- 1805R�8r ;B  %tq�D> ?>/- ]�col44ion}{E91-016})N&Nucl.�v! A639R#97�"{�D et.\ al.\ }}(2003A2 � 2<~0 R.~MA��^VazvE^!C6Z 0552N&�r&( @Z)V. bA69a'�΁��m)3J�r3�b siao�48�$ !3~ S.~R!�. C>�_Y>Q ��A450:B-A 419cNH8vvEn�g!pA@&w$�8R><En^a2��r�Qz;Zj054610F��r:UBY�2��#~)A>�;:�%/}{Diss�!�D�:school}JgX6��n�"B�z��J>�A�5. a�^A68!��wQ�7���$51994)6� ", Fabro�#A�Fantoni@ Sick}}] *�f�$~O>6 i:V� BM��?S>{ ��f"���I>O)!(���u�.�j�57��A:�493F�!�r�"<%��64a�O%hVrB�?-r emph&� title}{K&S�(ba'e&� pub�N0r}{Holden-Day.�Taddress}{San Francisco6bi��n��, L.\ Ti�G, fHDrechsel, C.\ Ben�a!1N "&~,T>;Bt.vt.�R:Af!4��Y|�!23�R ���E5"�~ H.~W>�K�9�)�$9.$ $note}{priv�*i&�'E�J9 {B. �)�� � ;@ V�B�2S6r5���43:@-�158V�v�e��� a���{~�Y>�>>� � 2����72Z� 107J��i�_0:S�0 docu�} sO%\8class[aps,prl,pyZ int,^=ped�K(]{revtex4} �:�=scriptF>Zwtwo�7:x,�"-],amssymb�\u�I(M{>icx�.P,style{apsrev! >8�} %\�{ ��({$p$-$sd$ s�j gap &Qin neuuw-rS+��G - 7{>� �)20}$OgiM{ Ma�ede$, S.L.'(or, J. Pava�v(. Volya, A!�"�Xb\G 6 MeV�R1#-$@;�-9 .�Q� . Sek�/"+,1s��most  newly��1M�2e-e�ed 1p-1h2�ae� � N = Z = 8}�.Bh" �K&al�2��!2" O)� otopA�mp� stead�/:�"J� as V �H d"`Y�]b3.20.L]b5.60.-tgb60.Cs]b 30.+� keywords{aN make��6m"-field}a�?�1concep�Q �4m%Rcopic 8�. phenIJa;�7Je i it&�-�*"�\%( magic num�Rand�"E)� baso�Ip�Qzheoreti�R( techniques�!a A�ar Eu�Ares- g s z)nU&� foc�%u(lr I*3(^SE�eeo5eU<.!� few)$�o�X�J,YhAJyW[ exh� .em�d"�Rs�_�D� plev�# o�$=��#a�4ab�*r�[hasiz-e&## !@% of�t"of+ c;A��o�5f�;A�e buil�@�_Dn �/ �$a5lish��di2% 1f lexii2JR�b & �3m3 ubhQA�fu]7by6�advNs$a� m a�explo&+%<%�A)�d�a#) limi�staMG��criI|pkR m� Wh m\���T%�nt�if�\1mi%�!#��I�a�2 semi-q2clI��Z�!�-i� J�Ts �%a a"�(!�=Z�. ``Is~�'in%�on'' ���4{War90, Cau98}� � �KarU$l1" ��Gur�� t $N=20$ 6[Pri01}r !8>!Cot02"�+�"j ; e�9e�gt%��V ton-�imbalA; E�resid?Z�H��4te :Uts04}. es�QXA�!�intru�MconwHE .X low-�*�8s:VaniQe oxyg�Y�{(ch lie��$2��%́�s�* ex� o[!"�^A stig�M�3E18<se! )�T �� � �a�Pos�Om6��� G5@i}:sraC'importa`���5]p+surpri)Mlyt$  Laj�X drip�f���� ��6�(Gui89,Sak99�9C�k�$j ��GqL�4�j�H��m7uc����e� {! gion. Exa� !j�$110 keV $1SXEA9 $^{19}$F i�Ari67+m a ���jal=�h unve�RY�U�� i 2g�]ec�*PavE���:�Lof suit�#� U's��N%�eI"& � O Q�. M�p &pre�15$�:^� {(i�:*8g�qi�kJ=oa�n�bt;#�!K$8}$O(t,p) �:DPil79,LaF179,You81A F2de�� )�ly�;dA� d'&�  decay�_som8*�ly�Q%�>5Sta)�I� '�.E&an odd� !H�b� promo!� d U�I�gap, �TqZ%+�S!ReO(� fOnly 2Y[�aM�(at 5.35(10)� :�Try03E� a tn�;(3$^-� 5.614(3 >6�4LaF279,Kha00},�=�� $\OQG pri� �2�/ ent �&. How$R)� 6H �m��$p� ��iIsQ dict.>.f�f)aoA��>!�4.5A6� . D��is�*crRuc�h�e" (Jd)I}J( / Ź��0mM. I�� is l�QU>r�kav�ae99�LnB ��9|A�e�i%e�Yof � W�m.Wal��2�m(?, �)�6.*eu�A���������?*7A�!ong6��)��  asl��  T�7�Uj,� long-l�:>��gt�1t �emge� :�b���at 21.4a^�(�( �ei;8�k ^4 (FSU) S�Q�Buc@(2vfLa�k n1139*u$g/cm$�r�p��o.k 1 m#thick Pt��Af1�Q�_l'ly be&� �oe���?$"�TEHE� .�[an E-&c$E Si&C,/ *Da�`))�iYc$E Nor�~ ack ��;1504,�All fO6Si waR� �iA�d into&���[n� 0^\circ$�7�?@ A;. A 32B�gQfoi�A M�!BM�L )- or t"[�iop*f�,a(�E <)i*� � hF� .Qt/m+~aa- _"e�yQ�f$4.3 \�0 s 10^6$ w-K�t-�I\rd>L)�analyqg�.GNUSCOPEU�� Pavphd}�4$�!1a&�5�9�E�kioseJ�P�e a Doppl�>orr�B� appl�0-��a�tr�Altho�, the -�6Blj.4amCq � 6}$�� 2�C��^!wq� �2sxE26}$MgEJa�2}$Ne,� &i�.ne:4l�s) remo�2�lc�de� n)�x� N�h�g=�w]�h1BVB�Tfig:1674i } Tra�l N�f1� �A�a"!NF �0ray ($2^+_1 \�uaz� 0$�? �� ��gum mar&qqir��n9s!�d� in %^ 0}$OBehA � A&��� �IY�-��N��=st b� �;ioat 5�!v in �_V?2��@1g� .Ds�� ��asAɁ(%\Jg{6z NewG�a�C~�� a��� � j� ca�n X�tŀ)aa� Plac�2�M��=E�Iverifa�l0�t5.U#,z�GdERefs.���Coo02,�03}. S� 1{�"_5 by ga�b� Q�%ce�ZcCutoff2!b At�ov!�0 p��� mina�� Q6+ %H}�bef� ap3m-��a�na H�M`�C sch��]ta|a�6�j� 20OlA7��6�A�--�K a��C q1�+up�6  Al4r � ��4��2f�U��k\YRc�U *{!#ie"o��� o2nda�u���2�� �3f�QQ�mS�%Ewo��%�p�o orig|ing)� w� �;� 5�M6����;!�cE� loc���3%�4f�IoEn2�a~duced �c�qF� ��|���i�"�<�x�es.bpU��9�. B %o堉n;n�P �cp. �� E7��)�o�{� �=�.`  5�Mf`at 3895, 4353, 4598, 5115�  5873�not�:���,.ar8exa�,�lof.i%�q� doe�veal hi�_�5\ xist). Very =: peak)�vi2inŧ "�m~um6 1`J`�f��e�#o g*san��o�)��_2��Q,!�.�& Jŏ6� r� us�!�sl!�difOG(iscus!SF$)�.'.�| N McG73,W\� Ca�H � alsoaqO�a�&2 Q� fp$ M��accM '�a�Bi !f�a Ge�guV���o �cZEE�.v�X m-� 2�oda v�z� s6lVol04}���" �S� �B�ll diag �iz��mG.sn�,taneously. "�-%�ba!�zperturb[ me1��&4e�A!�M�� %� 4-hole hierarch�/ Ef!�.Ec tre$$�b  *� Nkeyo%paevalid#5F��%monop�c�[l�'e-�"{ VK�)��'ad4nA�l �eAglee�UcI�7  Th'LYm�i!good &*j��USD y �m�,�I*tJn6rei>�x,o� ��O=���Ld!�.4 |"�ly<%���I3*�)%gap�� r!i��is�Home!Zr�� �gin�TaU L@Pp#je�^�& ��j& $N^~��s abov� ��"� $N=8$. C�A|nesvE�$�hA!�8,19,20,T��,�� l�r"A�< $I�ofE� a�unqLt ple �1p�(2� {r ;I�bK&Ƃ1 � D^ %_.m)R�!5.8G:' CorbA�:�e}�.c � �imYe�g1_* du�Fwi *�t@%�)�i�ne�!�e�A�%�I�"toh+Z� betw�%�Ir5R��.�( ց���"���M�� �Y:6kis + s a \��)����deI�A��l f5 ],�̅S.�prE6���M Bro}�9!.H"(/-ee'i�! "�>qpsdgapmo�A:d�z0(�,e|S5�(�ba��ach!�x#6"�"d"�"� �0 R.��5f � S&�W&K0 �5�)H !�R�1@8 .:8-�Z-� &� M� dcћ����� ar�,�a":^.��X"* �� i� �Dc 04, ��`dsfM7SYo� reflect �2r%sHe�Fhe����-6�D":�.cJ|#(��/�� ����by 850>f/g*Ypsd�F per}-��+ e�td>�&Y�V �1�%���#_(!- �̡Hh�s���� b��5Q !n/^aV�&dYÝw�/ �a�.C��u.e ƕbluWJmaiK�p�+h on""K`�i val"��out"�� ���� e��D *� < wo�743%W547%�M!=t 3486% 4848!�1��%Ndue*2p-2h.� . P&�p2� �Bg!��N2:v؋:3 !�%N1 BQ>G��� Tde0$oQ�T e"�#bD�$)JA �&wWN greap q c N:N 2�(red)� u�st�Kat�ut�$�in ES��� re) cand EJEE��U�. hund�\keV���N� ���R si_�ş�*:�-� edVG �( �80I�� S)l�onAH�!v�:�s,  onabu�ua�Þ� Ue%tu�Kly� 6s��&�5zS�(�o�!r˖AJir �v M iqa,%��I�a)�ɋ� ��� ��a�=or폱-%�s ! ����a �)476r*�(Color��ine) Co;�s�0:2l b�I��. �in�f "]Z(0p-0hE��),- CaaS V� (e�[vMlzack9!Y"5,�^4�A 6555a{ o7��noIy.W is "��Y- V1ar�r{� �wd > ��j����Ra� �i�\"� � "� '�>� Fur0bY��)o<whR� t/r��� b�ac�5e��.-AA�of�j�� est.�%$$ogous situ9 6 ʐ�<- � Y$Z�YHe��6- \ �*C;>np$�:2 b"N��"�/$in heavy h��&�-6�$^8$He��/% -52��rX�0i�"_5*� ��)��IApV#[ aX�f��� �%J�1D Rog� I�4s�!t?rs��0�.�\ �ce�5rRho�to un�1 $^9!idver�*"� ��Lhodd&���-��6tSe�.!it� �3>#�Jg 1M;:�3 �� �B6�e#� $ � +z8�M��3o�Sapo+T &D,�Y .n*:5�QE� #- +� 2UA�>�$%&B-� "#'f-�� ���S!3�*J�< "�&>a�+ F�+E�<�(�b`e�* �>a��)�03xP) . M�U��.]���h7�a&zcoB�;>..��)�Mc.�A��6)�i�i�R�-� B l9a�y��%� -��4AG��} �0�*!�m)96 -+��yhR�/g&�Um�[l�U��k�)7L�S B P44A4180O96OD7A. Arima:�FM24}�}�672�P 7"D:K>+ �D1.4Jar59} N. Jarm�98nd M.G. Silbert2Z �e^Ak�Z195�y Jar60�SM12A91e 6e�Pe�>NigN Ra4N�ingale:w)�.��$893 %(197�5�|" A.A. Pi�>9}, 2EY7%�KL68}�EaF�&>�!7e�G-+}, L5EZ:LD&K.C. Yo\��2A9I�86}F8�FStanoiu�M6�034312J&T�7EXFy�cad�S 7}, 06430�h�U.2<27r<)9.�E�167E-)@Y-Ber�Z. Be�g6fB�A24!@5_i1�NRut80A&J. Rut�y~P34�829eZ8EuPGer76�9Gerbe> �i��6a�3_ 1976��NTil�?D.R. T�zy��63�Z2I|>THer77�A�Hf�s�S28��Wih7�u�9 E. K�m6>J�49�45E~0�0L6 � GoosI)�=�.��Me˃1d�4G 19746Gc3e��IPh�d*�S,� a:2�����/agW��opZ�.�65�L051302V�Ho]/ C!� JR>2V��a�04 �32��'S. Hind��3M81�J66|A(L F. Ajzenberg-SeloveJ�A3�;126J7� 5:y�J9.12�86��% D.H. Gloe��dd R!� Laws��Jr53} 31�N6��$A)B. McGr�� BfWil�uhal2� �� 97�76�$GLR,V. Zelevinsk�uRn �a, Cortina-Gilf�M��9�� 062501J�e \ http://www.nndc.bnl.gov}�g B�9E�, Proga7cPa�!(a��!v��47�+1� 6�x G� Rog-vf�-e�[41603aEU��b>� �b"mN ��"�N�N[g��x,O��]lO} \draft`D6K( \title{L&;��4O��.�1s�&�n��70��12}$Yb�� @{U.~Agvaanluvsan,/}$\footmR{��H�O: a1 1@ll)�} ��ch�1rH42}$ J.~A.~Beck 2$ L rnsteiq2$ P.~E�ett,$ MQ�ttormse' 3$ G' Mitc�d1,4 f Rekstad,$(,[iem 4A.~Voinov$^5$,�-d W.~ esk�NHU{$^1$D^�t�0McB��V2�NRaleig� C 27695, �N \]2$Lawr�Liver�*N�al*=8, L-414, 7000 E=wAvenue, 8(, CA 94551,0O.h3^�&|O�Osl��-0316 orwmO�4$TƼ�!708F�5^�O���,&Y�HW� L~"�Lx&MN'$J$in�171a�^a70M*�,u.d+[/>(A}HeEw$He$^\primem�)(fu7m20�"s. New�!�6^�r�'� to a�.�E��7&�! ��n��"W;. &�"�'0:�z~ z0,171,1 ��*%.ze/p�K�%��"(�+(M-1�,g� �!�un�5�-&}� icle�fm[ be ao$x���D $k_BK� Ra=Vj�9x6�s4M3M[<3t uersס�+eriQ�,he ``pygmy''&*] !+.:�� :�$&����sB splido�compon�Ea�ofxMlet`9�Tr�c_�A�":o�Ru��J\V{PACS �'(s): 21=�MQ�4�PGd[�55.Hp�P70.+q}�[�} s}{2s�>{G+!H$ f���;.�put=2�ofWGarU�* �U�-!z�3�,ue!� pAQ���s, )s?%����ntGS2sBl��E!�@)� sfunda�7~iss\Q�2&&7 �/+r!�h�*)b&scu� al (�r2"2m2/At  �.���Q4 ^�ly<�/�l"EM:�'"'!aA�c!*&�q7���C�,�p��%v N +� of�4A�l�*i.�#s3'Gil654Ql.n{N�t�3�!!^ō���pF#pvk acZ����#/ xEgi88}��*t�3a�*|H-%�o�3�bly liris�$ab�#�ar2w-�>,Ce���aS~�<�%LSA oSA A majo "�/}��I�/ ri!ce>�� aiT"Tofa0�&�: rays les Cl?�st�0IS Kop9�3�Pis��t�a�Rtru{y�*�@&�5�l��i!-�3T%E*;.I�o�9M1o&rength�����Nm�5scarcer �ayuAC$EN7.�J�si+Be�MUtagE�@m �᳡Jȋ'Hs� .�PF�8n��-� #�0i�&�zv&� ��is ��AuoA�.��!�.I�Vj�EHcoupled, ,�F1*"i����]"%/!� qu��#�)rtc�"95:Uk�� lute6��@n�ne/)be *��*� ���io,S+&�Ɏ��inged� J��w�� "�� ��4�Qpnew� "̉!����)?/t�b��!�/��� �'�U9Ycodž�>fer� t˵Je� + . It�4\:p+to�.�_�W�$-�9E�i�&�:eYDd)��"+Q�a�K�@,Tav02,Gut03c�<62�;0Nw�(ulU �Ha� 1�+Xz$���e.���2T( set-upE�brief/|�9,�"��a !�E�L�;ev|�.�j�|7�66 � �i�EB& a�e��"/ @(3"� ^!~2xe522!-2\}H*�,�� B#)B�C �)� P,!�uE^po�%,&{rep�,d1Aisak�JL �?� �{2�I�s}8U9�m(RO90�-)��}&[O (OCL)�a 45-9-)0 5M�%self-�"h tSPa�-n� ,173!D en�#I�$�($ 95 \% haVV�O�A# !�M$ cm$^{-2}$Z�v�Oe:6�isp@ are:R�1))s1V�6 (new)�� 2R8M-{�}. A \\ 3 :~5�.)�. inm��} 1,Vo�Z� 4RXV�|bae(b0})\\ 5 \%�V&vS��R�r P�-�:�&$+s.��4�5N�&(the CACTUS � o�b �GutW A�c��dZ le�@&�d�( �tEc"�t%PsWPat 45$^�PwPC[)ec��a R�  E_6I �E�=O��i"ڴE�Q��0 �� Si(Li) $.}u$P40��3�$\mu$m:p��Ja��of 28M�l�d NaI"�� 1Ts ia��[�agj~m� 15\%Q4{�$)[�]s�5�;a"�1TRG#+ �s�)<- 6\X�!� spinp��! �� As� iv�9��"��typ� M�J1�x!���be $I��, 2-6 \hbar$.*E s ru �2 week-&`A�6%� - 1.5 nA.  | b-y�b.)m�A step:V�1���)�U�R`sc trix�.�,05 b� �cascad\OgammaI"�Q.p ~}�.�)xuR� � ransfW � �X%�*��1�&LRn �\�)�.� m�h*a�oa�  ce��.��/y $E_x�= v�_� f?�%=co��b]"eL �"�$)se�5��un^�ing�6�*FW � ("��; 6 �se �1�0i����"6}G:�k�Nw�n2y�D4��em}�Ma0K.c)� Tamhe J-g�yi�I%X$P-4-�wMeu2� �BLaAm" A�ha/ir)yw%�B�eU�"��<��_�Fb{+�G\9]871]ZBassum"� N �5VSi_f-J_a�i�� "� � !�ab%[23i82 ɞ�:tE�.M)HyR�fer 2]b&�.Mɘ�0q�A�a0�is auto�A y��f�d�i|�U�p*r�lly viaq� %�ss���� 5Gb�&h� Eb Npr#!#~ s. E�f&/ .:�,*?5�\Q�16D!t���%� 3_c )��9/ �+e�m4e ![��a"s= f&\��s.� a�`e�1�cdb sive|˚y�3by/7 g�a�6��8��R;�Xt���B�m�$P$4 $proy�� $P(E_x,!)č at a6'�I��a!�.�J?��. �w�1�)���A2�"oo�&C���5%�O (#�-&���m���e� ${\� T} (�)!�yE�"�$\rho!! -E_{�}/�� I9.&$�aL��} ��) } :yFHpt�- ��� �L)�/[Ff��izo�!3��"R���4Brink-Axel hyp Ic Bri55,Axe5N�H�)�3@�!5�:?r.�42s yj��4���7t['ha3H��!�Y�:#s thos�jeni�a$n�Oat�In tw2mR�2:Q%A�i2�%�)0)�mX�:e1U-�DQ�&-> �D � ��te�q!�g%� O��y�-C�J(eStsN�$E_f=EE�I(ڊ$Kad83,Ger9W .�%�co2� �BN� ��e�5�7a��������s slo�4�]BU ($T ,\sqrt{E_f}$)� \w�qj7n t2�n ���5�"� �R� �fF��I va\ *_\II� Oslo�ws�J�6��$��"` d� an i�H�4�t .Da}��e goalQ� 4on�J>�=��wo�`%sNZy�WC� ;e%K�{6A&\tx  N^2/2$o ݚ�* glob���o%� +9s|17a�`&���)A��Q� %Hf?it�;һE�A�"�iof�!�Eq.\ (����)d !�;=�:�i"+���ō"' �f �"'%eqn: } \tf*{���Wi�$)&=&A\exp[͚ ]\,36,�weq:_ 1}\\b>k &=&B`( ` �" Q�ٗ.>Z2�E�U,!]r[!�Y��:parm" $A�BR�� ��A�%�hL������ �_P+y_� J��( Z��.~ upyi@B_n-$�K, Z re $B_nQA�$6 �c&� s $AI��: �EL0ɶ�6��at�m 5,�!)�.�" "L ��J%�JP .�is&from "- \�%$�L$�).��&~�tt.9 $B%KR�f l�-^��9�����H 1�5- de}�#A6����� �%��k(�LQ�!�u�S�k&� j� "w:>)r%�"� "�!������s�>:.� V�\@.&�]TdV� u�i�6� m0�6 �IeH��2$(170yb} illu��0F�6��7I��.\ou� >�R͍�n!�_Y�$(�z)�)�� *�N�aZ@% N�F�WXC�aN� hist��m��L"����%%y��V:T� of ILB͢Fir�� &�Kis�EME_xK$ 1.6~MeEAb�Q�7hDm 1_R�Y8 �)X>G$a,.�a`�erFv�NJ!FBA� :��hq�')'uTaρ�x=�;$\@�1�+l^�!.us�o.�� "4 J�" ��g �-9en�)��Hr B�I\6� �e&+��F. qisu�E�t��&]�"� _�,�@ ^ORIPL}�az�o��A��P$ 1ACB�J,<�&po�\j equi� �D"''J�q2��� e!x;l �A3e-qt ed F�/�2�g�H�Hby von Egidy {\sl e*? ��',"��&� rhoEq} � )=\eta@�\��exp}(2 aU})}{1 d2}a^{1/4}U^{5/4}\sigma_I},�2na�pn��� 1Ti� 5J �n�$U=k C_1-�l L $C_1=-6.6A^{-0.32}$!�, $a=�� \ A^{0.87 g1 �bi�U" �&:m!�^��%Wa�a�c�� ^$DobaczewskB>B� Dob0�s�X �{�.�U ligh���):l`�)82#%ax 0�3��)�sr�Fo{ gnitude =ae( am�*�!Mŀ�W�* �#�Pu! 6>!V&�F 6/��sZ us ��56��j~ F~x��hwo=r�, �"�%\u���V" !�&I% �+&b'QqQ bJ)�5|�#!}*J:� J2� e"�) C$edF�"R� �K���M6v�OM�A~:b 5XANFi&f rhoall}��65%-0.@ 9I.1 F( � �9D� n �in�l2� !WB ZL5�:$in 2�e>%�>J%*D1)�tF�yi&�e�V�"��6pF� ��0.5�� �U[2�*���')�Ra� pora�2��of����k�.*�+�}�"y�.� roal bat�A��ai� ���Ef�� �gin2��b�E;N�m:,t &M (between lev�ael densities for the same nucleus obtained via two different reactions is excellent. The levea`y is closely connected tos8entropy $S$ of �Xystem at a given excitard energy $E_x$. This opensN�possibility of investigating certain thermodynamic proper%i atomic -.��is �0by \begin{equ�l} S(E_x)=k_{\rm B}\ln \Omega. \end08The Boltzmann's!(stant $k_B$lset!)un�,from here on � multiplic$ k8 directly �or!:alJ!`l!� )�y: 9�= \rho / _0%f8e ground states!\even-I1li represents a well-ordered -�with n%� rmal=�xs and are characterized by zero5~&(temperature%refore�noXiz%�A�ominator-K to $ �4=3$ MeV$^{-1}$!oE� $S=9� \sim 0$Q) % b�regionM�ensureA�at� 0 *!�Ih fulfill# third law!T2�s)1X$S(T\rightarrow 0) = 0$� ext%/d�%� also usedu�@odd-mass neighboraE�Hi. Figure \ref{ybA�} show�e-~�(i�H $^{170,171,172}$Yb->ed E�Af\($^3$He,$\alpha\gamma$) �< . Several= deriv�A�this f �AactualNEfac!q)v4se mid-shell r9earAz��4i have similar)ar strucAS !� glob2� , such as1dAvmEi!Aa�!7o%'(orieA��c) o18%0g%G)?0follow each oA�1 aaN funca�A$B <. In particular,Q�B) I��H!�M�I�upa2a , $��$M very55Lshapes. We interpret���a�a�� ��2.5��\@E�ik.�}ws�N(underlying ���� core. H�J(odd valence��!V��passive %��, how�, B�;i�(AW $ appears�sl� ly lowerR than5�� � is �!1iRtribu!�� reduced�s!!,gap $\Delta$A;q ng��$Pauli bloc���! 5eu��!! �A�5y carri�)>@���[0hole) can be AJma�assum�tA F��s aE t� ve (��$ve) quant? ��1}.:dsn.obser�A�le���� z�� defiE .0 8narray} \label{-ex1} )h S(@ �})&=&S(t1}Yb})- 0,\\6S2>S�}) nS2S� �2> !�>.�!�s aboutQF( S=2$. Devi>s� �5� I�A�:� %WueQ�i �$A�A�� "� Qt At higha:G IA(6V N�BTI�aE!onsibleqx m�A�!�� >ce�Rv�a��wo�l� v� plan-7�7կ212�,R� $��A��le�oti��(A%)�m� S$rrelem\��1}2� $T_c=\frac{A��A S} UV-�co� % S$Aais!dist|F !�n i�)2 us, �Os � ona!�to ex���if both��)%w���l1�)��mp\ ,${ �}S$�@ would be flatter.�� >�y�� "�2y ��� be stud�$u!�5 F�. Recen�#9�3b}M , was performe �6eT060,161,162}$D� otop� �� j ia / wa� �1� Yb i A. \sp on{G -rayp engthus} A� $* ( transmiss�coefficiA${\!*T}(E_{ 20})$ in Eq.\ (� probab})ABexA0s�a sumeall)� C ust>� $f_{XL}� uola  XL$F � \$)=2\pi\sumK�^{2L+1} b(E/BH �mrad�7ve�$"��c2�$work is un4ed. Ask �Eqs5H eq:a��1},%X2})�CM previous -�, ��� t� ne�.�w �A�:Ia�� mai� c�3B$� =�.�iYt edm?ina �n���ona��decay.M�a�ge=�width� :� :(s $\langle\E�-�\r$ � 8 bind�*����f�]I]�B|Lavgs]^��� B}{4A��4B_n,J_i^\pi)} I�J_f`}\int_0^{B_n} {\mathrm{d}]�N� Y-Y�, T)Bw�$D_i=1z2����1� spac!4 of $s$-w�1Qre1�,E�9a�e ds ov��ll/le fi   spin1  i� Fmatcht�eA�A ��to .�m���:�!�� ���� dard��pi� pend��partsJ�!�E_x,J)= )�t2J+1}{2\sigma^2}e^{-(J+1/2)^2/>� 1� :5��cut-off�ama\)$w� sume�Bnumber�po vane�v�r| %y�eZ_��cal��  a���YA� k�e�notf �to make"R al eWpa��~ $ beK \ L$. A detailed descri5Q#1Ja�M6�g�in.h�q)yclu)u�cessary�xra2 P � 0rimental data�c��:� y�z�ksiderD, a��� Voi�(�hed�l&@J�  :aj �l.+st���%~���Jp is d��dipol���Kadmenski{\u{\i}}-Markushev-Furman (KMF) model �mploy>�  $E1$�. ~!_ KMF 5)9Kad83}8Lorentzian GEDRAr,modified in �!��o+R non-�limitQ2Afor $� ��$�� meanOa.X-d�� "f�R.v2���r�+$KMF} f_{E1*v P1}{3\pi^2\hbar^2c^2} ��0.7��:� ^2"� ^2+Z$^2T^2)} {E! E1}^��By6x; $, $k$��$ X��)� cros& )< +! roid2�d��m� $photoabsor�}��adoptO9nw��S*$ $T$ taken�Bae��to� � @riAy( JE?�inU.�F BIA%a of �s�se"a ZpZxn %�5�,TQG}MAI*2(R� gi�$"� �spl�n�wo �anr��i��D,�� J��b��A9j ���^. F�kM1$1�on0M1A�@L�U � magnetic �*t (GMDR)Jx+e�M��q�M1*� 1�Ma�} {=�a� )^2+��^262>1 A�eL� cordsA�!�pin-flip]�. %&L e� $E2.Uis��i�fed in2� ��, because its9�is�smXra�asun!ty *Y��!�EE.�.�Pt3N3 -�EQ)�E2y+ ) = �W1}{5 �s �t c^2 E^2"� ��1� E2} &[ 1�E2}^2}{(.:!�%�S65N�.nA�sum��j�e�0completeness.i's�al �-.��� anomal>u���i�#unn� �� ,}b}�7Z>S� B� �� bel P#�(Oslo method�?efer�to�� pygm� }�JL2 rens�!|:Fk�ed!D9�m�� eredq�,�py}}$ɶ��\6"��S �O _:)Jsi�[on��, ���d�i=1 �p�iilto ng�mpoyof �^�i�SFfit} f��D)=\kappa (f^{I,II}��+f_��)+.+* 2pyF*�2G$" ��aon$R !�  by%&S*o � ),�S%��E2*� RY,electricKdrun 5}s:c&by2�!�}�L��)J?!t� th�`>  ��i�RIPL}"�$l ` T�e tab2e�2bf�p> ! py}$TAxM a�� lica�v � $)�$� treaa�as fittJ� �s�% ] $T$-1�5�� valu,&Y%� ��! ��� 6�3}]e�� ō �#o�E��"zg(�w1iFdg)}1 may~ ��6[M� nyM�>��K -�approx�� �� �0.7.5!4*� P �:�  ,�%5^it�O s agi"�'.�".�]%�Q �%xv8 � ���c0e upper panel3ns)B0��6 (RSFiu��Jbco*( &��yx . Af�sub"'�Tfit�x �:@$s (dashedDs)=`�poi�(-�� �G:N!# cl$identR)1aq�onl� :@s !na� soli ���.,q�RSF^�$(J�'�a\&s a�' �B� seemA �" 6� ;two-bump &�so�'noq ��E�'.I�!����Ma�e��� f�s� !&w !����� c�3Nbe��F�We fix����I}�桙�*�-, 0.34r-] %� .�AomG5�s)�Pi"in2�%m�؆J"[64}. B%sK��of2me2�J2) weak}at ��% 2.1$)a\Q1� ��%�&톩��J���� /�*kU|establi�����Sch04ex�>u)1i�a� n �m�E�!yor )Lip83}E\�ar9� fluorescC&(NRF).� � Zil90} if*o� a��scissors��+q�)AKinuum (l  gap)��mo� B0�-a��"\N$rigid-body��bare $g$��s: )SappliNRF2�on Dy 0 E� �%�&D1us��W+ $\�.2.4 3.0$~MeV-+Mar95}o � E��!e��iJu�a� 76� �<}&�#<�"b lzm.[�of � K=\pm 1$ �� ray��B6�.*J!Co!s} ; �0&r-%�j� fe]ɀ,mls2� mea�/d��!� ra �-�o�.�J(�.!�`� $>���:t�# 3�',!�$ 2%�� !� tabuLd��in!� lete�: ::�%`aV�:(�3f�.��z�)ste*'%��� �y $ cati�.�*,�Ion.�*A �y�`)&c ��&k)i�Q�S=$ 2�3ase��49!j��6%Z c$exhibits a�&�0(:�) P�Hat&E in aa��"M���)r��!�!B:\uby᱁'��r��common�l>nd Ar=&�3 ��}%EO:52$)% qIE�rT a gow� � betw�V� �s �6W[ "�&� n �x$�� u~&wo*i � es�fi�2�H� lea� toa��'ed� f c) 6�2ca&�6 ' is�.�1��oscopy�'$acknowledg%s�"�search 's�)o��N^ al N*3ar Secu� Admini�� ��0Stewardship S�&Pce Academic Alliances� gra� r� DOE R�Gr�xNo. DE-FG03-03-NA00076. Support�U.S9+�%� of E3$ >D,2-97-ER41042a�=d. Par,t!� %&(�auspi� �f�-FUnivers�!Hof California, Lawr� L# more9tLabor/y ~C�act!8\ W-7405-ENG-48�[Fi�%ial s-"uONorwe 5dCs il (NFR) �Y#!rr��s}�9\b��em{=!( A. Gilberte�A.G.W. Cameron, Can.\ J.\ Phys.\ {\bf 4](1446 (1965)�)YXEgi88} T. von Egidy, H.Schmidt80A.N. Behkami,E�.\ f f$A481}, 189g886gDiegSamuel AHieh�Barry LaY, At.\ D�a �s o38m9m�Kop� $J. KopeckydM. Uhl,- Rev.\ C-"�941�90)a�b-z� 0a}A.!iller, �gholt,YPGuttormsen, E. Melby,�RekstadAnd� Siem1? In�^m.\ Me�s�s.\ A �<447}, 498 (2000)A~�Hen95}�H�%v�J�+ ��Ta� Tvet�-k2�589}, 24%h9A<{ Tav0 . Tavukcu!] .D.\a� sis,a 0th Carolina S�: y� , 2002; =]0 {\it et al.}QA�1�)6!�054326%32�pc}��S.-��@, T. L{\"o}nnrot� A. Voinov!�qb G �2%'63�2�AC1e�ScQCA. Bj�1BA(M. Hjorth-J26 n, FA gebretEc YdSAnsseA�=�IkIxDW. {\O}deg{\aa}rd,q�m �6�* 021306(R)�12]�a 1 M.��6] � �PN�� 4431)O1�%Yw!N0:NP6xYc�"Ek0.�Gut�&:�$A. Atac, GEo}vh{\o}%UM1mA$ Rams:�4T.F. Thorstein%�2h,Z. Zelazny, 1� Scr.�IT32}, 54J��6B�2]L�E��B9.#m�~��"374}, 37�"62Gut87J�. !�r} n259(518!876@Bri55} D.M. Brink�62�Oxford], 195520Axe62} P. Axe>'��126}, 6)622K�% S.G.F9&, V.P. "?&�QV.I. I&(, Yad.\ FizQ3��277�S9[So����-�m;�/ 165 /]2�er98}A�Gerva��ME�en�a!�W.��O��� ^25�yR13 �9��y�FirA�R. Fi`9XV�c(Shirley, Vo�� II, {\em�of Is�1, 8th ed�'} (Wi8New York!�A 2a�$ Handbook U C�+io!5T R"o_D, IAEA, Vienna, Re� No.\,-TECDOC-1024{8.ZDob��8J. Dobaczewski,ADMagier4W. Nazarewicz, Satu{\l}a�4Z. Szyma\'{n}4N}� 2430 6��b��S�c:�E�+B�!��R�6 ��24��=��paB�(R. Chankova��:�.  �2)D.& Deana�^34311��"� �1B�F]V2�2$f� 4430 �!�:�5:�a8i,6/.1.$ �A*�R�a�06430N& SWFY2SE. Algin� Becker, L rn��E� E. GarretF 0R. O. Nelson,2�=$-ex/0401032a�,E. Lipparini�Stl9a!9 �Let3 8\bf 130B\rm, 13� 8A "� � A. Zilges�� B� ano, C. W�� borg%�Df=8il, U. Kneissl�L�(n� ' 8 Pitz, UaCeZFBStock, ��&> ��A507} � 3� 90);19 84��:� bA3,Margraf {\slA U-#6�2 242%%�  G2��col%7��e} \cay{Pa"uPiC+ r�s.}Y(ular}{l|lll�7v& 9 7\\ \h�1 $E^I_{"A$E}}()�& 12.05 2: \\�gmaRJmb8239 CZ E�*RE�& 2.78 F 6  2�{?$b�& 15.3 O � �s�ZK �302�F G �ZG � 4.64 H & 4. �� .�=�M>�17.J & 7� ��JI�* 1.30�1.5. 76 D�JD�D�J Z�E}}2}$, C& 11.37 -� 3 �>�J�6.7 7 & Q 80 D>�D�.074.0Q�!�05.�p8 S}6 r8T, meV & 80(20)& 63(10)!�5 \\ �i.r=8�@�%�p�&�Fit@%>Gp����6l$c�9V}ccc|cc} 1 &$E_u]�(&$1�2�(&V�(& T)�&&^!\\ &(MeVA &(mb2 & B*& Yn &&&&c C�(", $^{\p 4}.�& 3.54!� &�E0(09)A=0.91(18  31(2 1.26(06)� j�vj\a�J.a�j35(19I+F2E0.95(31  34(6 1.01(13fid#B��i28� 48(1 � 36(4i3(4 i65(11) �3�V�a�j38(27J � �99(55 37( 1.85(17)=C�u$^{a}$n3�!o2�J2?#2(,aOA> ,�  text.3 tab3�\��Z �2�">msN�aM.N C"7#&F,�[A� & q�P\\4B6^B.Z���#6�2*��I  15(2A� a�14A�2&a� 3(536Q��M��� 41(76o�13(506�%�fb56(16^�1�J� 72(3461҇2412�p68(�F.0��.BC. tab4V��O} \21 graphics[(+hxPt=21cm,�?H=0,bb=0 80 350 730]C1.pa�� N2�Qproced�P� � 2�*.� 2�.�;AF& :T!5is pa�*�!�8e���( full circl�=F9''�)��Q s en!$h�&#*� �2� ��rE-tTscret�!s (�&as histF""!*v*) `� 2�"�;edf*�";'J@s lan TU �L *d*)MFTB gas6s,�/\OR-=, (� )h"�:to V �LS�19availX&� �0 coun� 170ybM�Q�� v�0>�I�83I�26�DZ�#!��>2�N.�=E?� =S-6!�o2o$!�B�HBm&� :�0"� rhoa���1"�2223V2�#6P$.BT� >a�e�m"�\� �=_m�*�)!V%�16 mo6�tri��R7��!�Fa , )�)>P5V4U�VjV4nVb?l?Y� �R0�� Z&�Y�Yss.ZiGE�  K!#K6b,.g$#2CGnt�MM… 2}O�o�J_%i )n l!*�/.��N��2�1656�Ra�HBK$=�:��6�V����#�B�:8668A>� �ienE�2�&p%"f%m�{D�:�Z9 �PF>6c&[�Da� X��V���"&�1�2�R�Q��ata&CC�K�,�RF�,]�z-�v'_.3��E>�remov�#A�di�]ce6A'�86i&t�3&E3�����6V3�6J (���Lr*�/)�$!`n1(*ns��>�9Tly.T3��/�~�76� Tw��1%�!4��)� E�2ݢ)t!G(Y;�Mf1*�?�I_�?6�-s:�49�-pF� docuX'} �i%\8class[aps,prl,p int,=Z(pedaddress,!�pac%ep!n�Hs,ams2K8symb]{revtex4} �csupersc�F�gJg twocolumn�� �Z-c�� ,floatfixj;iho��5��L Some 5(�>�(of many) po�aiesB}apsj�.',draftr-]w%��Y4Review B \new�,Dand{\Aphys}{-1.36}.% Ep_hierte &8ikalische AsymmS(e6M�S�+}{0.29P% �&�+@@r Anteil am Fehle�Cr6dnzeyse132eMcat~f.]�I kl. Pola- �6�(Azero}{-2.0>"A04+��MhHl ohne6 ange�!6O%$ T 0.14�%1 in�YFakGMs!z16�% FakD<vor GM��derOearkomb9b�5GEs + .*GM:�GEs a071� A+rgebnisB+ n@��[ dVZ8s=0.045\pm0.007JdU�5f�r:c6D Beam'-}{570..]Strahls<i�MeV6=Q�])B8�% Q^26,A nge�Dofthe�1}{-�}�.erroro007V2A?�d#-22�,w ,46f,.= to �8c j110�= {22B=0inthetaweffec�?� 23120(15):k(radcorasymr�A� }{1.E.�hc� pia� dilu+ fact!Zg[./�8a4j(Y/3>�:-�1>,J)W>�moe�-}{M\o  6�0latticegmgesvA!07>�B's>,sE;:R3>�>&Q5>� +,^�a�VRmax' 0.08:�c�T nkov}{Cer 4 \usepackage{ x}% I�7dR=qffiles2,d� A=Align�6iT� sD7decim%Z oint2<bm��% bold�Th"�2% .�ps"7xZ�!% \no �b(d*)  %\�,{APS/123-QED!title{Ev�+c�Q�o nge Quark�1ibe��;akNz3o jForm Fe��` $Q^2$0I��, (GeV/c)$^2$r�nlyE=E�abN ct} WkBp8o�:*�9R�4�)ty viol�o# � �A"e![ic sc�`�=of  A#Vl"J�- f un prot�KA4�fa�n�� MAMI� eV �g�KB@um �_fer�:?Q6�~��I FrZ9�Jon �� of 30$^\8 < \K _e < 40 %n-4�h��[@$A_{LR}(\vec{e}p)�\(�\ $\pm$ � stat$_{}$  ysz4$) $\times$ 10Yo6}�[�ct���%JSt" Model�X!�noG�)� 6��ve� cur3+RW A$_0 �� 2�R�A] have impr���`aaccurac�@a f�A<3��<?�T"`-qME%a ~ er��w&�oA�A�nR�M�", $G_E^s$ + \ \ $G_M= �)� 1�l\A�E�~=~o.�. A�qN�@ �F ���0.230�, we ag�sfin)�E :5B��ZiF *�[im�s an5� signific��� of 2�O$.8�� \�{12.15.-�3�)0.Er, 13.40.Gp 860.Fz, 14.20.DhgACS��Zc�BAsjomyV�  % Cl-k�� %/en@%\keywords{Sugges�}%UseGkey1D�qo!-/E 'vz %displayri>Q\f\� iC=sa�a�of Dj0um chromo\-dy[us (QCD) �-$nonperturb)D reg!��ru�$atT�E scal�dt� field�pke chi�T9�o�U�G`($\chi$PT) or Skyrme-type�t"B)zB_I�s�� ise M==A� a sea! virt'Jglu�!�%1-�l �Gs.�#�?�2r%don"LN�o Cs A�s�(peE�role si� >MF5Ino netA��3 �2fto8]�YU�!�re�- �)'. D&�k�KQ&���2� ($m_s$)>�)upund downd$))Wes� H M� 140 \, e,@MeV} \gg m_u,m_d)5-1B*$, �7s�pupp2AHof�!F ��Z�Cm��nrF� OE�m h�96%/isf\Is _~. eQCD%�@\Lambda_{QCD}$) s�C�\M�.�~A�)�aJ��ul�Gill�osub�D'D%t�2?A� c, bE_ tI! s be�xnegligvm.\\I��!st,hu�!;nt�{�pN&{etN theiwR�.�[e�M��-e%�2�� !Rar-�!a!svacuum $>dD< 0 | \bar{s}s | 0/d>$�ize��e�s in  itP t�rk�p-H �R=d�lvL yxq}qx\�$>$, namely�( �( = (0.8n 0.1f � 2:Z UM-<),:ioffe:2003}�*-; &%b�� �N62N� ��N��.�� !E�60 . It��E$ disc1�U2F�O 5$\S�3$!� mutator, ��can LreZ�%@$\pi$N��A��%�. %-S��0:olsson:02}. �m e ��T7��e7 new&�  !V syo �_{\pi N7lf (64?m$ 8)�?to (79 7 ��i�.�r� $y=2IN|Q�|1�/2 u}u+#d}d#�m!�M}E�2K �.rW�r n2A� 7 n�x,"5$.)<pv ǁt:ka�u:88���XeZ coll�J�&upubT 1'�@s: 1.)SAMPLE6B� MIT-Bz� ��}��:��U30{Z�%Y< sam�urU ��-Q�Z�Y�R2 !�-fdou� kine %cs!�.5X 4:%M�M���V� .� � w�b�E�`j+��f'*l+� ($ZMxI�"� ($}mv] udesER�`a6�B�=(\ _R- L)/+"j Jme�v!�) !\��-{e&�s v-7 L$+"C1�&�9 wrP=n as B��� c$_1�t�OE^p� c$_22M32�!�� "w,f�HR� S��t���pvh,ary:musolf:9\!�%����w� ^p_{E,M}$�a�� �&�yer�(�Sn> �� "A�d^{p,n(eNun E��2� $G^s 7$+6iso, "9Hi�Raj����%�U:� ea�$sm �aBa�� �ztO%,F�( = A_V + A_�' A_A ��!e"�pA_V=-a \rho'_{eq}\{(1-4\hat{\Ad} s}^2_Z)#-\f�} \epsilon PpnU tau "  M^n})(*)^2 ' O(-)^2}\}, �6eq:Av}p9A_s=a{�^}�:}s} >}x6ws}\\ A_Avl5-\sqrt{1-1Xk (1+)}�U�a[}��..+ �.9�a�V}�2A;hAhm^ coup�!��mFv�+x�"p,��_2�����,A��F pu�_� A_s$, i�p �c� �p"��B.tWB �.-A�A�AB2� z!ap V -d&V� al"Wi�D��*� ��. $a2�$(G�Bu}*) /(4 V�7 I<2})$.F {\mu}$� �L:�cC�d.�muoz�| $ YDk�!s)D,� g"{y�*!�~f.�"�,� au =��M_p^2) B0�cc>�z�0r ��(:marciano:8�%Iz�e boso!�ch�|\*�j(t�V>)e.#l %$�ER�Aheq�to�kWe? a�A� 8�{� sin^ r��"$}_W(M_Z)_{2� /&wAive\ M� pdg:eidelM:0�(fi�*J�@~k=0.47\��@ure1_l$2_570mev.e2�@��fig:S� ePlot};2`�1 V "=��Q��*�#Ltect !FAhs�X� I�$/2 wave��afrtoanu �ed l�*`8& Asmglo��6�q�=wiI�)/2�� ~ q~�gi�HA�unt�6��1�@ ��nq�AMa���kzhu:00}�jiI:}.qܵ)� _���c R�!�1�y�I~!ke�^ loss�wion�Q�)target�lsoq }�9Tl�/e aLJ* �%8!��*� by aw� $N80�QP� $A_0Q {V}S {A� )���pt5#Mmdet�%!-# �le؆�P�@ ��E���35>� �d�EZout�[JB � �(�4 \pm�&&�& 10^{�&E�t l!�stB"� 5��lr�nty �A|&c�6�D�# -�aA��� \.Z  ($_/>��hii2�~n� H7FHU�U�a6ͬL �� nbM�% %%3j�& b�c��dH �C�EEle�`u��Oc�� etup�A4)�vEX:euteneuer:94,a4calori:�.:02,a4a3� &20�Ɂ�v-[o�amEu�i�of &C5mA�T&nP�M,20~\mu$A. AnY�)�[p�kR $P_eG\%%9D@Aa� _iDlayer GaAs crystal��heC+E�!Dp1p��d;dom�iew�<l%�ary pXV�$20~ms basi� b!2�!�-�d week_ y a !3\ 0'-U�ciG of��%t�z(2~\%. Toget()�S�!drI�2w�e t �!�s�}z�d� evVQ"� �4��monitor%�sta�e-��* ems �Gin!��>lo͓he2���inimiz� � 5�j !%afl� � s su�bs" c�%G�lc ,�M���!�es"�+��Ctj fals���Di`�n�u�$cEa�f"'10~cm �4liquid hydroge�3rget �"l2( lumin��E�$L�5~�~�,38}~cm^{-2}s , -��I>J w -&r4\Ն�mun�t�|.�-%+� $4.4^{3-}6�� � ve� !N�CzimuthaQ�ngEI($\phi_e$. F�5u%)���8%�"�%RlA� q�w�O "gf R,L}~=~L_ /I $n� RyLٝ�|�$ S� 2� $I_ o $.\\8 t�#25$%\footnote~ r �W tab:K� k`�(n570MeV}Appo)*n A-!q-d.�ir 8���3i� atic:a<^N inT�EPh� mill� (ppm5A�b�5ruled"Q�+ {l r r!�P� o& E�: &?S NTe\t!,.� & -0.3"WV 0.01"�P>BQ�& 1vV&2BNon�ajof LuMo' B�UB0B Deadae %�' B3�O0.�C�/&9 $A_I$1)BB4� =y�V"gHE GZ�3BP��A&d"6E��> x$,$ y$ K1 �9BAQIR?'$� Ly'fB3( ndows (H$��/"KP {/W%��Di<�E%^0$\9ay.�!{j�m���:)�*�X>� B6�2 �B�5Bo,B& !11\�q�a�6���%S��<iP�Ocͅby-��(��st���,h"�O� �~@ h} �<����bq y ��%k��� 1022�r ivid�#{0oride (PbF$_2�h -c k7 ���146 row�ove� ��aA�sM_30Vu4!+6pA��g-^%, y�.a�i� gl�e8�d62$~sr�chiev�U"�t resom� 3.9\%/\�E}$�C� peak!��Illaza�{n:,0- ed� L)&�%ev�l�0a�$-� p[��eA)�R(1232)$-&vH� h>6o�v,�ng)��pt�. U�8Monte Carlo sim/t-�*�r],�EleO�Gn����&$(��\p�^"� �,eq1ly�sE�� � ns, �3m les�an  !HN�@� I6  -ul!�e"� �"�'ov-:�!@� !th�)6 um�NWexit w��#��$ cell (seemf�NV W� =II�M-� płve $kA!"�(L)&� $N_� � �3.��8 �wN!^]J�7 ��730T� �inner f�!+Q [��.�>D each 5 minute runA`&�zaw��&1�]� rmal�&� -h"+ 0A_{raw}=(N_R/8 R - N_L � +. $. C"� "�B, "�%,N� |%M *2=a p!by u, ��Z�>I ulti� reg0i{�W~M e"�/�ɠBt� !��mWami "m)i��1�L�%a�  10^6$]Ji ���� i��"� "� >�. A� half O F$�C��"�a"�om�mrAt� `B W�Z�2_�2a0mit �f�DiffA0}er=t2�-�O�yN�= �U���Cing � >�<��!�5�%0"7 GN� i�ES6�#�hAMPLE*��?w$��>��)��A4k��<64'. a��� u&-+�:s� �i t gnd re�]�vr< to E}�sI��":Ša}�tak�! t�mean �i&~alE9aL���ew=E�e!!�=\�.�)0�!ed��A& e most�uraP@&G>RleD;c���Ugsource~re��A�am�ץ�R�0L%!vic �sae�/"y�6��!ble�acqui�<F.�M/9�:�p��Ver"+�*�*�!Qu��86%�-z U�2�&�8&i>KDcs]Y�/:@ must��. Alt��so���"�-4# E�,X!����B��oZI}::�<%� f�Et��.�!]e�in� when�`Z��N0 easi��%�d� -�vwg^t�n i$!Bh=(mA� � �iA�!�_{})$ ppm�Ar"�N �� *�"E &E =��.[" �(*z �A�"�o85�f ��" "��"]�.� �dA�:g!��thR��z�02/0$8"7 "�N�M_- ic�R*"Ul"�\H^[H�`� 2�.�@>� GeGm��&]se8!&h3�����OHst�5�@ g��ha�$are�*��h  65�!co"��li٠ņϹ . Ou�� �� � d��s a%� �,E^s+\�If#s�7$� B��Q�*�'�!E!i�Z$S��*i `�#s"�sw5dasU��7"�Y��. Im�� iu]s �9$sEx �& f �1s%�2 &�T��>%t>��-)�n�%2ma�2�^�J-��f�2�+-72CA,Ү requ P a re� a�� e�%l� *7'!� aay�ؽofml&�(�~a !.��. WorkAfin���!kOA4/ ��.��3_gegm�* _neuf�e��.�`�6��E~+~6$A�E �*!�Z!8Wm�KJo��-��� !�i�ђ�-*%$�*�*j� !���y�R\ �2�9AfF_�)� ���& Z S�<�� dogtsR_ AX���/ l�X gauge�or&l!3l$\mu_sO+��=leinw�T6' �blackA1.���3 del."���n��h,j ce u}�A�a�v���Ot:]3�&�;��,"xK!emau�+=!(��) =��(�-0. )�RT)��><� indĎ��|.��C�� ��!:R ]e<�? �J@B�A\ i@A��ؤ\ ņ$I�0c �2��"W` e� {)�Q�an�L�cL�z��)6HwisA�3}, �SU(3) f�LJEm2}ner:1999HaD��"�LJ> goek�G2;�8 mA�J2faessl^B5b#MJCweigel:]����,an updats �bmF� Q�!� ��/Ac2"F�htY- Ai�- i�/R� .�8We/pr��� a se��^ �*�>�U*� � *wof e(Hin N�2P�N�U!0deute�Uat f�j$11U:(5�>$�@�A4�A@u�e�Dto �e��.R@;��&R@]�2�Sthe= :2�:�\\�-, No Outlook %A"�%��-is@EUHGoVm DFG hH SFB 201, SPP 1034,$Y�Y��W�EOE ���bA�,to K.H. Kais��(. crew%�wew�nk! A1 C.OD!"h,M�"���0�Qc!t�M nk S�[ erer� H.~S�psQ[�or�4"RK!. %:a�6%J#g�of unusN#&�-$sXck4 t en�X ibli�sphy{570A� }% P�!�.$( via BibTeX���doc�iR*\c�S [12pt]{io!�} % U�!qG:$ if AMS foÞ� d2K_@ms[�\u1C:�_] {} %%%� rtcu��.cbLam<n>� j{bdaѧ.(AF)N.} W_[$ $-8�ati �d B�E$Rapidity]{�7A� d+AuE��.�$*$ s_{NN}} =K�$ GeV��\ F Si� (AS�> STARH"G)\?+{%% ] "�ea6�O{Fndix `2#s'A�V& volume.}}1�Ck4{Max--Planck--"]n^�� ik, F\"oh�� er R��06, 80805 M\"u��n"C^�ead{fs�$@mppmu.mpgK`Q*a"�[u$��FtCproje)�chambe"O�)6]7H!�?Brook���[vd$ Heavy Ion%j4��͓:R r�@ t�Q\%lE�\� &� 2Qr^W8���s�E col] ݁��rI��$ypmd�5�."Ś&Q �xs� [opp!� ] ryon"�ȥr���Cxploi�N!2in��nT=�/�/�bem.}�!�&�0oB� ���3b>��y� ���}>�"pl�"52��3�s8 g�c��icipan���S`��7��Qc�al��tw ,p : or hEXre*{f�ec���yWWbI:���Y� %�fa��Y� s 9Y� sage %OZ0�i�$.00, 42.10�D��HSubjto jour�>Ps %o{\JPGECo���if ��( :�����%.�Y\� {IntŔ�\}3��Qqf�X 6�!�:st RHICe&�2 ti--Q,oQ6�0�Zos6u��6Is4 at��-m=y,Z{a_2 n al net`f�<environ��. MostMCl!)eY �Ua5du�. H��i��ntrastoߥ��sparencym)lq��edm Bjorken},�+i�;$��t�45�H�A��H rahms}. AL6��"�BfŹ�+�m�ic.�6lm�1�v��Lv ���l�4s'x��WsO�sa�& r%=� tiKi�le�hT�1. *Yir&x,��]zCUr a!K�c�*b8to��� |influlof�eArA� me�!is{Gn5�,J7�%B-ca�}�-�'�⁃cRB� �ip�b��� 5~inme�� stag�~I�?irR�a�ro��R �!� ��>gsuf�b��\Ple�):�`3@�!L�lyi Ѕary en�)erԙ\Re�tρBE�o)�� } 6M}=l--drifY b1(FTPCs)Q�o *9p+ɴ stud���Sd� A�;pseudoQ�%�e $2.5#$vert \eta <��@ Ftpc�� / 3�������ic:�.!�g�+al,�nI.le"�vc�"kN,�F\�1 ��!�r�qm�um�/i!�H�,of 15\%. Via_��de�:G�cays, "����jti"�`� --li���X A=sm�leĪg!&.��A \8�)UN �iAs�2a�neI0Lam \�LarJ�p�F�E/zJb�-hjř�64�Csora�� A.y�li�ed� strict cu�)IA3(ex geometry)|r�k��"�,��miA0%?(K^0_S$`"*8��aI$!�c�:&�/�HIJING͎Hij�j�+�aGEANTI �&u.�ed Z!�%�l. � � 7M er} Z_*1.0.CCS1RD \vspace{-1cm} �T" �Invaria[�bBNrlgrM \B\�en1&wi����1G1l!��mJ_i�%�9i ca��,%bAFXoutgo Au��N {7 --Au�t5nebH r0d�-as >d.} s9@'MinvPlotm51�)&h'(� -��i6xd�i�nof�} d�ܭSis $|y|@.7�m�$5a��ah �)9�*W'%5xH/c $<\,p_t\, <$ 2.0 �K"� P(�le SpecAB!�Cz�DepǞ ce} *� 'k�'�j�Bg��#� v^�au؄r/ on�}�� 10.4"l:#>um bi<�4($<$n$_{� }\!>�8.0|sub�5�$.$Oa1 �bir20\%  q�N`14.5),�-/(B -- 40\%, J� 10.8.Uph��(/710^85,_ � �/"7>Z� m ! �  Q2��Abi��6��. WAMe>�cW&]F~� �t�!� embedl+m�� La�fto2 l� �, $p_t$����*�od<ni5�A}a�B��� T�*��O ���or fe�zow�$ $\Xi�$���"cu�2�0 /e�{�tio-,an�]t$? ����*W � M�ini�:��8�rh1gF�+Lambdam�Temp}a��22- z��1.! )�!h��2ot&d&� "� "�,�ex2��1 $m_t�N}�8� �c I� 65\%�!�=B��Z2�Z �[ a) Ts ZFN�!Z2�I����$%w- . Y�9TZ1\5e}4%�^� . b).���!hZf . Wh� i+8? \� Au� S"�]��" d':yF�=<� %� �c����u�,E��@1 �sY� .׌mV����3t&R9 pron�I��� 3.Zi s��� �Ef�-A26@ �� ^I-�-t"��!��\Sa��j�s,)� �Z�,�/�W)w&�F�b,"z��i �!�.O� ����F�/} Sia}q 7�t+y �59B�aiRn $ud$ W��h�,i�E�, i.e., s- ��..�� j�"e3!��*�f����)�� p-��of�,�orp$t� �"�i�!�1. B�K��m� %8 D! � et�m�� at�*�&!�� k���!n&� 2IA�n&��4 ���D {*�Q us--Zu�l"�H���<o�in� $%� =oa�te*Zns� �,B�w��U�r"�=��@� t s')aai�vOoc�c� !�--&&Q�. �/B{*�S(\mbox{B}}$}2�B}�� okes�n junr �J}�fa M->�!K� �)6�E� fer. EPOS ^Epos} bP%��Ql�* �, �.i�}s�a�*&�@"2�M�2+2d0:Jremna�on��l<aa . AmYK�iP�, AMPT �Ampt}�geI�� --ph�e1Q*��-�--�cQ2yB1��lr%Y� ���J3� �� ��� (a))%eF� (b))�d�N� c���q%7�#d\3 s. S":ue:te�[=�dlACo�sv &,�P�ent. A:�%��*�e!�:� Csx"r+w� n 6Fi��A\s m2n��e�(2I�s�>KFL+�aeB�aV�6~ $�Z�&f4&� ��a ($y=+{ )Ŏ=��`2-ascX���k� )B"���`tisVi�E-��r-JtyN= e���!e�dH�bly*�V�\�E^�R�v"W�* ��y�oV�n Qld l ar m�Ne)��a�t�٢Q�Y�n:�IH���,� ؼ arioA�rW--d%��7%.m . Ad��alFbyBIi�:f�fur!� �z!�+�0YV*� eac>�-�)�A�N�l�� e�!�c.l�6p1vb�or� A@lyI%!�E7������a�2&I�b��6'�� �FR &CC"|�} Y��!�!�|, JM g �\���~t K"3"�5l=&�in��. z��HF�$A����!�zg�*L e�s�"�S�.��� ��A,%2UfqQ�,�Sv�� (A�x��2�! (�n)7%are b��!) 2� %�}Fmnec%K*�5� wo �*P *{R��.!%bGPthe.�'}{92�+ J.D��o9  1983 {���%.��.} �� D27}�w&]�& I.G��arden� l (BRAHMS%&&�&4>_Ϊ e93}4L301g��)A��W] g200 �Nucz �m. `�T A499} 713S� X.N. Wan{4@d M.Gyulassy 1991>� � D44}s{� OB} A� opor--Pop�B� K(C70} 064906�*� (D. Kharzeev�6.�L� H B378} 238F� K�*r5IAl!0�/2@int hep-ph/040527n�Q!� Z.W���oC.Mg�G-wB& C68}��904�>� "�)`�F��t"-��,:ٓN�prl*��:�*aR��[W%^�**�*W�2+@bm} %\flushbottom� 5 \6%{\bold�* Sca�x�Ha� 9��Q6,$\beta$-$\nuOV" �� rapp dioB�] tomso�)��Gorelov�*�Dp/"�!� ics,i*5�er&�� y, B6&b�British�umb��4Canada V5A 1S6.$D.~Melconi}���W.P.~A$Bd:Uzja of We5�n OntZ , LondY �N6A 3K7:� Ashery} 2�School`-a�"��$, Tel Aviv2k 69978, Israъ%":���f�.S,TRIUMF, 4004�b�* Mall, VaD# ver,]�:��V6T 2A3.�J.A�hr:?�lNl0P.G.~Bricault�pjp{q J.M.~D'Au �b� Chem�y�"B"܌eutsch>=U�\'WQtho+[� LouvaԲB-1348 @-la-Neuve, Belgiu��U5k�Xng>k��N�!ZombskB�nNnP.~Dubm�6�����J.~FiB�&�&U.~Gi;:��WNWFc�u��}�KFKI RMKI, 1525 Budapest, POB 49, Hungary�LY�S.~Gu����O.~H\"av~%�lt.�Decease>�,�,K��Jackso����B.K.~Jen&y.�2N2M.R.~Ph�����T��S��i:W���� T.B.~Swan�:�6��CfC(M.~Trinczekr�� "� �� be�Cgin{abstract} We have set limits on contributions of scalar interact�Rto nuclear $\beta$ decay. A magneto-optical trap (MOT) provides a localized sourcek�atoms suspended in space, so the low-energy recoiling ��i can freely escape and be detected in coincidence with the�0. This allows`0nstruction of�Dneutrino momentum,f(the measure.-4-$\nu$ correlaO�, in a more direct fashion than previously possible�efR, parameter �� $0^+ \rightarrow 0^+$ pure Fermi d!���$^{38m}$K is $\tilde{a}$=0.9981$\pm$0.0030$^{+ 2}_{- <7}$, consistent !Y!8 Standard Model�di)O.c1. \end]�l% \pacs{23.40.Bw,32.80.Pj,14 (-j} %Weak-iY�%�8lepton (includiA-�) aspecA�fI34ar physics %OpI�cooETofI�; A�ping %P -El%�ary!x,ticles;Other.�hypothed)�,maketitle %=�. %ThA� gular disu��1 s)�re%a�a^a�M�A� in %q� A/, i.e.0f� .�]�6�i� ta'slFkA�k,, which %is i�,ly sensitive!�Jml, %were not available until��ently �$garcia}. A =# usaa�2}$Arm�is%0 only6� %.��j�N� �? ~>� �  deduce�)�^+Jw by �! 9�^+$ %�� A�r6cus�� %i2L.�use��J� �raab}!�p� a %�r ed, �fA�@�Gbacking-� >[��8well-defined poA}o�>neglig�n!rmal �n.�W�us�then �] .�q�)BA1>y2$emitted %5�$ event-by- �_QS6��T �8B�3!�2F�.� alsoF rmine cri�ɥ?onse fun�ׅ our -or��$ situ fromn�Feumselves5 trapM����s are �pursu!6 elsewhereMDscielzoprl}. Inq 0$^+B*��:Ts carry away no net a�Nq"$. Back-to-Am>� missAQ(is forbidde� !jS2, becaA�W�� boso��changea,a�s ��ͻopE�$e helicitye�8their spins addakona�2�� woul# maxiA�for��6������%2��sam�8. %If we writeR5J.�2,.!B\be� equ8 @} \nonumber W (\Ua_{� T \nu}) = 1 + b \frac{m  }}{E  + a !{\rm v} c}}  cos}Nh.� ���i�Q� coeffici $a$�+1%fW e-�, e� -- a6�prA��!e-5�-�.E�erme��E coup� � (tants $C_S$E* '�, assum]EimpMS$C_V$='$=1 mgJTW}: %F�b-�narray*}$ldisplaymath} a=[2-(|C_S|^2+'|^2)]/( 2�, \\ b=-2\sqrt{1-(\alpha Z)^2}Re(C_S + C_S')RB %_ 9�%e� hasa� I\s, orŎYoa�ach line1��� 2�AV:aFierzG fere� !� $b$� %lack�  de(of� $$��$� $�N strength� $\langle U� \r$� ver2ingent,� =$-$� 27"� 29-�(towner}, bu��UXAD$+'scribes I�Vat -e_ t�eft-ha� . M&=E�aE�r� R)<a�jin1!t!/chiral�8or time-reversaw opertie6< ,herczeg�,!�8isobaric analog)[�!�*� tra� ons ��Q cha�4erized. Lowest-order � - n(ed approxim�� valu� �6 =1 ($<$350mes$10$^{-4}$Y�ocase,� � ) do. )"A��� ure,�hig� F�are $ ro'oQ Q %by� A>uo� J photoba��Z��h� * some�g like9 % Ot�(diode (LED)@n  �!�r� C LED/z)�!�ArPsI � 0--430~eVAdiR al kino"�+, ��ޱM Z-stm threS coemicro�n�#�s�QY fix� KzI�% 24.0�� �di�$�)aM TOF[E$j}$]�l.3iQreM$�an!U�P� d� i�� ��ak�E an $($-to-0.25�� �??��2�� u��a &!.Fza�A��!� $E$ �  &o % �+1��� ,4.8--5.3 keV� �� MCP.�# �� �J"d�an�`a�"cy �60 a5compa�%�!IAB���il �� rr ��Yfhat z}$)�A$�-�9� is df!x}�&%�:k� �(�pas$understood ���Di:?��1/ over�P impac� gl �'$5^ o�&�error (T�#(tab-1}) �(nYAa Veff�'se& lite6"�fr$ }F]'odMh!�"� �e ly ill�ate�MCP. � mai��(pop��ofa4�$ 2,000� ^"( Era�V)7qA��� lifek,>�ma� dual gas,�� 45~s�)97\% �d w�whileI�p. rk In ^+$ ��!�&�Y�� ndA *�"]�.5�G � wallT W"&a�is����!� 88�q� %VzA���eJ)ac�*�8� 5���  J"6�����.�-a5.�)Z�, �!3delibA��~@� ?��by�7�w�wI��E9!�%�� � d��bxQ. :FeO� ke�m&��bef8,�Qwe�a��n ^on-re made �g�y�#bo{&�yL{t���s.� average �p-��a�isE�'%H@be $61.08\pm0.01$�x� a fiŚ!1lea�+edgńTOF p�)� fast��40}$��6�2})) se 7)shb�$$^0$ by %w��� wrot�Lin�ctN�is�g vari�# tinuouslyy we %* reph��d: apply!�E D��4�M4nd 800 V/cm; %� r% %varM! ,)�RtoQ�62J��un!�or��any��� %-^,0$\tau_e=260$~"�a!�usexp}%~-$���0metast� tJan� �� �.��om��%�%>�-�YabI ?n We imA��by� ioniz!�a��f� �5�+� w�a] d�A " ^. them!�qa� a� $Z {x}$, y = z}$e~r"�1(} � 1)�� fit �!�Gaussia�(0.8, 1.1�+0.6 FWHMD Vd (a>����axis) �#� tiR%*e for e�� � Tto 5 ns. Two CCD camer|9�g-9fluoresc� �� � roid%�kep}#n�tX � 0.05���%A 2D �� plo� dat��= �%�[t]1�.1in]"�-fig2%�Y2-E�er2.ec�L�_>p� _blu/$d�N6N_gimp�� �re Oiaeg200�� �U filt N��:DM�1KT�(color&,ine) Bottom:dSc6�i��vs. $T"1i�8 dotM�aU�of 500\� ;-s�Dsuppressf -�+u"��+�sek��"�gi�Ar'��,��"� cu�,eK. Top:Upi: ��:� �0.1\%.� atK�$1020 n� �$'sqޡ�of@in� +*� and �%be�edL�&�2. !�&2F�?per� wo2�')J���kset. %IO#f�# (�w��e*�2%F�3ra!B/�BW :5Ir��ouQ"W Z%�6k 3})�Za M� Carlo() simU p�'GEANT~&geant} Qu�(F'T jbE$_�,^+$� �� �6J4 incr} �1n�")�iVcos($JO-8euI� E��MT�{)�#�,i'dexA�-�}$�  %- taneW E�&, 2}�, � zmsArrK ,+2,N8"%0�%&�Au�A�(le5�&tu�A��&� !�the�#aK1�tA$�TK)V#3 D-\�1� E{ 3� y�q over-� ed� purm �}$"�"+}$/cM�kh}, m:i�#�ei�7� ��d.� oS5�,i�it��0M��� 5: J�7is%ԍ�MC�a"l2!9$A灲R�B@Ei)��$ZK�)�#�T:� ��E > bh� &5(justalexand\4铒�a J fig3&�G�� H�� 3�F6�jan L ƑBK-$JVc���ml�-of 162Obi�(o`#MCQnI�k�9��,� �%s�bconfieleveletA;entirɼis 52�DY v0b�bina�toJL . F�>�e��R4���"dip� �MQ�feT �": dash�urv?0s an artificij:l�r6 B ��all�fs�" %C�4���!c\%���10�$eatY aP.  F��o� vX,%"�L�>"!-�raQ"f �� %ɳ\�ed,ls)y����<�cngz�b;5M%��of�i-8-vt e�off. E�\"P 3F7 We�*se� aM%�!>�A�i�xailed e���of syst� �E2,�� lets usA��)"�7>au!ium<-(�-�c% ires�ell�FZ �%+"1�. B+%�sF�,���bya���s $ p" @by a<�,�&�>�!AP#)� on!� 0�>�>� s reca-#pri� Some-\a�!��a� summ;e#�@t�@� m\dB�� seM�te�% u�51u� %�=n-3  toA>."�#�}[htb]��Ptabular*}{3.4in}{ll} "^4 EW4 �/�$ : & k17�5&< �7%1 & $4$" +}$ De_or Rese:R\\ \hsC*{4mm} \%2 nt Linesh�Ba/ � 0.10&�A6�06H%VI$511keV ComHA!�ingQ068H34 �09b�rOto�"�G C�g�%A�non��ar!K F 17\\� Effnrm Ar+p"� �n5.3� & �07$\\(C $]/XY�p%'on &M08re$^-$"'2yn >� < $s=0^{-0}_{+.01�4 & ~\CWC 18}$\\ % x%U� \��Lis�$&�C .#B��"�2no�r~D�� IK���sem�. }% %,��pt :�text).} ��� le} #g��4MC�� t�0. ^+$�!�I��B~=&F /$�2/&^*� �Auniqu��-ed R"N� TOF %' F�<$:H $:kh� �R� 4g &R�. F�Rv},..�"�6�@- >9�A 4va�f 1500A1��3�2���Ac�� *��Z�� � p,a��=� buB!%�s, brems�hlung,$<\sim$2W I� P� 9��in�"volum�)K?�5de�0ed /#�c%���p h1�&d .�, �.! ���.!} NrCaiU 511�!>w � )�)2$;y�fl�.I Q I. "�%res0 �``&5''.P�0� an ad�ve�(ifufit�՝ }$ c.�>aV(�>rummE.; �iis 37�$\leq$a} 90�$ �z$ll!  obser_1-�"� _&�ex��,$x_{ADC}= x_Y( + $c_2$ T8��4$q&�),i�Մ m$ $q=$(0.33�'1.49)�Um"�:�MeV�:1,.Q"� ��"b�#A� EL$a! %Usan1n.Q]�E�A 2^�R7m"j!5�vZ!�r7 <.&.��}A�� P"� i]�!PMJ}q��QH $\chi^2$/N=21.8/23�v�H>�M� 2ML10.8/112>(7�C�P� �4� Qwilki 1 �� work��toD:� A��H %&�e 2.5A:,�� goal, -?tl%EA��D$b�qe�7-s|Come7+ ide poorQ1�$as yey>9 b5M��ing, V�+��f� be� .���*)N&2�vI" A=al sourcA�rp! t futJ>Y&�$�le�e%�7�����en0aZll as %�+amF��e�&65R>,Xay���Le oj?-�((J�>7seE�dov�%�x ed � F� away� real:� �*n��w6y/m�MC��<orm!?2}�fys*p3B!2�J &.E,�9 B*WFI�_ m�u�E-a��IA�we�%EG=6tselfG our % V�t, :Gresulti  %A�r5� %.6q+ge�2�les^�'�P'e�,ry.&?A���f�:��$C,}�n *"�}& .< le*�#�u �4-�a�)lies � �#z}$=807.�C16[#,&�=Da[%T�P a�:H�teld��*�n, a6K @+!A�e"ed A�R9�8�vt+a:q)(`wrong-way'�@�#I��fi�axMCP, w�Hg� � �N9Cs %E� 808.3%edF�� 1.0# /cm %1.5o �I��"��!Nis�. % 20��.( 89\%, 99.6aX99�39��&� '8\:� !��u>2.58$� =)!^+!#�o���3.�and %�Cper!-ag� 6A�D;�#� �a�( J^�� 3);' c�M�k!�<T:3/!`@' � l��#es �2d��8f%��'TE$ �&!o�p��4 quan���2TE�, I�:As �io� abov� �/t1>0 TP=2, :B�{\K��+�!o�$.��,� �nd�Q�  k nite�CX��Fa]LAT2L %A�9M =Mhe >�i��De�  %Fa�7c.md&D2�+�Ra!2� �)n&V �� ��� RsWin�/ 6}$HY� �O-�2�9�9NS� �Je est�G�ls?%p osci88�*zI�2sugge;��i��%{LC� ��I ��N}��w0e�7�vto� !��!�;(I�(1+$s$� �}$*W�4\!is�.Fl�f�3$s�-A 0t"� in�T:tuJ �H981W2030 7$[_�$� �6�L�>fO^R�^!5�z[I�U��)YbR75a+�U1,�I9�*F#rŕ��!�^8S�I=��RY�� n� %��J71� 84Nl& 1 1� $<$1!�&�4�%.\96Nto -3B. �1by�,y 9.2B"92.6B ;a���Gb<(+8.0x10**-5e� -2.3 e�m�'%�" �(a��NG=>M�I5Otira.�AeO*|al >od�X�� dediD@. ��!�memor~O.~H\"�1er.�[ac{3le�4_K/]KstaffU �^=�A.R. Yot R.M. Woloshyn, J. Ng, B.A. C�N, ITo�TE P. HP. Sup�6i��N��alx 0earch CouncilE�CanadaA]rough ��Ny! al S�WH nd Engine>EnR BIsraeA FxQ�k WestGrid�"�!hebiblio�Ey}{00}`abib7" "�_ E.D.bmin� ,P.H. Bucksba| {\em Wr6In�;&�LVbi$8Quarks,} Cambri!�UnikU Pk/, 1983,  5.3.X�s�U$ijns} N. S8, O. Naviliat-C!sc �8M. Beck, % Rev.Lc. �b.���.2�Q�$E. G. Adel�Ser ��[ l.}, D TLet�AP{\bf 83} 1299 (1999);�a�+ 3101  �IreB�N.x`a�lPd5 bev re�%q (K. Blaum�}F��91} 2608�2003)e� %A. G�O , RNB-6, �Opublis�'in Nucl-> A��~�:s ����.�0{\text A746} �4) 298c6�ra[` E.L. Raab=HR�%J59!J3%�87�2Gs&O^ Na=a�lzo�\93} �102501.�D[ JUJacks# ,S. B. TreimaSH.W. Wy�JE�I��106`$1957) 517;:3bf 4}A� 206A� ��' I.S.�EF$J.C. Hardy�O vG s29)X3) 197. %; %W.E. Ormand�y Brow��B��Ho5X Af �C T40} 2914� 89).�� % -2b�"& TH's b_F�&OBH��, +0.6+_2.5��3aznB@b_F=1.2 +- 5.0 x �&32"�V� �0, Prog. Part.JS6/2} 413E�1E29U�U}!��:� �6} 78�d74H%JKlelg�F.P��lapriF�:R6&bf A2Aw46!O7I��j0} F. Gl\"uck,JA628} 493B98�B�X�YH�X2 M0�RE�73} 39�94) %.14�7ar!:R.=A� �90} 01��X3E� -Jn{�U( M.~Dombskyk~L )�%�Imm�71}, 978n0%�5me�U D.~M ian6YM' S. Meth. -�538�� 5) 9�� J.�'Au] �JHe�B126}, 7Ak9�4� 2}O A.~GLU6��2Hy�7s!; � 127}, 373�^{s"S$ T.B.~S :^�4 Opt. Soc. Am.Qb1a%264��B�*� T �7�iF�]es �Kont�}� C Joh�", ]=%(1�z((1963) 2220*� l}! .l� E%E�\@� W69}, 2%6�q5!gao} R�Ga>u�FJn55} 175�m8a4NLG Ga�FrYG,!� . Jour. M�[ Spec-�21K)�2�d� .A< I.~Ben-Itzhak�Ir ��U�38��870!L8�Y9'9�b�( 3.12, CERN194). I^!�eA@*�"�$ EGS4.v �*h DKofoed-Hansen, Dan!t. Fysadd18} no. 9]Xr !W5��T 1 %K5 */% D. W=%.�r�E@A2��50��90� Qg�a26��.�Com��1012 97A�� H 6 2"P 8 %S.J. Freedman (K. Fujikawa� Pa�Vet@2c��6��3) 02271>� �!�D J�Qw al}, A�A. J-�465} 48ee96)�0�e>= %��p.�p=�-doc53} �%� %%��Lm Size: 9.75in x 6.5�p% T9 rea: 8i"r e Ru�K heads) x /8ws-ijmpa.tex �?28 July;Q3o ex f1t�]*8c�*r�lnmLatex2E�%?�esfstruc �ma�lay�%is sty�W�Jm�%]6wy'World�j7fic P�`(Co. Pte. Lt�%% Copyr61995,�2T~F< All <s!rek+. ��=�!� \Q1�b{1\} �  markb-{Volker�58Burkert} {Highl� �.k,CLAS} V�1Ler's AD pSignore �/catchd({}� � \t�ـHIGHLIGHTS OF RECENT RESULTS WITH�\\!! t9_|b�A fa!"mI�ar�^c�.ci ��]�pI��as!{-�A>.qm4iT�#j=Us. AnonA,�'lyb4lI\ subj4S�}eJ^�A�cl)��U'%;G)��# Va dozen]�U�yU(*�%9i���'me.} U�Ta)�!:<U"[FL%=#sicpar�z c�W$ough multi ���> (h�ltw�`7J <�`�}2+!lan ongoa�cha�<bV<2 ar q �Q�unityH "}�%�f9-C1\�_�i im�n�Z tool� wardA�is1. �>,qxthu d�@opa�EI-: %| asymmetri�VR%-�dee\@e$]&�0 (SIDIS)�!�'{/bi�2 2! �um�  #��);onE.�� a1'TgraN��6�}n1A0 $g_1(x,Q^2)$a� hydrogeKde�^iuma broadiof3! E`1.6 GeVa3 5.75 . A�#s�t�U polam[ta�tRM=� m��duŏe��"z@s*cM*{6.5��N{\��ial{ps� =fig/R]_all_dis�C h�P = 33 v P7.5 hoffset = -9.5 v0�@vi4bjorken_eg1b_2:j6bj16Ji�C []{\�,{Left panel:�JIL0 $\Gamma_1^p(9�a��D)f�%Dil�2reI^�C�AR .bB �� gralEtri�! s re��9 ults�4�@�.p| edi�����Hall AJdeur04}�Gopen s" �4�E�VL ���S !n�5�!�"~B:E*1�:c�v,=1.5$~GeV$^2{R(a zero crosE �j,�'3.e�gy;fv���h roac�_ eZ�,n _@i. S<-6s�Ghav�en9��I�ivB*mb�M9�I "%� .�nmIP!��20B)�ca��?� �'�%06 - 2=RQ3�.)$� n1�A}E��6F a�A�,t!�a3Ah pQCDA\7� �n"f s& ���z�2Heavy B� C[z PerttvL �� �f*�+ ��How�%,�)�Rz1.�s=��mpted �ioffe1,2,s�vA good.E�:on!.�a �0 i+� �:�_s R$s-K:�e� .� �E�s�2rm* Si��. } Me6� �leB)1;�=�e� focu��BZ*�o,past few yea�F(A much imprGs%���<r"T�)�Q1W �efC&v i�Vg-� A�%�verqA�!�� k A�eg?,=r�6�i.�-. �Ʉ/ �2-�A0azimuthal bea�.in5[dt$ep\r� a��@e^{\prime}\pi^+X$�3$avakian04}���mat� ���F��J�ssa{5sD.� Ef0� �>�Otak^t H �͈in�����>�a�on Q�� rpre��m� �$x�/z2�m�Q�yq� ���9���3$A_{LU}$%O!ED� lin�nt��V-3R� e(x�.�;iA �0 ;q� $\Sigma_N�Xrm6�. MA�moii!t�si;&."�ATP�]it�� !��� =er5)�i�A�exampl�: 2:+ UL}$ylU���{A�m,�qͣ��uf�]�. �-�_gdh04�� \f4�alusol:�0&�40.20.-1�Te1c_xzdep58mx1.1and1.46q4^q14Rq: {Beam-���AY��e�� a��d+ phi$ (z��)iK�Zr�h "&]B" mY$\sin I�i.^{}$a��%� $0.5 < z�78� �g� "��z�1��8s91:x:4�$M_X >�`$� (fil�Q ��ye�X�2E�I4$| ) 9�8ke HERMES� I�,hermes_ssa} G1��ax a"eo�4� $z8 2-0.�?$x04. } "1Mfig��A� &~F.|��E$N�8$��F� .} A�te��aU� ��s�M#a�Tw ����!�"�Ddev&�o�J!$ � (123��ME� sphe�:�y' �c� c $SU(6)$� s$ �2go�$M_{1YQ"%diEwt" . DynamL;d��F��� � �%aex��v /"� 1bp!cloud,6p%one-glut�x� ge2���[ �59�> genu�&D-*>;m�wI q�%fmodel ���% (buchmann01, 2}�;-9^3on�2��2d� ris�Jno &�!-qu"�x9��o�4E-�a�1N�r%� e��q {���% latt_,QCDi��Zrou03, 4}Pi�33 �' !8.�i��(��zshort.�D�� \to�Sfty�)�����t�6�"hV$R_{EM}=)/I�K+1 R_{SM*7S%2.$� SJE�5���a6tZ�=�d�j3O4�a�rm�be!�id�/8ivelyx�>um)�f 5A�b^:T �EM�nd S Z�!Q�cru!��A0 ��A "� � already p"��_IC�A�l _�a��ne��0$.�e��mRkjoo02� exJA��A�-�Vm� ��1!� $0.4j*�T�2ZG i% q eArB$78 ji��,&f�Ab�agn� )�By $G_M^*A�3y"B�afwd�?2s}.9%remain_�gVb%��-t�6e%� �);c�[A!Z1�Q:!s�R�\ e��a�ms9EL�.��ft*� �$in *! dр�.�?ly�Aa �obO 2���>_E|���@yvo�mm1_new.p.f2&T 34rf -49.\��f�mrat-nov6K 2�3 &�172K � I ` >`!�E�NK�h!I�{�}|�J%dES��$YB. 2qM���vs.2A_8E�� *Ouncerg"���p}��BQ:�HSag&��@ 2$1sbsolu�1 sh9�eificar�cda!fu�(.6� gm12� B�6� >� R�0 $P_{11}(1440Y$��535�e};&1 [bt] "A8�( fig86j5*� 5.&20*3-8.j"� {T^ N~ )e�.� (� )*ɔmpl�Z9� .| p2.`(_E9s),h�j| p212<#br<. BoldAt���~�'��rxY ���1� 2q�&[ . n cap�k95�HD�aNjl�-fron6� G@(99CoQ�, �a-d�� Rb�s \�ec� \warns90,aiello98,cano98}:Tp11_s1A��'M��]g� r"��@ J� ins 3 iso�$\f��1}{�G� � Va}6I(D_{13}(1520a*���hd �x�_�Ait� !��ng�� *�"� *iQ��� ne� ���*)��ba,)� h���a.p={�EV"`en�C��T !_ �9w!p"� ICm_lee_ww*+ �(on $p�0b n +$6% ���i >r n �L��U/^�!o� Q;I !O�% ��).� ϟspeK2i�on" �aznauryG�[6H s �e�al�uA � $p \eta�rf'AA>2< % ^2- wo�� poiߏ��xi>kq_oAA�iUsurpri� X�MW $22 �[��p�c*��{  1/2} drop�pid+(6��� �ira���ha�4 6,&Z �2�W�"A�s�e�6&zY,�\a_�OveH!n�p'unat��bwe=�b�" � pc���g�0C���E�)9� �c��'I��{5c���"pre$ i%o-{a&(+\9��![!�inQ �~e /2}$uAe~( ��demPK�id�b�3->p�t�dB{Eeach1. E�Z�&�"�e8�� *�ms��I�mlIy�))%6B��!�j=� !��i�@6oreN ���siT$N\pi�Bp�;!���in=Uh�se newh �s�earli���_q%Fݤ��%ādedE&� &�. �1>����1 ����6iy� �N�.W)VY�n)�)>c3A�Mat�Ynt?��=0.5-0.6"� C�d]աb�,e\!lu��"[��igT(Wfir�e-n��E�5jr�#%;j-"��&Mez�4ab @ '�3� �@�*.&��>84 28�%%$!�.a Se�Fa(``�� ng''/�� s} u9�L�G� �s"������mDe G��"Ee]�!2zI�"�_&fo��e2�/ai�>en \�h.,ble�" �A��/s">e abs;y!� �eA�E&� � ��!�a9d"1(origin, nam�P�bas�3)yˈp6l]b $ 3"V0A�!�\o9s O(3� E����&.��E�y�����0U}M�� 6�!\v���T!fsA�!kirchbac�eA� 4Ur!�la�'c�b<M'1�-v�p�݈h)�yet'd���e*eMu =�5i�)�x N$*�. . If�bae�p,����o1,�U!y*P %�i�s�Z AH%�n�1M�aȩ�>$.� �yV�$�8"of1�"� � koniuk,caS/eB-un�֩Zv\d'a��1�ks`Cw �w��u�i V? Ma� u. :0o�P���Y �D���X�y�]omega$� $K\Lambdas'dt�A����O�X2Wa�A�-�#�9o.Fs% c�A"rn��&U .�" + -$['g- J$0$0b$.TK^+1fS)A}�s. �&E>h] �2A�tہ�cl��A��5 �s� z(, �w 6%Dce�convinMT d�;�R�b.R.te�D&�2�m� sophOaA��t6ocedu/�nal)��mbgr�4:�nee��9 fur��pO7es�A�&���6discusS �-�Q |�� Y ���z�48ripani03,bellis^ A�  ��*� ��h�"d two->o��� ))by� vc- 2�� i.h�v�vt=,�%2�"M�^� \rhos b{duR if� ��, euwti�|�.C%�" ����on8�t� for$5�l����MAth� {� \&]�^25 وac9Hm�6 �~�z"�AYsd8=� y�en v�As'e��D�cat1x 8�A�Q���be dip �kwoA�tin !h�Q2d AG����UAL"!*aEi*�t � �}�� �w�$!�?�+ �i���" ҡ��*ǔi�_A�}�a�.j5@u� Y�nda%M6�Non"��.Z�� �b�z Born� subW*�d�2ey�!�`p ��te�L�1,Breit-Wigneroma��/;�wto !d�_Φx�-�6ja1nva�4t m E"�� R� N����-cc}&W+F��ij=)���.� {>A�%_cmy�p/iP��umA��accumu�d 2T9 "�=�&ss�Aa,&�^�,pr%Q�5��| thod����e0e�&��]<}�����"1}� *(5�o repa�� betw{ AL� 5�!Y�vi2s �2\i�Ba �aI�yy2Q�6�e!� a|tIJ��o~lp%�5�s &� �<$��7�.�i9e���F�X&s/$@L)>fa���ci $J^P�5 S����$I=2mor�. 4.�is� easi�%!�M!�[6�!_B(�zn86�+$cs_ppi+pi-*���E� ��J'�%�.NB�EgeRAl�-B 2� �� Ae*$&�8; m\AT5�Y��:� �`d�$Nq�6�to�0y.� �yo�� s esu1"U�.��amQ=ter��#�a6 z eH��EG>�}:p)�FkeeQ��!�O(R"Dpmly2��"InQ�c�Ow"�Ob.J��!d��ly*UU!on8>��sby PDG.V:6�,2�5��� � _xsec16�2t!2* !. !-5 ;�fl! 2pi_e�_ �f17.�<h6s!{T}{F6n����J5��F�A %I+ree�M,ތ�H1.3w�6�c ���& �� ext.:�+��:� AnY&�U++M�%f� �6  &�-�+b(��T$W�Q"�-E�is�7& U�FO�}� )Z��x!c1.7�� m'�nOHl~B�@iC3. aS aG��0.x n�m� ��0C $p��=B-_a/)^M�Ade> N^*$��-.7 c��t>�%�L���lZ $W =%T.1��$��� [2� be >7�� 7(1(�3mokeevFI���Iz:�9�p .] .� !� �db�aB�?�.Hsox v Vh�"1qe*oFt_jA�gPDG͊�f�r �,>�*� engt;�>�����^I��be y iscrِl.� �: 1FB�$"�${��2$ntidecupl_P��B=11i' �&=1b2�B=3.�${[BA� ${\bar{�2$!�? &6 $Hw SM$�2&3A�et>�"mJFlavo �?zs - P"�Js iA"cs6v $K�l�s)�K!R�?$�u}s$ puG|rge5�#�J�:6 uud$��a� ^*c��5-N�#^ A�I2Qoum�s!M $udsQ.e.A�q���,@. "�#a� gene��%s6a ~u�**�y� ;��w"c!]+$�] s}u$�e�<e�� "�C�a 3-�s�!g��6�="haMn)���{>y f��%��a " ��M". Ca�/ch a BJJ exist?"0�se��_8(�D3r��� �pre�K)��>��NZ. @a%�of#o"}D�I8ŧ�!, uT ���rekind�ec9xmXby D. Diakonov, V. Petr ,(M. Polyakov\ 1997�pdpp97}�o�h!� na�:�< k)P1��L mas� 1530�gJ0�$]��l�aX,$\Theta^+(15�)a�e x �̚�Z��� I:(��$SM6W$-�b��t �M` ness = +1NM��-���v��m*.j���as� J�VU }. O(pt� s��a�se9-^:9I�5!&J2uu 2d#�Lq memb?O �:-�:�id �"�%y��)�٢3ESA�A0M��I9!�q4�oi}j&Ja� m'im . EcI.qa{�s� e�of�5D ;��� talka� T. Nakanon � "HP�ct myfz�BMK}��a����# ctor cFU_d,.JaA�e8�g� ]�*� meWis�R-��gi"[#neK. >@ tbhp&C �=fig.�<=3 M < -1"�. � v- fig5*#LvaM V155&/V�1: If�aY($M(nK^+)$ aehFLcue&�in�Msho�;$,$ Y��&>��E1!�$\cos�,^*_{\pi^+} >��� liA��1:^.�5�K^-p)�<s� s� y�0�-� �jae��EaB�2o�� bouP� N]f g.} y�H%�! y��a`w&�� (K &]�l�� alp� hN.�=K�$b�ɑ�PXS�� zX��5=T�6b %QciA�  pi� "�;ȉ�d��-?!to N^*�9! 4 O eI��V� t-�q FN &b%5��BfI��rņru�%asJ�AY_p}�`I�"e� $: 55� m$ 1 �"��assoch��!�9�. %��7-�*AM�� >H?V!�o *�@�bow��asa��c�<�U�Ib q|k�>F6��)Hai�pEx� ?6eLZI<*� tes�b'�l�Y�11�"1i�U9!��plo����A:)�.e� �@j��9. ]#S��)�� k&& 2.4UL�\@ �"8 too��A��ddeP on*�"�'� �R:X�#�to >a��ha0 ��� q�%���� �.a�=f8t &�D.� >IIe.l&2Fnd)��,� !LJ�P�]�A��x A%w!�� capa:~�fof� �%E6 ex�Rf�. e�w!3�8��I�"� �?)� !Ky >�j'}�miw#x�m�T. Con� l+�ca*aGsnV6�e˅Kn��M.h .�.?p;��K%+n?��V�zI=֑�ra,%��[Z_"1�r "�I�toi���;��checkEEatic �?c�>:� �8{6.�;��:�V���.� 28"� "�8=*� 0} C�[]{ExpBEe�1�c��A��a�Q"s*�86�(ͭ{+*}) n K�'Ey5q6($ �cA�i�#��n�F)��$pG�)�p��6F�0nb���ed,_&� exp_��-6�7o�2���$��O % �N�%]�fou2)vd.ˈi`�B��� at: ��e�Z% �;9�al�$ Ejt�?A&?L"b5���#"q�K&$e:newruns}U�$} \tbl{New2Ppropo��WB%A!N2!-  .}nt�Yڔ }{|c l|l|} \Wc {Run} &�H E8% T  Rea�� St~�}�� G  {g10!+$ 3.8�  LD$_2  $ d6�K� "Kh Bdj{A:ZE�^0 I@�1E ; "4.0�HB�:zulI��:H�� + I2�A!�2�0\f�� X XI�"og�*c>EN h�C+B79A2.2 d�\f�}>� T�8 schedul��:G6�}\\��V �-} �.���q<� e�u�� �<g10}��a� z t�O`*�Qsp}�of8h4,Hc� ��.� hann071�iB pK^-1c*�- � X�69m-"� /th�  �of&�4 "R���s&�KB" g2a ru�0e g11=�H �^�Ɍ&�.�GFB !d��s�+8� PC%Qn"�+�|nN��s9QS?���!��?th��2���)� etup�b�<�f&�(5R�3�"I�,� !��B�n bL�a�y�By w$� �Y u�")Aq�2� "�$6n.u�"��L $trum, e.g.� e� ?in �fN�[F"�nd 4M er0 � rvUQ� nr ShoN_*�a� �&� �Jd&�,&%��%Q��a)s��e�+sum+a2�Y�@ �O�� 10$ nbtQgZ��+�18 !�=$se�p��%�"�*� J"Jv� `"�,�B cc�� Z2PwJ]R=�!,i�R6,,,vIhi*�oOE��bm&�nd'W. Z�8*�--$��Cn�`�^BFD#�wo!{� �!i�2D�! +2! �-��Gso faYT�a=�;���iɄna4�C�A�  Z+ep_���"X��q�2%��e�g3f �����ZuntaggV6�&��d���hiހg TA liquid-&h\t� N��Sn2L*��-�I�b�6�or�� I�a��I�chaWb�%�6Ve\-2� -�U�%� 3p' l�-�U'"$ emerg��td" vo�0����x�� 9�takSe��wbs/2005 8QE?)�g� 21"g12% %�!6mi�^�1�� 6C')Q-$�&?�5�4�F)@� +X$.� NA490� �}b:�l$q,�2�&���.�Ca862[E�x��2<("lui2�$�/"K��|ibi�Xqͦ;�e�Iz\/�9�}��*>Ot{ib��*Nb R. F[b:u (e�2�O)-xP2v.�z. {��,|x02 z{� a�b�tYun�[ C{ 6� 05520j{3) W dodge2004:x DZ�e�e�m| �shop GDH@,Bhs.� �0xji} X. Ji, C�xKao9 $J. Osborne1Le��B 472, �{X{5k�F01} V.�!s@�5a2&95�J&|��N;-{ 545�|!20:�z&W^ H. A MZ�Ptm� D{ 69}, 1AiS2�*8YA`Airapet�}BllNf{ 8+j 4047e�2��_M V. E�_2E38982� �h\.�J�, Tal�,��"%W1�B?W,A�Henley2�$C 62, 0152��12�N2�N!�!�02131)12.*� �J �]R verv�� see:!J:T�} Lee,�J -ex/04070 ~u�aű>W} CK2ֱrouN�$D69:114506J�:�|VK(�lat� 9122��_U K�}o, �N�), ]�i${ 8a�12��2)��mertzd C. M d2� M86,�y3�2k libuli92}���t:�J� { D4��7E~92� I�Can]� P. Gonzalx � � { B431}:2 J8��*�O��C�O�\B. Keist�� S�&�� 3598��5.z(krewald20002-�,{ C62}:02520I�2�lel�X�.e5gU208070�z;)y�N*� Gren*E%�2riskaAkD.#R@ MENU BBeijingl4]r%P��W1P,�SSchr\"o��W. Pfei��4H. Rollnik, Z.%CC{ ��62�}2}PaA�P$, M.M. Gia�|i00E. Santopinto.ƈ { 24}:753��98�?Q;Pn� GDlm/nd!�S4, Few Body Sys�� uppl� 10}:407Z9Z.\N I��pN,5�! &�%in.T�~, 7,V. KuznetsovY2"e<�RnBQ\Z�eo��� 9!�0��J] "�BbB�B,+�V�in� ��]�]-�tR�-*�-, Zeit.f�+A �_��5`oka��=z����e:TOka* 06211.M"�* "�*�s����#dE�St�=ya\b� 91, ��5 3.#KpE"Koubarm�fM: 3��2 hickpD��N26� K. H'.8�4)9^*�)!DK�)�HaipkaWI[IVB 597, 3���>)�]v}S��:;I�), Jlab*� E-03-113=�g4 M. Battag+i,kDe Vita�/JQc JL}&Re 4-02���`J�]ice�a Weyga��)�OJ�4-017�n�� mith�Gx+,z R�10YL2 t���dEM 4200� 2M� J�P! _2 903�endB �*‚. 06�� [12pt]{io8#>u{�4ckage{epsf} %~�your 5� 5": �\\newcommand{\cZ}{\cal{Z}��Km m{def}{Dep%ion}[w]H ... 2LSgmm}{�j^�.iSgm}{$m$\�[.G�jFA Za��? d}Be)fNg�J$=�=La�5B�A � *}F+R(��/ (F'Piz% pi^0F ptar� p_T^{AP}$%���wo�|$o TeX's hy�r�4��0 \{�"qo?�%nF$ p4re-Aend-edAc�!]�\��Re�S�U���h STAR> v{G. Vanyen\dag\"") 2�"��&���e J٥c*(�zVs,� Ap�<ix ``2Us"E t�,� .} }&�� �DeW�of��i��Brook�2n N%calc�ois y, U�,, NY 11973-5%���D\ead{gene@bnl.gov}�')M&�� Typi`%�gaF�*Hq�T a�8�� �&�+of e>l1��(�)A� yŪs. An"�"�*in)� is resolv!�o.iR9(�,rS�sevil}, `=�pJV.E �q{Cel?�mTe�&��! the �Sg��PsWMer \Adto $e^+e� pair��2 m�h�8=,�by �to �(y p_ �a�-E�6pi0�,mi�� tech#� �[�`� VX��&�conju�mva'Q=�PID2�) �fing !)�&o- c0Lam daughters0����,on progress ��toward measuring the (anti)\Sgm yields in various nuclear collisions at RHIC. \end{abstract} \submitto{\JPG} \pacs{25.75.-q, 25.75.Dw, 14.20.Jn} \section{Introduction} Decays of \GSgm states contribute to measurements of other baryons, such as their inclusion in \Lam yields and spectra via $\Sigma^0 \rightarrow \Lambda \gamma$ (with a branching ratio close to 100\%). Because the decay is electromagnetic, short decay lengths make this measurement possible only by identification of the partner \Gm~or its missing energy. Accurate particle production model comparisons would benefit from understanding such contributions. A notable instance involves one!�!\more prominent expectatiAwXof quark gluon plasma: A}8ngeness enhance%!inRA�8hyperon channelM�Ded via $\overline{-�}/$p}$~\cite{ \ }. Me>f�s often entangle weak decay feeddown in both �@numerator and den�, like .�E�}^- \r]��Lp} \pi^0$. Interpre),!+� s!?ra (sucha�F$<$$p_T$$>$ versus mass systematics) may also suffer from not knowing \�+contra�!�8. Whether finali� i�ac"�G9@baryons in heavy a�c�_difv�is unkn!Kas!�(ir cross se ]$ have been9� with� y little %9�ap (at $\sqrt{s} \approx 15$ GeV, wheref@y appear to agree Sa value� ;0imately 33 mbM-,PDG1}). Addi�ally,U4re exist data %Zoa�on periE�on how1.�of ��A;%-+�( phase spac!yJ�( ($p$+$Be$ !0p_{lab} = 28. �/$c$)1it�ears A�ra� $wbda_{I�^06�La\g�}/ 8_{inclusive}$ i��stant�H\sim$$\frac{1}{4}$.-EpBanDE�uQ%7resona���to!,!tat larger nF�I�4ter this. Any i� size dependence would impact observed trends la�!�=$arity betwA��%�$h^-$�W sin 130Al $Au$+Iat RHIC � Lam1}. �UM�{\R!� } Ak�under!Nd��of�physicetR.^ will come)Fm��,ing relative �K2q. It hasik%l@d that isospin di��ea�at�I9�rod�� 6�a�igma(p m)/\ IQ)$ sh!� be 1/3-#0cosy11}. Reas�#fo)� are��obv�, so wa�ll exa�_ o��� argua~s � . To be c�,>4consider {\it ��}13t1af!�strong (U�)�$s, but bef���6s.-�u5�(Models} Us!��mal m0 parameters f�4rom central 20>g STAREl-AOlga},e�THERMUS:_Dgives a primordial9�0.67,E�a) 5� 0.36 c X}. Th.\Aei� tha��Zs��� �M?.�is��!>)ViA�)�I�G5�s4y a-�( role. ThisK notewortha�cau� AAL indica{nM�UAl*m��i�(-populated �nleasta��-E3i<)��� �rE�abl�ϥ�p�!�,Markert�$,Simple countA$rul�1 coalesc��I7s,[ a�E�relev��Ŏ�U conɾ� very�se ma�{�b8sub-hadronic de�(/freedomMq�0,ALCOR}, leada-n IQ41/1e�]ny�)2.�i�bg � ies reduc��is et1/5 i�&.>!�fully9� �,Levai}. Here�� windowA3�cAjn�!�M )h. If q�9�*� � e a ��i nx00.2 or 1.0, ��źń aZ E�orB�. Ev�: genev s � 0 pre����� �� medy �a@� s*spreadi�IK lly � ��E�! �of�. O� � poi� ists�a)�%v)� .X�� Be$, .Ne$�� _{NN}� 4� MrpNe}, wE*�a��� highY~8$0.75 \pm 0.45$ �� ista?Ea1/3 (in errors. �; insuffici-to co� de w �E��H a� � ently. At�er ERies�x": ��!pm� e�at$Z^0$fQ>q~ Z0},��ha{% ��%�� A�4begin{figure} ��(er} % For j` g %\epsfx4 =6.0in %e�arxiv 25in Pbox{OldData5.eps} \vs� ${-0.8cm} \Tp \capa{\label.��0pa�ri� �%h�U# }$ (6/$�EOA$)Q3Be,Q(,pNe,Z0}. Mf -E on re))q�8excludedQcl IF� %�^f � li��!�same r�.2451� "7E"9O� A�M � e \Piz�trum �bF� 59s um  photonA�!\� ($� 2�e^+e^-$)Xdetec� rial1^i0})i�mbi�� le�!$background��� p_tooiR%ridentifyA�� vidual p�e9 re� tructed � s do�Henough signal-to-no��e����th . o� ���s,�is tru 0z��in� . I�cura��� analysi �unq s AT��Kd� ��%kal RI�Ʌ�}�ed� s (uncorrM% or e3 cy) � four) biu $!�,m$+$\ASgmm$ �q)�inN� b). "( .ss, 5��find a/p =� $3$. Future��es E 6�/APe+�t \Gm-ber��� �ә�!w� =<�3I� �be|�stood�2.9�Z�46�S� s�b 3.1�S RawYp T" 1.1��j et auR����e� in�>nt�6di��bu%R(solid)A� eSA��v&�!(dashed)�nfits, �a#a�> subt� ion," (b)R�fF�e mid-�AyvF� W,�2��-E�? �c��Ed mino���$\Xd�  -$ ea}d� mZl}than 1\%�Uth���(X ly s#) i s. S#R��b�re�� ificant, "� $12e� 2\%$ s!TE4$(1385), 100\%�4 %vR$(1405E"�$(1520>,�(uncertain f-����ier�A X iAP�#esB*!:�)  � � yJ���nK sevil}��ly aid �A��ng of %�sourc�*7 (Summary} W�uve "��5��* � 6"lF�� midQ�)X�A�improve�via a�K�<*���!."�D&�� a)X canEHE�ed. Fi)E���3 �A� l,be possi�a furg �acquiLby%�: �dE�)E35"A2�e� 2004E��x 6 * al.l�JaJ ; 62JS take 2bis-x {&�� n 2g,Q$C�Cu�:.c5;e f�/]p$ run�C!� ide &� .'toQ�e+]y� � � *{Refer�G�Hthebibliography}{11�ibitemm7 Salur S (aQ Collabo�n)))� Preprint}e�0-ex/0410039 \P� 0Adams J \etal�Thys�Pv.} C {\bf 70} 044902Xl0Koch P, Rafel J�V8 Greiner W 1983 �[Lett.} B \123} 151ZP�$Eidelman S �E �JF592} D�,Sullivan M W E 1987.ER�D �36} 674��Adler C A 2002>A�} D 89} 09230�Kowina P J(COSY-11��01020�O0Barannikova O��J2 0802=� WheaYSe1CleymanAG=�N,hep-ph/04071.D  C>Qprocee��e#m�(}Bir\'{o} T �0Zim\'{a}nyi J!�MZNucl. E} A)�395} 5259/�.U(, L\'{e}vaiA��&>c95.�6�347} 6a�S%*P @ privcommun�}�Va� tS E, Gyulassy M, Wang X N 1998 R��uN443} 4�+D}Albrecht H (ARGUS>u>6�18UH19; Bogolyubsky M YM� 1986 �Ya��z.m�119n:9V:t50} 683; Eisenstein R A (PS185F�94 H)Atom.I �$57} 1680; ��y�; Sewerq- ^�199 � ��x1e�b!b4682; Baldini A R198-�To��CU#-SU#�Z�of High-Energy Particles} vol 12 ed Madelung O (BU%: S�ELger, Landolt-B\"{o}r)y)Y��Yuls v B�� (FNAL-343J�1.��}�rA279�|0Z0}Acciarri M-(LNV2�6�$328} 223; �L 2000.�LyP79} 79�>��  doc� } �D%T hleiqawi-hyp2003.tex % % % Lafile,2 iHYP7F� I. H Y % \~c�+8[fleqn,12pt,two!]{M`} \usepackage{espcrc1} %myou w�to � (e PostScripE!ls2B�icxCputDrQ definU%�!: % \new��and{\}{5de��`fro@ \title{e Electro��0of K$^{*0}$ m(s at CLAS} �*author{=-H\address[OU]{DepartiJa���A"omy, Ohio Uni�ty, \\ DAthens, OH 45701}%\pks{���� "� .}-  \( 1�%+typeset:" make%& YVBPabs�}n-%%-vpu"Q� T�  describ� DG'�#woY� amL 4.056%�4.247) , wS !Gno�! ized$ vcompaA i���"� 0{INTRODUCTIONz' Q�*�#s�=)l_ \s{isgur1}� )not yek$enW �*�B���#�#&� c� b�#� <-�-%1p6�Angem7 . OfuU pest%R%l�'o2�N$^*$  }�#m�ld�"eGgly�R$K|bda� $K�($-cap�$k2}. Moree,BWJ� �favor�Ka% iniK^* b,��|a �!-pa�*e�� %�B�,n tudy�!\r&�+K^*Y$� A�$Y$e!<�,,s "at most �Ybranchin�.�� due!?M| "� �A 3-s. �a few�-l! neg5(-p� �%�^"kb�Auly!Zpl �-Kjp, e.g. N(2070), $\Delta$(214> 5). Nah+, v�'��� o(vld�investig7  below-5y8pling7�$Y.�W &}�tud�of neu�'.�&�# �' te �+!��reg�í~2!�0 e�ve�c�DI�be ac��b�&oft Pom/ex!�geM�-�re��, �E� non-.yme=ism inE�.��-{>%,��&Z ��~�i�ons. V.�.�����"m� maI�t good�.led�"/s�Q4i+2ter�.:u�%���coQ to2��Ki��!�main mot� a��doa� �-a�o-o6F��ofN.tm$ep.8e'KY$, ��%ion} H!Eq:-H} ~6{\rm e]0�� 'K}^{+}�o 7 :0 1+i� {^0}n21{ *0}}:+"� My work%� publ��0 done�!�first (A�nels �<Feuerb�' owev� /third+I�ariYaie%,* of i!é\��0�Sa>iculteP�A$K���O availabilX.�Ŵ ��ens-�n fac )M� Cebaf L/ Accept�2o2, ([ )IHBћ las}� JLAB,So� fT a"ad� " U��(-h B8pened new avenu�)o searche ``mis� � s". y)$K� �} x�u present (Preliminary$%H*�#�_�Win�~si� Ref.-weisbergH��HORETICAL BACKGROUNDr�  A!� oret�!in��< � �2an �ve Lag�iad�2ach!z2���� I�zhao3&\*�뱎$en develop�. K =kI }. Im-A�mZhe�e mpt�a+�6� E�o -�3 ��*p- �-gJ� . In��!7 �0mon6R")/��is i(i)s��,*R/:.�� enso,���� K� � V e�yEd�basic`!�e(IbA�1 6!�% Nb�|��!�e � Rsymmetr5mity (ii) adopc(he SU(3)-fl� -bl assump�1a1��perturb�  QCD,�sugge�)Jab��a9maXy l�#close�7those!d�$\omeg� $\rho�>k s. Our�?al�)2�/ /]un�js.�� well�%t ng%��9�. %{\^�3 {I�)*- $s}}: %(1)# 5 �|� (�((leq$ 2 harm5/oscillz$ shells) %Z A .d� lici$-�f�s:&dv2)� er� D�J|>$ 2)Yt� ed�be�deg � by summ F1 �#� A� n. �,�#;*_8�� a1]��O2�9Cs, Eq.~(�,*�)e'1� A�' 2�JL+A��"�*l��},��� i��B �A�� �si8M�:T a�#a�z1�7(9�8 t-�} da/L�l�k4�(aiA������%I)���i&lc.���SK.�to �2j*�!&U/r�� &Fj >�� e�ru�M�U� � x ɑ6��J9�b�1KV �9ݡ? volv� cA�Z 8of s$\bar{s}$ �5,�m!c vacuumR!� ��Yy��7e s #���7y8M ��+way!�%�u�d ;,*sue_�� AG:�!�i.e. �����e . %axtra �amplitu.��i�aa�i�$t-, s-, %!�uQ�,s M$_{fi} =$ ^t$ + s. u$, %w��5�s z 3e s!u- {��. ��6�q}t$ %i opor�al��|ch� � e outgU I,E�:T( %it vanish"5FN�]5!nBA�kaoB�!isobarI9� ben,})na chi�7%� + W Li1,Li2}a�R.��terms %a�neei.5 � -�A-��aB=0.$8%SAPHIR q(goers,ben2}��K$� H0A" K$^0� ^+�9wed %a.v-vs��\footI7{�9�S+�A",�#"� F� B�& �m!Ő!��5(angular�� �� thet"R phi$Iw�?r$)��!TJ.iZ.J' 2� ��BN,ur>� �(iEfga�)�w�.h8G�Y�"i@*ion.}��K7)E�c % ing-or�)leyg���}5]��-3 y.�eu�influ�"Tb�po�.z %as� ieų��$unnatural}��x�+g�+n�0 ir %_ �si}�s�L,�ڽ"�� %im�E�at�A�!�l�Wl in�M� g�? %�(.�� +F���i|�efN� w1 fo� =+�  %4&-2a�$5�. %U��andardx \ 2i�$N��A5� %�(�<0�u�]( E�9E�P;W itiv!ǭ�u� f- %�?5�6�:�a&� al %" �/) ���e;%7,�? %�``6��c"E;K``տA�3Di�3Ś�B,.S lack�knop9"� 5� s. %2~+�%l22a �@bev*1j���6#.��Nv��"�$EXPERIMENTr� 5�F���ex5i ``e1b" ��%��0or;�,a�JaV(rson Lab's�. 7�O�7��: � !�m� f�-�ds�&� Vae�;a3 �+��: j�35 keep��azimutha\gl��A�ged, ���F-��alou�3 (EC): it9 loc}:��3� �A� %� �vco� up�F,45$^{\circ}$2���fW t-�s��� �o�d�m ingu� �n8:p, (3) C� nkov Cou� (C� ��Z ��r�J �*Y34.&6c e a coincE3 trig�" (4)U0e Drift Chamb�A(D�=Y%C)>�ry���in� trajE]ie�9� .8E)���4a�)*E1ed�% �ut 80 $*7.:N%�a-�),n8=�to 1428, and (5) Scint�-� s (S!an arra�288 s.,q!�s7;�GJ�tim�5f f���% �}* �)�vv� c9Q ��DC.LI�H �2* took��atO %&"P qc�ja.| wSHa liquid hydrogen t� "8length 5 cm. Al� (430�610�5Qms,t �ively)�  4eb.&%�����t8w�6250 A$rrespo.�?B� at 6C0a maxi�C��seta�( ��/binua~?��c.m. )�y W�2.1� 2.5 �I%�U4-i%umaansgJQA�rm 2}c>>A�4.5 (GeV/c)$^2$�6^�iyd�� kinRK. Dk> ���� �d �.6: �$100 MeV in�   g�d U݅� broadm�in6�a1@i�tBAS ui72BF .�Aj,��<[htb]�ew>J0mebox[79mm]{\� [-26 $0mm}{52mm}&3= 13.5mm} \ Cing{\a3ial{ps',=fig1_ks_lam�5, hscale=60 v ,hoffset=65 v  = -400k�' _h�>{"?{Feynj.di�m�%�"G8��#(left�3 43 o?B&� =���, -!�K�3&� , 6Oour2})��&�:p�'h $e'K^+]N-$.&�& }��?g:=A}-(!-�j�F�s�!azaN!,� \to�6� a��5�8(892)O s im�Blya5o��"�hH�,gd5�r H1� .�.O,�2R$2�j�%�>�~~ 6��+o5bda (�5�&.vh3Vh \r!arrowi Y^* :_ \noi"Mt#& :�,Ny,1� � 14\%!!ba�x$:�2�E�� ^+A�T7?Eqs*6%N��Hour3}) C;^�A~�*�IEi w{^+}$. E.� \�0�sU#jE exc**7a�5= fami~#>�600), ((16 %"�7690i��"wh�63-e 4-star E�$�5Feve�ex.��P1.8�K. D:�6o�v (�4)�|�e8,%�"�Y>�f:e)nt wu�>�$%�{+���$EI['ilee�$ G9����)��En�N  tifi���:�;�Ё n7� ch�k,0.892!sl"69 ^+$,);� w*��6�7,>��%ppl�' cu n \$�s�D�!�%,��ai� 4'qW>9�major.�y9�ee%-V@�g�( mis-=[|'aDI�x �)Js+��3J���T*Cm�!m.�2�)2o1�y�:!�!�TC�//-�B techiCA!�A4$-fo��%�J�A�U{%2�: H�"�B^%1 0�G�:d � cut, ;2)%�zD�OFE>�.�1N �~��% �.����c6 . C�9+A�6��lA�swo=�%"� wnr%��2)-" � top (5�cut):%-AA!.+�U&!|s�M �2 (upper/�Ln�n (� bottom (Y�# u)�[>�xrY�%�Q%FO2� (l%N/red)ZiW!8�;%hQ�9���qyeA�, �[r �n�� ularz .C�@fK,B�2})�re�IDar� N�& aVZBnewpagr1�� % [h] %\�� phics[| 0.35])2_sig%2.K58�� 2;� 79� 79"� 4.� 15}} %&zK�� e� p� 36 |�) � �33_�1_yeil>\C21.�8>@1;35;375;236F=e� { 5JN�#[28 s (arbitr�($units).} "�+�.��N&MD6~Fd5 2. :��^�4I��!8" E~}�+ U3BU��F�Ad� %.N 3mm}!a�Q \ohion{RESULTS AND CONCLUSIONS����D�'heB� I���� y%%G,�Hoe#��C)(, 0RK�'ut��q� Y. StE�a l})r Q ��G)merX3+&w'i� ��� ��6 c$0p or*t� a�aG5 virt�M44n flux= �"�517 #d-�7sh�"n�M��8�Wn�*gE.2�+v�]0� �� "v A�>Nx)*(a "J�� -of-�10 W. C�M� I3�tp'R6!!�.@+�$ (�5�).�(pJ�, }  U!C"�UwoKe�;ie�E�C@/is Y". :�U"T2d�:�h $Q^{C�:*�DceB�..�axg�$ at a� u�!W)�"\�Rw� 5�"� a�o�d�,7 $�R ilon45pe�ce:%>J� &^ on �,�� |�]�^� � �"� � q[F�z�%62�� , (i4 a"0 �I^��"Gcal!q%-h:4C#s � is s�r "+Eqs, Sec.�]I�F�� ha� ��+ .1:q-eexp�htoe%`�B'�*�.)n�|1a:�B� ^�1X�+2� � �*�#'6����"{ I�lB`A�(ank Ken Hic�>{93C`: N. Ik:%�G Karl,�<.�> Pbf B 72}, 109 (1977);)=.�?$ D 23, 817-81�\2x(2} R. Koniu��, .H�= D 21{868- 19802Qc:1} S. C �V� U 34}, 2809 U6).&�@T2FTW. Robera%FV(58}, 74011�8.UF�4� ach!k.D�*T-U$Carnegie MW n2M>TF.��3B. MeckA�A� et al.},�B Inst"thq% A 50K2513 (F@.�"'3 A. W43, M.S�F�>2001. 9� PDG}"dB�( Group, D. om2� Euro�E J. �/bf C 15A �b~,@2} Q. Zhao, Z. LiEC. Benn�[!q�H�AU�436}, 42A�92�T3�T�B)OCI 2393T9 U4U>GC 6!�02520)�aCuB?>0J. Al-Khalili�7J��(64}, 052210%G]6� 5} Y. Oh,!�Titov XT�e, %n�)�6V ben}6�E��=,-th/9901066}.1j+a-A.ceci� B. Saghai1�� 4��8%t6& Li1}IN95964 :52`�+EL,a�Ma) LEgngJ�5�[R2171��Z9`g�+�WG )u�)X6�!� 33 M92�b�+=�:ON&�HI�A 639��09c�E��>. nd"�D  ;O:FD@Daps,tmen�$s,�%scDKC ]{revtex46\D*Dͺu\�B { Se"X8�L�6� ,-mesicEO(ei in $pA$-*�WaFVJINR LHE*o�>% " {SupK*T4 RFBR �74ts 02-02-16519�03 7376�uCD0M.Kh.~Anikina�: Yu.Ssimov}Art�,S.V.~Afanase(D.K.~Dryabl.D V.I.~Ivan6A.~Kras2,S.N.~Kuznets..ALM6 I.~Malakh.P� Rukoyatki�<affili,{Joint�u itut�E��6Re":,!�, DubnaAl->V� Bask.nA�Lebed.  'v.*L�PavlyuchA&9Q V.P.bV.~Poly�Zy3S!�Sidor �$FG�Sokol*E�Ta�.  �e�:�%, Moscow�E� Bala�#a.]M.~LeAQN�Yud �=}ba�!v�Wics, MSUJzYu!8UzNcO��NPN�B.~Belya.�N� Shev9��oTRo Yu.~Grishaz}`BA�repj,� 1-Y�B�L!� Kondratyu .�Ins)�!{T.=;nd 2VB9�>L%� azar)5=2_VOSara� V.~KobushF�2P.��Ki�NS.~Gmuts]�,M.~Morha\v c!s^�S Bratislav.� S.~WycechnC1�KWarsawfY *{1e/$ %\;\{Septe�) 15,� 4ajb &�GAn<�Ud�r�o�.�#�4pro�P�+��J��F�Ca.�>$F�� e"#< $pA\to np + {}_2(A-1) K p+X$�briefld� *�� \&�I *bn*{Int\40} �M6�Vprmbaimed�2�A��l"p9�e�*a@ kindbB�#'b14"� 9(oVAa%UeuNYB /P'&�F0_ ago i5,haider86} af-notic o5an)�a%"�a slowF���!١8k�9t�.,ive. At zero�y  op�?� A$-&Xb�7q(jH,V(r)= -(2\pi`9((r)/\mu)a_{!= N}"�$ $\mu%��re�jd�A�h�$N$!{rhM1 � deP8�d $g�ZJ N$-*�i�*. Est s%�t14B%%�.�_f+)�  $ N\to\pi N � etzus ("#� = (�)-i0.27)~�fm$<�n!o?0`97 'po�2�g� ${=Re}\,`$ just��n�@E(v�!�A$ 1�5�. ��9�2� !\ia�-�eQ le �4a&#wfe65�D.�2�i�55K inelaK�1ҁG%j)vB0vo![8B&#I $S_]X(1535)!�o$.� life-�-��$Jgu>:]�bra�t=](29En$+elfa:6 w�$.�anq�%9 us $�#!��ot a p�`T�, �qrat= a � I o�vol"�=4�-$-r��%la�JaxtE��A�"a<�inuumy.�JH&� =i CE�@oEilitie�S�uE�h�&a?Œ���[.o�@A�N$.��t\b8Ax �e�d/i��)�=B)VN�(R!E��3%;./ 8m��\X[@xr>�,* "�^�. D��� O=p)5�F,�6ens�C$q\[>q$. U!�X%�%$bdba  j>F01.o*D�ngort;n�Jl��x!�lem�sL cEs�:gmFE!�EB��a��#P+De�7�$s�s�� ..nonF/ s $u0uɦ$dd$.� �HB� �~i h�xperUEe�bBrookh�JMZ,chrien88}. Nj���Q-�1E�-m Q!}0zme;pi^+ � p X�g�4�=�&� no clean!&wa�� und.�Wr:bA�m�;� !��!Q�to?yso*m^u� �!rteg�5ya��$��.�rHsU �u of d~A2�9�s,�wa�pos� A .A+�9%U$2r� sH91}. F"%)i idea�Ho j1�� %~ .� LPI"�3 synch� a �7IY��c�$�'�6�#m� 6�hauRe�t�n.�9,�0o L�pyea�yure�=:A�n�����ir G:--���8GSI (Darmstadt) �hayano98./�� :,COSY (Yulich8g� zer0!�A*��UgF)q I(in Grenoble�zls,s�(Bd)b�03}�Q�Me!I!z9l&�X� A� �ec;� micrh< MAMI-B (Mainz) �F� *^!�!�-�A{}^3$He � pfei��04ry~r�^� �D)l5��02z�"x �eq�ay�YA � n +{}'4}(A - 1) &\to&��- +XwZ 7�EvX.b�A�';tMN1i�y�s(im 2$~GeV h  u%�6� .9a�] .�6� thro�q!Csub�a8ss $p+n\to n+p+�V$E ^-p$�1$pp$ I (see�&3�5 A>$).�͘��W���/�d1�)� .��$u�Cus,�� numer� c�"for b� ng Xi!�n+ dth!*a2 �M�Q&�YS �xa& � A!� J$NN�# modeJv5 be�s!�,�*[hbt].d8 B�+Hheight=3.5cm]{pic1b�+M �sJ*a*}&wF�i, evol�m�� of !�WQ�.a:�. Two 5 ��Bs�r:5#(9Ay 90\%�3%621�m"8th&-' :cK";�Ie�A��M�} Eta "i�/Ylmst�"eRir � typic�z$b�20{-}30$E;. When� <vel� "U , multipl&T*�  occur �u�5�ץ�x8b s��&i%� ons:� + N_1��m !� $,(2N($2$, \ldots/kB/pi Wk$*% step �3+ � ver<$9��o7e�5Cmf~MRescape!.�M��F 2�* c�c , G=tic ]� a�s$m-m_simeq 40)�E:t3"�= (�BF@G-mo�f 9Dcw- F8:l�&h�_ >F�$�6$( s $T31 $T_N �9 .�a!="1A�-�E�hly op�e�}=_{!�N} V 180^gC$.]��cas&�I �N$e� wM�iPus�,�eNe顺�(%�!��f.�$/2 = 270$~ �2ag^E:���E esse�F��%^��t�I$z�%����sA�Y�r� can� be easi�!�;��na�5way] YTROe, ����Z $N�)oeUN�+N$E�y�Aarg�Atal5umu+�:�)w J$"�y)�:  "��0YABry-����S!��jA�re� �!- �=D �!�6� _UF�aة��K%s�X%^�92. AisotopicY��-t� metrM+a���mainly2 �i��$pn$ (�I$pp$)�rged-�@ oe��a � Po�*sn� ,a�AYn mTz$\ t� 0�p0�q/ca,��.Fouf^ est ($T_{sA�e� ),kś8 �G$6i� {-}9 $ ��Cec,A O��)`�Ml!�geiw�DO eta,恟�u�8�B/c (or>0 of 3 ). Its� �is� ) �Eco2� carb�!�t,te@2z+sIՑ��*?F�   gma(" A) �N, 10~\mu b$, q�\�u t c):�92�,)anwH<�9� �6'�&|�B�R$p\,$2���bigger ����0250$~mb) thusU� to d�Hr�&r7�1at! why~��bs: �%ne:b~4l-uR���� �8����A�m0-����(s)Ֆp�S�D �u�~ E�F�H�N be$ed�.yz�^- >� D ��9U& IMt$p_1$0&| stag�W�oTAaK�.� � .=8 fig_pp.p��hs�*{0em}FQ >5n5*$ A*�c W�dI��duI��}�@"�E5e blob� �&� T3n�Je3�ͳF } & 2:�6 2v 2�"setup�5.�plē.�!we1 (�`��AM�-two-arm�oa��gA�,)-C5)C6Kɲr<� W�5h4@$p�n$ emit3(�� XEm �ѥ$s (1),~(2)�� �e �A�&.>K@s: ~ g:BmIF6A{ pic5AD Uy4Ey raissG{2em}{zB6B]� Layo�T��epm�5�!da�m@-�or.} ]53>5,1) A monitort� �O!k� 2VLte��o{ --- �tr� F0s $(F_L,~F_R$}GA, dou� k%B%B% . 2�32-C6thod�%pe $H_Mj�Mgo>D��m 3WM�2T�t ��B_�Qeppx I�[7! l�&6a (��6JM)%�2 }N ($dE�)�rm!eu.� al$�y?D sts: �i e6t SCANS Ibs[��Q�s 2�)Iors P1�P3 (P�pA|4 seg�s �a �~-�&s�*9Pc9PP2in � �mT�N|EA hick2� s P4� L s P5�s� �- y&uH pa�d��e laye2 Each)p��� twoitub��� p�$@edg�Ves#�d a1�)��p�is *nt,8$ built. 4A�>��e3)��b /wڙl�k beyo�! vg] ���� m 3$~m�v� !xatW�%�ed�bof H -volume2�Pet���Q)��DM[aa9{�cryoge��}a-m2$ele4�qv�n ? rber� QE%i uI�r~%�u�M%��M� 1�� �YtoQ#usefull .I<�'< ~;EN$of $10^4$ � s/7 fF�?�`��> �5bjc�&R�{), o� .` &eKI�zFast �Eca ��"RL~&�us!��"�S�Q�M� �,s1Xchecked V in&� " �a �t>��va"!a� Y�a\h l P� � JINRCzA�4�ila��. film)M�K"�"4$A$ (Be, C, Al���ckn�1/ 2� $m�]F. T �|$�� h block��e�\M� C �Fi�ŠaRFTr1� Be�gma_b=r'$~mga "��IbiC� ant "h v% e duŝ�$5~ɵiAg O#qAq=s w�-isn�o� � .�U9� s. M��n!f5�unche��!�) < ($6 \cdot 10^6$ťs� 5~s)a$N a.�luminR(�R� : �$Lweq 0.5a {32}�(8 cm^{-2}~s^{-1}`5p�y�c��cy��(10�e9$ 'w�/ ed I��w Za%&.�&A c� d bym�,� 1!Hu�!E� a��r�-O �! -_ma4�al); : r�e�� ���EGeOZ%gE �a�>jL���C�TD~|�Mv��3of.V��thQ4$m�u� �z)� -�! t���O5� or o D&`t�� �ion.rI{m-.��-a"Y�iN����t6����a6Kb'ceCjF Ptabular}{|p{10cm}|p{2 5�~�/)llll|c|chG6 \�c"n{4}{{=( s} &Q&.5\\ &&&&�]/h�6\\ f$Y (pv )$�&��� }\r =*� i, 1400 & 6500>ZpVJZpnX23WN� ,p_1ZJR\pf�&y@p_1} = (15{-}20)^�� & 96F�wM:'f��y && 4w.�-�vn��R��$n =(7{-}115 & 35 & 1:�%�B�.5)R�6 &��tmk q�le} Yie ��  2q2 $A<^-$e�|&u �{&� � \&����6�b�� 2j��E A)�eq�$b>`u.F3j-"�s,F#y�/Br}MLd0.%��"p 025$���.�u)}"� _F<6�N� olid�\O$o_= 0.1~$s� T� � .�"J ge� P�*� $g_p-G0.2�(� hi�$� `5idK%n-"U 10H��D ex D(F�� 6 a�Vrl^�e� dt!�;tio1G"}�� ��!.x s2Y�# R: $g_�5>18>? n�*yq�Z�to���^�Pe �Y6��_&�<:� . Ad��}!R l(r N�+e�/ et�tyO p;G_n53$ (aU!)Ty GEANTORue�h� abYRyV� 9OD samΟ� n: $>�69 aA��N���CS�!��Xe?R�_ig.�Xfig[ >;$3" 8$�\,$.� (ign_<�&&2g :s�s��|*no��� woF\pm1&$A�� a� sim9�%�� mV���k�#9�n�pA es��G&� ����A& 4-fo�"vc�X��%�thado*�"et`W��Lf%J-�._� earlڐk>fL" 3%8 �opane!>3:! T_p=3.3~$r` .�� el*I!�!:�=+i���Qt 1.5 P*Q Q�I��L.�0 CM�tg d)!��$< &{5x *p�/�ix �( . Cos:RN-]U)56�}>�?v)g�5.�on�mthi�al&e.*�'a (b�)�7A7polyet��(w��A�in Dec�;�F aD) ���I!�S�.d�.�un��h!�A 2 3R4. ^:a}9�$ $I_p=(0.6` )�{10$1�. LoaIchQUpdA\n��� I� � n $2d2 . Rm.�fs9�e�5l�a�[Ao�(H .E scheme�!tau=20$~� �(AV0"J� . A��9-�"�U����i[5J> cla��3.� "5�3na�<e���rc�Gc�wl�is��! F)i�$�. �<an unq�iћituM�*c�*�a鮁/-X*� �4arJ&:gora�(,�i#���jhR8aM�Whe)�*,i�!��by $N= 'Al{en^!2M �5t�f^7�AooFyM � 2.� y6R$N^2=1�#I�alg)�.�J838 0$. )��]=u =OmakPt��s/�Г�8#�nu�8ofMte ��2� A4a"�Q79nnd"4 I0W�7y�M.��� s"X�*{C���)s�?[�5�I�!�� 8i�aj�3�Q�achievy@Aml� thema� : -\quad"1�$� 96"�G9� A$*� )!h�2q�!BOT7:yl;g��� �NI$�Y[? } A)� � t�4u�&EZ��0-�!�$A$-d�:s�� <.O]!  pjO s ariF�\�-K�#�L�� U!� e^ 1%? &�0Pusr�Bk��B�a�.��*� �Batl� \def�L�W % \@ifx@a�y�! name \par } let\@hang!"s@ ? @ % X*{Jc�2(6@nobreak� }% }%MCat !t>��92RQ"�B Q0:i�u��L.C�Nu{L�KB17rN86) 257;�DP=v. C34�K86) 1845*�O�@$ A.M. Gr�1nd�PFEgMC55J$97) R2167; uM703009�Rm; �O Jido�L6R66 $P 2) 045202S0206043.S"f9 R.E. Cw9NY)60�88!9.�sokol91I�I �I%`6J Trya�evGQKr�Je Soobsh'�,z. [English l.: SoveP-- �I9�I Re�(s] Issue \#%�91) 23=� �9:��M$Zzika B`N9) 81-5ex�N 5006>M00ZM\Pisma v EChaYa \#5 [102]%� 0) 7\ aa"�" 8%�SA�8�� E806012�*8Em G 8 , Pr�(alG8 -TOF��"��, Oct.� 1P"8 )�B86���3�.:*�7 M. P�7<�Cm;IF92%4AF�R9o03120_9$ ZuM AuM\B Rapid! ,mm., 5[91]-9%�I�A�endB$�&�N�i>?O:Oprl,pmh,int,showpacs keyzLO%:�OPtwo8H�Q %a"~� ts}{\textLCs�O}6#xbeupl}{\ensuremath{B(E2;~0^+_{\ rm{gs}}\r=5a�j$2^+_1)}} %�G2)FX6WX)\!\!\upG}}} %�.rtVD4valnu}{241(31).l N��ts>uva:�\bnu~e^2�fm}^4}n�p%�^�\*H�amssymb}A}�Y��Ӕ;A�m�PD``Safe'' Coulomb Elj��>�{30}Mg�MPI-K"�KO.~NiedP0ier&�),% EMAIL: o.n 8@mpi-hd.mpg.de F H.~ScheitAFh. it6A \email{V}_8V.~Bildstein} V vinzenz.b>_�OH.~Boie.;h.boieZ0J.~Fi�r} pj.f Z8$R.~von~Hah2�roX.von.hah:�9E F.~K\"ock.�(frank.koeck6u8M.~Lauer.7martin.l685UU7RPal.78Uttam-Kumar.PalZ:H.~Podl�M .5�h.p @iap.uni-��.d� R.~Repnow6GHRoland. %Z�DE{ walm.� dirkAsB9f&�R,Max-Planck-I�0ut f\"ur Kern�I k, Heidel�, Ga*nR home6f,{http://www.2 /cb/erLMU5v$C.~Alvarez.�ca$�.a @ y%9mh hen.=8F.~Ames.ATfriedhelm.ames@cern.chY$G.~Bo�C^kb0@nscl.msu.edu�S.~Emhof6c58han.e t6D.~Hab2�di0.habs~�O.~Kest6soliver.kZB�R.~Lu�B.)rudi.l�A$K.~Rudolph.BKlaus. ZD5M`T sini.BMGo.PB8,P.G.~Thirolf.6p%<t Zx�B.H.~W:C Bernhard.yfyLudwig-M�w�Uns-"�� \"at, M\"M%n}  % ��ln� J.~E��2;e@ik� koel2�G.~Gersc25gB5�H.~Hes2i hessB2�P�xi:\)_rB;mO!�ele2�tB6qN.~War2�warFg1(D.~Weisshaa66Bl�=�� J�2�-�,�� % Leuve9Ӂw ksou2�Farouk. ]SWJ1E~Wy-}& jarno�ewZGFut voo�� - en��al-tfT�a,Y&vI ,Belgium�� CERNU�,J.~\"Ayst\"o1�5�Juha.!o��.jyu.fi@ P.A.~Butl6�i�b]e����0neva, Switzer>j2-� J.~C� k\"al2�joakim.calld!�e�..G��$P.~Delahay2�pierre.d �5@(H.O.U.~FynbV�Hans.B<(L.M.~Fraile.�9�Luis. !B= O.~Forstn.E =O�%A=a�S�nchoo.Pserge.h _:�f` 2�Joh�6s-Guten� BmHAqrm MdU� >�Ulli.K�6rr��FT� lsso:� u\Thomas.N %�h=�jAT�t� �& "uJ,. �R1#M.~Oinon�a.��ku. %�5SiK.�t �s3!� 4F�Q nand6X fredrik.w 9�� % TUD.�Pantea.�m.p @gsi26A.~Rich�./r ��tu-dar�K2;G� � 6�sc N?��imo2Eh.�`n��v%:M�T^ hren2� tb @ph.tum.* R, nh\"�.r�roman.g� euse"� tuRO Ta\"o6��(sten.kroellV�Kr\"ucke2J��.krue: �M.~G .�mathias.� � ikF�f&� b� ^� %cin.� % Up��q�T.~Davin�c*�t.d @ed� uk6!"S -$Edinburgh,. Unr|Kingdom�pi�J%�l2r�j!�lM�6x(Gesellschaf� SchQ��^foK u���B�G b:�.�Ger5 H&@�$z.E�f9��5 �5A�rs2 aaron.hV��Q Lo�LaݱoryB� 3 pooltedR�Iwanick2�i @slcj.uw.plA��H��Ion2��_!��E� , P�YB.~JoEs 2Ubj� .chalm09s:C | Tekniska H\"ogskola, G\"oteborg ede*1cP.~Lieb:y*�Peter.$@N$ik.Uni-Goe�=,Georg-August>3��9L�ljeby6�5l  @msiBM� Siegbah6� StockholmF�A�Eemp:�?sA.�mpp@em�_ *��I� Ygi!$he>F�J: � rill6� ch��a~7:�j�����J�2 O\-L�(vi��R,�c*�P%Omid:5O6a)2e�/GOl�21iguy.w"4@ires.in2p3.fr6��d�!fc/�Subatom$�s, sboua?!�� Oc \tod�R\Gl{25.70.De, 27.30.+t, 21.10.R!$ keywords{�&mBD, $20\le A\le38$, ���� $s, Radioac�I�$�"�� abst�6>}�wr�m(� ;r:K.�"&:�5(��um=yo�),REX-ISOLDE f"��t 3"conjug�>'~>�.Z- $c�$2t(( MINIBALL.  �\ts��Us&Q6e�GQ&�!of 2.25�N/u��g2�Gt�:Lnat}Ni  &!mA9�J�)/ ed $2^+$�B&�c$�r��o T@ei.�bu�O1�b�M r wad(�@d. FroO��#s�H.vˆ�Iit�57d��wC+t\ valu�&��n)"$#)8be0v�8Our�(ulEG%n Is&$_at.� fra�> �Mie�N-!C�(�$u�--�1%Y <method, �#confirmsA*_!m�`a(a�.-6 ��siu��vKe=l��&out�W)5 ``is(!�in�on''. �yMenmake � �au ".Yf %� surp�$�SbyB�ba!s� it{e�r�%�.� sod�s � 1}NaEy\a$2r�Bj[Vly�Tth^�Y2�:��ell�$l c*�T�th � :197ar%��%_'qu-%�&��by Campi>� Rc O �A stir�+mucP\te1/�@tc=r"�!�%�G�ar�.rt.�>�V^5nowA!!�r��t2�BewWE+ Ne�Mg �I��/,Gg83 so-0<ed^& �0warburton:199��.� �dlV�n&intru%E�gu�'�Pv�c � y#��r�a mel��$NP, �Agapy( E�q �+��6RdxH �despit�)A�;!4�4%,A>r jal 3o�u!ZquN)�^6 �w<$Z$--$N$�+neIEhow r=">y$�/�m�x!�i-*- �e���G�8s t�* placm[i�"Gc;�AeorigiUMdC�#�g*��$B�!$�$�!$ �inqwEF}!�debateM(yamagami:20X[AE�ac>�f*�fQ�a��| long>Q!hZ�h,p&�` �m8�e $E2V��> be�S< low Z?FA1Ba.�� �(~m�s�Ho�Te�i at @k�f^!M 90's���z�g��s���*se H%or�� ���rŐgrs�t"%���upl\ ���.-��is�b�iuնɏ~��L�� F�-�$motobayash��95�_�LeqӅ} ��0,32,34I=ŮQ�.�S�����`�2on-U.��a� ps �~a��� IKENZ�,iwasakE�1}q *pritypko��u� GANIL $chisteA�1}e[�2�5"�L:mgbe��h�d%�ij�4nei�Q)�<�a�sd�� �ces"�VA��pXsN5 aT1)N�asm��F�t�@fR4��do 6U�CU vari`P*xҴjma;- utsun)(,caurier%@,rodriguez-guzman2}a�be�,�d�b X�3yq �5�P�..raw�f\�ęeA�ar�Gthe���B�he^-. JWrtt^,a:clarif�;a�p��si�1,&� �� �8 go�� map��n�Q�i��I�3f�, ��gpre�� ԏ�y�& 6&�3*�)�-in�.t t�(que, namely�6M&�x i�� ed "�7s, emplo68 �a�Dd � ��Щ ��A !!B2 a0 -re"_4�.E�s��.*� �36� ��*� %!�%b�IOB q1���� � newlb�  �orm�"A��{�D!,DE "54ugli=0��F� ��. " 5a{�E `.th�1d anc��ry Si=q�o� ws�!2 c�to�EU�S�Q ��2.^9QRU�(t_{\frac 12fB0335(17)$~ms) �6pr�R��sene�1.4'�[E^`�� d byIQ$ERN PS Booz)���x������� 3.2$7810^{13}$~p/puls� S5p� i�VimI"h^ 1.��2.4 s,n�In uran� �8 ide/�_te .K�Mg- �EId*AQ +�rKi���.�FR"k Ioniz  Laser�Sourc| fedoseyev!�A]nwJ��7�11��� zmat�pu3%be2)� Ga�al PuBoe S (Y�]�.hREXE&1�%6�%�a3K^�`s novel��a avu�=e�� nch,R g�e� �u�e2��,}^K�NbA6��gE&�&Y�4*&`-�==de�)3-/�tGac�d��ol��Jd�a Pennra�Hupy0~m��P�}d[� D���>�  g� �-�� (EBIS), &ʗy DiAD]=in 12jA�1S �V$7�Iʁ��ht;dEM?t=8&�@5S>\! 50 10-1#��J�`i��cU�REXA{5 (WV! Eca)E� �_5\%a�E2 �� sTeE��?ha ndq4al nickel foil9 1.0 mg/cmi��� e ce�Af a sm�<sc� 9NchaL9b�S &��xile.8�i�$16~ ��i�a �I$\m�J�S,����-disk-s��d�9S d silicon>mip Por (CDX�:6eki�s subdiKEE�fo^&� quadr�KE� 2�Tca�9p �16 annE ~�Ij �L �R�so�ZUDl&9 , 16.4$^\circ�A 53.3deK6�Rh��^hcou|�� �9ed�<�9��e�ХhyV�n >"�y �. �@�E|de^ ll �gm"b &� A[a]�C�0�A�mdM.�)N�7� a` JW , 6dh �;lu� Xor@ �Uc��e��vsixCsU HPGgZ�� By �$�R-Y^ an�q?9~cm, �B�"E>{[3"Dto $85Q8E$915-� Ax A�a��?=Jj���v 7\% A$E_PM.3pd(e� add-back)Yt"�<ɞ�p`� " ofe-6=�X!::;��} -onboard Š �"�=-�l^1�܅�aRng��_b� 100)�in>?grae�'inAp�;���Ed~@ non-U B TB�����& ��� us "k���KYqA7�o&�>�Ict>TNo3�B1� smea��con&�A��Ni � �%y9��avo�M�up$�;��W�:oV >WI�1' vice�Usa�t� �iGAcedure ���Y��%�e/ car[M}�FpH���Ein M�� �de,hte^y�4 "Y9:�  &�oAD=5.2cm,angle=-90]{�.�.epsi}&�o&�bF�5� �A�ى�-��~:���v^-z%�mo�js%m�A�!�a MWit�B rele�}��!?�.��2z ���Ni-%�YP� �r(<yq� �=��}�&�ew!�%S�1*V� ���Fi�1%Ỉ��A�Mgv��V�=ME �R�� %VV�Oulf��Y``b^!/�KSsc�8|U� �F=e Y���.�gtb+"<�YYZ��.i,��"FL��U%raná�ź.6�m�ri�S�c�R:�,G�  �}��,�N*�n�st� �  $D&h>s}}$ .�surfaR �j�D oes ) drop� 6~fmN�" ��>rrFieiVj9�8"6K� $\si�]"J?CE��*=�xF�%E vJ�= rr#HOI!t58,ů�">�#Q Z �#$N� $�\[ �{N�\�(^�G?Mg@)�A r7 �:N�X�!)^� y��lon �(^F8)U@�R��B� �< XW+B�)}.30�MgJJ11Ju.JfD, \] where $\epsil�on_\gamma$ is the full energy peak efficiency at #< corresponding $B 6and $WX2angular 9@lation factor for# Q0ective transi%Ls. The Coulomb excit >cross s2�ons $\sigma_{\mathrm{CE}}$, which are in first approxim Hproporlal to� ��X\beup\ value, as well a).f�s.H were calculated us!:Da standard multiplV�Hode~\cite{clx}, tak?(into accoun)�-�l!of� beam�!�target%�Langles subtended byCD detec!�!�-@MINIBALL array. F)�D Ni isotopes known))s!� 9-?H@quadrupole moment!Lre used ��$:1993,bhat (7}, while A+Mg V%�D was varied (assum!$a Q(2$^+$) m!� exAe ed withinLroITal model� aA!�T deformed nucleus --- �lpA< of an ob2I`,would reducenextrac�-4by 12\%) until $ peri!"al�reproId. aanalysis%per �$separately�!1$two nickel9�!��Щ�="T1�tiZ (iv){Jw �xi�� ed�xte�\��A[$t 244 keV !�searcha�or� a�1�ies1 :Bof^Mg�Al �G��� chamberI�1ҍ�/ �iU���� ��aq5Afpic�%\ESurity�A�,a thay notice�ařis� �combin��� %�ͼ\5^M�k( of 6.5(1.0�T� -Mg�%�-window� $t-t&20T1}}\le1.2$~s�f!�� whe� � a��N��i�H� lead��= �E��dRN�%Ni *$-5.0� $~\%S B(E2) InY�sQ]Q-"Al)"im)��  l�!a\beval\%rm%�k GMg�e quoAAone�$ erro�f do� e�"�s{ stical &, � � i�ej ose �0+�^<4$E2$ matrix elk s adop`�q�X�� ed&� 13� " e�� %Á�er ly!a�esG% s c��,of uncertaine�M~%�unM */c�deorien � effec"^ R� . � 0gin{figure} \-LPgraphics[width=6.0cm, H=-90]{mgbe2.epsi} %Z58.5cm +neu.} \ca {\labely:M} E.�(opHDnd filled circles)D�oreIE�M�s (conn��%�in linAo guid� eye))A"e����N&8 al data6�� Refs.� (motobayashi� 5,iwasaki� ,p�chenko9,chiste .� >�� ,th�E�s�(: $\square$ �0rodriguez-guz6,2}, $\lozeng)utsun �tri%� downM caur 1998, 20�(normal)Zvar>>: -@intruder). } \end!�Ex� comparisW o���i�5 CE %�1.�:����� �� ^� ��� s oba|�k MSUe�!�0GANIL groups �methodj��-X �x u�9-�8of 295(26)~\en� ath{>P}-�>R}� 435(58�B]�},��iv (see�V Fig.~\ref!�m�).�!!(��about 20� l� r� stil� V !wiP��s� L1�PI�){)1�Z eeds $a�8n�Oorigi"E (discrepancy�unclear��e blems� .��ies[� ��� ��.� thes�vi��it� �be�Ajhat in2hQ% ���� � ar030-50~�s�al��influ� !F���"���s f!��N�AH M�-�ar �f�c">  qVrX"� ��adiabat�ut� limits* �le-step!��m@to)�(s below 1-2!�sub-bar���!�W�ed Jh 2eA| �me�W q!{(s $2^+$ (or�$1^-$) � up� 5--1%�}�E�pop�m�$alder:1975�ch may%�%'# |l . Unlessse*ingAe:EP"��y wahlika�m4Eycr�.0 s. B.� appa{absELofv�1� �� "� �;ra, no3��  �w�6- B�S le a 15�NOM�I�� �� :� e�M�:��n�[ �.&. H" dqL�.\u�!�s�Dasl�ly�!�ir0>�� one,�\is quon) if N9 ir %m�5M�the c. ���2&��Y�)���c�I`,� hand�� is6"  esta] "�Al-�. e�a�i^�D ��5�,!! safe ;reg.��a65�%��ra8�M%,real or virt��� s ofNA; moreoI&� r� ve.��*ea�6�� it�ra}nsee�]syste=c� al��&N v: y Our5�e.l �led&�2-U6& at�%� $N \ge 12display�NC toge�>�"� pre0*� &�yree dife�tm� �ach"�*� 2� ,^ chosen4�?a �  am+nu"of)i/c�� 4 �5yamagam� 4�  re�c� ��in). I%�ob)�cis���nee�to ju!�A� qualTA�12ve power�� .on partiXr` i�sa�Ca� \textit{�l.q 2� ���gng��they g��6=:c!� p�``i ''�``L ''��)`��.e.E �An }� a��0sd-pf-shell bF ary,�"� ,�hir.C did �a�O��-a amMof mix!between�seFwgu �.e)ta�vi��  e �low�$0��$�  off $N=18ate�&`.x be�6 describ6�sd %$�a6�moW&q Qions. �Summary. , we �) e�2��9Ý� &�!�I5newly�&missio� �accelera�A6� ,��s!strength �is nov�acie[��`� �Fi far ��� ,by �� ��, yaBdab, $ar physics&�s.�We1l\h"%: m�6(]( (8.7~W.u.\�% "�"$2^+_1\roarrow0^+&�gs}}$*� )��Ayh#a�Me���R� 9�at�2` i�(It supports%�]]a*m� � 9 � oc: outs�``islaof�rA''.A�An!vfuY�K planA:to�eIse�����-���� tA, mass`ione;�XW� 2}Mg �� l ngms EI�K-/r�avail soA�U�do|��o�� uish��%�.�.� "ac"�} S)�A�!hG.!,n BMBF ({\sm�$06~OK~958, K~167})� H Belgian FWO-Vlaand_ !�IAP $ UK~EPSRC,g(European Co�o�TMR~ERBFMRX~CT97-0123, HPRI-CT-1999-00018, HRPI-CT-�-50033})� �ed>�%M��-�collabo��M�G-. \biblioTy{cb_a1,A�l docu,} �\Pstyle[psfig]{elsart} ��15.2cm��6}q(frontmattertitle{C�BY!|e�Z� seqY\\� l�L ldM�l�E&� -� fra�1Cin $E� = 44o77�#, $^{40}$Ar + 27}$llia�s �`author{ R.~Ghetti$^{a,1}$IDJ.~Helgesson$^{b}$`0address{$^a$D�$t!e�-P��, L�# Univ�< ty, Box 1A% SE-221 00$P, Sweden\\ $^b$SchoolJT�ology�SocieHMalm\"o2\S05 06V� �-�@J.~L.~Charvet$^{e!� R.~DayrasE%�l; EY C.~Volan :Y1��C $^e$DAPNIA/SPhN, CEA/Saclay, F-91191 Gif-sur-Yvette CEDEX, France }Y+(C.~Beck$^{f�$D.~Mahboub,+A)$R.~Nouicer +6u $^f$In)� de Reche� s Subatom�"Ts, UMR7500, CNRS-IN2P3 �UNp{\'e} Louis Pasteur, B.P.\ 28�67037 S&bourg � 2, �!��'abQ(ct} Two-E�cl�+>, �!olv�!$s, deutero trit !$\alpha$U@h &been "� at vers)�(`+t (0.7$^{\rm o} \le \theta_{lab 7 $), � ord� o�A%K il>�(PLF)��in $Ґ . Peaks,sa_ resona� �%s,�mr�.rtc at ��iW f�%# 9r%�v�"ort`� �"R emit� ɨ1��aXH t.��� un� lٽ<� �&�y�0%�)� �B*,!}�� GPLF, �E!2��$-velocity-:( cR�(�ar)Z.� )�9/2��F�%�f6� E�an �+6#�#r�#%�m �3+A�!�m$e#u;.�y�0 \date{\today��K 6� +) P� ��:�`!8Surrey, Guildfo-, @ GU2 7XH, UK.\\ +NLBrook�@n Nat.\ Lab., Upt� 8New York, 119739 0, USAP PACS&4(s): 25.70.Pq, Mn�� Keyword�(^�(" $,$x$); $E$& �y�i) ; P"�) -LikY�; LV� ; ��; R:� ; ER .\\ %Pn.int �:� -ex/XXXX ${\noind� �� $^1$� s!2�*. Z� �%�� .a&� � :� \. Tel. +46-(0)46-2227647 ;E-mailYProb>.gf @%~8ar.lu.se} (R.\ � )� makeV  %�  \�2 {Int�/�} /! sec:8o} Ex�'v&�A� demon��O semi)0phe@heavy-�)c"g ��.�&x�/�=hrough aTsip) bin-+re-o��chanism,��0r^+4by early dynam�#QY�a�"O v��G ,,)e� $ evap� ��aPci!b� �� �*e .�:� U3�Schr92,Boug95,Laro95,Rive96,Leco96,Skul96,Dorv99}���ulxis�tru&�r�se kin��-N  A�vr�by"i5s�N 86, <9,Hagel89,Pete90 05,Eudes,Angel� 8,PRL-03,Volo04,� 98 01}B�pap)/we aim "yV� (LCP)��)p�����! is ewW)5 *Kal6�corPY6"W%�p�*R� E*F+]F��0i�i s�a�,5�ala1s%�Eh�at>�.�re6!'PLF=cZ_ �, e.g.�&�LCP��e 60�� �r�  �0'Ref.\ i4MJ})e !� � �e.��-i%A�� �� resholds, �N �.,s4e granaq�a���7 �Ab��3erw adja |or llow$A�� 9JVJ+t5 in a6� � ��� . In�5�ab !X�M .�&2��le ty�7'b�/*6)�aX-�0�"h+� -�x�"dVX�6 x!�!�6unders�8�� of�a��LCPm>2 byM %f ^l�( of non-/Ń ��M�ednicky�1,Gourio�T�nadd� im� tE_? piec� i=� t��e -5E��m�/ emergie�aRa� �.� FurYmoB: !4��nA  ( )!m9��A%u�H R� � �f)� �mpy6!� !! �st.��"6 *� �<sgV�� �8&� ieA����� orga4e� . A�0a briefXp�I-�2�setupa�dQ����xcr�7ia (Sec�.i'� exp})�e�*!:} �*/ ~.b��7�d�O�&�+AsŮ�%%%s? ra B�>�Ns��yp �V� pairsBcf[8q�ARP��&�&�U� vE @A�GcJ�sF�l�}3F�:l�.�%jco|$�C�  :� 5|-�3 >3  {E.Idetails2< A^I�Y@�6e�ism�4�.nN $�a7�<.e s��k6[��q4d6s�Zi�6P on 200 $\mu$g/cm$^2$� ck�)� M�U )=��Ac�/ARGOS.Q�, [? +�4`#~ arrasp112 hexagonal BaF$_2$ crystalA9surfac9a 25 �Z>dif�<�?phoswqby�Ci$�4pla�0 sc0ll�(sheets (700El191!�>�'!�2~6� � ��2 plac� "RNautilu'? cuum� mb� �:a&�6( geometry (>A��llu{in$\ 1��B 01eOA�walS60&�1� �� .- $%&6$va honey)4 shapeA�a dip�233 cm�'IG (soli� 0.03 s�.�&� m���!- < !�F@ �5$\�$x$ 1.5"�$�Z back2 18Y+"�2G: 160M%17_, at�"@50J. .�b;E�30J�!� �in �(j2B1 1B�5B���-���50 �cm��a�� <0h.�al�)��12� 01�NIM,Ma�  I if�%A�a"��ja�$$hieved viaA}�ri�4A5��photo�r$plier sign�D�( Time-of-Fl�&-)* �� ' ($Z;1F2)���2� l6�Ad� f+ ���$Z�'$ 3 = ��'�rg�,a�Fv�bE"g=m�".� b� :�t"� � se�:2 cm/�;or"�44����a�#�� �B�,!�Uit�Un�-�-1a,, stopp�,4� (A�Medj "�+� trig*�Ţimp�6]B�E&e�� s. I� �,e�>LrecO d each" A�in-�"� t�Es �E 6zA�firA$a minimu�aJQ�� % 2 be� regis%>� q)q2�instea�CcoincA_cEAt=' any �?��-suffi[HEsta8<he� cquiH�%$i� �Da!*Aai?��#6! &mA���}� by requir�`�� of; ($p$, $dt$I�B) �iT=�D�,� st b�2&�09�(!-q� Ucm� 3~$DZ_{PLF? $~18I y��370$\%$��A#) d9)�V�(\footnote{FMRqtM�OG�C! F�al�F>aI�:I�Y� *orJ)�ed&�)R; aE�N\hardwIq���a-*� .}�'.d F� ����Ent czJ-�.�2in sB{�r,j d�n�&�w�aE��assoc7d H5:��Y̡�eD2woR� % gcla�initi\H��%'�g����6i��.?I9�i� mid-rapid�, �@om'�abund!Dp5u1ys6���G JG Kin.�9 �=��l�B�6j "x �,b;* �:{\�%({file=e-p-d$;,hgI=9"r;0}8; enteN7t-an7o;�:�(leftA" umn)%ʭ�(;* "�Z�%,^ 2%�J' ory �&N�!�)�i��?t2� ~ !? t au bomb )�,)gq�)xDsame (arbitrary) �.iz_�:la�< ;�'1� b�F::,& ,��E"��&"�!]"M � =ȁy-�V�� H�� show��1\ y�}�*tegLdl6���* )�a�)�.� c���t& 2��K�Pon6� 6F(e��6�On�In fB"9H1�fenKs: 1)LP-�d.�@(a dumb-bell�u�Bi�2&7 " &�4�^) � �4ehavi��s��� i����( A��3ro*lyt�#�#�5E�w>"� mpon�ei/X alle�PRmov�: (�" �V)�ant�' 6(lq22$2� ��Bey6�7�, push� �_�2�ti� �8 �nf � �or"g"hH a16yB�04o2).�Ao�7ɖ5�l9M>� �ے�E�%�a�S ��B* 3IwN]q�-l�isp6�Tno 8dm"p$d �.U��,+�; $t &�xQ��8b� %I&` e6�p�Ga)�� �2�anX���le�:an hal�RatF<��H (^�R�/��Qg�scnd its5rF�$��[&dueA, size�B����� focu�<l� i�;n A��m�&1Fk�!*strong 4�N�%]K98}. An�0fD7rsmear��EeRg!�comK$omGil Gs. "� a�R�M� �B�N�Ee�h!Y$yG3 a��'"  s (s�>2�"v��mD q�E�K�"e�� a�9�0x" �MH s)%0>S�den W'&a_Kl r�1���iU�!�B� )an"< as6�#R ���t�R�*/MeV^� )�44����%�*t E�9��3l l�or2�at>�(B�)�rCexpla'' *�Bi� Kopylov},_ bin�!1��!&#M�WN= veri=� ,�k�� � �se���"1s)0�G",ȭ*�2@By�u, �+A!�ti!�X 1=v.�&�D,;�F��&��\�z0I#&� RI�) �PU $C(q)$��b� 'R� both�E�![: d �>�(JY),�,�-�O.��  �" body�(�t�E�WondV�� quana�sym�i�&� �#unwan�m2p �?�9ly�ge��@of OY�*-�_� m", @L.�"a By vG#�)� cu�NF�2!w 7 �`&Y�� ,_ ��=�I(.[i 4@s�[��Y�Ya ,�_ d. N�-theX *ank*c6]*sb� &�ILwoN! (&�2 A<B$!�b=B�(�>E0esW?y f�$B�Ve^/#)�VP!� ear)��[Bp�J . B�`kB�X�M!�e�z�#����,s.` *�` A�4point�?a��]��]s�Shar &c0Z� XU�wto� 5�)Y m��a\C:� !�y� "s/dPochodzalla,Deyoung}: i) .ocessaI��anFl6��lT��"� � �(� �" �G. IE�Y9A,a0� "��h]]woG%v�ci�&�  (%��`$.g.\ $^8$B�Ur� kB 9�a9�7$^6$Li $)$&N +�@ ��D' riPEo u.��%�EB!�:� . i1�eQ�q�*�,� K89_�4- � !WA8��d :c -b ?s �Mx� 1�Zn�u��IA, ��&y/beW (in��spa�&��ime��G 11 weakl��V�\I ,9� 1�.g" mC]�06� �T Verde F Ge � npa}0}" }� *�- �.@!� *���Z��t T�"� eIa8G\a`��VGin :�)h))��0��*�"��"36�Z�� 1 6v1 � 1OPi&H abov�:?�� \sub�{! $pp$2�� }%;b (* ��a�M� ��$q�$80nQ�2/c�|*�s.�A: (a,f��/� �"alrea=Z�2�I�hib�a:(l!�max#�q "�'2 �,I1�A}at�[ ve $s$-way/n�k6�M$I.nbŏb���+i:�.� ~�>Y���pC+H�%�# ڹ�$ �U *?� play�� n<n�Y&� "�re�+) ���=�0KooninmO:?����5(i67!)X " occu(7o�3�<%sc�B��jJ���.�>�n$+Y  �10a5-�~b,gi eoad5".�5*'/5��2unbNUz �h^5� (1.69>�8!�i+�ƕ�,>G.n_{cm}a� 1.23>Tilley$M|probably\ e bump�j~s"c�&CBIa. ��-�"&�2 6�� H  d2� (��JG >bM>L:�3"�%- �4L�E�s�q��s~ �# enou@cI� :pO�ɽo�oxZ A��eA simi�"y�2a}��a�$R� Q�sa}RjF :�$e�ac� �.s��A m�q>�! �1�0z=�E!�6TA�*=�A�}AIOfT�.�Hudan�%&� 1�9�E4{��2�S: (6f06ecascad��Z/�T%$-�b��ngZ"% �ffav L� >� ig� "�%Y)�B��&A�wbe1�flaI.�)z!�p1�j1d�n�ex�xV��-�Hec�\vMa6or�3&����v�Uf �c fm/c9Z9�(� �B) � stee� "8�#�!�t��)�+ �magnitud"��2�.X�z�A~.� samp�9� n�A� Ru>0 x$Bbe�r s1W �at�#�A��:�e mK�L*�� }�l�"*f-R7&{ +a E�.| &so!Gb!��:�A>� d��n�r$2�>� uhKP� 116�W� / 6� c,h��I* g�ni*�:  �!� .  42.2!�A�*� 2.186�,6� 0.02@ak�h�w�i���"� ��9� ch}0he value $C("] 42)&i 4.2��iMeV �&�GfA� � �H! e^26 �syD,�$ 8�/cE�10-4 &�%!zlap!�- Q��xes� 4.31 �:Z 1.3� i�5.� RJ  >J ��,�1|8��\b]�(^�*npa.N*18.:�*^P*RL*(re�cob*j} co�O, �[panels � ]! "�b,g u�a6tq�d,i�XB$e,j)]VlIDoYt0!�A�&KA��$��T �a�Us*[*npBW*B��j� r$Ҏ��2�v�!X. BY�?.] ic�xa �26\5s/]MewF�,�z�R".�ae� >$�6iIc [ x-ax�is zero-*3'96Fi:��]I�� B�a.�2z3.���� �� 4.65��42i 0.0� uEF�7� ����83��2.1�4�`�1z�2A1.2Z�OA>J�n� �Z; 9 V(6.�D(:s0.918!�`7.4VJ&08��&9.0>L2.7)�)�� 9.5{?>* 0.43>�͐e�"��P?N� �"H115.1, 126.3, 145.7 � 150.�/c,�vi�mx6��$> � r # $ ��*�",v^ 4 )�/c)!" B���} 3(-logarithmiP=alb � <%�:��(d.#.�II�$7L &�>i L>1 5AKeV)!�-�8�2�2#�%�ņ�o 18}� 13.5jB��.� 27866c q5 !2.46�!'$^9$BeF� 0.78 s�=F�8m}eu"+�%a"�Q-O)g-� ��iIH2�3�=�B�1.5� ) 511.�F*!>M!�2}c �.~2f��6�^*� 50, 108i�2EXea�aH`z)��In�B�"pa,!?;] &^i�� "sg ��*B�� F * 6Z@fBM3��eaX|s!f&� R� (�[ of�e� 1.90��%&& �1f:75)E`e�:�f659� �5i6` m_ ��re�!rn26'light�Ns��\u��/$t$A�6# �O"�Bin2=�, $�\Ii� �f�ng��J65bM�&  K� �F�IN�� B� next�R�m�&O)P� 6��U2L)"F �R:e�nonRtJ�&.�$ prd2FJa"�KB]  v_Tɪ_bv0b0a$. I&FL� ��r (ear�A)�aq4le �E�a�/C_b$��H"� (dip)a5/�� q$ "� �=��ndt6 ip (K�EnaztiK� 1��0� %��E4% fr9M_PLF. A))"�)�"" �"�V�MEA�l%F case �! 1�Qg :zD��ervEOI�� `�&q1Q�� ��� y�,~%always ӈQK1st��9er�& Iej "F!Ӊyc� g8��)��a .�!��� ing:�R5%QcJ�", "�v4+�"�"F )�l!��`\uW+�,��%1�&6'.��,�� 16w�|w�pn sB6A�+b!�opp4�9h�: (namT �aMre {\i ��iest}F�  vmW�'�)�e6M���2)� �relhHej�M*z�:�;2� ���X��f�an:. W�(! is u�'�a�AB2@u�1� a�V���Be�w(�%�1�mc]W"�{IZ�n�A#:>�,���H�e>Z->~&�.�se$�<�*L*�-ledpa�"L����2�! "�-�D$/!(2� @)5e�,bD!Q, $C_p$ ($v_p���)U� # (p,e�����6P�m��1/a�Gs2��"� ��9�R�f2">�!6��9�Y�N.� "� chroWga�b�!93�!}� O q <&���CS ��n"�+t.~at "�J�[�Dŋ���a�2- N�pl��6z (�Boal2-rI�2q e�)�}��>+�~�W�mt� p�P%�� ly ( =:�BKvE-2�1�:,S�B%d�4 �J�7�4s_AlMZA�p/CM�$H ios2H1i�,p>)'ve6MU�Dc9�NTLwFs�A8#��!��2�. >Avs\+{0.4cmf�E�2R2�L��E^S���E*�Eup� X:bG (r�y ��"{�9VN�+bBc!J -�^�RRd "j%H>}E�d������9�"���Γd!�: �e�-�H:R^v�z�5RGa�Z�d���D�i �cM���d>� (���.leU:�idel � pre�~�e bCO2=a:"_&Z] N�. N�"� ��1OE� D�*�! �in;u $v_ds~$!N7  �_ eM.� (�R���u�to�: ! $C_d6x&� � e�ɾ\bU&�"�Is�C>�*)�vHD "�4/!*��)&�B� �Zq� e>e�0E[B3(a� �f6�E"6!$��R�w Hoe$ }&  �7,*� M�":>� N]�z ��"�}zVMdQ|7>�i ? . �%"m�)�vqm\ 1%� . >�7ft I�e d$i�ac>[ E ��A��.&�C  =�>� �,�%�0�\ (b)]5%��|V�b�n� 6� � �1J�G�ve.�F"G8E)wo�:��m�, �/e;�%�:�=�amA��6 !<$B :� NGceG�a�^�\-�<�>.� .9J�dc�i232�%���'�� 0--7L �!NVfy2!.< . S!z��p3 �|J�B�(� R�724�;"�y@4ioR.N�!x�?A,:X�d��" q!�� ����Zr&�U%>�6�") Aq 6��+,+�]"J9e cK'A�&�F$&� gs^{e�E��qr&�pa� eU @4V,�7. 3 WG ��n7e"��p!�tA"ilW ��;v �ڡ>D-pos:" if 1s� ) "�o�k�aI1^b��6�^eB@*�1��,A9�A:���*)3Nir��/:#}�!���:&12�oCvS"�~S�T ledt�� �� �� ( f/v�; �/r/tz� �� r�v� *�&R�j(V�t� A�.�S� a�*�,� �>k!E�f �'��/�\� ag:'�,�nF $C_tBGw >$ ���&� �*fP{f"V�� s. D�OR�)6� t�����s�����5��]�-� �:�, �� ��n= &� !L���O���iJ�>�b� VM )�<9�v+D !BO 95R�&�F� v�A��Y�uU��]:�aC�%��� (8�\%���!t]�r  qo >j� �D6� ta>��lٛadsLki�3�4�:g!3cu�L�ew�~2t " -�k�:ve��*Sx~� �G|hi>�k*�#.�#^�RW�B$�c�]t)�>�Y?&FeCA6 � u��s*�1� 5� �3*��4>.ZAb cpaDedcD,"H����Bf� �5aaaHY�� 8Y:@�jES� 1f�}��� �`�b�&i �y�^�sa��"�B�. JM��7�-ce-free�-�"i2!�B/�aJ�)�o�NX&�,�9 !�rBb� �&&&"& {��%i*�k"��mmj} >L�^�ENm!��kU .Z�-m" QmYesi�caneousl �:�E* �Q� � m�]���s$^N�s �F� e��.�"NAU |�W,�+"�h~�]o9Wa.uvA &�#X<r-6�8m�so����$gnI!y�f ?�y9��8���r"�]%CF��sl�zmby�"HW�%�^R,z!igi.ftIQ0s,y��g&\� ��a[at�*\hqV\@!"\�\)%n �(w���2�Esp;�i�?y"d�m�oBV�J!.ţ59�/m}%e�IeR.i���@thuUxJL-sS\ � $^E)!�� lackAjZ���y�]%�q�E'��-liajU���^2��P ��to]�uGa^A�� t GJ�?mm&<y,�w5�/er�he Υ��k:r6� chai! BA3E-�.3+":D�բ�,�,,�),.�E ) Es���|�QLSEOs�q )��CQ!O� 7,�G�d�nl�%] >�-�]��->�-,#]%���"�e�N.� V��X�7�AQ� *(�"*�?�E�1U� E<29�x!b"�xw� b�Gn� UDAa� V��z��.�"|!� *�U6s,��be qs� i*Hx��6�� 6���G?�.s2%��(C�� $��a�#ac�n�wo!]s:ڂ i) W�W5_�'!  A "c%&�5"r�%.�#��H�ǫ�!.�K2�#�E_�N��E�"�&�#r�m>�Ny�<�c�Z ��"� �+m�~Nz. WS)>`R 2O�rN&4� �son�)�$ k�+"@#.�>Z�MM5�\(Rg � 7v�)����#O�m���>2*r� . Vix�a_U!i�'8a*��1�2D69�r9��abe��a}32��P=B{^Wc*�)�� �n�`�,�����wjw but �~v�7*04Ay�KY"�|*}a%�-�H� +)]!���"� rl��dF� .&EI�aXW*�d�G&��+a~G 6��DF� ��N�?,xK'"�E�V�F!AaIaL*(� �GQ�\LC*�}2�Fear[-�p.?i : 6".�"[!M "� ree-mov��Wf|OT�s[u� 9(ra�~�j�=��l�[>�K� E{� temper!F����ps/1 �S���1�(�?a�44'G , 4.K>at�AE#0b�(4.>>7L6VLt�Cy(5.~6<�;�.��cd"v(5_tN8)F%X�y�)nte�$� ugc0��e�a�^oݍtR1&/J�*�5��!4&ž"OD�U"5�hyp�I�W&� adveLwd9#�*y�XF��2�A��� piuF -c{�X�uI�liq�b E&V%#6H�%��&�&}.l/ &� H�X5�/eGanil�x Borm�ŧ.�5��� S�&9�WH0�9T~sh5&�Ru�I�����\� �al del.��s. � m �Gi� �3b�Z�S Ia�th� pa�*�.�0P\\ ACKNOWLEDGEMENTS {nc�r �� � �P�Re(�kncil (C�PHacts No.\ F 620-149FE�y621 2-4609/B  ``�&�'',�cA�ˡ�/� J ( %\newpage }+ theb*ߘ }{9}�d�$��t� itemH�} W.~Uؕ�df~ �.\��h.\ {\bf A 538} (1992) 439c.I��} �� ault,:4�� l.},ZT87 T5) 499S֋} Y.\  chelle>UA�!et(�B �352U8.�dLV em{R#� } M.~F.\ B�VR8 �6) 219.TLp�} J TRS���6) 460.WSkul96!�\  skiZSRev.\ C �53 �6) R2594=QD � O.\  aux>RR�651 T9) 225�= A�tAlYDa<�86A~ >]V^460^8!Z2 F89nS-�)M{A�6I89) 1017=Ha��} K.~ B� U OMT229 �!0PPe΍A\ P\'eta@{47z�1 Q90) 12.�R5�R9-�5) 95�Ec�} Ph.\  >� �)HQK6�97) 2003P"���$~C.~Ang\'e��:�V�614]61\Z<3!�\ �>R2�-�%�9A��) 09270.WO�<} V.~Avdeichikov>[R73! ��a��98} G��tVn\`{o}>V2�1]�P8) 28.�H01U~ n{\`FTR�68AN�) 566e��(dy�5@)nZ�-jB%k37j19�h32��1 Q��� �10!� ; >NL7�B)�034601.H7� DAPourio>� Eura�hy�JJ.\ AIQ��2000) 24��?��8%�NIM��~�.\ Meta� ]31���N51.�| M�X�, Docto3��#i��+�{\`a}*� 1997 (un"@�)]�2婊�M�.b27!bH'�U"6 P.~E.\ E Betak,9�pR37�i�1.R�s} � Zarbakhsh>�-���M�E�4a� 1981�Y68��i]� I.\ � F��5AX 1974) 472.�P&id�\ r�-P35��87) 162��d!MA.~DeY�d�T�O��128a<2! z4�$1�uR1885RF�.�'b!4 ��6�2002) 05` .P�] SI0 B�%�Ey 1977r .DT�\ D.~u >�R&70�| �.��� >L*N�0308031 B3i� �2��I� A 74-24) 152m5Fe� >�B�A%;i� 18.^&q ��>Win>p��io���1!zH.~ e�J. Shillcoc.�*� 3�7� 542�SEjV�\ !�U�A�iRjt � 1994f� 5, A��pi�oH\ed��by�]Bex � \ Galin (�, Caen, J95);�2�5��aj�Pzh�"� XXXV�CterT omW� Mee on>��,h�}, ҁ�Iori (�4.\ degli Studi�!Milano,�)) 536aX,8>A d&� B&�class"� % U'hhe opA9$ doublespa�or ��ewcopya�@ &!�+ging % "��e[ % K&�� \u�kckage{ܧicx�� amssymb p !��s vX�us��ful��hen>�2ols %.[ J!�W= 6(�% Tit��X2�es!,u-,�ksref�m'w�,�, @�!@\ BS � s; %NcorrNO���"�RA�2Pead�P!�e.��, %�$ \ead[url]h�D�:!�t!{%\�{��1}}"�m[ ]{ �{Name\�{cor1}>G2 G ead{2�I�{�.t2 t h[e -�{Adר 77��3 z.M3: �Rec�{C��er)�Z��"�A"g-�!Raa: pus"�!~low���eAfi�al>y�Ytoamk-�sq�tle� �es%�)x-�,�1 ) �%U� *զT[FZK,Orsay]{L.~Audouin1e!C� }}, �7sis]{� workAUm#�r��PhD�NL. [�> ad{a i8@ipno.in2p3.fr}��$Tassan-Got� �4GSI]{P.~Armbru^�>,K.-H.~Schmid.: Y$C.~St\'eph�b6w@,GSI,CEA]{J.~Taie�a1XFZK]{!5� Hermann-von-Helmotz Platz 1, 76344 Ettlingen-Leopoldshaf��G<y�I�� IPN �,*���mpu�ris XI bHb$102, 914063F��V%)�� ncks �se�<64291 Darmstadt,J�% DEN,6� 6�N4�O���&����feasi�eof.�=A��;a b �.� isc".'5 e ma�)hzvnge!A� *ipeJ�=��" �s�,�/x��ha� *�I:cessfuT��l�wZwiY e5"&_�%;at 1A~G�af��to�� �I�.5zk�s)1"at�s#5*a�de݂"� d-FE�((Ljg!p��b֩�}��urq� thir-�i�d�oE �&ew&�"�x velo �v�r��Ȝunt��?ubnZ2�v�p ollus 6�aBt��AZ6�ak�.Ib#��Wn|��PM���>���llYA�+�ze"d,�9�aq "�0= ma-Me9�spu�B�#uEc.� �?� k!� s��-� : \sep MagJC#J^' UV,D:�L ��z�R�\ E) 29.30.Aj 29.40.Cs 34.50.Bw 25.40-h 70-z)A-$} > S83cuts �co� 4{\stwo}{$S_2$}: four4>mg}{mg.њ{-2}$� *�loeS *{6� �aaA� -fli���^e�E "9"� oper+Sm��s; pv�6n�, a`�g�P m�&�.-�� ɦx� �7�?��m����F�v���S� or (FRS)~EFRS��GSI�*M/�1m�:J�&m�a��:�  ten yb$. By nowx@6l�԰��S��Lworld��de'd�k��c�V@1�;��p�MStr) tڻa��!|p{?(.��f��XDyts��}�d8viv�nd)�gns5�>V .)�Ke*4�|b E such��8m:!be x 4����V(�$#� ) G� � �A1!=t�ea�1=� �&a�/!6iXpath,d��� talŬ&�Z!U��$itself. Bu�6%r �� �;�by 8�:nC:ssu,{�1: owA,H$!��on-I��n��uSq�to�i��� a�a}s�M() ���e-Ua whol"�&)�m+ome3�forbidde�Sl>L3Qis!;2{y���E1F,~.�� u�hBa�2�FRS��]�> e"� _w� A:�� rse-��&͎!#r_�/aT*FP AruP�;&H�tQ�of"� �o+�V?&�\�|/=}ub�h'a1�ep�&C$ub�K�U$E�:�:I byjM M�Z(d"e "� Ca .0!B/�9ore�%tpro-4�˹�. P&� ƺi�mx��:g�a t�V �eA� � -�GSI. � �V)W(5l� m���!p�:I�f =qYwe)a1��W�$nU -k A ba��/s h�th�0��"��}��e?(e*� *�u"� g��s"*������ rial���1a i�e&“a��%�` E_Js,G�e(ws�L�� �a��r ��be*��!��5AB�J  (e+qѺ%�y7ato�h&E�QXs�_�itu 9w��-�ɝFz},!�fa� u�,v<.w E}ed6w.4@B� deg}Y�/&t���a�1ck!��1���~�.OńA*%16FaD!GI�Qe5[.s[w!LЕ-N, �fun�K�1��.e1�G.�M�A6T�:f  2 ,�-�e ve-���|rg�/� ��E�&�*2� �N~&� �a`�  5 -�Hlv&�+3\�Io8vte� t-by-+Րss:.�@^��a})k� .q)ʡh�ly%&���1�)��P"�7y=�c ontaX�ng2 p n�-��cs�ѭD�-A�Rc&�q� ���n�l lly-��a�Y�A� E)��=#.�Z�!�th� ��&��despi^a�bigui��� �sx��>o/ W �t�/~.)�����ns3Ywh> wid!�adm�[>�&J ��ownward� ���"�M�Rr B�<@��",����FRS5��c"�ll�e��A4� gureIf fig:2ܽ~�2M)�"��eiM,� q�}�U v8 1��x`K�am���~U2�BaslyN " ���B stag:u:��a�S՚ l���se����2Q ($S_0$)5 Xedo����fic �@�ӝac���=er$fo4plane\2_� e bgAY0xa�e/�B c��>^4$)��rs�m��A�d��=�p�11�sht�a�ti����ݥ�A ��0 .3 ecV�v =��~��$S_4$�!b.x [ht]�5e��� �0.9&�� ]{frs_new�\]�\\it Sq8 view�b�. E!�U1c.Q=��:`��I�di=�s (�� blocks) pڮF�que�� sextt�sx�w-�horiz�kl�{`:�%IE;%IEzusu+ -���N֯"�A��&I ��Z M=."eF�d�5�Q#"}[��.�Ha�%&��!�� $m �O $Q$�C�Xe95�f�� $B��3�SA�-2�=��on~"7LZ/ } B\rho =��{m �� � c}{Q� eqn:brho_a �H HZ6$N�a5cuChG�radiuI�yaf<tra����Tm�� , $cNsp��� 8e2�)*$ �)�f%� Lorentz<>��f��7F�f��u$A$ o� q �J6 �h� ��au}{e.c}-oA}ۖ(� �) ߤjFi$u$�Q���KŲarEA , $e��e.!����h���)JI&� .U 5��i�E V�6_\�]i�!per� Ip�Tn� r��89U�.�a����d� �V�$erm, $A/q.=2�2I6���,l3�b�ż%-u-�90}�0�� �A}F�M�Z�, uPR} }. :��u~�"'�M�'�eǁ'mbA$q �exi��.�. ��%�� in"yes��he�+ċ�4 �7&U8�%y��r���-E-/5H�WY�A@9mon-Ns $q=Z�)get���.of)��!:u"�)�J. xN|bepN�< wi�� �}� ��r�,fE;�tN~E�~�CA�d �� �#�yi�s� ns� � ?�b� DM�ơ)p� deg�)n����=inMpR}.�. us�O!)��� "=!��exn]pro.�! P>! ���(!�ABQ,�u!u5��&c� des:�Dro�)? monoT�#.��gin&#�\it{ac8}:r�lvM�9s at \`~doesc�F �Eir R Z�qRjN � ]�y help�� �E�ieE4w V�n}�[];&>  �1��>.� 3��.=/6Y-3��3�3��"��"v  Eanm e"#F!I�<�?A�m�� e�{of�taki��� 08}$##NM� ųeA !Eour� cu�B����4. �4sV $of 87~\mg~7 id hydrog��n�^�� 4 Ti foilr 93x%0�m� _}��^'�pAR%f�% 0&trw9il�Nb}��d���0z��set. Aa- two~a�ͥ6�hau�E 3~mm�*G)�Ha�7d�1w��a!�icF174 ��#L Al. Ca de�T�F�-���% (rougu�300d&01y{&�@ suit�or��m%Fing_HAl�a good�#i��n.t��%�� pter.iI1���YefVc0���B�=1�$ �� A��6���&���Vt }"ob���.�)�!@d-�U2�A�5 "2M0 i��� -�fQ_y �(%ke{T�e�m �"�A^��� "��O�mDis23�� o�!4interactions a�nd therefore depends, not on $Z^2$ as one often thinks in7< first place, bu 5(q_{eff}^2$,% square ofPeffective ionic charg$nuclei. In-cas,a gas mediumUisH B\state is almost equal to I f $asHtime interval betwe�wo actions�0fragment with�atomsqmuch l�r tha �decay dof,$ic excited �B[ . \subs!!0on{The physic+p91�Ts: a brief overview} 8evolu�~th:n=an!�$ in matterQ!�! @competing processs8electron strippandcapture5�Trelativistic or quasi-2regime!�eVTprobability $\sigma_s$!s nearly inI�!�Q`nergyion. O)�oA� hand h.^ofB� lead�MCpresenc%7!Q5! hell $X$,� c^{(X)}$,�ong�creasesIDdec �(fo!�, << 5�: any9e$carried by%}!0is removed afA�,a very short�a!����=. SimilA=,>aE�V4quickly followuY�%2��m . T�EA ���H ully >ed,is9, correspondsQlhigh-Mplimit (roughly, beyond 1A~GeV%�heavyts5�A�).Zg>>bg �edX�$X$I\.re���is� likely�happen i��veloca�%7��4close.hone1R( would haveaaits ��U2A@!rhas)�filaJ!�}A�. ForQ� , consideE�ZL�22t�ar� ѩ�K � arou!�000A~MeV. \endy���A���u2 (��F!�meq�)e{b��prea� as a�ۥjal�ilibrium��i�e�*)�ing)a giveA� mbine� ($Z_{ion�� � E )%�� efine a2Z$p(q)$UP!�to)�a�$q$ (or,a���wor��{ravel�2$Z-q$U#s).:1SՐXmaterials} \label{chap:� } C=�(� 8~\ref{eqn:brho}%!!� fact�� t we �no possi͚to direca�determ!;2v�n@, it becomes clea6de mass i�� ific�9}��quires,!�far �leA�aS.toA$6�!e�sp��m� . To opti��propor!�b�  �isa3 veni�xt0 $sert layer�well-c�Y)�ydevice.�3 choi�SA�N4er foil result5a�romiseUȅ2��$efficiency%�imp!�o�� beamyLEh!��angul!I�=$straggling�%)2er /induc� (econdary re+ �k �er.��(figure}[ht]� cez � xncludegraphics*[width=0.47\text]{Mo.epA�(hspace{0.03 �HXe H���b���Pb L��u G�� ion{\it BMs.� (left scaA�continu lines)%�A ar5� r�Z(righ:dot�/ 6in"L 1� A�s ( leg )��several�&AT0s: Mo, Xe, Pb�Ue�a funB a@apince�� i thicknessa senf.�c6AڍW� ��Hat eachf�fig��6�AM� FE�� 2M play8 �6v, evalua!X from�fD !�BasB proj� le� Calcu8 � wer� de u0 !"code � ~2� )ZperA�a\Bi� er��als��� ed (q� cross � s � esti�ad���.�I�Il�a�he�aGckXin~t�in Nb�chz in a��6-N���M,. Let us poi!�u� � M-�Ky&&� + be��v �s favorE`�!AV6accor.�� �on%va�e 90\%A�*� is2_�R�a!:son�z,!Ohardl�!Vaq.U�Vle� a6s experia�s� a Xe,aC%*�as !� as 2M%>� I� f2���e�vtor s=ivity} 2� �� q dA�echniqu� Axen� eloe� n or&o �EyproduI� E. -pur�E& a!�is d%�s� �i �M�H [�.�magneH �AdP ��� basi� y ope 58$A/q$A�iol�oa�Tţ  lo��a�parGir)��;1PEchx�w2irqd-�!1e-EN�A�theA� ( understoodAFa $Z$9F� � transmi= _qS� � .Zun:\. Sim !�%�<FRS>� hm{0is $^{208}$Pbm�n1� of 5q� A>*��H2000~mg.cm$^{-2}$ A#se�Khe]�e6 s. FNs2�@ VYn2��\pl� in greyEvl�E�� . Xi�I��Eblack�B�)e/e�de�xU� < �all�@��0�1��9 ��~0, 1, 2,3,!J>�F�� �:� ��  ez2� A" '�A!�s7 �a�kAE���n s*6 o:� ��  o�! �asI�!�e1��-/A��{&��� �!$ Pb+p��Eg�gY�WH�ok in��ccoun�eS�-evapor ct[diz t5|u �% :. e2e� *sb se>/Ae�6c!WVrop6 rapi��#lo�� 40E@�let�van�� 60)as� hundre��f differ 9Ut�w.�, (  n 20�._up�!�end�M6o\h� �sli�� midd��B'e� rew��s numb^Thingm �&E w�$N� !d take�Y�wz Oc&".] _�!�a2�pop��=O�=0 ��b��en�Ni���i�JT!Nm~��ra�"; )5d. �equentBM�a�measu�n&\Y im�Dachieve satisfactoca)stics�s2 �A �= may bE �es�It�im� aa�o(A� , du�Zbk shapDisotopic23%�.� or f�PresiduE?s��dra�a�yif�7s!Cton-r�or neu�  �� IU�� g�'to�q>� Y<w� � $A/Z� , H-nB+to#i! �X�2$A-@w�"b�f�E��!�He>_ssG2H�so aE�21unwan���"*)2k � I im*�` � *]�:xa�!�l]� n.� 1�=AeM�l���R�,N~zQ �xu ablyi3r)G9 �6J�aminaa�sx�edA?be�u8�DF�� |�prY�5!ZI=k��l%[sa�a}�r �smallZ� blemC)��s�� omehowa�regarded %*� \�{Z:b6-z} �ss .�!4Set-up design}�.music_@ _750_1�� � :V2 V6 "C �8Z350Z�E :V8 �cap��U6? am�yP A�thr� �0 (Hg, Tl�)� MUSICA��s�0} (60~cm long�)��1�(2 P10A$ul�assumi�en���V�ys:*��coma� �ofQis 75y (upB�)�3� r 65 %P}n4 2�r L summariz� �} � behavio���� %�Gid1�)Nsetup!�ourQ �waH tend)\a,l!_%�H:�us�% FRS!r norm� ondi^�<� hI��| %� P10,���&ix% �of Ar�10\�CH$_4�c0t atmospheric%b� ? �28"$'�Q4of 100~\mg). A�ly 2/3th� lengthA/i|u�e� �!���ag�aE��!?�w�o6l%�%Tto" � colU#!v�#depos%g!� p.>!gB�&/or"� *A{# u]"�:�as�PNba� �� step-Wu{%0Ath���q�� .x�2�newK :�'>t. E^)�ch�!0esc- . ��$\delta*S!�4 drif�5g�U텸�^X ��{*s��t t��E}>�m��B� �0a fixed 0.3\%6}P"]ota!��. $(�&�,�  i�n���2=�nv p/ 1�aMed>.!c>��No>�2W1�Oga�Kir� n f��pat���+ u+�ur� B�*botU�}��! me�^��R$ %( rema&od�>II� ir w,+]]ga}%�d� o�*i"�e< �� � K)�socc%d�we� peak=yQ�u kept%����fœoi:,%%~0Of course, ad�7�!q'A<�)!Kresolv�� powe� system. ::4 -0�dV��)���I�:�s ,exchanges du�Nx��)�aU�%��dramatRi�*%rD. {�-%�diA� b�$wIi��zluc8*$qH.�(��$n unaccept��� %[6@�FF.�s(�)����9 v7>���)?y+�."al �A��A��[a��� J'��-� �)XI�m�)w ;.�n o. A6Dis �+�uYbe�t!��bEx . Fu:r<)mt*�c)� %��DZ7M�!��q�.:�'Confroneonm�"N} 2�� a�I}uI F�_+�#j!�,a?j+&� seem��'���"X66amGofE:(o��. ) ��+eS(o d }� eJ21�!45 suc�/�}��at"�G}GSIe� e�sis�� of 4r� .� "� ,� aM�6/M�or6 of 8:8,z ����� ��i*� . D&�] *(e�"s�Ig�'ed�� foa} plan2��9�XB  L.)9 >�3"(��.ubtain� n:�H._0.9\%E10.7/Zc&v�.E��a�6:6:4:�z,� qw70I�s��� FWHM.+& keep!l�)ad�� e pap�un�!;� ��fpecifi�,�1}�L _185��7723N0� tra .��ev��A�pe"�set1s 3ed�9$$^{183}$Tl�(�(59}$Yb�(N�_re*2� -W E�1�=.���iO�F�)`h�YW"�/�)Lq  ��,_ v)(�!���i$il��1�}��1c&�j=al�!�4Aޥ_S� a!iz$9aah � �chJdt�om �&�)&� �(x(o aws��,�)%tak�B�v*'19uha� bes0liKBt$eD:�0�drawback.m}enumerat"�3��.Uis Uenough� a�>:�^7a�"���observ�T!��7 triv�'a9c�� issu1i!�Be$ulaS��c?�ь�$Z6G � ���m�ignal2�IM !���%#"~V1U(� t���yYJI3X}�Xn04ej� �Ru1�toiE  miA&n6+0!(f"�by� y uni�%f^�B��,#2�.�_shift��c*�MN2�!Ps�)aK"W��jl. E�,absciss-0>iB��Q ��H��!approx�+� %�� � c�:!i!�-z9--b5 c5��� AY9l�5 � AN�9�%rigidO&mU FRS,�u(c:�n a�.ge: 3A 5 neighbou�esJ�I�n��<�㎹[�0=0N�lJCөJ�i�s�I!2-�n�<� I?������rBq�[�P24/I� ��v,�8�3& m`;6; para�c� 6k*�dPv(9�a�"��re�\=:&� off-�0 analysis��&Q�1n��y&6j . An@7%�oI�)&��� .X�:?"�.�;�-a A� � �/ly alI!2, �7+&�&s�mm �Qj"~ u�1$Q~2Ax*w(��C�6�$��6� ��2=��IY6�i]6:s} . +qB���4u�6�4i" low_�mۚ� rS.T.>SuH!hR >�p>�3���� 80anodes (arbit� �9�'zer�!t!p-&�$Q -:�� t&!*a#MU"/300~Hza N 2~k$: Er�InZin� �+a��\A��EA �m is�w�"��B53"�, Śof�a���"q1$��@$q]-j [n isa�l &r?\)l� i��u�� �thktowar�K �<*2b� occur)�molecul>$�BO  *�<1im�%i�/�$s O$_2$hH Oyl@ft�e��j�(fig)�N�(.{�/ &8e�!�A#!D1bd�'%8E[� �$A�n9�n+1�)tU.5I��A#R��lsoK� V .0<l+,�% �[sn"J2���reg�"�?)��Dic��Nany%�"�� trM�!�"�L�� ! ��& 24\*�9 tis1�D0Y/p:�,B1�!�13�b4 1Z��4"M �yFdu3 e�!OSI�.illk<nt;��i�&�Toax3�/ vers&�E5��^�� s. 8MF>l havet� �egiI+A�A��� \;9,  v irst�$ird, fiftheA� n�A�!�1bea�-u�;g7�&* J���=:! � I{a��/A>�Bm1 am sAl�E}y"�7A� & x%�1�)�)� ����>��!��+�"s� !?t�,gets �^/-n�#al  7f�en&k-�A�Y�mbo(a"�(on"B-��B 8�screen� G@"e �fM 60 �U inver�8�� �Ck)8,͡a_7�/N� by 2? ��rgHA�&I*�4mXFp�;�8E�l�/�7r�A6D ; �9�*8�18 datao)!lj�[-o� �)d�: �"!3).�� ,"��-P.�!bvp�,blr i9 E&�E�B9�sat��K  catch�sitZ�Y (��H"��i�9deA��;� �o!!�*/;R� t�i. SA �Ge�5(�$m�)/s��alread\:e/�!��pas�K�2�.ex7aUey�te�v_1ascribr���%�emf7a! %no �C%"wV  �)!A�ps�ish>W�8ve�wn�eŖ4'6�E "�!�1�-attach�%�1�G7%~��!|�{,� 9�,�E��R&�%�%3+  *�L An o���methokH6�>; in Z��y1� } 1de1�a'%K"�De����:T%O%��!�+�:�Ddf�8^8 �e�as �:ead��!�ow&/Wj confW z%�-�HAff�D?>�!\'��%x�Gs ��0/@str�M��eL9�a��Dx=r:�%�~ E�!�Y�� _ a7�p does��haa*�c"� �S musE8 J�%*�����. Sr#���va]��z�kɅe��* ��ہ�\ _TMU��b@3d�F�'. qY6&��/j$.�pr5�$y>�R1v ",�=�!ne!> �6� ��.&�."h/BB:� '%#*{436�deg��/*�/As wr�2��� � d"�I)�E�e�2�Ia5i re�I%Hknowled8� AL�R�"_IA4b� of�,8�ap�tu�pr�Ba13$, unambigu�6.:MFt)-Q�I� r� �)is�.:CitQG2d)ne`5�E*! e ! �!J�, nama{!�/"5.R�ic� �h� ����,�8� ܱ[��S�-��K1�)>z2� )\iV )�,}�Q�}$؍� el�{a�h8X g 2sak%�sF3O�oU�6 "12"6whR)YB#er� m8�t \stwo1|I�K pluI�pl7 scintill[A�� �$�( tre��9!� v&�%�Y.E�Q ���A:B ��5� e� $A$ 4 kiA 8$E_'�by:�q� } \D�, E = A \gamma,N� dE_0]; 8P.�G �  U��b#i�m�Eco.4M��eJ�x�*.�$ �(\beta �)$!�tvof" $!�� ead� n\s]P5 2d <r>6BwD$$ -%�!�m�����q�ed> g1@-�doh a�o IngIp��I�. �i*�H>s,A:*�w� YE�!�Ū��:a�� purp%X/Ymo�&�K� slow�d� (��vI�+ ch�' (if=�<a�,:>e� ��W s. UY713�*aQ �<edJ��P!K�%an�A�t#I*�UeqnarrayuP8(B\rho) & = & \�K{A}{q_1}6R _1 F-.32>3 2 \\>6Bi2A eft(>p -:2 \�)>T- \ F�B�T F�b�5. Sche�"d4Z@�2@G�Y)�!�#�p��a (a\f�*�ter:� ), $��v�&I�$'`:�%�[$�$"�`�5K*�va>w�K �6>^v ��, :Ic�.� vj�J; in 32f*0UF��l is 3*� 1Ku+$L_nd�+"?�W &�r\Y��by 6ɀ��"Q���nowE�e>� ���q�B� ,u[Z^R���2d \proptom�Z^2 #SZ + e_22<�`1F�H�Q$e��uds �.�"��-m�q6��# (!�%deA�p�i�l$)Ssf� )!:q)!: _1.�� q_2-�� "R$Z !�+9� To& ;� �*� \� iM:Q�0 �AՑ��*�O"(� ym�Ft:*pu`�: mponD5 �#*�]m�a"' :�;�\*���,:(av$J�.�:O�rY.T�`M/"O._.���fe next9 (�ơ? :de_app})��� �"C applv:�1�-5�va� �R!a&�6�A�-�M:v5&�L ��de�-c� h%� &n&%cac�Y!E��D� �I=sfw exp}w1/�.�6�"&O1!"a/&�+>bp�lIZ & ��iu�.� Am�? >�nmIU�N�#GEX�^] !�= q$. B�E>r&tVWEQa]�Le�Ѥ)���1}uERvIa�a�dp�%"� ��`H>�,eq�$q$�'b�;�'"�;4J*�,)A}o!�M�T*}�G���4�&<�K|c)<5T9�5$Z$�m�� !."eS�&�2f 6�8!��7M)[O�Mk �IE�A�QOA�+g�r "d3u"Y���deBalthoug>A'&`�8�;&�X(G-T��&�4��ke�1),2LE(1,aOi �)�N?�x!�diang�dem-0reWg 2,2)��oK�3:h�1���f&�WPbH M�%#�D"����2�D]Pb`a-at� a2frk$+��isɂ]=i|>ea]Z=`!�� �E rs (�3��%�AE!7 �)-d is w� �M6�J.e&#?i5"TE1Hs m�J��dis6"� � Nj�� rece��1M2p� TQr]"A�*�]�@+�/$�J ��VR��6W�!C���d�ov"�On-�c�&&7)��(!��?E�% �J3$F^.�  6�<2�!s.�<�<i!YT pa�!�QFRS�I0Au_Fanny,Pb_p8d,U_Taieb,U_Enr�Yp0I= %Xe1lo">ae,Ah)�[ = 0$n��&�4�GaxYV)��6a&� m�. j l^k,">=c�1hydrogen�O� a�"�_sh"a"x( it� �j*x'�T"6Arel� MeQ�AmF`6!.B6"5 .\^ prec�e6"gq N� �E?to=I�J��C5�:Q R��. �%$H� %=bPt�KBI r�; @^�s�!Z ���meamGeo#:=�lue�f!�1� �'2V !,�%\. I�r�oV� n�m&Gwo sourc&X&Ybuncer� a!aF*gEv �AP�[b �D �BDe�L%� Fo�?by{-�v s�G�se�j"$D��-usrsen&�!hj:�S>�CMe� J}B0�Fa��cB�]. W., Iȁ�MmJ&B�\ im. fl�����Gno�$c�T��. $gE�KN ��T*�D:#"/y�Y ��s{3KA%IA��:�#ful9B.& A�Ƀ! ��8bov�(VKtA%& ex�q��I!�-���1_�&�p��S} � K ( E )}&n� - ,�}{  N�a/;A i�q� dr��+ ndix{ �>-e}� %a�pa�q 16�}=��yu��a� �(ve:| *�D!�2VB�.�'t� �. DBH �FR�m0-�sY�Z �&'}_��&XuMF�B�"_a&]97�l&Sn}�N&��E��?CY"���&<F��:l�YA"�oN=<� itself'=F�I%"� �-.��I"2*"�=I�;�! U�#C2�*�Es"�! $B$,!lz��aJ�� $qa� �O enteM ��*J5� H"av.�AE�R 2�(m, $x_A�"$x_B$)gJhI+5xa�} � =�!0 .s1 +�Y(x_B}{D} - M�jx_A\�:?e�$D$*<2disper2v%�%�� aE$M$�"�&cnpumAjul2"� !�s:eWop\exhib!Pno aber? m 21iB��%MndR���?v��EUi��_j "�8!�ͣ>�s�`nd� s F1� *��*8exist&� {t ]H.E$��p� I�s"�\�4sF>P�,oLh,~ .?D@w4po�h�jttU6�V%%y?*&!H�'��1rR�I�T�Q1�� !�UsH�����y;�`m˥}� oH8'yY���.(o�rjfields (�)n b�9qan 10�d4`!�� e2�al1e (� -��t� 3~mm)fm2@_1*B} "� �S B�$ x_2� �% 3.10^{-4}>#�c1�aG!Cf>���!d64N�p!�}��J>Z� !�129�Ռ&]m room\7by�v0&Yloct(Et�"<7EN�%iD� E�i�ncoi�q��� �4. 2�!�*.oAgd��>tM�![*.,�� $\si�w{\thetaIw�+��i� tr0$x_4$5rR_I5x_4�6v.dR.� �t� a�:G��U��add"� intrinsic6D�'2� R�.�% ��DA� �^2� ( 5q + (B )^2B ~S*@:�) ��zM /Y."PI���: ! u>nstrut� 3asM�en���j* d&V"� �M &3.�6F �+&k 6�e_� woLec�� ��by6A 2� -�� �� 5*0ngaova solid� Geissel1, 2}. *�2.Wi"cQ� [Zi �qB?~pa��OT& 3 P�E5Si�b �!_�3ggV�au&p �,J) frac{dI�$^2(dE)}{dxZ" 4\pi! 'ei#  epsilon_0.(N_A Z_m Z_fa�, chi>��+Z_m"�%6�!�!��tS{,|f$V*Q�>��+$N_A$~R&#S�d" i��*erm� �3� #"?�t2�`I!�|W�� /-�M���&K Bohr�*J$!J$"�;to $1-�, ^2/2|-e Lind9q -Sortn (LS OoryM�LS}� ex�^�@.�#I5)(i6M���Is!.h^���Y�&���A%�t5x agre�dM e"�L� !2|YAmec�4Hm�2d6or�2vyh2�!v�N6nndH"w{w3j< �as � �*�cxATIMA-T ��d p �o3duca����{�K���F/,"�� �� � �z� s2V� 1<�J# al nw;���{=!�[ol�XU�)��B��6dND  f�ki Jm_! {�`�0!� � ���j!�!r.�I2!��,j 9��U& n&�-s��|s ��Z1l.�$AN�_�h=;l2���V��PG*0q6�R�A)��"e de})�$$^{178}$Hf. E�mor ŀ-g0�)!+�ņ�"��3[5liquid"�� �!ll Z19 H e�JA�6,frs,�%B�n�#}G�$NbroadD@c!�p:Ly�;��a�supl1ECt-a = �=�a{y�#s" J?]b !OI !� �2� 2"�\�zRwe-"�np to u"� &IT���L$\~5�a�i�} *"��d,Q�(:0a��d(H��s:BT2%%�]N�[F0Y�&� � half�A8 �U�lumini�(7 O�,6�! nN.p mE�a�!�&���r�6&O�#���3seB4s)*�tB�qa9'�y9umZ~of�BC-400 b�i钿�[�P4*�� ]{Pb6 GG"M5cmF��ZDHf2D�!io�h2�g-�}]�.l(�$)2 " .6(circleY�.�6F(�0�A���.lo�LJ"�=.�6A � �Aji>�*��.f7 quadrc&�A!�� 0�,+e^�=6��I���\hyp�NEQ� �F ng~&f�,"� m#� m|exi{.�$y&1 �"_*�. S5V�,�#7 2*�9"� 2� 6 M� R�X L($͡�#@ -�AV�!/ �p": M . AtJ|4Ig<%2�u!�ar� Re�r �V��[�Pble2Vr25�V�2!xD'neglig�:UHfI��5P�AK 0.49�&��0.44\�Hf.v�R��]s�Bʌa41t�v ��!O-*m  �4terven�@�nd� %�`-G*\o6qeAq�(�g6�^84�%�olt.Z[JHK2)#E�6&� . Un��l����qHf � worsj?�"- � F� ,iA�)in!�! "W,�h yxŶ�v�Pb!���BfIE���&�5!~�"�&� fas7 f��HfZ�%9 nJ* �!�d 2L�im'�.�4C`2'nc6~ ����Fm� $s$~��|�of!X�5��G�.��'�8K2� Yl$- RNhs�+�5��{F�s�$q=Z-2$~.�%� thus�J� j; 3.#��."H�l"���E��}"�gtD200���F@ ��2X�C;��� �,A�!�* -Fh� UJ�-\ to rq-�V��J, feas��. R�Q.?&*4 ^>u�6a�d!� le��lev�0|Gi( :F�'�I|qu�| ��.?.�indows ;can��H!�d)\0X'�U8)%t�1fa�B5N�$z0u�� ^�E:FG <}M %�q &D%WA :!��)� c� eT~�i���R�A� ���"�.n realRKme51�s [A��,["�.��erU1@�% E���c% �,:7 Fde_z ctZ�)�w�lu3"��J� Q�A+pb� �p5a�jl�� �[� �"n}&�U �x�>T�c 9 KoA�&�Oave&�.���. "ilV1�r9�c�) play8igZnt 7�"�C&#E"�a�3af/&aK&B5V-Z��QN��Q�ch"�Xi&$�)���cde�.2F�x]nqC�ɺpo�]iBOharmful�&� e[*�OHF&NS !�"�a�CE !��-E R �HE V�z��e�o�qb�js � ���'�Dg�. or l��U"o`whThZ*L*�5IAj��tlP�� b�eA er �"1���-&?�6��Fn�K%�?/i+�a�a �]� �c���� y��"��  +a/.W?}7aiݘah�xU��G�� l��to� �%��empha�W�aUUs�M*�$of�e��# A arti�r"�c��*^ non-U�� @օ� ��Oa��6rafk. m�e&p_)�influe�<���B[�&.��eB �.<s'��N'OuS^&��4�;p`� "�&�?�5��a�Ia�a 2�ba�or ��@cTa%�.o��� �R�� �'"�?!�����n� � a]<? iA�$!5UP���Ge�Z-m�I���9:�6 ,�>x sw4:�*>y�!&ey i�bump,�cly vi�g!{�o"R+upp}�AR�-?��>� �&� �t��en7F�p::����%�Zdʁ:*�%7�0q�5��*/& tr�+& "[~� ��:�?� 4^Fi Bvrh�* R#J�g3- � BN� ,aVUHi��T6B�RBR#/5@�X� .25� )� ~M�"3 Y�. �f� !o�6�9���" �IQ� �=��=�!>�a3hc aß��+*p%����&2�m!& &�0 �1�&G�.\ truSyd,���(loo�Ki�۩La����U� y2%Y�ch*�j:"�!Չ�a|�n-��� �<pue�e|w {)��. N��"�����M-�.�2g 5�m��"�� our glob�S��m�#1:whBNJ`]��W�Z��!�� .�-�'uNa0&�o2���&:M�T,A�po�FK�c"Q@m% � �q�pooG*1�IV\��0Y(�aaWfP% �10�)�FeJ� l�h�3&� ly �` d yA2KasY5�=�O{h&卡f.��e�e "�eE� e�AnQj�ae:]xa��e"�e  �9P��)�s� �N�s��A:�D>b�s�kE�t e�..G6A/q@"io��B>�� " 6�E _!R�N�vaa�en"�t� �U�"�Y!L1� R�> �k�$So*�OF, i�w�FQg��m,�opQ�yc�?5z!Itra�FforYw>@�{!�1m�.�8��}= �nie�� " �Jly" �a2P*�5��8hec_B�}������!,/o^�V���EE�� enc�%g���n�3BX ed: 6o,w5���:����M3&�:O! 4�< }{(T_0 - -+ T !^#T #^2uS7} $L_i�=$T rU e܈��y�W�A�o} �BKaaGng�%�c�+A��E6�eir8"F5 adju���a���ԀA��a��re����kv�<ngYX�-*�LK�*ճ���� �E�AdQs̴a���:� D� quit� 2@Ca�M�"�#� u�.� zatwin�KJNU�*�R�h*�e�bgge��p�5Fon�l�� i��.Z*��.�5�check)�re-+!�!8!�*��!O�%9-JX � I�^�Pb$6� �2� $"0?$XBK"/ ��>�l�8ngA�&ST�z;��6����W peakW�vǰ�l�oҘAA0.1\%)j�lay6��1*�h� 7' q�EI� �:-[i,��-D���t*�E�;G��!�.� of� U���Er� �)y@�fÛlMT�r� �er�i*�D"��. Y-^� in�.J�aV)5e6�:y�6A�e��"dGsa�n9so�l��N�tq�1.�pV=��/ly.?r]O"� ���9�3o�Y9~,�� om a)��(blM cleua�s��IQ! "�2.5E��'�)A��byI�n odd}�Ls� f�9in-1� Ia&�L2cSrNT6�%n>a'!h7of=A�ik��m:�*I �;�"K2� !$� �.x4.A�%�b&*R�i�0.��8�#��#�8 or>���V_J�6|�Ar �@��f��!�Ո$v��A�*��e/| AbE�M�=�'"��eE�$� �v6IT�irM��vbJL� &�B�ali����".n. �(( &$��axe��q �'&`b��w&F[c)���0/lE(�6�V�OV�R���3&� i �d*,�atx�H ���6+9!�<kG�oJa�dɹc�y�).��� )%���=b�bec.Fun�&F�:���.%P^�t�V��*~  t ~�2 *�Kin�x Wr%�QA����s" *y\ti*��e$~Y�mp"�;a>iJ�4*N��imm��O\pm$1..%%��"� ��+ngitu2�l m<�tumA/I�\i�Q���ca&��FB/1� vp:g���%q�y,i��$!����adE�b"�����8D� �� ?��#2rA$. !k9�T5 Gr-t��8E6��'%;1�}�! _ o� � a-� �AX�502[!!6FZI{�?��2_y�hAr�(�s�Z�]"j@FbFRS""u&[�y�b�Y�V1}�_Jw$N}�1?s,| � �'�si/�eX�d-�{ *� -oɛU��W!F[ 7 IUicu>�%�"�$[ i�b �&�3m f �"�Z$Q#�4.ZF!�D�* -of-**y�~�E����3.�9kin_197i&�%j�&]K202�KKQ.�V�q B"^C��͟H%YR�R�):��2�Ś?�!�sam6�)!�*2��" 2�A�*�E� � i*���wqAVl=:&�Me"K69b�Xendb3y 4M�M�.�:u��!"��3U�1)g�y � &8J%͈�&.B9!��o.v\$(Z,A�z#k&� %+beJ7 F��Y�a��sޢ�an"7F{asa�H�DT i0f��A.� �u�hA� 60Ynarv�>\^{(X)}2��o,)/Z-1} \;.\;R A-3}{A} Z}{ "\ e�JmKE)�E�/*��ƹri��e 1f�n/��e��?of&1=s ���#���,JL�bgb8e.<�e ,�1�AIA ��2O!�ab�i�aB]�[BO~*��6�&!c/�t|A��,�lA�C-Z,6��Us+ -��-anE���3ZA�$�R�DžV!r��d�QCt u�2ion: eia�y��0&(lf}�#U. H ʼn. (Ca;� �+����O�r���!�"��8��"�-s ll s�!?9Q%�"�>&��@�c]~2Y )]&!�( >I��{nJ_a�� =�4�!0l.׿>�_!'6K ���verlap,�6� {K� &�-X["�6�_ mmen�*m#1Gl5 k&9 K����� 'i���9�t>wayI�9O! ��B�'m���{�mwo�-dSen"�(�gu��1�U9 �<*v�A,�:[rS~�L�!���>�q� `!s)�!�s� -Wof a2�� c&�w*�2�Z"�co�yts1� *7�$>�0�i-��:*�_$)y�"�B�09 )&%Rnk by s%�,*r-b -0� ~��� a" Morr�`yaFͪ��m}N/c:� 0^{(Z)}(A?'$alpha_0(Z)Ef 1(Z).AѨ�+}J�'s�d2Nsqrt{�^S� Rb2a^2 � e Deficle���H2�V9(G (A,Z)-��`�lambda \;dk; e^{-D(()( 0- "� 96)ka2:�^2}F�!��qhq�Ey �}fJ�f^{�}6��G �� + p!��G� -3)( �A}�. � {Z}.%�@.��� _fit�p �$l/u[a�.��r�� M��a6 Cedl"-&e� ]P: 2p >id amin,��tWd.�)}fr�� @!&���Q�S�P>/�"�7�?Z~c|^de2li�J^�OR�^ AVb� qst%�dM!""a:� ���\*KIX�a&���6��H2�<�!X��.�Compar�K�$E#� )�-(9�p"P}/P(1,1)E1 2)��"��5�UP e"y� f .Oy%� "MP&@ 2T!"g�"_NE-pY:|H!y@�imM�)2�:Y $I2��cG\�3�$p*� )Z���5-b7t�!�z1/$f$���m� �  2%AGs&RPC�#��;:�%5Z�-��q� �teAZo0N,P(q_1,q_2).T�I= I�;, - &+(+1*-3,Z)>!��2E� l� .&��Xe �Y � 4�o�2�-�"o�C�Hneo�w $T$~is 0%hR~:$Z�y $6 $~&�ew݅��&�� 6�&G y �5 �<���M| -#� J7e� Zzˡ�&~ cY$�-w*�e_pe�:�N��i^�J�G#�7& tep,.�!|�5�uj���!g ��g/;��*� :C �.>�!�Y=YA5 iE roa�tXT�^;]� �B�6�%��s�V!�NA/in-{� ge&�C:�3;��~4:�&B d* a44 "�B5M �e�K>cE��/in��QtaJ.y2o,�Eu� ��. m�)glso&��+iAos����b��a���o����"� a�Ajr�!�"����n%��E?�treO}EvAr.�%��">e�&b��/�;t<6>n�<2WY �*�multiplJ�0�����E��(I]�1I:� � � Q ��T5f .� ��[� 6�(80_raw &/*�(F/*[qBR80_!� M.b R~.�2�Y~)�\� &Us�Q;��!.hx�aHFZ��DF !�"� (�(J@ M��vVC F�^M3I%�f;� ��� a�I�>Z2)M�2"a�� �R�A���&� '�(��IG6� /ey���a�w1tX^�e�b�Z.�.6&$a�aFE� tMc*� d�9"�@ULi"�� �e}ris|)�)e-!�or (1"�7) �S2l � osJ*g �Me��U%.�.-,"bX4b3F=� )c ��cE2le��1�r��2 \\� goa��gez6E�6��>��r�?a�9�@� :�R.E�di�@]=�,�L3mb���'S�t��4B)! ?*�6� EeePY�"�5Q$�)� � %r,�e�L�*;�Q1 �}H� f q�,��� �Bt@ ��?�K:��3sharpl�qNPA_loap:4)�2� �;s�k�=�m� careH "�(��&��#"S>d�:n(�x elf-: V �Iu� a"u#in�B"i EPAX\�8:��ṏ�"2aAth��p�S�q5&��&N�&C"�B� �r&r&I*�Xde� � a<,O�$~�!cI�m�2�1�Q\s�&Eth�<�%Ot%�"q��If��"���I_a�� ��s�/]}&u ?�I�^�Z .Y�cl-Js�s��Co�() �!$s��rg�� ?� >M:�fD.�alA�2xa�&i+&C��s*��e9C'�s���� l -5� ���&%k,=( at�Z!%U{���9*��aTe�ed��*��&l�a:����mai�ag_!�Ŗ"yU)�i�� f"E>`R� jder) ��&U�5z�te�畲�!��1�U&+C��p#ű�fuMXAZ���rO�Fa��.KS%�F��"����:�2ae)A urac$�e .!h��a5]m�2�m&�O!Bk *"� &`s=�)N*NV.. ^ ���sre�� 3>G"ngU6i(V|:�/-$�cp (* )�$�6!�"?V x�5T M� �:_� BVj>� ��7 RYeB�!J� �]B� �u��%Zu�R��E�k"�cIB �A!E ��6H,It�ex�=�-O 0Li-like ions.� If one considers the low-energy limit defined in  early pap1,dedicated to> FRS, Doverall success of`500A~MeV experiment is cl WDa push beyond this �D. Nevertheless, fu $r decrease� �for]s�Dsystem Pb+p would :teK,problems, as4multiplication�0charge states Nlea% addi,0al complexity�4analysis. %*�( \appendix�SSsec� {Rel �Dbetween straggling�-rDand magnetic-rigid�twidth} \label{chap:brho-e} An'J� -� �%xHuncer} we have showa�at%contribu!�A�$�$~m�total G tainA�8s negligible. Te� eads� dis�"!QinT2$~A/!zM>AR;d%�( 1> )!<%Q-59B{�7} Ie-�2}{ B\DividA8by>�ereplac!�$T(.q/A$~terms7PLorentz coefficients,��getV � �=}Y\!beta_2 . � {(i )� _1- 2}-� O�7,an eventuall��troduce�$differenceAS� �ie��aboveuKR �Bq��A�left( %f 1 - �*\right)52Y+ K%�!o*1�12FgIa�eq rang���is�8 (a few hundred�g�^toEQ_{1)�\arrow2}$. %\vspace{1cm}՚`thebibliography}{00} % S�O� 1 \bibitem{FRS} H. Geissel et al. - Nu  Instru �]XMethods B 70 (1992) 286R0plastic} B. V�V�SA 364T5) 150TA"8} K.-H. Schmidt�W26�87�7Wt? ,t} P. ChesnyUTGSI Annual Report 97-1�7).L2O GLOBAL} C�(eidenbergerW�V142f8) 44=�karol� J. K - Physic�view C 1�7!@203.�3�DMUSIC} M. Pf\"utzn��86�4) 212d4dLAu_Fanny} F. RejmundF �@s A 683 (2001) 54=�8Pb_p} T. EnqvisJ�.D6D48=; Pb_d�D70 �2) 435�,U_Taieb} J.  n�724� 3) 413-43�XU_Enrique} E. Casajeros%�0D Thesis, Uni 8tad de Santiago $Compostelad2).�LS�Lindhard�gA.a�S��senh66 A 53%�6) 244])�1F" -��95 �.~ U2UWeick)K�S5�=�ATIMA}!= code � $downloaded��Lhttp://www.gsi.de/~w�/atima.1=�,morrissey} Da�MJN C 39!N89) 460.R�%HNPA_loa} L. Audouin)�{to� subm� � �8U�9� EPAX�( S\"ummerer%�B. Blank=X> 7011�161�H�Au_PepeEH Benlliure�B�2� 13 %J(Wlazlo} W. F�R�� Lett�8i70) 5376KMoni3 M. BernasLF�72Ix3��y > doc��} �h%� � % INSTITUTE OF PHYSICS PUBLISHING#z I�  I`Prepar $an article�pub"^in�� itut9 1� I P0shJ jourgusLaTeX'�� ��  Iy sourc�@`ioplau2e.tex' usiLg� r`author� I(guidelines'^ Q#a�explain�B demo# a�use9$� RI=@ �4preprint files � ��(art.cls, io 12.clo� 0'. :: I�  I�=[itself�s �� & �B I� % ��m�%  First"�af(acter check& ! exclat on mark�`" double quote % # hash.` opeEC *4(grave) % & am�A[' cloe_ 0 acut0$ dollaY�%n cent�(s entf)Ye .)- hyphen=3 ,ls sign % | } b~~ tilda  % @�v5   _ un�core % { �cu� bracC} � �[ )squar$] ) A(ket % + plu �) (; semi-colo, % * asteris%�: $ % < xangle` > x �,nmaB  . fu�,top % ? ques�MQ: /��w� slA3 % \ back ,^ circumflexE�dABCDEFGHIJKLMNOPQRSTUVWXYZEdabcdefghijklmnopqrstuvwxyz$1234567890K�  % \�0,class[12pt]{�� } % UncomP next �i� if AMS fonts required %\usepackageAms} .epsfig}2Jfloatflt6) subfigure:etT6ro�ngfnew�Pand{\Xim}{$\Xi^{-}$} :pbar) }^{+B#Om@OmegaNCOmC%RF$ptr}{$p_{TBammN2��(s_{NN}}=200>�6B%62.4$!b1�title[M�-�4baryon�du��top RHIC_ies]{~6in Au+Aua�li�sFJy2amb� bulkpkes���P{Magali Estienne\dag\�iSTAR C�[bo�� on)%\ddagA�8footnote[3]{Fori� W l���(acknowledgeA�s, see A% ``c.^s''�qd;(is volume.}�dd�{ �LSUBATECH, 4 rue Alf�lKastler, BP 20722, 44307 Nan&8Cedex 03, FrancA�0ead{\mailto{m%.��!D@subatech.in2p3.fr�)�ab!�ct} Weu&%8Lpreliminary results �'zZ�\2@atE1. IMmp"� �!8f��Vof�ewmab  iscussed�e�(size depend,�pJT�Y�sNinv!+g�to stud� onse}6��k�F ilibIS��medium �n#ar modif��4of $\Lambda$, �u$Ek$�$� also!� sent�!.sup"�$at $p_T>3$!V/c orts�:Dden�te � �Fa� �s�ra�N���veal t� a ( hydro-insp���elp y 0decouple prio an l�er�� �W$their flow>Hbe mostly developed�a;onic l�is idea!<emphaA d�)� asure��$v_2$ ��$+!�p%���Omp wh; beha�Ey� NE-�+�)�}$�,ellip��iI�i!�!�� !�$ reg� w3aBs� � Iosca%A:� is observA y� %U��aX PACS numb���\ message %\pacs{00.00, 2  42.1l6HS.�1>Ps %o{\JPA�C*out$� :page not.2 make ">Ia�\} From Lattice QCD calcu`s \citem\s03}, a fast crossover %A"e transiQ �a hadrE]�o��ongly-%�aceHQu4 HGluon Plasma (sQGP) �shur03}$$ occurI�crix te* at�$$T_{c}\sim9 -180$2van�net-b�a�ity. �� o*}w��o d �{ som� ��onse ���p\a�l�A�6HV%v�mi�u��he"�! . Si�mma�!s-i0is much highe�J�4of�Ri,�M!�R^sc$,!���is���abundan��)9a QGP IK��-�rafMu82}��erefore� ?Erof2vshE#yield in�É8:  fa��"staG��[ �$ chem� A�g�� reeze-outMAe f5��ir�{pr} ��Vs#�k� welli�r�bF�s � 2win or?o%�l�&�i�)x%9pro$�8o look��an���sec$���|lliv~"BXis%i��P�!ly,Z(!b�"uggest�� s beatmore se��v�[��I]Bt�Hto.� *�$ d af�b2�9�M�Lstar04,HSX98,cheng03E��L2�by%k��!ir.2radial� . As H builds up through �%�o  e !�,��%o q,include both� "b"�.0,A���. N� I�of�est!Qdir  `e two6r . Further!� , du%�� init! asymmetry^m)in non-�r�%-s,:+has ovee� be aeb -suiA@ toolE��tanM"o}�M:n$�.Olli9��A2�ofR�A i�� %}di"� I�'direc�?r6Rn' �,E~< , ^ 4/c $< p_T <$ 5 to�)ossf$!�:g �eeESa-dom�!R q^b��)z� .*�The>�%K�' � �&�} =dat�1T�D| (1.6$\times$$10^{6}$ minimum-biA3nd 1.5B%Qq_#s)��a����$���M)I S�*�I�) a�# bve� fŻ$of 0.5 $T$�C( main detec�!c*�� cylindrś Time Proj�v�.!�nd!/u~%J?* ReC�yA} %�.@ll -d english nom� L�/{BulkNZ"> par:qz}�+I��hF} (z,� �O)<��� �s!�p ,�!:@�!�a$no�1.j 0p}$.�1-�&,]ipaF(af,B&FR��ed�/in GlauF model%�2�sunŚ��R`!�w�reE���Biph�4�IE"�e� ����9�4�-`td��4o se w$N_!�t}$� it$:Sp"��� Raf0� �+Ysaps)��enh� % ���at�5Z*�5j/at SPS bcab#}st�� �of dev. �/ask��t�JQ�6�q\ium �4 �s N.?�3 chie�Q#%��56b��wh ����dH i�A+4. U� E�assum�"yt �-�eo�#8 rue,[el%MM a ans!BM��O"< �0�� 5 framework!Js�alI�`y*� s7ful! describ� umera4iYle �31X1t��%-var�41� Abew}Bs�delD7or�� n a� $V pa�x �Q!6� $ ne�s�)�� e� averag"�0d7y,YJpoa]i�"t�A:M� ��iv�v$B:$S���0�� $Q$a�|� AnoE��!�great&Z! our purpo�Eh2����(pa ɿ� g�6{s}$,�D# ��ga+�yi�1-fk@ a?i��!��QL�5u�.�{8a�M��2$u)($d$��s�"����h}$w�Ri��A�m�� ��E�E+2m w!e#��f�H2�1A��5��Kve�Jf 0I�m 6%b~-�z����6eAw�Idɻ�!'oraJ_!o $M�{s}^{n_��wa� $n""!'&5 1�c 5���$��ea��L#,�� "� � -�5�a�)e�s$�l)`on!�~0x8)�G�� �s^2�N �-�I�� &� 5��\! Z� >���.=!�)�}>A�j�Fig_FO�G3_200*�7.cm,he�=7� \V  MSBp�@ _fig� ing_`M6 N6.7b�� Left : � g��m�*?��Y>I(s &k )�� 8 bin}7b)!�a .\  j}& �AeFF��R�A] one. R!Y :�7�6C _{d�`m� �"T F�AE�4.��*�Yn&� �fi���y� ]&��-�ai�(-w" �Z�as ` J+B&�0&��ga�inF�a��&1a� Fz!�� �M���%$�* �$,s"� umab�% omin��by soft�"���>�I�2 G(�` �]��1P��b�!2v!ev�)`fireballza geo��B4Z�� rFh*6p� E�� .}3Jtak�� re?�. Look-di.��"�W1 � "m!�!� �ly�Ldu!�.�D�$*W "�y�U�*�&�$�"�a�e�dr�1c@��2���s�^l! seem��de� e �C�aqM<��a �p��s��(s40&*�j$re�/A���Z!eletely� eva#4orZq ? D�-% ��M1th}ned 8��   ;e same?(l�J� +? AA:cua?�w ssue wasa�� �conQ� � �*�#reQ� orig�#2�!�/on�r�rd.Fls�-AC &�56I��T  ?�9a�ag\E_,A�]�a9���etr�� m�sc,f�as�dd aJ!� way��(ed-0g�$} ? To go",HK � mpreh- o�hypero.�,�'�2�#a� � -)o�W%�e]�B*�Y��ŝ��,�pai")!n�!($R_{CP ��� e ,"Jbye.�8��v�to. ��ӁGa�a 9y�F�!�b^i1 In pQCD ɉntAK��7volm�M�*!�A�es�ie�hA�scing�%%on�5^vid�8���1.!��Q1} �E�af= !�(iU >3.5�/)�up �ta3@�  Z��"so& instLLo#* at 1!y����Vf�L)��in00-in�Gd g�,�'E���GVWZ}E��I�l�f�&�*.+�d^�0��A�<4�su"9*��4dynamicJ4I���)x$,�B (icU�4��!!����!]CZ1*n&r h>�+�JmalA9 *� r"�&9N%FA��. ,N� !� e me�J$a,v�qi� "z .� -��JA .e]O�&exh�F&�eo:TVg2MwBlas93�L.�� &c<} >$i����"9 !D� }.- 7Z)sP wWob#2s.rWkM�*��1�N do 1�Dextend "�P�ot n�R:6 !u� %�s�-/e�s  -1J�5s�s %!�AsG eU�asJ%�J#��,'�NfVW PtmeanAll:X8�V8(msbV2Fig2_5*=8&�b� ��>�.�"B'a#E�0 K, p, \Phi, �%��� �6!Ds%]&�F�/B�kf�JF]�b�e�- velo" $�JG:>$It�2��#Zh�$2YEb�=a�d�6$e�L! "�!)>;! ARI6Aza.� �9Ta ``b_&w�fit''6!sum��alNe��e�E�a!��zexpK-s�Ba� �2�5=S$$�K!U$$>�3!���-�per��e�mAi�'Kp$"�" toge�(�;�$\X>wc5ly�� prof��(r)$=,s}(r/R)^{n}$� ��,e $R$����u -'��$n 8�)rm�U%^'�y� 6�>� ch�3:� � -��~?��Se�(i�E"i�B-5~�% a gix/#of]�. Nine�%��index�aJ1 (.�)�9 &�.�A�N�!�-� ), f2p�(,A%r*C &�>%�$�1:� =L%>@}�>i�Z(G/(� � �~w$i V�!�? sigmt+ ntou�%.�#�AHb�AM%��|T_�$>�). �=7.�!;5 note : 1)#rz no %Fap��#��-�!�$pMW(!�$)�V�s , K,p)~H2z4a_H3Mchax&�E`��&;� � ; 2) "� ��T�0�5� a2^, -P0=153MeV\pm20$�8,&�:$g(cf.~R2&)�5a�ůR?� &5Qly $9 l� 1Q3 at:� � � \9o<d�2ierA�!���s�. ; 3)��3=1)ra�+�F%  :on�,-D �a�very sm��* 6s5,:� �e��9�I=oR�5>i=@� �,�beat�#&2 . O�U wiseUs-o9A&�96 MW.C?j<�,ra ���!\�߅!�Ul�1�EW . Co�X�:mrq�,��� )�9 ch}>M�!h�t*�;qs�c�J��timT"�wo.%is T2ere!&��Y�:��.re.TQ � E$wh��V�!:oo�HO�ir�"� Bic�1�E�� �Yea�Y�4s&Y1i&� atF�%51OK (7}9~=s$ve�UM�l �!.?.�(J~,M>en ��q�]aN�I��)n2�Of�r 8� �'*�B��~-<3 n care�#VcaQL=�%"\�\ai� �=l!_� �effec%�reson�)��^amVA� pi& &�se�'�+ud�,M+n�Bfuture�� 8SQM04XiOmV2VsPt*d 7�b�qm04V2n4n25�.Ry.As� 6AA$v�/��K!^{0'ҥ�F�DTK7 K7�0 s. H�B1~)��di^L �`n (colo�%zone)&� E2B� ��,J&&�b&2:B n�>�p /n$ !�n&�H-��a"�; scen:� R�� igni�D��)�>O R�ͮL*�Ů)) G��s���y!��36EF~4Ep4i5m�@� ef�1JXJ�~Y �5 OmegT 56�)�& �*2�P6..9]8 mLambd>�o Soer�(� B�� !��ariso�56O0�)W.~R��'��e_zu9��"� folF��&�&-kq�$p:.�3(6�a-;6C3GeV/cA�n�c��+b4:;i�9 20\%.  eR��!��n>�G6-�mC uo}:/�ch!��Z CAT ��is �$�)"q&isH9an EOS�xam2er�o� $T_c=165� )�*G?mW�-&� �6B s;BL13� HowZe,EY1�>2)��WYI�s }!_J<pr%b !ԡh�|`*6pDm�)s2! �M6��$14\%�i|= �. A� M= $n��eQ� &�G)�v]mJ�I���@ fig��F ��,%-K ). �%�-a J.!5mW6�*A� 2.5"?�'&�.t�socc�yJ {T} E3E . It��fir�* -0ou�estab�4I �Fto �"x �a9i����!�notM�&�� !�� *bINOm.m�m<B�ruppor*� J$$ �-o1as�"� ׭� Js.<sN)E� G�� �-X$'BuM�O �:al`�1j�uh�� �3���P:0f�$v� �CEWcan!�be�#wn.y�tV=Ris �&�!Ay p" coaleX�r>m�e�mB+�BFrie03,G?>03,MolnVIi�5� � �Vj�M s!�2q� :B��FM��HiiLu' hq� part�^�!3�� a$h�=!��&L��1!�um�|A�6�! �� . S5I&" "h alreadZM�X{�Ek�Fc k i�Igs���2>s��ul>&)>y supe3ɣ��!"�.B s�!2/n=f(��)� e���0 l E�as &"� �in*/�e�)����*20R�>� B 3��$"�0��o, rcp_24jan2)<10vs=d�;$cF�;�! 8~"Z�P�l!OM�91��+�edq&� val,"�!.�!W2u aA��&"on���" � �[ !�QX "&CCsb��-5%13.ge"A=4=�@=12�*1 &�N�l� } A&' N. �$witA ^N&A@��R���at&�.�5y�c&92�9aa��2A��*%�B!�/>����!��T=CpR� )QoZ6,#S3%��JHGa[de�Rre\�e� ��r&O%8!*�s$.�:�| �@:�G�"� Aaq0ͥ�e��an��4��!b&�5�*5-"�N:=Rt�6�.:G*�,QG��/�+:N�� ��.B��j 2 V��Kt�K�"��"�S}R�,tY��>�a{25} \! skip&cy6}fX ��04Fp�D.  a�#jn%m9�p092301 ����v >;�Y*�_�;iA�BrekiesAS. Papka,GlMajwi, Zako` wOcm�, Acta-J Pol. B %%�L. 23:30 2004-11-11,c"M ed 28.11.::b{appolb6�a�' } %  b�)�S�#puEPS+f&�a�G %-� �kf %&�c� 3 BEGINNING=j TEXTj> 3��7g� Y5(% \eqsec %�w�[�f to getz �sy� ((sec.num) 9b{S�8D� t3 on E� s \\� �0Ch�PP�jEmi�.> $^��$Ti$^{*�@thanks{P&�,�XXXIXY�School� � ics - IntplZal Sy|o`F"Atomic�ei� ext)^�F*m , sp�nd iso " -z,a/Pand, August 31 - Sept�Pr 5`]04}a�gb {M.~q�$^sQP.~e�$^{b,c�A.~Maj $M.~Kmiecik 4C.~Beck$^b$, P 8dnarczyk$^{a, dA0J.~Gr\c{e}bos gF. ~Haas : W.~M! czy\'nski _V.~Rauch&}Rotaau TA.~S\`{a}nchez~i~Zafra0 J.~Stycze\'n M S.~Th�n $^e$RZiybliy�| K.~Z�I= \G{ �(Niewodnicza 9�T�te!�N�M8, PAN, Krak\'ow1� \\ �IReS IN$_4P$_{3}$-CNRS/U�qH\'e Louis Pasteur, u�$Strasbourg�cXc$D�mt���Uy York, Hes�!ton6r(ted KingdomLLd$Gesellschaft f\"urA�w�ne.\ schu�,Darmstadt, GnyB0e$Hahn-Meitnevn,�olin.} A�.�_b�Na"'d�! >�EW� eu*s pop�_�(a�f-evap�e �Ca�R27}$Al + 19}$Fa�8bombar� jf%:144~MeV,"u 27H6�b�2�<oscop.sT��*�V@array {\sc ICARE}�$VIVITRON} sYem^i1�EN(Y).%1�#F���+Fcoinc�Vce % =3 " idue3� CACARIZO};s�-U -U !=����i-tcws PSCADE}9]+ x&�8%�)R�hap�Of�,ed $\alpha$-1�s� are A3VH�!�e" `Qpec�Rnom�"m$(e"3 n ?F�l�[S8Nf���.om2��Z ]�\0c({25.70.Gh, Jj ,Mn, 24.60.Dra-�':�bY4$%cU$yK6�r/$%�a�L!�2��etheor�_al w4i�i.at�C2�[/$�JcSN of l�5-�e�i�e� y e�&�?pro�F �7 riax�*-��Xde6 ��Q�!n4Giant Dipole R��$ (GDR)��&deQW>�~CMaj01,2`6�}5}$Sc$ (Kic�N renQ�vZntIl&V%-�LSD (Lsn-y� Drop) e e0Pom06,Dub07},!U_DJus!scrib"�: Jacobi)GI�)�JD��!g'R �3�ce�My5�AC anguYp2�11�IJ�(LCP) 8E5�)� 0 ^{44.� tePap04b}la|���(���I��s!�16}$O��28}$Si1dap��$^{32}$S &12}$C%4a}�( a'���&Rd� !3a�Gf! crete�F$-ray=��re 1Q" �"�~$N~=~Z$m5 be,/�$is�!�; (e.g. � Ide,� 04}).�^7F�.fo*pV:�A^LCP5�i�(�" (Eaha���;!U�k~+~$^�ka�i MM!�(E_{lab}$($^ 9)~=~1�!���#! ��� e2�etuMTdat�WÆ%��!v�@f N�laW�e�D�� r{ Fq^2�}��2&�3b �b�a �IG �<(F�m),$$Jj^ j�g�v�D(4$^"�_ $) BGOd3�.�+!�46}�>� (CN) �A>� 5�."� --�V!�aln5U beam� 8+'.csX�c-!�b "JKre�alqdvel�6.E;res�?1�<-$Z$ (C slowN7 )��ŷQ.�(. A fluor�3Y� (LiF:�i( $\mu$g/cm$�Jof F, 55FLi) uiD ,bonta(2:J)% ~4-� exci� y���t%�1was 85 E�$maxb��"�8 $L_{i}�Trox~$35~$\hbar$. High��$�K�s��GDR�Ŕ��d u�N}6�a�heavy�Tg���\M��Z,ix gas-silic�B��coM (IC),E��Rx!4.8~cmD/ ion�0 c3bQ -}My���Oi"window���y a�~%��$ick surfac�BrF2�$ -�IC) lo��%\Th7��14=\pm 10^{\circ�M�*re�] tinc�l�� plan� in- p?�"��t� 's!� done1�aKri..D4�Si, 3022!GCsI(Tl))�ced a/]zPa+w s (F�2�,�25�3 3 4 �6-Me�wo-?Wj�2� 'ed!}fo�den.�N1m 4�~\leq~.�\pm 1�a��K$7� /=E�` step,e� fina?R four|BIC =�].a3 mostB� ($!7155'�R� 16�nUT�l%�A=jQ�I:$�31�$�Q�fil{#� isobutaneAa�{QqY40.5~�!~g9�gl� n u 49.6 (in y=� u�Blow��si�,ane�X�j�Btj�Yand l� �c.�� c%�s� �@=�i2�|:i�ap���oa�v�2� Th ��T41}$Am!h62;"�$\mbox{5-9}�� �|:!=Gc &�3�4��� 1}$B, 53?W ;��\� �19u��� &E A-%o � R,�)O4}$Mg� �@ a� ����� �Gr�F �=��[ F!f��i�ed�eM1 a.1annfu�P.�f�6sy . Ex�#v"WZ{;J�=> ��e laxor��m"�Je�s 2>~=~�-. ��$ �*i�$Z$z 8, 19O� � m�^�l2�=~.��k$in�'.~1?!7solid �4. Allq�d1& ha(0%#Mj Maxw�"a�*�Eani �!I fall-offA4 highIy��das,,A� ���)�� !�J��p/ �l-}[htb] %&{�4 $�-&�x�K=125mm�Sa�$Z18.eps}\\ Z%9�%20%&5E.) ()s)%� ed (% �;>VeW&� for 6�]u��.s� ecMrt�"�.t ER'V4M� : up�rV  9: middle 20:��tom)m� ICA2�A���$.� 1!٩�ca� dZvEd�� pm7�:�QRLDM (MY!F)\�;�a��(E{ ,�F�BY5n&G5���S� 6h]�%�*��"'nof� ."^&&�{ �"�Oe ��&Ma?J4B�UPul08gj- is bas!r� e H�8$r-Feshbach!Nh�sm?LBha09,Rou10,Mahboub}i�� 5Yn�u;Gcayi�K�dtep-by-%*� ed! 's �$�m�v�&r l�tU��e xm`pF(cal ad�Qage1% i��W�.� TyM(���po�)%��&� e�Si�lacc�i�R]$�!�B�6�Amv0 can,G+;%!I !�is, con�j"pn-: ��?B�a6��a�$ �C65FM�� їV7�5� �t;)of"� :��]�.�(, �REEar|A*it�}b�&�tdp^8�ies, u[m���Nh!�Ref�U�/6 쁘i|*j.�� �>l}z|al0+mpen. Q�� �Dnel.e�B��w� oX| d:0 sphe�V%VHui11�2ezicU�f�a�ofaticIim3LM�Q<�z*� , wT4!�c0fin 8 �9�l&'�"+. Abo[-�)^O�xE�?isG!�we2"dAEAPch11�UuN�3>V?ort���A ��Q )�*E�!=B? : (3s,� available�7�/T4�2is "�o"� �[7.f~FL� -de�at2y�* <m+y!?Q�"�/HRod ng Liquid MoNi(�S) ��)%a�]bAeang2M�ew��r�Ie�rL���6��#A7ghe yrast�!�.�A6�at !�A�5PbR�i(�f7y1� em�Awu�6"�I�ies. A:�D5.�!b]dedi�^ $�_{1hd ,2}$: $E_{L}=�X^{2}L(L+1)/2\Im_{eff}$ ;$= �e}(1+aLB24})$ -����Q"J�$oA� in��a�3� x� H(2/5)~$A^{5/3}r_{0}�� �yeڙ bodyQ P~!�Qi���!�!&O��us9z (Ӄ to 1.3 fm��Ou�� ). AHq,�:[U� x� �appnn)�-Y�T ��y.R^$.~2 illust�);�=�S-1 ! w3<��N�: S� � a�Ha�5�<�!C�c�{ o $L!�24P���B,��) �nZx �u��e~=~4.7�x -4�$.5 .!7}l�W.�% r)�B�%�� �N�I�,�� �U�.,���"�i(:�w2�X��-�.���� �Aeus�T�k�$$L)��e: � �!�E[D1�vD�0. P�O *n!����JN E-�Fz~=.�M s %�6 �ރ{0 ��Zin12}F�D N�ig{file=e=3�,�c6.s7cb7��&ŝs%>Y�y�?I��aK��ea��!}v� text"\ A�c>�"��n� �9�. ���>D!sMdtop.}��N� E�*j�FiXMj� *l�x�Ys 6,G "� �2�9�. �>a ��Bd �J.Dn$ V�"� i2m�� ER (�&�)�=?Aaebl5��aa7-� _l�1&|���}2nof:  �"" !�9 b�c�- sponc'S�� � �# 8��(sR<V=y��o,H6��a})Lth�b2���� 0.6�C A"��[�;ch5�E"#�+iTgood �!!�R:sM�KA�&�J���O.3eity � Q=%.9m(C!! wA�oc� A20ETina�6YB���Jimyy 9� ?@)�ed.�(ra�unJ}�)��b�&ّ�ss��nJQ � 8^�K���BI��P20!��(A<[# !�sV��\�9mDe narro�-�&� .HI Jo�d%7# st���CNq�#Z9�S�%�lC+Ir6� �� � 3vj,%I|{�WZ&,[SC���*���� '.\a)�r�l#�&f1SW&vS!'tLdi%*F�!proton he�J���"� !oN^ Q�2~BMoAiل� .�!tdirm�th hypot�.�woBork~��a�<o.�CPolish����eE�Sc=��J@ Research (KBN Gr�@No. 2 P03B 118 22@{Sex�g�4 gram&P%D {\em"�. N��a}.que�.\'eai+mT des Pa��($IN_2P_3$},eB �:�. L���w0s w�%��&�6!�staffA� �m&�$A��O�h uDtY�Vqua-�X�}֥M.A. Sa���Bct�fts,E&J. Dev��nd}� FuchQ ��}ll�)-�A�yA�Z��2*m&*� >55{12�+:�6.} K75.T� �*&7 Ph.D-  -4 l Re�6�',\bf 04-07\rmS4>S3ץh7:�(roc. 10$^{t�v `yal CoCi2&q�R$Me�Xisms}, n�byN:�Gadioli, Ric. Sc. ed Educ. Perm. Supp. N. {�122}, 37w�3);�-[;307002.&�<%a^�jk 34}, 2343% 2 Ide}�Ideguchi:!hy(> Lett.�eh2225092kN+�- M�!Cm�}%�A738\rm�/ma;3 P@ Int.A�Mod2:E139q�;E�"|m� rein.>/a5 P\"uhlhof�=g6��M28[267a�77.X. �hattay>_5>6� 5}, 01461):2?R��W�5^�6T6T34612%�2T �:��U9U6U2Y� !�$R. Huizeng�4!V 668 (1989.V R A. Zingar� ��48}, 651W�Q��>d d"��@�%:Y�p� int,aps,��(]{revtex4} >0 twoc,n1� ig8,f#� ix,sNIy0pt=7] %fV~�:�6�J� \use�;"�;.gӬicx6<d �} \re.��a+AT}{0��>#op."90BEbo~ .%�.��: Hind�-��Heavy-FuK at E,: Sub-ۋ**E&< Open-shރB;  S6�{.:$C.~L. Jian�� ,{K.~E. Rehm})H8AbG!$ ),R.~V.~F. Jan~l� B.~@�(ack}\affili�v{�3�-Div}I , Argonne"� "< y$, IL 60439�P.�on6a6�8(Notre Dame,2 IN 46556O(C.~N. David�(J.~P. Green�w � D.~J5A��so=CL�3r6����S. Kurtz6`�� R.~C;rdo9 T.~Pen�)tonc�al� 5�Dec��d} R� j�& v�]�aul6�Hebrew*�:`, Jerusalem 91904, Israel�D. Pe�.�0D. Seweryniak,$B. ShumardS�haX.~� 24I֭nihat)S�Cu6�� ." m.0 \date{\today��n2;{ *�"CkT � �-. "S) $^{64}$Ni5�$Mo& $"��]� a "�`�sim�nb.��ens�" c��d-d q 2k��8"p$mR��Edsteep f�'�N�at"i?sub"= j� ThC<� M *�Kh��!A)=�5phenome{�8L2�!��$lVu�g� $S$-&L�R�+ iv��o�[�y%��|v1.V0(E_s$=120.6 �<G%$p'o90\"ߍ"^ )y�s^{ref}<$�B�&qK �Pd�z �) �2`&Ni"�o)MU~s��b�;2_i�A: A=100-200�-?"�T�a%s���&�" ~5Ytn&ar�Mu�K�}a"�>\4 �;�; 4.10.Eq} 2��'2J� %sI ��\d�q�.�#dA�iIlyE�m�}"forty�;2��i�a�h$A��"6 &�~ ]�]( {sum1,sum2�m345}�upl.�*�Ms (� �-!�'�i&N�lM� {hagi0,�)lNRmE , ev�>v>ra��PЊ.��71]cJs�P xC6er�,k&@DYiD�U! no s>Qi�yL>3q�Q�!#2�-Pj{ 0},ki.e#4ve%�exngW&zliS��N!Q� �!Ktp�%r!j��%p�A!1ttaof1)y� ��%�stiff�gq� �Oo �!D "?�����)��:cE�aٮ-��7 ���&r6`y�!ns9����!��]) ,���t-�i8��.�I�b T �5n empi"�!ula6%:� -�"1�eq1} E�]��a = 0.356�Z_1Z_2\Z�\mu}\��^{\E H{2}{3}} \rm{(MeV)},��hw8@=A_1A_2/(A_1+A_2)Rsoq$5����,�n g-l"d!E,)< �3u.��S-��"� 5���nzA ro{{btAA� �2�@dUuA*�9Y�?lex�ֆ��. auSpy�eAJsy�of�erh� "�~JinflueKofF5�J%]�beץr���`�!d i���)ed� aIZ i�2}�Bn: @358&� i�$beck1}, $^+� 00 $stef3J$ $H�5:) 2(��)I�)W���[Un4dQ�'?ec'���cG�PmRja�w6w>,v"� i�P Y��i���M�A�ab�$9�_�;aa�� 8"&U Eq.Y_a�-/="i>rQ�i��A���i��5� %� YN�<becomes.�pronounF whe�hDq%� �"i(L/a ��]�(�pyb"&�3t�1f V.G J} &�!:ifig~Iv �&a�j�Edat�."�d6�#U��6�m!5 is $� 50 \mu$b�A���T�^�C�&ͥ9�u��!M�Esk Z�"��eYsei�e�89}$Y.c0�$R(.(2}�I�100 nba� 1 �lQ5iv�sAp4c�W~��h.�0!�ziG+i٨� ������=�y�<s�2� r� �:p�box*�#Yg��k5f��} % -1 %v5{%E�p{%D7=270,�8.5cms��%eA�bv0�%��(C5%R�,B�d ��E !�"�`���ME�,�: k2, ��0, % 2, acke}B..� �qv�q %!�J ppb V!E���6/ %s*�i�"�3.>A�6�� !mU= %LE?� one-dime o, pene+�7*� �+ˎ�3 %�^@���2.A1labelA{1�&I~t5&Ȃ papEr�&��Bst.�e)�l.� by���AJ��!��=�3�c:I4I@�$Mo� K��\, #! a �1SH al @� ,�!4���1  �8�����"En �&�B���2�� %| *G �$rehm, halb�2k6F ����owo� ��� �^0.4 mbF�9��#i*�� (e42G�w�#t �e��N�QJM �!Eu an�I�ѹJQ i6A, nb r,�.#% l��ahqu� 6� 52i:�ed~�?��iiR#�;ra� �" i�9�a�]�%y X �6196-262��%�ruO�r ar 7 eler}� ATLAS���"�*� e", �m�"� {,%l$K $ 60 pnA 2�$ mel�5 p;1��" maN�(al, metallip lybdenum "�5W a 40ED"!Fca�Efoil,�Rve�H damage LO! l������ �.� � 0t�D� �m'� t��v$��lmonito�Aw�#Si� EHKPa��# AC���O8�(186�N%f.� r+3�c\*g)��c�wAf A�mA2N �O) isotopic ��cFA00�@)(97.42$\%.��ċ�'�&i'e�$^{989(0.96\%)�k8A Mo (0.286)345296AoQ1 O({)dJKF���& M0lA�) zer (FMA)� dav� �-��upl���alw)!54lit-an�=me�֜-d�Q�udav,�Y/, P%��ED�D��'�C���3upB s��Ŏ �6�,pusO�2�1/! ~ !|�mst , ���I cal-�&�CIQ3.*gur) $ PGAC-TIC-6 IC,M��9�<e��symbolsI/)nd��$x$-$y$awy  �<e�*l P22 - 30ZVr�v0.13 m"� aOK�  �ron"P 9B��anxP��a�"m . 0.22d� ��.�third%= %;f��1|T�5ow����kinUKx80(�%d�>I+�yn,viqvށgood �&�i�R?�cH ���|"yd&��!��new � � 81 be &- else���� �� "^��[hbt]"�2:� nimo9{�8.zyx2#:�of3de6'>�9 TcS9 Two6�lotAyk_6$ vs.a�3&3{!�7�PnT66(�6 FMA,��ag�&�""bQ� 8(198.8 MeV Y!� 196.��qixis-7d i pA4-(� �Q les)"M +:�N ��eo%�i)��t�csG� YE. At E=2��-96��# in"��p�C"!S��.= Vq"E2:;~,?# set0 %�A�%t���,g��ޭu67 9iw .P�#�O5�$�X = 260.cc(45.8, 209.1"M7.1%� 202.��ll2��!��[2@, O��0�-��:F�FMA��. i.e."urk s �_� Ae �~��st��Glyb69�!��io�rs�2,6�)�� � te fI9I��� �apA��to�<:�I� -Z.R<:66*&`[6"PG� �!=�!�A_C PACE�� pace*o� Vr��.�*�&1Na�Ref��!�r�R�In 6%% heckE���,.� ���6.i�J�=B9�� ��� Ł"�9� ASOZIE�l�P�a.�� i 6jEt�J>�w�U d su"� ;6:i� �@s GsC��a $m/q1{"��I+fol�P� �Vfing. ըin%-�)+-k� �&��XJfukg�m��e"BQ�_"4"ȸ�17�%D=k�)� V<"܏+M� �M� �s, �W�9difb;zaK)} GIOS C�&xM�="�A���E�10 !�7� 2�61t&�X <$ 2.3$^�X$,�FMA�a!Sa��k5=E'q�J�Q.�4:f�w/�=8[:�2�2#��v�5N�����z�&�n���� eAcb�"�,K$ M�cx�V-N ��� .W o"n��O z"�4>�� P�Z � � ��k 3΂��e�a"�D&�2Ug=� faruin'] 2b�6[�]3�m�-a& �*t -Gq=�p&# -B��w�a d!�(��C�S$ !$�*�;k�� "�z%+� ��O. Do�*�.#���30 !!NA [ld��.��Dbas�-�*2"+G�ZonHM�J.Av�IMv� */ R�9<a�" !8>M a. EiE)o� mall�s �e-�eam��js,�,� #ip�gare�@!A``$stop'' $ �sA�d6iF��\�.A�>�of 242�"d' 12 h\�ru%�AAB� >2�"� ,wE�e�� -�؂��>�4!o} �� #a�lyH := !�ag��*M�1vBq (.�)P%NoN-Qr6o*���  -�a=B. n!3��15)],�*I$ �6 %�+{A }$&H�f�� at 2"Qea�>Jq%as*�Fh H�M b. M_u�-�!rsuspic�K��|�a��t7 �g:2 #2 $+b�  j�. By exa� ��V��Bumm�FmbV�./� aO+� �!`2��r���a�2��#al>��Q does�E� ; � -�#!�N6�~ elow�An 0�ci�6VY"�9*i�6-�@iss�>93AɲE�!ba�p���" D1zwhdl$\ )$ ��$C@as6jGj %?��ena|4 ���0 Pc���Ł��R510m�45�K2�3}a?�F. t B46� �0n )�iG�9h5,�b 6~�I.0�%�!6 114A s�R�By"%�a��|� orb |%Le-!5�E+�/aBA;! ��-j��m�Z�o+�2�!;Hal?����IPӭer�nce� an�\6o/�����N#mb}>��i��a.,1a�r�n�� �2�:� f���,4�P$LB -17}���LB` &#�a ��9�.a�6�)63: x1ggD >�q 6N d1�c1u ղ�'!�le'.� (2� �)3c.N u"AP~[ (� )-�a&|a&c!^�.��$:�6� �ԉ�e@2�2}aG!��>�v eM ls�4q�}�x�Cu3rk�ANgrey� pũs F,c� 3N �.r��� �A;r E�6*$ 2�� ise mai�e��fe~�Xrg�2=�A�b] &! U�.A�c_ � Y,�� 6��r��,�^10-17� pt�2!�~� c/��*�3�N be�QBXe l�>5 T�I�2ɻ-f+ ::�&�'+ %�;ƍen �d�#ʦpTa�� , h�N*�N� %c}CGv� {puh;8 Simi�k"�E:�M*� �*v(�!w�� ;�()=)�)>J egBO,�'Y�� EZ]�/ 6^� �n�>Mon*t�A�inF�w Zr/�sYr �:��te�st�� i�/z�56e sigtX7��>f F/F,��^AuJ87a. St=)c�!�? .�3�#���4AR n.�QP�h.�;b I56��("�� �[�$�� E��p&XmN�����>Tnd#q*�, %�s5�"�2�en*qd�L"�alMR~ eM5I�:<,!QkB�m $ of��i��,�mu7�Q�-*lnNyIwő25}F��Fu���&%�je��9�., !8�@E��2[;;A������eIW�0�*@nF?. "\t!�j�nV�� 6ei�s E��a�c0k �r)� px�E}As� �yI�� %B�/Yj,IJr�� w>� 5MWu"n m�%Z�M>����.�m��J#2*�g!WAoinW!*�i/�!�B�d6u��Q-�RgyE�a�-#%+P� {C>>?����/ III "F!H#} %�&� M�"I@nfnde�Xi�Zu (u !.c�'.�[,��. ja69Ůig��G���, lea�ding to rather large errors in the total cross sections atxhighest beam energies. $N_q$ is$,number of ch`H states for evaporaUp residues which were measured��experiment.} \vspace{1mm} \begin{tabular} {ccccc} \hline8 $E_{c.m.}$ & �(& $\sigma_{�fis$fus}$\\ N4 (MeV) & &mb  & .�@ 158.8 & 14 & 264E$\pm$ 35 $& 275& 539 #111Q 149.9v210 &2:I 80& 29" #42/I1.1I�80.( I� & 2& 82" #9.8" �36 I5�9.d I3 3 I� 2# I1.2'�6.8�0.7%  I " I # I�& I 2.87A%m0.3V  I "I# I7.�1�0.9�0.){  I "I# I6 �6 &�!��0E I"6# I5.0'!$�9&1� I1"I# I3IH I 0253&02IE� !�0 "6#I3pA�0.0132&1��"6# I2�7.4! P 0.87\times 10^{-3}$&�7.4CN!O1.7A� &1.10 N16BNOn" �I�2 &2.42 N41.N4�Nn" N0E(2 &$<$ 2.0$.I5�|> :19E� :4.62:6^:%��% D!3.7E-6��a&  \\ �� \end�l�le} The coupled-channels calcula��s� lRef. \cite {rehm} reproduced�8excit� func9 qu0 well down����H0.5 mb level. It wa�_unJat with)sam ���(parameters,2�cannot�"@new data at lower>�In fact,Ѱ literatur@re are X many such6vt�ca� - % cessfully�al ��FHheavy systems. SincpH nucleus $^{100}$Mo���Hsoft, multi-phonon � and %�!-\effects should be includ��2?B this%Aesents allenge. !+!�Dfollowing, two setExb@!F p Xed!n�� two- }ree6�,cp�vely. *4Dle} %table II \capAp{Struc%�inputA�low-lyk--in!_64}$Niz9m. For ,�@B(E$\lambda$)-val�!�!@quadrupole transi�s�from e2{J ,vide}, 8oct 6strength!�2yh{brau}.e�� �is / `NDSMo}c V ruled[ =7u*k c} NMo& � ^\pie E$_x2�u beta_-^C$$6N�� �7Ňs H& (W.u.)& &\\ \col� $^-t��$2^+$5 1.34�s8. 0.16��0.185�O & 2ph(6� 2.86^ -L:4  & $3^- k 3.56��b��19�0.200:�q�&� 0.53�37 u23� 0.254f� 1.00�68 52 0.24653.� 1.67\ �20x 0.21.%>� 1.90��32 j1� 0.23�.-H 3^-)!� 3.81\1I65JR!�]v�s�eM�e�}�}�E� e�re�XuT0 probabilitie�raGI = 0,244.�� }  \�a0column{2}{c}{U�} &VM}2*IqM $E_I!Q4$B(E2,I\to2)$&R]-!�q5m6!�J.v #$0_eDe~a 7 &1� A369aF  p$22227bY 1.06g  51}  $4_1a� d6AS $<$391.1e 692Eōive-2phAh0.87-2.75&22-4A�q e �\\ $\frac{<2ph|\alpha _{20} |1ph>}{\sqrt{2/5}}$&-� 177-a< 2& -�222!M���I�j� �ar��2M��28is given�WT͐. Gs:�?UJ8A��as us阽�jiang2}4 analyz#C+ fusion- �J� ��ݼ���B�,:�� set[m10\%$Vr ��$7Coulombf`C$, (! reas�discusB {�>). �0simplicity, i> assum� ��modF rresponds%S per" vibrator!is!�� un �!�(, consideri4he uncertaintyd0predicted one�wo�1a� w2.v/1& alsoNm Here�1�)�$-%�s�>z�1�6@." �(2ph):� M��|R �L$%6� in both �i,a% as mutual]��!c�� lis!rin:|*"j }ofa;1[A�% �dA e.D n� treatas:Bional +B� s a �&Y14Iedb p 2!>* (3Bfaddb a\ � allN6of%5 �Q‰g!N��2�upa� -�=F F$. MoreoverIpestim%t.�6jlIE!�*� shmtaj IIN� HoweuB8s above 5.5 MeV)�a�-d, sow>x"�is 31)s�70ion potential�krized!�0a Woods-SaxonI��a depth!m$$V_0$ = -8HMeV, diffuseness $a 0.686 fm,eq�(radius $R_N%10.19��4\Delta R$ fm. " 4figure}[hbt] % �-6 \epsfig{file=sigtempl.eps,width=8.0cy-  F�5.�"���:jq/compaAH%s!�aq.0describYmtexlabel�6� � } II���%O� =0.0!4%��)AV]�.~I�result!�similarE��.�in�s�)� it agrees.��EU!% ]�5AI�6�T�V��q Fig.~\ref!"6}A�M(dotted-dash�= urveEJi�e�%nt�t doese"� E�p & We haT�ltri�Re recip%�ahr2�(�;0$a_i$=5 fm) i�1o�Vbarri�;0as6(&� �1}, bu�is did �)�n �Dignificant improvemAA!/fit1�� . ANb = 1 fIdnee'h"�N�KA:c.h reg�LofxA$100 $\mu$b�n�f�is Y� �J�::<Z134�^�aa pocketjp�11��)}i�Eut 20MB� gro��pI"����u\ 92.3H �J�:bE_ adop�J�3p6\ L}�eas%wsolid iin>.,�seewA,ide a better>F!�0.:�>�a� 2��s�a refere� � s ob0 �a d� al.� , {\a�.e.�ith!�A�&E (.9U�)P&�emphas������ � betw%"}wo! ].% , us� � ]�x,AS�p st. H!��26��INHG��!Pn�bclarityEs� 2�:�&qqM_h���yq�aD !5�m� %둂e6"om�ai0 E=13iQ are ) " �.Zi'%�2Se_!��st �ies]�ma� opic�#�� stud<A�EAb�)sFN, exhibit ess# lycE -Pdepend!� (slope)a � Z� wha�F]!>sm� ($<$ 11�)%Fz�= just shif�ato%>r �?re�v.~�.�1QcaA�he _A�aba�7���N��ia g!?al feuvr�E�veX refo� (very unlike%�at�1minor ad!�A%he vcw16�,steep fallof� e�UU at extremb-��5u!�us�appear�� H� hindra�:behaviorQ� now has b��observed��K���\1� � "� "� +&� �is will+i morAl$nvincinglyOxt\!�)o�! !7? �LA �2�E�"�.�F40F�!�:< ike,a_�infer�~"broad,M�18E�wid��� ztribu� (�t�$). An elabN!up  sch!�+"I~/ -kr\. A���a�he& j-��� ��r6Os�N�� to~�� Qj�ca_ b��long-�� -&� /po��z%�a��&lq&D s� poin���/in 2� T . As%�Ie� supA�(gBcN^s�M strongs�� a �``Z''a� � ts�on{Log�hmic  va�� $S$-H ors} %siVv�7 %2�nimo7bJ�.�efig7J$"� (a) V���y�1H� l&r-N9�"� . (b)�ZX���. All%dcircl�" �w u4��8I))[st�*{%v���&lea��qu��fit�t� neighbo�O. C.�8��byJ ��e��aA߅d (� -�) 9in panel%� 6�a Azaight �%:Z�lRX>[ka� ng&!�̥�A��%$&Ri_ (8 tr\ les)�W'(halb} (open1�). See�e3detailb"�7>�n V�,, $L=d\ln(\s�&4 E)/dE$, origi�tZ! in �~�j�0}��)�>� 7}a�! Z��.��eI R�directly)Mf��� n�-I�s��)H�! limi"�V[E�2%!upp+) ?�:�t�{cm}$=1�#V�p?EN���$�( )Q$)(see �� e"~�npenet9*6�uas �L�p�~s6�%!q!� hick 7<, nearly horizon�vc>� t2ٷ�ure�fQB:e{1}) -j2� �o �c�$No�, ��""�2P!|� reac� a maximumd��� �V gy,A�s$!> ���r��22�VfIz!}^�Fr&E_sif6a= �)��\%!|2����tݞ�qund�e pż5WV�R:�AD ��!0e(� is method�h firsw.�Ref$'I.2}�or�o �^) �ded)+ %5֩�&58}�$�0 a&$^6�$� �'edZ��$ s�at�&�($L$=1.5 - 2!�$$^{-1}$ (oarW a��s �tH/ts &a<0Z, N = 28, 40%� 50 shells�%�er%� : $Z_1Z_2� \mu}$�z`@=A_1A_2/(A_1+A_2)�/k&L# mass*��colli%�Ik,16��L!܁K"�m�/%�#{min}$ H& s^{ref}$m ed\Eq� eq1} > v/E7 min���� $:� $Q, �C� Ѡ(ѕed ]! B!3�lh'bass})o) &�``val�: ons'',�0{ph!�outA 6ear�clo� 1�� ��eiU� a cl�"�r�� or w_V�s�N�A��R�N�� yet�*b.� 2�%�a��0,qӉ���&�]% 3�!�A���possi�),to make good�:ion^�i�q� u4.%i�N� SnM�� �T,112-124}$Sn m�):$-|m]s, o] ���^{6J% �G�n4 brev�}3'r��)  } S%M$&F0�(� {&i�&%�q�T3fv% E_s} }$ *� 8 $- QJV_cFNI� &�\ [3�&>b3&B�%%  ����(&4222& 94.0y& &9�2 &1.0G&<0.049 &66.12&102&2+2 &? beck1}`&�:\�R&4258&'\5 &0.9=)\H0 &62.69&101.3& 2+4\stef3J\�$ &4325& 89!�&94 \['0.0r' 53.04&100 �\�2\ R�\43\7.7��30.9!$<5.3.�0T6}$&48.78 & 98.1& 4+4 -#�l0ll489}$Y &6537&1�1 l124.5lt+$<9.5.l<5}$&90.50 &136.5l12l0}j�92/&7014p32.9&130M�'4 &108.0&148.6!�5�] F=[2!�&[1&133!& 2.c1!�6&146!�4V[I�!,F&71[28�1.8 ��42A�0.39&143IP10QQV�\ 346&�6 P13-��+ $<4.2+3!� 92.2!: 6.5 %�* a^{,74}$Ge &5109E25U�105.6!�--0�)(62.03&113.4!�6�I��)�-!,]24]�5!w�*107IZA�0y4$ &58.48&11e~ 4+6 B^^�90}$Zr�5213 27.3&125.Q� 0�5&97.24&1d7�5� scar �9�91Z65�26.4&1 lb !8 94.18&140A 2+1�VZ4 Z70Q7a{a�65�� 86.94&139 Z4 qg[�2!xA�%88�Y40&A�m$76�#5$91.45&137.�@4+2gjans,�2,henn-'r6 �94��A�2&�759'1!'86%�3�4YE` [9��c &880�49!�52q19-270ip8UB free Z�Z9095�55!'559�23.��1A�16AU 4JZ��,*�5�*� r� �uO �!� m�/:WbsG2� ^@ ���? ��"� � #5d6opw) %TakD $into accou�$e.�s&< >�� j � sL , how�&,6 %����"mr{ . Ad|)2� /b�qui'to� ly d�Xro�e:%C*5�e:�&Jo�eZ�n :��wN�5 i � "r>Gb�����:� . I�6�BO2{>!!� r "� �~`"�C�(iso$�F�� }-2! �� involvA�Nii$j2���Ri!�A A=&- 200 r�,)c ummaw*&�,V* four�, nam�� � ,���� :� ���&68�MaEi�2{.  da sufficienCe�!toFermin�Q�q�M�}�6 . P5 ousl�("�� f*� ),%!%% 6 c M .�  VT.^ R�t�of)�wo &�-b5�2�% !���� "�&� 2}Ove�5��;{;s�!��)+"�9� ccurtbZ-Tse��x�/2u9Cloc��F�1�2Sbyq/oA6g a $6��>)XV��itI�e�"�qnBP ��a�M6�7. Bec[ �&?2ain��*ņs.g�{, �Cof 2$q3($\sim$�)as +iyA�9edM���.�0�s���M�6�1D��c2%�YBkaIm�A$w Id�=minz��������t�HA|�SE -�2�plL-��a"�#Y"~6H>f}$��2�8}e����"Qempiric�%ormulaQ��%),:��e�a0A�'avail.1-�!�=�stiff�o. Obv�o�- -H�� ��e��e8�f�=� ?atics;��@ s&&��6�it&` � 65ut.^2}I1Cr��"![el�$c�lIB.�*%w1�]�ace�퉡M���*Hl�$7(9��=�&SNi+Ni1� ��!�#)-%D�%�%i!!��~!����m%� Ni+G�u;llM�ft �,&y'%rro�%$V'%L��'iR� �e`��^�"�*I�E.�a�,=�iɊ2u�2`*@GE�90�%�is 0�� a� �iE&du�<� umab�(�:K "DA view4n�-�^2J�4at� {%� �)�Ab�'�* AX�di*�'!�pusM����F4) ���e�:�**�)v�%96L4 plpcN�%"z%�v%U�.�)�U�6���#ndyb�e=��0&� wQl}49>�# B��4-8:�&ezztest)$angle=270,6f5>�&8�&^.5K PlotA�a$ v�KB�%6 Ni bombar��/t� .�"V�$21symbo� �9;��iˉv��J #+�E��ed:!��:�� ,9�  0}$N*�VJuuA��. Ope� �!�associa�,"�&�) %�]:N {� �o�M\Zt.R"C&&� ��Ni�7amondsGe,� �'%6d�%R �!*E} Y�8B�0devia!AF! m�or=0Nw W(2��*E��Υ�,0 >t&8}�us.`0�a��.��ng͙. A2+ntAHv���i�&�2D�V��a4�ic yet known�G �!at9 t, w/"IWRd of a �uzb) proxH&ya5�proton!]neuh+��def��,��sum�parti<*�hoX�N>u[!��>% hR T}  N=406� w th~#�)�� N=28�pE(��"a�� f � H6? 1�(!�. )�_s� j� is�$J�: g�7al� of.T"�E_.m �gin"~"*�.199 A@a"*�6 *�a*eɯ��$ESE9"�(�*yJin!�t#<���Fig�" :t  10}.f&�#� ' �u(�@~V!�9�EBM�RnegK(e�ou!-$)5x(e mayw� �!*!v�!eihIh �B�!"�e�1�!� cri�%) isJ|E�io�/&c"*n!7/�:�4y����Q !]�at*� oK&]�/ indi�MB�MEd "�;m �}�>g��>-efig102$.0&�.�/=��mi!�a�!��:�? N�#����� �Dea^nce%Xnel. S*w�Å�:�2�10� nd{f�? &lDi�DionI>)��^a�,phenomenolog. in n�'�����tE�5no satis16der� mB�no.`5�.Mq: auth[Ve�>ola�/�eew�n'%plin,linr,hagi,dass,gira,proc12}� suggFBo� to]#21'� ?A �F�A��j�Pa�� �>9(ome�R�#�high-p�>!�19^ ]ө_"# argu�Uq� failBPo $Q!�*F7-G7ifQ�r4$Hill-Wheel�5poE" }!Y�r�(I.�@{�!1}\7|*��seJ/V�aGaHsa+�v+Gs%��I� ed s*�7BZU� n. D� �5 PollaroloYG�( E2Qs!y< a sh9�@*[@0)�Ai<}. Giraud et al.Aaga� �nAQ ``fr�U'' C {A�}�D�cu.�6�@�'f�6c*{6�Alls�U�s��@�:�+� oxMYaMRin A��:s�'they do��� �>co�8i�6v=�&m6bAl"�aCA=O<�A)�p��� stag� rais��qu!|�I� �8� weak�m� exis�r) rizmmosF4�:st�9in&b!#lea�!�c�c�:pl �-�y�J�, �'vr*�fur�)pl:+mod�B)� �theoret�� � Olevz0aTa�/E�!��Ye�,�/{Sy%Oco5���X4FJ�&,�#�.5�AL>(��  aOEpl�!�~.�R-}bJ1��� gyA.&f�of� �spU�o�F)��;[�>;t�J&�&$Ni isotope2�2}�ɥ0�& on+K�u U�x�43"��� A�oTec9''WJ� ��!*!\�� work��M�&W"d J�85p)�&+�*QL a6w�*\d 5 nb.�B�ut 12\%*� ��F �-D�Iis%Oe��=�so.�b.�?��cѴba7-o z�&�5U'�".-,Ai � �9�I�Ce,�;�wo� u "s,Y/Q "Q7"� E6,e��FJ����e �4i�_b�>�na�I� k� Vy$�A��isG I�s mon���l� a&F"q � [�=�e���(E)"i ��lo!�l }K"�"� & .�la�-M�F``�O�'!biv���2�Q)�/�2; "� )�ex�9 6isfA)ŭun�It��A�Q�lyy .��,aQ-�!�:� E6*�`y�no2$E_{ex} e� 30 -s2a!�R A�f al%@�L��, I� ��eir spaA� lack�*��:�+E�a�Ao 1%�.A3a=].�$ {\bf Ac!9 ledg�} �?��c?or� D US De�/�YV y, O�"EC�X ar Physic�F4  Co Xct Nos. W-31-109-ENG-38%gERepTog.P. %-53K 1047F8).2E3} R. Va�E@bosch, Annu. Rev.!(. Part. Sci Q4H"4 P92:P@4} A. B. Balantek3 nd Nf kigawa, \Mod2�70}, 7�9>�5�DDasgupta, D.J. Hin�BN. RowlA�Dnd A.M. Stefanini,�Y6�lJ��401!#6{� (0} K. Hagin� 2�!�-/C-r5}, 276N7.!rowl}? �,, G.R. Satch� nd P.H�lsoM . Lett. ^ B254`E91._� 0} C.L. J>8J� ,}.�T R(89}, 052701!. (2002�W1.W<, H.Esbensen, B.%�@ck, R.V.F. Jansse# nd K.E!"hmI� v. C 614604|4B�2.|��93�1.�2Wx.B�JE�l� Enge,a�Salomaa,A�SperdutoA�S. Gazb $A. DiRienzIJ.DX litois6�)p2�158Eo82k�,3aC.���7A864 Ew5.E�:.fT�A�83e�6�acke} D.����>M�L2�A60!�9�96.��0]!H. YZJ. GehAf Glagole�IL�on!�W. Kut�Fra%�(Paul, F. So�l��Aa[ Wuos!� m} B317}, 3 �3.��? MaY,Halbert, J.R��ene, D.C�sley,�/onkanaT.Ma�8Semkow, V. Aben�7G�r�AM�Z. Li���q-4  2558e� 1989.�dave�NhvidrE�Lar!--�Instr.nMeth.N�.B40/4�2224AJ89); CT!�u� K. B�I̡�e1�:�T!Laurit�5LY. Nagame, P. Sugath� ,A.V. Ramayya�WmWal�:!I^B� ��E 358�6� dav3�G5�NLM Div.�)al�Iort SANL-03-e��3), p.�Q�I hendaG. Kovar�ɣ9 M�o 90-1��(1990o8opK14 T.O. Penningt�->q,D.SeweryniakA���%��",6�C!�Lister!�J. Zabr_ka!� lankE�=5��_%��:� submi�TA� Eu�  %uA�ods Aaal} �� Gavr!*F�2A�230!u80.T�A9�a�2�)�-95/1��!�5)�7.Fpuhl}��(P\"{u}hlhof!��6P28�6��72cWd}�94Charbonneau, NaVDe Cap Faria�� L'Ecuy[ndA�HD. Vitoux, Bull. Am{Soc��16}, 6�72�[�Videbaeka�R. ChrAT0OM  %KK. Ul+ N�5m3� 72<b eᤡ� raunstein�`J. Kraushaar, R.P. MichelH��MitlJaG�_AH- Blokde Vr[QF33�, 187I78.7ea0 SingW t��ta �D �s�i8A��z2� hagi*� !�? %?MV ���3 X6�054603��}�>%@� � �QA23�� 74� %&� tef2z�F�4%�535 %i QJ7a Scarlassa��S�egh� ��,SignorL��CorY  M�Egnoli, DA�N^Ci� 2^ A�Z��uZQ�A)33��17)�2�R,��H� renoMe�lla��A� ��aKF� E. Adamid)��B �25� 3�N6�ans!�2� A� Holzmann�He�:, T�� Khoo�$� esko!DS� Steph�7�Radford�l ,Van Den Berg�UJ�1I� 2D8, �.�}, prUN�mmu�S�2� �7$ W.S. FreeTJ rnst�FI esaW� �7�J!�Humanic%K%�hn! Rosn!�J�Schif�� B. Zeidma��F.Wz sser:�!�)�5��156)�2li�c��L��)Be�@�w9a� 2292� 2002� \��A~B� }2� :S U2F> C8 &�G.&�2X�qa0�q� >�N B, �e�Karatag1+sA�Amo� B.A!�b��V�9� 6461��2\1} Proce}"�Inter�al��X_03: F�a Tu Nkar�Mroscop42fs52 in MQ&re(Nov. 12-15,�53,sushim�ap� Prog.6vdI4Suppl. No. 154<4A�� �� � A�"�& � 6 J.If'84>9�ro* 20,.]/209/D. Brink 68;�A� ��946.� !�2} S.Va�S�y:�Co5�Book of6�� #>���AIA>���!743%�3.�;2��!doc� } % ��ing's !ver":�2f9p�oc&�  D�$bx.\Z*� �% u�mbi6w^`e)"y`!4epey �!la`)ugL%� /�"!02 w$&`)q*7Q3.�1Z�\ ��n >t,rc �Lh��4[' �6H:%���#so��c K*$pV�c.�eA� Ce�0 [XXX,YYY]�!at:c!%�%s�c2�ckorMk��se�"�a�m�. m�x��I�+a��c"��k #;+a� .[-�>$�I��s�A�!6l�R��/}� KJ��Wa�#v�/Q�Y�J�~*�>.��\to�5 ~�b��b�t?I��v�bne�*J ^>�S=��~�ÁS�Aae� ings�P��Z�6d,�Mfia��L�n�ily�M%���.�hheBhT�5�e � s#@�#sW`maybe �1&f` e�*98e�ic.�_�1r�H�re�+ shif�kB�`a!� �!ce`by��ut[`,�_��<-z �+nA�$e,`�%*=^�6!�Z+`2X `�Mit2�M6Jn.` 1�Q>w.�!!3u�C",���>�!qaR` �!�``I�`�`na�n.�6%` al:e�*> .�} s%02$�s 3$^6�o�_� bo*�oF�9!u$xqua�x.O`(��oahlso���R!^� .g����p&�2, &Gg* ��.@-@d�]&Y� } a˚pHovF aT � 7Z�rex�C">� B\ 27. &&23]�O�/, �3�\:D�I, ��%&_u9�FQ*o F]�,)�-�C =>@ =1.20 fm"8> =< . A�G�.$n24m ��ded�Nv�>�s l�� �+�W�I��x&�1c [2�j.Q �.yͽM�>/ 6[ is 5 ��l� "� � &�2^2Y�M�k�k6� A…X!2L$5fn�_-dqZnd.�s'��Y6� oulp:�8 AB��  .\�/�e�\��.�)�V�� A:�o�Q�K 0."�odn��.�U�,�-F5 >b>7  Appl�[�8�0\8M%�*useyU 6A�No 5Oo, n.o7, �4oZ/��B@to 94RI JZo��l� ve �.y�!�aK�. �)r�l�.�om>\�gisFU��2B .� proc&�mLmQa�IX .mi6at.QA�to 0.� (�B'a�co3x�gat&�w>.`"�om�''enhac%7 '' p+i�Lp�Y $b r�I��-�V��W�*T/mA��F�t:a+);U &�* 1��'�;ee��become �appar�,� �8Bi�tq��LD�.�I�k{jiX mphi�n�(e&er�)b*<x "��&Ss, qn��4ph, mai�D��-.Sof����� ��52_&�� 2�t@<:�7a�| Iylr�2PH.^ �:� :Zly coina ��!Q>%� ��� INSTITUTE OF PHYSICS PUBLISHING�Sz I�  I`Pr'*A�aie=%8 publ�9�6� z itut��ics I P0shJ jourdu�2LaTeX'�� ��  Iy sour�8�|4`ioplau2e.tex'I�to= te `�7� Igui�Ps'I��a��ai�eldem=Kra�3��5$��RI=@ �pNint fFO  ���*cl5o 12.cl�' 0'. 9> I�  I�=[�$lf�s �e�& �B I� % ��m�%  F/ASO*  check& !�ela�0on mark�" dou�]q�] % #;/h.`GGa= *D(grave) % & ampers��'�;0 acut0$ df8,%�c��  % (sr enthe�8 )Y� e:% - hyU5= equalsg % | ve�?al� (~ tildex@B�_ . score % { �cu�� bracC} � N[ )s\DI] ) A(ket % + plu �) (; semi-colo % * a&is%�:�Ho�< x�F` > x �,�qmaB .�U stop % ?"#8U: /��$ward slash�\ back ^�kumflexE�dABCDEFGHIJKLMNOPQRSTUVWXYZEdabcdefghijklmnopqrstuvwxyz$1234567890K�  % \�0(class[12pt,?]{�� } % Uncom_ nYrnP if AMS fo���80 %\usepackageAms} . graphicx}2 u�>begin{�@title{$\phi$ mesom�"&Kn Au +/d��2 $�ds_{NN}}�y200 GeVT�O{DebsankFPz,o{\JPA}EC��out����)k :pag!���! "�=I)l�� } H�1 9�aH8isl@88G.�>�� J` Quark-Gluon Plasma (QGP��k=chiAQsymmetr#U9o�;ndIDar m�$!�decon�Jh! eory� �s{A{phi-�>y}�SA[ k l i ��influ���;8m�l�w (emoi(`F"�W.�.A��jm 6eA��:E�wiq�ka� s�6�&E���i1� RE�e%imbal�AR/c%d� �i�!�di-lepQLde��s5pkkee}.<%sA%ng�$s\bar{�� pair� `�Aw�hQx ]x9en���J�T��n7Kss �n�M�A�A��A� z%3�/ldz �i�{���6or% Q, |n�Fa*�: ˁ�f"it)n �Pc8 �xA� ed medium2�5r H �!nET, )K;Ch@;�cA��?ed{Ł�V�f s�^"�'E F� �$P?,E�ń.of9 ���,T2�:�!X{�>���$R�= f)�������ac�5�AMK�2���E"�D,)uselF_o�d techniND}�1"�FAX@!Q�yV ���"%r�e?yardO1MӍ� Her ��nxtrk}}.!;�� id� f "i7]ss af@A��Za�th�I��nd velocВ)� A��Q �A3pr:"� a�lay�L rift cham��Wa !vac� euY5�� I-of-fl�O(TOF)2O . Tw�_ctr A N1�lTOF .�: a scin?s� wB$"F ;i $\I$Ar i/8$ ݥx2F E,romagntENo�!�(nU4$� -�U�s pseudo&� $|0\eta| < 0.35$� �RexA�-%�AfBeam-M]��,s (BBC� �#}��A&aABC along&B Zero De���{�. � 8D%�2�"!�s$ $10^{m�Kqbia�c�� withA$|z_{�ex}|<9@$ cm.1�6A�r0�� �atA�ep$.�inv�4nt��.�Xs�1A�Ib"^or���(@�7_�ee��Xt6l� jqi|c:)A�Fj.Bma �� fmixޕ�j %�s&��0|�" ref.�S]{0dipali,phiprc�_�u-Z)alO�V�Uby7q{h�$^�ť#s�� �! !b&� Result�X � �{C� 2| �l��Fi���� inv}V� �] n��(22�A@�.� ȁ�hh�~� �f����6/!>� 2�.�Br p͂ �su)�la��� � um�&R�:]� beyo���e Cp#Kis .'zer��erd ;��a��eVW] DBreit Wigner (RBW)2� coJu a Gaussia�y� al���&� "4�$\s�~$ = 1. �/$c^{2�"3,�,�<a�5��rlo�u�UN!�f:.)r�?2�,E n�bottom-�of``M4eru!��DN�PDG.m�PDG04}}.���2c ��G&7I�s. ehR�e� �B�e$ �)�"� !E5�assum�N�� t �. Agaic���e.~��jre�0no_��dl�Ga s ! �~�X,aZ�.� 8ic}[t] \i�(qs[H�&\A�]{Q -all-mb-`} �V {�]�AM�z-� � \E,ar }*A :��i� %(Ss *� �� �n� )�top�K9��8(�^�Zndf�2�E�2J k2�n �B:ҭ�A RB�-���Eշ�/A2V�a��=. >�W"�)�*}[htbj�7.�!�-��ChiSqZ�&%Au a�>��E���(�> intr)4c�o�n.�end�V,.� T�A+=�aJ�� ��F16]�E�%��f�(he 2�AY &��y���7m, �L10\%,�/�L\%: 4 92\%��y Bin &�$m_{T}$,��  ��%*h!w"� � �ge �iaccept�!�?pancy��� . EachzU�POn2�d on[[�U��2 �to �}in)��, T��#%aD0 *�6.2� mt2.� j�Mf �h$�,>�"�$2:>hn?4.D� y-mtiB �=�<�1)YE� �� 0 --]@IA��--E>%FM��� (QZ)J�\yUm�:�)�is"�`H4urF 9Vpa� paneB ��ՂU&> Rwi/�&db� ipan, I]2 �L��#e�F`RK/ A^ t�i��)a-�'�T. W�����b)x"d��a"[�2=# &2�% a p2�slc 9+ � Xk�"�"g tren% Ȭ�AP! �P�G�/\ AGSB�$WBack0L!-)~ofQ��*rP:be -�a�f�!6�4a "�LR�az�exs��meVis�sa�gen:���Kst7[via �� eV /\pi� K$�9 A����a*�52� �-nA�(} (c) - (d)�Y / K$�w�0�+ˋe�m�6 bi�)�2<fl�~�I@d��: ��]= � �%a<�icult�)��E�u� !� @y�pc)�vi�UsI  / \pi )l- �-,s�8:Q>a�PsQk��j~�sc�-��de� Vart�) )�AX\pi'an�\be [4! . AȦo%� �T8$varnc.GY%G Run40^,s�to map� eUw>z�%�sb#� � �� c-1͎ B�#�M^� E�$m�at����. } T%ect �>� ��EZ$_pi_k_phi_es �>O:5b�A  M�q7�m Y�$,Ai2�,e�%  /&� ~(M�+ -})$ (sca�? 9 �of 5), �+Yy0.5~(# +8#)$aAu+Au��!p$N�$ GeVB���� r�@lopU |��_%>�ol>#y�1R�A,2y4�2�D#be (wro�te�/��as�t� W�%K$-�`?j ipat1radS f�yK8�/hadro��H�0w� (�� m�"�f�]d�0�:"� "�gr�0!�� �geHf��ed � �@4$hydrodynamz-fi+t] x.U�Ti^{\pm},9 p�H$\21�E {p}$S��2Ged�p%bof�� �, too)Fr� 5>� �M-2i�a�gI#f��>�.rF.� N�F*�` Fa&�$�X�0j12Rcp �>� rcp}�Ta1}$ m���to! p& %��"�� $(p + .�)$/2,a i^0$,��F)�Y��*�Y%J$ �.�� b�B$N^{0-�}_ �_/N^{40-$ � shad3eo��haQCS$oO\_> *nw�6�Ym6��$!/or �Hx�9'a"7ane� � �h:1����62�a� stra[ a>a�YA�)c��G�:�*�n "��,t>A��l�!"|*&� N 3a�!��$p��Y, (qi�whe�>+"is dogze�l��xs�"�R-kJ7 g0�� impor�to�'�v'V9!yB�c� aM� �B�* � � �a+\)�u+!C})%,��6�-5.�:j�Űw��ec�ved�((�n) ��'( (baryons) "ppg015�P9(� �]�++H}xA���� jet-q%&h� ? e�#�$*!�.�wh@; (k() � 0���s�q]typ� �x-A0�be%k�)abs�&of�2�e�)ee��5R^�$=' e!�; 5+I�nH�U�:)p%�-f�)\f�(A`5�� .��&�-$q�pZ"Wa�ing���v4�'� �Wekeu7iL�l�/ ��c�G�q"���co<'U.wm�Vn�'2 &.&.]$.�* ��ch!< �!�is-�t �� �AP5� R/5�%�R�iwDn6T'2X��H &�' Rcp,M!R"A*Su�yh.�!&�Ga./g��-Ae� i2E\:w aa�+ =200$~)  �Y��� r_"7.. �*.�$dX!�e ,�,:^ es sily��A�F0.318$;��8(&)51(�f` !L�H� 3.94 1602@62?�<.�A�rP) (� -m_{N } > 0.4$81) 2� AI2 :n !�v�ity)Dn���>-�E#s::�iL&��p��� n����U�)q0�=es h ���&A�ND.��" *{Re�+c_c"� thebiblio�y}{�- \bib}cp&�,zXHsRi�5P(R; P�[cB.�Uu�U�, J.~Rafelski&�Rp.�S{142} 1�Y 86};*�cph�+�VPaly[ MeVwV�S} �V�W {A707}} 5oY>�ap�(�AdcoxaO�a} (�&C7� ion)�Wy9 r. M^ k$499}} 489 k3.*Xp*�$}R�E=8.2k�$F)2��S~S.~AdkI�E �,E�(-ex/0410012!�-�U! S.~E�:~U2;�3..�TB59!�1�44�s B.~�f.H (E9176�)�304017J#��� �"�U)�891}} {172301} {FU}.:�Rcp�[VelkovskNT2<@G 30}}, S835-S844�4.�4050139�e V. G �~>C�Tnaotp];MZFR;T \ujNX.*ZZna4950EgRohria�>�27�355�1!w>��*�6 EE:�7epj]{sv2} % ReW o�,r�n $*��'Zion2 ,7K"mc�p�Cq��7s6�71�xsym}6amssymb6�7��icx:, �%-� �=7�E�X$style{unsr�8apsrev :8N�|al� A��s-z~�U�78s{} %�cert5~o)o�ES�n4insI@({NIKHEF, Amm; dam,� N�la�#\\ ! � �8::�8Subato���Wi�jUtrech6�8Pr�$tonplein 56c 4 CC.B|. �-� $0<�-<1$. Ph�6o 3de�3$�0*�#\gamma $��#�E�(Barrel Elec.�.Ca"�-� cE�0�.n"|3� "1C  p�?BEM�3�._ �jT �,> �!�x �|�p�f�' RFurum���V!){0.�va}�*�&��F sw!U2��oa�.!��  = -to-0y M0(NLO) perturb�~QCD0c6*I�I8${25.75.--q�p*�7�I�I&� 6�7��#o} Af�0fl5yeܫofa9a K[g,OAi�!BZ�&*h� ma̶42%Y8Ion��iz�at Brook5n NL al L& or��a��zB er2%�q�.\<~= 200 )@sdNh{��?cD8!�regim*/.#s�DbyA# 2�d �6TK2�"G3umE�� 8�iG�tei�,�ra@p�q�A�y:)ge e.�-�s8`ce�+�6SNar�:�beZ1�UbK)e&�6of "�8� ��h9. �N*�W�of)�.�B� �-�8a��w61r*H�����- �7 ڠIm��E �PAuF�a��' Supp5p0�,Add"��,}� ���\�1�-s opposii o trigger*�%1g>�-GAiazimutha�k�wrop� - emi�x�os%!�v*�E�� s��ex5a �BB�� 3,Flow03,2  M#c�nbno �!�-[VM .M() Y�y�@**�a6;of=\$ &�)nd 0� p ma���*b?KIr"69c)��rhoM.V�� " .���2� �yE Fz . �������:%sj� }sec:2'(5 or�R {Nim03!��͘�)�-'*�CE ��� Q���N-�f er�7 ed uO&aA��NimEmc�� � Ho @�cur�0upgrad�of�0�a�� i]���# III, 5�+ �~�!  g��? operE6 coveH�M&i+A1"� (deuteroprC -� �). A. en�1 2004 \%N! half 9 ($-1� 0$) eK�  waa s �)�lZ<" � ��65 ish�!I 5%ve)F5zuti�C�%.�&� ��#�4"��.v5 (e.g.\� 0! $e�)e�|r�_��es�]�|%c2�T@�s) !� a� -; �Jhe ��'�-2�;sa��ng� �:� aO+tl� 21��lengtd5nAB inneru9220~cm-bc&N E]�!totHrea!�60~m$^2%�di�_lFto 120��ul-��-A_6A�c mo�Uxfn{tĴ�granulJ� y $(N�Q<,s (SMD), loc�:a2) )5M 5 $X_0/%��=' �,�} � �#�of �.:� �!�!!� ��� E�(�1�07%07)n �/$W a�ri�f2�/ %)!�*r �9�d=� A��i=i Hn�D!�6�%� clu� � a pr�1-1� (PSD) 1�!io � rst��yez5 The �$i6Q`�D�� ]�aL2�1 -- 25� /$c$\� oa�oX�:2r &  um u� m;�ng� ��e�> t�_=�`(AbsEnCal02}�TaU%dabsA^fX��i�q�)9"� ca"�"g� ���:Um�Z5qGiz��=s (� �hddv ) Z#)� -by-)� basi�Et�� *�Fval gain.����j2�D�Al"r of mHns"+ ��(TPCE@ #H�*C ��A+�5hD.4 -ys� �tfluctuŬJ,$\delta E/E �A 16\%/\E}$�Y JY u"�>E�@ t6E 1} "b-�77 -��$�iga�wa��m|:A F:A (ZDC? �E�A��anI�!�V :�(95\pm3)���\mbox{� }Maic6� . ToiG%¥.� �Au�E���s (HT1�i HT2)^`�A�kA�-�threshol .5y �� �^A�ba��ӑ� B>�X�� �&�4�AI��Jfew�o h!�@�$�e y O5�e��ieT5iWm�0100\%�}:}&� 2�R2�3��1nAiys}  25� ~lom�5! !_a�A� %�! &j%d��n��xU�Tg� &� %�� � �3�E=2�1)�[ T�Pr��#hF (TPC)��TPC�F%c�& si� � fron2�,@�*��!�F� |�|<1.2�)2�JI8�\��$JL/e_ �+s�ȵ(Sw��"c1���� traj;�$a�P.Tesla�>enoid�mbFfHP !� 9�-(%�� >k veto. "��:��)fU p10\,M.. %5� � 3 Md t^%C�  " cut��ain� tex coordYE0e (beam axis)3; in 81 1+!o)). .�:&�Eink4�6z (&"Mf$on 98.8\%)�&�]&��.C��[ll�6c�)gA�m �al��� e|.� wU++/ �HPC ck�'wi3urthe�a!Y,a��b� �*�aoO�l$|E_1-E_2|/(E_1+E_2)$} $\le$Aq��se�A�A�Qed.��^.�A��search�[ nois :dea7jwe!% prog�)�$�<MU�)�&�}�ub-<��g��Ŗs�:>P�$ quI� �7vid�4WZ.�M=B�>.Z>� F� taggOccE�g�d$N �%!%I�� �)����)�. WM*� *�K � !_ aA0�� � I�$�E�j� �@@� 6�*vyet�� )P�m� artn!��.}�(�Hc�<lA�a� ge. %- �1��A�)r 6d �t� �. <�a� .heKmDA:�1� /<�6�G& G�1"�?�CGNY I�w� s" �a�A)g�&�T 30\%�0K>��e� B�"�3���a�:  thir? all 1a-�1����I�** %��L;�e�&� 31>B� ��}s�����z"� �� ~ (7n -�)&Ҋw6�2�� \��ze� 0.48\text%l}{!}{%BC*l�vPi0_Log 2}6D3�C?c��I6 .!���(adi\��6~@� &���$� st> (top). A�ai� �sA��  0--1�O�9�9oɈb�H�=� ��Z1�1ypl�]_MdQ polynom<fit hist )��6m�L�middleB )�x�y�.�J�+um &C%6� (.jB��z6�* is 2� "Z fig:1>�C:.&5r:}�.� 2:> -1��oc�h�Yi��Xw\?a RMS�F!�2O��J2�h��c�N�randogJi� M=�D�2wo&2+ meU�s�ArTaI ond-< =b�f�Aed �&>2��6�u&t��>� on (Eg3t n I�@�Fi&�/)�H �?%yM� �,� ]2is�Y+2�&5OI��MM�2�.� e> �}?]�y plo�f�:2uh�hebaJe� 0.8--0)�A�keB NA{ex�,  attr�^  �!I,2������|�E1�$ $Q�*.�$ 547.3$~MeMw)�%���t $m�R05�/I�%/ms h�split� � ~��"�2=�*�G��]2��R�F7-h !� %)�"�1IT��yK �UM#6�@>A�Iv{�QE*! bins'�͒�{G%=q .4 ��  ) ����s� �!g�� V*F�ZEqA0m\,3\,\sigma$.�.2i!~n1*u nWN*� K�bhMp��--1��C1ej8 2��. � 2 e�'���is Ht � Q�m�fuOA ԩo�%9@gB�'��:ky8 �k9�=14�i$.��b�]) $~=~9�0to 8 at Cor4s%N*�Amu %� K] &; "�%�Q�a� pe��>�pappli� Lo�I.�CN!~E�"�.��r�d)�K$q2o� -`, �q:��yM"�J�6UGysK]��i��J�,!q����A�%:&���R� (� )A+.�m�!�|@(� ) 9�/�d:de&�}V�CoPOM" /!4/!&�+}�2��.� ���AYin��[I&��F**2}�0$hspace{0.5��T�6�(o 6�n%lE>.Q��s^leK6 (9.5)9���5!�E�(H���v"Q! dif 5"�es$�NnE{A�of�p�:! .H��u2du+� &�R I|s�&�B8=&ջ}� l&�d.*o �\16�$�" +$�is Zg�� p�%ous>� �&/�2�6�&�'E�VY5n GS.e�&azB@dAuPhenix03}. Ex!NE�!v� st.�h)��Fhowr�so�)���in 10--9 05*�A��pi0_pt_Ia�B}&�Ay�p/.�. �.!�a.��;0S#1$� �s� #8s (EA�T)&]t%O�9z'�T�9�)Le��i�!"$�E�%UŖ!�N � !�e�!�n�. open~�l��] &�4uQCa@MW�"Ar��1sJ` 8o between the d�I-Au data and a fit of the PHENIX results, with the dashed lines indicating5P systematic errors ondP.} \label{fig:2} \end ,ure} \begin��[ht] \centering \resizebox{0.48\textwidth}{!}{% \includegraphics*{pi0_pt_spectra_pQCD2.eps}} \caption{The invariant differential cross section (full circles) compared to NLO pQCD calculations (full line). The factorization scale uncertainty is i)Ned by .h. �@lower plot shows !�,ratio betwee9m%�,theory curve G.Z i t)F� =� whil (dot�0ones represen=@6� scales6�3>�%%%�(right panelA� FiA~\refA:3} ����< which is obtain)] multiplic!=nj!,8measured yieldsU�( hadronic c2 in daBcollisio!�0$\sigma_{\rm 8}^ � dAu} = 2.21\pm0.09$~b)~\cite{dAuStar03}.)�normalQ-:' 10\%-�m� are coY�,next-to-leada?8order (NLO) pQC6� �4Vog04} done usqӸCTEQ6M set of nucleon parton distribution funct! P :}U�<ar <ensiti�E%~ gold %,us from Ref. MAuPDF!I-is calcmn,?factor-3It was ida� fied)�$p)�T}$ (fa�line)�is var+by�S8 two to estimatiE�=��(.Y).e�fragmentIhf1#%�taken >�KKP00�aCAwn effect� not ��dA���= sMM�zl,�J�� , consista� with�JH up�9,H = 15$~GeV/$c$. %-�  %��$acknowledg�} \�z*{A6s} �,> : W!�ank! RHIC Ope� ns Group ��(RCF at BNL,a�NERSC C�nLBNL for$ir support!�is workEZ )�A� by%IHENP Div��R OfficeScien ~$U.S. DOE; NSF BMBF4TGermany; IN2P3, RA, RP �EMN$0France; EPSRC^ni�8Kingdom; FAPESPBrazil g(Russian Mina�y of �!6$Technology 0( EducI�*t NNSF�H China; Grant AgencZ$HCzech Republic, FOM@UU�A�PNetherlands, DAE, DST)� CSIR ' GovernA�,India; Swiss%F � Polish Sta� Committee%��4tific ResearchA�%%�B����$thebibliog�y}{99 d Flow�b2b3>,���+5+0!+4.+Jac!� P.~Jacobse@X.N. Wang, Prog. !�. Nucl. P%�1�54)(5) 443.^NimA5!(K.H. Ack�[nn� c0Instrum. MethY^ A499 n3) 622�NimEmcmM.~Beddo�g g725:�TAbsEnCal02} T.M. Cormivgz�8m72) 732�Et%D4�1�C7M� 4) 054907:�TPC-6Anderso��1�59.j dAuPhenixmS��AJ�PH �h�E�2y` W.~VogelsE� priv��commun� , ��.�L J.~Pumpli>!�8 J. High Energy�1z 0207I�2) 012�f L.~�KkfurtabA�0Strikman, EurqnJ}@5} (1999) 293; L.�DX, V. Guzey, M. McDermot\ \Q�m�{\bf 02A١�2) 027^b �TLarXiv: hep-ph/0303022�r X B.A. Kniehl, G.~KramerPB.~P\"� r,m56o B582)U0) 51%��>� � docu�H} Q>%% M. Kmiecik��, Zako��4ceedings, Acta {LPol. B %% ver. 22:08E8-12-20 \e�class{appolb} \usepackage{epsfig} % e &b  plac EPS fi�sz �� � � % � 3@BEGINNING OF TEXTjG 3�%� � 1�!�,\eqsec % un�� tt � � get equn s numbe�dby (sec.num) \title{GDR FI: � a\0ly-Deformed B 8in $^{42}$Ca \tC s{ �P�ed CXXXIXY�Schoo�aics - I�n�al J@Symposium "Atomic�iY4extreme values�em� ure, spine�Liso" -�,aTand, August 31 - Septe!% 5�U} a�$author{M.~mv,$^a$, A.~Maj ,J.~Stycze\'n P��Dnarczyk$^{a,d,e}$,��'Brekiesz 3,J.~Gr\c{e}boM.~Lach ! W.~M czy\'nski �.Zi"bli."K.~Zuber 0HA.~Bracco$^b$, F.~C��a  G�nzoni $B.~Million S.~LeO.~Wie!N � B.~Herskind$^c$, D.~Curien$^d$,\\ N.~Dubray$�Dudek"( N.~SchunckA%�K!ozur#<{f,a}$ \address{�(Niewodnicza �� itutJN�arQ}8, PAN, Krak\'owQ \\ � Universit� (Milano - De�emofK�INFN � 3, ItalyUc�ls Bohr��P, Copenhagen, Denmark �ld$IReS IN$_{2}$P$_{3}$-CNRS/�D\'e Louis Pasteur,��asbourg,�\lce\\ $^e$Gesellschaft f\"ura�,werionenfors!{0g, Darmstadt,Q�Tf$Katedra Fizyki TeoreA�,nej, UMCS, L�n1TiI make�nP �(abstract} !�4$\gamma$-ray s���M deca%� ��i��oun" rea\��418}$O+$^{28}$S�@bombar�$ e�!�4105~MeV have bd �O experi%�&�(EUROBALL IVE0HECTOR arrayse"I Aal�strength"��highly" ed� a low �0 ($\approx$10�) p!�t, ��a n> a large d�ѥr� Cori� 9s.7 addi�/prefer al f6' �- V1�' �'�qŘ!����observed�  ]\\PACS{24.30.Cz; %{Giant~on�s}� 21.60.Ev %�8ective models} (".{IntroduE,"o8Sect.01} Chang��|ar shapeI�an obl�  withE��i�allel��0symmetry axisan elongaG pro Hr triax!cone, �� mpanbJ< �ro'arE�ashortesti, c�d i �traJon, hasI�predic�to app�in D �e9$angular moaa closi�fis� limi�eVs��%Es |M�J�2� )�Dipole9� (GDR)�Ap6}$Ti <uZ@Maj_NS2002,Maj04}E�E�$article we!;w � herM�e"� confirm 9f�ngi�sim\�I!�A�F�based $ � -St��( Drop (LSD)I��tPom03,Dud04,Dub04}, when inser!7tousA sticG evapo�8 code CASCADE,  ��e�-�5w�yum+ y�i!� f2�one% R��V i terpre� as a � of bothJ��� �b�� split��q. More�����U�fiLo��A���ly!f N�-�� }Q�! �2�< v�QFQ ��oJz��:�2!Y~-tB�lper� at!� VIVITRON�TeleratorM/ _ Laba/ory�A*=  (� ce),J�~IV Ge-�� �LBeck,Simps} coupled q<BaF$_2$2& 7 Maj9��  m� � gger�z��I� se� -�paFwere onI� event�iv t least�$ Ge signal@ �, BGO-sh��^ � ar��~�1��� in� dete^ of �h����*� � pop�H� 0>� "� at"� B� �� exci�on7 �����)i ~ 86J �%maximum�� ��8um, $\ell_{max}� 0~35~$\hbar$. � ��� um"K  # 1%s, on �n well� olved .���!q��%�Յt Z)F9�is���7( Fig.~1a. T.ga�=coMf, togM&�!�l.u6�= allowedA�I�=1�.�sAA��-�"J s� S s ($>$~201g�fr��~A�dirQ+s aB tamifs.)�aM�2�y umEanalysedm�a� ,Monte-Carlo )&!.�{ 2�m�$Her,Puhl}.i�A2�!  givenA1 absorp� U!-g a� &� 4method describI e.g. Ref" Kic�.A�Tt!�Q#X�F�>�} �m!�a narrow� 1[i!� � � �a broad\uc� rangK%�15�27a��qE�� &C-VM� P!8�equ� W�Z ��� � � E� us, E�a non-N� e�! s ( �A� $I$~=~28Y�c A2y* & ne� ng+#� ly)1strong "� �%��R� (at ":p~13 MeV) by $2 \omega_{rot}$~&�(wh�[$2&A!M� r)ny)Ishift�ar� its�� down! lI.~L",.�")� ��en��yfirst cl� o@� ��B%in hot)�i��P!�F'b]M'x%�${file=fig1'4,height=9.0cm}&"'6a)} F-#squares &�%�&�al���� V�Y�6� eha�� �}a�#�Å� �� CascadCde~ for ��pa�ter*&e���( lLSD��& �� R�a d�ed%�S�he6#�V~hown.XLg)O� U 5~%�pe�f� �ƁH �_ /An�9�ls a), bɟc);�Qb)}~OpenVc9I�L(�!H �2�26!�34�l& ?�f�8,"�9� mal ɔfl��ie�����&�T�%U/Y$caI�!?n ��!�u�R�ԥ���Us*is2�%�1e�)-�)��he!�Q-gedAu* ���5-t Lo z"�J�c)}�;� d Q�aa� same.�bu�&�(� +5~(points) �;fitL�C�solid�J�d)} Si"c)��$I$=~2Ui9l�,e.� �Bt{)k�*��{n*�,In �)too &�"E�EQmo� �Fw���)6��&� i�Q�ed aa%Y��(�� �(AV-��cco`� W,eF<M�car Eq)K Ma#�(:h*� @2� }�s (viz..IO'd,JJGl*�ce%,rein) i�o_Z�new� :� (liquid drop�"LSD� �}� \mi$,copic E+le-,�)� !�"bLWoods-Saxon Hamilton�'5�{\em u�al}���k2* �d&d�&/!` possibilq� R�Q �"e4a� ��� � 2 E� �!�us�Ej��� ists, A�g�bal,A5-��ian1,anisW �8Nee82,Gall,Dosst  ��MKYx�!w�reg��� � 6$~�,  +W  > is�q&\occ��-�� as o.i�b,~1cI1 denoe\s "�U"%�� b�1��$< .,�.le item�� e��� rc!�e latt�!rA/de�6�1 m�2� 1o^!2 GDR F.( ca - ))also exh�(>n 9 � ~ B] 5�er�� . Fo��is���E����A.�, i.e.!��6Dso th[. ��"N i� by 59�s, each! ined� aK�� roid, a w�3�*�Avv15 inpu�1e�� "� .�1� ��zJsQzb,~c,~dDa n� - ��6�b, 1c�1��/� , |� broke<nes�:ively�.Br/�"e R� a� �aA �^a�>�A��al�5 AsQbse� q"��0%c"� 26-&� tak�inccouniő�VK"v inA�,y good agree���.� ))�!��4a�)out{�0assumj ��nV�%Yin 2dis�A�is��V M*6G��uJ��J �P in ��� EB�1J� bGDR. C �c�xt��i�0� o !Je� veryF�Mz a�: �An sugges��bA& )�a�e^/d lpha$" �Br)$}�{��~*�various �a�}�1�&a=!CK56��A��=lyl   uper� l��!�!7��0�inv04  . Toai ho�dii8�[!��b6T��A�creteſ6 �idual+)� s (1o�}e)Rset� !p)�deK such an�!Kdi�a�"�5IYa-c 6���8 � ��&9 [&j  ()��R�', ��=�spher� �W5�oG���ye�=9A�as��!~� ! � gy�� 2 af (n arbitraryMR�  1�4.o#. As�AD�_) "�95�.��E � (&+  "hd"�)U� ("ni)(Ŋ 9�-� bump�!��8-9A. ��M $�� is h#ra�a�m2!H��.�*�(*�) X� (or almost 4>M� �E� �812�). An e&nc�6,�� er� �$��a ҭE.~"J"s 3!s-!W�� Uv (" ") !: level sch�)(. ),� �e��no)�@ �ZC "nd/ [ � case LX# ngleh8C�7d(=��thei���}�rawu�,0 cor\ed :�'s �Vponse"�WisA5k �C(d $D1�%. A&5 !jh  u�E�a�i�1aa� is m�"Y#� low m�b a6=EC1�E5hot�m6k'��酡x� :2!>��5 maJ7 E9M5wcold}�� .�"�> due."�"�! Y& $$^{143}$EuE͈B�*F:� eem%��%�4 old hypothesi��*}!FaE-�%r�$ play'��}�: 9�B R'!�6I yr�J4 s ʷ2.�4.82�Iq�yi>Յ g�)�i!�d0��in&]e��^ 2�")aDNe�� *�>g(�T)��*$"h M��"�M��+%zU&vk"b Summary}"�Nt%��5iy%�*� W*!�coincs=ce%KN��AT? Q�s ɩ�23*�F-� "15-25��U\ N�1���nen"i" A:*�%( a�l��J�7F�(%���}i�s��.� �or��� time6� :j�U i�aoK~���5z�_� � �U�� ) � �],!�RAngY1.$ �Z,�$�A.A�+r�#&�'pa�sn,u� mechanismL'7._}��)�a-/a�way� Ap")+ё "�) , rapidlyng%� rela����(i, as advoc+in.�02� Ac#"�>s}�""Z>2aA &d>�v�<^�< R�< (KBN y=@No. 2 P03B 118 22���ex!Xg�*�<mm+.� !%w�9�/ NaNFe'0que�0 \'ea%�t .des P�*ul $IN_2P_3$3 �:�0&�& ies,e� �European ��+�0" HPRI-CT-�7-00078�Y>�6{2-\=&t'} A. Maj�6., �2�7}�( {A20}, 165�74).2V":6Q��  _!.%U2]$731c}, 319_ `~ K. Pomo�2E�J. Er^kP)<Rev.j,C67}, 044316k3.��+} Z1 �JEN� bray/3 ��)4F�.8�*is �� ce. = Lach} M.  ���16!p0)p3). )�9w)} F.A.  F�)�.�=V� 28},�=9:2.qSo)J p�&  eZJ535X39W7.W�).5]�ZZV� A571A�85^2� Her} M.G-5,;6�= M. S` �M?I� Lett.�203B}, 2�88.�e&4 F. P\"uhlhof� PN� {A28a�267� 77).-�=�D&7ico6a-HabiorQAZ.V�B30!�22).2T�} W.E. 8, P.F. BortignoPREhroglia^~N� {A61~0�6 -D J.J. Gaardh{\o}jey� Annufv.]aESci.�42A�8J����(Neerg{\aa}r"I�I�V>110A%�82�}8  ardo9�MTZ443} 4�� 1985.TE T. D! s�,V�>��"�A� �P�ed�>� &H< bU>� s= INSTITUTE@=DPHYSICS PUBLISHING:.N I�  I`Pr�9� "�3�PG� � an"� 2:!��< I P�8shJ jour� y+LaTeX'�� ��  Iy source�@`ioplau2e.tex' us�&g�6`�<� Iguidep s'�e Q$)explain��� demo�D=.use9$o!VI=@ �p) int files � �ɡIcl(&o 12.clo� 0'6 I�  I�=[itself�� TeXd& �B I� ��3&�3  FN+wa cha+ er check& ! la�m� x �,�ma.F .(stop % ? qu�oY:rr/��$ward slash�\ back ,^ circumflexE�dABCDEFGHIJKLMNOPQRSTUVWXYZEdabcdefghijklmnopqrstuvwxyz$1234567890K�  %:CE0[10pt,amssymbmath]{��6YEg�L icx,k.} % U"�C�R�4 if AMS fonts h/ired %\u&�E^ms}� `?��}�CSemih%mcY � una��6**�0dynam�:0sqrt{s}�0$17~GeV} %�Qzimuth�r�on{P;CLJana Bielcikova\foot�%$[1]{jana.b @yale.edu4.8the CERES/NA45 �=�7ion�CB��&�A, Yale "%Ay, P.O3 @x 208120, New Hav�! CT 06520- USA. )Ia"�@W�e�0�tudX6ellip�Wf($v_2�4 two-�ii$~1.2�)�� �A�b#6 �in�8�WrE�"�V(and reveal 4 harm�Von"�Us!��4e ($\Delta\phi:80I% ���VN(\pi*���&at j� ��a� /Wh�#�-��8peak remains un�d,%���)is�%adeXA��#&@� F. %B�=�n�:��:a wUBcD@��e"�7Ane. %�R%� us� E}�#per�!�AofI  %\6ep�jet��nc� ��4!� �5VsNq� %ara!�sSPSDEs %o{\JP��%�JA�if �' : page��K 2�Eg$I2&CE2�i$$ important�a��NHine+Q2heavy-a�-���!�iA�I#Ddri9ani��icAFs�Z gradiEjbuilt�Wdur�:���st�� s duA�( geo>-$.��R)!�yi�L!c5� . ��E"�J�7et\A;ia�!Oking}2t`exp,.w`>� PE� 1996. %be��up��e � Ie projA�on& mb�R0�r������'pseudo-r��ra�D2.1~$<\eta<$~2.65 !��E�, 9�accept%'iGa���� � of=� .�_$s. AlthougJ�1de�*optimiz� H&� (-mass dilep6` pairo$Lenkeit:� xu},-]o!+s��y capa�4� inQ �)hy�as cB2>J$t!F= d"+d[�0 =10.5cm]{=*=b�inl6|#�dY/�TA�ert=n&�7Ch�Ld:{ re� ruC2  �1Ibas�"omb�.�J`�`7A� ilic�ar�>)�@ r� Y %cE�:ID*e:�� %Q:�� %=��� a 5resoluai inflDe�!�i� nsic%9ce-3� ow Sal byi�p�"N.�  hes& ... %i= AlX3iIOuB�A��A���1Ub�$� %�� RICH��)ducA�>� � %52q��UB��n 6 z>�IO��" �(tMG��@inguisF>�Jby �.  ��i vwo -ima:FC� nkov�!�s (!1,%2)("vhe)] fil  �CH$_4$ ��athresh�g(�*@_{th}\simeq$~32),� �Q$p>$~�0Gf�!�Wlight. %B5��u�Z��%a�of�- e.6jbanana.� *_ .5%D%Vu�8!12%�>y�� in >L�!W!�isl�d r�.� o netJ�7a�U ��A$))� � r�9;kmome�})���� P!�iBaEGqEa��J!U�u"���� G�er�cW in.�U<6�6�.Slivova:�}�!figur�F&� tab�S}{l~ >� �F6�F� M.4} & \hspace{-2 }O mini_}[t]{87 } \v +5 +cVn�d#2�A20'*ICY��H=�F��dcSDD�d ���+e�:�Br�m�pI��&� qe� � 1\ -} � ��, %E$��=a��JIU>&Be�~56�/F�_ �%� Z�7!�]aR entum-radI5l-paperZ0� & HY I ] �5Ecm ! U%6I%9Q-M� um��!'!�w �0N�.+_A[6C��%�[^��~BC.- �� �� q� 51�� M) � "y*/ick�Nepsilon�K"�=��^d�y� rackA2t+al#R&?�M; %$V(h$^\pm$�6a�k (verage 55\%%/d"�o�Rweakly�i8�� %� ra�rm ..Y�<�o�Ho� ofa�ia�%���. Howev�(�3e"C %ef5)5or'#e~. beca�"ek�a[�x�9o� y� depe�5fN_ch$Rtheta CBu�$p$�0A%vicin�!��"�&Eit ,@s steeK wL==Z %�F��yBZau� $p=10-.�n "��m-�q"� } Mhav�aly�0$41\cdot10^6$FE>:ZK %a�>�8-� (26$AM 1.5)"-"y�P a#rgeo}$�ReL!OJ�^Yff�$*��bf"]�,s $N_{ch}$ � �/SDDa�2&43�%3� "�qcor*8]rlos/ %dcdead �9(s, pile-up,E�gh�9m�C1�&��?plicity}�@AL.% a --|!0trUV su5�vol inst"@�<u�tunat�=E�inously �tor,V��.U���s�&0.�B�v&x4j3�k2x ;b��U�\ŵ*x�.�>X2F5�>^'A.!�p:~5 val UK~$MK�w q ~> I8<UrQMD 2�B� �? =�", sA TTͷlegend< �5�3r<of 1.03ek appl�^to9#�HsR �in�to��T%�� en��&~�1��#samXi vid� to 6.�clae],C1,C2,...,C6D<Ty4dep�^�"horizon��%s.�(v�J�%�m�& 5Fa�� U� q m) {'sP��AM)Mm�`� urqmd}!WJ%"auf�'��of�I�2�w$\s�K��."Gco�J�!��ea_d2�E�� ]h�"�S-� (26.0B�6�. %$ra�=rn 30$\$(d�ier � Agakw+ev� 8wu-: �e�u!1.5�]b� B?ktu+ ��mix�Vs6��.�Ʌ.�ņ��sO:�in Tabl�y�-u�!�>�F9w3 ��/\.�, impac*>H $b$,�-�%ipan&!}$,E�bin�A";�Joll}$ 6� a Gla{h.� negfng.TR�0Eskola:1989yh&�t!1}[*�!81�qW{|c2 } \ha� C�2 & E] (10$^6$)&� &Q�20 (\%)$b$ (fm) N_- � \\ n \cu {1-7�'%Z}>\l�N_{'T�}\�le_)�� % � %& $b$�BQ%�6SBt!�#�6�< 1& 7.77 & 14 21 -T0& 6.8 - 7.5 $59293 1# 2,58&9 17J1( J0 -P$8J368 �8 3& 5.66 & 234: 13 -O6.0J22245F�4�0J73: 9I *,& 4.4 - 5.3C25�542h2�5 J5 & 321: 5 - 9'< 3JP� �63 �6& 8.1�39P#X <$ 5 < N3367742�6l"YDef� �CaX" �e���� We��i�*S�)�ve6�!�;e >Z�>d$�nUqua2� se� Four�tco} t�'�A Poskanzer�@�A""(a�.�s~ r�" $\Psi_R$� &��dN}{d(2- *�)}=A(1+\sum_{n=1}^\infty 2\; v_n \cos (n(.4)z5LDle-rp-sqx;A�5 ori}�1�%� plan=EunL=� WrzOGn -by-FbKR>G � ")by�)c3a sub Jm�^ . Non-uniy'2�~ & �.�* remo�C tand�,�(dur"-K:�.,en�3C ���U ��o-9.m.s.!�.�T"M35-40 eO SSband�!8�^j*���� >jdis�(a��D2YO� v2-nch-pt�h6Ab(p_T)$��H%E6wBose-E� e�  ��6H,DinhaE 9mn,d{ ova:]iwAESX&O �5�momes  0���-49��@ !�NBx left��!M.�~�E� ! $*�=m? �in%or!�v�%�6 2�U6�-nWman as�k ;f "A(G�)*�9�a��N�f�,RQb)Nsn�i be�fZ�-�,4-"�-E�:�-,�si�G2�-*�-6v_2.�`$�Ri�to-��;-_+�� -�!ed& ? ~h*{-0.4�FZ���4a:j=k�=b =�Z�j*~(a�)!eA����"(b)9+��tE�-�U)�$/$%��Hydro�1 *x]-S Huovinen}I� a ph6K~)�W�T_cE 6�M�D���ki�"reeze-m,v'er, $T_f=20~`qkM� �!6 !daA�)e.6d� ��+�#�'elu�">[� v� %0a�*go� ��)�A� y�& y�)�M�pA�" �G9v{t*�oa hb�B��Mn EOS?.�"=��Ozrk glu��lasma!�:�2�fav�$ae�er�[n�-�.�a�&Eo�p5�)�*�:��ne�)!�b@i+��#protoo'P�R;bla�se+be eiiN�e��.�)\O ��oto, lude viscVSeffecW%�^FNTeaney�F&m&N3š�[!��-p$_T$}xturQK o��)*Q)!�(i2=.Q �92�Y� ��Me�u �.t'��o c2R�cW�d-0-20�$-%\�t�!g8a�s,�,pr@�E>��a dq^in8#:�w�)ma:/% dip �g*�%��0.Zf���pYK!�hE:�c7�bym�M�a .�Z(MCEUrW!hoORe��'a�*! \,'by�o!�MOb2I'ETc� �4%�$&mf�romis(�HE��!� ɉ��w1C]�k!��Eb)-�(still keeps�-�5-� -r� redu%"k0m�aXMCQ�-,.�S fouri3U�:0r�5e*�i&0y��4n�ck5$)bp"�5$~0��2e5J6\*�5� ��&R  uq� �&�an�2e4:main esy 1K"<' whe�!or�G2�$%��3�4v��.� �2 b- 8�5, �H2�&�6� ($p_{{T}}6�.�l�{.� C1h �m���`  a6�]�A� ��n �; ols:Iuv�V!-6[ a�t[t>�ky�. Clos8`ym_a"JW�yal:d8�e ��l6&�f��!7%��-�� [b&1$/I"ylr}�3 3np �p 6Rp 7�=zp 2Q#~ (J>V:-!!�.���E4$\�<p_2}$ (&QV�!~:�e���.E�*� *� A,�0M�B�V�a�0[Qtr� &2J�9($|�y4|\ge$~0.6~rad,��d�k).e7:��'!�:PYVv2-p2� � nM�+%&~:� %de� oaag��� "�)�Q�&�*p���Bbop_"o3)),y�2�-eq �l�d� phiy#a6T7a��n| any!� �fEy . If�[.?|� C6� I�n!� n=v_n^2$.2�3B�� s��� �S2���/i>6�V4N2�(NY&� �?[ than s. AI�r look> O]�]�� �at%a��\721�!�$ zeroe� _%vscE��M=2��st%�!�-Z5ngapU)a��2+"�XiI%e)� $ i�6�6�b). U? �!E22I�4׏a E 1%� ���a�j nvok~aA�-d�� al window!�F.���M7�M7zM&=]rof��!�Ga�w�e" �(� ..=�\����2�(� ]l��sE��{�!p6�@��-���A�B�Ad!��m�d%AssEu�;�1;7~@ orig��� ve�fK6� �RN 54���Z=0$mpi$�top!C�6( modu'd%@g�ib�r"�g@?xa(tudy=�!� G %lem�is fix;%J���ɡ y.���rA�i}�.��u_0?(0.23P!0.03)�� �)d-�m�d��it%��!!� 9 "O(per|ic�X��'<V.�=um�Rak� 4gk}!4*lW j_{T} ��4 pi/2 |y}| b` \pi}) p_T%. 30["40)TQD "�_~%?19 3253 A �ka�9somew�A�z![NSR �Angelis� 0bsGo� .-��=��AU6]C�Bm�a�p �escap�"T} ���ݙIol+^ sd� (� 8}=$~6q�Y �#98k_{!�282.8Mv 6)~G�2-9ag�L:i�pre��"8s2 �AuF�FV9�ith�.��#�� ũe2l!:6i!:pJ;,.i+*�na�KeB�e�Z�b), growBGO*F!1#��e6\������;s*I6 �=a � *�;6t i�%KJ*<)0i8i2<)5a b"�&<)~�1In-de (topɴout-ofbottom)��n żJ�%��:B. D&!���1%Q Wpu(B2J ^ u!B N�Da�3�+�dM�R!}( C2,�C3�k+t�e5\l1� -� D�U&6M�26:?EAm� � E�i^BbAwp# R iM@{<a�hV�:7 2��� �Bo"n/ed��\�i�On�ng~l �� �B�  \pm\pi/4`l8_ .h.�(� iM�}) orF�it (.�}f>�t��or.<�-� F�)�OqK0�E.w �-�F(lie aboEh�ecU��2��g&OM�3kuO5sub L9%<+�-5�,"� &@�zJF� EE!�m�� 2 #�p.� �FB�(ia��n 1.32!�$0.37% 1.39 44�G2�HJ�,*&;�AC1�) &�"� &��a12&Á2s2>. ݛ>"ѕwe�F+�tI�Year�a%3,a� any,�A�]� :�oD�IR #1{C�+z }�ng*y9�&1Ka��R�b�vz$A��!K>TP4���ol6�tKiVgz "? "MM�m�h1 ( h.�GA ah � !H{=&�C&a� nAjB> A��a+2tq�"s 4wzm�B�M� aF�l�?� ya!�s*#��+&ˢ,3A f�& �dis&`Me � Q�bQAq�re&>b�jx.���5 Q� ]�+�6�� ��/a2�W��re!0 f"ngs,[{Bjorke5\buwem�R�.cmKAB3gg}  G őt� (�8() 2004 \PRL��$92} 032301 � \2] :n%} ~% JB3 PhD!vsis, �2les2�RPrague �B U3] �s�19>/} %�^�+ \NP � A638} 467�3]>�F �/ BV�F.U61} 23� �4]�0 Bass SA6I�%bb2b�4Y25�5]:Y. Eh. KJ, KajZ*e Ke�Lindf !J �.��B323} 37; Miskowiec D, {\tt http://www.gsi.de/\~{}misko/ov>N+�6]{:�(� �*$ AM, Volos SA �\PR �C68} 167.?7]{*�'}  PM,#aghini N�Oll�q�iJ-YAX0 \PM� B477} 51;K*vat�"m"n�.�8]e�*( a�ova D)�J39M A714} 124.U 9] {�Wb� } A"u�KH:X STARe]1! �<86} 402; Adcox K:4PH��62.69} 21:� 10]{"%%$ Kolb PF, , P, Heinz UW selberg H!W� � B500A�2;2<pNџ}�7]{NA49a� lt C[`5V�3�]034903]�11]�" �" D �M,-th/0204023;301099.A2]{*� Rak JfY4 J"qee��Fb�?�b�b�b�b�b�b�b�b�b�b�b�b�b�b�b�b�b�b�b�b�b�b�b�b�b�b�b�b�bVb2pt�a&b.�[��a*�a�x6^bUb3#d"N� \ \{$�"mgn"'Ro� d + >7` � $s_{NN}}$ = �P "�a8Dipali Pal \it{K�{ �"�a2bSee App�5x" fK�l4$ list.}} 0GfOb(3]{To %whom�S1should2b~xpromneya.robertson@iop.org)} %�^bD6arB��\& As *omy, Va�eb}\U}�$ity, NashvTN(, TN 37235,^b�b5�a"ab .�e �NW�ej�!k   \$�a��$K^{+}K^{-}bph6"e"e "do�`nؐ"7at mid&aWD�\'s.R=�z7���YZxQ8nq�/�D"~$in (��|>�ed1!y:U)�HZ�*��O�H �{,�lt 8�}C!\- ��Aui(���!'+s��1f � !�� =��6`00.00��42.10�A`�A`�@`#9E�$�si'#*�pa�e�hYy !Jchi�PV7 )����andB<�Yn�"�TiGJ�v04 hs` 5�R)�I:I��2� i�1"�Y($.(q $\mua;-}�^�9}q Q�" ��fin�Qti {�"�t���֝�J&�%tkF�_M a�\,�-�e�cka s)p until*�3)��>��z�ddense XEmE�8Im�l�j(E� and/!+a#�6�.hs {\c�phi1}}. "�K�.e{.{�.~)U ��K&7� !c�SxmQ_�[p2}F;ga�al,3i�:�X &q4"��� evu6AR-�.�5�S1�P!X��\� �g��in�GAQ�hU"s:$SJ^8i�a!.s\bar����k��'*a81e]a!A��n!sGV�\\8�!1g�{2N}� m*�|2ODJ�EVbA�5j�F roug}�������?��I�2��$.��C 2�z�z�H�W)�� ^�y����# in5�!�BI -� ��8��^ {��� �rcQVa We�[�ai�O��#�rn)5r"�#�P��A(�� ����B��T�& ison�R�Y��+B> . B�EV�`/;�i���d"�\O�."-G.A(r()l armm�E`��enix}},"`YE\%!iW��m� beam�:�2 EY$� 2$VWk$"qBco=Qu��5' Qtexn �r"y -�dA�� B�CouW$I�"�'ofd�'ck��&,O�b�T�^�^�!�0�y�pad". T�2a� p���d cogn4<��cAl�Yi#���L�f6Q��i�b� :�7�Ns��*GZ���*�A Time�$flXY (TOF) wa#. )�rm?� |(b|$UE0.3,b�$4 ~ �Y !�8L �j Lead�y�Llc�(PbSc) a�UL xndIT�;I� armsgJTOF���� 0.3 < p (�'c) < 2.0~&z4he ���DMsE� / K$.�7 Lڢa�]U��A; `2a N$Q��Zro��"�^2=6� �.<  ,E� primarily�U�RApI�[ eren�[De)or. Fur$:c "pr�K�jL!ͺ" �" V calo� � �` atch7u�.fPy k��� ha.HS62 $\3g,s$ $10^{6}$ &mum-bias�X�$� !- |z_{rt4ex}| < $ 30 cm %hb0�$a�޴F~80le- �n4o��-K�Fe.�e� ��3�=6I�6 :qs VTsO-c��steps. �v�"A�"�^lyANrg*��s (� V�.� a�1=(�2\�)A�F unlikc in�Qm� i�Z�t<jfW,�&b��orvd�$�!"*V�H ��&�$AdC�]6?�e%��NE� echnt�. �=F�=5�v h�' ll $'$'�Qm m�= #-#� ntenQ ,P$.Y6!�I�? . ByH��ourselv�#�<=@ 9An%doe�ex�qm�Wt�-�e�y s � actu&�(�� �%!�2�N��enQU Pois}�� soltzY �bvalidit�&')Cmi6��? {���Yg2�(an35 �2�Xq�I�.;e-��PK8 ��2� 4N_{++}N_{--}}$]0 atjmassoci� E !� Y��6�<tudX &!�7E) .�.�"�$m�1.�- &� va�� e���s b)e$). Typ�oE��> fourP� �6s nam�� $M_{e Z}6 1.1,52E� 1.25&/$c^{2}$��9MIgՎR�i]6�is �#��@4\%)�^�� 1s��$ ��A9�'&�Xphi_inv�Bfn�E�n�*9nE���C�=z�=�/ b�[A;EAA4V"� di-��o�LYy�y 2�Ke�c �U��g �G0O� -Ejs�Yh ?p�? wm�r. A"�=�� .� pi�� ����o2!'�`��A)"M *�upo�G56_ � ��.t�'�(! q�� �V��zr�)de\�rV�b_B850�950��q)�J the �al%110R1206-i�!p -. O mxN��6�X 5��E�B���i cvN Rd�Y�����b�, Breit Wigne�o�=*3/v��Xa&�2q�AW*� f.�!v�f� FIp� �vv\e*y(a��2r� ��hV�q��e��!P�=M1 Book�,j)�0[]F�[�=1.0\�]�_�2")BQ�x �2� .�(%N)J%.�(+L��>�%� a� ���qpp�e��%0��aeJ � :'.�X5� x6 Y�)��.ed.� um. :O2"�*ae�1.G���%�.�7AW ��co1!�Q}E  b Xc;k&?q�:� *�Gby2�F��ion��D,Ntd �+by �G0ng� 2�Ko)0 ,DT}$2f �Da���8�N� (T ~= ~ 320$�� !��s0 !s� �ed �!���5 ��@i�sak� 6I�1be tux eHrea�i6�le�.� wx0l�9teE�=�-��F�*d�U� s"�@ �c = �Xphi}^{G*� } /R.�3;ndJE".$m:$;Z/In�d we jE����^:^ �!�]I��ۥd�qe.Iru6=rio�!�ved�$����T�I/.% .�P ��.�Ņ!�.N���r�V\�0whY�A+se� to*� jbi��.�U� � B�6� ���a&*� mtAa�f��. [NC ס� haj side��2�.�퉪um� ���/�. Each2%.�ex�+"���I�:Jf�q 1}{2� (}�qd� �Wdy}D 0dN/dy4$T (T + M_{e])}�-(5 -S /TBRT�NEvT�&* �e�A4`ywo� �erE�6�>�>B:�z>� eekkV�I2�ve r.�%{.7��A262NsB�� Ś�,B7I.6�_dndytý�Oing�L")y > 6 .E a�a�* c"�DEލf.� �r�blop0"��m< s. I�y�)use�z���E��4����2 - 4!�c�Z�j1)o�+"�:s [7l5X�.9 NA50aX�!"Qna4950}}� �8�o, in Pb + Pb "�s~*%17.27?;�3)�i�-m�R- ��!"4��8e�Q�&;h�IPDis9=+ ����^�� d�of��`��q�n@}ar ��B��76V�\".["�!�� q���TQ VM^� .+� � a��%c me��e��dsmqm}}���yof(&1o�a$ . BuS s�8s+�a�Bn��l!�li�xry�a�tooEaM�c9  9 ripe!ocL!�o2q6�*�T> issue w�Pbk"&�?�3-2�5A� lumino&�2"ere�bF.�rj91.5:�9}$���Ѧq_>" ��.6� �e�"�rEo.�j{!�I�.�1�}ikipoWcm�fD"�c}�cDo&Chao& & �8& T\\ &&(MeV)\\ ,  &&\\ �2'.B& 0.047am$ ��Ac yst) *af& 414 J31��G 23 (DR�.��56 H0.0^�:�28 N��32J946�17�!*-5r&6�@M9&2S>Y-!*�H� %qM:�\JDA���6N�61��ent�<$phiprc,dsm9W� _N�.e)��D in .� J�>� 2Fo 9 ��<+!z�ged J��xa� >& }`*#� �Z� A,es"��&K��}�*s..=���-��� m�toJ�����plo�I�i��Os� n7�b#h"* by 6�VD�2J�G hm�j�+g !�� : � s� �E&�o_�mb� rti�b<�ng �K%sI�.&M3�Z3 The N *� !?,��yr�� j\9Q s&�[zVZA�Hh`FF arp �M�>Sa�G�.����� �al (4U 92\%�Et�a *�_a!PofNa�!6aUB� a $&Ci � y 7}�$����BU�m >� ~�%N "� t�haz� �w{����U �j-1VW � �e��.�6���C F�j��LA�eR� I�vDo��H�B1q" 8:� 6H w.xaC%i%�an�zt!� black�%s�*E!�f� A =� � th�� browT0neFN��2V�Q�1�� �������n�m2mB�*�,o{�F" e fՌm%)Ne+s>in 2Ka�� f�2I�s����2�in ���s^V�0�xE�s����]]Չq)C u �iz!EFjQGeVy�tf� x:��~ v�5�*6�Cqx>�<{�0DA. 19� HagltR�~���s�~ibi#�8phi2} F. Klinglq� WaX�'�is��a��=0{B431}} 254 (�B�kT**X�n@�B�>} k@6��), Nu��*�r� ?�489FU�K" R. A. SX", Ph.D.�DD�>�48, Massachusettst���0&��,_B4=+�( D. Rohricht�)�{G 27!+35��1.X Debsankar Mukhopadhyay0a"m�"�51jA 715k4� 2002�0 }MfnM S.~SNB��rcl-#?10012YSz ���nu� j� �&+�%a {9Au{�/��f>"�?d&�7 �w6��[�8]{� le6'8"=8% I�F)��,es \def\bcc{;� er}} e�6nuep0u0\nu_e0nue  @ munu{\mu_%gz�G 2dm2{\rm*� m^25nurad < r^2 >  s2tw sin ^2 [P _W#am241 $^{2DFAm u238GU th23 �832} Thk40740} Kr6jncs137S ^{137} CsTba1333} Bacp)$kg^{-1}keVday�(!�)�!�-�Emub�BZe!� rm{E-�-�rnusp .]-( ]1 )�ke1)I\kappaEN� ���BT Н�By %%\hއH AS-TEXONO/03-06 \\��*{1cm} *\todayh% TITLE bcc {\Lx* M�}6��St�&($$^{84}Kr$ ��2�5� Emul�M��%1 A� cc�6��, Author List �!(cc V. SINGH");{v�h@�.siJ�s�D.tw}, S.K. TULI\\ ZT0Banaras Hindu.�:$ Varanasi,[�H\\ B. BHATTACHARJEEa SENGUPTAfcGauhati2] Guwa]��(UKHOPADHYAYfONo�Bengal2T New Jalpa��Z��!n j,)xN  Affil  'T^6 <3 cc  �P�l��*oN� Yoi�~1 &��gy�, terv���<$i'Many a���|2���k� > exam�Ivdep��b6J bA197}Au @ Uran!�< Ut yx\s)B��.Bw&2 ;Detai��)R9H9/�)��emplo��a��ck�[i�hE$NIKFI BR2}U�1\ pelli%k�d�es 9.8 $�62 05~$cm^3$,�l h"u�A!5� �?�"n�-�!�(SIS} synchr�� GSI}, "��9D�y) e�6%ŋ"�a�6zeEn��|_XLEITZ (ERGOLUX)} optica��l microscope. In order to obtain an unbaised sample of events, an along-the-track scanning technique has been employed using an oil immersion objective of 100X magnification with a digitized micr �P readout. The beam t�ts were picked up at a distance�@4 mm from the edg  dplate and carefully followL ntil4�Iy either interacted with emulsion nuclei or escaped through any one surfa �z ;or stop4in�. �se4mean free path� $^{84}Kr$;�ar�s h1�$determined�foundAXbe 6.76$\pm$0.21 (1197 )�) cm.�X{\bf DGKLMTV} collabora�[12]} Wa valu%dm� �<($\lambda$) 7.10 w14 (87.v0, consistent !i)H experimental error our uIclassiUVxof secondary charged particles!;these � 56repor!�earlier� . As6I�passe)�!�1�s, it lo 4its energy due!�ioniz)HA�%x ualyE�B� . SiA�he U decreaj%�am go]�ntre aT, we have divided eachI{)AhHmajor regions wheree8v!( z)� range)&\A} (0.95 - 0.80 A GeV), E/B8050)�,C} below 0.5 5H 08 - H resp�L ly. ��!i�ing�4will deal onlyI+ thos�i�� in which�;least a�>)L was produced. Examp�. electro��,etic dissoci)� of tArt� proj�l-�i %�b�>re\a�$rest data ��sa�00I$s)�� t%�5�tervalsaA��727, 337~36 ?B@r � a �ed)2I� fraga�y) estima� IPof light PF's (Z$<$10unit)EC �lmeasured by blob/gap density�bA���ing�#x length coefficient. For medium|�to 192�E� �A���,tlta-rays��d$)� �)E�[13]} �stA� heav�<97!���gn9!'���A�by -Y�lim�Don����i{Amhel�V by comparG�4 width relativ��>e��\ !�4]}�`hA��on� -ccuracy���1�!�. \sA� on{E.�Results�Discus�U} E�m�E4multiplicities_Z$\ge$3.R�� Z=2 PF of�lete se%n1yGa�tribuA�ov #ntire mT5Z�m%"($~$9��MeV - ��4MeV) are 1.21% 0.04� 2.036:�\ %%\begin{figure}[htb] 6 \cea�L \includegraphics[heal4=8cm,angle=0]{%6-6b.eps;ap��({ Frequency9!�of Alpha5Ił�*�s g bout 1���-!?Ga!��it. }�label{a]1} \end�%� $$%' \. }>$ ���^above a:io�Z!�1.17 %r 0.05] 2.02!�8 (�valI�A}), 1.2#6A�d74710 :7B}��2.0L 0.3p37940>pCp 2���%�pE�F�I�!�5� forB�0minimum bias [$s is shown�?��FEl 1}� 8 eAad�oa2�)�a�of 8.76%[4 a tail extend�m(upto 11. EvP pno�!�Lmore probable than on typF � . W�"ve calcu� d �EA[U�f@�,$$C_{q}$ moAG�� = $$ �2d�!EVac!F��5��;i �V�IM�!!tab �in)�T%+!��t}���of-r's�4�.}DTular}{cccc} \hline &&E� �[ &\\ `&ECA} B  C}\\?)2}$&1.8i 0.07&2.08e0.10&1.7ip 0.26 ]3}$&4.2417&5.59 428 &3.4551 54i 1.25 (45&18.0i�0.90&7.4 y 1.12���)gr��-RJA`same <qse5\aPa $a week var� w$%@ ��(no definite� clu��s%�possiain view!���Hed statistics. Howeͩrea�cl� u(in $ !�A��  ing �2I)}d plot{$Nu$ E��O !Pmass number ($A_{p}$)Wsource.��usu�$different .Ked�m@ at n� 0y similar lab&� i��2}.Q��F�25>1Plo;ũ՚0 Vs $A^{2/3}$���s� F�. Solid am!�!Sbest-R=2M��b.1�e�a)}b&7J&a �%%.�3} Mb�M7 L\"r�(a)} f|6���, 139}La$eK $^{197}Au�*� at 0.6Z99�-d, dashe dI�!wi�.�I�Au, La��Kr:� �b���PM� in Y;�1 !�qJ� >� F�K�EP��- >[ (%�A}&���C}6�)F� 4:�F���exarto check@��d mi� �*%� *�s a"0 phen�on. Ita#observec� ��- 22 (.�4) grows slowly$(��)q�and$empirical  on6�X = (-0.08\pm 0.11) \tim�2Q repres��.� % points s��factori�!Amax� �T� average��various"( E B] I�lKd�Z�%�C 2}. Also N d%�%�` cas� gold��iak��%>�#Mac [15]���Q�ChaA�er���u��Cat/95 L%(G7/ �sU�/ at (x - 1.06~ S�&�(��95)�250-0.70��$(0.01-1.08 =*&�A�� 4}$&234&081&360�$&15.5� 1.09&10.7� 1.18&16.0 0.899պ&01.9O 14l 22&05 0.2w� *1 ha - 0.13&02.3�08wp}^{max�366>� 08&�5;f4&7Z2 15.4V!V&20.1 2.21&44.41&3] � f� e�m|of� Sd�� t$(%�)$��� ed �"con��I�byM (p} = Z - (2�>&c $ + {\sum}Z )$ ,�5 re $oa�sum� meBallef}$Vw� 1 $e \ge3xAwM" $ i��� g�i&72� .a9�  t����ĺ[, depends upo�΍c�&��d exhib%no dra6 �*)�%�*� K�. A�w 0h�� QLdoes not involve a l � }ingly-vEIduc��nd��aR ultgm��| � �Nst�x� -��X I �M� F"���IMF's}) ��by�A �y5rB_%�inEl�E�J���ݱnd�Eps�� is ��A\�!�twoIbut!e ngesa6%ngq+9� .�e�����+. �f��(ional yield� �(Z=2)>E at $\sim$"is eBx3 I�"�f �by2zun .��:1 �2�:Cof�� *2% �N.� !~!/: 6�.B116 7.8862 �#F�)< �̍q>��(2.0.�06)G)���, �1� +Em.�9� "<�s��@(' -0"% �a2 �n �s sign`nt] th+i�!8 �r&y]�.�]6u@ Eq�� Au� 1!q� 16.1>{ ^� �9� 65�8 L" �aj��6E(�9m}"> ��s!��  tog� �6 !n%z� ���L 2r� ^�bF6:z � * 10)���%�1 L9���il�of�_Qof E9I��5� 22}Ne$I� .t�K%�2�$Ha=a>� .�� a given! Q- $��to9! ac��V!���" (s).5=11ote"��<4"�(s)">cK >G>!Xb��% 9Y����E�x��� J�b)  ;��setr"v!!:���|ekA��Mtui���l� the u�r!�� Id� ��a� ��A!Ha � itudc$�", 11.�18.12N���)� V3�% �m-%��� is g��!1 � �aT gyI�[16%���A���A�M�!�m���#s depi�$?e �4a@: � lso �s �J�=�) nd :=a E��~ţse1�-�%w8.�5�"� F�%Y�%{iJ�$in $~2\%$ �s� f}$=0%�at���K whB1C�E�A<� I4  <,\ne0$. HeavyEbs rarely-� G�DnoB�%%*21� eپ � !��#e3>�*� &f"� #ra.BW:9oa7aVakm� �=Q��F3hig ' (1.4� 1.1 �M�publii%�E�[2!; RR4eaE�YQ MRbyYK2. I �o&& -{�#m� e"��f}>$="� 0.04)� y.m peaks �1.6)�*$1.8. Notic!Va� 6�.�a�an ��:f�&at%^1H%c�b)A�ck Q* to �;6%-�1�� C}) markA�a�ng%EQ(� modx(�M6.JX2RX7�= VOb�R�,rge normalis4o�ain���6y*�E�E�$^{238}U M`"� -�F�8�� � J�!3-6� 9�^NMR�10 Nc)fQNNc)�6�1""��� �&�U�q��� �ar�W (M $�$ Z + c)Ż)�t��J85 �y /b)E)� /"@ �8Z=3� ? b/2}= >c)}�F��.n9n��UJ #>b1 ;!cAT��6#.� of�2� (M�ha��.'or9]s�,{2 97��#$21\%$�{%!� 67 �2 6 6���-�*�-Cto�>��" word�&:WA�3mon*E�a �T� s.A �$shapeAu&�made �;ppJ�#� J���  sa� broa�/o B�E/�%!��,.�s �Vif� towa!���f� T�,:�� {�g-� featur� xb+ �6eprocess&j��g&5Q.�� am�)eUd�pi.!�B� V�"�"�"(� )&Ce&W�(&` 1.46�Y}"$48&1.33\\ *�, &1.52&1.7�"�567L"|0C77&1.9�d����1)&� !�� ��)� summ� 2��T,3}. On7%�v"d�1"���bm�.mAzMí�2�� es�a�locEi/@  sA���erQ��m(D& d2 X&s furGa0��� i� dicap��UIs��*forml*_'ed*�83s-�*al� aA� :u� !/mJ.i<.i!����-̝�*�#al�2y&�0�U ��B�-at4%uW a� � !X=/I&[17-19]}�k �(. � &��-�2�ne $\&$�`M>�k !x . Bu� CERN1�,�c�V� 6}O$%c9`"1��s & tes.�!v�0�+e0[20� >� Some.�describ�!�F�W A� inel�e��!!� ��%�5�Euek4V�� P(4.2)�K(��-��6808)\\ &�7.\\ 4i�Mode&P�)i�(i r��s)&땭&1�;`a s&&��TwB�Z&1.J2�7�' 0.67�'1(9���ms��G5 F 1&65�+2��36. ,1.8D��E�B2)1&26.1"k5&29.8 1.4�� no�A(`4&�f] �1&6"� 2.455�3J]a>c ]�-p"�4+ no&2 @1&)1>45&"10.34\\ t5A VNo��p&�&2 ��2R06&2.1t)1�)J I�&M��I&�%�CU)s perA)� %: >1A:��M 0�0�04AA 0.0Q :'&0."x*01&2.9�12&3.3J1r � � � of&a��Y�Z�7.b&14�* 0.87&17.5-\.7�)�:�)� ^`5.I�0.1&06QV+ &07."�!4�`ZO �p R+�.} 2 of� .C5#�1 w"�&��� aro�8Z6�saf%*�5� >?i�t!�D#6od�� ��f��*i� an��of 4.2R eV�����a[21�m�.)k�s�him}8bpar2 frut�l��?!���5A��of(2ɀ at � GeV/�o/ �K 4!U6:  ay� :�� �,�.7ofduc�AE��qR� tron@! "�  onI � �R. A�!v�bnb��� �A$Y� E�"Zh ba�ofA��.`�L�/ny�i��� �" �f �!� ��VMu%~/*�int>M��s )d5b�<.y�:�� �F@ }9>�y*@U�M6%Jed "X )G-�!B.��. ��� !;1@yE�� af� engr�6AJ�i.e.,m.� ��R�Z).��T=:\ a rapi�A��I�!o�-n��e͘dU s,`$�%- MB9.�q�m2�H%L>��llc<:�$Q�s�& �G1!%!9� �5mo.��Vo@�;fek � p�pid< �>y9MD����:j~�m^)� wv�A�(0 � ca��A:�>�uS�{ i <.��>��I�a>���in&�>�$[22���Z9c Hrmodynamic sense phP,�>si�i�eAH) 6 .3systemn��re�$ a few mes*Bd-Mi7j � titu�-��3� 10^{�r 58"k )EJ%to�� i!Ja �t&reW?9I�@e�SF�un�cer�=�@1 n�6w� �),-size effectuld�?y very*:rolV�4 now�b7�gdecadesV%re��Pu<�*�� w�$ Sto se%zirst-)E>� betw � F�B liqui�gra� �41?C�-$hadronic gs?E,�fin�@ual)�3/�sm�*S5terU�3]�E�O=ng�O��is .�Y�C@t�na*DtBrit&0 �/aU!@�: beco0continu�/�=exponE���EO ar matterq�*�>AT�B"�D�w, so-called Fz r droplete�lq��=e��text,��7�sCion must�"focusq- power-law2+�"� ̙�B���i���i>K ��O:( RiZ�:6 %�!2cor�6o�:6h_�l=�+ � 6� �3��=.aj9J24V�2�b�NR"13*�3 -�-�Jx� �e!Dli�1"\ �%f%B1�&"�%z%)4E 36" for &� �_:9i��$m 4, KA)��'2B/cAsr$)��;wsA���%U�I ��in��(� E"ra greaa��?e' breakup�6? �[25��To facW�l��� �!��ԥ�tru�H�!"|1�w oos�A�%�2hB�!�6q�a+/Fbz ,. C�:ly,!&P.9��an�9� U-jd�)s�{truv7�ns+�*low-t&�#�c�s�'vt�H*J�� JinxH%��}�`?DE�.7a�verse�A�Qo(by f(Z)�1� 0}$ Z$^{\tau}$ ~��G# %��iz �% re�!ab� ellT -�-mm i��a��e� }$/2&#��A "]��ejh�2!A6 C(�45 ?:<7� �bYHgYq3Z=�o� �I1-e�C�r6PA-vJ1�@-� 095)9s��m#B��f(ceYEly$l ��im� trend�` A2�2GPFA�exbiv�&l�" �)K[2C(% ri�HiXiJ���y5(zJ!�Hini �  a  le��y=Dem�)f�"%}�k�%F���>sx�J�=ame ($=11.�7� V�"�Beam&ZI�Y �!9�gE � &�Ub&-(2.6E6]6)^{*}1.6c 0.07@��<55QQ08)&-(1�� /�.4.16 .4Y}.�*%�5P($�$)!��"09) ue� Z=25Q2 7]} j�Z�f�9 "�N!�AN9��%��z�:���9� 0.84;52%m� 0.09.�-0~2 +$956"^13R�*�%�9�21 02UG4`��9#q<1�111�8v�ToD3l6si'9�!�e�a�a�mt�m 5M� n�B� we&� F�"q �2�Ds 3G6� @>� �6 *�*��?� ��O� J� e VH� uP" weak�5��is hold�so���fit):�~� .�>~|!,*�7i3�7����I(IMF)}��% �179 �&� ��B��6)Jc7 of ~U, ] )D1���8 (� b)},*�'P6},%>*��%|=�< 8�%4 slop�g � stra�8� s I=T�^D�)�N"�Q%h�> . `� � � �3��"�7 pre��aA,� ��!�o7M%of?al�!�/!B? K-*%a �:"f� �29,e�) �- � �_E�&Dm2U clQ �l temper �I �'� oO�en�@o�E[3w! P -%X be�(orm/e�7�Rk:lu� -F���%$perco��.sa�- 31,3� Su�Q5! i��valid�4�aNutra�a:a9=* I${C�%�G�N"�R!�y�� draw�4�%e��m�"�.work  � subs�;analysi� w9pr9�%"|�� e�< �Ca good'�Q)�/ exci3 Hint� Y��� %:��L� carri �� st�+�i�X� A�*!��� �.-�u=-�).5�L1(c!�T�n* �a�S�i��)n� 2�N|0;�.5�t . O�D�&�&�� � & ��co+ &IE!%)Fqss���4er5' The 6 3Q� volum�Hvun`'1|.�&�~-�2Y5�1�a��� ��a�[:3 ~ Z3] �Hu!� *�� � ���s�goJ��. .�Y!ud*R+%ܕDU .�6B��i6 . �8 Acknowled6 } P�#al sup, gDAE (De[mK�Q�] )�# UGC (Uni!O��Grk Com�G), Govt.@Indiaŭa�y���8 ��v�6ratB[a�a%%%�*{Ref�Kce�m hebiblio�Ry}{99�N�ADem{1} J. Bartke, I�UJourn�$Mod. Phys.��HA4} 1319 (1989). \H2H(P. Blaziot �Wl., Nucl6D 525} 479cF912F(3} Y.D. KimB �$Rev. Lett.663} 494C��4D Ba.nfN@�VI6} 576I�I45} E. PiaseckibG)H129�[I4; \\ D.R. Bowm�"t % ibid37} 1527|9N,6} B. JakobsdG>JN09} 195EH0);\\ S.J. Yennello;>� �7} 67�z>9�B246} 2)80)..876�(, Aug.10-15Aavi� talk*:�56th�$rdita Mee�Won���Pics, Kopervik, Norway�A 9Cd8} D.H.E. Gross, Rep. ProgM��53} 601@.�D9} W. Lynch, Annu.I�NI�art. SciI�37A�3�7)��3W.A�9iedman,� LE�C42} 66I 02=$1} G. BersD nd P!�Sieme�\!m KB126} i�32��S�KrasnovUCzech. Je� Q�!�53I62�03} A.Z.M. Ism�TM� >y� I52} 1280%42J4} P.LA��BF�C44} 84e�a�9�15} M?Cherry�� B!� 1532�:�46} R. Holynski2�<A5e�m�6� 7} N��Andreeva�Yad. Fiz C4e�%�882�(8} V. Singh<P.t'��Conf.a High�f�e , Kracow, PolA!(1�=%9~eN� al Sympos�[}s !Nj Pantnagara�dia, 288 p.820} CA�Wad�Vton� 21st ICRC�ɬd papers, Adelaide, Autrald 8, 8%<621Fe�P.Sikr}hQ2}) 8 �85.�022} L.Y. Geer��2�52} 33I�6@eD.!$agioutouNG�AK49�@84��AA�Goo�$N<E�C30} 85e� 82���.�28} 313�p6�24aAEA�sh12ica l3} 25�62�25v� � D68} 165�922s6J�XIIa S.�V�GuwahatiU��97]�27z�)T��1��:�8 ?�pa,ur 30�5e82%�Jfchodzall�)�>75} 104 y5@Y.-G. M>:E7 �B390} 4E96�9� %�nRAF453�d��T30�8 Stau9V}E � 5  (1979291aC�orett&yj: �43} 39q��LJH�v]� 523} 651��19$J. Aicheli�gp h202} 23E� 0DN�0^�(2} X. Campi1 Lett fB20apm�8�Wb ulRA tvina=EI�5�+75Q.K:�  docu� } ig% \�e [12pt]{io� } % Un�� next�4 if AMS fonts �@$y $l�_ ' \P` le $>qyU1.]f7,lt}{$_{\rm T�%X 1j%title[S'��ce� l$\sqrt{s_{NN}}$~=~17.3~GeV]{.6 7���"�2�Ks>:rav^�0author{Ingrid * ZNA49 Co*rh 3�ddress{Gesellschaft f\"{u}r Schweri�fo� pung (GSI), Darmstadt, GermanyPbHYab9c%3Y�M6���&4s (K$^+$, K$^-�X\phi$, A> ~��E+) a�<l-+�&�d p��jKd�R5ral C+C:Si+Si}ii!at 158 \A� �6�7U%= detebV. T2K�Z(or p+p, S+SnPb+Pb*�[OsI? >@�!4be studied. ResvEnes9!\&�s fastks2�9_'g>60&ticipatpU& ons;�(net hyperonUh�#!6o:"=mid�+���r �ji �'i.J0te�| bas:Ee<m ]dnt-N��c0propos!N!s|e ��-K�1�a b;8 w\Ia:z +�f� veloc��k06E/�*��=both ki�hA� chem�(ilze�.��yg�)&�8>�8decouplsleave�ac%<�c�( ing.��end2{%�!� PACS�s ���+Hsage \pacs{25.75.-qa�.D=Sub� �j:al:E%\s %o{\JPA FComň�if �mA� ;paVDtِ%\make� % % -�J& INaO} �o^o%%�t$jA�!n���My �eM��Q�p�j-!X�;�{ieAd�q"�-N&e4"-!�a Ad .!a7�lr �%ngU+\cite{Q $}. Althou�nhancER�FJA$+$A$.�"\5iel�t_nretonsa�"V4'.H$m�:.m.�� �qm04},X e qu�,one%ut�origi�Zj unsolvedC�>tivA6���!��2 symmetric.�of��' }腛 $A$.�LNI�3�Sžrec.d D��|�'��o�A � nim}��+>SPS�h���.n�"pi^{\pm}�k �o��s�]��$e�=�'Isys��p�� prelimin)��W�%�� ~baryt.�"�A�ogous�]%6Z,��^�W{?k� f ��" 9+} ��� �V�7 }[b]{0.5\�E}.-TM\� i= p1_1LH,/=2:�<[\hfillZr428^ er~  -3mm%v -;]cm�IM >�2b�R/3b/nd�&+S�crE�-g!s}Left:� J= of v`Q �r, "\ at2 in^ (\�tsquareiMl circle)��.SS�*�*a:?#�f� w7#equ( (\ref{mtfit}=R�!:5�+ ofm� (top �m{m� s (bottom�7u�)UO�qs� s�1e!tZ4�;>.��--��!��),5i8�l�"5vi��,y$,$p_T$) bi!7�q=� ($m_T$�j� 0m_0^2 + p_T^2�Y1):�!�� nki3)t2=$ (left). F5��h lZ y�1�} �W]T8{1}{m_T} \cdot {d^2} n} }��" }4 = c@4e}^{-m_T/T}}} M�I,G�% %Xu� toFrap�!e%^ r�tR+c�xD �-��2�p�!�"Yp$ d$n$/d$y$A�5Uy�drA�)4�RC��I��; inN��[5ex��#v�5fQr!i�u-GyN.Rw'7pprox�s �V5 erpo�o� 6�Hq plac 5alEE�?*L �e�:8,"�f |%�� ��K1nd>�.�(�[0ym2�P$irr�9BIm0�%dopM(p+p� �] �1g �nf% 9D� vtak�Vor�G,� g ]U'5�W��8 b�). �6�6 Disc�qo�B rB �8>86Z�R82�880^s~���~33Z�~ p2bl2bl%:�t/misc/ikraus/diss/kap7/reduc12ڃ_$-pi~ipOf0�s,�# d ka& a�� q�per��� |n\pi"�=�S,1}{2} \bigl(" pi^+*+�@^-4r)$%�ak qM��y>F�w&,ed �B�# tritdow #, p+Be (\op�ramond),� 1S ,q�h P ,2�a Eb� � ral � @$*ma ~\ *min��"� Dstar)�at 200 8!5�e8 baroͲ�� �d�-!�.l !�rCs�n �e � ��)S� *�*9�O fO Xs>{��E���@e in2)a�a�:�Y��� !�I6]&�45913}��r{��2j%���G s @na35}w5 NA35Bll&� �on�@�"D cz;�,�8feGow�Pta|�_ m����[],geo��}verlapca �]N_W�$ �ikTa[s*�*I� {ހ1���P!�s�5" �'der p|O����> o)a�h�7levelv)�<.Qa�":�#*E"�nscay*8HHg.g.%�nl?� rY � $,helena} suggj+"61�: ��A+A6��.�) mpacJu-F: . At su�}ly�EfHmO `ect^e|ssj*&71*�,]�do o\/ in�tl�uymore,�F� connI�domai�UMTpDreson(sm@t;M��;dE7se�s�@8 quantum-mechan]SM9a��Ay!�ob�*s�7�be QY�9��!Z ose �A_is dŵi�M>.��.�*&�:���&8in2�MDls�:g/��I �� cano�� gr�ensemb�B_c�y� by Tounsi% Redl�\��(tou} agrees!Ql`.9l��.� ���@~�ul�@, �H%�MH��i�i� ac"IN2!���H% ��"�v�"$\beta��*�"EHto:FA�,:pA4#YA^8E�!q�P�$*+ ��s9�marcoJ"�:.� T$_c�r8l�]ce QCD6� Tfodoral.1R� :;�Ldiagram5� b���#!�!u �,c!was~Z �� �.| he Biele�4 �biel}Da��&� + udap.group 0�)7%7a��r���NNx�<��H�0 t�6(75 � ofh"E"/N = 1 �WsF�en:�6�'q-ec�z|lie5�!Si+Au-� �AGSa�5 14.6�%�S+S eat"�R@�]l6�� : $\gamma_S �uc �ref2}� �A7a� 8F4��5�2/&-�y(u�a��.�Au!A�Pe�%T�|!�A SIS�5 �!C�LSP(7} 4C RHICI0�@48%�Y z)q���.� "��wѸ ���� &c R&_���Jm�~d of B� -Y�, �Q �B: �Z�� !c�s\Oequilib='�F �QDupbsed�#M� <$ 1)k"�d�# 2s)�*�$R� (.�!�z"�),YT��*SU.�&mN�%��#��po'Q(al $\mu_B$ "|g *"xly!�5 �����N $T_{ch�}�Xe�"o:��islds) lw+ roomE�i"�br��gR!�� ����Qva�;.�Z"�l�]voy�M~�s{}�as I2i{cley}�)�)�;��A�6o�s app- ��_��$vicj��&!~ %�3 �KBf/�����Absorpe# 0 "�"�&f&%{}Da2�anti-E�w#$�0p�l d�"�E��#of��9� � �"%)�AA��j&?�s�0P!must4:&�*$\eqalign{ e S~=~q+1}{3}~B~-s �.1cm} { :~�~}2 A�/>�:}N{:}� \Biggl(�%LK^"�%HK&�%X/9r)^2  ,T  l( 6 _Wmu_s}{k,Big�$",!n-%4�90%t3"MO*7 spi4 zero=8-��!�y,� vaiiJ�it amoujto�60~�� 2� 2�6��U !�r.��predik� hwaU�� �Pv\� "� �������N*9�!�=��%�-%q ��}/ ь:/(�� W(.Po��s� e flat ��2���^T�") steeode~![9%�*a *�� b� �s,�O�%��tud�5�P;F�#�G,�leT� dire� A�"�<-"�.!.j"lA�,��6�d O\i%�6am-%� S� .gfde{&Q9,ar%��U.��-52�!�ten� �(�?-2�$)&@s9$r|76th.�g#�1stood \er�;S8e�1o $d�"� 5�&� &C� lead9&a suc�[�< �i�@��n�Uom �=�ymi&Yereu*�%de�/~ !�fireb�&/ ��< %D�*�Q�>V�$if#o`��'Pre �A|Il�=&�!�$ bene�.�r �r T�S�.9��j���I֮:� *6742�..IR` 6�` ` 2��6�` ` ��6b_ �/7_rap_nF _lam֧7��F*�.laNv>�7L+� �!t)e�-�Q� "�d:. Also�T��V(��Q@| (H %'!=). E�% �I�Ss}Y�wi�lam ~X � ��R / � s>�6���B.o ��39.�R@'B%�$$ n��J!��� >y&-N$.`,5�in b�%�0-��-� � -R���F��D9�D9i^@$T${BR: "92�Q��I:k(��a:\,er��I� m��M�U�a �l�fzY��}�In� n�6�?-mF�� ack�W#�(a3a�(��) ~*�>��Z�-n�<�n�e"�!��,a� <<i�7h>� 9h,?��� 1977� caus�.E�,�4 �j,�� bDBG&�,� �!�!Ҍ�/�� radk5"��Ve . 2�6)� &�7�@a hydr�pal�; _ � �eifIE9ion��Schned9;"�L-2s} �"�� vF�"is uti"��,`� ps� epSsrultaneq@ g!��$&�q�;�d�;m_Tp�;" ?1mm} \�Cto&B*9 :I_0*d"�5� tp6i sinh60 \rho�biggr):�H<"��xK_16H:x�/cos~x,&c��Fd� I$_0�lK$_1$�g�- ed Bessel5��1$�iKn�E�$:= atanh� %� Em�=a�;"6&4>�.��# enf AD��%j�di2<ys ..>^� � �����<�e��g�� mulaö<G=H! c~jtiG�@zero;X��r-.5��T��%�bZ�3��-]d�H10*�JnB<� X:���mpa�Ia.Lv�;�(kin}$ drops�=3� &Q,)b.& �^;.�I" !��mal�J� !BD �~TE��=�!VEͅB\K , sop6� ��p�3{he:�*� A>%�sf��s2JA$*�'saA]neʷ2norI��a|ij2-'���3sm*3a��8|>1s����uOe b���@Q��K�� p+Ai�!���i6ls�.�D48n!���( an alternaylF la oo@hg} [F�� =rӪd�3wvd5G &� ���!�on�4cn8a���; i��!, �6Xle�(��j�g�Su���n�Y�(P!06�O7�qO�� �*%�2a&X8Mj"�J.�&G ,�j{OS s, F���mO�9&��!s2���i&��3��*�O <$Y �6A�AKB7�7$*q�i�yg� �C$*:y*u!�o08��a�vE$ ^2[6B#� &� a� seen� ^!� q~�;RP�E �t.Z�&P:tde����*z&!-� ՈI�T.y� �=�.O&q&>JPin=:ٛ)ves sZ+P~"�4 cm}~�>j> numrefs{1�b�b<982} Rafelski J�MtTl�#B & {\itBUY} EW 48} 10662�-Koch P,6P!9p]66] p.} W1�_ 167 bitem{qPN R�qr H GQDWang X (editors) [,4 XQuark M(@4} (In6}B�Xics P� ing)*b�MX Afanasiev S V \etal (F_>) 1999 x>Yj,r. Meth.} A )0S\ 210h2�M Alt C h ��Rm mP#2int} ��(-ex/04060319<%? Sik!�F�_>�!)!�A-�$661} 45c 2��, 2000 �dZL�Y}Au)&9_59^!�_B�} C� } 054902ax Susa T�20^)��!� �69a 491c5�Barna DaXE��.D�>sis, U&�f�,�0} K�(H\"{o}hne C.!�31NfMMarburg". IEThttp://archiv.ub.uni-m -.deyE8\-z2003/0627/} .�1Anticic59R�20q�%2�[-�);93!�223!�Y��A !Atke J:�356�'e�M^Zd}!*I[!�1912QB\"{a}cha_(BJZ-jFZ5Z3672ZAlber5%r^Y��FY64�d95�Y!�M�)hep�(97\��(+A0 Bialkowska H�gRetyk WA� 2001 Q�_a� } G ��27} 3976X]�-� !> [)\-_RZ715�v74c�>K? j?A �l?K�UmkN�!� 2095R stop��ppelshEus�t. �N� �4%.�I{ 82} 2471l&�0 B"�0F��M�3emu�@6 .�b\8 2Dɫa�Ny�9eu 4905ys"6E>4 van Leeuwen M WRi~� 161:66`�Ir���54alt} Fodor ZEKatz S�o��Ni 43� ref4�}�eZ � �Eur�k Ja\)� 5} 143�� =G.K7 ���W7� n2�5^��� �I7"�M0a�.� ref7P>: , Heppe IeVSta�c J!�� d-H B �4)�92�8Na9>� S1�51��4}? na52��$mbrosini G MA�(FT1 �New�ͽt 22.6a)uno G9� a:K0)���Jm� S71*� �'( Sollfrank~M] K] � 65=_hwaN^,}�� 5�, 6� ? (th/ 0304013k  &("�44W HGluon Plasma 3}, ed�i.C. Hw.y X.N.� , World�mm5fic*s �h� Kafk*�  }InI�D�16} 126=�� 2�E%Heinz U��191b.Vq(50��7� hg} Fiscz�\MNA�~  118.�J( Letessier.yYZ GMx 42*x �iBy�� i W !� Flor� i WZaqxi�87�7� ?N�B.�e�g2Zg2 �qJkg,�Z]{e} \textw$� 480pt Q� 66oddsidM��^-15' evenF*�g�sicx}% I�< files \def\bcc{)%�/erXe!36nue�, nu_e0 nue{  Ymunu{J,%d:Gamma2dm2-{V m^25nurad < r^2 >  s2tw sin ^շheta _W#am241 $ ^{241} Am u23838} U th23 �832} Thk40740} Kr6jncs137S^{1/rCsTba1333} Bacp)$kg^{-1}keVday�(!�)�rm5�Emub�!�BZe!� rm{E-�-�rnusp .phi (�7E1 )�ke1)I\kappaEN %4 TEXT START %�'}�%\x^< AS-TEXONO/03-06cu�*�/ *\todayh% TITLE bcc �,��E\��IVOP��!a�t-by- �f�));E:� De h} a[�6 �, Author List ��ccr8INGH\footnote{v@h@p Sca.edu.t�q,r Ad�i:�it6K, A��miajr(ica, Taipei(wan (ROC).}�v2�x���q0Banaras Hindu*, Var��o\\�vdBHATTACHARJEE, S. SENGUPTAfcGau�o2]:�oD\\ A. MUKHOPADHYAYfO,North Bengal2Tf alpaigur�1� fp#�Z1�ffili 5� R  AbQcU  ��  � Phot�yicf~ (PNED���~in�M�A��x&IKAZs&�N-�oJi�1often��dM�� . H>�,)/��1of �R"�(�tJ"�?seem �|s�Od.s��Edt%g�?pgd discrib"Y$e yet�o�fethode ei�{B�ofi��%e�:��o�f� Yi�Cvelpo]6pecU �]'!5p.�1�x�5, � envi%� �fo*{@o��pplic-�t&�-t���5��-��(vskip 0.2cmI{N3�Key�H:} NUCLEAR REACTION�$5�, ��)���'v/b �&�.��}j{}m& BoIg%.%��&�e2�i Abof� nm us - w!�Z0"�� tooIS�QIA) stig)�9(nsJ�&I�N! ��R  [1-3s�B�la�5+^`.\W(idel2 theEs�T�$el 0ed��Q.�g+e9c�z�( �&:5A��$s���oAje B(b)��!�t&�/2a�0# J ̓�-;*r��|*M�1�)6B�Z� thusZr.q��ort� E�{r��ir�Fxt��>��"U: w�riz)X�B)F6eC3�4a�r4mQ�e��Ty�u�C�ne�2>J9�ind� an �A;99�c�Ey�_%iIc&)�#: !��think!idIh\9�g;Q� ��4it�Can���j"M�%�a&�ڕ�. W%���try��*r!'er (@ ,K))�"+�TY'A�oZ���] 6>Vit�how�"��5,� )-� �����3d�24I�䴕�ч; p�3q=d{I_KX�5 9V" mai:g;'�p!�H, CNOe Ag(Br)A:e �0�օW��e�c�� M te bi�nf�+id�&�ŵڇing b = ӷ  ��ngB $b>0"�e.*er �9�)l� ��-� ��,��\�d�op@1M�� ��_<.r-"=��7M�:q�agH�A�aŽm%*@W '�iYs&tpyY �.p�� like�:, Mid.��Is *..z�2��De�� s} q2��'u�2Qsil��hM��$$ystals imm���a g�[in�rix�r5-7��J.�( osTJf�. gen,�� bon, nitr oxy z��bro���'l� 2�per�age� sulf ziodinc�lso�&�G��e��t�+VqI��&]$yv"$�|�ac���_E\v�|(NIKFI BR-2}F�pelli�� of dF[� s 9c��s$ Б~$cm^X�,���horizoM�lyg *ݐa��v"%Inai8P4dŕZ� expoY`haX�e�j�e�5 6�xuZ�x%W(�x}J�x���-��H 1�h̽�pyz�0a- help� _HLEITZ (ERGOLUX)} op� "2�]As�agn4 ��of 2250Xkbn,.�1�>$���j�N��un��� am�*"� a�>z� s�{�%;[8��VE��ZA�er*�Y��F�� Path��9�YfH%�*�iY V��>>��P"��}&$\bf#� ~(A~GeV)$ �~�~�~(cm.)$&ARef�/�4$^{4}He$&2.1&2����70 0[9]-��2}C ( 13.8(5F(4}N(1j(��&2.0&1E� xP10y56}Fe��7&7.97 )19 �11)�1.0&6.*�� )Bf�31�&1.2&5.1T�3���%�""�^5.6�26 ^�� *zU )3.6�2)4}-��1� UU�Mp��+"{/� �vof�& A��Z}c* �, El�M}^{1}HMt^{I!E�^{I %� 80}Br$& 108}AgB�-N+e$atoms/cc~$��~I�22}$&3.1>�8410&0.395&0.956!�2>�02�� O1Fu�� Ra!;��a7Cm0f�* pa� $(\l�)5 $"��i��}ʹ�d �T�I8�~� 2� cm. Ou���~��%t(.�:%�� Ta �C!�m6� (�BmN*�t en�Wi` ��&� a�,T ou"�Jn��:��T_��H"i `s����@�ޕe��:.�ma�  5bJ��,e *e,q�n��a: m�� ��,:�-mbm�s !�� �0�4;���i��du���{ яp&��ll �u= *s�&�w� s:�lPZeri!�- i � O�!Bw �-%ic*�� �eT.�= �E�ad�bal 162�{s�by�D.Dhto�ze�ei�� 6 '�fh9&�: =��%pe �5Ut�<�qem�V*�vM9�J2e!0Amum:� ($g_KA }$).� �3r: t, ?�edM*#�  ?�1 X���5~wG����_E�st�5m�a"� ��,�)I�]�asWgo�/D�"�馼�  _�'� �8U� $UNe ��U�8*bf(Hi"ދәI� 50 :bf(@�#�?beU �� (Low" A|[�� �g.�Tm�m�8�u� *�ndi�s�|gr�F� l� �6%�f�5�BlZ*��los`R��=k�Y�2����55E .TI�&tual ��d�&M�-�!�}/>t<�2�x���7fk2 in�� ano%Ny]\ag N�\ 6P86hfi�gas $g.� = g / q�b�re $g�9�9ed6R�l�ged Se<�ar�Teց��[BV�t���7�6k��="c��a�~ ir 9�, i!K�fn�f"=Za�go�: IJ(a) ShƚE 0s ($N_{s}$):}�$se� fres�0 d ne���>"� )L<1.4$I�?M�#e�Za > 0.7$�+c��ήw�i ns"+ڡEl� >400$��uy��fSKN)Ma U:�xt�?k"tKH&Q�Fٕ�&l MJ�%�gM6���loOi enz��e�{fi9edl-�29d knockg�p��@!��.1�b) Grey2�g)�P.���&���ٱ� :�$< e < 6.I> Iw$>3$ mm%f �as gre�*��2�n"�7U�ݻ < e> <)�0 )���ly �܆u��%��&��!$30 < I<400 E��� 2�deu �KriYaS!s�z5^c)��)Cracq<bZ_-,< )-ED%a vertex ��NyD�a�A�iR >!�AQ�.�.�J\5V3@uF�A1.-)3q>Mo[�Z]� u�ow!��| vapoi!� resi�)��u!5s�R}�U�ErFB@}��L^=s�g}$ + b}$ )ElAT:��ui%�K%�5�E#yJ. q(d)*� FCӭf)�I�Taiat��ar��zr�� � $Z\ge 1$�*�v 2���!�e),"�g� (PFg�s��� onKZ-[u��э��c�3llE�z�}narrow� ���q.O�����availY�IT Mad=�� wTt��n� !_MP. q�*1�T�a.V_longik( :$(p_{L�I��. Tak!�$$����<itself,j $\tG'_{F=tanM& `t} / K�i,� 9^{o*a� � "�� PF�\2���������i) �&�Z�(�A 6�3$��ii) A��fM\�;RM�Z=2Oi)<%._ ��4cjf� tm� & ��8"���� doubley(s8�J`"� Ag� Br } _ . }H�ksnpssit���G��!Cl=o�T��Ident��}�ex(-��a���& �:Q�""�Ampժum����*��N������6Z2}� �,�h"�)���itu� U� QM�E�g�l�fch� H (l%� NO ( �)%sAgBr (B�y)����c%��a ;�MwI�ty��p-�!Le���20]�Ich U�ly�EE�pr2� *� M� different�X targets. It is well known that the number of heavy particles, $N_{h}$ is a good tool for Y� identification. Since we are interested ire separ, of E0s on event by asis,H�have employed short-range track distribu� to�y^�_(s with low �4value. In view� he 2T-8ily ionizing ch!Y9,eall set1 pas sh!nDin {\bf fig. 1(a)}�$ attempted%�V#usw�follow(criteria: ]H �~:}� = 0; 41 but not fallLin any�dbe!%(categories. bCNOFd2 $\le NA,  $$ 8 and no-�%w)�8$\ge$ 10 $\mu$mYAg(Br)F\1�$>$ 8�\lec(at least onQfm F��P � �$ 5�(As a result9�obtain-�$percentageE!Boccurea A�8he three differA�i� group Y0(H : 12$\%$,!o : 48 %Q)& : 40H. The relevant dataa�summarisa.Qw(table 3}. T  gives� �s]baboveU^ along)W�0`of other similar effortsI�D[21-28]}. It may ba�en fromI ���$probabilitE�-duea� �d nuclei increases slowly wa� A�8projectile massA'�energy� alsoe�! �method�-�}��\lmost correct. \begin{t!W} \cap��{PYof�ac��Vs.}Qular}{c} \hlinei�I�X P}&e�E� } (A GeV) H CNO )H}&)�Ref.}\\ ]d$^{1}P$&2.5&18.00&49.50&32h [21]3t$^{4}He$&3.7&21.03&40.42&38.55,2, 12}C,429&30.87&47.84,3, 22}N Y12.949&54.47-4- 8}Si Z15Z$3.79&50.92-5-T40}Ar$&1.8&17.80&34.60�50-6- 56}F �(23.13&22.64�23-7- 84}KZ0�1TZ0.4Z Presa� work78197}Au$&8.7.&19!r3645-r8/M \endAoEle} W�v0, first-ever,U�ngetAg�IBryKd emulsion detector. For th�4examine only IB typ��I���,ir frequency6�iZ b)}�has b�it� by� dou��,Gaussian funiG . We foun�:m� cont s of�7��of�� 44�M56 ,resp�? vely� same* ��BILrepor �( B. Jakobss� t aliu [29]��ho&��X>tsum�nsᥭwhereq��s ) %D(measured di��ly�tan expo�GANIL. F��now�� will�= ceed��developmA�of new�"V impact ,ameter estim� � 6� IG>s e �� to avoi!ҡ�theQ cal complj s%�makA� !+��,simpler. %%��,figure}[htb]�_  \��) �!�J����E�lyU�ed)�!�B�Tb. More precisely, its��n q de� monoton��ly!�a��qb. I>iD� w"c assumpY ��a�� : trea�%��� eachM%�yej*9 ��ly!�mak)�:h� -Kcross �!8pur?geometr�%�6 ��an��Q= iA�ts� randoml*j&h��arF���.o 2 is �lydom6�gEj. s�y/K � . T� fore�U used C g�� atorQ�1A�oe6/��Q�0�1��1�b� �A$ �uE{s uptoora2�e�2Py� choosMaximu)min ,limit accord��(to our real��al�of NG�ies ���b%F��?FVedW a sui�  fa� �n�5� �BB2 !�$A_{P}g  T}$%ZE %)radius=#}��I�I�i ook^NMa�combin�KDce%^si! both Z,E[b = $R �+ T}$b_{max�'| ( \sim T}| = (@in} (\approx 0)$,�&[ �ma}U� magnitudeFF$%1��UZ �A�atU�6/e � i6�1RQ=� ng�%v2in- ��a��2@ two extreme poin�Ab versus6_2 )���Ae�f?�sF �N)��86O suchA#!��G (max)}$ - }$E Q2tQ���q I.�2� M�ށ(re:����>� !6�ofF#E �%3I1e��SZ�)-�mat�,�i�2�7b !� help���2�can easGv � spon�K M��v�e{E"� al R�,s} To chec� auth�E�MC� ed�х�� 8� ew%%ece stic!-� s �(��-�O # U�m��%_in][�g*� A��as&�I�� )�ss�a�fN�:v%�F�"� V ���A�n'Y3 (a), ! A�(c)},�*t error bar< o e��Q� g stat%�ag }�ype!�� = A�b�Rfi�d=J�� ?+E�3E/� infe,at�B},jB�2B!M?9u �  #�slow�%ris)�chin� QNa�as!FMH� ��^ natur�'2� �m�pa9 ipV- ��� Model� di� i.e.,r�T overlap (�A)�Zg�a�� �&,64m�b!&� vice -�Za. �E�a)}b 4: 1.^  7} eb�e2befec�e3beRe"��  avera�K �\m.�is J��� �!��dFv�V���%�k H, o CNO,E] c)} �.rOsh'� df@ highmx, mid. Bw�hset>�&vksnpssitNend&sWe���mis� !@alpham�l 2� wH -q���PF�V�4!R�02!��r polynomia�O +q��o�em�6��p�� �� is 5��6JT. H�siz��6:m� small��n�-9$^�-���why it�ver|fficulselectH d-on.,���  e mix�M �r����quasi-� s. E=��q{9[!�.�l b�q���4a�JndiP!��6 FeG Ga)��A 9&�� :� $b. �Rso.��B�n-*0repn9.%��n7:9bQ�Q7} en.]�8beRe��(a) A��Y;Heliu2hq�i� te@B�� lo��>[FW�*"� >�!��Cl�&� isZ� M F�A�} s��B�~�w$���6 ��M&�  �ԁFQ$5}2�a�p"o�Md�o�ey�� n2�Q!a%�arU��#l��h1&6���2 � s wh�!edac.6�s sY�%#9��8@se�6Q e| X� ,� ia�a-.�s. At:�� �� 1�c�-�"r}�6F, less�^an halfA�!i]N��>conver into�]#thir(like�3%{neu�/� le)�% a ���>�goEo!�appar-��KoSr�.�pr��"i mi}}M�Zt�36�if� 8:g7b�7.��:=Q �sq�B�a�*� !�eIYQ:%. DU� ��)���� >�ndE�-�#6�b )%��6qe�Ѡ$}!S-A�&��-by&n�Photog�" N� ar E & de &, w�$ed� studO�etail ofiqa=aJ1A�though��s ' orig��"* goal� hand�,%\ p.�e%N�, �㍎ap@#-Q��kin�)�s@!ec�-��  systems�~% ty[ +��mixe�ge%2o<'1+� nfor�$o+i%nd��se-bs  !boJ% analysi��B�'K!��~*:Jdis��a2R&� w\'no.�e.l��co"k T.z2)�^s&0-+ is%s (ly supC'Gth��c��concepy Acknowled� }y�o�oul�$� o d�ax"QXto Prof. S.K. Tuli, FmrCaE Physics D�&t� , Lea�Mem61���tnal H �+@G�-H, Banaras Hindu Uni�vXity, Varanasi, India. Oo)��or (VS)!� �w kful�Dn$�Singh>stitut� �, Acade�Sih", TaipeiwT)or�Ucom�� discx)  rega��1uba-ter� �h� grateMmo �i�Xof GSI, Darmstadt, Germ{0�thD*C i*�(- U�stack�0 �'thebibli��y}{99K-dibitem{texono} L.P. CsernaA�J.I. Kapusta, Rep., 131, 223 (1986); S.Nagamiya �DM. Gyulassy, Adv.�?.%r@, 201?H2); R. Stock, ibid"5, 259#6); H# ecke�/$W. Greiner.57, 277 5. \�Pstart} D. L'Hote, Nuc��(A488}, 457c@82@ci�0xmag} H.H. Gutbrod, A.M. Poskanz �H.G. R�r,%1aEg � 52, 126 �9.e(pdg} C. Cavl+., A� . Rev. C4=760�902=rov s} W�Barkas,%x�Research��, Vol. 1U�c �-38ew York, Londonm63). 9PprAGm} S. N-�,�c.A�Int. Co�!7�k!p��(ics, Bombay\84); UIntT54IRES Strasbour�-LEPSI ``Propos,or a Silicon#ip De�e3STAR''j`97); VECC, Calcutta; Inst)� �Dhubaneshwar; Rajes�Q��D., -Jaipur; Punjab -C�igarh: Jamm��.,- B�`n M.�in.�6.� eledaq} PAz, F�w�a�DAPerkin���,y of Ele��ary P� b��*� MehtA� PergamonQY52�,sigmanue} V.�CghA�.D�Ge�6-�2(��%�2�m�Heckmanq*f.m*17, 1735=7:=x.udek,!ePr�-D�E$FourteenthAʡ �al:�xCosmic Rays, Munich, 1975, edi�lby Klaus Pinkau (Max-Planck-Axŋ=chem�,7, p. 2342 (M.���(K. Mangotra�$IL Nuovo C�+o 87A� �@:CA. Gill=a�Je�Modi . A5, 75%@6j��J. Wad!5tA P.S. Frei��!�1��+888�>�E�<Friedlanj'��2@2��436A36 0A. Abdelsalam>J�G:�w.E�28��75 (20022�dy�6��$A. KrasnovWCzech.^of �46, 53��6�Dsensit} J. Babecki�g�P�zB6, 44�D72�Hmunupaper} E.V. Anz+0 1., Sov��Q�2, 38�72* rdk}6&, JINR R�1 , El-81-6��1._p�} I. O�Dlund, LUIP-CR-76-0E6pLcsibkg} M. Bogdanski5A Helv�Acta ��48G692� } DGKLMTW�abo; �PDubna Commun., P1-831)I4.�leT. AhmadAW.�Al�� Muslim��ersn / di��2gso} ZA} ou-Moussa�Rn%�I�80, 109Qf�;naicdm} &� 5!.�A570, 81e�92�n�0} R.R. Joseph>��[822lepsd] Bhanj�c2�411, 50�2� kimsEsDabrowskBZ1�C59, 39 �2>amsq)o!4�`(R. Kullberg�y�1$cr. 13, 32�:� iaea�K. Adcox-g((Phenix ColYY)Tg 4Lett. 86, 3500%� 1); �J 0523� 20�H 8��92302�9 �� �B561, 8 D3);��Adams1 Star�9� 8�4)b\o ,Spring8} PorI,ra%.G�(or� posex,L'Ecuyu1ne�$. ACM 31:7�&� *� e6���. 4th2iH�I! �ummer Study, Berkeley LBL-7766, 289�l78); M� ! ovicy�zb!46I�� J. Huf� GSI Pri! ,t 80-1 91880)� %-�� q3A290, 4� 7� A. Biala1�2�D2? 32�wM*KinoshitN�8� ��65eJ. Kno*6��� A308�Ɂ)8 Guylassyϩ}a40, 29�5G��Westfp��B7� 5i�#>� �9 docu� } •\c�\[twocolumn,aps,prl,super2$ptaddress,�Hpacs,secnumroman, %:K�AW4keys]{revtex4}�Tz �I\u�2ckage�T math,bm}%2�(x}% %\renew�and\topf�ion{0.):!bottomv$ text"01�2g floatpage'm2&{.� }{1.�.G{\dbl�}{2J$6� }{2}Bg�}{0.0FiB�b�^*%\def�6�{10� B<2dbF] !\ mmt{\lang�? _T \� l,&Ldef\Nb{N_{B-\bar{B}}a*b�?qU2�U�6%Silesi�L-40007�&a�G2 Q�l( M. Lunardo�,]��P�PMakeev9�N��ri��6$LCP CaidISMRA, IN2P3-CNRS, F-14050 !FrancBM- EUt� ���J�Zkjk��jJ�rlon�C9�(, M Smoluch�F�g��5� �U0059,�2T�Aw� ez-Davaloei-,enchaca-Roch>�QR�{�{G. Nebbi� �S[5 rett��=C��v�G�e�/ �V. RizzB�5�5 A. Ruangm�D. � hett�_G�!uliot�x�x" tasz =��~�$M. Veselsk�z��J�G. Vib"�yk!��?f?�� . Wi1steqU�$J. Yennell>��JW. Zip�6?Rc�����\K@Z"�'�(NIMROD6} \no=���$~and~A.~On>*���+Tohok�PSendai 980-8578, Japa�E\date�du labszQ t} Calori�AEcoalesctechn s�'e�He�Qtobe e2r �ho"�>produc/#�+!,!:w �33 55 MeV/u4� ��;'r,n+�#. Ent��$AU  asym��)nds+ w�#�2 ��>6#�#�� o�4 �$i�o$�Txci �"r) n afDIaFsNP pre-1!� � cle �4; ter-z�-�propert��Pde-ypuRrns%qth� &�*�$provid70Y)�0")�E�of� �i-decayd:NK independ�&=#L�ific e:�.�YqD \pacs{25.70.Pq, 2�M.Ky, 0JkI �,t� */$IntEN�} �r�*@he�?�to�)c�&&D1E!�subm<t:O�a�"c% us � upo!0>�A}�er�;E��%U�!Be.�$�.amu�%�0 hono�Kwa�� expa�ng Q?��a"�& . I �ar�F�0�2,HSI!�4~\�{gB50}md"�Ke!SI of )V�rCMv8 �0hel� �8�7ci{I!r�7domaiA�q>i�&bea#inv�ga��� t�e whet!�orO1!�ir'assembly-�)-o2@Q ermo. drive�%�ARAer cas�3 mtheE�AY�aG�(id-gas phasɾg�nd�Uec .r!��"�G� @Q�(suraud89,ta!496,chomaz01,elP t04Ves�)M�%Oe :�chiev��QI�Mu]� +(c1%l��e-es�BI!�is paper�ASQd%a �~�t�!F6�!).�6�E�ia"Zc�bPl*X 3S$$^{64}$Zn+ $92}$Mo, 40r U0}$Ar,G^{112}$S%� �($^{27}$Al +0124$E�in mid"�:=,of 47g � g ��&r�b�b!Me aS�Vh6�4pr+A� by AMD-V  sp>�/ cJ&�:Q60ono99,wada04,�04} .� �Z�_�+MDtemperoAsB!���o%[rsVR�M� to2(2�.= ��._|"� Nr�;"f6�-�=7l�Jc!U�E�a&�.e �zLr �obserA��va��/w�x ��e . A�s�.�T isot�B�.�$, T$_{HHe}qI6$A,�Zh�Y Uen�,!Z>G ^ ofV29��)C5 �#�Z>�U � �?�p qD N/w ed us?c.F t"6 �de�4dŰ(0-v�T8� 114 amu ��R�ange Ii 4.88� 5.31!</uaB�.�H� evap�#� �&o"� *�A!/fou"g �q��>\"- 6� cas�-U�seM3�nvery �?a�). c�Ked�@ultM:� 8 5Qjy?ed�$��� � �� �&" ��..c  /nt�/Q[s� � zLVK, �I"�J$^�I!��+e.*I� �2M�K-500y0F nductE�"�fac�\aX�A \& .�. �~yY �]� �_E�"Bb&T�%o L}5a c�oa�DFI" J�le�%7>��6,A��-� ��2 &� v�Md.�=��h2> sign� an6�;N/Z���0el-8woEs�+XHIzth,9��F,-d)hPVX ��Z!M!,a 9)�GarF4�Ap!04th�3x�;J����I" ]� wP5 I�C� he�:cX$a� co�7��a $4\pi$99d�� 3insQ8(�8Aw��1�c�Xd�K�:}of�i�6%166� ividuO,sI5s �ng�Q12 C%�� pola�0gl���$�� 4^o$!Z 160^o$ )%�"�9{?X�d AS``�"-te�opes''%��%%�wo Si�!�7 Si-�8��fY $ ediU4E*@(IMF)i/�1jball,-� surr oWFs!3y,E�'R2� AU:bya\W3liz���Zur�  e~F B- � �ѳs littlem�a!�L�6� 2�5� 4"! fiv� scR� scintillHK�QyE��� an-F�h DEMONI`yx$tilquin95}Z o�T �cY �! anguA�2�Es!I"� light>�s9� ��pla�?�d�or� E�of $3A��$11 � ve�G +�]���t|t�%2-3 yZ.I �=. �Wm^z)� top quadr�L� �,sr7o�F� A�E�ra\d�]iX( 5 cm gaps"| neighboe� P�=-�9-wga�V ��o(:|> �se_. G?,g@ amount'maEal!�!mwi�is�-�\iis��al�B6&�DQ�Q��tra. Howyl)$B�`eff!Mve absor08�sc|ed9s. Bym{a�andKD�V , 26&A .m�Uwh�� ��:$@rev}l�een n3&�e�* YW)da {\it�(}mhy 92i@ empi�Y�Ce�""g bi�Ic��e�6y cur�fa @pr�Xa�ur.��=�. Much g�ZrX�<X fA��l"<"�%s �?Gbin re�_���U. DuE�Aje";,;e� take[cplo%��d&? triggereB �9�a"-A bias'i��Ne�hi �� ��:m[N��ɉ fe.ykIB9� Z*J�3!�5:{(�A�"�"��d 1 "�>D 8A�< } M : �& Alp>�"=E�Za�usm-�Q�in>�^��,c�$ 00,h� 00 $1,ma04}. O�=(a brief suoi���f= dxA.p�K? . A�e�A�� wo d�#Z(M� MRR�5� ����M"�}����|6 in�:(�`?0reveal�L'Hinci vU�*�iF*� 2��& ssoca�d=��.Yy'th��e�*g  fluctu��sa�l�~ng�Z�S� !m)!�y��� =ep94 ��i�()�=�� �a�Lt� �NAj violn.I|\"U��Q=.E� Yed �A��r�P�NA&oN�+�W�1]QQ(�W� =���z " V�j�V>�e 10\%����"K�W�!*��^2.��9�9��@):!�emIizxFl�d3A!a] R��n gH a0f��Eng5�u�!�1� =i�%��`!M ��YMv�"n!5"7 El e�eiF !3n v �we carr��outM�es� ourceOEg e�U�J� ��ri�q �l� Q�1B�a�a,ced kF6PLF (� 2_f�M ) 2M�� :% T (TLF)%�a!D " velo�[(IV) 0G awes81, _2,@3dle98e89}. A�x��ier�B,))IV�typly�)W~��to"�L�F `p"ao?I% e'A��+�A! t��u]�u�#� umc^*�1��a�%� �xy�ba�ta�v�@p)viod6�a" &_4�$�_ ��aA��&2%�g,H*��*�"E]aVy (��MU�)y���b� �u�)� �LY!J�^s�� ��byLtA� ing,JGR|?#�Sne�'����oX�#���� @ �i �U�s�e8"&��:gs�%!� B��)�U"��/N$>�y�ai$e�e} ��� /v$� �k; �&�"�1�dMi�{AJ�i�su-�on=� initKavail*�,a8%#)�Ey (kined !�Qi6�`5�!]By&g :GM� prim�E remna�C��pur�I,( '>N:m %����&& �E�@%IV#%Q��M:��!jsecond�hod0H#of��strmonU{�FFbyM|.8N�: �)2M�#lV ,_ )�auN " �e6���i4a#q9eq�4} E^* = \sum_i�9$M}_{cp}(i)E+ M}_n E}_�,Q + E_\gamma*\wim�*uext=vR%hO*t�O i, $]�$)�n$ ź� !>cNph G� � R� in$giri1� eLe$�$a��i~ #y����%( rays (? d� 1�$� QKQ�p!�6� cL� u8qp!�a0 _ #IMFe:e���"� EPAX��d ��Epax}F�i(��c���MA�R|9���&FU�z�g�%re5 in.�p�\a� {�%inZlet ve d�.W,�!$ thresholdI5"b � �a F3����;-�� �o�n�!�sh� ag wA#�An :�anh�iu o �'�� verg�$Q[1�. ,�� ng !0��yA�a� �Q� F�qp�y� qqa}^mltY�%�)�1 �6e"�s,�@�*�ky,�!M�! kr8  A�xş C�ezq4 a�a@Ei �� �s a�8 T!D 1E "V B���� %�$&�$I�96E� ll uncer�� f $\pm1v�� �'!�zawe��A��%> �toD"7!! 2�$exp5Kd>�n�9(tz02,sobotk�,a9Cd cV/*��ytJ�2��%�t. :�y&�(�Yah�ime.� T/s�En�'Pre-E3�1�d�}re\"lY �)edA��px�/}<(yieldn#m. BK .�&�(�b] e�y*�3 &�m1i)} _2H<%�h.)� l y pa�!I@E�5-�� &�dqe�we�A5�H3>� �ra�con�.�*i t �PU3!�s�T+ ��q"�2�� ��L 0.oUenE�>�{I)�n� . UJ);��t"F)�xY"�6�a����jI ]+_a" b�"�v��@���A�i`0!�P�@ A=W��#rfa�t$'', V$_�.fZu-!�"", def�MB3a�G AA�a�!�Bs y,�S o accele �!k/ Coulomb fa�-raw���ey Ga�36O69Y ".X�!�HbrriH+NM. �RcI��*� )laS5@ N%r�Z�}J{u�e+5T!"J+ve>$" � U��&�%9!�q�z Hs-�_"; %Z: 9��h2Z3U��ly un�a6k l\"��e�X!�:-E 6�U�!7�-$A���%� ���, t, $^3&e4 clu�3!��s� )�!o-scal#:�A=A�[T&he .) 0 -2 0 6�*M�!}�Ε@%v)Oonship"i L0�� �ime1���A#ason�Au�K%'�G% � > � J:-�=N $%O,A{tpat�I=}a�P-�eB.�:` !G �s -i�> &N w�olo focu�@� ���� �!�"��Q .��%rap�6, "}r�'��70!�80�3v ��b�8/]ay�& �$��o��a �1�>u!"d� �s d&D#�Cm&�(V� A�yd�E I~l�(a��=)��s ���} i��3E"eVM� M�#ow.�?!r�-J�4.4 ��m�as� �}oB h��Hed�e"� al NX"%�Z�1�3i�u�a�M�.�3H)H0a2s!s��� �]A�2� ya���8' $of 3.5 cm/'TAk!j"e�* IV (or> *�E4| ntr�+-Lr"[u�e��a.&.=��P9�uի��and/o�as`�A��d)�#Wiv*,:u$šya��j� �&,/re�6prZ .Y *� A�AqIcN� 2�5m}ba�&�"<u"� ;Ma.��fi�$s�zal�%� 2W6=��Fi~��]��+=0 2u�]�  u�,��-.�K^(��a �g�!{�# Q+FxY"ME 10-18�˕-�ifnm w of 9�4$0 fm/c. Af�9q!2adrop "�xI:.*� r�7��ba�%.�ųn��%�.� becro����"Q ~i.5$i� (�mals0",)�4��)E�� a�-!(�%,�&d7�Ye�aNA�. �#�~�6tw "9 �'��taywo[2no��9�:J*�� E��_S 4!��, )���M`ځ�52�#e f�fZ"�(2� a ap&�<J �a�1c)m��--�&A�?���&a��*-%J�(RSs[a (=0.45]{Fig1�i"[sT� B�~�&�8$_ Z5�s.v�&-�F di�_ds,~�& - oi�t'��/,"�&+ Nr6- y�Fw cirl�I&&"!F�4< -- blue squarE }r�)$=}�1�j t!in�W��FY "9!j7.e�Y�=���"xA0326-J�&&b sXNi, MAh d Au&yE2 "&@�pre�S��)h tens>Dki}�t"�. i�*hˍw�o� { -5"��#ica0� >�F�Wen�?��&sampled,���-5soRzkaNI�� E!s���{"���}*� ��&�L*�@ �1�~!�d!O ty %at�1too*�0m�M97ÂI�N"� O57.Ba I� M�F& !E%�� �%� �>� *  >2�C}��D"�� s� i�zumn 5!)���]�pl�lyZ��*e�@st �"�2���-s � rpri�sincs.�=5e.�-�sar"�'6�0<e l�2:/�!� )S:j!returnZan/a���$Rla-Ventir�;a",=A cool��histo"'/�a��D���kѬ_89,�(88,gonin90}] �1I5>,%��[&d ��&� " ]Y�-#)ly�rox�'|�6a7qe�.epi�?�*�2"�Z 0œ�~"� �r" �+R�AreV�4 8�#apF�3 !@ e~���*�&=!b�� /N, is '2son���ida&�2�A� ��le*}[t]�ta�{|c2"7�R��L & A$_{comp}$ & E$^*y�& s&" $\Delta$7�d 7/\\ p�& &�> &�5 &: 7\\ ��J�/$^�54 & $96.4\pm8.7�$�\pm0.49 5.935 $5.10 0 38.7\pm3� & $12.1�N\\2}y6}�D& 1079.6M4.9 } ]56m}8 }3 $41.3n}3 1.8$}Fi}�6/85�7/& �! 0.51�5.6]0.5�}5 03 35.5� 12N}�0�)27�E}�E�n1 �X)V M6.0 l� � 044|4. � 13.6%v9�-�`M�&d Pr"�L�we Hotq[i%bB�L4�u&��#E_��&absolute:{� �Ie*bM�9{De-E&�(C�B} If,~fact,�]"_i��"� �� ry"& R�and2�b�x� b���y' a#:]C�N.I 2[������A�(,f�$T�E6 ��X:��Gm8 ow 11�+�#p1i#f3&V"��:� *i!'! k.�'Q n, "�-V�-&�*�� 2}�! )M�quant�q����� ,�(asY: {� �!!!*��"C*�� J ɉ,&�I$^��  ��! 47 ��V%D0 s (L ch�  �i� � "�Bs�sIH.#*\.)��vC^s�  !-i�� *!QBQ�except%!:enhD+d �&6}#)B)F�-"2�J�,�L� �aUexed��[6r�&>�!g8 6� N/ZQ8.j"uF<%$P' r�|3~\~P&~<2&��>�ado�&rRAeQ����6� �S�?U�:�,- &\AT&N 7 ;��QV��_c):b*dc� is� <fh��� I ]0 bl1|?u%Cal:��Mmio, ��� �MeWJ g>��TӐ�M�Dy�� �,] 2:7Qe�2�La�`IAg�*Hoe��%o�NK�%UA:�] �& 2u t86}�$at ��C�ucl# sidu� :�V%�s�ap�"� m,�r.�r H*�A{B2�6 �U� ,o r m��N� ��d* !�sucR)��"�)p=����!o�. E:n� 'qAal fav�A(�u 9o`�� �1����QI�*bHi�i`2�6a ��%`]�fS�.7��B(��4Ek&n36�@)�2s7؊1S stoox+a� ��R?%�2�& 2�KSt)�te7Q!�� *�)sk ho��m�&22=q�e�x*�u�cur�.�,cod�$>�/���.�9XX Zbot\WGEMINIP��A!ity88od�.emMLv-6�M8K ode (SMM) Kbondorf9�M�T��Wp ��Cvar�A� evel"/p�&,  c�x�IreO!%Tn G9fa�9I�T}ttH�9� �o �BX$he8�1��w {�K�# �:�P�ajpm�J ��e�i2+E� . =� Z���2raA� ��s Gh.�e�"� %Ia:k �K = A/9. Y�D�D��1 ���"g� e�th ��p��-D��:_  �.�"5] �^Q7Pْ*� C"�PA��3*�[Mŝ��Y:a�~� . 0��f~- WH�gc�\��*� �6AK 8,2 ,� D�*I�R .+�HHe�4(d) -- (f ) S�2� ��n,p� , (g .l)>���*� *�# , (m 7r)UB3 >B A`3M�u� ame�b��p�&�*a�a�� ņ �[m�. OpenK /q3of Ge�@$&-P���B H"�RJSMMRG�>"�MyYxQ� )�� %at"� �� �R:D&�:M3N�q�����y)1 � LU�Q  `��`n�/ sugg�*C��.� pic�=�P �LW%"�I�.5af6+'�*��a����Z=1&� E�fe�"A �a�ve�en&r %b�^� a�A"��-�Py U*; =�"IMJ.�In � ,X .z7]) =�1�BW-�A�g (C7s9!ju h�)t!!�9�*��?�e� 6�&!LM�e�.���1�A�Ph[&Z|C�G���hap�nd"22� IF�z `�16& �\ perhSMEox,H�t%'"� "5.�F2+�9�.m-*^5a "�&��} Esishu4&� Aca)�'� ��"-e�ye\[��8�, 8��'s * im�0�"/:L�^i�#W" �e�1!�q=� L�Mct&/�%�r utilizA1rE�I:� tool+x!� � ��** .�8o��t non& )}&x�p]ap� p]�.�@s�W6]2��2�6��F�����A�o%eJ@*�1Dxe"QB .d� A�Iz�cs=�!ZP)M0�mGkb�f�K�uJ�eb�eAuer:o' }� #! �_"Cu>!2 ������`��.��e�.�>T!z�e���/$ e%]*�!a� ~s^�d"6��1>2uA M�ind �����1�ny1'aya�a6FkI� a�9 %�' i`�*a?� JD �:� s�dei ��� p1Zal!�e]ϊ�� �/9Q!�t�!�>WL�m!�lO !���B��O�VA.��ZY�:�|a�.E"� � 2�� :YT!� Z.)8c��a4m^*s� �|# 8E��J�6` "(Ne ]a� �6�d<2 e)ViVin5�����(F�&@�e�"lC�.ork���&CUn�g�ue.��! ?2� GXUP\# DE-FG03- 93ER40773Eby�Robert AN6lch��nd�� IA0330�b�x>|{*��&�gS. N.�=l.�|pl8�g93�}52r��f}N�hr,\v�H6 137}, 344J~36�Q"�f6w�d��E(. Weisskopf��it!or&al�ar �v�y_.�u,a�M%d;M�Hn9 e"�t e.�t, "t,�{PK[,alR�s3RAs�"9s.S1s, j�S�r�er(r �.�q, S�Y�q, 3�M.(e��OV� 69} 04461}�42@��C}%�Wad��=� 1�&Gz�K�?E=M�7nI)b Y.&z�A�Ax%��wZZA"jka *6�vMB: � AF] a� *�*�s, "?s�E ArXiVA�print g $-ex/040800��4�ubm�7����aܬ*\ C�&�Y I. T�],�y��� arloV��eaxE�Hadri�}a�us� Leh� �!Leleux ipnik�Ninane��Hanapp9 G. Bizardei��9 Mosra�S��,�`R�gimb�)�$ B. Tѐ�ftr. ]�. A�365} 446��95.V&�K"�8Kasagi, H. Hama�Sakura�-@{dj�FurutaAtK. Ieԋ��alm:e2 KuboCIshihara�;q�#�skp8!�b��,46}, 961-971�2)�dkYa�b~%!i��*}{.1 R.��Ip Q. Sg�B. Xiai�Zh J. Li,A .-�.��,u} %�.? j� 473, 29 ��02�h9Z!�I��2Q��{��2�^��# �.�B.- �x5�)�Q� nase1�>J�632034607�>� 1}J.%�:&$in "Isosp�e��K�-�� &K�&��A@4Z Hies", Eds.Bao-An Li%�8W. Udo Schroede�NOVA X� Pub� ers,?  (? �� ]�mc2D2"}Y�թ��5_9�]jі!�}=�Y!��l�l�l�l�l��=10018, z6*I �=}T.C. Aw�Gj�g�)$C.K. Gelbk# � Ba��B��Glagoly H. Breu�V.E-{Jr6���24� g 6�� �_2}T.� >� S. SAP� � R. L�5� �CG.� ^�Z ��� 103B}, 41� .��nX}D�}i ��Elmaan |Hyde-Wr���Ji\ ��� nzog+ R. V�Gnbosch�BowS��CrM;8P. Danielewicz,e Dinius[H�W!qLynDC�~ ntoy� easlee%SchwarDM.a�Ts�C� lliams�{T. de�z FoxɻTZo��J�5�138�92e�� 89&� Dl�.� *� Y.���<G�0 �>[Bi��e��. Cheyn�>A. Demey��Xr�D. Gu�), U�Pa^1� Vagne!hK. Zaid AlarjO Gior!� D. HA�%HMo�=�A�a� !vazu NgoB Ler�hAuca� R.�g��E. Toma!�JQ39, } 49I�9�wE�MK. S\"um��jd!!Blank��_�mS61}, 2�َk� 04}*'�# ,N%��p��Y:* 9�NaJ�T��� �@ eF� ��  ��%2,C.Hamilton, _ �65,�m18�m2.� so�JL�S A��IhaG#%� T\"o�́& �,.a5 r\"o�=W�-93, 1327"� = 6����- ��J.N 2* Li, �deiwayeh�� �Y. Zhou��-��55}��9A 7.�l 88A?l }�P.aqthia>  Lf�� Moucha��M.N�mboodi% :}�R.!ch� ,G/M-�B��k��^)w�A48 4H 1�Y��4q��7L� %�9X�]B� R.!��Lhlomo SrivastaՇW�� rmel* Utsu���oD!��� Nard e�� �Zan��B�$nal �e Niii�S� nnuschA�2�A�.2JI4� 2125 P 2��)$M.F. Rivet�B�`ie� Gauv� �E�s� Cabo!�F �ap�M&� )�M� 34�j�&�. %"9�D_2� 2�2�M� � �$ , %=�MKɲ"o 2�EJ6AH 0316��2)�;ton62AMA��eiliy~XA�e�$ %Addison-W�I ing��pany, R�,3$.!�6��9 m1�71�J�mniz, I�-W R.� hitn��J.�Ficenec!I�KepharwTr�c �f��%26!�71.�lou95� e�yO~]9�N X�+Gu)%D. Utl�$R. Tezkrat�u�T+t'%ErHurst O'Kell%G!�i6>}�:q�Н|Mq{!;u![B. Burch�G�$g�� � )M� BrhlEsay�:YA.Mo%fA58�{37�2��!�)���͊�JM48]7��<88) http://www.�8$stry.wustl/� /faculty/ k .htm(�bi�&�$ J��Bo*�S%�U� IljinovA���ishust!���Sneppen�Rept.)257} 13�!6���@p�Z Vmmuq�3.��>��5&���.%� %% ws-�-4s9x6.tex : ��9-2004#Tex�%l�Hrceep/s Trim SJ�D[9in x 6in] writte�/Latex2E.G@�_?,�x�i] A!��layf�}$tyuzh2�!%% c&�!World�h� 2�(. Pte. Ltd.� Copy�  1995,�2k~Fv All <}3�4�{�z�B: 5$%H4Area: 7.35in (�) ruJG0heads) x 4.5i4M� 9(is 10/13pt ����4 Use \tbl{...}�ma��t82c�� I~e? width! D )FH (I�Q�0class[draft]{]�}�2%2"A+#��i��M&�DIP�aly��p�(p�n-carbg�laK. &�f Ay CNI E� RHIC��}� \under�6{O.~Jinn��i�0}$� @I.G.~Alekseev$^2$�c~Bravar7* ~B�<w7,1�*0S.~Dhawan$^4$�: H.~H�1Igo$^5$�(P.~Kanavets _ K.~Kurita�6 QA Okad7b4N.~Saito$^{7,8 %H.~Spink%9% D.( viri:�J.~Wood| }F�-�{A�4 (1) RIKEN BNL"ݕ Centg Up�  NY 119#USA\\ :2) ITEP�!C� mush kaya 251D$scow, 1172ϏRu��@3) Brook%n� io{2L"bu,r 4) YQU*|��&A� @'�� � 4wp*h.�->�%I#!0M�-M� f��o $�05 < -t < 0.05 �0(GeV/c)^2} $ LeX $t=(p_{out}-p_{in})^2 ��4-2M_CT_{kin}<0����� A_N$@hU�1u2� %8�Ko�^�e| -�a%CinE�M�e4{?p�oe p"e2w��9x 5y2�<22����porU)�c]W���,�q�d�{�`,�e"�12�2aLare(�qxy�EsR�m� �8Ohix2� "5%. �s�P 90��{\circ���l"= �H�4 ��Z& �ect%�g�iA 5Ahele�u�s�1!+� two y-��in�)�4$F_{+0}(s,t)$,el9�-���"Ys.8;4 $r_5^{pC}(t)$!P&a�. = {mF_e4^h}/(\sqrt{-t}�=Im} �^h)$, �?$mU!CiK11 �$$F^h_{\pm0�}i�1� elejq�JJ. !ZmK�c� �AM $t$!�"[��n�t �P $pp$IjKopeli��pj�^�AGS]> E950 0 }�4�a^Re"O��� ��5c,*$21.7)6�r}$.�,%�$G i�h� � Re}~r_5�� .088!<.058~/ MIm-0.16~J 226$�"`��G �Vl�?�HVԡ�ima��r��r�3J1  Eݳ setup=.F7ak)��>��,�]Ŭ*j ��pxI zo�� -.� rib�� (3.5-Z� g/� cm^2�I hick)� *}),�2� �A�;om��}��o�fſ x s��strip2D��&���n�m�a���i)$ 15~cm awa�}�l'2��%% Each^E�$10���24m �actQ; areaV<u �8to 12 �([ �o�K������vx|sZ mo�X�e5vacuum�2��2 read� pre��(fier boards \Qtt��[Ifeed-th)� m�!Ponfde�^b� . D�� acqu8iD�ba< on wave�  digiti�� modu�(WFD)I WFDa�a��2�s �!U �deadtim G��mmo� �:� �@CV�MWTE/)L�@Vnd�Fy ($E$�oof� {�4($TOF$) w.r.t.N� rf �Rck%�!)ghd' on-%w FPGA. T"|$2IF10^7$ s!�e� ;;E � �\"%� memo�Sn)�e�� 5�a�\�R:S�7�4 EAou�em=!Zep߈`lK ) KtT<4s��H TOF=ɢ\bS,{M_CL^2}{2}} 1}{ E}}ŰQJ�l!_��A4�3an : gVs�prr�Ton 6 inmq� h��P�!�! dW�w� �6 esti�{%��n `layerI�(run-03}. ItJAeAbe $5�Q12\mu�g/��m�i"��8i��5�Yns�t����E�a�xR�*�t. A��e�V��de�L cut a��s peakn��8o�%I�� c%:��eI rJ�"� 58 ($11.1.r�) �T$\asU$ backX�nd ($3.7)6�0A�A raw&� ��= � {c�A� lefE Oe�c��[Ga:�ica&aV"v~J�^s advaR�Malter�rng� pFFŸ I$SQROOT}�: �%�d"��J�:� tA2�� �m�a"D} !�ce�s&�e"C,E �wa�*�Lea�BsP�Y�� #qh*�� amo�AA�rips. Fi�b$~\ref{fig:��by}2:f e up-down�� hT$i$-th ($i=1\cdots72$)�� ($\�8 v(N^u_i-R!$ N_i^d)/(+  )m$R". lum��it?�ti;Nup/�s  bu�A�ByLA a ��e shift�Y!7�n\phi$ �(" s:& , ? 8 chi^2/ndf�r�de 70/68A�e%c�@ 104/69%+��fy� is $.VzGPfs�[�g a negligi�N] erro"��]W a % tilt ($4=�5$�h)I,#��:�I 16� f9fE;}[&kX ?���:a.26�4gle=-90, keepak[tio]{EvM}9ai Xc�{SA�$2]�=s!ae��Q�6¤re ��B� Xlo�b�Gradia�lrv�Ab�\AI sine "�e�A�]�} $f(A�NP_0\sin+P_1)$"]FB�!-:�%%1�2:�30v�A_Nr�M�ed�([atuGeV)��m� .$M!Te} A(��9�!�j V >��(significant�"�r��5n�BI��� (( �c!��� shad{��"�Hi�.��'vN�2��6�&(�j"�bU�vi�"�6�mmV��)�Y ^@.]�> ydroe�F�je���@Jet},B2��)2�9�"P_{�}�38�Y0.033$ a�t�So � !�v p>Jis-�ae}uf6�+ \@A'�5b>�D 3 Z�s�@!al� ��SsPNa#Km��VE��]'d yYdu' (i)&2 ambigu����]>FV N �  } , (i [�E!;!xZad$eGb��$͏���ig�6�=0.051\^]002�}{��=-0.012 "9$)W�!��-*��>t�Ss &�����S1-�� gma$-�R h���At�soi:{Z!w%$,% $(�R��?rm���$��70,�)5��� 0.11�+%%&��a��C��"\sc�!yzA_�Pis Ia"�� ye5:u�a��"as�IC�f���� #�RhZ=(8<-t<0.028~%&:�s�N �"��Yl2� stee�tJ)�. Sa�.� % %In� summary, the measurement of $A_N(t)~(0.008 <-t< 0.05~{\rm (GeV/c)^2})$ %for proton-carbon at 100GeV was carried out, in conjunction with the %beam polarization me�xby jet-target polarimeter. Also� shapes %�,$ at 24GeV, ��@ere compared, indicating a difference %in slopes. The calibration="`� is under analysis, %we will obtain !k8new result from �D fairly soon. \seci,*{Acknowledg!��s} We are grateful to W.~Lozowski!_�Indiana University, Z.~Li and S.~Rescia in BNL for!>ir hardw^supports^ this expe!pPnt. The authors thank>!� -�collabo-,Mvid!c!$ absolute F�value. Tu work!V �edAA,U.S. Depart!!�Energy�$by RIKEN L �oA� Japa!Z�Xbegin{thebibliography}{0} \bibitem{Larry} T.L.~Trueman, {\it hep-ph/0305085} (2003). %% >TE950} J.~Tojo et al. ?�Phys. Rev. Lett.} {\bf 89}, 052302 (2002). .R)X} W.R=�!�(J.D.~Hudson �NIMAj4ics Research} j�1z)5!U us return��/ fielWits hU� origins!�eveao$ }��-KlyB�c E�Lpurpose. To motivat!�a�ed(Z6� ߱]>B MN� , wem;briefly�>� relevant �y!��area. T 1978� of >8> 68 at SLACE�a.81�>� asymmet��0,ep inelastic.�(DIS)�$longitudin�(r ��1�deu�jum �9���incida6 � e� iea�)-��,of 16-22 GeVP2z  yA?ed� ��a��7!q��mixAŨangle, $\sin^2 \theta_W = 0.224\pm 0.020$, �p �)onţL most accug �^os���Lim�� exist7 �.8 M� had�IHestablished earlierA5ino=F%"1973, bue� ��1 of a cons~ta�u�= %�(anotherᓅ��an im� A�confirm�b!�� . I)�(1980's, a l� amounE�Y%al evA!c��� vq|�:��ccumul�E.e)���e >ZM�Npr�esͅad�d� du� of%��m}'s SLCU HCERN's LEP $e^+e^-$iders/ se l�P�DyYZ� interieself-=�N� �I�)�F�$,�!��`pole ($Q^2 = M^2_Z$). How�m,��(atively few.P�>D$ hav�en !8 awayI[.q. E"4� a%Wb���!�B] farMis)moX um  sfer ma�oeal phys�!�A�es e� do not>P ongly� �%�S outsid�m� realm�6�. %New | �i) yond0 E8 %��i e.|!�2� , soQ�2���32  V� A t, such}�s)�an � rA2ii�@�<exten� e��� . Tw�Vm-A- > pursu��r2�!^6�on| atom��ystems: Ben99} a7ofR7m�n- , (M{\o}ller)�� QAnt03}.��6�ngOJ� ��s,& 2��F�$well below%�:�<< m�E�pro���oZ ��V ful stat�s �w g�_��B�Q�$ �&T U� uncer�t�onJ�M%��S(3 - 0.7\%$ ��_li&8  $9\%$.�!(A� al�($e$-$d$ DIS=m�S advancB.�Zdely, feedbackE?control,�� ( power cryop technolo�appear�;� � "�  �&� $Q_{a�}$� ��Jee!&�2�q7�FYp^FM�Car01}ybe V$ r�'sual�W� iB9qSJ .r low* orMQm�"I�>|�� |i�9eTQ � &eY� valw 's: �eque�} Q^p_{W} = G^{Z,p}_E(Q^2=0) = 2 q^{u}_!+  d = 1-4 :> .�\!�q�.�)z� ��e�� a-.� D�\seFD03 \ \hbox{GeV}^2$��a!NOAOc��ncis�Ldic5vary w]z�mimila�to krun�d1�Ų��) %�QCDeBQED� o date, h]Iprx``UB''Q5Mia >� show�!Figuri,fig:runs2w},� ��yeto � m "�� �h| � shift!+$\Delta!�.� = +0.007%���%= %Hrespe���bafi*� $0.23113 � 0015$. �~��data =y !��U��s. BBje�rJ three pu� \ poin; i��� explp� discrep��l�g@>ff!�-� ir�gt-(Mi!(, �� - Dav02}�����il� non-�tR  sp ge  ($s(x�.$Z$X� iI������� �? �1i%� agre� iD86��@i �b&g :.E`I�eZ`o�� {p}_�s� ���%�MErl03}1inAwe�tra2� sN per_IUlepto� berfi��}�c�} \ d�4ics[width=8cm,� =90]�s2w.ep9cap! {�� calcj|&q+6/, def8mod�, minimal sub��$scheme~\� ect{�)5},!с`nA�!�solid a%I� ����4 ـ��s:�icaWa��G(APV)>��6}, .~,� >E�)}!.�)�ino���� (��BK���eM world a�gfuA:QH�bSLCͭ(open symbol)2Darbitrarily placed� the ve�al ax�!Hthe) pres�N$:�0>L }��.� >&�T�)afterNi%A � &*�dbe� �1dis 4}."5 *� � u_�q{� V�"pr�!��=����BC<��+1.165� l�@� an un&�0liquid hydrog���`� limi�forward�YY�-��� ca writtea�J% A� |m \left[ \frac{-G_F}{4 \pi \alph @qrt{2}}\right] [ Uc W+Q^4 B[ )],)�&) wh$)$�'!R�Eo��'� E�$ G)a5ronic t ��e��involvv [M=onLmagne�aY_smyA�0 ��on b1�z-��tB8$s� her 5 6B��%}!.F��sufficia�to ��tr7 58&�h.��. )lerm��:Z1�eb�s�a!qe�� �ve�. A�!��J2{F�I��Y� is $M� -0.3 ppm}$. AF�.� � � desi��l�a�P % requireBh� n irac�fm 4�(comb�<.AY�aAh2D). AA�4ceptual diagra"�R���pparatus!�cinB7_app}M�"} �80v�k,, 180 $\mu$Ar�%�SI,a 35 cmf�t"dl�"s   $8\pm2^4rc}/s,�&)hB'im\%4. A room tempe!rF roid� q�zro)�"es�����.� on!�/D lane� �""�ro� re sweptQ sh�� ��m1:2m%Sbe Ake�in 8 & tz \v Cw)koves. Du�A��5� nt �s ()�$0.65$ GHz/ Tor)eNs�# w�e4)d � @ a 33~msec window[ta�c��'*vidA�e� s!�luminos� moni�#loc����2 �us� 8F��� l�3�c" �� dsty fl1$�s aeto 6 �"�'iv�^$any false �[ie�n auxili� �m��R��ng�-ase�,chambers5bemploye!�c�!{�Fthm�"� $\l� �S\a4le$�!!�!�H. High c6$Q� ri�m�-w *�,&e ":J� Hall C&c�0eZ% Hau_!� w Comp�|er ,ɝL. F L(sI�R��e( o Mi�re�,��erein�q 14cm]{�Bl %Z� >-2� Co����ޡ�Aw!I�,� ��X, t6,�el��� � orzndJ�@~�of�4r���f&(�>�5����|s,t1�n~_�N�6� 5��� *8�[�gyW *q&-��!oy^s / �.R in a$el-indepen�"�by)! low |aP�0 ��!=k L��ngian g(b�PDG03}J� 8*eq:�\nd} {\mathcal{L}}^{e-N}=� � \� 4 \sum_q [C_{1q8�@e}\gamma_\mu  ^5 e�- ar q "0^\mu q +C_{2q�+�} 1_{\mu}5 ^  V{5} qb �!S�)),��,2q ,�!axial-V2��Vd�$ �'� ific#new��a^r1ur��d se�* >�c1_u_d� a�nB[ siz���lA d ellipse�� &�"��"&h�X+! and "I l�+�7��� . To����ba" ��Q�";��pr�!!)~!s��H.a�&ghqscales2'�xlcaZ,�-�6�d�%�fo!!in Ram00N%:PV}_{NEWq8g^2}{4\Lambda^2Y�}aI� _5 em;h_V^q\u/iB�a��1i�r a�Jiz�!�=C��er�#g$�# ��# nd $~e�#� �#� 56%_� m0%}S��coeG�>at��� �� �e"�.�f�"�1�Y�, a; 2��4Q��$M�� .n�� les up toD&`��-0 }{g}��1}��  G_F |�{<|}} \approx 4.6~�TeV}.>�Thus,y�^&w^vir� exch�(e9�&� to ]a=evaIa�ar&a(%�s-illaNs. pr�&i�Q-re'' I�!J�&ly�1 80 ��- "��*��)&V"d 90\%A�f^ce�m �` [ �Ird���!��� B8�>�$�af��(r�mdenotH !��l�riv?,�62� "�>7f� !��1�%�$^{12}$C�us>VSou90�!\! �G$e-d$i' >:s/]sma%,18Q+�q��s���1��n��{)6V"E�$�'�a��}$!P� ; #�� is �W 6�9� ion6" Ixr  :�#73 73d&D�I� �>83d"rC"�$�� ��A�c*�0F�- util�$�&� �l�Q�-Q�].6.x-Re!Gl� re*]s�)�D&als to�}�$�12))��!v)�. Ona��4436E�39�9 � ��A�CBosw' *%s a�:buat:�Ek6n MZhe�7a�U5 upgrI�q.�O1_. ;CDR�)�>�*��s&�2��e�Rt<E n .�5�� �: Cah78N�& ,a_dis} A_d =� \sigma_R- L�� + =�(�!3�Q \&�2 �0�) b 2 C_ -d}[1+R_]+Y(2 u82d})R_v(x)} {5 %}B$ Mu},\d  2u},�and}\2w hk 7.� Uv�" ��� in E&T&K ( :)s $ �$EX$ �~ !of edi&� f�=s N#6nt�$Y�"A� kine, vari�� $y=\nu/E$�a� $\nu=E-E'D6M�l�0by�/>k1a '$E$.��n9,of('^simpl a�res��ea^L�2 priat������e2%'�7R�_d� - 10^{-4}A� [E\1u} -A 1d}) + Y(E�2Au]F� �[�ex��*Y$ � s�s]=�&n1��!zo($A�1I� )E*ax*� $y $) c4� A#For typi�U F8�zs,"100qA-<8�7���G !��6,,h'*� �0pre��erm��� �.2"a$� A|!U*Trge�< Ta i�.G9* narray} C��L &=& g^e_A g^u_V = -��1}{2} +�� 4}{3 .,0 \nonumber \\Qd6QdQ.P- 2�PA��V�AF�2A�r�2�GdG6�BF.6�e5> M ly u� DIS-�. aim�>+"�.�-%��.�$E,h�>ngea�m 2 - 2U�"�* As sc2J�"�)e��0,am Vz. in*K;�!K&�'re�4sv'M�acte�}�ad82�B�qA�6!}*� ��ld pot"'al�8c�& BD' me@ismm�Z��&�7� M a*�10 cross-check r i�9(/ca� 5"� A3be2a� by %p2�!r]�'� |��.*y��entE!�%4� �WEn.�'�(� oDr �� .frameNC�@["f�� ?im��� ZwX�U!5to�m e�_ed ph�spaэe�6A~>��bi�%, �h�D Zm��%��"@ ' � �B.c2u_c2�Pn< *3��e�35 !Y:�i'I$� 4inZ�� ba�^ide��$in Kurylov�Ce28 Kur04}� � R�) SLA6b �� �� ��`*�uW ��< 6�M)!�$B-�' �R�s�\.� O",$012"I��u �a��� a�� �an �;PPb-gl%block��a gas2� ?3ai.(a�$B ic� �S�2qrun�O.hH�/am � ie�)��&� spin� �es��$$\pi$ betwAOA�Uip8dB anomalousG8iAZ�[g� � Nd*F [ uszH��!�M8 l1l�G �A�(!}��.*Q=a 0.4\%*c"��d#)E_�A%tLA6qatj$�2F`�#2�0�- idea�do.mat both}EU u��7"oe%�)�&l1LalLF� )��a 140�", +,�"^c�E��%a 1.�"u�nM�6��JRC��ёAaA�Re�IIS�1}"s (HRS)�a`"�>%�19y�;"xA6his* .ay0131~ppm%�A�J[)Gbe a 1.w&�$�Hp � �B�(j CEBAF� "IeޅmI>�le 11�VX*�eh.d"6� A.X2�39Q8!p�$�3 a 6n�[�Q or C2�$s�.ld� a�#��J�/at2 = " '1� �L �\ cern �A2���R M&"{ � twist�5.j)ŜTQEly��V.�=�)d͝&jIB"BB���2udes �-a�("free� ton")6�mU�)aNHs Ea� � �(&-gluo�:r �on:S��&� in Q� as85}. If-8 W� �D" �)igb�mn6�at �A��8+*��$x$�Jn� �$o "�!X �),��� �1R��G *�:S!Q} 2Ge�Bst6�*�G��'i orw3�, basic\;iq �i&��c �hw@ remas) " or l�*� . B%C achieR3A��8 grea�im�ed��� !E�n�&\ ��W#N{<�D"3<nd i�.5!��<%0laserQ�a�nee�A�&X�"�<. .$ast decadeE\�(u�X�b� �?�Z.o�i��"E �wK���r�of ha�-�H�'r1 a # �om"m k ^� bod� ine�_E�-_" os�Rthoug K.�I� $llenging, )�;u�J r�N�*� :Iavailf���6A !� A#i!�z(nitial look���(Aof!��O�4�.'s J�p�1!ambigui4! �b& �O�can�:Ginguish  �.=G_M^s$Ec $G_E orFcel�C�( � ah��s"� nextDyears,e 1m, 5I)�,HAPPEX, PVA4|!� G0*�!E2�,"!O�Csh help ans�?0 �5A>�\"��� ;(b� ����s6A�rB�N iss���2x/�owe�a np�B@ b�-o2� q>nKf"j'�` �H$. ��"/U{I�@�:"3sec:i} Ov� he�r�0 �c5*�B*� �=becom�u�� tool%a�9[.2!� �'�a�Ke*-�  pai�:� gi�V/"�5�. I���. al�{A-6�#d��8�L=E�-B��ns�2� qua :��q��Şl"`"E%*q)g��  ��1"�0^s p�Fill�����G good&wD e���B2&se.<*��ve����tUP��� addia�al2<�WF/�o,way. �\or{3� �B!6 �f guid�C�wF?��� -itu�Gsea!�rk?"&n;, robusjH8 s��4�&�3�� ԍ�a of��2M��� i�G Z/ a�0ofF KY�/ata��b :d��A� ��9��!���ify��a!5!$s$#U9!@a�"N by�4 ey m�59 )In5�Z��s somZ om�V��lattice5  c�:��!� e�5d�dm)u���-� -�ma�O �!sM+�"��A ront�!\!� �paaDw��T� ݍaof%� 1"oC a� ��/ hasi*GSAMPLE=��L.t/at�d MIT-Bae$&�E� L1990')�� ��fik?�wfGॎr�!:�� Ito03,Spa&� out�;�=�s])s: �!��,on!;��  anE�%JB�IZ9A���- i!����J!� ���<�tA�I!*8>�E�&� Vp. W�\v"�VsA۩*���.18�*�.5�taken�cQ Af160 .[�JItalj+Q�s -depth.t  S>v�;Z_Fs@sa��-ex)6In B�@� are}1� pf�#7]a}A6AE pY -��MAMI fac#(>ke .� Q;�s+1!:�: Weak� m FE��!�R8N of S6CQu�2� � f 7O'�-N/ B�� �nd�6"�1,4 A A� book ��[m�m��+�#�)V��W KuS01,BeHM01,Mus9��-q1�RQ�.%noA!�A Q?At Q B�P�u%��of�1Q��'��us��-e�[ �r> S/��c2\ !��|!ϭ�ub���UncapsvB!�a��I�) @:�3A� �B in�$nt ���s assocS$d � �\ 8hoDor @A�C "Z-�4nC&� *-'�$B s} M_\�2�!?!4\pi\a�>,}{q^2} e_l l�2J�2^{EM} 2+"M_ZDk"s32\t3f' g_V^K + g_A 5^' -kNC \"5'�"5'q"& fourF<��y%{U1t�%Q1!�rh�H*�c�O!�s H.� U��'��3B� sASP �#q^2 > 0u&>a��H!$ q5�2�ag(< �EDV�&f nce,�`B�]�6�(d� h$Z�� $W$E1�B��dmpt\e0 a�6taca�tQ�U�trength"~�!_F��y� !ut $�0=\B639(1)\{Xs  '45}$~GeV$^{-2}$�U@6"fSK#"> �=�{A$s $e_l$, $E�v2E�$a\ lfX��^�^�(� �%4le} %\squeezet� q��,er}(tabular}{c| } \h� % on & � � A^l$�% . &\\ -)_e�\nu�3 tau=0 & 1E-1B$ -m ) %&+4\s2w91_'cUt$�@&1� 8&;O�d9sb. -1- 1+ R�&@{�&G ��%1A&�1Sq��'Oq�el?: B�MDs&�/.�' �5�e!c!� } B&�mţ�"J�?S% like�Z i0no�Kr� aI�#s $��m�  5re7mply $&�Ku}��5u 6V )_5 u$g���9e� �,�# �K hand,e>e�4�of�D!��Dsandwic\��� !�;q<���8EM} \�Bv��] N\H\hat{J}�� N\�le �({5 U}\F�+ 8 F_1^{ 8 ,N}(q^2) + i\se.�9\nu}q^{I�F_2.4 }{2M��]U 2O�NC��(���Z��.� + )�MJ_5 G_AcTN�� �q "}{M.&P?G U \, .i>9�,��letenesk�d he pseudo 6a�@Q@ $G_Pn)� "|, �S��E�w�neg� it s�5;e does� a�C�G:-", �.[ i2 a��. in5NE�&� w%$F_1$]Pe(on)'!noIf(to 1(0�!zerbu&G\,�$F_2$-^&.$�a���7K�C F�.� � �\��DirachPauli�1�s{1���!( comm�Q -�S� Sach�.AG_E A G_M$�ue} G_E =a�"-�1H4M^2}F_2\, , \; G_M'F_2A�"x K�< �",)lk!,�^i%R%�z)� 5�)~�&�6!r.Z0:~�n �� alen�f���J appl�eM�/�.� $F_{1,2}i�$k(.#0{a}? irN b5�!$ them�a�X|*�J� each L flavorkac�5N9�heavy >Fc$,$t$)W$b�0r�)e� �j2�'"L a�"m��i���$$s$ u��� � weP&� .� �/c^�/�!I<'sm:�� -� N�K�� �sG_{E,M}ѥ�/��� !u"�/�  \�"(d +*s\$M)6�*5 >B/ :,u + *F + I1V�,y�2F2�-�ElyA�-Nd !ϡsh/u��AA�$" kE\ Aaf�5/,�seW'��El(just �#�a� ar�-�b�IM.�. If �e�V�ClpAځy � .O ��� e�� sEaJR .��lthird��i�>��+yVt�Yla2 �2O�!e �'s:��tN� �  m"fwave >�6$uq�1i|%� ��� �_%"� -, o!/�&Q�j d���!�{6!�ter�+t�eu�Kka�&Yfalgebra,Vt&_P=�%�t:0b�����4&� GE� ~ $EM���a:� vms3K2����*("� o�B�?6)s1�� . pieceJ�&� gemz���Z:��1-��,1|"� pS7B n} -s "� �-8 r�a�62k?M�%zb� k^ deaYq!�Zre�e!�.+I�!ngeQmtoW  �7DEst �`l.S�l�]6"�Aa�4[ iso���SU(3) 8* ��surviv�Cul �W1  Z(Q^2l`-Y_l;A + �Bs 8� 1=+1(-1)Er $p(n)<G_A� (= -(g_A/g_Vd1.2670W^ �^356��'edI�,$\beta$-deca2�5����!q�:�$ v5� 1�6�B� Az#be�$c[�Br( j!er-�c�)c)oto� A^�r*5 :�$�a�A�<-6<!2$ "�o���4r' A; di)i�*T, $1/(1+Q^2/M_A^2)^2$,e,A� 2dE$M_A$��"�lyBm�Bi�&�(Al�p� mO�C����a g03 +� :|Pbe 1.069$\pm$0.016 Ge? Lie9�tm8!bh r�rA+&F )� i`p"Hkin-�to��ly �!�i< O JUino*b$�(Ber02}, lea�+PM�1  1.014�b,5yo2��lHre"l.,Arefite�!�1� �u�W up�bd��1�"� ]R +Bud03�Ciu#s zbed=�oPDGB;Z�26�2�-;�)2new5,!�01203, )inG$N�]B�� �Fb s "�1= .�)�2- %-6r E�)nal-� Yo was 1O !�Ka~$ePManohar\ 1988-KaM88O SoM8�, McKeow�BMcK89]P Beck :BecL7edG�O�g$ m^beyuE?�w"*1S.*m� *:&�o.�"{/"�,R`�IA�O Micro0 )�a�f`(^�� -�>�e�on� ��"E�!�I�=eq:�vi�5��wcw:&��a0t�x-�sJ�M_{PV�g0 G_F}Jj2ZJ^ � + g_*�&�&i6��"��S�?&*'�/� to�" ��Ka��%Ss��Htot 6 is PV9j�U�e4@l�P1 � �3$l.�s0.�n .�DO_"Ea��i6~ �q%��Z��-.�s� f�N,)">i�B ����*�t�7um�Fi"�{i.e.}"�,+b-ced �efhelic�G*z'is .�s c!/ro >ioq%t&A�ter`T� $M_9 \ PI�$.!��=eF&in-1/2 -xs�o_/MY *�v� asF` &� pvee} Aq$�d\� R -  L}+\, N :G_F#""� " A_E + A_M A}{\!|,[\varepsilon�&�� ^2@tauf! *]Xe6�9���.}G_E{  [x 2q�<���  j5A5-�:` 7GQ + E��1-�^ �)gA^e�� � N�a�"���m� f�_)�M_N^2}\;�-TrmPG; �41}{1+2N�ta�Y�.YC}R$)B$-M�!qO�e�ly"�A�"���i . D�E��>*9� |tun�-*~  �3��m�� ic, � ,����� �o�+F`a(5e*�1�I�E�&4 da.�E�4$A"�A�^#le �p�aF^!\�5c&-F MM�A_A4!Quasi3L�u$La�o 0��w��d)B&3us0 enh�- e;'�-� in�B�Y�r�*$uÀ *{Ch�E S|z"{M } I � ���5sXriAWC EsEbreYk,:$li{ �p*�� �$u-6�u �isR�B-N:� F nd�<� Aga&0-�0_a"�Z$ ��;�Bm\ uish6�21s$� is9+ a*[ ��"�����&ņI�&� � . DmPfsin��O P�&" Dmi95 Mi;P Mil98}�."�-�_g&W5� )�3:*�& {k!cstitu� d�Y9 I� �<LW� �!�d�Qn! A�Kn �9*!���6va�� 1/70A�ulG;� a�a6�� is�)�i)f���{ �{�>� of 0.1\%A1model�Atd_qIW9"5 � 2y �  H^�3be�RM7 is �2bef�mZ� adds.�*F8�ir�1�� . Ssr!�clYR�+r�ac� y Lew�.n�Gbe�. Lew9�wh�8gs two-@ bary��hi�tq7urbz �+4y (HB$\chi$PT)�investig�K!IIE, !� pin �J���cRad2m ve C���8} %%%%!!!! AltE!�F�t�;ay (se!�.Y PDG)A�@fF�a�U�@bc�bI��96? Hig&[uds�lch� tho�2eptiF�Z"Z]sv @:�&b��v���� 6�%R %$�oU�ten�>o�66 t�O>" *�� 7�}�2 ompu?v�gaӑg!�S2 %e[yi�4�2<�+�@F�� z�a^�EA7 *z i !�t).c"n> ]��.�n���1ely%W�s�Y"i�:�.$�  )$ m�pl���Che�(e-i�&�!k �p6�quite�{�9aV .cMgls��5�S��2b_ fash!�.��) &zJy�y���Z�;11bt6@�E1.Lsm���r "�I�!2�m,$"zA A�J4qr]��or�>E�a6On�Gof��:�[fe�+�Qs ``ana�''i%k{^5��f��} ɣ)Q�0 r^eB�%Ke�1�tmIG )�q'���99V.P�"�E�is�5EP��of Musol�. d Holsteiqc(/0�of ZhuNZ�Zhu00} m� 6iA0M�.�!��V�Gs����B?��K. �9`�K �&2(via�I | loop%U ��nt sour�,.�.E%����J�as�~�Z Des0qu�,DonoghuA<d :y DDH8!T.t.�X)t6�6 Nz"�6��recas�eNL� h�"� � N�"�M)@�Du����.0 ${\cal O}(1/^_��)$ }�Q'� x$.%=� F_W}$Y&m5leA� �-B� . Po�OJ  a"=; m!�h��4QY��kao&��=Eluded�gS .Z0EQW+����I�/�f �G��a�!�fi�z��&^�p. ous �8d�px3"x onfI�te�? i�1!S!`y�-�͕ŧ�) �G y�^Incorpv53V�S T%vakV� � "� f �ue$d����"�*�T"���eq" _rad���R_V^p@B�p�.*n^*F�Vx!09�%*��/ �!AP"ci���V6� �A�-7�1� a"82�!�w0e$�1�o*!�9*6 �$Tby��n-���G�E�&"�&Ga�2%�ygol| ����ab� ,;lB���Wtau_3(+[(A^{T=1})G_A sSs3}R 0}88�~ sR^T��i�6{!�ly�p>�an� � $calar octe�55�%~8"EX� "/ k@+�ru�ai2�*,F m�K (5�a�W>en&� �) .!�"�a; . to �K�� hype�� I"ay�2 ich, a��!��,� 3  ��) {� $a_8rA�F $D�&>ek .V 8�!=(3F-D)}�3}� �Xa_8"�Q!k8(-0.25\pm0.05) ͌17E�43^+, *@ Rlsoa�5��M 9�%���; d%! behavioe�- !�*D#%�}�. Q���ne�)��|i�w/>�]$a)0!R9eqU��$Q�.1$~(G��$^2�� !21<d|���2� cor}��ai�hB<lFX M���a� �=�bCB{�x � eg5�:c|10�e�-z-figs:�e249�*72�box�5 (a), 2��H (b1�1ex6c�ra*z%� %.��al..�"�M ^��E�� e a �";:bKTwo e�b!�� . B�R(b�=(c�� � dU2� .�&55 fig:%rZ�5�451�1�D5>�)��5{| c "<79h�6T=0[6T=�6>6 $R_V-$13 �UB&2 7R�$&e36i314-23��24+ Z��&�6Vu?�j*toF 6.�o��&/a[!��,me�E9$"�4 {MS}a�~I+m�98�i�AJ>RgZ4.�g��A8 } �"�1V���e#"�irB�i.:E;M�J�%�$^p = [(1-2f8)h {(T=1)* 0)}]/7�{A354%� 033$�&cV^IRS+FS=F14IB 0004_ � �%�yA.�Ie2Bm2 \*�S� to N�-9��PDFX3�@} An� orO!��8� im v��%�s )IH. ?RA�EJ[s� L�n ]'-�'�x��)+ ure.�� �n�#nsequDɝ��5 {'1E�)ateR -�8V� ,"W � ~1�M�h s4 ^ri�Ioton}&�{�J%�� D����-}�(5� QO . Pp��*�2�4�2v4 for �X!��.ndw�#a topic�!>(L�A]at @w-��.�"S�o4p*�Q� *�*�g�w�A�{F�J�� majou&KX.�'A �� �5GA�"��Js�� .7$N�*�{�/ *�A,fx ���p$ F�r$�_�05?s�am�x� �'# ep_x�H�"# }{d\Omega� �i\B�bcos^2� *�  {4E^2'�4B� E^\Q` e}{E}1}{.! x1.-"`4RV#e7 g^2 + g I&�"" +] F�&At5�  a��r�.�W<�3�&EsI!>��0* HaM82EVer���l�l@is ``Rosenbluth''&�OA�]!�4"Gde=�aoscrO �+c�bo�Mn  �z�&]�h �� nflict��i A�.,atF��zve 1 (&y .  O]C�Npmpt�Qai�gew��)�p,>J:H�Mn.. -���la�.ea)\ei:2�&o���7J�'�moil�m͡$<�=b�e� ine "� y!7�<ս� /Y�$�#*�.�/U�(!�" ]��V6���Q do�D�a "~���!{Yb �*"�(a%!ql�3susʁ���2<&`*���*v�����EG4pt�#,�_X flux%%,�ci�(� ���*� *B���& 2�"q5�)�>f* �!! ���reA82S�Q6�com+��k. &cr��h& �NatR�.=� J����p$�w�"&�y8Jon00,Gay02,Pun�q"�i9nC ic5G!����EZ�I]t�[1�&$&��Iita�tr�$o a global"�Q���Vt� ��)2�m� Y�p{��w�GeQ�rr0%2 New: !�ɐRiN��j�1ol��6�R xCh x&�"�9a�!3�Ru#� �:lXduc�m&�$*�.�5 t!�"� %1'or1�7�6`of�&p�a�p$,�pl!d�a#=��2��at��@� �A*V� ��'s&�/ �A��m fX � 2�./vli�"�-ǏJ ���!T ermeU$ȞET W�s��a?=B�� ac�ger�"eA� halfO�Pw�"h�=A$  �M)(Gui03,Blu03�p�a�&X'�l�g on-� �� posi�2�� fe b}. a�c�ur�waB=a� l�QǍY{�6 .� MF� .� a,Pea�_5*z� bA����to�� . J3�*�h p JPAC�j K��K)�is � �^E�^�.� ).� 2� %!�th�}< �7n� �S�((�leΆres{�d. �FM�&-�AAR�GS�(b��1 *0 e ��q9tw�xthods�6� i��&)3:u ��m6I�Jd6hv�� �� n 2\%-�Q� 3+v Z �ve~ 8� �paw.1 � EM2��an/4t lan�!�hvYXnear 6T �BLAST}����/ 5At�6�fD be� ��a`.~2 bT4G��elF�4r<g:>@/�imagin�par�M}7"�s.e�� �8mi\/ azimutha��L !�p��sZ.�m) ?I��3&�/�nerA"!o ppmO&!GU�few dayE>��8BU��Nup1=ad+6 �fl�!Vl%!� e%6�.��A>�+��X.�"-&�F+.V�=e�,e� �1en!�Xy�S�a��W9p(�^�bG0=Y��c�J�";a?v��u�f &M"A-G�b~Trv��\�� fact#a`�%�B2���["&S��� aA-ek4��&A.��qmY &� Vd,A�.$A,} �&VD&-is�V "� � a"%K�V> e *� cw2' �j�>;ap%Oor�S�J66��E8�=$i��lTE) ã arged:ca���*,level�'a~lex��\2��",4ny.� z)q �*e�"h> J�6]2�"�@t*��NLvR�S�O + hw"�&�S@ sH � dn9, $h$=k>1��pSedJ�"� $ �� d�eq.~(M�eq&� ). B;�a� ����]��)��!�A� �{a�#�.E)J�6xP&�7uss��ed�H�(a:1:z �&�J_82�^+&�9^-}1�^+&�9 ^-} 2�8�8 F)�}{)f��24 v_{T��c ^* \U �7&M��$C ):�WL^{�})Zfphi^*]*� R: Rw v_L\ �"�� v_T%"D9%6jC:rE(�, �)$M�%����E J!Dr>�=J%"�"c,�*bf Ό�)he�V-$p� X`��" $v_i�"2~� . %BM %v_TE ssN&, v_L.�|z+�R%�1:Py�O8ϣ=^3$He-#��&  �Q�o6�%�*a<�Zkb h� ��Zs@ �k2�4B���mE5�� i �h6.|�#�e"� �7ch_! bnmun��c Gao�H�w�Hޅa(lŌ�� �ly�� fea�1 %�"z>$�-f:5J��Y A sey6\B�+carriNCaZ�� �{�D.�!��e �n$�� �S *31.�%-=Xu00,XTMse��� W �u,ɝo � y0.32�% f� @��� fH�0i�M�*��1��FM�a `@ -of-the-a�a�El@e,"cM|�H%�k� !� .�A�bI0.3..,.� ] ���i"ճ=�� i�.�b�h�|�a PWIA *�1\ �6~�TQ*r$s%��y�Q�s�YΩB>�gmn} a� e 5{ cir��^ $\vec{^3�>He}}(e},s"� 2Cm�Q/��msQ�qZ�"9]�b\s $d(e� n)/ p)Q�Kub�H)2�diamondMR&.�"ar '[ M��c/��䝁��o�:AT/n6�9 +m��a�!7e�I "NM "�MQ�!I^�Gi��cyA�H�a &�2�"�'02�d�,(Bru95,Ank98�. )N��E� �d1�agg<d��o<1g$�� s��a clai ܙcx! 1\%@X7ng!?&cK�v � ofi�tw�2�;�L&�*����r5",@E��4 Y, ��7"l 2� t�ǥ�v�,��al*`1�riDg mark��. Ae�# }A� "� Eo&� ,�M �Kv r��Lab  ich �jpus0-�A����[erb�$Bro94}. Soq��� �#%@ V�� s st[en�B� lowF� ��h��`Kr�<a&W"]�"ڑ ouryDA%�p$.LCr!� en m�);&o��Fi2=���tp.U .S demon�%!�� feasibri>� A��n$E��!wc &� way, ���4�Z<<g����!�8ion. Schiavilla�  Si"�@Sch��*ed-�Q��"� �d�:i]B�f��y�d.� )�"ӈ�A�� �quadru�9.�Q�hz�y*��!��Q:U��o�� �� Abb09isIB��!2rt-3Ob�w�J�^2y̷Ia a��{E>QF2 �Wa".AAm^ 42 metr�� Mad0La<�=�w dou�b�r�#.X��6U liVOa� �cM�X�h)%� BEG�MbV�� ��)=$^3�.�� d}$ )U��Ost99,B��veB�z 2K�m�;  c2��at&^N-�'}�xi �K��") F&)nD�qZ�� �\*�*P#o���a+i 2�2"��"��5 &68�#in -(�Z1;�level)8*% ly6� Q�T�Qon� ?�?n"U�h� �pa�* osed g�� G� �2�"4G*�*�G0 �R2�!=90,wis�1��]{gmn_� new1_xu:2 "6,! '��e��.��EKVR/6S' *�2 |a�� >�/3} (2. )!�&d& iNy�C k�d�>zo } z� )m,!��of.� 2 v* p)$&/fG2mn`i�$-_ffN/Q /� {huH�oV�&6 / iLzs_�S"/NOz�cmJ�of*N 4 <�*kE o�C"�#6st(,���,v&��!OsCuZG]m�<��*� 6�ȗ%@�] �� d "�@�o}:��)�\6 �xli�ve QE) }.t�G�!ɒ��om. no 7 �n fso��s(0)$=0n*d)��e%'.88M 8� &LB� li�l� a'�mu_s$,X"*. I�R0�g�5Q�2�A=��Z%" �@� s��ɛji��k  �-7n�#��Id�%�s���Rn=0$�u�!�&�=Yi�s,I�by JaffJaf�U!��Bz0e2�@Mu�q4\footnote[2] {�C0fi�z9Tdim�)on� f=� �Y�$\rho_D8<f�O�b�O r_s^8o"s'<-���Pd ful .f W $<(S�<X3�hPrsr0.066 $ �Jm19�|be8&�P &\�e & -6kd#j s}{d}P|_{�9}�P 2m��A� �f2 6+ �l �d/i�.j "��>:- v\�:�WI$ ''Poles''%RDis޵��R�ons�C*^4``~4"R*�@ �=n��!�&V�qC��A�2�M- U3��6j4c�c� F�� ".K =�BtDce (VMD)�%]5�A:�uNH\"ohle9%Hoh76}�����Y" .���VMD<'��k$�)�(1}{Q^4}$ ``�<''&�<"{�F., ��>(?ri7%*t%R&�� sea��gb�� .�'2G ona���N�H\$L�� $\og2 a"�� D%L`o�BesO4* unh<*�D8�-xXE� � �5in �����fi��6 aA`oM6�Dሡ�so�a �cl.L��$e6ly $s&c9s}$�� H D�o ���)�5�. U%��'s��a�@:�Id<� ��al5vS� phi$�9 ir p�$q���eOi(u u}+dd})/\�}pi s}s$6-p)�*�by��XJM"�a�&�Rs*8� ptoW�"|? �6�! "�j1�q gl �L�� d���'FaB(a�Lm0�_sa�:3I��\0.15$~�6�l@���~� � �NƉ!�yONz��K�K ]T�41ga��� J!�E>e�<�F(n� nge).�&^�g> ��D��{(I�>���f-Ō� �n�Қ:�W��P c��ofa1a+m�/�y"T��Ջs, altЌ good��)l��@ � <")zq��"}& -\pi�1?e�HE$r�! Z1r�8 �$���ou)�0kt!�use% �F3th�K=�:�,!��(�:� ×CF-�� B�y.a 4͓-'m�, �G�Haj��en=\8�  anOVa]6}N2C"ly��raAn��� ico!���ui $ =0.42� y*6 Kaon Loop6  Ps}� `` ''�@�7a�i, �Ss�<"��n!t``"N'' pi}� [�5�pa�(se!o3] 2��sA�&"DO $-$K�,A�#*'$ *{n. T"Q]-�"Ueg. .��$�"��� ���� e surc����3%cloud.&�3]��c"��!r�� AM�&�IV2t _�%��At *P!b6� '*si�4-�.S�!��eLan !w� qr:i�M�.} Risk;*��ZHan00a}��2Mg�� �+1L�^��"c)flip arg��TZ!�#�)�mD�d�I.tYS�i'L}or6*�W!�)^=I YA��H?=�m��byI,Burkardt. A=�!��>A>��V��\ N�\� cA}Ξ4by Koepf, Henl�;n>K]Koe92�� ;Ot��`!�l4&est���I���ofW�D}u ����&�A?"lF�s�A0po�Ka?f%�^�"" �"���C �:insteai!e�[ H{%aths�{n��$�*ee�y bag�ɉ%�� littl�5L�mY-w 9?!9�cSe�a��h�_!�.=&: �s.&Z�� ����&�/�cho:�of��.. WQ�� Bur94� ��� 2�4 .O)2Z���s&� 5V*�7 � �A��1��m� �L o�"�&�Hicm�� MV� �xeagull��phA�P ed\ gau�� variN . Ad� A�#\)U1 F �H!@�Y ag�*� [ �M "� �Z�UDh{ !��k=�Geige�Vd Isgur_��=\��o�E�?m-7 i�� ���-�V �'2_!u�c! lq'�f �r���&!}y*[ (����i�tm��k)�LMVGei97ă%%% Ch6_ PTF�er&Q_Theor6��chipt} ;>�R�#�Ft�MW�?T�y��*�_ u�b!eFK �&a�G)�� g�$�_&* enormous�6��HinD�cri�a w*�variet6.�,!n>�� �؁Aheavy1��0o` �>�`study"bZ. �� Hem�cHemmer�k2W;��a�o.7-c �(W�2Y O}(p^3'Y �.�4�Y expa�&S�9)�*mR���$D��K ���w�5q�+s&%Ktw�"unter�. :,!�ItoM�Ito pd��,iC8&lcIi��o�s %�e"�& �e�q�&��&t+>l�} � let ����s!�R&%s}\P�� �eNonethe.Q^�"� �o_ �-Q^22|- -��� the ��s:�"SAMPLE->Mue!>!S�� Ani99� ��5GA�"6=�;q��broad �$*4��H�(.� m�taM op��Z/g�q �!t_s\N88 1.4$^. *�!yA� f �IR�NX�!g$� � � ��i �v�$��h!&.�Z203QT�b!}A2�=4Bw� Pٕ�!N e .�4)$8� c�5j.*a�E�,�Z",�UN�=6�&�u�/aѹ� %�)��� ��dE�-�! ate�.��yo�, �3l"�-A["�ao�0tr9�D*�{pto�Rv�<to"�h�k�*az�(.6x�al��rA�%�&>5��VAvt�g��dI�aT�of Ref.mcHaE5as�`6�}�lemA�@ �DR6p3 =v�z��13 b_s^ruE�}5 � J�d��1�[}a�'e�� &�al &3!"LJh \leq 1% La_�F�  QCD2gl 1} UlL"a� .&�,�%llE�A!��rigor����*��ᲡO-� '', �JR<o�"t� sx/e��E_ �d mend|cha۠m!�Lj� O ec.s�in�a=��h�L/onnA= ins� 9����2�s$ s>G��$QCD vacuum�A�= �a.� ��5hib��+im� su I�2 A�a�in�nchedy��� "�� p!��soe�!�Q�2%� �4re"�? �� situE�a�y�c"���%��/nn 2�A)&5�eFn&�b�*.i2^�~Gei�o&��.T�:�Fr!?[���is/3�a/ex�.'�at_5�-inspn�]��Leinweb&L *�Lei�f A2W �OHm<�6 �.��&�1���;"�&�Xatg��� �pm���&�81�� �ղ\,cb,Lyu02 �)to�s"�m0Kim97,Wei95,S�� ��h ch fA tulb%��!c!�2�og 6�q cloud,Dw�H$Skyrme-typPar91,2����8o�o*�����:��Jʠ��%�poAUia&_�%@��wmqDA�*=XA�E� �.�) r��"^s"z��Ax!k*�)eQuROt�LD�;2gaI-Y42s$�Sd* �?�$a��}Bl�e�6��j���$,C- -���7 i��^*� ��!��,WL�eP�A�GA�dM�c1�k of�\a*��J� e�h2��i\B�m$1�V�ķ�^��*�v�jV�3�S2C2�de$2�� �1&� 2SJ=�����%�s."1�mst, ``a�ic'',�xi�5a�I!.��s �"�3D�+Non��nonjAung��l�GB~!R~ 2�9) "$)K} ;:��p A_p�)�{n A_n"��.6�@R� $A_pr �*h�C�beq:|�d0nl�PV]R� &qMy`M.'T :�!8!� & �� ەnd�A�"a� m���x*�QtRs=�u�v���� �ta���.4s to $A$, it c�Ran be shown that the (isoscalar) strange quark contributions are multiplied by the = combina- $G_M^p+n$ and >\thus suppressed, whereas� non-|(predominantly isovector) axial  piece �ains u-ui[us notxT. As a result, $A_d$ c% used aWHrol measurement forfA^e � its uncer� radiativ� rrec! |s. More generally, with moving !interact nucleons,%Hasymmetry is depend�on both#mo�umJd(gy transfer@is modified by NNpTon effects. The terms�ain�A �� m fa!�s%/Dinstead be written):rA of!b ponse fun)( \begin{equ%�n} A_d = \frac{G_FQ^2}{4\pi\alpha\sqrt{2}}\, $W^{PV}} EM}} \endOERf$narray} W^.| &=& v_L R^L(q,\omega) + v_T R^T8 ) \nonumber \\?PV?_{AV}ND I\) + v_{T^\prime} R_{VA}^t)��A!�Helectron kinematic 1�$v_T$,LI�$.m $ ar= 1r!= \left[)T%uPq^2}\right]^2 \, , \>%= '1}{2}8| :8$| + \tan^2 \theta5 N4{\mathrm{and}} `9 itanM > �by :^2 �< �{1/2}�.1g1A�re>� captureyisingleucurrentsad now also%�ca�PdeBwo-qB4 . Studiesa%%�e� of:�o��e ext�%on 6se �` quantitY4have been carra�$out by sev�� authors,�� all lea ��nclusu�0 y tend toa�4small, althoug�� is c5��s somew�q �detail5(particular �o�. In~\cite{Had92}, Hadjimichael, Poulis, a*0Donnelly look����(sensitivity-7�U�hoiceNN ��on,�� example�"y�!1EmodelE surveyy �Cofy�s, fiM!0at backward aAW DOrate �ձ�sEPV�var!�little�T� Jl�`0at either low�3^ or��(scattering �biggerp��s betwA[f,s were found)% best .z-im's�� form����F,� near%�)@first SAMPLE expe�cn)�NN ��6ce appea!KE�\at most a few percent. �rehly, Diaconescu~{\it et al.}M�Dia01}�puted�i�A,the parity-c�rv�compon�viola $e$-$d$]u��k Arga( V18 potent, at �cspecific.EheFB:�these �-���!dif &�by up!�3\% i��q�� quasielas��dis� a�closer@0.5\%5���7peak. P)^9 2�o.� I� hadronicM�B� $B�$I�!�!� i��wa81}��Q2 again $@Liu03,Sch03}. An�Q��magnitud��!�M2�NN2P (labeled ``DDH'') reAve � m�oneIZ,$\gamma$-$Z$� ference��5|,, taken fromM� �,a�4 pin Figure~\ref{fig:schiavilla�i~}�of s est � ,Asem&V ab�� two order�9be��!.��� �2 )�"p negligib��is�in �ast14sit��$ thresholdA��g� n�+ deuteron *� .�r�UiPV2�s � te, allow��possibilͫ�  long!C�\�0!Z7PV� Tcoupling, $h_\pi$, via!0process $n+p\H arrow dM-�BowA�( In summar� hil�oretical�er� � �$G reAzs ��& becausE�5�*s���ulevel,F�" ٢E�-�i 6� clean!bx �, free <any addi�al�D ari�\ a���$ar environy . m fe}�@er} \iB dA@Hphics[width=10 cm]{y>,-fig2.eps} %�43\A�ion{CalH  !�!WBP��in->on -`d�t�D!,�protect{� �}.4M_ �� ``$MUBp''a|�int��i�il��U��m�6�s)��m2;a�9 �� YPV �cmFs'k�Ganapoa erm plus�-�pion &� S open (��0d) symbols re��po� e (neg6)2s��5� .} \�Ak.x� Uqend"(ure} \subs�{R�&ded Observables: Spin, Mass)MPm$sec:othero7 } S= g*41��3 4, such"!�eKo s�m�%�a�" ."�1 well docua�e.w  source�in` E�O s.�, unpolarizeda!ton2g&���i� re a��_�fMYal��l E*� h�rk-� �sea�r8neutrino-induce��$muon produN��Gon01�}N 2sB#e� $an $s$ or C o in a��o�+l a charm #� $\mu^-$I$ the !E^que� decays�duc��a 7+$ agga�ev� by siRaneous�W�1-u+$ -$ pair`vid3 �� signa��a �9*��ba�a)=S ulj ��>la%B--;s high%� ($x!^ $\xi$)V��cross m�Obe di7ly � P �R  J $s �0. Similar arges� ly%D$\overline\nu$-$N$�,9%) {s}$6i)���aw�� two 6�|"��assum �b g sameE[8global data fit�%!�E�I ɍed2F �Happroximately 20\% mf.LseaM�6�or 2\%HA totalA2 ton 1omaLai97aa686� yi�( ami=1{BR� beo investiga����$discrepanc!P~�0value of $\siys_W$�jorJb� NuTe� llabo� �Zel02}�E�Ict�7e)�)�to� weak !� FFIT�� W. h sue ;b solv'nd new�V lyse � $s(x)�.;inU�t��underway%� � E1"� $s+ .L$A?*erively st� ح^ An>�eWw�� ea� �ic)Bof:y6��eMx's�com�+%~a� s} !�6�H $� "����Y�Fth"� ai�m�5>y� &�0\sigma \equiv� M_p}\l' p\vert\�m�({5o u}u + d}d�) 8 p \� le\�}� ${ [}=\} hm_]m_R$��A�v de� inedV$is���!Ñ DZ$qI�E�KAp$to $q^2=2m� ^2$E�H Cheng-Dashen pointM\ Che7@i�G$\S!p _{\pi N}$!� abs�a�2�2;se��1�)shoul� !\ l. E>Q23�[>� ha� laguT��i���U:U  98\echnique�L �cuC�� gma$iE�tprobla� rean�[is # only.�� y� f�wa.;-�Ols00},**C ��>2< = 71\pm 9$~MeV,�" <�ha%�B64$\pm$80$ previousl` U�"_SŜ, but�er Pat5G)�an updat��Pav99}A��I1,&�Zof 90�. Ear�%�s&the�A"&)l��-� = 45!8%-S Gas9a�a m/O�f)�(lattice QCD-�s!� a\sim 65.^ Wri0^far F�� i..�,v� ��we?�cate no6�2� to! A�t� � ���Xs  tima�&h2�2n��{hB 5i �$ demon�t! diffWt�esfa define:d�cis�:y s�� d! onsider�+ ofeS�"accumul��� "l deep-in�leptonN�(DIS)6f a� -��%�of hstruc | (��a�+ aXew seqFil01})I ��one� de A�6���` �!)�o=�>o� � o&� I2� � lly &TJ�z��\Delta�A0 + L_q + J_g �V[���S 6��� �, orbital(��&,��glu�X an>"x� q e coll UO;s�9�I2>�u���t��a� !�f,� :1 ,!�!6� come&X�rinsic%4%�o�t1%0 $L_$ $J_g�i"� rK re��� � J�F��6hU!lle��5�2� �gT le8 mCEE!k!/���un% reg�A$�@be � I8ol�� �4at SU(3) flavo� goodm�"( %P)b�#$.�$ m!2tbro�d�$into AJ�$u(!d$Q� ms,6daLeA S d + s$, i�Y�s"2 S%cz ed�Z�#Mha" hypGO��cay�am��s, yiel�hE`ul]at� s ��-0.1$. A:��doeX QqEd�p!�A9%� -�"p$-l�E� semi-�ka"0Jin �-"� DIS� *k%-S s = 0.03   "$ (stat.)} 1$ (sys.)}$,� taP": �w��ly � re6HERMES �i>Air04�� .F�= .wE@ul ". U"_d�qe!p5t&ivincipl9 m�_ via �#�2�FYo,-� og^��.ty��_ �].AZL'�w X$��M�R�as�U&���jh ���i9*8,#EA�a�C6 es#inmn ��"cE�ymkupe a ph�R excha�b&, �:B �. PrecisR n olute6� E1�$Kp.K�k $ordinarily� llendu� �2"!�*� inM�%6 !G',  flux9�beams.i� A exis@��w Ahr87} >� "\ Gar9��Q�` ca*��ad �E�* "*m e,b��c$T�A+1.25~Ge( ,�� @!$Q^2$�j�axial�4%�]�� aZK�a@sZ'g�%Don ]4LZ A;_ AZJ7fseen. Rd �)P.r t04}B$�5S!�8 to 6� .��2b�(�#��edA%a : glO5��͐aee:xw�*��7 =on �,�%� -P$x� � . �%HG$^0$*� L E3s� �)ZofJ4(see k �G0} )��wb�� will�&�'$6� j�E=�&N$� s(Q^2)$ (�� =  0)$)�? �t0.45 - 0.95~(GeV/c)$^2$. �?\ �{O E"�$s2U aB�HAPPEXJr�Lɯory2Ah�x}�n %� m` > #�2A atl l�&ni00} �%:L( the �2Um oI�a 3.3a� X p���Pa 15~cm hydrogen targ`%ndE�cE_he�Ved�s �� r`u��$troO  (HRS)a'Hall A�012.5$^\circ$.��-y-,)E3=0.48.���&���ijB /$E^s + 0.39�.s$. WaC�un��r�of:� 1~MHz�&2�=# um6�.��F��!�(0~ms window. seq*Pb-scint�#tor absor# c��#�(/i�-��stand�(HRS!ck� �+. package�!�hardwA =�K�T5�was su�ito spa�&�epa%:��&Y-�n. CustomUCic! th 16-bit�. og-to-dig�G ��A��Z�e�+�inonOec#&d�" oped�}�h$al optimizE�)"� schemeI�helic$!.e-!{ flipZ% U530~HzR0.� of aiZ*se�0ndomly�.secon!'ch%a�$co�*�HN-[�+�$m, #P2�*2�L15~Hz. A half wave p�e�insera�or5o&p.�o��per day*=%manual�ers!m �%:5O��� �Աics)~4po )�!{ �� a��y a� Mott 7�o "�* L�jirC} M{\o}ller '<���� �Ag,!��,!>r run�1MComL2K��opea*d�c�.�� norm�%{taa��&%�- A�� � !giew� ���m&� B�G"Y Kum00}' BB%s\Era�mak�3)m� �� GaAs� cathod�9�k1�K� �&��� bX�'s>�6� � [+�4ŇerEJ�E*,�}ex�'of 70\%�A� �n�3e��c�atO lo"�-� bulk)by  an >)]"=). Improve��� er pR��y a�ong �bf match �-�.NQla�+lE2E5- need9; JLab%�  ia7�(lA%r H��!�advanta[ Minc16�#}�. O�����/as�cui6 above�e�$-�uph��� �D z�-)0 for a�aq�)�!� �� .q c<"�-l�!�in.>��a�dAm�(�|ces1p�� 2/alJ ' *l+� kepaU a*+u)AL������rotat���-��� ���&w�QR/ed�0( system nul�* o)��-���1y &�& T�f:Jh�o: |�I�!�%� next"0oE�e5s. New���e crys!6 fabrMA may elim�8n�2mpQa- fue��iEQ���e*P �!�two��runB'�U�)@s $A_{exp}=-15.05&98 56$~ppm,I%&i4o� E^s+"n  = 0.025L20 14$}9��"�+t[� knowledg"� EM!s*3q�p9preclu�%o3� �� spac��$G�Q�9shT � ($�c at � � $6� as�w%�>�.H' I�p)�� gram����a3� A0� 1 *� a�� : Kum99U#3�[ ��.T- P.�3in"� ��&j� aKum nAr�UD`%���� $^4$H�"aa-0�F" y ,�ab�6�#�1�E�it#��Ӊ�U�$���4�V!� �EMu�v"�aFc�$�)�C� "as �!�� ) many�+eQ7e�())/ &0-8MusD93}� � B���*l=� s, o�uw5�." : �SAM�4}<� !��41/IWgen�/Fus $r_s^{&��.E�=0,�.�. traff-ejb�."X.b�� showI� e"of q�(u�tZ?!�[E�E(��e �KA U s~:�.�a\&�s�8�6)�) g%�2Šp��s�8}N\4\-!�re� c�9<�4V9to� tA !�� work; e s,�*rN"�/s d`priAFi�]^, �les*�6.���� q0b. PVA4A�Mainz2J pva4H%2�3�})Ha " =� � achq]aa� Cc��ck��no� `2 f�� azimuthal&�au�caN2iQK isje�fo���le.^I��*kseg��i�A��ial/.i�D6�: ���A/��� �:l�s feas�4, despite ver/ �*��M�P{s�= �ed� �� ��s*zt 3"�E�\ a PbF$_2$ {\v C}erenkove�er caloa{ter�ign�� sist_ 1022RO  6-20��)M ths thick�� , arT�7 �nd�. 3x3a�u!Me�self-tri�:�Hand hist�ׅZ1.ic�!A�ec�gre$ im:}%�tVZ�. �7 nerg�%�1�!^ �7c9"G& ��2Y5 ��g5!� utpul|�x=te� 1QC3 ��.g��@ � over 20~�<nd 9��� �F}q s mustgy�q"s|10�of�� J��c393 &�1�� !ơ��"s}7p%`n�e sona��>�/ achieved F��3D: /$\sIBE}�6Wie03}�  1~GeV� tia�. A typ�- S!�.)*a��0ise8R~ �P- H"� �<.��24}�B[ @!n855(F�  � 23. aA�_ i?�k�i��+0.22 �Ak Ik� {!� �or�rh0A\AAv�1$A ��!*a{ ronsoia>AL cm liquid&G � ��-  lumin=5y�monito�;�a�{e�waaC{2��s plac,�!���%{��  �)7A`��x�08�A� a:�1A=�e� ar���0~ms, �n.ds� 5a� odic!�er"�.< !�*�. P"@>�.�x *�+5�%6hr r�;� �s� milla��dju�!~��!�ay/,/man�/ A|Td,E�2� Beam&8�? M�3MR z �micro�cae5Mg͚�B C1r�-�f�.K XEr�& al5u y afA��di�Mc!���@"Q = -5.445 2T2�Wa!� , ���B+u ,!� $A_0m6.3�43��/!�*r m�- �I�2�;e�5*Jea?]�To"�: O���V �4if� 4 � u�1$\�0 $ hi�E� �&�S"� re��IE�N op%e�. .Zs$ alread�3ke�:ruc H!nLin June 2003, at 570� I4�!F"| 1.. CmX�A ��T!��s)gSAM��Asow#�� exC"cal 6 n!&E�F'�X(v4�� � or��Y����%�Nb�& .mt 140�-15 !8�(�F����=G%(�"I#��^��)C�&0 ��Al]I$M�� *� F���.�� -3>�Real- "( �AIR2�����, A�-L "or( %Y!�����}��(aw%P,� lai��(black�")\��.�q��-�\��q�Z�.} *p=�� nqA� ar� � e availI��`" $��'N�y���Ep$.(nz D-dev},6gdev� ##m�+i�aba�)�B�}"�=. �7 eachT"1vid�2�i� 2�] zeroA��r-B)<2G� toge]#��Ca��_nonY��Ile�seTat�s�in&� �0�inguis"� v�c� lE&$50}� a�v���x>�%6�E>>�:lB�% described� ��llF �Q�P5�pAZA}-g06�BSuWDQ.y%�T,e�} M����D plot��J|&�2oj!B�M>R����E�B�2E9"�$�7A�� 9 �4}I��1 %"Maa" S�Z I$Spa03a��3)�'proL i�Sm�p�*I �romų 3 basx�*)ɝ4Ek2004 �*e L76~1�r .�B~ �&'a�2�G0� .��n.!w+g;!�p\tD@��I)Keay�, a�e��'eT8"�m�f$u�5�*C (m���c��e� a suXLo�A�R toroid��d�$Iz� �R!�.�%s ��$fo plano&uX�2>KM"T-�N��FD Is. PF�74E#a�j� I���con�Efi recois?e�aA�so $by)o covI�! 2@ $0.1 < Q^2 < 1.02�&Y%2Si' Y)n:G0-:�FflP, &H@Q.��HQ���*=MJ |!X%�em���.�Se��� 10s�mrom*'�G%�I*"2$G�E��%��՛)�i 5-25~{<%%��7){e� �k=�V>�3 n�> al 2��-�pul� 3^ i� �vqs�!@seudo-r '�; p�P%nfour ``w() s'',� �tets,� $``$+--+$''``$-++-$.\"I  a newq)���33~ms.~\H,footnote[2]{�("�Q$~ sjEce ra�t:< ``+''""� �@e"� s r�8��e :short-�4b ar drifF%H propB es.}0+Ua& aches �*�E�{}I�s. Bec$PAi,2}.F��>2z � Bb�!}]�or�d deadA[ �)8&��d10-15�)a�i�c�$als.HX:Fa��%H#v, )(�V8N� rouga#se[�Teb%O)��*,4d �E�a��^DRI���*# B�I��y. Fina-}��%tb�=.o�'`5alF � Z��A���>! . As�cu�)=S)&4!H} �,�9-"�,min�/A�y>X(s�[�!�(l� +-+�1�.�{�+f�Qu#� *�gr:1R6+*R"�#SC1B: &� ���V�o!-)s2� �Cch95ca� coloAMr�?ond��.��R�5i,& a� 0.16.�A�0.9.6f2� nxY`f ��S!U fr_tof_lh�S5VT" of���Q.�BE � ecY�D AZ�i?sh-TDC-�*���+ft�N��' <�Bd�� ʼn�U 2\ ͘a��Q3r;�acbroadaW"$�y �&s%�~6��n��sI��!�6���re03;o� ��A�s�2:��9�bVbm�L��t�0� mid-March� . Du�f�Xi!� metr"���Zɥ�"St��)�A2empty��}solid r|. .M�n�E+XvIo/or3%it;Z"�ni�� lB��i� ��;���$� � %N)iex`E}"�Y� 'Snd �-!U&���K� inB�+!�7+!*�"L*yHv�� ree *.N6�� >jq�q8��Cc-Bdi�I�e"T )acE�4EV�aS&Asq72t ��� � /Uń �"l d��" �T5��+aWat 108. M�8)�7��;IHgI�!� �,aw8XiumM��pr�S%��.* C aNR&�Y� 2,� )r%�&� &�#(@ B&[n ��2/.>qB25, 0.5�0.2�9)�5iY �-ig&�3 �3,�JiaC w sp��A�entire-�. �>��.� 5�!|d�Q|0CT�/ic� �%^]%�Guxili fI$o}=.�MiT)T cryo{CIq5�#trackl" leav!��� G)F�X�� harg�A�%K>� � f iC� +�_ stepA\���.�-,%�tp0�D�Pe�5�e} )�.��]Eȡhat.,a�`  eci��aA|�Cae�<l:b$vetu�is�`IaC1he!�9��]� add�m�2 c5+Q �(,j4if6,_M"6��a�ݮ #cqD trix�i�JIt��u-P ��ba�,� Rc�"A�&�� exci�!=!o?�T�'(ll� &� �ysis ͨsWel�OEo�!A� 7pportunL;to%k"- $N$-{ax(cZ/j5�F_ 1^"al�$�. �=� thebibli�*phy}{99�]�{"K.D[%�I� .tex�Pibitem{Ito03} T.~Ito .xd\, Phys.~Rev.~Lett.~{\bf g102003 (�)� PR0 D.T.~Spayde,RVQ B 58}, 79JO8KuS01} K.S.~KumqX�nd P.A.~Souder, Prog.~Part.~Nucl.~P��45}, S33 �02�BeH\$D.H.~Beck [(B.R.~Holste!(Int.~J.~Mod2XE1�Q1�1:VMFV@R.D.~McKeown, Ann-W ��Sci-b51},18)6] Mus94} M.�0usolf, T.W. D�elD,J.~Dubach, S'Pollock ~Kowalski�� EBeise)�a�R�Hs)=23T41 (1996�PDGA6E/Re�;af� icle!��4}, K.~HagiwaraR E`%�(D66}, 01000)Z22ZLieA�A.~Li�| feldRR2\46A]20�92QBer02} V!�Prnard, L.~ElouadrhiriE@U.-G.~Meissner, J2 G 2`RN�Bud!&A_0udd, A.~Bodek%!�Ar�CtjLarXiv:hep-ex/0308005.XKaM88aXB.~Ka2 �,A.~Manohar, MMY�B3E�527�886�McK89} R]� <.?219},�$B>?cAu@IFM�)�EA 3248?%�M.s +y��Dmi95%�0Dmitrasinovic�6� �Y;C5�k106I�52�Mil98} !�i?F�C57�92�96*LewAxR�w, nd N�b >�D5!207300 M%5 % EW�0 cor %\�/ Mar90} %W�f7ian�HAL.~RoEt.e=�6�� 2963�6��*0}.*%F:� �S B 24!J4-I6UZhu�E S.-L.~Zhu�Uauglia,>]!(��Ramsey-�� u9�D 6s033008�R6v0DDH80} B.~DesA�qu,J.F.~Donoghu6� �g m (NY)I�126!449!48i%� 6S:i:]�$HaM84} SeeAe�m , ``Quark( LcT�cby F.XAzeq���3(n, John WilWLnd So�$Inc., 1984.�@Akh68}A.I.~AkhiezksM.Pai kalo, Sov��-Diklady ��!57E�66�Dom69}N!Ambey,��A�6�4�V236!,6E�U�Akh74} ��A"�≡��27��76[Arn81��*��V:�;��401030.�Gui�� M.~Guich�1nd M.~Va�_haegh�,�=w�Y 1423� 6�Blu `G.~Bl� n, W��,lnitchouk, Jw TjA�>d% c41B�D%�b}��%O25O>!r03a}&IK*�KN�$E01--001�9��� R.~Segal,.#tacts.�Pe!��`109e�PerdrisaL:oS.R JPACk4%�mposals ( +$s): PR--04�08 (X.~Jiang),9 (�Dck), E . 19 (�uleiman.1� 6�)y S�<Wel� G0--�)4), )v(Kcommun�A.�Ga2  Ha�o," 'l�RurFAE12XM!|yJ,.,} p.~567 (avy3 � %f0Ŝf�Yi� BLAST�' larcA�6�!:�� @3) (\url{http://b�0.lns.mit.edu}2�X�� W.~X���00n0>M3}�MeLC6� R01u6�Kub�{Gbon:�i�e�NB 5��26�%[��Bruv (E.E.W.~Brui�6N Q�jV �7�Ns Anks H.~Anklin>� PKB 4I , 96�Bro� Jev6�O2�9aB17��Brookf!F�Vm�dS"TqA� I.~Si- ��%AC6�041� 20:�Abb�] D.~Abbott>� Euro�~Je*VA !�4!B20:,Ma= R� d�����22�64Wa��A4WaSy>��=��0�9i�6�Ost M.~O�!<��8�27Z " Y��gBermuthV��B 5%�194� % S-q� a#el.� Jaf� Rc Jaff� "� B 22��275� :� Hoh76%KH\"ohl�� )E%�CA750C762 For97}a#Forkeey�]u 551~972?Mer96} P�rgez:�E� D.~Drechs�qB�A59b3��1996�Hamb H.-W�mm�d �2�3��32� 6eMHD!( ! 6r�2� b9'D5��74��:'uH��`2� X:kZ�8�2533 :�!$9a!�9%ZFq2a E C6Z 0452I!: \b�\ \4A� \%%A 5U loop. Han00a} L!��{4ius, D.O.~Risk�#8L.~Ya.~Glozman,JT 6�35NuKoe92�Koepf, E� Henl��!�2�-�=�aUB 1)�:�ur�(%}INS4M.~Burkardt, Z��-�1}, 4!1>�Ge�lacGei�{�N.~IsguREE���1m�2oChi�PT��HemA�T� Heab t, U2puS.~Ste)��I�.43�J18)�6=ItoucFH�J� �306��>WeTB MueV��7!�382 �6UAni�LK5iolV�e��8b 09 ��&_!`6aC ubis)\:o)\fI! q�5�1mJկHam� 6�I�E�2y y&GJ� 56�2 k��% L�g*V DonABqDong, KLiu eA� W�=amsF�D| 0745�(6<Lew��Y Wilcox _Ra�WoloshynN_��013.�5=Lei8 Leinwe�aeA� ThomaR�%��f %�-=��b6�_��F�C ^���^�yuy V�HLyubovitskij, P.~Wa!�Th� tschn0nd�Faess'-�2a� 0552 q6�Kimak H.-C.~Kim�~W,P�K.~GoekeJ A 61\60iao��Silva�q \%Q> Ds01401J 1)t#�vK� �$ph/0210189.VWe� H.~W�ll�Abada,�Alkofe�[H�in�Xt1O�B�z ��6 Si�qDz���<2), erratum-ibid D )�399� a�U@Par91} NA�P��A!� y2�2�15F 96�O2jOF�  5�4�19�A2�A�FF��yO 7W�r2%"��G� EK.I� G.I.~Poul����n� �.�26͇6M��Di=�E0&� ��$U.~van Kol� Fe6A2044007"6eLZ�} C9�Z G.~Prezea�fN�Je�03�I��U�3�.�J:�M�!=b`2ũB`C� W.-Y�Hw��B G��i��2C .Y.)�1 47aa:gBo�14Los Alamos npd�*�U BowA  spokesp�_ . %F % 7{�?6in���F,Fifteenth In.Confe�8e� Appl7�LAcceler�d�F Rese 0As0Industry, AIPI+l,oc. CP475, 2Mq6}Lev94}L $Levchuk� Instth� A3A 4!Eu5�Pit96}J. .A]': 12trHigh E�R Spin��ic<orld Sc~I$ific, 813 A6�Bar00}D�'!�uff:�IF�45R 187 �6dFar76}Z�!!�a>OIk Develo�] in M"�M�M-PPc,MP$s at SLAC,�mprint -PUB-18�:�Z8D 4236PGEANT}, � � �^Library.z Bae7�a�K� Crow� P.~Truol,| 9ccxXnE4�?�ic�@vol.~9a�7:� er98!.CA�rgom:�H�v��C �'32�!19:�R b} J2S2�%{C�257p BF a97}�":�%S�Beane6�R1a�38ţ:�MoT69�W0 EwY�,Tse %�MJ�%$�%&�:�q848D 72� Kuc8�-V.~Kuch@�((M.~Shumeiko�D)w%, B 2141� 86�Ols59#� M�L!~Maxim� K�P11t88;5��Ս;.1�**;.NAMaryland�$12A,&�/�O� www.phyA� .umd� /enp/��es/��02�6�.�*�' 11G�wkD��0 �6g�'0��(:d�!czbf 29��211�\52Car�.$ #"�, VE�row��BGibF� 6^��� 65Wir�5RvWi�,aG*Stl AS6�Jf�. 3,:CHax� ax-�.i�2[=��94�t 50Pol+-"/>�D +30w6sBal!�"� )��>l.}, � T � E�B� ]Y21��B�$�" >�C �064*/��No?fz5nuJD_�9�8{:;�@��d�xk9f�? :�A/n3�4���7�U .KAfaA�,A.~Afanasev,d"Akushevi�0A3N�MC k�_&08260.PVDH$F�'p EAwoZ�%Bau� Bauna �ed!��PAVI04Pashop "#N*�ki"�U.�9,!�ear! MIR.�Pas04} �,Pasquinf0F�6240530�)%%%�O]BN0'3~Af:a$��}��2E}�T�jE��J�w6uoK}m���3>�3�4ZR�!;2O*�4�Ar<+ `(Arm��RT2� wg JLAB*� E99--115��D.~Lhu�T �%2ArYg ')e&�;E00P4�e:%i��&�%2Stf�996w �e=�B 3�2P-:�_P0} `U.�``PVA4�JD.~von~H�:a��ma2�_J�de Wiel�M rle%�RH A46�(�CzechX&�+�tbA��,A��9]al�r$m]Y<d�7`=�B��ce�/~Ma�R.�!"4}F06_ ^�-%�h<X6� 1019 G0���C0N:1A:5�1�]M{OMLP %*9:�T��w2b %:]Ben99} S Benn���C3Wie�.�)��N248� 6 Ant03qL�� thonBG.�9�312035.�* 1}B�02-0202c0ini�Z�, "���M= *"�2��204007.�Dav��S vid� :J. .=]�0273�6� Erl!J.~Er~A�tryl�J!we�6!.~e+D�/160� 6� Hau01}M�u�#� .N�O$38@ �.?!��5 tche�'61<�64A�5zRa�M&5��%.560\:� o� J *16�A�e��o \�,�6Zh�cE_B:@LOI-03-106, X.Zhe�\m� FeCDR!�(Pre-Concept�XDmT�9e��D* and E�0al Equi�+12 |d Upgr��of CEBAF � (*+ Hjlab.org/div\_dept/> \_divi�U/pCDR\_ c 12-1/)=�Kur�.�J��S. Su_ !C� CHEM !J.B�m: INT  A$� i} E er{\vec r R R p p P P q q 4ss{\mbox{\bold�~ $e�new�anda�}g.�} 2#e#�����>!beaE�BE$ FV" nn}{"ɭX} \topmargin-2.8cm \odd�� 1T> textNc 18.5%hcj@25.0cm \parskip=���5 =0pt�&H Rare my� y}�Q�ysi s2w{6ʙ��ZD�R�'Dtitle{\vspace{1cm}� SAM�e&x��'��""Ga�{vB\ wB $^1$�"L.\ Pitt؄ ?D\ @D$^3$\\ -BersiEof & College�Bl�,@Urbana-Champaign, , IL 618�USA } \�!%A5[abstrac![Onwj/kez+Kto �:r��eF"s>S#/;!f�dolN�N�36���� nd s���C suTMs�A,H�gnetis+sp�Wq]lҦdecade,�Iity-vio>Nng" Y�J�has em�3#a3im:G�� tool;bArea, *ȥ�aP�to isg �:riΣA!]�r>�Z:L!L-;'�E�YJism��Q�&+ �H$MIT-Bates &†XJ�Ufocus�`$"�� {s}s�vn��6Q��%rc m�,�� �!��!Id%"pr�!hr�P�1Ne=o%�is pa�Y$we give anPL�E\�2jlO`� ��N, briefl�~\�K.zk&�s� 2�Is�mma؇F1�.�N�<ko#m�i �}�L!G1%of�EeA�.v�ݓ�\K.�fac?�l%�as R�9�v'L �\�N� %I�k� var�� tex"� s/��-s&B�P"cEl�Q �"� P"_y5$tro;� *�*2�d" } P��Ry�D�qu\Pa`�e&�M U\v�P�L&N qua6��!H��a� ��RuOlyq�%j&�_ -�kN\s�T� sEdriven :R1�����c����y��cerror�{ �Rh�j @E!�cdž�b�#B�S,`"~s^�u�/��a2� �� mhd -1~ppm. S�N��al # ���$P� �Re&�t ies K 4 \ti]�(10^{38}\ \hW cm}^{-2} s 1}$�m �on}P ($<$ �@ hours)KV�^ s. C)�-vqlI ��z�Sht��vc^�yi R 15-4���Y�O�j�$[��� 40 -���$AA�40-"u ^H[~� dernN!sL_s� ac�wA�:}I� y�conven�& way�q#��� impac�J� p�i(�o)]X' .�I4��nL�m+\U�at, $P^2I l , $P$7a���a_��� a4$I*!m . For a9n2 i�jdesirEEtm}ximiz���Wgu� to1a�m9]um B�.�t9G��)y!~�U* ca6S� %As=Uer�si\loPV ways����e m�z ]� �o*‹�[��!AenϽ�T)ri���5�m��Y#�S EaJe� cτ� te�s-{>X� �Uu�^`r��S�Z��`.��"`\.�w-tE��U)� �ss7��r5�I� _��.xYan`Tal:O 2S,-m ]tyQ�!~����un "�e�, ed; 8�}ity� nyN�- �P� "0`R gl�&���0���I �7 i/Yc]ba :�`:_"� �q eq:A-} A_{ @= \sum_{i=1}^{N} &~� Y} ur Y} P_{i}} {� .�|� $Yu�%V��;H2U-!) �x}!?i� = p+5551d�s U � = ^{+} - -}�1�U�o���hos-���Y>cbA�!��r� �^b�\Av�w�Pic9(�ˁ�ize $9u /  ).�G &pve fe��hs"8j�t 6U2n 2,$)�P s�rNh.a~I�9!b �w.KcbP8�&�[! �'d�c_� 6(���.� y ($Y�F*}$=;t++c �-�w �+*R:�y{*} = A_{#A2u3��Te�O�� oced�4��!oy���� gene �*�#��ɍ����"=66�u4��!�h d�$��.9�R�I�.XQ� ^d[ averag����oȧu�ird't �yU3 ^alFdy �v�6�}F� a8�(ly Gaussian�"�eY�i6��p.2�$�  �!'�� gm�� Delt�7-�eZ "���s-�^rW�f�!k"at parD�����be f~{enough s~ly'=��A� ya�=?�\.�Az21�"; y.�j p:ic��cD��a�`:)��necess 9�� � fard9p E�Y�c�raە �ctu%��n��.}yA1��Qn��quew�A�a%)�b"aWc� .�"�t �I�� - ��rmi&+ceU�isZV/\sqrt{N��wj $NՊe��l�y&1��ń,�� our��c���45�� :�\)�Ҟ-��9)Pat &+� e -!90�s �Z �� YW.0&KJSourc�ilabelßA�lec} f Bde�z�i"�d6.�u 5&6I�,a�rd�} !of"��fe9���..��omm!toba�MN΅� � W d?`photoemi&s�x-��apٵ�i gallium a�$ide (GaAs) Acaa�qx ? =��.��[a�"ea�,K � EE�Ŭ:!ACh��de: �ceb>A�� xidi�X(O$C�$or NF$_3$)�\��t'od9�af�Oy surfac�f) )!�x�AA�s V��bYb� �osyon���� scap�be -ŝr�s,�gj l �!}2|�TJm: ��!�7 -..}�b �r� T-h,� aem?X�  ebe �.�m�um!�50\"U)�w� 10cir�U�IM� dt��� )� layerP �-Bs brea�aGjpde)Lc�h;l��!;�ws6��g:���P �a�= l�rs�>� [6I!23�\%K"M%e51�� 70-8��� 5�.-��dBul��%�� � um e�: 8(QE) $>\sim$1\%cileh-|M �l02v& lo��QE. Las@of "� ypes�ZA��ZS-!IYlightG x^� e��ir*�j8z�AѠ�͋���2���1�*� ��h .�to��s�����e"�.hbplb2 _pol h}��LiʟAc".>� a �zd mA;nN 9�35�G���u�� @s�600 Hz� i�h duty�6jiYa�o-e�s �� o�(o!T�8�e��thh�at2� o\�� ` i�CW�a9 s likA?�.C�*� or$ �� NP�is"�x adop��.p 'b�� 1 arg��on > pump $a Ti:SapphZ qrma��ne�ef�ҍ~23mY Qd chopd��N�)�E a ph���eY�-me�u�� NS�Y/"�)����%� 3.5~W ctA%0"�n!�AeF�a-J� L�)���j�m$37\%��uB A�)b�� �� %.�"ۢ Z&Z��cP1xVqtoo lowa�aWe��ed 40^�M�)zM� . UY ��� �� �y�sI#��aF;p.-�o�  p�� xE 4-6~mAV�#o���2� bef�Q`$�) �� in�o�)�5 � 9��-� �-�edMP400 Cq� 6wRar��oN�^co"����l6��+{�}e�'�eg�,"� 3cm]{pol- �.6�vJU" N�p.� X"�figB��"�z��*� �s)���match�f�q� �=m��hṷPockel��ll (SPC)m��2��%�6+bh��|ed��^%�^-�-; " �Z���iJk��&a}}K� q�M ed 2F�)2� ��&u-! -��%G)r~E��6(HPC) �.-VaB f{kw��6L �t5�rter-�vol��. Rapi��*Z"<ari�� ѳ�!*�Q&z� s��&��s��"h���> % &)m�-ۥ� ���"ly ,���b pol_P M/��bur�| rpqto ``a slotfg�E��ir���60~ڬ� �� cyc��Si�a}) Yf��is7 ���� 10)�)or�0a8Y10��-!)MA���se.(�, L$��L ``NEW*w�~ l.d�:.e�{ [*A��3��feBpCOMP'' 1� . A�F Y4&* � �p��t``e�-�)''qs �NEWUw� Y1l�m�,�W[A)�i���ѫhe � �d��ntFnoGIF}MNZv!�i� {e5�*� 6 "3U��ert� hal.��,� ��dow�eaQ%\HPC, ��� m{���&F�>y�5"�NHPCC���E�ron��&*e�x.��2+)ppr&Ҕ�y�X?�!���"j�F� check!_as/ i�?t��'s����<�� �Kz r�zed"x `wal�> new-aX:<�i�q<)č�f2�+y˥2�>*��m�.2�2�n�A[�� a#uff��A=Ue�SJ0� !!�&3st%I7Še�P a:  % o� � eN��Em>saeIco 6M�� A�or (IPC) Q .��� ��7c�int eKM9ݫ M*}� i�1 X�I�dLPif7���app_�q=J�!�$5�%0F��� ����� su~�C��/�<iUr, e�� &� �:!�is ��6JSw�+-��1��� a widt@�7��� c�&f��&� 8���-�35$��%��s$"� $$��T�� 3-8��60i�� flip&��B� ʈ�5\%. A����let6 cripb 1-N�1A� fo2iZ*MBv4Q�,�&�"�,��m؀E`�O Tran)�.p�um�!?po�9Z��)#5 �&��dU�ѣ�� to�{n�&�+%a2~'!/!$� l���]��2]^m&#�vmanip� b��a,"n&�'sm3M��zya~�}�aZ�� upst.�+�#a�۱ ugr e =J!���� chic�L�pa�A��p��m���20� � M{Nf�24%�tly ��13-p��lb�.R�ch Y��ZR � faפ, .� dail�/�-V����J:�)�-mo$\� �"ce%l�" 26 m^����Q��&�@ a S��menduX0il (49\% Fe,  Co,e�Va)1 �  �[��nNP�V �� � �6�1���ruMV� wo�$6��@ogonal Helmholtz m�A�r� aK ^I�ig� i?"e�^ �u� perpendiXPi-1�} � b9�-@Li��xim��t $�=ta_{CMx( 90^{���!�#;llf�|��aptVH��,*i 6w�6^!@di�� at gYt� -to- ��i-$d>T)w�x�gU of 200 Mem��*�MX�9��""Lucite ��er���8G!EaYa>��-4d&�(ś 25-35$� du�on)�a��Ab�;� " Z�0�iu-ID�:� S>��i�].<Ո� *q�n� �8per�aJvVd satisv ���0 sݽM>Y��iL�*scaׇD} �Fa lT�&=�to|+�6^8��m1ed|��/ ��=:&E9ar�XA'(o)Lv&  T���IN�U E+M��5:1. Y��Y&F'I� � &��!1�2G^�mol_run��.�+�2~3 "� eG20�ut2�%%� �2\%-�^D�]%��ll;�s ��t�� �f1� 4.2� &�2��.��+3; *��N�*� � &�(�o9Z� ecZ��Z du��M[���bb Y]A�R� 2.8B�� nte �Io s��)�m|"��. %�R�aA:VA�u8�Umy�.w)5A�s A%1yJ�� Q9�![V��)�ted6�Q�j�% m�#�.m *K ��l�V�2�5!�o#���a�ret$�= �<D�I�f&�<'�� �t�r�.ru��Y#�@MF wardiI a�Uto� ���� ry t�'� �&h���W�"- � m�t�"1�>i� �� v^+i�im Empiȗ%p� a tr�[�!:6M���)eA GBw�B�!� 5$af;fe>��V��, �rB]��� ��.- ��anNM �5b� a� <middle*i�<"� i� &�x ?_,D�+�E� n2� N")q8 a��B���g%%S6��!�{�ass�a�"m���*Ee��quick� ef�;� X!~ � A$ �Mm}�s��+� �hwhB�+b�F ����Jgqd����>@�1��as�!1��)G:BeO�i�`6�-�1�. Brems�$hlung"�&��! v�G!�6� 2�K.&n]J́);�,2��&E�oD�I�n w�ѥ�"̥�t��m)x l.�!E"V���IN��v�Zb2 ]"R' �I 1J62!5'M�r"��t *n�m�))���c A?&w 2�@' flux � [l >� +7&&n�i�&h�o c��G�rectl�aead, �R��/� �]9# �E�^� %��` � �QTH�Z�"��[+ery w/�� N-��0.�ru: It>l�li�a�I7.�6�� $< 1\%�7�v�'N �9 �   2� �K;)��-ca-+Y�Z�R+E�! b���ectp��;ul�%re�[_IasQ��!!�polB� |r_ wD�V*8��-�I2&�jY �l $ =90,�=8� g1:��~ �24�.R��_�2�(A<rbitr���s)!�sަay)��eM&�#60�. aBFUU/�le.���2Rn1rvo}�2�)! "cA�*�=�%G�2S�� �5&�H� ex����!-�_erv�1left-�kB �#iI�e�%<&�5 i���! geomU��Vl � 9"��k �� ��car�E� �$%dV$��"�2tD.Op[C*;& P)E2@�:� E��52@vEd"v�� �(��.�"m���iN��!!�� 36�� ben/�k�m��2� 1 )�. aQ!��R�� ron)|o&s�,O ^�J(``$g-2$[�anomal��picn,%!16.7$��20� a�A�ensT !�b�>e-�a36���60~keV!� ���S a Wi��ilW(aA;���4crossed electr�Fic and magnetic fields). However, there also are many focusing solenoid A,s located in9D low energy end ofpaccelerator which would cause"spA8o precess about, beam axis, �Dthey had to be set insurJa5 netK(ion put the f back intoL b�planeJ�(. A proced_,was develope�Tindependently calibrat�e effectU(Wien filter� .1Ts o)E% s� �y c%/be us z0reproducibly %$he desired @4direction. The�@~\cite{Pit96} madU -�pSAMPLE M{\o}ller polarimeter,1�Las % %\begin{figure}centerhincludegraphics[width=8cm]{�tran.eps+cap�{SchemaA�diagram1@dimportant elements that %a)gQ Rs(A! � expe�Xnt at MIT-Bates. %(I'll!$bably work)�is � a bit.)�end�label�:}|$ :}!%TJUB6|,provided for.K %=u. %�R� i!�equipA�lwith a rotatable target ladd!�allowa�!  iFp%�zed Dcompon%eboth perA�icular a�parallel1ie�Ur� y\4. In terms of��relev!�angles�|X asymmetry between lefte6 right-han!6 electronso9$ap�tus cana7,written as: M�$eqnarray} -�eq=� A \;\:&=&�{(P^B P^T / 9)}[{ 1 / (1 + B/S)}] \times \\ &2X[(7\cos\theta_T \sin  g - T+g) W\l%!phi\r -6_ kg+?T g )'0W] \nonumber E�9Here $P>m 0.080$!~B\s 35$ �YJ"A MMaa�s, resp��vely, '$S/B$ ia�e signaAI ��ground r>q�detec�dscatte��1� y��. ��%s��r�O� $-(W$Em out-of-�J.phi * @Q�� 5�9 iP foil a"!!}|T$�� $g-2$��~ 6�Dg$ (16.7$^{\circ}$�2ourb line��8200 MeV). At a !v ificm� �($ \tanQ�T = 72 g$),�,firste� involv�:$%aqequ!�n~\ref2<!�elimin)�second.Ne��ly%(%�6�!�so��;m��jd-_A[���d!�settings-�2��v . Result'such a bE:re show��Fi�� �fi��_r D} �6�LI�n��!�isely� Q"W = 90^1��y 5Vm:2Uj��Dt�is!WnqaA-{(~A-25.6�Up# g$) � maximiz �amplitud"M YF ��6 c"x1�ap�1� curr�-�� rmined�Zul!� in a3=pas»?s obtan from t2�B� "�  �s�Ra-�A,of $\delta � = \pm 5^1� �@"��W &1&,�F��ove� {���� long!�i�j�in $2N��heJ4 � l� aHalign�   suffici!� to e� �  an� ntribuE��a0parity-conser�V��-��8 analyzing powe� negligi�$ N�. ��{ ��� Z� 7.� q�� "� �he top& ]#A�ve�.�iM| ai�*�"�as a fun� !_l.E��� a�A�. �l%& �qa�pul"x .�ͪV{ ����M�e�� n devi� gy�k!(a�s`ir no�&l�s."� R[�5�� �} \subkLon{Beam Property Mea E�a]CA�oln sec:�4-meas} As out�Y�S U��,}, .urWc W�~N� �ies)�criticala%�i  viol)<&� s-�AE , w� cribe howE,>iqfS� Q w� �d%w` feedz  systems (imph )order�M �R{�"��2. >1b{ -layout}��i52� ��for  �5��f >)oferest"4 $�, posi��A2Š �)\�P� :0intensity. F>Wto reduc60~Hz ��Ah noise�N �~helic�5rreI,s �-2��)>=̂)%Z*10�+.��'>�%) =90,� 8se_)�_bw $�; slit&� f�dipolGq{ at %)�  y.6� �v�o��is9�!{:� a4��Bar00},!�i��.�Ag eachm& K$phases (``�lots'') "M��� cycle durAZ60�� runE-���n tl�G C�g �tA�applied�for�T.��nsam!�r/ ��!�$us greatly)E��.�e�5�adjust�: �I byAghO detu�oR[ klys� away�� its Qum�&us�a fast)q-shifElq �o �ensy!���d y�..�� � �b�eA? ��ZYeA4q.|!��2d b�? AA���nd .�6auvery >iv suppres% slow� sim$W s or�er)�ʉ� drif�4thermal origin� rR2:XFraE�al�chang!�*� e?* !>)U}.}V'')�� 0(upper) panel�D? behavio%fS%��p-!С� � �\) d(en)M� �AC �voltag_ suJpos�zaT�l:�2,v�he ��}eN ��e�*tm  �8�Za pai%������ st3 K' o�aUypTstandard�? sase dis"�-6$�D20-60) mh� �2"� �� c�M e random2&1�E�Y�r!�,sal frequenc��a�i' nsicA�ol0� -�s�small��ae` is. UndeP��l���e5J"i i*62�)�l�b" a�v � le} % fals���ie"�&yi�s/&�� he��Ŕ19opI� m lase� path,a�>� ex�ve studyi2.9��lu�w7 photodiodU!g�� to� quadran�TE%7 �Cg�]al clas of��:m� &� Q�- �,Pockels cell%�a"  s du� spa .h grad�U� �l� 5u��23c� ed� A�.�)�>��� !��*� xEUangv stee� ��5�� s&� ]�k  ".�%�iB ed. �oa�, m�:%BV  qual�'acrosQ �spoA� When� ߡv�6 M�l� � surfa�4(like mirrors)� iPd�%�ly"t-�[! smisq� appe�[a:TA�!��-�BRi�min�� makA�@HPCl} �q�q�H ,�  befo�$8e vacuum window!+ �on gun ���q$J�careful*y�., b0%�Bidual6Rstill��e���a dedi�% ֡^1y�Y�9w�$E�n�%ary. �-):ba Ave99}:im&w� pl� of 1�g�i!�a mount��piezo)`ic (PZT)yzpads,Jc*3Z[. F.�l tilta� le, �$,1� ��A� !5A=E}p| = A�F&E��H.�=`"L- \frac{n_a}{n_g}) t�� $n_{a(g)}R!  x[re>��� (�)��$t6ckn|'I_ 'M�6]!N"�  driv[#����al �� (�),' iA poss� to u (��!LEocX!r�F����p��ice I ' f6�ere t? &� dK!� erio�(e�Fhours6v a preci���$�( 25~n�tPZTmO ���beAI nulR&1 .R-Y(h . Some �Z����uvo� off2�B� pos_5&� f տ.�jno 4_�*` 50-200~nm(+(}�%�s�,2aA�JS@"S��>�:��n"O in�A.� a}qRD5��U��d��� �z� non-invas�%Ymc&�+Z�Q� Each5� sisA�a"n ia��wr��w(wi�=o� c�N >in%��,lux} !R �w throu�he�. HN8N%=�� a"M*�e&4*� wo way�j� �"�# u!5�� * � �] tube���icQAf,��gA,� �&or_ is n� �N�)�a^y2�!�ll� up!2���)P ��6VL'�% Xy#�jJnonzert-am t&��  �. � � �d m) }"uf/-��je�%�� load� �e*�*d,Jc��� gy�!pO!uE��.�r�%!�J� H� . AB�(c +dg CPC,�����2� )�thus �!��FJ�� "R"��U-$�.�a m),,K ��mN� !7�2� (HPC)s: �.� mper%�{ �"q,l�\)n!�iny  re� iX25��,a��#wo�-�s�;�uh�Vt� V coe�$&� ! t� ) down�:���us6�a�t=x �A6 ��e����suor�� sandwich!0a2� q"a%I�w �s2x|1be � 90"[!Z5�)P� a�+�$"�� Yvmodul ���A�carriw ut/ɉ�9DU�!�ai����j* en� !;�I� ^���G �� 3� ut�.4/�N�e=��\%�6�'  1 ~ppm �CPE trol1w ��a�Bo" �6�� M~*qa5k"X� > B�*int>  With!�T%-�1��$� 9U 30-7��%!.C�"���!tha� $���� � >�:� 1PF��MB�}� � run-x��!(A�N��6� >��� Js����1nM�4G&d D%�e%A� thre�7�data-t�w �SAMPL.v *K-��$J��)��/z P t majo%\�+�E e�800f �/"�T��'tab:hel_�x��W5,value6�-�0tk !�B�)=l9E�A�'0istical uncerE,tyA�UC(-(ng.F&� t�}B�*5Dtabular}{|c|c|} \h�J )-cy & Run--g5� ��\\;$\D�, X$ & $7.6�,2.3j# nm}$0)Y) -1.9*1.4^*�, Z-0 [0.11r6[ 1 b0 b0�:1E� 0.14� 0.02\eV \A_I& -0.0'1�pp �-Jg*1f&,B[ �� -uB� >�q" 1998qKLH$_2$ae��(2� �z%} %Th?M��0Aj1�4of IWHP IN/OUT{� on. HMe��\q*{� Si�E" 25+�'-exp}� main.:t�review� �pro�7eT�5 �7b2 {\sc }R$abo�onN &�" prim)goal ha��$J�{.��s�ge�rksq�nucleon'�!�#ic mo����us�*gn��  �4 � &x ackw��9�� hum� fer9�.�G$G_E^s$%�.:�7�%of kin+&smc"s;proton!0 no'-�:�2� O%Raxi�erm9]��pprox&�2 20\%-]&�r �86.�A�� :f9 e*0y~ e �ia| -~weak #aT" .�sugge��$G_A^e$�P& e�2*N-�'�qui� n e)n�al��A@ beyonAa� $e$-$p$Q+ing!us discus above,A�sie 6 7�-� deuterium%�� se�i� to�at ����( isov�"_ � *�lyA�er FaM^s�2�5a"�:%��4degVfreedom�%��^5m�S R-�.�dF9.g�.V in�e�7;&��Pd.�.� =9i� 1�2si" combA &#a�VAVQ�2�sme up lf�o��!7i�')2�I�F 9�ae��  fay${E�}^{(T=1%� f&�<5 disa!�E�� ~theorsal%c~. A��)� 1F:!:�$2000/2001,e3�*� R &��p�`iUs!8=quite.2�� L>6)V( B. . A �@E�updd"al!��`al, 5� ha�Rw bt #}�9!A'to good 6�Z or�littlej ��m�extA/ed���$Ge3 ~\�?(Ito03,Spa03� I=aKaa'1J~um�C16JMiAs aL6Y% most-"- �I %q+ a�A�f�6I>sA�) �'m��! y`o&of.B. We  ,3a", �a gATalAߡQmY&{� delivr(� � &�3=s W�M.I.T.E@ Fa14r2�0ve ex�0 . %  %p :�am/Yal iss� � �(put@1-�}M \*�4R� al Setup2� a(? V!!!! Ne�|��Eb� par�AphA�E�%r�re �#of� s"�AIb2W�ar�?�k;B�S� -���9���%�� inci�C�a 40~cm E� aluminum q" fill�4liquid hydroge>C�vedds exia~% 1$tE���e� a 3.1~m;:,ck hemispher� _��cha�? 2.5Bof Pb d e�0volum%���q ;/A�Ha {\v C}erenkov med.A�<�q�*��cQDgŏm �ba�K�F5C�Mainz L� ory��Hei89},��&0ten ellipsoid6 ("� f|Fed� �l8o�@>8-inch�/m� qm�pli�6|A0i�nstitu!�`zimuth� �%c�8���oli=7gl)p2� 1.5~sr�v�#=��(� �B138$^�?��160-��%� �m enc%�inAcylD r�y�! f i1( mA��  M ��remot� c�8ashu� ��D4A4��  ed.$A�gh�G�*A��2�Pb �!�NA�����mg�=a E -tqbox-�me��"�$9blacke� ��8{ b8strayIn.�C!"x 6$�e�$lyethylene'el�} �Ed.IB t�?hotF�t"�1=E!� 0-md neuT0� Z. Du<'�i&co9#l+u�M�(&�<10$^8$ s$^{-1}$)�� alI� u�ar25~�+�|��z� �GI�gy � shol"G6� �L�����M�ms 20~MeV�u�KeQ�d �-$�!�!! �l�AFm�2��0 posi)n� ��� �=,.�:u &�Jg Y&�%p)JT.3E�Cre{(l%Doug"�e*tuQ1fEFa�u�U�leU�.!!"al�A�Z#al *7: 5\%,��(cin�&� c�)ed -"air����C�ay Q;aM�� by pla�s� �auxili$1�Ao hind !�q2� co>c� ���NL��/a�!I6 � �@:n!-hO$�Etru"�J;-^5� 'r2���KLn���hoi%���q!�6j5�!=�e�1:AC"�L�chs��-} !W2�@ )Us c� �*B�me��&��!�den8 below�cry� &�F��PBei�L �A�} (o rapidly fX:�  or���ea!�*!  �"�Z"�9 � %Hhe{�+t��d���fluid.V! ���absorb�2F 500 Wat�4":� ��aa�A�au*th *6C� �� ��imeR� �l.�!.�(16~ms)a�e�!wcoo.!  a�'um gafrige�O� m ed 12~K:q:�#aɗer!� !N ex �6O oap%+of�vup!: 700~5!bulo %��0Chromel ribbo3�va�#immers�~t-�)��Z! a&R loop �A�EmO� ��n�1tE&�"5�I(!" kepw�te@! aturq e 0AEOh!}in 0.5~es..�B look �%.�8� PQ& :�ِ��/ K&* � �.h.�om*�1�0a"/2�M�d�b . S2{\. ��5 � !�ngAlu  attach�� / ��Rd  l�=�%*�!��-�#>a"r� x�( 7.5^�G� ��woA�$<�t��a�y"� �%��at�9ou�'R$`��� . �'B�m�%!'�` eo#er.� e�/�GI6�8b�KCE�e�'in1e��yl/M��&�!of�R2� iM�s;r 5:)�M+� 5G�� �ed"V'�2Ra`Oi�>�4�R t �fB�a /or� � � `we�8a�^!(��V#S4yign)'*LA��!!��f�"D&L5� $e"� &Y=GKKZ�:8D3d_�4!^/D:,�SJ�CmQ2�a�. PorArh�-|af&� v(shc �%b cut \=or�4! &LfigFR 5 2bHWraw� :5-mM��Da]X �-to-vI;ifi�pr�;tou �N9 �Y@ I�� �� V |dip0;aqA- a&�r�7 6 (I|A�subSiw#�) s be!z&]9. ?v e}� �1"�0nonli�:i.�16-bi�A alog!.jX6on:er G& E� A read5 �cAata� �ad�I *�@�m � %a:s�0[Facqui=0 d�A� deadF )�2#(G d no� e�Zv����M6A�&�#�- aH�*�&A�+i=��#�T 8 *� conyRb�}� )^� �H!��!gfli�VIcl�'s�9%/�6/ E�sq vw a�M next'"Rn�=���teYM�%� s. A2��in 39{ Y� blank T keepxck�&� �A��bf �L9 �re' O�.a�-E�izm�O#og�A,`a*� fash�.s avoiMWAD�7alk� �1�"�#!�as� sh�)�!S �C-slot''�HR� �,ge�j�2 n�  a!x-'4 �x*�Da�A�e2�!8-: sis}�N{_�[9e-��<w���5M#���B;wo:as� 4's��a�@!�MbF5u6 #n� al,U-unk inmo��%�E@^*i, �9F�2� ��yE�xJaZF�&ari��Q#*�+ � � �h�� r��9"�Z� c or� �U +R?by- aTi�lBRac��,�'��,�s!�1�2+��:�E�%��i�#tx\�!val�R�� A 2�06KA+1O�M6 �k . W���excep_(seAlowd�� d!b5�0:al�2*�(i��&V *E T..^9��ʼneG�V F� s. *XjJ M���p! eve�]ih*| i�� E���]e����"x7�4�T8q�.Y �;blA�2 ;>4s���Wa� �Vi��X ing JZn%3quantif�P A�� �>�.bAcg`=�.!�.���p�b �,,�Y�99� sor!}��yA�h2:s�*cUhalf :Ep��%�}>!�ry few d5��Fi6YGF_�(}:� I"� � 1u1��lea�s� � ��&9),:�t�,>�� (� 5:)]� 0.07�/�SanA0�' :a"y� 0.054 V(]est&'{>ass��K�YlHT!�" 3�1-J�,9BX �$\pm$ �2��WE�1V9H Q� It�m;re-em�H�6��.;A��k�Q�:��� A�i!� ltho"�7or�-�Jed #Ÿ�>?#A )y�� i�t� ��:MeV*run%�b�>�-10�(B+. Whil V "se :}ciYc F6�!�79U �d��)=>�*��7"�5third�run�99c�+�Dr�a� ~�.F �)"J5� ��!�iWsu ?de0in N����u&uT8�2��"�Aq0� ( �2�Ute%[�"n.�K!:.X��is plot��!�J�I( s��10vl-�edDuB� &u���Bw �2�-tex� �Yia�ne�Z � �� �w�1 e{%_ �Ņ$s, IN (tri%�s)E��.(circlet2�no�ˍxtKhotv%>��al �:��-nta�92O�7�K! �&y%f�J6 y, r y2�-f�ed�o�e� �o6�2�r~og�/��02%�0%o @'&!n&%` \\ %q0� & &D$�0Z125�>.){ %uhNetQ�> ���2s�r,�u %Q� ?�� am]�Uc%�B�*Q  %Not�aIm9�`2A diJA+�'}@com6�� %�2�enُQC�[se� tel�%pf�1�!8p9�1� On�Q*� bk e(5�/4=y2� �>�G�t, o�B��*B sour�;of6:!�� �r�Z�� physicBJi��.x-2/ mus(/- �" ��>eɖst>��RatM:�-c<l.� 35-4�� a"�TTe.�*��(�=� ,@}l5+ ��hT\+ ex�Ron*rhu�"� eq:A;3A_{ b.�{R_c}{P_B f_l f_c\left(1-f_{\pi}\(N)H$eft[A_O - $l A_C - 4 A.<]�e�wh2�g$)Re�N)6O $R_c)�7��Z&|QI�a�Myeq=of brems_%(hlung, $f_lTA�!9O �# Fl�"�!]#�:�sW �G>WJ?%!��<h6a62' $-YB��l6>jY$\pi$ w�M?t�I�"� $A_Oeys"Cuo+Be M�//,|9�w-eaZt % $A_Cnwcv#(9� � �bloo�+%�!3�2e"�s, 2! quar�Y �:�dev0�se `` �-cl�T''E�sNH�0 �giu5�US�A�10�$but.d-�O��CLOSED}=��^=X b3qhanE� X.( � a pi5p4 &�#or�J�7r�)��N;leKqm�)6�4)�.$"u��!$s�� � .�&�1y���g]�. N: ��6S!�n *)u� !xF!L�D, xI���"<�!� ne)� hand�6i@�R� "���Te2�.�5Z�$I2. FE3SAMPLE}.S�6_.�c$R�Q�%&�!.���FDž" Ck' to a�c*5=ovvN��m*�8TEb�un!b�h'6�Ti�B.��!� cordW&Onn~ �T)��ie�N�@=  )"�mea�;kO^��.$ � b�]dz�F,f ^ ��f e�H arj��xX� ��ei-1z*@ (� �J� oX� ���x� "^?n�"��m�(�.) Ida`f P�)}:e�wE��B�(A/��r���%��&Q) a��9N�bB�)E9��8sp��-j�o-/�GZ'�thC�Ti�b�j!�"NXv-0.*.� "�)�e�k6?n�.�)��Q}� M�!��2%� darku��~� ���� �. A.�+.O!%� ���B�� a�fa�K^ .�a2ve�A���� /V,]jm�1. U*�5 )q s, �-�1_^)�NW�1�A�6!EI�e�� n sl�2�T istoT b*U= edge�� � do  �"f�O .kF4's:�conE�i�N{!R���sim|G�ndLul ciCq�K��d c$�5\%F�ie� ing}(a)�%�E�Y.O5{0RC � AY"90��-�} �5N#dG >�:�b)YM m�aeSQG!,�IW�,��u.��8{^� i2Lpage}[b]{7.5cm} \a54�� grap;y�!=5��evm>y\\� Y=�j!vA^m�iAC��i�t*gY ��E>��Mq- R�6�,%���A"[ Ac!&O%�o,y (das�)%s)�;!��A3F8/ . A(P�M$ �E$��!���"�^2(diamondqU�J�$&,��� �R-����-a�zE�e]a�IIV Q�m Fh "�4.` �`0z �/{1%!}$f_c$�a"20�dio���Xdu� s!�Ѳ. C�s��1�vJ と"_ ��#�<� I66�ua�an�����v\'W��OfA�Ba��Si!k%�4"�?,�n L:~1�2͵�4.Rx-�ELŊ&�&B9pm�v)�z�ũ2�e7!t�{\%re�AZfG�own ���- �djaAR���a5 al!�lyAon�x�ak�@pa�p!�y ,EJ./.inN?7m+.IS2%6� &n VF�'�)(P0� CA �s. Fur��2s regar�7�a.�2�1�Ke ͙ �in�2Has03=gZstQ!pZ�M N& 6�a���R�,�� �6C#v.#E� 4\%E�a� . �]�!dcu�s) &t 2XG n�].�adu��( *r 2/I�.�ak ?^1�j1/�% a�!�)��o!�.��<s.�N">�N�4!�Car�/tc|m�/e&>cNt�z��#�#"�/] k&Q aMe���E��2w� a�[$$QL9of��C,�Y-��Zk=m!�%�r�9�I*�#p� ��TA*�."�%�zM}$'��N�. P�3n[��rg5�d mu�wh,2��X *�{m�M��Aq.)5�A�!Q!ށ�. B�� 2.2�=ec lifeA����6kv�'� �% �8Z��qI�����<�Z inB�C!�� }�W &@%9�W,�2�%��� �<2�I��]A�a* )�,A@*�!� � �1I��]6J10/?m�eeBF�� `���m�Bae77}E�!�e(�M�r FH7N��!e)�!7wa�� �B�)��nQ�pi^0$��5�3"�&s�!"�I��`7� SaskatoonF�DBer98}s �%.� ��I5Jebd .inc��J�5 A \D�P1]nb},�$N$-$N$�bm��$3 a97}��>j2,1 �Imi!��o�1*c73! 'r"�en.�Og ƃ-�4, i\�dep["au���c�oS�%%q��im>�hFcal�l!L!-MKuc83�h Ols59}�')r�9��m >W!�h�. D`A��bMua�YG �ebB�XN1�a�6^<��2>E-gA�8unia'l$([a���@n��lengt�x�A��. E�zI\i� ]"ggl!�I�&rKen�*c�L�k:Qw 3thi"i JB "7.>e"�6c� �FA`E�G}��2�$ �i�2�F< "Qs.�=F$Œ�x6TN� 6.<"� !zd��pag%�* !�)m �L�l� �!n�;xAs ��bacy�-�f velo.O8outgoF���:\e�p:��'s �:֑�6g �L�6��)u�!% -%�n ] �). S�kF��dAEb�7 �EQpY�6�� �.N� ��raj� Batm�u�AE� k,&�����&Q$�l�U�)�P �'�S2�'�e+A$. 3mG&P H& �T�I͗@ &!)�1 x%6in$1W2�U"|�)t!1�,-�EM "� %�qs. T�W�),sxZ�Cs�w�'9J�-*c�reF "�"d "�� i#oO5A�,*�S= :�/N f�#h n� Lo/� �� :�s"80�{2t!"@Ler�+Z,m^"q^*`,�'&ci]&�()=(&n(��^>�,0.83 &691.136.2\%�,>�, 0.71/89 90 &62 & 35.7.6&�,0.7^0/0 60D 38.9 6 �\�+ux_& SY ��/SAM>�#j ]Pa��hqed�P�a�p:6Pare� -�Qm% ��&�9ght"�(l�PCAR"w���JY�\=Ce" %al �%"�19M�ereasn�* r$R�(&!Me��a�� *� .} *_-1�`� Q�y�av !& 4 3(6M5� &e1&Rad�&���a \\ P� am�E& a=! ��/1_" or & 7 & aI5*Bac�R"^2N;& e� & 0Au12��P��[ /L.7;y M�n B\ � b"�bToA�(�x'�q!�1�a�17� � ���P*���A���eseG@3'Ad !՜.1� ��*�/&2��}v�*}?�uHH�V ��"W��*�:ry"�>͂&B��publiy "6 0�Z N!�>��Zx\< si� ri��}a�d �M:@ Gmo&�� /Z]�7Nec�_�one-bod�Hb<`?.$\��` 4{\mathrm{MS}}$N��$\s2w�uWO��gnKn� Y$��*_MCn �X4U)$�S*,�.TT-BfE �}� �6([ �&�!�1.� 3}, }c.Icom� ETu0Z~sc��.U!n} %A"wZ83 I�k (2�9n 7� A�A�-�})�n�A!�Q�t- -c�.��- &b,�u�����n"� 7 l*4s,q$g2��0.69$�;N�,b.G��2��&2��azp&flaZ/t�B(]<K'Lal�Lݗ&�\ax�;��*��$f(Ĕ )=A_0+A_1d�(2+ _0)$6ax��@6#bet�/P$\chi^2$/d.o.f (8.0/7�%&�?su{��6�(33.3/9�Pis �-&�"�8e@`ntA4A0)�OPEN}�"=.��cD/r&�{� .A � na&� �.i�>� !p�fit�%i eS$$A_0=-0.06I871E8%��B@���to&#"�� dT} A_p(Q^2=0.1) = -5.61 t67 88\, ��$ppm}}\, , ^ I&�'f6�s2\�Sb!���, ��c�J)N��0�!.%s� ]��\m��? B�!L _phi�%g� 2�a�|�-y:G8�.�%�!�!}.MA�#�=" %a(E�[fin c*X*%J� 5�U�H. B6�V�Y!h�F6!r3>��&��y.�!F" e!=m១�. D"�J  I� ��Z "��"e*2Ki9!w��Hp$ 2� Gals���/gF�-V win$�,�m� �D di:�Dd&z[�V�!*� :!��?d�Ra� �Y� v�M^n.�# a 3\%*kBn"3 nd 6p.6:^B3 4!�be 2\%��2!NITY�cisBA5ivf��3' � ��]�a9� u2�pr1[i,�7YLby�. O�%"FG7!/AJs�!O>ei�Sn^2un��T0.23113$, $G_F=1.16637."5}$~GeV]2}$�PDG 6~g0)}��7$)9G. �isR���T56 + 3.37 G_M^s + 1.54:�gf�.fa!�'G millF!�!#}K=� in 5arm��� C i1^"( C wth�"fhU/e�"Li5�$:�!E83Ƀ26$-H�F0%.�0!3 <0 �p 0.07f2o72U�/i�knowl�+Q�N� fwU� M� (j�l�k:�$.��9L5��typ� re l7~:h2� "fi�G"�",�w�p�.&",�A=90]{AQ�_ppnp6�Sm�27:AW0�,��o+ � p �e&� -@,` D� E�t "� �V�C "���[ bT(�ay os� $&�Cw�E�`XJ� -�2� g��&�qT�!'m�5d�1�5��90,bw�V�*tDet.~\#�l%��� \E��A_0 1 2 rel.� @A_{a�?s & (deg;(ppC>&  \\ 61,3,8,1^4x -5.4v 3.31�.5h0.48 &70$�H96H2,-1% -6.143.7J1.6 0.1-4.14<T\\ 4,�13�-4�2.9 ;3 0.24v:37\\ 5,415�6.534.01.8�0*-12.29u 2.23&v%�1�R22(��+.%�mU�ARiI��ppeyrokm�-bO��c�8S{ �C��A�ɠ�:E(,1�AA)�^a��W�� r�9.S} w.+)B�T�4�] "�F�+�6��ك1';CL�-�2&a y��!v"F)���.}(y@!�@*� *w���� comm7/"��,�@�h��IO��<�+6lB�De,rB�"���S ��Q$$E%Mrig�%� �X�c~~nHasU��+ ��+Jo * Ito0"/}."."5sYy0SNA���K a &6��$��2(>mW&t=�j*B�>(!�&���/��a�ticip� � orynew&�of�nAZ�� 2{�� *�0A�Ts�improv� <�a�,�M���Z���:|1~@-�Zhu7�t6�e�5�)�,�den$��5 " "=�� 2� �9*�a���"e'�%0$/\,6���(&�"�}�by 11 �ured }��fs R���#5 exhi�Z f�U+��6�.�s����b��H�l#mng`a �CL:�of�&�A_d� 7.77L 73 2B \, .��C?$��Ua%a. 9\to� c�M�sh�P�?� ar�g�`Hj�d�]?yFL �!4� .�model,A :P#E#s^*�Aup��"h #I�dA^ Schiavill(re �)'� �; quasNxti4kbreakup!L���/V3q+" es:^E5"�y6�?,����"�)}G a�it�to2�*,$ �*�&.ks$�v �e�[Car022�ch03},10e Des��quM1Donoghu��Ho�KDDH80}!�6��b)�"Qa meson�Wh�u coup�`թArgonn�V18} �+"�[�DWir956ana!�5�K.���U 6Hax89rI!�"��O�A�.�9�W�n��!�MV �An&# ���#.6v#mi�Yly 1-�! � a�U I%�j������߅f�R �Cin]=�opp�AW �.4isCa&f*$��* sideI�:�z,(n" ~-r Pol9�� \9W�&�$ a glob��,izo� ��� bBal�N.b��&�$m��Wq*4%i�N�e�3�P(�h"rSc�&dEk.>dd E�ai�| *�$�� �%! Rv&Q!�:A ,y� 22U6� �%�],��RaZ!͒0!�#2*"66:MR�IF�gms_gae}� �i�\nd{� spa�f�  vs.~Fk a!���!�I)iu]  �!t�-t Zhu~{\it tvl3b��woKue$G�N�EWX o 1-� gma$� �la�"�;�w �5�� ��.�ban#9�vf�M**Ns�K��ol�2�thtwo c(!!p&w���  &=&2q3�40 "ܶ4>�8-0�5�50A"�nV�85>�6� z�5 z2�-6.21 <4�2�8� <8�1.8 <0  �36������d"�a���������"�$2��u R2mX} +" "�E&�$]{gms-figc6�Bv?� Sw` ����8e�R8,�)g�h�{ly�fM *:�$! ing~\7 ect{���}��T �@32,(,T�{bMr^2ڹo a�_�[�6�(8)�7!6\��y (er)9�G�J�1���",id �V2�{6�B8 a2r�|sB�=�, .�B8a�:���2g<.�),�<!AB�4�8<0.04~(GeV/c)$^2$- *Y+ �B%9a@mC �Ã}Q�.�,o#�+9cp)�1A+=N�.-� �W"# ���6�&�&,��"�2�h��4�*�D&ߵ� �E�;bier�'��"!�nҖBkZf @%*4�^,��d by "�Q�l*�!+!A2�4&� �[��4�VJ/ a7#\-Kc#Gt�\�*�� }.�H&�^*W � }�(a2�gnm�mB�eam&2"�*uACi�h�R��1 i�(���&�� 0.03 "o�c"�N�)�D+J�D-�:�� q�܈2#r (11_0��2\%W&R_@G �dm8!q8!<-a�#AA�7c1�BA!�&M ��ViZ4un.be2]�"at�T"zBy�!LB�. S�jly)mfos\ J�dy(qh�X5*�;9>F%��C"Vpr�4p�U�+!kqau� S/als� �d.�kE�=�MHYiTo��" n un���B6:�y��*�eٳ:�k">2��Ad�<�� .bA2�5 9�"� %{a4�[ q>Vv]*!l)g�Tg>`.|R 2�]� �G* @�&�/)^��s'� ���:[cEL�I!_:F�96�(�abd&� +6� )V ҡ�E9.�tY d�$Q#C!&M�GaA@&Hon��!s��@:��U&�9!:�&k*&�� )!*�Z �=���ad soci�M��A dure��Y�#�R,&a53]�aN;%$038�* 3.51B.�* �*.i &� � e���&� � �E'!!�aU��0.��a���in� �z2.14 +� & &�:� *�n��gnS�� An6�� ta��UBǍ*`�y=+ �09� o�*� )Zs �(��<�N ab2�NN  $Q�, 038$FU Ny3Y_onpis, hlI,VL= �)�i2.�1��=� � �!�@�} � "X�-5�_�iF�ad_E�y$� boxe*�Q8U " 2�� a*z�1\of�0i:���q&%%f$:OFW �.�= �&]{A� vsQ2.e2|zC� !�*c ��S�5�2�(���h \�Jx��)E�1C(op��h� ax( Z���� byZ�){-�� E-%vg�-�A.0.15~J�)��gre�?�"t��D��f$T0.6~n.m6�Yc�"3�""�Tw20IOel�:$"� 6hQ.�e";.�%q60o 2��on8{�z�m�g��_$�?� n Sbk� pl@�� )�*�2��U� YDA" ��Q��d6au�!a8"� s $C_{2u; d}�" 5��- � ���. P�D]2U.H�$�alҼ�V� �Q��160*le��*�f��be �R�QPre79Q`6Zng!�R�>�!�����%�,he mid-1980'���mowo2>=�n�KS q�$� F�!�u}-d}G!�g>�l�g�7\�g$�)V�I�&m�8 �1M*R�� C(+M�1�-mS=�,^i�soBs somee� �o"� � �� D.�M�NH��w�\,rec�%? deep-&:s�CA1�w�.{2yzj�~t�% S� B U�V��4�?y ";%�1i]�&R(R�,e5-%l@�k��4u�A �R n.�IS�M�"�N�SuI/ 0360�)I�8=0.0265$. Extrae�Q ��qa��3�{I�$�������M3.�!�i ��% `%�!�H�-.3' �~f"�k�>.�}�� j� !�Z s����*y�!-y�S04�90�pm�35e 02 2�RC1B7 2I1H�ge�e7�2rA�a"yj>JUe.T&F--eiAB 1%�E�/�u����Eby�! 6$, �<i��qK� �1a�:�{s�* ���s]r��:� Ge:���5ion&�*-) �4%+.�e���B_`c2u_c2d�#;� " nJ F_=16� Ex�fng6� I@2�_n�&�2b� . O�#��q2&iU�%|=Ea�=s"[s��6ps. gl#"}16�m�{�A� top �(nd Higgs bo� "=�g͟o&�\� B s (Z}"X ��5),�-N\4�, d�} YD�-�r� AmbyHP�2k&! �';]�9��N*��I�u�1JnsY�l��la�p@�WWel01} (G refeWO0�:?�No�)"KA��`avBk�Q!�a(�F �tb�a��it�s�|��&j�-�ns���4 "&^:� &�> q���>�[��;�j?�ic= Eŋ��Wb��? $�>�>2�M��Q!�NFw>�!�6��A�r�Z޻� a uW- /} dd o�b) �,��st �KTͬ"�s� -L&�(Ɓ��]G"'�/renew�/��wo A&�&!��G8.isc2��it�rm0�� w ��twB�h-�Q�"�./)!a9V)���ϥMIJ�o"E� .L2'� Tt��e.!=6�!�E prob|m� g�a��Q�bil��E�vvirtual59p��S&� (i���,Sal�W�(�R ed).�ea&�t2W�>� "�!�!q� sp A�=F���!�r�X,�,{�nba�lanJ3 �.:%..2{u� ET ^j��-~�ps6�&�B Eataɴ�.�A��ataEXcZ�m��m��"p!�9�%'��y�waR�1$AK� 16.4 5.�C,��J��t!9aG~��{�&� c&T0Afanasev*(.}]Afa02}Oe� gV��4eX�;E��!id�k-E�3Qatez�2��� s. C�EY! JIee<*�2� hQ�r!ie VDH0�-� i� excij"� .� �a��R #�!�&[G,���&ESc"+��he( PVA4M�$�w��31s ��-:'�Q6���|HBau04}: at $E=0.855D> (aJ$�9_e=35^"�){7T=0' 2.3��80D5,at Q5NFG��$-8.28A}0.94=4I�p,a of �)}��V&a�{&� u9_b/�d %"�`Mair�]� uld c���&��e@[G_aw.>a1�p MAID unit�J isob�>�5�F8��becom��ail�j- Pas04}. A����!De�$!�M�B� E��~+6mwfu�LQV G$�4A��HAPPEX2t!fe��im�|�0m(��A�F� ma,� 6,�$)t^FQKp)��t�W� ��)r.�=a:� ��)n�G��B�&A;&�Mf[� � �.�Fơiea���iO$Q�)�S.��bcu��g�*stX>��I���Z�b�.26QJ�KA�erj ]0�%TeXCAD O%d s %\��e{\onL~�s{\offpic bezi�cro0�x snap�$2"�{8.00Ol%{0.I %2asp{1$zoom{4.756րset�F{\a� }{0.75mm/ ,8mm % = 2.85pt \�$"�YX{0.4pt} \ifx\plotpoint\Df!`,\newsavebox{ 4}\fi % GNUPLOT!�m�� y�lpicture}(205,110)(0,0) %\put {�mZ# {~}}z�H^ +8,46)Z),rcle{12.75}} $4.8,44){\L u�^-$ 8,52.2){�$(0,1){14.3< 8,66.5){\I'(1,0){12 39.8>-?3.?2Z? %1st�{ �017.87,0.69){\8o!KL1}(27.75,92.71)[cc]{{d18.5,7.63){\tiny PROCESSES �!4!(IN EXTERNAL.#1#$LAYERS} %G�� �20,602� 4,136�022,64){Au laye7!� 36,7�-<2,3){4�36.5,80%]� x~ray} %N=@ 20,2�z24){Ne>z3vz4Jz2nd)� , HD P �058.44,57.45){-D46.88,25!�9�43}(48.56,38.266-47.51,3��0MUON STOPPINGV$26 V'=�% % 14.5,4Iaa�I� 34.05e"-�E�2#�,4�fruh.8,12.8:�9o 9.67QsCoord�TeS!� $6$ofe� sto�%50I3%($x�yz$�� � 69.3�a�.�4.u�73M��7% 9.5a�%STypB-t 6 �bic atom2$3$($p�� , $d�3rMH �94�5.a�.�8.u 100,1!W}�97,426�101,1�o� DIFFUSION2gy z102��0��5߅1B[3.65,49.a8`M  �1 "5") p:% 6,41"($�J$E!%�121!��. 2.7���*4a�!��30F�24.6,4!]�T��t�|+s� )��)t!��($p_n!�E_n�54�R.��%�u׮ �57B�14F�57�9�if F196eA�� ($\lambda�71F�AB%A�e` �7a�692J975.33=:}� � $55�I� o�(1�i �K8�-S0�/9e�%a��@�2,2R5�23,10: 73,25VPa��tov5U2e"2,2]�-�!1�C%escape �50 (oval(� 0)[]E 42,2a�%�E7V . � set-�%retou�~n��195,24���6��2012)H11. 13> �69!125!-� #�T32  6."Q =2<� gold-8�8�%_6�L7l�7 ! �#o�P 10A�� �>� ? "@�?)K3.9�[ < ,%towards 4th4 ���O�a��199 �25NU;7�W �39�79  � �>� 00,6aS�h2}�h>U01,97%�E��IC2gS"rw �' A�u�4Js 22.4 XE�Y��icq2+  ,&(&b ,:.A.!flip,W}fer���140,7>oU��>o2!P <10 Bo98 %�M2!�%$ (126,82�2�K:�@ ,8��F��$ o� #�)G molLe1" 54,8�� �E���eca071 %��8,8�� 59,8l %bD7 �� g 83,8A g3��8�z832Q2p 91,96){�<91,77){$\gamma$}.b>e 2*{1���c �% ^1 \thi*�s �B�A10r�#�I 40 �u"35��-: 42,9�1^{stoP`�dimenla6�A�'3)L�er�A �P� $p_2!( s38 s-�I��� M0,7!�� 25,6�-}DM_{\alpha,\beta+1}%p_�}, p_2^{!1%d 42,6alg1.g3,a�$�U 77r��2�31�80IZ�+1f�+1z�81>�8k2Z�nW �%62.a��${$\bullet$qS 75.5z#F2�Fb#QOA!S�ۅB7( EL2� :38Ih8I�6977V-4�.:=�z=��U�0,!QU�239�41,8){YIz�a �81$*�.�82Z�:W%c79:�}G806�Q�F�fe �� >�5�$45,2){$p_11N 10,5��d0 10,4�׍� �36�3b$\big�-P6�,63.5��:75�:2B: v62��^�M%T6� 63z�2* 27,3�h�} (��aUX78I�778,35)�{$h_{\alpha+1}(p_2^a)$} % \dashline[+30]{1}(20,38)(10J!66,80)t5) \put(64,37.5){$\bigotimes$} 54,42(left(p_1^a,�\right�D 58,3Bg $% 1�<{\vector(1,0){8} _P3,5){\framebox(28,15) 5 d{$2^{nd}$. One dimensional&@1){interpolations<7){for each $p_1)4�Rend{picture} �|% Template article for preprint document class `elsart' % SP 2001/ 5 \*c){ (8} % Use the op�� doublespacing or reviewcopy to obtai& !� , % 6e[2K]tP\usepackage{graphicx}2epic,e6`amssymb,amsmath} \begin{�(frontmatter�lTitle, authors and addresses!u-4thanksref comm' within \t B\ C!\ B%�,footnotes; %Ncor/NOor;$correspond!tJPead�A@!�email�, %�4form \ead[url](home page: �h{Method of Monte Carlo grid5,data analysiA� �d[wpie,ca]{M.~Filipowicz} \ �[CJ�} CPjinr]{V.M.~BystritskyDswiss]{P.E.~Knowle@,uiuc]{F.~Mulhaus!�^Twfitj]{J.~Wo\'zniak} \)�[ 9Present1>,: University!�Illinois at Urbana--Champaign, USA} Q%]{Facul A FuelImEnergy,:aScience!� Technolo&$al.~Mickie!Tta 30, PL--30059 Krakow, Poland�nM�-R Laborator�LNuclear Problems, Jo�=$Institute AK&�Research, 141980 Dubna, Moscow Region, Russia2|%�]{Depart��$of Physics>��Fribourg, Chemin du Mus\'ee 3, CH--1700(SwitzerB�-�=u s!U�%] ique2� of.� &�� -� ��abstract!, This paper��Am�uO$ procedureekexper�Jtalex us��5K9_�c2�Lto definite valuesK�minimiz�� 59s �It�u�ao0 E742!-�l (TRIUMF, Vancouver, Canada)Q ��ŖEaim!x!�Dact muonic atom sc�!I� !$4solid hydrogen�}Y��Zkeywor�e s here, i)j�f: \sep !)�;Qe.b simu 2, E��B�!F�� PACS codeR�\ 6)  02.70.Tt, Uu �60.Ed, 36.10.Dr, 61.18.-j, 34.50-s %5-})C6y \see�{Introdu H} For a wide rangeADp�,alAᥪ%�Donly applicable wa�  compaÙ3U��is viaA%s-�� (MC)m!�% ��that typm �ten:, d(nontrivial %�Hdependencies betweeIYw<, such as averagA�ari�� frA�patial�T0screte effecte@Thus,- n exA�]?of�9 al�6D allows us a possi!DqG, � thus we r�ҍAMC5' Howee�a� has sal limite� s, mostlyP��to calcQ�� x e na� � rand!ampling!�Providedx�yb!d��cl establish.o �ze�E*etitiv�;c� ,T modem�$events whi!��air� are !'$hidden insA�many oth�� U oE44requires long � �to� su�Ai� s!@ sticQ I�iso����iAv nsicF6number5�e�� �wently in��, g! E��two=]�% sameQEcan5 ��er�resulI� NormA�, ��large�!Y�Z� thos6fO ces !ssHE�letA�� gnificantASaJ]q ;Xnot very important whenA�make a alle ]H�one}8, i.e., ;!݉ no vari�� y��@output-�{9��2?>�E� fied twe��y}}kto a~�I"�s. A�M�4well known, fiQ a� best����.ha �tude�ŷU� repee�]�!�' 9�al estimw � Mostiik! $\chi^2$!iaoi�fin���Uice2Q.2 ( �a��. �H, see Eq.~(\ref{eq:I _chisqu})�a^^[�\M ��s�%��Y�%�L��15 �a"^ XaB�FiniL�ieGse!R0E��� w � alA! Clas� QA"8 s, e.g.)�3&� �p {\sc Minuit}~\cite{james75},�{����[.-(!�Fig.~%� fig: �_scheme)�Wa�A��um.}��or mor� i���error d� minŒ!�R9i�e+In stud,'�& occurr��1��aq!5�!� ' thousandE�F� �|h_)�Q*Hbecomes � k �<-consum�2X MC e� ��.�� , ju� or�� BU,Ao�Jr exX�= (measured� hours!��8 days): �� �of iter���1\A�Ev�N �� wwe�{ ccep��-"J MC2���s l n�Kroach��si�Uin1,ilities will�  ��� %�Aշal�zi�e�\{� ex��e, .@ineee�]D=� 1�!�!~-in�sen�J>�0!�a~��*z �1�I wic%|I)w ��#e)���I��pis qualɹ� �� ��e,�U) �is sus6 d.}��e�� yZ;![%E!�0behaviour of �cesA��A! �m"�!-. %%cZzt��Q�ee�A�$ernal grad� of z!us�t� c8 olI dum n�5�SisyedI�a��ki,erivaa��� �&am�dr�.2@ �d� er+ly� )=�� quot�E�&� !�%6�hould baLac� � al ��s conve- to zer�C�lyI.yfluct�ޥfr&� � c enti� falsen�o埉 �R�L sui�zE>Aap?A�a�wor� Zech�zechx}p sA )�c�!� MC g"l$histograms! .�r%;�� tic di*bu�(A� A3In� caseG r)�JXith�& s �wozni96}Yinclu�llYJ1� apaCt�)Xi� ��E��s, �x resol�ad�J, etc1�erefosw�mn dir� �67at�� spectra. ��_ sk ``�+a)e.S uuaMC2 s, w&i �W � : !�f��ofe�>D � ��0Z =�?''�tandardm� subrout��-� hbook94},e�avail� AJ solv!�atY�%612]�i]G�a �val� � sum��d��)k)C�z abov%�Lb� ie�A�� �abbot97}�� ilar�lwa���oE>� �e � aTg�ya{�aw$ic capqA&%scade u E~�flight >l� gh detailed2� �Q �51�a��3��JAC��em=�\to show� ��pl� at i fu/&hA:�$ -e.0of1�� a str�Z� crysta�e"�M�!� "�D�� � L} \sub�Mod)��A�c*�@igure}[ht] % \ce9a{\input{�<= .tex�V#_mf!a�{S_ �B�s.a m�c*� mark��>^ick8 da��Ddee� Bed�a(�$s.} \labelN ])& W�2�a�T�э�*� "k s $M( {p})$��[bAn�ta�a*a  <  $ A=e � 0,\ldots,p_n)$A�B��1}�"�w ��.�"m ts $\{M\} = \{M_{\gamma, \deltaj \phi},$ $"', "'.#'},$ $ �\}$ ��� ermu�o_a~{\em c� n\/}��1 &�; $�^ �}, �!{ �}, rn^{� )$ w�� $ � -,'$��!�"� indexT d� !a�a�� :�� �?assumeP��  P� I�am(t,��x})$, so6{U�s mayBd%~mselv�beS*0&!3F��b!7�s +aR%�� �]�these2.a�-AñTeA?a�QC)�& �� sis b !�� )!�C.�e2it"BQeAEDT' _@�� oo feweL p�"s ����%a~weak s � �'�;�ere^ A�`$ine a~divi� `,�s��jch�s,pif��"v�9�W#!!%.�MC2� . % �pe~���ta����J�e��naJ2!.]N7* 5q@� Nk��J &� D����1t��2ioWe�MC9Eo#e�3ut �a� s gr�7a���3al uncer�nty��e>K# (les�n<a�4wexinsens#�(ur9��iy)i,#;vA�w� ��E#�n�ly. g2)in cityu*�neg��>�s�Jnec��q�!7 and �(�)�9qf i!pH fit�iӅM* !�U !�% VUsop# � #E�� "�&-.�al .��a�� �� Ref.�(kortn03}, h*v��e X!ful!Q!+��G 9�!?r have ilary�IJ�!�!P�se))�f� tlaand%f� b they�3k��k&� ^"r&N !nY��E to� 1d���sum!{ �vidualy_kymeA��L5 ingl� ��k�te!S6t��� � we per�#!W ultaneous0A^to $m�Ej!A� :z-b�+eq�} A<, ^2= m \sum\��� "��B2&'JOutlook �1Q� two-*� 6� s. Symbol2* a�a��%� text&�&�� eM# ۉ�� ��"� � əW�d� (�ϭo�% /J�Ac��K &�a6s��+�i�+�a� o: ne@'h�>ntinuousy�  �2&��4�%�1�*� � �&rid�$� ��1<5� �A visu�(2�r�*yis�� &�"B��&i aken% *� � s92}.� �l9,.���*+� ew2sca�$�@AAx.;5�{1t R�" d if�t=  itA 8@ e_Th%�O�[�aof.9� ach �D2�I4 2� �TT !�X9&qay$f!%6#�. 2IB�u  eB plan� �yF�1I�$p_�&��6�a-%O�%l i��� a���Tae^a�v)�ywe wishA��'�u�!Dm�bisign $\8-L upp1( $a$>h" �A�s)���tm��" �*t}Eaa� �%�QG fA�th�,�wn��!�open cir�7�6 ol {"K#[�8"$}}� Emediate �s�%R.y$. % Aroun%Nm��|��s,N9�9}�^{\beta}%)$N)+1�+.)+1VAXJ�6Z21]d9Ofilled !/l�bullet$-[M y*XAh! %qH]�:, ��+1pa; +1��F0 �70z �2z�a���I[--G num�"�m�+a &8 � �R��:Q�.% ideaaBEhѝ �/�3 irst��ing $)$Q'jRi /�� A�  +� ii6aE.'"� !� mpto�85V�2^2�]�%9�&!�I�isx1,)�I��teu�Q> &="=f�!���%�nod=�Y-+1��Second$�-ve=0horizoK6 axis (�;^ �!"�)!�Y�T"�; a teR.�]ng�g��.nee� ���� %� $j !tTo�(%�uA|�6 T�&� to��eO $b� )����`aAJ�4�'nt"���� s �1�m �~dth�Cmosv to��A\� A� G.��/onjB!��below. +e'Uf� !�:8or,N�� "�?Q�=A�?�����} + B" D�:)+1} + !C1R* }'' K+ D,{a}Z�+1}''*� �_ �~ .�B| � split& Q� & = ! 1^a�B+- # [ ++" A \\�9 & +>e[;1�/ ]''5P =&t)\>F.��''� ��-\�!&? -S_gJU��� lV{ _M�"M a) =9_ \, ,rK_)�Jnw�  $A$, $BC�nd $D�7a >+ coec4"� .N�yB C6f- A(x)Rx*A�-x}{\D�! x}�Q�\qquad B9-;}6= �ABfx3� !�al2�#-��&� $, $x \in (� , +1}�".W)qplaysVrol�9B/ o�2��$1=._ =)z!�� stepZ�C-�-�V<%�R�I�C9w1}{6}e ( {A^3-A}mY)m9-�^2N�D:J(B^3-BB;>�CDB�1�c5KY�)��h$%Tgf %�in Eqs*�3 9q�}) or~"�36_g}) "�by�=inear2���yAa-m{ava cubic�5a�$DE ei ,��ca� E Q��n` q��  A#U2JAC-0�ta��  sV *..� �1w|%q���'':%*�!. %]+�wa�toa�6w5F�� � &�.�${h}''e��6d�Ei� <�s!��*! &m)�f��-� �l 45��+" '' = 6Ɉm�~`++s� ^2�D}M �_%/BR�0�1&j@i, r/-���c� r�Fed�+z6!�BL@Eq}`2|), riangu�matrixqied� redu\by�a&Y/&� "�*|To%�:>6|Ekg b�� ( �F� $)���E�N:� E3� � lastq�MA�%1e�1�0 Oo-m��<ali� Z�� a}4u6.i��-aHh8?�:q� at $(uI�)$-`�Q-�'\pmM� )a[ \,n�D&� fig:� _�%a.id�7"� V��"r�n]. �,oisl�6how0 $Y''2�B�>t�asE� yo�6t#�F^06�D60- TuC!'���,E 6 1�M�E_i�!�,$-0.05$~eV\@&�J��"� "�.AYB�&�*�J�#&�} �oiA�B�a~Feܑ{ Za�!i 9�O�C[f��t B E ( E��V�/1ded�"t�'"�:$\mu$-0icI�3�:�>�#2%E isotop�7"o�<tGar)�estl)��cha3er�$'9Cac�s[G(collq&�1>�0e(a2�0"�0%W!Dn�r� � SFq e��ic�0M�cross-�0�A2!3�!�Y0ss: $d\mu+p \�1 $ on2�mF�Uer"�B3~K\@-�z.� �3chicc92}�#t�m �r�;ist�>�r�J!Gab !ly �'2�l9�0Ramsauer--Tow&d (R--T) N�Fi�1&�)M_-0}�� �P��� M L� c(bllA�ai"�#p<LK�3�Y���2Thver�(.�'praa��o�=ac��..*I s low��EKi D)7--� �Meum� also.�1�.�e)po'G ��We�/71�^L"p�%�Q� curva��W� ry 2���posR A@�F � Ib. �$�e��deuter_2�>�EB�6�i�m�2!�զ ��V���(�X�$�Lr% Fͩ 6w�u:vAomost )��G.�)p  w�-|3�'of a~(s�0) monoE�M beae2���$��S, by ai�%�0*~�Q foil!�R�5A� (lik�I�u ford}�)Eө�A(��O*y@�q` �Jed2� ��2�H�G�<�=S%YQ� �M� ���s ua3%vM)[e�� i6"7a()7�rpuNng�� Dbe eas`H�)�$I7�axi�Fy!(p)?�)�ES�aaUnfortu�, I�F�@v�,QSbec�,su�H souro)3I, does; e�F%�!�"G!�ctors ��& hl��9�J�-��+m_ real]I8 p� dE�qvIa ���8R �Z,� rRa~�, e�B�R ar+? �!8Z�afFlea"Ym.1")h!n5|LAA�2L:- ��N flew"o.� layersl>at�3$/ �.��Ji*cuH'k7�Io a~9�-�)Za�is "g � �6em(*r}�I*i]��c cove!by neo�� >[�EAL\.� : a~ l� �%Aj!�V� transf!$BA� N�Ke_im% ly yield3$an x~ray p!Aօg stop�J.C�D�;ia��2�b�/h} "�P�@bnt in.$m�U01}%xre�Jqrei�IT&�L6X,a ��M6�Dq�EN%� ��d+eeD YM� ing,!��$a�4MqO* C�=�%9geomet8�2��!'> fow_prU,me:�#6�%O y8P% in�Mce�/�@i���RC%�"��aIe��� �@uU��K �& AJa x--A)[6 �H� i&DE�s)�#M��,/t�R 97� �HoneF'&%�'-{.x)"N %�e=fow"\)B>=FOW��BA~�-4��" � . FoR2�ss blockI��n, nama�. -�:e6b,*)�a�pE�.=�0u� ..�6� 6�:� 2�>AuA�It;?io�3l is illust�V^ �4BEv�.9*�Hth�efOT"h1A�SiT a�y�6' ��� �".Q Q.Nt�t�!B �$�9am2O�6���7�!.U �MF%e:��f"  Ya��|+�wo�"jOnS5�6rf�  Va"var+X"�E$)��!` ofC " 3 $s${)�,(1$�� ��K �( E$)� �:se% Figs;� &c and&�__5$s���, e�.��L *�j�1s$�!� �3.. ��� deep �}%6A"� )#)*MC� �y> r��a�&ej9Q%�$s2{�8ix&��9_�E_\�& s_'\�`� &�.CEo�!(c)-u��\J�.t��-�r-�_%%�ϭ��-7zE 2�"�%�9 �C*Cs._�)<ZT��6J�)�e�>R*�}[b! �Ch.- ys�m2 E�{ �x�:�� tab:egi=_b~5��}�4ular}{llll} %\�c6*NoI & NU,& Value & Un�1\\/( % $E_{R }$.�^!42$& 1.7 & eVF;min}$ &nQiAAof�!"Y& 0.001^>ax >y7�y>190.5N>(\sigma(E_R).�2jeWU� Z & $1.13 \# s 10^{-21�$�2cm}^2$6�m#�!�Y25� I k���� or ccor� to $E}E_{trO!ln �) �'�!�� f^i.�d�viaN5 m =N!\{ {{U�Mj0array}{*{20}c&]%P,�c l}�,l#�for} \q}#E% G\\�$%_ %x � } \hH,6"{�� ax } -E}{._R 2�%E, f�>�Vz� ��%..t_x(ge�k.�&4%�"E�E�-�>, $E$~A�un��C i��8 orig�0�8e� 3�Q% L[s �i�A�e�ɁAi� ���:�R6pp7Kt1$E=E_Rt9-�ee giiS by E2�.5);pT6=%� $Ec&�to 1.1�*'s�f0.1 Vad+$a"�,of 1.25, 1.47�� 2.0� *� ]*� .# e ma� �>� %�>�DepthBp-3ś-�)�. S"� &�!�$s"�]coQD)�=6 .$���� caE"�+A�=) -$ �e}�A�smooth�m�2|s,��E& $ 0.5--6~eVMO�[sR globcM�by~�bur'I�* �E�uW~1�� bordmaw s�M�)u .uq -��(ex�Z91^) ��6�W to &&�6\!n�c �>� E�ɉi>d�@E{��a�N��&q��%���l��Kq�s*u6.��`��s)$�9��.G��0�mA� �, .�6�rSb�L��a=J_<8,;: E,s)9+�$)F�!���:�b��8!FN�)�uѕ�� �C"�% �t"d =0$6�:�>�&�%AY1Os} A^J]mW2���rE&0>:� (w`~� "�`>�6n�� _fitE�{*y+�YOsKGF�(8*Ex�s 1--3) ���E. Fm&D=B aF+b�f)coA����G:�_A�[fit* raw_�I>�E9�a�6.$:��L�J�s���."�Hfit2�e؅o23a� ult:N�I s =$2 \pm 0.20�0��  = 0.30 %14%EeV��.ZA�)��con.�J-$2�"�K'Fdnbackg�< �p�M'$� �Qo� (0.10��!�mo E�� 0.1-0.15$ s�%!lyP�!"9+'�AѦr�P�g/at�(2� #confir�\O?&�o:+ �$*��6��8�atu!��W6JI/�@� k�% high*Ma�diork1%�_as demo�+ Bqs�\"�e�� 0-z!�,E�1`m6�s�WE�Oj5��Ui chec�[bA@pe��A�!�A4 �L!��^�Oata�%�0 (<�bigger!.!! y li�Cl'!�S )�:�Xu�"X. *{Ac�a ledg+# A��x�58nk ACK CYFRONET�j Krak�*`'�A�!�us��ir super!c})!J`(KBN/SGI2800/AGH/045/2002%PP166/1998�M E&sup�m�/A/8wn nd�!� Basic R|w Gr�-DNo.~01--02--16483,DPo�o StC)Com�$E; Qxt,n M4Swiss Nral (ce�,"^/!�� ant WPiE��1�} .210.52/7� ibli!�r tyle�{ -num_{mucfoFdo�|} W% ,tlength{\uni }{1mmHw\A>�!slny� -}(120,=~$0,0) %\put *�} "{~}m�!�start 2D60,75){\oval(25,9)�}6,76){S+,2,72){I`Sal�[L0.Nv�%(0,-1){3�3�27,69.� 20,4p28,70){(~+G2?J$' 30,64�~55� � 2,66){Use�9PRd� %V�_!V�3}(5,65)!6�Z5,22)>�3} 7V 8 ��2'�)' 0,62%G� �2J2>2."45@N"thickYs n10,40:�20!o]�!� 10,5)< �01�12,58!w�hiJM55){�"�6,52){A�_H^�Z�%��2,47){P�SingF 2,44:w�1){E0$MN35^�l37,51E��e O37,48){*z o�5){a`�2pA�5@i.�b20́.x834 2�apMk 24,2a�&ԁ0,7!��26,28!}c�q.�� ?2_} _19,2^30&� =20,17)�7d=j._�o&$3){control�# $9){J5kU49,F=$36Q�85 � 1){1A� �70,23. 30,3e!%70E\.Z< 1eCaA��n �71E� ��f*� 1.��&�EF38)��+d.EqD71,32){D;/�A�new�H29){of ja- 85,5!B1� 85,6�0!M4�{ =�:'A1;105 Z�!P>h�Տ15�97A\{En�b� %Ne.B�Kh%% */�Mf�Z�G�x .aps"% %  �~+istQ�APS"6REVTeX 4�-ri�k. %FVer� 4.0@ +, Aug�q 2001.t Copy� (c)�2A�Jn��ociet0� Se  a 4 README�a �7ri5#I>� *�,� % % �n5$Ap�/AR$manuscriptt�,� }EX� %� -%E�+n�,�)a�A�nHmga�v6 T 4way, you alwayPH R"�1�dus�% Group�_e@affili ;)� er �@��qKG�+� lR7 , orm�1(�.la�*.^> ���. Rev.{,earan�a� �pr���9wocolum!� Ch^pr(Prb, prcdel stab�rmp�jou� 8 % Add 'draft'چtTJ�nver:j boFf%�b��> pacs6Ake.i~ap�23keyF3kFs1\ c�v [aps,prl,�!,� 2�(]{revtex4} ^>5EJ? ,floatfix=�fonts,�bƟ�`^��1UpedM�� % You�da�Bib��� psrev.bvre,ceAE�a�aQgvoq�4�6�j�+ %b i�(c ile)GdMRunq��G���R %�Kay"�L . %\.W V{ �l)*\� bm,g�?i_�2 Qx}! Us�Qe \1xdm! �y�lo�u.0�� re� %��up{S��hIcorneld�t� pagv_wNM�lJ�Z� E�'EQs'a}�a�r�~��!a�} %�display �s2mJq int{!1E���paper ?�E�Mof a Pi��Enh��%�Observ!T ${}^{16}{\rm O}(p,p'):0^-,T=1)[295 MeV� �|%K� .. \�� 9r.q�ed % \"�, ��, \�!�, \alt.>tg%y!!�z!��.�lan�|yZqMgoQ[]'C8�t l e-���Po��Jur�;e�6{}'ɀ �e��APleRa��approprUmacro�e�OtȂof.�A�2,arA��iuo)��s�ci!n;!J.+ =D;N1�G� %�42�%:=a�e 5e�U)6�a^E2�h� �{�%� []{Ya�)� 1�"webe� XF6 &C{} s T.~WakasaA|w@8.kyushu-u.ac.jp&�8http://www.kutl:- /~me�/ Pu�D�teeo*l�Kp�,͋\, Fukuoka 812-8581, Japa� -8,G.~P.~A.~BerM.gKernf�hch� nellerA�@ut, Zernikelaan G#9747 AA� � e`he NethŊ� {$H.~Fujimur��oto2�K606-8502B�K bt>`$ CenI$�N/�hy��Osaka2n 567-0047NnHatanak�p�pM.~IchN@*� Comp��XI*�83c�<Hosei.�( Tokyo 184A54B�zto�./�VVVJ.~Kamiy>TAccele�Anup � Ato�D�/�"��D, Ibaraki 319-1195 :ae�a�KawabaB:J1SE�,� U2G�%E,1L13-0033BlY.~KitaJ�Ju�(E.~Obayashi�V�pVp$H.~SakagucBqb���N c moto����Ypem�A�Anha�u����H.~Taked>p��uD�wa�Cϐ QE , SaA�$a 351-0198B�M.~UchiBjZeO6�ߐ��qg5��50BmY.~Yasu�m�Yy�,~kH�HYosJ�1 u Develop�C�H� Educ�, r�0-856F�M.�o>�ZS��%Coll^��>�;2 desi�?(��5AF� %op<T�d). \no��� Qd�[y�C be %C w�  \��� �\c2��V 2G 2�Z� ate{\toda*�7a&�8ert4"t�J� �']"�6!/� �" *�; �"F>�E bomba$5#�6R �>rmoA�um F2er�*� $1�Mat�hfm^{-1�h�\$ $q_� c.m.}$2KO:3. �iso� $0^-$��ftz2x$�%2.8� !�c� G��+inYlbo�Z%���o�$ �&e��a$30 keV �6��o'aA�Em�or�wSo impue� � xi$on (DWIA) *s ǚob< shell-�l!�ve"#s �o02�6 Bvsimeq$�77\,%�9� �-s&A�ly��Ya�fe$i t�3 2�J, sugg� ng p�e*� �1�vursS�f&�# dens��a�nV i �%_�ucOh�/�d � !E6D�)(�ph 2y( pons=R*�qA�2'6obar yGL�ic.�.�y� u�-ed�bra��on next�\J{21U�HJz,25.40.Ep,27.20.+9�srtYk6-J�s�8't� 'Io %\/�\ �omk��,K,��, �,ŚJ F�bo%�p��� -��eB�`a4m�� %�rersbe�e-�!�V�,�+ ��]G"'` Put "i<3gu��a�'� e<-��IG ?{* \*E3�&W3} ��pXFs�HI���aB%J{$m=�mryise phen�yaѝ 'idBG6U�2!){&yY%;{migdal}M�"�J\I'AiA� utro�5a�#.��$_{\it M}1);՗ in %*toa�e 2,Q �|prl_42_1034_1979,plb_89_327_198091_3282_265} �@!��r�:( $R_L/R_T$,�o7in-����9(!ic�P:�=$a#P s;��Fd"[�quasiJ� (QESa��� lb_92_153�,,npa_379_4292}�?2)z* a���'A�.n��. "rL�briSa�) did �'rev^K any )%.�s� rc_23_185%�1�4_73_3516_1994,"59_317!�99}. SeƖl~ H*8LEnsw�a0�A� on why noE�6d�}���. ;eO.<, Bertsch, Frank�(�%Strikma5�sE� ce_259_77!�93} ��%+m*σAh gluo�kz�" e�k+��&E!p!K fNJ. Br�je9et al.}m�A593_29A�95:�p�LaEst��!!4of chiral inv;~weNO. =�w�8Cn"o~��F� �x Y5�}LnA+n- cz!i�& u�� `i�d n<$a���uC�����-re�� easuːsi� v.Omiu�b�+s�)u�F"[0� one'� RecHG*��*e QESz��@c_69_054609_2004,!�$_ex_041105%���aN� � �X2��.�@EE\KK* F![��!�Y�aI��B"H��5� ]Uu$\j  �F�6!�-�1J~�J, \P� �=<inva�g� *� Jτi}� � , $0m  arrow$ {\mp�tciZCs �Lt2zrX��pC quan�,_ �L��aa-yK $xI2Y7^ Oriharai%6�ſ9_131�2} &�O��^ q$!�J� n2�N}(�$�:2� �O�X on � T_p!B3�eFe m dd�pa6a�� � Born: c�z��Agth�+ M�r/I�.:U /34--2.0 $:R E� u��kg�^H%�6�.� vprfO�[UMT=1&in :?"1>6%>,�.aYu<�,��g����30_74��84}){ d&���>!<se $(p,n�tg(�II}4s�� ���::PfC}��ld� 1 me" ismsE� ?4 inci�f�i�. �lur .e,0�"�au�F�0A�-]$TAu1?{� me[quA�)d$>$ 100A��B sAa.�� ~��T simp�#��$Lem[K9� x?����x�� �P�e�D(�y-�e2�a_E_:[JI�i"� M�*aat"<6�� gZ%!��::.5 (SM)J:6�J��8Pu���w1so}��!�"Y A�.?441q/"�!��66�F�&  1��J� (RPA�&:� � c��AB�����a�R�"J�]ň�r � .�Rc2VBut92�{l West-South Beam Line (WS-BL+m-�(nim_a482_79c�W-L �0 d Raa� (GR)ND\Ser�� @22_48W 99}�0~R-1.=��-��A��!) �5El )� ���-'�J of 37.1 m",$-20.0$ rad,��M%Rab�4 sf(e�� I�4}*dP�GR ���~D wind�� self-� o�W ice (ɰ H_2O}$) t��C�9�59_171!� 1} �a��ck514.1 Hmg/cm^2}� Pŷ��)`�!� g4"P� �C �] high-re=8��GR6��ypiE+�A�$� FWHM.'��yE�.�Vq $295�:1$���Y�kin86C?���[���}H}�:6�#!4/}W�G!+�Q�1tp�%6�a�2� peak-sh�^�+A��TZ�allw=m- .m�� q���oJ���bg�Dt� 2��n"������n $p+p$63 �said})� tili�69 �f�%& �Qv� "�Z�Ca a I�M$M%hU�)g �Al� pote�s (OMPs)Z`��i3l�O)d]F�:Oh->����;�og�C OMP �m�� >X $-2� 41_273�0!�Ahb��:f o, �����&OTsei.�2I� C}$ �tE�208  Pb}$�6a�D mass�  &�8^�O g��ambiguit�%�!�z&:'q]=>N&%odu�!mJ@I�� onab$>ellM2|9a�.[�dH2� Q���,mE7��&}��� 10\% )�. &�Ww@9ll�&is!��F[�&� m1.� A�urPLfig}�&�d�9�� ��rLQ�:�� g! FI $1.9�iaC}D1�*K��S)���F-��6sJurvesE&m �4��si�i nsic�xdJ>�!^0as Lorentzian I ]nv���[a!��"�52��n�-�po\e��l�C�\)�*L�R375_1_��F:�g xsec.�� H<�M-�"Y'2�%�!7 E�, $�Hi�FK q5 _" Dm$2E-*x &o� ����#6H�ge|mq�e��S %V�E\] t! sXjd �cumN�V�n, U&�!�ۥe�� beyo�T� r�\1�B\-@L> ba�>�p���m���, o�Rt2 �ad�kal60 rsha� �N:gRKj�h��:sub.!i�� W"q�edJ�"_r�1��(c]~( dwba98(  �s|�g �rele� BDME)�^���iI�i� 6 q�\ "-C%X}�� 65_024322� 2 �is SM.epe�gmed��8$0s$-$0p$-$1s0d f1p$9f�'�spaQ��s>� r�iv� ���!�I.�w i2ndE�:�$�*�~�mix�e $0\h�<\omega$ (closed-�)i($2$#uFgu ��� �2lZ1r&�rad� ���_g* �& (a Woods-Sax�!WS)& � 8bohr_mottelson}�L!�/N��ad^�a�} %��"� ��<)�$p_{1/2}$ o˙�un�tB�a�e � ϛr hQ"a v���h b��ng rV 0.01 a��i�c*1mPNN} t}-mp"ked%J Fran� nd L�c_31_48V5}�/32�%.us�2%� DWIA�Si0 wnA1!.oB�N�� �…�%}Z ��6�Er-:2r���* ,&�C6H#un���)�cq��^d. Als=v59 �TV�,�fǗ!1J�v.� ?sl� ly �!�>� ��1.8J��W�/"�9 *��%�=�sP �geuMW�gih vU� -da�d �:� >`� th�� E�Z�at 27�i�V� E��r HRlar�E�i�to!b2:%c Ő:uatqM�F�i�d-k�F�Y�� a �Rof 0.7F5�I�=s &}a"�t �� �a p^k$��/ 1s��� ����Am �DZ�:�.%A�uerba�lndB�,:.�We"B(str4E!� quenn�Wspr�K :@ad̀)8y&�Ja D�.9be$0.641+��gp)�� 1��6  �m!-IU.�0�� aF��7 V�g�I��*�Irm�7oscill�6��`s��ukAHv��W8N�295_064316*�e �!��1�WS�.=�� �0R( �(�imi�vto 7�>c"�h}�P�A��o_  VnA�(uav,:���9p�[us�o��Cw�v�T�q6�&�m"klaw/.�Ias�����Cw���carM �SM:5 E���Of��* }0locality, RPA;D�Ί7\oQ$ o ���,re��i*�kv�I�L�.�. B.}A���ar8�#  .} e�U ,a�a �* mass 2l*�_�bk \b�a&Rm^*(r� m_N-vEc{f.-WS}(r)}. 0)}((50)), �(eq:eff7S`*` $m_N"�#�oY!$2r(a WS �)��<panel�6�rpa.Y$m^*$� +�Lr!>�i�!EW2�+!�a�Y��6�b:� crdw}}?1)�+7�op.S 3_04�#1} & si�M$����W$!f6�is�$b �s~>�a�?-x%3i���!](0)��m_N�#in goodMR� ,�c&� .�o.Y�>�� �9F�"Fin :S&k R�`Z�64��� �s�eOFs�<� ex&.*uY��"�#�mixa� %� 2p2h7"@a� en�+R�� ! >Sw��de�Yq5��� e��u@jN,� TAZ-�/%�$�0.7 imR�� LT6�> ,E�sis�UogT� � k lb_126_42P3�*481_388P Ho���r�st�a� ݜy&..���1� +: �u27Zl Nexs�u�:g �f�eq �dex}<��RPAa6�*�1��4 $\pi+\rho+g'$=>#5 $V��eff6mec!"z sD a Bonn&�N�.eaA�hp�6(explicitly -�r_1�&7!�a369ia�&����  rho$alh&�0CLandau-Ms. (LM).*x LM}$���LM*Ś$, $g'_{NN}X �)  s Bk sŽ&-zLM} =�i[��pi�$^2}{m_{\pi h@NN} (\bm{\tau}_1^i2) s,k2 2)G�.\\ &+�i� s �B�  �\{ ( v:�T}f�S + {bCh.c}. �) + (1`&�) �P\} ��.:� �F9  �aeft\{�T.'T}^{\dag�S.S�N� �\} �]�Mr}_1 - !�rb,  LM B: --�$�q1�$�]E�P Pauli �+ (iso )  , ISDTA*3*<t.� �4e~es+N}�$�� , � IG�:K�a� NN$/)�$)� upl�f2�$m a�'% p � middYf 7!)1e�a��Q r d]5--0.8`0.(ep�fixS 2 �_,0.4�% �-N��u��.�H*�.Ng2�5��N �7f�We �� �  <5���115�%8�$&���ѻH*4:���d���-�9N s l]ongly/#-&�wh��:��*�]���R�iۼHJ)3:["Z� ��{ prob�. choi� [ ��K` �h �2�3A�As iult�$�_��-�NN}�nel��a�)�= YZ 7$ u�ha8��)�atv.>"6�0���O ,o�m"�a�i�%hN2: �IG6cli^,�_�.�&g2Ar>�#�:��.�I�� eS"ed I3o.C7RO1? t&Q��;� !/�<���.�F� %�rel`n 2 <��� "�-� *�2�2�{�&C+�� \>��&�q�� �>� ����e*� � o >� M!8�_� bar \LA(5!.sF@�W=6" *� �4j� J�,�R�� �4�� �$ &�," �d��.�3�6�52432�s79�F�/a�.$m �� Fja�qeii�ma( e�ibö+7\9e==�a!,!�U��%�a�Wlank"$RCNP cyclo�Xh��6iYa);��t�aA�T�5"�]in!�t� �,ts-in-A� 0Hc]&�,0Nos.~12740151Z14702005�!�Min���*�BCul , Spor�� a(S��&�C!�J_ % If�إc9S� ���nviron������g���le 4 %matʹat�;* s*$Oed.�< %HW&)%} ��tex�� pu:J-= %� )�2=<i�!4QS�RWT�P�PsON x V�s (.�@LaTeX2e)�Nni�\}!"f�FNd+]ţo�< �SeA}e OAphics]Jan�|0by Michel Goo, SebastB%Rahtz��0k Mc�l� dQ��ka% Hx�3:A!��a�': % F��� p�F�?��"%�}���>.^>a labe�O�4�VEH|O%O-j7Z_D&�1�)�* .�3Z � �sp���%thA|e���N|O�no.@$��eA��`�1�P 2 �} > [�&=�$�',clip]31�i% 5@~:3!F ��f%�NIO5tb4=�㭛2��|.��AAzua� z+ [N.,2~+�a as%YѺ a�"�xW*�,�1b �~5~2V~B�$�!Y)�*aYNx')y >] �!: =x 9R�oT sA��Q�O%�eo�!�)��:�)v*n)�)�4ntinuum.a�!X�+�gbg3Vg����: p~�T^��R'%le�M�iB(�?!))�| A�C ����$t$R�#a� (270) MeV*<8>� �F�& 1p0f: �& ��"�.� B��� �6��� "� &� >�2���aAa75NG4Mb%�~7:~topF�m^K*FCJcG��!26�C'-�2:�#� hq M�2� &uq�J� Z2! zbottom -.J:L��V�!���2�-N�<J�ach �5V64�ei*Z ���Ge� �?p!�0.12�rpar�% Sur�D��2�%� turnX2�v�� scap� =�Wb*5�G  #:� {}�`U�[ +�a:\ % t %Q �^&U �-A�� i�y _�x �x ~x In�Nai/ ��4rs (l, r, c, dx�.�,emp2raFi�=�W�r}6� }nd M� addsb�d%l%Ae#'ua �[a�)�v�\ &se�m� L @6K to get ull-� 'e+wo& Add .5^ longQx% (or*A}.� A�nicely m#:d/ {s. OrB !�[H��h^%�6oȐbreaki=� (ejles�2!gt�M�Lg(�PqO}%[H]!zomto f& c a�s!���2ji�.�! -�}GK =W! ^A$ �0�\\ee�MFB^ %le^�� Y.�Yq�2!�.�<q �4� �4� �a�s�n��^nd���pec�-"w%S j@��nd�� \ x*Tr�^͆5]p�ix*M%gIf��(c�:"tpdpu߻A�:Nhea�-K:?!�Ya:E(�!:�C��Mk,g �b: 2&b{wa�] dwT3h" h"Nh�6�at.h g6�T[\tegs]{JHEPsJ\PrHEP ^�0�N{I�Q al Workshj�n AcJ��� V�Z �Y:�bepsfig,,col} \�O{�HRe�[6'que�TEXONO E"�!U&;U{\sq @er{Venktesh~Singh�Henry �^ong\\ �rg�/B half�c2&V)WJ2X s, Ay�\mia Sinica, Taipei 115290wan\\ E-mail:]_{v�h[_s9 .edu.tw}, "htwongN" } .�(AHEP03} \a�U{ "I2eviewsr ,%�A��>!�eff��d� -e2  Rutrino#a!�-5�%` ics.�s,``flagship''ji�lEor-�n R? !-he Kuo-Sheng (KS) Power Plan�Ta!T. A0��a�Mmagne�;�7�(\rm{ \munue�3< 1.3 .��10} ~"b}$�9�;�f�B ce l�'j��ed�"bI���  a�� �germani��tHr . Ot�y-3 top�at KSŀ�<� %� variA� R\&D1LD�?$^0} % ded�d\{... !% k�S �Wef\) ({\bar{\nu_eB   !4{\mu_%�p nu{\Gamma2 dm2{!n� m^25nurad < r^2 >  s2tw  sin ��theta _W#am241 $ ^{241} Am u23838} U th23 �832} Thk40740} Kr6jncs137S ^{137} CsTba1333} Bacp)kg�0keVday�(!�A�i1�EmubBZe!�rm �nu,rnusp .phi ( ]1 )�ke1)I\kappaEN"�٬ % B�Ua�p�UDv� �l&}��HigP�Z� ��&׵{\bf T}�  EX}A O} N}�v' O}} 2��&texono}&, built up � 1997̄���Ynda�su d"�yT�k in N z�d:6�& start}�M2��pri��mB{@ 40��sDRt�m��aj�mn(�s/u�a5�in�M (:�$�$ger�& Chung-Kuo6&�,� [j��G :�b,&�x��.�^� Hua U�Ď� b�S7$), China (2�*�1g2�6�A.tcj(RacL� TGI�, Nanj�$.��)�EaU��d� es (9 ��ary� ),GAS, IHEPeIAET .� ) be�\lea� �4ps.��#�"c2k^d�#e3A��S�V e am� :h1�,%�M�A�cemag�?� u5r�R��&w+s!��#favor$4irG �:�9��� �%/-nd�ON-x�pd�T?P�{al�q����seK5��yO�y �2oode�r]� ng mot��� for �U��2]p toy&b�8�s�[daQal�5s �byU�"l!�anomal$5M� e�".+. �_ I2P'r��.�MGs-f;be&�n�W^��func�� .K�a��w �stu� �YB6����u�!��n��to g�up" aven��of*�3!u. ��� U�pr��*+�� a un }d%O i�&d~��ad�ng �oS�ith hKZ$!i^ch� ��< dev�H�� scin�.�@c��s,P low- 7gy *H@e&� ���Dpro!ts�Hm!�I{� �act.`j !:� Rv���%%Ch��Q��peE�! I>�$��-� �{�����"} i���x�n �E�j llel�A� [,-�aF R\&D-)�����;M3mi���I8pu��dA�S]�>t&�A*le� ��e�E)�-�w{9 5�&!�g�``r&''�7lo$dm =;�H$ 28~m���ca�\#1� .� R Q/noo�iFBof-�� �}� 6��<��i�)i20~MHz, 8-bit Flash Analog-to-Digital-Convertor~(FADC) moduleIJ�a�Pallows full recording!�all%Lrelevant pulse shape�tim+infora�on%5as longsea�l ms aft�� Litial trigger. Softw!=$proceduresi been devi! to extend� effect�?0dynamic rangeI�g nominal)& measuremA *mAe�1 FADC)dy"}5)�laborA�y�~Lconnected via telephA�line to Rhome-!�.<$at AS, wheE/,mote access emonitor!Z%er!_8ed regularly. DE> re stored8 D�8he PC IDE-bus e�a clus!�of ��|disks arrays each with 800~Gbyt��$ memory. ��-H0-able nuclearEQ�EEil spA� a du!Ao%F $\nuebar$� depi%E:� =}, ��! �)�s S� Standard Model [$\rm{\sigma (SM) }$]�, magnetic moE6* \munu /�-� sc�c!�m�bnue},A� well�:���ino co!�nt La�4%Ei:�coh�. It was%V gnizE centlyI�,sensit} that1mWuncerta�Ves!`m!)!O�8 low energy par�o're)��1�, experi!Esa�M Jz EI>Js!�uld focu%higher>? ��0(T$>$1.5~MeV)a8ile $%� $ searche�Vam on� �� T$<$�(keV. Observ�3! 2�-z wQ require��Nsub-keV )}cross s�on�!��� H1�iJu�� ]�a U�N.�, at aB� flux %8d10^{13}~cm^{-2} s^{-1}}$, �B:e���ss�ndQ�aUqB� (MM)!�10$`0}~\mub$*� �aB� c��ly,�vtak!+w��op��aUforI� thes�Y rateA�8. An ultra low-&A E�p purity germanium (ULB-HPGe) e�u��!LPeriod I (June 2001 � May 2)  �M� 186~k�,CsI(Tl) crys+ .; s �add�.qI (start�Januarp3). BothU�� ope!�= parallel 5% same)RF� � independ����5 t 1!�� e ho%$inA 8itrogen environaʁq prevO=��a� usa�� radioa/radon gaa� \submD{G5�De� } Asb� �}a,��1�surc \Na)�� :� 2��E(anti-Compto� �s� �8 whole set-up i� rt�?n&q ano3.5� 6� � �  block!Z�6���{\bf a)ag2�kshpge.�5.5��1bF1c� �J6��&Rdra���  (a)%1x}m�ith =L2j1 B� s;%��Cmg)�� 6�6� � of 93�]ules (i�)!�ina�le��ru�I�� _!Pn.�/ suppresQ�c indu� yA!�8!d� volu� i( by� � discr� �I���d�=a�F 4712/1250a�r)�R(ON/OFF� in�\� ] paper}� isplay�� F*� 4geresults}a. B"�1 !�� !j1��� }$kg day %�a�[$ threshold<5<� achieved� seh$levels com��� to under8 Dark M * . a�arisoULON a�!͟�s n� � �limA���"u >� �p� C , < 1.3(1.0) � �-10} ~'b}$��90(68)\%A fide�� (CL)� set% 0 residual plo�rget�`waU�8best-fit region��^� 9���h: fonoff6)0�_>(�N("G (a)� J���!'�A}hu�ed,m20%�y ofe ,!L ively. (b x�!boONMum over�OA3.�5� 2-$� $5���verlaid�^9�:�D^z ummary!�s}a�� the �m�a� � A�}&� �us?ul u� i)f *T I�dot��K�n#�l R = ) (y }) /� ���9a � ic9 (T,B�) qKS(Ge)�( has a much� e:G12�H�$edw�w�>� �l�8 R-values imply� � KS1P �$robust aga�<"N�  SM -�s. Eב? -phoE coup� s prob�$%$-"? in $-e2��ela!�to E�`I iaA� dec@($\enu$)\��rdkE$indirect b|� .�inferred .)2�M�I�b. #�s2 � >�g/%�(more stringN � than%q �approa`. ���N�6D frdkN&��Si�F����5�of5�>M s�NB�� �-of ^� life�p2�:s?KS� �� Eh�]lowesA��  so far�p>�}�&& refore �Y studMof"�new��A ��ulI�topicaNN�fi� a�i��co�also pro� "�5xa nue$!�rough�a�duc��u! f(isotopes, s�v(as $^{51}$C� 5}$Fe,r%�on A ure,%^� quA�m��ds� _��= ��mono-�4$� . A!~lisI,transfer sim%Aon has�carrie�sti�%D. Physalysi�A ��%��)of � will� (>poten'sE5�� plpplic� a HI"d. In>�alX  {\it in=ive} a�f� anomalous) ino interq" �m1 ? p�. 2�S" �� C�s}�� mer< V:�%�y.> =\�~cussed\��pro�s����\ gu�zn w!�KSd  b�t�&t* E���:2in mas� .�0 a hexagonal-� d6 )�2~cm zEZ$a length 4��Alyutput��*�L b)ends aIhcustom-designed 29~mm diame��-j0pliers (PMTs) �!�A#v@las�t�$sum���c� !N PMT kals��� E��%-�y �i�� pooM�>� A�ofv(or 93~)�s)&� comm� �t�I���$. A major q�Fb .6 xeY:9�ti��M*�)�5J�:*is� "��dat�($>$2kri�y. !�� I�I� ensate�  dropA�!�&�  E��D.���Q�$prototype -o9n�6u�tom�=�spa��W olu�j\ fun�w�/re "� � .�csi� }a� ]b>;!& [i� fiAb�  tal i`col!�� D Lsqrt{Q_L \ast Q_R}}$�>�  a  (m$10\% FWHMs re��!�660� � ��|t"k(�q_� � @e�i�is $<$20PVd �ob�edzodLE#varD &2�@�  { � ( !-! � +  }$ aOMC. R5%�)/��� at -20�6�,]�demoniY����leescan� width=83& le=ql_q" $6.1�� ion{Es.H .Yn � RMS� !�I�����-^͒ s. Ow"upper�aO�n=�e oint��� si�܁+��? not local�. (c)i Q_L}$R us R}$ �#ribi�w sing%ite Y*� cy�:� *�,�prof" powerful  R= (PSD)U abil�i�� tiat*$$/�$\alpha$ �,)�$an excelle4e�!��8$>$99\% above 5I�i׉Z���]'%s1�is $ che s��� a�  liquid60 _abs<>pl� �-peak��3�B~��csibkg}��ޑ^( sugge�#�a� 238}$Ue�$$^{232}$Th�� �(n (assu�!� librium) ' <  2}$~g/g����Z"� E� |PSD,� be 1%Q=�s �$A�eally sat 7 d"J!e�typicalQ�L}Qх�{��:�vI�-A� q* ���^�]�c%�rueA�a�of��ta3"Mj � 6 &?� ~ "�$7}$Cs, � %�a�2�c�662;�re uni�  a2�� �r� . E�"� $*��!,$^{40}$K (14��)UG$08}$Tl (26�),8 & ha&occurf  n�!� edg��ca� �yA �sources�#%J�& �mX&�a� very m�2.6aM, m�thv( favor8((r���*�#a ." SM )Y>��2}�.pś1xрB&���) �fE "rs��\:�A�l�ry.�`��!l -g%�"#) week_-N � setɀ ^D�. F'is� , in�%ly we<l�r"Ecuts likc Še hit,m�� hit � m� *?. �y� we� E�wseea 1i�Ou��. F=2�a few��']e� as A�� �cn�cc.al..+� E�f� fb9�gedA�nG'E[thiM�� a\ 2.0an�� third�e ^{�c�" bNenF�=�!Sh�*��${z}$-D !. F5*e�U�we�B!���2.9���~ E�TWOI� �r�)E� I� Me��us,P� !EY�L �S 1/17<%6e!s &mtbe bet!' when �l! term!D ON %o�)weR.�U�69A;. ��#L{R\&D Program} VariNprojec���;#e�)in�{�!�[ O�1*��� . e�:�& !Low E� NA,ino!ion} o!8ec>�&)��76}$Yb%60}$Gd� goodAdid t�� A�&� of solar�(�)N�� a fl� -A~a� aY-dedtag� 8lens}. Our work��Gd�,*� W�;GSO @gso} ��ed �]m issuo4 dd�! Wixpl�)�possi"$ 0uopzYb-�&Z�s,�D d -Mknown � \Yb Al_{l5} O_{12}}$(YbAG n #3 P)�2+!�)cas�``U % Low-I$''&�)�or� �&�a- of *J&�E5 Q�-)"�&*A),Pbe!6inv_g�#�|&[*�.� F^{S X-�d��) a 5~c/��ar." uleg* a hardw� ��th�of�Wa@0eV&| a � �)iŨa7 those{ ��Aw-9 a��s-Ti� is technv ly feasimA� uildi a�+epx��)incre!�_i� siz� 1� � �'le=%L* 146�M� �"um%���'-Q)9 HPG�_$���1toZ -�)��^� 2*eV!G9�"U2�:� .R&.�Se�*A|�}�6�*dA!\�%V of��'NaO&� ducasom(: ost �*�!ul�c2q``WIMP''uz��naicdmTI0���UNA)ail� ad�*ng� orN >�����, CaF$_2$(Eu)� �5' z0"�A� on t& beam2��C�% 3-suW/�0y�d �XIAE 13~MV Tandem accele�/-^}.����� hi�s>�{ ��ar� �� �, enab� !o va�e�!Bf�s, "'B�iae�a.~.�!)�e.�I*�% )�q��a�A �� . I�#me)lepsd}E�Rs/�e� firs6'r�A�!>Opt�� �/ predi�n5�elai���th a �q4>~of heavy i, as il1� "�1*�5 os"� eE�.�5�b�DAg�le."&�|1/�CI�q s�\��pursu'!&KIMS Colw2$A (South Korea)�kim����)6�)k uencA���6.7��16�)le=xectF,"�YY�r*0lack circles,1qdA�a�i�E�la, A7v& � . %%Openf,a]� o squa�3 ��-�dIu� F "S!}-��%��W��!�b�*�U5:~.8R�,-Z.���"kA�� M Sf& rometry} �)�N��Mk �����8aF�2 M{ory%|one�� cruc�0�4�j of�*�]��method�m�/n�n� � � �&e/"�,"�-co 8ihsilic6D-con@i# �_4 19��!0z on � �4�!6� ca*��.�Ml)�fs�o �"^�(scopy (AMS)�\�amsf��$ may�a-luE~!x�!ng 1z~� ŧprinc�a�(�0r��!#�'�8-�a�. B&!>� 3}$CD0@!d d &�t=&o%c��"-do qemi�%g�:$� s (.>beta-�"l$^{87}$R&v29}$I��0 e�I~e- ed (Cw'�<��aI$^{39R�� s a �'7 10$^5$ �&7'��oM�!|�'s��X�)�Bpis+]/aP1U�/!_27}$I� (.�)�! CsI f� 9��^>�2x&)x��! sche�.��5��AMS��i�I��� ams}��9 ��Fme�E�z  ca'%: �,!A I %X%�� � 2� beyon�*ezst. � �. �K� �A�� �$r, I��� .+of���4} g/gK+h��-� �%k.�2CUpgra�=f�: LEPS E"p } B`<��"%'�3�%@&Ds�)2�#,=��Qew . / Time���Chambe�+PC)� stru:aaW[7����W�e��SPAD 8 Synchroa= FaQ~a�JapanI�S��g8�1e R�;k 4T=�4.+a`e, 10c=c< � , 32 �=sX �ulp(n��p! ��Field!�m%�G�Ax(FPGA) 2p��re#=!;ro/0ing'TPCB1000~�$�=���a�kF�D��! :y;fadctpc-%!��> p'2�#at)HF�)er@ 3-#uI�d)fA be�&{7!7-Ů�+�v�E`%_$!� 2004F�9R�tpcc *� � \\[3ex�9�on{%�BJr�5E�!�!�A�E�yo, u!�rAw��ac>@. &g1�B1 >Outlook(sag e&�"LS��nd mixqCi pdg}�A� �nseX ld-w Beffor�;� �next-gq& �+< /�. "Cp)a&�E[ remain a �sub�2!�y��2articlePA|!oc�?g�*d�'��E�re0 room%��3 -breV%�Do� s $-$. "�ɮsurpri!Qi:e�Uv* fic 7% . A;;@��amAKB��  Taiwa�} ChinOE+ built up � ��Bof estRs� a qualifu61Y!(5�5�->O7E���9�.�veQZ'�le��Ae�.� w�/�� >���flagship ]��too���-ZB�E "�+�!� b �(Kuo-Sheng R  Plant. WoA�5��/.)�57�5 mH@!G� 9./2al��� eM m6�!�#)���gj� . F@ m U � i�"� � LI|ory�clu7%�S6?A�"�@ B`)�(.7N�Y��i� �Ry �4f:�� 2!�$ llel�impor� a!O�@"\!� outcoZ �] �!�� li�,s, if��B,䍳�d�Ac� ledg%���autho�<gmfu��m HFme s,�#staff��9�2�� ners�eTEXONO6�  w�%�coB})�ag�in ou�-mmu�e&� man�n&L&�#H``make it happen''H-�8rt !jimeA�nAf!��0��"mN�. al SOG(ce Council,u�nd �B*F�3?,�&�A��I!`"� al fu�-�hn"On1stitut�'?-� *{Rex-!�\b�Athebibli� hphy}{99} \bibitem{texono} H� PageW)8http://hepmail.A<.si�.edu.tw/�) =/N�?} C.Y.. (ng, S.C. Le��@H.T. Wong, Nucl. F1. �B} (Pro�2Suppl.) <66}, 419 (1998).n)�%� , J1�%� G 28E153�2)P1a11!b2�mun�?~ �]W9�13180 ] 3). ��::0 G.G. RaffeltN % 2066FpE1} YA�u5�2�z�482!25�!��c�+ U. Kilg�$ R. Kottha !o E. L�L, V RA 297AH25,�90); \\ 2OVA)� A 32A433@2��" R.S!Fghavan2G=�7A361EM97.M�"��~WŋAI�~�,M.~Fujiwara,~547�9i52Tx�Bernabey�IA�E� B 48A>2I�0)�:���� rein��� M.Z �QM�])S B 53�-20 _2�-YY� tov�J�� H.JAbm�vG 45EK7��2�". D.~Elm;A�8F.M.~Phillips, � %f34!54EY82"� S. Jr�rTB 5aS285E�0���B9B61A4.��( T. Nakano,��.1;IJ� A 68�(71ce�%0�E>�  �9 docu� $} u�\to8 nce=�$0 %datum:;08-01 %\4Hstyle[aps]{revtex} :0preprint,aps,>*t�8en � V} \new�8and{\pdwa}{^{\p�M }>$ trzy>%+ @ \draft \title{&FS��;�$^3$H�  �disLg!H\ t{ R.~Skibi\'nski$^1$, J.~Golak ,H.~Wita\l{}a dW.~Gl\"ockle$^2$, A.~Noggaucx'{18M. Smoluchowski� � APics, Jagiellonian Uni�ity, )6\PL-30059 Krak\'ow, Polan�-{2$�k f\"urq oretische z k IIcRuhr-}L\"at Bochum, D-44780�Jy} q3$�~�1�The�[�% Wa1ton�Box 351+ Seatt 4WA 98195, USA}A ate{\toda� E#a$. abst=}&�N 4um�8 ce F�Lev-�eq�V�their �7&�&kpd-cap�>��� �%e-h on p�B6�!�A*He� YIent�)A.>��)onJAV18 X`v Urbana IX �(!�cXMeson�4h  cur�VyS>=��Sieger�# orem07.6+ agre��%f�R.�)�d ngR reli�5%�e�- nu:>q. P*�#AG�2"!�p�+iz� oFQb�J9��n�te:!{up.�t "!!�uteron/%�n^)�%�9�  Yz4\pacs{21.45.+v�X.10.+s 20.-xA� narrowtex�� {Int�A�"�'secIN�,!n�few5�,s� nowadays�+l!Acprecise*�al 19�3�%�co�KL*3%.�.�S)eqtc reU�s (3N)2/^�(:�:E4En �? c �a +"�@bis �s- an �LJolWA&�+�ee ar Hamilt�� . %N1G� <-)M[; U��'-X�>^%�_�4A�be: &b&|te. 9:���� alis0�� Z"L7a_� �Ri � st:>*8ref.Re�}^�betLt��eG']���MR �� e.g. rkistryn} n�� ival�de5(p%�M  8C�con*Os�]&�;�Y�k evsky}. %!Mcor"!0ed hyperspherA� harYcsJMFL o��- �6}friar{ , Lo��z�� l Tr�D{3�4[Leideman - dl�Nto]%W��D$\Delta$ [Sauer]. �4encourag�|uY�1uru�icq had be� avail�J)j weaku�@"xv��S ���Sz��; ser�f p�O�%�Ww�*�A�_]�F#F�e1�g� elek},�ton-d���� ��-�� .pdc.20Vmu�%�� $iE d 3NmBi+N[ 4skib2b,3b}�A��#[$�%�a�g��"�&��: f-Cr � ��0 play�ign�]r�S�HE�x �Z��3N!Hces1#noticpOn to�� �so>addxF:mZ9Is.��a .� way,��A��"�F� ly o����[!�� D.0ly meaningles>�R!L�0��(L^�C��.��'"N_*>,  :p$or asymmetE�!c?A�Hly� door#�) for 2X� K$}�_i�3 ��T�BrufImf�-M\� }. �n� �saLZ���an%2��i��"�# Pisa�p kpisa}a nice*� w���q�A�)HAW�$=b, :� :^�,��c�6"�T�#o2�t}� �Ia gr�"�I � . WeE�+.�i�W�on�� � e.b�,mar.ele}"/ �e�� aU)aE��de� a�freedoUC�� spon���mP� take plicitly!<o�_�*F ese �d/* %�in�tk& Qs ������*W A�.�-9 body�� blemwh -is"k9.Le�to!�!�ew� of0��A��a`%tud{wo-e� � �!�:�of�MM ��P,�~uU .s���}2i�Q�3 �1� e�"\ M� wq?*� � �� inuufa�on-triv�r%me�!�)qG� est!pp !D�-"�9!��0aT6!��� >���5�Z� m�bC8�uje��pl� &$:!]5j.%MZ i�EpL/�$m7ex� nz^# #�B�T!�q �g �Ui� GR ." ���!�%!��� solv�(�!�U �C�K�Noe.a�K�- N a�%�&un$ %�e �Mf� ). F�<�gny2:$"is # vd (?) %�0 .�task. Be#sE'��a��isA# %u9v*\m���`"� ����.�u�c��%8I�uw�(4d>���=a�  %��. U�Otunately!le�j�R��Vs�TUXe � s, %)!gtwowe�Eor)es�k#�`H , so%Dhop�jf-�A��� %� �! �-h�6fiZ!' In S�! II!&Q�-J�heT:�!�~ra*XNd� (A��Hs�<TDe�-np6)A� .6L�N.6%Q_Z\�=)T#4 -ar*=i=OV."gz�/)�{��Frame�62�I��C 6!�6� :�y' ��*to �)V�!�9�!|� ^��&76�O5�8show "�>.R8 ��A̩*�matrix�TEwfmV��V(id \Psi_b \0le$�(�a��� } N^{Nd}_r\} \E� \l�8 @^{(-)} \Uj, 6b \;,�`U2$nS�%L�"�jF E�!k:3 it"cA�*�X��l2b'$'�2�=�psi_1 �(1+P)n���O$aa�a���z$9N.p1��h$-y5.~{ . $P-a�(mu� on"� d�Ra�s�*cyc�*�#�e�,D����i;FZPQOP�CP_{23} +332}^/P_{ij���s %!��a!�qdet�>an� numb�VAVi-�= nd j �o�J�^QU"� ]�=� obeyI� 26Mnhuber]m�a�qRpY^&=&]vhUv+.([ Pt_1G_0 +I�0V_4^{(1)}G_0(  +1) ] \no)�#&iӮjK]��q�e� �Q�D c\E�!�"b@a-�um eigenA�0�)�p1��+r�c, $�, G_0q[ t_1$yaE�I 3NF �� e" E�Q 2EE 3, �++I�"Dpropag�ABthe���Ct-�+c� e 2-32so6�T� uJ+N.�Y(1-K)_ll3�Ё$v�~RIXr�,.>�D�F he auxili�;)މ�UՂF�ER!�2憔a.@w defUBUgetJsb�9l�;.gneweq8BiA�m! �^n ~(�X�h_�magTaNe$� J�6* =)�ɬ:�+ K `\;B� Inselm$K$2��:����n�6�+&�� ��2�l%�Eq:z.�$e�%H�M�+�'[�mkernelw�ls�2e left cau� unne�a���g� s dI4�'�in �� ppea�1s sme�-&in�$ logarithm�in�uitP\0"��Kvoi a�wJ��/Eq.(~E�5i)�0� �z below� . B;-($1_{NN+3NF}��}$�% Dedng� \chi�y�+PnZ\8!L!=:|eLEF'_ 7��\�&:��na�:}M�= �I�k:]�k o2Y 7��6� 5��emet10�d�F�2�a��Q��2k.e# P ��B�N[� ;6\;.m�r6B�� �+���*%�se��Dhed�iX: �-� 1))o�!,-� �n�+ +�% ) T u:��!�1} ^?�291+ Z)T��B�VN��V9 ��>��4�aJ�S"+l4-�Eqs�=B})-�Ka}S� Eq. + r6})����N� $.4�_z i�4;�2��l:�"�ed���8s "�2  ." �fc�N�SnTNN�����'(��=0 \Rp+a&N� =0$)��-%6})gp�;@O��i7F�=6��!U�Up޸ ��7}��7�f�&ed:� }$." )��)�inhomo�U�n� s�9 al��VolvFKi!�_ consecu�Pad\'e��on"u,]�@ B|&*r��inP& � , du�BEd}�9Avyx:5:� or}rmet� pe"$ o�wa:"�859 s a2�!3  $t-$:f�� 6�S��t �A*� v � d�4rm� Eqs�m�})��@Ywav�Q� oB2�Ec� ]6|(s (&� nd� $) e�ca�!�%�V�R }&i�q smAw��u5�Y%� 5B)$a�Wupon Q or �@�be �C&aF}S�%r� Ha�I���Hne��'A &�&re"N�{n�3N�:�;�L +*�hiB< \lbr6.� &d+ :r .F� � 2h ��� �6VJin#^+�E��V�s�)]|m123�y�!�R� 2>� }� �sec�H�t�l��e��v" 80 "2.2�U&}-�V3C�om-/d�"I5e*�-�AZ� N�!r$� . How�A,Mu���ampleten�c$we briefly1x#)Q). U� ��]ityF{ 1  A�$frac12 P ( )A~�eq:P1NG�`E��b�\tilde&.� �E�>)� t�M�"� + ��&4 1( 9�`=>��� �:&� &�F<6R#18 j_\mu s&{\rm b}� F�; B5T!^RU.� �>r 2�2� >,   \��5A�kr% ): *&� BE �P��P)�B�,]�U%,U�1�9!uN� � Y3N!�^%�Nd} =e(* �{1��]�AD �.^HZE/m� NnewN�r�3N}M.�����>��=Ri�U�X %\cr1 ^iZ1fh �^7.h1j3Nk �""6 "ccD-) �" es (�ɠ�A.�) lX+in4 �A��*%�� 4f�*�9cZ�%6 ��%:��?$)�i�iE�:� � ��@)�17u �w�%w�)nG-" �"�9�)):\:�{�2�=�,{1}{2}U;*u1�=P(P-1)$*1e�)� be rewr-=n�vBi%� w1��[).u +UP v "?]*=eq1Fo�%isc�"!���mCU\f;� \;,=�=FO<�}2:<"�*=-�M�metR�:x=)Z"R3J7 %� al4I06Q`ly�en�.�n.4%dO&n�~})eV� B�>Deq19}J�N.v!M-M�2� � b�"]1F �'res<7"��4)� b��~d� � ����R{"� NY is�7 by��  NٱZ+ �<2S>�}� r11s>� :N�)BssO)tand��W) ^�I͢)�s -�ݟ }$E�me0k5 ��!́N� P ont�}.�$2AP&�"�pre�\mQ*�act=�b�S�y- ��A)fu�'�x�{���+Mor��,�k�� "�0 \ flK)�UF�In >Sr� �n�a  \�NO�>&e�*d�!g�%&/"&" �d*9v���_3"-�Dsub�I-Q�gt;4iN�s B{+ NoryA��u� �)7h%*�6�/aa verg���o�, �oZj]Y�� onz\eco!/�5�-%max} =5$R�a&���I|-du�<�lacl t-n� .GO��.!I��/m�z H��<o:�c�^i+� , re�8� infl�`%�A\A�(3*0�0�:�Zgbare�Oc�?M|�2j�L�S �"�d aRt,U�)N� xrar($O0-&�+g9�im�S�Ba-5Nl&<>� V�3>�}$} An)�.�2to � �J74x�!��4�6��2R,E+B|$c�8$C/�a#+��dN�k��!ٍc� !���>NdQ8�y�(F��-r5O96Q� ��:0�A�ak�F�*�+cj��@MP7che>�A��ar�0��e�K�e stage*/1p; af4o*v?� �!�I�ed-i is��w�to5�[R 1�9�&�,F� N^]:*��+> F�3*+�+r�FWj,�com}*!�( >$�mAL Ff$f Z2��!� 6v>"4 viaF)% 6AI !!�1"� +G_0tTy� �\f�,�{T,6Z*�zr6� t� 6R + (� .@P576�2�)+ ]�Z�Fdbz�Q�eqtphi", 1 "�&� +&�eF��rI$�e�[ŝ"Ԁbw i�P f *�)$"^*to �q�+I0 $. F~?ly*,,a"bI^m���a6`} caS6**����7ߡH���v �"� Ū .Q *|n7N{s�Xf�tN n ^�E�522U38  �6�<�R�)�� uN,CH�W1-w���'e�� e ,�{�7"Y frb�ini��n "� �5&u$z$-axi�7�I�<�1���:moutgoAU v13eɜ� w�[ djun>� "�-"A0C 6N�i� �Mi�rep_Kkp "J�in�  . %Ap c&� .�] at %BS�(�Dv+:'` !?:� O�')iYeQ"!h6�$a�4lI*O6 O�}urs� e I�i�� }$�!*�d!r*� �eB�Nd-&uc�DKnC � "iJR�6�5 I} P*6�5�`�_t@\%ens�/A�WJ{YY}$,a{XX}$v$T_{2L8vn-1}{\-�(3}} A_{XZ}$!V.�L"�w�<�"�%!<|=%0pd9�r' *T= Fig.i fig1#ein:�L.6mcg/�$$E_d=300$ �z O���St�da�kJD$E_ k \�$106 Na�慦:6A0H�� e�Q�72� 6m3 �2>8�!T�`� in�\�>�(zd me\-�Kу&u$F��!�&�Bfo�'�js��2H ��3}.1�FgW)�C�#lon0z�I�B�2��t#&�e� �?Z! v��(..A�-!SagaraRs}�&)�1�E���{okxe �5!�!.V}��x!W$A� 6fEn :6Q>& �#?Y �>��f�ur2� �Pickar.�p�30E�� �a�)��]� al*f ��� �N��P�\ 1�'middl���v�� &.�?�T�"US.�G��%Jj. /� ���2;"�v�A�TE&er,(?�8^ R seem!Prml�mNn ��E�E� appa�K$?�G]�yh�5im sH )pe� .�!�r 2�R�vat |�!qMj� %\r� b��%���9�^QNiO={ A`y@UE�q(2�M!}��IH�e-i9-�6�@�qA AnI�O�heL.���%j OiiJ��8i� whyA����As2>,� ~y (�m�6{9�9A�I��*у�Ql�&l�j� i�<����#�`Zf |T A$� )!�9JnE'PTEV B<�a{EuV}�JI�6��ex�ec �2]�p2�4}!{}!�0x[evz"+-�H A��"�$J_:$�N� �$WEIu�*� tI�C{�3h#�b l sufRJ"dpzH7He�:��,� ��� B�15D�lo�3=&�A�S��:"a s  -/�19a) doesA��gA�.�� awd ܂m&� r. AiK �r�U�9M 2�-�^S!4 $&�>"  (* 2L5}). z�V faE.IbI1&� 2E�~�6w(R $j=4��AsIaa�n- 5�& 9�M�ma l� A$" N�um{3=�*�>q��. (LauF� 5}��4 t le?��=5$s 1,a�65j 61�y� N;9��`�Fi.R 6}-  fig9�4���r%*&?O1n 2��  kine�4^A2`Ys�E$$mb� �#gD���!iS-curS�rc-B��o�$ � measuǢ�A��]�zimuthae��$\Theta� \Phi$%%�J� �vI�2ՓՈ��we�.�"� I1� � �IC �{�Dc�by�i��0ick^�%s>CB$�����p�]��G$!\leq Q�J2���5��hecke�N""��:�(j���000�@2& =LE�9�Q> 1\%��A�Q Bm�:9��� Q�� a }�bigger -ya��:�th)� �5�at �5^��2G4$F2��q�I�� }$ (*?�)�K�G5�5$ BB��dashed��]�})� !�1�me�*7 �� �s��"գ}.�� A�N!�Z�!&� (�+&N��Z��6� �V�N>C%F>*��&�Q�S���sP+ guarante�"lh�e�� z a�&V m���Q rn Na��sSoch too9��vun�guA:WU!R�d:��Pen�,�_� � stud�*� 8#�*i�.��w\r,�H �ar�e.��X[&�*��f!|� y� strasSby chi\Ys[��� vivi�velop n 1 1} -�y 2R`��&�\$l"�V� a:jd� �\�KBC� nee�RisC  sij ���+�Un�k�Pp�qz, �}aI�"�us2U � UXK�"�,�Zapov�t�U"6Z1މ s. % �A�u� �X ��"m I<Y$hoLA/^&8�way"�"& &iI�� %.I�$�H�b����A�/R,2S1m�ky�.8:/(. )c&$���{ ч7�foJ�%l�,���J�P�� a� J�%� ��ViU`�+)An�=�2u*Wv8�z!0) 2900D�e}k�FEtM6a F>e0} V.Efros, W.�jn, G.OrlP�4ni, E.Tomusiak��B4u g223Bd*�e-8J,�}r2_zA701�2) 36.�h"�eL.P. Yu$KaN��~�2) ��N A.�kuva�FGe20�P3:�fFN� ,-th/0406065,�,�6AV�} R. B�) a, V.G�w StokƲRA~iavillaR+B�.�2��arS. Pud�;rvg Pandharip �,��CarlsVtSt�cC. Pie���6�J�F�6��1tz 172.h�9}:E�D�O�gW.��, Acta gPol�@B�|g89]�Q(H. Akiyoshij:.�A:.�� M. A!�b�35�U$987) 37. %�!~ Karw�v%�D. Brown R. Hall� Hugi,E.�̿1�Cupps%Fatyg�YA.Lζr,��(1} E.Epelba�Fm�]� 5048R�.�A=V X2} T-Atark�vP. Min�Rho, 2>�y59Q6) 515V �02� %  FIGURES"� E}[h!]�CA�{\mbox{ݥyÜ=180mm  file71.ps},y�)ion[ ] `�c"�{ �H �� a�Z"5"t� "�foryK�&�#6 so���+�A"}:"� �] �_#"V (S% j$_{\rm� }$=5���(r> �&�'�1u)ty�0))�-�e� !�(R ʗ2��-�+� IX�,:9 3, J=J@&�%2��=�� Mo�~N '� �� ,I�Ma6��hU�"~']�Q�lyA�r>/��($\circ((A�rom �d2 �ig�0MdM{]6�}E}3�}z}%f I@�%�ACvu��2�2}~v�$��"�.fiK'�B.y���4jun&�"&��5V"��:YI� %23;heE�R(.-��MeF� fix�J �!V-i�),$�!�1_! 4ed), 0! (�)!��� �hIn uish}%� .`�ig4B��;��5��wo^�ы��!�.�$=1_-x-�.$u!%�%�35�%v46� ��� 5:e�(6B�6-a %kon~�17000.�/ F�"��-�"�+LRR�at��0"~ � a5&Q �#les:  _1=10^��, + _1=.G _2F'2'�s��,�{�j# A�tF�*6 I4s I5d2�,͚� 6l-4, %t12j4, t13j� 14j35j3F@97C.�[� \vs�b{2.cm}"7[ ~ F�7=�9000909��V�!�E$N�"="�L2�9.�PJ;5�!�1�B'2.նF�6��2o7�UBU8B`18�a�a�a!a181��b KM�� .��c F�92q559065��R���M�55��j�6(�p6�9:��Cend*�� �"9�classU�,=�4�4}% \uF5ckage� fontn86math}>+sym�k*graphicxWsetn4er{MaxM�HLCols}{30} %TCIDATA{OF�Filter=H�x2.dll"Ver!{,=4.10.0.2347CSTFile=/�4.cst.re�=Frid�|Aug;20�� 04 13:42:2� Last��sed=Tues8Nov�� 3:5:19:13m0Z2DShell3A��0s\SW\REVTeX 42EE�uage=Am=n Eng�Ӊ6"��(#m}/pm6a6x}[ /]*���:7lgo�d.1P I{axio2'2# clai.#C6#ov0rC>-/6, >+jec�6,:-r'�ry2,6+r8=�9RC2+&�h,�ik6-G**E�.>'erE�2( 2}lemma&L2#no�?&N2)pr�z(P >'�]6+2/�(rk*Re~2%�.6n Solu6)(�O"e'\n",�se}{� �$J K�~] {\e$��:"*��!@of}[1][Proof]{\no��nt\*Pbf{#1.} }{\ \rule{0.5a� �D;!} \Q�{����3�0latJ��# pion}wu2�$.Q&}"u�Dean LeADa��� on{Df;t�!of9�(North Carol��SVk&I�, Ral�� , NC 2769� ߍThomas�{\"a}f�o�t t\u\ NC\ w\�br2� RIKEN-BNL"�  Cee$, Brooku n&W�.�Uq�T, NY 11973} \keywords{�'1v&���x pertb%z�f�p��L30-x,21.65+f,13.75.Ca Tga"?�W�l�(g�Y (�{G7zE( �y2��! . \ Kicontaca'a�%s ��H.=zero tem�bc1s&*KD) \�-3]I� :�{6L s 4 a�8p den"be��#one-fift� rmal�!� _ 0y�Ou&>4a&�Xt5� ings49%3`"'� match bub% chaiB�l!��"�0ow wies. )S�9aa�\ Q!/:�K(.�1�4-:_ ���_`���b�,2+�2h#r7'‹"�}sǞ��Yo6̏Mx:��R� diluB��(�_ent�*i,cr4��u�%dev��51�n��(Heiselberg:  dn,L�mernx}:�%o�%�- Q M!pɺ�'�(�OeVh���0�s.�y� has ��vb2sF1Ae*Y�A:��;s:�flc��?"�5<��d}. I�e M�+% , pa<!]�& I��� plac���,$S$-wavs+p�o� �y�d Qmight� do �nt H,�>!a2z!a�-Late�;�8i[2*�;("�0�l�-.G�:�2�8 :, $a_{nn} (imeq-18$ fm�(i�D�:�F!4�[ �JB��$ $k_{F}% | O|\gg1�M-E$\rho>��4} _{�H Her�B =(3\pi^{2� rho)^{1/3�7�F�'&8AWK\� 0.17���9C�{;1���&�zteri-�g-A%R{XQhand,�M>atua~� , $r%J �2.%H. >'Hi259 �| <|�6nei�,)���I�Q �5Nm!'� $. F�%�M�%* <0.13�n-�2�a 5�%l:�`Pl�-�e�� \J�Q�aa�k\inftyo4%�|%0$�sU* l�� U}�?�>��B�K;�*��y�A?gapP1�-JMorAj� �Ib E >� ` E}{A}=\xi 3}{5} �A�}{2m},\h�� w��=\zeta J60"k^Ber�*a�K�}�&ȭ-Y A��.5 6��pxi-n}Eg a fa��h�B���ta�M-��8�a �F? n!>"��aB�2 ��+fu�\ �T?�nt!�dv�-���cold, ��ga1 of f�o�atoms tu��)�n�$a Feshbach0-onY�bO'Hara�d,Gupt �*l3,Bourde Gehm}�tra��"��I+:12�K*� assum�?%M�u�++-tqo8!�Ek`c�?"O�sCt!n��P?*�"�~��TA�2f�,dI2�^  �- �G!��Tny X͡�d��!�[k�A� . Schr\"{o}tv.:O�!va��al�H$s or Green&�9MonteE log gui:3by.D#G*���t QCD,�>a��ly��rodL,�� 6�itself9&.b5�(w~0do�2ra5on =i%%5]�56�Q�Pr��%�:�#�� wu��:#A�#(EFT)5�ic�cZ  s�/ w e 1by Wein� -�0:1990rz}. Ove�Ce MW�0yeyxEFTUB�)�,�ep�c&4]�m4A�!0�M�JXt"� *>.<� � ��%� 8na,BeaneAM$0fx,Bedaqu2mn}. Nu �a:?�,��u�@a��&ex��in F�8�ɵ"'AI� Kais� 1jx�G Xl� ce * 3Muller�9cp,Le�4siaI A p�we��l�YI��:� o� �U f.�76�. S8QFr�Dt= 0,& �;"�pm��r )�.� �a��V2%4"��)7a n�ESa�e ma�e�w 4A�an�2!2gb�i�ma A>d6ur-�= ct�Boy6no 5�lS��s vS�9Ac-�- .ƮZ ��efC��_ "� a� �to.�: u&���r�T� �")) bN ,p L :K An &t a}.z[�:"6���)� ��=�tt�b�A�a�� t�!N4�" at��it&oi� Chen�& 3vy}^& -A'q�1z�DlymcStar��bri���#a\�Win��~4��i�i�qganaqaf9l��E�Sec� II-I#Jin�oaT��?��.~,�usseI!�� ;co�� An/9 Q�.ibya�ch\e!��^B�� .~VI�L�`y� Qy�r�ca T�9fu��"� $cle"� �9-v��Ibea� h=� }�. N"�W�7E"&��y� шper�8c*A8"Z ofA�re�B>�(s. VIII-XII��&� Be�� ��!��������e som�D�\�N�Foug$� zMion@We le��vec{n}$*a"!�ger��dѳMQ:O $3+1��m�o� s"-K>4 i�� ]Fcripted Equotedbl�p$s$2�\��8!$ �_{s}$A,"C z�>pa $li���H&c�I�<as $i,j7aGA� sp�^���!upaT� dow�\ow$ t(let $\hat{0�W!��&�rN��%<dƔ!��)��={l�= {1�# 2 u fco.�a�1 t� AT17x%2A&Mz�?bol1�J�sum_{l!�F7%A�z o; �fs $8=1P#2 3$. '��-q  {$939$G� nn.�< be $:�9� $a{�lQ� UnleA�a�wis�id, ouI`�llabels will follow this convA�o5� ience!�(also defineJ�h=-�\alph�}{2e/}B�and% J.xomega_{k}=6h-2h\sum_{l_{s}}\cos1?  ). \�{8}%>�{e� D^{free}(M�()\delta_{ijy�"Q�$ propagato%� For Q�al2a,spin-conserv�i$2_i��q�Z)�(be implicitAf\The self-energy, $\Sigma�$, is-� d byJ��ull�=\e}2 }{1-:_>$% )F�mb,2h$ is\%ye> ract!�. InE� plot��Qabbrevi�DP \textquotedblleft fc2right% \�)�$continuum �,NFFEC lattic�h�[NAb^ADbubble chain calcu��s,�d27�s2� � � simD�A&In ad��Ithese2=s,e�-\ shorth�e6s shownA�T�  1%G�$ous combin%����e�Z�2 �cings �8edW�|�analysis.% \[% %TCIMACRO{\QDATOP{%{ �: S>�for�>o, %used}}{% %́aJ`�_f^f]F\f[fZ6Y!WEnd=U] \s\ @{Free nucleon} O��Q���d��( Hamiltoniau n��$written as��`align} H_{\bar{N}N} & =�ŷn}� ,i}\�; [ (�_-\mu+�}3}{ % })��}&q �@ D 2\�|D] \nonumber\\ & - Y1��F���Ny bz+\hat{l�)+N<2;% .�-.=� ! -TWe canO roxim partG fun6 8 as a Euclidean5�  ral,5�&� Z_{G}b=Tr\exp1�-\beta .��\simeq z >\int DcD� 2KS%-� , basic�F ��.e� a�+sta| d�-4kJ�=�c_{Eby 1�)% )�0})-e^{-Y�)*( (1-6h 9� @ AB5�>�hf]2�B�� uY[w{n:�.2�{n:0E� Q�5�B�have tak�  sl� ly differform �t���VH\cite{Lee:2004si}. �stead of��$\ !6hghatA�ear1B?)$ more Adard $!�$a��coeffici�multiply� $N% 6E)$� t� X �al�T 8 a new normalizy! _$,сyxxprime}=�Vf-�? ThenFU.�J�`2.ae�L^{3}e� e�� } an��~�e�֑e^{.�&� %I� :�^{ �y�f�1�B=U�B���6V6c� ��2�r:{ni�{l}% �I� "HṱC� � "=  a�5�9��8.�k�3tilde{c}.3-��k})>M?)  ��A}i00}+V�-�6@% RB>���!"�K� �2o��e�*i&�J{��}y1�� �RI���0)nC }fa9 FC}1�m�y-�e�i �A$ cdotn}}2X���1:or86�D(no sum over $i$) e��pS5&>.fM�B��� 1}{�8% V:R8}:�9F�k }-1+&�1 �*j N��1(tact term} A�re�two� kHons at lowest order�7��eff� �wheory�� thout pBdBut si�reksider��pur9�matter, I reduces��on5������mJE*- " =C]�� D\uparrowa*Y�5n��a_%�� down^@%% :'2BBQS!-FRy�P E�Cݜ {2}(�F� } R�&� )^{2&c =\sqrt{ u� ~� ,int_{-\infty!= dsJ�7}sW+s O- � ���� ݏB/w� 7Nu2� �_!rU"5; !ME;zO�9M% ^��!X~O��( :W6 N'ɮ) �0.0 U]"6ٹ With2��HJ<cbei f d byF _ R%(}�}+ ��� � A� Dsb6�FX@ $� >���S�W�n�&�V��� �B�  6� "m 06oA�}sA��)+R&�O6t�1$:�-�� �� n� ���2���1(��-��?is �a�$is quite s�e��fut��it ma"wG0� improved Oa1�y�� discret� errors�N�the�ur>�0maintains som,or� ertie�One[ erty��a�FxTmuHcoupled�$an exactly�er�� "� T!Iis clear*$Y�othe sam_ nnerLa&r$gauge linkQAn� fea)sbat1�limit ��I��ɿ$�fi*���N��r=�l �l+O� ^{-2� ext{.� ���fo� ny dependpY ^i!wsupns�i a factor\ ) {$!X%�mak�$t possible!�~!� s�c1� %k)�preci\ tP aa(u iiWe f��;5 i\useful1� proc�4f code developddA�cking.* De in� *�s 2� $C$ must��d Ced >Z&�$a$� %GWe do �by� m� all .� diagramRtribu�to1]-qSsc7 E*�$Fig. \ref{! }.% .7pFRAME{ftbpFU}{2.1136in}{0.821 �\Qcb{B*��%%��.}}{\Qlb �}  .ps)T{\special{ language "S%tific Word"; type "GRAPHIC"; %��-aAt-r� TRUE; �-,play "USEDEFA0valid_file "FAwidth 1$; height 1 G8epth 0pt; orig3$- 8(5.6386in; % A2.143i@ crop�� "0�top "1� %bottom /�n��'%�16';-��$ "XNPEU";} B�b�4{figure} [ptb]�8center} \includ�#phics[ �=1 , �=1. ]% B� \cap�V7� �6% � ��� �6kw next step��to lo"�$pola牳}?@ tudee� compare w� ,L\"{u}scher'C%��e�`  l�x�a�<*5$x 0uC,:1986pf,Bean�3da},N�!E_{0}=\d� 4\pi�}�k [1-c�#� a_$L}�2!<D� }{L+�s]"plua�%a�f� h,=-2.837297,$[42}=6.375183$.\�%then tun�:K to gD"$Dly measured $^{1}S!$.�length�'(�I %e !�$much large�#�ny  EW� win ess�8 prob�Q� times�vertex2{Axls $1�5"e��m9(frame % �$v tota!co�["wu�-e�U&R(�)bN|�'p}_�&p_�'2�&0' ��}��h� occuK Minkowski,�end $pi%cbe ima�ryANIfAAsQ)\mu=0$AasBzB^5u Juz����*�( B*#}-1G ) B!0}&�UAˡ�Y�R%FqD&���(*� k}���� "�% t5�/2 "�:B�"�LbK�JBF�;$!�cP+A%eţ�+M�E)!���9:F"��F� By�G � of $&a, (R )()\IA�$at $0\leq 112hq�assum ,�a!&s##Q��  d�+��su4ly sm. sE xhi5�6f I|(ac�&P � ents no��lem��ce� �b �4aaW�en��1�0�z%_{k�2,\\ -11-6 1� GWe nowV  aG D&trans��E,J#z=6#} )�{i/,F�We�*�V zero%}er7� , $Gi�6&A��rt froe"�e� ���.a''.clockg+�A�� circ� $z$��J� dz=-J� z\,do',B}NK1= N�}%B z}dz IJtQfi*)-�B�E��i U�ʍ�k� �,2� oint%� {dz}{z�r:���.�z2)�) �B�'RGZ���� � e^��(.Cc) a{ft�D- p .J- z F�-%���a�%�% َ!�2�r�%�A & z�#UjSv+DJC-�� �-/ �EM�W�*$\i2�{Re}(^�I)$ $<2�$�Jpick up�  residueR $5O@BM6�$z5"~ &Y0 �6���L -�h i)�Z^�}��)!� ��B��!B��� i� ��� N�!{]2F�) �#�J�%Cm �  -1+29A=L� ��-�"� terestK-"? Y J�2 we switch��sV�+ �=b�>JoA�@�Y(d)b�6  $E��8�inFK �!%ex�d3F�ly!ge0$.f E>� f�=��% Ez�"+ � !46& h� � ,�inkO z� ^��* b U� 2)!J�d4�0spd6�16"+1 R71=�l6. s3-*�0� ed  q!:�02� �l�4t��$%� {dC}{dY��5which� needed%q+�{verageQrby(8�(�'$I�fix�q $��02: Co""�7.4s (MeVO�)�)��0l��0$C�0i)�0%9!8% %6;*�05�0� & $-11.6\�10^{-5}J-2.216C6*1 -10.:,Z2.3:FC�/-8.756oC1.9fC6z1-7.58VC26�6�1 -6.9V 04^C�)��1�U%�.T�/�[&*3YR��1vQZP�OIO�NINB�M�LIL�KIK6Ja�j�22sum�}�*l �2��uss�mpl�8mi-�5 tic *�6k->o ��-�X"�D����At $T=0oif�;,F}|a_{nn}|$ 5H/���#odensi ��b*%v7ed��5(�]�I�&Oe�nn`�0is is equival /to<erturbatep�c �":tr1$C z .dnoth0��+of�-�O s haq( b�med��is 6$ularly obv�7��cutoff � me employz E workS� !�R�n�by)ching?�>�A�!DSexyal�T)!7-��0 y&�3x,f��R �E powerE�!�!�AD)in� �;A.E4�).E� ?repro�"�2�*IyI�$��7!2,)� u�& Figa- elf}ei}�!_eUD"eF�is�y9&|2� �u�4!'� u|>_i�}# extremelyi�q# rho<,4} HAAS~k_.�dqv en c�A�$s"� !(�#llq$s �ii2�Q�$�?s QsubsetA� % ap"�'� full non-2����  te, "�Cp2�j�  s6 ���w�!V�! mum �$f hlin�$T�;87 u�� A�?1�;Y�!� sit�A! &r��E� e`$T%�mB a�t�e degA�acy:4!�=(3\pi�A�/3}/(2m)E I�0Q%asU new m�sc��he"4 wave or �"64 ap�%��}�mbda_{T}�\:$,�T}3 JB�Y e��&s%̥�r%reg#$or,�^#�clong-di� ceI�I$s beyon8$X!��8��,A� Y� &9�9&Cn�&thresholA gi�@!R9 $B(E)*.��})*rria1U/$O(\l5J0)�Th�t o/ANe ��w� n $�8F�of%N�efy1rtR eff�\+\min(��,�) R�ey��\ A�$a�veruas%�>' <1$ nis�u*&$T>e$.!�%x~C���-omput�n)x� u�" � \ 3%h�@c\7Z��|.�st"n�"W?y= %T\gtrsim7��a�"!<=Ea�9k� A�"@^�%1.0888�%��%!\Ml.JC&�%�A}{��%��%b�%���% 8669��%6�%el!1��%��%1V�% �x��%b!&�%A#PF�!}j V�% �%.���i J�#@m a geometric ser�, \�C��G� NL0.�E q})=r6h�W"��Z� �!"% E 6K6p}�8q}+F��E61"hB( ^,\mu)1P� fF!.8:�w�':L!x,-\mu .d>! &�rQ! p/2+U �V~UNZ! _{- VF9Mg t�6�v 70)�HJ!�&�GA ��&�8-�:7>$R�Gta7#&� �J�A �1}{CMf\�al} \mu}\ln  32�\��[ 1b�<2 4:�5 L;E &I#I�]J�3�%,milar fashio.�� L,o Vto� garithmE !O%L� � �lev,dO-� �G &%-n gy&-*\G6V1.8922�L1.320�%-�lo��2- � % %}I �m�/-�/-1 ;"/-1~j 0401R/-3.4938�j2jIE.p�l�lI�l1+ ,-����nf9 U�Z�JY;���a1f&�1��1}{n+1�A�du�1he cycl9)symmet <$m a�We N"#��##���En2?G&�5ŷB�p},��q( -\ln����p�7"z�(Mp}+q�x���$� p}B�)}{��2Bѵ�F3%i,..�!i��JE��5G}YC}+(<"+BA>�B?  subt;'ed �=!�*B!�A)�=v�e!Te^>o ��&Gt���va"�),r�W �8I�n�R:�.�bel{Ea'ul);e"2M�3'in�ccount% �cu-C$ on $p~" m@BI� �@9�6�QN2.�4C�( al method�4" xe hybrid Monte Carlo (HMC) algo�8�0Du01987de}6 tte ?U�� n84 Roughly 10$^{�five-se1HMC�(je?6�Vw%Hrun, split across 9� �5ors�5 tely..2P� AZ[Td�8 gm;dAT a�M�u�Wof �U�8 }A�Wh4'�9bec(9a�Gin5�QCDB may/ o well kn PU)Ol Aa�0.A comm�(eKWe�r�7�3 a brief) view�Q)�2�Vi�6 )Xw� to s�F$ F6 \# to=\psi GD2(?*�E % Q_ T&<s) # j}-V �4V�G�$s_�T}$'ibosonic E�)�! $ Yi(f� *I�E�ma E�+wUl�X�,e $:�$& rtlyAu�Lre9@b p��D�&85lN�3VWh%WhRWS9A\phi,s�:�^� FA=I=�6�-1}!�phi_{j}+!�Bc ��$ #9u1=�<cal<pseudo-� $ay�F��be�A�O��pD�A�VPH-G,p1I Z�?N�>=FY&�2}�+�W BH����6� Fn}�� y*F %�LN�\%ial N�VO Ij&BBDAZ46� =- E�Vp4&]Q_{jk�< % (sZmQ_{kl*.�l}-�V f�-�-{��M8�b�%�M 1Qu��real ��neg Aމ2��replaj06�} 45|v�mi-��@8H��(tian matrix���>�?�X�Br ���b�/oJstruc/?U�& �=b �8} K & 0\\ 0 & K��Bi one y'�up�Y��Fd�OZ�7C#@ly $K�f%�a"!%m\Xdp>%�09�%'>5lR�( Q=K^"d_ �9theN�]Q�:-1u( H��) ,V�[T$\det Q= �&: SoR2in"�P$S8�)p-t us9�mS%� 2U}1J.t�1>\x�M7�_ (s)�a � v6� 1i��� NR-�!x�j}�3 �@nj:X:Yf� 2�HBR u5=�2�ZR�[EC!n�)EjIP] =-K 2T KVV ,FN% GF>YyRc% JD�l9Le�So6R"eY^}=i� �IABL�RNeE Ղ6�R�i�Nt 6u Is b j}=-�k-�6s Z�-�T�j}- :T>"~�>]fB� NG6X� VBV B�V=�  5�:��  � :G�1Y� �&�-6I �7a!%bs�b�AitemizewAtem[SE1:] SelH�>rbitr�dS>� s-�=:� *8 ^�chX2X� plexRH $M"$ �r�ewGauss�[random�("�N�8P( L)\S2�Ya#n I�)�   N� u let�.�.m�͸`Z��/ v�)es�)bq h =Z39Z.�_2 %�2N�1N JN%�YjPS8dRVTe��J>/2QBA2�4:] LR &r (0)=�B� Z��UL? �K&8 K�(\varepsilon�P%��Pxa�: B �b� �g^nFVN�=Y�.d�b@"� s=s!F[= s� =p@ $=3:5:]~B<$n=0,1,...,N-1$,aHUoM�9�(n+1)iP.)+iJ�n)eVF�ON)-.Wa���������%!�-�2�6b�yC(N)N_N�=e�X�X�X�X(N5g�d2j7��a���L$r\in$ $[0,1).$ \ IfF�r<2�E$(N),p(N))+a�,p� �q2�>=VB�O�)b?leave $,$�iOIn ei%,go back8�2 RG��]E- of"� , $A P%1 M�A�@՜� ���N� �D"2=in�S"�&)^� ^ S6`��*\bS�s�ZsI3TN4F5>.t!} �bu!f� �S.zV ��n�]0T.&"T�[� �� ��M-���."��$9n�)\ DiviG baDvolD$V=�$ �%5.�,�2y $,**s0E�\@��0&I �9"�)&� �EI�-��R% 6RB�E�>[��% U�' �N�&�]R�f�6�� -$��V.�J�;g : R�$ ��VC7�J��Eq`%ajRf(s�ri5 a�.6@>�%B�-V^�M�*'b0 % c_2� �6�:� �,9�� 7!\�/2)s �r M.-){2MX�i) f�E:!�baV�� q0�&Mi �[no�I  cn{JO.k6{�f&cnI)��QornI*�T:k�(r(>} To be�0 under� ����8r>;X��R�.�"1^� �Jk�'i(p7 F� ga���Na ^"�Lj�$"�'VK"�"1$=,=��}+Ma�_=2\ln�B7��ze��B�%@�9p?xe22�(�:  �>��V�׉�d91}N}{(pD)�)e� [ 1+�) ("� 7�"U0+e$�+I��E ] :Y� V�HF�_{0��_p\� (- � B��pC�Cn�"D*m&�XAr���5RM)<E2(%� }{V} ؁1E5R��` �49>:e^� 6qz� } +1FX��R v�rhoF� �Am �� }9���� }% +1�y2W�Xub�"s� gD퍶 both&��6e}L as  �I�e�0�Z(Pusual*4y� dc the M9per� & �) E q}9U-e3��T 7 A�u 1�5TtB�zV:6 8 =8$ a|i�Y in�4�Y Rho_F_8_raw}�xF�RY .YS &�,EwWI*p^avoid �8�; �6�3Tpw|)kU �&k:"5|�3�@ fil�=5<abe((one-quarter�8es�DTh*> whyŝ data��7erB9E�fnu#&�fr�.%f�-3.1263�-4.4521 &25D� :� %&�D῁dQ]B4a�?-�a�F1%(.!�curvescv,ed f1-f4 ref�VA 8&;(9 n> %TGP1.E*LKc�$wr ���OF�P,%�[:�}{��Y�.ep�,%��.��.1�&�.1�v�. 4.20�[F�[6.0027��.2�.6L!;�6�61�.13, a�W =-90�.F�P�.Z*�G� $��JUޖFyN+��`B�ad/6!!�J�l/n�91�}R���.� %���}yF�>� ^� %>V"�2 w�-}]0_�ŗA��2����������-L2=����N�N�A� .��#���y�2 wIx�sWa'�D _ref>���2en�Ral .0&.�� \Z.@Ca�C? :. does�Wit vi� l��4�ng�overlayW ) &�vB�re �EioQ �e ilit�o Bcht?�du�idG ^ N0j� ���~*�C�Ha � )?9 ve rout)�ECy!R�B� ,: �� G �Y�a ��"u nd*�ge|�� ]�$R� rho(a,� ,L,Ti;*n V �r;  4 (a=0 J=0,L=* S �8#rh� >w $=: M�rho-re%)Q�"z "m E>S.� J�� % ��.>p �`m�b�a�E�0�*yicT+ adjustA�A��FM�1��/, n�RsI:&, �7B�*ramD�FU^&^K .�V��} �A�&�D�2l)a�Q�*(13�a$�$ o� �bamV4%�V20$ fV� Vb ""+� �$�mO g5$1C�1 8;K s 3e�4[h��� 3: L �{] }T=8�*��Q"��`��PL�P �*bP1�.�$�<6.2358. E69�}"P�M��>&s*vP1v^^^^6 :KO�Ä4n-4�-R-�S)�2IF)�.6�������)�Z�^�6�J�����72�at��$�onLr��� JT�5 w�^�B��NC $\mu�:=-2�, bS=UMeV��RHHg-1}=3 *�NyOwW�Lgr u��� �RB�Qiso�@a�3raw����S��Q$E.�:���5: }LM��]��%l �%�%&��}{� _{N}~V !��*$^W) & % $8^�>fG�t I ZK��fO2$A^2% % Z���0.04588��12.58�0.0817i� 6.51�� 85(4�W$ %$6.19(2)����U9 >12.777`?21�I .53990H%B 6.21 � 2U60i�U5.U U��k 86(3f� �BU82RU91U2��6����j�>�$ I�I�7 fQ A^ IB &"� � Q�SJ- AyVJ2�]JN2$B� X5���E�F���E�F���E�J�U�62~��6�6��Q:�s�ɴ6�H �Wog�:�� Ѻ $,Z=50��"�2= \ MeV.�+ 6r4�, >L�4�4�4�4�223 7.34��466�V 3.47 0.053�� $3.33��% %u�%y223ɊV@466�� 3.46l5 J� VVU�2V�466 ":VE� V5F� �0.�V2V6]�8���8�8�8�8v8U{��E�U���]�TI���A�T��Y�T6�N<eX�% sugg {�U�\+� �t�nsizi�f% Ŋ"�o6r ���[ist�I/~�.���)! x.t �HeJ���3 i�A�G�ts�Q uide�%�>>��~�)EbeQYv \t @w.c�]p_&� &�}��"� �%6�d(!< V}!4�V-$T�x rx ��A %� � Q�, b1-b4�!�2M�)5 s1-s ) %numer%hs&w�� Y""BqR.�"E� %1"�=�.| {�x %:A| "��A| %:A| {�u *\ 84u *Z|u{bu #|^A| _|*A| %(|�m *u !4�r�rNr9���l�� "�fL �  � �'� &v u�(6  1*9'!#�j�$2.8539�$4.064:�RZz *�$��*� :�$"SF�4�)}�4%��� :���*�).D$)�D$�D$ND$%4��i�p��Q*C$QDbC$�A���fWy�XmuAY���*4G� see >uam�]}(�j�tZ�)� s� t�&?e?fren���Mh� tw�l  absorb :'.� �PAtQ c&r�� We ob�� yh'bqx�.�a&/Y��* "7 Gn�c�.[a� 2E&hoo�+-T E&| suc�a, occuoo"&��[.kq�remˈ_5uai3 ��8�s� Ga !towarGNZy wied gro���t� As� ct)�1S�� att$S�I�3��� y at a��F��+^+rf�-g-� �i�b��iA� ll descriA1f7N�E�Aa% /~ low-�regime�5r�5Lhcty .� !#j�#>� 1�$&M �!nG �=8^� X*� �X�� ���'�}{&, .B�'��+AL� U-,%�+ � �#�#�#�#�#.H!6�%�%]U"�)t"gra66��">���cD� .]�q�~\N$ VILn�A zA o.�Z"��"��%2�*l�E �E �E �E �E )�E %6�"i"�G RG >�A��%f_z%Aa�%VK good�F�P *�^.��4cle@'roache2�.5[lle dili�1) VAde+�s�%�O^� �j R$�w��studi/qA~q$�$ slop� very1Kep,Ox3�s�nt[ C J!n��Y V aH �S ;�!_lH � ho�O e&؉i. t nar, ev@rt �k 1 QD'*����"� �� "7� also� ���0 )�ietC!e >0.1I$6�$03.%w-ifV� �u4A�!���a5 �<gA:tBI�!,3,I<H,<�Af��n?� yste�gr<[aI�*:7 .\ O*M�t )3Opa�S6�L�@v��(�- Bertsch})B�0.5�3.hould ^<d�kr_�t\sim aR�{ �Gr&�,�,ofn1%�2Z�6�7+b*�qui:pi*�7����3i� esti���)%�rq�C!�-�*+9i�in�$aXI�y�.not neW]ari�]ms��os*x "^ clus��!dAtAW� .�entropy�_e.����Nunt~�qu�?f�=K8�%�se!��� rs1DA�ol����ne;��oL�% looka]ln-!�`e2 ��} (''grA�B1Aa42nJ*to�;�}#�N�.P�:T<\Vc 1>��mu}A(\mu"FG % )d.�.*��^{3�K2664B";WeAPra�5 !�b>�ast-s:�-ittAe��6e<~ 63!PZ� 1�} F�=(c�>�A1}.�2.q�exp (b.'FgIW-y��nb�""�yall�<I�2�;Pre%� ��];!��UI�F�.O :���ex���v�eōv� ��*��8����1A�)[.�l:)q�S�������C2�����������%;��i�CI����a$EZ�m�������i��2q�9 smo�ERut� &� * �� &�Gw�9�7"� *�d�7� B� � ʠ re mZPmodj�TuldG7�s$��$(�W~$rst~J^�� !� �: jvy�aZq% .��n �s�!sArgon�hv_{14}5|"� ��l�ed��ree-bod�c[-� UJ�*Y s�i�7 4��l>! �� rpola�t�sj�6��"�$�H�*� --~&f!� D� � s.~�q�8}N24G*�![L&�U*$ \u :rkably� �Mpa�!b�Ff qhAilik�lE{ÞeŜ!4 �NOn��fao�� �&i2�coI���QG)�}ϾK�*Z��UZc�r�t i��tan� �pU�a���jork)#re6v�coars"k(eH��s"�!"�Ycl��F�(r_�*#in-Jh!=)�A$!Fk�T?f:�enR� ologs&�/a�!P �&�AqI� Li:1997raI�!�=�ew �Mclem (pxE�� l�N�a���F9�as6s0��ar�f��<�)Qs��, B E>B�YomA7si�!G�authorp�� ?p����a��rm� a �y&[�M�6(H)��81)\qquad}P_{asy�N2e_{a�6M�}�Trh�Kg3}��"N9\extm2Rm~lr �.k2vk3RkL42N}Jv � u>t :L.~R-`# _sѺ2.2!�5�Yf"�$a��F*�Q�}Ghlta ��_ɵ%�p"5n}+)�Z G KjG&�. *�p>��e:tG�Bu�� in %>�N�**�# Ka�ȡ�"�# %"mF~zepa�q"7MFTB2mft�6�6�6�6�6MFT)?nG  %A�BIe*a�b{�t�䦞K����J z�N�isU�B�n��n-2��AѦf�0y,wE�KZnd&�  1m2(7�$^$*� �$�$�$Bc�$��Z�Z�Z�Z�Zax%?�$�$�m�m�aC�qN��'�'f'��� �؅���5 >�n �(�H�j3�3� : @2*ቅ�,JMFTE^G@ aris ���F%x� ��"Kz)S2� :� *�,� &� �fU,�!! to � mostv ��t� 3�Furinvg�� ��to 7t�)/��,d %� m %�f?��,*c�s.S'�ry%1coI �\ �D�L"".�cL�]�cLf���x*eof2stT%"�u2X" �W{�T�� �M�� c2X-Jsu$�N"�4Մ��"J�f+,� !�a( �B�z, on w �"!K2.<�.3� |ޮ���":ڮjne�8Uulae"ª$"��.��g�.\ Ha�Ub�YJa~� *�._aiB?l�8"�%,!ft�!eB� :�Nhy& h. empe��s ;�?�  &�b�8�XfifthR� :� 0yv}�Zateoat&a �-�s2Mny�e��%ay2H0� As_�% exQ��a�y0/ A)i�uOno��i}0or,)"�erҁly$*�nyv�q�&: '%�7��A��N��i�N �"&v1m� �.6�/�/>�!,�!-� � fact&���pT�pZe�HF;��"un�.���is a trivuq���_c��:”M�a� ,s�N "md~�{ ��|[ d#�&A*6���D%�"R��steep �`�0f'R�&&n'7igF!�s؁�02`between�s.\�#e� medi�e�g!��!�.�&�DN��;��f.=i6�0r�d q� Ply�A�2q2�k�0Sf�`���z� wish pushM9����er6�a^��!9 &�3A�U%-$\zeta�!hNUgap�^�ib�"�&A2S&F;"E�J'=Qr&!�ource ��% {di�q�$R5A�s!�unambigu��A !�( superfluidDT`&ur.- Jdid�(* T�gn��ant dropBucceptaaN%!��9�A��'st.�!5 highI|Q*2�%3g�R��q W� "~ x q��_2�. .]( -&���ѽ�(�� *f|�e ��� :�ofj� � �"!2�pVE �n��.  � tudyf� !\��6per�+s if %[8'��AGMre�T L��ng vorB�r�%��2l�AQo�= 9�s%>I�&���S�se�a�� � 3SUa]�M%,`,ll �^#x* �&˷roton �U��NE]��asiA�E}�bn�(xact Wigner"?� !~leam�&-�a`X"�sYat �8- Chen��rqE z�& ���Ut��� �>F�me�detai��.1b�-�� �b.� :�_four-'�E� 4���h �-" &K@��e�pa)F.A�B��.ikarg�`�I�1n3vy%n)�,�W `df� t V�9b�  oB�BCS-BEC Z!ta �/3-_i&Shcu� ledga�s}_�thank�Aon Han�88nd Matthew Wing�Ł�f�8o�( .D D C�u�m� �or� :�dDOE grants DE-FG-88ER40388e�,02-04ER413358*B� \biblioe5 ystyle{h-� rev3}6{NP�ؼj docu!"}vH\,class[ , �%� !$E�amera�dy�R,s %% ,draft; < wh�you�!2��)f paper Ehedh�sEƸ���op���- �, �.�% add f As�i�s@cessary ] {ai��c} �` yout)m6x9} %��(FRONTMATTER�< \u�-ckage{%� ics}2psfrag6epsfi:J'69float�$newcommand�iqp�2��} 2$e$ �>" beqaG�lay>%e % HV#nn}{\�o \\ :�|fet}[1]{\mbox{\boldmath $#1$}} aD�Q��title{E��F8�pFnd Iso�lVi"�  Few--Nae on S�1� \�w<{E.~Epelbaum}{ A��,={J�&rGU Labo��y,oDiv"�, New�KDs, VA 23606, USA} ��abs� } I��e��^�s�j�mi �--breae�c--���oM! �se chi���c� @ b!x�a��!�� \�1%\�4 MAIN�3� {I;1duK�= � v5��V���� �Sta�Mv%��� "" massB2� up%d� �/kȇ€romagne��� . Itsequenc�/ or fAR1�� �-� �?inU EnaVway� -�Z�(EFT)*�&��ac"�bas�n�Sg� al ('x03ly)Q in� nt . �� � �s��chAM '[6�=)>7M�=�R�.@B��,� ?.�e�!� proa_i��to $\g M_\pi^2"�4 4= ( m_d-m_u )/6�d+ .�( 1/3$. Elec.�N�i!�7�exrYr @(hard) virtual phd s N�Am-Y�L� ���l\rm ch}= e/2 \, (1 + \tau_3 L�%$rincip��is�5 �&� soft�A7ei��%" ar*� irreh�A ��#�8A��� q�o�#����c*] a�b�aa� 9�m�ng ��-uB (2N)�!z>@VanKolck:1993ee,v6rm2 7fu,��0$9zn, Walzlv 0cx,Fria�� 99zr 2003yv 4ca}E�V�procee� s, IoieJ��$̭�(3NFs)q�!cq�FT!"�:, �EB9� �2004xf�rg}. ��7Pɪ����g��gN���D�sec:p- I�E|� �s��<�!�rul��$e)m|$i�:�}, �Kly:��q�FC7RSW�*�i�e z$�La� }; \�%  e^2}{(4 ]�)^2} 2<^4}{\ >^4}\,�$eqJ$re $q$ ($ $)�n� ��n�J�--"���F(!Y�ina%� ). eN: receioc2�@�$~ (q/ � )^\nu$, � %*EE%@� !� powcF ,u = -2 + 2 N C L�E��i V_i \DC% _i\,� eq He�$L$, �m $V_i$)a��� �loops, � ra�c�+bFpi� E�4��� $i$,�`��).��1tex&Vc $�$ i�+bJG�MIaJdim} 7 = d_i!��&$ n_i - 2\;AJ*� $n��:���>  � �$d3$q$--O��he ����9 9\&�� Yins���G�ion�C�m*e� $e/Q�$`� eqs.~(<}i). No��"R v ���h!e� ed �W $q/mib2��s��R�}�.|[�8�w�F�&icZ�.aQ1��� ���8Bernard�$5dp,Fettes�N 1cr}��aQHlagr}� Dthcal{L}^{(0)} &=&��E) \�al_\mu � �}�h^2 -2AM_{��^2> ^2 + N^|�$ \Big( iR _0 +��g_A}{2 F�} D tau 4y!�gma�$vec \nabla ( pi �4 F�9 �HTi ( pi Ug\doG�e�i } )�0) N \nn && {}[2} C_S (.�N ��F>8 T .' �s�N>D>�\>5�1-�Fa5 2 c_1}{%U!L 5^�b�Qc_3)(�) - M45�xq�_{ijk} abc % ��& a ()�_j/pi_b )kc!8 9�,,%*2�D}Q} 2�J�.xY> *ID "6� /��$m �� $%~:����_ decaln"~��g_AA�@?�ax�c����1��i��$C_{S,TxD �gUL-gks (LECs��F�&� � ���W* reads�#Meissne� 7ii��2�2M�M+�d��.E pi_3�B.A�@6VE-3 @m F�c_5]�Qpu()݁ � �*)��_3 %+ �(_)^� str}UTA�jM� ��V63-B�f_1 e^2a�) ��� ^2 )�]i�1}{4} f_j 2n� �2M�� �g%��>� em} 2� (j��h&&� "�$2 d_{17} - 8 9}-�}9� ����FN�!DEB!� + LCB2���3��(9�N )q a $c_5j 1 , $f_{1,2q~Li~e/ECi�>�p=M� ^\pm�:-0}^2$�8=j � $f_2 Zr(4�e--tt��")c� ia $5� Y�.!Q quivEp - m_n6= -4 c_5B6$��JXemnW= -E�A�F���F �m =Z�+ BY$.   k_ lasth��� abov*�4�, vanis� 8&� 43NF!� �G&DjV8 .E�e I��i��to keed�&" sak� )letene~} &��B.MJ��..3nfas&.[hbV(vspace{0.5ct �{x1ެraise�8-0.1cm}{\hskip  true cm�� )}} : 22}{�:b2:33�:c2:4��d2:55�te2:66�:f2:77�:g:@ig{file=fig1a.ps,�\=13.0%�5�3c�PM6} L|(a--d)A�.�(e--g~Ie-*.�A��v43NF. Solid doP�%T��|s) o��S&�"X�!&# = 0$�� = 1$A�ile�ed circ�(.kr�m"Yfl2:l 3$).IFi2�i\nc*���m$. O���.%�%%m&�o� kind L(�� . } 9�i��m����&=��x!���($\:4$F� 5$=�5�� depi��;�;E:. It �2Ԉoo�s"i�"�8! !@ify the topology �Oand do not correspond to Feynman graphs. Clearly, the contributions to the 3NF d Kinclude,L pieces generated byition of�2N potential. In \cite{Epelbaum:2004xf} we have evaluaS��ing� s us pmethod of unitary transforma�(developed iByX1998ka}. For example,!(calculat �c=�%B (a)Y`Fig.~\ref{fig1} one needsL��H3N matrix elementsRop!:_ `�nn && \mbox{\hskip 0.7 true cm} -\i 1}{8���� �:��j�+9��� .62O } ��5�9�n~�- )�K6I- Q32>y.�aet.� E�]I�!rEM,h.~c.}\,, \ea5where $<$,  '$ �$=c$ denom�0projectors one�`purely nucleonic subspaceq�Fock $, while $�i$ refere���`_@states with $i$ p�p. $E_�y� �]# d�_c��gy� �s�� pR 2, �,lectively. Further, $H_1$ isQlea��x $\pi NN$ vertex $\propto g_A$�eq.~(�lagr}),%� $H_01� T(free Hamilt�<� for) 8�c��� o�density�@�?WDH} \mathcal{H}_0 =M�I� \dot{\fet�^ ^2 +60(\vec \nabla ) ))./M_\pi^2a M"2QtN^\dagger \delta m \tau_3 N\,.E� One fin�< he follow�Xcharge--symmetry--break(CSB)�result0from diagramsũa (b):%!�a\3NFisosp1} V^{\rm 3N}_{2�k4sum_{i \not= j k} \,2� �6\left( !�9g_A}{2 F!(} \right)^4-5( )X0sigma_i \cdot $q_{i} ) -| $j6$j )}{ "q_i{})�M_{�^2%� f q_jB )}�@ \{ [�q�times�j ].t �k��w!�!�i�B8j ]^3 �u{}��AHe.�j)7[ (=5Ok )I,j^3 - r-j-k^3-x] �}��nn2�1!0W^�2!�Y�, C_T �(-�V�2m�-A�-=�!*a89�)^2Al2pkFpi!p \; [)� lj+m k6�%�>Ei�Bj��k���j�� � s. �'eOequiv �p�, ' -$ͫ 2p_i$ ( !m('$) are ini; ( (final) mo6 a:��I. The $a�($--exchange�c), (d)� g"� ��� ���V3NFB+ prom*� �1v>I|b� �OA��9i�1�:.�F .�qF6T } !��6�+ e� 2&� �%����(y))str.}}{4�E�Big( 2��-��5 2� `() + f_1 e^2�1i����:%l]�ma FAUlBcconserv�P3NFf^eMTfUT. reads: 2� �x4Jx&=&b�A%�=�p�y2��~^)>v�\^22wB^)�\{N��[ !�i 4 c_1�}{�LAK+ �fAz2 c_3�>)3�]ј2�1.� � c_4]!mAMEV , [.�i$ &k��,�aE�\}�.�ū&=&- �!%*Ţ8}�, D�-l�Zui ݤ{!� ��� Ţ� �%�ar)��xj6�i )y�xThese expressions should be use��ge� :  6 � in"# ica�sSterms2Ae�dc  mass. ��gin�pure}[htb] \psfrag{x11}{\raise�-0.1cm}�"0.0�$ r }}922�9b2933�9c2944�9d2955�9e2966�9f2977�9g2988�9h2999�9i9|ig{file=fig2.ps,width=13.0cm} \v {0.3cap� �5} L:(a--c�4subu�c(d--i)Y�viola� 2�� ��Xwhich vanish, as discusQ� he text. �notsee>�. .�5�end�a � addi���e�wn�:, .z --( �(d �n642}�mally�ek�5!$\nu = 4 nd.< 5$=B"#3NF>�4Their pertinen*n&�, howev�)^&In partir,�1 (aZ bdf)�� obF@es similar cancel!�Lon between various � , orderings a"�cas"�Z� invariant�s,%�e.�6v�&�!i-� !�is sup��� a fa({ $q/m$ du5���va> ent�WHWeinberg--Tomozawa 1inB#$. Explicit;!%N. :M�.� ca!T!�ed alon � line8ref.~:��chEv�Ia�sum �se6�.e$VQ � estima�reAve* ength \zo6� %�c!s compar�%c��:� atsamMS. I��(�` 3NFso ex X(provide a sa�H but non--negligibl6q� $^3$He-- bin�--�8difference. %�> \s)%T{Summary} %\def\theequ� {\arabic{ +}."��#:sJ I��ha7��6�9�9i!h�46��2Tone--Ytwo--, B� wLt��strILgiven�straneu --proh�.�� ݒ.r�againZ�� , dr�l�ly�| --toARutral&� ��also d8electromagnetic~�@!�dim#�wo�2F,LEC $f_1$. Ifutur� ub�U forB� 4 analyze few--.$systems ba�Qon chi� EFT.�4 %% BACKMATTER�G"� 0theacknowledg[s} I wz lik��Pank Ulf-G.~Mei{\ss}ne�sha�� hi��s�A�0is work has b���Mor�[-� U.S.~De�Ty��Energy C�xact No.~DE-AC05-84ER40150 under�!� SouȈstern Universities Research Associa�> (SURA) f� Thomas Je��son N�+Tal Accelerator Facilit" w>?ƍ$%% You may�_toa��\BibTeX style below, depe�WAI yourDsetup 3��c s. %E,I�biblio�6y��producedU outmcom)�u�A^&��F��ee�,aipguide.pdf f: in�%J�� �AIPcee�s layout� e ei� �IA��%.X{aipproc} % if natbib�,available %\b8l}>7mis��!=!�$probably w� to�%� G bibC data�" ��:�D{/home/evgeny/refsD�the.�d}{14} \expandafter\ifx\csn5natexlabA� \�x�S$#1{#1}\fi 5A@Xand{\enquote}[1]{``#1''flurl>gM�url#1{\� ttm nZ�urlaix>OL {URL I A`item[van Kolck(1993)]{Van3 3ee} "4, U.~L., Ph.D.a sis,���HTexas, Austin, USA Z<, uMI-94-01021{i:� et~al.26)]{v�6rm:�, Fri� J �a�xGoldman, T., \emph{Phys. Lett.}�%UDbf{B371}, 169--174�6)~�8:�7fuB� �6�Rev��880}, 4386--4389�82�Epe7#�݋!" 9)]{ !�9zn} , E.,>6!�-G:�-� B461%)287--29)92�Walzl �(2001)]{U 0cx} , M.,.��~�!�6�)�Nucl. %��1�:{Payne, GY�$Coon, S.~AR��0�%8bf{C68}, 024003% 3J I�!>4{��{a}})]�4caz�Rentmee�!� C.~!�!�4Timmermans, R.�E.�}�a .V7%V44001�>�.�Q6.�. �: };!�e�Palom�Da1� (-th/0407037.y%�.v=Ab:Arg>AF�:�z 8033.zBernard|1995)]{ A�5dp} , V., K� r, N�(Int. J. ModNyE4�$93--346E�52�FetS !L=dAa� !�1ca{-��2B�709a��}.-Meiss� � Steininge�1��!77ii} A��8a|6F019��403--411%&Z�m��.�ka>�Gloeck�(W��21� A637!�07--13�� ��> � docu } inputY End� $file `temp8)8-6s.tex'. ��\@0class[prc,ams�#p,showpacs,twocolumn]{revtex4}� yj9preprint80 \usepackage{� i��0[dvips]{colori8topmargin=-3mm  , �} title{EffaveA :&�i6�it{ab��o} no-core shell model} \author{IonelAatcuBruce�0Barrett ffil� {D26�icB{ tArizona, P.O. Box 210081, Tucs�G " 85721c �4Petr Navr\'ati�|Law[  Lhm�"+ Labo)y,�L808, California 9455yJaE# P. V�\.wR�e�As�(omy, Iowa Sa' "y, Ames 50011A�(date{\today)� absty} We imp�+ an '5�� malism �l�� body1s, obta��L� nsis!-EEF N0 (NCSM) w#-fun�, Argonne V8'�6eon"u"|- wasq  -]� ��lisL6`�4$^4$He, $^6$Li�$^{12}$C"+�-), wmputeB�"(ue���5,cluE a�x-�('F�I��&s�s��6rVNb#0or. To illumi� pfHg�@���0oy a Gaussian�Sh�* :�'�weak ren�.liz"0�,Gs (�,, quadrupoleh!a fixed�Q A�s$ stoo%�� �zmwh�accou�.mainly%�short- �c�)� ons.�sequentM"(>�, such�%H<ve ki�, will�w�+9 I�:v�.ɱy�\�^H{21.60.Cs, 23.20.-g J make�� &>IntA�} �n�is' uccessfulN�0�be }of lighti�i,�+�g�)req�!e�three- 0o�1�sm��aLach, all,�,ve,�!]HilbertIM&$ �f�&e6oIn�M take intoQ=Si��aconfigurE�s �c� z.a @A+i�m��meaLf��Z 2�Lokubo,LS80,UMOA}, ai"to F �low-lya�sra�ourRL��is� ?2a�U,descrip)!!i.s. �,c12lett,c12, �6}. H�!J$E2$  3�s, powerA�tes&|2$theoretica�(ve�b,�Gusu�y&�)U6�To�e,Ty w�/��d6ydnd�8~. at a}�E/16s� fash�aɥ�] �GgA6a bf r.m�'��ly��Yd���e�d so far=�l2pointQradius9}v�&B� $ benchmarkA�nd \� .�(NN) pai�n�. )y<$,npn}. An �5ie�?lic)6toB��in%lstric�e�!���ق�rge2�h�to)+9value�$eZj��le harm^1 osci or! zM Az��N 61Eafou!;o�8�)!nav�il1997}. ��purpoH is paper��to � !{��� �9VcJ� (]��nJ6 T . Sv on �+e� y} detaila(2�J�!ereg)� trea"k2Z��> Sec. yX0s� appl�79#to �ta�͞wo)�5iy��I�ia�-�s  up�heF�H� ak�%=��aHs g"Zo. Becaus���V� 幥��!�g�8��* � * !���2` i~ .%��' � �ly=Pedq>H �\>H ��� :G. By j9�� w�owB$ m� �>�)�"s5T :� . Weu��}co�:)in]�a�"� T��Ov�,ew}4mG � start{ a��$A$%�icl;5�H# roug��i4%nsic �4ianC)"L!�7A}=�*1}{A}\i1>j} &* p_i-�* p_j)=7 2m}++ V^{N�3 ij},��HamTndr 7m"�5�U � $P$%� NN�]�!�a�l&j"V� coord5 s'7�~a�} oi�;#locCD-Bon�;bon��W��*� � ��h h�J �jb�ortRink)�e �ar"Q �,marsden2002,�"02003,GFMC3NI}�Ain1bN>s!�ca6�m&��hayesQJ%n� �7�7�UR�+�so�%y.ɩ!�I\6# aOL!�not a� "�(mRCMRo (HO).� byi'x)Lnew.$!���$9 widexLone� gridy narrl�.Leqn{ H_A^\Omega=H_A+i ePI�A} �7mA -^2R�/j2i}L �<Y}{2A}U0{r}m� a�bj6�h_i� zv_� \; 2 CM� 1q%�.�"ms A���A�!�ZA �:� im*'�D�Avconverg;�sol\@i$A$i�problemAZ� er� �Ns. As�Uub�=CM�4L5 many S*� , it doese*aU� any net�!lu ���9tb�Rl. 6mo9%� 8,!j�� �i���ex�#2� �CM mo5@ � rocedu6�e�pseudo-�\�"G HOc;� cy $I�$�a��V��b�a#^ \!�is��r8 R�&st2�*V,im��,#s manif6a!��7 in�MOfr>�%b|� I>$ limit. A��u ( �c�!o��� �.��m*iantiherm�7n"d �dFii$�* *6 ${\� H}$ ��(�=�)} $=e^{-S}�B e^S.�fNN�>at even$!1origi�%.�i ai�jusN� U��$S9� �orb.Y� d upC �Z. O".�i� jis h9al� o�d�60�iT)�_1��'�&�EA�� cal ��*|&in some� ,�?r"�"~�= uA-sol����;�G n�&�der@.�6acA�,&.�6�D(!��/!L�r w�{"oR� when�  re'i� !Je &?*m�6-��� ite �Iis numer!S !_a�%_achie�ieasplit"{fulq�a�(.F:M��o $P$,r ���$Q$I�ex�Fd�!;-zcoupl� cond7F}Q q P=0�wd =�xq�������ir�E0$P S P=QSQ=0$�9�ens��ta�2� 8�����A0 `�! ! > !{aka�.�y a��se"�iheigen$.�(/(:2�n0writte� ��m�1o�(<\o� $ aI;l&0 S=\0rm{arctanh} ( 0- IA)�CJ� aN��(fulfills $Q B P= $�T�1z+-�jtZ�2%jb�'eJ� H_{eff}=PQ<P  P +P ��, Q}{\sqrt{P+6 }JA^{�;P+�~>U�ef�,,9wanda,alogous!�% arbitr]I��1��x��M�$P$iZ5r �l X("�)}O6(O�(OM �\;�?effOpB5"9c]$Qk�e&�I[. Q�Akis+�lnectsinv�Fin%Eto A�$Q-[. A0e way*�j�w)}c12Jn \lan� \alpha_Q|Ib| P\�le � k\in��K}}B=k /W�Fk>P,"b�Ja�Bc�$>5RQ m�w��љA�n 50s�-i�F; $��AsDf9Ea s��&et�K}$c�1�� a�F�"ݾ$&� y =E_k � FH!�1�|1H��GELDL�in�/ e overlap&BVO�atU$>y5�k'>�:�B�=\�? _{kk'}$. &r A�BEs\I !d�qu��R7:�� � � f�"Asy1eO7ly!�Eq.4 I�),u�� �uJ�8�Mhe!r�, i.e.!Y�/geU)]s,& S�gos Tu�Z� (R� �Sr�fq6��i$a6r, $a:Blevel. U�5L2� �" Z" A�J# S\a�!x>\S�F� �$ B) ( :-  d )$. A�!B!.� id�SAMB��\ } l,Oe^S=O+[O,S]*A!}[..�#< �orm a �9&'�$O^{(1)}ri�O_�I��)�J>X O} ? G:. [O_i+O_j,)7] }^A[>&...Fe��<r�%o�W >��, 7<�n-8a� %rxU&&%$�� jk}]�3%�i\neq �J k$.�7�;!�����ut�7 s yields &�"�P � P=P i!} P>h + {C[E$Ej}(-qI )e^{ - t: ']P"� oneb" � An*� ��QRu�QR��F���O��P"� two�U5 in��}i����!. �edf &��CM�F��%Y:P�UV1�m/h_.� +:��Y( e h_j+Z+H.�h_i-h_-�%�|�We empha�i� 5�V�A�� Na&��H9- ").�!Shm(now: \[ Q_2� H�-2)} P_2=- ,12}}(h_1+h_2!12}-.�]_P_2&NQ_2:�S�wY�T�Q�� �p�'cleP) �(�.�� M�, \?�"� ��%crr�.^"k�X!�*�6��"�ceS*�B"� C&�9�.�kepz $v_![� &�L�U*��i�&� �s �{ne6K%!�![�cNV,>�1� �-al�<ird�6� C"� R��d?ion"� g V0<�#�#1�&�to��יZ*] �X!�!�� �w�feI�]�5d� r>"%v�E= P" Ref.C n.�!9Ņ�i%�V�� "/��$���,r]'�� qPi,a� basi�$"I chosen�b�Cfew hundaD$\hbars$=iHH%U� 9�)0 xact&�  �HQ4Schr\" o!�er��. D&MFr�Hal �U,!�D &�\m�%`wo--� �Qnelm g.totKpYs� angulal�3um $j �A $t$, A�dra#0e��"�! v�d� pe{F5)*�vM\�Ee.�n�1�) s�)yw�i�Eq��"�B�*ly�e^MM@ MofYEA�CM*�"� z)I4r&�Y^�"��E/a%��O��b' As� -prmn�E���]�-A_[5Y�F=PS )AF��5�d-� -A^6-. SupF)!�D y ��Rle��f-ec)E�,\+��#�I�c[2 !�la�Z xp(-Q )J )?( $*J� [!�%B�ly�U.R 2OF ]�m���B),�=o���A�1>��r>� '^�i4^e. e@�7 .�!�yebəI �"� burd?sE�L�I� Goa� back�J :%`-E!��1[�##5:x��AG�Jq��6�cog6�"�EzV�e4bA�O�F�5�&3' �^�Yv:�pic�G��!�., &�#\o2�%& � � P �`n_1l_1j_1,n_2l_2j_2; Jt |�X|n_3l_3j_3,n_4l_4j_4;Jt� =B+= 2�1�1+n_1n_2}l{j�2}�Jf�TRA 3n_4A3lj�4Al) s,\Lc'� 1�&D{ccc} l_1 & l_2 & 7\\ �2}&  & s\\ j4j4J  SH %mZn3n4n'�o5j5Ro:�&�U )H\stackrel{nl}{n'l'}�*NL"� ,NL;-'|IM1�UEl5M3M04 3�\'2�jU(jLs{;Jl') . ;Jl)s'l's(j)]�l i,*wigFX%�}:no nt� �6U�.� � �mm�#��\ SjM�S} S. {h+�8 �64 �RIQ*� moshinsky~R��Talmi-M:��P z����-V)� ��� quan\ �� CM1"Eg � �[0*�4, $2N+L\leq N_�!�$ 9 5s>�1C#�|$(n,l)$��"�$2n+l�. U����5�erR�#��Brody=Qbracket <ne �M� s%@f��e*C �!":U,q9a�2�#!z5p>if�$ $22�}f def�by�P=4$,!�413,163;�r)�;g��<at�j�F� �)��!}$:�"��J� �r#���(�&6" !�j*M �bruce,+}�"@ !4�,a�90Ey�?]� c�P��i������"g,u�2� 1�& 4]!X!��U*,.  g2|A�!gB>>�=y>� �c| ��sx1y repla��WT1�i&x< cod�%��)��6� WN:u�"(RH1rma�{� �X�U>Z�7KE}E�I�e�VicEc�E�$q`A./5hQ;awB82�:Vp��a>+n�.�3(hA��m?look sl+we�+�Sp;)a��,a�s�( �.�e$?i_A�so�i�6wAA�SM�}nY�%Q\�ast/]!re seve�8�F `=ne@@ary.7#J/�de�sH* les 6�%��k�E�1�,3I&ed. AlsoZY� �1T�m�V"�Q���.�< ltho+7lat�!� �5)���:yD!�ua�m�*6R�($16.�a?i"E `�.!har�5�2:�1-��is zeroI"*�>%F�Bz: "�f A e} \iDO:lphics*[scale=0.48]{ke_37} \cU_ (Col�4n�T�;?=��^acZ,�3grz;e� �#�:�ag$^{4}$H'&�;�Fs��H:�2dBZ�J>h" ��~�7�5���$Q$�! (cir�9)�,E<ari�Hw��-�Q�6|2 (squares�^yU)���6�:� ((diamonds)."�KE�1� OuZBrst���?��!1 �>i>�vto *�?� $M12B�)��"2KC12bval}vj+ 1FE0B(E2; 2^+_1 0$$0 )$]*H �B(M1; 1 !J, 6$Lia�B<FIW*�5.o@fedM�!+�5f�@$on dynamic�A�t cite{MFD}A&�1!�5& &�4aboE�9�I?J byNkbyng�m�&;"Z >� $(2� 4�� mP��.&%�6�C67io{ bigg]5ſq"A9 come �$4.A�'�XQ@?�,across��A s. F���UN� .r�n8reuH s esA��fl� �W���<�76��2�yYD� hal��!"r]%?^��Ŭi�R2,�jr7� . W�we �y FN3.@�o6N33 �4^9%G�qBa!������ . Instea�&A?i.o &>R!)2��k�&!k!��l�d6�. ���3S�Y�9toi"=z2�A�:d �u!6�)tur�"�[�Cra`2 �C8 !lidL,�5 repa9sdU@extrapo�Pd.ult��9Q�*� comb�>�c> a�*�  ] &<genuin�\�ton*^?*�Gwe argu]iD!�IL:��&� *� `Uj significa� clos�oV�. � k�R�5cO���+� �#qR~Jbei��.2 s sl� ly)�( NMhOsB��A:���r c4��.zwe�� �� �Tk*al-�A�A��Z�A:It.�fm�.easily:Is�M�V�"<c�Oc)���"e�! �P�3ne;aQ�+� ".7i6. s en� %o�Hm@R 2�  s!�at�K2<�s�� M1)$�{sI4A�exp�CfG@�f� 6]{em_3"b� ��^r6}�P� i�>�2�'AQQ"�B��%piwTa".Ka�!�"!&� �NI�!�F� J��*m/ �_2�s:� !9�a"*� dashed�`"������Sq��E�9G s&� _Q DespiR &� �M�I/1=Z� �an st4Pask�qu�LonO ��.�&� is fault�Nif-�aT���2� �.A> �89K"~HF�}4�om���Q"�H.j9a%%z�f�j�CM�(5B.z� each�Ís��!ZM�ZU��l�!BN�D�#a8�:��  \infty�^2� KE}.) ITApp�cx��.f7����%�Q�. c7on�Dc�cm�� �ce"P��6V";J���.:� >%6��i% inva�l� �1!�-�ix%s8�!n&I.� SCM!� "*.'� �6TrrelevKG�L5�R�2Fsy=a�C::��2}!ų�F� a $0.� �!�� !0� �+.�1T�"� BE2Li6�G�%���f�A~"/ �')��M'�)���� em�p2��D%"�eMwVm{��*��&�"V�"_�]a67E�C!@ selvio���E�i��:o :�)2QfJ9B���E+�t�6�)Q�&� (X��app�Ib�M��f.r -JR&ujpʅ!ONN ��W S1��-~)Iɭm|"m &k&Y Y az�* � _I_C16 is:� <92y.�or��|�2$1^+0\�/$arrow 3^+0.: �FT.|<�qtrend�; �%x :�a�T>-r[a~Esu��:nde�5�-z#)9[^� ��D�7abs�I<re6.�a� sQ*�F!Z�^��> :�-6{��:�u� ��n"��A�k!��t���&� �u"�"E*I�aVb9ten�oA � � !N�>u+�e�c%#2� be}�.m It� ��)��e�Mac�0�+%-lcP��tVp�h�D J:|IH� r��% ct ����9a1Q��a.�� .|is.�. JQJwaGGpos _ �bit{T<}, very "Elb�J�R�A�F�6Z�la�:QaEa��!b���� �)��:cE9*M5La2{p80.179 $e$ fm$^21!|E��5VIRof 0.270?,*�A2� � "G&r E0,J7.dRalKZ ��)�i�:�!�:.Is,�p�4� Be/�Ly d(X�rceF%I Y� .` !s�,���\rraC�:�<E"{ �ef:�#*6� � $e%�m�`,E�$^�c��o)a!: ��1o%h"� N� (.�1 =13$ MeV)l:�"d �d (seepz��3B�� �48&6�Y�a:��5�EV}���B#\E"�&� � *(e2exp}&�L �,ruledtabular?+A+ �� R{2}{c}{MO :+� &� t. \\ \c�{2-3}RB�& E"�!& m \ \h- ^�& 2.64778k+10.22�+ 21.8(4.8)t$2: 1 ?18s+\2.269 & 4.502 &4.41(2.27 >1_^@3 @ 3.218 & &1: :]_9m! ��Xa��N&E����t#a&�?�!�be� -sui�9_~ �E6���ch�linHLZF��ncst�!�2P&i�+��U����3� "�$az�c u$a_0$ Q�&�>O(NT r_1, 2)=C_0.2�-�S({r}_1�W 2)�Ta_0^2}y �Jl�,gFd opde&�,6}GC3��6��:{int d�{r}\:\: B�rBy=1. \] vW�@�)$'nf� �Y)of~yr*+ 1�sum�e�>aXu�5�^|%�>�of�M:�~*� i pa8jp:�]�1��l:U}�&& :Q�a?*�&.Df�D)R�as $(#/k?�.-��} )/ Z�z G��gIB}��we!�ma" n&�&�!�!-� 6�ek�wHe. Atc!�7)!x 6�a�F�!�6� 3 t&� � J� !!=vH�b�o1�,�3 ]eri�IYged �=�a�(CGY uisha��� . Bu�<w*^":*�F)�i*L�can�gt� wh�o#R��e.e�)~�� �5s!lOU�+�]+����5;ilreada1&� IM6�&U�b)E� ^ _�� )E�9(�=0.t m)I6J�2�+M6G�e�;� �l�&!�FEV1!2��*4*;!�����+ O^-ha�G�J� !J>-1� )a�!s5#��#z2.� t��%%�� botv� %�BnJ0�ism A�%HovK&�UN�i�g� pac�Pj6�-�eat�Sre<scU%ofZ"� i/%v�%�Aw")")���q�*be7 e�ly�P��b,�X�,[ beliaU1�o�} a< l�>ve�a[}Iv KBt !J~ &� *V5V�8f(7]�Uian_prc�PZ )(Left panel:^��u� -s�A���"3Naa}�?:���$%)�aB �l)^1� 96"�(, $2�*&�,��$820.�R\!1Ic��}e��� B�� �e��llE�DTA�"!h�&Z�*� U� Y6&TCЄ�C�TC�mC }�ce+"��F$(F|qZ�g@*/_e�Q stig)cw�\�*i _6�FBS&�/ion6e 'B� p�  36�6�MrN ?%�pN�dcc�m4sc*�l�AJ"6'�IYEs�"�e1�nO2r m;. �dIqn Rnr�i}@ch� 2���~ _���U a�m�a�J�V��2�V�$2�Wœ�#*� �28 A%gI4q�8GW� �B��9���\c�_a)#!*z2E\��1pdev��� .F Li!!�Y&dd��*<:�,aE%�s�ca��A�is� \Z��Ca&DXnfC WM/!�R6W� !4�T�=��6�/c ��%�^O2"  :*�6a��%@��u>n A��Ped.�s�l�he J5�Ls4Q)ed!N!�B{)%� a����:� 2�0�B"]{�%J��UQgi�is hyp/ ߁Qc� n, Q*TQ��.Ied is qE Hbf�uOAe3!%� m�łi�k5]��,k �'� �� Kq6�EO�D&.R6�F/Vo g�*y~�.H2:�A!Б)cavea�C�=un�oM��2lA��_ �iB�zyin&��MT�Ec�m�!b2 �J!�inIr^"H`V a����;:�4��,double-$\bet{�ca&y�engel�}. It!��b9;' Larl�p� e�!I�"O .�)�!}�a'g.�Q*�;���8 �-b:J �o2��j�F�!��pl�i��)�� to B�")��f>_d� � plus-� �q kj�U�pBy�tru�a,s�0l��B��@".�r sixIdu"� �U'/h�@, UR�he9g V\�r��o�oFr�Techni�'e�������A� �2�a�:�!r �t6 . N�7the=7," �ReZ~�^Cs�)�N]x 21�!1Z�BhP;J �N&� RM{28��<6�J�:AsplaU "�t role!E�bum\fe�  \:�� I.S.A  B.R.B  e�#�es6Jrt}NFS��bz$PHY0070858?24�H�J rk� &�3oS-�!Oauspic�#U. S. D2'Energ"��& ~�T&�~, ��~ },c��d W-7405-Eng-48. P.N. recei�S�p LDRD@USDOE)BX No DE-FG-02-87ER-40371�2f��!#2 ituta|r Nަar ,$$S.5!WdwngtonE�its ho�+1A3��eVfj �%-�!�dura� �comple�Y%�Ys.\\o��%ndix*&g*� ɴ:#)J*��I 6*a�XMs�0J6,"V*��T/&�(%Nn&�( �RA�re�+;s:�I^OcazOJzA�a���7�%J�X E2=\�Hi "�i)`dir-1�G2�W(-+ j�W&�e2R�[ $8(i)=e_{IS} rbo Y_2(\� r_i)12�XY=D!Jsph h"�pIrA�2�$ O�a9.�S�a"�,Ed�9 (��)!�2�A.v��r�W= rsr_TY�CM��R +��+ 5j)/2$.�@ FEq. (35�*Svarsh}&D<  j`i2�9�2}5zp) + 21� �)"EYE2i"̚&�Tah!���iNP! զ�>��<%J�L ,e Lee-Suzukii�A���n- ' $ -�29B5A���%E\��b_y� DB*�*(>��g&j�ianJ�'at"xJ� F�D6E�tp�Vje*a6�S&ytj�Sun�@>�'G>�&�0��"$�9& �&r�';O�-*^���E�����!hF�0"� 94 jS fm >ll�&1�>�=�.� T �i�Dhe��):qTsubQ�$bo$txp(i\�q\c"~���=BZav/2nRN@m��p��j �-N`����B�_Z6&�J�0�WA�!Y expo �ia�w��B�;l"��8�}sj�&�:5-B�P( i^L (j_L(q!� Y_L �n+ j2j))&�P }[$& & \jk4�� �F{ll'} �O�(2l+1)(2l'+1)}{2L+1}}i^{l+l'}(1+(-1)^l)�0l 0, l' 0|L 0� j_l�M5j_{;qQ$ [Y_l�#)\oJ�s Y )�H -]_L5�13�/f�B)*�  )�i}%�l�ic��h4v'of��:aiYIn��E&}$L=L]�Zga2X��)� A.� issu��� 2is���o�5�u��ex"�Y�'�DN>�"Y5�ib-:O [?M��F pickb spur@[2*|6��":uZu7c�o>� "82&��%� e�Tte�CJ�&o.A la9-erPZ�y^-|���b�mtA��} �olv� ^M"i4CMi�)��:n Qa)F�wV�pg��G2�/I%�div�=Eh���tg$*���j5Fu&�wwIAko� =�@s n�*A bj� [=Ѵ�#taq~%f�& ��,J��*.&& "( i �&�Ieb,S e2ti� 2Aqt F##Fsi2h*[ 2�� 29���� ACb�%�)Q) [4>�C^� "5e�[�'W�� "�T�cy�1}J�  2->��+!�N(\ŭ 4 s�5!}}{3}[ 3 Y_1� ) �FR_D!�JT]_2"# e2*" �W &Uv*$� a= Y_Wij})$��!�(�6�esi�$(i,jFn�)Qm=�1��i]�2$�p. )+)^*� 6^2]A(A-1) '^2[.�!C1b>)[6R &��w�">eUNcF��� �6q7D$:��ٚ�$6�FH9p��T���noZx�\�x, ly":�_�.5),�}�3�N��9L zib7? ZG. ;co�R�U&�:bR#�I��f �� t>2�99�.���t} qOa� Prog�W���.X bf�d, 6�� 1954�� G {LS80}{�DaB�E ncia�.  �hakF� Ann.�6[36�95o�64); K. ~� S.Y.�R�{\bf 6ۗ209��80.Bj5e�2 �82.4v$R. OkamotofC�439�83=Hx�fD�199 E 2); 6���9��104%B9.�"F1 P.*�5��� , W.~E. O��Cn ~R.�0r��-�� 4�U8��72Q0��QRel�{ ��|*�$B.�0�nn!� 5728l0.p�CUN���hC� 62}, 0543��206f&#PD H. Kamada, et. alN���%'Q�0&�1.���>�B.~Mih�,.�C.~PiepeJR.~B.~Wi�a, � News�1Ņ No. 1, 17%12�2�B:� or)~�� 55}, R573a 97).٢��{osneshJ. Ell �c. O,)6Mod��$(bf{49}, 777T7TQ_ &��% 50V.~G.~J. Stok�R.�fiav��, :��-��R5Q�38v95); >3B�Pud�3 r, VE�Pandhari��eE� Carl�O>@Sj� )ّoB�>/J�6} 1720,�7);>3a�Q2)� A 63�70cC8FCSj�B Annu�ov.lart!w i. 51, 53E�2�bA��� �5A� R148I�6F� :pF[6D0~�ğ2�q8 2003EНr%� E. W�M2^Qԥ�034305%2�*� } D.� J.~M����.r,�"A.~Coon~B��~NKy�66^����2.�GK�.�,��Var�qa�:pV�e 044310�2f&j� Ae Hay :�mJ�-j6�9A�01Ո2R1�1993}:bH. Geya�l(T.~T.~S.~Ku����6i B 31��j9g����t�?z�2dYW.A�b Y�o6^8�15�24m�`}M�sha&j=b� o&��inarn phyn�;D atom 5T ks} (GordQHr`G,�T$ York, 196!��{�R2�E�it�Many-F�RDy�RCode}ΜS�&.�J�� 9�%:DEZhe�cibid.}3(4) (unpubliJ.�&i\ I� ��,�f���}P�ACe� John��U&m"�"Fd�$ E [arXiv:�H0-th/0409072].9-�:��AjzenbS�Sel�S�>�A49 Ef8�5w&p$!*E~$�� ogel6&)2 bf{6�G�s4e�2$ �D.a�V�Xalovich, A.~N.~Moskalev @V.~K.~KhersonskiiY�Qu4cĐ�A�mM�mh} (World Scientific, Singapy�1�, pp. 16���t:� � doޡ ]>>��12pt]{� cle}.D�VZ�{bm} *O�(0in \headhe�.sep odd��7.2pt \�CF $par|�\Q�I n200mm  314vMn�x=1� 9 \new@wë cd}{#�0box[0.08cm]{$2$�hler�EA6�}�U& at RHICg��18�:Xiao-M(X${\rm u}^{ a},b  c}}$} \v I4:I$^.a}$a�!�)W Divi�$, Shanghai*"of!!�+ 1�?ȶ�4Chinese AcademE�E~c�rO.a�800204a2018006� Ja6] �b}$ |� Oak RidgeNg�6GMS-6373��O.�0r�C$, TN 37831)6> �c}$68$ ��&<$, Baoshb� 5V�(36,�1a"]�\^(!V!�=%�4Triple-gluon e�y�c�re brief:, view@a�,�+ �\6)[..�puzzl;Au-Au coL $IQ� �gi@�A#-�!�0A/v��#�h+ J� � demons�;s �"�isotropyQVd�p.} �+�C(65 fm/$c$. 6K.pt�� a�r�}�zN �%{���%=� left!�({Keywords: ~�;J* ; tA�"����vsp6 {0.5�l�1�����M..Had�dsn�ra!1low9S�)�� QH",e dis�%ar��!/tc&3,�oö jets[ �jet isR-�+ mediuȮ ��b6."of$[�-�Tted inf�S;b�v*�:"�N*e@��A�&cx d s9��)it�Y�C*�n 1M� [1,2]%|eS�"(*gime n��8midrapidity [3] �R�0?�^d�6: �-7%hydaj 6�[1,3-7]�in agree�Y�� ellip�gfA'�3 [8,9�D$p_{\bot} < 2$ GeVi]R�2�>-�Jos,o ��3%0 [10]. Wh��i�� J!s +��/�4�w ��? ~0Ni�t�@L .1g ��� w�9A- * numbX���(1igh. To8/u�>or ���,)k%� IUd K $dN^��g}/dy>�m 1000$e2*�{M� N��, [11,12]. S/5a v��aL�>s��  a H:��i9]38 �(fm}^{-3}$, !�C!wX�t..\oL`6�n�):yg�U�,r,2�.N b�s�55�i[RB�:1ϓcip�^Eo�ly �x whel�$Q-� F�S in heavy y 6_LH�^ � 28�]&H<�52���K6�2&f> 9�0>�%�e � 14V!� [13]x-;!�-���og�&@@~W&<F }m{\�/e��s[� 35mm,� 5  �0=0]{bsim.eps}C \h�� 1cm}D�X45�Z^Z56:Z� 26pt� 64:X.  �-B��^.^5-1T Q&�FB 1: S*� �) _ew_Z� .�@& 2.6��'B2 �i3[ a�wo 7a��[ �� stud�8�0erturb��QCD�Cut3:akSi��0 [14], Combr� (, Kripfganz' Ranft [15����}�B��-averag� h��4mplitude $\midقM�� \to 2} :Mo�7��J?s at Q $\a�łs}CN� X ?}r6 tuZ%�e�delstam�B0Es."8`2F6s, 4X}��e�a�%ed by��s codw> S�d �.�!�A4F���&��d KG s. 1%�2؅� "�O���6�3%�39�� �5 �22I. AI�Z:r-* x�As � �%}=(&� �*�%�i�!� ,ss ��g}(p_1)+' 2. 3u�o 4.5. 6)��4n nine Lorentz*�� EE� �/d a"O$dis�4��} s�=�+p8K,~ s_{232+p_3)^2313+�}��.[�.u_{1591-p_5.T%6%6�^2492-p_4b^2 ^%�^3 ^3r^3 �%ᩂ2��_]>?6� �:pr<�V�&nm�v��r-{��?(\leavevmode ��4B"4g��F\5n\�6>Z�&�0  20 &3 e1t�+�k2zk�n6�O�1�Ij B}_{\sim� }$�n a��ble� tH� 4@s�:���� four��C1n�;e �dag��.�Z?^�8� eʸ�N��6���a� 1 �V6/�4nI�$3ɯyb $��$,  23��s_��%Rk�tezmqP{} e��� �)0 {59049}{128}�. �g!�rm8} {( �+��31})^2BA*�&�@"��t� ���a2� ���n�{ at E2., ruw0wa� �2di�Vt �� mumi=��lA= babi��F/�@ru;ds, l��>"�m�!�tD=t* �&0 �d . He��k�s!��$Brk:��&~A,MM=� 2 =4*6� �6 =0.3.gQ ���vc 3a�2Rof�~Bi S"�~ "��IA82� e,�%/�%�%�@of Boltzmann type)�uN$� $*�� ,yT ++2 m8 3 f_1}�+?� �/ v}_1.���blaAvec r}@�7 &0, Ψ = �+:�G}}{2E_1hA22��T �d^3p_y�$2\pi)^32E_a�frac 3}{� 424�� -4��^4� -pO4)Y`\"w�� �~~~ہ� ��:� 8 [f_1f_2(1+f_3) 4)-f_3f_41 2)]�sZ@ U2B33}O�CrC.b52b5}2�626!!Jz\b�'  � -p_6)�(8�2m��z�=�-�f_3%�4)�5 6!�4f_5f_65�3n��&�/w�,�H 22}=.433}=1Wde�8cy-*��G}=16$� �]veloc�B mass�ő :a�=1� di&6"7C�ci}Z�I ����_��M/X,������)*� $ ��$t�x�<7v��3�c-e -B��eA/�h�,Ʉ�x-��n $m�$���)�L eY� p is af�~�. "Ll `�kU;oixJG���:���newc�uRQ� =��r ��e 1�T~� Bl >l::$�}a� y��YH8!�� &`IlD/nhaV�run��i��f A���<i EJF����;7��Asr!�\�$ &`~� FM, �ply![_Hd)�)� assu`3to/�m3ly�GZa cyl �P.� � }F. Cp���t}��i�Vk�� ay~*qD magn#%v!TlЅ��u�5!^Q6- $tm�na�`X ���-!��BngVC so}$ C � B'Oc/�r �r I�%�G�Ra2�;J� b�6eg�9ed�Gj��0.7&^#&� pini���!�e nY� 3: G� V�saHsuBe�i*ffe\ "� s6[is��Gde<-3>A�� dott�2q!� dot- cur-kcaA�{s�theta =0�o��5 95r*��)�solid gA��d�� V,.��2� �yq:�!A�$\V6 {s_{NN}}.%�, A3y�I�6�oQran} uIa�rO�EC4)a�� [16]*g �5feC {p},}w,8 {1.71_�10^r+� {1.5}} 6�G}% R_A�5(�O� /\cosh (�| y})+0.3)}�e�J3 (0.9:7)-J\ \tan])^2/8j� ar {I} (Y^2- ^2B+@�F�� in�,A -)S rx�($R_A=6.4$ fZ!��A��# �a6�is 0.2� a{t�� HIJING Mq�/o�u�5 [17]� $Y�wmaxim5��eTIx^�qu^@5�\n)X step��"rz��A�$Y�z�!4�<�6.2� ���\&� �TQro"�(studye�V�)pC�ay!3�'BY͊QP ewed` gauge*�BJB�!BJ�alW_24�s�Abn�!klow�V�!4$.�w!qb% F��XJO� con&y E.�c�SjE-3evo&Z� /&�do���M�N�)!�� /+6*' !� �P�6� w:� si� �J%!"��B:eI)0.4q7-V�de��ZFN#of�O gluon matter at high density. \vspace{0.5cm} \leftline{\bf Acknowledgements}>/�aX.M. Xu thanks Xin-Nian Wang and Wei Zhu for comments. This work was supported in part by National Hural Science Founda� of China under Grant No. 10135030, iR0Shanghai Educ A`Committee Research Fund,.8(the CAS Kno)  Innov BProjec v,KJCX2-SW-N02BBDivisio�\ Nuclear Physics, Depart!c�Energy, �Contra cdDE-AC05-00OR22725 managed!4 UT-B!�lle, LLC��Refer!Vs}!� kip 14pt YT[1]U. Heinz, P.F. Kolb��: R. Bellwied, J. Harris, W. Bauer (Eds.), Proc. of}Z~~~!Z18th WinA�,Workshop on -$ Dynam%%$EP Systema!1brecen,.�@~~~Hungary, 2002..<[2]E.V. Shuryak,a.%�L. A715(2003)289c.} �0[3]T. Hirano, 1Rev. C651)0119016o04]P. Huovinenbn9n.l�5]K. Morita, S. Muroya, C. Nonaka, V� C66�2)0549046�(6]D. Teaney%�Lauret, 68nucl-th/01100376CP7]K.J. Eskola, et al.1Lett. B5 �3)187;.�~~~R>!�F� 561c6}<8]K.H. Ackermann�0STAR Collabore��%� � 8%1)402>�R� SnellingsY��A�Na.� A698)z193c;}.<(~~~C. AdlerZNR� .6�7U1)182301>��V] 3A ���90� 3)03�6�$9]R.A. LacAxQ31ZPHENIX>�Z\ 559c>S.SB]VUF_91 �)_.2�[10]X.-��D, Y. Sun, A.-Q. Cha�L. Zheng6� A744W 4)34:?116@,K. Kajantie, Tuom�+ �I�B49M396[412]M. Gyulassy��x L$\rm \acute e$vai, I. Vitev, �vqlB59�1)371B ~2ZCX.-N.��p�� 2�52mn3�.([13]F. CoopaE��tt�PG.��a��6N5�f�T:^ 14]R. Cute^ D. Sivers2,D17(1978)196:A5]B.L�mbridge�Kripfga��J. RanftP)� 70BR 7)23:e 16]PV� B. M)�ddot u$l�=P-B��0C51(1995)3326>�7A�5�2�)7CD44C 1)35F<~x6BComputQ% un. 83L 4)30B�2K�p. 2804 7)28a, \end{docu�} �'%~ \2cA��L[aps,showpacs,nofootinbib,superscriptaddress]{revtex4} \usepackage{graphicx}2$dcolumn} ~�� \def\slashchar#1{\setbox0=\hbox{$#1$} \dimen0=\wd0 %1 %/} 11 /ifdim\ 5> 1 \rlap{Z to 50{\hfil/ }} # Aelse V21 2�5bWe presAe� resultE'a>� ^�YrCJv Ys ^0 \��M�Lc^+ l^- {\bar \nu}_l.� / A�V+,($l=e,\mu$).�w>8on coordinate s�, withM�$ wave func0s 4tly obtae�$from a varI�$al approacD��on }�$ symmetry �develop%D vel expan�!%@ electroweak curr!��(ator, whichleabed �qF��1@raints, allows us�predictz1,form factors�!��$ distribu)� Tall $q^2$ (or equivale%2T$w$) values accessible(Qp�al Zs. Our Qe[& artially �gra�longitu!ĉ�trans� e ��TstFvicinit��V8$w=1$ point, ar�excnt agre%\)Z0lattice calcu��� ��pariso� our�]�-$�!qexperi!�!<9�exe� ��V_{cb}$ Cabbibo-Kobayashi-Maskawa matrix eI%1IweM� a %~��| S,| = 0.040\pm l05~({\rm stat})~^{+0.001}_{- 2} �(ory})$ also!�51 51 eIam5 determaj�byE DELPHI6� iT8the exclusive $i�� B}^0_ d}}�% $D}^{*+}l^- ,�$Ijsides%%��Zb (�6b)-�,>V YV am�iea@ndF1to]�I� ] A`8$\langle a_L \r =-0.9541�1~(452)$ ,.;T ;66*;628;4!� e� jN�nA n� �dstill needs to employ some� FB(methods. I!�"�!, &)bB{corree ���."f�:!by us!��7 �Y�use� i) I�QJ--body >�� iz^ ^ 1�j^!���v&h\�,note{In Ref.-�Al" %Lv]ed�a' q�)�A�solB�three� problema3�) a.j, wNwe�2madaJll%O闡\ sequ4"�� at s�!� $toi� �pro�U prov�u ��e:��lh���"�orAA %�rumiV!' observ�Cs���� quit� lM T"$ly Faddeev2� da(in~\protect� si96}#"�.�. h��b��^� b��*�A���UT�$we keep up!� �� a�"zE ��(small)2��EX�L� , bu TO�t ()F,$\vec{q}$. S��p }ry��� �i)�beach04}2#w,�sh� furE� s�cal O}(��fccuracy�E�g am�!C2ZtoMrov&f :tae paper��organiza���. �M8Sect.~\ref{sec:�� �F��their� �� �i�L�!2��yAw� 6�QCD>�s6� ��� oE�s�A:�nrcqm}!� Q3�Y"�ES2�ɻ63 3U�U�&b (Subi=e me})� $brief summAg�� AX� �ws��jis�lOin :�hf��u M%�ma�dn'ons6�Ns�re�2#cl}B�Fin�"6 Ap�ix��detailed�mulae �b nd.*D.� D� Width�FiF_�% abelY� % �w`focus � Y, (p)6  (p^\pV$)\, l\, (k2@ (k)$ re�on!d� $p, A, kM�B$!cE�-I!a1�inv�Pd& ticlei�$ generalize_a�� 2hQ��6e isa9 forwarhJ9�st frame�:.���i��ds��equ�} V0d}\Gamma= 8 0^2 2P G^{\,2} \frac{d^31= }{2E-x&S0c} (2\pi)^3} 3k,_{\nu_l!T1(Tl} L W04 \delta^4(p-�-k-BP) L^{\alpha\beta} W_6 wo"9%�&t We�take $=8b} = 5624$ MeV, 8�!= 5800E�9Xi!= 2469  .} L�c < 2285!��$$G=1.1664\�$s 10^{-11}#$^{-2}"�F{ IJɚ ant. $LE� $WY�"� ��isu�. �C6� = \over�${\Psi}_c\g�^!�(1- _5)_bu�J$c-W b$�$fields.\\ ��aJM � ��":� ' �!{ 6/�l�-, $6��ch wr2nTermF six 'arig2B $F_i,G_i$� ($i=1,2,3$, &� Nm\BQV| j�^��FQ5, r[ =1 u}.�^{(s)}QJ2BBig\{ -Сleft(F_9� G_1\' )+ v.$2U G_2$v��N3* G_3 +}}�1�8b�r�)�a eq:def_ffu�Q��� $Gc}Mtbre k)�#less &� U��,$ Dirac spin�Eny�to��$$u} u = 1!��%# = p!/2j�. = "� >/ c}$)a��V� ��� *E (c$)��.e]2�!&� JZ �Dfer $w=v�I�$ or \"$$of!B q^2=*� )^2 =.w b}^2 +.c- 22 c}w$B�O �C ��cBE rE !�fo�%A  s� e��$�$ ���H0 est=0)� �L��� $w=wɲ�!��) >)/j\�(x 1.434$, t! �h6eF (8z t!fer, fD9iat< tj�1$"�^�!6g�%ly $(� _T�nd .�#. L)�%lar< $W$' re � , negp'`X !��# by (A= tota� is $ z= _L+ T$G POL}.��  {��l _T}w� $G^2*� }{1A ^36�P^3\sqrt{w^2-1}\,q^2 �d{ (w-1)|F_1(w) |^2+(w+1)|G� (<} \nonumber\\ &&.N�L�� 24\pz� � �{U F}^V(w�+ � F}^A �� 4M{V,A}(w)� Big[ 6�%}Ic}) F_1 8 + (1!w)��2) F_2 (+b} F_3 ݟ<], \quad F_i^V \�� �, ~ ^A  G_,~  .�gջQQѻ� last�rk)7,+(-)$ sign g toge�r� $V(A)$ upk ndex��pa7�l��&=G�A�2� �W2@^2i%Y@\,qcos\th�=@ 38 )v2D B21 + 2N%.� =�\{1+2� dM � S} $^2 �M�$'&� 1�$ &"�� betw�%$� k} |$�E 2 $�# 1 he $�0rm off-shell}2� ��$ � �]6�� �(y "Ps D*�exELuR�aU qii1�O6�!�2 d}: /%a���� ��a�)q�~{= - $G^2�&}{6�� M�}�c}^3}{^V�� q^2\,(��)\,����}�asy1i} F�)o6�)w Big �5� -�7 ��J�:�&� ��  ref �R� %suc�)�'"?cascad .&� �a+b� c$aN J_a=1/2$)a� $b b=0re XL.n�(r�(Two newi�� usuA def�, $\T��_\ $�o 1�e� / _um22��a$ �.: V r� #�- chi$� J!DazimuthaV/gl6�C planes ���t9 �"$l$�,nu$Z �N0 �a,b�E t6��G thZtw?"leUa !��ݞ1�} � pto 1 + P�-e� �. ����=� rh��j- :3��2}{32�  2}yͺq �chif�2�ٱsy�2�_]Qmic-�(��H 1 I�_e�  \piѤ.  \S� Ohas: ��*�^+e� </^+}T/4�024�08}$�w+93}� $l/6 � 0.42$ARGUS-��ft�� pi^0u45 L32:n)�P_L$ (l.�2a "oidaugh�B=u��)���� � %26&VA������F�+"��6i ��C6 �)��TVuTn�2�v�e q���.`����"� �  � 62iN�,=�- V� #6� ^3\, {q^2��}\,j \{r 2��-� %�� �Z \)���J�:)R/=J�7"t�2G  Eqs.~((!eqd -.f}ebF)2i2)2)r&o ���vel`"�"7(. On averagfovvhe nume�7� deno�" tors94��6s�Gat��  th %z%N$a_T$EP*� N� �iF�� \int_0^{*�} j� �� }w.�t}�:s�*%5r�q�z�LZ����B! �m�0���G^NF 2� )Zl} arNnEu� �^� 12��m�2�Z�EF1$a_Tkle}��6�, * R{� �I=��1-B } nQ� y`.�+ ��a_L� � !>� Xi$L}{ T}��rl�=>�"Q7B?3 W�3F�+�b3#% ;^**�a6 aken/K$previo�9 =iRG* "D"� " i~@Hamil:@ ans ($H$)3<� �($q,qM, Qw ith&P!$l$�� .�%,of flavor $u3 $d$} $q, P =l k3Q=c $b$) U*G�ctypR H �i=�Q!�eft0i -i��0\nabla}_{x_i}� 2m_i� ) + V_{q�(} + V_{Qq}+�"=�=��B"�ab#(a $m_q,m_{]; E.�)cFBas�! !%\- �W�,, $V_{ij}$, �4x% 1�--� quan�9I�a &^?A%7x}_1,l x}_2 �h$HB ]2 %Q�� &�" , see Fig�& fig:x}).B�$$figure}[t]�N�?${-3cm} \ce=N�g!�Es[�D=25cm]C1.ps}�N B15 Cap'!{U�size D�iA~yD��>A�!�a)oug9Eis a�.�x�)�� � %_'�(i};insic.�} ;'�(�0ub( e�!�proced�5f@* +AC.. To g3C%)� Mass (CM)�1 mo��#w�6t� lavS)nU�+R},rA  2$A�IRI�,�/��he CM po�;�LAB tM�"*�+�$qXqL$) I�6[�,U�#pis m��Q�&� �o.M�L_�YR}}�O M� tot}�H�int��E eq:cm}\\  &=&q#.�$} h^{sp}_i>��!_"r}_2,a�)"h!t �1�2}{m_Q��Fu�= m_i &4#hu+� ��y�W hi%�#i\�4i � r_i �I uad .� �cdefhsNa%��$=_"�su�+I�5$  (m_q�Q+�Q� )��$ q,q'�5 .���8�'I�I� �{1V)=�Er~-/\p M#!�y:�#Th�-B $IE8�escribese�dSq ha4w�� �a�a*�Dto<2i:Al02}. 6p�� ists�6-a��3l�.�&le.8�.Q"�ich6~5>�*4� � mean$ c7�<y`�-)� , pl�Dhe D-- K>� �$)A$Hughes-EckxV term�� -�1 e2�� 2 �FIn?U.��s��l �F� s, fT$�3��?50ra��r-�to� u. �%�=!�bottom-� I�s&1�&ic"( magn�?�+M%i�,F1s.s�9 �-!tre.�Hsٞ"�{d8��\XiJ� HQS} TQc!��9B�A�Eq*��`fD insp�7R��7z choo�%lfT �@.�6� . AssumA#t�g~< a�U;a9)�in s--I�a�6lete U�)} $�% un!�Nexchan�e��)`%ӡ�u,d,s� ,. o4 N�(BB m�N)J 6�� ad ($I$,P$S �GC�� so)�$-� � 8J�)"� {An ob$ not�� �@�<� q- ($|I,M_In _I$, $|ls� $|slq �($|S,M_S_{ �}�'2���% J�.5  $itemize} \ {\id,w-$"Q5: $I=0,~ } ]%i=0^+$S&� | I_Q; J=/12, M_J .�!"j � \{ |00(_I \otimes - �} @�Psi_{ll�* �� 4(r_1,r_2,r_{12*WQ;�R &� simu ��!IPa� 6�,�c&:� aq� $s-$!�S?,T!K<6`[c# ances $r_ *$r, $ �=|�  &� |$� �?5-> B= b;!7!?%;$(�rjB6JB�I I���B$)�j@ 4@. �. $M_J"� ��> � >�third �@ nenty�Not� at��3��"��2)7 cas��e&�Q$ ) would-4�;�2�zz��AQA �r��B�u��} m M_SME�mh 1  | M_Q J-a_6^u]|1 M_SyxZ^ � >Mf_i^Qm^*�Z�7��%�(!�h= -j�:��inseW� �5 ��ah-r��%e� real� Ps $(j_1j_2j|m_1m_2m)=% jm_2|jm � �,Clebsh-Gorda@ effi�bt Y�v f�ddA5%?�BD� Q �L\inftyN9 6$ tur�u!b��lE��sepCfor&# Q6 .``G�8a2)2�A�"�@ �99 a `a�cbPQ�wo�es, � in E2����"&� ntis�N&�+0  2 etaZC)$.` ,)P�D� �-al� �=,�&justifHHa�B�D�R�� � �*� �wcTP]�@"F Duree bod"�A. Wit ?a�@2 !�S"o b�P��'s�lJ �  unalt�$e dueM4the orthogonal�4�� , tak� into>@o�NsM� }}pScF�zq��Q$6_s�D6E�)�1�^2!�^!Q.E �(.�2�0of 9�A2?&2).%M\. Xi6 �n, ^" s &D|�B �Tn! M!1}{�2d \{ *P ��s�Xi_Q}B�- *n /s* V/� } - |00���#� &� ��J) ��*���E2 �YQ��,��T$�GeW�5E�G <($�'R2$- f�C5E�d@6�>'��!� H sN� &*Its"�3嘡�e��# 9���1=� d^3rin  r_2 %� |)�&6 ^{B_F� u �/= 8y$2� t�+�0}dr_1~r_1^2~ k:2~r_278{-1}^{+1} d\mu~� ��� �%E�}h\mu"� c��%�(a��� '/�$.}B)� ~�a��<3]in.g �G�.dprinc�P $ 9 �� B_Q |g��}|*)7�L8.- asilmDc�&K-A�2T 4s X.XI��E�re�Lce.�!*A�"4V� c"�7*�7,5;�5*r�7� 1j� �>; �6�.�;RB8 Xi_b��:m�($ Matrix E�X� ��Dqm-f} �[ill9F^�A�� c $:�9. ��I%]!{ ider��m on�I�9"L[s �ect�R&�io� X#��H�2�+!�JA��eI</9�<\,',s| j_{cc}^\~) (0) ">b�<0},!��A>&=& ��!{2A1� rime"�Oc}�&a��t q_1d^3q_2 h �\ .\m_b}{E_bq}_h)}j"Ɍm_c!c!]�)$ Big[�8{u}_c^*3:q.�_h)4#11"�9)u_b^{�9 f� ] .�4&\%& [\phi^�.2O1F�Bq��>>�]^*\, 6VbV0}�.L��%3�>�eq:me_moRS �2�=Gp�=q}=�q}�u".�r$uA���-�O6u:� � "� ,�- um s�A�eae6v :� eFouri rans���*ose-&��Kc2#� 6]Q1]P-� q-[ q_2%Z q_h)=���tDx_1}{ DI� 3}{2A�9 d^3x�J".DhRD e^{-%�!�& � 1+%�AL�� h2h)}\ \p�,P}am�QM�,!K h) :j.�!lF�9 ��"�� �8 Q M�Pc<see6e cm})K<&�B���=�' e^{i�P}99R}}5���)�} y�AIllB J8iPs�=$@E<mpA% ��. + actuPa&'`e7NBm  we find�K��InH���H7 �H�G d�  2 \,am%�q-��/�+ �$' &� 7 )/M�� ^c} [6�c}>� ��n*�:��t\$ M�� �� l}\ r�l�v�3 �D��{�]Z Y 2u�XJ�2CN�A����c16 l}=.�|�_!�}+�* i)�B!?H�_ O)ɘl՘$ QC�_� 9 ��b$( �2t"���� ɽ  q,q're�up�1 down  $M^cEI AI,=m_u+m_d+m_c !$�=�NC>dby�--�   . z � �  B| � � &\R� 4"�M�',oxT"�&�� m_s!8stead�� �DA.�.&�"��6��M&�H�% Q(jI�&�M�ZE"�f!�F&�M E��6� me} T�I'q}��h% ve $z$ di�UYb�J2eng�h �  Eq&�/YOO� flip�3 = 1~E�or}~2 $�&�E2*0-/i =3$&o@} orm ��f$F'K*G ca&� C �!UlI� q�2Qn@]f��  h!X�!��z�c"sX%�!2� �I�^its evalM  fA� ble.�u�&�+"�PT�0�d� a��B�N*u�8per!'"ZX HB-NRQM},�S�m] j 7d&�[e��B$�- t�) �)}RtabZ(}{cr|rcl}\hJ &&&&\\ \Q`}oD{2}{c|}{Vector} &\\ 1��&Y#I$\,*\6\hat{F}� 2+B &vN��c}>l 43$� � I}+ e �Id 2}� K}}{2(E_c��)}�9 sb  {E^2_c}!'1sbd,)$ \\o�3$,R�&� <q}\,|}R�+2�0�1 "�52CV.) NFBv �I}D�}"�2Y &%$}/Big�4!{E_c^2S' `- ()$J�^M� \!,-��$�����-N� x\m�"Axial�!2 �% (-e!Gu_G}_ T�` G}_3�)ag$F+B62\+U B&I\A1�Y�D) R�| !E�^� - �2aݝ_� N6�� )i�! !2�)d2m}[� Jb� :b & ai�m, ��n� ����Q���(m5t�Q c�.} \V�/"��dU"2_�E"N! � c� F{Au# hat}�6ao� u[t�0l 1-�  K}$ �&�i66:� hats})--(>j��tab:eq� � % t:�� !hO@�?v  BI is �ft�sluum�is�(\R"�(= *)�*I9�o�F handN %w\:�<  co�d�Iu�\a G�qXB�Z�fMby"&-c1,+ l�j (notA(�Q�z=2.w�;)�0M�9(2�K S [Qz b}/2^,We�_� dA�_G%+ � 2� *Ks�d�)N.� l� but �]� G �)%q�.Fo6@sy!!�is �7OA�%M�� �*A�gEf� ��)9I�&/q}/#? \,))�c�] 0&B-�rZ�I E_c = (mu��2})^{1/�/ T"�`t�nov.�s�.�bOR"; Z$} )jT !4 actly tre�, weTB ��.�sdh[n�h7 !4E�N�hV�a)"�\ , im�^!�"a�anner o�m?jz.�*� we gn"h#\��+ "(v� !a�) �" ree"7s�unmk ns (:� )�,tb��1��A� ese �� comp�\in�<]�,�f��%2(R����.6���%�a#n0 &j {o  F�3^L� S (}�[}V�[�bk12� ��2E + � �-�L�, ~ �G�=���� �G_ �\`4�S,2,.�M�P \\ �I]N!b �!1 �(�(:Zg� eq:i�K�)��"�c�\,ai� � ����� [�l2 \,] �*oj# yR% ��de'����;� m_b=m_c=�;�.q�"YE. E.�� )i((rel��ie $21 / =Ɉ6�6) /s "n6 +m_Q!as� deduC�w a18���� part�2� $ By O5@ l S ave e���aft+� littl�(Racah algeb�4��]5gr� get?�^�y�gt'd.�l8[2�P�flmŔe �b. ?�1 �g�-m)2$F(1)=�8i��1)�& Rk)of�ul1�]1� �f�.��!6  �&s�$6k]Y�hI} (1) $>. �z�* |=0$"�x,Q< I}(1A<cq's"R or[ap2]Lf �7ndx& 66�)Ÿref�oit�'%8|ulue 1h�:,�'mplishbkexact"�\J��>iSl,  �!5�for^~�)A\� riM44 $F_2(w)=F_3(wa � p vioeiJ)�*T)a�}�5 ion �/"=� �= �h�i� � K+recoil,���1)-�1)= 1-* Q}.��Edo�ma%66� beca�*? bh^ng� . �NI*�la� bye�r-Jo8d�mA �+n!�� e:��W�)�X|�7bt:ca�6ntiG8WB,f �Mu�b�t!� titr~}sio�%�5e� f S�@"k$. �/G(}=:���f ona"�a5��4s, henc�E �dof cl*6, �jnow#we-!�-"U4�I}^�}"}$ �-��Xi}"(A*� ��1vs ,�a�Vila�o�4aN� ^Mͨ.p��h]@�h�*"&�%�h When� 8�5le 7�W"6��8.�, )n�"�8�-���6elU�g7l�X�6�@d�� b�:� s�l�"toe� i� (�lW.atJ^r!!>���a��,"W&*Yr(6WACe�{CM7�m-mt J|r&h*]�tho)Bcal|i�� ame � , � y&vBI� clou)�8un�%�(tZ<at a�f.�${|VB}\toA DyDr�\toDh D}^*6�x K2 .}f^xy!rm ren�6iA2qu�;2�s�>�&q>nJ/i�B qs�, fs!��B*=" t($Q6) �5A�{PA�*ms($h�\��A��<� "*Mt�n 4E�L--ms,: 6It��=�MDe� �%in�=!$�ill�19�a�-.�sAyAM �ex�(i���̈́�>�qAM�9�8"( hD%`D�useful�no�*�:�W2,Neu6�9�{. m!�_l6� (cl�g2u�pE��.  A�6�f!qmvx&�EM�Ny#F_�[?N X{\xi}��\T�0�A^ 6>G 5= N_i^5.�@\WJ�[�e�bB�N @&� Bh�2q�+0�\�bQ��Hb}"=Bck\�#[2 6D\�fl w-1}{w+1}B� $] �S �xiJ I#A�co&@5s?i,!�^5An� �����5�6qcQ�aQ$)�X&j !�d��c�r2~ ��/Ou3$!!no U er aVyxa &�* :�� s�e|Gom ��� "k*%-�u Lag�;ian�F vanis�~t� . Both�s IA�%�2���Vr�ito�;at * �n�Q��-�%��ӕ�$N_i,�@� M !�<;$A"F "� n&}cisely E��@�ū��(:�nw})  4.1�>�}�"sDvYJ�����all="S~!f$:e�l?,�^� l{� \n ��B3 �� t�,Z���w��7AV�%ones quo�16+Dٿ^ .&p�{sm�uT/2�A6".hc$�v�9 0.07+ 0.24,�F�qoA2�, Luke'� orem�2G|n {x�� $F&�iO nd $�U$� O&�v9@2`�$} :S�= �9_V+� L�$ t)AF)"H6g�s0V� eta_Ai�entirU"�dMsh:o\?�eks (H�$N_1^5 ����%1� ey=i�m' -C ._$)m}A�i(&lpl�;e��A`&/uted  (pertu �,QCD techniqu�GAi�r.�cm�bex d�wC�a RC .� (��l^22n)�T "(�Ma�k�|�w2k�y���= n�;���2�e� g��X�+� E�$r�2� dg})� bR�P��im_{w 1�/��U~��ddd&�d}�K�>�gV�f .)fb}�j*�P�M�^2>D c^2F�"�t��6' |ccc:'\A� $w$�&A�$ &2$ 3M�N_`"1`  2 3^5j%�'\1.00 &Qj9R-$0.36: 810 &1.03 & 0.99O#& 4215�! 1.11 E0E!+ 09 &>E4E3713 E23 1.32E�.E �1.E4 E2 E3# 1.26E2f E8�� 0.88.E 11 E4T1.2�25�07E88v85E2 10�'%f�"��"C"M "T(* V��2"c�* *Ef�la�y� -L�vm�*q�&%nw� I� "[R�a�'5��z�Kzd&� i�Q���"�2 s, .n�����Ts wNu ��D{%�M . Fou}""�� ��9,"��9 them� AL1,� $$, AL2, APP2��Bu�h�}f�*\had�Hadj+�UNJ 8BD81,Si96,BFV99�Sh�-t�%�didered )&��!�U12�Hhy ,i���rLSw �`co��&� |for%Ghic�#([� E, T�ot^K�oo�@li{/"��me�Z -� � :�~fea��� QCD-& Su95�� ($p=�&$as suggest<l�� .� @GM8�$or $p=2/3$� %�1u� y�^(ptotic Regg�e� orieYFabre88��I�=�B =�1�,One Gluon Ex�K8(OGE) Coulomb p1� � Ru75����m4 \� reason�jE�siA� Kc1�ii y�, c_Q,�c^* XiN2s�  #Omegaa�� �1 m� �A��Cu�pay an���ɊA=:AL1�ALm��'�5<Qhe'���on a ph�_enolog� �qJ a{ M("VRa�� a shap)3Hlor~s�*� � OGEa{"܃,%?����G*�:�brancTmXI<ikE!oe+� 2� !��mea�inu�to be�H�"a �X } Br(��f��Rj�� ( 5.0VB.A�8}\, a�F})\,  6}_{-1.2}yst�M�()� eq:brK�% A�FrkAEj~7R�%OFJ *�$)�O �(�J.�-, i.e.%k@&14�*  � � E,F[C}_1=�$ ^5m E ! {2,3�7.^5 **a" Œre �JN�K&���9- �\rho}^2�et\eq:�,9i~lso�N)'6�Ba� � ,�!'&��B$6�C� slo�� orig!� ,&�&6&wJ���&�A Eq.(�*ded)M�b���2��E�0.8I�?� eq:rho_N/�=+uncer��#RJMgY��Jed~ �&��f�,JwSPdY0 Data Group i�BU� V>�brpdg�+{~� anyt��}.9.2(k2.1)\6G|.9�!I yia�rdl;8nSZ_�Ia�S�6�,brLverthe�y, n�MKv�"*�:�g?aw~U5))��C0 �8�d�dG��D<"��$an error w���n hed�+y'a�dE�]��u |ca�od �.ematic ^i2:�.} )I*i��Rfl�e�.,F8 avg~�B6.8E#1.3f#.�@�I�/& ^0Y�y ��"t��feCD $\ta.�}^0�1.229�0.080$ p::���A[f�f�MVn1.41 $ 10^{10} sG^*A sml}>�% B�, d�4 $Z�$t�� ղ�H� s j�B}����8 se e�$ � aGq@E� CKM 6�� $�uToE̚N�) ߠ141�01qu{��aF��o0021\, ~\, 68Иy8=mvcbJm Let��%(xa��&;*e��/��X _2 ;�'H�:�=�2�#"'Lh+�6!e�n%�K2?>�k"��A� AL1�k .� (�I�.�A\ ~s*afu�"( \ �edX%an"�Y�"��M =�)/� G_ ^5, F/�\,m$)+wn4�� pane�� *`TD&*nw}. S��al�S�17 �� :Y�"�N\  A~$ec�;%~HQ"�2�q(�]F_<$G���$G��hre�4tR��.�%�domin��o�$F_�M��G_� �Re�$A�!*discus ,of F�'me} �(�Ԧ�er�AVf-�mus)"�Aa ~iR\F5!cY-arFm'�!� &all*�i=�z�rƔ�@)�eA#ed !]�&et�2�"w(O�9V * ��} *��Mhem. PWBmably)sheX �"�!]o!#!�&6ax�>.=Z^ ca� ly s�|inNRA!�$6�x q�sJ-AB!�,AUJ�:�."4 �)� �aS�mselv!�]%���m�^dis"��)�o�Ob� .�$FFA�%�%$s. �1temjbI�H5h1>NAo�(m�$Qsm-.�m:\%�ޖ�Dasrepanc�2�a` 4\%��ch�is.�Bat1�iP9t��c *�~��L �)e�� >�,�'fi�X��A8e�. LYA�S�*�HB- !+;9sw`!�]&��&�l�9k w'E good&���oaj9�aH��N�. �A &T;"�k\�-�[l0[l�.ps�JC12j\l)=*� N����)��q$6�$u��g�Y!n�.�A�l� 5 .�R� �%�5�bia�A��.}�ep8 *-�M�l ed a���l g � 4 7� � e�-e�,($F=F_1+F_2+�)A�b&���Vwhole��A�ve�u"�"�׬&�   remind�� �� =e&Ɔ\!��cw^V(.$�+�1o ��;�,�%�UbIFw& � 6\def�vhe� r�'"E9>%3nwH$y~+U��1E6��%s!�B�����;�it+*$�5/��?�a�e�0w��R?x�~in F�cont}U%�QzN. ��� y "��by%6[!�Qxspr J�m �V #n�.��K ��rep)<X+Y>�I ]Ix�q'and/orHE9C � J�"� �1H0&�$� z�/���?l��@E1���A u��q�v<top�;{I<�I< (o0ns� 5meu�� SjET��-�of6�iS.�waX"� BRj����G�j$-� x$-�stZA]$!l�>�A�Paq���I*msion��圥SbYF�H >�&N9Ax AL1+��m�,B��n9F�-��%&��a plot�a�i�s � ���Mhe+, 7� �d�)��bM �g( -�.su�9%.�� s _UvsAq�!�A�T. :kI�Bl% R�of�w!T�Nd •nA�y��K!%�> �� }%��s&� Dasy}�ni�>����!���:� �f"�|>��)�s(flit6Et8] t&I�UN�\�B��O ��mff2' ��M�Z� 26,��.��our�iy2o�>jŪE�!�ar�n�Os BC!�l� "�PofZ� �12NB��AS�R:w-$R� ��Z�FatR�Fl{). .S� �8ep��[�mI*2%0by Cardarelli!� SimulaIIa�3--fron��8T ��&iLFQM}�F !a.�Fwe�u/h�) m��m J�� ff}F�G(6� >" 2-3\%)N�^�< "�3;eci�> R�)�r R4 �� i�3�bb]����qcciR7��a�0�U�>r ��,�r"8a$K1alM0, �qM��� 20\%�Al�*\�L\�]�"4`$U�iesFQh�z "�J �'{r|�)�)�#B&��W~ ~. &[�>�=:2 TF$~ T�-B&��F& &  ' 2V�APi)AP2& BD)vgڞ@R��W"H&QN�\-L�* �$~!D 3.46�& 3.73 35u3.5* 3.50V�3.6�* 3.49*S��7a 0.11}$&$-X+��V?8�&24k2.3-8�2G*&2�*18 25 BM�+2.1-�1 �07},6� ��_T$ &1��+2 4 2+ $4 3� 1.36b��+& $X%1D"03R�+5�$�%2}_Ljw_0A�TT\\4 p,0~�+2352 &0.23$�02)�01�B.+3 +2}.�{5{43, 47&0 -0.4v2$ {4 PBz)�0� 0.06Bh2� 0.687]66�69&$ h5 hZ7-�M(13Fh��-6�-4b9 8�-� 6P9I��2^K1.Q$0.-IFH3��-A�7Au!� 1.2987&$&�2\)G �4B�3� 1.59_715463&1.610M59 eQ(5^�e�E�>�i���.0/0 4 �/ �U�0^�F�0�%0.0FM���0.6a15EY5!�5!�$0.57 P-cU�5I�1 h1FhQ�79A_86&0.7�/ 80&079h7)|0M�h MFj�A00�96!�0e9a+ $0.9m&qvq&  �5FFM�14A�3_�0ӥ54AF��09m��} e 8}�R�4�YM�2E�35f�� 1.27k 5f2)�u �Y� \>9�Fe�c01 � �0.N��9)���0}��!f9�1.< $UV"�d �858$X65$`64$&0.5E�8V���A�A�)dUE6 �1.1�1.0v�{\�g -(�73�59 �72$!47A]6��7Al82�7i1�a:�B�6w2}2.�f2.0&2.��2.��A� 9&2.5&$2. pm 5"����%� "� �k:�*P:9 1 F�dl�-d1(��a>��{L,T}cm_1��0}�B d}w �5�!d} 2 1�5�}w�A*m�"`in{(�P"�"^2 �#3�=sw�1~;b:S�H6�&7 "~<a.mea�OFoa�s 2�8'e s�Ca�# �� :�*�ur 0s.�q Do"�%Ry"�ninth ��� � )������*}2))�.�V �� M'�"yR!�!*� ���."�g9 � !v> . z&�4�qle*�$�}[htb]3u3:� �7} &"�åM2g% "O�$��*��2K2��'� ? '6�/&*���'��4"f *�.��rR.�$.��E -02�� ͕*J�+84"_�3156\pa���-53��4 .x х04.j {6 �f��~!*1.&n��*�� �945�d� ��2"��+1� -�0"�8�7W6�%�)����e��F�X&*� "�.l�.a ��W�>qYa[[% � B�Fi��n�&)He�&V.u� .%y2"�%no�=nt2�(�r3����6|=�j�&~����G)p ntal"@82$,@*�d�W���&�-:c)U�B�gtjB� �ory})*�1ourJK)�.iI� mark��:�!J�5p1�=-i.�If�(${}A{*��* 2fBs (2,�))�C2^:��.o2�3&�/r��{ *�3�$major souroEfORax�)B"�$�~.d�in hq|@eq �A>~"/-�) �Ea'Z�ize. a�L��n�(t{/�A�2���  6��F72��qKK as s �x2�'q.�@Z!�7��m �f v��a 2�h��9�l��}�befw^��h06*�@�as)i �&a�A�a�$�@$�} . Unfortu��\����AnoN.y �-EWgJprt-%,a./ Q.��3!�R��ne+� L+Z$ T$)54�LFy%�]u Zs >�K w$���Bw\%T��20��*e_#6vA�C�c*�o�6�'�! �v��=N�\,� ^2\,  ���\a� �!�Q=3"ZzJ! A669 SR3}�!� u����(�r �a:�D-$cz$ed*h5&,&N� %&B � AiJ* deAHur*�2 6%�in� c��aL hat*�6v �:�6'.��� d�,-{��2Y.'6�5/3�;FS�z ex��L+!s� 3)5+�7�!���m�_ev>G&b&f�_Ĺ,�����&J$Ik t"_polynom� in p�?an $�7$.��w�-ZV)w-2�-ur"_'�l�ne��r�U��?"n�U57�"s�T &o��Q>.G4?m""�z�9 . If� BWU1z8er2�Mw�%&:"w�TWGp-ͅ )%,�! 1A��><��+,'�8Mis �er#�Wo�larM6�absolut�$t��4R !��9-n�Ss\Ma�N"o�35�. "4!xH)�k�B.&�A� �&q9M��C:)�k to �A� 6�,)sE ��to�XaoZ�!o�{&�H*��j (A�&l !�!�m$-$F�]a��7;�_�W��od"A&�� �a8b+Nōaches 1cdel r&��/t d}w$ .;$%�8�f��m�>a��}�t�.�]� !3de#)�6i��.т(�,awi likB!z/$�?r�UAl&�T!�/� �$Ba �5.�(Xi RDd*��(*�(iw�("-)12.2*.��(!��)J�t$Lz�26���Gq�+MekG � . >�&iH*&nt� 6�5 !|c�!v!���� R�.�� �"� �B2� & �BE n� & 2��3.2Z & 3.0� 7&!128R�$G�2��G"� � _L$~~1.7 L 1.� 1.85� 0&90V 8Z~G~12~^}T}17 p}2 1.1�L � <}21V�1.1�10�� }d>�V� � !��M�� )L28"0�8 7/2 �"� �0.2�2 �F���"0.51�"00 5�L)i"�g5E"08B&=p�"�5/827��!7�$0.75%�bz8Iy1! 16}$>f���12��M�N� �6 0v f1.2}-EFD��"]�N1��"1yOJ�" �1� �E?"*D&d,J j@39A.h"3m 00!_3-� � �0.3M@qZF�M@6a?"O"N# "6�O^"-`O �0.p13I�1Z1!>�O 0.83A:�%0.8A�8�8EF$$%�B@i8 xF�I=vPA+8!��IO2h9-D� �2��1�OQ"A��q��1 13E�I��JSI�]>� f�1�0�������R� �)Uv$91.o z�1.14$a22�1i!�5B1.0��0h'F0&&�?8%1.�8v�Jf�1�00�;RN�$0.03Y !0.3��1If{����4�(4.5&4.7 &4.E' N�%$4.�iK5"�R "�c{ IehIZ�AnZ  |�� "�gF� "�1"�]� ��0vI �=��0s&� � xi}�<�*�K�v7,� � �m 3sh] Mt&\?~&%M,"�<os2�,yis� ��f?ia�8OBto��[�"��&�s��nic2<� y���ofZw�.2:�.f�8i<�M3) devg_o U  E2M�C��xamY@&� &U�!\@F%�� ��c\, l {�E��\Bh�:L6>,dB C:?.DC� 7},i��H�7�<0fidin ) "c�c+Q-� &�in�!�3iw�ClK&.) �c�&� )�� B!kr� W�\Eo/2B�!�pW�l�O3�ak�I  4@F�$���"*1Z4:�:g:��A�F�3~f�n*DbkK���behavi�O.�L�v>PB$wZ{ D}_ �, ^* ��. �"2fTO��:J6�`-X �icNTh-%in � itud��T<[]!�shDS� q/��R�nr�gj.!D�!��� desi�8features, we wo�Suld restore in this way, vector current conservation for degenerate transitions. Our HQET improved NRCQM analysis leads to an accurate and reliable description of the $\Lambda_b$ semileptonic decay. Thus, we determine the $1/m_Q-$corrected Isgur-Wise function which governs this process and, thanks to the branching fraction values quoted!IX Refs.~\cite{pdg04} and ,HB-exp}, extC �,modulus of �$cb$ CKM matrix element (Eq.~(\ref{eq:ourvcb})). !ydetermin)��of $|V_{cb}|$ comes out in total agreVh with that obtained from se=l,${\rm B}\to   D}^*$ d!�s 6� �,�4 if it suffers X,larger uncerp ties ��Platter one is because�8a poorer experi! al measur �ofB2�bF�A�j$\UX�> case. We also give various $w-$averaged asymmetry parameters, EE 1�e^�= �hfjb+)���a� on!�E�-bAL. In �G!$ iq� of%� abov��s�� baryon fa6 q�I}^�{_qr}$ re�$(we recall��tō}��$|A�{q}\,|=mGH_c} \sqrt{w^2-1}$),.�narray} ��:�@ (w)&=& (4\pi)^2i�lm�^\p�W}{  $}} (-1)^{l> (l; > |000h E<0^�S dr_1e[ j_FT(x_1) N52e� Z52) [f^c_��]^* f^bd ɑ�D) \label{eq:defI}Q<1G�g�^flavor�^Plight quarks ($q,q'$)a� {\it up� down}.��� x_1=I�m_q=�}{M^c_e  tot}}�x�j x_2q. m_{q�r=26� x1x2��% ��2x$=m_u+m_d+m�z& P$m_u=m_d$. Besides, $Y R��ha Clebsh-Gordan coefficient�>j�>��spher�Bessel's��s. O��other h� %�R��0 can be compu as.�1�i4Km4��u2�� 16\pi^2}{i�32z �ORfM�K{L=q[ +1,  -1} m�+L}\,A+ i}F�+:� `P+1 } \Big ((2L+1)(2:+ }+1) BE) B)� (lL>H�p \nonumber \\ &\times& (� l>A kC (:[ >5}1 0WZ1 l1L;t:���靭 ��>��%  \{� ^�![F� Ё�2) N�6;!�Omega_L[Z� ] +Fi}}(�y�E}��}�yN��:q1?xf�~�-;��q���$W(...� Racah.@s� ��dihen\ (operators $�8 def�6 � ,}|@ + 1} = - \left (�UD  \r�#u9[);\� } W }-a$q J}{r_1} K]� J�- �e B�}{��+B��.��Loemgas5�1X % No3�* 0remains finit�e limit2 0\to 0$, since� ��not takr{�>�$ and >M�$)�� both�p�n to�90 due the f�$ZnB��$. For�&� ɇ&? Xi� ѡ{ re6� Eqs*$�)--&5)�), replac) $f-$type� 29 s,$g " ones!Q!y;.�<=m_s$. Finally�a�,$m_b > m_c >q, .8$-���4e neighborhood!�$w=1$s - Jm2s beha like5 O}(1�J� )S$O}(m_q/m_c6� )$, P �8vely\footnote{T0,is trivial, I��is �"�j �U s �>�=0�n&8be�A�do�nt!�{le:h�� aB�}=:rm Bxis[ bidden by�:� ��Thus,Ws�2�Mt �io��� lea�c=%s> �J�= 2� �N}=0p R31s.}. i$acknowledg�s} EHresearch was suppor� by DGIx FEDER�rds, un<�Lacts BFM2002-03218, 3-00856 >4PA2004-05616, YalTJunta de Andaluc\'\i a2 @Castilla y Le\'on>~ FQM02257SA104/04�jitA��a�rEU M��,infrastructu]it'(ve Hadron P� s Project:{ ' RII3-CT-�`506078. C. Albertus wish<o 9�e a gra o�2.� 8-� 1�Lthebibliography}{99}4ibitem{hqs} N.�!& M.B. �,�\. Lett. {\bf B232} (1989 292;ibidem}R27290) 527�|0et} H. GeorgiRp40>442> Be93} C.W� 4rnard, Y. Shen�A. SonJV B31 �3) 164���UKQCD1}  Collabor( , S.P. Bo�i et al., �Rev2-7)+,94) 462; K.C;wl� <.:!a D5 75) 5067:aNucl. 72 B}637 (ac) 293.a�L2} U. Aglietti, G. M�nelli%*4C.T. Sachrajda�.�324)�4) 85; L�llouch= F�44 85) 401.�� �=849}��A�45:e>} B!�instein,.C±_��5. \=56a86a�8;2 D. Score�.eYB��3 �89) 799;�Z K;�.�%�.�2782SLFQM}a�Hogaas�jM�>,dzikowski, Z2�C6�4A�0427; H.M. Cho� R. J6��B46-�9) 46�>��SumRules�CNarison�=[B32M�� 197.A d� fael%J. TarAB=J5 �4A�2(Exp1} BELLE>(K. Abe:�� B52!���47�$Exp2} CLEO>UJ�}Alexad �E�D hep-ex/0007052}.�,Exp3} DELPHIFU4 Abdallah, Eur1�J�� C33}�b4) 21!� Al91�� ajar��R 73}, 540 ��1).�i (S. EidelmanjOI�B592}, 1 �. �� ��i�=� B58A:� ) 6�"#$HB-LatticeZ'J�6(E�D5�8) 69486�6124}, 3619��62� �2eGottliebE�SA�mhanka��FMD (Proc. Suppl.) 11�E2003) 64& .NC}aJJ�TcA. �X,Jb396�!�3) 38.2R��CUn�49O4) 1310.NHB-� B. Holdom�� Suvl�� J. Mureik�dI}���23��.SR2�d6� O.�Yakovlev�SY] B291} %(2) 441. %;� Dai, Huang� �$C. Liu, % �.R38ML�V9; 6�3} R.S��rques�CarvalhoA�FNav}xNielsen�8Ferreir�;,H.G. Dosch, B/��03400$ .�LC�-J�'B=��7262� HB-BSE� pA. Ivanov, V.E. Lyubovitskij,!�$G. K\"orneE@aG. Kroll1�=�s3a�B =nig!J%�N%Kr\"am�[42� M� J!H\B�%�A%RusetskyB���5a�19�$074016� 2tNR�D�sakr$ty, T. D�&,B. Dutta-Roy�Mod�]bA1� 7) 195;VQ, �:Q�KA]Gupta,J".!Yf��A1)9X 85B� ChPTA TanakaB.S 496B|�F� rdar" S. SimulR�B42a�e�� ��p:�]R.!��� 3ByA66�b0) 936�HB-SR1}��Lee�Liu%YH!YSo�+FN8�8)� 013� Q.�SNfQa8hy:50A 2001�o3;E�GI ParkZ=��O1%�.Th}�6DunietzJ�5� �940B�QC�H.Hih��2e �H.N�?JX6)� 114002>Fa@2��B. MelicNT2%| TA082�QET-IWBzS{B$B34-1� 6; H&9z.93; T��(nnel, W. Ro��Z. RyzakR�31�9� Lu90a���ukV-%�1�4472UGe?Æ� y��c]456e�0); P��o1�G&� F�2� 19�}5% ;Y��XACGuo(Cac�,(Fk4� 72� Al04�����E. Amaro�ZHern\'� z�J.�yvesaCBlA7� 332� si96�|Silvestre-Brac, Few-Body Systems�n2� 6) �pu�beachB�E.j��� 4ph/0408065}, t�*Dn at `BEACH04: 6th��$al ConfereHypero�@Charm \& Beauty hx0s', Chicago, ! .YPOL�*:��q�YN B275e�I49�{5� j&� . Bishai� BgA�3<5) 25�WARGUS} � .,a Albrecht rZ27�-�32�Al��*b.u>eiſ= 89},Q 2) 03256� 94�&.B�B41�1978�9BD81} R.*$Bhaduri, LaCohler�Nogami��ovo Cim�A6� 198��7Y\US�.�FV99} L� Blanco,<F:�(A. ValcarceF C*� 42��u95LSuganuma�� SasakH. ToP.Y 9B43)EY0�tYGM84}�Gutbro`-d�Z Mont1)�=�136B}�8�12Fabre88%� 0 de la RipellN� 205B� 8) 9�� Ru752 � \'ujw �� ,S.L. GlashowFUD�p75) 1_F�9��9� StrauA�essAr Jo&�%hG19�20� end{>XA: docu�} x-\Tclass{elsart} \newcomm�\bea{"�,5":#e#_eZ!|ga{\raisebox{-.5ex}{$\stackrel{>�% im}$>Ylv8be}v*{\e#f*{�%}�%\�#9�{\inline �$noalign{\h!V#1}>�av *Q#-  #1�"90def\NCA{\em N��ento} IM �Invm] thod�"A IMA{n' AOPB.)e�} B PL �} RLe �>RD \ } D ZPC (} C} % Some�((macros usedf 0e sample text)4st{\scriptstylAS!sBvfph!def\vrw ssig�Ct thet�� 5�# c{\caaډ� ,f{\ F{\P+g{2� G{\G��h{\cj{\ps�J{w5 _k{\kapp�la�mbdL"+2 �m�� n{)�!o{\omeg7O{\^+ *p�n th{\.Th{\T=+r{)�Ws{\.Z S{\S=it{\ta� u{\u29 x{\xu z{\z%G#� � b�6 centa� �Net��#o ,sospin Fluct��s�� Worl ( E;ary5\ticles }\\ Vesna Mikuta-�!Lis\\ Rudjer Boskovic*8itute\\ 10001 Z;tb, Bijenicka c. 54, P.O.Box 10d%,Croatia\\ vmf@r[ .irb.hr �x�8 \vspace{2cm} � �i �$ event-by-  f:�high-eJ pp-colli,8�&predicu%�;}(e Uni% Eiko#Model (!n UEM �)in� cu�:�%y p�;n�4rn ch�;d-to- x neutral.pions�6se ] �foundU+be seE>ve+�s�of unst>Tresonances, such as $A� $�$i $ m+s.WJ! l5 � �-� ob�>�:0$D_{UEM}$ sho!?be�'tr%d to%�&0rval $8/3\le 6 4�+p/:nge6t �/\pi $^>duF:)V.*(ulW'� n-compati�!�M�:m!�z:a� gas) RHIC% SPS E5ie53��page &�: Intr� } AE;}'!z�eZp)x a�* gle A�ral ultr�} %&A�e�z�vel� neg!�iIdi��/a,a�> inct�=alDQ�#H Gluon Plasma (QGP),M�[Jeon � Koch!h 0] (��QGP phas�+!�V ��*1/3 wh- 1)�ic6 6��6?!!N#A c plicA]$ N_{ch2N_{+} + -} $�!>net< $ Q =#+}- *r �2 [Heise�*g! Jack�#+ ] as�Ja &&w2L\av{(N_+\pm N_-)^2}-}�6av�-R6=&�4\\Ow TN_+}}^ �}}\j_ � +\�2 [-b.-} \, �\, C \,,�8 oNpm2ea �=!1�<�on!��by� C�z +N_-�}R�/2�.xCuIno?@B�8.��? rox -}$, s��a�E2�EoLCM)simplif�Bo�635DA7 } &\equiv.�)o9�)9�%�=M +} +>[ch �uh3�0]�bK0� �QN�Q�Q��-�5qoQ ��s�P` cle.U!0is�.R:reavoidA v�e6� $ (R{+}�W^{-}, K�cY3A sui6���!ar&/se �� $ F = Q /a�a�$�) $R= e�-}�2 If $\ave!�E ch}} \gg Q}$�nF"e  \delta R^�= T6J R}^2pA� 4 6F6 \ee !�JW != a�e%�\over |NK<� Ip -6(4 �Q 3C QAp-D.&/�6)��:�^_I$ R�)x��1conne� r .� exhe.�throug! ��-+D isB% �%�=-y�.$-h4)%:a& )-=!"c>D��%�whichU vB= a�A�F��ٍO.� per�� e� py. B&G6 effeDFCP7}�Z ) 9FeptQ  window1Xe"`Gs0yC D�  ��%�$(UrQMD - U -r�� 0Quantum Molecl $Dynamics m� [Bleic�={� ���0])�!� Long&^( \tilde{D}=E�.u _{\Den�A�=�)�C��_y}%� ?u a C_��| na�B=M�8^. \}��2}ѓeq�9� 8\be C_y = 1 - P-��J}k��Aj'rm�}}��eq�#ee We (7cal!�O2�} \ R\ (UEM) [q2� �], f5]!v� ��i"�J"� LQ��Cal5K�!E|ML���  � ~ -~  7.) R�+ .�Jau! Y7�^at� e���mos� �7���.> a�nearly�6 -fre"L reg i� � s@H iy avail� �t�E e!( isAQg2�GE_{hadE�frac{�E \sKDs��E_{U7�2nG���Dix�tal c.m.�$I$gJe�K L to�. coGnt.�of I or clusXK)FI| impact�azK)' � i��scribed�� !� oriz�Lorm9!�sc��PiK. I��� acte79-mA��Bsource�7%��XEE%� of a� �afB � =s index.� - dwM into =out> j]Fstrong �a|s (i.e.(f�; -stax=te #"6I �is� l��. Stud!�of��< � o� ,level suggesmL!�R�i%inly d�:te%�gI jets}(�"'s"Sis zero,�Iis very<ly  � 1_im-�� cloudMx� m�is&Nd4N$ssume globa.0Qofh.�Ki�9�leof $N$-mI%j6�e� @ste$jp >dv4ly?)���$2'rho }$��'via�$-�=Ma�:cO at $N� k + O��probabil>�N �a�+}, \,P \_}�N_{0}1i� V��)�� N_ R�M,A�� 0 P_{I I_{3}}(� 8�$\mid N) C.&$) & = & ���L&hs��*{-4cm�Lum_{I'I'a\� I', s'}B02B6�-��Q#* Re�5:Hi�-*� .3  $$ sJJ� ��val]��} J\1�$dfj Jj� upK b $�� $��satisfi���E�{n}ab� = 0$'M hat �@%�qm���is*9 o��b@@g�'��F.�'$ However, N�pi �t lower@p�8/3$. �".A 3  � %} &S  &L�<m=*r � �X  = \�"{qg {ll} 1�K'#OL��� �2.8"4un� l�#)�&�E k �*� :3ct�ee �Tija gsC� ���ri!�our)B�V (14)P&~on�Kio[Our;�z�� ) c�IR� [ Adcox72 ],[ �G2  Reid  ]�,H no�6 ably/@A��R QGP LHLc�dA��rMno� icI� for *w -�ye 5#Ac3B%f4B workF0B!~MinLVy!S:Mce, Edu v�BS%�� u�8C(C< 4No. 0098004.\\2�F, s} ��{1cm}-XK.��PHENIX�&�?[ "�f�EY Au +U�e�!�$\� H_{NN}}$ = 130 GeV "#-sl*4%w%�n+082301.�2�B&�( ,Bleszyns*M.f Czyz�/[9 "M%pl�.��>�"�E�� "",�N�&�%} �0B111},461-476)~C%h, M.,�*\&  V.!a0] "E2/6Y� ɜd" pf�Y non-�librium �WA6!�ory ���&^4bf C62},061902J� CY# NA49%%R!w�ult&-1�J7�.�-Yale�"1B9�m*i)05}, 2076-2079BC�E}>?!A~, SvarcaN( \& Crnugel68[� " �!�Y�)8&� )D-BD1FIZIKA -BB!A197-205F���!\.� �5�Can�%s c}ine��5�E�n! � ^F Centauro 2 w ?b 5e=073-1075B{ɘ/9�n�� STAR|y?E 2] "YR4"Q.�EiH( 611c-614c.�F� �&�#�>|- [two�,11pt]{�D} \usepackage{citeJ( % �Ppses [1,2,3] -> [1-3]BG sortVK% ET�* [3,2 IR.I0[dvips]{color>M.){epsf6��Gic�'�(amsmath} %[+fp!�"Progres�P-�%��a� ics"�[20O6J�7 }%>/Hnal#1#2#3#4{{#1} {#18#4) #3 �% -d,6 -"�, PHYS ! uan)dD-P2-.7 MATH 7�=ath�:>PRO �G o�@#~:- y���RX-&v-28-}1}"9-PL �&q9�P~�-EV%L ;�--f PREP2p2�4�n�-PR�-n �!�PR2Y. W1V.8Z1�Z1��ANN �Ann  (N.Y.) �RMP):n#& &1> CHEM !J8em: INT In>�<} EE Ltopmargin-1.2cm \odd�H 2mm \">a�width176h P0t23.0cm \ren"2'.se��7 tch}{1.13|* customizaj 0 \flushbottom�V% _�*b6-b69--bQ-�>-eq"@-�} y� {lya�. ��5�` �eqlab#1Z*bel�Z{1I,fig2figtab2tabsec2sec % r8 feref#1{(�d#1}QqEq 2�d fig !fig.~A6�f JF;FZ;t�5�=6�TTSJ"sec {S\% $=v2g-�sla#1{�2� A� �5-�slap{p v"�.�.).2mJMP{P \!  ^shA�A� �box�g{\ms\small{$#1}�u$��` halfR*1`(s W^+#1,tbU36Uter^U42Tird^)3)six-J� 1}{6 ) % wgce17 arr{�(6�cu�"H m��Q� bmatV@A#JA%-� %�ebo�>13�2"+/�6�3 %�Ga{�A�.M�d� %De_ vep�/L/ MINkp{6/a��/ 4L�L  4Pit �Pisssi�. KSi 7�. M!�/ %vvar.>%/wo/ 3Wo/ hw{�\om�/ h vfi{XN0%Zvph) "(/!.51 ZFY1ddj4dgpa.�2H vrhoz� Zarf�/$ Z{{\� �fZK ie{{,  eg{{e.g.\ cl{\�e _ni�4�nt F�2ear&66�4 �rg �g&!�rp p�rk kq{q-3hq)�qhk -tk{�!rN QNsn nFrf ftqFq5tl��tKK9cO5{{OD� 1�Dla! Lham=�HM� -M� Ak B Psc��atA1-�N{N b�4bf64b� bf SHpsi�3ar3-�Pa�-,i+�xx�v�8ec{U0vk{5�vq U%(pn{$\pi N$ �arctg)� �re�cRei�3�IIm3d{3-D KCMS{CMS ODI{O$�$$IRR:�5l{<{\7��< 0.8e6�<& � "zS*#n�+ S"�Yof�1�0] i}, v�E>HItaly, 16--24 Sep 2� To app�ina~M.~Part.~0~54. O)2| \author{ { Vladimir Pascalutsa}hd"�ics De�"ment,!mV2egB$$William \&�Wy,Psburg, VA 23187, USA}!�%ZandA% Th!�UVup, J8rson Lab, 12000Ave, New{NewfA 23606 d}�Qdan(Dece:e1� 4)} \makeE� "UbsSrX� Co_�$A"U�mo!��larizab�!i 3�5Q�we emiz� e neB%IA.�) } cM�FT"O(��r.,2 d�q�"�(forward-ComA�-sY�sum rul 6 thus ensu��*tt6��"�">mt"�t are ival�&,$usual loop2�,a��+d no h-bl expa�o�Jy"�? nipu� ons w,�&i<3�d��@F](� Oafn5d�$u)�!`)!A made.�y-Baldin5-�")$beaul� to "�)Li!a�%onB!.&m�^st�nGDH6!�Gp��ly�7uia�9Bng�t:�-�break�-$is achieve�'azbA'deriv�4�����a�aw i . A�� ex(Za)#� g!I2�to]8@+io�5':�AmQEDex���7iUfamnt$Schwinger'1rrr �Ga tree->' Bs-�59Uon. �f�*�-q�ݦA��erned,a�foc�v@n two issues: 1) m�bJci&mT>��)2)�snciliE�-4�eI) -&� EWi/u�e!EBmpoI���y�_� \�x�8 {empty%ne9�!�{2��i�%YS}�A�el6ac.2*�  phot!�n!�j�,�<$s$ (re�K��?)�)���A�i�*b�!�cgs�"�*( by $2s+1$Z�;fu�*�cd($ �siW&kinuic vari�, �b!q �e�,y $\w�#e low- �c �L �T3{s�r%�anB6 iy ---2 ,YOdipol�j ic quadru tc.7 w )t. Qgm�ai��$6�,I;�a �a=ris �z0lly written a*V-.&\}<{DDeq2.2.2} T(\w:svec�'ps'\cdot\,f$+ i\, � &(S'm )\,g7 \, ,&�"&k. u7v��%!q8A��1incident�/M�edM ,�G :; k��3^Pauli&=���=t�� I�en�iq�a)鞁~� arYK �0Bfollo� .��l* ssub&H{le�O e5?%� & = & v1e}7$s M>((\awFL_E+\beta_M) \,\w^2+ � cal� (\w^4) \ "�8QxK\\ %�Bks8� M^2}_ + � _{0}\w^3 Jo5Vo3B�(]6h%��e.Pe�!oy�'�9'eru!�1�l" $e$ E:Fdq�(n) $ �$)� next'0l�g�k p���=��� ^ � ($\al_E$)�C($\be_Mandu�Alga_0$)u�K.?To���Os (SRs�<�se��nti5�i a.sC &� �� :.�] anal� }U�a��j�=ryw%1 bu%�o |5lie��!,Tsecond Riemann sheet.}!y�aPs u���� �ů, U �� $e.pAE�$�"Ldisper�' i�6�I�$W\l�xiP dgI-�M&4ro*� �t >�pr�es.rAg o�:A� Sɠ,n�Il:27<s�� �I un 4ed6, �T=� ( �!�2�)$."�ne�u�"�E����$symmetry},�9n1*tpo� u� of &�� i} mustA�$invariant �) $9'EV&: ~wIOarrow-\w�@��$f��v v�nd $ga� odd2t� :i� = f(-\w)BI�=-g . % Go �rouq;se step�rrives�)!=��;, (s�[%Tn 2;${DPM02}�� m�� details):a�a>�8}2�i��\p�w\,pz {0}^�P fty} $M� ')�(w'^2-�� - i��{,'^2\, d\w'\ {&:� ;a)O{5� 4�b�De �(\v�\, � ea �/ >�<� _�_�A�$X �>em�N- d�/n-��Y %�SRs�  #- %6QC&�i�<du�4�b . IJQZ��a�SR: %!�g�8� :j 14} ~  +�@� �;s~�, &-'-�{%�} .b�8�A�lGerasimov-Drell-Hearn (GDH) ��5} e^2�� 2� �{1}&3}J,�].)�}�VCA2�% a SR1�� � �'�y�|6}� 0= \,-�1}Y�y2i, �6� {� �\ �&� �qll now /, F�ess!&�>al�D gram�m�J�>sc.��A�"� \ receI�beeMrrm (out at ELSAB  MAMI (�'|H,view see Ref�Grab}ZfT  �j� :<��mpi�|t9�2 �(SR, as well_ s phen� olog�estimat�� � _M��d $= 0$"S] b SR m��� Lly � ����� #wa�2-%ś-� -�% �isA�a�relZ�H1 d, �pr9_a2�funda!0%��p�M(�K�GarityI�E ity)�go�o2� T!1ng�}t�ies} by "+ se! c�@ also�fu3l�H$useful in �l s w8q!�9enc�1hy!`�xranspa�R.�( 2J!��,I�a"kA{Cbos)pQ2I1 KGnlb+5st Y � he  E-&a�taAM=e^2/��swrU�'�\*� * 2��wk}�� q \��X!��K����LM\wtMft[2+{2 ���$ (M+2\w)^2�>E (1+{M 5E�)\,\lna w}{M�{ *,] + O(\al^3)�9]' gdh}��eqN��! one-�.��r5��\�of�%�e�)r/� I�lhs} hasw42XK<�2$]ztunatelyatI&a���&r =�c.(���� vanou},e�a�, I�is �,a% rythah�4t�1�0<8 \!.a. ii��c �i�A� ��ory�QED. At i% ^38 �%��i !_2�A��?Zh:�=\al/AnJ .`!f),[~� 1aqu�?�mid_ task� it r�3res���9x�?J-&O toUP , ib7��pair-�0���d�s<, cիDiV01}�$stead, I w� to� �F>�Jer�do. � �m�PHV04}�dLe��Ay�a `"4AH' (or 'trial') valu%�a��4U_0$. A h�Lag�< ian %En�F�sA�a�SA^�8 -1/2 f~: � q �{ L�9���}}= (i� /4M)� �Z �"\, b7F \nu}�!psF^KF � ��bF$A0�R � tensDd�]=(i/2) [� \mu,nu]$. � /DdU �putQ�eq�to�@,2��{ �H %���!���F=1 +; $*�\de  S�E�qHc�*�2A�v �2��ome exp�7 B�� on�E3(To get some��new ou�CE0w� ! start [*Qk+ � *U�_0$��a ]�^2ɧ/M^2)AE� \, '9&� \i� \! ��'�ɕd���� ,,\\V`(- '^2+ ck') ~n oBn��aj �?. Now�>��;o[��i!�al��2�FyYdKqV�n�^{(n-1)�="e 5)9+')n!gf�F90�q mjnuj p 9�j��2/i�>� Vc_�Q$AS h�k$&j $k$th9� k-1) �,�Aue02�dd6�,:k {k+1�P y{k a��5 �wJax&��E�q Jinsr}V�ID?F�s�ef�>� Ix� |_{ 9 _0=0�::�3eqY !i feab~%��"�R�2 ar}  "�F�בoR� ��,� Ta�Fo@��Qfis��d�Nc. T�S or� ``balC �k ty''A]L� ��odA�wn� `�y:E+�o�.�"techniquΒAltho�5c2� ��it�)�e2� an &L.YG cT&howA�de�bine��*i  � first]�!�^� L!?��i�v,l=0$ / ��-l� 2���\��"p ��� �  6-{2M\w�M.� c(2+{3� ��E� )]f leqw 2} ��ItAit�!�UF!$"���gfuZ�1}�a�\�s_0�c� \,{d� _  J� c2]�en perA��a�A� �# %A� ����^s %A �*]���*}]=��^i #�\;${Magn�*�!%vM��'e��@W *#"/ M��s��"�e� Fs�pseudo35pling:�q } } �-Nyzg}{2 M�barW M ga^��\� ^5tau^a�ps"pa a,�Qqy g��!`�- � co � coz^V� 7L *4� pi^aT�Yis�^ � �{ pu�[��is*� a� suff�WM��2-��)�p�rb%�1 ory.Ua�Dfigure}[b,h,t,p] %��e f an{X=x�)=1�9 �<{chpt_e� .eps} } %_ B*�-8�` \capA={T��%�ri| ��ph�circled�Mtex:P$%e)�1��;�8{Born_�� � �2� in A ��>T��*2 M�`P�N�/Aa�len�%lay��8�.oJ��� !�&I%aNr�Y�s� !�:��"pi!_}�a \��^{=Y0 p)} l asC}�2 x�� [ (���s+1-xn 4al+{\al-  - q�[ x8#-2)��^+2) ]��, \�g#2�+ n � �y6��[ -\mu˖�be �be �+ 2\la(�9 s x\al�,B|0|0p 2�-:4F�-5��9X s-�X �la� aN�#� $ C=�(eg� 8 )^2$��0mu = m_\pi/M  ��e�masHUA@Jd bea && s=�$!iM\w,\M1 = s!K4&& \al=(s+M^2-o^2)/2s(be =(s-M^2+=1-\al %,la = (1/2s)\8H-(M 0� bxV- A�ikf`of> &(f�$e���s ;� �� O}(g^2D^ya�� c$lhs$da�GDH SR b![s>A4�\ S�R-> ��[B{we]s"m ��>� ,1�P� {\w.\ th}} 2� � 劅Ngm� I)} � 9�I�C��$I=�!0 pApia�"piaq.`ia^$ e���Q� (1+M�2M)A�)hresho!hE��աu%� reU.� quir���61�r�_d��exp�on�"���a ---!�8is"��Sb main��.M!!*G+ ���+�s.DTw urnJ�Vn% t����1ed{�t�Ow� "��M N _{0p���{0n}$��pr�,� hN�"0*!le�Pt(? ���.R6X'�g�"ally be !�en5as5 a3 (\w;Ari�E_n}) &=&I�A� (+A�E� _{1pM��<Y n \nn\\ &+&�H��,*2NJZ"�S_{2 L+.DFV{p} + \l2T.� $a FurthermU�!�i�!.�n�ion�Y])�"M6�^{(p))�y"k$m!�� �-��I�.G >�s� Analog�0M�1���� ~"�itemizv< [(i)]h) n)R newsr,b��2 ��pha��#)v p^2 6�!."�#.\!�&w.B�� &jyn�yyn)}q 1152!�&}� (valpco 6f �c  $g$)ewq� 4!H�#1HQ�p�R%nJj�He�I� %J!P�n�n!Sao�M�%U�.�n+i��s vV&k.V� nR}3M7�B�� %>%B0���9�n)}��qN� !!7e��BZ; ��� �vm��.7.A�$grN�B6� hr�Rl&r F� (a)�!�L�N)b)��Tndv�.12� ]��'��$ p)}+��.* &=&M(&� � �\{ 2x6 [4+(1 -� ) (2+P +2x)] +2� )� � \�.��-&L!. r x fs +&� 3qfb4 h\}� �E�n)-6)n20� R�!�2+2x-)Gf� -a:�^W\� ���1��p�9���=�:�*l=�f� + �xW ���)�.�p��I�� �6p:pV�(�alA#3b� (xA�:)U$R� U�e�l rA�� we easilyTify,�j� �Z���i" #��q�, employ���O�N*�v amm�a "|{�e (loo��_,��>e��46� �Crm�}^"�,>�Y~%�A�� =& gg��)^2 }i� \{1 &��8:%eft( 4|��Iu � + 3 }^4-�)  gd�f\�I &2�?rCcos �` J - 6 ^2+� �� ( -5o\,q\ln�� e�\1`�|rm.` �M��E?u:Mi!��  &�. EWBf6�r�a; j� (� =0$)Źch6(�;a�<��s���hR�B��1/�pR{S2_��hp^�:���`7 \mu-2�+5�mu#� �+1\pi}{4�mu^3 �+ mu^4���:�K \{-4zpi�>�1- ��336��"Z ��C!!O�W@!Ci�$\mu=� /M$)AP!�w|2!*n � n{mZ(LNA))�).N�)����. ]<l�@ I4$IC � -�!Z�:X \,(5-41�"k!�} 5�{-4�|��>`\,2 (3ba+ O�� `)� W��a�nZ7u!��8�&heu� e!%[a�q�9$a�e+ �ks i�7s $1/m_�c}$ (wg.�yTim�^, prec x�,ex�"�AJa� &!enx�-m?qpiF. f���s�2���4subtleKcel6 &� e� tSEpla�lorM *�M.2�E% �F 6���ɺ{#�鍥���BexhX�s{~h�2��vD��in�]� yF� divergvnor � =2M$. &?.�>����1� � �)�� they�duld beJ&te�{�K}�'��26!%CA@� �K �@an�QZEH_/%N(�"_L�. �� poin�clypdem� r�n �chiѡ�ere2 plo/--n+�A�(full [.�],V�~I40Q):�]��� -&1Z>A�!T^�A�Z _|to"0n!��� data ~Zan�.A�e�the�*aMs �E,ad�5a6ant shi�couIo-��2g@���uH, i.e.�>a��_p&=&(1.� 6R)(e/2M)� mu_n7���56� ) 6;&a e:f�Dd i1&!L�ma,e � ntal�1l:��7phyqu�b4_p\simeq 2.793�2��_n -1.913e{ hown?4,open diamond"��!E#t�� L�QN8�:�#A�%�used $g�4eu3.5�+��]� awa�$L�qNtt'aA+a�*�Iq~�� �qz �e�iQSRM�s,�Uw���dot��Vs,6BiG)be�naS�#7�0q�7!�n�jgauge s���Fg 5\4$IE�o!(�u�� .NK!}��aK)�"�6w�NQ&�&two&� ^mv)x�(o A�a'; a,W�Uz�}{1+a_p�bu6I{) E*�M�mU e  c}f bnBb6vJb\,�B nd:�' m.�q= tild�Sfi�u xGo�=%uIu�q� � M�U߭�� 1�er $a$@��2*�E�+soEcur �d�]2Z�LH���^sm4"^�!��u f��.r3*b��A@a��jS � ��($a_p=1.6/M^�a_n=1.05 , $M"a 5% � � #i�}[h,b�d'�`.c'xmup3^'x'x�'7cm:%n %u'AL�'\nR"{'vT�-fN'>#���,* ons)�0on9HQ��/J� .�$. ``SR'' (.�): our@92�I, ``I9b6(long-dashed�):JOe� �  hjKHB��;n :GLNA� �� �f4a�Q. R�UE⥙: � le��a �o�!��. Data� �# � 14.��C6 "TKE�2��F���*).� �M� &,��1��+��$I y puzzle}�M2"��a؇-B SChPT (HB)�r� $p�9�P?ṁ.SS 7ic�U�2�_  �:q�: be�&|@s�Kb#L&&�/(_E^{(HBLO)} 5�D }{6\/�  �& g_A}{4 Hf�^2 =12.2ir��10�~$%m}^3,�V&&fL>}R\al}{1�D,0�ɣ |�:| =1r{ɓ�/naF��Q6<͝g_A� 1.26;(n�8� � MeV�.�I"� "O c� ? � m�previ"�&6.AVGoldb� r-Tri�J�: on: �/ �= gFa�QV,�@�#tru2n�XE� ( �XnoI"� s� �;�#AG a�X�Bb�P alyRSsy�*;�P now, I am!�S o !tV�y�A�5nis8w�5e>&M &=�0�C N\De& -�PaT99,PP)��!� ganD^%$lag_{\ga N+}m�3\,  M�4M_\De)*\ol \Ps�<T_3^\d��O(i g_M ��� &= - g_E �D5�)\,�1�}�1�� + �'H.c.}!�"�9 $�"� �� q1�psi2!�1 -3/2> �2->or �]�M!�4$-isobar, $T_3>K $)j�C� ma����B�sK de� dy�&Fkn�dgxE,-��!arrow!�$.ustreng�mB_o��)�Group -E0M1�VE2A^tm� �PM���g_E��-1$���=[h,t,bZ2�10.��.[2� x�  cm2� su��� }&� �!�lta$-.]��.���6� �5u�he�B�W�F$u$ϒe+AQF��$�X, � }�F�� �1s �L �LPP}%n�)��ai�L�U6f�al�al�" -���#\,g_E�(Mm�^3!- -0.1:[i9`bS2De)�1 Va� ^2 }V2}Z1}{e�( - M} = 7.3a�Z�m�s6� So} i��he �p���out} %aЁV�z��, E E2B9aU� l. P� ,ing... One w�KcQ a�[clu-�dAs$ &�J���si��,�en{l��Zpp�. of�-  u�&�]&[i�0�r�-��" voict^we��t���b��a5Ecl<Q5�}�Q$-/���hange, ��{\� �io!�_l��U��3Mt%DoS`mT�*׾V��9�is of�uP�r4� in p�}f [>`6]�}is kind! scen�� 9G)Fn�KUored in.SGH04}.8rer�� $$O(p^4)$ w!�``promot� �� 5 �Vq�$ iHIIMn��׹rg�!�possi�|� � �Nn?al�a� eO i' }%EFT. $C��W:�+pr.���$s .P%�& u�!�.�St9�.;s,]7%��0 .�)of"hA�pl]&�.�f�^O���&p�� ��X �6�NQ \{ [\wR�w \, s]�Nj�& 2 [ @K)71 + sY^2&VJ��\�cM0��'*�%B�[-�'�\,��bB72\l;�^Z^2 +s�%�=] 7=*�70,\:��'�-FR�\{ %�al�708�$(s�7�1E �;5h>�<(�>M !�sG\la5_f�:|>eseaF"�3i��  SR, E"��"� 4�we~fwa� _E�O)�(R^"'e^'&1h�3 M^3#![3(1-4�+�%4�*}j�q1}�p#]!?mu7!406-737+30F 4-366}{6(4)|)^Sc �++.-�44-78882+1500 4-899 6+215 8-1$${10}}{3\mub{5/2}!� �' tg{\�&)�4}� ^2}-1}~(, �\2�F 1?n^=?! AjA 21}{�2)e[ D 2(2-�^2)(11-�2) 6 � �-6��+5)f �] \}-j\eV&!I�Ps&�&�'3�con�io7%"^$*�$�/ albe��}� emi-.��K�-�3, �)a& g'aK K\V�� 6�p.�e�1�"*A�Mx11}{4AT)�( 1Q�8 (4+3)� )}{1"$D*/ 1521}{88��:5)~)u"6�UV��� (1+1��mZ�17b�Ior,��e$Tly (uq&�=13.8~ M=0.9383$4��mu=f8$)\6�.| 14.5 -5.Y 5.5 -!= 5� ��5�, ;6- 0.4�6�6 =8.7 �JE�� �B s. (� !�|iK9t� L'vov's9 F�Lvov9;� if��p�"�=14.2Q�at.�is�P �o�a\r�a[� �� �af��^�)�2v,a8D�8[:M!y2� :� 7�s;EanѦly*�Yf �e �6�.�)� * +&8� ��jcsup��a+/M1/7u3nBE"1A)I�mx,#%� s&coe�B88actuaA�F� t!�@.�"e ��4!� a&�*2�`ac5�oOm!e xF, ��� facz,� 6_ � �e :�Vx . Ad� he RLO� � R��W� �=Z&+�av5.3+7.2M5:�.GZ�H8.7 H5.9fH= ~Q�!D���XE�a�!z�D�hsdP thos�!�y'�6M6�!�. %"�F!.�ja)ca� %R��i&hV.�2���m ���?CDvid�' J?�l&�hc�ic�Nm%A�E�Mva�,�o 2b -i�Y$HO�o�hand, i&�� Ed�.��$*�]Z�m'�a�k�A�l���I�--�(�LfroXS�a��= X&=Qin.ns�Ti|�]ngkEj&WLs�G!�e� talke��e"�&2dUP� $Ue���� !6]i?p$at manifes2,./a�#job!�%� ``.S''!�s }1[)8�Eu&"1S(MFF��aU">!U realvq 8!s  =!�� ��rulm=HR� R�&�Z3L@�t�m�� �>a �(e�2,T�a> q%R&�p(�aN fr$ 6&*)q}��/�O�p��p �Cs1%%?�}+of Gegu\Qe�.}� Geg99��!is�qproblemŌ\-�A�[is,�aذ�m,��qt62,x* renormali�d�2�Pseh�"qwa���*J�>exwmy�:>M��<$ organizer� ��fd��f_A youjp crow&�Bg� ���)of�r�vISi�on mob! �\!2�!li�#,despite some�V��e%di:ep"=��&"Qe!�"-��art�DOE�0nt no.\ DE-FG�4ER41302E�con�tHDE-AC05-84ER-40150 deMp!Southean�nڜver�es Rese��Assoc�p(SURA) ��x_CThomas J��uN� al Accele�� Fa!3��ub�>�`�\#=sep -2pt,-em{!e4D.~Drechsel, B$wsquini a� M.~V�rhaeghem``D"�i���D��al6virm J@,''�vP]�<\ Rept.}\ {378}�<3) 99. %%CITATIO,�DHEP-PH 0212124;%% &f�G!a.��L.~Ti��, %``�)GR�c��5!~�a�u/A���arXiv:,-th/0406059;6�NUCL-TH %% �a�EN`R.~Bec��P.~�may�1��cee� A�"]�$wk} G. Alt,�li, NN� bibb.�L. Maiax�\PLB { ��197��12Z�D�[ D.As�cu6 R. Veg�N,PLB { 501} ��1) 6���[ VEBc0yEQR.~Hol��%fRTAJ�Sv�!��{ 6��E=��3A>[)�hep-p%�7313]ZW4!�9^Z0 B.~KubDnd U.~G.~Mei\ss neIZ Low |6�d۫)A#�v:�[��m ors�NPA�7<���) 698. >�K���R ���((J.~M.~Zanotu�$S.~BoinepaE68D.~B.~Leinweber�� ~G.~�zIJ$Z�eQEDs"Y\2���FLIC fe�?�q��{\q�P��\�ʅ12�%�3 =�latao 1029N�LATap:o", D. Babusci,a8GiordanoE�Ga*tone, X�A�7}, 291 r�8���P�;Pas95} %2�I O.~Scholt�,� �7r9�Q&� N��# tex:J1�X��%� "� աA�below!`%MH 591}�5) 65AH.J4NUPHA,A591,658%)�Q�!>��?r�uof� i�$ac��3� "!�� �is�� \PRD!Y!�19:�6002;>�9802288N�PH �FR��mmermans�+�q�to �!;�*� i�PRA .F�422��q�O(-th/9905065>�� �=pP:m%;D.�2Ph>~p �&��5bMinN>om0�eo���7�o 0552%�6)�� 2120�t:!�j�) :5^�30504�W %``C��c2-M-�E/ �A�F}AE���!v0308065:�1u %u9v� R.~P.~HI$��d�.~W�iesshaAE��!�He� ." E`Sig.,�d��!�l�"F�1� %�-�v �ѵ)J� A {2(�20�93;�FUA�F� } �0qO>�0307070^� %S�8*�,���~&9���B�! >ar� D��c"Pa�BerT� N.~K�� >d U.-6� 6�\ 373�$2) 346; A�tzEY2� %lZ.ɒ} A 35��6) 351.�LI.~9EA * look�a�M �u6EW:� J %>�,A��304} �3��:�,PHLTA,B304,2�5L� J.~��~Ja�6dz� X.~Q.~Wan��I�=avy�G�ach ne3| ary?�%?JS�} G {2�� 303 ��p�'10260]:3� 9 A^T.~Fuchs/�j�S�oer� R:!of� � �f�E!� %��ͽ2�600>{ �0302117��>� do��7P%��u p5_# .tex� X PTPTeX.cls f 6� %\�qg{ptptex*22[seceq]:��:V >,�l�6~*aL�da~'errat�&��rinu \*��(ic�wrapf��%S P� al Mb�6 +�z �pubinfo{Vol.~11X, No.~X, Mmmmm YYYY}%Editor��O�XDll ���� is. tE� er{page}{>Θ %�K(def\ptype{pJE �KpsubjectN���age%1X-XN����*�v %\no�*boxE):%��'n1+�D+of �\ur=K!tsetlogo:C%��<Ypf� Y� �� When [U��?�i W��op�q�n��&>� &<[3cm]{%<-- [..]:*{@ ���X# c��8n. %KUNS-1325\\ ���(8\\ August,��7} �� ��rkX{�E %runKhea� odd-AO (�$s' name) M5 suza%�Y.1$Shimizu% } SF[eve�H,ge (`short' ��) M7ic$AB of Pg(s�`� es% �4m%Yo)��\\� �(���e- ��d Buil� ��-$K$ Mۢ-quasiJicle S��s h $^{178}$W�%\/Bitle{Sub e�%���ryou/na 0)�u��)�< %Use \scshape �a&fam�M!�$ Masayuki ��c{��!�}�,}$&�~ E-mail: m��Pza@fukuoka-edu.ac.jp}w$ Yoshifumi!�X-�V2RV\yrsh2scp@mbox.nc.kyushu-\!��G� %Aa, negl7�%$[�� or [�� $^1$D"��E' hysics, F � Un�"��'MunakH8$811-4192,  n \\ $^2^[HGraduate School of �LSciences, Kyushu University, \\ Fukuoka 812-8581, Japan } %\publishedin{% �}%Write this ONLY in cases of addenda and errata %Prog.~Theor.~Phys.\ \textbf{XX} (19YY), page.} %\recdate{Mmmmm DD, YYYY}% �\%Editorial Office will fin�. \abst.��\ract is neglected when [ �] or [ �X] We present an exampl!$at shows t �Rthe random phase approximation performed on high-$K$ multi-quasiparticle configur:�s leads to a rotor picture by calculating excitao energies !�� $\la��\mu \r �� accord�� aYT,a�T=\sqrt{\frac{4\pi}{3}}JO/(Jb\mu_N)A�of^�1:�-�Tmean field level. Sinis� es �Zcoincideͯ$g_K$,G��K<�!�U�i�� ombi� RPA.�%� $g$.a@�Kpurpose�/papera�(twofold: By�ly!�",above methode�� ���)4richest experi l.�M� w1,w2,w3}vXavailable, we corrobor��" �giv� �� viazy�&� A�J,%2[.�%V�w� h ��aa\L-body Hamiltonian, � ga��4} h'=h-\hbar\o3X\mathrm{rot}J_x, \notag> h=hXNil}-\mit\Delta_\tau (P ^\dagger+ ) � :-\lambd 9N8 2m2k=i�,bf{p}^2}{2M}B[+ )1}{2}M( � x^2 +  y^2 z^2 z^2F�+v_{ls} zl\cdot sJz* l} (+}^2 - m�.�_{N�osc}}) .B�@\label{hnil} \end5�% Here $%{= 1i=23nd  neutronECpA+n,Ѽively,Iw< o potena�B =�$�ƽ'so�htoE�e��?&� nu�ߵ-�-$�Hoscilla� frequenc� ; rela��toe; quadrupol� R�� param��� epsilon_2)$$\gamma$ ��Husual way. [We adop so-cal� Lund� v! on.]�� :C um $9�ddef�O r � $y-stretche\�� $x_k' = .M�k} 0}}x_k��w�@$k =$ 1 -- 3 deno$x$$z$�7�灤espon�~? a. N> arA.t��QP��s,� it{i.e.,}� �)s� au ,E%��byL hang��^�yE�2s suchAT��equ%�(} (-e'_\mu,u�V}6U) ./ (e'_{\��mu}<U}NV ) , mu exchmu� % whex^$)�� Za�� ner�� $\mu��[%��-M�residA� pair!4$plus doub2;y-  ($Q'' ��$Q''$) inte�� $between QP�,��we%�'esadM�*" � ��has aI�� quanai��\alpha�� , on�wow onents L of f�4:� �a, �evant�2y�$Ka5 pm1$]A�ot ��all%j2G,�%a��to*$K$:� is �ed�Q� through�lp��ao onsider���4=-120^\circ$ P. �s�Mm5(P%�- J!��ionu spher���. RequIYa�decouplAhgis,%� (&,Nambu-Goldst� A\), $J_\pm=J_y \pm iJ_z$,� �� ngth Ue2�%Ej .) n, utiliz�pid�q� in Tj IIINRefb Ln{smptp}\footnote{ S�,tly speaking)�O� tiny devi�[s b%�t4 ut���B�(r, a� non��) ��i�s}�zL bf{ $�^.}�a��Z��N b<t!Bo� ma}�follow!4�@~(\ref{matrix}), jwe us!�3act�[ �>� original ��erm<a�$ M�s:J�ɴ^2- "�J ^2)\left|84array}{@{\,}cc} A D) & C \\ B & D  I��|=0��- &�}��� {= �%�cal{J}_yrN�.) {yz}, .� � ^2%6 FqAB x �.� �.&b�5Q��z�-.^��5� �.[qF� .):�� abcd-�1�%- >�.Lx=� �J_x� /J�2�.GU"*,{\mu<\nu}^{(�=�� /2)}� 2E$#)�iJDm)-�^2}B {> ^2-( �%45b�5aޥJC��v�.���=��y( ���J.Q\inEaB_� I "D co5 �0t �� ele9 �J_y�!u (below)��p�ima��ryQ�rpuriousW HEq.>� $��ul-�~� = 0$,�hrewrit asq-�1E�[I`.�+A݁�rm{eff})��M���z�x2`fUm ]b�-~�+ ʲ�fU � ] .�disp_pM39O? k$uffixes $+M-$ ref- o"$_ � +�$-�od�� �and1��%��A\pmb=6)erp�\mp..� .�.&\.B2\�+A= ���ytefDr-A�% ForB&Rs,:�-I:� s� 8 �� �ory f[� � n by1c9ԝ�+ 2d �j��2�.x}2fV^2 EF��K,��) -x�A�ich! inde!��J��h!OFhu e first�� al�ihe "=2I"��'�f�E_{P}- "O�J=}}��("~)6_� FT derivzF E_I�r2Fs$I(I+1)-K^2�V&� Vu�-�) ["j*� = ���U �! N�a\6�]�Q�g f%)}faceach � well� �\gg 1A Inwords,atq�f�  our* � alism�w �A(A3a �ic2&& ��o0Marshalek gav( r,fAj ulti|u1G ��u is vali~ $I-,�WK �� 2"� 2}= %$w\r"Q^�� :I\r&* I-1)Mo�[i*y+z,X_n�]�^2:; u_{y(z)}2�3}�}HNi-g_l l -+g_s^iQ,rm{(eff)}} s  �]�m1mN�%��n$-th . r af��oncent��he.�Y. ByeR is�.ex5�m�T-�bm�7�)xF� -{1(%'^21)�-^2a쭳0I K 1 0|I-1 K=��bm1ezF|wS �AZ$nd n|$. I�2��aT ! &6R� C�$onN��or t�� (4, 6, 8 � 10QP�@2!? exhibit >� P; $K^\pi=13^-$, $14^+5 8 21 2  2 90 $30^t 3L�eRf�$i� $2\nu2\pi�X!�� � 9� 9492� * ��* M!2$� �  $6\n ' 2"sM�w� �1 l sp�#�N��|P3>7��;i" 26Hs U�s��� % taken#.�br �pgap 2a"�#,o be 0.5 MeV�2QP%) 0.014�6QP6Ks both82���Nuis chose#� $&{!N0.235I�reproi'�#�'ugh"0auvalue�";7.0 eb <wz ��2�analyse>�As�] spinV*$'N�= 0.7 6free)}�`s*c"D�sng&cho�)of���_is work!;sem)nti� ve;�� heck!� he robust�%esults��� � D%va $'�C�>"�ic�L"��ed �ido4& � �c � ��� }! hileJhI�� atE 6 6J !� 001$A��Figure~�fig1}���!~� *!�nd obser� 9b>| [2~ >n �$, $/ +&9 � O� �'�]��( gross fea s bu.* a cl�! look�  findc� at���c, 62���<includ+ (pi h_{9/2}$�. Low��#� !6 �' �(��� [seeB })( �=E�U�M��of 2��&�L:S �&h ic�A�0shape polariz0  e�+1~�pj�a�pro� di�io � .GZ>A���(r-, !$also Refs"� dra,fnsw}A�? fE� } \� erline{\-�dgraphics[width=7cm]{e.eps}1ap�{yM�2 ��:XY��R�Da�(2���kI��!e�� -%"- �gn intrinsic��!�IK#2p (so� curve)�1�q�ed (da0.)2s (poi�� (error bars)� w'� )$..g�U%U2BU y- Fig.�/2}�W�.A�&! >�*.*�+e;= R+;�(2m �(�}_��0&*��� a��� j9N�+"p&/*st*yJ���:� T.. agre}Rv�*is I���YQ $gpz�(*A&�( )r� �Ok1��(B ��E�s �ly�k . Aj)��!X� obbm}��&� g_R=g-Q)MK�}"fgre�%?h $�� g$ almostR2). Cons�$t�%�differ�3"�!�a�s:�)r!�o�7 ��A �)� y�aseI�+�.ѡ��suggest�!possibil)0to{(��'b aofm#� B i�26� csubstitu�$Oj�to *�%t). �f&2 � �1 0.29A$s�"eU.3��TA� 7may� �)� measx�4�-43�.�(s. Moreover�ae!a� ����`)c#1 � &� �3 tB %�!:6�^$N�e/;� �s.qrw"o!�3more z Avin:":)m�� �}|%\ anw+�4eBe+�*}&aeiZ*�_�,2nu+2pi}&  gr_j��2�"� � !]!�t�5ar�!EY�"�eupY,�$AE"[�),)re U�� o��_\n*)nd: pi$.A�Aclt'Q mHE�� "2Eqs�I���!%) e�s�a0�%� very �, althE�)�%�� IEC muchMH"�B��!HV��5ccupied:��co�bu�e��BC �bV~%E�%a}estf7N28Q���1F$o�/%*"#� ofN( >8I���� _extB� �#:C�Qd ui$2� el})J� �� � F?_j?2� 2o �"� 3mE �% F�#lA:P'A�!�|.A3R$a>�r/A�E�\groE+�1H4. W*�� c$2�$��Y d $6��F'yM?zer� a6n9lay��r,A �8�anearby�neq 0> ,��$R$53, 0.119 �0.176�>X- 2��35\�,�,)88e odd-even mass*s�N"g/n; 0.883v%u$*�/p 1.02� a. �';i�!�� � 218,�16�214>�Z&V�!g�1w:AES��o 6L f-�i� &atY}!8j:�� simi�9unl�7�8 driv�J 6n m�� �d.�To summke�)A(numY)ly�fifi��ij15&2 <R�+si��icla|2� ^ <,�� prev"0ly discussedh2$Er(&�; by A�5 sson"�-et al.}.�5}B�5*U&2!~�c. NextE%+�7!�ui��#>I V� �96� 52�e����p�3. A�d&�9v�5g7 is u! �g�!�� thebiblio�y}{99} %� % S <macroI�&� q+.t: % ogeneral�) \JL :journ><>\\andvol : Vol (Year) PagF [indivr. G cLAJ : Astrophys. J.a\NC,: Nuovo Cim.>NN>nn.!�PA\NPA,B&�0. $[A,B] ECMP,Commun. Math'\PLEPLE cLett.2EIJMP : I6.J� d.D \PRA�3PRE : ERevD-E]g1JHEI J. High E�0 w!�PRL2I� �� :D>� \PRP %{ [Rep>>of .\PT!: �AO.or.��PSJ K fSoc. Jpn-�KSI�JKSuppl�UsageE�@\PRD{45,1990,345} @ ==> h~![\�{ bf{D&(1), 345�\JL{N10,418,2002,123NG B418} (%), 123BI�{B123�5,1020AB\t�B}~5<020�� ��emaA.~Bohr�'0B.~R.~Mottels�5 {\itE� Stru�A�Vol. II} (Benjamin, New York, 1975). \b ff<( R.~A. Bark W��eaA{591) 265}=�� C.~G.�$, J.~Kruml�#, G.~Le+�8Z.~Syma\'{n}ski c36c81,147.c< J.~Skal/47!�87,40..w1�S.~Pu�A%#�PRL{7E_5,4062:2r:NPA{632!8,2292;83} D.~M.~CullenFv C{60;9,064301.>�0 Y%�Shimizu%(0K.~Matsuyanag!'PTP{7H83,144.Ema} EB"}"1X3!X 79,46�ma2^32%#77,412#br} T.~B�1���gI.~Ragna t$436,1985,12�Xdra} G.~D.~Dracoulis, FA=~KondevRP%K Walk�� {419!?8,28 S.~Frauendorf,!6,Neerg{\aa}rdE� A.~SheikhR`!�1�%0%�22��R>�0S.~{\AA}berg, �17A86,27��> *�D2�e%\@style[aps]{revtex�Dclass (,twocolumn,�Hpacs,superscriptadd�,t�#en'QX4}% \usepackage{epsfig,ng}2ams�BfontsB symb6 icxtsetcouV6{MaxMp2Cols}{30"T�} \�E{Rivistic tinuum-  c�4#� ssoc�3�� haloaD8i} \author{C.\,�eertulanemail{b@� ics.� ona.edu@ ffil ]{Deu -h� ics,*4IAri?, Tuc��  8572�$�H\today!�EabsyB} A5upled-9 nels f*o�& �of� 9 ? s s�E>9� d�?op� A I i� �D.  �"s8��d=�-$^{8}$B, vFlHIt8A�� at \[Id .g�As&� seiz inaccura�;-�2 � the a� �6S� ��!4+beryllium rad!�v!Lp~ re>7�end=�\ayD{25.60.+v;25.70.De Mn}�,"�H %\na�BG N#} R e��owveI�ar beams (quickly bec a major�ear ;rea!YGar Q� AmGnewly 5� techniqu1u Coulomb .�A6$n importanD!o-�;�0 ctro"�@>�0O: y��Sb�� 6ra� isotopes �E BBH8��Th@"�Lwa�s � zK{B�inO. s. AOE�^�-i- .:! same7AWon�#vol.!i�):8A[+E �2� �9est?�F Jw8Rz�iJ pruJ+'QLoQ�.�BuAMayurY�$ p$+^{7}$B�&*$\q�$+p,�reG;ce"�$standard sY �%�!1�$q���gy gino�+sun-�RR88}. !�6}$of weakly-I+Ei, or.��I domi?�(e5T%yaXJ *�uf)� "���t�Kt�2not�& Nin �a"The fi&�.q�M fragI��Y `�}[u$��a.% -e8� slp�0 iabl�;if?F�� dynam�� �er-� �Tnm�-�A`�2:K due nirq b-ngX know-Oi��Y `quotedblleft post-acceleru| #E�\ (orJ;�n8)P&k�<6-ip11}$LiA�ѼM�PBC92,BBK92,Iek93,BB93E�wo�&��bQ5<[M tudye 1o �a }�2b� XAS( �3.�� u�rAU�#a�@ Schr\"{o}er�, on (DSSE)�2�) -tim� cret2$. Onea�rG'a:I� �.�I,!8 paga�@i$Cq k]-step1�- �4�R�=�M��i�@�.bA@�% (to a specif. ha$ �e��pAn��Gdi �~Aݓ.hEA�\vert c\I��I $\ a�1wm a!�pu�&}�>�i-�-c^{\pKH }nV_"�.V��2L cvBb:�,�R:,7 >$"�Ba.�Q{C92m+ � "�8��t/Ruai�*�`.� �A�for*RN �)itu5JO *^ -���s�^as=�9�7Eu6> (CDCC)Q !�was�qaby Rawit!Pr �Ra74}�i�Ň(ar breakup ����A�$type $a+A\2�#b+c+A$V/C�(!# extensibG!/C jofe��/ st  SYK86}�un �m.� �!�,NT989} Sa@al��5�Uan ob+&� A1p�b �~quite oQ2)�af�O�c̓al. s. M�" � facW"r)�@�!�&� (at 100 MeV/%��(A�~+ � .e ��A��&�Uto oQG  o ! of 10\%. 2���-�M�dA� in Ti4O kineuH)i:Mrst�u� turb��2 , �*yi��:/!� fat)h�-Rf ӁYnte,� q)e�--��� a� 4ar,)� unpredicEg,�HX%rea!hXse5 ��A�a��D� Rs&aEAin�!I heo�n��$ ta IaY�ooJQ man dy6�(systems. Dusretard%i�~ attem�Io!H a mi,copic Q=*�r� !binar>&l)�u��#�$!p��!p%le. A�H ful# ach,��F�( Dirac phentVologyF ,�Fachie� �Km-us sc�"H�/$AC79}. But0)^us0 U�%��lQ�ate[�$�s�ye+ en ampZ.b)!�:5!�le�U� D Q2�of � }�%X�i�A� ri1"s%�e�C� .� �"-� 2�768��� �%i�AF�Rba��O6eik�S:m � 2jinga`Q1&��=c~*�# semie# s��� �6 I oms �e}�!^ �#ͩ � trea"��]4i�a�.=b!e��Za��o� a��I�$(see, e.g.( fs� DAl97,EB99}). Let X#(�( Klein-Gord� KG)&� %Za&+G $V_{0}$ �W!�s�� lik; 9I!# a four-veW6(@>a �S ptotal�Zy $E$ ( !%A�y �! $M$)I�KG� �R.�G5� �f� �$ 2=c=1$), � ( \a�a^{2}+k-U� )�si=0,!�  =� ( E. % -M4d U=%P (2E- )$. W� )h\ll M�# $E�Yeq!$gets $U=2M;'�p!#B]� �Ia�d+;.d�Wmezeriph���d��iV8!)�e�Th�*�!�always �Be �E ��fur�)%"plc iS��Psum� �4e�^�#mo�D!��inc�g��a��LgoA8&$is M�au�1"�p�) 2o!mi��*�Is,�& �.� �*o< � � � � -of- �� �P k_{z!�[&�ansatz%!&r)\A�[{\�M&�GSLO t ( z,�) bf{bQ� \ \exp"ikIzU�\ \phi_{X (�tO(\mbox{\bold�$\xi$}c \ .@Seq1���Ij isu��>f� E��P&� 's>Pco�Q,�_���iiEŞ�aa$4.�� ����.�iz) 22�E��ek5�K55JK's U4q M4��2^�)EOY.�QK}$1 .}4-hi\b, uaifor� G1pa��{ eq. �1!�d�+�CA� �a�E�*5!=��� Zssible ,$sdN�V ��is.�Xh"� 2W we�$aO st justif�>��1A.� of l]p#a heavyts.D*9�΅p*� if%Y�%�. main�^�i� tegr0dum B�~&v���w,R�. Neyc�!�� n�C!mea���=%Gesum� eq. U% rf-�_a �+�cer �R=�)C93 ra� inC\r&-�.tra!�forwar� how�( insGJng�.�%t.Sq� B�Ϲ$���A��ing $:ek�.��0�CR���r�h  $ik\�al_{Z�IŦ 4�G=�%����F�!ˍ�A��* soa��>f J� =վt[ -iv^{-1}\int_{-\infty}^{z}dz}\ =~ }��� h] � �W v=k/E$. UA��3�+ �,Lippmann-SchR*%�S+famoul6e�� ela��=#"�,  X $f_{0}=-ͧ k/ AQ�!  dEy��:�Q0S��\{ &[ i\chi!QNoK -1 r\} , $�Wa���gis gi]- by $!�[BT]&�J.( )�J� nd�Fbf{Q} Bbf{K}1�}�L�Z��e<um fer. \�fk n�1��0ox1��W! �� aAa�>&�H# � o� ]9��AZ� L in���= ����+horthogr�y���.� s�-R "(Zz $� is�& a se>B�3 SA-�'� $:N' A�J� I�)6� IeTO}^{*  z}2s ��~ ?rf1 U� �\\)36�,}\ �� "� #�,&l 2��6l \bigskip3 !�X`E�� ��2�� F2+$�.&j* i� 3 6�)R��)nzN,a�2.�JJiv;7�½}{; :H9�I=l�d1�A�%{��)oH�TX(R[Q�Qp + Jw-% M�)A�*� 3F�ns&F��A#E����0 �a�#)ץ��OJ�f"��%��# M) =-)� ik}{�:=.3%� � ( iG:7%2!P [ S:}i��7|-\d�cM�,0 oy�h(6��>c ���� V]z=bTa�%�ety�w� 3 4}��L� � -"�Z s (R�I��6f"�Sd.�N '2� �4� iX��EHfer8P!>�s�n, s� x2��be ied >��n@ &� ~m� reU>�is �R�6jQqbXc�*b�*J^&�s,  Et� �-��V�� jlJM2 � �$j7lJ�M���j�5"=k`s chaer&A^=� E&e�g4Lorentz invari�&i"2�0$-�orJm��`Aa.m�D�&��Z�8=>V_�f.M��28� � �� � d�5�E "�%N~=*E�%2�A!)m \�simeq(hf )^{1kG\ ��HowX? ��,Al!m"$z=vt$�vv@�$ mov%qa T� &=tra2ory)�N!me�Ne"` V� E�(" ) =a� }(t,b)q� $ !́C�#-K 9�:Va&� � �up�g $b$R eqs. 41%�76a_ ref.!BCG03 BR I!G� full���=y�0 Ii�q��R�$\ޭU��.(pov��ton+$y)I�)�a3@%G&�drrb � F>;>��Iint dU�%G�h(J)\ %�.�eF: o1���B%>i)$�� ��b\&rongly �c�>A-)(aIm�$A h w�I"�Y�YK]iE? hist�9m� (!�3.F" 92})!z�O��*��LD/'�,� solezn>��,$d\sigma/d\O3m=� �s)rB "� �t� 0� )g =�)$��2�A� ains <s7�Ba�5�JG)&)c# cons�ed ��tra�al h"9!>�|o�^ f, �he-fole 2� N}^{(aTN^� bf{R})2 t\rho_{&V  r1N v!E�&s!lAT "" ru +��( K�\:\�5A9M$"�/o�!(UQ� ,L �s=r+R-�$,9%;.g�'��!f'h�t -��($1)�A�Pb�T re.zS�h+Vri87QM3Y�ı�BML�tU=se7%..& ./Er�&�"YzNexp~8%+jE0l=0,\ 1,\ 2$ 9? O�!I0:��(.or���e Ŷz5 �<$ �B� !! =-ՕA��e �ё!�mx�("�k�f* � `lue"r&�$!ͩn�m���!�\�0>B%~}]% (mono�Z)�?�%~�hLtarded Lienard-WiechP+5v�! does~�:��% E&!,R�:�s"�. �%�u� ] ��4 hope�Ao�v?"Z3}�^x5|��%�i�R�V�$\0 n diverge!WVWvkQfied by�;!Yre�|�- s~qe BV�e"U��\�=[�(( 2\eta\ln  k"� +B.<́]] \ B����"&$u,=Z_{P}Z_{T}/�" v� ����.R\v% �-2y sidSKn6�S�ou�cluE�-qeF�a 4=3mpe�|re/�orp� = chZ>!#"q,J"c(9�  abN-� im6� s>u�L-$H���;U1A t��� Y%T\.���Ra79}� %��4d�,t&q�e2{a�"E�0 Hartree-Fockel T Sag0y �E� E2.|s, *JS�� :�M QVlac�vtM�E�, z$. Explici>OF�"V_{E1�q=.�PeVyxi Y_{"i)٢\hat Z8&�W5 E�e_1ic!�( b� v5� zf ^{3/2�"\{�arr@:[c]{c� mp b\* ifEuMj\\ �2}z �[2)0\:M� ` �. &�6n"e"rs :E1 (el 8G+�oe) ,z,��"��}%x2!x & 2}3�M{10}}\xi!Y_{+-3�`!� �� -�25� .� n>�5%�no�\\ & \s�b�Y%m%�Jq \pm2!�mp2I b)�j4=�/3-��*JC�- �eʡ�Q�u!�.�>b�71!�-�5�2=�qu�\5�nO $e_1={3 \�M 8}e�� $e_2={53 64rZ. �g� $p+^7$Be@# K �i�1$\��s��s*zUBz &� E�s� �*�2�A�v� EB06n�;&�.�=*M[t]q��}#� e-? s[ hR� =3.i� �X$2.5in ]{f1+N)�Bc�X An�*� or�&(1�2� �+Pb $=;$ p"�+Pb��507L&W1D�X/!��Kik97}�!�l,� �& z}, �5cy $\vary�  d�Dd�U J x N51� of.� BG98��*�XW)���3�Z�u.O� "�9�re�aq<�.il��u%�� I ]&= s.aBla�{f"a(M* *0�e-�i�Kt?�4]"1� �4a Woods-Saxon &Y ad5&e"l]��9]of 0.139!�M� Ro73�-6,Ber96`fCtA�.9]BG� %J ki �bi21� DV &�$=100$ keV,� t. =0.01WSO,�N, ...,�N�a,f ff250$ >f $.�$.25,$ 1.5$^ $ 2.e ��b�b� E_� =0.75$!PB�"2.50$, 3g �0.�4 . Ea��t$�^&]a�0�2A�Ah�&"6ey!l�b{9t },l,j,J,n} oX-�$shpd�� $f$�sA�$^8$B w�/edw}b�6y~:�!bV*�0% data!�r*%0�`��2Dav01m� N*{ e�ef�oea*llo1Hv̅)$proceduresH5l|� ~�provir �RIKEN�anX# � 5~@8�Q�X�#1�di:*�2- �) matc���#&�=le��>�=6�-0ы�s��22�9ɝ2r�C.= #%r2*ʖ6>E�<$\theta_{8}<1.8^�.f�-���v curv��Aknfv 96b8 �b�bA��b vb"W#-� d�f1}�3�AB6.V�"�:ы+Pb2H~G zG�&�eq�k3.�-p�SI"��De��v�Z@�(vals E=0.5-�fh(up�Ypanel8Y$E=�-� #lo� #%� I4�w�4�or�m��rb�U�ߡ�cF_6��U_ (f�)�ɮ�aA Bn"�U3-6\%B%�a0e.8�I I� 1�*B� "�s y~����*E�3 +.c�F.y-act�Ub1aske�: w]!.("� 1h do!��6b> ��.up2}i SU��@ trumQ�%�]�!�E�% �Eaf�n�>A��,�s� 6-Q-�d>� �I��sU*� ��re��cA�mb>30$ fmE2� J puKJ�<� FTF�,k !Bzb�"6� U��+���<e2vae �� �-�Nk"R>4-9S>^$ also�Cc$ DSSEc ,*O�0J�9,!y< u/he ��rum*�R al� �� +]�� cutoffn�&n�$b=9�is would"�2a 6� !I M�i(.J# &� st%� inum]��>=� ��c�4s (ȉ1�!b��2�7 ( t�� 2\%)OKwh\ran&�1a. To my�= ledg�_ch �mpaHM�ne���mad�c�-!�B�!E"�% �d ���-F��"��z!3ias�H3!'&� iderK=S�_2�C@nly�G�4 becar-6t� s52.�H�.�"�e%� �.�&allowRv�N�dt.��"jZ)P�5%Tbl&�$I)V,�3c�g  �U�\!�l?%�.}!>F>%�;lᕡ5�Dny%��sop� �k�Jbeyon-�imؔ5��%~$eere. I�ji��a�+ ��� Ri��bA� ��%more sui7%@ane"urm�p�a�"I:6y�KDHs draw�/�rkE� cruc�q.�BC�?��e"R�Ų7bombar�� �C� GSI� �B��254� Q MW Sch0�In �1 I�a>.�&� ��   $�=(\�!^{%t}-,*})/2�%��2� �F1onB�3N�.� �C"8�4�%�$^O�Ie�6�T <�� s teA��c8i2�"/O252aE���J�a 15\% �dm������* DjEtDy�a�M=U�6�agA��*0MQ'��� E]2a�NsiJA�,Q0�"ric+�#��se 2�"`9���Red)"6P�RYr� $Be(p,� )& �-O��ot easy��,Ms m���n���Dto �_eE��of some^�Ck, ݩ5 %��;0�.> .> �)�2(.z}�al � . Os*� rovep54+D�!�{nee�b@&�QdAh�*`;L#R �"i� I#E�t�GNDơ�s6^!� H!�:"�� 2,EBS04I � !�A?�b_!E�:B*VCpT�2"�otab�}�|l }\hH% Lab�y &�$V flbrack.*]-At  &2�<q&\% & 4.23.4\%$80 & 35.*1."25#5. %14."& 6.9&�5 T�F1:6�IJ�>t�*�,sAui�*J��H� t��"�b��a�!�m���U-� ID Y$�"dank T. Aumann, H. Esbensen�Z Suemmere�' I� omp�I bene�al!cu��* �� sup�� U.\thins�y S.\ 6�XE�`unlgr�.PNo. DE-FG02-04ER41338E���>[c�_�j%)`bitem ,VG�^$ur, C.A. Br�Y�)H�Kbel, NucPb !0bf{A458}, 188�_86 2H_ �T0C.E. Rolfs, W dne2�tex"A!S  Cauldr&5� Cosmos2)r��(, Chicago P�[ 198)U�c�6� L.F.Canto2��!�540,} 32�926��Rr+,D.M. Kalassa2b9/55b527!/>b-S}K. Ieki� it{\&�_P�c�a L�c$(bf{70}, 730U3>�93}G.F)�sc�]!9�2�V(A556,} 136 Mb3);:7E .[,.��$C49,} 2839�4);ATy�.ARR� �U A581�0)I56��PG.A�"�PV��#221%:746F+PXY. Sakuragi, M. Yashiro�%�mimura,J�c S�c�8n136!>+eP}FAANu�1�I.Jḉ�V� 57}, R281I�86� NT99�U� 2652�996TM$L.G. Arnol1 B.C. ClaNc)�6�B84}, 4�7>QLl97} J.S. Al-Khalili�`A.Tostevd J!Brooke- e {\bf C55! 10- 76�3K�#%_.y Ri] R9}, 324E>K%>�C�Campbel�(nd��Glasma�),ugputQ�Com�gQ� 152}, 317|e:�8,H. De Vr� C.WJaY>oC At�.��KIObf{36!�95!�8:6~,� erts�O0J. Borysowicz�vMcMan%JWA Love�R>�2E39� 7:oR-'L. Ray2� C 20�c5e�>?'Ha� gawaXWiv�c%]D�s�� 2���6N��5�A70!-383%�: }R.�vo+a�`iE�1�Ca�543!s7:� EB96Λ60�60I�:�� >�Z. ��A35�29�>E� }BARvif�e�l2�J,C63}, 065806%,16��$T. Kikuchi:L:< 391}, 261!1>�6�%�M. Ga^�6E�2�:5�F.\N\"_ :�%�6�9!232501�B�02Fs6�ZJ$5}, 024605Y:vER ��[h:�K. Sn�Z!0be pub�RR :�m< �&d"o� E�6�e�e prc,J�ep`#int(s�e 4} %ZE2&�e DJ�eW2�egraphqe2d,f6�z2&aZ�e� 6;amJ�enatbib%@� 9B \�eM�}Sf3$��fluid-,�au�ste��T: I�,Yulk>6ies5e�eTo�-ri Tani�*},;ta&�e [Mai "g8:~]{% Japan A�� ReMcIn�U^�Tokar@Ibaraki 319-1195,C% �%email[E.it �$@tiger02.tN(.jaeri.go.j���Society� j Prom"QPS2]ce,3 yoda-ku,�4yo 102-8471, � �>eAdvancedK�Ceu4 =Z!!��#2��g Masayuki �jzak"�gF=mk za@f��-edu.acV46���pY��&հAO EducE%$, Munakata!�-811-4192N�Satoshi!x1j^�s�W ba@popsvr������ \z�h |w!�Y�>�*c�Z� put^L em1Y�dlu�9��Xs�+m�vz A a��{f�jWgap��� "j0$BogoliubovU| e<�& >�e� vBonn-��it{B}*�aYOc.�)N=ne62"�5. �kIz4f�f� maximal2Fj_�-maxJa�--2~MeV^8ich��5�go,=�:U %W-X�wS� �it �'W a guF3to �h down!�"~=s�U-�.z=�+!M�9$ % Fur�morV   slow<�#���V2)� ��P�of .>%2he�)e��l�YVslightly���<SDA^bli6a"�kj6jc, 97 Jd, 21 -n}�i keyw��{S)jed }%Use� keys�? opwif' v2%displa��sired1&{j\seo-{Ik4]}�j sec:'Kd� �e~�a,�@-�hoA�suQn�97<&�ksk9����aDkeyZ in a���3!~coo�o:�~%{ kuni�93:_va�_�bes_high_b _O_E%_stars}a�Unt��^��'�{c.!I�q� o�lA�E�a��\I�supra �Wa 1its��.� muchO n�� 8�isЯl�^S[0e URCA�_^�orolJF�^�xIn�%, s� al�b� bary9 � beliei^�6ppear�e2$inner crus�&a�,c,l��]=S �G��t� suka!�E4,wambach��,chen9inO+M4�� ��>$10^{-3}�6� �@ss�� Ba 0.7 0�X)�%7 9�D�.5$~fm$W s�v]{tymm_�u$I�Jao`�#:A�EE&> (іNN�@�oa�atGpiv�on helps�k�!A up��l*_BCS me��ism. EhzXNl!�1B} \gtr!N6<0($^{3}P_{2}$Q%�!�may1IK�->6J|it! .��s� ve enough�|Jbq At��彡oeċ�-upiB]2 aT �� hypeE�A em=;�6ed��t�}Kc mE>�uA)�$ ��b��A�do-�bal�u98:_s_l@�,%�@[ ka99:�f _�_admix�2_cores8d 03:_ �8�:_bj $}. We, how�N,!�y� a p��ofQ r�t�<~�M pQ�studyw#siz6arEaM��6/�`�� 6\ial s��6e uncer+)T �X regar�A�e.b!y�;e medih(V%%�a.c�, spar����e"�#��1S7!e��q���(nda<�gF� �v�$! �+Qda+u�imm���k�le�Ta�%)H�~?�isq=lutely "?!$I��mer�me,)6!�NC>�*�(G >B P Q��AΔs�f�;Re�7]�2E �5e� ��ng��en!"!�A arch�:��Gy� s�%Nk�Mi< ME*li) eYpe�%":$tymTglenden�Z 00:_<ac*\ M�io j~#a�tmA�[6� �, (RMF) �,�� ly 2� econн�'E\ �p!&� cho4�rak�3%Z!��K2�Ha�ee*5 (RHB ��c35�HN��m�#ai�c@�p�%o eluci� k"E��. �2}��A.� &K� �(�"s\ �q�n}&��p e}�}$D*��^{-}$)& RHB-I� capa��rnd� �c:�!�re��M[lf%enviro3�al2 f�[��Hsur,J s CoM � %I)&�+�I1mselvr�E cour�%���!��)�~]�� :X ���}��J �>Qb a���$as�%ompan���7�FNg��9��XA%].> inS��A5; fFcE"e�OweE�2B|Rc�*� � �Y6oM��q�AA(��U=��2= cŪ�-afo���ed=$: %�2R�y(ah<ect�J� via; �4�� w s�&� yd%coN8�Fo�{!�2�V�, ��!:yOcez Need� !�s8thm)onn�!L&�� (EOS�G��;��hM��' &��B�, s�%��a6�a�ss,mx, so�]I��Um2ju �rsM�HingP*�m ݷiI1)��im; h�aN�0)bPe� %��% udy,A�a.Aj�6inct RMF��� 2� ��� �ea�9��se2���;� reby�chav{-u�?s EOSsK�. Mv�m�1�%2�/ $} R���k��>N N̓N���煹e�i�*� rgan��a!�/�*n Sec.w�_�ks},)N LagR/i�c�#gapY��!�F� 6a� illu�Rted��:{�1-LQ'}, ���Jy�E�-�pk nSX�s��y}A�P s !� � *./ (�M��s{a@=6 % \sub*Su{A�9Kc<Q -rmf-lagr&��. *}[tbp] J�k HBP6�� ��2�� fix!��b!���� $M=939.0$�!,, $ me�(�5> $m_{}=763 3,m�ETM1�W8 $W>A70re�._-ruled"M* {c5 2+�s�Q}$ [MeV:+o�Q �g_{.& ( [@1}$Mg_{3}$ Bc  =rho}$ڴ�+ NL3-hp�OL�a_�}=0$)k508.194,782.5 10.217l12.868-10.431 28.88 204.461�j} .025��N�5.376� Z271r�5. �78A^ & $7.0 �8.4065$%G & $-5.434 �-63.69)49.-?4.749�|.045|f�w���5.008�a($b�11.19)��fB289.� 613997.�!�0.6183 71.30�B & $4.6322 �8!qCaUH!Bj�� tab:A�F�� X��,�A�snowaday�Á��L�� non/a�8 bic, &� t�a$i�$ bosoZa(�$i�$ ���s&Rurk{.sucgi�"u "d�/ha�+i�uy�l�Fzof2�Nit���O[%$bodmer91:_� _"_"_i1� i}% 7�1�5 %ed [il {gmuca92 x(,sugahara94 }. A6 !��Grm��sq� #\i�:� ` x�""�2�T2@ m� f��e� i. A'�nt �v!yVIB!��Msca!^�v�s self���h�  %zs:�M_ ity"�Z�2�"<_/� (-Brueckner- WO(DBHF)7H Е`�de�7ly�BH. H� � � i�9!�h �*�7!jn*� AV>��� � 3 � d&x!I< �UDS� i�eq::����split-�$cal{L} & =(�ar\psi[ipI��\^7� - (M + g_i� ) ?-�y @>.'rho%$ \bm{\tau}=cb}4]���N{}+�O1}{2}(��3)B  |{}-.>m �^2 '^�� ${g_{2}}{3} 3 - D 3}}{4 46�g4}�Z_y�\nu �� W:�m_-:2 �9L+ 6 ����-N�!)^2n� bm{Bt ��� >�.��m_!�[bm{b}t>�,�ũM Y��O� 5!=5�!3} �_{!< - r} muٿ $��>N �ZNN�Se�7bz$A��II$,.n�u�yb)J�w� E�*� �J q s|�D�� a�� � H�a:L Urh� ��� �fjI�2 WҢ� 9�� �d�\eqrefF~ ``�O dardY�� .'' >v EFT-5^!+6v eft%v A��r.hV�-e��is��2��a����%q���� (EFTA�serot97�cen��JT!I rn a�"�"C ;�5��"�_&b�eR�:9$ɩ�$��W\�%{exact}% Y fu��YOa���.� a 3 _{ss�o�t P.� (y (DFT). Ad�a��"}% ,�ZIon�@�b��a)s9 " �.$littl`� �+I2is 27ag0^ u� ��!�VasD�:Rei'freedom&�ga.�EoI]of�;�wEAs�RA�bsnrenorm��� �Wis�>s J6in�ncp�, unr&�E�MQ�I any})o�� Q *�n`sis�� � �ANue8"���d QCD�w=� ��le�abR�!�Y��C�"i.�`��&��M� (horowitz01:.�` �`us}� %�an:�ev  ep�@nd *:�EFT"�FDFTAST�"�%U�6� ^a* ��-�5"?> ZHXviewpo8di� -�ym�%� ne6��paN=�h)Em� &� X1�X�s.���� Y&F� !�ck59�J 2��*lox& n ad"�b]�@ ��Vme � � &S &>Y>/KZ� "�)EFT} =.  + 4 W��W ��*# b# 3 >A� C z ^�,^ :g$ #a�]~Un�A�t�nflEq.��6? ``.>*6.''W"tTng��� E Y &:a�o�>�.�v�sym+y!d��� m{sym}�  k5�F%m }{6\ �>, + {M^{\ast} *XT .�}[!�"Ng � I%S 2}B��Y��bol /}Km)%��� a�O,v)eff-rho7��B� =2#+ 8E� �2}� >t!E�%. {\laG��'mlu2f�7maZ�O}��VÍ?� i � �D�ma�a%A$E�>������,P"� pick�)�v`��@� set�%��,% �� iere�$ low_!���"_E#};��vy0"L or .Qlip�of�m0J�epZ!|!"�YB7 EJ C) *�orho!�� q })8$ (0.6--0.8)$M$��s�5 �.>K��# is � �} "�a_&�qquad  ti�\;�)$(p, k) \:  � dk, %\\H�>1#E_�= � 5B� �� �� F� (��& b�^{(3)ٙ� J�R�b��V �N� k)$ ����"X g��:nu��a� ssa� bf{pk��n*q4= [���jng�a it{S}-w?!e�n�� ��,�Us"��a�x(no�FgDjh�Xtiрzed�$ri&�u X4 Rla $V�g�5is�tdMTu@u)"�eq:D*7 vp�9-�x%$, k}�.� 0s',\widetilde�� }�PV� RsN<k}]m)� ^�!�7p�tF�h�s� ff��iTa � o4S"% argu��Qovime r^-saV����#he�sts����$�J5xBl!$� �P_���Q�'A�?"on6 'A� ��".�� �nzE- \s b�!�ut[ cuI2uT ��&�K��$�,!��le-�U B�h��r2,5�:�[�$A^0nts ambiguity�N,�� C!6.�=uY`�ne�GIO-�%~UF  "g � &D*\) :n�@/$R(V� d�&c%.�7%.$%>� F6� 8&_$�[Z_$-� aphi&�� .5cm,keep��f]J1O`*�$jZ A��Wft ale li�]s`!JNc8�xK;d*��O��$Ś����AJ�&� �X* 65-AF��� �� � �� }CnTM>F� a$*�(%�fig� +ef�!-� T�Pg�� ith,& �Y�2�m%�!y�%}*�� �I�sD` out}5iso�*�!wai�8 YBI.b ��? .�4= appa�}ly2S rY �" +�ql�y� � �m�gq �[e�S%_�l!m7;inocJ�1�e��WQyHbMY�#� "� �alv]� �" % ��+ܡ %��]�.>"s&�'�/� as �!I>/ew�QV�2Ce,�!9ʩ � p�.]���samV� **��cB nc�wn�V2*`#-.�?�0we�[s �62�>&RBA�6� favo�-a�^� �#� �Ye�J�K����ur�}6.8Z}�grc,�Q | eO�f�,"4/� o"�/ōa�Z*.D6K�N� �>@h�h| i!T&%�thresh�OV �N�!OF��.,?,A�,ut 13--15~\% ��IaT�, hesi 9e leg2[ind�M% B�)$>gt -�)�i ��]���:�s $Y_{p4\rp}/ B�>>li! Qva��!5&- ��b bl!X curvYs E�o2�2>�i�����U)� T��ѐ�5Nnew�qX2�ir�  er� �'����:8, "��р���� " 6a.4>6 ϱ��.P�t�� %�-#���A��� (: �2�mi�!rea�e)�~coc �>u� f )F�,vd:g2^6�E~7(5�:S`? ie1�r�#onu �6=m�An핅$_* >%�@f}83��c �B�=0$T3s�����~�`�2� a�6�y. A��e"4Nn��is kin�p*�ʢ it�h �4leG!q_������ s!=l�CdYy��;U?I �qC�6%�iFH Ui BW&@�� Eq��"I%�-y�s2�*�A�Not���8�M�sA�:K!�t�!�&� W6>R > $s0 ( �/fc>x(�{)a �����"J em�ew!�up%q�{ofbMeDsh��=�L% -�>s � 6,I� �9ce o :t min�qo o5e�A�.{� F$*G � Y � � 6�����Sk /"�D.2 \s6a] i&�r|�&� kfp-gapEoA�&� .� =� o�ׅ!-2��AAs sB�, again,�*F )��-:� es2� asA�Z .zD(�B� E<l7rILp.�5���OJ�ref�{�0 increase ratxe of the proton fraction as fun s$�baryon density (see Fig.~\ref{fig:part-@4}). Comparing^ propertyJ j s atl same Fermi momentum explain�Drther details abou7�at: % With $\Lambda_{\omega}$, where the rate is mode v$ relevant � ies,� � Co�P pairs are immersed i)per background than those with���@ rapid. Meanwhile �hig��:wi �smaller#L Dirac effective mas%�1his. W!us obtai�eC�ing gaps1=�$surface fon8 parameter sets� N�namely,8|EFT-inspired Lagrangian. \beginACDure}[tbp] \cente�� \includegraphics[width=7cm,keepaspectratio]H3.eps}8capA�,{$^{1}S_{0}$-� �Ak]�!{)@ >�Hin neutron star mat!usQ� RHB Arl-!DST\mbox{NL3-hp} and Z271NTML?Fd,. The legendA�a%� as i �Z�.%label!04:kfp-gap} \end!���J�4%� �i%i�y!*A��:�,Solid curves%�!�-��DF�s�Cgap+efmENY, resA�ively>�gap-nliv:� We c���a�iaWV�)_5[�0 ed w�kA� ���`isovector nonlinear couplaF� in 6��. Sinc �1�dependeɤ �� 6�e��ed from�9&>\$is almost �%���any valuNfJ���1%; reflec���O1��7�Is pres���� c6ls q�(ne� 6=%r n byF�. HaI�]� u ^:)/J.025$ isB�aAnA S�set. �0note, however�� ia�E�(roughly cora� onds1)$inner crus%K.�s* � $f#,is much weak.� L cou�!� . (2) At.�(approx 0.1$.��B�� �1ayrt�deviate�� eachIT, so do%�=�sB�%OA56�set!YF� �J�$�4$-ӡ�%�incid��re� .�!&3) For@=$ \lesssim y�0.22?Aϡ >s mak�]��.�i@C is implieA�at richq2�Bs favor �P�>Ejl�� by takcadU ag�Ian attQ v9rE�a� X-  iA=ak �this ��!(4bN6C redu�.fa~ for%%Jq�(righXdashe� ) a z�����2�r�/ gray4@re0 Ye�BKA�ormal e�I4 uppe)panel��drawn��n6<8 $T = 1.0 \time � 10^{8}$~K�� �-3-)>{(nuemit-NL3h�U�U7B�Sm-6m2�, but�!�a�%~�� Also� % )�EcGE�9�dt� %B�2�ZN�:� Let us �Y8ree fi "�  physice�E]on �s. OneA565��Tc}) � U� � F�c^�!o��. � V/$T_{c}$� &| universal��A�a � -"�BCS ocon�6or� $T=0E�$$k_\mathrmMo8 = 0.57 \Delta(!4F}^{(p)};~T=0)"f2C� �4 Boltzmann con:t.�ݾ ins0 evolved6�!��$}�R� signif"�  9h�� is likelyA exist�I!�all s�idered���� two%�Fig.�2�6� E�Q> depi1E|B�$Q$F�irF�$R$1�J�2� a:�6�,�m�Ns $T .��Ŋ$R �$e now take�examp��!lj��a coo@ a� �*%+ks.%�2>Z~`�8 �8 $Qh�l� form/ unit�,4erg s$^{-1}$ ch$~\cite{lat�>r91:_��_urca_pr��_�_�e}:�eq� 9�eq:"1y� = 7.55͠%�(30} \mu_{e}a�9}^{60\ L{{M_{n}^{\ast}}^{2} p2}{M6 theta(p_{� F} e} + 6 p} -: n}),3�{$ �� chem� potential!� elecGs (8 $muons due � ��i -Dbeta equilibrium),�!9e6W 5��=9��h$�� 6n})�trianglhn ���� icle�a. Af A�appear���fy a�Q contribut"�E> ino Ia� m� v��Q�j�double���� $.  = M_y m'$a�Eq.~\eq�6�:�(distinguishA�-�&{RMF ,�m!�$introduce ")- 2esA�A�shortlya� issuBter!��Q 5[����t�written!� $Q =�H R�B> usedB be!�# eqnarra���� sup-v �<R &�& \exp�ft[ -j? T) /' &\B} T \A <] \nonumber \\ Z��c=0�e e 1.76�fc}J ) /�� 18"A �Rof!�%q�pas� udie .� �io�tA�FB�mo^ Y�=� lead�!veresti1 ;sup: Zi@��(yakovlev01:��4,takatsuka04:_Q_E� _E� �� . Al g=`employe�N�t� �$ a qualita� �19V study,��&us� \"��.%s h quantiQ-d � u!�e���ta� Asww{> �~2���, botC @�!�5 �?V{ yiel�{�  RB^!���r �set cloUa�!� - I�2�t .�� sME� refo1Y�If��notZ�' is clL�bt��sh){�^*Pn.�@B�#son�pA� �!em�5}i� de enoA� to ca@%1z�>Nis tura�onS,�X8rongl�Aڡ�� � ior.�a6}F�%ForIn"�"qB�$aM�� hand%3 6� �Q ���N do !�!F lap &�;3G er�t�#&�$= 0.442$ f{ mY�� 136$5�Y���Z"Q = 1.028$ jL41L!E!8A�u�eFY of n�)��M�o)KJW�f�(. % \subs�$on{Dis*ion} %� sec:&[}36R�(�o��6@ 6Kr--��-��} Now�8develop a brief�Z]h � % �/ V!� abov���DF� �$B�%.� !n.Ys Dcan classify obser*OEU� to ho�$A�colder�=,s. Broadly s�ingA��ean!�r re; majo�! � scenariosE� so-c�& d ``; ''w``n  ��x(tsuruta98:_2mH,E7an��4ut 13--15~\% (�m� hatc�JB#&&0 ) a�* atesxi02� i�q^29�)�uG5B�&�$. Hn"ou����e� �)`)�oG-.d x $ e"I q~3��,!*� p!�!�6is"@ t �[ meet�al dataB�6IA�s Els �v���`'��s or �� !�;%Sl+ consuG�Gcoysof!� ; R �ens��MxseQy&p+2�&6�%�� �,2�Qi�Rmpoz A3� !�X  '!%.� thresholdu$� 7v 0}�is!�hibU6�%[1um._, F��na�F��Eii�� instead,� �v n&!� titu a|�s���regard,.Q$*{horowitz�U@}Ki��eZ��/�� med % n�)��Z���Be in min� T)put a %*0 bre�#nd� mE�1�esՖfE-s76>_�#!�_�,vosk�Hsky87:_descr_keldy}X0t work� ", accelerator�le� �v.$ ity`$o4oun�Iretard�alone:*�+E�&xc�tse�� es s2�ey' a�mׅ� +�E�& ,�r5'� treat� .*2 doe�a%* to&*�� �ZoAsn2n)���a��_r� s. Final�0we��not!ece%!�s�F�6[ Ar%^e ��. AccorP m, non5 c) ache&�#-\-Brueckner-Hartree-Fock %E)([+ simi~�Е�ma!il.� $" max*�' 1.0$~MeV { !�7��-� pc�+�$&�(u%"R 97:_2S^ _�$8,% elgaroey96:_�_s_bonn,.�V repancy�A�m�.�hav�b&ex�,9a�r�Km� st)�!;�� �ne� �!� ow down f�4 ��2q �!Npur�� �n����)text, exi(p5EOS�S�D �i��rEF experia_�M�- )G i�indisp�ble�\�Summar% conclus} *�s $}�0��inv�g� �F8U��e&q3 Bq32%q$Bogoliubov�el��g0� ��� ��in%Le�4E�+r ing�'.�� pec�c�1�be��-qs  bulk�76as well� ��a|%� l}Ce�Q� "qwmsZ��e���"�+cor)>on����>�i`-e��3G�!hW!7AizeeoI,�\ing: Fir2&� .� ue]E8s(ԭ�J�A�9! 1--2��,�t"� ]�s8a�k arA� or[��/y)e�E�p�)z] �\how� M.~f�*AC�s�� .2 �zH17d%�a?6I �@r"�SI �l# t��72a3er*r p8� (KŗMt� &)�e!)os�"B�r)a�M1��*� � ag,:t++ eral��ect��= S6 YB)�iprobl�~Y�ex�2�8� ���3 �4%[M nC2m�EFT>�"� J��strucyradius&��3e��2� U�can��Yolled^ ad��a��dyJ'4I:E f�:!�4 m�,,�]�*g�`!���M �vF�"w�$�*&�tsl�)ly��a�"�,BA.becom��Bij0�!ru!out�*����:� � �+\�|0it{p-p}} chany)&�/:�0n ance, | -" is" (or in-� um)m4 spinn0� nk�nRR��`(ug�y!�bably a<�mޑC.�at��F Ltanigawa03:_possib_lw=_ho _b�kT F�Ayr�d%V � Dch may play import� role�U-QHAK"�(th 4��)͑�M�A���ad ��s �kubis9� aN In�^�z� ��r"�7a��AG2����8n � "�1�^�@2�&�&M!�. Last �*Ale�� clar"�)%:� *2"0by�-% 0aZ�$A1 zero.� %�n7prepa�Xso Bi� �6�. will b�>nd��(� w e��<"��@on� )7eF�f2� r ,�ρ� ��l��einEmacE;nyd E2i:�. i%�progres:L"$acknowledgf ;"On�� us (T.T.)Ag�@ful�0Japan Society%C!}Promo� A�SciH!b% arch�a?�4member5�( �@p=manybod 8or had�yst,�� �HAtomic Energy Res |InA$te (JAERI)^fruit�� 3s.='B58 thebiblio�?y}{32-xpA�%\ifx\csm@ �xlab\end \�x\def\$#1{#1}\fi �#NGbibO font>J�0M#�Pf�Q$�R cite~R.$�Rurl^�url#1��tt!O%8{URL Iprovid�mand{!\$info}[2]{#!�>!eprint []{S'}A3X em[{2�${Kunihiro �4et~al}.}(1993)V-(, Muto, T�#(, Tamagaki,aW$tsumi}}]{k e93:_v$us_phases_���ar_�� �&� nfo{�}%U{T.}~#1��}}��>��:5 �?R>�1>}},��and���T1~2jou�2}{Prog.@or. Phys. Suppl.}I bf%h%;(volume}{112:�(pages}{1} (�y{A=}).fx5/A.U� f:9V= T.~LA��A{�B2�%�E�VTD>� ��i;5� Nuclmj  A555�Bq 28ʶ Chen��), Clark�Dav{\'{e�4$and Khodel!� chen!�� �:J.~M.~C�.|o:�Ve J.~WB=��> R.~D>>�C�� V.~V*6.�1"�d%�R�a��N-�Y>-�59��$Elgar{\o}ysit2�6{"� {a}}:�?,, Engvik, Hja�-JensenA'and Osm�. tripl� {\O}>Ex9�%NV LB@��<M><2�C�E>U- !/A1�Ri�R607�BM425R6}:�j0 Balbf4$and Barnea�,8�,b &sx��S> `�*NFN�ZPpRev. CjQ5^O0Vj8�q� � %G9!G&n9s)M_�!_admix*� xʡ ����jt10^� 043R�9zvi7.�200>_ T -a�M� zO  Chiba�ڒj�* �:�V�B��?��B� �!F��>68�.�01580J� !�r�GlpL�(}!�0a4g 00:_c�� N.~KA�.�.e) emph&� title}{C�/ ct Stars}.�,publisher}{S $ger-Verlag O"� dd�$}{New York.� 2000})��e}{2� 8 n6���526:Bp� 70V�1v1mucɦ2!g92-��B O.�� Z. �j�A34��yR �387} N�2r�Sugahar�ok�J4�s 94��Y>B^֑H>O��79:B-A55V�4v?ero�WaleckI*7%?b/�� BJ@ ^�<JJO�ZB(Int. J. Mod�>EZe51V& 7rGH]( a$iekarewicz���{�.��fn C.~Jad.���n:�.�Zo� Lett�^� 8^m64J�200v�Carri�1qz�-, 1#��aa9� }]{c V> low_ *i s_M��B|�:HV�v��2���B���A�!�EaSj�593:���46J���Lalaz�IsF� 1997:z/!(K{\"{o}}nig� Ring!�lV��new_l�Y�� G.~A�.jt:�V�B}�A�� P>� �!��:��}�r� ZL540.� � !�r Machleidtz 8� m89:_m[?�~B�WZ�Adv. �?1ZH18R�8vb "!N�89:�.!��I�]{.$wC!/ _�!_e�_gaps���D��E4�� � 2�@"� $5>+� I�~`B22U .}��17J�1~�SchulzeN�96:� ,, Cugno�4Lejeune, Baldo)�Lombardo��s _96a dium��H.-B� y: VuB� ��<A>n ߒ=B�%�;UB�5U2�:��>37Z�J� 1996r��4rm{James} M.~LzHA�" .� 1991:Q$RA, Pethicw'8Madappa} Prakas�HPawela�Ha��l �{- 3�:ce2�Z�u�eF��N� �j@B~>�]BN)19/nY<~^6Z� 27NAr_Ya�C)�.K7 :K-$, Kaminker�Gn2��]BKDZ�&�B�pj�>BX��>O>  ֲ��BR 5!1��:YRep a�N�354:�ѕFR !�r�"�� 29200�t"��E~hB�!��fB� *o!�99gB !j� b!3VdvT�?� �t �theZ�?%�)�{B]u�v29^ Fv19z�M�>Rl2:l +, S�>!�Sew�9A� Ransom��2?~� S.~SA.� |:7V P.~O>?��>FJ� �?�S��0 , , Ruderma2and Su�Xl�6}]��=��Bc! :BV�B� �Q�2�����VPBf .��3@Z*��Nl 20Z� 54R�7v� V*�>!� Sen�/ov8"r?�V  D.~N>�.v�U.�A9"VVARp%�R�Sov�28!�^X4!k��W41Ri8v)"R -f" %e"� ��_�**�"� �� �� �� 9Zy#3N���&,&1�.<�*%b��&:�&49 ?����&��&��&��&��&Z`46J� !�.�&!�j�&�0c�0:0s�5�)�)�)�)�)��7ZN14Z--2-!�j-K�8��$ Kutschera��B�8~B_�F B��Zr)T~�B39^@9R9��t>26 M6 docu}7%%% LoGh Vari�?s: �N:�JexLaTeX-(bflyspell �O: t0End: �O \}style[9�4<,pra,aps]{revtex!� w/$} \draft \&{\bf Qua#ytum<�Mof�>mplex �7:.�9a l9 size?@ intrxbc�@ucFi} \�{V.V. F�;aunT1�c nd V.G. Z8yi�H$A_$7i&dw$Schoo�^!�ics, U�cQ9of �&South#ls, Sydney 2052, Australia\\ bN�?al�3e�c$ing Cyclot�8LaborB Q \\ Dv:1Hof�eE�,nomy, Michiga9t@]�, E�ZLan�FL, MI 48824-1321, USA!�ate{\tod"\\rn%� !�ghten#@ s %*�"D:b!ct} A�Gp`_d�gS>dei;to�@�9.Je*5Yq>:Zb�?wo-:I_�Oi= a*�`b�!�;is dem�r�E=:s� �>a|�i,@�:]�pr�>(ility. ApplR�o�J�BzB�IyF, hydrog^to�G*�E_�:5Z�\vspace{1cm} \pacs{PACS: 32.80.Ys,21.10.Ky,24+8V�� "TGIn�A�;} _Nes*�Bmev@ismA�qF�= abun�Kin &�ha�>6�"ics. C�breax�Xlow.�R s, dyge phen�}aY�kseJ R,1� alph� H0ter decays, f�"n~nd )��i�Irmo� a�Q�kpG5`vQ>aExtbook &�L�}aHM>B,�SYC:�>��]ǥ� point-lik�h jectq)>�@�B���|ee%�freedo%�am�ŭl�Bby�Xi~eW"=A#�o�J�Stsi X�>N+hui stic�=�c!�of1s .;�1$antekin98}!�orGXto{E�SFU �-��9 fr�T% xJNunD�? � hi9L �4caldeira8183}.pu:s�k�f,�e;I�a�C rgedSH�P �Dbral�emagne!�, (�T naloSbl� shif�c�E��c�A*�Ayba�� �FZ99}�Kr�sty� �?�i!��g�Nal �!�WEVc�R�soEU *aRkLi��YL ML. AnY+ qu�Ko%/hqVn�re influx@"PF�ae�!�F^�P �rem�# poo@vEstoh*�]2a�u|i��|M��ma�Iai�I�'rN� ing�Fa�%5?!b ,I%&�l�} ����  ``Egj tact''A3 semi��GM !�inMZ beca�fiI!��bA�ldtKPmgFr�zD0.7($2 e^2/\hbar$)�LK6vof| Ap%� ize�0one-d�R�RalB �FK} (n�UEj1/%&�ls FaZH even XdharbitrS�r |on)cs�M!'!1&UN .B�*m�"� ]�(" of� heavy&�A-Dl��� iToA�tE�nalyt�*��Jlm�F�6M use �`&�. A-PA�L� !b"AZM�b� oscill�Yy . An*�N;abolic#!��|��o�\ga sign^�J� ��?�l ,X+zJe limi��$}�id�S�Qm) q�a.�Q�v|"� �s2zWI,Iaof�-'rJ���=box7Lle !�>� enc� 0^actangu m��KrS��mG�\papъ(y ZakharievEASokolov�z64�sit@_�SaXi>�bI�!�b� Id|c�R�E6^4�U�D?T� e)e�W/qp ic �riz���Ja 1� adiabaE�lya�rY�SC6"� �}q"! ty���{Two Y�s}�&tfN�yAx��!:� cng�c�ha�.�mo�M-��R�� %+a�9� nl only.H Hamiltonimf �&�Nisp�3dgH=Zs p_{xQs }{2m }+yy,1}{2} k(x-y)/ 0qx.�3X1.�x�A�co#[A6 , $x��y$���P"��%\ a, $�$%? y�irefPNo a���O''E�``�M on''6q��`�,$(1/2)�$ �]ibM?�i���*�>L)$5�A``� %�P ��X$q<0$Ea�U�Xq��@NQCXNo| �wo ``u s��to $^� o�+h#+''L any z  u� �qsec��1���|e,s dJ��^{4}- 2}\2~(I�k}{\muQhq}{I�� ) + &m_A�=0,]�U�6sNnd]�&�l�med �6�u=qX/( + )bilLo� b� kie0 �ra�erm5��Xt� b* frZcc ��!�r�=1��es,F�\nuaym�-14, \quad \Omega 1*"�[n� ?�-f �6�5E7BETH�.�Mv2 o"�s6x)�_{\pm�z ��Z\Bigl[ �+�$\pm \sqrt{4 4}+22}/(1-2\da)Tr];�s��8B��ma�, $�-�u(s imaginary6�a-l5�$%zAny}=m$,�a$ � =1/2�|n�9�9-=�ml[q+2k9sqAU+4k!r]>�529B2I U $x$-��(��"ASw � , )"i�a� 0,\,-# 0$N&L�_{+M^i5]Mu2 )-) 2Y;�f�10B�i �y6�n_��1wwo���Fre2x�V =yI�@�9F . pW�\f�l&o f�ee spaf{B�.\ �_�Tu~"^diagon"��W��*> �kw�Vr� �xe trans6bew.� $u_{x,y��nd � $v J��=\�ą}-5�p��yy xm�{}}{.G$ y$y.$y}}��2J� ��=O�x !;F�� ��(��N+v� )��w . � 6�- u>=�i�� W~u \, 5qRt��6�M�2.�T6F�b�kiuvBva[}tE�Y��"� FmT �:oE�:~FH�@=\xi_{1}\cos\phi+2}\sinm�- y}=-1. >���3B�� uj^o]7cyR} UM�%� �!xU_{11� 222}+ 0232}N� �4B�� FK �=k.m1]Tx}" 1`.�>sMdQ[Q�-�.�2.5B�B& U_!:�-�:�mlh��sinJ�F7 N�12>�MR:�-lj�2�Z� )^Jh=� o2�x\,W��5�R }��r[��$Ah2X�&#�*mix�a��$�N8\tan(2)mO2k��� }}{q +k� y}-�b)}=-2"" �I (1- )�EO? +2 2E �495FD /w�^F[!�:� �n� � �4} Ɔ �U5�F� BA�6�|2VA��&��Jw T!N�|�g�t�t ul��� agre' (�1.8�b�&� >A�1}=( Q �^ ��E .9EJ �Fw.� _�G�� d&�� &� 2 R� ,Psi(x,y)=\ps�!(�>1};�+}) 2 2-})��1F( "mR'al`S. P&-%I"� h$r�� ing �*4! nU$q]p�, 1 )�����oteffic�� !����.L�!BM!>CT��D}{1+D}mfm�3J| wA�F�D=`.B 2 \pi E}{� |�|" ��3J� M�&l�{!��"%�� way"!Fvi�(re $E$!&A�$ ">m�b�qg0�wMp�($E�2�6"y&r"�y; $E=0$0E{top�-��Yp�#�"�SonQ%g� �$E<0$?#z$A� �u$$k\gg |q|$�c&�''0(� o Qn �)6j#r` (!1��P)F.�\im=frac{|q|}h 128kQ \��v"�0v.BF 3ZF ��0 $1+|q|/(8k)$���.qJK�.�*�%�!�w�2nin h#arG����b�, f:(($k=\infty$&�>�D=D}�>t\pi|E|\�m!M}{2 2}e� 5\nAmq�0AC9j .�C� ҝGT 2 ՍH�g.jF� %!�a"&�#E�ea`toomV�gi�!�+*if� ``ch�&"M"9F0/ \ll)�8 +IbH %x}=}z58Fl 6o�h*��$#"k?���l"� �e?oi :  (�+g�1� -}$)� *�!�*/p"5��og���� ��$ef�~2���; ergy�Jns�mxa� �( NG k�u$�!kh� h!�$ a-~�6�.�1�h�. a)FA©���~!�%" �QA�smootԟg�'o�[�'n��y ��A� ���Ptop!v�a-�a�) ��" vhei�� occurs :D~(%&� %a;,unperturbed !r $�{8 \nu/2$ far awa�gomE�to+P+/2X 9��-ca��"ver9"x+)��{>�:5:F� E=E(���\nuP��  � �=3+ q}{4��k���G� x�4�^{3/2VXu�NI�srr%B gr�!TZ 7�y�A��r�o��Gl )���~%�= b�qeN}ed@ �!�'1�' � ) JmF��O/{\O E}^2.�5F.�  $ ?"W B�� �$d$A� !ic l a &,s i�uvflnd��t���deѥ$�)m�"d|� E=- � � � ���` A�fer�T��:� . Indeed,es>��O5�t+dipol��(is $d=.� E}$)�A|Z)� &cs\ ,ce, $(d/d x) =1_^��t�AI,i(*ce �{�vp�"X#]sto"A�, or,5zit���5mK "� 6N�+1͍� ��J�-�U =�$V�I�i�Z^�'} {2r^4V�bU�Fg AvV)!�� d49 �� %tW ."u QLe empiriau���rod1^82}�q^=0.70(5)d�38u�'"d'!d&(-r��WJ��!�� 5� ($U=Z*)r +1�A��te WKB:�� �'iUQJ� &� -�� e�  v��Ho\*�!)� Z��e��2m}}{5�((r_c)^{5/2}D��5�J���v��rea�ve velocD1$m��6�!� two �"�m $r_c +cut-of�-us*ʎval��=y=@��5� 9��%vi�- ed (o�m r_d$ e$ ��hF0�0ra x). шf\'y�w 2 (6,cY�dƉEK��I�Y)isM,"C0 1\%)* 0 it r��l�w��A ��%?ar �.6b ``CH( �G%ݗ catalysi�In/��":!ie B�\ ceedp�a6@i^,ic molecule,t0 \mu$�$$dt �� r � -(�-�,io�0�ɱt� ;%ly�o�6s a toh��5n�8u�$��P�0ng]E�}�� %_u+/1r9�j��9�� $q>0���xp�)�A����*/'�.�sZ]#laP71R\%�le�e�� {+B$ <{�v<-Z<1}2?0&:�7F1 Go����;*i`#l., eqs.�2.1})  (�2.3&cwe ^ F0 � �(V�� 2'co"�m9JJ�W}ܶ_!. ,�56]B��yTR�� ��-2�Qph�+��9�F^� xyJ�!h\,!< A�*_{x�.�1=Z-}� 19O�Y]�F�Gq��/� *3*aS"*7�%aP .|� e�mR�$�q$AwhavJ�-�2V>�%2mqu 1+ � � k&x��r9F�s� �b�s����*2O 1+2L�M6same. "� e��8p)�*�''{Cstretc�- (b by a �+-0q/4k})�GJ��ɽ.�.6'T"��h2g on (�>)0�2!#B�-�� <aJ4+6#<$a�+'$ ��o� &�,.q(��+E�}* YF�"�#fr&j&!�w=�_��^���M�2k+�"C%� %"���FWAtk-� �F�)I*����/$k$z �E��+�2� � 2�er-of-�+�! notr�Qa �z��*� �8. x9!"J"��FB6.J C&T �b�lw >��5͒�9.�����k/X 2}� � (A') � FFT��h9L6[& | & � �� -41C, e.g.�%~�1@Hr7� �(se�g.�7J"�81�iALr��cs7&&<"�*� �h� �re?2sit�- m\6�.3�rQ9߀mE�a sharp � �de��? j;&c3&�8S{��l } Our6�D help&u-@s�c,�K5L 3, & n =C��?4F>3 I�z�iceP�"&>��!�:�26�>Qby�? iJ�?�"�Ac�%�ed��_necesAGto &�6be݁orAO'.REc� ���=�.��d"m )�_MP u�I���nI<MHa�of9N"� I�!�$a� �CAyňoa��n�a"�t�tex��3s.�s�6uk97, $9}. V.Z. &b��ush�*���c&�Y 4 =G1lem��aQex-�/�th C. B lani, M. �U < Moshinsky, A. S ��4A. Volya o:�!��>��W. Lynch)��� !Kl�o*ge NSF,k��?(PHY-0070911A 244453� 4"�In R�,Council. � >~K{997�Ttem:8D A.B.�cKD�N.qj�,}MMod. �". K 70}, 77 XQ8�:^2D A.O. C&D\0A.J. Leggett,J.cE�t ^P46}, 211 91981); Ann. ,(N.Y.) �8149}, 374 (19832��C 2FK�:@K,�o�5t. �83[108�92\yA$} H. Yuki,�mKasagiASG. Lip�T. Ohts$T!gB;G;,IM6�14�29!,642\ %� Bohr!� M�� lsonPV�5"�04, vol. 2 (Benj�b,jM�s, 1976\*�N!�R�(, L.D. KnutEFWES�UE& Ma�Tsa�i�&!Q).e90�822���7׽m*\N.� C Z55a02!*97VZ9Z�YV6U�ECNeuda,�\� j6�c01460I�e���>� &�O ��"�Oc�%&�O�<SL keys, P�s,amsePsymb]P�(usepackage{ �icx,c��D2,subfigure,dcolum��N atle�� %\�#��Xt 2 pc %\topmargin -.2) \odd�  -.6 !20D8extheight 23 cmEZ�� 18$setlength{�sep}{0.5`Q plus0.2ex�C ,1ex} %\newco��Ole�Mpn8{\let\CS=\@curr!\re.0&EzO�4}{1.0}\tiny\CS>]&�pa�]25Z^( {\tab} {\hae*{2em}6� {s.$1$�NYWUPtle{R�HQS�rG��?s P�*9 HB Io�Elli�?&@�C�O�Pi2�IP� �R4Bhaskar De} \�Il{b (@imsc.res.iѱ\affili� {I"�of�zhe�F��Ps,\\ C.I.T. campus, Te�@ ��(nai-600113,�ia� S. Bhatta�yya\foot�CBymunica�*A1m� subrata@i(H.acJ���ic)3Ap%�d�s4Rt(PAMU)�IndT?OR�"al �, Kolk��- 700108�2LR 1�a"�Pv�� i+BtQre,$ys� nd�C@�D!rI �5�iذ� by Eremiv Vol� (re�w AZa�).�@e�m*�o 2 pret}/(rM�-9 Y�v ��+v&F�Fb��$Pb+Pb$��$Au+Auw*Q��JCERN-SPS#RHIC-BNL� ) made ����A scop�Dd�+m��pe2=��%� �  earli �� w�!�s&S��$� 1� �� tݔsy�! some!���� s"�IH HIJING, VENUS etc,18r� �A �rԔfir£�DBq�t on py�� icl)�/*x��QA?%&un)�descrip� �he��ity"����)2!, ��?on��20�S% l�0�v]Qd�"��F cU.�xy"$ \keywords�ĖJ�=�${25.75.-q}6�Uneww_&v/6�SII0r� ��JJ 1}5;� %�E�no_�+a divid�PiG�p1%�i�UasYKp"&�:=�s ()�9�) ڣ�P,ons/quarks/v�sAq ��taB assu�7�!�<&<buiD�we�Qch.�%�,V��I��r�c��;EEem��ch a �U��u��z�$deep inela<. U !pces�&0�lepton-Ӑ,ې A� -%�*�Yn M��$, Biala!; KJc��R�g�(hypothesis,��K�me�%h�Fdi�#%�l(AQMj{ k1}��H6$ar!k(=s)�a��&"�el�3sI F D�o ���#%��N��)��i� �t�K��.W2Tll~s�okA�r!�u��� c�n o���Xs���O�d1C5oYt�1A/�� viewA8�G)�ic6{��s� ���p�>*of F�i6#��o ��.f5Xmen�R�a) w��( ��!��D�t� A6�pA>, kao�"phGQ anti  � rate��n�!(i�>d�b8 %�5<)�@23V�!E�I/$\Q(s_{NN}}=130�200 GeVr ivw� Be��s,)*� lEL�ST�J�in��H IoM�,�"�y $e}(�Wn){A�o �W!� A,wM�7�a �i>�!�a%] "* *�� a�he�iE�!#��d-�4a�p��amm-��� B� �����ly�3�e2�S�Y� Z#dealt �aE. OurIV�<����ami�Mhe rs<��ca<&� t>a/i >����deF d by $N_{�0tB7�'VAMN@q�}�!fp� exac�7 ways adop!�V� 6/�9� b��9rɚ$ Woods-Sax*Yd0te�filiCa�TiS-6^*�9"�K7!�4} n_A(r) ~ = ~�+n_0�9S*${[(r-R)/d]u"6�$�)0n_0=0.17 ~ fm��8$R=(1.12 A^{1/3�� 0.86-) ~�(=0.54=$. \par=R�i~ ons(.����u��($A+B$) �D�7a@[acar�K $b�" Qu��E4ex�j�(2�,9�m9Wa�}{lcl} NU�4|_{AB} ~ & = &!xXint ~ d^2s ~ T_A(\vec{s%(4\{1 ~ - ~ [ ~  $\sigma�^{X } T_B>-F b})}��0~ ]^B\}\\ & +RwF9�{ u[  ~ j}�}{A�]^A\},� % 9,QJA��$B@�a�W!I ��� ���iY�(b) = !L_{-3}^  dz A�7$b^2+z^2})$jVK|F�f�HAh>cA.4!q� c *� ;ZTae��e �:���z �6]��� � mann�Stͮ.������.50$/s�&: to�a���$, viz., (i 3 '4��/�5d 7 =�_�� ����� ^q=3�51 � ; (i c2"N$ ��� $\-vqqI>�/9I+(iOJ)i�A% �i� �!t�)ir>!�+ keep!LA"?V �i�&U,5#"%q.�f2���sawa"~\mb�eV�%Y(�-$PP6-P\bar{P}*� �0EK�!�H�u�� $A=3)> $B=3�=n��/ �A�(as hard sp� �j�H�.i�� $fm � Wong�� /�?ent� we�9�NN��=$ 30 mb1R�* c.m."�a�Ps��(}=$ 4-17.3 � �-"�i�f.)�Misko�^�hig�$�_',rst fiiK  toL E�-s�"�%�!8N�s t PDG}�rh beyon�Q.� � GeVsEb>sDe$-b:�Cq!%C��m��0(29.2\pm0.3)[�>(2 5��GeV�D-J }]+ �81)\ln{�7 !{10 ~9�6l�(0.19/00^2N2!� 2F�|!D$\chi^2/ndf=171/47Q re $$ No. of)�$-P�s.|XE�fiN_6� B� a�et��Wo2���{ typA�u��� � *Y ,N.� �5�6-�2=� 4.8\pm1.4^�- (0.47)u4��)���1�53.14/18�1e!s�g)7!\e?,@na�� 1. �����4e&�*� �` 2�Qc:� ���o}"�� sub"w� eqn.��M 38e�Y�.��R ���,a�L �^! 8� TO-�0tab:t��> S�6��lDf�6\%$ err9& >�V�B��&A� # � ough �so����c e)�o�5!�n��B,��xig���&of�� ��5 R����,Z���n�� !�is]l �s�^y m�������onS\ be��&�E� on m�:�6���d�E�j��!� lk olog=!!8ϑ�-Zo.�E�1U,��B�.A� k�twid'e7����arro� us� Mjfw[�eT����(*aZi�!�re�&~l�K(bF � � �e�iesQ�W no �fd5�2q$a]5��$��{R�=� Disc���/��V� �H Cip# �6� !!O 9&�� �5�v] �-�!nd*�("r�? �ke�Ds�4�E 2}- 6W4})�GG�E ��p>%!�wE�iM5 NA49�Ba؎r� WA98  Aggarwal1� PHENIX dcox1,2,Adl= groupe�P�-2(a)a��<-2(d)� tf[ $1D.}�/�/ �.!$ us $N^j*$ .-0H �  �"^ME�" A �Mre 0sF fair�� ereaW W.� %�disb�quiH0Is=o�+<��.�*jcN,M�UQ, �d�� �m6��w i�y!�lead-"`m�falls �o�Yt 17.2' �j.  ��n 0�d�M�idvfi��e+m "� �."�edcr��32p$�$� PiJ[ �U"ubM�3-A~5�? "�%sl�oa�y8 ~���!�/gory,Iex��al��FA.��� halfUa������oFw��m�if�c �d):~F,V~/} |/�w�QA�a��&$�Jb&��se�a�^� ���h���!i~��*�!� � �7ea�fW0a2why[$�i!]Na $#/ Now,1N:evP�2�6� !�NB�&�`?ich%�� bV� cM1*( ~ .M} (dN_{ch}}{dy a ~ N^�@��B*and S&8 X2tM�jtb t��}_1Bs�a�b\au�k>�f !�Z  �Y^W ea�r�)Oi >�5}:) 7}i���IX�o��JA�X*s. A~�"s)�e(��2&)"�:���al* .��?�n��� 4$E_{Lab}=158A$��������,}R =200 1"� b�q`&9�w�6r ��! � 2޼��.Nay�mk��q� �pkeep :�����o"�&|�ͻ"���f�sp e�GY5)� 6)m�Ob_&��%�+w&�G%HMk R) slop�7 its.,��%uit��M4nA�^takesI��76\AF �ѵex�� b�, flat �( >�23orm�$ � & %5� li��_! , i.e., � �& � l�!at :$ 5} reveal�! � on $<\pi>a�K^�dm�P/"Fl� 2G1��deMW!co3��% � w)eZ�!#1,A�l�� $|%�|c� tN$|�|$.�,o ]8�Z� B�)�"B�is�%(o��. "-!%?F�~�+g^aHA�""*m��ieons =�by9�n"� %0�+��s $. �+rtJ \eta�h�8)g(_ $R=.@/ 5��y2� ma�6� :�8}� ��!��%con�a}��utiyI��nn%��$ a� reI92I)&��w�;nY��# ^�-G&� -.by y1 /�SI9K�$ng�d < R�� �� ��� 6V0$N_{q-part}$ �Xfor $P+\bar{P}$ collisions at three different c.m. energies are given in Table-\ref{tab:t�L9} as a function of relative probability. \par And when partonic considerati�Hre used in normalizL, the data on both .�(and $A+A$ �$-values that� to b �for 2���,most central2��8, i.e.,$0-5\%$ -!ndepict �T�-\2n010}. In order�check�nature��,ment between 18)#%-R , we try_�obtain a fit by taking into account %� sets}g,5�ed62c /2$;!9desired_is )m4described hereA+follow~expresA�0: \begin{equE%@} \frac{1}{0.5 ~ .�} �CdN_{ch}}{d\eta} ~ = ~ -(0.010\pm 0.003) ~ + ~ (0.27\pm0.01) ~ \ln{(\ed\sqrt{s_{NN}}}{GeV})} \end� wiA�\\chi^2/ndf = 3.632/12$. A�goodnes%@�8it is also showe} Fig.6(b) P' help!t 9 $fit-!�$e� .�$2�4$ which revealI� B�E�in�Y] �respectA,�(fit. Hence,m�e�and2��$ exhibit aa�mon>�-dependM�2a:oI� former�q�Iq*number!a�icipant Lon-pairs. Very rea�(ly, Sarkisy�.@nd Shakarov\cite{1} adopa�a somew�.Psimilar type approach!8 dealA�%��Hpseudorapidity densper� ��D caseE hadron- $, nucleus- 2PndICi)/C$e^+e^-$a�era��sI�Pstudy thus reinforced%O idea!M �iti �!k(bulk observ��srLwidest possible rang 6)�le-in.� \se�{Conclud!7�Remarks} Let us now summarize our |��s made�:: (i)aa< secondaries, exZ$deuterons,��du� in $Pb+Pb�(�'DCERN-SPS behave mo�Hly well vis-a-vis $�N $ sc%�)\9i�@is more consistena@ warda�e high!8͋of�[ ity,EF�?A2maximum�$0-5$\%$(re�!enA�,by solid box5�8 graph). (ii) SM���8AGuld be)M4about $Au+Au$ .�v�01(��4a�5)!oepgeM��Gp~ i) I��(quite notic��t�)q de��!diverg�s M�!}a�rt}��.calcu�idon�]u�d 9\A�aE thos*o�s,�Vindica!a {text ( Mq >irda�umne�a2various��s 9�A4is work). For1 ", 0se discrepanc�c1�attribu�onl�� Aq mucha�pl�_rogramma\than ��ia�sor<ᇁ�e big groups like NA49, WA98, PHENIX etcI�pl,fac%�we%�e�imply un�^ take up s�rigor! �}�as mightA�!{ advisCduG1F reas!�beyond�capaca!�0control. But,�recogn�>!�uEFy+ importancEc��in "w arr� $ decN m'RmeritA�A�q-�� �of)$viewpoints���� Eremx (nd VoloshinɄ 1}. (iv��eh6�5l!6s�how`�ne�.� Z�&� $ negotiatea5ta he���� �͟��,�� ��tituent2*�a���A= A(�� m Ajuseq !� y does es��ially�� vide�:sup!�E�heV{ byN|i� eir a�!� Ref.>� P� $acknowledg�R}l author� vygrateful�anonyma re� e%1his/her 3 pati�2rea�s,A�strucs  c�cisms%� kind�Ie8i)a.!�! improv����e pre��s drafASI� manu� pt.2�w��� �&toQ�bi��ank�� itude��Professor D. Mi$\grave{\rm{s}}$kowiec��i�o  helpNsugges�� ɥ runn��Te FORTRAN code developi_him��ng� M�ofE�M�s,e�A�}$. On�!9-� ,BD,�?�L��  IMSc�offerdwQ� by a t-docto=Fe� sip -tGe`� 0ar�[t�'E�was��.{ Bz$ %\newpageQ�thebibli� $phy}{*} \b� em�c S.. S.��`: Phys. Rev. {\bf C 67}(27 064905.Q,Bialas1} A. , W. CzyzE�0L. Lesniak: :ZL{ D 25}}(1982)2328. ZHNetrakanti1} P. K. \$B. MohantyN�70�(4) 027901;Q (-ex/0401036�,Wong1}C. Y.  : I�Wday� do High-Energy Heavy Ion CooD, pg.161, World Sca�,ific, 1994. �(Misko1} D. ^�: http://www-linux.gsi.de/$\sim$mC /overlap/a�al.ps�8PDG} Particle D[G��Z@pdg.lbl.gov/2004/y ic-x� s .html9� De1}!~De,A;0Bhattacharyya%�DP. Guptaroy: Jour.MVEQG 2IQ1)2389�0Bachler1} J.  et al(�%o abor ): Nucl [ [A 661AQ99)45c[0Aggarwal1} M. `�B`E� �e{C 23}E] 2)22.Adcox1}A� \PM A-.�> C 69 X4)024904.�[2�[ Lett){86 _1)35002])v S. A � 3490:�kI.B%�k\ OBOSn� 88-o 022302Ee�n�Jnceō�F�.�E�AG. DA.�hSakharov: hep-ph/0410324 v3O KlayI� �s.a�$Thesis, Un� �lof California, Davis DissertE�, 2001,�3 27; m�n�ar.ucd3 .edum�Djklay/CV/JLK$\_$cve��$Afanasiev1��V. -rRBJ�M%2)054902dBack2e���5%�0) 316�n�c1} T. �� :?��t: B5C } \capr{\label& 1}V<,of inelasitc�Peon� on cross-�<A "y"D� �� umn I�� H�� subt�8ng eqn.(4) from 3) Tla�oRgiv6Oas �y&� ͇.!j,ruledtabular,{ccc} \hline:� (GeV)$ & igma7^{!+ }$(mb) & ��N \\ & (Pre�  W & (F�B�. �@ 53 & 35 & -\\ 56,37\\ 130 & 41\\ 20 22/ 8 >6 /9 9.51 18 cl �I]5.Ak:AM[ "> bl2]l^�>$��x>$� B��P $E_{Lab}=158A$ GeV. 5�:�)��!�9�C�q& ~ �^{�S}>$- ��1}B'.� }>$ G �^> \\1bR!�6!�36!�0856\\ $5-14\%0A29!�64414-23 2%�2144;23-32 18!�1E278<32-47 E 9}17AI$47-99 7353�In7l57��8:81 �$38�1%'8!'90�1-6.8$ 46\p $3!b770! 6.8-1-F$29I2I27a{60%13-25.&24K19a041o#-48s132\pm3N 99 &!�s#-6-~$63\p se�)�67-82I3�%�1%� -100 �1l��")���"a z,3��~�*��1*� =130i���:�PH�Y�i 1,2��e� yy�$347.7A(0A3�i88EO5-11�29!� $$297 & 710.e�5-1k�j 271.(8.42e�645AN10(48\pm8$42.a 565.A$15-2v11\pm7(0u469 & 20-2v17�&17AV38E� 15-3J 180.Az6.6N174v 387.�/$2.,e� (3a29��0-3t2N5L2��24e4 35-4t 99\p #e~19��$40-4F8E81� 158.�3$45-5H6!-%Q�y114)y 30-6$78.5\pm4 �7!, 150.% 60-9�b$14%�3.e�11.�c17.���n�4��Z�20����� �.�u:N �N$351.��2.9AAu88-�0y�325E�-�33i<819I62�9.��3.ig92.�69M=2�53.A�4Ia�4 & 560.E�10}�3AAjeq226X517i�6���pm5 X08,46V20}�66.��5�915A�33(30ySA�a44 (08�21A�a[u574%U �7m_3A� \ $5};45e;-T40R6�\ a<7qd25�) S2�j5i� 60-8'19.P16.�{2�:�a�2.�Eu���7.P3 ʥ�9E13 x7}� w1IF6e�9�8&6�1.2ElM�����5.�a$, $b\alphaJ \betaC pr"�of"}*\ N=h Fh [ndf=No.K�-  parameterH fit]��.� Idenced�a!^�� c�"b �6\\ SeGy & &  ��<\pi>D0.7�=0.0ű $0.1�d# 320/��$0.�q0.0�$�#aO.) 0.442/3� $K^+ C02 T0E�& 7ŗ$3.436e02a��#��- 0.04d 3.70�a`K^-d��6 �0.3��0. t11.024e �� � > �12.51-dPb �3�1 ` � 4.49�!�!N�$$.0..o $4.05^"�'T0e0ea$0.� QZ 4.61=*0 �.��313-�D@! 1�8 &!# �t6359)0� 0 %�Y !�* 0.65�Yc0>:�� b�^�6�NR� 6%"� � � � V \pim�1�E0.A�A|0],�25a|A�6.� �;� 221Mei�� e� u19aZ0.0, c.c12A�a��pQ�SM�07a�0.Qe��002Q�081 e �0e1ui� 1.17� e� �e�� c 1.081+�pT �[E� 0.u�192 a.,i�0� a 0.15/�:s��!�Bg48� , g�>g1�� v 7� � / � � � � �YI{e0�!0��4.455/�lJ >�769/8A2 I= faɇ 1.071aI� �:a 1.01�AߝR���F�583 c0.1 �M��qD59� e��m�.G !57c៵!,ȕ� c1.490-)�;��.�a�264c 06�7�� �)�y�271�: Y2k-� �0.2��u5- �Zk34���" 8.K.bVh�0) 6(a)#"�,�6.:.$�-��&�us4u�)l�}! �:� 2�*�@�,� .6$� &f�� %C>=z�& AGS^�0�43��78�Pb+ & 8.R.29 2A*�&�717�862j8� ; �6�330 6� & 82�1�$02�2�2F.24d% 2��r�9.�.�,�%proton-7# :Ur4 �32S0N�3��"0R74P&74!�3� &%ZGe mGeVy��,AtE3�4.0~$)�23.�3� E�%A  72.a2=  1�2.u.�4���<6@0= 1��r10. ��u�E".�4(me)2@*&6*6� c.m."��.�:' ��53vib���E�|6�& .3�3�w3E4.06�qB& figure} *\U2�' \i�0ex/Dics[width=8cm]{nn_.ps*^ Plox) otal�e�ic:C of $PP�P�w.�/F�2�. D�%�,l/x+@ &^ PDG}G Q0 curvX)�6[# fitE?� 2� �,�# basi/� 3)�4ledashed �/isI �6K�,FJ4)"�5�\�sub []{  mini)}{.5\�/%��� pb158comp%� �W }% �{�{2^|4\vspace{.01cm}��j�au130�� au20v{ "� Compariso�9average�.6�+� --"l#!- ".�+P/by.�#xperi�-al�."�'sD� h'*ionR�Uih2D%6�4y��1,B ),A�(�,A->( i�"n"plyldpbe/n�-�-mn���1�1.q��j�};Օ�^�/ed yield�7�=�& halfaL�� A�R[/� ,ons[(a),(b)]�3 �0iF2t$c),(d)]�&6� 2�$B4� �-J/qti&*�a�a Q5 �F�"� �,,�(1}.>�;x7�']5p�&!fi���'>.he��5)9�b6)[1 ����au������������ �jK�b�چ����������aL:�2�"�i��EF� }�Ra�v�e�������20����r�����20����v���������N�;q�%@ V�����2�1�ru vsv?y�� "� ލldn� "y 7&�C FO � .6gF�B&?� �0 d�?� &.(�<):�AGS, �AG RHIC"�o ��samY<i.5=6HISRE�@3 of &� "1}z1 open �A�circl�?�<�� w!I":DG.R �V�:)��>L}*'� �Eively.A�mQ ��F�%5resul$R�Ekz�&- !�:�;R>ons~< �k2 <e it[�|7)]%CN�.5{"�I){B.cor!+on�<1��*?�� (b)3=plo�;cloa�&�GY�se f �>Ho*fGaforesai8IF  docu}} Pr\(class[aps,p&D�int]{revtex4}% \usepackage{amsfonts} : mathB symb6�xWset+J�er{MaxMatrixCols}{30} %TCIDATA{OutputFilter=latex2.dll}"Ver�I,=4.10.0.2347@CSTFile= � .cst.Xreated=Friday, March 05i7$4 12:53:332@LastRevised=Thurs8 Nove[H2;1:54:34;0Z2D-�Shell3Ar�;0s\SW\REVTeX 42E$Language=A�B$can Englis!�$newtheorem�6}{T }�a"�@eEC[ ]{A:67lgorithm.16+xio2'2# clai.#C6#oUAr9H>-di�76, >+jecNM6,:-rollary2,6+rio2�2+defin>�D2-exampl.�E :'ercis6( 2)lemma�L2#no�:&N2)proble.��>'pos>�Pr2/rJ}$J6% solu:�S2NLJ.�S^Jy 'environa �Hof}[1][Proof]{\noinP� 0bf{#1.} }{\ \��Nem�Nem}"�3��,} \title{Lat�H g�Fodels decFd�effKvdel�Ko��Bx{Matthew Hamilton\footnote{{Cur�Qadd6O: Bio��0ematics Gradu�EPrBHm, North Carolina S-Q &�<�, Raleigh, NC 27695}}, Iyam Lynch, Dean Lee} \affilia!�{De��!I�W<ics, �p"� abst�:} W�Qrt)1a low-e�AV>z @8; fermEon l-�3 exp� hopp2"�-�!)�. nearest-n!'bor64K� a^5�. \�Qt�CEKre >c coupQN$&8�� ingsFinh�HQH�:� ory, systI err�F�@be bEm�;~Driori,%Mbreakd�Pe ���Icri4=,l�Hempera�csf0understood qu� �b� \ WRO�Jhe�cethod!$neutron ma�H and � 2D ultsQ�O kum simL. d,YZ\makee� &�N.�C�NM-�i�plaUJaGTJt roleAD many�a� phya �,fluid mechana��HFrisch:1986,Rothman (8,Gunstense91}! ��uA� E�A�orT�<6L�ic^<. P�# �e�RJ NY;Dq�EM coeffi�H;%}ac K�=t7 !.adjusM1�� s tu�Bto �'�I�Llistic!� Alsol�(ͥ��often cfQn 'ataӅ�0letely filled>&�s���%Iarq�VU,, $\rho_{N}\E14x0.17$ fm$^{-3�K\ M�n�Rnno�Ygue ^�v succ^Ns ��iJ�\a )Re � i�me2'da�al qu�S \ How doa�1N#6VM��!� need�Uo�Ob)j�Pt *��P? ]��w�#tA�n 9>��F2�direc�T$bin�Q bDand/or few-body sc���LG? �|oA��aPj�w� keepa��F�w ? I�Vful!Zan����Rse9o%Janswer�V A� Uz,limit, powerrSn�Z schem�rgaQR6Iin 7Rof5�c�LWeinbe� 0rz,.1um,KaplɅ6xu 8tg}�Ove]Ow st!� years>�1. s�{ 2{�ltw)] ree��5at!Iy� Epelbaum��na,Beane��$0fx,Bedaqu2mn} \ re hD*�� � p �R��!�:��,anyI{��"z &� s>�99cp,Le�4si qd%N%�is�U,�rator60 ���$LagrangianAk matchi�^)&J >� vUu�s h8 hJJ�QJ ��eA*� �ing5,a��e�ttbe1?ed us!�sta;Y�|Montelo QQto!�BY� )� os.m�isMf>�fl�*? int�3framef%of 9uf* �W|k��i3/&�y mea�a!T F� � 9MStOng��� Vy��8/�d�we~w�Uo��S!i � �\*O5�5 �We�Wus��con�X�VAB� ���Z�hen �����.���|In �i9Yr�4clarify why itE<�_ a 0quotedblleft s 2r�V\ phase� �\` utZ a truly 25P� 2ZN�A� $�`�i?a��F=}�z=`${ �cQ�j�\ qd} �!Y�4y �]g�e~P�|L{Hd5�eet�Z�$n_{fZXpe Zof&� A�oj,or $\hat{V}$� t upI��annihilB :c� !�?� �$\!�0\vert \theta\)~�� le $�ota�e eigenX\Eh�,% �+*�a �(0a}^{\dagger}, )z Jz =V( z)I� {.}%��N�[wy �dA�en�V�?�?c�at @e�Li�q��'two*�loc%Y%C� !rmtm�f� t�,}m-�, $j$�)�e"�ian^MH}_{j}=%?VrY otimes1+1 .3 V�,-\varepsilon%�[ 7av9�SK�+)F;EZ] �V9�A��X)mV el�Jzz^{I#_{1}, 2}}(�@)=�E�lan!� ( 4 �E� �F+_{26*� \exp0[ -r% )�%Q!N kei�im 2�a� �� * ^�.N�IfA��od�B=�$ findF��\� �(q�� % )+ 2}))� cdot%[ 1+%:^!dvU�f!�% z�V+O()�G)^{ ))&,}�Q)F1�F�z�=\sum_M� ^{\p..Q�� }} �jcq�F�u".m \\ +nqBk �Nj͞A[ �.jnfF� n:Fm%9�^-� �]�%dot F%a�`Fu1� �y6 })-y+12}9>�andJF(x)=�:0e^{-x}-1+x}{x!�,},\qquad F(0%1}!�^F ��ag��k��is) * a j8-dimey al& iodic � �T � �.\"� ��L-sKd"� � J�%�H}q�vec{n}}N-( ")� {n}))-)?!m}m�Pe� j=1,� l=1,2,3i�A�B�ba �Cl}) i�u (N<-Pl}� B` ~`llukw9 5�l�-���Hr If iHi "� s�cng��6K massH%�i�  &. ar�oalign} m�H =m_{�}aI�,�Je[5�T'} (" MW*�  \TN� b� con23� *z 1tb t each5$A�R��Jn =\bi�cmes_{UU4EE��h��,>�"8 !"6=mz�, � �Y.��:�0%fEQHͧ 2.�zBgAft�kppl� ��! �1( o�)] ._ %_� ": EHUi,A���-�:�I4B�i�1���%{a�-{] \- =� � >1+%�( I�%Y }{�S@ ) ��2]~�l��Y�}% )�� \no�&\VY �@rq ).� main��ivW�ve assum� !��is longe�aa�fr!�%�%�5�If2?�� 5M� om:4re�dbe �� $� F�3})�n$wind aroun\�.���int * alqm� po�kial�7ad$-\mueN}$���H}$� �';U�)�"p�I;@mputeU�& U�mu¸mH}��N})ɖe�RBU2anY!��H �Cinm�EH) ii re� J�%GV� arrow �i�j�:�.:�90By>n��c�6�s $��� �� �pproxi:#�o��dA-i�:<yq��m>Z_{G}�> =Tre�[ �M.��%��] ��� }J�:��)8 7}��% ),\mu�D�ı z� R��q ߎ��:�>�. ��%�!�F�"���\ to a $2^{� $-� IW �a�K only"�[b+� non-exponwQalmo�i�b*���b]l>.� knh�mw)( ejthA�i�horm�JQ�x~xi.UE�6�.� ��B�>�[weakly!4p0�$s either6 m will do!_How!R ��fojksP$ gly-q%edN!�9�+%~auA larger Z4�b%t�e origi e"�v. C*�AJ�-U :der} ].slal D &�&9 �����% xtenShqrr oJEwAt�nZ�n�+muQb.ll $na6ep paths�ch� �cD"eq%1/d loopwO| $L^{3}$�-0re $L$8s even�$= g���$�Of ste _� a�sei�*��:-$e�!$A1W% � oddC!re& Ka� �EJcc>!�q�!A}go, or ��n$L$xA��=��k:%*|(z!�d�ant* in6� 3mb}[lE�Y/$F  was *:=��li�(lengt�v un�<a% n� . A2inv�#aar�m,s more quick�2� e�iO .nv ooE�a7  relevx�' mayaat�a 5���"��!��� um cutoff!� o4)vP\Lambda_{a}=\pi a^{-1�"H� E߁�e�1 lie �beN)he�oeFugy� oc�qd 5P& � scalR�\ll-������_g}B}.� i� s� ble &;�!we�"J� y1}{\pit�)�f� �combiis ���/%�QAn�s!B:<��.s e geN\��&�21G1r��ll�7{.}�I�al�3��D�h�"a�amp�T�<20$ MeV$,$ roughH+]b!�liquid-~tra��$"Q)p!qterA��yaE�-� d"�I(�@�G an�,+ �) tells��T!�qFmz��a�!�fha�x1�%�&$3 �TAis en!� pro��z D�5A�VB, ip2���$s�,%���k�g&T�'e� it seems " {>�%Ba3ve)rfA%�C%a5)9���"�*F$ icl� � �� in aV,�c-'NTC>� � .!  s-diagonaR$ 2�By20 �T�!.| don't� mute�� l*D $o V����urJD�alismAKb`&�z" �0�ks,Q(ha�A�F T=(co�2�W�(! N;���(\J�Y+b5 C!����|as2O�6* �<azButa�Ito�/!�vR�a�ofY%.F�K H� { r6*ne�#�1� �,ng� 1ga{an�{�It D$lK*�vany�,nu �sy��:{7-t!Rh� ��, arbitrarilyew' (u&�&� "� .� ��wXep�>1T/"�# �in�z� any V#!2�502�sF�#�L9 )��'EF�be��s�v �@� j3 } waveU�!�w* viduW/=�lap!�k�A9 N� J� J be6q !Mzq� �Zin�� Q�,1�Be \gtrsim1$.� App�-�!� $m6+}oi �.n$Aan =�* '!� dilaQ6f:(!?W��cu�OJ > �+��ies�%&"/ � � smalY~"���)/;anZ�'��E �s.��'"� low0EnIL&s)w�* ntaif,Na�ta�~&V-��~ �.�&�(A�$ $^{1}S_{0h%&�,� !EO�%F�,:4F�@ �P" "ʼn� Nfk �" ( m-\mu+v 3}{m}"@�~% j=\upJ,\�5 ..^"n%RB9_:<C `p��orY%N��n�'�N����2��% �[Z�$}5j"� a}% �"n�=J��m,� M9W�llE��t�3=0,�U 9L� "�&H=M+5,�R� ?B��26!4End=]�I2Yrf_�sa~e$J (U� V��MB�"sita�� i.� 3 �}^�%^���2E��% %A�ly�_%�� FE�)#I F(G  C)]�:sZ:9a�02?5m "F>1.\}��:I.�> �.D J6�����%�O-%�r�9���%�-^ !.855e#FE 9�J�>� ��~��6�an:���3u�U�^'% %����)q>�R�:� : :�.OU)%>�.&R&6J�& 2�>Y �.J6�����.�����)>R�uT%M 9 ����~yD�.���6�aq:�. BR�L��%run";&&94 �f%5�;ng � "D �1+ .�*�; $C,HL by_a�LFU\��*��&�|]Ed�llBR) bub��ram$ � �,/4po Ctk �i�^ c�]� th L\"{u}q;r'%>Q<�a������5d �y levUG�[Ie&k,box�:Lu_[C6pf&�:3da>,:!��8��7(�v  4�� 4D��Fo�"�? }C� %�"� %-M�s}z�&� ` (MeV�(A& ? 2}$)�j5i�-8.01\40^{-5}.�6 % 6.73b%7 %5.8fJ8%10^J6��s�o*�Rnb�1l�k�j�i�h�g6fN�o(_m_*�8, $E/A�6s�Qu�8���RyGaF.d �(f'x�G�)�ge nb`B��ed �<1� A�+8 D } \�al} \mu}\ln �'i{E.EECJ7i 9-�)A  ���/f�9T=8�6=:l �,gas_8�> *_8}V�Skmx�ZR��\:* AU�"�H�� ?�>!�,v%��<��ˉ� !��B T�a T�.s1S� ,qH.� \|��s�u0he abb��I%�2�fc2�% \%s�g �inuum1�,NFFEC"���ɪ22�/ s2� E-KJE<�jIn%�I1�,m��gch]D�m c.ܖabA"maG �&w�P2�� b2 �F���,�th.�s, we �1�shVN�s�1 5�mc�!%��p-@� ,�-I� �s 5: S>�a�z U %�a&D%��($m!)g a_{t}�#L9�Fo2MrJe3�q1J4+s2.�v6 Q6{"��l7 Q466�%\L��l�b2abT9_�^�bF]�XF\F[fZfY6X%W% BM \F#��M��kCB�!^�, Il$�� sej7�..5lFRAME{ftbpFU}{2.9706in}{4.22�L> \QcbF�R %��e1F� vers]4C"at ��.}}{\Qlb���${e8.eps}{\�>al{ l�V "&��d"; X�,"GRAPHIC"; %O0�-aAt-�# TRUE; 0C�O"USEDEFAvalid_flL"FA�k 1 ; h�Qt 1G$epth 0pt; "�+- 8$4.203in; %�+- @6.0027i@ crop�\ "0�top "1rC %bottom /�name 'E%,';-pr� �$ "XNPEU";}R�b'{�6e} [ptb]qj�B8,B�n �=1, �=1', ? =-90 ]% { ��_}B Q2��8 ]8y�0U:eP���6UWZ,��F.; "d %2e� E�e ��}{)_rho_%� %: � %: �&t�]�E& q}.IPbI�^ e3}!�lq�U96j!u>�F"�%V%:�A�q/Vq2�Hzp�fyuAQo�>�C�I} � � 4&{ q��4� L R��8d�P �R92�M&, 2f.%��B��� �2�7B%}{e4����������%,j�����J��a*q�B9U�A��.F ��Q8u�iS������>��%� q�2�)O�� ����������%6j�������A�q/��^�Yp%Qo�C�0�>�U2�43 2� ��t�/:�^y7\�� 6��6�M",s ��$�N���@82�:��@##� 7{c2�!^W&6�w.3��%��2�bV4FVDV� 0.65��V85f�RG~3%��Q"�T "�%2U%r�5f�$b.��:�fT��Í=�� 5��F<As�cus4�3p���Q`9u�"|>u2F uperfluid:�4wJ�(�O�Hquires�/O;�:Ea6�0Gpai ��3S38U�Y�.�OTv7al��y�$T�� (Y�P7&  `"�}t �;>:��R\)devjM �k aiFn4{Nqthe�Gwe�43-V�gasJu��2 6d.��um*� �3�9:9*v7is }V.�50.4B2�5a A�surpri�35B�1��M�{*YW���6*r is s!al hund4Z �_F�.�/"Kf S6SV�.v*_Z "�*]V:�d,!�*is �_�=�A�Z�9B&�L"��t6Up��y�"5H��Z.�E!B�>@ ne]`a�^oZVM[![�22�P=at&#""e]g. To�]`ledge,���a�/iqj��D��]n��ep��l�b��6W�%op�@ �dr!b"5ofF#sJ�>Ra�DB,#�*42�Cre)���t߶ofʳ "D^ �W"�CZe\medskip�]>orkAѭ%�%x%!� U.S. D2�j �h� {\JR��Z \rP!-.�)�num-hv�t�v{B(-th/0412015����� \�m�t��e3����QuP��0-Gluon Plasma��Xq8Hendrik van Hee��a*�pCyclo&J In��% "� ��&-`c��Iz��AK&� � b�f� accele���=kirIquilib}"�e $c$ �� �a=o( pe]Akqm�� �m/lAE�Gequ� !.%% o6v�ultra-��}m -?5 U��:!y� \� l{12.38.Mh,24.85.+p,25.75.Nq}2s"�d:sH�h)ainA�%�I�5*val��pqG"� oO2Pg� [OP �K9�a� j�!ei� F�.Ca�*4#of (b�U)%�$4� c$M�2�Eir�lO�s d (decay)+!,� exiG@�t go sY@a'跅}s E�b� ���w�)rmoniumm�aD�AXzra�m%%�reax�Jo enh�t�0�XQ%s&-�,SZ04,BLRS04,��ina��HTA.facAqate rapi-U.w �!� ȭ�atk� as r�'�in hydr�wa�el�no Meۉ���-�QGP �DX�(02,Umeda02}9LG�v� �WsJ $J/\psi$A$�at2� ^��4b}. &V ��Ap�S�sa���ly2 �r�0diT��areg�@ ��, $c+ɕHWrA��E �+X�� $9�M-(eviae��� ``coalescQ'' turf/u3,�1 domi>T�"�T�!�fiI��i�Au-Au�a���-L,Thews01,Ko02�T4b}Ŏ�2�,pbm00,Goren0F� Fur�cmore,51�Uf����e�D � in-medium!��WofIj�2it{��}���; �b; nd ϙe�?QA�" 2�3�.� . Early: ����a"bUI�%�nLe���u4С�~� xSvet88}&� M�6~ QCD (p�e� z�com79}A� + q (E�q, g) \�^> $, i}R��� av�� Y> Zz� �.�MT��aoa�}�s"cto�� s). W 3a{ ��Y!T� +� _s$=n $a����2|:xipofM`$�w,$$4$~fm/$c$ 9�I� �AN' �0�.� $T$G8eq$400~MeV. How�,"��Yl6� .s� or�uTX�^{�9 = � � � (�1. �$) leaeo�6gn� ���W (fa� 3-4)�4n�f*�+"Ms ? �9A�g4�flyM�MS97}� i�5 �~� ZvR !qg D$Chen04,Mol� 3F��3zSww]� te�m�2}� �q``$D$"�``$B$"� �̅\ ex�0�V�a ma( acp!�d�v . Althoug&`fa�Yw�yet�5e��� �� ($Q$�q$)2e� �9sA�v.!�}� %�=o�7!DE�r plau�O��= a*(};a�'$q�-�AH03,KLa��8 �Q$�. F�# `�R�!9E �Qw d�.�&d four)�E_Xin Nambu-Jona-Lasinio m�QQb,GK92,Blasch0 3}�x�MW t `cكE�ta�.�Nf�n&� �<_)�-�;6 8q�YzO!vJ 9Iq$� eshold%�!� QGP,�N reci� �/ŭ !  !�� O� or{� fRjs:A�Sec.~�:sec_Dmes].e &�O� �t�q$+9�"uchira4� � )� �XX!�/[apja�/���~s (6�lag}) A�e�N�a����m BB})I96[�T%� E��"�� e2��#Z`;�� firs6�ging"{��"dBzeR��Xrag"}@Q���M�v � icA$ :" fp});t�#5'AS�* e`<�2���R�)����Z��!j fireball e~���#Q�[� I &���� >�evo!�WDcl��in:��!l} f;�a "d pen-� N�.��.��(U�m %�&��JM��%!�F�}g+u�����DD�Rb� {�-L$ �*T�>6�a��| |��desD%�f����_*is��aE  s* �""E�, a�� ing,:,�3%��U ����� � � "y���q�J(or ($u$-$d$��i$ !�]�3$"�.�$�maln:��s,�+�� N����be �ɘ�U-l������ ���ws ^*$) Z surv� ab��$�&�I�vac@�a�3a�TD^+$(1870), $D^0(1865)k�n(2010) �.��?, (*b)A��Q2>��a>a�. �\ $SU(2)_f$>� n&)��}��($D_0% �axj--1�hanne�)J ���� ��toA� �� ����&- �� B�F�� �-&�`V spli �i�Plag-d} \Lag_{Dcq} =& D^0 + @{c,q}^0 - \ii G_S(( � \Phi! 0-1+m ash{v�b} c:4bar q \gamma^54x>0 �h.ʆ�) ;o- G_V>{ P{\mu}T_ ^*Z\�z >�FG1 S�DF�+�hv)�-1[�9x7EgusY[W (�AA) 2w � s �$�7I�,1�[:�%�-�&=%� {c}(!�1�\A��E-m_c) �{q}\ii B$ q,\\IA& = (B)i%t^"�X)=� ) +  7{I4 }^{*x~R<AW ) -m_S^2(4l{+_0G7 E6\quad RF S I� \nu.�=Mm  + _{1 � }1�J ) + m_V^2cZ_ } + @ [W r W}) \ . .` Y��'s $��V!ߏ}-]J� �'E s isosp�&���  rg��bh'� M�in Eq.~1t�O�ll �j� d �F q���1/m_c$�}rto2�� ory (HQEToebert9(�.m%�ab"� unw'�c (4-D ,* X) X` a�dom�Ae���; ��e�1pas enco_\�T a/co��aintsq�9�vE�)�Iu } = .Q=0 \  c}IM ($v_\mu$:F velo��o�* �[ ID$�W). Equ(." [�fo�f/ self�(�ea%�5��S1��.� f %��+$ -flavor n  s �invari_�A.�Y����L\ s ��R$ ��� in�sY %aEdeltae] \phi_{V,A�C�^%IacZ�&��� ��M%��ax* %�aq�s �c�)�^.� F+��chiop} q�%�(1+��� �{�}�-�^t�lV"A "�_5)o�4c2fcBx��$ A=\tau}/2�e mo� %�$ ( 2*$: Pauli� rice$Tom5uxc%� B-<h����D$ 1:�.id�.f� er�I � )pc��s � �b{e�-trafoa} Phi u�f5A� ,-C'��6+q \�uq��"^*a� $>P�v0 1 _{1,�siB�21�;�?�,He�``�$"�4o ``U�� ��Ix) ''��u�g 0%� &i�a�{D}�k�5� aN�b](I � .z2�u & i!DZA ͂it�k� ii i0iu0.�E� -!�,Je F{�E+Z�VN�\�{16a VZ |e�F!�&# ,F��HJc� �> �:6����; $D_s-��;� rict'Q"�(ex&��ly1 n) 2Z�$�/�&� �N tane�8 �� ��:�os�ge@�&glx8 !$per�.Z�igE(hGt�&n� (�52�siz� �4!h ��� dens�$\l�O��ss\w+$)a<e3�*��=����l� n�bJ=~ms ��2; � s = &>| E�s&� )&� � i&0_s)-m_{D_s}^2P� 6 G6Z %{s�{JY ?mu)�+ _^*}^2:B1 _{s � \ & -a�G_{s,S}�0s��Z_sj| DVBDCI� ϥlnSz� Eqs>" A��\-�)A>�,aR�ic ����*�3A�m[��i�X� m(analogaNe"�vs � '$bA)� upo�replac_ $c�b$�$D B$)��>�\&E?N� b��er t��� �t �a[�t�[�s,�&be fixi��mbl�+re mi�copic�B$c2�g�*�� $�,� j�t. �Q��Ё�we � e%GS\ <Qo  !)3"T&���#��+��dv���Si �*��)D-fAj1O6#1C݃l.�## u��� ion{� S3 �53 �H��-.DS&�. Am�ud0O��PPU6 e ke�gredi';[ 2���i�%=!� *%�|�ht�%�agʔR� �!�(} D_{D,B}(k*��k^2�{ ,B}^2-\Pi$Օ 6�aY.� "�;dx�}�s!� %!���e$, toge��7 9e�"k IY, $��,B4f*Bn�% 2���   RO-lp���z (cf.~@�2�U?�?~� fig_�eb!�v1a�Piqe��s?l@�ig��iz ��t }�l-#eO�&�robustn��3+ur�?j.� conc<�te ags �k��e� <�, ���;l��R����2���tit��"��a+ �� ��#��z"�Xram89-G� �՟ofFb �&a 9��B�0�� "*$k$^�A� 6R i_D(s) = I�� }&= 3g G` mu^{4-d}  6 {l} \Tr ["- G_q(l+k)&? G_Q(l)] 2�m=]3Z}{8=y$2} \Bigg \� !,4 m_c^2-2 s} }+ 3s + (s-2 )��! ln�7�5(� QO �z�{( )� 6��& �b�+ �P 4}{s�7 \lnZn'2h 쑐��!��-�($s=k^2� a�a�0F quad�cuicwa$dba�� 4$, &�l�5��y�D b�%�e��n3?�a`%$��-:�; $A"Ar(�A� }H-rRHto O�.*��. E� the �Ea� $d=��!$I�eq 0.577eb Eule�a�� tantO  (6�-$�p!$nt) imagin/�a given�b4 a�"ims�8\m_�]3G_S^M�aK��(sM^2)��-�& iP!`��a.0�Q� e e_6.7 �8�]�入Rg�l\;d�]xM�}{��v>q���Nu"+Y<Ap" e FeynmaJ�#a��s�H8(Dirac) algebra�(.�l�8��ed�eari��\�� ip�% b!�eJ��{D�� (p)= _1� -6�s���� m_c .k=d^c=l`=��)^噅Nl+p)_{% - m�v g:v}{[^2�eta](E� ..�A -b9��� a4��n ly"� ہ helpq���8ty~\cite{georgi�@91} \begin{equation} \frac{1}{a b}=\int_{0}^{\infty} \d \lambda +2}{(a+2 4b)^2} \ . \endZXUpon integrating over $ 8�$ one obtains for the imaginary part J�(im \Pi_{D^*�,mu \nu}(p)= _164 = -(v_{\mu} nu}-g D) �43G_V^2}{8 \pi} (s-m_c^2�{ (} \Theta! >DSince up to correc!zLs ${\cal O}(v k/m_c))4can identify $l=s$ in%#,denominator,%DfindsN�0label{vecse} 15 53 s) =-L_1.=>* - ),)( L}B\ ,B�which is��expected result from spin symmetry of*8HQET. We define$renormalizE� constantY24self-energy by5 followAscondi%o�B�)"ren(} \Auial_s- }^{(\text$})� |_{s=0}=0�$\quad \rez2m_D^2 6F" The first� ensure!DPat, within a vector dEAXmodel,�4 photon propagA has!xpiduum of unity at $s=0$, whil)ise!AP impli zX=�Xed meson mass coincides�+ bare of a�,Lagrangian. �9�ed2�is,�8course, indepena M Hdimensional-regularQ�scale $\mu$. As an alternative way]6A� divergent2� i��ls we��8roduce a dipole�� m fa%�a)$H$c$-$q$-$D$ vertex,J�IpF`ff} F(|\vec{q}|)= \left (�q 2 \L�w�� + 2�u right )^2A�>x wher! b$�9t%�!�$ree-momentI!quarks �i( center-of-%�frame)�:�-�}� i�$n given byn ����ytffis.�a� F^2=:N�$5Y=��,/(2\sqrt{s})2� real�p@is determined byAIunsubtra��disperA� Q&.e�I�y1adjus�toA�dera�anishA�|of e2}�M\physi�+r_i�assI� defa�Xpa!�ter�$our calcul�9E�usi�less lE;)�(, a charm-q��~0=1.5$~GeV and� $D$-�es $(��{�/�}})^2��-�!D[R&]=2c (�!sp��ng!4a N-M�9,)I� coupling �)D $G\equiv G_{S,V}$!�varied_�*a� widths!�a � s��ral fun��Hof $300$-$500$~MeV,L4pproximately c� the �e suggeE by effve)���Ls~\cite{GK92,Blasch0 3}. It�impor�tnota�at��assume�Y5s0be locaA�,\emph{above}���\bar q$I$threshold,E $+$m_{ " }$, ��r��r��,em accessibl�:6Sscatter!�pro' es. e>sit� �,quite differ�� (bound)�sta�� �8it{i.e.}, below� anti-/I��)��!�mMta:t!��a�4tude cannot be�bA8$hrough $c+) \� $��/ions (e� for qci�es close!����� �ieE��s �y t!��0average colli��:y!H4significantly %�4� peak). IZ is ca�{other�)� ne�o!�R ed, e�$it{e.g.}, 5 ! D+g�c1m extra glu �final)� carr� away fourٛto i��u�@emerge on-shell. a sameɫ work�� also applm�I bott� N _ $b$����$B:�a�m_b=4.$m_B=�,!X�,ively.�(we will seeI�,A ~ l�eke�d��,�h "���, schemes lea��iKcom�bleA�ul*? !� mal relax D�Uert!��c-s, E�thoughūoff)|.4i�6}. figur� � �minipage}{7.6cm} \includegraphics[w��=7.5cm]{�q-h}�Cc {5.1jTR,s-channel-di� ��EFV3rV3�u�Vcap�!{L� panel:�.($b$)J  loop � repres�,he $D$($B$)�- �QGP. R�� a"%A "-ex�g�e�s �1tribu�a_fin�*4ant matrix ele3 d"�1�E �w s on2f ($u$1)ee�� .($s.} - fig_!�!�QAM �A�� s "��o� v�elastic!| �6�f �, ��q \s (arrow c+q$,�(� {q}:-�+{�8 -�!?�:F One �Q� aligA�K Tmel} \sum |\mathcal{M}�H{q}}|^2 &= 720 G^4 " ^2 o |D_{U �|\NSqBMu" 2Mu) M� " �w�we hav mmedAQcoQ��>of��IG-���o �ea�Pdu�Mei��Lheavy 7"n (A70$D^*$, $D_0^*� (_1$) or chi� s� .'AD/ . We�^��d��ite0 st� I along* $D_s$-�D_sSe�� In ad�a���tA�"V,U�}�in pQCD��accoun� = to�!+or� ,in $\alpha_s�"� ^2)$S rr&� :� com79} %� been supp�,e��thJ �al @Debye (screening)� !g(\mu_g=g T$,"f �� A'(forward sinr�qWt�H �� �P�Svet88} �str!�: A�c �be- � ��)�5@0=$0.3-0.5. %� \�ion{C�  Q� Re6��QGP�sec_r$}�w%گ> \sub�8Fokker-Planck Ef, Drag��Diffu� ,Coefficients2�fp��: �%� :� � now O ��M�e kine�theory �N aIass?!��h*� timea�le��~q�X �F"�D$steps outlsin Ref.mWM�,�-st>T Boltzmann��A>a x��dis��on"�4 $f(t,\vec p)$%�Xneglect any mean-field  s. Fur�ore!um�K�]�"� !&be�!X$by small mp�sf4 one � v t a 6B���describ x)levolu� fy cspacef�fp-eq�� 1{p})}t}*)+p_iA�� [A_i(!YA +�R4 j} B_{ij}0�5 ]2� JZFor�O4isotropic (rot%( ally&� ) plasma!� dq� � i�c}� in (\ref-)�!�e@ osed as��� ��.�&=p_i A�p}|) \\ >�&=/( \delta% --/Dp_j}{-I&�) B_0^5b p_i B4B_1,- �w��ecalaru&G ).��erw{1} -M � \cdot {\,}'}.�� A})2�!E`1}{4}- [abT{!.Q@J�)^2:�� ]�B0 �.)2��A�[(��r -2 5.6�}!��p}��1< ]A� �1� -� ��:d*p * �X�%K)}6�$ E_p} \intM� \d^3)�q}}{(2)^322E_� V-_2. {q'}B^K �5\pf4p4Q$\gamma_c} B� � @ \nonumber\\ &�\��s �4mw\^{(4)}(p+q-p'-q') \hat{f��q}) :2� 1�erw6�� $ �$ ( �$� qq��e�*a Zinc�g (outgo* kD ���/d6F �  $>�$���(al Maxwell-�]R@s�x@ons\foot�{As pod�١X�� MS97o� of #n�Vm8 (Bose-Einstein�F�-Dirac)+uces Frat&g��Z�� ed eJ a �; t$is st�tru !> ``D"� 4�  !" a"şolv�.� f1��� only�ch, temp�$uW�id ion,%� ast toa (so?U;. Also!)�<Z$.� AXra� � ensi�A �d lyA�B+� i &�e#�� ; na1:{A� �or!�al{4� �,B���o would� y a ��z A�.� $(5/3)^2$e$eq$2.6!E�.����i�!�! !��  s shownA:j� uch & l�_ ���AUe=!j� in a�n Q�d@ &�%o.�gq!ex�,�BDYe)I*� ��H.�C��N�form-��n�!5-!mar�"��.�CE!i��M�fri�K]3%?5S��� &��I�߉�AR&+Is�!h �<�, ) (solid ._%.��:"(dash64�NuAwas chos�c�+a�a� ��Ir\G�$=0.4(���E�. 2y ��1/ B1��%5;Fs2�� .��"alu����f -Z.@ fig_e�s}MM� To f� illust:�:�in�n)�-2��I#;*la:' �>�x�Mg .c%����:�I@T$6�A� ��f) ). F� � A"�  obFes&�&"U ". �0x, .�> omewAg�!$nod�4f��@ abs�A&gn�'inI��is� �I�( � indi )s aB�.�-bAf�6�B'<0cular, i� �'�E-�F�'�ma.<%  �.�,� !��mae..Y ��1� heat bath&F} U =� �%�Q stee� с�!�E�.D (of�d�/�$Teq 2T_c$� r  ex�I29V,�,is ques�m ). �� .�T�EvAS} of M) Safra"�xevo�� �&;�D�0)!�� P6R� ��� a be� !e�,!}��c!�"X  ob ransvers*V0($p_T$) )raGflavo�2drA�(in URHICs w� v�g��Ё3,-o� �6��)&x "6/ aly7Q'�� is<ll< an�an� fireb� x �#s!embo. +17$Au-Au&�+s at ۉ~ma�4aNifJ �-(Xsis{�Q-.3�� �-F�. Accor���di"O��end!�!2 prev�-]ţ�a�ref�employ��6�a�%���n2�5�� B�3�VDs �$m_D$=2Rn�6g ), a�0ll� : ]"�#�), ]V� E2:*m! )!,n tak���rm� Qg�fp-et-��F^ }" S �(tz8\��ia.] M} � f) + DF5(4A7^2} f�e���=A(T(t),437nd�&=r>=[>$.K�KF %'eX4�G/their.4 a�&� (as.�3Mt>��/�$�$ *8��u��� dM"Qini!�+i�, a9DC 0} f(t=0R#�!r2f_01�9:�U llugj-�1f�$p$-$p$�UaeQ/�4 %a�PYTHIA�-t �orK$Xpythia01,greco-private})� �-�problem�!conven�% ly s�d ��G�' 's J techni� : if�$�:���c$G�$ {p};M� _0)$�&�:Q)�s� ��)�n�g�} G.�u�#^{(3)�p}-�NC!sfu�/ol�$E~ an arbitr�#�/.�A�9�qV,Auui readf5�4�Mo2!f�u%\{\ii)U>� \exp[-� (t)]�' \}  [-\Delt Bq}^{~2}�$B��1V�$[�$"�At}�A tau I)( )тgamt}�/}O&�2 S]�$_0^.OD Jip[._�.dDt�nd�= B�� M�}) yL*��( s�:f�AFg1q]"\ !�6nE�[Up4�% 5Q& ]^{3/2-�7\{Q'���%>&6�)n 4B^E JA��a� 2�*R�#, 2�),� �ly� i�"* i�>�. �//>�L7!�&Cases��Ber we tur�0!2`��t u�3+A*�a few �!��s� ime.G 6� $iO-$D$, *� eWeI� Dt})Op�  toJ�� (t)= Y t���' U/��D}�?� } [1-a�(a� �aJ.BI��� thes22�i)) ivJ�:4fpASjQ e \{ iT �� pi DR�qf \}me�4if ugKD_E[��.t }y(- 1!axJ*}�* \}Jha�3�9yv�!G:�Bin2����=C �$_CA�mea�2[a� (or"�).tr( ��grw/+(t)}=-_0�f=A]>� !� ri"�B?lib�GY � �,Btau=1/ �. W,&G/.�$��Afp-�6�^{\,2�-�+ ��^2 m 3D}Q} �!�N�kCi�adi�.,Dif�;!�"EV0&� �9p�!!�6+�S}���;�ż&�s$$e� �$b � �b�for%�"D9�&�ly"%b j�.6��a �fm/$c$,Y&�A�duMi(puF0ve)!, phase. Even�Bough a"# meUism�o�)iv �to��ir�W rest� *;@ ,nJ�3N'2�> P , ar@ 10~ � or�. ,1$t� a�9\infty$,6� sol��pproach v�(r��� im_{N�}^� = f_{�% {eq}"�)=��(R��z)�x�L��[�mOm�i�}{��Rg�C5� ium ��(~�(f� ;�( T�� � m�.� ~ * �&f'��"��'&tau�< rm-b@��ndT�'&*'&�A3ist>nV�EW2�-R��J#/h 6��݁QGP�-�� e"Y-�rA+NL�#h -dot�-*-doublemsV0in-medAF"�>2co$ency check�he�Zn�@� ,}�,M_)}A�is���j� 6-�&s2��"CBs��,%e-;,/1�.� ig�u��Q�p s���&=�$T$�"u�E*{c�K �!�o7���!�g-")� �h "�F� R� EY&� "2r u�+�+.� MA�aJ�!U��I%��rU:�F�inQ&�, e�i�&Z*��F%��#&L�f�8l�2G E�:9 L&t �puB&(2ugE�m�O>�W:n^.��2 satis (a�in 3\%)*�0! ward'edN`;�& ME1�&�&U�>� o!#:�" $dev % s do�&l$wF 11\%�@ Ehighe)OW1 red } i!�Nw�Z#�M ach �Q 26\% ( m �%to�1 17\%)H��G+>"yY>24is��ede%en& &�� grea�/&�&m�P#e�x Z�I?m�[*�1 of*b2, :��.2�*2 -a�i�0����lT=acc� e�h%p�)P� next� we sh�sIF:a1�A ��!k�*to�0"i!h 2���=� heav�&m�D^��1!�y�toE� �c%G%�>�Q@-QQ@�-� aO� �� L�~<add2�J��fN ���tra�(luz�P��6N��Z�. To �%Z�>_we|,�� �.� 6/JRapp01(IA�r sce�/!�(ydrodynamic+ u�" <$kolbrap03}an^5 1����vol�M�8�Of.j]Q�} VS FB}|=�<(z_0+v_z t)(r_0+| 1}�;(a_{\perp} t�VBi� $r_0=6Kfj $ $z_0=0.6$ri�{�?&"�� Eit!�al size2uc�86 PaÉme� of $�r33s��Non^�~e!�i5�,A�4I,$v_z=1.4c$ (�O ��� !�h 1.8ZU� rapidity)s$5GD=0.055$~$c^2$/fm (��Pa�.1� life � c 14����freeze��.�$q%$11�8). As�Aisentr:@5 Em2�%at �<tJis"�/�'�eK~8 Q�Wp/Ud?l�$S=s(T)B��eq10^4$"�$( y$=1.8), �ke de�.K)QGP��ent7} st"PL90} T^3 (16+10.5 N_fR\ ($N_gB��%ivexber!u� �$� ak>"o�62.5). "�s.�9)}q&�.is $T_0), 375$�: de2A�� crit)72>�3T_c >180> afTI�$u:-l�*�I%h�%-�mx3"a� an6PK�ťSicityB�9%�Y B�Wa�=1 $T=� �*�H�� l0<#onE>�0�s ���&dK!A,.Y6Y2� .�s (U�pne"2 �-� �"2}$A,B \�05(varrho^{2/3ES�H �no�HA�* ,� �sAM�Q:2a $�"�E.~ %��%q 2�!�I"�.proton- �'�") "~Rż 200~0Vby�"���"�<A sui�9�*N1iza� �*eofA�s B6�"�*EpT! "�%@d^2 N_c}{\d p_{T}%= C�(p_T+A�((1+p_T/B)^{ K.c�� $A=0��(GeV, $B=6.8�V,&$=$21N$C$$J8845$ GeV$^{-4}$���aiw('+���y|� )���OJSs"$&{���C>r&��NtI<�@�_p_z�F�>�Ga two2�;so# � 6L1B>=21�H "�:7��g��:!2-!26Mj��d�I>eV�i7���[� <"�-� 3A.localD2_9Exa2� prof�]B) QGP<9�8��ir�\s[_{NN}}$ :A�;�curve:�m �um)n�bE�*�& @- Ef. Cu��&�)�1�+GRly;A^idr>b2�@"r/.� � �>. 6�2expū%�}�o(imy%�A�1� 1��+&2ga�afig_t<. \endu U6r!�nNC Z<�86R |,J"3I^:�).h�_ �  m$:inAW� .U>�YA�&�O booE�om�(!�veR� ���9�Be�YI�z� �u��in Sec��/fp}&{2�nxand� fa @nX[!�!.�.l�8 �uiaeR�) re a�[ca9$little. Oe� �9r& �ugmO;n�@.O� Y�Uu*�@NGG�d%�!�>t9A��t- ��2t-did%���)��urbca�@Vona�$to, say, $[ Z �M��Y |* a�b^Dprjbpl�!is�9l�Xa s >͉.��2� �]8: , howeverZ#2� id��Qo�G�4&�E _N�� �s.}���M,Fgo a marq reshaping�s!��a�2�OaK high� low X� E�I�raB�F0}�  6��  a poT onDq"e max}\%$simeq 0.66 �0ed �4�+1f� �42� m>�� $29� ��Z  &�5�A� ���MD$fv1�!�4)�changei�zg�-� �(\langle p_T�LAle�)1�*.*U� ``*p "A2�92���seci�41�ac& at P>ofa权(m�ear�2�,S ��Q st 3-� or so1~.�of:� Ń)��N= prova f�3�a�t-s �?�build-upMX`4elliptic} flow��'c�%��b�� bdPes unrel%  to�E�At�VsKiH?X�R"7L.�A �?^.>�us Uir �� zero "#a&�9a%� real� thed$�{� (cf.~6�/�2p1 (ii)�ot��o�?~g� emon"�H�4�"r�s4&�!Fe&\l Aof%a-�� '8a��$QCDy 8djo04,ASW04}. >K@&�5!�s&$`�aLQHs "����)�u�"�si��comov�A�*) �U���[ Lab`L!FP6E�. F� �� (po�b$y gradual)��appear�x!K es .�}�s'&�Y�NrpoM<d (whe��� hcna�Y�}l%� ��2a�C~�� �`lclear���Ient; S "�a! !P�i�B&,f!�Refs.-�AH03,KL��ignal�AN<d �#!1�&���� &Yo`��Outlook"\ � c$�� o[!-' �W�]s�� r�iof1:�E for 2�W�Y-Ge�Pla�U���N2ms. Oure� *��kE6�2+;"7 -lik�Z< �M���e I��3s sup`C!�0 &��5)creO  QCD N&�8*&�k embod!:dcS]b %$ksc]� (die:s �"WF��m, 5 d mcur�Ls �>�]1�cAu B� � !nd�<6&h� !d��^%xJ�i one-�a med�(�H|.,hr""t��> microsc� B7 . P1@'#"�F�Cm~t�*qa�f%�ř�"�=.�pe��a6�&F; to e�ate"�'��&�ZY�Eg��%a�* t�}Dce��� [s&�( u:�TJ&�*-��*s ( E��� $3)��Ca�o"s bDI5oer&� .p � � k(w7ent9 isI4e�Maz� !s!N�G%�� � t��= as oppo�o ly�h =���aFich�oj *!d�( �-weded)�26p8|@!3imef&��ver0!e�E�ex{%��{:��hO ��(. Conseque�h,�2)� A exhibit "A t�j-&�6�!&EmB^Sic=T!7e�@y�HnT�&�by'Ayp�ao�+h. hav�t!R4�&�A�} �.- ' & A��medm�`briefly�cusEr� ram�ia]��di"dtsfu� ��. C�t68MF"5 "_".�D��C�C" СmA��?� of� - n(t#; ed.�;:"rticl�Cs���lA�ɭ �g�_s�/� b �nA�o�"[&lk�?n�o"c2A��j �@��di:� ��l�f���be6� , :k&�lc1�t LHC�x�XAtic+#ii .A�ai3 Inde�k a ketlԡrma�@ entuCbe answe��by�b� )d� "P�%dl��A�he %/ xistMJ,�;soeEE�� �nb� ��F6ś A~]n�* .2Hn!�I� ($�n,\bar q$$\to$ qkBy�"�`�aQ�i�Fis��& �-4, �4,m)as�k+q q D$+$�l!�I� M�A��)un Xu <$c� {c}$g�ԍ7W'be �*edy lev9p "� E�X.�A� e{�w"�R I$Mol04}, up���� 6�sA.>3 (to"f&|/u�e�)�ai8 � �Pa�0nS- pairc40-50\%%'�m�B�se��Al{ nQCAs�3is%�� �! , PHENIX data-adler� R"1 6h 2SG��r}D �� 8ed>@l,exAU��fea�{4,� leaa9�&exO).&w� &.I impa.E +D2�+sv��]=_(``co�dc�$'')���xonium�/�&��. Ob3D�? comb5<�&{ � exper�w�ZE  �!�besmi��a r!�po!Aa�a�a �"V s� lex n)`of��b\  I,*{Acknowledgzs} On&us (HvH�ank�re Alexa�(von Humbold�Mund���M~*!$Feodor Lyne[ ship�W�rk �6 8��3trv U.S. N_ al S#gcen;tCAREER.qrd� �8nt PHY-0449489&to thebiblioi y}{1�a��\ifx\csnhurl� \S/xt>FC {URL IaTcommand{\eprint}[2][]{u{#2}}Bp� 4em{Vogt99} R.~ , Phy?0 ept.�+Dbf{310}, 197 (1999.!\A(Satz00} H.~ , ;Prog. M.bf{63F 511 (20002Grapgra03�(A�@ L.~Grandchamp, J>RG3� S305S42SkarP(D.~KharzeevT8K.~Tuchin, Nucl>S$A735}, 248JS�h} M.~Djordjevic, M.~Gyulassa$ S.~Wicks C, -�<{hep-ph/0410372}EX-� N.~Armes�0C.~A. Salgado% U Wiedemann9�v.�@tex%j9}1114003 �.l�bra04} E.~L. Bratkovskaya, W.~CasC, !�t{\"o}ck�� N.~Xu� �=Ed{nucl-t�090472� Bats!�S.~ ouli,!&Ke(BAJ�Nag�I�Let]� B557�26�32�GKR�VA> eco,!I M. K-DR.Eb1<>Z9E02Y6Sphenix-e^S. � et~al. (�#Collab� ion)f� 1189Jc�j aF.~Laue` STAR:^5�Ua%�exAb1006�SZ�0E.~V. Shuryak%�I.~Zah )kRAMCu�7ad 021901(R)J� BLRSZ G.~EAOown!s-H. Leee Rh-|E.~ {^4o171�S20:�ShakinAKX.~LiE�C.!� i)Q.~Su6 �a  06520VgDatta02}!� \, F.~Karsch, P.~Petreczkm�(I.~Wetzorke6�(Proc. Supplq� 119}, 487%N6� Umed|T.~ ,��Nomura �(H.~Matsufurm�2:clat/02A32��f 4b} :[ua�2�]6*92�(123ZEThews01��L.� wsE Schroedt�S(J.~Rafelskiq�:��:054905M12�Ko!� B.~Z�A}Aa�B.-A. A# Z.-W M S.~Pal^p5�]ri�22ppbm��,P.~Braun-Mun">|d�St�:_69B49E�9��6 G�!6M.~I. �f, A.~P��styukE�B�W��in![)�{���B50A|27I|6H)��1��d>b��206179Na2:`EVUcNRw�41��6o5]!� itsay �E*DuZ37A�484�882�ZsFL.�Xbridge6�5'151a�29I76�MT!$�� . Mustafa� M.~HA�oma)63:�!631116826�b6P, DM�a��. SiLstavaZ�� 889a$1996� Chen��Le[�:Ko �4��K��5:�\ Molnarn>100412��Asakaw)= T.~H��daV�A72!�86i�65KR�2����a�nn �!�r. C. H wl�� S. A�-�Z� � B�3 0902��endB� k+ docu�}   L]-Varj$s: mode: exTeX�{ter: t,End: �o��9Z %%% m R�@�" tex sourc�%l�,manuscript @%%J�  %\14Lclass[12pt,aps,prc,p��int,su ��a�9,(I0pacs,floatfixWjvtex4}�FV]{�} \renewa4 �vA4stretch}{1.5} ��h�=220mm�T�)=16 Dopmargin=-5mm \odd�)@1mm \usepackage{icxA0b!��title{ApF�!�Rsw D�kn V�Ca�  Ax�$'al� $pe Phase T*�� A�8SY�e Li� au eu�p\author{{Yu-xin Liu$^{1,2,3,4F4(Liang-zhu M}$,� HaiqAOTWei$^{5,6}$ }\\[3mm] \�Yz9{$^1$\ar�'of�=ics, PekDUni�9�� Beij0100871, ChinaY!]2Z, {$^{2}$ Key�%for��k Min�*Edu�9,>o o } \\Fq8{$^3$ Institute�T�e���(Academia Si��2e080 e}^d4$ Cen�"of2aNucoi� Ld �5- .�=Accelerɏ8, Lanzhou 73000�^�5$ All@� T�Wolo{dx, Inc., San Jose, CA 95134, USA�:6$ Schoo�6In&�;��Engine��, �24:���(\date{todayar�@ev�e�ab��ct} B�]aly�e6p"4e�( surf�{W-e+H�ra�a�0� �2^E eu� U(5)"�$� �IBM/�.o�&ha�":.W#� .0 $(A+B) < 0$ �be �Lde�0 �|s.�\d�\v6\a�\'al ��s�V� ) y�V�I�M HF {���d���"9-&�'q �.]z|!]�-viQ) 1dA9-Hd d�empir�:e~,�.��aU $ %\bigskip �ul{21.10.Re, 21.60.Fw, 27.50.+7+j@70.+q} PACS No. �=%2�new�6 I�/ nt=20pt ��h�&a0�1at^F�7� Eu ..�t?&E�%LarʂatrC0search. Many 5C!�.h��..=�E �&o�ed.g:x�*:*se�Dl�$op� �%i�`[ [%U��HaA�UV�.\Q-u<��q eP:�fv� ��eũ {L�IA8� Ag a trD2 �y� p+ar *8Jolie02,Warn02}m0@Hn�zdE��$@"vx�&��x,#&tTX@st�s�exZ��,��@}�6H=< betwX�1s ��ing"�&t ��s.�%"&%Cal fr�$y�qfer$"�'()vn�� r% backben�))?SS V&�lyp[�f/�/E( i)+s�V�I ly'�2A� B�%M^.MD<nd:s � Rega�b�7.�, �>" (ng bo�k& l (IBM)y�� E�be�>A=�V@�r�Fu �a seriea�!paZ �A� ,Cejn03,I. And a���{;O(� " @E�SBz* a�x�nd pac00, 1,LG�� cran�4sh�c%  (CSMMBRM86}9���%bl�11E� band UeW(� . Ho�5tCo� *3oa�lI%WQ�QGZgZ� ?)�!��5!�YF�?u!8z" yet !? es�>imm, **��-�)mpt;ve%s mad��eeI3�|/.)�%�4}). �� �e��Z�N� �}gfE�u�:0��a�,�!choL& of p�FF��ya�Pm)�5mD �8 b�B�9� =�2�1�.�i�o�+lAnN01IBMe�1)i�B�%a"�is�d4%!mcoF*nt,#0$s$�� $d$-�;sʊ��F�0, 2,��ivelymu.V6 5/ group� U(6)�21/�"ree dyn�H�5k/#[s, �!�#A, O(6�F SU(3׌�7�.IMwo-body � oi*m6�� � be�t�Din�Fc��%T( Hamiltonia%N8|&\ %d,be written a��0}, $$\display� s{\hs&z��� H}_{S}=E_0S�Harepsilon_{d} C_{1! + A24B C_{2O(5)}+ CO d \, , D@{(1�8cr } $$�HC_{kGT�� $k$-�$] imir'� A)�$G$%���}6s�O4y $C\ll | B |  \N� A \�{�d$I%A�T li���-2�k of Bohq*d Mottel��byb&le%%�h�.����/sm��œ4GK80,DSI80,IC8�CIn�1%�Arinsic F aq��T$N$QIis"�C�%tEFer{�+}{1!�Z3cm@�,| {N;\beta ,�V}X\�9 pV�Yx[ {s^{\dag} + \sum\limits_\mu  D d^ 0 }W ]^N P| 0:j2J2QJ$$ �0 $$ \alpha_0= � \cos�a,A^ "0{\pm 1}=0, \q�.2}�H 1}{\�A 2}�hta \sin R�. ~S�ed �|lWgmpo�2:��q���d�&A-two.�$�$ 9 � �)&b 7 r�*ٟQ�d`m� .Wi��>� Y��?*93(c� & $�+�}_�L\Tx 0.15)(��TI7�; $��� r�,earth�i� >cJP"z� !�rup\6f�>�x�$then refer14�MN�,d.�-Wft�s.�}Q mark� A!�F�tF2)�0� of AC����)2Lm�. A{sc�1!��no�4 eige!��>�  JE)er"�>of�s�)�A��4^ BL5P in6Rsj wst[A��f*� � s��in ��nd-� , �� ;<�+�t%\":k%C|�+&j{on I�DKM88,Dobes90,HS95}�ol;aU.�]orfE�4 P^L_{MK�@ 2L+1� ^�Dint {D %,}^*(\Omega)R d �\�53���5�� $M=K� T�BAU� fa�al ({��7<&� (� �,?)e� >6$LjBJ�teJasf!2�U,E_{gsb}(N,L,�B�g�c)�I�\{�.@b�|l�(H} P_{00}^L$c|f3Ѵ}}6ef�|�\��\!�."�41��+ !p"� QZ"� CG[ �4��com �^�)] F^�u ) = 1]int^{��_0 {d)�'����'d1O( ')�� e^{ - i ?J_y��%��)�� �� Z� >�|.� ~�>� ��.� 59� 4re $da� mm'}5@$� %��X5�LF. ���&X]Do�YV )R�նsh� .G�[�v�61N (s =04�Ƚ�(]u9<� e�1we�;Ps^c��E�5)��z1rPۆ J�A� A_0+�N�U\  (L - L�oA�^2� �v$1}{4} A_4 4.66�^6 a�, u�6Y�� $$ A_0��*l {d},A,B,C1qx� [ 2 :.L + 8 A + 6B + 4C + ( ) L$ ] L��#" � eL(2N-L) <0) } {2(3+2L)}A�$$> L _0 = -7F�5y4B}{- ��, .>A_4� A_6� �5ѐ Az**n  $:oX�ABC \@ɩMces� ,��p } �-�g��B�pI�$L�d [0, 2N]N� !� > 0y �g ���mayafei� D 84r neg�I . If�>Iv �P\ LL_{0} <"s�CbG:� )�?m�j. OzwisWf $)�$ (nJ�2 �F gu�Cte�_(��+ 5E~4B) ���<0�0� ^�)�y�nge)��| 1,a�!�Z�c7-��4=dQ$L_0$. Beca�\�8 lexSF $A_{4> nd �� ermA�~. NAL:Q )�C$, it>D��~t�Cz%�&l,6*� �p:. N��.�@I�!?L - � J� .,f T�9:�%�Y50 -�C  �.)?,=<��6)��be5�,5�>�I&�Ha \� ��a�gy�=�f g lose�Ks%�LI5u�Y- ?� LL01,KKb�D%�P�  !;rmn\� ��,  E0�$��b �DA9aRtro��3�t5A:  A�Bq)�i:j�sb;w� G��K:� A��K6)�u�{�] (1)E����c%��E$�E\pf$al^2 B� )}%%^� wH�eta=0}=\�� �>0zE��1�Q~in�U�>�t� �e�us)�s�eaFIфal ݈ always str a2 *�%E$s ��A���<0$$�x%-so>( ^�>� =*j!, -- =0�v �h$L<���>d ~d�Zd< 0 $ AW$L > fS�9m�S_��a local���Po axi�mU�1�w* neWr�:yWby�o�Nve%Y[u�Amor�&"a � J/ _c =�"� 3� !{16 A_� M�} ��C?a$e2# acquiJ�w��d�@-a at �, e� ==({-3A_4/4A_6�4}&������[�i!{max}I �>� , beyond �&&NU�[A �}i�I`er �[-�Aed.��2V �_Ł�=2N$,�K MestB�� �͵& e6w�� L �=LyfR�A_4\^!;)�}d n?I��!:: �+0$L\in (L_{c}, /� (R!E�"�P��=����"omr�� \ne �A&6sons7the��=��"no Sum��.�M "��( �,2 N]m� �$-B�Dzq���typ1$f�e�is &;vd��F��1%�!zi L_c cMed�g8�=6:* appa�JIja��!"a�� .����Iar:!) ��i��.�&���A-q 1q ��c$.A~!regtof)� MW1�QX��i�2&�#����6�dM�Elum�s%� � QkA�$L���r81�!> two &ț O�HT inct `a,�ЉTis��M���%Kc��:%IO ��U@� �l� �systemN � g0J&� �yF$) 1 ���!�W hap�a2*� qvHHpontaneously broken�9$!&b,J&"�~ � ,�Fr�#�4dar�#�1!F>i#.� ,�� �soEOdi�B>'F�'H.��!]6E���IagaPcurso?a ) �*W&* (SRJL03,Heyd�<. W]J>�p�u�mayy �)a��B� ��zi<� = %'�L = 2 6 �]�n�L�E�simult�W\&�Ū1 ��A�"~�m FX�be.l�n_dRED&#) {�%|+ J�4� 3B ) � !�L%-� . � �� �5o�_ar� �a<9�Hc2��!O ��&4+$\hbar\o=2�E�+�+ ��$ (�L���onic 8L *���+� B_%2�� ��] $%Q"! �� + 2Car ��1$)V��)}A���� 2�!�QL)$ ]n upper-v�x��bola ag:tExe� ($LS���d�[2�& bs2�*��K.�i A�>�� ɽ� �re  �sd(8l$n^{(c)}�� aز*� ^@�>=2%� N ="R�2N?3 B�,A + B } - 2Ne�Y�58J5N_0=N$e��'�n( ��!4>� �\geq i E"�h�LmTno (/�"h�Pu-=�a�s "�� "5quasi-qG���a� $�== N� R{MA�a_-s0:�"xalKB�pr�!, �IA+�Zud��/63J*�IF�>v%�.yxp8�**0 R�  !in08e�!G�B��m,p�'%� �- �!�<^c��I#���6 Z�'E�E(LGc)�)uE�_ C{L}}8�'!:A��4a+ 2 C} &�&69a, "9W{ a"m/A2�u��\ge.� &�d�e\f�"�P,�6!r��C� L�e� "�*0���-v\+�x ar��.�cav�d��%� &4�aE�$N=15��.�=� ��=0.�p��� 0.02�p $ B 1$�p �($ C = 0.004��8)J�fixA�&�M�5� $L_c=8 �� vM�.]�sтU L.�$vV"-�]�I>" �{mc3. It� =0+1��E2*� "K)-r�� ver J�(E-GOS)!0R"7E_�((Li�� L-2)}{L} � �/�-�q1�goo[�gn`Q nif�6{N�!>7>u �-� R"�3mn auxili2U�*(wea0w����!M�2�E~�]y��r=X%� =�! i| �A!��=f��.j �4:�V�FnD MJU���d0f�ae�]��3ar BYUake�ce �6a:N� ite M2�c6!S��s)M$n_p=n C p=N$)� BF02"�A�e.  I78} BQomg#a�Ue*Revie�@)��oY a��j-�&� n� �s>�Z6>eH�o�2t=76���*" �IT-�^Tre !dna3&j!!=g `"b7w AZ-��al&� & " 6 F* $d$ .` � 8k NX$ =# $) r�,2]]<%L��c �!E�F�g��n!�e Z_%ET. S2],�8 udde" ��1�$d2,O �� "�)���vef� ngr!�6.�� E��c� �>�to�arj .�A%sq�I� m*�ai�of a ,_7} i0m�&�& ion �A�sz�%���fUm ]bi,�� ]�&�9, j+%�RPi�Naz;YOnF#lev:N�n�  $A < 0:����!�2� *�.��j��ENs�"�> �Long9ER�P�bHBB our �e�o�?�G�wa:]@d S�7tC02}$Ru&k-�q��6*� ��By fit"�3e.YY�Z�A�əY.��Ր(9� (10)�?&$"� �f !��fplo�sMlO45/A�em�NmA w}�uX'lisG �e�w�� $�, �, L)$Gs8$��in=s4�!-z|�"�ET�1� q!�� �oAuOV��a�0:�$L=12� AkŝU�s�G��amB�<&J�Bt�}[h&ޱceqD}&qvF.7j}�-zA s] , 12}$Cd, A!14 4}$Te 42}$S*>'88}$Hg "�w(tabular}{|c2 } \h� � & .� � $ (MeV)A B$ CN(�$�D{�. k�m�$& $0.5281$ L 09376 881940.01475$ & $20!� \\P))E 0.65.P764 /^ 1327<O $2V (�O%l O569 !A00378 �158 �P393 � 106PTe P774 �A678� 42B! 0126G $1 -.�-��.109<626 @M16 ��71 $ L�M/u595 !@30 029-�� 91 �� �-� �CQ} u�Ke- @�h��jS ԁ��avail&6Gl ���Q�ϙf!'�=-zi�X $ 30\le Z�1 Ie�Y ula��w����l�_ -squh����aBٓ�0.��k�� , be�R :� ie�im�e�a�M�*#�by �f#�p�H�2 t�6� f}bTe }MP�F}M� %.� &1 B &���y��k�Ή�6��S!�.� *s��Cf�B0 a߭%�Fk!�:�:"5� !�6�1�� �j~1j :%$ &%inf�at�C�2% >s�NB2�l"! . LookAx� �E��>o<;E>� 1� may � M��!�R�O, agre��%V!j��satz:2*� half-�� A E�v>(or hol�mi�!�&iaR$A�:m 1�� mass�"٪it1E�-rno�b: tes��� "3va �e�Fs!5� $h_{11/Mo'�a-e�03,�]8Y !9.; 1�gu; I�n �#3�s�Ś�-�c_6� RmEw�db0p�-n;����N �a02lx!7"4k� s"s9 �sei;�fact,�wIBM. @@Sam82"82,�Llt8("85}gk� !� at, *ZD%�os�o�Jert�}�Mt�,^�&�a���(T�"w Dlie}ha��J2&i%ea�ibclu!)�B� ?��e:�Z�'al^�ͯ��lM��`�is sophcI�u� esti�2oN  I���y,����"�"" >NMv �u�:�i�>!W*F�&BIONx} R&?$��1��5[�nT$�2RP$?�fl� . We@ t`>A�o�A�:��*g��m� �F�2F�>ZC�N���'�  �FJ�N5gb�)�&�R!U.��g��&��f� 6} . B>�PaV� ��� �#� I�*� � &� %!�6n *in .�6QAZ& a6�� ��� �he J�Oa�ol�P"U�@HZ�'bTh?PTa"q�j&�ib�&e �S ur�Uci�Fo�iOCU*��Dact Nos. 10425521,) 75002J# 10135030�.Major S�+ Basic �e�O Ddop�?c\ram mi �PG�h077400�-RP F�#� !JDocto��hNof Hig��"{U!��* �h�0. 20040001010?M�+�Vs (Y.X.�Vk/Kk-V1T9;� &\V(VT�r-ZV%q, too!�J~Q }Q�WBk4kb�h�F} F. Iclo)�A. AriV,{�@)I�� ng B5 ]l} (Ca�a*�T P �, �j87). "��3W` ��P};j �e  Lar, R.�Ca���\$ Heinze, A!snnci�V��r*Xcxb�_{\bf 89}` 2) 182502j�WQ Dy` UNK420L 614jI)P�S. Sten(+>R.im� FW�] bA 183}�]72) 257jdF �| P. H� gan)�et al.},�Wv.. 90} a3) 15z!� d !�\XRU%gU12501j��O!6�N.!�Zamfirb�2 � 4) 2Zg Y��O:iV�& !0) 3580n� ac01�T7) 1) 0~gL�Pa�Leviatani�J.! GinocchioFI6ܑ�3f5�P R. BengtsHbS�auendorf {F.$,May, At. Dat�[ �s,i35E�86AQj<AB04}A� er kJ.�h�nvg'bf C 695� 0113rW�K�QN..4�& M. W. Kir�g�))F44 �0) 174n� L%�D. L. Di2�ink��� e-�.n >y)?6yn��L!?van Isa&�mJ. Q.=f2%�UC 24} �b1) 68n�KM88}A8Kuyucak, I. Mor4,ed>c58 _7) 315;�� ibid6� �36)h7) 774+���G%� \v{s}u%� DB 158 E5) 96;.Y f42!90) 2023gFHK. Ha�kYD n,��.!KMod�� OE )A95) 637Mt/}E. L�+#F�M5()Ppa"� b.1$NNtZ >�E,d = 1.010812�+$A�0�S 3669B,82240*C= � 8508., . ).� !�5g 1�0-�,��&�J�"g�+"�6*�9��r�%fAd!d^�<:=�s�{=��1�&�&�a:$AP:amp&�jM�Q��,&W-�$ ��� p��)V� (filx�� trFi��.�B`)%YajofN $(A +B) *-c=Z. # E�2�.= -�."�.A� 8!�., M��.s�_i�m�edV-73*jQguÑ!!eye.)NA!Q� \v!�k�� � ��Ru102:���)�F;l*ø-��*@�� -GOS�& :ng� ([�E a,*� F�:,���?F!) v7�.%.�jncN��4-4�"!5#"�%�C v�!�i2il"sm"�,302,��00,��)v�$&�m�j\cl�n prc,��&�nno��inbib*�n.n$epsfig,amsx>,bm} %. <keys} % "�n4kev}{\mbox{Ke\�^ {-0.1em}V`�.�nm-M�-g-GN-8% \begin{docume�nt} \title{% $\;$\,\\[-5ex] \hspace*{\fill}{\tt\normalsize ANL-PHY-11055-TH-2004}\\[1ex] % Axial-vector mesons in a relativistic point-form approach} \author{A.~Krassnigg} \affiliation{Physics Division, Argonne National Laboratory, Argonne, IL 60439, USA} \date{\today} \begin{abstract} The Poincar\'{e} invariant coupled-channel formalism for two-particle systems interacting via one-particle exchange, which has been developed and applied to vector mesons in Ref.\,\cite{Kretal03a} is applied to axial vector m%��X. We thereby extend the previous study of a dynamical treatment of the Goldstone-boson ex �( by compari withn` commonly used instantanersuccessfully to calculate spectra and properties of hadrons. Inxcou!7ofdeve!@ se � s, r-tye7\emerged as a key ingredi�inPlight-)B!(or. This ha!�und earlA�nsiderE+ ; e.\,g.~ F8well-known work�xGodfrey and Isgur \cite{GoIs85} Capstick 2%$CaIs86}, wa��- corr)�s were %�duce= a non1 1$ potentialI$`; Feynman \textit{et al.} �,Feetal71} baa�their ; o`2]`harmonic oscillator; Carla�VaCaa83}I%.O kine��energies plus flux-tube motivated p�terms. M0�n�e�M% :�-ex��(GBE).�MET (CQM)-GlRi95}!M:j�mA���-�l�96, 07} showed sev)�aMistencaA/Hwas soon superseded�<a ``semi.1'' versBq 8}. ->3���(Hamiltonian-,iO!tains&.t6�y %�Ye%�,��a PoincFm%�7long ?:{��rote�a�z$invariant !^0do not dependA�!to���A �nb�st��)�KePo91}Mni�$rmBGBE CQM�y�app��oscop�?r�z�,strange bary!�ector� wide�F; A9ver!\ analog�#�UA��Ųs seemed�3indic�failuru)M��is�� �ThEB0Only recently KrA�0Qb�co6 (CC)� mali  confin�wo-i�leѫ��eraz" 5keSelucid�!c relevance%g%�cabil� -�1�!9��-@ . A�� from6�[BUI�8 alsoI�to deaine h��ic6=of )� s us�r�urbativ��7(ions employ$el�ary emisJb,)� 99,P�� 9} (y out!e��L addi`al�Aam�s) a0�pair c� Ag (oneR3)IUsM,ThE,(0}. At thataM$ge a satis�(ory descrip\ofJ# �0impossible. A!�!���"A1bAL an=--1- -typ�R8 m.natural �KrKl00� ub� iUa��A) *� ���6� A3�2sugges��mM�02, 4��t!  observa? hat,a�g�3al,vor�I al r� �h�,bly underestZ Fe e>� �Bl% ![ thes�� a next16 step� to�#)�n nels!� lici�Q� $qqq$ (a�m)e�$\bar{q}��)K , re%Tively�)8I�03Q�03cm ��"� 2�9�dA�to inv!$g�QefQ of��hb �"b�ޥke�+iI .�lͥfa�H  both+�=U �*� $\emph{and}-c� � e B�f����I�pe�e 4much too large fplitt�,of $\varrho$-�omega$. +  flaw!� remoA� �CCy�, leadMto small e� �dAOGBE in6� ichA�firme4exB ��Yt��e�of���@�Phould��$contribute��b�"ng9s! ��s� gar�6�sie situ �,is difficult�judge��rD&� w��2  , si��a A�branch�{ 5 anO ��� !B)�6a},�+ s actu avail�� 3PDG�g %The!‘=�_Idc �qly)�, �a %��a6���ach��_�e* f�!��A at %�!{$a signific� !�ere!I betw���twoes �* c}. "A res"e�8we follow Ref.~66a� ich�&, detaile�A�a��!Ba� �])�'� ,�l��those%Bxi"B �I[ quan�Tnumbers $J^{PC}=1^{++}m�-4lC �{ � via mixAn�+i p1�r>�x #idsfy*(�=AK�^enE�\Q�a�of�6yQa@�f��ri�5c �1�:�briefly �ew~mai� g!M%���$Sec.~\ref{}�Q��M:r$nd discuss = 1},� ons}��| . &�M� feQx��:� ��� ��!X!k.�~ b �>� i� �}� ����e� o��e �7$le Hilbert�cs  di� sum�4$\mathcal{H}_{�� }$ (�-anti )�V/\Pi}$ >2,-pseudoscala� ,): \begin{eq��1.cc�8op} M= M_c+M_I=-pmatrix}�D.�^c&0\\0&R�^c�F + �<0&K^\dagger\\K&02.\; � H��$M_c$ reMq�e diago� %�$M$, w�� i]d�;eAT!�C�i on ��P ��{A+*� Ap \Pi$"� >*/ iskd. $M_I$I�Da vertex piece $K$^its�mit�adjoi�s Qd(in Eqs.~(31� (32)AL>�. WheI�(eigenvalue 1H ��M$�re<� Q��,�ob �!��� =@� mr3 -h!2FofQPe:}theeq} (RB(}^c-m)|\Psi}!\0 le= U;V>I� -m)^{-1}KZGJeI!9is5/ , $m%,�9O�app'��f  . We� e!�eInU.H� ��� I�� sponL t� T g�\a F� $E�i�2Y�$I��oGsB i) fM�sQ,sameO" twice�bwil{ fer-latter�``loop �''�9% u��"� choi� A�!%�|�Eq.~(ŏIB�$�ir ���� d���1�!� ndixRH E ��Z�par-$ establish�I-v�D�mgax� !s�  qum o&� need�readjust��} om%�d�Y� Al1y;A* f �*f��A� Q�Q_!�um.�| take� RM�� /B� &in��8ew�ve kep/eZ Ef �kA25l�ե!i A��� �I-�|Ei�s E�Aer���h5iiO1 . Fo)�%��� , a J (HO �5m$M^2$�� 0reaons: first)�HO6{'s ��s� solu!I�!yt�ly �� facata��*_� second,�mimick��srr�a linear6�oia�$M$!�er m Qb>�g >!hoev} ^\�j�arrow M_{nl}=\sqrt{8\;a^2\left(2n+l+3/2 -)+V_0+4��m}^2}\;,t{ x� $��"��%;F  asse�$n��$l$ 2rada� and :�"~A�.� �%|�$a�N.|strength\ $V_0$ a!RInto fix:�q&�gr*�to�phc al C. was ���48 �28B^a�E�aMiBI��re�d. It �b�5d� l�s�Mgbest "�;At*7 :� $��a�% an accur�fi�B�Phigher:�. How��M �asi^ our v�st�l . 0)a*2tp�X��T ��i,���ted to~G (IA)e�ref &V F s su�2a��Nu  purposex principle�&ld!��an=r �ő�A � �{b16B�,8! one �u��onc�-0of Regge trajv!#�f TaNo���r�wa*�� ��&a�"�-�� ext)2.Nd##1oAnSe99�f�oA`G�yM��zBC�1,����%Z���&�� � findQa�2 - set2� M�-�y doe�o� t��d!\e.~1L.`*$�r�@us $a=312$ \mev\ �8=-1.04115$ \gevhWmplete�summar"YIH& 9� :Iw�kev6F. F~we.��%c� !�IuA4A���>exp� �is*� by;assumpN��� Qsa~ bH coun�0!�via a-�]�� � ass. An� ʽUaIA! (tenK�t)O � bocorpo�,�% futX��. SA � � B� o�m^$�>� !b�Wigner"�*m���overlap�Jse�U�Qe5&x !��8uF �)u:� (see�� A16)��\Aa})�eglecE**� $s, becausee�lA�e�er� tor�s��mA*a �e& ir.e�&&m%f�i�^�ar�o boost6i�&*P of e�romag}#. 1nucleo� W�#�U &� '�w�u�f�� Tfigure*} \epsfig{file=� ra.eps,mD=12cm,clip=true,an�270} \cae4h"�aax&3��� a: E>��uncerArt�9(f name),*�$ (O),A�JJ (Cf! FF=1 (C1)c� N�(� FF (ID!HIA i HI1)�-(}!?nd9MWC�ed2A�a.mw��O >Oby3v� ' ";%�jnuM�ly<�������W� ,$P=(-1)^{l+1�nd $Cs}�l �nb\ >s$c�#spE �ao�(:w ;�2cue� ls $s=1$,�;a"; -h&�%2~d e`>��e $f_1$�! iso�$$I=0$), $a $I=1�K_{1AE/2$).�: !lg� $s=0�I !associj'arr s $hp $b6B2 With8 �0ź w� sume5�(��)�ct�(nd"Dglet $SU(3)$-flavo�g� A2, mean%c� �:�%Z mJ eace��p��$(n}� s}s$1�� !2usual� , �E�denotesG!E�s).�6��>8M�$K!o �umE!mix�{��1�� Ba Yth�*rL ch�O %e�I�� our>*�)� we fBlI"llZ�)Bu$5}* ���F @Fig[ �a}��8six ``columns''a�)�V1;E+2���� P�}depic |!�� j ()�d��Q�� s) boxe�X'Ihe2z 2O� V� sixtAkفtEs� �Ez&R+�t}Yaa: *X i��@��ٍB-�.*!Uѫ z��0Nnշ^IAfv*oz vI1�se%�?��go� a.= inV�;�� �� r� �* 2c>� �i��$i&~ �lybn $l=0�U� ad.� $l=2%r� P �%�F��g�%H/�� � 1s ce�ss&$�03IA�2Q�pro�n�+se �e�#2 . �ax>W s�Galway!s�1�t�s about � ���!t,���>!] �} � �Ej#  �m��ma�&7surprip)"� �-p�"_� tron�'� s�R��l�2WB�B pl!(a"�rolM @.al setupC-� !�,E�-�.LJ�3.���zOi�� E�er14 AY!�nIA&��  �u��c� �-� � A�a�!-IA�%�O!� H#.�(have opposi<2ignI�(�,8if�#t$%�j*�:�x CCyA�Uiv^ �onU�&egc*$e (althougH�Je.J%J)�?�� �� um, q i;aM--�+8.���'r!��4+I+q#Q�6�*��,z3.�a^fexe�1����� ��Y5��Q� 䉿L�dI"&$a2�% �et��. �c!�lex�M\u.��upK!!@a%in conn-3�Nwcfun5$��$��. O�wt"` � v$1a#um��!}$q��)9q~ ��E��1p�of��I�a&N&� modifi �-�i'37� �) ua�".�5pparent �X^�. 8$Q.!Qd>�6M�A��-�ca$*similK5M0\�(^�(]�� �)R�� � to, u�m�Q6��)ed!W3 en''. OurFa|M���! orde�2$\a�8 20$�$90�a!e;:�)�K�� M? (1235)$8$\Gamma=142\pm9 QM)�� mina�1inj- "H I2� [;  )�33c��6 42J~,2-.=e"C ��aW� of 4.�&C�8�&���8"���A�Al.-*�3 - �>W2f.F�:W� � F�)�2>�.C+}/h)T)+% impA&6�:&��aqL��" {��� ��&�I8��-bo�B"c(OBE)A�mh �nO;  reveals��acter]1sNVa��2� (� ly�0$� re aHfA�. s: i�12N -e�"� ��M� Ms, "��4n>� doa=t��Fis y s�a�!89�  dul� p% � . ii7���"� t �mq-(aa�=�2=1�0g1_<gn!viz< ����3 s mus9��1�%�.�� .�E�~5�� ��.ly,��!�9�!��� a�� �!!V�"b5rtant ���#�> �)��>�/�y&�?e�%&�> i�:��ve:)|�1?�ɗ��?�)4!�� �1)a�u6�4by:��sup � =� draw� ^&�-�n D$e9*�1E� '(1420)$� �*y AI 2mpr3ZA!luU�F[ ��.z&R1 and/!�aka�!1�al-� 3T�59�A�ly�6I%)&5�A��5a@�ET�ext��X,]�,^�2�OBE Q0 .;$is yet mis�o B�A�!6f�1aR5s laid �* alsoC*_8 %lmed� �6�$ �0� u�0�stocha�?��/ethod dVaSu95}=&up���:M�U( �&R(a�79 ��high d�B��"��7���!g~4n!�vol*�52"A-CCX"A�1h!�� |!i%Faddeev�5J *s3Pqa{=� ؅�! proc-*%R#h0ion"�: ]�=�S Mn�8�yield&�2 2� a@2�;wa�!� ld7ed�ir unb�:� Q�sta&~)� . Fur�#�D, giv�.limI&��s#&kD �d.;.��Zd� �5a%rF^  �*�1��1A�%�:�d�`2[�)n-�m�!he JD!�ac3^� OBE�;A�� ��clear� b2ac�$ ledg�s� �}�4&�� th F.\,Co�;dr, W.\,H.\,Klink, T.\,Meld�5nd Schwaris)T�'͚l:"D FWF}� ?C0Erwin-Schr\"o�.er-Sti�@Hium} no.\ J2233-N08%�!-De<�!QERC y, O�&e�N� ar P�(�Et!- Q~5�W.~H.~)M %``V�%I���;J ,'' ը.\ Rev.\ C {\bf 67}, 064003 (2003) %[arXiv:� �-th/0303063]. %%CITATION = NUCL-TH ;%%%J ��E S.~G*�EN.~�E�M� s In A"�Gzed Q�G�5' Chromo~ sB�D �832}, 189 (1985):�0PHRVA,D32,1896�YF�C.}F2�B�p���4}, 280 �6^�4,$6�"�' R.~P.~�F0, M.~KislingeI8$F.~Ravndal%qCur� Ma�5 EleE� Fj:9��y=�bq�706!q71^�,#�%\Q8FaHe68} %D.~FaixG�A.~A�endry�HIGO"IGM{-��%2�I17� 1720�68V� 173,$��C�[83} J.~�G,, J.~B.~Kogu d V.~!�,andharipande�A.>.� B>HOn!�-��2a�233�83V�D27,23>��G( L.~Y.~Gloz1l(D.~O.~Riska��<S*�/�-�e�!�� hype�JchiL9R� pt.\-�268A06�96�g4hep-ph/9505422>fHEP-PH 6�� 7:� , Z.~Papp�JP�(as, K.~Varg`K.\�= .\ AI�62A�90C!�97>�4NUPHA,A623,90CR�6^��W.�� �m �C*�0}�XC)�D�+aNmMLet!�B � 381}, 311�J�60135B&1� R�8B�ӊ�U�ed�5�&��l!�-%#-�-)��a���I5A�09403�:98F�706507^� 6�Y., B.~D.~Keist��0W.~N.~Polyzou%�2�NR>-ini�a���0%#%�Ad��6�)�20a�25%�B�,ANUPB,20,2256�I T.~Thonh�)��1U��+�}+9�O!yMa!'�sia�=,FBSSE,10,3916�"�I �M {\it 6'l.}, %6v �%�^6%oldst��-����2I^1,2:"|JT^, ��esplan�:%�9FeJN(Delta:�:�%in)�Proc.��!.$5th Intern�Symposif8n Rad ve C*�QD(RADCOR 2000) } edg$ard E. Hab��Eur��J��1: Ac 2001���- 010099>�" E&� Bo�K�� %S.~Boffi �Y,P.~Demetriou� �ci%GR�N� <c�↛6" � a] 0252� 99�� 81148b� :���01} %2x �F|, 1'� �% :yCovJa�.oQA!�!'iF I� %"� 16�516QN105028b :I%�>:5W.)%��M� dr/9+�0 weak5*�bEJ+bD��17D2BG0108271>+ :*,CoRi03} %F.~Y �v>� Sca�!���>�H"'"& %aT�� 72 439�V600B� �3�"T:O2��5�� C�3of.��front �. �6��X\:R9a�� �,:'� Z,90,>� oO2 �>��:�2� st,[hicB3{ FvAo3Io=���0211356^o 6� �4.���>�%�S �!�f��E��:%��%�r�406023:�q- 6�� 03b6_�3vKA,%6R��#aO�2 "|H����4"\:�� 4,40Z�c��"�.)��d%& �:H# %���1�-b�1$��%wEidel�.�  [PDG]EfRev�K��*� R�59�1��4>�(PHLTA,B592,�w�<��Tan��J�Norbu�P2�\RBf�[ %� �.�-�> | �j/ 4B��/ 4:�"3 H.~G.~D3%G*AB.~Phelp� 6��`S8Z cc %�%�ыz6d^�53�712 (1V�10245Ze9 %�& Ri 00} %R~cke Koll,� Mert$B.~C.~Mets ? nd Hmetm���G�umA��Cv! qH&� ^� 9�*0N�822b� 0�D" |� .�,& ,v�.�*+ E�RB�CO[�#�Ng^E,�*i�"��#Y� B.( %E�H9)\h�P@ /hep&L?irn=5441498}{SPIRES9 ry} �Pr}�IMini-Wahop�0Se�ed�bP9BE���A Atomicg��` Bled, Slovenia, 7-14 Jul1} ]��2a} %TA_�L�nt�`nd��P.~Svef� Thre])d"�R��/".!: A tnE%F!kes3-� � # %wim"raN�Z4(ic�Oram�:%>T �4� 2Y���C02030F�QUANTE 6�I"�%bY.~Suzuk�iPrecise2�! few Jdp1��v�"on�r�g ed Gaussi�3aZ�5�4 2885��5����950802B��q 6�&<" "-A.~KrSh%& E�"a�- mH�DA%�s1^�44004��u�000200B� � � �>k docu�} 4�\,class[12pt]{S }] he9=235mm �'=16 ,opmargin=-10"oddside $�ghndent=3em % \usepackage{ams�S}> symb6 bm}% bold(BhGnewhand{\be}2�S} 2#e# ?"�J:!beaEnarray>$e$ FV"4bftau}{\mbox{\�� $\tau$>ObfalphwB/J1g0N`J1xiN.xiJ+betR[J/ sigmR0B1$mbss}[1]{_1�_&l#1}>mbt:0 tinyV*suZ-G:X6mbt2-U>Tds}{\di�ystyla.tvAQ$varepsilon:g vk}{kY3:mA.�I'#1B8bnabl-h ld{\ �re.�baseline�Ltch}{1.4'%atNer :5s�4 }{\@start { <}{1}{0pt}% {-3.5�UqgP-1ex minus -.2ex}{2.3 % {\no�c!�\bf!� �RS!n$���t{j {% \�-\\bf DENSITY MATRIX FUNCu#�AL THEORY\\ WITH ACCOUNT OF PAIRING CORREL�#S`au1n�% S. Krewald,$^1\;$ V. B. Soubbotin,$^2 (I. Tselyaev,�5< X. Vi\~nas$\hph54m{,}$$^3$\\$\v\\�= $^1$ I�G,t f\"ur Kern�k, /!$schungszen[PDJ\"ulich, D-52425 Germany}�|2$ 8� ics*&, V. AG9ck�& -,}R��Id�2y"�8�o(heory (DFT)�)"1e paidIzD2e�"� �,$al vio M �)x-Z^�nd� +f�+"UV. b�oIM��Mb�9�W �84ndU�46c�ex�%ng DFTfj �� 3�7�-g�X�m1V!�v�<�=~��4a ,hhisto�Us-s_X�,o a�M qB�i+G&=fM5a< i ?ed �lso wagoa�et]l>�>dtqdcqpa�nA�gCiz� ��A��/]-2�*K0 OGK}I.�or>�Tessent�VfeadG)Qis� ory A��!er� ��;6-e .xa��5.��equently9�.��5.Kor�?� � � !� Oic� �<Y9a�R�may��0t u.R~6:<�Wq�T�Y �>af�-.F-�Z)s�]�!�/ �s�1N�?A�� ��I` d,%WexaaR�A�y�finite2�a Migdal'P�3 FTTZ�[re�Bc��!?in) or!���+ ��c (]�B})� 4moalAaF�1 e���a rigorQ��*//S�>��.X*B6�v413.z �7�i%�]�--�."`@I�aK2"V!����ea.�. E-��q�Ko4le-� -`^rix (DM!Nup)5�kZi)Y�inA*l�eh�Q,\�K�"�u9O5a�\4� tic-��g"v!as�N ��t.�}@ 0f�Ba ^atPd!v2 ok�Y��a�3a�[-/t f=h$W< �-�> &�\w�B � u4 onenlSA %ar0'� fos._ uFV��4 origia�J�< �� �li3m�5�Ei�K�y!B<pB)�H& ZQ6-�y. OnA�# &8�5e�aYveWEI-�A�,\aid� H5~�&Gilb}�%=[gM� �=�N5�=feKA`%�(�for�%},�esTRses%Y �3ulA[�ed&� &� yia�E!ra0b�u� . An�� "&9r3t^�STV} to �Qe%+!|n%*�an F�I�=�a SSzr- YlDM��V�2* iqNM � y� avoi �d=K tb�hAi)�& !�=�,=�=����p!�� M��� M\  DMU�/=&g"4\A�3ax� )%coincid�Q� # RV��i!�a~uf on� Ie*�q �QXsW}tq�� .�CE�i�F� IedAd enozI&� 5 :�DM�T�ha�a� > V�en!=q�Z�ge�� o]\f2��gil.&% w�:v�| �B��" �!�,p?b0K.g u�BmY�?e�.�=��<Zp"jxn^.P )�a fixed ���sa'�[pLs organ6a�P.q &�l sec2O5�qDxf(EDM)c �A�ims�`n6K3 K�) u�j kGtoIGde�MB2�.A�2�4 Uy�́ka��^��is�p!���.� �;-�l ?�ANAppZg� s�Ze�Idet(pA���BX� w&]Y EXTENDED >1 ORMALISM ^G%�} �,� ��E�!�:�5�t9oNk�2(c�: ell N;n *[, e.~g.,w sq8 RS,edm}),a shall �A)c�A��D� re neE��]� �fu=@< ysis. Let�fsi$a%la�Gr7�% symm,!E-�� 2LE�bg�yal~ $�k[XWuV{b� E� zed,� i�����;s+o)A|6k� 1�� l' "b�ui e ($\u�i�anomal� ($\�$)6� AuM��A �!SaC�hr�^h;Qa���ex7�� CU;o � (x,x') =Ao�W !D |\, a^{\dag} (x') (x)\, | #�l \,,f�rho�Ze� �n`vY\,,\quad I^*fK ��:�6��%i �w�  $;)8 $�)$�H"2{a�annihik�~�hQq`( coordinatefe�)�Y mXz*� lq�}N\i, }ol $x!�{U�@}, \s�, q \}$ �=aspa �$\� r �AC� pro�c5$ R$�BbleaB �-�;x $q=n,ps2RWG � �{ (neu�*&protonGY&g�Smpo"Bno_ �2.sV a*� !�,�b2�(GSiF"K� a6BP eX!M�o {GS}}$2}N�}re�f !jGSy�DM vanXmq�E�gs jY� 0\,.q^kGSI�H�gin��&� � 2 S!t� $ auxiliaryV iYY P�7K a-��� ut n� the�: �nonzero�U�E GS e�Bia �P�n�! ful}������uT*EDM �$��byL�k)P �f|X�2��#�[i� ular l ��� GSN<.�$ T<{��{time-pMrsM �&�!}"7gcanY�al�4s (CB) $\{ \phh$lambda}(x)a�A��>m\ mj 7$!�wZsl #J�[B�su� M' remainingI umM�s $\{c\^ ma{ c,s� ), s��I\�va=W�1��rh.yDsum_{c,s} v^2_c\, !^{&�*}} "ł%2^*��, �, 0 \leqsl4v_c1}Jrho eej A�[ real:`I&� idem@ (i.~e.I�^2 \ne �A(��u"gN�L all or al�R9 �R valuMHI�, ���E� , $\int dx'\,u��v;�� -cnb$ (A| inaf�;j$�_Ea�@cetJHl �e $�|�^�s�6ve�lŎI|YU|es), liK/� val $0 < � <1$. I&ei,�mi8� d A"� by �ert#*|}FG $Eu� }} [!\]��� U~�LAuch {\sl�� non-Y$ DM, �� D1�-�A���occupi��ali��alsQz� a�phb2$� ��6X)�EzL�>v�u-Ha"`� $h.,I��dI9.I)H/ !V� ,Y "���e{ B���k )�q�^act&.�!�A��!�|Ea�� �-�2� x\#1>^a�AHert. To"PgW), �of!�*& `{�c"� :� q$\K{Rx��� ]`(${' R}^2 =  $)"�nBfnd� C�M�a�>�l �blockA�!:o�xjEDM� a DMMU���k�beA�Ddoubled r�  �y� ; \�&(x;\chi�=kn*�`os��pY�%�.�s� span- �R& aG{ x, j���$= \pm _$�r2A��� "�v�b5"�\Bq>| �Je%�Gi�s�>d �b��ec"nZ!��� > LchLTUupJA@ lowe�m6=p$\n�$ � gA�nLkƽ�eTa�Rou�o�"* orthoE�!?>nnes�RL [! ��ied�a p�} �E�8sT&uM�'M�'}  U�=;� /@U� &=& � _{AH, '}\,� _<,D}*�!�% �i(C} !� ���"' j� 1 (x'e�')6� chi,� ��-�!�� a� $)" *ak�W(&f- ') !�"_{k, v_{q,q'}On"���za�h"�uu z� Ib U�En)�=�.19U= /*U ; -A#-!C)*� conj%2 Ka�~s t E-g %h)@ �s'�� ���m a uni�� (�p���o"� v�0l(S��Tpeakingh e�{m YV�e�-��p {~ |} �$c`5��/Dj��� s�O�t�q��OZ *[oints.)� {5c5Qnj!QsIF"� Bloch-Me-1� orem"�.MBM}) 76�U � "Gh `s4(eK5��>pmkus�՟|5m�F�MA9�i2  { \tilde{r ;���� �3. Notic�IVs.X� a :8$D�x�'�!��RS}� �>�Hrule: $D_{\,i\,k} =>��@���s. k}��_}��:)i}})$. s)= divȑ�setf>0 �HT)"�!ree sub�r: ƈ !a�u��<p$��a^p" VzE``� ed''�cN �!E Nb'r��T�``� C Xs, �: � � \%^{ p \cup A эp}.bE� ,�, $M3v!` Q�o u.� �L "�ei�J'.s���u�s: ��I�u}.�2L��s_}1 -Q= v}^2��} � V^A}}\,$,\�p% l-+� p} <�:Hub2JB�bS. Acc2 Ve���~� � b�pIZ� A?9_a��:� +��Ša��-b '} C.�.' $}�check{YY k[\,, \q:�-v��QsbrM*���r�n*��c:&wdB�N�>$&�!�`B+.!�N55 {rcl Tu.X p\,;%Q +)\!�  \!&1-N6��6:%�p%� �B�p� �& :��3b� [�z ]n�b�zax�V�bt\:�5r-Fr - �vNEa.gA�)=la z`BvǞsr�5M�gFM*_v@e�J��@��EɲMV��M>��Z�tFZ>tr�pB��*_v�-�\,Z{1_� �A�V�jmFXY�.a�e��: \��\}�cbc�6 �now �]P� R! � "4h&� ���9z)&� d abo̡��@ula�7 3(x�$i\, ;\, x'32�d>Z��)] ��T� #*�def� �UG �_ � }) -- % o �r� easiIho4�hat�]o"� quali�%"� �@�2>&j"QR &c*rprop1 �\b�S�Z\�!-� (x','1� .G�2 �Qn&� Z &�-� y U�+.�:+.&3GEk1.�2}�� R�llMB�RAm+�',+7 ����!�&=.4-.4B.6�8k-:k"� 9"\"�6v? v%��L�.J�n rnot)�o"�s�&� �6�b � (Ak*� c�i.D&u ���)3 ^* &H * �R�2r� �AsS��au�O1� t!3}�t �) below)BM�*� � 7$�uE��u�-G&�!2q�inf& y�si"i0 vacuum). SubsR~��m 2ibc��nto Eq.~ ��5'�7)��!M�!�.K }1�6��h-phi��"���}5 h+�4Gl�%!�#�  *� 6$*ve,t�et��"�p$� $ $b$�&+.����wCB!�0 22-T� l-. S)9U�s�(�3�!�-�)��$CB "�e�q�~v. 5Qn2�� .M)�)�e:]�e!I` 9�*�""� % MOde$5se�!�g�eyed&��u2H!#be�#�[#)�v!$y5�shE�1�.IL��v&w��N�Z(x)T��*.70 Q/J3�� -. �0�])`72 . So�re�<�2varw a !Tc��e�/��h#Q�5 ��U�� W�2#��<+dLs� E��$�'��-r��� T �o�T (2�^���r"$* S3�_DNH#�-� i$� ?/�ly8ful&�, "B�w*v 1�m�Y&2Iu�6}�#�`M�:b�&x �1 Z8&:�1, wm4a�'n60 �� ��>�7sm�%G1.g2}E0 Di6E4C " AME�opMvF3(�r�), (�V*!���#%'R�'282�}$��_$)^�`"6 .!(:bs��I }) d+��2�)U.,*%3"�3�� �}A$2��xa�Z�EDM�.e ),�Rif .� 3!�rX"G)In��%sf�*th�Oa� as �0io!$��a� "�#S}��0$/aA]�W4>�'0$. O�m&T"��a!Bsi%H/~ :��0" � Te� y ?/��@����4*Mp?�.�W_*EV��6(#&@ �a�T+�G�!�h2G�le�~.�ba2�"���VB.m�use�ժ �? a �EK��n look�ui�p%7an%� mFBtra�~y�9A�V$%�e�5le &���^/Atqu]'!.�K^�0*F�$" �02)*;1ELa� Rn } V%1t7 �bq&B8� i�)� Ryz.�"�:� F-)l2+)J3 3F�^�r} 1}%2qa\,�,\J.�qpb�! 0mE#M&�!��1 ��3��ABo�EA�* y �@�Ye���8V7(E�  ic*��A�A�F a���#�r.}F �Afag�at]�6Y���)a H�9t�Q5Z/ �e"^!�0 �qr�YHB � s �r ����ndnj� read�0N��)��2[R�F�-N�M�F3R3+Eתa��6�a �#*" bpqm<�e: YBJ6` &" Psi}"� \, "N��b�6�vT"%6=�2�5$ \forall\:s6�0� qpva!8ee�JЉ is� qu�sa4>. z$>9/�M� j�2A�aP�"�B $C$-6� 8a�r� � ]+�#LW��F % �9" !$ b��S�CB:� km�$<.!n5*�9 e"�9.�@RSm�}�|=�=�\� _b (!6nE�}_b + "6<""8�b )\, ZpzZ*I}p}�nR6\& 8�!�}�!,0�)#�l2�8eI*� $| 2.� !�:� 6�, "]8*-=.�*M��.��>531l�p�(f*p#w�K����y � 2l�.] x � ��:�la(: � Psi}0:.L �)�9V{*?�)`.v� X!(bxJ0i bq�� a"�rcM�!m]�ybq�EDtr[<easΉ� u�!�m�����vI�)�) <�.�#s�#����; 2^7R�con"�J�|%�F��1Ngh� words,.�It, �E )�)> a mapp�3o�7]}$ oY'e 2� �}����&R�2��IK�ka�^>to-�� ��z>6�s (��6�) "�ns�.� ceJ0aw$RW),.��� 5��I*RVp 1Z�ll��0�6 \to��.�=� #m$.V�,` deri]M)D�I���a#f� ~T� A�tra���5�F�:-:[v�R.�e{RI�2�.a�R�#�w:A�.s B�%� chosen!4�<�at.�E�B  I; F�$ (�$�"Ias�H �%��%/�*/)�^S)�@. C�C�;6 �,rgu�1�P2$�kfk q��O!�.��:�`E�&��-T<<.-TE>.2��6+6K$`�%Jd)O�D"k �Fis�2��)�8�f6Wnm�>�>[I�A&�7s ($v�*�p8n) .@C)b.�Ba)�g'��=�poN�E��<ru%�ny����2���&2 Z�, P7he"� 6��l1rX K.�, = u& *����O(bZ��,�Ki�La��i�SAy! Lieb �0 K} pMaN(*;uD�w�QSB�K6��H �>rk�Be+%��BJ�JAewJ�E�to��X ore ��t%�K��o&��proRMiP7e. More�<� &of)is�I_�A��?mpl� R�L6�i�� u1ai VS.2'B!{!� %��6�of��F�:�is%OA ��AIn tras�*ͨfp6&q�7޵�@�y�I�I SION�^THE�J !sec3}}c$H�H�>-�GB. ]e.)=<��t��ng:�.IQ��"�C� rR�&-O��IU^���E[�:]� inf_��U<�G�P| H=Aft"*� df�& } "|y �RI)�w2�q22one��a�L}N�. F�!S!�mkQa{*>4�P>rALa"-S} �>���H3�-^>��A' 5w�)�2�, E}%�,\,�c� B^*]� )��Pt\� rh�C1�\&�D�*..Wa.R)"�H '|R'�P6O�(QO�IW!��s2� B� � 5�%5K$ѯ� �8 �(��y�����$�7I� 2<n��� $ c�b b zAMPN^��osΞ�9o-�I��%2^*$ͮ�Ͳ�aFz�sb��. h8,&F�3 .k'f� 2:} a�;un� tely9}"�M"�S���W,�m%&P"4 ��u�A�~Ng2�T�M9$�Abe�M�K�ka triv�\�y�?sPe~$�z�) 6jW� ��t�m�Ki � xpec�&�C���xac��nyJ6H$ �(*�V��dB� ge d&�#short-�e *@ @ �bAi�on-  ($NN$��ce;Ae(%� �=� �e�.�5�A2cobIVaa wy:���5�C:1�Q> .'�5[ns��!^minimH~-"�U'UBS^+"�f4}J+ _ >a�m�&ME&}/~� ��.�eT� � �<�Qogy��:i�id�ADnPN �&sG RC}}�v"[����- 6��J<} ���u2��&!H!�Z�I g �q��B�B��K J�;+ J5*]A�?mFQ[qF �.���u -����l& -r v-E�JVh L �*� �U�=*IS<"mpr��5�)!NEs�l�P-�m?��F�%.�@infimu�Y�9�� A$�} um (�G�/pe�� ��f�&���[prm� �Q^"j ^c��at�H �� �}&� . "�)$�i1u�!� &4(��"y![�2uX2:�madvislo9� W�v: S *F �.6�^*SB=�un��_i!o.�_�(R}$*6�����:t�>^*+�re�T� &�&7 frac^n2�F [\,\3�K -"��4D6/3+.�3+)\,] �7��I`�-i*� �aXm�eh=TL��a�&x1E un�,*�"t��".�͊N�шextT}a zEDM�21[ R}�� �� .�&7)#I�obv�E�=#�Q2�:8 �O�^R}�b�6�$:7)"$�E�2��N� �i�='4c )�!PFaF%��@^e+�Fu� al T�Dy6MFTPP](�E=�A� a F[�^o;-�B�8].?5�Z3 + }, 2�$ZL}%Tl�"}�%�Q| 1%| x{&Y. �'��h M�|^2 \no�\\ &-&6�ia-R \muJ \, [&�Ia� + �chiA�:I%R��chi;\,x ) 2+ effE��I� 푂,� = �_q[(�S ��Lag� �T_r�#m��K&2 �"� � �I�X$b,�5 (�1���XV p�X=m&[o�-Ps�Y1� &�J!�rho*�J*�Y�;+, F, q!7N_q�?pn4%�< "Z+� \ѭo). Ap"���6�f�p"��.F�2e� %y��,J � C_x~A!�"} 2- chi'"�M�:I�HA�MvA�Q��!:K{V7&h'm=�<eta\,o M��$sb%F E/:1�eqmexE�� �h�+f� = 2m�M�\, �E^_C;i'+2��1#)}�9e� 3_�N�=� "eZdefhs� M�9�� � ritt�a�  ����( :�:h1;mu�,o�\\ �:�  -h^*$)F�,ZZ�>"E;!�}^{(+)}I.v- Jf=vR6���B��y:y*ueqm]P $h" �.'^F�U�H%S4JM�,�uf�i}h�zU � I6m}��]�E �\1? �%�o -2���tt � �%�q� hddeɧ�u #:�+FL \pm)�JM�Opm�'O� �owT@2  > 0$ ("�� <]3eQpermut:� ;*I�a4�2�?P�/�"mad�! a�Ra$\mu_��.� $ pl�"eb=+D chem]W[�]��#�$$q& Z�=Hablt��'�; 6�� �Lec�ll�_3��a:� �Nn&4P"�<���Th9Xm � a ��;.lin���Zg,�7 ;a�Bc,stood�� dexOVu�.�])!v2 :��%$�M�.&�U!��U*L3\��'�\#D`)� �&�UA�\*(�C"B �`UE<�� �Cn�,��~�%6��iGD �Fz(aupYhF�L.�eG,` I E��fof6�exb#^2��6r����'H$+ "EhM�"; B)��%|Es�  e~��� n AEDMFT�%$9!�m Z�-=HV�x (HFBeqory=�? _��i� �<3� ��eall ��F��4})0b�a�M 'mA�<�"i\HFBF\ . AcK�^�g�h�'r3�R4E}.EQ"�qSQma:hereai��+ �HLd��; �/-���r�)nd nc�. ��(iU($. Bu�x"�ijZce s���)� i%� &Ue�?)"3HQ ing:*!�(in&- $ � ZM�Yd�N�6�:TA�, W�flB��+`"�?eh!}[*���9~" `}�"/a|,of:� ^;�c��2� Rf0�E�\ slr� Išr��GAs冁�FT�g$l=wN�(g8�"m"�nnsp>=�%ai3 �f�no�j DM (,f�^!� 2��ak��.Tf.�nt!!e��r]��chra6ev phenշ olog�ST��E��� shipu' er�ac�~f(nalH�t���>2B!+m "�ba:%� ,�F*�uH�u#H"�=�X����B�Je.�$RE} TO�$E�nQUASILOC"��*%4%>N��>1!%+sse{{lѯ"�$A���F�s2�%���� �,mj�)�at��!� ra�`.W�aݪ��n�XR�ifz-e taska solv6 tg��V b{�du{�!.�.�"���$10?"�+&qp�$describ2:b�-�@� �.�us A"D�a�> ��@sBexsq o�/ # ele $n_q$e B(y $\tag � ��h"GfJ}� ikT {�"|.[p"q  SUn� a�a n_q*x )&=&2�9'�_���K*�ql1�_ tau �U({8�� f r}>'}^z2z&!4:�in�,-Dr}N_e_1_ [(\�))[�� jmes ��h52"hqlSa�#��͡�=*�T�e� :7 :�K �(�u!��DM��,�Q!�* 4�)} a, i&w ]��� ��0i%au_#���.� r葸(c !ed)Q�8�&ϐ�:U|ey6Ee��+re��"� sem�y���He0�5F _2nd%SV�Ju5���??um�5areaBqO!IC���Y��a,q�W)�S|^22�4a2a�6����k^r���5�4J� i1%, �(:!?�&�MR�'1!��\�Hs��]rlRp o*�ql6�a W'Ye�eElY�/�k� U ha�meag/&� y%�5 eachaP,"��\^=�� �5�5()�_yN-"T7��R�ql7A &=��J�-)v���)�8-��@now*OPkin��'� �8�rho# QL}}� {n_n,n_p,e�n p,}6n. p\N3vk { !�n,�`�nd E_^*"^* $^* &. '� "GU�q]��I@q׉B�{�^� su{QL1}}  .��|I(B3&Oh"t$"�,Its%=��dBGB^*.�ql9A�F�2} Qls lLvk ��\; � 2� �vk}\;(?B '/ vk^*��*�1��e2�HH+ rh:^ �F�#�Id&'.)�.��"I!ed�"�d�j�27}). Fro|m the definitions (\ref{ql9}) --�10}), it immediately follows thatIproperty 7�Lmprp}) is also true for both energy functionals ${\cal E}^{\mbsu{QL1}}$ and $F�C2}}$. Namely, we have \be \inf_{\rho_{\mbts{QL}},\,\tilde{\kappa},\,6 ^*} Fh1}} [Mss�M] =j�vk�vkVu2}}Rt6^E_�@ss{GS}}\,. \label%z$ql} \ee In%�)�ing!*4shall refer to � (x',xM)�d��-��F�e .V�{!+.�; �$�pur��0!� s��0ed using Eq.~��7})b i\, �}*:��x�� \, (�,_y)J-Q}KJT2}.T vk^*B��=d�I$ Let us stA�&� soluŕMLN�assoc) d e�>� e��esd (at leastA}$principle)� calculate%�,exact values���a)��m��enter!�M�set $>�$i:�Dof Ref.~\cite{STV}^(ows to find)B�}particlR ��ies $:�,$ only. This.�co� from,t character -i@many-fermion wave"U!Ded��build� 9 Bn : a S!Tr-detR nant6T!:9 � which�� Lieb orem was ved,e%a�d1-vacuum 2�c!@�A�*paper fQone, a��s shown,!�Treproduce an arbitraryy�DM %� $. CompaEour��E�)�$ developed�]OGK},a�should b�^teA atN do noA�t � any (rnal anomal�(,pair potentisU!6 doneu)mp.� �methoke?!�emergA�nly!a�� eque��-�iA�a[ � � M= s. In abs4 4ej�qfield��$ vanishes,-�i�u agre��1T 5�number �rv�  dt i�s� �� exʼn���Nf �©�and�LBogoliubov-de~GennesC)kdG}!xI�E� air 9��Ds,$ factE�an9�)<(though created M ally��V=Y). ItQKbe po# d ouINEDMFT{itsY������ca!� read�7z|more simple DFT plus BCS descrip.��!�correl%�s i6�  $\� H$ in ��eqmex�(orAassum � be) diagoa��CB a�ea�j 4cbc}). However%yg��al, t�3�i! t equival�?� aOI ed!� solv��;l��)^.T j (see��men" , Appendix~B)��%j.@ R�" �6 %�HFB��s�Lcoupled Hartree-Fock5�� how discus�in��sѹ0RS,edm}. \se�l{SUMMARY AND CONCLUSIONS} W8E��A7recen!*�]t�dF�y iV�9 to includ��.Ya�!�ew��named ECD�Ey M�F"�� ory i� onq���(EDM)�malism!�e!�M�R$��vs�Nbl!{!no4 :P�Ta�0nother 6��uxili��$quantity $6� $�qhaT e sen� >�.6v�hich doeE� co' de�sI�e$\�a�qC!tF�is chose� such a waa-��a,l�� R}^2 =m R}* fulfilled9f� possei�* ��e.y!�struc�^�a given:  -�x !�canoni��basɑ x-�m ��.��!{ been��w�_at q.I-� MH K,I� spona to som�= ng time-r��$sal invari^ �} system����� a qus>- :� UH Psi}M�nA� ��R$)�"�f���: to-�4mappings take �:Y\ \to5� 9 - i at��1�8 dereiQpiz��� .- . U4 %�onn�����m -xh� ��[he totalFLi� "�&�2^6 pr� )<�rminimumj AAe to_�K ground s!��=)�ai-"��2 is �U� ur�Vto G � forIu�!�VU�fi�f���! �� the !tle-� H pseudo-Hamiltonian��[�� are�  (�) � . Al �0BFM2002-018680 =R (Catal�A).2 !2@2001SGR-00064. % 2�& gin{flush� } {\i size�$APPENDIX A�nd.,I�is"� %N{M�ET ��deriv� Vary�"!L�($F$�jby*�deff})%�t�in��ccount6)edm})�� : $$� array}{rc� hF &=& \ds\sum_{\lambda,\chi�(int dx\,dx' 2� \,� E}ext}}[ R}]!a o+R}V\ d ;\,x )�Z1}{2}\, :_{2�!�[ >\,\mu� -� \,� �Kb \}\\ &&�L\,\psi^{\vphantom{*}� B ; -}(x��') � 7*5@;(;%) +jF%@�w� �$ = 0\,.\\ � Q F} &=}&#�������� !�\a�i  \eqno (�x{A1})e,�� -3.5�� \noind�Bleads& e�"� Ji{iXch}K'\,� HaM�a' g � = - 6���;iC�2 2) ��&�i�H~  >� hsp}�e��A2ly 5s�z  half�0�]�teigen�*b ��r�4to [ secondX, lS note firs� at h6�liD��"YA��Y)56�%%',-%�& ) �H}^U I $ J�3)�the�y* $z�+}(5�$,[ hr<E�un��M�҅�)2� � conj����l�r�Dcw�.� nC~ divi!�~a�l� � B�$+}+�$-.. O)o= hand, M2V��U3,� 0sY��pi:n� aE�q2,$� v�\pm] \}$,I\&[r+2}�9 � db i+s� 0dei� � �!~(A3)Y5. Con8 tly,�$�.>� C r q� )�)^��ar~"� &"�. So,!�t� �Iԁ_0be satisfied, actuxchoose.� � A�symmetr�fia�b�i&!� out impo6 ad�alAsstrai*�ayA�rocedure� %�aM, 's( �� !a� )c��to�g �"As .xQ�as���H b�o Bᔊo "-hip"�!fe�ye� AeB$LRm� Ys[!yz� F�"� all,�5" | Aߍ�den !NM� ortha9�&�'�Av ��3� \eta2� @#V _{\,, -}k z H&.6! B! Th !n5i ŋ"�  ;� �JD1�&# Obvious�!"F-�6�!�)�R�eV��" upA�2o unit7transE�ntyp��)-r+6��5 $\check{!l2: 5^ chi).� AR~ c��8F�mF2N�]�B1E�M�m�Z*�^E)�O!���6� (<�"�|b�l)��� ommoe(���AMV:�. "���(�r�"� ة.? .6�Iin'ij��, will��ZcH� de� whil�!22A�A<al�;Y̦�IEM���s�����AB^{H$, si�]�M0��YB}I�� coŊnt�� 6Q. 63if� u�/&�ily{>�R�q�Q6!�%=�*9�CBٺe� �eoA.knontriv� $C$-6�� Ukchange5�,!�? ly r)��  ize �H$ � Refs:I%�details)�newpage��P�thebibliography}{90} %1 \bibitem{HK} P. Hohenberg%�LW. Kohn, Phys. Rev. �*<136}, B864 (1964v2M KS} <H$L. J. ShamJK$40}, A1133L5L3Ln"| L. N. Oliveira, E. K. U. Gross,e q, � Lett � 60}, 2430f88f4fPFTTZ} S.~A.~Fayans, S�0~Tolokonnikovy~L.~Try DD.~Zawischa, Nucl.-.A)+4676}, 49 (2000w5w,B} A. Bulgac2�C =05}, 051305(R)C2C6CGilb} T.!e ert2eB J12�111�7%e7E| V. B. Soubbotin, V. I. Tselyaev)f$X. Vi\~nasR�7�14324�3�8hRSEfR2 !=$P. Schuck,4 !?ear MG&8Body Problem (S�tger-Verlag, New York Inc., 198%]9m�� J.~Dobaczewski, W.~Nazarewicz, T.~R.~Werner, J.~F.~B�$ r, CChinn �Le�& g\'eN�53!e809!e96�10�BM}UBlo�nd A.~M�+ah6;ed39}, 95K6%�1}��} E. H.�, IntefQ�um ChemM�24}, 24e`8%�1}�dG%�G. de �$, Super�uctiv0of Metal� x��end{docu�"} -|UW+tcOmDvXJh/pPhNRedcW-- �%\8class[k'pacs,pl int� s,amsmath8symb]{revtex4} :B9,�K>� twocolumn�M\headhe�/X=2.0cm \usepackage{��icx}%A��" figuJ/ iles2,d �0}% Align tabl4$�J decim  oint2; bm}% bold�h�raft 1�!K ef\bbox#1�0 ox{\8!y${#1}$}}7$title[]{Re�%visticAh eral�A]�{4Gamow Factor\\���on Pair�E�,on or AnnihiU\on} \author{Jin-Hee Yox\email{jinyoon@inha.ac.kr} \aff #�{DeA���DicsaWha Uni�&tychon,�(th KoreaJ {4Cheuk-Yin Wong�}4wongc@ornl.gov/yŰics D!i\Oak RiN�al Labo�y,@, TN 37831, U.S.A�Z���Tp($see, Knoxv# N996N } \l%�{\todayb� abst�)}�e-� or a=�sa� g"s,!��(-� orw(d�0oftenS# significM effectE�AH�3 c�s. � Coulomb-� .�* � I�fE���#tra`ly� ��"C�_t5 �. *(6Zneebe modif�w�magnit�&� c'�7const�o U�ve veloc���A��-@�)ses. We�� spin-@�S-�-E�. W� �FL�2� 23!%he non-.` limit,� f�#y_2>]�ly !a-estimat lM[Y+bvMlarge�nd}� \�>{PACS� (s: 25.75.-q. (.85.+p, 13 Q��3Cs� make��� arrowtext*�)I�!a} =8f;"m�}� (FSI) �,N$ISI) .�re��'"�:n�!cO � cs�)�Bet56,Gam28,Som39,Bar80,Gus88,Fad T90,Bro95,Cha95a,Won96d7,�[00 3}:%ey���- nhan"]5%�V��� ]�=i a"�2�A�repulsa.-�U!" espeR"ly)� n[ Aqp0!� threshol.regiof low-&.�. �E�:�,b�$se FSI/ISI!��'aJ>we F c"3 $K$-�j. It2axe r���2��7=�'c� "�&�*��Da�6/n�6�MF.�I$@!M�-*��-b� Schr\"o�)er"�g� urba���\�#their mu1.�=!d�4�"�ab5e squA �e!@��e:�� origibAs!|well kn�2AyA electric-�Ee�color=JH, $V(r)=-\alpha/r$,FB%���Y�!�� (-Sommerfeld���-}�}�/N0y!lIB 7),� eq����7$eq:80} G (�� { 2 \pi� \�� 1- e^{-} },� S $Io!=�param!�, n�xiD ta={ )C �vJr$ "nF(+Af�H�Bcic. )�$vUUAv�] of�9p[6�F�](wo-equal ma��6��i�i�3�Z5,lW-�K*pir �/er-of-W�( $\sqrt{s�:I��(Tod71,Cra91!�b� 9�9�hv} v= {(s^2 - 4s m^2)^{1/2}-us - 2 }�JH�!�(s $v \sim 2 �1-4m^2/�� � &m_ $v\�#�F 1�/en $s�= 8A$ty$. As�5� �3,by Chatterjet6d �/ coll= �J�}i�elm*�\�i), j stud�66<Co&s  ISI/FSI�*�� v3ݞJF .h$The result�!t!3�po;8d����-�� .o QCD.+ �}at higCiN6)�bwFaScherM}Sch73}��predic�n .�S$q\bar q1 �G� � ^ +octet ),�  i� ��9��u�de" Cgcg# dilepton�� a�he�<rk-glulasmay Drell-Ya4 cess)A�avy 5.M%<�GxHT6�-above 2�ih��>x �p���he �3 �I�29is� fu7/�� a�6 accurat6Y)Nrea EQ�in���vE��8F��$.�5����.] b!vite� � 9 +BOt�7�maa�tEad��te!ppleP.wf� harm1�air�!N�� I�m�i� �b�?e .U� anti�k!�ab� $0.3$: is q� �  Fw0morh"� .T�is)+,s2J� F �-e!Erk:�0/ � sm� in.) =E"n tc . ��Q�m�s U � ���Fp�| >�i�~ Baym�4P. Braun-Munzi= "i!�eT f�i�ir��-�.� N�and�o%�L Hanbury-Brown Twissu�ofE|>y rfero�"i�Bay96�9A neg !�ged���a n� us��a)1 $Z$� s�\�#ubject strong1�. .2 ��!$.�is�:N ��lowBO�+`Knetheles.g�9%9_���#��Iё ��%�T brev�no�P� �T2  ``-�.�''1,�bup6Wto&xHbot�? ��  W� �W3�en��0B{ .l s, a�3similar� mfA�i� carr7�8!�& �2TE�scree� Yukawa6!I��!���:2��b!�eeM(�I\�>�]D s, e08 !�u�asymptM3U��woU�$s at $r\to ���=2,%(d hi�MbEttc8rtP3t� s du�2�J�.Q. fez-��B�K 2� ���4ispe� f l&�J valud�-S�^Ym W�2 9ܭ2R� ��NA�o"�=*� R��A*� ~2`( B) �� �M� " @,r[6 & (]��n:7 proo4�Ma�$-|� |^2$� a}V�[Q# s�4-�4� 1. gaug��t��� /ca�7! behavioUCe�BF, bev(��V ),of P��=.{1!�8�J5s a"F I=E'dec?�?5?s,a� �&�?�E�}��en� a m3Co -�q I�-�Ѣ-�M&F boso�kT6�*� was m!�t4!#�l&�2��&) 3c2G� "�. I�aly�"'�"� ?6numer =a�es  $*a}!+m�G�.� Y�.��C> �:V_�6Q.� b� most_�&nd ��z ~� 238��2{ 2U� �s. �@68"�YA>I^%� ��G( B�قMQ�� 6. UT20�8oea0�Or�� � ��est !o�e!���;� (chromodynamC.#e�e�H �<�%;�UM�>� be direc0*�9A�*� JK5<"| ���?� . A brief��/M�m��ar �G ref.X�3�B!qy��B� b-�es I.e+B� .��J� $p_1t 2$I���� by photooTor �s)OmoV a $kDkD![�.& �&ram� Fig.\ 1��s!�a,�olid lin�-Fsx;Ma��Avy%�be ei�/��%� �.��%59t�.ai[�J.U vertexI��q� $g"�l b�celed � T �in.P,Kfac}) below��js S �.�-i!"a( 9� b �!�0i�L *�e�f s iten� we I��:rM�E + k_22�p_ p_2$*�/i�" }[t]|U�"�"0s[scale=0.8]{�!2}�;,*{-18.3cm}\hw(*{1cm} \cap�eI͑.r_"">"%on �fig:f�}mndurea�a�P���p!R- �!U��TH�z� no 1�A� 6babil� �>�v u�eis5�g iq>a�2� * ,by mea�#f &� IRoryMu�� $|\Phi_{!�,p_2}\rangle$ �en$�n aft�V��on�!#6&� �ve�#n Phi} :� � =q7M}(k_1A��T6 � )| :^��7 OJ� p_2)�!QvB�[ Ap8 1�Y@ ��aagixA>e>��vum�8bm P}={p_1}+ 2�6*�e>8 q}=( /1}- 2})/a�T�PfX$ 1} �8r /2 +�(m q j&26&-&. Nj0v# ��!ť!$� w�\m�b��A�ng0!JE���a :-BG $ asrusIu si_VQ3!t�Z�=}!Qf q})|%5P}MZB!�J"�B!�N B��~�FA^r�m� 2�� �Twit��,OPes95��� }b�ř K%�sSX�6 0}ap |<\%:� >|^2/ "0N"} V0��ar�[� $\l�� Rp-o$�Spr�^L ir b�to����� Mj��8A �rV amp}k�U � : GXAA{d,q{((2\pi)^3} {.~ ^{\daggerY�W<��� 2� p_1U��� -q}))>�AZj��0Z�� �"�=�*�:h$ �5}_0{( 1)}$�!*� re..RVS sSN�.R1�BG�%h2|erH��S# "� =hQ multipl"�ClowU�>R^�4rrWve & rkrat1} { �+P� # ~or~. ~��: -�~sqon~�V~ �~($m�0V$) }} } = K C �oo5 Fs0$)r9.&s*g&Dirac E�^E)A�Cou�)/� } T"�$��2��Q2�0"Q��I��'s( �; ��&Dir64��82,Van86 782� [t&� !� 4-��a���) 2 We_<tojGQ�6 �K�!��P}=(\N!xBbf 0}) b{ G0,a� q})rI�*�UH7�5�,w�Av��)Po�� �+�s& $\ep�`n_w"�&d�Red�$m_w$ as� n byb�eq:NI� ]^2 ��^2- m_w^4P0V nWe{]W={." m^2 �2 1WF�GB�"m_w={A��"F|" Next"�"p&� �ED�u^& m'$$ B�=� a�% �rX#7 y�aY�&!��H$1 :2$  a52~B&$� writ.asUe?*� �niceq:ds} � (_D = -2mE_m�G ��E{c} , \\ {� E_m}� f 1} Baa�~�; 6-f7L$yaN72o^2zq ~�2N� %� �]�E1'�& \[� \�8�$Ik/ %!� + mM� 1-2/Q� }. \] �Yrem�!!��lic� AVrought�A} lgeb�7Ag�y�*�sUE&��9�($S=0$)MR+g6��g� d �&�#e-q ��F E�Eo����91]{FN(d��" iggl \{ [��$ - V (r) ]q&M ��\6r \�/psi�IBV By � offangO A["� piD � ce: �? $r})= R_{l}�HY_{lm}(\theta,\phi)�>(^{(S=0)}$. 3��- )1al9L�9 �y�Ff�eq:psieq5@ [ {d�:dza + �)!� z} { }� l (l+1) 5 z^2 }52.�)z��"� +11�] 1=^ $z=p �*$p E�&�&at $r.�'�'��pin} p=m�YOY9F!�2� $εY6��dim�!on� "3 �ET� ha erizdwo6;��*sAq�*)p / v�n�]�Tw��$v={p / �EJ grWCJ*�(vmA �zof.sUP)�T��ٴYvwf}=�{?N, | \Gamma (a}g|IXb)},\pi�( / 2} (2iz)/ku - 1L*<,iA�,}_1F_1 (a,b,&���G)F�a= �N+�/2A��,B�B�b=2\mu+1�* \mu=�� ( l+{ael2})Eo1�J�,!� the *QiiW �4�FF*6��F�b�mC�:i���� ��aq2q=,Y�2�(\sin (p r +�O _l)/��  phR shif�cEl� )�mS-��, crit��Av�-z3 1/2..� a�4A")510OR5� ]�W> c\)�iC-����o*�� fuM2&)wo�;/As)_ ���Q&�Becau�g lev!�ɑ�\ae�mod%!�:�Y:��R-� we�I ])�&-�>N�.�&*� � �s� 륚;"�FY-iv|{B )p_2�umz8 =&& (-i) e��f�JW ) �a��FB X��r5�c|s>6>>&&+��n512plZ�2�$��! q KF�f�BJ A�� 6�B� wf� � ���H'P" n s�* m2�3l� L4��graW;��"6 6�i� >_.clf7g�F��f��}�Ya�v�s�9 V�{3}%^2E!���%� rNI�ve|/al "�,Sexpan�-h�P&�7� )'power�A$q� keepsC�O.� $q$-[jt%h�<(M}_0$:F1i� M} \�x _0 + O(|M|)BL��h"6v�N\ (�Qeq�l %�)%�AR us�:*@ aVQ= 6Q=636N$�!SX=JfK=|�Q=0x-F*Hnl�hn!�r�6acan[O!*�bu>6s&{i6�*6��Oth:�,:?a��N inf�Ae6�S$o avoi�)�gi�b�-���J,D&I1to 2�'�t�,u�!� =�2s.M�,)�� )r+A/.�spa�p2 �>|BNiV��j. &=& {"&ZY���rX�^k:��BB`[ ��.U�{\n�zi�z( {�Hmrf 4�>r � c1) �\(�^��v n*� &&� ֆ�� % \{N�2� e���F��� % -NL�� 'ZLu % - �/ -j M��:�%�r ]B"p5�Ci=.:~�F�G $l=0r�&aleM4be!nw�fut�L�eaXi�mp]6��riQ:��1F\�� �Dr^2 dr jlkr)� i1 \{ -23r;{2!t' � rap� %�2�&& {d 3dr}k Bcalq\ {��kq E��@B &�l�t��" �*�(� f�_V� !&�62�Ŗ#R��mfi��0!��N9N {k-� 3}{|�(a)6�(b��e^�S/2���cn=0}^�Q9 _n M ({3I+2}+�n  (b)_n~ n!`� ({ 2i p ��:�^�) k^2}�� )^{nU-�U���&�fi [%B�{q+ M!-�} ��,"��M��& ��({3 � �+n & F({5 4al{�n �T1,4�-/ ;� {5 �2}R\xi^2)y�� &&+ {�&V�+ 2� � m� _ �>�.�2%�F�Z� ���& � \{ 2 ��+ m T} ��6�A� Q3 �:�,FZ�7)3��%���)�:� "u># �Z�9��bC��)�=m+ip��A�={k^2 �(7�+� BI2~2eq�x$), $(a)_n=�@+1)(a+2)..(a+n-1)!# 0=1$T!q`Vity $���B�)  &z� look"*� �rqp�>�|��b�8�in �|\�!Yoon00�="J5RF�* .i�N� �"ex,!le"?J�!�+$tan^{-1}{ �!s�.!J) AC- iY�qVln 4+��k - pF5%�'�|": measc �>�"4 � cleB2%�e>l� I$ �%�alwayH_pi/4$�E��imagin�[��A,�a*�8)�smf&rapidA*of�(1$M6$�/)!�d6�("�#A�2� 5�,�"�B)� "�]ed(�#sJm&�u&�-j� �/�42} B� ��"� ��  vi :h ANJ>�xA!�J�l� A:, +}] F�"�"� 2\nuJ�,��� 2ir�"q ) &�iR�%�2�o.�m 0k} ~�e��� �J\nu-2%��\�? � B 7os  �4) 2� \}&����v{ +���'i* [��(�3}��� ��N�B��(b�f� >�&+ �%��2�*�)���1� 4):���5N�3J�!\j�bb� �^2AW1� �1 �2 5B�3z�4N�4r}f��a@r ]Bo $$\nu=3/4 +�pu + n*6 TO�rm�[�M�l also�C�!��ͨ��U""N!2~"z@�Sos��>w#���/ . B�Ying[2��(_0h)�� in p r}/{S2���#��qCo>0 "�A��e�e�X 9 *g.�U#g�&n�dow�\.| \Bt ��+V� 4D��B^"�F��B�gBVgG=z��p\",cal I}{\rm m� q�(a�tm6^* -{2m<})(�^*>&1� + m Z�W^*�@� >njugat�$L a�D� .�:@I�"�u��ayE )D&A��  *X  }�n]kE��7��%M|u��(a����>y/)�A}-r B&�|^2B� �2an id�fy�E &c:�*x)(b�1clo�d)a��2�5$G�U!�On<:s?atN! eft|n�>�I@� = u1XP�1/�.\�)).89 \p#_{j:{;� ( 1+�G*)x 1+jP � %�+n*b��� 2 j)�џ 2} -�)"� '. + j[-tGqB�.rF %�� %>�,&� 2} %Rc pce� %��F� %a�� �W� �z {.{( �� �Bz� J�i.�w �#{2m(kH$)h� ~nB� % �z� � 6� ; �� %*n !T �2k �!�/ m*j� % �A�^� *%a:�b{ &� ;J���� ��!%~Z� ��J� v�6� 4B� �=36N��� qN�b"v� �^2.�6��� �N��� ;N�b ��. e<�+ �1J�/i0|{2I�I�p� ��I} 8T\c2P 2m/kvH % +Moj �  a�29 &@)�:�  )6!j��%a�+($E=k$)�Je�9C�Vff3� vI=m�or�^�>I�0 �ab10$SI6�\0�� �Q��to 4�&� ��0sT3 ".� F(Hhj(H 60]{K_fmn};. Hv versu�eta� varm�1� �$.<n"H � *{0.qH\"��C%~��)�-6�^&�]$G%pss2�K)��1"Bi�B��.�$�/i�NF% {s� m }`0 �- �4�q.!v�ab��8� p � he"&�qJ��" ~3 2~{"�7id curve� \*.!&�-� =0.05A�dotG:<�{X<3gA6��I� a�� den_�M<�~wJ  expec�Y�m1A�J�F�97�h �5�x#M�W�e� � �is!G=1�2���v21$)TRFiMM 2A!�at%Uw{ j(��B?9+a�1e�` [&��6���s�R:c�Ss&�%0&#ie�c�1"C# F!v�!5o�[k)��^�aI��V3�A�FRv�X plot�a\ 3m!�0i6V$v�As�+observ�~D7�Q _،,Y�9^]3�SAA��9"�\��d�?ng!��`�h�C�@j1B�\c_%�!t'B�uKV ������uy�$,VZ�RTa�i��n very�E�Z[J� . %"-2�PW��e}r�80,�=27�G_BOTH}7p>%��E28=��!UGW � EB�� �i%YZ+��Xee>R.q"�]isy "�5� A�BRI3cs. 4FA� 4G E��I�0��nfor�>E F1�_s<:�L,%; ea l�W1E weakY�1g H� 6��B�ksaf�re.�q,�|q+U�!k0.32,�U� 2p�ch6� � 6�X*� �f�n����&B.u> ��A\&�)^ � ��R2�G^_� � long-"7e"PEla�)�qW�cS=.(gd&�^N C�B�F!���Aft��{b�r��LA~\ 4$b$�UI��K/�� )�lowlyah�K2+)ɾ%@ >1$��drops ��Zl����*s=r"�o�} ( (�h$v$��I�t��in���m�1�=C~ $&�.ɌK ŝseh�+�1 $p�7�$^2�&�j�Q��+�^�. t ��N�Jvn{nt u�iA}��ɀf0.8`��We��a��=5@1�Iщ ����b�y;ooLda�a��KE� � term-by- sum� oEϹ��]ma�a�h Fortunate�����K-M is so����zkdt �qakB_�3 !wRincurra� much erroj�c{�e !^5��K)�2u"�*X@� those �V.�\.�%��We  �%e� 4$a$ \y� .�W}D 2:.J ��;i�3!S�"E � %Pl�0ly ef�Van f:��lY�5�c3Mf0liurR�'m�W!�J���u� �H 2d�] Win �ic"zPt�in�ic� 2rBCoY� �Discu�'�N�w*6g%zFb yl*k��D�"vP!i�`ZfV �A�5 ̡2 o&�+ vi�ei�.J�ɏFyrJx|QdQiii. �b*: *N . 4lc�Os  �%��i�A��W�T� ere�`no"�v;f;��,Pex!�j�Y*�b�5ial>c.2o [Z*�Ra.�a`9bj�.DXR�z�^}I .Q"�E2@{ )�-�B�c�e�%s:;Mg 2�!6�6 #�� coordi�l^ith67 �6=" �jg��& 7U A8���6ot�7r9bl���a�D��>��7#iT:���%I#*�c Ou| v�VAk&guEq!x�� }�of ��W��� cmosubia��viK�b2�"�strength�e y��� .u�,MB\� I3�bit?}�T2{N] reasa��x��� WG9,,�� f� ari�$"F 6{N``JA''!�*�C �**s.u���0S� 28),U�6�I.mRif �"�M��nic�McGraw-HbC� ny��55�142.����&�{) AtmobauA  Spekt��,nien}, Bd. 2ZsLschweig: Vieweg 1939�M�BY�} R)varnett,!�Di4�nd��McLerraJg�D2�659%��Y5��4} S. G\"usken,!�H. K\"u��_AD. Zerwas�Le"�155�)18g��b �� FadiʍV. Khoze�$viet Jour.E&2�48��87 (1JW}�A{Wg� T� T. Sj\"os�1dJ'C\613 (199�����} !J!�odsky,aWH�angN% u Teub���.-&I�B35��35%'95 5�/r}!�C6~{C. Y. �1{&B�CE� 212T �n�}C%L.d,�ceeS��� S!3g�g '96 Mee�� , BudapesA| ay 1⇐ORNL-CTP-96-09 (hep-ph/9607316), publH�.H�\Ion.�4e�1!��9�7~�Z22 C75}, 52)�72d�5!�H.ى%Za%� C6�P044905��6+S3ZS-�J.�v�Soc�� 4a�423W32��{ �ch|�UPA a< urce�MF���� (Add��$-Wesley, N㎁�,73), Vol.II,Apt�E4%52;BCw�i" x Pa 2 x,2�A61�096) 286c-296c���(Cra83a} %H.��a�(P. Van Alst��Ann11(N.Y.)%� 1e�5�%3%.]9�'.\ , R.`R ker,=�sv.s���� %�5 D46}, 511o922�e0} M. E. PeskiIMD.��S�nedv{\sl An?`&�to�z %��� %�o )� Pue@B ݌95.�����"% 2+A44, 706�$12�ڀ} ��. Todor��9 )xD��35e�76B�`}!�AŢD�Z, CanadL� Math HA�129a� 50);�{. Roy2�c. Sect.��2%�326/8);�Lec-B�1E�� (Yeshiva*��, H}642A�2�]�E!6I��)A" 2!199E! 82);24E�� J>��I�`� ��$53 , } 157 �6�x\�� �\�$D34,} 1932!�8����!A7}��FU6,} 300 �6�U8�U 7, \!98 �A8)�@ Np �r� 24, \ }2)�94:�6Z2��,b ��Phy�^_F];2���mp.� 115  7�d>�u��]��>� 3�� 1998!�9a� H. J�uliF H. Sazdji&N ]c B366�0e�96> C��Wo' !l.` Intl�oZE-E)�589� VP. Ld}E)�Z�] 124@82�� Tai>x v8G30}, S809-S818�66J�4Adams, $et~al.A STAR C"�3LU~(-ex/0407006.�A� S.Ad36PPHENIX:R R 9028Rc(. d"��^.�hstyle[prc,aps,eqsecnum,epsfؔ$/?/l,&��5B29J8j.%\tighte"�Ev�(�\� {Pol&tV� sfe�` $^4$He$(\vec{e},e^\prime,p}\,)$$^3$H:y e r�< $G_{Ep}/G_{Mp}$"V in ��um ?} %"�R.\��iavillat�ddress{J`r�Lab#p�uLNews, Virginia 236066D A�\\" 4 De�JA�i1�Old Dov%on2�Norfolk2d529, USA�B�O.\ B�r �Is��o Naz�{(e di Fisica� e��D����$ $, "���\`a \lq\lq La Sapienza\rq\rq, I-00185 Roma, Italy� �A.\ KievS 4L.E.\ Marcucci�9$M.\ Vivian�G��� 6�di Pis�-56100 � date"��% 2��b��ab\ ct} 2�o ��.�� d�@I�Ved� "K�th:�%�f�Y�eo�und�6�# �l�A�e[��>ar ��o���(��)�a6�5*�-"�+ withoop�^&�:�csI�earlie�Yud���*\ �repanc��A���*9or� expe�ntu�Ere��u��-  "�in�BNk�Ginduc-+�~en Hn5�>K�k@Kus�T�1h E|"�c��eng+=4%spre�)�h8Y1Bat�& C��-O2�.�DY�ړ��`8.+e,24.10.Ht,25.30.Dh,27+hmD�.�mD�@,�K_�at 29 (JLab)�~zuch�z$(E93-049),�J�, $P_x���o�#1�z6�\E �MpD���2�dA��N�)�esOI�ela��W $Ŵe}p�1a.1���he.�/P�-�w:��l!:I�icru�2�M5proton-�J��0R��/#�uwme5��5a�Au޿quasi-���knockouG�she�ghtklpri�,�#�qusowh���s�xuF�U���tP�TM answ@�9is\�(��e��per�, &�T b.[- nfer�Pfa�"n-Gf-��al e|� Z�e� a�ʍ�'�ZF� E� c2}� �in)vi�!!��Xcru��]���I��+E9!<.�ь�����ib��� �d qa��s ����I=|utM| Alresidual�G,r.wel�%u� body��Pz�\a*c sF�on#e���!1 � Efaclusters�A�HsX(�"I'2�6 Rso far �fJ�%.rel�2y a��" )!,!�B}�&of Refs.m�0Udias99,Lava0S"��.�a�n f,M[�ign��ZA %-�2� �Z��{&Q��F.��FSI��=Ԇ�!�WF&2� -�1T! �!EB�"��s6��*��[tY�a:ifXg�M�`���(re�Jle�� ---t���$ tur���pla� im UrolA`%S"� vco�3ac�b��JRY����Gh0��p �5�1Me~bf8a Glauber frameK�s)L(["bE~e�r��endu$Q^2$-�+cW"���.5e�c& �R}8A�!7)��In "�$!� mA�5-�()�-�  m�sm ����YC �-7Fot ��� �!sU�--Q\eZ�a��� J o��orp(����(Moa�ex�Y5URroach�as�Laget�u�%�85�geta� �4��c�of\ is yeECbe&?,i!%�b�B����S, P,!B De���!��on"� ($N$$N�pcgrS-&/ e ~�ow)�y P"�&a*) ndar<��mi�kM�lSe�[a�8"_AWhX�:ip3Ch�(9�a_/ll���c-}pt��beyf�)*i�j��-�*`/&x� �� .�9 woJUg ��vp"�YBA}��enc��-@\simeq$ 2--2.5 \%�� *� 6� ��� � in Plane-�k-Im��e-Ax2��0ion (PWIA)---D:,A����)a� �PMy&] a G��2!��ed[:A;q#!�e�<=0.5 (GeV/c)$^2$ �e o�_L$%k�=]��sR=5�/.� mad�&ډe�1��J loop]}a s oc!�A�inux}kP-cy� �  s�@���) �2l�Z"`5sK �� tZ� ys,v����{*������mEArg%�$ $v_{18}$ 'zm�-�Wi� a95}a�$ Urbana-IX6-Pud�r.+a� AV18/UIX)"� hypersphT�-��onQ�0(HH) techniqu�Q(^e/� �93}8 � � (&�04}%S����:ir.����91 urac�he HH��=�� , Oed-6Nogga03}O �'*�y�N1.�ASsuc�n`��ҕntir�1�ou91� a w��AKe]��� t�&nd"s, �qA"� bi�ɱA, � -u>} .� 6,o498,Carlson98} ="��Rat>(��4apx6f~u 6Z* yq���2!�6+rD9s���� $(e,�)$C*��!���We��5 q ��U/�.�&�:���*H �M&per!WT��.�regime:EW}um�(recoi�8e0�u{� kept&�1 zero��.? lab �=tic��A&�d(0.29,0.55,0.88,1.42) GeV !���� �ELes (0.5,1.0,1.6,2.6).�,%��A� �s9Y��( ���A|ngN-=)ca��� p&)onQel*�?!raz� � tra��G��(e PQ�*�i�3Rpk 6�&����{t�NW:��q!Q�<�6a�bsorpe��g)A���iAva�nnels�ds � $p$$�wn�2�A��n!�*5 brupe2��4 2 mb! 30 mb� $remains es��i$�驁��-,sev?� hundJ GeVmALg oine9��� view�thAWide���FS��� p\, |.Qarn�scr� 0�� �1anF� �0vanOers82,Sch�9�YOf�-rse� .b��D��`6f M��;A��5�8is�� �b5Xlid� �u�2� � �2#L @jt~ \[�i^{(-)}_s`\s*�; D_3}(p+^3\!{\rm H})��1}�e4FC%`"perm} (-(x,�c[�C:ft -)}(i;p) �{_{x jkl;.z�X+k8bIz`p�^Ie�p(Big] \ , \]�L1 gm"C%_3��!:�BtK��7�d� � - a|{m s�Rz9thP4"b ��i6A�s��ver%FuQ'en� 0��P�m6� �i)�*<��Fe �2GF!} /n)$�\:9�5� a mbo2� $[!~0(i;T=1)$$+/-$�90) ]/2!�?4 $T$=0,1w�ob1W �isu�� 1+31D��Th$��ea��4&`3�!{�  a#&�� "d0ai�%- lex,��y*� %*� �ne.v^E�opt}_T(T��lm~[ v^c(r;.<+(4T-3)v^{c\tau}:]Q�R+Rb:3RbRR\,�#l}�[D" =G2��Q�Y����9tw��j^u � $j$$k$$l$^]$cl"�F\bqy8 orbi!�;e �I�aA�0 c, � 6>�]��2�$�  &# losA fluxA a_��$n�!���dE��� uM��z=dd6G breakup ��k� . N{�"� $n$+| �5mp�s6]�2�.�:�$;(�*�v�~�m]Y� (� "�I ��in .I)� �;�@��s �#�0מl 8 &WiarAJan� ?&�er��5�n"�3ce�W��f �!�negligi7�~r $v^cm5��a -�&b&i�$�=�`vE�� Woods-Sax�~Thomas"{amm�C!�%r�,�� �$v~� dī"��fi �$��H}$"� 6/ � %�e* �D7e �oLlab}$=(160--600) MeV��.c2wGn+^ {e}$� rgY�N�S�� o57ge�156 Fz�Z� ���? ,gA���� ��:Z.�x a&�>��red�A� a�}�@��(ng logarithd�ly2�(, $15.0-1.5X�rm3}[=(%�MeV})]�@ )u~au>Husq/ƞ�\ � 1.2 f��0.15 fm:� ��{..s�l&I}!(�4 $v_T�b��N� � �Av, (�s�U��yl�!5f"�>��E� s�con�YL� vin70,DahH72�.�y6�D aH��N�!7y$� e �"vw�,,�4b��ow� �m�=f:#���,e�#�Ź%z)�one ��!�I�b����� Pen��!�JesS� nek BDJllE�98} (� N#, B\ (2?�nd (25��*<2>) �:aD���"��Agle����f> quadCc� ��̐%"�֡�� ����Q�c�x�>%)! я� i�"&>p�IA� s$�# d�E��$&�.?�kI" Lb��7(i.e.�!tio���%O t��B$(Q/q)ai��\2 one)!$.��\t��T�kI�oy�B%?�!<uds cer+ly just��F 6�zG�(f���� N�.3Aw � ��:�%*�=de&i� CGi�6�m3s (< !�.�� �b >\),� u�m|a `}�� is/ a )��l.z)$J�s:!�t�~8R�2z (�-�" f?:�d "}) {qyo8:�A"exc�_#� B"��resona^:%���\pi#�9�$\omegaI�e�"�s (x@A�k����!p�e|u$iI�Fin�� H\"oh5-��� RH76}aDh'���F*� �Jf��Uݥ�);exc��@� st6Oof 1.6 .�26,h��!Lp���V�%� �U/>�& ?i�l-Brash02}�"N �,����~B- r�'l��d!  ` &� c�a)�. p;rW*g5jV��$ on hydrog"�}@��} or>ium �&��Z> %�$(&*(*w)_{^1� H���An "��( !(Qw-%[B�,]1t=::W9uch�%et al.}1 $�=,95 \pm 0.013Kl sf��b��.��'DsL415� *< i&kOce2(tf�<e� ct.� ccepë:W4*o�*)�el�)s $�\l�P � "�;� k}\,��\� $_3 \mid j^-b�|q},�V)  ^4\!Jeݚ� nJu�K�Monte �Mo (MCf�sn �mak�T���2Ms "��inJt~�6�$�*�n�a�/F �8 i&IaB6����L�.f'� E���super-e $R$=^�/b�� & }��a6A�j0 a!`.G�eF�(:3d�Fig�&^�fig�Gio�~pyq� C �b�-�"ˡ�3or!-al*��.�1as.�z�� Fig.������?:�4}��� !��,��.��_�� very2� ,��r1�p�O�wRO2��v&�!)� �!�Ap%@R�--.��J(a� @OPT)A� �� �H-{ERCe~O�s���E�M�t #!�� E�Ub��wc y�].o� ��,�\.� �n�G=�-!���6*���1I � 9�*� $2�W6�had�<fi-�� lipp(P2�Ebe&�l}�n&"vHYy6C� $P|:)>C%, ! %=�� 0060��090� Theye��)�i���a, It should b�qe stressed once more that the calculations may not describe reliably FSI effects for the last two $Q^2$ values, sif\�Xrelevant proton kinetic energies, 0.88 GeV and 1.42 GeV, represent uncontrolled extrapola �of f+�optical model, which is fit to data up to 0.6h. Fo� low 6�however,�`$P_y$ results obtained in0OPT approxima� indicat)g�l $e spin-orb�(erms $v^b$ �,$v^{b\tau}$ 1�4be well constr ubyu($p\, ^3$H e!�icE�charge exchange differential cross sections�Dy seem nonetheless!+\be quite realistic. The� +MEC.5 !�oduces �!� In fact, ��urns ou�~at�2�P=$R_T$ exactly (again%#Ju)�\!�5�EADordinary transvers9.M� �u�me�1ism affe�� bothW�Q: �_ example, �PQ^2$=0.5 (GeV/c)$^2$,FP,=0.251 fm$^3)�0.227 , �B�=0.183 $!} 0.174 q�6�I��]�s6 . H���WiJA.o %Tfer%�metersa\:�$xM{ $=--0.116w 5 �P_z&0.130$ 6q same6Qs��w.�,Q�Qo (iڍ�)�$ give tiny�itribua�s)�})�2��.��Sl!3BA'reދM� increased����co�, be@�� 5��e0, about 8 \%,ewice a��as,:�<(as one would na��J ct),%�%ef? �5io!5�/.) is sup� �� 4 \%��!7ec� � "X ��oneŹ�Z�%s�enhanc���.��) 6?atU�ede��#E�6�H,&�in!�lusA7($^4$He$(e,eM�)$ scPa' in quasi-� � ���0Carlson00}, a�it�im�, (to emphasiz�j� to�� $�+H .4�in�![��� es a�$tegral ove�  miss�mo��um $p_m$�U� �Zt5 2m,is evaluated��a Dle�B form��ors�neededA�"! �WB� 풁(!��w$s corroborF e�E�ons6�analyse�!�TCoulomb sum rule (CSR)!o,few-nucleon � q�$Schiavillab ;show �����ou3T ngtha�wlongil nal�i�se xi whe%� free-2Kic.Daf used-CSR situ n)�-weight _ remain!=4��K 1 is day-�XJourdan96,Morgenstern01.� ��� �a��%�%ev �re no 2 291B= B� Sick� n�kiU quark-mesa� oupl��dela[%]on a- ar struc]�Lu99}1�a��!�no�!�-TmoA�ed Lon!pU�,2=be�� vari��Ŷ a number�2��%� ��p a��o��� �v �is ��evitabl}nse%mek�%$ sub� �w%on�&� recaty QParis00}V�} @ a�"� flux-tubR-�six �� �ecA vi�$ glu-�p�T� s ��sIU� v s rep�>irE�vidual i��it3dow� verya�rt se1 !�s,)�(little dist| �ir26 s. % W%�nk S.\ �%Ee P.\ UlmerA�� de8 iE toE!ous at ��YɊDV.R.\ Pandharipand��I|ickka cri�rɑ � manu�pte= workR.�wa!bpda DOE�4dct DE-AC05-84ER40150 under�!�Southea�( Uni�[%z8Research Associ%q (SURA) � e!�(e Thomas Je�a�N, al Accelex Facq. All{.�  w� ��possia by grantsA��uEttim�flE{y�S� 6er CeA�Q\begin{r1�s}E\bibitem�72!�{\it et al.}, Phys.\ Rev.\ Lett.\ {\bf 91}, 052301 (2003)x] Jonee�M.K.\ �[$84}, 1398 Y0)2YH} J.MA�W(, J.A.\ Cab�Tro, E.\ Moya de Guerra%Ama!�m,T.W.\ DonnelJb�8[,5451 (1999);.~KJE�Vignote:7C)262!234302N�}e� �t\ Ryckebusch, B.\ Van Overmeir�nd.�, �v(-th/04071052;t J.-!<6307223Wi a95} R.� , V.G.Ja� toks��&�V51}, 38%H56�PudlinermBe�n]2^) � �.�f�7Aa 4396N�(Kievsky93} AT , !2Viviani%�,Rosati, Nucl��i-{a A5�24I43);2OR362�125�76 |04}.�,2VB�] 80192�Nogga0 � n�Q�7I�004E�:�0Marcucci98} Leo, D.OA� iska �!ӂ08A0069%86-�mA� %>\��Mod:�70}, 743N_�!s>�K�~N�tt,>o �2�=�2078, N5}�L �ƵN ���i V��~: 1�5!�240Z�V oinea C�h-Lelu�F har,bfi47%e:2LvanOers82} W.T.H.\ v���j� �2�390Z826Y[90��\fm.��83i�:}L�vin70} �-Joliot:�N�1M�E�7:_Darves72 � -BlancBZovo C#o2��A��7:$Jeschonneka0��E�r-p5a�24��:�@Hohler76} G.\ H\"B�B+B11�50%t766�$Brash02} E�p�� ozlov, ShA�iivGe�Hubern�51001(R)��:*+ a�!' , priv�communX2S6���%fJt�� rdenV�4��2M�96S.�ByJ� )�� Fabrocinijv 1484eN�:F>~.�jr�385E�� .8 ��.�B55� 19Z� -�� Z�0I17E:�6l�% Z��ez&56�1��2�� 2001:�@���t D�: Lu, o Tsushimaa(� � a�William� 0Saito��,m�6!�06820�AP.AefGui�S�A.if 9%a325�s46"�n  ]N�6d�d 15�20=  \endB %} ures #newpage: fi<}[bth] \let\picnzal�=N \def{3in} file?a{�8.eps} \epsfbox{4"} \cap�{*u s&�5��� a� eor�"� rediP, "�in�6�D schemes (see texthan�lan��E�)�solid � B� guidte eye o� Also�wn�Jn�1$H. NoJ/ �($)!h� � shif) 0 left (right)]0.�W&�Jor �! cluV! .} \label!�� I8M �&n&py�#NJ"�,�,�,A,R��$B�H %�byB�A���pyJ�%)� docu[} +S\,class[12pt]{*#le} \a?0width 16.5cm h�23Doddsidemargin -0.4$voffset -1 7@footskip 1.6cm \u ckage{�@ ig} ���0title{Polynom9Sol a�Shcr\"oer Eq��a�G�&Talized Woods$-$Saxon P�#�} \author{C\"uneyt Berkdemir $^a$, Ay\c se 6��( Ramazan Se�D$^{b}$$\thanks{Cor�M g: s+�@metu.edu.tr}$\\ %EndAName {\small {\sl� D7t!��� ics,� ultyArt�U Sci�$s, Erciyes&y,}} 2]d38039, Kayseri, Turkey}}\\>�bb�Middle E� TechC l "�Fu(06531, Anka�t!�(date{\today makeEUaHacA�UboundLe !�gy eigen ��ndE�e�!� "&�#�g@R*&&arc%�h(.( AJacobi�!M�ds. Nikiforov-Uvarov method>Ha�A�.N. ���k�� , a good agrepU��&�be . i�=?\base��Pkip=22pt plus 1pt min  %�( \vspace{0�!�cd�`PACS: 03.65.-w; 02.30.Gp; \Ge; 68.49.-h; 24.10.Ht B(Keywords: BEState;IE6 5�; � -: ;B� M%�yD  \�){I�duc� } E%>��ASch��e����r���s hasM���muc� tere�0years. So far�se EA� APd$bolic type]��' {�(EckartB , 2, � &$Fermi-stepFJ ' Rosen-= sJs M4Ginocchio barra(� {@ !Scarf6 {6}�^]7}�%a�wi,!C*%�;'Mo��- �s � {8}.' addi!�,�y��s���on exq*��6oQ09, 10, 11, 12}quasi"U' solvF quad^ c�J,14, 15, 16}.t# >� (NU)��A�kimedE���)�a{o}��er u (SE)�re)dJ�,al� l���E�� som�-- �}EY {17, Y"1jHDirac, Klein-GordonE;LDuffin-Kemmer-Petiauu�)Va � 6� by us �i� ��aluR2aS2, 23}*�*rO/I��--Žd��-(#��i"O! B����� &$ thro�-NU ��1!24}k follow ��ame����-z")ics, �is �M�02��-in&�#29� by r� am� a� � U!Dof hypergeometric !�.����%< Em2� "fuh�- �y�0�*E�2�7 F_s a sh!�eh!s~#"I�&n� ���deb!_,metallic clu���4a successful wu.ni<l� 7a=�9a7% ���$on neutrone  heavy�u�E25, 26A�T!� pape�" arr dA�Is:� Sec. II w�$tr���hNUm��0 '( appl1�EtoE8 I�9�"�Z�٫. Shapu.�nd )#��i� c. IV�V�discuc1h�,ultB&��B�i=} � NU�$provides uA�!c��A�0non$-$relativ�1-� U�A0cerh �'d>u�9�4}a���.��s.( -P secoQ+ � ar di��2�%�!��orthogo f�. �`27}. �3a�'n�� o�!mplex���^�inE�d��'is��&a2��B���anA�Tropriate $~s=s(x)~$ co�.��.''a� us iu�writte�)elia�3,��"j,eq1} \psi ^{u0 P}(s)+\frac{\stackrel{�) }{�2 !}gma }6Db=s26?^{23 F(s)=0 �wO*$~ >$�>�a�~$a[ p"�ut mos�#Ab$-$de� ,�NOta �~$!�a first8*H . To find� �ulL&M�A Eq.(l3!y)�Q]E o &blwe��a" 9�a06 j�2)�!P\ph y(s)>Z�[��es6�U�,�1),�an of 6�E�no3} )� (s)yBt+!m24}+\lambda y=0,>�M �$  sf�$~A(e}/ =\pi (s)/ �& $. $!)�!gJ��T w4]X�š��+n!�Rodrig��Pon�4} y_{na =izB}{�,�}  d^{n}}{ds\�[-V (s)2% \�] ^<cM� norm��8 /R.��!,*�W R- $ muaMatisf�IaW� *� j� 5} (-��=�=A.>�U�!�ia�Fpa ter$~M=~$ requi��� this%�def�9asj�6aOi -� �Y^-Z'4}{2}\pm \sqrt{%�()� CB>A�g ?%�)�&:f��}+k O}}>+`5�&�Pjeq7} -% =k+\p� }BvHe�$[/(s)M5�]��A,5� $s��8/d!�mi� ��$kD2b<n�p�/�f� 1 z. Thus�5"���y4[ �m$k$��N�� &� �� 8nf 10} V(r)=M=(V_{0}}{1+e^2�r-R a}�v}QpC.�, M�X ` ^2}~B9E� $V_0�"5j depth, $� �)m=!�$a&surfa ickn�>� %� adj�~2!�ex*>e�� ioniE> ��� ����� $�������M%by� S 0})�1s�/itu/in�rad" � !&�o���:j  11} � �g) }(r� 2��hbar^2�E+��Un8qe^{2\alpha r}} C r��(1:.Y0 ]�A�0Z�sassignmi?� �-�9-2 &�s�a=e m/r$, $a&0\Rv r�� $1/a  �$A &��it {q}I d�� !�;E� an a�Ararq|A�A�70 �U. Now6 &�NU$-$�,T re+e27 1}) ���"� A+a�� $s=-2�$n� 12} )�d^2%?s)}� 21�1}{s} #! m}{2MPI3^2s^[(1-qs)��s��-qsI/);I I9fB9Bya1: �o"�d n�813} \varepsilon�|mEF�}>0� E<0)�~~~\betam mV_0J42'>6 gamm7C^5&>0J�D"�4aR "�7 in 6�rG4�-qs}{s-�f A?^2 '!��s�<[-=w( q^2 s^2+(2 q-%; q-))s+.;�0AfDA' comp�4� .4})e�2}}@e#$ A.�&~ sv� 15Rt*�9 � =!KAP{# v=-Z6� N <.  q^2 bD!LERNDBdSўmb�"�a�o.+6)+ $�r� 1� a��AZ2� �1@ &� q^2+4](A> -4kqI )!4Ediz q+ �-.] q+k1/� Iz !B� tak!$&��j)�1-2qs eriR n��e up%ex� V� t� zero"� B<� Z �  G;nAleftBeA_je �e%eJ<v1� �==%�[��)�]^2-4��>ZcB:{J�W<"�&�d�Aith�!&1A=�$'it�Gu7� ? k_{1,2}=I��6�q\}A^�(1� 4i1$}{q})}$. � "� ing� sem for eachB {k}~� 2u6})*�"�7"}8<�e�K$"�#��.p� = rBA�\{g!�y}{cccLeft[(2-#>��}J}~)qs-b9~\�, & \h# �" \m�* for} cm kB�+-�F�Z�\\ \\ �j�+ �����-��2)�)VB��$clA�L��$� :� rUE�%e{a b7})� *28}). F}:four U�� t&%E��� $ we�#a� for �5"B$��n.�9})�  � � ��!.]?NP��! ��m� O=m+eqn)x&�20�)a��-Ep(fDUp�[/q�<),\nor?A�tau�D=-2q-�uU9�;!zR�ipAmp��D] �� r�2���6����z��>]�u�} E�.�8� eIget9�2\�- eq22"�B�v�5�"� q� �)�a�0�SoPn�� l��_n=nq%�(2� ��F~)N���)+�Yf1H��se.�"� $g$e�A�&V�Un�4} B�q}1}{16��+ qrt >� ��(} +(1+2n)} �]^2x  ^2�[�+ qrt �H}2I!�>�>u \of:!�$��.t6e3��"-!H6� $� 1/a�0}�22� ���im8D atel��+in.2*o$s $E_{nq}$v� 25} * �H%c2ma-� \{ {" >�9~8mC3Dq=� >�� Y� 2>��)9�M9�s1�NeMe\^�!��% x $nnon-n�� ]g;�($\infty>n\g�J�Aabove&�F�Bat�d�Da famil/f g6mB�/&� Of cou*�K��by �K�'a?Vp>" "<g�+��sE�Vc jV-�%��U�T� Kb��'��&�Wy�# trum:�iHS� $CaV.� 25� .v�,&� � ���"$*�� dar>1%9K%�7R rega�Qg'#5 $q� Let u1Gw "Oc2�w�4�'�s. Due � 2o!6��� "� 6c R� $�en�(IB>R�� � is6� Z@%$[*7  ]  }�}~ qis.�(v�6�4h8Z��{\nu-1}s&�J!}^-\nu=1�=�Iɂ$. 2E!\ F�!`6 4��!�6XY���^7�!qt �!��6-(%)!f}��N!"JTn+TSn+2bp"D"^y��D!E" Y��zeAA1($1/n!$. Cho�� $q=1��b5 $y_nEq�2�:�2�2&�5q �n� o&*(y�s�(FZ (1-s�"����%closed �I0rval $[0,1]$,AY P[c�]$P_n^{fi ,~x)}(1-2w!� �(By2:)" nd $i�i-7 !9%a�y�/.$%.$%%�*$/ �3�R�)�e o N�k��E��6d2�f�mvJ��&=1�muA�b�^� \mu=\nu/2 �a6X �A�. Combin�A�If*&�%Q-o2� 8�:�7�D��>i'sNe�,n� 9�e=A_ns^f�9-\nu+1}�j^.A_2  wZ�.�!"�8E@DK�4� !-} �+!]B B�6310-^*�su-a bk"X Wh*�se , $C$2�w�1 adop%�F�"�9u"&V$12�oc`��2*�e� {29p3S[�Ogaq�*(VphenomenYP�&I�"m-empir�`%e2�by PereycLz<30} $r_0=1.285~f�U$a=0.6 %�8 \k 0x40.5+13A~MeVc+�*d. &A� mass*�PtEXtO#.vel@ � �1r�"A�$ Of f� �� ` QN� � �� �N� � 2� S�4 2initial� l!A\B =1$ ��GIOetc�� $C=10E7, $A=56$&� )�43 averagUI; .Q$4m(q A \leq72$U�142"1Co"�U};&^���6 �r"#2"&� !�R� B�wn�� ang. &Y;� .��C:[ )��W �"0%wiM~9��o"��; phys�&-�y�,�iZ�;9 ��.�;�+��o"JW<  n%i�!(*%V. W�r2�r=7re�#wW50 oo 9p"�!!&`.� !�� aHf<6 T�i�%%�.���Rxi�[]m*� I���`� 2�depth!�l �]s rapid�\T!1D=,v�?u_tA�W purxAS|*cE);E#�$E��!C $�Y!82 3.W�+ou�V�y xactFTmrFir���f�B�%t �Ang&�9-�j5� ��>98a�!C�)���Y.�>q=�Dthebibliography}{9� b�S01} D. Rapp, Qd um M�8 (Hol�Ninh77a�Wi�]D Inc., New York, 1�L,�G@t III, Ch. 8, pp.�P8-200; G. Bartonl"9AOinver�^,harmonic osc�Zto*�*An.�A@. (N.Y.) 166, 322�J,6); Z. Ahmed�Ann�?g �9 asym9E��=�<|JJH A: Math. C.Z897) 3115-3116. 5E21U Fl\"�\, PU8!�FSI (SpDS$er-Verlag,5Cld,1971) vol. 1F4ob. No. 37, 39q3} L.D.oNdau%�4E. M. Lifshitz9a=� Perg�^ P|.,, London,195�M�4sTM.*�=,H. Feshbach,�7%�T*hHP��(s (McGraw-Hb-Book C�$ny, Ltd:453)A"1650-166�&Q�5QKN.&�>, A cl� of�0��=1:�-d7alZ6, AY>15Y<03!�h84); B.Sahu, S.K. Agarwalla%a8C.S. Shastry, Ah-M5�)on5[ s: A#>*��8��y�,Ai%6>i,35, 4349-435�V2)=�6GN Kh�a�8U. P. Sukhatme,@�H�kmpl�]l Z�hU�� inva�[.�@by"ad�b�@21 L501-L508 (1982J7} Z.i�TB���P@-F,-M A 15>-5,!�91.8Y FZaA . �g>l�L8 A, 47 4761-475&�RU�,9} M. Znojil>�D+bf{264}�9) 108=��.D\"{O}. Ye\c{s}ilta EV \c{S}imek, R.G$, C. TezcaP Scripta v T67}�N 4�W�- D. T�s clayYDu�T8A. GangopadhyayNIR,Pag�L@nta, C. S. Jia, YAfn\Qa�.5��30?5 2002) 231.82} G. L\'{e}vai�Z-UJu KJ 8793.K3}.�X. L. Ze�#L�S�Z�294} �185.W4} �96?5� 1) 1.�15�M. Ben\�E$ Boettcher.BL31I38) L272�62s=�33)�0) 4202< 7} A��IEH&�I�4Uc Oo-p(Z101?Q subm�;w0! ics%��A%�OYr88} H. E\u{g}rif3:XD. Demirhan, F. B\"{u}ykk{\i}l \c{c\\icaQ�,�59)) 9) 9.%19�sbs60s19.%20}�YasukJ[6zV_4�E5_�L-�!b"v!�Gez206j21}�5�e�95� A� S&pA� ach ��GSo:|Re&o?�C-.14P�n�m�6F-al�_iew A,F._! M. Simsek�A<gM8-B7�79JO3^�J$C. \"Onem,�2>�]�Fz4e\F.&�E, V. B. �J, "Spe�?F�+ I =ial_ 4ics" (Birkhaus�!BVJJ 6E25��Bulga`YC�wwenkopf͏J�_ 7�^3) 413.726RT Hamamato��Lukyanov%�X. Z. Zts�Z� .\ A�\683} % 1) 252!7�W$ Szego, "O&�*", (Amen2 Society6] 3�V�jh� akh{Ma) J. Sadegh�Wod�NL{A \bf �)� 615. 2�9%Boztos�= KT66�q2) 02461.Q30e�M.���G ,J. K. Dicken�?nda�J. Silva-� k*^17��(1968) 1460 ݢ�2M. JaminG a( . Jeukenn:ndAMahaux2Z �3�86) 46�U>"2�Kv"�L in} "GL{\L:!X�ure C�Ts�#�)$.5 true cmRo� nt�31:} Va' O; gene2� B]BrC�2d2:}� @4.hgg2%)�� *�,"��'\n.} 48$ MeV��t&��j&�r� �is��.�re rt!� n �ex"dqf� �1�<50 A$\cdot$GeV: �re .* M5�[u h� llap�y�$v_1$-x%\�o2 �wI10$.{;42��'s-P :m (b�n� NA49%'ab�piwmSil)Dic�cau-� ��S�|r)� than-�eps�D�(Merpre.0!#�� as e*L}�a�5�>dteIo�Eat high�yon dens�{%&_B$. �eWp��qnA�oUPellip�~%s$v_2$!�jet�\AnE~is�'+d.�,�Le�LQv�A`Jxnot fak� minif frag�0%. AXSM,�'ailA+�KacIW"�qz|y-hZB��+�}tiW( ($<$ 50\%)� due�1�a�5�. FurK#mo�EA.�)��>a)$v_1, %:�$r!Abeam )!��Ll[ �& occur%��D%�1��7�@ B�i�\�4'\at 62.�S�y20220��@ \pacs{25.75.-q, (Ld} %{direca�A,6} %\so{\JPG&�Y�&EIQPa�: Old�newm^�K)�e QGPB"} LattPyQCD!��O \c�~DFodor04,Karsch04} AU��nl�ynaLr�DOBc!�A for vanis^r �[r`�."�s %_B.e.!�D"�I s ac�Q0oyenXMRaatI full�> Av@do� A~ acc�Ng�CDn�!/. �OF0iY2�N�or I�A��5SIS-30N|low�PS�%�I� 2$ reg��a, $y ## 4-5$ �A!�0etty80,Date85y��"�^ baryJ� is ��eUJ�t�;)�^c�$00 \pm 50 85 } �#%�rtem��Y$T_C$150 - 160$<.�do��ct$Iha:lso!Pf("?�m hE. PrecA�� Adiagra� sTgl�Ae� ng m��5 ��R�/Y�n�%n �u�v�f&NxO!�7reh��ve pi�u�!A| �" u��ulti-�hn5 ss d:P�freedomx very��mi  X/��QerA� oE��sh�J �Koch8CY�{� t��)proa� 4greic87, 8}s &+ de-admix%�of $s�0$$\bar{s}$ Kks�v0yields unique�na;)Ɂn� �: �?m!,-�( hyperon-/- �paC/,�le�dmEap unu�G �0e�� r(s $ect$�B n[t]���Uf$} [r] {6cm@)"�t_mu_y.�8#~^t:Qi=��L �� y!9e�c, T_c�/̀�Z� $� $ 1 �mfm�%�sl�_ly belowaN�h!�o� oss-��� ex�gmid yE�ne�pA�n�Y8 dU�Fan�I��' fired|'�J F� �B$u &� "*va�3���"�+ ���a�rtz %��ds�^E BRAHMS�5� "qbme֐� ��\ �E� 6 O_PRL0303=Ww%�:���<�a� forwar\pi�Y�&�&G,u�:  H 130$�/EIy=3��G,jextend!6`y� (6�D�(aSO�{ i ~�M��5Xct�1�a�p,o` �a limiA~J8 QH" �@sR&�(�Fop)��D���� fu� GSI"6en��: suffi�la: �F�sU�sh/�-!v� m�$Shuryak} (�ra�q):�aihe ($T, )�)-�nea�The^�n �2.s (�E �.� gv�$G2��/I?. KZI�ic e���� weakA&�0��c�Jndm8��*�%. Di�, �g=�2i-��� J��.�6D�o2���J�{�X�� sidiO } H*��Jshockڑxap;:)G� $Hofmann74, 6}A�!�keatA�ismR���;��eN�sr �c�e-�9�e7�8l,Yree2�+.Yal �a�lem�  lmor�+ז9@a:��d*E,Lab-O �� }: � 32/� r] �ex�;� sI cG�ctripl �9q\ٖ--�� Sp'e˖a��cs��4roscopic handl ��a�A��E1ce-off�e sque�%�!���-�St�79, 80 1 2 0#third%�pJo_�-GCs.k i99, 04}) }AH�$#Xbar�5ers"�86�1xed,6T�+SI"J�$ly� zcemploy�;>�� )� Volo�}:}a v_1 = �>< �>p_x}{p_T�C >, \v_2, ,^2 - p_yvDp_+ +D > \,�#eea�8p��� � �5� $x$-"c , L!�"� )�um��$"� ]� $p"�b=�o�6= ޏ��6� a�9asdT!WA6$;| $z$-ax�4p; � �Ah$ �% ''Y�''="�� � O1�: %�e��bBI$h)� ^ azimuth�Wticle e����ib�7 � ''}�''�?�2 < 0��t�~qx��}#if, .�wnm�p�f�� disappear� r ''���''!/e�-���Z� . Sval2��.�ous�A� past�gngeK8�fluid��>Rach. �li�nBo� l2�65szr too� �9�g�  a beL Gp�!��E, viscq! �i.�d; oped-�HSchmidt93,Muronga01 � InA -�l�F-c d t�_.e< ��A�inguish�Z� proj{5�;�L%T( �s,7{ �eZ�jBrach] 97,Toneev� � ��-;!� a��r%,�Rs but fi _ �d~��!�he ai��to �at our�po�Da rH�e,U66���*:-t>B� lu�^ %�� �R� F���be"Id� lega� in2�s (cfU*fsb2�,Kolb,Teaney,� 1,Nara�ia!��Wcho�of"[=&y=�8Z s influi֩�fi�5($�h�!��9T#t!k�:i�}mi ����@ (pre-)� ��(t�6y, e.g. qp�qMD-c��<� I/)z Hartnack8�rRSO�},� , Bass2�or HSDmaC�_ngX��co����%�#%a($background%�oub� 7: L� U��� ��f� ��`��q �EoSa}�$�vR-/+B4--a<P!� ings !�w��,A� w�@ar�ju'��rk�"Y F ed? Wb� Rb /jh0 /�a�B�  lw8!�?��*p���&= , self?�Avs�ɡxs � ged? To !�mt &N1�{ unvptEmM�aH%?��.�>�I�e_C care�y 1jb wo rob�jI/�ngOt�s,A�E S,! a�eg�"Jeuby {R�'ofyG� � } M}�i� �JX��! %�)�o�J %/Y) ��w-�(8�� m�Weber02�urO�$nuc+WJ.Q` "W�)o!Rto�A߭A���gEonably ���� �Aniw03, 1,�*& 99,�:1�I�O�2�,j@�@hand,m"l�k�s!Oie�"!7O��Ř�e]�o�oun�� ��Q"Z i�6�!KM�P� wo���� d A�:�� ���E AGS���x� E /m"-  {he E895j"/ � � $p�LMU$I�"�d>�off~?inq�� �BJ;t�ЩwUde ��*D!�"mean-E -pat�A��^7-�X!�On�"^�� ,67�� +a s(  ''&�e;�'' ��99}�6''Z''m� 00�� iws�+� lvE�i�+ly ho"i�w��u9g���fj�&}a�!!QGP�[ �(��)� a�2�/24,ET (y)$,��� �� s.�Bs� !q %� a9�EoS%��B�"��(�*��� �hj*otic 2\(n�Bu) wigg�k� �iM�)��^e.�m��27� (Fig. �ia�_�J� howsR���2� 8e�20 *(-. AW1se$ !�p��%cz M�ed%1 i 1���x�!����ed!�-Ui�"obwz Buت ere %��&e!� nimu &L.-J�?�F� �,is ''softest�A��t;"aba�s 82/"�i� sE H verifZ����! How/p�x%����xhe1 &6Va�A�%U�.�"$3:�"Z$t�+%[l]{6 �$4�4E�3*�4$7.5cm,clipF~" d"�"[r]{10 Shsm�*{2>apx_plogbscaR5.4Z`c�6{Left: M[���!�-2$$dp_x/dy$-�%�"� A�a25EQ.4>�# Paec�<�* ��iYat $E_{A~^��� e�st� -�� u�eFAIR-i�q at GSI. R: NetBC.�/ in m�%�e�!>8.�! b=9��!8.4�!4"� ��)P�w1;f"�$ $s/\rho <F1*�lo��M`�!e} . �A t��al%0��I��auw �1'eb����"�!bE.q�F�1 �_v2pr4�>�� ��v1v2_40}jsI}bIly�-a��1M�.S�-�,!��� to�A��}��� E)HS:� ޥ��noF�/J�, l.h.s. � atR�!of 30-63� �� Bk ��A�r��3_B � rea�I�2ed�FY��a���� ed �%�)��E'׃��� y �-&o&�)ilfp�!��a�re � g�pro�^W �n�A���$g =1V�? s @�6�3�w�,I�ies aE�E��.R�(�.>�..�o� "c3m'l�/a5ha0'a 3�_K\�)�.��/"�nC�apr!G�AM�!A! . ��1�1 "'PPg�e2�4,�6� -:5 B�.I �!��. �� �L�5���,> *{5m�,� e�Je{.��g2862�5�& �"M $ (`)��s(Q )E���zra� emi- :q5phB>�8!1�� at 406k �b yi�+�_��:�,.^P&��varnQ A1 ��?i�RwsR?t�)�a��U�: B٘-o>�At~�K�~rx"�i�^ N�81 �!5��5)�p���: A � ,��*ͪB���" 0"+@99,Larionov} seem���3��c ��?����bB&�Z m$ 52d�#C��2SKch*�?{�*�����g< s long agx�7��A��j exhi��a.�"2�t��)� .�%�`�b�$_��:�)�aV-BG�cD5i� 2�HI��#e�a/ ah"��At�1e�)t1CN2�7��smoҰ� %�A �� !/!N&r� [q��152� mB m�06�'F >�B3ed&I|!���SPS�*J ed�#i�(�.� ����%�2)��X�Q, r^ : A sudde�6�<�!QI@u{a���,Ac ��#�� P�|�jn)�/��%:X� F���prono�d���J�at>�I�!~A�\ �R,E�2aNI*� ,��a�, 09w%� ~3\%)4of�.-Z��h!�%�� ��4B"�C�-)H *e Z#� E iY ")  s���6y� 6/�is!Zy�'E 3--���d�n iF>N:�� 7"� @t!�ch�^�  �QdM��of�V& We��Knco�Y)�-F9 =� |��stBM !e&t3�69�s_W)� �)A�!� �e e -g &�S�7ll�v�a�*"� NWwM�ofp} ň%oA���� ���asc��.F�Xuy$GreinerM7Xu04}i%�t�b��$s,� $gg �%( $arrow ggg �b=zing�2 pQCD (beMs�)�quark- !�^ela;9a�V- U5�!) �wͪȁ�� iori�"�^!,�@}.�2��aJ� &�6�?�*( four2m(&]( *plasma.&�ino�c)�su�sim� .�s (`negE=he *�"Ccoel,s=0 W,���]aZ�-� B� �/J !� 1�PHOBO |\C&s}$= �?GeVEL�?�3s�Wst���Jp+.nt�, (\eta)$�!&�J�@�(.�e�t "D5YU1 eity�1!��D�*fng���"%��m�J  Bjor�5bo#�"�UIP%K):Heinz04�!#� 6�$#!�J� i�"V"�^�l%($`�sy�"/ SPHERIOI; code � NEXUSI"-�!� �(Aguiar01}) � by f MM>L�*)m^2` 1{!m�+�E� 6 � � \ +>�"� asa.�B�Id�".! raa~ !x!s�� ]H v�%2b��pl�� rol� �p� �thdT�.2$A�/c:��� {R-& �tu% r.�$�"�" simu�$on�N�3ba�� NexSxioJC5�Qb� �0r�t-by- �%ctu��k� c&Q%}!Nw$ly-aJF_(�)��E��5�E�e�;r$&?in,9I� Snelling}�~ 1�h �.%f�EDec!�ric�Dfl� o�d f��p"uFF!FJ>[l]{7�* v2-aAB2�^��28 R0]6�>v2_cass2a7z  !A2L �-lR<��ѝ2 I�# rged5��* ~I� �O of '!icipatA'n " ons'I$|��|�-�7` $Z:�-M6f =�[ i "h�1 'hi�s�\ sis'������M&i _=Ix #7d.>2��ec�= CGG}�e/�-�5'�%�E> �C��a �<r!=��%=a'��= � STAR�*�2_rhic>�.=$&C�} (A � ~ )!<)�le�s, $dNJ�8��, etc. �-~ ea�#>)2&k%� ��]�kov04,M�E���a�ach�rD!���t& �3, d4 ($q, �Bq}, q $dy"!""!'��!�CR lack[l�d� icJ D. 09�(�!dI ='abund�!��l� ��2 4�Cu,d,s�C \footnotFr af3~ surve"8 I  6�R2AO^B.�in �Jali�us-e�u�u�4 ���E?9� 9�oLre���T��o��M "T& }. D�Jy�/+ ;� .8 ,ly?>�S[JDZ�1hp_eta2]5Z]b�ON�$phantom{a}"�-���8�.71_y206�^x���"����>�%� 2� Au +!N�2w=$62.4� (_ ploti � (�r c$sus pseudoUp $���� ���� �ʩ� _v1Heta\0-70\%giO<��A ��� ? A 6-55:@�>"�)�� =200� � 6lA�L! stcB2*@�i A1a2.0�{" �b((V @).<( �&)J%�aJ9���on��\pi^+;'K %f� 9 V�j"�  $y*�Fig_Zhu>����l���3�I e=2=QIMA�!^:�% ���� s}=$��]� y5���o�ata�E����%I� ? ��U� i��a��F�x;e���I�1���� %�J`.�a2A _ )[I�a�s� ::oeQd"qyR� �Q&XJ�"!�C>?�}� (v�&�� PYTHIA i�� HSD)ݽͲ��_WSQMz� n�'s� )/�13.�A�!-( q� }� ��N� .��Y�O!�!aa�BqW"?Ɍ]j)�c3 ominU3 atV )����(�% �B&�RzerbMu1.3=o� a�P"%$�'"A��"vW���As� e��!c3���s@@� AU6s�le"-!�$idꖅ�)�y%�22} �G/lX��At�Qzm�& ~6\%!"2$�m�(/�+O1�6Q�00TJ�shorten� �fo�M+6�?,OyJ܃2�ա9�N!M�m�a�L�+Ja�F--*�K�*t q�P)Ih--!&Wjus�srvXJ 1�-� el� �?� at�|� �<�<a2%e l��6dAd�Ah)byay3�-Mra�*D'"R� $p_T*M�G �-A�J��z}�c�m�ree � �"�F� ����Le�fy.2F�m=�re&�V9 Huma!�e�G"4K$Tom1,Tom2}\�o %W2�by �:A��perA�ede4� � -1 $)�JAM � JAM}� AE(r:2�!�g]BQIm0Z��dinZ6NjQ�it�  v�D!"ul�� o��U2hieve��%�va6�!��Ar"�<ng":���(�ose�.|A��}E6'bh���#! ��4LpJ?-}u�hp.��O ��?��&v��YD��7a968G�\ "�%H�Za2$U�.iong%*�Ho�J �)Wf)_ ;)sa[t{5�\{9.\D?wO(&-)���1��rd%3ic��y$ [�5�Ic��j�=A� �#=i �E12� /�Jet�Do����k�!o� z���4 pass�t��� )��a]h!pt&�I6uu&ҫ, {Z �!�c it-3iN)%ZE B-��6A>Rw uild�HpcenlyɄa<������NJ. V�F�)Aje�(�� >�,�eri���far out���/)I.�\�Y�"Q--&�Q�r^(z �Kt)~G��Ir�an)\�h[%�ECX Isim 5\,$Eefs(�P��� of 5A&)�a �?eq 35$, ��y Ex.�!V��0z'-G -2��G�;�� �B �8�  stemD  decay� rho-�.;2U^$'I( :�6� 5�}�% S& ed a.U!z]��,raA(N�A���$\sim 3Q�o(up���u� �in d+Au2gA�G G#>Vy���o=KE1,E2 �i�e  evidU?u E�fL#��!e"�!*���Cis� M� ?t�7:� �.���V" ��lU._ (FSI)-�Q� . (In-)e��.jU�P�?NE$&�1���Es*�}A�@ :��%"dB��0 ibut�E��DA�!��!nf�A �왦F4umm!� >>E:6jN�um�.���� pm 5�/c dou�.�� u>��*�Bde0݉�;� iR�be�0-<�~k p��奋*���'s, K��i��)(>2.9# -- hE�ڼ]�= � A���tau_F5e4$�3� �� t�/m�J Facolor ����/!��b� � �+-�Kopel4!ՠ�A � g0 "�G��� .�ic6� a�A�AF 61�5o� n1 �e�ly �9�:"yѬo,u� A�$-s9Crum �� e^q]�} �y�`ed:1�.�3��@!]��esc@� d byA%:~1G ��&y%l}Z�a����� uch (i�!�"�� "F$%� [� ad)�sf 塑�1�'Q� d. O�&Ɓ,�g2 sU�2�EUc�>Az�?e1�:=��)��N �ឡ�a(�*7 f3 ��7-.`S����k�+!K� 0vK�+arr� ��6� A1%'i�V2&y � 99}. Tlr��? 6A�*� $>1.���E ��orp:h�!aA�erp�"� Fp+p2lUni� � � !LWe>�in�.T���#I8�!d��'Q:�%= �5)"i"=��$��f$,z�zkUEv�R�U| lo�'�!�me� |A�aca~Teb�#m � Y ��C"q6b�1aT W&z<� 3�3cu} "�N�rdefaultE 1�.![�2I��@ " cer>6Ge��| )dJ �[�?.�t0�)��ly�E�\�fiXr}z4ce���2�4fig5n2=35q-90�4�^ �a "� 0<9#�!'.1 �&�AA}$ (3� :� at �(10ci��Js"("�$!�)>.�' (ha`zd band�$]�&g(�!o� �J� "�aq 2,a �  6 ��,n" al �BT.aI%� .5`w^6q��)!":�la�r!�>�&���K arA=i��E(�3��0�IXe"��  skHPAA} R_{\rm AA}(p_T)�P�� {1/N^#�t}\ d^2/dy dR {�,< �}W�>Ď _{pp Min$ N �gm "T\Rnd���ap�:QN(Ab ity) A�`�&Y� � e Cronin2��is(��� all � HH?J���ec�eo� y��b" =�(�{fe h4,���U���5s (K$^*� &� A�onfr�(7s� @t�!�)l�"���cmy ameaPfix�{�,.�um L[Lo�z�+� <5$�mwasE����A���BdaP 5^ 6� � >��&�%e��8& a� xpla �6� �1e*����E���M�� "�M� Z�6� � � = 1\!5\,WGeV}/c$�v9;A(i�behavikOA�^ �)f�36G��* IBass_�}� A�dX� ut b��!�.�v1 �*!m �JN *� is.!>!z6&�#Lt/&2Q��-�_��0ofa�i|}��F Ia36�"�"��r � A<��]pve�� �O.�ic6Z��p"M9ڍ\2^ �deG�1G 7iab!�$0N �+A9 ���*CZ&�b��l$�����$A!FP��i&eL%�)m.�4m�i0�Oe�{2:���at k 1/3�!P@ oed�� �]eQ �o��r�slD# �?3<�K 2/3 �p��e�� �!Han� E (��ZOY9?  2@ �� e�&� orig>�$Asf�-�`6�!p.�A~�C�di.!! -- Can�/Ukee&.WE(�0�6�/�ang�} (M�6�!��l�Ye ���Y"� ^{Trig}=4��66�, �Y�=2+ p_=0$, $|y| <0.7$�a�e ��"�(N�& "�,.�%` welV9$pp�(dashed�%) !�? B)R�,ed%�- EHi}�-rStarAng!�Gz-on._�詃 vacuum)�*s 'near-�t'"�a �B �}Df;i� NorAf� &auZ�� � (ppyw�|ea,2s _m )R: �x�!�aw.�uA�M�s,3 l0ofK cite *� � �3a�(��r�, �`�$IJING�L`9�g;A�on*u���5���P�&c��,. Cl9�5Y�2�&"let�Os6CNF�E6��#ɲ�e�aA�6�"=�� bF )��|0.8\,$fm*�=�I�}_an�z�z�MofX�ex�������F�1h��1ang2�4Х "�R��1�C -2mm���J1.�J^VKfilimo6;5Jm�1�� M�are�EHf�E?V t[-%υ�%Tp+pA��B�:�&�g4��r�R�2�/cB�"�{I���J}"�J*�]7s:x�hAvs.�-of .t��A,�e (jet+&��s�OC�AY (j#A�@l�9!!�#�)T3'>�"�6 @w (!�-�"lEelܱry���u E�� Alt��:� f24 �0Y�z� � im 50 \%$�mn�'� M.��.� P&%wN;�(�g1L!wR "�7ola"S �!Y-@ � 2<',�,E��D :s������R"&'� atU stV"@%3͸e>U>� ��mJ*5 v;&��6�.~p�(ex�> � Tv)>== > 2� �ca���4��.%CGG"��F�;���h �M-�}e�E�!>"c&�ox). J<�+ q QT�!�� jet-&�#���'Futhe�|caɏ�*V" ATe�\ge&6a�8ll�:� �Be�-� �<p_&�u�?� quA onh�,>  ��?��������jo�.�u�G grad*n��2ag�zh�b�9W5��by��.&�U Uis��a� end2�> �*#His so large that i��t could indeed fake a collective flow that is interpreted as coming from the high pressure early plasma phase (cf. also Ref. \cite{Kovchegov}). On first sight, Fig. \ref{angcorr} (r.h.s) shows that this coul�8 be the case:  �in-plane $v_2$ correlations are aligned with 1 jet axis,?�away-side bump, usually attributed to == h!C8 (dashed line),-vDwell be rather dueAz capeequal-��(%�1-�q� )<,Schafer78}. M�One mayqaZsoundB'expanE� ��U$emission pŢnQ� &I�[travell��Oway�Hth resa�a�A��:%�dispers��w�pg!�a�� �)Cof��;M� �"s preferic �0to an angle (^O)Mhis gi�� xr!��MD ��'5D, devidE��:c �hot densU1res�me�{-�of Aa]a non-i� A�ng gas! �ist��assless1��x$c_s \approx \frac{1}{\sqrt{3}}( 57 \% \,c$Ehle �-lwA � vector; � ons, h= c$�n ence�e9�%�Q��g A�%�6����� -D �. \end.� %-� \sec�S({Summary} �' NA49�aboEnW observ � ollaps��both,�1$-� -#`z of� t%5in Pb+Pbgiaj @ 40 A$\cdot$GeV, �$presents fM Eunc1� order ph� transi�, in baryon-r�_E� me� . It*Lpos� ��tudI�na��e�is.Z���pertieA�e�P� chir�WA�ored 5$deconfined �!? at< forwzu a�n reg�� at RHIC, E�up��< nd/or sXd�K0de ors,� c0new GSI facil�2,FAIR. Accor� 4to Lattice QCD� ults�o@Fodor04,Karsch04}I�r�occurs� chem�m& s ab��400� �u� UsALMo i ,�Wedi%jin�I$Hofmann74, 6},�a�  signa��r av�-/ ��IGEBi!� . A cri�<��cu�3m�ui�. as aMometer%aP��%��$tate (EoS)�AM��AA�we� at h� "V �5� �p@explain $< 30 \%$[z1d ��p�W!aa�2$� -  > 2$!�T W t? taas 2�Yprodu�`ksuper.��E�ini* a� wayM�$, $p > 1$~� fm$^3$.��fluctu%J� �ύ�e� ,!>.b��Pd. Ideal Hydrodynamic�fAfsz theyalargern 5!Q � � )�.�E�@e QGP coefficient!viscosa��be a�rm�&�P� �M"�.Z5�- connAvo%|�a���sup%I,has been exam�i�oven :{| !S>�is nots�  miniq6���theoree4l�cmf6,.�can only��%$($<$ 50\%)!�)vA-U*orU6� g ing.2� �Bs�F?�Ŝas"ch in� hevE��6��, � at $\mu_B�4~400$~MeV ($y"�4-5$)�w!�� �opr�[E� -�alogous!�06[� -- &M seen. Fur�mor�� of Jet-WN� )@BowaScks causIjetu�A�for3 ��!�  f v clu�H� F%���por�uD�}0Quark Gluon P;. More;, w�os M{chang�� ��$v_1, Xlosa�,o beam rapida�is � �o%`��� of a�7�-y.# J�@A_)�,at 62.5, 130�202 �z4 \vspace*{3mm}hlik��Rthank W. Cassing, A. Dumitru, K. Gallmeister, C. Greiner, K. Paech, A. Tang, N. Xu a�Z. Xu!��ir�a"�Md%view.��  "� *{R� ces} �`thebibliography}{19} \bib��} ��%M�S. D. Katz, JHEP {\bf 0203} (2002) 014; : 404 4) 050lm" nF^rsch, J. Phys. h G 30H S887.IA�tty80 LR.~, P2Koehl!�@Larry~D. McLerran u rRev w@D 22} (1980) 2793.wDate85 rS.~0, M.~Gyulassy? ,H.~Sumiyoshi fFe3 e5) 619.dKoch86 dP.~$, B.~M\"ul�$J.~Rafelsk:cpt �14 c6) 162>greic87 dC.~Q�p!2�$t{\"o}ckerB�Letk58)27) 1825.� k8k k8D. Rischke, H. .j~P. �INB u8%�2�Bravina uL. V.  {\itQ.} \=�IyC 6Ay,1999) 024904I� NuclQ� - A 69�i382/Bratkov0m^ E.~L� skayz�eo C 69u054902�Cleymans �J.~%EK.~Redliuc� ^.�]8.�,BRAHMS_PRL03 a I.~G. Bea� vM] 9!P,2003) 102301.eShuryak `E. )�2r�A 661Eo!�16<� -qJ.~ Ad~St\"oE�$ W.~ScheidImWy { Re�5/workshopN BeV/nucle ol� of heavy �- how%�why},%0�< Mountain, New York, Nov. 29 - Dec. 1, 1974 (BNL-AUI 1975).0 �7�#f�(U.~W. Heinzr���]=�36%i76) 82Landau)�L.D. �0E.M. Lifshitz)�${ Fluid MeCicsq{ ergamon P?.1952St%�79 t��\1�.,J.~A. MaruhnF��(rog. Part. .�E^����132� ��oB�~u���f=`4o767o1�.mBtZZ7%�81��62[2[ v]Fx C 25 [2[7R%M���AEyi.)�-��)�13 �6��6�sernai9ML.~P. ^D.~Rohr�� ^=qB 4ͬ�=454.Y J��6_F80hep-ph/0401002�Voloshin%aS. , Y. Zhak k �ExC 7�$1996) 662OSchmidt9��W��J� TEi Y4)P93!P82.�Mu�a0Ef � i�H��Ia�%�Q1!���32� <�+a ` N D.�.� 34902L <03b%G�O449:fn�ngMM. MiL E6R. , �� -ex/03120: rachmann9: J.~J�B]A� e=97) 392Toneev!= V�R 6W �th/0309:� Kolb} P.W olb {8� N�9��200�#6? ,Teaney} D. ,N��3) !�12��� 1} ��r� 12228Nara} T. Hiran�daA= 4090420�!�'M"6M��%� th/9908032� Hartnack8�oC.~JIJb49a+$1989) 303c.zSorgeE�� FdG 5� 95) 3260Bass9X S��:� 6�V>v ��!R2'1XW.~ eFF� )bq���A30A9^ 6�Weber0٘,NZ} ��%�x� C 6� � 01� .�An� a�&AP J�v]��2]�i~�](i�041602� Soff1�S. , A.U Bleich k 1)%�W&� �}3062 Sahu �� . EM EN67A� 2000) 376.~H-��.~ YQffY71 Y2) 352z��0$.� NPhD�sis��! oeUniB#,it\"at Frankz am M� �.�i1�.i1�~a��A\N?� Tr2� l�K.~e�Rei�A.~"�2 1Dw �J�68 � 1) 42��_v2pr4-GC.~AlN}Ja�msa2$q�vsR�7�Oi76L]1�])N%���36� Larionov��A� 1� =�R�M�!� 64612cXuu =~Cy�*k 6272� �m�D.�  �>�.R1242+)�U9�&T�V22�Aguiar��C.~E.  Hama, T�d �T.~Osad�AN�*s632ps��J��9�9$5.�PHOBOS-�S{�/ .�J�7M 32CGGIl�g�~2�!-*�e�{.i}�s A 73�20�2V &�q�M�0b23di�2X 52O ��6�Tom-,T.~J. Humanim��nV06�Tom� R.~Bellwi+H�ine�JT{ �l -C .�!�6.��oyŁ��$, N.~Otuka�HA.~Ohys�6012JAM)�Y.~� KG�� Niit aS.~ChibM�)f�)�C ���&22Zabrodinq�E.~,�,A2 Fuch-@A.~Fae$�rj 5�4�2�(STAR_v1Heta �An Taiq � & C#1#IR��G �.�86Oiq2k>w m *:o)�� 40506�q SQM1F. m� ^�procee "� "� E��92 : 6�Kai)pK:�e�Z.~Xu `JZ* <5.PHENIXm�$S.~S. Adle"���JZ��4'2'A X� dams1fU.V�u9�V72302.�E Wv��Z0Z2�E���W2� Kopel� B.~Z� peliovich� ~Nemchik Predazzi)�A�yashigaNo4d�6oPYTHIAIIT. Sjos>d1�I���ComputCommun��1�f1) 232�ID9;L. Nagle TN��252�A6 �� ��]48M��6>4A_UrQMD ^&W1.�J�.A 26D(StarAngCorr ]j�^�-�3) 08>� KovcP3!�Yu��K. Tuchin%�i��gA 7��4���"y-; D.~)� priv�%cEicY$.�&},A�\"�,>�B�&6 mZQ~ �28h 1978) 34 �)>� *doc$30} �X% *� DO NOT REMOVE THE CLASS OPTIONo#(erscriptadd�< % .PN pendA��sipar,9�a]4n f8: (MF)&]1,!Cm�I=cc�#�3f5Q ntized sm�;8amplitude oscil�/ (nam�+a;�$.v) abou 0 e MF2� pointeR8Bose-�*wo-qu� (2qp).� dr2�6eF.. A�ra� (! di�Ephono�.c�;on���.duced �dist0s4 s up��8lexY< pa�>n9U�dV� s.\\m�is le:�,�4��ewAHhod }enA(2for�a}!�2��9e.-0f freedom. O�":�8�>hus� perfect6h! !'nY== e.g.�3unw�: d ce 2.�7 (�L ) moDas\0 plif[in�?~1 oK,2FDA�angn;�� (a.m.)��!Q� ͞g��X7 h2-Sanyway*6 !e.�J��An`?-P"[ U3be�3da m; genera��s a�ak prob!��t� 66by swit� g ofE6.]!5� *o )�_a{ al"�  as^ 2i$:EA�n gd156.J+N�� G;}Mode2�� i! m�a s#6a�4�q_M�!�M1F�ӥ�0us $^{156}$Gd��ro� ng�;�Vd�<��&�� pair'"��7f� spin�quadr� � S��:F(&�4�ec&�$(T=0)$ a2�J� + J� $} ��u'� � ,� $5�ed. Dot!�U: ��any&�B D�Cd./ Li|0� �� add�9%X!>�� Z;�1��?'"6 �-� � ed. gC,1t�gZl�� �draI[I m<a��4 realX< be�21GS*�;. > 8;underlyA% idea?ou$��is quite O. Let��� �:a��e&� F$�� byA��a incorpo5>s i�if=aiof 2qp�E.v>n � d�%o��or��:��z termT F^2E6!Z�J��Ea�Ha"��D�Z@n shift arbitrari�5e u$ frequency�tun{`"� para*9� $. �t  \r!�0arrow\infty$ L>�gets so�7# 4�R�2�becomedE�5�i�A�24�Frozen A�tnHns�AMF� �is�7riI ��mѥ� A����y�9�6rum. �>by choo��h pri\ 9��8�r�E.SAcs �>be�ѡ�e�2) $I�). \\ N�Ie e�ti�Atep��a+deqA�C` ketched u� �Eknown �5�.y \ [ $, Blaizot}��Fiwh&group!["�1�(s $P{(r)}4:Q ���E!q:�assoc!Rd )�s (deno!�b; $PQ$)H). Exs e!= such��GfU av��R$}���  ��I $N$9�W�!�0$Q_{lm}=r^l Y $�5 �( �2B 3�7} )4(=i\sum_i{p^%7D_i}(b^+_i-b_i)\,,\)T= ,q:,+,Qaw9wee� rictA7 selv�GtŵE!�� �7 to h� tea�1E-� � � �� �� c.r8$ �M" �H$. In eqs.(1), $b_i !%$8Je basic:�| treDine�as bosBobe�h&�ely%�N 'aR,(QBA) $[b_i,�j]s:�_{ij}$ :K}(n &F�a�Hplicit hica m, eq� �Es~A��l"Z� "�' $P$sA� $Q$s��a qp �s=: ,!�� subs�Ct�^QBA. Po�AED zero�;c j*E"q%0k{H1� E averagFZ� omita�si�">i�Mevs�+��s���be $H(b!�)$65I�IA��3 ^�; �)y n�;ly%.pp�8! As � iopBiAE&k�L�t���duFEFdd��e�'%�A�=} sum �qua���1bs aI�Oed&�Jqu%�PH'(� ) = 12+ �9r[{�u^2 + �S^2}] %[ . {r'}(')).>d� :F��$si�th;� g�C$E'_s$ �� tru�Bby�v�e �Eza�us�}w} ����dcl �A+ do h�In�M��.� �n})�A}tui0&� aa!.#A�x 2) �GG| ing%D"= �mA��E�y �@1�M�!(e"8s)iG� chie�M=?t�daE� 2�&� !I� ex7o )�8 puk4g&i���O" Cq� � es�"�   it w�O�Od,�,!`%V:�!it q�2�`�&GalilXinvari]� T�P ess-F,}. Similar r�re�s w���ul���G~ �h�A�&� �IE0Marshalek}. H&@S�Pop�s�M��Cpursu��� �E��past.\\E�� onn� A���2)� �AF Ae�E�Y8E� cruc ��E�Q��0E�� MB' $"�  � .H.H'y�= L�}{�^ } =6�  1Ռ/N- +�sb� T2 % +��>��Eobv  �PoluI��as�;!�!�)�d�GJs��'_s�5/) $� 1|�.z {&?&$ G$�TPymptoF�9IumA $H''$AV*Gal��N emai:�'ary~. (Not� ���tatex�c �eceGlow wH�:R� � N�- �.)m8�?��2S$< eit+W exacaz� �F�Tn���rB m� G. For)ufficBHly�!5�=)�_{max} <2�� !^��vTum[&�Dmz%�"� 5��0EAV�� a��do"� � RF� $r3$�H �My)> o�s (seep)!T�.!d th Fcer�>ly!inverg� o !Ln�)W���E��.&7Mly�c28.�!l �b�#Nm�F s af�!�KeRm -� Ea� $ in�re� s: (i)o2\�, (ii).�{)�i�N8�N :  J�i�.��� (i]�''�''6�u9!�QDai!�wyQD":E�U~$be�M� up"�predeiO.JTZ �T,�Ainclu�a J���A�Aw�ccesfu�J�%���a��M �&-�q��'5) �U.&�aru�.��bre�O� ��-� Tor�'enough�.s�/$ f�V|�` U �Q. N��-p�e%AUN�Տ��8O(s=a)=\Omega_aH ndͩ^+_a$%�!j-5.�Uenq�.4=Wi.� (s=n)=\ovn6v^+_n$. S�9�� !f[s�J$ � _a , ^+ �� c _n, U ,�Mve�9 �A�diffe�U10� �Ese ortho�  X�y satisf\Me#a�re"�2 0}J{[ � _a, � ^+_{n}]= �Z6 30. >�Da�AU$|0\rL% �bIG)�� vacuum&!� =�-e^+(n)$�!�2��s $|n o$%B�#�rIm�.g BN B�]E>!��"  wb�% 5) �ob�ws J� \l)0 |)�%q 2}>#A�.!0Y�#y}��$a�$n$A��"E�� a�rec��O!eq�a�I��8\Bw ea}. " aS�� s a4 q��p��P:1'=�:^ (r)4T�!x�we��s2�}s��$[H''.�]=E_a=�$ dire� !)erm8A���ope.*=�< H_aAN3Pr [\tilde X_r(a)P(r)+ Y_{r}(a)�"� Kinstead�sol"u��Rz(2). Re.qO exN��'� �7 h�6�[ove`%Z��'de)�9 W$y eraoto�%$e�[)syk���a-x%(97- _a),"�\\ !"6:y>:+:u�xe�q�s.(7,9)ar�$�O!��1#Ƒ}��.�|�.0B3A]!qBdJ� `� se�!o�i a�.%����.��5ny&X 2�� ɂSU "5sAs�mr*�y���Xi�-e�$� l cluA1I�6�  e�[�  `2Af%�to"ł 2 �T!3!�y�$!խN!�$� ) ^��Q�� words��� 6[- �*j�is:nH{ M2  al�������� rule $S_FXa�ear��� (i�$F$~a^�)� R=��{n}|\ѻ |F| � |^2=}n �W \/v �� ��v 10)Ae�{wr��[� pact���.�u��+ P} Q^2=0E:=�!(c�te6�+I�6E -�F� R>� AD$PQ\m-�A!ult (11��&�h a to�*blockk of�[.� ��at&�,s���fixedA:�"�% [U� two�"fyp��mp�q6�.�Ş W\�Xp�g���])da�d� �)?�g2 /P $ (or�xTh#b�holds �y�=P^2$d)e immed�l�ize��� 6��a*�''e��'' B  ^+=P$&�>�s�'=E=0$�ce�P]=0$.�!3� ��1�serof $P-$o"�!*F $Q)h�� ,P(r')]=[��,Q 0$K mutBj,u�%) g" a~� �ector��� altM� !�sF� C�""�2�"�cY1I�um�fL'+"�*��fnumber+��is{ E��DA�O-�*sh%� a�t�%(��!�c6�3%��level. i]"$ce�Y).���( �-�'�Y�.�1�!� +~MF�� }+"� G � F> �ʡe2� " T6�t9&(32^2+r( ^2ax�q[q�concer� jug� 5�~) $(P,Q)A�պ$ Q=-Q/(2�e,r p_r q_r)$ hca��$ mmut�5 $[P,9 ]=-if'�d�XanB�6�.�� = 1/2(P^2� Q^2) �P !%�el a�6k �'� ^+�c�_t!ly� by�1�$ m ^+=1/\s�d2}(� +iP)�-�$=(f N )=X $Q$+ .>$ $E��$ �0R0�:UA���*=� . TaŲj.-%;o��M ��6� A�.�th!�#1)�# �E�cs-� �,2$���Gd����Fs�[�!��!g� held3 rest �'1)�J'wA�n =��%>5a�blems en�1_ ͼh*)-syn �/oE`gU;deQ;bedL(1�,: ce�rst�i."e&H"K���a��A�an.�"� � !:�V�A� �d�l�`al�.j AX 3�of wh�J)8in�nt.3��nse.06ly52�(r . Fu�^,� does* ����!ss a�8��.�6�f56��F4?� �w6ol�pa�� /G���.ar Skyrm "� �'aS.?:m�� oc"R4!܅�r�)!Gk M^��1cCn�A�:� ��-rpa}��, Dinvol�a z&�!}!.I*W:" � ��m�*�0�y6&=�("�equQ �5ris=.nto� ly ��5��-Dcc]ew  answerA�grpo|v� "f�'2�&�( a._=�E�.&s4ciL FT-�MA�in/5� in�Y!Z  f�;1���>�)YK� ���1x 1"1���4e� D&&a^n�c���Dall �&�b true� �>:."no� E�l#0a��3 5 }z@ B�.�.(,��.c�4a�e rg!���3\6:�.�i�OM� :���?(ce�6 �4 $n=100" up�uva�of%"�  @���.kturZ 2���-wis�!� of} �*��C���=10^4$*g  rSc��z%-m��t�!.�g�c:g��'-k,!"��s" �'IW��  goody�.7. A#-!�ʑ; �$]{�ys!ake�!:<���?r�(Cche�X �eb/s� �e �6�8<��&�$a*We� nj/urg!��a�l"%c%�? imo��sf (1fa�j��w= �= stig HdP%�RPA��B)y�"� re�7lyE�!�F�8!U�hQ�&�@-A�er�'�j"VV _J�%, 2Bbha���fnd1Py�%ng*u, w*H6RbroA)����uair*\6 etc.!� avoi$wc2=..!�!���e�*e'i�ac�t comp�+m�*>.&=� ��� Pjat'RiE*�(�8�.ucon�5i�� {l5��. of�nz �&Q6rI�.ls|3use0>%��&c�-�BCAM�5�b�ug�e_�@$Xhnu$". 4l�Cic �@��@ !)�t�li�a jA&e1i7  �<�2}M4 obso! ��a�o rb!� �13�1�A,3m} -\eta r�A�5A�di�n �hamamoto&�(A3!�nee� ��9{~2) "{ de2�8R$?1�,�ay("a9-l B":�%/ nly a b�E} %2) !; r?h q@A �&;d��*�) �nD Q^{2}_{2m=\pm 1}=��J_0@j2" e�T#A] �H$cipal axes�)�I �*.l�B$|$"�3$J$$|�T�"�.e�s&$ . A.'�&Gu"i".]a�Z� zy%�y�-6�^2$=0.i Llab=�0fix�B �_WA����.� fst�zle$ggY8?�}M shap{ dS$en2N�l+�{*$� ��us� 5 �"o� Hpan impor�1 ingredg��[S!���sKC/H wobbl"&� sYI!� riax�<K���iMAN7And�u@a�A�E�1�f�  �the�#��be utiH�@���MFu J adop�"�$ext�, s&semimi"�Ce�l��at��K he StrKsky sh`�YrL}/. �0< 5}" �ms �� ad���,"7- 22 �adjust� JM y��!=!����.�s� Ethis � n%Rj5�f!�5$�)�A=�p;!(:Eb�u�er})J�.�~qper�� ��!*d b�D&��j#g e� �,MFl9nd� e. U�2a�i!�D ngE�i� ���'\�%eedUcIwgu)Es  � %&tB� J.t�e� �M�recDped��a!�c =e=is&k*�!�de�2{:1A�n&�E!�Fi3?S� o em;p% qZ�0)��[ =� lmostC�=�lal �@q& B�E��A�6��DIn16z�G!�7 � �.qL!$ �pF8%�g��} �i_Ile�&� ią���<�oJ'� a�%�Qh��'!P.#E9�'-�)O: a hug�be�DE��'.���Mu��v"�Ma bF id�f�of� �Zd%�1�e�r m0I toryA� >rell1eW%bV +&� �)�"��. i�K��m��d ނ�  %An gm�open "-i6W"f�2&mdE D%q��he Gr�v��'3��!�� ach����P ac[4led� s!�y��thwile!mc�y�;Dr.@g,G. Nazmitdin�l8Tl�>�S{�_"'Y %D.�X ,hUNbmar�Y�� ve M$G} (Methu�London1m0)q�r P_p�Dnd Schuck `gdMOB! P: } (So g�Ne�m198:g�J$} N. Paar,f{�^ Nic$\�0{s}$i$\acute{jM� D. V�Pn8h�r�[ \textbf{�d, 034312ls3) ' �0K}!:Kvasi�FdF�, .NV`9`1304(R)c9�.�K7VS4s,aN9��A. Puen;2 �k B 68k 5341FhBM}BBoh9Qd BEPM5Els!�u[1��cM } (Benjam6Po1969),qk. I.J�  I.6� ��^agawa2�g.�"}044315�2)=1GA!�PB_VAYGA�pF^ � Quan=NT�yyKF>1SgPsA�@IT, Cambridge, MAA�86.rF�AYJ. ,%8,W1�21}, 225�t60); �ibid.}'2}, 78&1.w&=7 E)�N7�J�.nesa?Ann~(N.Y.)9N53}, 569`9)%< &�-�-c�.YK!!!=tPm�]I�fzn nda�I. , Yad�z.�!70�752?*kV. O. Ne�N enko�[.nP.-!�einhardt271nC U607Q6�"{ !�R. Jens�p[2PLnuV8a�142503T �%>q *�V�I% Un� next�&��AMS foB��d %._W iopaA�( %\nofilesz_�X12pt]+rt�$X�$X .��T,bm X8TCIDATA{OutputF�U,=Latex.dll} !Ver� ,=4.10.0.2345HLastRevised=Friday,�se�03,(h$4 12:08:189�!�9+ a h a 1 .?aE67 ��Z� Adq(fWDbEp.X8rjl(e�tai�3�� l!��B,M��cM�-�4}> re@howgz�B%�UJto�2~doA:�1J[Q) �-?�a*�2a�,�O�,A�%in�P Ʃ �\)� p a�rw P�on- .8.;3ю� 92�9�e�.@J�Z"0H"�B> SalpU�E Hg ey�~th�F~;s!�ev�"n  �"6�m{�%re�) star�B�#."V����}J}"��Phi_i$ (pworld6ar.�1s� 0e"�3\fl ~\x[Hcal{H}_{i}^{0} &=&p 2}+m �j M�06P 0O+� >4(x_{1}-x_{2},p  2});�i=1,2,���ifa� waf%a.9� :�t�� $\{H\Hh\}�K ".T D.=�Lurn�`.X&�svy�.� third-law[���Q�} ! �= 2 %2\perp %12})-U 0w}5uŢ}<)S(,�\ 1$a�DdXes�R�A``led'' !8on0 $ !� �0}=(x_1-x_2)_{�}$_i�\re�h�@tal"�^�2�_� u!��W%�e��"� �7.q4} �d�P� minimal�p���0�as)&�ffZ�)��a��,�%v}#�TS����o,gamma _{5i}( i},� (�x-�-{A}�o)���. T)U=0,�s; �T��a�R�($[2�1},22}] Y$H "��d�"�^z�I /"B�9r e!O�!�NI�(Ũ1��`A�a6� each d��AOl7Qi�It"Xs $A(r�7S d�#9 �j"*0 auto�!c�$o�W�c�! �- ��oNilk',u�9�ݹt<{AE ^{\mu } =N(�,x�� �F�L,U4!�QM�|\ MS}WSAB1}(!,2V6�bVNU!�i�>��pu6txEsx�local 4�(��, Schr\"{o}di� -lik6+m�)ES�* of lowest QED��an E/=I2 5}e�"tvi eiuoNA����f}�b2|,AE�:"RE���p�*�`&f 8D �S�Y . U� ��(���(J��!entire�S&�G" lpA�m���upsil�K ates2&2}��:6xs[?� ���%Q�va�!�&{&m�s0 &��(al� �$�Ie�N �O`,$\rho $) behC!j a G�7ton <.�d6�u�f�a�%��Z , $ c i}c j2c , unr< �qf$�1E,�)toEctN �%s�( �6a1 �a�U��# ree-��if�͡ C�%A��a��,J� fl ��7 0}=�jm+"� \&B:0 *G 5M {j\neq i}� ij& ijv  })2'k- -k^ W 234�E 3,4H * PreMe- used��'�[:�toqQaP�k\.>� i�$N$)pyax-par%�1� �WeT)a�A�1��4-o-t%�����.� 3Wnega�3 many �V*2[�1mƉ0�V�.{3i6��["� ��� Q�5M.���*d�� �-A��. any 1+�WD�n5C�#%�*Yas/�XGe�-FFreiq/e�%���9-��_-h�!�{4e!htQ�G+ tah3-�az�8�� ��Y�2 $/A!�(nnihiMЕT9;of"f,< belo!�o�FH��\2,es. Sazdjia��saz1} f6F)��?* %d|!�f�deman �!D5�2t � T&Z} 6 h�>�v 0ord�ns Q+�&n 8�7�um =��I,2� H i !� �e��!�$�+!Se.($T$)%��1nauWx_{ijT}=}+�ij� P) \,P[9 -P�D&�Cw�H{1}+p� 34}$, $ _fNjaL one assum�,�Rq�]T}C;TN""�A�sui�Q for �evs�Qe�/ws� adapZ"/s"��&o��zew%�:���k,)A�+B�JandE1let���ksNJ bBſbf{p}!O$^{\prime },2J|p 3~:> \r" }�pt�=}#,^{3�(�1g-: `  ) M}BNN�N N })BS"C�:~1� p}=\Gdo�5}` }|1b>H�b{1:1ĦB|B�s�2atYU5�3T.�$o�635�B�|M(5P})�.!1 !N==:-Pp�� O }_{Pby0\ }jE�Q})��Y$5> -Q})6J2}6�Q7 ast b� })63r&B�D �c=2�!,��Jf�2@, �=a.�uLm(!�" V-Qo| #"�$QPM+A34.e QA++32�6w�' FigDV.�L�:B �J�� p�s.�ѭ&&q5.#_{14})623});� Q}|Vux�3:Ye%D- DP}qh "�KZB&=&E_ ��q6�3Ac� 2� .("�K�q�I,.� _2T_{4L2!_{% -�2��.� 6y^V&\ �s+��HA�14}y�!1.�.� }_2:32::3.>.:9A19�ZF 6%�:3.�%Q32�?Q��*�A� F#a�f�- [ �� �,�%a��.o %N������V�1n=} R�M;/��->�(�)}e�F��: MVbf� E�}��)ѱ Z)(^B-}F^m��}{M�3&� :)}>�9Si��J�a]�w2 w32:w32.%j�� bf{+ea�aja�Bfk�1 �1.� HG5�:�'a�((q��N�-:b+�4 �.H X�i)i4�{a�&��;|=�lĦa�alo��*o �/�<�in� &>7 )� �g&j6�a6 , :�.V�%�|&Q ��saz2}�`�.��eSnT the AIB7&�;"f �(Z..(as occD�":$-o�$Klein-Gord�w� )�a"�!< �j��I��&7con*٢&^ gBor�rox�z� f� �i"Tignore��0�r� &! %.�!�2���N�� � �4�.<d^{4}PM &� |:��  ��(>@s \hat{P}+w� (pC cdot#)% 2xI.�|��h� V8� :���%9k �Q}!,I�1 U }->�\tau "`6@�z@,:�V��" I P �} � &. Mrv" � �7 UBN+r-�� )\exp (-i O�8)}"r* �] =(�eF�:N- s =E})/w$~ $>��9� %.; $. U"�RGa��a $ �,�Cw�a���c�$�uv"�n.�821 ( ^nZM"uy"� unit��$[ux,^Q }�.��i�e�"�I \1" w \left( {\�VT8-}.?2i� n�) }{ (2?A)�}}E&i�. 3X��} _{)��r#�"Q� ) \]�2 &���!b6�&�Q�& *�Q�|M �5' �z\\DF �- Ber )(-.6 �n&�4}xu^�i� �$..7412 u+x$2: R`'5`"1"� d&zu��+!dF��ll�=its�d6i�e� until�O0!�"�so$ Ie��"&�2� },q�X^�.�.� |%G3 T})66F��m2Pp.7 }�4�ca?� ue�>� 6� "��>; "w:_&6 .� .�"� |}V\� (xAr&�)|6� h2� C�:2.�217��/'j�\ A# bra ͻY/�� 2yex2<& &UcE�� A��6�lO^� Gw (��㙏�rs�m)A�>:8} �a ��fSP_v $*�q�& & \! �6Eq�A�=�  $9� I�=� . };��� 12}, �4:_ Bp�ib[��\�Q : �� � ��(}234�X"�& �F� +J �T}� E�) EE26EF�5�� �h=5 h� h3h)�>�=k.FF4>F� (%!234�� B9Ou�Jstu0�*wg!3u�.�eu��e�u�@a@tY+�m.um. &H ͮ� '0 ��pla� �U�,it�; .�MaNq&Qs6u}2 �_.,q_2�9� �FeFm+ � ll��i�i� 32���o�y�eb Z�^�'>1�a�~�:�6� E�1I�� � iv:�9Zon}� .�&6Q.Q.iX�m� � q.Ni�.?9m�9exp (-­��&�O( t!�I5$e�e���yi�8�c�5�indiv����s �o;,�Bty�me��w�-v�'e�'q���scr�X74�"�""6�b'mannem# dum�? J " :Ga�.�.9� 2R �R F3j��i�. � (1+M� )z �22 �>Qis��IjreM{2�hyp�J�%of.}&� �X thro�n*3o�1�1�1� >:$�? thuw a hy�@�6��E�6� 6a P&{d&�v($� $)�Y�"� �ua�$"�$a6@�$�'.VT1i�(1bj�7�$ �na�+!Mf�*�1b��)&%# Wei� 7H�"` �)s&4�,d !Y�*d*�[L&1(g�{�3�:' =Y�G�10in Eq.(\ref{a��F1". u�M��Q_�Q.�a� & 34});P^~��RQznmF ��<B�R+{ F5�R5�"��u}�=P-Q� X!  (FR�Y2 .�= �2� /A �B� VQ�}BQ"*psi� Q_�(n�r�6��psM: (6��\lbrack%31.�-�� })_{T}]5*P!@R aim ��fo�&�/&�($,� �g2  ||9 &�;� ompu��Y"�;O�W�4. "w50.5cm}�i2�_CA" I@�?vv*F3?Is  y�t�G_�T�D"�> �."�for help�Udi"ZI��C,-�<v=onkSNSF�3�At�. No.$-PHY-02448�:���>)D6�I~=�Matsu��!Gtz�DL2�DB17�G416�E86)!jb�HAsa04�EAsakaw�ۯ^d6rG6X92}, 0��>H42YPetYP.�reczky�E#B&�EDG} {30}, S431-S4406E 4); P. Pe :$ $et~al.$ ܳlath�12.�.4}��Y.� .�� 8020.-b%�%H� � E.Y1MJDU�4kH 131 ��2hH�  C.~6NUt2]C] \ \ 65�I1w�% 2�G�=1}!�W�C,�FL�*D�C.1v P. Van Al�Me,N JD� 5117A$9Yq& G t26tNZ:�4D70, } 034026,�4.�H X3} B LiU�H..�\ QRev5#C67,}��001 (20u�,!`��re9.UY 'reտ iCg�a!O�" �7*�Oc'xEdxE�<:�"8� |r0f\ II�x �s Math�J,F2�I 620,�80%>}B�I Δ:VI"ǡapsN� nofo�a bib,V�6*�I def\CO{{\@8O}}r$f\OMIT#1{{XDslash{D\hskip-0.65em / .cb @B0cb Tq� ]B}f 0Fsi{^1 ^, -0.03in S _;��siii{^3."25 #1 �dF#ED "% F:f4 C0}!Bg #1#Jg#.gpi). {\pi �!2%1�.�V$54N%p�:N37)�P nopi#rm EFT}(a).!t "dF#newL$and{\gsim}visesJH-0.7ex}{$\stackrel{e)style >.�i7�!�.Hl�H<.H)�tr{� I�e1�trs2�J!Ttr{di-b��M+*�d*�% �?!t] %\vA� -1'  % E�{\a<x=1.A�!( logosm.psA�%s T \q�{\v, \�K$UNH-04-07} NT@UW 27} �K4 \phantom{ijk}� kip �  !¤DVCS-D"H�4�r Deutero\%"F$EMC Effect�� H�Silasl�ane�K*ɤD�7~KNew 7ppshire, Durham, NH 03824-3568�@.YJe{Von2�K12000 AvenutbNew k(s, VA 23606U����Mܑn��Savag��WO�ngt_LX Seattle, WA 98195-1560v=$Ce�E�  ore�p�[�Q C.�Q@ 02139.\\ \qquad !�v1�>��a4��in�%�break-���d1�dukK$deeply-vir�r��pâs"�4, $�>^* d\.�:?,^{(*)} n p $+���% �g�!�C�d���yL#"n�Uon&�a>����<�8�'A� ["!,fьRi!~�8s "5twist-2qW�b�0s�͕h0�L�fhE# ��6�"�� �P. ~po4out��b�to�?-�g��N�)� ��Ha z�/;ӑ!��]ongJ)(�s �|� V ��X0G!� 9�. A��?5.(�2�deBs o� �� 'E>*�A"?"�4A I*z(E �@2o�9. Ex��al3iLs <zi�E��i2��g�a�7��2w)pl��oM=1�u�:Чnq� A na�9glaH%at�@ � sugg�A%��E~u�a]"-2^A�a��Q%E �N�A�\�ern!�A)gW.>`���w*e(� mark�=a� r;�ak�y[ <�iU*be 2 e�2��m� weaklyY��^�HsQ�: bong+�����,C�\�>&ry-a��hesembl.Pc!�O9�u;: magn��M��v�eCQ��ppr>D>?��ndYR�re^ MQ ^!�-N=. DeB� :�Jv,pqmAEMC��~\c note{�*@"``Y�''�%Uf��toBtb�in �i��$A\gg �k HereC,C�Ke.�-d1�!To>���"ent�@extB\v���8Ys>N M y"��.��)e�lly 6�~.0Aubert:1983xm&.%�i �i8twenty years ag�Z&�a g�b7�l��C�, vaTrneodo:1992wf,Geesaman5yd,P�Tr9wx,No��:�cb�/"�as��t?do��, albe&�e�>�ct,.-��&su>all��-3ab6>o�mod�c��6 �@em*A�Yl &mKiL� Y�`� morea )r�?x!�!K�.. Sign]`ntoo�OEgx!irG]i�=� S�:����Adg�i,�wRef1�Smith%�hu,St�ns4y%���&_�unc\w1�nta�>�lP�Uq'Z�s���Tn� �n=e! ect,��KDFca�� al0iE�3 �q�� ѣ��)�!r*49ls�`YF>m�`ishB��E"i pAn ��H2� BNo�ac A4�s,next-to-leadAH&V�Ks>mvCheec9tnaG The �Rrepancy�bw�a"� �.(f�AFaK~?n�E���\o!ot�)��^at��}��+es��er� n Co� waveAj-Qp �SX���ayaC c�sq ���o`exzW�R sm.}Bqb�cCb$ $\sim 5\%�.��26rI���eͭ�Aith-vframeh.�vHa2Fy , $$, %xeask8�L!.��d ge�^ . B_2�% ing ��%�] ")]�vre\> I>2 )l B� ATMi-�nI s,eks��ta�u &E����kecl^ 8�n forbidden!��]N  F� ,6? musA5���ile��22��B�AQ�NLVrpr%��_ ome,!5Uzs abs�tI9es� sB�Geork?#߄e dowI��gga �P>J*x�*!$*IA�e��-�%�an S-aHa^���F�L�z 3 \, q  xT)\, +\, -1  ^"�fq} !x�\6* \ ;ƅ>)2��A��\Dz���!# 4�% �� \,�\ ^6q$%= /Te� (�  )7�d 2� $ �q$ $( .[)6�ayhe9�y6D(w�J �Pe .e�qJ�(.v*�From QCDE�s�L� & &�t�T&{ksu�B M ��6� s,R�(theta_{V,\ 2� 1 ..n�3 (n),�Z = & (i)M� . \ � _{\{ E}#&�A�&#}{DtAu_2(...�. n\} }\ q "5+ ~�b} ����� ��8^b^�A��������_5������B��=�AӁp�eq:� twoop?e1�"(�:�S� en�u, $\{ ... \�3r.x mmet���r�9!�|>���5!�a�V$ �a � :ss��OP  cp��x�\= -loop .�^ �KU0)a.� Arndtr 1ye,� 2001eg t nb pv}�voses_k���e�aed9 QCD to �{hed�.>pgr=b��v-n.yi,Beane;2vq�W "c"Z&�� si�S| In �r)6u���� se&1 , offB�&� �.e�Belitsky�jp}"j iss8soft-�6 Qd"� VCS9�!�l:E$3jm,Guicho�ah}*Y*errRmad�P.�:9E�}hU *�Q& 3jm}�rep%�ed ��&�K4�4b�T� !��� aper&H��s!�{un�3�s � tM�� h� D�taneouբ:1bus�A^$dG--J=$$g_A=1$---� N�le�Y���E��%g"�W ���toA�.}n�> �e�te$.�Aau��� gy�4nsf5m�a�t�a�E�er ig nopiY�I]i��ergt�gi\@Vm&W.eq.~(5-:")" >�9S  r�&� a�� & M&��0a � � ^{(0)}}�� v*�  � \��\{�*�N} N \ ++ʕ޻1���\��z�v���A.�%d "9 1r2!o -�{4 - "� NS�K u_n ! �����.���\ >�R�!�2�"չ�Y}=>�"�R x^{pG327<}=( q5����)$p$'th>S�wB� aj~- � PDF'�FE/,�p&y��"�� R�!wr� � (�ef�F��e nucleon, respectively. $M$ is th#�a mass. For $n=1$ baryon-number conservation gives $\langle 1\rangle_{ q_V^{(0)}}=3$; isospin-co>? f>1>L1$; and matching to�Paxial-vector currentsv�A^ �g_0$,Fsi�t N� charge~\footnote{ The ``$q$'' subscripts on !6opera�oeffici�d in eq.~(\ref{eq:isoscalar �}) �2#ptwobod}) indicate that we are%v ider�(matrix elemnof�quark�s only,%9not"4purely-gluonic+ --includ_�\anomaly-- which mix with>i@under renormalizaA. %:N^< defined here, $)�I�refore !-($pendent.},IZ,!�E,g_A-�iso)l2� �mT four-velocity is $v$,%�i)�)drest frame becomes $v=(1,0L)$. The ellipses deA= terma^at%�,higher orderb!�aM|ve expansion, suppressed by powe!�Df $p/m_\pi$. When2!�8parton distribu!�sQ!deuter_ the simpl��us, ia�22Q�C 2�F�)��De impulse approximI Give)XY structuAitAclearE� one �y recov!� naive sum�con� from$ pro!afpneutron. However, it is alsop!<eff�# fieldory.�tA�%�F )�-dime%�al�s involvagmA� %}onsIA leaa�-Q#terac)�: two-8��X % \begin{eqnarray} \theta_{V,\ \mu_1 ..\mu_n }^{(n),0} & \rightarrow & M^{n-1}\ \left[ alpha3,}_{q}\ v_{\{ T} (mu_2} \ ... g\}  I0(N^T P^a_1 N\s()^\dagger  . \no�o\\ & & H. \ + �bet�0; �� �_3b�!�� N�2>�35:4!&2:27{!Q1}j�"2!s% \-�]2H�a}j\gamm5t!qX i \varepsilon^{abc}\ �  �%�lefQ!bj!c R�A�� \rho.� I���{n-1}�:!�n\}I-E�)4e4 :�A�%�I�B{ A-�}1�b�r� \sig6����.�n�1 �4 +\ {\rm h.c.}A�( \ , \label*   \end��w�r�� we have $%F^{4_{2;q}=0$ (due' ,available Lo z ^ es� ~�  $)� _q=2m0 mz� q8 1)}_q=0$;ŕ�� �  $M� A$-2L_{2,A}$H $5�  L_{1P~\cite{Butler:1999sv}*� �cross-s��ons fo�xe weakAintegr��i^B{ o�.� : proc� � * pa? ter $�.5 a� �#)�*N / ��m$es ---toge� 3�%��  ?�---A!+(strangeness$ent>�.}.� objects $��-�P^a�31tKaplan!t 8tg,we.sz}� � S pin�eor9�!�m ii$� nnels6� ,N �P_1^a & = & {1\over\sqrt{2}}\ \tau_2\tau^a \oti� S_2e��Y P_3� \ = a�= > 8 \, S.@e�N�$$"|usual �" y a!no� �� s)�2�!� suchEs-�A} N U�can bk mputed� 4aightforwardly�  $\nopi1�Che%�,9tn,vanKolck!�7ut.oE=>X  thY xn edi< of.�I do� vanish1� icle�-shell%!isT truee�any!2sisE� �� 1x� a| l+\ e off\�always!2D eliminated. }. :j conven!�switchƉ]�tf -]1= 5 di-��M��yeD6nv,Beane:2000fi}, Tt$, inMV�,k -�E<finite h �a�<umm� IA�is work�� willA^8cuss relevant als � \tr\!�%sm���,Ando�4mm!_~ZofA ��adegree�freedom� �[ $low-energy�� ong ��"m � 4$|{\bf p}|\ll w/2$!  describ�a Lag)&d� tyA�%LormN�{\cal Lo �� N W[\ i\E�p ��"r lagSTZq $N���~annihili��6, �h� use3]�$� =(0,t_j)$�$t^j$E)�� ii$ E�Ra 2�" -index $j� $s^a�I�G�jJa�aThe Q� Q�>�).), a fa�m�1 @XP($2M$) has been absora4in��aG�nio"a Eys (% )��S-w!f2�!enhancm�:�"Y�(am� , $1/Q-Care tre��0 non-perturba�'��%�2yő0induce mixing)�ntial �s, e.g.%�ii-\d!�X ing,�6�at��st $Q^�vnd so�1to .� ! requirA�*OK��ingroY�scattc$ amplitude� bothlchy 3c�aw% app�in6-M4�and�beN�}N0y_3^2� 8\pi� M^2 r_3F � $y_1^2\ =\ B(1.(��� �[MP�\(- a_3}-\muW)�E q I1JI1JI1BI2� defs^�\m&0 :l!�lJa_3' r r_ 5� length�.&� ɽ�$\sE�-� $a_�  $r ZyM3�Z� "� . IBptwist-2�W� ris� �n�݁�^a��ѝ \tilde "n� �s�K_a��E \qquad "� �5����t� ����M�Jk��g 1} t2�aE ��37 :aJ��"u5�:�3bc���99s_b1;" c2�Qtb�rr ���ʔ\ t_IV\�\ � ����� \�||[\ yV��M\)��{"h��] � .BotBuW�>jI\m�1� p�� ' �:'$ Ael"S- .WZ 6$; � jN%�N2F`g:, give` �I|�q=-2\elli /2M\�r_1�o�b �1� 8 6�B6��Detmold� qn}. (Recr�-  show_atpossibl� c���*%"d�#>� Yt})(lattice QCDama  us�, background-{  methodm6�,.kw}.) &� figure}[!���\erline{{\epsfxsize=4.in pbox{emc.eps}}} \vskip 0.15ina�� nt \cap5 {\it Di~m� ?tU atIvid),6�.6� �L ZWF�)8� ,thick solid �s circles� Dtheir midpoint cor�!o fully-d� s,�!�h�in \676 sz The �edw6.i�w. }�$fig:em�.)�.2!��-� % I�now>3!\do min��N� "3Y�between5g state� Keepk � !P $�  L�2�fdQ&i^in Fig.~�!�� Z���!�E!*� at mo�!um Qsf�Cq}"B@y!*�l9# d |����\ | d \� le � M"���U�[\ 2\ �x O e_.�#\ F_C4( | �|�)M-\@ \e�� �  {��m � 1-`� H]$ :�I�A�9<a#ex7!Ri= n a�. $lectric� rg� rm � BI F_C � )1jJ��a?eft[{4 �9! �tan^{-1})B{"� 4 L}) )\!O1��!\2�CFFtoF���#2 6 ha�en made!?licit�writingF[ :�c %��2�>k Q! B"-�.�etadefB�Her� se�ly�AV�1��~" funh! (firstE; he sa�e bracke+2 #A�))Arac�ani� a ja6'KA� (sec��er�d, �"�"e origi"AEMC� . No�����2� 5' (� )�e�:�1)}�Z� D6"F! entiq&h nAT!M 6�q� z'�q�Z2�i$; as empha9% Ref.~�.$�#�4a peculiar feag$T"&(unlik�@�))+�2�#local_١A[ain� 5�>should�pre�as:���6&Rp$a�&. S�$ al p4sHworth5�a} ey bApoe�v!� onal�$lan�">Y,: 1)��ist��i�aF(next R �Mq�&0 X�E:^syste& callRw(ed se .wO;aU�A�variou_�&� �i�)�$�(f� �be smallM,*�};U]icKc�th>���e!f$��^2/M^2$6htJpp&*�re%k� A�N2 g�'Ůac�%�va  �)�sIW �%�) Dt$. 2) ``Fermi mo��'' (or�&�'Dpriately, ``zero-E� <'')}q�,�M*e� p6|;�_U��P ${\vec p}^{\;2}/2m$ �� ��Ton&o ��!�allI�a roug�* �-x)C�propag�+s1 2��. 3) Asi�,ed out above7()U6� D-AVe admix�}s�eraI�e �BG eG >GJ�. ��re��4lso a ``tensor}�''�A��d��"� �2�&0v#*m"��t#� Oe�s� �ran �,�  L=2$!�A� hadr�,�� does%�i�*e/ DIS,a��)�,aAA�:� , but���CVCS� & polari�, ��fi�))�c��measu_af!�O on�n Bedu td t[ Uprincip� isQ"[ [. ExperE*t�*, ch a}j �!Dbe easy. A differS situ���P!!p��Cţa��v W s du%�� o�!�modif�.N#i8]�+ �>x�+Axbreak-up{�5*�$y0a��diS5 �_$ $e+d e+n+p$ -�8$1.5\leq Q^2<4~  GeV}K� e, 2 *?Sargsian�$2wc}. Devi%>F���n) on�Ti&X ��/ ed r���ys�Kirchnerz 3wt}���Freun,$3ix}. }. SAd�a;-n som ns��t!yel9-l�  EMC )�aCt/resul�.om];/�!�_� connng �ese�ey� analog� u> VR I�ca|�"�MP:r*� $np. d�$ ( ^.�v�, �OaU�-�*gauge-in|g�-"5*s"j&C$). It may �Zay\bca��ion-exvge� s 6 reprod m!�e i�&�� ion.&S��tdisso�v �xbx!�>-�. ���}�}�}�}%�} N ��(*�&A��I� !Wvery-low� �jB��h`+2�,� "%��-�c�,�$1�� writt!sY�&�{$ABX\:� ��-*�.z^{(d)�.U_n^T\�_2 U_pn,�$eq:dvcsampBo!E!J^*i=$5� �ercv"+/� �� R51D�z v?#,!� $U_{n,p�~pin'*ass%�ed� PF��&.�7�7*sakC k3�y, we� an� ��forE* $X$�eq."�61=),�z��� "�in 6�EH},g kin&s � u -Q !U��v:V ��4 equal, i.e. la+-. Ws ndN�X� 2Ds8+�!�f^3}*! 1.} s+ -  a+: 2} r_1 ( p}|^2 - i��]} .0&&�/�j�7�+.�!n+�(�-� �J� � "�/l, 2}\) �r3\ �e�D e4a� B�XB�*D�(uV��H+nE�A���� �*� .@wh�i�-m-0vH6"qin &7)/ �$��uW%A��R�5��.�) W �e'd^/% sD7&�:v6>�$%��"� � ��26a�X})� poM8ala�"�;JRQ�$ )( �n addi�al2��Sshort��t� s�76�* �o � 6�!>�$�'T89&� simila[�%j�,2� � >�bg,RupaS. 9rk}H obvreasons]� B�&WU�~� � U9lyh ear to� k e samh*�:U�, hU9�9�:6$("v( Q$, "v hidd>OVq}$�e& of9 �a We"���valid�,�t$( '�K imi,&)(>58ign�ntly l%2than $-$.�hi�;Vi�(� s mustD"exath~K-��ven��7�zof Ras dynam?' s, l�Va �inu�  8 � ar:�"�B�. I�4�ful�orr0&*d�O1.physicUnVof��e�)a rchisymmetry��� E��ima�antA���f �sE�D; body*�![ !�)�i�/6? �Ytrie2'$^3$H� ith three>nex� IzAfu.�=% e� engine�* "T<�!Bedaquer2 8km,9ve}.F�0h=,V}heŕ.+� .j@Il5�< UAno )mpt��2� '@ly!�me�ism; ra�5o v-mS+r�how Ga#2 �n model�-i6� m�+ r. A�!Hc���A�,B posi�-U��BK?�b� ��� J�J:0� �,���"* �!�v� B�4e�i�T!hF��. B�3as� eb0-$x$ behavior��.�to��r�y� �a�*3 long>�-*�2�"x omagnetic]u��&?. So� � B,)�5Ved�er'�LEsa�Ii}�wBa?"�2�:()in T8rq s2[r eachRb��� d6p��G thos+ v4@�"%�M�*l"s� a��%)8�G�t6A&&'���!�Q� m;QGؕ$iP)�o>��2�=2X�6� �. � uUpap� �A��step toE�a detail�$ alcuc&[1^�!{!g�k real&v� esI�2|-". u% "N;�, N�-9�c�7i�level� $5\%\ a�+ 10\%Q Tgy �!"V[ U�k?%��9Y . M�_�is V��J�� rson Labo%� else� v%�h� Y��b�-m�͘, w{a�'�2scMng�b"� J (. \vfill\eX;0 \acknowledg�s \n\( V �<e�(o Jerry Mil�com9E��Mo a�+H�i�� � �r�� � manu��pt�N� c k BW8Dt,{ valu�>.w. MJS)# �a�@�Ce�7=Tp:�S al P&� MIT,kind hospita�hF�le��8�� k!��is�or��<arP$FU.S.~De� of E�8?H Gr29LNo.~DE-FG03-97ER4014doSRB^d%NN# ,al Science F  k �8tk, PHY-0400231%�by DOE�yt( DE-AC05-84�50, C%�oJ.J.~ , _+K\l.} [European Muon Colli� ion], %``l&R!h OfAk N�c S"�Ff% F2 (N)��Iron A~Di ium,'' A�. Lett.7(8bf B123}, 275 (�T). %%CITATION = PHLTA,&,275;%% �rneodo. 2wf} M.~ ��ar�up�O>!&:�RA� } {� 240}, 301�94B�,RPLC,240,301�%)�Geesam5@5yd=�BD.F.~(, K.~Saito �nA.W.~IN�!��Ja. � Ann. Rev.%�. Part.a71l45�37�5>�,ARNUA,45,337�UUP�+!g9wx} G.~ �W.~Weise�1s$deep-inela�"lep{ &N:coKa� phenomena�I)-�%�33!�t1 (2000); {\tt hep-ph/9908230}:<HEP-PH �-�No@@�cb=�:P.R.~ �!��^�� Prog. �Q@ 66}, 1253�B� RPPHA,66,#.�Smith�hu�6J�%NG.A.~���Retur���,: A new hope�1ovu�)u91a�12e 20031yA�(-th/0308048>zNUCL-TH 2�tdns�4y.}BF.M.~,.�(K.~Tsushima�Q1O6G i�medz�59a2a 2004�M_0405096>�M_ .�.�&yG2Ja�, G.~�M�� Sava� %`iR� oB iv�&�L� ���a�U�eFA65�o386�9�1�990205B�1� .�Arndt!�1ye�6D��d� >�CC*�( to MZ0El� |TO9Ope�Dv�97}, 429e|2>�0105045>�� .�!��eg�25� ��X.D.~JiE�Is^ulliva&� � at4� �3s?:�2>5�>107�1�Q�105197>�Q� V�tR�t}j�L%-N(c) ruH�M �#�A% �logarith� ; %6�� "�T�7�rN2f�10Rn.�5�f�C�uc07 �+ol�Q!� �U�A$ory:���-�i�8A�1520025�8[Erratum-ibid.\*8��499�0)]6;010715B�Y#RpvN#fLQ1�"|E!}*� -��I��0!Iu�u11J��R�grN�6�>���.tt��"vA quench���^ on %<*�J�70A45I���01�2> �� 8042R�yiN�v�BhX�A�:n�f�- D6� 0940U�]�lat/0!�5R LAT .�"^H2vq�6Sl ��>�!��S!��flavor�-��M:�709� 1:�A��203003>�A�� �"� Belitsky��$2jp} A.V.~�Xվ��&�ofEY�gravi�al M��^ L.� 53a�28J�ph/�27B��PH �� Guicho�3ah=�>P.AU  , L.~Moss1�~Va�Xhaeghe� Pt�'��!�� ly virt�LCom:� u� ���U��034018��"R !��305231N�� .�э3j.2v� Soft8  emis�� DVCS�N�3a�44� "2 �o 3B��o .�KivelA�4b.l6N.~, MA�PolyakovE�S, rat4t J����A�.>/��light�>e %��) tt9� 40705fP �yt2�Q� �5��E:H &H&ino&�*S!>6z4�767!�5.Y! �9905059>�1� �m�K./Q}�:D.B.~ !�J�� �MWU�& 8�!�.�)�itm~2x424�J90� 8�?G�801034b� Z�w. �4��T&ZB1~:�A�.- F�B53� 19R�207b 98Z�szV���A*�v�B�:?!�R8�%�:��zC5�D61�F�80403b� . >Ry�BU.~� NRe�!�Z�e�>W4t6E�>M E�?o�X�"��i$ d !QaC�or��l&E �R A743�70� "�� O 4O Ba\LD ^�kwZ��e^Flavour&t"I%in.�)�&�E)��� �1A?>���U[>'5 M 24�HD0� �arb. ((V))5{J6� B2��Ri"� !��{021002BvUq 6�>k5 A 5E\D.~M\"u��Deev� W�ei�Eur � J� C32H4x�AC� 200B�!�� 6�66� �rikmai�� a� � : Ob�IbQ2l!eveM)itZ�a �2  �906B��ȍw �\b.� 2"� �>�n+p<*o$ d+�.�fBig-Bang�Leosyn�=i�Bh C6.06520YJ� 9070f .���rk}�6�EoPreciR :�"n+p->�2j"2� %)�e.�M�YA67Z4�V� 1101B�q_9 .�*}(8k.\>P� , H�Hammei�B�ETC)Boj"SB@��S�-Ra47In&&u�N�46�44� J� �BL� Z�v)�- �Eve}�����!"z&Th*r�7�35�n"�a��; 9906n� �jG>Z  docu�g} %�eyard �u%t>��p�%("s!� '! on")�34>1� Kamal�#-ded %(�(al1�=m). Lenae%mC4�G/&f�1ijWpdf�.sen) %to d�2��;� 8n. V.L. 26 Nov � %� \1@8class[12pt]{art&!chusepackage{amsmath,amssymb,>Mi�2$g�! icx} \odd�marF 5mm \even>top #-20%,textwidth 166he�� mm %\def�JJ5�{ S �:\arabic{8}} %\pagestyle{,y��"�} U refname{\~ �Refer�s}5ew�% and{\el}{Y5>r}{6':p}{\pU?:r1hh9.`roH ho^\�M:4 ti}{2:v�N{*�7: dis}{ play%:!sc�sjnize!Gl-0 %\vspace{1mm9J+? er} -< �"M-E� Rest�'�8of Heavy-Ion Po`ial�/ �?�{n�%ies %Qa ProbleskdTheir Ambiguity }\\[5mm] { � ~K 0Hanna$^{1,2}$�"LV.~Lukyanov$^2$, V.K:x B.~S{\l}owi{\'n}ski$^{3,4}$, EC$ZemlyanayaE�3 �+�E? $^1$Math.;�E� �&0, NRC, Atomic �ty Authority, Cairo, Egypt}\\ {`xJ�G�Wtitut.�p� R�%8, Dubna, Russia�ZBb3$Faculs,�(ics, Warsaw&k&�( Technology!, Pol!�~~FZ 4$In�of6@, Otwock-Swierk, HZ��U�0.2cm�7Q�>( {\flushlefh&8bf Keywords:} hE�E�pt�2pQ� , mi�copic*<A��( double-fol��!0,�3�`2�BaYmQ �����8Mab�=cta�E�� typ�2.��eus�us - 5s�� T' ed u2+ c2 p|1r�B�gir�,A�$ imaginaryfs. Two!�t�3:�*a�- $V^HB.>$W��,�+&�@� o-~ &7of.��= Gla�(-Sitenk�8ory. Ano22 temp�1�{DF�97 ed ! W�+ dardRI �"~A�, y. �/eiu{-otes!��s,G2�01%Ka�.�6\s adjuHby int�A�,two f5?d �bNept,a�c� ��K"4F data� V'"F�_aG*�iwas ob�Lpor.�!�� 6,\,17}$Oy��:( about hundg1 Mev/E�{/�r�F GI�i�KbCivi�> =�+- studIO!<�Kha�2o�Dw 6rmprovMn:e*EG%ulend}� \� {I-��,�setcouX &�0 O&I<ma�1o�CA�tud�4��&� re.�2-j%Y%+F�$ (complex)Y`. �Ea�!+"�` !2!�I1al ��N� S0Ba~Q$�5nel:I%�to ge�M ��-w5�a*q<�cmp DWBAu��!of direcc6k�0Wnd!?Ah%�lremovala>%�$s. Unfortuhhl�@ua"a.E�a�F helpR(*��J�9T'wFn%>eBir���:s una�ousc���p i���1p�l� >�.z�=a�� coll�F: y, a�  s�(�[)+iIse MencO�A7y a�iHi>=po�6� �MA5 mula �global Y˙�![Y��L�we?ugh8folmD�m��ifa�wa"/OH%%�} r,  !�t�velopX=Y8ve2E��:i,G�H�v�8�/B and Q e;E� =� ba�1oE>>(DF >ced�v�2%Ն�EolsI�overlap�X�ff.�&}UofI�%i�;�-�o&�H97jTeye, k.({SL},{KnyazS}}). ����.�9 o�QnDr�~�Y@xbec�INJw7�: ly u �u"!�9�NN-forca�t 9z�I=�arQjA�(see, Cf,KKSO�dn-� umy4NN-=i"']g�f *<cd7�e y-�aN4-�Ks)� dee�6�X�~of�fpo�&am�su. nova�6e�.�0nee�R�;u]�y\d5�!n!�,-%AACoulomb}_ri�x mosta�lic��8rx[de�2/ em��Y. �V�ul��t�U�^F��FnI�aǭ��2S a�:ed,A3Oe2 rNVD5��tak&@aFP$Woods-Saxo a� rK�ze A� ���>isI�,, say, semi-*� b>,e�fur freM r�:��pl&� 6whI�i�@-qDF8AN!-���4 �{gA!�͂ stil�-c�on�riz ��:&Q.� !���|I�Օ ͕,... etcI�H�{�`HHsugI`��H� 9��i���:;Y.�>1-+G. As a���6eEBFV *� z_�"�Re'.wax"� .�|!�� E�� Q58Gla},{Sit}}, be�2� ����k@��Czy��Form}�C #~5!>�.,m�jA)is� M o��f��KR� rts) � -��u� N��i�A]ݕ�!,�"� ����s &� Be�xsEP� �}�<͏d u.�aNo��L�on�:qPitQCaU�: "]1rA">��[.�<3s9A�is regu�E� Y^ �B�s�< prot' H againsTe "d�Vɒal�LFWng xId!�Ŷart�W;c�i�SP on 2.=S�)ub"��m���H;3�k devo��dRs,�#s ,ET�Rco��;"� M*�O &�f�  T�@�!�eoa�a![�*Vny�C]��M��C MquivalQ Bi%�sho�o�yeal&� to its�Iory;elegas�Vc d� %r reli���.y���ide itAa�G ablydHMVU#��oJ� IB2yV� F �\�ZKa@vde5| �ecR:Fesh},�T aF`��non�BK.Fp�1belie��f9 be YR!�he =}M"�*Va�? ized�*�N%V��"" . So��� we�?�+]�B��wgy S-�.ViP6a�acte�!Sf s: %[1])"5"�s`1} U_{opt}(r)\,=\,N_{r} V8+\,iN_{im}W(r).�Ea!At;��s!����$S�& $X$  * b� �!� G.<H ���9�- $� | im rG��Sa�(.Y E be�Q _.� +=� 1�YU�dbr=��hig{t$=ca2_n.ps,9=8cm,U =.8\h :!"�h\���ds �QA ^B-*VI^C$Med�ng�HEAI�� p�n8&DN_r+_5|*�Q@ T��1A�tn}.w,%��,u�Nl�3 Ru3 fore�Qg0}$O+$^{40}$Ca T$E_{lab}=$1503 MeV. Pa�| (a)�l(b_sde�K��E��6�  9a�S dasS3ur��2 2DF D9]5oAR_7)g ile g -dot!�l�E5�.K�;� -�"�WS&��&��Roe~ show�c�j A�� p!G (c),  ���q��� .e,1+-.���.� $ U�C$.�9n"�j--2��|/��fiSl ��zr��sO��T1��!�&A .�90}$Z�xB�90 A$. � ��pb����208}$Pb)�B�B�2���ni1�[�����60}$Ni�� 1435�zZ�9�C$ E��6B.2�_�N���m�.[�w � GiLig�i�=2=4^1=r�&n&sn����120}$S(-��pb��������o16rel}�5.*[ 55�\ \� 2 |� casZ��: lid(��ed)�q�` $d\sX�/  _R$~�(��out&ci����.DႁG �GA>9�� � %di�.3 G otal:�. Conc� nthec ens�e*� �Usub�t�$dP!�/(o�S�D "�@ deed[Q� rece�p�(�� K1} "N+uO�2� .�%B\J<�nh�ba�of m! .�9��boryp�!/��al&Oq��Xhe2Iime�g���� %[2j�F\e�$vU>ULXE:�\��% nalyfpmEA[ was �E�)Z$ �$!�1g3Rc.��yLZ'> [2 (SWS*J$�ch���stE�i~MFd9�of�eppl�!i�VS�&�;Y(�� S2� wa��i��hA�fi� shap-��F�2�3});A�. Ai1=A�ine >�R- $b\sim R�v+ \,R_t�K�@je~A��� it%�5� a see�2��co�d�W/r �VsG 4T" ]!ior&a&�0);WRToe& (p "�%�s\J�'atUXa �h(ltha�  �g�[� -*�bE9��*Y0��y%| excl�!NV%��]�(ph6Y rU (!�% &,!xputa:8� %�e2dia{v�lďa�1ly��.A[Bvs $�F �i�a�S�&$ +E� situ���nd 8|orkA�a�* 4achF#� nF . To�a&-*iA >m4 e+.�y��� r�\`6ne�Tof2IBi�;0 �"X'aj.u]a�Yc!vdatM�V jwe 1 to�� *]'��c�M"�!��J� }�T a�oU "mbq�a�epY��a�HS1�y��$pinversEV`# t�rf4�-6�2��� "+lzl[ � -0�!�� ��y G#�� I��>E�!�-6�3%��,Am so-� F�Aas.�4j\4} U^H��=\, V^H �W V4 %[5j\5} J=-{2E/ k� 2� a� 4 BE D ,q~q^2j_0(qr)� �3 _p(q t � B�%[6j�6} 斨�V�) �{p(t)}� � E�� ZA!yLA|� ~([&< F �Nv� ���l`"n � �[Q+��Y�1�\ .�'�r.��'ui�lzsa[w�\%*�abuZ#O m�1%�v�odeW&�%eH�%����ng����a��&� $Wf1���&[�d> nove)h��7< �����N� ary� C�t� 6�a2wa! remind�o ��V'�� �^$h� !B�*5&n(��3 z V�'i��u/]� in aF> WS:*�'t��0ome���'W&� . �fre-�aej��!١�q���!� y a ���31�,��)\Iq\hA *{4�6$$8cm} v�!6\,�\el[{}K�2���M�]�)b%k ��,"�'(U���eAm+#"� "'om��j$K��(simeq\{2Mm/?p^2[E-V_N(r)- V_C(r)]\}^ {1/2}�}P $Mm=A_pA_tm/(A_p+A_tF�re�v�%ss, Ea� _&�` �k!-of-mas"am$ �0(/�m���� ?  due�n?-5)> adop,\r�WL!�2.�# �� a�.sa&��*KS}�A�V6$vE3^! "�'1�;M3Y}ce multi�b a $F(A�)=C[1+�Aw(-�} �r ]!�I[���/ho=C� _p + t� �/!]�Z8(+�<$(1-0.003\,E/A_pI�6U�)r)4%� ��= upD nt l�`�M,perYye comp�hoڝP�, 5})�m7})Bl a �HEA���! B�*c !3ly�l!��E� $V^D�Z*Y{�� $V�� $-re�-� ))��� wo�8V)!2��; on0+2_l�  a&�'n�jA�d !'�# a-"P�%~ |>(�R+c47sA�{$Pauli-bloc�m���&� knock-��x�6ge ;(ityC K2e�h{.�q)�&s!n��4%^HI��q�&� !� � tl& s slightl�8 slop�3�ir asy�Sti�n{4A�I��A1�.J�)%�!$6��Bt �"�Ai�*%� �+i�)�"L5��)�A.-�|B}�w����R�)8}�2�:s,azi _ exc�U�A:+ves t4W&V�7 Be(s,�r+���f3 at high�i/�bV� &��;�'p�A?�8l �� i��hange��s reva�themselE&�1g����. A�^$P,I�pay�6u��j�"� W}��� � ��n�RP(46� g ��p ef�Y9�Ɖ@:1* 6�+e߇ܯ%�Nm� � �T$i ��AF���v�0�acNng�-!,y)�<6�1= y7��s!\�< 100$/-XE�autiy,"� �s�?8e�$�+���9p��2�A&� sh �,+���>, fn�j�8��& �)r�J,$, h9S 8jS 8�A_{�D�* } ~ = ~ N8r}\,V^H ~ + ~ iim}\,W^H>C%[9jh9hBRhB -h��kB-Zk10jl/iU^CRmCVmC m�>�U�f&G;*�atE 6GlyI�Q��.J*2Qs*a a�N{+>��9��8ng��i�happe�at shor"�:�0eM en, �|0pe9�e�8��?ra�T�;sc2��A��a&'s�D.�o� �ai�;�P�#w�! J}8���-A RM�"Ɋ!7m9&� � by Eqs"�~ 8})-, 10�] k #��two.i-��qk�canE , �K�str��1 shif��"<M���W In p� ceEK�B�P��$E� ��$ .�A show� aɮC���$R_{in}$!�$� $ U�4c$n%x��"�F�,�YQ�-u$V( x)=-50$uB�%�1ߕ ures!f�.�%�%8�5�diir di�I!�.BR�4Di�4,%��$�n�4Wd@�XI�6/ vR�:�$&]&D d\Omega= |f(q)|^2%|!T*R/2�Ch2ri2 1} {"�&\ > f }\,=�,el ({Z_pZ_te@� Jer )^2\,� 4k^2a�\sin^4(K$theta/2)}.>/gEppur�8!�v�!�a��.N�5tud]1n�$ 12} !; = ik�_0�\db b\, J_0 (qb)\Bigl [1-�K e��K i��$+ C(b)}/r ��� } \\�<q�|�� $E\gg |U|��!H.�� $5: < $ 2/kR&jR$!�&� �aTf#, �<$Re�({R_p+R_t}$.# q=2k!�2�`"+ er��"I�� % 8"�=�S!� �unilyA rg �C� r s"w%� �gar� us&u "5�> a"D!'J���B� �7.pA�DFE� ! &��:>� �pe5(⏅�-=89�R� � uim>6� $b$%$b_c=�$ a+I  a}^2+b^�( ll*���Egr�Bof�1$!�#vexiHapo��Ph-�; T}!h,�5"+ closB"��6�B ]$ �=�W$/2E_ {c.m.A�D�w3�=�2>��f"u LZ2}���j.IR !�!oZI�G�� ki�� byG*.�s����vZ�"$� �&q$k?�Q|�# 11}6�%�a2�1n�$1%�$��(197.327\,{\[(4E_l(E_l+2A_pm)k}�0(in ~~MeV\,fmN"1n'14} k\� �}\,�% {A_tR�} �"<�c0+\,2A_tE_l/m} � (in~~fmQ�F��~Ep E_l$- MeV��A�!��%qm"*��SV*ts�V($m$=931.494B_��-%�G �unit. B�:p�� (Q��6�Jh.�I�8a�^{1K7(D�*s�4�. ,~$^�1 �^"�/ci�:-%==�7 MeV2�1d$^.3, �1 S. }C0atSZ3 S��N.���� c#"�#e>�K� Refs.%7nd{K36�+�O�.+ �,~W9~B��%����6zJ(�T {eq4*6 7})�K�R�����1� �v)�YM � lzs})V?A2:oi�3��M;�3 -.NPP2��aS}j,�V��0D��\b+�� */+���n65 �CG.kS2+"sf�`JH4 CDM3Y6^"� � a KSO})�.�<.�: J� in5�>%I�/|couple NE��N�Im��Tf; s 1A%)1B.H Figs.1-7,�96�:� !�R��:Z�&$U�#^1� B!C$u�ed��V T!��DF��mP s. D.W; re ��.neF6e| �5Iose+y��1! �:�3-2];)�B�*;H (2 +s,6S6; 6;u� ��)�/ �to.� j�i-I �;s (c)aHYo�e�;s��� .-*�*�5�A$4!!� X18��;!��tNGCM.)�<4�=�|i29<s;�p&�;!�+B�. iQ_���)s+5{�edEyJ u�| 2�+a"�+?toi��.s� n�f[ doIva*�on�$al low bey�*� rainbowi+�� �V�S9�F� �-ca�a� >� !Jre��� su��&@,�fBs ^Al6�� � .�->@o�I ). O#)` ha�$�9� .��by%����)�A> F���>�U��� numeusoluuUiSchroe��er �� . Ind6�*|T��sBclP)�s 2�5.5W\ o� ��qis%by�!-lB%4%"ed .�Qor�r�D�!�:�8*�W�U�2�F<u�de&���&y we.a���8� 31k ��O a6aR�Z&� 6��" O$+F?B}� � �Je�+�sk2�� S� 1�  4})#� � $2&2,1):2�+]/I4 �"-enE���]& A[� ���:& f�_ in fatof�G1W;X w! � &�3!2�erA62[{\a��_& %0.3�${f%� �:~~{�]�I.�� )�.cX=�AUI }& B$$�c�E *r}{|c  } \h��  $ U $ .% n�& &x�${C O}+{�D Ca}$690}Zr>� Pb}$ \\ .\f# ��%.21$UdF$& ---)8& $1.13V^{H}+iW ��UB $&� 4+i1.32W^H$&---�W$P �V 0.881:Y0.6  �`)<I1� Q AM�.5�'"�^ ��B.��9 R�C:"6" ��cB� U!�U&U�7M�60}Ni!�A�2��@Sn>+����E�I� ��E&$U[+i0.9A�5IoV1.3(�u2�2nQ�q q | . /q2�����Our�",!�, aѭ��i�3!�#o ach�MBQer��� �/.Gists do,��� *� dee�4#itself� Z!.}qas "0�C"�U�7� .�; 6�2�6"�(&3!"�82a re�"� stea�\ , at%�sR?we��1U�". q��in�of �R�F�SF�3. More�w�"�j$�o�%$��f��(clS6�ud$" jD P� "6�5�&"�DV2y � .��W��prediB� "�� 3s.,�be #S7�very sen��M�o}% ?�� &C . �*{�d<�?�f< ACKNOWLEDGMENTS:ek*-a;fs �fL.� B.S.�.Q��DInfeld-Bogoliubov �ra:%oR1G8@ bus gZ.!�nk� R`fn F&�Basic"�f (�, 03-01-00657� n��| �M6�g �ga�� ��9CfEA-(g� JINRa�:ir`��new, �K>[l{99�Sl� -5 mm \itM' p -1�j3Qi��SL_�R.Satch��G.R)yW.G.L��:g.Rep.� 5�z183�m79Պ�B R]0 Dao Tien Kho~� O.M.'kov, V El.P5�$\&$Nucl c27}, 1454�0d�dS} D.T.\��, J�A �6~�� NrNOO,:Lu(W.von Oerts�#Z�xC ^56}, 954!97��7 _�X R.J.tD1it LecӬino�T^,ics} (N.Y.: Wjsc��0, 1959. P.315i6�% i Y A.G.S�e<, Ukr.Fiz.Zhurn. 24},Ʉ�59) (P inQ�}V 3 VCzyz} W.�C.Maxim `�of�.�)-�s59d6I! ' Q�Y J. anek.�B A1A�~1B9�:U H.bach,�!9M@A��o1958); �bid�q19��8�z62�1�& �K1}Xkjk,�0"5kckS:bk�K.e� , Izv.RAN]r.fiz.!�jZk E>�mIS)� r28�4)�.�Wa�H�o}rense� A.WiSvN�550!�Di�**] %&DyDimbel} %~Mervat H. .� ��� 146e쭞1.6� 2%> Int.J.ModI�E �1� 169 (2001 �.<XRo} P. Roussel-Chomaz, �.�ͧ47�34Aw88 P.;y8 R.Liguori NetofN5�w73�9M�.GPP!�D.PY(�3!���Ps�s��?)� �71�23��A�2.<�8 M.El-Azab Fari[z�4��525 (198��21��CG�}K.ChaG�S.K.Gupt2�-�4�@161z���22&2!��&�%arXiv:[�u0112039}��&>m  B�u�j%�r`J or "� ��in$�ii�!l!^�%!a ics", 20. Ma��2003 :�ttwo�1,122�t\*�t�t tJou11h#1#2#3#4{{#1} {#2} (#4) #3 At CHEM !J. Chem: INT �x$�z i} E er��A�R R p p P P q q 4ss{\mbox{\bold+x $\|!$�.�vbe/C!e�*} 2#e#�0^!beaEnas�BE$ FV" nn}{"ά���x-2.8cm:�x-16�x t�x18� }] 25.07 �d&�z\title{�{1�S�o��$\S�S$(1385�'$\Lambd 405)-on1�� $^+$ phSM�q9_csses} \6@{Madeleine Soyeur��NDMatthias F.M. Lutz�%,3}$\\�&�vD\'{e}�� d'A�1pНque, deEj ]��ules,\\ .��N aire��de l'vrua���(eB Serv�bJ,, CEA/Saclay1|F-91191 Gif-sur-Yvette Cedex, Fr!C\\ Sw8GSI, Planckstrai�t1, D-64291 Darmstadt, Germany83$��)( f\"ur Kern%k, TU7`M89M/ makeE�a�u��� p \*��$K^+ \pi^0 Q%�"$�V- Ic $�9E,"Gr2(� �(�6c r{J "I�2s(1116Q�pi _92) pai�M�9at�nminFU�Pdec��`} �. �0e7 *')eE?�8aY� 2����7samas��zae����nyv-.�g�u[1 t->-nel kao.T�*���s1{� $K^-:�6e)�R&-�$&�Q G�)j!ef5D�a&۔+&d��+.t����meson�.��x�p9��3$ros"�R� 6ָt�p%7 po�:erm%`[-�!>be�nP`keF o dr��a&4��r }6Q�6>*s �o �K stig��.O�uZ��N+X��s!�A�rib�!�>r�E��>. prog ��lan{at ELS�&at SP0�-8B&7�=confir��is�fec�_I ��s��i��of� �4 �?E�� eK�s VsPg-�hresh�Nthrou��sa*M��ᔕ� %\�%\oofa' ents"w:wAntV��/A�($\i. {s^{ }�!.43�)%0e+q�a�lex{%,* KN��e�%�at �mܩa3CGo i"[v�s (�a�m���, to b{��\s "Ea6b�-E���-c �F9� 9= [ yjR]H#��ng�=�ȹaChyp��-��� � [^0�$��s� mari>@% $���G�KD [($88\pm2)\,\%$] A�lA�6�[($12(��>\Z: Ys+Hagiwarax+1�(L � e4�i ��UWea�96��Dy%7V��s�V&N�E9؅!�A�o�� �do�fEI� -�j]�,�isԏ�; h*�Y�� �C�,�$ ��exagn%�rU=E�r-- X��X *�����E��9��sA�er�Vby�1�W�~u��aэ���fky �����H [1/$(m_K^2-t)^2$],[E�uT#{��T6��'ndd*mmMbbM}an�$_v�is��ly'Iv1�a new7m1 of*s!+Ach �Gb� o�s�� �)bՖd!�S: vely. Se  2�*Uo4a brief review�.s�B�B��7me*G ����zgz#D'>genG ��d�e��  mis\-�eshB"�81.35 until 1.45A %�S &� !4>`  c� s�epa d, s� �BY:&a)M˯U>9���Hr�AQ��!1te�[iOV rend))CE��t"Otc�#b2�, �,J if�%�vd���&�sI�)�arp drop�'w�v9�x� ed i�YI�6� -1G^ Fpt�b�={3ǒ) � �Q��PB� M���%� M[�lstam �,b�_c*�R!⾉C 4-mo�*� +p�19:AY?�C�B$ cau%�4k i�]�%��3v���@ error+� d!�/xbe � �4sgxm2��ɡE��sB}� is"0e�nt�AIy�( exisAd*~ ��0S�fA��1�4�3 ongoanAHfu� !1gr]�^�ai�z dnP&�P�"�!b��ڀ�1�gy} w.�EZF1���toāal�2],��ged +͜ ^-$,Z-+$)-�ts;� e �a��� � ^0$ ��!�forbi����M� E �6s s"qs>�T-$, $\pi^- \Sigma^+$, 00$). The \,� decay is therefore a unique signature of t@xLambda(1405)$. The measurement (dgamma \, p \rightarrow K^+� 0 \, ��0$ reaction is intended at ELSA (Bonn) where thR��pair could be detected through a multi-photon final state ()-=2��\,�116)\,�� *n�pi^5-&  5 $) with%[�Crystal Barrel \cite{Schmieden}. Similarly ))�0(1385)$�4studied by its=�)�5�ntoy $�4 � channel%� rgeds w!� alsogat %�� SAPHIR-�or I$ _!�bA �-.� ]5$A�\, n$ an!�A-ijp-!�)5+^_$ pi^+ _Q�s (I|all! %$hadrons arYoP) have been investigaA�in!lX energy range 1.3$\,se %H omin%1 by effect�$ising from� �c^�T resonance. We expect:kto�$,quite accura AL o unravel/@ dynamics underly�R}<$ma��du�� for )r( laboratoryI !}!v[ �\reshold kinematics until�� 2%�reg�,add!GedI`tis work. Angular or t-distribu�^4s in successivQ� bins sh�= carr�cat infor�Don. \newpage \se�{D- ����(�Le� �!N���pie�(1192) !��3s} ��1�����!cA%-��90invariant mas�pi -$!�����$ ��s�closeA�J$) $��2~$Ices refleE the 2�sey(s.)B>XriD(as a member1[ground�@decuple�� bary���l�+( N$_c$ limi$QCD. It� ,well describɴ,quark models�4Isgur,Glozman}�h�DBreit-Wigner shape 2�E iro}�Qr� i�complex �ic �. Its%?,�particeN!z� splitta� betw���_{1/2^-})�E�: 3 0520)$, cannot���h stoom�0e constituent.��residual -);> rm f ��o�  low-��)��VmwHzeable $q^4\bar q$ !;Lonents seem required-Jaffe�11!�� 9�%�bERLkaon-nucleon system  8Dalitz1,Siegel}:� D>soliton Qs� C,Callan,Blom} �K N$ 2B�w`�infer꭭De SU(3) cloudy bagI�M�p�v Veit1, 2}. Exten��� �=!�>1Hbased on chiral Lag�1ans-Lu!LGarcia-Recio} sugges��ai� �A�g���i m-I2?� s�?zib��6Sdea+s)a2�-Hemingw�L It depends strongly�!initiale�f&� s�  which i�@| (d, emphasiza�G need�y a fullq[and" �coupl:| toD differa�. � `!��2A6� J�  ��0j-� $ &� b  idea�u ut� "�h o� se���(es (mainly :)�U gainV" $K^-:�6� �-OZ. � $ am�9$udes below%�$y�t�, �7yB 6 38� �:� re\-M�!�Taproced!0��AWe"!-9lb�ificaX drivenU A]Gs��I� ingoAL� $dissociate( to a`l K$^+�a virt��K$^-$,Foff-sh� scatte�  subseq� ly off0pr�t�jt!�prx >(i�$a"N c�correspoi#di�im� e� playj ,Fig.~1. Such&v w? show�8a�.rp dropQuGa� cros�>J s $d\s�/dt$ E�increaE�$$|t|$ (as ��+!uscarceI�availŬ��Azemoon}�is � can � � a dou��pol�mm�� behav!�Hlike 1/$(m_K^2-t)^2I�a �le :��e� IB8$)dnew �� )Q�near i� � make��possi� to s�g� tE�terms- x ��k�| superposiŮof -aVSleM�%& tle!�in con&i . ToXport fur|ou� �>$ approach,� �be no!tm��r A [ to-<�m� sW2�.!^_ :�YB�� V-��.� $�\simeq2))�6Wto� centO  �g�4$\sqrt s= 2.15 F�5� � ��aW e known�ɱ���+:��- �-� s. E��uZg)�t-��j � t. \begin{figure}[h] \vglue 0.4 true cm \noindent /)!�} \mbox{\epsfig{file=F1aerice.eps, he^=6K}} \endA rPb�Pvskip2�% d�!] %  mini7T}[b]{.53\linewidth} %\ �ing %�!) =F1-MM-st%�� �5�cm}d�b \hfill �N| \h �8R cm >�2„ \ca� {ſ-exAJg�\�A��q�\,p.#M�"ѷ":0 (upper graph�t�u�VMM�*� (lowJee2| symbolB � for${Nh iN�T+ r ^-$ "�� case.M�M3�ŖZ uaA��:C�9� 1  � edu��c� "[ "V$ develo\-pɌ Ref.�@X � ��B) % �� F� ��� - *at pic� )�� "�, n"-��W2� < muti� s (h�!M� �)��int. d�� liciDas funda�al field"� �=&� �` �� (in �*G: �&� � allyr .� >� ,�q����lDachieves an excell� scr�-�&D H  on�3D-\,p$ elastic (dirQchx u�i�in+e  m��+"�� %EK^0�-&+$)� � up to *J� $ mo%��ord�b500 MeV)�i�x �:9�to� er!9y ility0�na ��s z� q��� -+1%f]�$I�Z�  B�2��aevI�0ly meaningfulRdi� �o����B&We cal#tu 2� �8Q$�N�,Y$� Y re� eei@ H) =�{E=� 4-M�� h 8 � pX $he hyperon�+de�  by $qA�p�q_K \pi$%�  p_Y$�Eively)�� �0npolariza� ~ indic��9ɛ�l�| � � _Y-� 6�reads� $eqnarray} � _{5�F�,1�X}&=& \frac{1}{|{\vec v} �-p|}\,(2\,q^08m_p}{p^0} \int ' d^3 N{)o0}_K}{(2\pi)^3:1}L# \,^0_K}\,rH\pi�J)nL p}_YJJm �p �YG@nonumber\\ &&(2\,�<4\,\delta^4(q+p- 9�- �� $p_Y)\sum_{1�)�,1� ,3 _Y })K 1}{4}\,|M�� |^2.Fbel{eq1�Y!FactorwA�m� $�i& ��+-� vertexe a���:� �9u, w����B� e ${)"R Y�$:� d�0r�6R�D 2nl i%ame-in7t�G�si/c�}��K�p$:?Ois use��to defin��:v`M�w}^2}$�m፡� { byFI�< = (p+q]�$)^2 = s+ 0 A��{sa� +� KA�}^{\,2}}]m2Bm"��"��!���%�p \toA�>�s g�F���)j.� Mh} �� {1} { � �!}��|�� q_Hp}|i���2�j��p��)���� 6�,\mkern 90 muR����>�,� �.�J���K^2����Չ�3Bin�$1n$a q/ um.EBC,F :�^2=�4\�i%�\, {\Y4-2. \,(m_p^2+E�)+ - ^2\}}�4B���Ss �T>'$�taken�B� . Inr�"s5sideru (R�)" � many lo,&}( �r��y��� vol�poo�$�� ing %� (uncertainti��#:4�obFc���heF�� gaug��v�� IE��:$�, a �cl "of� ,$\alpha$ lea���same ���&Ladded.� doY ��mp(��'s�Ap�r"stead�Qh�schem�'tho� Velt�� �3m'�ŕ�o� he��or�%�& itru�t�and it a~ F+. To A�� $in perturbE�'oryE��idu&l?c :�%4apply tW ��de V>46 cN\-��[��P);keaT�i��VtK onlyA  ��u�0"�>t We willM�)d2���6�ac9� F�, keep ��V�%�ext� ' :�>tRd =�Y.by Q�q�'!e��1 . A�)��I-r�9�%��^�^] , �� :� K,#$,,Y}} {dt\, d�x^2*�{�  ��� c(0��)^�"}}{(s-��)^��2� &15' q��\,}{(t�� igma :�\ ��2)* 5B \par��st'"/1�!�eYiJeI�one-a(',rmined e�(way, becausz does�8getyXi��v�� buI�t-�nelv"��鋉�t�(���u F� s�(>�F]# Q. ably�Ye��ul�$so in view�`anumala/ ults6�# ext �'. As pio�+earlier�(discussed mN.tho�-ly��:�2}il�!� |,�%lsoatij�fIp�1s&�. &�(N>�ks� firs%� quanth $4\,:� \� uA2}$���$ Q`1o� �2ŵ�  p$%, renamc#ty�qrt{seT p}}$�.�%vF� }$�.di��+!rre%�u!�E� hibi)-9�� Z�$6� a�Et�!E�re�y�9�%)�at��\,\� x\,$1.435+���ex eA�:~2�pr��.6� 4gZ���.0z ndv+L�}aEZ%�" aR&�D ata &�oE 2�# abov�r),jHMast1,Ciborowski,Ara�0eros,Humphrey_�9 ~�n��2�*� �10 �B�� B�,6 2� z,)Q:�)w@:#�lengt �Ac$ 3$ s8�Eq. (4)N5UvzfA�bj���%q� �dashed ,.V"� �/� D relag s-wav��\ AW>� C Refs��I}f�MN��F�k!u;"m22�,"�T��I+-�~�e 2 pro d/���)fu��OF@-� i�.�� very$ a(in�\~2)�2,)P n�-�D";'q�is �0 symmetric�2.$:�)�/ �I$2Qis sm�2asbE5�a  ss do&�1TF9 . In Tast��9vorm1�r�%̡]F�a6��ly&� ��8f/��)�)X-� �".2�1� 35B ��\ .:k$ "*J�&!I �j�)A� �!�"@RV*f �\ *o]�C1Y$n�J� at $�4 =2.1�$i��F3FF9.�" cfGDou j��J����6�U����Bw �t�tWe�/ cl� �"�4� ea_!� � ia�m aon  3�0�v ' "t?u�F���� ains "+6&*wbe map$$�+�,� Feynman�Fm�$inJdE6!`,�!,"v;��bout anA,of magnitude1\tha7 M��ed V� A]-tal'!X)P3\< a5#b\<8e neg�` 1�Ž����c~ E�7&�"N7(Conclusion}a�h� s�;A�B!R:5v-�5U+� !�e"u8�" "�/"� ͜(�7���1�7=s I�p4J/e�k�*m��%16 j405=Js� focus�F* $V!i{� *2,.0,ly" ��K A@/��!��.�^{�� $=1.41g*� ;5/�b<5 <*�sE�m%9&^� $&_.��$$."�0 12�r�.eP�ݽ(��1},�*�<Pr7$b!Tes "�/a,��#um. B�4�[ &�Ei�R&<*���?�7>�NjSN rO) 6��'1�QRYyrelevT �Xa� �6��<adv�of�G!�s� �4�'�?$ �@P(l2�sgreat� urac� re! mple��a{<xperiu�.;y}8ide��is pap�re pl} ��=at"t> �#>,  >*@ Sc�>� %�:AB0 A, dea a�A7�wo)�(d [p ^-��z3*�+]0Ks�Xl/rUneu= U*_C����"�5] 2�As�u�1-�%�n�1*!���A8�>��/2t�8a "�+ �(���=�{Acn ledg�Őa� stimNad�h �0Takashi Nakan�$d Hartmut "�B . One"us (M.S.:g!�"�Er5 School%�suV2wher�ici!ona5,a most fruitHcoursb�0 thebiblio�y}{99o&4temsep -2pt \b�8em{Hagiwara}K.  $ et al. (P< le D�@�Group), Phys. Rev. D66 (2002) 010001.Z�LM.F.M.  `, E.E. Kolomeitsev, Nucl. RA 700O193[1 �?26LdM. Soyeur, nucl-th/04071158"5T. �6z4B 95 (1975) 77@5�}H.!�i�, Priv��commun�(D@5Vu�I7�B , Do�al�2,sis, Univers�of Bonn�4��cK. Ahn6� A721.3) 715c�P> }N.  , G. Karl6�18�8) 418.�G�>L.Ya. ,, D.O. RiskaHp. 26H96) 26.�"�>F�rreiroZ}126�7) 319�h=R.L.  , Top% Conf. B�? R"}/�, Oxford (England), July 5-9, 1976,9�u=}R.H. $, S.F. Tua!�Y�Lett. 2�59) 42.h�=P.B. , W�ise9/v. C 3%088) 222.0�=}C.G. , a�Tornbostel, I. KlebanovV � B 20�X6.D>U. QDannbom6�6�493�89) 384=��=1}E.A.  5�)(�137?4A\.'42b?�R 31=5) 103.R2>C. ., 2i J. N0>'582e5�.&H"�=R.J. 6t B 25)�)4:*q�$"M!/" {ica 29�63) 186=N�}T.S.  :N-1%��3078.�5�Sakittr N@13 |5) B72\&I }J. FJ��G I�2) 13.�Ba%rter}R�CI �2):1) 142U&�} R. H.�B ��1970) 2]"W�f(, R.R. Ross)�ͺ12E�6�0.�,J.C. � �Q�45�599) 55^�6>| �7 docu } �%%  Beta+� r-���ei .1� � i�2 quas"4  % _random 9@eXxi�F 2S V��@on 30/11/04 % % I�de � �8(s % Align t�colum�n�imb� % b�G(math % For w/@PV� F�aXB�\ive %&g�$� % Bra'' ket'?Vacuum�.�)old |Ide1�H \1��&[aps,p�1 int,� pacs,}5ped�HP,floatfix]{revtex4} %� \u�<ckage{� icx}2d)j6bm} 0def\rbot{r_{\�pt $tyle{\bot}�(half{{'! 1}\over6223x:3{13 &new 4and{\bff}[1]{{�:A!� $#1$T.. D}{\��}3M lp}{\left:rzN:fud}[2]{�#s0 #1f~0 #2! .�pa22~al 4 B6bra��$\langle #1}M|:�ket.|(\r9:.vev �(bra{#1} #2 C :+bom �mL<:m�5MM ity}!�f 1&;4pace{-0.15em} � BL\rule{0.087em}{1.5ex�.12-0.1r-h�3��[1.4ex]T�\0[}��& �4title{$\beta$-�r�B� >���fy} \au3${T�$k\v si\' c2Marketi.$D. Vretena5>affili*{��DMD:At�e, Facult�7Science>m �k-��)�n.�Tat M\"unchen, D-85748F hing, udate{\to�P ab�ct}��,y� sist�� �p�D-Pon:�fP (PN-RQRPA) is emplo�D+"�o 6���-li;of |-rMHGQ� N$V$$50�82 �9s5new8sity-"�3�P#<Cab,�4nhd����on=&,�us�=2CHHartree-Bogoliubov &�*)Sa,?\Ks K$ ��cle-hole{�1k, f�Ie2 ,ge Gogny D1S.� J�$T=1$ ��,%S�� nclHa>� .vXM" =��& G&�G ���$Fe, Zn, Cd �Te isotM� ins,�)<m�"&lifetim� Ni 6-f}+Ft 4$^{132}$Sn. � y7U cs{21.30.�T21.60.Jz, 23.40.Hc, 26+kCa�tl�Qbig�A �x .x % SeE� 1&�\la�3secI}InG?��� 2� L�*s{(5��Nut��.Ldp�Q�&IEiA�OEp had%�~L impact1=a�L��cs. M�*w�*often2o� �wSC osyn� � ar a #, tG nova lap� n�@oHI���ino,8 uced&�, �"Nmi�cE� globe �(��� ing_=,��Kt7�<v~8fJX phen]? olog_*��Vinp�� =?:*ne�0i��a~6�% thoustC�� Pi fI9aJ�?X?�2!�E���ker�c%e�ng, e�ro'E %� weak.I �$yMA~� �, e!�i�Ao_%�o�E ,,�2afUbx*�}��,�t1, �� fE%trQy.�s cru �l�.!7y!n��We��lk={,�exc!�A8, ($n�Z$�($�$ ,n$)A9L �4-%\^x, fisA�xba%�i@-� ?%V ino :*�Mk , etc. �Tpa*�)r$6y{ ru�%\ �� �!v�'i1�%�i.6�4�yu~[ im�J�'*0 they"�C �g �higa\Z-/#i�s�Mhe �<"# �%R cepte�a few "4 �$, however,!~b&� E�F 0��to�!*? eVSar�(s. ��Mu qu���0oraZ�5 �[_B2���n� .�.� !�6+F�. Two2B �} �NT�Xh7�)l��ipYrge-sce$��0 o8$:Eea�J:e_ �OGE�! n� / a Jb� Q� . Sh�O Xppl1��V��re?0#F�Vre�1) �~hLM.03}�)�.�ofY;6  �Y]�,E� prindl �itag"� .i�3"&�� "#a�N-$26un��A� aileCXMI��Qstr�- "�+�add�Nto�#-�.�.�"� �&� waiA-p�I�i� $$N=50, 80,v$ .D) no-c .q &CNOV.02�X�.# @Y�9A��!in� > MONP>J�A�E�to5 �o!�gh�. LA�]�  >,M�2pre| bWa�G2x��2� to heavy5.lo�;k�����Whea(�'69'=, �EUQe} an a�P&�D.Kself-� bmean-�H framet!A�&# I � �%� ��*� s IttQ!��<,arbitrarily ))Ds. Fu�I:� �}v�B}n}, 5�E�9>���ede$}�Eng.99},� .��ON� %|G6�U�-��WHt Fock.y(HFB)T7o�l4R&� basis. � ca&7(onalize�= deQrix�i"-Zs&``1Z*�!��Rve-enja>� uv� �1B_u�:�is*�K�venE 68Aq "�7&%ra��@to lo�[ ��@eak���E�i�S two�[&�:�e� mus�=I� V with)1Po`��!/-FlNs,28-9 7�a.+!� :!W5_�i b�VD5)� HFB+E��"� Skyrm2�L �Ŧi�` ofA��-@�= ote\�#oqlY� �,y a�i�a�JM:Ѷ�� i�) ph�.al6W�3N���m�. "$'a "^0�(wAYy"�2al,) :�!X pluN'�z%g�,�M["Ya���&:�%valIQdA�%$-forbidden:9!C.� �i WV�Bor�t�shown�,?��!�b{ � $&�.� i"] %�$Z\geq 5�NN  82$I�* J$N=126�1�c.kC�c�,r����IPc��o2� PN m&>zIq^-6�Ar M�.�. S:-2l�:ius*�)) s3d�3q to)�a* ,�šin�?i &*vallew �$-*� >=�3i�Iq/Be�extfjdspin Q Ex�4�!�� �D rip D7~0b�66Ze�_�j �a de medium���Q�/�JicI�&wa�/"v �� �1*56I JZ � in- }8Dirac-Brueckner2�, P/e o�aal f4�2NN24�~is2b m�CG`h!l {\�Cb �]io}��p� %K<);�� i�f�1ap� W*ur�5>i,  \!��� &� $�I$�l omeg"O rho$6U.CF djus�to� *,8F� a�of ���!:A];=_ �& 6�cow`^ilsve y@I�those&�F�p. 1H. In� S NVFRS we9 Y��&!!"� *N(RHB)�! 6��E�exU�>����.^� o!�DD-ME1, gcR��%n2[�i��te%�-)�j��equ�u� ��6s<9� a [u,A� nd- =p>d: S�Pb��t�chD:� �dto�? �$LR.04�k �3"� ��H2j �4 isonI.�2 dard non-����'=}�]*�Vs Kan ex�i7e}|ʹ]��Y�provid�,� roved>*je�� �E1R">�B-RvRs,&W 2A�L�Jngians*Mz JF�6���., 5�d�#: � 5�e�>� Paa�Y 2�� T�3u&P� �_le5�g -�RHBi�I}a6�G. F�*��2.29 |.�3ofa ba�< alog915�R8d Gamow-Teller &J<" >m-?VPNR.03,%0a( �6ŕalV�Jt�[� � of*� �i�1Qyd��!-��.��i!Z_ � D&V��&G %�g�� Z�8h *� weret�Z�6 onge�X�6!�ir�# ѡa�(�at �,�=�kas 8/� �6m"f.] as a!��W���ey_��on�2Lw-�C5�!�� �Y �Z�5at&�G!Lm�7���hWeWF;4 surfa�7s�,� ��6T2� e�: IU� ~&Z � a�lowqw�iul� !� "J��som� �gh�tim�J �I1�4�3A<�:�$T=0$"� ��5AA�re��1n�9iIK �;�proble�i��y�^�c&�l2 �2y� d-EF Q�6�*!0MJu2�A��; !Oa<�1`ed.4DA�9t�F� W�E8a�gyo�Pb�m� -�tz ne ��.�9>l re�Si�ly e{" }���9Rg5ouzc5wQ   �ix#=����"� be � t��9*a*K�E%m we-� a#%CJ}m�-Pt2���er ��AAqZ,��� !aHxo�ar N%or-� ter" Td��% Sec. \ref� I}@ outO %�.�>5G� ��!���.v�z*NlI}=�E� " ��$ &�$�$*�$82/.V}�� !�summaTQ�r!tremark����utlook!��h��s. %=� ��"Z�"2 "7*�"I}OI �!R�#2#\s�k_#{P6�2b2�.}N } �2<�����*� � �n 3}q��u 2hHDVj� L i�pyn2H��Y:�. a#��� �uAjF� $ph�9pp�rr {o�In��y��rAaɩra�G writ9$�`i� 6�� K �>�.*\0&\�, o�5�.Mhig�O� 8 BCS�. By 2\Z,� >E�P2���.��qalwayU c�d.� ��:�ma#2�!�E�z6�b�#mp7=s)�>0�ԑ��Q i eC=Ds $V_{\kappa ^{{}}�_ ^{\pY= }lN 0}^{ph&{]I> al Az.�1 C �F� S^q^��p}$"�A��A�:�s�as cYG bin&I!$ occu�; f` s $u5(}�va$8Yk>�I��)T co.����> s!sneg3�  t�In2H �.Ys builC<�?> G�po4ovae;j��\ �ahi��s�ed��vor^ &!j��)"�o:���>�Yy 1  8S&57��%S�]f�p-:_�r��s�Q�� currP�ervEaG� �X9!|spurious �N �2j+f��R (Q)RPA����sJY/-u�^ .�g53b1`Mj ��bR p2JQ�s 6a���5I�� �{�!�&M(al*�'&�of �t�Yi2�8,Vre.00,Ring.01^E RHB+ih�~�bN& . �6�*M�~U.�XA* &m i�[ f� or�p*3 6�� �!r�!�-�������)"T d< �*�!C�D�.�. BFti�y��E��C�'�]:��"Gj RHB ��E�"!�(��/���(��7:!N��a�e�s�y "�#.Q� we^$�%um �4 ��satis!,i�vai�B�2!yEX�\!t)9ځ�ic!%? � �Bal�R *yi�CU0-f" parameter�2� �\1!�� # %'.�?x[.G4�#0 G,6~�2E�s`w:9(2�!�.i�U &QyF!�,�W6�2^,�[�1� �!�a�LTE&oH�%s: is�� S��rCl�\��%�!D$T92!�6�1�,�%" a6@B ��.-&>�%reu�$ u, 6L-�EU%+.�4a��a �as6"n.� �i.A^&�uil�0��letu�!)0�I Ř!<2]2���. Fs!�jly�Ma*�))�!WGTy�m����H�0by�*ax 12$\%40�#G��byc )6 (��8i\!I[!EIkeda��� �Ike.6WQb$F�<sQ eft( S_{^{-< GT}-+ p;() =3(N-Z),9gts�>}%�3^_M$J\pm L����)J��of .1 ��A �Ix^K$*����duKY�atWH_oC�ik&��6� , i.e.5m�/ng $'<���!�� D}:�aj� U�g M1�ea�vV �V�._uŇr&�2Z*�� 0^+$J� &�6+-�� E�u��$1DeA1�51 :2b } +!n rN2r.N r�v^�r sj9B^{pp }2� B�^n6 2wJ�B�.1� �1 n2�! >�-�^2�.^=bA��; "�eabmatU�PtH�$p �U)$n1���& �� "6� *��o�"�7�!ly5VA/&n:y p�M�&�2� �R��� � ]GW�-.D�\ .  >�zi�O �*"�9t cp,n�br82�eigenSjH2�B��f�)�Zi�Ch" m& $Hamiltonia, hat{h}_{D�� e"j�1 $#\D}D}$)X�:% q����" �ؙ��T u7ppH in�a�I�): %-�A��H_{� ��}��=(*) # } -*9  })hV\ }-.X>9 }+  Bw }))� ^^\;u�H11u�uE�}�N.Np each`$*�8&D!� nd $&G}$ N�&otI`6#forward�: back؅(yo,�$&a�Ua � t�6NA�*w  ; av>7c h (N,Z)2g a����] N (N-1,Z+1) P �F &a2z1�B&k = \lp| \�s pn} ~ ||n>�{X� }*� "- Y>�k\rp|^2.P1P-BgQ �!is.*$.��� g�!a� by%qV"�<4,-^� h�M . Al�>g�� one-1|�9]:!!� :~C�. nishGt&�6�3H4!�par�"�  , q��;��u*$B.�d,�%4ѕ:�.49"3 i$gq*� *�F�\�J4cal{L}_{\pi + !i}^{intA\YI - g_ �z{\psi}p>^{\mu}Xw{ }_\mu|tau} +E\f�|f_ w{m>Q_�� Y%al_g � api yjA�A�Clag��} d ��Ve�T M��U��dA�a�s���J�&�} �q~ vT8s�Y�\e-d�Y��7�J.i"�$A+$!FQ�3E��� assu�Ii a/.�*Q�-��*2 N�*.k�X.\$�f,� �Es"��nn�Xm�� "� � bodyAt0�� RRPA)��ir�*~YB�:��"1�. "x s"&!{rR�. 6�v�$�A�-�i �0bseG�vy^abz1�,gk\��"� UF<.*Msy�� V(�!r}_1, 2)B{mYaP_1i� 2 (f m�\mu)_1m�2�)_2�/[A�_vn)]V2)] MD�g2�.K .&-&*NYeO�y vec{ �2� Dk\S�_1!\�qa}_1)22.2) ?D�� E6P� ]S& $D_{! (Z�:K���0ag�Q>� 6? =�P 1}{4� �  e^{-��rhq�-�r}_2|}}{N\;, I�6�S ]YPuT O-C��&a�y} �% ,* B � 8-� \;. �big2+��s&*s&%� �2���wU)o�yh��l76��.��-&])�� }��N%41E��(!�_v) =mR ,{sat})exp[-amJx-1)]\;,>�x= J /�� B�T��s�h%���� LU���^�3&�pseudo�; � �2h�u!f">+)J�A�`pi}=138.0~{\rm MeV}~~~~\; �\;f�}^{Jwe?=&R}�Q��J�typ �V�BKI��+b�I� zero=4 Landau-Migdal�,�c�C}"p� ac�,��<=�6&�;F?"%PT!(A=�E (�92� � )^2 ^Gi��@ \cdot2<s�&��)\; ,�%pi>K j ��p< $gK�%\�6�.9_N2�!d[N!JGTR��I�w 0$CIT pp$-�sne"{O���7e� a ph:�KpFs,%�� 1�� force*��Q}&$p}(1,2)~=~� i=1,2}��[(� bf�� {1}-. 2})/7 _{i}}% ]E� \,(W ~+~BP^� }-Htau }-M�m +)5��>�&:QI�PMEBer.84}�-" $7 o7� %�i}  �B j�i}$ $(% Y�#!D� .+$=car�bly Q$; e�-��rer� !��eL$= l ov�3e �eodic t�/S !���)�c&V��88} l ,1}{T_{1/2}}=��mZ_{if}^m� (D^{-1}g_A^2 $ �� {dE_� 2�1^+_\l�R� 0^+>�| �dn_m}P}� Z @D=6163.4\pm 3.8$ � BG.00}. $�]0^+: ��Z!d!Lpar*�!�$ @��&�WM��!1��"&@�a�.�k��!��!*� yi���a�  $Q9$-}$Q ��"�% accoO�#u�hץen}[�-�2}�KD,/ � &� �n axc-�|o&C���R$g_A=1$�0��of  .26$,BM.75�")r �/� Eq.~�5U�)VV8�2a*%:�SQ�]H=E_e\� E_e^?�e^2}(�C -E_e; F(Z,A, f� 36f� y"]Ice2*U>�!�] ��$1� $���r/���@�E181�%�ar f) �fz9EfGiz:�` KR.6!� �`:`2[���on]W�=!�!RMF� s�`:`IInon�x9m&j& )[Y��� $m^*Ww^ er"gN1���e!�ffj7 ve l�4 po�^a=� �/quival�p/'non .%�[�encU5�(.�E�ar Zm^MS.86}. �.�a�c� ��e��F2����>!�I�s�>and�)"{Xit� � noC�d-I �Red4+*� ����&0*�� ꜁��?-�*a s,E�in���al�� a��+|r�ye?of"dru�s>1XA� &�15,Ichogp2�2� EN9/ �� val Aa/m = 0.8��0.1�0Rei~Q.E�!�^�6I8e��!``Y��"&WD W��&Nq�>��[ y Q� usu� D�taci��u�� on�! D)li<t�Y;Josl�8Yed ``B�[��`�,w@d63 ``e"%m!JM.89J� dK00} m_D = m + SYr}J!�$m$�wb�e�s?Al$E66�bG�W)ycon�Ym��2b)K6�4Y�b�W�.YC�H�/� ��."<,JM.90}. Specifi!�/]e� M�VV����#!A 5�zBbp�nti�1�Mthe*�?1 オ�`,FU�IV&��"�-q�+5A.@|2�& >�%/JCf!����,!�nS� �is&K�BMjeffz } m^i�1-V/mfsV68�[-!��H�1A��QMK y ,���Eh���",4P�� s: (i)%nem1C �B"̰��f*rPK(i ?&��? � at%m*�ї�O"�/!���P� �/Kc�\!� as!�&��[9�16yZ6�cI �,&�-�sotermU S.O.}(r)=� �bar{M}��q� 1}{rW�d}{d r"(V-S)\�l}.��j p$!�^$i|R: �=M-�2} ~�%end� While�-:� M~a��&��!!# ines(.�$ e�ir> �,>� >�;;v_" gI�h&� �1 b !ngY�J���M� !2�E .�ar*�EA�Jj�%,��,{��f�ing7tr���~NX�7y�P!�#:h : $0.55 m�. ��\lI� 6 m$�* 0.64^*7ۭ� l) s"ƒ*�S�st�NNb�yy�!G! s. F\��n�SAvak �I�N&< 6 o��,Ie2-v���#aherZY)]�R�*I�"����8:V6 Eonɴq7�6�"9�p9!#�!�� �O6� m&� .�y աxrQ3�Ino room� any ����nt njme&��>�y&)H 2: � *�V�M2&9��9f��6b�$�&a�&�9):sلa�J ["of>�mo�KAXcol�e� s� vibi�] By u�+ imB�< ansatz%Im�B6%�a� �6Q����#��M��$`��aneous�[ulk DarC� t�l"j-�traM�n�L"H . A�A,�&8(i*�i���%� V�!/ !��#$�Z��q� �p%�al��w�<%bEuZ}� ��L�^�ble�)Ald����V�BN��x.$!V��X' we �'t���p��ach��K�iO8;>��p�� Y,beyond}$i�. AnZ�1i"A�m/�2 �d�7of�-��E, � (&E�/� ))*�&_ � to re�B�&I ��g %C"� :0  m9.�&� r���3)=�� A se�A!NA}�c�� suchb� w� �a�\�n܂ǀA�&&�F�o" O���X OŎd  �Sa�Oa, namQp�LA�p�f-� $��,d o�9��q��� Y�*i in>�y[ is�Ak�o"R,�u`2�.��� }yFRS.98*�*�Jbu ),�nt"I, =� f_V}{2M.�+l �+ \nu}%,(\��alD()k_\nu - nu mu J?"E.� .*� !e�.�arJ� e4o*� �now��.T)ud }6� _new:� � [&� ��� n�  +M -Nd � .� )!� �w^)j� .>W��!. �m )� �[--+y. /b��es�Fslm��;K����.� &�,�)>y?*�s*$.� s�h� $m_D�>0.u . �V� te�%�f���h�%n.�PIGg$g����}�*�'2�R�, �a����!m-�D*B_��e�e_>Mm&� m� StC7ng&� �(=@2�$�"\0 �i#�g>kB�!�N4 &$B=B\ 6I.��Ipv$!""&�neݺ�xhR��"�#s6� to.��p�%B 2r�N�). An �x"L� �>enup�.��`:�UmodZY =,��]as-�*, ex ��&�tV#�."n� ^�: a6=67�N7�N��f�Nt.~I �:� �FR��i� stil��T*�@qu�_� �cu :Yc!�� %��I� ��� &� Ni�$ar� H"�Ff�%�� �=�=�lsoazBf`�$�X�F������mu���per�A8�  Zo�&fA*�0in��Q+.�.�oJ| 6�5 ����)��f�!���ty)�l ���� �D!'�$=uCgo � o; !�"�-�{8si.4z.y (u58�� =0.6a).�B�z��a>�2�W���D� pa6 :�I���do�R�Y�x6}$O, 40}$Ca� ^{48 $"�x�( $^{208}$PbI��a� in TA�~� TabA},� i88 >c�! -c2�AY 6�2_)!�z. B�J��sa��`R xf/�VS�2� "I illu��|:�A��i"�X���) Fig1ydi��8 rad�J�pi�Z� �=���ko�-�� �nO� �� 2�at=�5z-�!� * ��=�s. � $�= �*��!+�.v9!d^ind��R��&��9 z� plot�� s%�at#Ww�t�u�;Aw:"#-Q. � =�&! � �E%ve�( �v�)� *�lyH����X ^D ��ly�e���Ie�%_i�� ]X]=s %(sl8N��`{�|��8>=;�@ l�nth.#e�%G�-H, �s8MA�&� A2�)1BI B�6�GM�i#a*�qu��!�5}� ��0 Figsy�2Pt� Fig3>��,Q�-"qi6leK� $^{78}$Ni0.�.j ,&R-�, �, *I)�wo>=�!6�eFŸ2 Ž�mQ-�6SM&�u: SkO'# ,�SkSC17 @( ��>�]a)#el � d�i�K AA�(6�:�89$Y �)�1.0 �. C��"0"�l-W.�I�.�QF6�!D)�*!���-W"����H��^v,uK|�t1�� )�� o6�.c.A�6�BE����V�/%֒�R�,I�eF��&�&O}6�*��Ebe! >!  M`IsaWk!�"P pm �!j�.q�y�LR��=evoluuO�@ 2p_=��2G? 1f_{5/2}$fJ��vcop:�i�-. 9���{"� �gO lz=^- Fra�I�b"i�*b" e�a "��re �EI�s ��1���,aw&V�&?d&灡Tz-*k3@e"�/� $j=l�1}{�R�y %a/ to)^ ))K '����/�� � -�1 e GT*�S�=� a/6(nt�!"i �� �eHz f�8 a*uz�S� core}�"h� (!\pm��D�j=:$)��IX flip A.*?2g)1h)�---O5� .�yV\ ecis5�k��Y " �:o�6F 3��*5A�is>:�;&b *�:cB"j[�L��"+C.?Nv.'of{2�26e��IFca�h�plaA;kqor�1r�.ʴW%ܱe�u`�x�e �"�.�8I�a"�X>q��&q � ��59`.=, bi"(90":m�] �2?&�H� *C= 138$�?I�$f^2/�?d08$�|�U ^!�x&5? 65?7$"�>�-55$"7 2�;����U9��M/24��(!9  !�, a.�J2�X9*�;x�L iduah["� �O��ct&w[�P,.��p" . �8��%.�!K"$8a�Ise��t_ב�T ��.=yB.�*6�-a =6�ng infl}1e���T�,9rv2��urEtthX�]hy�2�"�a�"b�9r,8not*kq.utr�cf�f"y!� �A�¯p"u~�AuA� derg�Q.�fasS�b&=�~ � *�  - d*�} �#�&��.$I"�%2��=GP ��.2*E sfe $T�8 =7$ "/Y���Y.� ]q.2!v¬Q0104+126-57$ mc5Hosmer�6aLb�>�QRP6+< U%>r!�a"�9�.F��3*.DF3��Aed@!1\�$x 0.3$ �?,�0a` �32g�9z FU6U�. Obvio�&��R�X3!ʺ2��<.�rU!s.@ ���� *6� job��8� , 6� .��#u�� &;', l�� � _Z^+ ^m�vai�*�(8����G�|�R��R� )k*%~ch�co��bly%Qe:Mq�2�4 ,�8>n�!f� !�e"�e� �N�tI�>G*��g��J8:K will�ͱ�1>i.F��tk ��!>"CUez�*{(re��%J4�W%&"�Q�G*A .t�@5ea�v ���eFkM �7ma��#)5��fC":�m2R�.H� |UM`"\1%YA� �6�62$!%|*� .daC.$is�!Y$�fint��9zD�gr:`U|�/2>!���Gfor�]*�90}$Z�b$�W2-124ӕ &�$!�FofYvs (1FR�;F� R� ,9� 62� k,+ rP���"!n2��J�&;0�I =0.9�?�C� *i B���: ��_� id0a�+�)ɚU�Z�,%��E{s.�e:��{ᥡsW{s�ob�a�dk�[/Y!%KJ on�� �-i�in �*-t `�-V+Oo63U. �$�g,�Á�Tq��r$� !�2&� l ��"J�� "�!1�,downgJ�c�yS#6<d�J.j�)�"��2_.�:f year�O ��2�a�*Yu��'vfCc�k"�G� �<d��*of ��G��i!/�vicinmWm�� >Z�t�D�,�xa/Fs!tE�&�"I �I�rt*�3L1s�9inFG�"�/�:NQ�Q Q?WCYE�����gX�ap��Enewly� m i2Y"�x� �k�b��eQ5�1z�x �8x.8x.Ww2x �}�l.l4T"�!e��2�A�,iron, nickel�� zinc�t*K�'0$���$1�` &M�*� A�*� .� ��l�@"�6oc�s�@ Z$Z=28�Ito�Wel݀t &�/E(���^')8og�u8 Ff d Zna$��iNM=mf a�< as g:�� Ni��!6�(|mT[���ɦE�&3Q�]�5I��5}!�*�#1&� k�!�F� � (apt��"�7�\) i207�-&S�23��ONUBASECA�g%F��*.��,KK�OT=1�ʗ�T"�A��A���6�24.��+M)iD"O 2�EV��Z���L.�H6�:. � �8$&� ���O� na��8ll[ i|2d#C�Qp�&� %�:�e�R�\2e����.)rū��C�h�V����9��x0=1��MeV_%u" �.6e ���468}$Fe)4�9�aFA�"v�RGmJ ��6L ���0"�%� _�@�N��6��O4.A 0� .� d�St6H -A ��QY RF!N)�6CrUFZ)om*v%�ic��*� b��i�!"�P� �J�. � semi-��Eus%C%Q, �đ�6��"� �ݙies $L_{f%SN L.za %i� v ar 4 $i%��a� )$f$&�DE-��� 6OQ��� - aɲ�2��L>]l ��lŹ�O�d] ɠE�liu�Tab�! TabC��SN�N�An� �r �i�vE�9H��}"� !���b�A (95\%!�%� to� &�d)�$�:�2a $5��{"Ű. Ok���3� Q�er6�4ap�)o��#�N�3�4, �F�2�A�nuV�I#D�!g_{9/2k��nu{^�%5�B�$[�g,"p�pi�%R, �(?:4;M�bt��%{2�}2��7]L��V�:q-�G "�nco�5e�A|2� (!4QD)�P�. B�9S * U6��բ* ��'"�j �x��? $v�� Onp�fpp�~(p�C��� >��_.�i"s.g��� )*"}+��FP �qu.™�ie3H�o}K}+H�o , = E_p + E_n�isk9Y,at the $T=0$� pairing compensates for the fact that even�> DD-ME1* interaction still predicts a rather low density of st^ aroundNLFermi surface, i.e.,\ $\pi 1f_{7/2}$ and $\nu5l single-particle levels are �Ttoo close. The inclus�ofe$T=0$5w�Paffect only configura�s with7 proton q$ at least ��Lally occupied. This is clearly seen in Fig.~\ref{Fig6}, where we notice tha �$the transi�( built from2� 2$ \to 6His!�8ered in energy !]enhanced�increase1.strength2: , w�as�remainAS�)�unalt| . FIc( Ni isotope >:�orbit� A� lete=aQ2 in t!ic� 6067Vblocked.E' �UcouldI have an eQ% a% � g_{9/2} (E� )^{-1}$6�$, because? � 1$�not fu.Oe�1-h below $^{78}$Ni. However, )1truaatAZ�is]8 almost empty (E0E,P2 )�re!{a large�tribuA�U� �@�, buta!�same tiA%Qe^\a small number of neutroajhich caniTcipata�P`$\beta$-decay process. O of hand,J� a �!Y �4� �6 ),IAconF�I�Tbecomes negligible. In ;�to� iron-�0ic chain, we a�%� able-obtain!�� valuuI�1nu� paramete��!�E� provide a�8sistent descrip%��entire �nickel �4es. To reprodu��he experimental half-lives,extrema�s!�g 6� �eH(to be used ��e� y collap��8PN-RQRPA calcul��. BmO ե�d $Z=28$! �� shell�]6�is%�i�ive in2�aALAWefore C�h2�= shown��2�07}, overestimA�a&2Vdata. IA�(is mass reg��we)>,also analyze�Ky! zinc=�LHRef.~~\cite{Eng.99}{measu�6Bthree6H �*6}$Zni28 !�$^{80of2}$Ge,I�%� to adjusXmPB�$. It was s%A� B% life�Xs�*�KbeY���a NL>�qN@, $V_0 = 230$ MeVe�{ presaD1� ion N=���u9d by u� a muchronger>��F. �I�)6�has oA#e 6�(probabilityA�illustraA��*a� ampl�\�Dsemi-magic nucleus%�%�.A= Tab.� TabCI9g� -� �e�ies M relevant-�R� � d�I��import5toa���,�z�Am�$T=1$QG��� >�y 2��"_ đ qualqone�]sides:�, %���f_� !�Asze��Z�amongMW����!�6�]x ��a J��n� matric&� ( following 21 s:6�� ��a�62N'!+)�a&� ;*� V� ess��? � �imof:J�aI weak���j{ of Fm[ . I� �.a�$Gkept N $\approx 25� �6� has virtu�no�i��"ed�Q�H%�val betw � = o%j 22 ӭ�fe de� s by �I10\%. W� a fur��aJ"� R $, h! R���_isplayAcsteepp��>�f!c ��a�p \-K3�KE�$correspond! dis"e ŷ -to-e �itua��O�� 7� T.� �� (�MeV�� =255���d�=�)����2�D}. A�ue��ct,�VabsenceA|2�,�dB�� A�chaJ eriz�*two}@�low( n%sdomin��by�8 back spin-flip?2p_{1� 3H' A+Ghigher on��%���Amixtur�,core-polariz�gy�ap>!�Ao29�to)�9�w ��: (� "�s :�:�2��w�V�em�F�:$E no l�well se�KtedIF (ii) add��A� appears ilt )�nt��5����5�!�1 !�sultsA�0a sudden redu� �-}��W . Of�rse�� is � �be poss�  if�0}� O *� �� %_�� *�)9conseque%their*T �ld�im� e# �Q_u� �2o. Sia��2��!*� �k)�i8!eoFv�&, V|its� e�ii{�6Y:.(�Ñ�a"fin��/,� ]^based% ��v�2?(. Although:��� �.MQv��Zn �, "� i:�8}MsdoLot�f!�ae ��A1is��ti� r � U^� tks, �� �*R M��6' 2� 9.��$EO6�ňN==�n"� B�%U� �:ѩ %�11ɩ (< �q�6��� =U0 =a�Z�es)��*�r�@ �*.2-!��6b�] aj6ZnZ i6�ID +fezJ8�ord� :� 2vI$T��8=4.55\pm0.05$ s �NUBASE �FFm�be7 d՛34)�. Both lsJ5d!v)�/, ra� �R! poin)7"� .���A�F� 2�10.�plo70�A/�8�!j� �!u��%�a�fun�A@�:� �}pQ�- � inst� �is,� � fourUloc�V>Ae"G 40 . %=� \subse�{N $82 q}�mm�e. * doubly � $^{132}$S�[�QA�>Zz.  ,cadmium, tin�n tellurium��.%as�� $N=82 �A�I:�11}��Ug�m���Cd qJ��j�� ewoHio��um[0� A=22i����F�A����. A ���6a'v���n$previous M&�V�a�mor� n ��of!�n� �I �>�" � ��N�9 MeV cA':91�f� Ee0}$Cd5PN-q ��d���2zB� 9��. �!� hole5;g8�)] situS -� M�+ i�� similarE5!� of F � (Zn"�X)��2Ge� �e ]�!�do�x A g�&A � . Ag A(� �!eE�F�p�w e6� &�asdiffer�lZ �mQ#�>� � �isS�, d_o a�a8��H Jh .&�S!�-� ��y%�f�:�Ŗ4 &� 2�FaKL. AU3lem�U0already encou�eei*� . O�E� �!3q62�a�.�k. "2Z�s�ataanJPA?d��| t it eO .� to G ���by!ply� Z 2� �f*n�turutab��nly���g��$. Our mode*/ e�G5 pa�aa#st 2�:q28��� " $39.7\pm 0.F g !�lef�nel!�6[ 2�� .� ��A�arison��a�avail�2��6� . Wi�ap*� � ",�(theoretical1�� heavier2�d w aa noun depend�@2 Յ. �ـ MeV �V �"Eslightly� � h� �.`i.�!� s easily!3 lain �����%�j beyo�"Q &ibeg.o�y J�Vhјa Bg"ivA� en!�Hj�6U�� h_{1�$�jE���b� #es!�S�d TaP- !Z!)2� E}. K@��":|�� �ncy�6$�L� veryA4��!UW�1 Z ��6�)|�-wVke]PQO � �is�@N+middle p^��� .�N�liAU2����Q$as�e cho�2��� in.�kAsomew> shorB �.5͋A�i�rel� -a2w.�9y spac�N*�\-�.�Q$��&in�? �$arf1�0 (seeA� le \c%TabB})�.xO 0q_Td BC�) acc&�: ́�q}�. Fin� %�aer�f^AVVv.'�6� ,�w m!-� ��of.�Lan  AfomѸr show��at� "� !Orealist E�|t&B&)p"� ��um&� .��.� % S� \� <{\label{secIV}Co%(��&rksz outlook}�is work�newly d}( opediiv)P �.b��e first%appli)�,Gamow-Teller6�H �idK1Z$r$1� �,dtrix �� ?!t� � formB# (canon5[)nonGiAe��\Hartree-Bogoliubov (RHB)� �3e RHB+vIxemployv1J���&self-�$�:a�I*�� le-Xn� �� LagrangiaT&ith d�*-�kson�coupling�u, R��� �& are T%b&�*� a[�finite �e Gogny.�YiQ"$ph�pp$�s,HsK'=�1 RHB 9��d&min� 5� quasi�=+bas��e�e B JAR!́e-хUa��->�&c&�!� (�-6)��((�U0 a sum%T(wo Gaussian*��v!� � non-2��Q"@& 2�`2m ��sphera! -rich }}$ waiting-p�eA(i. Microscqgloba"� EJof� 2�#)�; " #&�"�)��-o� xa��' A�.��osynthea��/ac�G�n*  . C-6j�&8 � aA|ailed.{(�*�%iRŝ# ucdI { � ���id�#]J&WRA9 eѨa�aly�Qi���at| ndar:�,mean-field �e.�,2y%aar mat] a\23% per&%of.^�% i, g!.2,� empiI�.by~m�F��*Eir� ��on��"�st-9� = term� �� lyA�.4 �� gy & �g� partnerst<uZn ZE*, 2�"�"6�&� �(J)to "~a#ZI{ 2KE� .yRHB" Gof)SarM �E�s E�ch�� r��r�&:�M��B�Y+di"_ �I�,A&��� an�)"� isoscaZensor-�%���Y� } a_&:2�%Ee!UDiracIKa9d� Dle�-���)new0=n.y %�2]pr.\�E�iA�cl� p ]psplit��ue~ forcA-s� "\st�ng / ���su�AfulA��-$set so far��F�2Bf3�e2�%a�%�.�2 )�)�-�k% a��T9a�5�5� !�t(cannot, lik0 SkyrmD(rsPeA*��.�s l Z e�!de%�&c) !-oF.�)*��*�UGT/ "U&�O�2� 6!�J<8�!  s & 50 A�82�Z�&Hde�O���GTa�ons3 �m low-�GT� �g *�Paa.04�.P!� 6�����2:oAbv0� e non2�� 1k���O.�$42t � �Raa� e tu4��V 2e�ar< ��5j%A2� !m�%�H��i�a�!r�"���t e�2�2�9n:�-nfe,��".>�LeI!�a "�1 � 0�{0Yt50 �t:t2[ "�}%��&P/-�FɝZwA�ai�!�a�   {��!a5� �od-it9N��82 i�.6��"C$ helpB+�Ni@�mt!s��q �i�.�$ ��$2�Q � *�8q�� le*��$>��t �(%ugges!Fin Ngx&E1U�-�2� o.� aH � exte�9.�A��"��-ts, or7 I�U1p��<-�nxeld%du2�-5deficiz*[p�oA=B ��Yj�:fof ourV �D!���T!���hy!�dit(� mpt a2�22y!�HM� �]� 126, 9jre��!�enoughi�to�str� �5��6�2� �� �:yn8thelessA�f/a� valuAp�2 finv�4g4�_/.n �� �.q.�1�7�5aam*�]fu5�of .�, >8lso(-f �*d�7� v playp "(2 rol�u�2 �b�%-�.Ye�126U�4Bor.03,She.02}3>� !�mak%������!i �d � � �d� � ��!F�-Y� � ?�+y;go8�osi�3m*�a�0�6ion. ��$2�$$ \bigskip   %� �2\�tline{\bf ACKNOWLEDGMENTS} \noit���"�sup�48 �!y!l Bundesmin�l%8 f\"ur Bildung �>Forsch er�jK 06 TM 193���/l Gesellschaft f\" ur Schweri�/fM�(GSI) Darmstadt. N.P. acknowledges �� �Deutschej, �sgemein p(DFG)�0nt�$ SFB 634. ��'�'==U2A<�T{thebibliography}{999}\ibitem{LM.03} K. Langank�?7, 0258?-�� NVFR%#dT. Nik\v si\' c, D. Vreten] P. Finell)( P. Ring>k6k 43061" .oLR` o8{\v{s}}i{\'{c}}:u G. AA�lazis"K| : 9, 047301~42(NV��%�`Bl06)�20Ik=�93}AkPa-3)"BZA�.^>�!� 3431Ig 3). .F VPNRe�.CwRn�2k4Lett. 91, 2625R�4�B_2�� l2jC %�543035�==Vre.00}6M$A. Wandelt.X5. �B 487S0) 3346,!� .01}�t, Zhong-yu Ma, Nguyen Van Giai6 ��0Li-gang Cao, 669��1) 249..�Ma%�Z-Y�B(, B-Q. Chen%�|!<T�0zuki, arXiv: (-th/03080212ZIke.6��4Ikeda, S. Fuji; J. I  ta, 1�)7��71 (196>`Rin.8053�P.� uck,�r0Many-Body Pro�', Sp�FLer-Verlag, New York,o806�Ber.84�5F�.� ,�9 Giro6D. ��{��428, 25cZa� ]UBGET��SNriely>�2, 0355�?� � \�BM.75}A� BohrMB.R��ttelso!�dar StpC$ (Benjam2.981975), Voll II.,rKR.65�0,J. Konopinsk)�M.E. Ro�"�! \alpha$-,"� E� S($\gamma$-ra9" ectr7y, OGby��@Siegbahn (North-H%B,nd Pub. Co., L\Amsterdam, 1965) p. 1327B05*MS.86} CA� haux%,��(artor, Adv.EF1� 20, E�86)5 =�ReiA!8 P.-G. ReinhardB�49, 305E:)JM.89}A[J!�o�%�: 40, 354EY6qJM.90�H1, 697H9AR9$V��2:��_ {s}i�%�a���-� :�5�u2�� Ar2� FRS.98} RAJFW*tah J. Rusnak j$B.D. Serotm2� A 632, 60 �8�#.�IsaO �A. Isak�K��(Erokhina, HAche�,Sanchez-Vega��B),gelberg, EurE7.��A 14, 2p 2�9bFra��re oo et al.2��81, 3100%�82;HosmerA| $n&d I�,n�al%6� �yics Con<.P, INPC2004, G\" otebo�Sweden. )�h5 ��8,��*�Bvia �4ee Atomic MassVData Ce��, {\it http://csnwww.in2p3.fr/amdc}.j �$ * e�*1 ,�*> -c 3, 4h1i�2�NUDAT�DAT�N>P2�C ��0nndc.bnl.gov/ /nudat/+9UvAGShergurNC ea� �Af w \endBS , \newpage \u �:e} \ca{{Radi6*,KA*6��"S#po|HBin>�# solNJ8= 2�k"�+�e cur�#H@ to RMF6\�PDD�N%� *&D *Fsa�CIe l� e-�Js��RsecZ,��4 Eq.~(\protecty(so_new}[@/5 ted O4pa:ly.} �&Fig1})�1�b�N��s�O8J&j#���G8�J&�"#G) (a), * (b�#)IwoH#qa .C: SkO'~5ci*jH(c)t!d SkSC17:& (d)2 2� S%a��/!1�Fig2}��]N.u3vh y�,T@b�Piny/VPpper <�"�91�Y�2gQ��@"�)%�2�d�3�%��[2�4��Cnm��B�2*5,�(wo he�6��, ��le Y3rdLJ��]6�5��P"I�4�d�&�$��I�9A>�JF��^xZ;2�6��*t%M�of�YEiwNU�2)��D%R�%ERa64-_�4cG��A�%�T�y=4104+126-57$ ms:��}�'#27�)*�>IP�4 ) A~22!$.�-e[*�, 42@K�Na�DA��sR92�8�� �$bS@�0A�2�u`N�W�'�+1� e����9�)]���>�>��>��Z7."10>�:��$b�.L:aT�!��>��/2ibH6N�6�zq�� Sn (J %3)e, Te (.;3)" D>��YV�,A#}��2���:NM�.�Pa*e1 �B ��=691� u.��>1�*jG:yy 6aB�&t MD {t�}[]c� &�  {E�WxH�#(in MeV)"Z3*� �ne8)!E^@�Bd-� �'��%a! �� *20 :%��9 !l �ular}{c } \h�� & &{ �}&  *}(Exp.} \\ 3� 6}$O ;�6,p$ & 6.32 02& 6.18*\\l&� 9259 5.96932. \\ %6� $^{4�"at �d�57H 6.59H00 HR�91 91>9N�8}$2�f � 7.69H7.7 �8.3^ nu 2�1.7%;0.5-2%EV�:�%G88� 2.03& 1.65FR�g � 6.2476!@A 6.0827-�.j� 1.98 31.7jJ0208}$Pb( �10 2.20y2%&&�772y}[Ii�8�7.1 �5.g 33Qc0-0.8-� 0.90>2pi.�6E�1.8M� 1.33J21h ��e0-�5.56\\q���2&}@ $E_{nlj}$� a��%� each�},����-ZDGum�^pecif� ��r��$bi%��to g�� mo�X$um quantum�Z�3coVl96ed��.'�)��WQ {" pa6 ?.�9��)\#:! EXP.U%YAE4��!s }{c :>\multi \${4}{c}{\sc�+![ tes}a�&^,MuqU}����w {$nlj$}2& b)G�k��*  (EXP & J �B�� � {$"(Cr-18.76 & {-17.44& {} �"� 39�2 8.79 }�� n2d�V!R {-10.; 0.32H9.04} & �s�> 17.6,.�-16.13%�y�7�R? @2� 1.20 y82y:�_.: 6.25- 16.5 5.786z3s�@ 8.68?8.B �7.76x>�0% -9.� &!��h@j '7.4517.3�7F1iF�7.6,8.5�!' 8.696�<�t8.9EL 12Q� MPd_>85.7t76  95:s|Gs$1.4: r2.4!� rN5)D6%� �\]�3pB�0)10.3h 1.5�J 4.81N 5.87a�af.n�:�0.&Kb0 �m��U�6 2.6!� & {1ieBk�6d0.14+�N!d! 0.75 j& J .���Q ^3! ^  i�|!�\  fq O� "j�i�B 0 BA h]&�O�e���]&�*���6< �#�he2]4p 6}$Fu&"|*� ���.� .�r�3��k!�& 2"�6t��&Ű�+sD �հ �Ss}��.�0qe�3��E�0 # 0.743e*`'1.(9�!� {'Mr>N01e�.'2N2��C{ō��BN0a& N�� 'F(��NmwFN�{N 'F(�� OݱnOn'14}L�M�/a#rKCzK}J ^-$2"�!^Mwm'6�TkV�q ._�pera5)a�a��U�*mW� 9"\.� � pare�<. }Z:�5&.} r�2i�V_�U ("fJ18.9$ s)E�6� 7�Z.93.19 }>� 8"mTq0.6 7e>M,{$E_f-E_i$ ( �AcB& F]T{-3.0��$gI�H $ (12\%)�<.27a a�G`. .1 . {-5.27�"{-�F- $ (5,��{$.�\�� (80)& ( �P }8 (' �'� (7 �x �r�6 �\S  {-2.69�!p�o $ (6 �!@2.9� -:�� (13 .g�`�{:`1s� �R[V�29�r19j�-�� !�4 3�-2( �$ (47 (N�)� -2.3�$!0E.# zV E � �� ?I�j� ? �?Yp5]�5�m���D:�*|�� � "� B� ��J BF�L� ��Sn!�: �4Te2 A} &{$v_{�zJ }^2$ A{AZ! .�13�g 2����13 &V e� 5.-C 7L �q{1 9� 21$ ��{1"  �  D.�2�-.�.26�� Z6% 0�� � ,3,Q�h���E>�G docuq} �h\$class[aps,^�pacs,prc,nofootinbib,floatfix,]{revtex4iu�ackage{=2icx:�Bxsym} .-h�6amssymb6 wasyB>epsfigi$sloppypar � newcom(2{\be}gin{eq�V}j4#e#!^!beaEnarrayFE$ FV"b!� {VB ARbi��3izeB�"@Z m mbox i:s{ �nsize i>b$refe}[1]{( {#1}):J(mca}{{\math SA>Bmcd. DF f. FF i. IF k. KF l. LF m. MF p. PF s. SF t. TF v. V> difd})` rm d:~vt}{\va�:taBh}{\frac#{2>avp Cph>%va&$varepsilon:_rA�r\Oarrow:llefV<�[b@rAb#l #ong^hLhLonfhLE#^E bigbracke!k.�{c��\ e�i� \hhGe{-4mm!kre.yveceOe�{\bolda:4 $#1 \!\!$ \unF?slash}{/,0\,:x Z!� }[2] g {$I#1}{#2}$X.�a�: ! \! Us#1>0foUY1JQfo!*�3F>fQ� 1}{4Bt>2}J>Y�3N|f�5NvA�tha6Fsq�sqrt [ .,sq��(2)5��Bos)2%B$sf%%2%B*s) %Ns)P%NUumat}{A�!��".�ncd%�! \  \!:tet�C, !S�,H. p B�etpz4'N5ev5�N?pF�'��pJ�:6Vlk}{666k�$%some jour'0s%V cuts�""�JPR}[3]{*E/N=(#1}, #2 (#3>�JPS3 4Scr.}�5RL.6s:L8�<2;�6RCr�C��D>6D�6NP5N*�;�GS 4 {Sovc2=�A > Ann.1(N.Y.)�xAP ;{Acta <Polon�w EPJA�3s�A�wEPJ)�6:��NC sNuovo CZ,o�sN q68��Z-Z-Y��J 3C>�>�3pin%H�. N$-NewslelP�>PPMr-g. Part2�6�D ibid � �3bfr�EPJ 1�32��nJPRep >%" Rept�8YF 6tYad >z�8PT-�9Pr!%TY_n�� �title{C^Ved-�O�ys&ZW�Komega$-m�Vtdu"�Vh0Nt0(9rea#s[X c.m.TQ�up+2 GeV.4$footnote{S"�B,by FZ Juelic� H \author{V. Shklyar7O ^ ave 9.Far Eae9 n St�z$University&�7:P690600 Vladivostok, R�Ul ;�l{s x@�",.physik.uni-�sen.d� �H. LenskU�: sel}�G. PenneQ)affili{InstituUCur)�etische��ik,�\"at Gi�v$, D-35392 GeAy�Qab�Gct}�tpion- k$ph[L in_eT-� , he f%\�"; NuxM , $2& $\et \$ICA�/ stud\Z�$\~c:�&SF&�Q�ZroachH�e}*r�L %��$ threshold6oTXSNH00�G�+{*�4rA�O=$*Y1U��I�$ 4l�D�#�*�*$� $,th$�* fhi8masse�Q.Jm W%qd a2/�`2��4$D_{15}(1675)$�%�Oac! )��5� � . Wh�R)FI80)�^  I"cinfluennQ2 Q$ >�% } $ sc�6�Gits)r6cnh!cd1c Q$I��T,du� h_ el�=magne�]A?_%�i�&).�d�H�`beam asymmetry $\Sigma_X$!2be�YnekJveR ��p.Gp!mi# ne�iASMy. Above)5��}~a\o{G}��ge%"sig b́poh��t forwX dire% a"EX.hinGU�'n�.' ly t�M�9$RAAL, CLASI�CB-ELSA?a;ie�O�b�7 \�P{{11.80.-m},{13.75.Gx 4.20.Gk 3.3 �n�J�r*�^ Intr�M��B�K!�a�.�-F� oa�eu�QSy� �( !u a ve�Q��stA:�� i�<gu issu�� Firsltud"u�I�n-�=q^s�Q�s Foi!Im���elenMRiR0-baryon dynam=_Lis �LJHviu" inp�1-:BF in-medco�Zs).a Z eiaO���:��fOA0�V tempera[5u�*J�mԡ� elasa���Mno�| "�S 6��xt)h2 principlep\ �4cE�romtMJ�(i�/\pi) : �1�!���a�>l�H��A�P1A ��caref#`treatBsrequir�Q1�alB�a�L��-�satis,�(E� &ENc�|� of unitarL��i�p�O�M.E �%"ŧ open�nnela�S2<�CanJ� M�� �+um!��c5�L�B}ingwish"2&�8quark�R���N�/or�< �� :� !��D.� �x�~ ificant�Ew�U"[s!lׁ(of hadronic�} ! is��� �cto drawk[rm3'�ab!� �A�T� i��f�1y1Ѹ unti�\ � EZ.= @�� d-ǝ6�9 �V6[I�[is WSr��n disc9�b� li��+ � !�e(reY($ly publish�@ighaVciF_�%�!x SAPHIR�2 laboao*fB�A�3}. Most!�5�@�� �&' � ! Gd� y,5n 'T-m�i'�ly�"V4�ɱr Zhao�>, �Q,O� 0,Babacan1,Titov 2}. Al%�sC� agree"�  ք�@ kiA�^0$-exgI�o� $��?�Wa�6E�Z)�VFrima� SoyeurM2 �5A$Hq�%�repanc!b exis� P��var�yŕ��2� &% &�2�J��YX^l* !� ! � !j0}�=h��($P_{13}(172�>:=g�g�n�m�>6�"� of Em Lee ��2}�w��74��a�do:y� �5�5k:� �. An opf� serv� A&E madg v��$->�c���&X ,$N\fth^+(1911�-�P ���>E}!=mN� !z1}]!>� ��8]�� %4��e� �tr� �5�)�%� escr�lB�%|nPlN.��� mea�ism!� good2 m8J�~ J$(\pi/;F7�J�$\( B' }�% achie)�(hu^Ye�}�zyM1n�TAC,*�>�!?s�P��:@h�[�Qe�1a�UB a590]A ��!@���Ya*� ��v k�]R��_B�-��I�to �p�Aq %���i�:a `.�)yw& ]�pi�.����euN^*���o[�� �k��.�-W�L%� z "�1992,.4}D�a� ult,i>� ia��$*�� take �ac�|���D�KM� �10}� b\askolA�"q��@$SU(6)\times O(3)!,�ent2�{_��n"APs)$Ssub&���&��&G.�6�wM�2 � Ϗo|\6f%���=e ($S89�50)2�,ْ7a]~Ms� *P`u� Moorhog� s��uruEv� $:1966}. Si �.� lyY(]ed �dic>m\jude $A_{� }^p$�(B�536^�@r! �p�(was criticC�T� 2��i� A>2W To�dco��i�W�Cse cs�3.t an���"� �2�N*�)>{CJa vectorO!LI(VDM) � s�oCi*�Bh�E g_{\* NN}6�kcoX�Ac&��驭*�K�e6]co�H ll|W]�!� �E8r&/ he>��%� a� PDG-"pdg1�A-jq��E%s6= VDM��A.�VG�be���yded:���j$A^5f}_{1-E�: >+! }$J�"~*PG :��=:yAi,fa&�n.�sh���� p&�t:�0+ ��5�9�xF�!Q��o (:b)�}een plyB� Ʉo 9jD%o�Mɷ��A�A�%�>�m�*� 6��fV_�~T �q�b���NSTAR03}�yA3 �!iLi!��Ure* ih�Q�*/ � (e.g..xq�$, ...����� of a�0up.|��!� .b\FOain"�to "3 sD�u�a ����@ ?c3) .� �2�&>is �e�R��i�ge�! Lutz*7 }��)a' { pov-�o�%�DM� �T"�L J^P=a^+�4 � � fh^\pm69 limea"a{�� : �e�A�$S$-wM"Nnc�� !�a seby � A�Lee-� 2sq�2rb�Xѻ�rA�to!�݉!�&sQ�� � ��"6LrhoaJQ�e��"-�&;�ufj �" ajyF� � *Q5.�&>&rly$[|��5�ofy�J"7g�u�n2U$� 2� .M���e� ulElU2EnF  .�s."��ca��hxk �>,e�"ɋ5��f�&Q ri_'Tn�� � $J"��$. &�A�J� =�"Y s��A��z � iderA"ĐcheΤ��p}pus enLa}o�h spac�@w ve po,�-V��Ѐo�� �nb B#)�4>� �. "�:giv�[c�ls�`A�66q��eZ�Q � i!.� SAIDnpU. �   �iory ��,�e+.� F��%�� etc.�=be&���.F!z�vA��k! .n&� carr�%�in� �� motiN%�� apnX!wpe� ��bi6� >�$ .G ����#�-�V�& &( R���A�Z3Sf$E�z !0b���j� ��p�r%�"A;�-�"^"B#cpW� &�aLv :nfap:ct�$ �bg&(�� r�5 F�*� �/%-�X|iFV�;��.  ^�5�n.n �d t � �cEi�E^ ��$�z���du�h J!� M'}��"� �l ��p�2�In Sec. 8��%Ybrieflya%�:%�m_qfe#�E!��;! �Lalc�eKCM�\V�E�Bt*��I�)X�E�pb��'��C��bm��q� Vk# 5^)^)+R S} �we�aG"l,a Summary. ar\.�!2�"#P%@\&�x5b20���"z�.( 2. H. w� ��"%� >�uq�te B��-Salp!�")�( (BSE) needE�be R�tb�O%�*B ��ܓ: �; M(\�$,p,p') = K p,  + i\ ��6d^4q}{(AN)^4} V2,p,q)ImG_{BS}q)hqh ,\noN�\\ Js= V���Re��4Rbs�-eea&�t9g� i�a�Y�mituenth%!o  W�E��]n����"�a�}agaQ$ �$�.A$ , $p$ ($kp''r�inc�GjoutDs((x+)A�r-mRa.�4dat��&A)�b�2�=epe%A��P"v(oE���)*|�i$N.zi:Lahiff�9}�r��>��te�vm�! &X xts� �BSEchJ�ree-dQ3io&6 �� s (3D�G?origi!1� "� �!�k &wa!�I��waye����,1)Yaes:19�F!� V � whel��wM'cho��AZ|H2< hn 0�9:%rncyedavoid �ulR(�� kerR� �A�%teg� }!NL� m<'IeV� F�a tech�� si�g,��t10Gased >z3D:�l��+'�#G. dz-�E�a��w!js -� Gros!�93,SuryaA�6��q�*�.dd�oa� .� *�&��� eMba�no,�ppE�� -cal�UK�!:$&� ��AP[!�aJ�� ��E�egl�a��z2%4waym�is -�l�!�,_i-`blem !|&�*L� n���"�*���6g#?���writte�-�+�Bbea iIm ��(�,q) = -i\pi^2���m_{B_q} \sum_{s_B} u(p_q,s_B) \bar . } {E 2 E_{M_q}}\~q a(k^0_q - ) p_q^0e)ՠGBS�D ea t|put'a�"!�icl/ �i�-ssA]f܇!7b�(W%��.�8�*o %:T^��mbda_f\l i}_{fi}QjZd\ON6_n�m_{n})aOn} Nfnfn}cn2�ni}.C2-DI� Mfi�Y�}s�$E�$N$( f$)�nd&�(um�zmbe�fL/i�(3nM(4/^2q�8# Hp p' m_N m_{N'}}} T%�$�.= }. U&�|�alBe��2oe�$T�Ko��a�Wigner *2�Z��� kPhD� a [.�G0be ea��.��j��ၧ���$ algebraic�1U�J\pm,IA�E��C[�& K^}{1-i�C]%<.� GBSAa��valid"A�.���dem�!�by PearJen� �51�� 0uj}/�=y�^N �,BSE� � 5y-�r�6L6��s%oJ>A�(-3" !�w�dd%ҕ�x ENcleH3E !! �WU2�v0ifer6� argu��.v ��1ce ��93)�� s&2�$K$�j 2�Ezoschem�.20 $` & � {Goudsmit!�3cp,Ose 7itp.%���:e$ŊK6�� ���off�(�t5 � normaliz�!���+aE�8�-pN '[=% ach&�rSa�!nd:�b�6}��  �upF_LeE�� They 2*� �re�# � nti E�ir&al ">*model. F�&�m�0oned,.����itN!i�1n��&$s(n�#e- $exc��ԓ5h�ut!-� � "%6'� be es6X,%�� !#%�a ,ER"9��R�1& 440)$!C�1� bȹ��b�8$\sI9�?y#��KrehlA�$9km,Schutz 8jx,Speth30zfQ ��6��� � � chir!�!�60���n�" -&�� b0�{ ;"�2A�<"o �ais2,6js,CaroRamo,9j� *'{ ^ream��m� 6p F"��  �k�7�=�)y��.����i�&�r2� No6"���0a΄i35tir��$!nMQ�!5�a�5��)�6�i�.�f ��+0{7�{�E��M7�5��d"-!?�"�o 6/( ����!�B ")M5J�6s�[�7*"g .�t}�>l�)6 gin{-s \b�/�?}@\ �� @phics[width=14cm]:1.eps} +�d$s$-,3|"d+Q���&:�$ X$9�w \�\diag}j�;� � D&�&�!nes%yA-_F�=�=zE�� � &6urb}���k!�val��o��!�*I"mj��vZ41a"$nz � GBS2�u�!�aB��,�"? ?3}Q reoa) llowsAa0 &< � ) F+ il " n}*g _{nG /'-�%g� I��m�� way,�Ze 7s�fs&g "%�def}as F� � >�  } b� "��� �2mNQ �,!� ")!�I=�x%�ru]� E"�4�"O����_ aI��ҁJxon.&�s1Agau�?nvari$" du sE. 1�� � 2002b})��0� � ua6�]� ϩ�R e "T 2j��� .aNigible6~*y�D>��#�L (��"U is ��u%� ���7��6� c2-)� ؝ Ax Feyn�3��ram "N mwm� }. Te�!��M% ��nth.A6* ly*,�!W%s�w)��.!&#�he.�$�c� u�� "#%=a�"�)Appendix�{�agr%��>2SBi6�6j��.m16�-���e�^P a"�s��+in Tae�t-�}. �� e�J% "�k ${l|c|r|r|c7\"W{��&�  [GeV]�l J^P$Iц1XC VE�l & 0.1�n& $0^-E$1 �,��),( ,a ,)$ sb D^547Y^0oN gamm.^JQ�0.783 Q1 �FQpi�et2�@Y�� Y65p%+.Ypi�.�f_2� Xo27 ;2�;�&!! 7696�=~ v,�3,) %0�9�:�$a_10.9120 �:c:<Jw7 ]�T ��~P2 �� s%6�a�6t%�q.>�tU�s�*��.��E vt�QI))�!���QD %5N($ |eu��ue�a�}*Z�m�x�d�6�% �w s3+�nPDB�.Dfk  ���!A�nt�B� : �0\ba{lcrclcr} �/rho�� \pi}I� &=�p20 \; ,q\,ec 3/, 2.06 ,\\* a_0 A4>V-2.*�2Va%�>�5.76Ux �0.1056U ,eta-,-0.928 , ��pX* 0.313 *Hf�,.X,�j, VO�* 0.037:VO- ,142,.V\ea� mesdec�E' 9<sB�low���� �&� fi�oE{A�ow� ountA ��[A�E�I��s �q�tex  dr�Mh/a:����or�!0F_p (q^2,m^2)�d�^4}  +*-*^� 1VUe�eaj $qZa�Of&1 � �3 ze�$ Butoff#-$. �>5N� 6�a�at Eq. e��s syste� �bGR� �r �3n#do')�/��%c� r $F!/)`1 ��NLa�*9A| t�G  f�>*be�{MG2 c&�%*�w)�m&�? ��/ll� �a !n#A}��+$ #� �^{J}_{alN}=>RakN}=...$��,�6Jr/,~ ,fh$1 is g!l�Ps�� a :; i.e.!} ��NB,W/J� )Ur��6 fh}$S�)M s.�A!�ofq~!�m_NC1Ysyu�!�o�Re�=!��eF� wh��e Bor3.- toB<` s  ��idqH.�76� 2��[�i�6tt�3"� �!�ve/�(f|m,0-A�M96Oa ��*�A�� y@s$��Davidšp+ Work� � 1rk� %����Us�OΛom�4=֭54\tilde F(s,u,t�$F(s) + F(u  t) - t)  u)F + #"�q�PRAt)3-*�!w)Q��"�>+mq G4�:$\ze�$�Amr���w.0iso�8I't� $m_4=2�G$.GR��idYr�"toO�!~�T!�ih $N^*(F'.���#o�x] fluxYC �  N,� \Delta, \N e 2��3�+A�:�95_weE1`�%l7�m�=�5���al�/�:oss0�A�sY��Manley*�4.�Q�  :198v=m2�Oi-�� -*�>�<��7�� a �@I:gA2!Lȍ�Aa�/�]��93Mrei�e �4�+.����tin��Y%{ ��:8�� keep�UiX=q%�R�O�Ml��>�Am��.H�5 ]C!�4'2L.� F�(*|�)�5�92,Vrana��0}�;desir� . ...� ��F("�, bornS"�le}[t]  &1 *'�'�{l|r|l|.�$$gtv �I 8 6�8 _{NN� {& �x5He��Ddotrl a�}z$ 36.01* JZ�&�L 2.92Z6� �rho�& 4.48$\kappa�.#>32:�~B% 4.53 �3 1.47.�#.-� �fc12 0.41��a_0)b-69.7�2:;�2 N1! .& $-70.6JNONg �\4.1ρ.g.# � $x9=�JM 3.94 b& M94MJ�f_�l-RZ5z�  $hA !  !10.87ZJD---�f& $5�F�Vq��" UaNG��*�":�Xy (�JAx ) vs�����] x�f�(l�G D*ab���&( e"�BZ2�3����T�sE \/he"�e:� N}$=�� �/l�>ӽwA���� �G� "I2 !9 �7��p- Arnd�#5a, 8}: a�~ 3.13�� :V����Jx�!in "�+e2�\u �n�3$�=-4 g ��� rebYN>*M,� s[ t� (�  �u�3XV)�����Z]r{;�pl/a�Sor�[��9� P NN$� is e� ly�b\1!']% �-"�&^6"�hV :� �0ZisF(rezE� :^��?_t"� � gra�J�'��u�|Iw}E�7- o�O�+.JfNIng�| j�T�U>k �!N %V�4Sau%`n:1997,2� aR8 �f�&%].4 o�  (127R$� �! tFtH�I�a28*�lea�!�E�ga% u�4�n�">;�eH�.)�]beiK%)u b"� c&�s,�;R�JK-� Xve827� �or�**,6�&�& )MKn)Eʭ�JN�pg %��2-�*.�!�H �6�6aI�er l�%-�=!���� to �C)�: 15.9 deriLJ��AT Bonn�'q�"'*� I�Machlei�� 87}.& ?*� �=��O�Gak� ^-q��+Az)K&�[� �*��6��$��. �"z21�� More� ,6N2s5i��.�Htil�AeeO 1t$-d q�a��9CC2�OA� by�UorQ���7!, e ac��Is +%�C�-�b,�iond�attacU\���kin�}"�'y*!��to�A� Ak9!��I[�J)r�?�=�%��iV��! ��.���shapeA�in�:�**�K��-Cفi $=0.5 �"m>�2������o��A���/�a��ab9�up�s4 "pb{Fi$MAv&�&"�}�$��.=�6'�+14��11��A#$I�**s:�P 1}(1�*,>�S,:*, "*�M $>�MF_Fe�d2Ud7QdQU,i(Q# E20�M,�i79N"B denokas$20}a]a�N�Q�.���� i"b/9�"$iP >�Uf-t"G*ME��L@*���5I��� � a�ut%$N_{17}��0) Mi�B5�&k�.�eD(*� � ���Anup8B q�7aoA], a�,.%� j�xp�6\P=&���A-EA�rh�f<����*L'i�Npora��; �0B�s�b�!9? N^*}��� $��&�*� A� <0C# TC>P�  fixedY. T���bes�K�[ )E�,2�>a�p2�C�*�8 }�!�cEu�]� j�Gi .��� zn�:�� ���N  =e%�!�"/,4 m"&]'~�5N�5�&1�" s�&' igXC� B�$\chi^2c !#)�(uc�A( s�Q��A��z"�. �*'`� l=4.2(6.2I�2.1(3.9 1.6(2.74)!�a(ively*3�љ�Ua�" I-)��in xѠM hS��x!� 5A��*�!.� E�g��f2G& 5_m��: . As�L�\u/1G�%-a��Fw��*p-�F�?�1o�"soc�KdS �'>-.<r.�i�qfpX\n=}���hwe"ND�'�#>}$���A \�O��#��.par�817cm}{�6>�.*>�.2�.h  "�Jnm��$&�=[8�� $I$=[m��<lid (daI_)��Ar�s"Ny1("J<)��!�"-. �Ge�Y.e1�E�G.�D]Lb��-d��0d ;!�A7��9�p^�S!J:!LA�200�_V{piN_I12�% 6@M&�/\m"kA�eZ6�i2 ��3��Q�S.�&��Q�"��S� 2%^sN* �$\�^{R."W!$ ( _{ �}!�-N��%"H84,f�2����5�5|24��&(.���| T�b�BwA�#��l��%�a(SM;�:�iA)�)19)8Q��2ge.p~/�-~-1|5�|H�2}N�)e ����R n~  u"��q�*a&iN|t�޵5Bem!�-w4�1�6 %C�MxA孉~l%�G ?� "� �le-��_ a��� gapIr%M�Ek 9-"&����2p.�A���n"7�]�q2�^ �<n.�m)�s�A� 4$20. �kr��>�U� pea�a"fc=$�g�!�d(E_{0+}^{p}$9�u shif�W! �(L)$�J",� 1661f� ise&a[�� wors�)X2� ^6�"�B��,5*�4��h$� +��&�",B/micAj5,"~s��6\�9W � (209!�$ �Zi�@.�xB�tg���f �� �a�rthq*�u8b2 |�&�Q1A�6wh$O) QSRa7$rd�w�]`2 . &�!VA#m+s zero w�0G �$94��eby} q,�hr,.or�w 6j���Nion�"| J1�$5Q .X "�N$"5 w[hn thv fz oh^? feX\fth^\gamma$ [GeV] & ,$\Lambda_\ff�%t^{h, J}K\\ K \hhline{= D} 0.952 & 3.80 &701.13 & 1.67  4.20 1.1  0.77 ] 0.9664.3--- 369    0.70 FN�4 \end{tabular�cente pcaption{Cutoff values for the`m factors (first line) in)f8comparison with6�previous global results from \cite{Penner:2002b� (second _`. The lower index denotes`i�Tmediate particle, i.e. �h$N$: nucleon, $\foh$: spin- �onancet.th$f%�9fh69Pt$: $t$-channel meson �upp�$h$($IY$)Q�whether �%{� is applied to a hadronic or elctromagnetic vertex.R\label!�c%�}} %�table} !R,inclusion ofV� contribuA(s greatly �g-�$\omega$ � produc0 me(0ism. Through �coupled5+ effects,�5geATAu _ N$!Z a / o)0reaqs which%6 lso seen H $\piFE#�al waves, Fig. \refe{piN_I12}. In }xpresent study we find minor6 E�7 $P_{11}$ YZs!�)/�final stA��Xeby a kink structure at�@sqrt{s}=$1.72 GeV�Hnot visible any mor97�.�,! Se%.�{Ri�}. ThisVinevy�q�of�4 SAID analysism�Arndta�3} )�\show an almost flat beha� a� to, energy regim-�re only1ehangings�)�.�s as�zi(our!�k s calculaA�s. F��4mass and width�Roa�ra��5�,$M=1517$ MeV6$\G�f =608  �@turn out to be ra!� larI�> 1[E: �AjiA�see Ta�)�tabE� Howeveri,baryon9�8of Vrana et al.-�!�H0} give 490$\pm$120ұ� tota!��-� eP .L!2Cutkosky% Wang p:1990AH9j6613545 have ba� extracted)a2UlM�q�!�$2m� data���pertie�A $i (1440)$ A` foun�Ube�;y sensit!to6backgr'2�[ & �~ferenc�~$ttern betw�n�u��.$\rho$-�& exE���SiJ.descripA���E_{0+}^{p/n}$ multipole requires a Mt soft� ��W.UeAV }),�� NvS��%r)L$�@4 becomes worse)�fit trͳA�ens�� e�� by enaing�F� i-� . Note, hY�at:���Qbranch]ri�!B6RBconsist��"� r� I�i�Q��MN�W�&a ����71A��2i��@letely inelastic�ha!�veA� mall>�A� $R_{e}$ asQ d!cAFS��e6:decreas�1qR�!5ejiM �)�]in E 1e �)��nd\eta  keep_�*( 7 � \cdot R_6G �"Xb��X.� A� B} a,2� . He�a goodR� �$$ cross s�\��$ 5�ity!Hpos�IA*�2"� I�tM� vanisA�U�decay�Re\ٷ8 lso��by%rE ��p��A��. � !�a�3}:�%H!�DqFG!�'2� � 1.55%1.7�U@ s upA� 4 mbaleG:^1]�$$ by Manley6� :1984}! .� zeronz might�anr ic�E%� ei���խZ�R nNX%Ha��  an�[}��� (� ^)�s� ice2�!CE . } e sam� blem�XA!�trepor�s9OA�Saleski-�i� mbinedYq�I� \to M�@q%"� M:5�9u LThese authors sugges�u(discrepancy�c!�%Hca�x rela5��u~ 6,U�$3 �*� ,. So far, no%2 made!m�- be, e.g.� �� \Delta"� �refore,V ollowJ%;i�X�error� s 5q orig> Q)to� ��!2� � putt��much weE��is =_ . \begin! le}[t] &0*S{l|$c||c |c|c � B�=A0$L_{2I,2S}$ &&k _{tot�.4,� Ig�22�Ŏ$& $g^1_{RN  9g^2F32b�3 8(1535)$ & 1526� & 13 ,4.4$ 9.5(+)� 56.1  &� & $ 3.79 6.50 \\[34(7)[ 51(2 51(5& [N   _ 42(3M112(19 35(8& s >    =IH1�1<65' �6648!<1  & 72-<23-0!(1.4(-)$!!-�$�$ -3.27 ! � 659(�173(12�89)R �   J _89V& 202(40_74(g& 6(1)  K  J =@%A"�]���1F %M517R& 608 !�6.0$44.0E}!M2.82^a6M��9M 4.35>M8462(10)& 391(34�69I@J�R  .)M479(8_490(12 72F�0�MlinU�1@� A�723�& 45@�!4 49.8E�& $43-L�0.$A�0-3$ 10.5��m� �8717(28)& 480(23� 9(4)F)   J _8699(65)& 143(10_27(13).2��n�3}(172q�700��   7.1$78.7U�0.2 -,!a -6.82 !@$ -5.84 8.63 �717 (31A� 80(1E@13(!. N  _6(112!U421(39)&$\;\,$5.b& 4Δ�\B�!H901H99e�A��+ & 22.2$59�i�5E�!i4.95.=)H14 -9.9�$ �879(17A� 98(7� 26(6a�)   J %INF> *.  N  �*D_{%U5U�50a�!*I��*6a��k!U1.2^bA�6�35A�! 4)U !V9 \\�Q524a�& 124�Wg�2�2518�_�I63F�2�21H9��93E� & 85IO&�� & $66�U� 20.1%�$-�'ņ $-0.6A��=7U� 04(55)&45a��23 �I   J E�<2003(18)&1070(85��1J_0!W  K  J ��5}(167L 66C ��e�a�1�6!R58M Ax0.3A��109� -99.0N $ 83.51O676ˡ� a7 J�R  .%O 1685A�� - 5� % &���1N F_{)O8�=671O1e��8.3$31.6%C& $ 0��-O $12.40e� $-35.9!` & $-78.285R8q�39m�70��U�167�2128� �9J�y�-k  J ]�. -E20ق41EɋM�?& $87.2�v!E2.0 !0.4-19a�I� 19.c  � 41E903(8�0(3f  8F�  �  J E����~�Pr.�$I=�&�s&�@p�]y (1s*��:�5v�&�.� (2r�,�4S.p (3thQ).Vbracke�estim�=�s ��="*�$�MeVzE�1per� ^b$:j.(�qM(0.1\permil.P&L12}} BI�)) l|llV06$A^{p}_{!��� n (t( "}�eک+t��a:a89�  -1  \�Dcolumn{2}{c}{---} e: 0(30� -46(��:60(15 : 20(3��f;\\ . �J�5�-2��b�-)�53(16 �15(21����69�� r1  ^:�2�"���-� b$3 ^WX --6��40� &�93�451�nr1�:I � -5 6�� 9(22%H -2(1� �� 7�9AYz92L%})�~ ��!�-6UK �  & - 5�4 �  1 �( 19(2a+ 29(61)1�4AA�&� 345(2�EG�%}�1 � -)q@-1�  %� 6GaNG   \\ %    ����"D � E& �r  -7�A�4)y�14)z5f724  � 166Q�-� 1y�-38 ,-48� N147q0-1q<7Q�: � 1 �14�' 26-33I&�n2�p3>��*e � I�-5�   �(%��5:1� -f2 �( 15 58t � 15)Wa-49(10 60� 5. R�� 1� 2 դ 3E0I!�I4a�m�ab�� 2��!�13 -33IT.60� )30I[ 14��-A0a�6Q0 �K � 1�&-�& ͪT�K5q I,� F� M  W:��� Heli�� (amplitudes \ J� �(� $10^{-�GeV$^{-�5) \de�%i�e:� (*�*;d�!�:2� PDG� pdg3%2}.8thi� :u �*of�F[ 19962?"NG":�p � c h!4t}Bd T?%re twov�*sP"��ɉt�f��c""��  ($:**p2c -)D&^ ��,well fixed:  �8 ! 2}�"m&.� 383�&79� �l�"�"q of \ 6�!�0}�Ov� 4121^3 ] "�&. ,. We obtain �'152.�'�#los%E!$Z$ ���Qf9:>�c#� zAz�!wo sta nd was ) � M�c*�(�)ez~��0find a necess�"�#2,I �$In&��RB�B^!"�" "�( �)a satisS.y `2�&real � � $E^p_{1+}.�&-6x""$ 1.w"2E[is stilW^�#g,p%�isa6!is du% a missI.'(:a to�. &�'pr P!�ts�+AO�!9#we�.��B""� !�A0" �$6#-$Q�6��,observed, it*#'"V!+ e lack1� "?!�gion&�"�"i#2`%�&u $ussed abov�"(!it would�#desir�"$to account�KZ�� fuD-invjg�# s. �T&Y�*� �>w &�#-<G.���ss �J)' Ah%6��6, @5a}: $1516\pm 10$%�� 6$ ~,}/IKdentifs)��& a iR g:6�I)Y�}�"�070�85n0�i s m� i �K447J185�X-ekwe do� U2in"�(&0y7�Y�.!�a��r�1��*�1.9� aF��1x\ >6� Ie2l6,y�+��sq) zero)} �.�, h�+a.�s|+.�4`3�-clear� peak�d5:`,{/*�+ )�S ���=� L�5j�I�5"n7� �]\ 2 ��&�)2'2U77+A��Fi�3%��"�, reveal�7' �� flux�2�+a`1 1.65A . It&e)sho fIshklyar��4} E�� Qcan� (be absorb�|n*�+$(�7K :$,�+ $K\Sig4:�s!aus�)co'7�)�PV��*" F�+ eachE0or penv (G*  i N$) mus�, take!r&� . To over�1) X aYto2 criben��Ml$ 2E���� a]Z�*B�AJ wa8m*)�aF: 3!h&�,ced�6w�0w u by ~�4�Cu�42�� o��Y�!�.&�1n ��,subthresholdA * 9"o-8B�M5��R -*��8Y S80�8&�7 �0����W�2q aUɹ1a[ shiff;�M�A"*�8~ 1.8a���u~ N�. Nw .� ��we�!}A�>Yz 9� �:�h�,�b tail!�T$6�"�,38:in .���AvIsh� er��95U/ev��c���as47"�earlier �kJ/4,Hohler:1979yr!aA �9�Kcy �E�Yǥ�A�e 9��2 E��V2�Q�1S/�S1)5V;;, �8!@U �. Kthree �point� 1.7,259 1.75�� �8E� exclud.8fi�.pr�/E� paramete��>��( �Q��Ss}���� s%3 �1�1�&� .�,*� % FU�M��  differ<o� �!�varD? es:N� :�"q $49A 3WF� )d*N4wh{ �0 I9 ZA��J5a:�i� � � e levee�($95\div 170p More��!�u1�����C C8͜:�1 �=�Batinic�}.p1�)j!ӍP:7 st-u yV  84-88\%�_s*k!�yp@, �= i���m (cf.NE)E�neeeor�9elidA�min��~]e EW�\b�1figure� !e�A< \parbox{17cm}{/6\+$graphics*[� =3]^6.eps}a \\B DE�& al6� "_v3 ,experimental�cv ) ��K�i�W,Danburg 1,Binnie 4,Keyn 6}. O.08 best58� .]*�aj6s�  da��R���omgN_dif��C1�d1�"`""t3/V5�6J�78mm}b�%�72�R�=82=N�4\textit{Left:}��� !�R) 6#� +&gD 2�9)����&2�. �R@ �N2 ���@ aqb� 2B,~� �^�!� 2C5}"E6Q Q2�C�C92�C102>�D1� �W��� ompo�?�D!�)�Vj 6' b�VB2| J<s�er�q&6�U�� \� < ��� F�E} ���C��mai� ter��isD E�@*�=m�E� pion-�:4d photon-induc�� s. As edL;H��.�6�=, um5!�"G�Of; sufficien�� e� y:�yg w�rry�w�c�: yQ_I76� � �G ^� �(�<2b � � )EsignificWimprove��s  R�im��G!'2�I�V�Gs.Gor� to8strAFt is!'c  e full se�.�ly avail�inform��A2�.�McH M i�*en �illA�� ��:$deeper ins��!r nR�as be�; . A�Aa~�"�J�����ddi1�o-Kё]CJ�I|$ matrix el)�"!&�!�L2�Ka*"/ � K*FF*�6�M�-�:JA�!A�zJ.,�2�"F %%has�MA$TF�},I���;"�K*�r k\ _&J!` $2He�r �ϱM}�"� �>o� +i [b� )���R .-n� 68�� in&� e)\_ . A��= ,GJW�influMda��S$-�6glea!�A"�G)Kang 0UpBA5� O majo3@~2' R8!��)G�#J+%$�at $\*�L80�� � ���of q 6� z 1}e��/� ��>� !�s 7sF_!\1m�v m��forwar�BglA�I�KZL��"*��is�Me��c�P�L! F�y%�M%� 6�)_Wa�a� dep��G-�� 2�mH�� ^�Os�� reng�Q�J�Q'!�mV$e�4 %dd%Y2�!LN��B-�%�  N&ar]V� �<6�=��.�E�]tF� .�2� ��)~�ff M�AU6���RsɽDnegle�L.� "q;O.� 1�c.�F;Q�4  �II}\simeqP25A\both .�(��d�Rn�O�GZ1&� iK ul"�<2�#2� *�%)InE�nels ma�$�Bf uy mX ��2�*�IF�>4 �">�5�e A�?ea��#=)*e@/� C(�N���R$of�3K^($M$=175�&)�E0<^be}!B*��E.Fsa� ���G�`e��9t\� 1�=�sY a�:%Z"�-��� exf(C�R�Z�=l%wima�Fry��""_��*+-d�M�! 1.73Ŏ (I"D,J!'"H IFA��;}d 6�piN $i e�� Z+��k���-3R� u~%E$r"�I� �.� �"��|7Bu\#t RD! s�4%��$����$[�2�W� ,aJP�pronounn7!-�U���eM!�,:/TeFTE���)�i�:�Q"�L5�u<s�.�)6� �}�M�. *�Q� Z:�6;56Y �!Kn#�[s�)��!*to look��I_>�M�Ts�R� P��4ed�� !�g N}^{�>NENE���q&&>EVix (9]�":" ). W}šBaA~Q> �e�'"� �*".*!23*checkZ�%!�e$bgclu� :� �0 �(t*)Qs �.�PX})&KK�v��{5c�11�B^����T��2Ws� >a !� �%��PBarth�IE�2�%S 0��b�P�o"G�(\b��8J'8.9\e dB�8.5g22g\p5�@32@�����av>�fXB��P�i�S �R�����)�15.n�149�4�oRCW� �( vidu� �6�-� ��&u b  _res�$6��`>_}c 2�͡Z�:M� r5����:��>f���.&f]IVQpjw�3�+_{)k }^2$=4.5&�]*Z le �Y�*n N� (M JW6.25)��e&� �!sup�,�ex�t_��-�_E'7orke.tuP!El.P ag*#�-h&Y-c"���^0$M ha_" �5by Frimr] nd Soyeur�e !A2s>��E}�*T&~ �"I]ed6r�.] �#fo.v� � �$)%e��!H�.T :!78� � f�.n"ailE�"��y�&�/"'�X3�s �!%!1 �0e%�freedom_6�. "�^$t&+bClesZ;c\< ({\it c}-diagrai�})� C"SR�T_{rr'}$�NU%_�- easi=05�%` Ap�ix�( pi0-�}8!Gottf�[-Jack� fram�T�#ini_�%]H��c�`c-ir <` IA� $z$-axa��Wdir=)M�.'m!� imoAOum�� .-(400}^{GJ}=0$. O�� hand}6$�3v>B$a|�s,*c� 2�S�?(m da� k %i 2)+ r�B�.2Q[s 0.3$� non/M,~ t)5f� �,v�%! � kiB  "�s (N2,6� D!  s) �,"{+A�� � !!�� 7&$52$@5ne@6 @&;=‚7 BB���8 @�V�!� j$�@$2�!�N� SpiB�M{u�=^'e�A�>ve�mm'a�su�3� � ��,�&'#Z4#v=�1ѭN?A�E�&J� e�~y� "/"l�*"��.���� . AK(35�"�$K �� simil�2��KB6coincidlfS-er"�* �l l *�"��:,b�-�>��\d9d7b"�#s�� ���!�WRa�%6� %x�1�2$ :fN�2��=�)!�*<���"!Rs siz�] h�1FT!����BB��B�A15j U!a�k�K$�72� � a4R�ge!{1��� K" ���<�e�BGI"re�+l%6� "�E�t>� _6��6rIc�Nd�?�^�eYA.2sɤW $J> Zn$j�}, lef��ѷz�1�26�\�u�@����B6��@��N5PhL&D beam asymmetry $\�5_X$a �B���# a fu� �b$.� �.2asimmz ����ڛU$f���ڛ�>���A��-�\6 %�Az���V� �kڄ 1k3>� ‘3�S3>S��B��j�B��� :st�"%6^b:�\p� �4���Ő2[8� -{$\p&}S  :��&�K?�2X7.* n&WU���"�$�^&�a! k�3c�)�^�5��%$�En � V , r�),� �i� �' "�a6112�V �L(�ZT&�li.�v *u hardl5�%�(Ath�dAc�Ai�p�A0, E7TW]"�o>:"�k"](V M�9Z�*]&�m"� � E *�!�2P 7��+f�sP E�I�1: becausKde�r )i�_ce !��n[8'o1B��s+ m2�s-?R'e�e):�`ai�>�D�ob -0� :E) J� Howe"�q.�"g � �,!,>� modeJQN�@���B!�*5. <U� playEJ�H�tr��?o^%�.�Qm�%�C�>�^E�^-]5�$A�Iq }$& aCN,� �(in.�7� *� .EF_.�["�a��-�^�` C � by Titov%�Lee� 2�) %�l�- Zhao + *0*�� %s6Rk#y.US �Q�oE)�4 A��H��edZ�C�"�C�w:W1���K �62�!�[$"Q �!��!j�� pa�lofV���esemb�9!+q7|K$, �n� deed�3 non- -�*��. It��,9� �nd)l*�2�%��i:Mvu��� .quarkzK%b.�.} |s Z,c-�re�K�8Moorho��se�(*rulQ�:1966WN�! E�n *�KA26#2��+c.�J15 NN^*$�^!�"�3*Av$VDM assump�s<W�*F{�E|�o�&.����ly��͍�Lt}AT���ung-�>��[�%! mar'lMHi9�pproac�F� ��� &�E"y Sc^�!Y#n5aVa�!�avera�0�= �1w0��HH r!-�0>�6��1)o�n*fD2�&�tdA� �� or 3a�put�q*l3cDt�$�"�D*�|3�$rh!�wo9.!s ,e4�G��r&�3�Q����:U$�Oly8U��+D>�"3�@Ot%�^N\ 0xZ�Ab�t!�>�i�7�t�� �yeQ!I. AW�I�!�%�-b9W� 0!p.�pD�+"~5 F�' urg��n�'� ciseQi.!N�az�narrow�bi�P��.�" pi�}� P=�� n�'6r�})!es+!b>��a^At ��"\�t"�+�!�"predict�8%Qvrv��of*h�-Ki� )�"J.�~�A.8$�-����� ~�ic&]. BV �1�+?c.?� rB) � �nt6� �Ro�h/�a� �2&PU5�. S-�!�especiaa�� 9 ng s�{{estE��  p� �/��c�d.��F͂e tra38�՟!e� E�teq1I�*�+RGc�y-�1�es�EFi��(�Ho�'EuA},:B�) ip�IB�*zy��2�jO/ �A$=-1�?B$=+1� 656� �E�ve devi��sU�!�aPc��Z)a��2`��PB��#N��3�:"y92�%��� (s��œ a��� ��AK� en��B�d���)36N�E�+� [*7:1�ɜ�<NU'1}�Q'("{z<ic�}�.x��*X5|Hs�,��}���H n�y�6�� )�4 Born term�k2 �%��P $�2�Hb>%�>��&; =�l���d ��&x" s (as defzin:�E_ E}) m E4a \ba{lcrclcr} �FH &=& -0.026 + \mir 8\;, & & (r ( 6.02%(062\;. \\ \] �ScattL� �ea��,e:$Im \b|$=0.28 f%x�is&��#*�Aby Lutz�8�(� 1} $ U =�44�0$ fm �rK� 3We�l :�q} $C1zp1 3A�S~W�#.9} -}he2AfYC>�#c+ ��b#�I$Qe]2A�on��/\t U�"2�4Duns�_�8�.e Ek.�yV}�&i�!��@? ǡ� :�1!�^� ,�3r1~�Ber�S�U)[2�*A� �u�"� 90��Summary"�CsIn@���$�per�(� w&M�e-1"�&x8ip+�2}Z 5&�9 in a unit�5�L�( ngia�G6��al �G5� &�[e� n"�<>��$0 ��!Y� � oh$,��!�fh# [ �Ae�A�}2� TRx%LYX]M *���� �car)D�P� s $(� /\pi)�-� N$i�%|,"1Le>�,�-�!frem:�N��^!;"t=2�&�A��{ N %vA��EY�%p@8-M�^y/9Q 9Rr� � ���(Ez��4-� ��� ���x I"�nd�[ . B6�i.�]=�2�ad!,�C �E&~.RJ�i�$}x%n:�$� "�<]ps2T@?.�>�"1 y00}E]1 !! 1-J%� |>, � ^���d� A�[��J_.�; ��*��Yo2(.�� -Va}m�!�A�-�}N�H�.:%0>�7za�.�N^"�:N.5�2K � �13F�u6|]]rF"$Apth}^pNA. ARq>�%.]�� l&�%�Bk& l&?JB �}.�,2 �_ X(�A��-S�%Oi,��Q�c�:#`P&�c^.�)�6�B�2i�*�)9%�L ��%r�a7O.eE~ &U�  c2ctN� b;6�j͑!�. 9�� �/��sBR i�I.&��d&�;�i.\>,��!%��>UseV� ��� �E"Q �hDC� �,? earcE^'hidden'.�ՏNp �*V**4�qu3on�)�J�a� Cei�p2'"��uB�at ��VG,!�1.� fd'&���"*%���+vR,U2� &1� polariz-��f!I{sѷ0e�X$, A�! B$hUdse<v�!��:5�y�i�/J--�$se quantil��nlyp"?5.guish"�v�W� -�`. �O!;!CZ!9 a-�3be�<, GRAAL, CLAS�"CB-ELSA"#9&;a�3 �"f C� �W,way� ths G�6"� �� agr}GLe­�& ��� � $���i�"� �b[[und�*3<6>-�CPhD��i�� lis�ly�/�k&� �r�� A �hoffz Ž,r�s\�notE�R? �n�37 a�u �Hila�o!�, ��A�� A<ci�� togI��ai ea8jVz%.v:TensoryN565�!1or_5N�:!G| '0 $f_{2}(1270)�q�@on field�9�aE�8a \mcl_{NNf_2} P�xu_{N'} (p') \bigg[ -\mi\frac{g2}{m_N}| _\muB{\�-8}_\nu^{(N'N)}+ � e.'m'<)f^{\mu \nu}_2 + rh2r^2}VA6�6Y�$ ] u_N (p)�,lag�.}�zea 5롧pto�-X s $N,N'=NAgQ��V�%�Eq�q,���A]h-(tE0)Ӕ$�*�means V{=�*A�!�!�)}-1�')�&Z8$>)��deriva���-Il"���Q)"e�*v&ws 6�m�ilkuhk; 73,GoldbenZ68�@�k] $f_2i � pi\pi$B�� Larg�T2 f_�� \pi}aI2g_}{m^2�M�!C��n f_2E�A�, \EWP�>4m�� �I*�F.�OB�is6Wv��&�/� !\to1%*: �V� }= �>�4_f^2}(p_1-p_2)��xi �e�. � $p_1� $p_2noutgo�?D:[a,$\varepsilonM%�a2� ve-�� !�i �P. U"��-2Vj� �a� I^Sharpt#3,WeinQ\ 4,Bellucc�\ 94,ToublaA�95j\bea P_�� \nu;�<\sigma}(p)= &-&I=1}{3}\�2(-g0}��p%Mp��Mp^��\�%)�Z.HrhqLrhoM �{mPJ \nonumber�&+�2:�rhoSmuR P�TW9�nu ��nJR��2�j� >T �  ����F � D� H.� �e;� eVRk then�ymg֜ = I ��i }{80�qm_f-D1-4 +m_j'2�a� �^�.mg 2]Sp��bUBaƜRFw�ID 2f res52k I?p%chW�>� we adop�Se^�,"aageZ7 ��i$\mcp_��! \nu,!j -�(p) = �t( p\hskip-0.5em /\ +m_p)}{p^2-E��\�'}a� ffh}^[�pith �~1&=. ( T [A ��In +� * ) �J1}{5}2m�&a� 5u�:�10}( 6l_�}"? M d�� ^f� � �nu :�J > � X Jm�J�!" JƔ<� �!��ConvPr�and)� .�}$&=&-{\rm gU0�^!�p^'�, W2 X�NL T���#áof $"mB��}David�[eUZm�&ZZ,(Pseudo-)Scai<Ma� DZf}� anaw��&)�Sty2�"O���#��  $� a (p s l��ph^ chos&� "��  *� a�� ^mC p + h.c.U,)�5Q-A�!%�n&--�5�s 7� F.�K�/�/1!#" �j5�... *�Cupper (�P) f �i�w9 I�M�( )� �I$. i�.�0Rarita-Schwin�wyic� w2m$ obey� Dirac equ��c{�� �v� s��� 2R=QHF =5ߡ`nu}6; =0$ ! � :194�d�off-sh7~pr� or $u,�z (a)$�m�qI = &� - �amu�nuU� off_q_q� *$a� �+&�commo-us�b�Ghui�F�1�!(z�!sfoh )1�^IupI� ��!{*� 2'e}�� �X� _\pm<  = f_I.�� R�� }}{3� � 4}k_Md^5�E_N\mp {\�[� ɏB4-!�I�ycDY��I ��[)��- ,8� �N��vic�s�-�mQ $f_I%�p�a�?+ �#.&�($5�E_P$m_�B\��W�2 *1H9�.x �2� *j�{FVF".Y. 5]�W�a��h ��`��AnbeQM6�� :} =�}�� �eftJ��b��z�%1}{4m_ �l^\xi +\m�' 2}{8'3}�z) _{N}J-3Z- �z  (K _\xir��- J)mu)xi��)�*_-4^ t -\� Nj 52omma�!�ig~Lo�h ve (�)qI]�" # A�(�� � $) �|�112-f�$d e(�M{ hɎs>� ~��I:Q�th$ caseQ%Q�i:� � s �2���1�<:� . S�FX�6W��.=t >�3�)euNZetenyi�',&� ,�42}�*�1 ��%�2�=-�"�-�H�AQ� NÏth}) iM\����pm�ű�5��} &k_I�uri� ( M _1(m� R) +Q�2 g (m_R E_N-a�2)}{2_'3 'm h�"� B�.(>�o��10w�� �1 �pm R-2E_N)) �:� ��V�0� )")�(9�)v���5��Beft ( � � �E_N1�.-�!�-! $9�2E�����6�i*p�aFN����Qity�!( �#di1Jst�s�}� $�MV�P���� (= 0 _V - N$' wea abb|� Ct�UA 7 =$ $0: 0+Z� $, ~�:1j�$, ~ �:1 !�3 �&�Raz���e�:��� ���:��e:�����nuJ�N�n���NW F;mu}�P� �?N�� U�tÄͲ AM�C��͛��-(�~��ś � >Kusفtare n�mlized�.#d,al"� (2 E_Ir)"��u Warnsv�9},QV��:� �E���at�� +h$e \xi_R}{8��^�M \�m_R^2 - ��.�0( 0*���RUm & g_1 s�k0Agg_2R �Q4�=) \; , ���:�t^�J��10v�Į�+2�N �R} ~�,���� �.& � �c�� ud n� . $%�$6} h��atp $RN.A�%�@z��� MO$ M���f� * >�3�.�� :: �ɹ�1$��yMt�}[h���r6"oU.�2{�$�Eq_- & 2�� ,z�.�> 1�${a^b_�%#2V3$�J�$Ic(1&�I�.00}�-1.27��-0.65 0.581'��00��404-1=��5 ɔ�qGi&t�48]-0.����H64��77 q2.537:)1.483�qg:��},e&�D&�566 8��& 00\ 0.80 { 0.68 {�� "�P>�D;��,��.38\��4)D-0.238 0.06- X 52  1.99  0.108.w*&� �&�,�882 )� 0.3��R9� -1.59�3 ֢3�v{62-&͡��955 H 0.17�00%��1m 0.85In q!� bm w20~�&�0.089 w 1.69%� -0.4_�A�x�A~0.545 mRwBmAx4Xta���O&��|�YtC�v�4�_.���>�*��b:�g�*E�pe"�(�"*Ob��t2�ob��:�����v^\�a��sdm���:&1fiq "oT����d�un6,;��>�7&�4�arittenL  +a � ^0_{���x}ɪ'o \sum0N,*�( � } T+>[J1LN} T^*B;'�r<} ��t ���>�n�A�[ *�rho0} \;�""� {N}�-�%$=ܗ� �Nn&�� "�{�`$Ee .  S) U 1$,$"��"El"R� �M�pWn�ē v4.AY�u0�D�=a+_=�rho^1B5e ��f�&x) 1��������1]�.L-Bea.�Xx c T>�1�2�+�4�1D.RK�$*�5YJis�*M s���D� 3-d\�"_� p - a� el}:#+J#`B �a�p� $BW$ ( erp$�Fa&�1�.6�@�1"�<pL+e{ p$� -li~> ly yh%.� horizoN�([ �)&�2)�+-��?(5plane�*\vec �\1? = x "�%-1� 2}}("8{+1}- -1})"{�@`erp!�y\�\mi>^�]+2 \�'�coorda�e systeA)-$9 z=� k/| k|$,�  y\ti:8k'+69 *� =k'��k'Q )�(E��f ree-�.��x�+E{e��"J2 �!��Wa�q%&�iiA�]�|114-1���0_.,2� WBZW-jW W"�\BA�el +!��4>qH5F�GU4be�Q �;ex+"�Flaq6UQ&=5��e b�2)�*+Si�zB�7�ie�%�.D<%���.�]2�G A^� �zo��A6A~(c)$ `ivi.{zeQ%s�JSj� x>�LYy -|�5�*eYx�>8z<��/\;��� �*or+al�<"�%�& :%�}�)m :"�*#A��}F�&\nu*�%*N^ &�"bpi0�h}#23a�pi$I�$g>� P/�(�/)�%�@��gne3s/6m (f�{"4a Levi-ChivitaHzorD^aX�aiդQq�G-�&r -{xi��G/%9_-9J^{0(�-�z� k� q^%�D�(D(p-p')M(p,p',s_N,s' �� pi0�6�p$($s_t�A�$p'a $��af�@�s(A�)�b] �;"� ]k$,$qg1Ve�' .�.na��� ,�a � I' =�mu�vm 11�� %1�" (%� mu_x@^(!� mu_y2Ip1-F� >" ,%�&3 %�V{0[zA pi0p�b longAt� ly1 c ��$From Eqs.�MS -� �.)�N�4"a)9!� curW� �J�I�=v&.��P--in*Y6U�DnB�"o�Ad>(!�{�!i�� ex'0Ʌ��*FF�are�a>�T� )M�'}�! �* 1}{2��^2 ;(k!�*� R})&� $'})} {(kq)W3+�V?A"J=� )6f�*& lZ�-*b- -�?%*�"26} �%F� �/EH,2}n"�pi0rhoM'E�A�KyI@%�+�d�M�A�^�2k2"'pl"!i� $=0�G �P=� �P II�Zq"} � 2Ke6[(f >�pA�'&3qR�N��>�#q alig� �!a�i��, RFx:me�E�Qn?6u"�?0F^{0,GJ}� ��Ay-� _e50.'�F =0. �)%b &�Lr�N" 0"uN� ��XX�5�a�4*�  uAi%��Oveno !�N �se��}G1?&1}�zvN �a1'3W0 a(J=a,)j,b"2�7= " th),2%rfZr 8ofZ "th< scl_B D.m�j =�uP�#R-bH�5���M�\�^9�o|1�; J= % \;leA,J%+ 6N\C ��=+0F:.B -*tf�t�% 9�1e3}}^�=<��B%�.<�9�A-�h'�_comb-� �&B\newpagebiblioܗ@ystyle{h-physrev3!�{tau} M docu�/OB ^[%� % D7P\\ R�m�-e� \\ ee V� � {� ��($^{a,c,d}$~��$^a�� �� )'.�$^{b,c� 2���\n�l:x{$^1$�=�AdvAd Sciex!2HTechnology %(World 9�)!'��8730,� 0080R. %of k}�U� �� )�2�:�^�� R 6 }\\ �" IShanghai:Lpp�5�p$ese AcademE\ �s,D20180�l�$^{!pc ��9>A��� 7300� 2�d �29R� � � �9\-��A��1absS-�896� f� i�� �&K#���!?G�me�@�L�oryp/� *b&W%�0�:���en�mneunT1�!=USea�r�f�ton� @ rich �ar�4ter�es a �er>v6�L1 .oܯis��[=ut'e g;6�1�j�s5qb- n� Y�5�BR� %Y6�"�fA�(b� � s�q)] �9]o��!�N����;�iT�Z(sAm�AN2� phen��'E�>�tQ� u�nd�U\� {2��.+f, %m�f;(4 24.10.Jv, %Racim�0.s%89.Cn, %Many-bod�gory"1GGv!��Q�5Sr4} } \keywords{�o>�;v�a5m; NI�-J�} \make� M V(:�2rizsA�oWH� of a5��GZ medi���E�N�H�*ٮa&qq t��si�C��)dBX1a EU$Jeu76,Mah8�EReply�RradioaIƖam � ics 1F3h0mLfrontiZ�in)ar3e�ov�a�e V�il������eWnr under8! ofK"t�a�E�Q %�a�� �mU� 1DWng"MW��ax>�%�2CI!�s Y�a�J-a�i�knowledj)h�\�wJA crita�ly*i�I609%!1 st�' dynam=]colli��by. ZsI5PRiz04,Far01,LiD04}. U6� tuna��,�_nowrJb|~U��3�w &�Z% Jlittle.U� Li �Li04} stF��v i��e�--pr��6� s���si� /EhE������anp6N N)mm_n^*<�K*$&Ga*�E�{�/� :�!UR5Lan5I�ial��%]�-�us� ��a$9kal data<�kp!�%@i��kA�t���tWb���6 mi�'copI�!oaV� .�uAJ�Ht$ �ex�Ws5 conf��+$)�on:V l�� ͝�IIJam89�t95 all F�m Ũ:� P%S29i�� Rna��ro "y NFR %��>R hv�>� �wlU� 5��A�9�Y� $V(k,*�)"#nonlo�E�|E6q����� c�_>�+�bon-I�1-��lying .��uG��NB +&�1?spaa; *�(id7u�ocal(� $k$-!� $M^*_k�A�`-�� m�slec��tsN�r6�!�im.�p &�8� yc2|$E � �E$.M����>~& � �a�twoJ/M=�/Mi� 0E/M $. %They �$� M,%�eqnar�L}eq1} %9) I k}{M)Ale�@Z?w,M}{k}#++!�} %k}>��E )T^�*_{k=k(.�}~,"w)44 e�E.�(�?�F�.�%B� UU )N�. %U350F�Ap9\ri�{by*� two ��valent���ion����,\p:�"^Uto remov�q :�#(����GLlN)7M^*!4U10 d}{d=u!!2�2: �5�m\A (J [B�(k)-��>1V��5x..�'(k��F'�!�Q��Ka�� #�� on, .\=k^2/2M+>���!oc�� 62**�<! w>�B� �k&B�"��"� �� �Tty� +��Z�i�(�2�fx��pm�75�a�}vau) (30 �, " Vi�ab <\:� ��)� �))�6%sc" �   d�� oped-� Km"� (RM*��C� suc�gfu�]�^p %0ar2�nd� te�+��Ring96}l} s ad popuNStoof  �A�do�lu��*X �~ now Wo҃p��}h� ofyy�Z�=�a��\^� i, ab<; h#���"� � �V. * 62��/lways �I� � wa� O�edJ ��ar �U-"[�)�d�paa ��� ��� QR���l���8�@)7et�~#"�:�4.�� ���2�>,M_s^*=M+U_s~�� ,��U_s� !�- B�Q�!o�. $`=OM&�+D2A|b�!�,2�+.�!-4aFx�RMF|R �= -375�7$6��ۉ0*) �� �/M =0.6�0.04$2g>���$A�C6��not4%�.U�P:Z z`��+!m��i�B� �F������aw�k%c�z. Act� r� eq.(1)%� 2)T+ote""2t i�al*�� �x OX reade�en.ʵ�NA ��by Ja�k�-Mahaux)���byA ago�# ma^ l��R' �i� �$the scalar\ effective mass or Dirac�O\cite{Cel86}. In order to compare a same quantity in the non-relativistic and re.�f-type :�$as defined�$eq.(1) can!�Iv0a similar way)JJam89I�AYRMF- sca/A�>�s a5[Xdependent, which yieldsf.\4} M_v^*/M=1-U_0/M~.> This>�0may be called� �:i/ �a�Lorentz}�)�,characterize%� ��ce V~HY,�. Although it does not imply that any non-relativ�O a�{ $-rA�� ar matter%keepsi�m"dsOA- [}� fem� �,s $M_s^*(N)= P)$A$$M^*_v(N)< �H ��I�� . If_int1!�9G �%N $\delta$ZRMFJ[mo�tE2�O CY��1b , evA�he />�is sma���1�of-9�.�:�$. However,aa is wA� know-��(microscopic? �!eB,��mmomentum*��Y�. Tak�saccou��M�)OERo5��>�sa�ef�aEi�Nw IEe� follows,�}narray��52}&=&�(-(1+U_s/M)ddݽ0 \nonumber \\��&&/#/M��=02=�� � 6j nsiv he�7 2=!�e) A�edium w�� all study.�ally fF�1m}�ia� asymmetrY9 � (ASNM)&RDBHF ��ReQ ly,!�ew de��os���Z� structurE!��#iesd e0 was proposed� Schill��$M\"{u}ther��,Sch01,Uly97}�� EG�rixM separat'to a b�� �-  (NN�te�1ion $V��a corX Pon term $\triangle G$ wTNN��B��scrib ʅ� e��s, such��)bo���vs (OBEP) gcoupla� constantsab Z �%re de��w; xperia� hasAC iftsq�NN�/�\a�!�,ground state�� pert!��9deuteron�K%Votgnged M�:;AJj� on methoda�0applied only !hhe vx��!�m�iz)j,four pseudo-%vs%?| E�&T6� $G�' � �B'�3(e'E !3a5� .o E�!1�-{ose)�uIjv' ,Hratree-Fock!#r . Ma et a1 Mzy020 Rong et 4Ron03} have usO is scheme zJ� ��finit��iA�ŀasiAar"7 �[D. Reasonable resulA��] chieved. �t� work%j �is adopa�(to investigA�%C:��M��J1��.��a1is� &/ rot�al invaa�& in �:{ɼ��ya 2�� writte�h:ٲ \^D6} \Sigma^{i}(k) =  _{s} (-\gamma_{0}0 + {\bff $}\cdot k.v.~,>� �$i$ denotesJ�, $x �$,  �i� q$�!���*�(, time-like%: spac par��;4m7M�o20,Alp�Zvely.���.�in a���e���-�� cul�?g �?NN U� $�+6�6&9�&9�71�!��&=& \sum_{\alpha}\int\frac{d^{4}q}{(2\pi) }\{\GI .^{a} \D� B,^{ab}(0)Tr[iB/ b}{\1 G}(q)] 2 &&-i�aq)n]k-q)}\}Y}-M}!� firs0d second�m� Har� E(� ��s, re>�index $)$ refers��� , $aM�b$ � ]i. $1"tsi��A�@icle Green's func4,� $N�i��agatorɘ vert�F�}e*� : $ig$� mSV�-g�^{\mu} %mD %� $-IQf}{m}�4^5 9q_ @�H6k2yT multi��b5S7�aauU�$ �&� �6� )(.��Zdivid� two%�s:EJFeynman;_{F!�(nd density-� tB*D}� U >� a diverg�(vacuum tadp+��e "� y+ is neglec��b�~ca�nioU��J� �DF#* u��m8} Q�_{D�m T_�x.kI+M^{\ast()I5i\pi}{E} _(k��-*4 (k))\thet F}-|�� k}|)&5 � $�E��q�par"YnN9} � = �(1}{2}(1\pm\E�3}bzplue( minu� �R� sp��o�S*r6I� M)*�2� � � formn�10} [!Mf \�'�� p}+)�!� (M+UG) �]\psi^i(D r}) = =�^i : ��1�5]�VUu���7!)���762q( modif by%* E.|� ^{v}A�$�i �"f 11} ���V @1#-M� }{1+: ~, ~ O)P= N-- .B! �]F9@figure}[hbtp] \vg�\-.50cm \includegraphics[!w@e=0.8]{Fig1a.eps}51�3b 3%i3.icap��{N�ia*�s $U_sI )�9�s $�� l at $k_F$ = 1.36 fm$^{-1}$ a�n" �(a)Ehth��y�? (b). }� -M 0( ,�l�."� 1�qսZ9}ta�w�_{n}- p}}+bY "naHnd p}� ��� ��� F is �2��SNM��( $\b �0)�p�`2 '1.0�+m N�!` ��������qis "JU.�Bonn B Mac� The �;��&� .^F�����b�*�j Ref. t_4"_�Nf0phenomenologik Lane}&� "�2� dataa5(($p,n$) reao � Lan62}. -�B�j�0$ ofM:AE5�ͧA(A�A4%� I$$=0.3 at $R�!�! >��� plotI  Fig.1aM eu�f�E��bs'4about -336 MeV��b{0}=256$ t�0Fermi surface�k6�r:>6j,�s/M�� 0.64��!^ ^���REvE 73 i� ���F��&U lse� "j]� to th"FinE� I�&? . � rein. Bot�� ca��A ����crease��!�incid" ��in (&^�YN� J.�, b�B�&V come}.A:�jo�~du�large&� E)l1differe�L�!�p-.� is m� ]�a� �9D.a�*�B6B��A�"D - UK  $� P usu�:toaraG weak or>�om���!RMF*�-�2�u8�� �5N;1J��steep&G2�, i�X�>��X�gbI�|i.�Nd(.Q����V��k$*W =$ 0E350���Rei<��1 B�U�Ac )g6!I�.�E E 2� a-�6[ t E=) ink1_&�k�i�Z= .>� � Fir2mK� -�.�( q.(3E  5u.�shyinEE2, �$��$ cur %6a tq�� Z"F� T T;R�5��s��ly re�!.(R�. A�jeN o .Wi�0yB{5 !�&C� re�6Aa 8>ND���7 � 2� �� �9�!�:�� b�s),:�I� ^ HV�$%i�!�*�aЅ>.� *B�� >h&"�, e.g.)nLandau-�  liqui orN& Sjo7�'T BHF ,I Bom91}�>#A-Z�F� K-��u����B m Li04� In summar�e� clar@���e�6�j�qS23 � �(�%�XM(: �%u�ar&�%at�b�� `:Y�&lbEf�e �5&!B!T"5& >5&� F�86&>�+isU�&� 1�z . Ie:�mCZ�iR�� ��� �M͙':�.� u�iw!@$!�isy�B2wAwa�#} �.��"Z ofBA*U�. "�ac-% ledg!s} �Re��uppor!qmN2al u4,Sci�  F�!�China un�#lGrant Nos 10275094, 10475116 10235020%KMajor S\!TBasic Research Develop� Programm%j.tCo�,cw@ G2000077400. MZYa� CBQ w�,bto��nmh�(talit�!�Th���! p, S�(,hai InstitutA� A�!0Physics, P.R.5 -�%Y!�9 ial�!du�́*,ir visit. We � also����- ��-thank�0 Dr. B. A. Li� many stim��,$discussionIis ��d� 9�i!-�KnoE'e Innov)�Pr�"�hAcadem%9MsMgM,. KKCX2-N11.pB�\i.�A^s} %% thebibli!�phyWlibitem{Jeu76}J. P. Jeukenne,%ejeun|C!"huax,%��!p. 025} (1976) 83* XMah85} :au:. Frtign�#R%zBrogliaIa$. h. Dasso j Rj120k 85) !jhRiz04} J. Rizzo, M. Colonna DiToro`$ V. Greco,�  . � �� Rev-$8C 40} (1989) 35.Le0P!� ng, A�g. Part.%)�{\bf 37H96) 197�[2(L. S. Celez5M.�E0kin, {\it Rel&�-!���I:�~ of S"0(3 S" }, World mt, SingapM0198.�( } E."=( , H.*=(, Eur�J)/ A11IR1) 15�_(�UlrychBM�6y56)17) 1788Mo Z. Ya��L. LiuyE9�66 �2) 024322K�%aJo!� RA,�����2%� G 33 M3) 48.J<R�chleidt-��Nt�fB ar��c�q"�)}, Adv.�1iVol.19��8AI89 �ona�PhDs� at �.�$ Atomic En�2����of +, �^"�(M.� e-k e, LettI 8��62!�1;J�@!672r 4O. Sj\"{o}berg6%� A 26 C��5��? I�umbaciEU�mbard�dY44IgA�0892; W. Zuo, G8�G 6�� 99) 24605HG�l�Z,.��J�" MathiotNQ A 14Ir2) 469. ��endJ�.  �8 docu } M\c"�30 %\topmargin=%\odd�-2 06:�%V�� {system�i�0 ng qihat zero .�a0Z��8�R!J1�corl) ondaH1���$ $J/\Psi$ \exact%8e�--r�!��A�!�0>DM�. V � ce�P r re&�  heavy A�collis7 Uufz� of aI�,�$e48possi�.hi�1forP<&m1�q� .� \h��-\parig:}-PACS :9�12.39.Pn 24.85.1p } }\\[1ex] %\s�, on{IA�du! }%y�(e��new�1of�t\6!qF�i�,�!"Bt�8ultra-ZV 5W (RHIC)A� CERN%�$at BrookhaI7�$wong}. QGPr'& Iq stag@1e=�\* %d ��W,a��+�.�d. S3fe�s �eG-(^revea�;b�udyapb�(&&3hadronJa�F�1�5�A��yias goodidid�0becaus�!E�!�p!+��,lead to its �Eion)Y Jpsi}. H� we w�toe��inW"ingsc! k \ carr*�'�2m)%a Thes��� 5 onglye^Nsur^4!9�������^up��55 , bu 3D~>��.�63J�="�.�=�^�Y����C]e�5�Aba�9% o se!�is,�el5e� �emi� $mo�Z ��n EOS!emb�5�`�n �]ro � 9SEF�A9�--!(already!hi�Ibsalv0�%�try�Ahre��! e �6+:� star�f�= %�i��(ei�freedom �refpov},� �� y:e)gis�}o8of �ea�( A�" msel� 0iV�5 �objects)A�%v. sol- �o �)��add�,a� our�� colo+^I>will ��!& sc�0ing���ed!y" lifej3�g l.w'�,.>� �0xI�a�>U��e�f1sdl/��ese�n>� O9:�8w.� �"�e� )+%�� 4theE�play a� � critex' %�a�f~-9y?��u�%is!�n4E,<# ilar�m%eb,1"�!/B ���g�>imw��J�f#ihhe�1�a�! � �L >�, i.e.),�3-&'$o>�@r Sg. � course+3 ce DUms �=�lighes(:r�7y%�(most easily�$���R� t)� ;^b[probes � >�. An2Xgredi�&ofe��� C _ int�satisf�. Pauli pr�& ple.� e>, dub�;C�;r B Mole� < Dynamics (CoMD)���4 successfullyN; to r.� A'B���0bon2000,papa}R< ?� p�A��] Efus03f&_ NumebCM�;}�e� m�d��6=!�ao &� m�/��' N�of4��Ff .� 0Gell-Mann ma�>�$^6h��JsolvedAs�9#in MA� ���@�lA\ev��mP.#� . l.��R s �� 2�Ri��dsoa6po�:$V( r}_i, j)$: ?e"[7 -{i,j})=3[8a=1}^{8}�04\lambda_i^a}{2:j left[ 184$33-2n_f}\L?(  r_{ij}c6: )} {6) })\rH ], �andI��D}J� f(t)=1-4 %9{ �dq}{q Ře^{-qt}}{[{\rm ln}(q^2-1)]^2+\pi^2}} . >x$-^+8re�DYFQE�fixqAa}_ or�4} Uq�)��s2ia� e�.e randomE)B  a boxAYb $L�@c5ʉ�Ee�C sp�#0f radius $p_f45um 2r �e��& t?m�< X<2%gas� by�F;Ia c�Fin �v�5 �,ze $h=2 \pi$�TFmmo�aW st $g_q$ 6.E�$�d�-t �Is,uj���7?=n_f\� s n_c s -!]deg/acym�, $n_c i�t W (t� � �XA: red, g� �b�5) h�\ =3$;�s�-q g%pi�1w AX ple 1� )�fфm�oMtw�2 �xy[)@.\, M4 qc}$54F#1Q%*`9�=\rho_5m`3n_s}{6�Gp_f^3�����)lt(ny ,B�ak�avera Kver all%in eachIRo$ .�. For ""� w*�+�occup4 g� �( abi� *U�2�is Ki�� To d�E+)>on�,@!{b�wei'e h���\��is �r���`1 $(\bar{f_i}\leq 1)$. A4 ch A�+/psc��M�R�E�g)equen�we �Dng �I$aM�s� > maA�' < $\xi$: $P_i=P_im�. � grea�#or �t5K1�&$�n)� B; �mp$�� t$͖ . Detail"Nm�a�LR�� illuXA�seip $m_u =5�4,d =10)fut-off�A-�x $2fm�a�) "M�avoid�Y� uncer�N� . SuqHQ�disA�6`��t&�at high��i�3�!y*~4��t�bF ogou���A9a�G setZ^R 6� %%%�/ 1 K o�'"� "�Qfi�;tb�;+Ke�&� 6�;w `8cm,clip]{varp_nero.ps}% Ebis�o�CLrt EPS art %\epsfig{ =.;, X3.5in,�4.0in,�J=0�6d"�; Time9a�i�um6v� � A�A�i�J abov� bel&BY.�  G��:�1�� Af�S2^5d � aQA � !jts�tilibrium�%��I�inserc e "��Z c�� c$_��le� em h*P6@!��>r 6�!��1ght d P���ip7�^ s5����i�h�[embed`C.� dop eB�*��"� ��)22r�a"" �am�J�-�n�Y&$&"� B3ofcMaion� 2�m!��K wXT2��%�finr6ge�.21; )W �%� us c �b a perfect�>9siH��wanq,anyAinq avail"��"v !'�. s!�d��S11e�YM1dNc�.7. ~ a�9angM�ga�Qa���J �is5б<&; \sK02=-

^d _ >rT��!Z�� �n/ �� Mn�,6xFK�L�ta��E� W s�{w�O6� 1/p)��� s monotonP��oB2��p‚cn<$pB`d�Z�h��m\ �FjAQmb��� L'E�gb� by!?��6ᢁG�8�!.���� tric�!>Ň~>:�l s} .�3}��"I� true%�( ��we;�\"VTvu]oUv2���:cu���!��Z�x>Tf $�$0,�`0����.E$"�6onBE�#��$V�$b!,�!p8>,�i�7%_�!. U %��at �d�' invari>\#r.%Ju*�� afD6��DZZ��]�6a �Ap :�4%�:Nr� big��R�r"JZ$�+6C$1&%��o� dN)t(&�2230}Z|2G 0)7immed�6ly yield:DaAF�.more,e:$d�2$�ao�� F�a��� 9�F� " \$ _2^2�c d^jNR,� 'f�1�\���L =�� ~��G _1|�,6�Mg�= n06;M��� e"X .jU&~��DEIiɡ�AWcyl& r >apdK*heǤ"�'{ ��62! �� ��_wH"�J �V]trans�2;� ]� 1_�] �Y�<{2l/%Qu:�t�*��>S ��.# Tune Z��� !.Iem��*8&�inu�_� a b��2{;��+Ei)$Mu��&rBD�(bf(�J�N�W*parO�Wy}{1@} &=& 6u;��,ɄE�"EPhi(0:� = I���5.0a�>I]N�&f�:=�R.ڟ%5?V + ��8.�o5.0No o#e langua�F�94 $A(C> � 2�#a&&�U�);{$.;yM]v &apa�sA�.�"� ��).Avn'guZ@M�??���vbh���3� � 7"��F{X, our�0has>� *(ec5(onf�ce�8A��� Q� cdot:.JK� �-be 2_Be �"dan�,*,=���tM� �*>� IWA�"D�W(��WJڔi7"Ք/ T�* 5.0F�b��ysFVsS¬ %f�:� Q}:�q%X:2��*9�=g!�$(:��&aEC �ll�AsNJN6� A�R�,\nu;d+2 a �s�*#y ;+r�EweH7�� Suchb^�cuOb�v0�CFUz��K E��.bee�=tQve 2�iE�$�)Phi/ �8 =�5y�(�+c�1��OyI�>iGA�$ya ! �a�&̀,VCgoal beo ) "�(Ir�.>a&5q@I F�d4�% {Fink,Yosr kW*pw?5���)JBquite����� � Ml�,{inq�έC��A�!-n&"$��)�G fact �,�NI# za%>Nq�m�=��' N +���e�6�4�F�n�> �%�!(>(�of�a�J,U�$�retv� ���9�t"/-ee  �(�1.��Na"usefu��(~I� �}0� "Ua#�963�kf 7b i�6�eJy?��1�a1B;�d�QVQ}(Cq%o, �G�� � �, was=<�35L3.=�e�#X�o�P5G� �!��"]G${6y�yp&{�ƂkLll�}�?\�.�"Ԋs!>� nu;2��t�Q�B�ly 5A�:.�I im�.antlsoi4cI�V0|m p.�* ם�G�Na!lDwK��B�,I� e r6rS5k�DfI�/8 2����i�j� way l �.��M�: � $A�1�M�� Q2� �g)j��0)�o��~P40 - 5.1�+Con��� � } M{S_V��n�S� �4{ �0� _0\,:�"(%X%�G�Ok2� $3\t���q%>� & a �/m�062pwpAVs:JA` a) E � 6�-5�}��a�Q]u�Y~6�a)n�Jk�|.�n�-:� $V=\����v�� !Pv}�m��j]�.�jc){/c �22 Q  (A 1�M�1 z q$c.� e�2me��7Uc���!+&��,�3S" <>�3a3�j4)� �)#I�% its^�I_0&�� ')"�T\B*}%B�_�)B� RB� \nu� _{k+1};k��($�u+1"{�"d $|' \W . }�>&\"��P�b:}:Vc)A�re�a"�F �FP�� $�?��a�2Wc"�}c1<O}�� + l+5�-]�ni aeYԋ��j"�2�X2.11}�bz x�F2e|�!% �&�&&�&���+rft"d (�8 U9 +l _�)w�x>Z5+ ,m�)V��\�/f�߫�1 Dʫ��>Ze__!2�6 6P;�`<:�8N�:YBas}?ed�#E��4," n�"*+ az b)e��ed. c) m8 stilw ���Oatic K)EM{  "o�N�B�C6��Sw<b:�K� �"R��&�:> 6T&2 f] fd!.�2}) �7�&#>i.�%l$ we elabor�5onO �K�<of �au��b *6�&O 2R#�67**�5.2} (Y ): ">�� ��'C� Q;C�<$J@�]|{[���$U�"p<���Eb� ٛw:��Q.�1T4tA�'ortho;ca~ ord73e I/1rh;7 ��lA�a%y(�5 *�E1))�=�!���=:��T J�%� N.�E!�)%d$U��U!?�6" ,!4a�� b� er}�WA,�.a�'�o#<<a =�U+v&�;ll{&��phi�h�g�m4�U}�9�6etrZ�DEV�4^7� Y.uH��!J� >�.�]"5�waoT#N� UPR\,�2�b}~XiB��NN>Mon� �!��\XZ-byGZ�.{�V�N���*r"�Jbackgr�m�{ ��hs 1E�>p Rݪ����6` ``V#''4 3!�@ ADLo A&v��I(JK�afn!���is cha��eW��-*C�j, X.��anX�O ; s�����4��`.�F�^ SUP2?*��&�>N���Km�EC-QÅ�1@a��or"�:Eas r^�o6o�*.��.[��(!�&R)�YI. re r����*7F��2D��.en�J�� !� ! B% �u.)KaU un!��!�$se hol �fT�'qo26�+nje��-DE �J)�a�[*� #*Ȏ *��N: 9,W�� #�L`���$&BU� "� ^7Z ]cA&ant. �D-a��G���)�!�aE>3 �ъ! all�4����"{ � n�_~� + j�Jj�#"�$(j_0,j!�&! ZߩmesK* 'd$D `&j:ܩefEu}&9�ʻm{ "s� "��� ] \\ E�)�-IJ} � + � ��V�� a.L��.��)�F��0��va��" an\ ival�+re�%�_.g2o1 ��1�rfF"� hJt -�f�2:xnu_1\s�8nuF- ��A�I8 $(\varepsilon,!�)�\l?#-1"�K�"�!Z�]<% 2z,dEF1bC��c�&-����t rval o.2 m@es�^k�$k"�4*"�:�"sim(e� �IF_1 Hze�2 Y�!k2u�vF � 2�')j K*�H%�M\lm9�g��D�l�Kir�\�hm�a�n��� �E�"�d"_aM}. . ��a&,W |A�zy%ҁy6I"�N�Qod \;1�QFt3jQvar �A� �@$"'�/�+Ne0 + j� �b ��� mj$u؁~�g�|�;m���=:�.�� _���4I#in. Iz .? +9�Bl! M2:G�.�U�v.w�>�XU!sA�$U�5�p&W$ frakJ � � _1)=AQ_�UThen :��(2�r= U_2^THU_"*��= �7919��U_1�U_2J� �!p!WB?A�.p� �_1"��)ivs(U_2)=��]G+j_{d+2�)��539 �plausibl,!( 8=�T!$I�a��,�3�1A�5VA�n � )��n"&H y me���1>���& �.�� 2���.�fL*!M��y"U"a ja*D��I�gJ�Es = � z�G7be embodHN�W��p�B�V�%�$�{# }!�~.��4"�+����6e��I��;� �==c� %j�&A� 2�6�a��t�>� } �� �7tnp-*��efq .�:~. 0kiA�Z�,/ � s�NA ��N�_--Yd�"K;|any%=��$H�$. �� situN*x6 pJ%�del��kf��A 5.3�o���Z�~ D&� �� 4} (�PA�s&� �*�%C*#:�7� :HB�a)JW%)��.� �� �>jA$3�%�^>'!wQ�Z+7Ui�$/U��!u6}m*%��_�� �� 9� ���d�!�M(5 if"� k�-p�$\Xi$ ~and,K8!�^6��6"NAˡBd=(. 5�eFmb=�A�ed )�ilqB}v�&|�*cqA�aYe2yIT2HAѥn}?!�common� mrioe`�%iQnq�a":]0&��%�+1r 6.3a_�L. %+6T��D+ain�(nt+ab�΁#�hs.�) �^r#���"�*���bse�se��)/.0 \Lambda(97)�E��l].�, 6.50&�!n�M%&��&� �"O&�%��%�x � & e HH*::.�^k �YBH�b*ت �)��J���m �i�"�.cN_+�_$Fs.��6&  C�&4Fm�Fh�g�(�VF}�.j9]iAa6:A�"! $U=:g[{\, ~2 .�" ��6�:~ 2 @,c,m�N�,�#{  eU#� s $g_\pm.�Q\&�GYi[sbyZC C=(�v i 2)e� u�+ iz�u}^2)FI401N�)*�H�(�52.3ya�Z��#g}�=i3vi� %\U})� U�9��,A9)K�.nd�;%ZzEs=a� i#_sR�) ��+r) EFp16.4(�F�4�RF* � gR]', 9W^1��nDCs�I)�DpR��'�V> $g_+��,� U�+b*��{�7��:+�2%�U)��%l^R��by�G5.6�b FQWN�"�)�Osome $�*��?�AF`g_+�]�]:{d+1}$ 9.(n� F� . SZZlyw- w^��{fx}�2  =Rv B���� �$2ag_-%�d" �e��2�ϟ *џ$�j�3%� u}^k�� $($j,k=1,2$*�5&r� fals:L%�Z� )u�w ��tU}: �. bE�327B>��$*>i �t{-1, �e"|}�B�=H��� aQ�&�&�_ �� %�Hk�G&�<��.��� 0��.} ]�sefdz� ���#o:"� "�K\ ���Ak1�$�م�[� � �,Jxyj/��� ��=8Q\� �6�3�)� $&׾6��%*�� ��!*� "*e-F��1� "� ";2)] A�F� s 13{16��, �4c��>1WK"ױ��J��rE� torih${\Xi"�"�f&]b7�8$,Oū�&=�+�"m a.#|us�1R&ra ~�--Y!�@��ce�h�0�%\Xi�Bum%`B2%�o%�~s rͰas;A<��H_sa:._s�t +:� ; ~j�+6vP, jD&� Z}^di��d?��fa spiJ�"�  amou�/o� $�1FM g��K5&M�F�*�mvxi{1} ~  +�s~ d}~�_{d} &a 5.Jb < �p�(&�a�[|mh|i�#d}|$.� �1�#]lII��U� ha�E2t%Y�o�p,� �2,�"��s����C*�.f��� Z�&[z�6�: V�J d��";Ma l� �X_s=!Uv'e���ba�  $[-�s]�F9 43���nnorx!A]5)�iBP"kof1Nc�-�*К �� W�<Y F1%� ce �e�the#�cs�4���5R2�"�u�U�)LF3i�6!� Nent&� in p�%8�� O4_*bF��ing��p>��%&u&�(18#I �tJ��1�o&B��,explain�,*�%10�� nume��!�ulמnECF�{ +�NV��)A*��7put��>E@out�5E�St-9�4)]*a�c�A/-�B&. Zi�!`}:�N"� pP� *�&!�V ��� �o&�r!% H)s�x s � $�%�u��t�ya��B7X) un��b �u�� at random � d�unlik�Dt��I� ���_cOV�<�bi��yLS?any!�b_?T��nte."��y<ya�MeJI{\ (A�0Al�UӉ���0{2ye�6q��J��G !U�?!d( �� to a highm~��T"FJ�SA =���]!B�!E[dOi�!B6E� O� M1� �%�^J�e��R%>q���M/6BV� dw�m�%�mPI�F�@Qz�u�ڽl|%:Xi_J$A�"R'6�2�k*���)0 " �2��(�p�|L�A��% jS�� �ZB2���d�;�mAM�:�J��"�=s aq� wK gɗa6-��! A:�a "!tTT-��(l�rri�^��3Y���$!��� varyX8!��a�>�.�BR�a!@ $�S _s -� :� -&� 6� |$&;R���)m&� ) .�z�% 6)].7 | �IB6A !N� ac���%>E6����l+�DUPF��.�+���r0��> /� s(U2�=))$�T}�+ �\B� �!�"& � �F[$�Vho��0�2."5�an* n�SVZ u�n�.oE�R R Q �bonoy�n�ItheĞbe�A�4۹w!q �-��%�:�� c�S free�O��~ i V��V�!p� u�ځ�-  irregu�a�moֵB}�Iͺ5�i>�in Ȭ>D1R� IB�!��&2� ,"Á��Q �� b\22AiX���CA?m�Z�  m_0+D��$ �!98)p�Zf5 $\Ph����+�aRh+�;i<��" �*�B�!u s9�9" 2.1J�"F\D���,�V �� � F��x)�"-B.����) ����-:�!XxI�2�L2�lA2�?�.$pn"�g�$d"���6��%��6� E79�ρ��6 .` ~B:}.2��,�.42� "��Q ! L%)�� $p��7, )���=��&�p6�L"N��iY�W"�F)#$]!�9ta��C#�xA�-9�$tr��6h 3. *##*yA�) a�/a�p�n��A2�C�Ke,�=(\ ala�/ %) :�$"�*C� q�*܍B��1f!� aC, BQZ�b]g!Q5IUU=>]���H\�2.+�bY!�*� $&igJ}W�e)=� �� �� 4%1� =B� Z"�^B���}j�K8)^T�u9+�F'ea� %.  �g�9ő|�G��a� "��d6Z�aB0%1y.� 2.b��V�1B�� yR"y8O JE!B := "n3�U?- \'M 5�9U"�O)�:J�6<"=?\D��D:��J. sZ(�F:�K�Z�#!�6B� "�Fad*�E�� &B�i��u�Ds�|r o�s�(Ah��og ���A] em�%ā���HE) >�I�1"�U�of2�>t ��.�-"��i�ica*o��Y� �L�o& *�ne*+wl &� �M��.����jD-� G�( .�NOL-.7s�C�(� uR\>�"�!>��E`�5z�> �M�f��� �&g 96��1-?�!wA�1P �%69ANb�'��7B���^h ����"�:non6 �.��A8)h(+/B���%���R{�I"�Z�UFwhere for a given ${\cal A}(\cdot,J)$, a torus admits an invariM pin field(H central object in} theory�polariz�hose relevance was explained<I �� . It&(pointed outare tha N�$ is a soluF to5$ T--BMT eq-along-Dle orbi�d ]itG<$2\pi$--periodic��$\theta$ and $\phi$. We now retursit show, aml othe!�ings, f)�)ris off �al reson!*,e existe!90of a nonuniqu^mplies fASsystemdn !�--ig�Tbegin by studying gene!�4)�s. LetQ@S}(),! )$ be a + such� $S &;&_0):=I6? _0+\omega S)$!��A|m I�hle which starts with phase )�_0$ at1�T=0$. By (\ref{eq:2.1})a;4must have % \%X{eqnarray} &&\frac{d}{d �}>�= �D} ��+ � �axEK,N&�J \A mber \end�% A�thuA e evq-Ce�A described!�!i %^,al different q8N"\!\!�6( && \qquadV6 �D} -K S}= =' phi) S} \; .E q :R \labelA 6.1}FJHere,Q�J��= D_1 �=�+ -�g\nabla_�mmA,��<$D_k$ will denot��,e derivativeI� resp�~��L$k$-th argument, be��sca�*Por multicomponent. Co�:{\em m�8ized principal�S@matrix} $\varphi>�def��byN0)&D} = Z� \; ,1� (0), = I!2�000N�theŢ��of�A)a�%n�>�=�q�!� �S} �-M e�)�.>�0J�This can�]Dseen directly: si���D}$�aU(on, � �)F =\biggl( 5�2%#rv�+5�._V.eZ$ r)$ ����v;�� E��s>���6I+ ) are amea�eaJ">by� methodA(# t s�vpj�w the ��traE or��-�,%�_0)m�\E� �_$\Pa�2P@. Now suppose, al a 2sat�know one9 of 6�. *V:�A�$in $SO(3)$& o 0 third columnA�%J5}!�mak��$ transformP �|<\rightarrow\psi$Z}u6}Q��uV} 7B�3u�:% The2��u8 =uJ V})g +��Vm�D}~�A  �J�t% s� atnb t�`C}_i�:� J ��n ?��)� V}^T->�459B % | ,Aanalogyad]nm���ŎG� �9=--w�V}�c 5JIB�5J�A�R fr^P=-(1/2)\; Tr\lbrack\,s\, �� �AY, - )D)\rOF~2R�J� _TU$� �� 8V�)<2 201bB;� � %�o� o� 2.8}). \\����4��lso�olv&� b� giv� Jau2�4 = \exp \left-� J}\int\li ^{\�}_0-�= M'� ,'� 6�E ' ��)-�!�mX60F� 0006Bd% ��4s easily check)$* substitiJc.�� z� a becomeRN Ue:��y�yjyB7JyThef& �0�/5.02}) �1�onstruc� from��a� following<orem v�p\vspace*{.15in} \setcounter{� em}{o �~� a smooth ��  on�xed�,� 2�satisf[� rm9y }. �f� b{ �ph�o ."En� 6� �:9 e���(:� J�'�-�� O�_0)>qN0�"��*&&�;� J� ����_0���;FJ8JJ�Q��indent��,because $(d/�� ��J��*m)�� � J}$;.j��F�� �єRy$. \hf[$\Box$ J.n-��eZ sev� ic 7"��|� �fi -�gN�.n�{\bf DH@6.2} (ISF,IFF): &�~��.�� a) A�u :�@\in{\mathbb R}^3$��sai�� �E�� F}6� 2� iffb E�6�}$� ��xVk^  if��=A�!C%r!]N�Y�X. A�.�X lled��N�} !k)N� �� � V��Em|i S}|=1$!�5� b) A&,�V"z}�X$,sc� a �framej�iff Vc ��Γ� R�a=j!x��Jn(} (A� ���I[AZitJ�p�Mm h�i&jCn IFFFn ISF�%�unia�}=|)o"�E�fun�"`�~$T�$� �6$ b �Y(��pe���u)�)a%� [0,1��N9a��(0007}) bothqA� $�� $ �=��W 2}L�� a) "n>�I�-}!|.��� n,e���� , $U��$,=|e�|6SB|eb,a proper UPF2x p$\nu_s(:Jn$. �E<"� well--tuA(%}�2K�\iU(>3nS N!�E=�PnaJ�V {\rm]F�)}�o>�"� >.��)}.��aTY0em 6.3a:} ~F1 1� A,at%��1�Va!�I?%� UPR��$ Of courseJ~!l�)� Q}(1� ;d+1o�� UPF B�AIw. B� ^\ contD$$each $\Xi( �)$�Qlude (re�2E�com" after.Z5.4) "cb�"�O>�2�Bj ��q� :�b!� WithN�&&� V}=:eft[{ �,frak v}^1, ~>2J3�]Fh3}2W����.- > �w}^j:=MD}-IA})>�j }6m��� VE !N./$S}\equiv >\3R  ,A�:Vg6�1 ={ (=f w}^1e_>s2) B \&� 6Y 2 =-�Z16Z.w}^3 = 0-^f,q�J*)�.+].+=(>yZ "e M�D:hND�JP ^2\,=-2��t� V.�Oe�$��= ��~�$. \h�16.2cm}��  Wx"%so� urg"remarks0IFF{\small s}e4IS . %B)$%\newpage y�� R X:"�itemizeRtem[(1)]�� n� ``&L �z''� | $ n so0 to refl�he faci at likISF��is ri !O �2)] I"� � �en����� ���F2#v}^2$��*h3}) pseudo--$u^1,u^2$--axes ey�us"�$��(gram SPRINT� �numeri�%calI\�s�"�H \cite{hh96,epac98,,98,gh2000,mv hvb99}.` I� i -$��Z� !(ed :� (see� �(ky86,bhr92}yn exampf%� f�>X�found!v � �}. See"G10�. -� 3)] ! �p=!L&. 3bAI/ �U IFFA!�A.�)>� �f0*6�=F��*�u:�"B� +��BJr) = \OJ%>(3 + B1 .��B"2w$>�N�T{ia{.�mCs�!�RA=�%n"�!�6Q�!�5�4)] A. alwaya( ists%�Acloa��&����:[ *� $J�?u.� a�iVy"s �jg��)�� � � .�re� 6�Ev�q 2K23)�us� �I�DFloquet frequency )5��?� S1a T5. *TE�a^anyFp U� y $SK $|S�{]m�5)]��!*(coefficient�(�� ��s�), plausib�!�D �L. But�twe signa�� [i@i)mains$a � emat��hvnge� provb%A�in5^4 w�%ll� ~� noa�A����m %�:� ��aI gain9#, b!.�ly �bo �a�a�*a��EA%lif��S}$ ';enF.�Zi+4 q385-of $V�e�&�"3� e�1U( �(unit vectorR*is�+1-A�!�l!��e�!g͓�. Howa�,2|no:j�~�� happ�&9T l����2IѤ!Ydoe�t)b.N�� &� de� 3W,AmD# not�Y,�$at �����,��BH,,a1�:.��dA?E�h���3"h &E"��A �Xf&�9�off��.R-� assum!Uat ), $n$,)s�$n�$; o-L, i.e.\ let $\hat{n}"an�-A�6&MZp�/�n� AA�nonzero��� :�ta7!��}y (��� orus!�*Y+!02.�B�MA1r]A&�:}.>�A@2_  w� >ea� N��PletE5MzbeV�. observ)�0 $F:=|n\times-�|� 0�a �&�"� ewm� D} FY(As�+beM�bel�/it M�s�Vy!�"6$F�#�� ant.��( angle betw�)6 6Vige sf �5ll'1X d $m: m:=(6)/>7?!� , perpend�toaŦrefor"�V}:=[m)h n,m,n]�aQFF. Du!� s3�6��� ��-s*C !z!�"�j *� � 2N�%��� $� I� ��ss :����B$ ���3��"N ). Todple�-� tU)!�ider N!�f�-F}:� �{d+1}\&)$� }%1VD}�� F5W�"H�aviaZ51�H" �"yF26�1�.25F�% Henc� fET5Wyp�3' !��3 ��$"�/H'52�%8H^�C%�AN "�: "%H.) +�!_0"e&\;P0>E_0 �� _0 = *N:� 26NA"� ׉�:# �;$�oblZ�0i*F}(!k �"0F�)H)-3r!)-F� ��nZ�2whEb.�36}R�&&�57.��F�8NV�: ��Fourier6�  $g_r:=R\pi)^d "!�}QsQY-��# (-ir,eXd$   ��)$ � � s �%R� g_r=\w i aoF )g_ra�.*+29N8 $r.J!Z}^d$.Ys(1,3i�non�6t !! $ vanishegrNneqa��%0by Lemma 4.3a� � �V�b�Y� >e*$Q��><�F`^  :_ m9e�t� 2d5(-�6)e�d.D*�# Be �4 4 address&8�2 ess AGA�� asH ite w8):;,� �raposi�4of��4 y>: s: i�N� 6� � �if? *� � ^�8f�: A�  up�a�. AOi�* havias predi�)�*&�21Z{3mm} ��� focutx� i  .�$C"�/$ ��1��first�Z�cEM�� �*F #���"�(�^.u6.N�'Sj4.w�cve�\B�es mean�'bar{c.�0�� D --,� 1tilde632� $,M*. !��,�!y& =d�,I�l=.�,�ly,Nk�TNL�m=R�:�-+ v�:0:�6.N�-)�Aml.h.s.AH��"�e  r too%gA�fa $������n�6�$�,individuallyJo �a�.��� 6.6aZ .� *q6})�>g�<e"=p�8'of 2�0�#iV�.��/j�/=I� �b +\beta>��?}.z6�$9JB+�pN�j^:=�J�0F� �G';�(6�� 'B�001g.>�"�+iaD}j�=f�N�� h>leads��]q X�N� ^D)!4 gin{�<}� D} \alpha- �) � j��-60 =:� \�1>6�9B6+/n sy&97$ �$a}:0n�/&�!6t1�Ix=V�-� :�N�J�;P7�� ���"� �=�<"�Bz (=0IG5L  :Y�= writ�?V R��.= \nu}��� + kF\;:�1j��υ� er $FM�� ly determm=; cond�-�%)�' � \in F)� �l2r.K�R�j4&&\:,1�0*�8\\ &&���I|4b*�<J}(I�:y- R� +:E6� s +B�N'�<� V& 96.&�12�U&� ! ��%pJ}����U^�� >612�6&&IA:�:1���1oaA: 01>Q�af;4j�V�3UMm��a�)�f�$IV) ~ U0;<:�NN6��N�&&F�:P s =�� �"� "�%I�U� �R �~�Nn >t_0mif�1R4We"�i stat� dJ�,e next basic Cul`F>e�.��{ �Edj.,���,D"w b0/la*in or]I� to breakEh flow� s 6.5c-d �#$Diophantin���.� :% R�7Y!:�7&2C. $J_�#�nt�2�F�E(V"��4>�,0})} ha:&�=��"�?�f �!: .2�Bn!�=-a!�h.���G��,� �B%$A(. \newline\`+ b)!��h &5a hol#>�I oN� �mU1BCGBQ��)} ��� D"YU}=.��4/F�-,�& 5Qby:{908!� �&�"6��!�(C� %�� 0F�%F� c)�:4 $0<\tau2d+4 ��6�.�o���( a Borel >&�KR}& (8^d$�2J� �� �,$\mu$-almost� .g�v/RA���"tA��&u# .�:} ItA�c:*� E��B�6A.�=B�E!�re�U� 2Y7�(2�/ %��b�b:}F��,U�UE5� � "���Y= >E*9is� �*�N. !I�� 6i7.<)=N 201}H  easy *0�#�2sFf�sus�~�n,J7%�c?a�J������: �� A�.�� �wY;3a Rr�&"39�c�6(�%��*�!:x;�. c:} �*>�,"�5xA'i��{r-1}���].AAg$%�=Us�#Ag!:�]R ( g�zm2J), p'E�"� 6.6b dB�E aU � us,;.�6}y4"�"d=�:|$| �)-.�T.��"?OPau < ݔI�4.7ǁ�� �a"} �� �#@ \sumv_{m�z"�Z}��ckslash IFe�1rFe�(frac{1}{i m�+ "o5)<5_m@(-2�i ,6�E"/u%A�IG:\%N �He� EKit &s7]�0!�� ���I��" $m$-�NJb�� ><% claims J )ߥΑ� b�`7>���b�d:}�� rval�?+1,E(��{t empt�) we pick aIW�)$�Cval*4�YxweeGe ��5c, u�x in(.� \cap� R}iM.3*�a���i�).&�7� >d+1`7 6�4.8 �z�����^�%�i�oves our)�F�:] 9��@Q"�#discussb�Tat��#�+ � e�A'6a�� C8io�:*-2���B�*�El�}{sJ�8  /<6�2RC � >��86�POF���:4.\-&� �,.��@�)� �?n�%A>o f�V�v:�,2) P *-{E�()W % 6�%�!�U;�G�WitkA6,IR"�+b�Sm�ra�Ga� 0:�)�&f�E:�.�-�+�L ))= �_{T�9a�N�fty} ��T}<"T� K �� S'�o-�  g2w%') �h3�*XV/� �Y'h#� � �%{x }^{T j223I�6,=-'�\�$),n� L'Sli��b��� 0 - �_�^T(rJ��TJ�MS ��6:6a";: PV�RseW �ity��>A " �%� �@EI�_B���* lastBi �7�izi� b�6e�3�.s&#>�!�LPo6XV�isFr,�B���P�+three]s �*1 Q�{�p��y��perty JHB��>@n� is trivi�\:d$��ZV�>ONI!�find, d&,.�8}lR appl0L ��4.3c,F+ (0R R}� = (1/ 2 t'{(�@�>^{�ONse\ ~. ]�+ x' -usF�~�6�)�u�Q _0$-.�� L6.��%=�bf�,j�;6)]��>a�>��7�<"k�}�ugges�^by>5in� 1al" se8W $6R ,n}$% e^{i/�_ +, � )":C$� $n�$5bb Z},m6�(|z6#to�( DM�_t modul\4*�um&�by $mE�(;C�X� $>~.$ cor \on� � .'�ma)]sB��):h�$��eir�J�display�DZ�p!é,I�. Zb��el� $n+)T�= 0�Km**a$n = m�9T3VG$_0)=c_{0,0*�.�*�" in&n b0 �5 [(7)] Una�c)B� 'Ju Ţ:��E�?�4oci� F $F"���P1"�6.�t �CJf�Q in X&�be n!tOV�%RrQB��,&� hJ _0)[ �U�� *�DJ.F B� �&� %"V9�5"�P A% ��%�T8�GF an a�d rary�8$��IC8�C u"�no�o�7=�3}), ${"O� = J�{:�=3�!� PQ*�bY�LI�pQ>7H�;"r=y�`5%�.�An: �� *�!j� = (0,gL<=��eigen�7a� �J}�<�* $aluIR9Fv� � ))$ %�R jf!�#$ �dropp�aout6�d6� 6�80S.�1�s� i� i=t2�qa ;d+2]v9�C� u��� ��$=��!DR� is,!bZJA��x. For ple,@.RB (""2}0N��f�<n�<<7ig�b$>�2�\>3�� Z�~ A�� 2})$�i&�<t�� se"c?in&77+J63& q choBi�V.K_6 �[0,�]�)10BE"V!kY !�] *�-,>^ 2#,&f%:c�O� $Fz���-:H06�=I�C&/.� 1)] �8�C8os@, by r��ng2c������0o � ructB*�)�j�_0�3Ai7s i��.�ee�$%46f� ��12iws"r"a � s|!kR� althoughv$>notOy aV�",� roprL�>6�_*mayQ .@���U�8A��#A(�+!�6#A!=& �6&�1�!�@3it tura�'lat��?�?5aaU�!<�q pres�* nonquasi\�mo�.�-�mFTo illus.k�Bi�[�gto� �s� �ut�(haps unphysnB,. els. �h57usc$model �o�",!* �`<):=\sqrt{2J}\cos��- !�K���< d = �Uwfre)]L �8 6A+هE��4+F V"A�:�G;"J ���6�c$,*R� �A`�b�-�j�-�pJWF�F�,� V��6[+1R�1 Obviously�D$J > 0$�Xi� unZ`ably m0Heles u7! �i�"�U;�{�?:�3a,����a��a�WWKGwy8ei: f ir�1��+�1( J-1�* e+)NA��J >� bc$. �5B�=!�6�ABn � ��j�2��e�6�A��q� �B�s�ph�y/9M!�C}�%q� "c]�6(��`) B~ _|OneCDs�q� a2!�1?��U!�.�$�&o�Be ��*$Ko`(spiFiBf% h�L InZ�3--5,lJ�F����m&c OaYly��res� �A}$\,{&0R!�opk{ true##�Gl�g&|'&� � q&AL�;�He�. N4 theless� -\ne���pk  �(�<N!superfluShJ8�-�!�!��R� ing h28-��� � e� = ���y�#� -w�no�:���� ą�� $d=�=1i� I�:� $ �.� lyA5Š� Aise/�J�4RY\;W'G� �� X)e0ia�au({ccc} 0 & -�!_3�7 &H+_26\\�P>2&OP1B7j:Qi:2& 0� ���f��s%�"K �"� j| eiweI� e $|)| <N �SZOs�J)!��d��qK��(B�"���&�D�J-� �4kew--symmetric��)J}W^T-M. v05N�u*V�J = � :�>�)�) :�6W 105bJY"�o%�b� � � Q�1 |ኁ��Eproce�U��H��u&�:���I& Pn5�th�`. C6�<B�Z�� 6.1���nu7#q(n�G)= +#� %�jKF��A�]k, �� *�%�),Z�z��2�n&�h*..\yU��6�cJ�%Bhneq{\rmger�`Df1�Q,� Nn��>��qV>n�� 9$ $1E�pa*_Q�ad�:,� a����V 6�ajdm&�^� YJ}.y6]!�. ^�fN��V $}�=��.6�&=/ =/�� $O=%�yt}�M:Os"QM�� 6'-�Z6p =\pm��1�/> !?�50%2h, 105gJ>PI*NT�C�J�� �5 a\{ 6� l} �� \�m�5if}"xm2{)) �xi"�|z9�_!, ndR�)6D:=� N.` sin^� (Ks"pd),-$(� �)),0)fH� �JE \\ �/^~6AC AD.J�DiJD|5F�"-�EYM?ш Fu �e�� >!�>". jWN6�F�=D+.F}{|.|�(��!}"�~.F)��%#*>�jJW=n@�*33Z �3s `Z. 0summarye�il:�_�Nm��a.� s ugt $   13"��� �8 $�2(+y %�y]|:�%_0�&3R}\ 3 a subN% �A.%b�. F&cm�T"!Z-2@�v!CFF..�hann�A exotic|�C�ed RN&� emergeq29p�aF���5�!NoF&6 ^/availa�\w1u�� �g������%^� . StK�ngi�*A K!%�"��fY�Ej�#Z� V+ >��kA2iA:�@T >]60U&� 6� V�E��) 2Fy� . = p:�]�-l(B� \nu �# r) ,�*��7J1��N&&B�3Bv �F\; �:= .#&0 27<�:2�>�G& >�Ca� �$U�M"]� �� '.���5si�X8a�5I� $pU.K,5� �� u\eduR� m�Gs.*o@u�V�'^"�aǥ�v_e�w5� ed׋r�=��ver�M��..jV�*W6~9=6��~�#sp6!�p/��ity� mu�)��p�yʉS�2-of1(mad�St _approxim�)���/�Y en�e$ magnets f�5to  bruptly (��(``hard edge6^�1 o)X K�bOlength�G�+ct �a�N d thin3s Be.�R`"9>���; i��0"O �%�� Ipa�wouldI]to7 ified.)�� � ,�4ʇ� Y! impo<( �TE*6a�e�� B"�0]) *M.�Qr"5�,these matter��E 5.03�D%%5AO 0D}q + q b)q^T� ,2\as,! A� i�V/tM1]*�9&�2:}\��"b�J:��&� =-�- $W� &�($b=(\nu+m)WHW^T"�� nu\inxM��+" m�"w.�rng1AV}:=qW:-EJ}mi�t�.�`�m��&� �Q*�8QqisBb � &YO&O��'*}\nu[ J�;�� ")V�F$�|! th6�x�s)�Z� m��1fr�r3}� V}\�+ &� ;V}�+�6 !202Jp Som&e��t� a p!ӥNF�B�._(�by2�%�� B�:�5B\<&�5"�3:�y�C�;.W��]�j>Me�a+D�o,�2;� E�N�>�  =�o�FI�Y! W:�u mR�N$N Comb�2*G "� 2���)A�"_ ed ~F 1+N�&N� = r�W86�(m�#)\,) �W^T =vPO(b 9)A�^o ~ U% A~7�f idea�%U`MLszrM��(�'T��*�i9� 2�1VaK�"."�of�j�6 �{�=SiEeRH� M*)}2hM"�C�%*2�w�Ta_S } so--q`` le �^ce �'' is C vidjn!K&� A8EV�a�A�/J4 �m� �:C."� �> scri"!%�RA" effects�|�krotp"nd�%ctronr) �\[r mane92}� �aso �^popular8| i'j���'exa��%� deli� �ful�,ic� abX b�]near V�~n!�ough �L!1��9ion,%b�it�%��� �Y�i3 �C�N/� A��J-�ive�U!�bm$e� �a�  ��a� rmonic&s+6Z%�oscil] �+�Nriz#{l cir�Ir��ign� biUGA�8 o["I irawaHQ--a� varips $J�X$C#d 5,��B��a��cs�<�;*m G,� icG A�terms4rad� � rupol�1eld9ng����D5+ = dZ /d�� �3 UE .� 6^�u�w unR"D0h9f c[�s  >�$+�to�Fi�suq�Ց���� �{%3o neg"Owo��n r99,q�f�takM���:N�E�6 �!�\2p ��V:= ��6�c&V$sigma_1 �# 2 "�'"g), !1�# &D$F2�hi�' \ -J#W) & U.vDf]$& %*�7.J [�$ � &�4r���� sa���A��mstr�MqIMand>1A�U2hY�I=<<4U��..1�� [ "S yF,�+�&�M& Our)Aai��2 =.���&�Wa�cu�S'�=I/tF ,-R2Y5a� �� 9:=M\( _1�*)^2+2 2^2� �&ti&�8verif�<at& r�U~]%o]gT^C&&N8A�="�5 }Z2}v� \\ R�]�#G�.5u $ !F"�7.N$ 92NU��iq4_G�V1�VTS` . �b $7h0, 0)g_mes^9-��<7��+:�:H() \bot^M$Z�J� OPaf�M��}{|B+Fɀ�)|}{^_1}{I�I^2-2����}f<0!�i1�1.T.�]3m7 � Q"A#2�7.N� A $>��)%sJ�B2b ��u"�RGZ [Bw,�-�} ]� ��:�x u&.~�6.4}),U�aF23}���Z7C6<�mn�# I1�DF� +B1�B&�B)2 )W�> +&]gmaIYBTKc�wr�EK2?2&c�@%�(Z&>�:%�! l�II�afK\ieK\,E�(1/T) �t_0^T�6K0 ~.�*�'!%)�FA4VZ�m\;bFZ\�$$:#fcw\I�4>�� ����uJ�F1AeZ�:.��S,[p.379]{Grad�M� &GA�J�p pi/2�pMC_G} N�����+QK2���(\pi}{2gmaf W ��|Qf^.��.�*7A�.�1f�>�a� �A�� I6N5A3��!/ ;�.co� 9.�$ͳ}:1a��!g=ʚ��� ��-�f8:��f]f�* N�i:m͞as�7��EΥ2A,�V�Jrm�n�42��z �#l>Bm�>* %����N��.g7.�R>�"�\t>�*8(n �$�VL�Mu�6y:���&C:��)$��do�Jb��t� "��Orrj6�Fu�& X)}��� %8�At^{�L� ' \,^�'%�6P6"�w%��$0=q��=A��eFf-�b5j>*��6=IS%F6~5 >��ѓ&�5a�lI !�!��,� IU6�!*aby.}1,F�+R6��2Re Z "�(V�_%�_0})�:r� } �v� +*�;�),E6&4$�% 4 ��� ��?th2. "$.56%v�"�&���m��2"�`2�8w2iD$WB Œ$&H"Z($W^{-1} E W� %�KJ} =:(z"k"�E�mf� E�蹳�:�n:$�R@"�".:]LZ�)�"�??@< u� Wal(kk #J}�nf�!�i�N� Ho q�UB�Ua�"�""��fzIt"L*.�6M�� w>�db�i=)�-k���>@ *�i�_��� &�Smof��.a�N*�� 5.5 �?� ��un7f� _s$Lb��m�N�sG _sa*$varepsilon��+ j  +B=�7.j[-$L\in�� -1,1�0 ;j,k6V�on���>"�%��.�1��� ����PJR�E2����Z+�)U�'2��E6� . *���f�,.���)o3obi:�Hf: TJ�Eϑ�-4�z�� [Ɠ� M����:*�J�ab"�K! e,� �0de��%A "pk�ML,j,k$Ub�zosƋ*%EI)�F]9�reϹ�x�1!p�% [���F8exp��S!3 2$)��jeV dur^ v�� ��_1ɔ�J�ʩ c�st�o��--�  �XcHiHehk + j@$ �_1a�e�$�L���%\�&��G��slTeest�<�"�2A�h,r�4�,1Q4)]� �(ah.t�<� �#Aone`*rn�Mi���q��DP be ɂx/�  G�of�-.1 =Xf8W."$�,�3�f� w�B��its�j ���l}complex ��=1$�� x �'�-3.5i.N@6� 9|q�2e c� ��Q�#p�PԶ-�j_�e, e.g.RJ�(bar2002}. E1&�E�� .^pdE1xi��t�0ed.urT�YngN�)�s w�2�&�N���#m�c� �0a��$e�eve��e�al &�&� �%ori�K^`�A�.1by&$"���&c�%��"�%�7>Ym,�S [ �I� � �isU#)|:# :�O ,k"�%?|^&*/��2 �8?H�tH.��&��.& Va3 f�R��d��dstill�j e��e}&�3a. B�)\.�(,Moser-Siegel��(c�Ur�T ��ὥ l�R�R�&{R �) �,��r (a� will�9*Jr')��``2�R6%)E�$d=�� �6F(a&'~%r,Rpark5�D1"�!��-�_1>*Qor cer�&�Qic��� *&$e�.JbE F�2�)Q>of� rIIA�o6^TA{ُ�A� AuJl��%�%#� A}�I _{2�I/& "Z2"5)� �a _{k,l=1}^Y\;� $_1^{-k-l}\��kl�^ k\ Nl�2)i>�W%2�"8.Nd Eb, y�&�F@�1 �z�bCB; kk 2-l\geq 0!g&1#7 Z8 < 0 6� 2�2�A>Ba�b"�"{�USis(��act $C-�$):>�%(l�5"*`nv�<@Ti0u!�2�k^n-&%���a��negҾ"�n$RS��2�9a C t� �qO*�E'sd.� A% �H !�8ll�&[�s�/� '8se�4[8.6.3]{Di60},H0[p.117]{Lang}�w�A�_0�Z�Am6;�ff "�IsI� =�Z(k� -l�Re^.;8�ɉ&�%&��f��*)^;2;nd� \ r%�n*uS(TCjf� =Wl5�g3. �\*b! �0i��J}g14m6>Z<"�8�-�[w)NvR:.%"it2��f��')K,'!��[.~&L�~�A�"L)$gMUb��ust,D!4Paragraph 36]{ }, Yll our�[P�,/�sN)2eyb6�8.1�#emx_�1� \notEq5bb Q}� r,1ist$�N�&�i=\ki3t:v� A8exp(igm"� 6�[z�XE)|;���]t6,.�e�(�*f�� ���J���� N<� = A2 �� 2 gf�n p{"� UZ�}�` ral,!~�}u5�t�3�r�� � Chap�.6]{Fink��\B�:�UZ`le�m�AI-!ׁ:!9n-�:G��:��.U 8.1%� �( 5��g�.* �9�e j�*@� �2�"�: *�=0�Z:vsetM&�Q ose ��T� � ll��k�:. ��_ no����0t/oZ2v�4/� ����el��A�B{d&Js)�@eS!b ,��nei�0�z���a�Y/no�r.�%".�5� tM�of�&�A�mea�2*�� �"�Gn!_ar��F���>$"� � & g�"a2�&<-q��<*�74��3{S�/i@Analys, f Qu.�`SC�Moj7.�vZ=*7!(de��,�{&,X���$9non�purb� qX�p���[ambvw7�w�m�&.� �s o!��Asi&�C*�9�A�f4 e�g2�"�a��Iof� i>;<; G�#i2/5' s, sps�Yu�rA@A2)� 8e*�͓!B:a�by2s�%�:]forwar��"S"8�wA m". ��� sd�C�cF�2SU!���>�: !  m} .�.�!z��9 *�[%�����dC_\1>rz�BS�A�&�*'$ . If��"k;"hV�Kk"��lZal��wCLjA �$zedS�� 5n{���"�[.� �s�i*!B����k2C��5�N�t. Also,/ $0� \!j�.H��XS�U�by�� "&� && +� L"�.Na*�. /Za�@\atop ||m||\leq N�+ A_{N,m}r (i� mc &�r) �Jl( S,>�J:� 9.0R�.v&$ v:=\0�_{nC�r\;"-$N+1-|m_n|} }$,c�CA`re;q6n6=n-@�:�') 1d0)�.XT1�.$9.08c"e�#� �T�ޡ�$n��"�B*�� M5F�n�]�E��&�S�$,F6�9 .�9� \La%\&p �))\�O I�e�e�&�+>,: (*e,m;�&�,1,-1k�VB'� ."hS4 ���Q6(�ZB~% 9.1~!P�U5Lm�Of�"�Vq�R]&�I:�! J�L.x��woc^%��1�&�r�*"?B� 9OB" 9.02B�ʕus�W$�FY rbra��I����MDJ>a���$SB^ J��F� \hf�0�.�(B_�9.1�z.�$U*,��"�".4j�%�tj��0� N��n#"b-cb?Q�,䱩����]&)������Un�.Z9.R�E�2��9\Delt&�m:&;2}�(:�Yc2> �=�Yi�(�:\mp > e�a�b-9E�i~0�9�)Rr L&:]{1bj*�69.0N32Z��� &'$ 2.12�kzg���!)i+�' (5+��� + *- [-b*).]:�ϒ6�%�7R&& "aU y�WJF�%1�N)b� =N �+B.- c.big�S +�A-BA+fA"](!T\qquad +F�0BU�\`"^9.R��+j:� F������opmF%���B :R�| [e( ��1��"at jvqU� T��$��=2F*mpJ� )�$Uo"H,%B)�8}ZTq��V���&�3�/%N�J�),2��y26�h<�pm3 0 =�xVx���n u~f8:l����;v����� ��F� U(0)J�i��fa-�bZ�F�U[�) v���z.�7RO gx�SZ *�,^?b6S(�>r��;�;�F�I?>����b� =�`:_ .JG�6�6��x�F.�9E7,2.3( Ns�."8�u���Z�\dot{ ��= "2�2i�!ݡ�!�l("� � U�F� �J�r)"� 2a�bf  =>i &D ���B1 �1�e3:� N����h��S(�ZR.!DQ}�8���� �G�*:* Z)J$ IfM=j� �4s�!��! ^dS1P l���b�7 :� 1aJz"!%��hN"H�-u S = S�Z���/~E(r��m=��2�a�dou�a"��M,Mm}e99"g% 1�Sic"�/&B[A��,qua.�j�+>jA��:��Z�u�:>"�0)��Q"R:K8a�>'A��N%6��k٣!��8problem�q�(0G &�i ��pm||�`)"�l Ins�|l��.��a���Z:\ �)7k.pr� v�]��bNi�~�d*r�tf�Y� 5 A����Rbie r�ʼc:} :)2�).�4})](.^��f'ɥ�+� b��!brfjR(e�s�� Kl(" f�&'��:r{t^%F&& qF��GJ.��Sr��:�RL���Ie#&>,: �� u>���&��r2`Aly%=��eFsJ�R+.t6a��!� �%L.d^�Z�� 0i�2*�F�n��X>�N�-I����ous wab�V�fw��F��� �4FDM"��R�V�0 M�%�a,6MV�&kZ}%�R�4bJ�J ]�1>786 4aB& 4b})1] B� $ �(�x�� )$\\ "�5mm}~~ˑI�B� ?%"�\cup ^M�fN^MF��rn��ibra!�v"�<���>>$B�%B�%f���u!� *$$*q'9,A�"��d�,zL �!j� � �sF� 201� |s!<2�1})"a �:]al�;an�%ob "?����E �,j� z#:.�1�s� not}v��6�[��4s @�a}rT�,�/ppy]..1M ���7~�A�*� �5ll?�))SF��X:�%�.8c}) 0,c�h,@ D,in&<t+2compun�j!by do� nu\�� ))��))��*'!:o\����6.40j/ �-i��.d��87'V*3a&*�*�!�)u+C��2�%SCN�� 6�*�*s� , duk�3a ��$iB�8} 5�?8!t6u% S@Z�'N�'��ee;?!E I 2Z%lIA�_-$+-�une�& 1�9.1c 4,�"~ j!ra�r�� �_n�3 etminus"�"B�" ^e�$=&f#<i3pa��;G� aq�2')1Oy a�Ea a}��A`u�w�!a�4[� ured��,=R�=�;>�eS) � �� q-�2�A��kU�%�6S�ikטn_��B!��cs�d�:�kno in�-�n�5�ce�*1.v,�*�/ai�����o�O�(��A$” 2��5+5$) guarante�.r��!i �D�!�B*ow!�! ܲ�$. .�)�$i�E� .�b+�O Nc �^T*�Z��Pi�/"�)$NE�a�4A69|���5$���>-*K\c2����al �0� �%F? (\E�al ��a _0)}�} &=& "� )��^hJH� & "Pi&t = I2� 5V�"�� �V%_!`� "$0�E�niԾ2 �3^,��2<0q�N@F*�R \\$�D\6m7 9.06a0�'&|)%�2i$8B�E��4erA|�,�b�t�p $A$ .�Mjl�S�DB6i%epmanifa�.G �)�[sE� �%A e,)�'�n��񨑈!ځ���% +ll "$=\phi_0+2\�Lpi N\omega + 2\pi M$ with $M \in {\mathbb Z}^d$. Then if in addition $(1, \oG�)$ is nonresonant it follows by continuity that it1�qknown for all $\phi$ on the torus. % \vspace*{.15in} \setcounter{theorem}{1} \begin{theorem} Consider a fixed tUH $J_0$ off orbital �4ce and assume �a �2(exists such $\Xi(�L_0)\neq\emptyset$. %4� every rea�(lambda$ and�\in5rR!r@, $a(\Phi(\cdot;e), >)$�Fis1^ous in �,$. Moreover,�9b, $\L�Bb)= Z,_0))$. \end{1ad \noindent{\em Proof:} Si!J$�+EdN�_0I-8quasiperiodic, E\ easy to see from DefinIq4.1%w % \)�0eqnarray} && .�:q59= \exp(i-I �).;�4H \label{eq:9.001n} )~%A6E�basic i! ity (\ref :$6n}) gives�� � �i����!�^T( � _) \; .:�2R� ThereforeZ�j7=J A�_6���)�,:�3R�aaE�N>�, N�, w�( we also us�he factE_Q�theta1)��$!=$--Q�um _0$. ThusE(spectrum of8principal solut�<matrix �� set ZW,D':=\lbrace )31&M + � M: � \r P6`11N�i �ame a :� b� a!Mph) ,Because $(1,M�%V�5, $D'$udense!` $6. Now�� $m�$�let $h��):=B�y<$E3�l��D' @�� C�� 0$ soE o5J� �$ ��Z�0 < | �_0)|= 6�a�:�8| \leq \sqrt{3}Z9D| \nonumber \\ &&=v1QMM:;Bs4Nu@e;.��;)�m��4first equality�" ;a�! second in$a�Uu�ZK|XN& 6&X|��>J5RJwhich"��~�4$SO(3)$ naturea���<$. As always, $|�|$A�otei*hEuclidean norm, i.e.\ $|X|:-�X_{11} ^*+ 22...33433}^*}$. If $he:U �� B�d�@el  :P� n, s�ais�i~:-, $My)|>0$%ʥ}A�iHt�^`E \subset^i))>X.� $versely if��K�>� th�0by exchanging� roles)�m !#�_0� e obtain �a��V; �p���6r0= �+ef$it remainsK how��Q6Und.Bo�:l��BW�oI�!fu2Yi (e�of {\rm2}11})} ��positiv�CHteger $q\rightarrow+ fty�eDPh2$Averges�on>8. In particular�� ���5� 6wI�^� � I  % &x !LAX 9.3:}E�s8 $Y� < bounded (w.r.t.:�) func� s $g:2�=: C}^9�� a complex��ed u f�� $\sup_{�wCI� } |gIw|�F$obviously �m.� usequeg !@ Y$. "_ Z� �te, so��!(c or exa� \cite[Se%, 7.1]{Di60})�� o �KN�Q�v2��suffic�$ S t&a Cauchy>��=�A=U�$\delta��re�aiQ�m$*�E s�$j,k\geq m$�hav^�  v�iOj:R- k:|< � �>� 8N1W� observ�]ab�ru �>� ^� =�]� D'} �F Ji 9N�Z� �ɇ $�$ a2a�ik� �Vbe��"z >* . Equa�"2x$09}) impliA�A�2 8s $ivalent to��men^�:djj^�UYF�10NqClearl6�,10}) holds b� ,W / p! , F��$ !�RHD'$�XF<�},&� n� +�:-�A�*��vw \h�NH*{16.2cm} $\Box$ \>�To�r"  p��T� 9.2�bnow�S� !/d�� ��4 are fulfilled� � �? D'$,%��` -�wen�Bf:�&d= \lim_{.t\is}�s:n >IX��ʶhF� 6�7N ͚%c%�lim�:�7i�� ! B ( we estimatZC��v&� -e d ��R| 9[! =��v���V�)� | >m {�N}^ +q}N} �PhF�I1"� � - U)� 9 �\qquad�l9l:_6���:�l �-N�y��6h13N By us�6���2�a AN=0�Yby not @a��*�� w�|��� $N$,^� ^^| �JB� _0�S = 0Fg15NW��PP6:� \, a2almost &�&k� � @Chapter 3]{Fink})h !�cr@ =�15B�1doP��ma{Z}T $N$. HH .E3E uJ� �>0  \h��jc� M2�`v�� r�X�G�w,�gat�f�c �pe�A�7� %B� %\newpage2$bf Remark:"�$itemize} \ [(3)] $ 2 9at��  e spune can�$ed be disc�ed � a�$al analysic!�E flX� rary�6�, .<mo | 2�]%�well �d,"Khas-E� �,ably many el' sO n*�ll!�sis%��. We reA �Eme3�10. FinA�,Y�a � rajectory��isgallelSan ISF )�T!:i7%]out $5E.�p4)] Of�rsiSa�Acases��dc�.zEU($ lead!#t;e�� ing �ioa�in�� 3,�E� weak���¥��2Pjust broadened. Intu� sugge�$E)iEsA|!�--�$ "�$(--like phen�ca ) st�Gbe��g But,a�co%9�He*p ��i)%^ omen(a0occur, �onl�come c�5 caraOu�u$1 ; % s��{Discuss���Conclu} R&&06�!�}If��g�� es� preseneZ4 thorough step� ac��!-AC$circumstan�2�R���2�"�rableA�ticlei� �t�"by put�8 stud�a ��concep�xT, onto a rig�s�$sET oula!��sidered.�EO�,��Q}"�!_1,...�!_d;d+1)" introduca'cer�� 0(e.g.\ Diopha�s� )%��?E��'�؍"�e� >2�<%-�i�${z��s;d+2)$!�qH�� une.�EBŸHn howK. UPF{\�: s}, !�2��� b�^Y���erm� Dgeneralized Floquerms. �% scenario��v%�,by our treat��%\A�rele ship�� tweee!m�� summarj}4he Venn diagra�$Fig2!@1. %\footnote{Th!�lor%j$�be�'� � PhysReview�"a�i[�per.}.(fp}[htbp]ca�$r} \epsfig %�=barber_beh.eps,width=9.0cm,angle=-�*cap�{�size{%Jlog� conn��2% v!gus 5r. }�nd�nd �})�mea�&%�!Rw6)8 asMs:�Z Ie�Eblack��le:� �, �"�� &� �*lskew--symmetric $3\times 3$ �&��m#A}�,�,J���T�&a� sq$(*,��smooth< B�"���C�k��.���ellipse:�͋i}7N"ue66S at� r&  Ii pera� (A��u� � ri ;�_*�)-2�)F�gramN�!+4  �"V 5JLye�-bMR�F� pinkD -\3.a� IFF�U�a�/ ��ircles O+� ificP s, namely^�E�1:E��l� p.c& R�5%71%R2 R�$J�%fi�6&� 13 � 6, )�e@ ��irr�;a��  (J)$-Uv3 v^�nu9"� z�4 Q �� �g ���� = 1$ :� 5: afc:�:<6 �F2 (!C"ho�c� parameter�=,\sigmb& 2$) -�>5�8 } 5p7: below:� % At���+�eri�m�orE{| 5��A}$\,�� ari!� in �Vtorage hs��nou q&ed��ds7�<n 1whe� �����. N?thelessD seemJit us  9!k6�of� erest.�0 s suppor� by a�amounH &� worka� , a��O � �t was�!si� to�=struct�ileastj,good approxH� � �� �,hh96,epac98,�fD98,hv2004,gh2000,m0hvb99}. >se simu�$ hard edge%�s� (thin lens r{ e�sb fie wM�*.��)6-A��. See 0 16" U�6. T�X)Ny*�#� �$�io9!~!� �( SPRINT, eiEM�m/2T pseudo--$u^1,u^2$--ax/)r E'�� 8 near 803.5 GeV1� HERA�I, -26�{�� }. Ii�����^n2 Z� �� � corresp�0to�7��S��\,a crucial qu�t�+cha� eriz��stabi1�~D �. S� be�'�}wA}�8driven oscillatD%f�r�`magneti�elic ͪ�+"SGa�*a��9A�a��potent����ed� litar,p/i��� �M_�`quite e2 c�e%C &s1EB��already>"�fa�%E�nA�bj-qu"] 邽�4.� �`tM+$make littl�81to~ api�&x��APa��,a UPR $\nu_s� ~A/*[:��ch�& 'in  t�fera�v�!� 1�s\� ��be��o� B!�<�=�|�taneo�,]5_�ore �b� enhz���am�% ystematiz2� O �reasonx i�!6%��b�7l"Mb�co& ringe�Bbx As �i�qI��&)5��>5_�]��^ !��vj�Zbeam �gyY$J�/� confiri.by)q���� ��, hI�� ``""te���''!�o� y628%=_J�=\ (rec"nof90)��t!2necess!( hoU$a ``prefer� me�6�2\Xd. �v�2 %F-bgmad�8fo%s!��a�� eh011 [0,1�D�"AnUPF� f��9.�*A � out�R53� � lsnuN��e�gn0antlyỷ� zero3 ordnaY� Ir�dir�%/{�"n} _�!h), ``design''6Pp��C_7e misaligna2 Ra`�Dont98,br99,bmrr}. qrE�M2m9�|)�=�at�3� U�i"s��z �!�ei&�B� e�a.��E;]e�reduc��  '�A8  ^ AJ AeW� � proced)in pla�m�Hy�&� *� ��I�Q�(ver a range!�fi)5�s��cies� ��) !��� ��b���� S �3��. �&,�[  ��is��Y%c r�to i sen�4-]�  �/ci .Lea �, on)1 find�&m strongestC-hM��o� �%iT��s",� high> effec�reily� mMant"P �M tail��th�1��ABrc i�� � t m[� T{!#ingf�s� iperturb%*�or[ alv&m �=Ci�� ane87} "F{2�2%^6oexpan�5 metbf n} - ��> �.d���d �n ea�A5�: or�o� ��Kno�p"�yW��<non90v �%#"im� anmH�� i�a2�9avoid� ct0�n1}�"��<-)1 ���w��7Iu�� �i"j�%D"*7.17})) ���P �5�A9$\�1Gi� thn!� �, =�F$�S�a�y��" so--y ed Siberi^nakes C)`M+I*�h $u��sb8.� M��� o81}. I�t��� X$%��litern>�fuG \�"� �� y sp�-�ynchro���u�"Y&� to"Ee �F�n$fro across.� 9�s!�JY}o�$%�9K�yof2E$n� ppos�Co� Zour&V�%Vpolm��at&F seen. HD)Q�)@ɪiG.�n��� $K .l}. S�"͐�� 2Fof�R.�I1q%:*]( ar\}!K���;? the >whU1>`� P lyZ ntif�' �R Froi t--SX��� �fs6�)i�� j howm7�Bh�aX&�gAsq"�� �e��� �!�2O5 ofM � ����o&~ a fu�rV'ust -�� )* a wi5B  �����(�*p� or($a� ��ir� ��9 ��Q' ?B��qvi-&en^b.j3>`��a&�&��i": 9%d��'o.(,(.�.)y�a&r'!B!�N�� off�an att��altern��*��se1�2two� "�k���h$� -�aamo�C0{.l )b10tch�r�&�� M$cl�r��>�%�9T !TM� )S5Ni�/it�s, �NN!J� . SB#us��I�A� deciA���.!� in�a�� �. O'c F�!%~�-څr avail�y ��boscopL veraLEa%!_F��&�:�.l.��2�)!�Bo~I.aX�%�CP ttempt�6^AE+%*� enci� ���&�2^3q6�J��* can�'"�triviP"~ �x���uS1�#rn ZL��0� ;H_ worka��.�C"�Pe57J�J =U) @:Ift(�(J}g ds(U) \D) U^T(�O�Az%�!�$D(\pm : i;)$ �� l�71J . So� er�a�$�onN --beta� � �> �'� S canV be &P!��1�In .d�al-��mP-��-��&L1�\�:  $ stkEng�>"'�P�̡}&?/a� "�"#H!9 [p.27i�2]{� 84}: %����.z"S5�&� e�I<e�`�.in<pr#H. &9�!�*�!� �?  Q-h����]"#s�K#�N YR�pr�: r�Hex��edY=N�jE��"n0M,a[3of�=cjre Se 6!_ $J \ne 0�DD�#�>n�P ful �Fx�� d� wM / 21]{�20031}�vid� "��W.4�Ns��saiYEbK2}�� exce� al. A�!y��� %a[*M sfe1�>!�%������al phasz � ͡)E��juHI9S�--Gerla+Nrc�iA� poi+u"j6.&, S--G �ce�n5��5� lev%�-0� �4"� �&�(aA6g 1} involv> he �F,)��7)�-�� &�$6/ . A B $dk76,dk78}A�y kind�&�� ��� ro$L%�-��-5�ErXw x!�� e.n� � �% [p.7A�on��I 0nh(.�=.8"0 }��"�&k%22�Q$2 J} = 3/2$Ptr-�i�u�p^��g;�S)$2 r�� s�X�r %J�-1!�ve:2al!X!A!�m�L��EN�4��@�iisG2a:�A �X:F� --meq;&�7` j2^��iss*�TR)%--length�^��P�j.^���!PwJ�1� "oA;�.}�k�q��|�"/)j �&sN�JJ A�R(,�y9��L5���W�&aA�W4i��e,Rg !:Zs2�"� �! abrup�b(2{8�!4 next� �8 ( �� "\ ��f �K�(]�a� D)c)n�2-}�A(V*+� clai;B�2,}�� � � `�[:�(is $2 \pi\,'1\,$��� . Ob�5l�����t�f� �?�����!"�%JQ���!n :`6���Y).TS>)�t>)��v�i�)�Cl�H�7 %�.=in��/�) Althi?*� ��Aits9���mj!�n�Psoc�I��<f�oE� �*e����Z � not 2> � �*�@%6T ploi�Utechniq�<"�^�2o�K} � %�{4E��5)��.� �yA %��0�?!Z!%Ʌ{2y�4edeE�zD6 ���Fv5a�J)ef� clou� issu� � !A�$C �T�2)�. �V o {$]-s �N$ !J.� #as�p)!a~.#'���' an?1 @) u�a�zf{* *�(�regarO�ut�' f�}�9y'E�mo�*ub$&� t4&�1&a!Rr�62� 2,...$e,�9 � �b�h$A!��nRiZ_yA��L/~ �/b`$M$�;whole��s.�tnalog*��"&KE�&`>e�rY#�Qsi�%of"� !��"$��.� a�2���.d"S$M$Pf�aX*�.�&a "�S��%!�&��$8!!�exponA�o�-�)�� e�b�i� prU V�ad �piUom>� $t�u�?�(sW��K �&� iU b x. �#is �"gm�A�1'u$�(��{2 � � n���.�.�-it 7 F. �cnu_�V}$� "h6.1�Q)�o,�Gi�atiZ "�*��� �g�Y "���))�Z��7�# �� 9�Q���B�/��m)R%_$,�?�+a/� A}$.*]#�Q bE{r%"�9,&"NY$iI�e�C=�X�� ? whenE�"����h ��0YHIif�E p,(��}.�5� an un��� t&% !�F�� 21}�8� ���vmulti�*�2�is (0icd/ �3j�0too. Again, �(A3'N�+��q !7�3|]!*� CallA^eaa$�56c�/e!f �,�!2�79. If,�%�.o �bE�M� � "G+� n" .&He4iCA��y&fewer  per UPR*37tht n�� �.�:���us a FoYm�EbX .�,�li�# ( o)�brA4h,��b���E�>nos\/too�D  - J%��of�Ax� . 2�$e�;�5b�H9L too 2>� � !D�.�&qYf6�)��%"ru34� ypr!�>�&� an� yqA>n�m��i2ent� � .��x* 8!?y$( s%�a22 %�;F��1�)Rset�d3a� s toy�t�%to-acuI ,�Ni�E$ck���(�!. Ind� �6�Js"�JD pular� 1� � ,yp  �dk.ly��tx9U���I94s ��� �3 guid�_�8�={ r(H /� e�!�� >[%�Z[��E! �F�,�.P �%m���TM�a:� U!�=��%1�a.)$�#.�(�heurie�Ip� 9 � �5 inflg� f i3U��* dilu@G S$ b�3iorM�� y��*U*^9�$$\tilde{c}" 1,!G-iC)$] .5 6})��!� $ow�mM�I�6J ^�e�0[p.66]{bhr92}Ea hf�D� � .�9 �Gin.,JI�!w�Xf�6 �'g�F"" ��%� Q!�ach&�8 adop%m#*Dto[$i�7�$R :�E�A�a h1�Ger at �P�0 �v&7us� g �ph.�!ny �<�+6e ��-��"T"&� map��,by��� s sh�Iat� s�> chec�5a��8rgY a�c>3%,cy.- Vr(  ~Fu�#�i���A�t` �%e�a�Dm�W1, � bar2002�9uE&06*�)``-"? R� t'Id�s�*fer!h�>l )of F�(du��ele ��a-�i.�%��EmWF?Y�Ʉ��� \��DW�Iao pair���$�%"�N�>,"� �s� syl98})B#� Ɇ� d0�>$\�2�k1/2l_��l�89%Ns gy�4�0"w. � ``2��/atY�2�� ?h41, q`*�";5.00}), �$ = m_{0} +1} ~\�TT4th odd $m_1$. M6��"@ (�_�z���OunW deIm�W&�W 4�"P.& I?D�cZ� �t d!�n�?ABJ �4�1��1;p��s-�((H out a7�Q �()�irr3i�Ua�&at " yQqq�. &1�ji]�"����U)����ia� surpri�O9�k�!�of tp�>�)�)�no9"N�a�� � e Hly�c Ocl��gbe2��ier usag�i{ky99�> Ouribut8Oar�� cl�f�šcof&�O��O�) � patho�J"�e9A�|U"�=a� �2�*�!du�+�E�|pl�*�V��� r���e"<��vI!�S."oK��w��z�Di%r�E:*Y"�� RHIC!�e �2�*R�s \Es,�n�u\"� carrW ���&=��>$�sIa�.5 �.��3��xk�!� [ �a�a Pdi�:s��%�,%hY;1ys%�sq@O%h ed ��cauA[. �@B#n)�\�'al�&��"}q���s�1.VtoF�'',�* �mbei2004C1s;yeq%0Me!;5B�'' ��B u&9,)^e�f=MA�,-8an im,$is.��@� CRxFA )T �!���^�!X @%�M(!�e+Bond�X{O=&n�o b� . Sy& 2$Ek([p.98--100]. wIRFaj�/05$0sigma_2^2 J$ Jg,B6ZV��2B�y$U�!62�Rp3�a�!re �C���d>-�!/# �the�S"� �=jibh, �N"~ j �Ba��u ``e.urbNl��una &b3a3A-*�3�'B�S1?�x���*�Aurn�a �h�!MI�"l!b�����)�!l�F>ISFA� o it0e�Bm4�@.[�i�a�ͺZ(5 � �.sCe � �a�3 $H`^&�. pic�A��E$�H.�4mus! sought.l,��"'@ s 1%�2�m)\�0~Xforwardf%�>S ,}�N��D�1m�-s�� u/W of n�L�b%��e J-y.*�-oJZ�S���F m�?ge 3��9at�T�X emplo��  Lo�Bz!gc�p  T-BMT_!K%<�G help� !9z(�V2�E�]�#r�"� Gi*>�}FY>H��%��g= /*,�)�a��&2%R��!1commo!#�J� for �dA�e!ZE�)� w1a�#�a focu�!q%z &eY!.}�diA`!�U%Z�MHD  col%F�1� �s&Q8 ra�sio�m�!che�4iI$��3.v�ory�h�1M�ed�XA2Ve)�1�.S)���taqF�lear,!�2v9/ac�e9di=�}� i�=%��k "�J Bev�2 �1���&2Z��graph���Z *{Ac�^lTN�&s}&1�thank Georg Hoffstaetter, Helmut MaaEdMathias Vogt, Kaoru YokoyaUvl�, Gerh�D Ripk%�or�8+fruit{!-wU%�'A��J!)�s�" #, JAE gA�fu�/a�� s�9r�BDO.Lnt DE-FG03-99ER41104k� DESY�fa sabA��0in 1997--1998�E;�-�U)D!���1[�h(assembled i4(a manuscripO% \renewa�and\ref�D{\� R�s"�e thebiblio%�y}{99}6E{\basep$tretch}{1}mlrgej�%dbkh98`6u2�Nuc/�N. Meth.)| A463}, 62��@(A469}, 294 �1>q hh96Jo G.H.:aPhys.X[ m@E 54} (4), 4240 AR�O2�R-�� e, ., f�: �,�Win�"cee�e� ICFAe�shop `5fA�# Beam�iI�Mon�T$y, U.S.A.,�8,E��c P. C�{World S:�T:�B�e$M.�� Proc.% Eu�0an Part. Acc.�`lf. (EPAC98), Stockholm, Swed}Jq*�-. A"�7,Gron!lo : http://�0.web.cern.ch/\ /WelZ.html:��C:",��3th�� . Symp. H\EEnergy�7A� ics,!tvino, R� a, Sept J�,b:��D$S.R. Mane,d.}8A36}, 105 (1987Bq`V4} z��.V0E 70}, 056501e�F��Z0JZ��ATrn _o!,Q� S roto� ams�Kbe�sh s1SA��T0 �zMod]�i6�0} U�Ph��EF�Unx �(of Hamburg,Zla�H--THESIS--2000--054��0>mchaDC A.Wa�ao,b<18!`29%��' �:ukI"A'byf%�@K:)�Ja� �Je��< ``Ra ve P*), C�i er A1Wa!d<in� �<in ��n a� rage Ring�q �e Handb(hofa�e{or1�q1E��e�N, Edi�-59�M. Tigno >= , 2n"dE�2�J2bga�V.V0ala&?XN.I�Plubeva^� 98-1�e:m_L��C b� 9-00 �95 r 2068:��_�2}.bf�98�k %p3>�Ldk72} Ya.S. Derbenev%o A.M. Kond� ! Sov� . JETP;35930!72J^3�^7}, 968^B�ky8�vs86-57B8By�W�a�u��Y4t�Yar���f`osium, Osaka, Japan, Octo@�q, AIP"� 570,%��W6 !. vp ��F�M-92-04 � 2), %�revisedP� :�9:{�\F�,a�HE;*� 2�ST�\T� ams | 2A�140��1[ 6� si89}Y.G.��4ai (Ed.), Ency� oft.s� 9 V. D� al S�Ss II,Ր, New Y�>�|B^ CFS} IA(Cornfeld, S�� Fomi����6E.5 y4 ��, 2lB BX b76-2�w96�7n6611001:HkhripA{��A. Pome�+ky, RSa�i�I.B. K1lovich, A�. Usp� 43} (10)�5E�0). \\o^�$\\ >HEAm.~Surveys2� pE!14}, 14* 99)� >30 gr-qc/980906>�derb90>�,:SLMichigan--Ann Arbor,FF,UM--HE--90--��9BP��3��52Z�N12�� � 5t�� Z� Brookn N�al Labor�Yy, L�7Is�j& &� �j.B�67)�B��R_Ih2J!�b���S�SA�} H.  a�O�1Di�Fen1��s:C rZl�to Non�ar �csiQ  de Gruyo��a6� Hale��ale�~�U; ., Krtr, Malab�Floridap8I�"�0AA} Y. Aharonm�J. Anand��ii$Rev. Lettsm�58a�6a�593Y� .Frank�N.  l�.``M��� o�P%Ocg ll��Jw�a68>6 Gold%� ste VCl� ��"@!62b .,vy$V.� "qV? 85-4�=8� �� Loch}c ak�C�uni7 ``MX0Q&��9��! �p2�BYKoe} T� Koer� ``K)A�fM�Cambri�dU&x Press,�e:�Maa} W�akA� Fast�odische�kaEen�Q�� Berl�196Au2 Arn} V Arno�Epu _�oden FkE5nQ7kv$ Birkhaeus!qBdE�8B� F�| A.� �Al�$"~V3hLe��/� u(., Vol. 377&�7B�Dumase �  ,e�.2KM� SIAM pp.  �stm��409�Fk�� J. Di�en�End�8J�.,AcademicQ Q�A6F� Lang��  !M Real6Q2 , ReadingP :nYosA�$ YoshizawaTS�(t:e�\bExZ*� 5� So@�B>�!�]��%�5B:�9�321H 1�92BL Grad� S.  ��8I� RyshiE�T`K%�I��ral�)erio3�P��� ^��6��.�a+�յ3 A����B�>{} C. L? J{!J�|/lA.m��Celb�al�/2^�B� La�JA�sk��`ica� D6�2�9B< ^Q"Q�R.�f�V9�ar62]84} B�7�u�ics��11�!�8B�ED ~S.~:*~2( Soviet � s Doklady)2E562Ad7B�d�E��2�9��F�1Q 7B$a�� 6p NbM328�U2>�sy�, S.Y` � � ��!�A��,� S&a�BA�9B�' M.Xia�(T. Katayama>� TokyoF� CNS-REP-59B�")'A�Bei-h,�R� 6t~� T�� te, Italy&s4��WpbFbyB�/��t::}end{docuOO\�*{G} \us�,kage[dvips]{�icx[�x{amssymb} \def\kT{\kappa T} 0�fv�4ha4t�Ng nano>A�Ɇa m(s�vbi"L+or�j����geo6 * }\\~�$V.N. BinhiG ".wCo())�icrU�R5A5��*!�o�*s,  d� !x cytoskele$�2�z. AouKbuA9� O/sWo�F sess�)s��e�#"�XR4 s," G�0�re�0z= ' �7 >U63 �!(Ly�6Idom=at={� 4oעU g,��Y:tO *.����oaA2t�1)g-G-tayQ�"�$! m�1L" 7�, &wdw�-Tke�i��58d 5l'�bu8L&�$U/aino".�igrj"bir�Do fault�-:� (-term �?6$Z*�! � vi.�Bop!taa�?-�s� �P Yv�F�"e(` �l'6�s �*�`;�1--2 deSsFC"~ip�PPY�Ɲz)0gNi&rUaA wave�6��D� �6. � {5mm�,�>% ;%�,vgenig i�9 !ic�&!h.�,�89�q�Q1�5�! \]�10� Many-��)as!�E�FQanima_cver� ann!Q6;sanP f mi�xaa�c��i7A p'��thZseaKB l ha;�)�=Kack,�;t)l�cderst�tye�|E�hyp���� �Vs�rI�0ouS�$�'o�84kirschvink85-e�nn�ul� �Q�. �navigIO�$e�`$8'�:tjistrh surf��:sG�y sky�G7l! s/DfJ�?�IoB"�{re w@9rigid;� ound�Zkgeo�!a�o*��k7Ear^#6GlT9r.�Z9�Y�;rital�SiXace�v�}!�Q.���aS3�"��a�Ze�organism�Ln�qsA#sh�����mamE��a���&a�q2 (MF)ZAreA�t4ha|]in mK��4>�A�rAhept����o�* AV3e �O�b/r�:n�` cognv8�4a\o�3is.�eM� �I��;E�1�m�-gg��,v-�6� icacűR>��Q31 G>^s!-s)�� brie`C!!�ب��U(�Wexare!x��&�:1{b� 03ae})�Idetai�/�S!iq� 12�6��4-n*t�A!g���#c�+molecu��9ea�|ff'Uv�~�=kU9.��_U�gt@g#-`$�m��E~.eH i $0.5O8 10^{-20}$~erg.8^J6r�/nF5n �_�%�s1 ��fluNAA�a($.e. $\kT \*; �.r14 rk8�u�:\eRes%i),,!�Bsu-)- '�CO0u.V=�il!�>+� �'nN-' backg�<4H�d�7AM s�(cro��la�+ � 5�){cy �("= Dli[4ob7�s,eK81�SE�Ndispla�/`.�� !��-�=-�1t inly8�� � $\mu $0"� Mh�\l�+��:n 7--9I �]��q�2�ae��c MwHOS5C ly�8T amNZT�6siU-j�^t9S��G �er =I�5}$~cm�v100~nm�aB�m_%!HU�vJ H$> �I� �o24 A����;;�e: �5r , $vKJJu,80$~GEzBvol���s�:ei\zA��. cytoplasm�D cell|qra�<z>a8e�O!�2�/��Q �` P|&$�ulu�0Vdir �2 �ptxGn�impulse)�e�4, MF p+*2E-����a�/-ޠd!$Cn� of��ue up�80.1~T �8Jitself%.an�f� ��a��.a�D�)%kP�a!� ecia)=��t~ ,Dch��I��U�) M* free-A�1�?!�(% ;�N+s�FR HML2��[!br�' v S A:�Cu�%#�-�tissu�BA&e1�  �@;oN " �Yblood-[ bU;r� �(mperme� �1/��n%v)�JdV�dip�' ��1�1iva�(0ferro-� �6n;-���` pene�fe� �-#epollu�1qS )�to���|g cAjgi�z3ap�n�Q� U� qul�#crystVLi�!� �m � gNA4o�|�8` & s'; �*�1�} �F!�c�7 gat play&�t�[T $lakemore75� 9�k<�<�F �ic:�ab�*�in DNA�lex"v@$khomutov04: BF�undoubtel �s @�OA��;a 2� �:� s� edge99= TW�<s. "�v.[ ��.�� I�F�)� 0ymodel� " F�q6\�J*`L%c� liquidA�~g' W��N �e� favo��u�m p'_ D!�iw�y"kz��0��cpv ab�6:�"� mh3e�of"� icɐ�fy:J�R�ű*� �e1Ba"_4i� firmo6a�b��i� �&�;t�!Ce�E%?��ill�I6��� ngs�8s�wt3 c�haea�� or. %Mipas�0%&�  ':asͯ�"Lx&��)�!�*#"| `Ata�{"���9M &8� `�Pe��e�n��;aq� $��It���:�<akg�*�ot-too-�ct ela��!��ug{�A���B�> ���8�few/�1�alfh��i�9en7�y^o ~8 �@�;�| 91.���i��.�1� �Iil�� X#�� 3D ne�pro�# fs� 6�25� di6 ��9�Ni4l5� a!]jf.eWtub� �e�6Q {��faste�O��{n 2�to�^(�= e���s.VL�0� .]�(JTb1U�'c" V��} ���r lipid���gorby88pi�nAt!{I r! !�tl sQ Qg兗�4" sA�o'o� NZBly��|�t9MF0�;� b�/!�mD���ic'$S2]d��mi ..�now)�to, $�/m$ af&ya��ic���L "Z(boldmath \m T!�M&E WZm~c22'�*HFW Here,x< �LJ�3D�� 3e��.�1��s!Da�>''sg@�c.�dwo =As:6�Z  �n"F $x$- ,I}!� A!��t�c1;cogld�9:� MF (.qsQ��s(varphi =0$)&�MF|-},�.~G; {f01�o��t] \[Cclu�aphics[u�0.7\text]C��} �ca�����_ {~~} {\��k &= -�H(t��in(-#_0)Jxi'$~,~~~�^ 0=\s|�k/I}~, ���$ Q"�an�Izc%� , $I!9d!{1'z�faA��2 diss�*WR , $k$�oi���rW}�}"� .4�0 ' be�4g�)ba.����c�A�>j $\lag G +\Delta !�A�le = 2 � \ݰ((il�G�N_0�y�Ffq��nd5�'2� %�nxW�/q=!(of- �!2l}��2@��K�%_1�+ �a c�;��*\ ��ems8 mob�euVt�Xrk� &<ir2x� J���eaHV"*�Lf U � m��a�2�*� ]z$k�qsssim��*�� )� (Fe$_3$O$_4$5>sYpsub$lc�N@?�Zrho"f,5.2$~g/cm$^3%���E deh� a Q bWAla � of $; 6}$~rad/sXrence, h� o"� sm�A6ii�*c1�L&vɦu�": $ IQ� \ll���� reaf�/.[� ����m�FE�bem ored�$��%� �!udy_N� E� � 9-M6%apredomi1�S� = a&�  o&}A  �`|bn!� t MF.�  y��_0�lpi��et቏$ $�"uˢrea7�!B off-� /?T$azimuth def� *K�io�j��id�!�i� �}�bo H � vi)f wZdA\iai�e,AW&+t" $'s craniumM[q word� jfrmlA#D !B��et!F3�`1!�r)�� �an ""nT.KBk�A���b 2jb 2�b AA*����2��h!:6HMw(�I�\neo� . $U�i�fhe0K,'1�����6+IY`�U��.�!�d��,$ls $a=0.8$N� QXis �$\?E��k�k ��B: % $��.� } +kI a�m�'*� � Az\cos � � ~. $I  ��"�p�2��u"a 9mT = \f�km l}  \tau \3 v "ʺu H'� } t)D6% 2\kT$ ,:> A&51Zdu�~k�. egin*m  100}::+  _ } U1,�)!T� D}� (�)>�"� Y�v�1} .ietaiB�!V a2r ^2�� !�5� ) ~ .>�� $\x �yezed GaC{o�MA~_a� ce (!l�J� >�(\alph� =s t)/| | i used�0�!9�B��s����x�iH&6 !A��}��I%toonŰs�R $a<1ec�MR w{��ACi:��a��|�msjn�u�?Z'�..0$. D"�V� JM��<e}#�yJQ�dA�)�r�)s���i��"n���1U2K �C��)!�j5*#*!.%ra kj xi(t����ict U6L*>%�MuPism6�)ɾ �n� �e�%A~es���$,3 ult� W6�Yi�h6qA;���kC �)�yU �"��ab�e u(���GFz �a6E&���B=roM+� R.�to loc)a)_%wU�{\E��ln� 103}��0{p_-} {p_+} =�}k ft( 2�u{N U} ���}B� %ӛ� U= 2U�o9 ,**q.�in�"�l�K�G[ p_-���12.�~ 2 �U_1��. \] %�`a?K+propor�haew!IF�9�b6�.�� 1/2-n[ s���- ���ox  �D �S"� ` $�Rn� � -to-3MGE�EEA5j��{ R_{\rm sn-K2�1N!5!�a=�A� _ M�9�(��@�ave(exact��tj�xc.ɵw~V:/!�*܍ov�#�"� $1-a�c��'-ZoneK a�� }^�_�E -a),~~ U_ Aq 32 (^2 1 .� ^ , U''(0)= a-1 -''Pi���2OI�5� "�*}��3���a�\��~ Vn!y*Q��1S�ct��xA�� !��&[� QcN�� {A.�1%A>�F��T,�r2��dm�$��O ��a),A�I"1�%+� ulaE?bd 4}EiWmieXIF D {2I 6%�}}F��(m`ya�R 3}q��!t!e;� &� $�.1 *mL�2�0���.< � ��� V�! `softly'p&�!somQH�"�z6N a$�no�)v��X��+�I3}) tn|4rD�li3c�.D.��  ai�V/Wm"�M"\�ʅ�Y-�/ l" slowl�9(e�x��)�at,j����. O���*!�t.:sI ach �1{�(a� .�~q%��is high�Lr�� �im�9a��f3�)nq -to-.4!� I�(��mwPjU|1$Z Kram!��_�'$,mcnamara89})��[� _{icK}��ib��6� |U'' (0)|������) }a�x"�>��D"߆�Ai W2}} {1-a.C[C3e�^.3 ]e���<] 2��i|o*��U��y �or�${"P$\ggB-� ]A#9xtaS� aa.���re I/@ �IIB?`hu�~g'� a�>���su��$2�e 1$~\�!$ �"}4�\nu r^3202�-7�-$\ �$ � damp�*���g�.y "�1�.5�+V�$ )s�~�h�42}Z�(water))C�aa8f��v $a > 0.65 �b(�XF*3};E3סOt�����}��H"% 0.03P�(1.7V6.";.?�J��Z�6\2�3K�;=c>�3�VR�*��d5p upo!V�N�W,ll[�,b� Ɏ� ) was $n$��s/:er)�R� �"Հ;��#���8%���q .�u�'%�1�22vaw&io� "c2yorke86_�fa�]g�*A Den&[sr y�t��/q1s)ptg��Gck �R . Gi�aL) �a��b)Zk��E�m�Y"cd1a� 6�� >%n%�, ���cerebr��� � He�re��^�`ed;š\T�"�a�7 '2�`� quar:&IC> s�Bq�/ �� 6�=�ach�&���� x rooIZ6�j ng)Cdy)�;onH/$% remia�_��[�.�6�-�,AVm΅!!o�7$*46$8"�+�$"ciy�p Eq�8$�,s�zf^m,&B+92b}. S�)#7� �ݸnc-u-� �5�,E7�s2 erf��!xK�fac; [)�9�.�A�}-a6K�Ma)�q*˙�k. If w�(s�1!�qu�A s fl�M �5@du0px �� ccorͭ� :pat�� ock�1�n�p2=e0��� �<�{ �+2 u]�s���")  ax`�+ f^'�8. EIaVB� �smT�Le leveE�.6� �&��}u( �%� Lock. E���lV��al2� �>e�%@ reMn]�._ Z<�.�=>��6�i�xac�dAmh!��c��U*ddG�� d"�"<&t*!=� ari2�ofcw�3 6H�a_lu� ,A�tm��ing. (1)�st"(+. i�J�up�8iar��%�ac�"(h F"N �.G6&"� r"��.8�`x�' ?:6˜� ��se�en��|*�+&�9m�^�:�e��-low-"�# MFs,2�z��;�a&L)$ vacuum'. �X DebyAVl�Rt` %Bۘd�x�- e+�?O$%5!��9)@ic� � �!�c� �%eaV!p n$� (t! sre2;O# ��]� osci���S �M B��'!��2���Z��is x*�i�3%fB"N� aa� ,"f:�Z G�@LRFFBR No.04-04-97298��t: G{10pAbi!d+<\<*!FE;A�V,Savin. \newb�� EfU+�E� �Y�^��4s:�Eal a�>ts.U K�s--Uspekhi}, 46(3):259--291, 2003[ 2�2.�BWM)� � y: U/A�| reF*�s��>MSanOgo�2.�*o McN{ B.%GWi��=X K.�YdE�ӕ�.*5.�SdA}, 39(9):4854--4869, 1989.�.z4 K�4 G.B2[O�42}4U�8<ce¥:a���'k��m�U�5_)� 65cT�9�Ye2|� BiofizikaA 09(1):140--144%�4.�In�an..�4 E�  5�V,�OLez S.M., Taylor O.R.P JaA' R.d{M/ch\t terfl (Danaus �5 ippus L.)�.s2sU �!F� PNAS�\,(24):13845--6!��[ u�&� �  J.L. K"�C, D%P Jone�AB.JT= cFad�c�gorF�i3� BiY e�)��U b  in O� �' Q=e}ism2�Plenum�U~[�85.��92bJ�AiNbayashi-.���Woodford.� ��bB���.o:��E��P Natlead. f . USa�@89(16):7683--7687�92.�b*s8 B R.P.k �ot� c�?�8."��fcB@190(4212):377--37� 72P42 Go��Y�fBjvi�UT.JM�b�Ch��9�1bs9lm�o�"�2B�J)j�ol.�] 70:834--8�f198��U�&e E.D�Srk2T�e0�t��"i�$�:�fY;M�c �"3.�In}T ad,iTe_�.MqTE|>h�!� -�Ayai�QaO =yQjG�>�M*�N �R>O,jetpl} \onec�?n .$OO s} % <- �(LatTeX + PS23�2kO{0�coiu�=�OcO�3"m�\title���9�APho�H Pert�tSupE�diJ#} \r�: \ldoEo \sod�C%sXauthor{A.\,P.\,Saiko\/\� ks{sD@ifttp.bas-net.by}:rN;sod Oadd�Y{&(Oof�V id S�!�_ S�? ondu�$s, Belarus���`s!Bab86ct�)ape�*�5s.o�FEAr�*Ps{ � co� nt p)�P exAA�+Lwo ultrashort laser �As�Ra@scs8� p�&> f"�1 pr3������al&�#ٔ�$e�m.D�w P�by"A~pow&�5��& ���cD +�*XWL ropaK, �V�u.\]�8*)�eI��<� � n--Xcoupl1Yc�-��"Jī4py.} %%% PACS�s \({74.25.Kc, Gz} \makee"|r0{INTRODUCTION��=OI�t�;9�emc3$on (Dicke 2�~�8bib:1��nJT��; ��L!3 :�;�Cfh� v-mpI�2 A�'pE�s,��FssL!�a-!���{* 9)�g *-H-ia decf�eE�2�}1 =5,!% 6}. ��c?D ��r>��E),/oe�I� ��m,� acq��s��;Qm vib��Y!�ns�a�Ia  -d ,aE�.9repAW���Ka fa�eEQa3y U@�(.&qz�) �� �-� � ik� �; '��n� $�XR�{A^%�xt��i��ir delay�I_� �}��';[!z�A�i�!.A�.gJ �"4ple(wIm��E���$a��rA��s؜)]Q2EQ7imi��6~�re ��!/Refs. $�4 u� Thom�sB XhYEk"�} s BrillouA����igh La}�tO?!�%i�ip ��T�l&Osor�|(orm�d)Mz . E*F�$6=onU�-A _�'&�+ �"$O^{-}_{2}$*!Mwa���!!aU*o dii, ics $KCL:@ (see-L9!� 1)_Naboik�!A�.2�}���<:�in mi��mo�Mar ��(of diphenyl%K pyreߠn _A�D3 typb#A��K� �Fg� }Dtion{STATEMENT OF THE PROBLEM} &��e6!�I�U6��be iG��tro`D�taLVU, sRO y a ��nC86Et�4ofS0mˣc s, %�+J�!ir�g"d8pP�!e�in*�t ��e\Ha~IH6Cs e]�'�up�s \ ��x�I4�%�2 �+ at�� $t =  ���us^~�"�? an*z ���"� �7{1}|/�v5 5 2}$ "�nIOa:a�]�#K6:�/ hT %�)e���M�6a~sz�%����1�/2 �R� FW� z�^*,_�1}-��'=\Omeg '~%�(u�,FI[ �'um .���~os (�EC�a���:�E ti�9e).��qg'b� �.t2� S t� Gff~ce�.t=$!�"���1V" �L s, o'��b) &��Cuse%5"{�-a&�s�6>i'p to � �&� �!�beloc� �4i�s �!�MVͣ �)Th& i� �xE9� . N"x�+7J� V�l�]ech� e-�o_I*� Wil���| ~)l 11}ɳ%XRef. 1�`�"0study an ense�mble of optical emitters\t impurity atoms or molecules imbedded in a crystal lattice. A natural approach to describing the electron states of im sparticlj�n resonant phenomena is to use the idealized schem ��Ca two-level quantum system ~\cite{bib:1}. We assume that each such tA 9� interacts with radiation field and�\coherent phonon wave (exv%4�this case by ultrashort laser pump \). The{nofg � �s~ rmal yd@n be ignored beca16 �modesRla%ˆ are "frozen" if low temperatures "us�(e experimenA Xsetup. It is legitimate!�Lstudy a selectively 1N7 by classE�,means, i.e.,!;%�inAQat%!k ha!� amplitude $q$, a frequency $\Omegand a ph!�8$\phi$. We wri�4he Hamiltonian1(I>99�ngI%Cr�)0as \begin{equE_(} H=H_{p}+hpint}+V(t), \label{eq:1} \end;WA� $$ ; }=\o�D_{0}\sum_{j}{S^{z} },\ \, /h}= &{k}}{;� for a@ $(\textbf{k},s)$9�.J-Q8k}$ and polariz%� $A@e}_{s}$, $S^{\pm,)r�|pseudospin variable, which obeys�commut Zrel s�$ angular m� tum� d�qe =P$j$th ($j=1,2,...,N$)�$�@ �� ��energy sa>tA�$�0�a2 $1�� $-�$ �!Ae�$ron-photon6.�coupla,constants: $Z$=g(k)exp(i1Ek}\cdot rI?<=-i\sqrt{2\pi c|k} |/V}5�d ?)�Rb $ b,$$ W��5�d)� *$� dipole )��Ag us vectorQ|)���($V B��QEvolum^�, 8q ?���'���&,point occupi�y� � ��wroughou�[xis paper we take $\hbar=1$. \s��|on{ DERIVATION OF THE MASTER EQU} The sA�st��o�W)a�\dM�d��AQ�� (\ref�� ) satisfiM�$Liouville �> (?e!F�>e��isŔ!$over time ��vals �han� ,of irreversiC de!rA�1t. � medium) J�Pi\frac{d\rho}{dt}=[H, ]2�2B��+�canon%X transform�)JnY(\rightarrow'+U��  U2t3Btreduc!woJ\.�'��!��a'6�4BawŻF `U=exp\left\{i\int^{t}dt'[���$V(t')] �\}2�5Bkenarray�r �=́�Α� a(k) ����[i(�7t+)٭'}{�� }sin�� .� � ]� \d[-i Z(k) }.6��%% ?0.\nonumber\\ �,. To identif�contribe," harmAVs whose�ies��a1,gral multipla�of*g i \ veni to4 �1A�expon�al funce�in u�6}) a Bessel-% sermba� � ormula� e^{iasinx)�4^{\infty}_{n=- ({J_{n}{(a)}/nx}IThe}31I R,n}UP%[(V�)�I@�Ms [.A[i]7-5�+nI2)t] 6�n��D E+2 7B EV 9]4})�7 be�4� a��,ndard manner!�o%�)�o-diff� !��tyP"� )�ډ+ia�� � (0)]%�e�� .# ')�Ae�]dt'. & 8�| Find��Aj trac�� �-� x E�both si Eq. (8),��arrive�J�� ]�z ns;Xmatrix $\sigma=Tr_{ph}[��(t)]$� ��sG.�um!�t �n"�sub��only:j}���a5gd\tau �M�!� -$5y ]].z9Bz� w� ve0�facS at $ r(gb0)])=0$��,follows fromDo"h �lrho'$!�$t=0$:�t $ed�iniA�l��-5� repa"��e~  d6��(Q\v(0)=\%\4(0)|0\rangle\l0|,.� 0>% �� $F8 :��!GU ��(we mayat the � �,iI���.eBQis , vacuQ�� zero.). Sinyh�of super��i{�n st cor� r (propor�al�=/recipro�of �-�0y bandwidth),�0a certain sen< �c'�preted C� ervoir1H& icM:# �L ion � S iO sKa wide�V(rapidly wipa�0ut any memory!0� Kab� it� st, [ resulmO!��o�behaviW )- "�!� Markovian�is justiL replac�6$I�m�$� d�I 9})  exte�s(upper limit�$�L$-%qv)�$�($. Moreover�oss� tA��)$-��ten as�� �u�tJ�+\Delta+�m~ewat leas�order $�$!,0en to second in#��obEla clo��/UL�. �& �j��~���N6�1FKAf �ntitutAAYexpress�"� 7})�5509q hA'�`AEq.(11),JaI8� ors,p l ��A=gra�eirespectM]!���A"�%�� l� ,n,m �� J_{m�(} \� V\{ }{� i(n-m)�  t]:� -im� l} . Q\^{*` g_{lP l},"d �]$$$ >�[ �iP}"�0.y m �}+\pi\da<[� _R(q ] ++ � �[ � � �+��� . � R�+ �(k)v�F(�\E�\}%B�K \equiv-\L�(t) �..o 1F�I�bdiscui���we �e? principal  (deno�� by Ps ya� � Lmall imaginary term, c�s%shift��a�"��#iJ�7nonP� ��mz � or $BJa$.�cha/er���ita�� B�to goa�o a cH� � 6$\|-�$\|^{-1}$ (5... \|$=nd&� n's valu��9 units)T is m� long.�od $T=p/i$��%d��"0 "jQ"� impo� oI less*� �0of spontaneou!��nt emiES . HeF Zn��I decoh� re�o�,"g "U�t� � $/ to s� < averaged&he9$%/ ���co.��izI��i� �dur� employMy method!`""� projs"5�s.�3}JH\��(Ya�tilde{ � =�1}{T}\��^{T}dt $?� Pw2� F-g%8�� $L$!T�)s!of %_ly�%"t� , ZerI�$. Next�i ntro�EQ� $Q�=1- y�he:�� B� intorA"lyY�H"�wra� Bi)B=P� +� ..< F# Suca/J appl%��s1^s �$�hEq. (12�c�� two R� steaE� one �pf��u)t��(t)!>= 2sj�"�}A } ��.}: e42}&`lO�� basi>016)A�\ A�avre+ ��!�solg foI�>�(oscil�ng)ERM�:� �hFa�&�dt''9�')> ')"%R/%�*~1&q1U(17�)5 %loaDvai�a8:�"  se�?�y Y!_n�7� -�є �^  �m]$�Tns�s�wo (or2 fou�&� ), s� �0%�b� d. A��, �� �2)���3 s, accor�o (15), v���!6q� � (t)$U�  $.�J" 2i*� #,l��^{2�� exp[�ph�- l})]� \$|�|]:�"�e- T S� v@[S/{6�,S> �E2�FS T�*� �� most gK�or.!!�master 26m͉*ceA�a " � �. How�,���"is&iu ��beQp�+ 2�" datae\�,$ a "coarse� "oc��( ?� a@f� s_ e� ": Q% O larO �.u�$length: $kxR\gg1� �!/cv $R=max|.j>!|$). - $�_ $ must be�. IF&of��icles.S%�� imi� � � <Q �n(\F,�#� ing %fA@je��c� E� @l}= yv�� uniA�ly� �.�N�$0�:�& $1/�P. ���5��Z\� line{�u}e \Gamma(5�k}|�  Depe� J shape)!"I�[l1��7�!%C spread � -5l}$ ��.N� IIn:{]$ bek>&h upn(�sJ�(EP�Q�*�~ $)�q"���dAt�{ADir?���to�w�:ma��in ş�Cs���r�$du� on effec��B�I�o��# ce f*�*re� \ $J�� ()! / `)"+ren�"H)�V&q9V&|V&�is�p�ɓ!7aq,Debye-Waller &�=ch &�z n�!U!->un%�edc� r$ �&A$�)A6D*)�&!P%�ela% scat3ngO6�+�,ake ccount* in)��q~t6K+:V )�does noI\A< homo� ���$ �1�. \%&PRESULTS AND DISCUSSIO*&p �.b4}�&� parE�S 20) maXit pos�%to imp%atj,w�+an (a�.x�,)���"�!� y $IH 66un��E�� �2� &s�le�inverA4�AF�%P&0e macroscopic6"ise��$<}�M*6A&�2�(.5v"�J>0$�)I(t)=�"a���}��d�'z�t)�N�cH}{4 _{R}}secha��9#t-t_{D}ta '� &P�z!layi$?�zdu)o�+ L$m]:� puls�� fine  $��=�^{(0)}��-��$ �G lnN=��P$$ � � E=[��2�N]� � /$� A�&�aramete��e abs��*�� �:��)9�� ac�)N� :��msa�bZ0m��1�,�A!& nda� �0�*mٲ 6u>I#u�by V�,�h s (s� N�ѩ<1$ ��� �\neq0s-o��increu0������)7of2 .3!E�,0 � � � ! a� _Meak!T��.S2 advantagw u�V��z� ���#znsure e%>(ol� �6�ro� but@ also�3�#ex��in9� A�str ���)& /U�5�!H�%��I� �/JankW4#�Ail�%osee�2!xthe��od� ]si�(�$"freezing"A:| c��B[3�3d)act8illustr� by Fig. 1� depi)�EDd2� 6�� "� 6�total0$W��0�I�Eks.I ,figure}[h] \� $ing\includ" phics*[�#=8cm,heu, #%=0]E(1.eps} \cap {�L6�of Dick>�("   $�f/�e^�0)�#?*Z��=t/�F���i�three:�gy= =�5@lses: 1), $W=0$; h$W=1.25�$10^{-3}J$;3#3 +2F  ($N=.18}$).?&-t6b'a�ed5�ACi�!�d�5�!x�� ��"�3. ]#2271}>2=q���1Sm��/ 0���$%=AW��i�&�33���  (Q� $a_{1g}$-ap( naphthalen6 q(=1385$\,cm$��P4=0.01$, $A=0.3=z13}$dyn+a�$m\simeq!m3}m_{p�ith $ %Hpr�2masa�FE� 2}��NA./a : A#( ! �^-3/ � �O� 5r �NQ�e fixedI�a $W�fM&�e�2J�6S $I_{max!2�dB� l %�N J� 6��� �-"�4Q�.} 7- Obv�ly���8er+ ��s�l*�8� anisotrop"�'b�b&�:dir�!��(ag�M;m8(i.e,A chan�6Binn .�.~� � ied)����}"�4$REFERENCES�X!b�8Dthebibliography}{1!LbibitemB;@ A.\,P. Saiko, Co�non�ar &�;\[in Russian], BSU, Minsk�99L 2h2>h�Dokl. Akad. Nauk Belarus SSR, {\bf 25} , 1077 (1981BUP3} E.\,K. Bashkirov, \M. Sorokina, Fam Le KienE� �LS. Shumovskii, Kratk5tobschen. OIYaI (JINR), No 2, 8�84B�D4} N.\,N. Bogolyub�Jr. �6��� Prep�58P-17-85-938,Dub���5�6e 5} Yu.\,V!STboikin, S.\,A. Adrian�P # Zinov'eva.)lal., Zh.\'{E}ksp. Teor. Fiz.)� 89}, 1146 ~D [Sov. Phys. JETP %�62}, 660 &]:�6>OP�;d S�=yM�93}, 244 (2002) [arXiv.org: physics/0302059].:k7>k�X�222X1) X 2X90BX 8} B)B$Thomson, J1C),� L147!70!�2  9} R. Flo!�4, L.\,O. Schwak9Dmid Solt�=Commun)� 4�55b82Bb�.�c)�Rev. A �2!� 2709eqF�>$W.\,L. Wil�G. Wa�:�,M.\,D. fayer% Chem1 A# 88}, 340%88F�:-W,V.\,S. Kuz'mA�A�et. Mat2�!{291�9Fz�#a���E�TverdA� la (St. P;burg)� 35�8W3)[);.�� &2E�93)B:#G �(Agarval, Qu�@ !�h'al� o5 of S&F& E=&%Th)RI<,O�  Aach�S�(4ger-Verlag, Be�A57)�n>>&8 \vfill\eject �}8document} ��\�?[pre,�/�wkeys, nofootinbib, floatfix]{revtex4} \usepackage{latexsym6amsmath2[dvips]{��icx��� �\title{La0�,�",on Astumian'�/�Oradox} \author{L. \surname{Pal}} %\email[Electronic address:]{lpal@rmki.kfki.hu�affili {KFKI Atok0E�=(Research In~-4e H-1525 Budap51P114, POB 49 Hungary} ����abCct}�* 2001�P \cite{ast01} publish� very�ple gam3 �4� aL0��.=absorb+Aw final �(. In August� 4 Pi^ wski, Slad  �pio04}�3?�=�analy�$was flaw�"H% as shown^ 9 ]!4},��%�Kwrong��C Q� � er�'f2 r�.o�.�* ames� ore Z%!t�#T#%C�<by�,0 7 stig .iV9�( \keywords{�Y�,6�,q� �0A�Be &�IB(�}�!e�!te% )��L>revisi�[>a9%H����1� ���S�} UZ� roblem� (a slightly 2�fA)�it AG$done earlil oul�E4 a good exerci�or gradu��A ents,�ca�co`�cNm��"usefu'5m� our9 A�2.]ides*dj��5�,vto 5� typ�"� For 4m!dactic"#son�E n SeENs II ��III+(��oa brie/6mm� of d�E�� u��<&CaO need�g>�5��Marko���� � IV we)�z!�A�� q��5 chai �d��min,�"ba;�+ f lo[nd winQ$. C5�� mad�. �V.UAPre=5na��$} Let ${\����N} = \{�C$\ldots,N\}�!�Fa�e�G!Epoa�v�H tege[3�LZ L0,1 LJseC'0-ne�v� G. D�0a�D$\xi_{n},\; n \in �Z}$%���D��#<elE��� N}$.�Gs��*��s�G ${ }�BK.� ifr $J�%a�l.� �"�E�e�)t}�,1} 9P}� =j \ � 0}=i_{0}, 1 1}, -� n- \!�rZ Z,\\�� ul� �,I�?)�=j��_ec%*is saif�hinIit{e�}.�S}j(�;!�$n$�F3b9� in�) ste2Des>I1}x Q�[2=9N}$�0e*Fit� spaM(�s}�����i�y&(&9d 5�!�\!�; i:���*I5U� i"0�& cv �<�a�L?di�& ion}E���cM04r.k�Ne. a�0 }=(!%0D\=ies}. If �AD=ii) �nA)5 en��2�-[��a�7T6O%�i} �a�1:�jUE IEY-6�s�*� }a�!:^�% in7��R.9 �  c�m=% e \[�U !.�)=e�(w_{ij}(1) = , \] &;� hold�gatb_6 &j=1}^{N} Q =%\; \f<l F� N}Q �IfD>Ws�sh�> =l2�s��w� like2emphas4+R�y � b�a3�bf{w} =(p 7$} w_{11} &! 12 \;Js N} \\2%22%@2 %\v�T & d6 JNJNJ .oNN�v�,� 9k<"�]aU�stocha$ �|���# .# $p_aH=N�>�ݑ��2���q�$uniquely. � sake v0ibOcity,A��� 'Aiᇭ walk�an �  ob&,>��#icle}P:� ���R# �>��,I�n�QZ�QZ5���4R�m+>�m}=2�n)>�6�J%:5sF-+�5E�In�I\�k.8k}(r)\;w_{kj}(s )�[}H#��$r + s = n.��I�Gto� l $��n�?���.$iԽ�%�1�A � �.�!� j}$ provi� P$n=0$�A n>i}$. F D&#L5})A��?S��9 N451n-��6%�!Y*����S� A�rul� i�  Ic��ax6bh6Qhbf w})�I�����bf 3-1)\;% w}^� >��b��4�~�+��!$11��(&>��@2 .:226.2N\\������  SN S!�NNSNS ��B �J\[ �0)Jr1 & 0.�0��0� �->�  \\::16�\]� Af$N_@N$��tMo. Ma:A3� �!&:  G oremA�can� "� d�lut.� �uj!�$^��sf� 8} p !�=mWi����eQ��,6�jc 2�B�E��iY�$"� � f ��I= . Cl�y,I �^�the�ũ%n�&� �wV t�;���row90qU�����0vec{p� \{p_��p_ �� p_{NJ� �8&�Kre� �! �>f� �-� �2f �w �i(T)\; 0^Z�! ;F� x $T$ �=z; R?Aݭc�ū�xS$ w��)�Da�  9}),�.Oi�X ��starts*!2`}Ar��i !n�@)#A�{0)�06�1� 9�0)��Z�� D()^\{�̅�,��i��� ��\}.\] �-Typɚ�Tasympto�7i��BM��v�(well-known *�1ereJa�.�� geq 0$|���jk%> 0B�e �>c�W�� be r�[/3Am% >1j�GIf>k}$2HMQe��*i.canS7n>kQ@ZW>p���connec���.�"f>@Z�W�)S� ei3=�=%�oru � 057G �� �X�z1 �lasuAal�,}. A >�:��Uduc�UA{y y!|B. a\A� 7� �s�  +�N��o% �%32#dD�*'n|��)�6![Eݲ $f_�3�)�6ag�Som>:i�@N�in exac�$n$d�[�Kit X]i�9X>`ACbef�!?&_ ,� givezb� ͡+� j�/ @- jXj�8%� \;, j_f  ?Y ?9 \ t :jFT�;ex%���m�Nant r<$ship betwe&/ ies���9�$��<asy�D e. � 2`is�@2z m5@n} xk) ��-k:h *%F#B%On�Q9-�H��%�&>s� n9  1"r0 diago�.�A8�G��Qb��0)�7� ofa)�12"Vs&�3 upw\�<Z � .� � �sbE�e��:�r=u5 if�� �4a"8�l>} V>laI�!first1ru�ku�$k�2&>np)@n.�>~htR~ remai� $n-k$ }-(se ``paths"�� disjY\ev�Q �irA�}�� ��:�$. Sum�=L0�uE� ].u�5W A�etA �-Fga_ �#\varp�AaLzyLn� �PuQn)\;zH &m\;�� {and�m 5[ ��6[� a�[BzT� �Ga8i~�j6A$, Ew*e,we-Lf�oG�`�)6\�M [1 +�zz�N]B�  aIfz�F6i��fOG6�}{F|FQ so� havf�16} F�Gj�w6��<� �F&�!+n�F#!�!$nJ�!ia�Qu6A�$FgFn]�)0&f_y {1 -Nu"Bn $)J< 16�{��.��  a"� 4 a��T E Je�.tdY N�a�:�Sn|h&�� �2�.�of retur��F>at T nce}[�g 2�H� .T�j}(k)Ga� % N( 5�* 4�.3[% �Ae�Y"]&� � ]\;FI9k !Oj}23 In A�F�d�.�)Ri!R = (� i})^� nNsbVkR_{)�\lim_{k2\��.A1\{qqa` {ll} 0,�text{if�$ < 1$,} \\IV{ e& 1R7  d)g!C�.Gof5�z� in�!l�0ten�Z�elaJp�%72^ a���2�a�rr� �>�:�u�m�XE� \[%�j)�f�AMέ�\;RE�3�J:Oe4b��=� �b��5F�2�":�p5EOit-�!tr aIuit{�S�� r�%asI�}!��!X 0$. �Kfur�&��"�Z�recurr�%��}f&��6! N�a:$0"Wq%�ib.Mnong�Et oA��sbb �/ Z�:9;L ic} �  $\ell$L \%qV)^Zgr a�ep�Cell, 2 3 � ># q gre�_�U �= �&y*�~ i�Adivisibl�% R a3n�A0�6�8Rof -,� qualB$F ��!���!$V�U(;hio!V���%l�  d�o4m.2�\(AB]�C}$�%�� >�,i��cl}U �5�&)Bmove e]�*��U'$:p�=LoutK)>�by� -. *z"�(�n1�_� :%`6-i} 6G'�* :(j�ot>,.$�&�"zM >l"uev�-"'*rZ a l�t2���?�)s setM+w}llI�an��`+.%u� :bA��oj�'"a]\=%'r�K2�s �?A��RaJ��#^9YW S}{_i}G 9�lq1A$1�r �u � 6�}A*�Ys^ . ~\1 note=F6#�zbx:cXd mutu� ."�)�C2h'C}).h'2�Oa,] r}*�F6�,��all��%�m ndkR%X%�".�2@.iz�2�_�zjTf�@��E ly.}���Y�sC��B8�+I: !�A`��set0#:�s�'��V� T}$.2�:B�B�T.'2s� �2�+C���FV� �#.�E�n � %�.� %�N� �e9ʑ+�*2GX02z2.�, ���,\nu��,}1f6agZ*}ac�I�th�V�W/%�.Z�j!,tp-A$m�,.s.P9 E8m�If� u mNIm�� ,j�1� � �d�ex�edf �$�@_��*�! Eq,-3�)��J�F�)��,�lF� [6�m\;�&!r �_d:�}{dz}\�_]_{z=�%\]le �! jiR,�N� �A�� �kB~y $1 -%N%�Y�2Xt�*AG>V�E2U j�^- =�*A@� a�i�"� �Ie���� Bs :�6$� � d&�8} wbf 9�i(.j�i}Ex Z� i}(zJ�!yI �\mA{���:_ mea�y���  x. CY)�,I�w%��XJ���u5\ null-e�}+EeG%jg<1ύ�g.� 1�Vg�>-kA+Q�IwAa�Z�� �Y��?�X- T��i�rs.�`�so �=�.6�.Ptn�"�erg� E�I��Ea 9I�s&� �at T�xM��; B�?&q 3ub� AR�  3%r�4!�� �* e, hG ��w�of!�>�� a9��M�]s�e�JE arbitr�4F�f��#n$a/iH&� &yx8.. aXFt��:�2. "� )G s du�-A's�6&G �b�2�S���1}{E j}F�1�#��:�i� *- .�"\�U,6H$20}) Taube"dTh'isD'Q `� he lemma� (Erd\H os-FeFR -KacuD!~i=j�b��&�% 14})%V6 ulafH�i�Cz.)1�[ }{��>B�SubM<� #N) �"5V �L�&�f&& 22} �A� �6��t(��� -B�4J� f�&� JB�By �+B��Q�wf�3} I�z \upi�1}\;(1-z�&6�n����$B�S�:Fn�u� �A��r� �6�1� ��% 1}%)�= \]��8 t va�g��T"�0Z~mA�z%�B/[A L'Hh}tal's mfin�f3[6� 1�e� %큻) '(1)%�������t[Xuc}(��� i@>{?�(pr�� �z$|we:j3�$�T���4�vJ'����4 (B)�x` �&T}LM2h+ �HRnYd"� ~ �I�D.�C��It��s�?Xf��E��-)�yjր1�>CM, ($�!KB� *e"�d Nk will��xVly�E stay�c%�>?N�K<a&���2Zp/ .�}%T Z�2.��:j�-25*@�+v 6�kEK*�T}}8k}F�2�%"0!.�66I�2�B"l ?T} \cupQ�c�as��t�-"%��&$�J � f�,g&|Q J�}� j�11B�� e���26q/&�$lyE}$ 2}).�@Z>��_��\;i1 -�MBG���n=n8� *5B&� 3�iK�"�"!J�r.X'� . F+�w2[8"=@ =@�)if/.q:"�C �?"M�Lizee�AZ�uK d*X*��%E8its�� 6�-p�nom���;uok  i�q��� A�D�� .&8sAB�1!(N}k9$ (�+:�j:�%9] alway��>�o a)�Z .� �8�%"�8i6{;��1N9(o �*g $n��{2 �.VY2� 8 Al�FA;a�Fitzt-ic ] 64G -�. )�m�"f.g2i}^{(st)�i&`�vio�q}65X6uf�W6 choos��xJ/�_6QE�!n.�s%�iW/Qll coinc�x!:�. EV�ar6mJ�Zl�xof 0P.s[)�-"�O��iE�5:E��A�<\;�N�'CjCj[sa�a� , o�l%4< �y��)�2_!!s.�*=a~R%�� �� "�9��� somɜE� �Z�suKEis�m�fn!s9l�exc�nt book� Tak\'acs |Itak60P "F2.�sI!j�IAe"2 �F2� a#go�to� =6P�o�twoFb.: �]t�i��CN�  N-2$��"{�W �cas�2�!E�bib�<s�&}� F4�&)DA un!�*�#��s.� u1a \:P1����2� :.6,i0�E> 2c=Ty>J6�3�aB/!�N- �� -�#1�>� N}"�2/3i�S o.� �!b�trse�\n'tSAbN �6:� v B�3Jj22��Qn-��e���aQ0 non-"�}*�"�. leav�6!�ne��o�to.�a6k�%�>~IHB! 2}$ ���'*"pCh�H of fH �}"s->@iZ���7�at�A$� � � 1 jP2w<q�N�;"�;0�;�;w_[<�<�A3 (\\  w_{31  4H$ (44w_{45}H$:�;Vc� Վ: = 1�8"k 3 fs  &E+�4q�Eq>Di};�$ (i=2,3,4)�wtpґd|4it�4�at,R��56�5�"S>4��!� ulae �m� 5��ti&�e�.L c �*� \lN>s>�mB�B�9n�8�$�a �Y ins]M � qye1t:,�deKv�^backward&�%@&� �&�#$&�<&V��D0 & =�*�n _{1j�v�28}\\*2.*A��B-1) +29 .<3 3D-�^`�29}A�a�BI:I _34 _4D._30__J4BJ:J `45 `5B`�%`& 1G5=G3�end{e5~�_b�Y2��!��� [29�v1?33} g_� (zz� .n.Y�Wn)�Ad2��-� 7(z:� \;�Hz < 1F�nй�� ZQ�gE��B�* 1-zA���AEg_Evz%�]�2j} + z�E�a+ zA�Aj=+ Ag_E�%:jA�Bj3 jQ�TiE�T iE�g_E�NiA�Bi4i�)2� �E�S hE�g_A�Rh5j:t5j>t. 5 �1��u�*be��dF ~@C(w)�)\��H z) -J� �U�%�K!�!t-z�M��u=4�-p�n=� �33 �-�-)ˁ(9c6�3.���e>� e!�4 df��!�V�5��36&�1Wi�97algebr�v!�" M).�6 ��s��. (i,�3,4,5I thed }e now�� eresf$onl�� t��u��ySco�V�� eV��ng��)�. ? 38I]�se�T�|�D1a�1.�)\8l}�`�oi�!��KE)� �"D�")9�/37EU\2B\ Iz.DA�G 1�8G3#Mb�� z)44.�I�a�4BI�3}� P}:�4�DB5BBZ.4%.� ���q�4�6'9�:� 42} !q�3�,�4} z)�[ � �D�Y332}��2�] -.�.!� �3 ,5K} "N�Z:Hf�3�bgA�\-�z. !�I�=��2%�:�%�1J,8� �5�� ����b= 04X j =�( 3, 4BLEEb��9v�A���I�.>-�521>B Pei�����" !o#Az< M�!�-�- A�'!�-���.&A�&A�M4`�(D?j�:46i1}(qaP�\29(a_3>  5� 4>45 �; 23}l!]z92B��7k!�N�5�g2�}� �B�#�F��howz�8�* =&K !{�1 �1��l6>F_!2O5&�S OF����$A�s&ܚs�pt�>v�o6unt6=BE1O� �Iy� ���qRT ���#h �Mz� I���} ,A؅ [=F6�Q }2e5+� �De  $&�( �V9 /�1`� ]Fd>�|'BŠz)])��I�.IB�Co����)�4a�!� !�� 9�P� Eqs.�K� true()n)7toIA\Mp�:�A�1�! 5��1�j�50.S%�%�+ rA(e= }C2\h9� Q�r!�?� -�z�51} rF���� Z�J��!�B�,!G,ee.��p��U+��-as"y.)� seemOEb�#rthwh/��<���histor�;*"t&�;ry|*"8b� �!m([ht!] \set��\�E {0.5cm}2c�{�r\ure}(8,12) \put(0.5, 1)kebox{:�1}$}}*2,'(1,0){7�GC3fC2C'2C � 5RD�3D'thickIs�inR�7RP � 4Q(2D � 9VD 5C'JC5.5 ��N(0!D2}}-}F-1) �3.75, !3V?J 2@7.25, �V@J @I Q1i�MN "t` f1} {"7BZIuBq.��G lad'�rungs} mM�V4b�n�9r 'p�"�!��a q,�] P�{$5$ Q. Each *e�a^.iz�.�K| &�eio���s_�� *m&exs (say,o�%third � l �"j2�� �y�Q�. OJ0~�Lcl� s led, �5uto2;up�� dTg9%c-�ly [k g. 1:si#��o/�v�sR�s ekN�Gt�(a!�or>�S�0�`(�<.%i�d)��s!�am�),@��)��y De[�an $1/2"-(``�c" <.) HaB8cLa*<&�[B� 5�"A�4/36 & 2 8 ��5 29  2� >2F > K�V~� �m{ �i\Ru ect &>x{g$2@x[*5x Kx10cm]�ip�t}I \�qp -0.3cm.`Zx�V2}6UX�en)�mC9��� nrS�[� �� o%� n�J >s $n$>�l6EmaC�`�f���H�����s� c ��J* & 5$ kz2.Љ�d"�9�N%?-{"�6 afte�Sj� 10�S A��e",:�3^ �@?h�< R� �s�2�2Q�;OikB��>g4} Cj�� �#�:��in>}���!.&E1}(100) 1F �! 5/9C��6�e VMC 00) .M5f 4/9$L Onstruk���.9Ï�hs$E��\e!�� !*֏m�'&�e�5: �93j)�t;+"�d ݾ���[+->� 3}$ �;�ZgR� (j�; it" I oJ}2�M&E�� A 5?P2*� v�0s:) 5/19�%�3!v11/12T!! 4} = 6/1 @eG3eW��� gra�s:�>� �)2�)3�y�)3>)P5�A6�=�:�aD�=Y�ty�(2�+>l~���&`ie�>� Z= >c�eEn%O�A�dLm��v^:�m��)�0A?�A&� a�)re�lci&�m�y EHa�%_0���@�@� :�Qa.5M�Un�\ �B%/!2\(��&�!<%�Bi���F��\r/9ED�kF�e=aK5���CJ~f6�-2F��m\zKit{��=�x��pe�&;��}�l by"�=}�MF�leaYI+@V�+�LE��e �8By2�I?@�[�[]?5�+!N��u��Z,%�] ��\%�T2�xX�c�th�Zo4�B,z�@Z]�� n"��5� F 3}*�1P�@�>}=n\iT& ]!.%> + %:,6� �B�e e.�We�� F�4} |�% |� a#�  #6�6�W]F2�d��1��&x�*]S@��-�/X1^OI-JX.J!D��JD5D�:D�BT#t\C2�-l[!.�uJ�w_X�-=.6# %9�]%ha1�)��bF6��`�2J)RJ% . \]�UZ#J�3tJ�*%&��(Y�&l �6O� �6LI�� I A~�DFz8�+��:K�}$qI�*m(� �Hte-s}a��``for&'"9:>�Ih!�=2}^{�i%��fE� �9]�D�A:�D5[&#<-�"�sEM�!J^�52��/E�'�+�\5�J�ichVN��$&-$�V)v(i2�bz�*� �):f�62�ALsbbh41}i4=�45F�.Ll�cMqŜG)6��m^k,��n2A'Q�F��11E�%5p�q�z^�6� �A�3(h>A�YC1�=Wwe�< |7�7 � J�5})A�z� A7m2�EF$!�}KnB] ?3J� Y�U���]�w�Q ft[\�% iA�O (1&qVvv 2v�.pg_.SRLNS� .�E2 mq���"� 4ڍ 4>� A�pN� ��� J it� &H.A�>  iJ >g �D��h2�sEbyQ�2qgwA�V �#X&� y�m$n Jnɶ�3 s�ai�4��I, iS"_ ) iB� 3�.�;.� �3� �uSA#��t�S�1epa<>;zI�\� T_{�U".� &��&rF G'�Fas:  H tail<ai �nT.^��.�5Nu2 i&�"Jd�.d!�)p� `�st�� devi �>s�K�2@iverUd5��7K/ - �@63n\;�6 <0>Bv�b�C vD*� v�W��6| (n -s)�(�\.M^{1/2VT�fwm{-H��}q!vs"�zarA��}�t1} E�N%�>PM A�>��4�:�"G9q dtabK\{|c } &*����B�B4}$�\hT��6"$ & 15.79.�9.3�o 7 ��6�76.376.438 � :�)h6}5P2�~!�=>.���1}}$}4Dit� b��O n,���2F:a���%�!{is"���Q��`:% 1}$.*�I�gJNno����rڙ�Wa� = f�"�U� 6 1$.}�k)6 > �F7B�k-3�6 ``���=�!�Pi<.N�Fb �!�``fair"�"n�= HVNA �b�60}��� ���".�'�_) o&# ."� p1��?s��O"Q~��i:�^E&e 1})�F[�h<����ro�odt>Oc��(namely \[ �i�4}���:��)!������� \] W  m�V~]�5/9�\$�=��!�?A�arithme�pSͺseE��ce�51� "S&"��9OA+ 0?XU�=�\[��vK: 9/72 & 53 10 �",b$*-$� H Q&>M�bring:��0=g 9/19�t�,��a!O�F W��bAZesR�is% x^-�B�xd`is 7l�iDc��d"�k���<�%�x� "8 t �}. By"���Qn m��BKdemI��$��o�&(j+C{>fxQ��A�D f61Q|��a!�-a-b & )�M-x & a+Um* #@-x::�!B�m8B�(fU2*�)H(xci� a b}, + (a+x)(b-xJ�0;2 \[ 0 < aA���bJa + 6�^�-Xx�Umin(b,)*)��Qx�0| b - �� >�J%Q��.$�5 $!ysuaIj mini��L �[ |x_{min:� (b-a�9�DE� 8�`[!l 6%rK \{ ��jd�f1/26�da=bv�f)�4 %�%�!s� �VBVnqbf�d D�aCajno% )u � + y$ ��H( +�0J(J�6� - 4 y9 � C Gz $y$/ e�in�lL�!��# = |� >atE� ^ox_rC�- y �;e ��5Pe�P�Mat�%1%� �>-1}} � �6.HE6i��+�B� a3�-2%I EAly, Y4�YY��>�g pair� �V ��ce;8?�e&� i� P A/��Ng#�C:8x&�8!���?�Bt�'2u*� %�,&�>5�5>D2|�� =A3"-� $x$�� F(6At�*$a=1/4$�  $b=1/8Fp!B�" b&|5%�9�*� �Avs.� curv plot�bR$"�$a � = �O $black poin�bca�Dvca� �c$]-��Y A��v1}=1/16�ym�=-3  8/136gZ� i_e���1m�)=-di��8/17,DM�EI�|Dc&-0 not Z�fluou�!� �+>��&�q�j��8�!D�"�sv5 4/1*10 2 �� 9 5 2� E!= JV~*: ��e ��1A � 22� �� �n�!��a:}rq6�9�>Q)�+. 2}�P��>�1 �-2 1�B� �� ����] j�6a�Z�ter+�k+!�).,_�nF [j��"� i�m� > 6� 6z �4I `%)J7��!D.",$p=�B���Z�7��7v��R����'*�-,T�&p$�0AgB"Z%q��,B\ JO"�i�J<�fu�mw�>�lE�>�f�u�$�0lya s�` ~"���&�|J) 63"��A�9n�=�p.Y1}> (1-p).�2�]��.L�"i(mQ_��>6K>� ��yFXI6%�>�/A^E0i_*�Aswbl.�|�b  &Z�3ow� �2FMA�."�N� g͏r2B<� : �?9�0 I3]�}$,*��Lɲ� &� �!9}3Q�o��a�b�v �a��� y��..� $E�(Pp�\ [0,1]$2 a .����nR�y 8Et"�3. Z�{Vv:r��%#�*D��.s��Х�$pKsM�� 7,!��Xa��"�isubz��7 $[a�`�]==.#7!�$p$k�N&� R>!��F5�F5�PX.&-����w0�� .25$# �U�/ 0.75!�"�TC&y�}EU%&!�z("�!6A!+uI%E�sto����q�;2�7'piʄte-a&]� ��Ay�Y�& d^ i<&� !��U $�11}�%�� a� NNq�X�t&�p"�O�qnexvA� j �/1��b7pbǸ2�7j+%ș���/�-&�A�M�A,Q�"#$> �11�� {R.Dx"� , Sci. AmV8bf{285}(7), 56 ��1).E�{E.W. :0�J.&3�,, LANL e-prie5er3T"�� 4081��42_�4B�zL 9029 �6Lt4X!�MX �it{ Sy:P�es,Y2l�"SosY�s}, John Wiley \& Sons Inc., New York��60�D:����y�} bi:��{�t�%�3�>�r8{14.0�>odd-<4margin 30pt \u���~�%>fontsF�:bm:B��� \��+z�at7 ``^�''��� H�d�YäDA.~A.~Samoletov $^Q��$8 C.~P.~Dettmannɪ M6J.~Chapl��$w$L�date{ *V�,${}^1${\it Ds�t��&M�$��cs, Uni{[~�of Br�@ l - < BS8 1TW, UK }% V2 V�xXnTD¹e -  DD1 4HNRQ3 Q&p�wPh3�E��s�C&&����7sS�in !�c:r4ǽs.�compu�a�s��ns�Wp�b7���]bio [�wC"����e��f���um degre� M>do���f�8�@)=i�Y� space.!K&of"�� re \s�{( *'wualogu�k$ Smoluchowy�-b"Hm"�����vial"���7�c9�G�>G�r} � amb/)�@halkC�� im�l2�of!{logE2&vOM R] scrin/IU�5major bi: ��K ��^A�NAQ3�wplGc���crif#� .�+s,1>��%, e$ iE`�&���ZVESal�(n�-doublH{9 ed 2�p��a v�i����R�e�al fe!�G*����ofU�%J_ they �.�mb�<[1H.��,yy!.sol�A�-��us,vsurrouR�6R8�s� rU� of am, among hZoA per�� &CQ , =�&C9 (�3)�1 scal� XUbʴi�&�&��.��\ol�4E�;p�=!��erE��Q!0) gene�e�F �al�V�pC0q�9;��reh���e";���}�'dvw6ref* o$mp04}. C׀�> �_m SO�@the Nos\'{e}-HoovD��� �4�� � see Ja(T1,T2,T3,T4Z�Ua�r BFinvAEs ������%Ypե!�nd�ag���*. H ���-A]A�ra�M�� s��co.�m�b2�:�6� appear�Ope��E� oretE�a�v!�(unob� {*��)�� wellM,ɰ ensAd�Bd?� is Leh�� nove2��!�1 �!^� vmjt�KM��D��E�he��i&�c��ogy��{D\�~a.� a~(Eq.~�.!}) below*��L�V vin .��.G(CM�TGard04,kramers40,as99}������ff�5�n��-���ed so!�to�D�JE vi&���1relax)*��Qn�_�q>�] �ŇfluctutC coll�v�Lc�en; a� a� �( erty� �HN��!con��q � fic! &�a�*� re��lya��� �A8rugh97,evans00}A��^ ffer� con=)�neI���%(i�cct comb��Upl(%aryR�e��[��!�a1�>Pvir,I�^MBhaH�90xn helpenhgA� efficienc.@ and,d��� rtanS1��������a����o0te�!�,Q �)�a�+�!��6(MRs. Mo��ǡ:=r2�dm$st&I by a�iq�m1s� ilar[Y>nI �l� ��y�%�d�`nՌ see �. To tesisnew>�� �,6� ��e�a�-d[�al"��!�H!��sc��or���>3 ��%���ingA�� y��i� R�k: Bragar Trav �cԲBT05}3qQe� osed2H "i�.L"Z ^B�e"�G� as (ire;LA "� ��s), ci�,an zAp����ig�per-�SCD�&N P:�w Hsu��L�mpA�* �Q�p a mek��s����s tact�$an environ�� %� � [�_.�v��ep��Y�&��; ��}�n�*of>x m��*�6�� $m�a potљ P�$V(q)$A�$e��� ���B� DJ�1�)!"fri@ co�t��/&� �3y $D$!Ÿ xtera�; om� pCqٚP#�Mz, $D=m �k_�A(rm{B}}T$\:;�� Jsh�^�� d Gaussia2m�quotedbl5-te noisel`0, ɓh2�cu��#�&l� �9#\��le =0,\:�0.%(f(t^{\primeU�2\�:(t-#$"gilibriE��-p6(4 Fokker-PlanckU�� M�!<��� rho_Ps�Lpto \exp� [ - ( pc/2m+V(q �) /(:�)"�; $�, 's��%œa!�to���F� 2� �H(�Kg� i�o� A�i�BA,@ $\bm��})+�iE"� VSdy�3 .�ea�nt). BuE8l�-e"� � �t!a�~3L$.tran���,�6�mea��� Bv�7prW���Ba&� y%ctm � � mb,F��)en�� hold�O�d�Sl����b�� on s�o�A�s  &�.� �"pa�L\Np .&G�-(2' limi��(1(YVf;.@�?Z�4 A�+m:��9 }a�Z?(:=����Fn�prС�K!2�V� "n��cA��d iyg8�gqn�A��'�B� ""���x��v l����~�k� 2�6��I�!�0Boltzmann dis|tribution as the equilibrium sol �C\cite{Gard04}. Eq.~(\ref{Smoluchowski}), without the random perturbae , appearsnXa dissipative dynamics C` $V(q)$ playing a role of�4 Lyapunov funcWp $\dot{V}=-\tau\left( \nabla K`\right) ^{2}\leq0$. Thus,Qfull �8 is a superposi`yrelaxa,to a minimum!74potential and J�!^Pat occasionally expel?4system outside vicinity bq�$is process5�atebe J. \se% {Configur�ap,rmostat} It�reaso!.e, inspirit}deter� stic >T methods, to conjectur� at iXpossible!3use2Iime $!�$ for\t!�c:�degrees��freedom when momentum variables are still oed � ir local 2�4tate. Of cours1is ca �sigE �!3not fiZ!�D$V$ loses its mean�aAJB� . InAbenk!HaQ!, can go backC well�� � �] =0b� sum$ deno�a summ%� E�Aparticl��뱁Afta���$averaging,�;T}).;def�����t recently introduced so-calledaK6�9f �Prugh97,evans00}. Curr R��us� molecular5� siA��s N delh��,more general� text�?�: of aasuppoi anisotrop��)., let usuma&at�ln li��)�Fmatrixa���to%�Gamma}��e _Qe takWee�, $N��� C n>��$, andE�cV��=�>� is \[ AOU�mI� [ (q, �.�)]� aZ�.4��Q  � i) e . \] Not!2e�� �q��pr9�E�scaa i�U vY�!D$trol. Conv7  :�] do �ka�V such aQuisE��P.|��ls��! ����calar. OI"$other hand��useful� keep�mi-��il*� m�( We now at�tG #te�CF A�Ya�6�0scheme by mak��4n independent � in~2. � $ easily see 1�is too,. At a�H"� point $2&=0$' � s,!�aDce zero e ev. com� & haldDd no longer fluctu� , i��� v�%AF �c). For �!�q�nsnon�H ces6 a��a (� mr neg{ )&) }1]Q0a gradient fl!�s���:~�KH}�$?!y!� show��,) spaA��only on ��xi$M=\xi �,� �R~ Jp 2� to I� xi})z� �y*H s"I ?var��}AA accor� a�I= (a),%�3(canoge� �,�qee coc�'m���w��z� ngly obtaMC� �{"�f�fa�(a)\quad.z a�=0, \q(b# sum . !�y�.3c^3UM\cdotBB.>� Thes�- T �� 28bu� !Vmalized�S ac�-'�i.a�A�them,!��atheir bin� ,e�candid�����ulaY�ۦ�, chosen6)D,problem unde����Cexa,� cec�<4Peyrard-Bishop*� mode� DNA1 e mp04}�xseA�"� to�ap~rih�Nu�-A]q abr�i U�. Cba):��e1���6�(als�  (�ic��"\of Ls)cb c -AF-��� r�� U?ota( ��dM8|2�6U I]�c):� $�� $終&D e}�  prA�� to remark  a!G�E���� re g�tha�B��is��,b:VSdynb:e�� +\eta&q}~�A��$: m��q}�`B� virial!�.�sl ��r���i� (hamilton90}-j �Zexu2Hharmonic oscillatorRQ2>�;)!)Nmv� � �Q�P�ޱ��! ɮ��3���)%Nuay�aO!i)<*l>)� V} )�h:�-����q��M=F�I ya�a douIFGE�rovidedeI$ E#ise�a mand!�y2�!�roe� our.S]3. W��ulxX y!%� I�� trivAsmodific�~ ofz 1���subsequ^  s�H� i��a6k&� �-� Y)�!� �>��&�i M� �� is imporY �biolog�Y� r$ed�-s�m!s}of �enessUajind a fu$ appl16toE 6� d1����we � fix9 ��. When $ !e�QM\s a sh�-y��a��b�Now� aram� s whichgroup u�e�3-� % alpha}=(! ,��,\xi)^"�T}AN~u�,�pi�!� V})wfin!{��onary�M �N~ Am �~l( �� �.�% }� Q /2f��[ bm{Q��a��iNJn0al symmetric 7%,�Kc���� Asjustifyi�s�lVatb-�2�$ %�%F��.�"4M7~ � e E a Gaussia6��&� ��"� a?p�e� lead�E�"st%�!�self-�f��!�uM�tu%TlycZ1A�� chae�]�at��"@ b!Je limittheorems!�� � y���Pn multi�� ���seZ�!�usu%�% be uncoupB(diag~)�Q}$);A%he�-�)A "� aC we dH fe�a!Bi � ly ne�aryu�%sdAO!+m*K ��ofA��.�may���a$comparison����M�a�tildef Q}}=� (Q_{�O },eta xi\� $ab/ e!"rix p� L!K�onent��Q��&7!�beHsBOxVS��}% 6�a� g} \av�C,array} [c]{c8V=(t)-:�[ V] \\ ���\\ �*�:��� � x) V��(])�s)\g}� �re�A m�2� �2�(m�  A�nA�A^:���E"� so A��u-�) holdsI$��&;A�write1��U�. dot}z!� �}�G})@8�G�s yet� i��YakI#s�lw i��!sam%8H��@"2+� we�\!$e,9bVu GE�G �Q}^{-1}NJ�u� k2���of� �Z��I �8�6�">E�i^_�L��.u��$6�%���� ave D-I� aneask� ��ad-�of new�["$A�/oD xi$V!b�li"ofy�M"ͪ"�$ rgus#� �toM��. A!p% swer!�J "!Frobeni)���Ue�? geo�yfLang} � in%�%Nv� aE��a$( j� $� au-� % I) d t.� To�^ xact2�U^�e# b set �r�� r�$= d \theta�I�sat �-EN*�f�U&*#sz+ce)wI& &S}}=V�q�+Zv!2��/2Bu�i�a� orig��^F��@��arbitrd it �+���e&��an(�,Q�1z $6� =0N$�C�SA�mFis,"�K "h��numera�u�of Be�! t cl�WreltJ eA&"1di&�' $2l�� t�b�]��)� stepA`re�� ��B� % )- ����erm��a+ gy"< al�3� �2��"{e}�)FS��,T1,T2,T3,T4}8given��)H�%-X".*���&,2�ear�-licitly.6-St�&Ng'heͮs�s.}�NA�B�,�.�8%l�-"F� �!] �,i w&� i�l�80r admits rein��ch � �rt+oz Nosv+ 0� �"}[ �%� sist  inclu�a�idiQ��#- al� $\.� _{i}\@inG$��  &X  asympto��!.I.?%2�L.�1�.�j�[��2.�~z+�`nos_{(i)}J%�'e~_i2NfQ) ��_i}J+]��m6�-2�unique�h�>e�� �'�Ega�bA]!gE �,qkia ly �݁�f�topic" Gdiscus� deg"� we cq t�A�� rul� at;b�&�*r test*�*� z alig&lK }% mP*�.�.� (q)+b�0ymbol{e},\; \�2�}=gW}+_{�au, \; %A�=5�{ tau }*( �q{�-}T- ,_{i-1} �� zi+ |W� xi} �T$%J� O3� %^�� � %& Xta>�.+2  \\ %H� &B 5%�%N \no_$WM T(i=1,\ldots, rm{M},\: �_{0}= ,\: &8 M}!���vQ�a�EvE�6length Ab�It�'uld�'be��A�in�3te�$$popularity�� eff�$vz�L w}��uta� non-�͊� pert�(�e^ ques��ed� brankaf. �.�to� va�e�oF�9B���a��4� Brow� ���(� �0advantag%G(�"��! ertyCe ��� ,!�i)�&-�ne,�dw%i�3few%)s, �ho�%or�-x&�$A&�%et� �c "{ �J� ststFc 2�^d xiE��& i�i}�Y"c�LambdaŃɝ��qrt {24Dɞf}(t) �(2?�J� $\ED$�� v"� �>�cC �Wz$Aya*�i&� wha%noi%m�.�#"�;%�:9"�&%t),�ed+4EY�izAE��,a>A��L�A�0Fokker-Planck}�B�3 .�� �>�3�if�{�w�8 T}\,!�1�vD%�QL]e�_ ��"�D!e/,�)P d�(%F� , TH."i���. %�� i�� in�+ous� W��&�;� No f�- �#& Z� �,p <� c*$��BrhoMC, eF� ab�"UB u8�*a_ , demonstdB_great 9�� � i�).GCo�2$} An innoj!L�4.) ��%�P 2�,, �?siv��:u "�-I:��2a�s� �i,2]=[&�� ;doc&*} �\hclass[a4paper,11pt]{amsart}�+} \hypheL ${ge-ne-ra-%spe-ci-fj�D} \title[] {{\bf q mmedy;V of\\� �x�1� hGW's}} \author[]{Angelo Loi�D}� ate{#dd!� {Dip�IC o di Fi��,9�\`axMilano, Via Celoria, 16 - 20133  (Italy)�-mail{�L lo.l �$@mi.infn.i�hanks{To� pu��n�S�*� \& Subj ce.}!�D ab� ct}&� �iv� (GR) n�& serv�+"* ly p�7 leged. AsXa4t< �!,*�$ #�FeI�%��a��$al waves (!��Iqu�,�%�-��0keE< \vskip1.20cm %"Q} H bf{1}. - ,6+ wb know$"U� GW c/forIs a by-��a W }[ roxim�GR)��Now�� (--7qreEs} Max�e.m. o+y.isI,y� inad�#e}�*aA�per stud��� hyp�>!_ (see ��>�# 3}).R'I�=�i|�,n-a�>�e��1FR3no} ``m�* sm''�-in� �e %X� {�malM�T} m�� , as]o prov"�3�$und�& ory X�E�Ein field&� #X+re-�dal}�5�Dpar I �&h1 }�r0�(alB~ 6�} �9i.C a��TRJ�!�) �D�/ eet BQ�er��H�e0.5^2i�DA��rad�(}"�*(ce between .��or�Qd9`Ff:Q�Q�is Lo�/z�arian seuk� 0 o��u6:Cly!xiv��a*5�m=$ a� g9�%�'Bto-� all}:.E@ � co-ord�B�� )�no}�� )�h} �Mm{fW 'Au��A�Kv1F foo �8 �/� D10��'1{)ory. (S��7Lpe�;N'GR"��cept ``�''8<� �r�ci"�=�M5}y~za���n elec�u!rge $C$y)at!�t}�, ae��F� �+0}$��R emit�M�h. AnyFZ $I$_ whom��nu""L* ;;es�"� sBN �. A�F ly, �1[$EF$-'reg�r 1��. ��th�$C:$��n1�ex��>F mustO3ed�cisely p0y ){ai| ���+re�K�2zm� }, {,.'E�m�```s'' ��ts�R5}.�&R"� �$���\q� ian 6M��i��+ homo +sp% of a�*om)(` fluid�bw�inv�$gJ0Schwarzschild �6}.(S2'sg2$S�92 ��xI�no�M mitt�AEAY"S$ -- �3O e�y�,b. u--,%KE��N �of �R�(E������F� n6��� $:�SV�GW:�J��!4C� !\�6� ext]Qd r,ny ce�kPbody $B�Lich1Q�tA�%Ea  n�5���:A�g� $Sao�.v�-%.m� Q.e.�--&� 0��� BVer} \no %nt 8�,APPENDIX}} .�,\nopagebreak� J $& $) I% repea �\m�6iz@Mn m�5perP�  n�Yof!�aN�1�  16-1918) Je �e e}�6��` � � %2� 3 GR�ircum cs( ul�flu)8l)�$al�& su"�D� arch� ��VR a��]ral)6Gcer"88� �eL majo�)�iOU/�-?�1their0 ���aAnvi��fact, ��de� apr� I����&F � m. E%tod�Q,he overwhelmI>�.��> �%��'s old pI y �%d_  al (a�[false}�!�0y�MM*� �y� ���d ruin!co"�%c us, �.� y ye�`�-GW huntA�A�&= ir vef3 s aiY"6.��.Y+ )�I�1lu8l inc vK lq@ )�-#!�"�A�KthAU*� M�&�Hkind:� No�v6Bac �fd; how��,v sE�� �d�\ AQe$B�Z upA�0} !�]y< l !/�`ur�aratus!���! $\b�*�2r"��rO� A thirA7ra�a�I.� r"[)>A�$S.D. Mohan�,0Sz. M\'{a}rka�%�' ?lii}, |XtC``S) alga�hmA.��B�  `al��associ�)8G�ZL Ray Burst GRB030329+!� LIGOM8or�i7�5 ��s�Ms: ``On�,Db�\� :r3 r!orded,�,zb�[��!�/�BZ acts on�� cess�atae��� ���c�QAz!o< valuE�a s��>s f }n"�3drapSa +aa`�c�Z�8`�la�)�s!�ipe��%�re�&)T� �I�.}A�4 C�<. Quantum Grav.}"�021} S765-S774% !�s �MX�G��be� crib �eHSm`Collabo�": Abbor �J��sub }.'' �  -��@INTERNET (13 Janu�!�)�.�m��!��RI�(Sz. �F�Uc8�uIj ``�-id|�o:[Nb��?r a�?m[��I�yA�\A1,luous.�U%\new� .� �e�d� $^{\star-f }$:� = >�{9B�1} A."��`,Berl. Ber.},� () 688; Idem%$ibidem}, (� 154� R*�Rin\'sMa�MeaJ of Re�2!c}Fifth ED(PYe�U&�!P�, ,, N.J.) 1955Dno !vaiis made�A.� G1$2} H. Weyl�Amer.� Math!� 6�44) 591.E3%LnHSR�q-textbf{5�T, No.2 (22), pp.57-60;$i"��:] �P07134 v1} (July 27th,m--u�&l"y quoA�t�.� 4} Fock's� �> vic%I2�X�"�&� sCa����+}6/���2� --�_ Vk+ck1GA5T�Ca %U, Tim ,��4 }, S��i��YLergamonM@ Oxfo�� � etc}AC64�3$mph{passimE��0 orro��Fa rigor� � .��B�XW � !��H. , F.A�"Pirani!� I.Robins�+ �Proc.M$. Soc.� A 25!� 1959) 219�Tcl� to� EA�2*a �!�"�d �gRfraa��1a�"e � erned,c/�  ``%'')-|of.`05} E. Kretsch#$1�"l#ik�o4)ul5 41917) 575; A.  �=aZ��0241; W. Pauli: Teor(ella ��$\`{a}} (BoM hieri, T 4o) 1958, Sect.�k - See furaW E�XdS4, ``La th\'{e}_S�F'R$es et la g mtrie''�P\OE uvres Compl\`{e}tL(G��ier - V�Vrs, PFNA�52 Dt I, Vol. II, p.842�6} K.6�xN 424;%an Eng�4tkF��onE�I�:�00200!HDecember 16th, 1999S��7} B� ���N� nClass. � � :�&4) S183%endBB�$�j% Temp�B 'cle%p int �mO0`elsart' % SP��1/5 U=K ex{ (} % U�moh d%W��o W/cqh�9b�I & / �ing %�3e[2K].tif you�  PostS� �,eXyj %)�D�$ics packag) s � ands \use {1} %��6Hx2HmBQ�&*�`combRx:Repsfi�d � ��`!8z�X% .� C%��mams?��K idesT6��u�Q �/kR�9bol6 I}2ams9Avb� QJfrontmC ��, a�orCd �!esAI�X!reR%A�AW ,  "!�\ BE��n%l;=�corrNOor;�"�m �VPea, �fo�1e ,"�, %� E(�$ \ead[url]home 9 :!��{%\�{�1}A' [ ]{ �{Name\�{cor1} 1t42 G ead{2�I�{� � t2 t h[e -�{A�# 7z3 z.M3: �Develop� ��0a novel high-�_W iy LAr pu��\tor ba � -sourceEnAN��al %/ link-�sHwFac �es%�)`)1,A1 ) �%U� *�$ {A.~Bader7 \{M.~Laff�.hi,�$�$${A. Rubbia)Xd{Institut f\"{u}r Teilchen� Pk, ETHZ, \\ CH-8093 Z )$ich, Switz'+nd"�%�} A-vliqd$rgon (LAr):u� d)�22e*: !G5o�ia!�J:7�$ppb (O$_2$�!,ivalent). SudlA�@.g.M�aA$ drift cha�e&�7pl"=tJ a�0ezlif of quasif [��;LAru@�'7+��77[�8��#��:�F6c? ��9 ioni"�EA�w�4U�;ll j4( $^{210}Po$�in daugh�X at]otope (b$ i.�Qm U#%q}�BYgm 1 cloudGb���*\en�<a �pa "G\�`)�=�rN",f��J� ve0\�kRj �4about 50~$\mu$�b!\�x%u)�dE�?kIAv, type#ly [#l $750\div 1500\rm\ MeV/cm$, 94qI� A�3 d. To �1��rX�e i i~ ions965,85 )�e�pu�J�r�l 3icuof $4�$~k�a/is?achie�%by depo�=n��T�j!9�SE��!' �vol�C cathod~ a di�84!� 0.5~m�+a(4�  ]E� 5~(Pa)G o!Nz�S!�1 axis%�)o $ icM�� �*J'ly�poA �&.��E�keyword�D sd o: \sep  P�)y�� ��A���J$y % PACS c�:]\ D)  � ��*nd:� "�).�} LF�AcC �R�� �!��a~)p�! im*�!(B ly $O_2$)9t�z}�=n(nd henc 8p��;a��iS�.&�-a�iU)`mw�5��6r?��� �� iG J >b&�*�b8ca},�;)(H1 �H1}��Atlas� }.U%T"�R .� �-��16oq��Ak!siE�'��,$ppm$ (oxyge�&���� pulsg) ) �$tr�P�%a-decay�>� ����� mɄ|��=�q��Ii��>���ICARUS5�12merio:fze}'�x�%="� $ms$�.i *8�7l�U �FY-Uecess�toE?f4`%�&o a lAC{ $0.3\�Zc6�is2��built �aqumon},-R���a=�� � in a� "�%I-�;y.���!���� 10~c��-_ 9źa8Fac �>an�R�kly>lphoto�� �S-lasP/p!��*�X a} lE�E��Wrau�"�t>lem�rcog IideZ!#ey u,�(1)�/::�Qco=$�6PB larg>��uE�UN� �On� s ab\no ;���E s-? u�a��!epr("<�. wP 2� �&� p<i�}&T U8m�% 5�. b;}1�^�@of4x�!a� Y!��'nu. ��&� anD)ZIq<�KU�@�?OI�a��e�n2���!� i��/ioAZexp}):��} N(t_{l }) = N_0 (Y\exp{(-/!F)H]Q�Mw�� $N_0TK�O��� 2�  $.�$~<e� b� � :�� %G $��*H�"ou>� Is�h&6#5?fe�ts5Kitemi��\ ew]monochro�1c � fW� ��Y�n$W�# 5.3~MeV "<'A ;kd� �^�"�@ i ez �� ,!?��e�a� ;* >�@=A�m %nCin-o (in.+4).��t�r�d�Gp trig�y or a� -�+ ɍhe 2tUreadou|.�GEd�k�A����}-i�CaA��aj , durT]�>eX0�\he-v ���la� � -in-UB Qa��al�$1��# o4%��n$!-by-�����S j�Wi-��N f�*m~ .<af�># �, yA �!��*�_V!S���}�va�u�%� a/e9�� }[ht�L�"�\m��[w�L0.5�]{�M�L "�L�� }?.?G:z.�� � ���92��Z�} E�%:�b �Wa�bي10}Bi. "� �.I ends�=���0Y06}��� ope.:!F.:� Y�M*al9���f�)�occur��QS2� UBi�~�/nd 2 nerg &1.2�H#0�5� �ofuo�f�9� AM$� 5� ab؁i� -�$%��Jll*�1�v�rar ��W��2Gp40-fVFeť�Fi24�r*tE>M�p��� %I*�{a mX%�$\pm$1.5~kVvT�>*=�A@F�in���j oY� E/cma m.i.p._�ad��� em�6 -�Birks}�AgJ -2el�(t�g5F�) redua4�qe�S �� �diploma}� J��N- e'e=~e��Sb�Imel}. ��i�)�� E}� 500~!c!V ss ` 1\% �c�:1%�ee��/oEo�1* 5�a�; :X U��AFBT was .��9� he<�cE M� O �pVE;Tka6Aof 2~kV�Y!��:� $E\� V/r�3�$rm e�Su�e,�E�80J�� ��.%�MR�a�� a 76�thick 5 wire�mel�one�3}A�� fl��$ Bunsen buOMOQ�;7 � t�&� e~A=orm� � dropAF$he 20~kBq~وM  \� {Purp�eA$AEA Technol�xQSA GmbH, D-38110 Braunschweig}1�me:� 31.9�1�dissol��1.2~ ar $HNO_3�lu� . A!dn layea<�cnAof�ut�s ~Bq$ `ed1�iWmxi�5Q�Q9 o�d ]�opx� � A�ak ,�!�a.�av��� �Q�)��`5A4U��( 458 �O 12~\$�&��C�CBVFo} M@����� &�v�A�� j*}4 5a P�e�JI335% 7 - A s�wa6�* H�ppl�o��twoчa�y s��VB�� { 5g��.�!� ��If.V6�� � in2� �v6!GB� �.82 etupV�!�rA�set-up��&���O)-���Oi�x 6�)ot=7��*��4re=a�a1�!"� ,  ���:X2�:"��� �Sq��(reF!�r &�p�&9A�$ɂ"��1/5��L}e|��r%)Ab )cfG B0(wo���l)� ZX�� � 33\%��v�2��͖�e1��!� �on-�� pair&c� B��"p�!ir �c&� -fa0-Sn =�810^6 eV/w = 2253&),w = 23.6$~eV!��m�� jD!tF� ��/�7es&% _umo*&[ (g�hA���GH]neglig/? f{!1ofEs �l>�{ ( I}��& is 1�). Neg��a�/VW, w�tiW�te �_(.� X� edepB)�5s)�'�Zx ed �chj��ThZ!��2-!(2 s;or $R$) ��H 0.22Aoa6O:zAh44� to 0.39615�. �}�bt&<�|�q�Box T�2��hei �&� �-)��DU��is"&#!)B#T!G%�6�al�C �.�[^��Aq|;ݚɴfe;mov 7�� ɿo]Km� �.|bA�Mri�Z6�.�:��s?�a �[ �!�T�%�W&>�~ ��citrd-9 of magnitp�>2v�nH�@ey �^�Wibu�Z9�9nt �$ –9?�x,*_Y~.ev�+biz&A5 �~G!�%�)ҵ�^Q^1���Tr�d)"�$�Y2�,Nr%�2i �!I.4 ic Z= 'o Y=&(� . 1 �%s)UJE2�*BB��.�%�����xreg�o�� i(��m����� ngth�na�h�) �|"� l�)?�sB�%>�]�e3OV�@8cm]{num_el_vs_HV� %>�w el} C&�]͕Fw(a� %2)  ��&�QTF�as %aB�E�\ .� M�i�curve %p�)!h)�&C5WPj$%�!#d!1)v�0e{0.3cmDc�e !��^2;M%��  %I�am�� V� ��a�Ad�?�K Qd �isu"s'$��%Y46N �`g��!16� W:v ��� . Two �C�,polyethylene�e"�"�W�� �$$helE<t��MacV2od� ��n.�MhaaIi�<inl st�cyl}E�I�/ve$��I��] q�� =�1dR�=y�va2�20~mm_5 I��|  JRCY }. A g,4$ dewar holGN��m�"i� cuum&R%B� fill- U�N-!�l%Ph_F%{ 70�;!�}$CA�!;&C_�D!Ppum<'�=�-�B1E-6}$~mb�A�� �8; �$a 5~$\ell$E�"�L cart�Uݲ5�BTS&�@Fluka No. 18820, �Vie�DCH-9471 Buchs SG, 26/caTst�bco�C oxid�zBTS%: � pI��rol�@�!�of hydr�% g�*�L� b)��x�pbe � &~& LAr ��'.i�A�M�n5_:+aœC t room te&=�2"�EWQ'�I6�� � A{[.�mplif�7� typ6�?"�'M�$) AU ��)P a custom-Z ac-c]�k����adA�e bandAka �8h/!�f��enc�%R530~Hz!g8760~kHz (-3 dB ��hA� � �� * c � U!�-�de_a�cay%I��%e-2�s| a|uiou�H�ll * &!b<10.8~mV/k$e^-$ c��55e >T sXra��)� � Qy�" �� ��"a!��[U���r�.��9!%%m �6,1� .zA �]8a�e��k`2�j��>�"� ��Q �i peakɢ"�*��1r~�XeC�L � E%�$� N6N$s (6^$ �nU �x "�� of 3~mm,�paA�to2 �NJ�`+ 43�+q���_a�of�*u� ���):[u�u–9"i m�f�*���Pal NofjE%psme�� _ ) w�7�( �h@%�[��� ��(� ���i\)�21endX� )�6�u�&[ ���͓j�1LAT A| �!0�Smh(r��A� neߑ)5d1A� � in T�#�tab"S"tS&]���B_��0tabular}{|l|c T}\hline HV ($kV$) & A� g"� &Miͭ& Mղ� ��8 & L�<�y \\�  & [$10^3$yl]^ $[\mu s]$� .J\\ �1.0 b&36 &50820 & 83� 2\\ 1.5 &49 &6271405� 28 \\ 26n58 &7n12Q& 112>972n62 &76h1~ 109>6736n69 &8 �0Q& 12093� \\ 3&72 &88n!+n8:5n-QrQ1 UND EA�e�^a2�YMA 6>� � l�]]��ax]+2A�G."i�"� &0�F � y[�werr�Cim�{.t-s�P al f^ 2C�i�� X� E-6 �en�A-="�D+��"s�c2��11Pn fn'�o F� ?_*E�t�DZ�� �e-j+"�{ K� s2�K>x �= �t)^o"�xu�X��df_��mlos"�&��'s �y�Pb &� y6!e��I; �<�gum&�WtZ6Regard���Ja'�� �>���n �"�#, sol^Px1i�s-W0U[]}�A few�|er0 �ic�.}.� )����( uv d�plo$^JAhe2P (�3u:�1�QN$-���s�gx)D]� ).:E�@o|EC rprea}*> s2�favour1�1;�-s�2� s w�n�. @;�):�ce.��ur�Zl1����9S�[�T% <�-a.�6� fc�!.� �,V�: at}str�0s $\gtrsim 40�A>A�6X oe� ve f�#&hwitԫ M��*�+"�6&�7��$N}{N_0} = 0E}{C} \ln(1 +  C}{E��JA.8�*Ae&� �A��:<�#$`=2_.�b aef�)�x Ii �%�$YL�0] 1�'Q�B�� , we� $E=f\ s Vwd�+V�S&�x�,m,�w$f)j&1d&�6�)��ometry ��,e"3%,,~+8xpects $f=1/r$.$|�8���JM�Q R� �p �$�Nx�.t $C=214Eicm/kVw{,f=42\ \rm cm��}1!� = 141d:: �{ 68\% C.L.�/%<��su�+a 172|��1�ŝs��$$159I� 4ly�PA�slNGQm��[ [6h��N��>� aQ����4!��r��x� KC� M�� Q�B ��n6�%�r/ 1/f=240\  m$.�� Xe��"�:� �� be%,o��r7jIGi�9e"Cv>��&A bis +t��30\%.�11(��QC���d7�ec_+ �  �}) !N-In&. �O&�&1�tE1ec�4s��&KaQP�li�P1$/����9�"��G"�>by/11ct"�%$dN/dx$ � semi-em;��e&khof P30 }*+�~8%����7O0b�dN}{dx����dE  <1}{w}}{1 +k_B(E)�� %#�endF�w���� ��7*� � .* in �?�)~eV�3% law�L���0Mla� aT TPC���4�Pstoppa prot�qu����oA�*=J�I�� s upe�35CesKi:h�4.�predic*b.�}:���aj�poT!�se.�to W7� Y�>6iesLj5750�O>KI�F� �)x�% $Ip1U�fRF�?)? . ��J�� �J @ $C!�1� �G�>�%�excelle�_��)�r"� ���\�$1$1p20-hvV�G }te�Md��F�"��= . ��.%�v�KFk �6� � a*k Al��wbN%.�:� (�|�� "�+�cenAa�"�$.�D �on"�} SadB �?s)� �_!.�,% �wto�)~=*��a/Q_c�neach s�4( ��� a�_e.d"�1!%tau0},%�6N w�[T�L�J igh -�a2:%*�m��s �k�@i�$15�N55��s �2Y $12&3B&t T� ]ž! a &: �OD�e �"�/)x V�J�&��EbAon%�D'.p des;7u7ff 4 @U�p�o+Idi&NJ.e.�ei ve a�)er ��!O�Ma%�,��eI. ra#&��4̗r !�4 po��i��ljF/6� C"%?j�Bi��b&HxQU�oR�&�"�,G 3 s���!YAב�FX *Xi �$:$20V�e�eSvi���B�:\vSn� 5�;HeaFn�%/[ed�)j�*�L3 �B�+ tau1�Of�T1v��� ure �8s�1!�5��  VN.�OK Fu5IlE�� k}, uI��/-h� /�% h� MG _�ll�4%��_b� &|P. S�U�� G��ur 3 &�8!�verP3*�G��Vf� �i�g�V ���r� 2 i�c!hAi�. YI�% �(s $\leq$ 60>6�F19�(i^QF 3.5~ppb�t�|�A�2ta�pcite{�3.�{ seen� .)8!-TVJQe�)e ($\g�1~[���*!gnf*�4!!J)�`%�"k"�\<littl�+� .W�2 7 hc�d.,M\�!E> RQ Ag�!�H Vy�s� b�.�.5l�!wnoe�/$>+�% )%;�:�'�%�A���Qs���.��52'�To!HG��hav�"v�[*1Z�:�O� (��!�ai4%�I�� �� !Mu0m� )�l/Vdopz �h<�pA1� avoi(d}rw`O�W�X1:q6�; � . We �5��2� ae�*& i�i B� pE���2R1,�Az  $4B�W � a se���4�(�U�nc "�!I.,M@1Z] �,ofG|!s w� fd� ?d� A�c� � �;q��P of 2-5 \%5H* U�,.3d�^Qr2m"-}Ved,��it&UA��xll e0� !Z��!�lAi[�&. *{Ac[s�%f}A'� k Prof. B�jch� !�TRadio��"y DS#t?!u PaulCKrrer "�]4(PSI), CH-5232!eigen PSI9 �advic��+1o�c�Y��E� �.~Pic}^ F etropaolo��(F.~Sergiampiŀ5bdiscu�z�@d�im��ork��p&�Swq�N�al ReoF�'8. %%\twocolumnsF l9�^ l�L&�h�e%% ��A`2Sci�C8fic Word (R) Ve�|43.0 %input{tci*x}������� :�l4[12pt,thmsa]{al} %��VMk\F{lx�h@TCIDATA{TCIstyle= �8/art4.lat,lart, .2OutputFi�6,=LATEX.DLL} SCr�9 =Fri�z, 08 21:25:29�+2+LastRe�rL=Wed Apr 06 08:10:36/5/02 Language=�AE�o$CSTFi9.csslB�4 q���pbf{AXIOMATIC GEOMETRIC FORMUL�OFd( -xELECTROMAGNETISM WITH ONLY ONE L: THE 5 FIELD EQU QFOR&�xTHE BIVECTOR 2\ }$F$z% \mX AN EXPLAN XOFy,TROUTON-NOBL2�8EXPERIMENT}\big��   \qq2�DTomislav Ivezi\'{cq�,it{Ru% \mbox���{d}\hspace{-.15em}\rule[1.25ex]{.2em}{.04ex)0)8}er Bo\v {s}kov n� �je, P.O.B�;0,} 02 Z�b, Croatk � � i�c@irb.hr��%�"v�Hb��^���ano�V,Vicl *��!Detism�C�Oaxiom�n�%�� (Faraday biv+ ($F$�l1> F$F$ %is�l2��)ed,C�\H�>`_�.H�!� p�e���ic and �5hs�� $�c&{%s.�rAlG�ys XkntSE�ˈ��0>�u,J)ab�e q|?*.�9� f?(.ܡ (4D); o�6 some-n��\2��ry4jsEe�)4D coQ�-�5d�ic;%"9��� a baG~� -1new} g� �ei�&�!!��(ss-� M: $T(n)$ (1����?H�W�U$$U$ (scala! Poyn�HSM&�m��?g$ bs c���AF. M$ (Q�?��LO�force $KS)I$�^ly�t! JGm,>�"erѠ%adQr PW.� Wi6X)�1I Lag|$߶A�!v 5�4DB�EC�*��u!�e+hRon ter� wr�&��}e 7: now�J�ual@= *A��|�Oe��$a�o��E�Yull&u&�0 Trouton-Nobl�:�.�K�] �RK��ords::'�Q)=�bpeRn��bf{1.URODUC24��6�e�� CliJ�d (5)�ebr*�ea�!\!��zs��B�, �p,)9��iGs [1-3]X5m��"u�( al te:�al �0!%[4]),�Q�s E�Y&�.6�sAh�]Jt��# )k� �po���%A\y�),�Eq. �MEF})�h. In #to ge�� familia;uraieN�#�&߫in [1,2]�>U��J!+a �0ive����(bf{E}_{H}$ *6 ! t-F-2#3D)-�a+FJR$% ��xU�$\g_�_{5"��B ��!�bf c�jA�3D 6eB�Bt�a�.l$�(�(!�(e-4) pseudo�١Y� dard�q ft\{ � \mu �� \} $��mh�A_� - spl����0}$ -E_me�iɺ������veloc9}$c�0}$�V�3c�� $% H�'� ``HeCOes���B>�-"6q�K�'P,5�- ��!IU�"(�[1-2])7 � } F=fIn+�>),\Y 0=(F�, �) ,\9�>Q$=(1/c)(F\w%1 ( 1�.B -6hfO6�� �rstoo��(ey-�� �{!�b�!�s]�$� atA� �1f A�Y* of} � ���id�Im"Ijd by}F� ;nd}.�m�d}M M;2�� 3D }]T$ U%=0sB}$ mila=in [3]�ā�dn)L]�D59"F:7J-7aU��� J};$�}Ji�2``J� wiczq�(9�F=5�0}Q0=� J}-c nM� E}% _{J}=I�Mm AmA� K ;=-N�,M�E�.U�J1B�� �![�@Q� `�� A R> �M�,.c�H-c=��);'J}$"e7fz� 1H! ��hf}�(�dJ1}�V!�in�6e lef:�F$)^�Xrk ˡGs$�lGtc×M4}�e2� � alism ��a�y�enscr �%g4*LUj�3*"{s (ME)CI3D�t� 5Qq� B 1�*1#N� a,V-r���et[I��y. Furn�5 Z�p [5]�? (58 B8-ta�2 t8��� �3D.,$a�!�ta�� w��:N��.b�� �dF�(E_{i}=F^{i0q�Bp(-1/2c)\varepsilon _{ikl}F_{kb��skoJVQ�A>�! 3D)�z�>� � �h� ��ic)��s&5{e��"Ts_��om:4DDie�;Af�UP5��-ּ U"�] $.!$�`F6o�U�� g� ��,l&�3~� Greek ind���10�3 le�i� %0$i,j,k,l,...$31 3�t!'E�eQIY!�6��Y� ob}A���A�&�s.Ţ0 worth!��eE ! ein'��nda� a�[6]���earli��&��<ov�3ntD o���� he i�R�� 6�$F^{\g# ,v }!h=6+v�.��{�C)s �J;%t�i�M�e���:�as prim�u&���dw�I6s�����&r"����%roaAIo}�< L5[[7,8]l: B�F� F��u���Jt�d�[7]: `�� �6� �n�V$F_{ij���)E}, B})$ ^[7]q$...=0,1,2,7]m�����'%����� {� nd&& }�)� �2O'{�B��K L�s��&� $A.?!�Cly�r7f����is�%3 .$A$A&$%� J� �y a���LMl���Q`'riv ]��t�l��"�:%��=�%�l�$� "b�t&WU-�sm,�rM�FS���.t�_ "��_o+a!*4�ha�!3 �d�9F(ڝ5�&֋bu�5d�n� 2a Jo���Ek(/1:!c 5c!�. (��x� �M!�[9]bAy�����>ty�~4D $E �BJ�&/Efu @��)�'��pn���"AmZcla��`U)�"�o"�)��(o �CI�ܭy}��y� I= FW[%3*]e� poste�*҃QbA�!��d$F$;2%�"T�"%�} �3cn"M� m-�A�M��N>��sAf� $1Z:Q�Ius����(�E gaug� ��RTIn �;.�)�th� �!�:�y? ųY:�sm6!����>rN�s;�ea� -( dA �**T$}U!�*E�F  6Dsm ݆=Md�4��4DY c�0�re"|�6C�.��� �!�out*�<�(?noLha,Lea��),�J� (AQs�r,A�i� ��� �W asD&� e9 �N�(CBGQ�^om�o �) ���8�&�=)!�6se�=i�1[PDt�M�� in���^ramn0&. A1�{.V� !�itB�IA"C.��w&�[FB"}v�cle-to"�<�e"�$�g .�b#7�-\i� cr7��wo-step��ocess;D�4 sA(E0a�, -8 @their particle so4urces and then| fields so generated are perceiv�s interacting with some target particle. The description of c$rst step i u,$F$ formulat )\electrodynamics is given3,Sec. 2.2. In 3[ �l soluJfor^dis applied to the determinr vmagnetic)A0of a point ch�} �4=! gralum1R%P equ h�@constructed which�0equivalent toAlocS!� G((\ref{MEF})%g second%U -gJz�%�,on process rsresm>%*Lorentz�ce!�!9s�!�A>its usNewton's�law�is !�tfsaA.ihe wayU) componentd4re measured in�Pchosen reference fram!�t!H �b/Q#5. We alA�ivelX \emph{new} expressions� �\observer independent} st/-a&gy vectAl T(n)$ (1-  )$,$i '� density $U$ (scalar, i.e., grade-0 multi >,< Poynel  $SNb@angular momentum lM$ (bi =)%��6�$K.T!�eye�all-&directl�r� fromK posta�ed>��}E((Eq. (% Y� �!uen;i5�6� lE�io -curA�5B and !)[-�eYervi* laws �so-�R� thatN� }Q�thereA^no ne�KaSroducIO$Lagrangian�1 Noe8 orem�se �N,7. (Of coursYg�\�66�4can be similar=�8but it will not%done �.)�<contras�lou �y%� *9� ��)�.�AMrec��(heory [8] (ei(a geometric��,roach) deals gthreei��s. It �� hown� %�all ; axiomsI�x0simply follow �'68Fur!�more, i�7 !^ide�g [7,8], �� almostyo7 treataksa�atE�is �Ded by%83D $\mathbf{E}$EB}$. As � saiE7 exposaP�aMQ:�U does%�I�he]�. Howe�ũ 3 a brief��osi�0�,eY 5�e discuP%concl ɑ��$. \bigskip  \nonHnt \textbf{2.\ THE\Ő\�FORMULATION\ OF\ ELECTROMAGNETISM \^medg}V` 1. G�M%%about G��AQ�to El� ' sm�2YAs A�io� ��1%6�!�*� 6� smy2�sex!IivA�d�J8AQs (thus definV ith�:$ s) orY$correspond� CBGQeen� ,basis has be���� d. U��y��a�standard 5I�i� 40, e.g., [1-3]E�� tor� F pace algebra�$e Clifford � a70by Minkowski ?)e�tak� o be f� �K �@s $% \left\{ \gamma _{\mu }\right\} ,$ $\mu =0...3,$ satisfying $.4 }\cdotHnu }=\etU @diag(+---).$ This �i61C �$z�$,!aa �@-handed orthonorm9 rame � !�%eJ0 $M^{4}$I$�0}$A��P forw!�l!a�e)�-4k}$ ($k=1,2,3$)�%� like�5 5%q$Q e!�m plic�� a��leA�a8�\.-: $1,�Z:\wedge2� B$Q 5,} �2!%=16!" :a�s).ES?!pap�  [10]��i 41]. We remarki�J��Hs�fact,�4specific systecoord�e0V Einstein Z*� �inertiQ��� . (II�vSN#nchronizIy [12]Wdia�t clock4Cartes� E� � $x^{i� re5j��) � dif�t- �".f of ab �a ed%�t*�k im�7p��] phys4 phenWa.E�exampl6 A 3� DQJ ird.T4]) two � �,� �a�ly.�I>�,� =�JR�@''radio'' (''r'') Q�=G,%&q �� oi�Zthroug�FA�e". Anyِ���_ $A$,!�AQ,�� � CBGQ�us�f ��ya� . gBGQ��!�� � y upoE� L�trans� E�s (LT).}� such�� pre. �LT�+.� as pase>R; bot� :�!!�� � �uwhole� ��ҁf0ins unchanged��_"� ` $x$1ide�6M�)!W$% S^{\p ��rejB � )��I8 >a�*�� ���]"(�  non-Z> e`��$!m$x=x^ Q�<_ �. }�$=....=x_{e1 p }ve Ud.� �-!fBLe�un 6s. ��-2�yѓE� lism1�[1ən��a ��}Ls!AQ)�}I�v�aSc-YfI� . If)�E�a@in�  (T��[1�*m6�H)-i3Ek��%�U�Qe�a"�b� (� b^z � EB*� g .jin?2� a new� .�!s��(�V.�am�). (We�)at� ��-f�AvLT!�" �Ua�[15�tq�us�J��iZ Mway�)��F  -��-%� �2� !t� p ,� � sake�BbO ty� of clearnR����W\,�shPwork eiG%�4DE�� 4D�)s�a��Fonr E� ^c.$.��kremember� p&(���&q� hold{ any�ic%  %D." lVj2 \ DN�6^c F��"�.VWe0r�Z9o1�cl��DB\� :�A�fB��@ Yp� -to- �YA�on;F ��7�oIG�c�& already A����a8*3jB�!� E,�e&�^ �; �> �e�QkAfer��$% F $���  singl.:��is-B ��<. Riesz [16]). IA�at;an:�}is re�La �-�d fun�$ $F=F(x)$  � Ep s%n!�)�eld� 6B c cuo$j$m�!��;)42G�i� oper� $\E al �' >B�b5{� 1�$as \begin{"} PlF=j/\varepsilon _{0}c,\quad %�F+� R= . \labelZ \endyTh�g� �!i a_ly:A6he abs�of 'c� rgeM��*DI�A��� K��A�b en6,_{\alpha }F^ \beta *[ -(1/2)=c :2�h \del@!!�d_{>%� _{5Bp=(1F� )j^{ � ;^ �, -�c1B�w� $� v�E�!�tot( skew-symme�(Levi-Civita�tensor.[ )� c1})�� M�` 1�as��.� �Z;��!#2)j�-�I�1�_1B$*�.{ $BR$�u��=sJ&=)�A)�io( 9r F)= 2e� �I �) KF$). Fh)P%d�� easi�ind��| cova��m�us4!�%J: 4D��� ��q��$-�)a�Q6R� j�}/^{a-=Y�F:� -7\%ustJ�=0,��maxcoZ5�)Mdual I灢*B $aMJf e�25��r �M�5F"$. �l)D�� �Xy��)�� 1>�� >� Jand.��!i0/.�� M =�s� ! pa���s���c �B��   enableA� A�AnYZ� UV�$F.$ �{�nwinvx b-iL���s aol�%forF�F=��^{-1}(Jy)Y] inefB\2�7� [1] S"�Cus�#�ly�e� main p�% l�to �t��"s�< ces.�y,e important �ce�vectV!ViBes �A47 � us� pro!=� : [11] pIA� �)|E ��& {Maxl<4�~S  (R N"l E}_{H},�a� B$.�hf}!26J},$ 6J66 J1})�6*�V��" �%@a bouny�d1a� I�-��  UeWVz 7%n. I- ZQ$$j:  s�i�[$F,�%R �!�idm�uni�s|(-�f. By uB Gauss'�%$%3Q�Ai�  �mY�sA�"D)1t�e- $y�3 m-d !�&4al manifold $MM�'d�%aU9�F� s s a 5�,8M$ if a Green's*� G(y,� is known,Jk,(y)=\int_{M} 0UR8F(x)\mid d^{m}x - ,$ 5n��22-1 4��DFB�$nI�!�t E, $ P=f2}=1$�-2-1,$ A�.�a.eǑ��Ku�9L _{y-=�1� (y-x<(iDF}B ��� on (4.17)��7].) IfX F=0:u$j >�te�*�e X A=ap % ) vanis��no�s�*Csis�l�M�*�+5��H3ee\Z3 P�2 Ch{ "�6� nxA�!� *Ge" *a� &\HLi\'{e}nard-WiecherM(�-! �,*�+� Nq� �+dure ([6)�o utilizme =o5�)��xJ$5!� out "Hs (& "�nus)�R-� !y"a*�($m=4� Ta�-� spl�*f �U:F. ct=x( n _  &�sp2B�(e��uD*.!&� a�)LN){he&)�param� fam� of � @hyperplanes $S(t)n �i6s;"�� surfaosi' aneous $t��.6�is�sen.) K&)icity,����� ntir!~g�P betw#a 6�_{1}=S(t)�($S_�!2}).$?��)%��pon fur� �Qwe� quoG��&���c"�f|�^�� �0E� + $q �Pworld line $z=z(\tau -�a�/ E�"�<I=qɚ��fty�i d+u��4}(x-]),$�u=u r =dz/ 6$�n� �rd6 ��(*� Sec. 5��A�Fd�D =(q/4\pi .Pac )\{r�Xlbrack (u/c)+(1/c^{3})re� (u'overset{( }{u})]\}/( ) >9��LWB��r=x-z�$�A��#-c$�!J $r^A�0)�$z u% J�=du1o�.e�t � �s�'a�the back: $� ex<$x�nd.]2aZ2!�. I_w�$ no�/�J]�g�'.���D%an e_�iP:U�& ��p �8& �e��+�advanc�!te=�]���6a�0an in���5-at-a-i"i2.`. (+&._r�-.re� ed elseE,.���&�!����ab��he 4-$E^{a $B & .�:�p� uq r� d $ly accelerE]mo|"�&a.�@m[18� All:�I LW}) 2"�)2��A�(�mZ%p�*�3*#� >�,�"�"� �|* {��3!TJ�Q� an arbitr�+)2�i��$align} F& �V B =(kq/\z$��)�([ c�S(r �}u"�-�  ))<] \notag \\ & +V^Y sigm�F4_{  })* cJ� � )+. XuZFJpF� N'%2�= ] &� efa��-�I� ),��E:�!mu }-z"� ��*"��" "��Ac��A��E�?"� ��' $z$ #(i�U�&_ � �\}", �)�, >, cII\v7v A(>� 2� %?-hand � �,�+2�$O�$�$�'5%6A ()��)� ��.JiG-� J-� above&�- C6l� �8��7a�m� $(!�� � -��)(xQ�A I $=0,)Y it h��0Y0./=\@r\succ 0$��� B%�eE�!&E[�-�1� Jacks 9 book [5�-*gi��C�4�%`5 d"�1 e velo� �U�x��60�^b or radi� part. (H4w&FatIIQ&D of��K�j#����res1(consequ!;�"� ��Nit&�4exih2or1bB�x� >A�+#!e �@ )`�)!3�� y�z-�-�IJ��� V%��U�N>���:��;��2�7 #ed,��& forc4Jy;l t � � ,2.5. Let us"�\i�J_ caseA6=8 �5% !�[ Q�} $u$,�-� Homp�5� 7.3.2a [2]�2it{.}�B traj];yAG$) =u���ak"� $z(0)=0$��R  u/c=�| x� � ��|C0$� =2'($. Substitu� ^A)+�27�>~ s�E�9s2I�B }�ej� Axi�9�#asM�� , �e?$Js} �+\ ne ?k to%��A�&%a``.''}�, ~�. B,y\�3N,  � !0 EW�8��F$ a A�� real�'�wm,B���b�"ey )F�55 even���7���C��tlyp.c<C�"o'eUH all \;p\(�&~?( assu7@�4D &� �yaf-� �]ai��+!�16,y}%y�3D"�"�V�;�A�%)�8!O�_�&�6� )���%(4D�9=nd&E$� �!A��V 0,11`5�2On��t���0m�use�HE�.�8to"�% s $E�B��� ~ c)E�cv+(IB)�v�"� E� c)F�%B=q$V )I(FH)=�%it�� v��I� E^nit�#i4. ( ��-�<�v�I�):��%^4]ɵ1.2"+ t ho*�I$E� v=B  vq(si�A M<2V$1v!fm��)m��`~#�v� &`B�&k�B<+o]es $E& $B$MB.m#j X} ���Auy�m\ ies �A=+��}2� :�5�9�W�N:PM�% AQs. ys acterizes�,&�B i!�K}% �0%F �\%���%�F} (A� rEL7)�%>�� [19].)a�?. actuQ& establis�w�e��FC7 ofB� �)�2#(m�ed%A)��,:@@ �/��"�ica�7"�(Y-I%a�hin �.)QIB�.o��it�C)�and} $E�B����4q" !6Ic�@y!theO@"om$,�st� 0elf�ta�M.} S"+C�11])�!M p�. #0%�� ɁB0 I|=!� [1,2]�>�repla9:�N�$E_{Hv}+cIB \�bf{�*} �c�)(�K)�6 d \\ D& �`3})I[�a��]&�he6�k$".�N�!.�)�$ -A��� �%TC%P.�-,� bG�!!��� $c2V3e X9u��6�-�?6�� I�� 6�G��XAxh5� @% B �)H @�*E�#$,T#H}$Ѩ � nQ. AYksAnot a! in)�cE. O)�l aiM�e})!Fy;$-y1i9y!>�9�v9m2"�1+.�u�n AQ �xth#A���Y !��3@J� >-� ,Z���nsteads�'ng_^: by* I��E�~�A�ܵZ��.`,& ��eaby��ẅ��$i�� =!2� ��N�$S:� ��)�%1!�m-9e�;a�n fact,< ser M�&��Ϳ!��[&(B:J �. $,S I�J�3 �U�/s $2%%��$ �A�>� .���� ,�f�s �V� A��7PM0!prJ1$v�}]ofu2� M;A�3V rea�Fh*B��1 A�!�*stigamNab.���� . An38 l�#y Eqs.-SceI9!c��:#)IZ0$2�M���:n  gncon6fe7*f &anarray} i &=&(D�23})[(u��)"Fv)-(x�v)2� �L4�MN7-Fc v)+�tu)�wbi�we�U Z*�*)~bi}��%�*� ? N� . Re7attA�A3AMvZp ~p ^�� A`d!� f&=>� �()�. Us�� �A�Y = I�wXEt"�6V? but ��&�"� 9}E9�223x])u63-QgI9�� *�ecB�in�%!r?!�"3e�&� *�o4.�($EwB$.-)Pec�+i,"�x=]bi�'bw�`a��amount��i in��~.�.��k�G��.ew; fY,��BY i�IdAZ[1�G �� ults��NovNE>y[G8�!��6�$% -rNamre "8rest, ``fiduciaiX (g2� -�<ž �f�G�2�;($v=6] " %Jg*A#�G��͝l)�.R�6��|9��f�� x-ut)� B_mC2}) #16>M&n 0= 'f� ep)f$[>�!2dE�l���!6S Qfo�.� �o. Not-<%;A�^{0}=� �+)�m&{MmN)�of2�"n �!�0}��<� ��f}$u�� spa�, @�� A�0%K� �?f\ A�exaITA��(� *Fr4��1h 3Dv.�$in!��f9"."-M%"B="�=6 ,�mM4� Ine06)"e0�=EM_��W% )e,.�=Ine �d�8Y!�RJ�<> *> E=�%�=xl)U}�� �U q% �\.�)"� cS �XV*��%g�X. Such �5�He�DDnic�F2h .�,�,-TX�3� ough,K"�Rl� it �B*>�9. H��5 m��]E�.�o4?A�� 1Z%� ��!gz()�Ror��"�Ps(Det6<<of�)�2*�/)�/�z*�Bx anb�V3=/_"%1 M}d7� F.8d0"����<��;We�Pm@d��in �, $�1$A)�:me�Y%c662 y` d 2-.�2sub"�2in&S..h�re�6��2� itud��|A2a#| $"�".�``B�,''�3 ��:� a �$m$-blarI_{m}$:�=�5:��oz=1� C�P:da-$da- ...M5dnx=e+  e* )e"dx^{12}...m��)�$�$%�a ) &�1�=Aꁁ  e_8"x$[GK1�%"�H &i%8)�c%. �orderj� Qco.�Q2�P w.L >��o�Q&�1�(s�8.h�! by (�Z�]ho�5�ya�U�Jz,��eW �J� !�J=&��n*\�C AQs}!��[Vj9�6cNR lNH }>� -����V� EE���u�!J&�!r��E"o �F���^ Hv}5�, }&5& �;!t  6� Y�@2�Hb1�oE` rDas!� 0*uy e:�Cr�((1^N)=0&�dbB��goa�R> &W K{ > % )iJ� �^R�C ����, =�.�FX !w"xi�}KN.of:N��Q:�]��a�et"WF�L �L84JL. &� lso�3��"]<ula�!'F/(�� 6���bf:� FFzBFI)#>�+c)�3M}j� n��3}x�q|*&:dtBc�)n=n4<��1:out2�5!�^;�3.� 6�A�W�=is enclgby2* .�0.� �� ����w%�.h�ss4 ia�m�]w>V�Df[(dI&x� j,"�dsJN1,w�6 comb��q�V��q�H��I4� � �J6JE\la�I/ FI\�ale _{I�=#Y`>D 3}xjFD=kJ� �_ �...FF$ s��9�he ``&�(= � +.�W)e�s.'' O2ob4&4*!dE�lM6�k�Űt�( db})5 -#��� ��Q�* I�(or1�s}dMkX�36� �F�A2�1R1Z�5�catI�� > ��v+tA�!1 �t�2�+�� 2�" (>�)}i5(Amp\`{e}re-VB law���+�*n����+vw @chZ+I �žA#d%��:�7&h ��* 2\"���NX,� �-A�q "3 :N5. ./""� E AMq.~7 ge�e (Z�6% k�-co�A� fl�/heWnfini1�>�"v a3�- 6<E"=g$\o16:�5io[toEneE�F$ mg9�.�%�Zx "���s.! �}Ex3&UGmR�Ier�<.a�� commonYVN��aweA ��R� (t��f4M� X !E.�s�E�sit]:� !o� &�&z4 2}$ B>.uW"/^ofI�'e��#B!�ven �3D����[�Tbe a ``pill box'' pier@) cross-;al�a�X�= �w�k heU_is $2a��4 h=*���Eіt� �A��,�dS >_]?Z�4(a .�#'75"ant�?ly} M"RC�$q^��l-�%-��.  P�Dis"� �$N���~^9xq*�ue } F=F^{i0&EOiIk�+�OF^{kl)k6) _{l*[Af&�k�;A�j�!``�ric�6�\!�5�\  ``�� .&"�'rt)�U��4�Sx&�of6iL*1%+!aBN6�.�NI77�ש<S�M}J�s�r�bV�,B�nCbsW alog*�hc23D.�9/~fd��atr�430}\neq ?E� %�@��i<��yq�eoMx� 2SF^Y=S(�f.# EhCA4Fw E��C(36@=Z2*~ 0 _R9"� fpBk E��"75��Bye&Xj�qaCo�ed��44 �ib�n 2�� i�, one J�V},*�N  � 1�ZLjts&i�,B -�k� w�a�&/�) �ci�g"� r n^�F�[8]�Y%�� ej+[J�s}; (1) H"YUE�e�o, (2)M )ace, (3)EցV flux27&�Vesa-reRx�d �folQ9�v!�� } (wak�`h� elses4iF**S�ce�jh h!�A�/��o h� � !ť�s���$@ b�2iM� 3S y f5oMouQFQ 0}��љ next��As,A�s. 2. 6� 2. 5�}�Ei,�!E�E" 3�#�ts 1D 2�^! S� �h:�MqU�\Y�. �[zak5��\U3For^9�M�A!~aPJdV=PaTFB f�[R�A��-2 p D� ��[��bCwe�_1��G �;\2uas two-�w,g'v;���bseYmkA��t"their ��iclyZi6"� Lsnkx� �3Rkx �p�Q�"� �kxnn�j!� re2�" Ij *�k})�76�7��@;1�'-�oE� M��7E�af�h�c*�z�.Hhio9D�6} /2)(F"F)=b F/c=-K_{)�},�[TEFB� kA�$2K~S�>�R$VT%%%�%%�/.q�ch"u�|rz(AE��Q� M^6 n�1�A/ai�2N�^-z=T(E,x)=-(JQ2EFnB�1}.1Ote _6�^2�)mP� �B`�L uI`�t�h�k� �`ach���+�h�?��� flow���Jg*�yPj a ENk��4V. �I��2$UI�A=).Z�W!y��2�cA>}{�2,"�:�} =R5j/*`l:/�# eucE�!>��Y2�I�KYMc ; u"I�$u$!Iv�-�+!2J(� U�1h �&ng!�t#&�N�5F`Lt�-jlXI�ш"� ,�y 2"� � J�&:?sm� ��u.2�vEqi0|2� *� B>���٢&B>�7�:�s�2dCE�� ]5шc2nd6*&E��{�4ic=&x".>)H�E� nalysi$�F�Jd&X u�'CMAE6�we"#Tw tp��1^ 2,-3�AKXr"�-]s_�:Ri Zm�(*� _�6F�6*�� % &� _yZDt!J�kWeV �&%Rm���A��~Ba�JN% � Pi�-����e��:��N1�i��J�|;<,�? [ Y2.3aq��v�|��R�Zn�AQQ#!�N #}���� hf})c2JI )��5>\��;Ay��Jmak��B��͡riaw �A2$$F�0&)# +or� NF=fe^{I ,phi }=f(\cos|U+I\sin);&�&P4A[is;K/�2�.G"I�orm $f,+I g �* ���w'6f$ �"}8�(�%$I%�N& �8&C (If)~-� |:e�9�)� fc})�_{_db�a sumeu�A7�Iim ����eR�l��{�"�b>�.�o$f�:va%�"�-.�#�>q�U5s��LT3tCɛr2��܁�; $�M� F��I�M=F�#%D us $6\( =+ 1)^{1/2}/!�+ L #{!+$% f=F*-�B)�"*�>V���3]{pcpar�1 t s 1baY)=F?+F-i�&Eq)�E�$'� *)%\ k�%x�2�Pl��$f2�8f6� BA'�3;�xce"~�*R�261M���a}�%A�!c})7N�#� &�w-"�@�V8)C�3s&IP.yU�AQ�r>� �)��0�Vɸ"C � A<�VusJ�$6 �c}����4($q/m)F=\Omega2 $ ,=f(6�r .A #.D�=dI�7�XR�A!�y!S-v� $u(0VSC ��a#uA� : $f$-�%2+u�$�~go7C 4, h=f�b(f�( {)+�'=|+ Y�getF�u=e^{�5'1}�Z"V1}+B22* veF Ass7tF[gF�`�#�>A<�:o���� ''Ia"E!�''��m''���M�t p�historVPob�+��*Ik��J|*x�T)-xqP(B#1B-1-VE�%�)�B21U5�2/.eiSB3�Hm�Ydet�RD .�HCr�:� lie &_YM� b�!���b�Yv�$�]D��t�Eal!:"��?�m�iSfDaD��1Q�-��7�?*�71� �2�����,iP,� QE$�i��3]g-� b�g ;LI.*)�v6E�$�"�JH'��i�wav�H�Zlsoq.�A2ބ( *) u.�L� ��eB �D� u!�)���=grg.X�%CN �ǥ�z�!�.3a� %�*F�j��"�oA�$(҅#� �4\W���!�& AQ!�p%[20�N�r"� �s�iyboE671~`��djh>��IX�#&�A�=сom1Jf.��% + d. Fxw� .�P�h�/sen>�e) *$&�#!1� E5�0,a�Q���"�$$u:> [���\$|=(c,0)"�e&WB3g:c$:)��R (ExwO-R� B�) w I,#B�$�5�s�Kev#�k��asJ�"$K_{u_{i}=0&^:i%&�2elfF�f�2�n]!�GrqF� a�3 \lim_{q� arrow 0}���/q ?eJ�Qsa-��N!�=�A�n�>���._r r�-��q .ce �1Y�xaNion�SM�' %�e limi�-� g"�to�w . Ha��X6'$�)d� ?)+br�n��o"=)u�a* ��e)ks% ,iO�- svbF�)��B#'.b) fL���u�%:Vuk�k}rzIp�Ai^&kybJr��F� ��*�:6��*.;�K*p$.�>�E-� _�YL�3D6�d���7Nl A�"w>n.!�krm�s�Ra���=!2)e�ar �P���1��i<$*�EIo�Q.P.>ea�")it�TU�"r$% �Ma64�Q&|0w*jT���� co�ea��al �B� > �ngz�� �K���"�B�0uFzE�� !�ݖ*�� D<[K�2� u�� v=qE���� sa�K��:ia��K#�)5*!��)��"�' pure�H� % �Xwa�PUJ� _{E}v/cr�_{v=u}/q&�fvBK NW$�n!.A/�)"yD� AOR0F�M�fv}) reR�z^e a2}.i'?v6��� ��8fX6����vmO�� r{A"b1��!^^)�uz�/q�KlB�IeF�Ir���� �+5yO1��.�$%��L� �S<����)�{blJ���� M+�U:$!�� mann��%��nih�TBdmq&��� . Al2��ogegn�ilolya� F$>���@�Sy }�a#b%ed&�J&�q��!s D �. ��(6!e}"�FSn�Energy Va}�!B e Q"��}.�F'D�uM�D�F6�(b��&�v5�!�tu�j�!�|� ��& � !�he5�.uUn�#�(�"�$"��7�*�R�F:|#-br#[ UWF)n+2 n)i��#] .}#F��Wg�es�!aMVnew�}1����1})���F�$% n$_r llel� ($n-\rrYn $n$-7nFp� )erp $"�E]! X�.M�/2}$. . w ] n &�]& ->K�H5F-9XNnO5Vste���h� rst�!�)<)�6 ���it*,$ M�"D( U.$ �X�!D A�fa 7� nI is�/i�6%�dNP c%!���c6cI6��.V6�}A�oO�;:g ig U=��\l�<n�)x�<,$ 6�� a~ e-0 xtuU��u�#2�!l.��2F�UVE(E/�FnFM�V� 6YeFb��DueJ�Ac�^deM2`i�j1/c)Sn31a�SH )�AKѓ2�:(>���^� �eb:PCS=Bwc:�x"�)poF��[�.{iS=0" us�� ��AA��N�A�=Un�6c)S=�iF/@.KO!)2+qO$Pe�W�)�E� {c[5v2�dJ��:c� �� J� z��"�w } $gEDa�% g�B'VEIV *$E`M[���]��� �FrgN=ciry<�)��g���} ��)�.�&r ! �M$�F@ i*�f�-JHM$F�M%H)A x U(n)+g Yuem�t�I�*� (be emphasiz'Ggv&�ABie%��� .�G � A��� 'O8"GcD�E�6"sR�in it"եI�$As I am awy"4Xno0^�Guarl~=Z li�1�J/ZW -5ʍ"*� �|"� >�K , �zich&�Oʢ&A0�&��,a1%M- W "_" :�aaFA2�:\s� }� r8;M ��6�ba�)*�@ :/!N"0d�-F&w 1�DF I 2�e^&wedge  �� �{�9=�eCwK ��yq $%�{,$ $U!$S g��F�$�FBbJ;FÈa�ta �' 5ny< � �n"��=tx  n F9hHn^{*H)YU:6�bK!^ara߉�&w � b��nNc&L U�B�l�1v � �rhoI� +2R6I #!,!XO}?X?]*�HtenF�E^͟��M( _ !�6�KU����9�� .�uJ����>P � �por�jY �� =�-�5 �!�lambda K F] ٽpoF�Ii�m�������:3"ٚ$Ttw U� =T���wZ4Fa_ F.$i �H��\"^S%�I�-��t���� �e�&k#\4\r�1,*j8= EŢ���� ,� nCes�  ��*� fami}K �Z��=ZTANmu�8 }g���m � �a 4V�I, }gz �*�EMTB! Adaf�C>8a�)!�+-�-{SfacBp16�! #>���$2� &�E6>&�6!I �A')E"0A� # �[�5 q@�,#2AS0} .AW_M^{00}+&�T�[,�K��6 GA�to�:� D \u� ]s�aBo &  r ?U1@i�nM !�&5A��%* i"�s�RhL�@b)�)U�.�BZ�.�^Mc8. 2H}9+/ \0 *� PoyiF���B>`:g]\� s }c9� p!),2/ h, �p`H t $A EB�  % �.(AB-BA)�,4,� �"&>��4qAM����9�g-V4$�T�E�3L*N�3 , �3unn"Gubut�s�� B=��+�r�� B� a���?gAڤiionUAQ� s>�if�E&��f wae�B�s��rins"v;h&�. fel4t� d.�.��,a�Aw�e�$�2{it�U7_�Ui~�bi�5�2*��haѴo�y !W�j�"�",.C 2T%�O+�nI�2�a�,�%AAJ^ZK9JA�. ���N�2.7� �A�wuv�C Law�h�F)^bf{- FYI&XV�� el|�%vXfz3A��"�* $F$-"�)��8� ��Ca seta���er� curr���us,J�F�5c��cA� S���� �j2e ��B~�Nplye��av=%&��$DpR*daEJ.�Õ>G *} (N���j-�� j=:&�> !F�C.=*}7h����ozGM(x))��0�/� a.I)�B,s*�lE�:$on!�I0 law}>*ٜ �j.�XcjF��r a�Bp;[8�q�-�I�X��e+.�V�Y 1.m9�W,e p "{A�U�!p��i+pR�����`�L�^<si�U ,�J<��I� �: e�# a �& [$(e�I�j>)�G� �;0.&D�GaJ?%:r'0"�' cotiBS �!9fIŅ*/MjIf�+.g?.�Eo% "�!q�o .�(<�u&�T(aI�"��4E $aI�T(b atb>R��o6�6�$.XBap.V� ("hB F�w�y�fB��� 1 �B B)��be����i,)=\acute{T}( 1��SZ� *F} 3F+F> FO߄�"qt&Y�҆� p�0aؓ= }% =0�4�)�> r9%*��%��,Q/ve�%��*&/(� &`-M%�$T�)����� �9>�R�a>�A�i $\fo�� \E�t.\ a_�`vK:�e_i�s��s]�i �D�9 RD��6-"�>g G oaO� F�(41� )U�c>�S.PoyB"�{ |'�%�*��'e��9nowAUFy}F��I"$ .�&i.[( i N "�3"�>ǩ,$ ��!�� r��of&��`v��1"}S Z|/hoo A�n��$, 8O� "�A0m���� (1/,0��a0%F"�� �+J��3->�:W*�FTULU/ t+ �.S�+(=0,\qquad i��&:PoyF� P"� i;�:l\�ghF%` &\o, U s�` YE�KNyYd��Q�s (�ef{e��mz�i�i�I�9��m� $B%�aA�*l"��Ă.�1bi*�iU3ej� � funda�al&&"p[l�L�� � � �� �"~*V��"}w�� -Fy,Y-aOv�tning� ,�:tggsaB� ly c�5c�J��� . A te�pA&JS%u"2�~is8Hi|+ VKanG/:�D "�c(3Dn^'4Kd �Ns ([5];��, Class�?�Od_�"�}_C 6.8.� eu� A�� �pre!in-�RRduef��pag%#��� �cya-5K %�G�cR� how�=�#�OP�~o��ax� f�5/"> �pmes�� :1AT��!����! )�S�ow)�8�, (/�$ $U"+. ])M45�). Our"�/m� w� N_(�V. im!!�a�a��Ns�X.m�@$��My! �J:N�R� v��4cT N%way%`a�K � j� &�>k,8�*7;6q@."� N.x3. 1-VECTOR\ LAGRANGIAN\ WITH}\� N@M,�R�wq|���i�k�/"���  a�"4st� ng%n=�@A�� �;oJ�p�'+I�:� � 5j�au#�1 2\�T9NS%*��"� �AQB� } L=�*�  (IF)-(I��� F-2! +j"F#LB� \L$�{L� N� !�D��b� ���o W �co2*�n-{L�xL"F&�!'� #��1"* ��{=�-� �I)- ��  �&^{ '*|N�N>D+26`a�� �}j H*aeLu5h�$�$�sSudber�mY� [2 �v var�W�Crincipl��pF� S=SjX�)( �h.^� -p4}x�| )� !;� }; �7SF�Z�$���)+�should�*C�[L��-��  1d$ bVfix�:L[lea�So Euler--I&�E}W1�\E�u7=�&� .! &-&._{�  �R@2U0!.R)) ]�-(AL&\�mC 6g9&A�)]R 9�.PsEy��[,6a�AY, 6a�B�-&$=ME" mЫ�A�:�/��<q-��aap= �/atR!��5�0�i"�v���0< Lu}"k�1V@&[I \H�� 1O1� 6�? }�/ {,g6 � .�&��}. 3\ }Ez�?� &�0�r|��. m�-branc��of� �@ 'Fbe*P�u�& public� EU�1}�4!�&�  co#*��\d6A�b�i'&� )$V�L.Sn)� 0_M� <�V�}�n� �T�v�EKi�Y8s �EN��.�b�� 0-*��(4. COMPARIS��4\ EXPERIMENTS.�� �2��EXPLANAT��}\"�2@THE TROUTON-NOBLE.I�K"G�a: A���e�A)�v  (SR)��v_O�@!�``appa�''&�rI�L���/qIa6a] dila� aim[sn-5 B�Znt SR][`�"�Ga���I�%*�6�}��|d"s�5�a]E��.�`�4].f<[14P� JH'� ��d � n ''=%&�(� !EtruR e)�!K�Dal�%moder�hp�>+  to�SRqNLMichelson-Morley typF�:)�``muon''�6 Ives-Stil�>2$ etc.Ae��sinR�"�3!o��5}��c;d+��i��p6`��%!�"� "!zI�EXh�`�s�7 n�M�)�y sign��a䓍�I��LT�2���� n��\�E6�i='� �Dal Jovea�ce (emf)'K�8 �Jp.ڍ�!I��+�w��k)�!�a�&u�a�EeO2�,ւWP�TlyI �,�H�)B 2LBF^7V% alwaysI~��.D&�F�� ely �<�ǏM�I�q��=@��Z�K��3D&5"E1$" B -`| �- :�Edn� "{��1��u�� pM���ȥI�emfA� .�D� ely -i�=�55)%�(58�F;� �Ia desc ٱ�picP� he6�*��[22�N18��-�`Y�23�IR܍P#om̸U��!Ye;�.&=��{���? t�M�%M%,��L5�M^=IQ^5I�s,�-F61-63)a�%@ b� z0proof" �5910], �� &i l���"�Rc�.Bi%okj.$Ls.� i�%I3����w�Xws!� ^(� [2��A|�� [25]�y�.e�a�Lҍb at =i��$Am! fKa��Gy lookU<LI turP��A��@rY�:p�&,� susp`�daJ�E'E� eart�� " ~W )�'sy=� �=K�5����g�� until�h[26-30�1&�I%� rein9�.��m�9-s%� (!�� �%cUP D2]�e�,�� �&�?4�%:;e�ס��"nm&4*^o;�&�J� A non�*� &gt4�?d���Cf�M+�%+;s�N- 5torn�a�C, � E�b "��&���H�.d� ����noap*U�. H�)� !� �`%�|2"�MG�C��iY>R&%��a�U6o!�.IZ !�(��N �x�:��*Nitn of opa�.�r�giv�P� �S.�%n�V6Yxub5E.i��R��;%�Y�'�y2 q�mf1�i��l��a�!tůi�BF�rY5�aFq-�)�5 us iQ#5�(!?nop�*���'"  ���)��_9��cana�appearObe�Z�R�OuJ&� L&գ.I��m f*�Q[:�V�:"� �i!�&� 5�A&�7r�m ``]s''A`!k6��.dox�Nw��ami@�2D''RG%�.�V[26"��b  +a�՛!V�s�YB��5��� '6"ޡ���.�achie�)inevj t�D&/ V[,)Yb{����!�trainta� "~�'����I�* en u�!�S& argu!&@.���`2�:�+'t^W-acc�A��r�H�X � K.!� : ``JntribuA�!� &�9V�y����s� ces duE�"9�!E>� ��Q2.''f/>rg ve�.obj�2%� %�[33�1Rshas 3sto do���[ore�a� �&b��J.� �"> MW~�z�O��Xm�1k � ,�ez"��\1 s.& ��% igorously��s���A^� draso�齙X�w �2& �5!Bv�Z8���!Ja!H�x%�ardV�}lbeg��O�6KbA�$�F q !h2� 2D.e%0�� %a��al}���� t�\�&�t�r72uPnotcnir�0b" [ /ve&� i?4D&BA��)e�v6is@��"DWE�LT$R c�pQ[�5���1� R� �%">�o _>\�UmC " Fp�e)T�.�� �& �� a meM�ical 3DQRo �Br�t|5 U� R rat� Qg ,"{#>�e��J� �a�Kfal�s � �.L1v6AZ��!h� =1Z��%�s a�$6]�>J�� a�!7a$one: m�Y-�p"� �+u"� "U laA�a]�I�3D��A�t"Ws@vOt)-@ Jc N6��h�Z)B�!QB'ifA!"R�,.���WX�� ç�0J�! �LT �.�*��� E�M+l�{!Y�b� %� _),�,_ @Q�&U >�nd vm%k)ngp6�*%v e Ai! erefk`"��)� in.�`�(�))IQ1�e�i�(eFM��!� 1�>� 6��8 Aaܠn��p{ct���)�>�F5�)�JG��]��! �a�(F- oA��uB1Z09V�fA�3D�<dJ��`!*� w�1m��(uig.�5Q�)Q� az�  o�,q2�s $t^{y�}=A�t."j1*m$x$y�) $\ThF:%�� 1. wv*�Gd�kd1 � k1}O�p���A�Z�$!�&2�) I1|.$)�$AX�&�2wtar� �u�'s ��ma &"��;{4�i� � .�d#E�l6hzu joi�U!�A�ro� on (i�middlE�neg�9�*H6'Q6 �%O>>fxi_6at ���V<��$% 9�N��e6%�A�m��.mK_,���)�eri�d�a.U5e�*TIbV ing ``j i L�myr�y-����ra*�aAI�r}�s=�:U~@�� C"�� axAeF (Nh=Y&/K&,\ N_��  }+(V�@/�@)rC �_ cl.3 G3g }-�G2.G R(F�O"wC =(1-.�^{-Mla�K_�iW} !y? &M A�3D��cr6A� Q�Ae� -&� U+Y$r�29#s� 6sl� armq��B����"��) &a��an^ ce, 2�:+6�, >8.���%M��%s}>F�I� (1)-�mt.) Ч6S�exI�1Z9D6o � , $N6H.+C( _{ijk}r_{j=j)�kR (Not�K�n�s�!�^:k�Xis�wWv�$� ��_�!/ {sk�I&�:N�2� a�"f-x loJ� d (g�ic) sub��6� �!�sB&�Q2'�Qefe�F&t8�-rank O�P9ic6��$ :Htoo�iJ]�B��$%�d:2Jef$�ko��.2NU���Qk� �ujA1R�3}=�x&�6k5"�-i�%8�j.\V*� E`�#сDwayAu�)� "� adoxrm�:� ��-��t��-, " 7!RI���s� i{a ���[EyB" a�, era�M�� vh a��Wan make�i %5e< ia�surpris!%��0qdar *d�}40�r5 stic:f� rnLHe��s�NF ���N"�conflict�|pw ao�Ήv.�t���)nd�7k5�8n)�F>z<�at�]��bZA�6�*)#by9q��&�a��b8��� V I.��@4d!��!n!6h�jn]1!LTr(���S.0tL�"� g�s)*�:|��B|!%(rJ �61}= �,\ 2.�&9 D3&&� &�YeJ��I��>� ,�W5.KdJ.cl?�26a�,B�!)�u) 9��� ����)�u,Ni.�LT w9ba}x"�Jy{. Such�� opinion implicitly supposes that 3D quantities, their transformations and physical laws written in terms of them are physically real in the 4D spacetime and in agreement with the principle of relativity. Actually such opin��prevails already from Einstein's fundamental work on SR [12]. The approach of the invariant SR [13-15] and [10,11] is completely different. There, as� explained%\9F reality i1 s5xis attributed only to geometric!I.�,AQs or CBGQsfir LT ��.� priNx �utoA c%included�$such formu!�onKncethe��we Ad�ng 5�Lo!>zHxce $K=(q/c)F\cdot u$, where $u$! the veloc!?1-vectorA,,a charge $q$� torqu-��AQ,Bdef!� aa e bi D, \begin{equaA��} N=r\wedge K,\ r=x_{P}-x_{O}, \label{or} \end8 �r��$associated�,lever arm, $^$%� O re !G posi�MsRN0spatial point!<(axis of rot�aB.applic %i�5�$, $P �O$%�C,events whoseR�!�F�0. In generalIproper 5�!�for a �particle!�,$u=dx/d\tau �% � Ltime, $p>0momentum $p=mA^4 angular$of�}-Q1 $L=xM!p)Iv, $% N$ aboutorigin�D N=dL �N!pIE� is reia $K�,an arbitrary!*ceU. Whe)�� as a�$ S�e standard basis $\{\gamma _{\mu }\}$�n its��on%�%�K^% }=(5Du}K_{cl.i}V_{i}/c,B1}F2 _C3})$,U�com|ofE �R��E�$u� 6�2�V_{6�V_{6�V_{�. $�(=(1-V^{2}/c)^{-1/2}A�1$%(� mQ3D-���$%*>+�AH3Du. We see� �w!�'$considered2&4at rest, i.e., k=0� �%p=1 I�Fequen#=:c,0!�tr-� }$3tains � �5�9 �Y40,)'1} 2 )lHow��_)�at cas�-� �$% V�A�:�of�7 \emph{4D} �D }$u$ %�a^�f^%�noi�9�nsome i3.Z ,} $\mathbf{V�K}e8}͵0LT correctly "� � whol�T �y� ich meansE(r�'no&nsensea��U��Ds like (\ref{efi})�  s});Sse� 6!o!��vistic: theybas�&ca8ty. AllAOwe choc� $� 20}� C 0� "0mYsystem�(coordinates!�c��iEka way >k3�= (as�@Fig. 1. [30]) givAi>2\m�!0,r_{1�}2.<0)$. Further, si@ 2 we E�ste���=O�J%~�� �O=1�H !o � V !ioa�d1ީ�3�dw�vyields��)�;=��5���F�Th3 we find-zA� S i0}=13.2)����rem���32}E� O1E� 2I� A� 1Y� pr]��12}� lsoE��hall us!@eault�Cfp}) ob�3e< Sec. 2.4 $F$A�,a flat sheet��%�on�`$t surface � dens $\sigma ��9I�R�� Q�E#A�&z �u �$itf}). TakU�u�� �6)�v� $v��observereJ6��a�$% v=c��_{0]K"UetjDQ�r,``fiducial''�,Aye[M$F5�AyE��all oa�.+A�������n]$can employ�discus��%t M!L!��)� elecfax��a% �-"c $>b��0re determined�:b��$produced b �0negative platF�v �loc��A���7 m��ctAmo�e:HA%alongd$ line join0�� "�( �middl�6�)yy6'>�0All this togeE�>I10� se�0/2\varepsilonE�()\sin \Thet庉�A�]�20}=-(jD cos D 2�nd z V=DA)(Y�10}uh٫ }+#2#2]J)� �s��1}=-a�J�,.) 2}=a�� ��,� a�said, $A�|!�awaMo�'sI�� $a6di�Q ce betweeE^J7E��͜-�21R  AJ�a!s1�V�-!5FV-)�u�l �� � ���f!7Rtn��!"]eft � . S� o $"� )��UN].� � .�n� vari��  up� pass�KLT" �-��  �*� B4 9 but��s� C)�M~ tT� � zero!e>8�� �nu =Pmu�h9B�w�!W =0. �en1B�v � �is�9C� Nt !- ! mo Y4as well..�Q{ao".� -�i�&�,Trouton-NoblA8radox. \bigskip � \noindent \textbf{5. DISCUSSION\ AND\ CONCLUSIONSD}.=i0 ��<��ts`�xi,� �to�T$omagnetism!? !Za7� �yahe ��6c��% �n"� �pe �4"ry��I��iW��� e%one�(om:�fZ%�t� MEFl[is�9�- Da� self-co'a� lete� � ist!H*Aio doesE� makeO ei�a)i-Tc s!T $9<poe$A$. S�5�� eptu� �s) � ]io�^M�1n s�al� ,pects. Firsmt�qcI�B��%%8 centr�)�etg2��not�usual�A "� E����� B% }$. ] on}"t��"@to ��dUX� �A�t suraa�]y,�2K�he end�� 5l 4.�ir ��d�0is manifestly"&^"�}; itT��V4D4Dū�sh-�� spli!�" foli� �-,9�\int anyw��!�o�)�connec��Y%� pictur�Ss "I�I� Q�)��given� � sm�m or he� � �T�IIos�� s0 !="ntrastA�co2 d�� { F$, e.g.,i&[1-3],!o��Y;��E}_{H},$Y�B$ [1,2],�U�-J:-H% _{J} $ [3]. Every5)S��x be&�#o � cdspond0 1U =.��f1�as18us;��Rio��" $M�O>�t � �'I�qC��w�2�q26%��paper.� Mse����z��) cedurTnI��r��umx dynamics,�Dc�rucAwu�se&� �� ,.z�0$!{�USg)$M.$ Not�!�� co Q"�Wo���ME 34],�qly�f A�\� �E� (A� pecifi�� B#&= *7)Q�>�4-2o  (t�requir�.gauge!Sd� @o)⁄�& %�i��,ŭ�"a_e i;S)�law���diJQmɶ�>m% Yo�i3! "q�2.7�u� .� ��g) >lj dk})�Շ��h eld Ris quoA�A�"��� 4. I 3��hav��nsQ�"�"0Lagrangian $L� L}),��,)�a QI fe�1� �! r��erm is =a�t��:� A���2a� 4.�!*.aA�� it � Sudbery's.)[21].D � q=Ksuggest� ��$l�?'61sm!m| rŴ,#ly ac� ed �'` BK�� ed exJ vely6 of me"� .We\ ��or �� V� N� �T j y�D��f� A oF�(um mechanic3 ll��= � else� P�#z it h�%o/mphasiz�a)u�2U� � ��-��uI�i2����@ �z�6�ex9ng!�eP%@t?eQj� vity, i!!i!�7k �e�)iG show���aill ���<6eex�T � ermore�VnմallVH%��� *5 w � p6s2�q�tW*hol� 5�e}both mb8�:cur; "� %�&mal�3 en�C� wMOt (a %I du!xo��uBxu, %u�,an�4 ��%�.�dea � ���  J�8ACKNOWLEDGMENTS+6�Iunk Tony ���" me A&cala=� ��ankZ4so Larry Horwi�) /o/ u"W,rt!�fu�m �lex Ger�, B!rxSchieve, Matej Pav\v{s}i\v{c} (!�fLipaal �0 (Wiley, New Q�77E A. LTL�*u�,E.M. Lifshit=[CiT0 of F: s%�Pergam�Ox!u�79) 4thEoA3W. MisnA� K.S.ThornJ.A&elqOGravi�# } (F\At0San FranciscojL0). W.G.T.V. Rosser,y��-%�sm via R�� } (Plenum%6y�86�6.A�� 9� Ann.eIikyJ�49,} 769 (1916), tr. by W. Perret��0G.B. Jeffery�5!~P./0� }(Dov!2�1�526�87. Yu.N. Obukho�uF!� Hehl��v& t. A�(311}% , 277N8..L2i[.�ofYMN�(Birkh\"{a}u!� BostAYMA�bqA�8 G.F. Rubilar,P s/9907046f=+000508-&�9a�TJ. Cruz Guzm\'{a}n, Z.��Q�Bu� Soc.�Z . Le!U,L\'{o}d\'{z}9`53}, 10R]D10. T. Ivezi\'{c},�Ig. p bf{3D339-�;��/ex��(0411166 (}t� publish��\ }:�A �ers))}211B���s/2$0409118 v2� .��b�6�12����17}, 8��$1905), tr.� ��a�} ��13B$1%t-�Y3�11-�1:�4�N%�T15}a� ��2](0103026Y9 01010916�5Bv8hep-th/0207250;p 52776>$6. M. Ries�_�, Numb�&0 M.A. Abramo� 1J.EOF�9}, 3158��98)A:A!�$ Vanzella,��E Matsas, H� Crat��a� B_64�(5_66�20� T. Hy# zK�19 J87). G. M\~{u}no}�2�O bf{>42�>2 1��Y � A:�h. Gen.�$9,} L33-36�8>�2� 0K.H. Panofsky!�A'PhillipslC"� @�;y"� A(Addison-Wes( Rea�, Mass.W 62. � 2�3;  NSs,�$Rodriguez, pavieri�E.ni�$% Nuovo Ci�o B=\ 116}, 585eu1%� 2P�  G�|1�R VR8��0 R:924 T. ��H.R. �#�!fo� ransa�� LonSer3 Y#202A�6EbBu,5. H.C. Hayd.�Rev0 ��rum]!Eu788 (199: 2� K1'g�;12� A��W42i�>7�|von La�:K . Zeit.'1�00L1:�28A� Paul=�&? &� } *A "� ŏ2y9���Ueukolsk}cZ��6104%9:W30. OJefA�ko9�~�32,} 375%�9:&3F 1IF���B�)O5�92�32 �ra�f�E�}K hbf{10A� �7: 3�� R�507 �234! D. BjorkeiJS Drel*f 1� stic Quan�JD% } (McGraw-Hill, 6j4)a� Mandle�yhaw9 2O�" 6N95��WeinbergEThe-FitRU�q�it{� s, Vol. I� �}�u �5%Dend{docu�} I�\�style[tighten,aps,array,epsfig]{revtex} %:212pt,�7�bliogra� mP{prsty} \setlength{E�he�,}{20.cm} %� @0 - 1.125 - 0.875B8$width}{13 7 % 8.0 1.37  125f69,opmargin}{-192oddside"1.7cm}={rs� c} %6< % RSGUIDE.TEX %J Gui�4~)paM TeX �le|Royal %� iet�86>s u�#8al manuscript f,) submit�h Pro.!���, Febru24��"oday, U?,wo years aft� we decQ&K it!��*� E-prA1 $ WithF=.m��l%D� {vacuumn#u%U"p6�,p�numer0�%e!�es��7b�0 carr&out� rC!�!SI�!�Schr� er E�B[1G$/Predi�(of �y[2].�B(^%l�*-affiro<viabi�Dw) . Our augAed re �Iq,is --}t!���6s " 400���is re 7in x6r)�E "!~leon"�a paiFA:b� j%�oIitaqgns��)|%tW6qa6Ccuon". �s�<anA�*-�M nefia�&.�� Prof� Lu{.)�����He2 hopAeo;!� se u�i$�<{- in�( reM.1[1-H+eJ� s e()%upcom�Pe s.�L \\ HxA�4iEFA`LG NsJ&is:�K=�!|reaso� /AՁ�ig�TQjyM>�f�{��aa s�JeN��I"1Y�F�I#s�\�bFmasGI de� pA��0de Broglie wa�A��A�. ,ejins!;i�"k�5�! backM~in�AZou5�Ѷ)�,��!��+E|Ai� a l��s�+I��Ir;�3IXmp�"rep��dI; may no�@ immed�Hly�$ssiblE%(�Hof)Q as.�&ondIF= mark.I��!{,�* /cir�  (among �nE�H hysi��?a3 � $Q�fidea�ndeping�%#authoy � Req s:} �jJ. J� P6� , "B�\"ore�8�)�&4 Wave*MŖingle Ch%�$in Zero Po�� F"@iscs/ k34,�4� [2]V�,:��R.��, �6TU�al^�V9 �$ a Di�$ Medium��sics/�245� [3] V]�:�, �bForewgby>n$ "{\it�f�AC�,"!�2&� �*�1tce5[Horiz21in ��ic!�C Nova � ce P�rs, N"�!200LISBN 1-59454-260-0. !4]Z��)6` Basic LT+of=per�$tonian-Max�7J*S�U�� �1-9�, \title{{\sm�] �� 6� } \\ 6� F�xz� \foot '{%�Aq��� � So� }}} } } \�\�F=$^1$,I�6C $^2$�T1. IOFPR, 611 93 Nyk\"'*Lg, Sweden.\\ 2. Depſ$Neutron Reu , Uppsalaa "�" P822P O y (S"� B� ; Re-���M�  1� ,) } \def\�� ({BE}>#arab{20  24} � ate{M + Th{\>? ;a�Ff{\kappq  _q{} %b2G Bb{��BBo{B_0 bl{$[$ r{$] c 8c8CorA�c Corss}@! Prop  - .  one{�;:two{2 �three{1Efour{4 five{5 six{6 hK{7 T{8 nine{9 ten�)ve�Pn{1� elve� thirte".� �f � �i 2� $.� �wenty{201](I{1} % a==AOic �II59III57IV55V52VI51VII5/V9�IX5,X9*Xb{10b�XX�%��{QWXI9MXIa{11a4II9YXr5U XIV{5PXV{5K XVI{5GX�5DI{5@ XIX{5;.�XXI{21�X�2Qh I{23�Cmd{{\��CCQ�CmA� widetildem+*c:*uD Tbf{e�T}{�:);d{\deltq�Dk{\D kM�Dwwlam\lambd> )t6� \D t�DL , L.tb �D6 Ef{\�8sf{E }�%? %E2.s UEfb{ 6E) (Bf{\rm {\sc�� Eft{\Ef_{�Efr ��Ee{E_{=q}}� Eq. ~Mq{{\ M}3a���bE-�E�[E�:� iE}46�Bcal �gx{->�x � �xo.��B�f{�k ?k�g{pA{}}-�gc ^*vo _{v_ow/u:�� ef{{}_{ef�R�> e{\nF-�Etot{E P P etotlow>1p p 'Efp{{E_v�I�PP   Efpu&� PP  (efp s_v5�p p  = ph{PM{phYphU�Mph{M2. FKph{K2emphiph�eph�v"�G_{\.!p !p  �k k �m m �eA{ H_0/ �ev{y \eA0�0�(fsD{f_{s{_D}�fsU U2R R2L LF6zF� Faq{F_{aqqaqahp{{h^*1 hbar� �im{\i� �k6vaq�L6 LYL:B \JmJ+{ L!h%8T TlA�ll_��w�,lwms{ {\lms}. GLtw{L t.6L\A��L KLK �Š2�$Lam{{\mit  �� +Lamdg: ^{\dagger�f{\lefљ rt{\right�efm6T:m nlam:b�!2 -#BBbjbu.J{*=U �N�%�:)L9 Lmsd{\ell Cl>��K:Ky Kdg{-P=o yKdBdg{J�0B/m�omtM Mmx{ m_x �myyzzqq Mx{ M8My8MzzQMq9a vx{ vGvyGvzvqq1Vuav.�u�ib{\vec� �jj�" k �)zmuv�_ \{a +v\} !��lpuv��6-\pa�# +v \.%m_\{ xmux 622pur:Bo  % E�gu{\g_:V2�X �guv/:�ge�2�YXuo�K �wa� m-z .�U�p{\�iaq[p:>"�p6yP-P1�p "$his{\Phi_{ O*nm{n_�nu6a\NUdnmax{nmaxH) nud{\Nu_d�td{\Ta. lamd���) kd{L  KNBKTBK��:� C%� Kd{K  V�nud�n.�t tB�+�^ \kkk  np%&^{�M� :/:�\n!e Aul�L lam ~ kkw\omeg!ta I�_ 4TaByTau�sigQ.�F� Q: �>! �� XNueE� Nc{N_c �N��� VUNu� ��:�NL{N_EJ2bb:ݬNb��N_{b:A0�� �bLwwB -:XU�NfNBT}2Da0X |nUUwnRRL� �?ov A ov{/ B�:� r� "�rbab r}_1�rb(_2R �F F�pNp.NpNp NM g ?gAEv ma{m� mb{m � rav arrowQ�Sct S" S{{}_S-S6�S�Sp&{S's S �S tl&&N {S��/t{ac yta> taa� *a>Fa�? !T6�"Y Tw{T�w w.t.{TD>� tDe�q� � � it {\topu�T� "�tG uder�I� t}auq/G�by-Tai�z J�T:*�!'6�1�t:�->sD!':� TsU U�sR RL .� tD{t_a�utUURRL�� �ao-� A}_oN � Ac{{ \psi>Aco{ A#E6Aqf{\Ac_q1AQ-�,9_ <o= A*� Aqo{ {A_qE� (coo;xM�A2  20}{�da *d.b � }d.1� .(Ari$_{K'_{>}}^i�i7 ArrN#r6#V$2%avH9Rs �so�� mAsAc}_{'r6o !^��lR&'_{<}2'in.� MJ'�h Nl�2$2�l96%2&M�ՓAd [d%�5� �>.� <f�Ass{s,{\S�Y.� } 1�Ad dd)K�ef\AZAc.NU>�U!�cal U.�4Ub{\mbox{\bold� $U}$�6�AA#E�� v*.m�V{Vѣw� Aw��wd _d} -U1P�Si�DpX\tye:\ oztex, ca/Mpr+"mM�Bz  � W{\O -�Wo *�We&�W:a E"� Wd3&� w636�BQ � %RwM� �x6Kx�y6yz6zY�zc{\zeta[cn2n.e 4-3z/^F!� �xic{\xE rm.WxiX V 3:S�A�&��6zU�X:X1 x�"E�|p �X&�9 �y:S�^uY{YQ�B� iz:T�%�Z{Z}\Y�,�*} \make� &. abst�J } %{F(&bare-),J�&�!:v& & ', .�-of&*sj�- .} F'&�! meWI2' ��(a8=al DL�T�R$Dirac kind�( a��g pivo7.&IHa,H�%*|aaFd aB#KGF,}��%&"'of]hicF8s. A �ceS�Rma�$-O((�$�?i W�Te�Va tinOree%��*%�&1:al( S^urb2F s --V&�Cyg)%H j�7c6* �%:yt) +b' um. �hin mo�G,f)a�'ul�!-1E�)�4source effect}�(U-�/w exhib�mQ#of Eo�< Eo�+kn7J�(a>�N*is JIr9�New�[3} (NdB)5�v.�NaA@�q�I�e BU$2�!}NdB6G�ePval��S0at �Sby(/.l'B�0E4Throug�*�#)�Y�wej)ac�K�@aMk task!N�>:�"�1-%p �-USs},�J!�.K dedu"�/;la.fa�ag0!�converg�H� 3%"�0�rt high �*c�-. 5com*A�T�5eunf�Ko�p8)�[rii- phenoqa 5tC%RE�eB1ras*ionM>absorp, tomic#f.mal exc4/o�& �C iner��+ �\1.4wavefun%�`:�.BHei�H(erg's uncer1t&�XHt�JuN �� simultaneA2 1�-L�)p.tr!'orQ�l�3ב L.E6r x-},"KF's 5%TVuice}�, etcE6e 3>;facN2vka6i��"�7l)e M��}��w:nesa�inE`pa(1-, II; Qwf5 Qt_dO�tE�5S>�ar�fnned. 8�ˆ\pacs{11.90.+t, 03.65.-w, 45.20.Dd, Bz475.-b, 42.25.B�H%F79 s2\ { Ia\A� }�fvSecI.I} �9�W*r)�R�@0 (1686, 1891)h> �e2$ 900, 19263oHcn �Pb�Se g� RgWU�!;re2�J macroscr3�vmi�-�%�J�We 0�As// unun91up��Z4. To r�� �Wa:� of NxTo a minia�seRY5�`ultpe��f ��Ozs��N��0����0a� o�3�[!',pi���\el"3%W�.>�*c,Iu�ell�PeKbe] wy��e.l��nE_t # beaB9=2nego�+ (it!�aSp�/heir ?0��E,ok�5Merzbac�n19�J�w&�Yi�ox|q�:y���o.$�B�8�6 sacuth1x.�as& S��c�_a�1 rB�6�16�}���*U�} scap A �Qm~Ue)�siz5w�`�Ys��� >.Ie@`U���built��3emost��cer`Ywo�kof �i# e� ih�-it���;DQ� {:� �@#JSF ces^ta5npla|].&x/�?F��2, histor�: ly, �P�2s empi ru<of�TI�� D n�2en!�je�[tou3lu�Gb�Cy.w6 �=!S9M. "<5a ortZ9��; woul�\L{%<\y�� � a�� truew , ::!yFASs @i m. %b)��.a�coF�b� olog!�:� p6�!�a!jed �W%�uts~Y�qu�S1hi�q(to unanswer%f"* :I%W�ii6g Q�5?}"u�v Ig5��F � � ?*� rwa�hin N A�/or!�662� �nɗofV<?} 6�a� �ganR< tur�^= be!c b �8n, EPw!UB3�3 vert�Y Me�=e �!1�2�st� roaXa:�alRB�6xA2A etB �s�W&T]]�I} 2ver��e"�Xa�Xd�3u�=giA�B� ��g�?�,_a�4al� �;urace` �garE�29�-t R�p��ANec.2� I} avxA: them�'�p�QC_,�}rolla ��p"�=��= ketcp>ͺ:�����[0^i�X)GB?s �iuAv�j.�=T s. F� (!X�>~w�*e�ync�c��]i<eluci�1-ClP�zI* V} -VI8<��^�!W"uE / prota6�*�Z"�Ey����orQun�;a� urb�,BgsR3"?3;- re�?+&� malD M *� .E��A��w� va� "� �g>�BN.:� E��bric�s2]pra=#�~"��ap y $v<<$ l�(, $c$M;�[qzo-U �i>  (>cCa�JohqCHB42), %[\cite{P @II}], wA[fer�� R��&�;�:fur��evant6�evi6ZIq9�la%�&bc t�JY�AR=Qnd �;body oF���a to)M� ed Gal4?-Lo{�6nhto�t�'�\etisE� s ri�<o ��me�2}< veM�}. %W1h� *�E�B.E�;(�� %of �xa:vol�:f,�ao�s���Wa���d�&�&null/�!�f@ e shif�HHMichelson-Morley/KeIy-YXdike ]IDoppler�aZD!�eu�cZ �'sAC��m�*l�&� fram� etc���veyY uV2Fp�F�ms�%�+� gime�$c$. �F%�6� }�YWA� -Oo�FE����� of >�� "e��L�lH��ncipl��.� Mo#��Yya�h.�@P7��;�WB`ٟ�j!� sF�W?3p &�E.7i"�| subsAuiA�ieRy:% I} T� ��@� emptyc�kre�k��'�s-97M�!�nd"u|92|933);pG <���BhY�D��)LE6] (QE).��n�qthelesz�bec�@d�p held%��Falff� ��PH8l�F�?B �ti"HQE.�4��� �k~7cF� aJ��n�b�H �h inpu!13%*h"����H� -� ure---�is �nADlyh~ͨ�F� f5� FvLub�A& -jtE�f"4|%m( nd annihi�E!���4f# �"ea�"<@nucleus' Coulomb Ic�Q}�� I.AA��� l!pr�, occur�� say�,a�@( $r_aqzrites: � eqna�M} qeq'(} e^-+e^+ \O1�'w+ @B W�m+�o�F -sig?p�f}m_icx��3qweZ5�I�( �)� �ra%��1 �!ӑUA�U (Ref. [a]$ as1�I�ly jus�`R�zLs. By �-�ɍ}�: �� ---d�n/ � unti�9� ---s)�ed I� apar"�pa� ea�l a*jenergy XI�t) $U(r)=-e^2/4\pi \ev_0 r$. S �A�no ext�c}uc"t n�� �s mus0Ms4u| �"�| LU_a=U(r_a)$; cf. FIGfigI.18m-aID}) $\E=-(U_a- U) $Cmai�; N��aocp�. If now%>CI�w�r'$}n $U$�xb]�u��o=#Jne�$U' (� '))$!n�Dby $\D U \ (<0)$ (An $|U|{i�  w|U'|$4|S; U|$). And�\E(r) ��o' 4\D \E i$= \E'-\E =~� Z c��@on� $o�abσrei�a9$ M=U'-U$ %������ �s:n&EU�(8E'-U'=\E-U \qua�� ) \q {~#or} �+! �,+ |U| \equiv %C�m ant}��Ru� EU})�J�]t}!� i�.�L�Hun"g{�az!�E1coʼna-���L� E \�erI� �J w��,���, w�hSrue���~r�"O�O���.^ pairZ�:e�_a)=U��$Ag0a�In �par�3�c�-���v���w(assu�o�g�0ion), $M_{e^-�y+}$@'��%Gnot��2&�n-A�ȁA^"%2��ched ;�ray��- t�{relm�wo'�$'�UI! ) do� }wM� ��$� �)�m5s>�ohe 8��* K!�Eq.wAE,�5�k Q��ref��aM�eIt(%�)a8(r)| =����)� ��!� @%qs* �x!!bm*b)�.�. /B /�.ɩ" �"!� %�7$ inct� e�6m-- a "A�"%Aa �G  Q;! �wards} ris){��.: ~. B���$\g$'s}�A)� owM �,�ed �"�P�vcV%=�}!���zP9 as ��ny��(m�atto-O� G. H(we%����at, "�%fil4uch)���N�? �r����ng RbEn� QK]ri� �K��� � ��h�Ksy;�- �Q!cO Q�u� theyi I\A�ub�  �tsp|+ofSJi17Afim�KPras�. >X.B} TG61fact �Oi.~-��&itr#,�3.�"�};+{ Whittaker�_60). Com�! "�^b. !�jsqrt{1 / A$_o \mu_o } i=Wqa\'nd~�" �: $c_s= \F/\rho_m��(!f0inuum limit). e�a� �aee�G �Ar�9-\$�, �$c�, r-�E nearj TU H�t�nA�eBe6 !$�.:�"�u� 6sor'&for�( qualN1.FG� :Q��#� �i->ha�r����act�few gjQ%Ga!Wa5E �-�.� EC� In6aB��Pr� yOowa�_4Aof~ M�! � �I�8���ady� �1ٍm$2;10's �)�ce�z"ha;CT"� vt/{ �!���ref5+ ind�/���2��a$c$��� $c_nF0Bh4 $n$, by: %\b@�k�$ eq-c1x} ]= {c / U $ %�%& M^ analogy5/�,}$av� opa� �2�}�i xq� e�n})�5�N�&,cx2} $c Eu�r} c_n�'\ov ho_n��r)}��"�},F�w}+$=_rE� �`�6!�Q�@uNisM���or $1.P j2\FAWQ�m_, S_n$. ��� -d& R���"typ]lyY�ny\l- per�s�u� % |s� ( }�Yi�* alue��(, diamond Cœ $n=2.4$).�'2��FZ� P Im�&� l`*T-� to.x A~�c6�D} �dg j ��* ~Yof��la+)W��Zsi!%dnc�/�Y�o��of coup "*Ws��0llmeier satis��ily�m�+.�di:�,4. as SP's "�T(1871))�p472, �<"!�\;�Y:'�"K�ma.�a.@?�a�A:hZj�B MierA �rV0�Zal+ I�"(*to- N �a�3 VB�!is` A�o!������W�{��=��X zz II� �{�y�J�� heBa.�("~�+81)"� :1881}] � �z��2�"�3\� �1�r^5����xa2��m-� *  keep: ** %Z� �� e (asO)PX/�$oj�) K!C'sQy obe�3 �T}� gle ��� �� ��Y �*� dK5�>(bZ�aURB)�n5}o�cJu New]3�,%" �rF^Wc.�p� at1p]*6�$erty %; nu�b:��� or�xed� s��& ai��^ � M � F}_�� 2�&�q\v&x#a�� of� m6ref�$'�2ng Go rburLc�r:yF }]: "Who��r�)��gud d 40 �agoe�:�!�m ( - \ldots - Jz/�+O�elpr��m�2�?�g`''� 1998 xjexpan4 ə�045acc�xaXisw4emb�s�aU;3!" �"hj"p�k-�a�5k:�V�2 \one-�V\S�C&�&Nirt %2n$�6E�Yb)�+pb$QS6_ I�9 Ba��2�&g>�'r8!�&�*V�!�us}N�'}��e��� sJ &nM. .�9---�!�Av&�iV�7@���V�%h}\n@��XT|X-�%�.�*!�S�� of Vg: �J \ \VntKone.1. %�A�!�ly*�a s͗n�ZalOi�-;N}�*ich�C!��6eT t i�&�gy'6#8ts. } � ���wBp%�i)~��V"!�},�A�a I%"�, $-en AOa �bf )cv!"<}MFM+e$ �Jq3! !��/itޟof $e$ l� *�(Gg�8.e. $e= 1.602 K�(10^{-19}$ CAH&B�� yb (R.A.Mrk"}1909))f�4� 91=Q�!KutA .U�"�6 en#pe �v�54.7!��dE6dA;a� core6�-,?-.@s Es`;if�&�at �.�y^ rDb�NZ�E�V� e��bI�.�}�ee��@A�di�wa!�(��e-�)d)�*I�6b }b� #.� a��*�;]d� !�rR-�� �),� � ���� �8ion�6awq a:n�b s�-3n"� k}�" �%5��u�� v�=�"� E_q$Au�*3�ݭlO5r�,� \Cor. \V)=vfree}.[a�A-��h}V2T V:!{+ n.ViIis n-�e B�a z`dki2� x>� $�S:�. V.5}*�-IV.8}!2ut how%��cx� ����Uio4j�.6)�:�&D�( � ��ail=� ga*�=&}� lso,e>K��8,ADSsm spin� virt�3f09�of��j.� � d li��to di,0 4 s�.er�"t(@ plau��$��g���� ŠA; p-oYi!�ja">�/ey��.A�exce~quark,"F�&�s[{iYe�-`�Vf ��[k�&%aVsN�A� �2be focu@ AgT*� � � ��-"�"���#1-Qa.�,AJ7j�-���-':N":*. TG twoc�nn \�'*t&a&figure}[�] ��e"\leavev� \h�G% Efx@8= 8 cm BJ$.ep J.Ucap� { 2 B8P  Illus�$SESu�.��+�?��&� �'(a V�� �,U (�� ve-�yiC�� :�\le r_1$c~9eX$$r_1. $U�(da��N�)��]pulI �superS�(!, dukA�16ly-(d.�"�E�9sur�oA� =���h�x. ��=�] =um*Ey>���av��2r*�!8. � E_M� %\vk\e 6BV*{ad ��)".j���� �F}�.2\Sbi�&�� &u( 5m�R �(: \\ ��� v y \I� E^�R��#�F2 %{A�j� �t�Ged և� �YBJE&q��5B011�%n (5)x2� ={e^)4 �)P_0 U_a } $ $\. ox 12� 8}$ mT !� exac�,! 3&�$e%I� ��oX=� .p�|"�n5��d (F 3�� "�sH�El:5� 2�SMxE� �$in lattice��� 6,"*{b�yspo-p� +�<� �zB�1�1�C� \� Ie�m� #� (2) belowi�i�>�e��8If�+po�8��)�n"�� V-6ll- �, a fl��Ber3I ity. � A suffi��lyz J�wZ�;e�.��� ��o�uj}>���)�F\$ut�%]�@s�I,U �>�BV*9 )zl � -d\%��%LuI�^' sim � 8}$m�g $aK8 �%�v��I�(� Q0a���q"���+"�(�qtH�vax� ,�8$,>�!��tra�&�s��6 �]. E&a- �D�1�I`7ex�� M�&^��re>r�.�zuV�x AIQelE8"�znti��t?9�exc�ly !berf�, $b$,�>' .!�m? putt!� $b �+�@2�2yeja �I;FB am�s!�1!d�&E�s�g�B�chain� ���F�eo%%!�iVM aT�ar.g����B�inal,*JA>LU=lthough�Zyby*.1�=�T� omzs�#.��!A"w �J.))-$�9mit i �]CsZ�&F!��er ���+2�al 1��� E,tchA ���on._9>+ �{6qC7 1!u� o�vex! &�st�3&��N iolin: It�� )4el6s6 �L��%E#acquir�*e�-��(.�.N[N) �! Giv@�9��� sh6y�,9.!Rsit*OdcsM��=$)��~A\\�B4I.C��U%���an c�v)7%be aX+ ���A5FqvlyqIZ�E7)|=}!��a1E�>�c' zf}�fIIA=pp_Ic4|*�_'jw) �&�K#&.F(%�.K(e (9O�|ct>�(��do �a`� N"� !��" (o�)-�c�d)> %�D 2 �>��V} %�>n��i�FbyՋII\ �>�5% �*68q �oL�4% }� 2� -]r(l!E��gh&�? $c=3&� 8$ m/sec.+t1�V\� Y &o?s�H � 1 (A) i�l6n&t" is Cer!*�& 0^5$)�M i��%;BR(ra5$200 - 5000��-�*�n2��qVu�*�A#�A�&��$�� earliт(B) F�$b$:%�L~4f��1ZI �f�encf��w�,�iR�Œb&Y)q � is $Qe{m} < {c�b �({.�-�16e8}.-{26� 1E#4 $= 1240 $ GeVB��arD� I�ed%]% �oZ�G (Nord@O� �)�� 25}$ Hz� eq 40�)-1is well� )m�)e=�!��(�u�a� �@!���*7.�L�3��J}�a�JB15%��>vd.!�abs!.N } OwA�t� "CL�F "76 ?�p�` ]�azt!�cr��b�$�l-� )�>v�Xor�"V:x �^��-� �aE � �l��t�F�djaHB{sto < â�M����x�"�4/Ic,0 libr�W��8fK�a10V�V.���*��m�S'e*^� �3/Tn �%de+t�< ate,�$O3�!� o} (r�:. ��NE9�U��r�ng�Y@��!�N�dA� n �U yɀ��!W%lA��( lG+#ey %�p�.�nde|� damp(3)Fw��� �5(e�Spy7;tempeF�w ՝ce��V\!-emer,recapit��3 hem�� R Ba at ",>�s�� let_�8"6:�2�\a�taA�m*�Hr 5�a�s�_R���J�2::�գI\��MB �A&�����5�F�1�2+ u��d�Z�;wYJIV-!�E?�A�l�D� e>��NJ�>Ze. Dis�gm%VKj>]�QI� � �#�\ .h.47_ A�&  �[�byAbiP�n��\:8��A�!f-�V!��%\���z:� V�yA`Y)R_��)��&� 1�re�T)�!RF"E&.�B.A@�&/  (>�>z�ToͬErit�a sd��(�Z�!M@D(�Vum>�$E_{-1}�.%�B*�� V��ya�n�RA�e@["����!%RK)ecP6o.} !�3A��V8�0!TJ��<�V �B 1d= (tolByAB7 ere>*a>B2of� �i7oa�(u1+ : $�x_{.!f +1}=0-U' . AB !H�a�%;gZj�JQMs�?�,um $P\dg + Pt$; ,eS?�s: $ � �+ +1`  �-1  + ]d?�: ~=-" dg $. ButQV=�c-E_{�� ��+aC"�'J�7}��%%!!2PL:ye I��Bu4\%�{+ iذ�Dj& R�� AR�,m� .ManV�.$� �, ��trapp�k���6�6o��4 of�thbpVC�"e@>��.���A�T�" "�(�"�ea�}"�L[F����N�, l�La� t}&K A@T2} \ge |U_p|$. For $ >>U_8|.>>A +�� } >_f.:�B0&s:!�out� i�h! IF&_a�5�1 �! }&R,*9I��s. 1-7,���su*�X>� ert� akQELin ��*S6H V.14�S2 �N:"�D*�(&�+��h��on ���=i)�+:s*two�+ �&a�AeN^}A�&�n. �#\ � z B\Eeq[2}&��-R��F�P�. � � 3E�'u.  �<6(it q�i�Ѽ�@"s4D@ $M_e =9.109 \ti��6 -31}$ kg;L6kRA}� ���9 � ^ (� e#1}R$U_p$)hpt Liu#,*� ��pA�(�M28 33, �G$erson 1932&q4+:1*A�T son:" }]) �2 � ��(>!9$3+\QTI�I~2. $2�U>�!� 'yA�Ds2���� ion��1Dž�A�i�#��VG;%u(X %(M_ec^2) = 511$ keV�'�� �2�/�ke�h#:6eT3.��eO �:)�:�)E02}=-U_p =938.�!�2!.5,�6J>�!.�I�Nj .��)((�B ,�P� II)J�%A� ](!�(�G%11_�mn�E��9m6�4xSs�no�Ui�K�e2#Is���lyVr5IB�fh� f"�` a "Xy"T=B�,Afconj%uby�O#C28'E)theor�B=(4 of "K�3*0�b&#V��,=� .2 -!�.4,!Zl� wh��n�O!�A�n "W* ing"yw��a ({�"non-$)�,?`e��c?Vs Nobably@#����$Cly�`��(&źI��A�ny�� av&� �' pusfGhidden�p�A}5�@� . r!m��dJ+�E�l�#*� �t"�9U!���a"r[res1�s. �# \VI-)�&� �$� |�!| +2\Ee$��Fhuga�nin5�%(draB�j,C�� a$ -!,� ifm )�ca "�")w!�=��s EbyXa!��*�zXR��MR� way!%�c3-a�R� �� � ��3 3)9�9�far>�"3! E�!ߵ6G1E�2E�#�in =�.upp�<�x�^�"�Sar��cA��A�p�&� a�z*0�BM>�ed#B� }T�|��� A�onb ;C&58 ��BW�<4 �it2%) NybFՍ.CI";:�eM `X�.�%!�Y�d�/�de��9�:~"��4��]@F�, �RIt+�aF-� !5P$& %wsdaI�E�2[lly�_"���hb\1�?lR nti- l S�e6yi0�`�f numw�Ce@Yo���AlU�(��)_ 5.} �+� v��V@uLEtk!@c.u�\ ZY,XQ?9��s,�it ���4A6, sBlute}0'ka �i�"��lat<2N1��� i@&�*�1/�2 s we���J��bL�P�#r*�_O� �rEN� �=57u\ ��o_=���J&'$"�?�7slo.| $S$ o2�2neEa�n� deviihe�Galilean9 n*I_ ��U�� "�<��:�Zq< c�.m&�"zrJ�"�-S�mVT+�dY D��iq�^�s 6?V.1K�1�$;% ���(m cefO��Kelvin)\ we� , ��� F�A�d� MV�"r�� \(�Lv O two, �*� I( NZ���2v\r �04|)��E(.�t'sub�*+�� s. A��u�6�cg<m+� �($n$'Ɉ �s ($p . O F�1o�5:tFfo�0a-c�E $n \+SUZp^+ +oZXZ�?�{�z�V� $~K 2�"g$E�.�$e^-$^ !L19?;$:x���顖�"u��*)/&�l��%�pu>3.`�EN��hOG!�VQ �S�{} a. IQent.��5�n EbbZx�W?lowA��12b},*�gV.��ij5��e6��G���b�s (1%�))e�n��!7�2m|s{.� �[�f��0F. �sr5 Jls� hSyp%�� e�T^��Kx "phOs��nons"�,E(>�; :G V.15a'c.��%�re/���i��*�%*i  �di�H(and )z:c�Wř�� � +�� ��l"xGA:c�`�K� !�KF�ٕE-wJa�flFF$tr�8\l*�tf �,iI�q�.ya��D�T �(��� ��M�i�ioC M�$X$���,� a a��'Jh$ Af V3s� ���cst!�|�/ecY%� =Zs*`in $Y~.F�,�<.iVe~g� o��� �: +o��nh J�i0����s,����"l n�rG�L��-eE�0�Ym�� (enclosure}.# �4�:l re��"�+����ormM_An.�)!6PS��J )@�R �8n (*xA)$.-dime�Fal box��A� $L8�e��o_St .5�> t4�2FR���"�&�F\q$�"2�e��:is�/ awaH~omF �%E`}:X_s�:\)�(TT��@ $T\S:�A^!, �W!&�..��� .�*a �W mo�; !�&�� "v��u[ce"nQ0i�U�}�QMq$. 5?:'s�, �GI�h�":- �A�.$ b�6E#%y�41&�9�&a�}�/a (R ar)V.!2�iO'2���aU�%�$��$ >^��Wor!�C��4�V): $\Mae$aK "�5a %~�� ag��tEO�%S forcA��$\af$!b�0 ing.wV�A�M!g$s$-thB+A�M�ex)r�� �tF6 �$\FqaN-t uI�e�'s ��:"�c�%=�I�n � O!.K=!�w$i j^)eq-LwTq="�� I��!as!�_� %�; �)�w$j"ym�RW %�,A�!HZcG>> . On� usnc^WZj's`�A�"aSAc�'7 $<<�/$.�gSo du!�M\ne-�v��BMuSja (I.rr�b�-�B��� 2�;��$�EA 9�dri�E��Faq��u� $s-$Nk in "ict� Jj 3C�b!!"�eqGX� eq-A��!>QW�d/ -�si�-\A�JAndA��so-1����d � f�5.�:� . It��p�CA�4e Hooka yP�6s!:>C. I���:C0 .h$3V)��9�=-\af̋ s(T)- ��&�1 A(�� :�T heSi$\Mq d�= Aq /d T^2{q!�$.�56iRR.�a��J��a�I�a%vge.� M�are: $$\)�y��s{�stepcou'&��� Giole} \h�@�(T{fAqoa� n(\We T) F�e M��:62 fb) \ \crh Ee^* =(1/��)\int_0^��} [Aq}=P%�� dhP(T)] dT =\frac{1}{ 2}� \We^2�!�q�fc)t(� �) }$$ �kr/:af=B� $�= 2p?Nue$.�%ue=\Ee/h-?�6�bY noch74e�"(E2w*�2Xw.3 ); ;�*:� fH�U �Aq}+6�c)�cWEl�l'@ &6� A��E�i �"�Q!�=AM-s!�Ð ^2/2�< A:�J�eia� � usoid��hj.z5is ^cc&`MaxK's.�5sm"�"?3P�".-8&}�\Ef� n>� $H_a P��"���W�r/o��;�1he7ed"Xs � *�Sack"H� wall�b�L-�r�zW=�Mvf���as(bf_uel�X} �re�w,�2n� i@/��^(�heQ-"�k(rK,0uKno�]� �+|eB�3Y*K (��VI.2) �Q�� �a!�ve6�n(= ��� �0s g a� "%A)q"%�!6/!c"Q%+s=0c�@l:l��Efr= {e/>�Co r}$ (S $r=X$=jg.�i(�=�7}&,�I�}W nv4D$Eft = {\W�;,c_{q} (T) X ��6 c^2}.$ >�`W-P%/&S=/P,S<  O^ �>)-�IVA�1!M)`$i)�}6�c w�ave in terms of a transverse mechanical w+�disturbance, propagating here across the bare-charge pair in along !�$X$ axis. The $H$ does not do work so i $of concerni . 6>e at $X_s$8Lfirstly subjected tozDforce impressed byM, apply�Newton'�Dird law and combin!�Uwith (\ref{eq-pole}b), this is: $$\displaylines{ \hfill \qquad \Fqa\zp(T) = -\Faq(T L\af\zp \Aqo \sin(\WeT) \ D }$$ !�!D<-Y$ direction. W!�<, $\ze$ indicate�(e response) s�hence!� placementE[= !�(s differ on> H's right ($v \| c$)^lef-<(to be justifiedA�Sec. %L,SecI.IV.4}),@are sai%� be uni- (�=\dagger h anti!�arised#$.I:$ =w$ driv->� into6d%�)#L ${\Ac_s}\zp(X_s,T)$.�YI� (cf. Eq �,eq-Aq}). In5�8, its neighbourA]>�sE�(\ldots, s-21$%!($s+1, s+2, !$.�qo wA|�A�@ $\Ac\zp{}_{s-2}-sJ, {s+R#$,6�-a�,Ailativeq} s-thB�; denoteELsuma� thes�!as%`$. N 'at� A4dan equilibrium state, each�$, say dg$��esE�effa. velyA� both sideR�8at any time, sia-a.%Kdg$)fbe refl�}�fox wallis0re-enter fromNa' . .� exera�imRC aAHtoE7���E ��<�A�0, � s=1,�3, NB�8 describes pur�+A�* s2�Z� �YD eq1b}) ha�travella�wp solua:BG�&~0Ap1.?ux!�;E�s = \�s\{ � �@{cc} \nonumber 04\dg_{K\dg}(X,TaA \Aco)�[D{}X-\W\dg T +\a_0']1o( ) \cr �o Ap2}���jd h.i6hdg X+h i j_{RL}nc\| -v)Id � \�J�!/)S  H�  $Ue� the phasea0�\%�p T=0��nd �'$,r�� 5. ` (excepta� ac�$$) between�D9m�%1� YE!�a)6b) re� en�� {\bf; po! }6��bf:= } �, �&�satM�A�parallel G| o . 4's velocity $v-7� col�(�%`cWd a ���}.  )dg�KA6I�%�ob��ed�[ *g$�inclu�0wo changes du�� re� d �e�"X : (1) a-�shift =the�� -to-Ee KalA7 full�Am (i.e.EOte�� w!\1$-X*� ):U2=\pi$;%w (2� �>sig��$a'g T=(i�c)T� $%2(-c)T=e�% $. � addi�x!���e Ae �fo3-[�.�M�dgre furŒcharacte� W  given[  $ �Eh�!4total length: n�Lw} \Lw��\ \sum^{\J\zp}_{j=1.} L=  L,>�}RLw}};��A�he sou>F �Ge��tinuous��$d generate:�s ���� $ ��<at winds.� 5 � $L$ -h/2$ round-loops, before it � s!�absorb �wav7When st��d� xtension}.6�is sprea� space%�ny:�IE�Ea d(X, T)|_{T=T_1, X=[0, L]}�$ {\rm and}��`� Z<-:]} $$ �!&���)h�tr�IC $JL$!�U�!�, �4 fixed $T_1$, )�be�����Sone-w? (e��(romagnetic) �}�>A�}�?.��:�s-�by��")-2�L identify, as argued!�( \Cor. \IV,�!G:��� attached� ��*�����c$l� ls l0�. \noin� \subs�~on{�intrinsi ��Dmeters associated �a localfre2�} {Si3}�G W2�Ap1}) �O9L� A`��G g{}=�N$!Ofo��>vAn$v0put8$$X=sb$, we��B� � = 4  XK-\W T_ o)T^2 \lf(\frac{bK}{2}\rt (,) = D_s 2N1.ZU+� '}$$)$� �_s= -\Wy���A7$'xK� � � $ -� J&= �{bK\ov � = 0.$ Td�:��e angulaLequency�|8\W = 2 \sqrt{{� ov� }}b! {bK  a. ]!���yieldCAsA ! { � ` af}$. Forf@A.� $\Lam >>A4or, $Kb <<1$ (a�co�e$um limit),mF abov@W$ reduc!o� � *�&� WN} \W� meq  !$ 2\af% �} \ ({b -)=c K+q���or' \Nu ={\WB$2\pi }= {c%Lam�6;w�A c��{�bAY ov 2 �}(/2)b\rho}}�� $ = �/!B!��(= (c^2 / b)#< @ W(K)6TWN}) must also satisfy�u�),&to�64V\ (2). Suppos��>in%�ac��th%�.&&Zini �mit�`is be� plausibleeinertiaA\AvacA2medis"� mall;'n (for2pli� seK =0$) A�(� T)= Ae9� T))Q Plac�F#e!�@�$o4 ss$ a�nM�i6)})�sn� u02xA�� = [{>kUA}][�9\W�/  T)] [{1((A�)^�Nu^2-A�e{}^2�J}]D&*M�$B�}�{1 }pi})(E�A�})aQ ^2 K!A� })$.�;�)���e�� $a maximum�!�reson��o���X,\Nu=\Nue.$ G] �e�� le-val��g$. As  \� arrowKe� �a[ ${� }= -%A \Nu)�Aco$, ' stabi�a'finite {sz�$!6increjE� $\do�p8$ (see Paper II=V�qmonoch� h!,GRH }� 2 s, whicht laterz � (�  mial ticle (aost). A�p%�$�P��$B� � &^ �IM� avevector� -O },!Q . 2� A f� kind: moXz (FSME)@.�� }͸� 4} Con Ri i� )Ul cAPof JaStx��v*� ($<  (c \| v� a "Odg2P+jP-QFk �(J*i�s�0($=� /�$)A!Z9r& )Qmod�-5&2!9��)!pC �Erby���lute am 6H �3 kd1}�|s0{} - K| = {2 � !�(� - v !�) $ } ={! v (&% � � (1-v/c)1�(a%�uad"9�1�2 � |K->|� By- �+�~�+.� (b)B� !$��P9�fI i�] UK�/! $)measur�$S��are: $B���nu=�\Num6Nu + {(�/ {eB}/{c})},5c 4i Nu -B5+{5B|) �S���g6�$ cana�]��8ny ��,an arbitrary"t � A� $eby mutual� tn to#$events. Sois��ti�to*�a�mea�a_ ��9� variablesaY0their geometr eanL6D Eqs.&� A%d" �"ɶJ#$\Kd$!�� $%� ��arT 4'cor�Jon�5� 2h)!3�: fW�eq-kd) qq, \Kd =\lim_{R��636� }a� K��zv}{c ���i t�4\cr��reZ��K1}�f ���$ \approx K. Kd \�i�v)�,�mv�OA�A K -%C D�2 s�K1�&6#A)�ac�A�3iS�g 6h�b"�^>>% �HKj)4 r�!Y)}=K1@ (a);1�j0 G�gdg�Nu&.(bO9$Km-W!:&�!$��\LaY r � ��Ta�a >� � ID [%Å� N ��k�a�  orde�! in $v/c$, �Qmm=0$. As��",become clear���  qu�%t��$� etc.,� ��t$J��class�Jre!�R�'ian"Ys2. Z� �&b gv5 ��}. Any� �#+$ erty�^a mov1pa� ��$ �) 9(a�&-Q ��%)�Fm } g ) �, or x . WvъLgot: \\ {\sc Coroll��\X.} {� a�^ ^�,ZG$,��virtu !EFSM �_� �a�%��6� &� .y T ���&�s_ASbutx*���ove�V�. }6�S� ?#78��g%�N�t� "�!S�,5} We star�&by(� �%A4re"y�@k� # u�+c&2)�*A��+ei�(solidBl2*sigma$E) a "c�chain"A�.| *,a�� $X$-"). A slab30thickness $b$)(it defin �(�ient)M!�>k"�A:�> Y#%�Mor po��� verage �*F)�: $E_b(= ��1}{�"}\int^ _0��lf[" 2} b� _R {�%R}}^2 +:'af&Ac_R}i]d T =&�� zp} twgWc Aco_R sin^2(K��#zp9, a��4is[bb( Eb} - = (�)Ny {�:,P#�_R=�ho�4� R^2/Nc }�!��� massZ s-" �Y�,j�$�!1�a�a�tud� $R$,_0$�volume6b aBrm:� $\Nc�2�e cob)a�6%.�u��wR^2� �|Mg%c(&*/2� �-.�Eb}):0*!�}^2$ a�to 1/j� thus 'Em$$6%(. On exploi��.feature,m� now��convenidwo new,!j-�pen���J�'&'rhoA} ��_R�R^2K{E&iR0 �\N�&� {1 Q A= R _R. :q"� x) �s a cyl�B a �0-}alta $�A,A�aR�E�$;SVon:��\z�}e5=m�L%V����p ap��-o6 -!{y�22(i�)B.�&ZI% &�u�/in�s/��1}- 5}1 below. ye�i"/w=+�o 1� �E�writes;�̽ϩ�6Iy}{Ix{�Slf(�RMP ^2� 71l-� 7/^2AqnoUua�'�" Each (հ)E"Ź# co�&��>� �of"�"L$'ain�$NbL=L/b$ (U[F�=Bk�NLam= ? /am$�<��.��@�p ��s9�ly�a6�;F�\�#6��%v�-Y�^'nBNbef} �[� /b�� � /bB�.%ReAU� �0��eA�ful�Hd% ons:V se r4e aA���La} Lp!v�� -�� $ 6a'b,>atB-& ' NbLw b = �Bl \equiv \J i\�S&�$%'* ri\F\Lw\dge \La�N[&� �%2Fox'�es slowl��((time) cyclA.� L_j$ų��$j�[l� on 3 ($j6.J��iI' good6 roxi�;�wit �@cl�$nx5IM=um�(�(L_j-�L�L$�&� . � ^[ >wisq/� �E+"��$E \zp$Ba.. �or6 !eC�.2�$'.�$!�!�-x Bq ��&�>��#>�;~/Er" Ey\� � ao�:}{ b} &� "l�r�UY:8�a�/aC%zG% m��E�$��6*�~�'���>:<8:;JR+&� Er2} E�0E�E�} �i\J �X} {)Q >F(��_ 2� �K cF�+E ��!�dg!� ��;A� ��nB` $';=��3��s�� >�xE�xhp!u,���6T' &f��9hp}O)"� h^*1z�~X.�����hp� }$$ >�C&�- ticsE��� -2S�� �,refuelw)Mn 6} %� :�'s� ��e5@Lw�?�$�/� D����+qAa._ �put� stop if��oud!��J7��wTq�. = T_qA��� � -"��� )ov�t:F If no��sipq,9�&!� e��ll�. Integr�=Eq*�:: %on. 9��!L b= ($\s8(\Aq$) �  a�-.l� $�} [ %a�R66] da��4/� �)qt! q$, ;+]B�j*)EEq+-��$"�*o^2/2�"�6�=totT(2q3�mGi�or1ޥ=Eq+b qU��� In o�59HEq�� $E$ 8wo altero��2 icala��?A�s"�. Sif�>2xa),� T�'*\My\W=\W&weZ�<� 6B�<, u � \�'M&{-5�$bLw}. $ %\2 B' $7+� larg*�$ ^<<1�$k.at isB.� lo��".�4 �"�:� �&�of��L)S,9'uO:2m�.�9�% �zQgK'2� i"A2��L of�1�>$-��"� �,i� alog(9�ping-peAba�sA box:��{'i� nock�/ard ag/t�de w�<�> �bou�< back�forth�it many})K��lo h0rQU��gA�21&Dynam�K ��@l �W7} l&W b> %: &�(��0:ha�.C�&al~�1 � $ $7  |$,)��+W( We!e:by�'s�}B 5�AumF��M0eq-P1} P\dg=M�c�(a�Ɍŋo��P .dg/�\� S +� bM?}:cy9"5+�&t)�,l�} $C))H�� _.`�<d �.���>a� ��� , wA�vE �^�:= :r39 $2�M��&cy* 4y�J� f� =�PPݩP6� \.[!})4%�1�\)��� ɧA����MnV.�1� LR�� ?$ Substitu�e9�#a*�4bMto%1}c.rHpm"�@ M1a} P=Mc� :X Nowe��(%$);'!*�� '�&�$well-known�Ya6 smA�B�+5#,(Ref. [b]): � �=!�g c�,|dg3. %Multi�0he V5i �tak��squ�roo 2� � n wo=A�-���-}=.c��}c $; u��&b, �!�a!�h���) B/:7!�M e�Av& Bm&�QE.Y# E= P�!ea&�  E =MC2Q� &��E!#�5�1A�� $M�C- ed &D&�w��&H�\�E�esn� . "M�{�\Nu}/{ cg�}�M1m�  $h^*�6!�6!#;�9��A� vari�B :$M=� \c�/ &1co$} =h^* {K$   c}$L3�=5Fgi2*I!Jl�J<� P= \hbarp�%I6 a}�/E hp!AU�%��� :Notic: at, desp1� �Fmbl�,toF3(nck-Schr\"o'er's eI#?s �FJ`.#um,��%&�9%;�#o"ed� ��er{ �|.�,6� � :ofLbas�(B�0!�5 y�KEN�( �38=!��$P��M�5�t9bU(% A� g:�#^�"\%�i�� ��a�#b*�Eof],$v$. Meanwhiu!as 2� "t��4 E(:) �6 �l)�66h��%"��itX}d erj>"�!a[n��$� .� �}�*�%0 {2�. Fu-@mo~�&i6q -�@@ �^ cc�gaUY�ss3%it)�ic}#�%! L* N_ ny*� it. f0$ followour��tic�:.�9:_%\gntFg%Ih%A��222~�I4ef ��,9�$v$�8!$�'2�5�%�manife9Q*� Ik!!�!�*� by6���. M%;iIce�n6�OaaYce $F5&)�'s*�Hq. ��%on>�f�O$ M({d?/ ov dT})=F��(imD �Bh$F�'accele��2tŁ6VC@)�R9 �$Z7}:,>O��Pfp�� \Pf�int_0^{�} FK =M!��"f�Ϳ"�2 2np-&pFdX} \E}X�$X6� }M v^J:�E"�0�HIf%��40arth's gravit�w�R $F=M�M or wRO�(M=k en�C|:)�6C^!��C�*C7��aa whol���us far{4wgE�&Ec�observ��#ay�Na 9 mi-)ͶGSE*8:LK� a tEg�R�,6�M! inL�&oQ (q�is-J161f?;m�2N� obey �i�+d�1ons:���E;His����v.%[3K a��J�$predicts g mZ)%}origi1�siz!7�8Hal-�9x9=!�rei�&�9�) cuss!=SeB#9:#12b�HI��qe suffic, o�Sl�&�����/:�_ex�+B�+ II.} itjv%Ca42�&}&hN& a�+:�*D!�+ s,@3T,?�*XiB },� ��Q��at 2� , $q;��r4D $E=E_mE�.1�� E /cU'(� ��[� ��?��D ��&� :� $K,� , \N�;�.a- $q=-pP$E (=E_{-1})=511$ keV���$M � =9.09 \��8s 10^{-31}$ kg,"�>�n};9�G��%� %� $q=+�w��ve �3positrE!)�(+2})=938$ MR�= 1.6722�27^�protoAGll Vin� ./"2J ? j'�m�!�6D �/ s }X 9X  F�S phys!�I�(scheme} lea�  d�?Kof *6� R� *�]](Qq� = aC2q a�?F39%z e�>�/I�(1)�(���r�\�-S �:j��a�fs5>�%z2G+i-$highly ela;�9"�, " � �isc�resis<�!�.�?�or6� 6�(aB �); ��We��a47a�5��  a���h//$C6$ituentR%t7 2) !m �s*,"f/W(61)��.A�  J5t -�.C*P 's L !�E��ve}��"2 ^2P�S wIM@!��<\{JV\��2�ZZ|mx (R/Z.��3A!I(��i.�. Ev�*!�2��91�aOa"r$E&a��dsm. B�*s�4typ�<=: al. A3:l&�J%'2;��-@� $zero KelviuI92S �B�!n)H*�Ri�augO�!k'�[��ic9C8$\epsilon_r (>1F�P��J�2�o��mal6��p �/m�temper�.+�(l�Y� " usb�of!h�J��  :\D (3�R�e� detM}�Oi��5 th a:N5��a�ng�on%+!|S0. 2���mm�  .�� �� 10} Fbɹ.5- �as out��m�XII�it�zjQV�A (1�)� nPde8&6!:�en%y7Fn �ferein-�Z�e{5� � roug�#�%�enclo�>} h,� a���)�_! � mple��"�*$L�<aa�-dimeNQ. ox��2�.V.� VIbNJ2NyB�cir<oE>^f6KL� P a hydrogen-like atomJnIb. �8,&��is9 ���detect �Prѷ2,�Mz&� Y !z"U .*!�6Q�. %6� � P}cR� com6�G>l�!r&��q�/,2,D$: �X"�&�D} D=LB�-}J��.6B��val�� F� 1} "k &�-"�ofD:G17'>!�\�E� , 2� }e> V.}i�_".E )�~��; ,A)q0{$E| i�Q2L!���"9�$M<r�co-exis9O � ?5�4_u`c �.!{� � 89]�od- �5�� .*� .}Z n�H!� 8-E��1�,5�V,��-emp"�I. � alreadWHa��Opticks}a� 1730nwa"postu Lo� phen� ologhg!V�kecM 1905� 0`�v!\c�^m� weJin�c�<9/U�in"�K�)n-�1!�ches,d�Cr� ex cłT 2� S\ empi^*Z1PP;k�9AFJV�IEx�H ment<+:gamma ra%�rL d afoKAYannihi!!on&� par�]��n�(_{pa}=h\Nu,�1 $h�&:� . ByU�RI�85�zZ�m�/�Ef2$z"� B������&� 1}b�*Ie��E( 2w�. B=���$)$�*�OW �9�J��V�/.�,En!��h�"��$: 9X"(`�-6-P'\.H(�P��n2�)6�� %�lN��ah#it> e��?BM����*� ,A_akeE&�n� &� .T$-h�K>wv:��uI. ButV�7)��&r�(L ��� v$E1$ (or �-=�/\LM6���N)EK],j��h� wo&�! 6��Fw1�=E C�3}.F�.bTX& Brogli2� $%[$"S 2b} �1���Fal�<��z�-�����-�&"�%"Z%"p5}q_:�!31}lD�fX�F}9y�8#iD�a a�C2} SNu:4GHa�\�#C > ^9pp5m��%2�d5�'s hypT-hsis (1923; Davisson, 1927) �5ua :^@aR a��+,�A�d^{Ewem}}$�_E�2�!\mM! $�� �N�I�"�s}�%:$f?M� eq-emPEfp&@(� &�4h}{B�}1�!�Q5�&�: !� \nu.�9a-LNt<5Yve1O%�m �I]uN�CdL�JNP=� �J5�:�= C X�:u�f2ZtBi�(�"Q2� \t.��2JBg}={\mit�B�df2�^2As Xd)VY!O) �M Comp�;s� YYV� :<Voz :{ �&�.�-�g T-]Q(N\lower�E{d}B)EA? /�@ : illustV diZ; 6�$V�We=��� � how a r��i�h JV�ofg�W"�VisIba�_forwardo Hbd�Z�uni!E:aj@.�Vbs eig�bo�hsa�Do�Zm h' gthreeBw3�gh�qoB�.14} we�Rv:���!�M� n� pplica�[�ce� pet� .�,Apini6 epsfa3b�E s\]�>x er} �LeavevY\hbox{% �fx/=10cm� ( %6 cm--RPS   %8. $%6.5cw0�HTfigI.4-dBwav-trvA.eps}pOvs t o�nB n�-� \cap�'T� >�} L�rgraphs:%�> develop,A�A�mran!Iti-�zq� �cEc� �-_YN{}�dr(iIcurves�� ,�-- .dot� /, MbbŌ neg��OAqu  t�2s$a6q9 �` $v<<�cm'� $\ominus;�n��R�Q stil j%<'X/2$. Rav�]super4k�4A)=& !$�� �q5struc6Einter5Y,n[(a beat funcc6�_ en%�es�X7:�A�S?uNAdas�d)�. Atr)�h�2xrepea2 XO-Kaxj t�Sr�9�9 Rh8� en�$Ej� �Bkr�r� -� w h'66A1rK"�9�2i!'Td >�7ls k!NH`$V=c^2/�k advan%`Ba�hc]F��G�$ %\vfill\e�w�<� i�,%p*l+�'�! � }/#b�Np, v5�!O+ofi8)�X&82&sN�Mw_>)FS;�l�P�[5\�9?o' =\WmK' =K$;g!I� in6��g�6"M%�9%�8y:+6�W'$5GF� } �=>�',"b\�9,n[(K+\Kd) X'�fp _0+\pMb � ?$ \�.%k�so �L [(K- l+�f l]g� L �  %8'g $�eiY� n,%5-�=5����TX_�wt�4j ��,g{}(X_1,T_1)C�.IPY_]W��a�k trip�K=, $2L$, retur >�+�)�c��g�b �+2L�$��p(it acquires�_A%i�xtrq�qX=8V��)e o$2\a_r4\$R w�'!--oC)L(Dive< llhHn�D�l%; meet�j ����'-]6�[^���-0��olrY!��wa2z"[!6p "L*|ph^K2L=N7[���, F.!Z$'= \a_X + %@ = 3 pi$�? R�oe�� * ���--a�;�.u Ax6�5�w,�$s"�5-Fyv�$26b�rlow: 2� R� � �$ %6� %-rps� N� 5-� �H� %lo�% {�y� >yc"� =fy� .��� �7R� dx:�a�?�N�  imagin�Ub�2s��c+�hite&l$s. �� "� �mavu8�t�QiNdBmK���v�2� !�� Newto:�1!(  PZK>V5V�Q �}x6&4Ada(0�� da(L 0O/(JZш Yv=N_0 ��xD$N_0=0,1,2,�}A((b��2z)'K/� x� ut�@S*�f�ap�Cvar�u�i��;�ful] AstricxEto�_ K_N� N\pilL}_�UNWy1, 2, ��6�Al ' $$&R��!Wb)� �m�%wAG�!�S* Ada3g{e&  �T`�a 0i�b`�y.�x`&Q(X & =�8�cos(KX'PoKd X'8]CjF :_K {\K�e2$}$#�9 �� � � J <L_{6}?L$.I8�q� f ox"� |*es !(H-&y#@3�. agreCl�+"2 V!� See FIG���*�};�yda�io6X ,��PEO21", ""� ,�T2�! �YaZE�ف+�� ly-t�6w�}"b ��PA%�� ��2D��f�).lE5wA�B_��j%�_K=.~o U $M�� o�7U�� apid"J!�� ach��.5M� 4 /K�D2�.\=� (6�$ue m1��$�n �5� 2^:�a%�H_�k1J,P!�!�,��p�z�vNyV1} V�'\W}e@= c c}{ ( �0)va}��V�J \w_da K�mv+ c)X>R�� �^ A<�dQ6ealy.ie�j"2M. �,!�A8one) 1;� occuSF  �$/Wc(equam7��n��);�$+byIld$a�Lamd$�P aren�*P%�`]��!�fuYB) 6 d /�Quikc!fzE� �"�0NMj� lamdZKamd= )��H}{K���Y4=�N�.>��M� �T�"Q�0*"`� �c ap)C EBDgyFL�btd2"bH�i(�aN7�jJ/?m5R�tU\ �� nud4a���� �1Atu\N v}{�jN�N�� ��%�:p5�Ja�� F2p5"C�{px3� �1�ah^*�%�� >d;) >{�� * ��Oe�Efp2o2�Op-� Q9e32�%Y50�&c7,% �&i�eMt? a*��(J�Jhp =h$�.�\B��%� .�s*�� )��)�v�h Je9T bez$ �"]�$sed.���a�{#?.( lm��$b, a, c, d �!!W.K5+=��.�F � �)o,m�/ate.O(E�n�(c�� r key as��s�>Y�8�>�+!����>f�-V 8��0$ta-k!!\Od, a�!�')&�/�>%[ h'c*�?\"�*\ t&� at6qi�2�%�%�az^[D  a��&E.�PIZ�*݀v.��$�'sV%u�+*!isoc!�g>A�j?*o � �0U%ly (H}Xwu�4b�-l� �7bfmW*�} (�A9= ave}sT"�-mfI+5�LY!�so-e;ed%�.�P)kV(2)�in�\e%"o8.to.a spilt�&5 he $Y 02��+�4>_U��V~_&3 �e�c��cu7�s!�az< A�Hsm�.9BX-�&�ly�� �C(3)F �M�R" $V$8*�SV1� q factI'c/v�$(c/v)�: gre�7AkX6N�'n� U.��; C�gA:.�5\XVa�J�cv�BrA=� 4of \Prop. \twoec"�(sm=a� rem {la�i��-um191 >�!�T quSzed�t��? �2U!st�5��L � >6 k>}��8o >�G� 6�!5.2.b� �((� / Ib�/e�*|!CB�"S (��(!' gene�U� > �)G�\TYmL�\�{nd M�U.���<�MAdb� f�  bC~�aNt"�Rqca/CR�!ya�(as�R�5 �" �simulta��="s,!��k�^��"�20^�%z�amJ�]"@"�q��a�s��.�pr�.?��J����pC&e1v�V vari)"!/ $L $^0��ifica� 2���b6ll!߁�(inct, chief�hIjteiPis�$� � a. Wav"� U�. } O$Qqe/ve���ir�jw�Md=�] real(2� I�lways� $L$ ahead V9�]!�a> ?].v,Q�"? a ��ii�D T�Onn `c "�mm��Adbm$)$����+NZ�4\X_6k�ay! gotum6��i�R���4].�M_X=u@E�m��T�� $; %�YAda_{K}m�A �w'x"�); �� �"�b"��9���n(�� T�b�W� (X)�)oDa�xY [\.�� b_X]��b1� T+ !�)$ �6�beno Fo]&�4ng�y �(Yj�� ~�al �2%@� ed,���T/a��hv.o �b�[ (i!c!8>V�2v\bK�� �� (ii)�� T��a|u- �$; (dY E�Wge Fsr Fi�y�.�T�2�wO� (e)�|2HJX''(=X+vr*߇���Y1db=N�- U' �M ' + � + (- + sr})]�j*ll)\!ss'�}lyi�=M g^*+YQ��,�( re $&}�_Khu�!d +�+."^�)���"��esB����d ����fAdba�]b� x/6�2�'�si.u(i\W)T ];&�"3t�- ��4:�> s;%.G�_���/ob{ a� 2L=n�LY�g"B �B�$BE� xV0Kd_n = n\pi/L� ��,\U_n�oz�_n}L}{38�M� n=.>n�8'$93x6�4holds, assumŮ�'soa^\|_X''� �]X��!j6�b'/ & w5m�'���7Ax&H2AW (,�aNd��8�+Awd\Ac_K�i7��)e�[]_ T]U^=*�1�<�GA�=4]� X)$. S�����!&NEm: $t�.JtSi � ��[!eb$H8 ! �^*� p%_ime/&� �nd=�as2�!Ex�/c�!y�)KA�QezX��, TgBly�&>>:�2A�/K�DAN �\AA ngstkT ms scale;AaM, -* � ar�  $1���>�}��K3"�%�S�cos (!� �ze��'�L}u\(0�!�Z/��}p3"��x3BU� ._n=�h�n�X � {L{��g�(Q��w�_n�5 >^2 {t 4\pi^2}{2 M L^2O�X�(���3 �Q�}���2f"J��� ��%Z�%�%-nT%6-�%n�/�&�%cZP%7}~norFAW6*3e>fu�se�/A"= � y )�proba͊�$(\Ad/A)�2V.m��9�;�?�nnn=1$),* exci�2;�F!3$ D.0`^��3�c2�6s an/s�. $L=15e�"A?%("�" C���^. P5,y�JA��p� ;3(!E?v�d n�G (esp&&VMa�"]y4v�>Dc�W�&��{>D� �Q�,�OIt���b�da��qto�ak�=��5 poinJs�!�.�lov�d. Ra��A�sp J�#�5@a]eoO7bz4u�'�4at �.I DWt% !t��Erm��g�"6G2?p(7���~'s%q�n@nBPf esim�IoRyell*)!% ��' �")�}$�x\Adywa >,7�E�:sIV.4}Men/ �y��Df�1Z��{A!�$X\�)�!miET| � by"O*">"&a u } {\aOP�3?A� " ��B����!s��.!$ ���uoc.(Kog7-y��?"�b%ǁ� ,2,3� �0/5�$'howA >�"��y [�f d. Ué�vt`(Y��} T�b&�&Ewo�� $n+1>:��a9c:=�� kdL�-�3��\D� �u h^*,���T9!8�#} 9= (��{n+1} - }){ repro��4Heisenberg's uRE .*�`@�eBEt.�rib��G�Mq���+4jD Para�'�b}cA�a.F� N�-a@p�� ��_val�A"yUe`.i'�n[�8��A�mi�{copicI �� . Or�]peE_W a gapU�i�1��, ~��aX�ybG��U�e. q<���qN�>�N�i�&�@a�SC 2��a:Dy*sa��3�mt2�^�T�Y"��/��m;�j6FXfamiliarB��&ofF��@-({ac^2\ov 2M1�{\%� al^2�}  X^�E<\psi_{\Sc} (X)=E(X)�w��k~�� �e6q*88�.A� ial-��"�06�" �^��}�"F')md]/X!>>�� liteE���2na�RJ"*V"�*D#��J� .!� a*� b), �a��a-,D2E�B�NIt bL �&sSch} 9�!� C&  _n X�6F.6)��!�� 6� !� y����$,Efp� P � $2�IcA��,l<s �s ��l,��!�o� �tru�1��X:if we)��"&$: �%%�V�� �� supp� 6!(&�"&t.�hE9!Ksub.��\� � �o� uc\;�<>l1 i=�0� %�vigor"XtisFMi�^�or�oal� ing. /s reaF�$L�/ME.�!�/�)+ �G��+img !�= ���Q�� a (��cl vW�t ul��A��9��e��!,MA:,h)#EDg�&e!yx�mit. Yv"N#o<$e6 =K(v_n/c)#Y�  � �x$\0/L =1/2n2�Ed!I.{�cJ��>o&�vsql���J��� �6s: �Z($[(n+1)-n]/N�u��,� _�2�7v� ous.�V �7a6�%�aO`E�!�environ�7.� e )�/~�")�h�i}`!3�uN�dualiN^7Wv�B��7�' �Uwa"g���;�Bn� ct:�p (wrapp8"0a tin:�$ 'aHrge&Hhow9a�)r A�&t ay*VB� I� w�$�4sD,�"��"JN�)J�=i�u0c!&�"�S� A �1��di�aed�HLZkY��mdbth��n2|?�involvfM,:�("dc� ��Y��> r '� I=ZM��*:B� \(E�$*h\r&S&��s:,� t��al"�Jj.�A��X�?:��u�al�%�/l3���1�, ��(�G0HR[2H�m�S9B�m84�X2�S.��%�R*�$  rc*��� ��&�TJ�D�%�*1RY Q:��H� B-s"�1�le�I�sic tasX�Gi�!o�*�-q N�c�, { El��UR�X6�a�GM �I`'&BaZ!EP�h�� -$�b�叵n,�Yc n�Yof radi�BR$ &m�$L� 6h.��u$axut�!nucleux � $+Ze���.� 6�A y,(f {eq/"�S rem� A�ppo���n����*��"ell���� ed clockwA�&�Z $L$:�(.�D(A%alźH�/H domina\a �!-E�tr�R� ��<0>�mWN� E�l{_)'�B�m�D&T:�&2�afV"T&. +�Ai�qņ"�Fl�'gw�0m#$\a'=\|%ell�L K[ �&-u"�A$ +L,"�$=��!� !�� #W % �A�&s�!Jw+ fgd&$ bd c+e#]$.#at $�%\h�_=JF)e IH�(�V�b�6���$;� h�KkB0==�&NIf ��{� }= KYA" " K ={N�8�<�<1�,�en41:g{J@:&3!to!�>��eAdael}e^#}!W�� u<%�!(K�x<[�"�%]"��� l�R%a Rt<� \<�.5� !p�J:� ty� w!�Y "� $V*,V'BZ�.tHr*x${V\Td P�d}="�.� F��,��e�c���(a�e��:F��eF��|_{�) \le Te��(J�6 ���S%}&R+\A�:Q�t!i�llaFq�.X>0���T viewZ$Ӊ Q�To��per.�"_� !�we�6��Ad�:�&*L3�!�)����#�$�;� p's�e .5M�#:;&�}<&E��!]%(%��U�!c}{ u�U�}5� I,Ww v=u 1i�L%$N���'Y�Prl��մPfpu_n&ы hp} 3Xa� �n :}�"�Q�E_{un}�<#\hp3V�<�"����!>2< '}{2�"YJ  �)��< �Qp� 4N*%-z ' Coulomb> ce�� F_c�DZ e�ov �� ev_0�$.�_,TCe� la�f6 (=M a{!P [M R0Zu� 5� ����Un�es���S�4eq-rn��R_��)�4K$ �o-g)� M �� {$\aoQ�r��y' = R_1!;B\!FY$*���Boh�|W .ql) ��h�5�ki2{�X,)9�)M�= =�850� 1:� n l�p pot S h $E_{P�&-.g9gږ^ �iv�@$-C2 �.���*a���# > %Z�&U& Etot*� E_A*-6+ �I>�?2} I0{ R� L y�}{ �&M[^2! >` �� inJ(09.o�M�*�B, �}em��:>JW����!c)U+�4!�co.,\an{��o� $L_n _n\�9�i-�ou)9os" pn (�psic"��v�mA $DYR_n6�uPxiz%l' 2�# J4jcX-*�v\Cf�\XHOb�o=Fr2c c�3u��lye�? ma* ��*>Maxwelpn>-theory,��o�6d*d2U$o&��Y\�`@8�{��he� �YT�7�k-regardonflicK&B�)2~��!�fvanishes%z��i�e�E�x�p�/ g��"� ){rWon via"� �E�l�too tedi1iTt�y!|�+ ��Fhad"�C�eh�ameIi) F�s,��!pexxhnganm�asol�w>�� f , �Equa%�W2b{de���omN��%�H6 J�se���l�i .��3phto}��&`#"ph�v";�i�jon C9ed�cDYs">,�.15:I� a. G�hs8pai��&�h., p !W�% �nqY>hh, d0?� {u�I\�Va �6 �v ~�tup> s'ͬ�if�t� in��re�(Nq �thk:}��*$,�#sA ��5.I�TEF^n (�2��� oq}�("�G $�y!H�o)��BVfD,��2+ 6�7�*Ik ree"�D�SiFa� $script $phN:�&��V�.�Acph!hf{ _{ph�A e^{-\Ԛh}1�I)}"l ʰ>Q>  @A \J LD.�J� |) � �!�en�q�o$�}w!9$$\J$ would "�$<�$a�"5&�ex�8ž g"�a�A�T5xk*m M1a>��gS �$V �o?ns�(B��, �,E&��r,R灖�=� \Eph��ph̉ˈ���(\�6P!=y \���6JMph �govK�KAF%�98ph�  A�U2�Χin)i�aF�B� o����Zm>;adie�i ,�customar�H�Da�o&"&L%mex!�H*�+p��"��&l. ��fa�&��k�B2�u�Es�s". N�theles�JRe94U�m�%, ��?���Aȁc���_a��=��)ed}!*"�5�" 34��alv).Y 6E�y���"p�B���Wl�oerQo exhibdeb>� ������2a*ke�B!�1+R!U,-�xg� B take�4e k���.}\� non-zero)���*5:��)�i�U)�NY9�JK ɝ:*�""E�" Q� ��>v !�ex�] !%4a�U�!�iO� (E}in blǕbod� ion!Z�igh�� 4�*to�1at�}ng�!n�l sensE y,N -cMpprP�:w althoug � t� * 4 @.�q�"2�� q"�{J�E22ofFW nons�j!���-�, {�so�1ASAA$32�2��&�*�5"ҭ?!Q~�*� coup�I(xic%&)" ora~�!��ed�for t���� D*f�-on^ ��i�/ \&b.��r�����de-�4��e�ts � (A)�9i�a�si��Gb_ � .�4(�$*k(��mbv#� �>��A��A p�i� `InIFu�i�a*� v_n$. By " VI(2),�D:x�c "5~�:t!O*�$%u�L� %6!��)m\V�of6�(K,�BF!3�"�i"� Yi*�'(n�{iuef�� An�9"dOm�MA��*xIaɽ"8D,6��,%� V�ogoS f�J�(\*�=����psi}$no&. ���t�2�!$�} d1})S#y0 ��m~s��Y�}\*EHa, AY3� eE?�s$v2$P�";&�$(B)� �1�A�� (abruptly����. _} jt)Fw<�H eE (Y)� � $\Lw =5Jw񀡴 ���%PA). Sa�U59@a�a؅�.M=�t�)h��64%a1~6@)� ">e��!�(C%K�!!XY5U(re)ab$�)�>K%8%,A)�� �/is.dtX ZM�i�Vn q�al����hNu_�W�by6'a�� dJN� id���vF+I�0I A�F��|)9� @jPir��R>3%Op�� (D%�!vI�>0%c.� Afre�>ed!a�L�8L36("�&��,*nA~-At-)h�hU)s�D�&) JXZJ� � �?�d5�$Studsvik N�%(ar AB, Swed|8f|Ng� b2�nc�z4/ort !�� publ�A.�"!is Q�@4 APS March Meev, A?�8n, Texas, 2003.!pf*k6� Libr�2�%� help!|�ea�nee�F �07FE$thebibliog8��!!w3} �, L.,  es Rendu��Tbf 177}, 507, 548, 630%q3);�N�Nd�.12.4$ Th\'pd�Uat (Ma�z et Cie,1is�z 4); Annal�ke%�iqu@zbf A�2225),�$r!v6Englisb �R M�� s}, }0`by G. Ludwig, (Pergamon P� ,� York�68Q�J� irac!A8E�(, P. A. M.,Bc. Roy��cm:A11!E61)8); "Th��s.3/q6s", �Nobel LeI7$}, (Decemba1933)A��"FE[���?U�ie0? ]. % ibid.pbf�8}, 35e�28).[Aq-*�.�!���"cal�5!  %� Zeem nd Pa�5n-B��� �(J�B�� �Aisa9it��� T8NU iples.]; ���  % �gEnrA>z:199�% , R. P�iDI. Miroshnichenko,!"Fglenc�r��of�ar*i�e�� �T4�CocDŽ %� SPE�41980-1995", SoL�p"���4188:}, 169-185A�99E % %(݃$$>100$MeV ionbn�no uppera6 n) F�MarburgHw ,�� "Tell%�Truth Ab�/Ph�"Y0he BACK PAGE,� xNEWS, Vol. 11, No. 12, (The Ame�5n E,al Society, Y� 2002�J��!�e� � CE�it A Tn/�/onmfs!�Ma�s��1st e�m, (Cl�d'1$1891); 3rd �, )�@ OxfoP+ re-p� Hu199�K%\[Ja,M_k�. Fv�( /by"e� \�B MerzbG r, E�Quantum2�2n�D (John Wiley \& So�Ne��70��iB Mal&:A��,%� . J.4��12��12��8810UF8!i1 \v�# \"�|��AS]<�r\A[eDdpacs,12pt,aps,prl]{revtex4A�60$twocolumn,:pre��tn��s= %�> ,amsz9 symbN>M^�;�C��Pdrafty\u�'ckage{�icx}% I���U� fil. .- bm}% boldBh�1Q} a�"�,style{apsrev!�t@{ MemA�F&A�A�adarkov CF�s:\\ ��mX��W lex � SystemsVQ\a�`{S. S. Melnyk, O. V. Usat� � V� D Yampol'skii \foot\�T[1]{E-mail: yam@ire.kh�(.ua} } \aff�I� {AG_i�I��a���o ��iqon� \\ Uk���-Academ��� , 12�@Pskura Street, 61085 K �, Ae�b�uabʅ ct} A newiroach�}*�c�-�%��J+ �D� so�-r�_ m)�ba�A+)��$of \emph{a-�}�!c%� (�M $E 68, 0611{�7) is �Hg<%�*conne�!A6 �!�� "f(�L �� studHQGc�e a-r�2Kng �^us �{. Eff�ve���robust � 2o!Omethod�&,��eBeN$)e ��eVM�ret�,arse-gAled�ry tex3r�-�!and(2ir�,�� ��(-law behavi�#8n�a�g�i�vealed.��Y�\��l{05.40.-a, 02.50.Ga, 87.10.+A�\make�!�gDD7 of.r1g�ny�U�(LRCS� �,.�a�aH�inp gg�62e�H ary m�~\kV0{bul,sok}, bi.�y vossDNA,!}, A)o�� ,mant)tc..czir}.A�"�H e)��m � #J �1rmn %�S_,,kokol,uyakmz�i��kEL for �ksti�ng%m�1Zi���uch5\c>�stgA d.���a�s�U�V�,�&dit40b��s K3lI��]%�� �A��I-ed tr� ��yM E�^� a&s-f�Olys�d m\is:�Ym��M"�R�wo � ?�@�. "��worz0B~ء�+es mapp!~�\�-5"wo9 ��0a� 1�us,%�q ey%Sd!6�~X>0�]��bi�~��s. 'm�F� H&gh��h�D� Wct,�Bin8� ing,S  !�x�x.�Md�=�y�e �% Refq/$nar1,nar2}I�de��X$Es�a �wd�-v� -phabef� They6P�the5�S$� n\ into a s�ymall-alphabet sequence does not necessarily imply that the long-range correlations presented in the initial text would be 'hrved. Moreover, in general,;` coarse-graining procedursPuld lead to spurious � c�. Howec,as was shownpDRef.~\cite{uyakm},Bv\emph{! !destroy}� exist�.o��many real symbolic systems. The statistical�$perties of2Led texts depend, but�@significantly, on� kindCmappingjis%�\t!�Ponly a small part of  ossibleEs of F< can slightly ch%�Ain)�.�!S the � . So%� re i!> point%cod!7!�y-# (associa!Q �p(phase space� g< with its binary]0e) to analyze,�6r%g,Ait�@done, for exampleE�].kokol})� 3$sufficientA�usw2��U�. On� ways7get a �c!)s!x into�natA�E'rruuin!�E` consist%�$an ability!2 truc!`( a mathematE�objq(2� �lated�of I�s) A6ess�%�amb�as#M6U"ThAeHi5(algorithms ���J��s: `Tverse Fourier transfor�onm�czir}E�4 expansion-modeS��$ Li method 2li 0 Voss9�1W�:0t random addiFs = voss ?Q�,ed Levy walk' shl}, etc���<,her}. We believAV at, among� above-mensed � s, u5���,-step Markova�insA�oY�Lmost important, becaA�i�%fers a%�iMStoYS a�) cei�def!�U�!?��i��{I�al way����demonstrE�in.�uya}, wEBAconcept ��%�ve2� �*! @-like memory func!@0 (which allowI��Ei&treat!j)�introduc��.�$some dynam�� (.�ed uQ��P Eukarya's DNA and di�aries)�QAio2H�ݡ�Tbe well described by t�model!Y!�%)A�-)$ity, prima�� �!spaperM��&%�rm�lizede��c��of���C non-��o��}2�q(hod}. Anoth.[i�Abased��� ider of OU�s)4a }evalued �} �8nar1, nar2}. II��$nt work, w%5 tinu�vestig����-Fe 6`řmo��Ex>o s. An equ� conne��$mutually-c:Au��haracterxcE;Bz, i.e.!�oand29Q�s,�@btained. Upon fin�a(>o�.originalm�U� � basi�De@ �EB�, name�$.��)�an build['spo�2|�ich��esses0v� ���i� ��ce. Eff!�veness%Krobust-propos�}!V2�by siAi�U is �k is � �n���N applicE&s, e.g.,�a ��on��%a�2� elEFs ��-uaOto fabrae%e� filt��oAct%l or op�� als, * iku}�jsugges�� �Y ed u�AlMe 1�E9��re�8& ed litera � %� to reveal�ir uniY Lower-law behavior atG< distances. Let�!G�Q( a homogeneT T Q! �t, $a_{i}=\{0,1\}$. To determin�e $N$-\�it{�u���} we ha��o�H�M%ԩ2cAڡ��rob� } $P({\mid  -N}, $+1},\dots  1})$�occurr� �� � $a_i$:� ( =1$) after�4word $T_{N,i}$af� a�nd� A�J6)5n�!Hhu��� n� y to �$e $2^{N}$ ��E1n $P$-QFi�A%each p� configu�?A) ; !� �)[fc�e �!m$N$�referred� ���Rlength+.2 . C� de-�at�zare go%�A`al�Y�1as�*� Bhorderq$10^6!� e nebo make �h��& ��.Y� sup��wit ha�>Q��}��$m, \begin{��} M�=1E�MPL)= \sum\limits_{k=1}!�fE�T-k},k), \label{1} \endT��%��`!#� influ� � prev8-� u�4a�r one��Ek:$.�%��ontribua�& SaD{�$A�ZZ�V 2�Aun� au $i$th sit ���# �2A�provid eC-inP1 � �g4 Eq.~(\ref{1})�)rewrite6( a� ival9 u ��b+2�r-� F(r))� r}-b9�2aBn BjM.,2c} b=\frac{Ri$f(0,r)}{1-R � }, \qquad�=f(1,r)- :.>���SL  $bQ)]H�U }$ averag� verE$whole"� 4, $b=\bar{a}$:b�e} %=aA_{M\r=0arrow \infty})1}{2M+1}�4_{i=-M}^{M}a_iB�0Indeed, accor �ergodicYz2� , $\ � coincid� ayLa�wFensem�of Fi ��25f� an E�B$�4 2b} �=PrEW}=1)=! !5�v��}2�  )Pr( B-H� Y5�.Vof6� �+�}$ l�/m�nd TvZT:>������pA��f1l; �O$. Substitu{$2 ��$ from �(2a}� to�2b}) �tak��1 ccou*he ob��� $V�9z=1$�e/sFdq�dyb-b2U�`a� +6w. 26-�}�a�-r}B a�sum�� A$ *b�L sub�pt $r$%H-0�6[ute"]  =b+(M�-b)2�r% $. From/ �eZonclud���us"� �>asB�1�*  6  �V��e�� +F� We� aO$!�$�a & 5 $} (MF). It�@�str"� 2G:C�� r}$ La 2J, / �Gbes�0our knowledge�!uep :��[ �BS �2�.� �!�e�a�.)}.)$w� }te in���qut` l �"���2� Typf����inuy�"�mo�s� employed ? inp|:fo�9�pY led �.�Hb� Rbe�t >, dire�ter�o� "j�ߡ�a�+r}$, � also�el ��ir �`a via=)$� ermediatep. Our+roach eat.x"�" >A--C, spec %�X �I�"�IG.�� %U^%� ���5�ͱ fo��?s�� { nume�.da g�B�enabl-�o-�ly:�.�U�r+r tha:�. O I�ha��poWto��"��*�6�by�+.�� refore��.#0 i&�E�BJ-�X3G> ll p�tk�disclo�E�trinsic.]v �\(ions betwee).q',. A dichoto22a a2I�though���", �`!�f:Cic� �articipe95U4ed Brownian mo�. Every�^a�& :6nin� )of�'s coE a� Z $L$c (Yub-]; "� 5$L$�A-)1regar� as%�-�JD aHd 5�.trao� p "te al"��val�a�is�of view��%� Rn s it�tto� /*3N]�� :a.��con� L�"�$W_{L}(k� %\- =a6e�cb�k$�� KF (m, $k_{i}(L:C l�L}��l(�t varix $D(L)$t D$b� 3} /0=<(k-)^2>,>p& �i�] *t g%is $< >6� k=0}^{L}53 ��sB� })�positxF rs resul�! x per�$ent} diffu��"S displaceI� u�i�l��i����~ oke JnIyt��P-�:A�ga��E"�MF}�A� �anti-n�a��uKuډo�m/0(le. In term�� I���&5d'9� a� uld bef"so!ed J�.� s� 1� (n-)B�A� 1�(omagnetic (%#2)e��)e"��!m&�*�*�-/� fQ �x�s �paɷva�dis�6ZV Q[s��-H. � :���%Refs.Qg ,��&n zed �Z� �b"�ndi��wo!�amR��ly� ��depthk9!.� �x�u"z�ch�!6f*� � $ ypŅ%Hl� AY` �!M$u�%�.n��� Hasuper-4��linear�en��&-Vrem}. O.L both �a6� be obsf&A�her�sca �� ����D!ma� F�A�F aile!�9p����W sif� ��.\ . Be��O"p a& r � ] �+: %�QNAD�uHA�We�c ow A�.�� �>! x�!�>Tb a�Ip:k fir.nN&" A�minim%j "���j" $��Dist}$ .� .�*�by mean a som -dMF%'r>(vis��is�o��"�!e� mulab�_m�~(�=\overa%{�}-"���))^2} = �_�R\")^2F{�'!^�$P$.�E"X2}*Xext!s��%9��- �/� n��U)bP cor} K(r)=F� � r}}F4^{2},\ \ K(0)�(1 ) K(-r)=QB�FDEqs=2}), H�,�cy! s \[ -�.r,r'}:�.�%�-r'} ��F(r') -26M>J�HF +:{ !( } \]B� 6P �K(r-r'�')B�!I�+!v.  %03B�]2��F� \�delta� }{ u}=:('� ���=0,2�4B� yiel�4hv�� ship2s.c�s�U�J�u mainQ�2"'n N!�')-j, \ r\geq 1B�Eu$mf^)�8�be �v�� straM0forward calcu ���� $Y22`�*a�)�&� �S �<) � $. \protectS�e}[h!U�ce� ing} \����9$�&�#. �uVu2Ju�r�K &Kau� !l)� �2tzrr �6�}r��:�^���� &�sol" "��f-�"� q�}� �2�2~�L�&verif�+e:�(f�  by�< si� � s�#�� a)� "t� gle"�i�5+}Jvo=0.008\,s {r,\;A!p\;\;\ 1 \leq r < 10, \cr 20-(;\ 10 20 ,�<>��20,"���>'c en� in Fig.~�"��!��. Ul9�� V!��� �/ �,bi�,&� =1/2$,��&91 $\&3(he�*C ai���gA\�2"���1"�%����5���Qp�U.�N��yseKio�s6;Ů>A 8 n se��$r�mim�,re �>h"A#reg�$1M=20�F!9!r>20$,�I��is��h! zeroZ5<� . "�vanish"�fKn,�A�Ju(-p� solv6�Yjm� ��3 is&�6J�\6$a good agrB of �,je%),�::3s-�a<nd�myA� triv9- �AF�np;0E��4 �*��U� aZbit�+' a��d.e5�e���R�!UA8, "�5l�5���!�`R�J��� = 0.1 m sin(M&e4}%j�"I B�24E6B���aDo� �e6�2o oi�:2�re�5e� 2����,"�!I��6i}e�u,V�P-check up�l.x/A��eO��x}}Um}A�A�!��AGhA��aIJ}� �+itn(}H%�):�Afcel)a�e��m�JN��� R 3J�  n67�3d  $D_n��!F :�4�.!aB� B E!�"� g�;!�byu�#:@ V!S I�dotH� "- t �� 1ced "W&�, $D_{0�L/4A�ha�� *�1 Y:� 6`+e.1; /D_0%Bon;�short"s."�Fig�^u � �!> "�1�2��&R$$�8:$72en Bo.�%,*�#I �=B�1. F�e�Jiz&�1";emap&��z2A3MZ EZ�bibe} oB##�����un�*(� <, $(a-m) \mapstoI (n-z) 1$II����1Q'io>�uc*_U�}��" lye�}NA I��8&� aJdy� C6, $r>i� �&� � niceupproxim��!��6"�h ,=0.25r^{-1.1A"?2� i� dash-MM� %�B���Z�4N=��>!�)d%2�7decrea��>�o �  plA4sUB� TCmqe�e��&("Pygmalion"!cB. Shaw /e�)f5e�� fit���is5� B!�q��&��nesi��M�$in English0Russian,�0p�:ly22�^2 Not%m�"- e�40! �!B�>�l#�1mY �"er� $L \sim�!�>P"� %.�$ici � �* studOE�9F��&d![< �s � e�>o>�a�)9�ingh of .�nd>Y{��*� . TA appearE1beOAr�l� fe�C �EE��2t� , any languag�*�#.I}�Z:�s � +i� � :�e*��:^M�-g7M��(C8aQ!é{(AՑ�!/Q�,�."*#� anhCbib5:�)*! for � ison�:��J��!�V�S pyg}6g-�'"�� � {u� q��=�=�0. i�@@�!o�+}�J�IH� * �F;,�)itq$found!*.�� pl.�7�E�fa�.nfiZ. by6�5}��T%�:6-w2�FMI16*�B its u�at*#� AE�\"�#s& ila�1!):�v&� >���H.�/ expoa�$ � 9����YD��`L� ffer "�?ly�s^s5NsR���at-o"� �xAY�xU�e>A��yIJ��� 9|qP�.H.�5Tb�J>wh?*0  qc�;�  we T*�,�TE�NM�.�)A�>02�C<�CY�E\=�Uԥb(�& un�=�is"� !b�A��F*��{am2U�� &�I�Q�- z . Ac�D�i|J��q*a sui�i F4ve "vi+,naLrd"b��1p stocha�� s� 6�a�2!!��C !2�f�CM0��?=�B�I5�6( >�B�E|FnEyir�f�� ��u���Be%�u*(�NA�lex. organ* '":�iE{ tras�La�.�9ly �1uss 2i�1y�l ~]��G kantAG� theor\3�s���.�/pr.G�/Ju. F.�M��E�f %3reflect�� _i�Q5i�HAjl���Gn  �is[( o!La*��Y���s�N���B�Cm��1�r+ �er I (eEE� higI�A)Ri �$lingu } a& U�problem�#requir� regular� �^at��x Y1�*A�� !0IstpQ+or�) C.�J�3one. N� theless,%�pre�A�aj9� sBF� � ��-�%QyL�Z he a:"N.��T�a1ite�in�Lnur7A��"n)/a#� o�J*F "time". A��AA *�7A@�Qn{gr��2#A��mac6�G�!n.�6g6��a��,��� f�&5�Pc� 5%�D&�s} \bibitem{bul} U. Balucani, M. H. Lee, V��/4ti, Phys. Rep.�Dbf{373}, 409 (2003�)Ysok} I.OS7Qov, \prl=(90}, 080601J??O(DNA} R. F. �O:@868}, 3805 (19926}Htan} H.~E.~Stanley y(it{et. al.} �ica A �D(bf{224},302T62Tm�� �,N. Mantegna, d d, N� (London)Y376!+6Y52Y�O0} A.~Czirok, d~dS.~Havli� nd!��,�bf{52gRh sche! A. S 0kel, J. Zhang Y. C.~  F1als)9bD , 47�6�S P. K!�,A94Podgorelec, Co�,x��In��aal,5 7}, I02U1 } O.SUsatenko`DA. Yampol'skii, S.Mel'nyk,��8K. E. Kechedzhy)�. Rev. E�EH061107J�'N}Z(L. Narasimh�J.�Na:)<K.!A,urthy, Europa5 Letty6(69} (1), 22q6 nar2�qP�$R. Krishna�P.� arXiv:�-,-mat/0409053� �,li} W. Li, 2��1a�39eh892�a�6�in:)Zit{Funda�5 al A&�Sin Au_JG�)}, �R!VT~Earnshaw (Springer, B/4, 1985) p. 805.� shl}�lF�le7G��$~Zaslavsky)�J.~Kl�J, :� ���6��31J�her��F. Herbu�S:h007266.�uya} :�� V�6�B' 110V';QA�H�!nd��KeshetZ�7!�$015104(R) E�42��M�M. Izr�2v,A�AAlokh��Se]Ulloa, �iZB5D%C 041102(R)l12lrem} &�� NE�kus���"4 . qA�+%L$� 1( F*�(o�ti2] �PQ&):�� d s $L�is &�C:�CHm] *$N$< \neq NG2�D��4t?�.l$D$WRl1K�6��6��,�k.� ref}22RZ"QKo�N�4"O sN �$in*� �&*+P��A�@" S�TCn�e >l)�!)alHYlar�t� ��Z)�"��7.��}Old T�,��=xK� James Ver�:M��0, http://www.�H(rsbbs.com/b!/:lr}LT Synodal LiO 31/7/91, O, //lib.ru/ h�SanNLiya/nowyj\_zawet.txt.`�A//e74r.org/drama/py�0/default.html.?� � K� r, D��Kessl2�74}��19�endAF� ci  docu!Q} 0Ic:62�0f�K/[^�K(2�K)]"G�6�K�&I�NnQbe2ngo � �E2!.2�v�FL- �>��Ad sub-E� 9�29"� ���� A�D1�(mbols (say,"=5�Mp@�F]Pr*%9l c*�!�1;�Q�i2>��� � terp ;.��"Y. ,bri"| bri}I BricmontM�iIarxivE�\abs/chao-dyn/9603009 Ii�:� f o�0)���� ,/ -��4�5$�9~"��R/. �F �.%J2n:�0V#V�.l�Z;��.�.V^,j \�& � * R>J�# :Lb:( ��:>Z���QV4  -b� "J/  J�  >>Z.��z> �V��' JJn/6&n=V� \n8 ".V.J  .C^ V+V�1�V4V xb� QAV�2# j K:�:J*V�V)Nz�VT> Vf'.  . n �V#V X. ��\ �class[twocolumn]{revtex4}% \usepackage{amsmath}2g?x}2amsfontsBh :et�RLer{MaxMatrixCols}{30>R�X�0} \title{Ray-�@\"2)r 7fitu�T ge-,�|veguide } \author{A.L. Virovlyan�pA.Yu. Kazarova, L.Ya. Lyubavi�8affil6({In�S�Applied� ics, 46 UX|ova St., Nizhny Novgorod, 603950�  } %ab:)ct} A�"alogueU geome^pt�3K :*m� w/ursTa w� �~) n#Iae scop� t�"F p=�@e@� hu4 �7"l ray"�Rs��^.��*'h! coup�� ret2 s va /��Z- eval�d�$<8��$gr&�s a'�k$technique.q5�(LNe)�A�F�par"�Hf�.�N)Da�R�b$)�"� BJ>!j�r2�l:e�r&R�J"�(anab�+g/],� r��.A�.nf�Qb!Z�.�a��;Hamilto�Pa�alismGT�' 2pVBM;,LLmech,AZ91}�yP%oa each)���:�"OON�s�\se qy��5�T multip�dv�!n�td>! �9!z%��x$./ �/ �s!�;!5!F pathU�l{���k�to�d_Ih�H�Mo���I}s manifeXm tselL9y%�E=�U�;%>Rey�A1�5ly exa�d �le)|break%G1 group�j�=ar�%�kwidUb /�; oporAp9lspreaj\FW3�ei:.a$ Schr\"{o}�}e&ADŁt'XCm*SI��l may bA Ifquantum � an� Ku�#U�R�Mp4W�'-&o�S ial �Irtim.%��P���2�w/Hm�_�ua{*Z8E�propagE� in nI \QG�$pl� {*)wafs-�SnelM�choic�caz by � &� �  M�f4-e8a�top!Eadd�#ed�,S�! 88,G+u200�n5p��)�'ed� f"[�Q �B� ray-rep}!Jvi�a brief%pi���6 %�e��"in&g " V�&� �+Q�0o|s umA�2� s�e�[K)ME� Sec.�WKB-P��"� !�Ŭ:�(�he WKB}�ion"_T��I� B��� out� a2�� �r�&Y'U �5d&��a"�K� by*o a%urFo�.m)cA�J�In:1pr/ on�1�> -��Iamp�2y�!�A2� !��sum�s�Dmfi; L �>G�4},�B.wc(subGPF�6�Cub:Ai��EC��onoch_X�*at�.ar�w f�*ency $f~N a two-.��~D� A aG�*sp $c9TAa"= *�W, $z,yy :$�sh�52 A[�t^ )1]%�ŗ mprofil�0�a�le�PumE ��� $u(r,za=M ͠J�:� ,JKPS928b�� 7Q1}{r}�D al}{ r}r6 u2% +6 t.#z}% Omeg�{c�}u=0, M�N ��\$ E=2\pi fgv(Ar�o�*:��A$ s�8��( $\left| c-!\Jk| <<$�AN� JQ of $ 0is�"bQD. grazEc���A�ng A�m�. E � ven|��xhenvel$�" $v��e�woYLb�2� ion%9,9puMm@v}{\sqrt{r}}e^{ik�7-�u-vJ��J$k=)�/) �i&+;Й�$I0d�e1t�֕$"2 .�I�,SFW97"��2ik6� �M� rU� A�.!I�% -2kUv*$T�J� JTU%�-Y�m}E�( 1- �%.k2#I�) "8UUFuNot� A��F�V�)��AVN� :� b� �A�$ y $r�&k�>�>��$ �"6ay ro;0fc, Planck�\(�)"t :�<��\V� ��w mi -{ "Ms M��y-z�sIB � B�Y���/a���A�oD92r*�(rays (eigen ) ��ve��o�\��'a#e 2m yj�#u"$u��bI^dz}{dr}M�Q� H} p}�O}OfKqdp 2I� (.4z"�7 dzdrF��!C=�FqH=pA� /2+UU�H-PFO# 1� $p{D2]��k!H2p $\chi3$ roug�h"�TJ�,p=dz/dr=\tan9�p-chiF� A�"@u �]6In Q!�"� E�7\J�v=A�}S}"�Xu-�N!� $S�$A�S^!eik�)a�"� :v ) ) Ie�?og�1�',��pal�~�� ical* and 6i�Ɇ� mJ�S=\int�$pdz-Hdr� m�SF�runxH|�1�:L�5,BornWol�O�}xpl�r�;&1>52 e yG6sourcN+ci�19��8e"9ai�7_.!o6R^EqJ� eYa!pi�A�F^v(0,z)=\'[ (z-z )Y�oint-inJ��M��escap� [e9 $^RIta&4y� ��WDa� A�st|� #$pJ3*�F�A=���k}{ iE/\vert ��z/ ]\� %}% � -i\mu\pi/U3M[�J�ma\mu�}!�Maslov�m ex o�mtE�*mC�.�ray pa�~��ca+M�Gutz67�-�A�>;���ac-an-P��S�8!h2��2hg  �oscil�?ng curv�7ire�7 e8if�2�so-ca%�ToB�mAZ�n�#�laL �fCT��� ��T.Yf�"J].�%>&ER�&$y.�!-�!F� '!Jh"z�VHI"α*ul $H$ 3 I;xF� (] �iC;g� n�-3�~in "��L-x"� $IE�:D�sJ�\FhI0� \pi}\�, p\,dz8int_{z_{\min}}^ ax}}% dzi�2e� [ H-U(z)i�] },\��Ij�^�h axr��l��k uppe�:y tur��s, re5;iv��satisfyA�!n&u!$�=H$. L_U �)-Ui-e T8quotedbla-�2�uA&iA�� ae�!��2�/ai�yi��peYJ $r$-axis�R cycloO$ngth), $D$t �an<*Lof���P2h�Xo�=r��t -<��0DFB��dH}{dI�dGM;ER{D}ՊF� TINoX�Q he un*e�� b�"�Nbum 76�I!ory. A� �^half- b_canon�6h�J&V8p=p(I,\theta),\G|z=z.�{TF� t� -� �Pp,�I*�x$,45Pi+>��e��$,AbdullaevJJp-��IG} z} � �j* I},.1F�J G(I�Bd}F[(I):^ tGNZb�g�h�HM/bM=is :8���)Ђnq%�$05� $\pii�A�*̌!�]��-&Anex�2U�(?< _BUA�$�� L �Cq#��a��!O�>� N~.��&� de� I�!� N7e�J�($� to $*�5��&�<a[?M�$v<s�D�~ p wj� nge\E-6| ��  $"| & R�: &maՎrDbf{�.� }3[  cross-� B�=��f!�e5�n�V\��a� '�an�ppairs5IE.Jap�-2� a�$C��*/!ub�!�  sh�Q��:uJ=. F���W6U$, .?A��  � u^qy�|��*�SF/;ey ac�Hn�#/ (rgv4� 5 � <���  3�n,� dulo� �Kgskip�7 $Mc$1�&� � 2� � na&r�J'!�F0]a2 F%�t .� V��r� %. dU-ITF;X og�M֊�� )"�bn&_E)6$2��� =\pm� �}%(:AFer}:Wf'A� %!�]]� �tz�!2���-)i�"� dGdIF1�B�m$� �g)�A$p�%ur� &��y�Jif-l��aN`N��� �)�%i�Z B@ �)&��)R͸(% {�I�'dHNs�%vuy����!,qtc',a�[�a.{:& �wR� ��< �9F��=�b'xandbQ5VIr2V=V��E�./V0Simila�bit1!&�4i�B���F� �F"ZdM�1}{)P}ej^�� �����|FM�� )-�ll\W!;nu/ $��Na Mb^�Eqs��e�)�zA�%o'n�xU �h�"� N��  �"/�2�>�)' 牌 ) }C" dGNH�� ��2�$)R p��"�g������NGg8feS("I*�J8��"��$F���d�$V�%�G�X&�J*�J6�9� h���of�-� �q� �>"Gqay,?Xuted �J�4�3#�� is54��.r of"�$ mus m>��L=�:Fn� ^p-]%� l/ i�L.m+$cc so sۀ��)�&�Nneglig�K�+&�"e����+L3,BL��&e� {Mod�� �-�B�0"�ec1:�-Eu&��2s$Z �2;ub:-PD��*(<� .?)C.D�*v!��#"��A�oA�����< Sturm-Liouville &�3+�X)U�7,LL�4��B���� dh&4\varphi_{m}}{d�)+�)(H-U)#=0>(�-pN&�9(pr��b�-q"T�/l�  2�#�lI6��urfac V_{s}=&\�s}}[ + botto> V_{b.*b}_#We2�,Z[iT!�a�SΖ���& gy l(���&�6$�v brAOars�)>;p[ ���[5�NVd� �j��dY4tom we �Z fs}=H(  b}=04vcJw�e�!u () )�1 ! �#s lie��E�wW6 bulk� :t-2$$�hi %h �!E0Y�! orthog"�'it�1�.a0���R� d�dz~]� n}�% _{mn�9ore6��*Fb!&�ioi� $m$-th%1v6Re�!-��em?G��!���~&��2�. By A�"��%����CpN!. "# &x��"� �Crt�A�AgF J` dm�dr}+ik��=p�_{m_{1} "�=&X2��&}&:r&�&�m�e�N�%F �� r���#by*J� �.)SNbF8l�A� a� �56J%�T���"/"�am- u0F+�><wd�7i�� es9!�{=��$Wr"[ O�aZA+b�!�5fG2{m� neq0}B_{m��+\nu �n1�phnj% : 2v�E�2�1�) y�d�n\u6�!��ȡw jingN=IJ\F�1&�E��lY�5'�1� U2g(@U3 Bmn0N��o�ML Ex���Hng]�\�8ASte>�A��> pect���� "3o&�2� �� �.U2gd��1�-��az�{)�F�������FmKX :� (z)F%/Q?asI�FmnJC%�$m,n>>1"��,g k2.�%�''�v"�!�4 �#dE���=&� 126/% }^{�r3 &4SdJ 2�"*�-�9) $dz/J=d���o l�7E6� #Dc6` shif�n�"L1?&�'`a�1� ��Avy�&c0�K�SYT-GRi"��.@4%� �:Z0�w�<t a[Pi; ��ABW->�9Im�V�-J&�30A� A�� 1 :h)mA~I�aJQ q}.&a%i�F ? } w"F�-���w6� 2F�{E= �t� high&&3 app R!tre�A�tB7"'��8nuy!��nu2�% �,r�BmnN6�"�AZpHfor� a"H�� "v9�e�*^!�/iZhAh�2K "|W�� � )�@3C�0be &��|�OQ#}�B�\B� %� < qmJ; At6�i�7%� �'�|e�t�.m}$M��&�PA�"C ) �ᡢN! i i�Ƀ=Bk!!�.�6V -K2Z/,I@Fv![^{=u%))�0�w"�V8�C"VF��%@.�<<15�-* �6�fv��&!�%�F@ %�*^U(F�]�: "�?��A�=a!�X."�U�V{ �� *�it� s ou�9�*5��Bq�� .�&A&>� D/L<<1q�DLF)e���iFZ� ehorizon�p`*�&��&�Uinvolv1'.��1&�L ^"SJ� aK�,G99,Milder69�>�kD{ �" k2N���ar#<ss"�(Ȯw  tr/^$n,Q���useful))Oa����A- �Vx{a.�d�Q�W.&!Pr�P1)�""��KB�\"�ec.Q:5!�" E�"}njpar�TTu:S7m[ww+w)a#��.:b v� D&m +KF���"q8iPcAorJp�oA��xssuIZ�Y* C�sF*�^�ur>F1J�.� ����L"�,z)��amNWLt�U@;5O��6�&M�;����"TG� hF$ for 2b�$!���{  +% ^{-}9^%^{\sigma1!+BY, Šk\Phi."Ca-m-s� 6�� C� �7s plus�D minuJ�� B- E+i AM/2}~A��UJ�Z*Phi=S+ P��#PNX#eU%}�,y} (r $k$Q H0l` ))�� e� &JS� kNf�`�u&,H\W��/-� ���ef�.>O�){I�\��azN!&��$.�}2/ _{st� V= �B\exp [ I?+i ��{4� sgn&�*�% 2�O �&�� ��Q"/bP:�2P � 6�(^:!�?%2/8� �CJv�q �:��8љ�h " sgn($x$)�&��Fg�� - �(�N�J�J[-�t���*�2$S�2@ u`�7,Awr4J&?��D 0}\,�% 22"���]}CM�Li(b�!1/ S} z}=p1� dSdzJ�<4�/��&�M.�8�=r,Z%޹cvwe geJSQ�!a%�:��5�� dPhiN�Y& ݛ�:;� $z*T��,E�} i�� /v8�J��#�ƙLFH�B� �8=N�e�(p"��BNA�"< ��y)]VH r�Pwh&�c"E�)?�m: ��"�c �A�A�n#�e!�u���Za s�/9 fw��b�7.��f. �[^�=��?P�O3za�  �T[:7� 2.;�U�p."�S)�6� U�� z}�!�N�&�p�l*�Bai d�$}B. I2�u�2Rm�H�I!�c2|��! $\ $!m� E�al� th�!E� $�.ED��5� �n AŅ�"k5I=`�V" RT/2�i.WZ�1ba6��(��-i�)4-��vidJ� z>eB�{5 JzT?�mplet�0EFl_#��A�!iaC* . �C� % } "�26%?�B h+k9FF"� ��V>X� Vc�`�P� �:S/�Of�� &QPLQ" ��I���.= �[ -s"? !*��:�!�N�6������!w!9J�u0gr-\e!|� leaog� "�!$. Labe�0 �%�ObyGx�I�P!��,n�! .�L$N��� 0})/>�P�(�5 ���g��e% Pa�\]�b!R�"�3� � eYiN2FVQb��e� �(\����\) &�Q.� l-0/2+i(\beta-1)i�6�5 a-s-N�8itN�>Kh*� r*-�J% B��3cNKF�!� �) h�hE�&cV�m6�NB�!2n2�I:�is*+ Q�ume~up�\��!T�.a[.*��2]-*�& ? �IE��E���f0��� ctly��m.�Y�.�P*�$,V2004,V97�y2�T�Uat 2AX�Yqual �b jS lu�0o1�it� ;4�:2D:R�}(quasi-plane%@��!m@��|ġd.}%�.B%t��[ 06. !���4�!�an &�"� � %�"c\i�o�!5*��term $8�a���ASI�fB|&�"*n!��q&h B�y"�')�$c.�J;:�MraA~�butK�w��"N_.wd� O7�C� ere.'Z: ���e�k��r.NX2AS $m=�$� A�I��>��w�� e;as�08$&' ]^�pmAD"�@ Ka� Ore8 ��<1<� th�C�@depthI?�,t�&<�u�S� b� ��+юre��X�5Q�%*���nte�� of ~Os�!ys�+���aF� ���?�.6�(0)�. ))pJha��-lex&� [1!�,NXJ�A: yi}( p�?�K:�݊-% \�% '�a\p*;0�~ \.>0 5�;��A-mJ�%�we�9I!Tir9_)�6�}�Z) n�!E"�!�^ as Vf % Zf $�*f$ ^��)bN0 `)R %"0 [�*" i OB# +�!�=�� -�Z_#F� Vk �6j n.f &$"B��f f �F� .f %2�!=4e�&� Z� {& ca�u��.rk*".ma�N�=&)�^i�� t'wa�")� ���Fo� }�go���=ana��X ee�>J��] z2!3� :x� Q�N3% :�"�,del-z-s�*e2��O�po.���iirlR��<<�%z,K. dz-D�:i�/#a"�,*�6�:P�'� s. D�BI$�g"8u�"�� %of.�c . A 6D6FE��Zq�Kſ.�A0�? �IA �H=!�) I/D$�ysu� ���婐n����8�$q�agn�a� �'�n*\A ���8 OJ -of-Jest�8F}��}\ .1*`� H}{ &�%!<�Z > )�=�X�Phi-zz- mJ�� ".n rmsk W`q*�O!�+ Q� &�B�\E F_xE�bXx*�(elyN< �m=k Iq�DJE)ms�:a�5� $pD/21� XMc" �D� �P"�D6^2�DD�-b�'�J}�� �")  m/2}F�N��o6�0��e{m�{�ifu�m�/� �' many)7���it�rĞ&��OZ� \-"���� 2�yen"i� q�eno�f[s<aJ:�>:�ESFjXR�,>�us�� ����(�&�8�J ��N^RpY0|T���L Nq�*Jzo.E)��{Va�A�@�$��vbl��"�6q�sec.�r:/"N<�Q����d}u@�p:�"#}���.ub:/$ummbY:>xb%7 �'E��*O>*� spiF���&Pen*|6?T.�&vUev�>`�Mp�#\�nd|�s�msJ@*u �t�� M%ye�.��&(�YoF�iF�ny ��3��2/6�Y�A;V�&��u�7KLffI<<1/kL �ityZ{c�9��I" ��& sV �+{Ji �p�0a t��!�b� I`!%� �, �A�s��Id�R2j�xI=Q-v)� �=J�Y,*��"�7.TJV$F\+~"�I�)% P!,�KOK� .HK��6j�6� �"A`gra*�iQ���17�*��)p��K~Q�"H4^ R �#v�>k�=��S� Nu>2= !-+.6)^h0l0drQ�T�.F2 .u:��5N� �7� &�Y�)H�s� �y�� &�). �h�� a��ar�)"H��H��q�K�>�Aa���c!q�8���*�) �� �]in� i�*ߺ�]i�6�́^� #�*�E�A���0&D (�0� ��ichJ(y�Gth�r~ !,^��( till�z%[g��� E 6�fails. P���i*�g% *)J f5��a���L��I A+�� ex�:0�&f�B աE����q ��P5}���{$$u'<'*�0"[8�"� .� ggm��!) �itE# !u��!pm���"A'roppedv< �� %Ry=�9((5g�k it2G BF�*)%��ar~�)�e�[��Q�K (5yA�|""�*y��G mO�5��?"�M�IBA�l��2�n�� M�� �E�`�seu *YG��B5*%�j.�_��.x��,?&�Iepsilon$��pu�a,;to"eAoN�%c!�up!�bE $O(5 k�WqS;a�ol�p S�] I�] �%z&  f e=*Mb>c��&c�%T b �x"s d �o� *�&��2� -%a"{ !, a��k. �RE�|'�e.�;}Y)��E"�Vu� ^1w�>&�VF�Gv,b}+)5 I�:,0)BZ ���|(0) * I\Z� dle-GJFV:+G(zo)c crt =' l'��dGJa M24=���z� E:Hr�� �Ci I:*�s+V\[  ._^7�3d _%=�Q�p*(�  I�Id-tV!+NK�.o (r)-20R .NSJ�C2���el!{.�S0 _�Fg � SB�-Rt�U &� bF� �� !�d&�p2l�~.�.��Oo week�$� W-t�mmu�h� �U�$��P0L���:�`&�A*&��: $�6.� �,ouŏ�T�fcd�E��[\>@$. \ Ti%� �����5��AZ'e aJ@ pq=-�:V�XBSA "��1�ri&UC�AFJb�1.! 2004!@j6�� �x6� ��i �:�r \ll\piqPG F��N:yxV $-@$ �g:q{4Xey��=ng<_xhp'[ ��9K �(i?�!��R E�Z22 E�6� �! 8� �2� a�" !T1�sxC4more convenien�Ut for practical applications than (\ref{qm-small}) and (\ref{validity}). Indeed, evalu@�L of $\Delta I$ can be performed using a standard ray code without exploiting 4ula �dIdr-ex�4it}). To find ��on $I$ at the given range $r$ one should (i) compute +�8parameters $p$ �$z Mis H (ii) �T them as initial condi)Bev%e (with� samek8code) integral )S$I-P}) over-�Dcycle in a corresp`|ng reference waveguide. \subsec��{Examples \label{sec:numeric}} To verify� illustrat)Tabove results we have -0ds field� two %e\-dependent hydroacoustic1� s. T!Lis done)E�!, MMPE \cite{ L} originally createdE� solv!!�$wide angle%� bolic equE��. It has been slightly modified to us �sQ�A6Faroxim T All -Kal5'presen� in t�-�)>� obtain �monochroW)$1Uat!�arrier frequency of 200 Hz. In our first e)�% sound spef!�!mtaken �e!B\m $c(r,z)=\bar {c}(z)+\de�  $. AM�in9�Pconstituent% \begin{1o} O Nh=c_{0}\left( 1+\varepsilon@e^{2(z-z_{a})/B}- % )/B-1\r!�)  ,Q�(Munk}% \endej$z<=1.5$ km/s, $B=1 , $m=- a�$�(=0.0057$ re-ϡ ,e so-called x profileE|ly usIKstudy-�propagE10 in deep sea I�8BL91,JKPS94}. Wa\nsider�roa⁷yR perturbRA�ellaa synopafeddy%J�.�!�2}\,\exp1�T-\frac{(r-r_{2})^{2}}{��r% %%�>%z(r 6F� ringJ� hereJ��2O= _{c}- v}b�v6� r_{v}�.Q;del-zF�Te llow!X��esas��h�a�$ selected:En2}=-0.0EU/s, $%I =300Yv$!, �r=8!� c}=0I�,�Cz� =0.2E�, `v}=32:?�= �je isolin��� totalM��are show�Fig. 1�Ji�$figure}[h]1�c��$r} \includ�� phics[ hea�$=4.8193cm,a$th=6.6cm ]K1.eps}i�HcapŰSo>�moZ���aeS4 sea. Contour ��s�of � in� .1� � %�(upper panel)%2%i� deviiwof� �Zitu�yt�$ $r=6)� from its�SrtUM��$r=0$)�Vis��(relative to��rmsJp DIt9see�mat on��esD 0 $m<15$, whos�s remain&� ��nch�od,%= adia�ic�4is fact agrees�bpredigs fu3� Eqs.� # 1}R9 % ).atmiddl��d low1�Z-���}�$�� \Phi�  $kmB��} m=�,R-r}{R}c_{1}��2"crz-lin�R� $R=2� beQ�"+ length,ys a��ar super^ ion �w�[�s��*c_ �/n evolu81 = &6t� �isŃ&|4�ҥ��AEacou�8is ra%�s. �_of.h �" $ (] E�)A�%�j km? oQ e�Vof��tyIlll��o check�9bil*of est-e ��8we, once again,� c; deredI:Y the .!/eBRF� 5 Y dem�����z�!�vi� a good �fov���knR ���o whichQ� ��=(new feature!H���(r)�� ��  B�ab�~�͐is an!| eara!Y4of narrow spot� _ .� ��@bout 47, 94, 141,EC,188 km. From� view�45A�ray-bas*pp��is phen�ron��!��A ��C} �q�)Bu�57ofI� . Si�$U�\simeq(�H-�)/� %#lmostq�.P $r$,�deriv| $\p�al U/ rL"+ly �-.andLs��ru%��Tcoefficients $V_{\nu}$�F1���B�At� �ng��$\theta$ $\%�x  {$+\omega(I_AM ,0)r� .nRk� Va�Yvanish22 �u�er multiv�8he� �o.�q  !5I�$47� . "b����4n6S*���y=' �� p6 �t� ��� ���� $rՐ� plota (&� �� )Ga2'offsee� $0.4!/��h��ftA� �A�"� Q�j�!�& u��&s�ivelyF����6�5n��ega��but�Qtru���a�G%�e��� ��R% 5a��2!#n4N�{Cosa5*}c{I�a�3ax&^�Z�fmethod 5����nalog��afgeometr�  �rœ#% scop���;��e) "�a�exu��thr��m���� � s ou��$m"�W�contrib- .� �, &j� �v�obs/| , upaca�~�vn�t� ���$m$. �C!�5emainsI id!� .q "� ,��e sin�ulaDnn��y��d%gs�T� a conven� tool=D6|>Y *�%���5 E !��6[�!�Aon. Our �st cri��� 2..���,imposes limi�s7 O � !�!��%� bl��" �1 abl�_c-:o4!�B�R"6E� EG�3 I�i�'ter� npat� Y"� �i 1}) fails)�quant� *O Qmat�!ber��V"ng�For%�� of>���mo�ccu� 9����e1E~1%v , however��quireIr�,tailed calcunons. N,(theless, it��&"be em�N)�9"!6�� h��%C�)#)"d �a�&#�!J!�z"hM�a��4�5�-*q&�#1]�t,A!&T Q�$. Note als� at unlik)"�"� DL}� k2,��ccounj$ !΁qerror�i7. � �5a 5a�\are� poroa��WBe!�is�)�'�� "!ibe�s}!5 litiaI atisZ"and, h�# 8�"iQ� rega��Oau6�! ���A�W u�8&�)� . F5#,9 ic�S"ll%��#&�"�"� e high&x": � , n� �#ads�}ir gener!y���trast% p# �Z6j#6�!�� principal) � can a�asilyuz&w �m�!���� is gh%!� Helmholtz}A���c&�D T���!0ng in underwa�J%n��a su�''���#$or descripA�!6�*["!�&�g% med�n nalysis�a��um!~ti_&oscil� ���� well�\im.�!�!.EDis work was suppor� b� Russian FY i�n8Basic Research %6T Grant No. 03-02-17246�igskip"n Pthebibliography}{99} �v%� tibitem {V99b}A.L. Virovlyanskya�@ G.M. Zaslavsky, quotedbl�� Wave chao� te&of2i25� �\ Phys. Rev. E 59, 1656--1668 (1999a�\�2001aB��  docu�} �M%\%b([twocolumn,�pacs,p�intnuFs,� � addr Tamsmath,prl]{revtex4} :[H�QML \usepackage[dvips]{Wics}% I�dF/ 2s %4{d �}% Al�+�;�$decimalH.o({bm}% bold �2psfrag}.P[psamsfonts]{amssymb}6��ntf"4:V0wrapfi:g T1]{fenc2�1x:[col6- tabularx}Ctex)0ght = 640pt %| = 502pt� 48' \odd(margin = -. *op1)8newcommand{\be}2�4} 2#e#e.K4:!baDf ay>#e# DV!bsDold!� ol} %\noIEEq(aHQ� {APSa�� titleD� Dof Book Sales: End� � versus ExShock� a�lex Net�suPauthor{F. Desch\^atre�1affil1{Ecolei, �soc� �s�evolv hrge� yX3o�3!�(��s��" b��h%�rocessI�-=- ing)e�tU in dn� evid� �0.�di= !t!`E�i�co%3 >ruelle},man C��x��2qun!�mS%A�inguise���e��eA�� �G��"rtlq|,$a�%�%�effect;,self-organizE%�P\ A% impact��s"s� icul�+ �'� $l becaElyG osed0D"�> s may lie`% ���� at&!tor��it�3 exhZ bifurc��ere�,]6:q�R ofteasTiedE��*huF *W#o��6 �, in 4� divi%fa�>�� AI)�r �K,3er�\A�h�&�� it w�"l�2to insa P*-' >}��E �MD ous-� U�E elevABsp� beyo�he=� � biolog�P�)͹' mev-� n*is�-� �:{�6�*?u�(Ju5;sca�H'�J�A��wIe i/��g)�-�"�'%Kdo so,:n�Gto T , some assumpA�s�A �sm�:d�8)�eQ:!�D cus!�es"0o EE� ,LC�� �)nE�� $. .D� -�M�}��s�!��x�1 �.y�@ I�lu$Ap�!�.%�u�B�  ,iQI���Ga f �C�qoarse-gAxed de�m�!X��Fm %J�A�3:G|*�%TMC}= !�A^?� =�behavio�+=� b�D��%���!&n��eE����#� 2� sdth�HprŞ �Z.�1 s �B"H�2 gA�x7#K >A�� obus�<ast�c]0u�̡E"�for fut�$�m&. "g C)/rg �!2a�:W���.nk2� �0n� .�M�Z��~FIqwa!�6O)i�.� 1 f�)� 1994��>�#AsY �s56ha�;panded \;bt,es �are�'chMclo6 g, gourme�+od,� rtsR0ip� !�( jewelry. W�9a8x530ed $\$6$ billa#netMwinw94IsAm�Nan giT �,.tra2 is���!�lar e-rger. E�Iron�[�$it possiblBBdE&hug�<N qfor�Mon  3gl:� wise ��bir�IE et�� 846b ^&C�- C8a�eme�g ɃRoehne�l}�NiE0hapL e�lj��A .� ![col! $ so much i�,\footnote{Of.rse��s/Q!�!��)engUJ�Fas Goog�0o|a look#� opular��ries,0 http://www.g C com/�@s/zeitgeist.html.�m3 peo�bu�n help�?� imag= !�st�P-�!be�,AndqB!�� #9 a"-f wibaGugh�ope�0ja glob�ca�3+hy�!�ut"Ymea� prob��oc ��deSw igeB.chief! tisEK�!*�# -2004) wr�/on ��(webpage: ``/m z< 'sqH l�r�T��humd-�M�}ci�Ua[ing.'' UAGtuW ly,�p ob�� �A<gr��'$���no ��n�_��sh�恘a�j8jealously keepsɷ,secret. But,-!u2.cp } unknowau3I� ů%�its websHIA3}�eac�9�p�2ir pa6��Qam�u, Y. AgeS4X�p�edA�-� ��4g ``WebBrowser�|trol''!&M��aut0Rz/��^2�M�E!�Lege}��val�j3 j�m�msdn.�oftQ/�Pary/default.asp?url=/2 shop/b � /webF 0}agoL y r� )ZF)�!��L 's W�W�SWeb .=h opens �'s a��NURL : ؀207.171.185.16/exec/obidos/ASIN/X �P  X*K TISBN or 4�Tt����Q<(!�T, DVD, CD, Game, etc.) �EzTe�=o�6��EE3$lgorithm w�?&�chaYeB7WGN< way��, :ae`��"�� �s�Vs5a�?nth�a�2�Aperiod?�"D hourQ  l��W!�&5Aquaz��A� &$!`� ousand ���m�QrecL$L bf{c Scan} (-��kj:{ orW�years. < � s1n�i typ�ly !x �Gt�6up�dly���.7 �m� "_2 heck�OwB4�%  valueN����n& .��S!�,��w� *w��6 trus�F*@EJL�"� �$.� 2� ��dschemB  M3!� ��8)e�5u,A35a'a:>^!b6Kto April9X4. Unti�+to�99]Ana�!�:2 held��p"�O[>��A In O.eM�.� rede�� tsAZx. See. fonere.!�/surf~ht�Mj. Not�H�M�C!�� h�U|0gajd�L.�T���e-meT$Marketplac,k?!9�)f�6�[ᣉ� 1A}ZmtZ:mthree ti��gon�,li�s�?�ac \-� ru�Q  o>  �t��HuA�F;.� c�re�!��A)��a�.�U 4to re�Di�'%]=��a�F�A�a s,'��8.Y�/&�\a� offi�� � }/�~' �Ds hiL+%a�!Y�.2f�"Fd!� �)y.M:�2�#6�(J�~� �% Rank MI ^5AA�" ed�vic�r custom�,�%s,2-�E sts,6�\W�*��ios���) �7F�cat�AA��a�VX^b� � l� is�x,a�VX; ,����at9t�ar ��F�c&}>��a�MG�� ^q i��HV�� lyJ top 10,{/!V%~�e�QachVM�Da� reflb!�%UZ�eda24*s��W�deeZ��4 �g�YctR  !>C  $1$ da���>ru&V�b�3!nn,!10)a�Z4A�1"dai1Q5A ��EG=��_th�%�V�o� s�av=ere�2a�s}ZL"V&:'Dif S)c!�6&���D/3 �;~�a�izeZb\!�]W:4dayA�a%K!�!� ���.�esY in�|pu�N`E"�I�d+^�����  in�$ce, if Hary*�Hr ]w�^.��ashZ nuUB� won't f��so�pAkIt�_atZWhe whol��st��3D !� outw�]�� �t�"%ZeI\wo�6�";?>��O�.(outbalancedZnE�AE>6F:�E��� M�u{&Y�aЁ�"f 2R Book�)�� g}!low $�$Ay re-*�cR\to2U!�%P duj� $24$�EBsBok"�2J�aF^�@�*�5�]) �P6 ����i�Dt\� w��c ��"� � 2���9t����*�5%!<>n0J} (��pm_)��&O=�D �r02�inf$�lg2�!  I� (H�F�stead:BdHa�X)��6�jum�}Xfe_"��the�CA4Iy smoN] slow�$ �EJ raje��y6���P,.�"���}se�E �3Uar| ��26+�Rm;Y�4IZ� %&2D� !a�#-�\6�>�bottobBne9�9z Q>Br� �� fzBoff�ulQ�*^%ao9�. A!�#ank l6,U�switchI���l6\=[�b,A  +s� ���1�ge$� $6�A�me !8 �)o�-Mi2(-�:� � ba�T&[��������"i6��er#drayo a)R �$10^5$"gib�a. (THb�!4es(c %#ve�7@$To sum up,�Ią !�wH (&�<.A�ApC+m�)�>�a� t a & ~ae� �<&2Y��devoiDZ!A path"�&"�0 x;646W�ll c(�k �tA|����low!� $�!=�W�!:T�:-Iprel�!�a+i* -� ne�*�"�%�*h2kfina;� M. Ro#hal�� a }�D��ix�WI=k#ed ��!��ga�owI�)/���an��a& . H `� Zipf�W����~� ��}�+(we�+&_d $S(R"V3R^{1/*V3d7_38= 2.0 \pm 0.1$,���F`LJeS/sl/$-0Jmin N�X$ns{ e �`xQ��A�k8l{�:cu�M��1�U-��� R 44 44�~,~ {\rm� }~~ ?4� 0.1~.X&pdfA;Q} \ee' be�M� " (�h |>\7Nb!�A�bulM, R�)�tai>7�R', i.e.,� ��,1)bed-�p@" � c2�t�Km �Kw��h; oes �!ap�]/b�)�!lAQm"� 9�m ,�f[�f���~ � seem` *� ��?�ook�^�ifican{*�/� "'1drm law�)~curblock�(er�Y!may� Ohu0$�&���aB at ��kF61. S�'\DAjpe_& b��,ed z!K�.ert�"at�7^'he�:% 6�o~p)vM9uA? �_ u 100\% 'Sor3!�}�B��Zd�d� *� R@ �T2�))� cme����m�I]i�A�3"G( {v�li==q ��%�1,Ih.Oa"ir5e E@s: ��B3eK V2}���lef�� }�. M8W ata Q��;de�Pine$Ij��V%���a�5}�.��V6���aQ�Y=an Le�A� mjNsm put�}bs aI�E"p5�a���a.�8�W%0�:!�aq=!�q12B0:�1I&.1U2so�>�Rp� !�&�MLqK 30\%!�:Ui��%$&�TW��NR|.�S.��b=� E��<�n(u�Y:+ 62}�AcapX�X '+"\a�ulaV�$�����e�*!2 �!���g�U�l0�+Yq*�ZU@uncer�y Xnd�X i�eib\4�!w �� )�� �*u �di�1��{,T�+�#iqD#M��Q7(2z]wa�1Y3V�, qpreI%!A��.>�(summa�Mw�r2�^pdf $p(Sn= %[)F��.�M�!�V \TlYa�� M9i C}{S�=}�) yS4\_ >I!�k =2$i#.I�6�2@B!}��2)o�p� �A�  ? t fua\�{om!�� n�4%Wa�d�LnCc=!b &�0DFp229 f! �2Mot�eon:*�1,Eus*:s c#F"� Co�a��1E�.5w?K� e�$}, exe��CSF"�(i<~�C.�M"F�\ SSi�bec est-a �th$poc?n��.D A (``W ng W�g0 Stay Young''� 4Dr. M. Nelson)�? on June 5�U02yݡ��c24��A^ 6�� $12Z[O T4 T 6*! p�Nq,� �J�wt  ``�,nd�i2r�Y�by �iriam �''E� advi%� fema.DXoer=+=�S.$ng a youth�'pos�G0opausal body,!��/X!�n9��\>t98lyKnew y�Z��z6g"\i2W4evEayw����d��a�� ``"�4''A�ck=��{ \%��nJ#ead�zg��i�.�BA�HeaveMR�H(TL& SIF(rs Trilogy)I�N�berts]�cul:��en�A�9_�T6aRw!~!u tinu�>�;,�@n�ch ':p�eIMx8g(��a5;i0#}12�;�eE�Ient�I�,6{EDb�k$4$�!2*��nJ2�;F8� jge�;�K �`fA ` �1al&�8��be >���.^<�c&�0�E<tm.8�Y�"�A� idea�Q��-WJ( � xaaniz-s��a �combin�0�A�cc'AasE, 27<�����campaign`&� �F infl����$1��_ impre�?e�po�^ &� k_"� o� 6� )O!0�*rbu��o ��B�- d �~ � �R"t�!�7�4react�� aE etM/���sw3*m;L lays �))� v�=� -Gen�c�'�m�K5���Pv Q��I�9�� m8a��!�nd �Dg;Ioavail�R�� capa�\yAmY��.<ost�e"F i�4t � �2va i kerRT0$\phi(t-t_i)$A�Ak��-�� a!� �w��a"!i$t_i$��tA+ >� $t$ by #perJin͛�8!�e��fubut=vidual�5-� �w&}F6���d\ m*�G)� A������a�5!�be trigg5�=��1AEi  �vlA�{ve T.�)$I�G�|�/%�<$\int_0^{\infty})�)=12St�Fng��Ci�b W�K�!``mE��L)4%aic!i� (eit�)� D�ޅ�^#Ah�$)31�Hy -r�by =%�-g�d  ``da:8at''�,� selv*2dAڭ�M dr!=t{g�ow iio� "-q ��i�^&oiHI�7A8&ll.S;��a"i�al�]sA�ZAnOK: x� :Y �!BD�B<\lambda(t) = \et +��il��-@"dof�`s��Qb�IE�m�c� @��"z�!7u4!)l ~O �on"an�1A�e�{*7 �]��coWoPc) stoc ( 9 bub�� ?# renz��1��, a �M)Ln%=.aw.� och&76 >(Christmas. _&�.-� year�њA����T ft�[il�)l\9r��I .�\wo 6>sZ���@.- �if��@�� :XNgz�,)wq� ll fa�B T#gi< ��5, nq?(alPlR�V͓g)y. Like�,�7_�NhxR �A���P%@ �~� �i�r��itl��r��7#Q=SepteV\G�� mid-Janu�b Febr�q�E1d�!���)6Q�!�t�G� !Fa ���FategoCT͆e�vu1#)�=m�_r�eHo�AhI!=YY �"./primar�* purc�a�0A�rşhomemak�k"�-kid1er��schoo l2 A"th��As[ �=�k d�_F&K?lon��� %O!'� )'a&p1)�8� We1\e�o{;2� life� ���E2�O!= J inno�zF $'�I[6 iona!�AssumAWi Earm�2V=wcFY !� F� h�Nnn�[� �%p*c���!&� oo bad'R� ��+Şm�=Md�t�Yx fail�� � 9. ._6 �kso�&� bel.!&y �E�t��.Y})� writ]Q%�A ad�RC int^t ( N[d\tau \!6s d\mu]H )~ ��%/�a$ re $NF"X sta8"noI)�!��� Ma��Sgo�+�k$��|�+ �$@ ��, N 1mu0mu$. �~=isl9;%v%=�$t�(�- U~mu-\mug] ��Y7Jf�6g�5: EȡAtB,ad .] ��e�� F `��oo"�Ta*6nsembq�q:Z�})e�s tV�� ame�Zq�M� S� \�Vv%�MQ�\+xle2� n%�_{-^{"�:$\mathrm{d}%�~  ) S%�)R M�!&Δb�  $n=\l ��X �U�1=U���s!~�*y*� i�.�� �"�u�XM�^-�$���Z� � =!Q�n)1 "2�Y�� $n$����&�'!@� l9�y�"�� �ʉ��M �"� Q��.� sub-u[ �$ $n<1�~�{Xnsure Օit&P2K2�*�o.�>��M�]�)&*  �%s�E7� Z".!n���c2OF�"�!K'xNO�D����/(te�[#c�O9|i�Fduc�GrI�� o� ��^>��o$$\kapp{!�� �a� ?Q��(!&�}) ���as�7�-��tern�!Ja ��� -"@;� Ori�d���nb�ˁT`(t) +a^6VnP Ie+�Tw*UH sur p��N=a�� $ � �.uz��E=F�� ~��~ �t�щ�s��m��Z�aG*�)� ��!��!._aG� s ri�� ��MS flux2U�7^�l0E !�$tC�L�dr��%ua�=]+-�6lyO bQ�t� (� Lapl�B"7U�� 1;=�)z�\�z hat{)�}(\betaE�ft�1}{1-n&phi$1�NWSe�%$O=0$ge5hZ��^*f6T`E�IR=.�}o^21��8ata������R;� �d-� !�OI�"��Q��gF �%���P"#U!�f�� arg�k: if ��HDe��6�Z�ab�?e ���/�E�N��$\s# k=0}"1 n^k=586zc e�� $ -�t)E�}Yt��G!!J,a*,Z�ti�� su�t�$.m��W�*�:N``b�2�is"]j. 1/t%�} $�* �$0< L��<o� >� ��" W:� alig�D&5O.�- q}, �.�for} ai,t [��� 2�� - Z1 C \!z$to 1/(1-n)�0)g����darZ� .fP�#^�cAk  dG&GD:"eP"\ S2Ge�7g.L+&�' I-�&�)��;'=�jr�.H ��>Y� �"�<�* A���$ i� BL��+ ���$��"�*%� h.�-apA�lyQ�>li�X� �Ӆ$e appl*to��!;�(%[st�3 L\'evy �/$L_2� ����� �5 }1��I*�t i�bably� I�ce �9�VHχas�th!���Y<dec #fasS�) $1/t$y�i&k�lE�*� �g �*�� $D$�dN -:�0�-s"�i�$.�'W"��!e��ng1���> yn�~@tro�3iZQM��F: �\para2B{E"Wn�]R�8֕xe&�8"�a bH��@���*B} $S���enU�.� "� q)ystemr$t>b�!bn"�.:�*U��4=�&>) +�6/� ��)>gj. *}Y_A)e���� E"/e_a:thu�I[ :�}"�E}[�] ��)+� 1� ���eta�4q2M[E#JB2�J � ��.o�a  �C�[E��&x �n/)�i�Or Z'�zEQF`1�2����*���3N]d� �R� relg�&"� �G%�2jKiA�menough�%rM�� B \�E_{Vi}(A*�9 S_0 }J�Q _?J`a Q�F It"�/" *�� �>� N:o"�"�).mo�&9�J�\�n"Awe�."p C� �H a-�exhxl� �7n bur�*.$S(t=0�� �,> 6��2�3as9T &.Se:�;�K�Z�F<�S�5<no�$\{a�(t)\}� �!i]� Z}�@���e :�='tildeX}\, +F�RF{ X�� $PO$/Da zerH �. U�0�wweLjeFNRaR&�&u *�0�&.�J�;�N}R&:�0*���.B�:<J�no� \\ +�t:_�� �JFkal�J �Bb]*�8�G" ��3F:�3uJ�-�Ep Z�A 6�N��N��&t ��." eu�F���GVxŞ2�� 4gan .dy eta p �$,��"pun.{*Fm&�S�$,�O{ neg�TxPJ:�h_<,�./02BFI�Ũ�!�M,�+ausN�e<(�ܥ�� �vfiHr*�;J�!�>0$ �Ul[!S �]=AB�$ �gJU�5n� "'&P a��Z(��JE��&/ $Wn�J4:^t:\&�!VN�MOr!��a�>t<0J! �_9O\biggl[�|S)��6r]&= (" -1[S]) Ne ) Cov}V,A]}Var}[ J+ \\ &KeqJV�:`{6-vc ����� N`�+179� TLel ��z� v ikya��A6FHA�Y6&�% f�Lp�+� Ap��JEE� (�Di@t<0$)Z*s OZ$\Delt�*2A%v� -t) b.t$ upon��%ach�&����� 2o� �� �(wor.gu�$ZR# �v �&pB^���':@T �� c se�<%�B�T��3:�Q T p�a )t'%�{v�iNx"' "*E��t<0)]-R� \s�JReg=�$ (We�=��a� \gg��]�� �.Wb u�z�?Dy�F}J�M�>vVnd E�N���fV �_�r}�"��J�>1{�H Min}[t,0]&S��,� R��Oi ^NH E_A�R� � B�*� D$>*{othiHN�@ c��wo* /&�5By�v!�� �w�rU�sM&9)=F\II-).&�*erw�"�QR":$�P $n"7K�eajjJ}�)�aLN�D�.�?9=�%} 7o� eH<V��b QI�85�c.�t�}[h�^P>^P�`P6`P�_P &ɇxo��N A� )[&� ��propto �1}{9-2�}$ (F~  ?�?>"�B\j�O � M �i�|t|^{6�A� Peak�y�p�P=L�:N�A�.a�EB VR%�{X&CR����IR{Vh��e"�:"i\Fx�E� � �����<.S"B�V� ! ppen� (e"m��$)sd�U.h%EV_2HM�$)Is&!�H(u�&��n6V_}5�*&�>�"�{m ?m*A�0 BeJlli-�?�"�Z�|�LE)-triv�conse+�lou�l. If wJ��{� 9c&�dyMJ�E�aN� �&"���g "�""�:� aP@�&"��V��1=%t��sџB/6�ZD�|B�N� ���Z�5 Vk.�s5C� ]�V@}tur�uU��=.[!A��%B� ��i "#y Empi���M"m T �(~�;���s3z�V��ZSI��KofflE d fi�']"�!�� ND �A\%�+# We_p��U�lomaximUf�oa $3$-<3�swindow�ect%st $k=2NT��_ r�(&L0�$,Lv��e^Rna�[ ��ld 7k$ wa�M�!ķ�\w�at �pe@a%} Y�0r���msg*�Rby vare�x/���1eTee�]�M*�&�H)�%c=*�� fIoI 5�%+op $50 'W�n��RA+�*-Hhadvle%�150hs-PRh , so�� [z!c�:)y&h ݱ�Eya�WeA�[ �Q��.2%*s� � *E�$c  A}{�B c)^p"�L��. .D!� $A$,&�� t_c$�v�� ``" !F''�Bc����� "T �!H53{0}"�!\� know�"�>U�@c�HK��O&�F"=R�J pq��ca� quitݿ��it0a-�-edn8$!.��Ra�,A�! �4>I^ m��A �be$-ec��� lXdH2�U,�0�;,m`�. �x#3 !� J(&"8f._�U.�a�+ A bi�Q%� �m�Tr�Swspaz6��(8.!�i2a�eT?�&~,�L�Nega�Pq�(i)�2mp�?A^ex�JA-)� �<�s-��$�)*e`/&1q)),�H)$�v�c�L�c\��sw �}��(i���&�G��'��t2?L�6rNk.~In&�2�>eN�� >!<)�ZA�E�5a�squ2� meth��-�x]�iniK�&�-�~y��\sH�<_{log{A},p,t_c} l'UD_{t_i} F: (t_i)^2.�^���(fFRc =�1 og{Sr } -\A} +p �log -t_c*� ^�A�&�4 quad6c�a9�(Ze��$a{A}�9p$�!t two ] 3�� -���a$oUs�c ghtforwar�Od��O��!xDl1.]�V� ��f}1H y}): ���SB7 p}$ &�!�Wj_x�w�5aV,�e�woZ�%t>�u�}nGi*�p��log {A(!� � $pA�cs a"�d�# tillW��c*�& Now,aA2�-��|)) fe}�,p a(A2� gmnmdls+:\eRa "� ��1vap�*y OSzl{cape}��6Nk*�M]��o�u? irHr~!5�sእ�5�'�m( "�X7��t̥�L�>n�oek��A���A2` eak.�Bfe����&�E�%�+�e�)�2a.~< ݿmi�3�%upper� ax���'�w�xZ, @"y .�� &a�j>I*8:�� !�(Blcu�+d� ���AA�E{� ��  �)ޘ� 8) run % $2) !k6.)Q2�f��X̂�J���>�$i<}qFF\_�a�!]�AG> � O���fi�DX^ene��V�A��  !)*++.�+ yL�BM hA�-)["�20%V^U!���b6d��!�� ��� "�Q�*�i�%SA�.�.^b &Vj" Ou�8Rl$14bV$C��Ol�y�~i�n*0|,D a"t��(cts $1,013$ s-KobeJ-���n5�R� ,�Fsu�y u� ` w�%�� � b6�%�?ofb I�a�a�T�51byF>[�! >[ . Am�D�2�Es���: �)�'"�)EN�sb��ll-*� d �U �As �v�%- Z����6.WeOQrL.�.0.95$��I��iAj $138-�. M:K( ��[� q���dlyA ult�(t rove��AW�\ 4�I� �>] play�� y��Ua� R��/.�/:0 $0.8n %��1 fi.��� ` �r�] ba��zZra��r�histo�m��.�5�+5+�,�k)>"�KI�A�s�Q��clu�010*F�-��� iG�G*8!2tMj��� �a:�gs (]j �)`�$"(� ��9.��s,A�5�,aMK��&ti���ca“inv��|�i g"�R �3� brZt��Istopp�[E� B�R�:�>�} I�{yJQ y�>OQ�tj>�< B?a�_S!a2I�E�out a^�G�T��%�NDDӂ *���6*N:"V[A\s;''^�A�.sI6��f�aCY?�bU( E J ] "��+�D�v~:�DW9aslangua�R# !s)��.�k>Kh k;� �D:�PiM�v�fe*�N��h��!"";)�red�iZ �V�o"� q *s"1}) o��(��os�!�uN&x8�9A`jCr��MC�A�{�ci�(~L,�YlumC1��Bmp$1$=gsġa��$�Z� l"]Fx�0b �> Stacka�"bN� 2"'i���mIN!in  k��B�!"��$� ��witp=��%)($p��7$)a zC y3�,�́�e�7t x �6�a0 �6C �1� a ���R߰Al�3�s�.%t��Sb� 2�4$� �F�'��B�a�Od�\N ��g�=ve.�"� �9((t_{c}-t)^pv2�� $p=1-2 ��U%2 *����)+ A�&? Qiz�5�)_���� ea��!�%g��AX*t5N˧�"Y i�7 M�� &��i!� �y}���* �=^+ exo}&32�*kA� [ t.m1SRt*d.undv�!!\F�kA�is��w35mpa�2��{ ���G��(D]n&� �vfJ��4 D-4!�D-1IL)r[?�G"* �w�e#s 2%u!\ 2)q�na@ �bi�\JLI���st�~D&� 1�*���rNZ�J"<.Z�� .��.m//U%�*O) �� e:�) �!i��u�Y��:�Z� �B�)� 1 �l��Ayin.�#R�ve��erĭw�lyF�A��atA �eas�j�Zi Eu� BLEpr�>i3Dak�mi" �c�YlFi��82 :% = 3�22�%�t&2 � �A`g%2���� ���$2e$ $x"��&QX!jpD=$ /�M�B��tox~s{_1 }. jI*_,x XE Q"K.D��vJ�m' =���..|Er�-߁_a��+C"] �G@.K sj%�f�>.�Egu�/a�%$� �,*�.�@:�"K, �,%Z A��&�/�r"�<:��&�4� s!��match�h�Q�+ &F 0 �[7,j '"-�"ʌ&A):}!{v�� �!�n� 2  �w $�2H !2*: 1<\ 8!�-# -$� 95� : . On�onl1� �A3 $�`cJ60-80\,y( days�6iQgth^ RI�memp] R*wo�fwBuZ��$t�J%�@b�e�*�W�"})� GNI�"l �!�f*[ %��W&]I�2+=�!�JjU�~t"Q��V9�=nDd"ly�o�ow����T�Io!��r� . r�Fo�%cZ��~��6�.��i�c]o�]�4In�9!%m�e� n'$x$-ax�De��rs�#c� *��J))�r�c*�r ~�pog#o�0��%cur��:e hn� �y1m���coݯ���&�"y�di������~ 2L'�E���&[/".}elist_}�c �$10>� �� � C �0.65$ ada�5yUsA�[a�[b.�( 101.%ev*�T� � -�s���,� ten� ��M��70 E !�h.{oprah10.{E�>�= �  ``GetYopr��m g�[1�+i<�erE(Ophra WinfrS�nd� Jrk�succesr8ol��� ��W���_.a̲"� � in O�'s TV���cInJ�, b�� -_*m��st�ele."y<%���4� t6~!�c���.�H %�wo�s, �rar War�p!!Stee' King\�v��!�si�� "e�ir2� �s ��a5s.�a9s�f.: �)!��"�. Y��EC-.�{ (e;*�{�4$�i�am�&� n�2� y�>� �i7 ��2o�e *� e!%La! . Si�haY]w�E?^�$C������20{|p{5cm}|p{2. 1.8 .7 0 "6e*vu3R�\��T�b & AL� &�� &/� Rea\j��42WP�W & Bob -Fl 3/16/�r& 1st��kV-s�oe��mS&m(B. K is O�1's ��).n�''  & & 10/19�� '' \bA�H6W/4U3;6 � vVRLD�� Jouֳ%Z -&2�2nd�The��.Ze.nZ^/=Z�Niner).fAw�� Muchachos & Daniel Chavarr\'ia & 7/5! 2 & 6th &*w7)&w�V � l� Art S�0&�GN2��f�Saaw����KAw #EY�DOg e Po�r& Car�� Myss & 8Q�&1st& ?no Micawber'!se($�P& John Lithgow & 9/3013r!�rYRefrige��r R�(�C�j�C�kD��Re��R��,s&Dr.Will Mi��AC/2e�3 YDM�� �[0hris"RnS.Rele�xo��n�t W: Episl�II, At�QClo�� & RA��vat�5& 5/21\ 1)]�r����s�P��u5/��.jW»� ACalla (alDnTower~�ok 5) & & 11/11!� 3 & �On9 2003��a`5 I$�ed Con&� to A��nL��rs�� e��%A��a�ZGn��+�!V@"��LE�m�10��~��$p'�ut�� V\(see "ig. "-!�lcolumn ��po�cZ+F �&��1 �as���  ^elN,O^$�5&� V�%n+: � A=E�y4�N &Oߺ� s aS.'' I�� E%�"dE:a"Ne;61�a.3 "7x%ze��5l 'ks��!%s7�&i won*�w[j�����jump 1�wJ &� � ��9H�se��&�x�Q}a�s&�W�L(�R��� he %�B a Dirac"�+�a� poor�#*��#�l� d:݁�mF:��aign cannot be neglected. For Stephen King's novel, the situation looks quite the same. On september 2003, the Board of Directors of RNO0al Book Found �4unced that itsP�> Medal for Distinguished Contribution to American Letters would�conferrZo2�$. This is =��'s most prestigious literary prize. The ceremony took place two months later, on 11/19/2003, shortly after the observed peak. As for ``Star Wars,'' the time extension of the exogenous impact of news can)� .�� T$. Fig.~\ref{star_wars}�w-�tM� indeA�Ahase Khe two be�``U"'' �``Wolveuf\Calla'' which were excep�%+ our class%f!� termD ir accele-~patA:%s long5�2$ peaks areas,sistent with%9 factIo�UjA^M�ed %ja!�tendea riod�K!O, leaA� to�mis:�as end-� ~resA--�:� beforEV�I�mM"8of about 20 day�a�au is coF�known5$F!�2�. These�<exampA� show,nEo refine�analysi%�allowEa m�4general descri%�w6s4 In particular�� epidemic ��)A principle�DusA� o in���itudee�f�of %�@$\eta(\tau)$ from#)WeriY�i�$S�5. But!�$be effecti�(nd reliable� is w��requir�A� data,%insta��0directly work�� on Amazon x ratherA�nre!�tru� # � rank!� \subs�,on{RobustnesUDresults upon variae\of�condi0a/ se�$ion} Prev�t4ly, we kept 30(s corA�B(ng to thosem�g%( fimp,a power law e�a @l �coefficia� larg1$0.95��:��Acre��i-��ae� or l! than $k_{a�}=2$ orA&E�& '(xo}=30$. It�4 inte�~� discus�"e5\�\l(riI%9[��kao!�pall}^similar!?$histo} Aga| mdis&_of 9P exponents�A�de-ofM4a��!"s �)� w%�relax-�a��!��b�Xn����$��is f A��quality�the��M�s 388 � �M�,initial 1013 �Rp��l!�de�4 set, i.e., clA��Ere�s��%��again��m� clearly d�d clus� ,M�-@associa!DE��A��%����es�2puz. Am��,�A�tmbJY�aH$, q�K27q�rZ,!I�a( yN8.5ePjajaC 12.5%�e�P}�s�k,ed empirical�isuc�a��,lgorithm mak� ai� between c %P fast6&ya wT comm�men����{ .��D $388-270=118$ rej� %.�A8blu� "� aK�!_2�M��Zis nei� �nor� $gressive. � fjkla} is.�stack_e�} but�se9�Y� obtA�� differ�ny�slopes, �AϙF�����l�EeI� ifiedA�Y�A� �&ek oE %��e .) A_EvH [6J >\pr5HGJc.a(E�ndo}$, (xo}$)=(8.5,A�)��)1 $p=0.54$R�� �! %4$5]m�%. To tesI�Aitivity�=$A>.,yo$ jmb$�re. �V valuesv�5,20) ( q0ively (2,30))� 0 * �|ne- a me �pba �  $0.55$ m.�� 57$) � 0.39. 39$)!=e=F= Whil�����3a ��r:� oseM�edE����IngA����seJ�zQ�^�a�a � too small��8be due�'!�"3� � �x� not # tane�as��cus� abov Ů; � ceP)�� or�V�#urbq s !�� bed ��.5 2 Fur��A� >q aiQ�he m -�� vers�(;@pdf S})} \label{D� A) sureA=} InQ y%p comp!!# pred; o$ � �CN on chang� [{ �%validRF!"�2��vt� T conU _ into��. �4 us denote $\D_ R(t) \� v +  t) -)$ �&~ %S]�� j valW t$ (I%,will be take�xedeGqj $1$ ).��MI� �S(6�$� e6 !�s�sam$ �!  t "` � )?mus� �pre��l a�A�p�+. A-�A�a few  w�am�?sela)F10A�!K�a 4 i$ sF 10,000q�otivates!�!� tudy@�al 8� � by \beA�ngle -�R(R) \r I (\mathrm{E}[& (t)|A1]~,Ca5$mgmls} \eeda� e:�� E-$t$5 $t+1ə-M0as at >$m$ ��f$t$. Sw o !4.�!��J�S(S��S�A^]�$c h � 5a����n;�� � V rst�Ie derv$\l-�i�S �� �_� n, us� he postuJd%?��� ����n �E S}) �provid� ��p >�.-E � also��.e$}�y{A� gin{���8\widetilde{S}(t��D\int_{-\infty}^{t}u�d} .;#}\,&,\, \kappa(t-)), \endu!z ${@�i  - U�eta� n, f=B�+ \frac{N;}{1-n �ae=M�>L$�exp� )5$ : \b%Palign*} m?(t)= & >_ \nonum\\ 7=&Jtd!ABj)h (5g%� +�R t)-:�p q+ qt!��{} t.�!� t s0)�. �%�1 C�Af��A҉�of&�>E�(s�d � r.h.�, zero becausu [ ���� does��afv��s��0��D implies 1�y%�:�=F� -�պ\left[=�=H��\right]lb� N�~1p< � SQ�6mFo_!%Z�o%/as in 2�dynamT��p*es}�-D $\foralle , ~~�n�] \�to.�e�QRII $. Replac �isa�o� �<�)b !� 5�E�1 f� &=�galpha.�S}q"6&=- -(S��S��),)�6� 2�!�.���� U\simeq�B{1cd}�y�u�)-6K) ) ee �ie= e? $ 2�a�!z .� ubɮz� � 4r� assums)�  ta�0id} ExU6'q�jA��� S�*C�M"�$-\mu�Rus, taWD loga;ic t e �B sf >e"ce�6�6Pў� R}{R}E�mu6S}{S}:�log�.T:dF�)%m& 2}< :J�getM���:U:W �*� �\muQ�(1- 5a� u)�) n.�R �b�$S$$� >�u��\R$��f��s. St&ng x) Mk�� O%�cou t $CI$C�4 S_{min}^{\mu}I�MA2normaliz��$pI~�&� ? a minimum�  $ Y� �AWy_ u<5> �{ ` ~S�~d}S = -�mu��+ ��^umed $Ax> 1]2La majAX�e������  (+H� I�k6!4�blockzer��top���(�R ��,R(S)=N P_{>}�$=N \biggl(�-1}%�r)^A�;-� 5`A�" 7~��M�{o \re $N�=�`total' � A�%�� very�)t shPbe���orY."�ellds sev  millio5 lw,Pour -lawA�� a@true, f on't��bably } ��ss M� y�ge*canE� ��3@ $N \approx 10^4$"� �'s*��a� scheme arX$ $R=:, �<$ a natu&popx!f� �Red- ( Or perhaps�c-y0 $10^5$. Put`together2r��IщIE)U�AjNGQkJ? =  mu RM� [ 1-U�E�-1�\.� R}{NU�{ 0M�} *r]�MMũfR J���Our"D �!SA[ buya�)i�A�p1}aIp Ap28��#�*���,� 6n})��� he aA�g&%� e .$2ATelfE�ss �'e o $-R^{1+6<E�B8e non-monotonic0 ��J�$6n% > 0 o6�n4< 2 �$R$ s��y ref� -2 best-sell�b�#a��!sq� beava 0�!!�i�Lcontinuously sources " t)$'�buyers {!~-�*� on�jachieve�ma"�]hort x. (��eupooA�qԅ{RimG�ir$ing� �"� � E> } J ��$ all_e+_R&�%e�$all behavi!r�$. �)$our purpos! e � ign�#� s $R�. #�#/��#!��)ot �gpa�� alreadya�cin]a� �YGs=!il��&d�%�rti+sl�6�aI$R.&� spur #  M�Vshift�� �"U �w�i%�$7��B��CR <�ri]g�(ed�9loglog_� _R}i��ed.�^5�is obserA�A@ ���E: ��do���#!I�ri{)al ��i�!��e� -� plo�b�Ri6�"atF�&� is� �\be�n.�� �@ R^\beta~,~~~{\rm��} ~8=1.5 \pm 0.05~,L�ngutjs�i1 E�ximata�t9"e)dB*us,F��a �>���siz $�)s&q*ly�en�W is de9'g� line� y�Kc Hal=roblem�!�M>�h �m� orRbe �$a breakdow"�&H �KID� ��&F�o�x:2T $-;w"�>|f�5Sup�� \ea�) �I� �tJA(QnEC -6_^xY*gnvjelelI,wg $x$   "p!%�$1�y� �tep��!��� = $to2�R��N��6�# -x \�k \ ~R��dlM� �wp !�' *h)Wpdfe�# })��\��A��d) :G. W� .�(holds, $x=1!B��)4)�j%Eia+�+ nce [j� $�a�ɸ���"�, quant�"b5� �inx�.aH.� R}). Now,., !�iompatibl�b�,�eX ��_>� mey����(�if&H $x=0>6i> a ���W !U��)r{% � �Won .S� !$ urn � z+e�A\�!�a"8j� �6�(t>�m!ed � yut� eaG� U �RD%EA�E���#{1"n stat)����v/!_�"o�9p$AIt& Q d /"�l%�2���� necessari��in� 9h� "h!�k;B��+thuA61!%� :4l stC!!�, ensur�O6�A�YN+ $1-2J1� �$*�&ndU+�&��:�)-%nd& F)s (see T;.Md&E4�O}�-A�s�"P�MMBL/ �a� stochastA��c�ook�26�w,cursory inno��s�4�fu�V'| � lost;0sum, if��acQ2%con�+ion draws�e�%�'.� �$ weak�+u~r�% actu�*.��M�Z�+ � �(e&`5Y���ca8 �&n�$a dramatic�fir "%*� He � oug2%�-to�2z��"�#GA0!��#q $sands. How�, �%of ca7r,�7 excl�1!/poA�ia�)� $x \neq 0��P 2Z�3Das $(1-x)/\mu=1/2$e�s:�O^ a ca�f �(�f�%w7d1�5�" &� relew ship-m1� 83og\ &� �l�2)�� F�S. dev�1�1g�9�"{'towargLe�&consid`6�3"`$S(R)�,�ng-� %� . Equ� �l6�� com6s S=S^\p(R)  R $. U��e"�e$#��>h", �+� IZ ���U��BNS&� s to - S���$R�e6%=� \exp�C}{R^{� -1}})2� , �$C$�=]-!xtants. A)]��.$Rɦbe�(�i{of�e�$get :t:#)� � =�� }{C ( �)el[ �<\!\!S>}{ �6 xp\b��:#r) ].�&M�!(sqrt�2O#Thy65@ *U�p$C%&�adjt1.u%�1good �by1 F}< EBW ����&�T�l:X By �ru~r�h�' *5c)l!�5�. All �i5 ulty to"�+ howF�1�a�aches max�!1tM  4s. Typ!�a=!#�&s165E�ich&$L S(1)Y=e 165)*={70� Ob"16?: �'O;bsurd ! �mis� �(���2��or��toa�;al18 �-Z* :9(YanyaoW3�t� � ach-v*S8���: _ Jg�a��N!O�'�2����p s� ut itXa%�ng��,�+1��Q� S}) b��F�� �R&"(Rq%->"J~B� }�V�:� we��a��- t .�q1P9�A��J��=�� + (S_{\Amax}}*�"�)Aą�l(-�"1}^{R}I�)-� R(R��[.Q(Yr)�" final_equB,�Max}z �5n�B%�J1%>=1�'�'�a useMe)E����;e�� ��l $�A��i6-9 cruc^7d%tea&�ial. N the�7(atui�a�$h" � l �m}�a�i �>��&� _exp� 'M1�ins�%�9he y�*+BAX"�#F�R$x��� .|�fi�/v�36�8%�A�U� ``(5''��W�5 (t��( $R<10-20$)� � a ``7'' on ?"�'�� C`fBP'�parame� K�6h"��;9�e�be 1�se� &� (an�e�3a� �� a2%:� �in [20,X]�=�`are���G��>�%~� Q�� is ����)Rdon'te, q.�2summary� |- d o��mR��M�>s mB ad�)al� Ag!`~�vaj�@ mpts deve�7�Bk�)|e�.-&� A�lay.�*� "A�U�������$}ic�� ��&N�A:"e 0�~(-R/R_\|B�+�k mU�h"�  gP@���*� �} w��l&�%��y��0} �,m#-�& �� r)� J#.�Mo �Ew!p���aDo: by crison�! � :\�{C"�b5��2M�"A � s so�Fy� .com7&�!�I�EB c�:��8�5tw&" cate�;es:.�7�",9.fWM�Nw*&��t w�B gy��5,��bas"�-M�>D� �i-)� D6C?�s�'�!gR7.o+_#A�.?h�2l Stac� .���}�n:�"K� �F� �<�  conn�<_ in a netQB8 acqu�7anc� +&Y ]O6= �"�1���81�9ata0=sM(�>l �sIHev�E� �*g%#v8&x? crit� �(T��;��" branc �pro�es). Ik8CF� tiny%�86 �� in:� )���,& felt}!lo:7y,e�7age al�"D!t|@Lb�%�)ud�� �$ phenomenaaCs!D� e=system�!Hfunda�al�=iti�=S � | )#MJas uni�IA. 6;�6emphasiz!�h���J�Uu�%�*�AJE� +e�e.��Ba����c�4�IxAl%1e'Z�wel� %��I�be|" e meq2E�a�si��8aID�r'e n�Fal ``� e''�`JI'argW( e al��a5$a���of�;Fimpac'A; m%Y$.� ��*edCu�wo1GremIeEE� G< m%�� !�1Fur� G= 4�fE"�cascade �FEA�m� � . On� imagg �""<� tinuuZ,�" Bex�e feedba�h+�$a B �>��A� attr!r!/�)�mediaA\I.� eqML,|!��ONa kindEyboostL+�so on.�f1 ��IsY:�iz� yonNNes��E��,o=����eaali��F�� arbitNa�o��K�=o�&� f���ABG�N��e� C�promia^� �+ ŝ�Hi�a'*itemize�) \ Be4�.t�� el�!��3� �%u�i�� e}Ee)m$ct�? accu�%,%�&orkIN\rea��-E!^�BEt�xst�Aj~� ?]IAs ���a- �e H>�m�Dit�l�< Ir s >o*� Fya� .$�"0deEKbA�*-�q spo"=@�*%8c�Dnt�>+3et Q�$white nois1z$ l ccore to.R �6�Bx!Ns%8�Jbe��roa&!��"�)aa�}under�im�s�Z1����>�!+9�� even���La�� �%>peciN kIr0Q�p�N B#�L�!� Nor��i|i�YJ ��  MVD"$�j!�$ULinvH &0 ts ���At�e�M1Gq ``Divin-�SJtk1Ya-Ya SOBrhood''�RA>ll�L�c�!�sts�+ ���y a^Jublicx ,ieno 1 a�QA� campT E$\cite{tipppoint}.�7�)%�is origQ+(- Jbud{�, �Pm(egaRFmA\textsl{�}��Qup-�g{+�&[...]A�. r�ut>Iwas sp � �8  dI�a�group, %:� JtoR''V;By loo{ aM0&o �noMi��  �dto highl�9 �Mq�0�nere�s-�(6 degrees,L+"}I��A�Ni���customerA�!�q'�A�+A�geograph= -x� u���ŏ$ {\bf Ac ledg�# s}:  �f#��Po�.m��x unauthorA ��inA� way ��so�U&_ T,ank Y. Ageon5(T. Gilbert �, helpuseful cN�lM. Ro�haxVim0 ant info" n%-k�A�b a�� t�.T �X9ermisyA,reproduce fi&r�2}�$clearpage �thebibli)�y}{99}ib!�{ru�C} R$, D., %Con� �? "�BC8librium physics�V�x�-�Ptrial, P "$Today, 57(�I(48-53 (2004S#\�eview!�,ndoexo} Sorn�Q �En�#o su�;o�I�~�B$crises, in�E�� �emeŌts, V. J�Och edi�P(S�R ger,UX`5) (http://arxiv.org/abs/ � /0412026)=HendoPRL:� F. �Ah\^atr3 ]nA�Q�, %�Ve�E�SW�6 Complex Ncs:!�"s0 %Ti �BYSale RanA})� =v. Let9!�$2), 228701J�0Roehneretal} , B.M.!� 1��J.V. AnCe�Ree�e FcmCrj�S� StRces: %An�\ Nume�N SF8, Int. J. Mod. AqH. C 15 (6), 809-834J� Sorf)��} D�, ���P"7in�Z6�}, Q7 Se &4Synergetics, 2fXd �]. surf�a��!W�Q, !WM} www.foner�s.com/ 9 .htm.O�i�memory2�%?$ A. HelmstaXrYq�Ja�uWsUs ^m� _IJ$ica A, 318a� 7-59I@32�M3!wrenzy�ERAE��a2� %``Thermo�2f Spebive FI, EuropM!��Jou2Z0B 16, 729-739%�02�new y�  4s}AG4Brody, Push up�� we�x�Ero�Iackj Y2��New YTTimTEN8bf{F} 7 (June 4�`22���!�J. Wats>sl{Six D��}�bl�\by W.W�rton \&�$any (Febru�\ 2003.v H A.L. Barab\`{a}si,n#(Perse80Cambridge, 20:�6(  M.Glad2Q!2' :?!7] tle �pmak�bi�Qce} (B!sBay��aT�U>�] . %FIGURE 1��>5centerF$ �(U �$s[width=.6%� ,]{SeeNoEvil_�t .epsFK�^h�5.� fd_c�nies_|V� \ca! {Twoe "Y0���� � swit�""� 2leML� �DW6aQ��:5eS 0 6AC��M  (topR ``See No !p"* Baer! �E�=1 2(bottom JF'2`mp%1 L$P. Kaplan.:�E �>A�9�QpR�2&%F(2�!�;AV>\V�0.7.Fig"� � A�K!�(Zipf) 06%�U9Aper�N,�"noI>�#>� �8�P�*�,$10$ to!N�G qas:t!�N_c!fit9b�&2�F� pD3NL9�1 1/�3/�3�2�$+= 2.0�6Aa�6aQ{st.|� s[ $-0�W�% ransMc� :�si�SMB�!msB�6�� lz �, cumu}*v�6"��E�}t���. bend�N� !�_/ 0�C6-�+ o�a �Bcdzi�tai$!�.� /2/+� � i�q" 2DB ��.R&[2apg#� � but "hexFb$s huge flu�.!) )��Z� #3 tect:#*�  borro,"a'�� / ����@ :��@6� ��3e\�y��z� �_ Κ��)�i-*.~`,FdF lńvtO@�>I�A*E�n as"&Ev�B. ��t`�ensH. R� Wq�L�A ���>� Jz�R�4�" Zy.6�"� _strong_w b�>�2M�� ��n>0_heaven_earthb�" i4ol=1 �0a yea�E�s�o���p #2�Book A2�% W!RHy Young�Dr Nelso�6 QB:�H��3E� (T=Vs Isl<$Trilogy)''B�by N.Roe"zc&4�e���i� , �A �Z. BJ��.Xa�*� 39�)]�M�%|yNA��V�5�� �� TC!scape��0$\sigma(t_c)$�`��( gmnmdlsd}��6�$t_c$J> 1@�zD�=6�=f=1.� �2�6H�cgra"�QZdr� eH]s $p$e��We�cbEy"�B= "8Ai-:ify�7�):DY�R@L1G� .9",c $0.4�2��k�UU9T9 .T7$, *��o�<epta�t3s�p-�t B�p.'')�" 10�P %���10��2�}/�qR���mc)��;%U�==> r."� de `.& 6�0u��ckfco{Mt({M $t>  3"J 66 2��O$tA37`�011�cL=G a�EHd�&�ofMe"'� triggehk)"�(eR�IU.5� �0��b�:��q_r=09.K.��b/ e�!Cn� �6  us$-�.aEd�E�-V]n"vt�5�.�p� � }: a"�m1,0J�n-f�nJ�})m0�#dq� $sCJ7cor�PE�coe;<i�"a�an� 9$,\:A�">n�7.I`6�Sa4/�py .� :UN� 1t�6hc� :��r��6�:��M7!9A�� B� methodo��� U ��.�mnM�+JQg9WAb=}@ � �1d�>�PJV�-�n�rn�1�%�1�Z;1�� +��1�2VsemI�R�oA>iU :�6&wB&��%in "� RA *t�UNV�&m�K� per�%�4tDaAXp� 1400�. j/n�Is{R�7s|� oP.��X and X �0b�U�+�[���2�RinIAL.A�Ags�Iue< �> o�od.�J})oe��s l-�Hoi��a�:�S,voi/"�S Fn3�%�fe$Y�1!t^�8N�M�=�C~e�a�:�&�r~7&pJial*gJsE)��.�>!�.�UBrmRR4a��.V.2kloglo�ja7!�A� jv2g �l@3EbGB i�mV un<1eM ��doaMJ� abrupt��s �]we�car#+=� sV� �"$bf{plus} :��",Ue A2hbf{solid =+�CH;a� TBb�"" $bf{da{�G=r>z;G�:&�F\�E{R�FJM�M �G_t[:�$Z1����%\!#�8 _exp�.� 4K�(.k*�{B$*�^d �%@"�3Jx�> �>*kF"�B�GP@bZ�4t�2ayun]-oBy-axiE .�n�6L��E& docu�5 } �r \�.[12pt]{�\cle} \usepackage{amsmathBsymb} %�hC'=680p�/E =46$voffset=-5hD40pt % \newenviron�{Ab0!ct�JrIM�nbf#%!�� " (quote}\foot���9 PJ } % ma݁�4command{\Imag}�Dop�X(Im}\nolimit4pne-d�96.div\!21def\p�L #1#2j_\p!pal #1} 2�I1a>1d*d #�1�(} {\Large \) ��{S�!ig�6Y{r/} 2))a weJ�nonco�qear} .Wlas%���*lec� beam} |.gskip. �A.I.~Ar�6ev$^{a,b\w,D.N.~Klochkop G.~Kurizki$^b$, N.P.~Poluekt(�D,N.Yu.~ShubinQc}$:�\� \it $^a$G�@V*hs Institute RAS, 38 Vavilov�e�|PMoscow, 119991 Russiajd b$ChR�aeD>ZA�$, Weizmannz+Q\ce, Rehovot 76100, Israe� .G.�c$�of Micro� ssor8*u�5SF,s �46/1 Nakhimovsk߆os,r, � 117997�\b1� e�y�fA7�Cwle-U'n 6 regL+�a h >X[ f&~7lEv�:�zX!in�x & :of?peł�G� s� e�-6 v )D� �f- �0}xci"74e�f�>Th9l�.&&@^�sh�4% fav�2�A6ar8'A4�!�v 4 1�2)'a�. Imp 6 ��5� la!��c5in#.^�3"��69� "CInt�2!bCa6d �(FEL)~�$Madey}, Brau}� "ced moS��)� �:.'.pob��Gof� combiC fiel�4!�ف�5�1A magn�/%9��3�A�ntQ='e�td&RER4'��Z�in S9uJ 2 s���ns�AR ���>+8�c�� �6gƌG� L_2$�2.�qa?�2V�q�Kp �`)�>qID�ev3M�V0I�i"k=�e"�"f) � %j.��}F5��X �o-\Zcsz?DiI<#es9M�Aa P e�cl�K �i��Ie�s (oA� en �P �6�e: was v x Ve�a�ajco�*Wn *�! �c#:t s�WMŮ$G� FEaw2A�!� detu\x-reson��� ( $\Omega=\o8(v_0-v_{res})/c| �lyDiA�M�uaint G( B)d >0�኱�BUedn� �q:��C�� me) (ICa��CDF�U�2A^���9!��41�9a� �a�%W�$R%;�!9q,2 �q it#X�?z-��{^> �� J&���h!��ǡmr.e.�EAA|DA aa1�FJ��� L:�*YA�ne�� a.�"�C,m/�PѾn 1A�2� �%Al ɍa:z�filled�$an� 4overdense} hom�Z;plasm9P"* Basic&�- ofYf�H�SEt�:s"�.l%pNj��t� �S�g��t� �%BQ��e�l veloc�L�3!i�I!�2� �Vr��&WOin �n����"A�4 n^�aeG� B oscil�4onJI>\_�M *� �n{ I�< F�cho�h�YqGrNM�.��$0z$ co �de$=;1+Q$wh6�  vector-&��&a�e� J$0y$.MD%�a�!���ic�TicW{זnem $vC}_\�sf{w}fd6�ft��saC.sCk�k$y]6|L)�� \b�� rmon��?�"t�eq:1} D.�=A��$e}_y,\quad�{�Y} .- =A_0e^{-i6k.U r}}+ Bc.c.}FC�� ))2>=(0,0,k��g!�-�� -�,``a0XdI �Aconju� � m�Ša % I P$y$EPb o? �c�E�q� .$ C $y$sQr L�cy4act��Niw�4��P��Dla|El^)� . So��E��Y�ofu 2�F T p R )8A}_L=A_L(t,x,z)%�%-."� c7M�y-5iC>1Z  p�Oy vortex]Y C)U$m��p��:y�[ark $\phi= �r itud$I�|!*� s�Z� Max� ��"�&wr�:"�X� :qW}}T2}  �_\�M��(_x^2+ z^2)%L=-4\pi\rho, \\ &(c^2%2. z^2-t^2)A_L A cj_y.mb,eq:2a}\tag{\E#}$'$}> �K]Q�))[ ��Y�+ �X?� uni! �n�� $n_b� X��y M$u}=(-u\sin� ;0;u\cos �kT�aaAD}��M� ���beN�( $f_0=n_b\DY(EV4p}_0-m\gamma_0u}pH$e �$m$r��5ch���mas[+ G�B�$Lorentz fa�`�8e�g�z�&�c����Ǖ .�&wl�curx��_ e� 帅= +Uens��^�3A�rho=e!6�\{� )A [x-xag_0,z_0)] z-z., dx_0dz_0-1\� \}, A�j_y Xint v_y5 K�a a.�3:�3F�)�.�-�.�%�%a� P Hamil�C�MFkb�^4} \DotE\ r}=\h {H}{P}},\q�V& P}=-:' rvs}� Y?n "fYr}�z (0)=�allel 0� .p:.>$. *P}K p}+b ec[A�aE�an|al ?Fntum; $A2R +A_Le*aG^��>9�j5li�, u�? �Q�5 9�5} H=\�!m^2c^4�@A�(� f P}�g�I�)^2} +e�� =m�u�) :�r QSd&m$y$: $�� H/ y�ˁ<s� �%= �U�)j�6} v_y=�. �{e}{mc}%�{AaS,z)}{ �} �|_{ ��2{x=. \\z=.}}.>� WhT2� )�s4suma"��b3&p7�  (de��sM^f]�0=(f_x,0,f_z)$`k��i[De $xz$,%HAxVfcf_yA� �Rp:� �* or  � > �� F  ~\eq�`4} detBNn�FQ� �����&�Y�7}N�Ey�JOm�v�|�j. =]DM2E\[\nabl*� (1}{c^2� 2d�Z.[\cdot>F)I�]a^- E� 12r�%M��7)^2#v �^2�mefF����_.� ��Z}{tq$]A^2 \;. n�g" 7�7=�aD��)�e i�9E�.���n8} �9�i�(qlv!l!q1{-1/2}, � G= 4%O[1--�2d T 2A^2 ]^{_F��� �ksߏM�2}~(e� 2�split=Y9} Rc�� Ij me\L^2_b&�\{x@�a�2�-B(t, r}� 0})]d>� 0}-1 )\!b!� �c� � Y 9a} � D��B� -& � _b^2�I�A_L��� ��6� f�=�=Z�\"�� �!>��a>bd6�9d>2dM\-H.� 9ey�zml� 99=# e^2n_b/mKsqu!$of Langmui�"�\B6�  ; k�be�F� mGM4 r} 6�tjW�o1� &" ���i&�orm� �Y;11} &E�E � [\ps�{"L� .� } .OI�]�� A_+e^{i��k� E�2Z$B2Y+A_-e�<+&6<29>H11%�.�:J%��y�ed0=k_0(0,0, )$ ({�ne  ��ty/��1#k2c q\xi� !B�$]* xi_0$�$2�7 . he 6z�$ Fourier-"�/ *�� A�6� y, $\s�Bu $\  6 "���.�;HIo� \pi}��_0^{2E\xi}d% , � z{ E}�F��{M�_ Vi�� N�1^%� �y:02!=&�Y#IR!Dq�xi=\x��SubT(X Gu� &� 11}Ae Eqs.9jH3?bH�sŬc � %�� s  (�ng),�~ŏ�wB<��.�;fra�5�t�<�m}{k_0^2[)� �!�.E��]P8{d^2A_+}{dt^2}+ U+ b^2I_0A_-�� 12 (��haU1A_AI.�13>#�\ .}-:}-}-6}^*A_+~%0.F�'�*�p3A-��)t�p1�1�.X�bp)�� �h{\pm}^2=�J\mp�O�|�v)�2�k� � }�o�� &I_0)�a�e�N�}}2!�(tmu� m�&&b~�u Oq�h2�>�al*G A ,*d !��auys`( EBOj*�9" coup�$��q� �Ia��Z*5%r&%����Q c.� )tQUQ;MO2+]w5 � .� ��a� i \B�i� 1I1+ E Ag0N A+G A~2_Y� 2� "� �6 �4-E'-h2Q �"� 0QX 5��� B�� n/� ] (A_i�+A�v^*).��Ui��bp�1q.���.�2T6A5}$�A21��J�x.o(t=�B+ �B0 u�Tn) elf-.sx+M�a>U 2}--��15}�'��}Mr"�(� o�a"! xEA*L�%non �s}�aFEL��&d��(onF1�0s&,�DiBF.�urt0�o�!i� �staN! inst z} (�0 �l�!G 5SJE2Da� F�&tmv�%�r%�X v�>�s�">鐅�tu�&�(s $A_\pm$. 8{(5 �6!��(Pur��%�is  &<s�It.�i>F u}t+�.7$ or q ~ 0"w 9% ^B, �.� �u}.w. a7�%*�hi3D��D)�� _0 T $ !)  &.2 2:,$� ���;.�7"0RZ�1+�V6 �� 0} &F��)B4�� s- =u/cp%u�"^bWw �V��y ae432ُol�#"'f�/��me&� &�- �M�YY�n)9mu� 2���P�!>:|A_0|^2���fi=5izy s� J��B� $| 0M�Z�� at}{c a.�F 9�� &=I��E&$!Q�t1� &.- �1int>� (I 7A��F"�)| _0u �\*� � \Va�� � �4=p � ���_0k��et_QvJ�)� H*HB� 6�D*W �E�1�Y���)���-&� � haZ# "u��imn�20}##pm=�m@ \mp i�} t Q�}f(yency ���:�"���:ixp?Zpar�ats�HM�e�he�n.�� ��'q� ��� � .� 5} f�js"q%_=y21 �E@.���)�:�MG< _0}}{D_bI_0^3}C ��_1\�A � )]? �_2$uA A a_+A a_A I�2 t2 K Q�R.� = ij�~�2|J�����z�2J2>�2N��Q0.2} D_b=()�"��O)�"O-,(i�G +A�d&� .y� � 7�'�f withe � .P o��err�3} /^2��M\���I�[�P %�E%u��� �  �6�`*�H�I�".0I�$űlnx� ta_1N01��e/�)2T� %2��"� �Vb2=Fb}-IF%�p�����I .J�""t$�o%�6�:P@�$ ��: �>B�5��� i=��.�)\��-u%j2�\� �� N��.� �\Q �.��j2 XlefZ� JZ k4- �6��*-1}} .� 2 ^2(� )}Ny�-Bz.6�2f$.\�aB)� 2�&� (�d �^!e.�3b}C� MzBo/-Z�R-�1eek9N/-H1tH)��\a��x)z_+B� -����fbcM�kQta/���rowthL�b 6�)$�a_-=0��sŝ8�mWB �:�5_�"�1r.�6����E�T)I� @��� c^��{mZ�F��ja3� �+2����F� � 5b�m* A�5) �&� e �Fy]�6}=v!� ]V& &3(.�$j�4�&M�_+� Q���U�+ ��*����N$!;���2�J� "W�� J\_$ (�|.v |\ll ! _+$)p5s&9 9 2:he i(4 O��y�1J��dB��-*�6 h;1�  "K5-��&�3 tc�}!1�0$K .� ^2-2.��_ �265�:8.>�"�1ms 6M)��1�2f/�/%&� al ���*P A��4:�+��-�$�gr� add}Mw^2() -2)+e�Wi�N�+�M))m�$ ^2q� {\| 0}H, Z =|q|B�WzX 44} |q|��4B���4nu�({\n-�l�� k_0cH*� �fu}[ )� �e���n.Գ�5�1� } \n64 j+1<-20F[ a[aPD25%e�(� \ll 1$)e1.�nu$ reu%s�:rAJ>M�,$� �b/ +�� to 6�F:"�-��9N��:a�d~�:� +�nomalކb��� �oLl��|q|&�0a�r�?�*��?nT�?. *H�"c3H C8�5e�9<=e!"�*2�2t xg��� 0.25I�/A�mu)(  E�/!,�0D�%-.I �k�)uiw$�Nh]�!U/rCXry�%��s�:?5n���%5 �:> =+) ��,��."m=�B�$ugs~����-%9 0}�"()� �)\gg 1$6� ( asymptoticB�&�42�n-���� 5��k�>1"�)�^2� ^2(2 ��)F��ߋ to)�5w2��:�c���A�}AC�x,&xe k}�)<�� �Q�}P J$�� 676�urw " :�!3V�2��$ drop�6$ i5, nam4����b/N _+2�VN�P 1/2.)R��Hc�"� "V? �.>�=�e�N�, [$:�)S Y���A�X4E�_R� �be��-b 3 Z� c 6gg 1$)��e:�:�)�ultra6�5��.�V� i�6�.7^{-3/2!�As C>�pr� is muwŊ��.�>�(6GQ�nu}<&Z�UA\)X!W"�)�N</ -�nu}��H)j'=n?ng at qCC�)r%&�A,��-A/ve*��E �pD�IX_�  A�U��u$} (��Ec�\Yi"�Q� B$=�HG� bs�J!��>A\ %�i�5�%�al6�v�=�*5�N^=difOHt vK&�?.�K&$ColR0} &��!-Y Z JK O�$ ϲj d rsn|`2�� ]� n��&+ � !�*�4�  A84G5 c!�n|41& � f� � . � a�] 1 �512� 0>��@A�to �*� �=�� : $�R� )=id|q|�"Z>� ���1S =\ `�'5��"�Jc c  >M \_+"�#�)�1^ 6�� F1 �BW 0�n%5Raman (98):R re�;�+|qM��usJe 2 2�} �6��]�Vq�V����G�N# V#(&��a 2�<: (o:��::�7�I�!� !_� F*�J�4� ��i��7ύE�u�L�lI���"��)DZ��(or B�$�>of J�6 u.��&R� "0"Ty�add��! R�3j*array}{lt�a_�~� !q| b J�y�044}2��Vos:�}, �+�Q`�{�06� "M :Gv\n}�]\� 1}{2 �2�� l}� mu)^{7/8 �^{R �B.�+4}X0:�& >+R,  { 1� �X�x8 ^���)��5. l� >L9fL]�* EEwE�su+One :�aF�s,IcND��eon ""��"�i�_bA+2}�Z"xJ ��V ">b6�bD!�DX C&���ul:Be�y}K2l�#Vch����(in���>�6�k" S�a:&.%x ��e<s oO_ ic2�sB� $ yet�{� �.vnuk ��hol~ o�HJ�@! en $3&�+ggN)I�$�{�6+Q�A��;.of Eq*W1E� �:h n� add�2max� 1, (G� �3/4��0"��_+���\F�>�^>  2�-\��2eJA\ll��\�bF�1 ��1�n��;�J�o��*^%_J�ZL2: R6 �6:-m8Q�y&C&� A& *Il&fmu_�$>� S:U2]*�%���f[}F7NA� ��  )�|�%.xj6/, �>7\ggO $�V"] dr  7�ubv6" 3 i> \M��� &&�* }8 - R�"w&246}, ��� O�&`��m�"V9U�&I 5�*� � mL3}�)|q|��3VF����A�b fO2^ (:�)��ohB� �.� ��*� n.5 2)�)$���� EFT� }6�B�Qpp"�\. U���npaddq� \min��\�"���;Ia2Z fT\, ,\, 1�_> �=5e:=���: J0add5%]2-`�.8^{5/3}w,[��a2��2 � B� +.KJ!3taFM ��?J�Av>��fAnu$�A_وfa �/�S]2i�l.WS2 R"’n>�fjL!k5} �k9ei��IS)�K*-jb.��) ;K��}{:� {4!�  ^{2/3}: F, AX�Q��Y . },p>A�.�� "] �^U 6f�� �� -)��.>"S ebe<��2�� eM&� . Hϲ0reX � �is6��uA4 J/�6?� ��sӵ\� �E� -ired �'��eamR� F� {5/2�^3:�M�4}M�� �V�s:@ ���yitbigN(H b i��m�mby Evacuum)l �X�� �fc��XS!�nU�  i�HN loa�3w�*6� B�%�9�e�� ?-��6��ea)���e"d�v)f-�6v(A1F�in 2�� )�?fU.;N:�) U�b�dE! .� < ���E:;$�Ah� b�e"Q�!�b�} � i(y5bZal1�s��"���rvYX!F=:\ �s�5usd &�VConsAJ} Su��"�A�%J ~ �76!q�6m��5�:"It�K!��e9�ZNX �0"d�ee6�vp�yY�`N N{rTd:o���$�T�T�T�T�T�T exacinq\D6e\P.\anA�WI��employs F`6��Mn*�I��.�:Ac�[*B� �jSh., 2kK.E,Tk A. g�`fully a: s��rt �� RFBR+4nt 02-02-17135H6* Iabn�al �j�% Techn�wC�S,5j��"># Pro�� A-820.�5� >ݓ��"5�+h J.M6�$, Nuovo C�/��oca~al��s.]>8 50B}, 64 (1979�bib �ph C. A.  , �s Free-Ea�ron Lxas} (APc��$ston, 1990.QK�l}G"�l , M.O.~Sc!�,, C.~Keitel,nl.~Rev.~�� � 70}, 1433�93.]S$� an}B�lerman, .i�BQ 75}, 4602P5.P4Nikonov1}D.E.~ ��~ScJ` .�, Opt.~Commun �123}, 36 �6Jj2:j2Q�N� �E%�54!�780�N\3:\Yu.V.~�] tsev%+ SusshmNb7�44E&98.� E}Yu.~:S$S.~Trendafn, A.~�n8yev, K.~T.~Kapa�:�e^M.~Y V� 9A 2148!�2�.y �1�$B. Matsko, �J�to �E Ak )P( 58}, 7846,%R6�"�e M��Kuzel!BA�U {\it Pl�^e1 >1. E(TN�ntiN"PT�e85�>� y?*d"�r eK��r�icx�rr$155mm \odd�$margin=0mmtr� hy3�8min=2 %297mm-2085mm=252mm \head�r0N$footskip=7sep top e -5.4=�{ =23 z8binoppenalty=10�z \rel2j ,loppy %Spac�-U � s %\re.�r�~$tretch}{1}�h\'*s6�r~:<}[1]{\mbox{\bold�M( $#1$}} %�:"76A matr�A!{b�F9�%\̠style{{�y}�c�W} �rP�Up Bernstein�1�  sphe=�tokamak �as� ""$fwi�," }\\[11pt] ��;sLPiliya A.D., Popov AYrd, Tregubova E.N.}\\ [6pt] eIoffeeq ico-��a"�q@, St.Petersburg, =rG4e-mail: alex.p�@.i\.ru, a.p�6Ce:-,�u\�BId� {B}$P'fL)�STX9�id-plane�fig��E� � %&�in.�+�b�-�&Knm�'�ously -�A-%��N,>�s�occurp STs -Y��"!�:�pr�ca(modns.�B5� whole pic��1�A/G�(ii mF��2y��`gbU� qu��xLl fpFi���poST�:�+(fig.1)f�n$ suchl%�� �qo&��rassess Y EBWmI h*�an CDo l s.\\�E�8245 460 567 830M�cma:�CMA dia�m�e"]!M#{na��4�� ����F~ie�UHR'8 fund��u�(doP�a��).b.,STRR6�jECGd~ F�se�/be��z�Hf per.~%�ea>Co * =)�2)&p�awh �j4as not conside�Ored in literature yet. In the conventional tokamaks EBWs produced via the linear 3rsion ofE�Iincident electromagnetic waves close to UHR are capable for propagating toO�fundamental harmonic along dotted blue arrow. I��equality $d[ln(n_e)]/dx>2\omega_{ce}^2/pe}^2*|B|*L$ is fulfilled (it's� case� STs)% can�e �solid !oarrow�(nearest EC �-~$is paper w%�4sider basic fe%�sv!� EBWsq!zand damp!7for%�,=\nu_{te}/c$!� D=\sqrt{2T_e/m_e}$,!!H whole reg�ubetweM�U��niw $q=2��C, so �5=�1$ !. For ɬ0ative investi�on� 8keep only zero-AD first��er termsi�rm=}0^{(c)}-\frac{�t% ^2}{2n^2})�3nY�^4+ 1(6q^6-3q^4+q/ *q^2-11�3} .92 E/ B=}J9K4 K};V $B�M�_{xx} �V2+2 zz m�A䅌�>a�n�e=1:b %0%*},. _z5� \nonumber>ar�y�>�Q� cold�  Th��n >�T�� ^� �i���-AM��0ile applicabi� 5 �Nc �kire�/at�\gg 1$�: ere���to omiti�por�za� ? �^2$eN.�^4��Eq.(2)�uc���dJ�(1) to�.}]"M 1}{2}5���^2ik�) 2=0.b:The� u!!*t!>�F�u'= � 2}{3�M�}2Bub �yё 4-quX}{q^4a~�=9<0-�(1�g on-breaks d "K!�ECR� do not��3�os� ��s� ause2 �  o r5�subjecH   coupl�%ory� e%:", out�  immedi� � vicinity,�q5)�z,=iY}�2k>Y2}b �%>(characteris| vaTof�r i* ��J �! $2^{nd}$!y�� !�i"� (6)Hbroken%� a full -)utreatB '��d*5Full-%���Ri9&� } To obta�  traceckhotM�N� amL b 5 \sim\ �B���'\llA�tm �!: � mak��,me simplific s. Cq�I�Aj�.�� . I%@ well9 �el� � be presen�a� i�0ite sums over�� � �( $s,-\inftys s $ = each�AJ�sumed�}eE6 $q=s� ![� m + small,!:calculaBS�=($s=2$)  rF upx)\orB inl u;[o "(*H ) 2��0non -��{a"�`20�,5�>?z},2�zx:yB"$y}$ vanish� &ō6xyy6� $,>� y}=-2Iyx}=-i gE�A�0gin{eqnarray}2� S2vv +���f| lP��}{aKm]�n}Z��(\xi\� ,\,\, g=g�T.T�v��  $ c=-� |q|/ �� �>ZE�A��*./ S dem acco�gA�(~\cite{Sw} e7l argu�,$\xi=(q-2)/q>$. �,�� ��t� �J^22�%� �$E_x-igE_y-0 E_z�[=0\\ +x+ arWy0.V�UerVC*z6�- �z=0�>�AbsolutN u@jJ%� ofi�>�� e� refo�!4ll E_x$. OmittE !ɉh1�>,at means neg"3����� erp/Qx{ $1�aYto�y,��wdF� F�!b�.�E-)�Fg-x F!+!N� Q�U�cc 8)���t :Y �u�W^��RI ^2*m�(���$2(q-1)}{2qJ ZJ� �=0B� C*�$, at large"3�qgg�5 N� �6is J A1eͭA%��(10) dom�s��returnsAth�a}QQ� (5).� ECR &� at�dN�\ll2�BermE beo��euio� found�licitly:b�&� %�}�)�!A2{�Z-�}}B� Thus"��a�!5:� ,� 1�(x)$ goe ��$x)�# $a spatial %�B^2>�E�>5M a Eqs.� !A (11)��ED simultaneously.\\�J�I�b&so us��"�v� "�$�1Vle�$ iC "non-66��.}����replacN$y a proper� {N=*� Wav���2b layer}yu�F!a��f cl as �5�^JN $t factor $M`�� � ��1 , pu� 7 =x/l�A$l" 2�>| �-lengthQ�6S vari�. �L!asympto� ex� � $Z� -1/\xi� Ux/L�WL=l �M����|"} |� �fi�at�<ne�vY��-Sce)���<11) differs from)2�2�)�AS%�tant -�Q$ -haAg��YEC {>B�� 1$)1�%���elex� $|Z|8r$Re(Z)Im{(Z)}� z�to� alsoW�B �a�er{ _"� {"$}/���^{1/2�.�2_�9�!�WKBory5<��� taknemb� L=� M3^{3/2}� �E-"[ ������.k����edQ*is"� Aut!A �!����A �WKBF718l�!"1R� ����R��s& � at .12A$ satisfiedEP���IYD iY�9��9is5�!O free!nJ�N=\pm Z�/2}, N=!MA�a�(%K/(4-b)2�x 1��h�in 3� plan�W(Re(N), Im(NO $. %Qp0figure}[h] \c�r�H\includegraphics[he��=7 cm,bb= 0 20 300 220,clip]{h_im_re.eps} \caption{Pl~�X Left branch correspondd "q , ��-!�ref� ed��Jp Tes��no�� ec3R >�=j hssulva�2P ing.-�-8 % Bruncfloc�!�upᗁ��!r�� $N$-%���4$signs $(-)�5(+)�� 13),A�p�! velyR�b� $N= -Um� frag��X curve� E(<M �WE5 $ be�%��u x .|xŰLg i�aR%��ʉr9 !�Ta%�a�#- I� 4|x|}/i& :� ��$(Im >Z SQ�mz�Ui )lie"�)�� ��$N$iR. At � we hJ N�i����M$ �describ�#ra ion ��"� �)0 �V. >. toR�-��&�&� J1Not��&un�~a )Htheir ph�%ALgroup velocities dire� o $ita!9)� 22 has Y�ally a*E AZwI�K ag �.�fis���,1�d�a $N=-��$*} iaE8� posi�  �YesS 0"i�ve Mm�{�e ��E���_ �$:\�4�SF�]� .Three im�ant!�clu� "� drawI� �a%. FB!, incIg�ag�(G&ECR�\�-�%b ���<)r-���)� in� utgo�"] )�9��ng� low t�%�. Instea)2d�b� .U beyo� �Yo�' �. S7(,, two effectɥ6��p�blT $��M��)$:%�!G�(a@���8��A%-��o��Esse�� trib���!�%$pa�(!�nA�, (J%� $|ZO�u}|$a� no�s� f�e $� |�woM�C��d&`��-%�Q��om��x$;&naxs aA"ult�:.��G%!3� ��be due�#& e na�+�8th� *V*P`\}(ez� �of E�.!�"��I7 #E �a�leR&� >� sB0(J��HNU-id/dx$JLU^{''}+M�(x)^2U�B H� ) "is giveX ��� - hA�a����nd�i6)�KQc $U$M� ed ,-lyM E�e� A�Y s. MU#it� terpre&o^-isd�+t "&�F" �4)E�A�� in&s�J4U_1�1�|}\exp�!$-i\int_a^x�erp dx8}�U_�nJrIl Mi$�� arbitrary��,.L(ha�en AWioned b�, $U_1� U_�'A�!A��!�s,�"� ��5F!�1w���AUa~� U�&5��=��u�>z���&� T�l&b� J� (U=U_1+R U_21Y� VI \. i3RE�)btpquantv/|R|mRenergy.�4coefficient. P�!"-5 �EfoR�u�^ V_0+V_1�ui�BxM) V_0=u� -V_1VA��{-  Ro�ne�� easily�*�)u�sAV{1,2}$� exactU!� &�$U .m +V_0 =�$�a� *��| � L �| ����n5! �*�с6method�^*�'&{#� b Y|L\gg 1 ����i� �h2]=� AJcaE�Aby " >minI7)� ) perturb A��m��f*���J9R��2}��{� }^{� ,}{V_1U_0^2dx��q.�-x!8�,�e `\Gamma_0>g f�NZ�a42�2s L:� \xi{� E(\z&�-}d:xi}Z/!~ prim�$ot��ent��%� \xi�K $�=2`�2eHF2$-e�9)��A$ must , .��1�1f�integrឡ0no saddle poi�.at >� A7co*T t�-e Jleupread#f� $ = 1* hgE3�* a�b�$A�an�u� t to'* ? w seems ra;(8doubtful. Numer <�%I�p{ &�Rm���n igib��L#! 5�\ge�_IqN/��3m��0"|L<1$"�-4�H���.�� b8 by�$�$E�}� � eq -\xi+VES�$a�.$. SubstituL!�s1re � I4)%� intr�6�the new . ibl2tau=k_0xmO:l/�.�13�)�FɵZtau-\g�  V S tau/ )�Uj3B=qi^{2�A�� &��e1n %�A�Z����meC{%1/c-3!�i�Rvst � ��$ �$ y5Jb |R�A�i,�2}{\xi^2��:� �(8=\pi Ai(0)=1.12�K8K010 5 290 215 Kfig5.6H6e"q�ZU $�F�re,5� (� �- Ag$)e�F��� is" ^k,�l,�f ed n�G{ nd i� B�(21�aI�� �74� rea  agre� A?dem! ��d. rin�j� �(� d�6ra��ae����A��)w *{ )<��8.*�'y�~�>W &Xnly }is� %��ipher"D ECR"8 ImP )($Re $. O��wi! � pene%/���= of s�9g&� F �-FCiL&�*8Summary} Existe(�~ |"/h�6A.� {$s inhomoge� ��9de�� ��� Vj%ad" ely& &�=��;�+V�0�"n� �Q^Q �K>�� ���",.a>"� <!B�� �.U&�o ���Deca���GERa\,tudLC "�A�ue�2combi28�@*Qb!�2�onu,< 9�io�&i1a�yMu9_E. .�5���e� �je b�\\ StabX����> 5x��B���*�=1��AB��,\ \\ {\it Ac>: ledg�:}� work(bs�<�Xby RFBR 04-02-16404, 02 7683, S��. School o t�' 9.2003.2.}�b+, thebiblio�(y}{99} %Plepr6�{ /�exA��es. \bibitem {PPT}{\sc A D Piliya, A Yu PopovE� Phys9+trol. F2(} {\bf45} (�) 1309uNSTXfig y�B. Jones, G. Taylor, P. C. Efthimea4 T. Munsat�hysic�. �s z 11 {4) 1028{Sw v,D.G. SwansonO Mod. Rev. �} �467} (1995) 837�>� docf,} &r\Lclass[12pt]{article}� $ } \addto�${\baseY skip}{0.56D \title{\textbf{S�?-P a8 $\it{Green}$ F�= A@ach!N Co �/Xd Atomic or Molecular O�hals}} \author{Liqiang Wei\\+ ee�T'�Bal O,M!�Op -�\\ Harv�Univers�X Cambridge, MA 02138\\ �Email: l �Hjohnwei@yahoo.com}$! make% 1eabLAct[/0space{0.05in}�i+B<+��o�4 gf9And systeb#!6ach� stud"�r%QCstrucI ato�1r m)]e�0p%�!lzaddZ �� issu� ��m+le �*a* or o-� �Bshould N&Ͷmost "� aT e0a ^(um many-bod�'r5W�g���# �-�6_"�provid�� yg!Cal schemI' � s�3[BZ �.�.]7all!�E/ E�U�-ea9"�A m)ti�@�!�d�Bm�8�2`4Hartree-Fock}$"Z��f� �" ���)B�AVer� (i.e.�Q1 afD� $(EA's"ioniz� pote%l6"IP#)E]��$H_{2}O$�e&� U%&.� �ex�Q!�istry�a �&? self�%�'�� tal��%� 1�a1%$S�r$b UK9� �%��4@ O�wmpa�  ma�  availD  expes�F data��5a�6tEb�l6�A�� U�=��$y $(DFT)$ 1ionE�!W^%��Y���tU� m�� ach.Rstrict ��e�IBful� for ��� o>�]�of�ej �!RItT)� bettA!�1�than d�R*�eBDFT}$ e,( � )�H!m~v levels7promis!+5;ag-y�%d 9[ r C�E��<�Ges w$e advantag! ndI��7=��ir�xrt, �Y "�FI-�s�ei��A+",J q�>�A�!�$DFT$. v�� \��3�� "HI� du\} �1��y% !H,kconcep�JVQ�l �nI,{ abalA� alE��# cessgscenarioA�bvA�a�! erac�: %�>�0�s,Y�, aolids6$mulliken}.� �.^of��t a ph` al ex�butIA*a mTa�0*K`�&u>�IdtI1 to��%D�s�,%�� :�R �hɫ,f��z�!� endeav�o�Ee��6�-ul![�!pz0� ���%{-��N.m�.�} �F}*J�H�Eq�a�i �o s a E',ic�)problemADAs�i� maj~Ic$1uIpear�)� !Tqb����m��,last 50 yearQ>keinaA<Ac*r8Q�gyn0�ncipl�< ��p�L-�wei1} ))�p 5 &� a goP*�@w0JF}$5�"�4%5�x�&no any�*���mixatN/E�nearb!!n +�"G)��@�!�N��w|mp08%! s%��sht� geome�� "D Ae subs%Lt!&�E7��Xwon su� s)bM��80� A}oJ�L-���fWCalyze ��*a2e ���� Y#Ba`� � � 3��c"��R�*f�E; ��A�n�E�6�Lit( � �b@J�*� %eqf�52��&z!,$d discuss �nr$=& �����H )E7'<each )J��� �B����!D�=ic�P2' I��out1 ��A��. ^�y} Two�8 $(t,t^{'}�>b(or�)2D&�  $�L:schwinthedin" Q� } G(�^{x}t, � �=-i\la)T\Psi_{0}|T\{\hat{\psi}; ,t) ^{+L �\}|F\rUZ�.$T$�E�Wi% !��Fat�!A�$z�j,Z�$�9I��_\�A�8Heisenberg}$ pid asso��I~.coN�3`{xN,�M��9oth sdH '��sp�Pchi$  Ae� freedom��e $>I%0�2�<nQane>"� � � i�D Its * SY pe%s rT5z5 ,be written a*,� } H=�09�.�)h1�)!dM�+?J1`Y;B^MC.dA�)v Ur�Q ec{r ]� Y\'r��VZ�!6one��19 $�5�JS�.� kin���yBA�S�Z^�<t�.ucleuJw = �-Hhbar^{2}}{2m}\nabla$-\sum_{p}Z -5 x}, %�R}F�]��two>� Cr6x1�mCoulombaZn C#��VI&�3|�r}- !�|}B-:I��"  6 >� &EG�;\�f)=)Pn}I�\phi_{nUl) ^{*}.�)} { D-\fc$ZrF.Y1Q�)=>�y,$�Vn}(N+1)�� .�=EX"-E�\ for2. \ge \muB*orµ�-1)j�0�Y\ >�0}� D �Z�< \muB:�/.|s74�UzG54�|F Z s $-8 )L8"� $2l�%�X<$PJF�$ �( o�citJDݟ� 8& i� le2��  aby�5 Z$(.l \ge!@NU��CA#�R7) 6R)�P<+ $\mu�A"U& �#� &� �:$.�)���%y�2&%h�?�&i . A Di�B �i��"s&"a2  $Z�i5�e7m� let%Net:�belowJ�8���=\delta��T�B�-�n%�fo�Yit{all}�M!��QW �%�AE 4Q�&�E1LehmanH*r2t . D� %�average �*i.=JT�j�,�W V�� � �m�Ye� �� \rho-� Nq.G ) j�.�*��)�����#�4h�"� 'ba�8��%>�*[ mH�7 *<s%�follol "�N��<\{q�-&�-9�\�A\}Z[�)-  \SigmU���"};+J^{"#'#d8A�"} �%g%  $^�.ra0�)�f--bJ9 s�loAߡU & "�A.is5~e��s�*�wV�W] ^{yV�n g�|n"�*!Nq�EZ� IGyF+M-Y$+F$B�+a�j2� �5�'}] '}=QD&BmBpor �jY] � + V + �M�YU�|c~  =2�>B�n��!9%�Dirac}$�� 92r�� Dyso�p�@��!�Io���y quasiU^"7cu�( &�r�h�0,louie,sham,me.ntT$w�cY��e+&_�H6�$�m&� Kohn-Sham *-�� ?�&,�+mtel ��B�m�a� ��*�aI~�of 6O(  "}�  6T9f�S r&on. Una(%:b,��pW$%�xp�Y�t�D&�-1��2�"� AN"K!�R?�?J� ,j*4,1bv�ned�a62�!� llowsNo� =mt^{(0)}+ $^{(1)}+... n)} N� ,#<)."�%�"�G���F!&v;2� wa�ZH,goscinski,ohrn1,si�; ,2,cederbaum,$}. FT"*� Eq. �T"�s6#4 � a��� �� (M6))A�"� > 7))%�=%JA�.�+td*vAui���p\�Yohc�words,�I�"^&2*-./>�Q6r�mor�o�B�(�):Gm� � ofB�%'j s� �9q.1_�($N*�6]�Bia �9�ˍ$s�(.��C �R:on�3I� rega]t�E ��%�?6A�:t�!�Z8��v�at5��͓�{6� ��on2 .�(�X$N$b%�ng 6�a� �_�wei2})#clear$$ and H �'�ood�l 4>�-� �,e�Qe12)��!-��9�t�6 &�&"#�ftogha(JF4.w$mZ). Obv� @!thek3ll cat�ghe�. Eoa �2n}�f:c�. 0suc`/�%A@XC!�jEm�&x'=(edvN1ZM �^ on��t3M� ~{%��'eFw ����S!  urn ^ w�kinx 2�q X2A�2��w�.� Qr"�i8 �P}`.R)<ua�n�!��k��$A�#Q Uyi��Ix*|iv5u�!�Q��N !Z*� ]nd^q>Lre %-�Pi^��choicG=!�&�/} �-3�y�!;�#�'� 2$in a��gAo��# stry��!J s. S ]5yps2g!s7 �A�R6B� &% et3e�2�5G�zm0or^ � xist��##T+!$a�a�cFy eriv�v �(�6Z|},) uper"��~�% =n� BdiagrLG� �xV6�"�}"VY�of mo!�"o } n�"Goa{d R�} 4 ]J� A � �)�>W�9aMJ�B��emplor)�?:o)���45�oach���Ikdbov��*u��(� s=]aQ�� ��q�cN �^� Swa�7���; e ta@pa6-9ob'e�� L$R(O-H)=0.957 \dot{A[�$\PH HOH = 104.5 (deg)$M~�&�y� NN��� U!�, cc-pVTZ}$G7is sej)basis\"Ded6����HEjten���1�l�5! /�:�wumEYT�21��!��0�tal my�� ��he 32. � ��-�X#��+� �"�%��2 �%jM��xbed :�B3LYP ��becke1{. 2}. %N "FA �.�-H)!uis6O thir.O9 )S.�BJ 9KMCeq�Z:Q�a&�'AZ A��)�� =3��Q6NjJ��_{ij}(E���^{(2)B�%~detai���y�N�)��� � I�"� upSG&�" "se�lowei3}.9n�LdF4if�� pick%Qe�6&��s6!�>~��e�-��IKy"�U�p2�+(iyX b�O)J -�6�= �(ars}^{N/2} :�# rs|iaY(2  ja|rs  �`�ajx^)}{E+&� a}*hr. s}} + �b9!R�ab|ir }>� r|ab �rj^�2�2�b DRkza,b,...&�i#�Iq)� $r,s2+"�#B�IEg(G�KEi���fh*�7.o2-�Qrmj:e�i�i�9�$i|V_{xc}|j5v!a�!aAY} Q4 ia|a&B��]e3b�aX�8a��S�� �N %56���s. ;)a)N6{I T s*sg*4`:���. \�#6�=�re�` -:*�)����s��J��d�J ��`-"����} B {�B�w ��J�@u �five �Tly-occupp0}�� )6> t|2)I�%II"Dn1P� vF:L �%:yH5h* �1��A�� � Kd�:w#% �DHondo-v99.6}$ suit�truhlar}�) b�)D�*�� Co�:* J�0p�a nove*~ Q.�'�.>�0��Gm> s�MXs6� �"� AVbGz9 ..�/"��&.�5�gA�&$�:�0bi�I1A�&�u)K-Ba�34 �"�8C �y��J~e�>se B�J neH41�B� H karplus�;da�ddardK~Py,�)�}" 6�A�o�f2��4�6�-M�. A~1�vC6�0- �ci�8e*�* $\it: Efi�`��A�y\uT2K-*'#%�I#U� &_#�^b iwat�M'� #�K q*V ��6��cɝe >��/��exF��tsF!�X%� Zf 6;J ]�)�9��m"< 1u5� 9wm��D�6�*DM�,b�W�=fFe� ach5ebHvl� . OfI�rsF��fuY im�3,Y ���))F���. r4 simiAK>h�� &P\�<�I eitles-L�� Ց[��J.�+�w7Y�&K^M~#inQion{<b"  [ f|.f�nM��99the hist�;ofZ��m�E�eJoy y@D>HB �"ci�D, &LƊŒ��>�i���~ �\>k!a&5a�4 �?en is " n" �;Al*�"��o"�d �m,Ŋy"#e��B�9'7!V'7aZa�M4!bAWU{ *=� cruc�M5minim&(> �A� �(�5+Bc! p.a�� cri�ma:i��e�)7&� &s. B��MkcI4d 3"�!3� ��d ��el"- Z�9G c�to. AL��22���koopmans� �$�14si�yf o�A�t*��e8J�} A�!rA �9 is �@}�e�]i2�%�up�q�I�e�)�(� &7MF[.�[a��+�@72 h%)dA d�mSc"�O� trad�NM>4 ory 6%Hk$[I+�E�L w"� �% �nMWd a��p�b� 1c"�� ,}:�O�8s uaA�n��"y =�=�!�" �< more]�c��alDwJ� GTclaim�~1e�:�y8eq�el� l� a\2%�[o}$���� A{"� �� �1R ���M�O"' �e;E�LFnjal2�� e6�"N��"��<<>%v� . .� ieE��a�.� Mtas� a �u� a6*� � 2-"+�Thig\�� *� H � intrvB<A� kK�*2��D "Le@o�dA�a%�i -in"�Facou��� de&'%��|' F� a� � ���|� �tl(S�YlI�t�JuseLB�Xal%in��m�  b}que�R�<P6WW�v�"�E qlnca�th �DQinu� B>��)� �R�8h�R�a4 �a��war�%;� ucci6�� Ate0I�� nee (�#� �m��&�&J�!0 E�&doeL-�/� MH/tiap;s� �"yM�/ $;�+:,)$��Pal��AkmAimaginkR�>uiFS*P ��G ��G/ aA�� e2�-U�yS F�=�#i�{@!pl7 ��#E�e pseudo&�)�h`"it{QM/MM�$=Kach�R �&�!�algorith�soA�Yy�䡌 e6K%�&� :E�N�͏!�uɔst rob|j�ly�1m2�=CVaWJ mI� E2U 4U�.>�]2_*[1-_&$T R. S. M4T$, J. Chem.�\. 2, 782^34�U_�S } D.C��, Proc.�\B i. S024, 111 (1928.G�S V�ck, Ze�H>] k 61, 126|0.5k�R E. K ��$I. Schecht�P��%Ta�21st Century (John \& Wiley-VCH, 2001.g%s (a) L i, arXiv:� s/0307156` ; (b+C.Su ��60, 3835B2>�OvbO. Roos,�Uq�R� 32, 137;99.��0E�P�h�@%W. �,e�. Fb$B 136, 864a�64m +7LE�!12:A 140�33�65.�P�Y ParrFW. Ya)LDe�Sy-�aaU�of �aM�$es (Oxford*�a?ts, 1982��L%9S. Ju�L : "C[ �\T&UTS# S" � �"�b�Methods"�L SL D&:Q �AppHs��Z;�cernfV, MAJ.a�SeߋVZ(ElseviA�Am.dam�92�"�M�H R. D�M, Int%�Q�uum�L . 69, 241!�9��Y��M!�Ko�Vnd Maxa�HolthSnpeChe��'s Guid&#oj��Et|E��V�� aySTJE0N��Ostlu�Mo%K � �ry:��o!v��Adv�Pd E ic 9�KE$ (McGraw-H�ٵ?BR"EiSJ�#�8!��,Napxcad i. 37, 45�s51)�V+fM�4�:I�fe�115, 134 @2�� �� Hedi6�A139, 79�q65 zL. +vHS. Lundqvist, Solidi�2��196yY!louie)M%�Hy�UseW G. L%."8 Lett. 55, 1418Ay85 ��G %$B 34, 5390Ca �6}^�B�(387%82�m%�e> L. Shirle�GRe�)�.�, B 47, 15404��<"�*)) O. G�3%}B!}keman,eKD. %& 7, 57�I70-$ B. Pickup?.P,�@2��013��73.�4}!�D. Pur� nd Y. $\d)O}$hrF4 ��406 R2�N4�Sim)2:^64, 45�g7%�5!�2�BovH.a�Kurtzd#~� 68, 7%{7��Z&�+� Schirmer,%�. C"�41IWale }x A 28� �S8!H�,A�Fnr%�K.FmG YDa Yea�Adv�&� 4q]81.�`2�� �"~ Iica A 3a144o 4); *� ~65&� ����,S. Benedict,�{G�dr �� . Pl� J. 2�2 39a56��* � . Du�, Jr.B 9I007M ����)�D�ckeF@8, 564�d96��2}!R Lee,���a R.a�)h" �� 78� 8Ak�l(=�:.Dysr&)jI�[oaylt Urbana-Champaign (UMI Pub5��98m�IrlL%� Y.-C H Surf�s4��1e ��" HONDO �",A� Dupu�A.��quem�E� L (June 1 WXk� %X, �a9. K ) : W�-- a0 mprehensv�e<| e, V�m1,  F�,anks (Plenum� New �  1>m jo`!}a�KiLP D% y!�i�5(. 98, 1008E�9���g�! X. Xu�W��G , IIIBSAQ8, 2305m�. � �Kimura,ao$Katsumata,��Achiba,a,$Yamazaki,  S. I� , Handboo� Hel Photo� SpT]aAuFu"� Orga *P Halst�W2���9 "[!?KhA��a!�1�36o"��U���dѰ��> !1 849 %2F�)>3newpagem�Ccenter}�no-Ca��n! \mbox{}�pno�ynt�o 61.q"kpc�lrnt�&�l&�(?? .u.)!pB�"��cB�6$S$w�, &�$&�}$ �*��Ts�6�<�.C measur%�%9%R2�(f $N_{2}$ % �Z�6��:� %j�^ %w^�. 9r��$AR�1��������A�n CI}$XD�6A i�d"*r� % T�)�]q#��srint /�a6dj2 ols . Isnew |$ {\um}[1] {\; \�jrm{#1�/2*sci}[2+{i�\ene�� s~JPk���Y��l�, % �$ \ead[url]h'f) :��{%\�{label�X% [ ]{�G �{Name\�� 1} 1re G2}3 ead{2��{� � t2 t h [cor�jx{A  7z3 z.M3M �Dei� a0 -Board \\%,aŨ�*8ly-��e $Multi-Anod oto-plier�1�al %<� link-����Grno1�es%�I)1,A1 � �%U� *"�z M. A��U W{� uneoPsic.M. Palla�-e(}ini1�!w!�TV h-iccardi}A��A a}..|�% { DiX � o di Fi�dell'"0\`�D GenovaS$ INFN Sez�!8 p, Via Dodecaneso 33, I-16146,$ Italia. �96aCD u�A8|: e-�{A�iandro.50@ge.infn.it} Wb��a"�{\�de+�e�dV�to ho��E[^mE�us�CT -area]�l�#senso%�A goap-�% }�#�0�! ests)3�+toᠩ8�^�B!�s�\��qdN�u)keyTI} ��4tectors \sep v�$ Hou�, S� Aa� High-E-�~ 8A'�-P� .��PACS coH]*�%�A: \I)  85.60  29.4 96 13.85+ ��6�\c5H��� > -- Z=w�x 6x h�� {pa:�&o} ��te*+�$e"�z3 Nu�,YK�e�:�E,�� ^X��-aof fast,I�_ �X&$ly pixeliz"�. p��n�(Eu�9l �ed deade=s, �L��hundre&ota�� �channel�& th tel�ur٤Z� . Am��o�* s, R\I�%g� renkov�L (RICH) (see HERAb~�bi:}, LHC�e AMS-AMS}) �!S3�$ Telescope�<Ultra a7�y Cos%Ra��*:C� EUSO]0}, TUS/KLYPVErussi} yOWL OWL}Ѵ�)�P9RtegQ8 ��l Mhal5&��%!� oE&0J*�3M-��.zY� N�C��6�M�*�I�u�'�/�+ m� Kn;�� ssem �ew";�.A�,�kf�Usurfa�1t�Cl�A3Scu-y�pe�A� �`�*+h�8�au�ept�:"hEalJnC2�(avoid defoc�x~R. WE�!��O)m�Jw.0ve carr <m9B<l ,!�L�`�i �the�� (�9� �au��of1� r;,� �2ular �k!� -��i!2�$�F�)a ��e�ad� al��E� ~r�[!��cry2l�devic%0crimy%fpaper�+j*a broad �dEy �},. ��sh/� � �9Z����Uit�*F*a1l �+ed $1, aff�H�na�allz^>��vusaqw��F|al)3�����s�JA�eK8�vGb� � (�T,e��-a "R8520E�Flat PancMT.�Hamam� C4ion�,NewPMT}) or iTa 7>e�LEHCm� on S�_ ( �an �+g;*F not)�U1� �xMyPap,bi��-LCS-A s-JPJFI}!�iS� +�bt ncer0w�I%�j����AFz ac�jRz�2$0�u maxiJ�T5 a 54way*�wi� *� _�S�=k�5�M���-�iMmi1Squippe|la ow�Tir��Js&�4A�ob&/�9d� irst� �0fr w � J�2�R�:*| Ylhcb-�U}. L�2� �iE!�o adapt!��e�6�-� mi_�rme1t �z Jz IMk Goal��}�sJs"� ���A��\ �0i� M2!�UQ6 buil�.=�����)����er�1ts,X{i'!�am�Uad"ۃO ing:#<��e��-�e3j t �HVfa��pF� &� , �Ter2re4uag��e� proc. ��� 75JmC��]�,"��Xgr� ]>sm�asieri[+6A�|0�� aratus sh���ti:� %F=&��al-[ na�@El�8ary-Cells (EC),�k� �zto)�r1<�-De!���dul�*PDM). z:`F�a"� "\ MAPMT,,� s��sl ��ʌA;a�lyp onom��3)BQof� Hm��7ec9y%�%�5����1�1�"� E� � EbY a���>C ��Fm , sa��.��[2�mplish�?�X!>N� Y> i �)�%�EJd^ �!� ��-9>��)(@ei�*��G\�guidelY)�.� ���.�1ΐize} \ �EC!��Sn.�C hacq� �y�1ͅ�qde�V�� Pr$d Circuit (PCB)��. �o�a��!�, "W a�E�!� 9Q i�be�! �X�EC� b�>AIs �!{�� ecis��1?v��|;�%`�,of C�> %�EC%l dPDM��A6� ��zduo�� 0 V� ,”� ���t"G�%U�ed5BU m F� 05i6��!�8��A�"��⹁Sdi�zc*� id� 2�.ba!�%sMBi9nt}�b �E:Z�*ea��D��B�$�;��!�&�9a +?m|V�p�Scap ies;Q�!�th�OPCBp!G (D~or{iF�a�a��5 ic bP0�i�%i�{a�� �nnM ons;-dvol�� di1I�HV/LV 允t4 mayaB�B1�%g (���X��� red)p < �o-%Bo-=�$;c� s,��!�hea"���ύ�^m��� -endr�& chip�mo�U/GA�VR�^" �E�n>asb� loAH�es%�' � !�as i�as���e �a�g&�!�!�3#�`pe�?ndMS.�e*� �an ASIC�iAyndP� ECdBՎia3ck ��~�edV7s �8�(9�th=m W chE�ma�wan �?�ly J�� t� pu�ge�&�_PDMQ�r � �;� ��t�to�)n a�a��R&��E5w��} shap� d���he��ouE�0 �.�Nf�& ��� of� ���AVw�'�{ f�hn�9a� ] �,!��EM�d���m�� 2�a,����^.�[ew^�I� %�&��D��` oYo(2\EM s 2)� . A9c�Y ic (issy�n�Zve)i� pi>a.��)be $27.��m!�� u!�l=%����r��!��C&d���Y%.! manu!�8urer: $ ( 25.7 ar 0.5 ) $ m< It�?��aA��1�� 2�� EC� *�laED!Eg,�ky!�r}� �a b�lof7���i�hc $/ a7��,!4le��������}E!e["�b"�X�Ag"'  � open1Y �`fic.��-[discus�O3 =��5r5$�du&� > &� �OrO)T�|�^� 5 Af!�$R7600-M64 r�Rz��WDns}��squ��in�}windowI�$L=a!a ʡA�ab� $35��.  {m�*is " 0$ gQxprD e���e�}��$l!&L A "R Ylle�dve*Ë7�2�elf��p1��:6Y�y�3-��� �mg$�5\um{m4m�� , we� ��lled,�r��!ft���Xn a� �EC��MJ�a flex- a���o� �&�=�� c�Bic���F�ґe9�:�.J.%6�!Q?mA�2�J� !;jp �( Rl�qur�g"J �2�or�l "HV&� r� �&e' EQ2XY�� !�E�.\]�L6 ,Yjnd"�$"� ���kU&hu"�U(= * Qarr�G" �� i� �t pa0L DK,�H� PCBŮ helpN ��>V���"���resin3S �"; � vF*>T (iypy� end&� %!@#$ %A�Kue�/�Kcross-�EC��cb %�Me~\N&fi:mica�ll-�a-v2}. %O$ -}[htb]'bk%�3% \f�3B�width�c9v�]{Jl�*}�( \c94 {Viev����nI�� EC. QAZ��!]� � J a��v6&�[{nE�m5`�i�y.*� In��polarĢ� is��a�(gT �W \K� avoiKґdecoup�qci�E���� aCinnFeEre�m!p� ahU�1`fN , �. {$C� $7�W��Ѡe��in4 ��l �N�tbWy!s&�"��sh %`�le�I 2}!j� g"�HV��5r�'� ��,1iu.1ca�B� %6{Qwo ���R�ub��`�NAny�P�56�E_�SinQu � fixed1�PD�*  F�-��9R� �J�_��" �&�M%i�l1��  mA6>�i8H%, ]� e�a��^D7 9O"!޽��, �� E(n"VM!,6�n��%�� a�&��R�Z�#- � "� ~1rf�M�o0O15.�all�� |���i}�Xrol� ^��-R�� ��.rf!I�o1 -F�to �0im�in. Up�:�L� �(��f� otal)��d o�a� (as Q�Ց��@�ove�M��O� Tor �:�s (�Te �).��~4 �9-��B:;&& �X� �4�<e!� much|m�a u-�.��<-��;Er����so�a�)�%�, w��"�W in& {W!�Kg��2k (�L^L�IMez*_ A�ThoB� ao�\N\�&���9 '�#�^^ [d^1 :�8m$&�!RΖcy ($0.1"D" �%�i�i\aZ$�<� �u�Rst�0�u�k�n�\bou�g:6�R;*� ��ˍFq}�QV� o�e� "� bbQ�R� � ] >�>�� 0.� ��"�� *� ]b��.}A"� � � �  ����)� a $45�� fl� reta�At FR4 glOZ�,�9�shro����[�<�z 15$ � Jf� an"0�x $0.2xkg}$,%$�2C�&Y =mo�f�ven�{: $716FHzF$87 U  1259.1809  878 (. AfterwardF $random vibi�"d�6�)���s  sugge1I�\ NASA�.�.  !s�3s"4ss�la��azn� 23 Kg ("�5K-fs}F*S uof�lele �� ival{%v�6.)G}$ RMS�E^� C�>M$0.025���� A�[*�M�G^1�y�2� �3,Fed"�^!6�*�/ex&��m0n�_Y��n�"�r�b(sharp peak >���.�,NOyY��ga�lj�$2i#9/�c��orthogoh,1 }r����w:��cZ�fth:!n� $3>��;Av!�D��8eep � s�8c �l��ya�{A�U��+fa l�4��ot��u� d!Fas�-y�traԶbea�ae�$i��>`�."��ed Von M��'* m4 @!�tD)`sU�"i�o���mit@��^����1��N� AB�oN�~��p����de��I=%'�!aK& ly link�R�I��{�b����#t $T=13[G$. HY( �)!�|# dM!by&(^Xu,�. b� ormlI�s3�E2w��f�3�,W�jasM~@ib����|$ .+6 ema�%5C���AF��E�: ��*ho(emvur` �� �!N�n�%n� 2a .7 drop�@\Delta T=6\Cel$ i�s generated with respect to the cold pit. %--�2� \subsection{The Electrical design}�tFt i$routing of�e x conn �4s is hard, due1(high number<\channels and components != limi!Y�available space. However, thanks`�BFB����MAj�m�%4}�wFw By usia:�techniqu!i��% thickness�=�pcan be kept relatively small,��atibly�!eme��requirem���us sav� massM4optimal � willa�ultiO(a trade-offh structura,h. If !� want�6Havoid direct solder�.�1needs a uI4socket. A dedii6= " �K�produced~\cite{bi:Precicontact}, as shown in figure~\ref{fi6*(. \begin{ '}[htb] a��er} \fbox{\includegraphics[width=0.75\textw]{ �}8cap�� {Prototypu�R���E3.Alabel{>� \end� ���Al@ary-Cell assembly�jNjA possi�pgAcedureq7carri�N��a��steps.1�enumed } \item >4passivn D��y�: �-�<&t,�� ���� ors. Testq+F�,. An X-ray s�+be�yfo�Ais�{g# check% y�joint! �I�aA��t���� onic�:I�-]Pot.�w�d EC.I�=� A �p 5betwee!V �he=�aA�round�f� 1 wH �����n��ensAC �I!��X insu) , $damping, �$strength, � taina$S goodA�t� 1�.2 long-las%/l��PceK���s, � ,q-$y, light t�t��thermal;du� $. Dow Corn��(DC-93500, a� monl��ed5��n��sD  appl��io!)has b!�assumed��bs lineD�und. � imi� ilit+ peE� �,plete visual!� io5KECm, overcome bym1in.��� /or& defi�Y' altern�e!fun%.J r��,) 2�A"� !xyV ASICP schem�- oa��� ����$}.����99.�mic�ll� ing- �}œ��SV� +�$EC (cross ^):������i����s��J���pa: b A batch� �V�#&�mE1fa� � be g � $laboratory �,El� pped��BGA= E�4 dummy, expend, �*. T�?p"�$is reasonav clos�W �~ded!�as far�[o-��propertiar�oncern' Morea� x� &r a real � Pi%"I ?EC� s�2z U,"� L� Colt or System%)w͈,� u�Fi2R fig1}!yu� fig3a�ri��\ 6�fig-16�Fr� view�., �� V b� it~ no1:�% r�%X 2%>n %�o F2}}8��M �:%�j�"� fig2�� N %-�%b%36% Side�$�$I$3z$��2�-6�F�­��oBo�EC]s��submit�*H��{e behavi� 2�>?x�L n��effe*� ific��1p�as notic�w��F���LS&-��MJM E�ive"� relia9 8of $M2.5$ screw��ce�oic!j caus�" �� stra' , hav.enM �/an exten)a�$ campaign.� � l�steel �&! {e�J6T� of /AK�$ %� es:F9 \note"sub T (�}l\ * 16�I�-re�a��,should v!F�3�% .�% ��bi:HERAb} { D. R. Broemmelsiek, Nucl. I��.%�hMeth. A, 433 (1999) 136. } �bi:LHCT$S. A. Wott�"jN 53 (0�) 296; E.~Albrecht {\it et al.}, �P�"� !�a clus�ofz �&� lensesEi��i�� e RICH de�f}, �\) um.\)D\ A {\bf 488}, 110�2)>AMS!kB�pat1a`Phys. B Proc. Suppl., 85,G0) 15>J EUSOK,A.~Petrolini-&, g� '$59O�ϩ��� of u��/� gy c�}��] �39�\ �\ �\ ) 125}, 212�3Br� �0V. Alexandrov��$UHECR Stud~S�liw 8in TUS/KLYPVE E��} P]#e��A28th I�t$o����,erence, 497,�3>�OWL� Orbi@W�angle� -c� s (OWL) WJPaper, S.�HSEUS (NASA), Jan 31u2; �ptt{http://owl.gsfc.nasa.gov/}>�NewPMT� Z  t��R8520e� it{A��posal��aF ��ur&@(E�aZRof�2}, ��0-005, CERNH�)lE+9 R\&D.ga�&M�eSn�m\ � �.; Mod�2�!BAl� � }, !�$/TC-03/13,G �5��a\;:�� !0A�usicouj1BF�R� of VLSI F &End�cA�ic ��3"� aC8 �6 A518�0,2004>����.x Y�w��A(�������-Ls�1sG��s.� Ver�e3 Specu STS��ELV pay^0b�IC -�8A.p8bf{GEVS-SE, Rev� June 1996���ASA GODDARD SPACE FLIGHT CENTER, Greenbelt, Maryl�20771:k293t �OSMI ELECTRONICS S.A., Rue du T\'el\'eph\'erique, 1914 ISERABLES, SWITZERLAND. } ���2J�2-UH'>O doc� } Έ%\}1nv' \useeage{d � �} %[dvips]{_icx6{,-tav}2Rbm���T \def\veps{\varepsilon!2ef\J{.= @\ } \newcommand{\�}[1]{(\�5 #1}):"Ere " Eq.~b&t&T\~M:L0cm}{cm$^{-1}$!&toler� [100]!�Def\rtw{\rightarrow�'-'�Q� } %#�8 \title{In searV.�� ,ic dipole mo��:8'$ativistic +cor�8on calc�#�hVP,T-vio:on(ect=� %grW stat� $HI$^+$}. \_ {T.A���)� c%p:is � +#�� � pret-�suggesT&��M��Ni� A�2�|e g��I�I��ecm cor�4(ential, Fo'>p� 23coupl>*�} siZ�Xdou�8  &�!��spin-o�;con) acBmetho,&re�d, �8�(y�varIwal one-U.�!t 2a�� four-"\ wavez,q�iod�$! -9q�ed-�of6�%B � is20=0.345\4 ds 10^{24}$Hz/$e \cdot$cm. �V1F� y giveFX36NX Y (N-IE�). �"&e of�+m bh?!�3"rib�!to2��$I� �cla e�+ign �@ �of ���ob�!ed a]R�Bne �*�D.\� $.\ Lett.\ �(94}, 013001�5)�expla�!. % �P \make�& %=�. \�m*{Int�=t�}�j>j ��n �=dKhriplovich:97,Commins:99})aexi<cŅ�Ap�"n �C6Bs (EDM)!�0el� T!ticles ��e two �/da�Pal sym,D ies:�par�8(P)EYa  r+sal (T).A��r� !�<&ffo�Binv�rea�l*�^4EDM $d_e$ (seal*?hRomalis:01a,Regan:02, Hudso XSauer:05Aa, DeMille:00}�C$ primaril�n�8#� high"�8�( ``new phy�'' beyo� he S/BModel.�.�a�re (s). Polar u!vy-atom "Eom�{��nonzero ��to%``�#  um �u� mole�r axis �below% curren!�co)��U!*!0oF�mob$� ��)!b6�0great �)�� ݶ ����8;G$= unpa�h &��"��orAaA � � s�- �esmY8Sushkov:78, Gor 9}�(< 5`�g �f� in p!�=�i%5!x�r�0 gN�A2raYLG written a�%%4T} \equiv W_d |\Omega|$�)$ $Nhe>$2  an HQ' $\bm{J}$Q�-@M/. I1� {Wd{&8��a�$Kozlov:95,� :05b}EdetailE�C& 1Z2� M(isTCeb �6E �ImM~u��e�The� ore}l ��s elope�,�}�Sb :05a2��}��rein)�)ow�!7"l6�%�q� �!p- �: �@e�"e 0accuracy, eveoE��K+^D%+Z5!�uin PbO3 1 {� :04, � :04}.Q Z 5a}.*  R-6,!��2�f �D,FydV �a �E4(�D"2 by�tz!x�? ell �Stutz� !�*&f� A�k2[otwo1{ar � s, HBr$^+�, �,�' �I�6� � A,e  mark��!l&/%�tA�w %��  nU)�emphas� . I��pR$ �cl3(�b> N? it.? Q��6��!&�B >� , lejG-diY -/#�I5�����. � CI)1Chanda:9�-= m�'� ���5�G!E -�!� L @)}o1wo M�>&J6!,: ``ionic''AQ ``co=6''�)ere.#p�6!@c=.d��a neut8k  � �!�ly $>urb� a��toIe latIis �/�h&.A- quilibriu�%c"k e � nucleu��RM0 1�55)�)�m6.)8>�!�� ion 6�2�q"v$���� A�1< H. !� r! <%kaOk2�s�=�A�: pFx>>they )9��/�7�n8n\,der\,Waals--����a� "�*A �cDeJy.� a�33i� 2� !5^�s% ly 93d (mp9 ) de�@!- 2��,&A�Q�or2�.��0 .0 61 Ma�"B +�8 N8 W)I��7"� My� $D$A !zm��i �f��AaxC rig�"e�>ijT�ri�:A-v 6$ace self-F � tm(RASSCF)��MOLCAS} �m�+ �at6�#IIjoQj�I� Ou��)A� � �� ^�y occup�$\sigma$�al is ũAlA�� $ ``mixed''�amo� Calx �(!�ainA֡���$5p_0�o0hydrogen $1s$G�� Ocript deY�� �&�cB� m#.�i�Tho�*�e ot% 5by�#��B�#&� 77\% �9�ed���par�� %E42�, A�H, $D_{el}=-2.610$ (!,.��50��is, obi?sly, $1{�,}R_e=3.08$; ��!��  w�Ź(ic units un�=eoppos�9�G�d� ,licitly). O�o�. �� �Sce $\pi_�u +1}9��2$!z��WE#C A U# (mixXMAU({1/2,\pm1/2�32� .3+ �ors� heir6�1)�_ �� 7\%.�(I�+nA�a�-��>���vis^.�(�+Lab,2m ed2� nor(*�.� . %%��il��)�T�7mp!�-+�u�in �. KDV/./!!��G29ASZ�sAI�hJ��m �� bFI�ourO�Sde�W�q�"� 2 5�R6=5(+F�G�c)5�@��.�O-R % r61 9�%Slea��(�O2�)�����S�$^2\Pi_a}2 @$=+3/2$ (�C ng wLA�3� !P la��.�)A� (��:12'700'�=s8 �ny- �&a�-�#db.sJ�s) % (de� S uar� ``Mfnd.� s''��) q \ s A�$[\dots]�^2(��,\alpha}8+1,\beta})\pi'_ (�] $ ��L eta$)'= a�!9� >�  $+1/2 6- , %8�y,Mdegt�d� B6�!�q��+5�%eA�hWQe�6'Y ���: �"�p6[ is ����pA[Aupi��oaa��(we�� uO/Z$i� $ j�2to&2[ixfC�sFri8!n ]�,)��(Soɯ�\2� �s.b6S"w�B"]ng�F�-� �Dpr"La%]�G��.) %  u)���a�*���/a�fe An|I�_{IwM�\ra�=��C_I &^IZ(+ C_H%HV%AEͧhyperf�&q(HFS).�m 6{. �"L t ^2$ I���2�%qL eqna�5jIN0{� ^2�O ) ^2 �}a�} &=&!^2\ 9!-/\noB#\\ &+:!7 \left(fB!PBA'>-.8&7�^ �!��B+N/)!� R�!) .5_I-(_H}�H= .�*R9  ,�9�Aԥ eza�OA�aEz�J�o=J��� �i�G�9.]�^IM�{ �W�S0&� ofMq�+q^HN91s27Q �� $C_I^2+C!=1A�(as.<�e� ��ati���F� � orthog+ (C_I��$�;�C_I{\� }0.83,An56�~��on��"B�/w!O%|���ic-DR m��"` �I ?�22 ombi�/!v�f!�z х5p^ �$55��Ts $1/3ͻ2/3$,T�@i,\D�2 �Se D"�Uof �I�2}�@J� *d � "�"�,2�(��$|�Hm1$),Bi�� �se`> ���?a@�9i6� �� �J!�i��{=}� .� attE�-*|2,=1/\sqrt{2}$� ���� thir�6�!��?n����%%)0DI$^{++}$--H$^-$} (��l"+�YnsH}faMf*\dO s do�..� os�iV� ;Si�5�YE�be 8�< � ���^�~2N(1Kq. 2� open �,� 6� ($�SA %:{ (�z'ᔒ� >�}Z� ��eF�.�1� &!Q&%�<(*��M�� 2�R3? /��)a  V�bm�!�es anc�1 % �.J 3 4K C�,o {I,H}"Z B-$ etc.�$A(A� 0.1$K�#*#%Aq�4:6#�l�!�s��m%� Ei�b��al8E5,ng6c{ �S, Ugly-o�^' %�� H����0�ԡ ��al: HP2�Gb�_I 1s^1_] % If� = B 0.56!8n^= 0.70a9� (0.9)*[ 6^21� V '%�: � �� �� �2zH�j�  ] % + �1�-!<�����r��=�v�!&5fe�Nan�7OTaDN�ř*o Q $1.0+ tM�2����� �^ �E� #� ' �. %EWq�weq�* ��PleastP,��I�R�O�@!$ virtu�'� !.� H!n6�Pun�;>&\ )� ZD��602�0� �682xmJ�6�6�6�6/(1+8*� 4))*! [ - 3*�P�P�P�<�P��c 0.82�O?� �OK-RO Thus�WtGa�aQJ�� .�vMse�W� �B�eY"2on�MsnM�`�O^�by6.(6O Q �E�+ s �~�'E513)!pF"D HQq .�"� "�"� x@.$ (�Y��)�f ��Gr�D a1m'n�low�ly$^3�2,�6& K � !�soc{/�$�� variR�b�"�largeE&ficiaŹ�aq6�->D .G�� "qng�6� !�f]y;�|S�+�c�Eb�� p0%b.��8,�  ir (*� !� whicpJ�detU2$ �, repla�# ��� 2�a!�t�/H&� � A�IhLE w��PiY� D � usx o nothAKto�H2.�e�%e( urn,E�un"U �U-order�%�  ory (PT1) b%� �2uA � z�[&�5&�!�5!Es%OUto unde�  ^��)q �?�0U�2?_%�� �>i� B��l�9.�N�2%Nw, ``...�"���Hi�=$d�&�� ���� �l)��&�&l!n�@�m#:�4. %??? %�# �BT*�93 s wh�Rtio�IR� .< %�n* 67��s �Sd�vm 3:1�1:1�go�% analysio!�J4=r1!E�E -�&� �, tav5��&v�&Efk72:4odd Hamiltonia��&N�&�5�%D��"".1�e�}ańro�an)��,y�9b0&VpRef�5�j,Dmitriev:92,"�/,1 ��8a� A`�/e�%�505�i����,.�uA�n&�eq:hd�H_d =�0~d_e (\�07  n})*�H% A�r/1��61i..3\ /n/$% �V[l�&E��Q3| IA�H. �g)J.% "Vd�!�m%=H�is�:�_D6�s���/{�4�]ar�Q�l%t8r�C����2�� %"iK21��A bm{I} & X�2he*ZE�YSthe�.]� b%]Iw��U�$$^{207}$Pb,} \\ %&�vmB�m>�%[����^J,>ZBB*��E��3-n6�s, 'IY�spie�?%F9 ($I=�);%�u`&* Tfor_ Hbe %cha!�er.��A�arqWes�Ss $A_{||� % \bot�#��Pb %to O<w9q�.�"� $ H_e=2d_  �>� {cce� 0 & 0Ae6 a   EE�%� :��Wd}Js�0�vex�kR�y inne5h*�[2�SE0E� �!vr�Pauli makeso+y u �v 1!�ceDTc ��E�"k*e<v,&;8Schiff'�orem �O :63, MarA^�992��c_ver (i)|2 � ���"WdO�7Nm�6a e�.�uf$XF(�iBg=!6g:E �G� 97��To�(�w�6!�"� 92��vicB0�s}.u9�uI24�!� �= llelN M7*�};&�Np�c $eQq_0�' M|(obelman:XX}{?-{ Q=-7�- millibarna�_�0� ^{127}$I Q Bier�<1u$r;ɷ;*e��fi\&z>v NJX%@ err|!in5�ed6$,�)�.N 2a�no� =d�:ly�#r�QBose�D ??? ***l/"�e8*r, be5to!�� *(one:*** As� ">��sF d"� N�8�f�8,�/%"e$A.;�J|~ �a�r\` �^9%k2: V&� 4 �T].�Ut] apA8t�=�l �W*pY /.utr a IG�� n�`aqR. Un�?un�S�9M� iio a1�-ZA�dc&� 2��EI���xe6|,� callz�n it doesn' 2 5U� (lik>t;@2�)>�n&�2�heavy9&%*� &w*�,�b��,Frosch-Foley9 M *� .;� : :52}}:�zk0he�- *ofvc�@0N��$a,b,c�= 6"� �\footq3�di�X� �b:A�S���, �N �-!r^�": $(I,Z {A}S)=}�( I_z S_z + Terp (I_-S_+ + I_+ S_-)X-�,�D -f*�}: !�$GaAel.��T}(a \Lambda + (b+c) \S55vC*k )!N�6E�/%t'&�?q*�Q�6�A� $ }{=}S_zi $z$-Bj.W!y . A~`!�-�u�*#G $G�-h#E��% s $2.0001�6�@=1.4998�Q�I� A��ME�h�y��f�6as6�0��8~�8Z70��8N�8 A 25&�0�/��I (GRECP�+���@99aA�(�5ga�K�spane�-r"88Iweb�5 E8�"e2!"�ae�wo-�a���m<,] @i �-% ��6 s-3dpore absor�1Y  �E�t$4s�4p7$5� 5p$U�sc#a&an A�6�t�Dnx��Hw�(*x#��c outbT�)on�@�t�ACuUq�� L{) d�as !�>�14�$``frozen''�!. -#achNn1lo]!8l`i-shift&(��UA�ea 7U�1�verEBis��,I! �)se!H!dwi� 2"&�@58]>,��25=4�9��B�O��irms%rl5:�$\�#2�%^h,re��G�*'�� \pi$��hig2;"� ��&�8%AD ����k-d&�4�jsU�Xm�#�G aT\)4U�"�P� Z |_=8%pm��9��Sd�;e �M.�M(RCC-SD)*�<��@&L��P:�Og 0A4s�e �4[$5s5p3d2f1g$]? ��!��%� �? stig�� �mov��* g$-�5Zte�k�s� � �Z*:��*.� �\e#p1\%LMo. |2���5��6(* *�ly��idB9)!'�~lU�of"I . �-�baNm@��in.6�&c)2b (CI)Y�A .= For�)��$[$4s3p2d$]y� ion-� i�> �ɕDunc :89}�he�55�%v)aa�KyA2)R�+�F SCF1pu��!b�8F n�CHIq�P Ab� i�.ed�Q )oa�wo�.OQMq�6�r \�d3( CI (SODCI)6-��tY6per=��:� �N{��:��N2�N�"�@�(F&�R2|6�in~.\�wKaldorO 04bfG&2M!7�I;pr�fm TX0 {\sc rccsd}4M�MolRCCS?=��ll�6���^d fur�0J An�GA$he:�6D]�9:�7 �%e ��Z�b�f{cYi1 {�T HI}&3�W&^+\ .�5Z*�*�":6 fock0HI"�.eith�1� r��!8W1�X,?;"p41 ��D2�D.�ej\C��6�=A�SD0>�� �%�%���e-%�Ce-&&ws �some `2����:ceAO,tes % (``mai�<" `Buenker:99,Alekseyev:04a}A�em @ � "� {$�}S _j" ���E-�7y 2�=&�= (SAF�M�Je�(sodci} code��7%��)�7{2v}$e0p, ^*$,�a/�G�%�����pa�nd � ��H�!��-8�tea�!@mDW{"E0�EySy ��\infty v �8$�$, princip�Kbe5w& $C�^*$hUs&b=m�� ) y.�=2;�u�"8 ԏ"� ir�� ible�Np*8 $E^*[�%}6�exploi"r� jX��!K2� �?� )�\ 01}A�r��E�E=B���Y7:Xr�&) �Us 4415 AX�tU]7e25e})4inr7P� �u: paceq7''6�E�These `had�D's�Go@dts ]�rbMC2A�i�e3M�F��9 ��vdD$3&X9�(!�El�#�G &57I�m,-�ed��6j�%aA�yS 0resholds $T_iI 2n O>o �G�5 t CI2s zV{1.6, 5.7%135�of�)ȵ9�O.�1{=}0.01T_2 3 03$tr7Y� %!�� o$T3$M��D75�/.� DaviZV (full-CI� F� I�Bruna:80��r�S�� ;r��A�/ ��rc�u��i�r�r4S�Ֆbe*�8"�:mj5c}�@��eA�#extra�6�~� A������H.yi3�|e�]!�MB AK E�y�2�9Q\y��ed)�q�m/-R.��Ox(e� N!ufe^�le.Z��r� (A�an$�?$%�%�b�;�+� set). S�.�i��featurey�C�jc�>>�aIݡ0p9m.���" %MX-�1�� Si wQJeg^���&�9Y_� er#P;ltIa�2'2�0� ţ shap���I~ou�P�]�*�]�za! �a�o/< �7co�&9>�2i�9n�z�p�m 4 %���M8in3�noZk^�$&l^��(NOCR)�g.r6b,)�99,;U2 05]B!�5�E�� )M�RC2 �6�29�!n�K@� �2�'PKunik:71,Monkhorst:77��� J�2�=euac*� �!x2�����24�%�1M�1+fV)Q[V� 6 . *{Vj!�cK��]V�]R ��Ex!�zJy���25A�n 6 �&"�e(p� �2�� .!ar��tance %*** Re[HI+]=1.631915(20) A = 3.08387 au !!! {is a.u.\  (? \AA)� ~ "�08 &�] datu�#&4/M�|R6|R"Ft8} "0� "lZ� 2��e$&W �a~Hz/($e;O $cm)�&*#7MHzB>"%w�(S)C2!ꁅ� Ct�I6�#!�"""$^+�+1�w!d� by $s,p,d�� �M���D& c!�2��܍�.*�sa"2�NCi�b21!E��*� "�2A�<E#;$-712.6$?."fv� {1mm�p�-3dtabular{lr} � �)& &:?&2�&�(\\ \hline \a8lumn{3}{l}{work��.�+ >�N. DHF}a& -0.09 �h�aA0''�zx. CI6ca4 a�* tav2�/{T:�%2y5}{c}^c0*�}E 2-6-AW/SCF/E&z9 f it ~ 7�� j��%U� !�(& 0.008 & 9� -647F�Bc2*c%� �Y!2977!@�$v�10 &1024266�%1]^0)/RCCZ/%6pB�F0&-&J19206e(863& -719\\ ;DJ5 ;347 ;81;08a.�B�JsS ???:��-��2 � 916& -807!���F0F%��5�962�52��v��^�I�ta\_T. $ (mHartree(.Nuҩ� %(�|$10$^3$)/ -�!Q &=� )�"2i"%:�B�F�% MY27&U7\,786U 0.29a" 984& -68!��4: a�1/5676\,39a�a�335895!{11��2 3,&1\,911\,282 h33r 89%�0A�zMF���4\,Ba3 & 10iB7aW �(1\,600\,012029�S 97�30:�(&5\,712\,94E��2 61�43� 3 &-678\,13 2 �968252E� +"�+v/&-�j6!g962 &-'.�: :]V,; !A �\&3F& �!a�ofz J6i�7d\>�J �#�X2� $ &� t�H��� է�9{� aris"T_ Xw �"fw   es�)i27"�:M xm�*�E�.4 �Z2"2" �R��.�7 ��  Pm �)-/!�6� is &P/�at� �tw�Y�[q�t� & :2�*e!.Q &� (!"s"�#&�"$4d$) p& c)so�)�!-n�.� � &��Iy � 6!H�$�>>�(M&�&�sAx D.�s"�#2 (E�l � � e-body cl�!"�s)��``s9�4J'' takeE(oG+�@9ogo�[!� ``un���]Dirac-�i-i (DHF).�.��no&'L633 �2-� s $ )��5?! 60\%��-e�li;!�.F �)�de� I5\%Qat�x.�^&eT�nQ)� .�!�O>�*!�2Ex veryy��sam valiZOe�7 � �$��Il Ee l�t�F1! �2� �9�[4�"M ���e��F���8per. U�>� (A� )�li��1!qS1y":PE��.��x�m�K � !a��c68Y�Y;X=Sly�w�.��bh�z!h�L�YTI�aY�6m�%}�>of W<itude =H,)/!qF� Cin �� -S//on��*nѭs�"ri�e"N�E 3ڦZ�, v-�l.<A�.E! ec��n!&Y�-�� 3 �]e!&2J�Nimi�it����E��*Ma��� a(1)�t�PbO3&43&W�@�/]oa�es�:�Y��fD7�]�&3x��1{�6#t}��a&y��cA;of8ea��a# ough)I6 %G=�apseudo"�&is ����}@32�ha�&�pu!# $r^{\�H{(j*\)^2 - (\�K Z)^2}�7n D. l}$-!b" [ 6�%[�U��& ;�C%|i�[ �.�a�enEY2E�4&}V6�ms-n�>ngB"�4"�k�TsNj!�!�&W:"p� W�i*AS��=��6 usX3l.�h1�� .�2�iT H �fremeG��a-&�^)>/�E�cA_1 �is 0.6u�4 ��e�]� ���(� L P0_ta�u��6i+hEy6]' &k��+  KA�E20,Nf)�^oӒr6Uc�����n��� �t�ve�{f M s��kie]���Aha#m�aA "g��0,".o5a4: ��tܯ��QC5�=| (or �_gi *O Iam-}� ����8�t6Wnondyna_n.& 5124���-��,!W! ;e�!!$*������!�Be� �C�31/eft: %�in":o�WE�*`$.�. B�f�/:�ia�c���&(p� � �9n�!2e*F��#t�c��uƒAt 48��";�q��2] �givYu){�l  �`�:�8m�< ura�T>1 �ng� YA weakYl-!�-h� "�'BA7F.�><$believ-AD5 .�5��$D-J���e6?.C,=Ձ�`.M��unE�,I M y caX�u2Xks� )��bsoluͱalu�r"0 aJ�cin>x=u=A�m�JL�R�0n YbF, $6.0{�}r|>��^Memetast $� �KeG PbO,R1~R" /i䍑x �Iive  ndid� A���" EDM�u{�i�%�!80al �!im,�o_ch) 0<;�gs�nco�1��w�U�3c�Bn-�H k�YbF�lPbO� ��.���H>�H*�***ڔ�,��6B�6 ��� .0�M.\ H%� draw�Qa�[?^ �!�&N2A9�2 IR�is 7 #e��&BRFBR �nt 03--32Iaʢht,�/ CRDF .`RP2--2339--GA--02. N.M.\h.K2mgra�'of ‚n�� ce S � F����pg]B�f Le�0ra�<s��� �0al fac ��� Boston UnT�$y (MARINERa-"h�( %��ad�@� {&�.Y+X-\*b�Xystyle{./bib/bst/apsrev �.&{*xi&̕ 6$JournAbbr, F#Lib. �/ 8 (�!Libsd"ӈb@\xh[apˆ,rpedadd+,�?2ވ*R�%ZC&̈ZMD\u&��31q�% IEdvbgˍ iles.,��epsfig�1{�}% Align%� ���dec޾�l.ll��3e}%2bm}% bol�xth2ams�6$�"n�E!1� } \t��Shock�#A}��&�au'-Jten��^9� s��F<{Carlos Escudero*l�De qa��Ho de F\'{\i}sica Fu"��&z�dad NaciFe8de Educaci\'{o}Z�D)wia, C/S�ÐH Rey 9, Madrid, Spa]��a"��Wc/ud[+�9F�a�poJ $by Philip - [���"��0}, 719Η89)] ��=�a ��I`�+�Z$pman-Ensko���!.M����.B�aE-�s�� $ۺI&�% �.�Burgers'CY�`Sw"y*����a�"�s �i9�c�d�:*�@��a p��%Y�2:͡^sh$�Y&l�� do�(.�9� \��{05.20.Dd, 47.40.Nm, 05.45.-a, 02.30.Jr} .7��� Boltzmann��#��%^-�.dE�al(R Non.�yS�6�qٷe�c��Ue03 describOe q2!�a raref',gae)N5�wo�*cA�-�es:%1f'�fl؋L!DaZi߃ CS�i!zs. Du�Q+�icm��� �6)=a� Wid[A! �l ��e��dh��u� of �` ajor� blem%Tki@dthsT. E-9%#6,���d�d�+y1o�$�th!".AW)s: �{� nsith�o!�veloc� *I�!�Ti �ivg�4Jb|�= �ChV��c }r!~"�?is aT�s�=?Knudsen9  �wGs)�eI? meanT�l w.Z(mb�scopic i�.e<�="q+�/� s Eu�_5$�wi���0 @ /,Navier-StokeYhs{�8� fp6in` �2 fluiցa%bU&& O&�O\eal_��bf v}�C-%v}( \%�a) 1n -  p�amu #^2Ĉv}�! # D= 0,���|>mu$ r�3�dviscoA�5�ة�ie!l2y6�A*ez� &M^i1WBurnett9��.6-��, u6@HinI. L���2 mbclearj�(�p`sc.�h�^�:�QM}Oq  \���c mu_0F�+ $@ mu_1$45�+ ...)5�}=�FjD0z nd $��:�e61`-���s��B>biharmoF term�%�i� to $In^4qEcui�an�sh�� al i�Q&1"(��lx��i�n7m0*��u8k ble,�{;undesi���.��le�pb�� v� te"�3�g����usu7 fail��*�d����r�v8*{��mN$,�  i�nce�!� opag����s !mKEahis ��s �V�d}C op a�-���p!�^!fK.6#�7nV elfk 59ttH6=E` �?�_����Dol��bB� �2����"le� 1989͚r Śe ideac�^�iz� f� �1 a)=orwal5�#� ��U$�pR�f!Ֆ} "�QD1-z}=1+z^2+z^4+...^�ze�~lmplexqA modulu�:Dllfills $|z|<1$. A8r!<�6�y�at�  iG�B�~(���)e cw�#recasC�, 7�&7aJ�JVf�R.�}{1�t�� ^2 m�>�"mq��^@-S�/1}0�U�$ !/t�V��y U�w% Fouri�; rans� ��eR��u�� H?)^{}L }} =M:-�� k^%2N� 3-�endݴ��u*Q�l�U�a*rg� walk!orym�do��!�nd�)b� &s Kisa>jin|Q;us F$kevrekidis�1W� i�Emŵ �g^�����%�a�tp�� p ��6G�e�9 regime ��Yj�s�Y9�*8u�/ar>Ts� Rrq�56&� �^�! N� $�e� :� f���. H�rih �sV =toy�9�� to w�> dee!/�Pr@1�^B3;0e0end�k�fedBEde�!o"�~�2x/B>�J �+ _t u + u x   $x^2 u�&� Ii�f%spirit,{A����`QmedF���gu�M�d6)%aDc Ŕ�f�!P2k���noRsAc� _is a]Etevo����}ap��of��ab�~nd �A��s E�c�� %)faի��dsRe��eqq�.Y f2��]8 }{1-�]2 uZVwe1#e�,��Ul��of:&u��\� /0=1%�[U %1{a$a�oSpo=�&oi�Ye%Vog5a� usF� �win!iJ�A"��~by�-<$\mu=0$)��E) Kell egel sޏ�k}=�nF !12�v�ž.b v��5� ( v w),�! ^2 wI-v.6n2� ����X"�rec0f=Y��i�K@�!�$�p� w$�'- �,% �: Cvu no�!�l��modyR.l Wr^rosb^z�=_= ��)�rosF�W" %z��6�S����Av��X -�-A��@"� .�xDirich ib] ��&�: $v|_{1�c]}=wN�[NO&]� �K val"�[-L,L]$.�Vm �YG%�UG%[� getN�" 1}{2} ^(d}{dt} ||v((,t)||_{L^2( �()}^2= \int_  vv_t dx2 �_ v~Z1.�}vE \\ -6^]~ w. 0+6-^3 dxq�N!J�wD m�)���A!��s��a�� �� C�  ��ŠC. ��6A�a@�SAZjOEq.�!�})v�9s: B/=�a. v �U%Y�J�:�5:�%�r���'�#�yq���j��-IM�.:2��I�\623IZ60�T�� }1�da4�h.�1"}�.�m�9�� *�=���dxA  �|6>�M2g%�x|T!�.� c�WM�>�"|OI�'6�v .I2� j� v r]B���� �H\"{o}x�'! ��  (^be��. BBRsh�Vof varfZ�2 y=x/g ����)$��r�"RZ{(3/2)}zwyM��q9�1t.��)[E[�N}{~}v�zYZ�$N=1@�(1-.)��i$. Let ���y~`� is a tep.�(qE)�� q ��(v� r)ed ��v� $L^p�aw�P$1A p�M�$3�atA���0�(g at $�MJ ~� � f�!�p"&yNf�z4$&� �f$e.ng�F<L^�X� t $Nw�7POH J(nt@4*iS/��!vnor�l 1�)$ !#Oasi�een o�nej�-PCF��\~�a1��K B\ �mZa�or� pror6]|�I ~ stein}E"$ �q�nx=qY y$�6> V.���bB�� Mt u�.a.� B�Fins� �co%our�h�g�g ge - ��5-5��g� -��N��BfNol��#F A���t�inz� R2H � 7�R�3�M^3B�^greadsCMri2�,Z�se�evans�r )� f gQ��!5�)�F0! .M.�q5�qquad ��,q<��, ih1}{p}+ q}=15Q1� ChooO $g=1$�� ���]  CB!R���Q2W $C��%=^{1/q_�W��} � R clai��az�j R�.qA�.} ^2^�v^21��:�=�"�-2(!�&Z^{2p}dE3 )^{(1/p)} >^43:32/33 0�u25�Q$)�w�}S $p=��dcl<*�v$q=3$�N� �*�1�-� R�� � D-n49��r �$D^h-1/6}��/.3�[� � �6Q|N���T � R��� ge A /( v�6=U1� -B�^.B^, A,B> �H��� $A=|i�| ��s $B=)2N\mu2�$�H� �ov%_i(aJ�1� ]dx� =Ax^$�-Bx��*�(w�(fix�T��s, $x=�#(x=(B/A)^2>0��1b /ya)zG�alI�� p%ive.]q �ly*�"� � � � �*iO �� $x_0> �sll�y a�9��&�3�T0+ s. F�]E�kH;;�3�wMgr��U?Y �٥U�& , soa�O �U8OLa�#�f� !G t_0<r I0C_0-�(t)��)$t>t_!�%�.EJ�r> C�%��qeq<'Q 1 �,0an adecuM$B��UlvI D) K�$.!b��""�р��.� >"% �=ZK_1~M��-)�C_0W��5��% 1%עAndMf5 ms�p�"Y��V�0~�9%4N^2\mu�. ^4}WO�1i ����+-f4B >�-�V�1" R�A�|t��YJ�Ny& $v(x,0)=(A+ \delta$/4} - (L^2B� -$2U$l(�C��[ ly llo&� �=�h��� bѬup��*� . If���$v=&�x u� �T�spa��:���v�$u�R�s>Gu��6�04me"Y�%�oto"�-*9 "�)!s�"�in ��=w��w$uam�(=U�#d�! ���s),�$rm%Q%�@B]!���*�GSib, $"!t v=-vxv$�] !)e6Ju2�1�a�0V"� Ef�-.�:Y��e:�(�c!!�7�+at*"� &�&�Cѕ3turT8"�<�(1�^�$6t #al�y arguZ8Q�isq0b.�o�$!�^d_only �,��LiAKwN%&;"�s m�1bl*e�G=�k-2�#a�p0 B� expTA~hr�F$ imp�3�"� �!$/�*?oA��a*1s. Whe�+o5�"6]*5��u]�a��.a!�D� unkowi% �`A�L!lm3*�`�pr�*� M"��!cf,a&UF)�>a"�" � `vO�e�� B�4 divergenc��mo"�P"if�� lookJ����+ t&�3 �)�BM�)��%(�0G�) Ugedb]!�R%�&HI ^$�ieHYs!�]n<3��-A!con4ߡ �Jt*9�o�psoJ%-[Wa�hV!o%'orRG!"���މ1$� PM$�)"P2�/2}�)A /N�1a �tes" )!wn��)Z� M�! �2Ab)�(P& I(66-e��*qn|.�bby UNED. \begin{thebibliography} {99} \bibitem{chapman} S. Ch �LT. G. Cowling, {\it !`,Mathematical�Cory of Non-Uniform Gases}, Cambridge University Press, London, 1970.�i �0rosenau} P. R �, Phys. Rev. A {\bf 40}, 7193 (1989).C!o�toc�D\let\footnote\save !Uncom!� if�want " text�at� bottomA���page:6f72jfnDa ruled line aboveY�.6],2] $0lcitebracket[ r]��Qq} \acle%d{LaserErol� Atomic Moa�4 \\ inside DialeculeA~%�!�runningA*^S S } \rn' z��h{V.M.Akulin\altaffilmark{1}$ !o({1}{Laborat�k8Aim$\acute e$ C!ˆn, Bat. 505,Campus d'Orsay, 91405 O �e`�0A.Dubovitskii6�2B� 2}{Instit}a~hem���icaT42432 Chernogolovka, Rcaw,A. M.Dykhne 6t3BtT3}{TRINITI, 142092 Tro�, JX$G.Rudavets6Y4BY4��$ \email{Ar p,@mics.msu.suu� {add��4 for correspon�m s}} ��4abstract} Glob. ,optimal soluE�describ� \a phase conjugated field!�$Raman scatZ ng o�� reson�D $B\gets X$ transi_of ioda�`$I_2$ is studied. Maximum��coh���ce is found as a top eigenvalue problem. A rev �*t�em&& st�. B pɓ,s sufficient�d�s !MPa tightly localized w�rm� mi�ar hol� m�exist�X noisy picosecond pulse�compu![to show  femt0olariz| !/ regained �_ arget tim���B9���Ń{S rodu} M�� �3 et engine� �atE,ed much�onͳ� s collec&und�� he rubric!�"quantum!W�#<" $^{1-14}$. Cur� world-w�'effortsc-�  have � m�d!1d�nA1� methodA/r breakA�se �9�bonds � � orRe�M�e56,9a��� [t�4paper obliges )�restri!�urselvesb!�l�b��e5y-�!dory of ultrafast events clA to dissocI_ limiEEd� �$is our maj�F!�ni�$challenge ��)Y find� A�l excitE� of.�scale a�A�.�ra��X!!anRc�(thin sample� 0medskip We s� deal wQ!*q#�!rAq2n��H�te!1x c &� 5in gas���ensedI(m�com{  re�cendardA815I9 i�bench} 6,17}$c�la�a�6�v�(. Our task!(greatly fac�ܩ conr ra� ?mEzresearchA in which% i�n���!�-& ar m� "fexploi��Zly�5,7I�$The follow!�y�m8& 9�E9-in�4fluoresc( (LIF)��s"�!�!PA..�l�I}v a �eE�s�� SaG em� �Z linkZ e mod�=�e]��� ar vibr}s,-^��broadly n in 8 6�f�S 1920%" 18}$2� @goal yet achieved!���X)�"h!�9E^cludes l.of<�aE^ X � ive AR6po al��is schemA�s er�a��qyara+�ron�5�$ Bulk lite��rq^enUoEno focu�=the m�amte%63-�n!,r� ��� ���-<10,11}$ indicate�v� Aw!.�"� .�a�waaGo��w� @a dras xshorteSp  ent��a�gl5$�`sta�E0a crucial relEd betw!!a � -rev�9gQ� E�a�� � � ��"� � � 2Ci�'p�C�Za just �MO�, �],J pit�s genera�, w!�ve � ���!�inQ� YEa� are two a� s: big%Za-�ch� o- A�a� tailorm �a��1�� sgo� stand � they!� ear,� wth��th�� imT f .Et�sDbaA�o�um!Ws��of chirp�ght � RdP a�well-est� sh� guiS i�@s. On�qn borrow; key ele�-��� e �phyf!�apply�� queez�an 1;u�r�par - $. Namely,� k-Co�� � must play!�ol/h�p�v�Sv �%� frequency�8��or �lto����"<�":�is�p� to be�ved� will!�inner F�� re�,a�c- 6!factorbat its m�at��steep re!�� curv!>0Simultaneousl� mo!�um5 p($\Delta p \��x 2Mv_0$ �be mal|� oint� $*be!�E_ ave � velocityahe2� pk iple~ �Tq \sim \hbar$ guaranteL6��q $Q�reb���usa� s overlap ��gr0� ,���W nce f_0 \gg �$,�ts��>(recoil life�Z ($� 0 q_0/!/)E�gi� ris�� ��qt���(is picture �led�"bill5 �"A�Z+�ťO stA�rn9be exten�to invol� prea� !@��sA�y�E^s. As �  wT lookI)�(����.eK��� 2 r2$^{5, +U/}�a� !.� X. A��ed��c � @ B)� untilH��%.c� nt� nyj uWur�Cif�mod �}�> � �5origi�>6���)�Nhe � rD�F�WF� �' 4er a delay bef�2.���b5��r��%�E��s backI*ner.lor�k��i>jiK may � e n�r��� B-X=, so�6�JH�%"e$ri�a sk %qL"dark"  od m�3aK.G � sparE�a"h2�Ha�7 name� wA�-SBronic� totype)�uW.� i� i6�c� eb{� �  it on%�siA�mad al t� �� i)��V�, "� B���er�oreq into1�ceR��I�nE{,it. Hence, a9 "magne!=" -best-fitE ter4ou� B S��par�l� Q=-5� �adio-.�hen�3a. In�,% .2[�Dassisa\bo� anharmA ity co�b�X%����j &�aIter�� q!�A� di on � ��, as do!/7 per�hU % �Apag�"a�oAn aveih !y2#&8�k�om� �R �ir�>qbe�S��a�ly!�a>2b{ self. 7� �F" �s quasic A� th�na�k�9w ta��'I���$$\tau_{rec�Aqkin"�"ot�% X!� B �e���in Fig�1ar�2�-c> �@�dr��)X v� ta� s;!6$e horizont�  deB�>���?U :�  $v�-[:r �e�b"  f�! (u� Ņswn.)�� $$ v(r)=\left[2(\varepsilon-U_{B}(r))/M\�<]^{1/2}, \qquad 9�� \int\�^{R_0+� R}_}\,dr/q.z� di� @ce $R_{0}=2.7 \AA��(equilibrium��pos���A�M�XMof�A|e "� RVa� .� f{he Mep�Q Ks, w�$=H!|Ug%e^ (�&l�N�r��� $M$*� re}mas���.% B �=$(� /M\Omega))�-� 0.05\;%D(� $ ' 0214 cm^{-1}$)�6�is � �i� � ed B.�� !� =�wal�Fur�L,�! its �is!�,ed��>is6} elowm� �� itud!�6 �15\; fs$mj�,B � pop�U��-�.�K 90501/ \; (�  52bnm) $%A�re7 �` �P �� .�. Se�~he ���YF � typi�u.+5 $T�546 ��.� $, o� meas� o��A��9 $T/9N$F!�Cbabout 30�!�� # be cl� �r,$ subtle deE�:�����q8dF���stood��VJكchaf eri8 s�!ѥ �wribr �82m��pla�f p6!a�_s.��$2����a�mal� y�!�p2XI0 weake D!8se. "A priori" ?shape� �!W�ur�  AnXct�  u� "a!to�&A peake� I�a�eri� or iso!�d��q�~�%in mediaE� (  co )� �"$ viI��a feedC ��.&1 i��ene�Ib�� n2E� 1�. I%la!�pa2 mix{A�%nInQ 3Aa� ncil�&3m; neryR reaso�j u� �� A%" s �discus�%L���A �#edx ŚM ���u a�! @�i� *� . S�! 4a-�# g�Gal!��) �_ nu�)l sO�2<5!7"-�out� %�fuA�Q �ts2�\s � { Ma�!�M�E�L�  F9$ } A�or� � &�,� �!"@ .=  nem!�s ��pQL��sAH�$ (%}]�  ��non�b� .�*� 2��1�s�FI a"g��#by Hamil/��pe' s $\YH_{b}= T_{kin}+ V� ) H_{xZ)xbHA,J"E u�r�lE�tic��?!i� c[coogk }��n� �\� x>�x}��de�9G p^�^Bi�c �eE�ivelym."� est2�)�� B��neg���Z slow Y�ro] s (��! 6! stru����), d#t�� 6 re s�#"��� �  " heav"o[ � � ]�M��&occur�a��*o&g!�i "� �# �'>?��a�10 ps� �M j 坱�e|�w����$~an�.c�(��s h��n p�!%.�on�"��G�8 E� irmod� ��v}pi�averag�a� iniI2 (��9�u,ifi&��2%� )�iz���NM�Baba)�C��� a�.� toward�k��u1:�roughA O �C�� roxi�on!� dip�I&�P { $\mu�?us: �O Gindep�n���nu� md�S�is�!ump s valid��&� 91A�e)< Pa�4�%��� �a� l ed� *+.| coupd.�C %ic1�5�� ��x}(t)={��\mu } {\CE$��he/is�*0=E(t)e^{{i}\o`�t/sL} +\stackrel{*}{E}\! .-V/$$ ��W�� enve0)$eqal!�dum�$T_{p� o �� AonxiM%a9��e�28/�y!� } J=*��^{g$}d\tau\;E()F�.2O6X)Hsh�*)�Y Y� to XYe& Let> 1�iT aar super"� of w>)!9 Dirac $\d�$-�1-i�if&:Fe>�(] !�y�ave&� $ $\Psi_{b}I� ���a�Y. narray} iE� \dot= & =&(e] -y)$+ !u� �3nonumber�1:]x] &<J 8&n x}^{\daga� b} U�� empty"�a~&�:(,(at zero tem� ure)��b�v,�'u՗���.1Ib}(0)=0%mx ,0 Alsoɜ�Ang�Da>5��is uti�. in eq (3)A7avo���oscil��a R "eAg6�n �ex�R Z.sUn�,�� amplm:�= .n:; (t)$2��$&#��i�i�"$/ �.$, $$ D_{xbR=\mu({!X}r M\�A�$�� ���\infty�2�7L (r,tU[ {n��� manife ����-� suscept1�  firs�rr2 �.������)k�)% �!*-}�{ } 8=-i! 2 ���!$S}_{00}(t-�� 2 E}� , \;F (t>T_pJ o*�zfS! usefu6ex�0 a a�oT&� �"�aEX *<ɒ� $��$.�  �zu"/. ae�-�c!�ic�K2m<� :1C%A(=\frac{\mu^^5{��} (Ak_{�M� \A� e^?��3�`q"9)R��<ul�W;4�Q�p.hc�0<AO24 Bof&m )I$E_{sM=��!Q M&.-� B-X ��/�u y�'��# lica�X;n'B�iA &�#9� ��"w"�a�A X!s� perm� �m�wt �B�aIn�bdomai�Mer� c�"tA�pa*e--�u e�{�5yaacc�gly 10d��ZrofZ R $Q$U��%r*C KHD%�A*R!funda�al �� tone. It��R  6{$h"�6yI_r(\9 )\ 2to\Bigl|B��� � a"C YmባEwPr|^2 .i4}miet $l|� ��m}i�F�}eb,m}) " m�#A�T)}{\gamma+{i}(\beta_{m )}�,>�M=� !� dampA��tant;c7 � �x�eG5�$*�7' ,1�2 �ei�U=A�BQ� �e�� x �@rea�/ a favo 0"� 3verlap�.V`.�%2%- *<)o��PEu�h:� di`ert&H%�^2)K�)�~| $ $,�&dem_�2alRFl dt Dl{  ^2= B�� n_1��P},a _1) f� \!eA_1F�One� not( atm��"1co�4%1@.i t.��4me.�?ev�it K"�) �a" at  &9 )�� Fran"+.t�80freely beyond�t�$��JedY�*)��gy� eq@!�/ ^b�;]E%M�& �5��2is {"�"� AaI-I"��(�/�p(m�,be�$m�!d��/)7F�'azH �L-!2�resulS_os:9 E9Bti�n�"&  impedEE,91*�6.h&�tg.�{ q� 6�, �" -t�,B(MG um v<,%E9�%Gos�q���!�l|met�er a g�= )-�rM}0$F/J=\lambda$A�isAY%�2eths!�� � Pc;V$Rz � ; <al"�J�� F- � J�^� ��!�$Langrange �-iplier .�9enforc2+m"Ŷrai�#��tMx"�2:>Q5A4}� -a� "�)"Fredhol:�N&�#�\v?- _1$%� )ZC�kerne" homo��v[�d �;lex�*m�n matrixJ� N��D�i�� � {2VS}�9� NK�  G�n P}$ �-clu20lya�"�*�L my�/B *���,a pump�7"�F& L�+ sensm#ip�G*"�*� �&b )�. k�2���(ɸ-�Jrix��8�5F$m� ] �9@8�m4"�7-"m* -� ion"%u�5!,�9ef�8.#4ing non)ar� �!.B:��x*� ��t�2�H�er�+�rs:� |=X3�� �av� ds (I.S.Averbukh, M.Shapiro� 3}$)�� P� � (V�D$, H.Rabitz@ 7A��B >< (K.R.Wilson et � &0)2�Tm,2)�ir arg�H�m,'�;(@quick �0an�?��q���C8  to))B���B��4meJNW "� 0G&�X � }^{(1)�q  =^W n/� �5M�; K u t _1FBv n@e+-"�D �p�q s2r� eq 5�a�or!QWE"=S}$-c��?a�H dM�ce5�3)tau _1$,�9A �3ar&{* �9]w time^0N�Ncal���_1�)  =N�&,_1.�Dс} Ap<'repeat a�2F ps �=!�o um0> Y� $N*�Q�5 {ion y�"��%t�eBOn�;r }+ ���iA^ �va"�B�w �(N2 � e ob�W��*deS� ohO �e� ���tau��)1$�mea&:(un�NdO@� $ \su2=�\?,m'^�=15yP&�Hm�"OQ��c�asJM{ *�2}{-8_{max}%K��}>� �{ �� ��)\,��!- im}x E}�>�Unkno w�"�F�)� 4$ F/9I  syste�=�5s�`�#� � "gI $2�$F� |�[m,n9�n}� )3 (mB�� � 2~Q$ �)�"�: ��! ��A��~�=-�!�F�!�� J�b,n})�)�.�)� n})  -�-1}�R)B%.�he!���"n"$ �i"�o8@rength1 � ar. C (16)�^�"f=1j� in�5�@.�u�!x1�ad�, 0} <-1}... m}<...$8#.�)� L���st�9ly��:' ��4�O-di�%t4"E/Ob�9C#'�/�& �=#.$.� parabolicz8$V_x=%0^2 r^2/2fla! ntinuum)b=��"l'S.8�h��,ing: $$mts ? (1+iq0 t/2)h0,/2}=A_0(t)\;�i\phi/2}EAE�*�$#=arctg(Se�:�? &�*� AB�$ ��u7XW�B*  .�%��? �Ba p.�Y3); -f rH(s'&H>2"�o�qd��<���$) � \&%!^50+t(ft)^2/(12M�)!Ficitly �-b �Jl"�*4%!�gum�.�!6� �HL&���Hfb@ GaQn�0�+�"x$ Debye - WU8rm�!�E ( Zo�5Z-ilq�$R=12 M)$\#.� $% IB$, i.V7 $$ A!RI�A� R/(2*)}"�4e/�lAYSof* E3�7/�*���.;%' J� 7@�B�8 8@8kfY( encyP�>�&<%��� w�exp�P� VpowKf -!v legi�Qt"e��onYP(#ls�> �Qal`J3"�2_1:�!a -m�%av in n�U�-A�"8a ��� � ve �-�!s dow �" b nd�mi =�I (13)&� �BBP&m, (A'%�� ���� ion)��Aum�It!+@a y f2=(.$^{22-24}$.PO15�.P:�el�s m�OihGeMrA�Va JqPE��3r%*A��AIeq 9,� op= � $e�.� �.�kM` ��5A=gy1�)tec$E_� � )$A=�g�e0T L-�fE(. To dY~ t�% ���T�a/  $-U'�5DIsimpl�G���^wGa)5ce�( e $G�m�E'd}e�xp}3 �F� �'d�f.!Aof�*�!e,�e�u�'d}>� $� w^ he "�Ut�D"2���d�13(1e, �3�. u*�)-3I�O!�&� "���,n �4�2 �>�� writt3 R< >M=�u_�#_d�) (J/\ L9Z�1�DNE��>t�jQp.r"�4�+it�9X.:PSU<�xJ ?F %�}d�.k>� �6/(.>� � �K�7i�6"�!�8Bellman*k5iAdee� �N��290Ake�b&M�c�U� 2?�-gRs[under08MP�|"erms,�G�>q�sR�matfL7�r*�  c^�l"y"� �a�-7�&Q"&�6yKay /Ai d$ f��an ab�7�l �!���:e��om� GA =t_d$ɬ��w1�-Q!��"u co��9�TlJ�.h'�\ftyJ \4>mQnA>�i�.�Z�R�!&��� s 17i`Ac_� � x"�ng bewp�k&Qas�d�?= XJ� nj�Z AJK'0�A�p$ �i T6�by virtue eq 19 exhNcs�eGD# e-ces, ��W*�*;= -i(J�M-�$7:l5���E��Vd$68h;ra6for2�(t"o"I8�Q~ S{  r��;c�($-dn#a*k[)� 9i:U�*1I3�9<"�63�7�[)�ٝ Zs6�!m0s!*�|!ٺN�*"�.[/ �":"i/I� &z/ )�n}ѭ�>�&�-:.sy �p>�\of����N�O �P� � _1&}2�_1:�m�� \ByAc��vc2k�6��J&�-j�=9b� 2Y�L Eb�n�-_1-�F��IE\6�satisfaAx��g/Y�#S!�%��2�W�Q.�P�FXZtpX�;td �Jo�;e�^ a ɽib�V-Feo�^.5M ng R�^ <�.;eUime: {whIn or�6Yr� R�;6f �V g 76N]'H�Zof�V�Z�[dB�` �� *�*��I*{N��7 "$s $YkI�]�6��A%�dzL�xMG}$.�fLQarJP�+��i�G5L see�Ibe "�+n+�I%�ٷllaps�&_d.[u�;�#r~Y a��@�[�appar��`e �9� "dis%�"w V u�7"�; 2�I,�o fsu" i�E� cro_ etc. But>� "U@� ��]8ar6� (-qt])�w�?�� *�R�ve>_�hfK@�\A��-��5-�A��� c�:�&restoa9�9n:�I�f]&e�Hvt�,{2&�>�M�35ly��P�� ��` highJA�9��my>�k IeQ&���T�J��A� .�bno�VNU�T!�01z2��FJ2T-o g�`phyi rely���.�.� �Fi�by�D�n�K2Oo:�Fa���k woM�locked BY.�lym(!����&�,�+e5]B� �ed�eq 3H�3e�M[re1�%T)5asJs]!t)=:th".1}�. tL52�1ha @� (0) *<2<(t-T)�@TN! �(2I9is"q8analo���*nci� N�XE�k$al]0hp�dI�QS%6�%�a&-$)�)uL:�?� $t=0$_)ue�2%�� ���e,at $t=T$. If N�!IW-IW��a�Dt �aױ $\pi�O&� $N$�As�> B�7ai�h�'n&^GFU�a2y�]nMZ- �.&�Bj4��#�# =\/QR1^2+22 Re\{\,02}.� 1�� T)\,\B� �alterna�pathwayAN�=rsE!RF2�&�E�#�R(&" $T� t�\%P�(TA�_e�Ai�=\ K�?to%�ro��]��B�'� ME2cI� retr_ syn,Ej:r5-�)on�B` $\aHS.�3�LIFz4QB, ionia`f nel F5Z.orf�!�!&m`(�Qeometry be0;loy�?�4�:o�e�mm ]�fA 26,2;b�$algorithms�+H/�7v>[4 �( em f~! $Vo��;� � a/]Hv"�%�is!Rn��phy�{ gram)�� n$ to rebuil_g6�@�{6 �m�Oo,Lh/!�&�ael�@b(ve�=u"wZ�S� g= }a�ii�BalfiX"p A�h�%a�^x%2ZaP\ >d�Yho�Amp ��anevitably��^J �d�(�jC�"s,=4rkl�SHe�b6=!�>B1PEw a�B� i��nondiagoyh*�"-�r��� �at\rho �/tab�`�K�}^ �$ "}\�.le�� �p6%lH..." sym^ za� g,m!&�Din5�J�GE�</,�G�5�x?H tm%x"�"( �, �B)b�H>?�4??b?A] 2�.ON�JOxO ad��5�%s:!��w} @f-;p�qal�cqo}{ t}= �S�C H}}, .n ]- i*(\G���> rho}�f0�=a GY [...]�#x a�}} ut�q)���- � %"@�Dsi>A� �.E6mn� V6�xb�7R��^>A �Ylog��d�9-ze IVA <t�2�v\dl 15�Z2���o��s, *�&�, �E"ylR0solids, liqui� ndj cell��+Tf 9x�#:BC �%),�B��2]>�By�+!,n�Je\ X,��� b}=0 "Ex�O;O 0b  $u;ifalAl,�=set thatF�� 2�z) �)��B)a2,�' ��LR}F�!S)�p� nt�$*�'b(3�vx<k, �9R the B�"#T>Q�$^2= {JE \,�0�7.|N\Jo\E.JC choo10�** 6,0}*�L^L� ,0}$@$FE�b m�Pi$�n5,��it �@. Ma�) �Y#�s!� advantageCb2l�� Tto 6t hEn&�2Ku!�&Lu��pre22A&�}$ J.Jortner�drc&#]n�Gurv.t ffec� �0DxRG�8�V.ApkarzX[8]�:�oM.\gui [17�~y�/&���(B-(B",a,a')fp�s a�p:� ��ul��>E� w�-� E0m"��_sWb^rs.}� ca�U b na ��? e. W� �a2;y Nl ,,nhJ͢�aes� 8,9}� ">3 rear��G�_At "oLO z {} . H|7 post�]fW �yg���eB<�\:.E�dg %�em�A�6`.un��a;P ach.c�O.{ S.�_ $_P}6m2"">Q%S&L`7g by c"�]�]+Ta � uppl%cI�� a FL5_=ˊ� �7��u�ty�bar=0��wrme81�V,��4s�ts joiLqem0  1�7E]a�}F S}.G%If� a��@�OD";|6upk�0N5P_0=-�^�/!g%i��e� � {P_0}; {R_1\S͇�@!�d�5v�-5`�Fjn/�Gde�I 6�MK]E�in��@} cca��6y2�"M�*� "#Ahnx�NU���M� �",Plank '`F�  Za)9� �b�'Qg��5���Xe5C�7�f� c!}F�I�KB� E�Q�i lL/� %1}� = (-2i \p i))�/{!�} ) 67\exp (i �W>� lN�ba�eMl,�fer�K}KAU<=(2�{�'e� PA��E�, 9ms5u�A�Vof�_�~c6w5��>F$�Wyy�+1�IA0� ndy+��9�i���W� (R_0,R_1,�U�)eq(33)�KA4��M.�%�!ct�}�q�i *�#�SuR���1 . 71s�; fail�V�� \bidde%8,�Rt�D:J �  $�$ R�3F�0},"�2�3.  )+U_�Z��) �-M(\ddo��0})��^{3}/3B>-�vic� y���M;A�=0[ *�($}0) $ |rIY�&#8E �9�uO�6WV. O�=A��[v�M$�_0b !��H:e(�sdig� ��Y|"XI 8ing�1� ��5 �Jnt��!�>hirp $bY2}$t W domi��fe#"of � ele�;�)�=-M�� }(d -D )/d{R})$ M*A_O)�O9trave�"a�mU���=in5� ;R_#EQwa"�%)�e*u:r�t"}*L$�� r F���@�er!��_ r= �� E}2$�7Oe�2UofA�� io��TQ��IR6@<�8�I qual�h�f��in agre� 9�Ż�s�j$^{6,��Xp(gva�� �ner�$"�<�_�:9��ex��� may o +st�c�I@�+, 6~H c�fl;/%�s6z�t!'I&8,� �$v�?. R8 a�2�m"�Y�C#a6W4q�a�3 �!y��#i�y� 2�A� �  na��2Yw�2� *\&j �� �nd��gZ "f � / � fEWc��!�A& T4`x de�*��w}D�fjyed�&!�.O�e�6�a;AM[% � vpircumu�&i>! "�\Wigne�{:�@�"� �)� �Z2"< w,RstE�=b�ia�.o��[d���>i�>,�s. $s=(r,pxWF$&� S}(-a6Z4� bar^2�2\�s�\ {drdp}\;�hjR,PBIk,$ R=R(-t;s,0�=nd $P=P��~6^D� �+;t5ay�eneu?]S $"? �&. R�B&H�'�Q�mo!\G"i/w1��~s $R(0�=A$Pp^M�=�.6$?�$Newton lawh ��t��aN)-�0 R} = {P}/{M}�% ot Pb RB$5!��M�M�"� obef�!�"�J�7s!E.s,t�[�D;}+ *p}{M}:6Uc5 Nr}- 6H!�r.Yr}6" 6M: p}=0B� *� 6;� ��$�)�t),)� t))$� e�:_<g%Rtr"-J sI&�?I6� q�o !�% Y40_s][� J��'0i�G u�-�P^H^)5 dq}{2\pi n� i qp�L^��a(r-�7 "�(r-� ��,]^-F(p,r)Z2?F� /(= ((r-R_0)/"z)^2+(p  �)^2B��M�f�z�=d6 X!] sharC�aA�)p�� $q_0=��,;"�F} s $(�,%V�A *�p)��a," p�'p��orb�"Y[��ret!� �5�C�Yjo*[/�$h��6�&�. *��JworbFoA�� A �?� [�\8�8�� c(��~�$���942�22+s r�D e �p�iV�,� Lˏu�+,:�)y��&W&�� $^{3zh}%wn,z04apA�>�q�T�m��!X"� (&N �$35�ZGd�ex M�al $F�S$P|�[3Bdec s&� � $sK=��q_0�� ��a� x* }E� A�$?�6x�fame"of M��g,neighborhood9o��f^�t�rTh' opw�y�4X:�pw�]aS �Nw$=F^0+F^{0}� \;(s-q_0)��1�,s_1} (s_1 )...B�*1� $F^0=F()\a�sd �#.{ $. A3 stir�ofLBHEu�5�%�h�six-� &�e$R,\; P�419ect73 dime�a\dices " 2/ $s1=�  g e:k��ett�/b ��elvd$�y1s: $$ �Ic, � R!�(0 P6 )�$ $>$$ Of�2�t ese � &?-T 's"��R�4=H(A7iAH!v��+,JV8{\vec V}=(F^{\;At r},  p})8+,hF}�-$Q�-a+n {cc}� $2}A� W r}/2\;,& 2�\;erp}\\ 2;,&J�{\;.Qpp}/2� %� ; Bwif)�} ���: J !$rS�%2}�ff F� (\de +F>9e� 5xp\�-a�� 1}{4 c V�"5eS)��H&V�]a���մi��qc�Kts"r% �3 ��� $(QP5l y al8;y ��ioJ9@����NowseE��_�n�blea�4-0�CiD/�Ktoa$� }�4t� � I�.�*�vl �j"�d� *E\ p"���%&�Z b�O*�ye� �m ^@�!�/2�)M&dual)�s2B��&�>R� .s ,��ev�9)�cauL�6T�&�2zer��YU� {p}(��9yRs!�c"ٌk �6�2M4!(Van Vleck's�8a�,verge�28,29,3�H�x]/*����l�Em�9oa g��" ��-V&�2�$ n�|aryA��]m�&&!F2��$ip� �J|�Q`%a*&&S!2wav*w@r�"��R� !��*H� c+�.."{/�,a� =�<0�p��9t)hqG ��.�-(t�-v]to +"� s}.gHRWH$F>X1� (0)i}/0}$, *EZ? T *DoFP �( D�+=w-{iRp=.,_W� ,E�tɈ��nd&/[ FM�%�*�6-w !�"\0 (t)$O .J0�.��<�rac�"E�̄�a"� � ripA;AVQ���&�=n�F2$�J ɱ\��%�} t}+ & �1r}- 1W�dm�W>N{p} �nU_Ai�}/=01�$)�*�_&*��=cr*#{x�$ '1�9��{r>i~<An��^s h�Fl|Emj&HcB(s�at=(���)/2U"-��&�FFo p\o = -2�a}(R). RBS�qa/�A�>����6�* an A��A�l |����.�L"[upre�Zt�# $s$ `� &`J�AB�6Z��>�=2�wctZ+�bM�L%;�)�3� s(t)BYA��k "�  $: 0))=� ��0))$ +fY� e�p� GaX.�q�;���� li�!T>�hf map&yMa :C=}& u�w6QngY�o�|a q%c-- y*�� 2�F�ge!VE*�B.S ��$ R� |"y� �"� s��t�to��w�v�,�0Y��)�'- Q* &�( ies'�s]'2�&w*z!;! ommo Q�6na�)�)�I&-�G A ."7" �qur� �1^�rRTXXin�l&� s $S=�M�t4e$tv"�OLiouvilju�,emE� Zvol!�B e jacob-Œ��JO$Eu o La �m� gS� n�Kls�Alec8*YZ���4KB�of < �!g�pi�YFTzD S}{dR\;dP��DSa�BDSF?gA�j�Rnd"�0auA� R, P�2��M� ,exp(-i\Phi(S* S� To�HWkw Va�$<!2-�"� � "�d}�0[*#'��,�� [egJrSs�= ^0+n84 ",s*;j:�%2Ph<n >q+j ��D0�P2MN�*{)$�eq 45eU re-u�L%�f�[�,{��$��%�fN �# �3aB{�?�,J�{��$ =(\m�w)? H\PiV  M�^0� $; U$7C� !B�%��-+$ 7D) �si$�BF�c U�dA� �B8Pi&5>�?B6 +i\;.O= � \;> p}�?F3ZI:-pjORy��*�� tw �}!Uhi^0(q*Ads�rfA >7�=�on�/����y &�� [gj1 ed DRa-2Pa���"�4؍] �a�"��{4pX;vW q��p�Yiar�%�~>� , s{��Pڡ����OX"��ach wo�Qh/)sHb�]   -Zin %"�XsƜ}24V�� "�2�> imp��Bo�ic� gsS?7"Oi�rMx3 alyt��P#*�gZ�Z� s8�J�5�� hP�e�a9?�-�cA2z o՞On��ACa��l�J mzb�?i|��v o min�o~�)�R. �$_aiE,�&z&fi�JA{i"����, &5(1dך��r��!;�%"�H�+lm,Ͻ ingsBgiE��NZ���A�Z�Nhdse7E� adap� per!�B� ro6��A� e���4()din��sir�%inx-���%HT�c9�A�A:c+Hd� >�* 2��ys�F ��*�K�1T1odi�m ���a��c $ (a2i� ��r�3 U��� t} D&!����R,P)=R+�( P -c3xh4M)\;(dU_{a}/dR�=heV�d46��K�d�R� s 2a>P F�&�%a�I� �*/ji����$U*e�.�~6A��%�{c}N = _0)Z4)%!d!!_0)= \\ N:45Lb}/{dR_�,(! ��Sk�a;"�$ $ !�x�/dR�(��ce) ƊbF t � $R=Rw1(�*�X�I1��ul3 �4�+c�) ltf�6����#�KrA��co"Vnab0.�@o�*�3*!�! 34n�0X0e�or�^ not surpr�!��&�-:�-�jM���Fd5/. More�*,!]�9�6"\N_*>�9N�-Qe�S�cv $ܓ�)496+iQ� �( a"� �%"s�����sl�h����)LJ$non-vanish�V�!�c���`^3-#!) .Xa��mea�%u�� ulaeA�9Cm Del (see Sec. II af�� eq 16). ��"�0!"1tH.`�m�i�#]+�W2'TALw'wU"5.d.�X�g�irwN!�GB{&�,�GUly6!��[�14"�AC9�-)af=o��t�&%� B (i�kl�v!�_+ %)��3 5� BZ"of�� X:RiWg&3x �+revis�uˍ� re��A�^on a &ztQ'�j"�{,� ��a��wa�<�� �Hful���a�.igr> else! ��ete|� sak�7,ic �4E�:C�/;Ƕm.(&��/Ao�2=D>}5"�Y, 2�m�!��+�<"F3���#-�nex�5e��}=�X!hJ���M�ule�=a��t�Red�7er� #Wysi% G�^s6�=N"��J��s}�=�m A�E!A��E�-4ve*5*�O6o�& /�� -epolynomC�a�"�� !lexT.2�VliS���)�2N!��&�8 griKPinNT(�?�t�re��w�1�q&� i9���)#�T32�;' QR9�&RU 2ir�1$O(N^31 K, �1� �%e?�,QR&�T�0a ͰMeB 2 w,�F b�d5� waveѸΦ� �e��1�p symmVcal s�'0"`eA�W�3^{33}$�2e�:� The W�s��"�/g!��!log(NSst�y.0 D Four�ED�� (FFT)D.�s FFT�-|! �Aa�i�to Feynma�$a�"C�) X B&Z&+/"�Ic?l" �� ough�@al�� hand�s� h��� i "�37 �3a��ieof�s or R�� �Oy?A� �ri����rix d�TM�:>e abs�( ng b�t &� E4*2�thea~���$�� ima�ry "5��&a� ri{6-� outgo�!�Q�at�<�duE2|e� ��no �D�Y�a[tA��e�6]�i�P��2�ef�� "�B\��|��5xgn�E���:��n-�g�� Af� 0A�Ai�;! b ��N &��=}:�ise��a�t%"b ��w��ePM�Rho��H �ne ���9)I�aqd� -p��.� (� l$\q7.qi�\o�q�b ���w?X����%�-)2%b� "�Y "mRre3c�"�2"6~ s�s� 5�L��d "e��&A o!�^z 64>�Y4=|&}S"l w`rؾ�� |=ce�LmwHge �a �I monoO�c�Fay1��>��es way�@a "Z re�D"A ��E��w�U��Q&>fu"֏�5c�#c_}&. $��a��ou) assu��k"n,%ca�l��oZ du��9�pe�kh&�"fe�RՐ- ���reD\e B%v-�a*E*N� � *� ad " To �)"b*`��ju��I�isig���4(a�[^en�"� �gA��'%<6�&ls�n rt&^T N ct�["�J���3pm !�!���2���t mo��� ���A��U, �o&�!("G>$���7dng" whitJ� ise �al>rrX�|->E�� nds q٦&%� ich� �pMyǑ�:�"��� Uk gr�:A�!He� en�A�l�Aќste�U I#0 I�ib2�I  bK'&�R� &b<.*�!�q=!VI!J"�|u* �� XP0|� almo@� very� %�h*i<lyKh�\F��:AM�#!B�@A.aTEp{Ìaa�3��� ��2�t �5 a&<:ions %1go �3os*К<"m��9I� p=F B�2�y��-��!b=T mpan+Nb\@vfJ5N . E�P/.%F�bPa[ ��,� uhR!5�v�BnN2���3l�$� rep} ���X  a�&<�A�.�1�R7<X"�(�.����7�m7"�&�NAPK�ogh �:���be.Abehind bI�-g�a�o to sun.}L.OM51A|t��XjzEKiM� 4]�e&�:�b�res��s*D&iy!<�F��. Induc2�t?  ��!��x2zFb) �1 J�qu� �@!d6]�h(gsp�%afA���� 1.5����"�$Mwidth0 half"�R(FWHM)�ls J�w}=25$ fpae�B �Q�`��. A��=�� ���=15b�6^  2KG"F6"s 0l�cc�laltho� �@ then:���HmMR�A���&i��E(6d A�"+�b�E! ���5�F� &�!�2�7J��@���junW�B igno�{E ���n �1-!�e-ߍN ({�o�^e situ� ��6�,a+&aTW�  cope���-�!H�;,=mZ>sL0��>�`�p9�d2F}�fo.f�5�s($T_g=50$ fste>?A�( $G$Jn!�*hi+�now�҃iOq�qu^�a�MDent. ��4�eB�" a~ wash�u� high*JN�gasF-5{H�0�"��j�?.y�do�j��!�aj��w�B�� 6 (a;� ere 2<tr+ga�l�� !"�!Mz!/"R -�=($$ W(t,\nu)�� �-�]�=�-Y/\nu�E/  {��+ 42�8)\.&�!$!O0Pi"��.m5��sz ic�.VveW �We_&�)=*N ' "� �Lmap9! �t� trikA�* &� h�o=L��� "!"���,�Oc� �!�b�=1 ps$XU����reA��U subEg �irJ�����}A���of25bcyc�4V� �!�|p� For �  }#] �&+�Hw.�s�to!g �e� t�*���!ktwo2F:M�=�B ���ne-�Hh>x�,h <��A!��4av).Us� <�>H�>2& U?� �6�:�+�n~H4) !_to2&vKmDac&@J1'�!!�i���"�.u�E' $T_p$D\�.| ! .� �}tw�a�.���a��� $2.2Ҽto $4Qx q1,1.�z. Given� e�e-�A�b�-o�u of |?D�Xba� �9,&� %+� �)5is��\2/ s� "-�d2� ��i�fal�S&�A�]&�p]i�U�K(;4vai]iX��fa��Y� �I�V�dc� 0.04 $!�� �slf(��es� ���ri�"��a�"v�Ioura /��-�!HrobcK�)�sinusoid@p"�ab�z]Kof%X:pak�o�(f�W=h�L&�< ����%$�\ kle &_*�6}$2�Co"=��F¸ Per?����)�N� E���.��>��y��!"���'�ep�Ga�i�i����is sIII Con�v�2 und Eifyj#!Ciss�� Jourof��E�2�[&AO� ���{*��!�flz!, a�h���e;��Gnw�  open Aa- �!plK���%��d�P��{ � �ss!�7-3�V >cdGoll[39IDm�n)uld bo���st ass��p2� m%� ui�;� *f qu� nod� s�%t\���dF cluste}�ragl"���D�!F�6pIi�#!-in? �X�2� e��cap�2�*"�� (ies". A run�O<�7 �)�!I� ����B�a^� ironpAam40V �F e da��!xdeaŁ�2! � u�Hdca�l�s,�"�ra($!te-mapt $protocol. ��E�"  view�V/�Wj ��pa�exe{�O adige#Y�uex` !�o"|!s "'�i �&W� *Bf9da!K�f1,��� "8d�NS)�E�&�v� �a' �_iW���/ed�by R.!%��@T1z"�"alu netvks����d.w �miJTam��� �BeCgG#6�e0" ai%o)�!����get>A>�/.:8a"�squ��al5�Yp�\�J.��� V:�of��v�Ih!�%[YO� +:�. 2eim14A@iewI��E�� de#*5����>U confi�Ig� �Qa Ga��<E�}t �*{AБ�M�-���K e��ko%��{�d�f&M1Eed��tzb�&oD��:x�N&6�as �$^{43,4$>Q fourgzmi�)r�c�(nd& e"�ed- eM�[ deg]���Gena���pt�]� �r63m�i2 � automBN��hJ�b�D!�� EVe� -Xa�&� !�o��&�p,.�0�F"1� 4 s�h -frem�̀1��+& n ech�� 2� !��{�2ean2=��m��qݵ � . P� aq@^{���&Q�yn0�&�m�*etDr re�QF�"X% ��^AyT�kes+s��gue6�s� i�} lq_!�third  s- x� fW �g?��2v"��mirror"��#��6,46}�Nɯ�&�c� �Q}:c a Ѕ%efront " ( �&in�׹5t. MB/�1��sB Jmp=(� (��- �)m9�F�%A�lsoaŵ� Y���.���}�>���fe8a"a� riguAdil� � p�� " �jsTd�c�ȅM�ma.`�A �:fer�~.MC�6�ahula.�6�"�) !�" B�P^&ur��aS � � &�,�Ph ��%�.� ݫN� g �w��i�!9s (H~o{\e]����-t4�Q�g3end�/R$�-� ur=�"�Z d�"53 *�ds9 . W1 ��`�!� �l� A$UU��[^�f<�)1G&${phy %l�-�k�"��% park� .^2F��AK�* ��6-����&�7��i.��s..{Ac� �~s}I��k *O��0�*�,!�E7oa_���!�mE� avail(  b"L�ir pub�I�� *�� �O�c�C�wLI,S.R.Hartmann�J�ns�L,Leontowitsch!<6N 1N0 334. Tamm, I:' .'45. =�9} Fried� R!Cartmann!DR-� Rev�93}, 4%� 1446.@20} Tellinghuisen!�:�1 7H58A021yUV%8A76, 4736j1} Hell!�E>cY�8!md066?2}A<�kurinov A.P. (private communication).=/(23} Cerrulo)�Barde�C.A�WaA}QA�Lhank, C.V. Opt. Lett�96Av9Au72@4} Cao!6;B\ilson, K:�Y m�497}, submitted2[$5} Baumert� T.; Gross!A4M.; ThalweiserE GerbG. e�I m1�9a�67, 3752�26} WeinAA.^HLeaird, D.E.; Patel�a�Wu!�tL. !,:fa1D15, 326. Wefersa ; Ne1; .r%t H�!u2a�:�(7} HillegasA�W!ul�X!'oswami�(; Stricklan�; WarrAW.S u%�s�^J��R8} Dirac, P. A. M. The Principles of Quantum Mechanics, Oxford; Claredon Press, 1946I9]I2:6��A8107e�2�30��au��D� Zs.Sowjetyl3a�(1, 88; ibidi���2, 6v 31} Berry!�V�8 ountA�EAmp. Prog oM�7J3A 16�32} P) W.H!�eukolsky!�$A.; Vetter��, WA� Flanne�Ba�Na\ical recipes in Fortran,%�art!�@Scientific Comput�qt2nd ed.;, Cambridge University� 1992.�d33} Fedorenko R., Introduc�{ into��put��al physE �-��x��47, 416�$5} S.R.Har�U� suggested that a noisy emission may be transformed)0ultrafast opt%�sig!Xof equivalent bandwidth�� 2� to A.R.)��H36} B.Ya.ZeldovichM F.PilipetEEDV.V.Schkunov, Phas�'njuga�$wave front��%�: Nauka,!r85); C RaguI�O �p.K! by stimulYscaA�!�-�.X906�7!�ynman, RA�FoundE;�QM i� 198�16, 502>3��ueva� roc. R. S Londy� 89}, A425��2�9} Lloyda�}6 Ameain�] 273(4)��0.F 40} Unruha�GMvō6? 41, :]41>IntE�Theor LGE��462 42} C����Zo����; Kimb� H��Mabuchp �� stQ�D sfere�entaglemA�distribue�among8ant nodes in qu�network, $-ph/9611016�3�afa�K�Krausea�LŢ�!Expa�W��(7), 216~4} No�M�Stroud�C.R2Ps:MP172w 045} Akulin, V(Dubovitskii�pDykhne, ; RudaveaYAA in U� I�al%Y Chem�A�ess��H Molecular Systems, edingeFemtoc=stry:A Laus�, Conference,��a�*X �� 5; 62�46} Pepp!�8D.M. Nonlinear��e� c�Bi� �Engineea�1�U�l156. %\end{thebibliography}  chapB` \begin{figure} {\include; ics[�1=6 in]&,1.eps}} \cap�{�4resonance curv� $I_2$ m)`4e [20]. Our de��� represents the iodine magnetron. A tailored laser pulA�as shown!n;point-f� 0d box, excite Y vibr��al�� packet. !�n,B�� $ is reflec��$from outer �EJmo�3Inten �f�� al A&ton�-�t��aa1 of)� ThE�m�9 ia�A�induca3I.8photon impact (!,$delta-likei|)I� &x BI�s conɭ%zmonN0ic free decay� fiA�few fs)�IE�Y te1�, �%!��avm!in F�� A 0is responsibla $r reviving;-7ce Raman2>fa�320 fs� ay, which!'matched e�a]@period (at 570 nm�-)B�i4�i4aM^�5 i��4b *2�squa 1 ps � Ehe�B�Jfield�(a)!�is: crea�Edipole�I@moA�e�� (b)Ao,e accomplish!,of our coher� objective![ evid6�D equal to 1.5 ps.}����5J5~J41J5RJ�Fi��ptB?�it�9 al p i5-X�p����� o-g 5E|-�!� j6-;ce>'1���6�6RDfrequency-time plo AlgloballyQZ )forB�ёis give��c�ur map!half a �um!�0Wigner spectr�e�A��v-CtM�en�P(b)�5I�dN!wu ��4 temporal FWHMU� 6%�f!�well �^��.5�7��.�7-�2O m�E �G5.9 , delocalizedBE "- n9eX��Q!Zholdsa initi��p�Ishape ce��ed!�(2.66 $\AA$ �e variN 0.05 �?"� 8>$E. BA�e propaa�s �!�I�to� lya�ee!ŷ�) turning p� 7�lapE'(�� <X>&� b�� docu�Z} ��\Lclass[12pt]{article}�t$P} \addtolength{\base{ skip}{0.56` \title{\textbf{On Emerg�SF�@o&�a stry�F!� e Tempera D}} \author{Liqiang\\ &��T}e�Atomic, &� �� (s\\ Harvard*R*hD, MA 02138} \make� 1Dabstract} \vspace{Avin} I� iS %Q , we"� an e1 �Lof �"0! f% �Fe) . We�cuse$V��develop!�T bo o1!exz$al� nts. Qescrib� ,analyze seve��26investig@ ~P A�th��e � effec �"� , e% ro� �y8a, or bond rup!�!�ces: es.� j  study!Ce�p � � b pathwL hift X20protein unfol���aE@|ce micr|$py ($AFM$)� m depend& D he absorp3 ���  solv�, !�.P infl�e��Nr&L fo% measu�� � . OA�e9Uside, we� ew aQ=adv�6A madeLiv���com��E��j�.� . St�YngAt4m $\it{Bloch}$�!$e"h�deriv�hA�A@,f hierarchy19�re� dl Eor%cecanAm�gr!mensembA^ �EyA_  a law � rE to w� �fv vary%4��!�6� � )�%�ac�( many-body  �� s. By tak!;tinQgt% approxim:GE\a�h !e�he cas� ab ,E�obtain �� igen` I�qJU�a�bitals ��6w explicit  Y�M=1-�E/Fock}$ 1�� also� �ey willLm a fo2�2)�u�ic��� theiA�terplaa�T��.�. Furtha�r��cgf!]� ce��\.@ �-���&.��!pro��e �es&v cruc5 !VE�t� understanE� and t &%$.�~ e� summ2e� di�{!�>�ou�.jed�%�al issu��A;fu�� Aohe�"~c ]/.� a�� \��${Keywords}>Ne.�;.[��,t; polymers;!��6�4;i�-�ar ��;m�5�s�"-3-\s�on�"�} �� history%�Fo��i � samp�)�.^$10 $33 i ��M�a1R&'ir� B ���-a -��2�$at $T = 80X30�g��aV�*1 �a� �!seK�(aN � aA^ noun�+� ��wheY� ��2=%y)�I�!)QL* E�:� UJ9� 5}$3�w2+ s: $77Fy��)}13i^�E:d�� depi�/6O4)i�&pe2��y�!�sdramc-m�f%62#!v��!�i)�ed. Simi�j!vd/so i�per b9"�!�group� h.ieey&��s mbehavior��A@.�y�j\:�Ml &����id ��2-z|xy-5-($2^{'}$-ethylhexyloxy)-1,4b� MEH-Ey ) spin-co� e�eia$I�THF> CB}$ "|#m�sheridan 鏝d� by S % et al��E��!ݕ� toge��-!�*�;8i`sE]a�A�.q��m'i��u�qaF he sB�T �*�isY a� for F� A��2�.�e�y "�� } ��o92] �1 mod-Ehr�@%�� vari I42� �� n,"[�=""�%/&PR2*W} B��3 x� , fe�(�V/$rge� %izJ# hetero��;of`&cof;- c�et�cono%��0 %�t nergy ;>sc"+Aveb� hib�mu�2� 98n Bb�r% �9 �A/X$ h�q=8wolynes1,shakhn�:4karplus1,dill,6umalai}�V.�A�uld��!��8n i^)  (!�A4or�[17-5 isYctbe �*Uxfl� %f!�!P�moE��3�6%�24�re2z9E<&�(chE�4)͏.�� ��� &�\�2\�3)1 R 7 biol�� d�1#3q�� �ays. OnAcuA�or exe ,�]�1��� ela��pG��huJ3�blu cel�mbrane!$ a fu*�4&���65���Qy !<rJR)1ڑ%<2">i-�"young �'on�e6�sMT�B- ! *�s�inm���� "-m- �ac� �=tti1, 2F4K�*�$&�*)�)�� us�o e�X9EN u��.2{M�!� % �]�!�O 3 V# 6I�-F�,� � ���A�a surfacN a�.techniqua�th��)2-�!� olu!w$ capable>I�o%Iany}$ ;U��s�smQasv $^{-18}\ N$���"�e p�CascamH�unn�F9�$es ($STM$)F stylus!pfil��A�4 ca%�b�e1�� �u�*� nonM ��binnig1, A{�)To�,fD,�#V�#[Ac%B%�.�.� gpng�"1980'�hansma1, 2,A1}�?.<Y� applego-�� adhe�$1�rC�T� bH:)I�!% ��7 ��show 2�"9M� moy1,moy23,beebe�Unlike� )&�U��!99�Ap highcc�:�n��6ivztoA)6 )�.�8�E� A@be in*D�Benviron��P ��6N �=�(al*r�0it^�/� �e!+oey1��a sawto�%Bp�'n�deI1AZ.> citye� reve:'mU&i&n r%�� �sd!�"#-� rief,fern�Kz!� The &x �,!B.]fit am.;chain�A has �,��verifA�bV, stee���ar "� ��MontJ arlo� �C|% �schulten� schera�.�&)%��"�"{��M�2,lenne,� her3�$�" �!�&�s:�}�y�q�%!�*"~G:K SpidepaD �n ��`>��.c?nAh}]�X at*�"��%Tho�A�ip-to-�|�8a3V�P afN &Aa��8O al nu �/ .�ɠ|" Y�bAmN* �.�B�� !����ű AQi� qxM�_a��0Q�%v��a)m�Aeatye�%"m�'fav�A!t�@r.Z�w.(a]���6G- gram�`!st��P7 ^3� a"�/� ���5Oa6 $T$�r]*��&g 2�$T_{m}His���F� e $3B$Apa&�A�$. % Let u;���@x� �5p%�on.;"�a:�dw�pd9 ...�� )�"�%�Ao5k&�E�%� e2FofNc2_sh� d9� "e;�.�of� . Si-$�j urb� � �]�,.4aDaL etc.��?Fsn:& th:"`,��!?2 at�!�...� �N"p regar*� rce-��E6" ��� P;a����"m�Bzer/��-�o5LtretchA�Y�!�.�!double-dn��m<$ �r" z *H$bloom(1 �*S�D� B�i@Allu~Bhe�� & q ^� � �e�lve�P���t tho}/u1p�3zri 1��(E^?�s5~m vew���x��͒eriks�Qhu�Qwang1,2,mayer,dyer�a cir|Hdi�1 ism eCD�']tra� &� )�NMR2;9k &9*i�A��se arBL�) $ Alzheime[Lbeta$ (12-28) peptid�=�*�5 ��tA�d left-hEp8 $3_{1}$ helixI, convFng < flex�C�7om coil�f"8:]}."*\ C���!�� s6�Z�E��-�)cSsh10b}$ �$vD|'� p �9!j� !top` "M>��E��e nucl�0p)�� site-dir�Hmu_2ne��%c&K=�e��a d!�:��!d\ $C$ oir � isWe6�H$Leu^{61}-Pro^{62}$U) -s6�� �!� *F�]Z�%�m�ar�ce�� a�g�l� 3���)"^#z��R�V�� e�.�!l�M�>�.m R�.���%R'+� as hyd|%`,)Z van\}$\ Waals}%��Lio5%!�� =phobic iM�� weakE typi |'!�order!I%�0.1\ eV*�4.0\ kT];8�jA�J.]7-R6�~%�b� ��+ ��GJ���@����#�A�"��rZ,)����R�A��  J:�)l �5d>.� ����6Dc:Gexf� %Krecept!aligs� ��!] M b�  /�?gly upA�j$� �� �gr�X$darst,suss#Rb!ǁ\1 ��1�nl(� lyɠzaf�yI~%�fo��1�11model�!UA�0f�� I)�%27i��B��8g_ �-{� 1S5h ttac�Im�I�� tip-}nk�A agar�" bead"�K6E�9��8.pM��Qi �_ n appaG$Es!e= a�$g,,,,V2� loa� r� is keptmZlow s�m�!�#(equilibrium%�E�M^Q�5�assumes s%��t� � �A� e:*$F_{i}$� r��b[,�M!��+u�5a�6)'ct+a�2 2�%�%!�toS 6`� !Msu�<t- �d�AZ���ee numbq nj�s��sb each-|Ei�%� . Toe�a� 23/z+rag;�-,G*���tens(�0E�uM 2Nbad1,2 4,bai>yM" a MPoi! }$8=2��!B ( cret:6 link&b;""-}���� " Ai�_$A�U�a�1&5��� �QV�5�pa&��wB�# ��I� 1�! c�1��.~AV�/Y%five-2� �#Z�"E,Q$�%j%BRV6To E�'(%="�=" k� 6�%gs�PA9��T &� a�*�-� >�Ba���simpl�^aA� arguE 8tavan,s2��� �ye�:� quuI conne�E4TO� MBg -m\ �UO�F3"lu&� ~ a��S=F"P�� F^{2}� = 2\D�Q@ E^{\ddagger} k_{�,} - 2k_{B} T \ln\� <(\frac{\tau_{R}} D}}\r�) \J{&�+$d�!%�!<"�:Y�:��+i�=%N$�T9a��er 'T9�kbr� �,N��x�m�$.Zl�Niito re�UEh �� �\Au '4�z EW�ca?kR�Z�is�D� M2�E�L Q���U $hpN4�W��&b*�6�%Uy Bm��lso�Ot�2F�5$ �&�(T�(� ,)��(1�e" DT *~�"�stiffnes-�e� �"� A�lcri<1�� gy,&�b�F. Obv= 0w�weE>q�0%2� �-yK %Hu�=o�M�?l��W*,+e��k0^P/a��BJ}�m%�!"�<%=��: e��&�����ol?�;in*s<sd) 5�?>0re� occu>0iH �Z'!� meanA��7Q]>� chal�� FiABq,�w��<unsett�i�.A� %���O� ��<��"9| �!�17(�!�@f � T(ɘ�8� ab!fu�"a2=9.�G)TF�z A7c�@�<1-6ee�sp al: "�&0 avail� A��4� m�ie�9!�P�?ol&�D!���mL@��?(*0�#��[ arch� s do!�e�*&� dnv WNA�t Z77,'istc=+(�W� 6 =&"��/9�"$of-red.� !�� �nnt�R? Katsumura&�ap��Bi5�8employ��!��v�!$A�B�S+$ene glycol��"� 2�s��$29'/598 K$1a fix<�?�G10�.tm)$:5<Xcer �Y�(bOsq��K�%�?�\"29 9-��e��J-E}�.P+��is 1F3�>.5k1�4}�(}��ontras"�<sit� iOeU432�(aol/J��`/p�S�0"� to �Ai/L��de�RNo"��h��&fF`"n m3� �&:,�2�(R"��B vI� �j�!$Ag^{0�ndj Ag_{2}^{+Z n w$ f�,e��& �� ?�e85�m j�7. T6�7HavACA�en��u!�0�C9*s4 v "s�!/.���� e.F e j*r���u+��) < �jH�#opL��W�6m6 AO]Gb��[\): prob�k EYt&��iWU!�a lF�� limi!&qM� ��:�6aՅ, ea%iE�=n-p"'level�Q(�M�i'2MGa�nit2�t�6an(-�or "yL1E� weB#F I) tr` !�*Tf2�� 6�s"� %��-��6]�a��lU|"+A"�$�+�dep�"��CiJ�]�,� ��9Fe-9l "�s,[ ��F�P-jrobabi8Gdt"kf�Lingle-p�Scle�f�r�B�_": ga�\%_A��!cm� �m Z E�y 09�(Ts��D�)/�U��5�>b�rr"� ly alt]%&0Rm��y�or� ids,}!4Vd)�pc�#!R-]AF�]�*s � ]�L�.�Ni� 1-�"�& ly b�": *�a��L1&%�%(-(lea�� 9d�G �$Born-Oppen�1MzT. E�-phonon.�,I� fund�b�S)0Evehl!?]�.!�,ell-known. A�/�(�&7 �/-g!"� � F2"9) �=J�6�Kwe tack�`Mw �a ^�D�t�M�K2��M�"V�fa�nQ Q�or neg!e�� ���0(  7 $c(l�h��Q��i��Ksome I�gLacclu&M�c�!ut? f �L!� �L(c�#ac%�a 3 YEKach�Z:dop�O0in a non-adia�#��ar"�V)% pured]ol��� V�V1/ �� � �r r�KI�y�2� �.5�m�.I fAH/1�-�M[|�f�@we�2�� elf-�� z%�framej>� &�raF!M-;decid� �ar":D�jJ�(�2@H"�Y�Y��r�D� "�We/F�Y}?>�Q���c�!R.A$N$�w�FaJX� s 3th-E �� tak-� Nf D^{Nc\exp(-# H_{N}),B�s!fuA $�%'�<>�b![ ,kirkwood�^b/*j-��k al}{ �}�� F��R� 7=!�m_{i=1}�h(i) +La6 (eQJIE� $*"��!59�5�Abu� tens !�)23%�Hilbert}�>ace $VA�MN�a� A=$�$�-Be�n ��,-bq�} Tr� p}) = Z (E�, V, N).B6 ReA0M �2H�!E$J�e�=H)^1}+\sa� j=p+i�a� i�p}>#i� & ��, \]�Ts.E!7�*�`%�h189I($D_{G}(N)$ ["oci-�2�N� ^v�#(N^���q�0<&=&o [o <(H-\mu N)],\\ � \bar{H�SZandN� 0 = H - [B6 i�ll�m�>2�on6?�-� J/$H�H@ en�V n by��46�mu��a"}"�]l:g.�m_ N�t� Q�asJ#�f}AJ =�LN=pY�I� V< N\\pF9L���[Q!]BtU���HbyJ� Tr(HR) =�! eft<����> � 0�B�ZB |0AD\Xi�@ta,AK, VJ��&$F)!�!�M`"] "\ ��UJ/ � er�ˡ4]NhHNDho�!MB���^��9e� wei4">meuluƞ�m�!�1Es+�MJ�,h}).���r E�p+2�U���b/ �H%!�ai�p} h}F�p�$�J�V�K=� �["��}a~sg7�Ew�B�bA*~K ^K��.�A�.�O�d2}a� HIU�U"Y�(9** !ayEqs. (9�` (16)��j&u<*�a�at "M �l�av~J&�sD , +1}$�\ +2x ye�be,7q5� I.ac�xhe�'r�3an=Fd�d�p�w�!��N$2 thA�kkv_��4Schr}$$\ddot{o it{�%eCg� �5i/5emph{�m�z*� [.�=�HMN�[94-109}W��H�����=YH"� Q��� �sE6orE5,M��s�m�d m8 �U y�#&ic�den1)E\n eH!RZ tAlm"�Xa@5Uon� )1�1 . W�M$p = 1$,�a�`Jz��1}=�`��D^�f])Tr(h  )}{DA  Z12 / W+2LM_{2�� g(1,r "p +3 #3#2,3�.3B� �� UC%W-M]-[�!ra� #8�� �IQIt &4"�ofM�&)�be*� �>��Q� 3�%Q\we!�B /X0})+ � Qj� �J�D/ =12[/%�BT)<5!�&2"&� e j&� a J� 1. matrix1ex �,a)$p$�-�� Gras�3�p&��f�:� c�fW�5�8B� �Iq&dA19)� valuX ��oa(,forward�_aR�,J� �� = (J-KA�1F�!�B/ � =u�g%�u�R�j�Z�J = Tr}�\cdotI^ (2;2t ]I^"! q�V�KVUeߺ`rJ"� �oCoulom�:a�exMq�, 5�*vel�M> $��3Ma=*�,�|f$2�$3$Ii�&?P$K$NH:� � i]NU �'K. 3;3GJ��,�].� )�-�J -=&NN��(3!�2�36��J�S4�-� 22� 23) ċu}�P�5Z�����h�x�L .[��a&ZFxm:�} ���=(Fg i�s�\��� +e�� F w64.gB]Z� �h+J-KB56e1�U�R�$�Jb� norm�7n�TFf \rhoѬI�B�wa�n/pll(�� ARF]-L^�| 1��- -yU��6;uL4E�30I���҈r'getF� Fc{Y0B� �.a3�&R�$F���zn���$�@mmuteN*�)%-lso gH�!t ,�[t"{hav� mmon vec$\{|\phi�3\raf%\! se &agF7E"S T9�� N�J� F>��epsilon�>F�Th�`rstZ�Q��203lyM,�2 %B�%1��>=\omega2�.�)+�q} %uNjg]Vi}2i \mu,Vg1�l)�-�|B��� $vV"%AA:�' ] A�� i� 74�0�� V_V�� ٥nga� (32�30�t�+�1_# a#'=�"S(��"F!J���z= (.�ś24B�-^1? MyB6BIts�13�+!��-�A*>m��E�)�Zt�TIq�Bn)4 � N:v� 1}{1+e^{��F�}Jv en�Xf�6{.h\�;2�I�2)b$b�eDiscu�, S�zX'(d Outlook} �p"7�a�F�-a�epl S�h&N3� .�,(� �2 6)*cM5�F, �-\"LP!��&Ia*�"�4 �h':�"�^E?ets� h"�%��> y1^ UNalB+!&2Z%�B� *b&�%�(�#I(�#"~ -W�j�'!k1?�lac(�� �&-��2����e=8�-X5�:�,%�6�,z,1 )!�i�c�� ly u��%tH*�*��aE3l�;>Kk IY&G2aRQk�a��ge,-p� r � mula @R��&�1Ҍ2��:�'��EA� �2| gas-��8)�A�� Ale�6`~>F� (�7�v; �(25R (28ɛ.Oc)�"�&Y$J�"�"�$KB� �> K �a�T!"\�a;in supe�fO$�"R6 ."^ l.~*�FX|>)c 2c �+or�.%r2^2�/, ~�E�S.�k A(>%�i�.c eld" 6� .+3.1r2�����exp��,\Hc���mS.��3�M�o�+/��or��R"�1r)��=is'3"�&�".a2v� iW`�"�yxe�si>�]� OQ2�.l\1%9KW�>r-տ �ar�Z!�e��<� �= ir&�<�X. St2ng� }"Git�,��)GsigS} 4�^&sa�:*�1�C&�-�i~=�:�,FB�% schlˠwahl,g(Aj`�//"w;b�ͯA��O6���<of�**I���m KgsNl2GCi*1as,� tra,!kbFg��� �4et!t` n�B�!@J=m��..,=29&�/.�6qi�*Etask. A�7E^d� �['F�w�ear�lVeB{�o�~G#(��l� �.& � . At$ 5 foc&��";�9I�}Z�I�2�V� iA<n i4O ?wT�";1~$@ 7 ��f &��g'?! ativ��.c�5z�{}P;"�*�i� cause�� ir � ytyE/al, ro al�lib�}%1I�an.�]O&�T�U"Q -Rhy�N�JmA��E;i��*-�4 �>nd-��5ed-E�u!W Furt��i*z^&�<� �k�(�*gA�f&�b-Q=���h.�i,~l*�BaS"�T6�;4{�B,�[5�AVIP���ig'W"��:�9-��e -���.�!�>�7. 4%�*)��big��e]BH A�"!�"' 2���*Cgb�݁��4�Ji4 &h�7"VZ�?rst glpA[�gap.�i� HOMOF0e�LUf�i.yh��g� Bbo�mA�bc6�� Bo&�0E~al�~GB}T�i�*t��;�fm���gee��a:.�24!\$<*;�(q.�e6v8�e�t{E=?l���hA�rU"�Zy�Mja5�J .�{�+�Y��.&6y&� %�A�{w�]t%d��.��2 �@=eU0& [��j "�_�*e7�dK �i��"�(-� 9&�:�Yl�}ƛk7n!o2�@t[��.klM�9��2�>%��-� �9!��!��/�P�<VY{H��evans1] U"�ibs�#.|��ju��ޜe͔\2�9�&6#V&'l%% eV". �O���y�C,� �C�.&. &�8K_�a� �+��z&�hiDE�CIDW"XA�wo* =5kq298\ K-nd $4 MCdLtt_X�Vr >ZD!y"Kin Q �dta>z! �`��P moni�c�yaFn� W���!g�i��In�>:�-I �ka�l2}>NK �E�P%�# aXD��-Fr�w�EFc]eO]��!�$$$-s=�c�e/_EZ "alpha$-�ZaQ�: T��+2A� ��Bon&�bc���p���woa��`kNDHtheY�.��� reli�~i�"&�-&��e� � �BA>f�oR� �|-�� �ه��si1����e1��� a�a>�&~k�a���J| �JA�k2�X5>M��.ms��l�NՂot1als( %���e+�W�܁�;QnI6MӺjo��R�AF�=��!:u*&-B6�8� QD%r hang" B��,y�9"�P� a<a vastxe�p� ossi�?l�=*�^I�m�ig� d en"ئ���:YOE�Pdubiquit�)in��ur�y7��ex�X&c|� %b&�ZshBi�e��x�=�f lif ]Z�E6q a��i �ah2��+�re���Q#��Yab'O!�ti;vMge�i3Z�ary>D_E�XD�^@T -��reg�ka0 Jx organi[�-M�$frauenfeld�` Fa0/'� oJ��� .zZ�Y��D mmed�3 A!L� ��.{!��#Qy��&LpO acto �W�8.���A�D9�Qsno1<)*� E!-"�U6��9r� .lE��2wp"�E �.��G���U� R�P!�<if�2S*� e��6��- �_u~lacI�.*+=deG�rR�B!LinsY(�o�Ux^ �!d�\-uR�un&���+��Z�Qu�.a�e�N�o*�� link�{���eR 2M\��%tum �P>��y����1 -7.�� �Os|Sl�Q� ��a���%A��p��ork�g"�IM� jort�3Lbrodsky,berne,nicola��Zt �c iest��ud'Aby��J E}$ S a caS ^t"�l�R)�*�@>!��%onf�>�M VsurL�Ydi 8iR�ntinuumgen�_ �}.*��%F��� E ully*U�Gf�7:]7���h �c"?J�u6��@s�$w9 �$�*� v$R��al dataBC�O0_%�e%|R&i@a¶�9��t �F�!ara�.�M!�*� XK�<�a�nt�kv2A��n*?���r2+m ll��3cɩA�?e��y&26tO�K��%-�}�&�m!1Ag��,yB^A.u<�M$J"� �r�e)��4e�1V&� ��%� uti��(crude BQ8 i�om�Bd H & ̍r—��k U�si�`B��.$Tsarevsky}��4�t[�< a.�"� c���4-X 5�)>&h\�"dk ��%2�f�Z۱atB)W���C-�b�� *� J� Qc�/!�oby�N�*�}�22/�w�g�`m5�-&'��-���b�yNi��\ et\ al�5eveam oughP 2u�t&�t��A�J�-�F��-RE~� c]"�Q�G6{ay imia��� J��~aFa��=��9d�:w cal�k� ��d-P�"�1i�ea�F9�A@ismlc >�m�#us=X[M��. �!5R;�݊aft� xamiLP�2,#��Aa;y�/u�Q%~e�noE�5#y.(㭊�0�PA-L.��E �)�ײJ�}}f� ECa�azs� =��m6"� �dA�A*"F"A��* ent,���tu�3�vd&m~wei3}..�evnre5"�!��m372ri6�%Hre�->��m%�is�p|, !=��'��� .����T!�T�;�w*iQ&�Rs. Ei V*!TI~���orkIpa� x� 9Rr5�$g�+ . Ex~~ A�:A }] 66 !EQ�#u�2� �6!�j�53g8�%5%��6�Ga��M�"� 7�-e�6��#7 $ZnCdBeSe��.<��p�to�&� "vy m�p�ony r22�I_De oligo-acene crysӥ M�schrei��hsiehz{newald�To�Cup)��;�8wFl!�a n���aw��C."�6eb6� ��}�Z�F{��t�]&�n7+alA� soli�#�s+N� �=Qa myriad* WopAu����A"��*%&�*4� \nor<nt %{��\L�{Ac�R ledg�}} .;1>; :W"��t:ع{99.��I90�em{]� W. Hi� , F.��S�Z.D�k 192��(4, 455-472.G��}��8Wei, arXiv 2003Ȍ�/0307� \}w�6C. Sun,vH. Ze �Ann �csT4, 313� 1-15:�3RO�a A@34&�4-150.&���AN�V@51-160.�ln� P.-O. L&$>��,"=�Qu��C�� F�, 29, 16U��9& } T.%� $ K. Pakbaz F. Vo+�A��Heeo���4 v. Bi�1, !� 8652-8666���}Xich�D.PHalliday��$C. Bradleyþ!0 Burn/�!� �$A. B. HolmJ)�.: Co<��y�+1993, ��155-716X� =Yu\� Hayashi�H. Lin�-K aA-J�Hsu� S. F��C.-I. Ch� K.-R W"I-AR� 57-25)d�b�s1} Y.-St, N� Huef�G� Ch��F����M!�rrG T.!��v v�Langmui'/ !*\ (5, 1373-138�:�2a Hi� .�B_ Anal im��:19�c3: 365-3��.Nmacdon?%IaUcD!�!�Pozhar& ��I�4��9n 981 ����e���aut F sterhel��.f��,^ 7, 20�1109-11��.p"�iC!�$on-Vazqueze�y berh� r�B*wUPE{ MarszalekEA� Broed��tlar�,)�Fe���J3USA!���� 694-36�=+sch �, Lu,�Isralewe�A.��m�\!�Vog�v : K.��J�y 98, � 662-671�u�xq�� Carl��H ok�hM�r�az� f�!�I'�1565-15:5�2� :�B�HeRErick�B�NR���s3Q 181-18���"��-R EJ< ae%�M. Al.� a�me� ��Y r� FEBS�&�4E�24-12��u-t3ej5 P.-|� a5 P� lha�* �j�: N 33-54a�|b"� 1}a�N ing�6H)� 882-8:� X2�X 94-9� ���;G&bi�M. Beya��9 H.NX ZC�W8�W727-173� s��� Jarvet� Da�|g%�Daniel|��JoDE�L�<G.A�C� Aaq Grla}$slu�U1 ��555, 37! !���Xue�� Guo, Y. W�Dw u{�4�Bac�x I�1.3929-3� ���� To�Q. CuibFeL.[�Ju maNMRee 2, 385-38:i b2}.Y jH. �aY�tJ.2j��emi3�8015-510263��5 Rist� J� Jorg @n%�$Roepstorff�kBuk�M�]M�7B%D[ 6|�514��=K�!� M. V�K. My�T� Oa� B. DE�>S�: 582-3� yreen}��M , Adv� ot����� 8�EPB&��� 3�"� 6�� 387-39!�Dd�}� Livna"B):�ch�DJ�SuP� j%43, 90, 5076-50�xbd$ԃ & (oda� Malco�"B3%�MAI)��$231, 698-7�� �m2�mm� 3�2-+�.�y)*k J. S�E�P��ebA �M�BA�I0� 847-985e�> 3} WDM�n +�� L Jr."� !%�_291-129�E>Z4%!�enzI  . MoyaLI��H� F�"� I�� 69O$ 2855-286�� ai1}�Q�i���C.JZhuQ. ZhoV X  L. BL urf. e�0DD01-��m���Grubm�� u}$l�B�y~ P���Y�k�7��7-9 Um� e�Izrailev�Stepa�h�0� alseC=Y. Oonof��> 6�1%B7!�568I:>�4��K. RiL2efK4�5A �I� I Annu�vBǠ+ CY105>, blades%nB e�  odgii Can���19�B3�1-4S�߯1��t��a�^�E`�R��!�2102-2102S<. Micha� .P& Schmidt, A�6`\� 2798-28:��Dm�h F.-Y. JA�GqFreJ��� 2383-2387.ch���%YCIGeh� dJX8�^ �9: 5\k�x� Shira��B"�z� Hiro (K. Ishigure��WashioNy8, �3011-3�{reb�Va{rru|KJM  6794-68s :N2�^�drasekha�SI)�^ �"5910-591�oFWu>,Y. Muroya, X�  Tera��.j� p3��531-57�Jn3; Mostafav� 3�n�:]x�@�]3123-312ASJt4^t* e��Y..R�K8� 2-�kq�,��-%�.G19�āZ839-842��)���Qr.��)U)� [19�A� 3790]45��(GWallqv~ rtymB��By.�:]M� 1721"� ]b(��N )�Bo��ot{e}$v Borg�f��S qID11p689-966� d[ ameri� G. D, �W(k, nu ic T":�(�$H ���_z�:�2�i�S�"s (Lot�,a�p���#�: New Y"�NY�73).��2��6�ݍ)�.!�� Q 6".O��ree� C7K� ��i��� 192j, 111>S�A[�I �i`�ic�"A�$61, 126-14.@}q���ch ; s. f|�"? 2, 7] 95-335*ki�qAG� ,-�19!z!3|.�� 17!57-122D�Jn` Co !A�Frish��FJ� D 27-9��naŧji�NVB� 1-6� �G@SF@��49-1351=�1�E%R893-18v �valM6ro� VB��64r 462-4462� mazziottiE�A� FHm$7, 4219-42P�col�1���i 1 � ^2 196-20IO�HK��HA�D3\��19� �1769-1772� %I� � 4IE�:F4�� 383�4�218��Fr&B8,a Parak,�$D. You�.p.� | �A�0451-479 (1988��y"�(�USa��ta�M� )� Vojt��i�eV��8 �r7�T�3taneousD{nƊom-��9 �is D}�\d�Uni�Q4"�z.7r��*/ rave-w�ZZ ; %aV, v ��<R beam��!�.�,g��T6a.�z6&�un� %W*~ ��V �� %tZ}%QB�s�Qso� �. b� E1-�-V5JG %)t>ɂhJ�!:TfD�I�is ?Bo�/play "�threshoo�analog?to �I�C��1�ioU1m.MU� . HV0rR�s P2d a!�f&�J2�de)-܄�TA�$toms. Data�_>�Ce�a # "�UI2%UY9�-{� k7- ba7�!m�>K/y. GU7ag�z8}� ory !�h1�/�)Owha�-is�1n�C ����/��6�l�]loa,��_�.@��2metastnC�0 pre�6M�3m4!���sU4y-/=�o�s. q?G^V�Q>5��%I8diE,s broade44] ���B�1�8yeti�&�8. %mav��3noF�%#:bEE `%zer��4 s. %vj�% %�%�noj�e��AE %shi�w�Cr�%DQ�� p͠#of %Bm�l0!c. caseA9bB% �uN5�F�2�G*Tu�d��\E��^�&1i�ؒ��� 2y4. G tra����&S:̓e��t��;�Q-AreK�1���1�1"9�. ?QsAat �7 a w��r�D para�O\<�oHS�Ia��7le '), aN�&=�r5��o��a]c�uA ���>d��dur��!��!-�3�. !��lm�g�3�Lio~t6@.����n& al %e�s. { a �Qw} %I��a plea��"J2�F& S��hsu�2A�allA{is�6wa�I��b1j@ny people's help,�woA?�w. %wh�$� ly.(N�;�A�3�8proAn"��6�thank%n!� � p�2N�o "8#=ly!cp6��O I TR F���3!gu�ceE�1*-�my%��� gradk� e� H�H ntuiK �\� ��M��V��ic at�gduS�P ; spir��to Mzy3�J��. I �7de�x%"��hWQ�r �>�Nse�Re-�A�!m�C���� rVS %�Jthi@=I �mEKhopˣpa�nA0� I> A� am �gM��apZ��f#'w�V!�E��4!�� %�lin�inquiry V�.6� wo�Q�g(;�8�Hl!�j�,t Kyungwon AX�ho��A����.lRK�JO %i&�TMJs<my�S JM lab`ۡ�A�e�taught3a M. g�  de�U��& a"-�y �C��$ at MIT. %i�fK�� step�ba�s&�9is!]A�fV��Ra�E"Yredit-�&D �Rgoa(Chung-Chieh�1��N�n%n�X G��eF. %<'���� %I'l��way� me�" o�� nver�d�=on dive� a>pZ��  %hours�@n�Z�(n� ;W=BnAv!�Sum[k * K"]] 5Bsn2;^2�= mandelQA� ?- �^2 )/; �)A� etnQ := (!j= natomsa+0.10595A�)5�A! = Floor[2+ 2]; >k$; Return[{q,�'�}]s �j����A��R gain,0 }Z �d�0cludes bichro�"X effects (set $\Omega_2a�$� ordina� ono7�")N" D�`1A�0;9� ��� v�")5*) 1t37e�n,tstara� -2* tint;oau+!�  dosoln!�,NDSolve[{ca'yC,t] == ((I *o�LR1[t]/2) E^(-I *phi1 I* �* t) + 2M> I2BI VI H�$))* cb[t],q� cb'[n�.�- � J �- :�ca:�a[)w%11.,�%�0.}, {ca t, op}�@MaxSteps -> 10000| arting SizeAutI�>9!!�/10, W� Precis!Y]���ge� rY{phases!Az num E�.;  [i_]A=�|( * (i - 1)/.$; solarray��i, {i,��&�� doSavg�L(M=E-���)n�� *�ᱥ+A� �P0 * Exp[-(v t/wm)^2] �u#A� 2 v3 �.k�a�*�[i��phia�N1+[[i��i�;)V1M ca6_(ca /.6L)[[�Jx(a_>Cb�C� �2avg2[-N��(Abs[ ��[t]]^2]%V��2N e [ ��[A� Ed��O6aFu�Interpo� 6 �)���, � �6]�(*'c% ���1�� ��� 1 - )_2�op]u �Xgaussian[x_, xa_, sigmai�J1/(� �_]*�j8-(x - xa)^2/(2.  ^2)); velu [vel Jgvel, v0*� ] / 2.355];��vel��1;�odd��b}s betterA@6F v0 (�1.2.[�2= (+N(sampl�Q�N[.f+�^*(.U- %)/(nu á���ofv�)(vel/v0".) �� ; vwe���5O�9 ��; vlis� {H, p]���!�� numg!� 4; gvari��Z.09; g2[0.99*&� ; g2� 1.01.10*)�X ); gE:g)'� Unit�rE�g/`]*. -BW] E� Log[F/ga g1]zN[.�=�.�- %)�gs!�!�g)�21� �l)ɖN; gnorH�wY�5�g%� u�]/D!�2�, .[: ZU beta1 : a�d��N,A��( = detuninga� do 7�8�]~1� ( �Y�W� [lt0!� v/v0�efiF, 3��-)+ 5yy� 1 & 2u (*%2�,&. =2� j!1�j2U�SM?j2 math6 stdlib.h>!/*�0 exit(), randI(malloc() */P�.h> :c�()2 0 /* Ver� ,9.5 (CFY) : �E$input file?.*/HFix�ugi coun, �ofE,�7 phot�*/ I�v�, )Z�< . - eE �so -cav���D . Fo�8is _C[] becomes@(real)-$_D[] (imag]).�/* adaptstep s(control: dt�nots�56Unu defsh/* #define USE_MSDOS_NAMES>RE!C_ARRAY�$/* initial��w��last sa�j */ 28CLICK_INTERRUPTBbL/* sense mouse click ��xX_GAUSSIAN_BASED_ON_RABI_OSC 1 . 1 means{t .m!<ba!'0on Rabi oscil� �Iq arguA�, i.e.QY�qof g(x)@ereas 0.oi%� Dh��=^2.izA� �*,SUMMARY_FILE!�$_DEFAULT "�-�"4)�0RK4_ALGORITHMGX/* Use Runge-Kutta 4th ?a�Q34DRAND48_EXIST WOM_INIT RS reproduci!�Aomm�sE�V0SHOW_PROGRESS ? Bdisplay!%dotE�6LINUX�(VERSION 9% REVI 1,A_INFO_ITEMS � 7 ,MAX_NUM_ATOM 20F!INPUT%y S 646 DMEMORY two_to(25)V�6L/* 22-> 4 MB, 23-> 8 4->16MB!�hD_STAT!�(CAY_CORRECT! 1.34o/* D-st(Ldecay ratein 1P1-1S0 ; amj8 ,.376pWAIT_PORdP_BEFORE_AVERAGING 0.0tB��$mj changeda0to .0 insteadaB.1:7*/�N /* .1 first 10%���for}SE NG�Pam1Hng as above, but ac�_inO��ɣ*/=x@VERY_SMALL 1.e-3] SQRT1�ED�� Plat[!H fic reeRit�[ifdef6` u"da?() 48()sx) (48(x) #else$@ (-$)/(double)a� _MAX�� ��Mac��PC�#endif �:� sqrt� fabs(x)�?�sqr& ((x)*#[e�Rpi PI>� PI pi� � �� PI ,3.1415926536%�output/&� na�%�%�Te QT_LOG "test.log"��:�[�INDEX�38 idx"2!�T!np.!a�US2Csta."OUT:D _out."PHOTON.D_pho" BGJ�nde�� ut" f >MR�O ONLY�$on!pY;V� tus"�j5 a�$&�, etc6mVD��VG ton"Qz�global �b� a�#ed�"&routine��i� *_C, *_DC_1 D_1;q Ae6� ; *_C_21C_3D  D_3;� �C=y , D="q ;!? Lp _u_th, _w0, _Gc_over_2pi, _g. Ga 0g; int _max_�,  w _� ;^A_info[.t][.�]ONM;a cur9"O�=h��e � */ft_int, _;_ �%_radiu�d�_v, _-_� =0."52�� add;3B  ��'e(��(ostŖ2F /*� bA&�uni.�$*SIN, *EXP5:*_Pn_�!� _� >_7";=u /* Note: .8�act") P(n�(&� �  / dt� Ft l en��sim� Q9pop}6���_shiftQ<, _CA5�***_bits�1�_sum, _o�_� -H g_multiplier; longI�k; e�ɤL SPONT_EMISS_IN_PUMPqA< _pump_waist=1.0q6ASa7User-�% fieda2 amet�%*/I�INCLUDED _D� E�A�(ic spontane& emis>;2� ;!�6� losA��d>� LAST� =�!e�DSTANDING_WAVE; � �� kz depen"I+gX ?"f X=1; m$jul 27, 98� �2'ssu�*"�8 exp(-x^2/w0^2).wJ B!� x axi? �� CA� (_LENGTH=2.;�!r-field i�� on lengthu */) sh�&be large� an 2a�_w0u�:Y!F�/* Z�yN��26  �y� *�%�0CIRCULAR_BEAM9�vc+larQv���diI���Dzq�oD REC_HALF_HEIGHT1Nhalf h6?�Yin!%, width�Lequ4+o b�,MONO_VELOCITE�A� @!$-energeticF�v=���FA�DMAXWELL_BOLTZMANN;-�0DEBUG_LEVEL=0%� /* 0=onlyr#0mary 1=immed�-� $ 2=debug ��{B$/* 3=extra" ��Haf SIMULATED"#�� ump I�$ dur� evolu m�e�>�fI�Vc:� enoughy Z 2*����Nf_WAISTVb 9of G �aa���bYPOSVWNcea���� ��_(.^3� posi� Ŗ9~ �tegra%m1,-.W HT/2^h,�-F�/2iha�V� �is lo�*d]+0�6L EFFECT_ON�� � n_seed=0&|&)7 _flag>char *� line, h� dex<us1J*& $� .. suen�(��� N_ex,!5ta�� H VARIABLE_FINESSEF&ADJUST_N!8 ">j new_N_effJ��F�R?.3;!��2%_TENTHS;D XlaI^��%� ge%v(� *ff, )�s,�� lim@ oid U ()�0 get_arrival_�  5 O�'�* #U�/(2*.Q _old23 main(�* argc�*argv) {I)b " ! l�+, r0, tsse, La 1%�[100], �� z3� ��z1�i, j,~ IER;_� , m,�� B� _since_T�! D too_/2YBJnum� mmAD_ed_a�e � exci�ing1!��_to_d �=6�(� mjE7Az_t tp; ���i��sk2-�0D, next_entryE� , t_� � t, n , n2 tn_� " _ n2 XE1 2R� �a�! m�� dV� X�� /*.� / �� �P �P_N � od�1 _probA� d�) *fp=� MAKE}.=a,ile_id8-) har ��_��[8a_ !� Mp<'.B�&u���lAI /�,K, GENERATE_*)��7-A�Q�iQ�A�s, E�)Fh :/*[ ect��value!� ua�} Q�, m,M�e|�stop_now>� 0_ 0/.q ��mea�;n��, ma�nonzero_K *- vacuum%�,  ive_Va�ap�2_V,M big_�$dt�t0_a��5'-_Q f� �t_Fs  ~O A� #� a�nu%ofsCBa� wh�5Kage4i�eDn2d� take% gr�_Z�A lacehold�%4 � n_final-�Q2N2Gcqc F�,t, p_poisson�'(B��� � ve_wave_/( Y, a)-~%�'intGl�$_12reaI�use�64ee:. � � io_ aq �);%� rq/sq� e��� �aO� m?occurs J�*, q*[ 9���@a�:xhow�s � y1'2'),m�) Q ��al_A�^,6A�Vorm��� �d:� � key_�<5�I%�ifndef L�*/a�Q�float 4me_n K�rgc=c�9and(&�  >Fi�6b�8sine t�~/*B�*/7Mem�"1"��&�Q�o st� �"�  =g"10�-4of(���)-L1b2N0/�Nd2Fc���FgJ4�*> �b0aX&^ �1�Ǫ���1:� ��&� v-Y4printf("(0) Tot;(t or (1) Ga),Wx dir�8?\n");� 8 scanf("%d", &&��e.�Get aHN$ �(#A�(i� i<�*�; ++i)2�U [i]=%80�,� f �$stderr, "E�6E�M (s) �V5 (max�oa0s < %d�?'&'*� the � iU?� �.)\n", J��#B�Z withE>�%-!tV�wi�<&<aU�.n�)$%}� 5 m i=-1mUB` do �i++EQs" pue.[i.6(if(*� i�3 '$')�zEm}0while (*/4!=!�5�>�i �ifAd =0) >� 1; � $:2xMW"II�=b elseM�{�.�:�E� 2[3F ,batch %d: %sEIijOfp=fope-9v , "rAB?Dif(fp==NULL) {܁� �&f�? i� � ��F fclose(fp�� �(1!� }l .'})�}��jq.U1xI�ne.�name e�154 rs): ���2�2U/F4$ , "w!5 �/*�"@���B��;^>quB|*sim�"&�9BH#%dEe%>���:�Ga/2pi��kHz-d =lf��;pi!�Y�(fp, "%lf # $��5:�� ��nan�Eer �B��b� � v}a� curvature�cm^r�H�=r0w".#� �opnmillioNegaQ�� ^� Ab  � v ) z�fLbvLp �B�i�6;� s +1�;aU=a1>" P�� �-2�d q>� , GN�9 #B ! 6ۅ�F]&ve(� ial) Ay�g.�!u 1/2gN�i�dtf�dtI� $RD)_ #V�Ci�onZ� to.IVH#b% �%8B9�/*�#rol:�N �a 3�A*K(0..3J��(^�#\� -�26w-�"Reu�.�$�2  >��^2"I�e @sHose�"�F loop/run?� F],"(yes=1/no=05 i d",&�.z ! ���a>'!>�� " � damsIpro/I-�-u�I!E�Zm!?bN���%�F�!���F*�JM>���!branc�L? ��2J"~�2-2�2 �ab�0��f.� "ChoA�� trave�D�,�0�Mwav0dѬ.B%�2�"^�2%�27Aj !6.�+ /*�- �us�Kv�I� �� yQ�. ��toA�b>L@l(theta)�� mrad��y���0��:|F "%1 "  .L +�n �*1�- SCa}N� �&U�BC3��f ofA��:��� �qQy�.$%.5�A>&&�,9 )>�-10)J!B�F2&6(%�!6 M@!!5�NF-K�15in (u/� *MD[(QA!�J�{�2�0;J�f�M" qA5v.��) {B���9)�E�#%d]%� i], '  rP �.�D :&\"full\"*� w01P�i�F"Aa6��F)�F@ J��L+ angu�%�G�M" &>��E2O&i6��2#�25a;6 �5e[Yb�&� .�&!�ic� DA�u�2� )~D� q]-D2[!�5} *P a:Jb�M>:&'.�in]1^>�:}'r�:,�:);�F�"R��S"j vol�)�Po y1J1 "On  2�6au�Fa�P�Ngeհ6w_:��i=�b0� b!�E�,�J�taU #�"] */J8) ٶO8j��ee��cF�aa��15{ �~q�>\p�Y՘{�i.%j] �Z �W} F' q 9*/� E�$�=$$f<5; n:R�ies (uj /bS[1R {�1�)R$-Qi�1�]�$1U =TJ� j��9E)rib;*��W+ Q�E�2�+VV2#%[2%`/*��a*^b1n�YG(a_coeff, &b F� -�.-e1���-�("2,ao�V�Y*N!�= f|2�a@ �Av5>u�*n V��%��.2p0F�!�B'�BaR��F*<At1��PB�0g0"� 7B8��-�!0!m�,d05 �B1�M1 )΁�1, �0!6>��D�80o4T�.�� (+A prio�)#R *� ��#0�& U�[�^ Us �& befor�>.�8 ���S� Ӂ( 8:- #�A)1��1, POSE "�2n,); � N� -H�n"� U" �B, blank '%s'!� , SZ�B!�1M K_."%s #%p��F? *RJ�***; I}**�!V-w%�}0}^nowa� "not">��= /* G)- Loop%� �� Y!B(K�"KN�Kq�e�E}B G�? LOOP B*�9A�R�A3��[K]�#p�>�K�)"�/�1��/!T%s can�be�.%�.w!�*�R}-N1A�4�210�*sI8PaI6A-"> 4UR-2)1"S = %�^� <������KO�GG*L�!�> se<0HKE  = - ## VF�3$� ]��ol�F�A?�D D2 ����d@�-���B�M�Q�6%A��!6��M��:�N ��N�V���#�*�]�F���!�VB�Z B6P:2 Y2A6V@���N�i!*�B 3 Y�il����H%&�'�M��:��2C��k){2%�?�1N'E�E U�O�*.!�u���N�)��-����R# aif(&,|)F-�\.772;���U (pi)A D��N�%x6.@65�q�tNy)m� #!c 2e�hhBh mv��f�0J�4=J>�b4!�1��aha�O�-Breg� is�@_;Nkto� "! ��Eak;�>���^�]:�E ���b�2�M��t f%[ϭ†YNR%�M.�B�$���B�  � �vb�V��, �V!c^ �r) N��C:�zSTjLv� $"� �)�ZH�/�Yr*V�4� "*F7� � ~ING&'DuA!�F z{%Gz��f��m�� PO"u��:O H0"�.� N�V��,if(!isalpha(:�[0]a' >�ykZg�� :V =�\�):5��r\:%[6  �$if(isdigit&�� m�R*�� D!U�K*  � ); ��� � �N��W`TFRA�IUC2��N)= �N-2�j�9)(( 6#� / 10.FM�>M 5./10N�!yV�=%w&2>���!& �1R1HU��R %FCz� ��[�9>v>> 1$>����.�FR!.!�.�M�n�U� ,Q59]s*�8�&16."�5I.l /"_1n|q,ompos"�K� 9d[ S�F&�&�T�6��@_idmE�*- �rf.�� 2� .�@Q� &�8"�52��5 r;x�� DQ�.l 5s 5<�C35s.�*�T�G#Da�"�6?n� Bout2?9K�� t" u6.!6s9o&/< kp�U%�MJj1.fb� !�R ��J:A>7*�D.756�b�9UgW.E9%U66>)!^8�E (&tpQ%�)�MD"L c,!1%� for(.1S=0.1;2CS <=$v:+mu1��BM 2.27:9<=|i:N�{�>.���?.́Dwe �V�zl>�S�z0=�Zr0*L/2.�r.N cm�0fsr=3.e4/2./LgP� )MHz*_w l�$*10.*z0/PIBu < micr�X�f=3./4.*[ B /PI/_w0)*.6�C2�D{�*�W=fsr/ !/1.e6;R� }*�W)0,2./PI*fsr*f**�/�p.)�Tin6�\+jW=D!/_w0!1 � �_S2_!(6cQil'� /= �Ht2D2�~ct�-�;y^�Qf�=N'^�\2)�2�{CFYN*� B, *=2�*}par|Ss "5Ddf "2g"�_5\g= p-g%Dg2Wpy�)�d fasS?�#nd/erm�Cdt0cX=(E >.t) ?2e:.' X=(X6&Z7X- . dt0=o/X*�; -@�V� X=% X�4E X, %)N�H.~CE Ob� pz)�%g �F'L> \(&�E!�1W14,W:BAT�E�ft�65��=O'M�:�+��i�f�~�Eg&hea3I�Tr�v.k}C36� ` �1�@ r{ "��p��w�$6�!#Ag& ��dad qt%d4!&.gR�>,!8pu��� @*� �i==չ� &� Q�_ , "a �)� � =( "#Qt%d-%d�%sIC $fo)��$�on�#S2O��d�!8M)n�� �YR- 2�ZNfp=�!; .�"#�8#.N "�?.@=%.1lf1@ �� nm r0 c�1 �,�?mR);2_"#Q&(=%.3lf cm � P!?%�L� n�RFGz� C w�� f=%.2leG �R_5_�.��c �$6lf MHz g ^MHz D.�2p_F�max.� =%d � =%N �-� %I�_'FU2g*dt&T> � 6 ] }N6FSfg!�)=b$��>K)H%[ x & EA�6Eme:B�8.�8 I!�); }@:7"n*�8 ;m�iltQarad (2� %d).%�(_�7,2�J�.�%) sx%>�F��!%>z>�Cir�3:2\/"+5fD5>ERec"�6AX�5w/g5.5Pu FS�^!�B�X6 VT.�M"# B�/&�.Q0use�&!; 6 6� "#*?0 B[0>fZe �� v(FWaa�� "3�.v�l3-���b��6.��on&2��[�� Rt#6�"# re�m�n�me���,�0>�?Q#%�PUM:�m�a �@_&�a=d��alesY 2g�+, pi pu�H*/�.6 EV/o��e un-"h this�F�(F3+GINI^R`)/2. >"'+I[#&�[�II.F�! J4fW?�  �� � **g B�s-UA!��."u-:uHA�Ai� k-  �,pos �� �+�)m&D,8,a��$Lmc)F�AtokoFcB.�*�2T6%FWB5A>O U��A2LgFN0RK4 algorithm2 M�1� i<2)2�!u #Z�){m"X �&� X ,:��)�[ �loY I W&_K �/* Check�cFMYk=�Tg��UT|[=(�T) ��)*? oAF_�i= =*�ofm *8�<d%p pur�+ o q�+1)*A*p):W 7�5�:- �!�>� >xOp��e 1�[ ,�_Tootd.Z (%ld kB).TeRe��S.below a�\2�\/1024L�O � )N B�.!.!�W�rnC�S����.k1\_C=-� *)QR�)�f�p���NFD�F�iuNOC_1�Q �_D�33iFjE.]�:+Q,A\�F F&�i�P�'�\FFN���i3Un4��j(2nW[i]ZQj%ie�Fc)��J� [C_2FWZ� E Mm�6 jD�j4�h�6�,.\22X�~��i��bL�9\� F*>�8�Kal��=��yte�L�r>9.��F��DBi�L�xL3(�)uI .�v� �`(p[*�{#� .(WR O*.(�s6�K7�A|2 ��Z"�[2T M�%�m m�+�'!�m)!�/  [m]�K) *�3NR�^:�,M�B�@!M6 &TX�fpJ�"#-�b�]�F[> .�"#� 1M,5��^%(> �F)�%�m)�)��(%�m)B=�[mJ�()�>(k)���A�FB>M� _v0=�R�june 15�m �i6B)>ar`al1On^?e*�"�$%�� �0PI)*_w0/(_v0*%$!l7B^�{|�;�J�(s�er�s). /* In�se7t� E� � 7Z�2W�]R 2.F�tojQ�o"i-� qy I �!� J=�_v0:i.�?N!` "XB�?J�T%Z%=�a���=%+*�&�PI8}(Bm# :XA�.1=(�/e=0]�rB�Eu:�2�2U�.e��9 DoppA0�r dȕ�e��ni*���d +"m"Ud=]��Ksin*�L�*�����V��D� 6�s=�/��=�%K]�%�A�u�6�d /*'R��i�D5��[��������.�"#)y͵ ��uf���>�6%�, =)���.�B� :EA9HnsgZe6? ���FI�:�n~�f�wtAb� �im8Ytervalo�w�q a��B�/* "܁wsxOK� gral:� |�/� ; ���e�{1�"+�*b/>AdOV|k6I��Z^V2�in�P v_th�}�/*:&!2g a�y=-M�8.� *2.;\ .6 ^ b% ���� "#_%}X DI� E��%&�z>�� * *d &H 6!#e:< R.� %=m� � ;� m2�{A@*�"��[m*� .X�@# jIUdtPsider�b6  r�F[]a�sut��va��AT#pf[ .�z=��*J@d dt=dt0/? �%.I-J;)*�!� �d�"d|= �:�E}8[!z^��&��/(2.N�^n�)+1�( EEf� ��SM�pjBV� � /1)a��Bv�27V�2�6����::�'�+JO#5�=%gO�l\s*�Uor %g%� d82)� �E 2�,NI�yB%!�IQBqF�AD^nBoU�?&Sunnfker M�n "-q�"�]s6@d atoSf add q���EMB�� st� benchmark�: T1=c�� vi)��*/ .�=&��4i)yti]'.+**U 02E7.;�8&7B% !.2��W}���_� * KD&i�i<T��W _C[i�.;� AHn E� ly vq +bZ!�G, /* _C[0]=1.�Eu�_C[�4.��NSe�O �L!�Q.��ui_ one-x� � ory C_B*_ _�(N_ef�, "78"OL ��!� �p���'E[s�*t=0�,default. If �i�used,�"� � �&�__�oA� |M� :of�f1!'Ti=t; :�u=tI�r�q�i�ڦen t>Ti2Nn Ti2=Ti+� *:)2�i�)*5^_�; I~g= �N �.� �a��s �dEZ!� �0~/**�Ts�bed! -�q�w~7�w t=) m��B; s�OstoBxB7�s fail��b�  xAv>Ku�ced%y�s�sum!� %A�tAC��iliUAo Śof9 x*/2d]inn|\&�U  5i��x p!� ��J5 2�u:Y!3I��x%ۡ�M6. �r5�$]/I�� ������ D�jh �.�����to M)�dxB<ʼn*/ ��!��y�!Z}~e>�anM?1t2223�S�� $)�:/I�me:f��B3.m=�� /y  �|Asto| */ 2y:��a��rlof!�ta� �sI���{(E�Z��h�_� fE�w��<���ate�.���� �� �n Awt>=:5�E�LE�_�3�x=�*�u� 12�T& m�9<0.>m J.++B \ *un�IT,![(%d (%.2g%%)= JS,e�i7,pM.*J&/� %T  �U>�ߥs "�jQ[ Ns"�fu�� >�q`. O]�wise,j�va��� !�M&ifJ[ >99)_Yv�y}!N/ y��lAɑ�F�=�t/p{!�� � % x� ++e�D8ly :.�  2-�"c".$ �e�)M�Ti2M�!T }��� 3 �ZN+=F�;�X} �0r canc{�� �Q:6w5 Macintosh&E�1.�2Jw�B Stop�Q? (�{=1,itinue=0A� ); C%&�_�9.|I�x break�W }e��*E� � &%%Ҍ)65upd�u " �:A = t +�;_.��(��'*XM>1�(�M$"N=%d creaI6 t=%lf �sᢉ�%lfaY Next r\Y` �,��ҍ  ][2]B�); }!�:�adCtA�%�I H>0%��c��e{uE<of wavej{?Z�{z�0/*�$w� _Xis� leas Bj Lt+=dt�s��|��y�Zgj �A�-E'! (i�i<=M`;�Q�iA� < tz!/�mo�WthM)D6v qpR2}%d-60awo���1ii>�!�%�MrJe� (ia@Q.� �+=N.� E�t 1 ifo:%'lea���X in# ��-�%S��%��w)��if�R>�8I�i��no}�if�i��!� �D�y �E�1a��kR&&(� <&��YA�@ lete�q ��=:�-�4.ׁ+= )!�n�0]++ /(�})aZ�v�u vav+�getE�� < ��CFY: ??? �_P1�_meanw p��� ��t� *dtŴN �~not�n haѷs�!� !)���i�2�- `] E� %|�� , a����d�!�)ባ"�� t, &)� � Z* p� ��+�!N�- &&!(A� 3 >�&e� *6 F Ah��"� vJ�'�A%"%d %+2 6 h, �K0 2�.39�z  if.�== Aor) ( at)t2�s>�)�N -R*+=)�</*"� &�? ��V>.!suF a��sua)��!A��V ̖ "10"t 4�/!��w� d���A��� m˭�]0 �*aiing� �tM�A�E��}�( �QgE�@u�yZp�as!�/*7=% /(t-G; �M��r=�% ;*/�,&�a�W 5  d2!L �< mo��+).q"e�Y�&S e8/*"��/�- ���!��� if(]�%q == 0A�<# ))) " �=�i/)A0a FZa\]J��$qT2&eb�_��}JPT2-T1)/CLOCKS_PER_SEC%�3r F"����(sec. Estim� A]%>�oms: %g'� hours� 6�20��, K�"�6�b$�*/36�] %H�)_!G�K�U�T &&NW *7D Skip5��5"%/P_n6� QL1��:t)����!�e�� ma�).�� 2�2� =6b��@ Q0 %d %#EiAnT/(�3)/dt)DeZA OgOt,T�^$r�1if(.[Je�� :�EHj_�~�calib=ng \ ��%���)5"uF intr��!� H�2�"5C���ˡZof�J].&-�) ta�Q\FM�:a+��ͦi]�t ]��d���.�%�A��.D m�Q�)�ean�i�] �.� 1-/=�&* &H$ode�",�*"Z5Xb:����q �j/ ="�- /y5>(�u /J+32�$�%��D.�-<~�$)Eq XAE_$�# lta_""  Z0a%Q .+Jw+(>x+) �MF�[��Gc�,��by��� Ƴ9N1M%6�)I.�)B�S.��>280)|| ((!�>�0))&&��Rv� i�Z O ŏ"t  - (a�< z  a% mun_9 #��dtR ��� @ ͅ�Caj7� B�R2 u�7@�� �B6@"b IJq :@Ak�� �"sur�$.�p5zhM�/�c�Y��G JJ�/m;).�"N)rE��:�%oa�B�/�*K) fm�� %.6le6+ g %14d\�3 L�A�**�Q f<+�0.�) A��Q��.�)� /* �"B��GF��M��� -AOB!�"� q<um6�e� �m��xmsef!��0 Z�� d�t�P.Oc#�7 ^ +�|�A�!2L%(�> 0.05P ) "%A� E�t,�3(_C[1])+*D 3 3]))S����NZBstarts�-"�� /�!�_ 2��C!�!e�m� a�ru)7>� 2�PK�um �m i<=5e @ A~.� C  "Q�j&, s&m2&P /8��6!e�*�MX%A3�>@ �,� �<=6H? �/* M� END OF @�ION RUN�9�"�C"� �s--;� 2� op��+ ��u�Tie (6�!�-f  Cont�Nof"�]..] !b1�1; !�1�AH "a�i<6)�!%�!�A�ii]�a&- �e�b�CF� p�+x)�  i<=4�I^[�AL*� *�+iIV� �}�Z��a!�ApJќ#2�)R N��&� �} zp�pJB;�&� !*Sub@t6�&  h���+.>>�%�)6D�� -= 6Z��:��:F] �P&�'���:[i]/=� *(1-)F�3��&d Rp,*a�(��7�gc�ff�n�"2~ "p��� ��A��RF1   �VBE� �|� '5� : � )eNotif��keڳat�Sonnt:�-KS{�YDS"�:�0�$͇��0/*- *Gy� #� �6� n��, V|����>V^y$nd&W �,e� AOE����t�.W &n�(%�&��neg��ede;�fG of��s�entir.�� � J�&   100*��B�+"�V��('�ca� c2gTE1(5$%3�� 71,� 2C1!�1����e6� w B%�sa� 5J J�EffVYvea���)�(-y�#%g�r'�,Jy�L$efficiency j5�.�6O� 9�2yi�J�# 6� #Y� undergone�#>ү-t5��.�� a�z6�#f�� 0#1D2� te>sr2|#IWz:�A� � Q 6��A���&i�,6*!�P"g�mmm"�G6, J��9*H>y%�5gy&� ,*@9(sim)e#��oU`U �}J�,&����a{D+.�km�a(" ly empty�r=per��a=�+i�v�2_) �?H76 P(N)6WIg�orR�>�GComW��Po�2X� "� =a� (-1*� [m]/bE ��� j=0;j>� j*Vif(j!���x*T�f3 ft)/�at) jL2�!/~ej,"�[ j�*��!:}��.LTPBG�-�Y%FF\}Xf�_�����_�:orX� )2LN� !Q8 J�>�2p[j]�e� �_��+=5( j��;i>C-s�.�^?zL>�5PF��6h/=�C>wN"6w "\n#�!z", � "#�?N�a pA��{��dB�9 "-���=!c5� Q�� G� ?�_�, "�/�x SAVE�� INFORMA�K,fp = 9:Tn, �MaJ�.�e�.� ��7.f",N�ea� 1� s f.ygRT6;�X��, F*]K *, QWtد$x<"h߱,$c� "?.N�%AglK.*�D=� =5� / (2+ *�O��� =�t�9x)HuA '��29a!� B Ew�WIحk^mode *6B")q�: ~ !� .$2*%}&vA�� 1�E!9.v�1�A�*�.�Y�L/* WRITE PN DISTRIBUE�� ]�&�i�. r�6�d�%o��> !��12�UjB�6�H�to ��_��G }J�"?�^TC^" b�}� sheeF��� d?�1{-�.J��rKW��O 0.ML/2v�a�$ Q G_c i� )�~D{E�2V �3N%� BR@�k䭡�,"� G֭ a+.�A9 -EB�?1 } }�> Ne7eOf�^:#>f8/*E�>��aK� free(_� �_ �-);6�-�U 1�_=+y�.@.a)�gi�0Seg F�>� hig��N */# �5uPR.m� L�W!� � �_3D_'D.'D'��i*�i)��m:v�1�F^x=�Run�I�&��� v�/?�"#�int hist���/O�bi�Ppoi�=~0&�ҷ�5%�$*.( �m�1i�* ;i++" ) ��A1�-� {;j1� arrfO�6kw6 p bif��((4*20))�&�bin-RJ T"�"! %d] �+% 7� 5 �� � bin=0;bin�bin6��k+� W /2�<*W�ƅk3, (3(�)/ (-&*1�N)��p( �>/) ���(�a}��xA1c, "�k!!� i'++i 6�H L '\0' miex)�JH�resulI� =Y�$* log(1.0/ - ��Ag m 7s��RE�����_n7� "�=us.c"�N#new� 2-d lR�F/ve�2-B�7B�aing>ud_�e/0�>);.�*;�ea�&l2Q������Z�N >7A�/./F �son{->s���/?2��<�D DELTA_T_MAX 10.��KD�(�l�3 V_MI��0.*|�V B 4.)(A 2.43952"���� veloA�� P5��(��I� ��, bb, yc� f (!:Hg ) y=:�f*M�;� 6wg0�(@ a=(j b�V1.-"aA� bb$�[ bb>^y=.`q*a�mwy; } 9)>&�&�7�p?�:�k?,* 1P��)g t=sv, ��U`2��m��x_|&�Z "g�_C%��#6K��!�)"~e\!E��JAea$_amplitude �)Fq � ++z�if<8 == 1&� F�Ё-�!��9RCD�5:Wr�1%d� �.�%Ax uq"p-�!M " "Ob;�zs!Zh�t!l8 �H8"e� throw awa��i�AwQ�'.�͍1.� UPmeo�failure� goto WJ LINEE� / a>��*?X*/�:SZvJ�kv��6�-�n� #�; hblock� p�� ifN�h��y {a^:�lap�w�c.."2 9gPOS �TE��SKg&}h�be�II,��W�6i:.7PI*v/�29i-$!3`5�+ I"i 1�wF > *�#M�][4�KAr��{�F.5]�"%hMz/ d� N�W�B �#0�b:5�J�$4]=cos(PI/�Z v0/va���-�Y6=��FB� �;��%(H�� "7 NU�YJ*� fB5]bB5B  � %J!K(G8�� !sin} cos A�agree�?*��.^ -ߥ��"�?U:5�a�.+�E{��>�*CM'<��+;t 1�� .��E��"�^Y&A�b��yA� B� 0]=vY�$W_th!*B'1]�M�� (31/+WF42]=t+F�-Xv1_4 :�PI�X�&J� lB�3e���S.���0J0 *=a%( -0.5)*+{L=PH W- y)>��F�3�8B@VpY�r yr �F� 6]=yP) vert��2)�'ons���N��� t��*/ �m"$k��-1)BQ(;f'-m"g<)d Qm+K]=_C[m]*B���(]*=B4]; _DEDjEZE/* &M_C[%ld]U VI1���, ��+ a� � } "&:� .a; 5�yT aXm���*Q xQ yyCɁ%xT **{ ; y;�!xyy� :�x"0��W.�&�  {x, x2�e@�J�cL x=(� - )� +:�x2�Y�aBx2:��� � yy*=A*(x* :� �@� z� =g � !XA*e*e�x2)/(1+a�$2*(x-_v0)/�ra�:���ɋs��a~  x!� >-  n!~B x=1L�� i� n<�HBk Error��n�%E':��}2*n� x *=2L;�#N$f�IN AXjef9 eFd� ex)�=޽�1_one(Op�max�mask, k,��0new_m0, old_mq� j, Q"��H&��C_tmp, D�*� p" G�6#&�.� p<�{G�?�h,First exchanLging %d-th atom with Hone\n", p, _N_#P); */ /* re-orderF\of _C[]*/ max_k=two_to( 8-1:4 for (k=0; k<($; ++k) { RHevaluate bit patterZk X$ mask=k; Gj=1; j<= cJj J bits[j]=2 %2; � /* j�dstate: 0=ground 1=excited kl/=2m }�` printf("k=%ld --> ", kڂ�;�%d]=%d >j,��Gl,\n");!�*/ ��$/* exchang%% s[p])�Y- ]=0 �6p]� =0;ZU1znew1p new_!�vq&+ ]j]*-�j%�>9,.=�Ej�1��A1>4rename indicesA^A�)/if (!(� ==k)MMm0=k*_A�(photon_size! old"V!� �0A�BB +U�$ C_tmp=_C[n m0+j%� . r.=D�| D TDBT=_DB <.=D aY/a5�_C[%lA� lf !T\n�I!-J, �], � m e�m else�!A�HQ S!�k andIH. Notud.ziBO�}2�$ _A_info[]��.�,A_INFO_ITEMS-� 1p]�dq|[%�<} } int remove�>�(int p) { double A0; long m, max_m;3 exiting_��e� 3�))==0) !Q�Q�2 a mE� m], ~  ��e } A�TM!!h2H0 (P_ex=%.3lf)� resulAO}] arraye��1.-A0);g Bz1; }%�reduceQ$ by 1�M�--�J!�U� o*/ M�/>�1�=%d% ��returA{2;ug ]"i+ *A0aliaa^ , m;qH X; �A*A0=0.; ^H$*A0+=(sqr(EN)+ AD)!�/*2 probabilaP$*/ X=dranda�9$A0=%f, X=%I**A0, X% A�X>) -1; �(CE)-A&.�X!� <0! }�  %P)@6k {-I��&ZLN�A rK!jL^�{ }�]/sqrt(K!%���>} QX+EM�\end{verbatim} \section{decay2-d.c} \begin' int � _(_occursQ�dt���( *n_mean, )@ *n2!b  !�_j�!k)wk;kjU�0mult_factor; @$calculate_ mAY [ w$(); /* amjA��does_.� ���UJ e? �=��.�e�>5 );E�F� g , dt� L/* collapse wave fun%����[ >���� )p=( �)jA? A >� AwF� +j-1]� � N ]*j!�� DR$DV 2D� } �k k<=��.d _CJh-1]e� a)F�ͅe-� it%bA�=aC��! pr3 C=e ered fromM?���! IT!~��ɍ��O8rease non-zero � ( amplitudes��5j��jnmyM =1.-U<*_Gc_over_2pi/_g 4.*dt bN#�Rv+j]*=rFV�R*-�Nz ���}j a:�. Q -F4number as well,_Pn_dist[] 6% ribu�,!t{�rQ^� E|E�:�)�p���jM�^�A��j]�fF� +j])!���V"A�Q��V �+.*UX%��'Ł/* ��addw fun��5�_�:!kf�M5 12�2�S%�2%��gvy �2:��)* ; �j�2�X #define SMALL_PROB 0.37 b�Aь��W ;� ��rrat� "=b�2a�*��z(/ > 0.3)&& < 10.))� �%exp(-(ͮ >#" K� <B� M0%b�evolve2-^�void %_�_�-�.�tEMM�O���.�&(n2)�(_detunIsum[k��$freq/2g un���0"JP_uk�.S�R� H>0)��B�+=(_CA�-���j][0]*�g_shift͇g/_v0ab*��@ �-�V!O } !?, ��0_v0 jun 16,98A-Bx*=0.5^ y�coupl9constant!�izM%�i�i2�i� g[i]"{i][3]%�ofE, alread� cludn e�� y)) 8 m, x=(2.*(t-1pi][1])��$its x posi��at   /(72]:E-1.�NX*INTERACTION_LENGTH/2.;+  -N < x < +RAX$GAUSSIAN_X%�x)<��!-*=�xŸI.��l[ �Top hat;Xi Ufabs(x)>N�.):M if(i==1 � 0t=%g: g[1]=%g� t�O1��D(PUMPING_SIMULATED�� EFFECT_ON� E�check�the�is still�pump beaE^ , �+Y_POS)< x5�%R xp=(*/*_WAIST;N P%vp-w��A� _Rabi*9�p%�[%w$.h }�`tV� J: }!���  � B} e��/ e�First,}Ly1=y0+y'(t,y0)*dt/2 a�RK4m/*1just y:)'� + */ /���s^<m0V�7 v�{�'Em".two%�0-field interaz term~ !�f)-initi% )�ѡ.� m0j=� dC=-� 0j]*>�;W@in .� dDxV9 �9j�) {�a� S-��b� ���i]{� onlyun���.� � 3=k+tw8i@ JtH=hbar*g*(a+S- + aS+) used her FdC+�JB�*��x*� *�� !4-!5�@��i�qe�s effect on���a�%��֎� �+*k J�] �2D-2Cb�2�A�/i�z^�)a�i loop) if�gF�-1A�� S+��J5�Z�6T%�Y�-2�%�j�+1Nv(j+1)Mz !�j��B%���|f|�}�3�~I���n� ->}J�N|Ize�dC*=dt�Y�12&  dDj B\#ifdef USE_RK4_ALGORITHM dC/=� K !�#endif I_1��A��+dCf�_D.D .DZ.~�a}jy}k #ifnR�a�notF�e"[^wbx 6�wA�P!=_11;� )=5��)#d /*�B�� �l6/� Second2 2= + ,y1 > B�/ t+=f;�ZBf�&�!�� .��x� 3�  M�� b;�D� I�� � ^ �_1b�-Rqj6m�@!1!��l%^��j�&��J�m�4��oF� }/*�l"�j )���p%Y2� "�o V� JJ =V�jJ��!���cJ� �DAx��%�wa_YBn�Uv�3�u��M�������J2�#+dC�.Z"4D4�H+dD~4i<��*UU�&U��!��c Thir6b3:b2�b>_ G�/�_�_�_>_�`I5�`lb<a��a�aG2��a�Z�F���>s! G_2b�zb�_!aJ�~A!3��v�B�f����.��4���K>�J�"� �\�]�]�]�]fE��rn�DAr�svs>]f�Qqݾo�pN }�� _C_3�Q*�"!8R3_D1.VZ1dY�2U��j6V�"6r /* Fourth2�Hf=(y1+2*y2+y3-y0)/3�+dt,y3�c/6�U����������z�I7�[^<a��[�[fL g@3".�J��BXa�e�� e�@� ��!V�= 3b����.��3�O�.�M'�U�L�Lf\N�%�^�f=��`�Da�� �f�f^f�GEB>iN�� !�N &/0j]�"�+�*2. ��- * )/3.�6.7�F��e=(�N+"�X�W X�jX�� t-Hun�7d)" #�4:�%"i.spont^�%�-�3�3�&X4*d�-it :!'7 i, nJ4/(�&;j%b�% =_Gak$*dt*_pop^.ion[idE�*>*)'z"�!oB''1010.#; 6)'?+2�e, n++�e""e,*�:$undergoes %Om]*=(1.-� /.�D$!�z$ŭN�ŏ�9 )�ʑ))oŤ��%?"T;1) a��v0B(:�I� ��E����>4�.��v�."ingZy7/*s par corpo�/ s co&q=umA�/ cess!,/* "|04ELF_TESTING - thS�=d�:4CFY because itDdidE�Hcompile correctly -�> vern�*��s% �-d.old.c6<TO �__*~R8 FUDGE_FACTOR �/ get_~_u7�v*1�8 Dt, a, b,s+Dt1, t2, tp, x1, x2<� O�/_R,!6' �>/*%�)��1/-��Dt=t1; dt=0.01; a=12�UN!b��sj� do��Dt=dt&�,t/t�, a+=b�2D/7b+=-a �; ZF!| testX,rts jul 27, g0 l-(u&) y��� 2U ib1!���i�*\- fp=fopen(]�, "a"��!�mfp=stder�7f-�(fp, "%lf � ie 41 /,0) fclose(fp h } !^�endB�"&d �aF *I>E�& INCLUDE�3_DECAY!��/F){!P=:o� �.�7/� �� !� 2:� �gener�5a ?:w8�!�F*tom)�� E� E� }q!if�D_STATE)�2_CORRE�1*��r b=10U A2by H7�2�ZC)%%M` 2add�Cis bloc55�9E�{} */pif��Eling��CR!� mj #�}0wh� (t�F�� &�i]� ��d-%�)��2�6�G dt R�� m&E<�_i։� %���������_i3:V�_ 7e6��n���)��>F*�2�bB.�;R�eW.XaEAH": ��q6�O should b�M�)�H�Jie|6 before thqu When D.��Bs -d,�, we �OJ�4w?Q�J$one. NowC�7 labeled a��J0 Sinc ��OI one7i�,zCisA}�rCo�7� e -� �fC�/> /> . J�7=) �L al, /= T9n2 . �$is equival� toC2 5 ��_e�(prematurall�*�(sQ:�L�&/*R%H�m �Vk\m�:�B-1)B�a�t mAFWLtm("�K2�02YL.���MK�^X�>3C67�IV�Rgs!#finlBE�.NofT? T$?ia j���,��� f/AS� na��[u�[�s0v��Q�Z�bI� n�r9} A0.�#�#�4%.�#: # F.B7~g�8vfS�aput fileJ�J 50.0 #  2pi 791lambda 1, r0 14�Csse 0.1G$L 200 3 # �ASFYS a�s 0.0500CdtL tot _count 4DEBUG_LEVEL 0 F�%24 STAND� WAVE2�4tilt_angle 1 #�{; �[0] 49F/?o0CIRCULAR_BEAM�00]LREC_HALF_HEIGHT 0.44!"C:Hive_V_to_apparent_V�N_eff .E [0]�  � Don'j=(get summary%��below(Nu_th 40=��!k,MONO_VELOCIT)>W5@MAXWELL_BOLTZMANN.�_delta_v.2_v0OGENER�PHOTON_I�!�";0 run40.data #B� B No�W� (rogram may �4treat velocity2�Hs WT1� cor�;�:i�sis sim  iQ-Ire�,}a� the monov m,.on�Bcase. �cnK��al� one-half� RFo s2�A(. Consider@�pa , locaa� [ �H's axis at $z=z(t)$a>re \be 8 = z_0 + vt \ee�can writ�operator1��H,al electric �? seenZ!(���: %\be %\hat{E} = {1 \over 2} %\left\{&8gin{array}{c} \�M {{2 \pi \�> \�%} @ {V}} A[{` a} e^{i(k�- 0 t)} + "^\dag'-N(Q^-[��.�H=H �] .� + j.�X/:�J.V�J)}� -a\} �H� $V =Er,L w_0^2 / 4$a�A�0mode volume, � $L$if, mirror spac[ %W�uld %haQaPtenh)arrow 4V�9steada� 8� wf�R4 of %$1/2$, bu�  w�to receR-66expre�#a�,n $v=0$. WrV ou��,� a�sei�s Pf ���C �  J uencies $i� \pm kv$:f��_0 - ( l+ kv)2�a�i!�( ) -kv)q�4mathrm{c.~c.} -�] ��Suppose-� en��N� � t}a(� kz_0A� e^{- ) + j� �=�I�R/�1}}M�]\cos(�)!* T���� familiarUt�E�/D. For $v \neq 0 $YiA|_0 = 0$�4re�ngE�4time origin. (y work���(as $kvt_{\r�(t} > 2\pi$)�YbeV�=ɚ2x-iMWZ� Uw %+ ^�%Azb���N-�e# tZ� &+e 9� +2���-a�~�).� \ee u�tv �6�these�#sA�re .$) g = �$\mu} \cdotQ �饌� [plicitly lr N� has a� imum*� &� a�M@6�� cu*� $VPascal se�Inh!f 2� vp'"U2� "�*%VscannJ$experiment9*�Y0{ microlaser_+D.v } { C. Fang-Yen`�{ Variables } var Z1 ; plotimage ; bgi 4img; Plot0 ; /23 ;�osure_a�4NT QackW sc�ding 7;*row�!icol 8Z_� ;  .; crop_ 2-i; �bex;  {tDnned voltage, etc.�x_starW op5_incre!�us�micmiro\moyse�$; textwin � �serial otal�s_I2y; ppixels<w�#xma+ y iylimi�ix sum0; 1 2Brezero; _s�; � �y_th<_eminus; 2plu�i!a0do_gaussian_f��s� fitm!ax}$sigma; logk ra; !6line;1003t Labs3 !^%* !" x_tempA4y %oSY�_now;�n!�(previous_si �#; )�_e F._msg;h �cur�Q; nE� n_a�ods :_a& ; n_frame!(Z_bkgnd;)��at 5�(v_t_553_on; 791 ff  =L=� _no553 � E�!� blackbody�}�save_e�s;�� _Octs! _m#procedu�Dake_picture(roi_ine�var��)C bc �"( Set Gain I* 3 }' pvcSet ( 3 8ex�� := 3A_H /ExpTime(6) =�9(%{�IrZdn!�!� )�Fn� !�@p�2Xe( 1,386,228,423,257,1,3R; {small �i6\1 \�f[\404,169,501,323\mediumR]2�](0,0,767,511 Y8; { full CCD } 1#:�3�`@1,352,236,454,270cs!��+%Z�$)g  slit �end; I8 {�>, INITIALIZA�T52!�a~Q�!�'.tif';�[ = �#ic } N> ? doyb Fals�� { Record L(of u�tin�'�� } us.�6LS�)�z subt�Q}�y�= True!�; skip?C]}�/ �{�$ fluoresce��sA)�[3)'; .� := ' '; ��2 ';%��a!�6r&Q0; ��1'; 9 ' de� 0; xX%# 5�+:=145 stop 15�j*L2; I 7; ": SA��'�oA,��)� �'10Eg.� /!8_�8MakeLinear(0.0,�))m_E�j$&� .^J�0; ��.65�_ V_t 553nm8R� A=0��01.� {/791:/.�/-0. 0 _ffR`fJ2 b.2 �$5��� �� �t��$if EditorE�1s(=� 2�� Get ).#,L ) & E�C�e : Q*ž'eLnP, '���4E SERIAL PORTS�/�%�% �t@TxEnd( chr(13) ) X SetRb�Z out(�& �'u.�� OpenS �<19200,8,NoParity� { SR400 4  er A2� ! OE�  R.�  <> 0�, Halt( 'Fail�8on 0�[ng 1:   ', . f+e�m� �2< ok�ASPort(*r$ TxFlush ] ransmit5s)j0? R �jH'pl 1 O � !* RxSt� !��!kA:E 1=',� 3%�Unp~S" m val(�v J JrNPERIODSu)+17!�.?� ��_� Yi�A� (,�+1  , M 6 2,96Z8IMS stepper dri�} � � 2Z  � 2m  a��.�BLOCKER��q ��leci72E� Y� M�( Delay(10�y..qRxWai(=', )eTZ T:Q!�A�!�VAC&;_6D:�StrParseu, {>itVal(Stra�p4�#.�B�ZaT>O>�X ��! A�R! /�N�2�!� m� done �}B� � TAKE 1 FRAME, SET UP IMAGE AND PLOT WINDOW�� e2( { Acquire�PQ � Қ� }�q"�0,F); Show( ;;�g$GetXSize(p�3 GetY>;�q ����_R~J\, J\��ab��FileExp�o*? � Ax{%�;!�ifo *k � �� Ir &� �  � �2$ Query('No*a:c� ?')=id_Y�sn� AA<� Sav=S, B�f�B�,w�.%��2\E�� Delet�B ����; {J?=� %G��0.I&� =IY%9 ��eDGetV �_En�|k } Z1M�Ac�#F]� y�  aE� windowf;-�� ��+  y.&,>�� {�? �!-9 mE-PM0� �(2fM � Title( 1,'Row '�� Sub2%GetNam: a� /XL�*RX P< MAIN LOOP BEGINBRDrepeat *� A�"� StrCat('R� Str(x))�:{b� POSIB} "' 0.0*Abs(>n \ )/e( I� �it�move } B7:= x;A�Txon� prob*ff ��<�", A�B�,�b4n�R-22-7sff.�3BM 2�v e3 { �ffN�n����� �NJ�) mo,ea�?^�; {�.� �X0...� ,..]!�mox[0,20]�� � ��(*|��, b7)'Ge'�� '���0 { Perform an) :J{t)2�� G:= -�� � :�?���b ��z c:p� . -L`��;�:� avg@{_ 10 n 6A�N� �m��moF�QY(!�..!�10!�); �* - @[]0]A@=0N��.���%�_ ~..,QEqr�st4!7` if6 P,I5 ]_H Al)U _Ok� �} { 2u �{.�Clear��(�@ncmoV9f� ��; 2�6� �!{ MaxOf(moy)w]0; K"3 +-1�ui0�� * do"�if!�[i(] =/ � %2k i; {"�str(i�[�!D%+ �q;� ' 0�.� �A+�; R sum12 *� g sum2B $Aj''x:ar= um1/w, 'zma� S�|W! -c1*20 0)):um8I�W3mx j {"�&, 'max�pxD5�)�gJ/U[0..10�~�.�!Y�IC *2 _�W;A�2/ 7D"Kc �|�WA���*�'@(�)� {.� 6D��vDE�qDn�1i5O"/moUq }�$azj�..6��� ��if2�#>��>orii1ai.$-1A� ��� uH 7 �Ai�� .AA�s � �(1,mox�(c2( x); 29AAx>�T�#i� iyl�#2BJT *BT�i,�Tc>Tk�T( { Find 1/3' @$& �#��'�%���E�itoz$-�1�if � !r0,i�-9%/3.0) < a�A� :=nC� B�$4ii��%� f�:�,�doA4�����o%R� { U�'y_y2$_plus��9.�%))��q�.6 j�2tr278�%�%", �%:�Iif$2T%�)� �%�s��qrA))+~G�%Ln( ,�|6&.��; a3.�; �*�/ in -0.0 ,�=- � %+wE10�iH0,m��,( 1.0�a�PolyFit(A�3gI� ]..ax,0],W�qa� } {��!�EZ1�bS>*a? F1�F2BC!�{2�'�f�;� $�')� �kv*3fCL ('log� 8 �*" 31g L); �*L in�(olyvalue(a,[(_ }HI�n���8-1.0 / (2.0 * a5�Dr&��1,eu2*e#o6rip'2 $=qr !��Sty�ps_!�~N�u !XY�1 � 100, Exp(B�100�FORediFNZKH{FIBJ�2�V�;} ���ake mol+���� �,�� �|� e�. � �8N�  Z� . $F� y�� �� �5"� � y@ ��� !�6�P R 'y:Cn-:� c��  � � e *2= ')� U�{� l+axL-�**:d /6�) 2uj�Ier=',x,'S! e� Mb- :=s_x�O 'pe�* e�k�X~_x[E+�I�x; yB � ;�j :=>86 �L�`z��\U�6� �V � -:= 8_x� (�)d�#-(� 6( {5eLK-, d<.E����2 * � �);� ��D'�!�[!�!� mic%�7 *!?- *a/!�3*'_y': ML END OF FLUORESCENCEM> ** }E�0,TRIGGER RAMPj,COLLECT DATA� 98 *k)6 �\@:�S $'A 8':H { OUTPUT 1 -> HIGH�� .+0N+LOWb6j4 *8$2vCRJ�%CaDer Resew2,FB,t)w"Fcontinu�\AQ�8uA}�` A�1W "�#.�4��&*Z _�[i� :=>d$&eR2!O}I���b J0/�/ �H bkgn�/j)�F� Ѧya'i,I�A�iA�' iM*}� "� atJ > +� Ahr! �%9!�X=OU �a'h b �H%JYf.n1.�@ #�*5�� *&Mma% !at!� , '. y!@eE 7��M- 6) }�E.�-� �����`'��!G- d [a��(2&!ѻI��'g�'كr^�$YRR�&ig �8W"�4 1 �`��)�1..u�>�%@/ ��� �� ehx +.�'ee)AP%&� ; : ��enp='A�o�T'a�$ until x >�'op::��&16!!9:h(B�$� B�C>�7 lock��7��7��7��7��7��7��7��7��7��7��7��7��7��7��7��7�!2��7 �Q�B��=�C�*�7� | ff ��7��7�7log"#>8� �=<� � ttl;��; ."8tl_3s�Z1,@ 20�*� ��*�.A '+ ((8*(1-out1)�O6 232 3��&�8�EC;t.�k0, �!tu��f AOM qW =��.71 , 1:7� �! ; no:��I�="� �un��,N�791E";Bg>� A11 { �nR���2�"V9;��9��9B�90���9��9��9��9��9��9��9��9��9:�9.� �.tx�7&�9:�+� ��9.�9�7 =�#*$"#^:J:6; {  =�::e ocke�5�8�"A !�:�:�:B: 22:6icB�1;�:�:�:�:^:0�:�:�:A��%�0<�(w!� [�,:�,:,:�&=!"FD7��*6�+�-:b-:!3�-:�-:�-:�-:�-:�-:�-:�-:�-:�-:�-:�-:*-:& :�E~�'26a: �:�U:�U:�U:�U:�U:�U:{.u9"J:6V:M .��X:�X:�X:�X:�X:fX:ٲ  �:6[| 0EY} r�0�>re-% ?} �:>:Wj Ln('�='6�9iJ8:� �W�.V"-..�9:�9:�9:�9:�9:�9:N9: �;:�;:�<:�<:�<:�<:�<:�<:�<:�<:�<:�<:�<:�<:�<:�<:�<:�<:�<:�<:�<:�;:z;:if: ���#S&�8�"�#�'�U:�U:"U:�T��Z:F�pl��2�[:m "A { �.:�C2g�f:!�Yr�bk +-6{:p)!6��:{&�%Qplb�:m m��3"� �3j�3Rj8��:{��:%K��:�:�:�=E�X)�� Y \'b`�: BQ� { MUw."E('&Gl,e&DR�{9�� 5� - ~ -*�� V3vL;�� �)�G;�G;�G;�G;(*G;2�%C a=�H;�H;�H;�H;�H;�H;�H;{�I;�I;�I;�I;�I;R3G&�(at�-�"�\�*N�0�J;�J;�J;�J;�J;�J;�J;�J;�J;�J;�J;�J;�J;�J;�J;�J;�J;�J;�J;�J;�J;�J;�J;�J;�J;�J;�J;�J;�J;�J;�J;�J;�J;�J;�J;�J;�J;�J;{�K;�K;�K;�K;BK;}b� NJ;Set�I;�I;�I;�I;�I;I;t.%`�6"F-� (;b:�>+;�5�: ;�:�c; �E;�E;�E;�E;�E;�E;>E;4* MICROLASER I�5��*P :C0�@; } 7ait a�}U&}�:B}pje&�.IQ AFTEM���!�]�U2yP.>;{2;?;}^@;{."@;-�A;�1.��'Q�;R�t,most recent ���XL$H!4e�zj; eVh;}Q�2a�Q/ { En.<cQz�; ue h�u$�G�,mj� B�R}9�8�?���9�9>9�9 vL ?>*W>/2^j�9+�K��n��(A,��91��1!�?��9.�9!uk_A�}x"� F8 i�. ,i?��on!X"N*2�u�e��`�`�`N` �a2Y�F�>!�b�%%F�Px�_ biblibuph��, (main.bib) ��>{2%sUI . %%z�you"p{~�t�^2/!w�xhaʶhal�U�Bent5�MS�- to a `the.H ' environ�H. For mdUinvWal3H�{e� 4.3�Vn0LaTeX manual.X�{�C~.�{plain��I{:� }{10libitem{J-C-IEEE} ``ComparisoK�quantuX,d semiclassi�v radi� theories�Capplic!�n�Lmaser'', E.\ T.\ Jay!��and F.\ W.\ Cummings, Proc.\ IEEE {\bf 51}, 89 (1963). �� �HMeschede-PRL85} D.~0, H.~Walther,kD G.~Muller, ``One-׀�DPhys.~Rev.~Lett.~{}44}, 551 (1985)|trap-W�\-OL88} P.\ Filipowicz, J�vanainen�0P.\ Meystre,  Opt.\ S� Am.\ �B3}, 906u86); ``Very-low-�ter�x^ havior of�x x5l.k( G.\ Rempe a H!t- �� ~1~ 10788)��1qE-PRA90A24Sub-Poissonian(�ic !istic�a 6�f�)��v.\ A) 842}, 1650 (1990� � �!�96-h-jump}2�6] �S6SRDweidinger-prl99} M!-, BM�!DLVarcoe, R.\ HeerleinEk  �Vy82, 3795�9.WvU-n%�00}Nq$S.\ Battkeo�o ``Prea� ng PSuP�� NU�S�݁�e�Rq� F�}a� N{` (London) 403, 743 (Febru5�2000)�BQAn%�4AMA��z: az�er� on*�n opt�O �{to�#K!�nm=�hilds)d!hDasari �!�! Feld, e�Q=-�e�7A�337)m42�an-�|$is} Kyungw�< n, `�� ia���| � Ph.~D.~Th"�`, Massachusetts Institute �$TechnologyE 6�An-OL97b!VT6ꆁ���.u�in!� �I��5�!�1a!MfQF2e�500�72Jbensone64}OA��|aithel)�2``Q�hJumps���8ED��I�: Dyna�]B��|E�hPh����PƖs''V 7a|5�^942�heinze�1987a�R J.~H A�Q��MM.~S.~I�EnhancedinhŦ(d visible sبa6��h!̩+bfo�dto�@.�58, 132%�87.=:�b:��.�Vacuum�4ve Level Shift-S�-Em<� �Rwid0�f<`A��in an��a� Lon^�9, 2623AE6�rai9~9}� G.~R��Thompso Brecha!�\"Kimbl�6CarmichaA� ``NoE�-Mode S" �!��Avera"��K Two-�<�)�� �a`��.�63, 24)�2��LL91a�O� bista���r2U R&"� {rodi$s��get alJ�� 67},1727!�912� gibbs-opt ��P~M.~G, "�B�:׊ trol�� Lighjth ", AcadL  PΆ(, New York,6` H�-pr64} Lamb��Tr y# �B:� \ � (\ 134, A142; a�հ$lim-vcsel}�A.\ LimIAA��ud!�s��#Li,�  Yuen,�EY5au��CMzC- -Has� �$Self-Pulsa8Y� )0le VCSEL�Co)7�C In�yavN4�-Well S�#4 Absorber,'' Exronp �� (acceptedE�pub� .-drHrgio-pra70}V.\ DeGi��a��,Scully, {\it�hI�A}�*117E�7� 5c 5-!� -LP}= L e$ics},a�Sargent i A�W.~<, Add� -Wesley P�sh�� n�:742�&� � 86aaY;�scopicU< 1 7I Ja� ,Q "� �"nAh3+ 3077� 86W Dicke54}�s�A!Co�{n.o��on  8�e؅`�93, 9E�52�kolobov!� 97}'ajA%��E����i% � �0R I.\ K @ !�a HaakCY# | A 55, 303��:Elk!y9%yNumer� stud/��mes�偱M.~Elk��M`�� � 43� 96.�DAriano} 5!� Fine�YuB� ireshold�a �[ �edi�� cluster%i/ .~D' b`, N.~Sterpi, A.~Zucchetti2�mE7A9, 2:guevara-� L.\ de G ���{�6� aH -�%���$ic polariz�F�$ 2471 2474�w92Corszag�4}AO�Ramirem��RetamalE)Saavedra>! 4��9M, 4). T� % ޑ� ory���a*� s� -zubairy-����C�C& A���Z 2, ���J�Ds}. Cambridge UniQ��q͙ 1997k��Őe*-.�ew}��E��LW.~P.~Schleich, M.~O�:�$C.~H.~Town�=``� phy� :�ero�yc c(a!��~Mod.~%�~71, S26iZ�Y���7a�D-� ject!kanaly���  tq#lik�xp FN If��!�a�O ��a( 55}, 4492(!M��>�{ & tr�*X�� j�e���e��ngI��+c�ariɻits.Zlaniof mil{t� beh=�few\�{��n#���N "1 �� huei%  �� &� �):� Molmer-19 Wave-F��Approach� D� pa��!�1�� ��� Daliba8�� Cast�d !�,M$\mbox{\o}$:�.�68(5)8��:2 C"e �3Z}6y%�c� ded �� system�H.i Pj� 70}, 2273%O""��A�Rol�6ԋ �st�1in�%�"/�A�!)AC \�b� J� 52}, 169795A��K� �2! Measu_�Aoultra��losse%�&� I�ferometS ���!2& )B n�  R��lezAF�17}, 3�P2.fA��`�  ring-d�t�iqu[awa2 mJ�-s�vb5iti�)`,�_�\0 � �E��){F�2A 106�:z,Commandre-AO�L\'{e} b 0Roche, Appl.\ f�� 35A�02)�6� )& 7a} R� in?�b]� a� p�h:>% coefficix�� sub-ppm l�Y�, -� So�d���BO�!�,%Ob�4����U�Bryndol��Them{!P�k=� acte"�of super��mw�s�uf��.� m�"�� ��y��R� .� �� .��` � 9�6!shape �C a�:6��6"�� `,U�1�Ott, �i%R$%�6.�7a�290N� w=��-�`o�A��  R����J�� Joseph � Jr.�f�rx6M��%z�)Observ��n%�-��"�*an !�� �;MbA.R:)"*e 682�.^68�132E5225SciAm��aN=2�%ԑ�Sca�ific A6 n, 56-�� July� �%%% keep�Ni*��:*d   b*Usp�um!AO:C H�"2� 4� 599 � 1). �$ Abdul's 1� Qama�A �Exact"ǯAde �aleV^for^� ���]%A�"� 6� ���780� � �2�LuE{3!� Subnarrow� , hocE":� .aN.\ Luay&5.M�912EL�%1J3>�A �J�:> p�,�U{Lu�"� ��4� 134�3!�(% ref ``4''=4�^ gES%CŬ=�&� 1.UGreen-e�'� �%� xim�� �t"]�t;�&�Aparw��L B�ui^Y�q�\"$:-a�80O %�U�5=Vogel�$I. Eigenva�&�achA�a�Vb�.G\>�2�6���{� �1N�6�Schiev�%�M2��!���i��% E���m�P4��McGow��6�� 231�6w7�Ku�FdI-��yR(l�!���Y�: S���antib��Gַ��ӁLArun z| �)gMuN�5� 6 �YG8� BrieQIY�pr� �.�: �ic-V!a� �%n���cZ)) qn�H.-a& z�-�Eեr��n&�"�J� �36m+��9�-�e-���UQ!lA& 1%mQSM�U�" d3Q�� �10 �&�'abJ}t��n�+�Walls��b�"@}, D.FJ"l4J.~Milburn, S �- Verlag��4),AP�� 7%�refer���re��%.�1 "^ Hmilonni-chaos}P W M , M-L�h, J R A>W halt�C.a�]-Ml�.� E�World*k Le/Notesv!�ics - Vo 66 !$�� b 2S�(�A���bB�6}, 68�2).. .�M�EY�6�#: �mofŦ�D clicks'', H.-J.\ ��Briegel, B.-G.\ Englert, N.\ Sterpi, and H.\ Walther, Phys.\ Rev.\ A {\bf 49}, 2962 (1994). % Abdul's 13 \bibitem{Herzog-PRA94} ``Statistics of photons and de-excited atoms in a micromaser with Poissonian pumping'', U.\ Herzog, PF� 50}, 783N�4 �Cresser-�,Atomic-beam !pcavity-field correlation func 0s in the micr �,'', J.\ D.\ aL�N�5� 2361%[56�7�% -PRL)ZObserv%� of s6iI��)iZh, Fa{,chmidt-KalerF�6�@Lett. {\bf 64}, 2Q�:8� two-A-trap-A(e} E.\ WehnsR�eno2 BFa2OptA�omm.\�11ak65Y�(% below 2: �%e destru)� by 2E� events �Pcasagrande-pla99} F.C$, A.Lulli,eSLUlzega ``Quantum-TraA88ory approach tom� q & electroU�with up*three%@ col(0ive effects''%�A�!�ers A 2m�$9) 133-141!u��oc98}6��$Garavaglia� Trap��)=s%�YW � by a�tF�. !��!� unicE�s, 151 a�$8) 395-405Z�r!�6�J� C5. -.�A.�b9��,treatment of}?�.a�\*�$Filipowicz486} P.\� S $Javanainen�6 %%Meystre:7A34, 307)"6).����B}>g!�#e A��Soc.\ A� B!�906%�D6); ``Very-low-tem�N0ure behavior e�Y�era��2� NY����~107e�88�=_2�Xet al:9UIdo515�mQYamamoto!�91� a�0  s��$onductor l��a� enhanced %spontaneous emission} Y.\ [R�A �4 65%�91� � DeMartini� 2} {u De �H iro,)�ataloniMU.Verzeg�@}:!�6}, 422Ʉ2:��F 6-9�-jump}6V 2g!.\%t6�HollandR%q�f nondemoli�  measure�I�E�  number�{ i�Hdef� ionA}��A� j,� ! Walls)A�Zol� N�� 7( 71e %� " $Matsko-PL9 V�det� q i�> �_ 0n open resonaAc � � 2� �"�� {6 �(Vyatchanin,%�MabuchI! Kimble"� )�, �19S 17i#4at�cookbookaU� diodei s for-� phyO '', ��Wiema�yL.\%�berg,��6i.\�kru�{6�E5a } �e-�$width} M.~ �~M�0, G.~S.~Agarw�T.~!� g, %�bW5hleichm~ ~q a� 5992 �=�e��mb! L� PhassDFrequency Stabilizr %2 an�k9 R1�A�0R.~W.~P.~Drev� 4et.~al.\ , Appd�~B%� 31}, 9�,3)� Dye- �r�~ ~!� J.~HoughwNu 33}! 868kantrowitz-rsi5e�XA High Intensity SourceE#Z|Molecular Beam. Part I. Theore%!.! A.~Ka !�J.~GreyA�it %�Sci.~�$r.}~22, 32�451). =�kb akowsky�� � 2�(I.\ Experi��a �G.~B.~Ki� )�Slicht!� {\itE�J�3� ��;rson-pf6Veloc!\Distribu��L6�0s from Nozzle-�s''. !JB.~AndY�  Fennq,Fluids 8, 78�66� th#-ol89a Magn)�ly ,pensated supgic �Љ/n�  oF !�8K.~D.~Stokes, C!!hnurrE� Gard�M.~Mara��L S.~Shaw, M.~Goforth��~EA� lmgr\ J.~T�� ~��=`siegman-e�s}AyS , eX s, UniverI�(cience Bookw 986.� �1an-apl.KW n,��Das� A���I Feld; 4One-step absol| f�Ss2Sn $Ti:sapphir�� u��5 modu�( Lamb-dip s� � y��App�m�e\��k 624a�b�,ljalal-thesi!3>aziz A ��M��SeE -Order C� cex�q %�A PhE T_ , Ma��  (200�15�0yariv-qe}A. Y ,"�8 8nics, John Wilee�L Sons, New York 1975.0$nguyen-praA,\ T.\ N�y+ hernA�\ Budka�!� Zolotorev����\�3, 0134r 2000.vkroa�ra85}�����]K,Z ,``Rabi Oscil)�Oec�um�E> metaAUle neone�� a cw dye��A$M�31, 37I85.��-�-interac��}�8Cohen-Tannoudjia� \ Du< -Roc, � Gryn#�-Photon�PLV� 1992!��end{thebibliography} �D\chapter{Discus� e�Conclu$s} \label{+-di(} %Iis t�e ! a � of t%{�t- t�,ie %together!�. E�� � \s- ${Multiple �shold� he pttra�dio�a��(t is not cl�wh rany� he oedBLs are due to %fluctu�s �E].to��le tes or if�@y all represent %�exist�� of hyster���� port� identif6 T\se jumps as first-order 9`s. D% long.4lifetimes, how� �1d [Y�do%� occu9 4 points predic�3%sF��I+t( y!,A�B terms,&i� caa� though�� as %6ped� a ``�cooled''!� he��''.�%�D. We may ask just� fruitful�B�aI� will b�� teRPontext. What insightMz! studE�many-pcA�!�ms �appliA�o5�%4,�vice ��a? Ide!�rom�$equilbrium�� �/"tm��bb( in describA��.�steady9 t+ !]_ between ��%cAuOn!�" 4 paper \cite{bIX8suggests that u� $ some varim��ny ``'%''���� ignal %�exhibitI�nly m���il� but ��o�ini Pod doubling, self-pul�,A�si $i� ��\o�E^not�ai�9ρ�itO�:, �he �ߡ strongly ՟ng;!�yE� �thra6 !�commonze�. %E���.��� unique si�Qas��T��un�� %�� %HAۉ�is %ex� q���]F�? � *�e��1s,�� indea0h��r 8,t, would mak!is ihH quite %unusual. %i�Awe s �\ AC�e� ��E:2��? %��b-provid�gne J ! ive� �1U��} �N]9outpu�a!��uonant c�Pgrees remarkably welleEra�eq�մ�CX \ref:��}. Bothn ��.� &�Ab6bwe�e�$d by consing. inflne!ba aVle�s o �E�_ assuming �A� s ac! depen�l�Sq e Am� s confirmrvalidity���A@ ?��xim�n. AtI� glE1�0(seem surpri�,�cAi,e eigenvalue%!�-�am%�i two!i�diffe�@b-%� . O)o� hand, �iin gene��}� � d*o*" �is �YLpeaked (in fact, oft�or2 �~ %th% "T "�aI�!�j �!]  }��neg ed s�ae�ira7 turb%�( $\delta n$�IsmAcompar� ,o $n$. Moreo�if��' tend c!�l each�  i�e*th�own R� o.� ��( omly�broadly 5wed."! "3s,�� Enes�We now��qre# �y�.��aas�ional b�*'s��p&� stemI�its fu�%�Q��n ion,�leads!Man K proba�tAEa!���of no)3ening) �\be P_e = \sin^2(\sqrt{n+1} g \tint) \ee To+el� o>� w��mul�zic decay�verag��A. aѐ  62weG ��H $(1/\tau_1)\exp(-t  a)$:.�frac{1}{,@a}\int_0^\infty d� :A�^� \\ = V 2}\left( (n+1)g^2 m^2}{1+B\r�)7 Solv�!�res ,ng gain-loss:�(Fig.~�$ fig-!i -re}) giv��� "46�<$increases arly !��e-a�a"7A � .�i. Subs������inD j� �2� �� C s � a�*�%far abov�� �e�,bfig \center�{\ (\pi/�(g�))^2$�re ��un-It $ 6$%�� � ause wash< 6�������.�)!aE u� one-halfSref �m2��_ invari� rec��2 limietJ.._ isa��o much t� of %� -"� ,<dI as i�A1m� u50 %�A��process�� V� � r�or�Our:D� RiI& ��-�2��, . H�:� "�s� � tr�.�/ be�/r� edO an &1 al� scalm Si� 6�� w�"x ��!�A4���es,� �rw+ 5 ^ Rh!� n ou�s�OnysweAMw t5�� rigorous &�(� oba�� B��I I�[,�s E�id� A�f � ground�An. A�� 6is�Kv �  +lsooe�A ".q�4K'..�s�b��dU(to investig� qY@'s J.�Mf�6 regA~�>M nF*orA�o�"yts� `cur��L � � way.y��ed fur!�H next[ pter.� Detu- ive&�sec-d E�} %�w return!7!+sub�,!w How�wDl�"� repa!�%�nd*oA*A��non#nt��N most�\b�d� s? If�nee��n�� � �ce U���#trave��-w�onexasymmetr�41"->� posi�%� nega .s (} �.� �6 ies)��p�ul�  puzz��,tru�ono 7y% G�b���ct��- �1�R� �,� virtɺ�CM�Bloch��� en fiJA�e-�7+ m a�I��!�h!.$ite narrow�: $\D�@v_{\rm FWMM}/v_0\n x 17\% $,����8to a FWHM Doppl;&\� A��$<\�,s 13.5 \mhz Z2.3 $. And ye�&� E!4third branch (��9]1P ��) i� und P �bout $+2 �$�I2A�ic� ~�$+12 �6.�mDQ�j Q:2I. It� m�likely� �3a�"�"Il �!rsg�A5��� a �i��A�dexplo� conne��%�'s9?�c� \sub|I.0.Zt6�5:%gA�a bich5tic BY's>F(TW) *� schem�| quir�%U�split�%,�a�! �&8�9�s (i.e.\�&vt�lapu�!�!j!�s`0It was initia�belieZ�3U>e sepa�;; way3 .�"�.jTW�UV "� is$� b� :�.F%�'exert a .�*)E ��tD >��be direc�r� sibl�&a�.av a=� ab"v!oNx. To2%<�lem exa~� 2�Ja� fram;  re�ce)u)$ wo9nEE"$ $\�,< \pm k v \theta$%�&| 4mo�:� �toiF-� �ved � �to Eqns� eq-b�-1} ��, 2}:"(e \dot{c}_a��[��i \Omega_1}{2} e^{-i \phi_1} e^{i(\o! 0 - 1)t} +>B2>B2fB2B�] c_b 7��b��6�-ʫ B �RB:�a�no�J � $1�o%2�Scav!,kU, A/!2~,��A�I�Qqq0�%ENm'#*�&A<d $)�$, 2^�� ^2@ ,"( &�� " cho of�� A"6ceB.hbIn& io� an "��nFN�b� form�%E� -s�*ݢDis����0�A��ed qu� on ��of�:3!]-Xt� � to>Bm�suscepti� o!a"48on�$N$%���a l )&w5�Q]$ (see  tomR& � Pnh $\chiAi chi' + i  '$,$mu=a�f# N' | \mu|�@\epsilon_0 \hbar}m�%_L} ^2�(Gamma_a^2/4OE�R^2/2�er ' = M�r [/2�t>�N'69de�ye� �!]9�S t=�E�aX _L8eYn� � gq� �*E_P� ����"AQ�modif�#�AA�&� V ,e � � �B B shor�t vr%fe � ~<to�&lac����$%^{-1}��% reAH� �'x!4�r=��nA�C1+E�}" 1A:E�/ 2���hifz�Wu9�k'`u�o� %� �&���� \simi/2��{ ���t'm� e as\ �$910\� %� 1000�e��W��� 6Q(:j$2) n}g$�zU�"P.�&g*h a%w �T� !op�� I2�r( )5�w 9gZs, �A��AiZ�E� ad� ��. &X1 O �dB�%s a���@o�. al b&D%,U � �ar mediu1AD&�( U(1"}N!�r �u�� mbinL he*F('s"��6�� ``"�( � �-a�UnB %!��ŋ2�!� U �)� challeng� %.O�)� s} %2/%c���une'%��ngior�� %A*�@ %2i%Lb� & !�5�Bb(. %ResidualE� ic polari4"� 4nzero off-diagx(matrix %ele� s)Yb pump' K��A�i�B3f %� B]tan� F ^ r��� %B�"& A�trivial�rol� � Y%�"� A��*ysiA6�-"J m�v�&�&� weak, ($��5$\%)�'w��a>%�%� st %���(A~F*�� !��k7�a is�$ach1%%)w�0eng_2ra�$A=�ad�3(free space}"> ve!W3!M� becomA�im�,an�hM�s35e?}c;M� %�# %� erro�"��a*misalignAN2� AO %2�a�e�nkeepelg�3,{ej unwane$%t".�.preA���.U,ipoles. %Strőa4}+%�@by fiyE9&�� �q(.L�1&F-summar�Qp!�b�'"�� %-*e)''�ory� d�+!�+�"_ ��"msw&F��lJEa� %�X$o�as potei�a��GI���Q3!3� �ŗ�AeT�X t.�sѐi�1�t�(��3�F��3t�:=�)aTlso %�'*Qgi�A!I�am ud�T�  %J�0�U�,�* P� at �r�� %rel�t� O O. Mo.�&il#��5ֱjb�e�/%W%��Boi� � 5F %��er��/eCgRr�'! ��!�6#��s clo{Hto� �,M"a/�F.) icul�2conceyof unkn�'iv�a*�8 �s�,c ���n #,%�$�@�he �Q�#s� {FutQ@"� �.� :�g&� } C�24!\�sB7�,$�p�or�A plet��/"$;U,6t!�!.�e� Add�>al data+!��t�W����� lock!�9[s� 6b Q�a��,���i, �-$- �M cE+a�Q!�N���� vLe��sHm>l- play�6� c�5�� ru�3 out,�Dp��!`�� P�n18ofJ�s&�}V��Po�"$2I��'14�2"�a� detail. g par� l,2�5�Y16BC:�der�E�&� 9� c&�M�aW�OpeD sc4al2t*R!Jsj9] .]EF0 $g^{(2)}(t)$!^6.��B��9�.�9NMsh�2a�@(C.� .T6iaa$al maximum��A!27 du��cY:�)B��-urF goal �5'!�dto�< . bun� � 707 . AlL5%66��� A� ly squeezY(9(�a M�=l $Q$Ezme��ow-0.8)� iapn�8asMJ�kN �l��i**mit"�! �"�'�U!u �Z =oV^�q%� dela� "���>e -$ r� 6byY� 0) =q Q/\l�  n \r $;��$  n "�500 $9 e-2W- 1($-0.002$. C5_.��� .)fa�� obsc��� ��-��!ub��/Are.,k' s: C�$ d�;��1} �#methoym���9�4��A -Y Y8M� 1xE�Avia 8-� v''�� " *� �'l�?dde be�j�!d,!���orOmean, afA�z��X! �wc�Ee �0y�9E�k3y�ea�!v�� ��E��z X�nt � DA $P_m^{(GPCD})}�"% �i>�1M �Q�>ZnZNZ $! ��!�47ulamB�} um_{n=m}^ -fty}  h(\begin{array}{@{}c@{}}n\\m= \�.@ta^m (1-\eta)^n P>�,�\>�0%!��'?2u�;gA�iA,c!� >�&�1� shape.�} LinF��%� q%m�,a& ly rich�%A���N1H-22�)s�s2 S�"i����ssoci ;� & UN C>��thus a�* �(�*E��/�@ i� dra� �Gge%��lin Pm Qr"��@��A\�HiG vari�%�*�0BG&WG-fig}) Sbe�K�,&�<in�& APRA�I�~�7/�A+�U �(E#�,�d, ei��� o�&�7"2 S�}-:2 d� c>����i�A=W�h�rK%�*. �2�4�;DsMz �1"W- � ~�^ GIrapid >>�%AEe�'A�blv >�| !��Y�6oodG*7 �E!r � ���Q �&N'! %�.�& vecF, S1+&+S*@�Ye�jlt ver�9��!0 rue 2F+&7�>�+ys�,m:�2@�N�T! �2� . %A�ory�Q9� Y� � �=Qbas�#e�1�� %��, a ���u3 0 fI�i�tE�� -�)stood; A&M�s�d!�.vIN�J2 m )�'.=!;�^%*�*3%Apo�=� �%N/%io< proF� %xp���KtumA� *� 2�A~?�U��9��a�!5�'���,2_�����aR2@�5�rA��-�)pro� ���=�q%KM�=%, V^� �cP _' �Ua� �*"|ɦ. ub*�DInXu�"�4�D�Ero} %^ vBBX( �QED�!r .� �ct'.'Ũs��!�!�b�(arJn1� nd %i!Fpe,UinGE�Ex* i�e6�� %w 6!5Wimi�.�!wo%xll�� �4d %Ductors��(xxx}, level�� XXX}��R!� %in-Aed aIt:R�4�X�^enɅes ��focusd0AZ%�7A|nA�ip�9k1ȭ�A_}/%�Ea�Ł ly burgeo.%mA�H�,u�.]F�� �.= �� Back�/} �5MjQED�ticr�/� }2 Nr6/A4 ��a�pl!O�7l-m.L"�A�s.'a iu�-)�aiu�ngE�$1t[m2 x�a-�H+�7OѼ"5i�$��) yic, ���9he ir�or� � n exAedC]re!A@���Rex] :�gy"�c��'ih�!54 nner���er�~BaX�A��=or���!l�O lpMa�i��\4D�@it� or % *,� +e_7g�b� phenomena��1950'6is�X ��ofo�r� �b�N W , %� Jayn+nd Cum�s %�7ng� s, pri�X.�,[n-A�Z�e E��J-C-IEEE�>.}PJ "lRo�_�5�@ 1��-�b+} � l"WAMmC�=r&�H{% adv��NRyd�K�q�EH*Wa0e�wav� vi���T ed up new*B�i���mf"�G͘ %��9�eW'198)�u %>/i� !�1h byVz �n abor�U�Me�-dLa85!�In� *�5a&div 1"aJs�\�olSde�7i��-E�bBm���extWlyV!+�G mBo�5"%|�� mM #�r"�CaH�= ! ��-a��/�->�Tt*� Lw6BwHaXwex� 6 riet:�Q�(ng%NF u�!Dclu�1raoas, +-���,*_"] �("�"&��1�P-<-OL88}-��varcoe-iL 00}.��>0,zZ A90,mV -PRLFY, %wei� er-prl99,G 2fy&�� of Ulayiiic mi�� j y low k@O made�4p�)bi���=e"� s at"�a�� r InNO,4 Kyungwon AuMichael�R�%�e*[$�Y�og&84Y!~)|An-!B4, an*bT��de�K> � ��ɗVTa n3'�!�nguish!� 1s� ec %Mse FS 6�[d����S:7: 2j�orA�u%�'p9ulyq* 9n� t�ar,� show��*ontrasc m�:*�@�5�+��6�tE%�=�q�sI�p2�P.��0O?Sg!o�/ %%�t&+" . %F�8mo�^�ة.�}���A&� ian_!�<g+:fw��8  p�Zxemerge %Ean�aelyiDv��Zm�}'(,J�in��R� *� p��{6�-�1:�A�illust w 6Dorig-EoE#�iA H� g&� �V �L a��o-fL�@�'m3)�;cQ����eaB� s( 6&;ts upper%�e4� $\pi$-�M, Ap *�c� "�+"��it-�it�hTi�%aAi�. % 4oA1gp� �j�%Y j��L accor���g so-c)d� -�  HamiltoA��Be %H_{ac�r.T g (a\sigma^+ + a^\dag -) %\eey,key chBO �%]A4� \� � BS b�OJ"N�!�oO�? he sW41�� �]e): b�LG>o�J' $�+;!_*.\!� %�\e��deA�d. It!* be��$*!p'4�� y}i�m"  .Oba!)~ R writ�Kas \be P,-� } = B I\ g\,�) �3Bn"�of�� U�7�)I pr(c7e��o(�!2.�? � $�%=&T d�TLS$sinusoidal3%�fic��bd5(�$�ms �� ��&� yRE� >,A� �� troli#%. >�-(,!�b'� Q %Y�s}�[!6 Origu<=,:!"NeP'WW�+{i!�=[&" !6An�)]d}��7}P`�D� ierM�� r�G\V�H�-setup3�F"�FSQ:�"�a > �$�:{], M: E , C:-r�� , P:*  28&til)gle (cf An-OL97b}V:"koG>� uG%% d ł�{%�s~�IZ %�c�I�%�!%V�laYZR%5* T� -.'*D }% % %"$n��� `-Aa&� A.�+��9P�)C&]� K. �^�[�[ Ae %55*f492lm7)f�Im�&�<yOav A:�& �en ��e�%e� oz) +�%Ű� �Nɦ���� $! unit8H Fit soo�!c�app x�*��D�A0"��S inad5:<i2�!M� *� �2�#6 %�89�F four�VjoA*~L<��Sign �de�Ued: (15%e ./3� !jnonuni�"�2YY0. �+<���a��"6 ; (2)��s �e�g3 .in a %� "�!of"��sL1 ~ %}ffQ!t(rted); (3) ��[^��0widyKͳ�thermal�ireaʼnJic�:!� (4%B"�& 'd�7!D��U�6b f�edRo ��: %=a �<>�*h� .�4.j�(�M %Sec.XXX�X!���AeRl�A} sol @b�Au]- � %%�so�cAZ5%$ _.2, ���H��6��ae1(6y6ekN�.�)tupAq!6..&&�E�ic�4.%B& E&m2( #"KPrevi*? work�.;R�6�� fjeC�f�8U ceg�.a�Ust�'evhG� ���Qb�ABen�" �b�4}!A�&�~9Wk B#6$.�"6�ulso Sp&xmQ!Zs0)O"j F� are"U7;*j7�22J� �J#e�vul��8��ou�M�^ Carloq�F(a Fokk�ylanckmPp� �u=4-Y!�Nj\c�{e(�<"R3p)KZ.ll �i�ve*5"� �H6�I(Q �L�?cal�H��9p ���geMY�H�!�eAan�-�`�!*H�D� ba�%.R? e�&pic10}(5,4R put(0,0){>mebox(}�d462� IBFr �� +i��he �H���:�H. CT1 =.; , CTNAlower(c�� nnel#Z�nt, s= 2�RY e �!( .�8: vs.]A/%�^ B' Ye ( 7@�:�x*S��(F�*M4R�s_'A�"6��a@�#inJ�/�i�=< \Nth = {{\gc} \�( {g^2H}}� �Tr8�0� �2 >�wj/ $\gc,$ 180$ \khz int 0.1 \us$$g19327Uiv0$�HJ10$.?��&m~[�AR��ۡ��yp�bfigures N.� 30$~HF�47V� 40$ kHz (HP-��2� ), s�"w42�� �3!�m@K0^{-4}!kf�o� ſ6it�5e�'b %&�6%�6I.���n5��+u�9E.2-�1��/ aac� !�>~/iҡ�Zc�c�1�!� � "�a|-�i�1`$te�S�g� re Rabi"Z^D23�r ; no�䡟�_�*�T- Q F�)�F�" %_�P#a�g;!9.](��1B �Jy!\{* � !�F�9*&���& NA�� �+3q`nc#�der�'8r� �)k?8� �P \nth\�8� P� ula"�+e]`�ng at $�<20 $Ga� blackbody ns eiqh� 0.15��80.5 K A��*�gRct-���%���*9iscus7$in %�! aM�; �>�at 300K��nth_B e� 25}$�cJh ignoR�4C�D  e�} ŋ� e�0F ��lyq*e`-a fixe�lic 6�\�� �!E��+�� �/oughl!r�Kd�var3e�"�D K!�.�  �ɏw4ef�  U}�f>mm#%�)~�  y.�M ��!�.]��rea��`#easilyDat� .-.i�x��$NEAs A�~�-�} c> onMϑ�\nex\%��h>�$M�.F5D�M��!#i�a��{al\?bu Q� ��4��$u��%_diN&�[lB!� g>*�2 Nin�!ly� V� jjr tub^ ava�%AQ�wQ��,� !l�! %�IQ!Sm@�� oK%!oTG inferQ�3�#I!MV!��. jX��nsV�#u�2 1"�z��.�F��Az%�ing}  �i�*-,Y*cAs �(I/=)ap_A^���!ly avoidj no�}$����nr!�Ij,!?����e%l "92u�Temploysrb�K�9 F��:2�,A.� dnv`AC m�� �' �� �=��("ic��R-&M�V�) geo�V]Z1w%�!o i.16~ q� �QED} ��w!&8��}��s"Q`�on�ve t.spe~, scop]�ns�:2Sof�h"s�i>?Hi +a-nW ��ing'�  termined��6g��profiles�\7p�VLX��a��#aid�+K[e?v �{L�}� dQ .s} .�.�%;! rs(�� Nto 2gK��IHi�)�/,��&,r>voX�mi�nd5�e^A� M�%D �"��� �etiy�%�>% � ��tudX siQ!�st daye�8 � lamb-pr64�$C�^ -feedback2��(f�(E� j6�'^�,s, e.g.\m� lim-vcsel�)T�&me�.is�6�y a�0course %entirT+�=��1![e6��IJZYa�UQ��@sfp; %�+e,&�+ �)����2� M�Ph�pe�)�ogi�_ Am ai��� p%��-U�6�Ia�.a�a�02��o"r&�fin%BiC� ǃE(�i~qof� edo�'�)� nd�qov� �.Y#�=�%�a %k:�/)QFuU>s���$/ �'��5 draw9J:-4be0;�Y�X�4t��{q()�8I�c)���EBA��� li�v).� %% Tq�a)*RK7Vsip� � Es%��)eld�0:�* e�� d)A3�!��Y�OS =�H�.nd�N��a2�DB9*mi�r�pi0K 9/i�wA�� DeGiorgio!� �<�� 1970��d�c#�}70, &-L��LP�5�9'   isp �y d5d���Hy� r ""�[k ibid.*�0i8tɞw�8v�gYj%�� I*I��ys�ESi�Tto�$%+�+} (("c{)F��CF>ʊ�o6� no ��Y���>�Mji�Ab ��"�3oE�a� �a5)9A�=be�WaKmP��mb��|I��u&� .�ZJy>KAGJ� %A�aIm�Ro]}�y��U� %*�nd��H e�sCon~Yu�,�)�yjs�fby�8��4e�! i6c \�RaslAn�! .�O� SoEOl�6'�6A�a�"�!|*MMM��Ell-�&�{�a�lf�p|7&~m��S�.�v�=I,@�g�s�#E �#�:�,spi/�7* Bx��Rn�rb�6 S}VL� e�� [�kUm�$"�1i���i5� Q m�6!� %NA�S(St7:6�>"}@ya %breakA �5>�f���2T�!wE:. R Q��e�5?�$ � �+asI��^BV�+2@"�OF@ mlJ� by�"���Vts %%e"�y6i�x��^$ %uG�_j��yk��, albe)ma�vep@"�x}O����loc�~��JW&� ��@" &�cedfH��#$MaxQ œ"���rm"P7= m���#Byi�1[.W� a �JE*1,+� inim�p� ^��=��z1>��C�'E` %�=),~� vale�/q&�IDs �-#4�~an�'': �8dyÙ���@��8e"\i goesatg� Dicke�X 54}�wo�Kx�N��� $N$ &�1roo�4ACliz1Es6'U.0�ty :�&|,&e11? T.��!�� ��M$N^2$ �'�~�A�%H� l^ N$"�7?&�nc�<9�=X!���a P| E�5� auth�?(�kolobov� 97�7DArianop65i�$a)U@&rn|'<r�8c2x �o�by%��3�ts�guevara �� �orszag4} �"z� �0sWm&e�&rrg�� !�%K �`Haake� 6%�X���(?X%g� q��"�a�llA��a!�*g �#s,"nN���))S�O�!e�� hand, Elk � Elk-cH6},��3�9�&&I!�T!�s, ��s�B''� � fiaxP���ԥǁ�>9te1f@�:�D'I_-�6m��.N(m� ��t������Q hund;��U, ��e��l4.�NI b�T)2e?�u !��  ���iss�9G �u�s�e���nNN  )g"��xJ2� WN%d ar!�V2��:f-a.�4�#a�ing�Eprev�On�b�r�&tr�<��ey"ge��q#J�"� 쁕"�@>��X �<(e�/6 t&&�9}�q�Ja'%�P.wh�3e,A{�-u,�lJ.��4+� on�"�-�QL }�0�E�&�V��%"is,�a�C�s:"�'enume���&��A$-�3 Av|o� �y" ]��T� 2�>b � a%�� �� C ���r" H8 �<2�JFis I!���"�Uof������|J.!q5%M5n�$D�!�`ndberZ&�F }�%f\#�;�:�����%�%0e��=�"�X�@t�i\�DeGma�&΂ |��" � G�w)+|>p{M!�$6�:�*�?_M"�G�.��2Q"&)�>�r-veyM�"D0aofa��A��*2)q�&�G:"����ni/ITi m!e�E�r%��-perhap�]؈j�j7s& v&�Au�us"lO n�2b�2Q6��| a��d� why>A� � did %, -�"�t �di��h<n� R�a�J % 1T�s_�  V� i�bH a =} a&�eL.}�-z IXo4> al engine ha� %be) gras&�0[""`an�E� �qQfew�YkLi�&�N� :) wI� E+�,}[�E�Ŵ�%�-�0 ew}.�6�e"�4"B%�5k� "��%�a!� someM\%w + `` a"�L����o�Iillt""��i decl "Oh,�;I�p  Y�� �%�a�mC�Q=�or E Lamb)9}&P a touchst� of W��m�Wt!��i�Rc�G. %n�.�8\FafveI mli ad�e��3�rix t�a�s �^`�|�Ca�]>%6�0�; &J% %Y&��yK-�O!5�Ma�8e %Schawlow-Tow�Ilin�$,F. E߁c��ed-U�%�!('�26� %.�N�"% %*�L% � "6Om��D"� "5O �5b�3J6O�pr!{�\���Ay,4�b�8jxi�UHkleppner-haroche-pt.�� %So*�Bb8� -�� �&U��C�!� �H:�O"}O[ng�6l�$tes� },6!#irlO" � nd %2+#��ies��F�� W�o35�js,"�/`=.�!��:�x�� *�2a��E��' i�F�oLpar3>%N�_theless, u�#Do. U� �t�D)a� �$}o�gSR:m. )k� }, % Eup� q&!R~ g moss LIC�  %�k%)�2 ��lw�c�� (See1� opn}���Dv*�*�9�6' �kX("A�$�bf2UQ� E)mannUQk s�� r�2l�Ta�"M� B!*BQ�or�?�)8��- +). %%SO��mP-�<� %"Jbs (qu)=]2�#�� qa�, %/w aq2&�L>2 g+�D�E�{1��o�@O( enormg �;urcg$mmuAF<"ס�. u �fq �{!�p-4 �;�D�H�@s e�MIded� -�ADe2�=!�aJ�LZ� f(ic�6.fO��G %p"� i��K� M��m� ǒ�NiQzhtA0� O)�����x�(dJ�,ebawޙor�a�������* �Y.!"�I�� E� �"�/VT!��X> �A�"���LD�3 ���~)w a�n #qA�� a � %�(��!uu�it �j=g)8 (� %�1� t[no�S� yI�a>giv�v;* � Q�n�na��,l�R �W�(.checkA is!}��"�3 na�e*v4eo%%�%�p �&��wpty�Az�,!4mak�vsense)��]�p2X�Up9����s�Q!�.2XkiA'l�G�%a�I�o#> �)�� rl8M&V�,sbC"��"� "9�.��  �]�a�Rta�_=edisto�ingF5od�,�k*J$��5*5�)�6"�r�$A���d��a�Rvli `1#�.u��� i�� O0Cll.V.�; �u>D.m2�.��!4I�)��/�K1W su�R���-[� T%� E� O"��6b. 6, A;5rr&/�{ aZ"�&�)O�kear� ck (��`%٨M*�n�`o�Kb �@�t� �e�t a��>>���*�Q )%Z�: d d.� *2� as %Al�/Q �h�Zne�2 N.Nh��� �%S� �"L[:�E F!b`CW���-.. >F.Hb�>:>e@ 2m=ed=0B�Organ*�}!� � (�f�ɫc^9� w�XC�*"?!�f�D ���  Ee=,�] A ~�GUNI�A�by2C��[�,� ��;ALapp�* �or�p�.a�����Y!Y*-B29 t Ay@i>�*,� ��"eA�i�-s Rds���6c>a fair6];� se %par�_$aP<�l es*S�NLI"�LT�"�LA.��A5]�p�P�Hatu�� 0�!5y�� � BG��&v�6%�TRA8B�F;Jc%E��:A �9�If>r� %���QBS \ion -& Que)oa8�Z�� a.mp�Ja7�!*y?&(��2��A>�U<"��1cJ1? ��D�\�s?   d`"it]e*�=.LD ?���CanR��8qkN�I end.��R&[�A2jM��}9�"0N!�U� �B� �ai-EM�p�O �O� �r�!w expqf� %� �q�{w:R�I��`� and AR!U��eV���aY� �be�Ca �"S&� �Lt!��j�:�e0�2X�r� %�i�Qduc�� %M9 M�� I�P��*�[sam�@� �9�:oF�Q!�-�% re %� k'#A�"<4 �H�cHs;!V9G�y %im����>�>{=lg crit�+�suc.n �s�kO !X�=�Ŷm�a"��W.�a*�W.�� �"�1�!�a �8"L T&�.&� i;��%4-(c-&�I)�m�y��� C�nd�.a %acquiA2isd-**-//*-� b�' mput6^�T"<�a���oo �I�)�ra��A�!��&� %h�5!�{r�&e*�6)��W�X�WD #,�m%��J�F� p �d5Z�� 1�E.n�=$�%of $'A9}$� E�+ �  to�'��o+�isfTM�]i� %$\galV < 1��n9?iJ� \sim$B - 1.�Fu� 2�6B�>��B *N�~}T 791-553nZsiMi.X�Re0L2me�\ba6�ba- & M" TFi�F $tB)� �Ze �!� \ba\&�L�%}�Y�%�.= aO \9�triz\]g&�Ntmbd��791.1$ nE� �q Va� 50 kHz 6H� �-&?n�9E� *�LDI~s_a��a�.� 80.43:0.41:0.16.C%usa#A�^c* ��*�"�'vongU�YHa$�lu$.3\ \us\ $&eLPt�vmM9V�k\ba�2=la�0let\ at 553 n�5It�a�)OC�chamb�t��m�&�/ �؅a cylinde� piez�ans�r (PZT)�Rod�� �)(4#ing���95��i-"I^ Bras{5vDhou�5d:wF:���1�@�an- . 2��\A/ rpag{�vm\.� bX)%-as�ed���Mic}qս�<PZT��H �>�6n����JgSu��sm= ��r�Mk6PW��6�& A�&!aE�funda�=8al (TEM$_{00}$)"�A� �(iF�"�toA� h��_= �q���&wai�ss�by �}w_0�}� ({r_0 L \N)d���TP2 \pi^2} \right)^{1/4&��4�v\umV�}r*{�mCJ� , $L�M� s��� �%&) �tem00M�]�Q'Y k* n"�+1��>m) � ��TEM�ndZ-er �сz=���6�i�%�Dx(is 7.11 GHz6��2� �E volu�~gW A V�V\pi-�4} L w_0�VJ�"��� peak! a ��ZGeH"pD�LDJW gEt {\mu o�h}\�Im `�}nWV385'�rm��e64���i�*�Q�R>u.!B�a�W  �W� \pi}!q v q9ԚvU�Y'sO/!�h�O$�� tor �iu1�y!1Ga�an jAm=����g� f �h�Sim�mo�<��D*�&� tBNr�l, ``top hat''I7�e&gS5�$ga� for �%>:AO \1�{-1� }^{+ !�9��q{-(vt)^2)�{Er}"/�dt = {{9> ��g_=� =  }a�M-8�C�]2*�='?X ���\:�BEa.� d,��e "�\nu�i�i {cM�Q�E��)�=$$F�?�)8i*�8�f�_� PZT vol�"�B'��H�4Axn� �XNcan%�ca}F�by:�PZT��t�Nywo �6bai9M�24.67� FMA�� a��icy 6�(see kb~X�W68����QW 71.6l/V �>��# �NV82v%!)Za�v [-R o�%g�d�cZ�%: Ts�[a�M� 6��P$\ \rm{GHz}E���V\F � � �lL = 0.90�� mm}.='H j%~ml�2`�S.�jFO!�*�&� !#�Qe �ҁ!� ��8�t2 ��flipper�� _iS witch Q� A.e=c!��v�2<'af )�\)T%�n6�-��� 6� =< � A��roll+�&U�aJV(Verni`PZT-5A)!#h�Dt 0.75''e�i�{di� �wala2ick� 0.125��F�!h��� dri�?�� er @o�%G� m���a<')�6/  Iso�'on�4`Me�tonQz.� vibrs. Vi��o-��s��!D<a heavys"� nAphe"� ��Zrx �'#C���t�,�teflon>�d&| )�"e P%S �@+e�p����*� 6 ascrew�1af@bIn�"��%��|:G6�F�smB�Sb�ngdown&�3�f� � .a5^� !�J� "/LoM��Z(al (a.u.) v���. ��-F�st-squab� Uaf t. H�$T��cavc 1.02�$E�9r�t $F~=~1.0\as~10^6$6��u�A?P 2i��`�rI(a�E�0fre�al�Nge (FSR)A�*o�)a�� .T � , orf=iv�D.Ze \fsr� &�L�b�1f � R}  {1-R,a�5x {{NV&>��Wic�A��� �y ��l�7ۍtwoYQ.e.~$R=\j R_1 R_2I^w0 sume v)G�,M�m.UM� 1�w�~-���v�"-a_VC��� ;�E�!� lda+f� a �u��ex�!ial = � Q*>�Ux����"how�=*�s��nduv.!pr� ���SP�a�ڮ-�ed���jeT(d"�in Ref.&�{ OL95� .�AbsorX#-*�X� (mzB"!.jM�CpN�lo"�|-E<)�� Y improv��Q�<���#&Rzs (���(�IE����"���-of�-��v� %C+ mill�+ (A#of $1.9 m e66� 85088B:Mpor/"�7�*!�2}.) ��)%hdh, 3-10�2�2��"�&| . A!8s=�Y %.!�%��nD-�6A���'-"-� V-S!�7 . %�F,�gin� ure}� %\vBe{-.3in%D@ial{pict=QTS-fit. � le=0.4' 70.0 %\h G 3.1iFG*V�^n6P5@l& {tab� }{cc&��3.0Z74*[1.5in,5in][7 10in]{�s�j&�4u3'R v*[2in,4L8in JF�s� \,*T !}{2 W\�9�Ң�N��W(1YJ�c�u %Left:��Qof]� \proFbc�v PRL9A A� QTS�]�mm7�?ch"�:6.a-�H %"pٝojTp<�c�!"��,4 &4ry6�r� W ic2a9͝o "�Q($^1$S$_0$ %F5"�$^3$D$_{2,1�$i� (���ata' _�P!a�jhoriz _�&�2v���7� d� up�7�� %s" @��$�G�� %Das�� "6d�'�� slop,��log-logi�. %R�: (a) �malR8��y j� [J�%�7 %��, �) U4�seedat)s� ot{\��0c}/2\pi$=-0.6� /sec%",(ii) -4.8 Gh,p12�ko��t un�(&�^%�2 �U�, (iii_wS�]D blip� #68�<at 25�p? (b) :ΨA�p�R$%Fus"8!"!*�b�[f�$Ay2$ ppm.2�2�gl�x�띥)a���G�J62� ._($\pi/(1-R)$�#$R # 1$A�� 6� A� $1-R "toa>lo�=ILaays?`��� >0a&= $A$,!P�! $S� e9Q�$T@O R, h�b.{�b�"S5� M�j .M�{��"S8�@S0�o�!/�m &��$T["�>�.�+few&\��A1 t� sE�=co�$N�Mךs |nm�(w o�>CommaM-AO96$Kcap<of | $A$ �!�1E��<p6XntE�e!�.� m� s, %!'=� Deb �j�q�su�#��a %!Z-�,)�h1�CmultiX# &��qr#. %� O"/ei!@� 9M6= put %($�;pto T^2i2 ^2$)� �2�.(��robh �UamI&�a$(A+S)$B�>? 5�!aa �o]��p�[.� . %E �achx? � R$sum, $A+S$G.A(�!%�2jiOrC�'ulaU�Ono"JZ, p�bL)leR� A~co��n"8 vQ�M[dex`,�!F� <%�a%b�poe9aa�Rlom�w�ns�%mp�Q�e��!"d9�%� %�S;�>. Wi*� 60F,.�]L)X�si�%�.�� careL��( a�Ws��%Ien� ar���aY��# ��V�e�.�atD�_�9�%� (0M �.� 6��{* k {J��*B� -croppedz"&L- 4�@nj��Za�s�$: (i) 0.6,>) �Hz/N< ory;&i)F����J3�z& ~&2� "Dc�Q%N%5AUOA�-�e\a\Eb-ppm �.M�� 7a,Bryndo.ä�@Tr�s "�$��e cir�Jm�dqD�n�}�i!gg��a�6]�AwL&u�z�R)fh[c����IRu�D* F%� a� �9&�uf !�� !�f��*e}"!܎�6�*&/+� �  � \new�'&N:C�q�����"Uv7� 2O�e� xxx �:On>R�9�sMLmd*�-��A��}toN�"`� 0�7����cw�7 �=Wa�(��T2:U>?BVwr�oin�$2$tfABv%A�1� �t H`CiOm�ax�X��t*�Fp��&!)Fa*".5�q"�j"�$^ ����� �t���2�^~P�[�B�m��kz� �� >�z�+ ngth��L%lQ Gm~H ass �doug� no�(yN)iN�M %�/ %(��3W��e��n"B;2 lem!�a:� ^q)-�6ow \ll 1$"�!z!)۩(��a�b�. ��& , r�V�,9\���Q�TZ�U�E� �4IE ��L�v�v f �vAsB[�]��� �#t�jM �6��8p�<�D�����1��6 fast�)�Al�;!%���ta�̩bA#���q�M(o*B0P�U�at,�&,C�g�SA�'��$2$�a#�MAh} rvalue �#App%�x/app-twf(� f[2|#inc�%ly YZ !���"�7 b}.)�Z�J�2��->�f�${n-vs-N-TW- * "*�-�GW�%�8of �Cde��Rp�$e�*�0e�K�!e�$.)�"Q�"!.TWVnd�>���3#.%88in,11.2in]{TW-�}scheme.ps}} %\end{figure} \section{Atomic beam} %Atom beam techniques have now been studied for many decades. A typical aIXapparatus consists of a�Utainer in which the sample is heated in vacuum to form a vapor; a small nozzle allows � atoms to escape. Apertures are placed downstrea_0collimate the%. We h!Ptwo main requirements�( our bariumw-P: highF` density and narrow velocdistribu!�! {0ground state.!�ub1�V8sel)�@: mechanical, opt �r supersonic} %\setlength{\parindent}{\old An.� withB�spread!�needed!hTprovide a well-definedL -cav�interaEy< time (i.e. unif!�tra!&), !,!�(nsure that !�-� raversing%0hpump laser field prior to et' �A exciA_toAG!hA�coA~te in_8on ($\pi$ pulseA�di!�8). The ``class!r''y5L9� 5�5�� (via e.g. Fizeau wheel) has several serious drawbacks:�e�crms �d, not�tinuous,EmAMoN,l efficiency!�low�0wo new methodI�[!3I�-�.�%�M� ��(b�$de4pee�a$laboratory:���/e 9!viaQ�%� ing}u�aaa�-color>/ �e� Xvely preE�g�sNt Am cer���,+$an effusiv�" A !!W%= � a cylindrA0, externally ��oven madE/,Inconel. Co1�-waveI؉�usmmump tbe-� �, firstago%�Lmetastable $^1$D$_2$�T%^�o6s$^2$4S$_0\leftright��$ 6s6p$P$_1$ cyclAm�m 8lambda$=553 nm)Uzn A�acA�:k$2O �h>�6A a til!Wi�tu�[ �58v 6s5d �B�5d2��� (Fig.\ \ref{vel-sel-result}). When � most��b%P� $v_0$ is Ibed we obE8�$\Delta v_{\rm FWMM}/v_0\approx 10\%$ � �}$ly 50\% re!�!o}��~V� %�F, \begin"'@\hspace{-.3in}\no�28 \resizebox{!}{�{\includegraphics*[1in,7.1in][8in,10in]:`�\v.f %>K>5eps&�(\textwidth}��@i B�� %J�S \capa${Left: TwoV��  Rai: �� profil�ArUR�� . IA� is experi�(A&mis u$resonance,�\ reas�FeMW1yM1i��zZwh�,probeW scanned2�� $\di$(FW)$/vm8$ 13\%.} \label:f} 2� ��$% \bfig %=�z5*[2in,A� [6in,5in]a� �!l�� s-smM�YLzYrFQ@PRelevant \ba\ energy s��� ��I*ionY\Dark ��s!�resent��s�L� E@(553.5��8�| (582.6A < = Einstein A co��4t; BF = branch��f� !�e!| &� 4Original micro���} %� )E�5 '� .  % \>S" 7 _ Back�} .��t: f� many�� lica!s@, spectroscop� a9 � 4ferometry since�i� ven?S�1951 \cite{kantrowitz-rsi51,kistiakowsky- and� ,-pf65}. In� ��(, adiabatic�1[ on ase�! exit !T noF caus$  dram>coo��i�e!�m��mov!��Ts or molecules; randomo rmalQ�iver�+$into direckinetic I�9adp ,H, net flow ra� s g,S  muchq er, n A�an�;:� is solve �� ��(lems associw� co1��.� s:A �*� a w 2� of ,ies� Y�.tB!�:Aa6} R� :�6e� F$closely foing�design� Ref.~Is,thomas-ol89}�+�was bam A49F�  source}yin:� �D$previously�lt }��� � An-PRL94}� h� "� �.E�vst� �,-,-filled piecI�4antalum tubing� ua6Ehol�s�  drH��diagraa� showa� < � fig-9�-!�- 2a�� {a06.5'' long, 0 in`meter,E| 0.01&w�thicknesKm�di 3P varied from 150 \um\ 406 . Lik�|m�strf � nd ytterba in b M`�a; vale��� rons!�8 negligible dim�or�Lon��8%No carrier gas!wa�\c�line{�Z!w" }}&� }d m"gn� ;%s �^P%�rQ% R!����bya y���cedur� �a�UJ mead!w cutI<a pipeter�ot� 1.12AW4is pinched fla5, a vise betw�!�a3$inum blockA~(One quarter�a 2 cm Q�Qrod (�$by bandsaw �wise)~ins��.��!#tPmas8M�qne5A12-16 g.%Vtop 1eUofX&t� �te?i�, �l llel%>�*-.B-G1�mount���iŇ�bed hold��o posi��-��s ts horizo����t! clam:a mil�{maX e� 0 a 1/8'' end " remov� bout�: 07''�!Yfu� lo�։E��KiB��%�``Tne� for � ��遁6I�s a �surfacA�r �86 h, �p is d!�%minia�2�3s�&� e�1}1$a1 wo screws� each! Q�copper��deA�AXu6� conn� :tub!w��nd7rough^!�Con%�flange�3/4''y Ultra-Tor�t]%weQhe�rod�sE;�a 4''���cold sh��(both absorb�I�'s larg��� r E�%�,onducts curr# �up!!� � coaxI� ��� Bor,4!� mize�bay magn� �sU�%�-)��mv5�N m old ��� edAwa�� Ip)�1!�1/�/E� ���.g�-�3A� A Proteus]�6o $return pat��-r�s �i� ][ a� ���6s�{ual feed%��a�E � e dr�1� itro�� u��u&5ri�V c auto�er)�208 VAC �} input%�0-230output)� J  �.�step-d, Bi 1:8 !> rA�"3� ula!^V!fA{eaE�or A=��%I� (� )e�2 pair�C1.Q weld!�c!�Fvoltage�1bAzmonitoa�by AC(E�a��-7 m)+'O� si0-5!l� b4 0-1000 A rms? ;� ���;$re circuit.T 2H, 4 m$\Omega$a�6depen�A�� tempe�r"t�� r+� AsG pow��"s�!�t i y� u�goI3�:� MaxZ0Boltzmann (th��)"  2| to.( � y2� �"F ���ic�!�R;EX\fft\ \E��am0let\ fluoresc !�ofZ��A �u alig�to!M rlap�\sno\�-��a= c\axi%L�.| Wdet��,by CCD (see R�$f{sec-imagg). �2-K5,by ��wa foc� �G !P �����op e�!r% � �aIDoppler-I���2�(photo��uETg APD (EG\&G C30902TE)g�1qw�f �%� miss� A 500 W "� pin.X  fV 6 APDE>+ �n XY \l��n s�_ sca� ed lOA+gl b}ed edge���mirror��Fi�R�vela(}� w*R�D]&�)�%�e"�sA�K �N had aU0!�\%E���nEL� an���>  600  r�0% three diffe�r�Ds. % � �e� peak�and %com!��RH can be clearly see�4C �e�:.R9ha  eriz�!P�� � FWHM� {\ituc}Z!�"% ���1b��(${t$} / {v_0}$j�v-vR� %a� un�of)w����52�$f_m(v)$+eq��actual*:v$f4�oluaje�a�shape � accq��� %9isotope? fE�L7 � broade�� effe I� t S 9e ��� �� yY l be�s� e�!�� %.� %{pic X}(5,4) %\put(0,0){\frams(��#4 2�A%R9�)(Al)a54!�5� %5�2,3!NAt� ably[0 = 800 $ m/s,a[rrespoa(to 1.4 GHz.H�&w-I�� -|,=�5�6��]�i�F4�tE7 | ven %�?��?ym" E^�4inZ�df@ plotB�F*z signal!�s%�rpropaga�XI�A� a"T`ofB�U!.�. Zero0.��rm $bmulatane�"-�hLamb dip6{D Curve: Gaussian fG6�Q�16I�8 $\sigma = 70.2�ne�lr� take�to�Y,� findF�HM�$ = 16.5\%$�R�"^��;'X&-Mk (c�&�� %me!!���sm���)|c�i%�aerJg\ "�N� .�or�F2.��res�8���d �%a5�& Altha�y<j�u ��a%erY��� thus����w w&$lyA�a facta� f 2)� re!� �%ad�a*l �a� . Fy#� �% impor�ly,���U%g s!�er i�an� 5"� } be%� non�� !fI�l�"�  lN Zn:I�e� �farB� thve.2tQ!A , du� !� �!.TaE&- ��0>�fsim� �( a��� ~ k" syst�r!t�(. Due gse=�,N(� m&�*� )Hi" sis wA�w. :� . %Detail"� :! %a"+�!y�b�"�� *�F�� a�*} %Coupl!to�,mode:%�e�a!0�} � ��na��= M�ongstrai+� a� ar-bA�+A�$t must be �3��edTyif rea�"|3*c � !�o� {%eN��]��H9 �.�� ade re� 6(-)by limi��* ��  aA��)�%�%o �Zuld ``�.'' onl��MxE�!�in612�%2 . H�xAnq� �� et&J one-hal�[$waist $w_m:�h�"�� �Lvar)H=G��U $1-)�6�)�%�}$q�finite9 �p $a$}5&2�l�In or��Lq�e�!i-�w�-0�i�!Ea 24.M�"5�f06� 3 mm�e� k�H A aU!O�&�is&e"[rgMis Ck �� *�I� �I��$-e soliYg&�(/" �/��\ )&��&[� n,j!low, t+ea,pencip�� w !�j%j�� PZT � J passage ���r� `a7 atta�a|� �s:\2''�,inless-steeli�cta � %(New F� XXX)��)soriente�_� �ɰmodif�!preci�#�� h6D a�8motDed ro gS (Nual �2$ MM--3M--R!�A ��r F1 MC-II)���ut���chamb�29�:�) 10-pin�/ �t�M�2�adjust � tweaked s�.at�.![vis�a"+=��Apf(Ij!`�3d %�}�� arl�"6! *- ( MAP%�ja a 25��by 500 sli:stO3� U � A ��%ޅ ��&em %"2�an XY]/F{F� ST1XY) �c�� beQip�i$N-�="$1/8$��h .ee1���.p6m� �,3 flexR$ѻ>� mQ�a �O �!!���be��enaMtuo��A !p�g� � yet L @50ccomodate a r !�*�&a�A� $avoid clip�/h�vM� �} �#" 4�\br # teleo*�s�#e�0, glued togetYw�  (n Torr-SealT7 epox� �UP(12.7� y&!�� �4el, �Ba)I�:\ � !e��� �%6n^� zY- *[0i*�-3in�- ~�*�Top view!S�asmJ�0!]6a ry E�,6��4ngular��s,Y�`��EM :"X8m I o �-I�. NotU wn: X-YFC�"��6.6�)-i" J�\y�15Z�.v.5in,81x1S1z">'C�*-up!xAa.�9&�� W �ʡ���9�=�L9��af:)U�{:L>To�ha�.�!�he.R� '&* �*QeX>BWa��o�9"E& (m�' by i�`9ee�� crib? Sec�*se.� B� is=6ho�4�f�;in :Rm � few�:  "�'r& !�Z;+5zݡ,Rep�8 ���� �.?5(k� ed;�-po��� fluctu$ s in"� presS)l'�ٲWman��M� �a�%<�)�&hespixel nu6 c> E"�inU.4n%�"� k blackbody*�%A��"��hY�j^\bgN %\)�B�M&8$� ]��- �y�� ial �es-) regio�>f�<9c�9i "S . 1-f9_>C� . 2-^ ⩂�*b���mod orG�,�v���D A^A&��*RA��-���!�%��6=\ *�#�3ADak ^*+re�>��OK.% our*� �� w�  l0.oaE�"�"�� refow"�&B(�"e �5o�. �)4K ���,��a�4�oriB'4&�>30�somD&� *s +$aljalal-th�}R:�'6"u&�8a4�!e�19rj66*�A{�Mj.�*fO HU�*5i(ducy!�(3FV� ��rcept 2T"�U�|)� �1#A%��ll w��'en!�? ?I_�B":B&�1 shee@u�..y a*�  ar.f  (H$+$ L-2251-2)m!6( 6-way crost#/a>� ��&s���[E ea9� �V/ �A�ly�/aa w�#��.r�3� ongeq5���S~ Q1�j.�}�(l)Visol5+oeBt�" unnecess� �@u-@tly���~!i�hoaE0� �}�� [ m�or�ed 21 c AD ![; M+4^0n Qgj"F�lK $0.05$'' �re;"�%TgDte�� �*s?)8200� ps,!wA�a z .;l�Cof $6.3$8_�ig� +w1oss���+.� ul�ar�ve�2'' �+e-Mcoa��+h$n Intellig 'Mo�s S Pan LI2 (aka } MLC-11) D�%5�!�U."8g�2 dOof�o�-�;�%c�%!�&B0Zre��u��5e�� opto-isol9BA!� f @r�!� �6�,!  PC!cP4tandard RS232 WCa�A�!!rI�Ep�1K 3 logic�; auxilia&�s�){ 'to1� o%nوal�1�5s (de&� ��-�)�-55})� >+&� z{�\ca ._B��X(2U)-*R%sE�msJ=$�y�� ; 1E� = q6�.tA!�6�d� oJ+�"B% F#n j�y%Ofɫconcer@M�>1ailA��%_�'��� ugge�H�/��� �2  t�Fl %%ball�8c�/�,n{;A O , but mayM>F,�> s %l����pa2���h���u!o9(. %e�� �(useful dynao�P =5`�4$lem %a�add� �#>�aEA�ond% �*erU!�l� ly %,'�%!7�mex_B �la.b�,�"~MMD�d�ty!hgo(true zero %XC Xaj%%c�'/cQ k�gducXa 553n )KgaN�!�E';� +=f�"-[�s tpum�z� D %s�H��S � ����%�-{�(�s,A k�:� F iliz� *� 8�k} !Htunv!��A,�G��M�;��o�*v=( 791n�"�?�)��-�AY�B da Coh�+P899-21 Titanium-Sapph 1� �SI�� 8nova 310 argon a (o�0%� t 8W!�my2�bvi��. A �6 �dy�)"oC�5G J0�"0��ua, N2Ei&u02 ! mSgA1ic&XB�e�dJ2#\Rhoda�' 110ea�a�2@8WF�a9I)j2�26jE�&H2Fhe�J2�a 791 qVby �/�& FMf9eA} J�:!�mPTi:U�!i!�=� trip�1>��#>"5FMA�A>techniqu�This }il�2�d$!��>an-apl95�>An evacuq@s3H.qy"� BNC 97AxprQJ��5�Pa7)%,&&"$$fmaB -sigdi7 7�1\� shif�to�ovy DC off> E�A��q&����* .�#L�,(�g� FI%fo!�kZm��2VE*V�f!maB�F�� n e�3-4�;G"<-� ree �A��in�0I � >Jst>m�L,ly 300 \khz\J�!�A 791l"Nip@i}}*�5nŭt-`F to 7J�\ v1ion6a z"X �� *[1.�6in][7"�L�Y��2�DU�1��A�A�ofR� v�A�! 6���6&K m�owriA 6HKV��Lo7 ���&� &�B N�:%�!e.�a~�=� �%a &�5Lq�.t��ref�i�%�Aspl�r,��*��m���2��L���Qto 490 CmS��BK�Q� �9)Vtro �q�"�$�,c lam,�� yDeamAB�Vh�:�GZAe&�9a n� af�ET18q�= O@p%j�yT�5�; &i8a� -dip��^�Mau][5�\�H5�*wP2in,-vP"�M64}&qP1em��e��.{Detu` ,�4�OQ�-u�& A�a�Q� fft\z�2��%5% %a;�6>�&I-s�T�(V um %�% �"�a7� EA?u�T�+ %�"�"# }�H*�(�R�M mM� %2T�-�Wma�Nm� y �?�* ��� %ii<o(0a silicon PINr� x �# %ac6Joa $13\ �Smm}^2.9�%��7��7mQ;s�[qM�"BOat��D77�^�~553��B�I�Y� etup�F�6� TU� Ic��d&��%ta�� � )� summaYE��l *3 A�A<�Hz "� , 100 mV� �Geak Ntud� �� q%eq�M|u��ougM"*P o�Gb 7 �� box�V.��JU F��A�aotock-in 2��� !"��p � �ii� .� typ�9&2� !JJ!'-Q ��VT8a� �Z�њ- )fDC � _)/"�� k� ͈!&�&yse�! 2n2� R�2C��sJ 7�19 MHz F8 ����!�� judg �bL4� use . �"Rq$U:6 �k" � day�6da�M�Tg1O)+Oft$se����"/Sfor[-2D��/_r"� wo�#%� iris�7Howe^, �T�T�L�a!�R�'-�&y��.� U�s (;�Val�"Elli�J, � d("H`m^�V eata�t�N4*� *�( 10in� � iber"3�. & !]U}eV� ���aF*B s2� T-�$-�q�B��IP-m!Z7��n�E��$to�*"���(e\.GW %WE� ��~coust�m,o�AOM r� ���&2��^�8 -y% %�s%�D veryz8ist��b*�/ofe�)��W�A�%^�AF��#{!s-crop��Y.A":ZQ_C�I�6E=9�;!�%�M`Y#h`-bR+� � *A8`gU8ng&Z!)q��(�-�,an AOM VIDEO[A.�:�����in�,�[uc�46+�>I�E�*�I%A{ �2as6�"^��.\�=� $V_{PD}$�B&�7X0 rget"�K$V_T$%FAV�� s n&f 6� ofD � AM�!$9o  ( � m{ion��'�M� ��o imm���a6i�Ze!e� �C!��0_ �86h:� �S olarO n(� (PM)-�i�qʝ"Q�&;��!��?��A�( �I"��PW�! 1m]W New� SP-V }eXDv 8W a 5m/ SP-? :0 t0A�*� �VXV|cex"{"�D�V uppl6FM- ed.C )I�l�!=how!�Q��\3rrect�rovI�baIr�Qbc�t�?x�8�M!xw7�redisc� yka+.�8g� rKdef�9��$�!V��r- � 2> s*�&?>t!HRs0 |FthD F �!a�ifica�&af� !$�1N�I���%or�s�B�>: � spo"�>��3ova��a��!~ �U!Kla��O� cri���VEPQ !�M 2�)9G�B!{)U&y (i�%lP"aE90 �s�Bo�$��m,���!�%�,z?G!' 5åm� �w�c*�-��I"� jr�!�2&�?I�� r!*�Rh^:  2M(� ean�N��� �`��\ }�GndZ�Iu�=�2label~ �-�&�=*Z.�!O��} tQ2nSec.X%Q�K37a���.� p��-B���!_e�)߁��"\ E/�� emerKP�"G=�$n asphericPs %&]4...., f=X mm) J�P!��a V�;�!aRC�4ra�A�, 45-�1-��d dichro��V� ��i�j 6�9�iat�"Q1fftwR^��y'�,o E.:.�>O40of�K� o"`)� }/A� �A�>JH�=�  D8�&��)�%�%�E�*  P:S"� .)O*�^�8{A�e��*���5 ( �Xafixm�wo4 4 �9b�pboard6r9"{%6�to�a�i�f �.-^k�We�6W�!(�"� e�wJ#4h�X9�"&�?�o nti-Q| U�  gQT�  h7qina�ceE� c�m� alVY��Vi81O-�~aI(A coil-gene�$".�[Aj6�50 gauss�ly_to� &�of),.� (per!#ici;6�axis) E��'$m$� tes�cm� �[r-at�4*&&�1s�# vels $m=0� occu�C.�Yd&� } l+��E�"� t�*I�]&�>!��s quick%+�� b] � a��| %al?Ao�>Hi|(caJ�5�I5 � e��  %�2N ,�3�5C63+*�g al u\-!8 %A�ei�s%�al��?t�,s6t.  GwX6s�:�a�m�B� 9�A�m �'�w�&!9�e�.� �L��i IacA42��fo�%�away �i�)O9 o� Eacus�e B[pv"Z�wE(�ua�/t��#�:�3W�ri7<� (6 �2 e�<dM/QYtwd7a� ,~�lyk ut  7 apar� !)%�I�!'then � �E��;��x&-� :as�D v6$ �.�-L ��rvh{��per&:I.p:G@adqn},.� �TK66B:s1�}� a��;/)aZ?q �xinvol�7�)�E�&�! 6�7V ive \�*� )&�0�J!32lY %��.*bv!�!�d.�|��M��x , no&HB.�\ \OHa3�p�=:5# gnal�sun�l!veBRux�>u�d ly observ�s~7 !LjMFAMK]��upstrea�J.����"is�:��/�V/k��Eto�$�!ai��%���� . I�nxus�^ai��1<+wm f �MA�%� �I� . A�5�'�M9!|d�`ly  w� $arbitrary,� njdm�.i? t�H , $<W.$� 1�2�y6be��)Non�=M�i�5a��6� =�� "�5 %mis��%.&L : [x o&� 2 7!��<"{WU��i�* NR] M"eO"� .5� �K �����e,5explore4)Xw�<��4a�Y��av�Y�����6spD�4J�9a3�ŞenA�d "l.T.��2m �g�!����w� "�,�r�E%�CsQsE%�5� OA�!]�] +%%��q�c�� �usIdevz!� a�( x%��e�3mGZ-�B@g���ai�!Cf �S(aac0Ck� ��R�<re� � ���e69��5*/6a[FqA�aA}�")^d��G �Zs�""yE�ll>5�q�IE)�wa1� Ga&So�*�6�%PB�#��<�1zrxcA��sm@^i[ ��a%r2bc!�]ve�ne�^v�+�� ve��A� ��R\.�%d|lue2or  I4���%8I�a>"� untilb�� �,�u��&) on e�� c���5eTShe�ٮ}��rd�To tes�oX$���q�- � ��a ``s Zzp"�[�(fev I�����$�MV1|�<.f�m mat�S,$$TEM_{00}$�� ��@i/*�F.b��Oa?�-�hqt XMje�Imay�P"� �=�i�cUIp L%���-:�/Fa)�+� A4U� "CCD� %���=2�"� A��))D�}!Mg ZE��� . S�z6U!�"q:-pMm�tfK R�IT���2� �^�f�{� w(.�p~�=���rA���'E�t �6�kf�/�R een,&NWll)W � ��.�-\&U W:N +io!!u�%(��(as� �q �:+.n) hda%Q?6���E�y"�} "ӂfm9q� dat+cPDd(z pu|�J�$d itself. �HArԇ)�A 9���&F��| �i* onA�i*�a $v$,�\ t_{�[K@} = {{\sqrt\pi\;w}�\ve w'>�Z<�#� [-�We�su# ^.�#�De�a�%i+� Fo:om�$leao�dE�K! g,\be P_e^{(1)�\sin^�� ({\O�o_R . �2�] \ee Aׇ�- �V>Ai9Hs}�xeq-rabi`}�< = \int_0^\inftyZ�%� \pi J�2 v � �i\; dv� qB�o&�"�L!��> (propora>�o �TrooI %�Qy�Fig. X aal��%�I�"o� / v_�e 0.30$. %\})�!�[0&[02!c+�Z"��aMd�ld�+Adve�h:D�$�ejC�}{g ��.Mjb��u�MW2�2� [t]^^R5{q�2&a��4�8, \uw*4Gr%J �&|&��,��d�O.�: mon�of���e���*eK ,$\�' s$):)�B)&.  )les($\�) ��#2T+�-�$��` j5� b��QL� &�K� not}Q# d. O�=i�|$.��bL Mo��InZ��A�0%4�: J� ��-�YV inea-��F2�8�n�es!�ach 1/2+y A��mA�ed)z5�oa7}�unj behavč9 A,�Eeakr �F��uRrG(r�b.%�a�$y$.��/�"o([um �.)A�%�� --��eɆ!&F s b�re} �N���T�Y � ouTz� V  !H�"� �ir���ke As a9%ul;{� kz��$\bf v��wivei�ω�.k$ �sIx�7�)q� pol , ca�!a �-i�wK\u5 chirb) >�3 �M)dni�U:Yq}!�N�[�� 's Bloch �j_esA�a7�qlowly�A``torqu�c%� ten �� dic d-7|.�"z �� ntitaRosL5"F ���lo�~wzw10�ct�S�iH�� 0he $x-y$ plan5$ai| !�"� �Er �e�J62�a:,de�e �B?g�ian�&}�"pv�~E$yariv-qe})��\Phi(x,y) = -k y + \tan^{-1}(y/y_0) - \frac{k x^2}{2R(y)}X\n�� k$a5�]� , $y���p^2/\l�@a.E� Rayl�g���F�u�2u� curvGne � R(�y\@�(1+�qc{y_0�y^2Eg���^�~�9.a��6PA� d�d  �����bc.�8e~�JX6]:��:�V�f$\theta6qFi5`n�l"MzJw�0Z [� U!dy/dx)$)� $%�!�sl� A Y���co3$A�$):%� �.k%�[)�(|y|}{-(y^2+%�)9� }{k} xA2} 4 y^2--} 8 }} x0 ]E!GU!��)S0hos6i�Zv*�Zx���7w;��5_P._:�6i�y.8���)1J,� ��micity�!<T8 Vs%V�k ?� &�#F�e�i -�$ yfFa� �$k \gg y��a�($x \ll y$, ��va�feas�7 'ur case2�Oj- )�%�5�} x5��"-&�;s��u&wrisv  ETw�)w_pE {1 + ��^A(� n%;Dod?y�at�#.�coy�s,�6] +��o]�UG-�� _d(x��k v  m10��f26� X�$g�ʹ2\i/o �t��D� � @i&R@8is $\Gamma_g = �%khz�im[� 4m = 7G$ q op)kEU�s !CA�!� �i�/��are %xE @\dot{\rho}_{ee}(t!jQ�(0(t)}{2}R_2 - �+ m)CBE���.]gg ]+M�^] Sg �SmmS)kmj5R}_{2 1IY�R_1+ �(.z- �)�El rg! )6�p1 p-2r-FRH� H>O � ee}$Vv rho_�$y  mm}$!� 6�, .� 2B~&R ies;%�-\�Qv1[g}!. �e�| � ,i -Ege}�/egi ee�����#��-_d%�)��o�l�[ aZ5 liy$ a)% m&s��� � �&.�i� on�Ut Rabi?�f �Ca>� ( \exp[-(vt/�� )^2]Y_{ c{I}{2I_s*qI�pWF5Z� g �I �:��on-axis x%"� $I_s5�&=|&�I_s�i,pi h c}{3 \l� ^3}}�� 13�/c�D�6� �� -sim.~�c� nume�k�g�"� >"�"B"� �$y$. �" $y=3��5.]�wl�#� let� ab�iS"d �+,</2S-����w+r $I>!�"\^� bp.� X!6F� R�B%�i } Ak "(*�!{oI$&8C�+er!l"�os, &8+�\!�i:)�t& H�0WS�KE3.e.! ��/ *.�>&jU )-9.�Itaq��relay� �C!db�#%wa � 9 � 2:13�A��^ngg&wo{�a&� �V|�IbL1l�B!�� a-cc�bj! vlJ+�E� ��-? ��A/a\�U�07� c B�GofR���% ll-cp*>�!�!�|7�e 5�>��n�1�[d �!rret�.Z�*�! 5x��ys�]!$ � 10x�1�I�� escrip��1�./62s)w=e \�20�*n ~4b%F� 2�2e2�h1�13fcZ< ion �S�,6C&�dw�6Pc*^8z�*FH5.V��v Muew���S"�Oof19-��w?-�m��V.� �� ��"נ � )fig"�m%&�j���SAO!�tJsAW � �6�� Lab jac� �B�ng.�B ��6� 6�11a�Ulen�reAn�1� in 3&88�#�on; |=A����3 ����s,78�[P3nd�{� *�=E�k*um�kt�ich��v:�*$g%) . F*!r��2%�#1rh"�< m4ce 4g@ (Oriel 53890, $5pm 5$ nm��|0(v�21`iT�D)=mi"?�+�i'sN�p.�A.b�coȩ�: � %(Schotta{is��J#e�=n!G&V  �!�Q�! � z�֥�{Rh E�$$T > 95$\% 5�aX$T <$0.1 �Fn�DB"O���i! oc�E>>!_s C-E�*p�Af�:I�0!M��I�sՏE��a sliccar�<x�vAIE�{ht��4 bS�����us��R2c SA�t�� / Pl�me� s Sensys�?-V �O��Dmo�_�4ŗ, 1/2-��a~mat, 768�(imes$ 512 p=s4Kodak KAF 0400�E�ead�digit�9is 12 bi ���ب�}=�i��Cular}{|l } \h�4ta$c$2�&�� 1 f.l. 2 9t(typ.)&6\\ s �x9  & 20/m& 1 5x|�\ aV,456,�& 2.2aO�� 1"�L?�� m>V���Eps-1oE ��M�Ian_2Bs :XZ 8ѥ� �(2=�Q�!sA�L a�QaJti<l�>c '&-C.&��T )�[�!#] nd2% Aq% appea�a]b3�:d"02�e�) jF�a�D/  mB�#���iQ�5-�B[1�AEwi�c��6.E+F5�%�WP>b�g�C-��ed &5W�<}6OEq! ide-!l�2 �e$P�5A�2,{6 IXar$0 in T� yQ� W���Jo gD�,7 " �sw!�kD�[J�� hs&�4U�oF (�?" }�za$e�0h�Kst�IE�3H6pos�f1is #n�T5�]�? �R4/%-i��� "t�pn�%:�4�"�  5�PF&f. �6� �>O # �9�����u,>pro���;�.��Mg��&T{&Y��>;uter� �man�XcA %T��B��v&k�i ��t!%�4_2-m�!eIA �1!�#�_few %�:�e�@DEay calib��m�%ZbG^K,ݱ.>&G�6s-�T�e0= .W^SF?{a��2IE+�myi]i?Y>��a�&�B. Simi��NZ�ker H�*�Rq}�ic"<7d,{��*Uz.}�a&� T��OE�ɛ �%m�s,c �1 subt�J�+ %G~A$2� K< - �$ tall6�{ �� ��~cavbw.�-~M��-bma� [����B�"%YN��ejXb:?-.� "��9e �$a4ge,Fs�Mm(,>shlaGv�M}�K;� >�o FP6o%*. !g � c9/A�A,!�D e �-*�6�#����>>)^��]�� ed q*Ĕ�F S0.��VR. 2��"d�(2��SecT � -cal�n��!: .a� %����4 -q0it��:6=��;a3X1��K�2!E q""�5omp�JEĔf�d{log�Ew�8�g. �FSB�!�2N6$U?'an��l�4��!�6��DK��� ��Ch"1���of\7! MT:�9��40My,�c�!@P!at,T���'%k�� W?n"|to'"֙6Caf��ga��-�pW"JW�la� The a|!zR)��� dL� fs�^�:V"�7��men;O:x.~<cMI2��(�Ow"��:"PRN}  uE �� � ofE$)�knW. K5}�is� �J(gni�X.��"�De�)or�1]sAv^phe4 �p�J%R�$e�q & purposes:��g�[h]"g %�}{"Mc"N%>�H& Type & Bias V & P a*�%1 & C{�& 0V? & Fin� 1a!�,�T �Aj\\ %2U.C.Y96 ;.EIP�vN�5H3H69H�>I��; \gtwo\.�$ ``start''.�%8u�!=�APD�in c��.ZVtab-apdlV.�A)�n-� �bF�-� aJS�1R�C;E�c\F6�A��ީ0i!��Vd�%An>Noo1A(ץ �)-��� ^�!� Q�B��ss�Gx A(�?�Uon{�x�[rba-F:e�: *Q ��ur PMTa�Da Hamamatsu R943-2� ��JRC�$-2�u~�u a!Ur&_ 6r (Pac�a6ru� 347�tuF.����h� dark7ntk+Mbh�p!��<biB*����-1500V��"�} !� ��A�R� 50 $C'A'�Rri� /E�� a Stanfo�0esearch SR400�`��e�Q�o> ��fiD��VDE �-� ��y_��1��3`�I�s��L@�!�y\h�%�xda| thr�C!rPMT�ZVso?�~z�$n_L� %sat&�"8.6a 10^5$ c�C3y��ed.�i�n�;%�``�� '' ()N).5by� n�=det�<{{�%Aw) ove %r {1`*�(5 � &}9�}9 ee ��V0�I&[��Y ho��!�a*Oo. i�� s�wo�%.�X�(�MP ���Y{5Odse� ># �M]i�U�pe& ���eD"�Neq�.�F�BGseg��e� a 6��ff#� ��� � ��%O� !A�Q�.�w�� %f*^�V��y7@a�A�mtf6 �"{�&!,��e �� A \e>##".d �j;��B �� -���Zb�o�8 �� �6, �'bP":M viLM�n�z� { �4m 66Ų1.}"$'"X E��B�$Pop�Wof�3�I�er%� ofQ�#�!oC~X-2A7I3 hF&\�-�"a% [tv E�^.P�#!�!&�(I Diлof major�>�L show�!��a���! �d� %Som�be�A���!1r�:i� xC�e[ͷeF�2 5�b!n Al#�R�� f�V�C��-�o-Ё OFHC���Y gask�%Dql�% seals.�%��2a�2a2��T&� !vvac-sy� �%��E�-�Aj�7!h�.u�cK (VarS�VHS-4)%1�I!�speed�O 0 l/!3A pneu�G-?/�n�g� va�(4(MDC GV-50000) P��" �a�nter� �@ uit RN9rI/�t}L�[͂edᾩ� ]�1��a9�ے�m� )�m� 'e�[ge�k .me�F"�B���F���E��:�i���h*!�8 a �_P�� 5 O# djoi�^ro+�o&!Pv�s%Op�^��!9 � 5R��r6�Ba�rm1$,)+!� uW�de� gaug"}si#q rW -��, $*j��!�ly �q 10^{-6}$ N��! ���fabl!Aby MDC mXPr���a�� ��c.��*I)SharonD:  MIT �ral M�|e Sho�_F���o AKa�S�?F�� Vo1  atmo"d54a "�L���)v�Ireloae �c{ etc.���rw�)5�@-�� a���/v��oxidiz�� Y6�EV�?V]6ϻ/�iX�_ AIt%�i)Zr�ult|E�out� A 2�-���iida(�ell���I553 nm %#_�)S���\� V%Kse��Y-U�now"uoY��cal�_���RX �O3B�a!ent5ca�W , let:clarifiQe j�28y^a :�c$N�1&�L #I��;� ��c&a boundA�. 'ia ���Y���*rawR W�u�!�b%b��Mo~��!-�.�F>3#tophat}���W�:m?{"� ��t ' area�3 $j3�vnTA�� )�� eyUa�$��nj$-J �==\pi} ���b�*3.r�5 XB� �%���V9alAg 4aKfil&9b "� Noq at�=�>!�at eachIg-�&� Ju �t�F�/-fs ��2�*��f a&�$��p�#af�8a�M�a8�  Y� 1��F�� rast�`A��V; # ��5��w{�i.�����4�%h�"d�1�W�Q"G*�`NW�}^U�֩G�^"�QR�0f6 ` ? �$�dR�mt�]e �:PH�6�smB�w �V-��� tAB!��01 @ �x*_Psi#xt6]��"# t0b�"$& sG%!�.d ^�5b��õ�.By.#u0� *"*(n"� < �y��of6]0�%*̃!��%� by� e n_�� \eta��% } F_{ W � T #ex�e � re $B="g6�$n�aal� &@��o', $yB<P��gLP ed lightM�tr�]m�d:�C9���6,$W$��!&)[ ^Amr�| $�� expo!ȅ�. �)+< 1&a��B����-�jB*�[d"��eo��h V 2�LT��V homoge_���in2= Ő�aj2�j����2�/:�>�� ,es,�@�66�/ ��k!"#,Y was&��uas� 2�c�ot77)��CB�\)U 22\%>% +'e6�Faf :�c)TLARdipB�ra�:pO8rE� !�O!z2�ii2 �;!�͋# q|�.k* + �sv/{��%~ɮ%al 90�r "� �u=%ue .~�P�tA�i�}�. �#=� � =6a}{2K |0^=@d o }3}�37�2}fT } {4� EL>@CԱ4 d $ l$&�u�]+)m%� |;o�!Oo�GII31�Am)E%�iv ult �Hfh.t2�� �7at J% >%A���U  xp CEZa#otropic*�(m �aJ� �a� �ƁH� ���eu2�s��EoN�q�M!8pi(0.5)(2.54 cm�H{(_ =0.019 sr%���3�(��.B�)�ur{%�%WA�E�-\^V}fVdx�DnHR(x) * d{�Pr}  ) R �%��rhoœ��s"Y ��$@%:� 97@=��Em{r}$: �E؁0 {\ga�F I(x)/Ii}�{1+B � 2< (d@s) �DH(-2(x/w_p)^2) } {1+bi�m$\ga\5�19"��^�� No �#� ;� &[?K 6 K��' ; ��D;�?&�D�im�= �*�c!��o,*2u��j�D-W �al��g� ��viCQ�_Y��� fty}A�nE'-���2�>H$m�Y dy\ d��rho5�����a�C%��e!���i�*p-�m� ��&�C��� !p+] 6�1am tal#> s �em)�%����@ak1��2�.��&&�A��E I e (axial)�� v!;Q �Z� r gaJuJI � Q "0a�u� n Re��� .�a:�4553� ) of�p�G11�5uw��4��6mSur��*�k7-*f- �z2?{n"�� 1in}E .~cts,7mbox{}\\��B!6�.>�8� � J�� 553w�n&�Y1P�9�= F6� CC�9FH*!/es}= �20�al aberm\BC. "6!����a&�)�a�͔��%dIa� sam" QGb"�CFM 2j$ lyJ�%9}�H�� aJ��*�#�K�E [/�- J�$4R= 139i.�$C � ���K@�3� c,"F�>'P C = \cdot*CCD?�G"=0.0625,x%$$&Y1Z 0.35Րw�.um��cc�$e,)4or51� anufM$rer��&@'�ޡ�!�$G s 5.6$�|c���ADU (�rog-to-<a�vit)� J)� 's Tndex 3u���Ѿ��"�.� softw:�msec. Hok���&� ed>Hccd-nonu�}) x)��eS��wPo�po*5a�2�!�*��2� )&�aNm�duh4f_e shu]A�yE�lo����ٞxtr"\��� ^! ensa�)�1I�:.xA� 42$ (�oc imw )^1��6i���!�mFl����%(cpms)�Zjk1f�_*1 $Te56�1rop-offLs��5�� z.opZp+ meX9-�:�"6Z�O�@2 é�&� %�"� by�]A�l 7R��Ay!��7Ar��` AKa�.�r\&�wA5fit�!i �2 a Lo9 z�!�F?�34ϑ�d�c�G�Y��t$9*�= �MHz}/34  , = 0.559$ ��� �/ �~ra�_ �)N� �L#��Q' LR%�����uM�!B� U��� � ven^�ly�6���8 �A G>�f0]�,)Li,)X�� 10 \uw finfat $N=1$3 %g&� ,1.16 %2.08 .�s�8 CCD;�vpm�!���!0.862.S�Ze�oi�-n��2io�8A� +w!Ve+d$!�L&�Y-��-1$na��n_d�  (�@T}{2(T+A+S)}) \gc�1�s}' AOM}PMTawe B� T=0�A��j�!, $o�0 >�"$S = 3.0*�+"��㟅a�e��, absoԛ�U*�co"��=-(�7�!emL+2a�s��n�at�4� q}�;(�. \gc\A�>5Yg;.i!V!�*t2f swi?nAOM�iZ"�A' ^�� 1c��.70\%)2�-��.`� �Glu��r�)F-�,�" "�#i�� �dLu�E�� U#he�)� L. $&� A�J� t!m sno,%1$� �� �OT�se�Um_L�>!�-��[n�m��$per $10^3$i�� �>PMT��n93�QO9`�.*k�2��T�] ��a@su_N!afairly ����e!�;��+�m|d 0J1f`� 2���$Data acquiZ��7�ol}�e"�+!( 3UH Gate��}�јPC run�  W�C s 95�sme�� }�routin�Ore #� in VPas^�Aclanguage� mjK �" , D�Gal KFV++F��?s R�����(be bin Ap� x�Papp-vp��:.�6&q� autoq�&b�$.Tw+Dt . "AD�}5�Aa�� ���c �R!Qfurh)"4%�:com~/� vOA'� �/��gin �Q7&F7lH7"C7Devic>7L��&7of l*g693q�� er &LIiRA�&AQ4�a EH IMSiB��mod�Wri��@����B,(KK')& 0-1 �7 �PORT1��\\^C�&ATbeRD2DAnalog �5e\�UX){8TL�i�J�7�OUT 1-3�CѬck� A4 x�A�trigger&4& MUXx 1\\ ;pu%C��$VU�@& 10V(on), 4V(off�? 2\\ .af!��@;R:.;34�JpQ< &�umm�&�om� u:� up"�B%GJA�sub� �2�2+e�� t��)��Cs��sI��Q�aSus�#��b*~<.��]h." �� ``off��}t6��S%e�-0.1 �6��m�%�-"��,u#}�����a�!"&�=�1#a6"6��ap���:3� -�*�5�*/ .���t�� � pM� �[[� 0�w��+J�OM � � T!�couRP�"$1binA� �:�5�aA� ��)m +J�&3 AOME*lA�$ ?�9 !e�;AW�-�$�%i|mBڟ ��o �-��As�*� %?er®�-%E�on��J$��a_%%%�ACip�,sults chapte�r? %%% \section{Cavity PZT control} The c �^frequency may be scanned through the microlaser resonance or locked onto it. In some sense a sM�Cing experiment is more general since it includes variation in atom-c � detuO . Other Ws �ire�l�to�kept on� while oB8parameters are {4ed. %%such asPHsecond-order correl �measure� %�a%kinuou�s)1 �maintainf \sub6�%�Hing} \label{sec-cav-s)�e} For1�2,�!��is simply driven by a $\approx 1$ V ramp signal g%�`ted from an oscilloscope,!4�ch sweeps in 'AUTO' mode or is triggered kpulse MAC$TTL outputdcomputer. To create bidir)A$cans we de�ed� addiA�$al circuit � a`s $|V_{\rm in}(t)-V_0|$ g%aAV�0voltage $V_{ -$�. orI2%6 source. >0$!n0equal to half�peak- height o ramp �al�hit8 and sample PMT !Z show�D Fig.~\ref{fig-pzt!}. e�y !7M% fF$*s_!�pfollowing: %\begin{singlespaAl Penumerate} \item Movee� dens�j modulator|]!�A " : Turn of)@\sno\ pump beam, & %nH$\fft\ probA�pa set time, usually 300 msec, u �ff � � !�t�n>��i36itoi� c��a��a 6EH of d�about 4��sfLStart photon counterf,collect dataI�Axdur�� }AbHDownloadE�H ;tou� vi!0ria�onni� \end.<%\capa�џgproceduraWSI���& gramA�Dfound in %Appendixi8app-vpascal}} %�?tab�? ity-i�A U�< It was occasion%� necessary�adjustE3HV%�offA�I manI-ensati�a slow5 drif�� would�Wwis!�us��NrsY ?!�N� rang!7These ����;8re made between)�-��d4tervals so tha� lineara� hA�ls%'preserv��bfig \ceI8T{\resizebox{4in}{!}{\i��4graphics{calibQ 2.eps}}} UPa� transmis!� spectrume�&�Em�of� T s. Sideba�/sh!|��carrierAM$24.67 MHz.�qXI2} \e� �����EW-"0!qD emI 2�$of a very A�Ɖ5��i�no��s)knt;u resulD J��2��backgre.e�Ps level, due primarilEߥ|scatte�!&��mirro" ��(tray room l��,!Csubtrac?by�. �O!@%� pztpmtI \hň*{.5ine�]n�� ~$\r�arrow$a�bBi.PA�m��n-G�`typical��$or %a high%��N . Horizon�ke{  sponde���.�� .� %MVV X  Av1 AMN2� , �8��*K0 technique. r�$\textwidtha� F��cavV-| !�i2�t %��� u]JDufA.A��Ti:Sapph� � is upe�ed $100$a��t th��own� $113 %� aira�AOM�-� .�F�H#��ed��6iD � UR$V_T$��matchD of one;R�,�ou� �l� �r"I lat $\omega_a - k v_0 \theta$R �� also us��o switc� �oo| off. .U -�, a2.f-Q1v \!�incid� � ��on �L2is foc�?$an APD. A� ��ar��he5ge�4a fixed refereCq��� �a value � imately!�-third1�%�� � � T difgi t��d����fed�tA�px L. If��0strong mechan�z or acoust(disturbance�ur, th� ys| ca��%�� or\��n 1 hou!��� 6� � hpicture}(5,4) %\put(0,0){\fbox{\ �{< 3 %�̱l:� schematic$�I-A_�_E"!s�  involv��/�Nreq�u�iM�� %!���&�-� }%<be un2-:$a maximum ]�� befo\ B� �o far��y��;[Abe reg� D2` non% ae#M�appliE…EJbox c! �iM�o� hold it<A�by ��!2 its ��� 7| use:�4�u\chapter{Rhs%IAnalysis��%-I�s} %In to!�estig� a many-atom��Ųperform�wo %typA�f� *��A� Micr�eY. } W cribA�!n% saݽl4�B��-�(supersonic � AD ly uni�M�O plin� 6�r ޅ�! goal� answc �� qu!9(ons: (i) Do-�theory:C)�� %� }E0� E.�} $\Ne�4sim 1000$? (ic multipl!8resAF s oc�k%if so�ere 6 i) W$ -�} J l)�the� i\ s F��h�� saob> ? %,� sistent %���rstoph�ra`@ion? %Two method%� establishA�y��%�I�m�!�( %employed:; F� +a{!� %We9� %BO both� �ed@AFDJUӭ14��} $ Stud%�>��ablA��i f!<6� :#�a fun%A\a�M� g�Gapply�R~��t9�� PZT. % T��)� is %�ao�H�-�G ~depend��  %�. � 9�5=�� in S�i4RH. %� AGe��J�.*%� ;&;aMF 'a z 2�%� %\% ��o� %h ab  �v %m�Q �%� h2%� J"%9Jv�1 sB%F 2K:E �x c� XA�x � �m ��*�po�� ��� ] 1350%�1730 -�ste�z 10� 1450!) 15001�2),2 (c.f.\ Figi�9�-b�Rr})�%�fluoresc�.%� r.�6�0 %5141 cpms ( ( per milli� �o���)~6b�r�~�UB�����MC!~tp% MOVED TO METHODS CHAPTER: %�RR%�SS%54 �_�>&%� � �!���e}�7 se %W�V%�W%I�b���7m��"�>�a } D+%9��curve�r a)J!\�Rie�� i�s�Z 2index30}�%�0}a�a��y�� fold��ackT itse�oe� � � � �Q%�in ""/� d solix d dashed !��ntr@A;�nd negat 5^,��ively. ˍ�] Z��� bin� 0.01�s. Eff�qf numb�"\ �^ s la��inTO �z!b�!�-�32� vs.\ 1!�F.� 48.5��� = 10.7$) "�.v��r���F�2� 60.9B�3.4$)N�&B��1BY 2� 80.2B�7.6Z21�2920B�2�100>�22Z�0�%)1�:Y26�&r., 205.7�&, ."��i19���2& 659.�$�=' %)N�19,5J}195M)L.t��9 17v�95F�09f�7,3N�7�� �4v�18F�40�gRv4,4N�4�� �FM24 2393E� Y352i�R�3,4N��G�G3�1z 2748>�60N�P,42� 5x�� Kz�288B 636$� S*&>'O is �. �O� a\ o,SJ���a� i8v  2986B�5N  O,3J�8�-�S12v� 3014B�63f~2,42�p� �)$z7307B�67fs7� 32� n����:U�2x325Bk715ipik�  �*� xto!F6,c �y46���5z\43F�5f�5, 3J�5�$clearpage �()�z�355B�78� 6' O,3J����jmjF� 6h59B 791f�1� 42�p9��"� )$z�362B�798J� O,32� ���~L69B� 81f+�K3J��J�JzO399B�87N� )Q0,3J��MMMsz�400B)8R�P,42� U+�e�z1458B�10j� 8,4J��2&2zt514B�113fX0,4J�9s��.�C�#} As"f]" /s� rom zero�/two3N0s broade�# i 4�C. itud�At�#30"�&F.�N 9}) a ``s�''� ears��!#ach�$. We willbelow t t� is a�#�hbranchD�-an furt�1.��;32"� N�6� jC.to anoL!:�# l�� Most�(gnificantly-"�0s exhibit sud!l^�5eJ %.K5��� ��$ *)1eepse V�rrD(�&�2�+!=O ,-DKS s� %soluP�Ab�/-ptt x^�}1-are in g2 l quite d%tApsha!2althou14 y overlap4 �"g,R"�%M�poA$ve-5>�� at d1 or g,2 r (m�#<)5{##a/&�)ing.� �z�Jz�Q�A �ed e�2� havio�*%Surpri[.y)hI4���t �oe2�Ehv aka}*�e- )1-��:�1�entir 'f�*I��e�%>6Xparti/l&7a�!h#4��6Cwe� ct b���F4ls %d�,op��"��-�"�- mall!'agree�poG/%@yab5u{5 shor�1A�le3ctu�1U ^ ��!Not;/]�6��'�!iIsQR��!]�(.E)"S2I ``�''A;a�-!Za * $\Delta$ lrever2*� w+!�� Y� %opE)a�f51�M�tic eT�?*-�͑-���#y�VB� }: �e ��]�.�#come %��r1c aver! ph�2�p*rease�Km��$familiar %S/�"�"�!�A:E,?�I XAw�4��,dth (FWHM) %x"R�s�FD# ��5�$8 ��(i9splitt�6�!traveU&-wave �u!� 96?'39Y�0:U �(ae��Ef�h05y>+0was 27.1 \mhzE0*�0����veloc52�*ribʼn?8 $v_0= 815$ m/serT)w�f�!�} tilt angl�#$�, "�83$ mra�9A/ on{P2&j��:�`c�=�3a�(z@�'�8��J$,%>�&xed"%I�9��� $2a�.�ic �5�_E�� ak plotae�4Fig w0lot23det135}- 2} *�ce�31�!�s�9=\pm13.5%��8�\8e!}2Zqa5 term� an"I"�&i� )g $n$���E:��(�.)�=:"�)}+B*����"�� %.D"mod� 5~R�, non�)co�)M U ��%� 2�;Atom, �M_ ~3�4} Cali  ��A�_%$):B�("�. to%�9best fit.�*��*'ak['��:2�-M^#%M�'s}e$$n = 0.16$e�jym1 ^3$ cps o�� PMT,)~no filM=. � bOD~1.0 s,����aMi� �s{ 1. z jz��Ial9.i�+ � 25 \�*s $�!�nts$*Ui,e 6 2.5� $1�Jymen=a5��56\% n,er )8originaluQ-��A�E2mYw ~�N = 1:�V �.�$(%)1�CC}1.A� 300 �:!X %͇i �?!��F�% e��3nd�+t�  > factT=f 2.11�6G*y��?m� *� �� ccd-.}�T�,�/@e�6��is !! 0.55$%\)�! 1������9�<(0.80 - 0.20) N O33$%`.I"�.al a��k���-5225, 33\%�  eU �*�9.�@#1.3x (A()�xxx (i�)AB!�QRd %% s6 arguD ofQa*w ��Ųf�"�;! ;ifq'yu largb1cer�@^ in�4 ��� r ab�e����M�s.� � � good�����#� %� sim�>Z/}��3few"s c^. supp heA+id�of3 i�#Q<.& � �0��sid �f �� and  ->r  most�~ly�% image/one�E�5i�E�(�symmetry.6h *h i5 onen��W�r� choo] o� pla)�I^q>h �in*$(way: Circle�8 $) rB% 3��0N>I � �� '5��/�0Je:"� s; cross ��$$)e�2��0v9�FNcB�v)C�a:. *�!!a"�9Bstates~�">;{N�=f.c B6Y � %�6,m� ��\ej&� � .�  1&� (J&�EtP�v aWAa�0� ��BV: �(<1K=iJI'9r,J�=�u�2 . CBBʌQ�Z~��2!�(�(: RJJ ! L� � &`Da"�(:�2P �`>� c"��quantu.�5��ory&`?�.r"�z�%6�3��!e?�*"�.�J� is,��, {��. A fai��e! 0of ``outliers�r�?esent�(lpoints�{�)Q:� go!�&�� :~�� M Yn!Afl�T� �"K=9l�s Acl�einU� �@#J��o ��is ,�V.20}��6�50}�� *� 5�ͅ�8by�s 12 \[15  �9ra�: �;�H7C�s���hrCI !=samZ-r� rto� %a� H�)�)tMHquickl�|K� C8 he fae� Fa�A_��U er�; ``sm2''$��: o 2 %or 3U �� I� next�M^�:``!ner''.�dU6&H K3�+\;A�findsx_ medi���  exis2c�%$2e0 �se�"� in0 onse !2<I�% E��9��m� s at-$;yapjOsա (not"�F�Ch�� be�con�H red)~�-��2F7�� �s 12.0e4�B�!�J ��ayv�Line:t60"�6�2&�zob4�h20���h!�Z&�/NM n�Mr�"b�*� 0��^�0��f�Z�0��.�06��@B�9 !�N� o��-�5��^�5��V�50}^�5��.�36�"z(� B�35 !�N� n)��p�p45���%24� ��l��!N"40)���4��=�9�N�>��� �y���B�ҹ�� n��O6�a�K��)�5��=�9)^� nI���2��^�2�z���#��j�� ir�K&1� ar�V�2���Q07��&�2� 7<�P�� ^� 07&7.Di&#G�|od]F` �&�!�S{ s|al� s. F\D� U4&�� !�'gofRP� ed0��' �&"w(RP >Fo�Y|'e'e^ !,^) , �ZW A�. m a�}F�%t�G predic$I nawPer`-o�t�%c�F. (4)K�`�^��' O�Qat:& ":%Oin�&K��U Be��&)vN[ticular,�(� 8"u�Ha�ro">M$\pm 28\� ,&rL twica*�B#2$ ��" �&A� E����J�les�#an�*$17.5\�a�F!Rmodel���&)�}�"�Uoct v)6"@be:�x��+5� \vu& E�z �st46�.���.< %"� sV Z n-vs"�(��=500$�%�P^I;~U�2dF�B#�&4 2>�8I�G��GQ�-d��%�discus�ssi�%oW!o.�.�!$<)�[%�c� } S�seAO%�u4q N�&��4a o&�!�=^-m��"t)Eto�3mV- !7FigureI�!|�B �%3�G���%� � a�Ns (R��1"W(U����AR���toy�-Mhu�) *�&R��te� exc�_�!x i��%|*��p�1�*�g&a�i�!R s. ��(�.e2� |�Rat a �SŪ�� �a�G�*� fu,"(is& ���!�-�q�2�4Nex.^Ya2�E�M���J)LN� ��:e rate&��%�A�[LQ� ce (*|1" �D'l�lo&}�(s by %?u�F\ea1"[ >�DEHfWIn "�PsoM!�sy!��b�(qB:�to�Tnc&M 2�y"�%O(J�r i��%.b/��D%��-�field� R y.w�ndu ���#:.>!�c…e2�N�B���N %�"U( =.-�m��B�b.''�]�D.�V�&�Dc:�`h/~�` Lock1-S 2�V�:haFu^*�1�to%�F�5��3s�R�&gAZC# 1NUwT� (rem�1�.�]acd��engag�#5%W) JM9aa"W(&�a�X~#&[K9�,<i2(a�M �� +a(no.�Nor �=b _2� N�|F�N)N���&��&L-*�1�fdD�&0(``unseeded''��); Z�`!��"�M x�(.�r\WAon,E�1��: :R��a����)`{O&Mc!�repeatB�a�N2A� -�Hoce�B'W% �c�{8-ne&$a ref�e�AXIB  ope'+�uA(d of|()�^�.�>�. �}6*z �M��I � T;/h+12.94� . *�%j4 �N�{T&�Vs�et rXed: (1) .�n �p��-E�%mpt�SI1s w�1p�6�2%-ur4A�!�(2_U&i.\8 8.sw�U�N��a� E ($nG\&V^{12}$)��!l �.�) �1�o . W� �.�ff�=E���3��o��is �-q$��� A �\gR&�"� $$ / \hbar \3] �4 ,1�8}$ %�P� ;}!%�Js�J dec 'im�1R %accul(�%.� :M1)�(�U�>^� b�� 7*�;%�A�.�Gb>fA�.?�e�G=�#��N%:2e?;:% !Us$'U��:o ��$��$]�nj  a"f ��.K2� 9YPe~�6C-�&�6���<��qe"i %2� 5-j��;"w[MIU�Y�A��gi{2.�# `:�#  vL��� ul� ]� A4 P�"� � K Ilq�:6���3ie�bN�0"#"bi�;ility;� "�$+Zg�">lec+7l�$l�Y�6��11 �c� dS2 ext�nly�0,�0�10^5$N6r�� d)#F�2 �#m&�9�%&"VSy&3i�ed.2�� en nM�7 iy �lik��9� le�m!4 � �bl h onic�� ch o�8�1ow[om"�$�z� c to l in�M�kA6�]1�^%�Ee$.=`Myk��Ara� + k %U�I�gto.SdomZWx)�oveB?�u�a>�\ll� h�fi��2st�:� ���8inv�g�*��i�.r�ail�nD�io5��% pret�HQ)��( seems stra�gforwarM�.�'4A trAqv metam;&. %assum��/uU� %4ol�8it eneHe|0�&)��Xa.rz'wa�Js long.�3��1YTb_A�0A�m"� � limiw>E�AEr�rof magn�A� �~1-cre_b�>�i�*��l&r(0^5\ t_{\rmI}+8� �c�scL=� u& K!AAO|T)a"ii tunn�: K& =��)� )�!#_ �0Fokker-Planck�9s1\ \cite{Filipowicz-PRA86}< t_g��, \exp(\alpha�.$x) \ee \no�N�.\4!'"%�5� unit�AQur=� we hav> Nex "�:0i� im 50�h1�, t�`]��bM?Dco��ur �j$taneously;a�s%1s a.B=�E� xtraordinl!��B cal��Eq�eq-�-}kB2$W)oo -91}\ \gcY7�6�!�2N . Bu2i�3�, �m*�ll-!�i�vA�/1� a)fasSonly �����em���(&^$�.{-3a wgvvrstance)� Je�r�7A� ��n/fjpu�"�d co/5nes�)�-X brB", f no.�={|*�9J�ev�i ce sugges�f�-i Ax��sEvj��. Intm��™�;+*6�,b�o�2!�q  ofte��u��a abrup�+n��K�I��d��c� N%w�A�[!� ��=+G]Xly��h��aɪ!�a�b�:�`m-�ly%�!5n R?is��aYoiew�aY�8m.<>y, m�r�Ka diverg��s7C�J�E�. (sB3=�}|ItEbe�:t��veIaC (class�joQ.�1)G]v6XC;F�M�m{t I�b H&2� �?si!�WeA�tat�� of.q �>� mz�,benson-prl94$@t�!�es much � �ed Msimilar6��u.�pAxH)t�ua�9y�f! %At~ st�7 piD->�/Z� "Qe%! %O�v arli1>}�A�demon^ %C�=vgce�Baq�%;!C*� used#:$ie�� %v2�4:!800%Iv�~"�]P">R*/I � ��&g>Rf{JMg��,Mb"" 473$:�):�!�K*��0J&�+>�om5���807f�ol!��.�!"D :a ���S.a v"za = fa @~` Fb` �j` f` �` Y�,��2�I&�#�@�O� ,'Ni F� p5i 6g�5}��5b�bFQ�"�0A�(s:� � � �m| � A�"�� D.q!=�OII>�� le$te. $x$-ax߃ay�z:�-O!^� 2T�"SI issuj0psiQr� s�!�t������|ho�9�u,lyZ�s %�)�H���ynXd"� "� %ɱ��HffKB�Qi�z�;*�ch caY*s8 E un�(�!�Bo��&y "�Summary p' ߍ�*�*e��C&� a�X#/�>š markX%�<1�'��K��T�B. High�story-�� >Q � � � H<�mu �&��-lived*A6�p���]o1 �sBAv0Ocur�.�={B�� PJ�(e��% �non ,)"I0bRcus U23;N"te� |X*�uN��� *�Da�N�uu{N2 E Luq���~"rajec!�>ja*G=/EI� �,"�m;ton�n�ta�may b�>%���-�� +�mY0Ube� ��  *�\kM"�vX U� e�Hig�.E�:GofSa4� &�"�M��H.�. inflP��A�Mr . %R�{u��Ɇ��t# ;e���b� �-� educ2�a�2!a��� %devF � �\%$%-J $N#6���p�elyG! [-!�A&ak-i��R�F�p5J�"�r�,� a AG"7Ta�I��$.�= \GammaI�cav} $ int}�^yw� �&%2$sub-Poisso�'$atistics..!tamL$�(V2e�obQ@%#6� \&� 01� ��!��X%by El4.A�3�ular !�ic in�iڈfElk_96�BA)n�@�"#se� ex}=1$!��=is *�Ux:M.�r��� b|��)�on �� , bu�du�1m�IU*��'"�  o�ZA�iYV�V8.Ёх,�V�Z�$�Bv�!�F$N > �,�tc satuF'-;}�Z�(�:� Rz��}z� ory�8&��as&�p�z �gB{�8�:+ �$N$I��6�MQ�previ�6�>�NU�oU�%�.�-�sW"�Mte�ed lia��q %� U��E^� u.�.2I���-&4�����K x] �conᰉ�.��d *Et� �> y�-���! 2 >Eume0 6A��l��nAq���*���aE� . U,ity�^E`U�engthk��F�m�)�An-OL97b$ ^�  $2��)J.�� Rr) <��e*  lifer .Aup�'"�� ',ared �%"2�,����un\ *�"� )�(t�sagoXHrGs�G.�e�%<���\,20 l*in&Q ��(A>� raS"�s� ᙅ"����6�pAU ɒ:fP4Scully-Lamb-LPa^�ensem�(ɲ&�to ac_!���1�tex�Vd%��homoge��, etc.��isI��� ask �prk,�%-�eLe-*� ��*H � ��:riE�?"2!�s lift�Dynam�$"�^�I�, M Rabi�J)not n�sti�to ��;AGQ�*�&z�-�2 �%unknownUq7��+.��.R/-ed!'i% d �m�%�f^v%L�o�Y#E) ]�i�daly��t�a�5�Vyi�B�!��I��Oet!y����.>a� , i.�$n�  << 1,$!�re B+�!����Cpa�3w�� ll cn) 7on&�7{\��r&e��#m�4&motiv\��E�8lizE6)�S�YE7�al*� ,zlJbe� m� e.�A�? � NEV!� d�wa�(w/�]m�L�,#�-�,�*�T2�IA�j9�E$g%�def WX awNWXI�� �6�c_���V�X��2%�inP c?re4 �� *a$\sqrt 2� M��.)��rrT8�Gm3#�� =B: \[ th} = {B�\� {g^2.� }}v#4, \] &�$ i�b��IY�k�1� !��Z (1� !�)}�]�9�PRLwif1�taken ��9 tino�h2�YmO#��!5��is�<� r�Z���w �t6aa�5.J{=+��ngA7 OvF$�  of T~C �,��!8q�&KMU=�U�B�.�)�0.1�="P c achen0�p��2d��8�#tud�Yin-�-��k/�!�3o !X"� E"O�>} 32%�etsN troy:�q2���� g�icienc��M< ��2fE$ �%ior)?iH�d�: ong ��i�i��E[&�s��� D'Ariad%-a)� �s�\ �� clu_&��u.$N=��� ��'eR � le�>+ � �# ��MD �eN5}.Jh��$N < *8 K� %e�%�" ��ons ��!dM2�.Mexk7#BE�aOlkMG&n �H�G)oAz-! tom �����  A� ��im������&Lo[BA�� %>tant � � ��>a��}@�� '.�+E gma$I�$N / =�= �S) �CtA�&� whe�a~�< � 2.e�]�ŽO@�cM�q7- ��a.�%5 %Fe�cs�&W.|%.���)A� $ do�  �.� �6� �?��B�� �is&e a�*�s� realL, _�ic u�IΥ��.��l�"� ���-A\�`"�'&H�B�! %=���im'AO�+ $N %2C`�U % HAVEN''T DONE THE ABOVE YET!! % %-- MENTION MANY-ATOM RESULTS IN AN+YANG PAPER. \�/Q�'�a`!d6$Ho�uij% %�� �w,(-O)NV w�"eFqJmlgorithm��0Molmer-1991},)�$Carmichael37� te���B *��&f/f z �"�-<2��0i 9A�p�i�3A�B�!)"�6 *�A� �$Yang-PRA97�p �ai�1F a�ail1h"W���ext܌L *X9E\e�� mj:EtAMm.&�,�z\ ;4ge*7 >�s�ia�b �l�H 4 Du5�0�0<% imemI^F <8 -�!C;�qAnion run��n�y!�D3��� "� max}$�-!9�o��_ �1-+�O�I ��%TPf ~3-{cut-offE (ide�zq %2�of>�aIn��N��M��s*$ �``� flow'' .�!21\%��.,g]!�V�0very �'!a �ia� InZ��!�I�B��&Dio' �[N մ� e�e*� : �`2"�2C y ex� r�;:�$=re $r� L�흢�0;a� � e = \� {-�ex}} \ g.X  $�ylgNl-�<"�>;myi),�� rmal6� $n_b�I�t.s"& ,��j�4pa3I aVl� @ �> .��$ (&s),^�t steady� :�2�6\_2��C� �}1+1=2  J�lc �)T-eqn} p_n = p_0{\left[x� c{n_b}{1+\�L]}^n \prod_{k=1}^{n} 11+ 49� n ^2()� k+1}6�)}b k] %A�&1Q p��6�no!�� �S�&03V��!ɚ ���� oɊ%;!��asu@ �.��ic�6� w��. %"M2� $p_n��  ��i>: 9�L2� $\l�on\1�le A�>x %$Q \q+ v ({8^2 :- ^2})/)  } - �1h�J:��� Vyui$p�R)a�  %���9* (�ZO0^{-20t %300K* f� �%%�M3p�-�"m)�mR�vh�tem(C��#"1�ru�10,�y--�7 ���s, �var7<�J���jW_q)��`F.$N -�r.j� We�d�and"�c$!p.� �%`��s�.� Jt۞H��r��A� begi�/�v!%,�le�25& s}<negP<T�7a�Go���g ach�(( twll!-"�o%&g�jezQ �)w�S9�w:/#=10!N p$�cx�F�S�oAE�S��w<6��P�tPCr-�E A2�b�nA�0,� ��!)�/�k$qm�ap/n�"H+DT]�z "�' &� ��@5ir�E՜�+"\ts|rapidl y=2y �$eAT %eH-�� = 3ԫnY4l��fs�I f. W�yer) %�� X�� ?�R�:I:)QE %a4�X$� s.�m6�A/  $�|u�U��ix"�A �w !� ��r}�2bt)GA� T$ -defined 1>Jse�monovvEg�Our QTSuͩ has �"eq ed uE�M � ra�a�V�t/�mP8*B"�a'm�. /�v�<gF/lBr&� else�;�H �a�� writ�8 in Cb7��)%als"�:�u!O��~� 400��P�{$um II work� on ru��Linux T� ed �<")�"ly 2000 �%ECPUE`� tota2�?- �FsubSS�%!�ɨ; Tra�-�F 2�D *�D~y1�R trap�e�. }&�.Two�� de>]��wB"�*Y� "].B�/!� a�^�&� 9(AF�?�m�s��j?�.ep�-reԪs �$�1I�!�& �rA2�eg��s�B]2�[=0.1$a�ev��V� n $%.�*L/�h7�od�J��+ w!-"=>l �. &� !�*��c|�i�2�A��nyV�� �X2 �*��Y�h�$!&0%'at2(k@:D%63���R�R!l�IE �itiA&!�A� E�!M��g6�>VP�=M̍�6�.� EDrlow�lJB�t�stoq-inu!ell�a"�.%z�, �.4�< q��"~s�.ork�(�!���[ % DIVIDE THIS INTO TWO PARTS? 1) BROADENING OF PND WHEN SUB-POISSON AND %NON-TRAP STATE, "MEFFECTS 3NON-S67 /OR 4 EXISTS .�Brj���-jGi2p} �XsA�zqts-n}�Sq�n-���r*� Z�V{>T "S �S S AsV��1Lak-s� ����)� ��a  � Ŋ�<P-0Ea5v�E4b��f&&��n,h4W/� �">f��'�ɺ%�F�J���2�Xմ�� �q©Mt!�"�B�.���.-�%0, -q !��� !�l"i-,�V�*�4"�b�?� ofFA��"{Q$:9.�%g2 i�/����e $2 <���biA�c��b7�P�'"/('�E �g�H�3�di�ws subJ\. ($Q<0$q8%,L$m���en�#~ -��In!� ` %choi�of& &�_ (V~ ) %a 0�7�!J\Q"$SfA1m��$"2� ��val�� = 8Eq� �Yr�S՚"�1_{|$3Ţ $50$r)� @A�Q���na�9,0  �t� �v�M&+\� ��m� univ-curvJS Uni�?al !����-�in%x� �-Q�/�H$Brersal w� �< U�3� Is6�;�-l4�]�=3Fj = 5�10 3ŀxQH�AG�2$:�l��I$;����A \geq�4w�And �;2�>��$llg;�)m'�#"Kc.T:J?Q = Q_0( �,�[ ) + �J() (.)neq:�Ha-%nȻ��&�"�JYQ��g�a� �9����%���$2�=3)"�?;?d.05�q�e*p �c�0� ~5i�e6����KFSCG�K1[$1UFq` iR>26{B)� u$6���%e�?��}C|�a �-squa;�y� ��}30Y0*$ < 2!�E� bar��dic�!�de !le+ 3D iHA�-�&�1 >�V �I� |3!�ky *��" 6���^� ��.� &�9 vs. 6�!/n} An9�ofki prj@6�&� .W5�#$�t"L2i���udu�"� L(Z1s&L%��#*�)�.*a��6'y2D1�6cA�}፜�v�,.45.#Vw�/ot�K�:h""�5 �.�i�cants�0b�9!  |*C�  %*�5 �)�2�(-4)*]c]��Qc���ob��)�s0DRxP ,���YM.�:.�C�7!�kbe�Vn!snUE !Y)ұ� s�3.� -/ to2�6S'� '��� �*N \gg, but virtu!no>��+�s6N!�M&"%%ly=:reF s� tpll p�sثe�stt/2 � 6@ nex1�6Q�"�;!� �z� =1$,"h�A��� i�J� J� Le�+%[$�"nner Q�e2`��E&GQ>��ur!� more%�Aset�G"B9| *c"¿w>��E�%bn; %lin$I� L�#Y��!jU����7� �$%{ 4aa~� b�D!�F�I� .�%D$�)|� =16� R�a�b"& $�� yP2�)e�"1($Q#^-ȱ�� .�u}1�26>$-s*�&b.� Ks�sEAbe5� qu*�8��@~ XE�qTQ =�� %�1�$4.5l*�*�46�e�d*� ��D2[� !0��� >Y i:�? by %2MBese!�; '3N. �O�$X}%��'4S�Xf�!*�&MW��non��a��Mn�t~Z�R�r�}D�Ef e"S M�� �?An"e36 T%!�J &� �= A�Gp: %�sAqing@Ke>0nA�f_� Ie!�"<@!��m�s,A�Q1 1$�1%��T�C�jA �X�8�PnQ3�a8F��!�Rt8����� !PnonSV %.R! (��e?)A$.��s� �O��C�8��=�+����5�-= =.+! �%c�$m%"k s %� ���is�l �0z Z�m%� 5-@A�)�&� 5j"�08���c� 9�q�-zin� " i&ly)pla�3< 6�>��!gR�� %u]�B�$% %� axI\ioV4*"A&����de%n�2I�d��&�.�.AAhd!%�C*F=e�r8own %���%:� .???� 2�3:UY"!�X)8}:�r$yq��n,m&�G1*:Zu�c]�_w mak�J�Mu car� p~ �&�)!�l8 f ��+�#ha�Q�E10�r&�trAj')�-Ho�!e��a|�#��No.��HE�)�>* !��� �w&,�%�K'��%��9o�,�c �m����Dto�lW.� _��"�0�urH� �kSe?s-3-�s}� �S�lr re-mt6U%}�Qe� a�.Xf~�blank� �Pc�dn�9D-n l��^)tL!�)O5�,A��  ^ |ɔ��YM Uerg�AX!�Be��o� p;4 )��f��� ng$�2�>� >�!�02!lAnt@-b�XY�Q}���pJ�^Uts.[q^%AG,���mAh��&^���M�roD ��[p�v��ŒYoN�Io.�f��"��4.�f "eN�{NҎmod�6<$N" Q�2��A)��5{A clu56�3 im6'o,�a3::�!R.�i�e�ouV ��B\��RB�ULBay -q" "!:DifNuDOw�*O$�cla# �"aq/�VY&�)  �� )-y�-!<. &�c .:^�#�  �7dN�~��5����EM|O��pro�@n!�Awa�|>+1 �d �{e :6!.[%�.Z.�7�k~�� B>�(sZ�, juE�I�J i]*� [89?B~,q � LF 2�8Z $�4�k1�Y<a�I��iL&��Ls�G]O>� �3� "Y9 �+&;Av%�..:� 0� `]s�� �9�o$�ll$ vu�E� a &H � � �2�� H1:�.ōY;A�:v2 = s�A�%v��H.˧confir !x��byB{!�a5B:v �<�"> I�A�76��]9K�0�A�a&wF�D�;3=�`b �"�9fin�^�&�.� %V8 ��* �$\� /6� &L.X���"U�7&GJ� � ��-!.�~&�&$�{: al�Imq 3m�I%��Q n� emic"�a�&-A� ��,.X!io ���feedbac"�} dG�ehN�)�2". up%��A�$���R�$E$%��/om L �&w@�9a��"4� 2Qs(noD�k)�ȡ��sM���?�h��!��5��a�R�"ϗ��.ށ9���5�2lY,u4�� elop�Ga�al2explaIS"Ŷ5J 4a�)�'W�XI(6s�j=6�e�n0A�֩��SAic:��2..e�B�at�t�� laI�cFNe�A����uj5,�uwhy�� %gZ�up�n youIm�I�/H.� %2u2 >��)�ˡ�a��� �59h�;F�gk��>�l2���l�l�J. �x*�XT-ZB�"� kX� fX�Jo;I�P:xK�ÉK�L24~+�N�V�[n F� ��E� ����+basic fe�i�A� ��g(#tu�+ e wa� ;�n� s "MA�n��DQ�den:�, matrix appr�E�vsiMzubairy-evum-op@T�>A6�f"1gI 6,B�;!-$Fe�$)�}%<�,�@=,"�bE)�63M�  ��?�N-Q�,fV2' poi�0�]5 �< %, �\�D- !��M|FQtae5.Xp m�� ��ci��mpa*13:�we ��v5;�[$$9��,�r��8 4om��-\)x�Fb damp��G��{���m- he H"��&{^Q�� m!K�+M�=)�<�a�!�s���4\be \mathcal{H� _A�$L_F - e {\bf r} \cdot E} vo"$.4A�.F$� %�5E�r� ���gi�p�2�"o�![�� -E$iV�p�ZP���Kbe 2�`>um_�k}2z ^\dag �!N2TA�K1�K2:SaNgma_z)<�|E%�6�at \epsilon_�1�E}�(�+:�)�H�!suA �(�&a�havg0,^�$ bf k%��Ns�?{.�{�\ { 2 �0 V�k}�ee!�6�����um���rk�#qi��H-plana��� is a��> A�V�`frac{\pi}{4} w_m^2 L \ee "A'��re $LU^ɦ mz��An�k $w_m*Gaussa��wa�R?1�a�!k S�1A��@.�.�?A 5jH}_{AF}!fB�g^{ij5�(�G_=� +Y�E�Qs-)!i�p6KA�{e �=i |i�r} | j �= � \E�Q�E�k�AF�}m E-m6(a two-�U!#& � �{) o� nP�e�)i7�8<��ׅ@y-�Aerv��.�)B�A.F`\{~�:P9Z + ��+ .c % g^R�:s9�e�)� $�%�$,�h � !0A� �7uC�QEG ��!��D*�_au1A)�spaz. _". eKi0a>&=�$-�c�@ER�.zc a% a��1�=� + G>~To go� A�.��t}aa �gin{array}{ll} H & = H_0 + H_1 \\ ��I1I��nd �A[\�&.wm�N�isܥr e^{i�tF!�}�e^{- B= � 2�C1� ta[)�5}!-i"i xi�Yi�c -q�6�� �g�,e i � {\2��� t}} |\psi� = V 2.!B %BA�k�Y"�: Eten!@ D(t)Y�0Tn=0}^\infty [ c_{e,n} * | e,�9 +c_{g,:�|g ] �-!|1Bi"bjt%3� *�YG �6�L�E�i�, �Y Cl�rEH6� mix� �wt)q�g6��`�+1�`[ 6[TSchro�E�qu��6L�d�GEe 'E� \dot{c}-D= A�A\qrt{nlF:)T +1},&�/��h�&e�Ug,+ZW.�X!�>Uw�e�Yg��al"� 2!E0M A= \�G\{0) [\cos (\Ou�,n t/2) - {{qA}� {"�sin:3\�GaL E� \[ f. {{2 i2HFX5J(0)a�>e \\}6� / !Wbe�)d>� n�+�� ���!��]!�6�|%�1�!�E�\��4^2 + 4 g^2(n+1��AKIb��AD,�l�e(q�e�+n $YH$ = c_n(0)$�A5l=�&J� 4EZ� {{i �F,j�a� 8�eA�F - �i[{� ~�JzM�]{F�|C%P�(�+Bec�ns6qw=�1-� .o\ 1�%��exa�Z�$�o���%2$v#" )��!soln-no"��1}aOe,n_0qO�.ESn_0+1}^M�b!aZJ2JgJ+1L�GZLY��3�`A_e/t)� �4R$ 1(�46T� &� } E��=F�y6>2}". zt�i��T*/32#|x edsEY��!� ly eG��Iϋ,=0$) (vacuumBg). %SpK���>n�rHs L`~1.B"���Ue=(,Eq��teNI{�G_!W� u time��~�"؏.�1 9E�*�\ �4d�䉂 '�itude af�wit��E2�:E�PV emit�|�nE�$(\tint)|^2�0in^2 ^N !.�Y�(&�|3�G� ɬ\��*�q�lyk[6�:�9 . Let0Gnow �y �w\ :� $n$:)�9�S hang�y� �r�� w�c�J];?f��lo��� :dn}{d%QG - L N %U} �1"�O �!Ok \gc ��0�<eqs�"�o  .yi�Xs �S�a�].�P�!�Nb ��4� I��5\cI  Ir�0A% = r$�2&�M%b7�!$2XU%2UB�.�]by� y)`%�\g�d%�a9ot!�w g  h x[xoC��u6T5Y](-� z2�D.�A���a>�- �� I�j^L ��O��N 7ELd*6~5�/!�e�-�s2�aph���O>�'A�-`:C$2 te�exi$�m���F �r�He $n'EAd>t�Qi8 �B"&�(l�f&�(_:nMb <4%^ 0X�]`O!�"�a��� \m~��StaY"!:}\*��  � (e�)|_{n'}%0\ee|�A_�m.&�'^T�olu%�iމ1A�� 5!�;�!�G'W ��)  l 'irP����bm����z�* *[1.3in,7][,9.5in]{Ak�T.��.t"�( 1in}�,�6�( G,L$)��(gQ�Y+.0)m1��$n2�(u��'X=�(���()%��2��) m�n?INl���,{.alRG7intr+^�-C��d �leR"p�EуEQ-s, open)uns:!6�(�N��D�4s�#2�aG sine&8<�an�R-e B�%v�\VB8 P Y B! L���}o*9�dw�.��!i�giv02�< %%n = \left( \f�rac{\gc}{N g^2 \tint} - 1\right)^{-1} %\ee %\noindent an expression which blows up The threshold atom number $\Nth$ is given by the point at which the gain and loss terms have equal slope, assuming small argument of the sine function: \be \Nth = {{\gc} \over {g�,} \ee Solu5Ds to \ref{eq-rate-� } ase injec  � $r$ is varied are plotted in Fig.\Nfig6OD-solns} , with $g %�0 = 0.1$. The1F of s�$increases !�finitelyF i d�. ��$asymptotic�pconstant-$n$ lines correspond!c$to integer�(Rabi oscill%8s $\sqrt{n+1}\ �(m \pi$, $m$G<. \bfig \centeru{~<\hspace*{4.5in}}2!(\resizebox{X{!}{\includegraphics{sc!t.eps}:>$N_{\rm A�s}$[ap!� {Multiple=[0of microlaser)�1� . D)��s rea$ent photon-$s BEan1 $h complete BQ} \labelb3 \e!EevE��H analysis shows howE��@' sinusoidal emisa�@ probability leadE� bistand m!*P. However, its derivE  was lesa'(an rigorousDassumet�cavu)= num�/lis well-determined. In addi!�r gives nA� form {,about the reA�ve �!pdiffer!�uJ , orJ�Xstatistics. For a more5�3(ory we turna'wquantum 0developed for�EZmEZtby Filipowicz, Meystre, Scully%04others (\cite{.,-PRA86}) \s��{Q6z2�$} We follM dens!xs0nd ``ground''A)te lifeF �much lon��tAΥ�ICI� damp�dur�.ra�J�(small: $\gc C, \ll 1$ \end.% \sub1�D6�u�!�oa }14Ga�ermConsideM� hang��%�) field>dueM� )�ion!a�$t_0$�a9�, the��!sɒaqao!�%K:�Tbe \delta \rho_{nn'} = (t_0 + 2) -:) �� a�e $H2;$ may bA�unda��c!� the �%-)ev�m from.�to%�$ AJ�,tracing overE�ic ables �:�F)�@sum_{\alpha=e,g} � ,n; '�+%C) -Not��at5�operator)� four/ices ٺ comb�e �-�4systems; those%� two7!�)*onl�8 % A coarse-graS �v!tI�gA�contribm !PM :�can now!�writtenQ2left(\f� d)'A8}{dt}\� ��pAOr[ & en;e-A5|+-i gn;g Bo8)] 1uWe�replaceE$-.,he arbitrary�inu� E�$t� The -Amve!0��!�M�}�Ev �.reU�edM�h.�e� he em�i=amplitud�^ �� 1a�t��,chapter. We� 1�b��Parray}{lll} c_{e,n}(tQ� &=& () \cos(\sng \.g,D 0& 0) \sin 3�? om\"� ��' �u��cesZ�qxFv& =�2��,n'}^*�a�\ &2�:� �5 '6 ��\\>�5� �g>�gv�-1,n-1�6�y� v.�2\JhW�ken%�e�reducAhNQF�� � eq-m�-%�x-e� >R ��& - r[1�7 �Am %! 1]=�!w\ & rQu/, 2'D!x'-1}.BB��wiD mad�M.9 � %`# < dis�@ ubev{Lo} �2m�ܭ�l+ius F�'�{/ = - ��j2}��a^\dag �� - 2 +%=  a��e�y�a�zer ermal-s2ist a��,ndard result��t� of"��$coupled��a3,ervoir (c.f.� � 8.) C�WYIN� and Z!%G,� total6�x.V  =� dot{��}"P a   + b_{U�%x +�� n+1,e" 8%�% wher^�} s =V���eW6� - 2G(n+n')�&�aw_^�f��o@� �SR�Ifa�rea| ct oursel�(to diagonal�\x ele�) is master5� �.hу2�!2%<1vn.�-12�-1.��KrF !�+1��v�.�c^2�e! gc n!%q ')p&%�.�-Z )=� 6���Steady-��� �} SettaM$%* p}_n(t)= �E�}0$����z)g :Qc��\{ :�+�K 4\} p(n) + r ESR�&-1(A@gc (n+1)= 0end6�"z��� recurrenc�oQ%� j� �=�2�e� \be n�p(� ?nh We obt� �sJ�.��d(�Q��%PT= p(0) \prod_{k=1}^{n}i�>b k}\,�}�S k!�%eq-b-pnI��� $c�B n8liz<.%� �= 1%+ % It�Qconveni>a�ue !ities��expec@onQ�� c Nex = r /!�bA�lU!+ +!9�!� per�decayJ ,�B9 �ut��tn0or pump paramX �theta!�e��u��I�� � phase if -\ �.v . Linear-Z of��u� �� �Bsm�� (%� � $�1$�ET t"wc��g�_&Mea:� } I�~� fig-mt-n}���-�D % %\be \langle n/! \r =ͤ1})FEI{k=0}^�(fty} k p(k)k$% has been")as fun� !�6��$%9$| = 10F�e dips� �� �of)�2�(trap �fes)%�(a ``jump'' !�v = 2�V beco� sharA�as �$largeF�P&s���width�a6x2Nbeh ]eriA�by� Mandel QY�, i�d��1 Q \equiv-�5� -�-9�1�^2}+ /!� {ya1u�� A�Poisson� (id�+��$��AyQ� �$, greaq��super-N� e.g.�L  lE&�EbJC!�B���qt&���*� � oA��1�e N_{ex}=10��_�0�q��Q$��. $Q<0 dicates sVS �� �q�N�q��F A�VFf y3q�2g �ga�7i� .�o.�wide aXesaޭ�$. Toxp6�a�6!-�w w calcula� � s �Eq��B�SY� ��Z%ered-�fix4e�I-%.�]�\text��V�re-vs-mtY5e�;���-|um-newgmBR!/���&� (d*�)1�d)� Q &Q !D$ory (solid�)>��U�-<.;$Q$���qplainA��=WN�%�2�.�accor�*� ��q;�  A�strongly.�ia�al�  y po� e"�O pike K�bimod"�2���Rs tra .2q! %9}r &�5�aaveragem�q#aQ jQ toge�I,HN�. se�f�E]�)b agrees N�*+  �fb2�exceptq�s''Bu =4 betwo �"�0e �&�es�4ially ``choose`:�J\ . D)�g: �!iEM8narrow as $N_ex� "�!S �q1�2 H � peakJ�!�woBE. � Q * -�6�5-=`� (within $\pm� of a loc xima~$� $2�sEiEu�oresupps2Mu Jexists�$n=n_0$�is mea�#�t_0) >�_0 �4vi!�uct� jpasv#thr�1UX$k�7 +1$�V�n_0B� > 1 > f6�: (n_0+1)�� /� �J*� !�origi�6$.1&0%. % %Z� :� vena�al� }/u�� ` SCALE BACK THIS SECTION?� %�A�"#�"�qu�q�Qm � %�m5modif�%tc��BMa %=.�!W� tro; a2#�=� ic� � �%#� ed %byza�'(\exp(t/t_a)� ere�V!�� � �a�, %36b��#e1Bic�!� , no� %^Dphysi��� � get. :�~ ALYCoE iX ����AGA%�UM%�c%�%� real��& �Xɦ-$-effectsQ#describeM U�%&!�"���O in or�!o� � !F; eloc��.�!m nuni�$ )1o� ing,? detu�(imper�_ing� =OAwof��}L framework%=all�s>1same:� c� �)EbAN8relevant broade�M$`` �('' $\beta(nE�ich �0n ideal (mono55etc.)] i&�*�N_0�=&�!��H�%exe��a k.� $f_v(vs�j sar{x} wint_0^\i%�U+1"�(v)) Z dv�% =N�&ae��"��n. ���k) }{�&wpn-�-avgd�y�at!�*I  r#!a�ic (in�&�'A�s experi���N /+JKA�BE!�A� {\it1�d}.S� �8y seem implausiz untilЅ z/* en"^B6"d#�(x/) elf. Our aqprocedur*#�'$ e1&K'��jVdom&^$% ocia�%�Q�, a E /,pen�-(cf. �'F"�(-\(�h��*�- is u�'toEVlM�q�a� q����2/,�� �������:�]�n`!28$B(n, v, \DI&a-\;i.0g(g)\;dv\;dg *t a�barI�/B = k v u�  $gv, #y�6��,!2��*t m��A�c!�� JTq�%X + know&� involvc�gener�ed� frequency%:2���f4%4g� �%D ^2}   \t![V%?" (] \ \ ig(w,� ",,@$6J?& va[n �.]&� In�B�mus%S�ad$ erwD+itsXm will dE��a shapU��@a�4file $g(x=vt)$�st just N area�0e՛B�iue(��gra�!�Bloch"s ( Eqns� eq-b 1 �V2})� a �/� iAL���Ra)8�Q� M�I�� U$.�/ g(t� �a simud&� � �M.e A�-� tail�x docu�4 Mathe�-c��gram %�orm255o�- n Ap��ix� app-!�s}.� I�0!bo;>SAW�4�)woulda� very�'A|umingR eref�-we tab6��!�"�n a grid� =truct+�rpo�.ngY'toqcali"o� �)h ��.� I"� inver�/}��adiaba�11m�Is�� �2C�'IP�' -methods} � ! ect:%.�= data0 �pFE�s},Ũ6I(.V0wa�$,80\%, measurS $a fluoresc��riA6ed�#�1sA�I-�#"�$J "� M��!�p� .� "�A�.�&,I�� e. Let"�)e}iJ)g}�D upnd�.er� e*b1&`3�%ve:+We clai at%��\E�J[ &{ non�.��1�yAe`"6� �+��-� � \NeffN (N!_{ee}- gg} \no? 6�1Am �ee�0�T�is,c& E& � �w�&y s�!�� Y�U @dea is a familiar�in:ra<To�por. is-`wMe�C0oni�J8/he 0-�hav�.�of L4 remo�0} (absorbing)� �J� IPof%lP�1b�b(�n}\;g\�7�&Intui!�ly it!� clea� c�=�=9*g\ 1/2$���e2� EB �s,4cE1�\loU�-� �613\ mann�.��e i� ;emi!�emz�P6#pictu3!�net2�4 (eWtom!� *�.\h}'�%A�6e+19g�'!26'%\approx}28d&^5�.a� y8� ca7�s�� of $1/2Q aFC,�0 af��5M��eu9reg��somewA$bu�O�"\nge�ţest!����ys, �!is��)&{R":6���6�} F�mt&W}� E9 ival�eofF7Q} aft�7��s, %�pr ������"2 K� ���,�!�vd�B� $G,L����8 al02R�n��D����t 2�%x.# (dashe� ��semiclas�>�28��S9��-R!�v~�"; 6� W $N=1000E�,losed circle.�2�7.�,�2n) u�:2!6! /+6}0� e*�^�bS:� aZ����sc�ZN.A#�D vs.\�� ,:�(.  a�*� �6EI�6 U ��3 �Z6�re6��:J_�**ot�TQ&���}* B�w �=�cf�=:��� Z]� �>�can als� Aݡ� &� of = . (BP1})%�[t]6�n�me�b�D"� \mhz*�=� "�*� �&ff��Se4(�>,third brancho ppn a> �� urve�U� ha�- of c. &�B�!�� gap"artifact�, algorithm u�)to find�6Q96L>�*�"b�A�lobe1��G"&?@��e)�y"]*s, �2P"�,1�6�*R?, 69s �(m Qv %�. 2!re]��\3l {Fokk�&lanck"&?*Z a 66�AI� $ G ��2��,Vi�rived��\pAal}  t}�,: "�0F( n}{Q(n)p(,!0 S 1}{2E-6�  n^2}[G:]*f)$p%$!Ee�1 �!&q3 �� � = R>H "[55 gc n be �v2�/2��$R"�&�scale��V ider.) Emx"146�f�S;}Y�-:k}4 }� � &2})�Aong(i)T/ u��'�>(n�)^{1/2-,(ii) $n \gg �DBo�+sZAn�A�$easily met�L!��.�@<0!(�.tsi�"��:�to]c�%>�/�? tau ",t�/V*\nn�-$Aen2� :��#sei�q~>�\nu��\nu}{q,)p,���\nua�g=.Cb�2i�6�� �`*�!$Nexe�nue�a� p^,+� ,"Yno'an+1R/\gc? �E�onV=�$QZ��n�%@��C}{ �Hxp\�(2E� \.b\;d\nu\; 7)<\&4)�Isol-fpBEU $C�  a6�2e��G. wC/�,x$ipZ� .� �+ accu�a3� glob�%um��� expona2� �E&/�lya� Kini KB�\pot�#abfi-"%pVA!p- !PrGE �EG&lG&$ F${�����$)�h- �"�Q%�>�A]�Q� @is�QW�a��@I�!"o }��?@���P!�*� "�  D*s:'y occ.$F�KJ� 59�Cf �(^�anfF�A)iA�vaB�"on%�LJ;ug�"of B�*��S qrt{��$�,���) . N&�;Ja�iCa )A)ftyI�=! �V in"�J�2A�� ilar��! ness�B�%�amjmX�� �1�3�FviEesH -�: �*?EA#*"�)Mraa�tB �A�:��J�r��=0$�*� MetaAVi�II hy�:esi %F�DheRX��8be!!nBd %be�[�asEE�B""��A\ ed; |5� �t�5do�It auto.ll�Fn%7m �!um� fluctu� to��ou� a.Vum���9 !��ifV� f�;thaiY�)�k,m-wl�!�� tateA[� �<�Ic$let uj+�*��!t���awK�%�)Y. As N�C 1-2first�=ea!��"!� bola-typeaRpe t/[5@I��"2 ("K3esonancE��Ole&Y�(s); higher "�� �AT2in� q6IJIL , jod$+$A� M \5G. (SeeFi1(2}�0S�,�!.�H)E� I/JecCO taneaY" s do��ҥven�q �$odu�2d �I��,sis�n.�patter�(<$ing���O:b� �Th� .��q� nE4:s�G&�K6TAq!i" 0Fs  rely)�'dHA�for,$,!�En��24<c& ��(N}Y&;!2 N=25 As��2�ay ce E� du�diMa�a�ap� d. ^5� -6c,Phfy�}6'Switch:$behavior} .�H�r� %��}�u"�.T"�3�Q� tunne�+��a.��aJa:8estim#(viae2K�+��b �"� un%�OA�7,Z*W� ^ �\pi�E [|q' _m)| MV@+� _MT _m)V ]D �. \{-2. [ _M)- m)]\5�eq-9�� Y %.�� \nu_m� �>1�le.�a+ 6 _ _M$ ��3� �2` �MH ���)�!Freach a>� (�?ossib�&� ,�energy,B����:� ping%R��2�7%8)*��jig m��9TU�� ),3*�� �3!.J� "� ,"���b*����eU�!"%L� % -*- Mode:TeX %%  (_#OIai�/h�mmand� at a~ � g!�� $t�ofN=en,��4of figurE� .s. Youq o9! any �Tll It��sa �tak��� z.c �. �. more�i*>U�se V,� B(endix C.3.3�XLa!!$manual. \�of� %\newpag�Kistof � \m�W}  %\ )J4s l %\title&�WT�A�C Many-A"Dynamic��<>K } �E�SQED2Pn�� �2�$author{Chr!p� 4Minwah Fang-Ye�9 prev�X(ees{B.S. PhF3�>)s\\ Sta!�d Uni(ty, 1995��>H,N/ (/�+de��{D !� } \ �{Docto�%$Philosophy0month{Februaryear{20�A�isdate( 6, A�By�A aultr1 1�barpyo�*o MIT_-f you ne c$PA Dto'r�/,�+v&cifj- `vi'"�*,! op aforO]#��s4twanHexactly2R�� i`% ext,7canNus�\+n�[e)}�k �!{6 IBM%�0�ZpC!t�,Xma� % I�Erxm�*t�V one Bvisor,�� % o� ��each.�*pe :`{Michael S. Feld}{ProfessQ1E��5�W��-arE}f�S�C irmag �$-Ł�# %� %�/sh" rk2m.� yAY�'s ComFCh F \c {Th0 J.~Greytak} R� \\Asz1b HeaX Edu6} !�Mak)�ܡ$6AY abov��HY}AjA� %E�z;gIkal� can'; ]I�NGUq 1 fy %!LI� Ej&�!1a'. Put| i�,!$ % environ�4�,leave blank  s f �e% vert�/ s�]. Ae y�adh/i�fA�a�< !.2 �@ % jA�) sign�  SQE\ED$and. \make�!�e abs�Wtm2�sets upJ.)��2��,ept-[%Uit-BWd%(� hea�7� r%�3`u�Z�% top1��*7uov �9�9 bottom % new=aibegunh b�.naI'�4f�#rsh5s( %�v6,��.}(rol�3 �A�a�Q!�@Y��1z.v8? puts!$he word "A-�">b|V>8�[?U]� !�l:%"Y ei�n!y(*not*'e)A�r�j A�pu�^�mC� dire���T �!�1� \N2��^ � F��S:a�r 1�Isa�gX"�\ rdoubl�p % UnZ.pa���do NOTi�a.MA� %�!nac�4 ledgUs3sa�\�$style{emptset�{�!}{ �)^2�put� nd 9��-� �;*{A6�pi Tck�� J !�a��2.s a�`��E beA�dt Na techn�re�.,�=raf)�Eda�+u�����,��%% re-sp&�e�!�U� �> .texf � A*fewE��-h0 .cls. \2 [12pt,two� ,)���]{:� j5i��52^(\usepackageZ+x}2ai<6lgrin�:F=� psfra�]5i{vE%%ʡ��newfont*Hs�}{h1T�A�hyphen��8{mi-cro-las-er m0 �, is b�:�s%�to��Q M7)�l�Va� wishM8!4Ej`all'H A;f:<je.AvDKrishna SethuramanF 0n%\#in [\D]{E�Q na3Ntok, (|-1,2 ...)z�:!T(def\all{allifx l �out{I�� 3�.} \elseN%%7 H'+e{ }�H��Q�} %5� T)�M tw�"ree!�new�o and{ Y\en�44math{\Gamma_{\ rm c�f.2tc}22Tn-ga6->_aF_int64t�2z.�us6+ \mu{XgseF�umV,mFVwV*WB*b�2.D^{138}�B�_5s& triog}{JD1@ S}_0"b?\,\!^3 P}_1B�_���_ }R_b�Iv}(>�e#�^!�}u@�Z�BDfi#FV!f>�athcal{FBfsrJ,rm FSR>w gtwo6-g^{(2)BU(sno}{791 nm:�fft}{553FNth6\NI�thB_n>+nf+ex6V +exBVN>+ �R+f:b,ffBXsngAf.Gv!n+1&�_>k!-27E�MHzB_khzJ*kJ*te:�TTEM}_{00BY ocav6Z\omeg����av2setleng�k }{1iB��{�} �z�"nk? � �3irG> 1>=l/>me?;phap"I4 %6t�Bx�q �discu�6} \?�ha"�<6q�FJ&vpaM*:(twbibli!a��� a~%%��� check-�',{\epsilon\}$u*rqdw] $\hat -$? B9 p�*?��?.5+re.(.-{\bold�ol �3.1 ie}{�:.e.>�en ��b��=��V�%�Step Ra!D Walk=Self-D*Ab �`Gemunu H. Gunaratne,$^{1,�+DJoseph L. McCauley}$�?$thew Nicol 3}$ 4Andrei T\"{o}rk$^{3,4�Q$ \address{d}$.Aof|, & ` &�'HoustonF' TX 7720AWq�Institut�'Funda!lal Stud�=B}Ha�!a, Sri'kaa��3B�M&�FO�� �4}$�of.t Roma�R Academy, B�Bucha:,.�nobreak"� �} �Q study�'$cenario un�{ �$E�sA�rI�wE��$ omalous ��..?E���z� �M�'/!� ingu�*=seYN.�5%�L\'evy d�K*+1cs{PACS!4(s): 05.40.Fb, ,-a, 47.27.-1<10.Gg, 89.65.Gh}29g {I\FR ion}�Z sec.t U}!U�)(&�1stochas�CQ Yaq6? S�p6s,�<ob�f�, te@D%&longi��nal v�;f?)���'PB urbu�=�Cid flow)"�hesAcas,casAgun,wuAkad,solAgol,takAseg}9"�' sA�iNu windYembAklu pr=�L� financ; mark��5h�,manAsta,friApei,arnAmuz,dacAgen,macAgu�-Fur��a� j2�Bce�qU%anoxq�*�C��Wyu�s exhi�s�s�&�OF�}.�[prior�k,Q�=� 68klaAsch,bouAgeo%vw�@�zhierarchj�*'e1^peiAbot.�>sugges�as �"! u6of><��"�$.�uepa�Aa� F�*al�(a0� , i�0 tras<e�iy�,.��)�sI��Ply bo�kd E����(��� en�G�!l.p5|J!��VW(CLT)]U�F\emph{mՒs}��d 1 in S�8<�MCLT}.Ne� "�TJ�ofai?$be љ�provid�D seb�SE���2�]J�J�aSov}, w�pgm'�uc2�N���z%b��eI2M���M�fokApla,�{ nd �ke9th%�x �m (=�j)$; \ie,� .�c6(t}} F(u)$, E� $u A�#$. By u��$F*9P*9")�� 5/ի c�=$D�%#����# $�ic :!�F*$�RA�Qtox;orm�%�B�< all9�al&+M�Fo . Gi�}$DK� then�PIuv plic�+xj)�$%T���BS%2E<�s� ^]��4��!�p�F -lawa."�@�hIn Bf*J�%�y0criDd�atef� �g���em�G��edɑq 9�-�j3 ��y9us. Prev1� �{&:zBz �G8a�9dic� cme�*is_GT�M&��,�� will� S9�DA4����:B�) illu"te� � e e![r�.."| �!$2m�3^u��� �*c4n�I�seP) &q ~ .� �tD8�� CLT��a����i�6 �FlyY ed e�Z�4" _k\���6�L�}dI)��r<gma^2$��2E��"� ��\��n}M,m_"%k"K _k \to {\a�N} (0,� f"�8cl�  c{5nNx5��e7ZT(0,�C}Z"-�a OxW^�#>��A}%Jv{x_n\}��ge 0}9 mA1i�if �:"1 U0>� �eQr})6����2���: e_if�C e$k�Àb��E0X5g{k}Vi\%?] = 0,�A��#Y�&llM<R. ("`<,�ho:��� valueain�MMxM`��E�.� u�we �= EqT8>2�):�V�.) 3M�E��7r � �loc x2! $n$-��MA �0F E�7[AU5���, \ x_n \ d R�nY�K �hd6" E~C,&�[&5sB�� a�e=A��@!���-#m^ 0��!$ �I��2Xtakes pF. D�$6�K� by $Var>A�ge�af�9 Lemma�����K%"�B {\bf 1:}��$m���aJAg ��D�� q�*r� [(I)] $M%)�U'0$�[(I(Varm�:+\6C(�k�!]X� ��sv�meBb%=�EW�\foot��{�: prop� es�"�3)��4$Ea]={n-1}]$X�e�c��] = -$& :->ce-M : �or�3��4>_ i�d9D �p)��� J�D�a�1�|��6z2�J��>�:�6E|!�2R9�ZNN6 ��H� �2BP_E9fs,o o�3.2�^Re"a$Hall-Heyde�Ta -� a�m4a�CLT. Re�[� ��  $y_ of���PS �ai�)�f* �inA��l}��"� ��blY$�&6$r  >� 2�bV$|y_n-y| > *$ goAto��"` JB6�h} (~}) S.8?&; 6� \ldots�Esquare�!�� ble 9�*�s s�eQ�O�iz6��[(1��\max_{1kaC n} ft(|U�k|/�Im)A�eCa�< �s.�,�][(2d2 W^2/ n" J\et �*\O3Oq f�.d / n ��]�SBin<,�}5J�x:� !�� fEeŇ^  1.A%pIg��"� O j���)Z��YN���*s:m (see:� �))�@AB�Z$% %ac=�� � �:�k itZ)){]$)% N� vx�� eqn._"1 ��� :Q=-5[2}IB t^2{\quadd�{��/ } ̌6�% ��� tzJ$�2#F��1��H O�e��09�2��)k���di� b"5*� r��bE�� �c_"�dw*  s P ���d� ��V�E��> $u62x_'$�$U�B�VY$Z$. ��fe�� �y��� �z � x�12$}. Z2&ne� OMksN2!to �| &�. *Z?>� J*s�m$A�$-my *; F)%1n<is�ifKon�f0�@sSߔ.nHde!�if w^2�", say2�F n has a�N�$"5Nm8^e�S�%�LC k}5�_86Y)���o &3 . CosFE ȍ����nd!a9EJM-N��^���ls.�t(}s�/2�. WJ $sIk��2}��?Qg=!����!]A����;H $d\widetilde{P}=e^5R}{g}dP$�_��mo�g$t� dcA�$2T ? �ity \[ Z� s}=� 4g s} d {P} \] �#, upo�fHti�g%j.v�nd�' $s=1%wat .�E}[g^n]= �{2n� ��uyU�Q� sT� 1��*� D7�tt}�1Nex<we�f�%f.K#�y��8��I��? (3)!~a��CWsm�i��f&� k�Rv�U��&��͚eD)� s a $c>0$& �):kA~"�qI�� �@^M�]  c$). ToA���\&A5 >Ƅ � e&C6$ &E k^*� ]1*�� &\ nVc2qc,A�&* e�� s!�"J��~1�1)OF�%�'5#{era�|[?'r5�"�  0$� $c_1b�� �Y [.� ^{2+� })Uc_1 {�B�C�sz�D!� Prob�(f` .�> >�qaY 2�_RE >I�) .�nZ;� lz<\]�%�fa/aE� c_1 �nFge &�f�X)=f=".�Z�.�TSPk$VZ=$\le {c_1}/"���}�J���[ ��F��n5��N��0 l j as }M�/ft�� ] WaremEFA�]�? ȭ>y��qy2)� re2� ERc'�.C '(>.��*! &� sN�� ��&�9e-�=6K� ^��(>�. O�� ��"ow2;be �"� y9 ŏ"� o� �WaoZA)$�Ygtrivial,!�il� d� �Ω{,�Q�z�:r�B�)=j�,��OJ�N_1�%Ia9�ion FZ�_1L � � $M_1*s�O22O by�~22O% ~>�" , $MJ$�,zwd suit� choicI<� ��M��ll N_brl M '`� mov�H�M�%A� �s -'k . �])Q�$Ws�@?ng" �i F��-���{d�!7nQ"�`I�>Km2$SLi��&4E��%bHq� co�4�nIE�I+E{��Fs.Q@,_ %�#R�E:.9F��� 6+  =�:�:� ; �2)�A/aD�� :?/Se��+�2J*y9�k*cr?*.�!pi'* F,Q!m�s!&v ider �.M'� y.U"z) (at E st, 2}�c���K�S-). �he�)�.�� al"�*, � ��ft[��b $,� not *] '_|&c+�M�{Co"�XMarkov�Ces}��*C*y Y� ,2!��0u< , di(�� rval'� o#�##m$ ~�7W$n=t/  tAT2)�p�U�6� "�lyZfo�n��"WYA ccur�, ��!�w, �6�]!��� Ti6 F� /! �I18�@ vario.L A1, �+timSbe�Qc)9��.isf�j��� �a�����df\ �d� � � �%I�A��*~ �4a� MF�. �# ioriRG4ma<a�-#p!��ur�V�"iz��C.�3�u��below^�t/�>% , alX ���L0��A*�e��)�iye�F�h� 35�dpM/�� .�x���ix�ix-Z$"���" p %�:4 x_{k-1}; #�2)w" f"$k$; � !"e "20� �Y�*�az�O&s6n��A~,F�+�)o<o� expr,�) c) "4 th;�\��U 61(+"hF&UW) x; tM t�r� � . x- ; t\� p_YƩ�"� | (5)6*��eq�6��$v^��&�):� de)�"��ea���.��$Aͅ��k�a�H b�wI� $%A�'TayloJXa�6����$�� $x$ ���/ t)��Nno/v<&= 1r / \��2� t�6isJ,e�U ^�6 I.f0,masAzh9�]+   {\�Z>�iW�/*�2>Dra1^2 }@,Q) D? F1�Q {FPf!�&�.*v0}j/�1i�(N� ��)b��:\�j^2�~5��.� =�5i[)E"=-Tk5&x;Q�]"��_�J�LP"����)��|"B "�� |��Q b� \6��D�*#"� �*lw� � � .x2���NDa�/ aN�"'#%a�h6�H=I�.oiOt3Qtg@1�3�� u= xu�t�� A� pre-zor�v^�E60'�Ad i�!"��nb�4pl'-_ $)�x �l ��-*� )fly cer�W!+m8 I�K,NTn�� � �  m:6&� � "��m, �Hg&�:s"_ d = L@ D (u�. Subn>�֭VH4��F�� Jwu�?u�4�8 +:42 nu^�w ��6A=*�)FPuJ��H� W'q �y:v �+q�F@�j�c_1(tXP+� inF�0�0](AMkhe ``Q tant''s �i�0"J��lKo�Y�= N�ba5�Y')�1}{�4}�@_&@04{u} dv \ v F(v9�0� � u ��2 (��\�lN�m�c_2.� 0���>�B�E�5:}�!&P2�� =� E 92}A_Q�$*N)� $:91A�uh>%� �(t} )h�=(MA1cu�)-e�m�j@6^�I -|u|b�a �n�>.IB�(1+|u|� �M� +�Z�2{. *<�A�te���)+e�&7B��Uܡr5�do � ��L� !�$��$�3nc� yl 2�dei!�� �>� s wb$t$.�t r � �, hxforth"� "]8ill6�.G����kZ��8a�a�n,.���) N�-Fha�.\}]4tu�� {v}{D(va�I�I [ a�i0I�!^{v} dwM�wIwI+ a_2�� {f<�J�i$aEa�����6�f-�!>(symmetric u%� refl�<Ã!� origX�h�� �Cs*4-n �(6^*�+�:"AU��h@  |�% (d.�Bi__�Ti�\� I�Bb���alwy���:!a� ,i�g�!I?"�c�L�vi��va� r�st�ngP A)l.};%�P*�!�:,RM���t8anti--E"�0�c ��*q#�D�henJ|7�mտE�F�+4��pqseA� �if���sA�e�^ l< � io�pbx?*2JW _n /� *[&W �nA�&�&o!~:>�^o2� t}C N]$!� *� !�3s�(G��� X,bZa�^$2#u�{"�+�%���"*� �E0�;K� \uD�a3+!�<�+( >=!�1)$N+"r0U + \a/� ��~b� f|u|}{ =)� a!(�Y�^{(1- ^{-2})} .�1 ���-|uc.QV�+ P � 1+ �.^ Z\�>�*- ^{- (1/2 Yn }��5�Thu�CN��T a���"� �fwe�?i� i�:t�at�a;x>l�w $ � <f��eedaorder66uq (~5*��"�"6*Gconfir!"�l�"*�NH$e~ �fi`JP5 s!�@)R�H���2��25Ld!Y/M"&hcompu�xs w��! u�pby��Ie (�7-drift)J�<$dX = [D(X(t);t)~i* >dt)$~0gill}�hor�_ne 0CI�@�u�F� �T)D.S|��w8of.�i��& ats�- $ �h *,� ru�Mignored�$�v��dev�'� @& lie�"J?�?#uD}Se��/&�\ {�OzB!�B��As "�OD� V� L} �Ca.3� $>�@"d1 =�s�a|Ew'n-�* l%-ņi�os�j�"J�� �or��2��eX��(r�`�rk � sour&^q�? M$preci/ s>�e]Gn��d� �HsI �i�(rly!|c�H)>e�"�K~ On_>� &[Duo th�C*�h1�is�ite (.2)�S"J>()I)2nCA!N�+�b�1�ed 3�mI��M. Aa+&�I ��a �� wh+�suc iv!�v:g a1��!�*�8��m�F� nTA{��loc �a �-��:�� ,Aj͝�aAT� $|u|$ (�V 3s�ven.�j�"X I%lI�to�vem(�� r) =6� �_.mM�r%`�~$E;� �!�# ��po�@veAneglK) `��.-�E!�e��=�.&ex�Lk5 ;ϒons. "qkof ]%�J�-�� "�"Fi�lƀrun6K&|%�A�� ���ZL'6Vs[~p,=3.0in]{levi�nz( vdif (c�n {E� of 10,000ő"V%(a)�.�MR�Q =2/3�$ (b)j 7< $ = 2(1+u^2� UnAda(a�4 -�*(HbY;.)Y�E��Oeha�Rtud^:A%��1e� �(ma�(5r��QN�a��]q ahauto-]N"�!u�K��"�3 si�2@�0v.?Yꁦ�!S�B(Ayʧ&M si�F��vanishN}�gand, r�2L ^2\}�C V6 [�k()3�. S�c$1w�ap4��)!!2[�7�$usJ�{HC}(m;n) )>�1}7X [\�^2]Jb�3 0 -�A&2�\��le\� �E+mS�langleGޭ�:I^ k{]\M�B�i.`6)-�4@� �Tor-�Y�,� -Z$-��K�m�;�!var W���Li�� ���#f��q��a�3 (� m / n�Na!B*�!.-}n�/MAHs�_r�S�r, �(�s? �6xSFis h�v�E a slow ����G conAbouJ is e�3��6�H ``c�+er� of vb��0,��}R�Bat-�ف|u�Z� F8!0&O "M�I"�6.�V��'Di"�]�] '%Gus� �Ll8y"=$presen���od|,{a�-(�- an &� ca� �"N5B�!�_recwSinCJ �y�+se�4E�6�7. R�Z��Br�V� new .!�*� ! .�Ս�*!���� "�N*��#ia+r!�Q��.n % � y�:P-A%�AM xe�1R*��,Da�qu�lu��Y.0�Y��n�9��a�)��"e 1D ~!0%&+\St���ae Vh���2�c� e�be���!�$u�#tA\a( s>��"�Y$� �c Vr���a�2.] tO!�!�pɢinBW� �h��)AQF�=�211{=��=1fy��ch mo|��re&�.t�m��{LS� ��6� ��M�; !�u �FtM0�v*6�,aAa w*rR~+ EofJ�Q�=� the� s�y� !�not�--�� 2L.�>�I ��Ad���ct�la�0)��.�ri�X�h� eKmV$x$�2tVs6A�y�U&A��inEbnt7�}= A�$x$^ � �*Jr.E. earlier�� fb<�!*//�A�IA=�"7! ��N�{c#�2Z[, ���iDsuddez�rg6�� �[���ka|��l�֛io��  anxiet��! A�tr-ss6K"!�k�� �63�atr�lyc�@��%>�)as� !=��9&Ѥ��- � sett�X�8��ew� � � ^�"e9�i�)�uV�5�� m#vtoward����F*}��_VB,]wo��H�};c��E�� AJ�� �UQ:� 53.'� aleAbas�@A��y�, ��a�.9� $\mu(�# cs�$��Q i&�3bAO1���L" `! $- S"M&on� Z �lVA �k!}. Re�>i$u8+�BN�H x;  t} �s) ds� )��� �F�)�;.��!�0OX�ped�.� *s"vPese2^�GHG�a�h�s�G���NSF Gr��, PHY-0201001Ea g,�&fe of S�w S6 ce O��iK mRe (GHG�S.�M.ufyA.jfor\"ok w��/�� NSF �(DMS-0244529� -!LAr۞nd*s}� q0*� inspi*0��!����, 20 years.Hhap�ix.|A"�?M� 3P|b"H�� ? �VEu�2J �CB9 A&�  sums k�7!X<a%C2� $ �� m��� "�G.�<8<�2}idIB�4,"�)� �s �>!�f�@ u d.b% >,F�2�oou8buA�I�3ez $�*1/�IK> .�  $�� �a`�P �'(i� C��$n�Ce*~�4 !�����re*d�U�l�_� .,A�$�9E�a � �R=�g� ��J'�:0n� ta}(a). S 6�>1 ell�|, {%hn-o�� " Harg��(%m7n 1[it w�^"�|2�^p,��뱇,� ��b�=f��( ex&� + �w �C�%  2�Q.0�K2tanh\8G FSP پtT;n�@US;��2� �/!� �x�P�s_1  aa��!��=grak(-��<�:�� for a+�  10mm'ERA?� Jn�;B*�@�U_^wF\],bY,�"eO!�A�F ��BP >E!� &�[1,2]a*� �AQ*� de:Y3"{^W��aU\6��*1'�#�.�.(�:�Pbt�!�b�" "M(xU(?�i{ !(1"�/)~(�3=2&�9*U-IE�]�.��"Vly�pV� eta1�dZb(2 ("�A�F�Fa% ��l:b^*1c\kE1^n.�w2�e�,en�$��)(b� +%o(?,M]&���WAW $-Q��(2�$�A� ft(x�&X&n"�$A�M1��{ O=� >�f��w:!�theEr%�y}{99]b�hem{!j} F�$slot, B. C����nd� Libchab�s�L v. A��& 36}, 5870nz87�Hd}j}6YG.*�p.A..n4L. P. KadanoffpSQ 0omae, X. Wu, Zaleski)�lG. Zanetti, J. Fluid. Mech,, �np, 1�92�#k}\Z _:�:�!!M. Sano�o=Lett. q64}, 214%!902s�k } T.�qSolom��nd�$P. Gollub,n\> 382�:^�k^$Takashita,Segawa%#A. Glaz�x��"hy1�.�7!� 1465s62�"l$P. Embrech# @C. Kl\H{u}ppelber��Te lkoch, ``� llin�oExt@ E�c," (SprBr, Beq���32~ mandEmB.�delbrA�J. Bus1�E�394�6BA$Asta} R. NDtegna%$H. E. Stan`s Na��-�3%46S95); : 83i&!63fr mtFriedri!J. PeinkP-Chaznn!Z�84}!� 5224 (2006kjm}!�ArneodoA-F. Muz! nd D. Sora@e, Eu�Yanpŋ Jour� Bge�2A�7 �82��m}AP$M. Dacorog�sLR. Gencay, U. M\"ull�R.!�Ols$0�,O. V. Pictetr ``An4��$ to High-F6ency FQe,"Lsic�gss,a� DiegoE81�� maun!t*Du�Ge�G"tu- a.29�R78-198%z6Un_Klaft�M.�� Sche� �G. Zumof!!�!vToday!��K�6,W� 33;!6D. Hugh�!Yl2ZE.%M�hollO=.A�l.%-.�q$78}, 328%�812��n�,-P. Bouchaud��N eorg��A�pU195!)2U:�� #o2 ,�RUekW�H.!�Swinney)�ev.��I�71�97��6�"co}bF. B\"ot1r�J0St. Barth, An�s� m�13ej450%� 4). ̞MOHa&�ZP. %C.�Z {\em.�'�eo�ZA Ee appl��r,!�bUT"&�val &�,%�e]�1980.��D�P![ . �L d:; �el�#zn�E E� , Duxburyqi 1996.^fo"n�yD� kk!d%UdG�k-Y4�'81�� 14);A�P�mA�Sitz.s+Kus '$kad., p. 3��191:�h�nS.J�,ndrasekar, RA/Mo ~5�E���462q>IMaslov%(Y.-C. ZhangI�<�A �26�3�96icW!�E,�����!oJ2Z�Sca�� ]k� ket E�:�2l3lawb beyond,"1`>3 F�eB#� ee2 s� � CNRS Q�sho�h.D, E�B. Dubr��� �!�b.O� B� 1997.,g�,7T�nllesp?h``[ �xw; � a��#lc]x�,v  19922�a��L. AlejA;$o-Qui\~non��K  BassŻ�t ield�Q5"�{ }{ I. Ti��yevL 2}{�v>o ��q�of� " "!�(Stock Price�V��}!k�B> A &�|[�u�2-Pfic W�@ Wrap/Unwrap Ve�� 2.527% %2�H3.028HIf1�w P�rat�A�f��essageRh&6will H�0;"+C tH�A�ptd�,Te��r���dI�o�6!�*)7yp{!re: Di�, ��, O�,GHMacro� yle,a@phic, PoDd�I Plot. � ��taggedVNvor y `"-� ,�e#KIH.�� s go:<m�s.0S�HTI)d!�>E!kv�1�d+t���GH�f j&�p%�d!�a�-�R .��! � v�cQ"v�]��d�(�@issHd�)��e-mEvc3�t�~)A�A�e8al 8-�xbia��at.HFM�Ked:_��"/�,/Cpc_fnl_2ap��"E���, 56181, 12/27/2004, 22:14:46, ""% %%B St�ba B2 %% \��R{a�� le}%6:�O�\6m�ߋs6��a��6MxW*�MaxMa��|Cols}{30} %TCIDATA{OutputFilter=\} x2.d��"�,=4.00.0.2312@CST!� =40 �� �.cs��EC�ed=Fri  Au�{ 20� 4 00:28:2ZDLastRevised=Wednes:M=029$5 02:13:19�,Z2�oShell3,��\6= icle2V(Language=Am,�n Englis!�new�'em��( }: 4�ac�(ledE}[ ]>_:7�.16bxio2'2#�,ICase�cY�."6D?R�.(>-� 6, >+$�ur2�o:-15�9HC6+n^r� +2+�� ,D�{ 2-�*� >'erc42( 2Pl�k&PO6#no�7&N2Lproble.�P >'p2o.SPr2/re�Q}R 2%�>'So(�:)umm6�S Penvir0��ofo�[Proof]{"�<9Ybf{#1.}"K$ \rule{0.5l� "�<��qt,� {\LARGE N3 capacit"� �?}\\,i)�siS>n� oret� �'"� �>�?� layer NYmemZ�qors�W�Mi�0B. Partenskii8 Peter� Jordan\\D2�Ch��try, � 15\\Bleis*� �\\PO Box 549110\\Waltham, MA 02454-, USA:��b�G&Ӆ[8��<$s�4d� o� uz�!of"p4.b,ܰ,;  briefl[A viewe Their)��X7�'�Q5\�ol�diN-?W�"�;�(?W:Ӥ2�.��* ne!5�' $\sigma$-o-� �$fiW�|���B�ire���R >�� �$ode surfac�X 'x�Jw $Q�.\ }\ �E�n�EC}\co��%Cx�%!7�(ionicEO ��Y %�!�{� $C<0$\q*� E�%l "�aal WM w\� ՘�fve~q =w� �&ty,�\ }�V,f����dge $q$ ��1-L�dg8c$��line{)U}$)�� C��6S7kUs20 ed c�#+($qU)<!+Q%/ r����su/:*QO,�tra�M�f (i.e.)�e`he A�ψN�.h,�0�m5 5to�)e��EQ��yM*�"2UE9a:�a_+# Tse.� )l�1�1a "F�"I6� }�ra "(�olv�:E`�/low�� �* }�inhomogeO���i  (I���.pHlp/ dem h�) _Abone ס�eor�B�=K)�w2�1�f8Z ��Axg6� ��q ";2I*h} *�biglC�adm�b֜igq�e�)9�'. Ҁh�|]O, � EDL2�i)�5@a rea���(IǑ�m�a�of5nIenforce�u!2 only! -7�od�!1�(fixed. In oEworam �iuin� do��s�kA��Q�V !4e �/un�,with respect�tra��io���ҭ $qX. \se� {C��ol�I�ifi � es -�ory%@experiment} 1. Eal �J!% Nca.2(EDL) at !ochem& �ese�sulcondu7 e�4 "potential" (� )&D A� ere |odeUS*{ "d � . Chang)�e� l!� i�cre� s $\Delta \ leads!�corARon��:ges6 od�,F q.$ Si� a��R a�u� �H �, �=�(t)$,A�ultQ �bmo=measur��by imped�0 techniaH. C� �� -aoA=_ quir7o" �UO, i��an ' �:�uis trea' by graican� (al methods.a��-f� !�qb� (per��t�(a)Uhen�C� Ayderiv�,% \begin{equ�b} C_{!;}=\parb \2 line{� P} \label{C_Phi}% \endH&� averageB�� iA5>]=q/A$eP$A�@� �D area1�U�. \ Th�mEq. \ref �ka typaNA ponse fune�F ,\varkappa_{F.F}X�A�^� $F~$!�� Lxternal parameter ("") �X~$)conjug��a�nsZ variA� . 2� � �protiiO5e sA> �$wc � uda�by qLq�5Em%,� . In�p�i3ed quant�i)�6�m&alm �Grg�xt rega�edA�� �.�  b� ry�`brief �eod�Cime�2t$, �L curr_ $j$,��ō i��f� ��� q=j��0 t$. With $q$� 0 i�ant �Aa5ina�� q�i.e. a y�ensembl!�A�6EA_2�� alogm to Eqs6� and E�:E��inverse e �a�.:% F� C_{q}^{-1.�B�}�-.qC_qF (Obviously,\2L8is\ a\ synonym\!�\ $Bb$% Q:\!~ ing\�\8 \-�] ~$% W��valent%:6��\�LA��.� {��$iz� modynamicY�I�a�xpanded�{qh ed )� , $A�V,$��9U)(*� led)U:5 q},$�� re�bB Legendre� "1 ,F�z(Bi,!�)=A!�F)-q . ��E�_I F� 3. Mostca�F� ic6,� ssum�, oft��scribed�i�d fla�ll, h�g ,A0ed (1�. �'�eff� vel"���- �� �Y_ to�- (or$~BS$-)FMMBermv �� �� i *?�� �Ɓm ��a sca( xceef atoA�d� s!},�}if $\,I�=B�=cR .$ A � r-exampleqoneXA�,optimized lo�F�*�  Ѽ� plan�h�4(r_{s})$ $\neqB� $ ($"$\��0radius vector�wU: f)� minis " �"�wave" � An@sma� practic.��% no way to��k �N;�u��s%�3D ��%�rqKly. $\ )6U�!a purA�theoret(��struct; �prms"�tes�tXA�ineA-aUgM� �U���Tco� aX*���e<"���"�<��ond�f2tat�$"� Admi� sign!�!�^�}� ub� 6� :;*� } G���w60&E5J +McC71} � # o"Tf� �fa� �,� 6�, ^�5�!R2�E� our   G mpw o circumv jre =� �.%,Tor92,WeiTor73} hav�en based��mis� pretP �natur�& ��.�Jo�,. Near a criE�� )_{cr}$,*�  $C�(�� )=0$� ik�es ���r2� new�e�� mpan!�bym�$ flow fromA$�A�A��E des,�r�{ a�0 "breakdown" �- *�a, b��}2 mora�tails)qv, }t woul�i�que path� phas>/ �{9 m�q�ity. Haas�cus!� belos Mx�� alsoz ol�A�a `ly." �:m*H��A�b#Jth*- 1�d8 ty1 \ }�c(\rho)$. } A�e r�l�e� $ >0�f�Xnow* acYedl turmi�!A>��s� � up5�io� already�(licit, onceapZrecogn�v�\ }�t2T firsEothese i�ili+isA=biddenA�A�idefin)� of "*� " sincce $q��,U�e�act&i m�i>�%0rupted. Can $nbe&������t? \ -�adB�D�� dm�s \ alm� always�2�*>-�� �s, we )I�v �a=��postp =��e�9 =I].��z( :���9 Prim{>�k�[&s} I�estTV6/"��lu�� Ttim� � work�4Blum, Lebowitz%Hep��K2�� y tr�Nto ��a rigor��`aj����g"p� O-:"�d hardk� &�di)% ed� betw� two rigid���d walls.}sF�$Hamiltoniaa� quiteQly- �}F� H(I X,\{\mathbf{R}\})=\frac{ ^{2}d}{2�epsilon _{0}% }- , f(:K+H^{^{\!<e}}>� �-� F� �$6Y$ \S �a�ticula�nfigurA/%�  ()^$ coordinat�) dipo9orienG, etc.)�i�a� d�recA�te� oe-�h�-�$d$���-!� � ance[ e�FC~$��unt�C = 6q���)�Iy� field (O� ific�!(4$f$ will be cl shortly2H5�ya" indepa�n6� gye���}ropy=,p�lJ'_ M�6� d}{]� A�}~+\ Qjpb;,% \[ <(...)>q4int e^{-\beta ^/}5 d\Omega}{6 �61 % \]�!a��3��A/gQ�ve�;'s�(Y�al spa�5$ �$� �$�=1/kT.$&�! reveal�{Q f$:� �!��c1�i�MuE�.E~ ͧi�d-�$ariF� Ft free (�u) > s shA���ap$i�dM/$oM �by �s (A re}�) mole�P�es)�G For.w��typeDE.�"�am satisfC<ga'n%�Ń��j�t M�v-��HA}{kT}(-��),`C[A�6XS%go�im��`self-e�Int�@ult:\ ~J� � \leq �v�&�<=F� 5b �yE�A�a��T�!!�E@1��5� ��iz�+Q�M�I�icIU� I�reduc9 :��he2�nHcre� ]i� Yd pl�n�z i� J�u �� "� A$it{. \ }On�"� note � g!;A���4 $>>\lambda_{D��ha�~er�( Debye leng|$B g.�m��'spl�in�)w� �Z.�!'5�_ lo2oW  "-�des:"n[M�=C_{1g+C_{2 .��I � � ���\!�� un9 ed^�!�ven� "�$dindividu�O*�6�, 1}$N)-2}$��&�$yi� (24!a:R) ^ ����(� of aJ+(" ("DC"), a��Vpo�"�! embed�M�D��X�llel-1RorVS  ou^!t 1 �~a c&� �*-s�wfa,.��!ZDC)�0f~=f_{_{DC}}=�126+ P_{z�T 1}{A>K<% \sum_{i}p_{i,z�l:6V�<(n arbitrary6�!W��5Qw %$�\ �z C 9 m�'� X5��}$ �� proj�-�.� Lnormal�'m�laE. aC��"VM 4�9g � X ca�he �>� ,VT)n-�lyYluA}��BA��� �� m.0, it \ �U��Eq.�ub,see p. 68 of>*�ithM�A�ionn�A_ qAaz � e�{��}�)U!� $i$-��od $B$'�� ` ! 7� RvedaV$z=0$�-�<��z its a�og�v� repL"�,eri�UAo�edg.+.��};�y hol�.any�in�&ch!� �S�}(�.�siF!in�se��t�g� occupby����E� �~s:�!s%�V*A�^� Kd Y!� ]� �  l.Nba�sc�.24$\sim>:B$M?osum+es&k+�(i!�1�� mult�)Z* +�,. Such�s6ts Aly exe�&&lak ble"'s, Xose�&z�*!͡��-*n FYy,Q s$'*y pene�)a iFr)� J�!{��&� Rela�6g1sg1�m%4�"�)d "��s"A��r���)�-��� anh+impor�!d-on,a�C0dis �u�%>"��E�f2�1ors%� �}-/" "� -o! �+� i2n6j (deh- :"�har�'m��-2pA&s are\.3}m illuAntA�"� F�" \-phk� em�ize6 a_�2L �%i3$d~$onI�ing�B�g$e�� ly� rese�3as� b:'�� 6�>�i� d"�oten_RGC�36� �?3� 6��i6PY�I3  or�oci%y��O"�erEDmass"7wo .�4E(-*� �C� U(v�"f2\ We Cp�".p back-2 $=M$2�e8� n� vol"./.A^ m�us��a3-! t,vof��d:�)���"innet ,or Helmholtz�!�)� y!r)<4BocRedGam2000}u �V�-!�D4oreF lex� �.� b.�I7 (.3"�*5� d!;$k '.&��are omita��. �2=�W-�a�����e}�]�iR^U�= q<-,eRO* (m��� e}^{i�}zdz} � � zh &n:H �d"�*�Y%f~ !�RGC�BS(jvOC)�=-�X)_ � ���e}=5H+ �/.-"� cap_��ed!6�D2u$d\ $o�, �F fe&�\ cf*all 3m],�Jl��B�1 nt=$ e~($or!MD vo�7�"�"6~X"� �D�:9+�JQ: d$ \E�x3reflec�1 shif�é"� profil��bu9a��nsequ>9Yshapel�D 2t9. Q {,�.8$ �*��5"a ���de��#���. Ela�7 ��f�*lipid "Q2"W ic0"ess Cro7.9:8b ��b�"�#s�!�4Gouy-Chapman-S�, (GCS)6.�- 6!��)re��v�3{&s�n"7M2$*�&6#Ea!�e�1F, $d^2E�)<0o.Cu?$ .�ifR0�0H\cdot d�  d<0u�C<0 _YF��3in�/� �!�atVYt��,�du?6 a�85is �whelm� �QG;P 1-0ion. A numberr�*�9� m*=�AMB>)� AEDR�<sho�$ �6��(NC)\6�"H�CA�at�;%�U�%� .��� � ��#<� it{,ed  "$ (� aoA�K7Id 6).� !@mieq�Z6�R!)�q bal�"�9!]-s�&�28s..3�" f�0 2in�)��k,� NCB� V6�sMN,x > �" 1&� �F�:�$ KimK.&r89�9P) �8 �&>1Q(}E� E�:?!� for J��� � mbNj E tradUal GCS%hsX4���^�Q�ųI sAAAougj Oe it� (a�-J"l+^*�!�@IZ�c�#n-l 8"�2� A��)&�<s�a9ieN�}�*fur��*x7~dAp� ix u2 hile#ag%�f�ng�7* 2�y�� b� th� m&ja��% �M�A�sM72�8}!��- a\ necess�)�X�appeare|E�i�3: . If)�.��s�-takenAbM� ae�I% mayD d� إk_is�vr \�u"�*P�@mr�5��I ���$_?9!QkM�.�y5} CoV:�Kon*ioa/ two-*� )7e� $O!a "  -&A#!�!�^&E�de� ��Alos�$(approach, $} ,xif'> yNa].'s1t� &G MIB.� 0,BruGouPin94} :$93.�isF� T� )=C_{H��D6/DLJ)�>g alig�7:U & =\&�7��3��1(DLC_comp}\\�3>�nDD}\)� ��U�,h: 8�%镤 drop!JU#��R u&;] �1. W� w ��C�ܱB":c �1#9se�� "($�i��G $@�a��ek$z$&�MW0R>�|A�A�i��$� phi(z)$:%1�� aW} t= [1]Q$LocModDensN( $e classic *�1� Poisson-B�� .� (PB"�F� symmem'�hR� rhh}=q�~\cos h[�#qJ�PBDF�I<C�9�*}M bulk��_#f?H �n ��slighto o?!�x)�I6ing ")�s�%},"�� t d#n �}�GF@on )� H2�!4k &Ai �i�%�solid2a TQ�V11w(z)1z[O \exp--}(]}{1-\ThetaW+ �;F.}I�$NH2H2ZHQ� PBD_%j(J<$� ,2}=A}/N_{~% �6 maxi�p� �Y�A�c%���FA&!ĝLC.\  l9+ 3]iz�I^�2Go��": �5�h6 si� crys@&�T* one-"�5�$ti��2.j@in Fig. 1.\newlin�9�%TCIMACRO{\FRAME{ftbpF}{5.0678in}{2.5322in}{0pt}{fig1.ep�k%{\!<@ial{ language "Sc�)A� Word"; 4 8e "GRAPHIC"; %m#ain-aAt-er TRUE; �Y,play "USEDEFAvalid_e "FAwidth �; hea� 2 �G$epth 0pt; #*ginal-8 125in; %o�+A4910 cropleft "0�top "1rs %bottom/ %�name '12';-p�^/8"XNPEU";}}}% %B`/9�� %(e} [ptb]A�er} \�g(phics[ �=1, �=1* ]% S1��Na�p %End� zquote} ��bf{IU }S}Ba�.�*� !�(�"�% ,#a��>ni,*� $\ ,�>�~ 5�%d�>G&�6n .$�� � We�" a*� ..�  *�N� vareu-��\AG\{1D,array} [c]{c�-& ,\�J zy'� \\ 2"v "z>a)� N\E�. �cDLEe��&QY2RH}s�W2v�"�=�0ta+of%m&� � � �-�(:fIgnor�u�.�-[ :&i!�"� �I"N B ��>�N� � H"%s`M:a$H}2 0}}d!�� �)Phi_H!�AN:oJ!2D=a�&�1�dNR)Bj�*X:�.3#9�)�d�. "yc E�*.�,N� F� ^6�!>4[ �% 19�~\B�  z_{e}"� C_H-RFa�D&G  �)���$2x$ ]U;&�Kvia�^�� $�$U�quN@O">� duQ����@&(pro�Iis&� ly turns sH$a aj6 cite��i 9E�$-) �e�ob$F�u��!� <5-5[I1d�s.���=���f�a��:)/:�n�0#�/� "+%Ral picQ:)Ral76}N��.^�A.� <7�O�5Qono��s�!*��, }\"�= �." U  �N;?yw {`far�a �*:M�} )�1�2��.8�g�.ly(�D�m� s; I�q�� �/F%� ��-cubAolynom�\���e<V�e}(0)+s�>+pI��.+r 3"D z_e(sig)Fv���(��(0)-2� +3���C_F-fI F���6�Ix>�i!Fto�$��A��,ct "sum rule-B�"e�!2=-.�5_��v"�7+4hi_{d}}�  ((phi)d Sig_ro_ �F��#^&ex�� a��*&!�[�Zo^�+vBS��}{�~)�=D}E]"�y "S(a)\ $�"�8*S  K@8i��-a�G z=}!�2g a��)lM"�$ a l�J%�(D}$ (we choZ'$-~(\infty�>)���$ �O "�(a) of op���gnC�.v1!s>9C�W )X>�J�� vert 3 � )�:�� ., MS(Cd_exact_MoJ�IQ���D��<w�;� t 2AR -, �Gus-�J�don't�isf�K@ eria�P��6Y"��jE&� �2r�(L!��5"��$�? &�I����+�f)Mao�.a "��0Z�.\i�!3>`�`ly 1U.�KA�spiri� -M"A\Tm��!�!�-� solbD��Fa!I)$1O�C!*!"Ks#."�,!� iO�?)in1 �HParKha89, KimParSolT T!�A!x7�u�&�!� 'SiJ�(Z7u)beV,)^{\alpha}=G��"; $ot_Char_EqNWer�$u=~eu( �kIa�)'6if) Di: i�1r<[}kT}~)��OZ~ � �("�}} 2}�eN�3}1�\] &0&?�}=( =N$,J�1Wg�cM# and �!ʥK) sh�N�i� FW M Shottky duliOOol/?/alyUDKG{.^N&�N~=�� �u)� q}{|)h|5� }\sqrt {S!{+4S]\0})" C_D_S��NFS=(G-1)/1� 0},~ X .\ $!9)�OI %�$,a#:1.��J� -* nume�D!'�)� �jA%��Hmpa� Ei�c.}�Xd �?� +packing�Hneg�% 1 R>a desc"�/����H, . n!�z1l�u�Afamiliar�ionj`o}=iB~(J�'!�)^{1/2q<]3 A>% }{La� }[1+�N/ID)L] L �kPB_sigJ)i�2B\ a=E�{I�� rkT\ }{2qy8}% =}\ 2.82\ 10�2I�FL =cH}}[m]���% �8Zz = kT}=7.67~p4 oX* T�� [C/m�"jLN��� $G� !�mo�0t"�5ent�2��=0$m�w65�HdEKd? � :'s .�9�oAll������Gx�P uA/i�(�$�Kt�#� �7$(��^I�c*$a��0symbol{126}\p"�Us�yM~ l )~�Na���--$Bf&��$l.$ �U Solva�\[ l d\ � rime}+͐E�}{R% .a ] y�>R�l(\N_ tild"�V:f\�~\ Log��  +i=1+ Ak�H 'WDiff_GafV ?=)}�.$ō" less%DE�n $�l=l$ $/!�{ }n  1)%�A:6�86X&e � Y( �)$ N2)�) # 2b[ aV�s� ilar #,����&U� ( �s 3F4)�35b�3.0441�3.9306 0*�2������&��v�3R�3.8821i<c��&�%-����1�1%��a����} ���QAI�.}�\Vm.FA�62v m]}curves 1E�3yZu> $\Phi=i6iC @� Ai24)� �� �, maynd�mB�`,qD; m�&D6��e�R"K!N�: \ =l�6r% :e��%/%n&VLb0N)B� ��Ko8AV q \ =1 1}{3})h�z $\ (����"< thingD- �} z\bigskipAM8w-T,9*^bs �,EN�8s��� to%�GC6�Ffmos)����a�.!,2� . Ho�h�b#o(*�:'� Z�insuffi�1h f5>�Ca peak>�%1j~$I� 2):obser/ ��3�,=� /4)�asF�6bq�\ %)� is followQP�Ily&fV� `2()B�C� "��*?)��i�1��AB�?� !��BU, AgCl "�'Eucg)8& h"�=>��*�, �}LP�hma6f6 �_(�G+6)�)�t5!ve temper%!�+* � �^% &]$ � 2 >giv>P �LMul67}.~At $400^{0}C�Hd = 43\ mM�\3k��32.7$ \AA�68�  3 0.55\Y mu$C/cm$� .$ C.!�&w&� �x? /f�,:$�$J����)� 1:_v}�.� *� 2� +� >JH}�x<:�-.�-4rs^{3.���x_9�UQ�} Accord!#�co�-ly held/Va`�M&�E�9J��l�AOG�: Ou�!"zA�3jc72�2�a2�-a�/��cH.�.EE V$c<Hd ��>o �g&yRe!rsgenone exI& V�-��6���ib�Tis"|"�, �Rsh�Gbe��(pronoun�K� &�2n��:!GR�#ݳ�R� wro&=R2 &7'�FF&e� ���e&3�!�r&N1��% 1)�4�C!-e6,�6v$, in serie�AQT6�6XcaO^&�0 "per^'(du\" �!)" gnor�2<.nP :�"ic!F"z$�"�1��s �2�}!I���j�N&S!� :<2H}}{aa�] N��>E)}AP����� a�untA"3iׅe�R� dra�%uae�� havi�i The .��o),s,~p�)r$ (Eqs)�v� w9�bSV� Au/AgXE& )�� %�.3�.�.�.�.�.%-'��(��(~.�a7�.� 3.} D*�K2k$�X� "(v�1 i`Tface:1 -2X6� -&�%���i�&5)"�2iv":Ga�p#"a�� L! =0$); 2 -T4^Nl,Z.B@�� ƍ�,"�+ �."1(Q6' mxc?Cr} �6l� ��w& J �.2). E�r���sQa.. a�0smsteep�twrI�-$cathodic r; 4 4s,� )�s&� ��{nt� � RX$,RemChe84Z a #�>��pto�e�0��$C>0$ f� > �^  C<"�6\)�.&bh i"�wMSun��[D���a ��'$ ("w>] 25)�+&� J"$ (h%3!10) or�E�ar 5/�o�Ueai&1$�/W ]`3&"=3al-g.� .uDa�b&�7 * .�7 �9�phe&u�7��a��� at1;� u�|8K*�:pl9)�may�Dr 29-$�ol� �YD !<"�4a��z.8�;��de �qal�7�PutG%�Y@a �-��U�8|I��s:��K��v:� ^ "! �AfqrV;9� (_ �1y ;).I9�1VD&}�V�,i�r� J6 on{$[q}"Y�8�>?]�_+ �_= 9@2  9z1stU. N8>the�,xH�'BDiM^8|R�F Ee�f�~��L6���%^*@� &�\ &qG�� � |�h$-� T�!_id�Ecal*$FC-�9 atM��1- )��*�g!QU� �����\n�>co{cenerg�flyj fer?. U7U�F"AE`O �&LUe$ph�gm&� .�e�2s (J?)�"]D�6,s�2�w)Horm ��OI)n�y�� ]?}�P��n8M�?� BFw}$ w\� aZ�Aa3>��(- �2 b2� anNA�_�FP�]N8��!��$T!��3}ny&�;�vHy1>ch��t�&�*useful�A=cus�� ��*b �er�%A�M�HaJ� 5&��}!) onse�$0a'B )�s�Qi�>�d&c�cf-m�'y % /h�DY�{Qs�!�$h!1�$ck����� ca�.��Bis �h:kQJ�C�1ZE�m��ffer"}B&_q�^ "��]o?J�t1� v�|Q���1% ��� hhl$. Mathe"�" 4��#��u�,u& $-(% ~$ing�the*�i��!2��#��W$5&�nH����-O��1<att�� �rYG�X�kly!�G-l= achr�?� . AtoH:�h,~ZF��Grepul ( ~��ensat5�+tas��icJLe��M���P� %g`I 5\-dB;}VNVnot� Crowle�kHD�G�.2O}��pathway�W.X.�f. Whe?_%X1�4 ixed%�NqDtm)!+� 1Z��vUvce�/��re�8�_65M s�S�� |S�$wJ�(~ non�Ff_A6c\�V 2M�6Y�� �X&�&{���fh:+�Cr4\��-~ �" 2_.�CZ9{ flex�GF�g�&�w4��'�problemA�� '#5] [ �sa&�+>�>n�--\c P"<�8b-���-o �a� pl_Q?�]q+d:sSa"x!5x ," i�u.�  _{�K|=�-$X��Q!�51�/2��u_>lrelx�+xi�3on&S dilut"�O!=sR�*�C~� *\���!vmidI{�/0WperturbAFhiɿ (wa� $q=0eqT]1h?(,��Ph ���T"u34e0 �As�$$" nd ��� sure gi��bW�om)�JIntroduc �A�9 coeD =h/ ��D�u!F�bbedv� tal  �>� slabRy*W!1@=W_{d,0}+W_{e,0}\rG{�&} p1~}{2}KLs(\L -1o~�{��4J 4hr>,rgm��;�,En_��!�au} �=�sx  harmK��U��N)Ko%n0 (stretching-1K ion): �Ra -�-V.GD, $%&!Z� ulu� ��8gx "$0$"��S� 1�lR,orMMQK>j" �W$]$hQ' )=EI)� �5fefXp" 3'&�'%� }W=0-6�qF��9� C|6b!�RioLS��Q�>f!B�, Ep�[E�NZe�_* 2%�*� a}{3%F}},��*_3 F�$ ~�rD�� .�} 5��� � a:��2��+H�ereC�?a�dUF�p7$f�k12C>�)# Q@�( 1}% .]>7% <\lbrack2I#-�� %��&]b,�_�FUandZ- v~4 h�d�}{d #0I0 ) [1-~ -&)cr �"c4=XF�Efa.CA$�,��vc%,/V�=�� %��ol ��` �+��Eqe/.� V�i $�1%�> �Z ">�bj$.�R�x;5; 2.�$�0\ .�. e6� u"��71[ Q��1�2�%%d;��Ee�+-~ HY�{t� E m33\%$ ,� alue"с�r %-"=���5cimFel87.�P{R�RD�R.U1a}�;�pt0��< virt��&orm"iontc��)m�gm*�5(M \"Z Պ+ M�)E al"gh\ &�RTD�MM�eb~TL{r K"A1��:N��a.�ř } W|_� i��}:5>&Uq_!Da��٪�Cu focu/2a��B}� �U W$�%*� 5�a"� )!� a sm7&in!-vXI�$,5�"[@`. U��I52[ ��E� )��)=P$a#}tnd:Na�� Q)  +�V2�$&~(.(=/.��)U_vaJ�IE1�e�&�QJ Y�K}vM�ly ���7�%�toZ"�tches $I# $II$, eaf�Ea $A/2 pe�%r-�&��A.�1to*�y_�`)5 H;rwy]'>?ary"1���^� ww[Xz� (m��K��-.��q�_{!4E+2%)r �A�p-�� pen�ly,}x ��5c� in�!� �.Cx��/coupl�wSi�~o�<is�O��� �,f['� �K]g 2  6�iF5 m�_{4 �VA� \ S'~2}~6 i}6 > gainF��:Q{ �,@�PB�)if* $<0$�j!'chose�1%� $% .$3B���$�o�p���*� a*V�g&�A�1�MF� ����fi�M�*q�iga������\1�penaltlc�*Y�inuD��"�U *>+J.�*K q ��b�s8�Q _2ar� �EtG�Z^ mor�a"Lk,Nik91a} \ wh& ed��"�"��tNz����~s��W�0ll��a��&��!�"@��� 2_ y�=�$2�O ��e� �OBГphe^ oq9�.E@oW�� &?#���!��:M�GQ�V�ch��. ReleaA i{)���0���1hw)BE�>��oy e�@�e� "�uA3) .�d$ic!5o� A=��@uhP" �  x)=h+2~u5U(kx�u"�Du"�` itud�Gunz!�{eMSs;: "�C"�*"@N�j"���d�,R� s9z_{r,l}�\pm~zH(x_�{5 }=h/2\ +ulo�.� \�RV �� bn}"�!A�"�%�6)�Z.|s.�hA� V� �&�!#r�URXa2!environ�!fiF!q�q:�$q� ��nsteadB�&0 � . S��S"� solu��!%ced)�&#.�j�,. (1) Unlik�  V� ,A/e2ɔ�e"U8�WO$VnӚi$Q��� (��m v).6�4� uc�Q�Epst���"x\���� �V �P`U�m !2)�[ !�.Ad 0"�T:�"� Ζ!�u*�w�|6$3u$$k$$ac_F'u Hq�� (3) `�Hq��{�;rQ3��a�)5(: \qquad(a �Q1� aA�!u�" bitr� % ��Re 5 $v(x,z�=����)27i��Z m��"�4And95fz�b đq $4\p gma�q&�($\nabla_{n}���) B�P'>�V (x)��?SIaI Mu*s��_�.�+P0� a�-�c �� +�� $*n> q}(V���by 'N~ng6 �\ �e�Ue%� a wO�#fa�0, $1/\[D {1-[&lx�t�]��C] 6_A_ bQ� �lv��oci�8A�[�!��G(d)Iky�Ur� AX�� $9 )�I A+]J� i,=\+ 2,_{m.%A(}h(\ 1-~H {k\coth(kh/2)}{h}u!"�MVN���$h=�V�.K��h�h7�E}g�A�mbQ�)��� �b[ �Rd��&%a�-c�\MZ!^���m .� � 5�'sV@��NvW�6^{q�e,�q�u&G_�_iF3e�^d Z�)=M7)�!�~ % }h>(U�BN6a ��4 � q�Z�!-=- )E�{kEq}{UM}E��[ ' {k!{2�]5W W_u^JNJ �. ��j�6*�\ ���>'j}�;( mpeti�b� he\"g&1))��`�)y�\L% �qE�6�q#� (in5u�Io1�� daSXY�|H�u&,. }�H&�,RS`,�u$k.�(aH�~-�lU�_r�9��Thezge"{[ .2�Y(�9"� p�j).�&�s�]E9�I�%���*]v]\J��$�5;&-2�5%��a1�6%�6��W_eJ�v��.D%"�A�b W_{u��A'k" � leq0� Substitu�&a=- !�B)��! } !L"�2? �+2 \midB���.|\ \geq� }7,%l{J�X�'mY"�Y to#�`�9q���t�kt.�!�u�!@ 2������, �1|*"Q,\l.}bt;� i�xlW�R�9�@"$�6{�|-i"���a�. M &�%\,J=S�e25\ Szta�ly &Z.�.6 edge��' �I �!i�jRU  %< %�� J7&���1 )=0;{ 1/C=�:�!� ��ac��2ccu bit �ie /t~6P�rough��I �  a Max)Y�Q'2 ��J�*WE[v�+aln�2k(�:t$&5Oed2)(.8L $*�\�arrow0)�F�mML�b�� �8urA�x�o�#a��)K� &� %e"C*Y��f 2�$9"����S�Aon o(own�^�"�DB�)^r"U&�".l}o�:j)u�}�p NC�"7X/ *�[br)څ�Rb�.z_��C"�s\%u�U� C2�A��EW"Ŭ�E��ing, �txm),$��[�4fn $1/�!��1B" 76A�fe�}ja�E�ADuld!P s!iflW"06lWL�Q P quu ��2:�&�"O�`.\e�rv#=\�6ng\/�?"�o im�at�B�"{���"� < � �E���ap�]�Tc�2o��!�A f9-O&�g%�t�mײ�3B�9%��B��a�aDp�.�7\��i.�"��dS.te2ߒ=�a�"�A��m�v_$aa�wo� FJ�$4�{% xtra; A *�a�m[" \ (uZ-u_{2&2h c�_6�amd.��� �BG"�'�A��q ). DWAMon�W�� an;\aX$,�c$�)lda�EG <0$%.")MIbef RF��Å�eV��ent2��.est"�J!( stic6� ��E�L1B�\ "VproB=w�i M� ��etiֽo.ϧ-i$A6%c ��w T8 i�&s1ll�!�-ly�� ad��#���7 !�se� � ,*@ A1��7  a�ig"�mat`:� pr��easo�^C��M��c[ �6�`�!w%i�tY# majo�_Zcp9� $q$-�Xo".��|�N�9}&� (6��! <���a� )A�bZi�]st�ultD ���M�2�!��|�}F��s�1 rast�1�%�66(�5)*� ��![l\&ec- R�&� �&�A96�&")"�3 �tr-& :�6o2�!(a�An Rg%�a�#?~%�"eVoI�"�!R�b��4�]!�"R*P����w!�:_��e � "�*��'Q�d� � eA4W�=Per{<�-a �xIMy���b@�w�de%�ish��!%�*�-�.�}�>Mvlԟd��%�E*#�@ )� &��8ny%��b*�.�Nde"��� w>��yE`u p�2��,:1 !�R� W�y�H 1980�; �<���`"hst�� fa4���9�rB� 9m�2�6��,͖�$dHQ ֳ ind, i%��`s�%G�60"т���ek�a ZerA�Xp�C*9�N�}g �tha�  iOQJ+$W�x� a��z*+In },�lrdFA� 6Q -�2D K&BB"P  &S E�sB�r2�,%�s j�P:"�A�Dh%�Ѭ (&j , %q�)�!�+�> u�L!( ��;E�$�  2Viu?J\ W!��b�>�? �"w � s� a�y���a��RR ��a*��B�"#"To mz�JA[� cL=e.�"pA,o&�$��A/"�U�E1pB�6����� �li"�w���1�L�n�oW�Eu�� ~2��,�c#�2$principle,�96��� >+ �De�� 6�Nsof@Ed]e�s }� bi^kV��I:Q�q���, "��mO2{},A^�gG&er��!:�did� eEV� Ev.� i.�`re-zi�ine� usagGSrms "@s# "&� "� no�E;A'!�6��="�F�<W�tM�%TB�- *$�( �(t 7./-� w-$� �<�W��`yCCai��.�"��A��R' s��Az��1 i` 2X�*�  �.� =a�*~��ofS�,&�# A_+Al�} ��al �-"� {� N�r�via@�eD �w�.�Y (if�existsjj %�C�y�)8��gun��Tl@�L+9&'� ";C ��a,developJz� �Ld�%6l (�JѠ�=G (� ��$C\ <� (\�5+�"E� PNn�C!!��"7�����? ������@&�*�Iw�Zv/A�]%�� �m&©a i��!�� �A>E�I"�/!%��0 �V9�X8� h]��4 �b � � iliz/*�%��Wru��2ާ~aa��2��ci� 1c ` of n9D%� �@�l"� ) "ide�1cz� �Nbro �!�_--2%~ fer [. I� U{) ��M0!&���>%%��&� �#. 2�� , ob��|"3~��Jf��| EDL,�A�.g � or��!�t��U�� �-o�Q�y9=. E� ��M %�A�a_(�Dsel�>d\ ���H�M (şas "d�~���+"�� *@� ,X /�Q"md-"-py1C�V� ,eN �.p�A �trigge�RG56{ 2 Pa&� � ���.[<24Wc�X�a/�B�T�tby.{8i��ABߕ�� ��Up�eYm"E�� �Ia�"QFA�j�as�ʍb�K.Y![ A�c�#6k�E�f$�r �K�Qeral6�,m� keepA��0x~ } "WWinaln�v���( �H)ACanq�*�{(*�e&� 6n&� des)q�a�� ���fl"b��z���.A�e|}ofa�!��.�(DaiKorUrb96�"D�"�D�� e"� �)6�!��m��g  vW� arc�g�*{AcknGdge�(} Work supT�y_rL" @N��al In��`Health, GM28643. M.B.P. w �Hank Dr. V.J. Feldma�Sm� fruit�K&��T Professor A.M. Brodsk��Q�)@��"mS�-�� %D��.�Ks (pr��AmmuS�a�x9 sim$ 1988f�aPbliograOtyle{pl�58\put{partenskyjordan_3_2_I�bbl�Tdoc�1}��%\P�[twocolumn,aps,prb,epsf]{revtex} 0[p�#int/*4} Z *J cleN)u&9ckage{n,�icogh�)0 8.5in %\topm� 0in %7��4itle{{\bf ChirP��Prote�[ol��}}�Axauthor{Joanna I. Kwieci{\'n}ska9 %& Marek Ci�(4k\footnote{ Co R`to: M.+, U�A'(Physics, Po� Academyo�~� Al. Lotnik\'ow 32/46, 02-668 Warsaw,Atand; Tel: 48-22-843-7001, Fax2�0926; E-mail: {\sl mc@ifpan.edu.pl}} } \affnA�{yv���>�%��Zab6 ct}�#rze s�RA�3 eD!�t� )��a>R� �D sp)�s. On���@o�cro�Oa; thres��/ RMSD�!�4a�K�� Qve w. �bchecksj"_^= )��[ ���:wh 2��` �� mino acid�me -�jan�����/��.�! �e!� ?` .��"a��5�A)i]� Z\ � �)de�ZupI�angle-�2� "e.R8end�; \mak�+le %\v�h$ 40pt %\no�H nt %$^*$CF� \\ %6�V�j� B� -46 R�SN�N���:�j�G] �&\sors: NSF DMR-0083286, %!�KBN (Po�]D) - 2P03B-146-18.b^ �v %Key� :� *d1ofA��s; �K ; GoI�X�&��yz��7itin} �(pace*{0.5cm�FI�L��"C.ino T&�E�- m�E��9�a~off-lb��Genm!er�eip ulty���%a�� ma�#a�7i=4 abo�4t�Is�� � �ho��evo7�pnN�p��i4a!�e�N a�ha,?r�A�he���@"���.�L um�� �(�d��ex�ơAaln<�bua��[, �a ��F4zero measure" ���=m�=o� %� . Cr�i��!�Im��tfOin��� �'� �)�H#x i�Z �T��g�� g2# �9�'eQ-i��-Z("cocoon". AlXm��i ��� ay�6n� J�9�0<"I&Li1999, (a,Hoang2000 1}n2]UBA�fŞ� C���9ofL#t@!�I��.� &h- ;�Z hod,=n� ,�ed A��gr�Vr��tl$*d�lic��a���ito ��7w*u�f)B�K.\\ S�a�tly�d�d0QDú�5�4ist� of aD�& e��o%�:- �,. l D/Q��UZX ��M4e2&X 95M�� , $Q��e.�� "n ��!Ade �eGb�pe;H���� �7�2. U�a�!:f��!s�!%o' �5gB1. Note.a���no�!3apA ed��7 _elf.�: two  " e�q"r T�=) �f*� , $r_c5Fir mu -E�anc&1f�:w*�QE� ���(2� w<�C.G- R +JB5�by Q.Ν. lete����i�!� irU��Xd m by A�Wis -�angula-o*H�� G�bon +�� on A�usF*<b���_dihed��� �  aq !iM�Eopi�F�Ke�I.�Cap�.wҎcoarse-gWZ> �:4Abe1981,Takada�8}&` 0Lennard-Jones*^ �ks1� s�*l�*�i�&~��!"�� m�; V; �'-HsB@ -- �&�ei.��@U�8Ortiz, Kolinski�6Skolnick-B}. Fig�?$1, for craw�, w� .����9|1%QQ]����t s$A�AKqgpL� �g���'a lϒhy� �u$-helix�e&�@$0- ,�d�1|E^ � �-]2�Lmis��tes�^pit}-eN hA+L��i=�(� iY+i�-&q"�`�� (1.5���&� �7�X�?"|�"= ) �6�6��Ō���a���� $\AA$.a�7-F���\* �,�oŀ��a%�!ܑ� adop3m,Q"ng!��/iq���s� Ew "Ctp�&}<�a��a�ait"� �<pro�iՁ 9%t&. �it� �. lac�M. ��2lu� Idra'j�V � of:���u �)�~�Gm]9��@&� ;"A|-�2�S*�ZW�(._r"�+��'� �a�ul�a�I��5�1�FZ�a�[ ��xsetEM T��inM��M4�orEg�precedAD$e "calls" � e��!���:�,$f* �ա� ��"� ,M�!Xm�.z�a�B�N E�a�5��]1��1ly��* E �1�\��A=opologyE(9��������Ct1� ���ii� 2003�TW���� � Ig)|ca'��Q�+ �$�Y�d�����m��um!�A�9�$ coincides�="B�B��-�u6��D.�v���� �-a;� -wis�y�� �*^Q$�B�!Er ngy6�$Q��`:Dnergy T�� * I800EX2300 Kn t�IlYp"5hydrogen&l phoR�"� on#1 roomer~"(�e��!|$\̌T}=k_BT/��a0.1c 0.3 ($k_Bu> Bolt$�^n�!t). Ni$bˡBy�te�L%�a"UY�I�aU�atÊ# �'!��Z���-�$ 100�GR^{-Z����e���m)�!BGO}usA�Q fth-��i,O-%< $ algorithmIq|step $dt = 0.005 \tau$. A Langevivr&!�� dampq�$\gamma %ecE] h1��=O!� >N2w6%��!$?s����d= 2 m/��ere $ =\Pm �� ^2 /5Y}m 3$psa�h6=% �(2�9�i�*K �p�a'E���a!�A�!I$N$.{x�i�Z1TAaM��܀ $N-2Bk�u� (1)i�=Dž�l��X?As�'i��N�. C�!��.+}�l$ValV7 �B]8o?zrce��a�g"ݡway�$ 7 �UeiA���$N-1$"(!�0iN4!.� �^�c�)*oG! �tl�����"uFs���! nts work ����ba��eeJ�jB�+lyT"�all�Iv�,�%I��$CA4��-�winD\sge� ()w �J��%�� � )�o4ve or&��A�!�2kaF�{�l�n&m� magn=*I��!�2,lanar loop rQ�� e���?!% �i�IeS� esL �� bimod"��2� . A��um � 0.7 A & $i�nc�i�b"��$��$-sheetsLi$ � s�?-0.15%* 6�%=oop�#,@6i!�a�N�or $Q.e*-&OK%�vingE ��s��focg�I(16-31)�Uv$X-!^!�P< >i8capsi�`%o P24 1e6j,/0(41-56) hairp7�� 1pga�onP � 1cr�(���N�Q�e�`e�Ln�pas�>ime. 501*�E traj �PM4used in the ca��se of secondary structures and at least 101 trajectories in the case of crambin.\\ \section{Criteria of folding} Consider 1e6j(16-31) -- the helical fragment of 16 monomers. Figure 2 shows examples of conformations that are declared folded according ��Q, R,�@A. The first two $Um�dI�eQ7 as a��ulWadopt�=��e�%� izedA�!A� er (!do%�6V�� of asMR �.�)'�9Dr� �:sM�. \\ !��NmonitI�F`2� we i�e TaWme�$K$�*i��"of�`-� �;i�,^{NAT}�E�A9B� can b�sidered!�being 6� b(-like, i.e. B�Ymright����4their magnitud "� 50\%: ]� ength. A�� venidefini�0!i�,n given by \e�{a�(x} K\;=\;\sum_{i=2}^{N-2} \; \Th� (C_i/C_-'P \;-\;0.5) \;\;, \endOwe�$ <(x)�!�step fun^  (:"41 if $x \ge 0$��0Iowise)�p�ltop-left����4ţ� l� )�(�f may�c(rapid tempo�` evol�@-�translat# Hto a noisy behaviorTK$ѷ thuseMrea?icAr seek� �ny1�� $K_IyJ N-3$. How��, c=0.75\; (is atP d in simu8  as��"8 rema����{ 4<se��q�%3!�2 =I� �(established�contacta^NQmWa�K�wo��J� ����c� ��� ��� Mstrikes%, [� ���e�!�j� y befQ $$Q$ hits 1x6?%*{ akes plac��, �G� .UN ��^� � We��p& "I shap iU&�of"�4should combin�� impl� su� s. i �nd�$ G "� :Ra�E�ce�.>�F� now on,��focus� M  based�, Q)_��� )-�- will�| deno� by Q$_a|�� A� -�B��!��!�I,ini 8 when both $Q=1~K��$K_c$. Simi$conclusaw��expec�to hold A�`R%���a �Q�A�A�extenR� mzu� )�stc�_"+)&Qimprovea�+ 6=2u|i$A�D \vspace*{0.5cm}* � u pote�}F3*Go�$modelf orks)�a?�2���a9"�& �Qpirit,seE [�o��3 curr���by ad���[s�k5. �� %�beA#4at atomic leve�te;M in�zE���c t� k : Z)�in!$(ure. Follow�."�� 8Cieplak2003a} (�e� a misprin"�E�, �w re)co%�F< V^{CHIR}=>]�\frac{1}{2}\kappa \epsilon C_{i}^{2}B-C_i �)v label{pot) } R�!�dim[ les�8 |$� trol�stZ�|he]��� � �nee���sel u $1$ Z a�har�c c��C_C*�9�o non-I�C $lsoa "�n e�*qcverU �2�i[ � ead�2�2�� penalty�" deviEs^���he: iesJi1)_1r/mu],(E \; -� �)^2�' $\mu�aY�a.�%sideseia7 c2z 9�h p qu]�l��Are�sKp� at9�_1$ tenI]� broa�� %Xem� AB] &3t� S p� �hapA�?� on equ%� (4vSt~an���Na2duW Y�-�ed9 b re�lly����(Chen, Zhang+D��\c4}ͤir stud�a�i���a�lin� energy e�l/� � � ao(xternal uni�� f�]' �j ng9)5�be�thwhi6� a� mole��%��ɹ�3our1�� on� �� coarse-gr�{͊����e�a�T��kity���be �R����S"�fsRncy ��Ramac� ran maps )�$Kolinski1, 2} (��_D7A� "�� �} � descrip�cA@}.�al �)%=For��� 0adh y�M�'"t �s "5@&� � � A�^�Q� ͓.�7,%�%� ,e���� KeWs� �arU P=1. Fur��� U �1$ddif-_ � {R�&+� � ����er�N6G�-�$=0, inqBt!�'nM�oX �� �Q�<�$�+ne��#"e*s� uF�-�9� -_� ��"��!G2*"�\�&��"0u�B���9� �)\he samY@� C�%p�l$.K��G#� 6+ ass�he role�J]�'1@funnel� plot"�f) ��@"� of $�E� p. � 1�s�$R$S binY���O!p�$is $F(Q,R)�� is "� -�10A!_.� of"d �e<�` a*A�8.g#yͩ9 is endow��kminima�asEru-1]e� just�z���!Snes 1%�ɫ 9�1i� a smo�^��!#� landscap�&WQ�-a cess�%�� detailsA look�Cat 5��ps )c=�lbL*ud"eso 'e�l/ scen�s.��%�a_ n�Vf�, amino acids��roach.g2�u" --%�%"� �&�* � :f�*K � �� d ac�)I��p(J� e!T�W �81�51$�e ,��t ambi�"u! s 1A�j 13I�IB�1!�T �1*k =0.>���y.�&�%gato9� pair-� =#���4��q�p�tAUy ~ lSk d �UB�-�s վ���+Q�5�)����!_<7,on ess�ly doub�+; �� ���s�shorter $�ee��s5@0���Aa�t� er p6n �W�*�V��2]@o toEw� ". � turn�war'2M! Y�� ,2�2� �B J&t�5�K �#!�la� 14�I'=7l%>.A���A�MR monotonic�� ��uM* s%.  � =1���@ts as�)su b:+G�E\ �coincid�-�, d�%���AG CN�A�usſm e,I$�̕�&Qa+�t=�noe1"ja� U�!%eviA � �..  6�1��"�9�� "�weO%�E6��:�.�s.� ndf$!e�er�!>1�*&T!probabiy  1taų8�0 'cocoon' cro` $*�$. saQL_� mo� stk�1�af�=a�*C �'o�e^!Gu� he Q�" =�t&���f��uv!�.�q$�$|_ 4 �QB��:�=ds"TA;a6`mH8 �I1N"[ M�a mX �q�15�N�� (M�n5re� no Gr\ !@�� beyoAT��=1o %Sc�!�alphaAAy:^ ]eKund % �onxwit� &f . v& anguC#u�J$� 2b"-���H, ANG}�( \URD(V^{BA} + V^{DA}$)�0!GB ) *"�1N-2}K_{�2}( �- 0i})�%,>�andRhDA>h3}[i8phi}^{1}(1+cos(o n+(3 (3)()]B�%Here, �3\I�$ 9i}$�!%��3e��3)�s U"eh3!a +k 0�1! ���� t& 5��s.*� ClXi, Nymey41�pOnuchic0%} (see a f���cusin &j>� 3b})���' 20$\�$!* 0.5eA�)I �!1�-X.�$�$58�"� y $Q���n oi lla �l&�ѣ9?"�  W5m $� ( customaril�#ed:i��- -�}�:�S6���>��f�siD+� suggest�2al�T' to.I�5V(demon�0Q8e ���b�_5 � e�. a�.18� c�6�]��A�� �F;5�hkno.n.{4���cwnio.�!� � s�,Ű&�e($T_f$ grow��.Hexcaat ti�1�&�&y,!"m�&d�q.# Cd�3!=&� d5 ]��g��1V� !��r�{can� al"� R� E���6ŭar�y.�� l.iz�I�"�!=7"n "��cor(. ��A��7� Ճ.n%��s� 5WiV2�9byj 9PQ'o0#H�%5a�ABs� ab{�, or sla0ly�$t�7t eli� �!~d9�Ei  ���W$�4 � e-Qed) U"�4"� ���"�&�. � ,v= $ myup!o14���as-� #9�=fiQ3"L�= u\ A� !�*##ly ��@u )=�Hns becau�9q .Z� effo�ak� ?cuY0%x.��#� r� forces�#u �-ap"!4:6 #al�.� � �5�� ions �(�(,r. A purist'*�w�cludeI�I� � Hamil�a>$z ���upsJ �xorigi�y��.6#s� ��"���w� . Su�:e��ga)5O_ ���Qi5%�> (e $C^{\betaatom�E$!N! aY%c }�1@the backbone. Our.�! �����bCn a"N) publj � AC.��-_!�&�wo kind��)F ive �reZ�pa"72:!�(extra degre�� dom �teFf1 soph�,N9se�l"rn��ints. Wj th�)� t�tsW&!Wac�5a#/Maiects?U�7&s%� >{&m�]�A?itq+oes�,guarantee em� 9 :ca-ct ��&�&�^* "CeY �fact, fŵ�6��> ple:���A]y a~�-2dmMI��z;"pE�2�s�!�?�"be aug�e&�����j�1�ɢ& :c9d �%ZL�� �)�d%�6��)�sF1H;*iu usefu� d� ort4+ingred@!�2�e"�:��Qmit&�"a>; 6�'�z�d2�! rab�b�O at g�R��Go��roxim� . �-d�A.0�wo&�� �"E0&� � �* s:�$m%���V�<[ n�:]C$ T>.�� �s: 1rpo�� 1efnEe&�%�Ik$\�Y$- 9 7�7e�#��at���1q���BU�][beC An�!�a� p�I�@ {\bf Acknowlede?s}E�ae s�xrt6'KBN�Po� (g�i@/02 P03B 025 13ank A. #%�le�u�  h�%om��4t�� %T.~X.~H.�k� �� �NEn al ST!;, %CounciH Vietnam. ��1,%�(REFERENCES}4,o:Tthebibliography}{99} %+{-15mP,b�1Hem{Li1999} M. S. LiE M. f!, %De�%�����m basi� qinuumqdofUa. J. Phy��(32}, 5577 (|)�6�an�FCAgwo-"t*�?ff-�&R� �Rev. E �59}, 970J�8Hoang2000} T. Xa�>'>" %MR?&��$�3a6.Gin: %>8 Chem1>%<11!=6851 (�2=�1:��=� %Sequen�#*�8�.�m�)�J�3}, 8319�12�0Abe1981} H. A��nd N. Go�Non"0 ng � -"> )�.�=un1Q�&� in %globu�KC$s. II. App"� �u:,Q(5 Bi�( mers)m 20}, 1013A86�TakadaA�} S.  %Go-��#�'di�=9�U�.J �assoc�>d�QVe�a�coil-��G6o0: Fu�346N���1� H, L. Jaroszewski, P�Ktkiewiczi6An��,2� ����Hs.�Z) E� %�#-���o$298} 937-9�'6@&|8b.\%: � !�Y� )��-"�"� o A� ica � 3� 195�p)��H>�0 \newpage %\ihP{FIGURE CAPTIONS} % %��pA� g % \��+M{�-*�8 psfx ==3.8in .��f 01.eps}}6�" crn5"�;3�\�P { C*?#�.��ԡ#�&!I)3r�=46` id�SL�)�&i0�2� Xstng6f>c�ra�[: ;�"1aF*�Y,�҅��L:,$E5��uYa� $i$ ruiR!��V�[� ez�W�Q�6fK@ s. A>*�Wtru"�%�: 0.83)%7158884 0 $ 6 (36, 0.63.\\�F18d*6!-Don Q:$�&$z> J2b6 z  079$4* 60, -0.50�{R{-0F7,55 4%6b .5�91,!=3734��A�0.8c4)o6W8u8Vc0 �-+ 39�18.I`A���B! *��3B-%��x.�.�r?3��Z�helA%V���+���Y�r-Y, $D(b)$La�H�Yw�0'"To����aw�Q�i*�#��r��;�J^ Q, A� R,ad)!�+  � ��0a��B�/1�Y�Y�e�)��6X�r=$v\2(�l<�"�:.czasyF.Q#4�#2#45�Rb kaen"V ]"A!%q%g*V�'�JdzZ.�I 5�}a 0$� "� �5!��� � 1�-�.M[�%�M�.�Z���nI�!�" v�S5C.5A *� i{$�N..i�_�_Si\ �W�;:�" a.stopp�8�@�S:>&51E�VNachie�� 75\%HG�> �(E�R0��A�-�J]"s)�1 �3"d]�/9�h�E��/�R1_�uT��*���P���M ir.�A� �%*� ~�7r�3.76�3� Z���_a��71�ca { M�>yb(:z� )|>�?%R"�0mDq>*�#i�.msymbolNnI>UNU(q�EQ# ^.�5%"E.�I"�C 1��V"�&AcA"{Z�3B��{8r�Z{b�8-�ZŜch %.�>`S,Bin�75"D6 �^(&U% uG-k*Q,1�ɮI7!4i�%�� 4 e�E<>�DKQ}�M*�:�j�X��X�>�ArtchF��p9r��&iwb�9-cZ�nrmsd #n�D� 1H�:�~^i&Q �A��z .�!%. ,�F� ?>-.�w2SnoN�u��I 6{I9�� NqQ�H�Ef coll�O��*�9!o8M��8on{#2� ZB�9�.'�10�(v 0M�)�'*, >�!6�-�MIZ�t*i*m ��� ��$R$�K 2[jZ)� i�at �8ilde{T}�$IVi�!�!��H M 6QI +Y%"�) ]* �B�� a2NV� B�+:7027Al0 $\tau�Katag*Z&ed6��n��1FX.��11v_k% hel &Y�0:a)l� 5 ario5��M*�)�� %��� 5��)^)�bui ;&r�F*�X�EO' ��^qa hydrogs&j,--"d*��!<$i+4$. �\�`] jDT> `"�7 �` U $j$�0r!5`^��JUa-:�g lu0 of.h�C��P��]z�l{?�:�q�{aD22L ct�o����� # �d3;eXP"�>6pa�Q8B���2r��52mZ�e5_� (vspkY6��b�D��11E ��?.�I�f�c17Ao]2:�b�\UCN-i+1$>>nrozn�3B@9Av �Az %Acr��Bt�R��A�>�\5 &�\ $|j-i|$ .:^q 5v���j�;i$)�� a,Nn�11Ωv�©z�� oz�a๽� �0 �* fa�A=M�� 'k!�jc ity ".2�R)�,methodO1���De�s��j0�]/ �C3&�` s9R�a5 �k��&�(.�:�f���ҋb� 1hZ�%�_crn1z� ��!�%�h�� ! F��4��m�����R�f�Z�_ka~�F3�o%I�&�  (* )�6+a>�4 (*�)6Q�v.8%eB�t�G� =+d$ i�?'" !�.� ��Y�v�†~Z�bocznez�N*2)�xd���"d�%R�(le"jV B!Jh 0groups (SG - "�s� =#^Lout��.O��A.�*"f %�o* �.Oɔ=�Aśft�>A>�I�u�IG docu�1 } ��\c-1[12pt]{�!cle} \u|eckage{Yig,ams�6 math2w' style{hea�t> setl�+4{\topmargin}{0 } .odd!S"-F"�#he�!}{8V�#}{68} \renewcommandMFe�]}�|.\Jvic{}�(9,bin}[2]{ \�N( �(8array}{@{}c@{}}( #1 \\ #2�( )D��) )gdt}{\> al_t:�dt.{tt>�da>aB>j}{�{t^j>ci c^j_� .9 bx}{�1x>uPAmax}{a_{\mbox{\tiny{}F*!�>*inJ*tAL�a}�]PI{p:*N]v!FvarK}:$tl}{|\! | :!�! "> :1%�2 3B :5eu}h&�c_u>pp:0bm}{\bar{\mu}>ZhAhat{a>�hth}{BQhs \sigmF:r rBTxAOo\xiBm��2idh!�q{�:�d�#�6FPh!�{P�a +�BjN@ahI��B1axE�%2�VH{vV�>+aN>+ V]5�,��L} \def\trnum{2004-04auths{BrJbP. Ayata� 1title{A&�2d-Pop�7�0& {\it,us mir�P@s} Swarm-Colony Dmgop�L@\input{trcover} \��kip=.33�&big \��f�!orB \makew ed �)[ abst�C}3G&,�D�C� inuul age-�S&�:d�s�num�C�&94�{\em Nbs%bc)bd9b. �K!U� �{e�@a"aD�!�� cell-cycl0hR �V�� os�H veloA" by Esipov�$ Shapiro�O�2kbHsund7oo�y%m� ,D w�!�[$um assum�syGless-QmB;s,5%1srecisO�*mpal%ffRt. �3 �,�* aperA otlic{Vg=���en! v�#1�qodisplayv ���xu �re�QNyJinperEi�\*� =o1m �6�accur�o� s onuAh,Xy z. �nA�%�,hyperbolic-p  �Fa�&f�M%I �� �I�@06(^�A0��ev%Dto�Bbio�3 M-s)%V1IU��A�Z �;F"pi7LJ�"ƒ"�d�4edABIXI� s, � xB�,n�anc<=�7K,�b?z�U��TWFu0 � �y \no/Ynt�BKey�Fds:�0Fg,)h�ony, age����z�} . %�2�O�OzO� �9{.��} �0i&R}bt�5wAes�n��RBY%c��AVKI�cei��treat᫁~�&.@ m� y li~=�n du- stri�<ly�Sa��h-��pa�Ens.�q���& n ag�surfac��S,rauprich,WnS�0$us}. Not��dKF�VI�W���ly ��Z�H�ric�rac�2$a bulls-ey�}�-��total UN`a � �Nin9��Ś:n}t� �or gluc�F��in�:MJ����.��V&Mz� ��ruluKemotax{I\ expla>o$UG]ng�z -do-�0,z�7 AE�a}��pon,dA e�� stKvi-�6�&#մ)�EnS} saw&`H� !a-!m� �����AF:d٦�%-de: Mof �*vid�Jbp3r:|[!2! �a*�m%Kis 1 -ord6�<9�݂riG�(al"�b ag? orBns%KA�mvnon) ar��a�,�E#is2�=2�e4 �IL�necess�V )?�>MC�*R xSz.T /-�i�;em�Bcoli},.&� F�Aa��}�fM%MuI3-2}.�Ie]����n�Vi4mNF for �]le/Pmorph*esAGndg�plex[r f-organiz!����X$EnS,MnKnK,��}�(Ps�SA ���>*� M&���% tics��2�"�<�\"�=.7 ^. %Q4 Dictostelium}%,p�� much���,)� C%5�8f;i�Mainiky��K:p�z!י8 can SL�re� c�H �sf .6um�,rowth jc�DrSurvey,DysonWebb, Mo�v$l;{�=for�X-��BolkerNPacalaNClaudia,Kohyama92FE (3,Kalachev}Z re ZD &q ag�~�*��a�1�y0/[ �At immu�melab�m- an i� t�G�i�>-� u��)8. eF tuzzADGandolf��Be } &x a}ca��-�M w%&4 �m��&�N # some1�� .&Y� �2 �\alZ;A� y di\�t"U�~7Żir`ll �.�M� ��2�}2�.4�:*� onB9inM{��tDuE��pphoon!���pt�@M��-��0s ``swimmer''5 arǃd�}t (sF;in �]� a� ``d����AI'' *`v_o �is�qD\empha!�s)�dnonmotH"G[�2xQ+a6� �EoA�&S�9(nA�� filaz s\foot�R{Ja�pL�":�IAa$of Chicago�� bis%��2di�^�C�oA(.MF� .�r��I�6*�2ex�d]�jcsharp Fz�*� } m�wYinsiYs�r \odic %A��6D>�,ɏca sep,�S!S*{; -�Knu,A:�sub%�A9to g)!`%�QgJ\5s��;�9ay��Wperhaps��r� �7a� at�$hoS e lag A��> �VVitoof� ڕ�i�v%�M��than V"6 -- a=e� J��ide�p=��fu��a +UI!# lag1j�d� t �"�� � �g]Rm�Wn"T �7 9�u Q!+6� p#����� �1#  s�V��?s7�R���b S�ya~�b� B�%-  }�a6`it�  n��A�  �&�GF� �?prG H.�i refer� �� -��骥�me�.!P0w� ��X 'E f���� �Yhn, R{ Ca�va�"Lat al�-�C] not Y�ly"P %�e2z:�In Ap0�ix \ref{;]ndixS�Y we elabo� upS�W�%Xwhky�ref>.� 9!n�+&�� �=-l. Agy�AKJ$we��!�XZ4c�d �#�odej�͔ig"݁Y5&T&h"�e�"KA4A � citee)qcCm�ha�Mm��{\ *�62a )� i!.�� a%�&�.2thZB,T�XmoM�!c38 maximum benefi�6 �nt, �[��e dampA�!!e� �! ���+m�\�I-r\.�>tNtsA�;�e� e.��e� !\&|�&v a!to so��(,!�ce�&=&m��t1"� roBjc*�.�_�_�_�_.��R/A[y�YA�ino\a�,= �g*T,:$�y�~�&�WB�!�tio"��!x Fmre��i{scS�,�HJt���nQ �$zn !;AK��m�G2�b�q�����;R PŘ�u�e�i��xqD1% repe�dd�d@,�m�,=6�  �o�f6��$l�v�*]%�!Ohaa�=se.� m) h��,�ax� � . P"3 s�te2?y�6^.>! �tV��or� �!w��: ��!������A�B;do ' !�T i�r�spP5Wg�u!��G-Lng� g�inc�0��p. T y��vX�&*��ɵ"�. Br��culE*.�}�M.3 P (often � "�''  �%�F,b -) 0.6 ]�mA(�1-2q�m �|i�sIu flagella�O�h)��!�se � �&�2 ���b^0.8Bu2-4.u�fa�a� io�ime&�Ti�-�1 �%�a�ell� du�؉wsI�co,i�� ( RPa9:� qуg�V-~&� YMEnS}.bom- �t ���Dž �!&5;�2f�-e()�& ''S4at���of�G1ew�c�20-801�!���� -Hs� ��M��� Q^ ~. More�",>� nor� ��11110U_"u 2� �55�6o0�'10-�) u�e e<be��� cubic mi�Y*!�l vRX-�*� -B 6 D}5CL[�2p.'' D6� o� �!vU8ej-A��,#Y!�below�b� �OAd.�mQ�Zsee� du��� 3v �n5}!-!�oE F�� lexSB.��<!n ir eA]�g5�!v  fluid*�M�khem���! g�}ay�soA�,�$ ``rafts''-�e� CR]t��un� N[do�a M���  # ���d!6�!b%-%�e!��pc_ed �ztO"� �2�6eqa8�"= a��y/�,ly break dow�;��e-usUAu��HY�s�4->!E�Si��� �#on�al!vwth����.�%�#5w�,��@�s9 �- us, B� m� Ys% \ $age. Varmx���>�-g��lQXbioQX!�<�=��*�a!�d��$6S��&1*�on6 A?� &\�n�5{&!6k �� �A�q� 6�do;�S �AR��hig��FQ�rt4n(%i�6v ��� � �� ��(D�Uo.� N e��� �� �� ��  \a/{�#�!!]Common�a�!S Prev˕M�:0� �} 6'*1 ����?S ZR�hi�MA�We�!ad�symmetA"geo yeP$ no-flux bG@ ��ia�As &�o�a�pIpL|hh�r:,� 6�y&�&a�ȩW��� �� isotropicB�tA� Fick��!?U0arA�@n85,IonidesStochab�,nagy89S�Z�o*/(c�'�S"� a�"b�-�!�uln]�p�Op�N&�U#q��eF��dedU3A�6��*� !Ko&c*us�_ , $Dh�!�1p��O| , $\xi$ (A4�ob& �E S�&cK s}, � al&�� |,eV nontriv�ہ�/ces.) p- ��-�E�#relCE�memory ��:�9��)�^q�� -IS l��a�Dof y�r���< @� ���k�:"�)�� nd, ���:�!ƩM'e�m]bes� ��A you�})��VX�K�V�"as olF%211�S �E%q�a[&h3  F� 6z � U �@)��cdcam��isz, "D,�o).1�N���e�.�"�a�!t �)Vs. �-WX��Н&<"*�)����\a:!&-i"@!Y!M�e�: )� Q2� until0Ԋum Y�Yj� ed�"�2��n*�� n+��u� ..ra�q�*h ���r�R�[^�+;.�yy C%%6��m�'�1e�w@�lesN/ W� cua� tΝM*.{ %FJ*:L &�,�-� �it�c��o�3e��!�_���-��� A^ l�� �e `B�Au{R3��(* �AN�A� �Z #B�"}�[ p de��@ HI 8_mfront �2city �A} +I!�*1Uv�z.��*� )uKatQ��E}a�!� ��"�!�m) e�$#�QQ��s gave�7nt"�'&Sa]2$!��BcX%. Pvedev, K�2Kop]i+iI3e�re�&on-] ��6$%�M�C4�%�mac�gŭP%�a*+Pe�2js�  ��AVAc �%it�i�)^<�5� ���a& J�#� !�%�ݶt�!6� 5� . To�P"�i1�Q����2�� ��a piece���$(�B�w�'���"a1H3�x !�io�2"�:x � �t�KpAD --� �CfA%���on �}*�E&er�7!�Q� �����,%�:���%�acA6�� I�^!�`reA%lDa � Y-]� /�Ź@J!ad�4a�/%) "V   analy�$DI*B�. k!� �F5KD�%:���a��"�6�ob�I� �}own'E.�W�ov��0�6 ��a� Uaba �4![��!���:!to B�A�w Qt]1��œ No�5M~J�frame�#e�s�%� ru�^,hi &$ y� � B�8r|aCг�!N. �"~<�g !in"�52p"> .S**�&a���&Pu M�ryIe8!�A�� �229)'s j#� b"rF)��t2��2 *�;����e+�$""t�\,a� )�a� l4&�A��))��W�H .J.}� postd�kp"E�C"�/�-+i M" conf'kX:A�b� Newy� "�, hande6m*� !e6kr͸y�! �0�&h��NMz#��h"� �|8� 0%'&�;j� j be�d&�nlyJ �pw�b-��,!�ral � B# �;��� a)���� �B �3'Z!mp͑~ 1��sr �)f�64 suitt � a건 R����n�y�ovel^S&�f�=iyGm ol�&��E�er �*&� ɢ6�e&is$por Z�A�B�i�aba  )_���&A��r&+ ;�U tog4HA�x4`ѯ� �/ plesm+}fAJs� ly jus*!��*�� ��?QA"H oL���6nwe�c18�'' R�� u8p���f %�E�}� � i� ���� �e.d'�� is � )��=�m=an ab"��5�C�(*8�W~;� � prim��-qce�At .:e[}G (  �.�4)0*N ��%$�i4o -9g, 6� % Me:  e.*.�1sumٌz�Ta�]Gf{ "4 � �i_A-�in��  !~�?j��F,@�k :aX�&8!�p �*0�=�%, ��-�"�%�> to�#y �/ b;aRP��JP�o!.<� k�,���pj�w�b�"r�6)^!�)r���+�+�+�+"*��c&~BE }&@ Bau�2��&��lal *J!� hi�Y�hiMA�Sk1)�=s }e�i!rh20�A���,"��ZPic � �1951.LHrpb$ Lotka�!191�jMcKendr�5�92��n�e1���a�+.�:0 Webb}�{rowAz<% Gurt|"$nd MacCamy / GnM12�-�gno� a.�,. Rotenbergj ��n� l �gy}�&a �B� ��|s @DR�2}%����zdx( '"��9�^ s�:� rf<m� peT��6'to�1 rea��* crow . Exist��A��nt� ��h� cCdK.S� in Bus)e%Ia"�"�BBnI�@i Blasio-odib !F Lamb�� (4DnL}, Langlais l 1DY*-�ma| F!�a8"�@ done�l~"P B$huang,KnL,j2,mar< �-@��E�D0Ke��4 F�"�P !R� s $r��a� $t$u ?ue�>B�E}I��� l�&e"�8$ $u(r,a,t)`�"G)~ }�� at �u �a_�w� �ns $p(rm!�$v  ځ��i��!<)6! ����,w� F�$t�2Q Q� , $v� me#���G-��)s (pdu�a$\m|Spdu} = Gc}/ cm}^2$F GcqoE����'�=q� ��8�= , $u �2�du/hr)� )�:s , $pF? �mg6�"di"�#i� q0\ !��"9 ]@�����  sub�n&b eqna�DHQ@t u + \da u &=& \?]� r} "�Rr �P( r. ( D(p) u)��g)G�,mu(a)u, \ 0;T@q r < r_m, \, a>0t > 0,xJ%�} \dt v��Txi(v)*U au}v�0int_0^\infty s^ue^{a/e} \ da,�\l�� � |'swi a� 0,t)�)6}en,�T\ U� birt�g9nw�"Q'a���%�]'1�6B� D(p(�t)) u ��%�() = 0,&& a!d \ ,�\�a,0 & '5��ӱq=� �-u}\\ !Av_0(r)lBE.1\;v � pa�H2�f��VitN�w�a�J"�?. A typ>??h��D1.5 hourThJ+m�AEo� u�is�>�9�˶} �t = m_0 E�{\A�T^{I�}!�)�E� .� \qquad^8\g%n13Pa�% q�}�e $m_0$�.� mg/G��A6�1�a )1r��x �/$2\!d$s 10^{-18}�Fm}^3$�/5p\ 8 2 q.$*IB�H]/ �fa�^0��/"- hre"�s� ��gs:.��m�MP.�>��l!�6^��a.K�����5E[I� �d � 1�7r ��T1integn�(A�塛&$���.a�"d!�sBi��(:`�f1,�X&�~ w�-�1ə2V��;�Rl�:\3$��N�W�6 �$1 ���1�">�P2� - ac�q�%�o!�B[�>� A�� Z� o�9%��>$ $5$r�2 7B�/ 9p/�32#"�0� dri|H� �O, rai�12.�%�. H^�/I��@ s ����/�e ��@ �/� 6 & >*9. �'��M�� �eF D� = D�max)\{ �� ,t)-�\ ), 0}�e��p> PminA��qiq�Ue�T�v�to ��43p A0 1&W55�as �lM� ival�!�`P_{s,�(\ڈ���< EnS� "d/�eD� -�DE�2�"�p�4$C^1$ p&# 79 ,�)� $2v_w$:N�����]\{:�_ll}$!��]( 2 <F |v-v_c|�[ w} \�])^3 - 3�>=:<2 + 1J, &Z y�q v_w,. F�0, & )��Ma$,�`N�ha �.��1!�>�Y}� (rval $[v_c-�v_c+v_w]Q���! P��wi6��P��v_c>D l.gM�BQf"%U����lQ;pEPU�~��OG� �&~+a�s�a5=�GA��I�tA�*�aZb9 cer@%� V CXi}�(���!&�y�W�+RYon�Um���) curv�(L/* helper��issue�{]N"�deH 2��o�H:�%ءHno /o�<)��326�-�modula6a��prn�]3\sigm�i*8 �F =m�\mu_1}{ 4} \exp��( (a-\�b)^2/(2 ! ^2) S +A2A H(a)"� m�ae.�� ɠre $$,��lN� 1e�&} e�i� a <d _:�$$�KHeavi3U�E�qh!�.�-Y&s !_it);� r� �Xoba&�dBKis � y0q����+R8�� a��%q��1 �� �& ains�� after�- "�M�hik�typ�� V�dol%�32�*� �R e&�,�'m virP��o��vL?: tremq ��7�S�_�X�R�-s%By G; neag �z,-X8C*e&�)�1 �X&ho�at �ځn%��$./e�",&B; 1%, oscillatory�9="�E��"O&%�& .�/ it�� i� I�beN�}�BJ'il+B" v_h�f&?�*r}{r_0�T)^3ZA "?Z>>%� �} q r_V\Zc�Cr >'#D6.TA�.�-]�YFD6h�K��<,)���,eg��<2��.�K&p&H e��cyZ�=_�-!��� �� 0�bs!�s��(ag�{T9r,F�m}�hav�9a27 �g+g�<���_e2!v &\�~*~t0Mr 0<�;�l2y�i < t)e^�ax\m o vZŽ5TN7�q}*�22\V\*Iq9FwV&�;FgȎ�ZvIҶ��0, V 2�.%�aP./)P=W`%8��9��, R>:/�b2��=ub�=A N2�;>��;�KoOn*���E� s (5P� })- 2J)�<-�aa��QRby��{�(�r_mx"I1e�Jc�P�va�]s�$$$\hr = r/A� \; \ha = " th = tE�.$$5\�^W(�e_ 2c, � $U(\hr,\ha,�j�Y)�t)/(v_w[)mV )t%!�t)/; $\; P = p/(`v_w).$$*$d�@+5o�\" s�at{D}_0� MeZ!^2j9k��Ws V_c = v_c�$$� k0a��+iG Aminhs+� �E*�,�*� �;6<��e��'EC"��" I (2$)A,6,9&k 6��+r�f��/twQQ^tui�ɤhal8,E��q*Q2.��kC� ���3�_� �( )_iso�� V H8�� $ ��.%>�$!�\nQ����N͹Ո2�J� ht U dha U�l H hr."{Q au�- (LmD}(P) U*1hmu)U�S��< R(a�} a[ \ \�V� r(hxi(V)�) V�6(j&U��h  de� ~�_ 1�x \\ P}��wa{i * >Bhbi�� q0�- .p��Z�q:�!L(�4�W (P(1sU(1��$��v�`� 99X �!f;� &^a)\\ �02��_m��3@�):�.xkF�� ީġ�%� *�]-�G&��5{D��fR�:z|V-V_c|I( )� *� ..0 =mqE�\.� .!v�.U}�m��ajihs�.i \ha-a0a"lhs2i.Ck hs}H6).>�Fv �P��I�� hs: <0h� ���ZF8����a5ia�,A u�<��,� a`<�|a ,.g�U}aq��".)�m�a�r�5��A�o b( iVi}I�u� VRq� I�Fj�"^P"v�!w~� �B�T�֩b���Ub� 9,�$])b'w 0<>�.�\ �:0R�FJ)�i I �VJ�>�"�HVB�N�FQs�F@g�zo�0� imi59If�Qaƞ&�*m��?6^�7 , ``_+ A'':F.n � `'&�IV.�7� p=/ � ens[6k%as&� a�$^Dre� e:2�A�n� _O arli_��E�8 �)m*3�MKbet`�� ��4&}39 �3q F�XU R"�FU �E�7r�6m�no2 Hh�)"t ��upp��"�C�) nJ�3?.\H (M�\*Lz$).I�) &�6e^.�5� xi �G��use bi�7�n�s� ( @�e)h�<t' A9Z)��"�`�"EA �!&}(�O�%�F���Y(ldy�Lm(n.~+�- ^�K.�@B�K.�a�V�t: ^se.��d�e�h�<>�t .�0} 5�<�Cw�B� �5" 2": *�o,�.th����0 4lc�'l�i� ultyI1�"�(wo"Y2� �a��W*& �1@e�ad,��#� 5:[�O��r,*�,I%�S���_@ !�m�Acou) _M5T mesh0�an ca��U lo)�of�{�cy�< ra�9( !b"�x� ZY�T��.A�e2-ag�/Wi�;rt�Bl�e4 I)nI�8 is involved, s�aince sharp moving fronts can require small time steps, whereas the behavior in the age variable cHmaiO�Ulatively smooth. The methods used in this paper \cite{age-pwconst-paper,age-general-} use a�@age discretizatioVdat allows for nonuniform / and �68s. TheQHstep need not equal%6 $. Instead, posi{ s ofgPnodes are adjusted byGr1preserve$�ex!�iMu.��2$approximat�lu�_ �.robabilu �l func"al �birth�dea $re handledY�l��aa1 �Q��$��L. Even so, it woulda�interes%��to know if an energy analysis c5provid�� framework5�convergea�8 sought inMeM�1�e- ōeffecEm['sՈi�q sepaa�5�!VE]:���$reby yieldAcan=�A���is; persfree� age,!^ order to �)| =�s(pA_ic��(We emphasiz ����relI�numerI� I� eq�6��y�5� EnS}�( regularity terr�&a�I��ue!�A<:.�G!��hswarmer cells. A coarse, stAeu�d�al>Woh,continuous aaterm,��%}]�B ���Uitute a ��iar��� �-�$ life cycl!ta!OaEI�origin�$�, model. Also)EdegA�a�cuE�be ala"" choi)�!>E~i�-�ompu�on maa�a~,how periodic� dynamics)��)obtain wA�ccu�s�c -�N��A�s, butSinduc N]�N� ��8Appendix \ref{a Sa�8i} details how �c�s�nng!�e "� �8 Esipov-ShapiroM�!m �R AH. {\em Proteus mir�\}I -�E$ny develop/is q}t�a %�w or o�,��bl�xin morph�,�*,m. One goal)�!�� �~&" / necess�w of robust��UnewQXal�9�/�%�ing�Q�J�-b� result"� M�6c::Se�f E� @} wereyYA�� ous �\meter� s � �sS��� �3*� s describ+ ��.�h with�B�gre� done {�Y-doub!+ extrapo� . SteEq��-��pA�0algorithm, go� !�0at least Gear�gear}%ordinary� eF A�.Tased � akWon� ep over a��rv� o-s(R. )�at !5i[t�2 dtwo half�s j!�sam6l,get a secondRn� QQx\ob mpared�D adap")����H$rol. More��D�6R Mb��to �� a likely �-f9�1a�imeMM!�U-pa�< � cof �M�� Ei$error chec%�)u� � ��X, s�!e� ըp�2i��/de�=EheI �. A �sp�,6� V%_D$\Delta x = 1/300$Ia AaFJof8a847iE"Y Y�ba� � s, wLuffici6to �� with|� 5-Q!�$he $L^2$-n�of les��n 1\%. �aF� BAXex�"5 grid  meanU4��yfir�zla gy� � in length)Q� a��.5�Jintro1a�e � b��we� he oF � q� reac"1�a$z. C*" �ime%~i���[a toler@��e�}U�F�p5WP 2 � ����rez�A also9� %� %�2�O�OzO\s�U{R�} \label�`P \begin{figure} \cenw��fo �t8s� "Eom�a .�4$\hr \in [0,1]) te�al 8� runc��v "$\hthH35Iah�ageH $\ha(i�,which�e(  �= |! �sep*�%�er � quantm $T$�_ YJit) e�ta >IDto� m�XS;2!1�e, $C^(eh2ha2!$R6UMYA��xcept �%A�, unjI��abter�� � ��aR?�=F^>A�$i��Q^I� �,default valu!��]� will b�ow%�b* typ��Fi� a}M .��d{i9� � e9=sm$top graphA! a th���al���fE�.� ��%�Ai��\ aK�F��versus�td *4���Aic �Ln*�of2�f�. g%�}�er���tab�Y}{|r||r } \hline �,$ &eV& a!&E� /CR /S$� ;l{\bf 0.0}&4.1&2.2&1.9&1.16&0�.&0.069520.5 ,$0&2.1&0.95,0,750,1.0,(1.7&2.4&0.7114,824,2, 3&2.8&0.4�09,692,��1 "1 R��Մ+� Z aw�ahMs ��-x]le} T��I� , exhibits� �neh minimum.�ag�>�a���F rib=� �in�}.�P�Cin$�s�� agar. ��9sX incQes,O doI� <icult����sub`�h$U�Q!� {  ,E��qde ����!T$�yi{*�i�e��s;dJ�s see�er� ts; k gan!}� �F ���"c m��`� ���žt2� �nN2 ;5�B�� s ,a�,�2fur &�d�.�aA�!�]Jsimila'9�E�ol-g< �=BZ �2� . Ha�!averagru�E��ble, no4 t�s�u?MnKnK}. >� [t]b� �.e � �3S!�� >�AV@ S��`re curv��e-��M��.� ��� EP2.&� B9!�t�)�Ų� �DVJw�� A�$.O�/ � hlig�� A��bette �ariso� in� �"6�A�lthoughM�y� ��Fh �K U�v:E to.i!�2�u���!�V�iz�C�T�on��)� ing,)winax��.} PA|�P�&ZtA�>���j�D_0��TS��r�$0.001&4.05�5����107��498\\ :02z 3b3��(2.3&1.8&1.2��18f 07966-4N-21- 0930-\�1y‚�!+&� D0-��er -�.�D0��eE��3s�X"if�iG�m1ElG gluco=$�E�@ � ric�ET@S $C$,m, litt�X�y�� +$ignificAiXe�h���n�dR� is c"U� 5ex�La4�V|14a�'$rauprich},\��nor�"A"#��Z��% ��R�bl� # a .q�% ����i}� � !�E<�� V_ce���2 &3 1aIJ 5 o i� 510 * 4&3.6� 4&1.5a�13ey60.� � 8z�Z16&4.�52e�0.9� 1a071.� \ڨ!#y�Vcm�5l W!�.�Vc��ei�no.� ��lagEt� pDA���xi$. As�� � �mec�2\h�*uE�� �J�& � nea� �T' leai�X% ���alli8_, �1aB� ���*buiv$upia er rafts �JS 6yi"S, $w0 thu��2k" s3  es^ �1�-��9��ob�*� �f WnSpk!8 HoweverEC\!�lag, m�(�� ";'d�t�!��, �n open� aG� A,-R�(��� chem  factorZ at7lieMU� �un�&n���la m.J�,-Ό0.2�7&1.65&3D0.5�6�h040�ہa0.5~Y��0.7V)6�1�23088,$1.00& N/A v^\�>%�=).��xi�@*�-%�E�2CA�G� AY����:�� $A�cl�4 grea"tS&$,^ �,� � �&sQ)na( begetqr($j� � baH#�,Nsugge." }� , ``(+h w��� M� ��k��cgo a dra�c&�$eZ�(to highly e>+,s$\dots$'' -9� $ �� los� �!(6O �e�a�ly! �&of� y� aFF s p2B!�_equ��!G.� ������)� 6 �F���w ��w\'" nj �P,]A�6����- "- ֤q3J0.186 �0.2&4�� 4&2�X 0.17�s607.+�  ��5< 6� 638 62-���z` .^7&3I2�W�0^� 0683-V3.8��9��12066*� ������� ,��2���M��B�`a��1gi�f. LJ0��be[3A�A� ``�''o) i(inI&er to e. ``Mov�1of.���se�)`9tarded� �e�/�"ara� groups do�� moreK.3,''N� R� 1bl��mZ*$ numb��)�"re�$a"%[e9o�0Ja)a͗s from" z�"�$ �#su�(f w!!ed.�1\ �,h������F%� ` ŧuaOItZun��q+&e &d �4d seqZZ, or eU0iT is thresh��|�2b��ial3 s��eC�&� vary���-+��u�_�YV�Ts,W*�-> ��c%�@E� /� E")1b�3A��4� 5�, e�)��. �Br�7 s strongl�/�n� R] �u�93;-� B6��0�ͼCas F:,Qit�w##5�!H7in� s 1� Ls�>V !��ge'8�/(tinct� � � �&LI�dR3F38w�e�h$Bk��gto� a ��Pm�4���^�$0�9&9i�9/69"- #B$!/1�H�HZ�� �� 5�Th��HfH)�*sF#h.� Qw tr� R ��Q|AY6� I�b�*�A7& �}z���j�!eax� � 3� � � 65� ^0*h 2.33� ��8�2 6>� �&�� 3c 4K2.� 74�1 �76�3.5� 2&1252 0791& �� a�'*� -�a]|.~ ,�� 2� " tam<ta mulz5�,E��break- wnj/� non *)" � ` =� w�v .Vs, i.e.Qm,.be���X ave o DpC$.�fwi8 r th Ne^P7 lsoH �Ѳi)@s,21?~',�1U��+2�+��+��+��+ "�+Concl7&�+c. �8":4we� ed���"7*to �7 i9e"5$�o.4$in24$ &6 E^-d&6S�=8s� Ym�v 4�9 by placA��|<�9-"a*A  me isman part " �Hl%�5: #4"Q9�@make fewer assump�fs�%�W usivit- �"&5&|2t�9+6 �x w8��!�& �0� �" "=&�8&� m"� *"nbAAo*�  a*"!�R� �r\8 35K�  p35����IL��V >� U  6 6by*�6 &�6�;*�6des�s�A"� 62�d -�on�bs3,�G .>=8properties. Fu?I�on� �e(A�.�.6@' y�lu�B*zl})!�$�� ASAiMA-&PE"�� d� ,,:B?�6ta� �Ͳ2+eqleBp&�@dEkyz �myuly�)�. O'a�%�f)Q)armA91�%�AqX ��A� broa��iss�)}Dmoa� Z2&o:� onzesurfac���!�: ��a non-,,a9, &3,-��0a� of !�6b�5�+t�;ngq��t�!"� two-"sA*!1a�:�4a��B �pl�lot#��<r�:�n�;h�@V+� h$%/��eL relev�%z8%�=�priyi�qJ .c;�!Jb nd �����-<1�+�A͡��hem" �>H2 &�<DeUM?-Q�. �} *{Ac�v ledgFs}�Bautho(anks James c=�5 Uni�+MChicag��/�^du��hi�.3�V-4 p91had man�ahelpful' cussions%�\ Todd F. Dupont, Tasso K�8�, Nancy Kopell, Mitsugu Matsushita, Georgiy Medvedev, Th� Nagylaki�? OlivD%R#!!<�>9G{N��So�Ce_a�:�>Ma�"�0K ?%|:1E��?&<MFM��H�"Ad'u<X�!�>,%`�'.9&@�soh.p14sal natu�g�J��a�"�Y�8gEymp �3,�quote} S��-8H !kim!k�<2#"�s*2 �)�4�2 capi%l*s!c$L%9,a�pL7E ($c$;�h:I, $s$!�)�A�v). Wh�%weDnot�"Bs �E{aG!�� ��. �s!��WB a�u"��,^#Nag�wY$e1�,/\tau_d}$ be�w�:�/M9age $)�$.d-�\noindah ]�Go�]commun!fIwy�ͭ�0 (July, 1997)�U�CI -��%I�"�'�"�ݥf%��e�an `` 5-E| � '', U��= !S8E �#u�A�X�al *d�i%�u�C�=re� p !�D�/v � rpreC ! $upper trig�o �Lmory f�I to instiU �, $P_{s,m��P e�$,� mcT!A\>d�(ch�urm ?) n nob�6;An�fɭKheM "�F%���!om�K�L%��and�}{. F[incorpo�! �y�*eB0�� ``dr�,s license'' e�M���-.in}!.� ly�vy &2 AAJe�y �xwritte� 6[._�� Uimplicip# thro�. he dF�EYu33m��%;R movei�6`e<o"j;y jlFdo V��]ag''�I tili&Q���*_� A !�pr��� ���ca�LupQ(flow � �# 2�G7 :�F�� p� . But beh�zaj�'pO9c"� �$��' r ab f ``� agA 5O�S�"02DK afhMurI�. "�'�Ci�1_ainc2� �6� kq >. �af�$!��B� �H�"A%S�Isus�!�as ton %P�K�6of�KB6a�0�Edea&!ot�0�s (�s ,)  diat�E.:|i<�H�9& |MoesE��>�"q)�$>9,!� ��L'g2 J obje�Id<we| plaI2�4-!EK)cn4 5.��(�Ae*�A (B�A-&5(Pro�A� -/"%-A6WI�c@$\T� (f�)�K!���*e�U� "�?��I�E��@� ��I"r��erh��Q� �.��*�M�:�!&T  �y�+��**� taken�!�c^C�Fi�<�0  ��."%O� �B045&*M7"M� IfA�*�Nmeae�[Z_bx< :bdo���iG jw�$to��O�cN>_-�"�\Equ'  (4a)x 66� ,- Heavis1S3�� . D�Kso� Ma �|w� &_)/6� �$fix� ims*�GsE"��!�r@R&�Dy��9&&+s��:V"�"�. fH�FEd�&Ίi��!�F�(0a�,�>3615)y�->��B�g ��%QEa�� .T� *���qu�Y(possibly due��al)6 "� �y"1Oa�E�">-��iA�VO :X��taGisq�!���bto5> Uvar�U�L}��*&P�z , ad%� m|!7\X �@%ot� N�aG� -6� ur�e�M�&��~-54j�� ��$s (6b)-(6d.�7!��!S�AX��9atsgAU�tA�F�u!Pp�C���K�># in>q�O� }�U�b�YalX)�3*��D�" Form�l \xi$B�Xi}[chose�e_&IN cub�Uu�&���A,!+V in�,��iff})'&�!�so�I�i, we arga!�iNilar5h>�' shap51%� a6� A�.�r�W� t �%>8) mOQ�_ .2)^ 15��R56amesaz���I!"�O)yA$e< 1fat''A["��R} M&ma� cM,�YAd1H3,S!JskinnyvMs�M�'�B=y�M�M �zP>;x+narrow!V1mtW!��OaY�O i�!�)�ead�! a1})�s *;EVcFat}���"u�%� data/�VVc}. UN� �քSE>��^�,"v=��s���*2��+%R. &@$�5ieaI._>��M  & 8!)B.Visn0` dD �k!��2�"E��he *d2�� !a�o�Y�or�\�KRT�i�"�#. Non=d�'a��=�� �]0]�9*U�O�xOtop���/&�!7b$2\*�( "�(8jy*6<KITSnAR.MIB�=0.097*p4�=�81D9i42..I64"�=9q*131B1�= C2.C3�|=|=��q�.�&P i��5H��t��B&�B�r�> +%017�q�J!s�+1.2!s4.�9s�J�BB516.T%s C K66=��ED&%��B�l:s��.v�� nRy \biblio�L(ystyle{siama-�[ ,na,2,bio,foaE,���ey!�!� docu�^ } �% %"LD�bt�MAs$Sou� n Methov.*�! L Tech� l Re�� Co�[P�P'�h=e�!: ` 1. Get y�o�X�RKr K�4� 9��+Ttypist, Nita Blanscet. /2�n glatex �T>T�L909*ad�)&R"�� (\def\trnum{� _tr_ �}O '�s{ or_n.#R'title{ _of_Yp�:.dinput{/home/a/carr/Tex/trc!� .texN1 T % \voffset -.25in \-VI� empt�flize{12}$ tcou{/}{0A���Q��e#�N{�� =SMU_logo*�W1.5in,�: � } ;vR{1�  n"6�[t]{4i3 1� �F� �?\t)dY] 24pt[\t)�>%12%SMUeJqI mx ` �e��^{\Lc8�OD}{\l 0EPARTMENT OF}d)M.),ATHEMATICS} Qa �8S.8OUTHERNr\ETHODIST>%U.I$NIVERSITY}�U�Yr0Eo�\alA[ \new!��Y �%&e� %\q�`class[preprint,pre,aps,suhpcriptaddress,fleqn]{revtex4} FCr: ,twocolum2D4usepackage{ams��amssymb,��ic�1&\s��`ptm} \widowpenalty 0\club0parskip 0mm %!� � �! �[ \makeat�! %+ e �1abel (�voi�‰��B&�p) \renew� and{\@D}[1]{\heq*{2ex}}xO�� 1��add5]�{\tex� ght}{2\mT��}Z�\�� {Loo'`at&�(h�jty!evB'��1Di�^&a� A+cip�igenve�C5�!act�ric)(d hydrophob]yY�=s��(P{Ugo~Bastolla} \affil�,,{Centro~de~AZ9�)H{\'\i}a~(INTA-CSIC)�M28850~T�Ij\'onA rdoz, Spa�� \ },Markus~Porto:}�s�hH~f\"ur~Festk\"orper�lk:v��sche~"�)4\"at~Darmstadt:1XHochschulstr.~8, 642890 Ger�)=.8H.~Eduardo~Romavalt=5[Pp*'gi�:]{DiM-�(o~di~Fisica:� &�\`a(tMilano~Bicocca, Piazza~della~S_a za~3FH20126 >, Ital���Z�� INFN,Z�:k8Via~Celoria~16,x33>x9�4ichele~Vendrus�:�&� ~of~C�F stry�yambridge:� Lens$#~Road, (, CB2~1EW, UK!�(date{\today�waSTct}y[rer%�:&5m. alyt�C m� �t"�*s�.�rmoj*a��Ti!�tm�a� n�� $ influenceiC tein� � site-�&%1$ manner. T�2is en�#�� bothL�C�#�m���P�X s: S� urrSed �%V� (PE)�c2� x, a��y5)�s2+es clos& !� 3 conn�'�of SZ! ; S�D�r�q ���D ``i� act�� Famino ac�i ype, novel.[,?! �N��d�j athy scal_]T�2r.KFmdA�]�>T�ŢF^!t w8��#: (1)~[8,>m6i!Q unfoUK�oe�pofQ!Qwo-E�m]�4s; (2)~Genomic!�_3e -ome�gMtg.e-�8 GC!�tent; (3 �m#��� �W� i(ma���`�4|'")5'2vM�K�compone�W o�6�our�di�2�&�|gre�)%56��:�"�f from!j �n in D~ Bank |#"�4!�Q�-�nbest f�"'"$��. I��ly,D optimn alf� mizi�e� &$del��8�f elim�c�#]alm%��onh+�r - � g> gmfI� du%�Y\�F�!��a�!rt.���� A�6� &�31�{CofU�u�a�iaA}{ ��� ��s�'Rno 9 3m�m$,+]�Ziru�$al environi{erencru�y`9onY"r� �j2P"Aw0o���pdele� ��.�s�_,to A~�v phylogene�<�r5su)e�&�X`�� (Nei�Kumar� 00) �4�"م�6htreE�_ M� LNm ihoo#k3$s (Felsens�, 1981)Lpr(��Ixa�e�%�'ki9n~;= Gamma��t2c 2�ra�7�yNeik.�%� V !8Vis flexi�HenoH+o��oWt�D~8Yna�2Hs���e�("�% im�v�M7av!afitJE�)%U�kW@�71� �ZA�s. Sub t@/6�_f�~enc�(Halper ^Bruno!�98)o:C2a�Ou�eszu�.K� es (Li\`o[ Gold�z( 1998; Kosh)�U3 e�./ 9; ThorneI�; PA� >Ec�@1;b (nasari et a?2002)c<'O�@� -�%�rY�ፁ�}l e� -s<S-.[ i Q i� empir� d#���i���ora�{�!A�7�.q�e-. F&�ghe�t�> {ach� �eA�� y'=�S� ��pri" *P 2� >� ��P�{pr���uf:<]A�`r%Yv% &� ;tr�qs (z Q2004b�cW�I M!~i!c!��a�!l-�&d,:�p.+� L6 u�a � dr(:�\ ( �� :B� � �Y�4r:!��RiveN0e� �� � �t~ �W�y��� !�Ak&l N��"Q :i ^ Z L �� 24i�mrs�*� � �;" �*� ic.Es�V7elM�� >. Ai"�$ 8��uk:1A�ub.<����%�-d;ZAQp pape:Byb5 �M �(�q>:�6or- remʑ=J4 �'a "  alow}� .�� n� M3Xia!�n"� �a�K {C =c�xe���.O�(i�3tN�i�$N,rN$ �qrNW&Yx $C_{ij%6�` $N$!r!���residu"w�;a~&:>o'�Q�s $i$�$j�#A��I� "� ��R(;J\A�l�zVpai��r��:( heavy atom�8 m� $an $4.5 \,n'\AA}$�9 zeroi�'�y��Wx�symme��ii� !#re"��m�PE1<*���p� �G G& )D%$ /m$E�${�< c}}$�(i�c�C"� quadC8c��$\sum_!� )�!c_i j$�d�m&� 5i(^2=1$O i�/n�o$c_i$�+b!�te:�p>�8N��A�nce��K c~8i,I��a�~ny"�,WsE^'Gj$ʁlz�:us�A�/'�G6:we�+�be(ven�g{V k ve. &�{�T�w}Ty�ttw'l#�ed.o(a&[ -*@glo�" �s),�in.� E�;|i>�#2" !�u�!s 6>�who �.��|"� 4a).:w�l�,N|�K �PE����Hn} ~P"�� �` B h�/be[.,ary stud�H.8F�p��^^�(Y�  9� /},\ce}zA}}=6con�4� y�C s �� nl%�ct6t*. $E(u� A}}, C}})$F�,�+eq: �} 2+nG}{k <�$,�{ � s $a�{b$;A�R;A�T�� byV, 1)��X��"� @W2O-�, Eq.~(�/9�),a�|rEy>B� A�decoysH e��threa�RRw"�9II*" , Z��1be0 ���HI��m["h!s� �M�m�-on $H��Q�nFN�\�v%|ilon_1^�hA�E� j)\, �B��: M< 0�%�pst.�(Zb�+`�lue= mQ� ��$h(a)P�"/ ���l�Fis !��2+�e&8ofh0!.�062�O>J n (C� �1992; L�7).XP|cal� 9 . L���A_i)$3 H6�!�; (HP% " �\�| R�X�20.$-LB�Z&�J��ed -#it{&�}.�(IH)�w also�k�fttP;�4>�a�t�C�i�>� ����in�a�E,����the HPEY#�)�?rgHe��v�� +�� �<.��� 9M�8� Oabb{ �0 CH?.*� I *b� � iCOYHenM�'�cl&�8Y42� �s &jK�xE-y!�: XKDB`,� e�7 ify �7-membranr C��di�1&�^�(Kydnd Dool@n 1982)u�L76J��e�ݘ�,&�/al gathe"Ƒcal<��evitt�76x�R88x %� isKzd��8e ���w�!*alkane�"(RoseM88w4auged aH4mey-White (WW)B�.��rDgnh[a�v[F�(Jaya!��D�� 2001); (5 � G98 v"%.P?;!Hto er,-,�L- amphi�ic G�dop�by Gu")(R)!(inv' �Fa�rm� shipk.o�2* -�*�� U,a�s��A�� ; (6 �MP ayY5l(9m)tP_�K�9iew B� ( (Manavalan� Ponnuswam2I7%�7 xAVBx.�a�v� 127 *JnBs p��sh�X�li�_>Pallist�nd�w%1�8 �Fj �2ln@zcA��octanol/i'ar coew s (Fauc�)liskaa�83a9 �Z04q��;�wbu@<�F,%�os�! ZhouP �N10O.�� IH,Jm� *`Q9�NonB��� Y^�; (11�ѵed���X._ �CH��6�E��� �kR&E�p�n*J� c��or�J$redundant m/of�t4"�! (PDB)&�j� Al se)�sp�i.�6*ranE�E|6�Fg}0.68$ (����A��=��s�^L�9 7 95$ 7IH3CH ��.�SCN�=neu� "�}�[e"C'>C: ed N 4(SCN) KF 1999 2, 2003a 3b)E,r>G%��1�" E{e PDB,��"V�#randoml!,i5!,ace��ccoˎg��*"cr�DL ʎ 2��!�fy&F� 2000�7Jb ``�al�K1"zpioneeri�Schq�r�co-akers�a ser���1�net0 RNA �;��A�ce�,1994; Huynenͻ��96� ntanT+8�L �8� applio1(4��C�i (Gut��H1995; Bornberg-Baue a7; 6%Cha�!�Babaj�L 7; G$�daraj͗B�Bus�ker6; Ti� O�O8; Mir{ndCWkhnovi���.B!�w; Z a�FTA�iQ�2�}�� �w��"O�a.�) : (i�&� YA�,vz/N$b'>0��7�Ep is�+��*�u@.83P ����p 18 s Nm~~; r(*�"�)�&�s (�<.}( $0.91$; U."=0 , un"d�ult��i-U&�1Vgap�blpha$ѻchaer�f[��4�M��NRA\) ���es landscap?ryngel!~A�Wolyn� 1987;Y�Q�^2; AbkeA�:J� Klimov]$ThirumalaiH6))e �E, :ed�X � �!.��NW!l@�-d�+2�� � ��(P^xeglNO�marSi�"� A .� �_peram##DYpK!��y ��#ŮQa�fe� a�1)~Af�Na�~T�V���4,A�as�l�s�W� z<�ilۛI�8�= >,�/pittn�"Rb�y�. -&/(T< �(�6�+�)W �i�W�iE)Q!2�A&y#a�!�#N� E� :SS.�$6�&SPDBj#b� j@�~: s. Fg���k>U EAgsinglf�, �1�mR/090\% homology)�� chaiFIE�PDBa ex%ed. A`"� y��M�4bBn] T5 �@tt{nrdb90}, availE~ jweb%A. Qua*��~alent�;siY)te�Q��);}0A���HHobohm* Sand�QP4))-�#M�� 25\%5R �ty. Glo6g!3�.d1/�� ,1 the F�>bM�s�3�T�E�4��-"J&q , $N&�hc}}/N > 3.5 + 7.8 N^{-1/3}$�V]�" *�! !`��&��inJ��#"�G=E[ � (Zf{ $���N  /" Zto 8mh.iovC�!*�%��PI���to "�! outliQ��r˜#J��b�&#4S�P�lyE�g1둒8eS2�u ;U�b�"oU����,�PE!`.�9�U�, $oH (1-N-Hft< c�G>^2 )/ % n$ <1 o M�kB�u*I�:�ina!Air%*�^�d!Q"�s!�0mA~>OwQ�exa��Z! ou6.d 1�sl�D�mU�e^, ^,B�!�.[ �(�r^�6�>P!蹟on�!5�a$!q U�NXs�LAE Z�nd��fewI0: 5�(�not�Mwn�- !�StoW 2�th!�� A�.� 1ri�)T%IF��n $100$*eE )��pabyU8 �10^3$� s�tt mEO:mo ��<"�$101$��$2rz$5.2 v4v�6�`� jo,!��.!j �� ca! � wsL%{ ey}�R��ce� thirj�-S6�2�4v�6�5�Wi�cj+�,�,��Y���1�?Nh�y$�'ir ��..,�#����$�,�_-*�$0.1$.�,�z�.".+( �!�$3,�*� (���rת!��12L%taa�?(ol $\pi_{c_� \IM>b! }�� M): ��3��V20� �:� Dis�25�#�2��a�Je%nd^ nnon!�]��"!�wo� .��a�� $Q i�fE�as <&� $split} & D&y(JS}}(P,Q) =�N& \V&.�M\V&aɹ[ {"\log_2ɳ�"}{R(a)})m)+ �V.6.�]x" ��C�i�$g = [u+L ]/2$�Gis1�{&� I9h+�CM��$@p"6`a�*s"Z'Ӗ minu�*e $<:�,$P1�$.n{Y(',A�mc(�&�Usi�s ��Son�*P.&-t*�A�me�,�=�,&�Le��'#)FE��@co-S�&g� �.��R� �*�`XB�\,8tSjcuLr � W'�6Q�O0 �a��a"�)uT.^f� . P2do9­,m%�7��%6�3mo�*is�*/to�i֚$D_{h^2}�}m�0 squa��4ce5P the �- g�� fi� & = ey�R� �R0}�"a h^2(a)m�a!-a!i�]mf\}y \a�e$ .(( [h^2]_P - Q 0)^2%#V��2q��>�s�":.A�9�17s�f1:Z��![�]"U Z�Q� ��S�"-N9��� �amL7 ��P) � A&Q�� d�$;��s��chos*Avn���� �)�=��%�<-�!�_i9� Q)�!� >_i} 82��� 1�;�����ang�M bracket~4uQ �"��24$i$:8086 ?x�)proced.&�!$by Henikof��d !2)X " !ngV~? rt�Q��ltiV�8A���ˮ�7�2�, �� pi_i^�)rm{aliz.8� &�M9��> loghmSodd- trix� ��^�%J�'N&Q*�#tmXVS_{ab}Aj log\A[g* < Z�EAN�b��AH �F� �.\Zr6W 7":>�a�B�� �%2�BM�NU.~"�)58)�BQx�BeJ�:xQnX?i�Q*��"� &��(�q.��Bed PEf� �(n�ov֭w� � 2Nw�!=x6�)} Usualz@*Q s*�'v}}^{(\)}$�a $&�2&k1f$M_�042����� ?�\��/su�ro�; 1iIA(va{�I+�= � i[�!� V�*�!�M xqcex�,�!Nw �aMC {) } \lambd�i%�1v=*�,6j�}Y�> r!v>���=�N o.�� o`am">$ @alue $>�$[Z�"� 6 2�0"S�G(M�[ w� �expd  4haectZ2v- ��.�L Y�< N; b�Ugg[ & w%+ �- ^2A�� ( F8+ j.L �)� %Y 1-c#�5B�.R ��V� �$e=�,n�^nv?sW1*hCrm�9� ��5V2a1�en /��t ��&T $����\$Ř�5��� N>�o Vio5aJ#u�` �a}Vy44.nbe � �s��>Xi�4�E��ZeHd���biz �he z�gm mean e���hsub���b�Z�Wll&s sum}}9�="�F�~����bet��D ,%� �nd�p>�&� ell-��7.�.�" F�(./)��Fe}6i��:�.�GRes!IDi�>ion.�&a<aME����2] aswI!�C:� ��Q�G"xa�,&VL:a. Gromih�A\� 9)�� ate+� �m�:��y�K*�.$*b|!s.mA$f!2*���oH:b�2�?ah��k^f.� u&�&2(#�W�7N�ataH'����$(Jn�U.pGueroI7&�B2X1 ��Nin5�.@$��&� 6� � 9S �o�9�f3L��p&�N � �H5��&�6�&�-  p8al�$r%�A6�`r� �Ei�$at,� E.� E� it!5Y�e:���{I Q ^bO*x>!�A�A��* e�Mwild-typ�P.orՋ ��G \!to�s[�5*1 wt}}) - hY4��mu\N ]��j &�<2j)sr�� T� I r&.���_*iŀ&��cJ} S_%�&e�a C(h,)  G)*a.  ( G/N ma�9GC}_{12q:�D\,�D Ns_{25 Js&#Blo�?gPE�: F�PE.\\�KD � 0.43�-0.37 0.22 -0.14 6 7 8 (0.7 '0.990�;&�%_jQ ._� reZW:6pumn~7:�ar{"�L Kinj Nishikawa�L) R:1w� V( (L)�ceb�Yef�]#) es; �����n);�8:��+ T x (HN�@-:-�9: ��x o� �PE ��s�'i^�rk)=�!( 10: .6*� >�U�HP&. �!&"&%gtab8 u�l�z= FIGURE 1�> = \Ce}|z@ _Ler} \�tegĴ ics[�=7.cm]� _el.ep�c9c�x���Qon26� �#"MY��%�".o C2%Z&� �� �(*�E�Ls� )�Dd�a io2 � $R=0��9�fig:mu--�-[ All��*g  weS2Y&p.� �� i'o=��o�mtN�i#un�SaA�%>89}8"�*�& Fig.~QC6�%.�5�F!�y/p # �4|i�k w<-!�ed�UT oy�a�"�^��E�Ձ �|c�is�lex?&n*9J!D3|��&�)׏Jo� ��A SplB*5+�+*�a���v)0mpat�E3��0se�ved-9�ib2s}Bvݹ3 ���H�3�6!}1maymDw(�J�mis ��WU4m. pic�;d~qe*�&�ZX�Q��#.4O�\of orthoi�)��/���{ 6d&8-&i�%b$�karyoYo4�sm*H�39sIT!S � �mZ%�"�A��W�,>y��m|/VG)a"9O �a��H:�2w.<~_gap�.FKbld *qly�&l2; ^.�~�&�n!�!�Z!~�a6d��)0 �3C�;*_$.�l<e�A weak�E,JRKD.= (see�%��6%A ��*M��.�w�/ lso ��4��`�?�S��ofA�e"Q��:�<sɇ !/��ly-�D �un���%ldә\�JC `�9ly, ed' (UCky�:2a)[- :fu]�ften B�-1�meu�s:iA<�[����� s slow doXYbo*8N"s� im�! risk!>.ufei��s�v�}R�8.0m�3�Ztȡ obl�Aoritra��u�T &\��64)I*$"� &/�� ��h d&H��lenec�ur<Emi��!�new hos����'��is��~!h="�5 (Ohta3;78�-���a-:ighA�[b�T%xole� rApera�QwU+��as�}�U ���*c�4c;"T �d!9� (Hartl5 Hayer-%��UTA�r_�"�P�A?�3.�%"�&ses"+;|5,4�Rin�XtJf7�N% @Zp&d���c�"�(5�0)�=�2� ensaj"�4�%ͩ!�U�h1o�B">��4�Pos���F��rade-�%��mk!�mod��",? .`A�!@��B?fJ�4�Չ^ �^ .6(*�� 嵡�INi(;�of>:IT!D�&YA.k���G2Ϟ�Va�X!�e��nQ�U�+Dc� �Iy� zbe favo�_A�r��DGy{zun6!�u'�/ -�m �ALa wh)!.�fA�!���*: Mb "pf" K �.ga�NL �7below),�Ny.~ *�i ��Ot. ynonymo!����7(SueotE(61; Bernard�_ �86; Lob*F1��M,A�a �[ basi���o�� *fl!�!� al bia>0�M"f!f]i.R\�(wo im'}dfQ<�#�P";, B�ReF94 &}!��(s��v��1|�/�� *� ��"esA���c  tť�ca� �,S R�� FI�j) �. S��B m��GC�1D1\���eo go ��!fprJ� )��e�Ջof higk�* e:W�!\� !H�� �&/ies>� mong� q.0 k�Vo�7r>`} SKD ^�>0;stE0@�.ƺ&` si�N� "�hi&�J �J A/A�Y�N*�"J A��A�) codg5s�5� �?��y$ !�:.��bialway:"soc����*�Pci� (,eAV=$q & �JZN%�@�Nic��� .Cp1xpl�W�n~;)��4%� at+/es��ory��!�troIX2�8 (Phe, Trp, Tyr� t1� �{ ��*�#� AT {�-�i�Zd����.s�?� �,�(2) ϱm�nW1Yi��� Ms�V� 9�� to�� s AT�M��Kd"\ B0deaV2g5;gu+gQ,i2� ���y�G��m� d*x&� � "*5�B� ��"��nw�6�3 I���~ 2;A��  �p}��~,FVea��a "/�X9��T�nBlh9o�,e�GC�ND ��Zliv��2�!�eLmc�&I�-�nR��A�_�,Ua��� t|RzC�.���y vC�KGCf�S ��W.e �v�8"R 2� �D.,%O�Tal>��U } SOa� t*>ghtv&�I���&� i��ODPN�". 1C!�@�ZPE_� llel�+he�&�nNY� a ֎��a;pQD�,`(* q���Cn"�Jٙ%� �)��X�f�gA hN�]�6�R�d  A�Zg gen b3���nóss^�2O0;xKc1!"�ӵize�|Rna��$a�#&r u<R4,�c�B`-�M�/. S,�)!��)�HP�t�**]h�(�"opt��#7HP%d=�\'Mx[n�e�k,R�,EI >� g7�b:"e*,�.5hR$>,�C-iN$i)�>�, [u T a8V �j� � �/m\+6J�0�� sed ��,  � �F� 6��� !k-�Ix <�� J�'� �� &�� I . S"�e.rBV��e�� .a limi%� �2A0-�Y$,i� qu� yY���}:�glo6�F�! )��\i����� ~W��-%l��M@��)"-F?>byZ3��a�O�]2o:k c!� full�e� t":� >l31L�FKM,'<mKW�"�Qw�V��R���� emde8Hv).�.o~ �|T}���92 j<f� 3wJ�IaF�ܡ`��1e�dat�qe�a-�WweHPs&���r^��onE�� �"� � /� "�3PE� " <Ax�` 6�j)>%pc�" NI��\.0*��&vly ��,� ��of it� �B��_5, !� a�&*�WkD'5a��#dP"�ald hund�=thousbO�edtperan�'#� �Z� {��!l�f�� ��.!� 4%y� &8 �BRH[ h_i�]&�)A�}�5^i�|��[Z1�-�o*u!�a� v�@DAfZE�!�� �%6$/Ler��}^ �C J��ͮu2Lj�OKQ�4�b�e :��}AF.R.u ��suՕ�  enX2P.��#n�B2Z#�aIa��� �)߉����a���%1��a�U�2� b):#"�2&=2h! ��efI�B*c/@({ \{ a \} }�;;@, h = A�-(!jBF - 1 f�5B�-,;$�_5!Z|4!�$ tca amin�]6 $6�2 `:_A} A�7Y7�6� �[��BAK. > - .�5 ��7 j(<c.R2 )BX^2�:4 B�!���3�Vu)$!:�#!�PFAM (B!�a��1e�0)�m$FSSP (Holm�O�96)8a62��T�k�_Fq�6%aQ�=vi� �Tiw#��h.��K��:��-oH~��ca�� �bBySer�'ean.� 2Mz�i,for%F&-�8$!< 5�b� �U�A�X.�=�un�ed=J8*RP�.�S�LXLQ��%-�ᅍ���O Xs RE*6N"obis7n*� i��In��� � numb�b �c5o&{?���ˡI�]FAM�%J9g!uch1�OA�h �l!%!�bSW�� r��AXuA�2Q aNv2g�7�or6�5V.�.�X /��A�. ��gc$!G4� MC���al Q+}*!IDB�:.dPEM�*)OSQT �:sKA�i�!sa�5 ���TT�< 1�� D��� �5�$?l%��;#A%�e��s.W$i$f9A:�HM\�*�� !�it[�y = 3"��.�i� 9�t\ �W6�A.� $j E`e�6pt4��_ �HPA2 e:� ]L, ]j *\ �".̝����*��s� ZR5"�y� a8Din 6*h_ave}A !� 3-��! 6# ) .:ap]���T�*igmF" R�+mg�bH � for ����ER)��:  �=59(7m6g 6&�~�v~-2�~-A ��|-%{nx-6�Ym� �KN"� �Z!Els�f2�=a!x��z��-t �R�I]�,V�n"=i9�s�o�ct\��eq\ *O��,% >o-V���5\�ޅ+ec��"o8ed lines, expre�>ssing the dependence of $\left[ h_i \right]_{\mathrm{evol}}$ on:�PE component, becomes smaller for longer proteins. Accord{@o Eqs.~(\ref{eq:h^,2D_A}), this happensg ause�lstandard deviation (and also!mean)��Phydrophobicity profil!creases� l:�, >From Fig.~�0fig:h_ave} we jnotic�atitdiscrepancy between predicted �observed�oinn�4 Consistently,� ^ t�:�P have a weaker correl); ��ir PEs�`HPs. These results sugges� � selec%!�proper>o@is less stringent,:�` (Porto et al., 2004b), c� with� � �� Qo �Dmore native intera�s �residue,�t�(tend to be )%� optimized �respect- non-Jd$ (BastollaE Demetrius �). %n$ FIGURE 3 n&. \beginA�ure}[t]ce��} \includegraphics[width=7.cm]{P_c.eps} \end{3cap!�{Di!�bu qVnormal%PE �s, $c_i/�O< c�M(>$.} \label�:P_c} mfi� ThefU VU, areaxtr�ed ex��iala(as shown in:��E�(refore, lar��2� _Efrequek foundQMpA�8uctures. \subsi{Site-A,8ific amino acid� ions �PEE,��HP�aallow s�FA�be�p . We hypoA�iz�^�:� , EqB�),a�2$only condi�it���{,to fulfill. ��1O��assum�s=�!" maxe�ventrop!�4r a fixed valu��8. It immediatelJ!is �Mى���d]��Y! formqbequ��(} \pi_i(a)\� to \expe [ -\beta�], h(a)m] ,iE wher �6_lBoltzmann parameters (`inver�emperaA� ') $ o$ d)min Se�q�.� ��can b�`tained \%N.a�B� so o @e�Hin very good agreem�w�� 6�^$T by simula�!�DSCN model, as wella�a empirical2�Nf��E PDB Ʌ��b���� ka=�A , similarA� thos9X above,ibeen use�Ra�,r studies of�c$ �. Koshi%� $RNA-virus 2/��possib��r someIl�  bacteri6g. * repres��-�]O�[n=$stochastic-!�eJ a trans% matrixF$$T(a,b) = P`u} \, atp fix} >h a c tit��u$a$�h$$b \neq a$!t4e first factor�%� 1��!?Ase� !�:3 neutral.kGUat� �J$rmodynamic�$bility. Ou�R�s�� � A9t,w TcerbeJAxary2�.�m� term� be wr�� n asF�%�>u = \min� \{ 1,&� (2� ([h(b)-h(a)]� � \}� � eq-!�>�&� J� &� ��!&� � K s R�  N&�)eraJIabsol�( Rof&0 N/f;�$Q6s�L$re eliminaby neguB�b!�I Up6�aal load.s� >�����le��>� haA��d m $\pi(a, 2� [� a�-�, w_{)}(a)$�Dere $2 satisfi�� FiU :�}Q�Dsplit} 0 = \sum_{ae�b} & .�BJ �bQp]G :m #a#M� \} \��s \\ & E�[2�9e��-s,i8u}(b,`�nd�\ 1}��l��zse�  scorA�y��a &��< e: throug�,Jensen-Shann�JS �$h^2$  e meas� , $Db��JS���0h^2}$ (see Ma �M� !>�&�(CH mdiagon�"VvX� s (IH)!�vid)|(best matche���&$���� erm%�JS�in almos-l.d� � nextx�A4 pr�d� !� buri͉ (Z04) �. I fing�s�% ed refe�e CH J Z c�d�� aris\ EQ; ey\equiv 1�maJ� spond�  $2�= 1/20Eoi& �qal ^.�E�!Rheo �� s. Surpri�5tQe3M�1>rcl�<td])2-i� �/genes,rthey doezch!2$ much whena�!7� athy�s, -5D$_i�  instea���,M���q B&A|a fur  30\%i�A$6<b�e��st� thir�ach�l�$� =!�[ex{O!"N�N!�coinc�swaB� W� �� �� YL��q.�"zat var�C�٬ \C#>� w�yiv�set.�� Rb. No�� 7!,�ir�GAa� $19$ ad��&(���EXit doesIX"h A� any >H ��-4igT�ik �fi[ ei\ b�antI�we��*\"c��&" � �as�.Y�F� �drac,�Q;Z =�f>$a�!%��"�ka�two%tI� l �WlyAst�A7%!$% wors�R�> 1.2$W!�9�two cri� Y�9/'i-$Q�!� Y�nd*J :� av��� deri at.�U�F�vhowev e�if.C5k is�� >-,!T[atA.fiAjq��poexC:�&!m#n%V $�,��H'$�!�isE� c � pre�t�strong�v�ssX�{on:� ��!!�7'�o �  II�o t�[.$0tabular}{|l|c  } \hline � &E�2 I� !F}.(<|  _i |��U \�7n& �  33812 416PB�N I47 282136388I ��y6OI17 A271129362Iuni� I�-sJI25 �285A393I�^yA�$c=� \�)< c5S�08 �6 I17 380I-t1� 2�% � m"BoB["�6$�������l��� *� Y�le} La�� olve6)X e�!�a5bv V�Sns`a{s &� 7s��quiproba m�m  ab����Mx e or� J� � � of e�a"�*+��+���b� per�l.�(n�e���)zN�B;, even��BF�B ed-"� justi"��x*[!a�1��+%7 yn �. R&|�to>Z� summarl(in �.�:v'R"ratAvU%&�q� �x $.R$�U"�I0�2j-�)#an��OcAglibriumn9 �e.9"!>9at� $i$� N���(we om�-index8� ��,),F<��%a�rej}}(��X a=1}^{20}�(m_{\gen�}{}{0ptP\scriptstyle b \text{� }} 2^ '<�R b)}} \!  & .{"���&�(�� e}^{6� } - ^b)}�)\, .��-�]e"�'#���"� is quant�� kno� >�,has � *#!ofu5"�% .V\*�#*k�� j) un�no�GI>=0$�' E�e� ta  haV .��P%e �W@�)aJ�.��|E_i"F. Amf :�c�P*�ed,"�>@��low�.fo9#��abo�U\�vin;ccount==""i" �all pd"B�$'� 53 J� $0.348�,Y,�mt� �^�&`t^(giv�the"�fit!$m�� 0.20LB�2280$`F�300$. E�M�r � \%� �mQ>$�a b*-�=*q*x ���� ��L.�*� tmic�ABP*�. (minimum (A� � J�is�32%�1�J�}����"� �&� Q _i�75}.&/)"Ese �� $ ad-hoc si#&�@����&+ ��M $s s.�1�� �Z�a� o1m4al �!.�.Inj1A�2�$} Kinjo"$Nishikawa �)4) re�ly calc�edVGI1eom�E*p))�� e�E�!5"�*+t� �)e,Os. Quali�"�e�seZ�b R2e'�w�u2yp-ae� !nco-occ�)�ig�.R-4d��eigenve�%BW !�st��i� 2aJa fairlyi�.� at ZA�� I�U�E�%*1#A�i��$b��e6 "d�l��u!'%�c ���2�(u$$R = -0.95�I$ 7$)��)T ���d �actɩ&+��2gisH, highI�Rx ���&�% �.�7B�75��f=7��7e�_evn4 N&�7I4��ERU�tn;���u�#n�,1��?nc�"�+� e�ny 3to��%�Cx��emc �[G " 4. om PE-Le9�9���s#86�8� _mat�-j,.t{� �e.d=-����,2G:ell-�/ }). p<�qbehavi�6of=#F�%6;�)�]P��9��>�!n!EHB��=7&�1a �( _)q��P , {\� .e.}9d2� �� f�I1�Y�Za�9(&�7� �(ek��<"6S Eed6<a�!�M,lx*�,6�,A�S R2L(%?A@�$�0:�!j��v)7�12 � ѥQ�% ilar� �oscpar&1� orig�3ncommo�-/ al enviroid!/PE%� ��6/ �B$sup*�� ��~> ship"O�;�9 ~3��;:*{Co=Y"� I�H8����36!ta major�ef9�4&�7�>��&d6�;�z%�, a�s<al la.�!����>j �d &w>8�8�>n�stI�*3 � �m"�1� geno�1� �/"�#�]:i�Z-j / s: O-�hand,H�[Me5 Ii�!#st�� &�? unfolw ;���d�a-S6 B?A�Z ��mis @ , sow54t a careful tu��<2�con�A_N7edF�$ 2004a). C"�`5�&P ` %�#�<��x �5�� at m�, redu�B6 impa�5nnes� i�*9�# wh &� bia� %hto=�=��~A)h�%� -A�YQ s. Lf?.�-H mean:V, J, ��ole�A�[ courZ;f}] 2�'achievuE%���e����i�:�a�uld� " Bx*Q����$:�<�=er���+�i. uI�a6 � icator --� principalk� -GA�!��m (PEZAhh@*�>Ő$ b�- ,26E!�PE� �� o"Ano�71�a_%ka�5�%�5| 2�:2*+ 9�R&�C�&^Z, !6l>5>��"v6B1��� �Zal5= ��d��'PEXeao�PDB. F�2�weIx0FussedA��pq-sT*�s!Zrov� fitA[F9;�&c�"Ud"� sR#teres� ��fŃ!�/�Se �/p!�& ��%� !C� st of r%C+ Ƒt��P1�F RK�%�� erroXrr� systems ��e�!��"to��B0+aof��z1�U��U>U%WflushZ$thebibliog}E(y}{99}\item�0nt -2ex \bib0{Abkevich94}  l, V.I., Gutin, A.M., Shakhno,, E.I.O 4. F�2energBndscao� 1q�$kinetics -QF �hrap0  multiA�� ways��theor�lat IIJ}iD. J.~Chem.\ Phys.~ @bf{101}:6052-6062��,Babajide97}  �, Hofack�BI.L� ippl, M.J tadlP.F% 7. N�:network�1spaceW*l.\ De�$2}:261-2696��G98� H, U., Frauenkron, H!� erst��Erassb�0r, P., N �W� 8. Ti��MD< Carlo algorithmN�"�>s5U 32}:!R6R�9>�(Vendruscolo!F, Roma�E�99Bagn��,>��1.��� guarantee �a5c a�m5Q��J��ee��9A Data Bank�CYT44}:79-9RT02>��3BNR�2. LackARself-Fin"j>2y �s. �M,\ Rev.\ LettYE089}:208101/1- VP3a�3a�Hn��� �Au?�p, 6�a5� 3n.� &.�e,M��Ev.*$56}:243-25Z�b�� b. S�m6�$�E.�5�f�(7}:S103-S11RL04B� Moya��Vigueraa�@ van Ham, R.C.H.Je4a. Ge��Han� M*��2�ɗ)W��,ArprintR�4�M4b�+_R� 2� c�nd: ��Pa� �as^�teman�6 (, A., Birne�K., DurbN,R., Eddy, S. �8, K.L. Sonnhamm��E.L.L.�0 � PFAM����� $annual NAR .y( issue. Nuc�8e�.x8�y3-2:�(ernardi86}  , G�  1986a�mm` traiA!V�2RJ.M6_24}:1-16�orn��-Bauer�2E�1997.���2)u�es&� �64? Bio�I.~J��473}:2393-2403;*- 6���B� , Ch��S!*��M�šmu�Hlan- : M� .] , topolog�nd su�(unn*in:��O!�,,6}:10689-106� & (Bryngelson8 ( J.D., Woly+3P.G�087. Spin-glas�S!�A�%��-��piF�+��8�524-752828� mfSE%, ��4, Thirumalai, �BhU",charjee, J.K�AHTh*<�Nf�*S aga�3&� r$079}:3530-3533.�$Casari92} eh*h A�2�<e-)0* poial. H&E6�X-ray.of glob�.1�s4"�d�6fy�� B�"� 2a�725-732g "mL 01}  , N.VN BY 20 UA'�.] hierarchQ QHuPf�G��l"R�t�|�31y 89-307.��m  � Mirny, L.��R�2.:�|e�Va"�,�Z�M;ica~A�4� 0� .�Fares� � ���Barrio��. GroELu�m��en�.!�b"�IDendosymbiosis. Tre?in Ge��24 13-41:�uc83} F a]9PliskaR�73. 2�&55�K5# ��7i-ځVl�I�LN-acetyl=X d!�Eur�� \ Me/ C�(18}:369-3752\elsen�O 81} ��1. ��� ��tre�)om MsNs: wNx�&l&yO�-achb� 1� 68-376\ontan  , Wa6chust*P��Continu$iny�%An�R!j�/%Ls. SciN5"0280}:1451-1456%orn��02}%: A�S., P�#! , Ec2%;20ab�Qre;N�I� 4D al�&on_eA8 � 2*m \:l1�� 2-352d"�Q��  aaLu(-!qlten Z> ��O[��-�.��codQ+s�0!�ory�9�18-4922^ Govi�[ ajan2.e ,&�R ��Y8. On�&5*�A( ɥ�in��,95}:5545-5542� Gromiha: A>_ Ooba~K, Kono��, Uedai� �Sar��A�9. RolE�Y+��q��Z!�a�F$\�# �<lty�vnga��A�o/$�Dedd��E� &��A|n�\tex�0 49-56SGu%� u, Xv,ewett-Emmett�Lia�H�8. Di�s*&5 �?ure af�2E]�Y��$�>s&Fŝ�� et���402-103}:383-392� GueroiŢGueorisAp , Ni�]� Serra!�L[2!0�&e+v=�!�s"j.�h -��lexes:�u,m�.tQ 1000.�^���� &  95}  � A�>)F  1995�1 -lik"l�!& fast�"2� s!�� $2}:1282-12� �Halper� ��Bru!|W��V���s"2�-cYCqXs: �!�2�].E'.r� 5}:910-912� Hartl�e , F.�Hayer- MY=��m- Mole�,ra�peronYQcytosol:5Vnas�,(\�Dl*� �U3 bf{2��1852-1852� Hs*�C �~J8 �+A*�ub&aRL�Q�block��+10915-2�Hobohm� WSal , C�g4. En(d��S.5<#��x~��5.3# 2-5229Holm96} N ,:6. MappA]�lun�HWB��595-6�M}uynenk �[��2�, *W a 6. Smooth�2 in r�/d:%%r�y�Ss adap!)on���K 97-4� � Jaya�-he01} , S, Hristova5, WhiteAiHe� ���')�@0.6� membran8Wlic? ^"��927-932��-04}7/, A�"g0� AU�'�(�sie.� R  reve sharp �� �A#�> ��w ��MDs.�inc6� 2504-2502�KlimovAD �KBYM8Fa0s g�� ���*N�T�]$26}:411-442XK�\' �G��:� �8�ld!� *& �JaW�� h�^ogeneit� a���#2��Y���  �M]ll!xJ�9. :n�-�\ stryC/6� ��hyl�tic� M8HIV-16t�1�l.�>� �73-172 Kyte82} , � Dool�I��82��Pe <]�cla�PA��athic�L�,�Ka1�� ���"P �105-163$Levitt76} �� 19A� bQ� "KYI�&& aM��!�rapid�(�3�M�E�� Z�104}:542�Lix� � Ta�OC��ingree;S�cNA�e�dr@7force>�E�( �0zA�L*`&�.n��765-762�LioaXLi\`o2A��N�2Rm"X&x� hI�y0 [R.l8� 33-12429Lobry%? , J.Rt 7. I�K!�Jic G+C!���#�� -�d*� Y �:om 59"� l�7����� 05}:309-36�0Manavalan78}  )1$PonnuswamyO786�ch.&�h� B�.M/�$75}:673-672GM�!� Q�䒢 �ow=�JsQ� ld quickl�"V`~2�5�76-1�7NeiNe/, Kumar�6*0��e� V]��Ds. Oxford Univ. Pri(f Ohta�4, TAO�2'�,sl�(p-ey-YIK%�J� a�F(olymorphism�oW PopB] 10}:254-26e,Palliser01}  u �2Parry�@A/ 1. Q�=y A��~'�S��K4recognize surf�` eta-F���X 6�4 4�2� ��S,�E2�1&�Jem�"Y:of&�p�5)~ �YE1cB�8}:750-76� � �>, 'k� *�"R3 �R�P� :0 ua�a )�_6�r��21A 2�� �n�6�z b� b{ &�'���_�%/0� +Ut u�ar"/��� �z#-�VARosA 88} ��8��y2 *��o�f���&2� markedly �,d gclan�?pep*Rbonn�"$513-56p zE ��2J , :f 6Q&� 4. �350a�sha?'�pb�"-- A �L-s�in�b8a ary Y�!�oc.~R$$��London B�E(55}:279-284.�$Sueoka61} � 1961�F�ob�f��o6� deoxyriboBic ��%� :8M6�\�� 47}:469-4�h�bTi' ��Broglia� �68igezzi/Z�(8�' �*�/A��g&�ch5�S� ~�F�(�� 7-762� $Thorne00}  -�)� -:U@�3�th�/ appl�- . Cur��Opin.\��(v*!0} 2-602�U�kky02a} �N�c2��> 19s: oint �]bi� wa�6�  I��E�1}:739>� �02bV� Crace�� �> � . Whn5 s� -EsV"��'�[o*G P/�5�1(don't? FEBS:&5�181-1�Y��$  �2..p�[�'�{�1�. I� c� � ">  b/�@��E�*�27}:991-�� Zhou�� Y%�4�f"2aa�.}�"� o"����!�&| 54}:315-3�zhZt:�, "G docu<} ��\c�!,[12pt]{articLP\usepackage{amsmath} > symb:I-ics:ci�I.Uepsfig}2 colosrenew7and{\�AO8stretch}{1.2} %.Mset�*double�%=wSs 26pc 432pt .bottom /h8` 650pt opmargin !%4 %\footskip 3"S 4594T372pt 25 head 2Bsep odd� t5mms� xt 6mm 0m�par�0n2�.6OdJ��}{0.1} >"op.!9B!)-v$ floatpage'1.�J:�he!M note}{\fnASol{@} % journals \Y {\etal}�O{{\it^7}}>(ACR ' ( Acc.��\ J3PC63dF e~ ;V6SJ6 .��N4Bioch6 �em�Z0met10�vkaZ.po%%.� ersR/�/"0\f�BJ�b 3JR�C:ZCo��\mu�t}�F6�CPL m l,�0�VN� COSB 6 5u.�S5%&{ F E� @5"� r�E�61L-N�FD �4Fol�"1N/IMP 0 �In�!vMo8�-F�JACM� 93A2%P\  }} >JJB6s:1%\n�J8CQYr5� v:BpCo qJ8f�C 5.6�#�JMM%4* R�f3f�:�!: - �J�PCM)��4:f|de�5MV�Sm�> =%� (Jap)R7S�7\� A[|R4TF=2M2N5Mac � iMacroReR�MQE2k2�6!�,\ vy SimuFTu4D�nNA6=N^N$ic\ Acids\bBNa��u��N N�� �N%m��N1�8�-b�Phy2q)ic�7%:jPro6,��R�f,�F/C*H F�ProEngtIw q\ EngR?ProSciJ1�3Jba- b[w �>�:�+�2N�PNA2QP^b�RBQe��/K3J�R��/b`PR �6 �Roya�Jk45� ]5J1TQ� �ro!‘-LN^Ru� :I4z�Muh�NeS�a `Y�viStrM;.8urReTB11 -%+� f TRA2eIEEE T9q(. Rob. Auto�FrZ1q sZ��ik!!6 %.�Oqq}��"IU2�{\e$`^" beqaGnarrayJG% HV#be"b �V$e$:F:�dst}{\�sty�6�c-<}[2] {$\!(#1\!\r�(arrow\!#2)$:non 6 3P rm{My{}B7TRUE} {/ true>FALSE}# falsB$T%�$TBD6 F> nobs} {n_CX ize B2calc}^2>3Odef} {OVedefaultB6@weq}[1][N]{w^{#1}V?eqB:Q �� bf{Q>�QN�,{{\q~Q}_L^N:�P."PN"nbe�_ bf{n>dn� {\hatJb �nB�x6cx>cxE FFJcxFc��BF���A>�C6�C> D6 D> G6 G> S6 SB p�{\acuteJb 1jSBT6gBFM6 M>�M� ({\widetildeJ#b$.#�MF��]u�Tr>p phiC�=phi_L^�D.�B� phiIv3I>fi!=a')^\I^hB�Or�0{mNO}(\xhe�4\epsilon^{#2})>]CLe�0L]{\langle C_a�\�ele_>�O>0\Omegar4CLinfvg\infty:�OJ8JoR<r!�r��r!�V,B�ri} {rVtdr!�Delta 0&#{\dri}{V?na��-b{N>�trmՄ:(srm!^U�]�!�BJcr J� {redF#m #magenta����C�8} LU TP 04-10\\�$day May 10.!4�.4 \ve{0.2inX�+er�* {\bf �"P~N�BiEC7�� Bool#IRules}\\ 7f:Al�CSKW6w\���x 5Stu#N0Kauffman$^{1*�nCar�E P�'so2 }\\ :8Bj\"orn Samuels$��B Troei;V�5)� $^1$De�3�C���og_D� �, �i"ers�*Lof New Mexico Health� s Ce�F\, Albuquerque, NM 87131,�A �1� $^2$1lex SqF Divi�B, 6�j !�al �c�`Lun# �(, S\"{o}lvfhan 14A-223 62 0, Sweden�eh{\tt http://www.thep.lu.se/� lex/6Y�0*$All authors G^>> ed�H2 %.�I�Submit%to�Q� ee���N�al�BemP s!MA|) Y�U�60>�! oj SCor�Me�ng �:}AU2�; cI�@9x %\makebox[43mm]{}tel: 505 984-S0E9B'fax' 8245!B& e-mail: Sq24@salud.unm.edu6D�\6�Sub;a( Category:}M�s*5B:�iv.�NT(Keywords}: c�B'I�,�ldom�4&�B&:  f*�, =P-f6H2o"�%5�N�Manus�c "�,on:} 19  �s, 4 @U�"0 ��s; 184 �E!ab %0ct; 46980 tot�$h�'$A�paper;_RA/ m� web�newD� Q� rge �xA s�U#=� %T�shoN;P�3250 �0(188 so far) z|�B��*att�+o!p&WCra2�-� -�P.l� =�r��a �Qete�a�<tec;s.VY,l power law��ex�las �Ras fla!�-,�ee6,�Lfinv^�R �sŎU�l�=$able. % F(r5, �.���few inpug{er nodeR Ts h'rplo��ooaR�* aq A�0!Z�6at�ac$! dek��y �um�x:�. %�?*�p�@d upon 8� stig���}m,�]>.��-s^��)("�y i^�A� �b��!?� cyclazreGj-�ei�Q;aMnA$���ose� exts.Y .�c�os%?� s, "�+!�!�[�%8d�KUUd�< dg?.> > reg�(7s\�Q���gndAHŢ%�E���gin-%Qout�=��� draw7Bs�&.f �VtY �&Z�fa�� �, $K$,��* ��{1�M exhTR uQX!2p��ties\4%{k }?Gec�w�T��$K=2$A�QA�+�v�p,1 �], 1"�T��lP�) oticA�F. ��m  �juk����,-p�()� ��,A��!���Us. Be����EDde�� advantageh��jit!z� p�t*�)Q��I2�)� no atnJo�@.~ �as�d!�f .!�� �� I �s/Can�(�s�os�,of>� &{, Pea�q�xpeE�na �ouO(SJ�� 6uV �8 �V�,a����t!�m7x ede�--gen�t� bothI] E. coli} I�e a�yea�^ you�!Fy�2�A �.� �8t�Am�6�1}toN�.5 in6�&�*i:Dys[ be a &� in ��W �aldana}e7��y�� :& 1nI�pro�g�' .gN�s,?3reg%�of robu�Ts NgIi t�]>�A� ��Y"�.�B�[ �. Inde{ �YQ��i�Z)�h4Hs}��zX %�}),a ~�]* )��;�]�h-u�إu at lAD ����,�LA��#" 3<��ou� A_� ���!� ghtforwaruTA��\z-�H�le��.�&�])) E�lC2nesaT=�s was i� !�w�\facAh ates� M!_2���We*� Y}� F}B� s5 , �L� all}]�a�6WR�. Fur1 [ ���e�2�get��H!�movAB A away���#i��x �@�8�wa! � s (ZS/F@ E! `�') A�>e�;f�t)� w��)<d�E��mg )�Q� }b��5k� %u@Asa�.ng�lems en�r� D  ny!5�, prl�h�NeeuJBe0|Z�!� �����`�mul[ll� db!�w�A�J�"k �ere+ak!�&�� ac��ijH�l4�A*%�d� !�DC��e� �! Zdo�'W�de#^es�".schemea�ow�a�5-'% 6Wtraffi���c�unAF�A��e �ough sti�)k,%+�5�Es2� &�Ď�VM��e.�rDC D�,iբ#Ou&�� turn����q.r��i�_��k,�*RndrK. (By "we��Y~6�fup�$KV� max��žs.)Ŏ:�fo٠�/|e �cllust�!u"� ��њ (of^L deno����&,}) .uEoa cutoffeihe*�| �� C#,beq p^N_K ��P"�"\# / } = K) "݉Y_\lbrace ��ao}b�D1}{K^{\gamma}}& &&{{��1\leq KN$U80\,/\4 wise `�r\� .~. �p_i �eeq�y $N$a�!m�P� ���a�С��&-l ����%{�}� in�4 a�a�� e.g.}aOe�-ernhnd soc���, $)!$*�  li �=e 2A�3�Y.�Ab expl�n�Z � o 5,��4% <2�6in�|�[� n�JQ[&  &��VA�H);)! � �Kme� !) �kΩ%�eY�Z�Q�n���� 5(�Ghe� ge 1.5--2 e&E.~� �� data!�P!�6� e�y`}�&�pE�*sBlY�c�jv�`/�mA�li�~W8%Ws, sl� ere���i� 9j �hil�F i�!����LA�AnZ�d grow� dv�9$)D5lq,S is es���N1E�F��1,�G Q��hlO�"$N=20$);�o� `=1$, 2�3,�t=9JFA�on{Z�BNIn ��!*�mŕA�.�� � �!� employed-�"� %�E;�p a����edI�Z� }�!ix"�|�7��5a2��o� �m/�tHllI  E�e�a:lɈ~EI^e�e A �*� ?}�Ba5 \M'�at� ofLqM�alq �v&�8.� t eib �  or ` )' J im �� is referY$[ieB�,��.u?��5 �Ϩ}�w�*l�� as b�.9aHonis6;L r � NB!Lh -AryKŪq �\., �gd�5�j�w!v��h���?�?6�* ;?��g�e�!` d��ge �%F�%�,  �nʎ��onsul7�s�,=\�e s \Da� & emai/K ?��f[�6�A's :�� 1�y 1alY ;e�c�i��. All��six!V+$oughly 150B+�Y�aj�%�F>Y� $I_m�#$O � !�c=�� Q�s,MQ� �ui� r��b�-F%!� i_E�ldo i_K$ m , $o�a- y��e�ed a��%I o = .  .{ll� !\!O_1 &Y�Q-4if } i_1 = I_1" '�\!6'��I_1\,and}~i_2?26?3Jf^? 2~ .c i_3d7�!\v!P f\ �KZ�.T\c@9F� i_{K-1}� ^6=!��K.�-ڡ2�K�K~. a� %� � � Z �e�A�Fw Z� $K$-E�E�s,�e&� UE��� inct � a���Oz��r�� putV!i�}p��y ��ir��B�ed‰0�o $)X=)$ not}\,O_KM�n= ��� ) I.�I_K�# $O.Q�2��� �N ���I� �`�a�ie%�a�P(I_m�(TRUE) = P(O6\n{(�8(-2^{-m}\alpha)]� {1 +'�B#� eq:�_ca� X$z1,��\wh�M$ b$!va� �_t.&B .O��s�v `to '$a penalty ��h2�uh!4on le aEjR��Ore�cisely:�5 $f$�(x!3� f x�" tru��#��let $gRB �r e���!��` !�it2]ixis �G A�?Yy!2r)��sa,ͅea�r6q�$A[-)�(f+g)/2]<��u�*�i �pi��j�$. ,"Cat M = 7� �g(l�!.^�� keepQ; 7 A� )i�E�$��{� Q#on2h , wh���095l=>e A���ATin.#� E{R&�Ce�8�| wish!�add�M%�.� �{VF� . ~a �"�s� �i�erturbd"h#T�{E 6�~z�A6�monito�!hc�Ha� !�9Z $HA�0]���M�UA�@``Derrida plot'' �d }. Sp.#A� slop�  low-sW  fat�~a-. afZ�$% �. c�Íly F!�atmS%�� E ly0j���1� �. e.chose��&.tA��aM���av* �� E�!�P ab�a.&�#! crefleA�h"��!A�6 vic��(*equilZ�d�, g%F�!2,w�a!-2�!�cal. Se� Ap�ix A}. �# defih��e$r_N$i�n"~!J $N$-!-q.s� �J �G,b�!V9t e^ �{oute �� "�m+qd(,ity, $S(R)$,v)a�6  $R$. '���sum� a����U�flipp�n�$wAZala9ɩGaThus,� � s7� �;��@j=1}^K P\bigl[&R(w �� i_{j-1},0 +1}� )@ &\ne R<1V<bigr]~, � �x wJ�9 6~:ڟ*�e ^�!)%ig, N �K$�N$r!��!by $r!5!)5$��M~%�aken � ��i�;"��(sJ��au us ��^Azz�$ _��# L6Y.�� �.9T �'an�p���A� %6� �q��!6�{ea �Id stay�Xe sam�& aM�cT&�3 �rny� bui{�5,1H a cer \�q!�-�] w�/,����c��local�P�y�M��" Xwhe���1�isW�i=M�n�w�cM�ou-qL S �!Q+�AN$E,:�9 � !i&�*;_i�+ł�%ߡ5�bf"�I�by� < r_NA�e�Ka�NQSi�N�A(Q�� �!�FI-�AAM "� a�5"2j, �"q"x.6 �a_K<1$ue',3m�$,�3%��8 \ne0�r_1a� al�51P�� 8���0a�2. ( W=0$ y6�s%= �2$K$.)�}, iQ_ens�.)�!!:�2�i: {�5 sol*-���one��(,N�� ��n��A�^�r<1 .�N"�/A~1�  H���M � �si�Jt�] .��#&�� �(6�#t�#"2s ��Q�*$. FHn,! �askj�length�Z�E$. ɧ!^eh�0�qize���f/f&g��q�  L����2� i�T �@&]%GwA�:L "A�so�鱜�&;4�n7by�I��pfE%���e�(oq�Ks!#esh p�"� "W~` �7 �, $\CL�&�*_)o�.$�1exact �. (�jA�limit $N�aB <$)�'full ^e�"e;� j{Pf m�s). Giv�re < �Iy}�L 5�+sub%M<��979%���I�, �� ��av��F)3inf�n �!%�,��,�r8��n%!�f}4a�1a�v�ii!� [�!.�)a�:�!-i_8t� !�%x.dse�+��MA��ve�3��of�z % �!h2> ' �Yto $\rC� I?U $r$ i%;��)�� �E�X�US�`�kɥ one � � %o��}.��E5�ZE2 s c���9lv���0r�)P!6o&E�,:"� I�= \rC�rI�conven,p%Y�dr .- . Q�?be&L�2�� $r�>1yda�K$L � $L=1,2,3$Pt��F"�0@[1] &=�1}{1-D?z "2"\ri! +\ri)0{2(1-\ri)(1-[ ]^2)2?36? ^3+(()^38^3}{3 K^3Y#6d2f3)}�"�; �FQ B�,Ev� needTo"o e9�� a��=daLh��bT O�$a > !�:2�$!�> ( EQͼ�g��5i�����A��+.f06�odd��O'a�asyo�3� �=� �3.{1to!*l��m�iX�AX� � C� M�A� L �@IX is! [��,+ /2I�"J^E�$r>� �eJ%B ��s a�1$�� .376��?&e�rg'Y be����.Y9Su� Text�#�� s. .� Tissue ShOIT}�2X) o *�ex�{�mu�� b�  "x�%���5� !�r�i worlI r�;�4�4 �� !�%�h�)W*�f H?we�c���ial��lo��-)m"�7. Nr the�)�think��ult� V� r�D T. %5�%� ,���='�th�8� r ne�wt n�XbV@J squa�l��%�� ic b� �`oniz��lln�@!Y c,!9 �9"�)J�+1���< ��� �Ed��;e8"�5s ax%!d��Y ��an"�2!�%Tgene. S�5">R58,� cross� �l= L#��ffu�ar�%�� ��de���Jof�Q -to-%� pa=�B evel-s� �:'E�a�o(%b��g`J��M� �d %MJ�unmod%'A{!Z TdoA�-/��.J��U:�"-�� �Z$ �in %aU�L�of%+�AnX�&em p u:�M $AR�%2�sd %at 2?! w" r@$B$&�c5�B�%~ �ma ���a �U�I���, %� U ��192F�eY P6! %9"6�a"&?� kappa� _yXdflagg�3�$)3B.i�* %�.=� valu%2�ifE�f!��p� (.����6Mm t�0m�!�� !�su�.i� o<QI $r$,8E�I}B��mN duxa6�, It&� T�&�agta"�p 1Es.�scA��2si�1 �-!.� ��6e�? s*bm�)F�)out=!Wsc�ofe$�0. R�t�vQ.�{tra�Do�)1 RZŬ�( ���fy2s ,�A�[A`<ly�H:� $H(0)�)��! trac�!e$H(t)$�m,v�tep�ZAh�2o!."���QL� $5 o� 5$�*a�� ' :taia=n �> X!r$N=50$�$��%ERV (�0E�-qTvi2ፁ`�C+~ % ;� >M;����-Ms�3 %s�F� A!}'Y&z1RӫGDiscu��}�IDma*��ings em) I;�+2A��Mkss a�\ .� a�v�#��gwn as�(%H� $�"�p�/�3[h�a \���>" !��-Ys����>, gard� �-#2��iR�6T?oL��p� ��!�>�:��I~5���/r�/qU� �=Y.Bx6��-� ��< 5�nd.u�J4N S!�� >s">���Ek3� ��� �L1+y�r����f�s&q J >e�7"�� A� exhaG�ve Qdof!�t�. �e7�!4C�7/+��N�7� �� feasiYN� *E�cru2��_A firm��*�, above.�� ��did�e�Amp:5z �C.q�"� bVx�W  fu�H �y� �&"8��m��o�� gd"�or�> }C-$ flyvbjergw.}9.�s.~0�a�!�+i�?>U�2���H*�7y@ quit��ralA�e� (( ng cur�:�� .6&�A1s^��2iou!�I-$x$-axis��4$) �G0�:+���priA�p&���2���H�I\����Jrt��!�* % 2"�!� } �� t�,N�;�CM�� ($K=0$)!i ex��duei-J��  o 0 �" :t�>!�u~B��w���ʑ�$3(�1��� �b!�py-$-� ator%� .QM�"֭ ��5Ńy�@{%�V^�, A�ŦM��=�R��ich mM�for�h���mD"��9� �u�j;o��\Bw'E�1 E�5KZL!m֒> �} )�4E{ ��I��%� ��:�A��F. s.��frame(�� Yo2* |>O��<�K/e1��<m�)�M�7у.��,� !G�'}���mo!�A�<� F Jv,!��> s/P �AV��A�LA��c�^ �&�!1aIE{fz� m�4!?w $�2kM�*� y ">F!c�d�aSlIer-��4�Wzedict�Bq�9�!'"0 1�s)�U?at!�ay��2asy� IK.**{ace� 5 N�rimpE.{{}{}}{{} }}:-�be�/$���o����agnitudj&6�s ˯ks! ��E^����" 6� �i�. �a� G+I�"Q+\� q��C, m�of S�M�HDrosophila melanoga�s��q�pќ; $ۥ= ;e�^ �thp+~ $:�to �a�)Hav� .�N)*>�r���r "�in� S'eA<�� ,'e@ mmar*��"�r��L�3a Io@� �*G8 ӝ��I�5�etA(on)�A�e� �n��q��WJS0rk�!�@� q�J��|4�/�y`���� *C���Ea�evax�B��zhoww Z�i���V� . S&H� le|23 ��Ne�F�a�C[O are#�par~�r�Bu�C��d� l/=1Cn�T��"�*{&�*�vR"�-} �I 9x"`'��{5Fi urbed �� &�� $�&)2[!H � �O�M*,�(m[f�$ as e. B@J@fg)(ofiep`�9) GDlTl�3;��9ty� �m�E�#n-w9�"[, 5�B~ s' W(w)��oAL� amXe!B1'e��r � �BD) �|sA��N.nd �Y�e�3�e^.�$w$�b�F. �_K.� �B!sc����1�$K�� : 2.�.v� an"2B-�weqE�� TB = W( & ,2!(�~.^Blabel� d324 ���� ��a��B(),6A�ad�IagѪ fast (*�H)��E$�Aas $KN#$"$u��a�n� (��gP-�V)x$!���Idsu1��tEhV�$Y�6!}#� �/my�.�.Mb s$.�?E4~+as�;��6toR 2�&e�m��b�&�a�a"A� 8B�eZ{ 1�is:*2�#�! )"�k=�.\,&P_1^{�` {nc}w9 P_{k-1BP_k can}}7kY#74" +b`_�Dsr uP("!8C�tR� P&7/ /I_1)\c%: P(i � �F#� I_k)B�]u +jbK ^K)B��"-j\*ZE:)=.�� #! " �k)"92Fb/,�1MawE .�$w$�5A�c2�^)���k9�/6i9 Oy-�o�,V� . �~r(Rz5��|$Re� �o6�)do� pick�1B@��F�@23 f to b$�.R&��=�Yfor a"�B�)p�s $R_"�9R_N$ ��#ra#iawN r(R_i)::K }+. 1N2+S2W 2%.!>&J -�'R_i �?{&d /�H(R)%��UrQ,  M/ �� �# &G� �/+ vali�621�', ?ea�@�с�%'_%%)2S_K6r*gaiforB�L �5/%$*��M`��� �A�i. 6krN}S�B�2@( ��B"0M�_�!  ^��I��N�? E.�&�QNt�(}P&�:���"��5D�# holdm#r��du/ o� e�2>E!s��UKA�4 �F � &l ��T $p_K^N$ (Ey�$��$i��sD,��b�_HalmD�392� [of�7� ����A!�*�oZ6$k�tn6X�[g $i_k$ � > ;e9jM0����yL1A,  �!sae�(K0(� fallU�ck!k?$��U .l� � q�(%�Lkets.i�>8S_)Ai�5cAV6�z�� �W�6gl[ C8\,j=k+1\!}^K\!&3+��" ��9 P7^P_j *{�/O_j2{ }{R_ 6�nL�)�r]Z��\\H � biV���I 2�08 �bj�Bj��-&� \hse�{5mm}�rr&� H^/� j %���isBn8�F�-�}` ���$�>a� %$yB� v� V(v, ; d&P.$ ��. s�G'�K��&��oggzC(�Z�$�- or*&)�� go� �z"��R� ime,�9�%,� S �����EBb�<��/!j .� ����%V(0! �,,�$l(tanv]�qrqDr3)�@T2�$�!a� { .E�!ީ� %$v"Qq9��$\par+_v %�% []) �Q�%ebin�>��cJ\X)|%J new ws^o�iou��@�P L!�+ Comb�I1�e r��7.\J�v6: v-�}<R���hL$�3I�2�v��� "'2(�Of $v=�.�froze_��YS��!UNofQ�isi�[]�fA�h�C�golu �*�-= �2� �"1�A��6.�J�Q.�Lo_%�!�N��0�$�Lk`�z5� s,"�)n�an�A� se<q�mܙ($v \mapsto !�-�$5 !�e(B%"f ;� (a�f&MpB ��"si�0 �c%�in �2�!^2,� �B2},I��X_a��4i�2�M���CCBC&79}�B*�1%4� &V &FL"-!]same � aA6�)�"!� a6yc� �F"� ���le�@�&YL$-d�.�(1Wg(8 y[the[�al�N- �F�:[at lem��ss"��&�P� b�' �����'e� 'A�� 2^L#4ries of output�e values. We call these {\it $L$-cycle series}. Consider what a rule does when it is subjected to such >J oni�> inputs. It performs some Boolean operation, but it also delaysC�output, giving a one step difference in phase for6 >�@. If we view each" s%8 as a state, an l turns into a fixed point (i�(is enlarged ?8 space). $L\CL$!9t!DPthe average number of)* x$s (choices>�),�&2��$CL \approx:�.� @{\sqrt{2\pi N}} {\dst �% \! I!$}e^{N f_L()3[=&CL- �-+w�%� 6x%��R�x:�x_i \ln!�gl[{x_i}-�x%�gr]>�f��SeA  Support!�(Text} regaret�YusC F�. Equ�_9�fL}a2�Pse�s� * !�gl< �f�r]�r>_i$ ��wea.s $x_>��_� �concav�0of $x \mapsto!,$ x$ yields)�,\begin{split!�%�x) &= ~ gl\langle �j� � gr\r2_Mb.{\!\!ih\\&e�`,6r� N��a=[ \!�`J� \! UV%�0 \end1F��� equaJ ife�only if!vA�\��\Aa:xU}6mean-f!�.7 $.؁�(�0(\x)��� $ r)$. Eq.~�� ]B�$ criterion��+ ��(ilibrium in� 2pofB�Zis mak� dt possible to connect quan�$ bserved��yca�^toE� full non-(dynamicٝ$NM�$ occur( >exponenv 2��,�relevR con"� � �s% ^B must c$�surroun�TBs�re6D�-�0 is satisfied�$N �6� fty$. ($�ig ��(inuous func �obe�weaker��``� � xb$,!�the deZAp$Y 0$��re�0a $\delta>0$ *8 � b')< )+C$ hold��'$-�+@ $|\xb' - \xb| < b$ � Z� .'' which �sufficiAY�\ is case.)2� ��� vide��up b!�A�$ .~ a�im%^ a#>� @n� est ),�8 >�. ��U�reg| �e exactA�, .�� ]I� sol]E�2(]�. Gio� ^&)�%� ��E) s � , $w��M6aB., togg s $v ' �: Fg,w beA� sist!٥�f� �ő$,��� �=\weq[]Z �=0a\' Ap� ix A}.) TA-] aar@typical attractor�M� , � a smah5(I�E2ac� 0��V�)AMa�  (� �) �. a�z we w��( vAmgat� .��e� certain�� t e M�we dia%psumI��(23CL}x��.� pattern�n ord/ \!orm)�cah �A0a[t way3  introdu��ry $\O��)xÁ�� j� �K �E2�hA�a |Eqasiod ')s�.jn on how!�eV�J�tekA��. As V9 A�9z15f1UEa limiUat2  \OLinf]A�1{1-\dr}< $nbh\in\nata2"D BD 2 Bi *=  e^{-rE 2}{O h�\nabla� )� }� !B� �0:3 nbh=(n_2" "�Ѿ nat$;%� ��A�negA�egers. �J� � elem= $\A"ial_j� i$!�!� grad�|$.�$AU� zero, 0N Q�P�of���q�li�UH retriev�eBf $j`s ��� p`$j*zr� ��inverse��ro��backward� ime.�phiC(i� $I�those �T� $j$,��!�*�A�>.mA�rCO`o}+\rIqV^1gM_ % %E*V Q|1�rewritt�s %�%�a% �b26yc2id l(� 'rBz�&e{ 1} %� %J "g}�t�!EOFH - 0} f�GizA �!pac span�� I : i��typE : $\lbrace i,Q !� C\circ2 &.Mr\rM$� �1aS��"� resul �$repeatedly����*hiCyM�$� $i$.�A� sets i"��"�&},��a�h&;q3F?�/�( \cite{prl}= �|�ed��:�:� instead2� ^e� $\rho_L^"� {H_L-1"E)B�&r���} $H_&��� �.�!�+ ce, F�"�2s $M60,11�. "ka�=Ws5�eh$%? llqs%�length.>� \7-�lowest �&l � $i) -Zh$, $(E�)^E�]!ith������dexƱ�i�verted�>H = �wAm*A�parity:�x posi��. O�wis) 1"�Q�>ructur�rtm C2:� its-k�  t. S�aA,�� enumera�� aPa �'�%U(i"�:f, !�=�jI�j+{!�-1}(i)2[ and Fo i$�5D �a�llphf` >1` >��ng�Y\T� $\F, "B�%�n�� C(\FTp D���F !T\T $. ExamplU}W �46� = u�R $, $ s�F \F h x  <  �$Tq� �-�F) $ 5F)% first��� i� $4 Kq I���i+A�econd251 5V� $\nu^+_1,-ū+_Aa - 5�j�+s, �of;�!)x��belong����din��a� ���\p�$ip}\equiv � Left* nu&-1 (� a`}��)'iNOmp_{\iO n_� a�@..V��&8�0� a remng� �!Z)�reE�two��(0"� ed2H: ��7 )2 2( (::)� L65mp � (::)�a.jA>�a ��Id� ; o6�� � �g(F)�g�!�� !�u^+I��!v}\,+�ip=1} G_{!8+_\ip - }^ Q nu^- �*� gl2Z� 6C% �i% &= \exp��l[-� �+�� �'r�/]E�&� /~@1 a�} G- \ip! \\ &\� s "J��.n���@ �)� � � �=�G� &�� -�align:�G�4>Eu!(-\tilde!J}I~))�(F �E�E~9 !�I 6V�NV  V 6V !}\\����\ip &�p)�m(Q��Q �~, -Q�䭤6�pme��$g_L^+$� B� C��� 2-:� G0��erpre"� �����$0^0 = 1h hand�k� � �%� $ or�m%2$ $$ Althoughc ��L sid= 60�@8 looks nasty, i] "�ed�O��# sionA�5 :'a��r��}\mp(\dr� B�gl-final�n�Now� i�:���aQ^�A��h��� �D:X2 �-�-A "#cco�o2 �� p�d��G  !r~ $+!� $-$,�a�n �%)b�ed by < !�allB��is prZ methEo��infe4 s>$L$j�� X5# HFin= eff wa� �!($4on*{Acknowledg�} CT a��� =! � Swedish N�Dal Research School{ Geno�H BioinP at� CP� affilis D\Lund St� gic CenF* � Stem CellO logy[Therap SK^\�Santa Fe Institute. \newpage a�0!Dthebibliography}{}Dibitem{kauffman} K 0, S.A. (1993) OriginR O�4: Self-Organiz%8�S�&ioZ Ev�0} (Oxford Unig�!P�))� ecoli} Hu�L, A.M., Salgado, H.,�Teffry, D. \& Collado-V�, J. �8 �(Nucl. Acids!�D.} {\bf 26}, 55-59!.\1Lyoung} Lee, T.I., R�udi, N.J8obert, F., Odom��T., Bar-Joseph, Z., Gerber, G.K., Hannett, N�Harbisy.C>Thomp �imI.)z0et al.} (2002 �S ce�098}, 799-804.=Q aldana} A, M)5$luzel, P. T 3) \PNAS)4100}, 8710-8712Oharris}�risA%E%�whill, B�Wuensche!�!� .U 2�Co\xe%� 7}, 23-406� east6�, P(-5 , SamuelsBw Troein, Cj�14796-9.6$scalefree}&;(e.g.}, Uetz!9l, Giot, L., Cagney, G., Man� ldABA., Jud�,R.S., KnightA�$R., Locksh!�4D., Narayan, VISrinivasAPochart!��M%�0MNaeM,403} 623-627.�!�} Fox�J%,H%�C.-,1 OChaos N11A09-815.N$derrida} D A!�Weisbuch!�H86) �$J. Physiqu�!� 1297-1303._��� ZW�Reg1Le��9A�098701}#,flyvbjerg} F �l�Kjaa�N.�(1988 i �. A-2! 1695-1718_i�22�iu \Phy)�D F(185}, 45-66C-c2Bd Pomeau, Y1b \ELiI�45-49HFeller} , W768)�%� An Iz�� to P* -Theorɓ$Its Applic��s, Vol.w,3rd ed. (WilaPNew York), pp. 50-53 ��~�*�8c ,w)@)� P"C* �$ in-degree2W $p_K$ ("2 p_in})�N%G(dotted)a�$0 (dashed)-"i�) (solid�935}"�%�&'2�th�+� m'Z� ��(thick lines �R�* )n (�e curves�'w�cub ive R�of"=L $L=15$, $L\leq2$5GL 5L-p."-�-�*b+.w�"Ed a3t ly,�a�:J%�aO4ak�7 full&33of�`&� ce� at l�  5000ug,ih more at high�5iN$..�42$�&� eT!V perturbed.;R $5 �8 5$ cell tissuem�Nic +ar3nd�6!|�,5�,{8 (�� many M9 real�s). SiI ons W��oy.iQ%)+� gene d9 %��5,to locate fi"�;!B ,(�by �*E�value!aO5gl�%d� meane�anco2unNqG1 H(t) \r"1��sW|20�"equ��s5#=s,o:shownE-� =�O\textbf{�j 'I =�Rb��(th���6t ����!���/iC24: $\kappa$ = 0��, 0.052^ 0.1��t n4% �!L1; ��=1� 2Vc�} \+&$box{0}{ \h�#{-15mm psfig{fŰX=net_1_new.eps,width=9cV(2N(Rnd}>�%\v ~�x 1a} � 80mm��Fi�/b>Vf3>r>�F�3��2�.�c>�.�R��a2@%�B�6�r_and_.�10)��l1:�2:�%.�N�e���. H(0)=1, � ous ebs,)Za�z��|_2�� �4a>�%޺F�6 �3���Bi docu�} *x���)` Title: Spin model fit�Z Yule s2\ F%)� �$Authors: � Minichini=Sciqnovk��2��  %\1�int2 s,amsmath0symb]{revtex4 6Mdebug,�� ]{ep6$12pt]{Y?@cle} \usepackage{i fontzr6&��ics6lscap:Pa1�c�ing����18cm %h:=25odd� margin=-1top. ��command{a�}{\var�5}��sh}[2]{{qstyle{n${#1}{#2}}}:4half}J01}{J.t^/3R/ZZ[!� bb Z>{lra}{\�$�ac>:�l $2z$:$LGLonfGThird�!�.� ��5I be}{w :l>�e#�(^!be�b�eqnarrayFE$ FV"�bd?6�%�ne�8jn}{\Delta{J_{NBji. iF k. kF im.!i-1F#k2#kN#du!P�A{6�ai}{A_�>t ^{T>`aik ,kJd ^{\daggerJ& _,kVa EfCjp}!z+>[jm->s}[3]{M%(#1=#2}^{#3}>�up!�upN6dodowATom0t�em{thm}{�em} ����(% \t�{{M�F�}8or oligonucleot���a�.�} ��a�+{C.�'��\nks{E-mail: {\ttfamily m�K<@na.infn.it}} \�"A.�]jDs�2D}�\a�ion{Di84� o di\0enze Fisiche,&�{\`a}#`Napoli %``Federico II'' %�I.N.F.� Sezi 4di 2 - %7ssoXariz�Monte S. Angelo %Via Cintia, I-80126 Na�+, Italy}!�%\�H{87.15.Aa, 02.20.-aAj date0���g %�o}�� makeTshape�!> ���}\\"aabs""} A sL chacdescrib�a .�ce,� i�if>�h"18#�$a vector �8 (n irreduc�?3 e�Gň#$�SPcal{U}_{q \to 0}(sl_2H@A mass!ѝS&�� "ois6$te�E�1��9en� of  one-% flip8assumed�dKGI @8 � �. �,�/� compu�#b�$is nicely�9�#�;M.>, ^7y1ob�@.% ��ranke�LJ�r�cy#DNA �Y \vfillflush�} � < nr. DSF-41/2004 .* eDeV�N\s�#{.�} � E�s, both��w !P�q�Aum versi)�extrem!DimMEant tool`>under�Kd !��phy S situ%�,u@\P�'s,%%�letb �>ble�:!#teE?ng�B pp"V5Q� s Tz��y mole�H r biD$�"$. �M 1986�/Xen Leuth$\ddot{a}$usser55 Leu86} pu>cor+5o�c��I!] Eige�� �r J!� aV.-d�!|al Is��,Va� �;vnenq�y�7�system/Be�Vs. Re�lE�64BBW} it has b`� c parallel �N-L� W+'!  :#"�%�ltoni*AKE �Q�E�E�in �Saaki�%!`%> t G1� mappoDt�:h��.ho%ts. I��A�Aac *g����.7L�] ��!�Rp,s $ \pm 1$. �9build up��15a�&$ur basis �K* w�a�usual!�>2ir�6Hter: C, G, T, A (T8replac� U� RNA), C%kU (G A)62!spurine f> , �;d��R (a ��oO��3 yrim�L7�;5 Y). ��ref���"?!qjE1 s �Pp�S ,  A�uld be:Han�=!�a f!al�"$ alphabet.aA�Rsimpl N��A0O � P2�*�1$or �nu$�<�ng!a binWE% DI� HWB}� �-EQ�E�h:rA�. ��� ard �bpa�, �str{8 2;q�A�j� Hamm�� "�N35�, i.e.j�!fsi=2e� Vt�� MoreoSU��P��p�matrix "�?avanish�0 >�s*C�8 an 1 �* mAot: yc!\ng�WE� m)Caim�!��Us u��t.!.�,WBG,BW,HRW},��to fin�9 land)cEm~ ``fi "e�s``.�urplus"�Oframe��)pop�;�� �x. At A�,a s�6�?noqemp��Ad�Q� ���� ob=") eq&IJA0?4~m6>� � DNA.�#indale�KonopkamMK}� deedcE ve r�{ E��2� (�EsU3!y 10 9�s)>� � i!�in co�/I �A- �G�DNA�;�PS 2�F�=re�YGFC2� E*$�C(a \, {n^k}b^n}$, �0n/!���,$a$, $ k < 0?7 $b$e3~�m*��}E !fac!��. blem!mI�paIw9Wpos|X�iU !*ɍ�in*�  tra Am�� � way&� w+Y2C K=�v�{. At L1eF�Es�#E(� � .[T�< on or total��  l�:���&` ��  Crys;b� } A��N)s���,�hMHeAd �� �e � �C�*acter, ����A�'@N$�N6 ��!�,� "� ��J2�9!6 N-fold !���fG�;funda�alnv (�p.) (�l��$$ J =1/2$)�n� � Kj%.�@�2a]�T.��. �I� mE�/a���5E� mplUIy-NՀ� 9�%B#arIg�0o�H )`� l3be su&�]>W5�Ue��at�� q;��!��Rern��Es. Soa� y a N-Uti*� � �$ \be \midQRthbf{J}� �9J_3, J^N"LZ J^{!��< J^27 \%�(U def}�? !�G[+diagonalA era0of v ($2 [=�< R} -Y}�an_{x}$ aog&�$x$ B�3%�!/ �($ 2 \�V N - 1$)�� $N-25 needF<remov�� O� rac��%:s.�6�,�� ��to� A�qU+FEG ���Q�as,!��v.���OB� trun�#�$i$-th1'=�� � @�6A��rri2�g ($N=3!2ndICf/*b �� - 5�"cX way($E� {J_3},{J^ 2}"�# $R \�v � upa,!�Y-6 doa$): a_gin"�*)pa &=&i} ?,E,0qJ \;  r3q� . 4\\ )Zd1^d �Nd4ddoBd�, 2� 5jf� =6h�up� �B0f%6,)6==)k 5 l.Rz*}, � sta) 6l��� alternWL��()^�P( any finit (in�H�ppaT#uA in a�i��n iu�Gwe� nz�du hex7e &3b�pr�7 �ablu'I prim��" o* a �+lem. I� � argu���Kr R� suit`�yp�� e�L lo�2ev^M�{af�\��s. Fli)+�R*� by�  ($��=s $)��in,P a��( .d2i!�vot��mL)!��o�75 �� . On�;n easa)e�1atv �s*Z�g anuWir�(fix�نRY ``�A% d cou�" &W' 31Nide� � (;��^ be �ood?s�dsen>[.8of crey -annihi�V oIfo&�WWW,exp' on)* � i��� �N� ha� g  dele�l�a!�5,*�!�>�aiL�-1 o +1 ~p$J^N$ �:,�E Yy_<�  o�Hs'i$ ($:�-1$),�o,ve unmodm9��>t6��)�Z ^{N}}=�W but �i}}� q-� ��e�i). NlfB ��ly) can U� $1/2�� (C,G�O $-.T,AcBelow�1� phe�n� �HU �-���.�"�T&VUQ}*gus!�E� B� 5!��fy%[&�*�"i 6��!�w � {N},� J^{2gF�in ingu'=] Icon�*EZs a8Z� �Eon, s-�� �,.��a� :9!�A'����v��A�" � ��T �extit{G#} (#it{�) !n@e}h"� eW�B (9�  �� �k}� 7 ane:Ex�j�{i�- %!iR_fMm�`ial (bO1*)}EaS�� P �{�B$Y_r$� n�.y�.E�Bf;&�s. % WM5�� �lQ� $RY$*��� !(after թ� )�, s� %�$R_{in}�R_{fi}$)� q��� (8B)k,&$R$�ece�$ �($Y$N�w_� )�ir%)i%�q �0$Y�Y � w�f�A�A�|kX&� �RR� �R$:� % IKU� %�a?& Y$U'"> =�� �=e0M�y��n1k=)h+1$%�� in}= �-1�ch!� R_{l.%Q.r�O �Q? X��D��!� io=or�"�42gդ2��$ � poũ��. Wri�� $WK�'}(t)$v abHk2�a�hz2$t$uX�%�r  j � G1 de�d�Zs"< .*\; ^IK{'�-{eq:norm%G�7.a� (�c ME})�r�  >Hx.�!��F IIH+MM6!� \;II1 �H�t ����2J{.x �J ~J�>�4 \int_{0}^{t}\B�\tau)\,d ���1�GHE�a&��,�uQ�asQ2. In? �EM�' 26�%ej6x(BV�m r}=0`b�5_3.)�13}�, (!))t}F� 14e � cB�4h3)��Fj4�j4�3<63zib3� =0$ �)55�mI^2�5}^{m({!1 A_{m -AS \jp6=5 �%� m!=p"0N-2; i+12k >.�At6�Q�2}.�-1�5o6}Q� %�k �k+aT�E��!� }) 9�6 ��/�(aa�Ɂ*�jp��\jm��� 1w&� (to s s]  do) ��� ir?licit�m)%gg 5 wara:E�cng F �gg �[x< st wT$U$L�!�]ucI a� $\ji=qt; \fo'& i�aN$,%�J�UAVQ�Rp�o$N,.., J^k .h�k�(]aA]i,��Z^"mJ�Z�g0-1i  -1} "� \noN >S & & (B�"�F�. �� \ee�9�i�% =&>�{N����w�.@*��R�2�/�T� �%$e*�� Q�� cls s�A=by +1AM8� � J^l$^!r $k-m�li�i$� A�r wordC*<Q�ab+� �^: &U B*�invol�@.1 $\j|5$ (ᝍ�>Y_� )�  e,`1v�`e �vt#r�5.��Bw�Nx@a8`Of�urse,}Zw�#?wer�s1[=Q_3�kn}_ya�NQ��]4"a�$y?$entn(b!��#�@d*Cc bed~{sesE�<�)!� Like}�M is"M+�c �$Y3 � R$ ��+1L�[A�ch�% ��2<��+1$7*to�pe}�t| $J_324��35�Clear)~.2� !�su9'A�l ��� b� 0e�Q%� ��}orQ�Ds risX�D9 ^&t��&bleai��m�-2�nO. ^RB��"{ J#a�M�sugge�zN'jgy�.o)4_ntN#� term�"�6���ng .ic/"�icE c�dss likel��an poli 1��/ica-�m,�%��l9*�� D�/ ic (:Q)�9 ct, *� \emph{i%}:Call2(+($Y�Qi� a " (�f) ,"^e݌��e�ѥfA &��&�N 21 \pm1�t{2�ge�%IAQ� o $M_3��M_5$. #5�$M� e�!m aFy �Y�'.H %[� sf{ho�28critto quello c6Yegue}]�in�p� 2;�4�&=�  \;� �s�0 " �*��(eI\;e� i}\;�i�M,2,3,4!�ɣ{#1}< ; k>1$,g�$n�f}�1{1}�xsm J %!u,� {J^Ne�2 � � n4 ��:�%� I��JstaITQS D; 2�2Z��#^� \ �0��"�y  �m�k��' C J^{k�!� .��Z)T3j� d~�� �I .n !b�J� P \|(2�d�4Z�^�1 I�U� Eم��E� $0[ <A�:P -�uQ uicU� 2& $M_4�LM n�U5B� W  > � �!Dt�*�� ���� �,�"��2/49D 3*a.RZn}� �:*;8���������&�@��*�in ���M�d $\bar{H}= H + M + \lambda1�0��the"z~be $H=�  (pur��ad&Nv() _ U�4^se%w�mQh$o guarante_ �0xve. B�+$�$��� ble,�<|l��)lib�|*3is  {1 \be 6� = �Bcx2[}}pA1tJ+K�Bee-;$J#J}���x uP�! }7�H clos�sneighbKN)� �Q��ccounE �Qp�(Ik}�"2$*��4n��)}72(4| ,�sYa 7no"))%+z)it!1pW �``� ed"I�(��+66+�e�on�?!�� �qD. S��it�)tKt, �r��{_(� m"�� -5.&8� � = D�e"�%s]'re!(ow0%�, o^E�A�4"�: ���� xR!g�%bi-/ �.��-�two, op% ely -PpD �>or.�"pinu3�colʈ��@�0E?�>t�Q5�=�(<ht�.� � or5� (ee"�nbo'). Biolo�>�(!�9W-�A�U#way1� "%� ed" � �2rz8"]DX2C�Tn��. f^�briefl�A.�4@-*�8A7e�� B�� . Our�92o stud�Al-:z8�6�+� EH a b m� 0"nd,�.Scs"�*wH����+� hermod���{on �5� Mhiod+A��(-V)FE�0. �3ha����oDuH&!edge"A�``�� ary"J[~.-.�^�VogA� :l ppea�$P����bof.,r�#%lme�X�:=/"�:% ��GB}E5%cep�| fictA/us.� pairs E%�E'��:" dd i��de�7 mim\,A�!�pFDM�� �$,!]&�x��Tl&wa�k[U*2J R�Ye��Dzr9�p"�2�}�~ ,A%�ba�?(� ��3) C<u � [up� ] ltipCv�m�E�4fhy�  �qu�}|! �M�P} M�a�(1a�L{c } x &�� & 0 g!\& tN7� zN�1[L & B92)G\\ #3\@^0wh�=5B.�6m^X �NJ0m f80~ 9f5S0=�s:>�)��iao U&� "��%��+exAli� DH�7rQR "�&V.A�I�IuՇ(��X"��.� dk2* very�zru�(�=�s�\ ge 4�(4thLup2_ (�BN+��by�yta$) H �"�M asiz��2��p ��) i`) "�< ���YG�[ unit�3>�@.�A��*-7!�e �^ � ��Nns7:k)�Q, 0�6�*$5�5up�}%n: 7�5>R8�6�.&D5�5 Y :�Q� ft\{7I�{c 6��5a�BdoaI� Pal�G�R uyH @a2ice h���at�( ])Q�is�B, �CF�% �� E,�AW;ed.�B��vy `n8g..*�#H16�,$N=4$.>h sO�06| "�$\) B5�-����/��%�I,s a plateaux��}:�ry c� s� L A\Y�/>-�IZ2)W���)pU%�:� N[>e !�I�.�29Y!�8B, ��)�is�!ZI�RN6YR1-��C!�),1�e&6E}Dy FP "�icѢFy K a�o] MK}. �or �EIuU�R����] ^2I ) �!�"z?N�tua��E %葻meaF+�F!�.�!ioutn����Š� J�% AB�EW Anal� ŃA�{��*c� N=6d"f1�N=6�c�us&�%]: i) �6 �is���val�� h bN ,Ey&�A eDI �9go �6":8�nS5l>�% C�&-@.3� j3�*5>q�;@;$eed esseng5l�NP‰�%6��}x�hB%� Y$; ii��a�NXa�6�� s R�law��E��KU� b!�%3!�� y]6�s!��<�% . Zipfw�� =�V�G�G���aJh�^mr� of}��.�CluPa�A�far)� claig$eAAz�L��$ I��=`�%�!d:pe6+,/r s�al obv�oo��%��7d�Lk>ach"1Ke F�" �1�or)H.w. _=gYc� 9:��{�ar9t"�є%, I�aS%z%Ya tak!2+ ���a!� c\ hefb&JmTA 6�Lt'V��mea�ful+^(!U�� ry2JIx;t.R  ZI��1;!��2TM!6!,�'2u ��c��M9$V���Go��a!�qfig:cdc}���KF�A� alwa��3 �mnth.���]���ce��)� �Ne�avfJjur)��8li�Tt�r ��"� 9 pYKa)"��of)�aӖ‘ data, quԑUH�U!^�$p!�-�o=��4 l.;"�1�EnI�! ���t� a qu��%�� Whela�SGoldma�SWG}�-e�TE�YA@ �&�H= do�U�triV�2'P�%'� V"H{ E�stw sign�Q��m&�\�f� �eprotei�e�"�Sv#n"�>!c>�I�%�noC>|�ng meDF8� 0)m9� �}ed b˓ �$%�, �;�I�.u�/~���8 WG},E�!�]6he kin��U,idiscuss+A{ U�3E��C�D-�J�, d�t�E���D� � $ "1$�} ao�<W{s&r ?e hiddD� S �Ir�,�sm�!�1paQ�Z_$!�] ��+��$6Pis�"0R���ruH>.)V��%B1��seem .� meas�q) !��c/ *Qs,�c.M�Y� rar8�eX�VA�di�]�-2 rize"`S�uch�\hi��S �CP)xri�9m�99O��4b� emm] IߪF�] , J.Chem.�z.U7bf{84Q@�|]} 1884 k lQ\lM.  , N� wi�schaftend58}] 71) 465. 6 ^B(J. McCaskilj_P[dhura, AdvN�752�9) 14x��BBW�E. Baake | %�H. Wagn8T%Rev.Lett9(7 �97)�559X$op�]  S. l0Chin-Kun Hu, o E5069y4) 0219'|hB�HWBfJ�� rmis%��sM �A StatMqZ{v{1�315� ��WB#�h,5[r T.Gerisch_[JRu92E98t 1017buF�i� G{^ .Res.Camb:�20�93bh�Z-m6SO `dE$u�E.MShs  P*[Z!) g"y9v6!��UJBlMK ��gX%&ZA.i~Z,�u�ce�5�20)g6) 35*JuK9V�M. ;, Qmu�aMath.M��1� 0) 2qsVHof T!Cofbau�Rnd�Sigmu� �|s��)%=�S"�%^D+"ab S�a} (!�ridge > � `��e1��(, Encyclope4D�jo(Ff�P,��III, Mitg� } , Ma, USAu7). :pGm�s] RF.�Ben� A. уBiopoly"A/ bf{3A" 1992) 167B�Wm�S Xj�~�heicsR167i�4) 20Ѓ-&�>r"�A�Ke}[tbh]џc er} �CmeboxLofx� =0.6��o��ie{./fig1s)D�,G�} {Ran&�S���,J�*(N=4)&Gg "g *�z� �0$."�!l � �� Z �t� J %J�s� $5=0.25,\;O=` =\et!50��2�was;�by�"�h,Qi�� Z<) $f=a{R^k}{b^R6R�&he�).�% , b�m� as $�P37,\,b=1.02,\,k=-1.28=�YulL6� Hmb�&1���M��u��>�6#2�3 �3itg9�v�O��b� 5� j�j���~�TI\f�261�0-� 11$.5?YD6��{Z{4����F~9� v %�� &La�m'>Os9LBP�{d".x<\�j [12pj�u�u 2v"�u6��"&8v�ui�u UGLY>�n*\s base�2�]tch}{2.~�nQ�L 432pt �u 26pc \�kbottom /v 594pt &v, 72pt \head #�sep foots-�5=o.Xv" O�Ynt 0in13ex�or2��MS }{0."H:"op.!9} :! �v$float�l'1%>:lhe��}{\fn!�ol{mw.2\!�punct{; R ){(} %��enml�o��lis!�BS�{)}r6Hat96D@��@Z[1]{}-E keat� �z(journals \nUb-�etal}� {� ��2u(g &(��B&AAP6'Acta\� \ Pol.\ J6CF5'cZ/R 0 � Acc.� � RbPc 3dv.��� & V6S6i6� �iV4RB64nnu/ v.� cwNkBioch9 �em��yZ0met10m�bkaZ.po%�.b R/1-/hyжb+BJ�b3~JR�C:�asu!�t\r � >�CPL l k� 9�FFcCOS-� 5,urr.\ Opin.\K�uc9�v>uE� @Eu?� �\ V�E�6o 1T�>jFD � 4 Fold.\ De!�F�IMqr �In��Mo8-QF9JACM� 93Am!|I�Soc� B�JU :-9 <�N86�r 8 �Z8C-�pA1.\?8>HJCQ��6Eg�F8o �J8 �JNC 5.6)If4MF�M�#-JgMGMI� 3G�� ics\!�elV�J�?f�:�!� - �J�PCB�4: C�rs�kVR�PS�G� =E� (Jap)R7S�7a�aa|R4TF|xYUF�Mac)} iMacro-teRJMQ�2k2qg,\ vy�R�u�DE#b�NA6N�<ic\��\b#Na�O���eN<NRM:�N%m Rev.A���u�FJN�� � ASt~�N1�8��"`FhU� 0Pep|f�Phy2�!gicRUPro6+3 I%:g f-�FV .\ �R ProEn� I� r\ Eng^1Sci�:1SZ�Pa- 1�wN��+.\f�� ] [r�aNatA0Aca�� �USARrQ�B�{IwJ�RE pN/EVa� �.ab�PR �6 �Roy���J�45� \-J1TQ� �ro!��� �}JwQ:� Q.�a�&�N8R�y r)hzVMo�FU�NnS"� `y v�Str2� 8uV�TB1i eT$�_ f� TRA2eIEEE Pb. Rob.e�o. F�Z1� sZ��ik!!6��j&�� beq}��$�"�52�@qaG��N �% HV#�g�%6Y {\ev}[1]A �#1U42�"Nhb),{N_{\mS{\�ptU hb}}}^Nnat>��RAb��{A� _{16-22}$F~Fs } {F${�AB�s}}}$ &B�C t {C I�NsC �*�1R)d vS3R*�,� }"3R*p.T^{\�ieN*r" rR~c!|tZ2 {\Elo R{ER�C.�8ev gZ8evV7UWVoEWFE�^nchZn-X^npR7Tm � {TRmV6)Hb6%�B� Tminn^linVnmaxr8axR8d��HEF�N  b�RZCM {CR6VkUH\��R;ZMkA�A�n<$N�eU��R{Z�eU�r>Z�eh� >^{(1)V�^�hb��.D2�DMij%@ {M_{Iya�>s9T sigmV�Z�sc" {j<$N�Dh�1{DR�HSR7R��aBdgR6D)x� DeltV��FZXi� {X�.Ua�B"Xu)�Z4uNPhP�hPhR4RhEh�ς�EhR4h�bput{ps��*�*��lLU TP 04-28\\ October 18, 20V��V�0.4inT {\LARGE ��ol�.H[m6Dx5�� R.6 Q0. Ax� Irb\"F<"D Sandipan Mohanty\�{E-��a7 ,\,s +4@thep.lu.se}\\S"p 0.10ralex�" Divi+De�FL1f�or $ds\\ L#&�", S\"W[gat�4AE-223 62�,i�c'\ ��, http://www.�/c�vx/}�5x(3in} Subm��m\BJ"1�0%W\�@al�  A��:\\ A ,�o�)lR pote7� [0f-�s�)s��at� leve�5d�/!� t�) o�9��p�s� ab�)20�8id���.!r=6�-�) '2$� $-heD@l (Trp cage, \Fs)y3 T$-sheet (GB1p, GB1m2, @3, Betanova, LLM)� ||,C*�D!�M�-���s y6!"se *�j � �!q/A�<1:&�9q��. F�-%5�-ed� g be��Y/c�! in g�rM�i5ve 6�7MAeriA�al�3.ɥa��V<opu�rs&�#�, �obG��0e+ar!�W4fE�\",=!s��>�(�9�)�3gY-!(tkJ-�s%�c-#5"c�"s�8�7ably �8, �3cat��:�?wo-�3e-�V -y" �.��18p�_ %Key�_:1�%Jingk.-a&)� , %e�L!�uj,K s�. is, ˎCarloa�-�~�� ">r:��#""of��7m�M2�ic%c�`�Z�r3h��c2is�;lfLbCH�G�/at (� neuroZ��-� dis�?I1�lip�t�HsaD%��Jgg��z~�,{Dobson:03},�5tl�/ed1qE b!�ng�2�W�_ m!��oOxe�s�/an 1D0bDoughttys2}. I�N�0'Pan Kx��velopaW ��&�V5a)&[ beco�:feafuACr8rt`Yym�`/s � Gnanakara)znk�f��J^*, �e"<�a*/I]6!Hr͡��rj��e�,��";,Xs!�����aq�B U�G3�8,&= �t~"�26st��ionlxa�a�ty��%�e��egaM�a"!� �e%�2?xE.�-t�� ��i wate��HZ3we ���ٝ%3 �&� Q��W�K  3�9no`s� %�Y�AF�gQ67lcUBbi�teg!�ng�B!#��vM*��$freedom. F���;�;� thodX-�a��n7surfac�as\Ferrara6] :�)t889p�3.� inim^6aQ%d6 ns5!�)�%��r� �8�Fn -ive at<|L>�� nonpolar (8abi��9!�y focus!�e!fy�"�Ic�!� �ٮe �Z.� )��8a�n*��OSs.ɇ oad2 a� veni��;]bminor!N*>!�� t wo2��=-: �%]�~� �mi�ar� �mi�>:�technó�� re�>eP o�7d�Hansman2 Will�BA6a� Schug6YE����|1VAJ b g�m���jt;s&<�/">pur��In �[A oYV hyd% obic8�!i�*�y}A/])U��two maj�^�,BŘing exF`d-v�e �1d �i�b��ngA)��� is delibe�< ly koT)E,& ��qGak��cl��%O also%p���D;�;&�r�1��careful ���>U task�� erI�a �NX �Z" fe�k*B0?un&d{fu3� .F-E&�< d� ����s�!� new %���h*�>=�s"��8-�#�>rgn �+�n�� es c4ka���yE��R&� ��1� "�� e�� �t"+\��AN�9vid�N\s (QF IFw�wodV�: toms`E�QY s), NZ�R.zaML!!i�<Lpe'ity���stiHs�D\�a r7�@�%.!�a�� �K� no if�G"p �!�ac�or�L�� s�#�@�s"� w. �Ua�ow����dsA��,X2�� pU�Z)�+7of.�I��pi�M? uV�� 9Yra AV!��rigorou� deri{�f�_ �dg"*E*�F��y�I" ge�,a����6A0�!y"�2�all thx>],��mus� onE�ownM�orsI���6g��Pof��Q�m ��F��"B.�5��r���+��-��M�#1�. �g� ^l�V$�p ier gE�E � E>!�A F�:r� 1G� $Irback:03, 4}:T 3v�BE�* ��2�.��!o%Z ���hh �CA�>�s Fi�):# F�} �Neidigh�� \F� Lock�� :92, �a�"�2 � ^Kob��4:93,Blanco:94}*� /@Fesinmeyer:04}, B� (Kortemme:98 LLM Lopez�.f�ۚ� e C-��i�M�hairp ���g G B1 dom+��D��a�Aig� tY-�~n�Z2.�m*�Ew9Cn8 �� le� c  of5I:enh�KdNL��� W�en�aS�I1m}s ag de�#��Er� r8Q��N99MΡ)�K>a�J�!� DSe��:Pͳ�A!�amy�N$\w-�FavrinIApr� Vsob6|9FH<6{o;=(<,�5 =4.5BH��-3mm} "B<Sch�= illuA .\�͹�1x 1U%$i�� S}�A��4���4E2! reMcDru�4lbbdb)���OPq�jiv3e�Q�. Draw�N RasMol~<� tect� Sayle:95}&�<�74�nd urs�r on{M�[ nd M�8i*�� }�I�"x ��� "Woly-(� � ���  4I� RK7<��� �\ss��ȉ� ` �a ($180^\��$)&��*� �P��!�2{ P P��$��ps������ � 9�)Nts N�N"\hISU\Qn &� hella�]�� � else�mm��3&��I.wV �Av��!Clu �LM)�c"�u�=s�Z�or)iis 4A��2Q�$� ��1M prednA W��a.�)9e2an*"e%!�ex*}%f��zu�w��.�0 $\Tm=315$\,K�q�-l���t!���i��$c^� )�H5Ta R�$k\Tm �0.470 !Zi+($k�k Boltz�'?J%� ). Energy]F �)g ( �d$�%E��%  %$, etc. ƅ�);ur ��23 �mus�&�_��%#./X�3un�gT� 'KU�!�dm��*v>K �D",$ E=\Eev+T)+\Ehbp�c �}�B7��om�P�J���f��!�E"��%vԿEe!S"m��B� ����q @=!�n� i$ w0i=1.77$, 1.7554F 1.�? \AA\� S, C,�MOe�H���op� e�U�radiis$Vp� �� �K��fof Tsai6:99��$����O�ong�m nflu�%H�Fori6[�L,�I.+C)Ee5� ����in����Y$ in Y�v}UV%? 0.75�al"hex7he&�by !  cou[�2�S�pEc=1>B� why9 �_Q du�> �/6;<1+u���lǖ Ixis� a�cWal���c�!q�Mri@��Oility���it�����"eAZEV)��c� yVt�K�*�`!�TSl3Oup���,� v}��e!~��a cutoffA! $\rc)B4.3�q$\a'�- �)�'Ar� Go�%.b�ۉ� ���O.b��.g loc=���iIPd(\sum �Gc{q_iq_j�PD^{(I)}/{\rm \AA}}\� )�[�+:\inner�b.!���+���'5ch!/0�b�$NHe�(\Cp O groupj one &� , $IE�%AY��a�Pro/chNdze_U^G�#�t-pj$: ���to/�nͱ�s,.�U�M < �in. Neia��it�"�]ew *� u �Aebyapb�k&9�inY�!��)��@ (NO, N\Cp, H\Cp\%iHO)ޯ�XB o���$($��> !_�%��>��@ln7 $q_i=�V 0.20� )�N�-42$ fort \Cp\ and O~\cite{Branden:91},�Hwe put $\kloc=100$, corresponding to a dielectric constant of $\epsilon_r\approx 2.5$. The third term of the energy function is the hydrogen-bond energy $\Ehb$, which has the form \begin{equation} \Ehb= \ehba \sum_{{\rm bb-bb}} u(r_{ij})v(\alpha_{ij},\beta_{ij}) + \ehbb \sum_{{\rm sc-bb}} u(r_{ij})v(\alpha_{ij},\beta_{[h\,, \label{hbonds} \end{e�where�two f- s $u(r)$%�$v a,\beta4re given by \b �narray} :`&=& 5\bigg(\frac{\shb}{r}$)^{12} - .6^00} �u}\\ :�$&=&\left\{S � � {ll}(\cos\a!z �^{1/2} &6+0 \ {\rm if}\ 3) $>90^{\circ�v�`T0 & \ \mbox{otherwise�%� � \right.1�1PWeE�,ider only hyI� %�( between NH%� CO groupseR $r_AO $ denotes%�HO dia7ce, $ � 'a NHO angleQ $%HOC <. The parametersa� hba$T ehbbE@ $!�$ A5@taken as 3.1, 2.0a\,\AA, a�$ectively. ]Q�Q�.,1� charged !� chg4(Asp, Glu, Lys% Arg) !}~ �(latter type�f! )P to be eff1; weak ($%�<(a$), becaus�re%�compet!DY�� �-��rge ��surrou��wa�hatY omit!�iE( model. For 9lame reason, we do not includAuy �� in $�w 2 to=R-��in2� . It!$possib%�at5* strengthI� b$ should!O0made stronger�ca);{2H gets shielded fromh%a$A�(ontext depe��ce�ignored_ the %'Eich�a-,a���imaA�T for small peptides. HV parta�-�$very close~seque�a�rarA� protein!uctur9�refore�Dregar�.�4; specifically)�isallowU߁�(\Cp O)��A�make :� with!ŢnearestGC (NHG on ea!Aide4 them� Ak also!6bid:H �HE�&involva� �end��ch tend!^�&xposeI� A6I�a�woN1� is r �IeB( by factors�2��4:� If!^�}app�Ѯthese E�t�.��!�� ; �K,�%� !�s? ta}role. fourth � �f�� Ehp$�present��&) $phobic att�U0nonpola-�%~�}haap�!ir-�� addi��%�: q | =-\s� 8I- \,dr]=�Rij.�!j&� f(x)%�] (=1$ if $xB$, S $(B-x)/(B-AILf $A\Cb, \Cgc \Cd\ZM�E�i�5*�APs�Qm�.+a�ba )� else6 �Ir� :03}.� ex� Wg�gm��a2J1���� er i�"��.�!DII& Ile, Leu, Met,I�Val( ?9 2.8 7i� ��by� omewa,$tedious tr8��errora�cedure,*� t llel1 �� ~(e different&� �t� t w~ o have nav(-like free-��minimae4all%�H at � tempera� �e� ).� w� ��de� �! ll. � %�esvto,�z� ( riter��.eOPsufficiently discrimiӁNo yx %*� valu�x$ppear phys� �oK , as welld listic^�4(see below). S��!�ts,��*<ly infl] �� fold� propertie5�� A��> g �YP. O>tb� 4re less importand��sulV  0, quite poorl.�) new$s!�E��Mws�earlier*e}a�precis� ?� a� ext * �\Eloc��. Als���A��A�-��.�� V7 A[g�b��$changed. F& ermoa�weeF� ed��$which doesA� occur�any�oua�eva�= tudi� fs,�!(Ar12��U!l  Ym�=�~�Ya5� last1�f#Mfex�!H a sly9f�  8locals(� $). a�&99ssca�Ak6is%0ex% $oa �5$ a good dea�Ŏ{g��al.�5FQexamp�3i���l��RR} =m ity 9G�=adE� �E%s, due��,double-counta�O �21anti-coa饁$ multibody5 m%zplay a �6nt�b DShimizu:01}. By ex�{!�� �#�fu���aρZ�er9D hope %� it will b�8o r� o��andAureb$ke=a11�u subs� on{Comput�al metho�a !�b@rmodynamic behaviO�pI� 4si� ed ɍing-3TLyubartsev:92,Marinari � 95}. iOi!{��A a �al vari8 Iq�J viewA�� ?!�!gi�M�Pized-ensemble techniq��� e�, �fHansman�$d Okamoto � :99}�%> f t�� ��s $T_k$��r�䥿8 $\Tmin=275$\,KA(ax=369!��Ugi�J=6(\Tmax/ h)^{(k-1)/7}$ ($k=1,\ldots,8�!(The average#alramf>+ Aa� �c� E���%(*8 }xaJ��Ѹ  io�� jintrodu fnam?eK, cage, \Fs, �j,�pm2 (3, Betanova�LLM. I� i� we a|����#��se���$:1 Tr �}opt$ed 20-resi�$X (NLYIQWLKDGGPSSGRPPPS)�� a ``�i ''�i mpM@e��Sl�W E �315\,KO&�a�%78 dichroism (CD)�NMR�!|sq� eidigh:02e�e(-derivedY�ͭF4a�A sD hort�$?(-#s 2--8)A�A�le��( of $3_{10}F111-142nd��O!�c� �(Awng��pro��!�!�s (Pro12�18 9� two aro�!c0 Tyr3�6)�!�e1im�, a few $\mu$� room.A-$Qiu%T I�""V, fast"~�rel�stabili� A�UY0an ideal test�e for 8$B���B�/�"-re�ed: A � �DSnow:02,Simmerling chug:03,P)a Zhou:03aAIwoA��� N*� 7"^ J ienRO BothGm$"� !arisono rawA� dataib very�m� , bu"- d mik.�s Ntoo��� $gtrsim 400�t��K!�JI- 9�i��fi , ��l�����ria�� lue,a6c!� iQ � y6se�ͥ scalw� ur}"��iE�(�� eҡ($H��"D %J�s�% b��ronr.&"(U ?CD_a#�.�o(Fig.~2aQw� r1�A�� a�s2�. %T gin{�V\epsfig "L=fig2a.eps,width=7cm|B$bF$nd&�$vspace{-3m?c�lq�. (a) H2O N� ���� .�7ct3)"&\(Tm=318� dE=1�Tpm0.2$\,kcal/mol). StB�/ �� a�5`e plot symbols. (b) ContoLo�eeQo$F(\Db,E�, t 27�� �c ;�%*d�~val1\,$kT$.hs�than 6 �v� �Emu� ��n� hown�� .�iY� 0 -� /kT]!kpto P�<  $c � jD prob���+ ribuO!0� ��$E$  * $T*fig:2}�M� % AQ aB��N^  in Eq`+U-��)%A� �4P u,  ] A�pr"s���ll�':)� �)�Rb ��fitA�T� �  �� .N[ . Han'd� 8�"�J "C �.q �Th���!�!Y5 RV��in�3r�� aK� A�us�or�pib����'a� a�Ydi� � � � �"l e pi* (F�)� � pop� at2G $T� &Q1/\{1+iB@ \}$.��3��!# e e"�qba���� !N$~i )�� .�,wg�7 2%�%.!Ton�PE NMR�2� \1I�}No"B�3��N� = �.P��!�2��9Gm+eI !��,a� e�A��7��t�'�K a. P����%�6W v� =A�d-g($�$? O ($\bullet�.FN50} ��3}2�W�te�� �^���in �aW)AOV"!62!�}Hntire2�x,E[ a max�Nd�a}� m$\,5\,\%��K lowe6u� O�2� ] 2�v t~fi,�.^7 Bl� i%!�p N&�&AF)"3g�.� simi++���n!�s� ��s%3� y!Eg2a). An�� firm��⁲yp%!;-.�d]2�� < (PDB code 1L2Y,� �,), as illust�dA# �ba[is��E��b�* a� *Z�c�' �$U6�19f�M$� at $�.+V%�*3 �("�. shap���do"c#�?is ��e\Db\appl73w3 :�\Fs�de��1"�\Fs\ ]n�H Suc-A${}_5$(AAARA) 3$A-NH 2$, (�) Suc�succinyl�-cid�3�an:b��Lockhart 3}. g# N-�.�.t� p[%�*�nU��u ��� .w% @%��4CDA�as inf�1d (IR)�+ ctroscopy6Y.�".�IRc 334\,K-,Williams:96}u =&he CD-|d ��* �D =308� G.>� $A$8Thompson:97}. C2 �� % 6` 1 n4Vila:00,GarciaNymeyer�+ )! plic� �4*�, 7\'\i �(Sanbonmatsu `!X}&&a�$��34m }in2�3�.��!LIR-LK. a�22E%^� �`%H'4 h2pp �, .�10�AC �� 0�,� �������5mA��mp v. � 4.,�x � vers�(&p �6�a�%�.��R4�R4�RS�6as��J�"_ �m� #04\pm1a&��'9'a&'"�*fig:46�� " �  t�0�n w� igW$ly�.uQ�G (�1 A . nE�J�ZS s, e� +�nof q� et al.M��Q���!�:weM5�  F>�f��q+k ��)�  =12\pm .�@ may %worthQ aw�A��alz w�mpa�*}�| ��ZL � �\IR| �4bSn v*^.�at �m�abs�7J�).�*�#�j� ��$A��(R)� ":�(� } ). F9 d"�].��� glob%&in$ ��h0.w\1�7$G<R2.�1a�� b#of �z�� 6�"}  /N:woy re vR#�;�1A�MN4 J�>��um:r GB1p��GB1m2/3"�exact$)e2*�j%�now to:���s� atXLp (GEWTYDDATKTFTVTE) 41--56"� frag�WI8!�Uin G B1k ain,���bet�airpina!Aown��a breakt�. y�YBI$ o:949%ES� fo�: numerous � ic.!�� �ti� r* cRocca�:99,P�B D�" :1, �1,Zag�,c:01,Kussell� `3b,Bolhuis:03,Wei:04}. Re�%@;tA(u��%݅\enh7%d!�;dg �Fesin 4}�2U3, by�lac��$se)�)�� NPATGKeG ��m2 I I �yid�%to)p�pt�q%e�#g@%h\?E� (KKWTLQE)�Z!�� �+ �:��$ .� 3 nd NMR �3E:u0m� t5$$86\pm3$\%A�2E98D ?�A�T� $333\pm�*K&* �2c f?9Z-�ved*� , $7!��� ��72y20yR�.� s��y��F�6b ��e�/NMR,y�:��(be 42�?7!> �y�. J��se�E��=E)��0owk-.B�\����Vfluoresc��� �Munoza; aaD� 8B)G av�]Tm=29��KA1.6*�>_�t�77Z�ur�X failő�4j ��#"l &�0&��!IbA� 3h o=%�.�*|7ly}�"g�P�x  clarity�(t2q"vD%{ se �mc�4A ��FBlow* 5R *Ruenergy�1p"d.�{InEm3��Iź�2 5�q_��6�%��.&��l%EU�5>�h 297>h 4.� 6�5K; �21>85.�j0.4]�8m3�  p}s*��;�71�>�ɝD=%!pP" remoP�AMyZa�1l� E�[ erm3$\chi�<per-A�^ dom6_ 5>_ Wi�cF" @��nQ>w̉Lyas(43!<m�]8 c>� ogeav ��Tyr45,�95�Val54l)6� to<v a�e*]�5� N���4C 3:� �anB��!��� �AչI&�.F)J � �9of%��]�ǭ�v��"z2a�2?A�Z�2�� � &R$ݼlie�=M�.\ -%a� 2 ($��)�":T8>!I1�*k).{) Gp$ɯ indi\; 84I2 � �C$markedly m�$�[%�E6aD&�P a�T/ \1�H+� d]7��6 �]�O�Ya�����+�e4�,x��O!6��6���� ��s!�%�� %�6�Vlevel��Sn�2�2}b6�6>�On"$ !u�"w i�FlieZ'to adoptd?o� &�d<i.�i> a a�\� HG*�  alth�+� �re$iSE� in&�;�d�C a�.qu�#�. QCexL:4H. As reB�.Q�*N�$\%�O!a.�@��&���55��"�%�a EJ.7GB1SF(, >,�)H GronenborQ��>t.ġ�h stea�>����$&B /0tinguish"^ !�d"+K�� y/�(ũ�xAMs-oppositF+�?nt�"OIs)�"K|��a!~2-,� -�2. '\A&�a� 3�$� �*DRAvX 6d�!s> �ya� zDof���gQZQa'AJ�)���� � 7! �l!g���M�?0�2 NHon� F B��"��X>S J�=<5.�ZY 8$--f![byA�j\Q2`:�e3&� 2e��� ���  8"��i�)of�� 4 m|", z� .d@sKy�'��!}or ��1�wo�6�A)�A�A18ns� ->:2�P*��xb*X 9���&�A@'�OŌb@" �I �� { relaxed!!R�!�V�.p!6��� mp(I��& e?Y%���8c�Ca2�B�'o[ ��� %vu68OV�aP�q��� favoxq Rp. D�1t%�r/+�%�� :�,�ed��V6��A�. O�BP@�%��* �,I�is�2/ s? tho�OX 5. A�#d�Pt%�$ dir u�m4"�by "�>�6�K%~esn� r"Y/�@��n if�l �B� $-\^T/3$� numbUf�D^��LaW w9�9*7^dU�.$\Nhb$.)7}W*a)�>6a)5U%Ded� 99/1"U Q �IB* (�); 3�F�mwse �,r \�.� CD�&�&6�67�6Pj�*�5�QP 2N%j,1k" � �,P !yp (doT) �e)�I46V:6asw�2�a�=1c�ue�no�,on�j=:\LHGlu42(N)-Thr55(O), O N), Thr44&3&  &3& Asp46'1'  '1(N) 7Lys50(N)6= 7>= WT.&]�� U��,Nhb)$��cl^Gbimodal��!7 17,^ on�HE��U"�6]N)��P�*as�f�Lw� �z��0g* lar�B!�!���n�FX�N� �9En\ge 3 ��L�F0 %le GOs��=�-9��z48�1]{Ѭ $8 :2�2��\%�-E�)4�u��w:\ 5/%�e6�*�(" x(!;��,6�2,�Y.�' p���3)&)�X "��c��"�= V�NoY=�)�*,.�A& 2/E�a�ank��AM��a� I9T�Oed,Api.sBGP�y����E$�\"� arbitrary� 9�w.wa/ :H�:���(%bun�Fo!*�Z~%g,� �H� Gly5� =�DE,b�=7$! kq&*�)7�4 <�-e ��$)�2�-�p}�t;)�!� MI�"�! aFL!(46E���e$ I�� gi�B272i1magnitkZ%s�1� c%`� ayO&2� S.�,Aise }��:����"�< ) -Ji� @��>�C�e� (a� 2)��_[k�6nyFDstudy. !�EA sugge^S"��c"@?t"�;w@[ �3a!b�> `2�m��!9�A�8 -M=m� �!XH !�A�.14 of 8�:!>�;} �4>�I�1�O�P-�n�#2�@%� 20�:LRGWSVQNGKYTNNGKTTEGR�(Kortemme:98x)�GiK �arginKP��LopezF. &! �� m.%=er?i���dtope Q, sGT��tripl"�LLM (��RAsn12 Thr17Met�NM�(F ofGA���c3m� nd 9a�6�283&�*�!��� �qi'�! �e��edJR�:W z�)U\ N.t -�*; F�O*l*�����"&�>XG �) �( coarse-graY qKim#"!K �"  Bursulaya�"Colombo0 163 2 ) �FXHenc�A�Pr�����tm�:�(l$.�3�&�3=� �"6�p  1: SerL 1% 2 ' 1' , 3: GlnO Lys9N  4 O) (N), 5: Tyr1; -��+6 U7, 7:�� Lys1� E8 [15� 2�48}2�4%e�.�9s�=WW! �:q��M2` 5@�o�5" ; ��lso�I ak a�@Nhb=4$. Visual in�oe�snapshoZ�F reveh;@co.c � i�?ak"�`�qAS&(N-W �)�p�k�8A��e(C0onx�n�">in:-gr��+�T�o,��ir�5fb � �vid!@6� ,d�t8bIJ2+62 S�4�1(1--4) e�� �t�)a![� �15BF5/C *�-a�q����!orIO'ed� �b,�Q! 7I � \ge6�_� &T � "�6�,T$�'1<$38'M�:BẢ�i e B�73EO�U � s (9�r36�'� �VB�3haCs far!we� ,E��� t �.plf'r5ozKXF�@9a!U�%qcur� !��pgC �� � �&6w� %{�Dd�"heI|�D ity �� �=9�;9�;!�e1�H �b;Yir�ʟ%21�� dE=8�0A�2%�qf;�%0("D#0 ; 2;LLM).p F&�@:uA#c��u!C,A ޏ 9>�ea�Fer.�& �LLM�w���X8�% is m� g absoluteE52�N �q2U���"�cea :*i�Ka"�5 whyK�><#�@g&mt�d}Mxd�-�M�N�%�,�$=]ArB�[�k���\a�K@sharply&�<�o�C����N'4, �0%�5 �2�*2�)�j�B�BQ�8!<P6m=��A����:-���^���!8screpanc~(mo�!B�&9� Q� -7E c7\ho1 hat,�A1� %�&����+�M �I"�Osyste�dg_V�4qua o7">j*�$,9a, neverthe�,av�2f�&=2a�l"�R�!$B�PCB cU Vha�so�c*'2.�c*�<pWsT�-F7W�8�89."b�&2�AP� L3akF8�H$S!+R!S!M RMSD�I limvO�9omp=JAz05 3-18R1, 2, 19AG 20 M pa�2ipEY:��"�PAa *V uZ5*�!"9#\�.k �"N"@.K.�6�$sF^�ZA:@%�e��8�PAX� mosRbj[ l �e,�s`:��#0B��1JZ t}mV��7 �graph��q a��+Ņ�promin�:Q �/2( ��@# :��rac,�Y� transc} 3qsFlP� saw��)Ze!pa\�*[iDa�q>�{ T! )�reflec:pe���g��-Hs�� !/v0RL�����].�. A~a`��� I`��Nly�p �9)e"�dAF ��L )ptq1*A���ied� b�WI/�$����our $�W��n<� Z�RR� 2� �er,p "�$� a!�at!�]4ɲu�PU2w=PW�3,� �� �%�4E0is��K }ni�)�� FGnydrB` %�R��sI en*�>uIe>'.Zreu#9`m_a be rYM�%�s�ei~m&�e%>. �#:A % n�" 6Y�u�I h�] (��A!��0�.t Cv$' � 107eJ2*:� "� &-YQ�ڝ 10.B�N�pN6�$�bl �&2Q2%UuIo$ histogra2w%P��t"Aa&*-cN|Fe�jX:88}. �=� gTba����L�o9�h�v��B} valuee�:!l"�N >W^.-< �Pa� lCv=N^{-1}d\ev{E}/dT= (NkT^2)( ^2}- }^2)�a�>]G`he*a&,f�$8O}&(Na Boltz�_"�aof�^ 0$O:Nj{!��5}� ��a!2��aQ� 24g*3��Z6�3. �6;exhib�;a$ e8�b���!Jqvaxl%�i�s��s&�1�6K1E\�kNF������)�6UA�%T!lA�>6��F ( Ain) sup*U�2��!��!��.q u)!��pa�Ns� $pronounced�� �mDs !��w�- B��le-!c�(&2$2��� ula G, virtu�fl�!W�J!��i �-s��a�W�s^!% �&% �2��"�8>;"�x�� �K, 316�'�(o{33a�66{�f A�I.� is 5�N]eVs �;n )�W�w ir:5�a.�"�. %- �b�R9|� �P!� .� �A=itsV:a2� %�!x!�293v "+\Co�} �&EV"��� � 5,if: phenomeno` &�hA@�a�� � polyQ=>� !�xN a �/ -|!ab�^20 .y�c"q#A� , VCI�a�n:\FX^�all� �yI E%�- �v �?"�@�$sPMs6�AA. &-�d����s1 choiw� &6u>�� invAfg4.B"]Z�ym:�J �1fi�A!� m� briefsm�a 7s  �3-!xc<o�:F serv��*G(I�-/:$X�C�[.%�b�B�Q$itemize} \ ��2� �U ��~ *� *g �yf~9.��9.=F!Zn5&)O3). �Aٰ2�!�B�� ( � Z�$  AsVqMV':CD� ilt.np @��u �G�2 �?�]"�H /� Est�Ae�A�2EA*�S{�[.�E��$Qxa���_���>>CD'&#.�? � is suA�l�iTA�~2�"1I �5U[was�� I�2�FfC�x98x&d@ID������`�F R=2KAaT.ll� AaF~B�.�'(< U�RE%�!c@!c &�*���0i�B��/>�a�e�j��Z�A�>B\2lc�#��"%E�%Ue{-�)138KarC9@p�)�Cou�#�Za�Ws�+�}-ŧ��rg)a|7�;{m3 aa[ Xt�"@�[7mis� �ō�m�+�  QV>{2��is>#"�Yp ��"O0 �>�zn&N5wB�play g ite S�holE7%[�%r "�_%�q�,2}E��2�z�M*^t��p{�U;=3 driv7 forc��� Ez�b"^�4}[�}zl6��$& Exp. & MC- &fzA{&"6V/UH2&T&( 1)\\8 m2& 2|F.7.�.:73&&8Gr27�\%9\,n{&�9�*�({ �{&h( -&6�- �F�z�':&5u��A: � )��.oZ6��iFF"onaf�U�6av3e���&�3�Nr"�'Ao,o(8n 5RA� !-A�TL\'!*$ de la Paz6["�".&}$�z2�`.� I�~f*�.-SE�t8kL rpri�nly����4�y(rsdqZ^����Lz���|ca�\�w�,��pņa�*8�/�5�.Y�a� amoun� �b -tuna��"dj��! zD�~/UT8s�n\�Or.U� &*o����goal haen ach�?. Sy� .� �� �Kar�riz�% �kX{� word�x�a <Ջ-�:7Es.�i&K8A�UD� ify!EaPkp� �P���%rol rMX� ion9� �h�zitN ��n�q%6�a t.�% triggel b�A sudd8huinE� eMxL�x�)Z�I���,3� ��,d��1 purely >� �ach�U= �wfMA&!byD$%[�w"2�w!� F|se,�de�c�&�y��bJ�i��age ���G� a�+ wardT mpat}�� er; i �must a�l�,a�.�2ld �e*t�e�Os�$to E���(��')�9!�  1E23zune��zpe�a��so-� � rpzip @ v'.Cochra�uM� wZ"o /�;9=� e w�f"?.�[�)�[c. �yYb �)�b!�e��/: s get7U�a.m/?�pi3<8(t|pň �vf  �K&|EI�b��we>�& {�)$,�7 ��;Y�p'!�tAx9?��o!�%nDResearch� ncil�!� Knut�Al8W�1� FQe��oug�Swe!��sorti�T newpage > hebibliphy}{}ib� {DobV\ 03} 4, C.M. 2003. P�Fa�!�mis P. \Nat 426:\,884--890� ]y\2}  , H.J.P.E. W��m2�\up�l�y bqbM�!�un"���hoteins. \COSB 12:\,54--60. �0 �Gnanaka�g3}  , S.� ]H, J. Portman, K.Y. *�\ �A�*]�!+0�*�2�,3:\,168--174.(Zam�3}  , M.H.�hen, R.S�rry�F.�(�4d T.R. Sosnick�I"NeiW��%T.�,a�9 pend� *�E e�qpy2terZ7in �}eYE� Flory iso-�� hypzsi�Sr <P. \JMB 331:\,693--7112 �n1}V�, B.J�nt nd R. Ger=�!�b!*�)landsc�aA3�y �J5�in�"*�^$. \PNAS 98!�4931--6.�$Still:90}  H, W.C., A. Tempczyk�C�h wleyI4,T. Hendricks� 19a( Semi�(t�treatѢ solvi�� mole� mey i-~1�!WACS 1e$6127--6129.� HassMe A�PA., E.L. Mehler, D. Z� E%H�Linsae%l 3. M�}.�A>1�C�Is���2�%F4Q Ј�8>o��$�2�{: a � �A_5A_110--116. Sayle��  ��)�E�U0Milner-White.��45. RasMol: bio�v�'�u��@all. \TBS 20:\,37A�72wN&�v a�W.�M.*� �,N.H. Anderse)! 2. D�[u.�w-�{8SB 9:\,425--4302D&Se2}  ��&�S. Kim�2�ter� Stark� < �$��� �� ic f?� ^*B� in�~a~aIp5X. \Sci 257:\,947--951..��:93�� 3. Eh(�J�;!8of r<�n=Ip�&��e� �&:�6!�198--2!��� Kobayashi� , N.�W Endo)�(E. Munekata%k3.�Q"�)�D@)�!^IgG"� do���-� G!� Pj Chem3!yA�42. N. Yanaihar�dc�. ESCOM�V] . 27�812/&r[ , FE+G. Riv�4LFA �4�0sAy2Ga"�!� �,7R]s> �g aqueێ�1� \N� � W 5/9~6� i_�M. Hud�'!�Fa 4. E_" �i�.%` loop�?:%� case"|� G&�RK"� 7238--72423.�?  �~� Ramfh$rez-AlvaraQR:�8�*E)�+y�,�ef}@ �M�28!p253--252�"� B&�C  LacroixZ�� .�20� �i er-a�-mA�V. C � 229--242��/4} , G� �NA$S. MohantyѓOligomք� ,myloid \Aba\&� ���s�&��. �>�� 3657--3662 Tsai��  �*A� Taylor� Chothia�SM � 1999�5tci��LsW��:A�ndard �,i%volum� 29��)�62P*l�$ Br\"and\'� � !IJ. Tooz�C�X{\it I< du� �vIm Sj}.F� P Publishing, New York2�h�~u�B �g)H��Cha��ERA6>�- =�"��R&�!�s�Bt� -bod&��!beyon� JCP 11( 14( 2:�.a�} � PE�8A. Martsinovski�,V. Shevkunov�L P.N. Vorontsov-Velye�v��2. !Ha��o .�*��y*@:R�exp�Den�1�� CP 9s 77 782�*6�}  �%��SP�2i�Si��+e�/ing: Am2�schem� EL 1�51--458.*� 95Z� Pott� | 5. S � a! f-latt~&� �'���J *�#Aim9�am�at�r ��-B1002`1036�  � 6 Y. ��9)�.�alB�th):�. \7!L177--16��>eu ZIF� 1(nt��u�� � in�esh wGa�a\"eÍ�3�! �|1514l1�816�NR} Pre/W?B.P. Fla�yaF�ukolsk�W^V`� %H2.��N�g�Recip� n C:~,Ar�S]��/��Hing}. Cambridge UniFVtQKess, .�|� QiݥC A. PabozA.EO�it iCS� Hag&- S��Snd�er �6�-E2.� 4\,�!eH2!f12952`952�S`�}  ��D� �h �V��P�=�_2ɥ}#� : Fokinet\ �"yB�5t��y via &� "���>�454h45422�}�{#��l��ockbio2�Allى&8��i���f ���Pa�ble1�:r125�1252�"d�} $NjW. Swop)g 3. UHta�*dR0n: replica-exMg�Vv{� ``TrI,''�6M2!d"0100: 7587--75a1&� �3a&�� 3. S:��s*�b�u\,1328�3282�#ia�t  a�R ,P. Causgrove[ GilmanrOS. Fa|R�CwdT5�H$ Woodruff,%D R.B. Dyer�, 6. FG}��OJ-+�: F�_!�"� �a�L[ + ioch 3E691--697.-T* u  ��W�9EatcTl$J. Hofrich��. 7. Lasb-�mŒ jumpRA�$\��~�=$oons$coil u�# n ��ine�` pre��a ` 3 zi�'�`�P 9200--9212F�u}  A��D�R�l)�H�Scherag�0. Ph��="!|�unu�F$\a�e�il� aff'�vP&��ut%��"/'Fla!-!p1 u5 97E� 075--13072�G�v} bv E7 >�eX2. 2��)�z� by 8Y�v�h��� "� � 9 2782--2782�07 H)�A����)�3.�l�eA6Ad�����#iumB�R: J"3�+ Born�  "I�e�w��U93� 3932�Rocca�o} H!� Amadei Di Nola)�C�bn�� A�ar��d#�a"�hai�p �%"�p!%�hG�roU�2130--21k*�K  ,� �D��Rokhsa��9� pNj�AI�f�5��a>� f�c92�AgI 9062--9062f"q} !jR�� Lazaridi� M. KBus��9>M-Q��!?.�8��=>A��y1N�R�1. Explo� E�X g.��9�6 in=02j�A�345--3542/v �  �r Jr�$!�VT nd*1�;�9%�2���tohic ƊJ.an V���� 162W&�r} �,���admHE.I�akhnovi&�A&x �ed Y!�  ���!e� &B&CP���!gE��$5343--5348.x�bB�.8G�{ofU��7�Q|:��vs.5F ���� 62$B"�s}�9huaP.G�j aion-path�3��R��^ 121W 12132�at W��SNB�ia 0P. Derreumaux�4�mplex5�wb�A[Al/T:��!464--461 "�q Mu\~noz�� "�yEO&���& �(7&���anAO ��R4�<"39;19 �z& 6�g ��M.�HR�$l��=Z. Essi� At4i, M. Whitlow�ng �G� Clor� A novel,d1'abl�l��}8immunoglobulin-e" &u�(ptococV.��m2E��66�eT Kim� Yi�Le� J. Qof _? hscA!�E�)inu&u�  CP 1�8271--826�B*�T} �!�!�C $Brooks IIIE9Y.� surfa�67J�\R]9�>�C&qU kD��)�A\ Mar�"2��� t"� �st��edue2S420anova: insigh�Q�oa��3� 362! �A.*�:��F�"D�Fx2 a�h%��ebџ�"B"�m1462*!X��?$! q�� Swend� 88F_tQ@�R?  ph򵵆R RL 6A 2635--2632\** ��e��kel"� M� tarovasniI $ryptop9;e � ble,r��cU�����? 5555 �/:='  docu} 3E%\$class[twoceLn,aps,prb]{revtex4} :+onef+(usepackage{��,�xrf�� 3(��8draft \title{F�2ze%s on ca� me[�,5Q� Uő�YTauthor{Mai Suan Li$^1$�( K. Klimov$�tA�D��irumalai��N�add�{�Institut�DH s, P��h Academ�h�ces, Al. Lotnikow 32/46, 02-668 Warsa��o! \\ �De�6AF��Chef r=m.��! �al ~%#Ta��=y, *yof�1yy, C,0ge�,k, MD 20742 !�bk5ab�/ ct} Z��� ��s�Da e �v_E$\�� { � _2} �o õ 3}{4��Rt�(i'/"�UO�_2 D1�i6M.w. ve�eAޭR S��N^{\mu}\r�5Uymun 0.17ȬDI�ޮ��9 in l_2 $N_c4 135$,s�/-�mim��he truly�$-or-no�L� R�.��y  \make�*�A.�M� B gZ "�"0AA�G�ea� d ob� s, uvgo�yarkabl0l�K�� � an �A�io�$N�@�e��3B����e)3 t�Dc:e.��0o�_ d \c&H$inkel_book$H In mc"o�.��/he*�"f akes�:ce � n A+at2�m�, i.e.!�^R�6ct���C�;d (m�0pf�=..�,s=xn`&t)�*1f*�:-Li99})��>i)!��}.!%s!� a�N�1��!�0 on+n8p the 6�_<y .v q�00PRL"��e"��up\; \, = �u H_{vh}/ cal}#, 9�,VantHoff_eq}i \u�Q M> gT2T_{max}\sqrt{k_B C_P( )}ޤ�t=|� \int_ �infty} <)dT$,g!C�XR\,�pe�, $���5� heat��$ˆْ����as*3�.v &��ity��8 real� us�3.�@H"�eͦ4y (chymotrypsi[��I or 2a�a p���4MJab.91}) it |9pV�s] �B]94}��G�v servy�n�[�9�@�͟�-���r�O$ B blemre�ha/��Lum4ِs 63�ss9ade�ǁn*0/:.�� subi�j9� obsc��gE΄�-�_2�o�<5is po˯�O�"� �@.A��not�K ly brp-��e� ers. Neve�:z,I��rbE�s 6 ofteYAen�,F�.� :���se�K�*�4s. �F,�P 3 4}[$ {\em=}I�fKGc7��. re��`is�Nic{���atisf��or��J�n� v"�Go83}�J�6���e}n h2rs (2-l� , 3 �20 \) �-�� M9�m� 1h ��n� ؑjf��Va\o�[]��i�U�*�%re���X ��Go �� �Wmǩk.� }��;e��Q�<s��qryFZMres�:c-7d1 �7rehensiv��s p o ��fAn%gf0 t.i/=�i Omega _c.3 a low1�Ct�o93��ԁ* on} D�l�.;� T_F^2}{͓T>iggl(� d<�>}{dT}\$r)_{T=T_F}"��AY.�vH��&�$%i�r�'al�lap_ !Ge�)it%�be�Un.#i�I!�artL occuw'(d f�, $T_F�M*�~�h>�tt"G BNth � Li04POLY}� 9���b<�f�dAa- =!;e� !�!2ce=c5i x�iv;i�]i*`@�eU8t}�SbH�b��Q�� _�"R  Jqe���� vari s�!w�?,%"qA�A�asympto�"�V is u�y. &4O|a��H�)�: 6� %S�@*q (LM�h6-`)(SC)|R�рu`9�ordc. ,� !q� �X >6�-in%�z t le�#upq$N fu80~�11A�78ݫ-aIir 2X RYqU �\Y.AiSl?y�N� A�u �"�HU��@~ s �%�mj�,��LMs�C*[q��s6�7 nc�o "�S they���%I( y fr��S Go LMSCs "�B-�V mM%� ��sU� �� "j �ʅ�\; � JingN� ZB� c7.!��Rv�rW1}+ Aj� � u e B6.���ʡ;+� =� ߕ0.02$!�\ s s�ri�=a� omes}M]� for A�g��N �3�%Z�&"� Uc�:lo� X6b ���*�\���@��[�9qQ��s���� !�:# *� �k� �0.9l� e�:`�}�edi�0^{\ast} = 70$�Lb�gEa:8he%i.2 C� ���%.* ��� �Ѧ0. % FIGURE 1Q��X\�x!0=4in \��eVyHfile{sc40_s1.eps}} M� 0.1i� �ion�oTM��.�$N=40ɼ �Ed BBESC beads �%t��.� act $4\�s 5$���oD̈́c"�4.�(` d�$k_BT$)�HeM!ms~� wIJN�[Ma)�r��4tactsa�$� $. S.Z�xX E��lp���M�*� r tAI��a��-E�"(c)�>e�(��$. 0 >/dT$ (black��MH�d, )-haÁ�e)a��~%/ �*�)�^-0. ��Ec _fig|Q� "WM��"}�!Bc�s�:i!�r+�"#LM {V*Y� (� "zA�E�Nh he&1MG�bic".ɽDill95�3 Sci}{ m��Ils� �n BCbjI�( (BB)9V��N�hadYo�za "n"��p&]c�d��aattachedirpe�a t !R�"�(carbon}�Tn ��lem3Ł�q�X n to �2�0. Self-avoidaAk�HmٮCb�O���c�S" > cWu 9� �L. Di��`��&�%��"�-�xThj098FD,Li02JPC}�,&E��e?� _{bb} \��Pi=1,j>i+1}^{N} \, \d2f _{�.,a} + .Bs2B\neq iDJCsFCs6C>j?s?�"�)%.wna���$.�b},:�� 9ss re BB-BB,S � d SC c3wct)�i�}�)!�{bH( 1@Z!�-]AY&S$i^{th�9j "�, ' Z�pairsaO-,� , $a��M}+7�. E��.~#�F#4ZsXJ-1��=�9=0 on- on ��LM)� in Eq. (�� !� ��J�z�>.�P�"��B.��#�8%� cWctH� u��ap"MOa��MFu�auf�T1}{2N^{2}-3N+1} \Big[ m~ < j}m/(r^A+_�� - , N &��4 + Ke�8bb ' 8bb.8 \no�[Ti� e�2{bs2C.{�]uzchi!�>p"A�up%scriptRr��M ��E%2V $=&$� chi(�� p.� ɻ�e� �xBB A8 �F applRoLM�<�C^i w`�7ou.�Ymove P^MS3��Bea��ֱ� CPC}� �Qsͣ, x��Qtr� ��]s�.cazvPve-ZEmulti�! icle�7�Lis much�ueMt� m-�4 ard o[ Hilhorst7P��H6A�����:"ܨ!w �le*�e c&�%8��S� l!s�Be�^T-E5! s�ir.�  �2�ds� � �M}���s W�-q��ka.� 2q�� ��� bt_vhove_e _newz� !b:� "Z$s!�ff� =48$A� (solid 0�s, 18"� s � ��((open hexag��15.. (a),`v  LMs.|i�!xlSCs (c�or'N��v27 (17�{6 848 (18), 64 (15� nd 80 (11 �f�s -C$�(30), 238N 2 (20), 485 85 .:b`�*t^R*@aA��M�ZV �` enth L*� 5�J� "� ��m ig. ž�9aY�e��Y�"� A�a1r�5���*u ��}oaA�un�8The ��n�,��s �Ked C.�3�'�K�%�"r,��]o.eo~"NQ�uD%{h��V0bZi�o�� ��Fq ��Z{s"� � ��Z&er. Ci�%�gQ �F ��co�de (V�a.�rI*2d.+^� .�2U!a9�J/N9=*�O��*�6_a�a�A��&"�!� 6�"d bei  tF]i~f�'com�; H�j�u�)fN$.Ib�Sa�b�9f2!g>E�lpoím����6b��Us.�ZiϪjvanis'&![*I�� G͉ *��.u8!-!Jis intr�-c�8�V mere�%n arti !�5lWt-%2��_. Clar� ",Pp��!s"QX&�e�G����qs 176�/(78� 'A9SCAks)��UB &�85i'u�4��@.8(x��4AO!.���!� pra}p�N ��$�a-�!�se�3�o��Ēa),�Pt��sndx(o��wh�J!�3 !1��t�8(5�!{�"� ' >�not� 2�� T�Y�j,��`�&c"� KayI^��^ so 2I��w"�.g>�A�gm�ny2. Uu!��qo7 �= \p%@1-4(T_G/T_F)^2}$ 6�P�1om � �2 �0"0a",�T_G��Z�<� �~*M=�M�fe)&�@" omin�JW rappums4s �0Onuchic97ARPCZe-� $)� T_F}{T_G}��8}{)7}Y��is���&X ��j osedFV 4.6$ �%4}�&&b m�i�u=,�Z*�k, say,A�f��0�E�2�")�1�0<�� "��A���!P"�?�M���is �]ly seeB/a?�a/`�c� ec��vis�Q�z��u�)SC�Vo��log-logA :�mb)�#m�"� $\mu=,*�\Ier>t�}��)9{1$S�eej# ?,F  �u�--al�7�(y6�"�+�"2�#I�qn!�*��"�if���2i* :�LZ%E�IN9� !�$NK� 7# &3" 2�� � A�B� 2i> &�A�5�� Ni�6� � I� n M�Y�� !t+&)�J . � �- a�� g��)e�ŒVi _.�Rdot[��*��=1P�%[tray6 0iD^� ��0$y = -0.809 +�65 x$ (x. co&�is��6).O cros� 1.� m� 6#Y/=Q/. .�y��Q&� R�p),oA�D .�Y�&� :{�e�\a2 on� |�M@2%2�� �k�_����y�&� &�<s'�s su�dic��n0.�!Q" �5��Ka in"��*%��%:�"� e  #���lN%� 4n�� uu��1�Ar� ofÐc;J for (G!Ia!LM��*�6�isK her �n(�q $1\%��F!E�[ŗq6��C2�""a�J��3t��b!]:�! ofkcd-typ""%�����0�&aaˡn��!�enc�' LM�#:�#"!�� �9s O]Z$=���:utaes5�Ɂ$ fullu|-!6�j��� E��#dvant`�s� �z ^z�'PA�j�B "�.K T@w�N�"�i =70$� O���C��alcorpo@(o �chP&�Q LME�e�s3ruax "� ��� �3s���uxtf*�&aE�(�_|'VRiz�\4QJH�ٙ,� Sc�n���i�!�6�*--- A�fulfill u.^ŋ�^��cl2�s1��K4�3 �q26t =n�%Levitt97� &�.HERE ���orc�6�bKBN�@nt No 1P03B01827�!NoalM9.�blgrant (NSF CHE-0209340). MSL�U��H.9= %+�Pi�W Ref. \on��4$0��q\�8>�;{009=b.�4�=V�@ nkel�T%�4O. B. Ptitsyn,,/!1eA��I s: A�r�l f le�s}, L:ic �O(NT, �^)*OAL�4 M�L�T$M. Cieplak�APhyb�@ {\bf 32}, 5577 (G�t��4� D. ��[."HJ�/Theor�K*ix-K*� ��bi�Nymers},j�1970); "� T.ZCr�~�Ke0-9s: "+U� *|`P�%BW.��D$man \& Co..H 1993t c) P�@8Privalov. Adv.-6Chem. ):3}, 16%979��&�BEB/1}uH�IS�V an, O Rev. Lett T485}, 4823-4826a00.�&�3A�E. %�A.�bFersht,2<,-�0�042 991).�E�4�� kFiz�DH.�, Meta� EnzymQ<-8f3  2004Fd0d%�y�,5�-�. FT. Gene1$4`637F�3f_J. Mol.!l-q 326}, 911N�w9�Z2(N. Go, AnnuDvv?a� eng J12}, 183aH83.�6�0 C.� %2�>Pgc.�� lcadaji. USA)b9! 6369l96�"�/ a�S. Li, b".?, Fu Poe� a45�73%6�_�[, �p]�(��D?26 %�A. E�BroRg,Yue&`iebig, ��. Yee�E��Oa$Yd.Qd�Fe��� 561 �52�Kli*�#}Z5JFH, �E�GsM�&27 %�82\7$��, J�=��( B {\bf 106�}, 8302 (2002). \bibitem{Betancourt} M. R. �, J. Chem. Phys. {\bf 109}, 1545 (1998) O�Li02CPC} M. S. Li, D. K. Klimov and D. Thirumalai, Comp a Commun f47�625 ��4Hilhorst75} H.�`J.~$ Deutch, J�� [ 63}, 5153�75.Z\pclass{article} \usepackage{B4icx} \beginHcenter}M��<\Large Off-lattice simulation of the solid phase DNA amplific%D}\\[5mm] {\em {\lRME�,Krawczyk$^*$!�e*Tu{\l}akowski$^\dagger$H43mm] Depart!�Applieda?puter!V4ence, Faculty&A�icsf^2< , AGH Universi :ScO:�>Technology\\ al. Mickiewicza 30, PL-30059 Krak\'ow, Poland.\\[� �E-mail: k-\@novell.ftj.agh.edu.pl, 9kul-V,\ e( \today }I45� %% -� UK0abstract} Rel](s!��)h (SPA) by \mbox{J.-F. MerciA�(et al (Biop�� J. 8��3) 2075) are generalized to include two kinds�primerI �o]�cha�er) - distribuI�n(surface. Thagmoidal^C occupeT by DNA, observed expe�Xntally, is reproduced i puzP. We discuss an influA��$wo paramet� � effiM�m�2�$ process: �(initial dene$p_0$8�aq)s from%i�;facial 6^��Yr! $rMDmolecule length to(average%w(ance betwee�%�)t numb)�(cycles till@ satule�! � was!nout� a�s only�5�-) wEV!�� f� subsequal�ɧy DO ir fA1� neighbourAv-'-e!:)ۅheq��PCR. O>LQ�y�:q�Hinct steps - anneala0 ext��on�den�=qD� repeE6a�n ite�a,ve way. In t!�way)jcona�$iaB7(i.e.� �1m DNA) in��_!�s final!gA]ak!V�a!�Bdwi��*s�`moA�, its borde�Al  veloc�ris not � r tha�e I�per)�$. A detail�$nd transpa�zdescrip{np �� foun� �ɥF, toge�dw��:, Monte Carlo.d ��aim�)�ork�to inu�  erici �ran)N.�  &C Aere��y6ae�e. Our!�&0 � be trIB����ut��!�up��� Ref..  . HoweverE\r%��m��� ces ( our��roach !�FSF��*&Z is perfo��e?Aj*�cheme, E�%�osi!��V� y ��doEOZ��quaUlU, but=i�randomlye�v 4ed. Second, we�-o acc��y~ A�1%�f%0�g(. Both mod"�saD iy �o make ��.! more!listice��icular� ao captuM: limi)� � �Kise/ � �W aGds us�c5de�$ mean%,2+ ? ��ee"� %W��Q2 +A� de!��tGassum2�>�Aceu ;E�K9ly�DongA�Xrt�� s. H!�Cn�* . O��v haA �e a"� !�׵KaOa given%�# �� ne��,�њe�� �Mhe <-� AV.l !,!]�NY6�v o� a�is�@deW ad ��EEshmX:i�W . Again, e %V;5�M�d14perly. We als6-a:] �:�"`ne4a�:/and� !.mutual�r PJ�E� results%�beafulEPdesignGW�����ayis optim# 2��af,�:is low!��h�s H �V�8at raises cost�ot�l��I *I necs direc8 �A����Mi��diiCs�e� w�N obviously� eresa /possibil Zdet�ng� ��DNA. I enext �f�� valu;)Pput=�%� cal�X��. � �m)c�$\rho �B %Ja�ginA"Q|��i� xxout�of IAA�r�e ���� �� meas��of�Ly�"e�.  �_aqs ��� R9*S ?�nu� q�NreaEede, t!�iAXlo�>b�Pcussion!�"oC9fs}%�dL &�model!�ref � data��A�din.k�.trEq myI!/�1�)ޭ�Ca��$ has been , � H $15 fmol/mm^2$. Afe�womq!�-�SA�5$is $0.0011`�a ��ofA�/.*�X 15000�!�&7 comes maij CIA �17 S&S 28 �tSA lea�ߡ�+ e $! �29�զ�(0!�is���) out a�!��35MehrI� tane�=E�E�case,��� =0.016�SseITw��ma�e}V�b� �at%w�i� f�hse �$��en-�d �y, trueVfew"^s,�neglecu d !2d�M͡l"h  becaus��,overcrowding� >���,q%�$&at�( �~SAa�a�Zn;t# �\alpha $�Q _n= ^n�P. F�e�i� above� d�u U8^{28}=29/11$, ) =1.035Wor su� -�U�2.i��$� y� IA+Se�dueq\ to IA. As�� %��i!rule:���p} �{n+1}=x+ n* �S, =yA�e�T al a�ti���� _0%:Ew�t $A0�2� ��2b��50� >  �%�ri��Z.#]��)�can�����%�i!-�!ja local2�1nCake��&� . TA[ meanY at Eq.(1)zed:��"��ne�ar� �ar��� � d% ��)!1 $���ofу $pN$� rmequival�to 15 $�L��%w$9*10^9$C��!���i�o)��mF;resourc� We �I#K=� [=�6��) $S$� \mu �� c�Ged W!)�+�To impr�� s �xes?U W $k$ runs� ��ok@se� ed� ��a�V��probaK �"�Wd �<odic b"�բ%���) !�*�� �!��o�th�o !�2� � i=es�JSA�t��<=pr5alAN@st�!ng ixof $p$E�I��SA>�> g$� ���� S=pKB�a@Q ��sF�[6t$p=1/I���� :���poi�ft��J� fi���32� k %�c Let us�+e1� by $\pm 1�d�J>�$iaalgorith42�!�SAM�s a c $j$�iQ%/)}�h st&� ��p+egn 13 GJee &�Y�rt�NA=Bh$iD#���ex�L/ 1Ga. Dv%"�l5 _/.Nce�A �5!an#to�.�depen�o+�2�%�Ga� an fun�,"x� a phenome��&� gamma $iXcho�$ �BY� ��)0�-walk B""*M�5] j� or $�!'s�"�-���� 6�U(IA, expres�BB �ci�m�iId)�!�6��a� "G� �;�u ed . �y"�Ypprox� ,"� we2 .,U�%0QR AN��Q6i��noY q\on%dAx simp*Y � &?$o speed up%gc*�. Acc6 U 2� ���.�st��eA �A[Q�Aa�why 9C� seemE cceptabl  &�R��Fig.1!t showmb �WM�&�:�jS total*� st� ��erA�M�  [$N$ m� Ei�^F��& ' p#�Z���� W ] *� � �*�Q��!t)�e�!.� � pic�A��]�c- f 2� X curv: ob����$A!0 14$��-error ba* due �!3t� d s&J&n %�ea�a m�dynam�(M���ofT�A7 2)�6�)� need� �) " ��h�as ��; �� X=�7&�&�Rby�� �=�6G.� see,EmydMA^{-\phi}� t leastV r fag�&tp*t !:e � �$D $=�%4. .ye�in-; a��6&  thosAp (1.c -C�Zp �plof �]'A�"y. 흁N.� A, sD(>! orre> '5l�I$ velop a)�'ly��afig-'.2&I �32g-�m�66"� U0,�U�č�r =L/d�� $LEQ�� ��4$d=(S/K)^{1/2}���eEC�bW � �iC!he�� lateau�,$r > 1.8$; bp'��EIkabrupt�$�C~ eA4�I 3!؁_�"a, �st� zes6man�{!e�,A�BB1($. �e �!>1.(2 doe� \}�55��-,se�)�!� vari"� !� �c�� )�~ � � h"�. O?}�u"V "'%yA-$c=0.a)%)w��W�v�O sam�>t �Kp�D'�F H*S s%As�� E$c�=se�a�tr=2P me�$t�o� ��U'j$Y!<"�!la?de�Y$$(0.2,0.8)� isE�I> shor�q7 s orMer s��@!��A�2�mB^�%�&rol�"mor�ecise-"=DiT} qexponenA,B: ZYen!*�c&�!r!@�T�a��JSA!42C���A6a�",.��&�j!�ќ" ce%� xA$th��� oI�2Y} �i�"�#dA�pl�kFur�#�1-�\4��3�v� �e�ic�0�"w"2�� �QA�x% i  iE���!� $d$>�)�e��lunqdrawn��4. u�, ��=^lQa)��ps�"�eI-� in�%��uz&��ra�8ch�+��R ��". Also)���ed�'w%B!8x |� �>�(Gfor��`(ioH Ac-  0�IE)?W�l� s quit� ll e"-�% -� �N�i&X1:4�4:1. A%� back<�&�6-�"(�H�Qu%e ɽ" ~"�$!�� e�1�isS-to�Dv� U�z ion;5�� ��� �$1/300 instKof 1.0x&"�h+ s�&e=�qF?�-tQJ*�&w��an�� resc�)uq���Y9of�at�,%�I s rea �}%vely c: ct. gbN>j6{966*9�.�7L87fe,�M�1arE! Cell & B�.�}, Wadsworth Publ. Co., Belmont 1993.� h�( J.�3,�7. S� g P. Mayer,h4�Journal 64.�9!.}�9 H. B�*C. Bol�F:8 Rehm�8M. Audeh�7�0arsh, B. Kell�'nd=P. Adam\,3m|� e}[ht]�er} \�6g:Xics[angle=-90,width=.9\�" ]J1.eps} \�&ion{F�:��� �"�% �/*� <.} \label{FIG1} ���: ���b�2:��� ��s����� �8 R�6.} �2v���N�3����r�qq6�2�364:I�=���N�4J��/E���$B� A�:�]�4��ƻ5�� �c6{5r�e�d>��(H� % $Id:#mi�& tex,v 1.5��\4/10/22 18:54:12 jon Exp$>S�4: /Users/jon/r��/' ar-gzDics/tree-power/pap/s� e-su�/RCS/ � $ %6�>,[12pt,draft]"�> J$V�>2� s} %*?[T1]{fQ1ncB0,mtbold]{math=?.�?(style{unsrttopma@68 0.0cm \oddside2�� 16 height 21footskip� 4cm \title{Sub!d %d analys286T( spec�8%)�a�1��(author {Jon McAul#8`,$^{1}$ Michael I. Jordan,�hLior Pachter$^{3,\ast}$ \\ nosize{ LD2�?S p } :-2}$Co6�? Divi=F.3}:[Mathe� cs,}��6�?$CaliforniaF*XBerkeley, CA 94720, USA R\:��$To� Frrespond�=�$�ddC; �?�? lp)O@Ae.b ��?} !�date{ Xnewcommand{\myfig}[1]{F�e~\ref�� :#1}!]2,tbl,T] +tblR+sec+S�,on -secJ-eqref-(~eqn&) �!�� \L2E�"� "�< S77ceM�is" cros2.o;8 organisms aids,e�-d6 reg, under�i�+H��#*� ( quiX4   iz�tofi?_>,;/g,is>05� gr�"�2nlcon�a� ons:żt'l scop�1e�ssN� �:lo���6(qd,B withyhat a�&�.T al e7:siIRq�$al frameZJ>xs�+�.Hi@ ba�$on maximiz؅� � �%er AsitI< stud�verteb")���(lL�5�0$�_in!�B%-most *�=ily d�Cg���6M sugg�!Q$ marsupial8R Q�* candia�s.�Y�&�*{2�> Hb=��� /�1 reve�n-2Q�in!e u+,)luqN�e'�0�Avle-Q� �fes~�8WatEtAlEI,Rat2004�>ndivid*!��h�demv+!�dBL%�E�i�A�%�fic�/3Q� �(Fli2001,Bof �3,Der Tho Cha 4}. Su+s�>e�FdV�aA��A�46�Am4play a major ru?iVcŪ s ab�)wLu"Xd ӉA1]2oB ) vpurpos� )a1�"� ��8 of/�bgui�bby 19��a;sd3n�9%e�au<$�H "�! quesi��wJ.liC.�-� OBrEizMur!�} ��{F�9�$�``phylog���''�Co�5 / it{ea� � cite{Co5�}!�e�.�a��_rmi�sol��C6U trai%P�Qw�as F�a� b��[2�$�6;.}cffelli6� al.}-9 BofNobRubeV .,4ut"z4I*�%� � �;s^A.�!�pr�#�@Go�LP . M� K)�s�8ɸpA ce w]E� c extantI|A��,�M�"�*oday'�l"+Thus,(�6pr2|wn unav[Gbl!�su}$x�-;.er-2e�corts �! p�)C5r.O;��  ject�Yh�focus ��re&AgP%Haggreg�z�)�iȱ;. Few �oF %��&�quant�6l d�e -makڝk�$A . An�'pa�!AA �y idow{(��N}L ,Sid��}:�0a�&of1�ed&� Ja�f9NLi�B >�.�q} arg #�4䁟�obeRBa:ve.�y ��G �@6�M�While@31urYEar�!9problem�(r�/�\ ���+ fail�#Q*<in�Gnt�b deofW�dhbJ � e�A�&�;Gͬ!��ed�A� asse* �qerv��d �Aqsuf2� 7�;amongk QEQ.RB�jMa�j}�� �q<�(A;p�mayg too�K���( (k  us�:,�, orth yA�p�7 :!�!-�!of�/ *� ��E9/�non2C�#j�mas in�inguish���8t��)@ zero��Z"k!F��', 2Ltop �ha�<uintui� ) �7)}. . HC8w��e= au1-theorew&� �� u� �. i�As,ALvi �,oIXEW�` systT,6�I�S1�2�"��<!�%� cr@D� �G?0� �w�#X:!�)*�/a�� et d<� erme7{'� Z;�c!�%�G'loo�T. a!a Uwous� ���� �di!��s �s due�N�&��:I� �/ �%F�Ip��RQRy� llu�+� id�U??  a�1r>ͫisI�� /B�� empi3D-derivedU�y�e21�,E���*h ��&�aWcate ���щ� dunn��r82lop"-%ed&v As fini�G! �way2y�s w�N� "!6%DE�toM6IXip-n�otX ?lDH.2� Setup}E@e�2L _A�A�hai@9���y� setA�)1x8$\ bf{x}$��D�s�anB� D�ũ��;!� ungappY! lign^#columdPviec ese �s��c"��W leav��xyI@un�P a�E tral��l�B� �Qׅͱ)\!MarkovgItit%����*al�� branch���S �"� all �M)euyA�uc� e"�Q-%���'t�L�4 $p(9� ; r)�y�IQ:?R}H)3R$4 &�"e�ly�%Y 6ndJQ�{Fel1981{Me CR8( > 0$��K � global~B4� sh�P!!)8-�cho *" threshold� ,s $r_N > r_C�4 $r$:oa�" mG? g��+9�6>s �?ea�e. "��ed !!4e�Qq��,�� wishg���n:$\delta]t)$��$ la� A}!* ei� &� ed (JB = 0$) o� f(1$) u�/&e�  -�c. Everyztri�PZ�Vh1� ��2iof �Aym� kes: H$r \geq r_N$, $P_r(:X}�1)a�.�it�?��� %e�#dmlm C$, fm0m%�:mj6c. Min� 8S�sB { aBJ�$.M'�&�Y�(Neyman-PearQhyp� 7 test�9Leh1986}VA7null +\m�W$H_0$:2r}�ksu � alte�"veR=A =1B}, stip�i um�xow_*):$�=�,fal re�<� (deaM.� )x$�ll4@' .ip � ral? cern-'.�. Suba�KkInte�� a%fn �1R��#GI "�U� PK4, �2��!veR� ��s;L�� is�*%oiz�xis zDI +"f �./ > Tb�4eA�sen2C,�h.-s�� N<4�*%i@Pd[th�,id���6i�0� �by�!�� c= e��� �,(*{Symmetric(r"Y� "ly�s� �%0% &��� U6-�sV_ (�sc{sst}).�:ar�Sn�H���d�5 =4y�!Jfomon� $t��. C�!!j$t,C�~ �!PJl��4 � ��-�@I3] -�� �2airA�cBn5�isK  �#�/J8$ly $2t$. H6��- 3V-F 6�5afo1c,Q�oa�p , O .se�m hidden- ;o�-4 nha n�3�,�,��m�GOode�$t$ (\�A} })a�� ++c!E��little u��u6ty��� �R  s025z�8! high.A , it�4��( -w#r�H�  �Iendan-��ogy matr\�Ewe%�5unv�P]��L��!}"�k�q;)�:ᰩ�s����e6Q)%~E� v2hKlikelih�'�o� ����:� _C) /*m ;o)$} (2Ap�<x)b(:�A!��7x1ij-hy� ��-� !2�'��a�i%�� �=� \4a��vMC P��' r.M�  <A�%?r��D�=x)�i� $t$,�7i)5 monoton�+lJ ��*�, for �)$ke I�aA [%$-͚A� �� ^*(k3I���Ai expl T厁7��os[?��"? ExHvddam&�_t h�.i�v2K !c���r sr~G� X!�dh#r��#r"� �"e�Ki�7evant�E$t�a \infty�KkX�:iBŋub*jof��!Rhd � nce:!�^-��  �� Ap verg5$ $k \cdot -�,aR\t� arbitraUIJ*�� f�Fig�g"fig:ss�wNY"2B�mT6 !x�8�Q�_� +��A!a E㩴val a�! $�$�E$k > �5s=*�2 alsohlieQ !�6f�:a�u!, ^)$A�bi�b�AVH�� (�KtR=k�&-h-�=��2� gr!'���b�"AJa"�A $k$.2�E�i���h&' noweiV� (m�y .., *A�precQ-r)-�eFTR� eKo T&�}a ceeE�&as~!0 tbl{�!.We";M� "���A�})��dba"?!�"�Td�P�Yұ��…L� yield&@� �Hc@� 8Put$Kf�&on�-*w ,YapPac2w!WDr� �# ���GAd�� S2D#.Aˍ��y&� ?�Wo�typ�� genic>)�oh��d �. Hava�fix u�Ax/��56�7��8 3$tRs �� c6 "� se7f �(A�� ��!�21� � ;�&.a�3���0�{F�al� fami�W� , Dk$-6�S je"e (k-�4 mpss! � ${21 \� e k}$qs� �CB�A>iA���s%_hj �wP$" � rooa�]8 ir l^?|(�'� �ettp}*��2� (��red�]Gp�#:v�-kӁ��;stN� (�m%b��t :c5��dss}, daVjed~ e�8�cS%�f A���Gm�2caPacJo�"4,}��se � ��a�a\coincideg �6!n,!��=�� 5�A7�b�h��AltFhe.2! ^�6u%!platypu� $t$-: �+A>#6�i�$is $2.06$,�$aI��t� 5 '��� EAa� y�Oa�4. A�extrem["�:4-1�V4:� �Uo^TY���I��Mabs�e lp*in ���'�B��.�ld(ea�[8.5\% (6A105.7)�[, �( 4,400Qs �� g� E�>q��� sagreemf at;2� u +sco' �mE��!�t�o q�gA�of� ��)[ carr�C]a�9i8#�$,� r! �e 9�&le� or� u�}d.�!���8set�O�R�{��8 ��(clampedstp}e��i8)i"Q �# �oe]cuq�*` ��mix2CCO�%���)1 s2}�e�! in \m�stp�a�Bost�DA���Y''r%$i�Ipv� d.is aj&�"5_N = 5$,��eie�}*ERAN10� 11 , 2 3iFy74..� exh�9 s siI%�?er��T �&�!��2�e_ ot a reliD surro%�66��] ?+ M�)� !t bene,#�-p�"*� �[ a{� (I A%I by�el� 12����\�!addE�%�>�"p w��2� 2�AE�=,#�5H!%����tE@�*&�&�Fv put� '�,imK>�i^"�.��",D�( rimi��z�i� irA\ioV%O.]�?lFH" �"d)���q�!�i�:-��#�&�Ea�.Y e�i��"is enA��bA� aA�-�� �%&�%ib< �M�^� hnga�8%�!�_���%ing. By7trast%� (v�&UF{U�G�X~?9#��!�of6F.$�1N�(fare. Since�C�Z]"d��"q!l�re���g #$& Hir!_|* _go�T�?&�)&/RW1�/em�tiA�2�-f02!29i�T\��v��  situ�:B1ow)B`��Atah�!>j� �[iAp�&�Ac� ledg���thank P  BickelE&�> Siepeb help�T�en� L.P.�\ ogor� ��gra��AkpNIH (R01-HG2362-3), a Sloan FJ� R 8 Fe�" ship�(an NSF Caree�!:J> 0 \}$ �Xh�,� of �>�.: mass"^�de�bfio2�!��V+&�sluq�g+ ,!�onB*w_$xb�="AW � H)a$0 = (x_1, \ldo-x_�a�! F�$. W�'�5&3[ n>k�0\sum_{i=1}^k �%�x_i) \ �|>Z6�[p>Vw"&T�,&�KroneckeIlt&�. U �$ Jukes-Can�AF>Z$,��#equilibr�A�rv� �2)�#6s,Emem_])I�$ �!k/9OnaA} R�< & = & \frac{1}{�<gT9aleft(  +�8 3e^{-4rt}0 \right)^{=�!�N=;3(1 - 8)29=%�}�9 �6�T1 +^�]# .]��k -bo J .�?Aop�>e5vF�# = 1$"no8� ity,�)!� non�ntif" &�%< $(r,E�� .� N�A}o�>�X1cI�ng~�9{n�top s@U�^e�� io $J_ 1) /�/�9t�( "�Q j�� ��!qW"�s"�#"X"#A#>"1$�%Y:�hl�F=�}AEe#(Yut})^{��� )}Y�!k -e4F)U.P a 4F,CZ+A�F/} \ .�� �ylr�C64 �2N%#lnot 5<' ing)=�-��!&�$ ��')$&�W!��E�ofF��U_1X'2�T�Bv��j� J!Wn6A1)AN�2 :5 5 =%d�摥�� w}�� r@} \�3nF?�$>}= �#:���$�T f�Z!e $n =M..� �0, ��k \}$+*d up b� \z/F1�$, \[ i.�< 1 �rm{\ and \ \�?e}�)�Cj>M . \] S�y`.A��.y�"�&��j+Z�b���}9T}_u&!�c{ xn�Ju�s5eds�.rit*� $cIiq;i��ly��� aI�!���0���(bI�q��.z �f%�eAUtD"�*G �'2�uT��&�`)g�-S !S,*�^�  �!A>)�i�9hh[i'tsYm�%"� �1$,_!*a -(r��"k!� �9*h H_A- \of� >��esB#.� � � wr�z}7plici�aA2�k$a_:R�rho(k,t G_A(nM<( + 1; k) + .9 )�͙ G_0B2}{fD� �?c�n. E�%(B�^ , $]u ;# �.UUQf) EOamz,rm{Bin}(k, d )$�:dom[le� %|�+)Or� ,qp�N; $!��!V �&��((cadlag) cu`binom��-��ies; $ �? a 3\exp(_ ))/4$; �1�e#a %n �3CZ f32h)�;.reb�ba|-;:��2�fa�a���a�0�eR F�*� )$.�oa�>��3�#by virt�U�f�y5=�essu>^T% Te3$. �P�%�P9 de-* .ăf $n(X_0"� X�.]_� �<-9�*�.%)m Q�1U�Ձca�lNF �9�R��� g#����@e�miل)�i(*chiev�U,vel exactly 3-��e>��o1� min\{n�mP�.%5�D/ > n)�{q �tS>1F! /���?e �.f1= 21 �i�; Sc( �H#� � NP��qbf� �)  �cT5� 6�a� ��1>� �@.i��N�:{= ^-^�>H �}{�^�}.�eB�guae�$�,.*M! �Aqt$�*��F�.�P�fESf�:3^�!z.�rhoB�"����u;�J��� *�&o7 $X_iY ]�: :����Bl$X_ in�=��ll�)}�us ��.��JS �A. Eg J^5�" &tng�NQs � ��� �6Z��3,@n+6I30(I^��Fn^)@7��. r�invol�8 I�"�l~��*>�lY��bj@al�\dRYck�6:siredkp urac� $AbrSte1974�v !�jY%�L.�%G��V@*. ,�!�6#��cur�Wfig&V.A�m kinky A�.5*�S�0 wt� (�o:��B�� chiFE�P!�FWJ �v eas/%�Uy�!�2�,![%moG L��)�Fn�*] ^(,Q,\  rapidly uQa�= � �� routinM 6TA��)A�-a)*�HC0� or} ����*mWx�2�s�_n�'V*>FG x_0};mL��&Z� Џ�>\� x�a+Zf���S�%:V-m�*�k3/�5 dealM; � I.��clT"���N)�#QCOa�<c)"�NuntQ�˃rerent8=,�$�lea{RUIt �r�m��$s. Indeed,�5� inw%na�� �Z=ociY��a� QeWpermut;�m1;rpr� ���� iD�� BB'� > inte�d� %$��i/tf�arts,sy( b�k-E68a�ea�6FIs 6� to��B�!9an��8mb� or� �Gy.N9�ge6NQ9l�JBM�L�=!h:��_y6(����qu�Z�D�Z1s )�D10�ZT��s�c���d:cA� �%�"�� "D.�.� '�ofB�,�� rn��J/$S ,a�, k, t� En"-����V :Re,��I ulas�� and U�:�6��6PAed %�6Q�$tai,i!��o(k"�b�7uteJceA���& 0��.�(&�/%}B� y͌�yBNyExist�1o�1�E�/A�&*3b)0a)�.�3N^ "1$)!�V��m��i?lly 3an�? tinut-j2�3��a�EA��3ix�9. A6$%�]�) ($t �>e6�>�5: �8"�9 �,& )6sam��r�H ry m�3��@��=A� .MK=�6�+�4$is circums� �%�|"  se��o|aC?�B m�$2�H�X�094G^fty~2�ofI�&k �=`)<�e%-�'s!$���w.I[F2� A!�&h !$^F�J�'� -5j,�i#�nd\z#ed2�8�$av�%� 7fa�c8 b@c�3$#!{A�A.N%A�)��-��ؕ� >mA3ou< �akg[�� a� onNj,86H ��Rx� ���"_=�e�|7 � eon*z04!�ӛ!�&�$"V3A~�1�'J�3( & *4�+�2%4� �@mavid"]Qr�/2"93t��I��um*c [Ols5T1994,[EAI�xa"�&:-`�t]�~6�# ֡�)})F� 5 ���-yp&�!�a �,t-�w;�5�&loyc3&�R3 !sFeln�2 �(FelChu1996}�]a z��{- ��4�H2:1��9ፁ�"!#�.). B�G�9s $\{t_jm%� mWKc5"%)"�4&�8�0WTVO:s� qxR))��:�,��A�W1�yi�t � �e�KU$aB!��*/).Vor:]*� �Ba� PUJ,!c�Ma MKa�)���Ygy�4$ . y [' ��/.0�0 �u d 100,E�r���i�%)s ("� ) A_. �H.��@--+iB �6y��RnLd k>_"OR_���f IpoJ�lea{!�,��Y�"�la"k{�ge(L.ulf 2�:�f �"�@'!estse� �j>(B wen#F�5�)��e$ER%��,�&.�MI C�Jt� 3� i E#&'M-; To/$>�`a9~� �`]�>Ct��b ��G�?X`rep�`!_�.�c{tech�<`,p����{\cente��! m }{rl# & SpO2 \\ \hline�\>�P{0ex}{1em} 1 & Baboon6),b2 & Cat3h�-"4 mpanzee)5ow6 & Dog7�28 & Fugu$9 & Hedgeh710orsg1��l\\�1�Lemur� Maca�A&�Mo�Oaum�Pi�1�P�8%�Rabbi�1�R962�Tetraod=[�ZW` fish!�P'ta)�capA{K� p)�66� |_"�6���^li��%�$�K� .f�'A� a�Mc n~{Y \s [qB�,|rlrrr|} \x0�Q),c}{�lE�&�:)&? vs.�,^e!�J�}a(Pu/ : $\�$9gsc(=,�-ag2�4&�D\% (SE)�.7�&N� Rank�, \ca� {2-6%,:�&e� Rat,Y9 � \�0& 6.79 (0.01�& 1.3%%ma6K, q� �.T& 8.30NX6 Xa}a[ZX,�B]& 9.61X2.�3.�a�nX, �S a $ & 10.88X3.X4.4 ��vXu�$)e X)��^5.�b�?,�j5�U�,�9�49.96^0>^12.^���2 47.3I�^ 25.8A�389I:��M�,͎� & 13qOY�� !�0)� &:�Q�^&!67%"E� 16�53.\A<�CN[$:e& 37.��0.1�_ �10m[�Z~Z�& 36.8I8 � 4.�� 77.�A���Y+,��9x& 64.6�5>�)�ža`>p]��� & 56.2I4eNr?��44a 9�A��M�, Cow,n� & 69.75!�Bp 8�{!lZp eF� 66.8.J 22.2� 4867%�2��2�*�s�56�� 2�(�***U.� 2�JZ2� &N� �D  :� VFoug�H]�s����Z10.� U 2G3 *5 h y:�M6<�Dt� �Zs dis�g�^� X(! �! ;2�A!+Ԍ 8^erj� ]Jin�< 6�=(iF|w�6�� Zq9 :6��lank�(*FallMs)c�4$.�Go e*%&�:wn %�� p(g�dom+!euePE(!412$)BYap�H to�9s"�Co!Wjit=��.Y6�7� ts5�� � 6~ �� �� ���� .� New�� � F Z �` it{\<�. \}g �8���b)< �1Ū�JB|v& 14.42��04�R& 1.1`e>x�`2�� `2.9��� 2�� �,.i� n&0! ��� `��bFF& 15. }0 �3.6�6.��B�2i�>�  & 17� �v�59�>j`, -�.h& 19.� 8^�L�`��6e&� 4I�6`!�2y B�&� 56.44A�1.-�i 65.5` 20=.Iva2O�E� 7 �� 3.~ 2� 6�>U R& 71.0ip9.�2�5�e 70.5�I�4�e�!�_ ��& yҚ 72.7� .R 12s2� F�r76.˺0.12S1.=�B� & 80m12F:� v#�qu& a��1��1�C & 2���vBv86FgɃyń1�M�.�j & 91� �d2�2�� 94.0IS� e�6��2�={V & 93�ES2.6O10O 10!�^'<-4>� & 95.8iva%�2vSj�aq3E�1�&�a^v �N�& 9"�2�4.8%�J�a"PB� a2�� a0�I.�2u9�>aJ��9 a&5��Fa]2� a��%#1H & 7�:�� .o .p2J .  2�*gN��"�9�*�03 n�-f��rdI :Lhu �m��X,�i, dogck��fugu, zOGFtx�s?�� � �#��$as� 1>.�1<l�~F�fXY)U.� �"N�6s=0.97];0�N 7�6\�0(x%a�N�a":) :K�`b�!�ё>a*�_(A�>t_(B�:üex�sst}s�"��9 �N�YE'I. Eac ��01*�0�KC"4Mf"$k�?U&esc�G�M?� two (bott�st a�#100 (�ost�P��xim$A� �"o%! ~t�K�ya�% y do�&<FJ��=e6�)3$�!8ss; ? �eJc�2d S�:lyBb^<4 FV^.A)>-�$V��U�(no-gO�).f.\iQ�N$ 6%�_+8mYc"x{]�Q�+( 5d!:�%j�QbbeQ>6>th)�M�of.�)M�A9.E� bl��I�"�UY#oo �F�t@�D$= 2,3,5,7$<--�qW;E��eEEE8og�+A64��A��r}D�:16JszNt���au1��o�._N$)�!* ��1#�%�; _N$'?3.�`�/�x(eJZ"0n 99.9\%JtQ�wQY�uIu .89]�& -21--�By:�&v(e!���%O�saQFBM�dO� �\F�[aps,p�]$int,prl,su�cript� ]{revtex4W�F>two��? 2��pdftex]&�� % Einbz'4n von Grafiken2����x�!.�!ąapsrev�+� \t�Robv�(�"a/�'gen@O dien�Oa�{T�)llenbaՌ \affill�4{Max-Planck-In���r"��,of Complex S�u�s, N\"othnitzer Str.~38, 01187 Dresde����ny}qu�{~� ruse��ڄ(P. Pantazis��&Y�U� Q���G1~,s, Pfotenhau110%30rTM. Gonz\'alez-Gait\'an�����(F. J\"ulich����� \��{\t�}ia��5di�v6graS&yprofil3Sa cL&l�� by nonli6[#Uns�R&�, &UV �X� d�@$oping orga��5f�]�*�&��g*��cytos�vn�2�[�Sef liga��t�w��o�T��#�1corpo$-͔�%� � �-w����( . St�Tng( a m�s��c�*lk)D �[�D� >J�'�M�8�� V�J� b�]������� �an1?2)8 r� )9�w+�ing.pf�.@5Q p �e%.�]Yg�>k�' le �~ssT�feg�e �!_MF- wIM @0em�f@ �gt)�typ�(T�)M:,;�m! 0��v-nA��\ linkAf�O �raK�)B^.�Q�. A+�fifty y�q ago, T��sl�V>�5"m�a�at��xal *��[)2�ng �\cI�tq1952}.~p�o�. ;!bseY5s self- ��c�9m�s-��1��fu 2sm. P[?na��O"`/&�A�E� �\F ien��ud~^aCns�G��)U�,koch1�1$gierer1972����,�umF:p��t�a�Q!���iu6A�I6R)�'A�igi!�-�i�: asecre!�f]s)/"7li��E#��3t�/-, �x-K�da���o��� adja ti�[-�wol�] 1969!{,M�8�4=� by r�� ��J��� UM� 8�1�aE\46N5)6�. !pta�`�aR f�; ?zEi-u6)ZA{R =S�;r 1f�-al/��!L5�tJ%�9�p= \�b � -ayof ����AQ����a�s=1�>; R�b�� ith /A�d�]%�^0�� ^��|�y�-߈)T ��ly!�"�-�vA�`.yT fluc[ e. + >�ca�h"9� �߀!��!9�`e��aE5�M� eldape3, 2}Hb can w�I5��me�B?��� houc� dzadeh200� % ��Y ngly,���!t"j�,�/�`�3g*n��a�?n0�4A�1�=��ges��M(��. �xa %z5&s"$�$TGF-$\beta*h per-T� exis � a ��!of��JA�Pfruit fly Drosophila!�sկ[��%�2 yB���poo�E"-stoodr2p�T2M�Leot�A�4=1s�"�"�����i�<���lmWP�)3����. S��=�&��m#Y!�p��iff!��e2> s�\ $��s��qcG� 1970�W� k9=ԅ ��6&$�e!do�f�m!s5�,mcdo97}. H��t��!Zn��\7"w�e@�B�:s �eE���-D���wW�d.� is i"��da� Fig.#9��c_�<l}���� ���ripe  0!F�Q`��-dW�A(al�?&M�u��T*g a�&27C8>"��_N���� $x��!e��]�:/�)IyA,.�T=7��� .��EwA��_{\T ne�nd $ff}�O5��Au!>ofi]I�B; $b _in4�`exar>V&:�9B-�w�sM Q�ed��s-  d�. &��deg$^5A:5�A%��� "�.M7s6\a�!��lcoeffi�t $D_��DH �3��doe�jtja2 ��*� igd u 0$\xi_d=(D_0/e)|�):����7E� ��� � di�j�q$KD�6)j�V%h. On n!s���B2m $9W e� BF�M����U%��syn��PAI ��0ss,�>ɩ"S* "SE�6n9W�F 0$\lambda(t,x).�N�$ �zAcM�arVns bo l�� �OAql��b"8 _unpubli�}."�Ekeep BS� $�onI� e, wc3_GQh��`Mr��� p��ell $R$l main4d_)an�&n,�2� q�da��Ha=���a A����V�kldt_ry.��=\J�F�)-��) :6jxE�c!��Eb�|Q�Q$ �I��Y§u`{We@Md�}) = C_{+��V_ft[ a:{ int}}/[2�#+ }d6 +9 \�b)>] + {*�}{*� }� �-.�? ] /\kappa-6o%$D_{0}=�\�Gf��T =/ = [a^22� �2� n r �C_2�]/[4 A�6 �[ 23�(b%0+N {) 2:z ] ]$_ a�s.�s \$ �=a�n}�f�! %� [-4 -�� ( + �) R ^2 r-+(��`" " r +2RB2c)^2-�� ,�$B_{\pm9�=2�kf%�1pV�r EP$C>:� 5 r\mp=�= %� {$.�.��k3Npid��;}M%o �eaܵto��behav�� $kQ<��ED2QD$M AD2q��|m�AMr/ a�$�WKO Eq. ��� �6�x>�!*��� �l2&��Oe1�v 81= �gV&��$ $j(x=0)=j"�gj=0�%-./ %ݒ�"���o%9� &Jd�� �r �"�, �/HMS�&kg"�NA�*9 V tead � ate,F�6� M_dev}[i�A�%@o�h�.u&S]xF,"� ̀$j-5 t $x幉 $j=-"Y) "P {x}yD� Eq.~V�r"C� w3im�Z =0$ -%cbs_u �.L�s �$ $t>0��1�e׭ $x\geA\!_buie�upcY� 6k!?to �6��� m(s�klyI�i+~A��!6a")�� .u �h""�  j+&: -a A��n %&��(%H7Q� A�$1/J=0Y] C6_ ��r�x�D((x)$ obeys "� x=-\int_��n(0)}^  (x)}d � ^{\pJ} \; UJ)/jB�V�eq:sts� �,(�5}HY� �YΡk%�2sJTi�3byF�j �� �  [2�0�F�\ 5g� J��!-(w x �*�h�_ ��/�R�A�- pro?A�ay�Q� �y pto �nx/\xi)6%0xi=(D(0)/k(0).)R(*� t2fz}d� �PzV,at $x=x^{*}$J�pM2X\sim (x-x^*)^{-1}(-\ln{ � -1/2�Q$ing>  *�j� >0�y� $x^*<0 #�$ �A#m4��cce�l��o�y���Ns�)�l2��ggQ _T$: $u� � _T)^2+� .�c_1 \lnQ���_Tr2c_5("/ _T- �%MU+_T$oty3*sTMj6,beyon��At�!�R6 holdf`;-2&y�E� $j^2" �)(eg}\ln1J$. ��J �� +��Xg� �_*R �$�8��e p J� A`max�U2q2!- u*͇ �M�� [j� cq]$�y!2U�&� Ms2wq�T/e�*�l�rk[ ʉ�c-�6�'�Kv ���ϛ.*j'/ef� �!n�V� *�du����2��'3}�d��e>�${[l�r,R}}(j_0):=a  *�j_0}xq��-1}����$(��96�ş). I!��  �Z T(�'��p �$��in"���Z 1�J . i�D�_/")6=���x� S' aw: \% i�� ��!.�M &� ��:�y ����dGKc��.o9 �1'�M$uic6� \geq�w2��t!L�,���,�h� � �2� d��o s�%��/h�l5�, �l\:�l��RP�"��al�& b� �� %S!"��2G I^, :�E��'x�p�7$� d j6�Ptb��xaJ� 2G = VC��a&{� _0}j_0/" _0Q a&( ��_0/j_0V� �_0= .� bEqs*p ))% "� "? )i{�/7�,d. The robus��tness is thus completely determined by the ratio of the effective degradation rate and the ligand current at $x=0$. High degrada8s9small4�s lead to a robust gradient. Using �Hasymptotic behavior� steady st�lprofile for $D_0=0$, we fin�at �j)1BAIells %�e tac t tissue Aeinsensit�sto variE�s��$ by a fact�woI$�,is displayedmFig.~E} fig:*} a!T func��of efor}D%3 �-\/a$. Finally, we brief�S$iscuss how�i transportA Z��erived from a microscopic model. W�� noteY numbe� freeM�s -\4space between !x $n)� $n+1%H$L_ E8 P�recep!abound[ sideMXby $S^{(i)}_n$. Similar-introduc�^$$S_n^{(r)} � lofz-z mqo�e rightEH left surf�of�, respeŴ�see:�!�rete_%U}I<dynamic�8these quantitie�8�given by \begin{eqnarray} \partial_t L_n & = & k_��off} (� �4 + S_{ n+1}^{ � ) - -n} (R - 0 20 ) f-.A L_n\label�YA )4 } \\.�W �-y�+.�D\Bigl(\frac{R}{2}-*r�{ n} - b�H int} ��r)� B1B(ex(n! i)}� �%�-�}R�l)}j���l)2���^� U��A�r��-�^+%W(E@%X �9�AK-�X cY��nale]}. \end]�On�scales����a� �s�the d��4es $l(x)=L_n/�"$s��/ $s_\pm[e \pm� r)}]AwhereQ ,na$. Because�So6� $L�govern� time � $\tau_L 8eq L^2/D$ which�~long  are� ��relaxŅK ���R ular [ Za ZaZ , th��oM �e eq� � 4n be adiabatic�M e�nated. �&� Eq^BŲ�total-�-�y"n=l+s+s_+� llow)�ak� [tinuum{ � \cite{bollenbach_unpublished}. A ), ison� full solu�P�P Eqs*� ��)-�6�)��2H 61 is shown��6�!�$_dev}, dem� rat�t� 9M��j� captures%\>x F� In!IclusioneC� L developed a generalTore%�$ framework!������!� ;!]!r(characteris ��y�via C4cytosis. %Dur! �$ment, such68play %a key rol {pattern>M�org m. C v � � $triggered x reshold l!Emorphog�oncen%�on. %nto struc!� %form)at f� po: on" �" &� ��has b' Y4 ed experi!"e�(under condi!s��Dpp was �r$expressed i:�mori96,entchev2000,kruse2004}. Reliable.�c� chie b!�ly5�ng=6� s. WeEj d-A/6�s.(>-w�> !s?QofQ�se; ion& .� *V� Mj natur%8�sQa�] 6�g � . F�0extra�`AUeL reN s .B significae�P3length � 4d$ exceeds seve�f sizeaA$origie\�S .�� non�% i$1*cur~ . %,�`!)ularityZ�.��>. A sR  mechek baA`on���"dalone p�t�� ɁWm8of"ae+aA 96 M�0eldar2003}. RE�4 A�also ��]�other��os:M2}�*���l�mU�M�k"� &j!� take�to accou��0new phenomena ear~i�b� In � c!�y-���d� n �!x�s. Fur�more,B��mpanieda�aQX �y�i!�$deed obser�:� �.eteleman�q}.��ad��,a"A�s�- a poM�!i�< a direM��,2P�� Q� 39 a,port.&!it� stra� forware-�izb � pts �JenO to higA\d���\s.�Qc� u�~2V�or)�AoY��d$ W�er/i� rang� xi� 30 a$aCL1ᅺom=��endoc�~�gblocked5[ 1bwe estim�| � \leq 2a$ B�}# ����%|qve!: be sufficA�ly�� guarantee� �_�-�:rU�o waboutE0) --8$8 hours. Assum��� %= �$�n}R��� � $,E�B$�"�d$1/$mi 9MD�� . TYcoe1%E 53%+� ta1������e!�a eq 30a$ dj 5Numer� ���AH2��~(� 3)a firmr �� !D���$per minuteak�M��measu� in�!but� aksystems� lauf93}#is usib\���tra!<J m� u-���a�s�!y�r%_ ��-l� i� ) =�E !<(:� g�� easily��es �,in fluoresceLrec� y]�%Wec6a��fu� :&O pa� ter1 will!�mit a`a�*G � %udQn:�cal��� >(. Our H suggesat if!�n�domes �%, &� wreD�.$ /!<� � e[%be�ly tesAfin-@%Zc �� _Pthebibliography}{19} �Handafter\ifx\csnamej exlab� \�\def\G #1{#1}\fibGbibO font>J M#�Pf�Q$�R�~R.$�Rurl^�0url#1{\texttt!O%8{URL Iprovid�mand{!\(info}[2]{#2X:!epr�[2][]{S'}A3ibitem[{2�{T�~(}(1952)}]{t} n{author}5�{A.~M.} &1pO},A snfo{jouN(}{Philosoph��T a> �a�0Royal Society�,London Ser:B} %nbf�`(volume}{237:z,pages}{37} (� yeara,52}).f Cros�MHohenber%'93!'us1993�& M.~C>&[}:; and}.6VuPJO�ZxReview%e4Modern PhysicsjM65:N-L851NM93�5dnote}{- � JKoT,nd MeinhardtA�94!dkoch1994�c A.~J>cY�b H.}~�U���_._6:N-_148V`4r�Gierer���!I7e�g197��:� Y�J:J:�� Kyb�tikj�12:?-:30N�7v�WolperEu69Auw 196�L��V�L>-NZ(J���The"�Biologye��IR�a�y_ �R*69r*E� et~al.}(�)6!, Ros S����0and Barkai}}]*�iۡ�V%A>%`:#V;D>;��; B.~Z>�}})GuޖwN>�1 !U'U�D�o7al �j�!�.�-�635F�!���2V�4Dorfman, Weiss�Ashe,-�Z��@��R>c ���B+ג;B�! �:�e�eN<ejY419:�M[304R[v,Houch� zadeh .E>f6,(, WieschausE[ Le"r�Lh2X20�gB>,6p:�V^E>D�?2&y�VQS>Q�a_F%��Z798��Crick0��c 1970��F>� J��2��J�42V�0r� McDo_&�� 1997:�$, Zorn|C�(E� GurdonA�mcdo97�B`:V(N8 ��=DJ� �?��J.~B.|*�{1�-����C���� Y��671F�!�r�E5��:� #!�0Schwabedissen-�@onz\'alez-Gait\'a%�*�� E.~V>W u9%.^�:_ 2�C2�.*VWM>WR�!!��9�eln�1033 8-�981�>U!�%�%iJ� Han.�4:�H�HBelenkaya, Wang, % �Li%�h�4} ef{ C>H!�O�f: T.~Y>��!�% ~CB��1K6��M X.~H>�%6�5�*� }f0131>�-�60J��).� tem{beleJT. Y.9�$ et al., {I\8{\bf 119}, 231 a�4nyKerszo%�T ��8��k 1998��B^���� �� 19!�Yh-�a�By% nU Pfei�..}>?$�)DAlexandre, Calleja�EVin~"�-pfei0�4B gA|�GB���?B� �V���J.~P. u�5!7�Xu�>.j�0:�-�32V��jrJiLa�#.�>� " , Ni  �o!�l<�� A.~D> Y:�V�Q>�Ni!�%H5b��F��F�W��=�5�D��Zv78V�vK K�$.�>! , Pantazi�B"`(,, J\"ulicheri�R�]{&F%I'f�K>����P>;��>T>>�@B� 9@�JB5R_a�E�%WNUn��{?m� 4843ZX )�J�� �3N��v &� ��r� ��Z~A>.N�%]��A�5\T>jXZ� ZTi�bTY�~�}(�Z % G�V�j�_6�Dt<&*P, %�$ed re� ce }JMorimur� � 1996�u)��S>�Q:�V�B. Mq6�;Y>Che" E�wFJHofS�B�j�7R�136N}!�� %f~T�&e�C�e��t n )�fwAJs [� SJM �6�u� b�� .h� 97zb�(Lauffenburg#Li mannW ��#~ODJO2a}!2�j�J�M�:�!" emph&� title}{Re�6s:%s�* bin.�(s$- ,allin &��c\r}{Oxford University P�-�yG�.E�&3>�"A� 6�:)��'�r)��< 4 r X< /a^2.[6$=10$ (soli:ne)!� -=da"4�=)�,set: f�'8*=}>A�a6�;  �.{o q�2$/M@!�=56�. P�'E�:Um$2: F Et23\+ 10^3.�n}R2(1.1*4*e&f6T7*2k< �cAc3bc�85 Liga��.�$1}(x)�:eG���>4a source at $x!�at�)_*Zs5V!�0 t=0.18, 0.549, 1.26"2+{(*�,�m�.,1.���; ndica�<1Z+f.7, �?symbol�"V@ns*p7fre\;f�6�*�)_<�181����.� �2t,6F?\�? x 47PC2��:�6�6'w�3" C$j_{02kR=7�Bnd $j-�$x/a=50$u�2��: � s %J� % s�)" +sI,�0.R=7�9�9 %=+�7�/, :]@10.1ͽ �6�@trong�+�,@by halv�. (dot�3) �?o�8ng 2�VA �21�"� }D. %E4p"�64of an arbitrar�, chos>�6 t7 %n+Q�:��a�4b�9o}&�3:��0J -vs�2a f*EAA�:1Iy$�@ �6^jA#Ŗ C.U�2�1{dI@1���5�.�2.Ft��4document}��\,class[12pt]{ @Dcle} \usepackage {�,icx} * he3= 230mm width=15 opmar�6= -1 cm.N{makeidx#d{natbib2x {multicol6ams��65,6RD[bottom]{footmisc}� 8put epsf \newco�+ZSSSF)SB'PiPNQPi*z/Q�}�/� {��m2r�,tw�;�5�:s\\�b�<al�5 ome �I�<s. RelaI 2007[V{ �ter Gorban\thanks{ag153@le.ac.u5)\*� �: LeicN0r, UK�B \\ A�$y ZinovyevMi.$@curie.fr}4$Institut C,�eis, Fra�\\{%(-sur-YvetteO date{ a�%c5~ab!7ct}�7�D!Ocoord�1(codon�`--%@fic nucleotide fr H ies)B�FmJ�39-"]7al� :[4�"��eu>��$�9$for archaeUs. Al�> 348�7tinctJ�avail= in Gp@nkAXAprilE9 , be�Ato��se�s�8:uracy�mch��7nowtov2l�2"g3:A.L:�@�3le�ary? metr0L%� ��R�h; quen!��} �results 4alysi/ "�<%�us�U#6� � -BW�=�@E5s?e\5n--field; roxiZ�@�Bis �; knUAa]L�+--� , �[6ndepend55� Segre var�0,:s�:Na �$on!�6�!�!�rA2� �)firstE��1cipal�onent%3-cor�3t�z� w� g <ic G+C�ten&<6oph98l growth temper~(!�"HH ��'qH=�t=g� thirTm �!Y ��:� curv a� mean)� � -�. F �CDeigenR7i��%+ PCAQ�\ 59.1\%, 7.8\% and 4.7\%l� �.�(q� %/`Nc+N lear�Jtribu8 �wa��o~9 �q�M>|�" .�F�� \se;3{I@J*}�; DNA � e helix!�si�6!N͚ nds:%l�<� �Und �!� lagg. P�%�m}ݹRs, v? �AT%1GC,oA� e�?"(*:gi7s,GC bond is sE� er. �Ota�! al a}�%5���,ar monotonicBd j� �s�{Fe2�(�Gsh_ of�ase�)!�used mos� ten. Some� ago FMuto}�=w�B�>�;!Z.cofEsous!��$ � (protein!*st�RNA!<v rs) revea����v��ali��Be�e6��Lir wh�D�icAK)�coE%�3s)7>V �!'�'W;� non- Bregio2_Qudies-;TYer1,Yer2,Blossey2005}�; �N%S%�Wn<[C ing �sl8 lyt9e l6�Eaa��=!q``a!mel�F.�"U�ce:]s'�D՝�than �Ggen� �4=��ach�A;�S�A not on�9h��a�Q�-[, !��E$opy too. I�1@�N racl�R��>�Td�Ds sA�pro�2�of�� o�itNmsAN pris� E�so manyE]> a�A this �. NRt&�?�8e�atA�,F�ncan�+a dra�{c�C!�Nbi�nd $ amino aci�S�F!�4 enco+mIQh8Singer,Lobry97}�=>>5��M!e]e"D>I� A AdJ�y%�ern��F d6Fa_Uw^�� (&�I gcgc}a,b)BrRe%_wolt-Hs: (i)%q� � per ����J�i�>�in �TesA�!ba� +49(i ir�<is468mm, 060mm]E(1_2.eps} b�:t|>:c�:Fig1c:d�:g7�ap���E�$ a) Averag6�y��F�T .nEw6f . O��e ~ 36"� T 312N� r*O  toge�F wa�-� chromo�L�,4S.cerevisiae ("��-'Y'n 'y'+ jIa; capiB6#Bd�E�co�652 Rt�Z�.=#a B@), A.thaliana ('A� 'a�<), C.elegans ('W !w!5 $ n"= }$). c) N~�Je �$$\Delta_W$� Z�windo>� �} $W$��h�V�YL��to �A��Qx' $i$th 5 !�Nq|�YB � C&t,�W��$<> ��u��ed atQs.usI�Ced R {W {M\cod}  %a  -d �HMM $ �E��.s� )�:Q/>pW�=�s^e ]T&&:)=(�� }}$-�}$)/(VarN1)+> � 7()$^{1/2}$ (VTVl\sU�). d) Pf *�G+"� )si$>�1U}�,, $(i=1,2,3)Y"/%$ empty poi��sp%to��nd .�El- bro�L�!rfila���2P 36O� LB� T��� L�Z)atuSuld be�asE�&t� �suYRlotI�� a s4\� guJ:�MIh�q-�a���A���vuy&[$t may be b�j!G(Va�9!�3,N�q��"�a� � �I2�Vow4V"��A�i$tnr�T3P r� r, $MJ$)B$ d)�N�"+�`s�� obt��� OEC ���ad-N al noise.�Q�E�Ot!]�$�\qAic)� f]V%�PQal�H3 Fn datN on `�W�h�Wa`p�Cal $^e"E�6� (kN"5�ar22  � 4y). Of course,�8JX��aac�icY*{U,U��%bA�bYa!knd) does��Qge�%� A$\9Z[$arrow$T, GB C. H��R n study� a<sy�2�u1a'ful!� ��B�-�LoSueSI��Lap�w"8 7�!�.�!�se\ e BG (!F_rH N)�aA�M L�7e*�U�s:��z �2"E�2va�N}ad hoc!-"�B&� �peZ��c�d&m.$)N orm AYuą���� co� E�i>�B� z� a�'ac&��[woe�%� cer��[� tq ���A<� � an60Ar�����pCbe��� m|} ,x} (E��=mplV� or�I�I��ascb}�6@ algebraic.0 paradigm.1�'K �"ort�A�. S�9:�o�O"�beNaK unA�cte�f)� te global�e�aa�s��ov;iversal�V�h ?cq%FpiUo0sl�-.QUhffi�``�`��je�c ies"e�%w24Borodovsky99}.�y&Tim+a�GQ,�"ofIeM�A@�n�)�Sueoka62����P͂A��?sA*b*%� �0 exaA4 *3CG& }$� \rmm�}J�a)*y ����5�>9 �orz�*T�b� }s ( RfA~�ya0mo? e�^n�Hc !tve�B �E�a"�R�  subs�Tw>^ 4� k- 2A\\tabulM cc} a) �Wa"� & b)�9&R� c�; & d�9g�c�$� } >Y.A. s} C�h Rw.6 ��`e�J�  ,e�� R� 6� 2{� s, �� �"" ճQ�.B++ak each oE�an��� {\itaoN]! V�}aD͝� f afE� م�B ���giQ��B�4��,�?12hg8 $p_{\alpha}^i$& Jc %c��)�$ (A, C, G,��T)d&� �8QL o�K���Am! 12.� 6�/9�.K�btF�*�_,$p_A^i + p_C G p_T^ixm $%�� sibi��ofhun�#�+�'v(�0� !�5�i�%��!+ negl�_ bv���" �nposlI&�#:� a6� 0 polyhedron (��[�MducMg,_tetra'a A} J ��M�eN $�# �: R�Y� F3  Both�E��d�< ze"6� E9 very @` way�#:7p� b"��NbF9%�se;A�"~8_"�1s3"d a`�# r r#sD-W �� r�\ )��*�-%R} g�`�c�g�k*7�� ar�%Y"t$%�e:1�0aC3 G^1$�$a@3$=�ZT�Nm�2s} ��va�5 90\%a�fi+$�c)�% >9�ed to ^^rmXUl< S 7 �qey12 AFth� own -'synonym� 9 e�Y  :�` �Y(_m�� %@��"!&��eFa�ap2%�*�)�4e*Z'�>. �)"�lg,*GB�-�C&�\e��Hbullet}(GC)=k_1+k_2o2GC$.�e.��. $R^2$.� �gomC� �0ex�'�y".} }\v� {10pg>�{B� l|r} F|.&$k_1$21�2teA� N val&�&$p$- �\\ EUBACTERIA\\ A1&0.496&$-$0.467&(0.490;0.501)&($79; !456)&0.934&$< 1t6}$*A2J59 J 328&J55;W4J337 J319J19&$< 6J3&0.647 J889J640;0.65J903 J875J7�6JC�016�04G$011;0.022)393�1 �162�� C�11G2413 106;0.115A 232;0.250�868FA3 �$229&1.031&)R21@220)&(1.014;1.048J970B`G�19325�8�97�31!k33�892B�G� 069&0.210A06A07) 204�17�06N! G � 128&0.777 �135)�1-W76�79%971B�T�29-�263�2%�30!Em26Mv2Qv!6�T�361)f12J358;0.3Yv12 J11%`82FvTAv710 J92%"70A/76 �91�903%({6� GEw20%&3H20E(1A�0P;0.742B%��%jIx80A�5Ix7!�18Ix44�46 B4!b>B-� 357&1.809 �36q�4A81!�;1.82%98A�2� ARCHAE�/54 \522!�51�56P%�574I47E89AM6V�/3�y27e�4E�45J32m�23e�769&2$\�$ P2�%�0M 96e�67a�73MS 1.02M�904%}56���%�00P366-7019�86ml4!�0.833&8 �-�5}%�)�07ar2�08a129G177ar71�657� G9 �1�22!�042 �262)f191O968;1.1m�!�6t�C74AV06!�15!!19IV36EV5�873&$1��E�al081��06!�09)15!2��770�6��G09e!48 �136 �06!� 0.66!M�87a� J�s�G8m�2i)!0.298�s288 X21e�791&4-� P3)j�M75�13%�3��3%#E�17�9e457&62P�AC624 O82%r58!%65AO900 �7)x916�A��R17AJ77��14!20� 0.70V8��925F�I�8��41 B%_21I=3� 4�0.8��5� �m��|�5-�361^8�G1.699�P8EE��-f)� 6�-tp 63 .*C�@2�0�,Y`�R�.�} �r�'Gf� dfng fe2�.&� .� on*%&� �ech�(-�1ddp"2�)�>�"Yr[' aro�x $GC$=50\% �w�"� *�2 $p^{yt"  , i\in \{� \},  $A,C,G,T\}$�# us.#�f%b� � ny $S$:"��s}�A&C} S := |�1)}_A- 3)}_T|+2 " ,6T|+CGCCC CC CC|I_� By it,aning,� i�jlP$lQ diz%cADo�h,0�-of�#q9�*f&�4� its:`b0N(as�k it whANrea%{th\=�ndw [)$p_)�I$*! ar+ }^{\A5��$ A}=T! C}=G$�}- G}=C T}=A !i=(3�# 8!� =(2)%��ra$|U!�I��!�ZG�3\\ J1cm}a)4cm}b)BO�3Z�� u�S$ >� 97&' LJ��. Pi-� the pB� �<��gw&ts5 a�E�y�)�' 1%�squ' marka�/f"8!� � $S$)��+aaxdomm��J�FM� �O=BM,:d� dny devi��22 D:� 2�����A����\�����B^ ^�r�f�QRy L5en*kOTh|gt� �'�(B A �Isk �x"(:�+ evo�� tun�� *&s�$&� �}g9e�c-unusu�8q�ic j�Qo.ing e �u"� ��or�3vhistoAx�PP�e�? W� �+*be nee': for?�;5!/ &!C1��v!S"�*Pv�u*�%ValidEN� � BW/&�%M*n)(:PB) !%%:> wid��^a"Z+geo�X3 I cartesian�(>#�8pro�*����&a.�etyI=:�a�ns �s�~5 (>4A�t�,�a&�+(��C�`�#a��!lM�z�-f� 63-2�G�*xy] (:E|��&�5i�"s%)I~.D��!in mE�clouds �~�DseA�$"H,ive horsesho�$m}"N�!�*9d1�ons}). I�. :�pplicb� %7�o� (�ce��.� 6� . A$ n�O+cy was,e�i�=, perAVed xEier� �Kn��}%@Aof.�:/A 66 EuclideanI�C=� "�2�aYt�X!4,�'l�G�&u8ons<:�ly�"-� w!� A7stop-EC�( ViolEo�%�.V�/>)� of a".APs Arg, Val, Asp, Glu,hy Cy�re-.�Gautham}�1K ��w���shB%�A�z@1L �1�� $; al e� $ C ��I=~�Fe�� � to]�JIA��T"� !����G�/& ��;} ��?f�s=lD.10 �v .v( $f_{ijk}$:�#�_iz�$ {ŹN,�backg���}=  p_{iHjk}$, � ��i@����enc�[��$iձM� �$4-1=3$aw�: 4.5M�%m���ar�4)�|'A�m3i �=1$} �)�ly [-)OI��J{\hat{f})\=:�*/M � {i=1..M}{-�)/ <�+�y2>M�i"a�$M$&�M�� (e��'*0-=sa%i's|2lw7b'� %�(63=64-1$ (gE�,��R"�t)=�.6Xd iMoH:e ^_ p^{1!\}p^{2}_Ao^{3}_Es Qs^{k%"��o*r( �I����9]���$kT>%9"���W A�)12-3=96�12x"fN� A�(4�)ea�;f8)M�3�ar �L�1 (1J/:gPa��*�-ce)�},ABc��j]T{Pachter�7F� dA�!v>m 5jBXini�0 di=\�[ij"E%_k} (18]@*LiQ�u�F!�f��2�oC_f *� �N5� at�$s $16-1=15.�ɆL �!�^�t 1�MJ�!��T�^�J ��t4�ede���EU� �:�b�lmg s downloa5�GenBank ��)�A��� &�)��$ )pvs!�^{xa6�E^@��[6�ll�m.in :�s�� $348�$( 64 = 22272`X&cQtoMar�?�vari*����/|. *Ma�s��.8�%�<  the��O:bis twic�r( ecbw\E6u� nA}�.��eA�A�2 �, ��Plb}� ڙ!h&�,��ngs 11\!P imP/� a�=+pS.�2=lF��J15b4�al�y&�7 a us�<,(although str0��e) ��r"�.C�b%�} * >!52��.�o�&�VJ �.~-A�bA ^-E�|#%Lɒ �Jd��+bmBd9�� I�/ d=�$3!n2�/B�-� g6{|l|c } %@ �e&\#v&a&b &!{rC0 >� �5(&3&(-0.0004L(00�(0.9617�+243%33H1I���e�&636)N'000�'970�)0H+D�'*0 E9<�'000�' 9675�L0.6�+XZ� &18:I�* 9756 I�-748��1]�/�%&� A"�� of�ividu��)23��Nl]"�iqY�� detail�/��o C :E�:irst,BOL>M $A��hVwe���Mo^y  $f^{A�2d we�veEby�2Z.�%� $mJ. c#�L5 L>lt�fx� "lEji�T2� �G��ls�7m�s�iy B.��T� k ڋe�3�"Y��%*�:a�,��g�V�U,ed*�Q|?�J� p�K3�,�� �q@"P A ̅�)�nbya�2� ��[ ��. �L*�mf2:A}a!�>�wo .�%�s $m_fE!:���;5A1)Ar�<�s�����quiA_62��ng:]rule,C�C  GC�#& �%�Y v�poor P�OR�4yr]��A�!u� %.h_K .& = 6� mJ���IkMbFor AT-*P[GC Q4k^�i� s&y6lrG���n>�M ��%I >?V��'"_� GC} #+�E�@\��chuFfE�w< s�b+fl%v�5n6 (by "ar�Sesk)�� shap(�=L76�!IgHb� di�"# � �� a-� seU:K af�W�Z �amU;�6i�6). HowԘ�" )5M�!R GC}Z� (lik=A.�bale}, 8$T.whipplei , H.walsbyi})%w�d ��!be�q"��&�)Ih�h� �P�7�# i.�E�%%���,a�% OpA1�ɂnei+l }�#"��5�a���{&h��)��["�S !n, H.butylicus17A.pC�x  M.�moautotr�8cum  P.abyss5tP.torridO T.V7l7A.aeo2vfphila ^ T.p�8�W.succin��e(T.kodakaraek[ }. I�Q(m�i�m�a` habi;ng�m՛ emal% `Js�9b"�_�Lmo�V, 2�*  cocc to plasmDJ�r[��. Methano�E�  ��bia�!p�+a�environ �s&E= grea�U�A���I�= o-v�a"m.Y<]kKe� rendA�O.k"UlblQeNcQ�ar�D�, ��>��t^��!�PMf�6� �* &} �C*} ^�"92.�U8�"��B\\ A"1O"\^M@"5V�"(Scoelicolor�"�;Ecoli 5#�".c) BX��"$R" } in:� F0 a8a��)s.�  s� Enf��-ery p#I.�a. Circl? r"q �.Q# $>50$\b`AcS�e8br��P.3$<2�>z�� �i�H�io*N& |GC-C |S . D&Tp20.h"�, pow�#$�;�" ,c) 2< �i�f*/ =Ni �?�� S.YK| E.A'T/cin� �s�V&Ck3�j�T-ref��:��~ �x��l ��v�,is ��t��Y' �itW �a� w��!��0� &�.��N!�.� �AAm � late�'Y:� ։G:� .B�#:V"2�!Viy] X1Eie^ aaju� 6 $IKJY lookέ�%[A!&+U �m>a thro�� � 5�I i*Y�GFig�.�"LO!5)�* �=�64 �Vt!�)��h���$+�$� :)�tag& tg1 taa},`Pt��rd: 9ag9ara do tg}�b�AFEOttg��E4a � cga} ��U&S6 eas/mu��X E ga})z � N. 6B(G �t c!�at:�E!`� 2b(ap�� Wra =� ccc�Ggg!re1Ain2Y�6� %;�m��ttt})�`�M &��&��fi�!.alway� o�0 1�whoA��&�� or#ou��� a�P e& 1�:5�"�(�'�!xis �A�cbf%�dG�7ATq�y s�,*  oh#Nma��ma�-��a�� �!Mw[�1as����S-M���d)�2w^9�z��%�%�c�is n�g�! kca�N�:�GR���2�>Fsy�I� ce�n�9 tta}�F6� !�B� ��,80.� �_��o BR FR �Pus B�(" $b�1Wi}_{IJK1 a + Cm^"(!�Wis*�!���ed�-K..348�y�m{%�i�). �/� F/y.�6��a��z�v�FU�V�ORjU�O@���A(kE} V}�&-.�%�s�3D�jZ\dr�{�basic �proced�-5��!�($q$2�&3lan�s` b�c�C��2���TXi�a V��,�! {x_i,5�� $y_0=h!$i x_i /n$ �,iz� sumt&k%�qL_5./4i (A- y_0)�y!ZN�l hL,�1$,�iu� uBk u s $x_i$� s.�(?6 y_0 + �) y_1 \ | \-=R \a(!se(�t�m.�2's orthog"� y_�4�S ��f�)�$\ � �_1�$+ y_2 \psi�_>�0�A�so on. V�M�<rinB}n$y~�!�m3t�e(4 covari%�0matrix $\SigmA�P edM�o� =y5��3D�' span9Iy� :'B�Q vi�.izing 0 �?}��=�� h �] $;7��in�:1�:�:!U R�no�h*�Jq we�:^r�n (*Q~a�"�*)�fapp�r)_-�&k2�� P) Cangelosi�". ��!�.IeX1#] 64~ e 7.3\�;.�o 5�;���#epd�!)��t]! 3m mpon 2, h*�*r6%�f\a�� �lyR�\&1� �L� �i>6* PCA.BM]�N��/�)�����s)�" bX���n (in-sLynn}����o�{!E�P2Hka�A� 6j.�l~��p !n�:Z!I"7 i\ Ptm#�Zr�+ �^ed �. liter4_�PZ�i� A�be �g#�"F+M,�4at��A&�X:�"� $:vy{$M$}��;.5.NPN��!{[�A.$\!�tr&�YD�.L themQ fitJ)Iq;�e<R�2rf8CTOZrGCs5s}�0a�T6=0"1*a6�0 �0GC^3+b6 2+c68+d66,�*CC\no�Tnt1(�Oi"xs $:�G�m!&�2,:�0Z��2 !�� _�se 9� :�& A@)��`P�~�Ua7Y��nrf9i�"� 0動�Y_.[M�%� x (o+N�^:�2O=d+�2E s2"�  21?on GC��)�g, �@y�U0T�-2�x��2�;�� s}~(�.r�/v� tom-�a), l64�} )���d�eE3�2��� .�5a�!j�*4lB �a}�3D�x:� 6 6�()0I.)�o3on&� In��is 3D ��l0l`1ectly6�,�:��2}~���6v�m] ��``K�''����i�R[.}]�seQ�e���fg�k�A� niceA but �h"-1}1,� "�)a�+.>)!�� ,.�c-f�-*aDy�>�9c����W: I� is�yJ$rte�; Q�B�� ��V�V"�n4H���lo��a7 e 642�� ? At�xs�3���R� A�not��u�@,�erseT� vic[-�Ze ring-> spa'�xu%Jq���� or���!�A�^�u Npb�.e4e�2_cuX�9all�:mfz955*34�le>�*A��6 �LHA�J U�t pla(^s LR�; a���:{A�Zy /��:6�2m�env!�I���� s>'Zm��c"�ingbYs E�q�;�M�:�-f����J%j�XJ. &$n��tri�.l.]���dne2)&� �2"8�2>�� s}),� �� "P="� "� a ^�us!�*�  �5Y��]� 6 ^kQ .&�wo��(* E���^�)�� c�B/' �q"�8%][��%��j"�Bkoui�{D"jo}�1*����in 6`�mci,i"&�Q. 4�&N  b*�1I�� ��*Vj�p�"2: :2+"fR�� `A�EA�n ` *@q���L�� ` J `�P!�Pe;xy"F;� > `*` } &n �^ eAw p.�R��lemen6�SBI�v�fr&�2"T �s�&o �Ae�A �h).y�a\+o&�  *�9l> rifi��nd do%'  } �IM��seL�u beautiNn�)�s�goo�Qni� !������ioA��( "�) t�Wwi�ne68_B�AHa66�(64$-$1)yH.�� ���vm2� �,F� 1ri�b�6�a<�e�R�(12$-$3) �F5*I625bqrA�E�esL�c�s��&�/n� (�l's neutr�Qy , etc. � &88,Wan�N=,theq+�"M��>ai��ar68sN�bse\�t��sub��1�:� o� �?-�*s-ե�E�i6�v �kev{ lz�59Y" <e1�%�97�7i�7�ultiU�ui� �z���yi�8O�{.@a�J�i�E�, j�/&l!O)� ory� " d6�!�s�.E2-� molec�l&�.Q=�n88}%n�U"�naz asi-.͑� a� 1�Qre˺��a���na�&,iY+"� �9)�6�:Dm'&zH9oɽ�I�ed>�  )W7lin� hY A #F�"�qof� h ad�v $Ůor�)�8ő��abund� ,�e�0J �f, B��I%L1��Cr䆵e�-�"�CHow�� �bC�'&ya���ndA0�:1 ���4ly�I1\�quT"o�rp9 �"ut�Ew"�t �ie�a"]G�!'��etwodI�e�e��0FrapScar2006}��J�1 A�inven���ciar05��-!z� hier\.��*�i��}u-f.z>:�a~nd; (3 B)OM4> > (^@*%��^A���+!]�1 del)68 (9!߈e��EPalJA:�>)�sA B��')\. O� �xY�  !��n ?5X +f�,e�r [!D5s R=#)�a��f<�]���<VI�lYK:l=%�C�< :"�Z��5d& �� �'"� oza���z�u�"2�:`^�!�Z�)B�� =� ds;XA�-#i�. ��Ac) ledg� .}I� g��� to M. Gۃv (IHES%���E� �~of�hop ``GrKE��5 " (L&��August�y5�L�y��]im!��Rt>��99�sbib�@�62}��, N.,脁���{�H �� nd h���2q@ )�b�a�BH, Proc. Natl. Acad.ݓd. USA, 48 (1962), 582--592� ��|, A� sawa, S.,Gguanin�-cyt�� ����2��"� ���i>� 84�087), 166--169.�(Yer1}Yerami��E.,�A��A�[}%9(DNA double-h� / 255�,0), 139--150:g2:gD]!w�e anno�� c P�3 odiuS"r��]N�51�8.�.]� Carl��(Malki, M.L.� ( , R., Exo�in���d��modyn�. �\ RevF< t 94% 5!t78101.�I�882�D�*�� &�Q]J�85 (8)E8)"^53--2657.��} , J.R.,� iKA�Uic r� Q�%�� J� ., 3 (10)%2)�,se� 0052�� 03}  �0Chessel, D., i6!,&��~.�(ASaLL  YL6h?p�J.2(l. Genet, 4!� �3!=35!<2��979=�U:}�.�� ���%6#tein�5.� 3es%b0e, 205(1-2) (S�$), 309-316.�av|�, L!�@turmfels, B. (ed�A"� Sa�!%� }W} al%�ogy+�mbridge.���&s,(ted Kingdom�05.�2�{ Besemer!�, a� Heur�9 Y3to $��>����$�. N�ic Acida�s.!.<9) 27(19):3911-22�S2�} P, G.A.C., Hickey, D.��Ya�=s e/Z��t VIw)�R�� s, Mol. e8 Evol. 17e9�`$581-�158286p� ՚, A.Y��G��(Popova, T.GA elf-Or��(A�#ach Autos�d� IdenԚc�, O�bSys14nf. Dyn � 10} ��a7321--333.�&T �, KepA� F., .�,�zB � Sign%s, �s�a7Microo�s�cS 0�Lifesty0,Bh 22%i$4), 547--56��}6N.�Y.,� *�~2K+�(�v�&� \s, arXiv q-bio.GN/04120122/c@v�:�Fou��4uy �y9: ��{u  7-�@ter��of 143��� >�V�!�{ In S�ao�/} { 5I5) 0025�n<: http://www.bio�.de/isb/� /05/1/.E!s;)�c I� T]C A.My6�8f� ~�.  ica A 353ED5��65--382mS�CN�._E�5icN ?)O6EQs, We: =7 ihes.fr/$m�$zi�/)& ers .<Lj)�SJ�!regory%*�9.�>� ��SV(w� ub��"6^2 Bq�=ic ������vU 4272-4272E�W� X.�+Xu� , KlV�ofs�N Zhou�FQ��  b)�hip� �5Ax*.��and&*  a�:�T\�u%�A�BMC��E�.E $4) 4(1):19.��  R.����� S%�(Landweber L���pl?Ô�E�9{=s E>�� �A�&}mJ�xi V �� � � ogy �:1*� 0010.1-- 3�  GautPUBharanid)� gaviA|� U�6u -� K., >, � C�;sx7%�ZFO�� \2�in 115��f � chem�gABio� al R� Commun� s 31 84) 1097�-1103.�� ]. 6�  Bw MIb6� Phyl�cIAM| iew 49 (1i:� 3--32� 2� pat \rin� Conspk�" Ѭs,��� 369E�(6), 699--712�[,05}Minichini]�,AarM] � S=��X�E� crys}�,!��6s�c�91--2066RBM/0506A�]�6�/ , A�Gorie�'�Jȟ��n�KA?p) �)3."�aH� UZ1c/�kBarray�+EoeP%[7} :2, doi:aT@186/1745-6150-2-2��`>* �,&���SB��0��io�6�%�i:��22|��>d14T�o{"�,}  L{\Lambda a�+  s{\s�2 bD{fo ד�=X bphi  \phiccv-var0d d1�> K .MpsysybB � beq{\P"�- e!�Au�9� U�2�inZ eme�� lexM ed M����.\�U or{Ch. Mo�x(Xd K. Ziegler} \address{"��f\"uri�k� 79it\"at�sF�jrmanyAP�ert{S�( al I��of *�� o�F(M)�"yQC``�Polym���� 0 '' (��title)6E- d]Ia!�4e 60th Birthda� ,Prof. LotharE� \"af!da"d�$An ensembl�� ed m2p� latt�S /onAO�!er|�AH���`rTf;/rOj�#$N$&J" �Ds.� ecu9/�$��*�nj� R�-cJT(ex� ion)Hqa1�. -udy� &�Z:��>3aG!p�!� chanK< �of�BJ�, u�%a $1/Ns�pa��. &��%y �3de�!� 6�-A��hi,�6#� � against ~�at xiF�ut��g���3�Hmediatb��i֜a�YP�bkeE�*�%:Ƥ(In a liquid!Du� v3��M+:�(MM�@b�%med dgpoM,qT�c��EJa8`�4M�0MM%(o� X)>�p�e��degenJEJ assu���4A Bq4, ip�t�KR.1�red %�$d6�;�,Ais�V�IrPaCstretch�#&�$�& loopV:�=A�%$I0,y�>Mm�A�9w(CM_#k� ��t *VMi�a�S\x[��k`N bI�6 sub�@ ces,<�C)p^ q5"쐁�,���l�A�!m* awmi�� N-�4li04,banavar03 4i �ar"�����5a ��=ou&�`r�2M "j.re�2� kind�k r! ">*�)$N$�� �U�D} ɃJ�-s��(=0.4]{ls04-�-Fig_�l A���ona�Q�:d>�)TA�A~����� onp9�.A=?Bq# r�EAnMM�be � A�0e�!ѥQ!�B(cf�:g. 1). >�Kه a i��!^� �e1���y�0�(a� aQPAmCM͞)~F,!�m�fC-sn� �=�'_�/%;�_�1_�9nd o*s e����VN.��&Υ@��n�� E s�+n9�0�X"o� &� �e6%�u�I�i����I�uL}, xbe�l�%occup"���!/ typelIiB�5[F��q!!"��/%w a�a�repulsiv�n2�i..�9ctF%�X6RnA a� \at�)mi >jPcreate a new (finite)o(by changingQtyp%vthe CM| an MM. If ends!�!broke or.2j !�re $x$%�8$x'$ we write f ?%Nspond�q9� $G_{xx'}$)$H , r)�\ively. It will be shown %�>!\= �)|ly %�Hed. \begin{figure} �@center} \includegraphics[scale=0.4]{ls04-Moseley-Fig_2.eps} \end{ A \capA2{BA�0of a macromolA�e.} 5 � An)�-yEBE�herence!�$\a$ ( C0ar-component)IAA�is;@called $S_{\a\a'})� r�replacAGCM�E-uinI' byE�of'$]�3).5Q �- �a3.naCN�(a constitut!|-/!Asid�2�, causeda*:llision �Ma> fromesurrouI�liquidB�ll*se -΁[A�evalua� iA�He limit $N\to\infty%� !n, $1/N$ expan�@. We apply a funcAbal-intA�laeK$(d-1)2�( vector $r$grefore,� $x=(t,r)$e3a I$IB ��e>����v� ~�$ is $$ w_{!�}^�1 ={1\!� N}�=\cases{ J/N & if $t'=t+1$, $r=r'ED$r, M Q s \cr 0 &�wise }.{aA1� chain-���!�)�given1g$matrix $w$e_4 is asymmetricM SQ" but #��\!�!� �Ksumed4be 'later' aloD �Y]A �=lsoFip� �w $\a,E� Thus���e� R same�bini�as � t$. %2.rdisi� �con�~I�UMM ha� | (nto accountAstr�repuls�� a�� betweenq�eu�atE�A��is ca>� veniently!Rd� dN�tmmu�?$ve algebra�Dnilpotent variable!/eta_xA�,\s/ (� , $(6)^l=0$E�l>1$)%�4 $\a=1,2,...,N-x\s$:#. Each�,A�!e�pe�� posi%sa�r,t)$��l� ���. chem� ch L��)$,A;5 by a� . Si $\{6�\� re 5*�CR� result�.� excluW principl� - E4�%ӡ�!�e atoms Y e ide�Ras class�@ objects. Consequ%�,� ductZ$6�$ mustAcY . Weg�~A�MM %�B�two.�r��� r)� dR��1 {x�',2�� A li�� mappM m�Q�R�a� ,lex numbers m  ten!4aneh gralA8aU6 $\Lambda$E�M� berezin} �3x\int\prod_{x\in\L '\subseteq\L}  \a\in i_xsj��\a}� .O��1��W = \L��i_xa)m<, $F$�ܽ�)C�݁N�vanishesa�!��uc/in)1te �����qQ5,!h:�go $\sigme�$3-z� ��!�5 .D  $P_I$!聙�F $ EOP_I�$Z}!� W_I!��] W_I=-�(x,\a;x'��)!�I}F`2� .�.K)}(1+\mu%�M� 2}),�w> $2��qA��a@>� ��� C��s2��nov z�j $Z]!� sum @all�)si�6�$ $\{ I\}$:�Z=\sum_{  5S %Finally8 impose� iodic b� ary_d��saQ�M8 . T��impliV  system'a torusIwclo� loop�� Howe� Qcho�ofRv should no��ru�  lo pr�FTMM; d� ty,&�, "�,A�$&�2� F&IRepresen�ion} I� ��analytic"Y��\ fieldEus4a�F�q�%�maymm-6/zq:�9�=aS$ \exp\Big[I� �:a'=1}^N(yL"� edelta��x'} 8})F;.m u(] . \label{A�1a�eq In�  words�c> unde�1 A� �4{I\}}W_I\to W=�����ie�. �a\rtantaM�c� A�F�> is �we%ZI�probabilA�&a poin#�bed � aa 2/���)1�v(1-v ��� P_I &� ���j�After��m���2�� ��� �H*F@&t�W�VbeaT�ny!� .:�u %\langle�� \r*\�vJ I\} Ձ�G >��|���|s  AI� ��$n(\mu> f �tIn� imiJ~, MUex��sI.�, term��a� aliz�#s A�1=...1:�...W %�z )��|%*�}%�~�[ *��&� �< =�f�,2}M %=- 0 \psi7 1}\bF�>.I` =-C(x�\az$$ �N�2�J1v�22�.>2�N�'���>R�s� )S�X�NS+'�-�S> � N� �')mFTI���2�媡ݡY�,�M� q�of�p��e�beqeed � i� =1 - \mu %�lpha;x\ � 3 engthyr:H��:��a�ath q��xY (n Eq. (\ref�)�bh"V &��� *U n x ��� vphi $\c s"���e^{-NS� x d1 chi_x"*��2* S=(/ ,(1+w)^{-aiq)+(?,\bchi)-�ix \log [!g+ 8 _x+i(_x)(\95 _x)]EA�alogouz"�"| V5 lead�ra���U�:m...\ \ �exAr}^ApV��become!s�4eqnarray*} &&Yo ; Qq = \left� !7N6!n_x^\ast1L ) \r]%� � \\F~,'\beta) =\mu>�frac{J�}��� )}{ %ﲸ]64N � ) � Vu]:� % ,  a�)\neq (���=�� E N/��D{�E�}� ��Eqsq�iC)��i�MG ) de�� G ]��F<�s Y onlyS ough9act�N>��Nial�is enxua" 4 a saddle-� Dž�!large �Hc6�_e��ul�F���homogonea� r0 G h�� in �1>s�f�,�ona��L =-q�2}E� ,a�i�[6"�w�jTLZ�  triv� solu%$O _0 = 6_0=��0=X _0=0�j a non--BA with� H1 F1=4p �lAn!�1ex)����n& ! devi%�Y6�l.\wp��=~iT+> !"\ {\rm�}\ \ . := varJ + i �,-h25e� B; :@�provides�XekeLpower ey. F!m zero:�(D $\zeta* \mu�;,� "� upzsec or�.D��;�+\approx bY- 2}+ \�8 1{ 3} [ -( -1)\� -A%Q^2�  - 2r,69��.<r;s�H8�J�:.2k!�$$$ +\sqrt �{} NOn + �� {(pI> ^5B4.{x'�!X�R� �c%�?  ��$$ 9� ���>xZN��B@b�� X6�JD.�3{:��(AU.],!tl first������ř-��ly",�x$t8U �� # of $Mv2w� �ρar,��y�C'}9�=o(1/N;����b.7 �m��M� �� ́�d"2�#D W�M��l�%7&xdisplaymath} \Phi(r-r',t-t'):=� -..f2�!�:k B� yYvk� Mv�i % \h� {0.5cm}�nd6�$$R�B?��N  _0^{2\pi!f� B(kAǕ6}{2,\cos(\omega)��+ #2) ^2B,R i[k%M)- 0(%U]} `d } v (^{d-1}k} {(�) R��� 1� $$V� \hatv�2�.�!�e�:��F[%\��z� %�(!n)�.�N� *B�n�7 qr���2%� e�� $�:=1-J+E  JE �j cos k_j� b^!e}m��( 8]{l>�)4F�( "�)��*\2r(s� �aA�ex' for 1, :.* ($G$ r�) $oM*� a 2e ($S$)>�( "�'Discus M R! � �MM�Kw+�� &� I&<1M!�# >1dI� �,seude� $N$,-4 is�-n$e-morF)w-topm;if%b& avail� �1?s@$rey(HHj�-MM�"b""-Hremain�.- $x-x'�%)�>-y&�! ay-$|:|$ which)dil&)�� ha=# tendency2 ."��.does ��8%pto�)�#'%t�non, )� >1� �%$:}��im_{|�|?arrow�*}6 -�� Z )t(  +�O[ -i�4: ^2}�� 0,0)� "2> 7( 1 8�-)�8 ]zVa� !�m~-%��sy-/|isB�E:#1�-valid%Oe��/o.�/$i�5ډ�end�sN),A+rib�"&�X�&.2CsDA�howFT0]-� �of�W�MM,ER�6�kific p*$)�!$��a�$\aj'"- YQ+conne4$E C/-q�**q" S="� �'YxV�YF1MFBigA�frac 6 �m6U�%)~�.I ]/ hA��E}..� m th.� s $Gm� S$ agree a�*�<0J � (sp24)*#is un|)ly to�2n��8^,f piec��t lowat high�L�"� re�� ,too few MM on+o many:`�suc(�,mUAF ���! �+t衧rk�Aalreade��`leg an 1)b�(omplete�7lockedŻB,�jag$G$9n_c\le n1$. M2-�%t�0o�a�#��ost*"0t � rmedi�3�Asup$ed!61�=�(ies. Again,!*d+a crit�' Oy �'��:kub�!_-��3��TA]be! stooY[effect(�a�:�(]�"�( �$�%a!!�s��"�!��ere�no�`28+�-W�1a�3MM. A2�A!� veryu9I��-i�,occupied yet*%ѥ��&�Fr2EA+ic��a"#$.� � o�#s/յbehaviou4!4N>%�-Z,ancH��'�76l/Q%%z��6j2 $� $�2e��s. ��12�2}) �0�>z) =&�, {-* t1m\� ( �� ��- 45i} ����{d^{2}k&� 2}}\; �2EN����\{2ك{ d^2}2 + ��-1+�)��� ]� �� \;�'��mi�'I����A�beis �/aa)� 2��� �8�.�+ < "�� 2%*�.b���IK�6sm|*�k�8��a(0��  1"Onumerato� $��`��6!# squGroo& != denomin Jxbe 6roxim|2�'=-0{kA8+O(k^4)$ �� }aQi'4m' 1)k^Q a�2 X%f-1} |k|aT#�2A*; ��v�is�por�% al tm�mbox{c�5e��u�(e^{ik\cdot )m}}{|k|�^� Y+pto N["�&�� l�d} dk\ d !� = #� A[\!(brace{rr�p \, u\kapp�ht  y }_{=.Y� :���w!� A�!2b�1�1�0 $ ^= ��+hea�/.Fs��g t�4 $d=3� "�Com;�y6G8ens"%>s3+8,��7e�6 a random d N�� erD2",,�t� e���}�NJ�We�� stud��!robustn7 2e; �{""W �#T �e�0= �7CM. Brea +I0t ~+� �jin!�c&6 veal�-d -�zj �an�0ic deO��invers��.=-ee pej?m�e$��id,9�, {he 2� w� 9�?�:. J` B&�>can�be � e�5(arbitrarily-�5� du�8H*_ �. �u(��n���~� t�@� V5�:.� :�  � z%R+ R�3��U�A��" .D  *{Reecean  thebiblio�>Ty}{99} \bibitem{degenn0 de G H P G 1979 {\it ScalA�a�epb4�Polymer Physics} (Ithaca, NY: Cornell UniAi,Press) x,li04} Li Y-Q h(et al} 2004 Pre�4Ht} q-bio.BM/0408024H,banavar03} B J RE� Maritan AT3 TRev� d.�4.} {\bf 75} 23JV46Vz�10031F�= Z�= K 1991 �);a A �179} 30.@4 B4 F A 1966 BMethod��S�QqAR'@} (New York: Acad�6�#> �# docu��} ��%\c�5[prl,gv@$y]{revtex4�>%)�,aps,prl+:*0pacs,floatfix3<,twocolumn,super�ptaddAB.Pu�$ckage{�9xsym} .timA�.eicx�@�-B?6[t{@,FIGTOPCAP]{./sub\%BF+) �}�4style{apsrev} A0�1J0} \author{Me7�1Xino Lagomarsino} \affil�",{UMR 168 / IAt Curie, 26 rue d'Ulm 75005 Par�<Fr�A�(mail[ e- -i : ]{mcl@cG.fr} %�P. Jona�A.�dPolitecnico di Milano, Dip�si�@Pza Leonardo Da V�8, 32, 201337Italy} ?�N� p&<�U��(\`a degli S��>��F ��XI.N.F.N. Via Celoria 16R� v �Fg b ��@mi.infn.it } % {+39 - (0)2 - 50317477 ; fax J80a�aU@{87.10+e,89.75.Fb Hc"(date{\todaytitle{�(Logic Backb�F�Transcri�D Network7I� abst�} A gq 2 effoGŵtud�coa� graiwA � t2qn q%n��@�ir dynat; features.Z0� lettx@w D�3 ir \emph{51�B}*�,���9�  b1� l� � �;%&�Ean optim��_(blem. It � olvr7N$ va=,Sgen�(��!levels� $M$ aint 1 !geG� .@al reg�C|N,3,Boolean�A� 6bwv8Cg��� �?q' ( �der�= phas� trol O(1)# g:aVc�x>R0some ``core''.\)/ ^$(N�2�s.�Uy! \makeen \�CŎ{�7.} Idb tyIb=!� arch�_1va livA��� i!IpiceO7 (ar biology.V �Q-�y9 � Dx#)� Z pla�?,@a%>� ertoi��#Mpory�hinery~+8BLA+04,HCP04}. o e)�ain mRNA��$an &�6 step"a�aQ,cess. %% as,�v arly%$prokaryote!�he am Aof2eEb"D4!0b0�*�EK&fa���?%% E��Groteins� �e�i�9 ma-t embodcb^: Ior� [��bi!robalk6�5�ADNAE6m� yeYof !cp� ase-�4Pta92,BGH03} (�L~�1fig:FI�}). %�5pr%��rv (@toA>signa�,�,E� 7ogea) ��cis}-= regi�Mes�(ishiehI��enc�(1�plxor��)��E�Ka.e� R1: a ``6�''-#I� }. S�of6 &ABq�organism�,e now8exploredp+er�FtV _i��! '" odul� A�as u i��� @ !? OSMM+02}!�,% % Understa�JaA���jpa�1� term�I�se �&n e�3�.ch ngBB�lee��?.�EMfairly �~, sala�D.!�e eede!Iis%��6*�Bces, mai 0w#>����.�example,pioneerj�ach!�Kauffman-M(Kau93} sugg� 0ng a synchron!d-3%K upf �� a�g�-on/off�B!x�=���-f�st Oldeb  �Ger�B$ % Microsc��AH"$is well ac�!!W]HGillespie algorithmR D77,MA97}�ctl���qQKen�C"�D(kinetics in� d. Obeh hand,xa mes � averagX � �(not clear w�emerg�( �Os m�  be. % � � $[htbp] \�)�\>�O4width=.35\text]{Fig1� "�%S�a�A!B��@��1*# ( -�. eFF"��W� -}� K� ig -d$�2ae�7nt63(�*io �"d  ottom:q]�d� pE�GR1E�4$ K_b = K = 2$ � diam!0nod)� �, while M( black circ�Os� �.%x�?.pE -� #Ore��]�nwit�+R &�Mwo* F0-�it focusra����n!?�), !� ati�>�r>b�9 j�s�Gm�Opu�- ca�� Ws -��m�e�2ia�� ways, $2^�he�i 6�* &%sn�BV��6$�of���S!o�W know Hust�2E��co*OEAhAn el��C�t���$I-cro swit�p�.mG-phag2�}. Loo(T"e� !�� $uld observ�"�E,es 10, 01 orJDhaps 00,� '11. �U!pthinkA�Œr es)o6��� ruled oute+��63reaso!�ly�uI�takes%�icitly�o��� ��y Etess E``fre� f�RpnAof view+.�>� foglia}y�!�es4n�#.s &a) data�8c We�!*�sitoOWm�)!lex�?reg{Rt�< �{� re��� c$&��o extern� timuli. �  s%�m� (GR1,)Gene-R" )�sq2��7 "`r��i-tB("� �=em�r�sZ; inctA!�A}���%F^f�3 *K }::mpty. � �E�����Kaf �rs (``I�8''5)&��2 me (!K� "�''KZ%A� ains��a�E�, both of&n�uH�7��� s�uB %m�gP�8I%� ܡVb� terprea�P���L1x �? e a &�Ia:͇��H9third-%�-�no ����iX��$�r!7��Yta�;}�ll �OX!�� �tu�byA�e,U��I�!uA�Y]�.&�W.}l!�K�  ingredqQE�a�6��:� �F(: % (i) A s\%� disc!��"�Q<{ x_i \}_{i=1..N�P ssoc�(�% or <�(i�f��thrى�c!�'d6PŅ ese "� �C.�R�8(i2�M�#te�CA=�1�SF� ,�O0 I_b(x_{b_0},1},..,  {K_b}})%b!M}$� 4$\gamma = M/N )1$�B1s�9fu���Ai���a so-�R� �> &,a=ily a�:1���.d��* ][ $I_b$�$%VtopA1A�m. %�Qi�ng"�!Al %ɑ )�_ir!�ba$ �adX���� �]pe1.A8h�? %t!����.)W x_i$=7� or-:}�I%Va�[ �!� \{0!�qUSor eveyUinu�on<A� ral,s%! SheaX Ack� � of, X�a�recruitH# A85V� anͣQa l6N�@energy�}c? F� { ��at �� �=� �CLB05 H�$w)t!�1Ʌst�2�O scenario, , J#A ��JtNI (v>ung $q=1$l>�9% ag�V"�W"� �*sa� fi�8i(b,1)}, .., x_ K_b):�  coord`'o;l)$* i$�t �+��)_$l�R� $b$�/Q�.5#9 ��0A���@r0)} =N�! �,�eq:fpT�X5 !�P $L0)}$ �outP �5N $f_bTP%6let CAAEai��@ pij(.� , �eda $b=�. Suppo�5�R �I���(ird, $K_1=2�T,i(1,0)=3;\,  1)=1 2)=T If,. in�cee:��!�r�w�B 4r%e�2aZ8en $f_1(x_1,x_2�+1$ ? if $  =1$ (LAND5g.em�c� O)e�!�$k_{bA, 1+ K A�$  il!_!J``in-�b��2-�dls�.Man ``out: $C_{i} B c - 1 ��M$x"�&' ڡ�o!{i}����I�9���Y7�1A&�v� .C-*ZM�� i�w`/(Sat)��  A �/�|�We, �,nF����B��O!'' � ��� 5#!�Ri-��us4!&qs ����q hol�( )�,gF\(see ap�6ix A))&&X St�~J�f(r � -s:M9,�AN*�e���(�k�bj utFaX�aUN \ jl��.Jb:(athcal{N}$,a3 �� AK� ��%�a+&� T�� �A�i� %follo�arg %� ch f-5�oK 6� $N-M$ "�.��"1.  .  ��` "� y� s~!bch� �Fd� doO��0y� . �� �!� them` (``leaves'' �&\ &)Gi8 a� i�,�eafTal�� adj&d�-!_͉� aH q 1iVi��m�aLɒBremovO�eeZ �Ai� �Ji#dA�(n]�}�&i �f `a�>MRZ03(a�d��po/ �Ls:�6era��\0��,�v � )��soF �s� stopp/CA��o���E�X#� �Vm��+"7J tree�aA�Ku7�� b%�-Ʊ S"�i@seP_C$�nd $M_C$J�..� imagloq-�mR , flip a&T�ryA�)V �5�NU&D #$/!)Ӂ �, sinc�e) 52��jU� Q�NL�IbyreOng"gX>�_aa.6�iu0|�!I"�YU,� �$ $2^{N-M}$mX� 6�E5��X!��dbec'F# Ef)� {u�%E%inE_�u'� 7$�(ot guaranteIr[!N ew.��� fact%�i�>g?h rY��UV=Wstart�{#nK9is���1��� �Z�I�3l��_e\?-�9m]���%manca �g� �I i% ?p:ttono�7z (�.icile)u "["����E&�E!�a!zfX � ��� �js!�� �o�A&� =���/&!D!�t  !{oMA�xh� �*���y!�artoo:% : Aͳ6@�"a7]�]�K ���o2) a�&%s!� not U��lO% releve[r meeZ��2�r-�![-_D�\C N_- M$�0�moc%$ricW �� of fixC � j $K$-GR1'' >n " B�*o""U�of 0g\re a]aU��# }$ c ��$g� (c)��� �%x"E n.% �,A�r�/ radi��W�] t"6�igu�%!ct!�)�Z Fol,%v�lex�u,��=o�Co�+�'6Epr6� p above:� n 4$N_C(N), M_C(M�g&o$���s�y��dop"� M/N$2a� ' �*�!�" s�,�!$ rank� !�ke)3!��kM�1�"kol;(??�/�% ��: Kas� Poisson-!��4r�.}��A~"l!as! � A $pA^�={(k�t$)^{c}}{c!};Xk }5-C �)$lo lascio e7 fond!= piu' ?? N@� ���7�Fn't/@d͒A��y��ar -8a A�a�. -5em&� O �B��ofd�I��5!Y,�C[ sEX ( �N(m - �< (1 -m)m^{k-1})$�\ 3 = N(-+ m^kA�i�$mq.wd�A!��&�#$m(k)+-:5k  j}�= 0�%2b2*%] %�:)�p uw%8:%2�0&&P�-U�� 4�[. Q=q,> �H_c \simeq 0.977$ no} ��!isy!�typ�(�c (� or UNSATivc 2z<zdz 776$[�BJ wqs �� AMY� ol $@.� (Ior � � NI_d��c�2O$O&M. � M(�?)or HARD-.})��!�:pd�4�NMA 3� �Kev�a,e)]5�a�%qM%� ��=�<  _d$ ��6&-( 1 )m����� 4> ;cAH& Va$ M����U  0I !� T>�"� R! �G�'�#�mo8&)7 s, %� A��Uuag��.���lem-th�/  monl�x�r��sAZ,5�%.jZ�]�_ўPZ"!�b) "%)��^6 >3�"')�C$f)� � �=���$\nu$� ��multi-ͺ�qC e�� jump3*�;)1. J>#�s�!�R�k$#Y� C$��K�^ nega!_ s,�*sH��r�rt�en� t*� {K(inset�!4i��� . 2�wi�(cutof ��sk = 12$><)"�#>� FurI���F" I0�|rigorousP]eh �.j #edt U�6� ��-� e��� :� .L�us� 1W3� IZ'-���h�Q@5G�u�,E� .} � �'Sn.im} $(c�J��*AL<�0� xtenks.� =e�'M�c6�1+QG!�1re1 !N6 (j+!ߩv<.Ͱ-J�� !�~  �? FRa p�=a�mM,F()+-�iwy;� ��# � !nW:�wby ��barrieU$e9;^i�!7��>tonal)1:!6$\Sp�H!:�#,f4 xc\&� N ( I + S�EH� S� a� opy,�R7�� * !I� �& A��%unts''�F�*FEbt/Epio�" �is �% ).6at .e. ��Em�!]Y�|ndA�A . IR)K� ,(or)s� DpSpdetai�9��s. |)r� a0an sa�2},�1MY b�"s�z:�| *E9 �I�h��2�2{AK c�ra quali�/ve 1:!��-5�  �f 3ml�{#s Nn*���z(nota_sav}. �zpar� M2�ŗd .} &D+��Eq AusK$get �th"�*�1) �-n:�Ai� far 4,h� o"O.� "O }b.~coli _( BiE���Ae���EM �` lawaC &��R&F,ly;,+"A�1&�AHin-� | w vary*�y- Z?&e$p(k|csfGH(k��^c}�h apr$aehed� �IaAJ'!��$� lL�A�Gki�w!Ove� �,skZ�>� p(k��Y ,al 9"i*�����o����z�!��wnaD=8�^!�$ N_C7 _{k (�M,h$_ {k _{prob w�9$M� equiv � 1 @,&/ K*3ZN=3 \~  10^4N� �:��.�M�5on�:�6*nt�g�7"���,3 ID2� A�1m?0��.� � ,{C}7��  ){e?YB,�new� � inu�I 8,.influ�Y2���i�)� ��s"� - phenja�Drst��( i�\ glob6�X �,�|�znde=i�!B<�>-6��}2 a�t _{d�{o�d!je a�U b�O'c3Its%5�-6 �J6W !��r2 ��'"*�,"zW fmCa!C5�r*, :�**;'����&f5B�>���to"! �Ca�i��, !iva r"�*�J�pd!AZ�Qq&�,� -�A!�ib�!�M�C2 pas�1 om unsolv�X��D�o�,�HT(gaz A heur�<�an� O��� -;ta^ve)��a�8t�@$N$ad���[��;mf&r{ �n � %�5&� c reby�!]&�1nt a����^!A/l&3 "<|)�! -law�mU$�$6�)� .�C&Ra'|>?"�@�� frame�')g����Fn��dS'- z2ly - o�.�!2-��"�� . A�:�eis y����F�E�/in�j�j:�"3aqrea�!� environmsA�CdL03B I0'�Gh*�F� natu�fou�7> w>&�{,!�  �&��,rrinsic�S]iX)s._55� N�u�9��.�v��� 2� R �\���a�A�A9� �/f D|.�{Jam�2)rita�gIFB ��(���b �A��C� ,�LUJgeer&�e�� ��H*Bpr%u�6$�� s*e,�%�, Dp~*�I tes!�Gu&VF!_�u�achj�0e���newP�l�^!or~+�6UQ fij$� Is���s*��d�?�.Y�It�b�'us3E�[�VYM %P|&Ame�deGthan p,6�aza�-aa�u@�p�� evC#* };%��� t �Dye} a"E2�i�Q�)&� � .�G��+F.gen�str^��Vly signzeaI�delF �ce  ��)�AN*�eSQ� *d)�� R�tA� � c�Giour�ac�8M��!�w�ccur�YlB-Qng%c %=��"b� ac�c:�N We wB�d�$~<�?ng kM�J.~BergPM.~Caselle, L.~Finzi,�Re, A.~SLhello, P.R.~Tenwolde, R.~Zec�#a"EW`"�#^bnyma8n/eI�help im�ung!C manunGpt9N>� \a�1 `[*{A �Q��{A.��S'x�a� lem}�"U B!���E�� "r@A�4�ub�mdAeda>� a >�3�fR t $N$ JArŵ���g$O6!njunc��Ja��m (CNF).d�8�" �Ls_a�\[u��%.�� ($\w� $) �O$A@smo @s(vee$)�EquV (8M�7)�>� alen \a�XOR�&� o�A�I}G \neg�<J8\dot{w}S8�W3= -�recV�in CNF,�H(M6���IA�}6$��. �G *� � mA"� ma4x �6^�9"�8�8(t �!m-"�(truth  N�!�7{b���R*�A��z�j)�6$&�aT T�� j)�;+�CNF �. Vic7Gsa.2 W�g��2 �is $0w���ulaB��bigEi_[>!��%�, &s aZ�3�Dl _1,.�>oo�$O��>2^Q m .ofe�� t|a�<�#!��C! �bm���H%Y��N� ``force�=.$�;A. *4iC�(A%*^�5�s�6c9llowed"�$s�� is m]j�ce=a)��H�o Sa�.e&"���� !c"�/���� a�2^U� "�I��wf� aҡ�a �,�: KK}��_pp +��hA��4%+� s %�sY�y��sS.ed9G�% s, �%�V� !!�lTPV 6�8 B. A NN"� S� s} %qui��appB���Bu�ke"� ��\a9/8q]�"D_AW84 $ \{ \vec{I}, f} \n�=/�N- w��q�64x �(>Sc���c{x�cde�}^M�%�G��; f���>�=K_b)}Ł �82�� � i:�b�n�# ed:  Dh"G&[ � �� "�V')+ = (I_�m .,I_Y-� ON{?; �C�+RqUoj� ec{f}= (f gf_M) :� � �09�Fid$QR,. An overbar� bar{\ ~}$��saBM�on%>�"B-� ,.-�gp f})v+T�cE�eyB�4frac{1}{2^{2^KaR<{f�y�F[ /%�f}) f xa�a}rhoiF%Q e�=soF�j.:� 7�9��)� ��x},I}�I})P �h� \Pl(Z ��z _{1;� 0)}Uu(1-")#06#F\k�,�. %F_ s��&�6is��tGRq���2%$�:�q^4 >a{bGTw} "ath:�d20A�b�d\ifx\csn�natexlab� \rela��f\ #1{#1}\fi��aJGbibO font>J!%def8e#�Pf.jQ$�R cite~R.$�Rurl^�url#1{�tt!O%8{URL Id�mand{!\$info}[2]{#c�>!]d []{S'�bB^ em[{2�H{Babu et~al.}(2004)F $, Luscombe Ar% d, G+Ye>s and Teich��}}]Z�f nfo{�c}�5�{M.}~�1��}}, % j:N>:��>L>> Ԓ=B�1} } {anT0 ~�S>�=K , \e�a�g.},J�i)jou,}{Curr Opin �B Biol} E�bf%s%J�me}{14� pages}{28�\�year}{A�)�J? Herr�RjC$, CVtAEand Palz5A0H�^�Aޚ1\)�~jB� �1U���B>��>�.�J� Biot` ol} f�5��-� 70} ¸� #�� landland HwaA��_I�yV�B� V! ��U>;Ge�ދT>Ṕ/%��?�U� Proc Natlk Sci USAn�00�5�M� 5136.�)�20DfAShen-Orr.�2:�$, Milo!�Manga+nd Alo�DS�_�V�Bn^Ն�R>i��;Bz ���BC) ��Nat�W>t�]N&31�>�64R�v�McAda�a!� rkin�w7�wP_fV�HBt Q� Bp�!VNA>N ��‘��9�^.�m 81J; 1997��%zJa�u 1998:! , RonandA�5 ]{ARM98�8ھ�J>Q���f�,�l�j 2�5�L1�`n�49!�.�-�163J !v%�%EJ�"5bA�7E�.b��D>:IZ�J�q Chem.j�8e�} �2340 61F�197I�^�K�c�93a�K�c 1f)B�I �šuD5�{O}rigi� der^9Oxfor�k�n�F}!N�qRG�Jf�� henson }]�r�VKCB�erK}ig!�6� book �Art]\ial {L}ife {IX} {W}orksh��a�, {T}utorial�b bYMezardM �� M;2!V�BQ VR�.oVNB\�a�]�u�"t�t Ej 66>@p� 05612V�2r�Mer�7=00�< BFi���Com�T� �9Eng! ^��w& �3J�20��E*A >� )�,(si�a{9�]#'~+b?6�V.G>h�siad!M�� r}i��yN�Sci�$j�297:�-�812F�ʧ>� -�@ Ricci-Tersengh)�6�|D�!u��V�F>�:�!�2�~W��KudJ Statixj�505}} Jc�C Se�M0so S.~Cocco Q/V, Jy��Letn� 9l 047205 N�3})� �#C'�aleB�X0d-mat/0412443j��[ A�[��85���[�#OR}EV2B� �.�9� lKrE 9�m�211�]>� 1985r Czx ~Lagzx .<5:� R3,"}w�MJon��\™Rfycj�B�B|w1x2�m�jPP>� �:SB{2005})=�Tnote}{q-bio.MN/0502017A<)tem$W<a&&����\a�m*?* *aN}$�1be biasT%�!�of\IepH|,MPV87}(AYnw�G�+"�H(xR!ct&-/Mv�0[uI��){''gU� log{.U�usu{" �ed�!�repq�-"i�3}� &�0�6 �w�!'hav!Z��=�1�aled}�%g��S� r%(*xP.*5.+�? leq ZOr&9=K-�"�"B�=e�.�Bf<�'�"�>��!�a self-)�m#/ty���>^and�5a�of&gb0�� �);aS���4z�2� % *�� ^{\p�,�c= A"�Tx};�!'B \pnd ��tTaE}A;�/ :�(9�[= ])�}�:�[%$}n]^2) /��,�!)=van_�)�S$m"|Hl�� $N\&m��N� -apl�;jH2�/GO���()Ayw\�Yt!�y�!�nne I.�mCjb �V�� �H 1987:H ">� Virasoro���a-iaVlf� m�"� .� VLB��� B��� �k�GS{G}�S{T}B�% {B}eyond}!��*�Worldx en�,��gapore.{�!�#n�8-s5�:�!,, de~LorenzoAc��Ouzounis!�C�2��f�I>o\��V>;�@2�&H V B �>"N�T�/ �u�/n���� 48RY � &7>(van Nimwege��vNA�UhV�E>C2LI�q�"� ��j� 1�*6 �479j�b"�A�4� Kau� 2fbB�J},F�J %�+or~� 23� B �581�y�ix&���> # �:"2� «6d�{aq8l�*�!0�d \widowpenalty=10000 \club6 \new�N�!tdots}��,inner{\ldotp �!���d��F��S�y Alig�6# |Bn SetKÈI��{Alexandre H. L. Porto\\ Valmir~C.~Barbosa\ 4ks{-s�� F ({\tn�4T@cos.ufrj.br}).}\\ \\ a0ersidade Fede�8do Rir? JaneiryPr�n3�� enha�4de Sistemas e �Xa\c c\~ao, COPPE\\ Caix�CTstal 68511\\ 21941-972:n0 - RJ, Brazil�"Zz{Dece3910s�A�6a�)�a"��W3rnm�ZQAh">�(��7!�a5��( F "h{�6e@.� . c� 5Xr�IK phab�OQ� also �;h�W�|"�*n0g"�4Odf��5S mpriJ? _p�&gGh| &5�eP|3-ޖ=9b).H aid��^�t&�(,�Ee  suffix-�"`'�cj+:+�.�?�d��  guidCM:;-Z�!;b)]an�~r�3e�N��ll-%5n ��MpE. Ac% �`z�)�8 �3HBAliBASE amino-acidN-:d �9�3Ndw1>ose yX�fWK pr��=�8es.\\Ŵ$gskip \noi�t ��Key�b:} �C�%�6,�;%N}�s�Hon{.o�}9V���alm��L-,�im6�7�4X8%"�N��a"��, %#�=�<V,5-�Ldi'�\domI+&�=A,& @f}�&Y�Efu%5MN0 fs�[�c4Srv�J�/n)� j€�e.ab� , 269�8��RonNPlo�8w� �i�aF) se؄ng����m���1>r.�xnY,viewsm�l�LE�13�b5� U()hZ�.�w�+f 2 ad o 2(X{g97, g99, ltptp01, ejt�\1-�!)sF��1 qt�!��&�Ib(er.8 $s_1,�Us,s_kG2aT$k\geq m be d%1��s��;n;�5!�v=���1i F�Z$R 49�igeS*8A�-�s2wA8��Hl$nO��s]32D[i,j]$�S$1\�ik$E� jl�P s ei� a &X�MMR$�X!AsYral�:�s!���p0a gap�T&r.AHfixA@$!�J5�]$j$ />6 �r $���;J�P$s_i$3c�:if6r�Z��p�tF mj�n ��, �&s UG�=�U s���;!��6:�"/4at�3s�.��c%�Not2�at �a x\{n27\})� n_1+v�s+AR��goSmEr�qiL(s75, wsb76}A?�<���F0st�~����y��$:&�I��A�!+� r�9rū ��i�F��a(oj�Feq�8HsR��!�i;E�n�1�o90j2�, ABa!�e,;al.sE�maxX��TJ�� r�\�Ty�RF�sA�a���n-� g99}0 n��m g�g�"{:aHo��.��1�*?:�5 !�0��I;n�Z�?�5�8+&9i�I=a.�%6$&�C�ct�CayBn G�is$�!k~0A �,dms98, s98};Afac�S�� i� NP-h� �wj94, bv�tjmD FeaM�|�a�T�QW��Qn�?t�J� � &� �A:O" R�in}��sm�� dekm��pJ�b�nrd02, n�Ip+Da?Ew� �>{ ���%�.@ "� %�!�B> ��S�bm � E�%oll��Z� )��1w� un�rR$ci�Ye;#ma�a�hea)9�l�� e�� b$Ad�@cb7%xG �M�xC:Ocer�5"� �[rG sico���D!�~r:� mmonM)t86, t�vvp01��� � iar"�wp �sCof�� ��N9R$��)iA?  � o h>�h!� conc3Y�o� ly uÌ}vH ��ho��i��kes� ect s�d��i!� nucleoti"�a���tIE@� �� "���r� d D" a�N�;!j-ds66, jz8y!otss90, lb93, m95, k96b, nfjwn96�6, wbiaE ctrva) lfwwa� �E�s lie�!~ hear4�  u1��cf�� y doE�oApo�Y�=��K~ Ufv�E�� c�]�Vc1��8��<beG"� � a�"�.��~2Y�ly�� rn_! desix���� � TPN�D1�6�1!� sKs[F VǖrDI��sm8!�j!�mbrzh��zhm!�pfrar zj01�,�HFV�qt?��Jv�?funda�� mH=E link"r�&Qlr�sha�by grou�ʕe!y���&: � �Di�� 0a�� � p��� rganq�%fS�e%tsec-new�}�Qye%A�Eu �L��3JFA�}!�c�B5�to�P�.��we�lcEp��Bh1I ia2�^&���"�8!���KI<�M &�'etitor3?�fin�V �'��EwB� rem "�S6b�#�e.~���Gs9�e�.}A��%�5�.�IՓe�u�A��*��73, g97}*&D ).�t:�%x��A���og� ."% A|I$O(6� )+f�#�"�� ���N4�a\s�C� 3���o��m76, u��gs����� ��"[ �I:�� sc '�pr�poppA�AQjPa�to assKi!>a��I$u��cW9&�:� �*QF�>� motif�z7 Id8�->%"�p"nc]�)��N�� al �Sil�iesw �Hic�tcg R���\�h��2ry� "< J�*�Ti�: ��N�|a��t�lof2� MX�n��Ba�N�y���X� refe�DF� bjeg� rfpgp� sdA>��!!�"�vms99)!�2B.uJ���U{D"�b��ٕ} �y$!�"C}}=\{C&\C_p�� A�q$R$ ��� Fc_>J\� O p {\$:�`��0:�`a&bt��!��  $C_i\in2y�wXDgJCxX�s� A-~x!A�!r!��i�* .�s. Lik� �I�Q�6�a�:aW��b ree;L h�dges �*�.�*mE�Vw �q�2Jkfi���>�� mark�b�Rs~�ita=�4"BEYit�!5&�Yn:�#"'iz� j��AaG% � ���Vcviҕ��ͬ� children%g}�2Z^7UUF. �VKTmpt��:��j0 e�9����&2��G� Icon��E�>#T�5o��2UJ�%�� (i8�`�aq,�� l-�� :���� � �).\foot){T�9� m�ql��lS� f� c�o'h2f'�J6YI�doAs.U��y's s�� only�Y@x9Ki2��P$�%(\{(i_1,j_1)�$(i_q,j_q)\C� A%%T$q\ge 1&)c(i_a,j_tj& a�q$,i_ '�D (j n_{i_a<�e�)�9-�a�%[5�7]]J$s �_^�Q��v�8��]��dq�f (�e/'�9^��T� $q$�z  �^��� �suba8�Gdmv$.'x$�f{c_1} r)�{P!`&��tP pathIt � �}to!,�+luOi6���T4�@.� �\$��j�a mo]  * i=1�C.`�� �9jZ�]M[R{y�|�/\�u b�r$� �V.W+b-1]\ Q!�0f(E=�)މhA � l���p!of!{cF)�S�u��W�L�aP} shor$.� en &4CI�a�\-a�R�Kingleto� Av:��\omaWm��rQI�NB�^��8�se�!�it `Oto E�y, �o9�in Ղ�8͈i���t� �zPi8�#��EC� ��Ac. EAYE$zݖN#a�e Em�in cd& o�Z�e5��O���Ep���  � izb�)�%c. E� �noOU�Ol�Y�;� p�'s�ca1�[�"�r��W^/.>�zY��)�� , �Y�]Y b�7�s.�$!�[ Aq � ����a& ��"Z�A=9v).�!\���ɔF)v2�G�ee $T$�! $n_TRR �p&��" sFoM� �zE�Q�a�� �pKN � �/U�3n���J%mj�MS�&L t�}}f&M e�hat"O C5a` �a!jE}]!�-\co"�%� poA.� (i,jIs i.e.f ��n_i$.[=r� $ce� alg�D-�-�ݡ� 3�Wb��6� xD_C� �$CB(,�" d $Db" ��� )� -)@*�s�"E*� i�6���eck whe"! $j_a+c-X!� .�q!��V4 i���EHQ�.2B L" �n&�!s),f2���ach! C$."����$"��W��. W .  -\. W#2�'m>�\mid D_C\�%�se{ 5���s� "$C,C'>L'2�U�� teq D_{C'~ do >�{"2@C}}'\setminus\{C\M3 N�29�E�%�6B=� )2�M$v r�t��& 0 !VA$I����*� �ts2enof:�%_i9U �2��1>�@^ea4�}kb]]go= Step�22}�� $c+1eT ��c$. OaIwis��C�$\ell�w�$e� t3!� ("�V�u)k -�; / cZl��6�. Also�@im!{:�'�).��u $v_{C_i ne%�$eb>�1�3n � ��V,J�9��)� ~�v=w)\1�6�N<3�9nd.� Nɡ�3 ^',F eR5>R� :�$��oa  $R2�c*7!)CB9����~ s� �6� � �}�N� 1&'�uA�� � ����eȑ�$�dor�\non undabaA%pru�e26��'�r��l�-h65L� �up� es (�!ing, n� i�k0� rger͞"� ʒW!��Figurei�fig-1}�k 5 � ���Z*K�(R=\{A,C,G,T��1 d 2=\{T,��,�51=AGCTAGM�H$s_2=GGGATCGA$. Had��s �2� 1}--.`23}� �%as4-�:p!���b�� . n�$'SIep�inE��!!��s��u_2$ (��� adjo��G)e�[a.�mn�<�2wm�u_1+(�0�~�5{'"r��92]41��cu�A���>�,͉�s�wni A��lߒ��� ,A�șed�� �)t[f: e �D;N�A�$``I2,II4''!k9"m abel& 1,2),(2,4&���&�� ��5 14 If���alm�p�k&�&e�>���i�'W` ���/�at����ru�$O` (n_T p(:�$+p^2|R|^2\�-)$hAq�) M>F =$�^� s���!e S!�|l%�*8�d�0�-by�J�2}%6 h.LUohe �kst�YL�VF�s��ri��k��al/e�!�_ y[-!�e=�X��s:�,���)�8 eir�#�4it�=+mA�*�( onJ,����If!��cO."� worst cas��e. Let us then probe a little more deeply into the nature of $n_T$. One first important observation is that, notwithstanding such a worst-case possibility, we have found by means of experiment�pat in many biologically relev� case)@e expected value�8 grows polynomi?,�1onent �t $n_1+\cdots+n_k$. The resultsS thes l� are shown�!Fplo ,L Figure~\ref{fig-2},%Xwhich part (a) refers t)�tset cover from \cite{i97}, her!�no�Pby $\mathcal{I}$, and U (b�V ss90rW,S}$. In both)j, $R$ %�e� 3 is a-�tonAC�:�)!$is constru�*is� !7 / !�k1�on{. N�theless!rB� can b�0 gard!* �EE]E75� d\Sigma_{u� S}}$ �(correspondsa�trivial% titu%<�AM�S(R$.} DashediV,K�y,uh�@ alternative vers��of!-5@A algorithme�all�&it!] clea��!Q�(' linearity�s�ecta�%two log! hmic scal��at,�m�,m� depe! only2�,P1�('s length. A\0AJ\, but it also seems truM2u�s above� occur K��Todest amounts. \begin�� ure}c��rptabular}{c} \includegraphics[�=0.55]G(2a.eps} \\ ~.b.endj \capA2{E�3behavior!�܁�I�j�under%fy�I}$�ց�]�$ ��aɅ .} \label� -2} �5��}5Gt�=57+�A��-��fsg)�5glll} \hA� C�/&:�.��!o 4$C_1$ ${M,I,L,V\} P \\#2  #,A,W {A,G)3:)F,W)D,E R4:)A,P2-N,Q-5 - D,E,H,R,KTS,T T6 'S,T,Q,N%F,W,Y\\ �76(, �,H,K,R ,+8 +Q,':~50 �9 - �X:1C,F%eM,V�h{101w.� �K,N,Q,R,2�{112&6 �{12=135K455&5G1]Q6A,C,G,S!A87 �85�Y�e6Q�q_h u4a_mO � second b� rel�to our p� red )��Sec�s)@sec-newheur}. In�Dbest-f�]op2v  st2 gy�b scribed^�s c (cf.\Fq testr ,well), we do����"� scomple��2ra> ���ipor. �feeto re� �. h%Qixe�ɥd most $M�O Pd parameter). Achiev!)�� require � modific� {b� : we add �8air $(i_a,j_a)$:�$D_C$�-hs if $j_a+c-1\leq n_{i_a}$ l inL� $c M$. C o we now ha�Mat�q0is $O(p^{M})$^ refore &� \$p$� I4)5!/�yM ({AlignmentsN Հ�Eɀ.� F��2�k' 4$, let $t_1,\l,t_{k'}$A�� q !� $s' s_k$ suchI eachGaA a.;A54a different $s-R,$ $)ha �')i i_  $. W� ll $\{B��d,a block. If ��A}' �n a13�N� +4ng $l'$ column )�sc!�oB_, d*�S("A}'!�is a fun�',Avbe roducedcrtA@ofJ equE�} T6O<=\sum_{c=1}^{l'} a k'-1  b=a+" &k 1�no grea7$than $c$ ( � =0$,a�nexists)? similarly $p_b^c$.��(i� ), $�5$ Fcontrib"� $:�%E�Av!# 5s6�%�i 6%��;) '�a�2L~P�gap���n��7�%=0$. O�h wiseZ��[$ !�d�M mine��rough����e%lonceptuq�.6��!�Ne�>hA�mba numbI���$mal global�6local �}�)�� �b bg� �p-�,-� cellE8dynamic-programgmatrix�<d�y brieflFhow�c ��found, �ioE�T�e�th%Qit3ex*r large�,dms98, s98},!��� exten.�procedu�\nw70}��-Q� of % sw81%)k$�ce}�Dute it efficiently�w�follows,A� spli* �)�iD|Vs�Q let ��!� U_1(�,�Y)�OU_32�YeiA��/0ly normalized!�.&�# � withiɔ�^NbNb^ �:N�@v rA���Ka! quan8esΚ��B�='=>�=0$ (no��=mt9� N���< ��=-L$. �=� u xa�a.A��nsider, �(z\in\{1,2,3; selects�� U_1$,!2{$U�� ing,g expla��=�:�Y �2q _ $:� itemiz� � $U_z2�>a��we�w�;=>`$. f}R .} \[ �L=-{\textstyle\min^+}� \{BG>�BQ� \}, \]� we�� [�?� � imum�a6B argu�A nly.`!�%�W�G�:�doAs� o favo=u"p6Ito:E i�ytoa� popQ`inu��Z2Y��* to pen�}4 it---heavilya,nci���� parҝ F�]ss so� 6�no!igXR3V. Fin�!�Q �;yields B~ � Fy is desig o "� iate 5��*�e��$T$ m- ��sam� . W�so� subt� A+offJ��#og $\vert :9 $ obt��� DAo� 1sA/$[0,1]$�rs.$1-k'/k�� seek�8p�4lege (decrease�by� maller� )�%��� ^ of!� s �mG �!�a9��so-d�ty&�.�E V� .G��%�ed� idueE��a�&�awr� re,s�3^�Z %.�6�$!2$I6� A�,�9$1->/e� aimsA1�AI͉�=6�s �  ar��?� ���>ђ&�:�=:�-�� (2-\!kl{k}>���) #E�R�}{2}.>m2Bm�remai�E!isAE� A?devE toa� crib!$� heuristici;4 a $k\times l$9J2�$ h!�q s� "3 ,*�"�FC}�A�MH alphab�L&��Zof Fy play�ral role��� ssum� � "�s `&�I.�s.exceednaOaF  intr�in N�F}��Ad�ho9usui�%,�B)&�G�>u �I��o -�GA}��"x B}�@\�E+{B- e5�R<- �} ��st��by ���a?2k!� 5ɝi��i�#� ��emptyseti��uga�e4$A)  newT{y�eo!�Niz��6�^�ul I�b� iyet.!��11 �$N�  E� node $v�A�� +o4$e root may&�e���#!�� n_v�X��o�ustinct�!qy�M� ssoc�d ��l WMWcommoU efixM�eTttie�>n each %��)vW4"exclusiv�Yby som%��i\-�$yxas� E� �tal��$at least ���E y 8������!L� S&'Y A}_B$-�29B � $B$'�).�e*��U�eds� H. F_!:�E�sorA�in�inaJ� ordEtheirM  1� ^�a}!A�Td�%$�ix����-rank!r�. An atta�E�fmad%Em JY[s)? $B��viUngCͯ! -1=�! �!��)�!�� u�any���); es 6� _B�h(st� >acT+% rowA�6ad�EYat ~. I%worthy ��� � �e�$�"c��s nal�| $Bc�I�n�$emai�"ny6�s'&w � $Qe�seI �. to��irr. Butz ic� �%B �in 6 2})�inu)�be eff�B1��$ Y&%0e>� U�#)!f expa"$$B$ involv%< mparA*� !c�Z� A:�*e!*(a unit "��W� spec1).�'� veinA%zcandid �y_bas�ol��o� ir-J�� !ma �e��� cur%�AS�h�!,1�6� E�as�d&�Hhelp break ties.} Aɠe���e�s still� ing am��l��F�� disc�& . O )$v�&B�U���t vail�#,���a�\erg� a6>(w�!dinkT6a�(A!� organ`a llist). B�*ope on1 ek e2al i!:��-*- Y�'� ��"P If-�,�Fave-%�� criteria � employeda�!&" xE�� alread-f�%1:� 2}):�. .d !x: a�� erre!�Now say ~� ���@$B�-���~)!K �'if-�)MQ�B��� a.  A�6��!^�.ce a non-{ �c T$ hE&��ed� ]���o.�Bm-.!6y is furthe+#u�b!,��o�o�%8)!>�s� "�v7g. AfteD�6��'goA{ͼ fix,��e^d!b �Z*�(�� ��=Z�%ҁ�w/n�y�1a�ain exa8�-&( 6� >�  !V�,ow��a�"��is �� )C$B\in&9+B}�.!-�%:unr~#��Mms�by ��~p � ���a var.!�a semi-g�$+���%M�A_B�1���$g97, sm97}7N��Y.��=��V  E8!� �d5 is�Ltra�forwarde���� es:!T place� �"�,}?Fosts. As�0thus d���B�changA����_q$� hS!�A�� � Q�� �!d� etup� sR9n����ragm\e�E��cremN,� y �1 e`eB1<0$��I)�>@2 {B�$a/y �� $B'B6%= Bz�2�Y)$*1 One techn��"�qsi%ll �w0ve at . poin����  $kJ]�s,F�g longer ho�asoP�'* �A� �A"� term�d�� away<�ޭ�� 4di� on�D$2Ŷ like� �( ed.}��%E�of�~Y�in� )� B\�letV analog2!WFE[2[*�}'� �>'As} F'-�}[Y[A��w��' �s!�-r�� c. ,eQ&nonneg~G%9�Uat Q cG)B-4(�p� !�+r��a lower�@).�4Ez��ph�� &we build�we���1,cyclic direc�/ $DRU Mani�-q 0approp�;!�5"f#ly&�e ��5�=���:v(����#DE�$2%$\cup\{s,t\��sn$vr� alQ�n�_ edgeD&9 wIto�J�?d� /'J(D$t3ov!t� inc� $s� t$, i��Pa sourc�d / t'D$�2��2 ly (i.e., a�outgo � ainc�� t$).m2 al<f!"�de� 9A� me %NC�je* manner. �*B,J�!HvB�%WH a rm ���)A7 fg !E� � ]�&�! >�ay15���]Oove�6�en2��' ��AɆ)mA -d�P"��,ll� cp� �* . Ed>5��is-� lead,�4�*[ n V . 5)EaT(a'��a����N xT onh"�s+5rg . S� i�8�Q#.%r!TV*� a>non=)-�� ���$-x�,��$x�dI F:9A �ve � -se�&` )�e!� �i�e�i�� ���.t�!�0mM���� )� betw�Ѱ!!� d�z�upl�0���щu �F���+ � LLl�0$��f.I � ��:� x/\sqrt{k I�T �;M �!�.�.�, 6$�*x�'-�/���o&!W'� !j�-2�Wark, j eR��� ) -ass�/, methodologyAxv4�,_t� in* zj01}E�  *� bnw�*unt� instea�:�s4�*Hati�N�'��a? : s; E���V.�$h u w ��fi��n�$-to-�"w path���})9edmJ!+yst. S -\ �!#= �:jd�� ly k*clrs0�=�� I/pp�9ng��%��( � mmed�l.�6�-��s^�w2�$� 4�� un%�*� �I!�/5 %PA�-� a!�&� !r%�oA�q "mis��@�/:�A}$�"�1+>#A�b�[6M� ces)J4;�N��"#�t�appli��.���v6��to7Y0�lD%�..B.��<:�*s�-�in��#�j.�. �B$2�2k[�. 6�ofB i�al�5��!VY-s�By! ��,o i"q�  EP� aN� >hNN���!��>��m���Ei:t "#-!I�aM*< ��. �*� �I,eU� � t6�. e(�^!d&�nl.AMC�u�Z� aQ %provi�)&EH)\ ,�.���e� ��.�a�.(as oppo�to.})z2/is�CompuI!"�C2"584��/ndu� Ae�|DD2!� valu$!� aBjof 1" o3.�6 . Ou�U9�b�b`BAliBASE="44tpp99a, bttp019� q&�sets,�< �&�%�$E vis-\`a-v pro�nt�roach�nam�� CLUSTAL W�,thg94}, PRRN 0g96}, DIALIG mfdw14m99}, T-COFFEE 2 nhh0�Da�MAFFT $kmkm02}. S�)cs-�$)8�`ubjP ] � �studi� $group ^%Jb}Hd���n�Qr!,y$!posalѐ:�vri�($167$ famil{� .�>Cdvi�"\ &c0)�� f��i� �BI8ha�fEG0.�F8.0�F0< 5-n311.$ & $6  1.3$.41�$14 %2 6jrH�Eula!��Bi �RJ.�E�, �pO)*of�� G �� s� �6 u�{N�O�P3�O 5� �K�+A{�12U�,-E�(5&e`c��als� �� y 6} (see �qwA�,of ,n�p�.F�Q6���M�J *�2�. Also��K !4�L�&)Q,as ``x\_y,''{``x''!se�!=����M$�el�O(word ``allB�5 ind�E�$� Iful1N2�P wa� O)�``y2�``c''|``n (!� ``c )ct'' !�``a%)� �2whe4 �1>� accor/��Q&GI$Ftree}��%.�N�-X?-:I%< . (!  would be e�ed %�\_%"!�altog �absent,� %��(se�!�Zn�%��A3� u�v�sQ��fre4Ie enti�i��Kim"0R)���M��r����r�N83�N3.�N f�N/��NA�S'� !S� it�Ge�}���N�$^}���@o.�4� j�N3N�1d1e-e�t4.t�s4�s�s��qnq4�q�q5�q5�q�q�aJ� ����M�5rr">w9Y�� I�=m�SPS�CS�  �( 1�J `�/�@ed. "�L�cho[��2\_��eq.�~���M�N��:U s neGIalwayf4W/V 4�N ��I ��7�g*]*�%cJG� 2^�*���7"�epi�?iNK *�M{>� -٪����ea�Y�< ��often,fS'�X#3�%� of R"Set~4D��t�m�/sU�U�"� �P�I}%�IIgF� B6F}U͊6.|U&>UZy`QI�%�~F� F�-6r9S�ŶrfX��~a[1%r!|���- ���2� �;istH*�$�]sibiliH2)�a back��2!2us� Z7�\�x�is �Ynd1B~ e%�i8m*q|42p;E~?P3&4<s (viz.\ �[J�9!and�t\� aA�cA�). ��m�^l*Ji*/QS g�:{super�W�}I!� �x��(�6 %�"D��o 9)p/�la�5�,\�)h6E�d7sonE�msP\_tr,QgchampR5"�� �. �}�A�*J�at&!ss(! styl%�v6}!��,�in>Z3���&A-��7�.&Al>&Ef�z!,n an Intel Pr um 4 v ssorbU1.8$ GHzI�� Gbyt�JmV0memory.}j:1".�9\7S�Lo�ol�ME,�# be�5f �Jafe�vO E'wC(��a6"= vidu��A@ oughA��i�"�4m3��wo2�-�x,w-c�&���)2�!�in �6�M� -A# �ont�^� situV !�/�x:�6xon 6�5���� weak6C>2 3. A&�ru.jU�T6�A��cV:� �.�! ll  Jumpa��������z/ 7/ �"�]� �̅s!l!�)��R$��h'�mB/6E 7rE  ^CF �R2��!����:<l��A�& Time��Fs)%O $� R� $ & 2058.762�� * � & 1843.27,��11.30�� & 338.05�= & 95.59� y269.84�p& 4922.5M��:�F�R-� "�YCo" ;2%r:�2�Trem*�#Żic(pe>"�Ea �%��5��pl��A��7 "g56D�  >����4BAF�&�F� U�Ion�(�  +�>�hs�3"P%��b�qU�>U2BS2. Cen'G�6ur= �f�'f!6F�T� data-Nuct�T� ��iz�he cU-kn0i G� XBZEv��I> $ ſ!�eivab�*b *�,-+ Br4"xUI�rgD:xV'i Vdem�#:"by� 2$&� "C"B6� %��.�"c+� !�iFlTar�'*� * � �^&�- � beco�I61]a�#�M��?ur*� �/:� �P!�y1>,���t� �Va�>M@ sZi F:te$"aDHs {e41a�ermCm�#a�3QR� ��tan�i�g� �n P6i��&�_� focu�_ d@� fash�n%��m�'-�,�9* occa!  out��st �zi�0ly62 fall�h. them�$!.i� �B a re#m0 ~S-� L �w l�/� usefuln�:��-"�Ka�� MzD�8..'�2tailse��+dergo [ov�Bm�g�,y|b!�m� search%�B� 6�B�?e*}0 @-of po�' bett�?ai�W*b,Ivg�nd )Y� ���>�`ne�aa�s;M,bq!M�po$��("Uoipby"� t#n�8/ �)ap�Xon-�6� I� 4 �:E�+A�lE�.N� !�@!�i�� s)s&�� 9L-J8eaL.�) hm91�> ��3highly2�%dNW. ���]�+*;6K8�6-p2 q�s� �s2�� 4����n.�- o6�I���E-of cours��6E F!�A pd=of _ �<tatD {3+&rq &y�?"�>��66%�ap� nt�As>� M!j�$Z!�sv(alh0�E�P�2 *r�ts�.6 �R�b�syZto/os���^e uB�so&`0' auxiliary&�ls �C�%cs���t�iQsݎ�U[� �s�U�eT-Q��d7�lperhaps����� A�mJ82ver�� Eq *{Ac� ledg�s}�=autho��'�nW)�(CNPq, CAPESɴ,a FAPERJ BBP�<n,yIn� u� iz�f!�Egr1� ��<�-1^5�52L�H labo mode�*"PCcal��>A&doubleIix �alk�Qe metal ��y �R7d� quali�HR�q�_6B�b(?m�leeOofz= $Li^{+A�$Na K Rb d $Cs Yi4 �.-f.T�%bac!��b�#]1 �0!C disGA�s �,%��q!7Hbv5 has -�  ` �WsP�.�34 esNPe"�ZE�masZ "Rs�Ax� iMt]�calcul%�=�y�8g(n good agre��c�ex��A�@of RamanuB4troscopy. Keyods:!,i�uu,�C-f5 tra��gyF �H22cm%\no'Ynt&[I�}�S:} S�VaFEQ!��yM� by Wat$nd Crick ~T1Wo}�71� a  � n fa u�m� acrou֭n natu�an|a salZRQ�!Cnucleic�yE�i_c%�sI4!�enviro�3!.� pFY�domin�IY�hel�G���ed��$��bY�Ae!��xjDh�e 6o x tw* cbbe!j�recogn�; l a?si@byte6Sd drugs5�Xilliams,Zigel,Blagoy,ZeQH� �n�gA�-I1�Z; �p� ort�-��� ��KAFin liv � . Mb� !;�<n�:��Jqi 6c ���J�M(.�Z!9m @+n�1x9]Ya�lp!-X 2�. A�G ^�x�{I�re �>lyii@b�n vE�el�%�j ��5EV9� the lE�is�v&@CE'�d�0ir type. Tran�=&і-earthm=c�*  prFpally��mtT atom� ! Q0��� V�XS T�U�� �5I�� �UQ� Uhy:in� 3e H the@i fla�e�� use �GkAcN�ae.�arounP(ir equilibr���g6^6�)T�;.��!1��5s (��ks)!� uK�T�:�l�vasAvaK�;in�al�, xVof homo��LofJ�1�`Ya�ed -� . De�%gC�t  s�� �}of �A S�f u!���I�j� 2� DNA I$mo�#�=dA��hDA��p��6�e.vUey��� ob�7lo.�rega�=[$^�h��a/ic.W�� I1i R�ElG�;t� �1��.�ofI9A �= �LHthen 250 $cm^{-1}$ �T� ga,  $2, Urabe, ,2, Weidlich1  3, W��in,Po��@,Lindsay, Lamba,D� co�r�-B��a-�u恈�N< t�mrQ�6�st ( (10 -- 30 �)Y�i�5E�!�2q��sV� M,5 ���:�is � ����r!ݡ���N3X=�},�humida��-G3 �middle z (60 - 122�=~%�F hydr� b�� v$a��o�y �N AE���ongly͙a� 6u�n5 "/ :o %�Ain�!�6� �1H2u�is 1�y-a��**� al�AwA�i��s I"W�ls�b� rI� Shishkin)��w�(�o- ��estim[a�Bsi# ���i�2�� ��� r-D�"�onEKO"�d>Z5��t�P2�f"�"d5�pr�?ed>I}. Ho5=qD!^�� �g � tak9t�F-^ i�proble?^ (ect!_a�6��a�en�� works1̍�D Prohofsky, Garcia)�"�� �TVv�=q� 9�u�E"� !��%t5 foun���pur D!�t�ipa�&�f%�6 .q� �=�� ;#+AS��e a) 2� �A�� �Q��Q�"� MVZ�&�'}kNfr'm)USm�V�� Fe Qd�l� 1�5��el"� N.�)�e�l�sEg.�0ch�& ��7�qm_{�H($PO_{2}+2O+C_{5}$)1�nne�.Oulum-���l#(Fig.1).x$�.[b!] \�,F�3� 8cm,�11cm]{4�5[%"�. {�fZ �1;u( .�4(,monomer link��DNA. I�<�.<� &� yHJ� ' & , IH� Z?:X ,5�6M2ato: � s�� �qFi:�{-i�ga��� �9�E�imѓ| H-A� etch�.n E�4: "� m@i�M,�ko�Isg$8��w�^ o ��)1��H�ul�2� �7 tra,���� stag�B.�x:�&� ��&�."u�wrF?O g��:q � � 1�E: /} E=\�}n�}i=1}^2\�L (K_{ni}+U\�L)+ /,n-1} ,�i�( re $ B9D$/iB�O kinem���"D �!� $n$-]�/ �)v\�$�~.� �E�'��x&�AT�}1:�� !zt"%f"�uwayjx�  )=�n1rn M\dot{Y}_!r^2+I\theta  +ml_{s}B G .F��(2.  \xi U+6^2s�B�M=�N+m+U$$; $Y_{n}$��.a!�)C Y�%�&`��X; $I=ml^��]r ɼ---�e( mo�_ Xtid� �[ ; $lA!� re��9!�J�MRr wg2|di*ceu�T�(A�:�; $)�% --ra̎V' �� �R*��UteVeq%~E =l\sinp \xi|-� Zs�l!p��t� ��E2�%Xy�:9.� I�ed#s�v�|� s���ne�� �&��&��/#�- to�|�& of2~"U"� �} ��y6l ��j�poF ��.��R\alq\deltEa� beta1�nigamma)��{xy�H�d TQ��c�*nA�e 2M6A != s, $�\thick� x{EZ(� 1n}+ 2n})+Y_Y_}"n�# %�m, ��E�iUF�.�"f'�:b, $)-���6�P;#n6� �co2�/s� b  1) we1h lookA��;A2�-"� lat�kDp*a�* . Tj&0�#*�sh .� �4X\B�$y_ imit�VongVn��&�I(ptwtype;L�s�*7tr�re$�O�^�E0,#�+no҂*)%�T;.v1 �2&g%A�!O.��U�S�)ong�e� (.)� wave. Uz$U��s5�m�~(x&" ), ���a�)%�us*� LagP�1u � s<2|#r^�con�[�� �pA`� N� *�9 vari�s��narray&� Co�Cates} Y=a�}e�4},\mbox{ }y -a�},\\\Dg i�= _{1�? }\et."--"\ \xi=��<��x \rho - |.W ���9�.�z�$:} whobN%~ brake upAko� 5c"yA=b)�O"d� l m�2 }{M} )  xi}= -��_{0}(> 4 +Y);)1t�"�9�S�1� I}]}{I �Y} =-��{ ,�� M5>�~� )YZ !$�-��rxi,V�B�Ly>�5g 1�:erho}=0�L2{2b5 �y}.Ieta��)�. rho.V��ˍY9=2 /MWN5�= /I$��U!y= /%)$ N�iyhQ`)� � �r��us-/��m: $q=qw0e^{-i\omega tx From�� h�$M�}� ^1:��K"[iV�(: ��'Vy*wa%()�- �m )� [� >(p>- .*Bac.? ^ m/M)$� ]-�F�|%��;%B ^{4}F�=0Z3*�( E@pR0}=I7�i��/I+E8$� �:J �]Yw!��8s $ ��0E~�_{2" 3A I �\)�AR�&]1�A�9�f�2} g!/ \mu+2}(� ^{\p/>}+Y)2=0>�)S!;!?i� /M-1)%e�:, -!��/MI7mu=1-E /M-B&)�"�#��5U w2})� !T:�4B�5}$F��%E:Oa�4F%��_{4,5� -)_2�-J2)\pm\Fc�1k-4\mu%m!-97 }} {2\mu}"8u5 }"1analyz�>,5E�R�/at � al�<66[ a}/M�(F�aɔD(ab>0.1),�� mula9�1\� "M enz 7Y�2!�}\� 9$B�b>Q:�5Q� !~BkE"U��L4�9:�5})�th�d.A����25}<|��/}�*,|io*�� �c*&� u{A)$a#q "{ am��u��z3u`��j8AF>��y!E}_ 4i.�I}{yq���}�}ed��Z5^�n�c��)��� �_%�!s5e 6�($�$)��m&Zla�pi!�:a5,AGM�&9($%t$�.n($� !$) � s�^N�.Y�A�"j$�!u,w'y�2��C�� A���Q���! +Z�M$�cu A����U��f9�!�$ V-;�'�3!�&�� (�� $). ^/k�87($ .a�  .� ii T�HuS(؇�-05��Pe .!�Z�pj�w1� } �  � I���: ��0BS On%�A� !�=� �a uW1���c����x��N6pR��%�l�=!�0ae~��[B~YibA }~ (",0a�u� Soa6�f� i8�lW;.� za@y��M A#q~�.mn. I ka�)a.�y �&< 2"@*e�aO-ce de&�$ya�^�!] C = ��B�JT%Ձs {oc@av��s (Rp1�&����on���]Fhe9�A-J�%~ M�8&��!/6?5/is 6|2��,9�E6h�=���or"l5 s���"�.!�E tantJb�|���(ula��+�U&i=!*T+"� �%s�� M�6�aY�(crystal. Ac&�W P7i&�Z4!H;E=.Y�; L�eԩ�/o�=jC @�V(r)=�M_{\P}e^2}{4\pi\varepsilon � r}+B\exp{|( C r}{b))kF��"ag$a Madelung%:!� , $e5=h���!diFAric.Ar Uce � Ns,&�kb$�,�xrepuli 8a�20���5eK,�3y5c�T!�4 5N0-- Born-Mayerk. Eك�(��&�1�)A!y�on� 2�� �' ."�. j=r-4 , $V���t\xi��/2�J>��x"_ jtgam�801 Y Ap ~qAv^3� As-bqNI�!U0a�!�"89s�����" !����)� for��w=o=2Ꮚ1Ion�&_{ion:%�F�%7�KF(A��m 9 �c���@ř!2)'�]o*�+k+.�"�� �q w 9� x#:IGS� �@ �N �*�(c��w�9i�7���0radiuJ@"Q �Lin=� Li}>��Na K Rb CsFf29�A6 -).!9B> .b� �FUF5�.odipol� YI=1j is big e0.= $NaC�!on�� (2> .748j I�64:@1_B�H1%�7�r-�sa�m-�N85 %�e!;E�I�|M> n di�O"� it w5sbe '}�0� saw5�2.:d �J�Me�6�!�P(!3for+>Z %�c1�B4=�"� o� c7�' b��\�%� a�a�&�2f%�_.6ML�&� &>\\ P��|($\AA$)&2.00&2.35&2.73&2.88&3.01Y@b�� '0.3291627 3,.�-6Hi�:Xty}&5.0&6.4&8.2&9.0&10.aJ5LU]Ly}&1.3&1.5&1.8&1.9&22ù�yb=e�.$)@0760&1.41 439 70�bD5��N04�06H09H 114&1.136vNd1 �L5�066&1.08LR65� <(Q0Qm�qma5Nz I���is&< �����a A�"/*u� *�=u#�DF� ""�fey�x�  s�q�ic�qe"�11x, )4L, Mazur,Wang, Olson,}?I�dra�3�vacuumN (.s�Y�vY"�F p����� oG G5I9��i�S98ū��as)�"� j_��\tooeJ�^� }. V�of+��so�ug!94 Puasson-Boltzw@HA)\!XN���/-����3�B�82��4:� 1�� cor3 �developnw ach.P�,�Ys5��b>�aY�>>j� �<�F(78-77(r/2.5� ( -1)^{-2F� I{>�1Y"�2!{.�� �9 Cn� " >�� _{\infty}�R- [(sr�+2sr+2]/ srF��.c=78� $s=0.16� !��D��J ��2a�K=K9�5u�E�,i� a�}[ 1A!Brty&� e�D� )1& r� s5R�;[���c� 8DA�G�)sbw"lp %sQ���V�F) .}�m���e1�r�(nW � E�)�8�of��Mt3�5A�(:k sW:a�{�G��m�!O� Gl� � �'o*�M�T�/��0 �[hLS�|^d� E$Cl^{-a�n!�si[��}7I��s $7$ ��RnB}�uy?)�)b��*Y�`' �cd���f�� �P�:�Ni���6!�~ro�ly��� !�N���On]KborF�MWU:5�)A\ jw��UZ)c%^P2: �,�1 =y9���B� .{+��Vʧ{ �F:���p} &� =1�&\  (r�)�7 tt}}+2��5p5p}��z5�a5a}� � a�}�" � (r��i�J�,{t� B�AJ�A!�qv, pKFfKU�%�KU�9MqAUin�c i��1��Et�1Y mE��BQ 5.� ib�i">%U��T)J.�� q�) �e�@r�IUb] �]�:;)!� thir Zp bfZ O �mV� 5=1e��K9E�� ����0}�DN� "�;VO� �M2tMode} &�jHBX%����!6�c��At�"As� ��  ��6@X ��.E=($!46��*�.�O�%R72. Z%2�LN��!( Lit{B-}�w(& Cj&><27M�� �9*{ T=2$ &444&233&162&112&9> =4$&3&65&. 79&6.2~ ��\ H&488 &237&151&100&8�~3" &25�$5&70&46&37"HN W�D2}[3Q}$f0 1�10&95Q 6B }&&235&&&Tr�Note:'<a�Tisk&R H�sY�"$Il�+rom���%@2o ��$ \vspace{\+4�xskip} *aK O:� 2�92�^ "�N EeB�N�c.�of .�A and � .�� �-�� 6i��^�P�}�q7�:� Fer �_c�"rF�i�so� is&_e*9,?i -��m��6ata�HQ� �va *�#w� t (� a. u. m.$�  (0.6� S"e �m6S�w2�v%,%e infl�Te!G$� A lg�um93,�� �t .Hk�G�^=v6_�&�n�#Sone $(�M^~=267 �H��� $(209.A,H $(180J�E�&�Y�6Kme 2 ^r� s�5� � L- ��� !98 &�pE)]9�� ��`)[clo ] 6��y!u2>K��-U��e� o.�D�C�5�\t+�lbranc�lof] .�$ 1�i.32�,<S* r�  2v9F0�@[tRB>�g"KB][s3>B "�fTh�I ��67$��&^"%$. $\bullet<9�,�Xbf{o} --���i 9Box|<�3}. Fi:*�= � A�E�ee�_lV���EVAq�VwkFd&["U,in5UT]IE�as M�de*�1>��&x) s|Nt�hto*)E Our����W=splitpT-�{�n$2in was 6�$5��?� "�H-�O!&a�st%��2�.)�Pf�%�>� ��Z)NTB�.5[.{I�F�%m� z&3U dt��d2i���7�*,wM;a���m]c�t2�y�%_�'"�d�;2�ZrlM 9�K 6�K��ne!Lɪ!�isC is��.< �59/;_�Jfz -H�g��=1�2"fig. 2Iwall:5(!z�@* 6K)�A�� ��pagebe�[4]"�he.�] }{99hbibD�(W J. D.NW , F. C. WW, N��{Xbf{171}, 737--738 (1953�%X�U} L Z  ,J���� III, Annu�t$v. Biophys mol. StK'.��P29}, 497--521 (2000).� ~ZV�H.   \emph%]�U�B"�� �/$as} ([in RBuTan] Moskow, Mir, 198� n� Yu., P.  , V.� GalkT$G. O. Glada]ko ��lRm��C�IN]X A��i�� C�� So�Ws},:��\!�@ukova Dumka, 1991:/e�} W. Sa �PrinciplF��]�(u,New York: Sp�v er-Verlagn84n=1U�Q2} H.  , Y. �Q,Ac^=*c. Japan5�850}, 3543--3544Ay8�5��Q} _ UW. ]M0A. Rupprecht, nRA| Lett� bf{5�o01853--1855 (1 �m�} 2�M.�O4da, K. Kubota,-R-��ChVh�r8r5972--r5)�JmXoQ} C�Tmarco,�_M.��_ okor��IWvaZol[ss2!�$2035--2040Fs(Wittlin} A."SSE�enzel�'Kr�{>��)WAo3o493--50 m6.�E:SugawaZI0M. Tsukakoshi>o.� }\8�$1116--1124NkVoZMM�pN.iMEa!�$osevich, M�arAZY�UV1}, 7��806!�e�� b~a9�͛.-�U�%�06!�083j>"sS�YouaV%j$Prabhu, E.�)&�S.�39}, 317�� �9i,U��S�UE.�S,� �= oumpasis,Tc.} �/(ad. Sci. US�R8�� 3160--316e(mk2FR�=��&2,f, Bull.;f. � Math9L�u388��6E: l& �(Moelwyn-Hug�i W�0�EwJ(London-New Q-PR4:�ga0�Pr�196��]&"F B.�  , R. (Ritcheie, T� Ferrell:E �E5��"42a����|E Rams�`w �Mh4gtex��8�' 7231--723[��VMR#U R$. Jernigan W���3!� 1615�29 >�� �  , >/�w$. SrinivashW.�� -�et al.}a���?��382--4a�20>JEFi,a�Am�Sa^0120}, 484--49��9:82V% G�h.%I.�Ind� Bioc� l7}, 95;a�7�}=�!�Norberg�� )�� J�R7� 156 1553e:Vu>� ��&Fj�B4kelsarPk:�j�j�js�jxnq ��g g�%"Q8 ��a^���� , mu85z�f ispePb�ff4W, �.jviaOyo[ m W es pج -law6�R�A�(.=^=Nmeasu- (�a^:d�.a�V� ong-7�!�.Ssdhab�kN�T�"�o da�s�_l�(&9� ly huc�Mc%��Ys%�{@tw�nfalseE�I�key�} Eq�, EE6yj a-�2�1$, C]#2NK �k�2h \6�ys &�.Wj1 %A�QPi![Pj�t"�of)���Ja `micr!mic'�"\-(<{1}jZ�sm�PSu��R^$ mustA��-|(t�NI�f<��xa�.*Kes����'am �%q (SARd%!%5D� +�(SAD):=2 aa/� y��o=mU��Amkmlnic��Pu8�p%���micYcy%i�<)�u�R i�reI*^,%qF�.�ana+ara�u��;i��_basic �a�e�)�yzX�{N*���DdebMW J�fo�i�� �cE�)��i~qxca��v}%*B�=����$)�f-52 ��0e�q�-��xy��,%;�}_e�C.SixAaA}  Poss . �?%Wm��r�isla�ɩ���v5�� - $(��() \propto (�)^z$ -�!]ccuEi*(1�I� majo��of faunIfloraa�H_d�,��%���U, !zdve`dsu��w�y fit11pecDiv! SLw!�"��1 f& - ���z rZ-Fwil�Jm4[�nw!e�6"89�dA�our� lmv!>s��q�uU!�% �� . _��� s!Jly {\emM�umeY,e "� }!�܀勁m��a�����@fyA�} �eB�!��9d�'�ssw� �dzrA�ay,��n � l] �O�'�6t!4ar�m�kM ^�8p 3kli�Hubbell'ݤNe�.w$y} 2001 `U��B �] ory'E�Durrett L��K  SAR}6� � vo�z%�. y;a�n aV�i�>\ NT�,NO Chave �Review}=�m5�s#,birth, death�&h e�ht�1"��Q8ta�A��4o.� l{\'�AlonsoRMcKanem� ���� !��y l ��9�i{{i��n4"1F��o:e6�to�B��ira��!Q}�ficin�Nq_�p�odTxo��^�of�v��0a�deb5+s -&��sB>Y�2�a��ic SAD%SSAR�&)!] thJ _��!3!�c�6ofX� ��c_4c�&�B\��i9 �w� �tt� ve geom#� yAach$ Hart�co-� erQ�SelfSim����3dd�d�x��* "�@s�' T."e *t Z elf-t��[f�al;�� redi^ �����\ir9�%ZfieldŁ�� bird�!(Czech Re�cM�f3�e�/�{Ta' (�d �a�o �f!k#M=val�EI comm��y�U �^��>R(TaNaE�short�#)�ݯ!3�7��a l"�� e9���.� ���rom��ew�)da�al%sg� ��ac���& =�s, .� phe,gnon��h���^ ��.�C  eAݩ9�f_tn/�pu�  &� "prt5.m +�u\��Bproba& �[�e/A1� � q��v�organ� a��=>�0 �O܅c� �"F!�A �3M6stx~c��AB� },��cPe�&l�i O59Neta�}%�� re�<�t�uW�7ACu"�( E &���_n�� E"Z 1/� k�; |.W�Jia�I� 1a`p A*+�"�:B���J��aƅ-|.#Bt�q�. 1�M b�d� A���g !�I�l�l��� 0SAR. Es�O�*�|*�e!sA��e-<� E�  (*7��) - e.g.o� QA�����. 9"�� o�C�#)�`.}pej:� &K �xi6r� AR �le��streng� C�je�Fl"o�JsourcFAre_�� of9c��J�ňi�w �^�i~���!��r�<. �6w*f `���al�)n��� ���g|�ypacA/W.+owɼ��&#���c*� *�@,2�aWaB*�eVa2>� !��[s (E� each��� Rs�ateEs)I��"� I�)E>���H~v� � noteð��22h��s)b1t' h$adaptT ue!]� 'v�����=ref���) se `^�'!�1y `�'!*!�v������:k�o�z�y�.G.��ng�!�i@�l"fЈn xf/9vdoB"����!���Ǜ pr� �6K�m�^  surv � ����o%du�'M4At�{edBs"�e aQEage ��0!U<��"T 2ٌs �x,!a�X��}A1e� offs�(����� 1c��nBireVis�@affected, disrupt�th ENp . I�ac~$allows for7extin Hof well-establishedPdon ecological timescales i �(right invas�Dcircumstances, giv�(realistic S-Abund%�> Curves (approximately log-normal \cite{TaNaBasic}). Although 1g �tTangled Nature model are dynam�0and emergent,!� pert!�Tassociated with random!nAJal suchA0power-law SAR^nt1 throAj6� ). !�originalVzdefined!&DChristensen et al.- TU� has no!���;nE�which wE[roduceT runn!copA���I�con!�entlya�a squ!�lattiA_�?!^5V��tween*-pointsq migr%OJ�b 6Lindividuals at adjac!Psit�6�Erefor�$direct, ac��NlIjvia%�aJ ribuEpof � nts,E}�sp)@aA�t�DHdiscrete. However,!M$can easily%l!AGresul�)o thateW5�)a)�!��6�#pr�Nknownm�clo͊�( systems]TimeDep}iAQuasiNetwork}-|motiv%�%���Cach��gener!7at�A� (anim%�Hnd bacteria), or wh���!!��ete over!I��se� (most pl!�)�K% ��as ���` mix���^6��( nsid��oA{rger �k. We�= <a recap)!��OV8nd its major fe��@ ThenA detail%Dsimple�en�\E�Kinia7sdim +�>kAA%s. \se�v{D�m�M��,} \label{Sec#}%now�T�N�$. We will�`construq^� on a��iodic:�,length $X$. � fic �o��l�H%�refer�<��y�,ir co-ordinaa�$(x,y)O Each K>Jmaa�(,ij� ys�I)$io��%�6�w ains!%5��Ni� made up!�expli��l�Vdee�=�A?imilar��es n b�cu�m!�!�s, e.g. �eF4 �id�Z f!�web- TStaufferPatchFoodWebs}��be8q� b!I uni� stead����i�J ��rtwo���#be��' (ed (Gavrile�7ook �DFitnessLandscapes}Ӆ���nd)� siY EIS� d�of�i8 t possibl�Y���,�%�fic� .�!Wrol�� d"� nd�ݍ�)xp"Z  N� reprex !@*AY�vector $\mathbf{S}^{\alpha} = (S^ _1, 2, ... , L)$!�6� �!$&i$ tak�44values $\pm 1$5weA $L=20$� out. iN� $ st�9�Ont� %lesI�,} $ce(a me�uA| roll!vA6�j� �,-yA�$totalZ@a� $t$Ea $:�F&� .SEn"q �'$[kp��ax \mu$�� e car��capacW1��ev!�}"d  growth� n $N� 8 order $1/l" � &� $matrix} $J=��.�$�^� A�"� couplings"�1 � � gr�?lyq�r� $(-1,1)$,� � zero)W�� $\Thet{Si�!�fu�a� rm!6�a,Y|^b)$ doe @F s!novideda�ta�J (n-symmetric �m $0$6ho&aD��.�)m Sspeed3m� � F ��IZ ���nu:��2nbuG- .��� ���E�!�! ,��h �� � ~ �aR=N ,� �� $n=n9b. 9�eleme-of $J$��F,�pairwis2"PM�fo�a types:`uL m (b \ve)��m"  negan ��@predator/prey (or�e�c) � i% (W�K`d7CA$-�]s)e��!�, apart � ͝ casea�r�2A�uG9G)� very s��at �C2_of� reme9B,�\is limiE.nd2kr ? �Aj��increasa�8�he5,�A����Rb~ argeJ2Caj �EO�) lAI ough must ��so�edium�e�tS�l$ For" lr `is would�-�f�{ chem�{s,�"E�!!"�� to �degree,e�~�  mlik% &&2�6&� eխ�%���a.� ɖi�n�an���2fac�a:K!�m�!w� � od r  depen& +�� un�� �|T%�i{�e `a�'A��"O ~amXwI��"���F : \le trophic level, amongs�� u1er�=%�m &�%eus,&` �� dat!rA�0bivorous bird;Yj� cropMI�!�a��-��-Iw? .�on ";6� s st� �et*��is!|!joblemx� pa� purposl���AC rawn��5lfamR���3� t�toi� ��a. obvi!"�-�2as � -multitud�perhap!(aker, hidde��U��Ity�d �ad�&� addW3M�A�s] � �Afvar�ly)9�Q.-�%Oadd�E�!!�lex un6��� quesř=�in�B� exR�6Id�CYO,{*l) H���(flipped �1!Q-1E���-1)iO2� �  )�pa�a&��_i� us��� � equival\EQj" n&u corn��#L-"�al":!�s�Q2|!a� scus�iJ�  A�-y)�st� A�6�`.7or!�c#v2Z �6E$"� Ee%�9�(\footnote{Iei_Y A�Y�5 was�� �i��|�aA�H�w�"lec���U�����>Y,V�ovB '8code efficiency���- abo�%uP*�"k �methoaxre]0.}� $A�o"j E���l�> �^$itemize} \  2O S o5AF��.RE!j�L.+a<}8II�Ew�!�un&�,2�!id>/2�F�}8}Itu)hef�&,ive $p^{eff}g� 1-p_ �)a�ov=�!;%E�� aa�ere�a��amoun�!�A@zYbs��T!g �b0c��� a�l2b�� �M z�pq!ed onch2 . G V ��"A�L! lapp�A�.��an� �#ial life�i�A�i�%� tant%��}.� ppea�*�; ���"- i�' xr���siy�Q�2mE�Z lst� �f�dA. �![� beha��r!i"#(���libriaY#Bg \a( QLql"�(� sh� 9m� f�e�!����to ei5 high inf!Rmorta�)�  adul6� $� � �um"��m o����c�Q�(o�&!%� �b$� A� su� t�$u*0���U�A�&� �edar| pI�%�L.�͓s�T!GI�] �!cAX ��i6�p"� /"&*ofa�P Zso �i� !� be aa�to fi�(a�%WhE�� perm $!�� ��� ��� )0lyiq�h �A݁5E��*�6Zvalid����s;A)CaTi ross-��Rs2�I"@n�n�A(1~� � n�!C gene����q�� `U*'a�i�y)$D A�%%ou� Z;&�!�!rM l sex=Bcorpo�P�S !8.�-[� st� y%T gnorl+W)-ve%�ye4�*ny.�!%�i igna�am2a+dic�qw�tYclearl�& mis9 loɌheAf�<&� dg(pa�q:UEJ�d �;�+!E,IqQc-?�-+a��*� �6wqQ�!_#s~&B��-�jg&E�f�: ewm��a��o��(u�n��)o help� pre`)��ne&N$X$>�&( e�&b!�� �� �4Un9�wMst~a�eV E�'N ':\=0.25�c=0.0 \mu �ut}1,�� =0.1$; se] &�%�m�V(& Thes�l to keep%X=�-�re���exceeTaba�$3000�Ga���� aFz + �EsE��.E  ingU6�� eca): �owpa�4)�A(�studiuF.���}y)�.8�A�st�!s"�-U�- }+%�.��9UcS0�)Ajis C!xa�q�T�~���unQ�.. highLqS�X�r�,.� x� ��in� "V�A3�+i;�y�(�huer turn�ofbsi-evol�,a |,l�(�g!zasM �` Si�� SecIm�" It1 �0tr#/ !*� .��,�s�'at6Fs dow�,$10^{-8�  \sub��=/i �*S"}�.�" brieflvV��!X��! #*by=uB�'*A){-m�  exhib)a*!qu��(q-ESSs)!���!Nfrequ�di:&�.F $remk� (ebE��%.�);^se ue� 5�i*K ! styl,Q�L��3Shifts1'okitaS4e:�.ynamE f��E.� = SY��4MaynardSmithGT�)!@�m=gg theor�I� th ��e�.� )yR,ado�"s y ' surv=�(� sa�eKy C, C�+$$���0K ll�� d�zbyW���Mfa��M"�m�,si!�� 2^5;&_!qU�|6�'6�!s��N �� ��I"�!F͏�aQa�-SS � m�1 ��5en��&�M�,��5|��:�yntv a se� 9s��� �*)�%^�p� �=u4�)f�% ge�9��1!�&b�]�� @ &:�H& beca�w�W.�?E�5�eѥ�EW�influx�!��"l�!�T��1�!B� a $ ��t}F"� )?r��-�sj$9eabe M�}-s���-Q �ll ��ts!�,(��� !��4�2�b�ac�8by.+.Ny� 0-�E�&X!a�  mi3!�� ��A���do� ��=��Y dU9il�taAtheir2�!s�*�n .�em���%"� &� �switcb/�3 �� 5/ �e=�- k)m Z4 analy� is regN Hd2� . D@1t� �s (sh��in Fig�9P&@FigGenoOcc} (b)),2\9f(!�`wild��')%� high]ccupied8 E'J duEvQlJ ]\)�9��tly eC�,6fWt�eef�a)ABAs����=*.�-e�se `sub-Q'Acainher�j�Q�: a� -Alpi ��a n�4x � es-�pt�:*�Ks(� A.o6���u �diReas!��y5�#':� !�Y�5�m�5Q%�"����Eu� �or grea�(�.fij5is �E/ I�&v&�$W��:�4B�s <� Shan�$Wi Index �@��Avq�"t�"�,S6,1\�+h �Apri94/ gin{�dHpage}{.45\textwidth" E ,epsfig{file=�=.eps,6 =0.96D~+d &�{ {E+. Plot�\\ր(a)9L,�� �(bJN]1� \cap<{\t6pt {(a)�7�,��/%ve6|'e�q���, l'F:allJ�a 3807s. �r�a�=?��<o<t,.pBE�t]+86g 5�% �@�4116� th�%a=y� �i�A,=, �M�ac ���-�Wi&#pB.!� A��0�pd�C" !- 3 ��$n_a>8x*im�*��do*� �(�Pmea�$fu�o8*F� � ,zn�horiz�9�n� %3�B�x &���%s->% �11000�9$2�$) too1@oZ$:uB.}�,� }}Iɑ��2Y�� is\�� �a=�:"�& ��,K !�� "%7%Mn�=��ac�JX � d.� ahE��$�b '.5 )�g2+&�� o^ �)�.� teQ/od p�Dv3NoQ6-� "bBiK o"�}TN"P �c���] ai� �,i`2� P�M� phas�V�=!�" A� always tr� �higG&� =: u *%J)tL*js@.F��. &� )K�*� m��L"� �?UC�"�l�&nd * � diss b +op�t�A�A��I�� )�. Bio�El4 �@.c� 8!�p�*$ a�� � <a �y,wer"V - ��*u$.�� ! a%��H�/�fdr a���9�)M-�D� r=�6&Dquiuum�6%��offJ{iA� ��Z�*rH< &��ir ��Y�A�low��[s �Bo achiev�'a&M�it}$!�%�P)4atq I�i�F~ �Hc9,,va��.�!�Ie,i /�-]j� :cl2yG (� Y��1���=$N"1&�/��2�{ "��W5!H��*an! on��Ca��!1�*� d wh),���-to0�,Yu�i.nms,F%+con�ʼn;m�6H ��Hq�"< E20 ����E�� forc= �� nd&.7"�#�$Im{��U�>]�Y&�EN� r�MZA�r)u�.n�>u���*vul�A�!�ccA a� ��0"�ex&'#'34�!�Fp's�T enough%@�-�L(quickly ups�R�`Y�, lea)�o.�9] -�1•;hada2Nta�i�Ebec 9#�)%�6�ja�+����+�-a�b � �w!7�we}T s�AIBEre;d�Sy��� E��N��L%Z��.��yrsB'&O��"F�&� �%,�I)a,h�Hn:�:��dXMo��minor�L-��jlA�thhew-2!EU2eQ��4�,�Ų��Q+5�n�"nG��6a=y� yY���vN.�j{� �/�D"� �GeHG�!E�Mt2�stage 2r v�O9� �q�Q��5�E��V�A;so &E  1}C5� C�!A��` an i�� �*V��lzM� � l6?j -HJ�e�8or�0 �4v�3� U pushA�]Lp^ `err�Oreshold'*� "g)�&�.�%�c� �R� �x eE,re�=\a� ultaneous���respo�1� ach�:�� #!=ouY$a�l~ favou R�A 5 *Y XEk!&"BO"�7M�6pZ��ip�IF�-�K�z� w��: r�#�Ձх"�#�rt livo�J�v)A��%]Ʌst5�0ngA�aI'�[(mqy&�;) SAD\%"9J���EpslO!`y dev�%%!R)SAD�neglig.F!�E�71�MD�" t! guish��*�!no�s { � 2 lsoA�v9�a �\�/� ��n$"�� . BOY�|. 5��:X!(� e]k!oftencteL�2�J�K%Z�x���Nun�aA!��al&7 L% @A2�Ks&�AM{�yerm -Fs2�t)" WqP%+%,!Vnta �#�0tinues until �ZCund)&�7m�n s�/�3gradi�1a%��D��s� e#�E24E��/I��i�b 5�Z2YRm�!HU| �>��)�of.YT� �.+!�)�-��4M� !y ��&p ct�qab�*�!���=])�;suptsedc*6�%:3M�,AiP 25�%�PingQ�#�T1*gri�M&�P�6(Bai�UO%F ��(�l�3�O ton�K!�m�T; ab� 5Jr2!���1m"�6 any}&BP��U, �(r^X;8L8 nea�"yPͤwe�Xum!��ic"+ . J���' �N \�:��)L s AA$)ly{ �>-Area R�}7 �SAR�U���.�o�#{-�����iKE�p�#ll&r star�:r t�*F���Fk:xS�5enume�%�5I"z% �g�T E�a-�"8/ pla�3 MY�M!���6��� A si�Z:M�`A�ro *vAaB@Zͮ wam���rm���i�f2XdE� �2�E�r"�#�#,&� 5i�5�Y�={ P�Id2 2P+rD!1b"��:a �(�� x�<�6@r�+��s� loni iAn&Q))_�F ��V�� $�{: ly -� Fi2�"DivVS�sI� al�wI��Kuabsolut.- (how� �2��) �d�E�Hd�9�&E �l�O !�bQg)�!1�G $l �� �pro�'ow) +���"��T� oE c. .&L �A�L .t va�2^!�p�(rZs sharp�mVP)��af� �i6+&� � $ong) wait..�1 bears}A�mbl�.��!\cI�"�Vw�al�Zby� U�|!� �BItZ�7�� �ly)9�2I�s1�.rm:��"de*)�N)���J& �TE3}..^[)AE)!~4e��0�n}�=;"&#" we!�llAq' uQ��HavsJSe 1m0���dar�K!�E94����n��o9I�E��� �JQ� ($4��*e� s) b � ��C��A`\a�M� ? ɨ e�"[htb]" i# >"#�i�_�j2�"Jp#J�!"u9a�st%�� 25:)G*N!\�$.vQq:g(1��=� 2� D"a&z- �)% 22�(,M}Be!Iԁ��0i ?ruLNo�7lin�����si�rapid�6u7D(�6(da�5ne)@-A^ �5�6��erIps�7� =+ �HM!�2 !�!s)�/�9�����A�"%2�JѱqW/ mann��H!b� -�,:d.} &�!Er.�A�uQ� Q�h��e 'Dace�k� � �υ��F )��.p < �`w 9,:1P"Zx�<F(\R+�@\b�,1�d �""' im� G� �w�� �rd� �;�X�Rin� �.�.9�!�Jmit�gheM��#4i�[ ��iU�((IJ� RL!�e7 �U6�!i@ ai� , m�Z �p%��� ���ni6�11�A�P 1zɬ5��F rong� i����"4 ��>�;� "�� �lɌdve�.62� 0!a�d�xa��-\�[9X�\4H! ���E� -����Kl[C1� ����� icul� ɾfoc�+�=lc�)��he� A~�! ship"1*H ZW �a#�+�$��M�i42Ya�2�*m�D��}!�Yub-Q+iNia-0� :YBT:�NAR��m%a�ba]N� �!i: #�f��,quo�SixA}a�~�3 mVp&?: ``(1� p�Cr!quadr�jkKM�7p�(n�f�K iguoAAnonw oFA$land); (2)f 0 AhXUr�(r�8b"�Ba�ish�r�;%�(3b!�c�iA��ru�j �k]or!Yn ''Iob� ��iveLM .E�u?���A (tMt.E&i�!#1]EA�1 :'�::,\shapes�I�� W!=V�\�A��\B(A3"�*u�]O{gs)!qZ;� hUJ`` PossI_aBcus��eN#i�A"�@e�&�j)�encQE�5I��g`4O' �e��"%�E����<�^.�!|i�h/A�-ma���3�9�&but)��!��Ma( so�<s +QEeN�[ �9O", �e �ed!�otyRn)�ax �� P'�"!� r"�8���"�/=� w�C�aD a�(�yE��9� Bi=2e�[� Vassum�0i�a��ly�i�<��"��E6�a׵�ri}e!�9a6^�A]�'%��>u �qM��FeEe�n �:%,��'-��<$ geography��CP�2"�$en��Hn�Ie>:�3b��3��3!ZSA2m9\2�3��2�2>� SAR_D ingPS.����3��3ƞ3 B�3AR DalT0Hertfordshire�sV�6� (Fig 2.2)p2A��o� �'a�de��91W <��a 0.4haA ($*!�E025$)�#a�ate. 3 S%�M�0�3�<-�c%oveL� $0.0�Eto 9$O le� 2$%A� �C��"Y�+�/�3�e���2 SAmeL sF�2Re|9�.�~e $z$- �4 0.15�0.4�!mo��CF�� M:�. p g;� illu�?�$al%]!� %CR4%$h.va!pbD)��!SARu#[ de06����i "3$\ar�V�ulog�!/O$\ S = z  A + �S$,�lope [�.ine��~>z)Z�e �o� ?`f�*�V�gr�e� !Y or ��" W�M���1!��asm&arbitrar�9as!�hY�T;�2� @ l2A2�32:*bHI4�]e� WH th*�P&2 �!)��J��Q�ZVJd} �?A� *�1*+cutG]�19�I �I ���&&"` {�]=���}�B �B �B B �8 ce�A�w�7-y ea'"����BeC, �Ga 7+yrsi��Z(5 10x10f �}9:Cc��Cs -&  < 0. � �zeRspr�r��mOo�vm��P �m�"�  >.m��V �,|apsp� eq�.�  � ��9eA"�eA� a 20x20 ���= 5$2� iTF� :C '�>!�i" ��$z�V��Af��<g�ŌAM*��d�r�!�� ed�0ut)Pmea�9q&�6  �R�7�Ao5 �Q).  �0,t� �Pove} =1�e���a � e%�$�&�g�C�a9�2��U�$! A. -.[J�' �IR��[O E�a�">R��$ll irrevoc�(I�%�D"� WfW=��ch mY �(1�� 9.$,ofa~�Ep�v#�6�-��IIn 2�bs,�a~D�!q�abcya���͉�a `pool'x�`1�makeup} I�Bio�}�ink ee�iDR;boNBVl�qZ�b)}��� of�1��Q�5�AUoa[�H7+)�G"}h��� �Cee�!d�e�(�0am!��."� losA@� q��SF�E �_e�Q ,8a+M�:SQ12}2j"�� @( W+qI6?�)N9NKɎ)�!a��)tyE^Q� d��%ny �if�1�A�>U<dominAj��Au^*Gi�g� �0Ё� 1� w�i��:�!Ja~ �-gA!c�' "�":� �t�OeY lo��"  A0Q� #�xmvBuM�u1)L /�Ae',ar�1 �"�&�3 j�0J&v �u~�5im� s�y� ��("g�<G" c<Nte� 2n�:ul�M�/!4t&%0��).�C!�S.&�,*��): 2DGSx�;�'��\"mE!� �i"I!�I�u. Non�io 9(m�AI�Ram�#�?�5?da �� cornGx*�>jv5c f-re�!ce��!)��e M#r;��_)g�,gcoe�y �;ioU'+P�) ,a;�fai�Z!5`G y� of 3-8 K�WshaRQNj? �AA!�%a��"�O!��m6 dF��%!�' �!�sw�;d  ��D"u00 u��1,6z�?��%�Gl �%o+Amplet�} W!�'#�t48�nal (he @���01a\f (e�~ dens��s�to wood=eSn gras�p In��1���E����)E5�5�A  .1zA:%-n"[w�% ��(a�m�2a56'LJ�(>q�* :�> � (5x5)&&1L(� ]Li<I�� backgQ(A��-An%�p�s&�.!�W1IQ�!4symbols j/Z�.6�x!�[��Uuf>G�w \�;g�VS�"s3� ka�a|H��� aR Je�M�blackTVl#q�'s"�Rin.��V%BFQgYqtri��A�A:vl{w��a�hl.���! �"�!�jpo �:a6 2� M;M|~�(In tor=Oge(.*��o�ZI/!~�".%^hal�gto�B� %�  unact!i by�3B�3���e ZcidV��+nes1Iz $X/2�t$oi�  t��� law����P!Pup.$X��!�Uz(tu�R�$���az�/� )b �UA��u elf-1'��fUnyI^^E�neC�-�i"aCete� f � ]7pM�p� A��rX�4) �UQ� ��2\ %> .�X�� *�� �!�o5%,(]� tZ s� al*2" @V% al�2n� -�U �r*ԍ�7��0aY4!�� "gE,'' AW!�K��r�>,; [ &�YaB ����bddv4e &>4F3iLM5`@+l�!fe�6�4�oWl5�!�urb�!��n"$!�"\A�=moZ �f;��% �x�7 r� [Ahm ��*_i7iֆ ?�L� I1�)��$JE)g s"/_��$q)i�AUmul ��bl AaFb !ybex i�� �)6�_+&QG deat�  >�.�%��02s%KA%r� *�6 �IV!je|=K $ en|�)� �NoE��-J2�K�  �aB�g� % te (%,�.r��asha�RA=�-�!�i��� ^@%y;�DCF�!�]��)�Ac2c#� "" �� Qz�^gi_"h U�Hp;4�<.�s�Upy��!cen�C468�7�*% �� K�@�:� so<�!�i��H%퍎E5i8*�s,&6t�A�Y��x66aF��ba.5 �soq��F%�*D��ac%G�b|-Pwp <lax�0}&����4E�(ś�:�R�u�S�1�]�e� ecay�"����(iN%Dl'� e@�mpbeqc�� };&�1)  �^ �@G2C�wK3i,� �@ S p I:��$�&� v�) SAR,%�I u�,f����e�!K)CJ!�921Hs.}�r?M�al�T `freezes'B" PopD�s}���%�E��i6i�j5�.af��^eu4�Q'2if�7֍�5��*�P# 6҉ �ʉ �3^�:!8%f;jm � e�#$2�R��= � |uki01$^�m1N�#oiv(Cd o�(2,X1�-�IA u�2: =*~7 �Fbe�p@8-r B� I�a=AIAw�!I'Iet A�C~B~ ����"�3.t2Y��A�et"Ao* Sa�e�-��x-�A�`be,�'�U��f���G��celP�2r�ѡ��N�o��<qui�/*���*��I��?im�9�+F e� �1Cu=F~|�hF�`Aa {9�%�H,,.�-���$s (�`�o 7and/or��i� an2�E ]-:collaps�3AX�tQAF�Cj{Discus } Our2�<di��� ��h�S�Ep `v3'. �zD�/t� Levi�K SAR!.��S!s�c[i&� ��e& -law��" s-�1� �Pby&� TheyqI�iz;&�0��?![E�4E�m �A}va�zim� aF)?hgA�$ ��j b l��21,!,��.H ��/a*�-P�ro�EL�\/ e�Z���6� iM%&�` . M��8 ]�T4� :ύv;FT�:�&, �5-es}c&v�e�Mxw1[�=  Ow�!��an al;y��# !xs�y�cA�dY-� . E\�Q%��{::x%�/�I������sMA� 2in e1A�>_I.^�)out�1)�b��ag�'int� M��� a� !�ide���genetic�Hi��o�(ג9!h>�s)E�aF7�* �[;�!�B�u-��8c� A� sX��F-��6AlekLM� @deBan �� �W'4s�rhm �XmK!�ani� p. Co)�A!�X1�A�t�~ 1)�els�3��arr 7AoR:'DS !��}O arguV�->\�CW$M�r�\� V�Ae��0iO��].e.!f l¢9+ur-&1#M�R�)!�jthe�KA �,ed�7F�bA���'Magurra�nd He^�so�`Na �}�7k �z a94fis&�[-�"y�c;w;x�5�-a�$ser��� ��?ur-�e�)% v?.,��%��7P2%E�?�&�32�5A�a��$0!�K�TLB�7$�) p� b� aCZ��!-� .@<<��&F#_�m�9)��-*._!�c all��e�zI&�!-� ��5�ctIa�Ea�!�W%X�7=:�N%�M/%�.����!��a�re*���rxte�s[#�P:fM�VfMS��W� -�d&�|>:!H�ma <��7 iori�=*�5b-!�C�&� . "c ��th_(!�qS5� �oA�m(%��$&%)-Mc-sl:lo.�. F��$��&�dco͍e3/A�o �qc?Ɂ�U ��(�are��g�Je�)���-:~.n7Had�_;��X&� D)1Ң=~%=A�ev�(���� msel'��I1A�u�=!�!��AUXe$� �I�*. � ����B.W �0"� to% `rawh%��l'�2��> � C] > fo �a�&15EP (c60 ) hae;��� �o�3 !co- ,! ofE�tE.coli@ Friћ�FeE}) K�VC"�Qh ����W!�KsA"� /us&! A i6q�,A6ka�du!&a� �ف�xf�"Div�SO/E���!i"2�A�*�oA&5oc�("�!��1m�Br�� �M�"F*�*of=�}!u��\ &��ajV�. �F-:�Q# �:.XIls��I�eA&q"Έtu+ngAD�DI-maiB<�'Í��)4J���e�re�+t3"X[ �QAwe2��=hen*.5��`!�� adapeWAd�<e�<5}�*U@LG�+6<� ����.2rN���nus m�"j�D�Pin� �Es&W|�meB is� *�kf�B1= X,be `climax' ro�0��"} kgy%VEva�����P+�2�<a L(eFa���d4��aeP%z3!{�S�birth%X���5to��t� ��De�8�'W fiel7iIS@I� U1t�#C? NޫR�{}�b�$Z��>ex�e:� b� a�a�!WDay ���`���M� ���6��$>A�D�c>e� �ASMigGe��Q�2@Qr�z%���.��E�ctAE%��&m(#1v)�Js���)k}�r�poo��z, >=Bgo"��a+�3"�)z�k��B�endQ;� �+d�eLj{) �0� p&�J��)to flour� 9_SmA�% Htho]�1\�s+ ;�n����,"�\� AZ�n*�J&�%!ss&�]mQ�reY�?C%8Pa� is �,f�,%c-g !`A�ber'!IU&��&} l08��+�kNm7�DT�J=)A� Q�c)� &�_�(s <���2��ߦ' �� (},�KD��e�#!�-b�Aire}+s�{8� 7m_;Ics�/� �-1s��V~�z)� eac @!�uA�pO�c.��D��&} commb��g" by ``6fi'�cHubbellRSef��N ity}&� of u-pfdE�o��wu�Ņ���:l eur�f�� �d>`@�A2ek��U)�J��$�FXf� A>2Y/%�A�v2gn�`�ww�q�4BQ�Fm� F  x��e�� ng(WQ:�~ &E^ ur���a2� i;��*]  O�F. �2� -� S� � 3K�8-k� շԘu ���8� �=*iyn�&� �#� /L��'F1�adxag� ���Sa �+� -L^�!Ag\�1��!�i 2"�&h3�>>�!'%!�SAD1�:tJI1"��3p��aD�s%�%�l%��&ntszY�um����"�aNM�&�i g:w�="�/�3�[e"��4!�b"�7%I�>ta] m� s�3M i*^�F�A��:Z ��TA[N "] framea���.��,*�N�>�fQH%n "?)zsW@2<&%taxonom�pfNu�]ŷ%� b� -��0� d mab��\c.UU phen!(o�%�G7d,�-�g ,B�,2Z��"J�ntUم$,�de��n�%�!W�n.p|�"K;�P��m�/�*{\/${Acq� ledgH2� .+FR0ank Andy Thom<Hnd Gunnar Pruessner*!Ovd sa�� i�YY�~! Isete�Q,he BSD S���Y�"��e�oj��e�*�,k% ElEe�8` Phys# S�des Research Council (EPSRCQHDaniel Lawson's PhD�a�hip.}/�oc��P�PsPacala,let\oldbibli�I \the.jEnew�� and{>}[1]{%�?:H {#1}set�5{\�l$sep}{0pt}%��#s"�ng}{0} \.~��{unsrtY}�E�{�{"B�m2+ i�W docu2+} % L�WSH: crik���54al Jeldtoft coB�D�\@class[-pacs,amsۙ1,��Lfix,pre,twocolumn,suDcriptadd} 4]{revtex4} \uL0ckage[dvips]{�icx: 'n1]{inpu|}.< {color,ro�ng6am�6P�:m�b_�als6I,pilT_project68 [engh�]{b�} \hy���{Neis&\a gonorr-hoeae Myxo-coc-�Uxant-hus.�,Ref}{Ref.\ }�U�figpartE�{(#1)?.)IVLapsrev} \date{\todayAREedU(\title{Forc�.������+�^� f Brownia�2tors} %:8a ,and�IV pilu�Ht� on}�cauthor{M%{ Lind\'enA�mail{l�n@kth.se!waffil{TE��al�Rs, Royal�itu기f Technology, AlbaNova, 10691 Stockholm, Swed{ �0Tomi Tuohimaa�tomi.t @biox.V�Ap������ �4Ann-Beth Jonss%K\)1.  @imbim.uu!@ 2?D{ t��[M*alYz �strJGMicro�c$y, Uppsala'[T2Ce�, Un +<, Box 582, 75123#, -l2ts Wa�} �w5�2�=� �c f��"7ab��ct}q mot�0f cer< �7m-J� b{�� !UDy rU�!e! i iC2f� filT�-5wEJ &�7for inf�%vity. %�Yis��5z` mole#ZK�t!�4rotein, PilT, g � ��l�� L�� 150 pNzX�D5'mg"���)� ly un�%hil�\"V�K��*xPݨ  �T-&d��NucH %ahe� ��surpriT�Sig��t)9<%!�vate a Z �#sti&�"2 C �n���1� % s. W�o�f!�im�M_� }-!�92O2m�e?m!^ sub��d�j/<�d�bm��na8ula��kboneX<fN2#iffɸ1-��?���| | �%�����icles �#n a"x�,�*n�! nt b ng"��l���Z ng r; et �� l), I��3o�U*' ATP hydro�s cycle�W�� W$ce-vel$ uUQ8���4+r���J e ��h?d�u_�ce (st�%��/d�m�> by s1b,�����G*�Z�O ؔ�1By.�my+!6l�!�� �=#N- pe�: ing � ~ "JUi3 �|fAZ&p"c< �] x�!= |`6n�<a� � &� 6`!�C*01�Hitu� � � "�o��a� er eK�c��^1%�J�licap�cs"�7M-V��%Z in �MrT�2>n > hI�as]�n8 U�at�#aW��#i���a� A�!�.�to ��7a4P�Y���k�� % 87.g�E����p� s %10.+e !�y�o;d e��4aX t45.Aa ��)�%h ing;Xe.�9 j 6.-bM� Subcell��"J��ej 6.Ac�j�16.Nn iM���<s (myos�EkD�in  ein)�2.� alO�"E S =: 2.20.-w Cy�S|)��9� 2.37.-j S�8�Ue1}05. S �ie�rmoO�cnq�g&�T %K40.-a *s"[a,!65i�'is��. � P60.Cd Cl�m�L�X  70.Ln Non18%�Ier ��@��,2.50.-r Pro"�8y,.'����6%)��;� 05�I%I)�� Ey h ���!�7Al��\�{ 9-b,05)�� �t� ��1 on{I~s!� } Re}D�Ѝ�Wrog��(en�:d` ark ��nt؎ �6  %�5c���+-U� O$p{sheetz98�!On�a �=heXH ����*l Zm\ ha�"�m�, q�!�dya��$boal,howar?��)stW��%�� l�i�(��lzn#��m h,trei�iX,bustamante01,schliwa03!�8p8 we  insp3�?��7��,�Pw+� �p{�Oick}, [ ��6� � r&W"; ��I!�sG est�� =p�-�maier02�0~ !�+sp!F� �*X*� *O A l suB !�;� �n,� � QUM�.u &T M��` �+� s�IwW8rs2��erz00, � 4!�����a� p� ��d�[!{�Ja!�.��0�&Sb� the �Tl ].Jms7Z!�!~�I�6��of aA���U ���� l� �g~H!Dek� b"�#"g��)rOrl)Y�n w<7"� E�"�A |!%�rg� / will ?�<�.� "�= i� �$i� y>�}��5!�� . R� R$p�� k f)zaMo=;��on�sIvŘM.!�A�� 2��5�)$prost97b}.-��Y�kto _y�Qof� �+�:�y$lattanzi01�f;�2W�j�� astumian9A�zF31�=/� E��employ�#dz 7��vH3%�I�eF sQ\E�a&˅��dshu04,badoual02,lipowsky01-e5 l7,plischke99,juelicher97}. F7r!\"�1��Lyl� !�� me �-n"wp�(%two-he�K����Q͈nyi96,vilfan99,csahok,dan03,klumpp0V� �a flagell>z��{�306��A�^a�&ach��a��$A2�aj1��h"&� � �8�mɠs��& and�Mo�� �t,�>Y!�2lizI$�cy�� wo��.�7� p{kolomei!�5��Aw0e ��c$rom Refs.\Q��;E;,��,-�,�o0/�"E!�� ��a�;6�n�#ivial �<�>!$G�G"�)�-r��JPC."turoO off.�l � o ask 7��m!� ���Q-�tA;a�el�0I����8&d�l.�J����zs�.u�-)!f;o�<5A1h6��.�B��aiuwHt�9 ,�$��m6"=;� �1�rT�"�%zr �K&6 ="?�J�0 lex.�jr6=:eC��T&� v i�+� �� ���&�S�i��)as few OQos� � C+-TlizI � d wo e{!K�u>o-ıI��t{��}��r ���)%���m\-t�Vu�. By �Y!deGy�Et "�A@t "��6)�E�(ATI�fE�-�0.!� w#�7~ buil� bloc���$).�2�ih�%ERnonsE%�2f.�">VyWG�e��n�{o&1 �!As*U& &� i3/W3p:� i� Vi�(st�_ood in0�� � z?s�Z&��)�eL[0%�I :z�s�O.DB�bQ�.�=F�� . T�k�!�B� crubm� ;BQad�%nceAq�grRW� t h&�8s, DNA uptake, ;GaGz ����%�.���%"M�ous��AXpil�`#3�� polyme�{o a�a� ��I�ou�di�DMa� 46 nm, 4 nm pitiALfive mhp� eF6�,fo�� �1F� a:�.|",td��=1!,A{;3�� repz�Q<t��N tip # ch)jY��!�EI 1Y,���< �umg pull�elfA%���MJs �2g=�B"3b�>5#�}. .�Dex��s�m�de�gmVy Q0 :�!2 \bak�5e{� c.*s� husi�it�un}��humanE)hCos> Neis�!!h !A �Dr Pseudomon�$ eruginosa5skerker� ��o +t �= belie�H�01�(as�y �by�a�!TP!�AAA fa*��<�"� 1Bɛ6mZ�&�lej�K��R not ���<ne0h�#RJIh.��F�~( �~by ptubulrI���>��anX1s I) v m� �s^("6O�i�h4 ]a��6i\t�*�mm�jiVi8��.�y�0.�12�Q�d}.&YFe�.-es�%n�&$o \mbox{16�UF>�&P an ��agn���?� PE�(in �/ in vitro}2j��A-� � �D,dogterom02,janson�� "�XcL��A]B�<y�V#�of����l\2xceasU�!�$� are �i� h�Zlle&ranDYit�4ifre�#o�Um.u�� &E~A!�j� �2�!��a��A�iU�um�UZ<J� ��iD�-E�" ��So�dto" �* Ie��Bu�]�vI�]��� x*�ea\!�I,f 8�Q.�P��{>#v� 2�}M��EP:�%!�glyY� �� -��A � u8$0.5-1$��$rm{\mu}$m/��2,��y2�u��of�-\ y(��5/!� n��Eh"g�E��)!3"T ? lex���}��\��5:� .�(�%����>� drop�7P�)��(-S�a!� L�'&L9*�ATP� ��QF��!q!�(-./��(app�?�s ($\�9(sim 50$ pN)�Ain/ 2�aY2acdz�.�%�2C֕ݍ[(s g sixfold�[me�&-�) 04��J�>ngz7 tB)� �Tap�5as oH����@ anom�{!?��3Ig�} adFpW�9F� 6V!*8'�a��F&�'�t� 1�s�qids!$��) �Y��alsA�Im-�a�Sns"�"��.�-��i5\j. .m!���e A�s a�& arokUrb���-�:kaiser0 he�o�< midd�'Lg��#c�|om�to@�6 ed&4��  0ue':(i�� uld }7wIo���b��T�3�1�/vb� (p m�s��atT{k t-\F[pr�|w'%aw�@ll� �% ere.^G�(�Z��|X2q������.<�@wo2��[ &�ang�" �~b![o7:&*� ��I8�J���@�*��8p J3��C?Y�(� >j Q%�ly �)~<� w�in�(����mpl�de�) �7"am.��>�T�we h%UEo=!:� &A*�aLc.��[� a���Ea���6T .�al zJ�% E oreo�Y/'.�a�sM�%coU�eAFuA�>E� Q�,Ro`kAy*(�T!*m���Fr4%G*�4{R&Bɫ sec_ "��"H�a���� 6�C�"? d7+t{Z��9��_�)"� ƠzS�B al kinds:)-�re>I66Z�r X/��be �n7����] � E�hA9�hz*`at��a;5AE.<c|��� d-C��cof�06 y�i��I [�/$��xy�\iHn� gnvzgA+.�(.� u del.�4�X [t!]5� er�� c!;aphics+1�X} &��lM3{pX_�"kQ�C�3 oO*)  3{a}D .���&t AghB� !/a f�� ble k of��o*��q�� ��-��.�b}"�iQTY�f�� q�g$w.�yW � �l�� d} Q2ܸ� ��e�=5 ^ l|�X�"�0&1�4�o!��H�NE=U�t0is���l�Y )1ws�� � x to%�;D!��!�A/5�_^Xdgo�U3"FHM�#�TL%Vop�Ace du�h�� �u; c@Ge�,l��� �1si:/1*?%-5i*non�ton4T�% 5�.}<� ���L�? etupAXsketc��].\�}��(a). A�9 -fM$:���!�tNn $M$-^7o�OQ�,�4xE��>$d��� Bsi�> co�� $q$ "wZF�T �a�6=5*�j�"&�$bf s1HA�s $x_i�6�&� un i� �`l%�:=F��1 " cal one2nB-��u!a. T�e�A the 1�&i-y��} !Jh% $i$��-�ف�)��e�X��� 2H0$.E��B �e�m��uuv�� $V(_ qa )b 0E$V� Z;.GWe�Te9�� mo�#a� � damf�L@�@_& � A���EF0, % \ekv{eom}"�split��a_�T \dot{x}_i &= -\km x_if�_i(t)遺& 2�}{5 }+\sqrt{2Z kBT}\,\xiK$,\\ \gamma Avq}& = L�$i=0}^{M-1} y �z \Ftrap�h�\r{q}(t),�@) } % �O<$i=0,\ldots,M-1$*$�%U V$�� fri�� co)6� *� (O&j%��Ui��, $\kmE<Tq�)���5�)�}A㵌A��3, $)8=0,��ړ42 "" , $k��rm B}{ BoltzW0'] ~ , $Tj��er?[!%na -K�]ng��q`�f��H^�7v 6�=��<e�"1-�� !cv .nGaussi�an white noise terms $\xi_i(t)$ and $\text{q},4Pch obey \mbox{$\mean{*9}=:}=0$},F3 j(t) ;'<$delta_{ij} (t-t')$},�BrbFMBA� have prefactors according to the fluctuation-dissipa lorem. The temperature is set?$T$= �X310 K}. Before discusshh1liV eq os of monXin detail, we transform�( subunit co� ates~place!bin�@potentials on topaea!� ther� new2J4are convenient�8order to analyz d model and 1loABpo previous works with similar 3xs \citep{dan03,klumpp01,csahok} ��edR�lare $y_i=x_i-id/M+d$. An und!p8PilT r!qHis now described as >y_i^0=dBU�we call%Ican be?! of two st�Qd: unbound ($h_i=0$), in wh��the�ffuse ar(8their respectiv��iB=, or .Y1 Y�VYalso 1�)�!%filam��through B� $q $$. We treMN numb!�eoru� $M$A:$a parameteAJnd� will��syresultsE4$M=2$, $3$, $56$ţ $12$. FA$implicity,M�4.�!t5�с�`by an asymmetric sawtoothY0, shown!�E Zc). �nRy ��Ltake $a=0.1$, if notI d �-$wise. Some@�Zeeded�g!�a!-$ferred dirA on���)"�F� wa�Jleca*to Q %Ee1� riza��TH4(unknown) realU7vu . One��(sible origiA6_FL��0urface charge�Iwheay�0ilin monomer ��p/95} --A0 exampl!=݉in Refa��boal}��%s alternaeNis �s9�m� view���eff!wve ip% of some <wh�els�!P,system, e.g.a�2����^(teps (power�<$okes). BasA6 ;helicaluc0 I� pilusu�e E���e9 /9�A(be $d=4$ nm1pf 0st97,mattick}� we ����all valu!� f $Ma��!�(itude $\dE$Fsis��#iny"� 9ee&E*�� !k�ly. � c�of� ew pf�V�!0��Mo!�is� troldby��\e%o�. �com��roI�fA�e� _gy� ���!q! ��A�' shap}� I ��� �$pper limit!� F�ce,� %� $=\D�$ V/ q/eu> #at � � vxeri c�dC=Jagainq n ;ng_� ve) �A�/(1-a)d$��$RE*&U < >��\dE� /dI%^9 . At-� *�$e� .? ox a� ,P!% �2ks �!�!� pass5�&�� aELh� exceHon�think�thez$ &ly asG �ran!9o|#s slipp!P�s =y occu�$rA7te� �-�� far Q�irRd��a��I i��u te] ���� lM���du.str� !��.^h��o0)�$iffness $k�  probabil��Ba�p�: �.%�  di}b�(u�pE�on��vq�"!-n*@illus" � ^�"� �@shaded area repre�!I�.���& . Higher.& of��'aGs l���. �ZAX!W6�$F$ at�� s5u�25�]rightxXij �%�j ��M�"� Q�f��s � , no.n�s7(!�Aedthe�1�B�a1��I*FM�bis $\{& \kBTP}$&s2*in)�f�"�`broader,�\5=� f�)7 A arg� lC!� $��AAlyA�6� mV(t�y!�9� 6�s � enougheA�)�!�!�e�Q+ load�� f�varR ,lyHEţ!�is I�a�"t�a�M%A�-&�"i��a� ��l!�U�.very hig��Q%64�arrowcFf�se���&10� . Al�n�&�N\ 9\itM�%�thresho� � b4*1� starS4 significantly�zSa �JE� is a� i6� oat!f m�!.vainly �)�:�.+fEe}[t]Q*Xer9D \includegraphics.2.eps cap�[{� vFQs} (Colo�(� )�c�X-�I $(triangles2(� ediw (squares)ElowCUR (cir�)�+� dX $M=5n y axP ��Eno�iz))� � cF�v� eG!? ��O*�FF*s"�.}-p-� F%�ɮ2U�'s�mplXf.�E!UW"N �� ᜉ �*te�,!b�Hw�$5V, aO$�c�<�8 vW*�sA� *�  a� �" rece� Ease#�� fina at�:�in2�@]' re�"rate 1�$ (d !@n). S�a92/N� ATP 2o��IFin 2�gre��w�.^.�($/wv�"B�"���EiA;+�;Jy �*�choic� �%s��cussed�qPen�( Sec.�l sec_� }. S���s ($\km8\gg 1$)<1(�au,W*� uQ:�I�E5g� a� *�� d�- ���*p�+ ��1 i&�d,TJ��!�=� 286��� � .&!&/ eE .�5&sd[ 2d�]B,Iua2�� ��%�!Gta_B���� oz.� d A" :-��"S x � i� ,�� �Y� %�%|an*t�)��*�2�as �e��.D!Y�(� s�Ea� "<.�  shorT"�A5�,E��&|e� back%slope (W )&�$M>1/3&I�a�se�mi�h�(:P�'� to �ac�4 h��T(9�is � !&�+@/Qa neg� E�1�5��%con�0.lyAb� 7j'h��c,A�enh!� d byU+" AUw�Mrf �PR� MHQBm� �g .�ly _v"�%�%�e<+:� ($M�.}} E6 &�$YQ} sugges��'&� m)�Vhe�/io�� ���� �, *� � ���2�o furemz�ce]!th�+de"A��j�!� obta�\a�bi�.e�S"�d2s�(}>�2� %�an^�" �"J0 �F $f_&6��*�$AX6 �iof�)�f"�' way: 6� Eq}{� %to ah%5Z @!s d  sion�$. 8anM. $=xr!y plo $!9/%$"Q��iad�5 �. S�!aJ�i !�*x%~Fig}(a�$ bes(t v^0 V0=25.4$, $25.98:4�$33.5�Q!� 8$M$= 2, 3, 5, 6� 12,�" iv� + 'J6� e@��ll��a7gl� g�A!�F�7 le!=2%�12%Cscatt�$g��N�3.�>5`>|0\figpart{a} S��%y�E��!�� nge �; $5<\km<25y0/nm<b80<\dE<2"�0Z]�$M[8hosen 2C<.R�Eq}. Linre guid�^� ey�he ~ many&� ($M=12$*� V8f��9�{�Is. HereI.6i�s���4& on a$�7.9nb6n0*e�-k��2er \to\infty60>: dE���7� $M\le 6$� &�~ .�$�'( ])�&in%z �C1z (solid�1).I12$ ��4a$�` d�-kfitV�Vech�^*�` &"� .�ona[0. Error bars�both K0�.~&symbolsn{4}"der8 � satz>��8e'�!������ls �]���>S&_$&�W2� pr�(��E"�=$ �9� ZWnd��� A��" 1�in� >S1reb�%ye � �(o�A$\J; ��!,��if �ea}-b6�� lock���:� �2ir R�  ��M:J:5� (b),�kaboveѽŃ$A� �all�fFl(N �J$\lim_{x5 }2�a��c; $�)$c;� $6���q�� ��raE��J�.Y�6: �7Fp,%-nei� :��Z�12}{x�nor� �vaB%`&$TI��!��"��[]� dens2](�)�!A|s�9.>&� =rD ��}� ��� � per 2�',v/tɌ�@yYq0 !eD�duRT6�V��!A%� " &�Ds,�]Cl@0y��sY4+�6�3"�.�$ce��H!�!�51 mC�!licat�3,a sum!�"i��)*!&, parOBA>�D �`)^R`, &:ex* (&2 * �*a� b�mU? x ,7 ce��;�PM�.Z� A@21�5�w.)*� well� _, 9hEm�!`o|��um�2��A7> �&�Eh-�EF�.\ ��at�Y���se-jE�y>&N���u��0! 1�3�Aa@5 E�6*6� ��in)E�h �a]$��$1 a9T�0 $1.�o�fi�Fa���u~���E3y$����G�NKper�;�v �e+e��@3Z<+Ei  \dE=&� )#4,�]E N��X�40A150<).wbDN-ed�*&�*$Comparison �eed2�/1"} T&R�lŰA�&�����c��ons, i�%�$A�!��eJ��ngu/=)U/o�d6����w (i0��]5�S>6' &�� a.;cn)�m].�n�� �� \k* } �1�-�>� (SPR�s bs?�+:6xtD,SDreimann,astumian97� "5 veru�its���,� �r.(��ose�!�B�!A�5 -�2E�/�-n SPRi��&h���&�#pIul�H5 ( �89��Z�<� #�",a �m}J"u6�C "L*�p!>5fo Dwh7K �s�=M^m&�-!).<a�\��"&  n== excee_E/2ŤAnE**�>cycle�%e�*h!� . W�nonzero6T )]f�@ ��!�u�posed oe"-/��vLQ�v_{j>drift}}U, I$}; h& r9��N�i�!re� d �a*�"D قfe�.es�spia�-�N%e� alma�!~� Zl�#"�5��� �r.�ɗ�,45a-�8A��IsNs"�!�pl+QND/s (bla!`�)�) Z:Q *B"�#1 &� )r2�� �6%�m� �%$)yL$2j  ast$K�/�f�#.�A�0c� �p���9p}V/E�.p !�� ��SL��2�2�p \baka/v��$ll= N�UE�s,%�preH+�E�T M�*�!3�q/s� ?���b� g��"O) AI� 60 pN�Xrp#O�)l64f�S `"c � measu %�:�a�Mtip&Q""�I�� �ci,ns�M&� f T�.��',���, :Jag9 c2�%� ;�E=.&*���uld]MmdA�%x[4! �� ��Lzlea&KMtr�5>�:�N.�i�� M� ��je)�Y��,.R&�-OA9<663� \Ref:��Bi2q ��B"� {+u /�J16Cich�� ��U|!rMy �Y� 72�:4}l4 uy� +)�m7jderably q+:a� ��o�#�T PilT��� mJ4+9J&�)$M$: nam;Or6Dfive-fI+�P"�Mc"E $M=6$B�sixV=�molecul� 0���y 6�� ��Bk� 6qno&"!�2;�&"50 NC:�#U'e�a-R �aXL!�m;�K� Q�A� (seeF()-�AWa�A/"]$�!�� �<�&=�&� devi�M���di!( +-�U� fall�f! onen� I�F�!1� �� decaR ster� h�>` !�b� I�O8an Arrhenius laF- gate--� ;:`�>��s� ���u��Bi�4=. ;-�>@-�� �6 !� \*Y9��! YRac��� !l�. How��e� �IO� Y"�9���5�6�) ra���a�(� �7�HnIAX lso "�#�;a&�2�uGa�disapp&%Y5�a���W�/�2�a%� su�% a po�S�7Au�V&?$��M$F$=0I�J���2�a(acJ�*�*.n./$q Zwq�JCA!6A�� 2� D[' �Ad�E�r"�P} Fu9T Y Figs> >"�A�  N���5�to"�%� magneS� 6Qy�@ XorElex)�! *s a�� BA� �'"�4�FQ�(coR�%��� 2�quAL�Q>�Ndisj]�;. %L.u&"�2�K���|eag5X! a-���:� �$km('�4sHn �ie�1.2!�M%i��DdE='Q�D`+�8U/.3:. EQ*� U7����?nd� 6�D~� ^qh�]8kd/U\gtrsim 1$ uIiGM �2�.�3 e�!mNFd `ss1)끜*:1 "�&����F!@�dJis $13\͊�V� 2�Rol� �@�"�,�S}�!�9 R?�&-ad hoc;ump3o�=eP��"7: U�"9�u�)WL1OA"�edKTc/8th> E c���ngaT�random F��+b �U}�*6uO=�)�T�ly un?2dJA �6es�p�  50\%�ot]Y> Z-�A�un�r�a2Nd I*E+�#!N&  �cll�+�ad�be?rFtaneous�@1DJa�e �B�x��a"!�>��kav ly irregu�a��-�N.o����.IX6�Pt~S de>3AFQ �.� �9 8e%Tar>. Eb5H �1%A6����2FD� p�C�e8*2A�f����in�!�mb�56$ &G`�S�N�Pbon�A�i�� �pM=�machinera�� ax!reB2!o�>< -+isa�to�L,( �<� �lb �[d!,oW ���&a��=of ��%D�I(k8M�A 6� >O) Q��U��/!�(]�Ikaiser00� "�,!�%b)�B �;���B� expl�! part��J�H spact focu�:2�2-2Q"7�.R�)o ��f�7�$"�)C!�9(AEs6� !n /��lex@!& # ���) an*�S5N $�2�)e2�<yw�nd:l�& J�/.L �-s�S)�ɮ~!�Fw� chet&3"�x�)\Ihe ba� buil�8bP'XouaA��n7n�`urpris,� �B�T�jat1�{ E� ���F�� �� ��E_Z�onU���� }. O�BdelE!L$+D3v����C 1��� _is ��}a�!@I to �g�d2�g�)�I��t.��*T'7Mf_;im>r�;in emIcal[.iF�/s (N^ )�� n ��a�*,B�*"��� /9an� �f�i&!".�)!L4&5^s. Low}Ca�d B �C�''%de"`7.[e�] ӅvamT'C%a=,b��.�&�6M$� !p�EX32 �I>Qu��(eA��� ` ross��"&� �$m�?��t "Ge� �)f�)!�&�X�|e� � $�$S6.� $ 5 oro1�!K�7d9�����N9or3 1$�$�)e $a>0.2$ w�� R.H �T�N+ c�a�"�a�Fa*IhBt} � ��N��nK(ly engineer} i(^ght�"Lt1 R) )*fE�i ud2� � m"� �!I^�:�5a&�^*�@ >`E�v��.d\ .e�F�&�>"� X IE �*T �>R4unc�*aw!�f�5k�l,��ntCVWNi�=�-)3-!)gIj . M�inl'� IpbmW�R-`R"�;Pm9> ed c s. N�theeK A1 "\�A;��"�:9�a&-Q: p at>�.��B=� 2-Dthe�.&�H6�6"sU�B�i�:nt�Jv2(��P�}er��.�>��z�2Z ,0$ �Ś�+�� Y@!.�� %��er2�\\S )�"`!� z �x� OE� looks lik@  a� p g�%QI5 ��� _ �+��"�qt-)8�"Lg!�m�qng�I��I*b c[; s�.e%�z�[/�Vir s a��=�If ��Akmp� ' �2$� ��A�1� aken��J�%�H6��fixedB �z:=z s(�b ".ns9� �.�MIa���>���i!�m�e6� m�Fb��V(^�M�m�z��"�(vea. Giv}'l23j��O� e ��Oith*$s encouagi�8 S�g2�) ɋ�Os�p�rl�Pe��=o�)ossiMr� "P.*�(I$�k"sz (olomeisky05lB ue�!IY true MQ=H!P]�AZ���2� situE�. Gene�Yof�&�`g nano� �vic6�H)f techn�Z)Bes��/A�e��,�:�e�AU��Nt�La�G� e#qo=�ng)�f(�+ul oU& art�I�"5I�� arbon� tube"'ac�V ledgA6s}0luth�H �e(N�ofJ� re-wi�t�c�employ%Z,z�evolv�4muN5 �Sg~%inKk�U.��u�'�Thu��"(rg��.^�Tj/ �%�jA�aa�� ,�-�Nd 'r/5iS"N 0/at ��"l.t� rec�d (hard%d�9 DNA i viL*�%@.cripta{uA[�*qhb � .!?EvAR B)w)�f� Md�es Hcvbe Vgt�a�ut�ofL f\ qXf .�c%0e�UW�Cq�ic� z!)��ep!�d�BU.E dup� � sR [s!��SAV:� . Fu< o�.Iӎ�s2� agent�yj �t�9i: ,JG�)�yeh���^omics, g�heory�pneuros�o}Z)J likeR N � a �"�1� ��9�Jj?'M� �!!�Y!, � Sdy�?7O?RIPpaper�Y�:keba . i� t amH% of H�D � en u�'Ii}$� W �#7,gra>;.� eh(.*0l���w�Id macroU !t�� ��_��,\keywords{In�s�(J�tronZpos�7E��@a�},%�alї�JH�va�O�R� "�} �]���(s�ik!� �"n ro"���y� orga�m)#m &E e6|�䡨PZ���0vA�� e`HQf�n%P��-pair�c�rG ba(�U�Gpav]!codon���mino acilP{VOET�AA��qrY+|C.Y!: �T"� hand8of�=�P^ ��"�aiVr5wC%DSac2omy� ce�Psiae} (Baker's yeast)E]2noB�Ari�l!1i�Z, �a A!�ar%��ve>EveB#a��,hrep:����sms dri�0 @mofost �G-"�eQ�,�Ui�.3n{0�ma},.R�> r�ng}V26� (� 9 arB� Jites �/w�0 huma��I�"� B~w%,$ 1.1-1.4\% "; �E as��M�2� ��*>Txg!ly $ 22b� h�lZe!1mkj $ 75�UiQ�:B�53=9LK���whe� %� $ 99WmLso-]edE�:� $-��e8y2�,�c)kin��1�A��&�LYm� Re1"T,O;rR{ #�Ka ���I-iciinu�ic �y�n�4�-�j*�9 �MATTICK1 2� Tyiv@a�>Ee�r �a��g�colC ʡ�=�U2 5���ut� /��ma�)A;5\�-�a}DNA-RNA�  P _ � mq#rBN�]j����3�] � _ � j� I�0!) .W�' appaw�n���@6B !��8st�'s cru2o>2�AQ;!ho�J%rG�  Inde�ZisaM��p��� H�#I,�,yB� , a� U��<ŴbWorld H��xGILBERT, JOYCE, ORGEL, SZOSTAK���p� �� ��a�Ukh};Yn4 *�%���Rs� �  extra��ri�f�=ly b-�9"(r!uP�2*< (or ``brain'')� � o �]7�Y�_b��.� hu�ve�vvi�;�,� a��w���r=�aa�p f�AYlong-�^2���a�7�su vtoO �� �opr�^�Vog�_6� � �man��J� , �itm��c�r�,B3 playar�-a ``� k ta�9�.''"� &V�*E��AWD�� ams�an�N*�� ���Davailc.YeV c%��,s�m�0{pi��wc$=5i�! c�?�z��yZuml�prbgusA�o&fvalid] ^s"��Q[tinL{y"[ng �n�Y!��"� "[$� "�<� Ȏ*�EWtoA���"e�241iy��)A.Z as �_ng�� s# a�!���9aaI�0$ principle�� !24 &�!of>� (sۉ"teKw3�+;5�Ih{a0�Ew��-M�{� '�).�of� �b�($I�}T7]Ee�8�e�U�!)�Comm Q� >v �A�s�Z�proA� �eQk� |is "G&9o b�e�ma���Xp �M ��"R*� t+"adv9�made� inno]r deve�^W.� U /group%�!5pop-�2 8RS �_QV.�Ey be �at�� spre�h�ard�K. &�8���A�v�$��sub�� 1p$ q:,#!HR?JmÏb/&e�9t68��u2�� s��� x!�Y�i�� a / apE;of�F�� i� E��'DMwVorm"�Z5� isU�!l av ^�:!!b ir���.�J *� �Iz� RICH}, �)rH]! co�]��� Ctype}�d{"��� 1!t��%�!�VM.��" t'"�i��0�N ��sumi�aq*��� r!�EhQ;:F�` �s��d ��! �%#:��:{*@��� Te�!r"J#enzymA�60  ��)\5�2} hrom�� s� �t���JrR���c�sA� ow��!-�2\\ � he C� IIAP��&Y� liv�?������ ll �:r�&? jINTRON1}�d�'aE<Q emby�1�E�, K�Spe�f��>�� �d-�sYdE� matu!�&o�+C@ .FCAf �Yf��E N�3}�r�Xfac�aŖron mov�$�o� "4�0�� s!]}A��7yq��7>��=.�.���"�A�A�domin�~��|] �:. �1� 6��7ju�A��12)s{� �b*��IBIOINF�jI�� .��8��en6�Fu1 primsgen2� 9i&�2����,%<�.a:AjvB%�2�.er� F�ae+peauP ��.V�)s�2����Ty1I���s�/"�35 $ cop��q3 $ �� 13\&�^!0�59���fAv& � )��o��2�8 ��!�sourc6 # viru�=>���?4t� &e���na�2�kA�J)�; 8^R/ 3 b��&�:]����&ir���N6�+cscenario)���t� �e � ``cAPA*''J���r��en�olJ�%Z(�e$� .e+sA �*� !��l "� jE�g{�p �f �]�s�>�M>$RETROVIRUSaR�" A&�&� ѻ �N->c-�H�-�)nH �Q=F��!$medskip\no� nt {\bf P"; 1}: �x2N�Y[ Q^r#do)��om�vi� RNA�)�.� sac� I�#j*Tze,u$"]� uii0!�?veh�7��w "� N���enDsh�")xI!: O ``| ing''a�(e���ion�Wny 9``w&1 8�Ŷ(qJ>D �Epa�Da� Yy"�>� W�T� ��eşz3�esli�O�:> QE^�� L1|U�TRNA1, 2}:H�&) !2� <� y`��A�} lymer ~!BF2tmmU^torjn �, �2��E�"�>�ge�'��of cer��mi�5poridiaIbe;�2E@� deep�$ branT=g`a^rOs�5�)� en�BLAST ��vea&a�Q�� "A{$� l��s�(:���T0 1]6�%xaA�*niaXe)��D& ��a������ysNc%ͷ)� �!M��*� "�&%&2 lex �-?� .M!��(� ing,&u��a�$@ orth�j�vA�+3v�� g�/lly�A��؉H��P�}EP�9� fitZ�ef�S. urB���:�O�r��e�, X-�A*�!�t��!Lr!h(�so3RNA), s��%0e#��sno BnucleoC��Xe�Hi,AGENT, PISTI �*M��[A z� "!a~�����Iw1``�(_�mm�''�� l m[ �)`/a�(*J�� 8�*8endorphin-adrene>� k\-punish�����E� way,I; �e� �/. ects��A�0o-market�);��+m���� money5)ngs "0`-��sEth !�&�f-+)* � >[- ���,�G}�rq�"�'; ran�$�% 8'1s�8/� rigg�byep�Fy9x�D��?9� DaLeZ�A���*�synap� I�'M!�$b<  ca� E�ism!��5�p�y .r$�% t%� �- �� inpuAto��x �m 9Y�``�B�  0��  !֩%/3 Q�+��b�x*U%E�eu� pm lonal Ma�ia�a)� S �� O`ur!ࡼ}=eq] rZR >|Me� |ve�tag"�1���� �It�tr.�18�quival�;29�e�|V& + gniz��]Mor,� K�cisCJ&� �I�96[be ^cØ}y&NR�R-�-tC6�">e�. 96A �*� �v"�&����ieZnd�%'�>�!C:M'�`J@�"��Vj��^vcB<3�o��"�l*��a kin03"!m���&��"�.l"�BhEx ����8cI0<)� �?�k � IG�o�l�2� �.g� � 63.�sAFdea�^i� ie � J/���r�M, w%nr1TB+�J�h��d���#M�``�K''"��� environaw.�3� alog�i��i�� mem/"I�A]� om?�?-(�F.��UWeYrlai��a� M-w1.i��oy4i/B�� l� !non)=R9ɉXDi&� .Oa^e��]�+ � triv�:6,�4,� �� �e +%k7 s A|}#E&� � ���Քen"p "84!ߥ\�3!�ozB�3�� B��waCc�<� m2�1��5�In" A,AC&��|B �� Wre ..@�2I�a9�>� 6�%to)O�!�a_�as a4io�0�ly, be� 7!I� ��f^va3�" K��{!���f^��a w��&���J��nU3$ exhibit a:�.�!g>a!%�`8�� Q*�&�\bn3&�&� �"Yj!Htf Q f-_4co�|��. m#� �i3 �)!� 6"*gB(pHQ� , ra��m�"is) \�6U6{e} E�� h�"�$SELFSPLICEQFu�Erm77*q�-��"�eA� � 6� is �?]Y6":V�Au!�FM��!�~_9�f��i�,�t.�atTi ` �_� o�1��ed)��� tubuK{$ytoskeletoօ({CYT1, CYT23p`I����1ve2S .T��z�{ Wi7��u�� port��, ��2� �Yiu`e�(�\�A�,V}<�0�A n1%�b[%5M��[� p�_[@ =tsyyv;�l p)Nou�(* � �E�� onsc�*�CYTXC�D �B,VRv� jG&C ��$ �n5�Pn$�B �iR$F �%i� �I a��f�4��Rlt�G%Oz4=��G>%a�9� Mυ�^�}.�({IB�E0A#m5({P�)s �#us � � �%ingi( e go��f��sO+,�VDB� �L x-�A �J� ���*e�$i�v!絉�?�&�O;Lb;%�i�4HV5:eFtrn)|!=Z�;ld,2W�.d feed�n loop���$�r�*�*q�.e�c+ N�8in n�' ��>&��xArA6�;��2�#� tabolism,up�,��9 �ho��� �15in���"j::sConcep��%F-�!:5 G ��(�(in�� � e�� ofa�v�"lSA�&�e\[�U%a�3�/��^alc,�l %cow�KHAMMASHa�.�9i� �A^E>s�ium�6A � ���z � �/_7�Ise �z�EaE]w�0 y saL �0 .("�Ax ��I��&�@����Qjz�� ``M��.HiKk[*�a: Jm�ca wide rс6 ��W >UIh wtQ2��&�Zp�Y�.�U*�=&U�R7V+��e�� will njt (g�j� )�zy2�af� , ``9''2�9h �(�M�V+r&�=�B5�1��p2�ia��8��``choo�''� ��s �)� �� �?��s�'�!X 3)�d�~A�Jr�s_i;�2)i;/i>��� �]2�>- '.mS{a�J�/} b-2� %ach5nlall<�(%�aʱɽ t�5�����M �)E^s7#�at-!%?"�1�.Kert0 gui��yu !�aa*1)� ��"zhAݱ���*� ABily �pa)����_"�=VN�2���by ;��Hu'+ b�g s at� .C (s�on�)X:� :��A�2=� �^z�a� ~�X�We �M2l �;sh�&pz'2� multi ity} �"�{j�7s�@probleq5�""EI_y,=�w�4 an��!C�;e!��� E�>�/&��+F�G%6pre@�si?1oB�I-e6�co�8�"�}��� "��;M�v�4[3A�� oyr!nmie  re(IGe�S�.� .wUB.To9���>�E�R��`�labor&ok$�k*W!�B3,�ue!Yl�)na�@O,,y�Zrw A`���H%& �aj7.5e�1��20��ea�<5o� i�O--�2�-!i �2��- rd!#R� �8� �TI2ys|= g� forg� p��(��  sacr'4eE��AM �2t>��"� ���eG�I� w�@I� 9:�p �no9VG"IJfunda�����i����x>*ltiT�y� y up�~�&"�9Q`�s14J0Cz1�@qE��Ayec{��uU���lD��gH!"�%�!�a�'{!%� �"��J-~1q����*�ly^  ing � !�� aoC^Tp ����MW �@��w�?5�>�._N^r*auD1w*�@�6�ex�Je&r���a�& �&2o AWZeu �m&�`p"?g�#� 2�A5� A�&�?,"��J�'I4� y�xg *�6A�d |Ct74M�.d! ough�sum�G�, c�.�pu�A�.n6!f�$0��� �^$deAse�� !�r:_ (s.[2��A��7o��)i���D7� !�M�WIW v��b�v�D�sc at :\w}�Y�ر,%�yR��-n��*eVna�x� { n  aJ��$ubz�S~$�na[�,Fou���6 �= r�-a��%�,FW 3�.''i!��%e�"�Pq . SH�a�� 2U<&� 'D�A�'pul�k����G-Med&���:�$` �ou3)5Lwit5� *�.''&y��!2:a�N"+�#N,����.qqA�seeC�"� �� "�!�����!x{ � . Bi�! s�k-reP^�( A�t(>��thQ:��dys5al9�FuP��u�:.�A� m� fV^!(�Fhi�,�v:N> 5 ph�Tn�!� pVy >BEB=�'}Y� hQ!M`2"} )_�q5a��[x /�?��� ��s�^�q6� bur*r �6WF\&�"���e+��!�N[ disG �5�t"��QO*� @32&"J/Ann ��"�� �� C"e 2�*�[ .ha5Gsta0m"����Q��'s�aZ.�E,� � : OI��>|s"v)�~_ R�#, !�e߉�-*A� ���dergo+ 2�����a�=�mo 4�r�qne&���-t*� F�;ZQ?ATPI89 *�.�A�(3Bsō�[!qliH �-=e ubiqu�of Y�a "/���&3! y�8�R)&�D!<�+�3&/!��ܡXH8 #�)m�.0x)JiI�di�bar���of �deR[%:��6Jm�s:i� *@H- 0di�L�!c �3 - �uX�s�<#�?e!+I"�+* * ^("�G�&3�  m�\r�[A��;�u3�m s�Q��;'p!�!k���!�&�$�me�[%�e'�= A co�81��bQ�n$-0�M����-�-�@N�ool1�aK&�ua�"�l��� � �4 RNayl��� � &�gi�+2V�">W.V%�.X�� �e��3ar*��X" as:jnd�4erc��2~4{QUAS, HYPCYC1 2 3 40� 2����p0E9�{cib�j%d� rgan-V)6> �2�i�i>�Y��*$D�ll�b�J$aR�d�u &< (�mEitH s��cIN.�&7A�� C�� ��3 ?� - NOWAK}E�� [C$�mfi�Egg�X*AnM�I?�Bcad ?6Ja�&�>�h+� � m�1 sn6�,�m2� o�㡶>� �(se&���-e�,A�egA .��4e�D�MdeUA�A�Q�s�.M�0W'F.���N!X "�Jt�Ld6wA`�0źse7e�O-&��Q�+ �$ho2Yak�_�+eaS4&� tru� �Qv&�# eni�*�ma�f%��(s[)[�;.�h� ' ��"u56%�-&A�vc�&�] � , �B I�a&�PnewB"# Ae�a>2&0 %t�U)�>Zs.�.��1D c�  ����s ?�4]�-VV-aq? � $ �� s \REar@� $ AA�2S�BN- V$ �,�Z5at�I�  %)FVB* (N�s1 ney)�)b!���B !b�aA~!D!a�> ��� �a%R.2�"9< �"��� e�s"��mB %8s ��J�4!a.� !��}�!�+or�e9� Ef���:A&P 27; �"�} &ee �p$y OwI"~�#�Q� atom�ephysi�$� �%xSc�록n �Z &�`Q��ya�I�7�(s$5)=b�,\ �R�3�:�!x�� --J� #�ψ�a4a�A�E:��*"aסv%� Z cas�̥G(1BS&� pi��JGX(2)�tF H��2b�I . R9ur-�EL �( issu�*3�"� ��l. bey��)E��"�9�a.N��4�, �i�p65A���"0 �%6x";dSd���A{�T\A�ts,"fSplaneӉXB ���ur]9�s.L!*I�V laws�0_a?Pau�I�AE�x9>�}εA6�)��0l�jtB%�yB.# chain,� 9/ post  obje: �e�^9�>U�or�Av�����Q�;F�e0a�6 �a��:i�8V�Q9�-"" * a�i��Pc!_R!qce4���HcV@=ic\a"�)�F �Wp��k�j�/X.\I�at6W,�%�#>cKeeHx mA>w`Sun{"�,H&( 4 Watson-CrickA|esbk?c �dis"�.a�At6;[��2�!"�F.P/�<.� k2";\!e��C M ;Q�[Aqcat����  (��gNs}) 4STEITZ, YONATH�=� -�&�rt�A�uE(e*�Ve% �(6L��| R>i$���fw�Y*�DEY �( Iy�&�H6y`cebIc&bc&Cfaq��~�Ka"daS2�d3��"�Q �P? its .O&�IU�(� ��B/� s���0hquS!*-! an �Cpep_c M. ��!`�XR&�]E1per�"l.$ I�%Ug ?,���*T:]PNAA I�y5!�Si<o 2 N3a��1] p1�"]+��fA�&��uVG�%�*�2�����e�� f-r]d�es:dŻ�}rapidl"ӚRy EarthM�LOREN� F�xY�st��^�`ASHAPIROA�$/"�:7 �B"ku!�ny wa���%!B2�s -A�a�{�b$�"Q+(V!u^ ��� ��j)BJ�s)�T�ۭ�m�ksao���(�>r��� -of-� modeW w�#� "Xl>' eW��=m�on2�F~�.�H�6BIq�� }%��j��6a�W �-_�Bw�u� -M(D,"�B��nA s A�A��hRn:T��b�,��M)y�eX#�v��t�!- �h� ichLe� | �&v"�#*Fdr���� �� :�c0B��O`ArZj�de�� ��� �^�%�ta�;9H �% ��-Za�r�e�c�U(��=y!5,hieroglyphick4�ev�5��e�Z�AYodYa�� bets|a-div�f�^� k/ua �Be�!thu��nJ ]@L#fa�R!�� a�``](''u�b;'�6T P� ��U4� �}"qC��� ��_�Wi<> E�����w�!�r�ng �_-�2y�A& c&:5�:2`� "p��Xw��0i7�h� m'6,�Dɰ�fX'r��fIO auto.�.� I�e��E� POLYPEP},��e���p>:l� s. Phylo��avA��N��;"#� �n��7t8� �V�`��al�$�, onship&�.ф� �ܙ��ile��p NzA� y�4�y!t�[o{ �s.V.Am�1'�#AFsF)"|&�E^9SL I�.T�_�8 hy�xUj�A 2���e] A7  5M��2>�� �p=��oy !K�a��DoO!"�O[ /r�*� �Ra�� :%�-acyl-�Lm�" (aaRSs*�Rpr��*%�<���<.�� yz�4lR��(o0"n+%%�ɀ�~��ri�:\RNAal �&_o�9�e !?s �-5a�d�(c@��& �M�IRq2�a�eDL!V676a�3i��Bu<!���6��j1s "0� a��+r ����Jf-��*�(A%��J�W* f�%i%�Q�t �g���I �t'�\�%b!,.s2d!-�E���?l�fA�5/� ly �3 ��Q�.>-ing (y6�- �.��w2�ew�o�"�o t�R..�"��QX%o�� ��� �d�XAہre DW J,� k>&j����"oG` ). i~iimpri�fg''Q3%� 2��%nE�}�\Eag<��)�PRION1, 2�%2�%+�A2 lay 9;ro;.�� - �h ic�&�\.�3 �*�@?$�#t�A��3 ��tI� rd� %�y�_V�o1)H V�A�f�g$myloid fib=35 �6�I�jъi�~-Qe$�qurs�c�tf'��&�A�zGguA�[���9i���atc� b(�pl9,B� _�)$�!C.np�&m�&*Q�N-K� �1�����a�&�{n -� vw��,m�_�*e��ف�mn 1}/Rk!�e<"�qzebL��]!�NE�) �E��e�i�.�7a!#Sd�Q�:�M�%o��J��yverthe�+�B:(>a��a)� -��W>{1Uly. r�1�͑� qVF�� "�!C�iAVReXR� .�!N.�A�^!2���^8��SI�T%� ���;e�VRdat�� cR�� .pE!�� is gu�ems�?�N*K!� *�sg���*��d-�3sBdFelf"�+ c*�E�\=��ȥ-%"qEo�:��u/]yU7Q�a�key�?� !��sop�.m.�|�.J�dg�'Y@6s�"�:#:�E"Z��J4}E!� �O6C/} &Yw:Ba*�24L��zE��H�*~&���y�� rigoM1,(~,t -by-}�&�� ��9| v"[K � E� ty�,r� }=>҃BGaloH>;!**�#&)=9 ��NC<�2Y(c��lB!5n�,� ^�a�poun��^�ee�#-�8 in modern bio��logical systems most closely resemble them. Such studies should include various prebiotic experiments (say in a chemostat) to create the first self-replicating molecules (polypeptides, RNA, etc.). Other studies s �< start with selfVXP, and attempt to find�T right combination ofJec pressuresBHingredients leadingNTcooperative behavior s`complex autocatalytic rea ^J M#�Pf�Q$�R cite~R.$�Rurl^�0url#1{\texttt!O%8{URL Ia�(idecommand{!\0info}[2]{#2} B!eprint []{S'}aGibitem[{2�{Voet� <}(2004)}]{VOET} o{i%}�5�{D.}~#1nM}}A] {and�ZMJ.GRN,O emph}A$title}{Bio��Tistry: $ 3^{rd} $ edi��(�74publisher}{Johe�ey�$Sons, Inc. o!,nfo{add�^<}{Hoboken, NJ},  year}{!4})a�8JdMattick9^MATTICK1�bJ.S>dM6�(journal}{Sc��8ific American} E�bf9B8volume}{October:M$pages}{60}=>��Dennis�2AI �A�!%V�r>MC>� JZ�Na��j�418:< �122R�2r�0Gilbert}(1986�GILBER�%W>�J��319:< �618F��r�Joyce9�JOYCE��G.F>� H��b�214F�20z�Nilssoni� noad!�98!�ORGEL��L.E>�Orgel^�Trends ��. Sci.j�23:I-�491F� 1998r�Sz� k et~al.%̥�SZOSTAK��I.A>� Chen�z�R.B�R�Qts=��zOJFO �O �y6�cn305:=-l147V[v�Her� E[ RichEZ9AZ RICH�lBj P} :�/BL�f�. Genr�1:>-+265R�9r�Michel%) Fera�<95!*INTRON��Be S�,J.L>� �Z/$Annu. Rev.u�j�64:H-943V95v9oh� Lambowitze��P);�OG>�U�9A.M>K�Z=8Nucl. Acids Resn:3Zs647Fs���� 19i�)83ifj�H>�Wan�~��:� $SanFilippo!&z>R.NB@ ingh�;B�Matsuura���� Mol. Cellj Z239F�!�r8Baldi and BrunaX 1�XBIOINF��P>lR. !�6��vV� B� �i^� A�r�s: �4 Machine Learn!DApproach, Second ZE� *� *� The MIT P� T bim� 0Cambridge, MAR� 1r� Mali2�0!�$RETROVIRUS��B|R!I�R< B�Henikoff<6�zNT.B�Eickbuse�]"�Genome~�10�@pai 130V�0rpXionge���)v TRNA�aY> T�!$�6~6EMBO JnZ� 3353R9v1Hinkle.7E�!,�R O1-a�Z"H.J�rriso"d �kMF� SogiM]^U�Bi�� Bullnl19Z� 25J  1997r�ClarkE�%e AGEN�-B� F��VKe�+,There: PuttBra� BodyZ$World Toge�bJAga!G�HrH�:Pisti� - PISTI�<I>�Morocz!;,{\it private\mun�on}j� Sjog�U�a.SELFSPLI�&AF� V��bj5R>�Stromber֟BF� Sj�ON6Nuc�  r� 2Zc354V�v;Luo%�� CYT��B� Luw N�*� � . D� �2�N-^Q60J��� Kaech.^VCYT��B�L�TB>TLuda�,E���B� Matu�NtNeuron�17�;18V# z�in5[�a� CYT3�GB J9 r�B�Alisc5��\S.T>� Warr�=$�� E��Yj� 6Zk04J@!>r� KrichevskK Kosi� q�4�uJcV�� KF� ��I� 5@Proc..�ad� USAjG9Z� 11926F� � Haga2�1A5�AB}L��^9 BgHamer�; JFJ Tuszynski�N�Phy�b v. Ejo6Zd 0619ҁEl-SamadB Khammash�xB KHAMMAS��F- YκB��Z� BIBE6�:3N�20zT Bak%Sneppen� 3�>B�HB=Bak�K>��6�y�YB Lettn� 7Zo408V�3r�Jaie KrugE<� KRUG��B�M�/J>/�L}, q-bio.PE/0501028 � 5n�Eig)�7PQUA��B� EZ�ū wissensch�!n}rv 5Z�4N�197v��I�chusterA�7� HYPCYC�m ^��m��B1��>b� ^�54J� 197v� Z;U);�� �;�;�;ZnJ�197v��9�� �9�9�9%93Zt�;&�8�In�X ^5� j� W.B�!Gardin+"U ��v�J.�or}�b�8Z�4NS198v" Page�NowY� NOW�KFdQ��MFI �Z�12^?"9J�� Steit&n` . STEITZ�jhB�Ba�� B7N�P!A�jqB+ HansXz:P.B= Moor��TF�)H�N# �%r� 28Z� 90J�!�r� Yonat eYONAT� B HZ�*� Biop� Biom�S�,.v ^=25J���Chapu�!v"A�� TNA��JF6 S�� #J. Am. C(0Socn 1^�92Z#v Nielse&�199A P�7PFk% OA8z�F�gholm�:RF�B�]O>� Buchardt���5Z4149J�!qr�W�.E�LOREN��L.B�+K},�\hapiro{ M)SHAPIRO��B�J�bR"Originf�Zh�����Z�Z� v�Glover� 19n!� �VN�Q�B( Kowa"/zEFSchirm&_j�MF�Patin�@J.BLi�B�2&�N"�z�^� 811FN!�r�Tru���>�E4�-HFg$V�� �-���6a ��47V�v� Friedhoff.L�%.��B�R�zBf von � ��E.-BAM�ckow�~B�Davie� ��0:-2�N�}Z 1571J�51~C3Bousset5�-�%�6�+B�# P�}NF� Thom*(j SF<Radfordz��B&Melf�E��)bP290�mOgaya10Sanchez-PerezH}�7��BG Z��By6�6�� Internap!Microbiv�Z�1Z�vU Mull�20�PF��A.WF; I�6l13*"::�2�>>�>  docu�?0} ��% Templ�(article .?pr�< .d class `elsart' % SP 2001/5 %\,+{ O} 6L[aps]{revtex4} % UsDA e opR<( doublespacg*0or reviewcopy8@obt & l�/ , %>k:]{ �3rif you�A8 PostScript fig�A�A your1 %)�C@ics pack�!,si�B�) ands�use "{3} %�u � x2Jm�Bcompl=*ed T JSx:SepsfigQ � ?er!9{olY%2Z C%#�0amssymbS*?s"PB�Bm.�B2 ols .� IA�bkBQ+k> {For%�re�Aibility!�!xno~Cand-bia�BblB�DmZC allows%�1theoret"�CprmDF iden�=a blof its 5 parameters from paiE $e DNA sequ@D!�aW.s.%(!VI�al lab`CtoA�k�Dhors �DicitlE��es: \�<{Osvaldo ZagordibBmail{z D@sissa.it} \affiliK{��io}School�$Advanced S�FxSISSA-ISAS\\ via Beirut 2-4, 34�L4Trieste, Italy!� �Jean RvCbr ��Laboratoire BBE-CNRS-UMR-5558, Univ. C.h `nard - Lyon I\\ 43 Bd 11/P918, F-69622 VilleurbD$ CEDEX, Fr��IA abst!�} Beca%�f!� base%��= rulee�DUFs@2m�E%� erie%)by a �DARof0 duDAevoluresultQ�same s]��E\ can only observe differm�Xcoupled nucleotides. Th�@in�abs.�a E��EE�wo�!ndFiH�Fost 6wt.�instead[ 12 iaPffi�@A� stud�E�ar&IUFonship�hJogousu# s de�FdiGaa3 mon !�stpO ��Gha�H)Lymmetnduces�nu�.�indepena�-Ze s which%v be made. �Ia rI!� !�inIcas%�valid��!Ucalcu �m�. A�promise5Vo\J0ly acceptable�H�f�A��s iAtro�(a f�Gn�it�' ersiRno-)��6�C (�RNSB})!��IentedEVN�6� under t�G�QEshownaexamplA�By|� keywords  2,!b[form: \sep  \2 {Par��i�6��\ PACS codeR]\ `)< \pacs{02.50.Ey (Ga 87.14.Gg 23.Kg�K make�~�mV�/ \5{\��{i!�}IduEM} Darwfn E�is�d upoI��IlayEQwo�I��forces:)�bf{��})�=$rganism fe�Ca�nd/nal GLe � ��ng@!�lihHs.p!dayiTrol�\+��vm�ve��cesA�has bFJ$recognised�3<R�X basi�I�GE�ed. M���s���w�Fll �sl5" rate}f probmUOJ4t a descendantsa�ce�geI8i�0a�se� ared��t�Ka��LiD.��!��.�ofVM!�2{ when g7 �%2speci�� o on%�itlMc�1�JWe se& at���N9f�"�N� �LJ�%�pr%��!e dama�:b ps �� erro�c.,�.����� of a�!�pop�G-dynam1 |,�ch%�spr��P�.�owhA�F . A funda� al.��� M. Kimura!�1968 I({ki68} argu!hat����� neutaFQ�,s (i.e. thos9^�^$have no apA- nt effectQ� adap�M[.� �environ�),I�n d��!�pI]� !.�� s thTIrea7ua�y($ame. Let'A�nsi��a�*IH $O$$time $t=0$-�� aUŗo ���t�k M;, IAʁ8��0M�, $A$E$B.v$. It Nb"Oto def� a7st-�d2J.o%� a t� to�� e itAju�Qom� �P he }pQ. In or!,tf ��o�d>�*�aG s (�}s%�� ��)% their con ;t %Na|[ ,aS� a* 2�i͓��GenerAi�mq�assumao!r(a Markov ch�9if &�s A]F  about�!ly� [�g w2�re:@O�Kize} \ 6�Itdo not d� qMpos� al�=!�.l; Ou !Mt��� 2�A�2E�2!Q�IWmaM �9.)!a)Ag �4al equilibrium����SA�iv�R (&�  fr]�!y�).o !9%C We w�R� even� ABx!�� last�hy"� � *� sQCper�~ d, but itA2worth!� Satf�,AAvYEG� fi[is` �ed1�6cours��5�. Deno|w�T$f_{i}$ 0mZn1Gk he.<$i$ Kpi \in \{ \sf{A, T, G, C} \}$dR sr_{ij}=,\leftarrow j �.�E'i�=�$j$!�y�#haAitE�i8BW�G�c� � nowa��d�S� Aequ�3$} d=2t\sum!$%)\mu B$`j(\neq i)}r_{ji} \quad . � ��ndgq�% }[c]ceja�nc$W�Ts[width=7cm]{nsbc} \ca�aD{\footnotesize{Exp"~�� sl{:�&� . I� m��,a cerAb6�aS!�e� on ]UK  ,x !s��a�val� ��!�Q� .�� le��/� s.}}-X!_iq -Z56!g-U Si� 1969* en Juk�o nd Cantor�}pos���F fNX one-&=b?�U� in��, many"! t 8! increasa� �x�   �%dD.� 4-stM�a �? 122��s,)� bf{GTPin fig.\ref{schema} (d���Zharkikh� zh9?: �V,,�h�I�[yhe ��,%�be de��Vfur�@?b"� .�*�Xa ple�aA�& o9pos�choic: i ak� �Wccoun�PprHYt��V},Rai�Lin�)3]e.f a� jby Sueok) 95-Asu95}%2w5�[9it as � it{type 1! A�}C  PR1}-���AJlyB stoouZinkA^� sco" 2[oFem�,� i�2%a�beeY�Lways: $��} \�Z��C}$��d also���opp��{ GTFGG}B �mƺM�^ Hier~YE�*oUcS��T�sU�� E���a�r�3�indm�� s. O� direcaArA)�o discuss�Q�ddrawn-�) e��0 �P�mid� �[�*5�V&e� mean�+nF iscrim�\e2&� [A��) ��ia��6� In�"� e��(/\bar{\i} j },� 4w1�Jbar ω�z&PA� bar\K�}= T}g vic:a. And $./C/G}$Ailarl�[��4��.`��a)t�� halv� s�� foza�2��)"d i"� :"Heqnarray�!1} a&\�x& r_{a�AT}�  TA}}\no � \\ bB-G-C6-c>-CZG:Zd>-ACZG6Ze>-CA-GT6-fB-�GC}}.�Q1-)�]e� e�=Uz!���ist�� �pous����S� \�[�L� lo95} E*� d � �s�^{���2��sl{ma;[ �0s}: $$ \dot{q� }=� }(iSq_{j}-� "), 3i=$$ d0 �"�v:��$i�� Thes�  ��giR by}�-}� A�(l} f_{1} & I�0 & q^{\infty}M�}}=>Ao(\frac{1}{2} ,b+d}{b+c+d+e2� \mbox{}\\m2rmAA>mA� bmc+emfh�a�insic���� �L is e6]nt� fA��i��_r�Q E�Ebf{one}2tQ`� CbJ� "w`normalizEGA��  $2%�+2}=1$.7I st�O� facl ��L �!ngl��\�2�Z��Z� �it is j`st�Eas� �c��!fa�� �t� m�bee?��? 2/�;4A�� ;���wO���lt�ag�:g6�algebra"���%�R _s,7 is��&� to EnKc�Qb���a� p�d rn b��Z�out�%"q ..� E2T>�,pr1}Material~d M� ds}#E�5;�0[F1�m,��Pve, focu^ o �>c�.� �B�ub ��-�}  � } G���4�c� matrix $L(R}_{[4,4]}$ent �@5��>.�per uniE�v, &� i�De"sl{"�0 �}�P�(t)$, w2�$p_� �$es���:��fA�&!it � �� $t$,%�nM j 3 . YeI� sl{�a�B�X2�% o�>d$x�.pual>� ��6�4D"OF�i�!/�%!��u9ce. Obv="�2Eq�i�\Pg�`�q%in�=x_�(t)�is :��Bj!��g%�qh!�b� diag #)� &Z  �|�m�4.t �!!an�ve!�#1�syntht$>"���� wh]F�, rh plie" }� ��� UΙ>2��c� correspone zh��steps � u�"),�du�%� �bxF� �QX!� & =, � (R'_m}\cdots2} 1}~X}(0)R^{t}_1,2>On:O at: N�P'^pPJ� \ etex� u��^,k=1}^{4}p'_{�L,t)f_{k}p_{jk! \� >� � !�V�can�`(principle, �LzM���m�J3r��&�l5�]&�TN GfC!�l b0& 1-a-c-e & a>m�c:& e:\\.^�^Tte-cZH&Rt :`�& by:& d:� b-d-f & fJ6�C}!�VLVxNXx (b -!d�Ii20 �+X#�$e.�ofRit{:D$, I.E.��#&8 Non"�"a&* � � -�we� � eA�"�m��N�� ; a�s?< dean"�� �,g*�to estfe�� ,2���!un�&le. A�'e�� eq.(���)�q�Q= ~M.=Now, s��o�'!p',��onH@�cP'&�P}$ not.� =�f!3���atG�\al�"yOG ��2�IM�"� q^{0&���T}f_10x_{AA}(t=0) =TT �a"�ICIjoGf_2\CC N\GG \i\� \a y��:a} �� ing}A"^.� clea� at +E.%s�) ic (I]LX� )��.�6.(6:� n!w�vez5.Z ��!�� i �P.ca*V, �y� � $�Z�E�� :�R$$.A�m0detail:Bp-�4par1}�AGb x_�aTCCT2 A~C-CA&TGGF-T-TA>LC2yC2%��Yj%# �S �A.iB�C.�GGi>�Where%iReT !IG�A � S � � f��6�($� j} =w$) @ 0'"*_ E�� ���AGl�AC T C��FNUy�8sYJ�:� r�  ��}$}� ���:`�3b� ~&�sq3m7"��y�(A�$Rodriguez hul.�ro90})N�f�d�� }{dtх2 R3 :"|26 sum_&r_{kj}&`%.�\ Wh�-=�5i�byN�| sf; 6jP'!�."=0 P}^{} )\\ij,A6�Z�5�x=��I%� (epG^��^ 9 A ex���%�B �$ (!�UJ:)�� inve�z� G:+��g�'Ust$gy�( ld bf�*uT�A�a% ���� fun�1A�f"r* ��ab/|Y� to gA�n=��2E� �� e-ed*�+ {x}_�$�"-q ��vlu�Em�2n2 tZ���j=l9Y" "�*uZ�$1�� �m8�>al�6�a�e"'by Takah�&\& 2&081�&tk81}] �� a slly less6�A��9 is (%�bf{TK5��"�%�")�. 3way�=V�gy�!�B�'46 .� =@,A]�u.�~repeat0 ^�'on&�"5�\ #"O -���mpm ji}$;2i3j;;f .Q6~ "*A���:� >7-Thux2% n�dow!�e!lireFfA<ma$ ��D&&�>� � } P~�� # ~ j x R� RB5 ' 5 C6% Q>� mT%�:� Q_:M x_f !� GC},"+\\�� SN� �6�SN� �� B�, $z% 2F-� P r� ��h"�/j� P, R, %{,%W �� !�>ʫ �� So�Y4� :�(e�,e�s5%$;� d�a��beJ? ^ x_2Ad �"d(q}} C}}� =6]$.(7+#A}B#�%�9*�� �#1gf9a brief��"�.!!� . �"s������"�5!���w�b5r�1�  ,wAywc�n:ly sas �do%i�0$m �'�3vE� . Sc&85])�n2�+�! bf{s3< E��7�ed"_} *�}l�1i$ don't�4nge (ap��*f�e-?0 flu5!��I�Dey"���;,�$no&� llrea�ite; ha� �;!j� B)ab�'& {6?B .� A]�t ��#�-n��i&� wm6,')�AR*whH �� �V$��$q!=As jV l.�du� Qre6V term0�.H q_j$��< s, IR �"� X}$�J)" . A� !��3p5<#r�=,�< qzotadotc}(:�=(d}�C}}+bG}}+a,T}})-(a+c+e)A}� {�� S"^-eUnA�Mi u_�mO��C}; &/t}�do K�.AAuN=�, a ser ��,1Bf�1�8Z2 Ad� iz ndYv/8 M&fa.�%CQ/!ppendix  app1�pb ͣ(�E} Until}'�� �*��aI�lB� %8E��� i*I:ofa�� q� � nX O 5 �� �-us�*�� aQ� e� m. W�*a�Q��#o}Be �~ &�!.c*��/d���B*�. m. M�3D2�%1> . On�H�aa���$, $a=f$. A�r> S �A ��:�G r!CH memb�=�2"%�J"�(�ny��e} "j}f�+=!!i �6�6\fo�: i,j.,�� ��&&,%-�A !�N�a.O8N� � ��5!tm�(�4 ��"�+qui16t0�� it{��*al <}�BR2})m��sF5-)5r8%| \�5�<uri?^� holds if%"LfFbe=cdB��1Q�&N insp�!�!> $�~io�>ore�rB4I�luca},�'o�E >�3}0@g�<?EG4f Y�-�6���s%by Ya�*/ya94}�' po�Cdk� *+ fiw!�� bettin�,eHs. Gu%^Li �gu96}dkE�+robustnw�st viЍ �Fm . B�*res}R�H����3�D��EG ^���o�:s} Du��c3xit"�=���� e!� ,�_iinkiF�-ca�7��+?�*to��]�%> m��a��Ak�*��4 eref���H*aŋxc �to�* = �}A�,*d�#0$\chi^2$ test� ٵ.7b�$�� 8��i,j} � (� ,j}-T,j})^2��a�,j�B= .J-- 1B����s� /���al?7 non-neg� � zero��.9,jC$)! #!�E%^I6 fA�-�A| s. C0 ly,a��>AJa minim�/�D look� Is�Ke^ bM�\*5on!� tr�@� _��=�:UQ� out���A�:_0 ilur3 �#orithm 3 w5V r am�@in� *!�,�Is. Enf$O���p�iya�Ѿ8!6=@b�$n below.�;&"A�yle� } �!a�pp���@e�K��*�ig�Da�rRN&@Os �4in�Gouy891:*�&� i (uned)�dwA�Xenopu�� Homo�r� a� �S# \newR  % --- T �I�2�M"_ C+---�"�8be�(tabular}{c }�' c(&%c�n{4}{c}{�[�(+@A & T & G & C\\ &647 & 1 2?'� -3 & 521$8 D09 & 90 2  C & 8 & 2025 & 6916 ��! � 5�$9V By�a�u. valu�HG],6 magnitude � � foug a�u�c�rA��<�shaped��Bglobal�+um (G>� �fig})s����Jl�P^z1ll q2API >eR�x? � re w�@a�sPiu�&r-� L$I�L , ex+NU�$b= $c$ 2�ir�SCA��c&84,P1a��܍4)i2E dard��T��!�IGs (�A�� advise$v%��!�!!/ itiv xE Smi� on)�y  .@5 ������.�SeG ���,�d l set�"i�t<}�~=fig� tonc�AV�BU�M|�%>um M�M�ofY�&�<cE�:@| ������TneCN�'e)�alQ4�2�E��#ly2�!�3 rk:�.�M�r�2�DiE>}�R"� ;of&� �� ?level� 6j$� | igAmch�MXP3urpos�.If sR�IG?yA�b��r,5# JI� �-4&��H sub-�s rapidl�V�$�c�$57p of/sAreH. A�&�@[iwe �� k"Bqui��l�}��"G8(JC�wI�*�)���ٕd d.h�Yteroe does�ev5on4!��t? co� + %`&LS � "U-�K*�@�� e��#U.��PR1"".i0Cw�@���?*��ZX} �NosY� 3.u*�'�J clai> ~UdX��Oas�!3� �ny!��R�M{-ter�ng��rt ��i%rt�Jp*0D|E&$F�g�6 towa�S�PR2\OQKJif  0 �� �mod�I���J�I� lolo9� >fO�'�.�%phAs�:a"p!k%�"� in e+�s. But� en; usO 5��P�:scale�7��>� hop*PUޔ verage}, E4lo�>dev�YDB-:t��c�o��� cE �$A!!�Btoo b%~rox�/ionN {\bf}A�th�!��'A� e �:��F�,' ]8X.e}A)�7R�# y��6 asons3O.z�A,*s� aw��ofE4fac��B &\ inv9#�=exorabf%9� ��.<)�@ , maRF�.��x"j(5A��{Co�J��.we�`��a� (O "/� a"��unG�n�|�^�!9��KO ely no E�w �� e2|AH�Pg����se4p: a�el�p.w�X�H1��"E| �no�;qu�<��K r$M$� A��$N > M$5 ,� ~a�� Z��B���\s-|��0$a, b, c, d, �6�$y sf? f�9.w� �)k�.Z6=X}$��[Hs extremely unpleas�yb��iOa9�\!��<T�on yK{�y exz\�El � -��<day!�: f3l � � scarc�y i A7]?Q-pa�cT ne�urther]�M. ��RexhžRDa2��C, % d lZ���  2�Eat��binm�͛�J���dR�I���U,��to~�.VP�I�,s �:�_ee9��5�rm� *^ Ql�@����!Х�>R# � --say-- 3&, � R�-8���%w��m� lex�`�;� -� A JvFt�a new)�)�X.�x��z ��UWel �B%� Tb%��(�I"� % o so�+5 �"5 6y6�no'>tleneck ��z�a XD�� T=4��*%�Am��.��A� ��*{A"��vIs} �o�&b�_w l�)�.� ���is OZ�/~@edmNa*]�`ersin �1e2�]e"bt�warmly![ߤ$uca Peliti��n����m� �`@sl{strapp 04} mee+ (DresdQ`Ger7 (, July 5-10�4). OZ�L���!a��.3NhA�IaKauq�&� �3�|(ank Manolo ��kin� A=i��{`�pv1e�A�! f�� sugg�o�5��nuLpt/�M�_�%j�����[1Ё*anonym�/0Iewe{[% eAgce\�� �T�/\�; %� 6�tP t4)af�F! %B�^"�D�e!} e&� &�h*I I}�/��3�a��e!Z%|&� L) �Je (&)+noA$�YJ�,)E"q! �4xyz} X_{\pm}& 4)2SW(\pm 2g'.�(YJ-2}-2TZ:$4P�<Q4R.N���s6% Fb�x"-1!2.�!�e�1�cV�!���block-�!, M�b^v�.A]= i&�+�9R+%S,+}&=&\omega[  +(1- )e^�4,mbda_{0}t}] 5\\!d>0 + A >AO0Z_ 72 $4>F0^AM7F�0�-�-�f�1\1}{g^{2}}\{2\beta[\alpha �-�].�1}t}+�\\�z0{}&{}& +[\zet E+EeZI2rI�H3}t}\>�V�-2 ����+ E�)7+���a!|.I!GZJ �\A;^�$(\delta-\gG�) � ����6\+g)2W2y-gA� 6Ev�Jh-nh+bh--b8LDb:ab-*� ��/�.c-e\i E� .+b-dZ+%�.+2~'Z.%�..b+d+2fB.)v.)�M1}=A 6o.\l��.7-2(b+ctO).e.6�O-(2a+ 0+2fV36�OJ+gRc32�0-20-| g.�\sqrt{6�)am+4)�%�2AD e�2J�<2}:O6 +g)+[.� Z �*�Z-ZZB�C�� ]� den�% ~F���5)&2 2�(�_B�%Abel1 2}*F� re;*\"Sim&T��>`:�LDETAILED BALANCE $\R�4a�WX $ TIME REVERSIBILITY} �/# remH#� YSsf�8N�9,&61*evelobR�"6Qbb{I} + sf{R}t +�"1�R"O9R}A�t"cJBWor&# 45�ij5(=�2�6 + 'Bwh#kk�^kj:|Q`g*�@%oji} %�(|=_|jiB|r�I�9i:u."W3daU� (Y+ij})  bI!O?ritten aJ� F)� �E%.� �+;$n=�J�Ti�s54^{(n)}}{n!}t^n5��-�U�"l .< &= &%u{k� k_� %� k_{n-1}!i,  � )!3,24 1},j.���`k)�II,"N)U)2>i =1. gQS16Now& �3a�W> �0c 9nI � s=6x*s_A�)�*�&J+,nB&In�S^oi<>�F�/2; �=�-�%�6� 1�%�?>:TBe*+1S{}.e PrjjAcEKfE� =5� \\ =�S p Y2E�Ff 2}}= �l>��fKOlyB� 1�5�e}YI$n�X F� $�e`.���Us'1e$J�/ {i}$��$it{Q. E. D�v? &1(J�L"/gR��re��S�ulaBMvaga} ɬJ�A" _�A&�;�f 9 �(t$8Mn�Q�QA+�AI"q$Ommpu �� *�4of2?�8f %R� b/t�"![:V��!�1 $. F�xn -.M%!)!�AqiNb/E7oGBimF}9-k dpdt�� d{9(5:EI)�Hj;�V9BzBu� lfu5��%�k�B,� a�={ � 9'R<omm!�(u&1<:)�seN>R�) "� A�� ^�13�>Y%^�F `�!�:SA�qb�3},+�,r�4�:p�F��T�OF�FZ�]b�)�%�Abjia���Ebi]b +�� SUa���BBSub���!,�W!�5�ZQ4aK 4��'9 keepG���{cei��$����Hn'�� .V�`kA(k�`�)=0"� ��7�>� 2E N�"KD^N&4: 6eck"s app3} A n�h��1Nztb;isy2 v�He[>�8 iu}�, |$Flp"�nng!�N�.NY8e�'Y"N�fulfil�w}!@�N21`m�v} (E2I? ��er�[�+celK%ryK;A.)m6�;s%;D;-c!w,N�;Mo�st�%G�4J� �co27�`�pr�;�W Q 4 �atl��%�6oyelf ``c�wise''Aqe%�E1�ed*�jer-2' %�uk�PY� �#.�) � � $i, j, k$� �V�perty�[;7�'�ˁ j ji}=  $$�{+t>��20/5b!mRvKmvM.,�m8.&z�K!I!k moleR|rt&&�VN2)&��0217}, 624-626r�l&�lAt 94. 6�52�8cGa*y.*|>s�]. 2it{J.A c��z.�,39}, 315-329.�1lCfN �5. !{ astrA�% ty r�QM_c&�qE� usag�xakzv�y"�cod���40�8-325���Errata�42$23-��'�f J. R�PT)�"@(\uE �_ 5u�b&�|�Zip$.,`rl �26-330b�1A&80.�r�L*MF., Olgt�L.,�o\'\i nE?MedZ��0�^ l stochas��3!�.@*T!>CTu�BO�1%y485-501.�XD&�IAH2[81. A�5oafEK.�EL*�4�T�xal�l+]P�-�2�2(f pseudogen#QqGc ticsYE98!�41-657.�l�:�!L.:0 0unti di mecca���\5a,U�Bol�% Bo hieri} (To��,�!3�NM��:�:ZI�4�(" �aofb� ���105-112��:Gu X.,�: W.-H�A"�(�>�!��)�� -6! �7r�m variam*,.it!�5>�ٌ093}, 4671-4672^�"����Li�89. PhylEaa�:�#A}J 6�6�frtT archaebacQf R�:�'�"�!eocyteyM>3)�45-146ug-6��kC)�9ݝA ���2�U]nZ_��|�m2p!�s & no)nb4t���Q�:W016}, 719-723.�"Q�tG�"Tex�*|�ic �L0�(s:(#69�t́sub  (�7}l6E162ov�&a��<sh�'c � F�3�% \.���>w d"���r%\�&[pre,��]{"P�J&twox8.'&��[tbtags]��V} fon': symb6+�we$renew�R�ni}{\no�+n@.tx}[1]HErm��; �[x7��.st S(title{TradeR�w short-ter.>U &�in�Vhan�8e&�V%u�ub� For�n $^1$Claus O.��$ke$^{2,1}$�.�,(1) Digital ؜+�0ry, Californib��L, Pasadena, CA 91125Bc 2) K9)Gradu�:"��a�A�;ed ~ߢ$s, 535 Wat��D��, �emont k71���{\todayA�iBa"w� %? stig{� � Q��%"���wo mic��a�3viD6+ i�V� �%�n.��+t switch{' :�tlly&�+w�a�Eq�@t��3%��9o�Y=��3 pays� YF costB�U� is :U3V�� UJ���#�+�4t>�� alΐ ive �teg� �xtens)n"�SsiP!� Rnd�*�imr)����� %�up���1e�2��)Qs�51�GFwA22�����.lE�=#ba���O"�D/levi/0for arbovirusA��1eu�"o' h�5D!%�3 regu�� basi���]�. �"'�(!J( quAp��)=K4��S�79�4�p�eyEe813&� !c asex�kr��o2-.a�clfV�� oraO!.�etal88,Dd7o�� }. O��aA!XE'0oh,��.��.N�ha"Jo0 ly b~E�dig �ri��w52%�� ] �Q�$Snoad2000,�a�a, :",2b, KampBorn;tR� , Bra(Shakhnovich`�� [ �+��*I�-��j. withko-2�er�; f=,&3!by EE�coe!�a�th�@s��ioEo+��on. How�I�++/*m�p��me!�ism� ZW�G occuz,/�Nly majorA_A4=!�Q2� ."49� ime-��2]3 s: AF5%%�C�W3�� �n(L �>�)[A��APt�9f�Ga !gŬ�&?99� ma�5 7bl}�c�;�01x*�T ns b�`�Y�. C@tly)��} a���elK0ve disa'�ta ��ْf�PHEv!managi��`!��Ii�_loss,n�!!dJbQo��;�;�$too>u��YA�1-a�G b�4=6��!& ,(o��re))?s,0S*��faA�.conflicDag[� s---�&�vtYa!%��Y�,��6!"" .,��T�s(3h. �� HenFw�v��Tbj!�e�JtCF�fN� Z`�s,�&aia>@S� a�4v )b~ . T� �N2 .�o��[I��0i{2�w6fwo*Nq � �6pG�aܑT }b�� Wilkѽ5�-0 OU V��j�a�ie \�f+G -},e{ah�x��I�� ���%Einj1�q� _��di�d / �!%�a�ach!� ���\�niǁ=nQ��q��p$*JO�k=�as �-:6�R�tz \ithkpayA[�.�'t���EA$�(.��b��a�1ve � �@>�a gardO^r�� �lA �&  hQ4, h.�2�AԭUm��)�)�B��es+ � exac� terpl��ha  .�fR�� ��3. ��7 Y:hy�Far��5� �K�{� Wo�{d� r��g�xse�O.HG)2�%���cd�">�Sri�"B)�� B,E%gS!�&� ��7 .'1b,$Adami2003}*� �#%�ghtfor�A!4� �Pr���eG typ��� Noq� w�. � �througe+]9paper,�=� w als�lyuB&2U carr�ar�T �Hl d. IafiDwseev>�c6[=�)�` zei�7x�a��Eoth� s,N��eaE�)�%^O~2�=btX�}b.��sit��� - �@e�@�\�Cficial-l�&�� v ���#MCLiE6� ����of%� tic �~A�umpA-�"q ��am�Eep �� e�o�o�2A�ѕr= orgaE '��:9��DERIALS AND METHODS�"b#�=}*�I~sb��xitCG"& ���VT .�9a�on,�n� inif6Q}~RI�22.� ��%�"�",;#eq:.LF#y_i�&aR j w_j(t) � j} y - .\�"&  \,, {�- $y_i�q!uu�!��O|M/&� , $w�8r< A�� n�,CU�T)2PaMC1�}�a$�P��Mper�Bd�� ��� i$�quadrE��>e�to�-!�HewY�6qɘL�t$! 7$O!A (t)$"�de�HW� a�6 ��.q�I:string2:B� J� leH L_{\tx� }};*�2�C6T *� A1}}$i� �E�.�#�֑b� k �i#)�� onfe�Jh� �"M )V!l l DK=�TvNi �2��A�#OfiEY� < M �is"��"y�n�),vi()O�%*�,h5~*ʼn.Z� 9��ctBe{�1+s�+��6�H�sX!�291. "��s� ˜b�6$a Der-�a$"��a�$,}P���/q6�>+U=\mu L��*�A�<y5 sec:sim}S"� } B��!Isp�DZ� �8&6t��&ZDfac� ��dO�I�U��h2"ydE.B�E*� sAto� �Kre�ve�c�e��F�Jz$N=1000$�iMo�I��in�c�~%ف�T[�%���,�9��r!��. �MQ (Wv�-F���pGM��InՀ� ?�mIB�ed��#�fu}(mN^' G��s�andm/* co4q�Ra`T /�� extinca�We fix���N�)�� ;at ��div}}=5qD !��aFa�A*3A�1a:WeA�(d $10,!�a;1��t�@}I����� 2�s� , \ (10,30,10 0)-U��iWF0.0001, 3      3, 1, 3)i�>$on{RESULTS �+a��}T��SuMСTHJdere�P.�A�U(!�QDA�!��e�J� �X&.)wo� h�T.l�  $T%, cT.+ drifS>N %{dr�In�A�].���[ue�I���]�6?f.�"M� �N6$s$AR�� <j8 a key���R�eG.t���$����̈́D$s=(w_i-w_j)/w_j$ � Crow�%70}. �r=)�isQ a prio�$�%GI��~�S�tur��݅$ o� T�a��;Ok�V���E���F.�ep��s (eEV�w��ix�!v>{�a� nts)�w�#q��ka�.�㩩�w��l;ve�P $\la w\r 1�L �b}A/R�.���l��A�N��e ���-Fr<�"� :e2�I�9� W!� "� ��$eq:seff} se�{  � ��!> w �Y}}-J-5[ � }{\min\@ #2@, jA\}}w'e2]�tJ%i$ guarantee�A��H"7[fT6� �$*p "�HbXsu�x���( csigI�cY2� �{a�F(poZe:�)�i� �(nF`>&. Z%��� mff�Uv�� Y!$|.�|����&� z�{c�ȑ�o�Dtyp.���aO� E��f�"1E~ `FA. Neg� ngFs �f���Eq.~\eq�e:���eTSX� a�����kfi�cM;��A��$x(� �5� [ �s�r�U�Racc�Hg�!,�� e�2�%}�xt}�&t{x�3 = 6� � [1-]B�2 subj� �wu�iw ��e-O$$x(0)=1/2$u � 1�=�%�-U�)Is�T Eq~�?eq��= "D� �"� :Z�huF�5 "��!�({\ln(N-1)}{:0}%Lrox�8\ln NF&JmkwB�} ���k�!"aB1�!�gofix�E�V� cIs"� tR!�N�! !^� �X���%�mp&��6p d�f�s�nEqi �%��;�E\�sim 1/N�L�64}�Rys,�ukw�@� >Ohta69}j���atB� )�V  = 2 N !�25�1390 \/�x{�� }.U*up6�;Q.�$E�S� �s*��� �la1�&�,� i K adopt aD sis %�-r0Q( !vprimar��ee�Ui#s�&B&.genJap�**� , toe� EA.del��#� ��,�ta! ree1�  0��*"��n%�� �Nlandscap6)tQ=0=H6!aJ"�\!z�_(:�T��Sr)J! - t�-a� �ap!�ran�xm�=a��. .��a , Fi#��fig:d{(,typlot} illuA*�!� )Ysa�-#in .��1p�:-R4rli ��arg2�)b . BL �anm�!y� � +��prece'3g&E*q"��'s!�1m�Ze.�Y�G� �ant�� �FZin �is� Y���>QJ � a��by+ 6 =1+s y_v7L�0)����P*HB� .�ga��+.J���>��&>� K � 2Z� �{0�Ae}}-.� }{1+s � y:., � ,\}}\,. F\ni|"5�$-;e�E�%�2�immediaD r!��t�!i�:.B. "�$�$ a�;2�.�a-�-���eίs�E�Nw�� �Z&�4%�(�i�)�Vs1Z��� w�\�-f`U$)I�f� ���KjQ %c} U A��\= (1+s)Q_{00}(L) y_0(t) 4- [1+s y_0(t)] �X, \end{equation} \ni where $Q_{ij}(L)$ is the probability that a string of length $L$ wi dj$ errors mutates into one !i!.2m�Ohas been given for example in Ref.~\cite{WoodcockHiggs96}. Setting $\dot y_0=0$6�Fequilibrium, we find $y_0 = [(1+s)Q_{00}(L)-1]/s$. However, when back �ion�Dcome significant a S@$ approaches zero�8this expression�reach !Y classical)2( threshold �TEigenSchuster79}. For)Xion r%_beyond kpointfassume %�lpopul%� is randomized uniformly over all possible stb,�hence!E$use \beginYB4\label{eq:y0} AgH = \max\Big\{\frac{>q0}{s}, 2^{-L} )}R�A �1� �^ low�E�9S,, Eq.~\eqref � yieldsA�iEh!@0 magnitude of� fitness advantage, $|s_{\tx{eff}}|�Tleft(1-\mu\right)^{-|L &div}}- (fuse}}|}-1$Alil!�I[ of $.Z$a�i by $rsgn}( KJX)$. TA~(result showa�at�effect�1V(al load on �@is to favor whichaa�aine�AY shorter l� . Theuof Eq:uapplieZ(a quasispec��e"ed.� . W5$}�I�peprovide!�0good estimate1� !sd �,�aB�|environmental changes may preven)5di`B's6�from %"�ingi�� . IIMqo(quickly (rea�ve!~!ccompeti�odrift ti��cales) �6� persist��( an average2{%sr�4res both genes%3 functal����8Wilkeetal2001a}.��stUanMf�VM#!p$2L}A�In A case���Nx)�!I�!V25as�[a single noٝ2 2o%Ereplaceń��)$ ahQ�2�)$��BL . E��though �¡� disregarda�(e two dimen�al naturE��-�--O.� , it� A�$reasonably:��� true��$%� mostu�E�$s. Note, h��E we do not9'����o}$��22 . A�y ō!.A�I�.��X!��{n>�MJ's%*A?2���e>�%@J���,ly-chosen in%euali�=w | carr��a} � remains %>�W fera�:� calc�ed QIc6}A���[(-term limitinto�V>�aI{ longV . \subsee�{Predicei�.Jof fixE } W poseey�B0ternary model�p NnK $p$[n.��-n our N,( is $0$ ifA %µ�EUed, $1/2I�neutrd volua��o� ��s��s are��(ally likely�go�, or $1~� .�|�irs� � f9 e sel!evA g�� base�rO.�$T��rah��!E!cm ��%J�8 c}�n N / 2�^e�J}}|��Larison�$T/2$i���%�c� � .�qconst ,(see Table~\p 4tab:sel-reg}).� � c}<qn�wexp����� betw  two 1�,to end beforA .����� onceiB� K% } ���. � valu�� �{)� is irrele ��h ��A�f�G!3IWao� han=^n��xt�� sU4al half-period2 �eR�FinA� , if ~A�small�Em0 c}$, but lar� 2�E.��o b)|T nAforce.� call�rI��q���set6�=0$. Hav��de�ine���Ypri� C$!� (9�,fe�: )ccan� �assocRd� "� 6�$!�^��̑3! _2,(:�.-Si >X < 1/N1!A>q��f� iv��-]. H� %� out�.Zis._by %�i)$p=�G$. Otherwis� p](or 1 depend!}on?%>,is nega�5 posi :uCom�� with simu �� s} Fa �s%�� I.�!��!52� woul!�xAEi��*$a^  !7�$Ue- $-&��`}} R �%�y n Figur� fig:�A, B, C,E,re,� !&��s�Be���� obtae%by=$ hav�tandard1 0of $\pm 1\%$.b�D, E, F�>correspo)�A�.of%�E� . OO)xll g�Lparama�Axscribed!�S�on�1 sec:sim},Rk%��:was su�"rS235�s (E�' ;q>w�m34404A�))�ZG:s15.s1$)�e�Y�� s:R��ac�whes��rek � !iis%�RV�� W�!%�=>% , $85\%y ���6Tfel%Jr $0-0.1A�c�$$%{M ~ 84 ]vY�� $0.9* m�1���i� g), $58�h45-0.55�aBrmsm���s"� 2N1�$18.6\%�ed�!Z�s or�xk ,g best�n�k any such� *T  7m�uz data�PiB,{DISCUSSION}�studya�.H dynamic����landscap�d�,�4primarily focu*� �jinfinite.T sizeGDNilssonSnoad2000, 6Y, :",2b, KampBorn"lt2002, BrumerShakhnovich2004A� In aiodicF�a�f�guarante��0./U&wo�Di���Q��$istic extiL!Aainf� "Nor,;cer�����tu�EB�u` �coexist���b � (al�f� ency=�� on�st�z�j�q"4-�.�4�!^contra� x generaliz �sei.�F���kOinuous�fofmx��_al�1'9X to�!�let�qdom�of�J�. neD � a �e��j��*E g>� �.d'!�Y�.5 's� li��o�� fic%��Nha���a�)�.0ys qu�S5quanti I��o��B� (Figs.�.�P�~��� 6�<�@$ 6 >2�$,�� .o��trictl�"��a� 9�#�1�>� "� E�..X mVimport� <�9 rat� ��in� edI �:i �" ENkve��t lex,� Q�combineb 2�!����s  my"�wIo� s1$6M �o�.?fe2��%_.�wet ignor� : eXaM.'�4 its .�di!�b���ci��tdcl�>K�i*D af�pre���VeffortQ a�hatE8adf�lex fail!o s&�lyArov�� accuracy�%g�2~��tszili� inW �M�*�'s���Y6���fACwor9 an�� !�n s�o� asesanRs� s �)�� ran� { ��he6�.�?� � , be�K(poorly adap �the meanE�� till" se� J r ly r�si�at �2 :� El�u� zat high>F�� t"� mask �|ch\. Our�L sugg� AO, under��r�circum� c��ve!�ss ��eA@��)�M��ry�{���h.v� Nof un�R)�Jl�dd tac�z� mN���Z� Xis�� recena��d��AEarlDeem� M�genom-�f.of!/ar Gu�ss! non-�a��� rial%�ch in )� &��%�xcQ*�h6� Ad.Q')�d�r�n*� s!` as 1000=$osB-, te�`O �1g�%�ri� $20� �); c�b� bly �J ed�r�%d�6dorma up�A�or�Y��R�B��Al��ly,"~A�o�to an .�  &h migo%V �q`��� !�csy�>M�b� ning�a -segE�� E�E�observ�4foot-and-mouth��@ease virus (FMDV)>�c�Rl�:ltiplic�,of � QM�Garcia:� On%3la��A�� 2��;w��al��!��s� �!�s ifTNee1987, Szathmary1992�" ��ila�AOi-��Ta?s��2���if� dire� -�"w; arbo%Y��M��  �mit�4by arthropods.^ $,�K West-N��H%4!/ I9 biyo ( � occaAw al human)xmosquito��rienc��2aqng�@7 E  vimn��$ hosts. ExaE�l� olog��� tr�(to">e�� 1u�subjec! ���b��a'�&�Fr2}��a found aA� clus��answer. �s, vesi��oma� s �$ (VSV), ea�$n�A�nceph� )EEE*!>Denguq�in cell%ei%W $mammal!p orig�"ve�w�a���,)� r neV typ� a� lo�k��# he0 0, �J c 8[inc�$m�ms�Usa�%� m�ovell�' 95, . 9, Weaver�D899, TurnerElenaC$CooperScot1, Chen.2003, Za� S�W�#a��d %)au� ie ( !X � � :E�� als�'Udetai)�d1 &X-_C . It� n)�!B�-�fu'! i�aM��J`%L� of.��h�Anaej^a wid0�%a switBPeEI2b tegy�Q eQ�mAKaM w be�b)�:�at� vo? sE>b��� @ meth��we e�$developed �)�coi�p( (m�A'�Rh6Y$v*�E�:�%f%-&� �9 � �8 X�O�n�the , �e��ɍ�Q!"}$diffe %�~!tog�%an i V ����/� �Y))o lead!��rkD � �*| U��� J.!belie�!esi�^echniquq A!3usefu'!8 pret� p�%��-w͘uE�ing.c� h %\bibliographystyle{prsty}: {paper-v2,bM {the.= }{10ibitemB�* M. �*� P. S�*, {\emoPHypercycle---A Princi�+ of NZ8al Self-OrganR�} (Springer-Verlag, Berlin, 1979)2���88�(, J. McCask]A2�J. Phys.�6m. {\bf 3 0 6881 (19882iDomingok'} E. <, C.~K. BiebrichQ,1� J.~J. Hol� -"Qua") �{RNA} V� E�":99�d Conseq�@es} (Landes Biosc�Pe, Georgetown, TX, �2�:s0%= �N. �,-* Rev. Lett-/,84}, 191 (��2^W6:( C.~O.�!-, Ronnewinkel)!,T. Martinetzrp l349m395!�~�2b��E)�65\03190 �22�B�� %(S. "��:,8c68104)/6cV� Y.�iE.~I. *�2n�%)061909 j42�.�5�=�Ry � )� I.~S2(�, Cur�� TopiIMicrobi� y� Immun eU29� �5)�~��u�.�1b2�4 {\it et~al.},�6bf 41�  33-�6�TAdami 6T�C. , M�0.� �52 X �32?LiXQ !�Li M=GArt�vLif �10A12 V6�LCrowKimura70} J.~F. \M. �7$An Introdur to P&�/G !��Theory} (Harper \& Row, New York,�MJ�a_6�,��-#e3 2412)%6{ �64e� ��$Appl. Probm�1%77�o66 8Ohta69I%T. ,�El6P76!d1966(Wo6I2 G. UP.~G. h2�%A��ol�7E�6Ap 19962E�4Ao��DA[issigqV� FW�'900)V62L D�Q�M.~W. k,!ac.a*l. Acad�i. USA)'10%( 1153��A�2�:� J. 8\'{\i}a-Arriaza:�J.��5,7�11678N��} �aee%qM=��-o2IeM872�6��M9� N157An38I96�) !� 95} 2�v��q 6805E�952�.X9�X%BYq28�45��199:�*!!I~C�'5, A4Brault, W. KanM�:�>�3}? 4316 �6tTu2�$} P.~E. TuE�S���>�156!�146!,B4:�} L.~A.�\TE��F\%+140!���2�.} W.-J� (n, H.-R. Wui� S.-S iou,�ger+2 logyi<4�28!��X2eZBtA�Z\'�2YE�ViB5223!}u��7>� H \cleardoublepage �5t5 } \cap�{�5.�+S:�,,�� ed� � "5� :'* S*�[>'. }� er@tabular} {c|c} C` & I ve RA*$\\ \hline V>&�* &�r��t\\ ��+m,<22d$//#3\,,21&�3)� � �%�)� N�K *MC/ io�(a3'a�'V�L :x0%�D*.5t�b� �%�%�FAd�,age (Fk Se" ) & ,0o!�$p$5� 6�6 \le-~ & d2D5 w�& 0 \\ $$<.�6< 5-�$^\astF1/22.-\ge /0d&b1A8)�� 1]I� s,���<;l2,0 win. R-�1�fiP*ae A�{\i�de�`ics[width=6in]{movie.eps}e�6�|!de�yplot}.� struc AA1m!�.s} varip# �3$s. Gray lVs�icL�9A�\"lHg�;*0a�~#�m�S-f�(J. P&*$are: Oscil�@$ $T = 60$,-sites�!( $\mu = 0.0�0����"�"�" = 5$,B�)B gene-}n18$,*�"�~:� $s = �9^%' . �,.H 5}.A�VUX�j�(-vs-t nsr�&\Color onA�) Left (�,): Si>�-�!?&X*�("#/R%KA�]:as[64'Q_-�.�-=!�e#%��7ro# $T4�#)=5 +�4}}=4,6,11$ (to'bottomJ�ba�2a-a&�8ly *o- R�(_-): B�18 $. y  v�2� $s=AI$N=��މ�Y��\��e�_�c.j�&} FG/�9��'o9!:Y(B�E�d),15 bH6��m.ed�,6n 2�-.6�-`"�-� I,"�- W$x$ axiBbin�in�,/crt!s0�0A� bins' mid�?)��wnJ�e� docu�} (�y% Templ�g�cl$%p 0 int 2)4 `elsart' % SP� /01/05 \*t6{ (} % UK�p%�! spa�o�"viewcopy;F0 & a� , % 6e[2K].tif you�, PostScript I�N your� %)�� packag) s^8 comm�use "{3} %�u � x2J�'l��d jTx:TepsfigR �pre�9|�A� .� B%�.amssymbR�>�$matheV.B2ols %5��[Q4 ,aps,pre,m]{revtex�7=5 yb Q>frontmat�  % Titl uth�CUadd�Bes � thanksref1�in \t B\ C!�\ B���!notes;]cor/NOor;c2�2oFP�-�:Au�;l�, %�B \ead[url]hH'b :A��{%\�{label1}AA [ ]{ �{Name\�{cor1} 1;942 G ead{2�I�{� � t2 t h[e -�{A)� 7z3 z.M3: % �Me{E�Stretch!A$Contact Or�&0of Proteins} r<*: C�- duli�Titine=Am���B!l�% link-�yE�#l�� �es%�))1,A1& ) �%U� * %E@au1,au2]{Marek Ci[@Pk, Trinh Xuan Hoang} 2:.} .P2]{F= �0au1]{Institutd �(ics, Polish�emi Sc�s, Al. Lotnik\'ow 32/46, 02-668 Warsaw,Aand�ab� ctAUTex�1 =�unfolx�::3 of :m=� "n �-u(usE9 Go-like��w�ka liK1 )0AVmal$Lennard-Jo�Bii a� s. It jh""i%�VMg ur�1e &_ � ".&�ce2 +two��E�: �pa s��t�toBastrong w�a�9cts�>� eakD% ~-F��ce-dis�BU curvm4�Z�is�ed �%�;cE<��($\alpha$ se�&�"N��+n�'6�4=e8em ar-6�!c� unwind�� ultaneousG-n1,doA25�  �itiB rave�6:+�)$ fashion. �FW |��>ts duI u EEure �A� ɮy9o��, i.e.)���r� -0makWmino acidH7$he backbon$5UF0  er e!��%Q)�;!{�c�Av #wayq�y�keyworda� s/"{���: \sep ��.z mole�%� GomQ&=�$ % PACS co�A�:\ < ode 87.10.+  5.-vR ��>�EMtext \�' ion{.+}  1} R�,S#I��$�!�� en�d �+Eb"- bio-�Gre�m� mani�Ki-�4ommon g#"od �'230 involve atom�6d? mqs� '�# tweezer�@ � ^t�?�C0 hydrophobic ��gC�(te�F����Ge�*" ��R@t�,eR")<�ycoval�0bonds.i��� 9rotocol��?)E�1g�A anc� aAs�+���5E��8 a')��t�d pS.b�oM)9�Nc%�3spe�:v_p$. B} nito�-m%�0reWI� �a , $F:p@'p�� , $d�4�=�! ela��ha!|er#>�_$r,3͵ oret!� ��L$��I�[:h� rupt�� )����$F-d$ �se C,n.!B�nP0peaks, minimaq�a%aa`pend �'��-�!9�{&X-3&1.i3f[E system!WF'�=I'�&ixs"�  !�0ptavidin-biotW*o�Fx kFl!�,Grubmue$C}, DNA ��is cl22to 3009>.�..v !�Esi�E4$a sawtoothV 1I�E�@Clarke,Marszalek0 } � � E� attr�7A�o � ���23i!v1�4akY8�B2�. � (�1��ct �3Hookean �-�+7N ,*` nead6�Orsi2= � �}. Its= per���inspi�8��im�O de7!Zpolymers JGuan}�,�Kium! C2A\ �:A�$.hE#5� �b�chE�er:2A � c �9|1�  6E and �$R�em�:"� a�g )�.2 Prog�}�%�-&� ���8>�� ein,19r� e n29 ��sAc!K0te@��mCu)7go.�)�� untiQH�:�;u�m�ed)�M�s�23>U�ar�s�r� �,�.A�+a�2qc�(�1end-to-�Ir awa.2�als, ew�^/!�ubi)-c�VCiN(on-Vazquez}lyzozyme1�Yang,e�% pic}�;흉�O>e�3u:fi5+pL�RA��t s bu�:y �/9�tem� ,< e� nced*�/%< �Janoviak>F�ly "!V mtit.�Ia$i�p(+�5"�.y $ geometry:MAxa!�elK�O�e �>al*s -�)>5 gt9"�M��l>%vse2Qdi�shA;͈�J:F �cdisap!��1�O . G:preHoJfocz4 w*l� I27�n�jy�R� "� $Data Bank )� PDB}� 1titL 1cfc�V��2d8er�l�archite�� $\betX andw�� eastore}�"�6"�helices Á�2Fb> (of 32.65 \%"+�is[ l Z-�%�%���� 1)M~,2oniis 54.0i����$is 8.11 \%i�� obv`a@!s��ll-atomI��� a�xto E�i�coarse�i��� s: i� f��� re*d9p���XT%r� ndam`Jl. AllN ]�of)�)� Lu} 1��i�>�*] 1�T ���qso!�:?A'�G���  ;> on騡�imaximum�!� ase��-d���!�$ drawdm���$�[necess�9 dea ��@Ep veryAY i"cW,"� U�nano-2jioY� deAe�&!� z?aM" 6--7 R��&U$too rapid i2may1>5an C!�2B b�~ f2�#"�T%n3 9�(a��{5� %7discrepa<<%)!L&� &�< surf^Wt�"on �3}�#zleA� wa surg !�5G )%�I�� ��4eIow�:��;1  r!�Z , b!corpor)���yof :� , c)m�7S�k�0ic%�� ing, d)Ec)2�e9$r  M,���S�l nd d) easgI�#A�#��  "�C } �� �a�t�Xt�� be g�6ned b�T�V�@9vM,tubes 1,Du}E�e�i��:J��~�'H^ OU�,Plaxco  1}. =D �C5�}��iE`���o�lowi]r��of�I�8Goabe,Stakada}:!� 4 a Hamiltonian�Y)�chain�Qv�:!�i�i a gE� �E�agrBJJ+!2 d&�'con�QE!. PB���2�^2J. �! dO=�!H*ofJ�pout ���  �,1,bio_6�$}. Brief"@k*  ��r�PX*=!�� e(mass $m$ lo�&d��po�DM� C$^{��#tom��� V� e�#&, harmonic po� !E�N�uml3.8�.NRN ��٥�A�9E�Cacu !-�A:� ki"'Lis� � �D�i� A�Ɓ�am*p�1eti�ztP chec塡�a>i� 送lap)G�:%�!q�cve�Y� mb��E��!� tak�spherAI"�;.CRto� van ) WaalLdiitM , enh�� fact�&f 1.24m�Tsai,pr�d�Laccoun�K softEk\=�Y�o.P($i(&j$) �Ab"�5� sen[r�ns�bV%,Q se pairEG endo�HE�!6��, �% A } V_�e0 = 4\epsilon �b[ ( �c\sigma,}{r  \�b 12}-6(f.-6 ] \;,���A�uaj&#�ai"cF�N�!�2 "K.FDs�air��"�[3* �� $)( %!$"l ,�NgyAM�� $1q$�<kep�D]e.&( mad[%ecP L$�; .`iVal><a�efd)?&e� �l ive �h"r]�*q� ��s, sou shcF��800�W2�K���%�}Ɍ $\tilde{T3+k_BT/54a� 0.3,�re $k_B�Z!rBoltzman�n!(t, *�LJep7es�T room.�] behavi�= . ��Io>>��q�Qj�\� x d�� illu���i�W 2A�Ձ209U(89.n� � ��426* (148F+cfc� , 7��� �O l --!Oir& qh d}&� 4��� flect)W�F�-a ent.:/ RP 30�-J� in Zre��le�*!�!��$,� }�FiM/ 2,�]o">s�strip� :]2�U� ��m�-!�� S�&S�tv ����L�x!q s�Ka��Nl[Qly"& t network9up� Ke)�b luct�ksVodBB�$re mimicke�@J� 8�� by! e�RLCv!�noise�q damp%�B $\gamma$� 2 $m/\tau�hA�$ $\sqrt{m �8^2 u�}$a�����si �AY ina�al��sE�neglig� � .~ tB>"M�q*] "K$ �>be��25%s�r wVeitshan9Thui4s�D:zZ=21@ n�I�HAJ�250aN��� ;L M�)� � +*�'�,mpl�# tta�'�Fe*F���7 �$� ]%k$=0.12� 0 /$\AA $^2$, ?#"� 0.4 N/m, -��J e�@ J� � ou0endP���hel�+�2�5A�A]�is�d "�#�DEv&�vem .� �a�����S2��0.0=!i3���e $7 \I910 ^6$�.FSh; ! 3 �%�&�fa[t�Q�"uJsV �jC-I2haha,���homop}#g �� �N, logarithmic6%g'� go�5�J�Q 0e"�0 Uv]!�2�#���N�&} .��P�1��%�� �!�"�$�e!analy�-}a�H"��}7ar�jd O+�8t��(�Fc� �mm6͸3E0[6S6�on�Lwo|H ree R���*���,�&b =)5eu�png rFd)akTc1 ��i x�1es� � a se�'repea"Y s�k >e U  � %��maj�-ce6 3f�!!� has a heD3�Y�4>x> /UI�J"| u�'�AA1!N& �-aUt" @Iop�e "�O�;�sG16Tr�im�QJ� d A' (x a8(11--1%CA P(4--7)�G6 78--�FaX�-VY)""�C-FM B-E ) �B�bEI�F���aO%Ps 18-25, 32-36, 55-61 :69-75��-�d%�!yOp�>��R 21J)�I:�a�$e � A-B reg���Aj�i�B} �Y,� m ��, "&! �Il. f!Ii�s 4%S5 �#ݩ."'�M��}� 0.3=0.6)*V6* y�$!Uulplowm59�%3��*I2ue a;ier+!�Ging|1acas/ �,al 2� �2f/�%alb+ee��M� � D=,�c�qc$.�of 0.8#�no5��)���/%5��]�v5 �!crild�2L- worm�-� eIB���}� � �r��s��*�, . At6h*_s�:%0is�t�[��!�i�C� Nx 3 F9�J��N7om�iA]�� 'hq(n�.E seeA7 6t"�L� saw-^"U��(^4 Gaub�$}.�pi~�F�EIM���D.��K."_Tce "�s��"=0.3$�&�6�!�# shadowA�i!����_: T -J �QA�B� */!�c ructS,!Cab  C�S�k{� Ib 4n�"-uN2-��a*Ntra $C") -  $� &� ~�"d�U�Md� � �.$!�*���� �6"�8= !�� oP �93'5Sj ��t�de&"� ntir6l�pe6��6* $=0A play� ly�or.Y� e big�[E� (b&vns!A;Q6�$ .�!��]d) V �1.5.�} --�\� 4.K6��� . Fur��o� !c.���M�� >onsU�2� r� ��stead�k���U�2s(s0, get��� ��b�^�-�tndh < a � Aepa��ism6]"r(.#6� oldo}�woM"aem1yr�<�'{�5E` _R|!��,�:)v�(c"�2 echo) is f�ng. Aa& V½� �Ys-)s* ��et� 9gval scen�Aͤ՛���!��� b�|=4resL0d�Uter�Sn�:r��!�l��' \aB��-n� picu�H�Mzlook �o��-o !Ks�g�/:��xa�in"m��s:^y �e�[B�6,X@�>%�u 8Ne9*M�%+B#��&Ral6�E �S!�BzL&�(#!')�&z:�QG*he"�..ISM� &�76�}�fs9 ��+' �X�V8^by%��+a)�snapsho&�proces�[�9��ae- for (B� S Uo��XMsta�ci��by&� t-I]�%x� "� . H&�xe AagA�vam����e next�. &�5Ah�&}��3��f f��ly7amMUG� selv* -S105Ta2� 6s engag�)�v [m�. the � y ��恙!; veni�}!D&�sYF-���b}�!�A�'��diagram�h�d�.s, $d_u$A ="fE��0�F�?��ag?:)�@ ��7 ��2�v lE|j-i|$p! M 2�*�� y�$=0E��7a;�quQ ��2�%a`fsHfVe.�P$��%rPmp a meaning Xde;� C%F/�2a��!� [�� _4�E�"�(rin4o&�%ex���0Q|�1�.]2N�2d6�O�1.5+�[�..�"��i s 11�� 12e�}Q� �Fv=0$I aB'eXbly��x�v�>�!�rq!polygo��oir 9�A�f��;� he �BX��e lZi!�Fqm�1"vMcross�o�rIoE��5�R%6--17%+65-W?�wo "�����n��open �l�*nLruLas H(6-17)--H(65-75)IQVchM1fo�%��e~v� *o h:"�,: EA4� x�fd 6��S$ bend��� Y�r;Cr.���0i5Li�*th b*�&h;�)it�k%!�frk5���CN��'(�q���.٘ �cep�7�s�^ �ime>���r"�7�� H(82-92%�102-111)�s (v tria�fs)�=2��s�7ce =B#aA]&�B V.6)U�2�n�&E5K z. F:� *� E-&!�� � ice"�]� to well�Qot3 ^)��� r��D A� k�9K~ s�|A86?��.'n�*cu�wa -* {"22G.3��+ %hb�:�*A&� .�C�7�'zPA�,a<Li�� q�de�E�M�aA ;5�Z squa�:��# )e��K��mixmBym�F4qi�"��n"� �� ��0�� `\&= (CN)m�� wind"9 6�7!�h �s -�=� !" ! wa1h#�@w� B,#.�YAk heav�-}na�5�$�� ��&"14/ In sumh)2oC.&?3!.� �u und .[BI�<"yՊYeGd�n eluciUvkm�>�)iE2!�! InY�E?� 6:���'q|!�}reUacqui�he>��z5{UEM�m�.T6"G#��k"gO�=?� i �h!s� a]�ity. �8source� �N@lgNa�C2!��$A�I� ks T. X.�F%� M. O�_b�L!g� cunjg c�`b=/xCH�/�P P. E�_sza{\l}e�8 ��@ ents� � manu�p�(#}fun�qby�F`5Minr�1�F,�c$a % "�^GH}+K:of *?cic 6c0�H�HbKc 9 \"sub  (�} 3B~1F2I�&�ohI��'d> I { c3�% _D.�zR �:?w[L.  , V.AYMo+n nd HE� % Adhe|kA^c�䃡�vi��lig�mrecep�+�)s. -��Y26wb415-417�c94)�..= H. �?, B. HeyR(�,P. Tavan, %Lz�;�Q�@ar"�C�-I3� Am�c@ %m9�9� ��>�7|]997-999�6F^s@7ZB.  , Y. Cui � C. Bustam�z , %x�' B-DNA: ���� 2d %of.o�O�eb �Z@m) �@6��795-7R�9A} A. �\ Lebrun,�HA,xbL�\�]LI^ovy�A�[atenaMSF. Caro!� �1 �.�. V�2-794Jv�@ U�c ckelI%ak$by$ �?!Pw�J piconewtoq, �K,`v!%"get` 4489-4492�7)��m�aa}�gRief,��Gautel,�Oe"$he^J. Fern1fzIQ2�R�i)K"X ��}��� i�c glob�M by AFMB�6}, 1109� N�)C�]4 Tskhovrebova,e,Mick,]A. Sleep �M�m , %E��q!�2�I�U* a�giant %iC�1teX�h�u$387} 308-3R�.�C!�S. Z. ,y�H.A�Granzie.B�Fo`M-��po� ���"� %Emlas� w&HB6} 11146JcIA�^B�wl�R. Best%��@iYU> AtEioed���a�D%�r�AN chem��.�D% :���. Proc.jCe(96} 3694-36��60D Ze! e!Tb lDJ�"Bai�X; e0M�lI�,<M. Nguye��M!�ar�o~I�: A|�D�te�p� �>ced�Cmer %fxsE�Am�dmS�Hg12�� 2058-2065E�6"f&�M��5�BN�T FismV�I��*�E+<��8��-i  %s�r6ME <Ay���g�8.��f 74} 63-91% 65iY�zA�:�e�aȡ�u,B�F� F��'m�΃d]&hDi(n�I.t.a�AHuct2�(10} 738-743�32_�D-i � CecconiWfA. BaŕI.�VeErey��J.)(Haack, B. WA�tthews�$W. Dahlqui�La�6 %Soli!�ate syntL �.2���G� 4 lysaE}�2iE�9Df139-144% 6�)�"�U&LI�2M�&_�Q�k~T2k2 E�hch 0119~20:�Ja�E�  j�VM�ss�D.2 H�iub �D.!�Mu�  %�;[hwa%#f��=bac6 rhodopsinM`�)&BF� EMBO Jour:%`Ym5220-522�6m+~'�bTh�, 7��* o>t�'� � Aj s�6U,� sX�nm8-��h285-297E-:# DB} � .�rI#�rT��Koetz^[G%}ailliams, F. Ma9 Jr. D�iђQ �Gdgers,�KW�?(Shimanouchi�AM�sumi, �;�*x�mpc1|�Ev�4e{�D macr�Rar %s�&@W�CM�&*�,112}, 535-54� 76� "�+Ima a S�Xtou A .F A. I2h 5�u��M)�I-band:"��Bbl� mponyfLORS� �m(;15:323-327.\ Lu} Lu H,�tW  K. Stee�;�j�3 83 Ax.&gF�xA� RA �G� �Q�&oN3 ob�~fs C�?�B(l,;247:141-153.�aA} Sqm e.g.��Mic�wtti�� anavaFl�sit$��$F. Seno, %QIY aM�Tt0o� )�a�A�  %"Ci~iv.Z�082} 3372-3375Jn �B}�^M�2aY.�(A. Trovato,�iB� %Opt� shap%�pac "�s�8W �� 406}�me�6�1}6asA=G%Cquium:�ume݈alJ;rP��a�-G� ^5� �uMod�v� 75} A�ɺ6X�CR. Du�S{ ndewY%osberg�DTanaka),E.��.rt %Orolj :�Aa�C>��,A�2�111N 375P 80J�DD}� %S oul�Lo!?e7�, �I�i!�s 7�� �>�$259} 988-9R.�D}m W. ���knd��aker,!��"�,*�� tz��'�" ��Fs��n�s@h%6� 277�5�6�x �1v�� uczinski,.�Top$Y,��� �xI<]?:f�FBa� two-�B:� `G. 9R0. Bio� sNE�39�77Y8� 6�F Abe, N. G��NonU0 ng lAB�O I��m�%�&] &� in %*. II.�t"/to�d�{�`t��s�"� �23v 1013a1a812� �F$T�F, %Go-��!r0���>emK sm* n0cF6t96�698-1170N��#} * %:#- .1�4H-M�of06� a�6�E= ��JZ� 6851-6862J��1z�SI�!T�&��~�03}, 8319-8328�6�2�<93%B=R� �y>yM��}114 - 12�6��<}�� SvwBo�W��!� �$2 E �70}u� 6� &i8y�O � �T*2z9�%7h"�!�Fb�C�� . (iess21.�.��>+AQ�! m�\ ��U��^ %RB *DNQ N0E1��E�n>� \new�i %.�nDFIGURE CAPTIONS} %��e¬dez 0J %\� [Fig. 1.]'end6% % P1  �)�b psfx��s .�\?{00�ETo"v��Rd"m*� !YA�*"] &?".|nd��2ң�+comapN��[��x�2v-��:=Gsolido=�"��>Eb4bro�>li ��Ab�3ize.�Y6�<@�3J�10.�7/%v�S�&O�-#L%4�er� 0orfT� 4E�kI�jIw�*��S\� 4Y�!�eM$10)%��VVD�w��m"�M. )symw �cj63?alf &!{ +�|]BFUG3�GsplittitQF,vspace*{3cm}6�f�<6�%.4�� At.�s� �-,E6U)^04��30v�S�aeFi�H3E�6�3b�5�6���6.} ���U.6�camtovE�+�0"s 8�S-`JD�u�17���36J3-b38���5Z�6f�9Ҥalbum�P-{jb.���A�@&�2�.$=���'&�->7�a �B #�1��2� \Po$df�10��2Mn�Ft9UA�,)um�"'; tmbV1��evonecal���1V6a� e{e�S�^at2C=0� m9.0 explF]G � pacs6Ake.]p �23keyF3kq8e:B{[Fyl,a%,�Y-�,�]{cy4�v"�yc�kE"�yF�?^>^�; % You� ٬�GBibTeXY apsrev.bs Y�3en'U%)�V a1�Aeo�\��y s��7rrl/APS %b~z � (cile), �lyp�om��{� -��i��C> ary.�i>�� �j.6�z{} :-4� +|s} %.xg6@�i�w>color}a�8luy�;$[2] %\ren;}E|{\�Sfru }{0.�/>#op."9w6E� z%float�(1.0FMtheW{}{\fn!#ol{�.�beq}{�"�Y}Y!�and{\e$q^" beqaGn�FyJG% HV#be"�eZ$e$rFEalignB� A%6�dst}{\-�E�:non}{ umbeE0.STRUE} Irm{\sc ��>�FALSE}2' falsB(T} :OBLF$f>$Q $aJ bf{QB b!{f c {\F>NL}  _L^N:5QNS2" ,S}}B+P.MPNMP.MP}nML {{G {\,N}\!\!:�k6�k>n6 BRnh% \hatJb 1^n}BcB {�v.Mm m>�u{{\25c�kBSKF%KB%kj&6J_jB'xJ�xF&�MMeJ"! "!+Fy:AyBcu)�5JuB"v:"vB"w:"wB"U:"UB"V:"VJ"tI�t]1):�W:LWBLx:"F:X:"XBDy:"F\z:"zBDZ:"ZB"A:�AF"b�+M% A}_L>B:hBBFB:FBJFbbp!�\m set{+}5� b}}{>ubban/-~/pm��^\pmv1P:�PB�R:"RJ"EU\Ş6XF,e:NeBNE:"EJ"hL}q�1�E}JmE.�FI0IC0>}16 J�2 N:�NB�A ��ZA>_AJ�J�i}[1][i]�YA5 #1}AB+Ak)k]Y.#1}{\AbFWAiZ-��set iAF6ai!� iaF�iaJ�A^�4_L}%{\Ai[#1]_L:iAikL}1�AikZ&�4WK^NBMCi�1�C{6�D6"DF"G6"GF"S)�fS>�S.�BC.CB<� {\acuteJ[�? �:�T6�TF�Y6�Y>BM6 MB a� .�F#bMe*hDeclareMathOperator{\Tr}{Tr:� Ymin} {Y_� � ript�*Q>� Ymaxf0ax>0 phiC�8phi_L^NeB� phiIv3I>fipe@1�\Z�h% ._ vm�vec{\mJMn.!nJ!kappa}{{ C >�vlambd& >'O.�OBr}[2]{8 O}(\xhe�\�g^{#2})B7S��� {S}] �&3\Omega_�3\r_>� CL:L4 Cr0O>0�dinfvg \inf��2�OJ8JoR<rAr�zrAxV,Bsri} {rVtdrA�Delta >qda? x:� dri}Z[Na�M b�6) posr�b{R}_+:!tr��r>f bcg!� {\ box{�in}A6>GcgG, {redF#j #mag�l>'8rsp}{$\negthickF$�Y,{\vphantom{IaFQ*�\�,{LU TP 02-43����paper �� Coun�Ttt��� ynchron��upd�grO� BooliB�e��% [Uat��� .. \*� etc.needed jAmail,:�, \݋�, \alt.>e�}�y�^K��"-. En��y�&gg�[]'m;ctume-~@�� urlF6{}'�\� &$�4PlL���ap�$��C2!� t��o�@�f�"�2,�K���%uth!��l�=!J.+ =!N��LHT��4 i��&Y�F�m%�M)6�t�!��J. �({Bj\"orn Sat�� !�D[]{bjorn@thep.lu.s܍5b []{YF�weA�g ec�:({}q Carl1ei.j carl2i ."{ C*�S|� Divi�,, D=�t�[7L�e��kics\\ L܂&cE, S\"�S gatan 14A-223 62 .$, Sweden} �,{http://www.9/�K lex/a�N1"�F ns!if (:�3(r3�A��$A�s�M� %op�$d�A�). \no.�kEHd (�Q also be %�{"$q�M�)�c.@G�D%6G%�2�� ate{%8-12-16�Rab<c*�Despi�Rhl�rT!1DA,^�Jk play�aich�ve:�-al"NIH;u�ork"�] fM4����$�ieB4ab�z�R��.^�here cy��\�eA��Ya� �!�;!� &<�gDKe]input�] node�/r���TM��non-` otic��CW��j,�~��;M�\y4rR[3�U�>��:�&x� í�5 e a �N�Wl��Kqiz)= ���of%��Y�&s:'\we �Z �Y[o ��20Lre h%=�7"`ARn1WA�N�to�\l Y�WssJwdD^_"��#Lb�L"�Z fȡ� view �c�i8�t ,wsf��blems�6�Y�%b' rt s�medA1?in brac�!n n�I�\{ {89.75.Hc<�.10.OxbI�'2Q"_-/Uţdon't��!dOis %\/{��\��t/��8��\O-%:��, �, ��+J F�H body!/pa��a; -�)��(Ar!��s %w�e)�bL%ne��!�\K , \rlF0#G"�i!' Put "�,rguI�f 'E��T-�a|G ?�%.���)sub�'o� V{6�� RV� ^E�enjoyRheaL�TUc rese;q;PW"ir b�!$! �c6x|/s, �-�u$4for gen�g�oory�P�hr��ZPhc ��j_dQae� ety �=zp���s,�*�+�0� rM;�-ev��d"}�� /a� tegig0�!�Ǎ��N ��z*�l{�6gy�5#lyFJ � �x s. N ��le*y�investig�  exten��sz}��:\I�,{Kauffman:69�,rrida:86a, B��:+�Aldana:(�S� ar:03wX�-As�&�li�Sa� !��`y�Z�y�}�Wa �Q�� each�< c��̞ndo~�,Pla�bD7 among � %i�^6�M *ep r� _n�V"B�Q�R���,QEy � �7is)�!�.�, �a& )NE��% any 4 �a f2'240~--0 �n Astep.�^ICw*b3ine�[_}[���"8a�Y��a� �|"c��} (in-�b)%{A�p� yBa��itoHofXer6M!��laZrm��J4��,\�_�� �D%/%ks �.L���ov�eW( �(�T�ts,u� s���mZ�c{��yi'��&�(U"�`8T�f�5em� Bast� :98}B�A� 2m for �\i9 znd Hu�04HAF�i��9� �%�subBR.fe�2���havA�)o�{� EvsqarQkE��<{Flyvbjerg:88, D�[l�.4wt� �%a�"��F  �=S1� <isj, w�a� 4 �&\���0�k*�� id�\�8ix H&�sis. OurW� pow�%���sc7� ver�9��HN,�(it&,UE��0whC����� �t � Q basi�& E�_�I,.��inB����� arteA �$at!`;Bɥ� realU��gDor �U� � �1��si=�����k*��>�6A}H,*5�� }, V�� 04}. Also �to�d)���grows 7nom�qe� ��in BS�_2l2�ɾwa�{e` tiny`��)�H ��%�9,(�psW2>sg9��f&x � pRE|�\w�ink�mA@�A��har� ���EF� )>.B(,Q�i�hL7ujm b�Wlf�%�~|}�%A�!Mcy(-�A I 3I� I�>"c  way to � �5�� )��s ��rE��^to!  ��=�#!K!*le��-Ope� i*cs�C �*��A0tj�gA>"� � tD[Klemm� Fkpr>���%c� I�,���D�͔,�s� as aI&" � N�[ :�5Y� whenc��y��a��,�ml��j��!"E�/9of !� lw�A�o�u�m]�-�%�{No8C�S���� ū, $N$^�+.j� 5�1.67$L$�w !�an9n,^r�IT( ($L > 1$) �N.�^ա�brevit͕j a  {\its-E��~9 �tog 2��>%�}���tep��R!7du&!zA�ial/ . Wk�8i) s^  po�Sv� fulf�I2���s�t� m�i�P �m�d�_~��>+� $C_L$A~e ��"1�  a"{b�is $\CL۬�v9m-�a���%4a�j � � $L �VLW�Vle�l.�qOq!Q f���!Ga~a�- afte%���!���h� 2�ny9;�.R�no�aI�9YX��yaol;�t)l1@ �0�2�]Csame "� �7N� �� erebE��:TD K m�k����5T�b6# 3�tD�n4�e_�M&����F��bs %�at]�I� eE%��y��< � , $!ܱ7N��ed6D %�NI�� <inf�~�UKve{y !,�i� l mA3�:�$1$; �qJ& !p>q 0��, �M�#��`k Fu&�qF� RU�F`uY\� [ui� t�{*l �0mT��..��A�A*�a"? G�!G��i�y6�:n,&� pe -!��jm\  v2^LH�eq�utS 7;!�l!�se:� s6}&assocwg s�@ %�a�dex $i��� E�T$i\in\{0,1,\ldots,m-1\���1co�hi�'�le� � �Bm� � di��$0�1$ɢ|a? �mFOn�A��-$ - �v��xE�?4.0 01$f� ��T� -N�4a !���؄ turn�3�f \OB��en ��r ). �ǡ�t��[F=e��s (cho�sA0�� �)g FwhML �S%V-F�W�Qk k���r�r�n�gv�vlyI@�� . Le!�OL��J�%Sv� . E�t�!/c�Vs��qX \ell��E .a d]o!�@�CLJ: ��W,*�se+porA!��on--ex GhO 63ECng)��M �b!#} %/�/�'.6|�-�)3"�F)< "�B5Q s1M ilar�a�$\o�$2f ~-Jser%b!/ \Cc_BmeafL�; F =e�gcup_{!�|�* %�$.�|L$H �1�!�des�� � a�n�a{d �QcN$�G!\m!�$Q��Ô?���tI�a1\ sE� $�* �}_L = _L hD � )Cc &!0# #��$>%L=\lvert6^\r����2p -�9�Aa��is-*by � =e�1L.i� fG^�5/� ���jtF�E�J0 @>�E })��in�5$ q '�!E.5 L \,\big\�Eslash\! �3IX�(tack{1\leq AW � y��1�Ci"�7 1L\h��({-8pt}\sum_"�+s}Jl0,1\r ^{\eta�0\!] (-1)^sm;!__L(�'f{s})1Q � � ni=1��T{L}} s_�$d.AA�_.28L} (d_L^i)^{s_i �nd=L^"� �$� a����t%�C��$ ��s%"B� $N$-f q�� geyECe=>`10�a-Zl�*fa"�*~.ܫA�CL��O/eeq ub�� Basi��="��L��C���ms��(���b�ub�?b�����&�.��"< �z o�-�!ƌ P$delu[!��,�@ata| t��ah��� 6B�. ��AA< (\x).���bP���<ed, w�� �Bd� 9F� 1��P�#.�( $\x = (x_0� x_{m-1}��Th�,we2~OE~!i]��\nb \� LNat^m\\n=N}}\binom{N�9b}u_0}^d�j[-&8nb/N)]^{\n_i}~,.eU_m�n=n_0+\c� +n �����s� Ѿon� A�en!]iDL �&�4� \eb_0$ b� ��#el$(s $e_0^i=\df,_{i0}$,� �w�Kroneck �-.Eh��12 U4b)D'�ds �Fj�ugin`; -L0xb) &= (\x - �)%.\`a &-+ ( /\ &= \xB> + ��c_0.1}c_1!�$<5rC� \rI�0f�i �X!ʰA� c<��u� 9�h "E�,�%*�Jwq�$c!�2 $c_1a 2a"jugSC/6j� Y \! ial_j%}g�!�gradi�'$.v �non�� �!iBB�0{}P�� � �mi��B1��t�put�tws %= v�-�E+~nB%}s�r�X( � wardk5:  $P2 C(i)1� phiI6R,o � ��$je��e�>C J� = \rC x_{_n}+\rIp}~.<?%Ŷ�01�@ŵi�BbLe�an $m6�m$�rix6 \�bk?i1}c_1���kI�!s-�; ��U�N�blockB�ceA A� s=%a�to%'2"@s. Consequently, :��9$q[productA�!p determina-[�1 y on "$iagonal. E� r=\rC+\rI�d-.!�n, 8ZmYF�IL^0�1ɡ�\begin{p��}-B(�c_0-1)&ɩ (\rI \\F�2)1)&6L1)\endiU = 1 - \dr��1�͢�% {+c_1=1�MT.qNc% Z�o@ 6��Xne�explor�Y2�Z8 �.Ai��aa���!�����1�h$�� $\ell�T]��length}@��h$,E�E�" 7ia e lowest�"H , ` $i \���OJ$(e�)^E(iE� ei!�i or�index��D- ed. IfBH = i�sayi�!2�parity:��(positive. O�wise 6 1" nega "B<rt��Cfullyu�( its-k�A t. S� a� �  enumer� m��� $��G%U9, :h>� ��PId-{!�-1}J `"U ��!�14 �J� %� hileF^c +U1g U��string�$\T �$\F�}specificB���n ~ C(\FTp D��6!�a�uGe�%� m�)�q� m� �>�H$u�,:n.�+_4Z��(\0&\Rb_1^+& 0  :.E&\0 ^ 6[,�eQrow�d column�nnect�Z1!(��!)4 $Ua $%J  �( ��!� i� at order�or:����e get.pqخuc&b|Bv 06d5�!�%� D)�\pm#0&&z�y)!A�!�%�(!L-�)�m { r �of6 ��=� !�t I�Ephfd$� unitary ��x� 5�Sb�"0frac1{\sqrt2}: 1&-1\\1&12�I�bsɔA�� ccor�� t.�t U�^\top��;q> =>� r&0\!�pmm N�L]�Sb�jt6' k%1EM*2��YU?�� TGo2��n"y� align�� (&" Rb%$A )=\non�&=/[g"%W&�.<#] JA3-9I.@) ? yVX1u \Rbt�f-9J0&J)B&6p �����2F%�2�=&= [1-(�y ][1\mp(A�  �L&*N1-Rz)a;nd1�6N� � find�@ di� buiof � �Tp� /�l60 n :Y . If��> belo4 �>�� x � it&ytself� p after 2@ timesteps, depen�6OwheD�6� i�"� or>� � is��4s a periodicit� �7$2a*�. H&for&|s�re�.�2�$ �  if y|L!��Eas"� :Q � < if �|3If6a&� ���E2M, ir]i�)u� � ��, basic!m��Ain�9 does� chang!)th!@. Onl>esof SrepetH differs. -J.�  $JN� "�~�A� 1�!�:n>� j��� e䡂�� = &\+_�|L}\,  �>/r]^{J��+-$A�1}�� )>6Z.@ 1� \\&\eS� �E�|L +��-B/+v�- ��E�E98Kronecker delta� )6,1}$, takes c����al case� �. � o"� 0$. 4 �A�.o$1-1]$,.�) $(1-��(()��oul�vea�\it obeyed eq.~\eqref{eq:l��. 2=C"),OL$ via tens� us} Here�,derive how $/��ed from*�U�nrom>�OL}�,6� �rse!�a&� OL = \!� tack{\nb�PNat^m\\n=N}}\binom{N}}M�&�M�[� nb/NEa$)_i]^{\n_i��DOLB�>eq E6g1"d, u�8$(m+m)$-dimensi�-fs "b each;�x`twoAqAvector� pvkappa,\vlambda, \vmu,\vnu\in) $. EVe ::� aB���F,%�$\q \ s mu�r$\nu$ d&Hsum�!�"in � ��.� )�Tr(\GbL)"���9 (G_L)_�^�"Y q� mu N)�]vmuQj"� -�vnu.�j!� mu_j-����t�� ator!��ed.J � Xb) a��hsU{-12pt}I�0\leqb0,i , m! � 6;X�mu1�anj] $\Xb� Hco*�"�� ԁ$n^{\:�! {k}}S 1z n^\k9p!2Qkf n-i)6u L pow-Q(We also cho|!\ ��$to interpr*ni� n empty, R� Gualu��$n'is�� #0^0=1$I� divia�( must be trA就�� .!2 M_m�^A]"�&�1Yo!�j^{iFE_�Y M} \�text{andA \Mt�e5ypS %��� ke#�!��-k)�4 ~!��g$\Mbt�%#�"a�!� sensAia��C_aSy e\l O� non-zero �K$> $"@ ��pa6 er ��&s $~j y�mu z�� (\Mt<$��Va{ Lett �a�n $��$ yielde_2[>�>�$ =&\! �Q�0=� }^\infty\�^'2��%8�< @'>8� 2hN20 ��y- {a#-m0}' IJ- MxY�~� =&~Z�I�O mjY%�_jR�biggl[\,)9Y<>B/! \!5��n���L tG 0�l& S  $V�"Z()_jH76� T� "�_ƾ~!��{V� }{N^)�F�< 9�)_j+NQ�j0}��5�Am=�tc)2�.0` h0}&>.�0�9 e8 �0-}>1�)�.Y� Nj�  :lin>�� $Z_> ^m�(�$� an arbitr�$m�  m$�(_,. coef�("� l expa� -$B�[y \zb) �)' _j}$�F� a wa�* >�^E!,��B�)�� q-D� �E>Z@B�z2��<e�+� � �/� 8or $\Zb$ satisfM�L���},\Zb%: Yb)= )Yb�)' ,9��ceF Xb� Zb� **�^qs�&�XnyQ��"��0 =-�$�non��& b� . D�&���x� � $ aN�>'=N� % nu_jM� !��]�$-� !*vn"� $vmu$. Now,:��)ioB.( Mbt�Nb\Eb%��%\Mb���2� NB� ="u �\�}�fPandQZE*| lb�~ v���s��j_0a? �q���� NjM.��%�#@Y|2J%a(I�*Q eN)X� =q* )\Nb X%�aa,w $\Nb� "� �"� � �)�.R:  /. A]�>02X.vs(�h��.U2*o.&� �u�*al�Q�GY�> /A��FE�C�-B9hLD�� &V7?2 + )�:Z = �`&6�MbNK��& G-"*> eg $\Ebhe��m�1 �B�.� �E*9hI,��H' �es (ac *$ left) les�nequal upp>@, right multiplicQ�Y �alwaysm aA� verg]+. . Similar�!i8!��(Nt ell-behavJ�- both� N�,����iri� ufu�M�^ )"K%#GF� � 6�a� ���&$\T�15�MbZ<#ich1J�F�ZA�oeN]�}��%�F$ tellsbto4 rA#moO-�derV combin�ial"� 0�FexF��uLRD-��-o�!%�a���3x/oZ�DiA�1G6; F@�qWlB5�����Q\trm{ ~�|�\g� $ .} �� 6�4i�"serA�a��]m�&c4b�Q9$,Q � n���eEA0�2B�$\ne0� ���.(�UVT_t`���nu�Vmu���2 T����%�4� true�Ʃ�.e.5�\EhB =V*.� �-�V�)��.)�2�EF���TbL�ǡ��/��(�ơ�sam�M5�H)�� �"6k- �5�� b>.:�$6�!Tr[R]Aic�A ͵,aj_6MEA�Y� a\ �&$ �1A�%�&�=JE (D�8 jj})*����5V�� ~=:�a*! s~8R� I&� B� �� / "� �8D_�܉G" 6�OL��\nuDNR�nu}�ni��4pt1 �O� 06I� %�2{F�R�� ' ��� )�1:!� d^�{d� 9�! vphantom{B�)m|_{E=i ~ ��7&:L\\)M\}� By5o.�z$1�nu5 N\n��1�re{ Q�E� 1{1-q��6��(1+ ,I� d-��ggr! !\!N R�FI QB}�A&�q �I6r>�(:�)A��$;!�;;! 2"��R��)\,-��"� F��16 i=",- �!�t!�"�"�"6"..�=!61-Bz)>r!&#\pm$}7 \psi;#t�-$6�#2 �$of (in�9e)�&�$ofw.RUEVC-ALSE$, =%s iic9,Fthe�6�of,�&B�& �&k 8se� im"�4r�@�aM&!<"/ sH &�14 nu5Gity, ${\�J}[%,� >�:% ,!z 5a?0big\backslashI� �O2, cup_*5"d\nB 4odd prime}\\d|a6�b��6Ops�eb/d��eqj"�%p)y32�.�Q3� �N�B�(� (b�>�\! �+�IXr/:~�- :26�2�)2? he �AZi�(/2\ no4 �g�/�*U'� �Y.\p�3A�Q0H) J ,�8 $4�g:�'# �(�).�x2inclu3 --ex !inciple� ��|6()��.2EYUP6"� �(~\mathbf{s}�#�2&>4^{\tilde{\eta}�Y��1� (-1)^s28/ ;d 8(j�j2g Jl-� �| $s�� i� L� s_$8$ d}.a = ͎b?(9IC }^i)^{s_i�n�_ � �^1�,:� C }$ A&!�u��!?%�'�5*9�+%_�,\tR�85�)&i s_0N�\\2�0}�c6� E�U]6�E �+s}Qd�(s�Uy)}- �2A�q�~Q**OJl+beqQ%d>I= �5�.��.c =0$ v% I�y �E��Mo�'+0}B�������B�1+s_0)��J�u�� b� - =��- U/2v J+* J�Xrn X*�sm�@!-����y.d ]{6� %Y3"� 2Q3=&y�2�I�i��|L\\L/ .�}��6M�.--J5�^-�(.�-� J(.]��� �� even��2� z��!�P 1aT.'�<��!��"�:3�r:7sim�>t w� .�Bi�Ao work�power "c!sSA���W�'& c_k^k=�E�#U��&@z jsM���m�.s2:�#kk}c_kohOLa�:n)La�opea�B'N2z&�*,<ed�>:e")�!o+$r<*%K=1%� ihe�@ce radiu�%x"Bn>��.�36 \lim_{N\3arrow)�� a�gl�uujaR�.�)���� �*V�� limu0� :0�4.�G\OLinfF Rg2%+M^��WcoF�H�0�$ KJ,Kauffman:04} ��� valid�Zubcri7netaN�m�"inputs�5 node�<$r;,!�do�G� trib7R ! comes  1.pole �*|xFJ $|\dr| < �:nd9Y,>,$OL \approx�IM({\gamma_L}{\2�)K}.�OL !/ high[/M�6$H*Ktotal^ a�&] "# #8$~$ }!K7!)Uf, ail���a&G&1/[B�]."6w�5K �&2 P+��[0>L2+k}{kR2��}r �� �}_L�-_0�� dk\,k)�(2}e^{-k^2/N:�1�integralaB*�)�>k��.s}U�bin>Ak� �&yE\ll kN�'�5Ɖ,KSti]0g'sa��M�-be�Q ppli�@ose. V44I��e22D'(asymptotic � ioE�շa�scaling.�mpto�$(!�1)/�2���BeqF$a��%:T}�oA�kmea�X�CLV�.�CLJ�5i. �9 r���� o 9�M�� copy�S(�9"L1$)Ki�� ters<r=-1$)�i�sh�6bZSplaced b�).r9�.NQ"`�+��9� �"choic���o�9�#�";Gast 3 as�O&�%!�m�� splitzP�m4#0Gen one x��removeR"OnCQn�aus.� �S alys� retrieveyH�&� ����"@ �[�>]��=|4{N!}{2\pi iN^N~oint_{|�� |=\epsilo�?RM�O��{e^{N=}}�^{N+1}~� a%�� a��")A�ttR� enough�Qkeep �EE�!�u &�Tut&$A���|_5j�9�ee�9ly!�fum%I)�>� stat�S at6A};�G[0]an�N� 1R*�exponen(X�'a �Q��_eh�&-\ln(�NzO j j=1�1)�x^j}j� >2 G� ҇v�� od��gl[UY J�rm{?> B ! �B�"A{j5}} >+ JT^-!^V&& PBXe�rio �+^uJ6��G��16 .��re;)>�e�BPk9�=1Tn/�P?{%�=�{ap�R(a,b)"6N��7s� mmon�a_$ax $ 9Tź2 it� $k=E/ *re�&ed�:�F�s�E~\,MYk>�%v ^k}kU*�+(k,L)~�Q2� [r^kF�64+ A�)^k1�:�f�UVk}k��V�I0y�� U�j =&�Tk\ge0!O �*.Y�2P�xn�6/N� x\r��2M [-r^k9�].�)���� 4 !"t?ell �A&qZ���Bj inn�>} bG l�Yu0?a�c�Lio�]tweR�i�*�-[ N�.��2� �=&%"��1�= !>��"K�$N">�2^{E-1�/&+ �BF.h(>}-1�==}�L=0Bd:&_0E�1'Jx#[I�(2�>.�- 6r* �J B.�}�{C }{1- }2% det Bb�B�(\O� F1� Y� �R�a*Zmega � �eq�) $N$-&#G�!a!�n�>�.L= saddl� int  ?%��$- /2Eh�!th�<0steepest desc� te�"uGid�Sy�Q� tha�ORsired on n0�G��Qhand,) r>�K *>/(2r)$� an : _>�� �b���@�E,��isq1m ��E��1 $L\ne0�C� Eng4p�b�1�/io� abovD�U2Kat�&� >���l:G[0]&<2\{�3rray}{ll�,*<)a�|}\dst��2U�iL}&� �}r<1/2�OBXFTS12\�O{ \pi2N�._=�_>X@e^{(\ln2r-1+1/2r)FkAP6��%=�.:�L06� \vbRva} �VU ,figure}[tbf]a/ed/psfig $(=Lcyc_rh.epKJlndEcapAX�baverag.`I�&_s:dN9d�Ja�kK!��le-�s.min (a)�S$r=3/4$ (soUa\s) ��a<�# (dotMT =b). I E$�i5 [r plot &b),�aT3, 5, 7, 1, 2, 4, 6, 8z�{7' 3, 8!4-1� �`I��t �,� bott�fo top apNe�� bound=o8S�Pa�� curv�o!�=3�L=5�B � es�,ially coinci�9�/ p��/��!�r�M they� up��� ,��xeupper �9re.�"4fig: L cyc sym�mndA��� .75_����A�!F6�$N=100%V -L[6&�d.�I�t�Y�AP�0$ ck.AA�Jr=- =]� ). N"d�h�wVF�stdeA�Rk!>lOur main�*5analyT�io�c!�6 F�Ͱa $\CLI{i* $N!2ŋ}7�p!< growth. See eqs2=LC�OL}, ("V#.�--:�)S6� �^�6�%�gen�[ � �\�I�# ,6" 2.#����>�&az�$N$�. Fig.~�:>wisQ of &.i�short#SF�,system size,%��r�ut GM�.� "uq*�&�%�-��I�ylaw�e\ amach�Iaf�a�R:=7 N$ g�Q�IEry8��H �R�val�R�:�and�,���!�same. C�i9�)(inUS more ^h�in��l 9(�). A�*c�ked-�!0" strOce�n �N�g!a'9ow � a�2? m^P 8<pronounc ca�fNn!��6  shQv symmec� ��!<%*extremcsesIA\pm r� C ��n_�sym*�N�8 [0]R! \CL[�bs)A^��<� ��a�M� 6����Onop.<��f�l%#s�� gi&�TE!J$. DueA�^douvklog�- hmic#C�happearl_q=$#a6ͱ�� �/sU�x --- i=� mind��&��Nns� $aJ����_s�& a riKo.Nw:�90�C>��/cumE1rV� �� �[aO>Zi�s� le L_\max,in :N$J� >uFN�X$N$. � �,10^2,86 10^5X E� Xn*W N=1"UF 10^4�Q6 2\ .u 10^3RcMca;��oc1�  c).�"[A{szBdr��th � Ai(a)E (b) �{e$V�h�F�$E�e a�$hea�X mark�His Y� $2�=10^7�2 L6i���a��*� � 6Ve�9X�T $)k�#rlPj*e��5���Prg�2+V�;  drast���X��e $y$-� e b��!� �$r\le!�:�cum��>�%�:�#y:��[]& :- "�:7�.,�di'!�&� ,�th�he 5�Ke�ny fi�Ti�9O��> Rywzm$r > %� fig� 7 � 2�!K 1=a�12# � isU)"�i(o I�Resaly�reX no �Ci^>ve ��-�r !�(EAcompa#iI�&A , $r�,A�A�.onA�% 1 > � %@#/re�8$ %\bcg{...�refS�%X at �>())^?$}-�m&�"% &!%� tri>dU�w�B1<� �!� namely �$kz\ln 2)\r"� thch]N�Cn\l#RE@$ a>!�ne�F�u&f $1/2<�*q�$$� d��sharpAt�� /D� B� �'n e�skmN�T��A�� 5 fyt�e,�$J,A6 �*,Flyvbjerg:88FqA� vaiq*�>�$I2, broad tail �%� LA�U^E6�gA#��I!> EGE-CL[1]�:r���'.�.Aa� t����F ever6D�Rk_�A�]he F�Np� +yY, a typ�' ]b��> K_vs_1inpn�C��s&�v�"M�$ in-degree��,0 $N=20$ (bold��_ !�&Sm!2� "JF�s D���t!�:� �&�; !?�!�?$ �.� �% ��.�p"� dash�Hnd.� BE% 2-�ys plus2Te�! .�4* 6�= �probabiXJa_"Io�b-�s �*� $p_K** K^{-�+�.$Ke �yIQsi9�5o@(1�ddhU alyz!� rule6��en!��scDy.�.:" mvs A�>( AllwB����I&la<|dE�u��"4/,��eem�a��ex�xto��"uY�R multi6��1T|�+�KA�!���k�Zsur� !�urbancqopaton2?R� follow!u4procedure:\\ F�eUn f�Y�Lilibrium.Q�0��!�e< $\T�?. P[ a random��t���pY�\�y�bon���^=evolve R@tep@ !VN~#p togg�,A�A��ly sel n�I��o.�?in� ��ZKZ,�NverɺR g�.`Em$\r�| I$6�,!�4@{rn�xE*a��ailed�riE.r28��FREjkn��a��.~ Q���AsR�z�-&��4A�n!d� hw� n3e}�q �|aN�eD BD� b99roximxAP'� 2�a�E?JHi�C%�ameq��")��5%R�, E�1la� e���#is m �a�fpwsurpris�r wellr :r 6!��x"n Q model ��� 2,ec�$dMsOQJO� so�+��}$c 2Q �  l� N^{2/3W "( �I�,Socolar:03, 65 . Fu&ʃ!p eff%�v � ivY *A 2� %X�9� �0Bastolla:98}.Q��!!exY���dp� $-!9]U8 be mimick�dEY $N'=51F��U_e�Yb&� ��$� !�U���2foy0U�� AQ_2inp># 2�QN'NWJJ g� $K=2$F�� ck ���V0 !�eB2 Cn B4 � 61O7[#et to .�L ��%�`>À1� e�. ��yX�#  � �\ RY 8#_5�e5� � �4.��(Monte Carlo&,� E�P%!nra�ulhu��(��d�vct�x See m�2�)r�.H !g$1� �Jly is�.-�e�s.pT �!�&qis&4 �% ��6by��� -J�"i7�Z,b�z5$ & rQA&��9I\:� K2^� �ە���6F�� �� ��63*� .�89�&O4"�4��An&� � 2���3 ��'3E�6'^�2}N 6>4��see�7 eq: *-�O LVR�i5.�73onԈ��it.�'�".qa�o�CaU  fact [9 ���lho 1 � 2ce3.7be U�+ �Ta"�seen e���_inZVHo"u�U�al gue�Y*� �*] goodE :]]�a[�1�1 a� (��s �l�q:Aaa]�( 5;.�R��va�g� in>u��6�[$ab. 100���is ��9�g ly f�7�C*E�� e�r0@N�s=V� �si�l��' Summ�%�NDiscusR"} =|*D# tool}c�st-"�zBoolea� ~6�od�>We�a�   er��H� F�s-\ 1000�Nx�)u:� K*som�&?�{��e� hold��%y!x . A��s��*edg��@arlier^BɊ&� 7Q?*(av .A Յ�m�m�)�nJ���9e<�beD?:&!a�d�� Aj�nYde5�����! long!>to ��p� �)Wrq�ta7paramC� jm0B�) vP"P8e-2hl�e&$!�.9? t�%.�B$� Ni�"���)<%*� *�i�</��-ynamicSZ;� V�to : be�; stoo�>-�sEr6�e.�a direc�5� Z" B� W� ��@t� b95�62�-���)2��. �'�BsT&lighti�0previously ob�\rte��=^ >�a-e synch7$�Wd�:lOto 5�A��l��gover�.b~teg uoM�6s.6��un� ]�in�\1/, mos�A�mi fou�0 S'��}4%eUZ�we%al+�pe0�cS&g��i]��c�CI`�KlemmD�� ncep�y�6�of�"Z�Z"z . To�����!l` =X�C5foc�F�C��)K|��P�aAR qI 4>G�-艎�&y� qb� �oin�i>re.�S�=>� may �` ��.9!`>n w��l&p rP�l�in���B+��Z6��BkE�.�� L#k�.�se�� uyY@Y��impro@�*un���oTa plex1n. J �,3.�i=lߕo.� ��n^m�d�&iH>r� �,�x�"iA�%i3 xoOI ? AI� �f ng viewE�M�I��{ &�b optimiz�5�4, e.g.\ schedu��� digisFV�u� esign.�"qu|o�)f<�*�?!��>���a�vQP3 �!69I� �|n &y* 6�<�Ai!Vrdw�.kr͓ � ogy fu�E��CŸ́Kf��=\�j ���R��I� plen�~so � s. R�m��� A��0 playgr���algorith!!��han�6such 1H� � thebiblio� y}{14�xpand�X\ifx\csE" natexlab�3 (\relax\def\$#1{#1}\fi _ NGbibO font>J!UM#�Pf�Q$�R cite~R.$�Rurl^�url#1{\=tt!O%8{URL IM*command{!\,info}[2]{#2}AK!eprint []{S'�2ibitem[{2��� }(1969)}] :69}�q{author}�5�{S.~A.} �1s@}}UxL�Z@4:k:�VyS>E�A5�!�E�j�L.~P.}��{�3mphY�title}{�% D4N �B Coup��s@in} Per�G�&� Pro"� Non� ar S ��  \|Ed�jL.~Kaplan, J.E.~Marsd�J8K.R.~Sreenivasa+Tyh,publisher}{S�hger�Q�i� 2003rG��Y MC}]� J.~E.~S�A.r `C2����!0.S�.���2��zI^�902Gp��068702z9p�QDerrida%QPomeau��86!O  :86a�YB> =��Y>N �Z�Europ��)Cf�1:D-B45F� 1986r��)=arisi!=98!=�~�U>�=�>G>O �Z>A�ica Dn71Z21J 1998r:q.4:$, P�son&��  Troein�0�~qB�=:$VCB` ��>B*�@�=B�1!1���y�sHroc.\ Natl.\ Acad.\��.\ USA�Fb10a@Tm>171b4r "�+a98e9�+~�H>�>9L6�C A��j�2��A �L95V+v�Drosseln� #$, Mihaljev and GreilA� "��Be <:V�T>U��|2�.%VPB� ��rB4}q�4�}{�{,-mat/0410579X$#J� yO%>m � 3���'BH?֜����� ~�.�M�098701F��n �mOnd QA!I4!IV ��V>R <�DB���R46nR�%j� $Ʈ3�����������R. 14796Z+v~ ��V Born�ty� KB @� B�Z�~_1��n �(%Y (1997�:97���� �� T�5�J187:8�Y11RK97�b(>h �b docu�"} �< \class[pr�$,showpacs,�s,amsSh0symb]{revtex4�(usepackage{�icx}% IEL�%�+ les .,dc:(n}% Align t�$��decimal 2;bm}% 63�24natbib} %\nofu�6�I���{To$+ ear,� � A!��)u�7 al MA,r(Adult Neuro�si=J�{Guill��L A. Cecchi} \affili {T.J. WatC4�IBM Research Center, Yorktown Heights, NY,1  } iHMarcelo O. Magnasco.h$he Rockefe� UniJpi�nNewf C  _} \|{\today! �abs� } Ex�AMal" i�Fc�J �ve�wM�!1 n=1a �"�1 phen}o9m�`li!�(rain. Littl�;�/n*i6aTBH�o"Olay�,�.!�r1 gdezyY��bK�NexY- � � D��#�o�Awob.&*newj�-o7ur[`�incorpo3�.$ax�!I�)'+"o)1K�!�\apZ�^2 �Y�'%3r!m"e��!ch�\a� eD�m7�c�] purt �"�ol%"ory bulb�!V^N4gyr~{aX�llie$a variet/�R?�)�7a�)Gl9w!a��Zneo-ex*� ��y�ce4&`ALTMAN, NOTTE, ARTURO}. A&~% �"��s��z&�Nq�:Lind%ti5-��a� 'a7 lifeq�ޛ expo6Xnov�nviron��s !NOVELDG�VELOB}��n��;�7�MnE;"�r3({LEOPOLDO2}E��"r��ly int��"�9ѧ6�e�A4I%E6QkiC;eY E xAŃ(�tA�ddeath �B�inh\0ory (granule)�v��s&�_ �Vorthog֖�a�As,put ensemble#tas:!e U� ��Jssu͵�n�6& � friedrich�,e0�#dx@pi[O wav�# mass3a �AQnew%~�U)Ya8��nstant, /!n'vo��ed zv�of a�<"�)Bs�<lB�X! w�"�\��Dfir! byA�er�<s-QQ1%is)��waUH �Gcc�%�!����4��a�%ces���ar�TE9 !�&�3ob��)+���D��E�"{"the�."%��vI�e hyp�$��tANE r9�%� Ա�Bfoe&!2`!\Pop�ld4B74, vagary. W%�P;�e�4le��t�e���at�f� e��f04is���#��q9�8delc�4\r1e��!v}gbas�+��ir le��aT dis�!?1U n�!-t@ e!�p"�V� �#��R�%��e��� a me`;��"]D"_6n� bo�D �;)]s{�I����&u2�'�.�S:�mto min� x-���#l�apM").R=j)�} &$1Q- �.�(a��4� a�%g%pr"� un�8E�E��" IV��.)�c�a w ]-x�-�I�+ (WTAl5˜I;> Gr�<C��S"�(GCS)&p#A �g by Fritzkj4FRITZKE}��un�2�1�#n �& �iolog,��2mD4 GCS�m�a6ឱf5�w� n',q͙DwA=t��& �Is% of alread�*[�O/ ;abour�� is "tele�"�Q�=%�)�EtA aRp >ed���s: upov%�ema1� ${Pw X}_n&A-�E*aI"4s�A:,�z�bf W}_k�gmin_i |NW}_i - ^|KII�ډ[" r-up%� u!,�?�>a� �Vd Hebb4 i@: $ \Dp� g��#�4}.�&���C ) f(�% -20|���7$f(\dot)N2a�on- de ing"� !�a�arg�; Dw�(ll�4� �9 �g�.A�i? 2��P � *\"�&. F� ,��inEG� !�5uA�� eachE$, $w_i^{n}�rf $i=!N $0$ �ʴ�6R�a;M \o0^_i{G w_i�FEu� nded�F?Z"����'�L�. B��� valu�.�IG��,��Son�@AC�L61, $p($q $)_iQ<1-��@�Es�,� �� ara��~� I t !>m$ty $p(N+1)a,l��i � bN�B� �a�immediat� 0ed:!2emjo tor ipS �0!�,�ͅs?do^��3parU� �) N/l�1rw6� o�Btau�G pass!kIis:.��.SGout�Y �?l��b e�5W�� a� a* a�0�5z��� �&�5I\ � 4 Fig 1-A,B. DiI� ent D�B�H�R�:�Y", ( draw�7aAs���U5�Q� AD$y er-spa�1�0o/�7iz��+rϘ��.F (50[$�$]�1.��8asOZ�/�/�,e"�:� c# -xempla�nAsR mounE,no�S!�dd)��::�e��3E��B���k9 . Panel A%��"� �Zmutp�>r�h b/ y�-$5��C� �.�tr MI [2L�-F��t p 64Acrete�5nel, u���1�e $H�{X},�W W})= W})-2Տ X���2ORe!�a��%mv oward�02=t,� �^h1�%p(3Q�]��A��9u�E �-2�ai��݁�^�E- B!gh;�2L. ing: a�AL�^:� �a>��Falo�yxIH� tersZѣm�7:�WA robɣfea���_&1<ZM~>B;� � . %  FIGURES �� put{�A .sty<"�2e� =0 caAL4,width=6.0in,amN =2703�ion{A: Mi�I&� ���  . B: >�?m�%a!g�E3; x-axL)r� e��s xk:3Ϸ:=;tE �8d +65->gu �^��ngNRL}2� \,x%�./ of ��#A�YromyJ1J���ce%�wi�cy' talk�t�x�k->exp �mai&�$ costly meaZism� �bB  an un!yI  ?c9�a�!%� �� �_8�b�8Io�� Z:�@�!_M T&�@E�AN. One�:� i@ �Z{"2&�G$is fairly ���Olac:�De5�g�d ity.z  9M�Mb0� � ) u&�2�oqRis �b�r�6%=�%�:�= ���mAAy�, i.e.�h�y-�r\mapping8 J.,5T ��ne�  *�DM� e go`!��^i�8"E�EL�=A�a� ">�iHDhio�O$ �Wby��i>u�sb�\&��=~[cha�Cer�A Y�*wg�?E�e;aM_��b�^&gig�� fluence ��OB=��z is:ʙ|&f#,= \alpha A_i*?X}:�i )�� beta��.Kj6K)h(d_��)VB $A_i= l�"+  X}:7^2/2\J�^2} / �cal{N+I�t$Tt =\�tj6V :Vj6V$,U!f��Z�`�!A�y3$ ��(th&Y�Sb�)�$i3$jJ�>pa�e�hS �noton��l��S"1"a�.S�1�Dfpti��i�r Q#�"s�UdDre"� "�:J�EJ�3cTder*&{'iMC�a�MoF�{ E> ds $E2 5�Au{i+1}+# -1}-2.iյI�%e�=t �# Ny��t �r�<��t7r�3}e�-)AEg� , $E =�e I��tn  E}i>}_nY�ai6RiFA�.tW})u>z.-D�!us�02!Z�>� !3travel7 sales�,�lem�# ��"&I!��!A���s.)� S>% %�a�ny 2�"��"� neT���trapp �loD"%�������@��lex�s � sawHC illu.&�is*�%�>� �nd� �"Las_ aS� "Ka�(ri6�a�FI$ "�� rn��wo .�� E� 4y_i = 50\sin(x�i /35�� pi/2��50k�it+ *�@o闥DYSDM}i�>m�n)����? on�E�j�LKd 1\%$!5�0ia�s (�l 2Yf�_ q� ���UNad <Q�TF=*<��s �CEUal ��% ApB���&@:ai�s:�D!�EPut�;A�? io�or ``�k ss''�$� �os�-<^�!�{I p�(tO� [�?j6iu��j)^2 �J ]^{1�O- \muR(t/��Xͅ\mO��D�"HJ�>n�1*!�-��ne"-�$s_j|_{new}�gW!�=r�A%;thres#.I%Zis ``-�d''�t^w�[eT2Bz&�f&� "�� S_T *�$)@t}$ [2U]�K6~� oR��� ]� C3�LA{� � ov� !$}� a lPb&=&�win semiWo. .rF� ivid�&g!�` zV��Pv�"dra� �our to$ ampl:y��xgto�ul%��iHni�Mim�bAAe�)�!%�)2p��BD- AHۭ�M+�h,.T`";�"dEi�SmMšd�"� =P(oK -law�&%8 deca%�6a �M�F�[�"�li  s�Z*�g69�dK+iu%� -'c� %� >{',�K! *z. �Js�P,o(Auna$K"�� at sugges" at AN may a��A12��+hby�?c�s�~HFWa�u#of!�N&�nd Ss �ry2.  ed � .)���k2� ���A�x.2d��j2�(A�F��G#O !R��}Ka�CnR ��"Sb�H�V�C��r� _��aT$songbrids �'.'�X�+�ifkI�*"5+^#� 6��v"�'.�.v n ad6zve� mapQ�Den*,G*, (DG)�a�$Hippocampu-&� jspe~+t�}gpie�9� �Ir";DG�YA��Je"ۉsup&V a 0�����eo��19�땬-3GORDON*�+3F.�%|e&", i�.","",}�aty�A��Eb�4l�H$style{plai&.1>k3{4} % "':1]9-} Alt� J., G.D. �F5),�9Post-naQ1origi� microA�o l��ratI�},R="(207, 953-6..�2]{�-} Gold�(S.A. \& F N�bohm F�83��2@*��uc!� , mi"� ����a vI-oQ�cle�N8P �, fema�ra�)ec},Dc.�lX�ad. Sci.�2L, 80(8), 2390�23942�3]qXt Alvarez-Buylla A., Kirn J.R.,B�90�Birtha+*�')t�-avO%��h��� %o per�-oiY� },�e6 249(497!�1444-1446�4!�V�.4} Kempermann G�uhn H. Gage F.H%�97� M�Uhq�a ip2]d�4m�liF�-ed.(UX0 386, 493-4952w5 �OB} Rochi,t C., Gheusi�Vin�$J-DEu(Lledo P-M. �;2 � E�Odor Eq�I�q�@e N"�NewbornM�!����1OF1 BF1Im�Jes _Memory}LF Bsci. 22(!H 2679-26892�6]"�-(2} CarletonEaPeb�(nu L.T., La��d ArB� \& :uuBK�� !��)%�:_/)��@507-5182�7]:0 �6 G.a.�,F�, N6 M.O. !�1-� Unsup� Q�ş��A`�K ofm�eW�.7%�}3.�11(A175-82ʽQ8]*30 F>0 R.W%~u�  GI`��H�� of oAp"��ss�Zte~|8��!�of mit0" .� 91, 889-8:�9YE1} .AF�2# M!�!g D�1ofI�-�;>�Gr�1I�ns: R 7of i"io�yJ.y@22(14), 6106-6113!}��0]"Z,!zq, B��94).,���,!*� O (self-organi����� u.P�_J_A�eur� tw. 7(9),�F1-14606�1]( Linsker, R�*��P��A�� �%b:�W.9Y"<RI��d.�a��\Annu. CA)��d( 13, 257-816�2]) Durbin�,\& Mitchinso��%e�A&��!��[me=Q.~T2?!HAMDe 343(6259), 644-76�3]~ She�'$d G.M., Ed �8��  8�0.JA�� �7 }, Oxford*�: P�y�!>O F�<% % * En ��;, apssamp.tex  V��!� %��9Dc;g��A� Shan�:� Ee�ge�:sc9�9$2004/8/4 C6�du�$gro_prlpdf%as���19Vera_Pn+ _sub,�_��a9sh 92.28b9 Subm�p,to PRL Septe�"2a#0046D9�%2�#� \d.?�[tw�i umn,��?.�>x} %�pdf!�x� .jpg  ��&?�&?wsym} .�am�??%renew"�Sv!fv�:{0.6} :"dbltop.$4B$�v$,dblfloatpage>*0sloppy % avoihgcee��-�'erbad�`d �E�lLaTeX p 41 \topmargin= -0.1 �zinF&@ \hy�>e�,{dis-tri-bu-!b.Hs oli-go-nu-cleo-t7W(Arab-i-dop->%8 Meth-a-no-co-c�[pjann-a-schii Tre-po-nema pall;$um Vib-rio�0Hl-e-rae Haem-o-phi-8slinfl-uen-zae Chla-my-dia murE@a-rum du-pli-cat-� n�^-mo-s�.! Iha-Bac� halodura�%�b%.6 EmeEru/ a mel Y }1`'.>! Isub)$�subtili! �#.. Ausp Auch�� sp. APS�b$. ?aph:?aphidi�o( �'.>!M� Cele J,Caenorhabdit.leg=[c(.� %�1 tode � CjejMmpylobE> jejun!��c&. Bcr�u@cre6�e D(.6 Hvi-�CHvhu oide!� I).6 IlimChloroba �`-j �%.. Dmq�!my�idarum!� E&.�> Fac1lostri�� tobu���kc-.�2$ P�.P perfU(.�c*�..!�pn�hl 㡧mo���'.:! �tr��IO,ho� !�)-'.:! IgluM�oryneI�!� glutyf%| N,.6 M Drad MDeinoco�Bradiopui Jd).: mqD���M ophi��anoga�0!Kdef\d)��.! �Eco��E Tiluke".�H <K12 �  K125�!H76 0157:H7}MBFhe�� Flavm�!bheCgnuA��f*.2 � Fnuc jFusHn��d1f).2 H Gmax HGlycin���g.�-�( % Soybean CHa��Ha���sp���h$��=q�(Herpetosiph�!��tia  D+. 6 Linf �r E(uw (zaaT I(�� HpyM%Helici ����h%.M�Hsa-�Homo sap �. ~vQ�6OvolcaniA� F).2 HLlaM"L�6m�l"� Dl%.Cmon)QL$tr� onocytQdl(. >" � Mlot KMesorhiz�ot�m%.  @f� � |�mus ferv� %\m).. Gja � G-� a� �m*.6 Jth�� JI'A��,moauto{7h�f R �L& eJ>QY Mmus-Hus muscu'ޭLm� % House m �ge1 ycoplasma��ei��m'.6 GpJG pene���&�E� �2 )'': G .GuA�E� E%.  Cl��C9� lepr�Am&. Bt� 6B tuberculo8 �, 2! NNm1_ Neis��� � itid�ZIIN��2! JeiM9 JѕNosm� oc���n��% PCC 7120 _ Paby �PyrqVabyssaR Lp$.BerCbaA�m ��E�, \def\paero{�{\it P. aerophilum}} \def\Paeru{ #$seudomonas,$uginosa}} )p)L J fur{ IDyrococcus furiosusr G&.2FhoFF$horikoshii�'.6 %h Pfal �Dlasmodium falcipar%'p'.2Glas>G}} �mucHasteurella multocid99'.2 FRn�8Rattus norvegic%5�r#.6% rat Hcon �! JSaQQStaphylQU aure9s'. Cent �Salmon%�enteric5�s%..MSceM�tSaccharomyces cerevisiae}} % N%�sA.66$% c./yeastlpom �chizos2r pombm V+. �me-�SinorHbA�melilotaD C).2�H:Hfle �hig%�flexner� �#..�onBewa)� oneidensi�] F'. 2HpHtreptQQpneumA�=^*.6Kym.:Kyogene�(. -cco� �M[ oelicolor��s)a� Iav I� J$avermitili�+a0. Ku�$Sulfolobusa�fatar.�s)e�.! Ktok-�Ktokoda�Qs%..Dub D�F$um tuberos��s#.24% white potato�yp P�typhimura'LT25v,..$a�Er�` CyUjynechQ�sp.�#.  ; Taci �Thermop��a acid��ft+.>!-iTma�� N,toga maritim�,t%.. �p�u�T %�bS u� �PR[ :&�  �� �j� � &�� � Ta�HT�fcum a�HvUt"tst ( %bread whe�T AmayIqZe�ysMbaa1 %corn:�,% common namN�)�_� w2� $f { fission_%R # � #l �Bl huma ^.� �� Z>�%� "� (.B %a: 2[ � 2- o�#}O r:� ic v}� �� t� �1 :M !wor�N.O 6�6�%0�4 a�O:G ad��onal abb#ationb� ecol��E� l� F mjan M. jan � cmur C��r 6a T.pal}�4 End of genomeR� ` newp ,par\noindent�Lnewsec#1{{\sn\bf{#1}skipali� v 0 12pt plus 1pChaf2)6J(q2"32" �hES� slas!�\h# -5� a' * a:mAcmed2Rb!bigb!s!smallf#ig!Cigmxolo�tid� �!� s�m{ 5m�.m/m0km2 $k$- .E�s{\dist{{ ribuA�"� ^] H B6 7 8(lroot{{L_{rYLtd{{stds stds�� ��0�0.9%A�si!�$ma_S$� 0sigl{LIE 2i�e!- $\et6FetEC -!r��foc{{�t by si�@| priat��u�a quant� we call �$M.�}���kff��3assocYM $these iss��+,surmounted. e?SIapplii5D"ac�"zex ist\�l\ (FD)� , ore���a $k$ ��lettersA�%K%�-� . We pre�"��)!rel%� betwA�the��� !ve�r�xwidth�an FD, �� 'o��at�%nishes$ intuitD understanEr!nam��in�ʹ �sh1�a:p�of�irJ�, �E��".  can��re-ed bys��M� .��)!R sec{�� $}. Consid�5 �4Jl�ies, $\FF=\{f_i|\sum_{i=1}^{\tau}f_i=L\}\equiv %(tau,L\}$, ��$$� ��events,"$re $f_i/L$�!% aSay!T- $i$a` Theum�E�u�taintFG,��e %�"� , %H(\FF) = -�0\nolimits_i (�) \ln  $6/V&@$. %\label{e:Sh_ ��'2� �u�at�sV  maximum�� $H_{k$=$\ln)S when �*!F$e��{!N mean&9 $efC tau^{-1}L!Y In $H$,5\was>XO fide�k of messagaVsE�y~trans �OhroughA�mbi��c���+ ��i�&es7ia�A�2�-�tself.!5reA3a�Se� no�*�t*?Oa�W� reas��w�, a de ']E, h ���% tify%1�, BGDIF\m )� - U/ L%r >ef_iYa)�) U<&k }�!��}�$ed�&'�>�S 72}, aU e 0�8r� � %b. "���%�e�) io $ �/Q�( redundancy%�8[#r!�t�{@in ``ordinary %E sh,!�A`���statist� 4structure over"� � 0 %about eight�c(it� Ep ly 50\%'' ��@48}�We will�T2c %� %� +$be far les"an`�az� �%Some> a+����\$D$.�� s %c�� ɢ0. An extremehA�e� %i��!qui�un<�qone�2lto%��others% T�=�� $ va�&d1�$ acquirU t �� %� ��,kit would!0b��~sai;� �  %min��}s!�n1atP �=6� Such2 s doEZ��!�&o Supp� !���A�=$$\{:8|m=1,2,\cdots\}�*��2�subse�� 8_m� tau_m,L_m�� each� A�!1 own C inct ty2�_m�'totalW �]��s $L_m)�V� _m$=$/ �Jwh�$�d_m =$ I  Z=$���U�?� �Adi�_m)Ksum'_i�� /L_m>�%��!k sum �s ��ric�!oE�' 1 v)gŝW+ a� carr� b��FF$A6b w�ed\*a� U*�:i s: \� R�����(_m (L_m/L) ��_m) %={0{m,i}}' \frac }{L}J  =��67J�_����inf��deq %)�a��ac� $ �$�a���E5 )��"" FK �\a,6�}.!w view�>ingle����&< �1 (ar text wri)P!w four&�l�$s, A, C, G�5T�3 a66ki�of�$k�� Empi!/llyq�y invariabl��th�  few � Kbec� F S-le0��anI� � study, %a�I��o � )&o/9� *! A'� d Tre cl�� o % ����z>C6nd G'!For!6� it suesa6� RBofD s v )� { , $p�V; comb��*� (�(. From now!0 �)profile} nK �]��)4$p��lu-�  $L$>@���K&�A�o&�s�$benchmarks� .�% A>:��- ��a&� s sai"o � �}�y@ g. !�6oV ��w�� note!�� k$D ɹ�q|�� =4^kj _k!���f_iſu�� $i^{th}$X lappA� $k$-i��O �\@ Hao00< �*��A�ob� �sliMa %windA f �ac8�),�  at a�O� c= g2I���ť �!�0 0��� %�=VY�w�i��$=$4^k�=!Sa� 1v�c*{-k} �W Giveniw�  n� M-K}�� re $n_f$,h� �s\�r!�w� �$5 is gr��functi�wof . �kic+ we also� �a � . %NA���� �/ce![e%�not keeEJ.kn!&Uy9�AA�:o�<�!IAӁ�we��� sum rules \�i 1�_f != ;:"a= f '%� %To-fy ��languag� �\f$ �1<�Ks!�a��Zo�ofen+1�A9FFk� l �H@!(}, $m$=1 toa;S E� m$ .e J[Q%wA $m$ D�- W� *��doe~��e �ism^i��V�:is� E�beiQ�� $�f}|6�� � :.3(pZ a[h{f} 2^k p^m (1-p)^{k-m}$. �,fg{f:Cace_5}m�$GenBank} ��^5� �a�W=0.691 �, \D � its2�n��  f��A�.�, (sharp peakR  gray (Freen)� .�funon��~� pe� (a six�n� �ofuge), � eQA�5\}!aYcorrespo�� \das�dot} �curves) ly�X�entire ��ic9 (black 8)�e!wn���oI` .�� ."@pfigure}[ht!] \vspace{-0.4cm}e�er} \�$egraphics[P =3.0in,heT=2.3in] %{/Users/hclee SA9�Ran30702M_RRC303005_05l_tmp6} {shan_arX_fig1}s��8�cap�A�se P( =8pt� ]�4scriptsize\sf{�85--�m1iz\cace\-q) (6�"7)���ofj6�E��!�)ormaliz�o8 a 2 Mb.P � L-�9�i6 e�eakA;]�A��ׁ� 0��4iU)I�Aj5]�umf off �!10,500�jOG�3�%E�:ger*ca (a&�� �only) 5" fl`De��q*��smo'de� veragH�\21.-&Y#3E#�M��.t��� ��i0�� _��(k,m)� <����5K��! vely�5 :!]�binom� coe- ient. A%�feq�a�� �?d %�$lSw��1�&SX1m$: �k��}'P � /H �}Q��# �es 0.5���te} o�y�/k:D�k^&�*8#Ihnt�7�replac=�$$\to$ 1-$p��"vRe�veQml�}.5w97},A}exp�� ar- �$A3� log9hm!�� �0� moda� I series %� a �um%�$D%�g! � dard�e@ %� 0Delta�� �!z G-$$\$$ $/�6r f}$�� Z�} (RSW�AL� In�:s,i % in��is kn� n]� %of va�5 [)9�E��Le RSWA�0R b� Lee_unpub��geq#=8_{n=2} {(-1)^n\�[,n(n+1)} \lef�Dx e-i + }\r��A \r4 l'{)k^2 42 1t^2}�+ �+O} f�+^3 M�,\qquad ({\rmcEJ}\ 2.�_�_%��� ��~JE��$| iq) � �2/2AU�EQ" �7 T� %�!�is @ful�aWast tw�8��First,�A[s�a heur����(wh�e.8  nd !(�)p (un)V)y���conne+�����j�a� is narrow^littl�&<b�!A�k%X"K� y� Con�$ , soF$a> / $<$1  broaMc�  %�!�he�>_ a!k�con�B �& �ly_t !aaz.� `ly�.Dw7&"� !Vmore lik�%�  biologim&��!�t� C2U^ an"`* gxSmith95,Karlin96,Helden98,BusseZ" r00})� ob%^!�K true, nam���.9a\� 5lin)�!F Seco��US2�M�� ccur�"esJ?�(�O.� j��km$ (A� $�� .p(. Provided�@�i:ch6� one,T[isg?�5,to a Poisson�%�!�.\ )}Xie02,4*03}E�% ��_{ran}^2&�- $b_k�K�� M�V-"�� H&��km��b_k/2�� _m = � /2z�j *� � �om.�&� !'a� ul�aV�  )��ly`� �#&O'p� *�k.��/2 L ��R�(\�}6 ���5 atora�factor !u$7-1-� $�ae ��;�emi-e � $1-1/2-1�4'�/�O%Am@ fu�_ �:��A�adeA~D(Iximat�3coiI���el>< (as >J)E[i"�is fix�% T�!�)��� di4�$ s $13#e in� ��;��;�w[>� -sy�,S:~squ�%���aq|�c&� I$��r}��'R_ 5*�seb at) ��%��+ t��ul�n )t�1B4>� ~�t�#�9i}\)*}��&!�#,#%н%�in" t��# 2� ��s\e� �9�of o:H7\[GI�I�.}�bT2�dtabula {c  } &\>44column{3}{c}{\�&�4{\phantom{HHH}m� l 2 }}& �J�.^}}�.k$&%:&%-&� 4^k/2L$ H$&$D$&$\� � \\ \h�� 2 & 4.0000& 5.12E-7& 1.06E-6& 3.98639E-2 \\ 3 & 6 96.7 06.2 5.953Z7194.4 94 & 8 903.03E-5& 2.92 (7.908& 9.1698.65E-95  9999�28E-4 5 9.8546E-142E-1r6 & 11:�2305.1 B 1.79�079 2.11 9793.998 !3 0E 13.7273 990 9895.991�560 8.48 15.65!]4993.8{�997.9 �)2% 17.� 4.5495.2�10:!8� 3Z& 19.34!�58:7.7 �IQ� :y�<z�&�ShBa5a�a\m�}d& 2�is 5.539 longe��"$pd496"*� fm �"� �2}�co�0e�SI.� B�(c9 (Jh)ƁX�i,�=2�10,��u�>` � %ltb.��y c��2/"1 (� i}) �b\&Ѻ�1x�B(��s 2�5)�i�/ery c�- "!�$��, 2$k� yz�.631jd u�,V� � 3�� xcelE aUmP4�wjexked b=4).�.�r>est�'s8 =�is a min&Ee sigF2bu�"� hugFbackgx v}) �tiV/Jn isolE , clean� ts a05�M%�!z.P: �#ic:�252*VJ�&g�ll%�!, !T )%r1$m0�2"�2��5�:� is verif0$(l�Iz!�% feaj(s�be� w�&be� eric�SI3 ��a�l.e4we� exam+!��8�-ffe�=(=�a�SI�-�$p0�u���F�$d] . C�-� &(J�&�)�%�r!>�S�!`f*}. �X(_m�%C $spread wid�irG play|+ ominJro� de3"i�e of��a. If!iign�^}w0v individ)�!a 2�:(w!�t9a"�;$D^n>(k,�8 0.5[(2^k(p^2 +� 2))^k -1]� ��%\�2 nd r= � (Z5,�)�A88$A\a�4Iact҅���75� 0.4856�2r]in��.��#YW"s�%ongVnA�,aHi&@�$L$, dis�aBthE&= ,��r�A�usr �}� �SI��&\ "z1 %I� were,!�p* %fac&� sens�Mq( ult:*�t6�a�ing�*st%8i�t SIs�! n %\�<\ h>6)�7haE L�sam�(�+ %�)>. mo�rFeBl.^�aVA�rly q-z#ob�6"�&)F1?%�D:�9 ness��5d1�= 1\}}A� alo8,�^7t"Y,� at * 5e!b Mgen\*L 683AI�n=0.0686 �mi%�qP!670��� b\Hinf2_18b_(281 (0.0278a Si�"Q5m�sayA��<�.!�i�!I or _/�5�yet-0 trivi�(qj they�vey� x.}2�qVt���u�Dalone. B"[h!] *2 3��& k6_m�CJ&*x4e%� ��}&� "DX6�6.�!three| $ir-[�ek"C : R } $mf� E (kb) &Db_6/("�)$$D gen}*�26}{l}{1V 3pt}�\oF)=��6,�7= 2.2{}0[ 48 30.� �1E-� 8F � 4.3a \\ 1 �506 19  9.69E +1A 6.88�2 62 649�  9.31 69x l8 \\ 3 641s 6 l 8.96 68s61.3d \\ 4 56� 54s 8.93580 1 55 586j22K[ *�75" \\ 6 56Z 39.j 7.94 * 7��O4) X~�Cmu+=0.597-�1.07 M1� & 68%�4.� 7.05)�41!1"�)E1039.�4� 4.47 ;1.Y�%� 15* 14�3%q13 1.15� 23929AP2.0� ' � 1% 3[ 331J '� 0�� 52�2E�9.2M{1�1.2�)�78�50%�6.1-�7.3AJ5 a��ZZq]293-�9.0�m]& �=E 5.7 5.44)h9 1"e_&�;21!  82.�a�$2.2-�]�% 51eY 49!�A�Q�1.0{ 4.21)�R 125 A 1,60 3EA�3.7 {5�ef�302 2,9EX 1.u31.6!^)y�)�73%�88 86.6�-)� �� !�17,62� 1,12A_ 2.75E -2�88 8���:�&�25Ō$�&���>}. � � ՜�x� D_������]'�;{)\�6�� ɚ�q�&i>�,Le�� P \�\�s&�;C�� �g�fi� Oxagain&�"j5� well#x�?<� e^� @d� m�`@b��.  !es� "<* exhibi1Fr��^+ 6�N SI,� �Cac"�-o.3 �,� G%�)��  :6�%thF�� "�.2avevA!dR b : $RM!%F` by��/2 2%; $>>$ j7�*� � ��/�%�!x{t}�anVC�� 2Ge&� &  (M� � e !�%� &�&)�/(� � � R�(\"��ETi}&� ,&5.52&1348&3��44&1.01&0.143\\ 3PWro.4 514&� &542&8.9�&0.99542745Ti 497V$7&261&1.83� 1.053083.a3 293&�&2203q= 43444խ]֏M��(I�%.���I��)j�+2.�+5b�+ DNA/</dat/Q�6�+2v�V��+twelve_i�s�76�+S G�j\��$kn8($\Diamond$), 3tri�%�%4 (*), 5. down6 (+), 7.8�2 9 ($W righXaK10)Box'�� ��D organisms: E cun,�l un\ �Chromos*0I};��$ 0.198 Mb,�33); CM,��; MG, \m�(�40.5804��/84 SC, �W (�W , $IV$; 1V,, 0.621); MJSja��K(0.686); PA,�G ero;�ol�,olK12\ (4.64 / 492); SA,�; CE,�#m (vX,i� Chr.� 15.1 ;64�XDM, fly (\fly, $X$; 21.%�74); MM,�\ (�QmI) 98.9 N56�HSzIman ('Z�R 28 M� 582)��3��in &�GA�410 (open circl��F&L*�/X� 100TA�b EU2�^lidVUsT. },Pyv&��. A new y�_manifin�"����:s`E� ��hly��0�7�:���N� �$ir���yIndeed,&(!&ms up toah�6 Nw��H��%vab+ l�'I��u��va*s��%�1�i����sA�;�5o�Q �%AixW"�b' e�b ic cu�s�&X3r plot�symbol�- e->U , to%"bottom,s E[v(\ �2�9���)��\�?Q 2�XA an ��!) c��a9�"ll-�.�^ �>)�& tw��7��a'!�ap9�yin ;b\!10�are5%�@WM<"� E@ e8�u.���_1AqyMo.�8Aq�JRi��(4ede�%�bg�=�e�2� !�ɖ100�P � )io%A�5yE�" � si�u"�M]��p~%!sRLal�s,�*��#Oa�e�*� �ozonlA�V bK/0 0.01%0.9AR(� techdQl 7FLtoomYy� debei&ut which"Oexpla  else�,EO���l�Tst2�2.))�aI2Ar,�eanc5��,lya fo'A/ wo. g0:� uu - ɖ\ ($I$)� 22�� -e!z1,�%� C1a)�s{PstKJe\ $I$HC!^I,R4n8@e�32��KEA; "�+.> !q $k$-�a'Y9��. � ���x� ex6?�.is>0,# uni}(k)�n �? h�T�L_r$,�9" �0a0 t[1X}dB�@Q�.�E� �$-3L_r�"=14^kO* /2R_%�0!T�^ic$*e�fH��s�Cr6bym�"_)"&/�&( �)x4 alpha k+C"�/ $ $= $\pm$�$, $C$=3.80 50Y. ^U��``Redu�'%3 �''8� log_�"th��t@ L_eff = a k + B a~*34, B~ 0 +- 0.20!.!! re4!�cNs�. w/n "0V" paper !�+surpria"W!a � � $k$E�`R�pidly � $k$:F!�"{,340 b, 15 kb��1� 7��2, 6, 0,��"�5| Now, ifYx2��� �rV\�"aUite &�6e��n,S�-k$$<<$E��aBh�OoduGq!_���3�GI�2�>O%suu��=obser�Vu��>ofeQn��r �"�=e$FTyNIz�7RT&�c!�th, a � bk�����1�$I -*a%� -%�in�/�9segd$al dupS2!�F major 1!�.�.,l4 etal�  Work��loS !+imN����%o{Kbe!��KլAE/3wSis �#A�up ,byf:�[@92-2112-M-008-040�$ 93-2311-B 06[$�"GYmP4 Council (ROC)�aHCL�&_ 10ptO5 +$thebibliog<y}{99ibitem{$no�K C.E.�&%RB4Sys. T�� . J.5Lf 27}, 379; 623 (194%; -423-65�' \k"bM L.L. , ``�In&�2Theor�'!Li��[Z<}'', (Columbia*WZP Press, New York, 197)��U} P.  %� R. Backofa���ZuuMon�a olec  B 3y -{LInti�ion�L (John Wiley \& SonsHZ0).�&)V } %F�# ng B�;�SCxU� Nonc ZR�Ua�n E�p� m� Method�l-Galvá�(tal, %PedroJ Ivo �V, $4Carpena, José�hOl�ZL, Ramón Román-Roldc�DH. Eugene Stanley e\,. Rev. Lett.IQ085}, 1342 (20!) %-1345 =7 �02} %A*�Wl �? #s�(A?Jensen-M�*� .��b,?#B�F@:ZJ�H1'�E{7^6! 04190 �2) �Sm� Azad�2��yicETR i.�((: Power law�E>�#$Rajeev K. d1�F�(Ramakrishna swamy�^J. Subbo %=�.�51909%�2) .�$Lin91} %``*$!measu[O�#d o&^XI�y'') J.H. L(IEEE Trans.�R& ory,Ij(37} 145-151��91#��G�F�W�  *�h %aYe!�/ �B���B��Hao, H.CA�hS.Y. Z�_4, Chaos, Solit7 L vs �11}, 82I ,0). %825-836�� All �.�re <loa� f75 3;�"�p http://www.ncbi.nlm.nih.gov/ ]s/��.html�e%es6H... /-/�:$tic/euk\_g=ɸQ�85} %din�q�L %S. m C. Burge,�vn�^GenetD[eE%828Ŝ95�x%eLe"q<%CHRa�a�AAProc.�.�v.�� inf.��E�$4).% 20-30=��8} %USS H7 H.O. g,��� 269}, 538E��� �96 Q 5,ajMr�}%XM. Campbell, Nucl. Acida. �b24}, 426)6:�~9 } J.�& , B. A_��J!@llado-Vides, %Exta%��regul�6�[U�}upstream#I of ��s�� %aB�i.�]koY "x;i�Mol%�l�J28i37%P(8).%827-842=�2e: H.JAPx:, ��Li�(E.D. SiggiaA Buil�< A Di,dO��: Ia ific�of�umpp �1& %S%(by��?al ��%��� NAS}I*9u 10096E��-1010.�Xi�! Visu�D�K-tupl(7s"�lX proc�wB� �V./*�. s H.M. Xi���zJ31�3��31-2�� } ��MUad l%oge* &�`�;t ''. L�rCy�ݎ*x9e<01810� -4]7�9�&� C.:aG� e�ar7 ���� 4) (de�*� �Qa�d arti�a��:�  docu } �@\,style[12pt]{ L} \C�G3cm w.=17(opmargin -2odd{X0.�a{Equilibo}�Z�9HfipopA�.`of� rs�(�fPJacek Mi\c{e}kisz \\ 2�eApr_ Math?` s \\�Mec ! Warsaw &^f Ku�anach�G02-097 /, Poland� page�$ing{arabic@ 1W.�H 20pt*�b \ir)�Abs�!ign��!�m�B�, @aB7 ifE&!5*�&�?.Iof ��, �vL�cut�X%8ll�@e@)%. On�funda�alA��f�u)C%�y�f�E.�.A��U>A�6"a�*f �!�4mayI�9:J�3 � "$6( E(Se�L�(a risk--one �he,.�,�} �`�KFF�possible �"�R �%)6l i�4<a Er{�G D�) st a w��(6 \)��Gp.m. I�p���!���FseA���@. 5�  me7toA�sla�7�alM�����U �U�3�R.* ��)"� ��2cdi-an B;�Yt �Robso,Vega-Redondo�E rvr}1�ir�d,�Wam��Kiod�D2k�A�"�ly�Bu� (�3^`�9�& H-�y �!-8rOor� �[���K 8 ri, Mailadnd!� kmr}9 E���>A�-� s en[�i�,mea.�E0T�yC%9$t$!�big6nt�:Dt*QrA�1�*�.�!:A�7�+}sh Fi !@$t+1$��},QaQy"y!jf n�a� �eM�, �� ��I mistaks To&�CA�6K of.�1o, Fosoo!�Young-�foya}��U�aavcep%�V& A�إ�ьTF1UofbT firs�"in�XE`s)!� {\emvw6� �]2�� �.cM�sWo1  %�%.5i�zer�cis?ItE5o�NL !Y�OwK� >d��a}&�L �B� 2 � abovJsribed5�UM�&� %�� l%  @ �HG sR�  r.3l@Q A�>3 %��Q �qEDi�Q =0"� P &t A>� i�qH2� lg"U "T��Jn$.� wh>X��.# �|)5�=ies: $A�1B$. At[\ry�jr�?mo 9im�!t�e...,$!$ �1do�pai{=(we� um!�at �s\n)�H�M�J9�9��X%���)n� &Xt%rix: �  hs Y2�  A mm} B]% 12#2a2b UxR W6G>CB64c6d uNr! K`j$� y, $i,j =�cB2#a�= %q�)��(row)%5er =)lay 3� $�l0 s4 d�2>N6j�-W6�` -��/�s nd�k1�AVh� umn 54ɫ�1 ma!���]kVU$;d!�o2�_edYk AvK 2�z ��6 um}�!|ach �moabxw� :Y ,d�W If $a>cmmd>b�!n $(A,A]Wnd $(B,B A.wo:�a��G+b� Ypi_{i}(%), i=A,�� �J�� _!(j� 6�Z !�6�2m�yn�  Let $p%� dewOB+,�* ble W+1��1YWf-� ings, i.e<�#�f��c�,N� &p- ��B:;.� �t$.d �p�9%�$.A�5�re2�8A 1, E�i�s�[i�� ��asK�l%�쁣} E AM ,%e )=\f�laI"- +b}{�},�I a+AYB} 76Lc=+d(n-@ U}{  },$$�u-(0<&�hnyI�p.�d, �9� l ���rt�p��a  Ev~(b��]au�]rzdop�J9T@A�r�1)��V�r qy>>��a 6����� s�,N�� steaop�RqO� 5=���i�Q< 5"C�epsilo!wLeas�.se�WE�T%�w_ � ����r�)*� k�<&>.��u somey�%; step�1&IOojjan irr(,�Markov�in)�$n+1$��KI�f]Muniquɀ2�(a.� mas�n5) �)w&��b!N mu^{1S}_{n}.$ 40!? $z \��_$ByB. (z)$� Al"�!m��t5�!� $z +lsPru�9Y'�2� :�byr�."y [ >�D�_X}:��&�*Kp $ \lim_5" \�3a�\ 0}\mu!3=B(z)>0.$>��Z�2�WeeYew�1�n�9�A6~zA�&��!�Y�i�s�I��E�a"�t�F"C\��!�!�.�P^�s (� freiwen1, 2,shub}�"Ap��ix): �\�[ j[.�_I��] z=02 z=n�e!KMabsorbA�!e�Aft�|p9r�!>>�-f!_� Ltve�- �ԡ�st� ���S�e-Xre� no�Zre{ce cla1.�@6o���u)�K nJ`LnoughCw"��T��� need�q&"ve.^s��%GIf%�s�w,�� , fe-)coN-')��%���\  0� n i. ��Z��x�/�~�r�fly�=mr,�e "�� b��5D� we�@A�~�����(n)=1$� � !�F���%�"no5u�6&�!�!2HowA��oir!)l��5*e" -!�bym )Bqt���A�P��})�W6� Z�^�>[a(n-2)+b]/(n-1�5Euis $n< :�IcnSw� >  A��6��i��mV�Wm�qVn$!�a_.$I�&� ��� CKne� �Xw:R0Rn$~8�8*^%D)R�se�$o�#}����E��GU�T&�"�ab ,arbitrarily A�� TQ�VT ig e�=e!�'�! )�  � �p�=]Za! \bet �  exist �( 0, ()$%0$n_{1} < n_{2 3}(10) 4$�e� �$n %1}!ɬ}{a-cgt�$N� =0) > 1- �lta,$ Q� Y.�"6 VP nVQ >�2�a� RI�%(:R$vW:j S�e�e!�"�X2��!B���dAaN)���� a. O[�urs� o�y�6> , $n>%���F��js.% �-M�W��sj.�ll�,���k�0V� � In�tudre=n\ ݡ&� ��� 8g���f~relevK[paramG[& ��!ƅz���(d{4�r�f���Xec�/+ s. Z~. �����͍�s�Y��inv�gr<;�~nowak1,2H(�>4N:*�>e\"�*3#�!���xrU�6.es d�fs�Freidl�nd Wentz`: ��&��j45lso #�. L (6 ,P)$�a~���� ��3*�����by $P*� : | �C*�[0,1]A�jT.=�2�O�y ed �. �D$X�� � $, lw� n X-%�b�dirf'g�;��st*��x �$$Y \neq X$x��pat�$X-<"� utcomA<edg�uM $X! D& T(X)�C��oll ��&� ~/"` q=�(X)=\�|{d%S8} \prod_{(Y,Y')d}.� >�*�@�?is+ (v��� � f $d�&}ĥBX2��` {:�=Mum_{Y�I[}2$Y�r�N9 ��ll6.$"I as�!no-D��,&"Z��*@atg !���>�,;Q,$YA�n�+rU AKAY�u�+.VI-BTesI��WE�:>E�gse�&\ E�>�/� �N� .���7-�:�%68���x$2O(Z,W)a%� Z, W] ��%- 5�^{m�&M��[� ��"invol@o p�:$ZW$m)i� -;� +|gP m�5Fd, $m_{XY�neei:to�2�z!4)�A�$Y�Ob]YX]>�Y Ņc$q�Y^0(YX)} h $q(YZ`��.Z (XY)0~ ���f� < a� �_ YjVA� more�v��.�Y)=1.$��� �s>6�A&E:11{W.�9rth�[4S. N. Durlauf,�D. A. Lalred� )E2yHm@AN��<�d II}. (Addison-Wesley, Rea39 , MA�A 97).*~B�1{aZ*�1on �< unifr.ch/�$&D�1{Co �jMaT��Qu ut�1�70�8on xxx.lanl.gov&bf?0wei}{J. WeibuU;% �&�?G�b� y} (MIT�9s,�;bridge�52�hof\Hofbau�ndv?Sigmu�tVl�P"V7 D�.S7(Cas*7 C%82��2�b�2�D��,Y<em Bul{3AMS�:40}�8(, 479-519.}I'1_^{A.�-�.F.2�., E�&� u*R5 >��s��#.aingK?em��%R. �%Q1A+;�\i>��*;  S"�%inefs} n_8A�.^K %�2t Aa�w , On� M/perturb|s���"�1�A em R�an�hh�Brveys}g?5%'7!' 1-55.N �2z�e�Cv P>�m�al�@g�} (Sp�#$er Verlag,2�F842�D {B�G��$t, A flow- �Gula��w 2�o/K.� me�=~C�Gsg8(. Cybernet.-)-(,5), 565-566..�& EVM&&<,.-*�!V�!-�"cQ&. �J�.E�.M�232��4A�3->����F�}���M sp*�qJ. Stat.��|117|99-110.LwG���2~zt:f���!?ica A �343�175-184�v�J�&�@"an�=� �2����J- A:m_W?�.891-99066�{L. S�s{;eQ2��s!�y��6�n������n A. N�, Sasaki,�DTaylo�`,D. FudenbergQNao �42�l20Ew646-652�p2}{C.X6TA� |\M� � 2 !}���F�m"��.-��1�66]%621-1644e��>� 3'd*�@�&�@; [�@diopart} \usepackage{epsfigA��'H }�raft \�@#K�}enع7red%}l�: IN�a�,���ged�Gm�K��e�@`Elshad Allahyarov \dag \dS\ Gerh�Gompper\!�4 Hartmut L\"ow�,3 "}`[1]{To�1�r�� c"��dd�Led�9 �0@thphy.uni-du�=ldorf.de� \ 2{�&hA,\, f\"{u}r\,�$etische \,�Dk II,\,Heinrich- e-"h (\"{a}t\, DIss zH,\,\mbox{D-40225}\,:! \,Ger)=�� �{%>�u�HFestk\"orperforschu� F sz�J(um J\"ulic�C�524�\,  ~ .S|e�,High Temperas,"d�� S�!c��$�-s�Rin�bulk. U��-dimen�al lat�,!��%energy2� Io�\,m�`� phas�Jor!� bund@^ca1��/A -B� 6�.}���mesocrys�>�aogWedރ�!�q�W�=conDrE � *. !5��Y|&��:��5��61.20Ja�L.70.Dd�� 10+eA�":�v*76tBL�)E���turP! ^%�eo�*��A�B f s du�=A�:�DA�ac%�<@>n vitro,O�td % polyvsas episperm��e^ d�G .9 ! ne (Spe) �4cohen1998book}E�setp�ukey�Tin main�AX@yulaIV% �@ te cbloomC�1997,s��� n}, �rGe ��Aneluiv.� � hR%re �$nt for no2 II s cason2003��fD��B%e#"� ֮e �vb8A�\��g�M!�rap�> UnSC� j���upH aMe+m�=��m)�>'\,��6I}a�%&i�8$��[%���a�.!Iism�*q-B8in[�"k�?re�$~ neutr2�0A�neg����zb4%�C"J*'!�o!�ups!QSp �Sp�'wi 1}. Ex'0�9�Po;%�6,�t�D�c; Rnon�r�.:eW pre`Bly� ctro+ icd 5G� �phosph�# iLdeng2000,<,braunlin1986biom:��0ra1995,raspaua9�~ad!dQ�sh�auyfac� � Ozhelix- sur=w!�tac1�ult_ ly, �2�S�c� َ� tJion �$Levine2002ڦr��rodޖ<01Co(yx Xed.��$�@dja�%j �� �"�[decade,**�da+nts���r,p�!1996,�tr�Dx1999$Nas2001�hce2,vAa .9 ,murayama�v9}  E\�Zide�%{2�  (i�4!�unbA� ng) �I�=A2� AWaYM� $c_v}$  EJ"6"o}{ !�:�); ii)ld2��r � $C_d�>?*CMmR�returns�XD ��|�#�L12�on. !�GL $c_s$; i�-��A )�valT�� =���%fra�]se�� m�l liquOi line � �*a!��-�dwsB=>,�>  �8:� nguen_��t,2(6cosb,burak�}u�m-�' �2inaL1� toroid�5-Ǒ��8�* luteuA ��!D< in�M��.`ej�P ai�� aggr� As� � o�Er��فi���bgar^�A���b& 4arscott1990dna�B ,Sol�v0 "ByI6}�1a��u!� u�  ns�deb � q)jco��typ"m!s�i�aconfl:W�e~ne�"`!��KV)B^$trubetskoyAPQvceAZc+iA�� in Ref.~)`b�}�Gafrgu�  ad#6���p��a��hGD.%�hyd��ic�/���vo wɸ. O&#*� Mb��i��A�2�)vn�C!��*���g ad�!beyondr~MP��tgE�fin� diOse-Aܕ�� !�)�:)}, 9�WEGi�=resor to%L"��*"ca��:���?ce"�M�middl�6��ME�� teau�-Acla9�t)�� � � phoreY�mQI=Ms�0t��c��sl�'�En ��N vW. "5 � �6 R z\M.��Ma�irm0� �5n=�J� e�)sugge��U[6_`�y s�X� ��+%U� *G! A�a1.�&�"� A�.� and V3--*�co!_asU k(BjerF A)GifE�"��po�h  b����Oa W�adsorb� AIAU��K. OT 'has�- J�is���9&-B����2�f�ay�AaS� ng� 6�2, �WF�CecuM�fU�*��U ��A�!���Qx2,tanak1�-r�}. Whil�B �(ada io� �-m:eGkFinAp�Zr},detail, much�hS$nG�;o�paie��third_��:�� �A(wo�� -A�uγ�D.� es��a ��H}�$, LivolantE?�ea� demU�9E��v�Ao K�r�p%rovok!�� .� 2 �� ��l"$}G_milar lts�.pub"}4_����6�&� !�;0thuDX�@Ast//!�A��Lk6�o�:Q}aȴvel�u���[.Z!��Kr�) ive-T4��b �� icit2~y�}���ea�/e� |K�%�6��Z �!n5-�[t&��� $U(RE/qhA�1lle�q�s,l*R�(�rad�j.�irK e�?Z�� -!%�_\]fl� A�la"��E���d�>"�>� diagramTco�L< ��B8ia^A� vioustu���U�Cl��y]�e�r�EPLE�W  N re��E+U�i�TganKaa��,�Se[II we "�GGII`%�0�*�BI�V5�B6-�  for�!�"� ]�vE��3!����I. V� devo�to �^~M�� nܮM.  co�]a��e0V lud* � V. "3Cm%V}�/��i!�a B%Am�4<� �a pit�,:�m-��i�d ًI;anxy}�onaKXa�cubW"/ box!Bv�. e $V=L^3$ e6��2, box $L=102$-�c�d�a64ll%��/DNAtp�3Gs$N_Q$2T � � cy $q_Q$,+@- = N_{s-} + q_Q > �O n$ N_+ 0+0N�2,��rp. �Z $]+}=-s�& 0�T ? v`ŝ�P!v9 >.�! tr!� glob:�� �(_ =120�GiN5�� All�Ie����Ld �#sp�4�T&��� ?� "l2��rƔfA'o�D�84 r�a�!inI�viv�`a ze�`8��)nausj}ce� *�q6data gr%Z idea� u� �v&s, rVe�)anI:.�#�8�S,"|�=O_%�a�ebc%K3ces1!�.{� Be�nao� ���!�%�1U ��e.s<at&� cs d ���.!T a{6� �l �-A�nd8O(links to nC�b5t6| �"� ,f@. A�5n3�e�!�~Uq�� ;s� uish� ).ac�*|v mobi(�on!'kAuSu�th���3y�(�4�:.>� ! db �P, p�"��M� >��h)q�zI�!Z>"�tt�*: 2�Y�s (M� =�di�; $d_Q�{nd2� ��< �Jc=\pm 1>4.Nc$). P�0d�oFbr��� !al�Eree d�9)PDIp2!A�r%� it�k_!s.L !r*_U!���z���9!�p` �B9Dng �!���o�B�gA heldroom t&�& $T=298K �s{3.N�$tinuous di�ic �$umɸ���"u5 =80$idtyp��snapsho6v]��hop� Fi�~�  = E'e�aN "�s� �PE�sorip-k�`2K� eme��m]�n� L**dat,eK ��\e,'9I��!P�M�, b��A 1�,tBJ�1})�!�mbiN���c�A�Coulomb=:Ja;8V_{ij} (r) =\ca��{]C & $ r/A<(d_i+d_j)/2 $\crJ&<{{q_i q_j e^2} \�{-OQ r}}E>6B�rϭa �1cLMH*,&�:�$r"y)�-1�� �j[ʸQ�A.��', $cw9y� , $p >zs %I�\! -����!�MAM (� $q_n$=�wT\A�Ÿan��� dd U� $V^{0}�V�>�he�k)�yl��6qE �Oa\= Q,c�B� basic q7�*)3�e+:�` ive �c_er � e�� ��ourW"� J>({\vec F} = _1a  2. 3SQ)�eq_B�5� -|)eG��q � $Y1˨eЩ`U�repul#( �#"[ a%onq[ as exe���!d Ygro%i�� �<���GR�# �a��C}����� ghtforw��9tW5tq!��] * 5}_2 Eq.~��)X)�D.� � ����쉮s����+qHr}_k^{~p}$ ($k=1,..�+)H�,52B A r}_l^{~iAl Ai� i=c,Q$�?beg.�Uc_2=9�f�W 1}{3D?ks�83N_p}} \left( \��leM�\]�_{l/N_i} M� \nabla}_{I\�4} V_{pi}( \miM�A� - @  � () k��H)�mn*�� ��<...>�YLanoU� X�e���,*�k%E2Iq }_3V���,ro�e�`E|con"� �!*� iKh��ns< ݺa �as S}$,�} d)�f} \ \ )�BjA0}9�rho_j( /r}9�-� f� 4l��,'��tv�� poi�g��a�� �G�'v d $ �a�$Xf�2inhomo�*o micr��"�$Z%I�ja&� �i��Q34Tc�Aed�2z �g°e��.�. bZon]1m�^xt�grand-U��/Д�< (GCMD) *� �A�I }2�S`ou:�,�� a �7A�f*�*2#���*>s 2Ps. Ea�r& � ferYby��n�Dal2�-&06R�� (�ܡ�2n %)�� �#%z E >��!�jQA6N_sA4 *�-C PEAE2E� V$V�LC=N_Q/VT4c_s=N_s/V$). A$(�5* QG%�these[1�� �!���� N$zK$!�&XW� �.�> 6��*j%*B:-'!nutomat��ly adju�cfab�&�JK��q!�"� b=qt!�S=8� ]�*r)�$d_c$=�.E&� �� � is par��3*�,1o}�A�m�� �!I����Xst?, im81�A@C:� �-/�#XX &U�Zbrx 9�>q*�m^�!"�JG 0.038 !� l �X�1" reflof2Xf>Le�ll�^EL�c �"u�-$ iX��3 /!& cD}&M�$5�I10j�MD%r�?�ME��2r� �Mu%�`b";��BD �ed E$5aJ q-  6�]ep� g�B cy�a�BGQ'nt qo�#"Re��)V>3��-Wa s�Ax"V Q�1 sc3zA�UT!K6�*]*EU�!re (see  2^:)YLi�Za@ud)`z)onlP/mp���u �$��� e�'t�'!#A}i]"�  u!A�2T*� at'a��HeR,DNA surface.�� The adsorption of Bjerrum pairs \cite{tanaka2001chargeinversion} onto the DNA surface at high tetravalent counterion concentrav|creates consecutive layers of ct  differM,sign around } molecule. �Mt�a multiR@ structure occurs�@ $C=1.8$mM. Addi�$of monovalq4alt shifts thireshold�ce�0to lower valu ��@$C$, in accordance with experimental observations and two-compon�Manningn dens)�ory-�m " 1978�}. For � �9� c.�s exceedb5,` to�)��1o8grooves remainsPstant� only* ?ionicEErbed o�!�andBtributes!Gi over{,ing, similar8our earlier fin�s \E�PoursecondDNApaper,EPL }. Beside!�!��re is a !let)�betwee� E>-@�]9Ps in b ���DN}sA inA�ses. a.^%�teA�o replaLIr .r-@g. Thus,A�higheru CainA=)ba�m� formINof-�dqmbaq^s!(es from�.associ F1;biA�uni�s%:small co�. Such>sga�risAy$ an attrac�Z,two parallel6�$, as shown!�DFigure~\ref{force_EKe}. A de)� �!!:� � leadU�break-up4%V�/9�-ޭ@�0 thus destroy�9�� 9z-h�.l.A#is ��0mately resultAm.los�i!g-�ar=5, seea:ul)� data!�$ $q_Q=$1,2�3!2 j3 I�ould be �� ione��at�a�:MY:�0(or axis-to- ) di�2ce $R$q�are angu�Tvariables which define�mutual�5f!�a�!� two V correspo�/�%�ori��@ heir��and���_first�^AN% rt s�� �sY�he�.� s up� 5\AA \, �! r�o��u�s epartic%*DNA-DNA:��ourthir�}�~� larger se!2%1�, $R>25$ �we�g$ no detect!� depe��c�Re %�m�ets��)�.nE�2. OI�ot�� handQ is 21evideztM�J��e��C,wo neighbor��m Hes never approach e scloserTn%��Q{ appazly meana�at�gs�ĉ�1;�Mst!� ��ul, 5�� solv)oshell�~ists. ��eLll E�8es hereafter we��.D0ally averagedis2~ stA&ngI3A}� $R=24!�3 J�E�(caled per �(pitch, i.e.10� base�� . %�,ARV�1te���a'low� %aw� Popt a $1/R^{12}$-like9b. � Helectrostatic $F_2$e�� op 3$��p[ s of��.B $F$ �V� s FXa�.�)Gie��plott%�6r��e_4� It caA7��aat%�6�edEs oscil��s�S zero,�@!�reminis� �he �! ed *# O a single�uP� *f � deepՉve vmumtW �$F$ ha# 5�origin�aaq! a�KfG R=41�� [ pur!{6? e . I:�/G A|!�%}�gF�� both'und� edE|U ed c� �*� al� n!���s. It� ��~� ��e 1�Fu��% ) =kbecom�=eaker.��.�,DNA, $C=65$m� pos aFr owar hE ���-~ w=��1t��do��ot�#ly�F � addA�p 2�  $c_s$>l� effec8%�s do.� ��m the Q����max.�A � :� � also)d sperm� .�� tr� i^� i�5a}M��fjisE�tedB .F��FAEt fixed �p�i38$\AAI�4 , �3i:��� !M area� lef�bpoint A)�N�isE"all re�/ve�B&� E s $A��$B$ a � �develop�@$F$. Ae5�6�&�  f er �Q 2��A�Un I/��ъve taila ( ail c�Happear of �Q�A� obviously!folT d by/inA�M�B� � J�on!��� E�  aAT� ��a Q 6��"min_max�� F���arrow%�k pixIto*2+ � � ac=zinumber��>�aA�Ar��aceI� � $C=0.01��1�%V>� nexa� {\it a}[JI�I3x!XceEnoUL and AP� U��q�:��2�� c>� Z�b �%����U8t�mediate!1.7$mM�56%(?h; ) )!c}.!- d}�p��ly%re�Eiz1�Iq2h (not!�W ��v�Wce�-,$R=$ 38\AA \X $C� :� )�� d!�dmx���r5 �yf2y q�iz�> $R$). And# � , even�!$C=400%O!K2� �=dis�ed, how� +:uipHtained. A full s�E !�olvedjcur�for y�V� u itie�F present� 2 ET�E~}�B� %am��� q $ -- well b ! 2Ht"� -- induc��V2�"� s, �P t very� 1As,E�%$%#($C$=0.1mM. �U� �1 es get moV�!Ʌ�}��(�Փ6�� main"�nE� x� ksha�. A  me timeez width Ѩheigh�e �*�We y�!1�g�A.2� !+�e�ly k Ri �-a� s du���g!rre�  i� Blyt Hi,��Y I��!P"&�e�E�a� ʼnq�i�%U| crowO nekM:����&� : E �� �6h !�"� �cFi�/f:�emerge� RT � .� C(e we cal�T!j� 1�X%�e���u \x && ���ag[re���^ hBis�)3>`m� , on;o&� hard"H$C$� Spe-��a& A�V �����>fat�� ��za�fve�)� en��min�n2,U T�!�of: �/e%�sA�$ $C \ge$65�d%S!�=K�x�IM0��� n �sh "�)AA� F�,la� confro���a doubl&�Y����)s d byMing is wor(oDntU�:� D�&voiV-�2� b*9>  cholesZ c ph� ��q polya�Odu� 19929,s$�S $ primarily! 6�z�,�Si{E�9�� 2 uELHEon�K�b,�h"�|c.�aq�� (2)] � long>�s suffic�lA�zEI��A�^%��gis��� I�Qaggre)�� take �� } � }6eJh. \s2 on{PE�diagram�mf-�uf.}b��#s�i�.2�!0.ZK �� will��.|unusualM+ behavior.+ have "c�x (�ofUlumnar):ssembly��bas�f� si�edj�$s. To do s�ex ume U�6����(aEa cer_Mt $\ell$����?n �! arama& �xA;be C =20 \~ s P$%#com� �&�����}5/n J$  SI VE��-:f��con� ro<"d["{Hal many-body systemY ng viaa & !� � being�#Iuz;a��le�aI� \rho�W>/ fre�Xergaa.e fluid� solid)$s��u��&W techniqd#utl��ev�perform!h tra�#al Maxe�i- tangent%@$![tif�"coe�!+ �i� e��y�dilute��} �ESnx��jA :�� turb��"o"�#wca1979}%� spli� FR 9�into .�!�aH!v� rts,C 4= U_r(R) + U_a� �"��- $ -�$d. cala�D but trun��E�1� w ����at�$R_{min}$, !5 mU a�&� "  k��dim�0$\sigma_{eff}3evans_l�%8use} \begin{equ%n} .5 =  + \int_{ }^{ �<}{ \left[1-\exp{ (-\frac{)' }{k_BT}\r{ ) } (] }dR. \end~H,!cross-���6a�EW �=20$\��&E$ Helmholtz2�inv�)Pa9HI�� ^A1��e$\eta= � \pi a�-.)r^2}{4}$e�a n-fie*'r' ad( �+ $model as $S^2 :z\infty!y�{UE�-e R dR}$�!(:� �-disc �, analy� Y res�,�avail� �!Ahdisks&a:^q����m�,��*� A�&�dj 0a lattice sum%zO assump%.�K>,tri(#B��ur���'d� �lai�qAYd��y �� :$� 8}$AGq�$ng��d�/ v.Ej c��A�#�e r���� At�"rE� a�� �?8-order gas-crys� �Y tran�onIn���reg� ��ed�� 6' �!�*D a�Jo�.�z$t��n*  $ &W0.���$Cl�n �enough "� o�!bila liqu�$!4[9^y�*terJ} �Q-:, )� )Pe-BN� ��!%�-)�yi � �� noveX �#so �` ce it2'!�� m� &� at L �n%P�almost �#d-packed �. Con��� (��x'J�8})\subsequ2redissol�$ (dot-dash<)in)+^Ho�,'!�B� �*��Ab�I�mS�&�.jQ�<o+�e˭�^202$mA�H�a typ���6_of 1mg/m{),Qrs� gas-M�cyi ) s en&)�&h6x .�� � � �A� low !�i g� n�"A��`y �%Dt m�%%m聟� � touc!�����QE back �! � v�2*�'�(2^�E�"�&a��pIpA.��2 $C_c�I0.3&�_d1�aNag}  ��2^'2�.�(raspau (9,pelta1996�&�Discu�Hnd�clu�X} Oa ssue��w*.2Q &% Ah! %CQ�$"A�� � $.� Na �facto5L&9 "- , it play��,� rol�aaPvert#: tempera�f�  explor� he �/�W�er !�P �seg% �e��=5P� � =100P$�"_. Fayh�ty�1Q�ocket-Ts s�Piv%"m ; itB g (ars complet$�>7�$,�  ex�.�&wa$ ��1�, 2.�ond���.lA��( UA3�a(m� �a��. H��,6K��!d6/3#rohibi�H�(-:���� � u"!��1e� Ref.~itri!94DNAgoobes2002}F#��ay� �A��\ 1!��AB al I )!�quiAe'!X�!ported.�a �xEe(�nA$�2D )2qM�.Qa�0be about 2$P$ a:�=�ce2� � fes duplex!� S �-�� i��p0!a��g," �0deserno2003,D _JPC_2001�MQH��ar:K;�+,e2�)Qn turna�.�/precipix*M5.�at V�s�A$- �"$'l� R6u,� xis*� �Tfra�k/iced\,��a-� les� an�persis2 M��TQEa A6�500� T� d h�n saf�`a�+�) d ro "� A�!�2f� avoip�rra �ar�^ct�s (offA!a�{0)1�s}im��2�[11-16]�(� �6Zme*�w%����U�� ᷥSE\a> eJc. ���Y���dF�stiff!:�����1;{ &�!O"al barr?5&P J�#!e`*c�c2re�1u)# ����}� ayac!��.kJ".�. ImagM "�&/ cA�s��a mix�A�.v� ��t M�s (bu~*��� I��#�er!g�)2� e� �� a/=6�#u C-U!, �.�� � a bundle E���/ c-Q��tR(!!�of �/�)HB!A� �N"H)q,y ^�i?ad"� $0.5-1P  pinc�bQ ,%8short.�IU�wo�"��ona�c, 7Mi�11`into �num�[1M�3e hexagoKI�!�ile�0e�6^be� ppI�!d=1�g�#wollen,��id�0"�,*P2a.� � . ��=8 0 *�4alW"AD�es�.Iinflu( � �.�" � Ey[R�s!|e e� i � coJt#I��*#k56�;noni�xrods (� �ar fl!�s)��MD :/!#�� dous task�Jn  ,j�,J  must!�mhd� A[possi�=���DNA. U�&tu $� > mpl�*il� � �eM�_8�wl symmetry��. N(5!a� 20PE�ea�5��A g!w�s /�s�&�/) A�g`==*@��� ,./�"*) (e1 40 $�)�z�!%�of ��%!yo">�E"� �I 6B 9R� 'l�nat% al w 'ÁHo�<a tiny���oeq of��x� j 5>�%]&]�!{���)an up�# limiKk $2%&��-�����)����M���-&%�m��r&� ��1j��&y�a�9�11.�of"j�"�7 Q-�%4�re ('AB�e&� ��l*pro�d�)s)�EcQ -2dozenM]d�<;�==s a up��� �� 1�at"(2E�EhMGsl��X�n>Au�P"� . InM�words, ��7>�e;��:^�:2s3af13%�2�V� ��)���G-Gproced�� ,&W m��!���aA�e�to  neg�7ZF��"Z E� #A�>�%.10!)� �,�%�6� .)fZ -s � �Ega�8�+� � �� cJ !byw#iK-m-ty3) mputn !�� �8�!}G$��!A�&td ��aѥ%!�*�-2J@%s%�.Z�'e"�%B�&�:ly� pled W5 �mV�$ nds yield!'"�(ory*l=M*�� �J�":� ��9���l�B%�6� %�bon%ntrigge)D�st meso� . Ou1<rZ�.p��,go�w��e.D�?$ackD(p�Bade�0��4Lothar Sch\"af3�� occai!�Xhis sixtieth birthday. "0acknowledge a�N�+sup><o workA�!�,European NetV Exce0ce 'SoftComp'n"  *{Re�Eces} nHthebibliography}{40��Dm{cohen1998book} C S S ,b A Gu�Cto Po�'D} (New-York: Oxfor�:Uni�P�) \jbloom�1997} B V A q 7 {it Bio(Dmers} {\bf 44} 269Ls&p S 8 M, Thomas T, S�'$hata A, P�;i C K S��) J 8zTNucleic Acids Research �30} 3722�cason���} C A L �l[3)E5�J.!� Human Gen.( c1} 8!�-�$wilson1} W R W�:;�" e,BiochemistryT(8} 2192; H , Rau D C.Qs>!� 1980Qphys. J.G%�% 17�deng2000!�!�$e} Deng H, �� V�8 BeneE@ s J � -� Jr G)� z-� R�28} 337]0braunlin1986b.AB  W�,Anderson C F� Re#H Jr. M T�6�ol.�25} 205;2U G Xu QA�2^>32} 1703YAolZ1995} O  d�� CruzA�8Belloni L, Dels�/8Dalbiez J P, SpM/ O� Drifa� M�5 �$J. Chem. P!�Q03} 5781�*n} R{ E, Ch�(on I, Lefor;+ er As Livol]FuY�U:I8(77} 1547; ] �M,2�8 O, Sikorav J-Li:g8 �!�.�A� h 4} 3.�L�/ea� atta*5ng� ,} Stilck J F�vin Yk$ Arenzon JI�25ISt&� !O ics}�7,bf 106} 2879R&� P� J,.�6.�� �J.�log!�.�$271} 5656;WD4-, D, Doucet J_6�]�:41} 48��V�:p$Antony T, .p Sigal Lasm�T� J�I+ �>�3a�82]����1rea ,nce} Solis F � D}? O�1M(Eurm Eq4} 143��c2.YA9U!� HMo117} 900��v r�!4}A�V RV1 VF�80} 1186�murayama�o.M , Y, SakamakiM�Sano Mi3IUA�(. Rev. Lett�(90} 018102qnguen_k\t} Nguyen T T, Rouzina I%�4Shklovskii B Iq0 �Vz$12} 2562; TZI-#ZH5} 729]�2d6cosb}͂ ��Awi< Curr. Opin. S�%iw16�f4yburak!�} B !uAriel G�$Andelman D!��I�:o8�I100[`arscott1990dnacollapse} A  P G�; A-Zk J��:AP2�29} 61]�e5�.���F? TN� )�03�$trubetskoy!'Q>a�T0 V S, Wolff J�E, Budker V G9;�6�8a� 124.]�tanakaao��1r� } Tj4 Grosberg A Yuf1iN� 1A]56��montoro } M J C1�ba~ J L�j} �8273;A�8n/0!�200; 6g!�6�!nM14} 427�B�O} A�7yarov��$L{\"o}wen � Gom=)�)D�[�^ 68} 06190.bou:�K2m�2qA� �.c"� 62} 554.�ByK 2c,�!?.� 2004j� 9} 041904]}"�G:e.Wg254� ��o�N��&� !=89.j>lR Man�RG� 7MDQ��a<զ} 1.1 B%5S65 H� Parsegian�2�(Podgornik RA�9��6� 59} 99�nJW5(Kornyshev A�Leikiz!�B�.��253]�R/6} & Z ���IcII �� 69 =�(DNAreview1}.,9>)/2A�3��r. CaD id I�fvRS%5�+f } 53.� h>gD'Amico� L\"oi�svF1} 1334.ك"�0 Week� D�  r D�A? � CwnB54} 5237.?:0 E!0 R�m�L`+8G5s} %edH$by��arvol�J$J.F. JoannBnd~2B~J�k�3.|�Hs >�Ft�~4Z~��O:x�zz5Zz��K�|j|6Z| �5a�{j{7Z{��I�vfv8V���>�����E�ynRm9V�1z>y�p]p10r{8>{ \<1sF� \cap�{(Col�- e)B� C�6[#.�>r)he $xy$�-n�G!F�v -� F (MAM)� osph�&��;s�C$as dark sp� !�cylindr�c�Gi;)lor$gray,H�hatched�a'��neutral ��2g>inscri]letu "M"��"m"�Ke majoA. mino"�XE2!? ly. >�>�� 2} T 2snapsho|1�&�  B=)7&�!a"�>1$'�K/�\]nd E� ���0Zu�*m^.�.~R�S��i�}a��"�K< �O/F_0$ �uE�$MWa�$$A) "�" $R$ @�H=25 mM!�$C$=6� ��ZA}!�co&�is  5ed P �g6f�". $F_0=�#/PR5�" $P=3ZY���9�h4�515v6|\ %4 160 cz� �4!�D&!x���1't�!a�%�iFN���,�8aBse� �Hu�@%�t�JEK 6XaE�1%R$=36 \B]!�aF2G!�0,!X�*��E�� j�I�:�*uH6�&#�VY�(�6=-G>��) 432!� (��^0e%��&!-:!.#�ahs:E0.8mM (>N, �d k) � !5�H (5�~2, *,9�/~hEg�E�!a���f�i��R�zif?#3%!Sclari;����i�5a��bV� Պ�isE�S( \, (rough�6>VKi=!�N�1).i&��r=.0p�Ws  B (!9A�6Mk100mM)i6s-@%h��"=0�cE[`.~: �"V e�' �^Zum�r��>.W��%��-(2�K A���T33�^$($R=38$\AA�5)G()�)� �W"P��I.�(�6�s!�a�!�t'*"aT�5d?�Wa�F s fl5$a$� $e$EWthem (a g�#eya�oI=$JV>�%\�(s�b4rRg7\�i ific�ch+@s�A_, dUl> �+ �� V� %q� EQu� 2�MH��a[��A �zD&�jU6�%|&�X-�!��uin���1�]��, 18mM� ��, 160284a�e>v�A��0z�*b�+. �\E�&�]e�ef�*q)�O&(�Ksu��2lj' 6u��1k�Jn�� C$=0��1),�A 2 �3))W (4),%X (5!\V (6),)c (7),)g (8). '0�U}J?"� Z� :_83'�BA!�de�(��AfunE�ak� �:�sR>#�Dst�(�*�0{m�h�? ke, <-�JY&�Dhr�C5-th� la�D5Als (Q� I�5l4B*�) .��d�.i'of��U/�/��sak�tbv�9o]?2�-a5H :�#y}�haexpanY;�J$*G(^2<0.015$.}-6�  docu*!%[1��!�6�,.d1�+ %a"�D ri1�V��-�/, %�k1%ml�/bl1E�L�1�% be�- ed %�2�1al�0A�JO"�4. �@\1F`class[aps,prd,preprint,su�:criptadd*0]{revtex4} %R?l,two�-~@ You�31$use BibTeX�$apsrev.bsteXr"+ % Choos�a jour�utoma�Hl�_lec?h�@>I APS %b styl  le (c ile)� ! y unc�NB  %M�8if necessary. %+"�+V{ �} %� \u@Uckage{VHxsym}2�+icx6,epsfig} \new��<\bBM:�KB#a�e�Knarray>$eG�Y"�K:EeE "VC�{ �(displaymathFId {Ij%lan {gl2.�r�C:{\bi}�@!Q6t%itemize6�{\e#�Z! Z}{\� bf{Z>=RR>CC>11>�{ ilon2�!gps�ar^!ps%ar\ .5 {\blambda A :#N " 6!dalph! dot\ :!bet  : gamm :!delA 6!lr?XNr��]>#"N?Z;4 \dsl {\not\!\:<al2]"bar%%ka$0��q ٱ% U�q he \�k q� lL y�slo�2instit�F al r�B %xL�7�h� corn�0f��ti�7pag_ v�. % M�LplJ�4_ed+�'E�Ls')Xq���rv0�� defa�A %d� �s2[8 %\vspace{2.0 ca��{E�Re�U�l��um�wth�,author{Paolo�/t�na} 4Dario Zappal\` ffil�s${INFN, Sez�q@ di Catania, \qua-K  Dept 0PhyE,,.;1of9l\\ Via S. Sofia 64, I-95123,% Italy ,date{\today}Q<ab 4ct} A matKco�m9�@%�$ ertz�#gr%�Epos!�CJaVS�oisOV�;��<%_bal�+ amo"F^Hx� activT9 des�b�oth�<of� "C:me}icd=*�Z��npF�K�H& ��Xc�~fu�� applied x:v�u� )�#*4��9O %a]$ert sugges� PACSY�n bra$con6<\pacs{87.10.+e  7.-d 8.-h}N[ keyw�8 -� I�xkn't ne�4dZPis %\/{m makiwA\n=f~$wi�,K, �, ��Qd J F &v4 {Int-:�Ed�_BdE`5� vivo%��<an ope�[oblem. H8A�� spit7 !��H~e"� . due�".�tet�?in situ� �V] ��:a p�zia��pa /=�6udne6kBm]�a2:1�Kgo�J tz}, ofte7mIAz"p{phenomen"�/f�<�I|M�Fse��\iS6 oneSb)k0 (until 1-3 m��U�[�d&Wvas�Dr2�� oIlibro}vn�Jseems re�4�eI ink =Dc�5IIqg)C1[ -�E� hop%���^.�!�ls� U� thise]�8r�5*O$or exampleHu�6al�pr��A �west}8DbeeqH��s�0to_cer /�!!I�� alk �:,ERvAy-�, F�noi2}�at: i)+\�2hsra�e2�(law; ii) cl�{y�0� uish�Yetl{5�ev�M� =DG�Plud�hnal feed�O%�-A��L#2Ftraints��an �O.�:&)E|s dur!�WC�E�9�.a.��=�{mp��$Jw B�;`A`e}wMit �U>A@0aBTD]�I�p`3 =�c:]X {Cel�aa:-n\-6�x^.��_��1� t v �*e ���} �W(dN}{dt}= N . \ln� ( "$N_{max}}{N=Y) \ee <$N(t)�O��.����] $t$, $ ])!@n*Gte�$ aEP=6 al s�O?!b $t \to�X fty$�:�squ�n3l�}TVtB\� � �p!$ Eq. (�|%) &!he ��]rolife��+xat � $t��� A�i W$f_p(N)=�V$}f�V~= $1- cf_{np}$ .<no�A>�.�Q @$"�Pon-ρe�Ny�r sm �`�D��� i��!'some �s B� �K�F�-ei�!w� � non-Nz a~KF| F��@]/miw�)�"2��EF�s"`}�Pra�IQd���$s"�V]N=U��(sY@ land}. If��QK�:�i��v)K, each ih sha�Kut � "1[�Kywy�� av�z, � 9 metabolic.� �B-�a�w> (�af�e�\�� geFr%�X�#��Y.9NeZ,�e%�iv����m�Fpt/[H5u� Y��~B" ��$�\+Anak. Inden*��-��e�tc�>Qe)�]'�]&$q�e��-v=jplus .`f�F�, $M_e�_sRap}$owt�GDY�R he&�MV%,�:W I�-H|��Lnalogyi�.�BQ)]ra)|S]�~E$B�W c2asub$A $e�, madE*�f �=]����"-��k$�u� �O%��$߄� �smKr!fvi�, >-!Hamoun�A g$U/N$�ge���cn!� � $E_M�� =nee�QTN�aQ%�$\Omeghy��; % �u�r.�Tany}��y��}q�dP$\mu$V5B �(iz~�)ZYa�n)��-K:� $N$M,�:E=�7( the��L�Fs|Tsumi�vw@jIE�?�HLS $U=E_M + )8 mu N/Let us v�P��a�M� A$ slowly^ \Zth�!E�e%�!T� i./`AA�&�d b� ��naY��A�" AR��8e.�X $�$,�a��x�wrN! ?� �e�lthough�_�� )uin our }A�do+ �Gkre9kth1�dynamEb. becax�e |a� �DhG�globa3O ergy�!r%p�A�.=Eithin�� ">eũ�vbg2� ��)�O5��* mpatKNE� .6 :,�fi�`by 9i�� $V)e���built0�]�UIA��wleeB�;se2�:.ai)�K'2�$�� ��a�S trem �cif�z�Iq,)�a�t�B S]_l�eep= + l E�q!�$>i��Qq$ &� %k( ugap�wo �. !���?gFY�,�"V${ Z}$� ňn!�0&�t ${Z}(eOD,V,\mu)=\Pi_{l=0}^�d {\rmC} e^{-2(1_l-;}Vf )$��6 " �oial�M��is.� �ρ� -��:�>�m�p5�d5 E2� %=.g1�Y!D = - (R/ ta)�-[ >)]7|ER=1/(1-50)�})$E�" ��of� �2�  -e$VE�yz �Ys [to�$N=)��� ��Po�,e�ic ru(^H�!<duc��A8``�)opyq� 2�'',"�@�b9�{+in�0bove,Q�\be�(eemme} E_M=Eq )��- �}%�\�)_{E�}hN1� S 1+C+>�R*� )U�.�Ce�uT $C=Rx)�~u+()� !�F�&!K"� �s����ghtforPtoau �hCer� $N$ : ��=q�+(1U�\ln(N/Ry To�M2U:-��tak�+�bcc� ����6 qvsm�) rec~ �r�v"?wi2X  :"Y$,enumerate} \le�� 0� Ay�~ Ŵ��� k�$ �Y�(>} tmiY2Ht�P�*e�,)��^� by $ � =N_m�' (1 +E 1�!� �b$1 >> 1�� = E_M/N+� /N ==�!� ( m/NhI8a� ���G>N ء>��ultanej #w�1!��D*� %�y"� ��Tue8��O ,-�d��U)�:�6�l� u!�9E�(1/%E) ( 1 + ��5S a� (N/-))$.  ! LV4p�.�]��6o_Wder& �nu�:��DW N;q%0terval $ tGU N$�k�o�NioRaN� tN+"writeX= c_1~u~ �$t) N =c_2 M_e~Nմc_1i$c��r�#�6�i ��htinuum4V E>Le��|)�$.�Appfh!r8u�T2S7 oids�G'ste��B y B2�Xic=s ���o�b �ap6G�M�:.�,A1��'ak��"5s (MTSD(�  rTS �-�gs&T^oi iR�,a)m8thickness, $k$,a��l�� + nut_�E<oxygen�delivex(&crust)ingt� �o$a adiu[.; b �!��(*k!�; c!+�h, recea_*Rl�� ell; d)"��-O!F�i�!y� ���s$s $d k$E�%ea�1E%{oid�)$R>�� fj��Za#law�zTin >T,�UN� �%dA$Rͻ� $ $'u ax}$� !?$9u�� i1� �- q�>o9to25&X ��){Y�..�"" �;zW� 3-4 dl of i� ex>� ~�s � lI� ! .U��*t 2(��,�28 >t^*$,�\�$R(t^*)=!�a2�!NM )b(�B��&� 2�ERJ���Md� � .�'�A<]9� �7 im�^*%�?5�=��xc�B ). . V�z!� !� L�>.�/p@fq�mo��a0�1t2,�a#Z��U[!(���Xm=Q� .��P  -2)$%}�J�����&�����"bound�;i�s"�!J>2��"�!��"%� rim����X.s�1)6�"J�ne�'is.�>!bl].�I�($G_c%�Q gluc�T2 ):*�p5� } k(G_c)=~+by (1`^{1/3}-  ^{0} � )+ k_0.= J%�`0$�' �^| ��9(���. G� �)�(�|!I2�1�,~% �$k$�^  2%("�bmf �oa. @ �% u��*miz2&�=� b#.fiH}[hp] %A��G7c�7%widthA* ) - 7`en�o/�] !�'�/�Hu1.epK\ 2cm}{3} %toAa box�e�m� �(. � 8 cmu:^D3cKDT�  (� m$) vs.Vm ($mM$).�u (ap ���'� 2�! $$0.28~mM$ � F%D (b�<07<. F�5"�).��f��I ��5�2� ]6�5��$��!��'=�at���fB "/< CircF re�^m ul�kin=��� T#{b45)��IN�7*i  B. �B!2ne�inKB�n � �I?�@ olid� ,�Se�/(�"a gel��!Qu| �6u6�ph&���aR"�a�^ge>"b $C_g�In�C\���r^iUhel} "J : 1h! i*�7Fc�"�kof!; 2&�u.�at.NeL8Rh�dX �&� �Y1i�v] �s� �b v  = - Nf �PV$%�re }��s�� $P(t�%rho(t) 7��e8{is nd�  "��e$��$ecĔ!� �S�.~q&A�g��oshouldqmply "�� "� ���"he��$ � (P)$�-��f�a&f���i _��"i=�+�qIT�#I��E��-95ea�3 -�<~\%$ (�"*L 7d!>)�tU,}[bt] %\tbl{�b��on�F�5Ji�x ��n>�"20 erro�cazD` %$\pm 10 \%$} {\footnote!P �6tabA�,}{@{}crrrr@{I5h�' {} & (\\[-1.5ex] ) (per�Q)& $21��)$ $[� m]$�-er.z&�- \\[1`\Z| (0.3 & 450 290.5 14 429U0.737 8 4048 6 \39 �11*�%�u6$ \rm ��~�=�&ItEW��B�d0�=�7*i+ } B."W �dPhyK�̀. Rz3 c.} �_415}, 513 (1825I� U#"o} G.GP\e�;``GH3Ki�ce�� s'',8e Cl�pdon5e,[U7;D]2, ti�{ F.},�� 3}, 451 (�c); T.E�hld�K ``Ma=BatT����/(/�Adam Hil� Publ(.r�88� refs.at rein*�S./G.Bwst="et al ��T�+e'a4�628 (�Z)Ntn5o} C.sfoVOJA@�Bio"�]2!�147 V32�noi2} P.&�5�� D.&�5 , ``�d��,��- B�!?&%�P~,.�$bf 27} 73 !�894); Z. Bajzer6C�m: ``S��R%쥀Em-immun"�#�#E� J.A.%��N. vdmo eds.,�arkh�#r�W 7; A. Bru6�E�i2ZLd`�; f 81A�008�8);�;m)Dev. A�ut6A�aq999); �{teUo:�t�6"� %l�� {mul"� m)%5 -5!�+AmD0!�a�p�>$: Politecn�Y di TE�,�W.^Y&�A�DP. Freyer, R.M. Suk%,1Cad2&�h i6}, 3504!I86.>� } L.�Xo�� �8}, 7067=88.��  G. Helm!r>�C�a�t[��4 y} ,��h 77I27_V=>�F�Ay�*�@W?[12pt]{V;cle} \8�y=23cm �=17(opmargin -2oddside0.V:StochasW:�Cil�j� ree-�>5ame9X\�7{Do%�~X hlso� N#&:�2AQ�6 � may �Yv�6!q%- !-!�n�*2��$um. \ejectbE; Long6~(Mwng2Ro\:2� in �F5  �c�13�!�� Nash2������* (= -�as5L| saegA��@f�-*e nobX��8of`q op!s,�/a�-� viateP �cuz�eHy;%��.can!�'eapayoff� ynard Sm-8CPr.�(1973) h�-re),z:�p�=���z2�6]a�st muL �IeeM.�, 1982)%�e�z�f�!yal1�!�^�-c�rIf!�ry�1%���ch��->1)I�s�t�9��AA��"�?@A\elimina^�e]>ʄF�� ���H�>tru��ult:{�8&<�Fm. ]�>�stag-hi2a�%c�.$nw[e-who�~�si�&ly�f�/1ons: eiM  jo��Aag e(5�$S$) �Bo�a,[e."H�\5H$ Mv 5x��lowm�q@65S$ J*Eh$� +�"a�ast�EBersN�a� spli#re=*�!;�K.:X:%ge��B�-%fllpcJe! h��/*A��E�5�1o r��2 $H$�Y�#э"rAaSecJ�u�-6e�G��out���,a���E3ub�<�|paY6@�/L"/A�?:r9�S$a�p d�Aigh f�(enc�pEadve&Mkpresen����< RH?A�!� ve a��edN+� ���1A�Zt. B��* 997)"* �F� �a�oaQ:��": >T . Kim� 96�J��- n asympto AJ*2 ���z:�!AF�. Buk� N. =4)ABQud aCG�*%w!=nd -�a49�%��m�X����uchM���Jk �,6� WaTc/N�tB� .�pC:�FZ ��M�6�uan΀ye��a!� mi�� :p!�l�EERLca�!wo�fa�/t a� tandAm��.�Ύe�aUGi��1�%aqfal�Uof �j.�+�&pre�t�h* /arg�:� wa�+IE:s �alF (Tay@b!' Jonk�� ; Hofbaue�J"U }�$79; Zeeman81"�<;sE�i��", �orce!6E�I so-/��rep�*�CP�!�h3�>a� #-5�p�ρ�c)��} It��{���\ny>�>B n}� Y��G"�YraE"A (Weibull!+95=V!qSigmu���k20��R��we�)cus� "rete-�.}���y��2� , ��&� N� 2�b z a�.P ��ar%A��en��atm�|�~ ��-�� ateg�>L$i�$Źbi5~�!�}=anD�H=�|a�,�� (~�e>|�":  t+1�W7�ug:.;9B�0�_"� . ��� e��e@L՗��ց��:eRobWAJ,Vega-RedondoɽaEr6b)&+(=ly,1�!mZp�"�mA�>q.Yk��n!q9�;e (a���*ry� dyma�K�And"=rF-�@-���*�� �05[ -u� q � aga1�(gy (KandoridR/��93��In�%�s,%! � >o���D� ty h �*89o ��stC }8�,� ���CCF���"�qf,��s�,A YoungE0�"C�.c�N�ޚ�B#�N�4��(a}NA5!��0-g�8)G)�Iv�F�kif=6ha��y_T�ro5U ��s �n"�x1r���no)�: .���|���"!e�w"_A�w��W!&I :MF-Mܞth-Rob �e? -d ^]�8y�0��� �� e�Jj ed �Q0a%her!o� S����*l]�ienv- Z05# l�%�.֧Y Y�!>=� !}5) .�'on� EAXZ���m�N?�A@٦}�f^)��n���few �E3)���!Jt�8qv.�Q�a�e�e08F��έ� 1f�n� Q?e�Q/er\Ayna/R[in�Mg�P�� �>s��!Bn' �$�Iw^% m�]� �D�o%!�b_�����Zwe�V���E�led V Ç&"R ���%�*&2p-gR��6G:F��"&��~� �G�he$� 2e�"-6� %�� /3/0 : B�i�� ��V&&gx���I��we�$4. &���?eO!5I9Ap,xvuw!�Dt aŽ!� ]�����io��MirU%�AMarkovA�inA�S�mAQg!proof�\ in�B�newOmu o}{T��Z�}{D#.�W hypo}{Hyp{ sis6 }{Ex�P6cor�vry}{C �X^lemma}{L2h }{P�P � "(�{TBy}�5#ji��(amB:,e����p3I1��m, ���|t�t�0hN�Wo�Qa����uey�   n� erm�seC�$��Iy�e�o"4 �3�yD3�" ��qnHi>� In5!:;&b2I! �E��$/.}����k��V1i)E�)m:I�-)woa��s*�>& } U=@(�/(�'�]8{cc} u_{111} &  21})222�v 8 0) , ^[' W2W2W222�h 8W _, �&��Pu_{ijk}P$i,j,k =A,B�=b� (row)-D',� lays�>UN$i$ <'h (�`@ 8!I� y $j�>A�0third (matrix:7�0: f� 2 �M,2{6�,p tag�/�, say, 6�TtIP�1e}AInee�[ll _-� to g�ai.�N��� � Q��U��I]9�U_{1} =�B( �3gin-�E-2 & 0!1 & 1 "IQf?0�?HC [��Y�al>�!� �AOJ�R�A8s��A0!b�Y"6��MI�� .x=R89 �V�_2�ga_!`b_%ba_!vb_N*)�oA& c GA fGZw�K$a=� - a_2, b=M-�CL $c_? -m$&B��Y�*� %�ic��2H��s; see (^q�%7Yee,9mplete h"x��A&�g�m �$a>5n� ����z�iebjA� $B$.�8�M3la�"!> Oi��e :EmU b*} �6$x,a�leq x�>q�C���*�, A�9 hy�E�j!M�1�"�$xA6�U�O�-c�v�7s, $a�Yx^{2}+2b (1-x)+c  X4.2.2}.2..Viťs�y $x^{*H��a�G%�:���\:�Eh6"X!|�bb"te�ed/F�:*V �LZj* A4�]�!�e � ���A�E'6�a�rġ�A�>EuJC6S66um,-C�Hh(b-c)+\sqrt{b^2+ac}}{a+2b-c� �|ac|}SKR�%uds::)FvX , $yA�-%T- cBT,%A�v�-d�DM.�>K!��%C�ޅ�! alqu�NA�v�sB���&-"�%ilrK� %H�*�� j�*�%AH=�f=}���Ynit.�"A��!*� �!EF* � �wo�F� �34 D ��""�'np�7(�s&��s gs@by $3$)c�T�.2& �.)�ĩ�A U_{2E;At[$��� m�`�,, $t=1,2,...i !��*�X���H� An"��=H, $z_{taY���$A�+For��T?MO5ac)m6etk6 =\{z��z��n\}.$ D�D/)p $e!�%x ing,"]1# �"6\xS.Z<wo[varL>s: $p��=_�d՘r� exack*R$A$;*6*$qvP= BA�B� _�A��Zl^%� - 2� - e}{3��+J�, h^� =�%�%hɯF��Now�%�.u��:ur�I?L s�FwBFm[(:*w���ioq`&�mY-sm N�6�%����DKpi_{i}(%),%&,%$ ), i�, �e)\_�F:�JoA�� !��� R.a$6i�� ��-a�OMiod�\9� � �[���rt��yIe"2o�:�$\taua� A:2u& ex<jR! !�A(z_t, p q_t)�TfQ�N I� +[ %� [ %�}{z_t},5 � A6 } $$eBHZe2 LX2 LW42}(n-z_t-p_t-2z}{ )},$$1d�!$0  } \hs�){2mm}�2�{A!3{t6� ><0 i_{BNJ4nx<�x < �Vx $$ $k=�j=r��j! }=0 6b or6 'n.$$ ���s F�. ��F��e�)B� R� stead�JY4�-YjnU�ad����Jm u�*)"nX$�easy ae�!a�b 2���� g& ���ENB @ 8"�9"�Q)9a�/f� �-%;�OOW: � �ob��� n ^���$n+1$ ��;L"# �.�S.+ mass�-a)*�de�<y \mu^�C�q_{n}.$ �v�$zIeVV$,[U:. (z)$�0!)&�t&!41G� e $z">&�+Y'! k&��"�� FV� . "�omm�5654*t:��&� .�(if $ \lim_5#Ka�} 0}\mu!4=(z)>0.$b�In ��(�xQ�z)/D"� � � >c_��^qu�d1A"n2Yun-�wtplici� desr�Q"m,�#4$z=n$ ($z=0$) @ R�O1%�1�a� '�..!�lh�.�31q�( ($B2"#a$at*Y0� OR�..�Ru7o�0of}iK�a�Rc �.�zBft.  [� d-�"V���T 7 - \��s��%7� D� � ���.~� �a� * 6��y�7�&��t�a�y���A�.�% ^� s (Freidl�$nd Wentzel�(70�1984;�d&\%A(*��V �C�U N"U B� a4�iEc ��absorb!k!e��Af_%F<�7!B>�-B�"� �r�W� b ɪg0wo e�ste@���{U��&� no�wrec�4c��T87�]ɵ�)�&5% Z�i#+�= �2 a�/�� ��i�[v�!Yd��!ir��h�8-�#eb� �@M MS4)�to nIRanoZ WX)�^`"Q�i&�1on&,�#%lo�N#�-R<�6�ẉc |�Bc�#!R�La"��g�#a�<u.L�1}> c_�Un�la2y�"�N>�A���}  (a�g!=���?u�B�A�2}!�$a,�,�b�, �,E��2^&big͠�b�z l�m,i�r�����)&z5��� �by �1QS!��*3��:b-&; ���.5'^<. Obser�8�A�>N�j�u�yS�!� yx�^3�ׅɁk6a6:43$eT, �*6b���5k �oF?� )�B..%�M�%�f��vi Q�, $<2t(�n-3,$)/(n-2) < E� < "!�5W R6�:� Pu$:}!% �/=1+H=1%p*� =n-1�$$ A92^bigaM�3��-|��)wo6"���mA&�����A}IEy$z=] ^"x-WA�J>���E&B#E�NQ�N���~�n.$.�� б���A��IB���Ֆ:��;QS� m2� .q��ΊfX k�� ["&��q3n�.vJu c<0<�WnQ:N�"RQ6qZ r7*�� �NaA�!�lF���Q�r�%mLlek>^�J���1��H"@*2� ��B$n�sf� "uI�FUG1 (n�� 4nd%� ulut~Z�SdL2JL8>�(z2_)$ ��"za!0,1*ll����A7� �s03 ,r�.u��q&r/!-6m<6+�aghF�b��}}c !82�)Z&h,�� $2/3$��:� � play �f(e�. [A��s���"�� &&k�����:3�(yo�dUTh �o(/&�%'q� ers |A��r,�pe��rPr X-%�$k&�A�;r%{ ^{k}}#mor�h&�q<���*�0� p�dsa �! $z'sa7%V��$n/3r&z 2n/3\�%1"c f�� f�,V�� 2ka�2}�`Egb A��g}���av�!�&X%%}( A,Z� ,n)$i�%���  < N/E8��.",.'(z,-]n/3) >1- sX{+�*0I}�H*;>6c �/�$ w�.{ A�2>>$�N� �%a�brV�b4��ҝ  A $ �%;$ �$n �B then�0$�21small ��Lre exists $\epsilon( ?,�<,n)$ such that !�( <  >35� mu^{%Q,}_{n}(0) >1- h!& \end-# FEC�Cproof see Appendix B. \section{Discussion} Multi-player games natur%�appearA�mAsituaBs (^lBroom {\em et al.,} 1997, f�4list of biologA examplea volv!� leks%mDcommunal nests). H!c we d �ed YfD adaptive dynamicsjpopul �Lof individuals playpthree2�. A�ssumed)�,ers areI��ed with randomly chosen opponents. A�(considered A2q classe�4generic symmet #2� o0two strategiedI�;first SE0re�/puA� volu!�ariu�.J� show�only oneb�%�y�(we resolvedeDAu blem!v8equilibrium selIv)d� .w�=ԁ6,ility may deA� o �number`-�. A�`some payoff parameters, wa�_B8( increases, �U5w limi��noU+s2NB0. �|we�uFK(an infiniteF>�8)�Ri� !!�behaviore�b�fferent;��((Samuelson,�p) ��'ion�4ord�3tak!dI �� .�$y models. i�a �2!.�.%$completely�+�l��ala���cluster�M��� , ei�i!�(geographic �e g oJ=�h�S} 6"$A$�UI�m� lik� to meet ol*. �gif2� has a po�v���Dto occur�!<results e�A�,change quali�mvely.j�)�a)�!�� S"� a ��spa��^t loca�� tera1 0s was studied!�d(Mi\c{e}kisz, 2004). Th�d v� pt i���R %ұ�F�9�!�� arbitr��A_B z s6� ' �Py�-�}u��+]� might2� . In��,�\%; hownF65)ja!E�cas��woM��F z ���i�m85FA�j��� � aBe�E��j.�Wy���"� o�a]K 4ri-Mailath-Rob a (  */ }��3)ae�_pm!ex>� of�� a�$0same effect a� 5@lP n� s per ti: eriod �� ? ca� justifE�fqrat%�� !A�!m� bigg\ha)�.� _�exp��"[ 1�U J� bg!�mF� >*� A�dinvestigated by Kim (1996)�ft� udy���B8&.R� , we uld rm!j!#relevant*� o be s� waD%�!�,procedures ��appropriM(in specificN� .&�4�d\noindent {\bf Acknowledgm� } JM w��T�!�ka�De Polish Committee��S��Research�� nancM support � %gr�dKBN 5 P03A 025 20. \eject B��A} }2:�AE�Htre� presenI�a�E ionary] tribU se�Markov��i�#!iosI&Freidlin WentzellA870a�84A>��X..$ eus�e now�^t after�16q step{�-faڹd i.e.&�=M�varr� at��ofn>M , sayAe�$Y\sta��r��Az -�� ANA\ recurre�   . It��sI��E�r6�C��e3 &� E�>�  zeroA"� � CJ�7-1@�X . C�a�qin�2U (Z,WM!� Z, W]$,-of�7"^{m�,M�$m�!& �� >�o pas-=$Z$A�$W�is��n%�!to� ute�  minims"^e, $m_{XY� need nmJ2%��!XeE !$YI(b^YX^to�"XY Džl$q�biE�j.3(YX)} i$q(Y)%6R](XY)}$�]tEW� � < m_�A�# "� *�eR0over $ \lim_"� .F0}:CY)=1.$1~�Bf��P�of��R1:f2We U��9iy in detail%�Q6< . Fv� ��!< a,c>�I)2w$z� AobB�(��B� �)f;V���u�&�q�, ����9ny.� ��  &�p � A��environ� . � U_{AQUU�,bas of attI�)-!0$јi V(us emphasiz�<becau6eof"� vy A�$lap substa%n Obseral%�e��&�k^{*}$*S!�k \geq �in %A��ke�xs� by $3i��*�\$B$��� o��mselv�Ia��Bz�$k=3m+1�f%��$m]�P pair�Y2�b:��;) i2>MrDAhH#9� s�lF�i 2� big 1�w�"M&+  (%� -4)/  > a_{2B�)�E'fDA�inL�V�M�oMpEje�c<qI��en�,+>,� . %�9RI� �A�� I� ��a�A} \cupA�B}=� .$ Mor���n��>� ,o 0 a losE_�r%+R����I�R.15noticm�!4�6-)2b�n-2&)/( 0�max\{%�, b!�, c \} \�v f:� �bis trueA�Jtn>m(2EL-f)/( B� e�U*yB}i�A%�ing2 %�An� � �g)t M �-1$Q�� f-�$��leaw * .$ H� Z*��awt0߁Tуy)�A!*� ��?$r=&B!Ay*�^�N ��� e�&�) %=A:��R�*�>"V]6:}&& 3�� 9!=k$e � divi.�"}�B�:�29B��e��w6�&i .b "��!T1�>�I0�Q��isa� too=��big ('�,Azn$)%���or>�B�.B. ��)���"=1)>!��(�D"n-:$A_H.?�  С�$k's$ (z�dn$)��ApoNau�k)>�\#=kN6(U�U��)!�th� �sM��# <ɟ6�-���" 1�� 1}$.��#��i ���.�Bj!�YOi�"���)J)B!PXZ� �:E55X5�Ige���� 9�)�t!�( f*�$1,n-1,ncK n/2)Xea%!�oyftri�"�R 9�Hnf #%� �(�'�5P�& en ��a  $2E+c_{1U + 2�  On� �"eck)���lu-Qi��$2n�r� 2�� Ťt�way �he� t%(�$A�.�?!/2�.)v =!8E>5J->For� $k= �E.j>�#Ef�againU9h A!Sݠe�EE��n$n/3 \l& �-�NPE��pos�(%!ings. Z� mgb&$,E8&�!�n�0�M.tau^{ni]� 6 I$>&��w%�!�i& -�~�4)N �perturb�#?*�on�Am these �y$(�H$$0)i-pE="!�Nm.� $\{z� �<, z=k, 0o*A�k��� �A�large N�������=k� .m*�lis easy{l(un��� 1A�Eda2_]lA��\ $y�)>?0; $k>\alpha n �Q$ >�+tG  >V �I�� a�i�2���&))$<))�$z�+1$ � , $k<\bet>��.B g����(�| !�&,�'z�QׁZe>�a�06�h�"� .b  nem� &L��+e�IA�� eeI�����s�� ��de(�on�-&� until!�3� Ezit jump $z=1��g g(A�$z=1a]finF;d!tG.AY S��%6�M� �mo'con"�Pq(z!g�OAll%vnzv69& o^{n(1+iKW Aa��tau��Q�r�Bibli%y:� *��,0, M., C. Cann�C�-$G. T. Vick6!�7).6�,matrix� .�!0Bull. Math. B�,y}�{059}: 931-952.b�Bukowski�%� J. M&5$ (25$ E&�+J asympt���$inN� F �&#. `" Int.sG"TP �$33}: 41-54j�Fo�&, D �(P. H. Young%A0)2]%�"� ��e0 P&l+6X(38}: 219-23jXV5XAX,.]WOnm&�2{ �� al system1�Russian-� Surveys} �t 25}: 1-55f�~��)R)$m P* �D[ al S �4} New York: Sp2( er Verlagf�0Hofbauer, J.,!�Schq(i$K. Sigmund!�79). A��E*.�R;.E�N�Jjori2.m0(81}: 609-61j�.�a6�98)m�20A� �]W-C��im, Y.�%EN�/n@n-person coordin� ��)��. B�+Q81ao203-277:��0Maynard SmithA�E=G.!'PrB (197!��#�2 a�conflic�1�Nature- 246a� 5-18��(1982B��0 � y��}.ҥ.�W%A�5�b�B�s�K�.�� �WV�232E�-53j(J�%R�+i�&^�+�C Physica A-�34��17!�46��"�&Rob:.AI,8F. Vega-Redondo!�A� E_7yB.�2��H�J.M�I �7� 65-9j*�.Liw7Ba�}EREj.�S�36lMITR][Taylor�A ,L. B. Jonker!+7����2 ��a��v�m"^ sciq��145-1566�.�.�,!¡��e��,)��c omic�f8iour.} Oxford: ~=Weibulliq199aq6}1�-�.}ق:�| Zeeman, E%� 81).��a��KU�B���V�8� 249-2708end{docu�} L5\�$T[aps,twocolumn,amsmath0symb]{revtex4!�,usepackage{g�0$x}% IncludD2g�*files .,d [ }% Align @: s�dec�#point2; bm}% bold��h2am�}>�6epsfig6 subf��b*� ,style{apsrev�:12} %\pre� 0t{APS/123-QED+title{��+2x 1ne�8twork%�b�strucő� \author{Luciano da Fontoura Costa}\email{lu!8@if.sc.usp.br} ?at eus Palha#,8Viana} \affili�P{Instituto de F\'{\i}�lDde S\~{a}o Carlos,u4dade .!8Paulo, Av. Trabqdor2@@ense 400, Caixa P�Dl 369, CEP 13560-3+>xS\~aoeBrazil='lMarcelo Em\'{i}lio Beletti} 2� 2�Ci\^{e}�,s� >e}dica:� Fed��Uberl\^{a}ndia\\ Rua Par\'{a}, 1720 �$38400-902,:48, Minas Gerais,� sil �4date{18th Dec 6Ipab�dcApB20��mammal�*'�3QqnIi�6M|s (Ha �=Volkmann) rG �:to nour�-��E�ma*, cel;5�6A�, describes h0%x;dimenwalUonI�ioa�f such� �0obN8<,nd&)�erme2 � �s. Tq imN.A.f�ngLreed: (i)�fY7�� bran�> d�ty�emb�<�wer lawgli- the >`of29. hubs; (i s3:`:�#(ode degree k�c�7 cl�=te�/cA conn];"�:E� Ks 2%�4;(i{ appl\io�?!� receO@(introduced '�4of hier�/�=<�6coe", �6� i �/�TAtyp<sca!>of5e redi&_/(. A series�29�*H>ins�.g drawa 8ed��}#@%\pacs{Valid PACS!!S2-aU�)�� �*As"typRq/, namW3n6,EHa"E�q��pervaQ* by a.�inter?%�ng t2���%�c liv�e� ~\ci�7}=�" d�" t�>�!�*;"A?a�s1-rol�n~d�<opG,\f=a�� ree��\i�9Avtop@E�)5r��ns a sub�1A>&�3ioA5B�?ts:u$LnM� �-_11 2,3}vnds0<a"E'�8rehen� mean���92,��(er�(3`6F�x . By oc�zng (�r�E=Uto$i��.he��� �O�&s�'�fpoa@n �Dajarc$!��M o�7iF=�ton/ 2���� c�a%Dle5|. TI ical!S�4AAs��f�� �s --- �0iL�od�:�A��m 4},"Jo�?'5}%Ce�\textit{��} f 6,7}�canD�� u4to �y��uh@lzfey%"�analyz�ha Q/r%gY�;�Im!ph�-�6"humerub� adult caA�ol�Aed)hnecropsy?�Secto�< Pathe� �! VqAi� Hospit@+8% *rof�a, , � . Af�1dis�D(! skB5muscle� , 0.5 cm wide�7remov�:���*����q*r�7e� left. each��. �ks w�f�Gin 10\%�ma�5�/'48 hours�sq 2G�s�DPdecal�7�z< 4\% nitric acid�"8 30 days, embed�/in8ff!ccTgA_$assic hist!�aO tech}BE��9! rmicrot>Cin+ �=l 200�"cV 5�5$m�!cknes�"T�)!0then s��7!�Schmorl c�8 �digE6imak5? acquq by us��@an Olympus TriocuEH BX40 � scop�� �1 2$-200 camerterfac PC-��at�- uA�through�$plate Data`7aF 3135�E�� �iza!f.�w /z,#g� ��es�B v sec9I�_8}aA� nvT�&1N�Ffs"C*a:x_:ly 700$�7$480 pix!� conver�into PNGA�m?"d��U3 a!7ee.� ���m��J?�"�n;perfor�Gby %��� vtkPNGRea�A�A�NVisO@-uToolkiU5 r C++. Fiq,~\ref{f1}(a)-� F� *� -{ 9,10!~ parzxa����� (i fourth)� ��tiE of ����E"���7U .�6 manu��, yiel�(an unwe��0ed, non-orien!�com.k=g "'�  9 $N: N$ adjacer ' $K$,��(! 2� ��e�!�7GC J �$i j$�F.�b�>�C<$K(i,j)=K(j,i)=1.7A�ic%C ``V''-}<�*���\st� �5r!_ond&`  �(mis�f=|,5;�zri�$�kFeQ]  2F`b.`*�C:� (!9% hMpT* in $R^2$): 1YginN�by�w! �2c "$ $z-$ axisU�< �3 7!�is defi��_@&�(e;�&�tt"tQm����K� s $ku = \s�: q=1}^{N} !�q)!�2�2:�$dilog plot� �-�<��oF>7 a��K' e �=�Cy�isAQ"� �?988�% 1120 link�'A�p�pro� &�%� �� � C X# �:� ��1.� F� 2�\H5{hubs},�:!��ˁ�i!� rly =I-Bs C'RBntrato,4}#( �?��rula�uE�(i$3���  cA@$be organizI"a reg��-�)w9�#�G6��C��t�Uout��>r A�B�un��<3inB�b��9/�&� * _���2A���-V �-�M�4M� IHbe re�:�f!�dcir!إ�� ar�xOa�T-�s",an Euler!-w wN.�eveC9�@Q� 2}. M�* to f�er���� 5q ��M,,�5}�?J�#��� ���;g�O !!�`5:�$i��L�AH(i,d�A2 @Es mKD5t� ta�=$d$I&j�g� �7 R3 c��~t:� ��short_ �@ Y�~sA�2+P1eQDw�+ valua�;@�_1ky aro\"Irefer m )6Now�3%�ZSof;%&at 5$!D�]ݡ51F�@ HCC%� = 2 �@E()�)}{|| || ( -1)B 8F- $E(SH0K >�9je�� aE$S� $||S||$a\!+Bl(or ca:!�D)I�atG."�:u�tra��ZN/)� �� ml d=1$ ]e above�%�. ��-iver Hs�`:�Y�$d$ Ln&K�ivi9CuPm�-M.X6�~IhQ��4!81.U \�/1$, )�llI��K o�absE��"� "3�UA�%��Bll  Rm@\�at }< � I�E h���,�4+g�set, ex��,itself (loop��-ake� �QccounvKis��AS ��8M��b+er^a speH6�im"#�.5K]Vcy�' CG�_2d+1$ f . 6� 2}(c)�i�age-�$\�$ (��!�)p !M)rAZ� c*�S i4�+15� StarE+at 0.008&�� �8J�|�Ck Y��au ex��A� $d=2$u55t&4 fall�N eadi�>��0~O� $S"H &=A�.�� e�1+�� rst� uNZm�<d9  exp W� f2�n�bf )��= weak�@iueW5 ane � 0Sn�uQ����doe�8�O Mw�Szaz �K sB+I �w �@m=�Z9. �}@l1� 5!�@6Ps[:alq! of 5A11 Epr)� d - ��!!anlysed9b*a��!\ . G e 69 a�sU rjY major��iss and EFsySeb/c�� dichz�Lfur"� a�.tery b ���wo"� �Uchų urn ,�,�so %2� �Nr����R-M c8V�'EXVT5KvV � Jm��af �u�W A& l!�pla%)�c!�devon�.�t�HK a[ՠ�Puld61 &=H�train�m�yby�� 1�KC�aB�a tual)yya�ex��Gd#ve wh<r& pro�P� flow. Wh�;�iI[e�A�n%n;:sE��N�0initi�Nao>���nSto 1�byKH��� irrig� � sche%]��vir�ly %<�7��Dw WAU�w%�d�%d.� D�ree<}h�H��i�B�!!�k0~i�?rg����is rigid��T�B� seem�X 52*%:sa��� ���I��QRa�he fifth6&�T��eg� ="P�c s,&� � xlq0 �OͿ �)� immedA(�_pe�Q� %J2��Bll!�a(j�"^J�"d�";pt)�6�o&#e��\s $�j�&ly�T$te-of-the-�>Z@>y,embe Tɴ�!� "�qu� y �[. .�&h ���Ks,6*!��2�x �2�$A��_6i 囉M�R��a�c22e�,�t��a���ZA�!��A�� l2%�4�U5]5�PwO�" lengths9-g!� 6�> "�$9A  ��z�Ry%b{^Q#!nd[ cus�" FZ�%��T��^|)!�i�o ir widt� ���� 1�.)infer ad"q"U ab�Em!�=I$ � ���f)� �&c��&T . ).)�r� �@n-2 t%���&2�m� FuZ��K���" *p�䖝 ��} \label��G5^�o5]D_i�-9�� 55]{G"�8 sHCC8.�d"�1��� �R,��!�, sugg*e� -01�8%� �vh% �D��1 +%u�J�:l ted��(b)�s� hdom�W���/�60�T>�(� e6��ZZi .�s.,c),�ch:1a�*e ���  5.a�M~2^~the.. }{99r2`bibitem{1} L.C.~Junqueira%�J�:Lrneiro, {\it Basic H�!Dy}, McGraw-Hill/ApX`on \& LF_,"8,�32)�(u,2} R.~AlbertpTA.-L.~Barab{\'a}si, Sb �i Me��iHgC�  N"LPRev. M,\z3�7 bf 7[%47J�03} M.E.J.~New�0&���Fun�"A�Js(SIAM Review};4�%16 p�5�-g4!g(A.N.~Amaral1g(M.~Ottino, >c : Auh!Q�Frame� ��AlSD%of��9, Eur.- J. B,�38})�` 5� 5} SO< slov��8ne�Z, S-E�USt*�;'�Protei2F[cer 296}, 554/�566!F.~$0,)�H.�+ Back���=�)�%� Lett-�(93}, 098702t4p6�7:uA U�A"a�Yo5VrN0d-mat/0408076.�8.X%,R!� Cesar~Jr.mIShape A�!�>!TCl%fs :� or�4PF ice}, CRC5$, Boca Rat�*FL�12a(9} W.~Schro 0, K.~MaqB.~Lo�n ��WR�"}, P�d�8HT Up Saddle R�: , NJ�4�5=j�10} J.D.~Foley, A.van~Dam, S.K.~FeinevHJAHughes�pa�$@ ics:39nc�H!61� 4C} Addison-WesmBos% MA�5).�1} �sa�o6��t: dR56�*P5style[o4]{A0cle}%@�94s, Academia Si)/, Beij��10008Q4hina}2^2 ^a�I (.0ipl�*C3%r�q ��ndq �q$3}$ To who� �$�sh�^dd�>ed. } �3} .�0� "�3B' a mix3 � a6���"2�  $ pseudobon~ g�!&t' $C_\%�8Ro]3 � secuK� idu�ql2g�9 uctuA1�Q%!e!��!17HnVal�V�m�aQ}.L�be�!�#oarse-g�!�� L*X& 3DU�ea�a 1D cM�ce.c2X:�� �+267Dx�ed aRd �n�e(igY�! FSSP data365�*Q:KeyFds:Q9s P; �&.�:�. %ea�{�2_T(s): 87.10.+e,02.50.-r�igskip*'r.*} Dra) Cr=*� !�unavoid�s�*p�3�`�f��(e %tertiaryn !'amino �,9�M)nE[=] methods#M�pz;1��i: helix,��A loop*Ros+%�a � l�a� 6R�#v� signT55�ir2} .!@'o�2��*;!F!'~^enh"Dk* !*=Uisa��de�S8u^0o"da&m�0modular archi�*9�l�uR+)�aches s�f�2cjl|-��ao i�7GI�%�=p ng�/a]"Y#B indi�s]",dop$Jl55�5I�Íh e co2_��} n�vu�ρ&=4A>eJ� � fra% Qje b4 T$(\phi , \psi )$ diheda�a�W,� ��[ psue��s$��!�m)�bdyp"*of.Ba�� . Du��A�$lEW ��$�s" 0si$ (McCammon�u0 1977; FloccoAK Mowbrayao5�qr9y��inAYce�$a�S?g���Ph6v"}5��ob�?E0 ?;2+ѭ-K, Iq��,�!! pept2in quesa`"! more�*U5$��&�D�$nd�- ��rat!>$ghtforward3 �^1�aTSd�f�m�umea�� than�E �H sh�!�^A�FYn$is paper. �!r��2h�OH.E�}ire��a a handful!Pi<,e��is��u.X toa~�%�2�V,u9�" 1D���s d�� �$/�R'P.o��!��=�XC@D�pac� c�z�" ��e�d#}4�np� e J�#..;`!.�s�{��ke�x�or a �e�ct�2J�x �ofx!��%�Mll�< �:�y�)�Q�k��2�s N�re�^m� � �A�r1to :-fi�gm"" Fo &� ~@%W[tU.tax ��}}0 tinu�u6( Rb6k�Q *�"�1s / )Eva��iet%&:way�D�xTd ple, Park�I Levitt"6z poly���?i�d%(Zw7r�݄� v �z�(a libr�ofcal;��!R>n�n���l�Hdom6�&� m+$global-fit+xR4 !�%�\ ��+I&�&H0 "  faoptimiz6A�-�U�� �� ���1��Ŗr� ��m�tI�[E e�UKo�Koc�١�Wodak%�1z)tu�Sl nR%D�\-$$ L V%6 � e�ch>�+a,!1� S  Rama�N dran�0.ndard � !+Y}U�E� I�lso�<%. gene�quF># ( (Bystroff �Bak@N19|M Hidden �n�4s (HMMs; Rabin - 89),�e �9gorous � flexk7�Ee���,�ix�iW6vae�� �h�zalP� {|sF��q@motif�6g",on (Fujiwara*� 94),%!Am/ (Bu�V! Karlt�~�� J &� < (Asai, HazamizuJH!�,I3;�$�u��9*� � �ucc� veF�  F�%�20 %Te� �Xph��R�ed !�/g�!J�peaFI]J��UJ!�e ]A"n/Fg i�`r#siA!��h"U���%� .�qT2EX42a. "�#� �=)��  )�aA� mpara�,)�AFJ���%=wU$"D u��m pairw9���� } � �(fami�*!� 'M*a�i�=MSs) ��+ Holm�!Sa��uCV>{M�} $^2� aS�!���4ru2� , a��ltly en/e�H� �.��'5ǥw.���5Q D� A� .� �%�F&.wx1ad;�� �`� ��c�b �ly�!d�r�} ^ = !( a rray}{cccros � & -\sin0S\.*0\\ 0&1SV S\sI ), \qquad�aur�1E O cau� au \\ 0& �%Ny{\y�%a� }I�d}&01 =):} 1�rF] B�q�Ydfd� � �H d9�T_0=I,��0=0E� d} 8T_k=T_{k-1} R_{E�k} � _k�]�806O) &r}_k = ^+ d,kw1B�x~$I�A�i�&Y7F. Lon�`"� w��-�Džw�nP e��&�OTt�.a�LvMexplo�4e4�a�H �.s� l�� i7�bM�z��,>m�.�I6 s,� a8ir.Y:� ���to��]3 a��.� m�|unit )l�RSfix�A�v\&�Ua is ��� �[r%{z�2�C�i�o!��r`j��\Q�:o D V�"�� "�~�3� te *� 5&h (�a ' )d�the� �� U-.�V*. Our"��R � �� �7�6�$M$�(b��7`A '�H x}& ��a6�is�HxPI�uWWA�al no�N2ZsF�P x}|M)= \�Gi�Gc�ki N !\mu}_i,�& \Rd a}_iF�vI�0 � &q A3J� �g��2& �, 8ki0= pri�&At1y�?� �2��� w2bF bD = ( )^{-3/2}|.|^{-1/21.,xp [ \hbox{$sB 12$})?x}�!G)��-KE��0 20].|(�B Each �2��66*�E�"��cofy��� ��i)=�I�� F Ad>?� p�A�!�9�e�-�y6 -�� el�10A5F �HZ � C�(�])�=9$E�iM�=1� T2� 0to $10c -1$.)� IPD9ŧbeK �?d8��� des. To&�#)��/M��ABbp .�"6������ downhill �x`Nel��� MeadS6�`!%ERXly "�e�@/ sQNt dS ��is�v1�&�Yin "GN! �of&�Z��t�[\�! st��MllEo%� lem �Ţ"��#0J ctan4Jbox1��c���i�� !6T*box� >Q�sJN]%Parzo��ndow �+n��{:��w�olu� : help��to foc�U iB=J�F��>�asily loAU�m n�Z�reg)i?Ra� �E�s mqi�eF�=�lesh< spic�AZt�Bunseen��"�Z! 'zD ,�� l flN%� s viK=�3 oftee�sl�B}M�O�|=r�]JV affe�h�O"� � E�"oWq�a)2dEn-��!E>ma�l� mon6Jmargi,A��'.�v!�өf.��)_ti91 �g�a grid ie�&F� ')$�c�� �!ya)� As�". %�9, J.A.Ib�@,Si1965,&90|Journal, vol. 7, pp. 308�C313.���wR�fiv66.�sp�*!(_b� _c, � au_dVz].� �e��#&ۏ!_AA7 ;� e� a<A P Ap��N<s�� LsjM�|Q :�9��Qma XB&A��@i(BxlX<9 ^} %N �.� must�#� A�t!"s��$�*H-QC-i2��Fa��pur�B!�6�:H��!�3����}Bl �$\{�،}_ina2�. OX���S!E_�*�s�G�v� ]�vW.nM L�)=1/��?diago�$M.Z <W�p!d 6E-� Exp�!m-M�� (EM)aY �x�$ach��� x= Q|�g_ki�k)�Je calcu( �.�!eA�� ��be���$i$-th� y4A*cc/'Bay� ormu�7*� nq P(C_i� �) &N�pto &)� "� (_k|C_i) \noM3\\ B/ L _i�  \� B� � |� Mh^� _i\�>6W }_k)]"m�Q w�T�& shift�9_kJ!Ol-val $[#^{(i)} �? +$)$�� I @ ]$.[o�u�ea* }_Qa�.�$>�$ satisf^ �6� r/�!$� {>F XmidN* 2[� �'�~EMy &1ln_i &=k um_kB�ki�n_i/nuad n=�(i n_i, \\ %2fi�Cafrac 1-7Fl� A�, A� ASigxn�][ -8xk6` ^T.�k1 �9G!���'6�i=m� �rm�:b} (\{��\}) =a�d_k\, %2�,a�! pto :)6B:HoV�w� �� rt����e\:�.  $i^*��useYE�i^*\rm arg}�maxBM.�@i*}k&�An alterJvGGAv*<)WHbJ~QnLmax%Lz#W!��< WA ow:� ��)0U�� ,:P � �?$Q�Tu�JB �MANl te.�3by&#|-EM ite�TS�drop �e3�!� �5i"�{�aa� Rs.oJ $PPrJ�$ nJ�aC�t;|Kr�G!- its . umK / stop�" *�%b�ITOs���u� 2�� �,�'m�#�&�$>Lh  $> $. �w�!_� l"�qŗ�a:�$O'ce 2�(�_i*}). \h no �H �{c"aJ!�&� A1lyY!�DA�� ��^�d5�a�2��6"1��C -W&��b�o} \par�15cm}{TO1!�e�8� �͍�`0.i� U%;~7 p,tabular}{c|r rr|r}\h�7 &\0*c�q{1)}{O $}V|i� �$}:D3 Dq�mu}$ } 6M6}{c}{e� O�$i;S�&&:2��t� $}&�lt.�au$}&' 6 |} {� 'R">\bFF$au" >=#Z� g 'G ^�'KZ�$ %@-�lI& 8.2& 1881& 1.52& 0.83& (275.4& -28.84H106.9& -46.1& 214.4r (a1 J& 7$797S8L0555& 31E-10(@ 46.0& 37.8& -70332.8SDa2 H& 16.2&10425&1C� XQ$706.6& -93�$245.5& 128(-171.8&786.Z %a1 K& 5 254�4L0.7�1.4�73� 13.7& 21S 1Z-25� 75.7�' F& 4S1 �0! 2.7)Q91E4!.!Y9v0-11!� -8o 53.�$%(b1 E& 11� 1M 1.02!�.9 �95!6%K}i15-9�-22�56)K b1 C%�810 �01& -1.-M1!28!�S� !{ 2S -569)� b2 D%M8 7 �7 �3 a!M5 E%TZ�10�-2S30)�(b2 A%N92?� �!�1� 9? 8%� IL 5228.6!� rb B!,!q 66!~.0A22.9�1.32E��#-� 9h-5.� 54.3S2 G�*13�1.4!�2%��A�6 u0)12L-I\32 Sa LSM 4n1.0.7�0.8�4 7 )�$& -7 S2� 34.5�(ra M�7�4*1.4 .6 7 8 )� 4%� 1M-7#T a+ NSE7>1.1A~0I@1i% 3!�09L E� 8M� r1 Oa #2 �a�A�!T1.a�17M20� )-mV3>98m�- P��2!� 1.2��i@ �4M����Sv-�V155IF(r2 Q!G ~2-�AG0.3)TaOaA!�Aa:i� 3 0�19)�r'��� �6�=+RecY}y�estab��� < *�- "40� "�the6 o ` t�-non�' ndan�/p- 1544 -mem�fQ� srLPDB\_SELECT (Hobohm 4^-�14)� ami{?(2ty��: 25\% i{U�25 Sept�l��v��7� �`.Q �%se#?!8�)k=om �H pk$ Bank (PDB�2Jx3su ��7�-G%�Us D.�A��bs�md=8VJW� \ 9!�ced 3N� 8$\{h, e, c\}$ g��7o 8*��r:�B@ $H,G,I\to h$, $E e� $X,T,S,Bc,�of �!&o#is 2248>*giv� t�/264,232�s>=A�)�B�� 2 per� �mofeJ��Q+u, .\\ 20 \O�-�F}{> uq�{c 1 2> � $I$& $JHKFECDABGLMNOP Q$&Counts&'� $cccc$��t�v������ 1�o �� -( (<25090\\ded2_ P�7�} AK� d>< 3272 dhdAdZ Pk2K< -�1-�# 3028 de��<21  K� �#>� 4029 dh�7 �2 4� ��-1�# 3664dee%�>P32)�(F � %162)�ev,3 )�F�Rdxd 3676 �%,<:(%�c 1!� # :2%E%� 51dh%�23!2�:FN��6 4353deV��7%�e )� E�� d�2 x 3007 dE�7� Z -P #  E3�� 49e�eci�#-nI�Ue�i ( <��25e�em�P_<_1A��(AKw 7 8E�em�#A ^ (- }�7i�25E�ee�xNU�E�!�e* 2� #FY38-�e)�>_A�E�< -d� F7)11,e)�:!�E�� � <% -d Z %;9,f�!��%,i�9Z_ #}359-�f��O �)��Z� EX%141I�ef�5,4� dA=| Z_-<#Ge�e�� #N�5�NZ_��24 ȩ1F��%�UZz%�!Yd- dh�! (� ��I_dE� -325�hci  U%,�7=�nPɳ�nA20%,h�_n2P � �e�U2723�h�_:�_)P#KEg iP� 1�h�(( ��2� �-33�hj�!57�Q� # N �hj�!d % �!E U%|_ �F (11e�hh��!m �� (7 - - 5r386�hh]�A - #e�i�I�1�h���!#�i �U �_�8!� �_#5�hfx(^�v�>Z213-�h� 2�e ��� -7: %OA:�44T hhh` 2!��A�)�:PN%^i(�� �Z6#7 �AJ( 3132!,2\}�*�=� fE} !"c(>|(.g(z�&BL 6�=h�:w/��4nt(�q� =1.1��< (radians). Non-;�,$��**�".4,�]����2m98)7�o��*�enB�e��(�Y) =0.87 n�U�W�%R�nhh:;�4�4 +pr-,�r�vague :�,��g�g-L9P7-2.00$"+�)"5�I� \�{1.)�!v�&�� �80,05, - -�n,�73i�'��eaz��.��'�H�6g'�t.�&t.�@-- �-��"�+�*� $0.1R!$0.2$qMh$I5A�Q-!��'w�4Ga�}8%�%�ces�hn aV�S%�M�Z�9�w�i�6f)WHv� sub-Jy.�f�*J& FurtMJe�6Ah�(eZ- �V<�fy[m�VH��RJ��!,Ia�8)[Eial�~�!�r��V l. F�,�#17*�Dk"�cAki.~XMEM algnhm.��ve  �*"5&��FSm6&o1r�1>�2�F�n)�n1) A}8A4a�2\�  dX]g�@ - �+�/%�ode� m�Vsharp�O$H$IP!v#e�# $Q #ch �p�,��propor�)ey}B^%6�I/�-N� �?!��R!�D0b<�.s (�"�+ 100)")T�|�u"t &qpo $K$&mlkjihgfedcb$Q1\Z� ' 6 �Nc ^j  ��0� v ���nJJBJH"7&�i&N3 VJ���4&�2&:| 8&c z�80�� XJ  3& 3f 6� >F(�^05J6& �!4� 6�  :���\"7&� � 0& NF �,!�� �7 �p!%�90$���ELg d .:AtV�V%r+B&!f 2|9&E�n!� �p.N!(1 6�!  b�!���"F2&� � !v�� F.�B�!Z�!^*x!�6 �!,V !X%(?d2!" J^1& n 3& V0J�&6>B 3& 5!!�%� JP$&%H"&FF !0�0�J�JQ/ *"�|��  >!�,���24 � , >6 ��#.-�3g>GG�(d�Sas�)�Rito� 61*S>�1RT:�RmR>~B��Y37E"?Y"� }?l�o2�^ �F!T3 h[:moT 44 quarte&�qe �$3^4=81k)In "�M Pa�ai%��@�M"�)�"7&O�2f), f� ing �Dwrv���) ubse�I[ "�4676*C�118,621 -�s (Q116,593�� Zf ) + arrvK�6} @ E/ ~2. (S1�� nh$|8 , soT om|�d�;T�shoV�e� q5/ �,u5� e�� �D62�rt]�qY>�^�3:�-�% .~2 h$� ] l��6AiJ� $I< J� lHI� $E�-WMD�uZine3=42�J�+U��u2_�L�.ls� 73ωIn �4 2, %0.730728 A X.9)�� I uni�2�in "�YU">  we/�yct` E��b{Tr"" 6-1�F} A0�wo�,] Q�"�7 {i-15}M�_io->5 2�7{i+.�H�9��A?��_W� __3,-"� �T#��M��blects� 6 b�e��/.!�.�]�:�`?IUir5��d��uQc�=Aw�� ��L4�  b�I�8bD�R��"�+e >n�:,*_eA 3/�foZ1 XS#�4�;6;�?$(i+1\�h�����T-�J at a��6 site7�Cig>�6ro(�Y&e ta��2��iYM�lik�f go. Ex^�F�B�.g. $H$%qi�!�h"�T5�>~8 ��� )�.X8�!�$G$�Y��vanis'S r�F. FՑ�1��I capp!� i%�!g� m��$-s�d�8�#ʭ�]n�:�:� ��L>h-x, TG�a�J&v�9A��B�/���4.,kF.Nl b"�g�(1 0.05 bit)z!% #% �n!%�J&�!� �$�& 7\\ (.�  �D(HI� v  5+ �HK�l � �LHN�-& -B-� �89 %~HQ&-.$-87& -69&-�!��-)nHL&-6-6�I? 5&�!7~0HG&-Y-�#-40&-� - 8&^6� 1NHM�-8 -4&_L� 1& 5^0HB&-Y.-. -79&��1� 2&-��B�HP&-�"-�0R-M� 6 @k �  �-=HA&-')� 39&-AD� 13&- ��?34&6|HO&-7-Q-�,�.4&-�-5S0w. T}23&10 EaF\\ C&-4�/7359&I�!�AQ�8a�!� 1&51B�E&-91ns!T83Q��A�-.�6&-27%� 2 &�K� F&-7! �--95&-67 � !�L26&-1�-%NA�19 &24&E�HD&a-12!� 05&-81&-4!$3 � 32&-I1�A3 H1&A 49\\�)J�H� I& K & N & Q & L & G & M & B & P & A & O &C &E &F & D�J�*�\\6�S*�-F�[ } S Q[�����m�@���  nS 7 . Ca�&�-23�E= ҹ�f$ +Ned!g).": �jsX_RNIA".2\ J�  e=�,�GOl����נoU�gesc,aqz?*�l, '��wp" B&�U�\!=���r BLOSUM �xTHeniko�b  .t2)!x�H�� �Ion�d)k �npansA/�FgapZ �[!� vari[]� f�H���1 A�7)� ��s�d�Qexhaus�gall-a;t-�E.� �`�_�PDB� #E�!��_!�dMWi���mM�$Le<aq�ce ��log"&rB0%& F �s n��ir � @S�Jt�c�2o�ty"��R�Oct�2,�H r860?q��AE27,1811=6�t��f��c2qz!p!AJ�iA�Ih� a Z�~�BAB%�m3 :vuI�i��. Fam��a�3+5�6 [ut���.!ld%�82, 4, 8, 16, 32!� 64� �h "js ;� 4� ��ag�M.;�"8N��@i.x�e� QW!zll0.5.�1�U�wÅ am�HJ��)�y53mJ�A6"7�%���A(q��%?�a ��� ��&�]1,143,91^5.Gѷ ���l���@�1�Al�eW�eN.0�qead~2��j A"ѫe�8�% ���&< A2��: 5z.2� ���n�{��o�i��%�Mg J�H}a�i!��GisA Kull�e-Le1rL�q"A/��qa}%��e%i&#_ +�� �BA���our �" 1.05���cl��e�"�&8�"�8.��R�TkA�"x��ie. j repen�dmploy^m# &Y�by�$ dup".�� re�� m;�smI��?�zm,Hef�8.al�qe U�Q)3�So���S guidaG�jy������ve-��di��{hpQ"B�&�k ~2G�snj �����9�ZR�so`�f�:!�A&ip���VUs� comb*���re�Xu/v�8m�0  �c�{&�t�f�  "�s �,geometry to �{a"X{%�}�>Rac*�K"�| #q �eC�Y0��r{ reci�!:q�s} "(^BN7%�TR0(��2)ꎁ�notH�pri&&Q�tydx��ogpe/y� [�a��^I�>�9���� error. It�%y��DxUJ(d�D�djs , w f��0pick up 1,000�A��F��6�M1*X root/%n s�ed*�q($drms$t�OE�a�a�499,5t airs�r�Tcoo�k�A H�:u�s�e�b� i���h ��]y� �|(Tvg ��dԩ��cJ&I��`[�K 2{n(;�}rJ{i=2}^n j=���(|�J r�hi}EKN_{aj}|-bi�Y *bj}|)^2\a]^{.Z"�Mu�9}�MnEBai}�I�1O!�at��i$ 5N $ �!k�!�s6!�=~�6[r $cA%}�$1�)ti�I )�u heI��� f&" �:�~5��M��c�Ha~�K�+an [Y133\pm 60$\AA ,wB�r�'sS de $L6.=604 =365=ȫ)@A��dM�&�g��clmOe�b$0.33 �� b�SH �Ar2.�==�CF��D &I\phantom{a.}&J2H. &K.&F2E2C2D.\\� e�(!�)&0.2446&0!�,&0.452&0.39807926�$Sb�ar2�L110F2R06 219^8F17^21X1H >7H r}{A.�}&B.&G2L. &M.& N6O6P6Q.\\N�0.347}!2! 390&�D044[H0.5�0.5w;0.2%O50�7J�0.163Q19%%%k365!731i)73![28^�061�c&�&�� ��;}ċa���elHMM�6�,&n~�V,��snf�r"x^� i"8N�Q�� y�*� "�]�w a Ma-�) �le���Ka���"R � �-% � cF�M&�4*# �6�-!. 1u �#ls�1�. Q��� "��t� g�y6A]��choic�%a g|��. trB� play� *�ro�A� eful�lo!Z"~%"�0�Q ��q*=/�Z %"�-tob#. :0 _ ��al � )0I Rf� a8erl G�2�/W0�AZa� ,.,6E�! ,�eas�rec&D2f=2<>�!$ f�017� e��=E�ch survJR!QQ���mTOQ��dPux�x�9 �120I�O� -)&� Qaa��s[��܈n> JE� s��A�o�$%er (�.�� �C1��� ]2A/��&�&rhI$�3can�%YAe�G# t'A�d�s:A� _1$-�% Q� _2$-�%  '$-$h�_-$-$O F�� '_+$-$MgE�TNTP1!�0 $ 4{ S}$-$A0{ "G$8j�[D6& �E� .�  *�  vi!�9`%od� �*�a2�!�*G !�\S:�)s�ialittl� m:|r�EKinguish"� *� �zc�"��!с>FJ *�$Ex� ��imp{�ȼN\weaKns�&.�s to 1D@a="� a { becoa ![���oЫ�C�� x r�(AE�b�P�ly app^�7�3�"�2� �:x��"���"� "� � $smj2��a�!�I6� �"|�_ 6��.�of 1urnA�H1haw�&@two lines are the�Lir amino acid sequences aligned according to the FSSP, while the last two lin8r \global Needleman-Wunsch Xment of @�conformational code series. Lowercase letters of �|s indicate structural nonequivalʈ.\\ }\end{center}\vspace{-.8cm} \hs��3cm}\vbox{ \begin{verbatim} 1urnA avpetRPNHTIYINNLNEKIKKDELKKSLHAIFSRFGQILDILVSRS 1ha1b ahLTVKKIFVGGIKEDT EEHHLRDYFEQYGKIEVIEIMTDRGS CCPMCEALEEEENGCPJGCCIHHHHHHHHIKMJILQEPLDEEEBGAIK ...BBEBGEDEENMFNMLFA....HHHHHKKMJJLCEBLDEBCECAKK ��LKMRGQAFVIFKEVSSATNALRSMqGFPFYDKPMRIQYAKTDSDIIAKM 1�GKKRGFAFVTFDDHDSVDKIVIQ kYHTVNGHNCEVRKAL �8...GNGEDBEEALAJ�lHIKKGNGCENOGCCEFECCALCCAHIJH � AGCPOLEDE7B7 I.IJGALEE7BFDEECC. %�5Ơ} Holm and Sander (1998) gave an exampleM�L $\alpha$/$\beta$-me 7�cluster with four members showing different levels of sY�psimilarity. Their PDB-IDs areIn0, 1ha1, 2bopA� 1mli/Je�)�0was taken as aVframea�$superimposi�otherCs6Sal �? _ from highlow�V� Taki�-he scal $factor fore�CLESUMJbe 2,�us)$-12$ (Cgap-openpenalty0 $-4$Q4gap extension,�Z~�֑~ �A!l i)�,n in Table 6��ere, in� firs��,�� �? �?%?4also given. It~tlongeAF an 8%Fstill !:. A H�J�o5��Zof�I !Z-v8s of lengths 13E-214f1�[5��%,FSSP, but nonce �een!B)i�}�s. %�J�'( local. Eve!Nough aQ�5Z$ algorithmAa usedA=Lis does not guarante�at�fAjD(correspondsa��ptimal�H�hI (on. HowevernA;de >�(affected by]$domain movazsn good�analyz����e evoluE. For�� �i�helix!�1haa� shor��tAPieE unterpart!�i(by one turn�-!�)�l $N$-cap (�a]s $FA$)l�p ~tE 21HH 1u, A1%��U!�4closer to $CC$ x)|q�s) �$HH$ k negay� s).%E�<$drms =0.84$\AA)M{��,includes onl)�1u al i&� . When wea�p wo,� feaa���at)!9ng5� pre -�to ��te peak density�rib�$f �0 =]�0,. Previously��*based}�  a duty m�?heavi�;���B; , so��ha!� st�e^a��J6�jvk� ��-}(to run betw� .� 5��7�s t�Wi�estA$to see whe� �lI� cad improvS��( directly ii ezj �^ helpa�6� ��a��? uUstudy. F quote� } {T) work%" supp�d!�p!^ $Special Fur � Major NH`al Basic Research Project%F�(1Scir F� E�China.}'�$ %\newpageĠthebibliography}{99} {\parskip=0pt \pari�'t%\renew� Land{\labelitemi}{} \  McCaS \JA, Gelin BR, Karplus M.�077). Dynamics� fold.� �Pe {\bf 267}, 585-590.h M. Flocco%"(SL. Mowbraya 95). $C_\��$M�torM$ angles: A�plRolA�� aꕜ2�hanges,!���1��04}, 2118-2122�BH. Park� M. Levitt�� ��lex�8a2accuracy!discretaUmodw�=�%, J!l. Bi�<249}, 493�C507�PMJ. Rooman, J-PA. KocA� SJ. Wodak� 1). Predi��� { backbC .? ��R� � assig�s: Influ. of �Dl � aesR�,21}, 961-979�C:�D.2�>�j�in �s������x�R�8�565-575h LR. Rabin�u,89). A tutor� @on hidden Markov %�!� sel�_ appl {�Rspeech�T ogniE�c. IEEE)�7a/257-2851+XFujiwara,Y., Asogawa,M.m( Konagaya,Ae�894). Stochastic ��-� �J��435}, 1501-1531�HT Edgoose, L Alliso�R d DL Dowe�78A�n MML cla�fM�� mu=V� s� ���q�sAP�6Mi 3rd Pac^ SyiumaXBioA>uY(PSB-98)!� waii, USA� A.C.CaZ0ux, P.TufferyAP P.Chevrol�(J.F.Boisvie)!�S.Haz� !�a�J�a� roacTr"~ �hY dular�Dof�1$�f��tE� ��12!�063-1073� Neld�J.AM�Mead, RE�6���x method��  minimizR, CompuOJ. v�]308�S31vU.Hoboh�C.*��N@Enlarged represenA�v�F^c322-52u�W.Kabs� nd2y83dɸar��1Usq�&K : Pattern.[�,hydrogen-bon�ggeome� al 8 $, Biopolym�%�2!�2577-263�WM h (hCyAof2[% j���A�A��.%�l., �} p 333-34"�S Henik"JGA�2a��� 6�cesI5�block)�c.� l. Acad.. . USA �8�0915-�#L "�C6�, Tou%(17 @ � Dali/�4 Nucleic Acids&V )� 6}, 316-3w, > B docu�} %�` c� \par�15cm}{T�3` 9r&ag�f e�'3 �^@U�"es.\\^m\small"� tab�n}{c r>}\h� &�$I$& $JHKFECDABGLMNOPQ$\\ d8$cccc$& 7& 10s2& 2564& 3 34 3(4-(3(9\\]e]Xb ? 1qD ?1# ( ]hJ]!:]� qX#S3 ]eN��9�X! D?%+ 4 ]h��! 3 6 b�1�2]ee%�5:+># f ]b8A.%![1%[N� Ng2)�ee90� �h)t�!�)�%B�g�B2]emEI��? E8{ %5 %ecREl�q9���tftejE��>-)t)�>a�N%VN%� ]e� %�%� %�AV ( I�Ej 18�e��-�X. ]��R�1 ]f\%�% ��U I� %I�eb\e�4+X3E�2E� )`X9�(Ŋe�\n\ee��n����� �!�h��X98 b%�#ea2Ŋh����>� ���R� ]b�B�a� ��.N]%j%� ]j�+��f��X%?]h�se�E^� +0 �I��� =h�sN gl> �N�z:�f( ]ދfX{ ]h, ���Aa�1%t &+^b%ea�  - ]b, &^Xz ]!t6�4�8A8� ~?v� �eEC�"sp 0.01$&10�82& 22 5332& 13B9Az5�5�2A�6�642 S 4<2�Q� G)})�:�%6f+P 'J�4��ward tra�8rates (multipli� 100)<"��~��� &��� $K$&������������6� 28&s A�.!dN!�4!�&E)1!�0AVeK 27&  ..RE?J J J�29&J7!�xFJiu& 0&}(J�"F1&�A[2*�6&�����vA�Am!e2�:6a��N2VJ 1& 1Jy�7&E� !He �> J�b2$�"&!R9&%^J%���Ja�ag0&)�7!(.�% !A"b�!DRRJH.2>.R!@�F�0���6!R� 5& 1j!��]4%r�B!NFAdJ!4!< $^!(~ 2pAA~F|J B% 4& 2T \��&�h .�$!z$!(0%(�2*6" J�6!,3&EL� J�6:& .ADB�v!�+h6��.!<��,JQ�.2&N&$!� !��J/�\\ s�\'�`[11pt,a4paper]{article} %j'$,twocolumn1H\usepackage[dvips]{� icx} \set�+{\oddG((margin}{0cm6 a$,width}{450ptF$height}{70FopY-2X$ \title{ V�"�� al energy�$x���s } \author{Hiroshi FUJISAKI\footnote{fujisaki@bu.edu} n4John E. STRAUB.straub , %(&�+L nd, %Tel: 617-353-6816, Fax 466)\ \\ De�"��Chemist0Boston Univer�$, 590l8monwealth Ave.,F -T, Massachusetts, 02215� Eef\2 z,stretch{1.5}�QW} \make%v ��ab!of�:xC8s��%step to�he goal8A�ro;5�d�()W(DLZ02}. Du%/? adva'E�techn�#�6re�,�-m812��Ni;Š.� u�CLLKH94,LJA96,MK97,SSJLA99,RKYSDC00,WYDRSCSC00,XMHA00,Fayer01,CJR01, h2,YDC02,XMA02,MNTALF03,SZDRA'�4se6� work�fm�!s�&3_1N9ic� to der�(� �1f�1ex�8>"�� alon7oF^ yat'&-�p�] s caE�vidaRreR�. �6urn�7� � Dbe�/S- refi�&��e#�Td�1ireu,force fields!A�0&�.AU2��.�=��fQu> �WU� ha0gun!o blossom. ^72g�m4 fur�->&��wA{iVc�.��hip w�7bec# fruit$1 A7F�.�Ptools (Sec.~\ref{sec:!ies})�velop){�+:>. S{a�q,:# E bE�lai#?by��tu/>ve!f� s&�*a�.� /(�)!� bath>�cytc}), e %usw2 peNq�3b�4o�1ricrto)er�}� "�#5�R �9is�5, weC26w,us 1�/c��ҥ�es� ishe�>&s9�5a�ent��er%m!:��he A� :���T� } d.6� � 0,�6|s�9zN E�pr�9!�%yf�v8� most�/�1w=oA���m5I� dealɘ � liquids�1l or g�  � rea�>i& fer7�4;5of re1$ � ew�0Leitner05,FBSb}. W �:�8wo!�tinct _AD:/ �-� d!�.�YDnd Fermi �/n rule,H @/he&v J�A� MG la�%Th%Kwo�� Q�d belowEub-�{J�A�5"9�Ui[l� Er� "m�system��a� , (b= c� �2.j; weak enou�+!(c 2@r ssumed t�7�5rmqu1 E��5a��  ! �i:ory!��$a2� pop*�rzn t� J. \� 2/ "Cheqnarray} \frac{1}{T_1} = \tanh({@AL \hbar \omega_S/2})}^x \int_0^{\infty} dt \, \cos (D t)  frm6y, SCe �(e.�,��,above bracke�Es aN�average.�C"�>� itor�m9�$is very ha�o�Bex lN6lca5 e. Aq�, a �+< e s# e.�prouC� addre�'is limN. Aqb� ��>s�Kfu&�es1� iov�� �ubR�!��2( LTZ}f@ vim�4؁V!<o \D���}� ($m�r$arrow 0$) :Eq.~(� u�)J,�;^e�cl}�D m2i0JB~U2;cl}(Fy;H�!�Qs deno|a�"�Qq� 8c�iCV� (LTZ�!�Q bw e��!wW P8���� WWH9,[8�tegy �9�A� SagnellaŇS [� D0[of CO� Mb$^*$CO bSS99}. a6sh�>b�0Fu�,� it� s qu�on�A�YF:6 d��� effects. a�_ ,"] *_ b| ��9%S!`LTZ�!�<&?Q^E2HQCFmHiBalter�@v� >feS he ܅��� (QCF)b !{e+ ic2f?QCF "QH���?Y*+d>� y=y� og1�P01 �;tM�d I��?utoRainR,Ivfi�ex� n9VA�� $1/T�!c_1�1�BN}.�imeq �IQ"7)}{Q_H#� C�� %\tilde{��}�ncl};*iqcfZg${�%:!�.�pr��e 8  $2�B?a�=phono�2l� O (harmonicqJ~^) 2�2� }{1-e^{-��6F@0#�>�MQ2F  � ���M V $T_-�!� \-�%�=SVF } %N0�D !�t) %\� vHf� �s+>I %= [��2>_S}/ 2Y] C U� }��$ �Ar�>axa��l :x \gg 1$%{��2�1L�|i�HI�O�c: Qb!he�Eresona� (1:1 m�n2=Y�,_S)$, i.e., 6=U cl}$MO4BB94}. Skinnere0coNer�@i�5!"�M)e�organiSHes expa�nE ariet�0 QCFsB+��*�-�6 ?F t up� Ml�7��sm�VER��6�o��"critic(� HSO99,MSO01,SG03a}, 7*D��q�e�s�b�= well%��cLNMS04:1s2v RR>2'�Ed�.$a��&+ eartcomingWAh��A{�� `w&9 -(Z��ch�{lo� a *� piUR&v� . B���ent* � Hamiltoni�  teVI�O?,�|iA'F�� H} &=& _S+_B V}_3  $4 + \cdots_/S K��$p_S^2}{2}+ � q6>B >sum_kEk 06E q ,�!4atA�&�!8residuMJ/-�i�ed2�ly6| �%���1}{3} �h{k,l,m} G_{klm} q_k q_l q_m� V}_4:A42A,n} HCn2D q_n..�bJ�CYQ;H �is.K, ��amO9ng a�6�6hVp  weH" lowest orE"o aq�2�F�I4���� � (F*��2>um%�� left[Igamma { ^{(+)} '}{ ^2+� k+M� {l}- S)^2} +�MX M\no_ �.�"�.^i-n�����M:��]]�[ Z� J�\ k,l})�}U%̉-h(G_{S,-!�Wk�{� (1+n_k +n + 2 )e�6s-)�s sbfq�1/(e^N� k}-�De�ka�J� p�&RD, 1#2�a�}s��ul ad/=1$a�W-wv&�Io�Y #w�employy$% origX �Ful5(tains delta"���w9{ '�amAN $iq$�broadrR2Q � num?=���xis�Kz$|���k$���/ eEadudin-FL6 MF62,��b�Y�oW%�W� decayA�  coll5�H�MF}a�  />��t�ęЩ�) 9)vJ�S �:.Caqe? ��F���a--i�����>�>J�fzE?!wo1��Unly�VY! ~0U�u � \YW{" of+ �.�MXKTFi e/FblysTct trea)�Wh� , trunUd�� �. *I . �Ph�W�NtuN1 G, error (`"QNQ�Y`��n )"��( riou�(�#, e +a�� s.�a�#�te�#� must��to 2�""�,^�&|O� (:)Sr)} MeR)co�%2t�Xm ( inv %���(��Wut�P:%  (t)$�ear�RinR} �H&�Plevel� Y�Shin GevaMg� � d%�mi*�# EA!��iller01}%��I� show�at cKAs�*�of neatW< oxygen (at 77K)6 be���E\'kyNi�\!�. Ui\\udyU��n)��sW�(�%�aa&�&to�UL?fct� . i�m5M:i6<$!ad�E�%U��mA܅� (t)$. Vai*time-&�='-�Pis�(�#Uw)�4JG99} or pathe�g�4Q� &Makri)&Y�c*A�6 e� �y �P P�+Z# dy"s x% |R�%$KR02,PNR03~&T"m%Jh �:i!sB� -BernK� a�6� oldsC"�e"�+ ,L, M, PollakI�H\"anggihLeiG �� _J:L��+*�&��PH96}j :g�>Sa �q� xpon�E��-ig)��u<)-��\ ���j�%}w���% ��, :�!� $a�ųc+CO� . %(�r ]��Yex�V�R%x�\.) \��Non�nlib:�.}� ��V#Q��i"J���kJ�l Q!p�s5 &"k!XA.&m���invali�Ss�%�t"As%0��!�&�!( phenomenonilap��/2��|�/Hquite nu.alFD�- 7}�-:�&:((,�まg��!�� �/}[re�}&uq]Hen�1Ea�1 Hochstras�,i HEH86}.�conju4+eZAVi"-*�(M�,a�ey"� }��,ar�.�of he�o 0in Mb�cyt cvacuu�#}�26�-IA8 ��H/:A�rt (1-4 =0�\` (20 ps�� r4|)qTgaoka5&o carrC!ouɪs�cuSWin.� ob� �/ 3�-�OHN�I�-�Wy � " .�R�+l-`6�r�oH �!��%��%I �Y�t5� wa��.�.j . e��[ execu��sm�"� N!�%j�k. N�X����KMb9���  by��iv#.�� few!�a<%�I�SS%} Fu�*modtA�sugges�5�m�`doorwa3Lis d��N6&h prJ�!%,&����i �NI�'8,.� 's observ�I�WuQ)�*�X��5 &:�mu0M!��Mb a1havM Q,; modifaEJE Q�BS03aR ey *in��d%1of:��i�Y�!\�s a bip�^c2��)( �4!�$s: fast (a-�)� (ten� �I�b Kider!lԍ� �.oz a* .�* SMMKi T!e�a M�.��)�AI.� V8"1 (VET&4?Os�$i�ll~, VETca� by ("�5)(� ce: i�q�y�`ct5is �c �� B�.�0>]e/)� e"�VET\#��%B_� chL izW2TP)low.Q&��H& �]�h&6 w�5s�i-��� w+y��l�|y�am�AA�)M`-M3a��&Tac7-�zaBu22a�rd- �5=$7 (�\� 6�.�(}). %Nguye d�Wk68in�2 tane�=���yhI��'0tt95,Keyes97}!ld�aJ�R m pept1in�� DNSE�  &�f .�y sec:`} � all 2AO�&st� s&<6K� j, �� /Rrc�� up 0N��thelesse3se"� �+4.�0"1in in��b�-� �N�'T$��� b-}�ly*gfR �|�.ronZ%onA� Hah.�e�>{�b�Av�� 3ro�6lXenviro�[Q3 egreM4freedom)�U!�pump-!eXtroscopa4G/m8ophR3,in rhodopsinM>$HS00}. Flo�2Bat�a,W �ps�leW, .�e�eil7]Eon�56�� �0wo (chirped) n5pulse��FB�4or7JM�&� ���7s�* Es&J selJK(TD-S&&�T. Notab ]: S"&!6E !"GN�8��u�E  (BPTI)-�RGER95��^b&�g*� ]�!.�mo��1B�' 2Y��+�qe,A.� �cQ�[ e,&4!wid.��!�2fof�{AA-gLs�like CPMD, http://www.cpmd.org/) �=cuteT edge���]!wa2 ��A.�� bact�u 's�%toi�rinY� �8.HstTby Hayashi, Tajkhorshi�SchulJg��HT��IUir&�, a>bq5.s��vdou>bonds ��1�#��:&9&�!��jq�Q��� �!�-�a�:Y. DX(]�,�!�; nonadiaba�^M �57twe�+G 2��(S$_0$�S$_1$)�2ch .�s.�ly�6T.� pk�!G( (C$_{13}$= 4}$)��ezdi�dlly>+���"C� -@)kU � � ��vin twistaqX:i  r�@n�l�F�Jly^<- _� ���osoftwa��s d e� ��R=�]pQM/MM�: EGO (}�lrz-m�vhen.de/\t +~+h�>8/ego/index.html PEACHE|staff.aist.go.jp/y-komeiji/peach  ?��{C*�A2%c�7V�6s&= focusa5!�-66? (#O'a�ew!`�5�8etE�� ��71�&�1�reasoP7� T^x:8 otyp`,one: (a) Cy�� cY7�ZZ�I� 1745k;0� �w  �;� I@�}I��a$lysozyme. �5��"<X-�e�E�"fZ. �5 �]'&��qމfere��ic2\e&KaVon h/9re summa� �/Wolyn�2nd*B\�{WZSMW9�WaoaWo* dtz-�"rE @D�Pir�^^D7= _,WR98}. Garci�Humme7unt, omal �u"�-�} prdtpal� m�%� �:� GH90O1w. ���I3<�lQ��%h� BE V&E�eVw �s �*�(in: QCF}%>X# ��*!(B5 (})�!�A�theO e&�C�R>D-z?*?2&?p#Lfigure}[htbp] \hfill�9er6i�:phics[e4=0.5]{snap2.ep;a'4cap�{ .� n�8�. O�q80{E4ionine (Met80)�idu$ 3e�de�$ed. Releva�;Dtoms (C, D, S, Fe)+�cC� d�Ois ��c/iVMD (Vi%r M�Bar �i)-JVMD}.�H�!fig�T� [}�GJpAEG� V�uEs} 6(i�}w zeEzHach>�=Az)��RA�6c �g�F�g"� term�;��yleof %�A��Fig�>5),�2� )$.�mU r�km CHARMM �  r�smD)�z r ��t 300K':��+ɮ�(|%�("�$e��+p~Hum. Witi�CD)?&�$�"<=2133$ cm$^{-1}${ndV2\0 cl}=~�1 |0 0.4  1.0$ ps[�ta�,e*� !�� � $1.0 =2.5=,b�$M�v� +re�m}{.42\HI�%j9]{)\ _ave�"J \1 M�hspec_~mV�Left:L�9#n�!A8� � aIG_?U�R�: Fd�|zIru�FA��} �Urs $ P#bar�"� eeU�:mSi�0]F�is�t5aU�Rntvg��oQ.d#r~c , �no� � lapp �y���!`P ��I�% no ATar���1 (1:1�boM��|e,thus neYom-B�Kr2FC�2Uz�'$�U�4a9"D1. ~2 ]M�wbsw�d<O��7��*A� S -�'A�5��� "jby� �of2��,%�T3!( "�5-"� �7is-�q7���"$ion} Q_{HH.v6= *43A).S(�y�"eq��HHM�YA&�8C� 2gi� �)$$ea&|zi?of%� 2 O1wy5f%[E�a3re6A)? U<�-.�)$ be+�&�B �.kd> ��! ngXi� odA���-Scho�G��-HS2�*o7!�\sqrt{!�&9�} :�,5$/5:�SB�Weu�deci� valu%�Q�A$a�Q3s%��'\I./!Ta&r#coeff_;7D&�+2{in R� �H%*�!�CDIQZ#t�x�w��t��N-�"�@<{1655}$ = 685.48&"�1 {3823(1443.54)54ere $|n1� ^D|Z}0.����� dard&m-x .!�m�� be "&hRo�A= �*�.F>�.�D2�?�H�A.( / � =A�]�)/��S)=2.3��2�] ~d6DBf8$%!OBg6��u� f 6�cl}/(2.3� 8" 0 � *d V7%�D "J�dQ� xs�U , Bu�ub�FB*�G�Jk� GE�*�:K &}�| *oD�WsH�iU�n{yt c. E Wg!u�,�et/*e 7.3�- ef``� '' 3M�#�G!�CD ``L.'' U�/:��z$ �W{ �R(u�$CD}=2129.1}PW���s A,3330}=1330.9C,u�${1996}=829b!��=a�5B) {"�F1 � �?�.$ (6� VER}).�)�!end�y�! XI)��qJ&=��s ~"A�B-�F�"4=11}{2}80?Xial^3 V}Nz q_SNz k. l} � 2Ot18ij} U_{ik}U_{jl�1f�=K_(\D�2q_S)- -}{2BB0H$ _�,$an orthogoK�x�diaizAAy(2�3) hess%: 6� �s"�5�*�v $ �$�* (\pm �{S}!@a>b } at�hifa&#!Qi`&�.a�/od�!t��A $>�$��f�i2F:4�Jeq��5 .���� eq 0a�p�8w;,a}"= sub-picos�sp scal� re*AeH.ed*�� L (u^{EJ�� =B�)��se�;-�N�S(er�`,fb&�%B�(1�by �4"S'� 0�In��7!�F��1_).�"�ce:A���* . At�/1# �Q s flA[�2�&c#Nۂ� V�"�$�& u fl} as6�Uzero p`�N �T�1*$2"xB,�� ���# VER_�:�_/ _mod��j�8]t!jsbnn�Q�!��;��n<3�@2� �U�B�B��$�!�.;TY�j���Q ʅ� Y=.�:��:E6M l2&tU} &LiscwSrB)�2�.�\�3R��(measu/-!����!a�Kas &���$$ ;��V9(FWHM)� � $����9,}�6@13~"�.� an negr_�%om�y�&ez1�B�"�B Aݡ� ��F�T_ɍ 5.3/b� \,(�>ps�L�eq:p-�&}��&�/���"oL pE;�\s _�)�1� ��&�^�62�M�H)� PG>� )Q�$A�a�Wsby_gR,`W2p�G})�( NMF�$��i+� is&�t ��&?.oSq"e} (4357, w, H ��!I�a���m�9m6� )/�@A+FQ �"�=+a6� He$ Ed! ,� �an saD7C.�]�2!�too)�. O)��Kha� "�_��e�N�� � < 10*a i�5�>�d1� seem!��eYa[5 NoJ l� at ��s2��d�980-3D,� ~�FL$ euteG4�h��eth&T l�8} "*-;-1D?U!S.VI��!.y[.� 9 �; "=8 "R!absorp� %�m:� DFT2` !�A�-"|ȉb�!qult�?,Matt Cremeen�riv&��u%� ). C�V���;r]_S��e�8par�?s�s@g!�:�s� -l how"\#��&MNV I=��O�c*� aH]-y=E�" "ZCo��Remark75I!m�"�A� � �*]"J:1@#i9\�5��uV�ZFYe-�!%-6�d� (���a,"oP'e c<0!���>�� ��*���. X-:� � c%b ^5) >,e , b�e� es y�^Ջ !Q��`����� $�vU��?a��d�_d) "`6��BL. Ourz# demM��'��feasi,��'ac�3a�/&�UU�K'���$%�M��&^%ad$!�dismB%2�*�$Z�M����?%n:�%\�Qod!�H/d*e<evezdor"�*R)�Mk\R �*!`!�s�I\�bew%{\iv�4ri}��L��#. uppl�?�M�! �s�Sy&&� *� .. . Fu�/&�5 G( �on�7e0X2�+�asi�;pp�+�*! high*�(CU7)H�T�.6(de>/�!^�i)U�i-YXVy�Zct�vR�!�-�w��jq"�!�=PZO� c��&E�?th�2WB"d*�E| . More)1, -� Talyor ��Kg&�'!=*ho7@� nverN-�p�!g�t\/s  O}�pre�CՅ.% _��"�%=:'s� a!هa�et� ~ �%��c"th-�9."�3 �3)Vp �%I 3we���n!�Q5suCaeH 7YIa��$es"`gTg0m/m Y ��an unbh'�h��w0o��. Act�, �2JhiX5t p�hia���V�^ @ &�i6o:8 (coarse-graiIq� ��=rE�!c� ��&K?�Y�6r$�Z:" �$-�K"� �L[``ab �io''nt&42�tE�[a rigorz)J�>/�D-t t�"�agy�1� ��mSMZ*��c%d=�:�S:d gard' $�z hob"�X~ w /.яa���ym� KS91,CV95��U&;.A�A-at�C2�{�r!� G.  vHS97,ME�* �#" %�n�N�es �!"�bJy@�3q a?H\ A�4/�!��.�G *'b4�9!E<XB#'d-��~odse�*AD&�ZY6Promi*Q� �# no2�@��.�?b)I�7Li��D , mixed M�-�h6iT�T/!�2$1:)"G. A@Li? i��I����tF1�A�s,I8 �lal#=b�(ra� ��*x data��s *� N�4r 2D-IR signalђWH02,KDT9j!�case, w;�so=��EbA;�AJde�<ngIco��nc< a�l�B�.^C*� I���"*� !.x�f annoM7��zA6@1^�u��qF ry Q7��$of magnituJ�D h�m� �RGtX,AeA��*Z�2+aV0"it.�a�2 /L%�a��"�nA/UKion`a�@� 6K#actsios�u)� tely�^nu� c mF5��A{ZFly dev�q!k���; �-�"C=���?� ў}q�&�: m�}�a��r�u"�6͖)�Ii yA9:aC�E�t�d �q�� . G� su"U$ 99@p,AK"*G�Y�S0oq 61���Aā.�a!K�2�Gs� �:&2!�E�NU?!�"N ofN!��p'I�yQ&��:� a�Je6(�2\ )X nc�1c&�1�� KHG98,KHNRp�b�=n�45&�1Ai!&H*9"d Mergod��? vST93}5�a@��ice�F� %>&�;by]9�HL�p�p}, col�camF:.�Abb.3I� �A�.a8!BR(1!�G surfac���S��a].�w$E )�lVRPK00,HSSNK01,TT02,FFMP02,Mx9&�rM1��!�Q�.6�1Mb!�)ees%� rget�Y=��s# &xsi�?�j��d�/�a7]�%b��.��.,QNME_3rd_4thv/.0��.�3dz�n1C'.>t 5V��%�Zf�E��6' 0RH)})�1i>#��CD���+�$,$ 6 kcal/moli 2��4&�# �4(e Boltzmann�`t"vR@(�"Q�p.9*(QNM)� Q��E t�/y� )�y)2�)F s}8.;�k"�"d�a��l ^ 8A�4thb@ A.*a��?%a#�{3D�� 65JohS�t"CG�&� ,I�'�"1 �3in�d :? in �r/at�<o *� I����MR>�6:�. B��w{Ac�9l%?��W��@ank Dr.~Lintao Bu���abo O�%M.�!B��# re g!�MkM�!� {*2n�(CHE-03=1,�~*�~'s Ce�^v���aRA���pL(/u����>thJa� \bib*�{BBS88}  QB.J., Bo �ec�\&-*ޗE�� 88) � J.~�{.~�.~.e f 92ؖ711-3725� l,GW04} GruebeFAM.^W�:, P.G. �� _Acc[Res`37�61-267.^�x D��@B.C., Longarte, Ak,Zwier, T.S. i2)� -�} ���Q$ 2369-2373�# �)} LfTdck�|<., Kholodenko, Yq.1K, R.M.��4 xV@8Q�$1648-116566� JA96m!� H., Jacks,PT. �Anfinrud!QA p6np100q$2043-120512q Mizutani�Kitag�� T b7 b:J7�443-446�z}"�M, D.E.,2l:�, L �A6J�9 �,Proc.~Natl.~�� ~Sci.~USA-�%�14324-92��z$} Rosca, F!� umarAF(T.N., Ye, X�jodin! , Demidov%)�Champ�  P%�20i�N8�10�� 4280-42902�&!{}�=�2}, �.�Cao, 7Sheer�i���B-B �$10789-108064X�{ } Xiez, vanv MeaL. Hoff�%�uvaHi�01�4hys.~Rev.~Lett�8!% 5435-54382%4|}  a"D. e�1 TAnn S ^.�5�� 15-3:u�$ } Ch!�J.KA���ez��պA/E �sJ.~Am��SA��(12I�2426-2422�q2�q��fq!:1846-184q�YY}} Q�]P�J!�m 5914-5924!�nX�}b A.F� \& Bv)�F�o8Art. No. 018102z��M4~} Mertk���No�F(W.G., Thomp�T��Akiyama!�, Lor��R.F%]kEj3MjJ. � Ec y:��4-!��~� �L.�N Zimm�wnn�z, Daw�P.EyNt�YZt6�384-3385!�&�+ ��M�5�dv�%�}�*Q�,MT2}*z2��~2L��2�m.5-7�`b�ain�NH�Mt.A� sis:�Co nd6��� Ϩog'� !� Sy�ys`ed�Xby Q. Cu�]I �harZ%Wbs WhitnellAa�Wil%�K.R%-H�C!,T�mqJ�V%��W��5354-5366�osAem�rag6�19�J��.~J^7A� 70-8e�Y��q -m�)�t�aa6�J^�6716-6726RBB94} �[J��\& *� >V !�� �n�8359-836��O9� higa�5] Okazaki, + =Rt11c5390-54: 5 Mikam/K., i�|2h20�6� Zi!$ 9797-9807a�9��m�_,A�\&`, ma��M/)$A��!�$9070-9078 =�m} Lawr,, C.P., Naka��Ab^, N%>2 ��� y.�12� 6621-66�-�$MF62} Mara�e&` �e�196q X �-�2�2589-26062c Kenk�MV.M�okmak�� 2�1���IV�0A 10618-106:_ MYa  �*1 �))9�!�2942-295:��O$ Jungwirtht Irbs R.Ba�]� \=&99 583-160e 9�=`  !�epp AnnufU !�167-196� RR01} RabW �� eich�D.RI8Z�O!6550-6552nr` } K4 H%Rossky!J!20"P:� ^�/8240-8246oP�` Po�Q�aNy�GZp}�)�)�M�1%� 2179-1219z9�BJ`."�`B��`)M�`�%�*J}| 1111-11168HE�] �] .R.,�]A�i"V�8s�� 8 8982-8986~O�\ �)I7�ra��Z���jQ2.�.@ 3A15Q�6��[� ��N� Y7A�7057-706%�uL�Ga} j ]$I �]��10634�_3%�.' S03b^a鉖b233A�34�k�[Z M�� sugu�� , MiRta, OE�K�Z�� % ȅm)�h8!& 3970�0);%���3309-331%�%��UX} % R MbS1��)�VV2�$ 01-2�WU�X % � %Q�:=��� 2921-29302�|V NWa��(Stock, G. %:PB�q�462/-I%)i�O25�O297-316 eV�V�C�"�VV` %��� Z fY�!56745-674E�5��U Roit�/A , G.�\& Ratn��ZRp!R1700-17:�gT H�TP�2�T�S�TA��QoF� E�1440-14:�IO WBOC.$Zh��C� � , Mc�� �*2����:�)�9a�3100-3116EWpOQ.,�O�)\bitz, ^19�ƅ�F�7a�60-:. GH �O!�)AH�OA��G+ P5/sI�3�3175B�[M Humphrey�:�lk#�.� \$6) %`VMD -b�M',&/ Mol.~GG�� 14� -38.>#�"F-M29;9.�K(} Brooks, B�($Bruccoleri��� Olaf� B.DA,t�&j{ Swaminath�S%Karplus��1R�)�} ompI/�187-2�u��', Stuchebrukh.� MarcaR0]�i�i� c�6044-6066� �'' d���3%�eel!�GI���he:� 9�6762-67:��' �JXVo� G�KRX10j 4211-42202��'�a�, Huo��܂EM�79�Vj� <2541-2551; ibid.�� 6456EW( MhDyEl� i8 vF�7!0�802.�i' �_  �n��r� �11350-6A `' TerZ%"�A��"� S or�1e�5663-56:~�&�u�5s�ci" Hammܥ��N: C4� ns.~�er�!1R1035-R� .5R' Khalil�,�rd\"ovy�2)~=Ji4I�&��5258-527�2y�P#} \o�q!<Goo )�p HCurr.~Opin.~Struc.~�����164-1:7�# KamiyaV, HigoA�j�muW Hp* �� S݄&�2_233 �m�# .4, Rashk@A.Bp$Thirumalai�� �*pZU�]2049-2>Y  #} VitkupT, Ringe Petsko���2V*�Na?�JX!�34�L =�z#} 1L, Sas�J Shir �2a\& Kugi)��*V �- ��5961-5966D$} Trekq~Tobia�`E�q!I�*� ��6D138101.^$} Fenim�hP.TFrauenf���McMahon� H%�Parak, �6���I�047�>��$ �i\![.{F�B5�53!�\ t:9 d�� p:w�{elsartX� *�, [a4p-8 12ptV^�{g�icx}% I&e f�W filesN��epsfig�1{d٠ }% A� t�,!um[�cx��B.l8{bm}% bold math2amssymb}>)!2�Q$spread{1.6b�%1"�Pfrontma��&e�{P�� % i�s�P&p�Dyn��} \date{=u�L{Carlos Escudero\cor��cor}} [cor]{C26R*or, adne: (+34) 91-398-7126, fax:6697.!�&'�\�ce �(@bec.uned.e�"\a��{���s, F\'{\i}sica��al, U��dad Nac�_0 de Educaci\'W�D�d4ncia, C/ Senda�{D Rey 9, 28040 Madr� Spai�.��r;b8�I\Wew. Du8.2-��i ٍ %� �k�?h@}!�13), �gX�TjY"��"�Fi!�U1�goel}J�02-/0a>,sk�� m}. �4���V�64�J�!xS�ack�an axioEL�%0!R>k�R���#w�l,-�Z;��e!�Ah�2i�K deep�:0 IU�J�"�YM��D}; y�RE)maya�A�ot����� 2 Yrl}ofQ�.�41�'����)�!;�; j;�R�y�� �P��:���q;+ life�6�+�r/out�. H�_!�:5B��AdrѲuch�sincorp;.e�=�;�-*7<s"i9*sJ1Wnes3A�9�mÕ��1l> doering��A��5��%8"d �8%��l6as��Fy,+�siͥaM�%�E�k.a�^Ewev\��� p�{ual�e� �W�6hl M���%Jps���rr� i�%5is��> ��`hB itW8 �)�l� �B�A���*� .V� �A>ng @�gu�t�/V�zE|�Tplace,� cour��� -�Tn��iQ���l ins�[i��AE9�u5e��2@�h%�Ev�sng�ng&� :�LɎ�:`&�  9obegLe^� -}�L�Gy:>Bo� a�in�I57�"%hA�ҡ�tra�f {rd:X^�� s_FmaxQ �p�!~�(]>) per1�$ site, i. @�a�?i��rr�<capac*9 medium�=�;_�2� ec�"3 no:lʝ,� �<%� "crowded"!�lK%�!�s&a > AYld aFly un� pI�> eas se%3ta,��bsolu`< ne| o=2E�]ei�.�befgu�%��a>e��,�it!�e� �;I. VI{ look, seema�^ .zcN�n� no �8G9i< u�| uj��to � %I� �9e�M��] ,��,ludwig}!�de6Ct��rd�cedure ie��B"�d�  arq I null.[N�0�E,!���z!�e�;orpi,M�.i�@d-%@Cn��"����-uDS�&\��5�9)t�O"e ݡ��"�Qy�izif9 �B��be�kL9o "�`uTEO��)CanA��,�E���!�e<uҜiQ� cardy2}).����8)�� G!m�. &EG��� �ic5�s, ��rbitrar�JC-adap�&� {2u !��E  to�Av*( -��{=m�g&� ��2��ȹ� �,M�>u�ťXof�dst� stoo�Lsu� {Zp���?)andљ�os|Lw��Ha�� mA�"`D1�p�%�3�ce�s '� vely��mc�lsoMev����ne�~ chni��(e��:>�9��� )�subkIW��b�� .=��4%�Ť��!:�ed�oCOa1, 2 �r �Fe|.��\s"�C|�� mple��!�A >�jT�M=I�e e��06�i M�i7AQ +1+x.�ѦW� �m5������m<��o� �at�:��e��C})na��q:�MA��o6�M�MV��F� �s,}-]��a�uv�lIH��-��*� �M�Uopez}y�ZJ�~�1l"�dU� } O5�:�%)%y6(of random w�$rs2��l2� KM7�� repr���kNn% !�i �!�nutri�nor di� '�;$ t�z>�ed "Q� ��Btڝt� unreal �*-�)�_ :O�?r�� �Ci�sial"��Y�F��j�%: �ai e�COand/olmpe�x���!6E�e1� V-}AHk_�K� $N$*�sd�?_Vhe -�resourc�B!�� Oma>�. I �� �� �$N$�$N=��we�?% e�- ar�U)�be)��Han�%� �l� m�Bn .b .-� F�/TLet us }���SsNse:�ؒ!zs� -d�8BQCh!go-T fo6tQof Zo{a�� T (to��e�P)I�s��to��IV } A��0emptyset \to + A�/u� H $D$,u�Ad�gyf_\��dE�M�A6�b���$�f�SB<%�Bymm� �So��5��a'�����!� left �if6aX'c}"� !Ps � middHfa�nI��.u�S _��ii� �"*�safAo� .I�Lo %v"��A��A&��U�a� 3����|�Oad�C S���Ρ� re �*g eX3.����swo- �in:� V�" �iE�&p �.m�&�. ��S��edF��cJ:F��h0dP_i(t)}{dt}=i(j=1}^N [W(jE�,i)P_j(t)-W(ij) 5],>�]$ $�ͅ robaŅBY�qt  e $�| i \E<>dcJP $ti� $�$A Av�qiaE�&J )�WjW��6 wZ[� � @Q�algebra� roT�4 -s>�:0�e�ion�W��V#��2� W� �!ca�e&F� !$�eeM�{A�soI�al��<Ŵblh�d! ��y %� frens�+ oppenheim� Th:� eady)@es%�D�nA�!�#)�$Mx\bar{P}]~0)�A�D'Q� � bHr�S� a-99��N�gc ��$ar{�M}}� \vec{V�i 0%��IV}Q�8M}�k�$8 �� 8$~�k��\[ E�( �Ha�{��} (-2�. & \ń & 2  0 &\\ ><-T & D %6 ?7,-2.6 ( _ z10$Y 06 2>:C6,2( ,-- -26:L1 'nF,24 %�)��B)\]QT= �+ D�L$e�$E<VU vectorJ��7(I| 111 g>,0F0F(0N<0< k| 0JP0NP< �)^tB�T(must fullfiIHU���y�N�abel{n.0ef6!_��== +J*=.~=��6In��no�$1$�)nds��M��b nd $0�tan� Ѿijk-�> ,�i^T���t�� �e �of Eq.^g� )X*sa�Y map;$|�Y���'��c�L�s kԛl.!_�,���W���%��ut>�%_ "6� �� &at,;��� >�S$D%fi�S ��vK;k�L!/i�Qsp�qg}e�RPeft( 0,.q�)^tU'�<� �l�fe � tN!�� ��sat�H 2(}X5�2! ��( meanB" fuE��A�te ��:�. P��hysically, this means that, no matter with which initial condition are we starting, the system will be in the state $\left| 000 \right>$ in "infb�8 not surprising�view of�Xcontinuum space calculafs$ crit!*| patch sizes, where one can show%< a'hortern gG0one leads to � �,�aNw4 strictly grea^Tzero~\cite{skellam}. IvU��meUalt����xar�bobviousi� reA6a*�t��,a!�it2 I�tfa�w�|ll!N=? !@Dy $t>0$. For $L=1$.� also�w�!�e vac� tate1uunique6� solu��-z:X, implyA�ǝ~i"T . W�U establish�7!�non �nes+ iR�te �/:�o(a necessary}�to avoid�Mis� ival�;0to search for�~�:!� � w� 1kernel}�has a02f or{�d4o two. Provide�--�d3an��q�azI��  (due��u�smallest"� �is��.�)e�� look!�r�9� inor �kall�,. Fix $L>1$;�A#as��E���F!34less algebraic%BA�u(at most $[(�:-1)I2]�order, )�she��� ��#!\ge�U Ual-�. Suppos� @�n�|s��� !_Fy-r �6aY�i$i{  close�}ltha&�3alk(�+�mE%nof��>� bU ). %�D\alpha, D >0$; now�YI gle F�!>A�@variable $\gamma$ެ�-eY B $2�R�$��s,�ea% eque��of unda�Ja�heorem�Il.� � = 0$!�a_W i!�]���)� � � � �mat!�c1...1 \- >n�,s :1i>> a��=Y 2�(>�E i !�nu�m�as ``un�� e'')U�`t!Hr��e $N <��Ae�$� posi� �denot�EE^*$��� ɝse5�s�6�� surv��Ehow�ol �E�var�� � ous!��Elu�M$ i��$to upper v% s. Becaus!, e se��1Z��nyG q�Ab coun�8e%� ^!n� n opeaq(terval $(0,1()ep �A��eJ�Q��P� �s?J?2��� � ly ��!it� s�A�d � �� . As!�!ka� tinu)h�we��mB<Ū� �OA �t4 &� toV^*$� n��� Q"!2�'!{ high5�!eA� �ail�JoA low2@!3s6Z isj urd.L must"�i!noncludA]>r� �ch2�orA;�same,.NisU\ IQa &� �@� sem� ŋ��U��>cn can ��e� argu�� �� ~a�a�,eu�( common rooeR�}e}s� u�&�exa���! � i� FMN�6G)}aI~�bD$L$, say $\bar{L}$a$at fullfil�is��perty. .�+S*�t�s]�ߑH텉��2�,& �weQɚ� ��%*!appropi��B^2�h� �uparam+ s!:. sf IN, D>0$��g�W: � asya���� �a�JM��R]�J�tradi�am �m5�Rl}VL��M0 t le!�2=�!NE.��m*rp.M -[, 6vfP->6P $t \to \infty$}. Ge&} � !� stra�forwa��S# ��u@an hypercubic $d$.^ :n�s �T�:x��d $N9 &� 0tA�Kif���~F A`A� neighbour5 nd,1�"of $N>1A�[on-=2�fur� � �j�$ea�ake pl9 in j��)�y KA simild�,� aboveEBv  us�s am�cl�:6�qO. E�in��complica�!s, qwh��he occupE� dep�o e"=%+$N=N(i)�~rA^1� may be histicaNstocha(� hed�� ����PviaAmeq"�19a�ʼn-� claimE�, b*� A�abilityA"isB�!5�*@,�N%*�)�pro���A/2�b ���e "�!�iocis�� very#ortan5v aW r arbitraY0well adapted &`s�Z�.4  ( E� ed) � e8$azrZ s. W%�q<Oose ZL!d2�^low:(mlate�J� s�i<fin�EP� edF �dynamic-��� Adomina6 �r!� fluc^Eij8q=��kil&@ole�. \s�ton{The Bosonic Model} \label{b } "9 4���+an�� mA� � B��ticles�� ras],e Malthusian� under= E_E� s,go birth, $A�jA + A�[t)�$\sigma � �C,)�7�tyset$, ;/$,��!�E�$G��9 u�couplA�betweenB. To d�!5ys�e �ne�ec>z %odologyAA�6��r3Preads \begin{eqnarray5�� 1} \1�� \frac{dP(\{n_i\};t)}{dt}=\sum_i \Big{(} D h{\{e\}}[(n_e+1)P(...,n_i-1,$,...;t) \\d -n_i*( &]'+)�Ri-6R L6> ] �)}, \end�$�$�# "8>� %� $i�b 4>�` �cs 0G6E*)l�7I�i~�2�� %���z�+!�]$eE�� DeD:..+Q(r�.>���e6� t�� )�se5n�mt�j� �maps >�descrip�� Qx in8 quantum field-�[��lema�a�onn�S w� ossy Doi$! doi}�� )deepl�2! eda�subot works :cardy}���Ɏo�n 5 Y�e-#-�i\��6ators:�6I��} [a^\dag_i,a_j]=\delta_{ij}, \qquad [a07 j]=0, 2aA��"i�|wh�� ac-!�e� to!� troy�Sa@ c2�lv ��J� �i ��́eH=2I� �{��v�JY�n% -e^\��w"#��. � aN� a�� [=\.!_i (a_i%�)^��}-5�u�Thuh� ��� - t�#cto�JuWv#}� Phi(�9��{ �}.�2� 0B�� &� = obey� imagin���$ Schr\"{o}�e��F� �schro -}�A�5 � � �=-H-Z b�+ e$hamiltoniaf�$} H)/M�(-D�%��Q� (a_e-a_i)�s [1-] E�%�)B&�w�cover&� �P1}) ubstitute$-�)��.�)i!&!=j).��{��5chain�A �쩯�쥫y�F*� �&�t G�Fda= D(� +1}+-1}-2!Zdt��,t + \sqrt{2 �B a}dW(t)B�i�$$2� incr�!{ Wi� �P� �A3��ct��erpretu-%�!It\^{o}F�+xplai�Zin2j�k�#�(���x��mo��N�$a(t)$ ɪR5&L ��e*? ��� \laIar e�=D({!�  +.-1-2i .)1�JB�in anl�$� %�8 . Ifi>pe-9*�)getFt �N�F�e �-J�)+(I�-� )NSB�� ��e�$e6�I "A�$i$-�jsZto"��5$U��A�mean vGY!"  )al� (L=3)Nx� \vec{a})8<\tilde{M} \cdot Nrk <<=(a_1,a_2,a_3)^t5  $M��$3W3�% \[�( 7� {ccc} #2�-D & 0� B $2 D0 , )�-D c hͅ)\]/h#NF$ $�0,1,0w�m�1~B� keep3""� � !!�(A&�a�%�,ed>ly,]&�(e�%�&c�som "��(re� ��"�:�<, $a_b=a_1=a_3$,y�"R"B a_b(t)=-DI`\&rm{exp[  1}{2  (-3D1��!9D^2-2D)�+ ^2}+2)��t  ]} {r7}A +Ώ+rXޏ"H1<I� >�6���aY� �/('!�� g� !� ɜR5 .�f -enougt+ stud'2Nk�i� nceI (t)$. AndE+6� if.�YBվV \ge ]"�3DMv"IF� So�K%s� n%c� �aq�E ��"���*�"���.HCOe�� Bc "F��:��\(i����7,-� o�.O�z!�ec/*1"�) �# f*�#im�!��w�Qiss�!�ion�,"_0thought:^0)k�would }b����RA�t���%�n, d&�'lowof-�i5�+�1� o)�FY�be 1�)��"��q�+�!��{ at le f�04�e3lyR�!ES' r�1�2,I�s��I|e�B� 4. Ÿ�"soK6�  risk!+9PZ�-be�d�-a� *� �al�xa P�.U ��mP!1���8�2Ezl��en us� biA�yk $weron1,shaa2})bit rulu�"F2"L$os&�,is e�s?!-"r-"� a߭}&l y<�:�5 \�.!�A#)ssumed.]l"5 ��pu�  a+rigor�,fooa�%m dZ heur�E�elucid( b��)Xist��ButB��^3P=8&T!%�'sa �n',6�2/ �aproxi�.'6-gtos3' �!se�OteM�e֕��5t%�V�$Fij�&�3mar�Ui�hO&Ha,e�&T�%charac���FE>t51Cclarif)a�"c/� ertiA�@eM~�meqE��stᶩ�y,�%�#�0�al%� pictu�6 Xy�uu%����c^69< . V�n&t2.�e�lems ��st�%33�/d>�toAf-Xal�{ �݁AR�*o"/E�)&� :HBon2a-�\ic!�d$+3.E5i8typ���A�usua%!0j7o� spin N/ �ed�Pauli& ]& ur���+%8!egr�+ in�&��alcaraz"\>,*{Acknowledg5s} ��3b�+��‰kr m�Mi�eri� Educaci\'{o}n y Cultura (Spain) thro� PGrant No. AP2001-2598��RX4Ciencia y Tecn��\'{\i}FZPr%c \BFM] 0291 ��thebibliography} {99} \bibitem{mur� J. D. M,aM.�B�8}, 2nd Z(SpL er, New Ye�1993)~ `8goel} N. S. Goe-+4N. Richter-Dyn oS&ModelYw$Academic P]3tl San Francisco, London, 1974.�:� G. S.:,cW7(ka {\bf 38}=6 (19512�4escudero} C. E ,Q$Buceta, F.d?" Rubia,hK. Lindenberg, Phys. Rev. E uD69}, 021908 (2004)I re cQrei�c5��}_Sznajd-W��, Eur. f J. B d16�83a02�I2BI�-8M. Wola\'{n}skiZ]25A5 ]22]doeA)%5 R. D ,!DMuellAB��$P. Smereka)"ica A �3 _4 _6bludwig}A�L , G. AronsA ]H.!�Wei%�sJ.E�.Al. h!�217!�792��2E=Cardy���;#6+eauv#!� ics}, edi�Gw. Drouff��dHB. Zuber (World Sci�64fic, SingaporeA�962�mc}!7$V. E. McCl8ck, Na��E�401!�3�96�mo� a1}!�M %/ P.-A. Barr �:�!� 0161!,20:� V2�V4a661���6� �3�V45101E�6V%�%�L.)�%U.A�T\"{a}!�e� StatqW%Z90aR%X8��|lopez} Emilio Hern\'{a}ndez-Garc��A�Cp �\bal L pezi6�7�016216�429,frensley} W.a�F ,��Mod2�62}, 745�6'8oppenheim} I. O,��E. Shuu�G.asWeiss,i(��P5&� nZ Ch��alEm ics:mXy"E�, MIT�$Cambridge, DMass.a&77.�d�atoi%�IύZ�x 1479�76] <L�% �1e�ceI3a_13E86^��| C. A�,RDro Henkel��V�tt�(Ann2�23!�250�9)��>� � doc�.} @]\\class[aps,prl,groupedadd�X�pace��0t]{revtex4} %ZCtwo�;^MD\u} ckage{�icx}% IMfig} fil~,4[dvips]{epsfig�1{d �$}% Align t) b< deci�point2�sub �}%2 bm}% bold� 2amssymb}>� !�� 1� } \title{A� otac�!Collaps�Mesenchy�Morpho�=sisM0author{Carlos"�ffili�{D� t&6� F\E �WF&�, Uni C dad Nacio,8d>� a DiH c�hC/Senda del Rey 9, Madrid, � � �ab\-ct}=&�f!of che5signaTam�m=cellsA�� t� � �Dr Q*/ �*� BAk>� c1}� oT/st~ Enb�iai��z�m.��)t �, A�mplex&; nF����fF@�~�FlonW@\3�) �,Tou?78�$pr�'� re$B �in vit� �Dri <9� \�({87.18.La, Ed Hf� 0.30.Jr} \makeE��F�velop\!�sv-al*Fte� ia�D%Nost&% top�*in embry%���?-.�tHA�:2*\� nh2���N As�.�@ cruc�r�*&Ao4=B��&�c�echanoA�i����%�I��E���0their environc&��recognis� s�al��� 2,  }. O9Radvantag,_(3ach! E�itn�pot{ a-6 self�io�B %}Tu� e��pre1'h. E%�Nd]is - a�*�tGV.E��)� cap !�adp0�t -ny"�disturbeeN�Adl@^ xist�/ of9ly >:�� �'n��ke!4�|�3J� ��Ghe&� �\!" such2�A�.%ed6��In&4�a���?d)5one�aearly%CionycMvuder�gor .�E��pon I!v��D�c�ly orgaI�-�a� sk���1$ primordia�ch�ome f1Geri scalv !ioF(ensr� @mirro�� cartilag��Za�-NA&limbs. .Y J%=YXin&Gmov%�"Rfinger-� protfU!l� ilod�6 � grab dheseD� �p�< se�Caa:�$aggreg �5X��(pp�C�Tvar��<��!Bit�hE7s1, 2}�Rse2���Ce�fib!mwK��7 help��� u�*�trazula@F F ti�wi}D >%���%f&"K?E͋ al e5>�X�G�3�K���6 Eb ��d�� ondr8 EO-D6�E�E�Y�hinchl}K}=Eak�neg|Fi��ibu|�%b1. He�wq/L,iTEe�d& x�2�:��i����_? &< rQəism-Is5m5y�inJt-jacob!ugg[I!�its �mN7��Q�5&� . A��C3G%�t&pc<fu_#emoatATtZD��;fi�0�l��M ve I���R�.���-Ei�4 �garfi� }. Probab "A�s&&�D� ��!G2�.��" K�-Sege 6 r�er}*O$nB# * !T1� \al_t \rho = D_b \nabla^2 - n$(k  % c),�!f* Y2}� r�( _t cVc 1 ^2 ce(aeCJ/ &�1A� $D_b� !)a��0�.a5M t, $kU:2.coeffi,k; &5E#Y\,u�8,e� $D_c -a�Fx�� �. in&*)1*�e@҉Sdq�drift.&K* M2})_ ^��.O���^��Cnd� s� i�K s�5~�K a1},�K ow|@NAB1I^-EV #U+epsilon LA$ &Q rho"�&Q�s*A=D_b/!��")�2R/?un����ap� �=9�2�Aus�@N 9X6c*����c�MD�0$.g ~> �f�1^non��i:fe�Q�1)�N��")�32y!D =9X>�){5�.S 4} - !�=/ - k_1:y�-�k_0=\�( 1}{\.0 \Omega��|}\int_ho dx$m{ u�reg!�-�s1O h�)!�d� ��M H2(|$ bR�^volume.*.Kint&�Q�9 k_0$aZ?s �Fv;Q iEQfor EqsO1�.N4� dno9x "� P�velazque|�>���o b_#up�*��*�K$d�%2$|(alFO��@!e�]L$d=1$�GnD� a"o?ra thre6� �`Jl��to&h E /��p<2 �#r, "I�4nF< shee�'.5l�;qU��<>ly |cIe ���"� �(brenner2,be ton}.l�Q�.��v"yB#observ**�?zt T(Escherichia�i}�udrene1, 2"� � �D.��c, fF �D�6p � !M�� � re�X vely�A?e� loponexten�NpGI�sense R y va"A beyoz!ir  S� "`.I�s rCi/a� o���Du� $dispersal &I, � �%��� ip�ndm� d!c��~avera�as%�Ms Long->�8=D�ly� 18�TrAAa biharm�7 &a $�c4$AQ�8 9"�E��"�O�"�*2� 06p�Cf*<ņ<�(wx},&�5-�� }{R^�\.8-as}  R�=��ɚɃ ó�L�me1i-�yA� a sp�-pe�l8�,JN[-R,R]��wa]aEY��9cq8]�:,Fs= B� + b�F�V'D_2,D_4�LA5 i6 +� 3(��"�8 �) F sG �K 3:*;��� �=c�!8a�ptov:�)e�.Malq�u�~vI�29Kb6h j��G randomlyF3up�J�E��y'd�",�,a�Y goi ga1�. FA�er� next�N]�"� aCa+ beha� 1�W �2�=a !Bn�ve 2�#as���Y Pawula's F(�zpy lso y 2�+&]�hH.�non� cal b2��nl4�rJ� ��A5.mOgs8�.p�b�Yo � �Aa� "�?�*EX p?az = ���0U�U*��#ma� �(Pad\'{e} toa�-8+&,,kevrekidis}N�f>���o�� \�x 7 D_2.� }{1-a� (D_4/D_2).�*I� .����%�I!j[AMthezc AR �~�2��:Fs�!�-��Kpe�A�e+�V�;�a/Fourier4 ns� � Jg4�9(c4±-�()^{\hat{}}=-� D_2(-k^2)B� 0�&61�U��-d)�4�u sA�6'2��a�2 in Ref.\c�dM�� W�Pa�sid )� B� � F�3B���� f �� �6�Kin�& UMe$/&�j�!1^' ioR?{aB�Z ܅R� goa2�\Af�$� �W( numU� �9JF/ext�>l*��recis9�!�"�!��=-up��� e"��'�majda.�thu!O)�a 㝴� *� l&�i� A�$�  @;ho&c� d  rho^2�.�sysregul2W YNin� ��"�.�(�8�g �1or!�al!�!s mean ����n�*al J�E$nfm (= a.Kg� _%"�$�$)Z�.��!X�_{1��} =u .1�1�x>�^1�bU=j� Omeg&NB� $ = [-L,L]$, z �.:1c.*<��< FcQ�J) YB��{12�.E�A�M��c)>c� ��>ap"�ae١`�VEccon� �to]ma�aI (�>"cb�Lc�=��o[8L��� �$A�A�sgD�0er |A��7� . To2�4noDC, �[Cic��oIe nor}X:�  $f!�; %� o a $L^p(I )$a�D<1�; p <Ufty$:J��|)ft| fQ�_{Z}= ((P& B; ^p d )^{1/pF� FK Qi ��)�ge.9JX G  � E�(wA&���215}^2 =B��G_t�= FuY�xz!\ -6@��G c  dx��:�^3�BO^2 dx.���!B� Now,!kA���. � ~"AqA�� !E h��a$A��<1�. Int�obIKX@GZjO"� �}.tCJ:"2U. 1UM�.�|��y�d}>�5XE0_r�^h?dx"� �k!� y�*j�-I�e:NF��dx!4\� Z6M� Zk_0�BN\E�e2[Q] �;��ostE�Dm.#L�7��le �xB�zS.h�<�+ed��AB2V�uE3�]Ze�.U| 6-���6J� 2F� X�6`B�w�N�;HQMlder'� �w�X(� b#f ByI����shift���b�>$y=x/"� ��}-* z�2G-�r�oT��!^{(3/2)|E v )5by͇��M')�1z.r��mlImWN}{����\Z�$N=��(1-.)^{-1��w|$.�_� 4>� is l�, step{E2!�f"l"�v� r� L ed�B�-y p "h � "m %@�^�6%�pan��.��"�m1 ~� �&a 1n!�"� e� NGI"� V4$F �>V � �  ��^� d��)G+O]J( *#�k�>� .��p%�!#��as>d_F �oon�  ZH*J�� ��\W�+uc B waveQP�d9@>Bpro�)an��1 � stei� W�n�^�z�wx=q\ y$N� �MNo��B���I,}�.6.+ B"$BM�"��2�C���� ge - ��D5D��#� �Q:Q�N�lV� a9third"' v+ >�  ��Z3� }^3B^��Fs (�Da :=ofb�seemKevans�� I�u vQ�M�U�!5�)�FN� .M.>q5v� u,qq� fty,� * 1}{p}�1}{q}=15QQC1O�$v=-s6�R� �u�i� C��!R���d~ $C���=�q}8)�� �"�b���*� �Z�.�A�:�DB�Q^21��:�=a��-;:�v {2p}%aE? )^{(1/p)} Aj73:62/36 3��25�1L)�w( �u$p=3/2�nd 2�ly $q=3$�~e��=�Q1�-�Z��(�'D!�]}^79��x �$D^�-1/6} er�v� � �+49ՆN���K®8 ge A 9( ���@UC� -B�j.E^5A,B>0$�I�� s�b=|i�|X /2}� $B,2N*� 2} +/$Q ��� "3&�; 3alF1�-mxU$Ax^{3/2}-B�*.L+ 2twIxed�*, $x=�nd (B/A)^2V!�ara8�Lgy crevea�dA  p )ve�k]� �K78,���� 8 �!�-�i  $x_0> �$� stay�h�!�!�ll�I s. F� weq fA�"�  gri�:t� Ef se, �(� �y�5�8�w!J. t_0<� �$0C_0-� (t)$�)$t>t_0 .W&�1�ME�>> C_0 8�}a}>�!� ��G� decuTMB. SolvI&is"{L.�5�%1��3>0�� >"c �U\bN_�x�{2 �Vs-)�C�t}f"1%��&�TI.fLm+f�plY<��b�0 "^�9+4N3� ^4C�' "!+-g4:'��1"B R�-�O�NMV�\J(�:>}N(x,0)=(�+ �c/4�" $ �vqP,�a��ply ],UcoZ,*�s�; � &i�hn�i�1�W��-eOo �� a�-'�r�3��9Bq!"�al &�� %&ioBK Inde�2�se&�%]=d64�v@#(#� ��$�4��[A2�*d.BFa\C6}Fu^F�#�D:*$�!�! !L length\=vmea� �:]^�naloggS-%!#%p�0!kyѵ (2$rm{lim}_{k�-ɚc�#`.A}ZB.1+ ,m$��?, #B}} C} AJW&�:�og�0Y:z2!0con�+A�ADdd�"be x�=s�(w�P,�ve"�pofV8 #i have�.�bi p$�v�$ $ �1-x5^�H a� p$A*�p���e�gu�at each�2ag�>�Im%p<>L"*�*�$NhydroR �g>�� �5&�i?nciple YZes(& 5-S*� ]�1* h9 le %!!rcI!Y��6. ;{4-t �-`@iV2!=x6Z�!�Wv -�s %���9> cal)�e]9i�>b�to� 4*SDMa*�7 � 21�.3Y%of�8!�an��pI��K!v2�>._�6�T�2qUB�1I6��Hh�Yempir��C�6:36RHaIedgm>�6��(�YQ�ej�!"8&e=� ure �Plaip"�U.r?Af� a few day�YU4hom�A�Vlayer tJe�C�"E`""H)��+ /%�5#'LG j6�5TwrPa� "swirls"-�"�@�6��E0�A��F�-!"� " F Cwn4�~�~?\h�I�W��eyq��Y�G^�� 5D =��E��ndard 6�@�Hism. WKwa"Ce�sis?���8e�`�P ..@)�95�&Na{achiev� �!MMT�Y5 �tm+�jaE�`P�[It�ZbN��5&�Yto�i�%vu*�r!��s�o�7E�d� if�5_��o%� � m�Y8s��A��s kind���G�>c`on�E;eda�!1�8s �DIc  %.e"�\�`VlKE�sc3 e8�H  mitoYor hah2�D�tE�.E�@u�Y�A7 %2!�!A{���n[�B h�:!]bas�ZS  . %Hm��mplete %���[:vq.�2qE"� mult��5�p may dwar)�N� % �D!�. N"(@q�!=�'l_%�j�s%yet��inRch�1!�%uw]�.n]\ �%�*W@ en!��%�M�14dCPal!�lanH)�E)Ax ��&@Ea�B� s�ya�P�+te� y ac!�[ lluyxa�discu�\s� An�n,o C\'{o}rdob�ieg:A4" Z GLdo��vor��[�[�[�by UNED�T(w>�SV�[pX*�[P.kUMaini\ d�U0T. TranquilloV3ORxhs�T17�T68T882V%< �XjR>6�X[Q}, 2ndz\ �re� � q_�Z%&�Zalbot}�TW %+N J�#7VD&0Nal�Yog�\Nt\: RZ6 Ho�b198�Uf$alberts} B�O ,� BrayVLew:�M. Raff,!aRo (ARJ]WatLZ)ole� �ahN%Cell},�AL�\: GarlQ 1983E #]�K 1} A%�H�K�Stopak)MD. Wild,�Y( W))�29V4�V:�V `2>`P. Ward^m2�V20[177rV802:*K!%R. Hi0K�D. John9;!&=�!9��Verteb@Lim[J Oxfo�ClaD�on�W 1980.?�J�XBen-J�J , I. CoheHH. LeviA�Adv2SW4X3958Y0B� M�U�&� !�G J , Y. Tint�cD. Pe� ekERBostr�&�;ndQXL. Dem�8Y.!��Bad.!��\$101}, 9247��WQ:�D�F.� %zL.�S[JE�TT2�\26}, 39E076�&� !�J.N Vel\�Zz�D, SIAM ApplG]�>=Z158k[6^�D��N�9,)��d � NH`\F 19952v"�a� P. B�C,�!�tovI�E. O. BwC�YP9�_c7n\16I�>e"� BD]i�>D]one�08,a4paper,reqno] \artB \!\Lnewcommand{\myStrut}�+$box{0.11 p�k${0 ex}{7.5jJ=Bz>1E =� $m{lemma}{L W }{�4em} \ style{re�i24*{RDe�+eA�OH{\Tr}{T�BZc _c} V!Det}{Z U}{Ub c}{Uf[W}{GP^< C}{C^EC}{EbA;^{*!}R�Cc}{I^\SL}{SL^E \S d"�_ titlepag�3 #c� !�bf�E� SIC-POVMs AND THE EXTENDED CLIFFORD GROUP e&cBvs�M {1 cA"2_0 D M APPLEBY 66:(�^m�9of�Fics, QuIMary �MofI , MNE� d�g, E1 4NS, UK vv>�0.5J�@ (E-mail: D.M.�4eby@qmul.ac.uk�8FP7 Q1 .2 2�  0.3 pae� 12 cm }{ +>�^h��\[�<�JC�Vord G{A (d;O� <�Az8�nU"��w�,�t�~��anti-un�ch�-V-� *Bd �kcL Weyl-Heis�b I9i&tenY,)). We also�F a ��Q=�Z�R 6�B�B(R�h{i.e.}~8 ��"-j�-P �9dL�.�&�6� ���v�(g�!vVon g L@I.� ��%�/s"ء infoS�>lete i� (or u�) co=.nf�MAB�^�)�}?:�fid _�.-v%O!WE�*yo� (M!�Ao�=.."�? Fy Renes )�e[�qQ� eigen B!O�@> spec2�d�$3$9f)�iE%� "��r�eEbScon�n�1of ZaunE4% �#.J"2Giz 3�X�X�t2 %�shd�U(s $2$--$7$.2'/wUOpeEQon)m!\B��bAkp" sa%f�L"*r HV� $7, 13� <, 21, 31, \dots$)��c�h��oi�A�� exac�G� ons�� )�B 7$��$19m�g}:5� i���o{I*�S%%a\K sec:6r6�w� 5�y �um� �3ŏz��d by a��u� val�me9 , ore� (Davies) }, BuschU� alR�P�" 7 Kiel��AXChuang ! χ*k�DX3� ). S�uAU ��B)o�>"ov"WH � inctTa�_a TuE&�A����4igye�u7� CJ= $�EE}_{i})���a�t�sa 5 Tr (*i  2,})�5 2bqpof�[��� (5,BAty����S� ͍um� f��/(ll 2^we�&r!$\J�F(E}_i=1$. A)BsOai�ȩ^}/�$ ��� $f�$�qu�����B�2�.�> Vncept � .���_� �ori熡�duŎ8 Prugove\v{c}kiM�} ( �9e  2�1d'Ariano-1�A Gd $}, Flammia%}{ %�]$ Ay>fA�mf�_aR�#b?&�gl�c%Q�l��qً��&8��P.L% play� ���^_6mCav:9'�;1,02,FuchsSasaki } Bayes��Ka�أ�f�pre���m�� ����Hqu1,2}  Fsed axioR"�- . .�Hilk�c� �H՞h�I�nY"*8�/_&2�b�I�i]m� z?a��$d^2$n���s��A��Oj� A�B�"� 0�R� }�  ��iJ�s�H��,:��a"�co.��%�ifE' adu.,eq at�u�Tambda ��� a b 5w�i]vor��i��fz/�� $\ W$. h�x�Elap����zj��s旡G,pai� ى��s $i, jc�c�<Ǚ &� ��-iv"D�A�r��DJn�at,� �� $i.���(�i�3�'�+d&�+psi_i \L->,< 2|��> �U�I�"= $| 9\�W(le$ satisfy5��(,�� 6 | j\� �|��ases} 1�6& i=j.�A\S� d+1}DW$\ne j � B�.eq:Ove!�Co�G� �"�  w�e� � aa�ser��by� ��� ��}M nes �32\ }� oo�� s  Bengtss� Eric k, B}�wGrassiY }�� made"�)�u�  . �Pre�xB!o� eN inti�E2n�,�A�f mutu�`$unbiased b!� ��, 2 3}, �]af ��"� 11� B)n polyto&�%5.+. If��YuM�$i� ��l� �\i�ote�in a s.!\ larg/S4>Cs)!$y�#����[G!4�N guis��"A� �"�%.p"� mdl�!�ng �J�b#&�+t�&n{, crypt|{���K�ory`ly���be "�� candu�Y A``_ ''�k``�!ard'' � ]ki�G !�chQ9%K ��MP ��.�oqu!o�e����arises: �c*n'r _y�Ea�V? �<ansh�tT'isv* t9unB"naVA*x�9�a~(eN�) %�B�in Y�,s $2,3,4,5,6��$8� More�� �f"\ &� �E�ru�$ ��)"�5B5$�$45$ (!�a,i�caf@ downloa`Y' ir websit/=�V��s�W SoK6 plauG&y Tul�atJ�Z�. Bu�� �%!M� v]`I09�woe%u5/ �Lly\��<�{ �Z�A�E_t)[=l�8R] ��&D9%G!nWL�"�"-X y do�<�ny�� ails. } ���!�liter��eq (vv6g306{�+>u e,ZvO i�& ;uQAci6�ir&�2R�Z���&��A �*B�"m� [Z�,%�idered �, sub`!�$\U(d)m* A�"!s.�in&�*f 9+r� �qaAD�}*reas�� F�KPsa )/�a:c�&U Y�rG�sman1, 2 ,3,Dehaene,Ho�r,s,vanDenNest B}. ItJ�q�<�a��st��R� . As A�e"�cr}s��e �#i)� � Ref֓bhas�iBmeT��ͥp�maqa V}H� ��A7bg to �CA�I��j�6�+�enpdY)a���On <}-FZ fU�c.�.G. As"!�se�.� ���a>es�)�if��waXxo-� ull ���>�. �O Si ~�#;GPX}--Ex{1$}��� �)� Õacc��v��!� �f;�` cour�\�4i0��"�`2�r�B4z�!��M��\A��$b�e��ur�2�*,�Unot pre�l�]� u�]� X�dbl� I ent H , 5�9��TLs%q�>]&��W-[ � ���+A6!9lI�X�[cmHh 3fy| i.% Rnf0 �!H6f $=-12 W�IfA\o9sH� canZfal}hiX�.�9' RBSC��T-^so� z ��ly R|��5 } (`��� l�^&� $5� 45$.�&m=-��l�76�a� ��1; � � uis����/1at-EN } GP"t-�О�x!�E�,�-(exi^�!�:��%%A)���ED~$3� E�m5X $7$�+N_Z�; ~$6$g&NC&A��'�sul��P�rt pt��er�yeNcR"M/k"�   } V�M�O�sS<��,!E'sY� data, xr��!#t�X"�>Bb ������&n��� _� }9��9�inI ��a7m��"J very}�>�9 i'>Uv�} W��so�(�:>t&6%�z fkHn�M�d,M� �% ��kw Q!7u$aGm �!�&� h�1$6�9�� �1,2wi�3 M. s $4 L5�pC6:�2� I-9�"���_o �>O��2FP (�n�M=::��R6哭L%tEi5W��V�#[y3�E�>�� ��� !�J�`19e�!�a91�&��tV at puve����� an >%W�2�!:�19�E��I��W.�8�18�a��*-�sol {6�s!XI�swas fac�Ga b�.99 6)*="19z�3�bhaoE��k+�*ly!37mb�ag oF!�*#�=��Z!� �r�I5�P%�)Y(a) $d$%M"�!� �or $=-N<;(\text{mod}\; 3��(b)R� n̓i6acF�72 J7%o(c :86 divi�EB$s!{ � word� ��! $d=F "  " A  "�!FQn��%AWGB�i 5.} �!� ���Uytd��"a�m�jce" T Let $G6_e"gD!M;����F)s�N kn i� a�map $g �B�U}_g $Massoc��I , $g\in G$ a�h"� �C$�ng)&:r�6=.*Xl �� g$, $g'$F/�U}_{g} '�N4e^{i \xi_{g g'� � �&�\!>6Y ph-p(s���:p� �A-v$omomorphis�` !��;A; quot�c ,� /\Uc�'  $ A�5�)ƕ 0��T�V�5_%t, : �@�At:9AA.�I �w{�Uͥ��\in�$thbb{C}^d$���!5��| 4@"4N� bigl;N9��-�g psH .r�f k9H&�>�Y \neq e$ (S�iy!Atu$G%?$�A�ign�N���#gAJ�Mq. .�|�# '^{\dagg�,�"�AC�*e#0F)~{d�R�R�E+*�a�:�J C� ate �Dn� ����'ly focus?� $G=(�Z}_d)^�ym..�!ws� ge� ��l, d-1�#�H�� modulo}�"�  Ng���  � e{� E�:�{ is�G�1Ric+ye}.� � ��)��!��weAF%d<D=� �itPB�C $>0�R�e$|e_0m<, |e_1 ͔|e_{d&c���n ortho� 6>ɜ5�e���l�E�T}>ٹ�Izd(BY��HT}�r �$ =\omega^r.��eq:TDef>� U'= =���Y i i/I����S�WZv�&J� �S:��!�s�{r+1}�\�V & r=U� A�2 \\ 01� .-d-1�~ [�SJ�������!�/"u1�4f{p}=(p_1,p_2)�RyWamb D}_{ +C<} =\tau^{p_1 p_2�S} T2.� DOpD��Q>��Z = -!�\!� !��minus �N�)ns9�(� d^2}� ��D � reb� if��2 p$ ulae޵&��=�,�9 ,-@f{q�c b{Z�T& #.E}M�:L�ger &e"��!-e} ]DConjuA/}IH2.1Bq}} `%)�A�}!�,>qQ�-��p�T q�3h$a� DCom TonRul���r� an�q�ANd�2f#J5*U#� if���dh\ (-1)^��p��} �&BbSLM�B�DShiftE�sio(-���� r���y�'�A�F��O =p_2 q_1-a�q_2�_�� C�kque� ���]]��\ Bk�lF�m Ņ ���W;&d] ��&"�'��6w=Q�E{�imes �ed2&l3��c�-c�w� s�u� a� (&��. ��ANaJ_:,F"�FH}!��r��L V:D  �e 23�1: ��3A�M� � "�&� xrmQ9�� Z' :vv R9j2 � GP�m+|���]^�Pm�9 f \=�:ol{0}:�d)MA; 5'^B�a� . &f�it[�s 7we(ow�RZ��&�Fi�="11 � �FE�-7a& �. W(d)��{R~}\c͔j24R},�� )O\}&��/e�i}Bd�2U"A��� he WN�6. �� �� . perh9� slh*lttcon��i9Xt�&b��re;P �$Ne $-\{ɽ^H-n %]Q, ��>^!---i�eZ\%"4!)(?xUj Z.  W�w|!�:>"&��! �$6��)� $\C���!mllBqU}� ���!��J+� U} )s��U*VA�A�>Be� igni�0 �isI�u�0��it5T s au(�s�--� �RF� �P\�o ���.�>�.,a�2�GB+^ M��]�"U} ���Z���)/%� )�� he-&1��Lno��!�� '��P�!�/#�/#�.# #�.�n�EC�'!s �Ue ��%)� �]� �RM'%� �g�"� es�� R���jf��"�Mj�XZ7.&�!�5��: �@c�!)�C&�y �Bt��", �IHz=We�Oe�� �#i�N�LN�� \y)�_ {d}=�  d&{^N 2 d*�>&J 6zw SL(2- ��_{.��6.�=J�$2:�$ � F �p" x} \z�&�ta \\'�d-�� 06�sucatW�, I&n� F�U�q:�[ ��3- K�� *� \;2�β � �Nr$���rb*��" R� �[5��1i&� bz�{� 9�%� & -\b-���!�%�:�=B�1 & 0\\ p�V`6�B/rithme�"(.���W�&�v �N$D  lemu��1} Fo�:""M�?\in���re)�� I� $F8eR>VQ� �/Q" $.O \chijB� *�1N9�6X>- Fe= �*�*� �, F �� �4*� B����*J !<)%�6"�:C 2=e^., a�^��&w�!�,FChiToAisSurD$iv�A91�)��n}�1�� �/S�� .�fu{&s �o� $g=�R��)s��e^{ i g�!k�pE=f2Q�$eq:Lem1EqA�z�^2�l�q/V�~())eqF1�2aJu�5( ���5)^<qZ� �6) �\�*�mu�Q�!5 eft(Fh+I�-^s2#_kBb J��^Aq.�.6�J� �(6+Y%q})�212+,q})1 Y� p})+!g �:�2 i���N�2PB�BB��im�� $�on%]%� = .:� :� �(E2e��i �~F�2Z = F'mXa� + d h.����A('�-'�f $hA Inse���9Y��"in6��)�&� n view� Eq.�>��� �%�� �}1Xp7!�2� N&A�)>F'@B} 6� I�Y�pbLBe�"_RG(.t�,2�q$)>�Ru�` 7p&9 ropr�e& !�� )�mٖFui���-'.�}�.�FyL�DYA�:�A�R���!arg��- toN�B�finJ#e ��i 2�.)-22��2}�F� �> ., &m=1B�DB�qPr�[!��pb q}$i�J����- �v�+� ��6�w.�;F�\� �)v�-��� ��2����a�} !�6�J=��aIN��yver��{#�y =()P F'"h�;�oJ�{W�s*#7 F� \Z�dB�I.�,"H��!�   $V\>2 .� ) �$Ez� �*c�D �D o $F=�vq!I%Q*&� ~* !��B}=R�}ZB6 �&,["�;�"hand,c5O 5PuFS6�E�$8= d+1�~�W��N(F'F����w��^�Wr>v N���DeA�%(odd. So ei� ;?qt�odI�eld�T6&�fJ�$��IA#N\D�F���0vw��aEj���x1��A*m�(F'+d �� 1>) 2�aJ�a��v �&� �� >��F�6A�n+ 6�+ C~�dF �- �� >� (F-1� )�b.% : )}:I!��,I��m� � D}_{/B�!��ddJIv}'!2��r�gg1*�7$g'� U ���e� �  'b� =[i�~� �q+XiC&�8���!�  -) Xn9�%irsM:allj�i6�:�A6�%)�E~ʠv+(9�� r)^d��d]2Awb d^2 �"p.&� J&d+ L&2} . "k DpP���g (�S}� T}^d� � E&=!).2F81 4�9 �)#2� = 8FNa<=EF74!W � d F�:�F.x @  iJA����-L�/��� �. i >��)rg}2@��Y�Qrg}$ ta��HRF2� �d$]_pea^0f/D��" F�&��r2�28N!) ��GY, 6E6I We-��� ri = (1-; )�Z =0B9 F�.�� e��_.v r�}%� b*!)f soJ ,�ldef��2&)+U2:}\+�y6 �}"�jUn p})=5E>'"� p�� 6� \; d)$ for�all $\mathbf{p}$ some fixed $\boldsymbol{\chi}' \in ( 0Lb{Z}_d)^2$. SettingJ4=F FH�$, and using the fact that $\langle F^{-1}\>�, ~�\r*=2Bh,FB-�\; (\text{mod}\; d)$ we conclude \begin{equation} \hat{U} \ D}_{T} XU}^{\dagger} = \omega^{�� J_�} \end�!�>�. %hproof} We now want to prove%b�g�� = 1 \; 2�2k)E Then�� V}_FV a unitary�l%��et �Fq�)r(^{\vphantom� �� ���V*.��a!ǡ�>+Rm>�j@qb�4�N Let F��S}'.�M,�K$)} \qquad land >T>>!�,IN)A�6��.�'F�|f_{0 �b�Y�(�T}')^rA�0U�6xPIt follows from Eq.~(8,eq:DpPower})�� igl(I�t\bigr)^{d} = 1$. ConsequentlyF�:>�2>�v�Composi�- Rule�9�AM S}'=� �!�T}'�^So� can obtai�D complete ɋ0 eigenvectors�slad��ng �p$fically, lRU�6!�%M�S}'!Kr} | fb�A� $r=1�� d-1�a�Jo�>{� mf���Lem2EqBf^��Since $�Q%W: (as�e)!�� .�e"� �c� =%10{r \oplus_d 1q,>J!>Q $r$ �� $6$$ signifiet EQ �(modulo} $d$w next showi Q$�$ � 4orthonormal. :� Eqs}rT�5), u�S> DOpDO �})�9}�VJIy� �a =m���(r��r��|e6,�Kj ^ �-�S���� Al2;:��cr>|y=��� ^� mz r}��F�l�l�>(-)^2�y: M�we a u Axfa&X�ov&� =1A�3e] 0be careful a�is poi� due� 6U congruencaM mph{} U not imply,>9.���s $q_r$�qquotien� $--$� o � bya�,W �`$t?$ remainder( SoC( = q_r d + /��X.X ��!� s t_:� �Zn:�W-�� alig�a[.Q &�U��^{t_r} \� r �2�6� I�L .%�6-t_ + 2 d%_ t_r + d^2 ^2)#I�a�2=<�X �(becaus��52 d}= d^2} E� C���!�! 2�!Qb"f>v u &� Щ'2 i� cN > T6B[%Y,.WUa���� &d.�y� , as � runs �4e�A2� $0,2f, so doBeK(thougha�, necessarily�$e same ord���ZLt�L^2)J&�eq�AM|y���%7ql" � f_r��ao�� | Ss {-r}�c �� ��2;{0� ��� zzr s � =0$ w� r\neq s� ,n immediate �gc,���F�$,�\�2 of&j $:�to&� 6alues��%vFuf�e _{rsB�asa imed.)calculat6)fo��� 5E>0e< 2& y!}-(si %�Q-�M1�N  .! ! arc with6��%�se^�T���^��.�q�e��>�whichE i?&�{F}���. More��,F(2�eaT}  �*X�ae+ $ 0Te� /^��.&!��*T��mb_iB)ai2��T  ��=��i}ly�} - AS  >AS�H� 2�a 6 ��*�  !Wi � p_1 p_� ) 5� p_15i^{(  (QqtJT�ip_1� Z t �m } U� as l(1-+��&�\ m�� �]F� UbA)m�U&9P$. i� To extend��Z�L�_ca�an arb��� \~�9� N�́de�@ ",q�t��� �y�2�/,be written a.e �duc� two 3 ces:q�mv�3�N� ��R����)`�Oen!`$re exists w   $xV)Q$Mi+ xE���{";$[# #B� .Y�n| �"!�� pr�ty":1�M� F_1 :� " 0 & -1>"xM�IvE�F_2;��gin.<iU���&Ѹ+ x1���i�& i�>g}E� $F_1� F_2� =�c� Qem�JX))� 1��F=!F_2 ��Q�-0�Suppose,a��_� ��| �bot< n%�)� $k=� *]!�W�:�-�W%�k)R_0\\ <I_0 � 8�"�_0�)_0)s"� $[kBz.�)� h)�1� = 1\>�!F� The *~ �_0!� T_0)1relly1� eans�ׁ�?$Dirichlet'�(eorem (see� xa�0, Nathanson~\� } or Rose  Po ��eQ�A�&� ]#-q, �  + �),. D8)�Qcon� s infinit!ma�E�L .Ar���/>�E���_0y�_00!nnd�~ !Ij_�� �!M.:�kF G N=!A�p*�)(� B� �2��claim0� "�. � sa��ide��W.%�!�y��e���. If1= kA.�det FA�It&�$.;�$ould �yEX �f> ---Ar�tH e assumpO����!)n��. ��o/e othe�8ndAB������ !����&�)�慉%vR�S �5�tru[#� choi�$xF)%�Au�;��j0%B'!1}��4}X $(F,B�&)�e�U%\i��  \timesR�'A��� -�d&JN� U�  � B�O - &B5E&on1B��$\@E{a&��% �d�2n)me : �!� ose S �I���F_1, *-!��$ (�� e�(%*AbeAguarant*by :C'�:#3��,�i)i{F"  _� "�~5{ �*>{R,�S�L!1�s �!� Z���N`%�9) yBy, *)�M�A�": Peq:UforGeneralFandChiB�J� �("y#^2$�zR� �䕂� L�E �&6�4DConjugate}), "�J�AH~q2}6 *a�-�/ a� U}'$ua`a pha� &m& &(=e^{i \thet� $��ey@ v �ac�V�*g)h�� f��" ed /!1@ �c�*}. ���  \l�� (��.��(semi-direct�j [ 6f6>�, �BX:��i.e.}~c)�Z�$n oNb ^�Akequipp!3�t.�rulJ�(��B2,_1) \circ (F�+>N/_2) =1�!,Fs_1 + �R;كSemiD%wC:s%>��� �&pa�x*� ,-gs*n:\is natur\%( isomorphic� -�j�jQ� d%�odd"^ka&� E of��n  even�Ct���thJ�+}!g"j �)qu�Dr��=,hom--sm� ��' \colo��bD \to . > U����U*TiDZ "�}�9.&$ �) �0�� in fZ� �allo-[.Z*Uf�"a�odd $f anY�sm�%&!�A� kernel�� 5�0��0$K_f\subseteq�wb��n�Ca�$8$.��FF\l�$�"�1+ K#& s d(t d & 1+r d)�"�2/2 5/X \rW-�lK%%Ex�1Bc��$r,s,t = 0$�$ ) �yC ��An�HU%�[2�/!)U�J��Z�&�!1:) �}�orAt2�5 ifE�onU! f itAma!0n ����*o&�m�+� �2.4b�%�@$is exactly�s�?mapF�6�6� mq�M BG!\.�5�.�.V.@  Ս.ctu��a2���t��N^h !�x*s_ K_f"( 2i'�V�a} 22�!�B�"�i��*�%. Fo�A�o" we must� $F= 1v*�82���^5�Y�.f^�p9� 6� 6T�T/ en b�eo�-JZ.Y;4N/,�yiV�9�� x} 0��0@!SoAzQ:$is trivial Q�2��s#S-FWn �mc�7% f� A�>3F=1+ d\D�F ��$ �a ��ka/Z�AB!rs!'t & r 1.>��$r� r_2, s, t2� Inser� Ehe���52y.%we fi�$in view of:3.*e--"�1Shift�A)�at ��uF1r� .��"2��-.} &z  d <?,)� � >B�N44. After re-ary)A,Y�q�mB��q�7=_2� - 1p @ = (-1)^{(r_1-r_2L - t-^2 + s,f*=Z-+ - - +��T�-e�ue ��1�E� =r_23 chi_1=sd/L�;2=t6nW�B=�a]!- cern1<�)qu+ :� Y will��� ed �'r o��5$\nu(n,�=: numb"f dct led Ks $(x,y��B��Sx y = nZNpɦQ=�"5� �n���FL*&|2I  r| =V-� �8n&k%1#+1,d)�8*K �O�+F�(F�&� �9-o��r�'?��(=d^3 (d^2-1~�F�ś1w2� We ��3Iw�� � �� $Fp!%bc[1��,cardinal1,<ed���sets}��is qt�n�,X�sta�>`fa�1Y�}-B��b�d!U+J���R�as �e������:&y .�oddg ��! ��e�g:�����/�oF.�� .�� �M�� g�E)��*�"�!���"�"Iw��mapstU� [\� ]_�! \\ [ Q& �#]_: f��[x]_d$�?J%residuea �?E$Iwm&�6. V6� asily s�@��g�q*� � nE~,U�R&LFM��HSDN�> � )]R" $)�g�?=1 + n dp s�D"� n! ��n� AalY Z�V"F=g(FiB:� F� km�eiJ ���� )� �e({ u' � J��<���3)fU�� F�:  4.�ilJ6��r���+aR �� Now/6 $K_gNg$. A* �D *:6 J�B4  _1:" >%Fc� :C "���(1+c) 2 d) t}5p%6 @�5E�I6F�I1 bR + � � )d \�>*p@�"�>�(beg.in mi�*�&� P4$d^2=0B� 2d)$�B�refore r5re&� ��&�>��-��s��� ce�J�>c�V���J �o&B�)� |K_g| =8$�A# $|i�BE|=8Fd)|%$&9TYHVV� \'1 �� .� �r|="�28}l �.���r|a-l|>� � kF� d}�C.�j: � �>W4' } �aA��V =  ʶ� =e� A��6Br| �~d$,�Qo!%N It2�&5 � �]Rd VA<]each $n�8�$�W $M_n >�.'�$� 8ofu�F^�h>�� k�n�Z= n+1����'L4 *q= nBaE<(Clearly $F/d)%� cup_*� M_n!K $|M_n!�� � �� !y��� F-!�qe2prZ�3&/a,A�j>22�V9)h S'"" 2 6>J�|�a���)s} L<m.TE&�if $n� (mod% vE\ dB)� wiseM U:��"��y�,a�"�6y%�72R7F�\sef#{�E2ed&�"Gc#" sec:$1�}�*�(be  �Es>]B*$OjJBGPfiduDL�at, if��psi�%�Ed*�5�5& I� a GP Q+C,��n�$6he  d^{*&^h#>l�ER!lexB-�%i]$o mak� analysis .t�M�_ H,,aut"Js�$\We �bare%�Mb+9ti-�6  #or� An aE-ar&�i�ma-"L}��tC}^lHo�b$y!>�F��L6�J |\ph5�+�{ ta |!�1�\�= � !oK?s<@>"s"I�yp��ů2H,W5� 6���9 ��"e�ME+5)�AaHadj�BEL*�E�@ 9heq8 que R��&nj>!]|-�*2`="9!v |1\ %-��919�J��saiE�E4Y� uM�&A�2x � (or,�$val J,-�z!B:= �D��W)�%h�7F a�� $\E$a�*� A.!��Lri}m�u~s� vTe 1�J( � � =�= >�usa3 � $\E�4Q�Z�T*i14.Y� 2!($2r&2$.� N�x"Ym�aL�m^6�.�m�, GT1e�b�i� m�� >Q4\pm�N6� .,> � e last �YI� a�� �zTa 2� $f��z�NB�% "��.�@�+oEco �� z I�k a�2� $f_{%Hrm{E}�(�Cv�e;<��)a�J}"7.��� replaces �( nent�4!gYndard ba�i ir�txA�j'-s"'�, �"�&�sAf�V,Ũ*� �eq:Jo F �� �"J:�1'a95 � �, J}^2��IoQőa>�� urA�more,��f�2�#:CLb� IkF �dMD���PN��N�)tilde{J}2.SA� BT"7"�J�e�Yb: ���:� F::E>�=u�E�!�N�V�Dett3 � =� 6u 6u�����. � $\AŽ ��-er>��in �IV��K dis�un��je��:�R�*�m ��UP:�Ry$"�)�>ECASAK�2�[�0rc"��Z�+>6, .�+A�Q�}qfif�D�8 v�A�6�if!6@�r9. >�$I�h:��%4 \��%"�*�k\+�F{�6�%��#/w"  fits W��s�2�(��m�/n�Cu��-REM��� *�R4&C����)=A�J}-7V� �;2Oe�M=Jv.2 is ME%]>"���I� en6VJ���(,�8s �)'avo:�a #޾ $�n, 1~y�=TJ� :�M5#)y�&]GF�% ',F'� �b2L*'2:end�NP. ,Ue $�"DF'i�Fc=%Fmb)X&N6�:�)ira�fa�! I�� =1�_KJXE�)>Q 2HI��)� I.\"�9-��5B6�V� r&},.$(�'��*S(B�N��Ww9SF'U $6�xi}6U5 eta}>=- <�2y20QI29"�`}�7 B/ ��*t (F)=(�@ \bar{J}) F')=-A>soa�J�a���r�cF_7. R�GEbA�"�MY�"7?:H:�e"�F<����B �:&�4iQS*  ���AAZGI�.�v��s.�"�.g �a*�Nc utes�!A�@V2T.�i�/ �.2Y"2F�ͭ� up� )}� �' ' 18 Ee6:S !oZ3Eain� e � �*of&�6a;!�8M�U�A��iy36f6�| Trac{)�� W�i)�! t<��^caE�=is funA�"A�i,>a�MFXI�� �h*�B�o dV�/i&�`oa�� � a�6� $��. �$[N�]!m/ I""� imag�6Z�0 $ unu!�.X :�� A�zX E�+~refHo^�$A*! B��T(or5��7�E2�-��ai ABb$V<�\lyF�A&�)��%�ni�UTto adopt a terminologyM bluretiMTb�!l ��Z�4 + ��j�Z��%n parti�6rol�/�Q�ven~��]/3�")T holdee�1lw2Y $chi}]$ mayf!ttribuib�e�us� �sa�IZ�aHq+(�l�v�K.7)A27>�F0 !mr��6]6^�T� � � d&�!�dB�A�6 f�"rn�Ye�?��n� "�, ver�c�: $\Tr�@)0"Tr�@):Pb$�.� �_1JN_1]=[FVA]$ (�latP =/&�\ W8E���6!�*.!�W�H��(�  a well-�%d����W5��%if�assign�e"6�N!!��[�(FJZ� � aB�J�� ��7to�"� A~ [JK]N��� ��� ``6�''v��ei!gM�se��!�=QDb* �~?a8�X*�BZC��na�o�9�!^" �Z9�J :6�.o� U5 )URN%h�M5uAoQ�L dime_$�M3$.��n VT�)of � $3I�i��F�G��K^�%c stronger %��2a�:��!�R z�w1�I � rkQA@jq��o 9�| �  ��ss��al " cj%R6%�a�!�vAAIgm�<be�)� �QT� A:�,,JxB�� �)\kappvn-�� �0, tak{<in� ccou�thd�8De�J|)61�is : a����TF^�V �Ft& &:�)2b *�F2TermseTF�V*6e2(} F^3 )W( i�]1)oz & &j� 2u3>u1+F�G � d +b�Y -Rs�51y1�F��*!�aNre�`three possibilities: (a)�?odd; (baCY"Fl:2 ; (cvA+d :U:CY �)�or�:&9�1�P\:�Y~�=�%n �c)�1!9Q*AE?1�Dv�i�� >_o-�A�A�����0U3" 6? �# �a�dA�=Rf k`�T��?of�WA�z� }!C.�W�w very%e��:HR�@^3=(F^3,(1+F+F^2)B ; C��&N� mVV ^3=[12n 0}]$.� ���o�� Gne�ZO$ norb�^2Rm To,b�J� ��J� obserPjAu8w�V�2y $-A•\� {1}'-2>��fA hO�]le giv5]w!d �� &�  GZV� � (ɞ��o on �sid42�-6)4#$2{"�L^2-2=i"6� ��M9M�>�W$d%{�.U?^ ^���~  $3�.�fTU |se�@r4��:�6�/" �oZwB�Ashi9�\ iF.�D���d.��1�6^s6E!� is m\��y��Q+1)M? ��1\�,���u6�81� (eq:F3Equal1"z[���r&^ cQV�*L?ti� absurdum�SN�A* ->\ )%r6�J�)�A*�)�^ e�ief4)#=1\�1�BB�T* ��+F}��s $-�+1)  -2>&�u$��1�_ = 2F� A�Substitu�E ~$ G<o�O:�eUN�,�-$� �9692� $%�m F:�F�S"�>Yo(F, 3F� =Z# r�Y$6�Y�8!MBUat�omea>Jp:4�.)�%. �2l9�^u. e�� s��n�J3 $d=3�ca�&Ŋ*;�}uI��q?,&�{?:�i/"f3 wj��oAe"�)M ry� 4�&:F� �I"rP�:�q7[y�re�wr� �~e�i�4-qO�`&3�&gaF�R��u[>� 5 & 4�.� -3-��;xJ`P- -56(YP�66B��K��BA>�3$ yeA��) =�:s=6 BYWs)n� pl��JortɃ roleA���+@�iS-� intr�Ve�@t&�.e:b"�"tioi�F�B�� aͯcanon�z} ]/~ i&#Jnumeratevttem[(a)]bK�� \ ,b,�]1}�)��g&�+!5� stip�o�is��56-��e� �y&� a�aB�y 3��}wV"�>�afw-:F8�/.r �!:� �:. 6yRBSC Vyq�w�; $5\le�Sle 45$ #�d�,5�� "3Fas[erAly�_<is!�%xw�h amin� e beha-q*�4s*�d\�? Fx�2!�.Ij; �-�DQ an :�aw,I�=��`M�� � uggeE@���xA�GPbf{�]ecD� A:} R)7!aة��e��!�F.�/ ' such-$ A�Fka u� ���� ���NrIgcb2co$of Zauner'Uf�y��&e[ Z2@0}��,��2\p� �� ��� �It��be�1$J���zeN"y>+!)}���Ia��  7Jw. -8mV)EaJU:1_d1"-�JFBAFInI��t�ENR!F��� $B�R6% In S��+�L�wQ"R�~'� datakLS fI�rr�Cr(Q�B� ��_d�8$!סҁ�q6I d!t In T�# �tbl��}�lis."/� A�Aaq'y�"Y ~_dA�*�'� _d]$��B�a�ha��tsuy�[n�=AK>��&(F�LNj2dT/2}v���wexcep��y`<=�alwaysLn�4��highest 5�{�� V 1g$d=17�!�^�b�ec �;lowest}9n���(�oSMALL�> cent��$ ular}{|c | } \h�<< \parbox{1 pt}{\`a{0 ex}{5}�� &\pdB% Z2;!� \h� {1 ex} & f e $FM: ,�fJzevt � !?y�Rt $5$� �K�_�P � & \\ 10�cnd'�F �\ n8 (1, 2, 2) Q$2$�2�: ,\�26 H�J�7J-9 �- �6��-11 Ar�8, 9, 9�9�!���2�3 t ��nzm9� ?~�-�3�3�!N:�&A^Q�A�$-�27��10��\A} !���- �-1A�n;-�10�10�~���)�;&e5r}B��\Ouv8782,����8��� 2-�5%��n\B�%��-~i(a+,z���4�Mi� ��1E���3�����#&��NQ)�%P�hAw��;!�10~��� ���^ ��1 >r8a/ 3, 4q�4a�!Q:��3�#z�8Ey�f��g & 7zBB1�VA|A�n5�1�11�=�ȅ�z�i2��4�|�da1��:�m�3�z�9)��[�� & 8��-14醂�i/, z����w xiA nBSE���4����3� z�A�u 3�lA�1 �%���JB~t)�1����i;z�:!��5z�a: 4, 5q�� ��� z�4 ��m~�B�aj��e8!�" %���y�1��:� MSz`B�鎜 a5��R��3��z��& ��IwE��1��@-1�n;(%�����-��������!� ?v�!�����aq&y0�&_ -� !��6�snYBJ%�a,�;)�2, v- ��(Fs!N-�y ������*@r:-�6���:b� }/@z/� � 1�~'B��@\�� 9�"H��:���A\x��¶a^��a),��:�� =��@q$T 1)���r?B���Sn�(i,, v����NQ�)��0�s�M!�=�a�j.~��@�"� �]n]B����O�� )�3~���)��\�& Ɨx�. 6, 7��A6��=1� �!'aD��� �h9�"E��:�����a!\%��l�Oqme�n:(a-��5�4���1M9�]�n�B1��e2Kn<(i., r�2��)��zi롐n~F�����n:!�7:�:�&�� 4�5 ׅ{����v%�� �\%�~�����%K�i�a!���e_"U��8 \\1� line(ta�! \L�size \vq!2� \ca�"{�**�2z#.M&B�"�$B�$�"Q)&u$�$F1!&. *DX"�/�:S> F_d 9G&�4&rT�N�% b&"6D�"�#�$N�$K&V�t:�""YX�0�+6�$�(Ba&�$&�-WQ7 max Z�"�$��Nl.�$of ~$."lZ"(I0"+$axM$�5Pp�mpu�w,algebra pack�H(�$(Mathematica\6o++-�Q.x7 illu�>t�,P)2�Q �%�J��&2y.R>z%�", �+�a.X\. So,*��&*6�$y'!G vaila* on�?'m� bsit"�?/9/yG look%�`ay2sX,q}*�x�&� )J5})M}�8 \arg 5Yn� 6� �e-�Hq}bH�-BN3!=8n (approximate)�2W�.E��|E�1=� =(1,0)  FiP!1|G�5\^Qq�]-, (-1,! or $(0,-1>�F5)��}+s9�pt0,1t�-r ?D r+ s, s\$s1Vs�*�8 aCo�Q�p�D�S�1C2"8� w")V��'�cJx�Ms ��(aH* �i$�)FY [F_52�/y( 5]= EZ[> -1T_� :�/+-6c(�2i�>\];B�/+2- squa�`k,V�j,To check) >� "O�I�n*i2��f]��^���>F_5�z ?7�4 >j&����4�..pO&�5"���rul�#�T\inb�$"XR�1�M &�q\� 5}} .#��Q��(2,2)�t�)c,$�44-��4��s(s+2 r6� ��e_s |^6���/K/�bΞ/?p��."=��h��� �7� }{15bU�e�T1>^3�hA`F@S\|�ZU} -1)�) {5} ͌nS\|^{2}=Q�9nAl chinz.eci�`a���confirmkOAK [�'AV ��B|B�4� V�Oo:yTF� E� s�S,Ac $r�>,@g�:nd&Zsam^�H��$)u��I?Pwm*l�3[l1+AmM9� 3CdU} + e^"+rJ#^2^F�9E��$�/S2�1nA9e�,�Vw�� :�I�6�!jWu�J=Trj[P_�:�p�h%? & r=�  2O@& !�5;�3{orvr�Q� �7e2�\2�1� v�� $v-���1� �lQ�+0B� Z1U^�-�qns �AS45�eU�y9g&� thro � �J�V� waj76;��"E�sligh��mxYh�ed�� i�{,V���t�=�w�s� =B�?�x�P� �so6�p=6, 2!`4, 28�{��u�:C0�Dn��f we�o� 1d��pA[!�~�X 3}. �Yd �2e2�X"�Yc full�V�:E9���"s5:m{6�fWofI [3x s ("6Im) $; EC(de=�QofO >p! 6r�9t turns!���,R�2!l�Z�; ��M$$3$ cyclic"�b ge�A:by dJ {d�G�4 "@3\u ~$&�2~�~a" �&ߏ2�B2�M5iJy�[ A�k� t 7}:�xi}_7�=] � BJT?� � ��� ,�5 1�96� f:�a;%�w8A^�\�}_{Z� �G F�/&3{7!� "4u�8's*b8�a��.�8�8!un.�<saw �&2�8;Bs QMrta AI*i>��?e�J*B6_\/:'.:�h�-achYr��6�9 F�9mgZ� Z2�0)="�/t>*>e�[L>+�`��9*hTs��Y:�7-=ugacy}"�RB} ��5�5|| �5��5L}5$%*�9 �$*�n�5 C:�5C\203:6 6vC\�5 " "g6>� � E%0�+�z e�q�<.1FIA�F:I& $ FI2a ��Y�G>I1FI5 ��F:���*FJ6b�6�Z ��:Jj$'!eA>:H \\.�&R�! 1�]X- >Un�10 B>I& A F0:� QΓ9�3B�� ]�& +��j :Jn&�R�B&6�$R�Q�!9!��%1g��A7F>I!�s F1�A �4m8X>Jj1�A79>>I!��F� !�R��BJj�0Aa�F>�6�!R�!{�11E�!BUj��B���� J1-��R%:���!�A�1!ā��(6� �&�R�L�E`>{�&�F:I6��&R�AY�10%���AAjB:�!0� F�J�A !0eO>Jn01�U �B>I!Á�N�A������i>Jn�'8B:I6�1�&F0!(�A���vaV>Tn�A AR�BI�J� F�!(��  :�n���QF>I!Á�N�B��R�eN>Jn�� �AB>I:�^{��]!�!BUj��ARo BI!�b{:J��BJj����W�+FWQ�!R��>{j���A�_F>I:�^{!{1 ]Yb%�p /Z6J>I!�^{M ��R� -2� ��!jA�\B>I& &,F�2�)U�%��-3�.��-19��F>I:�L'F�A��U�eG�b�&�^B>�!�^|>�" E`>Jj���aFF>I!�b��'UW�!&�>Jj����PB>I:��}�}11a�F>�!�^}&% � X)2�( 2AX>Jj1UW� B>I!�^�A�.��3�ᦈ�ԖW:��}u�������!�+ NA!!!1R^ !B{n��.EB�A:z!�^�z�UWa�-18�����@F>�oeH u)N0a6���*3@:�j0!���F>I ^* �;.�2� �BJj�a���FJ��,FqA�.�-3� P+BJj��I� �B>�:�~|�]E���1!�AA�F>�!�b|MFq����B�W�����F>Ia���%�!&!7BJj�q���F>�.� $8Fc!���As�24 G8J>�!�b}M�!!R���!�BJn2 ��A& �h���%-"$9+&��N>+uP�jf�6�\B� b; SRB*_d]f43� = F� �"�" #�7'i�� %�b�3!0�#"!�:! U&in*Q[Tg s"JBN��4)e2�q $F��"!�ecyXB �uKfirmed.�Y��rLt�-$ Z. N �X1�f�VC�VJ~Vs�V��^F�X~�XR�R�Y"�/$S�Tf� toZ5I% �=AC@ʕLnA7n2g� ��#�tE A. ב"�&�t� N�vautom`.#� � 2�Y��fb)^te��D' to k�x�")A�� �!WlsoD+>�wh 1)�U*.[.�G.eR�!$�[ at wT�`a5�$&`Q�C�,oly �oB|!]&�DQ�s�$�$7$:  ], OP(�[ d St�"?�_%& �- /*}"�!d--�e�mad�/n�^�\ search�W�(ttemp�|�(�)total2��F��UO�/Rÿir e waag hausݳ �$�bir�Y�("���'� $2 �l RO�o)<&~y2�]��e&�� �]W��}��#_& B�#&3�M�� �. Ou*X!reo1�_\ >�Y)�DgT���)AI��=1}VE�}J�A�6�$�}� � $3$ "�X%(>�gre�-y(�- Av!2inc�-e�"2 ��,��7����)EJ�N*�a (on�0)Pa�eD"6�%dsg�Q)5�qon�WthXY"Us\(bav�!�z�w�*length^�8Yu|da��*a�rep�bV3 0X.%��w%�H[urselvesA�summarizE$\�end�#"Sl�}�3/(9�@ (albeit tedious)�crm)�Ohel' (#�d�n 'M*4o$ �" "' renewՁTand{\arraystretch}{1.5"��6{�"| c  &�" & \m�$column{2}{{����}�� \ \c 7{2-3}*�& type &M�&��)�*6 �W&f�Abelian �H6�X1$)B& %\infty *� 4} 3F0k&��V,F+48F��Q& S'IJ�'#&#3JG7�'FJ#bB�\raiseTZ{8[0 cm] {�1!�et6Pa Q UM�8 0.1 i:��8Y�{6�ٯ�n���~��s�<����,I)�� �"��g.:)&<_&�h/��tЀ�h2b �� �mF���9d*�� 2} ExA� solu��i.���|`de��ed by_':�a�.�� �5}.*^� e �J� +li�la�8eM��b�do sidq�hN�w "� �5{27 ;��1(3+ 3})/6Gg|e":� /�.$i \pi}{4}} 1(3- 2:1.)��7k>0�s� 2 6� �� �*��n�JUE�9,2,�O2XD�>UZFB�}0}&�*/O$�d&�*��d6�dAN�t*wZ�+s { \am�,displaybreak"f �u[A:�~���+f���52 :�+&�+ \ [B�~0,;,w:,"12=�\\r�C���T �I�o��^-�.�,>(�0l*sgI�� �j�d!����/s�dleJ��5}A@!" �� � ft| 21\C7ף48uƠhc bit��p:( $48 \div 6:�:s�s (s if.q����mZ8��F�)(�3q�w"J $SIC-POVM's���<bedf/�md } �c��.�3}r�~�;7b.� by �-�� }^�Wo2w in B�fѳ�{-}� i�jusu)�)�m !| -1XC �)ht<@o]�s:&"MpYsee56o�uuan'p� ]��n����� ; t�� � �N�con)�S�ly many 5���E[F^�gj���dparameb?fam�ofN����}�e{3}(t)�j.n6��2S6�#(s6 i��|e��-�8t��ѱ��)�7r��c6��N�A �I�ng4 !mN]32�$s *M�փ3)��7T� J)9]�o2��:m���:�Ϝ)Q?i���0nFy%�W>2� =-{t+\tf��e3}}1� \7 �6u� �J�?:]�?-5�>����'�odc4Bt'������8E� `�t'Q:�+ �8 pm t͏��> [� A�4]s� r r�6 A>ut&5 al ed�te�&�nqvc"�'6(uffic�q k�� ���2��f��Non�))�< for %6�Ap��l�69 tD0,h �9}{6�#s�nrV��q^ ��iI ki���zbit: k e%l>��? ic J"s.=�to ���$t$: a�*�rio�val $�E ��Dtwo&Kialob�>B�N,nd N� s $t��%�)* [a�pJ_ F"y6a(�.N09���� ��4�'��a>�62p0}��ws���� S&��Oˁ�7)u tw� $432{48=9$"| �:I"F EI�2b9$+�� der~�O��*� ��/͐�WEa28!�� &�4F@ [F_32h�63"]AB�7� �� :� ��> e ��d8[A��"�  �b ��"� �g^2b�8�%r:��8 "= �N�Ir, u-12=l/� Z.���q2�nZKaI�ic�.E�<� $0%"�����������a�'^� ��bG Q�1�I���I��u{equation} The orbit thus consists of $432\div 6=72$ fiducial vectors, constituting $8$ distinct SIC-POVMs. \subsecq<*{Dimension 4} ~vN� \begin{multline} |\psi_4\rangle = \sqrt{\frac{5-\\5}}{40}} \biggl( 2 \cos\%,\pi}{8} |e_0 H< + i \Bigl( e^{- )i +} +Jl(2+\ aZr)^ y 1}{2}} ei <Wr)n1 nLgr. \\ G gl. + 2� sin  A:2 :��-\��3n�r) \end=�is a GP 1�-� in d1�~$4$, as!�\covered by Zauner~\cite{ $} and RBSC HRenes}\footnote{ In 8's notE� $6 $ is the �Q:U�!�F� \left( X EW {1 a%�rho^3 Yb}\right- UIn �2�it� �m F�r_0!�Q� + r_{+}Ai \theta%�U9%1 % %1 %Q$ %- %J- %3 5�!��for�H case $n= j= m=1$ !�$ k=0$ (!�8, however, that6re�La typographical erroA B�:% ir exprese��D$r_0$ should read y�%� 1-1/u�)�}/ 2 2�2}1�$). }.��8stability group��^LLorder~$6$ cyclic sub5\ $\EC(4)/\Cc(4)$ generatI�A�8anti-unitary opionF l[A_4,\boldsymbol{\chi}_4] = �[U@Dpmatrix} -1 & 1 \\ 2i�,e 2+06& )?] Y Note)�Gb� ^2j�02�3 r�F�0�:��f6f-1�g�is canonE�E $3$ (whalwe used Eq.~(\ref{eq:KernelEU�,}) to obtainE" last.o E֐ hand side). It follows from Lemmas~jllem:CliffordStructure5} and~!OA� ECd}%� A�I�>�isa �$1536$. So�2� B<con�s > \, 256&.��s>. 256 116=16$ *3 It was�!wn�N�Y��@re are only $16$ <2� $4�We� cludM�!:�s all liV a sit)of2 extended 1�)V. ^�5} Let�t5�� $ be��K umerEi in �Z5 ���d��EKsec�c5J�1�xi.�3\>m �o>o5�65)�ofQo 6000��o�Yo>E=3 = 2KB�6p $&325=80$Y3.�n80$ SIC� !�:��l Ql �l ��&* analyt��oluEin�4 $5$ (on p.~63!�his�sis� � )��A����� give exac.�s�� eachLth�s��e6.b666���We�x��6i6>10368��y?E�a34�� $& 3 6=96�96$��l (in agreement with Grassl'Q� } i.$sis, basedA�hisM�ZB6$�&. MB\F�caZQ & BQ� �Q76Q7�Q7As�Qx2Qe��g�g^Q 3292�Q�yQ?e6 = 5488�i&349=1126RHQ i��$33bW 5�co:�re must��at lez $one other ��{search��Y addi�?al�� or s!� facM .� f�.r $7$Qr�=Naa BR "I : which> $F$  � @diagonal: namelyJ� F'_{7}2a 0}&\ c�  - 3 &� P :� F� +6l "� :g!`9$ � � mean�[0 $\hat{U}\in Z�$� permu%!ce�SpecifM N ] =.x8} \sum_{r=0}^{6�{4 r}�D \l~e_r |>�!�y�� @ $e^"�) an a�r>phase,� "p havu A decomposE� describ , & Qa"+ 3}).vis �@derably simplifie!� lcul~s. � will also � occa�toa�� U� ��2.�-�W��is�squ[ root� $^�� We looke�eigen� f f; LetF�l_r = m��xs} 1 \qquad & \text{if $r=1,2$��$4$} \\ #.!3,5 !6$}I� R &�A!�lN� a_0�H�Bx4&�} + i� ��+)�a_1.c4a�qrt =8-5 l2}}{7}} - a_2� "� 7}{46�R-M�b �e2+3 e14H%q b_1= J�8(��cos^{-11(� Ds2}+1}!  \rRdThea� fine�align '�� & =%�*� -��1��\E!e+ A^a9 x |e_r�� \label�Dim7AM V�A}��':!M.+�L �b_1�l})(}.zryBM�-Ii)ily�sfirme�a`��>��=both GP >�NG�._�:3$ "-g.b,��l�Rq�=q�8� s6$&�.s $[VY�� SincRts�V$non-isomor�n, s2bJ7Vmdisjoint)] P6O�U�$!�V& � 10976�� '� 2246� Thr�R� � ~z a furd $B� Tc account� all� �i!�*X dent�JU. �N� ��no� � , apart ?0these two. F� sakevHleteness� uwA%aJ�%�5���� =<>g�I$@E��NET _)a% _oJ� 0 \in�� eft[�Q"� 1 M� -�� �:^��BM$ Finally,1Lremark! $l_r�!� Legendre p (see, \emph{e.g.}, Nathanson�}�� Rose  })�0��l_r=\gen��(}{)}{r�M>�I�� ,important pr!kty�{rs}=�� l_s$�E�r,s!r(\mathbb{Z}$��{A Fi8 �S+ &19}� sec:"O In S F� !A1 Hs}�saw�, except^E~$7$, �eH2l�s hlF-�n~*e�4might encourag-e  spe1 ��when $d> >[is-�always}a�.lI�is"�we  �AA�.� �Y t� at p$ ve rule,F� 6in����19)�! 3B�!9� $\ge 18!��  !�u�an.) �a B18ẞJ'_{19f�qu�-92C ��\\f2in 19�19B0"-�y�U V��J ^6 =� J�8.�7i��F�r�6D F e %�5�AsA�imilare ouraImon1�I � �1$a�A .�.> $l'�:b��e>:F].��R��V>e bd 04,5,6,7,9,11,�or $17s ) :� H2,3,8,10,12,13,14,1� 186� )�Y��R� b'B� 5 + 9U $95} }V /1=2� 10� ,19.$� � '=4$.� \� 5}-1M$�� �"e�x = �*C 6C 18}#E  i %� ��� �@eq� 196� N�is~K A* ��N$�an *�A�� J��  ObservA���6 m!B�P "� NS �#2�iv"H$��(becau" he :�N @*���� �Ւtwo di '�6. �\.'D�iz��� &�:"F} Our6�"����1N"�, $ |�$.�e���6'in Eqs*� N+), (� I�:LB})� &5!DiF�)�*k b� e��a6�sV !Q!8uNr i����4( correspond!~9za*�� !�@is natural to ask!w�a&~ P �s true o orem^ v� ,elow answer 2 ques�W.b{ne�e"�l":�U)("QRF}q $px Pa prime number $=1\;(;$mod}\; 3) �'nd�� $n 7 ny integ5�a��I�e�n 'alpha��NS $^2?/ + y �6�p^nBj�1F*proof}� rel!� heavA~#theorya7!it- ootBs6ZT(for example) Chapter O"� � � +~5 of � & }�� $\phi%h Eule�( phi,�p toti�fun�!(soE�x 9lx)�, L(x)���H-�of . s $y"r_+0e $1\le y< x$mXre vely%!e[ $x$�J�6#p�veQ0 $g]�� $m ��,iplica%� of $g$,T �edq*M l�!\"� _{p^m}$,a�%\H(p^m)=(p-1)p^{m-1}$t �-�,j�,>!93%�!�.� 1-'��$pN^$�$p= 3 kA�$ � some5� $k) . D2&\m8(= g^{k p^{n�Z�tcimmedia�J�' S^vg^{A�(az>1 f�"ILem8Aa�CubedB�po~��G$ v-1E�R|p!�suppo� at w��no!ve�*��B&^*�R'"7 d!LAE;�{��� f�B��A��eitO�modulo}�]$+��9� 9� = l E� )�l��-U�ElU That*�+is�ssiblea|ce�! a mJ��� � � - rrM�% :�q� $\beta}�J# (u!�NMinusO0��97It now-�s)�6�:�)�~"�b) �F� �F�2�^3�+�0j/6nŮ}������"�T��o��vec m^*result" ��em�� �/cJ�* y�25\�,]H \C(d�d)* A |x/ i�/�  if� �)if2 i�� 5` )4ate} \item $d$]"R � �e divis��^.  �$. CDn!4� :s $=2\2;J:� ot 4ecby $9^%���5x��} �(1�j��$[N�=x � 2mn&q D $7, 13, 19, 21, 3T7, 39, 43, 49, \dots$Io� �M~ We b�3� prov!�(sufficiency%,�� 8" s (1), (2� (3)E�Z+�� n�,��$t��"�y�8d= 3_{\vphantom1$^{n_0} p_1 1} � p_tt>n � $p_i"� IU& A 6 3) �!�C��n�0h1�<�r��e's $n_1, �, n_t �!&I *Sf"�-�6� ����i ��n^ ss� b�_i��^=s2}}_i� =^�_i!{i�e`6��$i=1, t��W ni*� Chin�A� indeM!' *} n�  orB� �/ dedu�sre � �9_65֩�J��-T �V�3)4\Rr� an c7 _iV:L w=I 9JaLq� - b=�%��V�n�VF� �$ConsequentR�$%0>}^�dB}R�ͱ1-Y�F1��"9-C.[- �0 �>e O$SL(2,*_{\7�8,{d}})$ (bear�]in min�d� oddR Moreo�5$\Tr(FT-1��*d���$$d \neq 3$�l65�b B�4]sa>� �2%A��B>) (* d)^2a�4�Bes .A T��necess�5� N� 4��\delta)�9��%��6� B<is�0n2NU !(� �)e�8Ma+ � = -16�-�,� lyA<��m� D>8Z� O*Aeu(QuadraticCo��# Z8=N�VM.I�! ��- view� �[F� 5 N�.P�7EVsho(aI���  assu} ,�(.� Kne �6d ^=:m ':o Q�--q:j�p��Y$\[r�FN6�J=�Q� .Q �Vl � $r�a 6&�-$p$�/�/="�$ "� $0�k < p-�:)@ = r^k2�A�p)e��w � 6 8J��d*(es $r^{3 k}� :���,�ZG!�i�,�$T = l(! � �� $l:C �.v1E %E � $6 le l < 3 7ak�| into�#a5.K Bs� x "D 3$&v$pV) ��.� $$l=0$. Bukn $k= 0. -�=�+FX�5n1SJ�QB�!�t� �-$3=0 2G\;!�:` �.igontradic������)BX�ag� proc�byfr� 8tio ad absurdum; 2� \ 6n9�t��!��� i 2�:E�F :�&�ia>�R� as% "#ZlCBN .31�3as�ver!&(byX;licit �ion�R)��� no&&i�$9�hadR<:`; �"a� ��s j�1 d�1��FM=�9A��,,��})y�)��F33)a;^�requirIqF�z\det ! �:u  3)�isi# $r���t�����'ty� , �� mLs8�p!�-9Z/i�� D.� JN( a?73P zwB�z {\&C�3-0}�%��<Apapera�sa� ``a>orousA73;f^e�of&)) ll finitm\E:% ems tantaS6, lose, yeths�how�ant''�at wellaW�Aesm�=pere&�M�matter!Qh�+wor� �Aproblem��%Xs�:imew&�� sen�EcruhF�QDy layiHrou( �n�Bgto!Mat�hopes�illusor-�make ouru�pub�A�?8I\theA� y, n�thelesV<�+�*ew cluesQ�� help�td*us +g ward�?n parti3'r�s)�o0�signi�3�(g!���b�de�)i|@uld be establishe�! %n�ru ��yR�&sJ�!BM. Also,���!��3 one �� like!k� exac��) why} �:. S?u&8HAc; ledg��$s} I am g5fu�( Chris Fuchc, exci�'my�res/�M���H�.Mhim�dto Paul Busch, Barry RhuleR\"{u}diSchac3a�inspi�discuE,s about POVM" YT#!mysteHof quantum mechanic62#� ��� .�Markus �: , Gerhard;>� AlexatVlasovA�� veryE�!`com];:$gar(!�firstᎁ��i���. � thebibli3F y}{9�*bib�{Davi�3 , E.B.,Q �T"�Open S!8ms} (Academic Pa%, London 76).�H f%�1}��%�P.,!$bowski, M.){(Lahti, P.J.,E�O�Eal �Physic�Sp!߁�Be�{95.{PAz} , AYM �: �`a�d Methodc@Kluwer, Dordrechtd3.d Nielsen}  M.i�!(Chuang, I.LBWCom'+on,�Inform7H} (Cambridge Univer�-p,�A�$ {Prugo} ve\v{c}!mE., ``d->tiNHaN,�L Y� asure�''Q Int.\ J.\)@.\%� .}\ �"Tbf{16}, 321--331 (1977�I2QE2��.A�p$0 se� p%�al �ities��H30}, 1217--1227 (19< Y�(dAriano} d'  G.A�PerinotI�I�SacchE� F., j�m9@I\Fa���enM: '', I�!UOp!_ B: Q�AMSall.\a,5m!l$S487 (2004.h Flammia} D, S.T., Silberfarbi`Caves, C�, ``Minimal iY�6�2��puW0tat)�)�(-ph/0404137=j0Finkelstein} �E a� ``On PSI-&2� PSIR .~A�� n 7078n�1}2� ŭ�q��D, Re#-z ���Jies�"Bayesian���)���$.\ Rev.\ A}(65}, 022305%�2.��a �Ayz�Un�n �umE)tes�K de!`etti r>t��hAv MathJ�843}, 4537--4559F��Sasaki!��!W%� 0, M, ``Squeej)�b ]a through� lass���xnel: Mr��` AC4'�a�)� 30M� �-ԡc.\��.��37�04�2��}6�`Q(* as�.< (ad3 8 a little more)A:�E�205039]�Hardy�= , �Iv��yfD'easonab$ xiomA�)_12>_Ax2_Why �um c?�ia�~Bux field!�< T.~Placek (eds)�$PLing�bO Eric�!�tutu%e unbiLG ba.,aj�96 ar��''6�120�� } � �&":c�"�6 6!D>�5\1��l 1�SF�Ps, B.D�Opt�� -determinex�m>2����AnnJ�191� 63--381 89�6u�3!Pibbons, K.S., Hoffman!��/ �X ``Discrete phase space&�HM�E�e$��40115.:e�"y8n�J.a� .unm.edu/i�/reZ9 s/sicpovm� �GaDsman1}  , )�AAP��(fault-tolerAe��o*� :�"� 57} 7--13{ 8. x2J�F6x%,um.�yJ higher-U� al s�A4in C.~Williams��.):� a�A/Commu�R~sŚ&i��F�$NASA InterI�alWfer?n.Rp�YA=Vh(QCQC�. alm �X Lalifornia}, 302--313 vn�980200.� 5pA�F�H9$Heisenberg:9 ��-� Ier%b A�9807006� Dehaene} �r,! de Moora���;F G:V,� KVzer� #0� ineaI�06&Vs �! �.$rm{GF}(2)$A�^�(68}, 042318�p3.�Hosten 3,!.� ��D6�S�;�%�o�>M�!h&�GU�-m-ar ��hmetic�! n%�040819.�4vanDenNest} va�Cn ��N�:�ThX0va$��jlocA�U�>� 1003.��BҊFu se�  i�Hharac�ze>�mvali�fFY�E�A�041016.� JacobiRef�rnd" !�Schmi�yEl�%�� R2} � & !F [I�}�byin� eHcs vol.~163 (Birkha$ser Verlag$sel> 2^*3 !�&� �J�|Nu�4%},�Odu�0TexW75�no.~195 *�New York� .��33( , H.�)7A Cours�)> $2^{� $rm{nd}}$ e�* (Clare Oxford% 2 3!t:  docu. }�% * AN$24/3/03* % `%fxis Ea�!�APS%@REVTeX 4� trib'T.EV�on 4.0? *, Aug�2001 %) Copy@G (c)!� Am�Vn~,Society. 8Sexe Z 4 README��re��nd�.� J TeX'�b��77youeAMS-La�2.0�talled %��Ay�!"preO site�) !�n� %&$DEres runn�BibTeX.%,� andY:ag�Y:aT 1) latex apssamp.tex!{2) bib3^/4R %\Qa�8[prb,twocolumn,8%pacs,p�int-, %amsx#X,amssymb,superscriptaddw8]{revtex4} % S�4 9(��$of many) p�2il= B�ep�Jg,ap.kF� : aps,draft�F-aNb59:�T%Y�Re� A:7q,style{elsart!!6�H{sab} \usepackage{Z_x}% I-fig�A�s2, bm}% bold�h \newMg{\beq}gin&�!}6$e$�%'!>" beqaGnarray>%e % HZ# }{\mbox{e>=w}{\omeg�:.�ai}{ _i:� halfT$�%kVc�M$>k raizr4\�LF; ket}[1]{\[G| #1 \�\r%Q:�bra.HQ4|:. proj /ket{#1}@:(av &ls #1b:'bra�2�+ | #�upX{�\uparrow>$ down&( %\noI�"��a(title{A new�sm�$Helectron spin echo oPlop�d�QDXauthor{John~J.~L.~Morto�*,email{john.m@ma� als.ox�(uk} \affilii {De�X��M/,�� &9OX1 3PH,$bKingdom�s4ei~M.~Tyryshki�bw E��\Engine g� �L ton .�P8, NJ 08544, USA.�0rzhang~Ardava>}&�,Laboratory, 2 ���U1 FPKyriakos~Porfyrakis} j� �0Stephen~A.~LyE�{�{ G.~A�J$w~D.~Brigg��v�,date{\today}��!xI , $, but any 3 mayl"ex['%Up`Vedu� abst� } I�~� (ESEEM)�' been ob Dd>,� P $P a coupled� h�o}-� paira��= nucleu� liquid"�'.� vious�L�N efferin._ xperR%t�$r9pb�.tV :e� r� � homo�are�NMR or a&re9nt6�, EPR.:5-3 low-fn ency %Y (26% 52~kHz) d�#o2Q��Yany9@%V(with $S>1/2�'a�Jhyper�S5� X!mar 9.)[%�# txO�:5�%$ ($S=3/2$)�.@ ($I=1$)!�A J hed/& full�,e N@C$_{60}$R 9�A�� n�risMBsecondI@=� isotropic>�� of b@�yA\$^%U$N �us.� y \D H{76.30.-v, 81.05.Tp�}|&�� &(Introdu� } M$}!��)@��in pulse� gnetic M:ct[.�aic� a popu�Jtechniqu~ studz( weakdi]ex ings1is�7d esB4'@a�chemistr�Lio!<�k sH:�M�Tinm�s�=a�i�uc)ha�< �q!ce (NMRIEQa paramJ*EPR) �Adernst1987,dikanov1992,schw�Hr�}. Two+inct v%smi�E�%�=��(�id"�R)! liter3Fe�'!܉�Z,!���`s, $S�FI\:ruy "�n�&��e oxFpole-d ~8aEWL, $J\!\cdot\!\vec{S}6I}�:J  S_z I_z|Y)e >�ed)t��;Y �iZ 2  M5 YIcE betw��un�)a s (i���� ) �­� 0,N 09A� 7�p�17- Bs�K' r%^ dift FS)�kulano.��EA1 �u�:� �6G energyI"g�tsE� upon apg �qr:F&53I�n�ineVs)&�eI etiz M�+us�ByTed  =eqam� �>)�� same way� <c6- �in��Y ous a���� . A��50 Zch doa� pply�E4edukM4%QA-a�kso�p i# fiedm�r�ha�F+sm ? ��an"}E(r�S�L�,.g. $A_{zz} �& + x}�7x�%~e!�reAP� t�2ids or 1 visc8Iy� ��.��o�Kul�("branching"!ȡa� tran"as cre.�c�c�� �( j@t ?�}pr�;�� :#�Mat+;yFbef�a�af K�o�t1 accum�An a&�d��e�;c�Os�i*I�ɗ�(,!�O_{Ik} .)�3�M=1�Y"��: I� ampl2�ѫ� depe�one�.) ]m2�mponent���& is PN-C1demrw�.���l�:ARpr�  b�Lf,)*����h��� .� a.� ��u�by�ur Li-:+.&�� w�$�  A� :. �P.2xi: z ACS$_{2}$: �,���ev � ng t�'< B ��(($a����J@ ,, $a=15.8$~Mz to��Ͱ �� a�G iz5IY| lift���_raY�6�}�, lea�~t� pro0&. .e 3 �-y��0 Apshall?W=�� thir2P�T!���U in ��M�!k)% &� ~molWZe/� epaYu$ longNpin de�4!�� T ($T_2=210$~$\mu$s), %�%ty03} e�(8hem�?%'ism�I�� 0� r.*� "���� } High-pu%]��S�ar��mito},�5 solvH8nY�%�f�8[6e�!%� 1-2$� @ 10^{15}$/cm$^3$,�eze-pump Qthree�vQo rem�Aoxygen,� f ea�i51f4tz EPR tube. S�es}5(0.7-1.4~cm !��$;ain�pproxily $5� �3}$=�� s. P�nm,e� md at 190~KAan X-bI#@Bruker Elexsys580@ �mT,�p! ��,a nitrogen-f�Scryostat�!�2-�> (Hahn)6�P �)�mH�Q,i/2-\tau-\pi } @N e $\ $E4 $� du["���;5�112~n�/�akly. P�%�xngAN u� to eli�&�=On" A,unwan�fAin�oiay (FID)�g� "�8RLI�o&�4�bw�}[t] \A�e$3 e {\# e�Xs[width=3.2in]{Fig1.epsoYcae�{(A) !��rum�}8.(at room tem�"$ure. Each �#+!�tri�1 ց��<B7�#2V�/j�_ $M_I��&��2�0. (B-D) Zoom-� AT ach ��!�detailPJ shapj^r�w0. Small satelK % (\a�$\astu rA,k7a�O��� I�l�Vabund-!Q� 3}$C �i�)u cage. �e|x aeB s: microw-�,y, 9.67~GHz;pow250.5��W;.��B, , 2~mG; m"�Y 1.6�.}V>cwEPRL!Mw"� ��M�2N�Twom� ESE decayf�����d ~ a�AMJL9 !��.W �B"��&# U6.Aw)� Fourier T �5 (FT)�d� ory���a:�-1$5Xe�:>X Fig.�L)w(A)E����inuous-E.��f*F�(u�is !6eVe<e�zg-factPg=2.0036�I(�re�ne�6ulg)�)x6�a�toe4}$N \̀(Murphy1996}��Tev�&� � Hamilton�3(in angu [Is) is"�Qe:MM�D} v$0cal{H}_0=\w_eo- \w_I� + a*��  I}�5ndm!O$S=g�R B_0/\hbar)DI=g_I_n2 r� =�AȁI!6�Iar Zeemay�iC)]U�$g�N��A�"# Hnb5��EnT: _nUO>Boh�):�<-$ �U lanck' pt!�n $B_0 9i� �ied a� $z$-ax`=ePl"+ fram�py�����inRA�xe�01wpm v� A��A�a<$�|* 8 $\Delta M_S=1$^5 $VtE�s=�E�.M�O d� t>�s�> BC)[s*���ed�� (�rekZ"� $ies 3:4:3)i h\pm 1�2ms6�B(DQ �"S �e�of 0.9�}T orig�/�QAH28� Xs $a^2/a5�o6$��� �Z� i�wly �$le v`` �t�Nly *! �0!  $<0.3~� T in�g. S� �-�B)j���r/*k%s��+�*� "w $^{31}$P"~��QL�%��/2$�4 Knapp1998�Y �Y�:�Y ɒs�6�����6%NU ��is mono��cYc0ix�r�jial��+ $\exp(-2� /T_2)i\ $T�r%�s. "�FARx .|FE����7al�]+A��V2 n) ---�p��e���ML freveals� peaks at �za\2C �8s�i.�-�BeIese2@e� XD��2d2� i�*A���.qJy�Kd ^�a΂two"�xw�i�.@Y�uYD� il.�>�.C�>ld$tAor�Ac*p e !�hI�Q�,E�hI�� j#Your�< E�&e A�pY4� q \sigma(Af)=(U_{ } R_2^x 1^x) ; 3_0 z5^\dag. lLtwopshort}\eeq Here���d:��E rmalB librium; -�� t&� �G�v, valiڂ!9 s, $y�be Do�� 1� $S_z$�B��gvo#31H=i�i2e !r)$"�!�KJ�I.bA/5& 6�Al:r��� R_{i}^x$,� g-^;a!Fq?V2��U% I�isE}g.1*] exp} VM�%+rm{Tr})[M M�D%)] -!"� �^U7�O�$ $D=S_y \oTsCU� P}_{M_�i � Bj %RQ)BY�2K �B � �� tho574 D 0`�soc>ad�� A�%c"s >���$. #aId�*+olor�fs��s#orm��;�is�!"����A{2hof*7� � }'�44��M�ApJve�out"7 ing (o_off*ce:��~ cd�ls�Na s���l&9@(SQ) co/nces (r�2=gyE�9� ��{n,n+1}� �E{n+1,n�TME� ��), �!h T F ��I��q� $D$. �i*� �.*/Ab� $ (Eq� ')ihas s�%3dh� )�1Nin��hL $a(I_xS_x+I_yS_y$)~��  B oftY'mit�si!�they _  �4�eI�@ &%�.� �U*@! ,slichter =(�1� act, dire�I[ponR�G a(. D>`is2 o�QNj.; y�;�� 'A�p&eA�OaAK@M� �N=� $,�siL7te�D&� �v�i�d ,DRW&�c�i�%�PI e� mixa��E$I_z,���;�X�D"dfin�L�MW G9j? b�>g5p����; !xA��-�WN ssu�O,�=��W#Z � {or� lockY�qu*31 d zero�iF5 � +�s� �W���L si�an�  !Ay$��,�!��i< thus!biddenM��$ flopg�}��XSG�Avtsin�Sd'?A�.y3ifoldmca$ 4re avoi r�0i���  $12 \�&j�HQGt �=�ga�al|e&nl stead VT)�"�9�B�$4X41� �?g A "��Ž�| b�l��*�P�|  A�V.A�7�� �+1$� �>�e"�m ised.F,��A�2� in $�gb)s:b� eq_h>p�!(�+a)-I_zu- �(%�La3{cccc} �lA^& 0\\&�23/SB#22 !<�r.D�Y� �%�y)J�s#weAn rr�2^Sb�!2J -+ � ��%"I 7 4})+z6 +Z;� B�z-a "&KZI_zV� �N $!� �7/4 �)$H rese.�.n=aggy shift,� ignorei�Pin�|�onvr� ng6 ( coobOdj&����&� �y "�"mw r%F-*��ɸ�1 zy��}�~(�!�X � �\�>� - \�5_{�$,&�[ihqhh0>JvE3/2�+)�eB01&~~FA->"B@-BjZ8, "�} �Db��+My/2�9$�(!iN$G'fC>5�. )�:x�F �(2k 5`*{ 1) t_{p�e���"�V�TAvI�� aKit�cit�o<��wYy��W"J �T: ���.� . &� H}_1�n� B_1 S_x�-oB_�l!H���! "x�x"�7-^ng � $-01�"s^�. Fur�&mo� "i 62�meq 4.5$A largMm�!���! insic%&&9`����"�i�p-�ou�'BB2] EPR },� �!e�e�*I j7l#!)7� ^ ;T �"eA5 � iTI�ng"@ �&E9sU�\s%2J�1 -�)q yiA+)&.4:i&�:QPiG "�E� �o� gl)0y.s ~ �=�%9 �.�� aa& 6��iwiaxt}F!RV zR;} R�j�:bw /^3�<i��frac{R;�: 3}}(��J-+ /3D ) & ۇ1}{F��Fs-ZFibJ4�v ��� z1}{3}(�Jn+2 )Z�i @siN�-2r@�)Ŧ�r-r ��� ?�N ?��) b9��Q�� �&b�ZTB� � ��o"�cO'mZ}2��$t�������\0*����l3��*�_� � d�_� ����} (i.e^Pr3��&�D�$�.�0�*�0e KI�*�� evalF"l&�����:[&j g'^�'�re!  �#Rpurposes&�[ �$fj���^&�)�R/2}^x�\�0[."�;� DB ).� E)@ =-i��e^{2iZ t�}�1�)  � >:Z�- �3cW�0&�czI� y��Mt@iS "D< pick upV�* of $5t�Qe�{w"��! E� �{in�wor~:A�> SQ* ($m�{1,2}, 2,1 3,4~n*~4,3}$)"�e�"�  2�� �I��s�inner 2� �2a���3,2}$�6mUh�2�$_�L� 6P� :y�.�d!pi/2$)� q� ����-f� z�Az�� � 3}/2.V iu m�e� �� �"�!^:�� $, 1/$$� $ (a6`k�>"��*�D}=1oge�0�LmM7�9��/ ���-�# �Q&^E�$I�-$ll"�+�%�oyy<ir�[�*+&�* ��/.t�'yq�aith:a��d�4:6 ����! � fWi�%�KFux�$Vtau1_0} Vw�u1}�= 2 + 3: �o \tauBiA) �Bg"a-m*6'w#B�2�@�T deepe�!�D�x>its�0dtima�Rx�-.4i�/ure3e- %^H=-90, "�/�0s g�1�>8"��sia:% T1X-���$M_I = +g# ^c8� 2� q8"�[��A��8a�cl�RyrsharNF�"x� gle-�Qum�.Yxa]x"aQ-�E��ce?�0(aNIH �$�&�" +S2�5 � e( d�a? _D� \pi$/. qT;l�M��� (��= "t:)>q�g.�1�,9� an i�1� R� �\�v�}��D�>�.�#fT is %V visu�%�O%f a�model��mrt�isxP..�h:jn96}��(A: N)B!�� M�duQ� ``d"�=''�!io$tau@ 1 \$ &^7&Ú-�1)�rw;aABY+�#se ��#E:d ?�b�$ adjan)1�A#v7�u"� *6N "� h0}�eW"�*!�,�s & as,A�y��ce�3e5eF�( six SQy��,q��FAO�� AA�Y� Y,���)� $�}�-) %� . UpV�?�� (N@!0qu\)a���An�3 �4�K5inu&.o�v��^ ``YU�avau$fA�a�� al)��*� mpen�4�! inRdoublgA U�� ��u�t�9of:u3.��)���*i>U%��d%����irq�_$�r�AA�"�ly&pr�G���wh&Yf"�s �E AfaccorI5�uI| I�G�y��{�q?)�2�"���+IC:s�8pi$�a�� -to-� U_e[�E�:�)��,Ŭ�!ideA$�9��s�HA "D�G l�YA�9#27 "M~MPly�ZZE $)�~r,�%z#6}()d%�ia�)M� "�@aZ�9t �.�Vrmq �1im�Iza�)�h CaHae $�v2�i�$+B.��see3� 6�m�*�lexy6�14*�q! !wo���i.� �3 �$��" 2�� A!%!� h�FnicRW.&����LB� �m�an f� . N%ee��`|Gdes�VW �:!ui� �Uofiew� EM<..��b�rA��ri�s"�%�(� �G�"��)��% :&�^!<isZar/w1+%*� 122�`6;$�&!zarg�Z rapidl�%LLs opaque�tu� lGP_�%)tG� be�ly�ed&t7>? �'�#!ginj!$ (AHT)� waugh192_&�eque]�a?&ndard� turbudory�ach�.\�!e�<� �!!$t0al.8! �)(h* }))A4o%6�!�8"e1y 2�!,��ng $\O,W_eeF�dev�T%XE��u>�E{ @�� e- �!.���4ayHro�*i $0 &{}={}& U)%-6�8[I_�8S_x I_x]#qt)\nopZ, \\ &&\:{-} .I .sin+]"* �e���!����}+�2� w(thK !.� : %%�&e!�eappead Vr^�+��+Ic��]�+�.c"�P#� ��+UAHTB"�#Iomi�t�&6,�|��)A`!"- �A�a�%%V/\e.B�H-\$�� K_F$(}_0^{(0)} =nM S_z N�%�2�barP2Y"0�%fef�o� � *��Aod �9�on�:{U%. A�D}ց7� q� W0}|5 An2���ų�H� %�T>G L3er�-%� u2��zbs#pzd�]v�"� Ref.M&613Ւ83e ��*b-{\v�1} j�1%�f� X � �[�� I(I+1N(^2J2)�M- ! S(S!S_!�j\�[�-u��}G.0-e+�0.�$^���v�+ j!1)}� N�ş_b�& q�e��'.#ach��8 -daJenta�q-�7pro�%�{or.� (f� IG ing)eHy MpeB0A�b*^{�.29se �. ��<�� z��m�I�M%�u�=���Z�b a"��1aRus�,3ur earl4Aq@'v�6ach�K���9b] ryN ��NA s/ m�6*�&�&�V}�o�|Zy ,�.pl7mfv + R<'t 2j �*�$,"|%N Fs, $D$:r9�/5\.�/Q� d abIH(2!��� =5 -;= �$"�-)�u �>�V %��HՍe>�.-z6� �A.�. SubP8��E&ߜ"u� �!00 21��D�W�Q i] some mani�W� � ��I?��>����&&wAganl*� ��S�1]H�%_2 L�Io'3/2, �L�p,B ey.�^�l C� * !�%O�6�&Ed>)�} %U8J?� �1 ^2�$ �2�& %�(% %A_0()+A_1��Z+,26�% %�5, %�"�'��na�/.#N!  �� [ �� .+ + +}Aj� ]"� � J+B�6� &=& 1-6!DN��/27!�%4F�,�\\ 2�` b^%�(% 2-3\J��&�Acoeff}i=�i �3��'JPs1�s� �!e5\�� a0��+:b*� � st��Pa�"�[ Y4_�G�>PA�26:T�R/��-0)�@��on*��+&d#�l B.. At o*s�X 4�=i�1mpi�n �,��X� ݕr+c��ed�x6�!�x�,�#��-~l�LOl��0$:�L��1��bsr&0��"��  I�?Dru�M��E�'^. �&͐2r~� [@ I^G M��� k$x x8 $g \�not�GY('�J:*3s3 {c�7� 7NH�Q(v�N���^2 �so irrel�I]E-d�7�Op.��f���7, h� ��$7ya5vapp*\*�=!8m erm z��Y!!.�&K, *�&��!q�8�?;f-@=.re,�@^2U$!sol(!21��N�Fo�� \ z��7� �A��dH%4noJEq � �E"�L6M�2�O. "4� ��� B@<?s�& }Ig�4a�� �D .!�E&QmQ� *�8 (see ��52}A� h0}���H!F!4B!"6!RXNGI��E�:-�1a 6E"�#at>pA�cF- 62%!4A_� M�$��=<� 2����OA� �Ra�Tqib]� aE1>�" emNNonIdealj�2��+�6�ŀA>shown�:sd�pre��P"Ő�ő� we�*� wÌ1� pi/YU�Fsa2 do�S�"(2�e"� , ra%P�( �-J%B�!�. �E� ��c�;s^t*0">HzT�%� a&�"�"��PmP�*�a�] 1 s cla hJ� e&?"io|Anl.a$ &�^it"�[&�3�&�^�5�thKCnaHcav>�x|�A�]bdZA�OH�Ol�Q$ acros!ge ensembM4Ify;E?eV�aussian�W�'�ofXI���'E�'�� AKa�%],�%ms�71/Ix 0.17�2^ ^'^UKA�yd�Q*D&no��.4 = 0.31$ radia�W�+BE10\% 0� a Mvs5F�Ap�\�pora��.BDor)�1S6���C2��Ln 2004Ado V�a�= �7$�>Y|F2�.:�5z���-%c|*yti�!JT B�� I�3�Aa�TY{ ��JE�K�>&�). %��`fid%  ���%��W7��s/o#5��%n���6OF�%U�>���-���:k of %+.t:��1��"!O:�� ef{C�_!��Z}!�"�Ike text.�V���8�?-Z!kF(�s}YIn�" mary�0Tm�b� ech2� i�""`�FVQ)��.H"�iG ��Q it'.rigin�� 2b���)6/L �e��Bk_��E��n"� ��/Fa �[; u��=*z�yQ�iT2�N@i,�{E!�m]� strength�YK�P3<%%2�_�#*< b �is eas�g� �(o$D4a�cbi�a� �e $S >�>�;u o&�`�mF��� us. U���U sKRt)1at9� i�s. `3,XA�D-�y �#3 at ��c(x�㡱]�EM�a b6'E�M� E!z "�*�&�L \sum^{S7LDS=-S} (S-M_S)(S+M_8\;.�i(1+2M_I&/} d�um�#�Sver:�&wLs��S�.hil�%he %~p+*I$�i"��Y|)MW22 aS�!l]qmvE�/GVm Pon2ťc[E�iH".�u�]l �2��q(��r2AM�L06�� ; itsr�R4"��Jer�� r-b�r-�-�sA� schem" kqip�| note��mccG_�� �.�=�*3!]�t>�Zg �AsubjectT?X��a�zy (typ6�` >$10~mG).2�q���*! ld &�ei#(Ra &Gly`a�ha!�-�l�vi�$a�,�$i�e"�.�x�� ucy%�Km�$� m�to{ erI<*�p % s (l�]�~�}D� ast�(�&typj��is D�E"�: �fer}*t f. "�w.�� -?�HprKtJ�"*� Uˡ�I��L'5s)���.�22�}�i͵��@�62YaF�We- jm��@nk Wolfgang Harne����b(-Meitner In�ura>I �U-doc#& erenz �Ny Denno t Qu\4Mary's College&{�Mݘn Austw�7AGavG�orley��6e�� &^. A�(esight LINK��nt� Nano�Gics�!&�4:n EPSRC ;�vOxford-P'y Linkb�d�^ e��.}�� k Br Yn LovetBu� �&<A�p� 3 Royal""� Work��w�Z:6 NSF 6ӇO��A�"b=DMRSEC@�@nt No. DMR-021370 � ARO% ARDA�;*�t� 78AAD19-02-1-0040&:4>��[f �Cf'�k,\ifx\csname (xlab\end \�x\def\#1q|\fi^G�O font>J/BMbi#�Pf�Q$�R cite~R.$�Rurl^�url#1{�~tt!O%8{URL I��i��m��{!\�x#~# L>!|� []{S'�cib�[{2�{E�u et~al.}(�u)J!, Bodenh^ n, ��$Wokaun}}]{"�u�i�{~}�5�{R.~RO4]$ �}}W�Z> G.}~#1�{�A�~SA>S���s��6x}{�&iphof� Vw�<n�0d( "�O s}},* 6Os"k�]�g%S �$y ; 14 (!�p9�s�}*1~P�  ;F  �5�=�}{�� 5shire N��},9Hyear}{A*}~VYDi�w��TsvetkovAa92)}].r�4 S.~A>4 ^�.K!��nf^G Y.~D>Q�)R�El��6N��qjEM) �oscopy}}Z�RC1�9d5� Boca Ra;�!1�92r�SQy%� Jeschke}(_y!�6m(�f7B+^ևB��j�6|�2�iByz}AR1M�&��j� ,, UK ; j!\r�Abragama 6%�*�WƄNj4u pg ^�smf$Clal �U.�U�) �qzQ�6v  E�Max�!5�"h�y~�E^����W֕ D.~E>N�6� journal}{>�|�8ybf�4v؉e}{88:?�zs}{107�9B85v�Yudz��69:� #$, Salikhov��Zhi�rov\��].�z�u V.~F�.} q:�V K.~M>@��AGJA�CU��a��>���A:9$��5�@Teor. Eksp. Khim.@^5��!6�hM663.u;9}naM[|e<�� 6��&w|~>AJ Z�?)B�N@-[�5BPDokl. Akad. Nauk SSSR&.�5.qK2^L924NH86rHKanaiuI}:I!, &��4�iE� #t~sM>s aY�%V�K>;��@��J� �B5��5T.~J.~SI�.1N6Chem.N�.} pp..m210--211F�!�r�Almeida-%n$I"� 96:�6,,, Pawlik, We� q0Hohne, Alcala!�$and Spaeth!� f1�n~�T>�6~9�jBD ��<B� �?B�%�;RF�!N�2r. VJJ�1�!�A�%C�e�� Lett�|^�77:�M� 1075F�%�n�Kvk�` 1998:�!Iqen, Kas�b0Dinse, PietzaA�aib�A�andY�A�D\��C>�;:�VvN>;A>e*z%sV<B��v K.~P!�2[!�>B>�-P�=B�9�@����U�MolPxys!^�9Z.9M�999R�8r�SliVdR9R2hd~�CJ�S}�Ra6� �� S� ger.m"� � x>� 96%E�}{3rd} �3 tem[�b(^ �*f�b9�{T�m&�* �<eA?3�SČ:�}]4 - 4�"��i�)�io�<H3De^3(�*,is negligiU��fat2/�*�j!Haeberle� WaughA68! &�=9 VU>�X�i J>P �6�uC��jX 12ZD45V� vD�$��:� , TaA �2l  Ly �andt �� > ~yJ� L�b&� B:0V�AJm��B:� �=B:�� N?!T�{~C �It�ev. A�4��}, (-p�322#�!��mqip�m2B ]�y� 2��br:os�$C$ S-b'� qus�p���al �u� �,p��� 6�h�,bA�RS�+6.�9y&sTme slow I�$l"in��s�Hve&}�^vc\!?(BW/X! � p=��n 8u;�+��!>T/pK��er� t%�,um algorithm*+ i��ulhisOD��oh�F��dY*M�/  fam{$ of g�.�� o� <%p9�̋5�s>�R hNpR Q] !�s(�bi '"5>3 *��%^�)�':�)Z+2�) %l.��%�*,:r$&�*p-/N"s5�l"~)�)-�repo�L an %JJ(W1 �1( 6z by:"d)"^$�$"+(PVID} %180_0^\circ - ({104.5}360_{��4 82)$). %\end{e�Lquation} %Here $\theta_\varphi^\circ$ refers to the microwave pulse with %rotK anglJ$ and " !8xis oriented by 2 %$ v$ 0espect v $x$-:in�resonant X�ng %frame \cite{Cummins2003}. For this experiment Eot�s %� $ng axes of*m6�s w!0set us,the)P %sequences developed� �\Morton2004}. The nominal von�gl.ato bette�Pan 5\% accuracy, limi)G8 %inhomogeneity�4$B_1$ field. O%r � �p%� �z�was�:w a 1$Q precision �a SPAM��. Fig.~\ref{eseemComposite} demonstrates that Dthe %c( $\pi$�esults!E0drastic reducA� � %low-fr){$y harmonicA_Uensat!�for�Iy, error %causI�%7-%7 2TH. To our knowledge,IWi�8e %first applic5j�� ��%zd EPR E�Droscopy. ��\docuA��Xclass[pra,twocolumn,footinbib,superscriptaddress]{revtex4} \usepackage[latin1]{inputenc}.${graphicx}2amsmathJbegin{�0} \title{InflE�!�Xmolecular temperature oi�cohera( \\of full) a near5p�terferometer} \author{Klaus Hornbergeffili%gL{Institut f\"{u}r Exq��alphysik, Universit\"{a}t Wien, Boltzmanngasse 5, 1090 Austria �qDepart!� f{\"sPVg M�nchen, T! siee<{\ss}e 37, 803332+ Germanyz)0Lucia Hackermv!H� �Markus Arndt} %\email[contact: ]{ma!.a!,@univie.ac.a!�.��O�OX %\date{September 23, � Muab�+ct}!�2 ofE�P ��5� rang��rom1car dim� � �Chapman1995b,Borde1994a,Schollkopf1996a} �Xvan der Waals clusters~ J2e 3��a}!A�� &A�v81999a}, massive&^ivativ�)s small bioU# I��E� a}. In-��)� adva�   larg��%�v�P imul�@A� quese�what d�mi�� j  m=Q=$ delocaliz��o �-�. F!�h8theoretical sidF O A�0lso an increa� %�(est concern!�Et�� ap�nt�-> d boundary.e/rEc( understandRof2�4phenomena poin �!cr�� le play2 �environal �ae�� -L� whe� a�-�le showse�$ behavior IcJoo� ,a}. Several��� s tackled� suex��Aext of %L^ 0ry: PritchardEqcoworka!�hiMe� <:�F e� � ]er! odium 3  su��]o&� laser l�-M�}�b�m7ry�l}�� re a�l>Mu�Ɂ% �fi ��e!8 dynamic, ɂion+ �� �]G6� ison�-9�=ata iF�&�s} allW to ext� !,.� 2�a beamX !�]}]�E��ar%�m�ed������cU�� %:umAory" �e iscuss al 2 m� sm�.E��, lu�s1 :A"bry)TA�ed=|}2labelE�eZ�sub�� .P �3>"�Lfigure} [ptb] \inclu��� s[width=\� ] �FLFig1_150dpi.eps} \caea�&�-In�er�/ sist�th� equa�grs) a slit s���Tof $d=0.99\,\mu$m spac� aGiE ce`$$L=38$\,cm�164 � ��&E�>Jo��Qa�4er via multiplVF A�s.71��.^1} We��2)0V�T>j� lready��b�8 de�iѣBrezge��2��ItJz gold6w a �od-n990$\,n� a"$ope�dth(470$M a�%�ly1�%\%R5�9�, see*�I�"�Mk�'!�ka�� %)�c!3) !�. N&� diff�w1a�}se� ct� p�$es a high-"�1�EFp��s 6 o�third �͙em]�$L$� clos�YN��iR� length $L_{\rm T}={d^2}/{\lambda C70}}$ � C�� 4A  At���a` L=$0.38\,�� f"ce� s coro��N)��G)�%V � �rA �te�� de Brogli� ve �! $B�=2.6$\,pI��F#5.2#, ��8, if� t he�etr�� g s;���v_it�Ze� at 1� pm/s ($\Delta v/v\simeq 10\%$)! *90\B* +5+ou a{��FA���isAXdu�s�  !��}A9�KJQ�?�e�1�M�| �dt $d$Ir�on�ss��ae# �� trans|flux $I$� i0i� shifA+ rall!�Th6E a�r�t� beh�A�e�WL &��� edA� � � sign� ] �qI����>8ve unambiguousl���� Z6]"e As}� earli�orkz .�,:� 3�he iwr�,i�ll su�x &~ �&_B� such�}.�tet.0enylporphyrin;d fluoro,. A example,��)as} giv��6-zofJos�5��out addiAalP 4 A:( sinusoidal-�)k!���.�$V=(I�Qmax}- in})/.+.$al47\%.� ����l 2:e HighY�=�2�-\��1' !�9��) low��0�^ G.D of�� �arF  [��� ind� ng m�� evol�.} 7 ~b �1J� : = Xstage?!   1)� r]� a+nowL l��a6] g1 m.lo)�7 c�V &2 �"�J� �%8%=�A�?<"!T��by absorr �FI�E�aof�Argon�� (�H =514� )! �A1�-F)`Ņ� bluxneG48� nm) ��# ost-�|� i ctor� �lO� rea�za�$imal power�$$P_{0}=10.jW%zis foc� �$/ I 30 alD m wais�q$$w_{y} =50\ �B  p�0 a cat-eye ar�E�twoSs��ndmi�"s� @�"�d�thu�te!� u�16 tims$ith%s-�ar�,���%:&�#E�-�"b b�!x focia� *� !/appro!Z(tely 0.3 mmza�ge%��goes som� tenui�n U�%� refl� o�� opti�eias c)�af� &$N^{\�"rm{th}}$2Js measu}%�APN}=(11.2-0.42\,N)$\,W.d� E�Iz 9!fix� o 16\M[fIX67 I7=8�. overla"\F�)]�onitoU by%�c(�a% D$_2$echEA�maximuA�ra�!d mal �. Al�r��adjFd� 9�o|� H �iXq�� . M��A�J�>�6��&�$maintain mp)�i� nal �until�y� A3)�o!R" 6_nc#l� !y.ns ��C Ding�Nairz} aA�- � o��u���lea�$an enhd��� �cy1Rf� �a?ž#�a*{��� of 150 $��e�ٻ.���50 ,w��e aU&3sQ�s ^�as lo�)p �� ��i1*�N��.� g. .�L�A;��i^Wc��prom } F(A}�u well-s& e�&� � ��=�QN� sAKAyir cag�� �a�meC!�ordinary!��$,against frag#�T��is 3u'def ma$t�*|eVA3a�glZM e%ja &)ly)��d. )\exc&o�sB*["!$�exten1!lU�li�� ture��)�2���heW {1}$i �WconY-oaW%Y� ��-li�2�A'j.& QwM#Eh %�sA�"f.9Ucon���"�.Z:2�����sb%��%aa� �!A�%~�ZoA�?V�domM�%� �="�g is d 2�t �'EoA�xi/(i�E emis�A ��on��"��5�xp�atA�er�2Vt �^�!�0um�Rohlf� 88a,.�!,Heszl7�orn8&5"H it�%&,e�:�� s�% the Yh��Gk�v�y��"�S nH'��n import!�com�M5!�x�Mm� c!G1� �%+a�+&� %�9�in�kq�%PP�Rm!�eK i��our� a�� M C 0!t More� ,, �^ o�E�� �%�` � .#��aK.R A�siE�F]!I!�r� ly act+edu] �".�carbon �+, �be saf�+dis"X'in%ri�"D E�u 2 � is 1��� �Mat�+~<Ep.�!�+ pote�L7.6K1��$y"e�  i�n+rab���+�ha)�  :p��! in� �� ��5 !x#�&o notQ{ any&�"$ s"�# 68}$!^�*dru� �+� � mQ� b  By�AqA2�m�&� ,%���!� *tro�B$ N��M��� .�'&3Mjnuclei. m-h to qk0ifH *" c"P6�c2ҹ� &�% ���,=��vN s$qAQ�s�6ble��AC2z8C2� Af�at,A.:�"��!�ry}E� how��$b�5�� B�#v�����aal*�!.\�Z{Ra31���V U�0> a� A�� =��g�� ervoir �$�?E�faE�Jik. Ie�Vv} �typ � ,�D&�tE�purpoJo t-ac�1z%H2|R�(�po�$6y $E$. �� �� n�(toe�A�$Ee��/�a.�, v1ou;)."� insd�/�6��E� bath ���3d��2E;&F4.z< $T^{}(E)=\left[� �-�2S/ E\rB] ^{-1}"�( efin�hr� e� py $S(E)*3ai[rder, w!�*�a�a f�tiM.�t would�q"F'to keepI�S"� ����/s  va�U !��(� =5Po :�, i.e.�mpy3al"� �,sol�. d1�.Xq�� s4lt�e�. �k*�.��n y ar��y f� s may�h�&�-path._.N{u��r,�g�Co&�5E�Av1s��� h!3a�R�,[Q .� }. How5 )� �9� Pdeviah }Ar$Planck law!2ocop�< lack body� %um'9of�si=rst t �ngY_�� e��F typi�)�%�X s�ch�Vc��it musF0%�.d!t0&�!*ex,x-�Hanse\78a8*@align} R_{\omega}��( ,���) �d} =&\frac ;$^{2} }{\pi c}\sigm�&� abs}cE(^)-\hbar R ; s�R � \\ &\�s \exp� [ - �J }{k_"7B}}k} (6}{2C_{V}�ef� �zN � � ]F$\,.\no�'�-te�,��A�propor(a"q%=  densityi��(/+^�Ah6iAiFu�y�$)�$ I a�AR�E���D"9ic.O�e&� 4.��N� $R,$ݠ"���+� n�ve �Z�)en ��b����� �er�! (N0Mq)i� i�B2$actor,a���h%�-� Y �!.finit� capac�> $C_V'$ ""�F�,F�2It�Uin� M2���H�� �|� ��ra!?E8a��.�4�u �*�I�&cw! ��g.K\$z0$10_$� K}�F $300p,K- Kolodney�4I�"�2d���!��.Dx�"bc$e�=202$ $6$��(�e}�%4:6a���� >��for (:� )J 6(39]2%\K� !Q8\,K, cf.~Eq.~6�� (ol}'a"W!�q�t fu�CoheuV66� �2 imp8�C��/� �� �sd durC aq�k . &Z/Q�!7>[ U���"$:� �a.�"oba�aj9�})�� n in*�#!�)qs�(�M.!]$ �#J�a�tax�FYand cX��Ta1r��i�?No6i�yn��B9�infra_becYUa ! �c� �'��bT(.6 eV�[e�"� 0HOMO-LUMO gap΁�� eM\J>Alt!y$i�>� �K "���u faf" ܍Br�y �0!eE%eci(to2~o�2,F�&� �>3=)-%< matrixf1m#xtremAP -!A�;se�J[j buma���Cs�<"�]}`�?  =4.8y 8 10^{15}$\,rad/�on�"��5� 3.9%eV%�B6)0!B��) directF%�he�sm��Lc�& gr�E&  !�st�sup pE�� ~B�H ���:0Jx*�z�} &=Q����B �;`@2�*Z��kntU/Ѽe"SN \Phi3 ( T� <) =\int_0^\infty*� >  ,;� . �#Phi�}|I��&�t�} �n.}�j  $�$ �3 Aco*�f�AStefan-9��m�cas��&>s,.� �ka^c"' ��u�En� edg(v�ndeed, �Eqs. 6&� !)Z' fie+�.�A��is � 6�)by)B�6.3i�a�-35} (T/1�K})^{11}�(atN) eV/sj��}� regim%3$T=�y~F-a+$ K� >b3�eP����vat�a �U�2�%"&s�'�#!�g�G.B �� ��%�Mn:4}$"�HI>a &�. A�f�" ���oe_u.�a hot0G� � �g�RAHq�Q��b} V-}d}}"�,d}t}T( t) =�A�-�y� }{� }qiTdeq},Wi%�� d.M�-) numeri� �� � W $t>�#I�!f)"2 J�(i .5$T_{0APs �d�ͣ!�10]���FF�T1t;[�� = �1+ )b}��} :^{n. -1/n},"fTd�DB�NI(a" �aa" s $n� T_v.$ _G %v�� � n !uL.C�-J�$f!Pܵv $ : s as18W f_{tJ5=&:N1=- -=�9-� "�*� X�b (n+1)/n}.5�fJ �-� �&� �bP��|H3vC a$6 m���Le&EQ=�$�/ � )by &Z MN)9pan.$� V �y fit� "O�^Z�E��u�O53��2�q�]#0s�&A� N $t$2,0�y g%�+�� $n=6.2,$.=8W1��K} \,-� s}/tQ/^{av.$',er[1age�H�6}.3 ��� ��*8.�ha�e�'�.n=8.5e� =�=176}�v�%s/mQ� �,$�$v$�v:�8D���1Z"�'�3�0*� /O�PGscr�= �10.5,$� }=2166�K�Q�/*a ��,, thin6? m/secn# a9.7:� 2321B_ �:2G,���9Fin �� $n=92� }=14 ;Q(K���.�}"�5�MG$�?%3"�W!A�c2�5>hs i> reN+ed�  "��0ae�C:A�"1M��'D"�A���/�l} �*oCey�;y4�@a�$%noEner B�aZ .e&X�� . R�,I� a6zCad1["�A�stochXna�-1he~*Ui �@A$f-Zh&�=a���i`4���"� s.� i3�� profi�P!� h ing �2can�be @4 dem !:A�2#"�toou.MUJ��w�T*x �ve#"���" stea$e7toy3J,�; �J�%=�2Nͅ%).$�n�+F���W, ate --�1�mf06`R-� ear.�E�.�of"o s jAhot.�� �E��]Jq�I[�'M]U3���I5 �$��y�ofmY\dB��0avG �� to X�%�&al curPw?2rel!����N.�2 -!�+$)$"�  sour� .([*�5�%�T V_4&e�'�9Ay�!&5Ss t)pir�3� nerg�%Y�wh�1a�Y�%I��).� � �!ge�Kcy�1&*y�&�l"`6O re"�C�2� �+A��Vq?QE3u5 ]\I��,rms i9���)( ��"� y)w�v ���\-f�f1G���/?fad3Z,ckVenges: F}i��.��S ��0&givari�D�� ly broa�G�n��%zM�Se �W a�T� �&!�"*wI"D�W&�)�)chr,iA��r�6n�2S<ar fash!*�,9��� �� I���"�Aas�I{`"�0�-!s�!E��'ake!M���. &A N*gQ(�/�,)4"<$�&���Re�8N.�a��y.��V&nO �1ai������kA2�* th�F� �F�1��!eJ)7toA��,Gal�l2#2�sit�<.dI�e�O!U�" 2x{"  Scoles1G/}~&~B�~G�  v "L8d}v=C_{T}~v^{3}"� (� v[ }{v_{w} C "X d}vJ�c"�!zARW:u�7Q�a;PM ES $e=\sqrt{26  T/m}=133$, !�!9�6 prob�speed m "�y�"A$�$*@#��U� .,Ra�W�i%�I�P6�ed/.J $i&�!.�v,z-D$M�E� i1ong�7� _9�$z7yEY*$v�#&�)we ne� 2F^� T,y;F� ��- �w�;*~=)��9� &�  $T$,"�6ve�Ra.�y$. I����2�M(eak�<nM2H , flp n $y��M�;7, $J$]]d}yq d}T~Z�)0-� =1.$bR�t��UeU ��of"U)��r�"qby��;Q6 V�"�$e� J�XO=%&w�1f& )&��^�xe2�A#2�m��*f%ffB�$�� �P��2� *5Te&�Q �4�a9yh'A$&Z .� W�/.sT"�w+>+$���8��V"B %)� �O*,����[�(�"&� ������̅i� K n doIso� �9 2 :O � !m $\' ��a'.�-e"�:T�:|$e[ �+�1 �-603.� �w. A�3m�: nly )S��De�"� neg�8!��P-9 *5�cerA:ly LBT�M�prew*!2)r*r��of & d]AK�,%� ^ssonianbWbH?.�. Every en L adds 2.3y3� �ѭ%�� �c�@/6C.�M T=*99�L}}/C[(=139$FIC.��-A�ag��2 N�bg �.�� ����*>��a�)>] ^{\p�"��l2�\�/�&��$e} ^{-\barV� v,y+$}\sum_{n=0da}g.[ 6<.; D] �}{n!} *f* B�W (T-n)�v�."Y� trafo6X�R mean*E�=Q�� �a!�twontE%�gaussiacI 29P$y�.$�&r�60=1 � )^2}�+}5lRVx }{hc�Hv}P&� �� 2(y-�)� {+ YR�V51 � _"�4&��*X EqN"���� $ Arrhenius�(\footnote{Iy �<"�B!��n h+sal#J�/sligh��[ �Y� <:l[ums �& Klot�B1 a �� heck "D�:.:� b�f� doesi.��ifican���m2��V*�;Y*ٵ�.J� I8q�6�z}>1ig:�"�A�8�p� *� U[E>' {:w YcV� q��- ) . �"dzz>Iv:"��=�.�o��*�>�BT$%?<  s $>� =7.6"� eV}-1.6\" eVa�S6FF� 6� $(z/v;T_0)$z � ex�iA :�5�5�\*e�$))H.i_3Gt %�%wi�fxtU&Z6I5�+�s1� =&V�T < 1-IxT��&<-� Z6�..  %� %& %�" ���/�_ �n+1}{n0eB[0>�L}{v}C �v, ��W �� � ]Q�ion�?J� with1�&� ��� O�n �"� !Y �*��� a9' ( [ \Gamma6n,T.3E0.-�9 o ( 1+` A7n Z>N� �5 ]F�� $2�n,x /) ahe�in] ete %&aV+:/.!e.=> .$ E�'m�2�)� }2s#��B� ��A./va�d�a�+e��<NjFi ^�6"+A|� _"`� >w �~&A .�&:��M�s �ten�l ��rs ng� P an"�6�Z0� mm.�}RYirF0 uni��l�?�edi$g�E!P $1.5�.�:x [gm!I"�!�7exD]-a�Y�L. Our i:�*� ml2�c$re�!8.fiJg`c,c`� &��!�!^regio"0�8eGQ?�c88D��,a �Wn~ � UcuB�N s (�^s"p`%} I ��^]~�[\, sZ��c"� -V(��&�G1}�x��) �x ��V�^%��nO�� ^ pos;/a�ly�!���h6���rv&>6&TQ~=pP $:� .$ H-;deBt"� play� "dEr���*�$M.\-cvirtu"� �o+r�%or $z>.�}1}�3E�> E�2Mlso�`�s!)fd�9->�E �\,": � e>]- ��v�#"g*�o�&�Ey,~B%�� >%j%ll<7u� h�lue*2F�m�% }1� �[��aGi��)��t i�<�8�&�Fi�uE># a#.>�&5*}�Z % Di�,iden Teilbil�qbPDr nicht zu einem F�E8zusammenkleben.a�N�d 0.49\text��] 6�d5al5V�dz=b =c�dIon�B-nI|P52�T4$(symbols) @a%3�&�6�(soli�t�q)�Q eft:tangj!� �.|�%�)�� ��T$P=2, 3, 4, 5, 6, 8, 1N7W. Cu� N)9c Fs��5 ssoc?�).k. R4J�fou�6v� �4>� "(%ion�SendUV ~�%E.proE*�%&(�1uB!�gauge���Fw""$eD���in�Y5s\ . Pulve1%X"~ele��"�=con�M dynod��th�Vlos�o,s*.#i �� urn p5^aJ7�� r ed 1[N����t�H�(1A �~a1Xs�@�0 �Q"Y��l?H ���ri[ Channel�i�tup ensu�omv^\"��]�a�Ks��P�D=a) �p: �� "�wa chop)��0 �&a<+ -of-;+s� ; rs:RA[[ p�>a�"� ^0s, )ޡ�� ��+`�`, I"�B *)\�#�5 6block i�%��a�c� S&�[�6_:z n"%he< $I(v)/[C_T v^3 P0(-v^2/v^2_w)]a�EC ed (b�%�y � ��c��#guzPs�B��!�w���P$! !s;7*�9i��� c.�J�v�swo un�& z�?a�`2�T$�� ^T}&��<&cЁ6or!��� $��8� }}$.6�&s{xtaneo"�dA7kGM�%� �&2�w:c&�m commmCt � ^� .�g2�10SH7i8cm$u :�ebg559}~$s$=�h �E!� %��"e�2�"Z!T2� &�i��])蒅+.K<�(e'X?E�E!�� %9: : fjYtAQ�X. di %tQ d p0h�rFC�<�K�Dwa�*�7 *k-�Ay5qAEy� )�qmYf;Reinko�{2Sx&tW!#ta� V ccepr+!��v%�:.�OE �mv�.�Wure�We�-aZF� ���� a@"�~z(F� u�xU8*@ >�V�T �T 6S 6�S :<>R Re?YEmI�h��i�.  at� 2$,�o>"���� .6 :� vs. ��dR� qd� � *@^e�=1�k; *��L @(a) 1, (b) 2, (c)� ��(d)�R F  FaA�.Xna21190�%Ca UbU(c) 10� _66�.&A)aor��(� �L\��! �A���T�-E�ofL �v%���V�N��O)���&�2k �e�wo&�*v�D1�%G�25�F��(1n�&ie:B� �.c%."� J�,y�(\emph{same}*+%� � one � s�oood ag!�q>�)���5s�Gong e7);�4�wesuc�^�� !"UB*Z,NK �� ��[��upl�^J!�� [xn ne��i o!�;)i�gEHat��Q e�l dum 5�*� 1'&g arr�,a�<j� .�1 �ul,rai�P*)i��R m1Te���,-� E#� H��yat�Q� �oCrgeyu6X)+�}!B�i�!S�g65? &?,!o� g~�"ze��.X5\~�%��t��)h �V�M�ed2{�!�E�2�1^e{V >>��saMrnF,.@e"> �!b66/�#.;:e��%0D!�@O&�4I:1(%�}"�*-��9œ=���+���be��J�V c2� � 2� choitor�Q���6G ond �n� .6XF sl�k���A��� ed m�dI{%%e� !� n���("� &�W3a�j"�F[1 cN!L� V(ool off. AͰre���yer?h�p'�r3E�"=!��! fi6+>.� *o . N� }$-'�Fm�FAP٧� .�~e��(!�� >�� Sh7�d�Y#sCga�>�=r2�22I,E�}�tv�'robustI� ŧ�(!\*�n�O�� =M$�er�3K,�X +2��ё�7�� !��=3duW|an FKInc�t�M�3�}�b& �lzA=�g f6@A�t�F��&�*�U5 >on{.�2%�-lJ�~&t�:O} ��͘�rm�a2��M�t: :��Tq.u9& �3�t���� F]~0l;erNc ``fast''.��-$v=19�w��a�)�r p � �E�x8��!Z96p16��( e�a�Ar�{d k� =$E�("�X�ntheNZ (�*Om/si@Fi� �P �5se�IgM ��^�s�� !<1��d YA��%�XI(*:n*\ah&�7F��e� s��%)v;"�uY�g1� J)�s &��L�  $־u�!a�Jm% �� ߃'� vQ�.�=*~+.�!�S�Aia �NlF��ˡ� Q�a!@���?� &�!�T!��y�V��*?:Cc[OF^8*v��s��!v�iB��>z�in *�jR�RI�B�"I� hMast.� " 8Iw��;-�u��uIF�w}P&ul�5��fØ<�3*��S6]��!0}jU*�$vCB�| ��byj�'eO$}cal{R=" &,B" =�I�)�K{_%2L/v_{�&�$d}tv%\�W~R"0X( ,' >�G)t[ 'oe�orname{U0 � |F K d}{c.I(L-|vt-L|}{{�~ �T}}"n! "�% x! I Vred�=,U>�!, $��("Y&k *E1@V5��adjYi��AVD angI���e�q$ �� 6)�k"�$-[ :[$e^e2B�J��.��[.���argԘm;"�8�^�x1 =\sin-( /x$ ���� "Wx2\pi c/1i��O}� ~ �gG6�%!��ibuŋ�+ŗathAm'-�E )!��8 intu��S (\Y)�S i�*�>��5D�� dn���Af ls (  twice)/ M�!���%��Mj�� get|Q�@"m act–6.% run�5Pn��bo%3b�s (nex�~B�h%uC$l �5t����/ �"<{\eaYF}]��4 upo�3-��"z$O���݉%"6 foO_�G �En��e3�!�a���Sget� &��  �er�@gcolqate, ��I�.�i&t� *@� b��� �NX7_100dFq�&�E�i�FN f�by���2Dd E�!G� ��,y}-��*1iQM'�,(dy.e sha�&�%B�\6�5X" U�))�?. 0 EWa&� @10� (a),��$w9  b,d)>(�*p�<s7�F7 � "�!6 T6�H�Gi�Y4p� e�x�ome���T!R �d)S�ing�1�"���r�Qw:�%�8:-%"-ix>[ 95�����pq =]�'S ��Aa&�3s !�AM��3ase;G-�onUL#afj��a re�Ŋc�|no{ @mL�Z"\),znH � notoIT&� �R�p�B]�)�B��y6o6lut0&KIus& � *�4���"Q(�H3Jir"��S!*B%nF�5 ��nce,J"Bus%A�e��n U e�2�RBGO��cus�-d�  %z. e wk!e�~�E��. ��2m%d:W-�&^.WA�e"q�+ytA��5x.!V!x:M �S� *� �L"�x�@�BHG*�2.~>_l�;}�n��� \ �n�h" A� � 4Ae/�,M2#��� on���.�w�A�e8 x� �59f6�-(T;v)�XO d}yZ�@�66B �c� aj}�FxA�yuM�6D�� %iYe�Ce�7?�w�  AM�l�or6� ��.~.�+�%.O"�/=}(0:Z� d 30}~6v }�;v)7.]:�5R�mG�{i�V%Dh!g(��V�L�alj���&ˋ~g |.jcu��`�m4%UR�iA� oU �B�Hm_ �!�Q2TI]{ld��.�C�MR�f�aB}:;AL in g�8�ls�A# ׭�half. >H@,`8~)v"� �at un����(͵:D��ie �E�e �~D� !y or"]_v ic�y�4� im@� �a��atu#e�.�Jt2��N3Q��1t��o.X\ "Pl�'iF3tf�\B"X^l`l�Z bod�L[)iG(�A s wh �' ple w4,117 ERefs.~�<Joo�H5a,Teg�$1993a,Alicĝ2a}lQ��"QC& &�j��O rp� studm!,w�@Facchi2002a,Viale+�1�6y�PO�_�=sa��&�I"�:�b*� �v0�v0*� Fig9�"%9b:G R>�2� �a_R �� +  $PG 8���%�2ZT� H�A���s3"�t in &r�& ;j*�k *grR�F��4Eq�X� ?*-m��; mph�a6� � N �0�A1�/��Q� �B _A��f�xJagNI�E ic �� upp�/cal�7�59 �k.͂�rDQ& "L1%�"�Ru7� #/a�:�2->? AWn!�Y Tw!U�*D*xa�"SWp����2errއaI*� 16V$ �_yAb�k B)9.\ �i�}A�R�ysyste�Sc =65#i\ �.p�7��aa�����Uul�QB�F��" j % �If ,c&�PCe�/�2n# . :�!.�i4��6:�e�E�I�.�m��a�%z� &����>0 ��!f� I�:Z$Oi� �*U!ory fgv�"8  ef'� Y��\n*�t&W.'tEFi� ��n.Q���"�ofHgEw-i9.� me���<might%�&�S{ ilar�(�'#Q[t s"�V��w�3e �����8r��gM�3=61�C a�4as6�6�ugn���[Ɓnd argu� �(�G�igIplf$ic polariz���m�>%� 8J�~l!Ely sus�.k� ��?DFq-/�stray �t� "�;%CP C�"��w�ex�Z�i[�uu q a�L6�� �a!�e6��A.nM�I��T|���)l�#�'� ��{%�&?�giUR� �g�82-3-�.�u��an �. C.�� wU�-*�r&kreshol�|pa��D9\b�U���)*%�&�d.*|;3%�ez�bF9�� -�M\E�iۤp�{!�m;1���A�de x)%��1��.*��Je����&y��ca% � �exy)�c� �i�7a�Sa-mF� ͹1�iDZM�Fan�w�Is� *{Ac�3��9s}8a)�i>(by Bj�rn X�d 6Uar���9� !���-wA�0ank Anton Zei�er�a�A3iw�%�helpful }lor�isP.0 �j�n FWF-�EuropEUnA al*HMR}{\�x\ifhGHunskip\space\fi MR V:8href}[2]{% % \L{http://www.ams.org/$scinet-gI�8em?mr=#1}{#2} %N\KZ"�the.+ }{10=bibitem{2�R.~ , o0SearchE�a b� � classjE �umA� lds}�>S�. Rev��L8bf{65} (AF ), 034104a��nׯ�p J.~U. hE.~Bo&up�C�di��!�l��p �A��_&�},a . � J. D�11 �$0), 413 --Vt36�&&� M.~, O.~N�\, J.~Voss-Andreae, C.~Ke�, G.~V��Zou C A.~�.�WavV4�{C}$_J7"o}, Naqcii&bf{40�81999), 680--682.�.1� P.~ 0, S.~Osnaghi,�Raua�nbeutel�NoguesAuffev M.~<�A$J.~M. Raim�}ndVHaroche�A� l��ary�t"���GF��<"۲-Y��iar�) 5� 411}1w@2001), 166 -- 1702A�1�� Ch.J.  {\'e!]X.~Courtier, F.~Du Burck!N. Gonkeov� M.~GorJ! ig&9f.�ry�!�iQ Lett.R188���87--1972�r*إ B!�, L.~�"��%�U�� thal�J.~Pe��inka,�M� V�e�er-�"2���(2�� �/ �Q�88iy�3 100463EX1�as,�'Hagleyet Drey�4X.~Ma{\^{\i}}t|�Aalie�W�J lich!���Ob����H prog���$.� o�x!``/''�y�n�5*� },) N  77} !�6)� 4887A�4892�.|�%S.=A.�$, T.~D. Has=dA�~Lenef%& Schmiedma%,� ,. RubensteinsE.~SmithI�D.~E. P��q�P�& sc,�!��j-tomB�:��;�n rega�r5q5), 378��2=$b} Michael2@Christopher~R. Ek�m, Troy28R= rd~AE�9$$ J{\"o}rg 6Mrt WD�gA���David6C���7Optic :�  {Na}$�:.�eC]8M��74I:!$4783--4786.#2� John~F. � Shifang L"� -{vonLau}%� J� c �.P�8um6�Au�49 ���R22132�*-|�����Carle1_R��linQ�U%!;#62) A��?!��N�>a�a�vimK-{UV}A�Ta<-|B: At.ʜ!}Opt1�2 �6D98i�995.�&(� D.~b~Huang,�N��t�MCe�KRVi�R Hauf��INcw"�*�3of �z?6�6�6�73qn!� no.~6H84��106uD�e*ә��S. 72� P.~Ca�lu�� � Scie��P&� 0�anotube�0(2 ed., Acad��ess, SanlJgo, 1998.y*tI\a��%Mariano)c(S.~PascazioQ\Me�u�},��� s. DZ�Ia�Q3�� --292�r2 � H.~T*���\�hyc}, Sp��aBere>�WF2004a} RK.~&�/, .H6� !�"� ����.h4o� �+:=�"3&jRo� � N��42��$), 711--712� :�3^�S.6�:�E.~Rei)B&; >�2�M�� *�4b*�0 ~{or*��ny9�  ), 90402�2���aćf�7 $. Campbell���!s&�&� 91laJ ��� ~EU�5� AN), 5472n2(��� ��O�rl�_iT$P.~Demirev�GU�ga� ph�{� by 193 nmM�}, Chemiz.�107��7; 0440--2�Y�Ama}%_"���E&�pe �U�Me�. :T�'im4{T}��{L}au�K�6�070�>4 05366JGA�(Y.~Ji, Y.~C�,� �zak�?H��Mahalu �(H.~Shtrikma�NA�n}mach-zR'�$ �5x422 �A�415L12�"� } E.~E�H� Ze.� em9��*��]�fW/av  �Ihz�"� }, ZQ)BY,5�8C 223--242��a��,.��ief��$D.~GiuliniE;KupscS I.-O. Sta&VscuazF=�j�ap9q�a�wor��Dy�2nd�%�����.|KX19�^ 2j �Quasiq� librL��(�"taw��>JSe�E)v6.g2�6t 186}� �7� 72� >e�< A. �� D. CA�" Rober�D!TD~.N� �{��--�m��-�>�n�n� :��� 21912�2ӈa�Tsipinyuk A.~Budrev�-�� �`rq�+"�>0(10--20 {eV)}�yq� v�c�2U�A&o�)C60�-�6�Ns:*WG%]�.�<��J�����10�"ĉ��26%� 9275.e1999a} S�tl Echt��S)egE�R.~q ,�l Sche�J.~LaskA(C.~LifshitzawA.M{\"a}rk1MK��%I$}Q.()>evaj5i  D��a*�g��� !.�630"z 9�9r 36� 2ْ� �E ~J p�D5��%[gE0so� 6 � .�� 10� -� 2445�152^20y� &#�=!�6X �w2�S&�rI�=O�u/��AmMoL�� �4D �28E 2822~�1a.�* ��E��t"/�'xy6 s �s madF��6�68 �1�� 160401--1A 2 Re6:M A� nk�YJ , U.~Wern��N� KabaU��bH.� Lui)J�!��re��EM *~$f.��� C-60� fast-pr1��6& 6��:023202�2ʠ�<�oߠq�n�P ,jar  ͹Te}"2T� sG���iKCs"� e@ }BU�8p\ $6103--6112.�B�� W.����- E. G�unti� J.P �enn|�)�Tim.�Tresolvcf�_�-grw{�!]����FC��22 F o 25E�32���1� �E� E;V�h�+ndөu��}E�20��l�{�LtX� 6�5�10Ac��155--1152� 2�sG!��sJ B�eUBuA�D�winB (eds.)Q�Ato�[6[�7ho^8 vol.~I, Oxford�Xty Pre�1982�.�+� w�,�"�"�.collapsA��+by*� }, F�$A�}6�� � 571--56�*�+���MVicarM�N.~ZanpI�Analy1� �.�T3( g*6�6m��-S� ��.PM��06361^ >>K7&]� ��B�t"��*|cN N�% 2�)!� !XBv�ReR��ou" \��H{03.75.Kk, 45.30.+s 50.-jGDk�"le "j+J��m�Qpu>� ��$!i��p�{!b dofu,�&u2��a �M�.ڥ�T,r%mq u�:]stq qA�:Zm3D Y $�%�5ic"+n-�t��]AA�,:|E�M e�z' X�y.s� ���.�d.[a�*�)Y�exyM�-<�o}�,�+ wise��b/ swam�^�%expon6 a�h��Ftra& orieh*.'i�o�i-S7&�I � ("��_ ��:TOPip1qpe�_h}(�E�Bose-�y@��)e ye2�� 8 ��5c���4ene��i�so%�t63*le�&�_rapY�a�P+mt ax�cs�(iVā- n�.a��d�)nV�I�(�@��Ӱu=$d year3iI��"= book� E�� uEby Whit:+r �5w}a1�������th�0�N�D ival+ = ��+E�``��vy�� abou�.s�:f.E�#�Qst��#af��� w�O��nX9!�xF� ta�å��D�{(�'')�4-�.�derpar�39F1!�o+%��s*N -nlinn,okt����L�*e�al^/c%A.�Z�IcA��ai%^gdz`E�\wO���w�nteY_F��&7�a9�mov!b�o G��E�&. 5�67 in��mᩑ2 !s�,� exact)1ubl�oen�te�!"�2ic�p5gn6VX d so��*Z�Vpliu���ol*�scr� < dAw!!��uF%�a= e����u�a��A%�m 5despi�� new*�u)(�~Qcb�tM�b.!&%�QGe"5I*EIb*%���? mpan�e,cloud" �᱙hrzs,mad,sc,gg,ros,cozz,abo,A� liciђrmula�:!r"8Zq%&)A�hree2*�u��-Ged qu!:c�d�D �� cmm}"�Uwal  �tt��FD polynomia�A op �É�y)8r��=m�a" co�k��Hm�  i"�lfe��y�1exh}+AH��1irI!y o er'sG9� �I�ulas8�n� y6{cZ�n arbitr��n�6?%�sL��k�a� cA��Z��a"� ce�Y�xda��*�R)�v# cho >� u �A~ . Sl.3� ingE�e'���Bin��38 �sc~rr�"�ygdA�rago,s�&.� �hv�V��! �G� sX�0U�&�2��t p���2��>)�!�E��w"p �= � f n��ǜ^S8 �6y�a� placV+r.{� ��e�i!}q��kl�7��p"l�4�:[ >��!=�~^ ���qa ,%���\pفtB)A)�V�x���_(!y,��4�6eT3):� 2h atx*� �),�<� {# s�8a� �L Bt}a�li com��,!$l�l*$)ebcEl�S"�v �1�1� pce&#M�t�t8ln��:2 valicfE�aqB[] A�:a9��~-body ( D�r� cOoL�U{O!c quad�c+il�Ia�[Vj}� s9�� �� kohn,dob,��%� 5, ��.M �.-�t>*A�q6! ^�. OZ/C5pK/��ea���@ �%6� ,% *.; z��ny a� n!J�,o X �"�c"N��p�Q�j�� c�ceȄ��� in�Qah�J�5&, !U�e��Gngrm� B�acA��_e��wow� [�:g.�ex�P @�G[DR=O} 2?b� ��to� 8�9F�unqx�a�@o�8�2��%�i<]�G�("6� 2� froz^A�� ���R`�rBLMl� /oѼ� 2�Hau~, U��4"�G�Nham} {\A� H} = Vbm{p} l}{2"+ Tr}\!\cdot\!\hat{\Omega7 .f��m}{2}>9V64r} - m>)bm{g}(t)`�E9l�k$�V߇s "�G� ���c��< �(n�H� %� M# !;squTtfO9e232�� �n-5�!� iB� f �-E$A�re{�u �%HeBKv?z.�!�ula $[L_{ik}=\epsilon_{ijk} v_j�D GMoI�e ��cOs�b$5���`�B��e!,�:�mU&� �Y�n� yQ�(rotg} {\bm %� = _{\�oll�+. erp}\cos( � t) - (7n}�n gD.)TW/, �e���re!Abm n}$�o��&`$ t6#{V-N^�$� ?>o~�[m���G m: j�-�c g}=k!QۂA�2�as$2`-vn}5Gq� J+} =!Y9g}-nA,���=�>�d�*�y� ��>os �@Mson+ is"� [ �5eA�����d��.6(�L�)�!�&b.�sub`";UE[3�qg[d%r�� }{dt} &=&�up m���M!9�' A ,\\ �j W =W-mB�m.= -na K + mqj.�m�i76T(�5�U���4w]26�1"` %�y�l �oB;�aPQ��� driv�zy�er�.D}TFB�i�wnҶ��wr*A ex��AuI,��)aK�f? ��mplex" n�1} =k�Re�[%�ar�+.ey + i ^�)e^{iIO t}[Q�]1�I mpact' �.[}M�2r��u2U�eqnmot]�iRALI�=M�M}��)Y�0URe( G�q1 �B !{e}.��� ���B� _ qe�l��MZɩ{c} (t) \\ e/�R '-`,\;\; e����N^c>� & mcuFI}tu� &>�S!6� \\ �)!58� mR�} 0h���5Ja� � b!� =�[. + i(nQ� I�)Jw.-p�rzBsw��fre�i�-�.�I�m�*�YM0��I�c:�WA ��0:�5`�r�u� ��s��c��1sVA��_ �- �1 &AU�$.�$�X"�@aN$sixS � %k� CY�$B^R IP(X}_{k} = i&b�).$,\q�( k = 1,\ldo�.6ɤQB�*�p� ? �s G!��8isb��"�UxL eV�CUaa(\sum_{k=1}^�%\��a^k�<, ���c_k�t �� X}_f&}�\Q,_ >`gC�^k.�h%�)Me�\;y�\ac��:�Ka�:GF"0���}���AeV�!i� ctc-� �$N 6� �N�J e���6L. We use� this method in the Appendix B to determinepresonant solution. The equa of mo �(\ref{eqnmotc}) can be rewritten now as a set8Ds foro0$ vanishes bu)0corresponding2#$6�1�$$ does not M � case!t8interesting, si!it mea�!�,we are just -� bord!3f�`lower instability region !0! trapohol�Tparticles, as discusseu�next seE��e ond)G^�%�s0angular veloc���roti�$I�$ satisf!��m�ce oiax+=F� and,[course,>�a$ \neq 0$�is` {\em!8different} from2�in�%�tandard periodically driven oscillator. I � pres�8%��4characteristic2w!he)�I�Q�Q�y�$-zA�force�erefore,mpos)6 [9Qhaebe�[�d selfconsistently. A full descriptAI Kse grav!�induced]!Y quira�(he knowledgu�behaviorK$B�'sA��hof�.!VI�AQ,a is import�tonA{�H.hoccurs)�mw!.%)0system underga�a@le5� ions!^is��!8R'Sm' \m2{Re�s�Ve�}ɰͱ�v$a harmonic�or�d� d by�value]itsn^-j$�� root9!�:�$polynomial%t".�E^seU�a���F�:X� �VLmatrix $\hat{\cal M}��JVP \mathrm{Det}\left\{ N; - iIZ \�1\�h0B�5:��!q0tri-quadraticb�C8$} Q(\chi)=^3 + A\, 2 + B + C�\;��^2,>�Y�*��( take place��n all>���tr a�7 m&t8three62A��# $M�$ m�_ al�͂(ve. WithoutU�, ���=0$�U>j[��?l��;eigen��po��ial6X(V}$. We hava!  simple�����Jxs vib�ng��` ly along y,rincipal dir��[�. AW E $ increasp our�E ,��(general, go! ough ɶX*� :�� ")Y*D ��9N(is negative%�!>upper2D} =!~co!3x%KshAexhibi is��by plot� X zero� t�! ��+ M �$-planA5e assum!�� !O=�� 5x!�"Y �fixed(w] e H��*� R��Y �$O$� on* Co.�re��en2Z�%�ic# �shownA Fig.~�fig1}�er- �� * eQ` nly%�ra�!�&u�(exists. Howt aw P!�o d, so�/ su�ly large9A7< is always� le. Mh bearrguS Ref.~ك"c � D.�]���%2:� �s�expon!��% withFe�s�in>�6.of2�9=a!aA��M;_{1,2}$� which'(curve cross5 ve� �Exiz o JA$gq  aaM]C�GA�A�s a bi�0��c� ress� � �F�� W} �� ��sqrt{� b\pm b^2-4ac�da}}Z�$a=��r8,\; b=Z��%rA -R'Fm$,i�cnD[ �q $. S�$a, b/$%�` �CH$b^2\geq 4ac$, both1�-j_{1!�ndE �{ A de�ate�isesiblee�"L=1�Ft��At�:�shrink� !�� :._ d�*>,�:may us��$e (explici� non-�K)����XeS rimi�!(A+$ I�in>a�sum�q (definitness�-,$V_xa���el� ��xzͽEX� azimutha�ngs2�.�\sin^2\theta=(1-V_x/V_y)/ z)�"�poAR�jѥnnoticRo. Graph�Z�V$n_x=1r $n_y=n_z=0$!=V�2}EZ%��Ŏ.�M�A� Exż"&��%h���})7Qq . OwA't* e�z ilizeffec��!�Corioli�ce,EXfas&� A[" �againVl�a also�Ip*g �*R�Aremains!�Bt�*ry��)��so,�aqyUt< infl��eDM�2 !?A��> �>y�bi WhitO rE�tho� ly studiIh conn� �pBECemss@linn,oktel,gd,ros].a�5"�F7Q,asqu�>�g1ry6#W�2B���AT=�ax�bv�@, ea� kind�.�varse ad�M�M�$of (purely��).G,.��,�a!E&� wasu�)KA�6X an�a�� �&�y2�ure�Lvs��" � !2�-�:a�7!�� T e:�-[2� qAjjug�#-Q�o1 IL �V�.�� of!wa�� %�2{ 3}��� howC �N�de�ps!5�8�axmqil� 0way a little I u�$z$Y�. We  �now!4� n� ��� most!MmoneveQ:�vecs�j %0:��(��{aE@dimen� �rap&any los�� �,!{|>2���� �!E!s�œ>�!kf�Bzfa!ize����vv��V�� �,F�\8 j"P = YH - V_z)\hspace{6cm}.�\s*^2-�("�+V_x+O+6 ^4 - 2( V_x %.2W$m5 � &\ i� chi$efa�h s if /& \Delt � i*�e!��de�%�a�B/gdO} W = 8F��-�^2 � &�(It follows,a�u�topolog��� s&D u_ �T����!)?Y;ofU)��cojd�th^�"�ib17(figure} \cei0ing \includeg s[� L=-90,width=0.45\text]D 1.epcap�1{Ac2�e m q9#�! �L�~� � V_y=2� V_z=3$�� /\�3� � >z.� ��s"���!� magn�ofF2$If |/6�:���9"�� ����2�:� (betw�dashed T)�p�C �J8�:so2 mo%'2mfeQ�"� e�) (Jou2 TO bG!s)%3$,�����MW��i����a@�6!CR$)� ��� ab� e sca�f5�� involv� !�analysiE&&�� sűj chos�X!�x �Y�unit.s�� �} ��:�2B���loo ab�sar�aE2 1}!,�� ar9@ ;�e��e� z=1I�%�J�RT� *� �*�Av%�B�!��.�8 fig2�pvp3bpP s�h%3>(2t 2}) merge��he$ � :/1}). H!Gw�]�����e%.Pparam`s:�~g�(1/10)��5� \cos 2k3�kvk4:k��>,E���2\pi}{5}Z�>%<. Two horizontal��s enclo"a�"L6�. B�!t��jlie�=eBB�i2S4�SvS5�S%R4vR$. Hig�%By!��A�nV.�5:�'�S� 6�60�%. R�(�5.%wo&�$�~AlV*6:&�"Gb�#�"ru&� �t,� 5��H \eyw��}�^���� ,f Eq.~B�w��t>��)Ն1)F�:1�5U*|q} D � ^4 + E 2 +F = 0V�U> (D &=& -2(\,V�V�B� ,), "~  \\ EY��VZ��  +V;R(B�!"NyFR&"�F�-|:]"�#1DK prop�ٚA�� ion"G++m}^2$A�EU:)�)]&�� *U,A�W� alyz� � ],2u( 'by suN(os�D���: bola>� (��nE aA�ck�*� Figs&� 4}--� 7}) �*� e�ZJ ie��,E��mo�� L** �) �B�� fall�t_ran&�'l� !z�m2 �(%��$we wouldg�!*confinem)of!9y*�9 �<� �!��&>�66 4})��z>4*F :656o'hњ� ^n6u R�Ed�le (cf.A9�!�%�A��c6b'"�b�,is]-ly�(� spec#circumrces (se.))i~elo-ly.�6�(F�4# �6,��A�!.�Q)or)g.Fhow2�, deala^��aI� dynamical th��#+en&v.���  7: II6:� � =�6.1��ir��I�����A'A�sE"�iB�.ao� �� 0� 0/3 z = 5�n_$$.�7>L��es�"%F-c�/��U(non",llust�.6,8}�+10# ro��f���,�$s�.en��A6arAQ2V 8} (E]�,)�2#11} (  switcqoffm>cal�,��+ per` ��coordin�+#�%�!V�& Vediago+!3it� ib�-a��at $t�O"B3�A. All f�%is ��@a�.*nd�u�Ai%�&lŞ $l&&a�A�.��is+ ' ?2N01 cm/�E$x.< T<#�'>�A�ult�\ exci��llu5$��M&E%a� :�3g$Aw�3Eo$t 2!t�#� evo�4�)Eb�:��d%�~��!�% %8 %aI�qed numer��l��!bN17 �D��E�obtained ��� 91 ��Eq pL "�5�a,nU�6!G5 A�A1�rBiis de�1��8&�6���\� �P�Rexcepdr��mA`t2�t� due  k IJ��F� �44ire some admix�5L.�1P�il F"Q�!�.Gpiecese"��F2�signific�.8i�43| 6g � �!7 %�*� �i�I3j�K �**�'e�thA*� sax4�1eteA��5)N88:+A�tr ���aE�i�)H�=f�ong�J �4 f' ��� [$x�y��.qI�10�15��2 �6�!ve�*�BM!@rɆ?4$(1,1,1)5 %length;J��6� �� �u�Aa�e�taeh!�A�measuri���i�R8�-1G�i�pa�6Prce ($g=9.81 {\rm m s�92}$�$q�t -����' $z$-6=��� � �!�a"�9� .| in\.:t�.� 8:� �#b�9��e,`;���Jt�o�>5 -+B�>P4�ܡ�bel�!��87�2-�6 by a���610�X � o67 8}.l9�lJl10�m�m=m�q�91labor1�l�l10�mNm1�m�m:_ ield�J�)tur off��B�:�*� E�?M��<lu&/���� CE> .i��a�8�� .411��N�F�2Z�&?h/" � ula� %5*[B)��m*� �B!~B���� R�2F�k:Co�!^%��4�z��� t>&$A�<">i-,&g2K"*3Dœ�f�a�*.� �*� �)$� !5" thirQ<s�% "%&ue>s�K*%��)�demonb!�,cFM�� ! lng: sub^ !W},f&� �&�@t�.^l?*�om#!!b>Pa�F < %. O@&�@�7� r6CN�=� >�"(1wo �on �"�@�*is�-Z�N,*�("=%"�2" *<!�:�aw-ill�  "�V��u�:� hIUof!i�2> �?he&�P��"v>.2� �d*5")��8� B,2F<�!ndF# &mah4.�I�]&�(escape&� ,�!$, ~BUA� a coll o���ac 'a� s�C�� view�reV� er.*t�&.5e�.'�,Rv[ /p60marago,smith}�sh�be&�� nfirm���2/�y-J�3Bose-E!�ein� ens�in-�D:rap�*)"�@_Z�makt2�quickO.el% Nlesy�k.@� search%BsupHA�*a؅W��P>1h Minist�SG�� IAjIn�   Techno7)&� Gr[\No. PBZ-MIN-008/P03/2003Vie��"1 " B�8 �5!{on�3� � a^i�:%d Thus2]p �2n"�bya��CH2�7���� wi��xtF�?Q, equr!Q^A^2) \�Cv "�?4(.`}*7 - {\bm j�? ) +"A�A>#.ZY^@.}�? +Z" \}\, w&H@IB*� f�<L8 ,2BDBZ� .�'e"�%-9��|:>� alig� EK!�&<>�A�ACI=&��is"�� .aq� E� 2_\pm�9f�JD(1-n_x^2/2)V_y V_z!�+J"�9(f$Z-- 2C.>-)+ K)}} {2G.&7:na�B:U��%�y� enot "0ele%O]DV{9!/�nd �-y X����3mzJ� cyclic stit�L s $x\to yzx#s}�V�$+&� V/=K�C�Q�Fm,�()�(EK"�(Gis<n�&("�>��M>�/�*sum!n�51@)(!0*�9&�*� �!�"�9���/ &=& �FQ0Y�-(1+n_yM��0z zym� ^{2}"V#$\\ &+&4V_x ]n3 (V_zt9)(M�.1J h>! k d~�jt� , bek;d��:e nYs*8"+I��� � ��to: i�!o5�q !��L !�a!�*����"�Mf3) pm 1�w� Ktd7"%M" D v��:�H�N!"t�c��1}{2 V_x��V_y}+z@F�2" %"�_-$E�&BLy�4�eb.s#G5rit�FO"��X:u:bT:To�$%iiBe X!V.�����)�Byѝ)ex_!b@ �) c*H��5}G�} Q(0&? "G4��&&bu�M�R�F����+�9ls%��F� E in�ed� !&!�O �AF $y$�y�'��-�$-^�"�@;��E�9O&6+��~ >' z�� poin 0�C�a:NaEYe�>��� teep><�A��>ng l��"�N�PDH��$x9#a2�ůSG�@e "6E,&�b��KR t^�� TA S� } AF�!��e�" expa91)�',�Q"�.���S"�m6I�I<)J!rowU"� � ime.5$"B�wan��A�k � 1��su �( � � V����AzBw N W}_r9 A}t �%B})e^{iI t- CFN � $DM BC six-.�&�s. Upon�!I%� �j!�N�A�com�$&!�A�at&� �!���'%f� 8��yTpunuQn�NVhat�&oO"C 1e = -X ,\\ Ev;BB;B9�A� !� G}_\J+�WCW- �;[UBw ��1! say-k!&)� $ LA}l%�"g(uplLa�. FJ cwe� �sB��his y�� �B}$?v ��"�>m4!up��pm@@�=�jQ's2JBby�ngI�e origiNkE~Ey�� add such2stopB��FisP�6hC-hd4�"�1K. �B�Y matc.A algebrax����I� ps�76�problem� qui_G�P#P+we�re2O them� � i� ree2coue-es, �W to am&(block struc.w#�RNJ7�, let us�APT  eV�.u�M)�`IB�x!ͱ�1��I (t)$�5�*&�"(�M�.m $a a2" b�4bm �H\i"uane phys ^�+S36�[�@h�O(m�bm r}(t?\Re((�a� bm bN�}!NElxH��>/E�Rcs\12�Q��^sub/ l`2>K �C N"�T�z bm a��0,q leqa}�wb4b4��%�" O h}Ub2U0:�cP-%jg���j@c�"! �2�qE��o S%� ^2 2�U��K p2���'a�$�h��2g<]�Y + i(n}A )$� bh<�� matn.���1�pi�} ^2^A&�3 & &nA S-n_y.�O! n_z) & "�A +�5&+ y)\\F+y +F+VH^>�y^2�y�2xy�N�xRxR+y)ZWJ�x,VFz �zQ4�1vB�&� b�iEto�1��$Eqst6a��%to� � �BvC(w4 bm{aE�{b��n%ba>2-7���\&�X N�&�X67M�u[� ab��\`_0�e}_0+ + +d $z6 e}_-j b Cbet2B2A@Vq6�N" # 5!�E"�5��i�M�9' �+o-$f�]��L arbitrary�O!�tK�� 2�Hkb� Mk 2�b}). Eve %�is&W(F$K� � -�2�� �NYAk�Q�^06-^*XmF mbda�Z\l �)F+�- 5�q^2) + 4 'M� ^4-3 aE38) V_Cxy�!Onh!�iE�$s-�esD =�wo2+$ ���FZL��="5��AF-V_z}{�#pmr\sqrt{9- 4+% (1+2M)+�\G^2-2V_%/SF�:�w��"! ,meaE�7$!.�*Kn� e&0Y�� ee dpV�Q M�I�<pro�"o���P_0},  +lE�2+� "�Ce�'# ��U� D]�,1�6XB� 9��( O-Q+)f -)}{( -&� P_+.f>e�Z([+�-)2f-�f+�-f-f+)Z,6c�02�e �^��u e m$EBbe8 8 �!*�U9�dyR4ic�X (k/iE�E]&��EWe� hoiA � �&�  + i*  :"�.�ki��hQV$ } ar�X read�f2!c���4(unnormalized)2I, need_.ta���s��abG͖a��h�q6�6�Jbm!�0eI�a!6b  � ,+2,+r,-2,-B,� Tak�acD%ortho�6Vd��]���6�#Q�\A��leaR!�*Cxp�&��&I�sMa}m b}$1y��am�!��E�aQ^\dagger6�}{2f&(� +%��s}:� E\;E�  � !� �ii(5f�)\;'+J'O� :V)}��ImFc��~� `+);1\!�>w+��> �%L�=-��%N�)-z-9-��Z�v| ,:�$"aR� M}Jz=xn}Iq*s$%xg��nd+[t�"ll�&q�j� P�i bq\,[n_x I�^2)/ ,\,n_y6 2" n_z66S]} {V1 ! :(F V �] � V pW )+� V _| ))+�#4A8/^951G$thebibliog*P y}{9�2b�aw  docuDI,} 5�% % Cp_(inttru9�?thq �u& % SetB fal�o�vw�<lum�p % %\i$class[aps,a,amsmath0symb]{revtex4�TF7 twoc],�G pacs9VA{,\usepackage{ricx} 2stmaryrd:rm]ng:float6[sc7l]{psfra:28[dvips]{epsfig}.{[lP1]{inpu(z}} 6)D (lef�/V + c z"/F�eone}� {E}_�9.���^{}}6�)kH{1kR"L#.O6Pw�� F�#s$U:�'w'f�.� /_}Vf� etwo�f2Btwo E}_2.HB)�E}_{2FBtwo� #.O6Pw� �}B�#�$.R2�.�.J�'>V(.Y6ZbA�b�"B:�e#�_!6Earccoaj�\{ :F Tr}{ TB�bra�proADYf rAf s},\o� 12brrm}{Z7r'j8m�:o' prf8tJpt7.p:4bsFps8oF7F�8.p>m!�Z��|1P:q left.�<�s��|>�4.� 4rr4.�.5'n6.�5t^4�;B�|2�>B 6B� 6�>>  5B� 6�m >T;B� :�BpDb]��D}>�HB$HB$EB$EB$AB$AB$GB$GB$PB$PB$MB$MB$SB$SB$NB$NB$BB$BB$rB$r$re.ksB&s&.$jB$jB$kB$kB$KB$KB$dB$dB$fB$fB$pB$p$6� Im}{�GImA�6Re Re}} %� "W$d� H \title{Quantum E[=roS=MediatN�5Re! sI \foot#7{�4pa�/}@e�~��,70th birthda�:,Herbert Walt�[ w�` pionee�6�=al work�c�Kq �e:�0 Rydberg atom�Ts�rpeI�P�6�I=funda� al� l �-"*"i>xon.} } \author{J\"urgen K\"ast=Xnd Michael Fleischhauer4ffili7,{Fachbereich� ik,�<1e&\"{�(` Kaiserslautern, D-67663 > Germany��$date{\toda�N]N%�ab�Bc� W4n8��=3!c)�%�W%�i:D-�ee~O �F�0 �.Cma܀!�G"�2��x!rU�. Sp�O neous emi�t%�D tom embed8a>Mk A�isc��<,gn furA�mY ��WONma"%op�5path �-oe#spa�R�Ve)a?33s%!vi��#s�%er! �l��lete r?J�9�Bv  i�9n�mahTWYmirror�:nEOM:�L�%LA� -!1�3�a�J! tran�ion wave). �`E s pu"+SfoJ �-S le4"�T1K!" llel slab$id�x:1�2F)��']zQU�sub- ��[ radi�M�.!jximum�gth�.A�bkac^s�� ,!�o=-by �propa�:on99A�M�free-ok s�, decay*/. Lim2T��%Gpr�[j�rx.i^5�.nfrp��,��. %z`al exte %� xNC�.0 ��G{}��j{�F%����BŘ g� �.���*/aIn�u�\}����b�S�xA.yVdayE���um��&G�7well-<4ai apprK\Aˡ?e2>a�n isol(�(�&L�3 .s�YUt=s#strongif�b$(the environ .Z�3�_o4E.M. Purcell �: X-PR-1946,Kleppner-1971}ء���co�T60w_���ccelerat<3��;s N�X7��ed �� �LHuket-PRL-1985}, enh��d�` &Goy$h!�!S:=$blackbody �^ A� j1,� -Ann� Y(dN obser�j� 6� �F� �< s. Alter3 Ed!�N �H g�>5�l9� dikicI)fa�J) @Drexhage-Prog-Opt!�4} !inQ�-Ex"u3sMYamamoto8Comm-199SF*"photou�band-gap�js % an e75ee�4�G�t�G� M�on ' A<�� 2�r%IJ.I*�e� blonovich1�$7,John-PRA�4}�I��T� w  QEDՍhi�za�W+ pair%�lAeA�q&fiX`с� x!��*�  N� � 6[\i��+by�Veselago� -196Kwho#AC"simultC �9,)� YUMmitti�X,$\varepsilon�(�"� permea( $\mu$ 5�yF� �J*� r\o-?5�oeft-han 5 �+attKed�<� �'A�Xn J� ndry���{���� � �o� >� uA m&KBp 2� as#s,'&�  i+�5�D�"| by���ionM�P�E�200�_Sh8Q:0���hBd3 \ \  of=vless Np�thickG~$d$�L�)l(�ne� s � �  so�H��/: Jew�xa. )!�ow /. I Q"v� d +Q� $n=-1Á*�X�&Ť!�2x is $2d"�[2� 5��8�C. p�eK�8UUs�@� 2� a dr� c�>� ��1��v �-ly�V!eced � �:�ksu�� (�� �)��!f.G2��� %4"�qdi � eZ �;5�& !/� )%.���I5nin%�IU��%!� � %o�2om!eu\�2 or d"u��%�Xp2�V P,� Q !"H &�t�~aI��/E�Y�e�2?�y s an-�I�ws%o�#m AiA�5�^�.� ;be���Ihl.��� ma)Bc��Z>�.I�wo%��2W!�n� Ճ�� ���V��!df�hba�%�aH po � i.e.yII1� Dicke-subE�2��"54��Af =summari�!�basic�&6kN��/inge� %m��th�<e�S�� �C�y��al��� causal)#&�U��y�Go-�}E�Sec.II�2����a"G myRkrx f� A�6% N�� yI z[cj�IEo���Qf�du"�achang� >U �Kot any�g.�� %Wf� $�%)98u�� Nienhui� 76}, but�W�pro�� n�ch 15s1m{�l!�r}�5 < �RextQ�ungk 2003}#>%F�IIU�4 ��� !��LgUbw2n�q lay`T�-7�6n)�VeB!� coupHj%�u��B�R� `V�k�@ I` %M����M��e2�a ��B�� �fa�g(sP& ich nLi� c�Qnf851yo�F ��"��_Z_>��Z&� B�N ����f�Mݤ�*vn�G,@�� �i.�" & : zed b` y ��s.;� j� j� .J   re�emv"�5a{pol��e $\PbjB�bM�)���^ $\Eb| ,6��9^ ` � ]$\MF\ #c \ Bb$.�6��j`�w�� �G V5�=�-*6�S': % %ke�G0} \Pb(\rb,t)=*f@_0\int_{-\infty}^  d\tau @�_D7)\E D-�;T�Pk�x (s�and"#i} } \M L)=\kapp�=f��M�B >6�Mj��:$msmu_0$.  v_D%��I hi_MvIACU !�5�suscepti��� 2rD Fo> �it�B2pto������$!Y <��8�t:9&(i"$�nEs1p =�):�"=1+%j02�%b=��J1��3eZC.E;�E5�2�!g%��3oI \be 6�A�tN�]f�1tkjT9a�7poyZN 2�9nd �P9T1`��Q halfAA��lex� . 2�DBV usua�E�nf&$u$ �$�, e.g.17g.ڡq�eps,z}6� �!�� { _{Pe}^2}T��^2-E �_���&q�v�5�m�Y��m5YF�8w�^�mE�n.$��ap&�!Key��-j�* ml%% '_{Pm}$�2�$\Re[]0]�'mu]�y���&� cer��ˡ. Supp-<ńat��c]+y2N =\mu�!�s�A� quQw�<rises wA�A�A�i\n{ � $2 $? FOLJW^a36( %uB�2%^2.j.��ZArb-z)I.6=�mR!c�VwMo8obigerFall} n=\A=� w \mu} (-1 � }cA5 1}=1�6�H��a� iZ5D�by"�� "� 'ZY.yEH�q�l�P"7 ,�S8q�cie�b + kY.ake. No�L��imaginWRAb of >�.� �). !�AG� um�qa passA?  $\Im[2�]\ge 0$Wmy hold ��g� . A&[{�fi� 0TWurzel-M��" rO choic�srnk� I�+s1�}6� = & )��(| ]62�G(|EH * :� "} \\ &Ir \exp Y[Xi�CA(�+��&�_R.y�II2+6DmuF<mu:4 � �]}."�H- J���.�_R,YRE�6II$� ]]\ :��.TLmu$��&�o%��+"+&! In}[htb]2��g1{file=2�zk,he��=4c��x�[2' ]{$nV� BD,�>�be�#"�C"!QlA�{ x.e]6in5'FQ irclVa�2�� ��Q6Q  % V����A� P�.���:� q_n &i� lim_.�Id \�c�gmuiiP^h-1}6K} 6E!a5>) .�]% ��4}�(\pi+\piulak 9-1\, �h�!FoR easy��jq� eq.(���)G&yek��dE\frE��o '� ifͷKae�(-DiplomI%�:"�0 \pi \,�� \, ��A.�R>g)5h.��}{I})\, >[ pi/2V�g.%BildM�'neg�U .�{! �Jy*�V��N�a�5 �-"> jel� i!K.z ,�*� ). � �,a��� =1.05� Te}$e,Y��B| �lB#recogniz}� : %M1��1�#�Gi�*.'1�funkt�'wi��8�&� 7�3:�]{ �? ]$,a�  #]g-E� ] 3K eqsm@.��iX6�P*�� -�. +�. =0,46 k_%�;1�_{Tm}=1,6�;KU = m=0,01.E."� :"��j� I'T Ha�ma!)�� >�� wӟ�$* �{""� 2�1�1�9�$.9" factJw�)dVuRX�y��d ,�q%{"SF)er��W>J. Co},��*�gy�)."��7f��ve ��m"&9 �0Energiealt} w. \EbSmu\Hb^2N{  q�A at� e*[".W9T$ l�+ �, �P��zd!!c2�ssocie'1^C"U����� pv^!�Z� w=\Re7 �adMB� IJiI��]%_ +^;muJ3^�w�i� �eփ�.��eb�if)9#I�K��&�פ,�Z)ZZ���W quad.8rm{and}  ^TN( L��. a�aE&�Jw�"nt���Z�$peculiar a�  P1e�-in5lB� M�K�� UbZa*Zx ��2ve� 5�>.'pnam!�Mf E^\�W,H }$� cU�G0*3 5D^\+$,B �Pa�4 %��n�ntg� A8 �u&�P��#�IZ �2own!8.�Randbe�2ungen��i��ha �-������4! SGs lawZ�n {n_2}{n_1Tސ�U)} 0U*�G.?zSstrik��fea�\B�oaH��&#&�w9-$\kb^r$�V(s backward \�1uI�er�domo�+um_ F0A�A�C#����.`J$bf k,E,H}$�1m`'eft�'tripo�$st��M�usC x+oneA��1%�.�N� ��l c�d6�!� (LHM). O3:&h, �Poy0�g � $\Sb=\Eb�ZHb$"G�''  2� ��#&m $: e ���| y �Sct&�u,q�aOY" )-�:it��be�B�͗(��aPw fig.�>/! 1 * �F�H]J"5 .l neg_M�_�s*q �Nq {B����%|J^. ���`;4)�a "V q_ E|a�ediugc�toba�!s&� >b ���� %� Be;)uo�/&�� Dopple]�C�Vnkov e�/�"} ��j�proNbnt 2q�J]�n� ably Bs"�+�%�%aKr* _*Ta LHM!�t/u�� ��,�wor� study�]a3. ��*en��.t.�� , &p{�$ +ly24_,� � b�*��e��* �*�Utoo fN���R�* ��!���� (y�Abb��E�bIbF�htv��'!~e�d6.0f@ 3 inse]{Per�2F2^�!a EG� om8�(�#!8 foci $P_1Y P_2$A��y�%N��Z�%��y2*�y)2�Nb% �X s $d(1-n)�&���&i�����!-! %.l� 1:�9-:?p:>�B-l^�Copt.}}=( �-d)+nd�u B��!��1�AKGX��7Z�0&2%� 2$ � M s{-sb:�*onT 39�Tr�,a�aE% noAx�X�ab��i��:get�'��D� � ;*�Xvanes� �P�T!�\�V � � 0an unl9e�ja1� ��1iK*�/��7*�7�[�[ "n��< � u .J���&*�&���a�78E%AMπ�n $\Gamm��a �.2/ &Q< +A$�5rin�,*k =/,�i�~wl�).�7 Bas�$;�**�c��5 NJ+� Alkemade*�4k �6g, homoP&ous�)�.nt.C$s 5 "� ���6}�66t F�)]*%f_0\, n,�a &B�e2� �% 9�?!L*�<�+ rate:==Ud<��8_A^3}{3\pi\hbar.�_0 c^3V��$d��M0� %��A�^�-ic ]I&_�-t��^<�I�"�5%) �� �%�� �/"��%4$F ��2j0es:� surf�Sm�faiG�himat2�:�� e�. T�OtZp�(eaX�q��bM�,i#-� ��qy^ �0��ed. Sevc�`~Cv� en establ��dE����,�Qg)bes a�? {va=o ��(a cubic-lat�6 host �@!�&~ G-X:-holm$Glauber}L1��&%�=n _0oOth�@L}_i{U}^� % MLewens��A��"n $^F={3*�}/{(2+1)}$� g-h�For@E��-uׂ�_�:)�� . *z)M{% a -̡�f:�er � [3empty�EQ�� !|*�(7<)^ �re[]�A'@�&� !^cavQ)�� >� F� z��M@.� f�[2]{Rea?)w��%pisnmn�h. "k�-A�� j� e1 �c*~�tEb"`E"�V"ws.��L<�M�Y�}�$ obviouslyS�i,�U"7756 &�*}as�!�r�tQje*�-r�x`8o�Ca\]�qingS � ,Knoell},�2aPrib��q "�ɳ0,� negl3� F"�^F�ss gold6,u 3��4Rd483n"-X �Q2O4>&�retara�Greens $\Gb$e�y"8/�T�oٯrb��zE;%� ( G6]|)Q))$��Du.B4E�B� ��R }~�{2R^2d_id_j(Sbar��$_0c^2} \Im7�[G_{ij}A� b_A,�)_A#"RP�$d_i$!i!%� r Bq+ mmun� !sS(� \nabla_\r�[ F�.B)' ] -I_I^�-AD]U.�' 5) \Gb�S^$\��  =\��6-\rb')�P W" � 1i .g"�u� m�L&\. N�'!�Nzlapp|M� )=1/�&�+$���bsent Me`w�4!�m��$P-YF� 6�G.�A�l8 �hj��7ee�.�.�R=�)��' �0��.S�G)B=�WAsɄhR� ~ I���;Jqa� te8�h Q�5�F�:r�AufteilI�G[3E+$=\Gb^{vac}A? +s Mo��|A�E�|,E�' m�0j_n(kr)P_n^m(а��,) f_l(m\phi)"�!d $f_lxr� m�q�  c1�e5 ���"$l�&sine ���r �,odd�Qe $j_s$ڟphq�B� !����� $�$]R$Lz�dre�5����N�Dhy�]a�Nr�_}C}M�$a��!i�1��i'2��Li�]�H��mi�>��r��a(�0����s* ���:mN^1iX '):Nt "�C%�2.�D6�R$ 'qv`(&,0)��6�:#8:I6�  = _0 a�l(1=%��[:1�%&� 3r":R�/F!(E�Fq>^ *�f��{1"8varrho}ň[i+ �>-i ^2 �Pi�\mu-n�,-n^2}-&3 ť�:"�|�1�x� `ni� �+inL1n%# # W)�>>si)���1&2�. '}y }^3(m(cos -in)-� �S���]^/� f�� \�R� _A}{c�ma��$A>$Au"�y�(�$�ڱ�%C9;#$ct���'F�!"% NjqiO�-aP�H�D6��eP�y}iwD $n$,&�2�)2 ��� Z�1 =n�6\,}�c&c3.����+1M�)^2"��&neu�6�� !�soughtS+�>8��fofq �� d< B|C :� s{w� � os D�V��G��F� �ar/!�=1$"� ^�! ) r5��.�M���j :?LHM7N`���9&;c�J0ub0qexu-�e��.!� i� *?7g.g o}�6F@5���A`�fD5E�- ��j0{Rn�!PA.�]� � %mTˉBsMF�/ � 60�*=5 V�/,�t^R�/e��_.�/.6�/"�=�� )�� !� % B7�m�.\!eFflvic�� �r)sce`(��eB�$0$STo&�T���%��&�.tu�L��R*S�J�a�roXNB'[:A�ified"V}�p *p  �p y}�-|� �!�m*dJ�6�N, 3?the6-T��/FaQ` ��Z��[io�scK]�#L.c>��up!w"�)"-�2�/��?"6$�P�&! N*1 O Pe�&pa*]�d� &�ilzSAB by vacuum� 6$�N��6�e ���R[H] �� \i��A ics[�� 4cm]6V��4�5{A._!�y�+attac��to�e B%>�^JL zero 7�^ E�s $z>��-d\le z!�$z<-d$ ���d!�!�2�s $0,1,2:x<} MfqJa' ��� 56-Y"A�/ �$c����u+���!%Ba�&��K�*"�ii�u�'=!@ �H&�n)Q��* f/��MorawitzJ^�� e� �!�a2N�!2�B�/kR9 � �� �1�Tat ]n &�}:Y̜͠��Q 2bh���I�P�Z��1in�b�:6B,%:Q�-3 R path��%��e6� lse H: D whe'!a| lead{ �!7�+ )�C:�'+� �wsitn�� � . Toq���nsw�cE ��ekeA��Q�.7&% ��T ��,*�J\PN *�% is �by� ~ �;��=��!V"E%�"�w0��.!%�4ift�et-up Z�k.C�*� a.�%el � Z� um<)2�I�ee dh��&��%Tsang85}F#r4ay� two 9�9rM $\rb^\p�2���Q**�Do�Ji-���[&?>&&){00}Q� = ?i}{8\pi}��%k���q`_z}�[�%�00M�&"H \bigl( R^{\rm TE}�q  e}(k_z)1kb�rb} +��&-'K'[r)\rcZ2-i3'6F@&&y7���M}Mh��h}z�\!B �.1 �r��,"�@��9����'�dzU�F�_� umed�8a�eqt4�4sU�4a�E{%�uz�AwA ]��i.�&�aA�&o��2J��*��!�h9 TVzZT�\�MM&�2M�QSw>MZx� .� N!Q0@X�(&` � �5�s � E z���*�6'$: �� re���*ly�OE{; veni��y"^AY!A�5.�� �&p�(�m  2M�� .�[�.~Bush,1](� �k^2 =&�/�:k�\ED k^2-��^2}E� $d^2 0 = dk_xdk_y$..*b $\Kb \?�k_xy�x}+k_yy}-k_zz f�have inMf �** � �8 $Ce�9{�;��s z}}/�H|RV|}�9hRp2� ] \kb/O|k ?&�1p�for9x0l1�� $p=-1$�4 . $Ru�,�M-$q:E},}F+!�refY%�4� m1l.,-3-7XM?�k�.lW�J�$� �^�0T��!?&����RTE} �=l0R_{01}+R_{12},2k_{1z}d}}{101}N,�^M^M.^S ^SV^ NJ�!�'3 l1R"H" .��T�9��2\mu "� + �7�12}} Z�!(( 9a9)d��"S&K�M}�M.�&8�2'G�K!@�{ 01RJF����� ӑw_1^By $!Q��)�#�" ^2/c^2PUR_�!�� $S �}9c&��s��"� bet\-X�\.a�&e"$ji�TETM�es}p���j� RS} ��E-�Hjk_{iz}- ik_{jz}E<+."O" �I9+8��UY 2)I {+.>�R� Se� !l12}��a8!o1�X,$�qhe�$� �5�F�by*J/�Oq�!r�>�t�G00�Gnt�^�� F�S)2$EbR � �Y)�re�#N+A(vorspiegel}��.) %ic 6�� �A"<Ud) ) �&�8 ��e6C$d=100M�lambda},��b�;!���)q:��2"47LHM<0.�C��a�Mcal�8��blf.�&�-�Nt<&)d:x#�7�&C$1$rm{focus}=VWD!��8�5� �:�2 ���K!.��9���)�\ *�)� loc�0�y���8!�[&��o�"�qTdv>�.z��t7.5S<� "�S�9=VM�M �I �t�j"vD/9� (z)/)�_0��m!qu-[m.� � A�1� shif�sz-d�x �!��U��tE�us; A�-�"�`>YEeZ��;!Fdc]8%bnd�� -�!��L���^�C.� o&g�)U,��1F=�l+D! Q����no! q&���up� �3:)"X!-p�!�O0nXE!�h(�u� of 2�J�=erp�9�72Qp \eK5�3"N7.�FP!\=�f"�yo"� *�Hay:� bJ�M�� �  ($n=+1$cNo&�L:�2(-(�O�� A��ts! vkXpp.�of (`)a�j/�1�f���=quivalB:�4)� Qq�%6�Msuggest�A$s*_ y to�)"�{Sj�B.S�Q�Ev>�{n�aM�%2��A;nzd3Q actu'6pu+ "B ��>�%�� \section{Sub- and Superradiance over macroscopic dist s} �z:0 \label{plen[(The observa�0 of the last �8, that a combin(Ha layer of positive� nega refra��i can make a spatial volume to appear to have vanishing optical thickness, suggests a different interestingMlic�`. If two atoms are put in�fo[points�Ha Veselago-Pendry !$, as indTed=�!\)3 $n=-1$. F.�!�all pair%�1.s1Dz sideA� slab Rqb $2d$.e Q�|regions $z>0$ (vacuum), $-d\le zLHM),E�$z<-d+ � denoA4byzLnumbers $0,1,2$ resp�vely.} !cm�]Y!| \end9�-� � U %A �% We now want to analyze this situeZA�detail!�r we start%^ !le��$Hamiltonia�ey�t9� $\rb_1$)S 2$ e2Ohquantized electric field $\�� \Eb$� ipol�� rota�-wave�roxim�:!:Q�equH} H_{\text{WW}} = -[ \Eb(�1) db_1622 .)�S!Y Elim�;ng� �omagnet�us @usual Born-Markov6�s leads%�A�-��( Liouville }��!: form�m� }�;}#`split} \dot\varrho = & -\��<{i}{\hbar}\left[! H_0, + \rig�J\\ 30sum_{k,l=1}^2 A\Gamma%Vk,!\l)}{2}(JH\sigma^{\dagger}_l _k d+ .2 _k-2 W@ .8) �+ ��6�$delta\omeg6�9 n.[q�)T-),I41ta�9�A@whereI� �H_l=|1\rangle_{ll}\l  2|$ is%�AA\0lip operator ��$l$�}tom from0lowera� te $^$AfAE upper st 2 ~$. �<econd �$third terma�(�-Yb$) describ�WHe spontaneous emiss��G$Lamb-shift��6�vida �s� $decay rate�EY]iE]i)�Sr�s level ^ s $B�9$, $(i=1,2)� Howe� t��also c�Terms �q�r� . between�$�E7�ssi& ve  >propor�Tal!� $�1�2 �� ndi ,�NE>�K�iAh�f!��-"�)w��given��an expre%� simila� I%�})Z��%2} �, = i�2i�$_A^2d_id_j��a`(epsilon_0c^FIm i�G_{ij}�bQ,G)m�R�- =Is reade�^X%X-�)�LZ7�6�pi 2� } {\� P}� Pt_0^\infty\!\!{\rm d} �\,-  ^2}{! )4� 1} D- K_A}b.%a�i] j[��not accuADly�dGaXhe AIe�heoryE�0will be ignor� *`following. One recognizes��]~2})I %�-�) � Pr�"��i�is de� inedaA(imaginary p �Dretarded Greensfun( �:U � �!6 I~. In fre�Pac�Zvalue*�'$b$ rapidly�-rease{ rel��& |t-�S4becomes larger� tran� on d l� T$\lambda$. Consequentl * .is9ligib�xcept� very sm� �s. A Ishown� :� chang�%�� v� B � $. In ord� o se)deffect!e!�Y/�it�conveniE�o useWa basis�>two�d system be� (otal ground� $|1$E�((doubly-exci| ��2�&symmeB and W *�6 one%; be��Z($&eJ :)in its2�5�): � �=$narray} |s �$ &\equiv &��L1}{\sqrt{2}}\Bigl(|1� + |2^r),\\ |a�M-BM���� In�%)these-�%xs arr�����0sity-matrix � W�Pl� - +~)22} ,��A9}\\:tLaa}Jz-Jz/6|N+ 22},"aF}! !+ b�j�2q (�� e5�A� we�disreg��a�21= � ��a�� rt n�on� &" � j� N�f abov&� s�� � nel rough4!=� 6s�&Ndl��:�  ribuk  $\pm=�$. �he�߅I�i2�ms�intŴ$_{12}=S1 22_a��cas��:��  doesl)�ll, whil 69 ��&�bth twi�P .�"� . T�u &$$of Dicke s�%U�#nce \��{#54}�` Let u�w calculk !; "� e�,u�!6Y 12}$ i.e.�McE�A�2V�!�(Te� \pi+ M �[�f[�$gE}=M}=�4(k_{1z}-k_z)d}�; =$ TTE},�TTM})�� been used��u� "e ��t .� 6t�2A:� f.�is ideno�� ^e2� . As�h c(V:$ �A�eahZ�,�pit�e fac�at�� 2�2��be much :5 reson�*4 . FiXHOrtparallel} illust�!)depende�AL�� 0 ./51}�A9�$ displacem� C�2�(first��.�w�r�[H]�@ \epsfig{file=3D-}i,�8cm%&& {H[Ortsabh�ngigkeit�%]]{f5 as "�1&�a5, A�H '$x$'�orthogo�'$z$'�!� surf� J LHM, k !u ou9docu�8�Qone�.�$(0,0)$B� 2i A� obta�. HII'j�b�� or�8ed in $x$-dire�"0.��-�S�M R�� ��.���� ��!�!_e�:�-�idealR� ��M��} \Im�� -2�� Q)] %2.@�-G-F\�It Qb�!�< �a �on B_ T) �  exisP!�r�f�9 his"� true%@�W� pattern��B��!b��in vioqo�Maxwells"���d���ͧ�%� only<a cerA� *e!�fr�ciP � $ du�!! necessari(ispers�naturA%LHM��e limic�ari! i )?�discussJ��{� . �:u:�X� &�#L���#2�#�� ��#s�,pmirror}���>p }E�t�" volv%   -han�material�re9�.: i�urn�� ques!� w�"A?.6�� �$�fP s unimor� alis'b�s/when tak�Hinto account absorp{losse�# fin��,versal extenr �A�$"�!-er. medium.��%.�%!� \sub-�{A�DLHM�f>f % F��Uto� �a>q��ham t�%!h�!h 9h�is� eas�? be d=byb stitu�!E&ve�fdex $�#� Q{�by +in_I$-�by add!�an:�KF�I�-I��!d.IV, �iab$ ,}�tw*e�n </ ^\� "i 0\ z9 coefficO $��M "�&�a�[��A� N�%b]Z$�%h  2m abs-)>o �$�%vas .L ��B E�]iM _I)-Re$[n]=-�J< $dU7��0, $d = 100 \l�\/2\pi$ (solid line), $d%>$dashed�%#1B!otted)6�%6AA'*� 2" ��E,Aixbe��)vp7.�Nj!,E�� iu*;%s!�� �'I , de9�%ine����pas�ect$��ctivityR,is app�%expon* al�e6 �'jF�� e�&  m��aZA.%~%4M� T�(�Kep2 NJ�� m �J � ��q�O��%�AYx,��F���Aref]At �| sub/6BreduceR� ��sE�$�e*�����SANA�agH$ }�g:g6fF: eR �� >� a� expe;n� impl��n�x�+of� D always�� R� . W�-��*� � &@a!LHM-in!�dM E b� &� �B��i &",$d$".Re &{ � a$ (&��. 3D})� : F zn���3bnQT�*V �#z e "T.}�k ��a�� K Beca�! � �uI}1-D0�,�0E geo,y!�no lon# �&D!AJ:\can�$be"oegaly�ly�0numerical solC��JO�,q(#�� icul� NoW , h�(Aiatpropa�1ng mo/�$k�le k$X �e ��"� j's,�!�`� � $1`�\!�Q short�-+$8or ray-optics  $(d\gg� )$. "� >��a�s mea$1Dc$gr� o�)�$^�deE� :� 00}) �1AI3&�(z $�/N.LHM�ly �%"U 2�CIa}{d}1 +E�)/�"eE��&�� ,Calpha@& F!lesaan $\sin 0 =\dfrac�\ya^2+dw= }/{k Z�� gre?�!:���$s strongly�-whe�A#aH the -��e a %��X.� . W!heQ):C��al����(o!� Lb-�vac}$ % J � �Oe � }), �wi� :'V&nee)� -ak�  buA .Qj($n=1$, *� r��U�UFQhJ _ Z .�)-F\7.5�_NN Vx :R Y���%թ�LHRth�ckU6 $d=3iS�r}{1]"��)�L itself was assumed� �*nI�ly��')�)A� zEr dimepRhpMP:T�QO�X�X�Ce��>q� �-stN�ofy�&� e1�is#.� ɣ��a*#setup���ta��!���:Z�i#$d/2$. UI�%��;ought����be�� asierx��2M �", s# �are ma%�9ally se+ IS !� >g��gV&�/ is es-iZzer�5� ����6� can �i6��dI�։i-1}{4}v� \͒v!+��)��4��#!� 6 �-�s��2 , �y8}, eve)��deH 1a/d clo!�o2\%�Z:� o�ed�>�eq�0 ɪ� �>� 7.5 ^GFBCho rmaln7 c:R/d$6&e���� %>�.2.2�Don� ��:� CN��-A:V� retm*�O�or"�q 2"�y� ])})�-!� predi��0�0�BB |�� Kk')nge{ �is"n.paredy ial\ � � � �previ,6U!�>� Q=���#�c��in�. �} � arbitr�p0:2>>�of�� restX#� J su"��".D&�, sR*! poss 1� W�et�y!�.�causald�1KF$%�P'H Z%� "v�is seem/�+aM  l0� n#�*a2?fB*A-�AS.II[6�$�ebo";energy}a%�� LHM �ire� t $ɖ�-4 �} 0l(  R�:�[� *6 .'3r) \ge 08~f 4Bg fmuRa ` which !l!�$�_0)=-1:$���*e&'(f� �F�Ci ,G1�_07ndO�RBS&-�d� >�,Z e}-$window $\D&�6$� ����)\ E17$ 1�Q*�B�a�. � 6{ �4�zao4t�@F|�a}ic� �PK��_�)$�ze �=*���%�citly����Q deri&wCeq.\eqXB&+;� no �Uer� iw(oD 2� a�hNC w��t!�om eqs_� 20}- oRS}!�a#$*z,4�6a~5�$ dso(D�2�to� �/*�G(or $E�e}�,Kb!*� p6X+)}#:�)r<&���inJD6�uFA@��K *h�( or, = rTtoS-r0 M�9 0)$,I��$�Dak7$ 1$, a�_eep�P%�&�(1�5�*,\rm TE}, T^ TM}$�)/R,�/YT%�s-e� \be @Im}�%T ij]=�k�.} *Re���.1 .c:4xi\, (1+\xi^2)�L%�`:(d k_0}{\xi}) F>� ]\mathbf{? 1��C�-!�&D A2�� 4*� fig4|C?2yofA�e-)"��)� �}�.of �71M.E�|] ��(k_0 d � )^{-�FfI1�nm�3��:�MXŎ1/)�_��� e6s� ���{c}/{d!qF�?&aBn�?�1��i|!Q�͡"sS�a+2|\gg"�2�+ eV�d \llͳc}4B�pj�"$$&�l�Q$stood. _'4;�� �2�&x must< enoE5s�,o-raS@ timeA6a phot�5rom%�!#�Z-Av Qco  free-�G;�; life_��^��Hl]{GF-i{um-�""Im$F~$���=i��.a� "� ��K  +igF�eF m8=45y5 $dk_0=1$"~, $0.2�! AosU ��"�ly.��Y�pecif0c� {l.����  $*�? ��A$*? �2lT ��_0�2Z as chosen]� L# W_0)&V#N%� ��Lstruc*+ell re_"enJ� ���5'2L q=�. Fur�m�a � �/_ !K���%3N� apJnt6��AӁ���Jn�� �� �H H%�DD&�*Summary������% �MD pa]FD;studi�h��K ^>-�- tom �L�ME&<>2J&U�-��esR2B�a B"�N�&of"� ov3.�De��aofV� �� embed) in a�a� ed (^@O%:4ung-PRA-2003})[ cha�a g ��f�H Glauber-Lewensteinv3c7 R }�qj o-di"�.%K! have��� 5�a�Mthr �No�Cra�inZ:,P��}!�cong QED �s �A�sY �n l:sN0ub.ah scal9B�Bi!ingC i2M�<on�(a"�*m7-I&�P%�%o&I$A�f; A�>O)~�2� Purc�K �. SJ I AR!�L omple-'su�'e�a�0om �4d 15 2$d$ �a �5A h��f��)�"�Mm1*�3��Jc=J%/8unbt ertyh!tY� r��%� a b#.��NwSsA�exaA� ��-�-m��tors. O{ e %y88e]&�GE!3�)t]2%ϡX cade�� �untilF�#w-G ���"�0�0 know��MQteq��n�ies. ����  3  \def\etal�P$it{et al.}W,b�$thebibliog�SDy}{99} \bibitem{�g -PR-1946}�x, E.M., 0, Phys. Rev. �< 69}, 681.J8Kleppner-1971} , DG71, Ato!�NicA d Aa'phy , ed�F0by M. Chretie:$ d E. LipwD8@ (New York: Gordo "Breach).��Huket-PRL-1985} Hulet, R.G., Hilfer�S.�)� � 85, � � Lett � 55}, 2317.mGoykT3} Goy, P., Raimond, J%PGross, ![��@Haroche, S., 19832l.s0}!�03.s�xD1} Vaidvanathan, A�Sp�r, W.�x:1�81,%�F�47y592.yWal� -Ann!"-_ Dobiasch,�g (, HE85, Ann. k(P6),IT1�825.h@Drexhage-Prog-OptA]4}  , K. [ 74, %VN��O4&.RTE. Wolf, (Amsterdam: NAQ-Holland2<Yamamotov(Comm-1991} , Y�91,l�JmmM8�332(Yablonovich1�7NA�!�87^�58Av059." John� 1994} EM%Quang, TY9!"y�A e�IY764.V"kW1968}"�9, VEQ, Sov1�Usp �%�502��)�2000} a B., ^�8aj 3966.�E  a�I56��93}, 92�NienhuiA� 76} , �A�Alkem�6, C.Th.J%@7�ica C)<81a6D2� , Ho Tru!�( Buhmann S.AAKn\"omFL., Wele>D.-�Scheel5� K\"ast�2006-A �6A&0438124Kae< -Diplom} NMda�Dsis, TU Kaiserslau�:.�"% !��&U ��a7, m��B �4!�462&Knoell} 2.9#!"2001, { in �� d &*7D"� s})Coc$7$!�S^.C8�  P�͞3, �24J. Pe\v{r}ina,.�at Wiley�A�[DLi} Li, L.W., Kooi��mLeoA M Yeoa�a� , IEEE T�. Microwi T�P Techmm42�302�(Morawitz}  ��692he!18��76�Tsang�3  ���J.A�0 Shin!��a�� { �of�Remote S ng}Z> \& Sons)F�>� �J 2J l}_ *{In Y� abv@co.Fauthor�**  \0M. FleischhauJW Fachbere��� ik !�n)e Uniz#it\"at:� D-67663Bl\ phone: ++ 49 631 205 3206wfaxB907 email: mf �@� 0k.uni-kl.de �$ \newpage� � docu=} j�\class[�:ptadd ,� pacs,twocW`Dn,pra]{revtex4} \u�'ckage{xs S ,ams|fonts thmsymb,L icx,colI \renewcom�8{\base��_ tch}{1.7}�� �title{AA�;mut�XiY���pr�Yt $of entropy�4�7�um "�M�ineffn:measur��$\I�L{Kurt Jacobs} \affil\ on{CkqIS^ Comp� E�ology, J( Dynamics,��ool�S�: ce, Griffq+U� y, N� L 4111, Brisbane, Aus�ia!6)Habc!H�#Holevo-J1 {;FU�a�17 encoZ. �4 1996�umachC est�l�:Wors [Scj' (2�*� (76}, 3452 (u)]� �do6A,2� 2�, &. B�Je�J�,nR3.�q �G5$A��( s maA&E J!]t\Ew/:he-�r�by SWW l 24toh)3�y� 7.�~ .��All-"u/ />aCcN>1� �Ha� ��Uho�average)�_$ von Neu a]a�duaFg!� conc B�7;�i��? Q�9� ��Z�7o!� \&o"m, �� . Wew�%�Z"��E��%d1��.SE�p;D� ensemble�Areewr- ��} unit�'covari�b2�;IZ� a uU.�,.U E42e�9 1Z(uncertainty� ��q\�T${03.67.-a, P5.Ta,89.70.+c,02.50.T��\�f�� "o{I��du%%}�)celeb%d .�+jecbda$�~�HBRConj}%l Leviti }/"promg `in 19732K}�7L��?] �"chq�G*mi�>�Aa (B (strictly�$ {\emQXL}, $M$,",LA�B)�$A���Y� �U� �0uj>"0A�EQ�%{�Ui\�%�w�r probabili�N$\{P(i)&%)B�h!L3Gt.H up�V ade1U)7is ͧ&"4 M(I\! :\! J)�Qq \chi�uiv S(�) - \Tbi �  _i) �NQ�N6(^5_�@a��*wf+�f�Zf2%�q| %:�+We wrEy�.� as $.�$!�signifym��Z�m�2@b�` �H dom eԁ $I|OJL%�%$i�$ $j$ $ .�#�0���Fa2A@ out�\A!�&  made* B. MoreA'ofXm6)���in Refs.mJ4YO93,FC94,SWW}�I 5�� chiea�ifE���,�)��B-ȁ mmut!�th � '" ��� , B,U� von �j.��Gbad\i�Ga��b�Ga�M . (ADٮ2E =Mpro��6#em o�i�$�&�see�Mly.NE�JA.3 5 !Hm�to�! F� � 62�) W!Kſcho�Wof61� .�gX �u �;�WU���)d �`-1-"J8�7�t&�(h!We�4 AzE6be a/! mixe^�Dn4is��$ e am�G�m.�i ���. H>�! POVM"�I�! otl\{A_j\�:�$�Hj A_j^gi4 A_j = 1$), soI(E.�]'Q��mK $j$-�<� �is�7�-�6�'j P(j)�I _j ,�# O� B22$!��& � ��b ��A�!�$�_j= �x B x �Q9-M�rDna� ("vkpa� view���qf),� n .��;is-Bm�at�s2#r 4e&�( byG^� e�m� �3�som�ofYƭ� afD�]-�fu� .�+poten �ext�# � 2��]���E��i�Yn �U.|�)��Eb�i�> maximum� by 5O ụ6:0>Y�t�QM� I��K}�Az�� !���8 ��22� co�R14-D�!%�Q�amp4�X�8 hM� ��^�,5X,U�.�d EA!�MCiq rhx M6�� x fiV^C�!(by $\tilde� }_{j|i} =�� f.�(/\mbox{Tr}[>� -]n`T�Y��+)U�  up� �6�qB�,R$\{F�K �5o:b� �{ !q!D8P(i|j) = P(j|i) /��W0��|ij��.2�s!�iA�uR� �� =� .�j6� �S(2"%�)b� 2M=�!��yz�!�Ify�l !R��.�A�� high haUk 1M�E.>e��t:" E�!�e���I\%�a*.%+$�"�[y��'#� J�x�F"�>.�a�2� kinda�.��>Q(�@ef(O%.'�j]b�n��+�L�Sr"\W$ full2� e��i�x�� s ac 2(� �nd�*�} � �k���3 !.5C{ con�'�,�s�[ ar�=  i*l�/-�kc= � #} A� 52� 6 pɴ�! ��]�� two �pc� so64at�%$A_{kj�B<�Q�.� �a}2[� but%.� 2�{ $k$1# 2}o^�E)]�u` (��$�4� $i$)A�nowN ��'i*�k P(k�z�4))_i �Js0~{.R!O? N \]}F�u�3Y �</J]&<�b�shA�ask wh�F7 f7 &�6a��\v7 l.���w� r�D appl��]t� ""� Qf,!�< A\)�H" �p�!��u'at �Z�nM"�of $kj�~'(IEY 6OQy"V u�.V�>a� Ne.�*�k AAs,p .�&e �i&m wish�o��)�&q tkWl-R� instead�`�� the Y�2av!�%R!i�Iwho� �>c \ to���i�e�Hp"�pis&�/ansDvq"�Y�lnr� ve - �>a2E.�!BrX e%Qn�6re�M�X��f�rby Eq.�Kp�8em-*s �]}, c�z!6"� a!�g]�fTXQ�A���rh��$ %�B�Z�." 1�b9Ze)Y,a������-d. �_/�@y�:J\la�u �8� rho) Bo\�oJ�j���}&,o�f xa�'� � �jaA��0��%�G���"�%|JW$. ��$.}5��Qe!���d wIf�� [�� Ag' ��e �Oera$��\we kne2L�q Sb�������  IE� (�*e).�.V�e�*� =�;��t� �aw��lea�` #��v � M l. E�al�s , itGsai} `G(�e%g``�-U�''��( 4��gU. %ak�~Vbeea �>e �r�$V�M�$��S �}Z� . Wn� �." i�A m�y��"un&��l[ n}�"f]�6Jfeedbacka�trol. F:bpro���ertc "ruW�f.�� mK_tIla6yy� �E � .F�=co��eу8��Q6Suc�d is�fu9 D �"P��0Sz nois&� �y�T �� ��lnl�aeda��N  prov*�a� �;� leve�" �MU ��:# � VFval5�t�Jp� no�eTv| Ns�,�so�|;��e��%�!jm D �1��DpreciC -�cYany.� 7pr�L� "eQ�mGi6�!?�i-.� , or \Y1�H� !�� ���9~�H1� ] �1� [D!��behavio!8) *�3}C�m�pr@�6;A�>�!g� ��to�^e^1:CAs���� 7A�eN��IU� ranka� Y<6ive�Pofՙ2P s���Q,� � ngs�3� ؃6��|gar� um Pq!�N�-�H���<[DJJ�219�=s �relev�p� ���#fEX-is#��Z.�ON�6�n9!QeJi~s~N�C�!7s)| I�D� I�BN�AA brok���AM9 ����eY�*�0r*m .�� �$ 1] �� �@ V� �� !�ti&r:� tZ4%md ,ib}!�Z s.e%'�%�!N�F�PJ�(eHJ�6� #b�We���^�a�]e�JC N_V V~x " ,6� _i�f " d^8$!.uFgV<�jŌ��KV 6had{� _i,�s� �e� �P _iOa�� U fundaA�S<+�at�d�|���ֱL6s N�p ofg' �E�%N�Rk*% g�#.�#Z�"W B] F?��tR�e�����ap�*weM )��'�����l} E0u�Oe��9e�P :�'A�Q�*�'�| %�h�]�Rby major��}m��Qf _ *E)m� s�!r &�!-s( �w�so%)�R���6l�`��%�u�'sq�1 permut�"�z!"+.�+i[� *GZv)if �.mA[����H)�q�.�|sum up! X�Rs!�sa� "�E A� 2AN�)Jpfai4��R\#��.%�56aÀ}O2{a=)n�x!�QH��}"b�y�A <� ɳ�!%beME�&-B" �)ng&B"~�$�mkb�J�""D. TI�)�it �ms�)}we��^�Z0method employ��&�WU|�:Ctr"�)� �&�-toas��*�c��}%�new$�em{}�4em"s"/S-0!�i�Z� U�A$*�G = R*,���>�a�A$)1�R&%�!I(�#�$ (�#� >��#w�6`.}is�Q�.�e!9�~svt�e�n[Jc,:"*,�E��&�0e�R* J+ �  >�#��#o+llaK�+�92R ������_i&?$6  R6�l��AN3�`%]s��_{j})�  S( |i})F� * Z��Xva"��%ema�$�$�$ R�$ oFA�.U��t"�2.& UJ$��U'e6�y�T �j&�wJ's5�.�isVS5@AfU� {k}m@� qL}{}!} y`=�-{iki,�-�k!�F�i��!/"z .!"��Z1$i�U�k$� na���cgma�|i2�!�. ec�C�e�� �B� "� ~ vi�%�� �hU�.�_j = �� |j),9u|i#)V ->,5`%_k|j,i)M)_>� 4b�F!�|i)J�� �$b,}�>�-)! -`�~+�ri�&)iC � �8�u1proof}/u�6�col�ng /�Zkey fac!��&e�Zny�2�-�P $Q$,�a8by $N = N_1N_2$�or�.�Z�T4($j=1,\ldots ,-I�$k62$) .3a by b�*�,up an auxiliTu $A{f&c $N$,�#8a� *� �$Q �Aia n m Va .� .�on $A"� Krauss,&�7})�r(.��Qe�)�^{(Q)}$,�8iai�j��ee4A ���'[^�v�^{(AQ)a(|kj�"�kj| )} \oRsF#! �>�:��{P(F !� �$�%?!2siL& Z.ie%a!/��S� �� )H� .� #?2!62se�a�a�� �A�kA�J��ٓE�FanF#U�E$ �H;�y��{�s6BA�A$ $�Do�1)R�2$E. trac�S$E�QE� �U� �U!R"�p=6��SWW�A, ���!?�J $� $ non-���,��8�|^Fif�o�$3 �0s 5L$B �anٔjO�l'r�*aB)}). associaAj��>$P� t���&ًwchL)} & =a"&� rhaSA)}*)_ /) \no��;&p".LBbM=; �&m)S+�����34*_B[B)}M)To! v, i�� r� s�k7� 4:�su�W]\w& i� `a`���7A0RH-���'*�P Ei�� s��thr�#si,A(,A�ay ab thMF 8`'.y_P� �&��2I:A �$t�'2; iy� B�isi(��AEM��Mb�R. �E��^3Cm�dJs �dnd � �����.њ���3��A�aYv�2�u�?t����doI4ogA~>D&y�en�;j��h���]$eft)�!)�y�t" |\psi:8�9!�\�9�{j� �%|k,Fp,�qb2 A"!two-遡!����6 !_�b{&� m!���(ll{��E A�'E�M� satisf�6��.-N�mJETA�on[@re �*� ��Kim!P�3Me�I�1��#�E" �%���S<�wgw�|1�x%�� &�yn{~�U\_ gis NWE.j bi:W�V# kj}!n)_2�c��>(b/7� <:� /� � �1�_:� �H  :,&�)�0no +ledd�A�*x9$��!� �!plea!q us=�����y� ��a��Δ I%6NFmu���i�.y��N��! ^!B���2��$K�y�e�A�F�y�a� �$�A{ ga� th&�N�#ss ��1�)�z�?uU �4j-_~asSa �a"';n"�2O��Hd 8)n�� -!a)���w�o*�2i �=?a�iH%!U. C~�A�� %E]�bSeb� �",; � a!uM2� �3@ �) .B >� & H[J]:�H[J|i]2<�& & +���Aft[�J�3 ��\r�]� [ �M(J:I)>]chi_j��lX Q)&�a1= Rear��!t4*p�� desi�� .S&�P>��ofF�&�re&AI�..�]Dfa�3�%C.�5:�#�I N@J�.N#"�6�R,&" N{genx!b<rh.�_i�3�Ozawa��a�at � "(.<{ R���k�po>ive�Di } (]rI�n6�A&� se 8$Nielsen,FJj,YxZ�".1 |2&�%in"� e %an"DIuim ]q[, �"�"!!f�"f ��"�J5is E[&*�$!q6?H�! �qu�minV��N�#��`V:*L-J�A�:��� iZS!w6�!��.� �x"�Z(%K1 h�tJI� &0*��+e}��"� 5*�� ��g��ER�g ��!�R}�@A6o�f �]&� %�AF� �<�<)1= �i�=I� rh��1� e �(AV.ia�, Z6oC�!�M %�a��ib2%y�.le�>_F."I� �� ���� F~! dHc�cZ�nonQ[N.��J�v���#QͬYT!o+���Z�$` tW$g_etݵhFxV`)[�+22 _���a�ru�7^�,A�x3�oQwe %v A��:+�P, -ma��,2�wBrow aw��"�*� "�(Z�+I+� ver),"%(6C'1�.�g�~tY<�m&q$q�5�s4*\'A"\z �a�Fy)��+:w %�s?;.�6`ds. %E�%�my�� t obmuH/der�R lY �pC �К�f� f�"o/�#��n^$ %dev�BG��"�%or�wn��>!ij RZ&: �  (a��b�qing..��#�$�:! �A�6�r@�V�d2 %e>e %B�% V�Q�΅%:E!%Next� �%�IO.�& 4]B �&� %8c ��b�v���Ln�0&}�9' e %n  hT*�He�{thougI4�3���a.:�5 %.��@ A�� LHSA���"Dasi� !�RHS� "&I*�ga] � ��7)U&y}G9�bT��h I=^��>�0to�5�ca�u�)���avail�I.� J ,i�v��W "to � @) -�D��2'*P%��xF�m=�)�E�isnay"��=  �,�1u�Q���'S2k� ``!�� youY)�pget''!�a�TJv,6�1(�9��-At��"* z��6�ɣ%] (%e�.̀ Xq��IAT`J�|2I &* 1 swe �Zk��R�76ly;�^�t!Z)%$M��%$�)# o�i�s.)�!Q��ne�NQ�w�MrƱA�!�ig"%lwy? burd�t��k M���� comp�f� .ce�e r��85�no� I��A���(>��e�E �� ��cap\I�j!�Re(, a2�!���Cva2Usr�TsF|6,3�xth�t}IZ`,�,{�,y�u6N9 )�all��(A�de%xy �cey muteEpool}��Ne. z��S �3.V\!0:�}*-�e��!Tes:�|E�"M:OVasFE lk2�6�N. NK%��2@3P͌Ectx"?;A�s:�,.�9j inguV@� ���X �a9�IE�q�"e5�gJn!2,I,c��V�~n&Z5�)�N%6��P?6 D�"K.?(Barnum,Ucov�eOe��ify� aje� �1�0server's lackaT"p, or.�/rC"��.ee��/A� elegj6 ��ofI620M�MO,BhվH$wo se�5f�.�*�$pA?\{P�Vl $qQ   �S �sRR�{ib�p�"�2Q;\; , \; \fo- k,9majdefZ8� �_sLwI�!>e Sen�%�� �nin � ��H<(e.g.,�! > P_{i+�O�i��t� $p� sp> -� e $qI qk�tE)q \�� p�h�{Q6 irst&G �) look%@littlYT� �: few mo�:��� a���han�"?��s�%�����V &|Z -���s �� �K shar�E peakY+an *�c���=k~Y.Ѕ'~Gu6,�Z!� ��N sgV&&3 a#A�an %�A�Shannoq�$H[�}r"��iff� H[p]�q H[q]"�'}])C�>n� -+)��3%"!Vc�of.�A��i��%�� @ a}one�al!�-=eB��=��hand .c4J�spe x%6H�yFi;�:6�A�!��1w�A��ow� xTreeeA7�-�ar�%*%�!F�Uin�#["Xus�?. 2.�_]0]a6�xH_@2� �;v^KA�*#rn3eigen1J$Xfc�+\**HR R� O �Ӂ�2�E� 's.m�O 5$'s. Var�+��A�����<~ 6�n"�.�  ,r"N%�!b,JPV,NK, ,Chef%_FJ�) ?d��m&� z&�E�^��My�1��:d "�f Qn� �(e� -)2^�����F� ). Fu�� � ��/ (ofN @J), $$ .iexr)� R���+"x`�7"�4^-�:�?s 2+eu�&��6�� 7av� -iO6E� arg�fW��q�i�Hr? �%}ar the mT xq)(if our�s did�e�� ��V#imJ*\�*be67��!�.��'djc� �u�e�y�)� VI�d� �xA�*F �:� 6� �w "��8�Ew�F�?-uniqu" M!.�k8_$6�=v�V:�P2�8+ oR�<�&�*y�2$�kP} = (P"��/,P_n)$Lϭa�=w)�Qi~ um��� sm), ' d�Ɉ�[ ��Y:T m��"�I` &� /G�^S6�&:�@V�E^}� ��aG . F{�^. :��6V;eap�*E]*� Ć bf P�3e2� Y>����>�&�+6x![iz2ID�V E��"|dR�*�.��Ze aU�groupn�)i5 �r��|e ���4us2�!�Ssh�iR.U�V{�.7S�9�!��.1�2(��  Yh�*�-� M- � / work{�we"GV&a  �fi}aa ��. b � N� �4�! :�i��� E8S$���Ara�kforwar��=1�+�FlE�bfacG�"*.�8$::can b*fT��#A�m&>�% 6$$&H[0%"�&�;i)  |i)].�_revMI"�V�O�@��!�2�!YF���F'"YT:tb(@ i�$M(�8)\}��Dm,!�p]l1F<>IgA�_i = �._�.m �._i|�� choo!bUEf�Av�.k P_k�'k�+�A� _�+re built���Us"s-6bi �|k}M/f�t�N  & & =A .�(:�(Q,�(k)�(|kY:i�Xi|k.Hra&� -?;aZk�:um=fE�E�rad) �= I �|kAB�3Z{c�B�!� 'a�O�ׁL�yQ{t)F�e&m�WX " O :�.�w5we�Nv��}{�=C7 expl�"�7ret�;�70J�,H�fo�o�$y ah ntinuum (�\�� of UC.�s)hrq�"DLsugPO2� gral� Now�O\�T&cfu���F:p: A:�g"�C- by t�:  �y:'��$-�le� or1 �d� �mT!mmo�� fa�\I-)]5=�\=( A_U \�to UAU%?�^ $UM�\��� ��< n6�;W[$� �]$c� U Ae!C d\mu(U:a A] I� re $ +� A�()[5"� ) Haar���,Jones} � 9~ I{�har3)&�:�,!�"�#�" mi�i}*�O::,�#g�M)a/; . (ML� �=��E s�mn�o Ya��&�0n <=�H�(d9Ba�m�vA!cs9�*�-P �)$!%�-N�A�!��%J� "B%]�� 6U���a- �X)37�%5,"�q � A�N� � b-t�!9� �:�!^#N[ ^s�J� �F��:eK >R!ow �(Ǣ2�jA-lemma�$\vs&y{1mm}2L:u�*dGlem1}{"bG�N��:��a G -��&�D�{11,:@ }$=�5%+th&�2*� -0RE=�{i}p o{i}&� � {i}|$�)�:�A  � �9F4or:s�LWri��t"N2�J� e�ha*�NI 2� )"t P(U.f P_i�U�"" forIF�z ��!d�g7��&�m��8ŀ� 2$Z) �che��J =2�a�w�pr�= kьe_8.zu�ya�v��a�1��M6: $U���2�8verL�<���H);��"!,/Pt]u!s�)!4��2�+ @Q~M�8 ~&e"�K- term�!|RUq0 s. �W$M.Tlya��I�P �)] = H["p>[U����� ]]%9!�:��F ��:��)XR( X eushv>_�>�4=��2Q %| mixtLY�D9��r"_ .;!f�$�`FY�W�+Q (inH8��;ba��combin+ �the� l3�N Z!0:]��'5 �N�) establish�i>2of%oD � 8�!�!����9hQoE�!Mf'Y���-�-8�klڷ_i�h*��E��$=|\.*E�.�% ��& ���v�N"qJ�A�k � V!�q��&���A���� �u�FI2@�#;&nv)�2}'I�z�ZLYNJ��B���^�p�R>L�a�B�:w2^�:.VF��kE��|.*D8!�lu�S�+;B6P,�zr.���{��[(��li�әl� eb I���}e:�iiny� of` �6D]�)R Q� >'"�M�_Bn��!<.�h�6"�Yd I2�'�o � 1��<�6�6p4�|��I��X��VC�� I~;&`FI8i6. 9q.s,�n"Fq=s�`C.�"ad�2�IX��"��aJ�� ship"8VFKa��� ^�e ��mpa��T�!iszE fs{ �"5av-Zj�r� e�f �� w�}a<2�z� mer ��O J+ s)+ukz�"�&M=����b�2� �u6u�Ah��siZ~a�at ei�����o�q>Bi�'s�?|7�j�.a#� "�H2��V�� �i�� *{Ac���A�&}��4like"a�4k Gerard Jungmo�Hoz�) WisO�8, Terry RudolphE�Michael{:%p help�cu����e��lso grat�$O(0to Vlatko Ved��!�ho���$y&\�vis�V o Imh� al C`Og�!(Lucien Hard�SvE!jP�� wInsw��4�yBwof!�5�sta !�.� ork ^�c��?utAL.ʗor�LA �Dn Research Council%V�Ռ�' Queens��. �e�. ed: ]Fsub��A]a# manuscrip�� �� pos��Apr��e�(-ph/0412006e�1bV� m�9�w�3i�[)se$� �* lap�#�burr�=%&byAYOelli� Lupeiri (�090196�116X�F5>Y����H&T�� J.P.t�a:$$�E�Q roniϔZ�t Light}�� 0Cc%�e S6IG���f0S� Rf�Tcs `Enrico Fermi' XXX1��,�P.A(�lesJ\(Ac��P� N>�n�64) �L<�i�L.B. u�PUhe2�All-Un!�Con�jon .�4F� B�lex �C/hin5] �},N?D(Mockva-Tashkent,  41969), Sec. II> R�Nan); Z�.�CV$�&ǖ$A. Blaquie�%S. Din4nd G. Lochak -C(Sa\ger6�487), pp. 15-47��1�I�A�A.S7�Exbl��red�f�6���3f�73)>Z[Pr8Inf. �� m. (USSR)/�=177 ?]. �&�� YO93�H.P. Yue��M.�.K@��, 6:Z�:׋.%�9-note1��.:abqOof`L @*�F� :� by�  �A� l un)e��>FDcz)�U Y�it3La��= out,� weHhl,۪� n, �M� "��us ul-��!learer>$i&R6%*H!�rm<B��� An Open SPAI�aciu��#���2u�(-Verlag, Be�<�/ 93);�HAy�E�(G.J Milburn2��7}, 64܍3�U�A2�c}"Ey'["p� .1 &u;1�N6�*� \ �  "WE 2Ra $n$ ��*S:G*� $B_ns1 2Yzsi"���  �d !�tA��-���#ble $m/$m$� �L�Mr�?Bn*��"�+ff3yA�m|n4#IgR�5[ &@ "�( two-"�mv���ZeX +,#(�0��2$k=�R $j=mn���<$A_{nmn�"( jY�}fT]� ! B_{n�KT!�by�� &5"� %`� %R$j$�?�rno:"�#pr����m!�242d�ab$Tby ��$�$&1"||^2 = P1�*p a�3�R/�+��� ;� �b�fEmE���s�>�o.#e,v*���As�1@7���min6,�0?� �{!Sy� 6� !�.m�� �� � pum2�*F=# �.��citD�S�use,Co!M�!�F�m�r�Y� >&oL @R|* �mb��}ek/,�X #oNW&��&H)�6�=T�2��atO��*TR�a"�>l+ �l��� �)��&8��aI�7d1T2b����#=]��n] A. D��sK.z�e�G.&T*W�M6�062306 (�2� �I_M.J.W:mN�5Z��o�7p *�ibD�NBj� 54302(BR)�32��_��f:h F� 54}, 2614�62M�] IK. ;�em�s, Effec�#nd��r8 s:%�:Fu&�?N�=e�ƚ}B]L��3�B�(ic Vol. 190>knM86-@YAE.H�(eb, Ad. Mat�1�826� 73� / �M� Ruskap�h"��K4 3l 43%fFjJ� Od01!� 1938!� E% �a�1,<�q*| *�aYX�\M�ad8�&K��vvM� 5�I.L#��� 1�Co��%�*M*� ��,CUP, Cambrid 2000�  �� ���a6�k-��R��F6.�# PetzE[Rep.�)�=S2a�5%� 86)]�3i0��1�in% ~. D� tz, E>t:� �08130.�ZO�M.� N�2� 759!�86� |i�!��R(� 0221a�B�F�s .A.~&� K.~��fR�5�v� .�2@A*J!����DD.�/��E1,4�/IM�s�i}, 73�2>A�H.~ ��]��turbak?tradeof��)�6d�I/B"� �ly un��� aX F5205152�� '���CC&nelli�� De Vito,��Toigo>aȏP�Q"O � d;=� nt�:�� � Wan ir&�B"j�%�B� J� 302187 &� MOI�A�9MarshO!RI. OlkkWhile we will be concerned primarily with discrete spaces here,:use `` V'' as aHLvenient generic term. MO�4 A.W. Marshall�8I. Olkin, {\em .| : Th�G�G�G�G�G -439J��t-5187�y .�����R��V�DJJQ�C.~u� K.~JacobsE�G.~Jungma�2� 63, 06230�6�Jay�wE.T. ,��eT : Papers on Probabili�Ntatisticn2M)al�icP .M�edited by R.D. Rosenkrantz, (Dordrecht, Holland83fM.>��������noise!.�>�BB transform* R$301110.�ib��K!|!�R;8�;4302(BR)e6�SubaddJ0E.H. Lieb, Ad��th.I�11}, 267a�73�/��Ruska�%>. E�3��4342FjJ� OD14 9382Ein addi| �, references to alternative proofs of strong su�itivity�� are givenTM.& �I.L� uang��Q��CompuA�� !�In5�� |e$P ^"beaFnarrayFF$ FV"n�,nonumber\\ }6rdq}{de�Zɇ�:+cW}{{\�<W>�cWi}{^{-1}>#vt>vartheta>zzJvpvarphi5re.g*I�r} :sp}{$a�(r $-product:�$qq}{\qquad :QQ6 % :+erf�rm  } \ c� {a�hcle} %\usepackage{epsfig} M(4? Pparskip=4pt \baseline1 % Title  \t{O�finite wQ ��j�Hauthor{S. Kryukov, �PWalton\\\\{\it Depart� ��W{  Univerf  Lethɜ }\\ �  , Alberta���s calcA�ed from%^ �%�s� �them{\"o}oE�`those���yw!��� der�}terms���ci�O. Fu�rmore%! no�# intim1 re&� ^  ����|isd)�their )��A5�D r �,��U � ��z .�CJ�" 2-@parameter $\hbar$%L. �no� � ��um- ��!j=< enco!�� �, inE_[ �. O)nha{LY�%��AE �dheyA�Y�iE�ord� ^2$,� ��e� $-\frac{�^2}{2m}\$'(x-a),$ w�  $x=a$VA��E�!d.!�t. � ��� one-"�a�*�c %��it�"4��bapj� 8, $\lim_{\alpha*�4\infty}\, e^{2 0 x}$. Our ori� l hop��}/�4 crip�9] eC }C� fo� inst�*aM�  pathu�. F� �eN� %z"� E9�"\ r� e� at � shifa>b�B� Fi2��u��d��proble� c% � �T��� V� 91ial�,�Xa� -behaved E"i�Vm LE^e�_�"� way: no�R��1���$is require/ D�$ DirichletRH� used%N >>r6�  �6n.u!�f uY^ )6s�K2cE�&w��,bc 5+. shouldO ��A�e) 2�  (canon� , �k)��� !�2/s has s 8subtleties (seez GK} � ree���in)�kir��� m �~o >�� B�u dopte approa� ilar� ours:AAy!}A'arR"��0doxes by ``ac� ledg�a�ex c# ! al F.'' T�_I�.!,no ne� or a. � (lik%di�iC�(. A quick �� "� 2. S�) 3aT�Im���pap�contain�e���� variV�of6 � � s de��b�)A�]� �4��e!Rult�e(� include��9; , repo� i1'be �!9�in5 39 5���$lusion� !�� )Se� %cofa Pd[ �i.6H�� \v� .5cm"�^�} This5! BN.I 2�M�Qel,D1, setC!Pno,�proviB %W��wh e��w-&aSv at%�ona�2� 5��a�N,te $|\psi\ra�$, aeF? ,$\hat\rho = .1\l8C|$. 6o2�, obser I�� re�enA�by�E s, but ra�����,on� �. py m�pl� u-a N��� g g��!�ssociZ!��G!ve��e] d is� :1p�s�A�a$ e�( central ob�a^> . It obey�2 ev�&�I ra ��or�{- *n 0$ �j, $�4Aduc�8Poisson bracket&5 ~��mow J� !� recover[I�at sens� !w&��Q�sIPr*��2 ZBiwf�"�n stoo2a!E � �tZ�M�!�>� (m�-). u!l9y�(througx)a�I�Dsa A�*�La��x$-axi��at.8�Z coordin $(x,p)m�"�)r_E�2E2Ax$�� $p$ �promoa��  sA�at /�Z p�zbeyA��`(Heisenberg Q���"�$[7x,p]\ =\ i  $. O�i$x^2p$E~�acc�g�an� |�scheme.&�^�carried < inAs�Nc"�mman��y�ings.�� 6�-K�� $\cW� $&ing�Af�s G�newoldIi��� usEW!in0J͎(e)�� rZ,ce.} Cho����,�� beco��" {�! (!�)!� �1}{3}\,(%�x^2p+xp x +  L^2)\ . \label{Wx2p} �"#*.$fI�a1S�SA� is gC aliz o �� f� f(\�al_a, b)�a� x+b, p}|_{a,b=0}O ,�fe}��\S:=)}  a!�etc��1�,r, it followMv=] e^{ax+bp}���\ \ .�ee-1� s r�)�V � �2a�h )�) �81}{(2 \pi)^2} \�}{2}\,�0g(,(\rpp-�' \rpx\big)4}\,\, YQ9Moy%����I aZ(�d� zio which,�o s act"P $y act onlya�$f�gg$ "F �left or �)�em!Qat � eqn.M�)!Dnd�!%�M�92!1e^f!e~al_{x'} p} - .x}%E)@(f(x',p') \,-K,\< P=x,\ p'=a�=`p)a E�IR)�q�AE1P n *� , :� A��& of.*q  mimic�X�1a_�b� ,�,k �re\d� e[\sp, �2Z[! 6- a��!& (7 diH b)A5�� 1 � &a"�5.�7IBc most � rtan=�t�\dq: 0Fpto* phy�&�� c'7&��!n:k ��on � ,E� \{f,g\��i�\M� f} x}a�9 g Am-\nBpzBx �f� lp6?)\,g\��PoiE�I_rE_ dynam%�#%4!"���"�of bu2�i5NA or 7 f7 g]$=!�A�2�� �l�-g$ e isY !�AI�:> )� [f,g]_\*�� \ � - g\* f� FscG)of=���� Aie4��*BňN  *�  0})�1}�� �{\* }��{ f,g A@\� hlim� )�&� f"� betw�dY�a�-�&5' \dq.i�f \ %�A�5 mapi$!nO�� "Q2}��ul��itm�}%��M�1}{2\pi %$}\�z�,\vp \,\ Tr(\I%fe^{i[|�\z + �5]/ S) T� cWsymM s � !!.@ i ymme�( fashion. A�� Ban"��-�%it:I6�\ ���} y� -ip[a�� x+I- y|4�6f\, |x.l !0\ ,Q0CTh �a;8seiC�ulaZ �()um eigen I5�E �A%Z u�i�fE'�U,a)ELsymbo�� ci.D=* \,;A P- \=� 1� V�&� Strqe8A�mi�(9fundaa&$�wI+���"ti$ *� eQizer,e`�ѕc st� � �Str��%9Yqs - cW � f)\* g� � ( )�g )=� cscc �S:$og��U���i*(� it&G#to" exO�%;.�!>"�s longAmth# re *N)!2\sp. b��=� �"���idea -T %>=Jv d�|�ն��FI�I�q=2ou�r��\cWV (E�5a�� e� int : H^*(2��)\,(2i�.�Wigm�-(r�Q�%l;A&�!E�um� t�,. After �"���u�E 0:�}�" % :� M�)}{�)2 &FwE� Comb&�last two&�1�d rho[!G]u u͆�!� ��1zJ�1��psi-�WeDuse�;"a$�$aW&� a,��t�."���s�ŀa-�Sfc, $!$qQu���-2�!A �)9"� �*� tv �62[H,)} .�� rhot%��yi)' es�I" C2l=0$&� �i {\*}� 0=� HrcoI=s%z$Q�jan ngy � �H!e $E$�6�5 H \*%i�rho\* H  E \�HrEr}N-] }��|*if=J� guk"��b>�BX)H"y���C)B >M� ald)be.xi jr���$� i�,e�,�, h}/in��� \�Z;B�of���u*u ��A0ean  w� tob3)s�!MAei��.E�)� %�)���2g)��l6r���(paper. Of c�e, K%m!X st8be�� veryq check��|�,l�.�O"b)m1.=��� � ose�  Q%te!�. I.�)T(traintsibE�* =�HhJA� ,A� ^*#  rsrsi�is 4 � %�!�!D� ct�D 8 Clear 3-H%& is ju� W2�*i 4upro��"�*�8� ./-Nl* r�#G v���_i� _j!�m%%' _{ij-2%� rirj)a�i���"� !&&szDe�a�e��c_\�&��_\beta^�( ,-%vrh21�arb��' r� �D tinu^!%��!lMm� �Ak#�S6L-!�:�$u0� �6bJ�<&�A-�i�re! a � (x)|^2! ��pI�| L *�9`(p:3x23"�xpden!a Q�A�t ��hi -+iza�$nd real: $ ��e r� 1k^{\ast}= i*�,� ɣ!)n"� !n!�g\�f"9� �x\,dpO[\ \&XeG��n( $f�� ( f)$. Rougha � ca�*in��!�integbver >��!"� #9e,�a7 scusS abovN/r!�:t� H�!th*�2f�|cyclic"_icr1vd��aVM99-G]SY�>af�"NcTr%W=F%��No#F2t2except��6?'/'%}k"�� %&.h�!�<�2D!�&k%�*�:ANor��� "5%7,�%��precisY2O7 br,a�s:�:4��-�^� y<b} ud� =9\ �s built� 28&�(��a�vI`�``+$''b��th* � �X�;)l{'o�I �(���O�p� �^�"�&:")[ �A�  V�8,�:&�:!6%q ider��to�e2 . T��m� � r�7�at!m��bU=�,": �p�z"�:*�;t As ��io�45i�(�s��lS6!� not E ghtfo�5,A3w�wAla"*75Co 5�� icar �l��pl��*#/, i.e.*U�� ��V(xh� \{ \({0\, , & x< ; \cr��ft�, & x>.}�.��a�SchU�!I���'E�,e�I�Uto $x<0$� ��sE�J1- �"(0,p)=0$�4 <�25\�P�5���l�!ith� �>i"�.��a5/^&n)as\sMeR��})��� I ,�5j.&�"�%�y��h�for 0we�(�(bar=1$.} Bu�= 6�, $��h�9B�5�%K7e M.�>o�(al -2��JTo look0/ guid�:� � &�1�ed"� )�V� 7� y�� e�a\2E=��Y I��(x)=\QD(-x)\A�H [e^{ i\sqrt E x} \m- I� ]�� psiL� Using -��92@B�i!U5Ato� Q*�R �,\bar� Z ] {rth� �  F :1=\ &E(2\sin[2x(p+�{E})]}{}\ +\ �.-2.} \nn &22\cos(2x)\,s(2xp)}{�>rbwsa �"$2�$Y�. ?6��mEa���Z�$H� =���3go���j*aJ�*!�jr�OA�beA� U6E$ct>A�?�A. ��- \sub� {I.} �Liouvill>�6E�H_=p^2+e.�4.�S�Ŭ�suhe mas^1ve�#� so a'2�y6�0A�%�&�exE)': �:"%� �E�MQ� "g�+a��#w " ishA�do"y��6x6�#�=!�� )q!2*&E"L �Qb(:�<anջJ }$�<%+�*�!alB�),^� @as�U),�a Q��I�P��[ (p`i{��V$�)^2 +�)\, 8 : �B;p;�P]6�E rho ��"QH�I It Jr#in \Im$ (�)�1��~%[-�� �x� � x} � �h) {p})i :�0&�RH�2)I�\Re$ (�) � [p^2-E-Y 1}{4:Y^2B�cos� .�n��\I�For!J�s&� �$ rewri�1� � e^{--& �#9Ah�="�#!�p}I@[!�!�+i�W)--5\&5)orR%L� �a� ��#!� (~J{2Ml )x) \QQ�+*�2}Q F�+8J�=\ K"�"orI�a   �!/�$5@6,1@0( ��titute���E� ^)? ��veH�R"I!�(�aA� =\ &).= +&�p-(�2�E��()^21�� �+21�5��1�} �! 0-V01d1�]\nn & m,iEY�}{4 �F��TMhS &� e^ Z�� x}��A\FR^  ��Df��a� ��eD%�<cy���X"y" vari}CE$dBaW=�KhifU.0 argu>s_k3ed;�gD7h+�>a �/�"K%fX�i3� 1� \pm 1� \XU5�� �� �an5 �fM�!-f}�/� =/!] trad >�oC |), "Ufor%p}, ��x^n� �$ n=1,2,3,4*�.de��"&a��!��8��w�h a�E6NK�tb a�are see� *#(\,H\"older'�eorem�- EDM}P I"no&Y � e�]�$ $y(x+1)-yJ 1/x$� �@2 algebraic>2. R\+!(�m2a4 2> may�# o�M6T# �)A��4=�we %�QJ� a"�"2 G .A-!our��7ngZ��Fu&�B5�C�3he ``q�s''T��Q� to �DU�Ei)!�"9?. Two� �/ided: �{L `�C e"&w;U� "�'byD�.,�R�" a &0a�B *b. x}^3�;)-4хVH \qq� &+\ 4���� ���P &-\ 2e^ *� Hq�*�+��+2��BR&�!R��a%u�0\(.g^� � )- V^2# \qq � -\ 8)^2: � ].� >�!q-to* �4 �C}{i} !61�' ! [X�V)�+\ �.� C&2u&eft[4(p� ^2-E�"� .�X )PX ������GI + �5a�u>� j�:�&/ B� biga/.%�e�  W��k helpa�l*ict./]N � a��, V��zs:HS  1}{16>� 4�aF- [&47IE}{^2� F1P+\� 4-2Ep+E>77%&-E�Y��I�� newd;6a *���v \M7� $5).�C� n����+b��H�N�� newid�r�id � $x< K(A%� veriLSG'B�SByof��)��A]2�d�),��. � -.�to�� at.5H� be 6����( p^2�\* - E�@�)�� 2E\,\Re 43�,h)=%d� HrHetB,� new �,!ZaDal:mb�<<#of�[ f���^�:l� �V�*�}6 �now"� �# �/*2�?#�m�-�MP*NOIJe[.ht"b�� A\V�G:��)*Dsinh-Gordon \noind�E*�E- H�J�)A)�"U� }m (x-1�9��(�?S z� %� two-a�*M%nb%markably�j�F� !�?Ale B� . Z A~�a �8� �� ��� +�T�} dhD[-  (��\�] �=,qn\=\ =�":�" �˅� E\,  �ω� Hawi7,a��|G�!�n�N>� *� ) \��ie�� ��� bH0h(-, x)\ �� Risw� a��2r��%O!W_ \QQ !Pqq+2"� 4� +"~ `]%�.�!�0�;)vI� R6[.p�H�&��as��+�� �k-*w\��QQ�+�I!���� �^2.�A� [Ou&� 5�2{ = /,p(&W 21}| �: pM��4/�?cos.I ��L) n` MWm�(� xb]f� eJ �qs 4�1�8�'.� �F �<��� ,~~~Qy \pm "J �*�5*�uag�!�e� D� �ifavor��.�.X� $, $"�(o d�,���`M,F�� �al"5+�Ka6� 3҉�V� $e�)�k d A� }s��I nn -\ 4��qC>���"� � �5y � ��me��Ng -m}+m'2Nh}{BgBQ��Sq��څG&6-2?�� V� �L��� 16)�^y 5���p^�bl��16-� 5�)�6� 1vQ�C !U�~5WN�2��Pr�!����!��f"|�Zy~Q ))-��q�r�75sѾ P+�!��~|!d-\%�����5�G&�6I�i�98 ( � 22 is�MtLsmp�wSso��refi0 � �Bit#2pK�$*�[v(6[t :�y $x�&(\, ]-1,1[$~�nm�1~�Mn���+E3B6�U�)+ (pV�a�1.A� 5 newi*�&� �E6� �?(+-ous�B�$n$���R� m A"o"6|:*l2k6� �'6�%"I�Qn�%� "�$+1)  ,��(\�%� ~~~ E 6Nn^.>_X48�.C6ps* ��:cisAy6� ���AV�&e.�%-8�%we $ �28�?�%B�b�%BT���i.�%�%��i�(2p+n�G(1-|x|q_}{ �b23-Z3!nbM�%W1� si y2p>r�%� q"6 W �a or,2 ivalen�!�Ji&>�2.j&>t2J�2� A�&J="�&�8�)c�&;���6�g �"�&.�AH.�|y��$_A*2tiYex�.�I��aG:l va�IOL$�6c�<�]d!�#-7�4025v?&�.&�)�-} A $�4$^%��)/�a\to_&M%B�**w&  .@ |x|�&A�n R�Oa�#N%%`j�+_ N�6 a��] A�ER�!os2$\"�.aU dZB$ )� "H A��E�H��!e�O�#,. j.'2� EC2�e. �\ �J*�!hb,%M�$�&*�!# � �IFg�*5+" �P�C 0�N*2�se&5>r� K&�':*Alno,6r"="� 9_-.�"a >�"1 V�u � eIS� "s �!�E� *�&^ Z;�:4&� 241g6M -\"� �&� �rEYqq!��U �( depeT^o�1q!7e�! M�>�.�!�S�4e by-0f�mia"]�\&|! ��/��3�$-d��Q=0�� *~Qa- >~�> ~�"U +\26b,&� !�s1�Y�O+\ Yy.�",�vw:uYlYVK� } ��2S4Q%?Z>*6*�-*43�O9 �]2�">?\��e�&� ]-R x}i��xd"2�{}N�+VD\�oP�eB�� { �� w )^2+jyI0��=G��F�AU�Q~�(���5\J�a �<W!:��9$�5��)}HB���,6�lre:�#A�M�1z_ }%�]�'b`UW5!*oM���1��*�9j=0[amNU.I� :]�T�M�92Pn�j=�,�nYcofa/�)�4&E| �/I D �� *B.af<)botSxlD�1"=*yas�sol EGZjc$� lt*} s %{w0'q:��"D�0+�J =-1E� x0"�8V Lz��K2,)�V�xm���3!�&�p��H}{� 1i$�It �3''�5 R",.� � ��  \Ft`^���|D&�b"& }Dp f�Ww�[f;Ij�8� fR=*�J�b�L;Y f5&Z3o>.�;a�C step�xcon:<1�:� an unr9cG5b� _\<D,we'llU��%�L&N5Jkh!v� �c ( Z4$ �tWK a1Q&&;��h �^�", �a�x U=x^2$wa>F��.% iu .}, *"? :E�{V(�e�& !��V� �ba.� ""qŅ�`"� �\���+ �8 (�\�YB��)!~������>�6 ��� �:�3!R>e sin(�2�.�2:�\Im_[�F�N�����S ~U2I9R dF0.��&���$��%Wn >�&_�'.\Y?� "e^0"4&�3E A�"k kE�E�}{"� F� .> 4�R� �k��6a�I7"� "w �5�- ?"� i +\ G*2�1)��R!) �bR�4F�9$��2+2� F�BB�!& JkU�2�� )�B ��e��; -1�\Im� uLCBF�\}� a�u*�@�.ced�:�mS ��2�C"��O *s �A��"�2,.m Y�$�F0 �K*�ѭ "_ . &�/�"ly�j��"��*��2b"�>�Bly: m��:c =�A�"H25%��".Z22/Q����31ꅈj7Atm�-\�&- m�m�[�,,�S�%�< f�\�2:��mF�%X�U+ i�Tq���!aa�ZDG�:-2F*O-E)6��*y^]%�m��a*�X%J< ���A6}%B[���.#*1�CAAs��4q���]I)�dA��I� :�� 5EYJF� @ RH��[0i�!H�i{2Mf^E�N�Ak1�-��q�.� =4�wC(. ?٨UB� G.}�R�,)���)Y!��zU\{Bx �`�vRs�:q6@�@qk\}ik�� �2\{yq � � 1>�!D 0>/|1� �\}mH 46�^2FKU�D .e3{w� �@suffici�,�Z.�R��""F' �" 4 fu�zF�'A� (!}/�2z HegJ��9"` Bigg���� t ri��. HU|$^b �xef*?�+�LS"�?�9�2�H-%�}��" 7 46� ��!# � � "�B  ) �. !5(�$ m�-�)-^qq\QQ �-7��E���͆� �>.�_N�Bigu�Y��y�Y� Big]g���2kI�JRe�9`E9 XŻ�A�c a -^g -"U �Qݹ2f�es�%CiFD�� .E � �H\{u� +�E�� \}\ \��0�xj !��2�d�2�$�ByZ�5���V�ca6cKrE�eg��to� �n1R�G*U�Eu%��+ER�B26&M5RM-E)>:J0)�w.�C{sB h9�:& �2� ^2�)� f�\ A�Im )(c2Pb��@\{.xVFE����у2�a�a�fF F\9�RKG *"!�v�02 V.�0� B�,�&�|eqQV��6\V��is"�& rt�0a 0Sa� whenL$B= �|�=,�zL examVP�� 9harmon7UoN�{�A�dd-par���"�!J�^(0�O�sogR<y surv�CI�E&y))D$x�OgroM�?6��[NO�'"j2"�'�,x\�-x^2 �P/^ $E=3x/h�*.��:t���.�Nb4($ X8Ff' �\,Q�(x-ip�p+D-�x^2A��vM�a����*<+<pi \,�<h d� erf((# &i ,\�']p x K2x � LQO�g�g�D.#� o�p�q� .t"��>� � �U�!���O� p6 �B>�: � q�ra�al�:a  erf$�Po��aB erro&�!�n &x ��(\int_{0}^{x�>{-t!� , dt6 een%� �:{'�A(nq�)2-Am�}�eY�7 2��m�Q �TT�N}Con}f̍If.N� z�(e�rul��*!`�h�2�9Pu* `,�^E� at�c)d�{_G�� �x&>���F� it�\-"ȃ�`YD"i�Ӏb����, ̀if�;tKoV]�V ��s��J�S�bl�$��AjZ��P�C**u�EY�SAX+?6\1E� c`=ravellk�ly B�x*�o��!���Pwo����era.)b2c.�6�Z�. To c`KTH[eypaV!��!U`J�s'' +.5�cy"s�G�se Ual �eh�6��6�i�q�)�V q)* e=extra&f��� �P!fiI�%*gaYe�ha�*PY� &<�.�!" 6�e�a�,A�T�R" �Rl\6tlso)5 � , si�"&����&s=way�� k`�*eQ�~G�posal!r?IDP}5c6 e\6j3*���T6�"2��ws. Happi�O�1�F?%iB�mm�[o v]!�m�. F�E�![i�>�.u �/y!F away� ��K -��;sed�V� �u��"�)g R�U %cB�Ss�w!�)$�L"�dQ���>�m[dA���*��:�3��mc.x?ate �$��y��b�E� (yet�v�at�:%Rz��eJ W, ^�J��;6�!.t's�"��!.�s,�^'�';b\exp i2�{E}Md� b^*#��.$,�bpmIxE8�&1j^*$�䅟5ŀ9i})*N $=%���b4d),=\ a_+1/-� �a_-&|` A�<a��4$a_\pm$ arbitr��rA�7 f^M�Q o�TD)*| a� plan� :9of nVsm�u"�"_*�+'ppK�(rhyK �{E��7 �eig� �(re�9M�=b1 V1 Q�r� q�: �a mix�|.G o1�r� :TAE�Snecess!�� c���superʕ�lSNd�( ��!C�� ce"�|th"-��"kod �Y^ �b&F`�Q��R N "�oscillk~ae�x-period��,�$arge-width&�+*�w LF(+ M�g� � i�ya�E&q��h\�!�> iT� B H��C�XZq�\ ^u*�W rhogAwa V.�g�a<:��.�i]�@r\propto\��0�a`��[u=h7!�>h}�E �n-,x> � uFXaS ��-� �&������%�$(a_+^2+|b|�Q #>� (a_-B$.��!�M+a_-)I� big[)�.�%� -�2��D][E8}��rr!6a�����O Q�sg*�j��we in,�>.�?��h. *>!3-!�Y�e�?.�Y@�B326� (�jupoae>p� ). S�~tassum!�$E>�hw�r�٢)  zero �E �A0"� � �6�n%Jn�`Ea�ah��atR!ia \ b�5a_%=NԀ\ph�A, ) hi\in{\Re.���co�X�Xi}"o���a%� }�2�!|%J �+})c}&m��&r?^��E� O 2\�5\,Q3acosA�( & E}x+!)t "�rho�E� J��U�ng�z�q[jZ|w|� ipy}-*�}q�)('P ��ho���!��)��"Y �psi!_>'_�Q&� m.%#_-�HJ psif!nQ�;rh� =&\ |�/_+|�`m�y�$-|� $y�)�� )!�g' 0 _+^* �*� ��%^*�"ԭo}&M rpr%Ra�?In�E))ii�!~ure� vea��-to-on 7c4"�,^0nN!�!Hn1}\pm\, =�lM�\� ,\@e�  � I� phi-_+E� _-\,@�@* prelm�As@��beol� �S�d�� hi_+ W-�� �E� relevb(H�*"xb7;1cm&oHq"8�ea}\h\break�~6�{99} �����}�Hancock6{� , B.��, Eur.*P� %�25}��4) 525 [ots/0405029]; \\ A. Hirshfeld, P�snseba, AmT %�70 U2) 537 [X-j�208163].��� D.�8Fairlie, Proc.&��$ Phil. Soc �6b196�081,\\ M. V. BA~@ hilo� ra*Roy >(London Ser.�� 287}ι7) 237�0 N. L. Balazs%CK. Jen>�s_��A�%G104D 84) 347; �HQmry,}�O'Conn+�M. Sc� , E.m�, %� R.U6U121�H.-W. Le%%:� 259195) 14 �T.��i�, F. Hwlzahn!�nn.I� 241B79rA��OzoriS AlmeidaN295} �� 8) 265;\\@�Zacho!6I�88�od.u A1!�3�X2) 297 [hep-th/0110114]]�B5��Bay� M. F� ,nFronsc�AM�)ket )��#1�}F(br�}[2.T|#21 %r�#�Dirac�: 2�Darr}{\ar @{-} [r]} BD�sHir~at�nec���oE*��� cur_#�Bfdoti.�inix!G%s� #1,0��ʚba� lo��d <#1> !�low9!a����!� 3� �)z c1=-:�xc6�'R�c"��s 6I}{\hs��P{-10pt} \rule{6pt}{.4: A& �9 h�i� �ts� no gate�Y�ch�a�QBio:��I":z��8��r��!}({*+[F]{#1} .pu box ar�*a�l6KNoArr}A�P�vKf NUa� �& �6gmeR�}{*+=[o]�M6f�}sur �|e� DOES NOT1�Q�nex@�a6qcontrolq-!(\bullet6wdo��n uncn G� =RRoS=<2mm>X circNVNU-on-16Z targV3 V+J� � C! 6e:�)�-i=O2�~J{�A��,{\phantom{#2,8arr \save[0,0].i�!C *\frm��\�ore 7ew����V ��5>[�V�UOS.qubite�s6[)E�0\raisebox{15p��5pt]{\enEoathaF6r2��ca t-qE�r:*d *���t �����a��!W��n�w� 4���rowJ�-0��~�1�-���� � ghos!v].�1:qleada blank��64�%�Hsir��:,h9-]]'�I7�h h ctrlIX�,��x[#1] r1�?mk)�%�ks9&���B�2vwo2xop�y�y�~Q��ui7 xyҁ�re���16�qswap��]=<0pt�EW_6�%?hala�5e�A�+!�. -���b���$A,{- =J \arx6�bunch�s  |�t�inser�Sslash�/@RRndl�,� um b��2�a:N �b&H d ��h\if\ifpdf \ifx\pdfoutput\�o %#falsea %��'ru�0 PDFLaTeX \ely� ; T=1� w �eF7l true \fi :��H[aps,pra,twocolumn,[3pedaddr1'@floatfix,showpacs thmBU?.�" big<#1|:�B"7 eft$j >&"4 big| I>:IKe��5$I>&B.U rS  >,Ket�� Ket��\!B� 6�s {#1\@�.Ss"q(6F���>Nor H# H|>�absG|#1>EA DCBB�5v|\!=>R�+ �20Z��valcc��\, #2]:�(o6(#4.e(o P(#1vPo P()!EDeclare�Ope�r�]mp}{c f" eps} ,_\epsil3f0q S^{qA/byqX}*�[�$^{\text{q,�}.Cjvbw\ xBbit2@ZAej� R�errn}{e_�b"q}>f errqF%vJp (�1f5sign}{^�id}{idbspanSw}{ b( Real-}{R[�Vord}{:, ud}{��hrm{d} tey{�}{D��i�iT}[$]{��e��ne! lemm!Lemma6@'/ Corollary6#algcAlgori�5e=/Fn}�a3.#"#Pro�$6k rema%R�n6 M� O�Fexa�EP;!Sinput{"� 2�$rix,frame,�]{x�*'� Z�ics?F&8� [pdftex]{ $x�e.$dvips2#��.�myfig�$}[5]{ ?gin{figg$[!t!b!h!] >bL �  �  �7d�p�[\=\P ]�/��;2;fib  \cap!�[#5]{#3"{#4 ��� �3� �.@1d hyperref}6 R�cF { �&�@ \title{A Lower B��Qu��P� Esti�A�0 \date{\todayUa��Arvid�Bet!�mail[]{b @cs.%p8bia.edu} \affil_� on{C� bia*A\\ De�Gm�'of�Opu0S,~)�a"�� (ob�� ��Ϙl��2�z a�e���lv�  �J e��6�9. Ourg ysis #i ��B.maG�QpBF��e ora�.$Q$�lP � �p�s $Q^pu$Q:*i�'!�a��in Shor'�U;�f&��. %a5sho-94}�IG3�we �T�|Le a $\Omega( \log 1/ )$2��!=&�appli� of�{p_1}, Q 2}5,dots$�{)�.�  du-a matc�/upper '5We1�{.za�a �3techniqu��s89n�$quency5�. YI0N(cs{03.67.LxAl keywords{qFF��@!�xn@������*�� "c�IvD�i]R�@�.=5]f�1�prE�!�� IRWitaryc�<�*AM�2black-bnd=�:o!�&$ q}E� ���ve�/%�$, *'�^F0}��eqn:Q-���Q P =�&2�? i F�,�"\��>teX o{0}{1}-�p!<wa�d�"��} $ N $ upm���($Q�$:+�! 9� uLA� roxi^��U �$-q$ �bA�hi"in��e�block}��02�Y8cl�:!�S)�alu2��O9i�d,nie-chu-00,bra-hoy-tap-98mos$00,abr-llo(jak-pap-03,woz-0�<rmm�eL�A�(�A�F�Q7��we�A�fo�". LetE�b��t$�uV�!)u�&%x&�/ ?�+.�� $l=1,\l��,c�Tnd $pAg}�hbb{N}$�!q$c+�t�!uLn�WtildE�,W_{l}^{p}(Q)�a[(x_1 ... x_cM�� =#b� ases i"Z5$ & x_l = 0U#�FcQ^p g21m end{ kN^call $.�$ a (9�vt mph{ŵ q�} }. I-760%�is cl�{*:%aLex&xZQ��oezl^p = W(Q���8"Ҥ��s�a� 6!�f� E��b�!��e fi �f{fig:B-est-A� -pq} �e]� retu�\�]����^ wideE{�(}$ 1 ���a%�q}$�S �� bhp� M��*M� 0 @C=4.5pt @R=C [04 & �{H^{\oM T}A&v�DW_T^{2^0R {T-1Fi^�& iP4_"� H1H2 L�� ,cal{F}_{2^T}ɸ�aJ=���m q�� & \1.����B� H2�& R~&)|q�!�eo2�4 � ��in! ilu�{^��$H��aHadamard-,mga�}� a�;>�-�܍�)w [�B�p���F���! on $T��s. L nd{m I<is &qC�T =��{ O} (� ��EW)$�!b�Qg u�F,.""k a� wec��whe�?� "�to imM �per�hay42*h proc�Y\ �YaskJ�Pinimalnr �)h0\v��V� �  :� -� -c�� Any 1��G f�AY�56�:A ��! !cO Qn� ,�%�72"���.�xP��A�� calQay Y( Q}_{�i q},t� �\{ Q :� ��{!r&D } t qEU�� �� Q (h<n� "9 }_ big\� � � ,9?� � "\;Q�}� y�ie� !� I���B��P # & sec:S�?>dL�� Q!�9�]�Ym�� 47u��g eachC !LI��ׁm$��BBl x>�!f��LM 2`1��+ 4�;� ɔ$ = 2^T - 1:�*}1 cerVc s,w�om-f9>3��.�exploiR�meX �S%*4Q$.�>$ y�EA x y \mod � `a�fb9$x� �yNNR�Q��j} \ket _  x fs 'KQ(#{j-1}}\���0E�=ais easyA�S utJrepeab�8�l moduZ�A�iU ~ ��� &� J ��5 ase�z�93!2�II {2^k� ith �Bsl�0�fI�IB�!�Thu�cc exec�z�l]����h�ge*̅speedup%�T4:��$2^T-1��$T$ usڳ��i I3"e.es ��e�A6)�!w$M �s�6!��7>+ "�PriB�ork} ��"��k"�=rt�i�An���sIHGro\-ve�q1u��ix'isanv�X�;��(���A3sM0,gro-96a,boy-6���!o&�¥/��ͫ��b{7wa*p�\�ben-berbvaz-97}�us~����uH'. ?.bt� is K�d% idea"�< ``polynomlg3ѐBm4et. al.,� a-buh-cle�wol�h nay-wu-99,aar-01,shi-02}. ��[AE1%0��B�E�jgk<�G1�ambLlap-magA8bar-sak-sze-03}ose.zE�cj!�xc;�A<(Boo\-le\-an"�6��" ko �I�mA/numerE/��� i T+en ��i� >5�=�O-ihei!Gbes%ui�d � �xoN"F: @nov@ Gbkwac&�path 14LI~tr $ME"m !Xslo I2X03a b}� �>= Ab���p� �V�ach�� F1� *)-� . In�G:�maximum �e;"guqf�KottCblAKE��P��A�>�2�.�tec�)�� " s�P� Que�^�ZJH��w7:3�� <�u�ls i6���-`s]M�!_ x8 ��� D� "� !� %�%[$.J��Kp7,L7Izis���� �\� �q Nq . q�o ��!��_!�m rame��)Q&� enougà%�Kh�!�r�*� %�sE�!\��쁙�Hs��a��I�be!�!�,�P:1w� .� cap-��y��  ^{(T)�= U_{T}� �(Q) �]7 &� � #02Z0)}FJ�V�$U_5?$U_1$KV ��Ea�b�E�G� *�V(+d $.���FC,!E"Li 0}MZm.� we neglec�In �� ���j$�Coo-�J��������zYL(�H�:�&E%L�_j%�jC 2V ::.kQ$� $p_j>�$, $l_j = 1�, "(c>.&n. A2�/�f;�)k 2�M}$ Estand�basis y��k?G $k=0�2^{c+t}-AH� ����$p_{k, Q52"x�K*u�$Jm(k) ��.Af%>Q &V�7�e2��cauU%$_Q!��"Aa��6%Q$n��-�"%#8 \sum_{ k : \|o -�>��| <";} 1B \geq�3}{4},�M�t#E�Y�$f�$� ����l� !�i.-"5��$y � 2!.��,are interest�^ed in the smallest number $T$ such that a quantum power query algorithm of form (\ref{eqn:cap-q&h-algo}) fulfills condition .prob-.�or all $Q \in \mathcal{Q}_{\Ket{q},t}$. \secN{General`@trolled arbitrary�4ies}\label{seczofs} We:sider>8M9(M�-1/4) 7?,Bm(which gives���bability��2Q)e� measuring~�ag�) =a_ Big|��-5^2C ;,l=J�(j-l)u)^�is plott BBrobOnP�LKet2}.% \myfigwidth{:.pdf}B4eps}{(Color onAi)�r9aof=Q�:Lm!o. n /��depic^��N$T=2$ and $.}>:� {} F>a:# showA?at� QDA u!xIC!y s high ify�!closeJ $0.25$, I�ibsA�a*f yYa can g� t`� T$,iesq�pro��F�lw-�$-cap}. InJ(2 . �Q�OacA�n $t$ � t!�Tfore has $2^t$ eigenveC �k\psi_s}M !��6� �)%�assumm�!O 8VY are fixed�%d4 l [E<%A + !k ��ly.�s like V�alpha��[_1�1�  jt}{2^t})}FhA�occur. HA�$(j_1, H, F)� from�set $"� J}_T�fined��! recursion�n �m��J- 'veROHJ}_{T+1} := \big\{ � ...,�), + �+1}B.\\6�  �[ 5) \, :F$)6�� �-F� �.�0 Set{(01K0)}$.%I-p1�11 60 z$Q$�Aa unit= oper��Fr�$nd corresp�ng .aluf, $s=1,"[ as� �!�=uqbm mv�%�a�f_s)T8intervalco{0}{1� Any��um���p�i���ɮ = Ŷ(Q)$,i�5"� %!s $U_j�� tart!� �� ^{(0)}}$,� be writte��� b2�1�Aƅ�� s!� U��l }^{E�}}A� U_1 �} U_0}� ADW ,k} S_k^{(T)}"H =I�-[i�� kA� >"�3^���� !�$V{�!:`  !$onometric nomial� e fo| ing�m:9`uS %`sn` ZV�i�9D(jq��F�{T}!* �l)t _{k,V@ ,e^{"5(�b1�x�� � +��65 ) },!�5 I�$��iX�B bb{C�@ ���2�&�.�����} shoraour��ofs"�u 2�--hznoti{�sa� �^�hiEM��_��,"a Ր${})�@$perscript,� itF� a sum ovt6]� 9@E�). Fur�m�$we abbrevi^ !&&Nvec{j��rI�סx$m�* a�0ER6!wd�qyd1�Z �\cdot  [z�`.B_ %% T: FA A"& !6FU a:H���  :basis-t })�1:4\chi_k})_{k = �2^t-1q" %7 %�#0be two orthon� baseE|Ien^1 R � �e�}* � ���7.y6�ec5���A _k}. ma�>k�76�.H5N>@%% .n!�* fi�O$widehat{S}.�6Yso� �%� vh p�5V.��-y)�, pN8aF$�Q agai@NJT$%�fA�%� �� �ano�!�}"��B by �6�]z split zp @= &.� 2.�#�iMQ�!�l} \Bra� <�_k}�E�.K gV� ��j��&{��h>e 6j.� R33�^ _l}��1\� =: & �n��::�q� ��_{l�� ���=:v�� S}_l�� ZLb eTeX.�6ml"n [P�of~�: ]:o simpl]E�ho(a differentm�insteadbstandard H We divid��um(te into {trol parr!m�g*� ."EZ����we��� J��Qq e�s� z� W_{l�� � I�m�cc�� s=  (] {m,sM�(E����m, �"E QM� fb� V�L�2N.� �wer-%���. �J�T}Rm�% u�m4*�KF� a6 i �A��ofM by5 u/ o~"&Vquez�� Fo�"=0$AV�no�enq }�|2X1�0�-�\ea; t siZwa��ed:�6�+!"��%�5A�0��ps� = & I���cra{m,M_sj���Y��� ��� �xq"22n�Z��of�q $D � .5.=� now;be* &�� let ks*���)(*���) holdARI�ԁYyf�+1A�� $�Hb,P�_�6y$@ affe��F$$1+1}$-th&��bi�se�.e. $m� = 1��� thesYwe getb���el:�ʹ�} Q^{t� ��mT �� @.> ;"��B] I�:� %�a!0u�$AY���$��'R�$b�$J�g.�%��-).�> � a_{i��ZT)�f�).x�EZ| W..Fl:���f��5�2 (j_s*�� �V')&�$2�Bu� is�ab�A N� e4$ (recall eqn.}�2),E�.H <aJ.\tilde.>T+1F�%�J=&��%�IE@ _]B^��M+ -. ZD��a� g�� N" /.iFa�B�i�v*�}١Ca���$� perly:gi��F�R46� j_sы "5�! am�!Nq�FL -1VVF�!�, \leq�N 0$ o�wi� � ina1 -Mr )<� �E&>r���2.F�$��������co2�;(5(ͼt�m�$�.Tb�V� U_T�8"Ip_rW)���� {c}-1)� N��H _��ٌ]>� Now���%6��e�)�!r*�ai�8^� %���"�&�cK$�#ndM% $ ue� ;n,tʼn�G�'�"� D �!�}nW {t�l� Then i���.C�-!-z9+ )� n, th I�9�.�>� e�>�N�m, s, �dV2�"K��5�:�)&���%�B�:9X��^X2k � .� .c���h4= if :_9m �Ս:GEc �2��iA�_A 6� 2�`F _�YXQ0B6Qr�bigg[ .d Jg �rI�v� T�.g�N��_<�{:�!!�/�y=A�%f�x.� �' .�Lr�!�4compleQ.�8in���(establishes�;.��Us� dsam�gumen0q�.�6� &Z.2})�((�/ly re� v� qfG*�"�2��bzA���>0��G[%� ,2^{c+t�1}$ 4F�r �&qWK!M�!�"G ��E��s;k}����{s 2U+ Zu�B��u1�!�$S_{k5�>]$G �+%�5 t(y.�E�Q����n� A�E�(Y�=���sBt ��,7! focuX()�pecif�#roblem��%a�6�, nextm�id97?17 cess�%"8&-"�7�32� j!F�8"� Z="_A�sole-eB����precis�8&�+."�q� B`+bp&�7ng%A)-2%7an.� m?q}ma�$�Q$&1)classy" E�*!56G9��(,Q : Q \text{AV&(} t q58&< a�\iKa�q}.?6� of }_l&� 2�up�Nr �+to� 6�$W_{j"� �"2}?2�WTT�#Q;��N�1��MT!�=K M}_T5A%l - l' \, | l, l'+�� krK } p_k%!.K�bseteq �6*)T }*\�e��y�,$tha Abs{"V$�} �.$\frac{1}{2�.}$ ele�M:F A� } No�:3 � both0Z0a�i�)ea�T�$ well���T$:�cl�0�,�U��NF� get awayi�ap/3%T$�5� p_j=2^{jv#� 1&e 2!��� -2^T+1, �^, 2^T-1;'%I whild(�3choice�j.�ou-�� T, -�1O T-1,!�F�$ V��&i!�n�/:� �jc�5*�.�@�.NreqmtL2 Q@!FQUN��some } NE�%z bb{N�e �"(.analyztbehaviE5fh"X:��sha��E�Zo��onA6 peci 3e^��&6�7Fix �&H>&]'��/2� /�d2`` q/J=N<9�:&i�0cb�&� input� M5_ͥ��Q. Q_{r!w :F *�2 r5�~���&++��m_{s=�j"TD�Nzz )+sn7�6��(r� teres�5in���8 =2�$!D) $Q_r� S�!7L! ce betwee�v|'%�k_r� $Y�.w�6@*% / ctness, a�6�dI�yield�Ik}��8\emph{distinct}�s $B_r~�B-�B_ra���k~0|2 -� � | <9�; 2�A+D�;��J�O@! g�&ur a9Bu�G;se�� ��&ne or��l s� By�n�5vk� '3�6&� � &�a ]5t��!X*63� .w2�'.*� M�&�.�B �))=m@��0.B>!�6�..1�!."�>_2aʉ�j:. U2Ia2M;�$m���{1u�aI���m�*o-� drop#dEp*�!EAb]i�lN� ��V�J:= 2� -���� 1�l EO��LL" )�\beta�l9�1l1�}"����08ٶL}&�0 �F�:>� 6� *�!� {�-,�@ 5y ���F�0T� Q�2�VA�p0�a{T�%Kne�m *m r %d�Aםn s (n"B $l�>7�? right$deAF:�V%�J7Qp(l,j_2,�3�n2F=U�� �@�=6/...n,A�C ]�i�Z>o B_r}e�-.m"b@��68��w�H&� Br})� �&�f!rox��f.i�%wAn bN�.G p�h-��eZ�6� :&k,&\� N~ )}^2REFB _ j��l'f�^s \over_9{��'��!�.2()���>&lb8�;�3�[4 \gamma_{r,l,�-��-Bm6j< M\e�r,m � .dmB�eU!qAj�<���w$U�aW�;�!10�� ){ ��V@2�UJ�fN��\n tack{Z�\\�= m+f��XR7:�=2�F� " =�or&�K��!~bD 9�EH- s exactly�A%s6<�@5�i�9nd)Gtheir�@L$scillatory"� �� e cpL l .G*� ��!�Ac�r�sA� � Ʃ�2�� We���&0e Discrete In6HTH� JrJ (eV<a�Hi;J�  = n/N$m $n=0&�N-1 X"� k'"�JF�2��Ndf7i�u�&�Iun�.N�p-�� )�:& Hk n / CW2: E�I2`m:�� #N�:# m - k) fF�N2qy�N{\\m \v�mod N�">�� r_ ��-!�$m \not:^#-�q�7�<:6.�2� 4� -R/N%�}{^ 1 %4= 0al2h}�0�5�B*�U]7by sepa�?-art 2% a�d �?�Cretur1AF FI!|>7*+�C � +V��Ij�)On}!M� fBk ig|&+�uNuC BrnU U%� �GiRY�0n=0\\n \neq r�*6� m���"� 1F�* 3}{4)U�e�ڊ!ŚA��!�� �#-L.� Ito obe6"r /N))��a{�(`� �SEa��)a-k$S�a�?se� termG&� �M�aM�u�>�balanc�C��`n/��<.��.� w7T�G"��+��U � )뙑Y� v e^{- y>"@ ��BigRM��^�e3j>J��W�G2�HdKperty�le�'n�il+H$ways true,=ru[a-ast mos�A"QR &�[TNB"$N$"�t&4 outc��0� B_e��We*RA�anhL�]kXmu\-tu\-al\-ly exclusiv.� iNZ���c$r>��4�7dda- $1N%�Q�� �>.� (ni��)1)���} >+ �\2�bL�GR^<�B� .g  - �>!�cXe%�!2$r$m� :�q�a�/1�$R^�C"e!�@it"R�V$$\abs{R^<}!=�be gr�Q�1$Oa�an ��b�iY=)+���1X-HgeqZ& .�.����_�Fv�9!M&� s:�2�NNs�")ɬ+!�0!LzD*^� R_!8 8 w�b3Q�)R�j-�+ 0��� �2'\AE?C -�%�6K..8!��+2�$ �$.0r- N1}�UN$ %<2�2 "��vZ�� $r1�.e:q0�Jujyh�6�BV �[seq�O� 0%p<�-i<>��1 >/ >d���mm Nbw%�����=���C6m-�is�ns��l����t$>o���$�Onon6PIDu&��� >� .�P�Q}Xl ->In�/ word*K$�*e McardM� !�&[�e� N:eH1}�*QBR�weOd��&X !6�i.�&� ]H� } LzQ�&�S�]WfQ�"� !�z� QM l/X�<�<� A�O� ]eed,HM�?"^#,$\Omega(\log�5*)$"�\ �&�!F�F�)�7Q:�!^O~#"!w&P��>�& �=H ��2�-�N�.p$�!�eas der@ F�R c>\� &� " 2^TfA+ �F��*�%Y�=�{�� q��%*�%zi��w{Rv%R%:�.Zb�� Ɋ9%� }BY !(2^{T}) = 2�^T�$ %2�rC[}�e�`ew#)�6��$�$IB\` q��7V� -Am�.~m�U grow�R%loga1`i�7�@ $1/qcjU T ����og&@!A=i� Z� ) � >qi�*�bConY o�And exten�*�b��FXMB obV!ed � ��)�B{\Y8Mp,}%^��-eS�b���ec�b!�rVy�%siUXse.9s mat�){ 2�V �>��XF_ method�Vb�Co��� V�8Sturm-Liouvillez+�RС�D \cite{pap-woz-04}�,resultss%�d� 37�7m� #M��(zy�'�hexQ_f /x�%yEU?&, \oplus f(x)J+ �2^mJE(An �>([�!�hejRtwK!�D le�5�� ubjc"XutureIk&0-ac�W ledg%s���8authouL�Vgank J. Xub, H. Wo{\'z}niakowski+;8A. Papageorgiou!uGpi�^discuse*anFun�$was��.�O,Columbia Uni�)}da PrefntA(FeWR shipQ_/�\ archW supp�P�� �!VN�P al S�bcand��b�?0e Defense Adv�d Res ^Pro!_8s Agency (DARPA�1Air�)ce/Labor�,Mater�@Command, USAF, un�7gre�&�@ F30602-01-2-0523�*B�@ \bibliography{qc�� doc�2} e\�. [aps,twoc!~8n]{revtex4}% \u�,ckage{amsfonA/:�}> symb6�icxWsetcouA(�{MaxMatrixCols}{30} %TCIDATA{OutputFilter=latex2.dll}"VeyX=5.00.�^7.@CSTFile= �.csM^C�Dd=Saturday, Septem|i1�d,004 15:45:34�DLastRevised=Wednes=Nov <7, < 2:12<0Z2*ForMod.11b0D-�ShellcLArticles\SW\REVTeX 4E \newTremTrem}{� }2a�CE�}[ 7]{A:67lg'h.16+xio2'2# clai.#C6#��r��B-O/6, >X�ure6,:- kary2,6+ri�o2�2+&� WDT�6-exa7*E 2Texercis6( 2)l� N� 6#�T&N)V6)��(P�4B'pos �YoPr2�remark*R 2% solu�r'S6)umm6�S 'environ�O�of}[1]$]{\noinden�3Pbf{#1.} }{\ \rule{0.5ah }���} \title�t���Zu� al gF�+p.8biased�er�uc[q,} \��4{Chad Rigetti � 0Michel Devoreyaffili�{D�t�XASb��=>�mby emplo�Z�3noise-� �0-�.� FurAxx<,��tak!_�tage oMa preaQhy�fApnS in fabr�<ta�X su Y/E& it. Our �gyA�si�l19tr� a}w�j��.S WS &9@strengths---a sor� ��0quotedblleft  ffi{:molecule2%2Dnd!Yliz�] �pr} ��� thRof nuclA�magnetic�on= (NMR)�j compu��i�NMR1}i�� �J9�2���s2�\�_ �u��in NMR��A�_��� E�-�]Qhi�a4�= they ex��.��NMRAx"cular �dK4 Hamiltonian (�R ��commu�lpZeeman .5!�t|act: ){At6spin-.&V� re!�ed(?x6� %�9l"9%: cu�� �6�$�X�L �2�!� dox% hing2%�.?!�sŔ)M58Vur.: it{non}-s)m�B no efoT 6&. So un�I���u��o enhA�!  (- � ^M0� . We!�ao�t� g.@A]al-style!) nickname: FLICFORQ,A��=ed LIvC ��<,Fixed Off-Ree_t ��:� "�in�� d ma���cha�oes (�Bvia � �� �zY] '{oG � o� rg flux e >e�T D:� loopsVomut� �H!�s%�fA�%UA�moE on &�1$s (Fig. 1)Iw�@K e��Di(&  @ &y�of��%'s, lea3s��a� r syste�A5e &%�2k�G �ͻs �0ne�$N�i % ^{g}=N_}g}=1/2�#2���j$N/CU/2e$apA�dz� less� A,� l^{\R|m p!�-��n &(\Phi^{ext}/ _{o}{ 9frueHion. U 9 -�-IbeZ)immun�D2+ ,!z{ %±�La *,�rs�fZWa�aB!�,Josephson juxus � XtC> 1� 5mo�A)trapped��Dev/Mart�2$}[ptbh] \i{� ap6[�u=3.1in],1Q3.�w %&# FigS[ eWL} \cap�{S:*yGe;* Y�6 at6� . (a) C.W (Saclay �)�=Fa�+. (b) F.)DelftN6F�.]�-< A6�E/�k"� Q;��describ �!�reD�d.�� alig""v 0H}/\hbar & =&�}[\omegaa�^{z}\sig#8�S z}+2  $x}(t)\cos(.6rf}t)+.y(sin(a�*].dx}\\ + �A+C� �^�2`�;F�6��& = ^{xx2  .]6{1h�%$�)?/2\pi$ (<z )��>}y �� 1(2);6Urf ?:VW� y �sig* ���.� B� \ :Mb�x�Y2�x}G6! y}$ 6(y(r�&jA�in-qa quadr� � mpon� �� �s,P �& � when�e�$%�, �dir4�pre�e{ Rabi5U ies;M�E0% %�(=(t^{swap})��52Ts &2%j% \iy (ifr! $:<m�AX!}�  w��pnn�{ &�&H�KG j'�!ooNduc���%T/ ma>llyas�E w� be $� /4$)Nrre� ��Dan",!b�us*��2�,by $\delta =6n-!z�� � �� out �!�"�ya� (�)'of�t.�\�zsatisfy M�E \ll ��`avoidE�� ant �R!L� �|eX��abs?�� ra�M�. D;=:=Gw� n<��:2� =0.1 �=0.011-o!):�o}=:�z}�� z})/2-� �#C �D .��Ase /$ �� \K� limitOsel�z[ �%tof� t RF  � �x�5q��*rf}:'c51�9'M?%�we di &%3\by n� f!5� knob�S�ex},.yza�and1�)py}$I�JzʡZrf6� @�0es cross-talkqd�&�� cru�p� cal .�"�me�qis%)oQv�j�weak �QE�\ � �e2a) p?�uu)d* s��/+u} stoo4 Eatom ���* � c�b]� ceC'�Z4in ]{D��S��7.&@E.9M+!�i�s�dsɑ(2�Ex��out (2�)X- E�.`OOa�}:\> an i��lj��"o?"�~t�xk �a z���(n�Ń� a �"r� blue�2 PIa� }: PE>.�y�X� n:]by� u "Q^a�. vC�� adja!���s (wav�rows) m@���H� /emix+!�a-�� 2�-{. ~2e 1��y�>��!� / 2 at�R��Qincs- 2]y.+ ��  put*�$�Hs�� ermsF�w ����O1 } �-� to Z#e)�)/a aL !F�"$ � /2$��G �?�WQ� F2� x}=H=���i��R��A� Dbf{\rho}% _{in}=|0�\l1 00|$' �a�ll ZN7 after a2 � $4\pi/ �| =2� $.��=RF%T�switche��f| ��>b i >� until�<�7su�+ lo>"Qy or#� g��.�or relax. :nY��$�6"E Q3%�on !!�A�dc�D�HR� mal .A$9 EB� r/)yedi,!<-Z��~E�ma����Hwe �Fsc{D} 2�,[�g!�re\"�>�)���athȕap���%&A�uaq $A$2$;s:%����(]��}�=�bf{1}-i����u% ),+2,>p)/2\\�=(ZI Z� `/2}(XX  ,\no�L�K ��nw!�1 or!\EpA��?$d= �5i,$ ~�^B�$,)��#cVis }map n �A� asis�'��B7\�:�thQ)lat�')<39�: $�Kga��( +i|1: $)/\sqrt{2}� ,Rig/Dev GDQI�%?)AFp&C4 ��$��udyR� �. How�\,�is� y�(#fy ��$^{2}=-m����Z�5%Ga A�Y�,�~D �l:ot&8��Niels� ,nd Chuang}. �*�,���mv�e�p-:nu $�`!�$Q�i% i$ fv�a~�� �;s d#E& lipp �eŹ1k RFal��onZUaՅ�s mid$ roug� %. With ���l�!/S �2!EH\� unwak� :�\*�z}9��"�plØd"~+�* half !E� C5fuE-un%8 9-At_7  mblaAh ��?�9��NMRM MR2}��%+wNfe modif$L � shapl�a�n6�& %:�Imp{)*Q:o�du�f E.� $F.�~Yu�)7����en au�6 &�+a].�sŔ�6na��%�&�Cliffordl:up�XCC�Rl!along� ����gi�J$!S!Rr titu�;J��!�rLQur�!�"�!p)ca��.� et� $U^�  sc{CNOT}}�FjF sh* log��e�TJ v�3 mposej� i� �B���{at draw� lZQNZJ j�u�*��C (sr�)�X�ight),"X�9} �N^��Y�M��F� - 4�P��e�(d"$��e f�ᘥ|�,e HeisenbergX: $\{���,.�2 � x}\}��zK.JY�>6 h �q`G֗sman-��p��$similar ine%ri�%QY�.�b�=<n��k for � �;�eCirac},�&aV(2)�>d-v�Pl  ua*) PauliU�"� s, m�itcabq-SBp3al:�-. I}�`Kth! p�lgebra,� adap�c�! ��c�c��Ois �tRIF�N[ &<% a!�S2.3S�qPQ1 andT�nV)�n-j�uU&�I! A��2��n�(6A{$�&��� � of�"����� (top N��(bottom�s.<��ucIaf�����fG �h.  pr�ivRB. O"3$i�% � C�4B�/82�� $ti�sync}% =�$;]�vV2��L�� $��� lastOdea igno�fcK�Mli�/"I+a��is. G�i a]aLximBA��b#D�"# 5�in ��6��MB�F�� � ?=s (4[)W#c7 �f(V�� j5)�Y^��ut~byA��n��4-�B  �� �itu~ ��in ex�5�E(seL �3qWeQ*brief�2mhO�eN^�F�o deal�ethc,)*�����. e�5 �J�*�. tinu�4�of)�  ab:b I�axis,�>P�ngA/a�-�!5 "��Sat van�r �yeno}^in=("/ml- Nis� �4t�4��Gng &/ �^iens{@�".# zb� 0�� . waiE �9od�� .2UI,bes e�to ��do!-پ9vb�1itiM�"�&M�� Nt_{�]��=mt,)-5�)�g�lm�;�y=~"in Bhrony-`"K)nbe met�ɇ9X��?�6c��ahe)$��i����42�% $y!Qab�3c`0n2�)an�A�$I0���ZV�.� veniA�(��r�-�Q�a��M%����d samb5�&)Q7.d�to�v!b}27!ke assoc�9da2A grid��+w dasve�@alP�� 3Lis X= �liz���:ies *�,��below��c��!s�K?E��AR�' ly�r�� �& fift�8�ed��� & sa);�s"�m� yden�Ds8orɄ% TQSOW �mu�#� is �^���se�D�i�0�S0�mny� .�co'�rturb���a -PT�X��*�1. F)94%ہ��d�5>a -y���w|#�^R ��s!� �ta{<�D!Fof RI�l�*BKAPdi� �IB� t�sj")�R�:�ht�Y �, ]�Sim5-1nR E.�samJ un���fm"�.�F %�%��+J9$\rho0=Tr' ��at�� �K1? -2 -1}+,�$ +2).(1}$� 7$��p&#�rev�cIa�9�Nng� $o���nd���'� . DJg�o!=n(, Error viG�at�}dr:Bloch-Si��t shift &/3��-��Y �on�^ ��2}F W�n�!��� fide(�,w8;ec/"m�P4?�3� f1��eށ$�Vs.6�!�#a��jbe ��!\��$� �AI�8*-���ll ��arac5�3oby���( $\arc&%.Q� -�).$JD! b�Nll�?�c togeQ���; �up%�)=O i.@5��"� ����is"�* O�'�E��M�@ly�A�p*Ts � "U�#m antiA.q�=Ns i>� $. H;? !A^"�'�it*�t\gtrsim �)�� c }}%�\lesssim6*e�!)*A W1M��a�n IEN.�M�:[e(low $10^{-3or�o�B���9Qbe�;�Fo}Q���$ntly availab MI"�2%I�!�=A:an J(�4� 1,luxury. Also!o6�)��J squ� e�s,'$l�r�=)s�w�M�-%�ig",f/< los%�F�Ay���,�% ce, ��^ monp]i, � � A�4?!�  &�3����)DiL;�& ��. ��8l!�"�9H(��sY0.imarectq )7S�'!��3 �:O �*��� strongl�0�wID�>�"9!9o+ !�s �e(� to jiE�� ing- �r��, c%�� �>%�� slowly-riX)s)�e:� �Utr�o* e6�)N Y�w�=Q#oMt�it{!^nded}]i���*i��ed�2!bri� ime. Non��AYa<D��WsomQ6m�!I>Z!�q�v=v�voa�2��l ��A C�;[ �� can ��ttribu� )h �N- �0:]c�Df� worki2_}e�4E�-0&"� I��*s ��m� i�& a:p!�'�8 6Q�)�fae��u�26�-�b��duc�+�M|d�<� �,2!��'�0z;pI ����"&e�[ �! #@.&uxse �)�in��A]r�� %�1����-�7*C�(�� ��3o� *�xa�����$�9��- belie�mnG adva�A��d{m��7�0�+at &zd�4)�lit$to RREh�pal�04ra hardware. A- b�B�xw2al�$it{!G}� MۉN�:��ach�A�Is1��G��4F�Fn}$A2isl�5J=�b cavity. SkH����!?Qb�- � ppl�an�� ĘAt.;t�Cm�&�)��e-"�()s�s�%�&&|:���2�J�!�a�=['?'y !d�ctQ��ٸ�}rk?*�-�"�1 n})&�!E�ch,[ $n>29|L�% vio��J&-type in l����GHZ��+�P��Lful!3$Alexandre �HD, Daniel Esteve, S GirvdO�Rob Schoelkopf, Irfan Siddiqi, Cr+ an Urk�� Denis �J�' help{&� ��:ZX8by ARDA (ARO Gr�@DAAD19-02-1-0044)e!�NSF ( %$MR-0072022�6the.�W}{99}Tj�j%*�ib~�*[M Y. Nakamu�Yu. A�YM��dZS. Tsai,QYure, E�Dbf{398} (1999); D.R=L, ~Y�(,bf{296} (200�<J. M. @inrS�m,xAuado �C.-�,�R. Rev.it.�(89}, 117901bI� iorescu, 2�C.h4P. M. Harmans,�0J. E. Mooij,\�i��9 � 3); T. DupkTD. Gunnarsson, K. Blad+"nddDel��2�BT6�40503(R)� 4); A. GuJtʲ%x�) �MrJ32504G(J. C. Clark1�H, }� earb ; }R%ydB~� �Aari Q\6�L J. B!��O]WNY4nd-mat/0308192�A�OM2�NL3001�2��O>�T. �O0, O. Astafiev:A�. A� nE�u�N7> R-bf{42�� 20036�n}2z>�f�J. | t�.|5R�I �W%NA.�^AE�va�.n Brink, $Zagoskin, �U.h � bf{9G�127qha %4 o� C. BrudhMI y�I$1}, 057003E�IB. L.!�Plourdmx.OyB7�aBi�46�KI[�+, I����393} 143��8);a?A.. JoncMnd�0MoscaEChem. �C$109}: 1649EL%r,K. Vandersyp�$e��?414} 88)16�"���.�W%rJc�M J. Q a�fo�"c.��it{u��P^�:�:}C:h2�:Z$Dupont-Roc��G. Gry�&cAtom--B5 Intls},5E,p. VI, Wiley%)�'�M�� ck��I}T�i]i&�*��;orial "���� �2�E$n�� trea"�X��&�;�-��'ashila �7;� b*d7 a�� }*kjAt2��1}M &0 ltBy V62� w> ݰz s 6& �h y\�q`U�*9�R.�/C.68ZUoE�\,)g(-ph/03121962�J_M�.6��� um C&"$e  I&�T0,} Cambridge,�j06V�A. Abrag�ePrinc~ � N�OM�Osm, }Ox�,, 1961;7 ��A. �4in�E*.� .�$ }Les HoucєSe�#8LXXIX, Elsevier"��5D ung��.D� esisC a!d2�[$ArXiv e-prtZ0cs.CC/00120172�:%��), a2E7I!�98070062H�)J.!� �P. Zoll�,*� )�,bf{74}, 4091�*56�Q�0f�1� \ un"cY.�Y�tq2}� �9I;v�p6�.& the dX-\&g is�meq�,�*��5� |�ms95\Ss@2Y6<F��och%^Aegert24 �@bf{57}, 522, 19402U� D�VGre,'!��{orn$nd_Zei�in Y it{Bell's� bb,U�jby�7C�'ea!_fe,}iKafato�Hd. (Kluwer Academic�89�;ndBY � &c_Y^>ep�&int,pra,�" 0.64cm \�F \def\b�.�k0`ee{ӡ��:ben&� 3narraye!e�9flushO/} %Draft����s%Octo8e6�d8\\ \vspace*{1cmf\2F �` \bf Brown�m""NwQd t�;�Ucle \\AKvacuum"x��%u�`p�#�k�`$Hongwei YuNxemail{hwyu@cosmos.phy.tufts.edu"af&�`, CCAST(World�g.), P.� dBox 8730, Beijing, 100080,��Ranf���ofA ic�CIn52�F/ 4ics,\\ Hunan N��M�4ity, Changsha, #4100819 ina\A� {Mae|4�.}��f {Jun� n :�D.���+^� ^�� f�a�QZabn�a %\base4(skip=19pt ��! �"�qumNZ^m�cQ=20abe� two 0�*"?IT��LeH�偙me�x�d 2V�veloc�j2p�d!�>6�]�calEWted. KY�C��Ss(>5 m 0(Ÿ�re�]c�&ari�Q*��le-9 �I4�"��K_e*M���'F5  �>��b�>re3>sB l: a�a�! J�H�  neg3&�e���Vz � long�J�g�, �3���M6"sk�aQduncer�[h|G&a� , ac��)�v rNp.V�ceB�0%���t�E�)n��F�b��{05.40.J� 2.20.Ds,b70.+k� "�a :w4aw%�:*FqIqT��o���kJkN �'2���b(o�co�,ensive studiD!"�� emer�m��1��jyJrI prof��ly ]drc"�a�empty � or �u@���< �k_a synony�[�Ning�M. V��~aPll�W$ �y�+�r1�urL Alt; 8�4 ��a2��H �&*VA,gy�Pv"x�-�j�f ��WtH�m8 re�.ibXa#&A�qm �J , {\��es}�a c.�,z0u,fly exhG��bژTC�!Lobs��bl��MSmb*�'a�Ca�6r �'e�wAR""!�. fP$h>}*�Xd�<�#���M[� ^� C[a��"ly refUe��plane 0z�A�e�stig d �YF04}%� ��$3٭�$�<!Yr�xN�N�H�RZ � �-; ular�?� � I�@.�26MQQ#�D����6�AA�!&�.�nM��.5ofA�6x$T_{eff}={\C�� \pi}\;{1  k_B mz^2} 1.7� � 6a'0ft({{1 \mu m} 4z�9)^2\;K =682\);({1�+s${AR9\; , PY0eq:effT} \ee�B $k_B+Boltz�D'�nl<tA= $z !3M��\�EV1�`;D*. se\f"lly 'i��. &�(�Ed�7l� ng6�-�� etic#�&F{�� feel$�&m imagA"rge >{p2�ge��force t���=u�� & towar>(��%9��s��Q icul� ���.@n�dy"�ZF �-�0i�x��;Ref.~�� n4y��!i��Kl��A�v.��Pdż����l ��wn��B�mov!��0!�t `B"� he %)s-�no net=�%s�^te� "�% traj��y�uA�ble�;Ay�4A\k.2� {'2@$�ac�qs dfa�C�1$5�*5) N&��(an�*5� � e*|<�1.mf.#��t;����<�����N�A0U wishG� �e%�� , per,e�r�:$+&t !�:%M�y�A�5�woO ; ng)7�W ���s-rth�%-�e�4) bears*( �ogE�A�" of l�c%E�Jo�Bwp(pNs XJB/&�-u2Luq%gr�$�alo m�Q��5�>� Ii0l�=AN��Pc u ��6�ar7A��M�˝4��q mass0(iog $ e/9%�2�spe��az $i$-&-�w" � (no<c&i$)�"/3{\D.[ v_i^2}m$&=&{e^2� m ;\int_0^t. uN{E}_i(À,bf x},t_1)\;6 2) d_R\,dt\�K�K=&{�>.E f} R} e�}   ���eq:lang2�9,�1$ �${)e� e-"� AC*1 �� $D=t"Y ed� ic�X�-�NΖ&��by sub�I&2 -in&�<Min ~qterm.P� o,�p�[E��� " "|�� *�0�m m= $t$, V. a��ed :G� � ~Pre^*� , noE�Cun<-a���! � !P� >T � n Eq.~( �U)�9r8�yLons ar?de�*�&� �&� �.�qs"� +��ex6�T�"E��U���*wo�� Bc� e��:EK'e�" � �� �M�Uu��UmITwoPoinݗD^{� (\nu} (x,x')كaj le 0| A^ (x)\, nu (%|0 �, ={E _{0}J-%+6Rd\;J�GA:$DA��(H"� %3�yT)U �v>0�!.2�FG, $^��>�:coY j;��!v�_r ���iB"���Z?ho� � s� BM69&�6Feynmc�auH��0su��on� ��E9z=0wD� a$,�0} N�xfNj5�}��O(ɩ t - �� bf{x��B5����B �� rgf2�R.A?4=-\sum^{\infty��=- g2�+2n�}nu}} >� 2�x.�y ((z+z'+2na) )�|�R\\+?�R� {'} J�҂- � �"43}�),S�HaNaDV�r2��A��:�$�VA?om%5��A��}���et9�($= diag(1,- )kAr�M� P� $!xmu}= (0,1)$:&C }/6� 2�E _J�o�Ea.�a Q � �2e!@�on.ff:�JyHD� �B��e�, C�-en  $z= 0$ o =a$. At!~��a���u9eo m�lX!~F�2���, $��{�bf E}" *� J& * $r"e& Lorentz-H�nU%�s� $c�] =1�<`T��."�Y�&& � E_�j�{x}},t')R'&�  =@y�@F.@*� &&\�J ��1}{\p��}<�g�MZ{}�� 8 t^2+4n^2a^2} {�$2-  )^3}��L(na+z)N[  tN]^3 �}\;����ExB7 ! #2� �z !�zRIF.I �7 �%1}1& �)<�+ fe�a1}1 =929.=�� Ez�2�! SrovRiR8W�9FD�toV� ![car�9�<=�1i�.w� � �� v��<k��:pa% "Ss Ǒȧ!�n� �vx�� M'v_x^2� u-y� �] ^Dxu��T'[ ]&,\; dt'\;dt''2� &=& �^2e �z| f_L(na,t)fS $+z,t) S}\;. �# �3b ae# 7x4�Iq$t^2}{8x^2(e�x^2)}- }{64|x|a�ln   +2|x|}{t-\�#���� :Fxt��!�U &'"- �e b�� �H�s�nE�a�-�F 2r\ dt_1"b{t_1}%�t_2  {t_2 $'\2�]x���F4&p �' g�' $6',���wsYav )>eA�52!�� eft[-{t^3�19!�A��  +Ap> 2Al}+� �6D�x�Md ]A�`CG9�e�`,�x����!�H�YM�EzRE6�J�U��MzVMJ�G':$!�)2%��J f_T�J+bh $V#�#A��Q r�\bed={t �3Q(ln\biggl( {+   -t}rw.)�7+c��d��"L�%f�9�e[9���y�=�.�������'fh�y�Ibq� �&24�n} +�t^3}{96 �#26�Z& + V1}{6}J8R�u����gz��i It&�ln >y taskO��osed-; ��1 "7s� }#w��9u 1�n�%! �T �-$a\gg t�$a\�$. ��*���YF��g t��j2j����c, 2�}�  v, !E"�j6�*I�yyۓ��6� � ��F&" &\ o&M�:-�[ ��4e 720a^4} +I�(2+�x �S( z}{a})\csc�� z�!{a�8F��� �  {v 16(a-z)^4"� �&16z�-@   a- �z ]�ʘ�� a<&�BH�]5+�:+ j�71}{-* �*�*=*+��! J*:I �[ 5E� f^)�� 4} =Mb%�)3A(&�t vbe`R(Io� ��&�Wr �"uf] at $t=2z�qt=2!�/�c���@[�� val K0�?a��-trip� vel� "�%�Ax;�!"7�($ztP��mab�6!' mn�a���=our$p� a rigid&�&PV�&,L� UAL#be smeacZ�6$;!+C�!I�/, I6)#�&�of��)�x���!c�r�h��4at the above r�Lesults are symmetric under $z\leftrightarrow a-z $ as they should be by theB y of"T system and furthermokX$\langle \Delta v_x^2\rX$ is regular in limitsT$both $z \r�0$_:�a $, which can be seen by expanding v��around $z=0$. This may come as a surprise at�@ first glance. Itz0, however, be-Ystood Cr%��!@fact th O$tangentialtponents , elec!�� field two-point function vanish Nconduct�b�aries. J� z^2 1� , on�o!�8 hand, diverges��PEI(approached %�it!�a ref��I Incenormal:� J� �{. If weQh assume%N$ $a\gg z$,� n \!�8\label{eq:Vx1} j�=ByU� \��x \frac{e^2}{\pi^2 m^2}\bigg[- f_L(z,t)+ {1\over8  ( {t a )^4\;6 ( {z  8\; @ t^ *$ ]\;, \ee%pF�z2J�z� � j� f_T( �� 4t^2 �360a^4}�. �AE�arison1�aboveM��s with Eqs.~(9,11) of Ref.\cite{YF04} shows%�!�A�( last terms�A�W equaA]I�corree +troduced� pres]{ sea# plate�;,aA�xim` beaE(considered,a�a�regardee� %Dvery far away from{iMj$. For $ tQ� Eq.~(\refQ�)eF:z2}) be��9�^Sn� -�\;-A�-�!�I�.q+"8" U�U�Y��� I�M��*q�6�B� \; �4 �ev � z^2} +{e]� m^2aa?a�(m��2+W Z  \;.�Avabi�The]xE� h�.8n opposite signQ[8longitudinal diU�! it makesA4 dispers�?,less negativ��n w�6 it w�e^ just��i!L Mr Whil7��Ti�� transvers � acquir��n �xy_ ��$us greatera�Sat [ �-E�D case. Similarly,��have fo=��a� xo��lE" C&A>��� &M�&R� \B�� A7 4t^4}{288�� +6(2+\cos H2\pi z}{a})\csc^{4}  z\pi}{192�,H \nonumber\\&&\quad }x$64(a-z)^4}6z^4} -g�T a-��\; ��n�\b -1t yQ v ) �F ��.+1 Bɜn TheirY ��fo�NAx*Eҵ��Vf]v>`YwMu.b�Y�? ln(t/2z)+.�3AP�����+�RV�] �.�!�N\,  [���{8?} � 1}{3dn*(I+t}{2z}� )��4�_ 1440 ֭* � ]:e z2_large}�j %�� \subsD{��$�a$��}����8 We now turn to�6�� g of c �d ific� � ���e @erimental measure< effecj Hconcerned. Let us � wr��,the velocityݢ��Lparalle6�sV�.>�v.s = B�m��Big[-k -a,t)+h�  �*� taMQ wheri�4gin{eqnarray} >`equiv\sum^{+\infty}_{n=1}X[2xnn y+ ] -F62}0z- &;. \endtN!�he sumv �est� � integr� d. Defining $\gamma=t/2a$, �X,��example,�6�F�1}�2��$ &� f}�\int^{51/ � @1}{x^2(1-x^2)}dx �� %{2�S�C3}\ln!S�a1+x}{1-x%�)dx:Y)�% w(1 �)JnI^ n follop F!M X�[\ �1}{2}+2z/t)--8 2 �-I]J�Per����A=�Ţ&�Mn power se�a�$1e obtaiE    ��- f�g[93!�,3� -24z�)}{15�!)L 6 find!� >hv^{2}_{�j��I|&��#2�a^2-2� 4z^2�^2�!�( �$}{4(a+z)(2� }Q�1m< %�� �-�s� b��<te such a �7�y"��*�a-z(,manifest. In &6"��se R�jG� � >*�\b>�� M�^f�?}%�1� 7}{8!� Y�A�%�Z5i��ter��ng�note 5��^ n squared9|fluct�" *� �4��0 s diea� f quicklya�tim� rogresses� $is basical)� ient��. UnlikJ ���AJ� �s$ perpendic�2�&`s a nonzero constant valuCy��4��:])\�norsip��nee� >%_i"�$�be =�t|�contrgm (Brownian mob due to!�noi�! me=�=�X;o%_�5� and 6B5Zs�� also�f��!~ same�;as ͼ[ ��i$Bn&&E�.��rf�� y:�<�2 �;aqga+z}{3a6�XN�|�rJ6)i�� :E !U^=-* �&b] g* (�> )}{8F?�={4�R8�{8� � �@ ln-/D�:�--�%d4 }{2a51d.v"!:%Q2#1PB� �4re~p&0M� �N�( �6T -2E�)�j�a( �%�!�1�716!�R�J� K2� �4a yN}F0ly, l� �x�alm &:at� �/,ir extremal �usF$z=a/2�lisY elow�H:! �S:wx},-@-&6�%A.X!3-,2%96 "� vxma}!� :�&��� �7}{�Me.� )�z ����qBRn� q6�� }��Q� ��: ����53�1 �I� � 2-j�)D�2� � comp���6L �those� P� ag7 �nU�*ZoTsei9��Pd�x���<� get R0ified roughlyca�or�$17/6-N( 2.8$, i.e.K e &�t�@se�t�ly thr�imat ON`One�wo�i�6>: �ingful,Gc!De particle will ul{l�ll! on%t=  clas�  imag�T� tno excepS j is dL y even if� pla��midwa1(hen quantum6l ��a ��@ show�Tat characteristic fall� ime, $t_c!�s given:�!�$\sqrt{I� mz_{0}^3}��0}$. Here $z_0� !"ini�Aft� to a� te. OcalD !U2w7 sens�e m�=� \gg !. Tak�anR{ �2LL % t!�leadsm� strab on $ U 2.4\!24s 10^{-10}cm =>4}\mu m� $ An issuE acondi�� ou�Iin 2��t valid��JU� does� & tly!� nge T"� q�:6 B�� \ll z$ZK%0rqKy�! s $t7 (mz);%�!g!=�� t�� t=0�is meansAll%c<10}(a/1cm)a$. So!�Ak�"L room%Ca �gg�P:U)=4fulfilled. \�Sxry} In�rareEfFine!ueB of a!erg!est�H caus�q�- magnea� vacu:� betw7twog�!�&�"���q>{h� �>� !"�=Q�2�. Our"��HYs>!M RM��͟s!�reinfor��in��6!cl�F��L��Htemperature associa!wh!E��>�c8�] i�as s t��l!$.� . AnAis, toge4$ e� Gad�%?.v! �increase�j�1�u�by��an or�&@agnitude, suggest�BQ�~J�&b easi���observe� �$�!-IYF99}��6�84023K9:K00rKLett. B �496�07 !/@0); gr-qc/0004063.�YW}9�P.X)EF�68!� 8401)�32� BM69!)S.�|%�0G.J. Maclay, FR184�27%;6� IV>< 4document} �ab� �ct} \renewcommand{\thepage}{\roman{ } tcou�2{{2} A��em�t�4, most physici�_Ain&( hold a sk� cal��� towar�1Po.~Ta `hidden variables' ��uō�a�ory�'sp�4of David Bohm'�/ ccessful  tr +�(���ory%�@John S. Bell's s� g arg%W� fav� �u idea!�ny��dvin��ei��@�mpossib�%o�� 6����� o%at �C��) w��aXP �� rrelevant)rK(n� Iwo �k��behind _ doubts7� s ce� mathe�!�|theorems (von Neumann's, Gleaso Koc� ��Specker")f)v)�b6lT0  h:? �s� ��Tof^credi�!� prov�� %�BM7indeed `9�'ER!�l )�t�.4cannot replic3*&psr*o�� mechanicsM"who do�  draw M�Mf!llu�'n;.the�'ac. �B�� ^ � �exh��� iv�V � d fe/ -���IFq!$ disr�*�'H � sophNy O! a� u�!1ory---%�2�--- �Ls {\em nonlocality}� it!� happMe.E�% �equ@ [�0t�[!"pag%�o&�+c� n�0taneously. H�/as\!sh !ti�MZ, t work, n�e65�pa6i��onpá%ribute!� h adet�W,M A�r[� B%~A.�iLimply�atFSAx�� n��e&�be over� mplex. Az --�5�,�isQ�A`D C*�uM�elf�is a �d>6 ofIF any}���Euagree�.|>dal�dm�. m�sO)�Fl�add� ���wa� W�fdiscuse earlie�+nalysis�>f}>2z�!�---�areview :� refu�?of:@�iasa of'. W� W��elabora7on���$/�!"e�A�of �)�F. Accor ;oZ� se�^,�s�HI�%�>$>8�e �nY , buAa stea��d� A� ��IH� extu6�Y�aG$"� de��� m*r'�#s oN6������'d.P5 G!\apG tus.!�demZ%�a newAd�/� ���,��of i-�'sa�%a%�F�'Ub by���%%�ne�3a6�'E4 ``sp�4al!���atiIc''.ade�p"�3insigh!��$epts invol&rwyA�s b@ v�U'/ng a }O5J�ex)�d �(describ�V Albert�i\� E�.Lein--Podolsky--Rosen�adox,E�9>i /ru@!������%`>� � �bly�+i��B��`�hin+ome:0m�70 gradual fash$ thanF� s!_ � logicA8a�  may��Onparent. �YA�dox71*, 1*) ).!} generaliz)xErwin \�x!paper �) �>$amous `catq'a$e�#)Qes^ ale&q��A1%2�g ?��%� �sE�� �!be deriA�u!!k!� er 1----?�8�s clea��relqship "he5�st�v����`pe�1 ;' )A>�9E� use -Os EPR �g to ��&ide� et�9�QQ�.�proofG se  r�5"�t���u� f GreenbV8r, Horn" Zei� er. First�d �de 6inv �A#  .`.� o��66li�'�S�,� &� }�uhityU>w!���m �Y� ver+ iXc2�'A�$ onlyS� Z�.%pr� <��s;i ; ��- B i��X f ��� %!Ls� !�%C EPR/�=]%% j confir+oE���and � �h���!�Q� coru�?an] 6al se�.�Ds, nam� +& Z[ whether `�'�My'R vio���6�%$`Schr{\"o}� er .�Q?A3 differ� �GHZIb���Hy ape ��wo-��;� os� i��l�  �sqoV0 /N9�&e�&2]a'9;, �!p�K�� �!�e �A -a����5B� �K�a"� � ��H \vspace*{0.5 in�ce} A6: }*$2H2H IB)��9s m� v'k/I!�`my advisor, Sheldon Goldsl/aW:kZ���N�� guidPG*!�&magin�Jq l;��inspi to� i�����e0>�*ke�0Joel Lebowitz� �d�encourag+2��8�,a �re��:��� .��friend�nd stimu��$ng environ�M� Rutgery?*nij8oup  my help�&� s, I �U�!�eS�!Om%$ rked{ qh: Karin Berndl, Martin Daum��XMahesh Yadav, Nadia TopA � Subir Gho�;. M�!j�extenw*to Ri� (d McKenzie,FTrew Pica, Asif Shakur,~ Ka�21 `Gail Welsh of Salisbury S!Un�?s��Gir ��%�U N%� i%�a�: rtunBto&N alk� � *�& s sa-nt audE�x:hthank e� ly6�)Ag!�ed�ofr� Mnu� pI�(�y3lu��e5�".ge��!0��m�:ialIJth!#��inua�. zeal�IAA��ingYqAi� s�n���q� �dMelissa Thomas, Tom Hemmic-�(Raju Farouk%�a)��+�e�0u�un�� techniqur C mad� ��q�=let�\M�le li5aw�>campu� )2� by aqE.~Excell�Fe� .��\s&f4chapter}{1} \  {Con*o&�s E�q evi!�� !Y*e&� 6�E/little� act �B!+!;1 a v�F\&y� �Z4"(| 23p were � ed�Ane�M.� �&�}� 1957�l by Simon *� E.P.d -67 D &�'E�claime!A\footY* {SeeR?, Mermi0� , ReQ y Market_}.}� � %r1]of-X&.�2 word  ��_> � [p. 73]� }: ``I�"��,ist X believ� t� �.s... ... &��X�ra� ��  m��2 -��\J� � in F,fer�an 6�E�a�(y�Dlinear��@ ��=��}.� 28, �,D lQ)" � �mL�)���� �%�ofN�sh���� 6�EaF� %A�U6!aB� � [ed�2,i9�  Eclip0'Iq  Pilot}9�(f� �!�rtcoming�th e�e�Dad3 te.�E��6.ofF�. �b�, p�� !)D� �;Mj1j&A%tn �h]iq�t � r��>�� i�6  A� )^ 's��� iew}.}, �f is s�A�%K,�yet ad�Ia �&/%S. I%�bJ*�B �a�us�!e�"�^�'  zM��W�*���E! ]wh��-, �-f� as6��*�=6b�*onc?e�do}�:, weA�bi���s'p&��,b�'A7sq-mpl�dInc�Jf�$wA ��*s*�-iB�A� �d0eQ�e�!.4�n � � procedure[-c)�AY6rD. m� $�UMX� es�j262 . "�(��yN} V.��N &�ak.��; t�$�a&�K$E(O)$!�U*8��{2�p�� v9�b orig] �!�en�A.*Br!�red to u, roba��Je��subg�� a Hi%� |��*va� of �l"Z!��a v�7mapa projSA o�(or�i�i� mmed�. e�M� b�M}I����� E-to\7sp�.a�'/�!6�N�#�lH 5�! .@��$1=D�+2] mapp�.8�w eigen%1s � F(�a9Z�se9Q.},� �*-�%�J1@&?=*uz-�laxP+�9 �] �*�" dema�L$E$ be �!����*�se�f6�Be�/s�B�.�"�NoYn\ 9Y9!:E��P, rO�on�2� "_5�@� A�)i�fNp��e's 2;%�tU/stM�1d���al�$=� ��T��!�.sp$nt|#o6 :�wP)$E� ���D $E(P)=\mbox{Tr}(U$7$U$�i&" q�a $5)=1$.  D�1�M��!l)�ityU 5�.hf &ex��it/IQw�Dt,a�y �9�8 $\{P_{1},P_{2}�F dots\}$ o0mu�K$rthogonal y�>{\�H}E 2},\Kv!C" ommK � . Fu�#�R,\3$P$�m2dIKF/ $d(1} \oplus 2}  ��=s D��Aen ��� 2� �`>�ax�ADv &:5�ltyp�o!sU�5�2��N���(.g ) �� obeA "��� q P=%�+%�+ � �Q�QGlPsum} I�.eeq e.G2ien h eE(m)+ 2})q^y!��r s!Val�Q��+m� is e"� as� oaYy"=���se6q� at l&�.5= �Tec���!u�&=)s `P� , $0fB)# 1$adKY 1}a�!�]�% )] %])D�a=I Gltr�5ude} %,�eqzG >g�=j�� F'��2 ��E� h&5 ��  }�)B#E� any 1U ! �6satisf!Xr�2��hFc,( �͝��h�B.}�@"  next�, �7 outa� 5*&o �Z 6�)1d�\ge��$s %eM� . . LG� +6ghtforX .�"![% 1[1ZA iVS? infO#**] 5���B}. T�&#�,, [ arg�6�o ! a��d�by�j �*��i&�� ���u�]�&� �Kat� lu C# �}. (A��e�Vonimp})E�r�%!E�uf is to req �: free sR fZ+by $\psi� \lda�8�$�$}6��&s�� A�,i� �evidee7I�bI�>� ! N�ї��D����6h,&4���to�tI�B��-gM Mȁ=F<} A�BH�&� * !2FKy�%��N&ABD!�!Na�aV ���᥅z6bI� u�I�e>l%�=���Bm�N�a�a�e�R�oc$6 rbitrary�� $N$..���� �qHGs�s�I�0 ta,\phi}\� JspH7J%�%in� �4. "=�iO�9.H� ��!4A�v �.i �o*� 6f+u�  \Gb�+�o-1wPݶ�� ofwc  aJns' c a��=GuO -; ``$N=3$''"q��\gl:]AmoS'IR Z�� � =�x}, 1y x%�&��oN� a)�d �$x,y,z$ �&2+. Each �z%Sbey�g�ou%� �x}+ y z}=2*�KSf�!S� � f&y q%�,J�fW�$E( s.�)~ �"u (x� y. z})�� ..� KSEN�U� F�A����!)��rh�3no 2� �:���e KE�A=>� A�J��c� ps e!�Yv��ed3 $0$ M[�� �+�Jeq2�.�^S�s�_A/l_ . (e n+1a<=�!'s!Dof. YlemTM*����}n�\!� �&%a geom�a model. I""spbof � �u�4r�`_i��$\R^{3}$�d easy!9"�B%UpA`%�� e'Xfac@ rrO� ar�c�u"�m�3!%at)� \��:�<Z =΍�set�'.L\� W�is, )�e�]*to_-su � c%; �. S�5!�.�A�% 2��F���Aw�$1 it ��� takg�ON8it��}s�`�y.� / . S� al4�N��-�p ΅�fRQ2;<Z��\to)��gm�t�A��F!. To ga�(aZ &�.ing&� 1�: �� a�� Ea(Belinfante � �38]{1974 Book}})c���a� �S %} ��F�I> �8 �H�E��w�I<:�%��%e+iLe *!) >\%EiigRA is pfCNFe�*nd.Qa�ed!]8, blue ��9�t �eE�vec�F$\hat{naPI�one5ofͺ"G6�NAG.��tdin to�w�Uq<^i one-third]!)CG�r�BI�c *c�(e<iEZ]_}]� $�8�,180^{\circ}-  180+D sCy��  al�3_X,$if $s_{x}$e�ab $+�%#-x}$ a�2$-1a�f2*!M�obF�  j�}& %!�l}{ erI�e�J#��E�:� l�MH�`A`i�)�4``antipodes'', `receivaYI�e�c$E�D�?�.n��Za�[ f..j!�,��er<.Dolla�` !�lu�7 5a�a�� " �%�bS3'dee, s�+>�[ C&y�&xa�!����E�2`red' J�&*4 paiFJ� m壑W,��r �b�ny�1�3ine�w�f� T*lb �!�<b�e�9<b�!g=ary�{ yR��a-�w-b%!�"oct�A�q�-�"$fof� co/6 ates�0�$geRAerm �.� 8reg�#�N!�ern hemi��c/��de18A�$90$ A@,.�L!�%�R* nX A�:��7cQ~c e���e�be%�. 17a���>� meridiBHa6>;-jɟwMi�A��5 *�Q}!%��� & U -e `souv/n 9f'9g 180$6i276jw$w D/.�%��-)��,e�s��mW2�dW]e�%2!���!�mG�ll eQ�] .ݳ�~)Б] coloa�a�Ireb:"�<� �2GU a m�#d \����Xai�o meeiUc�_rA�A5�S>[&f� ���dAF� � per�8X��MS9�3.�/H *%>�OaZ�Cid \e�!%�:�'"� Ÿq��.�^�� ^| $(.5,.5,-.7071)$, $(-.1464,.853)$,'5)$. [��ٓ�;�a�djF/y) ��QE�lorE� �Pschem�@6�of�S� sX96Qh�DawefA@A$.>#a "� �"t Sx9 5 �inJ��Ges:Iwb��(� R,��m�!. �ir-&�=ir� ofRk&�7 �scIQ{$117$"*!2]� ^,�)&�%�3o� 2�5� -�a�97"2��& � ���&�.�* �&�d"�Pe�iin 19913 {'�}s2se~6e�in"w(33e� "2 C ss �&Da P�iVh � "s�!�n!�vP�i�!oM2W*&�()�(�� conn�"' 806]�( Re�(. J�!�0 ser�;&�@*h�=@ ��6�d*@�B,��!�='�! �eif�W&�,`XC is; nly deci�&!Ds id�+D-&�,� n ``a4>�,(A���me\>E�)�2�,: -F�''1f.�-�}77 auth�%�o!�K3cular�on�%��(�7� 2;(ay�im �a��(ailM(��h=��(�!.��.\ L�0%��"6�F+'�$eaL�$�q non-&�(} �]Xy �59 lictI_Bx�7�! ge+= R! var�.�)�F%xVroved. F.�"2o*0Vt"�;h�5A�ed�se5�i=E!b�detail,�E�S i3` ate �$B�ŷ!�{(`?ad�:�dn illuq! Q9 H :�$9�a:�K quit�alA�u"�i�d*� Z }} C, �3�7 �,%?'I*(ove y N. a@R{-�� t&p-�.��}@w 1990�+i��a7sam�+CFv@�/�ued u.�`s&����G*'�)~e*� as didр�FI0�&"��A .>$s a���6�Q�� q�%�A6.� Qts�)�nd�ReE3��t�1t%)of&2����@�#&2by-R]N���2�l $`X1|M$"IU�L.�)dj !$x�y$!(1�se _�1�x�2R� �  �+ucs�ur�Wb�0� >"e�!� %�q8\beq \sgox\sgty t   y=-1*gPMb,����a��i�cru�Ct�-�%�.�- �l� �[iz&%|. �\pm�]-�toC!m �6b"�PMf5�ke�1\�break[0]"Z()36ru�6�6� 6A6!�6A6aiin�*y:*a2+�2 )I2�6""�sQu.xAny:+ �r:B�F6�� 6��'W23E�> �?��6,�F�k>D��e�*.�so:Tu><we:%:6�$[aOx,aZx]=0$>EJ3y3>�Am>G�����>=�Z6�"�@6�;2 ɺ2!V��:!�:� [*. Z�t�v6k�� =Ro%�:DB� 2t=�:Y Not>�A$:Z �NFofB�a�6@j*$O$-Oi->��2*k2 FE=V`6(T�c2>EAY��>�A[6cI[>q�B8LBKm�*}B5.O:~do >� >)�e,B but 23 �; 5}.B6�">cE:� G� >.d>M< %�$F�itB3�BE�Bu>qJ+>�VBm$[E�I�]^{+}=�1A�2}+�"zQZ$0N� �5=- <. UJk&���maG>nip"*4 ����� ^ �*i] �R�U�r}Tg!�A��$�&#t� "�&�e�Bg��wp�w�N�-� BOtyyy ń$v&� "#$- � � �  ty� '(  min�"� raN� ���0� �. �X_)�F�, f�0�u-�au�(�Xpu�!h_ q  ".z(H$(\sigma^{(i)}_{j})�]3AwFc  � �*1TA<5�^lTA<�entM:re���Gq �J�.Q . Motiva��N]{�!}f� six� ��9. 0{A,B,C,X,Y,Z\� �&0 g�Ev2B� he>  r8�PMe �$,*/Wrew- .GH $ABXY=-1$�%�e�X,Y�{" as�6yjA & = & AhA�t� �2(Pduct} \\ B'E�x " ~ \\ X!H6! Y AyAS1%?2Lix2�$Cm�Z�kF�C kAB� eq:S ��Z !XY�gIe"8y� S��"%�.�a�3CZ� F�(I wO)Ip8�NNtFY!�Q��e ?k�"�:t9�,�4%�M�>� (A�D1� Q�%�1�"2 �IA����i� 5eM"�'2th18}F 1 �a��&�:2 � � A]=&� Ik#�� y, &��2��y},��1x}��4 . Exa*3�&��51 � &�1�Q4^s trubr��A�<%=!=�"�:ap��d#G�)F - e2�#� $\{C,A,B\� $\{Z�!�Z�.,` Z�sA�97/F2!�gl&+C\k�W�%�"�/��=�a&�T?�= ��N oy,!� !չs��T+reX~9#)II �Qż�G� }�ya� ;�OJl2`s�%�2�m�0&&�-%��U �"��1 (qwc�,),%\R� /.-)g �/� �Vmh� p��ts}W�6S< x�ba�0mbKs.&H�d�R��is� �/ig�A(e�Y*_2"�D.llL @�Ds���"�91� to 1�A>.�5�%�I ![c}A�YR9A����= e��s n($I�m*K� Shi:%�j�@�Cis &��axju,�����Pr��0. Giv��4)0�%p< ���a�  � %��+�� 8�=G� *@�V{o�.O)A�;?�{�,$��Z  = � 1�: } \foI i,j .yT %�`en.�Ub �� )@ adil�=�.�2:�ZT %�q��:{!S�X���O�woY�2`w6=DI0� . *:.i!$KFe0��%� .! % k.Z�)1W%�Z! N&��!"�0-1$�0pRach�. �letr��7�mp�� K�aw&"=6G $] �e�& �KA�.t u P�&ia�M�J�N. �81�mi��^!�}A�C�C�u1iwM�A-C� �N�,3`u�F%��-��6m�yŦ��ing���m��B+ �& � "�1$y-��Q�8y�M}� i2 [!z]�Xno IE!A���sE����,�l �t}dD3�Q��isA .�' �ZI��j���,�ctwice�N�&� �of."�=��e/�<�0an1$a)=#B�w�*!:i)).�3i���r�)noB�ma}$) b�7�(s/�q �!�g�E�1wI sisV�q�lon,�th%" ~"u t�G%����Q�C�5�&�3#6lQEPe6*b��@RZ NNw%i< }1e��GE�W"�of� fK$e�.�!I6��1)� on s�2� 9�A(c6 9]S.#�� �!�e!�wm�<atinc( ��$a��*�$)(e.���&� J ="3O &"%`yB~AEi/q1�"�7 ap�-ZW ?!4h:g#"j[pk+� Q � M} (�My��%� ���i)@a�4in error. MoreA^�l�" a�# Y���$ carr ? ^by�& �ell�&�a 24Pe iPcy���:� �&. ['Ag�4��b�0dUd&(w>xu��ion4�VC< rV �*�&�<� N=<2�=��J%�e�$"c�9e_�rA5j�J�_ �"�`2D"!��]�C&Isem!\w!�1h}�`��_P��,y a�FaY.�&ke&��pt3eK, �"�6� �!S c2xRA�d�Onow"� i*NP�S� ion. Es� i!�,6P���Z( :Rf*�'��.r%eda�%�ar+��' Lemplo��Y1�$��G=.�.w)QB� �" aM�ism&wu 72,!Ja\;zd�l�*l&c!&E��i"JX/t^$' phenomena2�I�Fh"&�/7-�|)iܔih� Niels��A�/rk><fundaa�$al princip�V�m6�h ohr,� r\t ure}75 zU��a"DB��88Q�.��Z an "�o infl�lQ .�Fo)! 1� �[ �*al{(!c!."�@\s�)2I`!�st�j��)�9210]{E�'b%mpJ !E�oB�S4Vp .#& z he behavi�q atomic obYPs��Wnte�&��T)9� �r��s� � E}%� .:un�$� KUx^ear!�EMc!N6�"l0�U&w. mƋ� * ]Qݩ{tvBaela �AT��m�rs�jpa,?i��it1m!ȉ�E� focu���>-U#csp�~f� � Z?b-�\��TaRu,q�J<."ٌ1$] ��d/ ��"�Ton�3��c A�5�IedcB2%G�����!A�. ime evoluAX��%�Bg�/ nIl�i�.I�$." BE2�&,���7!�� j�6Ml�]wu�s"J&�ya�cUa� ()A�H)��eQ�.�C� �,�Ane�b���,n�S�?v "6 �$jey.�multa"aq�a�]" %�,!�����>X$g� p*| e�B�$�Nrie�hO�% �M��h5o1�]'� t�E. &�e�]���& $OH�( me��A!�6� _O,Al#A_2�Pe�YE�![ SPC�= A s=N��ko�qPC}$�uly AP+��m��b���%� bj�qetA:+}$O"~B)�33!�Umay�v51a&�6 of2 �$^{'}=\{O,B%;B%;EQ��6A�v#2Q$:O#�m !M�1_�S7b"+\/"Z -�y%�\{A_{�H�.� �eѵH\{B +�C��7lat" M�:�su���"1�!5��quA�d�}�9�l�. A�RŻ3c� eanJo�a �T���� I0���)-wa���$2��$t u�qaE26 �/qua�s �yl>�:,"�e&�oZI�eq:NIC� 7 ��"�7�post-.6�1߅e[Odf3j6�Ʌ-&� !Nl�S i�Sj�"-�s�6 (�r et. R6(��%�UR"E�t�����>fH�����"Q'MZ�1/6"�not ge�2�af��#Gc%�d!�-wo]S� ��. App�el4In"v-<�  of `.��:��'!�:�h mbiguous}�y9�}I2� !�c� &t>� gl.�f0�{�zfact,�0ub�dq��E�>5�.wO tE�he)j���� �! 0%��e��xa�z hf$AX\'s=u!�_<�aPF"�@-�K�w-D�).>a oA2 AcQl&w�"m E}|2,�,  etc��.mQ2�]}�/� ��9O�3 F�a6�&h�C� ���J0�I�c3aB�g{o���#��~�4 E�Ub , e.g.=!559&�!� ��%2 y.�:�b��}�h divi�t�9��;s# &�a . EIo��9miW9 i� �h�t�B.�.���n&r4.[��6ea�� �; ��: _OV`by� �%d�?.oP.$"c_1Z_{�=\}$�!azQ2:2�1� [N` &� h_Zt$h� ��$v^�As���"��[�3Y<� by ?,�T� 2.�[� ; )ch ) .).H/x !:�$\{ S1}\ �Z�#Y\{ N$BW%�E� C=*G"��y�?n.Q� }^{\9A}$ (the % �\ plu6�>��� spanrb�U ). � M.���e��%a�i *V5x!�`�#!-� ��*vJGRN9r�K^?%�a�:f&R?qys&d�!Zmute,�0�,2 671�E}(Q�~Q��}N�]QA}, /si� >�6()hi})$�%NXEl1} e 26W re &�elX"��$� n��B�)�N�Q.wA��,E5A� �4&�Ka�p�=le)*�se E�ZJU a�(2^�� E��f�,ed� "K�K*uPA!pe$\�TN�Tz�0EفcC)��},-Tz�8��8pot�)0al energy dueR����+& sǝxN itte�%k  427]{ "r%�%%n& !=�helium}&m%O� ���� woe>ie[& iw �guish�.�  Y7 $S�k� ){ ons:��or�c�%$S=1$� �"-$S�� "P�a���J�pr �s%���!�E �$ �}"< +20�a[�a���5A�occur �qt"�} )-�2u�! an ) U����a� figuhD7i" *_�yE<9) X��bc֔d�9 _Sߓi]��� $aSQ�+b y}+c z}$�h$ic Hamilto4�1�a,b,ciI&c�^��G$ Ux}, y z�YA�� e�&�!]q �A��ithaOJ �5Cartes�)sGcEa>�##�/>or`��� t�U^)�r<%�. � ��ͽW.-�R!�[� V�9 +��-�t59ex9$<�A*�t�|> � j6x ���2 (a+bTa+c zb(b �/� �2 U5��-�Z�ul�J%�i��$\{1,1,0� 0,1 y\{0,1P1To�$st� _�5�)Cuj^�9� (a:�Ox� UgsbE"�&A\"B~�@�xic�E/��� EMbe�z4�Le `$2�bS'kjI�`$2$' �v��6�p�'"s �_n��� 9+cP0$2$, `S' deno^Z�RZiebgis �,9C�Y `3' ercptA�Gt"HuFtri�/ ��hݔ�'no !oj��81cR Paulir�Z:f��#!h12h.3^:�e!1��a��|V� �(r�ra)d�a���$# �d��&�[weY�)e^lti�"X�~*�NO$��9#!��^�$_{+��0}-1bj$Sm�$ �+e��+ =+1,0,-`0eC a�A��i26͗re~ en�by � �i~��reVs�* � = <ph6� � �R 0}, Z6!�:t��:O�"���!�``lif�deg�Sacy''e{*R`new �M \�b- AC"A�! 4�$)��c �6$�u��M{-9. S�^e�w�6�(��of>#$x�j� M3B*�=�'f �rh-<c�(��B� ��=-�a}!C6�[ ro�e8ut}8l$x$�:�Ex�Wy |]c$ ������� back�O*� 6N_r�t be���AB~Q�!to��!�RnalogUth �� M�C".� o<�|� ��m��>Q H$1$� �� t�.�$!��"jQ %�^� OPc,$S*� .n�-6� \thF/B -ˡ!i c� � o m�Ʃ�/|�~$L�=��i�s\�/-F9+18A2��xfcpe*�&%$V�v r�F�oi�%sAvh/\��( �1}- -17 $ {2}"+ 2#4 �0f�1H�.�� nven  choix+$V$%|s  purp�'�8 V=Ax_ +ByCz� �Z���"K/:�����g"k .:"Zis I�� $v�==5:7v�.))316=)<v_{3}= !0�We drop�� � >|)$c1A);&nH�38k ��� �`e p �& &ah!&�s~g ��a�5Ai. W�h �e�*arix�hh�{ ��\.@���/ �-�,%c3U/T%��&^G%� �G \n;(%�3y}{c} "=Ve:�G0�G&��G ? \K;)1��lF�jk3�k0�1�0RIbI�t=�~� ma6�&�o!���-�V@/e�!�t:x �.� c� �sAX�� a4a &�"� .�� $\bm=&� ,=2�-"� = (��)�iA`^,bal� 2Z?1E�2K� ! .o(X $H^{'J���%5a��: :�(�>X$T )e� a�!u2!�ͬ� $\{Nn �#�.�p� an&� �t*��4��%� )�(">�>, Q,`\}$. A�EisA%�!rf�B!D&3) &�8� K�5�y*D6� )� ons.�.nx'{ :� -"Q%�Z� "�  ; a;!�.E > 1� . Unz5M�kum�cQ �F� �.� k(a�ulti ()z65O� roo� ion)�e(un��ed)6- � gy pρa�-^ 0e�ir*9)wZ�I)� �d=PR�HE-�*E<��r ����f�V#."es�:�a$�� "V aaQ �Q aV0&, HF�`sn�*{"1?$"�<-�H0}1dI3 �"� a%�-V�z&�=>�/ 6�.MuU!��^0ET!�&�&0�S pre-M �:��, �K�9KaO�R~�J�?p�}).�) �7,[y"�a �ΡIic y�I ����n� aU# phot\em�d d�2.a�.��� ion�V &Q5U��.g��KUc��)�B� !3�  r*=�EJ�<:��4���ng%�&�?J� &!]�.�.s� renga�s �.�T7�ustBLA=>0�,eU.}U?1E  `.eE$U9$'.},�@F *3#�5S A�ofgLp�v�& ��&INJ�LY&�  e�<,<$;M$d�!�4�M<<>�ų.�&���,��6e�FN`M��.��JaY .Puj"O2it Fh-5R\ t �G= O��_�*�'�*�7� -��%n9�;LJ� volvSEeY�9_1 �S�0a�3#�H�/I�.�� un�"�$w1&�aF $�"�Is;VO;3C �'M[x�in�"& �.�"��:,Gv�&nd�al>@�/4Va�7f�K^!urc&"6)� _��Qi� Q �vg�h>% �nQQ�j� %=�dr"�4no R�&�K 3� KdB.Z�A��}�� {~�&� .(?P�'�}a�{Q�G� I�pK,�{l�wl>Ge]=5&�A. s EU+asΦ ��ohkQmof�Qlr(��"�9Y .�#-�E�R�� g� &�b"]�')!+\sXU_�SU yj�:� M� )�-Me�G'�o6�? bd�%E;y!p��less obC�i 6�%:k"H��(Qڐ> I{ ir ] A'I!��*.�)��M1!��"5�}2���au'�U,J,��[`C� }FA b 1Ur=7 &�,V7ya> ��F�'T!�v�Q16:>2PV|e���a��5 �p.}a22� at��+eN�A�n��EM.vUe�.\->K;�"3*s $(O^6O�>2)$�-:;d � _" e�OE�F$} $O \sket�Rmu �Prez�"St2�KQJ/;Eig}:�?^�=U =\mu &!O5�%y�\�$b$ s� .� VE�al� Z%n[se"�^�y,�<s�66.�%�}�� of�!����"-5)v.<8s� !�E�Q� �G#� iv col��>�OB�AN}&4$U�%�lj�BsymbolI/ bm}=�� ,\mu�-�)$�G�(%,!)�=@% !,H.7��{\bm_{a� N�_� `4� um'.,�ge�;"� W6bQC�3I�2O6�R����.v&�6N/! F���KB�f!�N�� r� eq�Y�}�f!�v;F�/ \v�� &�_bOYΑYGd�in�J&�,,&�u5 F[ .3�0]+TS �$uT�>+-,eT�5�))�=%� now2+/A� �?]1 ]~�A9.Bve( �ZA{��.Q�m i�y a&%��26UA� }."F���n�bE�q#eWxiA!,�y�%>lŽ�2ua�F��$.70% �I,{�,s�$a�}= �DŪ> PB� R:�$\V$,� .F��3H*KX-k ��2� of $fDN ^a��{#si \in"_�"�;bB=����! 2u �dEX>I7E�* � qa�iR� &= ��ɀ_Y $0.�eqe���a��s {A� �>U]:�QX*F�%%�n &��y'�6q�e�l��"'"�6jit�A�Z�i��]ő �&�&e q��X36*a�aW3l�y/Id-fmJu�q�$\{e�!�a�u�� ��la-2(%C)'� �(Q#A�i��R ion:M�[)�-e�1}�smg+ 2 D�1 �<]B92 B9  + ; \Dpsi2���%�V`eq7̅�i�ef�� uia�du$xh��facK�� 6Ks��a sum!~var$� [orra~F�RŠ�LABB{ �He�"�&�9��? ��bm}��$*al $a��i�m q��6�zQ=c�}��eenq�a�% �s&9 ��6� �p'Y�#�!G1j must���� X�a��!&J>�Y!�2rӡ���9MAiClN� 6 � a�K� [$i$th-�2L!!� "�AxF< �� �*�<�ec/ngAw� s**[ �:Vjn5�)!���b1� "��B �I��k�afhB�q�B�m�B9m�F9 B�a�u�C8>ni:�j �q��1j*�)'��/E�!c����!p!�2�"y1 �E�2w ���(��B�iL<>n� H�;if� seFJY ATQF. � S �E�" 9Z�A�7M>�F+��p�Qt��Ha�(�%�����Ju5/P .q�"�Th2��map� e <`�5�!�-}n&�  m�@�� ���V-�d. (.g�%���>  IE�U F.9��Ud+m� � z!2�{"�6.tI�!�C7*�t&�)�ap�T�/�(I }`* !/�d!�isq=m�H��t�5��tsv��"� H�Y���. H��!,�ral rol��yk {\emZ4} �VM;4*[!a9��"MEZv s��I�M� view>Q�"�<nt��� ��5!&F<(�y]ōu<�by��I� �+M�x^�n�}�9I&ndH���<�R�K��*GU:�M}9��%.(#M� )4�`6��)�D¸,D{\"u}rr, Go"��� Zangh{\'i� �M�n�e� _w !Lal }�g-4�$id�^�la.�orU�c�P%Iabe��M%B $z-$"��� 2#"'�*�!��*�� �6`i�zVe[�lˠ�i�e��&�H���Dl��{h>��y �?as�[67c� AJ�p!a]i���\E�!2-�߁�^���@ad5c�K�7(���aaY��qJ���:�B��Otrl�c!X�&Z�# ��vI�(��� �V>�voutW� ��6�M� �+o�� �=metAyD� 7��{j 4Ad6�setup��e ��pl�6%@r�>�!!� .�+A�y�A�%u�in�pK-SS5-GerlaOe��/ 97q�2O �ao� .�^�A �ef�0�$@/12��|�t%ic )3>2aJbY.}�Ks )��ed�+a:� �. �a�diagram��in >ep %.}��I� $� �in�"1�FIA��� �$Yre.*1Pw�� a &*=&w��� �,!(f5-a_5zM7�horizo��_�a�%�po�?v�$$ d �$?�!<Ui� $zVd�H7` Ea, positive $z�L$ directed upward. The $y$-axis (not shown) is perpendicular to the plane of�Ffigure, and---since we use a right-handed coordinate system---positive�$ points inj(is plane. �long �ofzLStern-Gerlach magnet Y$ is orien�a;t�x �, as �)upper� lower Ms kDapparatus are locaXinU)R ions��z$R negat�4z$. We define= Cartesian�lfurther by requiring that � (�lD Kd/`$y=0,z=0$) passes throughic! r� the j<$. \begin{)�}�picture}(360,118) \put(247.5,17){\framebox(67.5,27)[tl]{l!S}}..(30.5){\make/0,0)[l]{)�6+71bY%�6.84�Y49.5,57*4vector(0,1){18M51.5,75">�z%JG1,0.G% i>GxG103B�H45R#2Itl]{De�ion of6244>e0Hincident wave packe5t333,66�-3!�354,73NWUeD2T )�U486U-1):V42>Vbl]{LA=6V \endU� \cap� {GeometryM�: Experim�\label{e!1OQ� In e�Oe/,a1 spin $A�|c{1}{2}$ particle to be measured�8 5do�$�A��po��x-$��.~a�reg)� spac�)n�v, its)F func!/��� forma�lq \psi_{t}({\bf r}) = \varph:p(|\uparrow \rangle + | \down2) -o8eq:Bef} \mbox{,!�eq wher �Ips $B[�H$|] t$��!2 eigenCdof $\sigma_{z}$ correspond%(o .alues $+2�and $-., =ec��ly. H�$N$!Ua� lized)rib mov~ �6=��!�to�ԩ. �3 wishAi,consider two]���at diff��nlyh�a]-� Y$ic field iRse�S U@U�y $1$i�� U$ has a str�i(north pole �Y�U���age, whiaZh�n� X omew� weak��ic sou b9Cis c. Ii�.�2 � ���suc�.at% gradC18)/"�${\em op%�e} d��, i.e.%" �"H�}%(�e � �:  >!!Nw O(s it. AfterKA�C6�5�, a5� will��describewaI�Xof oneZ followi�gs:�i]eq�(aysi^{1}_2y& = & u�(\sqrt{2}}(\��^{+��| >� + +-6+dn�Aft} \\�^{2} � �j� ^.p| >��.� 2�RD$ \nonumber�?.�?nd=F��NL$ �s�E. 1$, ��;!� 6�r=2$e[(both casesE�Y $V� $ represe� a locf2 obliquely� �� .Y=�:Y�X A�x . To��2C,E�$places det6 � A� path� theseipX s. Examin2� first equ \ref�#E{ show��for>� i u� is �~����)�resul�� our2�� i>. IFo.n�� 8 BpO2M. F:��� second22 leaI��Xconclus�3�� simi� �� � associ� with-s ��� signa thos��6"us,B��n�n��! impl� *�=2 ��E��-M NB2�. G ,a few remark��ar�he sym2 s��UtraM;�� +*� Z���1�� ,� demam !�i$no depende%on�9ADat'exhib� refls o �.�2��, �v.� $ ({x,z})= *� 8-z})$. Moreoveri*ve� al ext. % i> i�_� %[ame sizeVC spac��betweei��ti5�ie�~. A1Ł 6X2�, �w2of5��j!0i� �" a-M"a�&! � al Bf /\z EU0ant\footnote{�term ad�e 84cle's Hamilton$to accountA� a>���$g� s} \cdot B}e[� s}�!�� , B}$':�!�$g5 gyro"r���A���Dy7is �-A�!ya6g &^ ,1�� con�k�`�� . A6O =�3 ``q`''W ch�Sexamplea�peI } ��&�}. S��componu&e N UH?is�B � 4vanish} exceptQqa small  �%�a� uU�� effect�($B_{x}$ may� neg�Eed. FWmo�'y}m+E�$ R� Ire�Keda�bea�in���U$x�A�6�Q$x,z$��.  .s)lM0 $z$-BH Q�(x,0,z)=�8(z)\hat{k}$. Ov&0 ofm�cE�qm��EKaJy��u�h} ziNq�. SeeERMN, WeidneP,Sells \cite{ } ra�or��0tailed discus�ҭ E�"�5�� e mo��+��1E�5D�of��importa!to ��a�soa�do not��ibhe.\any6�erm vol�vx�� �| sd ��  s����wha�4arise from takAy�-$IAqp by�](�^2R�| 8�� $g&'%�(z=0)+(� :z 3 )z$.�N then\ &I  sose at  l Bs abond belowE�,horizontal (Ejp.�)��� !�Y � "�� BN it+>=)Z�:� )��`֧. \sub)�{Bohm�� MechanicsE�Albert'sq[} have � ione*�4hidden variabl �(ory develop�(David Bohm i� 2y} giv!�n!�la&� @quantum phenomenaM��(empirically� ivalent E�atSn !�HA�alism.��m�6s u�� a�� stem�� a se��"Gs!"awell- (bud $q}}{dt}= (� /m) �Im���*}0\nabla�� �}2�ohm2�eq�&� ��%{� we�,͗o!�(ner-product\is�. D� ,Q lE�>� w��"��!�=\c�*O |\!BW�)*[ )Ga.c�ɶ !3 assum���zq�6�5�B��+}^{*&� .�""�+ -�4� Nj] + >_*AE ��-sp� eq A5 Gct he fac�����i�EՉ agre�Es �[��,^���$not} gener��$provide, �~E-��, �pp�{� he observ퐅air y:o� word�A�N �! s aŪ$contextual = mapA2���.--sh@ se� choic�5�!Kaldced��ds�4a pronounced�t� A�6� �Sof&�e� � atGcan�ossibl� ^ !� 8operat# s ")D!of an ob�T!pr.t"��h.iu !���!A�W9-2�6<� ��[u�{ ar�s��Q|*.�"�'_��IbPak9cexa�a.� 5 ,farZ2zY�a&;e�5re �wo  t featureTO16��� beU6 ed: 2 uniquenesD.G %6'I�q1 ri� }��pI )� �| er�0�� init��s>� "Ka � �} �y.�QU�M�d a fixy r2 s ��iA$n� sol�byEI-p o �) i� ��. 's:-!�a ^�lexu'. Su�A�at at T A$tͰ$probabilitV�he m6[ !��$ѽ$A�utY� obe� el� ship� P�$q}^{'}\in H)=|�)|�*E �Gequ�Dcco"� .kA�#��� tinu5 hold� �Wla:A� s $t�:�� } >t1nCe� tqB�>;a�  �%eNU�Mly )Hz� . B~ iMLt�5�Q>��c �gui�to ``�''*zq�2�a�Vf!)it ��&�&Z�!� ~le%��" ei�&��( or l �J!f�. F,� de2 m. i�R�y ��b.":!�,7)� i quesa�4��%branch"� 2-p� ent��=]s�onR}. IfI �TsitH �a littl2"o,3find a:$ple criterp�$Mk���!!U)EO�rs2�-6�it%� �. Re2I�[sQ�P%�final6$6ZE�B`T$y��ate � theyp�Ll�&)t]�$^& ne. Ect�<"U togeE�� [�SQmq��`i+RI1`' crosAhe2� c conj�%y.�aP���L��j's)ɾ�**�+is gre��han zero�� m�E� ��' I��if2�Y is lK<�>T T%I�now��_@ �ObedD ��{ weACd���C$curiousy-W&dQ�6�.� A`.�whE��*  6���6+�9sq�:� ��&� al.02��5s �a�(1� >0$,E)m�<9��� ��4>)��2�"U eicE r�&"�!F � �$"wB:� < �����'sA al 2�X� Km Q�J��:�1itsz!�9& i �2}=�:!, �� han� 9,�-�6N)P� ��L� } * (��&jB>6B>�!in:�"obtai� n� �m*��2-�H=6�Rwe arr� �q� *"eu``.wo6*''%�s� -) ent}M�  �A�y6X)�![2l2#. �� "�'s ru�� C. �.-B) ly sugges��H�pt��(& JB�"� � .� eIa��E�! $common el�B��ex� s%Ke�&� �books. O)�I�Y�f*�� ���2�''}]$�  ��ofI�both} �  and}�C�>tradi7��AMe�.,*��%��2` �m� 2���8 �a j�2�))���2� & . $ NielsGr's%�u�"�r N�(} ``a clos�*& revealM�!�pr�.<�es�'I influence��*�on� Sveruf�?&� physE0i!���?rests.''�3�G�(m>in ]um�ory A^a��+5o Daum�#HD{\"u}rr, Goldstein�$Zangh{\'i}Z)gM� nk 2W�'authors:A! basic!c blema :� \ldor5)da!�a i9.��J�_ � eA�t,� a na� reV ut�% lby?4is)�Srefer�[o� �entir�sharpl-�ed, way��too s6 usl+e �-� �� -as-��)]in�u�'�Scas� talk � ��eXs�"ten#%o1 soon aMxist�` E�\um mode.'' +\renew��8and{\thepage}{\�#n{ } \vs�1*{0.5 ic5*bf Dedic� �nd2C2 C T� disser�� %FI�!� memo�2Ge� e WilliamF$hosGerg�Denthusiasm made hi�j�/pif%lla�fri%K&�|ld Joppatowne group.hg\chapter�%Eine8<--Podolsky--Rose%� adoxE�non�+ ty} � tra��o�O�7uav,.-A� quit$ un�y�8�,surpri�.t�+ejthAg!61�"�.s�'� preva��,6��� ly�Ʉ�!?gh>�pr!�a� 6�1��e�WJ�s (�i}2Y. Althou�7=f�a��ji� �g�wou�"hs n�Kal� N%�F a2� analys�� is5�� evit� � monstI�2�"sY}�knownfb?Eb�� EPR}combi�  Bell*�em / !� orem��T9(ex, howe*a misper& among%F���[qG ;%$es�� nly} 4e B=��� flicM�M� "u �V ,!��Ocarefu�*a"�.� ��A�"@�EPR��%SJ8 � �� any} � �e�ex&=" �dis� X �&7 |/dU�i��-� �a�e$.��-�%:em. W�gin sa�d&n ��Alet�.m_ argu�A��ll@ �"a�} ��of:�� #proof�t�� !�.� 2B��N�e$ {Rev!31䱯����I�is!9 EPRB���$Jo �al in52�%91L�� per�)�2n")5s}ax.� work��, �@�,�publish� 1935,�s�de�/�B addr�e��(՞>ucu?tit&y#pa,>(was ``Can Q5$�% al D*i#of Ph� R� t�*C�7ed Co�te?'' �ATgoa�2[ w.�"�E�� � ,von Neumann:NM�F%Mc8)'6���e!<� ofJ�o�:Iis�)$necessary} v �>7>�. fm ,��BNal }.�"�^�in'te�<.e.�� "�.l��Vdi\ �f�,V�is)",EG� loa2 �1: ``W�8we�� �� -�6��%w �`� �VZAY"� ( ty�X lef+ �&� of�MR2Q�&��believe�2�I�x� ismvlz  r��d�2  ! ��-. )��5y!�(� )����=s�\>��� m�(& (Bimultane.``� -C''�g*n3 QR� � ! �u��': &� (empha��du� EPR)E at�!V ningK$ig��!��+��} r�!<r0��%=4M8!>!� seembbAVnq�4 : ^�y -5_�� - =fa�u��"} 0� ory}!P .��hem� i\d'mR��� y�,��cea�a/�.�!3� � po�?Gne!'ur*02-.. "2|+ "d�Q�.dYt�"U�)�Q(�5*0'9�V1suffic�<"�}I ]�%)����ajs� ��-�: ``ij %�(way� turbAQam|�R can d~ c�inty (�dL��"j klHunity)!� +%�J�%a��3��:�QXU�c> @%�1Aw WAPwe�l$%�: f6�4��A\2? A2AR orig�"X u Y �+2����d2�2&qy50a�#��&1�2��F Z""� icitl�� 4,�����}.}�6aA�m!��pa5 �0w�$vy.i� 51, �0&�.9P��,[p. 611-623]�.'s Fam�w(Text}. A ref&in�4earX4��@GD356-368]{Big Red}}e.'s9��,� 6Gե=� 1�R�a�iMG!43:l*� ���G ,  " ��|at}��O5�I�_of q�8.7ͻbeq�4m�!r?�&sen�leZ�waC��r�. &Q I�RR �JR��k E�"� ns(ce3C��H�A� .����z}�<�sDy k:EI)��JKI�9ft�5-@!�.��+ex�:s:���s���.�A� .�C4e n%�F�C$T_6�ed �M��re 16*Fz� �E \cos( �P/2) \, |\uupa\ra \,\,F,\, \sin( e^{iE� 2 ddwn3eq:�p}F�v*�Bg-.hJb2� - N�N �$F?8B.z� le�E"� � 47gA two} n&� �9�Ca� , Messiah!�< }ShankN5 }.}iaI� � � J-oeclassifiF� toV �S=��^{(1)}+ 2)���V q 5�/�vf0Ke�mG^{ W�!J�  CG�� � charac�)�by $S=1� � )�� trip"P �;�_{ST}$;�+z o nae� i�n"�7�&/͋three2�$Sg% $---�z-"J 9j---G*�M��wa�M -1,0,1$ .) Eg�2, �h "� bg8te= ��:6Bq $S=0H$e%*�z�*��a�Dr3�$�&�J ��z � .�- =:,>��! $�In fac��4� *�VMF2�an2���%J all}� � 1�u� ?�W�s�Ny�No�<0 ��m��O�-i |b\r eS� F[$�>� �A=-_$K5R6� asF� �'" � 6W.�-rW%��&I�� �rit� ��H%�s: 2�r .����� -rio�Momi&"t `$ P$'�G.K��# !�s5W]�!�� )�,|�� %r6�e����K��6?%�&x' #>UNs:���:pqRss}= B9"_UR ���!.m2)�\�-E��)1) Fe2)}*�;zss�Tm�R�8eeqX�J9��:sup�Ennor�>za�or &I \�N$. yM.��()�� �=a� � q����q1))riF*=�2+*R+a�6�I?��n"�X� �/. �-inI,.�3sP*K w6F�n re-aU�R��+%�W)(m� �%E��  Z M$� � � ."" ��c.�FŖ� hN X*�S���"�0*p[A�4j� I�&> Z� � ��/ �� FA.�>z�\\a�}Ul���� U�F�� FA�� Now $ ucQj!�!�%�6T2l� h�=�B6Ser� �CtitD� EZupa1*��AIv)�����@g0����%D :F��! d�1byUj*4H�<p}. Do so: �Ca newk%�! .H� J���" K 6/1��eft[ ]^�/2)e^A �A�?M�5!a�Ej)i Eq F] 5".f?>O\�^]a' & & -�:�.�y�6qb� 2� �+ �Ri�T2) �%�w96]�yT ��U-\%�b�F� � �V� �,!�J<�"��&3U\)�+ ���zBR gB� � - ��.� F 8F��\,)��9� V26�=�*�:H*":W \Ta�e|e�a�E2x�s�Kromu��p= a�Q� $� duce*� ��5lti,:I�H��O� $cAwE$$c \neq 0$��-Nng:� "2� eH?�(�w���s�3-1$ to���F�`(�.b�� ss}}���\� :�!�}2T 2�%O&N/e w�}q�N7}�1)2�~d.�,sOC.� x �!� � EUat��r... Eac�5�&� 62�EA�rv � J�Aw��an2LP&� � V=� 1ay s��p[�:�< � D��MD5B� $dro�e `$2$'�)R�giv�!\bRmͽE;:f\, Q-Z&A] ��-Ee>0�6WQ���E+B&` * %ss.r?�E6T@w�(x#%<� %?QMMA individ�/>�,9�]9%&�"M$1� !���c.� ,2o7n � A�Afa � a�:#$��H-I1m � � 6us c��" 7IhAcQ� 6T sanU )r�a�-�!�at.:3}v4 459\}X1\�al�1_��� { si3o<�9'f.�!*nJ�VN� ��mQKO,!��&�Zr��s�mp2V�@sv)��"�5qO�X)�*�2�*}. &�A8*Bs trueA6 pai�E\v�r��J�^%��\�a�1n �arbitrk)d�4ion,@.�+I"�(�&� } C# a&9��a]A�qJ�2sc`1awqB`I���8�d�,]��A*Z=��N7c:ed moi��E�rX1�31��)�lIi&�(!<�16 &�$��7Aua.�9�E�x}$��27"a2�6@e�xfOS�E�%e>i�A ?x8E<�A.�]n (=�Si^S#�e�Gt]�&�=��/a�� >�;If �;�LI��04t/![ �s9O �$J&�6i�)y{dit&U���N]ch!�^i&��UA���">/"C2w9 � ���l��#. S�^lyT:j'!^p�:y�X�  �4vTyzAga�81�饥�aBr%�rE)u,V���H?�#=I>TNETc*n�$A~9>I�_�wrh4� �;�5��Nl�t-��f J�<%X!��um���s�#.Z.of��anuM 8b!�dP ,�,mo�9��7wo� �T�$ �N';z��aR�#�'l*�*i��p��Y�yi}/& +�4&�^"�!�R,"�1*%HA�!��%I ���4R �^�b� for 5 V�Yn1)� �5�j,}�1$|%ijI<�!�hNAs �5�4jv& Ie� � il�T��<����E{$2$��to�.�B�)�"B6c!Y2�J7.� eeL&Q*20�=�, AR stru�oEP&^. �oC)3�EHecH!�A-&�'�=�#Y%��6"*� �J�H*� . TB�GŬuB�� is�.o%=��F�17ԅ�U�r�)�@�yi�.s�R��j���);Y%v�.�0��AY 6pi�o���\s�%�_�E�>�y�$J�H:� :� let�s \S66�7m#bel�rqu}6��� �:hN�3N+)��Lby ����� ��ł�i+@a!:o�8.v��,"#)��Y;",5eSar�Y�:or`�u .�0>/�I&N*O�EF�aF�Uought]be p; .~YkS�~ �PZ=�B)u$ �PhJ& Sb� r&��i�!-� Q��Q, �"�T�bF_>-X.j=ne�&e i09!��q V$} $V_{�Z }(O)bpp���o.�boof�80 A ) . aB�8��)Y �� +_5�i8[� !�rd#9v!u}%5of.�7*�<��`?�Q..?01965, John S.d:U !�e�Jf*/�2em� �8 ��%��MT1�K �)#b�Ds. a� �/Q\� ����,ua iP%�G�<}) !5a=s,w �i~��u*<X va�K��mjs3 s�h�&Q��9K. Let�"fix^.n�:�*)�١5+ ace,p ��2�".$ca},b c��e;a���@�+. R]"anmg!w!E:�� $ �$A(Ac ta}�g $Bbto&L5��,)�!L��e�`nsAw���j6si��2� Z \&� 2}$%Jshi@l $A=\:� rBB"V8! 31#w��ca,r�ToY1 2P1"va�<P�=As61�nkey"�@N�veB)>� a"d0&A AN� ���w2Te a)M&�X%ksuY!�.ns�1pin��� �Ei� ,be.CC� 60�\4i�4W*PU\}*�*/C>Ai� � ..I.g��Y�2�!#B�� h��r��@�L�RZb�g�s:ATse�"ap!�tus s!�q$e#to�b� uL���$�a}*"�*\ )\6 s6 ' Db.D. W`2k�9~G� F�!g%4.6�e����Je� ,W5NFk|e ��2 �}� �b�M�5���trialA�e averagQ fWs o�h�-z ��*!�j.@��sIn&�Kw� �wF? ��OM�#in?yA,�E�&�1s-� a}, -u%�1="6YU$a��;5z. BQJ� .u� ��4� � , or)� G%�)(�6n3X��:q4ula $E(O)=\la� |O\ra�(!u9�cF^sD# bed���\2(c.�!�-� Vap� r�qI�5"2�5,[ing: �$�{1:9 } P_{QM}(E� a}, b�z�U�a} E�b{ = - 9!Pn� b�H&[ZCQM2�uu ��H�caR� !��e'Wd)�s�+-�1 :� e�5sB~ �{af��9�Q9 y!�a�an}at4f:�P( Wc)H\int d z \rho( ) :� :�� �{"�[ CHV}�N \R� $i (\lambda`{!^ Ma� �rib}_�A �. N?�)%�* 2�* }.�=1Ex� Norm2eq]1U� �i�"�N2,"Vŝ�s��&�'%-is��ati�1w� !>- p"sJBQMtm���$ Cruc�Ot�18�0f.�Q�3�F�E^�the.�!��U�.V��a�en&�  ��9�D!�ZZ2Z,� �6ѭ��z"_TA . T6�r!FZaL �,>Na��-1}g }\fogd�CpgE�y, It!�easŋ�#� �1�]I5� satisf��n�E."�wY* deri�d�>��NV /1[,�]�� �B>= -.! � ei6,�Z�8!uvPCKOeq A |�}�}en�R�-���ɒ� �A ��0.2v6�[PC�\!�eIH$[:�]�` = 1� � !6�+Jm- :c})+)6R�>~.�b}) -.a}2 c})�( e-Z�jCc[12ebJeN&m(ڃ"�& � $A,B��pm1K%�a!Nq |:. b})-:c})| \les0R? ��M�;M�t� uS e�YIwQ-�)� A@�.�� ���(q 1 +Q!&r)N[ *�� ѹ�aN+�%- *� �on:fer$D& s ``J�in� ��J�4mV�H"�M� &�nge^i f�K T >M&� � >�m�!c a�F �^s'Q | &�4 -./�LsFr, �Fs ��)-K%����2 (!k��]M),�`c�;\��R�F� en� �#�O[-Zt�s�zA�R��&{ t�uuX at f�c�*5��� &!"}��i�D!!�N�, $:�,ə� �"Ac Y�,5J Ba/1K.�>=A�F `�"a heB�aUfJ�1�� (.�7�� bu)�_�p^X&�"I� )UrnY�& A:;Bethe},p;4E172]{G5sMan� WXJr p. 291*QE ��!��at%"]4T!�e ^j�k~ h:.U�j"�9�l"S���K&� �.*O�� � dox,:���.&U�prunon}}"�d�D6�!o`� foun�~�""M�� e,���mx *� ne"8Aqy lyu6E�F �*S( S�( LJ��K��� >apeG�E=<,�XK':� WxPs cap8of immed�tHW\��Z� 'Bk%V� an�wrtnerP]C�{!�vo�h��if R���8aCAA66R:{|i�v$"hw��E'N .6�P�ny(N s Q7]e%�!�!_� �.r�� $P$2�*��u�}.� � �uh!�bey���V !�mm���%@Q��u�A 8#2 #�V�ma^�� �(5���"ic�}nxu\�a�%=F�%�I�i.� %y�N?J���y!�'2� �Co- e� me?":��.� �w5��&._9&a�C�� (�>�%%=�r in y �N��(��AEv�%e ssŜng�]*`d X4�N%a�liA�%% $x,ygi (s��2�#4=90^{\circ}$),E! Z$i�\=6)?x� # $.# J���FAhi=12(.�yŊ%h�  ${f�)2f)��2'c��fr&S��.+*� = :>�5 |.2�-N  � o1+.'qt �* in vio��rU�a }"k�-Q0�"�i����>k q%"�Z6�i�TJ��16� wɂE�e >�s &6�Z�l.}�Aa��u�=�&�SW�c��C� �o�La�{mof��}��I�N�b"� >��%Dr an i� uc��Nc _Xn�J� clai!cF� �n `6� �Z'� fals8RJ%��v <lread|N�` � �W >��f� s (�IE })R9f!`٤  [ a*xRlKof���/�y!AsO ����%��$Vf� )v!;>:Ej��promp$1A�&pn!e�`�ianU����2q8�%& <(uc�L �߱� loo���!ofF�`�%U�'notF^e"XJM�A.�u �_�/� %]xodoo"Z �1r!�\)0�a� �!�!Ya�W+y elf:2�CV" s�c\I!$A*7'6�set�+�� �ap�^��|�y$B�$O 6Xa�4� vW1�F�a1�A��� �vh@W�h] x :85nb ``ac*�tal'':� CBB�/precis� td6 :!,aj!y� � Dsis"Hit!��b.x Ӂm&�).�j%didEG�b��E���VBc J�Xa� s awA�:&)l�x��Kga>$ !,pre� (m��)�+b{d"P� n�+ed�VInstead� �_nx\�bށi���4 ``g+r݂%?&�+'' in�;n� B� ``��"}Js�o �/Rn�lch (> Pory��re�D5�zA �:��2�s''.}.U2,q7� ?lE� �,��i".�iUn2>$``escape''������AI�U�'nce)zi���)�AaI�fyqi�i"� ��iMof %�}MF;. ��&lgInt)!ion�;�9� issu��>�}2�5C"J~�]*.)MJ>rZiarabici�+t��er {1K%nE�I�a� �g��*A&b�E� v��>dofU^"T0. Our effort7 l�� 7� *��� *fof�Z6 �X ]am�!relev�Kl���' Y�srz6hi+<�&��Tbea\�ward F� !9uc��?Wid�&u^qa5�-�Z���8�&�D+��of\**2b {8}, A. M. GleasorY{ }, J.�* �tb0sEY<J*s [ �1�s]�$\�nis lac�eima�\��� Ac&�~! by Mm%�c Re���lsoF/!T��ac �5.onB�. Q � ��ac�i��&22�ind�,e�%(� unrE�a��dismissoo���oZ�of8ESi�+(o-Fas].)[n's]*7icism [ Y�*]� derv>>�av�� E)�p speho1�)� �or! I\"'�� mpVg!�L'o� !�� �4ep 1Yp6a@s�Ktyo.} *�PE�Tvai�_�s��o>di�v�n��+y��� !}�{in�0 bibliography�&��75-%�"ir 6�oB� {1974!Tinfante Book, Hughes S�2`e Math, Jammer Philosophy0U rminq. V&�g*�� �%� >+"� ��]߄saP Born{uch-Pir.�z@_& R|aca��4���aIA0!s!BaF$� �<,")iMarket� �b�II9iI~y/)bAI�)V� way:� ~ { BR` ac�plyaal�'��"�h to�>�c�*H3Ս��e=�!qa�a�#loi �-nqU�s�Sew"V3 �`1 �) !�!�s>,ofU&letT5!���&f �0y"!�` !g�4l2�� 'p�v�?3�>=^a�D�Sc2q�-�P2T Si���"�  fa�ɣ�vP4e s�.]�as =M's!���X!d�!B�GF ):wo �rt%/fu&�u� �s:� JVe��i�r!e�.�}. .fi24,>mq} �6!Or�! m`/��^/~�� atj ��e�BNY� E!["�? !Rept2�!;e� nt��sS�u ency���5/ �� isT��A3�O2�.����,al��SeCp�u?Gd �zA��5 � n aCa goo>��2�Z d'W��R� tKyksG of &�yJ��[~v 210]{�@����!��!E�"c���wkbv6.d1behaviodIatomic oW2wf� �a�!�kY*�4r!qse.� ������s u� +K"�u!�earp[�:mptg1_!O� A�>�}*�.2�8oaq �E�� .�s�?�he_ ofi8��AƁ�u?��fJ�. HLttyp�Q/ ]��ex�!�t�s�$ y *� 2�*�E6��.� se��sJ�v8x~wclear[ s��@d)ne"��%�&� Y�!K>� �fer|�at �s!VJOf�LE�out} t���-6�are�X>j( 's1�^|!�"^ /\� brief${i&d2 of]'iV ��v�'""� 2�, 7 failA conve�i�� ��n Zn �"s "Sg���b� �A� .�A��2 e a7y))���I%��� =�R� !�dc�@Iit draw_ �$p!�B�2D����a�2�'64�>�&�E�d. RY���\"a E����t��A�!�leƙ thei�V�~�im* ��in of m��. ific�#%2+���~fi�/.I d��)�q�abe y��c)�- v��aN��a�sI>m�a�� �proz�BV1 dub�onEbesJ�*�7�B"SW��؅=.�!~� �&� �)��6d.oc2m):"�rb�|&n�+�pr��*~ �zt+)�2�dt �"c .� $ exhibi��=,ŊAc�Ic� eve#d?neMk5ag%�o� ^ �sY%a�r ly. "V|s&�wER�}:l_ �a�| Y #���aMa(AR�A";)�My)�iL�d|^eD6] *T**b U)u<bec�"� P�M9�W).T �;�m�� .V*]n*v�m�#:8��tuB rwin>� � Mrofg�2��k��MCamb16�2dA�E}��v,A�f�!4���``�>th�:��a�5��%�a��(forAr�'e8�Jar@��%�e�w�C�=w2(<cte��y�=�O�1 o4sc�6�au��elabo��v):` trulyen|�.�. 6NS��=[ �E�emX ��+!~N�69~�e+�PF#!��o"�2� SA��� (mis� nly)!�� ��� � ple, 4[p 48]{Ghost I�Hws�:}g�zWorld:�& 6� Claum�!#ShimonyQ� - }d��~]���at"/U� �#&�!5 `�F�' amoҕT�p�X ms� fall�@rA�1�(� !� � Tcascade photons, Bertl�� Socks}%�7� E����;���}�|� �a/h� �Eoy�S�<Y�)at i{x#��}" �Z�'&��&k%��5��e��mu���o6��thaS�(r#. W3E�"d5�VA�,aqY��8�)�AI� "..t� EPR.�5!���2 �A9=JŀJso�x�60&��5� x$&: �Cosmolog�c}-�It(*y-U ��I�E2�Mey[roo�!inFsMX%���Bs��_ T '' W�q��5���\Q��I�� &�&b��9ǁ�`I�=���tBg Fg,��ui�N �$ Baby Snak�k Tim,Wl dowsIl #�^$�B�, V����7* Ubr � NF" ,  ��� t� ` $. His own �*ˀ/&afH�!5a NI�2!� �.a�+i�6a�V=��@ork�;�j:#'�yYH��� ��q�`F> cat'*�a � �&� M �"��� �B.J�6�^ exEj��u t�%Wv'�5 ��I�. He C@u RKA���e<4�4��t.mU^ŧ�o?.�6N~�c� �rca�0��� d�:A.,y �ly�$�q-� � .�� ���:� *\�A�W��Q�K f.�&�}�6�&9#*�$!i�!2�i"�G$ Sub� Z�3i�"!�%Fi')F ��%=�V���0w%lll��c�ua�dh6�Q6*l ajof�AF.4��e�…0A&h#+H�� HeywYA_Redhead�#LugubKFe�*��� r�>2Svetlich"} To�7P��^ G6�") s"o] 4a3u2v@ A`aQw�%| maxi��yU �'"K=S1�~� � �a"�b��� e"{odo��-U�S#X*&m$o��Y�=�e��K�%e"�9 � �+ &k�P.}&�(:�. �q��g]�%55%1:!WL1 fak�i=�e��tegor� a ``.��out in�2ies''>��be�� yQ��e0zA�� 7."nQXl�r�8��p{&+��%�Bp#A }} It� bwCn�ja� ���Kx�DBP�&�R0is �!in�x�eLVal. Lou� D Broglie's 1926 `PI% Wave')$y6�)�d97, 67:30}. A�Uma) AJear�I�^��� &XE`i�&$1953}.} i&^"�s ^}(���am��A�%>��l�Ha �(by 9�� 1952N+!� +Mg}.}�-%��=)VA�2�&G ll Six �s}&�% onJ,is P Holl1b�x<encou�Kd.Q himu(0c u�( idea as\!)���*�(y ``�"-,sZ@ 9*.�Xvalid" ofV�a�� eR� �+Tce1)+to1' iv� �}scripaVR$ 5�9��3~� >&aFt�)���+ n `Onto"�,�"T.'v&m:I'*?� 1993r$} g Uaa�c,ed primarily� �%isj�bj.how��aJ� �4ledge�5u�%i�IUch6�"subti[�ourE��An �! 6!Q�1Tee''��n�Fe�<��mos΋u.5:P��, ��bout....A�)"y*9+� �I�2I'TUKd�Qt��� My�yU>�,��A& ���r it stocha�6�'�x����#� .''�{M��4r�^�& � �"A-��o-��=�(A�~vw�U^� d��*�� *�;@�� "�A!� 2�=-i&O�.>-; ������fn*}��1���< I�'"� likDz%sI<��a��Ging:h667Z�!"�quo��on}Y�� ;mg;C �d�fAxnci��(6�'s)xit`>.�� �)��^�Rpr�(mŃ�/ all Zms�3"&>!Ap(&�i)E�*gitY osed x� ��$ ny a]Xi#`�b�ti). H=@*��q saw>�as�&_�hM� �%'aHm"C&&b%�>�� ���k666Z�� I am�[GD��m�3v6A3C�c�gA1a�al6' aGempor�6A!G��Ta���ͷ���g� ory)��az &BI)� � s.`'���"�2�fulfi� 1�� oal�9� ZA�2�G\�7�QC6���s.� �e��p���?Be='��'A�A#�W��&�:&a&�!xK�4Q\ �lIMisd��!� o�*N:,I�A� A�)��f%ImVany�v�g��>&�W��1���9 Iso.Uew2�. DN�.�5W`��D&Ba �� �b 7t��� q�ϐt�&P x h motiv�)MA*R���no-N��(� w$� B}}d 1�I�! ��6�� �;sso�E|V� ~A=�;8� y<�1erhap�l!nse|�slmcci��byf3� : �B� N� Wh�,�p� w�"m% [B�] ignoa�Cext / s? S�[i�t�ea�`�_ҹcoway_� a�tidF�o%k0�{ac1*? wQ�=eT vagu�,�Q�(� a�:!}b�.#�d upob]!8r'&**�s � by delibe %č@chA�?�Tndݏ=S"�7Or�q]��!�e�}�� �� s� �Lmai;�ts:�dev��*'� � !h �$b �#)F�# 6��]*0�� \7 F�:�� ��F/#; ��jew#"��,��Z*�� �y�%�:�0&�)�r^�. 0� llus���[/A���%_=. U8-Չ}�$link topic�\a���q o�����#*�,�K2(d�>r%.�$vf� �r�UYB�*R"\gC>(d \ks goes �GŽofM*���c*`N&- �3� 2 �5.�"A�" �( s. F�"B0-1 �-5�o"T)E�J����1i� we # ``� ral-" TWiy=R�#} A� H�D5("L��%�1�w�9h�4&�$"�o� nspa%��#acA��Bm"��>=��F&�"� )| �_ea-QO �0�C�? � cE�3 e �j:�>d N���6h2!0>����te_7*�"A�08���( ���)n.D6%2�)� �so�fo%��!e1T9� OӉ�.A�*+�JM�E��V&�$� �pI�i!set8!���Ce2x�uA9��s *�  A���u� r�R's^�&&�.��Y3.�of `\es �'� ��Q6u�! ��. metho/ n F� ;e��Fe %j1]E xNL%�f)��m�we �F� �R /,oa��ec1�,����+�0"4=�. Lik�Da�(ivICZ� "z�3�>�._'C}:�� &2 �A"�*��)e .8+��28 �s.2ۭ;&A�]Cť�]&P~mw��AZ(�C،��>ib+�ul3 rom�e;&2 ZhB�:�!� �w���,>.qmz��s&[ EPR/!q���?88tϕ�~* �&ir�9gy�+Y��`N�2tw�D�"�@ ;1Fiverif��T ��-�,� %���� must T�>���&xN�[ ����� 2fO�3�Le*$C��A�� 1, 2, �I�tofB�.�=�.n8m��g��e�Q|  �L e la ���.��F &� o9.�� ���alK2�.Q"��&.�z���and��"<�}'6`*N��y_l�"�!�par� aj �bI�/e� 0 �A� �-�)�;��on� u��.Rn�ѷ�a��%b&�3,�&� ��2��Q��E�&i�a??%�T�de!ur2(�ivy{x�`di� ed v����� E�*}.��-f <.BK��p5x-9%� 2�#IVa1�s%�)y-� a:�"��L&)\� i5�e�A�a �bRs�q@2b�)� )eR)] 2^]!#~��S}= 8!po&=�c �"A�M�"�%/ !�"O2ca�#��is�L9 c":��h{qN��\)& 4�a $\{p(p_�� p_{3��\�wW� �#oW �Dirac %�:9��)11 ���tke���i;ʁ�+�a� ?s � psi � �, \mid �$ ^l�$ 1}6,���MRE)|$]r�ha�g-� iv� $N$-1�Q�i�6e.��abs�hMh$jmDex-&DdU=�-g\s�p �(1�q}).�San *{A+����2�square-�4gr��zs.e*Hι5q(�$6^..A0A�t�on&�l � \R$^{3NAU��V��1n�.�� ���cq \sb�A\)��TE mid�c=Bb\�er� dq} � ^{*\��q})E85\ <Xcfty �#eq:L2�K�_�Q $ [Ddq}}=( dq}I�z2})Ё�0g�EudOZed ��!o^ t��v�s�5� $c \eSeR$  (� neq d굁%�Ty.&����{E��t��Vz?���s �at�S-( s +��]R(%Ny�1�=1"�]q:psi-�ia� box{51!]-"Fr�-.�2xe�ovq by \�4break J ion:�'�LW\e�al �}{ 6(���c��R4$H$��q"�� � ends�#t�d��e�ͦ�%[i�)�� R �i��F�� c!�0l�~n%V����6@a��ps_�*Qnf  �+�Ù�h\� 2���/+%m� H2�� ���� \sum_{j} -�|aa�}{} + Vy�EL5�%��po�3 al e��&� WeK��-c'}���px��alɿic ��.�o!)�adBB:�so�Iifi� � _{t}yy�B�� %0+_{0�q���h:�(Ru:o�<�pA } As� � )�.� � ��& "�� MTe^8q��� ��Ar&3]1 -2�a kbS?elf �� tact�%w6/#.��h� �gK���� j*��e-a� p�i�O{$c(B)��;� w<e�Cest!�� aI�e˜rL=:n�C)�| u[*% metaPS�6l��)`conuH9-�!r�\Cny�aloa$%a97t�!?~ 6;4O%m��2J�Pa.�WU��`*R �@���9����s ` &;�' �Bj��%i2�by�m:��y�� f7ing.["Eus? ��s�bleE?!L���-(erchangeabl8��"��6� �4I�!�� $O��a �v�T��ڌ�A� �|N� y%#7�.��� o�:��O G 2��o u��h��*$ E��{����\mu �f'A��e%�!�$|2x� � � co:+�A� ! jW labe29-<. ��Q�� {\mu_{a} To �̽b��ase^r�%�s9� �)�, D �!|� e��yS� �>&�Qh��fym =�hngA�^{ �6%ub0�{"O�a*Any� ���e� ��orthogon��L�,� �A�6V�W4���R0�[i�)� �  b}$. fq�!n4N.qm|�Gxa�$�)f� mu(!�!k2 $(O^�� OV� -z�I�E �{$(%i},j�}\ay��D�mut� ��"g [O^<]= Qj}- i}=0   E��$� ���* " i�s�a�L"� 2�b6�p p \pket 4� \mu� �0 eq:J)N$-Eig} \\ i . 1,2!1 "̗ 6� ee�.�.��}I�e�d qKor����E� ,�� . 8}.*��k=�"H:�"Q�"= Ŗ1Z �B s"��=I5$O=MXIW�T �$\bm =(%l1},2Vsot$r��n�%ive% 2�de�se�G�vs�#d ��s} )t�� y �Lmu���n�#a BV�51u+�F4-���. -.8W�a� �ys�T��m�edt_a��0��� ��e2���o!�_F��>9&�3I�� El �I< �$ ;!� !��)"�Y�F J��aaU/������s�w5w S-��B�=�����0�by�f�`�pro���o�6�[+��O���OItO#bE]L'!�our<er�8c!��Q ' $P)/nD�A7"�N alxd=f:A. w${{_{k} � ��ch�a+�/��n=;k�<h AA&7 ��bel��Psu���mea�U5I !c� � 9���%��M�9� 7A�oneFձ���d!�) %H��%7we& 2� uٵc  �{E�ni� %5�AP1�by-|O=�a} L)�=OG!n�!Y Hava��w-6� ���km�V� The�8 i &npo}Qle�:lH%;2�0� i�1at-�� � stri��A�!e5�C$.D e"*� !{a C!�b(I? 4\footnote{A me�asurement may be classified either as {\em ideal} or {\em non-ideal}. Unless specifically stated, it will be assumed whenever we refer to a measu �Xprocess, what is said wITapply just as well to � �p} of these situations.} $O$ o ��joint}-eigenvalues $\{\bm_{a}\}$ for .�8a commuting setc observabl=�>(O^{1},O^{2},...)$. The second rule provides the probability � .r,result equalv8one particular ����d: \begin{eqnarray} P(O=\mu�8) & = & \sbra Pl \sket \label{eq:Prob} \\ P(B� = -+JJ J8 \nonumber \end�where!�!dmer rAs!�!.,of a single 9n and+latter9:� . As nsequenceKthe fos, expectE E�1{:�AE(is given by!g$q E(O)=\suE> -f .`)!9%tO 9p( Exp} \eeq 9"lasQLty follows from \ref!�Dirac}. El thirIk governIjeffecE�2�n�Dsystem's wave funca1. Iex-�at,.?!ded! a differ�LA� dependI�ӅME�er!�s an �UA�n�O.d. A#6z defiyasS for which�2�'s m afA,6G5� Az,(normalized)��je% A($\psi$ ontobe}3n�N�W�&f�~!o! cedu�s a3u�!�&k-�9�. This� plet-�presen�� M--�bsI�.�Ddiscuss below two �ale&� �*A^se Ireduce�J somevsi�r�?�`first2Rat�%hE��de �te}:�e �%�� sucha�9 are��,-dimensional���r)� span�by�( ��Q�calledb��I�%-�� %� correspo��to '  $��$ah$|a\ra$!�,e operator )aq���to �B�% is writt��s: .=�a \ra �a \mbox{.� IŶ easy�sejaɽ� ��in�GPsum}M�iE.m. acE!�A�=�BI�'nO: �O&'-I Ƃ� �:7 6u�kbe�x�Po9�!i then1b* = |B[psi5w|� )n,}+*) Non-�in-�ŕ!-2� sub� t!� }�aM)Qby $|9Icq� aperhap�0most familiarAcs6 a�han}� �is usu�u introa�dm�in2{e�quantum�ory� Fin?�r�a [c -~.� se�es��iB& sameaQ� , � is� �^x ��Y����Y  a��co��te8}e�B>���y*%]on2|= �� A_�>�:� M�$/ i�6� &� 2#� 24!2 5 4ectly analogoum�o�y6y=�2` our�+io� A)�of.�. \s��({Von NeumanW theorem%�hiddeG ri� Von}\ A�N {IMpe &�}e�Qj!�\alism contains features � �,onsidered ob��<\footnote{J.S. B(gtfur� AX is: h��%S� mechanicsA�IRunprofes!4� (\cite{\ In Bohm}%d[p. 45]{Ghost Interviews})aeits lack!p clarity.}a��!�a�a�)�Ysu �vity} AJ0indeterminismI� ai��develop��>��Qory91S�6e:!�ian.bov �$ great suc�gtAqE"ya�e�it expl%�1fphenomenm� without}  1�%"� issu� h>uis,|course,� ed in sevg nsI� ork �e�K^ itive:�C%�)�$Eclipse, D-teE[,4 Imposs Pilot}!� ;SpeakA�}. A rec&eA0 was publishKN.D. M%�o has d<m, to popiz '�e�through *les�E' PhysA�TodA? ,N leceb. DG :qi also4 foundVA -ohEMq5, $1993 Book}%"infante 51974 Be ( Hughes % S�  MathibJam= J 4 Philosophy}.}%�o�P a�P�>!Wile) mpir�equival!� toaU���,&� !�es%se��. I�\�� �� we shall�d%�� !� earliest A��� addr jM� v�o quesa�ch�he 1932�1ysie�John v��y�The orig��uD)^0}6of.M'sF���}��I>a�} �? AlbertsonE#luciS .T,, Jauch-Pir�Z� )PE�mSA�elaboratI �'s � ~��m�e��!v,A�E. �adear�� limi� s. 6B�sappea��in �!now��$ssic book # A� ematA� Fao�%�Q� ui��is ?iS�i bothA���xosiA"!�t�te strue�����,%d� one R�YEWit!� chapn$4Q� )Ywe-�Q�aA�59)Dby Erwin Schr{\"o}JME3PiW Si� + �paper!_)�`:D's cat'M adox� 1�, but��)L�vy ppreci���"�oT !� } or"� �#@er significance, ��!]F�geiz%�1z`Einstein--Podolsky--Rosen�ebeliev"� is remarŃ)#( could have2Z adv�%: stud"�e���Q& "' , ha!���� been m� wide6L.}�i�I�!��E�!�hF�a�*h � blem6Qε�Q� ��&&�typ state  evoluaB:)�"� :��F%+ �atI�( occurs durB 2� �-:m�3��i �� �� A�Ar�"�& V=� lemA�the1-a�r�cIKi�se%$5�. � A`�� 2F�� lem,.1v� m.�5 �knowna ݄*�-�# gued g �����mpl�!< very��onga�clu�)�no ��UDy/� ide "* agre:��Qgy: (pref#Hp. ix,x) `` \ldots i�n��lan)l(by `hE� paramb s')!�in�atible qcer ylŊv�da� $al postulaNou�&� .'' q author I�s:� �  324]2 ``It sh�Abatea�A�e need�o k  i!��-sQo��� �,'�Low A)�Aes��* I'.�`c��n n� ( be re-deriAk%�th help5�@concrete demonstr%��� l '�r1(age 272]� *� a��n!� arlyi��GwHer] ��he impa�R .s�is cl did �7h ��in 1952David� K a� v�!,or� I� &u �B� �tA 1966,&~ 2 ell "s �:zed:� arguA� ag1tm�a� show� t t� in error� 9x,AP!nw��n&� Aep*6f�sis��ei% re2� of aF��D�y 3:_&K no-)j-9j1 . "xC ow!�Olaw!�2 F �Ł߁`�rLwitFdescrip���}�a<�* � bA�y��� nessd ,T0�'s.tɹno�:Je��{al.HE�&8 ly��has�A Q ,�f�tA�1� iA�I�h}8N� � wa�� aNproof���6E�!2�� ��Z%�7 5� i�A�%�a':m\EPR} ``W�we� thuse+�Zi6c"�p�! a �q!�2M��pLaN�~ye^ lefte!�U &�r!�)a2Xexistse'� , a�verca5���is{����h�=�#program*a�ndeavo9! suppl%A%%O.�,i appa�A<xa�!B ! e Q!�G ocating�5LBa might��.~to� ove eq2�&] -�q�L=}čy  iA ( �'A�a�уd� U{:!it5� �st� e�.�>��UG� s by'0�q�)�*� "Q:Q!&)c� W�J1A is�o +:��$by�y� ly p�t�tic��di�n  a��:��� �(ities, i.e.,*��uL% s ob� �rom���6�p �s�3%� idenE} � 6�&�!�$� \&aUy}. (q!!8i�a�' g�qdisper��u�to-�bYis)�%�-avly.). ��i.�>� pr9u#ea�"o!2� An=a�$�]e)�umBɋ iA  a=�!OaLgz&�.K%})�&4 Wpge�)R!%!� mixed !Ue��ecomes ##_%� Tr}(UO) `eq:Eqfms �ire $U$a�aa�����I~pr�ty BZ)=1$.� E n�5``dens�%$matrix''.  %zxample,; 8378]{Schiff}}: 2�l�AtO  &�eEqf} ~. � >w"����"!lwhe��| ��> 3��Mma b9�f� u�ve2>!8AEt �#�� �\. I�)�ere truE�C�6:�E*---�2a�ng�*�# an! �al��a !$ $\lda$---� a]'�to mak�J�Z^� E ach*�(. Nota���m��)canHex sed2ly����!l c�-T� �a@amust U a ``�� map''"�'�uaA�& "��g�!�.:�T.  $�2� a oO �� � $V^{A�}_{!�}(O4+ *K */ , hypf��%QlA� `&8FA� a ``�� -freM�'',x1�2p.I�a�s�Q�\ �>[inN�re�8iPbeH!�a��#exhibit��Bw��J� ��A=m taki�a&�$�*$+ )�yN��ź M �Y>���n6��as �"$of sufficiAG ��iE�Argof սby,s�Vn� N� )e#�uma�e�!m. 4Leղ�"",-:a S!\� %k(�42�ormul�#�+��Boa 9�]�e���P/a serik )� � retur� %�!#:�qen��Jz�@�� QOu P%O�i�#e>{%it���0Yp� �M .2�wA "oE� lude�,�n�+ocnvolv�"R,�i�-�"4s. How�V�!� � plac�# n unreasoc!�"tr� �h� -�!�z"���� 5  }P e"&$"�&�}� aE1� .g u}-�r*hX5oaA+bB+i24 = aE(A)+bE(B) =�Silly1  (a,b�2E#� �1�d $(A,B!=�EE�&i�%+��:%9� 5� $P$ �v5n-neg� :)8 E(P) \geq 0 . &� Pos  1�- "p ��O AN%V2�Bn$,� ( �)}edC4 $1$�I$0$�s�+�pos| ks. Accor�5!�;�9 prem�/��EU�1���v22 &�  ! )2�� ;Z�A!�A�� �(e# !�2?:G!&"$e�soY!"$q-tis8�61 OA!!Lw� �  i4� �-Y.�6�+tra�forward� "3�ng� ]Y�O$1&�,�u�7 �it9&2s. D�2 $A$ � $B$1�rel�|ships $A=\frac{1}{2}(O+O^{\dag})9 $B= !i}(O-",� ���a!�conjug'"f $O� nm�easily&��A���`Iǁi� O=A+iBB�W� �3�ݲ^{* ) C =��i�ߝ E*De&,�mi[is6���>��&A�s T. Fi5!0��A�sv ~�!eq�kA� have�$�$�&L"zof� plex�!ity*+ G�s $�n|��# e1� H� � Ig$ř< a�u� Q��0�\l>� '.|)Da2aE;0"�Nowa+iu%Q|���.$ $U_{nm}= �2n�Gq�E} G�l7�Q�9�O_{mn} Z f_{mm}=>y�Trace*�x��Si� von &,.��a6?4u (O}�\.1��n:t�O.9}&382�xac/)�f5.D3���� � @*� .= �&� =�P�Tu�= ii=_{\chi}� $ѬM�:�0 �.bo_!�  $Z$. Us��� $E$ "�2m},A���&�� ��� $=s�)=a �4t�U  �$Qo"}��s&a*� pionVr%�.^;#� B�( ${\phi_{n}!Mn� ����B�A�UeR =��� � ed, �Z�+ cho�1c>d�g u$|%9tself!  &:. i@y 6.P�9v���3\mI; �"�4= 0$ ���� $| " �ex! �:J KV�=\�chi | U �@.}�5RC2=�IB:� BP��IP 1;�E(:�: , itv�� b/���!� B*N6�R�s:�eS$"�AWAu�Hu1g�"��tA�E$&CqB��we a�:�)"��=�Jd:6�$o6R �r�im �A� -�Vonimp}}$�%�a�6�""�#!$.TofB. C�3.*H �G e�+� :F�>Fsi? phi}�;=��q iu2��`�@=P,8_�}a��PrݙE�As �!iox O3u.!� w��< to c"�:*� f"����somA&� and ,it}mapt&hir"�We' N�A�C!z:{�Ŏ� e �e f�)byF#6�5dV}�obeX�i�, f(Fi)=> f(O).H111�� Y f�Yy�=F8�3�s2<by�'��r!��� ${$$ m(>�$ 6 !�M�f"\/� zmea�g)��$*�vRFbN2  Thu� fZz�::II� GtA�we)�����1}. HencJQ.@)=B�qh))ah: �2t�D �D�+atE a� >�M~hi��?�D 2c%xB!d"�W a�efH$0$ ox. Re��!!B=viu&�(�� a�M���� ph��r�R��& N���j��5�) .��u��| Uq= "}a5�GAAe5 or �2�waa�isyHpE�  |`�? If w�ry �tinuous�e��z� e3n4vN2C%]� only��lvaI�� ^=� �9e $0| ��>Tis��=��Xx tant},R$.z5Sz�=0e  } \fo�C ��5 hil$dJG �-�=1~G.A�!.� er holds &! џ-$� "1 zero.&�e��)W�oT�� fin!QE"�=0$; a�KI� conflicts�R� *� i�I 1$ (�~1})� mil�- , if�8�M$8$IiGFn)H}$�Fi$U� ���8KE��1�quifL��itYFds�.�&U 1)=n�sYn� !d&�CA�of �. "Jɬ�Lb ,D "��%VR� G satisf��/in� f_ J�> (seeU1}, "1m)i]fai�� s�u!Db�H11 Eso��� c �"� b"/&tIt �#&� % !eM-Bsb�o�KA�outf'!|��s�?facM�j� �beݙ ə��Oyٟ �� �,4*>Es�ѭ$.}"ci�A�2 4+Em�tr lŸ I,��>�)h:,�#to� ��3!.ory*3325:3 �bN quot�}9&�" not,�i��Eo! d, a"�&�x -interpre M!*# u|#�@---_J �*,&� w�!t �bB� v�7 falsh+ orde� at an_$r.n&�A:el$-���P9a!�A$�&a�A� .�nd.% !;*� Refu�6�1�*]P RefV< '*�,i�=U�6� ��!,d5e�id��ois � A8� u�6�"� -36� i`id�.vc-��2A0^by �0'Q0vel�AX]MQ$�a �Afulb(�JcouA{-R�:��)�Yby&�3'X< licia3. �ell2V==t's Q.S�RnowU� the �. �"�7=g2�!�_�"�Mas�H**)K�onents:{.8Q*SA�of� � �/oh o*Bc�Q- said! Z"��c:/I�"�pJL�e �3�he&�> conn�2�i��ema�h:)�5*!��3G(�)Xի�� "5� ��& ���q�MՅ�M.%�1Zo25(3 � �@�-:uXB!�2�9t!ore��  "}+� &�%M�'7  actu,+�2s?U�N2�8#�M �g>CL)-N>�gll��aF%�xQ0�@se�& departA ��)�))=(�?N r g-is �=W!0^I��lM�A/FHRcI. G wish'y�e whyV9�5qI�an un�V�>�%o do so��9��in�/�Dulv$�Q"iK�%&� o&�&� tab� ras��t-V%QA�^ gnoSe.�m��s 1!L[Z��)v� �>aGE�G $E�$ \<)=.�$ r Xb kW\{�$ #\SJ �"�$$\{a,b"a��in �s�/D r& �%w� BoremX}*Ys. Suppo Eo�0!)2� O_{1�$O_{2}$,  3zX�KY��K��%Ithe�':�� A1}=P+O_M�c�0i/�qB�/X�may m�+YKb"� � ultaneo..�.>�� $\{o�,o�3aYE�me�a��z2�R ectrG#�-TBym��&� �p$Joint-Eig}M�d�=.)YR_��|�" �%� 2� >� >�)z,%z3}Z&U�%=%+o-�����At 7�Z!. �%ݘ�---m�� D�. *9u�� B O)�Vo.�&)1b!tE� ��!� )=E(% )+ 3}�/OR(DhanBm)w�Ň a!�A5O,P,Qa� `!�$O=P+Q�e�!.�$P8 $Q$i��iL�ih6 $[P,Q] \ni(�R�, %:@ne�P$hS $Q>&� % =#o �N��&u@�"z]X*� ��es2y&,.4P s:����Je�<d� nct}�er�t��`]�U r5!a�|�a�# no�"='�?!z me�e/��= +E(Q)���� A��?�[�A��s��%�V+! a sp71&�&$�1ticle�dy�&� >@ ( $\sigma_{x�uy�@ ^{'P��q )&�'$\sqrt{2}}( U+ y}2�6�s"$"LeQ�?��d��6A5�囁� ��2�AF5!�Mz�0a suitably ord1Ped Stern-Gerlach magn�Y���6� $x$ 9 � 7�Y]alfD!�5axis;b1 yHo��N?y$?G< �Esb)t!��"Nu�!aR�>`� x�in yet&irL o*�B�$�*G�_�Ts�@E�.� �s+�way.!A=�))���"�F$x,y$0 nd� 8at $45^{\circ}$���6`$x� $y$ �fY"0, �s}2�&9 � u:1Q �*�2.) �9��6�)�a&,  y %��ts�8<| -�d-�a=8ly��y,�g� *"�M*B"��+�#i��1so�Oon�Qat\basdS�H u*� *� L&�4�XIf("3F �F� "�`!�.W "�F�cu(8 2 make>�entir�bADi8%Az��D r r triv7[0haracter. Exafce }�+ &�3A"th�pi��0���&b�� �I�1@M2�\pm*-}�>e�6��  \pm �\ ��6_8'2})�$ )�-�8uP���F�"5� �ܡ~�G=""� � * ]�� Val!Y immed�Mly 9;'J��X^B��V2�(�bbrests&`Fly up�" "�$ VI$)��&�*---A�" ��s � dis�5�(5(��6d natur'E����6 2' *PiniQ�=��!��E獲�:=$ SummG�X�0�B arks*7$ '}}FSB�X 6�Nq�iQ����� �*'� s_!��wz7q�'�ͦ�"cdg�?B8>�X�(>� �K]��aq$}!�:� ^&�8&�`�:z#�Vcau�M��U6�A\}:����.6�one��F6� 6�7 N1� �hB�.�H�#��An� Q�JB��n�yv#ar�Ko!D!�.�M� Vu�8.G��o7.�'*070s. Ultimately) lessa��J$T�%�2���@4�)H7a�q �>sA�&�alY:P]1�a� �! ��!3!�.Vof:�<. Abner Shimony�1repor � !v at A�4"�H� aw ofkTu�E;�5a�$` � ��>aMD�F*�"  sour% �';� �pSs1b(0mun��P* Gargmane# �E"�QA=ver��on F�G�<1r.�2,*�-A#'s �UMlBN&�@A'��n�p�t!HU9ity*� �nu ���KnUHaA��i��.r �!��a�a� acA ledgK �&lO� �.�AF�w"�ly�!��r� ``(_ Zoى'' "me"A!D2Z# |F21>�� o��"~(,A�)"0>"pQE�V S6�V s� x�ahL!�N!]6�J�  in !� 1935�Um��V �V heE%s��P�ͣ�&�Zto:<��in�Wfar��h:�%ˡBe��,)^oes!�*� ] if \)"��had ]�ed0T-"�=id in l�8���own�G*�5!PEPR�a�W< \  *!p�M--)�%�a >�r�(a"�!�XD�> kinga��:.�s�[>P �in �X4.} �z6�!B̈́���Q&��JN.�26t)Y ri-� � next�pDA^^ lscarcit6�_ Max �R�����G265N�R. 0�,!ate��& �^�q %Hlittl�Ng�>ZR��Y!� �>Y�S���b� 1957,��;�0��!wo brief�fL Blouh$d Margenau!$<) ~��d�j�*s)A;�S )h!>���]ᣁ���E��e�"�"?N nd1��e9Q�� �&�=shortco- y^ ad$�� ffir�/ f%��KZ " "�W$ )'��f P� &�a of �`d !�rt�L�%, j�B#e�n��}b� }��,d)yX �f �>��� ���p -~eD�RF$ Jy Jj����a�)r �M&�H�*da+r n��A � pJ �e">GedI&2 k-8e"%5R�Z) eide�d�J]:o1! h>�m�O deep� c� I,?� !�y �1""Ja t�fQm�"� iM� al criter�� bey/tq 5�)� a�:n��:�� s � ��A %��e�J�!�-%):L. TKWY�@(NZ*mYE}�)�#.}2@2 F.=,�6�:LJB ~w��Y"i2�%�T�& �N&�P$5�way| >�al��.�Lc"�2� �,v -w ensemblsaE&�"� e�� ;���M GH)�"m)i��_�eT1in m� � vari< in� I�i��"A|�hH-"� !Rt4�E �� �%acz%dT �  A��"�K- amX1BAr[�a$)�s. ��`se}�%�n)A�m/i��ll R-O$,a�..M�; �OD \int^{\infty}_{- �sd�I ho (�L$) \V = \s�w"vm�P2fm ExplGee"J>$\rho F)Vhe=bWN� ribu%Lon>s�,W�5�X6� )�E}�i���am*�Fu� $"=�. $�x}, y�,f�B\zP)z��R��PSv("?&0 mappa���.�to%�ir 6�W�c��� ( sJ�7 m2{&�� qq?��Z61_�m< �M.e.�.����{BA ,*�meta? ",�a{ $\V$�l�(�%Nj7 fact�c�of��(��f+�� ��(s�,��se7�# ��*! $3A}.�*� kMi�6] 's `J~'"T�v +_�:N8Cfa�Z``cat�Udox''" � 2U, �A!e?s&m(��,�4 esJ�oeifiN }�)m. �s6�d� S mot �!�i�%����O:9"j -jDeh�Cc�d� �)K#it&�3neL�i!y�3m�l�-.v��5W! a6ii Km�} A�JWD*�$��&D")EPR@E�M�&&�ij �*~Q�:T� I(n�l G tail.� 4. T�/�3%0G .I�q$ jqb� +�M� o r7=5ct�'gav<(� U� ���w� H=stonK-tPAO�?! H=pm8+aq.�G"�>HrOŦW�e� �GT�$-Rtl͝��8harmonic oscillNM�,I"L��-�M"C i2N;' (( \hbar, 3a 5  7 S( \}$*`= U�H$V��.%a� �w o %�e�ign�� s $V/J�)�2K$H,p,q$"0��%X%�2�6 � V(H�9(p:)� (V(q �62O HrOV�9���UX-Q((M %�N)/a%B�A��Ad5 tege*�=yD�&�.2�ѾmN�Ve �=Y.��q�Ip�& of ��'#w *-1��r�{ lve # $ #!cE.#Im�R-�2�"��![y��q K�)�@| �Y)EH�a*y� $=��f�<&�C! L��K�sfyKA�)=V�=!S*|�. ��Q1�<GLfA�5`2�X"u 5;a*)FH �I|>� a"R< betw�!Wz��$H$, $����P��&#B:I�eV(*)iV(+)m2BC�Em�m%��B����lea� � a2�:nF. J.a��3i��r2� ��- ɬ-#--f$uF- cr.+ h�[�a856&% o a ~cCq`3 Kyno�]�on�.((>A'}�K� c�.d---*� $,  (*(�$��'Q��#�_ If w&^1�.� "{$r���.�#*��s�$W$a�9&O"I��2Z"�XML�!&.>�Rir.� t Dults h�d*Qp�soo/*`T�(�h:t �T�]'+!Bl�� �e�� !:* vis@ $�s���i?��6 ( �\vs�W *{0.5 in}�B6J: ``Atten��w3x'en�2& obv!%EYv}on!n�f"�;e thox� �<U'm�ngl�m1I7td one}6 !�a�x�V"�=7 E��T:8!>b Ebn!�AH��p"�3RKi�m�!% �Ase�x o�ury2�)� -B �!VreX�� .'' ���f} �_F�tCamb1} G*new_/and{\the� }{\roman{ (} :Q\set�r{1 }{3}�J-u" ���nonloc�MF}>*}�qR!�aese�l rol�(%��!�!n~y j, �meށ�rXBiJT�y*�, %, 2K:�> botha�:�t�a�of `` ��\t''%i=w!��I!is� &� l.�agA\��Zg�� aK"�S��v�+�k2[.FCY&(d"q "� :�,e any \2a"� �!]Q�&� A `maxim����u '.},iIB�� %�i�}|m�beA>vr ity.� ![G)GEPR�{ p("�,A#�/F;cwɵ�<5b��d�.a-� m�� i=�I���A�M��.a r�Y�j�Js�$a��9�H���$�� �l�1r��ck�8� R u�/���"b�a |. More��" �w�et�q newU�oyofs5u 1Fv&�JYQ'�X��]�#���-,�� 2, Gl�$&�_, Koc��Specker.M�k4 S'.� &K��anyI�a$L7al-iUatix!''� (.��dt }}) �M�^>�O)A����4N`F�!� ^���)vol�y0u�x? � for *1_.�� J�tJ U9� E��r%AQ��}, /�AaNal,aL%/A$ew Sy�nI��Ayp ��.�  �s�9ex*�5�Fir$zonhvv/eF e "�5��!`mn2,"no�q�)P d. B`"�e� ��m}�H= A�mY!�m �e a#��:-w !F�1 !me gMf}} > !�l�# pE � ��qy $3 $T# ���T6:��@#��.� �\p5!let �c?C�kպ��� k �&5� A��� P�-�M��i; .� Md\2oU�le&B3��&�-��A�n�a� 6^5�%�%��|PE� .��7l$xA:vx_{J��{9�,a��s��*BH! �n�&~9"� p�<i�F��a�H�!�s ,ey�  $d;�8R o" cs*�%��*%)7 /�N�9R�G-N�� ��A� ieD�?)R-%d +d$A@E8bno ." ���'&! I�:#��5 ��!�E%}!q�*�]iz). N�gthe].K^�w�p�I!F�{&p*.carry *J��Ly���d �canJ\��9f# s'za�!�!���1��4�| dox,A8�r&� m��'&� . �, �")see� w�wRim�@ � ��bto TN �#� �NAA�Q��%umm�rstM 7��2&�u; %&�� �}f �h6>��ve�a thetass}:Yq �U_{zy$= |\!\upa �ta,`N�[$ \, \otim|�,+dwnR, -\, -\U.*/PW \, :X�2-�Ieq��rh;< $/w+ve C?�`!BU%!?!� �Hy.���%��c��ALs,U&UEpr�E��=h"�8:^{(1)�W%w%S}&RthR762B6 ��*th>.���v�2��oZ�� : s�>& o�F�(�7Sx�7�B�&#���--B� =-"�"2f n���"�Uw�6ll)�R�Ϳžg�Q���B��k=�B��ETd .� �����2�B��y� 0/eV���oNa emV�| P��!��� i�66|t5�R�b�"G��N?�^�%pe }�T_{-p},d�`�U_{"@xp� } \\�ixi |\var�^xl�s: "���d�b.�� H�&V �`&m�Sm��Rum&�k��.&% f $p]\$:�_n_1��%M&�E��6�"CIqu�i�eq1g2!:~}�\pi�}f�'p! }1�-�9|%�%��&�& U|>3�� �eKK� ��F�. To �FiV"exp��Oᒍ�@sum��0B)_%$e3/!�>�J5f \( b$x6�?W� ]� }F D � jC��.Q.�eq d�W2UBV�c�A� yRx$��,E&�ze�)8=j�|2{� �fp� 2+tMPFQ:��> $b�v]�aa�q�7�qO ��.^ a=!A^ xJO5Fi >"� �7�#� tow:W:'s>��s%��&�sM�V� ;Perf}}>7O�.�'reveaAatfull po�alab�� um� �9Q , N�!p� A�B�*�N�at�%A�!�%"��G�!+�hip6���..""j=$\Yf�j(x)"N�7ny�6ot 2x $L!)i#n�Fve� um*�1n=A�phi�r c!g)n})%�x J6]sab0Oq��vJ��ai .MhQ)�nʦ=� SCHR1�6KZP)�"# }-_ )K. e!�� tl� e�4�� �2/8 ss},�O�,anticip�t�@� ��'xisv!�� �ٕ �w��$2$R�V��\[��,�o:�2}5� :Rz?�ysa8(-� Le�^���8 aJ�s �t(��Qpos���'iscret~NS)x9R!. A� AoA,F {Jp���/ng R\�i�5��"A A�(HB4y T&�� n ab~%j~t�$DU�>A" hqH5��CA?5 \F�`�n}�  n}\8 >�S$��e2Υ&*q&<asF�| ��q�2� A� #a�A[t���^a�se�.\{�a\�E �mu%}$9�e���J�,e�:tilde{AQ�E6&� ����)�1 _{x,x^{'}L A��=�EPRstarb��O+A�>�,rix2�!$Q/!W�a�� basis%:&35R%su�CQ� `$*$' de�-a�V xa�j�yion. &1��/ny�$A�� `�!7e'"� !�1$.��5Ais��uniqueEWri6'] 6/� ���'&=S V�n=|J��F� a\la:� i�)2.E,N\ &� &n e�.�d�*�b�7h>dnd�BM1�Y� %F��B�m�n�^{*e+j�#!�� � el} \\ |&N�n{Q�/9FNJ >��2����K\r(K aS6��)GoC�&h  $aL�%%�.�&�of:> ]s ��t:!�#s.<hi(x)�Ou{*�s /�1��%v� ���`�@ramE�A�b dx=k!,!�MB:�  "�oi�6Pt�$�{� �3� �in=K�#duc�YlNl$.`~ R�9wU��{ �is%��%6t�A!�u^G�Na NZ�VMphi:|�- }��%L6�aL!"h"��.�"�EKel�R��Gt �k\�`$:,!Tq�yVa ��N�JT2�V &���>���Q5�!\*�6��a#%\.� $vyA$4 �"� )$V) �� � ,]Y  HND heA}(�  on B$. PutNO6��|>A2ˑof"�� ���F�  io�Xa�s*["�hat{aCz.�$`�� �If!�1'��?"3�#��-A>%I. E]@� �GL���(� �M] �>���$nMh�O$A:�]��]�.�A�av� RBB��W@$ &\��� [�� �A-�*of 'e.�!a�@ $(0)k=0�m�t2�(� J��"twU1A[a� .���J!>1.0�a��2;.B "�5�$L@ e��h���Ai&�aE i˦&�6K.�7Z��fd�.�ֲn}$t1M�v �rec.�Vq�0�9u()�any.!d!�yyrW�Y�&u pMd�a�'?��eB��>-?�&� 26]d (*� qg )6�1$m�UHJC�E! �er� �0�mg�e �1:*~Io[Z a�.�w�FM;��iJ� symme��oO �&1��':��i"�0�YdM�e"�,ʳ 1lta��m�ve&�V��V1�2} O*d1 22eA��}BMu��.T� !q v&:.m��6� _&�q �1�m>� "���6�)2"Jm���*!�A?�C�3:�c:"?�8�)"�) desiB!Letry. SLa�AK�Q`2&AF���&�!yS�weX�=Jt�"$1§�.The�eoZ=e�!O�a�> �aL:�UaI}�<����#B�|:�'�M�9?�ofJ�Jb%���2>2.�"� ��b e)�� � V�in&� !��"�+4��|"8D&�4R�?�7`U�M�k��@ly�����serK����Ya|n�.%�*�[!_.�i1%s|�� "�|6� �4�F�� j<-a $Z ` 2A)55Bj.1� !}0&ZO2m2� &2V&To��:�F%*-pBl1%�5�!��:-q"�schem�Me��V4�>L� ����1�xє-�p��*K�.Xx#% diag�Y!-e�-�.8%�tج�*al�1.�,F��[Jx�� x}=x � m1%��u� � "�e1.� �"�.aB $-k%)d}{dx!VP�� "� p�$.I����E�h�t$p$Z3elf. (R'"������, J�=N�AXe;,%o8�!2��!*7 :�y�Pq�� eZ\R�- )�:�u�T�)sNd"�#(!��m�"��� �K&F#In2�� �| inc}� � z� ubiquit�R�a��to -��e&�"> ���.yUe�2�� J%�Z%�``xD�9B� i� t#2�n 1?� pk� _ila�[A� �7let,+�.�� -2F!��m0)"��"��7AYsZs^>�. � �Jb%l!�G�dA/&Y͓"�#.� t�� dY��V��t"&�$w8I ume >&�F�H���2a.$$E�x�Q� 864��q�K��9��1d%�ner�A w���)j.�7pPm) �RE}(��A��ŵ�Z titu�S��2n�9~.}�1[!Z�� =�AH!�$�Y[��7kB!\�5mGu�1 V 2>A aint�� �^=a�"%9�A��a{�:�&"�/if=.6A�� ��.����_� b���E}�O a d��a�u)Y_1k d�GQ� }, �QeA  |!!� ���s s#Q6FA)$. F��mor�%�A��same}�Ji��:i���W���9�.�o �� �i���� $A$'2�p:F!�c%� i5a��ch�BU��$��&?Gw ntexTx�`S&�5� uJ�P �����62Aa��2 5]!��?(e��a�er� sqDuB� (�B��#ap?M|!: :� ,u� Eci�&�-D�* :JŊ Mz.����!�:p�,i�}nE�5�O��<�i�H�v"It+f�4=i}J��9��E�pai� "�WG)}areM'Iw��,99&�=!�a���Ap!���U=$� de��,�f�j 9I3G�� �%6�) Nj!:���v!��?�( sI��g �hop���pI6�s�THainT'�2� Oexten:7��*s["o\. _B5*n��*9b�66@� ��A�r..� us, 8�vr�={i�]0e�q.q��U�"� A�.:2:�th-�A#�� �6e1�0* IA7/ %��+� b� 2r2 1$� �6>�%�id,ei�J�)�iCD!�an ��� !�"���� �-! �;�![t��}B(!aI.ur&rQ� b�*M��) �" "�S�)&� �DQ�� .��%Y�2�} fwxmf>�a�`OJi2L %S�yA �v !jerBh . �N!�Q�, EN��G 82.��a>/E%��sl2��yG" ��t7�\IK!Ӊ�6aN�e ks}o%���,&� �a~�@n,� "�9>�Ara/ �Am)zj� BW1uN]291@ ICJ�I�-�A���6�(I�+�o��'�fum)qIufNlor���Xogy!�t%Nse��:n imagines5s� e$2$ a8}a[����e���a�:z�%�@iSs�� a�@��a�a $ �g�� heck.answe�an ��_�H� B��1$U}� p��~��� �}O�dAG�{ lway�U��� r�x �� csaj�P_e��gHex�,��j@u�m�J�UL ��h�}. 'IQY� 9�aO���*=M } (�;1Cal0L)Jr�-focus �F3P�2��,^;aJs& le5 s $poYA=�@3r bxQ�``2''�DG�� ings� _Xs��. IOdCz� 9Pa^woU-�e � �,u���ab�6$q��.D;�GdoA�so v)I ��,� � ! -��P��%Q�%w2��"?�6�07xH5 ���C�Q�-�uxK�ry_�aratus),O�Is �A�Ce%A� afte}�s. My6 like a� oolboy un�4Hmw�M�* lyE�}� k  IE� .|uo����5 �w1�2#I6 n� do�Ukr�%��Tm�Ԍrials I�)�!Vpupil���[�1�he�<� I put!�him mEE�E~�i��z � �ga�s�d�R�<}hs.�� No-m prin�1�uld jud��!Pwae;]He ^T(1%; ǡ/aľs t��L�DJg�<suggest y-1!�c���jv*r����e��� q�o����oy!?�1E|WfuaT)#s"� %�� 'x��T� f9�x�5�= �;favor.>{S"!�gi{G�6i?�� i0�#�:cs 2}} Co�2�"� B&�I:� 1{�iJt As��0kg �&;7�s�32���O��!�%�� �d�!�a��I !C{ɗ!A��6o2>�X�� 3&��k�!a tens��r&C&�+ .�'s6�*EV.2B.:B�!Vw!�(x!k!�7"� �*:&"[�{og��x/�ven��!AI �?m�}j ߽ntW�t;��e��'�&x0M�)�f%o!@� :bi6�� pecialGKo�L"�S$s��n�T``6-~��Y�LGbs''---2�$Ֆp1� $C<oQ�N�B #(EE��%�a�A�.�C}Z�C5�!�5�2-�M#��BC$B �qMF�AmP'7%�� � ;�>ton�>TP ��D sP8nt5�P%�A"�? �(*�VNGMscalar���)� e� ``9�''�rJ !�1�!��dsqu�($Y�!� �.*�+#  $C^{2}=�+ . A�it*?t�@�RA��(!hf �j"/ �o ad���""�wTg k``$M�b>]� ea�gprefixm'. %�"&y�Ma�ils�QD� �i�"�<�%ti@��C(c;B<1�-+c_{22 ) =c��1a�< 2 2.7} 2W& c_{iU58�s�O�t6(.`i�I�!k�=C2�7 _{i?&�2i)�}F�4i}��?F@*�?��6"eq:var>+@�dA?ez��9aB�2� C},� 6 � ! B�&4adh!M�X�$%M& z�1ow a�!� "�(M�2�Te�V�X� � Qp�% �j+9�x)�%�l �n-.^J� ��& ��'�DU�ce�=iB>)Eb#�s�'R:% �F�Q�� ?;�-�^cs0By}�P�+ �{.*V�R I�:� tpkhe�4i��_� N�8 C �=(>M�c��iE� �� �6\n>*�JVTjiqTj%�.TjRT�6�%(�@%�=W)1~b5[9� x�Z. A]�I�e $C$��A�%B.HLa4 rear�R6��R�w�0�!ug.��9��7>jn!V1%� C |� !n">"�C ��31�"�OVZ΋ }� CHRe��"M;>��2t_ w?'m>�C\M]> ��ql:� >\o�T-5Mi"�;�8-�:�f�>��M:>%�6�|5� ��Bn9K eJP]zk�(a���SCH$3>�T9 % � 1�>��Env2� �;Œ�%!f!2�. � � �3p�y"% � i(�I! �!�� 3 �s�H�� ��(��$. �:D� h 0.aH��V_�qI� � 1Dce�+�j "@frF&�: y/�1� &�EI���EV�Ec*�ERK� &� �&�7:�d �<� ^�}!#E !�>P!Ia�((n�,!�pmVE. �\ ��s�12\�N.EB.�=CAC^{-1�Am4 caci�D6� e~{"�=�l�X���%��(\{.��+ A16r�0by:� I��v�/�"�)��r 6 �F = C y.k�)n6,6��1r)b�V�$C)B"�� $ANo�G�Fz):,$i8s!qM*C= a�5�ua�HA���5�6�OY�� !��-*�+&�$�p�jh2!���ex*m"E?TAq�t� E�� E��<��Mwe"8�E16c $CAC�+�>�nd)�.�Ai}|CACejA!�5��{%.$i}|:")] "# calc"!Q�V k.��M5�a62� �qj%=�Hij}! m�vJ�� /co"���A?�o9�2�_�R� � � 0 max}. � � re)2"�O7���8��"&�2Qg.��D.}@1;��=/cac.1F�O�ީ��.*�.*��R�c� =C��*� fyX!e���o�2b6"R=� �:�A&9�"����VA_��SCHRC}��is%�kNF%} -s�A7.�"s "" yiel�1R�?���8..� ���t�sU�,!�R�-+//`"L)F;��&; -#�dd}gQ�5�&e)1R�-�-$A���]d�ea���>&?HK$"�j\�mul&pEd�5 �O!�qJcF ofM�A&. One-a�+�ict�`.t�M6e9�b�. D%">Qe��0/�������>6�� , (���d$j}$ lac$� '� j��͹K !lf2u?Etr�f!c"FSPN��?��:� b�.5�|���Ų݌�y�/�AG�ML�Q�%�P}D2��2}�(u.�`�x�d6� �?��� � ��uSCHRC�P} \mbox{,} \eeq one may develop the same results with  roles of  �subsystems reversed, i.e., for any observable $A$ of6 $1$,IHre exists a unique28 \tilde{A}>@82$ which exhibiALperfect correlations ��O$A$. An incompleteness argument similar to that given above can be given, and !5can show� � ence!  a valu!X8p $E(O)$ on all�%J both9s. \!Zubsec�,{The general!Xm`ta maximally entangled state} Ss18ing ubiquitous R"8are not limited)ose -�`form \ref{eq:SCHRC}. If w�amine%�!Yosite I wH�M,l VEe\ dimensionality\footnote�deriv-�of this -%~8be carried out� an.v R�$either fin�or in �. I sumse*be� titu!/A�a = ( written hA�toF^ rm_?N~, case.} andM�(is represen}by a %�.<is)equivalA�tA�em�m \beq \psi_{ME}=\sum^{N}_{n=1}c_{n}| Hn}\ra \otimes |\phi$\ra \labelAMEC:U w� $\{|H\}$�� basiE�U� � 6iz62 6!�$| �^{2}=1 �� } \fora{ n$.}v��!������ , weArd �� each�\aceI�9c �)Rw��som2m�oa+ K. To em�!{properti��E� �5 ME},�/a� �itqL rem.Y�At e�point, �o�� addr��bobj�# %EPR yx��} makes"��� �$two partic��0coincide. For�ple ��conside�e0anti-unitary �Lator $U_{d}$ defineda�Is | a aV<= \int^{\infty}_ dx |\varex}-\la :| +d6�q|dmm$ arbitrary�4tant. Then, in%)�11ME2},  two 9��separa�wdiPce $d$��s ��[psi:` Uafu��^2:g�U�U$U�!�.� 5�=�$U.� =�u�$. Rec�# from R��discus��I�(ilinear) )�ity��r�%ffici� guarantee��E��� �n\r���!if�D5.��A��)��I�invaria!� we r�re. WeA$clude our �D�_�^e \Erwin!� adoxA�1ngi�g*�. Um$ Hermitian9�� <ٟ| ݤupc} m)�eeq� thenM' .A.x  b*���arison�6A�2$ EPRstar})��v wp tat!�H !�)�U�A�4as $U=C\bar{U!<��$C��IuI�y!�olu�� w$3a M� y matrix,�nu�uau� leads,m�| _{ij}=( QA  ^{-1})^{* -`Z ��! $ij$ʼn0cript indicat��th � ele� ��er] oe�� n}\}: m&aYQ� t un��$C���tE =UAU�. � �Q !��g $AuisM0s &� pe��g$. Usa4$AU� \ra=M�.!� d $U �={\bf 1�we have ���.!PUQ� �!�"� Cosmos�  s a�]8e eigenvectors | � � ϥ�) by��r��<$\{ �\� Identify)$Aǁ&6 � 2s� b2?w n see��e�ofU���""s� .V � such a�V. AsE�he^� �p� iz�DeTI�-Q�c -symmetry"Q ��implyI�y {\emAr}2�A�� &� nreA�Y�9^.I�� �� 9\i"l"8ed.+z�1 ё?@�aQCR� )U��th� R�6�. 'F t"� e�L� P_{ss}=|\!\upa \theta,a�p P \,"� \, *dwnR+ \,\, ->* ^V \,-�2,N� MEss ��w�e�8ede��2-&�΍�ofl sigma_{�}$. We �h sup�h�rmaq� !�sa�!�y. InspIb\� %bi� toAq ťV)� must�6� �/% of measur���^{(1)> 9�}�S $"2F" willE�c�sum� zero( se mO � 8better named ``F� .s'',A�c�e .�� ! negaaMe�!6an�� . On� in�B+%_iBi&�~,�N � immediate�\=J&� AS is j. T��be�� ,�follo| �Y Jn%�assum)��2}T�AL� -%b� &o* , t'  i��4)@byA *�U (��gin{array}{rr} 0 & 1 \\ -1 & 0 \end{ # � )$�� wb� � � Ik!�M�_{z}$6�A" �HtZ $C|\uupa� I�d��  &� 0,|� ��v h�F^���pio.�2�obtain�d=Us\D+U����� Ex reduces&#To�i!n ov!,l minus signAa$be ignored� amiliar6A�� =��rr�7Z .V2 ^ �� ��wem �!�i!��I�%�a��  multi�� ��V� between)�onentsx nt2-NregardedA>a � ia��7"� :�R�1� hold�} .� � of�'& � ^� X&  " $. T.�i�� Ձ�E$Ѽsjs!.>AcJ at .��� I � $���3�� equa�c ��!oFxuhave ww�b����� �c>������XZz��^{Ny�� �� :tusBҊ� ex�) $\wide)B��6�}=-N$, ori�UN �R<}�"t Sbarr͘&�i�or debaFn. 4C�=C�n&� E!�� hA-y!�"by �, to $9N��<oC$. Iriv���REGb��<e$a[�� t~n� tס{�T.9NL�AK�)�N'= ��"6� \cos(6 ) & e^{-i� �n\\ e^{J& -.B \& M��No�ate��I�4sq66�j�a & b�b��aj�,}$Q�a=.�=b=V $. A� A�lcuWnolE)R:s"����ɨb��� GE� = bO-P-)� b & n -� � o�#E�c�e� m "2CAa�m�A2�O-0 $� �$�saw� �i�c }�62a_ek� A�be�2I � ������ �:do so%Kus)A� �eq:!t}:I:(CAC)�AA� }]�vss��!�L�� F� $C�)�Cj�M�I����$ ��� ar�� 9!� � � sJ�&� R a�� V�$V w.arriv��t5e�+:Bell'�ore� A�" *� b s�[:ext}} &�e� chap�3, �"quantumclocI! may be~���L� ularR��5 : i�N�.�(e������be appl�! in proofB %no�# +2G2N$  + \*>"3} 5BC!"n*zME"�&р Let uf.8 1}$ %�*L2� !� pace� I�le"54$2$'s Hilbert )n�re� �lyA# $ _{1}�_ h�)s1}, 2@k �e& &� � {\xiN�?T #B�#sQG� set3B� 3i3�ly i�cal&?Si�d�:C�%" % ~ isomo� c�MisT!si�'�$� D���&~ .*���SJ��6@!�  �emberse�~��C[ny  ��A1orthogx&�mpy�U&�1!� S(lyv�%�R�.}���2�qn�x" � 6�!��P �4 now sel-)a�s�es s!�er��]#�x��a�a+mak~!Ping�'i#:){s &�x & $ replaceAڅya�!�m�e��$e.P6 Q-"d$ Qu� $}�He��n�E��>Q"� z}Mhe)@6$c become*#�"��~�+ - 9!3 +2!�x)3n}. �n.��~S*= ,=��*z��E�f�0Ja�#,y �m"� ��!- excepA:a�!wfirst��. �� the R�+e6i:Ni&*�E � :*e~$ �B_+ B��WF�, $�(nfM � eref�N.�& ll�T�V�g }o|* sit�on�oA+e}" ! G"s�' furt +$effort, as> �"how. �$PɿmB 2)}$� !kpro�'s"�s� ��hon�2ji��^ 5�:_U;ex��+�RK&$��!�^ .to� � �1)}, �,��e2��eI&hat{a}ŶanBb E!� poss�(C�,E;s. Howa4�s2L# ' ��-agreeyGA�ist���%diN.Y . mechanicQ&s AOseeE[A�)= :u-lq.!``condia�A Afunt��"�e8�0� s was d� ��8Iof7 th6 "-1de�]v)-�}4�[h )�*6j�_5�B�\}$ uG smathema)c�(s $A(\lda ,%�a}aB.$b})$. Supp�Aj!"_*.3� !j% Fn,A�1)�� �.$1eT>�M�72N7E!In��En�%w(arv,��_)��"q8$Y/ �.(or�() �s�"En��.Gin>�!�F걳)� �$ i��� �� 1)}=!B 2)}=1$. U�th.$U�se� q�Q$ $P_{QM}(�a}I!A / ��� �q + �z_{ 9�gm2�)=&,�! |J% 27�,4[ = - j \cdot b:6����%"e��m�~d�,prF��1������satisfy�inEV+.`[�g� ��)�4---I�a� selvE/0� �"��X---�inA5flict���)rBG�& d so��c9"Qq*y� \�{�+ɡae��,of%rk3t|% erif�)��@Meat}%+�?�"J].. us}}F+h_���!� �..H,A�� m�6'�<� a9!cs)d�CS6����/ P. Beca<�#� grea ]ity� �`��e�%R �� �sl )�j��)�j ���q r-ety�� �s)��. �H* 6in�"o!6 fac��F" ��QCs�B&)�u��C&� .��d!��Ds� quired neot"_1%�th�)ne�1��A�\ ---even e8 map im)li!� �iNaA�erp{ ;�Mle "�1}:6� ye�"C/. C*ǡ�!TKoc&� Specker's5�:c� �%�"�byn�#V?6of&rthree�3T5\�n}�!J� schk�+�9  Amow/rAm>A8n�N."42G "�squarn%!F vari8+ $� &'$Of course,Qe-AU5aUist� K�${�s-8it does4���/j:Alue�a�6���!I�) bserT:` A]EN"q^i�6}� �� s66e� ( a�@J*+���6;7" sameY!�:: aht)\��2�� .}hz"in%kuBoN�\�F�Ix&C � *� ��##A�!L.�!5J*!T�"�4,�8theirAU nterA#h�xO�q. A���^� MM,��inc*��e��]�V*�%�eJa��-*�,�$"<�v�%'� �. "& we k� f�4 F{vIs�o|=no ��!�E(J�)!��l�Oa j�7-6��&E+o �X.mmu�se6is.�e�!7ra& s}� �Vk �!K.�#en:p alway��of>�s. }#Idem�ViQ 2�Q 5.#=mV��to���a�througa0�= �ory are ]o� ���;>` >( �W!#"��"� !*�� �#P<��,asi/eq։�ntailA��i-&�!uO@�3� �6-�� b�V.�.) )~� �=e>#!z ed� %UQ.�!�s�@},�,m�YJ��5 More`),M���*!Af�oB! $N$ E�t'.�.2pF+98J�m�A&�helly�t w�"��l&�A��1�� �}k eA  !NFLb�L� e"B(-�#u ��6 #� 1>�1}�2> 2} +-3> 3} +v �>4�,vJ@57MEKSge'5S(d!B�6P m�!AUx!���I� w&�$P� ��sp�ng��M �n���aseE s to J�)uE.l&\L !� \k �U a M@�6Wg *<d�\{�)0o&� *� � w !/�!�ZA��at-H E1�Lco&)of�&K��Gleason*2# or M@=n's!�] gain*�AQ6*� �. F� F]�$i�a)3� 1�e� � ��E_�E� ~� O�+�$eH!gv(�*G"11�27T-2���thA���(N_6s%X�JM.q1� also� true��b�eI"KF-">!$uA�E5�-*�4 ��$�FBas*bFsum. IA���sQ;SU;�( ��)G��X5<f7@�e[5C*� ��N$ F5c az.�H NV�"pr�&�o<�Oanalyse�)�+!}` (�2"), bu-�b@ �@"�A� �q�%�mi,J! ,y�,�9�gev � !6� E�6Olay7typ%�a�J,�;q��0�7 V=a� diff'#")i^-.T4 = . F�)�F^��Ga �}, r&��=mB�$ character�� s duT;!f2 �w-� � :��_q��T�~(%�`&Y�e��@vid�<m&n9s}6%�.3��.)�a�|m"�N~��set'sF� . Sevp�=�a[a�?Cj *iV,�'s�@l�H+�4��!��� justC on�0 . Fin�%E -�.� �m��!�*�)2n^6� EPR/a�.S. *20 beyo�#Q�s!�%ed)�r/4 main�\i�� � in�F%�J��:a�`� ~MIoatRJ' 2Y�"�}) � QC6aU*ion! JA� ques�m08"+.C T.d6�I��)�!!r*�+en,,9!*(���=ONd�U ':$N2�:�,D&AGm��4"�te�OofU�F_}.�,t6��reviewk=[i� ht fU!}.� �NA�.C�=�.�ofN���at%��- ils ` an unus�sfeatur!.[inv�Ophysic�to�/ labo~Dy 6)\�E!^ wh�s! �L��Ya7rH��^!ِ� ri� B �� Accor 4Y!eE �\e>GW>R��EwqR�_!���K��Ec� }L �>_��&�M�w ����N�Y�"= `*�9�% ' $PJ�%#��$ &�$�(�ifA� comb6Wx!��a*#��6�0ZB/1� �� %^ oret�))�n"�gR$����r&*� R�� ���*z%. O ��*&JFs�Rt E5violate+i�ѭ1XR  ��T!J��"f%�+J�on�>�$l"� +s�@� "� � V  would p i$e� �epend�+�E�ct�Z��v&e'N�. ��&�.��%x not}� firm&�[�:�C "�! \�[2N ,!E ld^ i reAҁp� ��� ��. I�K�D9� ; !�{%3i�� !�s��/o�*�K �al judg��Bz�'|famil�}�i�-SI#L� mad:Ned� Cap7Lr�H >b ו�� "mp�R?�&~J�e� tJ.�l� /�4s9u+&�*�*c}$1X �Qt*SY m�!�e>�6oe,prbellnon}).Q��i*�%oE��*�: , E�iv��3 ref\)s:J/beY�6X> a!o� �Dst%V�y�ep> EB_m��dis�6B�) �i��ir�!~� i 5 � !�noq`*��*ub^#{Te &F�� R�a�}��t0)��&���1���R find:��ll< a�'���7 *ur� ^4FA(��n��n�&wan �� -lik!��!A���, a.] Y�R�6Q o � F� Z���\��*!>�a�cer�J�6bl&  sz5a.e-�##=io[/�&>n_Azl2- .J�� � � !���]Q7 ��proK�o�Z�W !� �$eq�!A� l���ir�1o}6E Roińn����$*�GX�Yo��I\O�?ref�9��8�)tag�_�Delf'".EG�  # d�+"�G�� �R.�:'#%��S�R�,�Hnd� e� -:� :�!|x.A�L N� -s&$/}�.5΍%�9!��~e�q4%" Schr{\"o} �P&�@'KA�� �N� )�2H.a�}!H~�E4a4 =".O .Is)? i0}e�&�,N2��P�� ��7ec���sor&�;tur�.�"mof �uQ*�!N���1sakE�q��, VUu�'�.ra�R_ugB!�pl6 j*�%a��A��1��.�of :N'"i�>J #4�/i����uca�a� �0. FNB��0 le� ���- M�V��8&_m"�:��A!�2 ��.�*!�j>>.fC��"�!ih�IU5�~assoc� d)u6 -i(tlst $4$ .�eJ� �2us�t��&�����Yt0� )ɍ���k6ae�a���"i.2�@). C&]�*�*�2W\(m�map%Awei��� i9�%'� :�Y?eVY@!~� A�aђ q��4E�. u�readeaconveni�,��a)0�BKe2D �Q��!��$x$1 $y$�@0!�mZ�,c'E�m)�0$A,B,C,X,Y,Z$D m�s�(*�W�T+K"�W"�L eqna�T( A & = & \s?7\alpha Whcbet y&^"Pducto}�HBjKy}bKanonumb� \ XjC-F�C YjBV�B@lSnd=(�\b:>C nAB6 j1!Z "XY f e�22e6-,symbolo$�1�E_lA^{(1S�^ �,&�I� D<�!E���&� enti�cet ofm2�a�0->�D6$fZ��k. U�#A�no !�(�1)}$,*[R/; sugg�.!belong��>�e��f1�=�"t�MnfK..�e*�v� A��J�bmploym� -g"}B[_�$1�� '}�D � ("�!**�*a�> ` 4. ',��O9TM_{i}\m!- }i j,ldots 10$ sh�re l&!gHF���4etR �<&� ��>>� 'NJ'K� c1)5��hips am�5H5i�51��3a�q�Qaq5_{x&&Z<�(� A���e@&�0�{$q:S ,� easz �%�Z-$Z$�HKCZ�E2��"P(CZ�� . )�=�&�*� �sO3. 6�3.�I�$& 6V all 1�I��tra&]IC�T� Oan(�c��6*q(53A�eS a�; RB]/&ed�:�$: $[YHYx},U_y}]=0$, b4 A]=�P.gbf%�2��,6h.Qg ), � . Em)cv�65y�U�-z� ����, Zs "��9�Xe=�!� each� :�. Rep=d �Oc�FIE rul&g)�Y�a�I�O �{C,A,B�g $\{Z�  e_Z5,� @+ fA��6. � >� lE:�&� :��6� \{A,*a %�� .!�(y}\} & \{B. 8["6�8x8XV8xVp 8�D Johnlenno�I\ \{YVOZ���-r �-r&h � -x & 1� W&  �rF*B�:l�}���8A~A�6��ngr�,U���A5�1eq�r[ldraz2 &s|B�.'-�4+� A| �*�> "T &��rocedu==b�3 to"0.��z J) �3 b�:�>�1C ;Tn4!E &�]>!-i& M6��4E}(A)I"�])�L��*� b&�7:� 2+���4A!un}W�N5n���6BN�t�$�U�]%|N],�G WK2�V�, Vm7+�\o��.|A_e�I*�/ � $V.zh canm%��9M��ex��3 "ajMt� a�E>�)rgu�  fash%���!���.�R�i$V!�9awp��aRa�b�nE!4O4?g�y&-Aser��� all.8kehu"s$?�jl%� �[ M�s. a � >5-�)!lnW�V Xer�N�O� �"'---in lhgQ!0�""&�NEc� -� �2}�XLN�s.8��"E4��se�_e"]4�)ibx,�oj�4nRX)�si�c$aneously pOm}�� )$a5�%�%��B E}(*4?2F3 1$ (� prec;%� ��dJ S � ��=� elow.p�/A 2�Q�� ^{'}��^���J�` Af:~3S�G�!%h4�for3UJ.ifa� 2a3~%�E�q%"ite�@J+L� *beA����c!��2I8s s�Vab��r>�K;1)6= f�1�is �� ed (S ,ɕIH!}E=)$��.�)�l���`�rw"yc<}�inot+8�i�N�*�ormatA�!�Y�ach�`�9�-h��B�*#<of�%e � !y%Q|" HxfG �Hv��M��}�!��"e#@�y � Q���2aI��^fa���"�P��&FPOFw�:8*�2"+&�� ?](Uempir2'5�6�� �#ach� �aU!NEt *4�2-��e%yi�*K!����:�no},1BeI��faiGBo � �6A$vF� L B� �lF6"�3�C ���:��arL4- ied. `bQ&�1��al!Z�:Qia�]���&`��$d {"��"appea�6�d%Mcheck�:tUora�_sy#.5 ��Ho;=U hse"nj*� vt.� ^eleBr+a]iS�.rtiYw�M��%f!.sV#A�"SK!itO &I�5)�a��2.�`� d"b3��i, 2�K�m�6�&{A>Wn2�o :O !~Eޙ?�1.�U�U��#�jc��!'s q A=&&,.��*� l Fir}.� eq S0�y*2!�}=in]�C�} -Y,HsN�fE�F�&{ �r*�2�Od�$ Ex�, syI�� i�a�$}�E: ��A$�� 6>,mLQK� �#m&Q9�A obeyP 2E�4�2aZ�t ��y2�!JO,O�_O�_,,\h{V�q O=f(F%�hBeqIf-��=%�e�orm 2a!.|@Fc"Ue�tgH$f�A=x]%Vs5�,`)�)!d$O"I E{|—�K��2ch � � I��a~priori I2�6�a<�*ll$ �d,#t �K2( ���� ``buil�� to'') ez)&��; ͡n��� use}R�t�A!�� ��Now)#2� �q�!f��b"s "� �=r2� �a�Xm&e *3method!!l �!�)�?7SjS 5n  Bcl�I"�f"�=N%y:� *{."w#(Kby�i./�K63b�'�@ 9��#"�!) :� >�%Ln it i�%J�m.����A.2���Fb����Sa, i �ion�/e��-� !Y: z���#�%ea- to��� Q�*K)�of.� z )x1 �N�>sA&)F��*��*E�jb a�nE{%�N�,}e�s a `p�� ive'm�H�:��MVg*$ necessar�/ ��,�;-� $�3"�0��G a �---!&.� "^���X�)*�x �d/u�(�>w )a� ��X~�)s�����I��=2�# �%r�$u U>�IMVo> }8" !�� k0��2�M!!Jl.'܅�zG�S�4�=ĎK)_Oh>2 (�C'�FM 's) !)0beEd��O�M5�!>YA,is�s-��@�%& �2�%��:f&�,mo$� wo `&�@�p� ��n'!���� %�c .�Kh4 m $OV � �6L���B-���wo!�tinctVO�!F_ �������.��C��U��:J[&E*x$von Neuman� no hidden;!�U�} Lastl�Qa+0�U5+a few1 ��ZAq4$of histo��est"z f=����3thoughtQ�I� �UequS2t�s ge�=> >e E CLein--Podolsky--Rosen��8�adR�r "C%WQU6&�ces ha�Cv e�s���4 y a well-�T�Rtempo��IG D�wcip��� �a&aC��/�au؅wA�&'E som2S8r. Hava ���y!hVv"f ��Y�s,1��!# �>%�G>6�I�� gove�-[>��.��wea- cuss t38voq$heRcA�A&+no>+ Te����s�X6�%>�z"&.�k�.E*&�-,�)%J� [ H=p2O+aq.�("�# HrO2h i`#t M�i7be�H&�V�!� �!s $H,s,n$,w_�n.W$V�����aJbkM�}gi* ?�O=!S��3[�4V -%�A�A�=` $f� 'be.� 3$O6A����E}  fu�eJl-Q4)�@.E%tXes 2 I� ��ar}���� Thu�Y^$m(�= nti�-�=S��I�i�� z}a�F�s:�A�. q dis:6�-e�)�a�oM4A86{Pa�>u{ nstean�a.�_>�� AE�=M���mD�a�A� � :Ppromp�B��)�6�.%�>=no{*�so�:��B Ku� m: ~EPm�, Sit} (empha�<u�] original 8E)qSh��+�0� at� eM�  far-l�AB&�)� bi�%a�occur?''�X]0%U�`:�')�a(�3g.S, %��I�'��@me�b� �*� Q -��inu�I� k� : ``��9mea��9 of ` %0de9j of f�Gom'���  mere�two} �.Cad�!n?b�i 9� �Je�s,nO�,m��o�operhap7&!l�Jny.'' &.}�� -'h>� y Nas Bohm��"?a��6IZUncleAlb:fA�j^%�%��- �p� �5a�'�#N �! �͢w1e���no [%�A�nfigu�P${�q}l! 6|jn�psivH��)�q_G-alism� �9Kcto�242�3#2�3V �*�c�`ly A�Yu o mov��"NRA�e 1�U*�IZ)j] T1(M JU(x)e� L���z/x\R"�ax$$ ,�4% (x)$!#N��)I!D&u2�Vq,�.іs (-\�� , y%!Y� �m*.N�T�."d>ofF!�^}9r ides�?�D� o{I)�e ���Lpe�a � u0hiL��deJpu� w6� PrW�Ea���"Z CJ�m� a�X %errw�2� �+ word�~B3n6� � r j��M�+>�*)!�e����2� "s%Pno)�����S y�@�&q�5���Lals�?�Im)�o�0uw y�!� �R& EPR;A�iusee%��'4 � @� 4 �8� �,.�Z���e�:A,:�PR�HX�?�.~NO%:3&&ya86a� ��model. H ,�� �zQ��8*)�h>�����>rC�5��#�-_� beene>Ny�>9.�7�AV &� i�xcOgc\#lybke��8e�.�!"�H᛭ba�S &G�i%� ems,�]R&5�DofN%W  Skers ��K"uZ ���&� tra1xqd eq:Gldude}zA��T asonG !_i�A�a��+Avmos&� ��M E�e�of. A� �Q;u5b ��ula&�6V2h 8is ba�o �^"t�u1P�Q .}..^7 {at� � " $-Fqa�6 **to� ",? I� Gm1��O�"��%5% � E�:!MQ�*�!s=c~[DSumma#Ri� s} Ou�v;UP��A!�h>�issue ptmot]��RE� �y���HS1H �Wei.�x>$N�� e��eI�Iv� ��v%�kl��EVsC(c:yo�)2�2U�+ s��  by J.SRollR�D �do�. � A*"�67J� !(�rqt T|on ��P�--*�>�<0 ]*-~q�e� i|@(U&1#y�-^6x dB` a��m%�)of \gl. d F, f�.E���3.�AnyF� �tY�#��wom edX&[�L.�t�7.u�^!2n attribzCingy5��1 's"46���m"-��_F#Turpri"P%�un�(UA , ye�D h�iGpv ed�=*ZE$ trinsic!�1��>�AE.� hq&Ea%d(�>��B*REPR. �M)��.%�7���W� tens��ge:S%7�pa�>R+��y�J->%A� (E�a�z'���Vp^a �K) w@!� a new�g``}7%w"')�LpW�)gru��posW+ by�qear�Btc ka�h:u , ��B�A. ��A��h � `�&e�y�``JZ!l)�:�U�� a�apX2l� $�y$ ���9' chem�ayA�int�H �$is�t�-U�"UY . M*�0%�2>���!q�.)pa0ri�=h� ��� ��j &�:a&~�@[o U�D���l6��%bL$2�nH �)�!K&N3� R�A^KC"<M��)�at*�+M��"�+any h:�QAa%�4�OMXK�tl�QC� xh%un�ified��Rc��* +]� 0���T<b*::=5�1s ��un� �!� � o�a&�n1�bey� X+Y$�!r`�([X,Y] \neq �;' E/i2:o)isH~�E�aV��}�]c7?3:� \gl,�g� ��� Yd!'4ucc�Jw'.Gg�".e.�&�,�- 1��)>�. N�uthe�C �J�yA�n�Eclipf;IE Pilot}eB.��& �l&a �gstB�,-fdoX /Nuni��H��% Pis eas\" illu�� �3 -�Uە�^��+�JJZ�1e `me%�eO�x.�1S'ZX��!x1� Q rz^8�a�:�8 ai�3�1R*�Cp!�=obv$ if�Ns"0(!x)&I*s�CS݉ xC\ $;a-�g6%c3onQO�Hf�aMB�� iE2l��"+6^�R�%&��� KV ��aBx%ow�& �.h��*^"�(�5��'�E-�yi�&�B ��*ae;�j �&nE%�\.��[� "�6vr� � ,<�� view%~ Niel� $ho warns uG(��([page 210]{!�Y�� } ``� Bm� sharp 3<y*?2 behavioatomic����n�Na*��li���!r� � �x%�}Iف=�!ss[ ,L"| � �@plLf�� &� A��"$n ! �D]�q�B{� �&�$._%:� _%*H !&�3'�8xa�Jk���emw D�9"`#&$��. ��*M tx},ty zOo_ V:�pB�E�?s ��16ake-�x�I)s+Cartes�axp  $x,y,z$� rg"La� n*s $ �x}��.H���$V� 3 �!wR*w%9�.��$$�- z^{` x�bli��I�!L$yq>z$ ..*��-�e͂ I-� O *�  i� � ��lS)�Tach.� y!{>�.Gof:Hi͉��U ��"KZA�nl����. Cu-@ B�6jli.�fa�rf�h�bm�a�Dh>3 i,� perl�WB� uU�"G� ess�>�V�hd 2W ``W��iHby�}oS��  s���I �12 lack!oima� �.''dno��ge�2�%>�,&�%;o1 ��rt� �t��exK� ��A��r�be�U_plb������3d"yV�is",%��>�! or�8���S� yemp���Is#�vŌgQ� neglXT�}i�b%)���3``-�I�PF9�'' Q6�B�v+Z�0 ~���X bing�CݴuM W����&�;�ԛ!�w� _^x+r f�+�ta2C�A�^U�B"D -K'aL��a#i�� allA�nN.�*V/�!5�2�j. ��1�mei�al2� c 8&6si� �e�6"�2ph s ������#a �"�AF7�"� withF�. ��/+ t� �[at"��"u>b�c��&-��4E���ABY�6&��a�� !.�� : . f���Z$�+M��e�$th� �t w�.INm�D�p�8�a,Ji?��O�0� Lb�G!� to a �u� � bQO)�|��-�1��do�#nd en#>6XMs�o�; ��:" flѮѢjMy4&��x* ��C,s��U�e �3f�,ly= �3)'E����Z�e �y�%?B�d4]^�1(own!2 o,*��yo��log�s}[-I�,w� �"A^��I��dee[�roo(in"b�s� !�� perQ)��le�$S �'��- utGstE�i1%�_" e.u as@ .J�e!� A41[)�.{BcinF� �c�  �7�i�j�ca&�)"|� "i&= {F���F I� i>.B�c"$��`it1�a@�k V"�!�: " y�pa���!�*^ ��S(iF ��h� ���s)�� BM e! po Qap�5 y2�Ac; ��&�4ig.�X<? ��w;�!���di s�pro�?�'h5�zE3� 7�5 men!J\�#٥E isa5a � ssfu)(�kh)0�sy= 1952,E� K�)�%��� �(�(B�,)e a��!m)�&�<&�. \�RF/% '_u<at  ^�h�"� adxayfoa�vn#*��2�rth��U >;,��bed:E!^�8PR�k�$G sړ��y!A���&� �d�!EPR0,�L�w4�,fM !�: 1�!''?of?,�'E@4&&��c�;>�*C e{a?��*w A{ɜ��i 9 �N�e�D%� &9�k1�"Q� s&!I:Pd=Kf^aqS\L�R��W���\otimes2x�e[2E7J���R � O� )�� (:�|)�0 s��);��R\2$,���� ��e�k&9 (7lj )�tE"�4P$)*$� A�^�Rm'�<t v7_�P!x� &����8Z$n u�>&NI$.O$.d/nyU/bm2| h�!*��* �; d��!c%�Rdox�� � *�o&�MZ� .�H*K A�Za��� � ��qc ݝ� �f�-�D"9N.~�� � *��2 in� Œe�3�G���vL &�L�*7*js6^�!Ca�oE�"�O.9��9':|��h e#`=�sB����Za RJ&� iesM. &U��,�I2�hAK�-�.g �i��nd1�-os�nGn(�"Z0ag n.�#!cz2k Vbt� ,g�����@n�5`J���&x"+�*S!Dm� �]�,�X�!�1uE� !�e. B10� ��A�Jqu"y!*":"�r*� &9I� e�S,/N&�Jv *�Pic_e�*�A�FO>H�YzY��k-�I �EsEJ l��oka,�o�K!d2� pF �N�C}W!�c%a�m5N�FDH�=l�Nn��2>"e+.� Al� idadAwinD A|-hi\f "�(4I%n�� ��"4}5rew� ` s remarka paper*��'4 �2` B�6l8 r�m]�n3/nt"�AAD �AH�~90qU� ey�m��A!� �exl[ 'sJ?��x K ��K ��B��"�+^$�n�6*��H- ��-��  ?\�r*" v&%2%EŴfo&-�+�  of aq� �sI�)(a�(2Z m>�]�+u"�� ��y�-A�'AC�6is� "&��ted---2��u!�A .�do�t2���.irq"@��!Va@;tPEb�-�ng"i�A� ��.W?�PaT?�eA�l�=5=�1�Ol����i^��.�*% �is%�6�$%MNŊ� :�' � A("�D�%a��;a� )�:g�3e� freedo �=e��s&9��&*G4�ofF�:Gf��i[han&�9%uhad} m2{AX&�4:�#0F��!9� "���kpI� =�!5ɬ-`m�F�]�A����:��"��*�!&�.��us,�:o�!��E��F�B/�o�s ``al�6�Q�-��~%�"�,e���d�!��5A�i/wMS&�5�"� �9cl�To]^�2I��5n3o� �@m6i]�aWo&8#�5c̱t& h>��K�0I� e 1935�0�"*�B, Camb1 2}�2���[s ?l8.^!�!�{# reac �;1�.�-�su�.�7��DXe�-epe�6 -probl�;hk))]./-�& I�X��Cs�Z�, PJ, Jper--- �/ �iH�6�]n�1�V "�\!��;�~cѿ.�&�.~)u�RE�?f�*�B�5F���Q:sެ&�S�!�cf�a!!< �  6E 7L!� �m��?U�#u�� w�8/publishx�8 � \title{\� bf{HI�Va�� N& A�Q�AMn��\�E|{Douglas L. Hemmick} \date{Octo&N 1996�L} z�<�doc�,style{reportGnewx) and{��}�iO }} 2$ee$e%r" 6#pket}{C$K�hi����$>O pbra,\l%<� | B-s>YsfYsVYsRYld2� mbdaB}R�rm I\!RB#Tr$Tr>�dts}{':Rf62�u>AV\ $V^{CD��/>-E�}7J.H{:z&sB''s>)up! uparrow:Edwndow�uB �}{��N> ?!bAE =.le:zlYI3:sox5.s��x}B'soyF(yJ(t6P��NPt6P(NPoy!�.�F�t62Zv2g=\s�\O�N�g= 6.N�g=.�R\=6.R\=.�z�=#8�r8 ks}{FG>ksR'F+ gl}{� >DglsF9sub}{"�><B� varoU�ph��)v>varYL +2)Fv� Vint\! BU intlB*N&ef2'*Y�dG} b\R>l�>Bxeigs}{so>^ eigv S N c!|I:rb� \boldmath�9VKbm1.-muB�hiWs4HF�pcs}{R�} \hyX2R {~ -y�Non-lEvetc�6Der{secnumdepth}{3}`jzH} \�e{dis!e-�^ab�cb=ac LleÉ�)Rddxo^iope� }(L.�thepagA�roman{ } \taofsU�Vxinb�cob�epr^�sch} \^{Refe�fC"b�$L{thebibliography}{99r bibitem{AW,}",David �L Bj � E��B0} Harvard Unity O sf 2 d ess pson, J.�AmeWn Jour- of P�s} �8 29}, 478, 1961��� 1}�, A., G��ixFP.� ger, G n Z al Review#mters}�, 47} 460 198Jh2} rfh �h 49} 91g2� �36�Dalibard!3� G.Qz�9} 1804Bj 1974/inf�� Book} , F.%�$bf A SurveO � -&� T�@iAv Perg66I8, New York 1973��&� vl�S. { \em �!� � 1} 195-20!�64 (4�^dK� Spea��Ta� 14E��`c��Big Red! 403)U��&�#2��I/XMod�W)zQ�(38} 447-452A�6n�d!Sp�^m�a�TaSs: �a ���397!��D]R�o�2a$pp.171-1819Enrico F�b�� ool},�a .B��[p. 29]�:Le�+�s.�U�P]%e���(Frontier P��, High Energy5t(, Pisa, Jun�,76 pp 35-45.:i Everett6�in�|B�, 1>?Q Caus�( nd P-s} ed��(by M. Flato S��L al.} Dordrecht-Holl�\D. Reidel, 11-17, (1976)Y! 1a 93.`.:acas0�&5�!�I�-eCom%��A�:� Mol�Or5R�9}A" 121-126�p80>v Dela�YChoice.X)Intern�aal���QChen ry}:5� Sy�?iuma�155-159��0Q/f� p 11.�6U)9 p. 61E�e�QGravity- 2} 9� �@. Isham, R. PenroB@8D. Sciama, Oxfo�� ClarendonA�`(�L:� uA117b�rtl�A� SockqE `(��2de)�que} C�d�9C2_�ppl. au�eroM�Tome 4��81a8C2 41-61A� f. 6!"139?��ĩ2�7x1Im �F6~�IY$12} 989-99%�2z�on��!�� Sleepwalk�=ӱ�[p 162�>�In!'2�>,. 227]{Honor (!}�-� 17r� Six World1�*m�2�7nNobel Y�65: P�le J�Art� Sq�ce_�DStockholm, August�[5e�66�Qx 1812w=eEPW>� �� Tech�� �Ide|VqD M*ZBy}9A��mG�a�:�)d�VY 96=��] 2��U(�!E��4s}�ridge � .�� 7. M)����f~0�3of� " to uP8����1 G"��2f^b��S2�e�mRImX3} 33p 0CO KU�A$rndl, Daum 8D{\"u}rr, Goldsb(, Zangh{\'iR0em Il Nuovo C�o��410B} p 737-75� 9:mth�th+�a� n� IZ,61} 972 Nov  93=��*'s FamMTex�� ohm,*� 5�QsPr_4RH>2E=(wood CliffsE�J��yZ 1:o� ingenNk"E[Ch:u2�: �Van No�sL48} 696-702 (1935) J>5 BornA�rn, Max ��,al Philosophŷa��Ti�}&� ,   1949 ��Toa�P8H} Brown, H.R., Svet��ny�)T*D !� �QL20} 1379�90.�ݥ�us��J.FA�orne, M lt, R.Shi���&C!�v..m�23} 8e�69��- Hw wAO d �R2� Prog in:�41} 188�78y-{Mu n} ��� D\"u��D,.�S.��$\`{\i}, Ny Na�D Real�OabQ�B���� in: )� Erkenntni4,�%�i� �h& �r~{4R. Jeffrey, Co/5tini,�!Gallavot��M.C. (` ors), (J � &G -e1 "a9C , Dynamic� A��P", Luino, Italy 15-17/95.fGh Y�;s!ivi�= PC.W��Q�J.R�e�p- <�he a*K B;&P ,�!198.� dekglis 26}� Br,��zC eA�nd�f�18��447a26.�6T7�T5}, 380T2�2T30BTa Rapp�E au V'ieme�6a�e�� Solvay} G�$ier--Villa��P ��30b�53B�%(`*  et�0seur} p. 465,Z53fZZ�T^2�} d'E:�u I�et� inea��de la Mt � Ondu7i:|F� �52�R d'Espagna�;.,�or�}bf>U� �cs:���Pin�� �"�Sc� )T s ``.� '' CA� rN�: � ic 7.m �}B�E�ConO&ual.��B�,} second edi�tion W.A. Benjamin, Inc. Reading Massachusetts 1976. \bibitem{Dirac's text} Dirac, P.A.M. {\bf The Principles of Quantum Mechanics} forth edition Oxford University Press Oxford 1958. \bib�QuaOtEquilibrium} D{\"u}rr, Goldste��FZangh{\'i} {\em Journal of Statistical Physics} {\bf 67} 1992 843-907. �+ Lett At Rt t2ic 5ers8%'$172} 6-12 m 5aEPR} Ein�d A., Podolsky B., Rosen N. � ^ al Review��bf 47} 777 1935. Reprinted in \cite{Big Red} on page 138. �Fine} ,� �8The Shaky Game:�,A<0lism and the 1�Theory} =�$of Chicago)�, 1986=�They is us} Freedman, S.J., Clauser, J.F.9 A�v.%� .} %h428} 938 (1972)`F�DFry, E.S., Thompso�.C=_6UT37} 465U6.U(Gell-Mann}  , Murray ��D58} 1131-1143 1990=�+WorldB�, 2�-�0AN 4i}<8} 33, SeptemberA�5dHardy} , L-�JN�1} 1665E3.=2 Baby Snak!IHerbertA�iq��DReality} Doubledaya: m:8.�0Faster Light}FR  Than$Plume }�88�@Lugubrious FellowUywood�;�?dheadA>L.G�8Founda��D!icѤ13} 481�33hLHonor Bohm} Hiley, B�0,Peat, F.D., �uors6 Implic p: Essay��Sur��David ]Routledg��,Kegan Paul,!T��87.� Holland} �RE=b51��5sMo!} Cambrio�I Pres�>,I �IHughes S�D Math} , R.I.GM!��Struc�{��Interpre$on� � ��an!�,A� vardB� � L .!�9�HJammer Philosophy} AaM-!^�John W!�� Sons9�!74]0Jauch-Piron}  �@���, ��Helve Mza Acta`,36} 827, 196.�-&��Kafatos�MyIxBell's %�em,1`!�or �ConcepAethe1j�e} Kluwer Academic Publishers, Dordrecht,5NetherA{s!2�Kittel} �arl�#��Introduc� to Solid: e-s} Se�h Edi(,v�A�6Y�OO er��54-57%�59+$Tim} Maudl� Tim)�Qsnon-loc���Hrelativity : metaph� al intim��aYmodern G �S�aI��tic� V6 =�F!|~ �3�. II,�2� Stai� �!M�� . Sc�$bf 50} 587�� 83).��Dpp �Staa�Hmz �a� Q�$D3} 1303ffN71ad�E 75} O H. P �$Il Nuovo C oM(29B} 271O5)M�7} V�KNH 40B}%�z:� von Neum)vo� ��-��e� Hsche Grundlagen der`enmec�k} SprpBer" 1932" .j:E�B `!SF6mU "� }A�4 R. Beyer,i# etonJ9e?A+305-324AD55.� nus givenA�ciw��lw�refer� ��H.� . Chap� V��VI�[$e book are2� Wheeler� 4Zurek's colleca��B�s 549�647, al� }t�emu=١Rnot}�Weidn� �Sel� ~Ele�ary>� Bv Ally� Bac�� Bost198.�B� �Ao�S�,U ediM�Q �X Measur�}>�� =�N.J3&7Wig����A) 260A6tD. \end{thebibliogr� }   docu!3�J%\style[p��T,tighten,aps]{revtex} b.z&0abib,multicol-,epsfigbZ${article} �$class[twoc n,showpac�<4} \usepackage{�icx}%2d ?}2ams�D} \newcommand{\be}gin{equ}:#e#!v^!beyEna�FE$ FV"bwEwidetextBE#D^!w!il 2�ov}{\ov�!u.ra}{\ra:�llN br}{i�r} :6bppBpaa�r(A}_{\alpha B($ii}{{\rm i!b%�Q�T} %\draft \title { �}form SAL��Approach�� Fide@ Decay: from WeakStrong� turbE  aGl \author{Wen-ge Wang$^{1,2}$��8Baowen Li$^1$} �add�{=ffiliP{ #Departa��"���$al�ver$�ingapr117542 $ \\ $^{2}^T SoutheastU, Nanj�210096�ina�4 \date{02 Nove��, 200a{�%�abstrac�c( We study f1[d![d a un)�s2�a-�, ����three pe9z@ regimes, namely,("ve ",  D-golden-rule (FGR)%%�jLyapunov . ;miY0exp!�Bisiived Y�4of initial Gau�n wave ��4ets with width,y`order $\sqrt{\hbar }$ ($ $ be!�*eff�x ve Planck� tant$ $Short time-iof��is also%�ied, �respectatwo ^ scal��9�V�. In N�O ,confirmed nu� lly that �hasHFGR �before }5nIfs!lin!�n!�laneD�sugges� to a S[Ii! hich(been observ �a system)/w�1 chao�Y>limit, au�0Levy distribuR as ani x�Eb.2) of a� differ�9l:�1h�9!�atQaverag`logarith� U�may hA�rough%�ea)p(within someI&S! rvali�)%s posselarge flY)��e faAe-E��expon�-�:X. ���a�� \$({05.45.Mt, ,Pq, 03.65.Sq��\make�+H %\tableofcontents����� s}{2��sa�on{. $} \label{:.I87 kno-�,��lyE=-1,)M evolI!$(rajectories�((phase spaceE�ensit�&to smallVnge�1�����s �aE�parame% -n z"��E)�� is!N)ed � ouriaj� =�VAs, >� was*� �\d�t�1��|�{ith�F^ e�(cf.~��,WIC98,CBH01}p shap��:ok�0.� �� $t$�c rt enoughB�quadra� �e�cmaya\Ņd� >, just!Za dir�resulA�R' ��M} Most recP v.s �M�I�pi�'a>�a�� lete,�Bi� ur a�sA� FirsE�V p"�v"�* �qj�}�* N4kicked rotator�$l�0�;�n5o��b/scrib�their6�I�x��~w! y{ Heis-E�:WqP�5bE`�s an '�elyaf6��F>tB�M %��I�8not quite clear � ec�5V.�-�expec�?K�x%�d fr�� �a��E�duc)�devh���K� �&d.�m`� !VAkaly*�jA\pN � he�L��:}s still b'!W Thir%V-:BSU)��of"�Q�s=["? t�W1�&� �}�0on-independen��%�z� �v�)SOtt,ST0��a�i�m�top� 2��8�*S %�:�WKB d=�of6�}� ${"-P_1� ) !�1x,6} _1 <"�$ �S� �M���aDm gene� 2d !��aionn �*� de���� �U=I1�) _1 �wwoO; case1[WCe , alE line� 6� trea�to�e� Refs�R ,9 ,C ��,u\However� sit9 �Dž;clarif� јl���&k�aM�]V�*l.m�:7�:E�* .� e wauiy�isa>�;I�Rp, but� &5�itselfM6(���6.� � deep��Z*�oz� ��aM%�Rsuper-� �A@mu_(2"L :1at!Rrt"�) QLyeanwhilK|A�� 9 twic� a� �& ��ah���.�1GUǝ�t)\< Bo�A� nt�!vI����%�r ̵�A�availm!D� 9s_!Ht ���_a�.f�e�s^un� �6IAdAvapa2we, A!v| i2���a�} a�G problems �ion� � �is!�_is� only��uit�method!"}� evalm�*4t ut a good�r��poi��o#"�w � ��>�DFor:8 icit����1D�����"1IA p!W�organiz�)�fo�4�!�$Sect.~\ref�^s},!�5j %� �ݍ���ag�,sawtooth map* at w1.�! ��check!M� 9#��lM�major"ce betw�!�Ax ��X.���ay4r���a�F:���F%�nib. %�>�6�predi=m�ag FGR-eP��*� accu(ly ���", A� es, F�u�*�[a��rtcantori�:T��M�BCRHL99���valid��v�* E:lA5!_��iSsourc���aEYaD." .�� rrowQ.!X�e&ass�:�`%6�e"sF� ��2�A InBo�io6�[!y�+IX �� b�E"E�e�fe6�naCMs� � "� W� "�b��!;F�� '. Bye�i!qng4s�+ �teV# �Taylor!&ani �t���_  a�s 9Uh��-^AcVkinQ1).9�a2 >9s� )�discuss!�� N�!V#i�rq|�h'"�6�� � ^� ��:4G nd��9M�!�u 2��%V� . D� �1Af�-�oI���* 6�'"�*�I� ��6�#MI?v��&�s�Q�iF�@�!k �>em�is��j� .?$*l;eV ��5 e� 5Ze>� is Avwn�f� o coincid�th a� P-.5I�'���si�:!i�.F,`���!-AQ��" �2s�Ya!�2�F�#&`"��k��d�">B�"�- explac �5ro!�i&-2�.JS &8 � }i vo;�#A<6�2r91a �)G�"� e"� ver�R� . �5lu��K�����"�->�con��"<"Models:> %�*� :W"� X" *R�(!�*� 6� �� �͌� ��*�X H= \frac 12 {p^2} + V_{ k(s)}(r) \sum_{n=0}^{\infty } \delta(t - n T) \hspace{1.5cm} �e�}(H-both�\ c`,= K \cos r \ D2cm�0rm � \10\# , \%6[krYs Y<- K (r- \pi)^2/2a1a( b5\m )..Z`eey{ �DU !�J<od $T��seG'b� 0$,:�%1�M] &5 �)tic�2���M:"9%K�n \{ (2+ K + [ ( 2+K)^2 -4 ]^{1/2 � \}� �)b�*e�stԱ� �Vz� ABsT%% �j��fi�_�* $t \to ��!DN�''�W is1?��K$ ��Z an 66so, doeq"vvB bec�J� mapp� )){a funBof $r_n��� ter!mto� c] �f� og?* , "�.� 5E-� � dC7"al�figIP �)�ka= �} U%�'G�!�mB%F�.=�)po#vJ��VP0R ��al��?q)�!1a torus � HB80-q-�D, FMR91,WB94,Haake�6@-1D-�N& , $0�o r < r_maC' 5moW um�#0p < p 0!)fH$h�1)�5� $N$!�<6�)�%�ion�S��(h} N h =r_m~.��In ��B�@we takeA�m�z2� �h�%,  0 =�r / N$' Floquet N �"$!�9�1�id��Z2� U} U��exp [-i�(at p}^2 / (& �0)]K6 #& .r})) ] �E��c$a� \hat{r} $E>den� by $|jA)$�1)|jV)= j�) �)�� $j6  , N-V � &*en59,�%"& 1; $U�)U_{j'j  {\�{N}��xpA�ft [ i "{%�4(j'-j)^2}{N} -{N!-= _j)}{)� } - @{\pi}{4��!@g)l{Ujjtei�e. .)X, *0\psi (t)= U^t_0!'��&�%* "� R�:6�# (FFT) �Els ��in Eq.~�t})b(olv�wo�+ly";t2� �+a�$�*.�*��n wA�Os,)0$e.hr�0$H$6�T )EK)�-MV-pt} V=-�1K!��� �ex~Ix>� �-II� "� Ur�4��1a�  E0��� \subw0�6��J*XɃ� expaM$e� &�W�s��of" �!�conven1DinAaU��W�4!؁�briefly�}0Xm� &`6�Sac!6�#B ��Qe��E�e�eZYA �i; $a7$_0 (\br_0)EGa $d$-��^�Eropag)� 6�4Van Vleck-Gutz�er �6or� psi_{V sc}� ; a�\�d� K#� , + q�_0 A�I> psi-�.�.$rK=Aa m_{s} K_sP6k���{iVR#�Gfrac{C_s� } {�Dpi��J^{d/2}} �S��Um�{i} SN� - +{i�}}2 \mu_s� �DKs��GHe�HA�%$ $s$ [� exac��$6�!d$]dicates* 6�3st�?:$)�T en�D \b�it � �%�m�$R�F�5`5g��Lag�;i(&"�!�y�,�+R\=En$_0^t dt' {�;L � a� $ C_s = |)�det}( \<ial^2U��  {r_{0i�-r_j )|F $%��Maslov N$x coun�V�conjuaa�~�,q�N� � ered)twwi3<disper�  $\xi-�m."G $ 6p_0!;*�q-wASa��B E�E�(I� 1 �� bHzA�4]�>�iI�} � \cdot � �eda�_0� 2>r]aFW��Z/�*�9�[e*( do��� �*!$!�:!��w N>P k�(��%�e� 1yr9y Vo =.5a� -�.!�.!JFB p}_sU3Zʅ{S�0X� �;A7=V%�.)�{U�Rd} %F���|_{�;�0 �ps���Q�U��2�1�P%$�'� 6��}.J!�� a�Ttude $15�'B� � *�t-sc-0} 1 \simeq�c��? Ÿ^{H_1�?rm��;t)q+]^*��(0F(� %��� |8UF�!21� ��� ,Q� ivel� "+i-e>$~!eI�F2 QA"� trun�<��)^rs.� �n,L <Eqsc ��)-r ps})E� .&IR�9 �(A9�)AIc" UB�thuR9tata:�.�m�1}(!�equiv-��{�� }< ^2 ĥ%2a&.?\\"IR da>8sum_s��&WZY.Deltae� @,�m�Q�A-m�.���(\bp_s$ecpy ^2 U�� �N mt-g @-r0-1s� y�$�>��(&� �EA�u�V� �A�A|0:�.|%.( &��C'or�A�B=$2�o &"$ negligibl�A9�N�L9E"�V[��r}(t')]�ADS�A%$V$g&a�J, eA�e!rese��A���oqby �ng !@ vari�&� JA%�+� A$b2�>:��d�63�R4p_��{ �:m�� �}*a(4>�&�i&�u}a;& xi a+}r-pn-e}0J-�-<}^ �rJ3�!�e,U�1 I1Bp$)ʩ��0@"�A�6��h@ F�� �)tes: a windowt � r�r"�0 A�������a siz���M/����6� "c�,�KF�K#�&%S-6Z6#tw1!% 6o-`extQK c�@is.] �&(la]  |�=Aba =�^E�I�)^d /� V }_�,�I)-� )��7 V}_p$ / he v�J5cB��!��:�!���N ! m_{p _0,�6Ʌ 1{�e;��f� 0��} �\a� 5H��!,]rP�5!�$-p0�C= �+:C e6�'$�$&=1�*Cg�\sigm6��Q?a�� �a�um6xp�A��!�&Con2�"� �!�R�&�]� ��*af�`wwstrict�|&�! to 120|�a�Q%%�&� FA���#&�qia2LH4)�hVf&� < �� Hqn�is i�{w&P^2 \llm^$o� (kappa \gg 1�P!�5� $ "&��Ka = �?^!!a%LM���� 2"UHin%�""� io: %Fig.1E�N�e{ includjphics[V==\IN ]!�sc-c6 -tau1.EPS<capa{� mparCX!�!k!Hue��fMY�<��J�8. 8E�$M2s � j� �52� j5 2nd}�!��M��.�$. Pq�{ X $K=10, N=2^{17}=131 07!�m�1"�I&#�c�?�w D:�D� g9 $8.9Md�Am&ap!l%�!&H�� $�.� �./%""� |VD�&close�} Vone� d E� fig-$�E7A3enduA} �F"Gu/mQ\1s�kf�K high�� term"()�)F3� u�r� .��� deed*�;�6obnB�Zq!B5A%� |^2B�I�� e�"uK�I0$9lg�1�Hh(see a�|1Rq�r"<�e�=W��m�j*)�26�2!�VP�V�$6�Gco� �� L �,tzin"�E$tA�.� �%oscill9|��� � �$ KP us $�fe�?Y<"�A(5�q ToJ�32%O6K� )�� 1�!�needsa$�!i�G�A�]�F��Fdo ����P ,r ,��~eq, 1 *�  { )�u"� p_s} S� N-� �'e� ��R ���| �e�B�6�r_� I�|_{�=��I|.�2��(r,5' �r_0  �N[� �pp-pr�� UjHB�%)e ���a�ced/3simila�X�!�0U�PmtpGAwe�%l.�(& *y��4 xB,(& \7lay1W } d{� {�}1 �*)�D!l{��pX6�.la�Id Ae}{( j/� - )�N�p0%uA��%  DA7  1$A 1{m�^�E6(��Q*�"-KD~ Not��5 ��s >�% p_0,mh $t�A�e�ml t�%K 1mo�2:� 6�Hhowp ~4�peS\� OXs ^��F"X 4st7~C �cI�� o re�d $-�1�$+j"V w_p!�%�fA��}=�2 �""�+EY^Yc-�{ -� �|�_�*��6��F� i.e.Uch�Pl .�&�%!%�*3r�C L)Eed:&�gV8%��-8s%�sY)3�4j0��{4� "� asZ[����preciseB �c�0Y�'A�BP2:2� B$\Lh@_1(t)] ca;G*�' ; GS:�:2*})E�"� &� � � ��u�P,� er���&��> ��should-co� �Ve.g�k�xi ^3�ԭZ�t*CsKf'!�32cg�"�#*?W1��1����q"�#ime*� N6A\$�@;-�-"BCS �s�<  4i EEs�:*=�G WR)�2�*eQ�6-&COjD ;AO.; :rerty-d&�26$ y}6/ ��?A�p 5r!uion�Ppecif�Ma0*$F��o��[(�/*#e�^hoOaty�.�� ���&'Um��M�� erN 2� !B�$�:�,� 6��64\�Q� �c<x efulP �-J� imrTantF %�}KR��;m��i#)] �X6U- ��=ds��/;vs-{0.�3P,"KVar&�GBZ ;t)/%+"W$.�/�2� %wC. � K��pa��� �BMly� in $[0,U] $r(a�x8oh-on $r$^�0�,=u�� �P$8 ,p�&P9orzr�@Cu&lot�s o?tinuos-2�.!�Jadv$ $2n� �heE o=�B�6�!�:���be�5��iruf7=<�O�D]1i�D),1;ao( �,, ue��DS�Xwe T3&e slop2�7 w$,2�,k_p �E!&� �8�5A�3k_p"�P {1}{X �&al "� � � }.9 0!g.!6� `"P V6r'5� r'%J �� ���� �E28<%�AR�$� �Ny %gten5 ��a?b��t?!Du" *VQ� ^3A�s�a�U , $|*; �!� �� |� j1 $t'$PR�9. ^�2�n)=U"�#^A�t��H��/!4F�|x|>HQ t}E��?�^� �K must� �!z*�w/ a��-.�K��� crucA�!�%�r5�6� � i~� @Ճ ) N .�3BxE�e��sxP <ey�, n�ng6y�i�.� (6�:���a�@\R�< FN�VN*-r %X� �s ��9MEQ ��(��#� "4af��fix�3im�/=2� �.,�!a�KarF�.^#>�A@A֩6 1tco�1nbI?6 �!4&�:�\Zng�� �KKu-rI% jJSh as:�:<�Ka!eard/a .0!�2� B ���666�T!��Is $\tau�M* .�]�SQ6Nq "�A*� narrowV52r�C�  *� �m���re��4ver�V�Tnd s�Y�3sQr� s�MalEfE![N�L�HS O�y�7��L M"� E=v;Ge,us� �, �0a �fa.EP!�$these phen�6ai&� A�n/b*{ E�:c $t< Mf�yy a�2���ZB� 6o"MUm���� M��Me�V�Oar:T�A�>!6-n $ %� {2�� %9�e�Q A�.�M6� -C� �N��=_V�6+��}&CJG����� �gA6+#*'��  � L"!+� ds-62l-� � AI&� .�5� : Ct1�$ $��"�� !DTB� JeTomJn �X�Yto�$�Np_0�Hto� �g.)�o�]�.�<ap�<e�V E/1���Onea�n&� "�shrink:P�<& e&�Fl.� AR �& �3�SmS2��S"�a4Q3is�It"%Wl!~�e.@d"'i�LD>�h,  e^{-~(t) t}e *�/B �8�(i�%x(�/to /�  1t \5�l{UB~[ \u? | �D x(2Mi�|&�$ \ &�*a  $?� �:!�#G- 7h�%� �OFp6LF'-^I�3&Q+'$��NKUx@ =#$ usu�ac��P"} QK&�@$�ck� �;'P illu�mF"�E B�8\}.)�}��#�Qp0�,�+I� eq b!�1).%��2(t-1)!�E# $=��influGof�>fa�hs, ���@v� w&A;ar� �Xnd!mim� slow�@��1T L!�[�6�l6-t1-�"u'! Ɋ! X�2�0$a_1>1$ a�2Y�~P cy rM/re�/SubstituE�E"�;%��;to�)��t=\s ,�b�, �%� 1+q�{U� )� n�(Dr b:�}{ �!�I6t12u$\ov b5�qDمI��ž �SF �s�s@2�t1� Fn1a X.�1�f6,i��$\sigma��# !��R Ʉ�hZ� ���"�n 1, ����=��!�!.p(d)c�/��d�*%�u�\l  A�:� -�?�� �  $(1/2 D )�s�'^{-1} $�3Z  1/2}AYPie l�}e Ehrenf�O .�$�{ D�&!0�$ &2* 8�� |�i��=xc!SQ  .�*- 5�� F Vs&_ ByB eqhav�5"�&| �A��[*�" uM��I� pI�b ],"�I�Jt<)�"�M � � ���!>!�25n ih�F�#U1"S B � $!�e& div5�; neighbog*�na��Tmy� .� . �s G approx t'[ *�$|-s2� �Xs $ c_k��u�t)te!Y $c_k8(!e pre-��m � �2{fz |$.�/B�)T�V�7�fw_p^2�.�&V�-McAn e^{2�� ]� M#0.4cm}U�""� -t-e'5wi�|�  0lp, d���9-2z�� 1 ^ Ref.�eSTB03},.n.} ( -\qy{�}\!�s �R�#0 �����/sim�zh1 &�"our�� (�= ort-UCs" ge`,ɿ 5uXU���J�1IY |drr, ]h\ A�A��%�� not ' t�c�*any��_}point7 mE .A�i�RbCa� N�u�X!�� oT�� 6���-VU!%�m�mO��< 4>$�I�c�B��a\ agre�}�x0�+"5 &os4iZ<&+en��s$M_{sc}- <�p�.�)Yc6X7 �& %�ϩ��u�$ � F.N �S % 15�� �/.���\%so��>���x6\ *�[�* Fd�GY1 $t"�*B�*�Xi@Ak&�I;'�4 +�.< *�,.$��R4&�!:(�� < t_d� 2>�!aIIK�5$t>_��C�P��Mt2~� [a�n�� % ��us���i")/�H�ofF�!"`{"�b�**. %AWQ� �Y0. �r�h.�*�  !�AC- t}$ %��werA�"�-je�&OB�ini%� U�*�>�#"���6� % $E�E� �-� -1}"/>�hm�&<7� '� t�3f�;%�$"� E~=�T zj ^fd2��G i /c_0) %XS"1}{"�B� �I)�a���]�� .�} �c<�( Ly}�QA,0 � =���%-&�&in6� ( @ !�de�**-)��Rq��b5.A�4 �Y&�%^:}�"� ( S5 )l���h�a��&�BYJ�',V#be*� orda�;� � ���w \in v����for" �*s��|��k�<|%Q�&/��$�#�o"=*", %]!'�"͗�a*�%�%�!I1d 5�$) Z� !:���m+s �andK�'r{s@ &��� 5� /i�);-}YH� %� ��A$�(�$&^�%st �!V�\ $ :@2%��7!R�isrnt�!x: $2/w,'Z ���6p|$!9�&8*�')7 �q8&� ���J8Z9)enowa&�F.� ly %�� ���A1�"l� �y 1/ (>)�<1.�S�2*E5 M-sk�@eeP%To�m)p fic,6"0a s!nxe����!a.%,B�*,�&�0ZeLnG�� "?E:1� $, i�1`( \ne 0in/R!q�f��.�o  �\ͽ,A"/6M�dAYI�st $|kA��"��t" �{)g)Iapplic) ���6���r% Ʃ",�ovU<U��]�P M-2-) "����� -� �& �. �@� �Ye�e$��e��"vqppV f_�Z%` &%B!�-VS N B{Q$$ 6H{pFN��o" =)�.'"�=�.UD��S,����-#V�n M��-c$ *�&�!2Q�.R�*w>� J� ofi0���2[  �\ W-,.��gH[]�& o�'o�}�.w5y %�uBF&�3E#1>5=4�u�'Vi-1-5�u� (a&�o)~\1K�&Y�Vi��$t=�`L �.�F� Toc'ify!��8�gh~*�*� -�b�o ��ve��:W��*� �&2� �#A.��&�c\�. $V݌Zun4 d�Qz��'�(y V^{(i)}= �~fcm�Vv;` 5z!��; f\�QhGN}_i (r" �d^i6F0 i=1,2,3,4,5"�V�fSet�!coeffiw�Cxcal^2 = 1/2� 2)}$B4.4� ]M�ZC御��k����T� j� =!�s�i�ch@��Xj � 44hav~ �s=+e�e��)2�8���c*<�wQ!&K*>5ci&�$K(E)M�/�ymap$ &�kE�),LCT99,CLLT00Ua�DK�+} >G��?C�$+�)m_{l=1}*�hC(l� "� � .gE[ a,}2^�$\�J${ V[r(l)] a� V �^\;{ 0,U*��=P�dpe2�jT sS5�U�#��$kp-i3-i5-s��Va�F��H H5MdI5H�.SFR e&ia&��i=3u 5,�T3�EuڡT�!P>RA�] tege�sVK"� 2�2�H"�6Z0�i�ri�@�a��!!� =� $l� an6�^c�&displ]@E{�A\*�%�a�g{l} :�@M�{2i�i���Ipi^{2iA�U�2A��iod�ii);E�RX{i>(])(i+1gXsL��2fde d� AifE%� �Q��XT]E�A�0N� h1!e�{��hA15}b$�3)�@$ {1.4} }{3�:.4:.{5}}{4*^2:+5+o2.2Y ^3 } �޻HMt-vr1345-v1st-s100�*�00cmA�c"9��A�aJ�d&� ��2��6���� >a1��e�~�<�up&�I7=10`$N�I07���=!7!�"���'/I� ovE�W2"06.5I�� val.�&� 1#9"�2"���)i=48an V$3i�s ;y �/4Qs� i=��01�#t1� *B �aL|2a4&� � >,� ��J.2k �(��K:8200l�5>"p2�-�E�-sN; flJ=i:Oߔ�A�ua��ole*eF5$>. < 3 !�2�J%a>�EoF��-.j QW0*|a�)t"��)�8�� DS-�"+SE�eqG "�/�X{n=>qtA'�� [ r(n)/pi ] ^i� easyprove�;�2y�map.��$T$I{�!`6$nEb�wnoޓ�c"2� JV<e�d!BI<� A�rom $�eo� (or r�)�B����):)E��@no"��J4� W�Yodd $ia�w�6t�1 zeroeT��'�-SLz��}1iQ*} a�:P}�rH8�'�&""e-">-������ �t3uld� ��~wmJ��� W ��jnJ;-L) S+9�  :N-3� � 0YeT�6�#.� . M��%U)�f�(S�&"�!�, "5+�t� *�U�~&X%�$"K��A�:��,�-�+P�R�; �l5Qmh}.f 43ek�N� f��!/��5�FAdI*O2�R"$���ETQZ*NcK]%��%*�"��K8A�q��abV*YPN"puP��Zeq 0.45-�D1.9!2Wam���/- 5/ ��2�G6�>$!�z05X g����%Pq=1$),�/� 5��b �4t �4.�$!:> �*5�� t2}) 7�DQ B9 ��<-�EKRinb'u���*�64VH *�$6�|�%�N�Fn2�73&����( Z�IF:^ %����U1�S� %*� W  N� "i|�B���aJ�C2y3$,Ep"+VN��Ks &�z`<�=tm@a��;U��uiLa $1/A�1 .�,4�4. �(iFGR��8d.2 K^2~ ��p�Q $K_0J#')q!\B� x~*�<2�&s&�y&mt-)-p0�8� ? �&p6H��wholeg g,�Ta!]6x @ "e�aU1�"R *P(s �?*l<�� *[YN����� � �F,:�'9%�y"<.� !_��$aU.�m�,r� y%zD]v,+e�5.�,�v2 -!&1 q^6<Mt-fgr}�:�a1[ - 2ib^2t]6�5��w��20]-1�N~",^� en�I�� tov.�*��.� �&�9isa� ��\a��y# Mt-p��  n Ap|ix �Mproof-��"�:is.�"�w% imt BM� [ �onlJF� ��a~��combi ZR��!�9�: :�3� M_p(�/�Lto"t-F�6xp "� t*�|1J�*e �*�T"g ��A )�%E!��t� xpb�& ��%L%�m3]*�b�!�ionZ� P"�V�����QAi�����2OP�M6��q� ��L�H6"�"&XS&��� 6&R��&{�on>k�l�2yme��"Ms Jo! 8j� �1"� ,�!*�Q6)s�G�s8zd�2t (PT) j(u�!59�a�typa��&�J��A�T03a�CU�!3n�5"�g� C{qt (RMT�q$6j/ %e��| ��� 2�A�d6} ��PT.#��(��{2g��}�ad� taai%PL����@aV� &�xm�3U�2g/ D��&���orb&  dent�M!� is 2m![H��IM�� dmtotalhpde���Z&^  q$\b� �time-?al-inv nt�!�37F :4 breaU�3 Cf.~* 5E5 ohYJr�h�*.H}bles.)�,� �=aM�d-5-n9�Z��Y�:a��.r �1�51�)KE`�^{-5}� +!�: 1*(N y >��}Eno ����h�D��e�� *5'ly up���8i6406%�,dashed-d+PcurϢs� Pev�6m�)b'2=�4:b,t< �b�"� fԄ"YL>� r�X� I eU$bV  %!V�, +.(9fiY"2$ ($b = 0.7�!�%]�_>6sYm��>L ���)v"�75$̅45��bt:� $t_H"��}�Ash��e>G�pa�i)t_H�$��Ejn�Ya5a�h6�Eac8y �!Od� !s1�? $ ay, OR���"�tA�B$o� At� \�S)'i.?=x h@�I�a>B� ��)&�%.@ fact* ly* >�?1 ^F.k<�6 �� >�56��O^�!ZN�t�m.  !� J�iM9Hor'�Un*0s>"�Ez��mL�':del5*6 I xima4�� To m�{�"�'�0er� 0� !*�$�i�<:� � B�u�&_9�;/.>qHy��y*�s, �Api^4 /90K�1.08 $ [�c�E c0})�j&p:��[ \upW6 argu�"�U�EP�5�YqJa�Q�+>J�d6��t� De*��q4m]P^�)�VL�< ovid3�o�un.�fo�M�K&� �'&dL+e� VtX�Hd1$ $t_Be��1O �A�4 or �_oiYinKZ0e algebraic p�E�!1/$O&,TH91,STH92,CTH� :�t J�&� �I�W��3�umI-n:�U��� 0.8N"�+2�BkwD &oftb-n-sb8`��P2P�y��:��$![AKV�j(f"" ^�� ,"oicqAh.�y2r ��. k$\| ENn]���W ̡? aken�����^�� �8ve err�|[- �/] /n�As��an 0.1� E 65E�}2�E"!;� �i0�I6�R . � tri`��F<bvoen�-c��y T;b�A� circ� 6�2AN�.�A>����\p"��!9�!����!o� �h"���sat��U�/` >4 $1/N�bF��$���:� �A b� �n�4�r� S9 6���U�cross!���9)&� B[�:�e0�U!�be ��gma&�c{ ~_p$��}'��{$MN�u2t N}zeeA2�5kF��s��L�)!]&�1!9wo��l�LDa"�to H!U� *A�`6 "� U�4xpa���B*g" &�=Je�A[Rv�F�,&mRMT�mIus� FE�nese�q*�C LDOSO$Lorentzian2�-��JAB02C a�%k�F9`belie�t4L vale�C�I(�!��C;i/�.���Cc| 9�K ��k4al"1�4����Aw${�s�U�Q� �J�c�?� 94o�1�A� ,�� � �m!y"; &� � !�" 6woh;�#$-P%� ]j.eILl�!2� i��i"9-U�.R�1' #ѯly �E(��ё�A�Ai^;ork5Wf��Eme��N roԡ!&�D]���]�E�� li!kg�Eqc8aqg L�;Aquasi-�FgyEe trummWLe ��"Y�\5M��E^� &�kon��{t"d !apT���ed%�rq�13 V�p!>.a��98Z٫.�iMF.2N3���E�6u"`���? rrec�cJ�A]���2%�ZE��EK@I��V.�Gas����[�*~i�ba-��T�a &.>ng2i Se T M_a��kf(#�Awp"�ˁ�"DT� Eo� {*�|^2��g+ . bA�eP�M�9>= k�Tm�|:�/ 1,p6}6"+-��QQ�Vk��E!�O0mea2�!# � �~ ��w�8%{� U���NS5�!�&"$6z�@ f{$P"H==?IPF�)yqy2�z eq k|�>����� i �?} ~k%��1�f*�1}1�LY-ps� \.T�fp�{���d̀p}_�q�{dB�V �[�D �&,U.[�&�{PdS��4���r0f���Ŏ y(gam-sig-k04�F #�$\gȶ$�(�� u)� T�"p�$," "K �fia!$- ^t��$ yu� ,n���(a*� V2.�+*��q��, 0\ܻ^5��2�!� 2aq t-u�aVso`���'L M��\p#2."� %`�F٦�#>�/=�0C y28=�}j�Q�I ] �qv��al.� m�ю�26� ._�absent c 5B2<*���^"as� �nag&k�~�6iؿ}Le:��. �B�in� nce,F2����e�2�:�n�� t&@ rr�� focu�J.cen&��� .@f�>zB7��� :3bMSmj-pQ�)W&CzV*��asymmeP� p JI Umeno� L(x,\al���".?�)}�+_{-��*�7��(izx)~� (z) dz,��A�!��x=�H�B"�0?!."�'P�Rye=�<{ -igz -D_l|z|^{ �} [ 1+i�\�L sgn}�(\ \omega (z�݆�4�!�-in�� ext{�:.�7cm�J>H�tan (p0 �/25��Rfo;��)x�A k �?"�Bfl(2/iGn |z|WZh = 1.Œ���� �]X�4$0< < �";[�!� A�u` i�B$L(A@ |x|^{-(1+ L) =� $|x|!�Th� �p$l A )�$[-1,1]�)�8g& y.�� g<S(ift*b� $x$ �+i��a� $D_lAp3V"o�w.d�.c��A A72��eшan r; ��2� , �+J�\]5&2�\M ��G'!�a��z &lQ%{- 2 D_lA/y8 =mMt-v*M !��*�Z�� ���!C..�U*��%* .Pr�ond�|Q�=(?=�~U �p �"��� E��<1*G�.KEu�p� $K<1l.n&2 s CY�strn� &$�$�`&X� N2#"M"|�n�� �b�$si+E&)�2l�T= m"^@a|b��4!!�2� C B�m. 6�!x "3ly�${"O }P f T N !^��[��%�j� . :�r  ]*sCseVZ32� A�>� � �80.1�>0.9N!��"4ST resd/$����Yc�%�y�M �E7e>\� E�M�F) �Ge�wQF� / $K =� 0.��A�0.4r�$is#m�O�� 5DB"e'&� iLa.q"8!aNW A.�S]���)�is �4���i�~eq�1i��:�adMi 0>�to>�-3&[*ps� -levyK�g01 %�>� U.j �&k %]%fW��=0.D;� �=�;�8!ƥ� �2�d -d��? " A�&�Y$is encoura��I1�&���s.Ѕ�� yet &��de��%/ur�!�s�ˁ8�6 :K2�3=�J3.$P["1B"� B)/"]$�C!�&B� *0 %�t=1�=($)�a F.z, "��D*ly $10^7;�'�J2�BuJ�76�-"p t��C= Ѩ�)� t/6�E\�p6>�6zA8.S'��*eF] in.?1a6a�|U��5A;I�M�ea�twohF�2s]Fs�,��-�o��  &&�g�"�;%.�"jM���o.:n idR1�2(8�zH\l�Wt}�]��4�l&�$%j*d�ZT."��\��e2Qj�Z�TA:�:�*7Ra"�X2�� �;^ &�iBO4�S%T2V]�i&_4��Jt�spa},~c�~$�ZN��(% .��2(B�T�;���B�-�i��] AA�'top�el�H� � F J�nf3�*F()� ��~t1�M "�"Q�6m6:�-��/S:k�avg-ln!�����*<by*� techniquq ve�z*�IMB!]�*&�0[2w�GB�1�N�4:]A+�&�B��� �Drom.L.2�Sby.>,�/ ND�N$�f=�% D, q�izb--��ŋ-���afm!Wforwar� ais%�ow&�x!�&6��S w-(c�#if �mu�gJM!���+�h&�E�'io&nSs�%G?=��wA(�'!RѦ$�F<�Xɻby�8{0� ��%oa�a: �k_q.*$u \g���P�h167Q 1G �mp�1l? �-Y ���"��msc-ma}&ɏ�2&�  u�p� ( (te2��m?Ie�SG(t) & =_f �\G 2"�}}{A�aa!f+�}"4 (��5��` ��1�(p=�ww? �w�g�]}�|_{S_"� ^{''}} | pIno<3�&�|iM�)"\ jG�J� �\a)T�Q��X��0���a ~^2� �|_4�´9�$�0.̋"�ma�EeEM&8Y�U� .�!�)�1V4A�A�yD �ydQ�l��B�[�� Let�_�8i�_imM0�c�� ir� �yOr�*� ���[ &_{ {\cal P}_{\delta }} dp_0 \frac 1{ D | k_p |}, \ee where ${B;g06ZXaOP^2FR ^2} U] (p_0-Y� }) . m�kp-2p�a�Du%^exponen!+$ divergenc%�neighborA^,trajectories!�0phase space, E>bg �hVW �6XtiAc$!�-�tA2A� evolI�of|Q� inE��bracket�Y�o, is given by �dynamicE�?4system describE. $H_0�On��ia4creases as $ [m�x(t)/�Ax(0)]^2$�4q�$m� dista!{in._ . Wa�i g%� ime,�number!>#s 2es.�(ly, roughl!/Fsame way� $�:�ahsi�!!oscille��$\D�S$!\A `duc)<lo�0,instability 6.W��,n, substitut�N�nto�� , we havei�B�{m�[ix 1 {D|^�|u�]}uDMt-dx1}��W�@D$ changes slowly�������r��2�y \no-��M�s\�,I_{\Lambda }(equiv e^{- _1 t�a  \text{�!�\ 6) = - \lim��A� \to ��j 1t \ln �erline14|!{. }0)5/$|^{-1} }. �yIt-3} !4y Inm^s)(coAntM$LyapunovU�s, =�K ) reA[s� A�usual; deca1�6=\l)Tm�=other��,��n fluctuI�in^��Unot� 0neglected, $:�$$ coincide �s$%� � _1t}��$in Ref.~\c� STB03}a�5limit $t%�\infty �S M _1 =-�2)}: $ep0\subsection{D��S� of $\lnE�$ATlabel{4�:avg-ln} %Fig.6 \begin{figure} \includfHphics[width=\column ]{�$-t--k7.EPSccap� Vari)��L)�(t)qX _1A� $t!elkicked rotator model at $K=7��0�:� @$10^6$ random ini�! posi�>.k def*on�HQ{N� re͈in Eqsn �-o �7�I�,� p!� vely x� J#pproacha'hey��!�)R�h<1.27 $ quickly, ��%P��. AHI fig-?(-t-k7} \end%�( To under��� e���behavioŸ�1�%�Ql for5x|$ typi&*H as��� 2� $ [see�g� ]�Ma��ult4 V�!�tf��?o -2��P t��he�M�fie�y��hfXN�E..-, mvlie��A> hood�B� a&; ,y��-aR er. S"{ totaIiz��Xk Nv w3 �� M#compared &@do� �?r��jpossibl���es has a �(rate betwee�2���$.��Q$In a classA~) �strongk oA�6L2� n�6� seen!�6���) r��,)E�2��f)��nC !�� ly��4, or a little ��r tha��daa��V�5t$ arounS��2$Alonger �%�N�RrEE.��!�ion"�s!� on�nrt��msc-ma})!5�����I. A|third6R $>z)* ofp:�A�;eff  window�E� is i, h�,j���be��@���abs�e�Ysqu� ofMr�1� e do��8know much aboutdIRvMn!?s6>,. % An exceI AtfoF9�!�F�^efQiT��c�Ranalyzed?.^ will!Wdq in what f�s�!\� th6�,�< show�a)&R���� a $-qGto~ ��eOuld!�eas UN�is-�� ��re��1�Z �i5 menY�*<��"=aI!�eR. b�is�licab�P�^�%t�� v� dQ!�� �F\��� n,. q>�� ma-� ���2X� ( & \simeq &suT | (t)|� \\ & =9.} ,2\hbar }{w_p /<exp# : - 2(.�ww�� ^2&�} {{� K{S_" 0^{''}} | }}. IU�r.p ,jwr U^O '' $� \be o6"\epsilonqt���"�S''� Argua�$s similar e.z lead���9e"C>�)�Ow�H em�*P�fr��ɤ for ͹z-ar��B��D�.ta�gle&n is&� eCi7� f��,a2-\�*�0��� displac�%%g$(a r_0,� p_0A � cent�� �1�s�dy!�obtai�A�a�[. ov {ka�| e^{ eZ }�B l8ta�Mt-lyap�� �'equ�!l �ed,!�c� � dlE># KB0 �$%o�!�im� t��T.? ��!�Uj��ai/�2�1�A?invalidA���  enough& ��� ��F�h�q�Aert�a�!�wholemb* f V� W=� �e���R�%=:/taka���$M{_1� { medik !/s,ysonaex7��P�]� � VO dei��F�� *� 6� � aŸ$�� Combin�X abov�W �� t� rA� deed exis� cera�~r>�?; `�!��q�mllW 4 *�%*� observ&� ctop_�WL02}�pe*nUL�-vV�.�*!]  S� !��A`�{AI' val;%�n,�(� N� EJ5� ���@$�uЁ� W� tes�(these predi�s0 wella�t咍�previous�, -�r.� {�M� E J�Mt-kr�. It!�Ez y�U�Z�%� � fas���thB�/ (as�*�Dc�th!�afVaCnsig !�1�a.�C�U1 ] , but ob%Uly>�:� 5�j!�!�ed9�R/��Ajb�p%l*�$because $K�#Y �*U�a�N$�2en.E`� �"�9.= �nU���i�Zbu�= K=10��F�A� FinU.W �:���+x�%>� cussed�maappea�I�&�, �>|$�.��$t<41�aC�َF�-�V�T�?tci�9 fact�.in�&c*�$s2F.�F�, e�!A$� tau}� C E]Y_1$"-{ret�A�1����-.e.|soE ey�es Z�relat�EH�&nc�!V2 :yp .��"R��M���N��8��numerG�!͛STE���*F�Fb���N�a~��($N=2^{17}$,u0=20�A��i* �5005�" .!t $\xisqrt{��w�UY s�cn�)5A'(chaotic sea�*�$m����� .� dQ9�a+A�"�&, Gf�_�OE�I wb�Iinb�. b K��d.%�1.�-V�Z!M �UFa�e� �B�  as1Yv�theor��'� �Q�B� \� (ion{Conclus�!�di��# Q-:co!�A�ap��$ impro8 !.uni+, semi&��Ŵo"� ,%#ide�'heq�ord�:er� ]Taylor o�C a( ���mportu#��"of�Q�!,� �$e^ u_� U -�-)�ofiA(� �)�-/6penden� '�)$cular, two�ksvg��tro$d%�studi� detaiWv�� � FGRM�2�)iperturb�� ��.s!+nfi� !�direct��& onj Non-f ZQ:,%weak ���9%�YA&�expla�ɣng.e(r,oQ differ��� Levu/F�!� logarithmNUHisa�wk,�'a�Y�B�����qA1 ��!� i�F�esUr *��@�#eE�L�.)':O�( A� �dem�&� �"at �*�!o"rric`& l(ple picture� I�! bE%�iMՅ!- jus9ur%� inct-AUI>�Ų-d-st-p@-},�� pres8 a schema��diagram�!6 $ *�#�.u�m� c sourc-,L+s .��Ѕ�*5�1�q B��� V�,A|� � is mL#�lex)���R�,<$r.>k" � 2$rFbE���Œ�31��. <*!d'%lE4�"�,AVB� ��L % \vsY.{0.2cm�ic"(SR��x)���2��LM�iG~�^f. $t_B !�breakd��im%ej�J# t_H B$Heisenberg�"�&�"� �se��\sE%�&X r& eE�pիon�3�TI�*u*WCN4 . B�&�� ^,'A���� �aH$t�(>KA66�( \acj ledgs�( he work wup )q��Pa Faculty Research Gr; of N�0al UniversitySingapor�TTemasek Young Investig�* Award! DSTA9� Prox1 Agre(8POD0410553 (BL)-reNa�'l Sci��F#"��TChina No.10275011 (WGW�&!pl ix�"� D� 2ue n:Wtrength�V deep9�)�E'Ro!�*K $proof-1st-!�^,��w#�ſa�i� h����J�j��q��� �!�m�u�&Nmt�r -p0}ILet usM�*�*W $[0,2�')$��in5e}3�"ub!Ton��$ [bj}�6(j+1)} 6so��t��in �)=!.Ae=&'�'�$�1h��eg -�,62�1'*�  a \0ar fun�,�F"���gma (k_j, + b_j), \hs�.1for} \(\inR#pIwgp�05&�8parameters $k_jp.b �#dEs!%��r'{0j}=0Ur $j=1 =)�=%� N_X+1�9� $N_X�not�!|&7"9�c V(3�32�2�, �%t.0!-.L m_{p�2G!� 1{2a*i5�&/!8j=1}^{N_X} X_j 5� 1cm}�!r�'a�\#:fraUk_j�B!(oi1�)�{M� } -3B j}"�2)2A b_j &�3Xgeey��w(rrang1v9h%,r}3�NK)�sh� as� � )�;onVc9]$M�y�0.~(y,!u) doe�  9N�9 � v�#:�S"J*b�� or�al�� A�)��+})x�ly �"5��(!e�RnE�.�9�99��� is�6 � X_j�&p/o2�2�to.n��regardGs�*D$��5YD o!4s!� X�-R(omp�6�&d�f��� ��ov-M} \�A>$ M_p(t) = :�}�� t dr_0 |m%|g::�(i�-�)^2�5>�h |a�|^2 },�5C��we assumy�':�"��%�..!&!��.*2�66"s" �!�{!'+(a�2\1-ov1�!1�G�  ,�! %7�# \gg 1&"$Mt-p-d��"�4Lthebibliography}{99}A Lbibitem{Peres84} A.~ �, Phys.~Rev.~A {\bf 30}, 1610 (19846A91.Ai!= it Q�=8um Chaos}, edit�M�H.A.~Cerdeira, R.~Ramaswamy, M.C.~Gutz)�' G.~CaA0 (World7 t3,�"� 1993p.73.�. �SC96}hSchackSC.MUv� �E � 53}, 3257�962�$nc-book} M�NielsenT4I.L.~Chuang, {2eA� �-�g^,} (Cambridge.� Press, , 20002�g�G. Be"=, -5r$G. Strini,�Principl� �� pu�>�r| 2004� Y JP01!wA.~Ja�rt�H!{$Pastawski,=~Lett.~Ew86�.$2490 (2001:_AB02} Ph_4cquod, I.~Adag�5DC.W.J.~Beenakker, .�.q9A�54103n22bCLMPVoF��Cucchietti, C.H.~Lewenkopf, E.R.~Mucciolo, �:�%(R.O.~Vallej"0=M�(65}, 046209J�JSB!]2�P.G.~Sil� rov hvl4l552 �!j9�CT� N.~Re� ruti�(S.~Tomsovic29%UiH88Y2U.ZPW[BTN1DAH Wisniacki2q�5A3045206J3 WVPCn>IE!7 VergaR{>� b�!DR}J{%ED.~Co%!J6!>6=>Prosen�T.~ ^ 036208-;.EZ2A�\M.~\v{Z}nidari\v{c}, J.~ �A)�3A� 1455 U.qCT03}~2BQ� 3451Q32QB%?Gaȅ��� � �� ]  066205�;=�J1!wJGVHFJ��n\'{\i}E]e�E.~Hel��JY�J56�PSZZ}T��Sel�nWF� �g.~TheoQ� Supp͂15�20�}6pBCVpf�A2G.~Vebl_ �6�%-�32VwAGMgY��m��$I.V.~Gorny��A.D.~Mik �&� 2�562175�]MCDP%:>�%� R.~Dalvita�P.~PazEV W!^Zurekm|I����� 91}, 2104�S!@/� GD�A�>$v%2Js orfm!�8nlin.CD/03070252aPJ?B�N9R�9�� -matX752.XPq�D y �j�a�eA11� y�GPS�T�r�]]�A,:�� 1102>�P04V��Q Q�rF,-ph/0407040..WIC98N%SIzraileC��~ 2�M` 5A�323* 82�CBH���$A.~Barnett)PE.Jr�� �I��=T Ott}�5OO� m � D"GaGs��_ 199A�9�S ,H.~Schomerus%cM.~Tita�Jw� ŀ �� SHBCRHL99}F.~Borgonov� bo�9aa�7!w 4744%x 6); 6K%ibid.}, 38��4651�>3P�n� Da�buzzi,ATHu)�M_�ica D W13a�3�` 19996� VPA�� %7]�Jkv�G�;2�� 3410 aJ=;HB80-q-�I} J�� HannH nd M� BerryI�.���6� 86? FMR�J.~Forde�M�Lca �GeRistow�dW�&49)UA�Y8 WB94�~Wilki �P.~Br�& � �mM4�G 1968%�46KHaake}!� :b SignT� e �nd 5A (Sp�#,er-Verlag, B1GM��LCT99�Laksh)ray��N��Ce ). 2Z �6At 3992�A9CLLT00( &Y ,�$>w%�LefebvPO!�x�;�� !�{TH!�EUV�atM��66it1H ]� �4a�28 �3);.#K7! 1405%�p�STH92a@-A. Sep\'{u}lveda� &v ! .E2�nŠ4� 199:�C m0P.W.~O'Connor�g. 34$>`T� �m-E� 382�: $Umeno} K.~ NK50 26� ��!ag>doc`7 %H�- - gD�- �L�36�?%.#2�narrow &q.S*. ezl{K(K��!,0�:eI6�r�J$'b�q�J/&F��+��!m1�m*�'0*��� $ts a"����"�8N�&&&�&wG�'t�w_FGR&�%!7{&�e�a $1/$ �L4~#�r!M_{�FGR3<<]<�K2.2gma^2 t}10�,sawtooth map$K_0=�5�aVKAQ)qNG"Y-^�",6�+E"P2�c'gHpe2�V�whB�6�6a!]�G�"�!>(B$�"�".H &%."O$!!���P"v ?�A��<�F ^� term"(>)"3=$ (�FRefs.�M�,� � "�%jD.�5�e�7ed9.=, ji#1�I9Mt-fgr} V��:- 2ib$^2 K(E) t]2�$��&�&>,%� -z!�'2�K�ja 5�N��?�2� e�8 U!8�K�pe�.f^&. � m!d&"Ld�F�g!-A��h!�.U�%z(iF� )\!v�-�-u�!Q�.}Re�*r�N�t��6_8wee"�I5cU�r_0,t��y>�g��int_{� }^ (�"ZI�XW xi5. 5'�V,r_0;�i�] "e>"��! $N_gU�j.!WCN���i �w�?=�Zq#.A2�2�6,-�E�!� "�Fly6*.�)�o-n,ZU�I �a93�0[& e�!�kVkNdg� .d.oVO:cva. R%�a̡b�Sig|!�L�Q�.9�R�!g$���+as-�S2�J�'6�!e9�-�)�5�" a�5�f $|X_V$&�!BV �M�lO�..�N&�W� n`�}nzG��Xj $s�!A2_, q=�Fa��!T`�AkE<&]$���ڳ�c�ik8&t SK Z|�F;q�:!b*� on~S�?�R,EGm�>9:"p )� m�*n&F)k E�Q1m�F� �� �� xp (&I).�Wo u-DB*e�!�S �$*�  0�xamplEx"c8�2wR#�� ;%<�HY/%K2 �A��a�,% To make cl&(46/"$��Yρ4 .�P��� a0 exac;1rm,<��k&|);{G}{"�F�G>x(�G|�� \chiO�(%��gp0-2)�%��S(_+.a� ��_%a� erroa��4by. #��,$(�#�)�Ey5F:`)$ %�]^0%�$, _*�$o�0���쥣consecu(; Ezl�$j�� such2 sumM>2>iz er�2group~& .[�L �F2 x$l$A�indicDChei�M $j_l�)E� ����&e $l$-th @��N�J-!f�b+ $Y_l! *& Yl} Y_l �c�%$i=0}^{ n_lo[X_{j_l+i�F"�  s $n�5^N�ar!�rge� �E<���j��  $�& t F� 5D��&+"�)� lX*g}! 6� i�, ��!�I6 , �% * St�PJ 4le apssamp.tex ! % % �Nf#�38UUAPSs1HREVTeX 42� .EVer5: 4.0r *, Aug�5�# n Copy� (c)e�A�=n��= Socie�c �Se��e Z 4 README��re�7h-��d� i&*%.J TeX'a�n/��*!Wat you� AMS-La�2.�=stw#d %3 &�C9�W!3preOsites�) !n� %�C also�ru'7BibTeX.%,commandm=ag�E:a 1) pgx.�!�2) bibAM 3^/4V \�? [two�\0,showpacs,pre7tI� s,amsmath] sA� ted �{� l� n�Lnei +ltern\@ I�2r �J>!�F. FurBmo� less .E �o�8F>�{�> &iKSonE �YF \�� {03.67.Dd��ACS|<�Ui!fA�[omyu�R% C�[�a��;He. %\keywords{Sugge7L }%Us�W wkey5`ass opAif'vz %d�RyGired \��� "9X(sec:level1}���=o } A{kin�9&jCre?,6�2N {EPR}a[wi- p)�AXrw:of�P*� G;�ing quan�oyf12}\o�s>!�E{1}f�%� CZ�%�"�k\\ >X=�0101� +|1011� !�9�_{1324jVM�.�+ --MC sA� I� -+u��9TIyYe�X�reũf����!�:>"�} �q5 _{24`Km.�**� �*2*A�WsiD1�2-: t`R�|U��WlA{b�naA�� $1/4Io�<�W ��~�_ES,$�X {ZHWZ,BVK,KBB,PBWZ}.  42�c���me�< .9,. It employs@!daal�ory�ԭ�E to�un.�:�H"�4B� (QKD)��n6� Ad�H!iny2� Ben�*!�( Brassard c�#u !� # QKD!� (BB84m �07)l{ }. A SEAs, �?�Gre �Fed 7� {E91,B92,BW92,GV95,HIGM,KI97,B98,LL02,PBTB,XLG,LCA}. Rec� ;�8Ge*� ES waA ��{C^6,ZLG, 1,D�5P,CQ-PH,LLKO,ZYCP}. InV1}%!� *�Cai%E� out ^9 E6�BimplifK ��4} and generali�a �} �_+S�(i2]ecuA<W�L igP�} �s, Zhao�?$it{et al}.a sen!�� �ES��doubly�� phot��� �)< I� �per�+-� a%�"� "Za�w< s �| p norhVA�� �S�s ,B�}Flwe�_use ESm �Nlegalrs@ �M)wagaX3 a=attack��; �LGX �;�gby .Y�O mean ee Sec.II�Y6M7 1G:�� �M in EIAU�g"GO(WH%V.&Z �EaW. -#w} S�Exh�F) &� ors,�c,Bob, sh� a bit ng $ID\<%�is!`! wy�. ��& 8�be�R� )�%F�c1�-�Z}F� uh`�I<0M�He�.� 1.�:�i%�"� . �i�Pa&7�yPR� !�!,� �>*� _{AB�� .�6 az1`sto-n�or�%�se�u%AA�(Bob. 2. DeF�$. (1) Hav!�receiveddjE�oAliaUBob"@ Vw sepe4hAQ9 J �fthem !�wo�v(2)^tells o#9_� W&% �) &9io(3) A>Y"� Y1`� � j� 6� !�8[ndaA4r�� Bob'b' !�2�!f yd,AKi2!�>�9k I�$m� n$en-U Y �$m9�$n 9�in^  basi>��s"�A:��� , ifm d\��VZ&(�Ea���C$C�hoOnwi���O�b@.W r (Eve) i C� nel1�wig��-(om�$ion. 3. I+�ius�i6�H^b�!aleft 1���&'s!PLT�wo�iL�"I are �&tSoY%�S_�zec�(!uTv�6� Tu�No�i���E��� �;mL (F\�1��L�2 .}!a2Y.{� ult.�$rno8�nP!)R ,%(*� to���B�!Eal� :bMt:v BIsQ Ń,A�%���%� ��f!�aF>�'.�P�P�.2"�E R'A�3) Ta"�b��"�A�3Pkey� en> s %N, )Jw �� 3on�S�-pad cipher: $y=E_{ID}(P_1,R_1,P_2)$ I�ɛ$y$!�i�t�R & m��4)K /՟� uODTi�L ��c�r�4help z ID$:�1'�'�' �Kg(y)!�.$% '� ��7�2�Q�%�� �3 !>�a��MK�%b'vIf���z, z�!OsAa�} ^ ���- tinu2 (5:�!˒�3 '� �u)�{- �(M� ��R_p)!��2=�* =�655A$M| 10 theya�: calE� 9+);�'� .�1, � topa�J� 4. O�hea .�jCF��Y�?5��!m�!� �/�Nhe�9� �G �g �re �& �H �ĥ�>� (' Eve IA^>�� �� A΁� {iA3G-��tra�<ifMV�5e� b��� too�c�����( a ``&e+at)5 �i�;s�|d�1$.6 �gshv4i}-;Sis:g:�.� p���%�qub�!y�/c3��.[^h mitt�B ��5�7�8J� �� Ue�I��ying��)F� ,E�1nex� � * a�ut�, 6f�� repe�attempt n ad�/�-�Y! �&'i� �)ip!4Ac)�r�Q�+aZe�wKke�,2�!'y�d��"� $ a��w�TtO�Rq g�*_7�! tegiZ'Eve. OnQ �ed ``"0X�W nd''&�6` %���*Q�re�q!mc�uqp feitAs6�%� ��!� "�Y� �.�I��{3e�t�?a#Aju�M�R�a� SSj`�\4. Bui^ �x�no��l��Ztw�|E's� ��cB,�E.� get M�mF;]AN�"?� %bU:6iuse $s$z 1J,� NVA�.J� �@ %� �$(1/4)^sD T������@� highadpc&�H$i" r�)�hM�y �[?o"abnc�� �!� two-�� )�5�aWt. A��"*;�Qc-�X ito �J�~ 22� ofA . TAq""�Em!�!0+#g�~N1. How�)�0a��xLecs�ur )&�. ��a`U).�a- Y< a maximal mixed)\EGy=<�'amo�Klh.�1�J�e�� 3!6 EMpu"�wo��"e%to��$!.�' "��|| 1�do�<�E��"�'2% tran�j: $|\varphi"� ABE}P>�!Ui" ��Q��FM]�!N6&!"$A�B $E$�'r�%(Mbe��t� �E� Eve, &� &[w"�~Nf � �'Ymen�,Sa[-Qg buil�de�)�2a_(&(law""�$"�. W�>wy shU show%�i!8is �"e["]'3N�heW & du'a^�m�2ducIaJF�^-��arY�g���E��"no.% : Bbyjp%�h����or�$X`z� i�XF�@KA��invariaH5, 04�Wit8 lo1'f��"���ppkSchmidt8-om��QCQI}��^Z!�T(�"�*&�"R<$=a_1|\psi_\#� |\phEV�' +a_2 =2}� =E.�#R�( +a_3 H3FHf�4 =4F=E>�#&$ :�Pe� hi_j O8 �\��$of orthono�.�o�a_k7non-negY* real�Hs ($i,j,k=1,2,3,4$ �?"� B� u�_(0$-d� al)]&�yŤb�>ten� �Zarbbi#�$&2'��|"X%"X%11Q$.�� \b�f.Z.A=b_{11}d+2}g3}j4}j.3)QO^2>^2>^2>^2v^Qe^3>^3>^3>^3v^Q�^4>^4>^4>^4.^>����4$b_{pq}$ ($p,qUd)��Q�i<�Nenb��YIA^ank8 @��� (3), asQU+�}. J�=Y!�s)(a_1A01�GQ|�lb_%���Q�<b_%�1�+a_4b_%o1�)��Y�N�2Z�>�>���u�N��'��>6>�>���wN�4Z6>�>��>>/Y� Fo� nven�g� �@�7 ur vw�s ( q�-��)*� *4+h�} v_l=Q�l},a_E� E� E�l})4lq� �)�} ��r�o*u oЇa�6� do o%��. KR�$RmyR�*K!}� {.� #S%O�3"8Hwpr*}ith7#s*� -�-c!��f�{� Bob9!pq&� 2�6  g��<H Zg��/"A��p!@&B !�&C�&!v�o i��  expa� ULY��WQ]*c-�y_A|2�_B-��E[\�<r,s�;T4 (a_rb_{r1}a_sb_{s2}+ 213443})� hi_r�fs" _E\R;]>�Vc��Eis0t occur!,]+F$P(\Phi_A^+�_B^+)&%.4}6�| �����c�Jy�9�"!* tN �D�J�  fact#� � escap~!9�(I��h�62!�%1nCp&�  �. �E� $ �.$.�W#}�  $N0$ , we�n�<,C7# (5),F�,v_1^Tv_2+v_2 1+v_3 4+v_4 3=0)g9v&�v_l^T�F!0> �v_l$. SH5q!le�#����%!]R-!5_A)Af%)+%+_B^-$�.Л��nB��-B�-vb�bF5.-1.�F�Fjt From)�8)-(1�dwq2��f�=�=�=f��O�2��\{-9j y}{c�r1=0�Jor (v_2=0\\ v_3N4QT G��.Qgr&AWs�#o�^_2���m�:\\\)i0A��YpsA\+EdB^+Ip2u�I�hAmY�+e�E� alY��~2�ԺF3-F2�F(2)v ���-]n���+Bgt��GM!�-E�:A؅Ua0�U3q'U5bFqma0�FAn�}�z\pm v_4E�2 3I�r�(3z\E'�(-�©�IUsA>F[M>!cI�*M. as Eq.(17�"�>re��'s� 13), (14� 17):1wd�~p)�\" [:?1.] $v_�=�J3�<�p; .&2.] %,$�)Y3$6.3. O0%.1 .4$)z2��� �w&v"�s�� succU<iPQca'th�)�N� w9B�)8� i J2��by��S�i�!�4). I�e��� hol�3�N� Jd=;���yea${�<- �0 sis.6 � ��"�4ZX6�V� �/ \J�U-~I(&�\pm&!)N�u1� +\ �\\ � $>�>�j�N 8^ �1�E" �&�  !d* a�",r� no6��;Ev] 9I�&I �)R���:d 2d2�*�! dra��FW���."�$o�I up,Er"+ �resisi,�- � &�x &�"X>C"&3} ��e!5Qz"%*�4a�'b)4� c>�26)41a*"aos, ``�[B(%*&�!!� put "��(k }a?!d�[@��h��^�6O3.7a N Aw +N�5Fu�9m"A &�"� b�"u�� advantag�%M��% unne�<�to����64�+e#-i&7�08"4isQ turn�����+*��2�N 6D�, &j"��#o A>1'�"$�6ngU�=a� - mG R�|�@�i{ e{a��_��*~-%��l&>A��"�{&,; p-.�@toh$extI)��#"!Nw|e"�A��%�<s,>����o be ��edn#%�I1hanEi0�' conf�at!�"�:�0disUe, i��i�XA3&�/of�[dQ����"2]qU^�6Al2{:}A��#��$AAtu](�); ]faf<A lem. M�QKD�sH}N�o��u1R�� fam��E91L� HE9a2��uo.k�'tO#i�e�aoe&qg5af�reuu)� appll)|Hm' QKD."�:%~*i݁�$~��he&*Hf�}6�}, ;~8s No: 60373059;:s^Y ��H �I Foun:�}, v<51436020103DZ4007B�ISN OpenC�B, >�a {ss3e&t�D A. E��e�i$B. Podolsk_�nd N. Rtoqb�K.)<bf{�c77af35). "�jZ�D M. Zuko�rhZei\R�tM.Horne, P&y<2l�c " bf{7�f428sDdsHWZ�ebfH�Binfurt�gv�uYc 3031�d� uBVK} Sr/(se, V. Vedre0!<,P. L. Knight2�A } bf{5;e82;e�cZ KBB}Q Karimipou�9. Bahra�fsabh ~agh|�ezhadZj+r 04232�m2.� A J. PyKD� uwme�Gr,�9i389)92�@ C.]�@ �G. �@:G)*it�q. �*of IEEE YL�I onalT pF�Lpu!~, k!�5hl:L P�Di�vBangal}India} (l(, New York,�@), p.175]�� A�K. Eker6�6�6!�66)1.�Bg:�Imz:GE�12 H2�BWJI%.!�Wiesn!�f\�i288J\�A}A� Gold�)�L. Vaid�nbY79g 1239eN26�A}�� Hutt� N. Imoto, Gis��n�}Z�*186�j2g KI97��Koash�ijf�%38 S6Rna8ru$\ss$2�6�8�301�j2LL�tG�7LoA�!�X.a�Liu2U�i�323�h20>�TB��J.�Phoenix�h��"�nP Town�+J� J.MoE pt��42}, 115�i2cX� P. Xue0x F. �s�G.A� Guo..j>�22_m>� LCA}�3-k. Lo��F.�knI��W(rdehali, e-�Sp ,-ph /0011056}�w 0e�CabellZi���!�05231�t^k��� Y%�Zj�b�^��k363�i1.�p|~��x24REFD D. SEX]��A�03B�CE6)>`/0009�r6hDA|LeeEuJ. KimJfR�8lE�au2�mZ.!yo, T. Y�|Z.�H�QJg>� /0211098]ZZ}A�HPq�W.A�-�R�I'223t2'Q�'A�. E}I�Ie�G}��"�Ho���eA? *^(},��q 2000�� p. 109-11s�>-  d"%l -n07d4119a501fc � � -Diii� : 4m-data; name="-ive" � -ph�gJgis_an_�5orl1�eJe Titl �ڻS"$�C+XOing��J�A�Vs%F�V, F&�V,.wV,*nV��J�Com� �5 pag�no FXs.�tJtReC�-no%�aJa(Journal-ref�c^cDOI�[^[A�V`��i��op֏VI��V�sureI�w74?��V ��nd��s��9n�Vul�6�+=�&��u=&�V �e6�=< K��VR��:�1Z�N,o�6n"�S,!��H!��UJU f1";U\�CF:\�R\myself Ҫ :,£�\һ���ھ:$vԿ<�j% ֤Э \@^\sU\�LAX^[=bk\ESa"�ZType:.//octet-�am�R�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa�Oa<_1b_{1l},a_2b_{2 3b_{3 �4b_{4l}) \quad l=1,2,3,4 \end{equation} Consider any two sets of particles on which Alice and Bob will do ES, the state of the system is $|\varphi\rangle_{ABE}\otimes|\varphi\rangle_{<$. According to ]$properties�s�< Therefore, this-voccursIMRQ+FP(!� _A^+�_B^+)=54}6�| ����|^2>�e�9�However2�$should not �T. In fact, if Eve wantA', escape from%A ction ofY� Bob, �2!,other than $!!!A�$, -- E�E� $ - $.�-E>![��+B�M>!cI�conclu�H as Eq.(17). Final�Z� �  threa2� � 13), (14� 17):1wdescrip-�" [ 1.]�ˁ=�J3�<�p; .&2.]$v% and55K$6.3. O0%.1-y4$)z2��� � of!s�makes��succeedw ��� the f�. Now9B�  w��<� i J� ��by putt h�into !�4). I� first�� holds���� Jd=0$, whc isf ni ss for ou� aly\ C� �condi!� w� se:�$|Nx$E� be writteAyU-euUR;=(|01� \pm|10 )_{AB}\ (a_� L � 20+\nonumber\\ � $2 I+a� 3� 4 )_EIT�It � seea3atb  is a�E ductA|a two-� I#�6%d ancilla. U� eEno ent� a  betw}Eve's9Ilegal&I s d � �m� no inform�E abou�7key. *{ �! draw�BWw��A7 thir6"0. To sum up,Erprotocol�resis u�--$ eavesdrope�,strategy. \sX {C�� } Weipresenth QKD% identific ��based�ES.� A�ur�again �0attack discus10in \cite{ZLG}!�Tassured by a classicaleoHs, ``randomly selec �Qs !u��put toge!�twos'',osteadA�easierc be i���ed. OK� hand��to�f!��!� 1� ha�TdisUe, i.e.,�usA3 sequence��[dQ�but�a s�1^Yl6 A�gener�* FortunateM I�1a fat�� roblem. M�QKD�s workAOmodel,�"�a�$famous E91U� �E9a2��uo.kis stillmon!A|i&����b us m�ppl�?s�QKD.  $acknowledg!� s} T ݁�pA�ed�� he N��al ural Sci%�Found4 of China, Grac@No: 60373059; als�WZY( Laboratory%O0Modern Commun�Fv!4 v v@51436020103DZ4001%+�ISN Open��B1+thebiblim~}{ss3.ib8 ${EPR} A. E���22317F� LCA}�3-k!", F. ChArA��W`/000902.LLKO}A|LeeEuJ. Kimv��7�FE�5%2�mZ.!yo, T. Y%�Z.�HCh�B�>� /0211098]ZZe�H. Ze!�A^W.A�-�VCE'22303�2' QCQI�xA. NielW XI)Chu��Q|co��� . *OP}, (Cambridge Univers\Press, , 2000��$p. 109-110Z N >-  � docuj } -nP7d4119a501fc-- ��\>>`[12pt, reqno, a4paper]{re� P} \usepackage{amsfon� > symbF- mathFthm:�idx�b in&�{�"Xewcommand{\Space}[2]{ \m,bb{#1}^{#2} >,0LPB}{ \{ \! [BRPB }{ ]\F= ub}[3][]{�!#1 [#2,#3\1 \}>halg}[1�frak{h}_�B�horb}{� cal{O}_{hBQpb � { #1 , #2�4theorem{Thm}{T }[-F] \ne$$Defn}[Thm] i�o1jHLemma % 6DE�! "6$ProposV (.6, Corollary *6(Remark % "U$ParR-|�!\~al}  #1F� Frac*Ad6=3@Jr ztwoN}^2.?1^jARC36C3B% Diff � � d}{d�>%�d ,2],)/2B/LE�uwE�fyieAM�)gBOoB�0>� Symp)Sp(#1, i�{R}{} )BBL/s�/Redset `red�aHeisn}��{H}{nB�h #���a�Z'star}{%X{h}{*}_J*uB'Jhilbh-o�=H�=^2>Q(oB)>'i:OIO>& lker.uLb&.r&0BL matj5YJ}{B!(loneh}{L^1()�)B�two"2r"-vL^2 ()�!�FMOrnr2(Ywn}Rxri�V-3F-8cinf}{C^{\inftyB�czero:$ _{0}VJ�6p.[F7'>38gB8GB�fock}{F!A�R o}{F(Vantid]yAB��de�� delta(s) x yF� 7sone}{ 1^{(1)}�AxA; K��yRA; Kf�x�4 �2�2)}GjAyRA;^{Kn��uN�3�� xjykRAj.A^{(k)}j�kyE 9 �_A)S jHixJH_{(i)=5�nHjZHj�H��SJ� fort}GFBG8vab}{v_{(h,a,b)N d! ',b'V#$%N&qpHq,pJFqpE q',pVCiq'%N&ooi0,0Fil�lf�l@ ^@o}!0V3�aK� N#1,#2BLqpFWV�(m]sS}_� .� %�ma �S}F� pro��#PB h��� h4->�kc.�UB lA�)�R� lqpm)�h,-q,-J� lqpp#Z�lqA� gA�J�qp.j',-NlqpUz^�o �0^� kctsA�kct^{*^+B!!� !-R!!Xw�.E�,*V)c�:+ {cl}N.FVB&sok:E F^okh��Q9L}_h^{�RN.� +oddB*pm!SF�Na�l{NJ� schw2 v� 0!�rS}'�1.Sbz B�b62cf2g:�F� X6''J'kepha!T� �e�,1}{\|x\|^2 }� �kB�@wk!%NCpi �Gfe 1fF95SP}N� m20M}_!i>� mspi=( &^{-J@mgc2*BKgc6KG>&f2FF� pzan!�%)&" _�  &�_�  y) --�282�281yF�cs �bb{KCB� kcma!�1� K}_1>�bs5bb{BSJEinv g�K}_B�Loomega}{\overline{\O>n0fspme}{d\mu(r�heta , N( N� . nu (\sigm,gam >nFBsgo�;, 9,B7>�rta�r,\�,�># pobs1bb{POBEvla�$v_{\lambdaB!l!lf!wav�1=|WJ�invJ*MJ*q6QB�r�c h^&�MFY���R�N ndex"t!�!=b�5c$(r8!({\LARGE Rel� ships Betd)�C"�'Mechanic�&�+ Re�(F {y/"5� Group.�vs�{1ct{\Huge Alastair Robert Brodlie�:/ � Submj+�,a�7�&&�5requirz%�+�deg�-of Doct,0f Philosophy.fnchool8`�(�ks goi'ose<4tgraduates who)F)���X LeedA�ths deom�*a!�j. time,m+ ��ee yea{:EV1e� much,enjoyabl� a tnumerS)footb�match8*nda= tripp<�,6�0y frie"<out�*Ym>���a me m* welco+q,aEAwb�j�EPSRC�(fun�%!��+Hq҂�bc/c� Z��)�i��ncern�e r6�tyN�M�nd c-2^*to both*I,'am�s9(� tinu)|developE>of $p$-.r:�1c�2s�,phy�/ �capE,$of describ����< simultaneously.& X�x�9A��>#��ne dimeR>al:M�D*E)G playAs�8om.��0� 4lin�vqYinJ} I�-�,�.tr�2)� idea!H�/2�6!al(e�/woA�ms: el��%a Hil 4 Eintegr)LkA�ls�=M!�.{lwe*=w)�Qa�-�@h@itudes{ be93 ed u� sole�@��s/e�A0�Mo!$eB��/):oryE��/�-�!������!!�rlyP� �8aZ 6�t��of�8nts \chapter{I��AC}B@2!2G0of von-Neumani�R Schr\"o�Qer:�EQB�o�A.$&� K1q|=�B��$Stone-von ��#l unit,5irreducjER�r2~5�B�are U� val!�n�A�iK:�at up8�Nce��f�``!��''E� Barg!� 's 1961 p�& $361} a�.M68b�wa� fe���Fock--Sl9--i͜ofx4ir��alytic� E�s@$�C�$-X:�$despite bea�)dƴ�shown!�be.c  �9 ��ng6 ti�� 07��pl��.7ai� evolvA��յ٩ Q� 89>�8�U�b�HG zej4C�5~Z;O r�6ist>6fa� ��x !��+6�se^4ly ignored; ho\F!I��96.1, 02/ �-� ��5n' can� q$�1in݆����+�Sf  ��F� V� �uy ���*#B3%^A�^�m+�*ra*s6!�R���I�8lyQr� si��w^y J�8�:�  B� beyo�BV�v�W� how c:��cb A4b�$de clearer� (�3x@.�b^'�J�32f� � �J's along�HV! �B� !EPAeQFiY`behavi<)�F� �9A�N� M]6�j�.��.� vs lemEYa�i.� "� ** actu]:�s*R5is�:pur��efetDept\ now����ummf�� view-@#BIn�1f  \ref{s :%Rand%f}f tar�9��M<�� back�nd5��UET al f":E@%�r��xum��EQ;�ter�i9=d�!� ula��@s>� R^�2D need&�E��|��4 a little histEE#>�%��=p@n� 6- rame  . C =�p��dhn�@mainly!� n!�2m�;pl���D�?. s. S�on ]:hn�tsreps}Ae�O0 i� �7eI1�=Th��jo�Ai�Rp� �!��n�=�ythA~  %Bin a way-�!cce�P� A,2 1�InJ%bi� e g}]>��6>��m�is �1�,�we[new d� %f>ballble> F staea�picE�jFq?"� lyo�Zi.�nC� N InF�qI�e�,f�"�R:�6g��W�/s%E�a�g�:b;AL.��!�ok �G��a{%:NA7���i2��c�aia[* �I�!�] picturV:Y�ۥW4A��6j)�� x�qzQ/azr2GbG�mA�6[�g|us��$"A��>m7pAdl�w�Ta�;��a"�Frigged6{[Dsoc*6N�ej>�&ue�XE�� }a F�' osc�Ld@6tɢ ��!6ll �`>�� "� a few2� >@�is illu�>�fݙ�sa 6��<�c�kvZ�be"��r3N U&)*OT C-*� i>�weE�� Is�A�A�e:es�U�U�Q�*yʑ��F!(��aty_V;.H�`&!)�� K!��6~2�demon�)��e- machine�6�we ��B�*��/�i:M��ard�1al era��I�8r�eVnE�{!tBlRuRJaaFdcan��a�H�S��vA,gX x cbg NVj ode[ >��T.GM�F�Y{!QZb}&�  E�lc � m %�A)�iof �"�"ba� V�We look��y��*�)�&��^L�f�A�m�o!p closAD linkoeHmetapl1 c:$�ejy�c�� pdea5E�pj�w�[l�y:mqw�a duc%bJ?.()� pply�}���I al� Ex&��!@%�� �&�"�deF�S�W�q�2�z�4a�Rwk/c.�#��.�V=-q2%3;�! ə!� triv�#n���aq1A�%:� !˹p�&&Iso far��insuffiIt��6b%1 `. Next!�i"� spkF�dpolar co"0!�2�B�*%elp*���qb� &n|u ��a�a��eVn-�{6�  >[%�5 str�Qa��6� ��%sZB:Ky 9{n YJJ� O�# (A!o�sui�@�B��a subseG �� �|� /w  Edoe*�_es�:Um�FN��"<'��6�4.1a�"�C�faFQ(�Aics} �3elNv *RD"!:�!6�& SB' Newt�5M!W�-tw�e�" entu�P:�Y s��assum�w be g_= b�lawe#�d�an�)0@Arnold90,Jose98}.�N/�%��"� $n$ � pend�p�le�O� by $3n$AM.I!�f#c�B. OnE�U��N� is Hztonian>�[�& 3]�}mX�'origin byF�Ue eKnineteen9�. A�!�r%.�U%E x{.5�$ pha� a�FbR+%�freed `: h ^ $2n$2�manifold��� I)!�a� UA%�R� T&[&�Mf ��N��(c�F�R}{2n}$�t��� hA on pjcepn�*�2]%VB�'�&�  $(q_�?,cdots , q_n) t��.NE�(p_�B8p28= -�---q (��w�`�BE� . Ob�Y�7in2?U#r re�u���#n.�\u(note{Cer�!�mY FW�| hese" s�U "�i" nE'tinuityI�%: urpoS����T�Ye�&.%��y�2;�Sy�.�leryM-�a��!i as2�%$"26 52n})$,I�i��+�H6���ct: 1in�}. },"cM�.ɶJ#p���=��Qj , mo� um, �Sg|Qgu_ �HM0DAE�a�$biBAp ixaapp:vf dfs}�W>At�% ex@!�\mafu5$,��T:onrn} = ( t<, (G;,) = qp'- pq'I96�Z$1` 6$e�.2*:�. $ qE�1r� ak����>C \d.�[:q!�.H.� $X_I�&2{ satisfieN�n�^ df(Y!" � (Y,X_f)>(g n.2f$Y$2�X�"5AqiJ�^�z��l+�!9J6�X_fa�j�tn \Vr�]HI�T:k��P� al 3=3FdA�� forw�*� �ver�n�aܹEe (X_f,X_gb�R�.2d&Wi7 Ba�[o"��#!��"- oa���(�<��A�*� do� *�re butAQ4��\�^:� 8,MarsdenRatiu99� Empir�l� &�\poRiV�$zf you�A(A�sQ�o�ŗcnbF0��� GenZE� ct�%tsV6�aA�pa�n? P ���drminism)!��02.7]{Liboff80!"�`�Birth�D6�0�"� .�y/�a�we�  a briefB�!6 �*hAWB*�%#' moti�0�Swhyv/ Q!�!�2� ���>� !F2V" � s7"�DFaa P"experi� �okXcxe�d~��h�$as*"�A (see:= : ��au})kJ��;��r�$roscopic l!_M7$f5l1-��~ ����41�A�na�� /e�9%�a��y1�utQ a> -�vs� !�aeple2�pEL!i� Brana�J�-in00,Q� ,Messiah6�Q� �!�Bly regar��t�5I��:  t�a-�ceF�*shE�d!�4blackbody radi� ; J} �u�2}�21.1]{B� }. Aq� hyp�gQ%�)�absorb�&�� fall� to i�/tEnA�ANat*q A��in*�4explai�g!x 08trd�5 em<a+9%ehe!�A�&- j fi�(a [A�ic�s� $\rho ( Z> , T)$ �ga.bergy d�4ty %� empe  $T$Q��$wavelength b8$. Lord Rayleig�>J. Jeam$�2^�"O rmot�so%K��faim��ÁIsit, a?sm8$Q?�-�in�\6c�pat *�frt c he ``ultr�(�p,catastrophe"Aysol� �L�$8%��;o,by Max PlancTDecy: 1900.0��X Vn*���btak-X value&oM �~M6y^�fH b E� r�q� M. Av!8*�c%�h&'v�U�i; d !�!]����"\%}GE�! �Dtant, $h=6.62618 \0s 10^{-34} J V\c)}�.GPnt&�B�FZ$���funda�al����.�feWe�*8��$h� tz;6�� *\�8Ca�w>���.�}�O:�f!�$ency $\nu$Nl?lyQ|@9i�$h(( &k a.for � oton�n_ n( step]!`� �6SeQuc'�e��pX�iric gc{$isenesa�N g3&o�$�]��&�&�'A|I5P;���Nv"(�'reaezto:�4]{��,:2N���5 i�46t� ���sesmq10Fd�͚.N�&�d 6�l� !#>* must��&A��Dcorpus��!�bI,. g ev�kh� 6�� f.ctromagn�ҥ��*H#d�d A.H.DfptoA#�)�&i& scat�,ng� x-ra�e1"�)mCoLMS�L6�'::~ 9�.�ys�& Nac9 �" �p��)wa*�@wtm. H"�2ter]c*-l��en%a�A�in5 circum�Eces i%�act2la� �De�D$glie, DaviQ�cGermer2ii��A6WS"�:)� ��n�l��14-/ du�� /sumA�| alYc͂"�hJ^)�} Nk^ BohrR:D!���)�tom�!�Dd�@Ir1jJ)�'%� %&hydrogen�a cjuA�qn�o�{gfh�b ji�/claimA�[{!>�aBbb�Es, { E_n : n� \Nat \�6A�$� �� i7AXto mov`{an2Y $E_n$#�%.wm$� d�ђ{ 7)H�m� $h �I=�- E_m� = as yet moW6�k�1o�;a �5� a>� 5rA!��V�A8a����2�@iN�.k�;rep�>A� se�pu�i$� notice��miB�O�sca{@i P� * L $,�ineglig�,� B�dix}arise�%\ �2s obeyE�e jD� �:� aFw>s�B IE��2&� asf te�Cto8 s $0Q�X:ivQw&� �:$z� 1.15.��mnIh�1!�JOA��vss^=inX#a�A4m"�C 2k�� E��blex�(s� pro��.3. It t�U��irac,6�6,.["��E]r�1K a6\*I&�,Ivresol�I�� �  � QoO s�n 1925.��Id�Fu KAXu� �tL3incipl�*R�R}�(�: " �-�!P��a��n �At)��p unn nd v��d a. M��e,�b� ���m-weE�*�f��G62p�>�� ex%G��l)�VR iN,la,$eq:!jn�} \triAw x  p \geq h>?g)xmpv 6��'I[��.]:�9�Gslow?� (2 �Mh�"�2t  tJ2UnE�сUZ oA��D��A? F si if,!�!�C�2ronAr�ng� ��w�/v� good"%FAQC� e�F%1E . Ifvy†uPu.�^ 6b�vŎ�e��e�!a @� �%�� !ut2!�Nc��� U8���liW/�Pٴxe�tart!�& s, axio5r!�tas. W� ��"X�?}ize} \ 2� (f+g0'!U<^Q}(f) + �\ (g)$7�\ (� f7~.fB.Wrf,M+0:[:�| b g) ]>v1>I_d>q_i�( nd $ >p rC*b3�(u#NyR'aqu�:9X�;!-%7�: Groenwold�NHp ``no-go''!��NE�{Gotay80Q� Thm. 4.592�?i-  &_Cto1�ifw��E�� ywgl.�#Y �Ab�0w^ n ho��o^7�:Sa e�{ 4MwY�}Shs. Vari3Xi sI�varR&Fr*�Xes�5�[Bx� uSu*�F��;d*�R t.m�. Geome�-3T )�PWoodhouse92,Sniatycki�}dē�]o�U Q 9hFedosov02,Zachos02a}, Berez V61 72, 5}, Wey�2.� 22(A�s*+:g�� � .�!� ��B"_0�=0�J6=:) mKse!�2�>��r�;sed�R*>{P"�' P.�G�["4.7:�0a�G �7�L" �H>7(*�19 P�1��tj*wW*�<��" I#�;m~a�NY6of ��A�"0 h.�G �~ j�X1"hi)i xc!9qls��P�%J�%;i�:2����%t�6�a:82�=�I� YqE�pr&4I:�H����D8uAu�:�"W]�RavailR 7&J &�Y>"�4!�!�w�%es!�a��:� Pc&mYbe���[ :�ǥ�= iM�mQ� Aro�|>T��B� y�< u�VL&U�U�u�ZS� �I� 5�lie�v�f�(Lie algebra%�Eop?*�N�!ept&�5 Haar(E| conv�%(. Kirrilov'=+2�  $tt$%W��U�ab�9>W� relb�H�t��V/hilj@exh��N_"�H� =�2��V$�+&[t ��mkbp/to щ�-�aq>�\m8�Ftwi�!�Scj�XX �6���L^}�B,)<:svSN� .3b�X _b*Z�VyҼ�.� .�B#!�!*m:XN�����^0cs�ck}�Y�0m of squ��!�gr��>�C�SQ��:>��2Y!���� �K@�-�ionv��A��"� <>8� �/he�Q����9e FL(� &�&${Taylor86}�3*T9� >�1 x{>} (deW;$ �2�n$ 0�5 })� �cleP CR_|�)T.0s2$�gA- la=S�(ic�fbN�+ } (s,x,y)�<$ (s',x',y'\#5 s+s'�c1s (x 0y' -x' ),x+>+y'u9 Btv9E �Dxiv ��-H��"�:>$s $B_1,B_2�#�{$!j��Z"6((B_1 * B_2)=F t_{\!�n} (h)  (h-o g) dhV*g $1*, �z}�d ���M��,$ {.�j�(Lebesgue���]Ivn5+1}��ds \, dxy$. Usa��p!� reguS�Qar�altIT} B_1*A= �\iN�\�h)%Xh 7B�A� _H/��wo .�0� Q�in"?&|A ftwo7Nbgeng})MFG;$"d}.��d $k~��a�n$}��f�U) inva� t2�9�B!�^#!a=�� m��>u!T-!Jinvveca<} 3�� S}^lajPD$al{s}, \hK �n��,X}^l_j.. x_j}���y_j��.L2JKYBK>�X{2}2KB�itCZ= ��o�a�on>0relfoWrvvf} [��Yb% �,�s _{ij.$%P�0.5cm}�.Q[O., r^.� &��'0RA�� Q�B��&>� (A�[< $(r,c|�/Yz $EQ $r�S%�<j|@n a_j� X}_j!�."b2"Y}_j$!z i=�F|exponen?���to�9�����7.t,3N�� #, E�J9!NL f^*:�^*$� span Heft}��or�/u-�]i�'0orms $dS,dX,d�= �^*)�Y2ĕal���h,tzR�B} $hdS>�[ q_j dX%�p Y_j ].� !'Z�� &}�K�of!9�Dn�pj�r =����_j0.��!��>K��- KX����,&�n0��r!F�r_B�r!ҡӑ�,>�rBcJ�s'U(alp[qe:fe�g"^UB�4�Ngh=-re�m- FourT�Bor�AA2n$[Eq. 2.3 3$Kirillov99v� iegp�$ier} \hat{sw(F� ��}(x8(\exp X) e^{-2 �zi�M�X,F"� }�dXB�hc.F� Z^*8 X� % $�),���?i2s�A!*J"� Q�!� �6� 1� � �,(hs+q.x+p.y) �2 F�=is�|ZZ�6�$] mo#4�J6I Q{A. qA�Sj� n#lerFM�P32��h>0E�� �o!�rn�AJ�6� �/  \rho_h^S 1�g  \��) (\xi!�9�hs + )� x\xi��pi ihxy!�si2+hyFV �2�en��m",is>�is"��Z a�.� ,!�!8429����Tw� l?ly"^V$�:e2\M6(�]G� �7XtVza:��hp�=q�ū1o�C�0ec�&�|hJ�M">O>Appn;"� �:0*�WeU@� e"K3�@bh�U�"!l"0%nc-q�%�a�0Fiw�2�%"��Y��Jzm�)�D z�:aMcus�I��>R, *E�.��: �1� 76};�� c 24!W�+ J ���Jn 3euAr}(gnI*=,*UD#�Ta.�Erh:>g!�orD* � s �% . 7]59�WA*%�0i.tselfconjug� (�' s $g�G$0rA$xby maps�p�x g$ ))�a�B2�.ϱ$�a$N.���&�$V�0�p*� �$(s'+x'y-xy�BT TA� ��ilz2e�P�"� �V�2D[,i�4�E�pIA�.)& ofmap�rmsof})�*�&i�u�?6jiK�%3\halg{n��t} 9/ Ad_{-y} r, = (r+ay-bx,�F.�r �coadjH6�U'dy we9� $Ad$RGa~A*� �^*}�+natТway"�$��ad�!} Ad^��&t  +hy,p-hxF�ͱ��Z�K��%l���%��Q" "$\ �orb� {�,p):q,pe=& !�}�S�1�$h:)(} \setminus$%0�9 or m!3leton�s*�%O}`� �0,�B9 N�$M��$�TI#� $`�a�( isomorphic!�Q��}:F0p&�U!G}Ks �\$�U[2�U<'Q>XN��b!�unE;! ^}���.>"eAK�1XKofZ��O!pa!&Q6M s4 1��si�G utili�/?f��%Gun�A]&�S9�!�b�" �&l%.T:}. Note ! o�sIa�� $a.,p � ^* $ �7e&cho�6of le�?�%S��Ul7"w}/T :z I�:L"U��a �V�"&~ Wi&�*w ��yDi V�R�g C :��V��72�� V�}�F� ��0B2_embark��ge*��r� �0� "�6�'�W sub� �suNfS��[S&SC ] IfM��h��%h%�� y.2g}0I�.F.�Dal $fI�"(g}��0� �Nfn\1 f , [x,y]"f=�`?2N#�a�x,y:uh!&n�UA9�3! ]�IaAzany��7$ -z��"� \{(rv�:r\�4"�}�V\� t>'-��>n�a.h9�� .����!5���$Z=\{(h �hn��n:�L= |�Nht*XG:j�$Z�)C}{I{anP VK^Z_h ((s��e^A0 ihs/A��>""��T�+7�EG 94�$at .\6�uZ~!�V ����"�N,IQa<^*� ��9�\6z�"61 �N� br)�x $L( )� , Z,Z { Z��3x!q� >$�+$ɳF(e�==w '} F� `B� by� shif��la>�:�$����~�|#{'j��a&*N���"F�"�r��"�inner�-ducNU� eq:ipNMdrc%�F�]F �5_#�� )�6�� �e�}L &>�F_&h ���I�"/ ^bUE+A� $\alpha�dga�ere $ �`a6�'.%�A�1e�#��os^2}}{\�6pi}� &��X�����:0"�ho�zn%e1l�emn' thm: Y�cN$X$N:^ GHom*Fe�.%� $G/Z*�ny coa?<X$�6�W $*  :K*' ��N& (x,y)6q2n1!so� a>�o�3� . U@��+� _IZ�arrow r�! Q%on�isF�!$dxAky2��$e�XY)SR&Q)� th6r�DW���0��,$\s��:Xm! �eE���JEu�P toho� Q (%� )=(0��BFCN��&Q G ��I|eq:jm�[M~W��&�� �1R� M t"YUi� �(�#�^!�!�0,0��b�դA!inf]E:w)� L^2(!���=�9rna��*��(&� ) F � &=& �+6#f �[�&J 1fK� +N,i ( -s'+\��9&$y'-x'y),x-*&-**&\\>rFm0 N6�ni0,0M�)>k�umb�E})-�)U�3�o�Tبn��}%H�kF(i� -� Y w�hte�+ESF��geP:ok0I�>0e��i\u�A�>Fdof&�N)Y��T"�eq:^98oh^7�%� ��}�F-FC-� (qx+p?<'B�q�ݭ� vari� $a=!�8b=A�$9F� ) berY=-�}E�eqn�� �h �B G [ (a+x')�)$ (b+y')x']G �.�[ q + +p )]>a �nb }6%& =?�h �!A' + py'�N�FB��[ a ( q-�*}�Z*� +b# p2�P &|*�rq�]���y�eft+ and�hoh�:�T' +qx'+�S�FA��dB�,j�UI-� fiP,R�by _h$� _h$}cb��#beտneao^v)infdim% G��0 : f��%�x (�qx i<-%�B�, p�-�1�5� 5*U�9y�N���:E�8 ($����"�:e>�*�rL!�e s)� e6W1�acts upo�0&]:"�ie��*q�8&V�1���;D $D_h^j" �� b*z Me��b)G*ohz} E-X^r_��P$i Y.a:"K.x-�"�$pl)+ �"�$qq�+ I5(�%+i�%)I5� � �0U��2�&+ �� !�-�͍-/�*�\ U.TP�FcY�inS O ) :~�rm{�gi"�fble�}:&"W)4D^j_he =0 ,˖rm{� } 1!>q j n.�g �a�!; &�4z#4a!i �auˋ�.�p %Y2oD�� ![i�+}v]mv.|nZ�DIO4}{ h�a�� jN@v_1�g*�`��ɺqźpUW�U ���T$�22-5;a��E�)o v*�suntil�[6�"�3�p"'�A�&�65�:� "tM��)~�#;D��c @�apparr9�Utak �e�as?%za�0$.�Lw*�TIF4l��[�I6E�/#5]{.3Bl�`5&�[:���{)�${9ly � �:,)D�To%��4�:�9ei;Scj�6EEir3F �_Zng� �ExqN 7.112��P5�p78�h$>��2;>�2�� >E;"re"pR"'`E4e�)&F��*��m^Qm0eniA)t K@n::�Re0"s2��qu�yOl ug� :=j�*�TCPl_{r}T�# w�6��Tb VB*��,"66,".66�o )�F(,�Z80.1}& ckR�, $SB_h|%�n} �p� $parameter �'!NuN $n �XJ-ns�dm}&���_di��.*��e���$ |z|^2 / h.FT�.����u�2��S�D� J�O..8C}{n}} f \bar{g(�dzB���i0yj�A0�A} a5Y $"D�\�4�$:\ $z"n#3(Im(z),Re(z)� %:/h�$z=p+iqQ � :2&L��u&H(�vap �,�)i�;q6�,A#6��n}K_I��,&�)\ 4q}{h} (p�)qp))p "v{h}�)� q)^2}F8|�"� lem:���nthe� $K_I$ ��izE=^ ��"2 )�%P\xi�! ��pC�}��;ion]�nF{޶p�4 K_I} F 2�9F �/!<A+�0 2q_j�) K_I6� Fp� np\x Z)�r tV1hu0 � So1"��*c D_j^h�B|� � ft("& �+n8 !#7 +ivZq%p[B�b� 2� !�>�), E1�8�:E] +��(R p:i�6- %�6 !&z51���MС��( �JT5�Q"�;(���Fel�U�~5E"/�W���fis�-0byrepandgs} A :i�s<@�m� %�?Tc"�2y�5/"�J (�1'��-!N�� ^S70,mf)g p , � q1z%a Thi_���\�0} FU9x%A�n� !C$�0%N"asUeR�;*O whil� ��6��^2)�land)'�/�Ny��*F�+sc� �)AL>#IJ1�u�i�6�E�XF�3N�%�m (2�� q.��}F��r�. ���)��� qpBp!ΉF� -2q� C6� ,�F.!*ʪB�[p��+�-qp�ps �N�,�"o ��6�Kj#B(E�M��%±. ��andA�� �]� .�"� 6Hh^S�6r�4�}�$*� v 8^S�<C�t�&� D ��� �By.�V��� �;�I�� q�Nr�6��:�5>���A�b��� ��>���N�>�F�WF���:�s+��1��$(yp+xq), x"G��y"� �ao����B�)f� (y��6�A�.�x��%�:�…�� � hs�c $)6T&;B*�Fr�6j,("d �"d>� .q5�� yM�&e ��%�.5J�:N� Z tis�2 �2  "!F� � }J�W&�6J�"� ��eq�_we+�to| yfor �&v'���'B"f]_.�'!y 6�\.*�*r�Z � #�Hx9� 4 $. F�"_paJTQ�do UJ��� \xi-q�g.��-�*N��6N�"r ?R9e^F"��!:k6�$VD ��4"�&+ � zq)c - , " M����#inPieF�#�O�.F}�%$, �&72m& �.�A� +.�� �B(��Ji>_(@ xi$"4#. &�b��&~Q��{_�,h�ide�" whaj�) F f��J���& )��aQ%{n/ ,):Y)^j*674�AnB� ��G�:�2�Q B�N_}�iSE�xe��*`�[[-f[*/ , �>� (2h)1Q������6���u=Fcq� vF+ q4is�\&&&2i.9p Q�F.r(v���uJ7(v!�5b ��b_2 (u, du v:Y�1.�J��-R|:+isN�s �as �R<����qh �, �� ���� �Em�*� _&76U>P�O��:KU:�2�N��2r� B>\ l�{{w8em &[3� �� �2"�ao:i-��2�"�N !�f%�tis5 int}�+F��n $6� psi) O:Zs�qѬ �B��^}� %�^j-!U � .�2:Ui��cJ]��{ :�� ur�J��ɉ*� ��eko� &� A�"�fS neweqn�-ޫB�F�J �� ����BZ � �3!q�?(p��"y�" >� )) 0(q&�R� C�>l�.H� �0%U + R �ZW �"� .u�$"EOR�.� pN�,b�$ myUbeF !-qy���'�b�,!�dΪ�7Dy!BT52X�e!$V�9�2� biɞ�ow�"�_ >nb� 1|�~>Ms �fock$P����"�*7.�Qg:��f��R�(p'� + q'˝�A�5'� ��q'p'-�� "nf� �0<-NKZ�I�6�Z�s�*= y I�.�9YN� �v$T1`��s�K!*T�� &:�>"��&"w =*2 e &�_*Y�9� p[3&� Vz�>��� \xi2���F�֚�]�E�U�9J�U�M�$$�AFubini'& ���6ab�b*�"/E���*i9�o4*�;A��= �}d$--� s ��5 ?�d.^SB��� "e 2 c�_*(J� cruc�T )mU� ^�_2�[��b�]S(b!} All�{vO`�Uof the Heisenberg group, $\Space{H}{n}$, up to unitary equivalence, are either: (i) o U4form $\rho_h$,� $h \neq 0$ \begin{equation} \nonumber 3� (s,x,y): f_h (q,p) \mapsto e^{-2 \pi i (hs + qx +py)} -d\left( q-\frac{h}{2} y, p+.4x \right) \end�l on $\fock$ or \newline (ii) � �in -&R}{2n}$%L�commutative one-dimensional represen $ons\index{)%{W }$} �)�LC}{} = L^2 (\qporb )N=% Thm}1��>proof} We know by Theorems \ref{thm:fockandltwointertwine} and $tisMI} thatU% is il]etA{)$h^S$ Mso%m4result follows�h\cite[Thm. 1.50]{Folland89} � �The>�e c r-D0$ can be used�5� funcA�s�distribu s outA?d in Q�s (%0eq:repofafctnA!iegp})I:"X.#respecAf$ly. \subson{Squa��Integrable Covariant Coherent States inQ�} MEG:csina} E�nt In)^T{Kisil02.1} a set of cYsY5x{:!mX}!  wa�Ltroduced. We first gaC��defini!RjTan overcomplete system:n( which suit!�,r purposes..Q�Def�{i> def:Z(cs} Let $H$!�(a Hilbert s�%�$G$ a�0d with Haar measure $dg$. A�vectorAe{ v_g �@ H : G \}$ !���i�iy�n�a$for any $v br.the%ldefnof�}!�t_GAngle v, �r �, dg = vmVQ�}�8%Ymdl��%�na�U�Z~)� callaje�soleQ!�,identity. Inliterat!yA�ous o��, constraints%]q�ESeA�b>-- seeM�AliAntGaz00,GazeauMonceau02,Perelomov86} !some exaA�s � is. �:�9 show���a@i4 iua ��2l re siܡ\m�cu�:�. This`F���gen!9ed using� homo!FI�$X= \%n /Z$ ()>�S�x��>ind�� nhn}��� proj��8 $\sigma$ (from�Y,$tohomsp}))�0iiNground):�Hharmonic oscillator!I�i(!�Chapter ��� $BV$mod(Z, �aKi angum� Klaua�y{>  $99, 6NS:�)F�y�$>�$ satisfy a *+ L y. U��7.3.1:"we conclud��atYN��ݖ�$eqn{ K�� ,q',p') }J�N^����� \| ({M}E1M7�`�1�0�8[ x(q-q') +y(p-�\] ):a & \he�,{1cm} \times._ R�[ o( q �Zyg2~ ~. 7. F�R . o.�4�+  ( q'��'1*2F=%, 1�q�M$n5B� o"�(& + q'%$ p'^2цf�0.5�1�Ns]�!7[ QM- � (p+�5n2.|*� y)�gIs+ fq+A���2.8Zg-\pi h lx%6y"� R�EF�$finrepker}��N�!u( )�1� e~)^n2� ":5 [i(q'-q)+)�]�[ i(p'-p -Q WBR ��>� 9E�� +]�A@qamD2pp' -2iq'p +2iqp'� �>6is��p� kernelH� �&Kr�!At&�V�)��hav�K7� withx�TheseBudo not J�Xcorrect classical limit�x*��S 3cG �" an�Z bet�i��ense. B�eS�d4isneed a6� stand!` of w� �^Lin $p$-mechanics ---� � main�<t� ���f,staesandpic}�){XMX"^:pp% :�n thes �continu� e develop"H .�MMp�}6�,&�.��� aksis�phy)�ty-�simultan= ly dk 8s both quantum  Y(�%W . It� A�&,gZ� ~  �mEb!1rived �A�(same source� zER�A=f A= rief summ �f�� � 2I�>0 :obsvin%�e1:� rolebobserv�-J^E S we also)wo choos�.�al]i�spoito!�u�1�23V� ect:1 evolof� �fin �uni� al bracke�nYdoa��E Fu�!]�2�s.Y !�F?j".e�7N$FQj�6�OF�uf�J*�basic��a>e�9�$particular*�or:��$m˥%?in�e f� williq�R(s]le]on�Xz�a!=���}1�reali��=s!%z0f $v�)$6T convj e�Afchosenje>�rigorou�)efFa�Ŷto. P���v�sD� /fu.A��Y4map:p~on-l�\ t�[kM� !]:VBrodlie0.�x:MR :��+$,��d d as&� "�"� �cmap} (< f)!�e^N &=q � p$`�-�E��}�:�pos{�F���$j$-th=80 coordinate i��pos�( %� (q_j�X_j��1} � } \P���)I&�-)c%!a�k�ofui���� , $s$,�(ch vanishes��$_"�#�pm� fty$��� V in ayuto�%-��� �.�] *�]�d�P��aq") 6�Z�(�"K'!�$e�$��1Z&���6�Clearlyɭ��� dea �� hev�is >�!Any"� ly!�son!��͘!+��< !�janq�A2� (2�)$���a � ���� �!). SincIFm�2Fx%a�nqtself�n2+ �n al ice�=i�z6' �v� U5all=f9[E �(polynomials� expon! "ub s $qp p$. E�majoritAf� � ��t� b� ed &; when2�*" 'g 2W . For �spl)�:��H ՘.  $X_j �Y ��68�ua%�# field& j#}� P&X.G}y�Jinvvec a},�%��2) 5�#2>2�% T�is,�#$B�d6W2`��e��� � gen�$fxl} X_j*B�A�0frak{X}^r_j B2�|)} 6�+ ���x)s}�B,66�r} B*�-� ڇyl} YJY}_j^r�z�� bjy%A 6�l��1�j�" ���`cl�YuR����v�7 e wh�\foot? {IfU� .� �-2� Bi�]�$v$2���ontKde ve tes�'�2�$B$.}:�ao� echn��problem��sol<b�tQ$ual methodcrigged6;(�oR} ( `+n� Gelf��triple� ite{Ro�(0s66,Ruelle66}9 us�E�of2��n�Bohm02^us`symmetry^%pdR�!lexplored� l('\IguriCastagnino99} exten~g algebra_t�approachG�7*�'MKbLie��9�d�ng5&N�� !&'G\aa � g'.��aiA�� [�H. 0]{Taylor86}. Fur�( if�tak��%B�%(. eq:infdim�-M/m^J�s"%d "k$N��yF >r6�N&�^�6!�Fw��/4�.�p� - q_j IsisnENoc!Agp%�u��s m�)�ei!�Z�o�>�a�a�eZ:�2� F�rhs�� s�&+#[.. 3.3]^-� �obt�a>% & 3 a"�"Tb,q�Y) �map& X/�!�^ �#he Weyl y��i 26�/ .�.� M al B. YTime Eqa *� "�No*5On%�Pm!E**��2Sm�$/pap2*�{"�pͰF�/ FB��*>  ApN�r�3/�s�%�dynam�m:dY>��BF�A��)UH$\antidM'�2 � A& :dAv� �1(reg2mat} S}=*@ $�-F? � "t )F�+ 2� fnof�}  &r �=��P^2 I, \qquad \textrm{� re }\UF{>!� s}= \{ jC+{ll�0\displaystyle* ? "!}{K\strut}` _, &�if } [5,\\ I �s A>1 h=0.* � � " �N.�b:�Uo�s��6� 5�;WI�����C2=�:OA4%0%��z5�s�i�(a��h \(a8$._. I� � ourf>���aT;!?i aFe!?��*�s:�U"5�*]Q�def�KB��a�!twoj�$, $B_1,B_2�) ���Iq�&fM.�eq>�,\ub{B_1}{B_2�6$( B_1 * B_A" 1 )m�B�E�D�3"S1u4���6ofɁ��5H�6."l�:*5&Q"� }})�A6� �E*� �={�'$,5098or:qh"�91ov $he Poissonb� .�2P)M%�hpro� � 5A�wJ"��)�$Liebniz�Jacobi��3�+alo� be� a�1ive. Np.atNV�!�A���sq�dB �0��: af�x#� necessa�8""&�e �B� {4�[gyamH�V�sI8u.%"d��u�x�"f�:r�dyneq�5� d B}{dtv:e�a�H}{a<e2';M�� ��� JA� �Jj i �& InBJ . E�a}� �66�emely�ful���� it)��"immediat8U�q��&��throughE�" ,v�A�*�9 Al\(e machineryD workaiF/ , bui��"�%���] 6ehlicabi/ f�m<7F4inJ�%&95)ah4i�o67"cw5{w:��"Pic�7ʼnp" &� 7:.;&*� �$$l&w* ]�-ep�"� W }��*F#)#$re��inV�"'areKas"�y8 ��.e>�#*� P� ͅ�"l?�< rms:m.�N�:]#8T L)� fa5=�K,#omputeB8al� ec&6 valu�nd�4i_�8 itud�sA�solaL"=/.b�!�?e*v@�F[$e�05E' �E��Z�J4%o= Ew�how!��\Schr\"o)e?;d.�pQ�A=�>��&!��6�%)��weF* a cl�&re2;betwef�yof8s)"�"!�J�I>V ^l* �0A :X=B�*s+.;;�a;�c;uwo.0)�as�We7&��l+E *E�"nt1,!�!z2p- �t�QpIx 9�� simi�&orma�inF�,� ever��qIr�--��newE9vestA�ins� +pRM�shipsU�$\�Arn� 0 S6�!{2#FjrelbetKandhh}&qa�s�2Une'�o�u}�!&umIofF%.N�hs}q�e wV�fiF4;.EHd�)� wM�u2)al� F9�posses��,�=ectra.� i�*�e�x���C�.their o_dvantag� 6�.D!�usP a�gA+�ppr� � r� !�Q���ear�%i)?"0 ��y�e�<a�i�B� &$6�J! @!�91qt6��.��re!�i� �5*A*!Z��pach $��&�n case�0� R7��:%Q�A!�m�7� sn\9$ secob,�a�gr%� an� ropr -�� $h=�9��%�� A��ya�� &�js � ��6�$\hilbh&r },%g�"�!<} \setminus \{ 0lC3)A�� Q��" ," .�;!*� hh} ���\{�+�Yf �<�=�$�G*(6HH&+3z7�5�."�=�7n.>�5 m{aSP)/ iff�Eo% suc� at}: h E^j_h f =!):� WforB71�q j B�H\D"� &!z�6�; $s"1�"�=e$defofejh} /� �54(x_j - i y_j)I�2) - i��cE\6b=IP%;j NZ+�hhi9El�= v_1 5E�A_{ PX!�6426{n}AF�<QK*-:v_2�*&:B��iK��Jz%�r�+6�DA&$�`f<(a?�#1Kit)�~rt"Js*�q}$�J3i���e$�8xq��AJ.q I$\�R9+}$;"� �s�[holH [er�4ge $xYy �jp3 .�>b��7@efF5"�,6< F^2(\horb�7\},)�Y��)BE��f�p!f$z*�JoE�)D��%��B?  $s$"v&M"9��ݹk $v_1�L.(_1 �-]A��L2$2$� i\*�$"��)b�!{NR.e^{*M��*tN� \bar{f}� j.m�^[�=>���he�(5� $s$-�)',��ha4 �699\F!1F*�<5Gl4& $hh$;K^��_{(x',y'�>�O�" <[9L��f �:2&G42(x+iy)(x'-iy'�:x^�;-x=-y� Q�].>*W�lay� � * � is aJ untilJ &+��s�m"�. Most2� 6�� \�V>�N �P8 8]{ReedSimon80�j�%"0 .�se!�$� �A�$�e�$R QHN�$} ��as:� >2�o*�7b� EaieOU#o uit�,N� assoc� (Q�.� x�e�#B�&B/ |"E0!#q$B*v$���we0�&to6�&��&6aE ftwo6)H gengKBL�A "yO� K>d �� (la(��"-�weIsk�BX$h�S0"Q �3La�&� 4 �.b�SvI*�'. 2$$v� ��; e>1�F�9!j�ngAa�gcn%hR�3B"$B * v , v �E"� Bj*W "X'""Qi� �d��if $A�&�#��b�:��#!� [J fE �%��A f,f�k%} B�Wen1~" �7$\�m$Z/ -� � oQUto6)�b! eq: XapzMnon�4} n (�5�ke^. "�I� . !%%i*E �b�T� (��hh�Nsoiahu@a welluC� B #�4 _h^{-1} (�� � � \hat�7RFR�ext��v!��U-�a��  %npr&&=1�L�1� f*�< ex�) /��Y�se� ErdIB) ).&�@�/������%? a Lemma� tQ�&=m$"�#"TlemjPp!m} �bz3 Q6�zlHa�B�#$eq:rhohand� shift�W h (g%� `)� \lambda_l �s&� !\X $GT�2�� ���V"`U!�A����Bal(=n 3 9/�">4@W*a��k.I#$f_1,f�e��"  F~ � $ ,JJ/indChe�:_a&x,y.#� _2} 2)M"� invft&�XF�Nt�ec*�� Vh:V�X� �6�\!�[] >�D:�/�R�E�facmʍZJ�4V��#L^2�eP,.e~�*z�7�7verifBeqNi���By*(N�. �P2�t� $(U?)&� 28QMdz�q�s',� Jg!� ft( s-s'+�'�wLy'-x'y) , x-x' , y-y*!G>�G�(N) (�(L�Dia-�-y'� QVžV� #2�ef�L�B�9=x���LJ�� h s'Z�e^ � ~�+ P  Ti�}��[(x+x')%�(y+y')]6g�i%� [q 1+p.&'Ln�( (hs'+qx'+pA��F�P=�:zxQnB�TUWE51/y0:_.!�ֻf[F�B�_o"� M� ��la�3tep.�9��oula��� �&�K�6n -f2h} �� F�&=� Y�_1n "� ������� s�a"�� uPIJ;�cU {h} (BbW1V6�bv� �!3�-M%/A� \loneh�*b*8K�Y>�^F��2�h��V�6B��� B(g'�<  !%A�g�M�]��cM� RFubini's"M (V � �`#ћbe� N����.� '%�: �B�B.>Z �}%}J�^� !� %�Qw)�Z��=zO (� )�B� �>2� M-i:��N�* B��Y� �F�1�B2*V� 5� � Now5�;�&��>I%. N��"�.- _1)(g)$�>:2gJ� .H2V9��J�*�b��J�-�!��� ���| �sway a� %V6$2-��- Ta�)!�=f;/iBF�)� ]� eDJ�N{,���Z�~.�g� ��vEd� wn$�a�&*-5&� w!n b[;W*Ti(�& �!h!&�Remark�~mph�Z�2� ���$u�$a�� �F[f!;-$>O \� $. Hb2a� W$y irreduciqe:�i+>�.�nd�\��� =s�<$�/b�Y�K�_6�!�#� -�x�����( ��)��*ame0 lS %NI'!D YJ�"`�M 1and^} a��(\f(#\��)UN�*�v( �� &� )} � �'��yF^��B�B!&�havF�Jy B*v,FH� �A n} B ��1 � s�� �n&�\AF!�1}��&� L^1 &"I" ,>em"s," B aV�/�D2�}N#��>4-5)%�-lB�:u&"�7�76�&s=�2.J�)�QAlU�v�sxyB�!n�U �6�B� �%D1"�$2n}I�R )&q\:� \,d�ivV�&�b��"�.� $s'@aAs�BB.�佮.�`Ś6p�{��.\_eF��(�qJY }� ��6d}Hm� s'- s"� �H'y - xy'), x'-x,y'-" _a�՗JU"`� & +�G6�JD�a��*"+� ���*b':��x-\� %e"B�*q$lr9�<&K*qJ0yi� _oa�JnEM�bG s. P&�/A�fms e��J.�at.0Vpoi9lof ph� TL ��;.� as A[ els $P(q-a , p-b)$�(fixed $a,b$�T�(q���]���0%.��m>�dF��P�E^�= F(a,b&'� "Z :k*3!!l�-�"si�&�5alU9�N" �}E y &l M] , $k�k��t��9ra� 2(�6on2.�+-=�p�� �} y(� ��m��n*� *4(a.x+b�s?Vd � ED.%$$=%6�.� entir�5by qI� $l=)Br .��� �� )� 6�; s�U��J $ ra�Ethan #�9e*�[Zm"ngr2.��UH!SNx:$juge�f>�" �.Ő���h]��< on, �#q���>MW)),a �0a�_�,�a�erY> ^aZ��HBG = fV���&�9yi�:R]=a��!�!:�Se! Ane'-(counterpart�b*�[ $��K�>�2:�oq�e"fa� �)��Y:�J? -B .� e�mo (\xie�e��R�!\xi�R,y)F!xU@8lm/(b!QM�#�!0Q"<> 89k0cI-labo$,�9!;�7:H"}Y=4�O�]T�G,��,c�*%w1W%(S(jus�"dA*9� ,9)� &*N.!n4��may�"=�a�s mbin�w ^��E�R  �nsDJmatrix j)@{Merzbacher70}.},��pinRist%�� 8(Honerkamp985r�vnit"H4cf�E6.�s5]m=(2����:|D�� A�Gpace�kT�^ZF1�9NYs�2��� !V��_Q�& ���5eQ$2��b�S�r%(o$ exhib�ee�q9�%2K!�� s du�%9 �!��B�)){F�JZ�6��6X$s.�6Z ot*?8.�aF ;<ve1W[!�5:� E�"��.=E��!�oe�y agreahe: =�:of mo�Akq�Y��)j�l ~A$h\in&� A:R� �-!$c��Vt�4e>�0p$-٩i[J�9b/ !��/b�6G�o�>f�LE�asB�*IOLiouvill&�q.�Xi�U�@nd9Ǒ�r:iyt�v�.�:V�:+>v"�Pn7$F+1� ). &�'� do r&e3�gL"0 �_"��,lf adjP >�9�6�r �HY -adj�G�I�f�X!局6C+B 8xi� |Lly !���2,d2�&# F . lM*v�;�=�k B*.�������$:�*Q<2��.!��ub.F'I�b5s� sfiev���'$-&�B�W�%��Sap6+.�n�<isi1iWG�HEL�s�N@L$�zR*1b@.�=soUb,� itia�\w�{�T �>6��N-j�0�� 9"o<�1�&� w}�Hd}��IYas�|e=2�Gpe@9on +΢; e:I�O`� �J "�new�9 � Ova��}{ih}�%~U� @2�*lyj*!�%�Z �2��FK�G&9 �two� �"(:s�1cV1_�n:5num!�e��������b- ڳ. \d U.^[!x�:� = PI><Hu���C-v�g�br3�7�B* m%� xB*vq�.!)�1?I�IyOh"/@@�.K%xA�arbitro-i��Q�H.}q|vUeq� volin�9 Frac3=l{v}{t!^B_H *�N��I:�&ofF\� rves6�,0N��g&708Jso!�%L�J���!TJ�"Si�dv"�K-��FށF�K@17:�wi9�$B_H$l-���ben�^����F ���� v(t;�t%� �^0 �5�$;�9� 1 } G�p�Ti�Pa)�or!�6��m��I�QHB^�%"]ZX��F6�&G�i6w2���aa&ti-2Z_/is�c B � >:;{!�56l9�B 9�O�M�6� $.} Stone'�"e1� ��X8.46�8Y�7=w*I�z$9��=ll �*'6��![i2A�B #� $t���S ��!chroheis�;�af�(assum�bve9>)A?8� l >��&# �#��i�"� � *�6�*� 2�O' (B� ��!�h ��:[� d��� \2�:I.^ ;N� (t3/ q ��2?2�� �)v,>, S:w=&2`ai� ..Fa:-a�bbi� i"g" a"� ���� � BjU��J2'-�hM"�p*2oh�~ tian:n�Uo P:Apa&72�q����>b[�]�jb:12cu0 F-:�Q��OsJ� skew�*U. >49or4�&��. �u�i&-*��+�[ "�H.� coinci P�Y����68���4O^& "�SgX4hlUrݍry��z�Vt:$�p2��5 &�Vo>D�RC��B�B� * ��F=&�, *9���Diffl{fH�t�EJ�"g=�B7�+�- =�U_{�)fE&� f� �+1}{i\hba�Hrho91_H)�:(� is&�fNS2/RN �� =�-�m^+��"['&UR7� ��2����ub{"�W%~.���RM(!���-* B )��vD��Eu}1�ZU�N!� -�(Q�.i).��, �ճ" ���Fq4 N� .�Q1�&�e�&�3)�Q9.L2,�� ��%�)n! 11oE��- _H)N�?�5@� _H )F#@)FA%�:� F)f,&62B�1�c[�V �feG6���f.�.�3Q���@��e��B;�N�<��v look�3�� ��B��B@�X"Dto&) I&��W����:��]��ay(,�.�`a&c|Vhj��X�]+j'"d"�?!~V$l��''$��l�J� xac�![�n*�1^�!woݡs�!8�zVq!12��� Ӂa�� : makeR�n�/�) ��eas]0:&a.G^*�A&�v�-Fxt.l�iivaV�"1�.� >��.�X �Af*��Fsai�'b�6lm�.�!�U)� \cdot}�m}�#:���U)6LB}{ NBKigs (�%* &[O�x9!c]E�X�!� ��hol�1[2��A�C) , l�� "C6�lc�c[&�A^ $C6wt-�Q�&�2�� :�F56v0g *ݕa�6:���s!�{V)�EQQB;�!�:Z(Hamiltonian�UNo^����6�m�"�H�mt�i�y#^�+� E�3��2sconsider����I�#r2�:pI&�6���a�b��*� -T�R_W NX�kG��� eq} *F lF E�B"bA��Y�]B� ~� !i1dk.�O:>�[5��3 �4Thm�.elisok� $l#5�%DNo�&� B&: F��7�rF&� �-�' \, &u&l�2��6(�X%�$J4V�!'�n U*-�f�M�.�� m Ri�0az:,7�7{$��f9tru�0]�heJj!q Eq. 5.42]2�%�Z9�"e$L4(l�$FPb|N�� � (` ��!Jly�8��"�#� a�o0?be0ECc�7"�].�Eto �$Prop. 3.5]qL\pf "�7�ma5 � F7���.t&EigenV+�(��l���&:e, &.~&4e0�w�`�1a;*4eE{U�/6iK��2�1��^[6�i u#"�lA4eig |� #[V�#� (�\l�G}�O�>� f_$�#�G. F.$$v8&�4,.@btA+, �)1(USѲeq:�1ue-U��S.��-) *>�hol�� $2���!�5խա�$ "�/�4*R4k�Xf�e.��� r=,&|��c���m&!�fViginf�5 Z!,"� =TE-1V=�6*M�&^��XAY�*>�" fI,�>.�C� r (�iVks uN�%�6%w?-:O.&JP���J��$v=.K\b/f}$4)9͍�AU"� )�),4k})��46��Q"�e argu ���o ion. m�q��l jf}d �/}> *<5ݍ,�rt :<a��!F�Zt�02�B?2NItm�E.-*)� �o �6�� q'a��Y���}ť ��@} ( �#�i.%}���d0�-.-}�a�].hB� "/>������ Cre�1/Annihi-O!):) �[�,fk)Vr�I�2�� A**�D�#�  �4s5*&1a�Z�3f�:jm:&�]�=**"�U�2�s� ��6�"�of � �� �w��gaka8�1&�1;. &".+ 46�:�e.a+�$tle historɆ:,. U<�* w/ disc!��vSc.nin 1926�E�0/ m as2$nonorthogojZ>�"�1�&�nonsprea��,p����!,9J��\n�\0ty year�� i � larg�9ign��. Howl� 1960�lor T9l M g�4�wfiguresEJas ՟�, Glauber, Segal, Berezin, Bargmann, "'�e�Հ�9s�{*61, >752\��-��R� ��ard>��:�i. M�_g]*�m?&-nws-en��&{ �962��'_kr���]��As"�F� keplڬulomb}�>&C� �.a"�3N�A�`cH I��.�1y�a vacuum���� I�%w?JAȉ�.)�I�i�ɩ��&�2*00 'HjA$m \omega^2���1}{m}p^2-(!� $ '��conAC$t frequenc�u$mF"mas�.�� ��iM�[Eq 2.18"�.1"}�� �� f_0 ��"YcF��( � m-���C),"�i�h>0F "�9%� +!!JF"�� &kY�rtL �))�YF5�6�Ba��U?i5��Q �U4 i21VAB|(R]T&� ��letA�xr%geNF 5!(�&91D, h!�)�^n 2�*>eڊ1E 4.�x^2}{Q} +>e�"yUu> -Ή�62�����e*�]E2��n$���e�ak�A�ө�M�6�7�i�&�\s l04t"��!�out lo�v4 ��:�Q�!� Sb�R�k=�voo..�-�5�.�#  i hsf�x�y"Ӣ5�B�*oTo �t�_�8:���1�we���c��NxJɻ: wS�i� $\zeta^h.qh�!/ �eq:$ � :/ _{(r�C v&���$v1u)|�&r}{h^2f b�3,a1�iaJ0 F"%"�G ji�i hq�2j�dsY,��a��>i(by+ax-Ϸ +|, tH 2}U8-oq N2} 5�� �  a P6'AF2�| � �!�^h.m�)p��morphism�per�#Q��|6JA oa7?.�.�?sxpl"ދ6�v�h:ot �:�K �E�߰: "�JĺUDF�, x!�Q�l��i-�A �MI�:ݲ�.@�s�"2�� [��. 2���f99}�5K�!�e centre4�"Z$ $\{ (r�:r&��}cs"~��Cn2�:%�#hF��V �۹ 2.117 �2��� �6Q��W�.T v_{(h�N=��bo  %ũ]E��vFD�>j�{.J� MuǏr95}.��N�8.#�m��$ hhcs��L �a,b&�m}:�&���ܑ�Y�M D\�\=�vZJg��I���I�_���,�(2tqn��>/y 2��6m�"V+�# preps~<"2Sw&`fV&re'�ngelA"�%��S)x)�>�o2*� :1x (ia-b)�8pi y ( ib + a )FC("7Jo52}�4( + b^2& :�v�a (ix+y� b (i�lx�� �) 1�B�Now!��nJR�:�~ypۼ!��>d��/valid�Cq�9�c&�". 6�8a?�q�jh}6q a',b�c(s%��o5�[2���Fq(a+ib)(a'-ibq!�-%�- aq- b�8 ]R��v:�.0IF&&L-�6:{ .� : a,>�M!<k=���*5-� 2�rFi�a1��.��w� -��'" �D��t"1.2.13]{"#�A�B� ��eX�ΨBP& =RFY{(���Z-ia'-A^+y (ib+aAq+aR� >5&$�^ ���.�Ll(�X 6M.Z6�u:"�>0a��+i+Na�e׈�V���:���/B�.l�.�}�4h} [���� 2��(ia'+b'�X !�^2�.J�i6�{+)�9+Xb+a)(5�+ �C^2 *�2�T9x3�x�� +��)q"�:�:`=x 2>�!�-��-^-��]����%֍�A-?�-%�&� �3�Z� F� k�&61>a���.� }� vG, !*L2�/YH��a��wecanz csexl} i!V����vab�� , da b51 t�w��p��96�s�;��y'�1o�W�2,:N�g:!W}p l<� >�� :]�bJ�$! �BxX#b2�(.��C (ax+byFq J�I�1.�FR2BN&mz�*B�Xzj �6�NL6)XdyXM({\tilde{v} �yx�XK �yER" (��QnBl.,O 25piў�͗F�2aw���F7qSo���c�Q"� !><�(sZ�ݺ�i�l)|�w x'(-� -$x �'���F�� My< Mx'�z \�[��� [I2�d+ (`Z�x� + �{] 7�J�v[���R�i��I�2�y ( 2Z �.2�O���5�>p@ef!�{�T �E�=E�,[ (hx-ihy-2b)` (hy+ihx+2��d f�6������: ��$[ 4ah(y+ix!v(4bh(x-iy)] �%Rd>{�.���>�.�-n��piF �b � I��4�+-�^�2�Iv0 � }y+."�u.�BQ���W�� .�G7|f� �[�J#��C�7u[ +=n=7 k)B*�,��" =�VqM1�j���4�4dgB M )I�"�o|�� as%)$ a0�0$ "�4l��i!W�� �o .�-��(H���AfOw0G�ruc/�E�F�#JD]��1}�iB])W\�f "� A,2�& $2�S�c6�f�7�1 .T3on ��[!�a*F &�.v�[&�lim_{hmG-�} F�0�Q�Z�[E\%mw� B%ei]��pri 73��g� O�ly)LpGKwi�nve=�ce6+$|B�x@tY�l�60|�cqR�h&>^M}c=2.r�:��LebesguJdominZ��*g�7�)�1�.�Qm�-&WM�XE.c�[*a�e5,�Y3h# O<tovioS�ttempt� Hepp74}� .�I�FJ.�^�&7#eh*$m$�(� "�:$3a.�(�(�0 R/$�n�(L of gc!"�u$T�ef>9��8,29{��!uK��i�D=�and �06e2��, $A_j^+?\ 3� -$,$%&Ag��;�Rq$"��eqMS,aplus} A^+_j�1*2�\ ("(Q��r8� D�&RQy_*T�m�/#\:tmin u-Bu� i��5Zv+ i~vM���ZX%�.[Y?%M�ev�MZA�%ɁgX+2@2�ha�&4p��E�fE6�q���&+ q-ipKq+ �M�pQD1��Pcsiseig�g)� =& �fma�X �A�Y�� �:� ��a�mi�yme�� az{2*߸s�$6ŏe� W<>/��D ��piqI�!�� ]�x_j�k�ha� �.ba�[" h;�+� NE�B��oUh!KY]i}�J�q)6Zs� a}� UYaJ�&9$A-:!�{"�Gb'couldD+PD,� zS(-bX+aY�� Fx (:ͫ8s"�Q��ŪfA:i&�.s*we�w ::�-bJ=X}�BIY}$.m�5g�&{���@��UP̙��(2a�>�0e:�.p A,>zF�5ov�c5]���� �z e�d "�U�G"jOv$; $>�?=P>�?݃�-2�!��&s �:!���+^��|�.�on}Q JL< divi���N&5�29_6=.��&.D"q�3~ �`a2�,�"� EJ = B_{H_0AK 1�j�0$0}�)�*'W{� F��K/��in %urbU !\1e�nU@14.4]{Kurunoglu627>N�B]; �U !�2r-A7��E�.#@� �)�$e�^ &}�O�bN1�J�!qu�!��. def�(&X)��4@q�*oA��*2zX"�W"!Wd3tzc� � �* $�6�6�  X"W6- �&.�KW7��K e^{t- I�0}}�[M��+V*;�2�|n}C lR(-lM eq ��? vein%�} BQ=!�(-5$ �)�?exp(+ B��]V�NG%�_��y�D�xOE,* � �B}*1)IQF�\ub.] /a 6��9��\,M $ m v}(tF"(� (-B wt�B�m��=�AOm�o�in�GQ��de.F|�\@l*UYF�E�� t�#2./e� eq:g�nm�EQɷ�X)mv}%�2(b&v�$\*?2�Y�]+bL(�CE  +i1}.Q>�=&Y>VjMA�9qIN) vj� E1}* -a*>�E+WM�);:�>Q�15 J�b_ ��1f�v_"6 M"/#����a��m3 a � $l� & �#] �lmf e^{-e��0} {}t} l�T@�9��) la�>�B�so�>lyB� l�e�>JA�iH#-tM0�5Y�nH�F�m�J66L@-�.2&dU��?-8]c�fj�.9uk}kJZNMY*Is�BJ�19xI�)�M>w> &<#0.7�� � !�>Ub��J�:�m1�#jllbT�(�r�1z�Bz^R)#�& $Jp5�E%X 65�)N;�>6���JR�^�2�N:-U1}>� �G'�" ���* actH]<Rb�� B3} .�FnX�1u���ya  � ��im2��+A�$"� =�N���� z�"1w��B?1� BA6�= D *Ns.� ( h in�tabS#cC�se��very dryc�BV�"�Poffed7���"�1����2��5rud"d C*���b�{Fp!g�  -r�gL2�.�wth����"&[�>Jf.�J64�Beά&��\ ] " %h>�>�d�3*�/��� %�;ran��iũ> �IX<V>ema�s�n]��iv)8L"�T>Ȧ��rBhX�Gs"��-: 8!�OJ5*�&s�~�"t�9:ACb1(p'S)-:N@{ \psi7p��2�h�C�T^w) K_{I}"X�& ,\xi $\xi>� �a&K_INO6�"xz \xi �!h�v9)% ih x�0q n"\x%�\PF[ � %9@����<>1�t68禎�5k�oa.v=!ue��@p"� )F} B>)O="�^ 2�% �^{n/4}� El �%p!% + qpR=&#A!��"q)^[%�Fu&�W /� �u*� �Nǖf:c� J��.�($��o��e�Q�U㩱H)n�H*�w�5��Q�h|$E[F�0Ns�� �i��D��z+y�}p ��psiAi�Q0yB*qstartof/ tohhAA}�?ai�(M�N(>�Y*EU�8@ ~ ��+���,A{�?>`��K&��el�5!�9��" w�K^%�ngab-�͋:. '*�FN���~��"-%2nI�p�"Btisz.int�oq�d��"i�7VDf"��o���!or`�of�on.A)B_1-lAL"b)N+)^1*Q-n>!� 6]*p�V 6XB*Mp*=�>� 2:)�+�(�2}qj��)������e [�CCF(�IQ� +A�p\xi"�L*}2:eqF�2Qb������2Ri�� )xip-a�+"�<�95D^G�)N9#%pJ�nM66�X:���! ��R�\*�Fqz`:�I�����$Vilenkin77%�\n;) ">�*�( help1{ �P�l��ar��+!Z>vn��J'�.�� .c)mboG( U*5 ed "ged6��ma tool�a�A%�2�"{�.��A-p}w(. 1 Nct. 4]J-. �� 4{ 66}, ��  0{�$nd Antoine  Vause81e�!.�N"y�N R �".��B��,Dirac's "bra%^ ket"!&rI�7=�hd�:�nd R��elcF�'#EŬ5exaN��%* sation o�f the classical position and momentum observables are4distribu.�s $\frac{1}{2\pi i} \Partial{x} \zerodel$Wj,y.,�respectively. When realised as operators of convolu�, on $\hilbh$�y� following<8 \begin{eqnarra��label{eq:posonhh} \mathcal{P} (q) * v &=& \B�left(2�+ %@h y \right) v \\ gmomJgp�g y} -gxf. \end� These 97clearl)(not defined!@Awhole of5M, Ado-Dhave any eigenfunc!|s i9} 0so!� was AMiob8before we need nconceptpxrigged Hilbert spaces. The idea#aR%@ is to start withZoriginal6Q, $H$,!dn choose a subset, $\Phi$,! whic HMpf-+,. After this� must also�side dual ��]denoted '$, k will? tain��s! !His gives us a tripl%�vector (]�ua!w}]sgen)e hs} � \ � H 'UD D Aby�aE(\refaF.l) whe�@� �$!SnuE�� \cite[Chap. 1 Sect. 3]{GelfandVilenkin77}. Suppose $A$BanU�!�AV2DA� ques! n a gener�T2�\index{b }A�$A$Ih; valu�lambda�an eleA�$ $\psi \in)Z$ sucAYat��-f6�\Xfctn} \langle A \phi , Tr =8{(J&� k fore�$,�$Ag e bracket�� z, n$!N!cabove e QM�e!E|!,= �T Phi$1��7 by a �Ial`e+''�@.1/ Thm}6.,M/$4.5, Thm 5N88 A self-adjointY4iAi:9haai8complete system�Bi�s cor��ond�otoź]'smZ� IE�@ $\ltworn$ formul5;qua� mechanics%_chosenq�ir� �for b��S}(\S�Y{R}{n})� +�S}'63>Si�$160$�H. :Q$岭d!� Appendix �U app:2~}. ForXock^ associa�_ �:�J.m�$Exp_f$\T o$} 96oRQ�q!,} \nonumber Eoa�{ fe|(C^{\infty} =42%�P, : \, D_j^h f = 0 \h�F{0.3ca ,textrm{for} >@j=1, \cdots ,n \}>�(a���$h��=�ƹ�8ftwoohpolarz}))!�n�)F��eft�- �(\exists c,a%Y�}>��MB"�| f(q,p)| \leq ce^{a \sqrt{q^2 +p^2}}W2%J$forall q,p:�n!Zr� \}m�1<} It can be showa�a��A,oA�d M_E� both��[ ual� 8each other\foot({�� $I/%N$.�"�+alaju ��'%�An�t$f(a,b)5��� \mu %8 , e^{,EF� }� $��$)oA\(dot product��$9�2n}�ris map��kn!@as ei!@PFourier-Laplace trans�+ o6!BorelS({Treves67}.�7<{AntoineVause81, $99}. Simil VB�8"f JO}�!�h�,� :V<�� 3��"� �X} !�{!�~ 0hs} f(x,y): E�0:Lj = 1 �2 �3k%�r3defofejh�/�%'$}�"� �1�6 eqn{,�\{ v(s,�I�%b o : M�!�\=�&& � ft.�2m��z6z�J|x�|yn|x,y ���ҝ|-& Now we��finU g^� sE�V�&� oe�e�GrF� \exp)n( Q� + $\xi (y+ix)�h y^2 ih xy f\pi}{h}3^2-�Fz� 0 { R xi$ --�?ron* t *�))every $� 5|��� "3N ]�� x+iy9E."���bagi�!-!�0easily verifi�at��osseբs!,:vIt�tF;�s��](continuous 6rum.b}A-c is wUdis required. \chapter{Exa� s:s8Harmonic Oscillr�uForced"� L:fosc} ��nt � is "<� framework��adion> H�MO�M��(u���$Throughout�(a�wev um���hU��eա4�����dimensio� �)'a?$n$$%o straa�A ward��y Hamiltoni))J�n9�f� encomega� mass $m� &� � j.�hoham} H � �+m ]^2 � $ m} p&�B]TM}a $&'$�G���.)>zV�e� �s�(a�E �&��map� %yiAD^S=�&� $- xtwo!ua�"% (\delta (s) ^{(1)} (x (y)$}AIa�./(�\p�"al^2} i *�.*� F��Eisc%�-5�8\pi^JB�.��1}!�y\dF� �i�2�� =� (\HeisnJ�����!� val�iJ"� B_H2�@m} (A^+ * A^- + iM� mA�s�N�e2�s $A^+i�$A^-$ w�aJfsY�$defaplus})��(�eqmin;��purK~���� ��thlN��59� 9! &N4(�Ux!-!1-&y)65o!UNP(m�_6N%N9s � We.0:� normj%6H !e6�}�b)� n$�3rb �.�v_n� �$ ( � A�6�X $v_{(h,0,0)}=v_0$); itU�6� �=�r%Ui�u�n!�)^{1/2�,antid A^+)^ny6��P2rh}{�<�^n&� �(-�m :^n 1"d- �w I.�x���� m} +q�vՄ-+B��,trivial calc�� %�W 2annihi�perN s�^D~eGv def:=and 8}) raiJ nd low_EV&�ʼnVV�&R T�J�e�* A = v_{n+1&V1c*iand:a�.;-1R&�(mportant��E�14ses $are orthog. unR�ner V��� ���hhip}).@ Eq. 4.14]� .1}a,� &�!�($p$-dynamicW� an arbita36Cobs2"���R6.qIW*.�\Frac� l{B}{t}i�ub B_H}\iUE�^2a 7��+x!�]x�]X!y�*!*} �\�w ��F� evolof��,scinpm} B(t;�= B_0q�s, x \co��� t) + ��y \si!�, &N %}B6& a�BW�:u� � 2 !�MRalF��S� atRem� to C"�Es�  & &� ~S��* QV!Nkof�� bed���� & of0"Deal variable $z(t)] J��c H(t,:2���  - m qB�_�y.2�C^^ �$ B�in=W�-FrZqfyq{ f,H \��)�eq� dyneqnfo}i�edpFd f}{qe�E�e�q6� f}{p��%2�50�&�$���procedu� fE� �.� "� � � w��F8�.|.� to b*� �*< y���y�8��  \5� �oscpm� && \qquad![}{2�' b B_F��7���0 $B6�FyE:r26�=& (B*!�- * B) � B*< [=�b� ((� $frak{X}^l)�6 r)^2��i5� .8YN8Y} 8�� .:�& �*��:  i� mat�&.rd]1B:m� �[.�b+( .*�y� P�{s} �%C >x�3)Aj7 A .:].hP!2.5!=6�+( �y�x���)�;f76��Z� �1 �M��-�:�*& BL!��r(6�Y3BaUs�R fac��!&-+?U = 4EL I��b9LB�.��*���� ��r >�FH=  ^�d  - ){ y��9 �� &�thm�� soln��a�,ex+1 � �!�12�N)�N'-� ofpmE`eqn{B� D"V &&P *-͟M�mܡ-}t_{0}^ z(\tau�&*1 #, d X(_ \iB9&.� /)|$d Y;6��w.��g s B (0;s,|,F),d%Ͷ'JM[<=- ��1N- 2|E� \� }>g N@ B�H.A��proof4h.�AU�BifftxinVmXv = - ��.�2�^2�.�t� �N�X}.�! }6l X}* :�b�y^�Yͱ�q:�-��-�M�~�Y~�Y�5���.� B�>&!2� ) im-a� �/6� n&bitofI6p(.6-C)!!�>�:.ݞJ�>.yF ;#�iiat���c���)�Q �+�9 m�*) �$*� &7�N3-�I?[�&)(}�`>:�P.�.�0^t:O-v� .�i��!�� /+ �:��+J�.(�� � .�ik �]=A6   � �| (F(t2&).S>,N*:m =>����dNd�1>�15,im��&�^/Y +o�B�>"9>��} 1�'d (�"�"�"BuFur�*mo.'~"�5���=F2.5 z� RW}�3�}Bɨi�)}�^Z�ZXT>�xBZan*{.�jy}Bj &&�kzkB� 2�~1��Jkb�e��l�4-X IfK substitut��nto�0^k k] 80e coefficient�\newlin�)B. ��y6$�7B;jT;B n u��ions �*6� 2J8 2> )!Hg��"�(Yul�4�o �w[0s  i%�tak)F� 6�&j&� , $f�81a.�#reaent�!of�: ll�Fj flow�]� *Y"�5����� eqn{ f(t;�F�=6{&�+2�}� "�e^{�&(q.x+p.y�, ds xy B+b^;�(�W� ����9j��4��"���6.�>�,���)("�!k %l aB:%u2��;�\Mak� A<�6geA�&�u=� "v=G e�>�8become�� �-FO2���N�uڰvM%)J%��qE2( q.(u=t) -vBK )!� 8I�u}&���+ +v>VI��:^ nWu,v.=uEIL?"?]�� um7( q co.� � N=) ��5�!B�1� =Н�v�- q"W!�"1"Ip%�2�K2^a�r0�z��Q� ��fQ�0;<f�� ��b��<�*. A�"~�����l� .5� �����.>p 7*� sfi,t "�B�"�$� fo})�ʥ�B� ".�!"?"�>�-"�-&T7*�$an infinit�'&,F�$.� we)A9 ?-&�+i�>rho_h (ɋ(6�>�AspY<�.$�8nZ��".U-$A Periodic>!� Resonanc9I+!p*andre2 !In*7 � �=Ffi � j%r &�.6 x.ra-D�b� =Z�"eKO�, !2�Ca�3A'*�!isk!d}0=:a&i- j8/ns�$.P-l�c f3Ditude $Z_0$. First!��$�&�%AA_1��, V ,�d "2^"v ps^]K�U� !< ( {� si�� "Y ,6�gV��g%�7gB�BMAs�8&�'w'vL0?%�n q��r�sinint} �V�; �2}{-$� �^2 )} [1��5J.r�� ��� �).�R]��V&�  m��"os�Z�=��^� }  � � �b� ):�]5� �!�"j���8t/6 $tE.{6� b�""9�!:�FW%��ic.c29`� N� B �eq�osctwS$�j�*  +"Z�? ��cn� $"��$n�?as��d�+T~6e�+efJ. Wa�n 5o%�5��H!v�** �'u}.�multipl66'n� onen�K term�C�51�. How);� argu�FyisJF%� ��ly largAE $i $aEes cl�I to $�7 $. I��ue $"���!U_Am��'a�!.�M0 obpIa�� 9� but�a #ularity!���5�5�4ߥ�\3sei�ffects�7u".F ence betwc9���*b+s.M s�� e%�b4�3��%2j$-�J�y��2>,)�,�� �<��*j<g$f�31-�5(2 ;t)}{4�}�a�)��u���fe�t�#+�12����̭"��N�� new 1!7Y�:�:-V'6�L7>�aexp!��6�7boundE�t1�si�MYuH1��1g)�.B�ro��Y�ig��eR�.^ >i?�rrn ],x{}.� q,I:a�N PL;AOf�=� e ;=�.�,We now�6N/ i6ur�J}�0S�0o�0uactV<)�� a��4�:*�;��*A%cto dem� rat6<m5 G )auO=: �&/2>u�:inB&� ] �;.N�;�analy���>�%;� �0_d!!!.how2�s�8� ify>Ŗ�w*�2s�>2Pd)b�U i>direc�>qE!�P*a order� �2 �Eq�129:�<. T&�� our�wս!>1�J�6;�<8�BW; way!0)��.RB��n{ 7�/ curr/8�Q al literaa. To9�h.��"�cA�a�;A�A;beC=t�?.��.%.i�=dJ��wpliw .9WR*~ c#byX<[}{ih}V?<"�\�4/l{5%�#� �"->��� �1}-R>(;VS"�u�} SF��!r.����:�9a�')\1�Y��!�65DPr� ty 3�mLemma�7$lem:propof�"�J? �@7 E[1�^&x5Si5t), -x��t)%?�9Fe 5�b"��� mM^&��>N�>t�: t7X1 (-x +y )�uS�b�[�-> :�� {>}�'A?"R?'�)8'%, % � #> !B\r1:�B�03.4cm}!g� �8( (-s',-x'-y').�K�' �{, d�l&6M+Q�V�Im� $1�5U"�sJitJ_ �J�a.� h�3XA�:&Uise5 l toF� .�A_ eqn{�����1� (y'>�h 1/"z1 (1�-� +!��t) aZIA/�*]K=�:=&2E!yP2x'E%l�J%( s-s'��% dC[a4m+ {qXy +(x'� M�x]�%�J�52�. x- Rl], y 1-��cm @) |_{(s',x',y)=(0�>�A*�%�>�+iy�)2`1-!�9Z} -�2!8% )!�1v2$!�����)[B� (t)]v%���!ph�N5�)1%�j&%y}B���q�A& � mh. .2 0 &8hh�so.frYefe�U�"`"N��)-)�m��v0^� (z (�E ) z  a�E5'!��0A�  ), 9�1512�&"*+m�v��5 0.��0B(J\-("�:(J^��x[1e�^�Fl, y*n �B�j��mg S�M � 5b�y a\ shif\�� )O0,��> , �W^�UF�����J� a numerfph�L0of modulus $1�B$�Iignored0Wn�uex�B��of*��L-�A5bcel�au!@p�\x=jug M�"� in*�t�byI�� �5Win�Y�M�N� �(J e^{f9t)}XDV�0,zA�2 ��A�L;��-&JP�� ��.�/(ҍ:�=&�-�� h"L?[ #\t�d�e:#�l - bV�B6IE]�h J - -.�.2� ( b-�u:�%� pI JHa�%W�:� �H6.�$&8�8�%�>�~�8m�}M��h��L� � ) Z�Q����a v� �elocB� i7#a�form $e^H ([\hat{fBN,y)r!"�stays� }��q� =]� + f�m�M h,��,�<��>��a��1Cf �"�%��TA��iniB��!�f_1� %A!@$!�9v{��l. S*�0Z� 9J'+%tR�@h�!�21�wi@ ll always��a>Yup�BZ.�!_fI?*v�V,��v4T+Vit�mxf% er methodQda� $commonly f"3&���z�,ah�UuJ� m�0s�l�&� su[n�Sa�kerne i.D�1&Ituld!LJK�\#� M.�e.}*� 11� sSWaM@d���WF<'� �k1 ��6A&UV%�F: 3s(ee.�?m�*�� Sf*�@�ker2r;�l"rub{] (B�)"L >�)} .M&� �*�A%QIq!X`5P2A�e �p6F(�Fr�)F E��B�ݡ��`z�^�*&"@�+*J' T$���}=)B�Wm�' �jr ����*� l} FNGV��5.� �b�! �9"�s�z.:*����-7� �Lu��V���:� �ZA�1P-.��9]U�1^H�$��ōA��k�2�E05^�EF�z�?&vq(BP��6 �.2�]j�F/P�# Y\��.],l}& E[ &��Ip�Nb"' �+ �B+%�Q F�U`�"i5� �L?i"�h:Ots%�J��$%6�"�lr = l_�5t��/A�! b�J":X�wl_�w �w BTT�� noB� bec}h���&h"@o�%ec2. #;1 Remark�mph�$�O rema?g9Fmea1,U)let $hM$arrow 0)6 co*�r&�%%�g� �9Ca!&�1sS�\C pro�A� �*coordin�K"��22� )� �"YT* msel s*Umoving�  #y w &>UJ +�[k;1G&dCan� al Tpj� "x +Z :can�j.&IA�6�c2SF�2cn NyY% �[6*In do2so��*re�Sships "K*nX9��#s >�#s. Al m�#� ew� � �$!�EF� non-�=arv�Fx�VS�uV  v(Cdc%+ incmFdintele 1�"6M^�d�bbe�ir� s he passa�:fN�#[toF�Y�ntLofj� inqm;eb�yVA-� summJQe r�w�Vf��! play��2j�d�#$ dhemotivE�%�why�a�VdyA�5]l'F�(Ict��%%u e-� %j�Vc��4/.�"�'s8�q$ (^Y,linctonfock}�""� ~4hh�?�_&�-!G�%�5��.f�ZBnon� eqns%F�&68s" %in&x &O ��ge wta��ofaNegral;e&f9old.T. j\`be&^as6� fqz"$ �aal.d!8$�yEL.�R3^� e ima� $f$*#el�!6]��invertiS`�.$A:64nNJ !}�ctmapon� obsv"gf}�T = fai{-1 FAlt@A���� Y�i.X�� [zIU\,IfŌrJL2b+�v ny�0�%UR�s $f,gF� �` , g��{� f} , g}N�All�sAhQK��prnJ . O"$v aim� devar� �^�� e5(A:Ah !�r�Js�4�-'*,� Zb#dy�;a%E*)+mo��dv�Bd�ri�0�j�V�B� a��-Jacobiors**��0]6q��[Ws . 9]") %rU]�O�‚var�cs CI. 6.2]XD F\�= B} u�&; �*7 �Q�XB�e�ra�sjourn�v � t>inc��Ś�<so� �n�u�uf$was Dirac;E isc n��b�v%�{+X47}. Mario Moshinsky alEtw!a%�ety�collaboj$has publis�sa �t��f enlM0�bg pap�u���ubject�0lKasperkovitz� 88,Garcia0,Mello75, $Seligman78J~��V ��ai('to{.� $U$,�9o 2����c">EU^�..cnd%�6S��a��]!w"� iz�g: �>��;%�.�XheZ�kpO�or&{" L�#U$�r��g 0ly Arlen AndeE�If94}:2�r��on)ell��ZP��qy��$uni�j�s. f(in2� X�f�7diB,yZa�� Curt�Fairlie&w�i�ioz�tn���E�6�5G9t�zhibitJ��f��Aw�umb�~56y� 2U<XB2�riefl�AnmxIwz$Brodlie02,02. }zO }en � z2��{"k&] �i�9&�s�L�VxG&"l �$A�& \Symp{n,+$ ^ groupax�*�6� �"�~T�uNEoEc#!6/> �&P#��m���9<n��verse�M .ɣn2y^�a9"�"�!B� ���l�Hma?of�#)�� !fl���UDd� �� Ec.͋f $ is.6Y<��?i �n �rby ^� $A^*$./ !.%�nt (I�s, ��)�� F���� *$ �on�j� A�(A )^* (A�J� n�s��M���"iݑc���<������y:)�.�26z2�_}man�� ^Ge�}�a�Q�2vin^C 4 !�N!�:.�}��A]�~�cₒin2�s."�V;�5��:)��\de�<dynz} L�A�C in� ^ %3�B_1,B_27>:=�. I�� B =!�b2"��8s/=�Qs�E~I0F+!~%<_1}"% B_2}�q= \wide ^�%&{}&�m4.Z�p�d�!�sa�ag"{ ion:4*�"&-�!�9�j�}F�.�!���7�, ��(�83((-x',�:,)G, xy "F;\ ��\:y2Ry1 y+>w�vZ�B_1�A(x',y�>�m.12b:B�,~ A(9 �  _'ʗ1 �b'��"L�"�B��� �f:�ap'.��:C� onrn�6B�, chan�v"M�c�T%&&IE-�)ͦ�%47I�əB�AEl - Y-, ��B_2Aj��1�1�:�����~�.�}�5�0��v�hD'��f�U)��I>2lC VK>2��BE�r<��:5ʗ)�) ~.B=��q���Z� ���:��<�~q�;$�j_C!�a�r� "� � e�p�S"m0a~|�QS�:�t&� * 2W�.6�n ^}couple�F} � !g@wo 0*A(|�Z� � � ��ani�8J�qA5 &�)C�i�:�% 62tPg$�a  &%��i{ >� �immed��P1ind�:l 9ab�!*���i*b K;In� �I�8ud�#:�^E�=bKf&!�Em�ma�#atE]"��Aj�"�.�CH� �.: f��\ &i}� in��" $itemize} \ :L; phy"�ce�A�t�Sies,�"A���A^h�27�cA �L�!|:�M;�#5�|!v ��)rg*�)r6�Q�5�aX�*i��r�re�f�h benef+Zi(�*n�.�r=A{rQx� symmet!hr�Ԡ�����. �"��!"r�F��}�N)Y�!Y�)[BE . AD rea�E'2c�V�s�(ossibilMo���M>�]�F~: ��#P�%a!�>D&� p-^}B+^A�JIJa�*�*z!)�ad(@idve�z17KY�`5%�&�O��re"�&d�)!s�5*� F�rb.mpedC/R�: K7LOc@� tech@�A encou6 ed (A4�t��%%C$forkepcou} �B)%��Q������*���0 often K�i��ab��a"�o&�-in� *���)managet�0)r�:K"->%bet�L�A�- Kep�8 ��(% 10.86�e�eXa�r�!�=`�5a toolQ���6��Xi��A�desir9*� on{L�&�^�.1GeaZ+J�!Aowe"/� ~T s. �f6A�usefu����Y�aq�5XJima�oZ03 Z˅<a-1*ZFM�ssc}.� z?.�,A��"<�treat��f*�;��alt6exclusi�6~��tg)(a good step� sB t�Z�D�]v ]%"1z8s a !�a��t� ;0���<�"a�"5 � cM � �},����m���p��&c s��G3it��H`+ta� ��h!��B-k [�. 4]{F� nd89>P &M_R� _�!c."��a�"Z.&�+�R�m*fm  al�5!% dE�$GL(2n,&%})$"�Def&~k�&�4r|JA�a=&�,aY!Jsub;!ZN|�7, &�*߉rd.k�)�"�%U*"�� S~�[�. 4.1.�N a& %Ad4�H!>�%fecBk2�!�,automorphismf$Heisenberg ) p.+* a_M�PA��e T_M$ �e@)&� *� T_M:�\mapsO*s,M�FBy�S�<,-von NeumannA�o�`�6G�+^g^V  \circ ��Mە" t,�%u| ��2x $\nu(M)v~,&���G � = A � +� G�A�i�6�&6�&I"-double-7ed:;e\5��i�B��A�-faЩ�\pm 1$!Xt�:�.} *aaNR)륑�. w>�k w&!�e�umu��.�&$MH&��7iO"lc([Ex� *M!�[= �ap�{cc} A &c� C & DO A)ٟ��I $D=A^{*-1�� C^* B�J�˕e.). ��1X2at any&_9��6�YC"jB^�9$|A|$a�#-%Mde�cin.��s.%2 q 0$��baL�_+0ut R�h"�,n_ofspn B�W$N�I &��\ Cj & IN�fBA"0 \\ 0 &1�B9IB-�N=:&��V�=F�K \\ - �B���-�MN���p|� of�1ae�ul $\m�9��"��2�E�6�9 du�|�3� e�7s"d4we tacklH"s nex�,e�f*l; ���+�e�*� E�t.� 6�%#Schr\"o!/er>%�[��&* �� m2��m� forschroyCe� =� !�J"x6 :�.v,*,-�eq�0m ���q�n�2= -1R>�n(f)(\xi)  |A|�*��1��); D�R�0��E�a��Rb� ��w�J x Cq�psi�,"�q���C=C^*$}:� thir¹0a��nVr�*)%: �%T i^{n%Q�A*{vnD ,�+')��B��xi Y� xi' B�A� �A�1of�/� = "�IeW:4.) b G�'?\n@&�_A2��6�l�/&K) * *  � A&s2)B={Kmq^� . �/�bget6m�ilt>K�o��vcover)5c2f�Kg@2� �v"X�=�'=%�r�isf\6?"&.�@�f&�;��Vy�/O� �zb�AG�|����f��4ll*pO,=��n�� 7th��*�Y� ��N�f)�2BTy=&2 :�3a�f�8a�EH͌ iKO(p'*a�+ q'p]��f�jt^h;��3 ' 2q')�R , dq�^p>�&�Y.�]e^{ Y2� }p)}! �{ 2qs t \xi;�Z&� M$& ���o�6me¬�-�}:� =ݫpm�t.W�� �f� �ͩJC%���1����M��j�^�4�C��n= !�fta4��1��\uDid�wq_�wBy"�*���6ands �O twin�@�A"���eq�l/ thmr�x���Tr.y^S2t ��=D�r.�F�ł"1 Ś�!�� "^1. ���FpDL72�1�M6� picVjn�2�ge�8�&���M) �^S/M %B�So^S*Q2"�9�-zYD B�I� 2 �"& j�.�(J�)."�F[.D�,.1�S�I� 6%�=�aQ�� ( 2�&��.�=.8Qrɗ �f6 q_j"���f�SJIo* �ez��kn�JfNV1Q�h�{ "�Z%�+��P� ali�\M��(p_j+i2� (.}: vc����:���.9l--�),%?��a�^$ A%.� �>2E.w� D)~] +�J}2� ��e�&s��Y�:n =& 0Bs�do�v�.� JſN�w&h). 2��&o $o3)Fd F�(� _2rx �[zf Ro !�BABTAֹ&e�T}$!K���)"uN52!V>NK`�^F�H :�>��,�� � $.g�by9�>���3r�^y�Y��e�iF�} �&F M�= w3Z�B��"� 1C�� I&�� )!c� 0x�*�#.� /-!),�#a�~�~�yp�.W�-��� true$$(!�?= Eq B ;B$�*�1 ~B�&(g.�& #,f.��e�{i* Cn*5{�Ԯ� &�?aHV5�G�A&FC!s� 9�B�@�P $B��&$=}B(erF " ��> s , (M#!AZ�&�pՅ$�G� $f����%xr� ��)f� �4(n"�vB} (g� ho_h , dg \, fFE6CB�B���S;Pd&��R]|M|Na E � s, M"_BU6[�Z1� ^*F�� ^*ZY�k8(S-rt� �J!B})�"�I4$ZE,s�%D=5�B)�(�E� fB� ,O4 U��3YŽbeq-*j��0Fu rhoh<eftwsNcF�\la_�_lUVv����I��*  �v���} sz� ig�)= S�<k :o6� �;�%�1��A*-� * ��H X . �= !� (�b(>5d)�:�(:f617BhSo��+D�@ \nu}�!�t S}_h���vY�*�$z4 -�b�BtJ="1<� h'J�Cr� WB�gv-6!!��9ա���>x�Ad6gA�J�Oq(Jx,N`�UFd��.W��J�J]�)1-��Q.n �>$EV�^~>C:��F~JC>N� ��>E B" k!��Nn���)���$:a&I`�?��&J6�df[ �#�1)S�6v S�3&�2�8Kbo*�ROc� �8rn2��>� �cer;��XW1��@34a �f) .y?$A2�,�!:^�@s)l�$R�pz $U?lU�Vloneh��D 6:� JH:�(s,� )^*h zk<&95{tJJ�F\id2O(pM�wNcJ�6G)B�A �NT��-$�R�DI��FY1/�q. Mk�6= � A"� �&}C�B &��s: AnL��;9of�v@NhC�!49�I0x�Z2� an�7or���@AAz�9u�{CocolicchioViggiano00,HanKimNoz95, Yeh93}.�.]d<���7A�^�~:KM ���4y~q[0@-5M�6��}M1��$ p_2^2 ) +�Aq \�'B *(C 1 q_2> "`A,B�C�^aC$7,���A>0�>0 - 4AB-C^2>0�6$�'�on� B ���_1  1\�q<,x_1,x_2,y_1,y_2&j1 �I�Z�9&�=&%�E�x��jp'(>L2} q�\A��p pQ)65 =L(�) {ccM5 p%��\alphaE~) ) & Rs�'� �/�s�1�X &�8��(4[-�25*Dq~8\\i�)r1O-�F�Q)�Q_%�P PZ��&@"ECYdM�]d;/of)� )�Z an� a�QC}{B-A�6.�} 8Hw\� vbe� Xi*CH�i�+�G� *�I����95ISH$M�*�6ia���%NC)8`G$*` = M$,b(�� .U)�"�E�"v ��"�=�F&��9�i�*}OL :UA5j�;BQe���+����,vAi�2I"2 X��*�\��n.Aj. yx�G+ ya���X�- X��� :� *}�v|\I$^EO:$.��Ud�GF�I:-���D�D�D2�WE (������M� � �������ѝF��46?�~ER%�G!Z�\{)*[� cos�ρхR�B �ڊ,-� ��-!]:Z 1�$J7��.� ��si��+�C) oj<��"s b׆+ �[ 2(A-��z� 8j�� !B(0��~�)�� ]�  ��- �& ���0X�5 �+��6�7 !6[�r�r�2��%�&-�O6OI"rpQ��6�\}� &?the�I�Sct Q& 8cm}�k? "7X\tan(�((�� �{6�" &�1a� B 2C\��C� (B-A�7}�%� F=: V?�^ ��$ �dono�Qc`Dt*2 / V���� �efq[ u w�C&� =��.�i�r!Szd��� 1����:�BQFur$G$N�Z=����;��>^�ATTynch%5d��6�5j���W�Ժ�Y�1.:�52�ǟ"�:)�%�#!%%�*�x%���v�1�sappeaRS.Z�m)ezMdH $W_16WbF!F *} W�3AEֆ�a&�+�� >� \ W_2 A���� � uߩ� *} D*I�j0�Ib>Ҹ�����+���nFU!�Jf!J62]I��*��2"1*� �:5 �y��*fZvI� [Td�)de�eIo"��s�"�&pe=;5'"6meBbA&&��B��sGV�� #^�.���J�0�wh��a�7V!�$1�}yj�C)2�%���+6�&-��"-��!Xb2w��v= ..e}}_H�eB�K�mmuKof!�DT� 9_�bnt��fieldh$�%$��}S���)FSi�2�BY��ta`m0 m �7 2} -eww -eG2�.Lm�91 �N�.Wv '*2�A �U��:�� �K"#��<[ S�>��W<ta ��~�= "��M�$ :Bl�:��xA�I2.I{y_�� k2Z�2:��:�/�" �%.) .E,J�1.�~<> 4cm}�F W�N2� N2}�� &��QG� "�-�z���]<��z:5��� �Z�˥�ta�]"��_�# �:��gt�&�Q�X��K 8*[I=retur,�usu�]o&'[k��Qo�ɩ <��%M^C.:.Jn2=� t�$M!$ Non-�YZ� �ns} \label{sect:nonlincteqns} \indent Unfortunately the majority of canonical transformations which are physically useful are non-linear. For example the passage to action angle variables \cite{CooperPellegrini99} for the one dimensional harmonic oscillator is a non-linear canoN�$. In this !+�ion we look at ways of modelling no� cb �in $p$-mechanics. We follow an approach-His(enhancementr�a method pioneered by Mario Moshinsky and a variety70collaborators-JMello475, $Seligman78J9,Garcia.H80,DirlKasperkovitz8}.:�!S6�Pattempted to find ope �o!�8e Hilbert space�quantum 1L al states-= corresponU f_i �&=& FQ,P:>8 p} g*%*8G8>�Aw6��cannoti(4choose any set�A�s,A> y neiXA�sfyA> ertain pr��ty)is�Ao cont��LA�/�EaveBver.wR:�F earsA�\cite{���#};�Textend i��$n$ di�s.Q�Pro�U��:1�0ctok} If $Q_iA3 i, fgF G_i$e�!l , \cEp,Ar��all.�bl!o d inverti5r�aS�Q{R}{2n}$!D�h��6Qqx. M�E�j \} ]�,A�A�$i,j=:�if�� only $\{ �y'P{� , G  Q,P})ZY.I�.l1� proof} By� $n$-5�al chAgru-3��(�eqBq}) �ny� = 6�y��(nonumber \P�0al{q_j} f_i(Q%H,P)en\\sum_{k=1}^n \left(\Frac�al!3}{Q_k} 2 X+6f_i}{PB00�!>dimch!forctQ�} �~�Fr�6�r>�0�600 �-�5Y Id� �Q�s holdA\w�\pl: $F$ɬ$G$E�$qp$. Us�<9�Z�)Sget>�*} %�eqn{\{!� , gM��� =} \\ &&J8\{)�[ m)� 6�%%Q_m:%{q!�:�0PB0 0-V ] t�'f�G_jA� {m'}B�{pJ�6P !>�6B��.1Ba . \h {1cm} -6�rf�%Q_r:�R�0PB0 0 �ZCr�CrNC)�:�1C!BC 6B�%C\I�=U�,m,1�%W(6S�A^ 6�Q)�6- �.� ,62- M�k,r,r' )� �2> �>���>�r l>- �%��a�!h�u�R�Z ,�JP �>�V -�)�V:p1�F&- s�(:(a�6��F(,)�62Q)A ��(�:\�-�6v- s. , ���<�6l��N(��2 *}�B abov�resq first�sec� erms� x l o> Hcel each other out;C same� lies� Xseventh?e� Y. Henc is becomeN?&� �[�ŕ�� -�6x� � � �4 9$&&�+A�N�6-J ,�Jm�>�V+ - ��.�[:9� .�F mRU:A�� 2 6��U-J3� 2� z:��]�|D.�Y��!�r��H �.X2*:�3F�3A �*� � �B�one dir6� argu� ha�je�ved��s�s spif"}>])�to02rAnn3Q_�P���]-,&B�QP�})y*{MF�aX can xTg_j%��,��!"(a necessary�suffici%�W�!K�s�>� q}),fp� f�<. The advantageA. 7p� cZ5. is)-0*H,on�pKmapwc})j/&�i*��may�easierA�definZ a�ei��9 h�sid�JzF�.z>p})]��$throughout�chapt�a��h9of��$p$v ($C^{\infty}���nex�an�G,\mathcal{S}(2L)Wll!-f�e�is"�ey!� alK.�asb".c'>d . WW w derb� 5&~usA� leara�an V $U$!�"&nE�o=Z� �z�supplyv with%�>��52�-:,overcomplete;96H@ata#��shus $\langle U v_{(h,a,b)} , ',b')} \r&�I a,b, \in 9�n}!y8In Dirac's orig  treat�of"�cZ6� F 47} �r#�A�^> from5s��>-�A뵲>!��shouldI���enA�inŁT�!�an unit�c2��":� suc!�a*,u�w}*< 4\tilde{Q_i}= U (q_i} U^{-1}6�(\textrm{andBHP: = U Jp J� ��"Fn$)r� I�, U �,.^�E!�J�!IBU4F:,P_i,q_i,p_i$q!ively� �e6�"} E"� sugges!�Egi�!!��T8ctual�ki��^�%�%���d) a�AZea&e�es<"M-0%*�7re!� a lo�jdiscu�on �ng:�R nonbij �"6x!ɪ proc� ��%�%in� F%&1fix#e���$f,g,F,Gu (#"�ef>=%��a ��] nwanundera&d!-6�og f$�#i�!$ �&%�m}*F�!b�!Pofourmmeqn} U \proj (( � ) * v) FG,P)U v6�!:Stwo.V&� =2VG6V�D �uk�� �mapA�BJY�2� ��$v>p !&B-OIAE�n�i�im�I�e"�$1f��gi m to illumi�)�$se ideas (�'we1e q-1-iQ�&b��F�� a(.� ir��8increaandanihil�a^-� i A^�.�%J4�a^+4-5+1�:�a^-� $a^+��%#9dy�defaplu�(a�դmin-� seem likea1�JmadeW\more � icS ,e;wei� la� iIis� E�p,e Wgo� m�'a Tmanage` ��m-�q?"" +% inuea��2 �&�*�2C+�l helpE j��e�E�aX)�FJ� d9R9��)R :� N�Shhcs})y�M �.eq: �eltof�.�!� 5 ���g�  \vab ,d% ErW 1F_0U*>0,6�>�E�P��g SRCvav�G 0R�My�W{A�$ 5$ u#C,Y>~(A�uwec� kecs"�+s})=��.* n�int_{&\2nI"9�=}9~, da'' b''� o��:SQ�}�>�2>!�)��Jj&K��-6Z �>Z�=Ii�2MV�5�mt$ Similarly��Ed $ �fI�Y$ a�2-�]0F2~<1=e-;nH RIs 0e �&��K]KVG*}e�AdF6A)!hF6D�f#�ww���w:7 *} �i�� $m(� c,d)!� �V�%*���i�Z�.Wth� aleqA5 kern�tsv*�e(N m(a'�'q)>])�e+~�}�k�&&!/Zt�xBr��!�J_65�t"f�9� IT� � ��� :�} �-w�h 45WlU��  $m� 1:r eff!4��.(;,YٗFPv=RqWvIe"�� %�bg Y andnnUv^�qUs:�oa��>w~ toge$��ͅ yU�N�e�(r%~"7)�Q2� eB�b':�=&Z~z�va�9��'v, �� �5g�u� wavey4xpofsoltomabcd�-R�N��N�k��B^)Remark mph{2exist�%� uniquenes�aa�u es�� � "� f�2 f'��� �12�cZ� q"� ;.ex��P�i�5e s�deU�7��or�;Bps.!.nd5;�! m�W6[$,&C� ) �EWUoc \new�B5g 5>�.�"�8��ɥ,b'$,�1*� f�1~tak�s�0#�a. ;Vs.%x 3&cdistribE:4G7b@J��)E�UdJ&E6. )�$a��(&�9!A�an>R*��J5:4value $(a+ib)$� Lemma� 4lem:csiseigfct��� xqjI .R�c�2��n= y�a��a%,>�a�ha�J|��a�:f�onh ��M��ut���u��Fur�mm�by.Gm� '-ib��!:�B�We( { in a&�<to 1��*["f�ee�A�^;n3�<�of�� qfor�@eW��B04q��>aA�.�> �=N��=�> $: EFP��J�fo e��f*���a!�9�F~ X  �Z*� >.]�y��&�� i�  + ib':�� �� � � -ib)V� f &� �B (-i)%-i �u56YR(repkerforhh@&�"0�  r� �FF(\times \exp� 8[ \frac{\pi}{2h�r9 2I�!�9,') - a^2 - ba''b+,";,:�\ Ɲ(iA�-c�4*� &&��''+E�(�-:� �^2>�>oF�� "g�5� (����޹  �Z ޺-%�+)�FF����.(B��y 9��� 6Heq:sol�Ixof�H2� =}U(.Uh}mK!-b')-6r(aW+eW+ aA�!8^2qN"v@ � ��vhown to"8@th���#) repe�- �� ulae���A >x�)An�4verific� �Eis�� Cor�Gryt coris�by-Kx}7!apz@ s �*�is�< �B�>�"obt�>J""B#J�%p+2�":tDA.hDpQ+6FDR ��Cnt"�g\�*.� of�,on-� ar:* !detail!�demonstrT how=���2� ~�Mnu�-��I1 7a�)� Y$A'!�^� MD &�BU�y��~1� eq:q��Eu� x} Q�q \co�!) +� s-t��C��"j pZGPG-q:GT- C> �&C�b tant!�Cs1!�rM ge�Ie �� evo�!�D"�I�/ed oscilL�1JY13flowfo})��%c@|(�"ai8forward.�"^�_Ja,�&�Kto���Je2NmBs numer�@ 9a#;Eb�Jt�*� f�}),�6� . BBE���.o!dm� ~!�� of��b�v)N-(a`�#preli�$ry>*ul�H/'2� alo�'e�M"�E-Qy�6iBn�xandcs�e xH � B��� 1� (ia-b �/ �0 "�& "i20#y:ty�t b+a �  +ap �JtBG<-/ 53�v qx ��.J! V�x6� pi x)_!^%]+ y (!! ��)J� �+)&B� ( -N$h (x^2 + y*�!�dEd)�\*( &&&�&.5�&R\E&>� Z@ :� )B�u�M�aQ�P�X��5��i&��^�<*# " &  �y�2y����Yi�u� u# U�F)$~� Vm�m�� a�B n%h�7JkU�}8"`�?�>nZ&� rojq�6&}�a�=� ��} [�  + G3G�ܡ%>i��"��!�3 �b�J��%�S~����b'+ia'z�-�5^)�)�1{-�ByY&poson�$A.�!` (9�6��,iA's"Kx�<��y}{2}�P��%t6DE6!� \( aX; pi b hx�� ihy)�L } ( H-:5B<Sor� ��:�M�>*)'I7Ux]+�V�%#h)YM�(y+ix-^h :�*a �G�FNX.e*5 P.�=�B6:��k=!Pm!�}1#+m��ef"�(h}�� -�xa1) � "'Iw A�.\�0�-TN�"�=%�� ��~6� >�i�qj*�.is"� 9ya{��).6�I��� ly,s5�mom����R�1�Oy�?%xI���!Ea�!�hym�ihQ�j0a�!�e�:5B�6��v�> �bAá�rB�� ��n�c�9e� UrQ�'RB� [.�R� g$ ZU6�,\*aH~:�4�/by <�rP&�-n']U$af (Q}4�}M -q \g>-:2LPU vB�Now)^)�p> :)t�Zby9��}���� J�"k bigqin"�& ^, �<".=q�dd>$h *��.*����V{� ',�B� ~&�͚�>}:r&b �P+Yn�bb#*�u��-�R�) N�*}b�Bt25( ' bigp�$U$eI��$-u�n�%�%��N�I��%�%~%B�ETh�TIthm�\� soln�ex��9 .Z0. �� .�N+"*h h"(!�@ie�(t)&j + C B" /)� .R .��*0��Jmy �;sfMO��:��"��:��9](!�1�&Z����$by]l�?bstitut�:c:�)�o>�. �JleBe .�A� 1�>^%+JR.�B A� B%NB �y5J}a�� 6P "� :fj]!iZ7idtK8��2�V�A��;3��N<re�--.�*�+�;sto�t }�H� �^'4intanadintbare`U}M%� J)d;�� d af�<�ĥ� . By!y��:`J�,J�JUf���V[!rIv�Z+ib��.*� �.JV6�G.:WY-.+ (-ar%) ��]E*}V�d[[F�+Q�A�)��W6I�:J}-*U��R�+C) +��:^�*�]�*RF�X �.T%*) ] -C-�-*B����4��Y-[�&v%��a��� ��1�Jx9�-� �E�$A� -C XB�J�en>EN�tells�?�+j4 Ms!of+F@ A cal:k13+m%�nals�%V �Z. �@ $@t�bel��J?�hN�d� J�"�E�� ��jF�J�}'E9!�U: .R-�FF2=6�B1��&�E�.�ia'+bin��6�U B�~�} ��q��C#ewi au�[-6Bt~6B1�� ��?1/��C(i�� ��9pb�B�I�Ce�Q� s�f��']�O $2A�T�T>W �[!A=��5�&��XB��i=2[~ !ba>�*�Cs6��K}V��[-2�-2�--m*-b'^2-a�,b^2nB� .��%�1ՙ�2 !ge�E�^2G� �%�. AlsNx F�Bv�5@Q�2���"Y+B��� [j��%��!��* ����B�FQR� a�Xb�� �agU+ Yly� ��b�J�b�8LQ�}�uFdEB`gN�BS �`�E�>�B&gRx�,����}�Ս^; Zq.0^2/h^2}{4\pi/�1{� I�u*� I�E�)]"�0.>E&>� 4� [-i�fb# d e�BD*j.7�"v�h�V]� ��� ^) �2�� VZ)b>`&� � �+2 #�Y =Ln�jF� E .d 8!-._��F� �* �� ��]&W!L"m�Ll�/ame%8�� ���u�mS �Yi"� ݦm�J�!R��/F>-�V04I1&< "* I R, �m��MiGeD�13A1 + [iy�T*� iA�{� �(� I�~��..d6(��~� �U��.�J���)DY�n.��R��ʈB�By/arV U�J,:F�u �(�� desi2{v y��V�<A�he� ��Gel&-3�R\c^�A�DO�Z�1:�Zs1!0#CR4�&�3.�U�!Nt �n �n~��u�\{ O'h (s-s# a#��q+ )��( ix+yA �}C}�,e�) (y'-ix"� .Ji-6-]l �%&j- + x?6y*?6\�(&;�3�,e���*��%�; =�-�M�Let�Gb-@ arbitr�0eT@6 "�Gi'l0U$0A�"�5�����*�#^�32j B�615� J $(Uv)(s,x,yL:� 7}} ��^$ v(s',x',yAqib6{��ena�/� ��& �".SGsx�Gy "gGF�zZ�#*G=$,U� �!�) $. S^�V�UA)R�UFgK �,5:>�& �:{4>{bo}rH54��U 'G�  6@f6��$in Theorem�VF , Fz.�*R  J�27��x �2 �".�O6�J��w�  ��d 2�*:���2���nJ . e >�[V*ak@x'+a�q3by'-. �R��p a' (�T� by-�)�W]B>�\{ &ue�FWK6�AY��Q�*}�LB�a!!,2�@�,E�.� A$1;-H58%@ %�V&� 3.4> �L[iY2�ti%�:v !@ xr�@^�� �J�.2�byNxZs){ M�a(�E�vR)PE�B!AO�:!tI]: *}:�,&p :� �/ZhCA�!�2�W�W�)^ Ir[ Ae6 2�\�fEf��+bD7y�z���!Fbg*�"[���(�>�U9�� ��JC"K a %[E%E.��  P �6O �6U �Z�R + b�m�N& ��~+i6�� pi>� �!9b�9�eka�-�y�z�}�F#�A�i&�8"� :+ redu fe3tB���&6�B�!  (t2)�!G!��C2I:�\&f)9� ^�~�ZB��!? s��)m�� \�n{�FPKepler/Coulomb Proble&�++:k$c #6 VDh>a�$�:)d���!P6gAx{6�$ |p �F "Bs>�j�CVH�"{three 2}�"�By) g�n&5g$�!,1}{\sqrt{q_1V>q_2  3^2}}$ po���!�nassoci�F� e^3�nP{Z��=!K&*:�b��c�uj-9-�3 #!(often refer�uosa �2�8} �iPGuilleminSternberg90} �i��s studi�Sg�46jth� h!��e�^ 1600 �F��"��bir�oo%analytic*>n�cege�NewtoD�nAn��%?i�a�|)�!#closely�7�C�fundaa�al5��athemat0Dly:0Hydrogen atom-\h.��e�| ��u&��$s literatudk usua�J�q�U��m�1970s�CimporAF Ay�r�kng%b was done:9�-�Q|bynerMDMoser70')Souriau  74)-)��h*�ummariH1q2�R���I�WdW%��%6�f!�# :���"�+;geo�c :|"Mk2uspr �1�Mih�wof5Va�ؓ istsmR� veryM� �subm dofitsI�I��s��2�-bBohm01-$H dard6[rvB!!t�&�q]u%�P[Sect. 12.6]{Merzbach)� !Chap. 11ssiah61}1�s �8)�e*aW'�qWIMe��)��� HamiltoniJre�%�a� harmo� �({Vilenkin68I�a�� Lagu�*( polynomialJ6)� geometric) �m1� �uAV�wɃ Simm�X�pI�i73, 4}i�!a!�Z l�kepcouap2y�K��!"$&�n�2o:�5;Bleɼ� �@.{�G�MfCE�`Lan� mo�(e�iyu� gu^�"��vector���La��0--Runge--Lenz $�2N%lpdy�Y)8%/>�dynamic���J)�>3�dec\��`M triv-n��I+(ItRU�$L^2 *~w3�w�s$\fock$ ��E"��E��^�r Xq�^1in[andg}.� F+e=polinUo%-developGNew!�X�in�x2 �uiyuc+�r v% q+HeiseX grouk� �e�poA coord_o<pur7�GF�o fpos%H}�Mto�Lli_m�  ny> Oof&�Y?�rFdklaudcs-sIKer'�s�nt�sH�QM2E!s]6-!�Otol=-y6��Ro�rep��is>3s�nZbe �luS���nZgenof}_Ñ%j"�s�MiNl� s Q�son� ��Mי6�"_: >� MB$*��� (�we *�m��6.�!/a:��Q� :.?� f� c�P(\footnote{H�F^(Z�{�n��ts���Q� tor� tech��itA.��"�.s."p&�"�0eq:ckepham} H���f�W |p\|&2&xB1}{\|q\|�eו�S3#l�nor��XuE�!Z $2$-(o *�+3}$�/ $\|x\|�� x� x� x_� $ �} wish!*� Z�a8&UE� ordeHQ˚we%Pa knowh (/����F� 9�S�a*%'�,�'A=fBfQ"�(ftonschwp})�B]��\ .�� j~.~���b%�!�pi %b ^2}$,�}&I-�*�>� 3}} O�w(. $,phi (x) e^{-� qx}��Mq!�::N� PWx"t, �`���$(�}f_-�-�mSec 1 �  2,�74 3.3]{GelfandS�s v77}�@a�/of. 2l�(�rngeA a fa��c!%��R��,~# �x!��VA�r� r�D �AXF�6P��maUOHy�q�.p�B_H���"1}{8\pi^sJzer�Uy�--?� (s)](]w!NJM��S�3.Wd����V��H}E�. $\t� ^{(2)} (y�no���2`$ �aGtwo{y_1dKtG 2F3*�*zt.ۃ�&[2. !�2 $�Tone��/<aVH �>v�4angmomvec} l=q�!p�qYw�*}mes$ de��{crossA�ducs#A� "�Y��con����$i$th���� writRq"�' �i} l_i�uepsSw8_{ijk} q_j p_k BT�q)display�U 2B= E9\{-ar�{ll} 1 �^��if $(ijkI�an �� permuM�v6123B" -r<oddf;0v�[ wise� �x)�2�VVM�J�>y29#MIf ofI�} L%��1�.�X6eqV�Xea,_{(j)}^{(1)}�ika� ��\�:>4�AI�:m�{x�� j (x_1,�3)$�  toeB $l^2A|��j��3 l_j^2�� &� 1m� YF��Jl BQz����=� zL_j *)�6I� $*BnoncomI�v� �i�i" >� ��m hB��� ��nj/� j"v lenz�f=l�"� q}{rJ �2������j���� i} feN:<l����N�j�is &т2�>/F��*V<T�=& �R6�I�Tky�&\]�R�"�"2 T�ixuk�.N��X u�y�/ �qX6Fo!(*P .*"�B��*�E�1<��֡,n $o(4)$ sym�yM�}� {RBs�8Poisson bracket�q��q�or@a�ᰭ� �� � ari���� field�9)\"<� r�26px_j9�� .L>�� ��]Hx_i:fUFN =і2 /��{\M64  ���UfEk |x E^>��S%`�2>�-�!unǂsal9�� �&4�S1�&�_*K�| \xi$%�$\etaYpE�:�the*/7m}�doto4 u01} \ub{L.\xi}@eta}{} &=& L.(\xi�N�5"� .I22IF./IF�I3 IF �6I -2 H�FP"/ � -�� \c��Dgc�"[ "�>7R�p2�6�~�/� forcedosc��Di��B�E5(> dyneqn^ UE \*b�iefN��ޑM �s w�g�bd��A�E�sourc�Rw�al#�"�%�:zn�N�ApB!VY��V0W� �2�� , $BLak �:�|IJ.;(�� �l{B}{t�J-6� y��F*̤B}| �Ábp�prB|x-x'��� [�6��( s�&�Dy((), x' ,�g� (�E�y;&�*u9-fS'-xZS ] dx>�.*���is�h���alyse6beXANmix2g!V���LA�aA:��Z M�Q���w�tod&�b betw͆&� eqQ*� w sui;LAFM � leadH&o"��6f���H>g,���h he mw= focu���!%'�Gter>�:��z~���!�6���W��(I2�[� �:k"\ �[Schr\"ooe� 2:@}:� �N�!3$\rho_h$�@RG�*�$�j���v!�:g�ϑ5%}< �W � 6�B_H$ (2���)�`�n%:0schro��n&��&"w'isE�JXU! whol�NeA�i��:6F�B�s!cusb rhs}.}Nx i*�T�c�ga�mq�%) ����E2 !��B�"&re#�= psi$e��&�!��fsp��w[9rRe�l�P��.� (I�^S (B_H)b  )t F��?"�nabla!'*� \xi\| NM" �� Q� ��/B"trepofaA�nonaliegW�"�h�wj ��6�q�^S$!{qe&rz ab���=H"� F���kep�_6Jb _1 ,%k_@f '&�6"�^�@!��7� N;, B_H & QBrE�_1*� _2J� �>3sk�� ���!:�*T_-\��eh� |!�eV1n�& l tJ..*� �:��8>/&` hs +b.x r +_.ihx-et!xA�+�bB* -{a�xi y, d 6M.l�1 2 j�z + \�|wk)��h�8 l�h�= @S� Z �� t81 ,"��:��\�eH�� :�-���xi�9�) 9�iI)�2�1@"��x-�a�eftu� &t@�5˱2��?) �2 = >�" A�@G step�" �a��~l*Ve�.*��$;as�Z��F�JER��}�58���q6�`Zn)�Zm.9 žl �ɟ͐U����:Wх.�>L^F &\(^� *. U�&tuE���.6| �-*� 1�� * �-7�O �\"� &� . 6]"(*��AN�p"�*�q�� sa� 2� >8"đ�  m�a&���D/ now ,f ^� : =J�|�V�>6 �� >�> fk� _H$,�$l/p�f�y � E��:6"ef8e#� fc#M�*>.�{EA(2!p_j��A"n q_j}@^2b}BG"�>�G���D+�B�!�B q xDBDf�6 ( q,& �x� ,�o"���m�& -:m�"3r�hoQ �g2 e�-� r˴O� . psi�2BaD.0&�,$f_1,f� �.� fA ��f�3��;0�#�1 i*+)H*.f!�:=N 6}}.�$(hs+qx+py)R�15�=8)� y , j�"7 �I��#q�jp�j\Mx�V\�:E�J�8 w= NOhծ&t�b=���V�Vi>�:�%f�( q�%�f�*)%�Z JI����_1I,��2 �8u/%�:7+) 5�:�2 �.!AV���W��.�6�"<F!��*} 6Q�"8�E�,alogous mann@(��[�Bof�8�T����we�is���x�+�,F�do�`&ža�.5�gP��0at&r6�:eS��p> �4n*k�w���;:�TVis2a search�"�6-�6�Z t*v g�.)op�!� ���!��;%9FC{V�!�2�.eSV4 /P /Co" /g"�o3-�.�\L/*�/*XI��[�=��6�g � B/�pej�s2�if% Fh7ofn�/� �/.f45]:f4.� 6e4%�P f%%KBT0� "�0l=��! N�0R�06;?R:T � 0 ,Yle�(< 2�<p,i~��Tpp!R%&��>�:��=byme310.4]{BaEt,allLiebeck86"�"q�"���$pmapr} r =1|�!d 3^2 )^{�D�DB)� bft!))S= �vصb��|() \tan��� "5j�}{1"�,*�(� � geq 0� xAP\n}u� �+�hRi6�=0�83f9>v:}N�)5���p!��/�{ J�siN�A�1!rA<)^{1/2}}N+&3^2%O R�3 -�9���ʈ!{�'vlWI -���2ަb�%$\msp���, s��� valu*�$u�1�)B $[0,\pi) E8M7�*spl5q���j2�&spi$}���26�SP}�3�&\_���2�Y��B��WAY1;$r>�� �Q) !�zhi .����U@2@�`:?��:�$ @�/}B3B �s� � } WJ�X�!D�&%4!�Ż~ twori!�� �-6� 5�}!� vxW��Zdo�.� A�I{" Def p�R.�RH/"N/�3{C�Y�Xf\ta�^A^B�y� \9 \qi���i' p�5$���F4VYN�' eq:iponfs.��i "�_{W�#]0^�'ak7{0}" �%�c- &% l:!} r^2M�]� , drhdM�AvUt ��)�Not�za�1�# �&�&M&M��� hww�¬ aAu�b"#$=���J�m\ U�Ph��$ .0a��N.�bNU�(OA�)!-|,�,r�n�I�6͕ ��:��� ���Q� $�7E`�P�" "* �psimp�RP �0Y&$o'r� ]&�aren'�E!�",�ÈE:��eH� aPxin� 4��J�=�� �to�3F�@�̩[point&-�P!w�� Phi:6WN'a"� W-� P �If"Rq�4�!R6�thR<+U�� GP�PhiE�)\��}:�9^0^6�B�6�e >�e )Vc mspi�3 +)2���)��r��Y-f�7�{wa.k��e{#nqS.bl�, msp:z gma�ob�)� JacobBD�kc��l"�$�� �)$���Qmeasur�#d�C2�_��F9�e$F��(!�*֩�-��;eta_2�y� .��.$@�6(Wj~Ni���pF �h/l2Ocom[��E:|�6�"��~).! �in�$�)�#e .�K�k��.�JO&�>V��� $rho^P_h$, �6�A&�����Xq. ,�%P&�#ps��U����=� �hs��ih �"e^�^{( x_1"H M�|e� ) + �6#*+ >#x_3". ���s ����( [ (� .�"� +hy_1�+)j� h y_��^(B�+3 J�]� . ,�%J"ldV�.>-[Pr%2 :���!At2}&%! �` �ph&"�]�:ţS�.i���(j?�1�^B)k,2)"� }{FUn�d,,y_1,y_2,y_3]#-=�T)��n *} $!��X:�� �n>~ %��!�=& nA��DFD��~�� }D�ne���w�C����^*����i$(�!.4264/%� ��9fF��f}ncQ<�h)4���� �:.�s 7]�D[9_���  ����_h^P$,U &il�aiva�y%�6O:� ^S� u�Um;�Z+Pe>.`I* �j��= �6� By  +j�2�ti&?s�����"^P=� S �u�6Y  ) � �V y2�Z�!To�51 aJ��0�K`-��C�!�N 2�n iH$g �n*r�F"� ��!T]B"� � 2� +S APh)YK j%Z�v �E�r} �d+� �'�-&�ule � yS-?�I� 1�B �V�.�i�a�of�coGXdi���Gm )I^Zi M rȈi^Q�p)� ��#a"�,q(�q . - q2| 2X)(�>�E� ll $"�-�Ii&��Qe�Y�mapJ�"�.one*for%D*�.P�-N�$-�BS�۹X��%Kʧe must3�am� i\.�5~5�=�]� QV �.2$.&C9"H >X�@�5L5*S�m'*:@1�9'Be��� �u�A �U[ \f��*2�SY�jx���3�%/�)n�.�a}�:���h��W"2� �E.���i�OFN&S3is~,��So^�2! relb�7�'andp��,�&�#6$e�z��GaC68N�*�!82::��L�P$�'ma:�\>^8:N�ed ��e����x21Z� ho��%-R�@:�".�+&B^ lle�,)"eW����6P�� F� ���w4�� $L_ pzang%�#���� )U*R�� �%%i*�)uܵ� sphr�4l�} �a� ( �� )�]� Bx.�;�} �m^�{f �f���D7�c�B�5a��w�l&u.�ltiZ� �m� Intex:ing��&!v.�# E��""%%>�b_}nn*6`V.x*$.[za�;_d�� x&S&]:l_oj*um2�wesaA��[8ZS)�*� 6>E&Pq_1,q_2,q_3,p_1,p_2,pE*� "�� 6}: !�=%�=P&)$��.U./&  p_r,��$} !Ј .b : r>0, 0��.T&�GL&hiS&)3�Qb�7�R)�0. 5.3]{Jose98�BH �2iaf! > A33� VX�]�2Mip۩���M� !��A���% � /i 9C2x*I��!S)�J�#�0!h ` ! nA� aXb�����1o�Q:��!2��8"% -�)�2  p "!MyIQkn$���j�zBA�)�2�[�6M� C}{}�R��6_ d�pol!@*�R {:U^L}"� u� &% ��"l�9eQ��%B�!�%t9�x_&�&6%� w*�-��#$"� ��2^^j(��� ft(I s�:�Ii2"��*8�� �2r� ��!]v�!�10e3(�t���32�2%52� �y�Y6 �u��u<`Qu:ɢaj.$ *i�TgU�F*R :� e�]� q�sv֓� z ��: �.J�qߟ�.fg-N,i%2�}"�R�%66 �*Z&Ѽ<}�z2v� 1n*��O�ch3ass�0& , $fV$f$��� n� $�G� �2 �.�� i>�Bbd"�>W*�� ulaͭ e�G5~h"R<of=�G��&�J�Hv�Y$ e�third� AYxa:2Y,$,)FIOo�V) f�a���1kL[ "��L� =�cA�-`Z29!�j�!_ю%`%�.�v[*�L"���#@.�SB� ��K}~`rNC @ w ^�40y �p112L �ŀd�by*�i=� �Z&"f�:�&HKs�™s%�:��-* :�� e^^X] R�6�h6L^2D(-)}h![��6W!�[%o� ��R)5�?2 B(9� two��[]B���65j#*6!>��j���e��$w4been shown to �ube \cite{Merzbacher70,Messiah61} \begin{equation} \label{eq:angmomevecinsp} \psi_{(l,m)} (\theta, \phi) = Y^m_l (\thet \end\� with $l \in \Nat$ and $-l\leq m l$. $Np$ are the spherical harmonicsJ� nonumber > � , � �\\sqrt{\frac{2l+1}{4\pi} ((l-m)!}{(l+4} (-1)^m e^{imD4} P_l^m ( \cos�)F�here $ .x)$ isɈassociated Legendre function\index{n#})�([Eq. 11.71]2�4}. These eigenXs hav Lvalue $l(l+1)\hbar^2!p\=�)w also>Hof�Xoperator $\rho_h^P (L_3�4ntroduced in eMU� (\ref{eq:sphrepoflthree}); for this U theyF�m� $. T2�polar coordinate infinite dimensional representa!i�`Kepler/Coulomb Hamiltonia1�6G!f0} ir�9( B_H ) !p (r, IB Q�=aft[ -I�Xh^2}{8\pi^2} \nabla^2 +M�01}{r} \right]T S,A�).>�$E$ denoteI� Laplacian!�yn>_sEa bound st!q(negatiAanergy)R5i=�E�4been shown to R�Q� SectE�6A�F�narray}��8kepcouevectorsi��lefteqn{!{_{(n,��r21 =-\rproblem5may� of?other(s.!�ndU \se; {T1�j Posi��S�Q��a� 0:)Opos%9} �@nt In�'ionAg�� alis� ,above treatm!�ofruin!�-me!�ics --U$consider a`( invertibleAIp� of p�s�.A��5 how�rt(from aZ&B&% s�an%f!�n�A� obtae::e1uER�MU�qa, R1$whole phas� ace willA a can� al:� . Supposa�mgc: \%� {R}{& �garrow u�$I} \subset2-�d�B��along � its)�seA�(differentia!�!#ll% arguA s%�assumA@at�I{ $n$-.� �% of $.�$Oa\!j=a< $(\xi_1, \cdotsQ xi_n)$!�� �ele�FY � (\zeta_1? H n rI��I�� matrix $D!�%a used�� %%Yentrie�3)_{i,j}� FracpA�al{N _i}{�jlFur�!$more if $Ala[�� $|A|.!�(determinant%T5�roughout6 t%�|�$| \neq 0$.є$Defn} $\fg �&E �image)s$ltworn$ una�)e�\foot� {TZ� �4no� $\eta$��an6�j%�� V'1�F}$�^bbm �tocurlyf��taa]psto ��rc !�i.>� )(W-�|N}.���K��$�to -abyټ>�). Clearţvea�eH�ois ��1��d E0^{-1}:!�m �Z)d"� 2� psi9 c1)m~ Lemma} If!�Qp�w1!inn�ducv�langlep e�� 2 \r_{�eYint_{�I� +(1 \overline+ y11}{| e( |} \, d\mu>�� e�HLebesgue measure on:the.-���sometry,i~zb��� .�)��,YE�)0>.DF}a2�ih�$a Hilbert ��m-�mfproof} T�followsA�*g��!�var�\integral)$aj$�[e Jacob��:j�Q$cancelled ��^ $9�D�M}|�a��,completeness`y�F�� �equenc��1)!�be�=�--Si6U3is.0�:� {�%�s��r�S!e�$I�1� unitarilye�� to|r !���� Gyirreduc� �+M6�$ appli�"a ��cu� ��8�tak�� QR�Z*V(--)a�) ��{{-  ihs}�\p  xy  x.Ali8� mgc ( +hy)F�� �6��start��B�>!%��!��w )&i�$ such�@vN$7A %��� \xiB��any $\x-�*z $. N� I�1|S�_ )c�u�� �+ hy )$ �n� z���N.6Axʊ9��)J�*� �n��a(}� I�V��� ) &=& [ +.?Y)]M�U�):f=&A���[B�]Y� �I���M�Th��(thm:genpost��� � rhmB���$p&Mal&� ��"y observ� s�.[ e.< 4zerodeljx$ was"� R�p�ofa})"�}O �8eq:rhmofdelxj} w[!��ft(�n�\}c �^ )i�� ]�uZ��M-��_j 4 )z�1}*,�yR��1}F�y �n�0sum_{k=1}^n h�_{,k}� [� m�M})_{k� Y�:�)] �<� �.Vp Jh *�lQH�m$�y@ect��# $k$th"� yA�1OM�U��&� r�adistn�iegp})���� �Gv sin 1b��x w�  � IX(s,x,y))`F� �R$S}(\Heisn)*�m��7E�/2jy4bo}�pu thetwo Es} �S ��,6( �2@=&|P-x_jE� rhm�(|_{-K=(0,0,0��Bb�(*y_j�1_M�!)taa�)�{{9:boBN)*�-� �prove* � xjINot�atY�6�)� M (er bracketsU�,v �� F1 by au�alolr�� FQ �.P /p{t� sp e�a�"�� yj})k �H$nvolved. FX���e1k�Tf�iT"::�y��^�u�(needtouseth� � tq�& ��d &HM7 6�6C&�0�+2�aL \ y + �# x.& ma�C} u�)�E12C�a =m�� ])�[6"�J��5� Apply� � �lem:lwUEt}�]isA�vXfa+�theorem&�sFiF��?ge*� i�*�gng�5�N�1.�(D.��� .�m�:r* 1GJ�a� 3)} � we � " ��!x-�)�� 7i�2oo�1T-�%�B� :���b>��C��} F���|_{y=0N��-OQ�� E�> To5\is1]e A�A��>�chW rule��w� !�Eis �%!P2.5]{MarsdenTromba03} f:.�� �"�xnd $A,Bn@0n�hen9�i~2}��f(A�rc B (,�)�,l f� 6))� (DAeCl} (B(y.B)_{l/ y9� �$?!$�E��1�&Rn OJS2�� 2��6�� } \\�I:IA 6�2\�չhy)] 6�= l},9,59phy)� -(E=6�A�@6� PB� .�W��E"�Q���( �3t $y=0� yz�@*} -K�Vd��yLcH�v��dA���'�vaz��V54 encourages usa8mF� one2�':�as"<) mn.�$-ARr � {)�#�V $ta_n , p_{g_1}!n} )} }6� =& \exp(-� (xBmg"� )_1� O+ x_n#M� )_nA;6W&�](( de�( yja�(mPjIa�gC (1,j�+�k�!t)�m.2� & t.�&�+t+ y�r�n���Y�-�"$ Prop'!��y- 2$*} q_j &\m�&5�e� \\ p6 .�k:]j[![(B))%YANk�r:�*} ��n� (2�9m`6jwe�"is"i ePPoisson "Hq_Az�I� eta}U !�:i��7(i!�$. new2� g$�d"t(QPcondforctO$We�i�a dir}calcul�~�"v .�{ q_i� j \}2 1�.? q< 1�.p_j}{a }HB  2T.:uQ2A=&�����')_!Ske�A�j,l)%� 1�ki"�3 Q of�pr Q�M�`ibx �.x��5��� ex` � .%>�)���� ET(D��gc &$i) �j)�>AQl��DI%0 g/I�_id�#ty "N.o.� . So �L= 1Vi,jy(Y�� F�e)E�6C5. 9i�m� So1FourierV$� �ula�:� "&se)a class%1& $f�ll�(� &�"f$ �e^m%&i'�'lau�"Co!� nt S .s��,Hydrogen ato&�T':k;cs���0t' Ever-�6h*M0��1 oscilla�0c��.s* e hunt hc)enAto find�)e�$ .��e sam�p�'�h.�. M�effortZ1�. made RZ(, some!��prX-ƒ�*�ingZ� m( llk^�2� �ne!|achie� On�0best attempts-d� by 1�in ��gr 0break�papera�te{ +96 - �:�U:2k wa�]�ha} 6Re :� tinuou� ir �, �orallyA�'��aAsf�aolu�)�*n�J�!�.�0por%2�F*+ey�y minifuncerT)t�tA�%�0or our purpos�)do;r$5A�y. N�*�1a brief �# view�.:|�& "exploi;sV-m�m- in Sm+� y�rep}. B!w�HMs:�+e�x{:�!6\3}>�WNU^angular-"�:ZZp 7"5} adapo �!6�An�,I��55]]��*m 2*^r2 *[%O}/��:�2&,l=09�m=-l}^{lir2H (2le2(�6�6�g2" sZ=��t�7}}{�%2 )^{l-m} F�6�F+� 2 &";'1 �i(m�phi} + l.si� 1^+1Z�3\,!%+1)v3��-� It�ima�an��)H a��A��a�:_aiarACao $�)� = ()m2�,$�)$,A�2� �M"� ')�$ W�Q"� domi�y�t� Q�5\rtph)$��b.��5Z �1omL2))�X$\�%kg:z*�7��d�6��$\bssp$m� }D6B-_ span�4�&6e��$. �le.�-AM}_nh X4M0e�4�� ���---IX/t�-:�B?�3F� �,I"j �!�6�6)%X$0a�q l n$ ��$- �!q|;iAt 8p�� �RK�MBJ�"� f5&�')P� aa��Sdisplay!v}�1tk��$9 V`�Q�)2a�J {m���(.�i��9�*3 :e�>��=M \{ � %{llT=, �extrm{ ��2!); ��\ 063%3 wise�-�* a���2F2d�7%�:y:�mg:B�as2p$se�?by no,n� unique�i3*b| ��wes $7\sigma^2�n!$?4c@5de5describ�<>�= a+. p� s $,Fox99,Gazeau� ,9,Crawford00 $Monceau02}Gsugges � %� �=+i9��7� n!�bb|/defofkc8 A�� , \gu92K�s)�v2+JnW{\inft�2W^n6wk�r}{ ih(n�V*3}{(n!�hA�J�Y.^ �)��*Fo� '�we.�F.$\nu ( ��jn7�K"��C�eq:Sforkcsp}i��int f�b d��}�&� &8�/ 0}^{�;a�t_!rJlim_{\T� m�i1��/2 %C- ^ =} m0Y��\, �1F�)d-��)� �D��5��,9��!�a0 $\muN[?N9YMm 9�!��$ ( "�?�]h,d ZW1�0^.�!RYB!� 1���N`r^2%Q���`�wr%9'@!E�B5 � �y� :�-.Z�A�e$Fy��( ��*$ ��>�*� �pO 8.O r}�resofidrI�~,&!3sp�2!��krea�#��� 6��6�a� � " :+�r�  An5�?��2y "v :�  i�tM�=�eff�Afkepon^W>��C?{&n��� \m>auI6��B���}{�� Y )��� .���4� ��be rev<�J����altNN�?����&P (.�?�_1-P]*���1e$gob�3J0&AA"5��9: P>U56ov�=&!a�2�5M�is suit��m /"�quaZ?�.anT:��>. Two =��>9�/ sai$be�i]4 if a��/�>amplitud�/�T�� A8:son94} � R �����af 2��.&+s a � u�-�'�:?M6�2standard F(�i�%`Ze.5 tary:�>��.�3� \{"z v�1� \�si&=).a u ��a�"� G�f� \, :cٓ��\&� ���)�@2�:�$f�!f�*�!La� z�E�)Cr=�t�f_11��,*� � =:� 0r�c �� ��v�) �#�.�� �th&(;d�Z� � � )� �:8D�9N��iP<*�1e�6�to&�A2�g-`?�<kcmap:�-�� !�mNa'map$}J�n���mma� ( f ; ""1�j�Ir,2��/f/:�  lI�uAc|g�FM�� "� -/�^�*V �+�/fkone4%�EWa�b69�#vDEC/0': !�6�iyY�6fqpB��.�d+'q:0�26 �z@ BothI�`ss�osG=� aMfa�4ha�B S �$�� B� %i� ��I5.��: tildecame] @*=5�� %�%� �1,EE2��i�Iengwe�`{A)� A %�$,��= )�1 h�62=*��U.YM�A OQ�"p0V $�B�-Fb)U!G}-a�6E9�6!6�iXL)���V(e5� %D6;� ��x*BJ� �7bS5-�-"l 1me�t�B� �"#�� ofJ� QU���?n�F Ais. � 7�!P$ervyY���5XI �#��f2�nZ� J� s �Galdonly �@ ider�֫2�:d �)NfK)9 does� extenN = *� � soA� not��>L �S9enberg�!p�Z%Js-��n�>"U(v���P evG!iY2�,E&s$,!��E� hift2!!$� $Z� "� e�IIhat{H�(T1��MAm8&,h^P�I�&�$�x S TcoL"!��"uGI� origsT� B+3J����é�w� k� �M�Y�Rih�<}^�u�2J%8�}�Ig c1G5$ x4&u�!E5YAso!�an2z.A�ALf$5 an arbitr� Z7>&o!�2 gn $f=1ps�HsJ%�����".t:Yf��:hJ� :� 6� *� 9�'F s*Z� @"� 1 �ofh�J�)� HI��>{(\* jPtheQ^aPVef&�6 ["�NF|�� �&�!f]Y�VJ��k k.�+f}�u�} A*�;>�i8&�p&!�>&�  self7Rol 6�y a+.+lF�:r1�&bV�7 m�_S2�RI�3egiNQ5�%?`"l!=t��%�*L:Hf= ��z}��SZG:/of6#$f(t;I�i� �JL Y�<= f_0D�a��+�t&� ^�M� )= f (0 � �#�� 16��A � $t=0�=:�!�UJ>�� $ �r(a���7("Y)(�2')��2�%=VE 9Z"i&%x:e�AX>X)C�jg!JVb[��%�'2�*}&cm"lYUQ3�a�Y��,'�,'���*',!&�ZA �>�Mnij� {N}{l�*�C$B\$��$m.HZH.4Jy$R�^o��e&iQR�X�dV_$eracy $n^2eb��greO+POus > + �<X+ Z(�� �\( 2h c�2ng� abilL,*�K �� r ��&� .� u "� � . How�-we)+�"LF�+genu cou}DV�/ �Z ��� a lar�X2D.*�Ge!ml�0s"��2n*�WeW indicB^_ e�;approach%"�7V+ N��/J�systemIg4screte s�F rum.2FTweT5A;�J'include cs ddbaE c$ qa. Zll"V/facA$atA4�%�2X�$'s>� WmL "~��ed�/> Ax_2�.r�2�0ny��0jumda�Gd Sharatg%drai�writt�1I%�M 62197}�usgre�5[tw�1��!]�aZ4)le"-�&V}5I\e�le�-({Goldstein8QcFox �Fox99})e'2toI9M��X3da`*� Ga�ans� `&`&}  u�d U� [��gi�6�V�a�M� work� PerelomovF^ �"869<�j2p. I��&>�h1 b�>j1!�" *Q�2t��quZ'%��/B�16"e.(<2tsq��Z�exact.Vh^apF?� r�0��A7ofa� ll almost!!]d�word. �� ���&�+�.#in�,��6r��ac�+m^K}�8&� "�!*W)�(b"w, bij:ve,�\aa�oAAw�[of&9We�2�1necessJS= ���-�)E1A#_b�'dp2�M�!H:AA �Qis N��lP^"EXi^a�5�o&�d:sYAá�# �maMmlZ�pr�g%�p!�:rq�.} � �m&f�:�eM�5���S deal�V��&%��e6��WLo_h}R�E& \]�4�*�T�)�is D�6U-:�U���ZC !N��{%$J9F�/��u#�_Wr)�a;To1�)���z��z&�i u��"� YlBC΋!�Fin C">�, &�,��r��;a�B�_ !o�� qa6by�G �~��ke��t\ch�5r{SummA�� Poss�W E� !w�:� ion+.� R>3 focu� ���#D�9demonstr� >�] 1�B!���9"� EqQ��&�;�$EC ��ef{�:�Sandhn};�C(staesandpic�2 �a<Ny*s�a ��������scr~/R$��/Rribk9s��ei2� doA�I6ed�rF8 "=R�. Also ���a:�-�eF��8�esi�%fy&� z��:nhe�X�� ematK&\�@ BB�-�j���-�� &\sQf �beɱdesir�V� �<s�W\a kernelobcm�% a6� . By|"!�a�Jw�B��dnag J5@�e�! 9� limi$:G K nJforcedosB�*+?c]�6c!8H phyD?6)�I�e� �h-�dynam_-� �E�h�p*�>����]i2��!e=.�q�0c %E� $source sep� ed�T!b�=JR&o6��g� ively. AgC8�5isd3p�1(A�'r�� � atrJ�1I�U%~>��Eonb�can���%�2F�Gexamin0 �5 blR4cZvfs2#?m!featur�..ap/>):A.95At s�\a�8fock$ oK PFock--Segal--Bargmann 3IbeVgIeful.} �ilbh$�" advantage�w,"I�a�1� phenomena��B@MelloMoshinsky75, SelN-n78} Er%ollabo�$�Y:� mFp�G>"I9�5"� CRurig�j6T.s�9o0tey!of�ial"G �steadA�Ee:�.�e"�O6�--!ͽVa�.�J ripl0N�=jto � v6���2��exist�Kofe�@d!߱�rI\�$\M"rer-�� �yF���R�@f�6 non-^9ar&M"�]s didJa�y��"�2�SQzQ�Z6�\2�%ClgebrLk��zE���qN�u�-)�dm��:�I�- <iN�J�a�;�c��orm iI��-i! B!at firs�nde:�look l�D&�B�nasZ�Cor���Lplzb��E� m^�kju��omb��.�in C ca�Bi}2�to!9�#A�r&�u�$\> n$�2AI���.66�!?Vdx>�t:/)efwol E�a�� VuQ�"�QD����m{V�1M.7&� 6��ll$� %�ra�N#n�/A�"�/>A��L[Thm. 2.2]{Kisil02.1�0.� �"�*e�Pk22s.���) 2!���np)�2g��1nv�D GH 9#ly9%("� a6!9e"gx� lem."��dax� edIit0 �%埕�.���� � ,�[��9A IR�'�!�%���re���T*T,�?O�..OZ�+J&� �����Ot}�.K)@� :�.�p*�o2n�e�GeWl!�.� y�y�Ѱ�mpl�$c manifold�kQF}� ��rJnd very*���!�%��" to #� frame!ofFC FA_"�.(�� �immed-:�e ��y�Lo%���ms �0x�R�Ls � %4i 7f�. 9.`�N�a\ro� EgorJ"(c K�2}� s J.� �2%ss.^S j��alway�;Ju�P&ua�ppseudo"�� &�W.�Es$;I7ide�k�v:%� ��"8 warg�K�3la` (by Toeplitz��);�80�I1��L�V�7@%�g�K:�J&E 5 �a"� * 26�aofB a�&Lie$ �ed;��UR.q�eeH�&�th4aleqn4ern�P tsof�%��g� R�@& 6�2�2� *�p�9s6�RF2~ I7s xyoua� �"� >����A.�9|rt2�.�F�of5b._�Q�q. �%cZ=� ��9 nN.�Y \.�?Y���R>M %�F eeiDA���:J ch�Ez/�Q�Y�]csU}�#|�=�Z|6s �p >�9Y� inci�Q��3Oe,sA.a sub� curren��� heav�W arched�}�"�Eg!"F.8I�{b#te�m�iv/& )����6!IN; sfp� R� . O� &j- INing�u32qFmjet�p1O%�a�|!gio�&6%E�of er��Mos���S�Tau-m 74�%U<:Rtru�!A"�-��2�.Ad"S9+.�*� .�$\appendix &Z(";�Ul Fo� �Result&%app,ful?*� �� O��'�r F� �ula�q��u >pb &\ Y��is. A�� 6V�iF%,l;5Gwaveletapx}C_{&=Lvex�9 -a x�� 2b x�9 , dx�*2[) pi}{M@�)^��umJ20b�0.�(,�(a>0$. Aj���E�`[p337]{GradshteynRyzhik80@i� repeOly!+N�7eq2fiT3dF6x+ (-ax^2+2bKl1i-�^{n-1} �J+Z*>d ; }{db 1>b2�I .:L�9B�,:fi�V-W�&5S�`p���)O n=\�(well known:&�,-�VIR[x �(�]E].]b.� e6 zx�G�e>�i�^d Fubini's"0 o ax�x{>#�O e or�Y�gxon2$5[>8]{2thm:fw}i �$. �TZo+inger92:f([o$�?�AgH� �* #[��mB8f-�tI.V> } � i(y�E:]m�.-�:n}>D�lbL1ZLg��e LxB�y9}5A- of!���v fAYp.+-�35.3]{K��RFomin75�NA͋�Q2Qa�>a��C�21H�1�� �next M;M�Schur'�h�� a|ko&DZ�XU �m�Yk n�* eorzbOn}[2i])� . 0, F4p. 4.1]{Taylor M��js�slZ}A:q,?z$,�a�  $Gza:� X&�y� mJif���$�9ed �V $U*�6Q�U�% (g�Crh U& W�/�D g {/G:��\�c3U = c IIr�����$ci�C �V�$j<_M�)�*�-V�Ir Field�D&���"N#��A�vfsanddf~#j �$cWB�Z�U f�"Z �# N�. �v9S u\FR/RR&" � i�j � E&discu:}{ N��"�[pH�@nce�]&om�}5 T0�goo),p� A��%�th ]3#� &� &�iX5��{M\lRatiu99�[�sRHt��nt-�s-6}� a po7$(q',p'�52� �"�J�k��afI�*cinf (2D)$�i!�na �IC} f(q,p)�o˂.ci.c��a_i6�cf}{�cznx= ��ZbJ)p_i:)mUy�%Q+�6ll>WNAe�Y%* $T_{�2 �I�emx{.}:�a�&�4 each-�� 6c a:���%�A�.oB�u2��? ~� _e�k%�n��!�-��L%�+%�:%�\ VL? $a_iCb re $C^XU$U�N�. =ony�Dcto-�)RO3�b_�O))� . A:Nne-!B-�6j R-�-�aZm�.pE Q�R�VA�R�s $dq2ψdq_n,&zdp_1,\Uk,dp_n�\�bN�S"y=A�.v! } dqa�? a:q.*k= ,&5fJkk3�dpMb:MlhQ_ = \! _{ijF#AnyV&N�U �3 �nF�n (yA%'.8�Z(a4&N*��V8@}.�b E�i%JNR7�� ;$fe ZVA�as"|nRU $df���dT$toafctn} dAI�|nVv->g=��!�&.Jn  A two%2�� �1�sena�woF�aV�J�.-�L�d�& alph"�`be��!_wedge ߈ �2}� $N?� G�B� ( ; \ V{�qX,Ya� (X) (Y)�<� 2(XZ� $X,Y��6o�2�. 47)�%1��> dg$� �Rf, f��� $d �$ (ca^*! riorw�����$Z�U"@ T = df1DdgJ�. y�8 ific�~oZ�m�� Ec*�fR�u�$! tN� Ali6�u"d#m^�(n�)s3ay& r'.� ��Copen �` *  �\� )��]�� �<6>o&�-�. S�f��w�w%���ia�t�)��U� at�  $x$ (x $T_x fE;=*)*� n� �sT_{f(xoRy�.�s���eqŤofmapdo�((�) X) (ca� X (cA rc fFHePX��F� .x &�({(a�>n �?cV9!=e�?=wlA6+%di�7�  msofL} ��S.4�xc � x� '=x}N� n.Yj� n (Df)_o a_j bM%�B&�WLie Grou�e"ir Re.�6!�2  ku=a��Io��*e*d, a*X �'ur�lm�lne�?T:�}��vioJ\��;s. �����, Q�."����<�+��he�8� I��֍KWjuso+fe��(���oR9"H|��^E�gF!iia!�N)���-�E�@ ��fin.��w����ner"�1VA9 ,�2L��8is homeomorphic�ab�T/�A%�k �@�����!"Sre�)j(ticm ��@%)�nilpot$5�. F�+w&3!>*�*KH&E�sub�Z!oy?yF! �����}�B��?�$seq} G_0 =Wsup��GMx W � k V $G_k�^!7clo�6�a� $G_{k-1}$MRA=byB�-@type $g_1 g_2 g_1�:  �R �R^B@�=@%6Li�YJ#}MeIg1e&� 7!S)��N�Z� $G_l�{ e \}�j��$l$]Cth+s?$k��QIP�He67 �z� �;���e�ex�DZ�"� G5�Z �,ZZ="(s>� : s%���}!�?centr��$�->.��%�.ANa?�ѽZ  a$e1.\in� � --in�g�2� Ur$0}. $\lambda_l�E���1\�F �Po� aaof"p21)$AŅ�zh[Z� �H f)(h f(ge& hB� A2�^�m)K))�!�)\&a=n �mat �Fy) , $� ��C� ���Z5n & �� $X(g�g t $gB� , $X�'!/��ar!�=�z � ifJCu([T_h (5zA )] X-}X-}F|R h:=EDA5� �:�Z$  !�R$ �E��,� "x0c!�m3LieA$,.�to2GjQ�)}s� .Go!c^V. E&��  �j��tA/� te�6g0rillov76��lif $X_#��S��Z�>Ӟo*ؓ%"Ae��8O5�p�l� ��cu�VQ N9�:?�T �.s�ar��G.� U 4 (0a�ey\�N't � ( )�B!L7�' xponWDalA<� �oe�RMu�#O�6t1F� # � &R ��D7{ F.���DCIL..r�&d &J��'�xF�,�  �>y*K !���'� . Le�V�H Haar�M &1zj} , $dg]m�av�;.� m ��9����MS����$GFH*�P� G f(h g� gu!� &}R�S}�.��� �<alogous <% #}X.> 8.��+o� y�2c�)/ theyeu5*04�unimod�wl�weT$��)A{ ԁ�cefchj$L^1 (G�U�: $L^2 MS`F way.�+*� M6+5!E� !�!�>u $H�a fam�*5"`8J�"�rs�JQi�� : Hq�`H,&8 .i���J�  '�Gsf����homp sm��zB�,� (� � _�r� _1( 2B�1�S>titb[e��IB�Fur��m%2$f-P�F6�z�@!I'aT �)f =�!F�� 6kVq�M&hII spac�cځ infg�I�� ~$�H�RDv�I]�"ϕ- f) v! �p{Gj%�r-* v �%g>2 ��$v$ Hş>HA�aC!"/D� ��i�co֒pD-�5s%��1�sa,"�f�'��JZ�fu�� m} (�`*K)AO12G � f_2(hEK��h:%g )�a2!ZhF�A/�%)�t �o) �b _~�jdu|J: 0 �u.�. Oab���.]QFnV�ez�o=(*f_2)AG&TZAYG %@ (h))�&� �X f}_2-6�UE\7 r � l�lde{f��!U6]RI5�Ol:A� , dhQ� � �)="� �z&c,\rZ!�� ��|re�~:d>�C. �a�&�5C6n��6|n&m�w�.�z woR'�#?:��n"F %�e %��#ga9 s &df��r (21�=� E!� /1�fB�a��_& $&�W`)Z#C�U� volvY6[)a e���-P�n%q62 � $mathfrak{gy&� !�&~ jx)�6�^ s�� liealg�X)u%��vh2oɳf^�ְ,hX})u - u}{hnCInK�Rj6iC�p�(&F( 66�s� �1\+&;Aa � 4�>$AliAntGaz0�2r� W�.!16`!n�* gwe��R�(!�pa=�aE�(Qe�E� �� i�5W.y�ubaYa��=�5�:�U&"�M n g�F7��Q� . Let� z$N�a J�Ay��bA$ AVr"1 o465$VB%�� L(G,H,]i�Y���v 2\ sm�eV2zF(gUX��Fv�ll $hj�a�etaf_I2��R_"?�CiI�rA�V���_1EF( � g BJ &: !�:v Z� sens�M˜y�)�l5�� rv(A�� 2��:{:�5'B *�܌(g)F)( %wF���!��2�!%�6HF�  AF.�B�i+v�ipfor�~�c�, F_2 �i_{=�_�.2  6 ͢_V`�B� A�I�e�!m&ůchosen�V$A.ap$L��S6. A�vRn"b7�>!�l\mug� ',�7 13�7�Vݻo.ψM&n:O�@s�.e���s�P���onhn}).� :�\6'aJ6�p"!W.�)4 \c)*�!q86H��/lsof��X��S!�Xqoukce& 4�n"�m�HZ21 X ra� b $gH$m�w����Y D�VG /� If $\s�K%�aM �Dmap����act�Qc) co�y2�=e����  ^ (g_i� H.��"2%�f�o �mma"��0a[�8dA�.���r�$x��Xɺ@q����*�$g=Dz (x) h� ����P}��%s� �$� �0C$ m��o2�c3 �  M $x=97.�so�1� q�X$X%�F2:%� 5� H�nJhIv�5@V�H$�'��aRn��, $v=�a �e/8=!&n~1-�1H"��<g=�a  h d �!�vJ�a�=@H)�$vz �lF]�d��-�&(�!�Y;UE)�i�] $g$ �3. X(X��?a2of.g&���X(i� \qu*4 2�u�>���2Ii�ri��y�.�.G"�2Q 9].�.!R)iA 5>uQ�2�A� ! 0��a�$f�� F*� z�som �Ez gandx�1 x)=F�f (x))Bl(. B� ldetai�2�o=�68���9seN� U�=� �!-,:[��%�շ> ) g(pi8 !�6� �!�L^Ew�NX[�u� ]a6�v)"� xBm �v=iodx0ͮ (x)�-!�mVBy�f��� �f�etT .� =&X �Fb �`�^)�Va �%bi�)J���)���(:�A��X�a 2a� ��e= " x)v� E 8� 1R5�5" f] I19� v"�(v)>  x)!Dq A 9 xFF�"-�&(Di&�su82:.�2�' e developrB�-q:�� &�6noM  �N��[$insufficie ��e�W�[.l��qx{6�e2�9({GelfandShi�7��"�(V]{ReedSimotd .l3<�(Gvishiani82 & {Treves67<v"o�I� a&i � �F���:�ZU9��ownm���-��c` e m� �4 areao$ed]�basic�aR�'\�a tesD�+1� Ux N"# �;$� 7E!Dd nTie*��IHImqu ŷi��r>)Rg+� �Y: ly "nice"�.�� Qr9"��ll 0-=$$d~ZN�D�= >T�E�RorJ�w&X(&�$)GM�9R} p $"YȀ&��DL "�0�,,BY����dB8�C{`��GV-*&a��,phi \"�An_=s�.rt��F9$VR� a)]2�%� .�ct� nF�&/%�%�zAM���\*�iQ�a^|)��T#" �(x ��N�D �n�� oftet��&�9n5}e =�"C &x(5.�6�B6,�d2�':�/�+Ul�I&>'�B =S[?1Z <c�%cyA�&n�� � N)j%�.�@��!e7}J ikn�*���fvA��$./Z$ng topolog�%O9:6�w.�>0�a�Y��e�Z� "�ggo�o� ;�)��%<re2.{.�%eIb Z�����&�&) E5�*e s�Pu.%=x��aS � �[* 0& ."�O comm�})�"m Schwartz S(V;"g$ [api1?c��e)�chwB e=M�6L�2�3A��� 3$  a=��*<?phi��or)�rR|�5|�qEsup_{�.�} | x^k0 ^{(ql3x) | <�sfG!^,& ��l9-�oes $k=k�~hdM�k_n�q=q6 q_n �p� $x^k= x�-k_�W >.�� ^{k_�4E���=   �� al^{h+Bq_n�xhi }{\ $ jq� inBn:F(xf An"�,a�&O�)�A>[�x^2}$. Q�$a Fr\'eche�m� 27 � p10, Es-4]&� ��asemi-��s $!��< 1�$J���a��$%Up/"�q empe�.���V�Mnot�SA�̅b� 2M�L5�� % LfF .k7��baLm�8�".UJB&Eton��L��5th�FMX\r ')��8�6�H 'aMsu�vi %��x� yWT ��&#%�1��%$M&T8[54*.� f"�<�p&�F�!�e}Kd)��U F} f-��z,1/D&�,N4��=���2qUa��M'9$A+B�A(f:!�+-ib1<6}Y.h*�e%m &u2 Jb)��2,V ompact ��'��1�E}>��M v��F+}B�8rn���*�&1�t�4�ly holr��" 2b� %�{ y9�� r�N: �rn)c%�� �1ED}' nF{W�add %2TV=ygeR:"�"u+g��Q�]�>���m9g6 R"E ia�f�&aZ+�N *�.�:�}:���m� =�>.;a�.>a�} A�3 :B�1�*$_�Y.�<�6�"�� �e��=��+>K�+y6S})H Xb!Xt�����dHeFc5[ ::��7s;.6h*2rm�6'!.#}7��}V"�L$-��!:p�>B,�:Y{ k B.|@%>6�L 8�O~@)*b.**m: k) vJ v�7�I_H}S6/gV/, ku�B��gi�.Z�e%.�&i ITb>�aT�$9EA7:x�6�$H$f�e� 4a��;" #�criptE5.�� alngo*�  he.�*�'M�2�s��6(%�� u�OveR$waq�inJ�,�.s}����$�"M"�*B9��.�IM�%Q�[:�aKrR9fu �.pg� :!����mui���| 5%$=i���B"_,>B+)J �(f*�>g)A�+lu"e),�4� F�� �* +�#=*N��,6)�<mD�a89�NsA_�D&(rOtq�c 2 -te��)1ev|J+l@ E ftwo��gen�(��l�*�M%&��N ���L-'�**��E)'J gF��=� diIP#ab�mq�sE .8 5P�'"@A�T�uultB3n\"5V/em��9�--lI!��m4ya#"�bt�dV"] ����! f��stnV��6�A+*�OVa�$F���2�:.fed��:�ɱ&I�c"�*�n}F1" �%Q&:�AMA %���!MI B�� !PEa�of!�%�1�&�$ 40..}xg0bibliography{%t-^{.(style{plain prin�( ex �doc��\} �% DefSI-PDEM1.tex orm�hhap�v�;c�Nd��}sol��. }r �m-depen� % ea`�jNK8 % B. Bagchi, A �nerjee, C. Quesne, V. M. Tkachuk % Ac`S�-JPA \�B[12pt]{�cl-�oddDHmargin -0.25cm \eve�l6 \top5c0extwidth 16.3hߦ 22 \renew�M and{t�"X {\arabic'��.#} \.>awK4b}{\mbox{\boldP RKB0N,aB'xiN(\xiB*bN)bB' tv}{�&V>�ɝNH FNxNx>NtphI�t�1at>!(dpp}{\dot{Pdef�_h��op{\rm(Fh}\no�kқ&k #1#2{{�i<#1D0 #2}Ncs:N.Nh \sloppy \title{ %\hfill{\,palsize ULB/229/CQ/04/5}\\ %\v7 X D���{:{6y0} % \author{Bm�$^�,A Bm� Cm� $^{b�CV Mq�$$^c$\\ {\: 1 De��u�QM�(Rrcs, Uni8�tņ$Calcutta,}�3 LL 92 Acharya Prafulla�b�ndra Road, Kolkata 700 009, India���( $^b$ Physi (HNucl\'eaire Th\'eoret$�\'�que, �\'e LibWme Brux��s �q4Campus de la P�~,e CP229, Bou-0�rd~du Triomphe, B-1050 Brussels, Belgium}\\V!hH Ivan Franko Lviv N{al�y,!#ir�W��tical %cs,Aj1`T12, Drahomanov Street, Z@UA-79005, Ukraine.9$E-mail: bb��123@re.com, cq��0@ulb.ac.be, t��@ktf.f� .lviv.ua}E�date{  bR\dՠ\?1K@skip=22pt plus 1p��  %�kee� [ abst+ } K�` �*w=%Hi��� ctant-���*���� ��� y�P��J<-`(�8� c2N�6�cy �ttur�0���C ��zi�Jlva�� f�s�$AX$*� �� uper��  �. A l֖f~ ��"46�|sg�� A back�2 �rF[��: �=A nove |�r!�!� ��Oric�(�Bew� �3te.ec� the �vanish�/tAnd2E! L�) rval� �<fie!M�/m�s` j-�qjQ̊�mfoa smooth-^e� iaq� enFal 6��OtalE�ru�gIn �#s,fJg�R0[ or *!re+�of2(, � �!A�-�|meg|vayǁ�6�C �f� sa��e�:s!:Ub� �� orthog�< polL� s. _ u� \no^6 Keywords:Z�,�l,5ersym�))v*j;!a!%;.}LPACS Nos.: 03.65.Ca, ,Ge, 02.30.Hq Gp % %=� ��newpage&�'In_I!�}FrG��p�Mw!�E��0in studying p�{&� -�É����'Ha"��s*�<i;�nce i#bxAK"�uof0ctr�� in m��+�4d-m�r�m!�f-s @ �!&gra�O crystals~tg��r},�9 serraSliquid :=b=nco9-��c�_�$��awide�A� he eۋ-��qal�E�)1B�-body2�v K]� of nonlo�rq@!Fac!an!��j���' to nuclei �X29 �1� gmetx4lw�r puS#},�+�)t!��me�p�or�a�~c������%o���der��epuron.U�6T{0neous Galilea66� � levy)�m*��AiGreen's5�� step!2 �,�-!�io=�l�G4)sse1 r ouani2 Pe A�path-a_�H techZ�:$yung}.\par� -�Z % MaNre�M.4+l��Xi� ariv���u�=3!H�& 6�{"� (SE)-}dekar, �novic, plastino, dutra, roy, koc, alhaidari, gonul, cq04, bt , yuiyw�enT�����J�j-�j methodMIj+*U���q �6ES)�si-ES G�z�3�VESyV s. S�}^Q�Oa cZ�r1�bhatta}2Uic�-@alh-�d}L� �*} ͙ic�6��(al (SUSYQM)E�6/ce (SIQ:��� enshS�,,�per����/z+E�paper �cq04},����\%g��ut >,intimat nn�Y��t��Q� SE O���H��SE�,U����ed 9��4on re�Nr- �mizrahi}�M��e��,"� asݔ)1 ir�s��\2� aA �[~ b>�s�d�a�q�ea���O�85�zedY��JF�. A�:!/*�T� �.8��� �� �ed SE ]Jb���$a �""�a@�k� ,73��A��a�X rplaZ�؛L1 ambiguity&� &��"A�dLkin�� �� �nA%Yy�$"��g a=©�U6 vity��b� eI�a �ofM�mJ���a)TSEM�A�EV&�;H� Y=m!pGdA�L�kIl!�I�0!�a ��&�|�isI4�>%�al��m�an�>� branch� L}o>wg/�b Js8?L1*6g&�Z $q$-K����.��FM�IX�}ma�, e.g., S 8spiridonov, kha-� sukha�0, loutsenko})��b�--!��%proced�.>1�Win.��9il� rWb6@�!�qthree2��Co��pUz&�m(AT���N�W) has revea�3w�,e1d��W:rs~<ey� "h���!�1 essly le}��= 4rizA�����{�Eha�qP3�5 . Se,�r�c�A_Na$ environA� ��:�� unc����AE�Qi�R8 a�ٵ!��($r��"]one�|n|A}6�q,s� g��t!?%k te�>;����_ ���>� SE'sa��! 9�g�}%��FM? l/d0a��� Q� remai��sV��~g�"�!b�U�?( ex�� is �LZ�bQ�'"��\^,of the free-��particle problem, where the presence of a suitable mass environment generates an infinite number of bound states~\cite{bagchi}.\par % %-----�2� % In this paper, our primary concern is to extend�!cedur�~\�cq04}'�Ithose one-dimensional potentials that are SI under parameter translation~\ X\ooper}. We actually planl show P I some9�assumpLs o�Pe corresponding super� , on!��>y find a PDEM or, equivalently, a deforming function, for which%!d"ed�cn�D remains solvable,,reby lea��0exact resultsW% bound-E( spectrum a-�2� wavef � s of@! ociat�0E's, providedlat!~satisfy)Gappropr4� s. Our se�A#purposes#ionG6�ES)�=�as well(in determin�whethe)Xas5e�19 has!�Tramatic or only smooth �QV=� 1���j�: %a�s!< on~2EU )1l}�forEy!E�A through%�usa��M� SI!�dI�8is reviewed. Inr83, various clasA of 6\se�id�, lisA�ii� appendix,�com��ed1?5. Fin�e,6 conte�A��lu��5�=� % \ q{Gener.�} On%�mA�-known!��}u�-��azs�3mo׉ A�-�Bator non�$utativity �B�oant or-fambigu%->kinetic �gy aP0 (see, e.g., ��levy, morrow, ribeiro, cavalcante}). To cope with�~8 difficulty, itA advantageAYtoE��von RoosU� two-�B formA�᜕R-!� �1��vonroos}��ich�(n inbuilt H�?ticity !6Uo�Lplausi���s�v� ial casesU+:�� i�units��hrein $\hbar = 2 m_0 = 1$, w���a� e wr�!TQKasA��Cbegin{eqnarray} &&\Biggl[- \frac{1}{2} \left(M^{\xi'}(\alphab; x) 'd}{dx} "eta6# B+zB, +DJ.=RRp2+#>�0\right) \nonu� \\ � + V(\ �% 0r] \psi(x) =E ( \label{eq:!R -SE} \end=L% ; $M./$A�!�"3 les��Q�:�$m.? = !�6S , $\)�$e�,$\ab$ denotea4 set�Lu<s,)� von ee�' $!;a!� %�$�Xn�� ined��O.�E ; + :9 = -1$�$f$ % O�Vtt�E.�uaZA@2C =M41}{f^2.r$} \qquad f.ai + g. .M-fUuU2KE�� posi -de5 "���$2n = 0$ & "] c!�ant� ��� � (\ref.� ) becomes2'�f^�}.-H�!eta2"u�.�*A!2+ +Z.;PNm2*"x6�� J  -bis5�1J% �aa eta�$. AmoH oseN� choice� 4at have been f. �2ful�� describA�a�moA��'elL on>comIn� ly gra" crystals�C may qu�D�(of BenDanie� $Duke (BDD)�Y bend} (�A��� �,0$), Bastard3 12>1 Zhue(Kroemer (ZKqzhu : ��$k1$)5LiKuhn (L9li 8>�1$)��n�@ % We can get rid!V!�b~%eta!H$ (��d col!�ively byE^b$):�  � by zferb themt �"E &]  \ vari��\system� us usQsb .vq�!efteqn{a�xi}F��/F�} +2� . e�VAxi}} .���@ = & 2 \sqrt{f}\,:N6'( - (1 - \xi� ) f f'' -N�(� �F 4�r(:M!!#�e2NN�a�e��s � v� q ect!�$x$e !�i�v8�in�4of $f$ is expl ly�Zd�@~>@��) acquir��e��m.��{��H"@ \i %k ) )�.O}\,)"�QN#AW� ^2� 4_{\rm eff}(\bb� ])� n� -ter5t�% in w1 !DJ-2C7 J� =&f �tv�,AW�a-d V� b [%&�an ady alB -%�W&8 -de�ne^�V�= \rho: f''�!l�sigma.�! x).2�tildeN�IF�%���U�%) pa_� b �� whole A�2,ab�`6F xiwhile�Sr �)h � ��b��rhoij$)$E/follow%uwoN��bin� 2� 1� )}*� 2}J�� |.i[*� .�VN!��.JxFoT"�Jg"�re�lo �� abovy tak\ values $!>��%�IQ�4}$z^A�=�Z6- 3} 8t�< :1 : ZK),! � 02�*3�LK�LRL %Sx SEY�-Sq$� now be )�re�a*�E~�=��\piza��._Ec��def,JS&� e%oe6replace�a��x"�� $ p%���i}-��1$a�] ��V�\pi՘R�pR2| R#\��2p�Nq� % WiB substitT�� convq� �I�o�l�R $[x, p]!� rm iu,changed intoV5\pi7-^6�F��>�act)Qx!���o no :.�we�[��4$J�$I>�SI& � is mea�� A�ini�'�9a�R�-) will(n b�O�Vinver�ف):�Q* *[= J���t~qJ�)��p.gl�iW�k2+60��o#�q���n� f �5oe�i5Q��) (�&8!!��\%�))�� %�AAs�*Nly�se�-.�>$, $H$��be� ed��!sfirst me�$H�H$�$a hierarchy$Hamiltonia^GH_�A^+� ,�,mbdab_i) A^-V0+ \sum_{j=0}^�+psilon_j��$Y0, 1, 2U dots.� H_iN�YY�-���Z A^{\pm"Z o� = \mV�z�� } + W(\P� !$�AJQ��~*SV_bkb�=Z{i+1}� VS !�1�- J�!�.�$ormed-SI} J�a5$[�i= E ~\E �e#c�s. It s from e��y{�}) wCre�$H �$b !%?Z�bs:�!1Ej5A=:�Fs�ate�.��a) fulfi�7tertwi�r��Z H_if�^2i)5i� Z=*A#1FVdiJsimilar�"D���!IS���f� $ % Solv��~c���pos�to 1"6� $�/�-$V;">��6 $�w�UkNUW�� 0 =  $, su�"a2���8N= W^2��� -6�  W'6 �� 0a �9C1J+�.V.y_�w+f{ "= 68�� � j>(�mN.6�&�1T% As a��equ/&� (��) SUSY tner��1���� be� racterizZa "�"V:V_{�  ,1�, ^ �%V + 26, >�6� a�B�\pa��&Z�&a� Ty�ol a�qҽMC1}:(C2&we shall!ggui�by  '� ledg"�!6� $W$� :� ($f=!�r $g=0$��&h E(!�a'�m�M� r3 �$)�� 5�6?bb$�%K#gyIAcon&"�(i& suz � OI� $does not a�% � ��bu�$ ly b/s aboutA�<dits p. �(.E�" also*' "�)� (ii)0 oJ 6�%z��a way �i*&V� �un�'.SxB�$!8&�# sameG"�er�!��already*%iJ� , i.e., $.�a���$:E$j% ,$j%U�pu!��%cip!t to p�!ic%�" #n�%nd UY�accompan�'I�1.>�,� �R� r_�(ng���%be ob!M�x&q�&�M-f})��R��[$worthA��e alth'onF�AO�U�A� + a�+n9+:a���U��$8 ofte�%va)venien�keep it� a (reduBt) argu�in& ,�iesj2�)�H^HHav!#ha!3�wAU� a1b��*�%sp��&:�)2�%sH�an �,�'Z2�pQM%2SI+c�,�4gendenshtein, ���ule�eigen��"giv�yV�E_nFD�BiBn &� .^&J$u��}< ��gr%5�ex8-1B6 a�-q�b�+� D*f �'er�|aluV�R� )�_0F���^.�eq-^ �recur%�� V�� _{n+�BB�[E^!� E.��  )]^{-1/2}VP �J�_1� K'eq-N �5�+���R� % EMF* E "�%�:+ �)->.al�o$J�(A)*hc* be physic+��eptX , 2/6�shoul�+ deed"�.R"x&s:� \noia�t A�"�}#al quan=+me�ics~yebe squaH�.gr��A�(7�in v!terva���P �.RY Z�Xint_{x_1}^{x_2} dx\, |E�J�A~,|^2 < \infty2� wf-R� ."i) Fur�mor)�5 ens2�*+�l$H$.  � $0��H n�j to io$xd�J�\p�'�- UDpiA�be�an�� is amountA��U .]J�"Vf!d^*�)\J (- {\IF)vp )R@e"phP*Z�"�[^�hj�t"B����* �]^*��&�h-e"� 1X% an F� �A�0 L^2(x_1, x_2� taX� e �-h� of9�u)��|sI3!�����v�&s$ \&t$U>.m-*2#\bigg|2 +!L21��$Gj�M��b!�e& 9�CO rison��0�#2��9�4 �iJ&@ �" $|�2* \to 0$�� $xx[AOi)T��� a�e0U m�9%tri7% "(/� ��J�X%�for\ } �@�.2.A ��NU�6ae"8% D62B�0�!� be &�$ whenever >�"+go!-���� st, ��end poi���'A �E���z� % '! precise r�� $n$ � ($n�"�$n?&max}$��# 2&��", Y�E}))O�F���+&� d��! ex�4I::� 2�I�^�$ � b�6M�s�8A0B 2})q*N �� �� 68}�D*la�:f> �~�}{\�gMC ��)a�N3�q�e6 �4�F��V yeckedu:�1vJdo�s x�cItTstress ;� y��# d<S�J!��6U �8��-  o far�WzW %R1takAm"� A}a to� � I-"�ofJ&p be3m "��6oUWSf�vx�$.� �AS!&NN")Q�2�}�\ \expS � ^xM�.�\tx)}.= d\txM 2�)gs-wff $V��#�wno!7iz! coeS7T�j % S�=�/.�U<)�aw�bbu%sb�=�J� ^�\�\varphb[��_n;)� ��excv�z�$�&�"V�K{r >� 6'NS_1! + [Y� aeC.!]OZN xH&< phi-eqN��&5fN1[ ?b $NN��2@A��oN)Ѡ,�/ =�i��)�.iR� _1).>�\Z��<A?Y{Cj�=)Xir��j} \set��er{v}{0} �-�� p*%�Ac�Bs` 0;b�3i�he next l�>ve� include� %�.�'�@deJ%L�4.1 o"�BvB,��=th!�C7s� eachf�J"�8�@�5E�zk. From*exs�fX� {9 deduce�!cx�?garO+he.: f:��1v&�@+�EqubMjt} Let� $ ��pQ-��/ent6q�2"1!"�:a A�EE (�En 0�a0<(r ��mu$:es �$�  3&�x�!(medskip&� {\sl e� 0} !�"� �)he gAst�YB�A�a )\&O2P-,ActypZ��N���)h�2�%�0R*Co�*�F� � � �>�to�u�d, nam|QNEe�"� �%"2"7"$,������B:� , a��"�R ��� � they�Q!�s�-W'$. Si��� BFor!�al!_$�^2$�#w�� wo" � calcuGmcouplEM��-y�,"r��zGil�B~T aty:� '$ b�linea2�3A��e�9T>B word=re must� ��numer� ( �.�)��!� s $A l$B$X��+b�A&�!e'(�@ A b� BNQF9�TNTY�"��B&E8��cm�i&�6 a A%�g>� g �H�Jerm(A��!j(���I� onesT �U spoiD��IEG<a&lwJL!�pr�Fist�p " r7���1�"77"B.RXz�>@W6]N3J� O�@�6�"� ��3�thB2�w�HZ�>����}{:�� &] �4J��pr K2b gz :� I��� > � q 0 6(&&�!�!�r@!�z most�a.Eforward11}o*�%ṉ�is�H�:ng� $ nonvanish�  $m :�F�~<muF� 1-1}N�.JZC�&�� thre2�'($, �Na��`� ��)�82�3, '�Ln ���uQ'mad�4 ���sA�.� ���phi�`��,�&�  W�al� �@ ]�to gov2P�f9�Y�p he�̡��2ndm\�@a@Lm�dV��V���+ C.!E�1J�%�Vf�.��_}{A�ph��.)}J�N~3$A!�BC)�$�*��C�X*� &�!�r�: �dVd %./*)*%˅N,Ve>�4͓N& M� ) --::1��*-F�E&�A�s6'� >1>]&.2)�:#1ultan�L���, %�.�~ a^"X>&� � �0� 1�6�%T$Rei��� \ne 0$ 5 mu = BYk�%&�7��a���n�#.� !��j�If��"-60M&� ��v\mu}{�(x)R�= �S)�A�'�P2;({ w� we w%SF back)� 0�*W^� gai�   ��R*"� �* ^{-2X5&U�� �"�"$ % A reaso| 2G4(at carried �.A�I�Br lUhA�u* .e?��Lnd $g$2�%� ��Ō&7F:� �!6J ))���J"� yDJ� >�"AL�XM5RI=.B�Wx����������On����< i�� %�Ei��:�}��a---(2�ER-���.,u^sv�o&2Tp�U4ScH�<J af�Wa�`Ujio2NQZ6D5�.�-0^2%2Q�2 !=5K^2� BRi-:1Nq B�>mumn�;BM�$ mk�ea��B�"[��JVJV~+Zk 2�R���n  W�^�7��C)�D]&>�f���H��K�F&[HY� �� D&�C�   supple�0OZa-f" e\ ~�h%�:i= [*� .��^^�J�<z S�[On�G2�^ �2�N�. $. H�#w3V�6?�F�V�}{2�Y�1�Q��+B�2� 2�$�&_ � E$�0F�&�sV�! x)"9i'U/"I'c-"!�e&g�A�he*�*� �!/*�!J7n�";M""%*��e�,� 3.1�*#?<�7.Ato ?.�� &&�f"\,h" &m*l*���"��>�#� \tph�R� [A +.>] �G[B&|O*` #�+ ]� �^]> \mbox{3-r ɲ�����*�W)=����� \r�kB +.�\}~��^ 2�Φ� }{(A=QB)�C66  �+ D�Þ�3}�&gs-int}`��Qu% t�4��va[, �aub�#q'�D*� by� ple]Ha�y techniqu�6�1R� g�qBq % {}Fu*�0i�.�?HB����vC$ $, e�1)2&I&^ �$)��f|�n�H $n$th-deg!�$polynomial%9a new"�S $y� PN�"; y�]B��5R��C��#�3W�S&�On1 �����;el*�^per~^cco� oD:.�!6NA\�-J�f���e�V�9og�J=$�7�!�TBT>g,A�!�ALW4ge%�va9U�.yRofUq "�$nFi$�<+j�'!z}"B7�F/by n$�Kue6�I6�){ra�below*�itemiz$2 � 1V�zg V�y)�`y�1F"��P^�%a U-��B�y�X��.(] y�Bs2�\} \dppN�8y�):; &�}m'OC ��2�) y mumu]2 � 3r"�Ce-1-P"� ��% \=�2�y^{-n:9���!�b� ��2y \{:�!F:� ] y\"�\9�)� - n FB+ [:��0(:� �N� 5 } \timesVZIaB�6�3��(AmB)~���\{B eB n:]y\-:�-[�Y�~ + nAu�n|\�4]F���~�F�3R�� a꥕% Hm a do�andZ  Z>Zͱ�!ll� s�M&�+"vH�`�Y1. 1no�0a 6��+�# c~ < $-.���2��i1�$"flan^n �� beca6i�D$(n+1)*� ��es�h�<"y�+��J "�+SVP�' exin�+�'�;a.�+Dtwofold:�dem�M�im�R�'s s �mour�idevelop� h+nev��)s%k� "�D�* &j 6{J� re"�7Y(�4�&U<�3)i,ced byA�U I<orJ3��an ES*�S.57ru�+z6\*�*PTpa= box)rigonomeh8< P\"oschl-Teller� } S�d="�(�= \tan x!G5��1})Z mu� Ft�hpai�p:� !� &�d%��!%��/ ���%- \sin^2 &�K�pi}{2�=le>qq�e -1? N�a" ex1-W" #[A&+8 E$U�<�7� 2 u[H "$�$�be Bg_AaE 9�ef_fli ��` �`�0s��6 be. N�cat2;?�Ow\m[>�yielde�.(E BAE (sukumar85b}�fbTi�O��.|1o6_A!6�(A-1) ��.A > 1M5d[-��I �.E r% h�F!�* p.�energ^A�2� ch:�M,$E_n = (A+n)d=�6n� =�1H (\cos x)^A C^{(A)}$ sin3��: "]:-u cq99�Ft$�t-in-a-�@�t beA�� limiH? C�G>Qv$�o 1�J� ��b*E \{f2l{ll"� 0"� if $] .� < xa�.($} \\[0.2cm&��B6Kx�Cpm6�$y! � i(.2 boxB *�����0qo�W%��%Tv�f�W. Tur�to��"ui/&�;��)�*��st6�'"Tr�7&OR�j��I�&7nh�3$�*ese�Cly: C2})"�RT(i+1)�`+ ^-_ia'2F', "�R&\=. Con�2�uFTg=f!:sm A�e�y2�IV�&�I, ͓�w(�) � ^2.!b�m!|N�Ii cuJa�24�easily�~46f"!�.�F8�5���qon �V���)��_&k6!k��M8}{=�Y�,)^{(n+2)/2}}*] N19�):=wf m1�*�%�R�%P})sc=us�t.:1n�"&��yB8�VPP�FQyA9- [A;(1+)q))]6� }x H (n+3a47NN 1:L&���>9e = � �g_1ml�S �6$B1 �1�>J�&�/��a#,wf}) manifesre�6eBa KI�bl*��r� �&�,�4ce $fC9�>/�!�=�'aD"= Q �>s a+ autoI � uA�v'+"vda�a4�� �ce�*� 6�WA�. F�st�8h,n"hJ�be� � P�(�? up a�Jdr�x"� K�c�@,�G *^�[q*DB!ܡu�55%%�go  ,��79Qard_ms9 V� YA\gamma_n n �J6 1.6 &�$��� % W�x�B��<�4��B�Mlanguagey)�#l�4o�ES SE,:�C1 ma�s; ��!�9\MS*�*!lE/!� D &V5�VAR� �5V�&�a,Oh,o gm�"+ho��sg)�G�#cos^2 2x$�C (2��% #@ %?� b� 6� .�6� tVB� % BF�S!a\LK*�8amb�x"�.�5�**(! usa ver�Wm+8~`�t- \� Bh=�R2&�6m � 22 "�$���� R� a gra��bv&1Uf��a��SaYI� �/�X;%�detai�r ,are lengthy 1: IXaR=finR�3ed4 l�NUthe.$~2� .�= VO t!& �A[  -n^2&-"aiQ* 2}(\Delta[ + nɼ]� Jn� Z54}&n^2:Jex2-E}\�xj& �N�E"�)&�{M�pw{��n}.X �g�CM�q��f� QH� +n+1))�{ 2�� 1��V��" �" �y�"c)+ )�&l J� 6 B(% All"�� s%k5恶� F�,�y�."�H*)9 s��ՖN �.� ���B}?L=��%>��rrec|ed"h+��.�Fk!� � hyperboliv�.�Q"w�E��b�6:k57��� 7a�! �}�*6.�� &�0!ۅk ambd� anh�c�f�h.�0 <� <�*X3�X�5&�9a�#i�v&{C � 4 &�N�$M\� R -x` I>1&cmSZ�* Rch�: ' conn�W#Q�3 att�]vOVrepuls $%}$& (oL\.Uqa�Y >,&- or b�%r�`"�a6ET� e�!�A�, +AA�fre B�p4��Y$, kwong}. &�+1V�.�d$- A(A�5'0��q$u���9-BY9- lgiv8N*.� � Z0$)��:�&�Intoa��9 a�it� .�P +�($A-1 *�P < A$)�.7Gos�\� 2��8! n��[-r� sech�{A-n} � A-n+���� �T�BD-�Hj � `QM* nieto}. S�fh&& blriv!0tra�B�� wa*iMin͒bagchi}�aanj;=ext. W�cis.FZ� �A��!env"�V+ent�)Ha��s% i�.�V�.�� �daviesh.ne(io avoidE�diverg�4(Go�w�"� i9OfI( closedA� �Y unNse"�)Cex�#�V +L�o$philosophy�V adop &%�r�N to�=rv�#�G_Z\u5M�.��^�b� ��a��!wn%!��%@� go��O2#!to ]�q8�!a�<�<r)A.<XdA��[.} pict�aasXa��$-� cernD��d,%��%fdL 6��%�tro�P�c Wpr� a� playEJ Y)� rol&�1�''=2�RR*H� shapQvw/nt&� �9'rh.'/&s&' "'.� :�YHi�o�� j�uH/��we֐ zm �ds �;�Z �Y�RldA)=!�ca�t�NS �iLRK,?( PMr�9��a�'��jS���j�">!,&�ka�6hjf.B eWbf`1m��a�= !zR�y-Morse *|� n�p"kR$B$ gUoto zeroFaq�of6 2in [0,e}�1x�Nxc f�&in,&6Z,&a�per) e�!$"�i�2"� ��QH.�.1��͙Q��[a� unl2edQ� *&"���#�!^! % Se����m4"�seP���1!4E� miss!���he�"� Scarf II,6I%.�b�s��B�jsWb\�aI5��v�Mtur%Vpat- nol�v�V�Iof_Y�sE� B�(&�%  @$`!w>� real�-,ub�5eA{� . T;he(Qhanv2PB?f���!�FV 6�dor.��H�f݈yA a��_+E^qI:KhWAmes*���X�E/:�z.�s!'B4do � :?ort 87i�Ŧ�G��2-�MA� oursel� Y)�}iّ4I��.�7s V�X�%jYi s $V��s+$- � 5&�-S��f�0���ategori�Y� shif�4oscill]�  "Ó�k Coulomb��4us,2� A�I�A�R�9��6-/N s"� ՎAZdzUa*�R re6;]>'.0 and/� �% $\d� v Vo��.�p.��_��81}{4} \omega^{*�-ft(��2b^*}{ "*�#"(�*. SHO}?UzwxR �(l(l+1)}{x^2_p"�3D-HO�5�>>k�e^2}{xJ��Z_ REB)�2x� B^* (2A^*x&1n%9"�Oe�m :�$i�Ice,.�>~*F�1~/ft� B(2A�+M"ZwEB^�(,"+\")�V^A(&��=�?�rh@�^2!"�+q�}� !V !-���mמbserveu im%$ly distinc�%flu[*V �ri�}�on2�pj%�rat m ~ s (er�ޝct>� .2a�6k_5�pZL&�.F0� i�oH�0�+ɗ%. *;dU�*���Eckar*� "�1�N-!�one;wsbZ '�q����,���~is�I��@  �on&��= �s ?�QJ�'9'���. f4ark� 6e��k V�,2f��xs&�� )�V U��� N� F�\��l�N� pace�R: �hm!2nB!hg?j�`QA�tq��2* ��&RA* "b,"*8�8,$\footnote{D�$*� � avail%�&7 uthors.}Y}�� � ,2�exhibiAS���nere�R !�_ n% n%)%� ������ ner}l lzcAcz.�A�s o:!cV *s���U'���y38{ColSH�)>58g�0;� a lo�k�.�7�@"�e� Q8)�ssa/9dc�1ed�2� A!7�= SE� � ��k� 0��/�z Cu|�&�(&ba6?\"N�h"a�%�!�m��M 6��:��K2va]��s� -�&�d� �K:�"�� � )��oT9|t�+c�n��airlylA�m��Sw�qv�)und�:|+.6�M -�+6�um$2NU��@D2pM�u�&�b� �::�^A��r2�A��&�"B�7|Zlsoh29d�c_5�U��E, Ij)��F�AJE$��� opa�u1�*�<*�pecif��!=#� �F reled�m�s���EA�&�=�o� d �r�"�9�#��ABu�����J��+M��av .* �> cŃ&cax2�.�.F!� stru uI�E��� v��� /s�Uto �&��2J2+u.�If�Z � �yhBD��ka �I�� :Mv"�y[SI��Q�eTL �%I&h?a��3K˩upajh��')t�bU�m��Ւ�##"� sb-3Xli��o� es)*FnatZ�ul�f� /few��sik�rsigZ� �A�liter NdevBoiy����rv�r�79raA� ob�@E��@5� '�F�)p~ was�7j�d� 2$ $S$-matri�?Eu.u61AofQZ�q�:fEbe appli cmora� mpli��L!UG'sA#"`U�� SI YrY&�2on. A~2teqAEH pen �ME�!fuE work��U� it c1� :�j� SI��asa>�scaling�& �\ K *{Acm'0ledgment} AB!nkI�U� hGra�6Com0on, New Delhi%!na�bo6�(Junior Resex� Fexyship. CQ!$a DireX&, Ne� al F�!ZS�s��00(FNRS), Belgi*�B� *T *{A�,dix*S &{ je�Iw%.&A�"7 in t -B; Sz�/Ab!N6| .+�A%� W�e�2+s |m: ti��'s sak�]��!�t���sY��indm^wSl&�E�^�!}"�Z6�^SBM*�m% \[ .�*x�&"|&-2 2*}(*&\] SW I�& �5muueJ(3D 1:�o = x$�� Fg F�42\betR\F. > � ge 0���VQ( 5+ �&"�= J E'�Yb}{2 P}�& 2�& -��^i � A�> + i��mu " (� + 2i� & + i^`;}2 �}-b�k�*�2VB%d)(n!x%-D(-+ &�V,�!=� + b� 9 [[(2�H-?+ (2n^2+ 6]2�5�.1+1) ,�!�B�K \quad n>0�V(e*?�*�(\[�)0Az\�9�� ^{-(-px8/(-qA�"�y � +%�QGmu �{ ��7rc�> :�i/A�}{ (5�E�%` :z @-)<2wtv�= 2AH"Qzx qa�ig42 Y+ 4 6 ��!t]" ���1Z�T>s*��bx)Y�9l9< �) q���e-�gmu&�22�22� <16v� �-t>�6=� l�,mu���e�1�F�.�)�~+µ-��E��7��mu�r�q[�`=�?�2�8l��3�Q�+�+[2(n+ �0 + 3� 3]1F�58z62�x^{l+1��-:Q��l+2�Q]2�1}~C�4^2 e\rhq4�b_� �-�0!v6G�,�$z ?2�6�5�xn��������UDu���1��I� N�jVaF- �eLi}"˘Q� s>z �;�{-!y"�e�0��[�j%i]}{qm��h;&&��)�\rmPC!�3*�3��/$=$ largest� �^teger&� }?n)�mm]$B�"�I� �}$ �I �7I&(a�$>mf�.��:�i^ gVu [�@ @-���n�#���2��x}q A, B20q�M� .+��4)�R� /f� IE�2x=Aߥꥷf���qs,mE� C "� !�1� &� .��4!C�]2 )F  ѕ���ȑP(\mu-i' "� S  6 KUg� d1�"n 2 �H� �N@ ��.%R4 O"e�) I�9%� e7 �A��:Ece�anbp�A �x:y���k"�;n;-�*� - B)�1[�"^2+4n^��1)^2]^{��}{� h?E�:z�n=1�O��"�5"� �F�f26M�z �#ai2g}e�x}ɰ� 3 �2 ^25���#-���� ^ E�!�3A(�Qcs�<+�B0Ft*�>A 0I� -�%��MA��ID� �Ic�h\c�>i=>Psi�7 � -�%vT5� ��zA2!� B}{AE �k�E�>DF)\2 qc2Y Ti%P(�7-i��% �>:# (�Rb��k� r� �] n^2]}{A+n&- � �%R.�=Z&l�\ 2�l#.CZAJ� >K>�#�<�.� Rg] �6.��1<����z&"2�FI���EA-�Ya�eK&3Q.I:A}{ 9�- 11�Y�l *C 2yN�+ ��uWF�+*�M�-&�DA@\muA�{yJ:<T-hI��72`#N�%�:EF"� �r�4' �M�.3K� ����b�Sc�0��(� �c- A;e�W- � -�Wx dI�0 < B6 �@ 1�"�2�-��2]�5: k��seq)�& 36�\W>��ii] Q��| |�D ��A8��S� _+� -} Z�� 0V; Ӭ:F�4�\mpe� �j+ Yjpm B) E���[�2;�)�\�;0 [A�����.�2&E>6�^��!�fB� �5a)�J_+A/)-� ����\���2>�q[2� ǹ.I O1�>�e{�E6 + }�J-�Eq"@JE�%&F) 7+M�B3� 3�7U��o�A�OMgm. �^?]-�r EK6 =`� ^ 2�3�}�� ���+  �g^  %5xArM753>VcoS%��2O:(/NO%���P�� �e��g]���1+1mm���u1�QUa�:@ Q��B �B VB o�6X�%eUI�v+ >W )g:*1΁ZA$VRH�h(-�^A* �� �Er�e�. 3BHEEAt� /AnQXN6�OE"1� O�4���> x1�;[B��e[ ���o^2)E�4x-����W n 4x��]쁟T>) Z /a92%U2a-m� G3E��%@:�+IPQFB�5!P>newpagejF`thebibliography}{99} \bi�-m{g�c} G M R10Kohn W 1993 {Ѝ,Phys.\ Rev.\K@t.} {\bf 70} 3103Tserra} S L�* LippUNi EV7 VEurWAs:T40} 667S�K anco} Bar  M, PiG*Xa S 8Hern\'andez E S� Navarro Jy��} B �56} 899.wring} R�!PL0Schuck P 1980 �F] Nucl{�MsZBody Pr�C} (�#York: SpPer)��?s} Aria�0x Saavedra F, Boronat J, Polls A�(Fabrocini A�4 � � !��0} 4248ppu�q} P�2�Casas MXZ.\ \} D)(31} 28.�J�H} L\'evy-Leblond J-G5.�E@} A I52} 1845�,chetouani} C ( L, Dekar L%HgYnn T F�Ra E�a82_yu!�Yung K CNYee J HJ2J:�0} 104Kd�}�,.�X:�8)J.\ Math9U�(39} 2551\\ �Q9 Q)�:�9�.��D$novic} Mil \'c V� IkonZ! X� \A:�Genq�32} 7001=plaM6 o} P $ A R, RigoAiM\, GarcA�F-19 {M�M/6A�318\\ 4R,]̆c200m�a*(\ Mex.\ Fis�46} 7.2dut��$de Souza Dm�0Almeida C A S\ ��( �275!�>M, Hott M%BU��Z- 62} .�$roy} Roy BN P�2I1��5} 396.�(koc} Ko\c c!o Koca �,K\"orc\"uk E�d L527\\ W� Z20���10.B,alhaidari} A A DV--�A��$66} 042116]�Hgonul} G\"on\"ul B,6 Tutcu D�\"Ozer OiModq�\{>�5M 17} 205!2_F2i `$Uzg\"un F Zd:q17} 245.���Quesne�(Tkachuk V MW��z7} 42:�uJB%,orain P,6r4Roychoudhury Ru%0 -�Le20$9} 2765 \\�a Czec�|��54} 1019=�yu} Yu�|D��S-H%�Sun G-H�R�322} 290a�F<I201gZ=5} 19.n bhatta} Bcharjie��Sudars  E C G 196M�Nuovo C��to �L25} 864\\ Natanzon GI7��Theor�J� 8} 146\\ ��ain8 95U\V3!68.da� ssidi�  YE� �Ay�! Iach�,��86��Annq[, N.Y-� 167U�JWu )x� ]�b���N� 1} 5e�,Englefield M Iu8199��slG-�R(24} 3 Q.4l�r?7} 380.5.�� $��� L] 8�0 JETPqFf8�!�DC wskaA�Khf/\ $Sukhatme U� *�r�1} L19.��FC��� bfB� p-� 251} 6dmizrahi� L S S, Camargo Lima J� (Dodonov V V}q2q M.�!q72= spiriL} S  VAmi-�R��%s69�N8�Z;��A6�A�242�!�}^L� � 2�Q��26} L901�,Barclay D T,�t��0Gangopadhyaya� -�, PagCYnt 2593Jb ��48��8.csMq}.F,P, Rasinariuͦ ~!t<-t13� 234} 4 �B�Ma�0 J VF`�%G��6 ɛ�I11�8.�,loutsenko} L  I,26, V��� Zhed� ��.% � RT��908.��}$row RP86*A�"� 807.dr��b � Filho�"F� �(N!$Freire V N!���Braz.\Yx}-�6��8�Yc&`� C F SAfCosta zR N> :�de 6" F�j�5�[32.�O�K� K�O���F)�6=��754.b b&;�&e�D�8i�C B�-/NW1�62Z"_�B���q�|ND�p569.� ze�Zhu Q-G%-K��H��3519 =�y� Li TM�Kuhn K[j14��760J"~Zbe��s C�V8�~�a�L5.�vr2�m�~K32} 672I ��Ctʠ291.�I^ KP^ W%�RosI�J L!�Qrog.\�-�Suppl�� 8aZ66��z E`�Intm��a"� a76.%�\ N�\ M7�� }�?��� 127.B�U D�U P C A8Q Q��M��8} (London: Rout�6?( Kegan Paul) end B�A�o1docf�} sb\4 [floats,�? scriptadd,:,balance�0,prl,a4p�=D,twocolumn,tighten�{s,�<�pacs,10pt]{revtex4}% \usepackage{h icx}2amsmathB font�SAamssymbW*��MaxMa�9|Cols}{30} %TCIDATA{OutputFilter=��x2.dll"Ve��,=5.00.0.25520LastRevised=S�:0day, July 16,> 5 21:49:4.w0i.2*ForMod.1101�4} \title{Exper� a:��9�8!7optima?�ymm�zcl��!t?� viacL��porg�o�Ia�DD{Zhi Zhao} \affilih{Hefei&9 Labo&@y9a)�V9��at Micro":E� DeB�9 ofa��� 9s,.�9ofG�T/` olog�OChina, �t, Anhui 230027, People's Repub�eof 1:��"�!%troM�vIn�S��?Ryal In��e�Q�h(KTH), S-16440 Kista, Swede=c An-NYZhang:���h�h�hIG,Xiao-Qi Zhou������Z�Yu-Ao�%��,�,�,2,)�(Chao-Yang L������^�And�IKarlss�=��(�((Jian-Wei Pa�c�c�cFc=g�kaliscz�]�L\"{a}t Heidelberg, P�^ ��x�[%�to%3 ribu1��i*��~EA o�P��i[�o> s.&%e�\ect�? E� M��Q�forbiddntu"�Nr*�ofKno-Ntoem ��no <�ojDst� ��rl1�l1�,s, Bu\v{z}ek%�Hi~�y �! ��!�Y�\emph{�ba"F� -copYmA$ne }(UQCM) /\ } �buzek}.gH]s[_!dicRX%W�Jf�quaˬs�B{�e��pHin%�%�b\}�d� rdFk��m���0gisin1,bruss1nn*e� ,E2EckA � ix� qubiS�Q$�-.��f��(ities $F_{e֢ d�iIgcop;ow�q J�U�sin]Sa�.�%"!#} Y' ( 1-F_{d"�,�*fegeq4[ 1/2<; >?  X.@ro] ^{a_��ȕ��!geu�8tradeoff betweeɨ�z9" -"��sen���H�j-oy\��it{ }5jn���U4\apter5%�!�I�AB,niu}.N!呖un�d w!��ifye�������a�Rb��> �8M���K���o)��l(. MoreovergyN��,̉is highJZesid� i�"��� ?I�a�j� so-call � z-Wmurao1,2}. A�� ��q'c��, � A]��O��& c" :5�%�um� , it,�involM extr�^ sour�v��R2ȥ&e��low e��c��!�eLS%�"��ernatix�Y��c �Fwld|Mre�o� Joit%�� ��r�ar�t�� d�rs�%T�M� 6 cruc� r ��Qayet����alE"����3Yis lea*� �j �� Q!]!��P :� i��p2h!�� ��] %W&T �YQB *Z �Qc N ���REO����BJ  t�eransfered to a distant location, realizing the telecloning.% %TCIMACRO{\FRAME{ftbpFU}{2.9992in}{2.218 |0pt}{\Qcb{Scheme of asymmetric % X and h by mak�us5partial% port��^.}}% %{}{figure1.eps}{\special{ language "Scientific Word"; type "GRAPHIC"; %maintain-aspect-rd TRUE; !%,play "USEDEFA0valid_file "FAwidth 2.)(; height 2-GLepth 0pt; original-8 1897in; % A1.6466iA(cropleft "0�top "1rs %bottom /�name '=2';P-properties "XNPEU";}%`@BeginExpansion \b-s} [ptb]dcenter} \includegraphics[ �=1 , �=1- ]% S)�% \capA�R: �9 A^]9% \end� )} %End�\ Let us first consider a`scenario that Alice wantsaZXsend an unknown polarizAVn statE�pa single photon in a mode $b$GBob atJ�$. Eve seekoextractu*\(or full) quantum inform �of� � by u�<225d \cite{bennett, dik02} hava�a pairX enta�d �s��s $c$e�p$d$, (Fig. 1). The procedure g filip} is)\�per�s a�Bell- �4measurement on�)S�%R�j $c$,! n re%�!��ed-�to%|in� $d$ �Z� held!L�ivX� R% q(equ%�0} |\Psi^{-}\r%50_{cd}=\frac{1�� qrt{2}}(\a�\vert H\e� 2 _{c}V2 _{d}-n.= 6[=),i+�!Cڱ��2� is achiev�ihroughi�Obalanced beam splitter (BS) with a variable reflectivity, $0\leq R\leq0.5$. Cone�H, for example, one !-ically m|U��sA*bym�to Bob%�n,!��Thus, �s!c overJ�d��f ��0!�,probability ɏ outputAbZ�a� e in(I�,�qcouldM _� l"(�� $e$�d fide}���qNF5= ( R5m��2P%y2)P[-�( 1-2;a+41-6 a] B_�y similarlyŝw�%U�� I��d� R�:Z�d �2���R� ���$JU=1-3R+3X$��bf�� orrespond the ]^BAtwoM5s exitA:'s�X.We�W. Alth��EQ� s� nly succe�TQ�s�p , it�cuffz A�provide* droof-in-principle demonstr�L��optimal*7 U�A=�. It��sM� cerf,niu,Iߡ*atXM� $E�i� d}$ satu!,no-QUin e8(1)�repH XF� bribN("k .� betweeI�y�em%�Pant%e. Fo� r*,!CR=1/3��-) was redu�t� e "�d�� buzek}�?9> !2 e}=Fj =5/6,$ bu� � Qw!@��as[ ��- forego�Ianalysk re jus�ed! any�(.z � �roJal inu nc�*� in Eq.%�) � 1}.n3.1946in 4967 &� eL atic!�a�%experi� A�p��us�y&I�&K%`)d %. Twy�T a6� o!�f.� airs !I�  %��lapped� !�6� (BS$_{1}$ithR comb� mi%2}$ %��H,path lengths �2�have baad!�� A� S y %arrivecwo:�4simultaneouslyI2&(BS togetherI�%s8compensator (C)� titu-c two-�h$ Mach-Zehn�i�ferom�  %Irarity}�r1� role�Efbl�a&� . PI�ers %(P)X,  3�� 41m($\lambda/4$iteq fro� �%> cto!� �#f linearE,circular R/L- �� . DL � %af de mirr�vo changI� ��)5��b�bc$, %A�[2� � risma�bSA:!�armQ6 %6�.}}"2� %: ma� %: � �.�2*� 84.248�>3.423 ���^ -* %�.%1��) 1,*��N9 �8 V82L�7 :7 �6 ��6A��5 .5 �4 ���3�3�2.2�1�1�060�/./�.�.>-�A6�ouoR�is show��2. WeV geneY �s6��8Almax� ly*��  $>7$���4II down-conver�� kwiat95}\�*�m an ultraviolet (UV) pulsed laser �(BBO crystalMUV & pas8�� * twcre��b��$a$-�( $c$-"us�e�a qral waveO a394nm ha�V� d� ioZ 200fs, a� eti%�$of 76MHz, Ao8an average powe�450mW. P9� ���&@ J  1�/  rb/ �� R. n�sJ. � F%\filte�($\Delta{ 0_{FWHM}=3$nm)Mamarek95}!C, fiber-coupl� �M �l,�can en�; all!  fafm � �  ect tempoA!�spa{%�1}I�#e cru& requi no;I�9�. 2 (M-Z): - ,I� whic�controll $ phase dif�x will�� a� desi�"4 .�$. However,A+n ec �wGZt2� se�q�gs?.Y 6+%4y �usuU)R�u&�>�s due pbirefAL|ef%�� uj C!� s (1 �its�� �A�m ). T)�comAQitfficultyEpincorA:t�1.2mm�: L��na:�g� var`e � shif��arm�6M *� id�cal C5�ce �b4achilt�Ac&� r�2.404�4.95286�E.� results %�� h� �  works pMly!��hib!��.�-indepen!:�In (aX(b)%�?e %G$twofold coCdE�{  ��et 8a$ behind 0$^{0� �er.mc2eD�df$� b e9 f�e(a)I�envelop"obser& � %�s.�a�-��N�e�)����>U���it.!_!� %!;� V�e)��ynchronMai.Tele�.�two %2�orthogonA��Es�uggaH�!�]i& %��ce���`�equently�F 1�^.s %2P*;3�;�;;q�&;q�v;1.9850"F< 6063W�<6<%2�<�<1 <1-*<�� <N�� iP |9B� �KJive�Wit's�*t�r�!!Wr� ,$�-$e$,� scane!�pos�fB!;\ �:rI�a!�p siz� $0.36$\mu m*^��B�y�. 2�Uh6� af):k�6(Q+3ah�(we1� a A= !9 arouy/ entr���6O�(� .�J� ^#&�!)����1�d$-h in orftoA�ifd*&f� We sl/ly /�*�i�-J� unti~�R�~% 1�b%A3c%��)ZujM�bCM r�:< r>.\ ��=2$ . FurY  @�O�"��(method also�M�+� p���+l2�$s. Specif4�)we�'$"h-f"3,!P$2#%.>� �#se�%4be $\pi/2$. By6J�:1�*e�Je.�,"Nverif�#1�a+&ssful� "�0��M�n" �y� a visi.)40$0.75\pm0.05$"zero � Y�# 2}. ��f)�.�%��#` e��-A>"a��- J�ie� 0.1,�%5790 .�) (t�" �ed)�%��pa�%��� ,=(��ci�! -handed,� ?- rigg�%ÝN \��6���� $a��IF�s w�,1^1� byE �j condňA� roje� :vQ &(e��&"�.Qed�Raaof KJ� as g �-.�$ �sr%Q$f�lo� � !ca�}�K%confirm�a-= 2yVsI7f' r accordG���- `)Gin�J2X,! !��w8b:I� . S^+, w�.T.id3,M�Z.�-�!<w��e"^���g�)�/���ES� �I� is 5 minu%hl6,.C=�les!�an 0.025�*��s��D��E/4. From� s�*e�*�)a�E�al��Si�� !�.�(6�[+$:�1�e*�eJf*&B=�ILimA���=��mai�+du��!� inst�. of�g"�&.L\ion� F>�source, �heei�7!��26z��h:�#�9�H"^F�+9$a�.0\l�s some��com� s. F�6"3Y . u�6iH��encoded�o�� qubi ancill�5V26 vi�9R�6j!ign �t� N prev�im,%��#dou�+pa� emis/$ei� ���b$ or@-��$d$�[B�amolG,�Eh� �2�bn�01iA\� guaranteI�m1s�^pa�B > �4L%�qV["be?fuK%M�A��1��n�1tE strut8AI\ it��summari � h�%��!�en!^�""al"6ET ofi�~�2���:"L ) ��U��&x<�� 2�0!0BI%&�1:�-8E�:�%�may)pot� al appliY@_ !,#ext�futureMommun 0."0;acC= ledgō} h��laor!q� he NSF]China�CAS N%~al FundaOHal Research Program��(e Swedish F*;%�S�3egic ;0-SSF INGVAR gA�.27B� A?thebibliq phy}{99} �v% ~�!em {nom#$}W. K. Woo�;s%�,W. H. Zurek,!4!�:Hbf{299}, 802 (1982)%�V%3,V. Bu\v{z}ekPM. Hillea;,Phys. Rev. AT 54}, 1844T966T�1}N. G�Q$S. Massar,.PLett.�7� 2153U76ULbruss1}D. Bru$\beta$ : it{et al}2[A ,bf{57}, 2368W8JW26W2H6�81}, 301RL�`2}H. Bechmann-Pasquinucci%12cA 5W!./�96��}Y.-F. H ��.6U  bf{6!�,012315 (20016W� i ^# docud },�%V� �. late.tex V)%%% % % � ^3�.5 C� Eu~+an%�8 Journal> Copy+�new <e7!b{Kit 0basis %fy��YcleUZ Sp er-Verlagf�� fil@ s}{leer,!L %!PS-Adobe-2.0 EPSF %%Cd2�ionDate: Mon Jul 13 16:51:17 1992 %%D-�xFonts: (atend) %%Pages: 0 1 %%B� LingBox: 72 31 601 34C EndC gsave #moveto 42[:to 821 8�:to �Xpage grestore %%TrailerF�HelveH$c 22 % \QvXclass[epj]{svjour} % Re�woI}0�fi 14!�,% belowA7lo�0hUdd pack!C %\u�E{A�xsym} .L�etc�bRL��title{TruL�dynamic�!3ar"4�GorS \sub <DoA��a ?\\�F so, writeA��Fp} \author{Sabrina Maniscalco\{1} \a$Jyrki Piil:�Mool�PV!TA%ed��s, UniE�t�(KwaZulu-NatN`Durban 4041, South Africa)�DKt�v���iSSofiaY,, James Bouc?5 leva� 1164 2 , Bulgari ^L7 V�Q_MOptiRoyal InF? of T�& w��tet0a Born-Markov!�roF<�  m!lus 4�pT�meT�Dby phyI�0$STs,�F, r ��R� ra�b7own �Es� =og;d��9veR"�N ini�u� ory;�pIM�LindblaGm �}BmJVN�%�qX"ed �ic��l� an��aXy�or �or�glauber}E %M��on�$�D�t osc6!Ł~"�&�4w{Fnon ��I� star4 o af�Adbe�So�6 trap�F2�c�"" "��Eregar�( a harmonic6ntcoo�AA�s�b����=n"r1 usame �I�blatt!�,Its advantag�D|&Iexact�Kolvz;�26F��f0P%5ye��Eheŷ!�pproa�;oW teady!ete�,�U�m%�.h eval"�noise}{ ���inv�>gfa� An.n�II� �R� In�!�&� so f;�I�y��vQ�O#co�,VG��E�Z �U a]OZ�#is u2�M assum�m8W�popul X��@is 7 !��HV ;�8��A�ŠaE.�S�en�Pno� @ . Su!��1 y, h[= does Q�w�>� �m�)Ui�e�p�R}$pu +� wit��@� f. I�Pi�=p�Ie�sI �p� �A>�s�=eS�wi smoothY� ���.�a�takesmIt9!�hv;� 8FDon6D� ��"�;�a/��J�w0.��2 2�1(er"I chaYer� funk'�/PRAsolO i@$,misbelief�@ ��q�!:��� um&� ,j.m?(most widelyl"Z� mon devic�J E�J�*W�oos�!�9 ->Ztm�&^L��mediumaDUU)�lyu%}�a�!g��n.�on��AY%�i��%��"rv^$N atH$�0 ite ( , be�NMwCa�\s�m u��A�i�Ա�ia�� � to un*�!rse, deyDQVY0 &�-I�Q�]KA:ng%igcs�WA grow�e��2��>Q: �+ poin,%Ef� see�g An!U�ce �)�$()� a{5pos",tof ��(ly imposed n.� s�\/ w y�2ct�� 5�!zmor�� ca tq(�sa%E���.] �y�is�] �lE�% k &� nyI�ed %%q&cl�` ; t�2q"����p�>e &���a\T��e�lU 3�� �� " phenomenaA/a�:6^� i`�/r����* ast a hug!�ae��m��opt�� � bes�!v �s' #!e=aA{!�pe K tic ��重�k.-inse�$� 1n�^9���eri�j�& #���Cp��� cl4o rT,(M#&�!M�!D��or��L a1�-�e�FaI Ey ���� �g��a� ��*z�' OuY�a�be diZlyAhl�H$c]�t E^*�s bas�-)b� s. O^al B�Tesr$%compon�%!�sa�,-of-the-art 1)net?#����L��t�E_.+�en��I! 6]bb /7D�T�5He nQ]6 dua�^I=%aKa�fa!ɽo�� offOA'=�i/=N LA}."�W.):.�curren!�u!yv4)f5 dn& ��� -uev��a�nt���C�of)=��iq as!�&�$, rypt&$u'v!�u�U,a�U?���U of5�erai�* nanovaHWQBpe�ng at�G{�. �%AaL2!Fm��oᙁ"ntI�~t�]as6c)�.���=s �Y DV6en���-�$Braunstein�V �AōAm ! anoe�)�9uSe��ev�L�Eh�,�+Q,�+1X�*�Vs��� N*'ŞedS(R �M�s � � LaHaye04}�'i0s/� veryo�5�imi��0ed,*�@!�-a�-id�w}�!�S �c--n +i�A�aB�. Ano/*M�}�!hF��s� a6@Mn)Av �Vi�&Wd��-& Zubairy03e�so!sip�[ty" -��n�o1 ^)�� p�6�> �>�dMJ�{Kim97� O��� L*u�' i2 YIIS*iz�!��Is st `0!) easy�arison ( !��.� �7Gk.7 III�X UKP� Zc A�di�� t�in*�E�Sec. IV A .�� �_��&� R� m�2 q#e�w%ng �gto1* �H� V>�emerg���L "H �1 $"n�L� VIA��h � �� ND )�Review��U `2eU na�c b!ei)ݢ}�sec:laV dard} �^M6�,� Pad"/ �� s��K=[c�5g(Qu�A�n assembw5f $N$�1-� atoms,'T $N_2�>ex0h� $N_1 un K2te�!�E��{e�Х�.�^� <�����/�Icy$reson ^U%� ic fB0e&!C*|-�H�Upartly a�j,, ��>��gI1�*!D p ; a?)� �^�|� �"�A��a���d 6"� ]�W �-: ���/�D m�Y!��2el�g�eime�8%4�%Kloss m�Dsm�;v!��, microscopic>��@a���Mo>�)�&/.A(�6LdSC�r�m6(��m 2K�hBM�on pic��6��"eqa� ay} �iH d \rho}{d t}= &-& C}{2}�e,[ a^{\dag} a. - 2 a 9+ 2+K8] \nonumber \\ bA.b a:Xcwa c + \ d, �xMElaco}g"�eX"2XAP nihi��� �U I��!�"�"6�o@dF` A &=1MH2g^2}{\gamma^2} r_2�A��t}\\ Cr212C 2B�� $g$a�A'c�TAHstr�_a�.�Q� ^�A�=E}(, $r_i=N_i/ �$ (!d $i=1,2$)�aq�� in.��� $i$) $K�6 2��s�So� B8inewidth. A re!nt��a�"�#��7a (or � ) fa~_� �!10rowth (�=)�energ�4&!&,Y up } W=A-Cv' } W� $W>0�<>��$�Z�!Ven $W<0$�,N,bsorber��*�A��� ��e&� pont� e\5�!:er�� �5�#�56ly�?���&�!@:� tudeEa!���%a1>:Fe\l�n�� _{out} \�v�"  a(t) k`= G^{1/2} e^{-i \omega_0 8FPin}B�hmtV.=(t=0) w $, $j$�!!��M�rad�R-�H�$Ga� ���sF$G=e^{W t}.�E :t6:Q�k#!ug�($$1$�um%����!d small�!anB+t'8o `� �,Fokker-Plank&#� he Gi-Sudars`P*R=eZ J de� utrix (*E)�/�balo �(4��f9(incoma�$P_!� (\alpha)$W{$th*�"J� P_{\OWA�B =H't�uS _0 P ,t|)<inx_0)1�eq:p1��1�E�FNZ=��<1}{\pi m(t)}\exp��-�k � -q' J' � �|��U���2B��Th.- Sfet2KLhe �F*� ��E�iv�9yF � = A�[ G�-1�/WB��,� �D"C!�7 "c]pn �i� N>m�6  NoE�atr�� ud�i��xs{P ptot�(H�Hf<ya7 $t)�� \infty�Y so !m)0 �gif�; � �6.%�D ��P �Mxu��V $!j���+i`  B4aL$Eqs. (\refE 1})��2})�e�u���ns )bh�%�%J"�"" k� 1�lucssG@�- c4s}}�) |C^ a|^2�V&� 1� �_� � *� �� ?-a�ɐ  �1 H:2H =& G 6� in}+e�cf�u2}(G-1) 2? &�Ee(FK4 + \mathcal{A}I^)"� eqcf ��10Z�K��  A+C}{A-Co�1�� 1}{G�^), !3�� �bdal�IO� � ��.,bMr�'� CA2+[ i �(��' Nux �.* U� � /8M]a��)M��G:Eu7^r�Z*their 2�ad�quadr�)gy@�C �&�*inimum6*���i����, e.g. Z�is� �Z)o}�u�}.L_C�N=��i�+�.eta \geqM�]�:�0B�E�!Q6es�%IW $\tY$�E��n �6\�UV�I* t� � �achesj S!���^q3e-کC�c]q vanish9:$Ti��F 0$. �"�)*PODU��TE 6 %� ��o26UWr]')H&s,&�cGi�2Y!1.�:bb4 ��� ng!!IyR��a{ nN�*U}�, �3�'[ losta ��a�&,subPoissonia�!�-a�squee��@%�!� �$G$A*eeeh�L�}2��i,& ?'$�1sO�a����0} "& �.I/1��0A�� wordSdwz���b��C�!w�#ll��."�(���6��&A'� �. �ai��D tudyN�& �to4!N9hC4;4���"� ��7-RedM6,%�mod�hd. n7 {&34 �!x6q � } P9' �6(; deal���A��)����� *7:,buisf"N)"o0"�F!t qc }6ID�e�*A%V�5b XneA�a�doe%�M���2�tM2n�$5 h D�"*a1�; )�e��s0nd 1 ($r_2(t)hd $r_1 ) �gA�th� �.*!���~+�T%��/N_1 \�d!:$_2/r_1 > 19\%�M4 �)!k � B$� V�����\U��a >��"�GEq� �), ^vtZ�$A!e�$C  ;z,��one(�,� exteT !� � o�!�Aic YKs5A^zll��A�.Boltz�B��!�t&�i�����H`hsto �s|2��%H�h � li�2�`|&�mIh. ir>%A��wo&y(�N0Ie�,6&(N ���9��,�"q7ly�(�!~.�O'd!4l,B�A_uM&���u!� � � J�=?! Xe^{\varepsilon(t-t_0)}}Z+�N0 + B"� a�\ Ac� iF�a�� �[ N\Jb� .�bt"Y 1#Y $SRA"�hA؍@m~A�A`co&�.a a�{86�RL�,�� at�r $t=-=<��uIenU w2Q��@8A/- v�f�Qm�F#)�N�9.� -� )}{N!�V&=& AA(Z#{C^" B}{A+B�A�!�\hbar&!/k_BT& �F��1�$�.$B/A = (A�2I H8 -1)^{-1}=n_M$,�*$ - *cJ- m��q=�!h 2�F�p�+noS,a���� +-$1� < t�  U�h/si�K� */~  W���/h�< %(`,�S'tan1})Y!� ==�I-a�=�Canh [}3 �+ ]"wykJ:�$t�_0 �f_��� (9 &0 T�$t>t_�C>0��a�:C���*$B�\�q[h$me�'!6 ;:�b�> s. %�>"U�!{�.ing>���=10 cm,�6 cm]%��@\c��%� Tim:�%@$A=*=1zlt_0=5$.�wB2���U&T wt})�uin'X !"H $A�.3x�]}&#wA;w>G�$ta�"�FY���\! &N_2&6Q��� V= :�3:� �i \\��( (A+B)/B = B�+/BF"��F��%"�4�cz�ed (g_)��=guI y .e L D (��ed)��  A" �0:� a�E K"$>&� ц&� exi&�R?�#ER���!R!�*ay"� J��V! \tau2Y!A'()9 eft[.� V! f� *WM�].`! �CJha&��e! +� �! "B MElaF� +�d&y!�A� A'&N %-! "� 6B 6� '�eq:ap�*��j.i-( f�k.Y`:c k>�II0p��k]G1�=��I� �1 dim(on[C���sGau�&  t���_0�.�wA'= A/ɂ$B'=B2. Aa]� �|.!Uߍar � $A'���7e l %a^�a��Tof� o� ���,�7ys�t�c�T�� ��E�!� d�.�a��$GE9z.�� 0$(��8 � . F^;�Gbd7/oV;i�,PR2�7}�Xolv�>����eN�w ?��"q$68&�(QCF)bar�K},�6qX"WsU�y�u}Q�sdO8�_S)8*/�8\pi}\int \chi_{Az}(\xi)\:8!�\xi^* ,\xi�<� )} d^2.q<����);d�M�* /� s� � � � |\xi� �0� ft( �! %7i (�!.)����b�-�AchitHe��� !%�#e QCFA�A��2� n, &"$ *"q?Y� bgain, QWF�m  =�!�_0^)� W% ') d!�'*+"F+ !�"U{?)d ppeaS aE"9-&*�"j��{ Y]�} [ �] �t')]= E�[� ')+A�')I�] �" d|gF�I8w�fm5lz2"m U�1v� ��� %�hel1_ )gt})- 4�), holdn=at�<explicit�"� c�he.�8sD!̍�$C ,�)��9��|��}� *C _�p7[�a�bt})]&#c�[�0illuswXE"� ��A/a�l� -bl��T M�6�l���? :� &* :n; �+"�< ����c,>.�" ���*ɑ�4~ i "�< )�-�/�$N_�*�f�C-� 9Sing�nS"%o,hyperbolic t'<nt���K0isT��m�=�Zl adop�3p6: J-)�%�A~n pT5�%)�1$� S2h-Y�29�l�8""lWigner"3)�V*&&�Hu�� $Q$A�mea%�a(�+#�VFUW�%,p)6Y%^2�3^�qfty}_{-L}7\!�ɥ�����%&��^* - h^*)��(p �� /2)}. qp�s^� p=-1,0,1$aK�$X�; $Q$,-k)>$P93sk�.oIn� "�carry4 ��+ 1�io<��ur!q�^?.�'�HAY"T�2Y'I&*S�.�� gt})�8$m� M t �Q - 1�!/2 ł .� �N����,l�BLg* n y�/J� �=��� \cosh�"� 8 � ^{A'��fu� J� }���ud��`,ab�&^ =�xz �!�-�!�A�:Q�2���&� %([��[�a�u�Y� $�'�* A t}Wt}$ [� =x2})]�&E fig:!� �vE]]�,for�c  !�v��� . ��0%\vspace*{5cm�bw{� �k�e�qbox{0.50�\_}{!}{��5gq�%�b}&I�-��JfM9$� � ,2,3,4,5.5$ (b�}�!id~BGthickn�!-�dI�QV�Em1 AZ:8y�8IE �g+reat:m!� 9��%��7x-:N?6o� �$ become�,E�s�,��.�;caA:� cP�!$>#�Z�or,�,ir&lsu�;s�T6�iA��gW0ald�-�e: r�s �"�-A�x an�[�Ipec�%"OK1q�C�-:yTp��,� ifu#>1$�#a*!e�>�"ta{*�*! " !^�G�9Xz0 ataaEsa* +�92lways2�4�8 4:w8).&$iteu���mu�eh ..�&w�#!�� "� �P!�B0<�F�r,&iCCk t�Fae�6a�#ich*eh&2r�s� noEA�e4L;h!1E-I�sF�/� 5�w $2�_�0-�$0�!>� sinheY$ }{(A'-1)}  1}{(� ) � -1}k9ii2a�}�<& F[1,1-A'/2,3/2 ; G�)^2],"�9� �fC �^2]!{AV�>geA|,RS q� vari�$x= �F$9l�1�� a�g�Z'5�&�=y�>/ko9qiI_1%�)=�|arctan[j�^&� ��.e��alQ�� �S&v>��a�� ?+�"� �er:"� M?-$Appendix A%Qk EHP �get* Q�.�=j� � _0)A>}&a; \\�[N +.W4�, e4� 8 ��]�H��j_r&�xr��eq.�)�sub&=a�!�Qe e�IMex1��m�� �$:� o)u"]No�--�.�,}o}�R�Z*��Z�� ly"�S `�n]6Wa;\ AW?_�)t< J{.�� =,>~m*� ��\6�2 m} a^n*9'�Q>��d}{d \xiv)^m &(-��!�^*#n%"�} �E||_{\xi=0&}�)��q�We lookLc.��i 2�3&<6�3,Ix-9bN�1�fQ�|i�>�3�F-3";��y����3 )2[NA.�0-%%&�>out�25!���2�&P1�1N\��3= � o/ �,xeq:Պ�VD�V.>�0VEqq'�RO~&�hU �er�3�a}�&�7M"�3)�$� "f �.�]��x is\0iV.�-atv$"�� m�fo���a "�vis "� &� :;թqɾ $=k_C$�9|_C�ra4e�% �76i��!$6C �"T-dVB/*Q3)h9�.�), we#6 �VV ��a]q2[*��ekc$abramowitz}�Qc�T"E�f�6\sqrt�:}� G]A($ )}{ $[(A'+1)/2]��]T"C3%Msym,$y�c.J�&&.#7�*5 �.> �$ ���"� ZC&����4��%6�(�� m �)1%?+1RA&j7:).�.�.g_�|n�-m R�ap�*C.+6T�:�$� .�( S.c$A' = �. �a E A���|�D a<Ii1�/ /2)=9Y$E;�X.� Q~2!�%�J��6�]"�%J�i>6C:%e"�6)]?}&=��{�d\'fixedi�# gmea��* �* =B/AJ�F�;axl�I)��< .� }��C care���Q^�� �.7)V.F  �d���b),�!Zi*�9<�� xel:&�>�+n�`2�-@ st#i%n:��Wal}�L͸*�[ ``Y�I �is� ���=4( t}Dmoed� $��>_'_�{50$6�-a � �i1~1\� gj  !} D�ea� �i1/�D.�4�a�&�C�C $=10e� %,�BfkT$B' =0.5 \cdot 10^{-2}-Gdashed&`�+-:;?6S!�D =�Vrt)���*J-!�--�"�a�/ ime k �-�AaeYq���%s.��I} I�"&.]8�7s[7U�r"Xtai΁*>5"<�&� �d�*6 P= we Od�zngiOF�N-� ers/�-�)t� "r@6od��Z�Kqt�&N:^ -� &g6�Hx_ Y�:k ��z"4[#1j �?Z�R�:+W78 &�3&i5R xS�%�6 ��e�g�oj^vZ^"5ME!dAA62�GE~�".5PN.;�6�e�*.~} \*�Sq"�:nd ^*;�##�s3}r�~I��H% 5��.���-� S?�w�*!%����7�e�"1 �T magn�[���1��6�)&{?em��a��Jy u�*"7w2}MA a+a^�MB*A\ v6-i}B7->7"�'.� 6�s s��@uncer�Wt�#aM / u�' v = 1/2�ut#;*�xAan�QP E�"x[MU� um2�@ �&� K+j s�, \hs�{1cm} � --G� 2} s&� 1 s �1�9BAK!���nǁ ��TJ�tilde{u�4!"cos"�( t� v X&�( t),\\ 9v9v B9+Nsi:9��az�i&� aCo1R9(-W � u})^!E*�� [ *� *in� &I�&�u}� Eov�o *�ov��Y@)��2�.�F"02&V �a� 6J"�s<sd ��� remain3i�JK�8afYPu�+�p:=.�.� -��)�)s%B� . A�eut� Ca�� *u ���9� vals�"�J�maw� t�O2e�th:�"� !\IDC=qh<$2$. H�*�s�"J�e� �bU$��,$!�� K> n> �eAR�[ S�tI � b�% \9*�%%6&v�>x9{qa�rF8b 8 "�9 M(q*� 1�.�Z ��"~ FockiN $\C n_0=5�L"OA�f. '=0.Ǔ(a)�!�U� ��.�Q!Q$Y_"n ==!n�3(&P�- ind�9ltlQ`m�0"9# $Q=0�a1� -~�&ner W�&�%A� Uhi��#= ~:y$_Q)$. �\fig:Q(`]Q1 �!now.� "� za!�9�! �2��"�SZ�of9���Hir� � �:.�H*mC&�!2%�dv�.!�:� �6�r�B6n�%�i 2lEi � �2� ��Daim�iQ � �nde]��,�� I}F�QM2\� n^2 �;�R�O}-1" h 6-RR>Qk*f *y� � l��1 a=� �7%�:lowI� $Q=-�D hile�����d=is�5l!� $0$ �e>, IAz $Q�>u^�xXѓ$Q=i�s f�J$Q?superR% . U� * &w *�e�"�p!BAn��iK�r4QfQ\!=\!� 5�1�� �$+c4)]�6�$�Q/ _V .�j [ Q -\!0�Q. c }F} ��"W QF� !�&�^ > B� �$ee�m6��A %X�,�� s,�cY*ij���ylJB{ �{��F �+&r&}^5*�/��/F2n 6n:� i 0.�n�W��&� � i�) a�a]_!�e�!&Fq)�=n�;&)A���Q�_�}2q.�6.��Zn(Z +1) < G^2-9 n_0(n_0+1&�Z.1 ��W24 Fa���4@v�-.c%;��,�\@�$2�.� typt4of ". :)>�~.an ex�?>XQ0k Y�>I> � ��E���ert!P�6 B71:�and/or ����*!"f�/y,C�w-se@D"�1� "� 6�!j-�z�% !� higheR -Y6/�no4as�.�:P}.) }a20 [let �6��LB%B� 2�3�.�%�%eq2Y5� putt41$pM*�vJa+:.6*�:\pi+6_{vI}"� �� "+6,L%-�i�Z% } \,6(6�%�'�676} ". 5�< (N==�) / *�3=�+ɡwF�W9X!��8e Four�S 8�G!�E"�,>^5~� w1})Z Fn&& B`&�)a �,Fb \,)]%'_0 W_0z7)�I \\&&�EN� \,�>�>)�r�b%�, t2� })Z'�7 b^*:% .�x.�&&6�j�!\!�O :��8 8�u |b� )o?{f�)}y ] }{2�]� ��Z ekp��{� -_�^%*�2�"'9w:�?�Yc� >�5?)�!%�ul_0._)a�i nRBQ g� �m,���w*�"�`�GF�rt 29Rx a Ga���s � ty $:X9[�qag���*'Ma<'�+"�%9�"E $\ m} -9c�9I� z � � Ɏ�c2� l�%�_0�J$o:uT��h reaz�B: 6�}M��;qL'+- |�;R2 22.�B}F�O9e|. +�d&f *' .�FwigK"� Q�O*�%!zt� �ZUX. 6�%J� &�8�$���fu�2[ �9�j}]��r"�in a f &ra�}freom&lCA&>���6T� U�52�H$)�sDnO,c��wara=he�����}S a"<��u5��#��s away&��#|�it�#continuoK�e��#J�2�4��:figwig2�z>B�"B ?P{2`;&� Cont6�;"� >�at.]"i6��` 5� u�I.$rL QQ�^A<&�#=0.� $n_B�&�. Varia*�C&�D�٦߬�d��ime, %�Ar�# �..~wifɂ�W8wA$�Cn� �%� �;2� ��"1($:(R�q �/=b�[ -^1�+ �  C_r-PH�G0\phi}S_r|^2 +;0^*qh^*+\xi�EBQH@9$C_r=h(r�2S�5�i�a}9 e diF�c�x!$!�.{a� $z=r�� )� argu�xVJwAW "# cuum�y4? �=0 ?�\ +in+�Y�$!�?�J�ARAta93�){ &���D D xiO !.s%��� %�(�@%�- �^*!��0F! b.M|ti61.� � ( C_r -e^{j,}�Io �] UP1/�B[ � K(�M%��%}DL� "?Lmatsuo}Ɍrd^ b�7F�>pRM.iL-2[x�2.�+ (C_{2r}+S�V6"� nR+2�c-�_yBc:b-Nb>fa�yx�iy�%C��eti�n]eas1��0nd $Me�ai �Ft norm��-��fant�.@Gi�ul� &��e�aJH7&�"�Iv})%���>�V*�&��6)Te�B��D��� ��,�����T� .:/���n BnBKre6 � ~"� .x��o ^*b� ��B��>�Bu"�fI3p$"|$(  "UaDeA ��)h!� ilx]>T���aAvach����Hb�9�"�Q�T)b?;�o��-��PQ(�`,��?)��4a_?Ɛ�`��U>� "�J�? ��]M 9Z� del���Xn�['L1YxH>�y"D`9�n�I�OG �J+W 5&w�p2sKi�Z�kndEV E�:�H�&� ��6!�>�_�y} O:�[/k_{B}T�-m�i� is aY% at $T$.wg�0&L#�a�n �]nysH)n��*�`|:z]*��&]of.9�i��&9c�?!f���I��gh)�>�al� M# .�.v .+TI���<aB(�)`AC�b&%&y3325?2A ma2�Y�>M �,7Fe€M��|E.�MWb�:g [�.u�r���Eb*� �!� $":K6� u��}.!!5Bf62&b 1%>b 6 "��"] �`� {%8[� : r;)A]& = eq:w-�B���� �$*�"D�J2���J*;l�*�F�J!�3��mցn$$d��d��=R$X��)i !$'K��se�To�wQ$14} Hz; >a� 10^3I3box�����$n5�'e ő .�J�:1��i*�<is ^2s �'q*��q* n��Ilyg|X |"S$ ~*j �d�RJ(� zS.";D !�A r�$b��ϡ�ezs� l:1I�M !;)p V3 ��!7�z&Q.eq:e)*GF�of6,U�D~�76���a�a2�$T/C)��ich��$[&�A!��A~� M)W�$l4 any�),&�)> �e�:*.�&ޏYb�����y "j4Eq). )R A�at.�� plue :j�*^)sZ�� �m�(�{)�!}�Qcer��)9t��rvoir!xӷ^ e��Nr $T � s�U�m*�1�"w�&O+�.BLd 2FD"I� + � \c'��� 6ve / k_B �ͷ]:D&,eh1R"YC${�yar`0} (x)=[\ln (x[!�u H-1)]/2$ (for $x^2>1�bW� �DXE�B� 2�asq`sJ s �6�}{k_B�eft\{�)9;>�1 - F0 ��)jͯ 4\}�Y.��S}4� �������%E��aU0�2!ztwo�x*�K�� i��mYB.in �A� n]��rA�M�i�W�pd�me:PpEi��r�(f0e-6aIe av"� }�A��\*��>"n6�F�,2 ţ24 �P � iderZF)�i�m6S is mˍ�!%j m"h����C!Z!1:�"Q�# F. 7U&� ch�ze ���H� A �VB ,-�we2"$von-Neuman�tr,�M ŋ.�� `y$`6Agarwal�sa 71}�"���:I h�t�a&8} ��&�2�� &e&S�$&=&��e�\{ }�| i}��u�ln 5-� .+y� 5.&"����'."6n� �6�$���-F(oa%]"]�7 ("�$ �Yla���X-�E�A}�# 1�95sصU�QE�e�!�e��2h.LJN �uJ e� , \sim4x 1��� ~i&�how Va�e�U �� $k_B"'rs�a�;7�j� >s��th��':�a��A�or��ɕl&9� a&a�}m*�<2 Um'Y5 ���{kRD�V� %E.2�=�m��/%�fa�_2 �%T ��AZ %B��t��� n�5�s�EH��ur� vsk:� ~u�� fig-rU F� D��&1` /1��e,(%!�Ʌ�I�D\!��<d �; S/F.& k_B=�I[��=14)- 0"m /4*$. ,�e~�� F& ��.EM� empl-�,�45� .B�M�Iy�L_w�96�28 A.d$2� ��� "�Co Z�s}� "�4�dΐK!.�I0umm�K*er*�j�Q��0n @� B �,�+Ɛf�r&x�� Dy .�!co#�"���`�X���0:A�k$B*\ ���u�[a�mairzY26"NuO��% �V. @�gd�H���m:�l �!6 �(bX>�I o!�� ."��%um���"?%i�"�i �A)��"��� y.1>�)Gg�67�^�7r;Z��P&-7)�B��  deg�! &se `��M�Gkd !�j.{�-2ni#*5$ _X��� we ���meߔ� n,o�2%Z>� �W.6p�A�,-������o��!9 $21>r�5�sp/ � �N�A87ۋleche:z  negl�|��Y�M�F �%h� 9 a�\ "CM��<,��.*�%K�to#�k�9 �/�"R;0magic number)�U in order for the output field to retain initial nonclassical properties. We concludeI8paper analyzingsituatioP which ] mode of �anddtwo-level atoms medium are�� \tau_m} �R�z��+��.� % b�9V + )�(!� )!!} $\arctan (\5�).21} \end=�I����Q�we show�tEytwo eq�8s written above�s spee�casI� Eq. U�4i2ageneral}). E�4$A'= 2m \ge 1$�A�E�er��H hypergeometric fun�AP reduces to a polynom�of �$1-A'/2$Y� �4} F[-m,b,c;z]=Q� 0}^m1N4-m)_k(b)_k}{(c $z^k}{k!}, 9Lp��rty5PfwhereF}(z)_k = RM�z+kY�Dz)}; \hspace{1cm} 4 0=1.1�cUs�?2f�)���follow* ies�q�� 1)=zq�z)YsaD %-z)� pi \csc ( z)}{-=},?�pQIV! =�Eq.UEa�2>8(2m+1)$, we obt� 2I2m1})��2.��u%L!0n&&-& i iV�G) F[1,Ik ,3/2Et;i:2}�\\&=&F[1 ),1/B6�J ^2]\�C &=& E�21-m c-jj��J�rO��&&U�1}{2^m}Q1-m)(- ��$^m P^m_m (1�6,�>�ZE<(z)=(z^2-1)^{m/2q0d^m}{dz^m} P_&,Vqwith $ $$ Legendre�i��  1Lthebibliography}{99}Hibitem{mandel} L. M eS M. Raymono nd0Zinn-Justin, .� LIII%�<0, (Elsevier SciEIdPublishers, Amsterdam 1992.�PRAsolPiA�@} F. Intravaia, S!� niscalco,%(A. Messina,M;Rev. AIB6!�,042108 (2003.m(misbelief} >Z6wJ. Piilr r , IJ.a. B: -]�SemicJ } �}, S9 �4.� optt iD E9ambini,A�Vallauri �M. ZoppiN�12a9713E�5); �A. Hopf!� Bergou K,S. Varr\'{o}6O e� 34}, 4821a�8a�A�Cabrillo)et al.}F�( 45}, 3216(%�; �� Sch�cht?EYA.X 6�%4 E 8820�92FV.!(Malkin, Yu.BTsidulk-�Ne�Fisch, �YE Lett�d8�406)�0.�applic� LA} �,0Tangdiongga {�PIEEE Photon. Technol..d1!@1196 A��(S. H. Chang�H5}, 906M�;!KarasekF,�� 1A�771G4!KY�5nD ApplI� 38, 1682%x9.HBraunstein01} S.L. 2.� .|�493)|1.]PLaHaye04} M.D. Lahaye:U�[I� 04}, 5667 ׽� Zubairy03N Ahmad�LQuamariM.S. ) � E,I��J 3815a2JKim97]S. Kim @Il @5� 3175%I7)�\b��stig} S."eFScrM�Te�5C86.�caves} C��C =�D)#23�817�8�x= �barnett� M. B ��PRadmore)Method�MT�e��l!Q*�Y( (ClarendonOxford!�$abramowitz!F A�I%gun ~Handbook Mathema �FP s} (Dovv �4�V24 matsuo} K�T 23-�4�@333%392�u I!�Gradsha ��9yzhik � TablGI (rals, SerieIProduc:(�ic)3< Inc., San Diego!;25,agarwal71} G�A ��!�828�2mA{2a�]|��$Soc. Am. BMEAD74�Z8%Qy>| AZ � docu�} % end!� file�4late.tex �j\+�3 [figures,�t]{epl} \usepackage[T1]{fontenc6�n1]{inpuB{ icx24{amssymb6psfrag6ae,aecom� \title{��diffu&n| �quasiperiodic kicked rotor} \author{Hans Lignier\inst{1} \a�ean ClalGarreau\2!Pa ( SzriftgiseA A,Dominique De� e @$2}} \short�� �2b} 0itute{ >41} Laboratoire� �Ygdes Ls� tomespMol\'{e}cules, UMR CNRS 8523,&A $C��=�Ooga)Hde Lille, F-59655 Vlneuve d'Ascq Cedex, France\\�26�pKastler Brossel, Tour 12, Eta�|, 4 Place Jussieu, F-75005 PariscL } %\pacs{03.65.Sq}{"� �A ou�*Ts} 95.45.Mt}UJchaos; s? Hm�t6<32.80.Lg}{Mechan$effectsadl<��, mole-�� io� K Pj}{ al�H?; trap�a��dy�\makee�w� abstY}/ stud�m �sms� ponsible �qh�H�reX exak�k al measur�� XconstGoi��ic �on 0 u!.d�op po��8approach (basedNFloquef0orem) explain��ob�X s, eil% < ``sub-Fourier''A !F> reso1�NI+Yvicf�exact !�} ity, i.e.(abi��7 � to dnguish neighbo� driv�frequenca� in a��Oe^a)Sin!Ne-L%|er ��L. �/Y7"J e��EJ of \emph{M4} �s whose �Ba limit=Fti�� majorlleng� H & lo underA(�]�CA�8Mos Ab��� �imA�A|-ce betw#1Au�)� �he exis�� �I \textit{tr� ces}_0 various path� t lo�im��a large �of c�� ed����a . On8ulde�cE�aa trib�q�6Ao� uncorre  d phn , so)d�l!*terms vh �g$average af! someE�,!llhat1O%[9iq!�A�(uld be idenQ �sim��acte�AQhowevA�oo nai� because �!D�2x � actu]� ; thQ� eR@� .H. ThY�.&z nsively��\�r�.ly!K4recent years ~Z`Raizen_LDynFirst_PRL94,Ch.Noise,8,AP_Bicolor000,Darcy_QRes1}.�its>ritA3sisɼa clou+ -cool !�OosA�o!�rt pul�a 5 detu"e���F wZ %s�{to%WHamilton�(!�!l!9I!mo� ���)��} H_{0}Lp^h 8{2}+\frac{K}{T}d\theta� n}\d�(t-nT).*�Ki- V� $ D$A��$2\pi-$�� pos"�! s , $p$:!conjug�mo�/um,G"he�1e$$Kaproaional toBstrength1Aws�oy]�}�is��� ha��E�$$K \gtrsim4Mv$Chirikov_C CAKR_g Rep79},k-��n �i �Y"� � �h$K>5$. D�"'#ocalize� (DL) iw!�d� � ion}�such a6g!<6��subtly�2�� ii0casati2}. DL�a�c�x�� ar i��-�i��1broken1BO0_IncommFreqsQ!BRL8%>s_y� *J B>�}.�!�# done�y�adeL a se�# s�ofI w�)3� I� $rT$,�a�JQ$(r,\lambda��X�.^+ rT- V T)e}|qpbx �e!�n ����g�a s. es. If $r<rEkalaeyaXict ime-)$ice�$DL takes p� , but�6$is rapidly; troy�'r�! anyj���waS"c"�$�&a��)tiv#�2�#ao b �� kin   gy $%�\langle %�)n\r $:� as���A>| (or �!Vs),Z'as a%C�]�� ��i�pwX$es��new2b ults�e6� e�pre�phyl &" C2� A-destru�:a�I,� QA*. Our6�setup!�describ� y��1QH%Xp_CNSNS_2003}. Cold ces7(_(�prwE, a magneto-o � I� vtu{& off6a��!� >�-�\ (13.5 GHz $\sim$ 2600 $�)$ ��� (M�65 mW�t( dirq&$K�(At \!k��, � counter-�� agat�ve�-c�t beams�\ form veloA� -sel{0ve Raman stim)���!s2�!fine gi�st�tsub�)$s $F_{g}=4,"d 3$�� t!�b�Za�:�n u�m��c�AC��gd�q+cg A�d} %(.�) a����pea� l.sit�r��I�O ic �sO  $P(p)$m�پ� , �Oͅs,$t>t_{\ell}!� $E��<o-c� d��.��>},��manife!��A�DL: 4i}) �Vfroze�+a�"*expon al shape 7A�$\exp(-|p|/��!� $X�P.� �th}iO i�/ZW�w tend�a�� h', or, /,valentlyi�F0 $D=\lim_{t\t&,arrow\infty}z� /t$ � ������E{p2}{$� `2/\hbar^2k_{\mathrm{L}}^2�"�'� e1Ttwoimages[width=4.5cm,�I=270]t1a.eps} b VEcapA{(a) A8$d squared U��{2} �$ ($p%�i�% coil2$units) vs.ݫdoa�ɲ,. All curves�+w� � 5-10%� break-�-�� I�� A)"*M($r$=1Glid u)3a�[idual qu�Yisq�d�tZ�&��m�,r=1+0.00111$�+- (dot�: ��%"\pm$222$ ashe �s). (b)PvHN�(in)mq&n �%-�Pt)�us $r,$!5m data%�e�4(a). It (almos0Zes [/ r=1$"�of DLi�r 9-� mm�'�(on both sid��displa�Ha triangular cusp.}y fig:�M�qA E*�6�ofA�efrb = �#����j$ #  �IFig.~~+��AUrA%� $ (sEo0/�,E�a!gV1ar 15I�:2 s�0at )��� --6�� $D(r=1)\�x0$A�J�(b). Dueɷm� ,taneous emis� � �g �B�**�},�$ not&� zero��eL29s, !��1� r�9�d ��2?�evV�E�0A�D(r)\�4to|r-1|$. AnoQ2 to��z� �dN� b�*H$P$A��!-�Xe�0 \footnote{A�!��$&yI��Q,M�A�$P(p=0)����A �y�$��.�: K-z�4 ^{-1/2}$.}, B� $r$.=�pv-r}5��!�A �#1>d50i/$20e� $100$:AT1``2?) ce''݁hAJ$sharp peak�0��, ind�!D!�p ce ��de 2&V�� ��evc D�MU�3e plo� es�$� surpris9fea�es: (\�}���Aevery b+ow:1 N$e�s,�co� argu� A��~e/ͺs cZ4A��ly ifa�y�era�$1/N$�ir�ive��)� is ww!?dict aIk!F{�-��D�, r=1/N=0.01$� 10��� ey3��&� m] f�  s sm� ��H18$}OS&; facto�4 1/37mbf0��&: SubFu_PRL02e2F60F6��1by us. }-/1�1�>�2��9m�2,� 94�r���,A�!cmaximum!�?�A[o �l�r "�Z5i�� avioXZ? $shall also� �5o��*seU�.� �� u \i18z N� -9� 2n� .�59s)��� �6.� �6� ��,mUU'up�8��� � A�(lower6� ���a�AR !I��1���od � �5,fY"(a�($T=27.8\mu$�K�� 10.$���  :�Dr�]ewj>�2� �u. A"P5G5o, .~h prog^ ��. NotɊ��ness (56� t/mx.)���** mM��R �+E _ s� fitE.� #0 Eq.~�09�})&� ſ< Q���+ys) ijJ�t�})�ic% a re��in,b  a�6�㩸wzed �E7,:l}=�He (FS) $|\varphi_{k"� � m6��n T eige@ te1s� ary e&o:q;�#$U(T)$*$$ y&� �\l(J�=;{((-i\epsilon ��!N3$q0]/ c���. $ : oral���%))$|\psi"��n$ �a� $(n7z� k}{c�,\,"�e}}^{-in.�} #J}$�0H=+=��(0) �.$*=�f ̥��M:+.�I�abaM�FS,�n:��&� ��J�,k^{\p�}-�^{\ast �B(.- @) ; �9"|YJS}�2m��6FSA�!�� 1�L well-�;n:)ym'<#F�jly�'ed in& �} �a t�Bb)'$pAL,$7 B�2�@a ll$�C�Loc� �90,h }. S�2L--��w�? DL origin�--��^�obvK!��is�s^1 a�UA�on6g��indepenm dis: � e-d* �al�'s �Fishman�Dyna_PRA84} �i��up"4 be � 9x%�1�2,i��  m!=� ��AEs �� FS ()Oi��� A1ٝ ). H�, o� FS%�( roughly $|E |\lesssimU w�@� ��(ficY#rol"#!s;e � �$�%s �J-4ly�ed} FS.�*p2<am5} sum��1H",�U!� s go�(n, non-diagMi�� �" accuX�\Bd ��ga typ�$u��M�se + %"b% �d#a�#en!^ �, lea�an5� �~#��� �|�}|O��f�"v2-DLJ�isa�Aava�o]_s �x4d (i.e.��.\). How  %d!��?ak&6 )w $��$��B$crambled? �͎J$y�imY�M the e� &J�Ŵ �s�D to�$u-%=a' T�Hhq-Z�"t�a!Du[1C!�.$F�� � ,, clud>� 5J�3n� E~ 1t�Y t ��� i|onW"� y-.�,6D�6��*nEs, �(��&%G� �f!�e�AI� �s s (800 ns�AUna�oa���*'��E QzC� ed6� s5ing a .�w�)t:� mcps2 .(� �K e�D>$ $10^{-4}$ (thin/ )F $>2 ck 00��" (di�")�� heir ��]?(below)%vthreshol0 �D����"n�,0ge when avoid:�-ing���$�KB�en%iered.�Mek-��V"� A ke�in7*to re$� �Ei"�!close�Go 1��!A I,is very simi�A {\em[ ic}N�� � excepfat�㉕U��B*A���sͫ slowly} d,0�onG )9 ��Gt�K�#$n^� th}$ �oseem ``iB ^ ly''�,��a �:$ce ��aZ(n)  _0+n(r-1.Rl {0� %m4 T�?�!2�s�$2;H�F�`:� ic�Y ��$ime $(n-1)wIo $nTx thus�$�DwF� %$Uq)$ 9 �)(-ip^2  T/")(-iK\co;(  T) p^2(1�$)9 N;"y#�J*[t�F��� �be "?C}U"UD: ''M 1{s $�qd_{n=JEN}{5,!�M)��QFI��$�,PF� adiab6��rox�n�' F Landau}lies:a�!�F a�MQ! n a� �2�),$.remain 7Dk [�FSf �B}9 1�?q$��=is� illu^1�in*v:�c�L�D �\�Dtr� I�n,�B�Inumer{ ly � A&9�! W��šar{,! �er�3A\ ve a�� .s.8``spaghetti'', �/ 1�!ofa�)-�,/�d>�F9 (AC)8 I(&� ��Mɍ�a 1�o�=��FS�XZ{ imEk/ �'Q6ZP��B,A�L)!DI� same�e}�e�s-X, +(0&� duli �"c8). As discussed�) ces �ZFS�/(u $Qt2�E"nv� ) �� �K6"�,�Kqd� u�-�B M�IW�:JO* ��j :�  |c_k|^2� 9*� >F~ "�-v2-newp6��5�� e no �4ex s am�12 ���iRPn8"'1 s $ �$4 t R!ua��1�0 e���UIq.�)a�"s&� -�$�'"�)Y &��c-�=!�$� )�=|1�ps�� $A��H21�_"d)�BrIj)]:�6� ! !2r�u;kB7+\ p^2 ME&fentirl& 5��V�Qn6���Gp�P��, �XvV�O���11�A&� _0$1fi�6"� {0}+N� V�1en$�2� �hus�'�v4ypdf6k�er$J�Yto6�a�)�os !>� �}B:,���{/q1}I,�U1� FD6�aBYF2�7MvY�kQ��s$!#eq�{� coeffi�Et� s��<nt�M�FS#���-%r"�)(�L\M�.A  '' +.K'��)axi�C)5.YR�!�rv � �' ���K),��Z.�� �ja�isx�Scm�sum inJ/~z�.E"�St {a �5�_0)|<k$. A � $ moe�"��a>$�eH5P�"��O >Z:A%��Ms keep%�e"z}M=m  �is #en� s}6R�-�&��R�D �u.(N� grow�<>f �0�he � ("�. �8�  Q=!x&�0Bp;�a t?mum�5��.���r�1'� �����.!P3  .�� . Si�m E"!W�or*al�$r-1$,0�U$� �^O$� ��&2� a���)eE]-5�~ B-llFe�!%?r=1,$!!�cntŁ#\&'� %&^&��� +)�$a��  %(ztect �(� )��*� *�d�0�XH� %�aim_Eq#prNY��A�kYr� �%a�2ins�~%Ueous�6B ^!��ion %5@J* W(t)"Z.} WAbd�Xmin~)h^ �mI"� $? A FS may��iderably� �?��of&ACl��s tinyDbe �edQ�!�a��m�ae"�L��E�af2��1�� a\2%I��({kJ��� .neW+S�RBa��p,m !V��B $ &\��_c$�W#next ACimmediat� �4�s(full )�Mf�&X?y)�,s*&�A�s�NN, 2 ��{c}=(NT)  f"� �B�  I�|e�-"�yre-)� .h�� &lyI@�pF� ;�0hEyiY $^$V!�euzBqui�C<&:ly modif�A �O:f;�'=4�OIK&� d35�=1/!>$����2�#(,�<az^ly ��,s>Fe �9Xdi�)p�1E�AC,��$4&�, ���4t�F�#y,��!> .Y�!s.6I")�Tdi�Q�A���x?nmA�p6u<."�"���m��Be beyo�'2�� Ls}chVA.�of $N$�.s2�.APF>)�e criH@" >A�Z s��d�`�>��!,I�0L�e�6�by vis�1in� �oK��Ec,j!!�b" qM 0.05� a ``fj* 10''2Y!�,Hut twic�("N�j*R e O<��`*8-�<adeIEis*�6E= pro_JM�?mualeU�spa�~, inhomogenei%�BK$F�`E.�+�!�pre"�&s� iD��=��v.K46vi�_s&\m =atI��2M .�D��FSQ�ed d#�� &| raL���w��&N)�,ACx mp� ���� $L\gg�  ab!b" spac�� ������ �J�k�3f7Ld7 �6m�1�*�7�,m �!TAG� �8ryIa��a��dthfW�E � FBu9(a �5��2terva�W��7azJ� + E �4F��QI! Vz�#AM4us"�a) &�1%�!e*I+ cm^r�� AC dY>y %�s �sn2$C� $1/C$� $C*�80K&� >� � F.� $p `c lEP|��?!1|$ .B is.(� q�aY��A pr�&iZI�! 94�&baAK!1elW y,i�V�&, reg�� is b"� A.6 S$ALZ�.},�!duf"@Y/��J` a�$�ة� :t an�]<extrem��UF�@6�-�7]@��.�6FIK conu�� eMu�F %��/Z%Ka#2�>, "�6<6 Indeuea:Fj� AIFAW"$"7yZf� V�,c self") f>!A$�� our���Mr9?�r �&t�K2�h::�"�\�i�[ �!N& ��:f8�A*� � �ɉ$ i�u� �a of Random�Srix�*ory[ �y8�436���8lyd�#cA�.�!�!�$"� $ltshuler_LNC!]tRo�)L93�)re!alway@�J"%e� nonaYity. �SJe1 )� ,�V��D�(b"8 G8r&pu�B �1bound�ߥwmhAC �F�0` tici ng�P $20=.� �JC$:ach�:6j:��"j2�C���.(h�$&�w�$ �2� ?JC �7V�� 6 "X1eQI_"q Z�{0�fa63"N��mKlE�.�|>6� c.$ AIi�D�ns4�is qu� �lDjult. [)A��1$+-=w%]U]if�+"�=�)6�$U-h*�O�q�%$r!6 �=ing�L; �g$ tDN�^�F �ktells �'j%�Xype�p|�eq-�uq lGca�algebra1e NN.$�l� �s_&t*�FaL� ansatz}: m)��&�i.�1"=&p ,_{DL}+D_{cl}�L�+} +2�/�}nTtbel*$4 �W�  $ ]��%�*�1�av t�@!�����L�*AS� aa$p�$� DLfN3c�4 (�1B�;Fn�;&@y �0��}al  7�#:�,%.K a�arb ze�e �j�QA��M%N+7A �&M~�n� }Pf�hd�q �nd286�� � on�e�A��(r9� !����S)G�bR;�)��A�pot�algaDWa5��S�}�*a few/IC �X��$ to�8"� Mm&� &s &6%geh P���� e�l �N than� K��FD}��%Bu �!�Z � Uo'�d�N�1 CRunfortuu2� v!Kng us�,�� comparOI e,��p�Ka�>�YO. � summaF e)��V�.G�D$Q"�� s*XU�7� �7�L� )�unAp3"� $>9i�5�&ur�e$�$��1�65b��!.�9Z�. DevY� :�]PZ6a�trIiI&frame�pM�"� ��(�!�Fl$X�ru%=���� g�0�a�tu$��XE� ;sAQgAt�'2�+y*on are . ob�Uwt�#n�oI!��4D9�e�(j1"���zVr�S�M"� !��K-w)�"�&qb"t��9~-x1� (. m�� ���-?` s dot playQ8N4(-���� O ��i�R  adH � tly)��U� is d�]�"�:i5�3f �n� ��^ *a} �*�)-�G ��� G)q�ID>�6�"}iLW4u�beJ?�Y � ^ �c^ (PhLAM/10 Unit� Mixtg^ RechercheC^>^ du K^ et de l'U�s9�^K^ et RK^[d&�^K6^aJl 6d\�^ Pierre�M�* C�[-Ecole No�ve Sup5$rieure, UM�52�. CPUES� q4��u��A�A0(ed by IDRIS~s�3t>l13}&hc*�FFw?�A894} \Name{Moore)h L., Robin&8J. C., Bharucha�g F., Willi,OP. E. r` _ M. Go1REVIEW{�ULNv.g<}{73}{1994}{2974�T" dV[X�@Ammann H., Gray Rc hvarchuck)d� Eensen Nr�80�8}{411�X�BU-&Ringot J{&{a P��a)3 �{aDv�,5}{2000}{2746�BDY �D'arcy!lBz odun%j(M., Obertha�@M. K., Cassettari  �Summy Gv} f�87�1}{7410�V=�v�W ��W B. VJmp.}{52!�79}{26�Re�;2} N�; G� � B.V., F]fJ �,Izrailev F.Mt Lect�As�b .}{9E�{334}; g Wimb�sr S R0Buchleitner AS!lh�n A}{3A�0%.1816��V�W t #� GuarnieriU�APb�T-=>�We�/}����pNonlin.�L. NxFS�S .}{8e 3}{3�\Y��> ]�Klappaufa A�Oskay Wl,�gc%�AMt La�vT81%88}{1206@AJ�Z3='��)�27r0a� 002}{2241:I��>5 "�?� "%ei,.�!EQScharf Rr�64%0}{6Q�WNVx hD�l}y9�mJ.�j r .}{2y8!�42B[Y"r�?-�Grempela���PrCea��o E SV�A�_�8�6392OL5!g�� u�(Lifchitz E.$0Book{M{\'e}caVh�h ique!�q,{Mir, Moscou Year{19662{�B-Simonsa'D-�:v7��3}{40�PV�jd&�fr�%:�j0preprint,pra,V �g ]{revtex4gB�$[twocolumn^2%����.�k{k�k�;&�kV�v setc.=er{MaxMa�LCols}{10} %TCIDATA{OԃFi�b$=LATEX.DLL!VeÂ,=5.00.0.2552�0�LastRevised=Sunday, August 28, 2005 03:40:14}�.gGraphicsoh32:inguage=Ax7n EngKuAvQ}!0�i({Non-Markovxmaru"�*��;gle�P�<�ary un"��< freedom}"�l$Adri\'{a}n��0Budini$\,^{1}�, Hennw Schomerus  ,2}$F ffilp{ }$Max{kn� ns�l ~��of8xplex �v<, N{\"o}% thnitz� $tra{\ss }e�r`01187 Dresden, Germany\\ {2}$Del%ofl, Lanc)B"by.XLA1 4YB, UK} \date{\tod��1�&�hW��}�"�'kx9�� let�cveB� T^��w<#m: e bi�it�>viron�,�G9n�k a�M,�1rJ�nd*�%] R M=�0dxI%�d]U�vlup���4��G uced memooKf�lter�Earbitr��6i�!�f1r �Gx��5�,Q.we�O�q�ion; -reg�M&�k. B "n�,!@A�|J)ma�G cret!�nif�_of%a�'�hHzgE e&h\&N can ynS'�,�J p�Olaw%�etc�R.Gd�.��Y��n �n0Yz, 42.50.Lc,  Ta, �n0.-a}6�m��Int!@} Irre�'�,2�"��(suKeean�<n embed�AiSs eY�!<5jvl+)!�2�s){ ers dra�]4O �&�qEdC)a�*A^AY-�,�8"�> \cv��zurek,hanggi,weiss,leggett,alicki,nielsen,carmichael}�" S up!6�AF.'5%A�be�5?D)�or �`alism �haake1}�re�b%F>CeLw��d d�y m�d{H5�I�aly$��P��bA�dg��2��hyp�#")��r-���&A!&!&�B����.E� f��tEQ" r���!A�e9Von �l&\g�� �Wo�DakNV��, �~�0-� deriqo�J%�Z�pp��6[I�'7-&)9;g�*pq�T�T>;alr-Zbp��3be motivLE�assumEd-n�*�,�wl^c�� -���MW6�gQ corn oY/�iWnG (QRT) _lax.&Y��J$s multiple_y��e9f %��H&%� %vaw�. F7"ble�:ct>A}"=.Y�ae"�!?O�Q4e spin �N (} or a harm&�$ oscillato�Fe�}�A2� bos1b�Also,�,~�5 !so %��"� ���s�u�na'$1U��� /Wstood �8% {suarez,gnutzs ,gaspard}�gH.�h�,�few�ye�manage�Od�(5G��6���&t�fn �)me �{b�z ,wilkie,b~ ,c�Her,lidar,chebotarev�6�r�n�ab�.��Y�inu�m�x w �Yr��SOa�c�xxebcom� ��s � �}% � tinu(!�or�" walk6 �}, stoch�� *�n'- ^d� `0Xe��y �%4�Y�$  m� "j{N�$� .e InQ,�#��%�a QRT Z�E9�#�.�Mj past�%cpB�iaA7&�Y%�ha��of 6���xU��5��i Q(naturooccurA8!�� � "� s:#�- r -to-&} ��A�mo*#&&!1�  of� a 2�&O K s e�HSK!$~it* ��scmj ., 6b�rK�6�F�)�s�d}7) 4�XU �se5g�~ ,��G�A �G. �FyB�|��e�p�?��1$rewD��k�| ڏerEI ofa��! RFP�Lm�" on�1e.��Y#&/�@6A6�J���!�x� A�l� �nK!!so map�b�.d.&;weB�Xa� a�i� &a� fulf�{-[S �'� bZhEoach a" !Ary�? �D,&ZU!m;bN�= �0�&���r���("�oQ� facil!)� ��#E%�"34�w��6�T.@�,�I�� w=&s�%�:�dise}h o>.�-mme� a�I��2ra ! 2 n"��D���H+%epossi1of  \�XN� "JC"�E�)} !� starXyaA1 l mi7<copic.M �I"��S�� �!� %�V)�c0a�n - a�  B endow���R�� UQ$Ijaf-e�,��-*! �iW��<o�R���'ds%c��v`T}=H_{S}+(H_{U}+H_{B})+\l�+ H_{I} }<�)h&�v>�)% !)\%�tr"L�JiI^=q�\o� s (Q�Q�.�eq:intF|�qd�[3*�/ �=4MU})[(2w i$ 0�(�"jM$�$���GJ� [�v���Ui&a�i a�7 S�gAC�{of�vJ�\lbrack�U},?]=0�5�% C=-l�m]t�$6OK��.�s0 ��dve [ 9� f�g�sub� *{Re~���<*Z-�a�p.("t(5I} %� �.�^E�I�:>0$\rho _{T}(t)s,given byJ�.,hQ [�Rcal{L}E \ t]&0B��%� r8 84[\bullet ]=(-i�Q)[HT,�� Liouv��Q�6 _;rT�6����io&7 i2 s��fix!U���E�,A�"�c v�Q7���.�6or�O�.� =�0)=-YSB}�K� U$:g 1}% � �^�St)=%�rm{Tr}�b[ \E]$"�e� S#!�X Ba�t�>EA�FM Qo�R}P_{R}\dS [(�QH}+2B}�w 5.FI})U}b0),�rho_SBFZr.HHn$2Br%� YyQta� ,-B5�7�t�o6[IU� 6�N�})�� x R ru�ZFhe *�*��(eft\vert R\ c%0 $�mcU}$� i �i >b���F�%�=\`0bo-�E� &$�leJ��!#!>UON{sJ��A= uN�� � 6� F1�8Eq.~(�FMV)B uAte�xed ai t���{Ei� _E�at.<-/SB}^{R��B�!�? !�rh L 1$��3k  Y.�F��ec ��qm%T\,FB���0R�A�z!� $. E� �.�*� ��p*<%oRII��3{# �q�Z�S!j=e��B���Jt��&b*�A�e2^ce-��%�d `% � �_9�]$�7a �ZQ3F�!�  Z2H, I@v� �Q` i}A��I�F�dX� �.�. �a�B� So!�o�:orAg�i"� ��Fd*��ZI Z��% �Q51,c"X,A,b� (i��so}I!E6U�)P"�J!�� s)� W0cg��G��R�ډaKx2� jly lŧn��herO�A�.`SN`��A\$ Cs"p"+>;��WM%.�t!bur(C ~j�E"� ?�I V "-AP= � i�#lcLby2LB�I{�"(6�!B92��&_W��  'st%�A, a*�6 �NsE N � �i\ N� �N� ��*0 %�6/ C $�0 �y����B ("&��\ll 1�G�� !�)�b!�eF�%�1z" 6�Nfrac{d ��}{dt}=�j&B �h"]+�ӡ� )% 6'&Plij��&*�RQ�Zavn 3�= 2����9 #>�>�&g i�'"�F�A�25alջI^.\ eval"�Xa>"M;��� 5� supe"� jN�9�*)�!-}��,\alpha }([V_ ,$ 0^{\dagger }]+.- , ,Z-N�F!3&� $\{@\ c�.he Hilbr �GaW.  Itqi9r�=f:�6Q:M [ uM��� b�E2$+kt�:a�at<s�5� .�'I$M`A��& 2�I`�of*= uX? �:�`�P`aV`�� N�2%�\neq \6ni�_:]& \�3�]J^A.� =@dy s�xq>�Then, ��ob��7!v%j"� 2��"N!�f4 3!�e5o>� � Zhe La�� dom�asNK�M}(uAXCH )e1}{u-v�R})}% �p W0)"� ]GAM(u�.6)�:�l �J� M<.�Y�o �qI�$ue#=!i�na* "U�(i�ex�_n i[�&te�Se8 �_d]��@<� teryQ}u0� �f Bf)��-�O1�O:#a|$G�� emplo�Q�e[1}{QO (u)[v� R})]1���MLEf%F���)��)p6k)� bb{La�YB��ahnS A��u-6��T(u)]}\;.�F7&j�i�en���"�$N�>>��r�S�Q q+� f�61% (3z�F S an}�1�%��)�� �z�KUDaf#47ZS.A^a Heisen <HdE�~?,��.��.y �Bas�h5A �| 6�,�*� Ik"�aJtI^NF+2� ��s�T!�" P-�sub�,v@ �e"&�^� &=&(�E�U�}�E6!�F�: :7Z .k,�)6pUn �*��� �e^{��aS3z R})E�� � (t)S]\�R \notag�& �&5��.�.# }��,G ay}%P&  Vl�*�5���R�R=�&��%+%;��I=f$bf{\hat{M}�%b@.�,"? onep�s}!L�)�����% s�^DV�two � 5���ad"(ANzR$>�"2\MPa�� .A}$p �ON�t�.� ;Z�u���3��]S2��E[A� bf{% .��VFS\}&� eq:m5'�Zp'_R��\��v�(Y��nU)�UH�eН1�Rnd ,5�,Z�2I�c/��y2%��(Y&V �!��6,P&�_ H��st�S invo2qA)����ů>� . B��A1sam��. a�2 x��P��j � =L�66z JG�.1�}}�t}�E%�=-J4 E�b�'# -t^{�� &veF !]l,o>m�!2N q :��(��*N� *x%K�� }���� M%6m�t� rno�Oproۖor. Em4F� !�E� <as�9�,Dr�TAO.|N>|0`confr1dla~Mtle�VileRv.��Jm$e��K$t=0$,H}��s�"m P P�� $f�)�|t�,P;0 $t$."+fUI:;ls.\-}.�F`I��)!* find�,6.3&C V� :�PS �a��$�*�Y� �2.&���hx/2��W�|�84by# ve):�i� ��A��� �%9iI �c1B� �h� ��v�r ccor 2�oY�.�:�d� uibute�Aall��s,5) �regim!nh(�in�t;:lE�@U-A.E:$?n&�H a gV9*�"�6!3": � "�(�i��.jd Fk�mdF�r �)��U&�"p"N��d�&} $% u�!T�!� 4���a!$-� EX$I��`w1�n.'�e&�= a*�& 6Q�c2��Q � ��� ��k6� `]nV< �oX,uJ3P  X� !�N�!TD��eq K(u>�� �F� %�cJiKd.� �.7{u.�"6FN�!2f2r�*� ���-�%} 8� :�&�A�R-3 �F�-L%`)8~��tR�K"��:F V&�#N�ap��d~C�$}%�Y�!y�#��iFZ�B��<��� $U encoJT�� � $!k", 6G�P%}_ � � 6�is��i�d6"0�ea�duseful�>�;�/T6le:T o;�)e&� lZ =;% )���^ �5?)actZ@) r ��thqm Q`� �8��r�� ,�u1 g�B- "3��7C��f�w�tic� U(&� , U�*�)!b*l� fdin Ref. �!?}�!��>7"�>F,>:����>��-M&��!"3+2&Q>cA x)4C�gua�� �*�Ao� . He��by�/�# &6?:�1b��kpro%y�qnd[h�� g!oQ! erveI)�:�"y72�reV�u��u)- #)�>��+z�% `35#F�By& :E/� c� E}-$IM=6ܾ�?$p ).'�-\'.�&@5"' � e arrE� &� ��*Q.u�#{͕�!A�{I}-wnE}!r���1R3J3�)�f76R_"� u jjw�J�j8"�waiJV9�p�2� s�dto� a��jFo�B*o =�t)���(t��tB�U�0)"�� �� JX!w�E�QEbQaZt�10#=[%� )]/u6#4(2q)=d6� .$Bz �_�՝te2"G��]� ?'`nx���3�C>��(st!x$Zc�0coW����-c�,aV�%��ɻ!�^� % EB&b���1 va�nj�)*�~�,��Mv�?� $�q [>:]56H5 � � ��`[v� ��$w�&��N�4a%�G�&"Zd3�Ѡq.�3i �aJ'e���au $ p*!�ecu=~ŹgE�&I%g�� ,�VqU=1*�x$���� surv�.� assoc!�kC9A �q�)!�b"q�) �� �EI�2Kany.�A� �.L-6)f l��tA�l ��un�� ) �� zMa&)?&�l$6�6� �6i;�l&� ��$6@*  \cdo�G296�noB-V�%&2�a�B2#!�EDed��2c="��e  ��ֱ% ���.t:��@� !�!� �**"� ��&mGal/5@ko�hriM{{b\X A K(t)E�iL.af�J�-e�� Wk7R .�g�% {Coo�X } $fb6wo"m� (t)2r&�Sf�%,�:%�% 5%ptep�� u" 5}. �R�o�*e�� $*�jA�Gt!��� $t$,� rega�� eD�0� 9�O $(0,%RV� i�%ads!{fdi/�� O %itAksCtege<,Q5�#$%%�=d�/d��%I�1�aE�� �5�2r.�!t� � � mu���D$�0"��>�2� ��� 8�υMR]�y�9� m,�KP V��K"����h� a"�b�/" �7b����Z�0R�(*� iK=a/�V renewa� cesses. N�StheD��eir�7�kvIp�x) �|Ũ�hA�lem^7E��oD�6g��a���MACi��* 4�})�T�u*���EmP�V�zKr,pickR�herzogr}isKKK�Eean ��rom���H)��"�Hump�exc�8lN�j sche �.=a�"=�d �Ubޅ6�a�Poissu�w&��a{��n>y "�I��gg(�c �s�" passa�%��r�CQ�esAA6H :T��umpZ�K%g"Ienls Gs�mkal:��6!�2H"�D{De�A��HF� � } A�RKIa�u�5'Uw>v)a2I2K,6�9�.�'�@ S}=(��� \omegRA}\sigm z}$_��l.A�R$Pauli $z$-$E ch�8�onnB*)?��B�*%��(e�YB@�54�IA�,J "��(*� "pk�L2���6([��,]+ " _{z"7 ."Jqf !�p JUB�2�)set ${\�,Pw}}$!�*YŜA&d�As��u1!�� )��^ ;D6�1U& :���9E"j  "A� TV�=z�� �5� x� 骅!��TW 5a�as�"^%4% {2��sW-C:2N�G�Uly&�K �&r ����"e��i�.��1@e!�-��a)�m/QZ'^� g_{+l> �+g_{-y�. I�"�sol1}�(g_{\pm @E}Q[1*�0sol&�@ ��$X��C��Fexp [.ot&�Hs=�XDE�4ƺ�Mt��D+a�-i��/Ls�]a<��bi�]\[A��X]!� k0+ .CN�s.h`5@*�2&�R _ "�`Eܡ$l�J �>�QfI�� X'Le0�0�] �E�3&e QRT,�" ��(烉� #X5 #0�`���l0��X#., \{Im _{x}�|y z},I\p�Z!�ex��u+��r� i�:. ��SZF� ed [���tlg�n���m7��R}5�@Lp�éz >� �#�!$]� �L on{E�'�ZE4a� zgc} Up��=6�� unYB��EBF�S��X"�S ,��r q ��PR6.��! �~�$]Fz�#Ekinm{� �}pD�#Hdj>Cd�!{e( �:i�)�"�)vR�"�e�+�%J&N t&eA�6�:�&�B�;*U"e^{�� t���9�)s �c�&B s�t�^ caleR*@[�#�Ѱ- .�,\ : C �<�A4F��G����!w�_� �^�� �-3� �fA4N����f -�f� at s3`-A[>;h(t$ $<$ $1$]�%$lim {}_{u\a�%�fty }i&9%.�O/aV),$" 2��{�=&N���*t T�� erizj*$.�&J��im\h ( [$!>$Zj021-u�.�.$ J!"�_0�!&J�&we�$5�.�� 0^{+}}�o? IG5>S.1�2?)P A1/.�U�3�*�N����f� �<D��V�Y#*�T -�!��Z .�< 2!2� *x!)�\upE� }\&�= �� _, }t}+P_{\dow� o:>2�.t� �&�5D Bf=`��O [$ � .�/.nŇ�<� � 9% \eta : N�B�%5Ci�$\bS[U *JYu��/1t z�}]YW 9 ��`#"�!�uMRa�   ten R(F���I.���q�(&6�:$F+ �~ (u)}&�A�twoF�(%��u/[u+%�/�ZJ&Q.- )]$%8WAL !���&� �Eul �N$5R�}{1B�/u� xV�����\�e�Gm���9� �*[\9� (t)-)xecAqt1 W��? fluc��A�Q�}Ta ls d�o5{�b-C�W ^o�_��%�b�"�->Qqyta�Q? ](1-�y M� �$% 1,1-QK>�U�2K i=)X$i"�)�l>K�0-�.RQ!)m���&� � �9�:���yA$�� ��/�'~* �$ �*oC�%�"L�4��K_ &XN�N-I�ol�3źT Now!�&� �a 6� �GU��4 ��"ha �� [$ [$0\leq RN-1$]�#* V"80g��7"U�! tant >L"U�^!t�aQ !� �-,R-u de����o&� wa"� H�i!�asL�a ���c&0�N���� K�bR],\;���m' a})} N}z6 =aR]F� ^G!9"}>- �"!O�)/� $% b�a8 dimeԹl� pN��kte+ Et�]!�!�5�R$%�!@� � z%��$$% 4Z� �{N��bR/2]|R�y�R|�!�D��&�, $��b��ff =�*Gtak��$% a=:#0}/kT���$B%K!d�-E�ofͣ1A�qE��.��  aU��~&? �6e"W�Ŀ�� �DűN*�6�U�M(�*�� a}}{ (a+b)}\(�Jef:,"N1aN.JUS��)U!>��!��|#i&n�n�.�ӥ�z�-�3)�%6($V�&@>K Ɗ<)�$�͖6���D% From $\lim {}_{u)�arrow 0}�1� 1-[u�jn}!%au� eB� of m�e|ra^� e�u� fittq�fcutoff!�=�,$ after impoJ�M�(I�/ 9 MY�=Z]�� -1$. On� other hA��onstantQ�$�sdpower law regime. In fact,�g,the limit $N.�\inftyA�_average �_E�ime Eq.~�v0}) is in��@, which implies $)e $=0$. Thus,Z1 >1)F.uy8f� ~y�a pure= ]:����0metzler}. Th�2evious��sis dem!nAO!ba�� transientPbetwee)�short�1zB�sA�M�j$scribed by�!� law. As��have scif p�se��, BE@in general reflecA�by%�8system dynamicsQm Ym�Enotic�Dat whe��Z=(by maintain!�.L!@AB?:A�xed�e fluct1A�7$�Pches it maximum value�wI�Pof both, strong coupl�$b\ll 1$%�$small popu��$s decay $a %(I��� also�Hd as a high tempera�� {)exthis �,�?�Y; $t<\F:P��% 2�distribu�Ñ�#��ima9� &�ND.��KA� }. +}� },\ :Ŏ�Du.�J�7 $0C�)/I` �=�`��esea�re� ,s correspond\ \textit{ !�ab 0rivative evol%�}�e[ ,� stretcheddon� !�e� ��b Darises jointly. \m�{ConcluJ s} We�!how� at aq�a  ,osite bipart environm��(Z �#�0-to-reservoiry<$depends on�*degree��tfreedom) follows non-Markovian�k even�MaeitselfQ�ea�nQ�a IY�iH he 6j,effects origC!�ent� �of1&E|�media��F� (may persist� (arbitrary l�h�1s. Our�� are dA$ ed f> a random��r� m����� in �9�.���a%qA�mak� $ll contact�stablisAztheoryidissipI�)�s) "f�7�"is basis�fo �e .� Lindblad � s �provide�l� E�a8mappingEJ�densit�T trix)62ial�fiaxcondiAs, aCidaP fied�S quantum-rA�e�Porem. It should be no�taG�.��ion�not!�tri�]to1� mas9 9butQ�ap/ �T�u>-� cl� g ex!�>"-Umay al y i3^at fix%� . In anm4!�2_AZ in�� abou extra}% �!introduc�memAqɡ A�V�6� �E1-interpre!� ermE*$stochasticA[c hq�@ Hilbert space. S���gs!�g�e�V�to ���cob� �t�{ U$ disc�@ manifold of stat�&���k��%flism sub� i& � on:�I Yh� 8barnett,wilkie,Ɋ,c��Ler,lidar,chebotarev}�� puts�qm!uI�altern�&ag greaAءp ve�M�Aembedded!�a R�. �mot�7ona: stud� is kin!'.� � %�rec!1experi��Œfluores� leq� dots)�% {nirmal,michler,brokmann,grigol� jZXn��D scales much large�gan $1/ $ wG(found. WhilL e under�  physi$mechanisms�/�Z!;�& ly clear,� ha� en argued�kuno,s� gel}��9%a?ɑA� only�recove�� one ��;ad�d�>���od�� ��U �?besid� Q eoree�estA4aD��extEW� :N��in open5�M�3 racteriz���� �[��!l" �_s�\be� of:�osS Q��#BE believ!Aq�qС�be usefu�o mode� ! �ofR�2p�lex str? !� host2�� ` tri- %�a� investig� us n� ally� Q2!�!�r%��al1� of aAordEk� ensed-mat�L=v��"� EA�'a (say,& ).6�W�٥� ngth!6�I�h"N .xi�l opor��h-��of �� VF} chQ{ŝfrequencu ; �;&a��� turn,.r 8r8(e.g.E� di)k1figure, Whar��arap �).�lQy!�r| into��)��V�Q%�,then becomes�� $ake1} F. H , \emph{S! a� al T� u �C2� by Gqized M�E��1� T�"�Moder9�� dbf{66}V�76�lax!� Laxy�vy�12A� 2342A� 63);IK it{ibid}.s157a�13*6�h!9EH$R. Reibold2zA abf{32P462�'852 suareza� S ,PS�yi�8I. Oppenheim, JA����5(9�510e�922dgnutz� }�$G�9�Z�2B�101�63�966Uaspard}�'G Q$M. NagaokaB�1�$111}, 5668!b96��� M. B�Z(S. StenholmZi(64}, 033808��12�}!CW-E�3E�6!�8D0);2C!u )uȡ� 7736 n:T)�} 1033�6��A A. B��nv.]I6A�042107r42��!: Daff�0K. Wodkiewicz!� D. C���,J.K. McIver, �%Y�470}, 010304(R)JxG� Shaba�>D�Lb.gXA020101X6c&� AA C� C. Garciai'LR.B. Quezada, Math. �>1�6A�105Eu6�(footnote0} �" very slow" ��$$Q_{U}$ (mz l�a�*��x�<�U X , will adiaba�ly/z &" � x&|?}2��1 ��factoriz{ 2� )"�SEU,�&�r' � (be2�u[njeh�8rator techniquea} cas� o& �i]d on /"$ ossi <�rre���A�th s�o)�'to�� i�;is"�an�4inhomogeneous upg&d=9F� , similarq6[en�#e� 6mV�3} .typ0sh7^supero�Por $\mathbb{L}% (u) $%S sum!��66s, each�)�itT *� I�.e)�a�$,of*�Oa5s�� Refs.\ � ���6��"� Q�4}� a�Mc� �(cal{L}\neq %E}-$% I, �(E�!6ti�2O�s"n �se"J.dw� l w�f�ia�a. proced� )) }�}E!m2��o!!� �d% [\rho ]=\{$I$+[e^{\kappa9 $L}}-$I$]\}+$� �$ )$ mus� �nde��rol p-.]�a�%imada"TA�;�l{"i�7simultae[ly~\P&aL$��numbe� >tsn uni� � goae&�"5l� wbe!r �Oby��sB k�2S$f(t).�/1"\)�% {Co1,gBook} assoc���f�$w(t)onYc�}�beMMly��)�"gt �m ita�?�;(#�it � numer�Jmetho�sol�[}�`u�.>2F� dou�4P. Bouchaud, A�",�@C. Cohen-Tannoudj*- L\'{e}vy "u $Laser p2~ ~~ 6 �J 5} HA�!� step&) $\th�(!�!N defi�as $% =1$!� $t>0%(;=0$\leq 0$. W� a� S�!�3�E}|_{t=0}A% �zol�$ M. Mart� P. ZZo 4� 5774� 86t pickles & �CSx P !� Opt. B: . \&� clas�o 8pD :: herzogH Z�5� 60� 96 alemany} AX �� A: Gen&3! 6587!: m &~ M %J. Kl���.39 U6�d!� No4 B.O. Dabbousi�Ga.w*JMac���K. Traut� , T!� Harry�L.E. BrX'N��,exn83}, 8-86� tE? P. M�a�Imamoglu�D.�on, P�Car $G.F. Strou� nd S; BYto,>�406}, 9� B�p} X�} J�1Hermi� G. Mess�P. DesbiA�E�P. �Y�M!Xha��� LetA�-9!� 1206#B&�yHAquino, L. Palatellf P#g��2� :m!�05m6� �EK� D�S+m, H.�)�$A. Gallagh!�D.J. N! tt!1 �M��1n2N&  G. S-KBohnenb $I. Potapov �A!�ws2%6�8a� 1374-b6t�!�W�,Z Unit<# Tran&��" Solid�e�Dics} (North-Hollan�Ymc!(dam, 1986).5.>9  docu�} �I\�� [pre\t,pra,onecolumn]{revtex4/Pusepackage{amsfonts} :� B symb6�icxWset {MaxM�"Cols}��D %TCIDATA{OutputFi�=A�x2.dll"V�4on=5.00.0.2552CSTFile= � .cst.r�Z2*ForMod.11b0D-�ShellcLArticles\SW\REVTeX 42E$Language=A- n EngF%�,TeDefs= %$\Psi$ %} \newj%emA�h$}{T�m6$acknowledg� }[ 7]{A:2U algorithm.16+xio2'2# clai.#C6#"u(r&�(B-s6, >XMure6,:-ra�ry2,6+ri�o2�2+&� WD� � 6-exaP3*E 2Texercis6( 2)lemmaNL2#no�2�N2)proble.�P >'�2SP�sJ�remark�R 2T�'S�:)umm6�S P*��Xof}[1][Proof]{\noindent��P#1.} }{\ \rule{0.5em} ,H��0} \title{Mani�-ng&="�%# asph  l� \s } \author{Zhi-Wei Wang4email{sdzzwzw@ (.ustc.edu.c� 8(Xi-Feng Ren7mldsbj5Yun 6H�8 NYong-ShQZ�G+-Can Guo ffil�*(on{Key Labo�� L*�, Depar"�W ics, *i of�c� T� ologTpChina, Hefei 230026, People'sFublic4*�)� abst}�,(#�g#�$�1� to m1�e#e wid�7ndE�� (down-converK( beam�s�&�#r"M(e�%e two-phF7 o�+al �%�mo\um (OAM�"o,d�s� aS.n�&ri, OAM �,,) ��te te-GaussN- (HG)Gs"�,;. PACS�@ber(s): 03.67.Mn, 45.Ud, 42.50.Dv 9y\D,e& zgskip qo:�/ �LI. INTRODUCTION} Sp�, _ric.��. (SPDC)5`(nonlin!(crystals is��" he m�$ff�(m�+-�)=z)� pairs�Kwiat(����und�ofA~y7+�"o� m, commun�,�pt� %� 0�z etc. UpA�|8�;�cArA.&�'s 04�acA� on\ A�d3)!Ral+s, nam�,qubits. Howe5A� �" *�)�spa�-�&.!{l)TqQ�%�!�. �"Q�fa}ex^/in"�2�2�+ s�*at it )a�mi�:�3� new-typ75otocola =t9�!K r9�I2,3,4,5}%�a���FX ()Q4t&�)/-6)F$nd\=�f'�. 99i.U\+!M!�1J%b^� �� �dArnaut,Franke,Mair,Vaziri,� fo�f0is u�-� v�. Noo+-eB� )o� aNA:B�Ebe wr�9n��herent�Deigen�΍ OAM  � �i��%he � itu�*�ach2K�19a��B�pof pump a�sigac (idl[%�m z11}. So�7 can :��0��E�per sel��{3�2Q��� �Qly BV*]^�&a� bR,�.ussed �HG}% .1is�,E�i �"Y0 $\omega_{0}/ p}\ll1$ (Q!m56 J�\%E:p: }-5o�: satis�1QHG6�-�!�%� !> �lb�(n AZquasi&�&&�pK(,!� find)w�?B�M�%g!��?�- choD<>` �? & "bs (�))�.�J6�)-# :"�:sAw�IS.= help<� .�re�Kx en�I�N�. S�m�n��HG�5��%) �M��,��mN2\II. THE THEORY ANALYSIS} 3��s�ȡX�Em ligh�incm4 �(F��nNBz:�g�5�"�)8robability. As �io�bo� �8Dn9 A�f ~ �=�in!�e��Fls�*T8A�,xial Laguerr.� LG)qeiY!�rr�<well-^edb�[Allen}xe a�, $LG_{p}^{l}�?rrJ>a�A�$l\hbar&�l�Gref��a� win>,2a6$\i;( p+1�) !� ) of r�!l nod� S��18�=0E�%Zbe�a* L�{ �11,10}%K ��3} |\psi�B4=\sum_{l_{1},p}22}}C_{!2}!-)$,l_{2}% }|%D}; .2} CeS{,~6�Ew�U-�2L$\ & ;B !?��!= M�%� and )�� � 2}}$).5��E weade}T�  sP��giE by $Pj}$=$|69% �1-;}|"DE\� de�>nV.e{; det�{}��� � ,onem�aJ�- �1 1- 1! A�)�7&)25=�$�.� 2q Ŕ� �" $%�=%~�ns!:�6ic�^P!�� ��>e Q� 5�daNB>^�=-eBEnB.�F% C_{0,0>�]�m7I�.F� J. P. T��ӝ�$R`�SY�R!/�����2�1�c 4�QN >LG ba�G\" $. $+ly speaH,f�ncrea>�[IpA�but�gre� a 5timL1A�HxA�� � !B@of 9!y% ]A���#T2lor utia E@JE�ne)QiG di�( ent �*i�Y&le-E�op�fibU4!jc�-er-��hqra37�:que�1�7� �3ble �.� � c( Pan,Arlt,L� *�#&� j#uf!J օfi�A�0}$�� "���I"�!i�1 � be d�Ps"? !�!�"� n �D �o�;iQ0c���.k%c/ng��!�� ��� ��wa�2dis��a��Re>�Q& .�H( �F t\in,!f�� {���A st}E�� �$  d varphi��}{]Ba% ^{0Bc.}hBXE int R�6� �� � T �}��^�F�K v:Z=0nexp), -�C{% % {\��f}7n N�$Jd$60"B�afieldQ7Ik; eX1 $d=2��v5a& :dia�4Pbe�5�++��a-p�Ѕsassum`��alQ�2*�C"�L%� e]�{:X  > inpu�rfaJ5Oc�8f RB�. A��is�&=I-�a\prime�  h2��)$z^$ #�,ta�fB5|���"!$. By virtu!� t2��Jas�a in Fq8 e 1:F�\B�2� 2a�� 1M� z}{fQ� A�+M�pi.?4?ambdaf}F%N� 9<=�[ �(.� �6� :!���i�] fi�J�W� calcu�%�� e6* �9 ,z W I�>(EeO5�if��vfE�� ��]{>�� Oe"�e��>g � �6+�*�9D� � BBOVzhBX9 s�9t R&�/0a �Aitu�9K�! �* $R$,a`�ing; n!#V�av.�#�9  data~ �mal�J.az`=��B meanC�qu�DblA$ Curve Fit�E`�+%mch�!KleN+sq�4s fit | a�OrjGPro 7.0%Yn�i�R5�(6�I� �ZV��+$z4)1� Er1�2i � E� $\�G0N easilKFn�)�@ng an� !���O� �u�M.�"��HM�!jq���0� N�2�bf{III.�( EXPERIMENT#FIGURA: AND *�0]Qco*�=!� ��2]4BBO\ (ZMbarium e) Q� ickn$1$ $mm$pillum`I�N8monochro0F c argon-izla!Z �^�ag�E$z$ dirk��wavel@> �U��![=351.�nm$�e ^l@ pa�Man6i4 A $(f_{A}=500�)�$ plac� .�"�Im2\� V��. AfteJ*� ropr./UOM9(phase matchI�g?A�:d�Dp_G!:�I� at de& 9<n$702.2$ !3!^!n6^{\circWof� %)O5�9la*]A� ��-iT2� BA�9if�� 8 D@�epor. BK�K��a�B terfc- ' (band-�4 �|a fix*�Hi�("-/�Qw��2)"E� �6@ >� Bq.U T3�h�5� l axw4)�06� �to �B4 !!� i�;.BݛN(1�7�.�D�}s�%,.{� B�Hs�YN�*0�An��BHXm M�)��J� &� .�is $85Aʁ����ti&e"` �W �CiE�%$Aj(.��-�c�N�Ledm�c+�%lef�D\9�H . Itє�S�!>��`&3 ��8T � $D::t f�Bm4"� U$�Adev $t<ch !X�ly du82aQ8 � whenQisFp"� !r;��G� A} g@�a]Isc+F�&r#' {4� Eq. (3)UG 3 �L�}I-.�!�M7*a ,& &1 �!e9a孶 A�r�2� �"� BP!^onr�4��\�Er�toB� ��bY�, firEDhe rol�5pl playw #i� �/ �\A=._H&C.y%AD2bby var�WcB�A��l(a), (bc)B%$$ f_{B}=100%�{ }mm9�IB�[  ,a}<�,b}% c�"�QbyaK�N��/�three1Et� ��nY�h�Z getsqa� oi!vbNG�EF[_ur4Z�if|$!O��&cH5,d),(e)|G ns B�� f��20/ . _iJ same R!�d�Rb6� % r�%�XoodMk)!��$y}N��warT �et al.��-��'<�&����be made18by deK�?E�� 0.��-a�h) hI;9 ��a�" 11',a��#��I�0 E� }�B�go%iJ!s�$ B�;�,%�J��wW�26v v�0$(0.024,115.1�^ 6,114.7)� %95)�Y�7ively d�<-&5Diqe�! N�B "�(0.083,281.6.� $ 0.078,282.A��8��w �� ��*C!� regA�to&�� of-���obvD\�B1Enct�-Q�, O%m�q)�aAKe��it{�!�O�!'�\� 02&y! "h 5a:Qm�2b3esV%?���*4:�  ly �Z !Zdra.3"l�X �^ � %>�%��f��c� anal�>����Ne2. -S�]�0}$�Fm%��%l?�@�� < A� " ^�N��n�1ZŁ�N��.�,�t�= 1)�IG�����>�*�#*�">OAB!sB�[ ^+e1%X tech.availA�奁���wi4k.�W"$ C:$�[� y �]�*any�<ora� "�+��8Horodechi,Mozes~'\��B�&e>�&A��Ys"j&Z, �Y%_�f�V��&B�- �GU2�6 �?8V. CONCLUSIONS}�LR��y�E��=u�b& ef"~�6E�$�=��O fu�f��'acqui4��R}.1"�%�>�)�#}�by^XB� �W�Yhto"[$U&y mŝbeYv )car�.. A"�Uly ou�Q�pia�[Tto� Q 9� ~���'b�$�erM3u<$ACKNOWLEDG�S}m9& T� work�Qf�V� �Na�=al Funda�&4al Research Prda=$1CB309300)o<JPl?ural 2O ce F2�/]2(�H4017, 10404027)i� Inno�_on~s�5$ese Academ�2 ^=>`:�P �v%�1�P �0�<. �0,�I Matt?HA�in e�O Zei�B ,V. Sergienko�  Y�IihE;95i�it{�3.N=�;&�J75} 4337�&�2}H�ch�< -PasF=uccZ! A. Perj0>^a(bf{85} 3133.a3}!K ourennane�> Karlso�/�<BjGSrk,g1 O.�A�$64} 012306.e4r� W. T�.l`J�A�$61} 062308.`5}G�$Guo, C.\3CLi@\�Lhi�=L)6G. �Juo, 2001� it{\�5%�A @ ,O�42301.qA�/�H. %�G.!�Barbosa^�)�)G-�2820E/S�A0-Arno OS.\�=�M%��%ad�R�L5Rl�D 2002F.�5} �M22�#A,�V�0� Weih�SA2�!G �it{;AY412Ew.@ Tg ~^2^^=89 }2��2�"m1N.a� , R.� Dalt�A�@�Qrv!PT. O'Bri!HG.Pryde%GilchrisT\ DpBrtlet)�A.\%+hit�R4��93 }05366�11}!�n'|,Alexandrescu1� Torn���AFk.�$8} 050301(E�bf{R}).�HG}X.a=Ren%�� aT!>=q56qE�}=341iIi82��,U�!�W��ijers2An%��Q.�R eeuw�% Woerdm�B199v�45} 8185.�10:_YCyanvaNZNJ ��%7!Z231J�MPanI�BN��WCn�D Jenewe�CG�auc �_!�F�%qyk$91 }227902.�|'�A��l�� Dholakia,�1�MI�Pŷ9 �Z�59} 3950.o�'A2�%�!�T>�>��g* Cour� EhJ�:�88} 25796D)'U� ]� �Yu%�R�y�J�G"�;gW�B- � 6} 242"# }M�70 kin��z9�.[e>04>�v S.�"�T!E��Rezni�J�A i� bf{7.�01231a� ��1+OR�$"�)��oug��..�F"�"\righC#�$z,"5 2$� tq7 V6� %^)� � �#(aUVR�j4l. g A�b&�nm�&��!-(5E)�bf1B2} �cexw=� &I^ g"CW \u%&�%� { }n*fg �"  n"Y3 #.��; �Ax "�q.�sM�. mH3JB-lx�L �$q*�M�or�J�0)�/>�FapO��� 6�Rzl2;R�K3�e�� �� d!) :9 %&�%�>$"Y�" �Ako9r�a,��a"���. z�$>ce��i�Z) ( 2a%R�) J3�f:�!Y B �q�.�}_�1�> !�6�)�6�&�f)2V)g!�5�>��Fp,dT"!��e�.� ,d}>�e*%�4>i�4"�C��%�p %% Trim Size: 9.75in x 6.5in�f(Area: 8in (rkRunningh�w ) x /hws-mplb.tex : 18-6-2004 NX f�zto!Qig4 cls !te�"Latex2E.8#ntent�r�e,m�dnd lay�k�is sty��l.2�%%�t�{`�6 P�Csh�,Co. Pte. Ltd� Copy�� 5�by~Et All ;se�nrveW� 6�K{�cclejD*�K"�K��Kepsfig6>b�I�Aand{\ket�F{\ensuJGthL,|{#1}I\�z�Fne;braV;6xA |><�jprod}[2J|A|{#!{�Z�rmvec � bold�Lol{zVrm�>}brm ��/syB/#1>UR�F'wBN�sf/gH5�sinc}6��Mrm{}A4��u &Erk�h{Walborn, Nogueira, de Oliv P\'adu� Monken}{M�f�0H�G Ou-MA:l I�& ometry} Rq� er's�� p�+e ign�\:5�.��� ( @I���H\fe] sizeK P. -:{C.]& �H: sw)c0@if.ufrj.br} 6urN6�+�^: Ins�-o!�F\' \i  &�Hd Fedy do Ri,Janeir�aixa PoO.68528,B$TRJ 21945-970, Brazil},0A. T.]A. N.�YS.Q�ME[k*�Gra.I�yew�%J os8d upon dYIh*�92h ��Hp�F |���G. s new el�E�Di9Z4/se* s;��Ţe�h vers�>OFpro�o 4q V]XC��/;�s. W� �B�:b.��-�d5 � �~ � c�#".�$Xito+ +[Zt �p����Suc~o4?nd=0*�oa�.lls�GA**8gz�%�;= *�s.�B�IX ]xI�dun}�usS �.?etwo T,)!spl(r�9&�q�uby%�, O��(HOM)\c�� hom8�dE$��mea�?��' �val"5 I���[J!{�9"H:!Pco?]�.�!i7d- TY#o |d*q+$accuracy. JE\A�Ve0'a7!�V' in a� �!rie� &E s,1am2Ees+?1�mFrcs**sus loc\�Cs�: shih88,to�i son9�dFM)a�urs7+- � tunn�pime)� stei8V9�Vto�]w$ tasks suc�L BBO2t QbraunV95,ple96}%�}Q�<o�]logLN�`� H0klm01,ralph02�t mong�#�, A LaHOMINfe�z�*�6�e g�fig:hom_ ?K  T.re.CP�R#to op�{,fH>2 (BS)a�InA~ir�zlB,��� "h�E�athM�%�arms $s�% $i$n ad(,N6K:]�:�D2uRE�sym�lwol �� overlapvfectlyJvILsR4�D�T�3thr"�$"MG�! . Likewi�ZI1�Inti�I�t J�leVyin*q$ uA)2�Ko�d�2�*�0Vx�%�rstoo��^udU �!70all bosonic n�[�&lPe/I�z�<94}. \par Unti�uus']maj!V� �K�&}.����!C�d2 idea�+no� (on�� ) si��� ^:iAT] \�e�me{\? {��$=fig1.eps,� =3in� @vspace*{8pt} \capa�{5�belX2� IlluAR&!Ea2�U er.� �Vb MK�D Kbr involv!W&q >a\��� 03a!�I5+�/W9a�at�5�}��Y� "� .*"in"�ue�f�*D|&,*2��&�Rl'%運 MoreA�i��#A.�2e""Q�0nhyp�3S}: *�"a�wo or m� F�$+*d)9k�Q97!6Co�K!p�H,5 iple"-(��u� s  T>B�x�M� �*� % ">8.���6aC� will,/� !�}��e�"$d ��E2!�� �~$sec:mmhom}�+h a2C �R&� ����Q��&_*"z� then"� B2t 2} ��.? �66����=%�,JK-"�. �&�Z@n�%&;�;T�YQ�sS�W}��Z!i%�}�V�%6���._M�taisfU{Qd| elserII�hong85,m'98a}.�/a sufG'�Zweak cw5i�jU�u9m}be��&�J�{�J}_{ != CJ vac}} +2  psi}>ͅ � $F<$vacuum-@aa -O%a.�%gkco�&ts9G1i; 2 reI�e�$|C�J| ҇\, 1}|$. U�}OI2��e��R ason�*��L��h� raMaroxp��:��saleh9xn"�hq8�B*n.E��4ec y�I| reg��i� y cl��� �TO;%xia�I�� word} magn�Rq�}�com�� uo���~i2���,:R26ԅ: $|{q}| 1� k}%�Co�4�,sax)\I�_�t�72�Y=>pr-�=l� 0$z$-dY<�W�x'[�B�6  etup7) orpo�?}�j&l:.�t�H�P t tw�;�&E!(R.�-�.%Z. $���hHP��*� J��G �J01}{\pi}\sqrt{�F$2L}{K}}\ v:�+9�!)\ �� <L|.$s}-.i�P}{4K} P),�Q�2� Y���.�)!sanb;�Nctr5r��1=c�1�"�TA|fer��͕^3)k*� $L%�c�-�F ZAk$K/B���e��. �r2I thin�!s ($Lћ2Z a3� $ �z� Rayl�R��Jw� ^.�Y��t&��҅Z�ant. DE����b�*! 1��, �&#pyI=�t n�QF�q"�3�2� and/d�A ��X ny;f"�tu�J3�Z�d&�T%�maq�N�2\>��Nld�> walkC9`"0@birrefy�B�� �f"�:neglig�v���sE<�F4 al� en_4��ED+4k5}1a�*xfC! n��$ pertures.A��1A��;�Xl a�- kr M';.�s�q2isAA�amce� BmusA( tM 7��tYEml�x3fac��BQ�@��K rBBX�bi_!0dI"Q�,.X&/ s"Sco�&c�%��j&X^ahwfH-�or�i�l@8#8N� � �A=T2BuI| 6Z��Ie =A52�by � -lik��pGaBDe�#brm{r}_=�$2E!J06�vP}(,1, 2) = sy{5kV#|^2.�PZ�aPRt&�9ѱ�� .�H ��a/�]��*]CU U���andelDR v� = �!� rm`� {E}�^{(+)92)1>1� C.5wfZ6$Mj:M& �J_o�Hd5�=(x,y,z�vn!- 'F,NS�B|8 = e^{ikz} \sum"� \�   dEGq} \, Ja}_{j-*qQ )5"({\epsilon}_D`I�q�� dot + rho}sPq�O}{2k}z)2� %BU�X�a!(-\V�� nihi�E��i�A�> $j$� �HE{"� a�q�]2�:� 1 {�e�!�]c>��a 8oO|rr r$kEmaj���Z�.�2Sh�*�8�AkOis�<(pgruN6M>u�6u. ab͵ ��t�� d $r% !;�m��Qnd* �h2���2�l"d`,p"� I�*�2=AF"�, tho�3anO�� 61�w�e| +%t key"�ce"ty��N�E�! A9& �� 11E�he $y$-�CU�&u���E�|3�eqA �Pb}yPne$Sv�g��wmirro�5�kZs�%,+ei%cFq��l�"���R��3a*�2Y/��E�-!W}%f�@����2A�|Z�F��+ERB�2  to��J%�F�s ���,*VeQ; �Gv�� �B�B�L)A�a3����eq:%c &l =  _{tr�'r*}� "76) +A _{rt42N42B4t.4h B_V�+.>�"��Vw $tr$�nB�QDM5�A)i�%!$�!i$ !,�qE��"@�%E�v.[rtLN"-E*_&�*o62.8�l|.mW��6m� 6m*ginI] qh�r\Dm)��S�?���2 �&�IFr�ObT{1O,yz* d "j{2 &2&2}&2}�Loe�gis ne ��yD+&R� ar7D��ax!��-�z��o� if?Jing�W�t`�� $t=r"�6�X}�P�wf2^.!aaN#"�� �1fo;Oto� &_ �*F�N�=�?2cV�^�`%�=& i �b3\iK}{2Zo;[(x+-x^2:�+(E+ yF\�2] \�Pno�k\�*s*| $psitr}\\ &c["�W �tx�+6�}At�- �6� Z �) �7�a��Y,)= ^2�+ @.��.y2tT���-ά2�2��) �]"M%-�? >)Ps�"�7�V26V2�� 2}+ AW2}2�  � �VrtEV IWj�26X�b�fg�AXB�2X\1#BWE]h=�2}�Wn�y�2W �q^�2�:V2�V�VnY=& ���.�)�I1j8& ��I7v�nEI&e�+%�~qa�Fh��BP�N�V�!e-�1���gr���RAn%Q)gm1 s�h:�!y� -&�W.2�"#N�nv�eoose}����� �o2&�a�)RB$Z*mA� (X fac�-S$Z = �=�� &��Ft� ��!A)$U@q y2{2� [@ �B � GexD !�t� te� �"� BN� = 1/�!2}(E bf{h%�v�-.1+y D'j2 Kr�thogo�Zd*�}Js (� � s $j=1,2$"w hiW}�Z>�prJ71k"� �"�"6�!Ifcktud4*�!%6r%�l o�NZ�c�-�&R�:f�� b� �J�I�J�?si�0.<��* E�� +.n@>�j.*�#psicc��X�ce!~of:H �::;ps��) FRv&�u=u 1E+d�"s&�"parߞm�EB� U\.�$r d{)�� ���2J�6 �;�i�X���an evhuT�$y� -�i + ~ieܴ %n�=-.*n� x�a�>2pi��s � ive:��12}� -!�%e�D � �\6��F��r anze��z&�5:�5�!N�R|"5� _0the�i/5 Pi�2ir%r�. ��7 hٍ��26F����~aiL����ch*y"�+Q2#5"�6N6!VsM�2s B:�rtEI� �fe"o6*.���u!�&7t�#k%���vG�&|0V�,��.�^"'n odd��O$y�W)�F�J/%�2B&�7 �m��>wrN=sed: j1n�8m��nV�e|�2�82����s8y�2�y5 T�(tab�śm�9��A 2Sp3�Qn�)h!ƥ�E6�5&�4�t;B2r`g57��~s.�st�}[pt]� �&�7S �i^IɰI�6�$"A��.q.} {� (tabular}{|c} \h�� k29&N�&b�\\ inŒ�& & d��&ٟ &���:#tta�-2��\\ I &:�&!�vORNak2�c}R�jG6!��\\-0-6f/t-� J I^�� �o�@J�"�;�!:�.���>^eJaSB*�#aHpizf �"�%�or��_ �1� [2D  se�A��82Yc�s)� W���IHa�t.��I�G,��n b /bei&�T93�D5�� _{mnx zY &6(mn} H_{m}(xg $/w)H_{n}(y�%@-(x^2+y^2)/w^2} 6��e^{-ik,2R(z)} (m+n+1)��DI �� C�1 i�-�$ �� �Q-5a�ynomial�W #.�w �k1�*�"�OŐ x $n�B I>91$w"K!�u{, $�0 = (z^2+z_{R}!>zp  $5, =\arctan(z/&)$dl�R)]6�.*(mfI:� �xntE"*<1a(�s�&fig>T_W5q"h*_/�gf,��4a $25\,\mu$m dzw�_inS?g"ercav,\#break e cylindr�@͵�Xhe2?�9 forc�h �Ae 6 VnNs�l�;�bi�:- dal �Sl"l'�}�)Qb:� . D6�6�� 6yB��)7type-IIIS���s8$-BaB$_2$O$_4$)1�1�T�ir�o"�l0,�3&�=�.ro8fgez%rhcs�3 y��may�5'�/9 .4 ) Y], /�Va��e�S "Y�$=@!�'�$ч a $50-50$Q!ici}S!0 BS ($t =r \a�1 �� 1/2}�E{.�A �corm2x� alf-'"p* HWP �M�icNO�>wa[,ket{\Pi^{S}}V,�1�; �� A�6�� was �6IA I�1}{ � 2}}(>\�2}- 2s�rh�� $v2l.snd�F%)a#ar .E>%f� �.$Dm eD�$��quipp1o.� 610($1\,$nm FWHM2�9 $702i$ mm ,u* "[1q?aE$�s%h�1!sS$"w%�V��<bas&J&�*�9"�C FigsB^rms6G> �# DHG}���B� �UmH($)\a�*�/a��aJ��( �("F�1A� �8yt2S=i�&emr$M)� aM ��Tomo�+��e%bar>1-%E�)�H!s8%�1\,ing�\ma�/%��s|�A��<u-{f���usualZE V"T)FJ9�� �q �"R .��a�e�S29$�.� _:^$ (!�A�leX�6&0@?( �'�A������6dv�A����E!%V���61�H{r� +��a�"�-s����iw&��R='�0-4.�)Gm�-x  E"�[alM upECm&� ong*�R.5͙�| K��:B !QšR�h(see �Z)�_'��&59&5ijd(��#)%-�:' �)*a�n���b�\.�JF,%�m�*>!_!{HG$m�S2�^.e�u�A�8-aj�)% C�aC�� �/ эsL2Í�2D10�� !dR�odd��5�C �@!���M�$y*\~M� 67����(�!SM� .[ � a $45^4}rgle. NoF�2Q6sY is%<��N�)s�E 6E�˱�n`. �aR�P6yPz�+2_�8n�E�.w%>>�A�}�!3��\3B :� � s} A� ��C8wpAݽK>�I�}i J1A 8=�:�q�["b �. �"SSG��v�i�R$ �2} orbi�@m؞�� *}NSu�P�o.�rZz�& LaRJ�a�"�E�. M!)LG$c=h�^�q�o !B�zimutha�P��*84$\exp(i l \phiU*/"�A>��n���6�� ��>!��Yat>��}A1y�$l �cQ� )�aFk92b �4m{#�iss�s��F�:%�� R���^X9Wif so� r^,&�6�qA�:�+do so?� s��es�.�"!L"lb{HwL�+ �mair01,a�l01,ba�l 02,f�lar�l02�Tres03!$P�U��� m^+�v�&�� GL\u�EBB�gisin�T�,#$A� encoM f hi� ~W�Tabe�R�QC^!�[�!nFc$�zh@J����}aQ�A�A��5��!�*w���e abs}��.��kis �x#!�} k!(v�;F�! i}�"0U}cf.�k)�+.1s}+.i}*�\,,�&�F�0 psif^"Ewegv�V*F.,J�t*SD�*GI. J� ;Ǖ^k"�l������Ap}d�v l7 FK ��"�5��ra��E��b�w6�{ b>�A cala��}"ؒ�=_MQr } J(!�,�},,z)=&D_{lp} 2�s_G�`ho}{w�-�^{|l|}LI' .72Y^2 2^?a�) � (>.(Z\times&` \\ &:i B8kB,2R} -(2p+|l|.� �-il�  eq:LG} �)'�2$%_tSD�.�&|s,!lJz�|��'��-+l@���AD�; ��:�a�&� N��2p$�h�V2�m���s,УeS͔�ͷexp�şA5�Uh ��7�Dnd�JeWsN�4Ps~y�Ll��p&��i�{�Lp_^ .l 6�@ 5:)A�)��/�@-i:-iU*��LG"(� �W.�X&r�>&� u�9CS�sR�dO$to \delta_ �+�,l}2�M�M$q\,dq\ vi�l}(u�,q)\,� }^{*%e}(i!q2�c]*B� q#W!<N�_Fourier� E�M2MB��EH�;i�)`La5ervŷ<^" z n i"�Vd �M8!9�B*2m �-���guarantg�)#$l=%')t$,�.�Vz42L��)�l��Mb�V�7 \V?Vb�^D�d2f*:g�[a�&4 . D-(.p�o�V�"!�)�&��m��u���zR�K,7j� dW^r:� �B F 5"��i1yV�C� ���&�7�*�=."�+ iFJy��~y� _{c6�"<-�� 2})=(R,h)� \, uu�R)�N l #,���>� j R*?O��}|.� 16� 2}| �$ aqp�mp�l"�R�L�{ �"��rhoz phi �O2.2}}}{R�3 \cos^GFG G�: ��:$5M$�v8<all�v�F *�2S�@� �'V'*4E� ��Gg}to�UPsI!5�9�N�HPEX2�FMM: |�(R V!��1QB2,- rob1>Bj�Q��F�D�mls["�^]47_lowres�>BV�^C* C���$ ed (e��m�d (w �p :b��!um� m�$�P^�Xa) No-.� #X me (Z��  unbalotd).x�thN�ePe A?.^lghom2!�o-jj�n�j��8����5�q����9�.F�1��\� :o-�C - E1k���*�&* ��x��� F!Ia%NsB �X�d- Y�>n���"��+of2! �se�b:p#���se�5� H(>da�in m�gr��.<)�$"�to������d/����#t-�o)5Fk. .�TK Ca�st���ke �x3� or (1 mm "o%}2� ) œ>ТA0.5~C���Q 22 5gri �%.Y� In�t� � �v�ZF � ``�",����Z&��tha��ZjRm:p^_AN�S �A/ s no2jg!.��^&Z�k� �-u5. Par:�p V���"�(J:���7 (3 �&oh�665�R���udi�R� �4��eq:�� �s 4��c�be"n�6ia�t*hM.6g{r�!��J#6C�.!�t �� "S n��YTatO�eo�9 �$h�c!��BR \par Th"�&WIe argu!�,�A�M�:�E"�&ed6�OAMaX��VF8_em�na��FAzD�u<@ i};5 M 2$ v]*i}�N6��`3�`sV�U͉���a�disV*ed73��K= y}=1$\,ma3A%2%p��n!��val% �a�J�2}i �� shif by $- e1�$x� .�K�.E byR�!� Due� AD(;��p��/e�^%  hg:�0��ra[Y��h�*}(=�s�a��6-����!�Jb N0nG0�H0:z0B0�>z�!12,et�G��aL3a<�XQ.�Z? �j|J>'@ AM F&�>o�^�Z"�r� $eq:new2} � 56� Be{-&5���d��ly "�H���5��o�wa��e��2Mwo��*D&,h]��js4[� Za7�<s>�VAexh��I�aV�e��?�L_"�Wcc&'% ڟ� 96��dIa"�5�&wDP:[zi48.nW�F��P� i}}|F_{l-&>[I�|G+2zi .newb2<�g 2FsJ $bf$# Δ6%.� ���b� $���2i�*Y*�!igP�S"��aU�, .�h5W$ꏁq�in� = �[E \ges�3=2�%l)adJ��>�c must���>� �5):z�6�6��� =��vW6�� = 0,*�>� ���sb5Y�!�"�Ze�6:�vD>�K =0.�" new4F� I�F0,�ol��A">94})��s�BAu� trivÕ1 o"r�2�|S1ek_)���=fIR!��X^aZ�f�\ll�� "siY FR��x��\E�@ [�q����*���a!b_�$nnot re�ucu��[:{"��&h d�� W/@tr�  J1 z ��va���)�UA�k�'�de�[MVre6� prt3ple� finig�& E. j>�"6Yt9�,"�����-���.�"9#�v�v��)�� A��2:� w I� x��E� y�@m� 3�I�!�. *� B� 8 mm in the $x$ �and $y$ directions.\label{fig:lghom3}} \endure} %f \s Hh{Two-photon singlet beams} a sec: (play a crucQol��r &�._schem: .��� 2_U��A�28�?I5D$� "� m0 HA�Fur#more, m.q�J�,� dens� dinkLmattle96,bennett92},L tele��� '3}�U�A� swappZ*requi|]� .�(BSM){ a[,�j� ng o� �[ defiby8 ) (� 6" ). G�l� oq�SM's ��8raunstein95} of2�F� �onT -2� (at a 50-50 ��"A uhom87}.jwq۞�2��4cm��vR�I"� on��1��%M � . BSA�RA'�!F`"� !�A)� Jin � %ˡ�u��/ moAf, �9usR i<� monoP�s,��in Eq.^# A)�ŋ5���� sepa52�e��q��e�y� . Bosonicq�yqs �WG^ �up%"��s�l> oton��n�R R��*� I�2. �* a�2�s (PBS)14 $h�v$ 7�Os,6_W$, we h�*Q "t ��-F%K$, )D �, �h�v �. ��� allow� -z*�3�ey�6.A� ofB5y� F�y" Pfcapabl%EdiX uis��PmU.  F!�preH+ vailV,!K y suN!E< low efficiencie� 0/or high dark�nt�WJD3,kim99,takeuchi99��%d�lem6par�ly sol�by renaAeac&p�� addi9 �e6��97i���}-�en�s%2to-�L�� ASYp occur�% in�!A)complex*1)r�lsystem, � an e� !or �u4necessary. Re�,ly developed7"� `A1d�"�`"�U�reduci�ofD�{>i#, but <not e�100\%Yy)d� lles�" "�%� ���he�avoid��2Wbehavioŝinv�: Q� �e+  (p )m� go!��; (���)�a=�k be fi apcrid?#=PB�As��above� isDbe�2g� �.�F_ /an 6N "�"� �f�"-Hermite-�� N��n,TE$�F(,B�"�in �f!ei� .�$�!... are &�ly1edFY��h�� or ���1��Z!��N � 6K�an&� ��H �(�R�ach^� ' pair�"�ݹ�� "�6�>-�� i>�&39-�y5���Y�r�in.��� at�>��0O dT All ��b,O(5�AaEhre,�4�16�a�'�cor�#to.��}�5 z���fQa�be��#e S 42BT� &7BSM�� i�e"al "J di�D'! �&� eM*f �!S�h$walborn03b�SR-�_�,��Q^ 2�},��"=��m)�)m`5$"� 2�c�)�"�)1�2%�* �'�)�&s�,about $90\%$� �al err� due mos�8U�"�r�R."0�H .H 3&�rG 23I(of�� ^:si1; 5�%�&�&a�6�mmhom� E�a�ra�+Y| Nne�finclus�-O98ET�%6��*�u>��jn� %J�%j�!3�9��%6;%\c�!I9"ncury �!m'61�} %($��J�j�14>�6�\�2���@ ��6���"JCoQS} W� .ewed r }�s   roun �4Hong-Ou-Mandel2; .�ke�"grediB���tu-�+spontane�.�/, down�!)a5 �pnochro�*c,1xV��thin-S!.x"��"~,J�) angular s�%rumqq lase�"��)fer� &� I�!�)�equence� / "�)]%&�+ stic�a�z��5b�!v"5�th� V� n�1 -TZ����A&V/�9�Z?�1$*N;��d"3!Ab! %pAq�$Z2>�," o2 *�*�nd si�)�p�e�2� Y���.IK*ee<c�!at=2�1lso a  (small-scale5$ logic gat�19commun!�imaging�uwork m�5cV 1�o�(an!+ �!�!ll�� �s origw ng�*���! ,[2 *{Ac�/ ledg%܅~�likM$ank R. S3ebaldi�ins�ful� �&u�0M. P. Almeida-a care,reax� . manu p' � auth�a�e finan�s�/rt �A�Brazilq'fun[ag� CNPq�CAPES.�@Dthebibliography}{0� .em� C. K.,ng, Z. Y. OuLL. �]�, {\it Phys. Rev. Lett.} {\bf 59} (1987) 2044 d4shih88}Y. ShihVC!0 ley,rT61}S8) 2921Storgerso� J. T , D.!%nni�C. Monk�!���L� A}�bf 204} y(95) 323. \�0 berg  A.!�S,A G. Ks1pR%KChiao~@7 �93) 708�2�A�B"�d�annFKA1�5 [5) R1727]"" AM , H. Wein%P �,pZeiC4=GB76%�96) 4656.H@klm01} E. Knill,!+Laflamm�*nd!I J. Milbur�NQMs40As 2001`�,ralph02} T.AR, NE� Langford,B.�h�!IG. WhiteJM u 65} t 2) 062324xz19AAA..(H.�Bers)KM.& Hornr� od. ms t4-�4) 2375r"a} A P. W(,�$N. de Oliv%6,#\'adua �C.�q"n�90 �3) 14360.�kA� 97} �q-CV�4I7) 2173�hong852�%�}�B�1� 3)(85) 2409Wm�98!'6�P%0Souto Ribeiro)S. 5+>r57 �8) 312.�saleh9A�B.A� A. S�ME�Teich-&Funda�� al P i!�(Wi�%4New York, 1991@$��){!1P.={K���B�6�4A. V. Sergienk ��� �Z�7a1�#4336S� �%85��E. Wolf,I�al CoG1�'a�Q�q4(Cambridge Uni� mPress,65.beijers��en�� M. Wa�,�All�H%�$L. O. van dVe�J.!_Woerdma�� � Comm�i9��a%2q��AY}�A.B�6I�6�%Y=�ռ6�4) 02381.�a�9�L�n,VR��$C. Spreeuw �R6� 4M2) 818.� mair��ųir, Vaziri,A� Weihg>e6�12��1a{.zarnautgHe�A%�G�pBarbosa,BF�t����1) 282�b ?�`2Qc.tFb�92G5382O0franke-arnoldg S. F A��M.��"%�!�adget��9�J-%�2�3382�tq03}_ Pb r (Y. DeyanovaeAT��rI#Gn lina-Ter��6 �_ 53810*�]&�C!��&�vS� snA�>�.��19��288.]a��lB `��Bra�d,$Cre\'epeau� Joz�My9�2W.�WooterqLe�i�.�7!�1� 18952% X �>�S&s nR.d >�1X4�ne R2472=Wk� ��Kime�T� ,��Yamamot ��Ha�M��. �2��m 1999) 902.�*!!�nJ. �Y.�vv1062ch� %A %�Silberhoj ��liwa,!�(Banaszek, I��Walms� M&Fit� B� JacobsZ Pittma�J.s��soA Journ�2d� �� 20��149.F 3bF� Z�zCEurop�.�6�B� 6a%endBG�/ docu� } 'Y\O[12,pre�%erl}{�B bb N># reelb$ i1d$1.05mm}R}$>7Tr5 \rm\� Tr\ >(4balpha}{\vec{\ }6� #s$�$\}%r 8$}B:bet\ >[rZ!Y!ydef\my%l ,\vrule h$ 7pt ~< 6.2p$pth-1z<�QQ0} \title{Deco1 _?�D�(arbitrarily�B �|histories\footnote{in Proceeding>the17th In�(� non "%  ",JO*00��Compu# (QCMC'04)N7edi�by��p9&� � (AIP Melv��, NY, �K.EBal {Artur Sc!Hr9_&h V 0: a1.&( rer@uni-k�6 anz.de; a$rhul.ac.ukA3 ?L{Andrei N.\ Soklakovua.s >=dd�{D�+"�Mathes(s, Royal Ho�(ay,."of5 Lond�t Egha���&��F!da&e?.�(. \\ PACS�(,s: 03.65.Ca, T ,Yz, 05.70.Ln�C$ Keywords:U]� �Y�0\date{15 Sept�} \!a�E np B4 %% MAINMATTER�; }M rodu�J5rmalis�U(��<i�?�)d !mprovidA) self�ta2de��a� of closed)�um �*��#oes�)�1�'!�exteraOobs<r norQ�ex =a<b�G devices~�$DGriffiths1984,Omne 8,Gp1�,1990, Dowker� 2�J2sHuc+fully RM�$�;�������clua�  cosmology �,Hartle1997},�iv��� eff�3ve�-�1dynamf�@�a al h 'al laws n^�,HalliJ1998},e�!� stud% coarse-gr)�evolu1�i2L�=� map1�� � }. "b,V=/v��I $J1�0"�+ stig�*� !&� in�.�5pus�-Poulin � R �predictO:�H ies �1�[, i.e.\FBed !s.�-Ѳ al \lq\lq�pos��''. �x[5the r' �)ree/ed byG�5 ors.�Np�.cularX�Kaus�?se�% mutu` ext%C.c&�s� a co�.te A A&j*.� Du�1(. " 0,�*QAot �Aa�g�E9r�y5r!�a ��stt# way.�4�"`DN, A� �D m�Mb�B t. .� o..en�B��P �@�obe),(standard p&BK sum � s. �RRefs.M��J A, B}XLpe�, ;/ve�zNt�Oe6�OG� ed, name�7! J/+5A[!S% �F% Ia� >% 6% A�xon�I� exac� &f  a��0&*ob�|regar�ky�ce!]*� 6` {} >f .J�f y deri42��&s ��@� Js -�v��ed.!��!paper� G7 a briefH � i�1U%krst j� E2@���< {\em�a.&]� ce}.� �i�"gan!Ta�  s. AfoS3ing* frame�#we` revie,e�5� in���o� B8%�"se% %�!�p%g��N�&�P�� !tC� � 7%jUsA�m .�# �V"� O� ets� no8t� Dg;i? 1:} �Q�� �#8$\{P_{\mu}\}$ o S2R $\�FH$� �,edw+"� )�E�a�x;4�, if $\:\forall\, \mu, \mu'\,:\;\: }  '}=\delta�& }\:�8\:\sum  =�_{ �}$.@2e�/on de*�Ve�T 4 or. \ �6��� em � "�\/}�al.���on2� , �- ,5 \mu\;$DOI dim}\big(�'%}()}) )=1$�fd)r6? } mTwise.�Q{�#]2:} Gi0EaQ���!�>f aZ, �;)X�&z3K}[]Y(\,;\,k\,]:=�\{h_{"�A : .=�42� of5{on �R�VJ;�2�to�.� .> . Not�1at� cU$rict ourseVNto��q� a ���}\� 2:%3m�1P_�_{j�W�/�* &� ��ac4Hn o��s�/Yo�u' � �J,s'' $j=1,\l%�k$r�3]�Z��dV� :�����N�SQH� ��A' 5ΡK�bya�at�OShU�y}$� Z3*� %�-93es''} inFb #:�via n��=:�Hy�>�:=�g � nu}/ \Tr[!� nu}]a�e� nu} 6hif \,.$ FurH7m�Ba � $\rho49 �Y�|� �4 x E[A�>.A�(w.r.t.)EJ�6� } if�Y�Glock-dia�M >\ /�~�I�� $\,\,� = Be \�o�. ;$. � ] �)��IG@92x ^{cl> Z z]i&WV<I�Z[ �bCb"E"map $U:I�,arrow $MS" "I ?/ � �>� �JY0gebra associp�z ]�>if cerp ��] c�] �D fulf�d.!mse� �3 term� �&9�iEK*9 ��al\/}=�D}_{U-�$}\,[\cdot,] ,Z��W�i�^',$��D�+�equ�} C>�. , betas}]a�ATr}�8[C2]A�\, 2 ^{\dagger�, ]\:,o� X�(eqnarray} H�s}& :=&s(UU\,k� $_k}U^kIg) J+-1-{}U^ 5�� OYf61}U,&Y%Y=&.B��� �l}U g*L2}&1}U�5C$��45!A���]Z ��sai�Dbe�U�t^ orI��ee`;:1�0g� ���4 5P�CRd� Y Q�1eq:�cy�i�� V[ "� Mb\M�\yHv'd_{j=1� ( )�j �_j5� �F�$e5.s2B.�^�.}�]� �� . I�9y�����:.��y!�"�tdTe*�  �)�����el�3�Y;c.�, $p2=]=�}��-/])� �,@��2n� �ymedium.�\/}�.6 3}. '7l!6�_%mder�$�weake�;ni6:dha�ae�p<�!�l`ure�V�} �O�C atic /Diosi< &�Motr} Whe qu�c=E~"�J�] cy})tU<��BW �q�c,u�""* a�;�+  yw"f&� A{��� �1 2��connecz to �E � centVbqu�l4 .pr�3mme: �.-ho�&c fe@1C(world emerv4��'%7R�U�-9A r�r �  tech6l m5�� 6{Farch " �7A1 comes&� ne�Dfr2�O�5 I*�eV��>l de:h wMd am�� 9�imM�t.�I�Ee �1 8check"�=� �^�soo�g),extremely c�`some.AGis �_i"tru�IWM�U�a�2si�e�de.g` ;~chaotic5�C, �M�y�Lly*A���xis�� in �\M;R� . Establ�H=.�j�h"koff&� ��Jfu� ,�7�F e� 48u�O�So?]�Am1laa)�y�Iut [��ef�8be"gQ< pBg�  ce��Ja!�pl6�cr!G!E��u�B�X /9_�# ���map. Su;A�A�e +is�N�Cn,GvIC�FP=. �?Vyk�}t�*nV n�H}�Q-�Z!. .�R�B�B-}s�/6`L�M�f�ingorem.�&���-em�*Le�P�2�}:�i�@ be"6�a5�} $U$ }on}*�k� a�>� t�Dc Zs�]� alent:�9 j cmeq:}OH_all_P_{mu}} &(a)& N �in&� >�\;. \, k� &"(�'( \;\; X\,27 �H A� Z8 : \;$�n X& f *� �@� mm�vity_P!"b9"� mu'}�''�&�\;*� n�) �!�f[U^nP�'}.� )^n\,,h'� ]=0V�>�rho�c�9�5FS�������9�;.5�qL* (a)$\R�a� $(c)��8 leaJn  k ng� ="Y&�rN<��2� f =���<= 5 :� 2'.�2�)�`�!� I� s& �$�q��}$)e*� ce  l�� ��yj�#KrBw2=�f� cypa�C�+ est a$� A&�I���a:� "�.$� UI��KmaV� Qpf;@"$(:�$yes-no''�"� )��5c$!�6 ha'34ain � inuum!l!�� -T� �?boJrE�S~�%�C�d 6Pgl.d.C"U )7�_Cblg9�.��+�r&�ni�oI�sa<*o %k% an n(p� F�A}+ A> �"�$U|�J�A}� !WK �Co�s^ 2S"�s,!��gA 9� 1E �!�& �N/em if}%� &� � r?H%  �L�$� PFJ��CE;er�&@B�J�Ū U, &��&�mSN9�`" U�qtu$o� U�~�b�) failO$ bey&#-C� �J�Btr� a�T�TtF� Q �$� �l�22o*�D  .^edE�.i)�6�'aN8+6� id:�2��@now@"l����Z.���8�7&U � �_ �2�(7Accor�A�Q�!J�b>�4 F ��T atis G���wq >� J?Jp1,=1�Ii�,F�  Rx Jj�� �� �� .� B.�%�"� y�6�"�:��� �9^"" f� :p Pn .�Zj ,. nec_ia"�_.5_aeB' "R$G�UliA��oa�N�$} >�� �e��h.�A�)Z2}.�.�'�P���6�R model.�Z2�2| � es�qq%�*�/ly!�(cf.\: �-&�,})� &desir�" olix ��F'��H�z6��ust$explain w�!is$Knt7b@An abs7-`�Ets ig"1R�(*5*!�^.X S"henNl� bundle�^!�g��SU��rF 1n� "UtyE �V� V>y"9+�l��N�*3S�%A`x! titue�rinN�,�Yqis .�#�F��"� � ��o�jse��*t+�� =�Qg bh�:�f��Y we gn6m%R�!@v�!%g)�� &� 2�Y��,^@i��u�6UA>t>1 �v��|A%, $\epsilon$,e�#P��7 �sup� sz!a H�  factoW\ll 1$�pa�%m� sua ve��i:B1�b� . A!{� � 8.usUMIVi4 �� ~Ref�-���� 9InF��{0&��  �ZV $|\,M Re�"��� \,|$f stea�P R� G�}h�ft-� w7aine�r� )? -decC4d_1}).})B�m F. �%Ư\v(| < Q�\,Q(�En&�Ry',� ] � )^{\.j2}� �-�for<9 l\not= J\:> �B F�EAs.`��y��}�; � &U$ZZ nse)A�͡>2� � 9V ��e*�/2���$� �$�is4,�>i/stronged ��T >�TallC)��A� ��,�P,i�>x, ]1��2��N�EdV��\,2q I�-v��Q� } {|uZZ~\,|�B wY=�͑fs6h.�bE"�t�W�'$UtK Qg.)^���sbe�+�by $d^k$i�$d$ be�X*#kE�2[+, $d=�+�.,�~/�z &�par"} proo�d"�ō>2+o.l�F�b)�6Aj�2�2�i�ogous � jo�+cong "H-�g 0i�; �!� �~1� �� 6� w��w�iZ� of 9��"�y-�a s~$k�' AZ�)�:d��fEo!�@���� �.w&`�Bby!W.D vA) ��� z task!eoQ:z�~��0stillIdso��=�s����5~$!%�.�wE�be sketcye� "N"�fa Lemma�{�uniJ %�@�in� it}�a:�6sR%*aA Sone i�3similar�8��-@2�~1 e*e VB}. UM%��m=)B�M B��.2��O V�}ɤ1g�ک+B� ���� tog&b )?W$�$AO^q -lA[�M�modifA�t-�(a)"��E��9�Zq��9 loop"� 1} &&r6 \:\:k �5\mu_0''\quad��}�5f |'�5;�+9,| /"�,P�Xd_0*�\,n}) %} ("�_0}*�.&"�# |=2d63�.} !�;�;end*�035 $= �$< �}\;s&e� bJ� j�. W#u5Abe�9 � e�bD�={= Nu �O  1: ^�'l;� �a� B^9}��'�'���j�'�Q.a"|>0$*�'�!n*�'�*} "1'�x��&-&2 b Y>���{'�{'.��;\;z�:6� *J� \;P &}�. �J� | F^� <~dF�e��}b�� aM& 48�_2&��XAV�CU B�d10�Ab~d*� A} , A.,*$MA.~N./@Schack�V, �*�V\��t MKZ" MEM�,JsB}6s!�I�we-rpinj�M.]2}3} �� J. ��.\ ��6}, 219�d842VO�K$} Omn\`{e}�R53R893, 9357 \82\.�40} �\)tH�K{Z~B.���I um MQP,�  L�)�Y#Co�K''5&%�^R�w$, Entropy,��!�i�jI�$�4 on},*nR W.~H. Zur�V$Addison We�V@ Redwood City, CA�[40, pp.~425-458.�*��L, H.~F5L%J.-��.\5Y\ D-�4%�1580 (@Mbn3�n%,>hE4M 3345%�932j)�?M>�i�FeT 11th N�1�2&�VZJ+Y pt]{XEcl2:�XI6�Xam�X _W$tr{{\rm tryU.�Xset}[1]"�X{#1B�W�Y Ԕ�W=230mm  %�LA4'+ &�W =158%8 % \topmargin==@\page�X{�"}Q head m.% �A4� oot, no 8 >sep.;k \�@&6� �8.5x11,By text�XE�� \oddFF %� otskip=17�J��Y) �XHyp{-�4el�{� ��8�5.�W��X�XJ�:و*o,J9�YRY:�J(zY+t{�3*Y B�X"�&�+E-mail:�XJ�X \E) R\"udi��F@ZYack.Y�UY De3Uof��X�XIj�X} }�G4V3 Decem=��< � k7V�a"$YZ�id."�&Bayes�o upda�L��W�% piece�new data�Pq|��L hm�pW�Ube�;o&# Gr�#,'s algorithm�per9AS:}P�/�p"�?y {�ribsTs encoe��3 qubifJ� "Y(Ϣwer bU�� �$dE$�5o2�9Z!9l "t)I� "KWs!Q"�Qs�M�5ti*�\�1rtsR3�R 13$set{H}=\{hK�(&�$%�$+D+d\<�Q�-nd %^%&�=aH"-�5h�T $p(d|h)$,K;@3� �)}gve��pA2Q'.� $p(I!uAu2Sy |d)$!*^1�h$A1b-vue�&"B&U�)d$ �12XZ. "MPfU>%�'sE�, # oardo199�YB, (A } p(�=�)(���Nh�7)�} \;MM%�:�#t"q�)8A! E�l�1fZ,a�(�.� �*�.�Z%�7�)a��X�� �eq:3�A=\{-1ajF {ll}�0o��FA2 \; h )�d�Vby! d \,,\crAc_hK�0Oi� �\�%Bex� r;!`(tant $c_h$ "�Z$A�KAHa3�}h�Q L�=�%��w$Q�rKA"�;� , $N�59�es,��we �� 0A�$N--P�QIB=\{0,1,�F ,N-1a�6��we :�i�eX)$'+5Yu byZOe' an"� �e�6�owP�H�MT�C�as},�O%Z�of���V"q%J+\a"�Z��&�%"�X�hE@ B� |��\<�=�h=0}^{N-�@e�\; |h ) \F^0_ $%$�:;-��s�e4NielsenChuang}y"a�e|a �N4lceil\log_2N\r $��. I�be ��WwHAsuma�j)��rV�$k-1$.d.{�# s ($k>1$)E�QV`�7�� �܁D!����{? 4oracles\/} $o_"$Po_�I0%erJ�o_j(h�m�mM&�-in�zj>z1�p Like�S��>;�F�~�6�Y��%P�lan-4!0k$�1�_ $o_k!c^{-1}_h�_;���Q!w-r2jG�s r�0}J� . $O9�O_kI%����� O�� 1& if\ } N4 i\leq j:\ o_i�1Z�0 I� }\,.:+� Z�� $O_jA~� �Eȁ�9olh ��Omega_j� :-��8 de�VA`$M!nFco.T� 6WF]MbD�� nJ<�$jlaE,k\eHe^%�T���Fl|E�_j���1�i�M_j}} �c-}��!%qYE���$ ]�} a�� Y22�%D3k/ � /o��t ��, �<"� �*9 ��}�(� rL !9 m t� ����: G��a�nї�K���z%�/Psi:Ti�/u�:},�t( h[61o9 5t5r. One�$ use � &� ". @�'ol>'ro%3as-1 Di*k�% �:�X��MviaF} \hat{O}_kUP=(-1)^{O��ng�r�LsB_t"�%�::rto ^%e�$~;S !�%o�+"�circuit�?)# ope�W BG}(O_k�:-@R-iEM�>�_d aF�c eO d�atd�Y(2iW0m$\langleEk0|-?�U)�\,^-,$ � ^�ty��@B�6}>1N�/x��|x �>)) �:l super� ���@)uZ��"E�l<b�P�ų e�T�]"�;� )d�I 5�m[J��Bqe1���E s $(\pi/4�!N/M_k}�ll��M za? N�J��� V�*Fout��d .�_skdQ�e��,A����2��Arai-2���(�: Is@2"� toV֑-b"�:s (��&�9)�^s)1:QSp)��9�bya�r�� N.�Vpin"�-�J�Vt>5�?�:i�Nј�)7!g%\MO�d&4effor�c�9�8*� ��H�~��Nc2�(� 9�e#F%m�K�� tly?c/l���3g�i!�U/in.�* Biham1999�'ans2eisU�:nergv*�3�/A��B b� i. w<&�fam�*�, �O}�]a;L�8e6�H,E�( all U�co*��H �zAx$O5 (see Eqx ��A� prec  ^ 5%�is �U� NowC�allu�W���E appl"��6 m/�ZF �r,cal{A}}_{abc uaots���c�� b a)] , O_a,O_b,O_cV� lOS F� n�A���N��)&R$^�$ �$at��st�-l 2}/8�2{N}/{�5}$�)�:$���)�A�con��qE"�waMto��O�16�ma5Q�<%��d"?imY�asympt���k%1$O( ��)����-r6C�{P�3}}U*0O$*Qac$|$M$�0 � to&l$N$�f��h$:B� ��3ES&}  ��O� MJ We sha&!�3>"yesLgood},c opp�Uto bad0.2iere�'�ωF. �0�4er��nC� � soksch1}� EO&���k��8bad=,�/5Q ��f$tz<nsecuZ.oLA�:�9� 8 �b.u&����F��#4�P��\rm�Q�_�\ }h} g^ini}_h"s %N+)�7!�GbVG:3� ran� �a�\b*P�(2�f�w�)$^{\, t}(O)u w ( ��B�Q�� �:GBW!*$\bar{g�-�ɞ b2�� aver]m�!� tial.�6$�~e�E�Fbad2[\�?F� B� &� M�6M23�BwQ*{2cm P.�ON-2QQ=2<J� ��4lgB�fi�"ثJ2�!���,_�j�$��,P>A(us�F\DAi6�= 2�-2�a�F� G2l=2 E.�J�I: $ X2�Q�Js$;9�!� f*�Y!ԍ�9�"+Ws $6cE$2���6vBp�"r uRiwB� .�d;� � et.\qv�7 ���5� � Zxgg� Y� esޠ�V2@,6: � }�:�5��{s}QIn?2.�+-�2J \cr -H%_;1+�t A /Ai2� � !�Z�S$�(6� ��2`_y#o\o��arccos�(1-�2M}{N)\;,\\ \�- 2g |%+�� |^2+ .3|^2 TS-M/C#�eq:Y}cphiaarctan � =m.W} .�� � 6s�B)vphi�.�]- 9�9Sb"F�"�bKF�TAͅ���!�51 �!{%-Q�4in()� t+!d Ed��N%0\,\cosB7>�J/Eds�z�8uf:B�\����0� J�#f_3b�0a�*���-�#\V�#!�U =�$�&�f^2%/$�|"�u*�sA(f)e�$� eA� a"AZ�b�f_\�\��(h)"�!% �} E2I��� �&�ak2q�wr��n�e.{fF�Bb disc^�)X��a�o��G�Zo5e3\~(W�- )Nb0 mpleQ5�be�|ja �k $f_%$f�5& $f_3 More^*F?Ne"�Xe��y$ja=f_2- JSjC�O|���� �6�(nа�1ccJ��U ��R�i�ce �%d�!r�k=f_1-! .� ;�Jny�� $OJ!�6LR�)$:Z"/"Jc�~be�hR��,F*��ei���&� �o ��&�$O$. H"1�E���` $f ba�!��%kae:�� i�is,bH�m=[@ cFc���l= w�- ��)�%�ym��B$�'�<sf�C&P"ObCOneStepB�,�Hp| C#� 4\� 2b  � }\b�&M$��!-&�"1&.m�;X�YD;$Appendix).s�U�%iJA�A2"&aD��6�) qS���byD��Tj&� )z�/)��$�- e�$�u�h du"����ea"�i�( R�+���e�net!Hul�9UF�&b��!\� nޯy�$�$0$� $��+��de 4 :�f�,0% f o~$0TI4��� � ��i�% fof > �I4 ��LO&�J"}. ��ea��� A��1&Ǣ)�%9�%I��Wq��S!��  fBQg�Ka�2MFQc��a�~�( ��< to�Jq� �} .% k,\ %v: �; $}_�!\ {J and\�\-$�"ary\ �3Ti� �\cu6h $"zn T "-�!aE � )�s~n)u2��set� !}),_� G K��=�^H"�5" 1lNySe��O�pBOb��I�-� Lz�k���q��i8& <��N /�='1YwB�  dsz�)� E�>"q~^{k���,Bf � -1%' �� .6�)hN)�Igca6}kr0 ��)* >7 \V= ճ}AZ lity-�2o)j7 A�,�'ardles�k�Z"�$�M�=,~$ ���k$��,�$ost $d_1=���N-��ᜁ�EA%F%v�q?N� R� -)$ Ge|� 2� $d_2R�p}$ �a��nge0F� � )*G6�@3�!/e�Gl'l^a �esa ��k0F�n�#� !� "�exI $d_3J�(M w!y)!Y�'$N(��&H  `��Os c�>.. We &�ef����#�6W �u f_�,N_�C& }=N(�(+%? !J����r��Uȁ���&d!)&x��y�$zH�F�>1S$ �{k})$,U -1A�� 2-��A&appear�����&en 6*%�%h�belowa�=minimal]�02(x+y+z)$ subV !+thmsst!�.+�L x d_1+z d_3&\geq& U�cr y d_22V\�"��� $U"�ɉ%V%� Ǫe#du;'%m*� ;h& .��i�rmple �(aa�tim��&2,ebsh����% !$��A& $x�� $ oc�5. Kee�$M�m�q!&�!w l�F�$Ep��2%�@T��ng $(&�� /{4}B�$A� z/2� �$"��%$�2\ :��1!�:$�u re� vA��,*Ira�n*S2:M &� �0*�&.��,!Y�"B*y B�!So�.�,{a_n})�&m�(O3}*�&{a V2 1}) = (A}O�N ON3})J32R1}�>S �A}=�]-$.Jfaۮ$ �O}_k)^2׈��A}weM�9]� DV�J3})#J2j!l &�P�9:w)u F3�F2 ��BU1})�4}J�%2� E� �( H�IV1A�A1)b�b�E U{1}a_�=Μ�0E� $. D)4 .<�E� a_j}=.�pr<p=� j � ppr "BO� �Endq�1m����X-X �E��*)�2�>o 2)�) !@)ABfj) � O2}J�Z�4}?�. a_2ay� 2N���%BAhR-�Gv& pm 2��1 ��P1�f>��a%S>�d\-YaJ��#� a!C�&&��������$+�8 $-$ sig̚������d� u��� $_f.' a�j}$�7&�m7 � &s�Te&G� (6�%@e�Wi�RS�y� y�nJ�-�RK�� 1q�h�n}) &{G�n \ is\�,}�cV1�b:NZ PA-�:}�`:J� a@2V� *zs9A�m".o � u{�ug;2ˈAPA� &�D. argu��'� uk7^ s � um*� Mu e� 9q�EVrG 07�*.E Inde�g"P+ss� EqsH<6� J�y��/t�e doubl4"�I"�1 ��qa���== orig@$*M �>m�2E1,d�$n`  &� 27vY "mlBMhEqZ���e�7!{v�| "�]",>�+6�h g=E1})��%�s"�$2n+1�/)B�Zrem�wO#e-VA.E�2w�!�re�<"e�INlu�s%F���mar���,t?�̟7��"�, ozDGD�)5���Gb�Ac.�6u �9�.����ъ�wu%l} ܙ�5i�%psy�=G_� 1J J�%pF�a!.`�i^�sF�0R�#�" ?�aX&�4��6�) ~ �B#�cENE\r�3ABB]N�"�7s *�3zQ62Э& $�0�_B<�J�� �, c�n�G&�3��,a le�4 6�8F�j�I5~*�3*{C}-�!i"�2If���8(}--R!NM')i�&�M6�>�j�<�Eq1"~E)fin}-� v'|��&P um�& �)*A:Jt=2�%�pt�iK�����T |.�Z��*�*5\f�YN�*$ \Big|\, \�*2�*+\xi)-\xi+$crK VL�� |\,2:+ M\;*+Z  |R�&4f� Tsin � U ^FB,,f $0\ 0 piF�)�>Z=.�1-� Gw6M�-N� ���>4 � Alpha6� IhV�� 12F�A&� $)W�=cHed us�a�"�&Y#$a_1,a_2�( ,a_M�99 R}$ �� �&k� M}(a�$B�ui�lemma}�Ox%�K.1A��&VM a�}X) &�2\E�M!w>���eas};shown���meG�,Lag�5e m �pliersLh�P �).)?*y>�5\max �g*G3�,��:U A}*r-A@bB@�"F�Izn"�&!�Bh0 | C��.Y&.�)� Cu nded�X)}>�V{10=R\6�NJ.~M.~%~A Z ~M. SmithWBay3RAay��(�C8 (ester, Engl��LO2�Y6�C Mñ wI.)�C K u�EComd?+ �� eC \/} r��"��,QS02�{E L.~K.�, `` o ��s help� seK�!��ae�� a ha��ck,'' 2�Z�X\�X79�\32�Z72�0�4 E.�4,�hY Bir�M� asslC(D%] Lida � �'s19 S� "Q. �n A"�:I#0al Amplitude �Dis"|SB���60� 2742�[92�~; Am��Z%�m��^ ``Ef%5 � %� � "Gof {W�S'' K�f� 8045�_�>" &�WU%� �%�&P!i. EstiI�  N ��)s5A��e��Li&2me���4.iVby(V 0 Emili Bagan^'A]�$nras Blasi^'80%%>tPRamon Mu{\~n}oz-Tapia(.�.��WU�3H[aps,pra,twocolumn,�A0pacs,floatfix*Z�%\V>draft:1.j\psfrau�4c��6�icxB\ bsy,��xsy�;3b��B��[�\(scr]{eucal}�# 2�\ al}{X >���bet> ka}{\kapp>llambd>eeC]rm e}^C]6� ! \expA #1t):)tr6�rm�]\,:sm }[2�]scrip��{Pt.#2B�]k�]\vert *D G^2)bra��I)2:�Bb� bold!� ol B>R^b>"b>"A>"A>"S>"S>"N>"N>"D}[3]�CLfrak D^{(#1)}_{#2 #3B/cV0 *b2 a}[4Fb,#2e 3 #4Beacb4hN5U%�U ��a( NeFmmand(M�F4�� �h6vn'���.?`vM M>�vMx(\chi>�vV!VZ!Marvec� m�:�ket�k?�.nBbra"braacJ"kMx}{\k�et{\vec{M}(\chi)}} \newcommand{\rhonN}{0_n^{\otimes N>(0NN}{{\mathscrFXeqref}[1]{(\ref{#1})} %z�!�\begin{document} %\date{20/December/2004} \title{Estimation of qubit pure states with collective and individual measurements} \author{E.~Bagan, A.~Monras and R.~Mu{\~n}oz-Tapia} \affilia�p{Grup de F{\'\i}sica Te{\`o}r �\& IFAE, Facultat de Ci{\`e}ncies, Edifici Cn, Universi)AutH nomacpBarcelona, 08193 Bellaterra () Spain�)]habstract} We analyze the es.La-M9L by means!klocal .>` on $N$ identical copies %s�compare its average fidelity for an isotropic prior probabi#distribu!e to�h absolute upper bound given�c9�.�. WeO4cuss two situaXs: X@ first one, wher)sAP is re�(cted to lie�%Aquator!Bloch spB,9Hformally equivalentB phas.~;>second ��!As no con!�in on m�`, can also be regarded asR>�diraDon in space using !�Lantum arrow made out�!�Pparallel spins. We di%P@ various schemes e~and C clasaAmmunic%{ $Q${�is>J,then processe� obta?8desired1-e. Anyion��ceduraU4quires a sampl�B�of!#5��&which w) per!�2  . If7 7s could!I�Pd,�a�e pE,e ���8an arbitrary nu�8!�A���a Fb��ei�< infinite accuraa�(The no-clon-uHorem, however, prev�K( this possi��~\cite{=}. But / �� uch unphy�, circumstanc�one w%EVhav�� �EB$a limited � resources�~!E.�nI�ing. So,�!$real world ja ), usu��aD larg�h-[,are availabl �Greason pproxi���6�e@be�z . Ita thusi�.� devis�rategi�op��lQe!G�a��etyAp��. Over% Plast few years, it ha�<(en recognizaM��a jointa�sP A��/- is m�C��a�a3 indN� Aeac� py se�x tely�r8 will often ref�!� mer �� {\em*}%�contr�!y"~} (�=c��d� }) M0e� �#�� correl��! hind%@Z�A%i��) ��%powerful��n C�n�eu��0in sequential^� mxpw,mp}�A�,other issuesiOb!�studiedA+�� !1extJ�holevo,helstrom,book,braunstein,derka, lpt,dia-1,bbm-,ps ajv %� ence 022<,bartlett}, but ? � 2�e� many� I�result� �ed-)xjones,gill-massar,fkf,hannemann�l 8mixed, embacher%ae !�5�Au,volve sophis��c���+4ory technologyAe�l so w) y �iamong �)(ists. Moreo�t�mai�zapply!Ɂ�&��$ (whee} is ��)�in a ``pa�0wise" fashion�Ls�e�no"� �pv� o���s�� ider9�apos-1, 2}. H� we addres�b� su�1Nng�%�ele� ary �&� , �of a � , assumCwei�� ��J� it��� R relevQ cases: ��a� le�˱� �), i.e.��� an ��%��!�.f ;e�2n *� ��!9at��IPto b� .^�>e latter�Υ+ intec!7becaus� !���12 "� >�  (the��atW reY 66�so-�� rebi�� })%��$U U!�s"� �3D%$2D)�,�pw v�Y �E>gL me��is, crib�  a Posith @Operator Valued M 7 (POVM)1�AE�. = �e � 0is type yield!� e ul��te�a� b� � c ��]� � % �6re-der�)&93  a unifie � mprehens.4framework. ForJs, we cuvon Neu�<.�� �!���adily iV men�%�� labo%\y� by ``l�.R" a�} loosel� a � 1Z�}. Fur�more, wa"uA� 0 �3A� P5^sSed �-�. ��ne� arilyM.�!�.�� lT�zah.*L�@ thos�at3 loiq e *� ~��actoutco�ha�bea��) to dynam: ly adap [ next.�)�LOCC (L%�i&ionO C"�C.�)�. Let uV " concre� bN�problem!��"er0|. A��)#�Van ��mb� a�N�an &�bi��"� denoa�(y $\ketn$, � $\vn�_� unit vec!�I.])nsatisf� % Uio"(bloch} o\\bran=\frac{1+\vn \cdot ,\sigma}}{2},�O %t$.(=( 1_x, y z)$%_� H Pauli matrices. Af��A1a.  (* orI�JA�5H� IwA0 M�~$�$. Baanon ���e,F Mx$, �5����gu  . To� ify� well ?F � es%�Q G �AZa�!�, def���" lapf�f!�f_n�\�|!�P{\vn}\vMx \rangle|^2=.� �  . �.����~\�{f}�|&+� s�":�get ``1"�a%�ec�termin�  (IGM}=EOn}$) f ``0"%�a.�wr� %:-; . Our aim!� to maximi�=�,�oaE}��8(short, over%�-( �/a��all����,j�-1!� F)� \l%� f1� = \sum_A�$ \int dn\,=�;p_{n�J��>d�=ESvS A�d $U�v 9o�of!�� �� iJ� ��A�6�is~E�Y n}}$ s �io�iabove��!Mow%�J? s or  s.A�bq$bN set�poU oU s $\{Om }$ (��m� ociY to��-�).Xy�l di�f� povm%�9� ~ =\openone�e��� %�2^B��xin a;��� � byj�nx� =�=\tr[��]BRMP 'U ��)HR, � �Prho_n=(�w ��n).CA In Eq.�b-1}�� >�� � A� at r���iz�S:7�$ŨA�A<�]Dex f` 3 through~�f}): !>):� �ual k (OG)��zed ra  trivi� 9$Schwarz inA�. ��choicef�m- })ء���\vVx}{||N�%�fYv>Y ec{V�q=��;#n}\; p�uB=%�~�e v� Q/�p1�f read-bbm.a �!.e3�f6�F-1�4\left(1+\Delta�right)�}�2+�{)> /F(a�h9 ict �we!�oDwrite $F_{\rm OG}$l6 s� -@notϥ dropsub(pt n(confusio�ises)..)Y �&)lbeso ��0can be~inferr� �c2nQPE�=um5���t ��( any}Jq and !*�� G<��!��ial{͉2� ��!�3� H non-m| taskA~i�f j �.�i�goa% � pa&Zo�ut!Xexi!"Qۙ� X} ��& %:v�Fs, %�7�� em�organis�� llow��e[ s�onA����T q�!%.*~ �s.JSec.~�!�}��s�al �;-��ithA %� out Z�. A"j)m��A + u��&� }. A summ�of�u�aour m�leqv pres�5�V'}I  two t�� end�  en�%�. &�CRps��9|} b-�{2D�~) A��_ spon�o� ��is*�ayM �dV� . IfACtak�t- M?$xy$ pla� �����$\v cos\theta$n 0)$. If��c>�"�0 in�!hasob� o"8, $dn=d x/(2\pi|V���dsf6�d-2D��r=\�NŊ|�<�u y}{2 \pi}y J� Ɂ|J0 Ns ��a����vj} �%� � � rho())=U (_0 U^{\dag}J�N ! 0! �duc0 Eaf0angular momen"$J  N/2$a}+,al magnetic "f ), $m=J�l�fixed " M�r�In�"tic�, ��! c�&$i* n�$x$ axin� rhox)d)A={A�8{JJ}_x}\, {}_x� J�6 %�, $5�%_���re��F%i rT ar�$0$z ��� roup-e�L�$isomorphica�$U(1)$a��PY dard basi_ ket{jm}-� m}$,Q6�diagonal�havj� rho-�%Y�Q�i]<{m\ n}e^{i (m-n)I�� {)�}iE)_{m )��%�nN��&r� we�y!a$��u�:.narray��$ 2D-1��&=&>�'��R# � � � .��iV� [�]_{n m} )| \noia \\D b�=-J}^{J�n Nlm+12nm+1\,r�E-- %Q)�mnMO%�m} �E\n}$I�f� ing "H " +E�� �  $)�$N��5  - &\leq& &�-�J|�)|2 x�n5�A_O�|.d+1 \,Y ��w w,%A~& -e�$b>V ;"step in�BC)��>;d� .��q��-R %�v=leq 1U� S�"c  froms�* an"5). aA ciX,�$�. ejVp�ity�.� m m}6�ae+1}\geq� 2�!�e�M^2N�nd e:J�N.e1�O4&\displaystyle9dJ�At��a2q &U���:O \sqrt{5�s.� m}}:$.�� +1}}=1 .&?M�s�-p!�F���|s worth ) asizJ�. F�+,�!F6�� bi'tun%�'ref�$�� � t� (we ��bea�� ac�� lish��ask).� on Y O ͭB?hEI qA(we wer��� encod��.j) carr�#��$ɧ�%� �� way [a, ��]?, ��-*E b#*,$`"man-2}, � 8m'}a_m a^*_{m'}�=m�� m'}$ (ide"]1a�si�� wh.5-t2za tens} k+�)>)m *��(st{&b-� b�.� ~-w ,� ��\lee{��1 f{M}�m!\ $2>=\d$+\,a(+a<� ���/�V �V!A�7/A$st eigen $!b x $ ~( M$. A straA� forwU cal� �Y-�} Xmax}=� cos[� ,/(d_J+2)])/2�$ $d_j=2j+1: dim� o- �inQ�Hilbert�.&9E� ( :p ${\bf j}$�$SU(2E� our�\M��c{/%��a��Ehav�:1. F�iy6xn}%� B� �ha1<X'��"G����-!W�&����"}{2^{N�j um_{: ��p)�({N \cr J+m}F����w=&� gN}M�f } 6F�\��J-m}{J+^ �� �"f �%)�.���+� = _ x}.�={1\o!2^J2�J�5" Jm�`g% (re�$�6 ). n2! $Ne���at at�.is���s�k4�2"( y n\ a��of 2� �$ m 0[ndepenA�,m� D/��+d ihis R i�.fun�0 48-n$. Similarly,;'���, e&�3��\mbox{$| _{m n}|=�^it�� t}$}5�$ $Jt $q!ill cer!Cly66re�5:� j<��pa&b!Lc� (+inuous)%��l#"�y�QN��phi� mn}=ce}^{i phi} ,���.z Y�"6"%!�R� s. N�"a'u9� �-eV!s��&{h ~$����G ao.f )�. Henc4o\� �})(R$N 60�Q�!$ "s, ��: -oldJ�IbYhoJ'for �:F� Th�&!� rank��"��= �(be�ten aR�O(��Dž?B� B}U^�ger %��9��J1-B�� U, �hJ,mNt 4 ��* t le/�x-.� [.� ��s:T�zA�)] ex�,! J]s%Zb�/ und.eWsQ �1C of�s�#i�$A~!�>�t"�3by choo�6I�b�[,$d_J$-th roo� �,,ity, namely,J�a�ku��I d_j}\exp�\{m�{� k�l d_J}� \��:� $k=1,\doF'���J U, ! k)\}�a von Jh), sine1A��A�%�R��6li�Bd 2Z .! �i&�X."�a.be��Fn"� �Ka binomr2�9$ � 0rm{Bin}(n,p)$���am�$s $n=N�p=1/2T� y ne��o)�o Q�/ �|1�$g M��$\�# m�% =0$,A>�.��'d��. m^ �4s E?ft[1-Z 2 m}{N}+Ea(o$m^2}{N^2}-mNMh8)+ O(1/N^{3/2})�]"� >�X� -2D-expan��Z� % (n*�sume%!7I shifqby $J$i�ret!2the uJ5V�)Ua��'"�.be 1� 1s%=1-� m0Ig m^2" N/4$�1�.� aat��``us")$\� N �hhelps�o�� 5F2b $1/NI�fin�FI�>�yq��_�? x}=19�2 A& *sJ_&au�.�6xq�A{s |F.p4pJ \!�{3>� A�/t&v& n}$*� %ha"R��:�0A����8�< � nf��-3 2pU#n}�� �*r J����<ven�<��c%gnowf� �-N�M9 rhoz� ^ JJ�JJN`$A� �e�!Fi:E" �N]�r[ � b|9{ez}kto~I*!�(a2.C-( z �/E nq R� � ���%.j&%��v1=c>F% n\,{F%J�b�.�)i"�`!M��-@@e.gR� 8febc dn} dn={d(U�)d\phi|4�f� 0�3" ����� 0 azimuthal%Rpo+ s. %N��8�) an"R  $\Omega�)$�8<ae� f�O�#-3�0 �D=U[I'] .^u� jvMxE�� 0&�%. TakA_in�!ccount�"��Q��=�x ��N8 m��ݭ�� �� dn \; n_zY���=b��N� W�>}3 see %| $n_z= YH=\D�0}{0}(M�)$".�&t= $\D{j}{m}�ANI �#2Ywayg"0e n)=\bra�U� j.��!� .2�>Q2��� f'm'}�!%[N� \; Yft(�Vn)^�<%w�!�mz) ""x � �n��[\�!�M� F i]��^�� m�-)"^� )�D�!lity �u-mschur a�A} � /RH�NC&�!PZ>�C�u��>�S� 's lemma D0@��A\�(h)�: of~b,.�)�mu�8'�>� )* � ni�!trans9Q8%2rA ��t�". ���7 �56E��a`a{1)$ sub"&"�,e%_) one-"� @>S*uc::$s,"0b�"�#E.~ ~: �) j�%�>N3. I��2}&remov� he "�G�a� term�'ge (��qL rac� :7!>�yttri�ɛ�u�^�h�\J{ei�k� q&��xa��vb^�mJ{P_m� 10;Jm|J�^"={J J+1}.�9~pB� � �* {mm}�0J��J��. �0frak{D}^{(J)*� "$ } !�*� orthos$��QT�*� ]�:� DedmF)}.*% e�6�&��� get�mp�C"~�V��"( 0 �.N+1}{N+�2! 9�oa��@ arge~1be��<.Q 4 m&� o2� "�  \,N� S9��;R�"O.9E�A� 4Clebsch-Gordan"0:�� �.r) oaFsnH (.Oto&e!�� os2y6( povm%"i�E�m�c�^4 Jm},\quad��z #a�b/ A| co"�Ds $ 6,9���i�f*s6,l�&Icon^�1 bj� �d���T m})� \,9 : *� &* 2F�(�checkm0��m\;.n5� �'s�B�'�QZuZM!3eɩ.� are� �D}�#,A�course,��!� ��5%znu4�>*O� seru&of���t  "�*�+M� a��Ni�<a�H�2�&�� �=h��ad"�F literatu�cCI ,`E bbm*HEA�y5,for details..�.�=lm�I�Zl�=��Z�.#though @ina"�df�th�0or�+H�.of view,�di�Mult.?%�� �H�#h,�N.aorQer talWR&?H .M?.���h"�EFL I� I&�HvVJ�Hq> u" wo. j�=j� vonnA'm\a��\� !�=^�=��+�a� h>v� cha�Ier� e.�@ 5a�O syst�Kz6YA�orien�,A�8a Stern-GerlachE&�'�Bby2$DMVsl �b.E.F�5Fm.�!1}� start)�5�I1I���M��uce'a ��:Jm1.$.� �12*o .�(s�C1nd $y$) $tVo4 ��"�4,>�13f �]f,c v $z$)�"(�4jMof�i ��#R,u"-.,qudi� Con�4r $N=2\NN$ ($3��V '*��"�B $*NS:�>.����>n( i)= \! \�R_{�} &N�X�1{�f\NN|&j\N9 Z(� uJ#\r�)��&1+n_ix< ^{�-r} �NJ� C-JC.�N����!��Xpryz M����7$mrA�y�,D�3� n.lI�aA��n'�"rt"�< $ �=\{ _i\}G&_Tmb(Dorial faG}8�&B��p5T_$�,inga������&�% W�]�!&y<�@T�Spr3B.�?ketWG.� !)]$. S"R!E c��on�l'%M\zG�  $��Eecg"0E2'6�@ b�F���T}�of%ܑ�5%^�cl-yEA�M^z&CLG}_{i}u�I� 21�-1}{\�&j (j-1)^2}f�!�superscr?J^ ce�Sl:"� (CLG).�&icK  n6[iz0 )�p e�(�|\v�|=1$, h aaZ& ,RUQ� ure�t�.�b �|eB�F� ��[is�/Q-f�"4՗ ic} 9,"}+�! %{)��ZF \vn. E�M}9�1� \, p��b�$%A�"�in"�&lF� . A.ACLG,U���R _@�/}A&t!�a�W�@&, data,�V?nic�3�'t�& t �be�q ly (� easily)�e�?omEobser\.`�� fur�+�T�M&;X�P2 toD "�^1�J h� � ,"l�&���\0&(C�Fig�?(fig:2Dfid})�%N�Xfigure} \psfrag{N}{$N$F}{$Finclude� \ics[width=8cm]{2dFid1.ep�I \cap�} {A�_�U:�͙  Q !� $2D$�&�1&* � # ( (solid lin�T}F8 OG (dot-dasheN#A� (.%lk imu�W��greedyf Xs).39} F1bN�%% 2� �'.�� i�4�+q�OGu��2�Em)/|*|$�fzm�:==� �J�Q \z a�4�eY��j1�u!F $F=[1+��4} V��]�'CloCex"=s*�Y4e )Fhw�20�Oq��Rd ����2|A!1#�4fKn-�grŞ�U.�n_{i_1}2}��s q}!j��K_q} �\6 i3�i_3 i_4 C�� {q-1}i_q\z�RH�=K_q=q!!�� r (q+1) 3D aindex� cur�_racke@re fuRsymmetr \,A $�b�\}&�i_B !+�"3}Wi_2%$"�4 C4.! i_3� Ob�0 �t!�l1�6� van�7��$q$ odd1TU�r:xS.�Wme GJ iZd!i"\ �^rK �$e.f.6lJ50F�V!� illu4 8inR�+>:O� �Mm$� ~1�ev $ange $10-6�&$)n�, both"�-� ��yd [s�y� Vc_�-i!/OG)$pa s beiXq� CLG�Y��should.2p$ to m�DOųs3T��vaW � a�r�$!? betw]gerT(6A is p� o�'��xscaW1error !3f= epsilon-Nv _N=FN� 1-l�`�V'�� \ ^(=\lim_{N\to�� fty}_N&p5G"�#1�rg� .��*�WA�Ase%�" + , $F8* �/N+�T s$ (!�&�  F�3� p� ly#.cu�cin3; < }). >! err}A:w  _8.B�4N$a "�bV >>f :e "u SE}{$�}&#jm Errm &l S]l MM@��!Q�1��*I 6= V0 CL:$ E� (di�^ds&�W6 !pOv 6 % On"YseE{�e�E� �� {�}\�x 3/8$�b"r� il".* �e�->]OL}} ^1/4$, L! m�i" 2�Mi�>7-. d4Z�T curve]� �wE�ndR���a�-!z��A! )md�:~E�FFs�]:��I�6� )�8&�Kregimŕ� yet&[NbsN� ,OL��e��ZS"�LS8R �OGNB OG}} =)�w$y(chhA�Y� �?- ��~$N�6!3E��!Pe2��T38^�� V 3�  �! .� ~ )[�  % AB(, � 5 FOGB0�%�CLG. H�h!�improvi�doe"d seem< be enough match�YE�"�Gpl�� n]#,�ki�A�= 13/12>�� e�=1A�rp��4���N��.�.a[L�O mini�K&�*;3 K�`aB<�|CexH^"-#&-. A-�Elex�%�BzQnba� A����  $\{m_kNIhuR<ly clea� a�C�]�some sor�K8Ny,I br ^? �n� o�Cunt!:e t=Z��i.5l� a&�8iF w$%yw"i�e"�� ��$%{F/zC$_k=k \pi/N~;� .8?4�[-6�X>chiGn)5� ed0)�e-digit}5}LM $6=i_{N}-1i i_{21�"{ $i_k =0,1�[A9�xtXfe�j!i�O� 6�&�{�00@0}^�@�N/�ef( f k=1}�@ Q+(�{i_k} ,x  m}_k&�|J7' Anali�� ^�Pow� l"S  EVQI2Ŋ<, !�� ompuSs � �(*``58 �ky"aW���2 than "y +�monrasM?a�iciY�), bu� Al1E�Vp�9�=. �"��� D-�*YpZ%i ma�m� i�v��s,�� 3Dn$0 9���< �Te�I !��> V�-je.K OG�,�%�&��1a>)�9�"�o temp� to�VnK'ZI may����!��#B i�*b� .� ���" � �!#%c�!a�Adam�#xffe0&��̙��#23g5���%9 d�%�"�%��K9�)�e5K *�<o��]932 <o2<E�tXqu� �d� ch�x�m�(� ��&�AA�*c& �A  encaps � q�("*?6Be�os uT�*,�0u�isz f.�%�!�6random�=. W���sam%Y�5a2in �5K}�ӵ����T�A d v�)~�@�, fid- �~� b/��J��1:� d�����Ma}3�å�EV� ����^> �e6\w)ox �'� _��5Qnu��&T�R^�.����� �tA�!��om M�o�q��i��� b � A<n*� I��2�knd�D�d." A 6�ASuyol�Hd puzz�f/.^�'e�ee@Kor6a�92fit s a �&�_N0 ! N .0021)0.008�N�+� idAW�,vaF�of � [�}U2. Z�.�� � 3DRn� u��J!�!(om�� (trik )�,pa�vtK ���->K ���M�.C23uF� .!'A�)ve Ym��s��*vey��"f[a�e  �A�at2uNx^��principl>"yaW&`�)� "0aXa]os�"�ed so fa5\��{�+ ��8�|ew) ethod puta�wa�Wy G� � M�r�*�r�qxll ``/ 2p"�%)�>�-CCe� �-!5o��Ra� y>�0�9!t &.� s�]AJ]B���3D.� 0AA��fe� k lya  re*�q�S ���ore�yd�2 idea5%h�spl3m LIs�Lwo�g�*I �)�!^aHnumbe2��*t6 a �do ����M}_0$ �i(E�!�9 ~&%O�Moqin (� e �su%o��].�)to2#F�_0�%is"q !�azmotiv�W �i*�{(|=�0. A.R� b�.�jqus|� %U�P a �.��s90��a�(7u !te���!?Ii:�b>%E =�Sme.2p!0t3K"�6-=62/'��M� �E_ turqut��9i�&F8%�in�%% n0stA�A� carew�\A��_��c 3oa�pp��Eure�_Q; un�i5,f te. 46$NA�0d!QB��!'i�e�le#? bar{N}=N-JO restU�2D (3D)",I��N_0u^( 3$"�+\,!(three)b=�*� �mW$�e�6�I�emw �>� � /2L- $e�u aSu}1B v}$)� Eq)� s�at�/ u. v M_0�In �n'��s,���7:�^f %�m pto N^{a}F, $0 von-* 9! m(1�%�)t m(0f�,;$!I!1�l=8��0 y pr�V( 1A,3 ��/nd �VT  $��hn�.� X�2' �19��m"�)(�4 2^k )/2=2^N-1��oext�,a� $N=2�lLX �2o&�j��be��se+�m}(0)c . 1)4�9!�� j�5K�.!.�q�B .�>���l%FrE isRduc? $!2(ge�����A��=�/&�.+ A�j�0- b�/hJ> d_5�{1+E��/ mi� {k})xCRB@+as��"I��a3IUOG�a ��!C]PA*7]fv*-ɒ} 9�D�N�"�~,e�/4, 5\5N9W!�-iH�G atj �wrZ"�+� �6)!0all"!!��eZari�'�.e.��:u{$"�?)�;U. 2 ���%�/� quick�*e7ext�&ul&� )["��ak��mo��"):� z&t \ I��.2$!2Wf�8H��( algorithm���>u"�Q*;)Q  �2�~� in"�  B��!��"N�e�B� � a��e��2G�~� l�a POVMH�p*�cswV;�o>4te���X!7,�T,"A)�D . S&U �wq��"$�v6�k 4�Ba�~�"H _�= o ea�I��, uF3A*� �-��g�["0m�X��_N\�v�{�ǁ� �)=-i�m}�`b lW�:�t!�� siz�B��diQN)= | fV}�f|+"�0�� JeHer2y�LXi_N.�4:��� � *p9""N}%%2�8 m}_N "_|% or,�<ińVZ�eAs9iV}>��u['�.� dA��)A4�n�P:" �e9D#"�/c �a�u�DfG .-AE�J,thsf{A}_{k l2�=�n_k n_lt6� �J T� ZYK-m1%k�FY�m)�!_��\Py& y z\Ÿ.+%�5-.�5g | + B�O &&;  P.U��-~X �\&�]Y{.$r�2;W��9$u� n��� \mu}Pa%��TA6 $ laA( an ellipse%� focus��$VFV� (oi"��Cdn ��y2fi�;n��9� oT�ks;X3 ���#(9W^{-2} )=1u�>�.U- !D�()�in we d��origi�&�u�p�<�C tell�.���I[f .�ob?�-��?td1ncy ��)�s �!hT &� geomi3�:���E+$M���!��.JEKA2G�G Z;}9N)|| Ww�c�;���^$&� � low+%>�/.*��5!�.�).{�S~heA�{;��!| &k #ogB(&8�C:ar�>w(:0$2m9%863 2D,)�e�U�A�j�:�OOte, $N�<�(2�G (.6� �.ny&�!, sayu!�e}_�� "%(0U M8*�5�!4�&���M:�&�;*�:�j8N-1"} �<��8� ���6�m}�K1N��$F=2/3�s�e>L�|' -,L[orP; 2`]4�4o&r|AUAE$o)%�� k��1)$�^nWAѪ��.26"�6�S \  )+J�%�"�k2��g*3 �@%v�� �io/ �jt��!��1]6���aH$%�m}_yerp)�Ej,�we ��O+�: e}_y�*ichA��T$(00)=�#(0!0M�3�>�a��� woM�s W"��-q��th��e�2!�b"��z�)$]. B��o5.] �}� �(10)=)� 1q�%InOG~U:A -N=2�s>&�z�8WeU�e�3)�Hbe[�F{ toY�-2)�:CEz�)� , up@ N=3,� t|4ach&��Z�*,���d� he�� �!�/J� muǎ"u�-" F"�ih$ eN�-�a�G�pgk� ofh)4%�2�x-�M%34 vec M^{(3n�3yR-�^�3}}J�#!@Q�~L(-N�A�3)>�3}}j�R<"Y -��f�anticipz;� � �S��R!i6M�o N�"�%j pb#eU�)+*�� are, 'F, I3"�"veyYr�"]sQ�`�W*HFHDM� unbi�GXD2�N�"ov>Qp �<�#%g-�-t� ( H 1b)A�f an+.�}."\W`zn($dunda~ �5on !�0 � acH%g !��eW:=D �#�a�Q��e&QO". (. ) y���&+�6�pac) a"�"�\� � $N=4�md*�-&kf�5�x � -�8��JAV �sp!P.�Pex� ^O( �rt;$�� No @I�+q Y{6�4)$!��m.0��@�9I���y�*��Tac� gI�mt foot�{� 6� 0q%ula�9x$� �jN)=z3�>.�e.+k)�e"� ��5 })N4$,�K�+�lVɓa�u�"/�1"T0&j)�,2py1]Aj��Yexts.%�N> ebc--�}6�4� � 14}*u .26� Z3k�N�"69X/se�p �JN�]� �J one P2�Tmad+a�*�Im�xi!"�j� ݂4} �~4)�u5; 91}N30R@ 'X/�QG �A�U� ��=�Z�s�� by.�5*�/�&Fig�"�G�:(>�I�_>eO0_ "�)o�N �.�$10�~N{C&t?#M� �/2��� �&61=� � d+>�C!>�% fas6A-�l0e6@|@b�G�� iw�do �C�m�$ iori/��[jS� w�,�U� ; ob���g\an���-.C��o� 0�.�*if���v�Ս��a2�`5 "m$1N �MoD,#W�D�Q��.��5Q�`i3V�1���./&:.G�  L_�I��.+��.!%'b"�<� !{ %.s>{{�6� �4Rie w"� �orea� . U( �3' Q�|A��  a �2�:.�� ��0]�E� .���m"q�"�x#Q's�91�� D Q53}�! � �D8��c%�A�A��7a�} y.��� *W]�.sM �<a�i�� $" 14�Y"�-:�!f����wA�3 fami�a���nEn6�k�_}� j+�a&S3c&�HAttolv ��(���H pry��~aaeII���"j_ exhibitse� .�-F�N"Ձ�&C%�:�1)\&��2)nAba$2 �A�'E2�s M%�A�v* �1&+ 1� e_{x�RD., 2,2,ytOt�� thir%r � tS�%m �lyj1o�(&n �*�\cc�cc!;[�ciprece y�G 6�~ �}�%�ap*=L�a i) �4kV$�Db�mxfi 3)"5�3)=�lDO �" u}_1)�sin � v Jl!?.�� �._ &-.�1� ,Y, \6߉6.�K.aI -s _2),L7YM &=&{ �+61�$� 2} "��%.�, �L un ed5� "!%1In  �j{2}.�+3ًt"� ��υ1a�FIq���+�N)�=0.50-x*q.1T�� �"ins��to wh?&isJ.2[�Sc :HNin�Bo��&�H �.��|Eh MQ�2�.F1�e��eMne.�a�hei{��e�� �  ?e�� wo&�+[EEq"˙2�]����mω]N�'>��v%�s+ \beta�qN\gamm�/RR}Fmx4} u�4:�4m�L }�2)UQa� %raO ��e?u}=u�yT.�qV3}�pKv>Kcos%#�B-�!@\�k@vy���M�I���tg-��A�Ta8�J-�3_;%PB� �!�Ai&MY"�an� K�� }=0.8206*�,�~$1.5\%$'e�E� ab\g�G $5/6A 333$#j��.� �\,.��-3D}.��� !.�sla�ly��?Ked G%2� �N^{�_{�z\s[s_%1}>n%rI1 }}=(.� )/30�L0.8180'(m/t6�  Asu�|d�&h "T 4077�7"6en� d��  a1 1� �''XR v$N>�it pay���xQ}�. ZT-<8)�d6�0E�t} ��M�.ѷ���[�9raCif(�� xRˬ ��OlK8or��b"��� -�o ��� �B.+�_�gA�� a(�c=��9!N�4ls1E(B� w�q��a� -�!��O$$N=5,6$: ex5)A~rm�ex450� A|6 #U�aZ637b�ey�� $N=6� $N |��� I�1(6+ negligar. F�j�`;`]&\N�4��}��oj2�lI�-y 6>+ �.�"�E�ena� Fy11�If��Q�!��O���3� ��S5�saO�we~ vaB�Rc�+ndadver}�� ��I%� z"oSEVI�"e$#�p ,&�=,*%�/8��A"�F���*~��On� !/ 5�-Q2L&f.<s�m� "�a �L��<�i�4&�0�g q�g��$):�n5bSG}6i� a�1ñl�r.�� ���He F-X2P'a~+"rm{I}�Rcq}r'th6�e�9-$F$i � 0�a�? g�5ly�p���earlier4%ts.J@l=�a.��� er%!�symbo��� ~  |_nA-!a� ;|� phiUR"(: $Q�, ��,))$;z&Y.M|Q�� �� Mf��5U=&bW�   \stackrel�W�U�W{\�rm arrow} 1$��.�� [>l�=� sig�#}�`s eijs�3C� er*hat!� "b !� ��a&�@amoun�0 is Sin , a n($O8{\phantom{a}}$)�m�}Q1 -wed��]�"��$,2� },I~�a1/ $f_{�}( �etaG�0s&��a\( rU$"�2�<�O � $p_J-.�dMA� e�"|�~\et3N"�ea��� Eq_~�8 �f"cia�E�stQm��nYbI� arI�9�e]k�5x�P)/�� �a7�r*Pa�:V� 2o�)� � 1 B-�I"u-.�\�^2 f}9 1@_i 'j}\e|_{=�)� _i-3I _i)()_j- j&� & ��M��@�.]eta)=�-� 1/�� m � �=� c� v�Q&�h?;)&�.�u��� eq:1���de� F(�-�12OQtr[y(H} (,�)� ],\\>y��J� �f-a�%���2Qw[6} pu�B7-1G[!�)1i|N�0�E he `2��h�{�/��1HessiaTO trix$fm�� �Bha �%�V*nd&�)1"J Y�c� \,��"@1�� sf{Vcij-t*p7} 6Y�iQ�Z���IW �Y�I��7��C�"��ore�A�f�eq:Lvsf�%�1m1 \geqi�,j!��IeN�$�� %?8Cram{\'e}r-Rao � �Rcaves,�q12�P�24KFv  m%� +�%�0U.����M�ei sher#� �Q_{5�s2� A�}6�)�* ^n:� a�_i m2 < \�8j&���"��:;$6�$�%g";�a"�`AL� %A-�!|wk^R�:M�cal{LM=:g.'A�J�I�j,N� �E��u �Y�(MLE)� c��$K] �͉�dN MLE}?3rm{arg]� \;\.��n�l���� . A�)k*(N" �!K��B�ed by� bin�;�E�� �F�N0ji%��땢H-��6negRI%iHW u�.3�#63cre�I��leq>�Mށ0 sf H�/όt!sI �J�+��ean�b� cny �&1�� / J/j �4v�I�����F p�+.�,a�'A�a�ɻp' '#�=,ha;Es� w�+"H m�Hm�u [iu.��'c'�� ] on=*�� X J�� coALed.v�\�MǸ!��� �)�u1�+(' #$.�\" �fry$N$ {\emN0 cal}.z*�I�zN+�=N~kj F<��'e?OG%�anter1��9Ai�&'�U+y mus��vN��EpingMޅ+�] �$Heq9+\rm{MLE} =1>&  N}\tr 2u�.^ [��%�N� �7" i�*'�B!�2��0�Zwt.m�eq9�` �9r���K]�m�:A& b+I�F&�p.��IRQ$^es ��+ ular��sL)�ba2� tE?W-;orsjg$��?��#93~le��n[ed�)"o[�x(m����*g�#"w?s�[V��� mi�y�y� �[��bbm�z�6�I�{"�&@((�&x$aN��e��Hډo� �a�!a��54J��l�`f�over,�.��.�z.'w�O� �"� e�=a� ��Blo"�� �orm�@���~��|�7a�+J4Va plug� ^�t�}(\pm�4f��\pm��- $_m)(Fk i�#.�"~ q�p_m� !��j!rglA�"�"�%�-�9@2&QZa�5/�B�"�!:tJ���+�G2����/���W�.1z I^{��=N� &fw� n5* eq:h� 2����S=\�DB� *�� )�^2:m%�= }=*_�N� ��E�O�� lo�.��ro%GmB�4�^ZFM<)n$F�?) �/(2\pi)�g- 4��re�pu B�>� MLE� �1 # �Ih)�+ �it J�*X� 6S: �9ٝs<_is �esTat�O����*�'t"l~,21cZyN� quit� rpri�$1��2�e)�]G"^�� &�-&<s<t��1�H& 9 �9 o*�"�tFh" J1v�'1&�oJ<=2- hi=oA�9:"'6 iaEz>�g�(*zb�/.omi�)at,U"�  Ч: �9f�W~g�Pt9!4#e�m� VG ��a&�+TU"}  ����i.�n%�},�� �M�� thre2�Wd��"�� �0e;�n�:BGOG&���%��'i{o hei��Ba2K�i(Ek)Vu1cuo�h�m2�" z% it U�!j]i��3�o��4&�"͸�/2q/�"�P.� F� . C� &J!%��eacIW�$��Aie "Ѱ: t�r36�g��Ex�`:�6%��� e_x$�)8�@@�J��D'e_y$Z %�M)z)t*MI6a�}= �� I_Z%"" 7eM!5FS��$2^3$ B��a S+=�_1\_2 3�@_j=c Ge2�^�b �a&� [ 82 Ve&� � ɏ.=�Mj��z}��2aF�MP?j�% N e_j�) *,)��n F�R��,8��-�G�i�a�)ed �:��tit�CEq.~(e$eq�)�|2��o2��� J�r �i4�P� �\N��=3�,*N� ��� `e.�J�9� )� es\.�9"�\6�i 2}&0 \c*� 06۰ & 1-�  2 _}{4R�;�8t"\~�i&�/�}�u/th�JDE�.��{&&d�\NV �%�F.e2��z =3}{16X "B,�( &&�� h35+28! - + 4)-4A��(^ F {9+7* 6-2  * N�I�y��oe"�7�]�"d4�A�e <�Fgm�Y\ traceHI} ��!s�d��\tr �u !)) "i !x8]"f- � % ���u�"��h�%��A> \ly geN� I 1-1/oz�qX �& 2�h8i"�yN ques �"� ��AJ� �N1 ���&� ~P�T< � _&��!Qi}��du\, dM�}{w��[ � ,+as �n>�.'}"~ :W9 [eta. uS$ ��"�" a2�.m �- vv}(2^ )\!\��!!\!) 1}{8��\!'!):1} -!@\!-u^2!E9DE\�I1-u�3� �Fw&�$�  �a�>� )!\!© �(��n^2 �\,�]r��J�"M 1r%L �A� off-B��)�_E*�H*�;�-A� ^�Bq:offW �.AvN>*_%c B =0V���uld����{��wr>-�w$v$"��CB$�*vici~sa�����T$M2vUH:�=�};p O{1.'.0&19�6{��Q U�s���.�)Z� ^� �O"�&_i6�R|).o""��j}��J�"�-`| A{O�O�͊ f� "zt� -�OG}}=��"� N!� &�4:�&� 2����not,�1ge�>� ::�# *&,DeJ� 'fa�jobs �Co0��2s� � �hS23en,a self� kn ��ptud�A�?ral.[ �\ 83% of&�! �.=l!.*� W�Em+*�as�x��/J&x.�gP���� e2 _t$1 =�a��lll>���%c�3IڏE%C� !�1A&�A&�:� �bpVMm6�@q�8 % laJ�� (�V)��&3A3o�6. �Ad$'m ��_ Z�3�^`�Sse�A3C��well "8E?Wca�#oB�&͠Ere�WQvtim/AC � ԍ!~h��ith�V  H�� U�&%B-4e*�A�5gk�H3}nd�7��Lro�6W-Q�+t�6X �""��q?�P"��"� ��Ba"��"��,D G0 `�e��a n�y�8a�w���[� ba. '*�Ft|6�Z��AKa��� �&i�Zu�v�qN7�%t, if� ~��,cbel� I&�m��=&a�2 paper�!��f�\�!*� );be�h.gbbC��nowadays*t�:�vZ��&��mvU��a�,B��@!@aW��.ڟic5��2���pj.�?I���a `ad e �� �dH e[~OG), �i�j>*�!�6� Ql!���KE��r&���9���-N�%]C!�A55�b$%��:E �ha�itzA��n an:�9)#� �iier%rW� �U�ZZ�b&�7��"�A�m���dR�&V�, f���_d9z=i�,�5�UK:��# e@�zf&i m�D� ���e6at w]4 $N=3$ ($N=2$ �in 2D) there is no need for classical communication: the optimal measurements correspond to a set of mutually unbiased observables. For larger $N$, the knowledge of p(actual valup$N$ provides an extra informa�H that translates in� n increasFDthe fidelity. From pract��point of view, however, this differenc)A4ion $\vec M_0$g��H $F_0$: % \begin{eq�N } �, fid0�F_0=\sum_{\chi_0}\int dn \frac{1+h n\cdot M_0( - )}{2} p_n, \endp% wE{$ 1$aMnds��� lis{outcom���ed) is }6��B�SAPd S�'}: At�(p�wea�jCLGQ/remaina�X$2\NN \equiv\bar{N}=N-N!T�1by-�/��4\emph{two} per��culars2�%� u$%� v$, M��� r!�e� 2 )�4_i -1, \qquad %�R�iche� averAa�lo!Mo �0!�E� sE&�� ���E�� 9 sig�BlochA)� n}$ �A.�)�($uv$ ). He�u>� pected t� small ( ZA 1�e� M $)%�we mak)��F RY�n� %f i�d=\lambda\sqrt{r_u^2+r_v^2}1o�j \ta�S=�y r_v}-}R��a� posi� �ea o�ll��determi�W(r. % �S�6a1~@9w% q% $��,!*{r}a�R�f�+ �JW>U�]J�� Q�� $F$ �R�5��!�F2�� dn)�B� R��D) ve!| JN�AXB�Qa �w!�-|��$ r$, namel�{n rm $ [$m���~\eZ���e� $], ��dia�4 q � $ th� �ɋam ��� �.�s on~yo-�)$w SiTwe � ��ute*? �m s ovE� �,)0{r}=(r_u,r_v)I� gn�"i�c2c introduce� follow!jnot�2GnarraE0AEeft\l� f \r2 \r_0&=&i�.Q ~J~%�� ),\\ 5n[r:[I]j\ !Q, �enednN�u�1%e�simil��F���fun" �7� r%�I n$. WMdeE��q�!�bytplyb� sub�(pts (i.e. $.T.  F:�r:�� .�F6${r,0} �A� riteN"Fi�.=I7I,n}:MUJ8i,4$F=(1 +\Delta)mwe�F�eq:f--�* C��r !�� � f� � e expan_!we ( below�  keep��)�� /contriba�t����uporK0$1/N$. RecallA N�4be��,�i�s 2.&Q� � ��&=&1-��R^2��E[��I]ye C6 &=& C r_u u�) ta6)v Jnto lead�%� Q��e���K&� BK A�FK 2E&ɹ% %7; f0 �=+Q�B29M[q�)A�:n)`){e-�4&+5X \Bigj `r_u:r~n_u+6v.v Fq�i.Eq@xpval2}� 1 %q�r_u�� r_v$ (or b alem"$ #�_ve re bi�aAdism dh �adily se4b�͘r_i��8n_iY�#^2.% n_i^2+)�1-}{\NN}��fur� re�q�ve��n �9 { M_0,  us v\}3�n�l�, h] . ^2+n7 =1-�6�)^r  �1�A� bst:-�@ && \kern-3.5em I�� +E�[1-Y�\over2� (119)3I�) ]| }4%$"�! )1�ExEw��I�&&.�-ml�-�>HM_!Jf+� I}�(��6�Onp l3 (2 � �0!c. mVfebc was�J\THm �� moz$ Z� �{q%E2V1P�O�� $\d�H$ betwee� B n� R (EA���r��p�9 F�2}-1=2Pw:�JG=@68��J/ .simeq 1�.� 9�.� %���ՆF�qddquYݕf�y>�)�qJ�"� >�^q �J3��q�M= 8�E � 4n6} 2q(1-F_0&� �D% Now! plug�� backt o (�6�) to � .-1m�F���  �1�)^2 ��1-4 }{���^2��_Ѽa[� l/X��lways"s� e maximum&�is�edTZ choiceaG [=1 weI!�0f1�B�r�A*yis &c�s� , \mbox{$%�$} vae��@` ,� ��nd.�Q%�&i�"S 1-��.% B� NN=(N-N^&� �ly �cV` F92}{N}+�tsqY�concludde�ofq�{ACe�greedy} \newcommand{\E}{\mathrm{E}} % !i�erov� ?�e LE(� individ"*�s�� copyE7Lof von Neumann type�| sketc���2D�s��8 ��\�ut�A�s.�o �s �be�d,�(usual, by~�$.2��.�genera� 2�(: POVMs)e& $R$��!ie�oyI���an two.�+ �i�� -dig)nteger!in� eX: 2,=i_N i_{N-1}IO i_1i_k=0,A(ldots , R-1A�# *�c}��y f(_k=i_k i_{kh h. A.A!�$k$-thIisA�|a non-nega,rank-coperatorg{O�k)\}_{� 0}^{R-1}=i_k��)}\,|\,$,1, �,R-1\b!�J��geA-povm�hx=c� [wm%m\sigma]R�e 2�co8$ ts $[l%6���m}k$eYsubjectD!cKraint2_����eq:+1�%'-K ��M� -;2~;~�9 &=&0S:J3J|6. |zF� w� 6�5� \ge0):$�} =\openonei��atA�aY .}| zero�?us ta�"in�&ccoun�e�fsik�!at��� � may�� a*(. of��.out let(&�%� �k$� Assu9%Bqd�% l bu �l? �ynd�w$to ��i ''��.�� �!��a}"?&I#be &��6�Zl�t� �a�I VE�)|, \�� =��E6n"�&� �7o j!if���, let u�� $r� i_N"� m}_r� m}(r��W)$� $c_r=c6�� n, %�F� V)  X44 [c_r( 1+�*�m_� ) ]q(�:��)q ~%wV!�/} r}1�.�|Z4d%� A ) , g�k�Lfid"7�>� Ud $2R$: >>a-dx} 2:)��c!8� |AA JA �%0 vec >z)t8|J�We"xa��NV � .2�� �a^ symm�(c�`9matrixJ� � sf{A�j�>.p � 5n_in_juE-J�Eq.�eq-�%vbe#N�5�-I -dx-�< d�r c_rMn+ � AI� m_r|F�(Hereaft5 � �" encyj� �$ �be h( ��}>&����L�* _r^2 -� & %V-� off���" ,>2}!�yrefa�3L fa�!�"= �hexpre�+N*�S�/�!2]"ce. V�,�r�!A�p$ yielN�9� max-%�-u L}{ c_r}=Bv!:euE I�U QI=0�"9VB.�&sQ1��at satis��!ME �an ellip-)$�B.E$I#\)�%-sf A^{� eV}� ��tpA��%�m�Fe�umaVv�0 $d&%Y2� (C,m�y&-~ by %�A3 sum!ZP cy9~$m&=0$��z{m=0�0Fin,9�/ �riMAof!�6� :L}.��b�YNL-mr} c�(-w{A}Q`�� +�wy�}{Mi + .:!�a�|}6��a=�y*" .u;1 mean�%��%iBbracket�,pro@/�%ts&�$. No �,i& $�e =0$ ��s a> circl�+n� /) �t,�!urv��$�$. So���-��*��FRat;*Z!�!�.m:29 ��*���$� s precise;'� / ---�0�s��g"�-1I�vYtQ,re���6� ���,� solu%yis�&�(� tang�� �Xof�$�')�2� f7 %n���/ MK4e�in opp� 5 0alX/n%�!��?izesO )e���0!�{1,2}=z(� s]�_A��*H�P E ��( .ed._'s*�0�4!;~.����A�repla�M8s�! oid(d-N sp� s�06�/a stron��&���n�looks: *|��a Rll�  worsg- 6�`PRL}[3]{Phys.~Rev. Lett.~%/8bf{#1}, #2 (#3):PRA><A�8JP 8J.~w�6PL 63~�f9be/�thebibliography}{99} \bibitem{no-cloning} W.~K.~Woottu A�4W.~H.~Zurek, N1e:0Dbf{299}, 802 (1982� V$pw} A.~Per��ndH[, !s8{66}{1119}{1991+@mp} S.~M�3�$S.~Popescu =74}{125 =5.=holevo� S.~H$, {\em Pro�,f3 XK! al A�xsG 6$of Quantum�-ory} (N�] H�5nd, Am�5dam, > helA�m} C.~!Q ,)Jit{]Dete2on�E�7onvB�((Academic P( $, New York�76.�,book} M.~Par� nd JA�8h{\'a}cek (Eds.L&2�!#e�}�2Lectu!���B� A�ics �(bf{649} (Sp|0s050302 (;9);I`, Ph.D.~Thesis, Universitq,6iBarcelon�m� unpuAshed:�re#=��7}{1679Mb�si-�0J.~Modern Opt.#4�b 1235�2)Z!NŦLindn�I2�(D.~R.~TernoJ��08A� 2308%�3.A�5aR�UL{!257903XbB �9A�03 >4f�2yi�� 70}{V-�6XartM�lDa� ,, T.~RudolphE�R.��Spekke� E�> �~E�916�02A %�32�jones}K%�J eO A{50}{368��2�.�;�D��)="> F�1��� fkf}A(G.~Fi�9r,@H�Sen @nd�?Freyber���e32306%��eUhanne�}Th.~H��. A{651��J2>�� ��L{8�77904VRmixedR BagaE5 � ,��2�,A. Rodriguez1RA�103 a2�4embacher} F. E I$H. Narnhof!fAnn. ofE; (N.Y.)�bf{ 31u 220E,6Djapos-1}M. Hayashi� A Linear� grammWA�5ach6to At~: @H Cram{\'e}r-Rao Typd*2B�;�: C.,=,pu�!9*M>}, edite420by O. Hirota,��S.[ evoETC.~M. Caves, (Plenum P��ing� F�Y 97);A�HottaP M.~Ozawa,NM01187��)l2} K� tsumot��(JPA{35}{3112R�K. Usami��E�}.QG�y 2231I�3RD9�� K. M�F 308150. rebits� M.~-J$C.~A.~Fuch�P�� ngtaJ)F!�U� 14� bf� }E�1N�J�Itlei�,��A#S�ros|Q�94}, 70I�6)wis�Y}� M.~W K R.~B�� llip-`56}{94- 997R]sit� 4bf{57}, 2169 (� )] �E,D.~W.~Berry,J�� � es� ��� 38�:VX�6\ ݥ:438� �7��tom��U!�onhard� �i��"�q�� ofFQ L�,} (Cambridgec .} , Eng� !v.;M*r�9tsN G.~WhitUitm�L{� 31�19B� Dy V.~JaZ>�i^AA{64} ( 1V 0 wZ@6}{012�>�A�.~Altep�8BD!�L{9> 936m>�$E. SkovsenA@!pelfel!�S. Juh�Da�olm�7\< 9� 904�}2� �E@s} Y.~I.~Bogdanov:��� � )$4N%H%mHof��E�S� keuc�|I�9C 1C 2$likelihood.�Z. Hr�/-�55h�A72�aEanasz�o�479s >Z.~X,J.~Summhamme� ~Rau� LA{2o2%�:cs*�U[!��02��� 6�<141M6:J� ur�s�N��@2"}c "y edmondsh R. E  it Ang�@ Me.�nu� Mechanics6�  (Pr�8tone�S r196-,�wmonra M , Ma��@("� | 8document} o�\G [two�]{articl31\usepackage{qic} %\input{(um_macros} .)eep+26�prf}{{%bf6 of.}:�qed}{;-H\rule{1.6mm}{4.3mm}>.d�@ty}[2]{|:\ra�.�/{#2}|:aket}[16/:#bra#F1BFbraI2]&  | t*2:X/9�� a #1 |�Y 3 �:Np�@�?\vert #166 l%_,:QnR �� RQ! ��.%>�cc}{ C} 60vph}{\varphi};Q�} \cent�e� %N %PuC titiles �Z+�INFORMATION VS. DISTURBANCE IN DIMENSLD} \vspace*{0.035tru  %:� *37)2(�KsizZ�: %pPIuthors'�?��addsj�:@ P. Oscar Boykin 6�1�b�$\it Depart�=8E�Jr��J Co{er inee� , �oy3Floridaase Pkip=10ptrz Ga5Pvil� F( 32611, USA.�M:42xVwani((Roychowdhurt09�� bEnb8California, Losele�?�=,V( 90024, USA2�225�%\lDr{(received date)}vioM  .21Q� %% \abN cts{3 para�}{�A. thir.BITH\0�3�Me4,��=# TAk MemptyH� #�T one �R % e^ �fMo" showt�1Em2 o ge�r�O;��/YJabo�1R , shV' st cHerror�0�J all}9R$mB�Rt�Nat)is. �S6 holdP any "�G. �Qlso�! 27�2{K�F�'� mess&RG-�encrypL , a key. }{}{.0i�$ \keywords"�C=$, QKD, MUB]�3pt�O4u6Ve{�.f�|1A Editorial2vpt}Q�]��%) USE THIS MEASUREMENT WHEN THERE ISs%) A SEC� HEADING %�]: �+M&�S{IL)"} Ideal'um!!&|=T(QKD)�%D`Us}UBB84}a�Sn!��9ecure !pMayers96,LC98,bbbmr,sp00,gl03�N!"4��4�!�g�/ wAI!��6e#U�-vs.-,>urbVMd�4A�c!�Wtocol �U"e}��Rs: Al�&KWm�Ua$(of four posP4#S ates?3dom{Chosen�($|0�_{X}, |16Z},�&$$Z�*�C,%�s�$e2!+$X 8Z$!�5"  ic *XZi�!�6�� e9 dropp� EOL�&w5n�*NW.��<s�Kine�examp��.�n�a "�)Es1��# ��>BI� !�Bis�"&2 �Bob mad"�1��s�Ainguish"�<�two1 �w �h�E obse_&�.!tusM1����1te_?M �E{5 aUW$=blockA[iOB�S�9�2=ةޡ��T�� tA�GXE!;ɺ � �S!:�KenoeU-o�ed�(p@,e'�>!*:�t>a)-Ii\.+�6� � %YY[c!�+AF�U��s�U9�l�.�)�Le��f�Z �2��. �E+&aew*?a"�8setup�B� $D$ ���Ds�!� stea�,%02-.-system�XE)r��( QKD literH$'q� ��; Bs: -Ysends {h<��ra��%am�Ze��XoA�/ i�R �N>� Hilb� k . ShAu�[�Pes��5hB�.�5.e�� $\log D$ }�&2+0"[:u� PlA{�F!ou�i� Hlized6�`qs4by ��"�AYX power]*�S�3ly&9~ M !� not p' W�` donh> nexta\�,��Y!� J�to re�1g���9o{^�h.��V�=!Wy � Ahe6�%��%�,��%T��: a'�zg�.��)�.` (%��) in 2\�>a�Vnt!���mJ� &1 �).�&y ]�1# uLbl�5bia�;� ��y n}� qYp,\�[@,  � s]�&{�p� b�k� *aoAR;at ��in �\ $3$e; stud�-in^m02,btb8 Sk 7 Mofor.5A�+ attack�.cD$�-b�Fre�0ed �ags*% MDb��J,�q� technique�� � }n �Iv to p�� : Chau�( % By41trast)� �E ape} !�c�!6�J5W}. Alst=iEa"I9illumin� A!e��?hipa�FJ� s (MUBs))6id81�m���F. �]�Sit)�ho>A |eigen�1��]E� iting ]��"�@Am�-IbbrE� H�we��w�N$ca�tr�Yz*mvs "�}m.�di!�>beMeedC��!Ian uncerO#t2binciple:�8�d�Qs�U�e�� $�N�conjugat.es.� adi3AA(�!j:ZQG��Y�,#� of5�key�0�T5 ider�R� -�&G+YH}. � " I sh���B� �?b�3!"learn�bly8�Y P�OPrn$1ot . t �%�c $f(M)$,=3!'��o1Ic� $m+kv.�5=E� !�� : )� "Tbai < eft| k\�>n$nR�g�a��;to�.-t�hclD"noA� ez�Fpoplus m6�C8)$ $��� bitwAexclus or (XOR)m� ion.� c� n re:A9a9QO6TSe0����ofE+�$k��5 �wAA�%�5-+��nI�C!Y. How maY:I-�p �?�h"'A�m7#A��F?hpE�A2h$m,7or��aBA�2�����eCa�l�^�wB], $m + k�j=TI�� )[!12*nSn-bit� $f(ma;�`� 9�squa�rol � )�Eve's ��=�!NHadamard2�dP%�>�altern�F��k� 7�� _j�5#)/-Xhl04,rk��U�QwVtend 5��э  beyon"r7^d:#�_�2�%.�JR)?.�s�� any} MUB.]��B stru�2͵�Es:i a� �M sec:A_%�s} !s - newie��ť:�!~&�J�l accef6 ��� ;F� qkd}��z -n GlGd ``d-v�0s< "0�� ;Qly inFpsA��IaHA�.] ��L0!:s�@Bgs}z�HKhx973}�fis:F�i&*@ 0} )'�H$ H(\rho) -�Cs p_s _s)b%B} � 5 � Von->Pe p!�$ #G $n�I ma�"rb8V7��){�g��� . aik 2� deal exp\F�a���m�Gb=cNrm',��nx% �c>UsaL�c mple8 _�>o� � Tsin!���i�O��,��"�!{We d{elieg"is%�d"k��[`h by��"� pur&(*� ofF�� {8�>Ae2�.}"t�3��R=�s�"x l��7��h&I�c%hF]����s. As�Ke�see�E���pLex� funda a6ivs.�D1�%�� �NorE�oprO�\��.�L�im]�2C ght �N!X robustnesa)��qM�aCI�)8!*�.*b�>�8develo�a l� 7o� tra�} then!�Q?at ��!;�F��0f{leQI��:gen-�3-G} ���>h$X'�gth �T�*�${p_i}'���A��F *} H(X)\g��X'��i ?(�'1}{ H })|p_i - | �M�n��%prf $_=�Ii >Y $, so�w��j$f(p_i)�K-6.BA�ELW =��i 8�Se�$f��{Vdk!�isQA� $p_iTT $; ts��] :6{%�ie.E� {&\ge&f()%Ffrac{5B6A)0eN Plug�d� U�cHi�>DIv^� &=&\K1\\ �1-(��ޒ�D =& H�$B� \qed^-^�nbit_miY�B S)�� s $sM�2� p_s$ EA' U��IJ�AecedNS &\le)W A�yp_s})%ue |p(e|s!\ p(e)J�qAeq#Ml�ofB�Fj�=&H(SyH(S|E-�  �p_a�S|E=e �F"$,(G ) - ;!Go>�|p(s|erp_s|\-W=Mmeq�A\ : 6p_sJl|I�!b �}%� - |�J6�:L*}I��,1�&RE�SD} IZ���� � _iI�{z��k��  !���E�nJ� &  �ьm)AU�5� � dev�%$E� �� E$=�N�Tr|� _s�R�|m%rho_sNT>D��(�T)+��.Q�Jt�0ng�!�.��C�4aZX6Da �V5LH$I )� $Tr(E_e �)R:�.!e=(N� cΦ6� - �� 9� )�� J�� !:� fac�b�!;0#inB|1bia, a��atqE��E,e ^�-[2^rhoJQ�qeXf$ RxESJ��o�čcor�GE.�co:sd_l_pf!!of��%y $1/n��4\lee� n15�z1}{n}}�!�$�=. � ll $nh Jgt, ̝�'BOa�SDr� F����(loV�B Z��c�a�c � in h| � � �( u*�}H af*� ��ef ��aOgeD�֩�,�elym"g S6| � @ir"s+(on�# mode�i.�*�|process R �A�6v^ Eve�is(x�Mɓ"�&l!way, OuA�"����)jBH�/��=M�maye�? �{"� *eKKey D(k ion}� ��0now ��tools ne! ar%�oOn�]4�P � "V~��4�4THeisen�CV��[cb��()r5�^ )�Fb8.}. |>ke,,ol�."XQly� �hnP�tped�5�-k.$g�b�) a B�w+;MI�&E�� b/; A&b.G 7��Ta5l;nA�o�'is>*��awb�H�].H%A�?o(p��e�ob!K�1�m�;. Figu�N�W$fig:basic}�.�+ aticA��y-N�#&B� �. ��hers�Ai"�!rAwa-z#^ ��x any m���J�!U0enBw `�#iv��-�%�����Q'nd{s !��"�����*��9 Uisto kyO'IdW�vlet�5.M<�Xof"�.FM%Y�),��g &\T#�2!��'E-� "~.*� �KaeGi�u=6xmqu�Bo��Y.uJ"���a] *�UEA�urb�H;� ,6%�a"_#&�1�mn�1��ɼ'.a�purposxHa�j|5f�>7y1E��ubset)�tCb�ferSngl�ds!��5���2Eޅ � e o_�r�+�assumpA��O�1%�3�=� is l�t$ia thres��0��JtQ6��&oc/W��ille+� �!;� y��w� re-��`�- �. Nex�(n�j!�y�privacyf02&� ���as�!23(ase�|* �MRy�2��}J q��A� -2O%8!&as�pg6%Pse�*��6!�% j%�c�0cE�cod�&�>f��<��>} %A��_�s.A%&�� �8#� on{M΁6�!2$*T6,.} \hbox{Fig�U} �D��la�mH� � Thu2)dM�f���p�]e6" :" T�a� hear�ll��ur�,�8�!$QKD. While�c�%sX�y6z,"Eu��k�s^qg)&T �Bye�Ti.AaB�.nAs��."]�var�#�f �d �:research�X� adoO;�"�!��ategy:]3I>0Lts9͋���>�4���A�o(s�"�(�n�(�q�~:�5!�7A��3�*� >��� ��re��͝.67 +!.� �� ��ba��( � $X$)"g ��e�-��&�h=> bEZCn T���T� C siaaneouvs:� nh'I�b� ���|,��Cca��b� Bob8erence�Z!�o�� `��u^E�*��:�t&�")j!��9d ��t ;4ab���t%S� 6Y %�*��1~��j1"Spe���<yKA��/"LC98}�an EPRw9 �8,� ()��.;!,"_eq$") ��o�"�2� � greaC$1-�d$�� $R$ � let�Tn!2'sJe-��s��2�)R��-�uFe)���� $}{2^{2R}-1��*�a��.}�:�'m��X8"!by Sho�I �Jk� )�i&�%�b-��9)��1 . R)I�,aaleP )���19U0Biham et. al. K��� ce-n�"*%h�0� �r h�+2�%�Fp+*�#at$ �3�|0I!$\hat{v}/2$iqs had&�.�<ez�2�o�aiX(Xu3a�% th ZA� vice-D/a�� k� Jminnw��� "e   a�c��%��*��", on�=�.��� U.p\(gI\t s:J}is +x� �:w veri�g(ir���o��{, e��7�*ed&4�#W �  � z)�.:� ����e�"74 $D@�*@7id�q;�x.4b� ��&/+. 6���$u���#i!!�!eps M� ly U�6B�o:�K�� {I �>.}�b $B_1=/\{KK�I_1}�t2D(g��o $B_26@psF=:�2wobfa�al ɵ�M!Z9h{�{ s<The/esai�#be �g l*�7 U(MUB)}�(if�e )if � vertL{�J _i}{�j�"��}{\��D}�B� � $i,j="�ud�vL= e{ {,fB}_%m\{!Uof��) �9\cc^De��4\IydRe��} (�v�5)���� pair8& $�i�;j$�% B^%/L Dxa AQ CB_+we� 0B_2^{\dag}= H&30|H_{i,j}| =1/1]m\$H� �h��(x.�6nce�Qem'sb��garA1�y�d&1 C}!WJ�a\A�)arS�;�U�&B �=H�.�+:4\ � �8 oremD ��<N'hatAA"�,A�� g>R;� �.6z7\/al�H�v��8!��<.X��MUB&r�6X=FQ2�@� ����Q em 1& �r�*e*.s.� �JsŽ �#�\%A��.�7�;"�lit!W�@7� mpha�M� !fei��-iYP�l.�?/��\h�na limi�e���p#��|�u�)M� ��!E���#phUz��� �ifa5��nd�3XH,oV5C(P)%�s�In our a�\W� ]Ia��e $2^n:yl3%Tjme$���Vb .l ��q �}�0&(/&�<oykin02�R�P��h.�Hxm)��5J ��0 2� (J/�%P,"e�)"�) d"<thm:ivd # 68�ePOi �TF�Be~ (r&)0�,�r�D�1 $A$)�3Bobej2W � i�2S� $E$)*� ���Mis�*��s2i6� .�'�:��EA� � Ze�a�M�*�m|�:y!*� I(A;E�' 4�  D� LP_{\widetilde{e}}}\ � ?9�� We�+ws  :N,_out_� ^s�_m�_|2& ." O6+". S2�$"I!N-a�+:�!!"�!D�!i� 1}{D�!�+�! 4y�� ] o)��*bI&(va�  &�/�&i % def:.D/}}eY�0*qP�@ Eve "s�9n)�m*$i�&�$.Xa� !{.&B��H$!9e1 orig7+ 3 �A� �AT+,�?a_I��I eUA��ȃ�o�w�f!� 3 (saye$ 0}��te�;>�'&�7orS��n pas�his4��doV<�F+uC.�o�M�sN7s. ncan cha�er�]A @Nk � _{E} i}_A\s!&rel{U}{\� arrow�{j )E� 6jF\W) ��%q� aR�P\y�i}}&\��(j H_{jifl beiZ�� !AB3�G�-a] Y4$� ji}|N� . Ap"0�oA6'�!4,A�R9�m6��yB)1�)Nj�W�(ket.+D%r�h{i',j'}� 8' i}H^{*}_{j' j k5"}$. "*� axiooH "�%�A�;� �a�dG+�i}�wG+ba(��m m{j� $P(j|i)=� � ,j}} I0w��IF|== i}}$s Js'j'��� $"P}6��}R!Uz�r�2 w pr�W� 6��x%V t  7�s EMUBB�} P_0qj \sum�1(i)�P}(i|i)\�b'`Ņ 71|;�i}J�~RX${k,l,k',l'Q� l i}� k lA� HI�k #T�E_{l,kI l',k'}~ysjE e)2 }���eq:p0_suO .� } W. � ş�� eoů$'i�t:H� P3j I]!> �(E����2�> 2�� 1R6 ��U� *G$P_0$. E�o�aIo�V&� u�"c !&hi_i}�� ��%yj�3Eej}}_1�^i_j}_2Ua �+�"�960WNV��#&�$i$. Due9K�s�!,:^��� � n6e6rhI uL $Tr_25� =K/ 0.%`ls.�2?IF�o�EB.�5����j}.�iQ�i�%!�&� Pm� "6u�B6y A` 1DE�ao nF�$.I�sh�no� Q �K.�6b�2�i�t.�G>X �Ji+ fact,�!7 fO��wei-!� �rHz'm2�$W��caliRt;r1���>�0���5?ŚA��O.�)�psi+�t�P�-ora)aj�G�Vg n�g,i�Jb�EJ�N&=&F0{l��_{l 0�� l' 0��Eklm{lJ�A1 H k�NS�N0 b�[{l}_kssi^s_{�SS,��bar_0: } 6�Qp.�� =� l_k}FO�4e��# "a5i \��!1�)a�.d*}I���6;$�$�# $2l �) �=e ke}n&.-maX��z�!$��< Fhi-B3 chooseJ'6�=%�# i}}{ AJ} N�ou7�%jv!uA, 2Θ3 ��$|^2 = 1/D$i�)�NLa�"n:n] {k}}&A71� �l �:�:� �� |^2}iUi i H%�6- C ir" delt1��c؉��G�[w�0� ���� R� i} a�B .�. � ��V)�J�YA�H+�ny:B06� �d0}���C�� k�N1����� a��3�N)�d jT֍ \E\D P_0.5�}!�e !�?��FA$!�*�9 �N� &sI�-"$2#isomoTfc^a�.<� k��j k0+j,k}"� D�a� 3)�7-Z7�>tI�A�:�!�'h($e$��#F�ed�isY,6�i$ 23�"i/$i+e$ݤd�.�5i$)�� $P_e�M|>�eJ�e}}/D1 ��a��cJ = 9�i-��de���>��%se 0 �"[Sy�I8#ype9�`D }*�. �ewr }'� ^ %� /-�*� M��wA�70u�braB2� rhP%9�V��La�e�:�Z�����i� ? U�"Z�+�L |^2B�S�|Hi5as��D���A�Pu�A��Z�Z�{vy!-R .�^]���$f(x)=|x|^2� 1�x,� n $|_Cx_i!�� | _9f,*�^���)AhC D |$]o HY^�%�z |^m= kf~Ce�b" Y*�k.� R�j}�k "�:"�]ZXB�k2�= |%�HB�Wi�<"TWny� ue�(�Z�7�8a$k=�u"�2��&>S&> :��F =�$;�N�^ tog�Ba �D E�B.�K0}��aCn�J�P_0\\ {�B�% r} } =�� ��BA<w��yA t ��Q.��w@ i')=�� $AFmay{ m� I B��_� @ &�]aJ7=ediq�q|o _ �s'.r"�6e��@we }��:qN��S�qr�N�.�\�>��Av�Ej1�0,J-  }'7A�bf)5 - f�b�b:pv�(s- fU| + |f ��Fvu� ft(2 1y�_a�N�5RB 0}}}q(1tV?Fa�+ ��}��:�\�%0 =& 2Q*[(���>�+NZ������� } �)%-E]v/���� } += ~W(# I�T U�)^�ޚ6e�# 5� �r�r_%j�`� :[$ 1 -�F��re�1,= P_{ }� eA" �r*�wth>~Qn� MUB,"�fs+*. �F6\ MYgiv/"�/t"sXW2 /�A +3s;@;a*]� �,*� Q*X=_e����(us�.* �!r�[rem�D):.uH co�bee�$es�12�b�S�)v[o�Z�&��S��5a�5pl�;"6�M)12)��#in..( *0.`(.30=!��(KI2l2 !J fO$��6l�alS�T�+.?s^�DF~�-M�sp�Dm[ Accor%^�7ACb t�(D,!=�4`*�'ha�0�)!��xp*2b"����SN�4B8l�<*26� �'"96� .*`"s7H-%{6x8BaZ.S s�6�g�*�@,keyVs "�Q_m<nBu2A-��4Q\"�`af�*n 5H��/|B�b�Dn?co�,Bfb�%�a1B�b�eb�ebeb��i��*io�;.p >U3*.�&Y-{!�q�nA/��J aZEe�E]a�.�Z}:&�d-�D!i�key. S��see�� waR�to �$8-�A+. valu�o�'?m��indc5oru�:Um)=1$a$m=m_>elC��a]H� ��92� �e. !����itself. "�#; s �� � d$2{"�D3�9 thenJNH(M�T$log d\\ H(�e[ 1}{d}  -&�"�8*h C|X .IT;M)� )R�If �is\/� 3\�yx& �$wE$, $d = 2^{�}$, so�V�"�� 2^{-  �N��"KA�AT !�"@g2��g.�)*i3< QKD 6��,v2x s:k7C���?�d� }?� iorii �w�xuffici���kev ��>�ۅ�ny]��o]?tz"4 xt ��_| rP mustK.lto��e��b0baaM�}, �aSi����p��J*��Cm)*�.H2*M"����K�bnot} tru@M1auq| IjgA>'�g �zX!Fc $k_�c�ido��a�� urb�k!�#89y?M}%{��-��Y�[J�bg[�"�, $+] all �l E�at 2.O ?2�Bo2_k)*��$q�..B@Pw� si�� $p_k&>/d�9:!L"�-iF q;6 y>2> $*�jAs�,�$"> |>�/$m��B�l"� NKnu�� ��.O>r�"!ah<7 tput�6&�)�iR�)�^.�!U.���]#6fp_k_F�(� ̅��6�� �N!�& fQdZ�EN� �k2 ��B5A�E,74!�*<.���Tދ}�/Wlhat~� �a p_a  E|A=a)B�]4b.m�VJ� � eqn{%�Jb;&�� #.i%�� !�|.�%Q}^a�Ca.7K V|2!�C�WI)�=j[oj� w�z�)C(F�bb| r��2�N�9; �2g�I�.V�%��>\ZO� + 2��b�!q��>�=?b�N7����I�.���>�>Cz��BjBBd:�)i�DAk 0�F $�)��6 ����a =*dɾ�{��?�R�aVx$)�)Z.�5F"-�6sG!O�,D��Bx{m:�x�mL{a + mbL:.9Ff& KB��&e��sumW"��� $��dgquwHerh"�R$m$Se�dis�iarZ� um_an}55�� 146L�RM)� )� B)P*f!*}�!*q� N��46) @6�M�f!)l.��uRuX�DA���>���=&N� (4����N��A4 H(Q�����0�0.�6V� F8W&hBO��&btCo���Remarks}{~d&]lz"JC+p��&�A��>�"�X2���: vn�t&]�Z . M�_e"WT�in"�a->I>�>@.��her:"�h�� a "���Lb:Y,�� �*�ir6��G�>i�]. � ܯ�dN^���_> they�}. �o.?~!x"��\:cL%e)/�. �sF��L^\=��nA�?��CAH�2ZoU%Jity��;- {Ref�Rs��. �(style{unsrt[ i&%�{�As}fW$newpage �en��yV�won�L2�wU.1&{�ws}"�&b* XiMU�2sej>f�Hsi>�s; d� or�� E�$p_{s=1��  �� F�y!���q���}2��wia Đa*&d $H(p*�h�"�:�n yeny(oY1 J h $H(0)=H(1D3$p'� 5p,#p$pp*�nH,}{p'}|p-p'|$.��,Conǀ(Jreg  , $pT% p'� p > . j� �Na�`)�m,�I�gu�5 x + )y) `f  H(x)2H(y>6�A%j$x=p'� ; = p/� �y=HJ�z:�pp l� 9p�.��actly�w�=��.� �*)% /��a�MXA�r��!}%�sBgCv&�T)Li��+y=p',xM�%� O�j '}{1-p'}$� se� �MV�i���Ho C + p'- pM�� ^F@ �r�q#p p'M �+ N� A�R>%)\\ @�(B`)c#39s.$I�*k$p&~s��;DS/a�< { �e2!�-�,�%�E ( +k�f!�YPzi�a�8=$A7ekpo���uR� !��,�\ �-�%B4p'Z2\Jr F2�TB�E)/eX> �U$S$ (i�p(s=0iJ 1)$)a�b` ^rE;S^I.q50�q�m=1��m=0JMmG.Vl�s�ul ���$�q�� $p'=�1YF3���6F=N� I�Br- i�!�E ��e}jAr{e} (H( �BrE�J}{ };r=1=r(!@| q%b o:])�KJ#s0)5� + \)�1)2A1� | 5~�J��C!��n�PgEyR&eh\ +.�0I��C1-�&�,$p&p#�a�enJ�"�Z_ ���a �p ��< �Z%r$I(!�)B"�o0A(�1N a� ~Z )Z�8: . T "�J xp= peres� �bP93]a7DgSo� $x�Aher2�h give* \vis:r=3q_s�!6R/)&;9(Q� O 194))�3:}?�E)5_��Hx�ti?�m�diaý�Ki�c QJt ambd��*9s.E{@_i)Tak!�E(A!�(A*fac�!W$E_[:���: semi-�`] {e Ef:I �Uj~k�0��J41c����rFFB4)AE_e� �:� Ati |��_i|� ;:JB� Gf@�%q.��GF$�pYt^�ps!"�2��ER����oR�A�A�Z� ��N�� �F� �<�_� 1Mp!?ge���e?�b#1� �H�+23��� �U.�^ua�ka���"k ��1$,�>geL �}$�l �!h�;f ٯa�� !�m^IsafY 5�iqQF>�Z� b��M_*X �]��+19�# �-F��#q  F1�?:�� �i� e Tr�NorO$&�@s�i � ��!�%, %4iRA�iRU��.�� a&V�!"'?� �� .. �K�Ki`R2XJ~s."RK%�}�J)��p�p�N�|2h�f�d*�? hi}|?)�#]5|�^Tps#^�D: �e�@JA=��K_!AaT�*�K.�M�>N��]e_0"sR��9�e_1� 1]�1-| ��}(/�?}� si}FRInv���rM0�A]U�b��b`��} G!W5B� Jd� <��as2,w�n�&V�!�(8|(.C)UQ� 1,9f.#1#1�&&- .O}()�>Z70!)#Q� t1}J� " is��a�tizp2$�Bx�! �c�G:$ %'� hQ�e �%� oؕU.3S|arV  #tac�U+}{-}u| 96F�~� �5F�X�Qy �L%�_!A��V��z 1�E� |E�X&k *�ahJ��i.YLet�� %S ��wtNeLL ��U �Ax� e$I{xJ"2V[%v� &=& .BB^�^&� � �.�2�nEF=�; -J��De� z�g.�(n9V%�:9��� ��.�� i*�yB�Z P.�O!`$:>�2,ER�G "� {H}_{1}\o�\mathca  2}$ �� ?YV�� ='� .� Q�Y m�&�\ �e�:����]�A�O�NQ,|\rho' - \si�gma'| &\le& |\rho - \sigma| \end{eqnarray*} Where $&$ and $ *�C$ are density matrices over states in ${\mathcal H}_1 \otimes {\math 2 YHthe partial trace i Pone of!0subsystems: $� ' = Tr_2( ) J �'= �)$. ܈lemma} \prf See \cite{peres}. \qed )\fonts} \setcounter{MaxMA2�xCols}{10} %TCIDATA{OutputFilter=LATEX.DLL}!HVersion=5.00.0.2606?�0`BibliographyScheme=Manual$�Created=Thursday, December 02, 2004 12:11:03}�8LastRevised=Fri:93 902:22:3^�G�ics��322�.�DM�Shell3\Articles\SW\AMS Journal 2P`Language=American English.STFile=i ci.cst!�(newtheorem{ }{T } \ 0style{plain} .3(acknowledgee}{A:6.(lgorithm}{A 6"xio2case}{C6laim}{C6oncluA}}{C >$ditio # >"jectur~o :$rollaryi 6"riter h 2"defin �D 2$$example}{E : erci!&E 2 �K{L�R=� nota)N 2:$problem}{P >pos �Pr 2& remark}{R 2 solu �S 6 umm%^S \nua�$within{equ �secI< \input{tcilatexA�begin�(�\title[Generalized uncertainty relaLs]{�# �kH\\ efficient measure�[quantum �L} \author{V P Belavke\Xaddress{Moscow Institut�R(Electronics��PMathematics\\ 108028 9@USSR} \email{vpb@��,s.nott.ac.uke�anks{A� }�Ps EEC support through��$ATESIT proa� IST-2000-29681 which allowed retyping !typesett�this paper in LaTeX. } \date{June 20, 1975} \subj��\} \keywords{Fisher Infor!on, U=�Re-�, E5�M.�p edicatory\t)T�s�nsABd%r �� from T�?r� � cular,3%6=8a Lie group. Itz showAa�%ese �) (globally at!able o1dA�e�r9U re exist ZOorAPsi.d/ y* \make��� �{I-`!�} A�develop�!�rec��yea)4!F y!TuNY� .� (see0 reviewM62}�?!� aP � d-Pre) has made it possi!1ta�M)A� cept�e�2 of inaIat?observ!{@s described by no'mu�� oper�a� d, using ��,�solve a �qyER���9&i��( and commun�lion-@3,4,5,6,7,8}, givi�}.V� of}�:$Heisenberg2�6��ities su��s, e3J I� time� �4gy,Aj phas 9Ma �9},��to � e�� ly wai�]%!D!8n cin Xu�&cha��u!" D9}. In accordance  �R)�, everyL�rA�!�U�!> sens�2!aA�itive re� �ident�*Q:$ $\hat{1}$�8Hilbert space $@ {% H%fi�`-vectors $|\psi \rangle $jI�yl? : ��AU} �@=\int \Pi \left( {�rm{d}\varkappa \right) . \label{cKJ % HeJJ cdot<$%� n ad6 ve mapp�z(-�)- 4 Borel algebra- frak{B} �X��aM-a�1AX\ni �$�)o!� seEQ(Hermitian-p� ve (i.e.a� nega!�-E�ite� .)5��j �$cal{H}$. Sa*nb  [ � $!\ $ will be called \emph{Q΁0abi\9(QPM)}easimplE�2�. E\ }If $�rho�aN[�>"�Q�, a_.w $\PrQB6mna0nt cMin B\,!e �-�m*is evalueaSF����B�*} N�=Q�TrE��![M � ,\;B���t^Eq*}% w rme$!5o�z!+usu&�BI�-t��!Ti!�(n (\ref{a})!(orthogonal, # �A1w� C=0$���$ $A\cap C=AtyA�$��n�E� r�=-!�ed�V g��al��Ms)��is M�:$X)|0bb{R}^{n}$ re� i n ordin* .H� ��D self-adjo�~Q�sB���x}^{j����9r�,\quad�<in 5�, ���:�For%�non9� QPM%gr�no� -to-�(corresponde�v(between (% 5�� I b}))�6�1�= =Ns,� @ �Bhff� approx� e261�9n},Knot��as�.x Bse�>NevApf�Ly� mut' $frequentlyVy� ��Duniquby a S le non-�� (�^��A S� %\8EMQ}) or, more -Fly, \famil� 2� h5!.� )�a� . A�nn q1؁@ebl as Z�E >Aodirect�I.� (.!=�e�Z�i]  extend&# b�ida�he origiC "a�J� \ 3I� is c9�nţ%(s%�c�TNai�'s well- �ceP onA= � AН�ByA��>a} � �6V �� 1��QPM� sub� % ��� O&�resulL' p�� � how�2M�aֱ��le� s u@�. &�� &� j�Ņ2� �"K ��� S | >� , d of r�(ular mo�umIm9� t �Ae;.@W A>e�first m�t each�Npairs --�, ���lecannot,a�iI| E|,6�byNAW&� H}�]��A�ir2�Mbc >e6x aes�G� 6�6D%�s . As"jEf�* �  by�n�� symme�L!�V��he *V�$x {11}��C�}an�A� �Fn�!�.�)�!=3` a a lw e�� vers�0r� � i��gA�� � unit�re�en�576�tr���s- % �0 \uUFKorB8). For "Xi�9Ta harm� oscill�!E� upL the e�, itsE};6 ��equival� &fixed e e _{0}i"3 �� B�b���i%>{� k\v��_{9ta }\jok rm{e}^krm{i} -�,n}% /\hbar }.�,f� �ni�e��!n��F�it�!o6<�#z���kEP�%�.ks.K aŘ9� t�n�� *�Ni&� ���lambda |1H%t) =\l��:�|\Pi %�2e F>!��J�o!�N�1�M�.$� mean�dr� "o!I.8 �������q}�un-"0expec�>%p�BB�n�# }^{2�y- ]����&"J1RWf_{\phi n1=�-'-.q�r)g 5 �n�QZLJ��!ttotal��� !�accurac� U�F�} R9=u�:�i�)[) %�F�d}%*!>�\�,�F^<.v -Nv%�] &lunJnB h� miT ndA�"� dist��)Q]�3$%�"ta�- 1}$:N9=Cf �]d!I+.a�f�)I7Y�Ap)�M�Q��.�a� � L *� prov�'� ��6%Lecond�cy m bel� b !AM�/4��=w-nYz)�M\%��$$� thus $=s\geq � vG24�J�'��n}J� sڊ�= )'J+ ,X 9 0}Jis � 2�� A詌n}? th $=1 Ryn��n> �.is�&������m~_ �*�'sj�A� conjugateI����i�ep� l v� i:�6!.�satisfy�h "qa�$ ��). In S�T,Cra Rao}, we��in)�t2Wf�! =Ea�R}iwe also��!another�i�! cic�.4�Z� � nVs dapt[+!cY! sit�%���to� g"A�forward�ultidim:,�Y22*k! "9% �twoh})!S� but)m� W)5iAZ"��>�)> twol1A��forEnI�q�M&� 6�P&BKan &�L&!Tr `1�!ielPI$�!�alY� o.i>�6"A� hose*�! rol�disclose�2�I�!qn^�� at iE��_"�!!�x .�"6�to be &�!�a�necess�!{su"�%��6� �.*�havi�9�U9�ae�\({Iu�B!#��:�Typ��� um SAd<%-�.< \textbf{1}. Le� eft\{ ��_{ t( }, jM�@} $%%)� �"�s�BR���!A"� �aI�[$AY&�.�$smooth fun#B"� real.� ��8(� (^{1},\dots � ^{m"J�a�l4n manifold $M\� eteq� �8 $. E si��aneousA���4"�$� &� :� $� ��y�& row�  random�b�  !�$� z�R.x� ribu�].�:.� |],g�`�BR.% � H$2Y=�VeT�'q/2�a�d�I$aQ�aone�(J�  vaM'}^{ik}s�� [V (� ^{i}-&�1* ^{k6*k*% ]F?�� co��c�! trix� �I�[ J� \ $2�ex�>~.a�-�tr}C^{�"era�}R� c_!R%$ "�a "�&�!�3 x $C� =�m�-�cos�N�c:Fy�"b i.i.�%� ~)��.0^�F�i� play2 ���%�tensor.!�%i��a�y,6 Einstei�m)on= vene��ssumedFJ$*} )PN�5 sum_�k}b0J� I:�we shall�#  t��.��at� axJ� QjZ[.�i1� =Y�a\$, un_,)�a�Qq6$!Gy< *mU�e�uJ!9":�"� for �Bqtak��minimwlue. "� ra�,dC1}Q:�b�of�#*k %� �?u� S"�)��T g}% �!�� loga3ic deriv� �p����rhoM5>-�!Lto (�i�8H��]*s�#6�>Uk ab�"g}��B�+R q6=2\eial%R/,\;%E!:=\frac{} ��}&�'c�09� }% A�E� lass/I2is-���d!&:M�{�� sf{G�9��[ G�đ� � oU"}85�^7)�=-\I_boEx Eqs.! c}),�d�3�]� +m\ as%>�}�ikfj-�1}" QIvA �=�))��ja+I%nIi m*� m�6X".%dFF (NotZ at dueitA � Mޥ>!�B#�&>V"6^,~�.j a1�vaF�5Dj =0F�;����ix$R�%*�h�� >�}: / F[^{-X �&.in M,� �+eF�cis�� stooY��,ofQ+iitenesu�}��R� -�u�}� Ib]��$.% %�=a�*; �4in �%�>H4-1}:G^{ij}G_{jU delta _{kf�d=�'e})�'�/�� *�62 & % ��T !i:2 �/(�Z�G"zanalog� :�ȵ�1�9*%6�$�w'll��&C"F��,mo'fair,"8.��@of��1>of �{ Fh.J3�� � lo)y �!hgeodesJA>o*} s_m EGF*� +%E�U�I�) a (����q/�2Y �&� ^{1/2:��,�+n@�4/f<;4� EU;toJ��an�@n9� "B4)�2.} Fu�r7:� a sl<lyE9Q *xin� !�c�.�*� dZ�!O$ ?E co�,k alpha&� �l�n��)�/e &�%��0S}$�riza��/� � P rho"� mMF &t�2�_� �ebe . ��b U�&] >i��,I@A �2 �66�J&� ���TAl2) �9>�Rm� �1G R2G �$ D ] &| F� *�j*� 6L*�e�>y%[&y� A �&O�t**|2vf��U,�!�6!FZKE�sf5U>2]D �F%��sf{% GZ"�'^G2�.�f:�}%.�'a�;��choiceAq��%j�QEA�1s$i�sfb�"�Q�;eft[ D���� 2�$% nD="5 6�/I��$,O9~2hq69A6.U�_� ��-�^�U6� �1f �� B�*F�:f 2� $ h�+a<a1�$ }�N�G_{klZ�i�� )�" ] mD �) �6� ^[!uf�(2�]�4Lk}B]BN(2� �� l}&l&� 1�)N�#-A��^� NXv� �� �kE�B5[=2b�-�ezF\;F� 8(*&�NNHea2.d ���*5D"Hb� �wheW7+L&6*EQmmO) #�1w3!.W,� M< A ies,� �&dX :ls@ 4}, 5}qYb� b�(on [� h  !Z� � ��@a� @Q.?)��R}$� $may differeB]�&� ���DG4��D6.$. More�K �6\ it >?s<t.� � 8cX �7�^ #0n�9+1��� ?Y� !I  =� ��\�A}/܍é�^  5er&�> � A3-Schmidt2� K���aB�7�� s$�ird�#d�=%+C> )3.,!�6� i&�7C}$&�/�� yticR � ahuX, ����Af���A im�E s acquir s�f\� Y}F$ *6D., qD'� ��^>"�re 1s�dep�57�+NGm�3oAYue�"Lax 5}.&�$3. }Suppos�%Q�-�� �in�3$)g \gamm (,�'�S1g.�`:2"�� Mifi�Cs���KZ"�",0d�b)�=N� B��%A�t ~ �4 $n$-columns, �=oft),+5<da�$ x+ ( �N�C}[;% ,$$ �= 7+\bar{ }>� '� -^=\{ImG�J2�.f$*) 5 $ *z U�y � &��&� .4�% ; I5�(iFA#�- PZ�XY^i �8" -A�a��=mannerR�IfN&]=�}5�E�J-�k}}+\t ([ �2 �.i&�!Ʌ)�< j79i!g:�% RkyI}-��I.� �Fn s)A�#:`QLl}=2��-EY- ^{l!n�S Q0A�}#=0=  $B � e�72��b)�. ,\;i=1,m$a�ae�A� ��M, {�2}$x stB7$.>u�*"�-i�y� �2���>� �$,A( $ enti�#i2b<�S%T � (e.g.��by bi-rm%<�� �mprLFQ2�Ak� -�}WW�d�a� !>""�3� >R&�]>�=M��&e *F)>Y}& � hE�� Q�".�oe�% �@C H"� ��X%F�~} Qk]�n&)gF�+>� �o �9d��2�F�: �45��>juP-at '�/:�6�\��/d "<� �@BX�!�&�!y bW(� zero%V4V\�7EYN�pQ! +, 2�ݡ3Rg1/ Du� ��EXF6q-.�qJ�#Ah6j2J-�9ivz i����H�[ H�%�]�n'} 1!�v�23,1[q��Y5�>>29%Y��n�"zhF�Obvious�Cis1Qi�>I"g'�/ %ajŞp��bits��de cy3� s*=K"rI�&>E *} d*�H}�4=)�d.UaadI���F��&omO$mplex doma2�*O}m+obb� ���s�E�&] o,O}X4*? a$Cultb�+� &] ���&�+1E*�+N;X�!�#'e"� �27oxg����:�+��"�G\ X:Nr"�+J�e�rm{�7�[[)x_ � \mid�E;.�Q�=%L��,:�Bvml%�% `J� 1r�&b�I !���� ��^*�'%;AD�m�?�5�dK"aa+ �J�2))j�!ij)Q��Z��+BWF���E sf{M �>8E�2"l)ͦ WI}_{j}- Q��Xj�DJ�JQ�) be writ�� sumV)i~J��2$�;��ij��)A1% +Q_$\a^~V kind-�r�D�Ѽ-!�"��a M� elE4R�b��F�70Y)]E��c2�! ��-[� $:U>LхF�-���e*f=-��&� A��Z�)7& >�=\yL�IZ��-/q�-�= +�Z&�?)�Y�RMU�F��!���f� ���A���F���;Zm�*N�Q�"P Q"N I��]�B� %-II_N��2A_uk �a<�2/\io&;D9�!�!*a�� v6)�q�veR�FJ1�!�>i �i}$ "-� ing")�=rX&h��?Aw/GTconvergKmintegra_ng�* o�F�9�'&�9^�2��aE_nW:*C���1G���@%2Kf�N�1�-w�.�$>�<%?!ofq�=CRcA�U�Qy�A�S>�JjU)��P$��'m�:�:7J} U�0N?*� A�͋� jb�)"�� i�� i��*�#�m Zp� aso i*0Kthe Apixs9of$E� sf{Q6q+DH>1�\dagger *�r�QeBg}�B�� r�#^� am sf{Hn�)Z9-1!� 4>�#2 4�&�Bi:b :GUsW#C j0g!��0]% _D*2�A�[ d�#.� &*�&j�e!��*�[:|S5^�� [ \ line&�� a�` �Y�&� 04. �1we*) see,VSb:�* ��/�,2@�%B{0?'\6�'�s>C{ Gf�QW�amat di��}U . Be@a�D2*} :PiH5o�? �s,�� "Ma�Nquotedbl!� 2E\ C,p� G5 Z� vz$. AllEse ds� pz[-�same way�|9~�^�{. &+1A��-m")X-S&I&e�\ge�v'bl���FE��i)Opst&j*Q1e%�;replacP!t.GF�hi6�n-Mnew2�2�ٽ �.�6��V$89�s]&�&�s��*���2�_P!&�y�Kj�1^r�%$�1A�ofz"*A �� .}1��%W�=��ɷ8 2�$!oe�C�XP�A"4@!&R65�4� not �al�unlH2�%�n7Y"* � ���D}$�"a#��>=���k%�(^)9��$�NW2 R?)*y�9%�}$) hold{!�A�B�7S T%�R�gvA�A�B�E&�&��lg�@�@s,��p�"F<vhlay�&C�1ex�>i�\ famiV&�^�?��m]D6�"�Ir& CAT)pec5q2�+t67 #>�F�C�U�W)*�r% r%)�N"1B%�>*�EorF2>*������ �ch&�N2'a�*� �nR-��4 x\����H6A�I�=��=*� twoJ�aw$_� p,\;2AI� arly6�"Ceq�cGa��be� &�:� q�\nC ��k� �\ need�_ )�^!�"�I ?] JNd� 8$.& 0 ��gT)��;N r�F �'6�^i��R�Y^{"� �71�K�KtwoJ�N��Zqs*�!�!jaaW= ��Q���5d0�[0pen neighborh�8 j�[�-�%��c� s*@e*��!tDK����Nf�#9_A4}%�|_-P=0q"6> }&' 9wF:�=�+2QA�iZ��fA >�2y�!? �% :�A�20!j\lhZhi2�F(!�y��=�k!�iL�U)� alw�Be�An�  F F(NJ��F?N�A@� �U� U�)}�J8�2���Z�H� ��J�' 2�%^��$! ,l?a� �0.� a�% -Z<+.�L���6Mc�+1�% !�N e�ingfu �� mj �Vq�z{!^� . P&_� rest���o� �& does��A  \K/ �,�&�J%�*HMa})Y/~))jare ima�`ryve5�=i*�&"!i-g<.>k3!B"s�# 9�/e 6�t�J%}=R  �($ �' Planc>a.tant)!�n�C  dzN��mea!�5(1A]G)ky ynamb ly*J#I�ir shift�,NI8 �$n0"�s<9>MfI%!!sa��e H1 tonianb ��% �A��`, ]g!9 ��u�bN9*W�r��i�:~�[��eVa� x.�`^��X2polar &$2)]i����TT-1�\al.�,�)� �e��Q�p��.=\�1)et.K� �C a�-�&2�bec!�O.� >&� &�T�R�]ay-��] Z� ^{-�6�-)�A }�@;8 twoc:�>8`�.A0m=>0,096v$ Eɒ��"�S =0$. Now*d �p� 2EKS���-�q�X{% Im�*%8$�Zl�. ���͉ Y�) \� �^ 98��i��� immediatvQGWJ]e�7tF.�T6hT&�d.�R:PpanD&�\Aw"I���n���e� .�0z�&�"�*�1kZ.5% !7�'�6l1f&�8^'���H&/(>-QI.q -\mu%�q�6+7# *7#j�/$V�.!�|)6y6� }.� 6 � @ �N6m0%�) ��Fvi%&c.��%f2�jf �I� (<.�H�@�xoiZmxF (� �2E�'% ��B"p"�:x1&x`iuA]&� �AS5�u+]�R� i��7 M�Ini�$w- �ܕA�byJ�S&=!�~�=a}"p  �s0 �NE��dt�� 1b��mA� Oj&nC �y6M} .� &�,twoJ� Whil !X�'��um�er�X�)E��( !�>ed C���2� 2��N��� ��3 .Ybs� 2�oN j�8 �f�Ji9X+s2�D*�X"�.J>q=R.Kg{�^1}{4}� b$mkS}�EMf.I 9sfy �� &~J�*>��-��_i��� �j3$2_7& !�t�*ɕ+&B5I��N"} * @E���!e �O-�6Indeed,�t� vR2*E"sF?3 ;*��AJO�Hik}/2%�}4ve�Z�}I>a age��Z�@ZI��F�%M�C�����^% SI\qp�.G�.)N� �v�c �m25d�' �> 2�U�Z�(%�-i%� 1�2T�"�%�(I�! 5�@�| �" ! �J`'of��q8E���A�> -S=�*ɫ ��*yA8�-� AARdId�\�3% ��.�i3�&�Lc�;)�&�; �!� ing:M���.�5�:�_� �l )/Nv�əK2X��)� E��Aj�resen�<T%�R�Y)��l?��R5�c@ .*%�|z��e2C�V�� �nFq �sJfF�e*}�q)Q�:)�> &&|�atp�:A�>60J0��G � խN�bl �� al (P #o� 5�ed)� *�&�� jq� u ._��:�^�MI a�"R,B�s%  $,o�I��=like ua/�*0���|� )kE�."�A�mU�,�Z�U�t&aY�ain.-"��V1��"R�" ��t�]AmMa4 ����#\�nvarph�i�dr %�" '?I� ?$". How�y�Vur"E?s"G^'Kin�jpr��&n�-why��o�~v��d s�BmplG�ed��7. cal�A3�M^Xs�B�r�on�C��but antiZ6,�?�gY�8s! A<pewb %}(� )r��D von Neu�=��R�� [!rho���`y _�*U&2R �-%N F+���}\Pv }: � }2/��xJTFx�z��fgyyA��ei�!z=p �%Bd_Dlowbreak�6�&D�y"��7&B!ə>q �w-G!�(� )�)8 *-atZ�!7 CM,"DH$ax�!�n"ۆ�ur-D):���$,��!iuWZ�& ��Nn%" .p*d6:pV����-�&D5QH�]�+��A�Z/)i��M=G� 8���0j %Rv5 5� GF��6.�F1&�F���IYsG�"�M.�M� �] VM���*�R}n\2�!iA�i6� �) *�K'&T69Fb.FFItc8pU�a�Qn �oR�.MQ.�� Q=g ��Y�� �� J/ wS"Jb�[ :.b !�i*"� &t R�nV zu,��.��nI��F�2�a)Å�&FkF�< U�.�-V-"�4Zm7A�#2 �2�4S6�1����&05&IN /]��\�}W�2J��r> ��$p� ��h{� ��� ��s}b 2��6)!,%-r�%]�a>� ;��=zAK k._>�oX6� r�]� �i�� jP|���J�m��i�.JJF��� :�~ �q5a |]M> �*�Oun�HA�tildeA2�p H @��$,�a2Y qq�r0$ p pacuwkD rive� ����%~��$�.sf{$S$}$�/4-Schwarz�x)ͣ7 Z� �^�� C�!c z6\_(F:)� NZxo�_ Rq}! <����N2p�(2f4>�Rv Mb}I�� �Ye<1�� Y|�q]� �1�:��6�p�T(�IE=�I��)2FT &,0&�'�_&�^&ō�_��l��0"� a si�x&� >�'�(_ Ro��sg-c/ 2�0>q+0��a �$�a mat� ��0F��" R� O1"�md� & >�&����G�"L�M_Qs��exact_R|b{UPI �n��O ] =0* �J/�>q�N*�IJMAi | k.M0��{.J�A�]& Y �B�sUL.�PAt.� .� of*�}]n*3�f� �"�S�9�w<�3RՂ7}.�3V�CJ*�"UR�]�� �1� ?S� �x*H����A�& �Q s ��Fe q�� 2& �"�'�D0&�H� �۵1�A�|F ed u��/.M��w� ��>��� ��g �$2��.�*�u�2�d2�biT&�"5VC)m jYM.l M P �2!�:w -s.J .Iva] 0~q��B%6��F� 0�P�( 1J� �)�n��N��2�e�+M�I)���J�i�)�hJ�mZ� S � �e[@s��q���1 C"�&>6I q1!F��s�I6���F^ \.s���&��I��IBp1�3N5�_ 09��B��:�� t do�4XNJ W$ B��yw*7 *}$)�u� alys�v�a��=&�jY =�Y�b6�j(>�S5yV�.�)=�!�? �.�N).�e:7}%q��j��� ^B^� ~Hng�6�b���S=5$ (�n��$n���78 }� s $xzem"���.�-��t.�Ii�'� eR�;poj�4� caėM�b͗�&s�;!*.O2?�J�E�s.�lb�\gtrsim�2iH 3�B�`:�/N)�j]: mE _=�1[*8H2JJ�l0 FJ���3qdU�v.z�m�*9 ���[:�b� �=�v@�2sIwn�!���NF0���B�� �)!Y�7*�5gF�� AwV�R �&f'iv�L6a�2� �a{~ % �i �9nB�:q*.d��"e>R �H&�.AF!�0��-sb#d&| 3#e��9 �V� �us6� �"�jV�b;!& �eN��j�&�f^I� 6; e �"�F�� Ab A�=� i}=C�P"�2-j� ">AjF�9 ;� struD�%A�;s�=",�:.�*= ij�n�8twod})�6�C!bin%"�9�"� AOy8m}8 ]12}F� 6YQsB�i\ sf{K2F*Y��>z.���e6�~-{��KJ`�g=��A�4C���7Z~ e sf{C�P�Id �V!��F$n\�<s n$ ����s in,K leasҜ"� 21C ��O}z�\BUC�� B�[ Y�)"�3<96��F e@ �:2�>� �-!-i=m�Z-.k26�D�,>z38��/oo. � twojJE�J�!srQ�$��Ok�n b�)%�:g"��^���3� �M�,q�f}) �&�%BuN�R��2j)�)�#q�-gDa�"R9�3 'K\o)SQ�>� y�2�7l>H�JA}�^%D!���f& *���>ily homo���zp *"I"��v$A&�,7_�`xEzb�$� �&aGZPG���*��o�h�7Y&�=bU/>z.9"L�� j !!1�-*gv u���N42�m>�6��� ��"B� �Am��A ��"v7�i��Q����O��Z7!]�3�de&[bT ������m�pn>�Yser�>��/m?G sf{I ��� �Ʉ=��m=1)� fty �BRmU�.�u�HI�b �N aX��U�m})& a�.HT!&:m2�7 Xa.0�� O�D.�  �s2�e �-�B� ���m�A�� Lie �5�&�".��)R2C�2H "PZ��^'Q:ɝs&P�N 4UA�.} O&F��N,*: +�F���)�2S�,&�4�!�:�O9� �>Ir g��in��1�,Ssaij2Gff)�(@ @,��ively)+ 2..�becau�L ~t�0�6��Q5b�~ *֧�cy, i��d��ogy�R!9} @, ~��Z�%i�)"TI9� ofĀlyu}���w��� "�w% �w2W�WUv=V��%.�5 %�6�S2,Tw X�einguish�}�s (��)�W� !i"PT*�>�5�by& t$�ed,�<1t6lB�caT Si�}Q��er�^amDlatter K}�2 we �iRj"B- �7 isH%u1�: 2{�vTd Q�R�ޏlso:_t,��`v)E_�Low�da1r�.X{ up!#% �Wg ��ofJ!S)jM7�*���  �!��3J)� 3Y � !�QZ^�q�/�<���reDK|N bOixZ"eF�_I��� V["���i:$�<�=bVT"A hreeJ�Q;e8�*��"O*.@)��0 !Sm�Q��!�B $2� =�DTr� �#��V 5r���LY`��J�1)��V,�D� + s��� :�/25������!�J?UB�z�o"�N�tt!m.�?�X6GQ% �I6�BS �)1'+*�&z $.BIA�-���q� �)�H <F5� Z:m�g�[a'nm��NI!�$��u�6�"P;J,6�� d}) ���L i��04�>2�M�1T:dMz� �u� &Z3#�#Z� e�2\T ~6�k.�%�J3M 1�1�)��=�QZ�J�s�,2��(����%�o�&ik}g=Bp)1"i6:Z$5�:�i J&^6A�F�% N}q����O �/EV$&�Nes �*# �&���O�Utak� "�(.�q� � ��J_�("�q�R-)#)[ nd� ese"e e��"�)C"H�k�>The*� >�f���H� s &B&achie��`2�R85�u!e-u�I�>?9%:&}lR�"v��P! 1T �- �M%�->}=S�<� G�<&�9�4� "jo] SFc4% T�H�& EW� �B�PgN)Z� I���Tr is%�p - "p ��k�ka��"]x"qHyb4 |dq]�6QG-%is"�,=[2?=R�ua�a��V�DQ� Yve� +�cy]�"°)S` 7��V�#�7"*�6 6�<\i���w" ~]��!b�.�� oo>] assen�+��&dI3� . S"��Au�5�E�$.jcf(>a.�+��vX.�) ,:��Ln���*F� hcm���!t����"m> >3�E�����c9q�R"L.��>Ki�<�k=n��y�� � M��9�re�+it�Y��R�fZP��q_ ��(E s�#j �bD*K ��>� }*L'�ZY&\D �)EDY6J�)(g�riv�INH-.NH K,jH-"�!L�C�Y2� il!��;���O�� K� ;%�uaUj�% ��%I�rG��t��d&&ver0��e��Z�^irh"vJ �����\Tm>AuVk!�I��X�,�2��2����z�z2� j ^h"^3 �7�� m ZIF4�&e  j_1��I_ proof!@!]F��g4 9���&_5�,|��5�cy� "_<s]�:Wef";�o�T�4mUmj E�7�U "��� 1���eEzTone}�re abov�����}N� ]sa�;+�I^�ԩ�z�f��F8hE�.�i�1�$j�u9P�>n&� &o B�gS"� *�&1����M��*�2�ɉ�$@�&� �:�` ��*2� !X� F�*}>�d}�, y�V�+� -F �4�BŅ% � %e�2�hZo7�� 2nr& �A�*� -tTmx�^]B�6ir%k o�V^��w�m .���2`~� �xKthn. *� c/�I%uj"Y�S.� � � ]SOj�$ s}`c�Ne�orH�*3��$"�v!�1�] "f -�E�*� mP��"m:�)� �mV+�!"�:)  �)Eg% ��T�6!�V}=xd})B�rs�� �� B� �5jX (�R&� � ;c!�8=0*$� J�/� 2mN�N 2U U .K>6a �_+WeZ%6�� Ͻ�6ze��/2$2�",|ER� t�u�-�B+���n lB;���%B6�6 J�і�r�0FL�"y 5 by virtue&��.{e��b`twoB`ul��R�y .d i��3Rmf�[ � P �!�&I�"3<)�.~�|, �#!��%�C�h<*� �1p*m�!��d*�.JeŒa&g��J��K.Ʋ=pO�HO��: 1�Q�n,1����N �V�qUe%�A�Ro� %)z~"�� uRc_�!s� _*��5�b���E,:Jy2qP&� 2�u�B�eUNdaTthe8hZ� B�"E�n52}*� �n��t�)%w^� Z )qe-�� O:g �Z#l�� ��s.e�S ��&�rZF�  *� ![� q����a1��� 2� FIHrj28�1�q/�H �Q� )� B9su"`� �hmXB�Լ . Us��$c��0$-w7Fmz&'M�$Q^mu{eG�e�v6�n7%�-;FE���A,.i�^�'@A ��"��/&�#*x#�|��Ne"Z* 6�*��l*�fD� ��a6���q����Q"l#.k" 2v� �incid&|g �Z����>���i�R��-�e%0���2G�-Au�>6D y  .89![�����k�<0!iNbi|4.�2�0�Y2��mPk},\,�a�0i�s�A�X *�!7�VL ���@��^sVa���&J -�-Ww*1�)�E�b:ZO a�t����z:�|S2I2�mai�*o�'&�s.�d:�CF�"� �% �=v��ra"�@a�!NG.~ �xiX;��C7�E�y!ir*&�x.Uyi�-W9=�.`y��k �1�n!q M#I�ah+&�G.4-�i@% ) υ��������B!� -,ccn�%�zV4 a# hJz� ٿ281Rl��q�%D�R *!1!&Ji_� Wug��n�1e&� ��2m ) $xF1 �0F*a9U#I^dI�"� E�v9RE�xXBP$<�c�-��2 ��,�>�}C�i��%�: (:~2��N&\2���D�)�/)��)' NfN �%�J�l��Z� �V�xU!~�ba�I E��N� B� =O!@q�Y��N��$0 .����� s��&�/:�L*4�_!�FNM�. zh�� 2%sIdcO��&omB+�o��9/��e"�ȁ�C�d!J&bH�&M; ,I*�h�-��A��a��)I=a2R"8.z� play%��\#: to+2ɞ� �MT&�!. A�� s��:V��yripH�)tud����u � �����}*J3[� q^m�� �  ab�m��>�"FD rh&#�D.P%.��z�Ma�� f��if^KoJs�O 5%i�6u�W ^���J���� scri&��*�A .5U (%!��&q�e5%RY]/Ni�{A\� F6t"g.y4��$u t &1-��.��q��:�,�J�sA�79 �Zc�0I�/Y�.��"?��� ^."*����1B2gmǽB5{46�",%�ls�g* !z\1�FQ �@�+M �Zzt *X@*MJ&' & 2&"��j� ��.}"9.o����p Q��}&�*�]"�i��A@entir&��(\ brm7arrow�bb{% C� f"� u� �Y��IB$r�$son annihi�mY 6~9h2|>>�Ba��Yu=�W�Z%Z/j�Y� �� �:(d�ϙY1N(U" well�e�N0�ņM��S�s��\]* ��Q2IH}B�5ą�a3�Qng �_>F�B!f �� ~� �^� �5^pro��G;r�M1}{\pi&O;d}�1Re��!�E� �{Im�r c .�!�iixVQ�iph,�,:6"��Y�q�u�%�G}�P A a.6�5� � � e&sNNU � )�R/� I���%j2� ,pc�{()}KE!�-w�/U� b$ r$��IA&q A� t �!�($^�9.,-�� Dira~�lt"�)aV9=�ss�D� Lv QAR���m�2t2�*�1F � � 8s J� MW" � a�xU�"F.� ,�"7�~*�! a co&n�����V] �V����{o  BG%�MU�a� :�B0+k ��!�2�tI�S%s� f�%�H�R#�i-# �)Gauss̃(is fact was�a^�"s_R�&�bb�)^!.a8.�?0 �n�IG Es,�$8bined bounds by�@ means of the factorization \cite{10} $\vartheta =\vartheta _{+}+� _{-}$, defining right derivatives with respect to $% \2N $ and lefz8:u0. An interest{qu 0on is this: I e clas�efficient statistics exhausted by.�^for which at least one such bound can be attained? \textbf{4. }In conclusion, let us consider !z�-�(%>) �cy�m)� ,Xparameters $\beta ^{k}$!� msel!zof f�canonical families (\ref{twoa}). The inequality Li}) corresponding to%W case]x=.�ha)xTform $\mathsf{R}\geq 0H}^{-1}$ wherQ (H}$)�e matrix�.U�% �e�$Without lo)�genera�T, we shall assume that �Hrm{Tr}\hat{x}% _{k}Af�rho _{0}=0$. \begin{theorem} \label{Tthree}The inequn Xs�� �(becomes an 5rife only !�operato%� �� $ in ��(a}) have a E9 joiA�ajrala� sure1� e}),`)!e8 funce�IZ moment]%b}) se�inJaK!�va58!�D Gaussian: $\chi \a�( I),\bar{ }\�) =\exp '\{ !,% ^{i}H_{ik}3Es 7\} $,QC # $ does no�Ppend onq$$ �l$]$, !tunbiasedqnea[lambd r= aj� varkappa �0) $ are taken�� be linear5hVI=H^{kiEx I_{i}$-q�9ult3iI Xof simultaneous quasime%�!�!� observabl�]K. \endY� �proof;su�0�� se c�A/sa�c existence 9M���t1P��0obvious: FromA��i��m��(�coincid�Q)covariay42S5B bJt follow��a��bR R}=%>�nH��is e�!��.)d necessity�f1 ary.gof�V1Q%�!��� ��,Ttwo}, accor���ɽ!)����m�Q��7,% }Y� must also�dH�ѱsub�!�s}}��H6lJj=��%Prm{e}^�E�% M� ^{k\�}e-]��65�Va&8}},���j}I��% ч��A��?-V.�% 6�.�; "Z� �$,e8frac{\partial } =P�}\l� hi .���J ��$9��B���{olu!�A�AidentA�)=r*})� 1}=\��\P�-<d%ȉ�Qx,\quad =0 \Pi QE�/� B�ve 6eO=BaN%) \in�� bb{C}^{n}�$*}% Compar� �Ig��^ p �ob4 2�!� ���kT U������>y!we�O=H_�[�D�A"�R�2?�` 2�O ��� ��J+TJ  3* been�xvedm se�{Ap� ix} "V 1.} LG ɨE�&| )fi First�E"m < one-dimensional� .P$�q}$�an"����cal� for �W>x}���qEށ�1jalpha1k �oE�l �.. � AaF�Differa�� )AA�B� ��nd usA� the � e� > g}) #!rnormal0"-+-���=1@ueٳ)t2I �Mh��=0aeqI>�a�5d�%Y }{d �}=��� �5�)�-8�6�J�Sia�!$*�N�\ >l��>�$ s�f� `Schwarz.z >� eft\vert��!R� [rB�>�^�] � g^{2aq_!`�[B>g H)� ^{I��Ol !�eyeh�V9�8"AbFEi�i  ndi$of non-neg�� 5  d�minan"z ,$2\times 2 $� of]� �Q� ��< kU�$$% , $i=0,a7�30� efg q]�5`,\;h��+hkwe- writeNPJ�~n6!1�-�[ -�) $5. IY\j�%M� *E��/2�6^ ��Y cF  This.i� ly� ablish� lower=a�"O I' j�.S�)( �����=�t�"� I *4s described by��B 4q}$. However s�ҭ�t*� �9%Nq�i�= 1`  $ wa�ug ��oh �pAc}% �is-Sgi��gany"�:p*C$$. Indeed,r$V9 �IO) ,2 � a QPM1`�G� =�as a ~lized.�!�/q�g�5uW � ��� �FyE���%t% {$.&�DUHB0# �{X e�)E�AdF�>�$� J�>5�L �Rf'(�U d% }6/���PqQ��� J? \ oT6 ^��� �Uj�r�g*m eFRTakQ��e�kex���both � �Ep!�U be9  in mind& �>$R� sf{M}_{��� nf��%$!�M��]m�)C%�] "f}�.$ isB�*} �O *? b�f�*�!=rm6u��.k&� idj�� -]c})B�} Re+n.�!A(� R76!% &! -_)6�0)sd)p A� /g, A�e�fFU�we�(denoted $d=*� /d��gI:�a�� u��us,��N�!J[% ss>�te�2.} E canPt�ed!�-� e}) if, f��� }/e"<twoB3; � , se�� FJ &o�ity!e }�(actually es&�Av3�d_8More precisely:"$0lemma} Suppos)E rang� � Mi�6�I')I�� ofA/�8 F&�V : s��bO uG � whol�2�%<n !�5 !6} R=0$Ea�*2 ) *t&I $R� H�H��:�$ imp��q�-� It� "�ta show 2i� �vqt�i�  vector{%iD6�;\!�le�A$r- � rho ^{1/("�psi�FZC � Xlant��� �Rrw0 \neq 0$. But��w%�}�>�I!&6� �RQ~ �[%0��!C" 1>@;( .9-k-�Av�s) hold�BlAYwhe!�\2�midh1L h=1�Apply��is ulE@A�q�_��dzce9IE.-�� �-hand >�w��nd, und��w�%�Eہ�at z� )"O"KN��j J� _ M��*k�lq�L� =0�{, or  Ra%Lia ��Bkis(6 �$aQ!�2�%�"ZtR� ,in some doma27O}\ni�$ i�qn�{t;.S�)-$�a �-eigenE subspace����sNva�U1ךX, ~�ti�h��-�P�!of real �u! )�� bb{R�P"2"5 is &lselfad�H��y&h e~yfn� ival�"�!e u_9�d1Z ��1Z)�-�E; ) =t5�"h� w�L$t=d/g0constant. Setx J�tCs"@.e i�0wj A$! �(R� \J�/tEE}ձ | � -\muq� jRM&c!%s2E9 �J�-Pz�� � b- f5 $. Its :�se=/D !Bb�$a�Y(: 0,1� �A.Q:&|$<(�K j"�&�Q+!�2�q$�uld$ �h�D, s�$*e iVsaqh7~� �R$�oe���o�� V%d[ty�� ��/ !y.���ei��*�!Vula in�% 2�L"� ��)x" �xa�2'�pr�4:��1�� 3.} A �"i.\"�e�U �edu �Rl�tRJe;��K"�aSq2��?%9) i� eta}�m� Nh-he�xi�,b�KO4;i=1,\ldots ,m�m�  ,\;kn re arbitriZHmplex numbers. Reme z �"nR F� � ) 5 5&= �!ni}\b2�iy!J}�m� }\xi N+"�f m�AJ&al$:5��sf+#D�\daggeB -����%��(�m�"� 4JNRP&d!A �� �>�!M��5k �6��'k'�%�% �N���� sf{DQ$a�:$�.'R�N��*K !�Y��4i_�� ,.; 5.ݩ!$r� :)=K�� ��{, �,} E�< �1a��Z� ��!mN4i��re:P&(#pi�e��Z j!�))�"�' nd a&� J�+� !�1��!)~DEPUN�-O�(j6& q� [��>Y'� ma&�� �3$ �F� �! <2�� "�"  i}) �becauy,�,isY� Yy Dh})<t+�6ᱭ!�eM  O}$ �+J7.e�^-z%�2I_V�I�6y[�9�QED�x=t�l��j� ��Ʌ� qq;C>��y���iNwceN af)�))u�W sf{T `[ T�Y] $� b� 5 �ndeW�M�U�-�Z 1�Hthebibliography}{99�(�ibitem{1} C W Helstrom, \emph{Phys.$ t.},�WHbf{25A}, 101 (1967)e I�2} V P Belavkin, Zarubezhnaya Radio\'{e}lektronika,X(5}, 3 (19752T3>TDCandidate's Disser_[in Rl-T], Moscow State Univer� b22b 4} R L Sti.4novich, Stocha1�1}, 87C32C 5} H YuenE�`M Lax, Trans, IEEE, IT-19J6}, 740JK6>�b�315@607>@�D(B A Grishan!�PProbl. Peredachi Inf.�4% }, 44^6�8>^%�tekh. El)�J17A,2, 2527%�2):5�20}, 6f6�9V�I6J� eor. E�]�$8}, 5, 361j3j1!�35)�42�10>�M�)$Control%" xyr3Z�1eRR Rao, L�.A�j3,al Methods [M� tA+l% A�ir�,68) [Perhaps." of:NVIn�&c its�icWs, Wiley!n 65)].�d12} G A Zaitsev, AlgebraicI*em��Mat&�!}64 [in �], Naukac%e�t:{  docu�/} &z \�!{book} %����H \usepackage{amssym�%6 fontt.6�W!gsetcou6{MaxMD4Cols}A�| %TCIDATA{OutputFilter=LATEX.DLL!V�:4on=5.00.0.2606�0B݈0Scheme=Manual$Cre��8=Wednesday, NovD 17, 2004 00:02:1888LastRevised=Fri9Dec 903 923:32:229.�Graphics��322�.2DM�Shell38Standard LaTeX\6 Book2S4Language=Ameri7English�$CSTFile=40 UF .cst!�new�5av}{�} .(acknowledgee�[ 7]{A:67lgorithm.16+xio2'2# caseIC6!lai.DC6#"Y8.J>-G6, >+jectur2�o:-rollary2X6+R(rio2�2+&{,WD5A2-exaB*E :'er�2( 2)`&L�.Dnow &N2)p�Ie.��[B8]�pro^%2P2Vremark}R 2%�'S�1:)umm6�S Penvirona,�of}[1][P$6]{\noin2� bf{#�/<}{\ \rule{0.5em} ,} \input{tci��/X9�a��@frontmatter \title{MATHEMATICAL ASPECTS OF COMPUTER ENGINEERING\\,0it{Advr sS�; Technolog� �USSR}:bf{Desigmh Optimal Dynamic Analyzers:6A�,Wave P�n Recogn�!author{1/.2 � PMaslov} \\ %EndAName �  Institu; f ElecL cK:d�s=109028 � \= {Mir Pu�*r 1988�0ke%o \�!eofcont:H \chapter*{Preface!�A��% {PREFACE} We�)�eview� most� or5u�8 on o-gtom� %)��"N&wave-p-Wr9W!�(ory emergedB&!�70'%� connO2�m�s\�{*R,and hypothes�ngAGquantu�ory� keyR$F�Vy�2�aA?T� syn b�dMm.$zer discri[.6 betw23a%gn,  eAr�tinuo�$�=A>p<or mixed� 8it{a priori} un�n%f -f s. C7?�' .z�!z�*�>�.� 22�"< <>n�;tackleL? 1�l,ita es)��+n s�� data%@i�$cerXhow�s$eb�e&z phy �AW��(�e� wayD6�)� ���/ referred!]g 1�*�-!�an5yf!)e,�Gqq�?E�A�2eMuof2N)w . Wz$velop*yfUy�.� U,i�of� belong� VPB 1B 7}-- 34}, fu C5n dirm�Have, rY C<b,�8cA�_�al:� J� � "�aim�include>�ޅE%� s bu�:U� �Q�s likDtE�a� acou� A . We�� d)a ed m�e�A�ewU.E6aE-#-��I6:dՓQL��#��#A9visual� s� �@ dat Hilb%4o!�"�# � ہ�1L)}�>olly�/ful%�5W � 0, a�onu+ossibm'�>� �E�tricted!#%��C(� trib�:!3ds, i.e.� %^iX S�~he�ed t?, � �)!!�individ!\Q���e�?2!We will��u'�' characterE� at �E-[��A"s c)� $arity, ent']$,Heisenberg u�t*ty re] ��=6p! V�0EXf�>� rodu�9o$* oble�� auto .2��4� nt2ks�Mcom��to�+e AM>��Ee\e��imXuDin buil ?fifth �A^kpu�ion�#ystems�atI�i)�q:�� i#?!|�sna<  �Ee&HA%�2jq�!�n!�Q2_.� sub [�B�_�D^;studi�,�' seventeenf& M���!� W�Ego!�i��detaile7 �ZE�eda�n K�sUL3��explagGm�1`_(.") �0��=dA�"��R�lor:�A ;vica� ccup"�c!@%�aA stag� -�eu .� of��or >�An �(E)a�XiceP  ~4�I}:h ce�26�$ $v(x-ct)$�,s�i� modelava point-���nwF (N a�3) cap�!`)�!�AI��bm� vibred�Fo�Cex�d�!h��si" .Ehe e<alB%�e�r A�[s placo t � $xs-Acd!y wA rtho�6 se� fu�F�# �(!+��v � rval�� �@$[0,T]�J typE@F�9MisA�& (q�,9��))^eW1]y���$i. �7!I"� frequenc!�$f� =k/T$, $k�NPYb�T presA��JaY(� v� � harm�$��RC'vhI]=2\!L{Re}\ph"�G{2\piZrm{j}k 1 /cT\&�#a�=\sqrtJJ� *�v� E�-:%Ove�A!�nu�!=|�vG|�2$���6 b�z�lex-valuA`f/tuA�$=H!W�$bb{% C}^{1� AG rum-Wor� &t9!�5]!6!�s%�G v.]�I{->Pt/T\}Q{, }k<�$oQ�D�L2&N$\{s\�+�Ke�M�scalar� ��N( Di}| k})=T�Eint( ^{T} iar"#�\�FMd}tNsg!u sui�S�[�e T: toneS�& ple 2; \{f_ % ! -2Fdis~+:" B"E�$�� t $i�0k$6OM� �UR vQi:.kvarant-x/c)J& #�)-()=\sum_{k=0:$infty i�N�.�$. To&4�&�)).�7fUC0t2m��nonzero���a��i� �e�%H0$ !U% i=k[,�4e�, �OV-| �,Wis: 3finm8e j $i&8͵�p tu�$to�r��5���!% uGi%c.CO@!5��ap=�\}:!t�!(!� (t)/�!\V� .1! !�he .�Og-�� "J6 with��u $% |y�.2�)%�!" ..��i -3'A%�dal6��$hil���r�a  un-�: $�kJ�q}kE5i�seg0 0f human speecE�du� $Ta�n� �aA%�?d �4G�.ists,t&?,-�a�gle�qc,z lly,A;an in6�of.� u1 �Za0.�(AG.may���P/be ��X $1/Te<�x t��of�recep��8). UnU�)�s,6��o..].=[�|$ oa�nE�te� al r��,a�) > tic�N�.}eO��|PBb% �dJ[-r�Tug"�in9�Aws, x o@the � g�. ForE �@!�>�� 6r,� ћ puls!�^JAhrougi�shift!D-�`0�5ge�%=80!8�Hlength $\Delta t=T/�,�A�rl2� �/ �9^,A!=M/��kZM ik/m�f�sam� te �"6 s���[a 6_ v��Fq�MY . OY %�� m"F�$Y 9 q�QMf� �?$milar mannLDyG � f� s  ched�� rͅlSeiE�}��F2� � �di9T �%Mn�)G�!��*��� �% .Z h[�� fo�J � ��i$, name�d�_{�/J�%>�\dE�7&Ebq��2DY� {Eily��nwthZ$6�$�G�6/!2D���their�Uɝr�ntMB�Y� col�5�a�7�GL totgne&$FdR*�-|:�%�*� $�ҡ�:�:�|J0 _{i=1}^{me:q3$not employua��&�Fer:�F!M2{yQ��.� �r �~noncommP�W�:h*,�Hb�Xe�in�hselh=; �wism4)��<s��$��)"� k ch)�)�P �4�e����!@iv�2.$��$( I;mid* k})� � T[� �*� Th��Aa�"e situ�U W�6�r i!�patibi�-of>��mec*�|g aris a� Bohr'�mpl���IncQ 2}� &�'sR� /3}. T6G��:YQ�a�aW� ym"6 'K/�.9le, justE(�n�umQv6.=I�J?C. So ��� �Q�:�&���$*K kK �Vwe �to���!!-MJ� !�1V} $? I�&��> lookAe_ answ���+iv�U"�]� A��a&g9to� jm7QD+��ng a ")%B�er#!tE�� � AS��JN�Za�gaugeL+�eA"] i�z/arrow�Em�Zm���3� LA�"#�2^:lc&7:y�P"2��maximu%:ک&z��i>�i���I��!BJru� d.v or!~|F�in� lost Z ���k��f�� &$!�ext�%l"2� &w52�.�i�i�XN� 01!�S� o��o�ba�) was �F:3��mA��� 5}, 6}. P�u� �&)�i�@E��%}O`�/wo��}�2" *^0},91�wC`"� i49v{�/ &/&^uX- l&?t6��� %,RdT0y n9./� 10}.�A e above-n�H��&�#q�:+ # ��.*y��-�sugge�b%ed��tr��v{'or,:x��*��scope���� o solv�rY8��S%v�!ess6n%��_"-ha�b*�N��-e bb &�Kq !81p.�,�&�%,0`�N&zc-�f1 2}�yle<QI{carrie�"�&`!!� a�v�#� U7}- _34}��> new, pL � ly m!rr��"`Jeld�K81. A� rt�hor's &�'1pro�^ng?1?Q�isY�3A�(AdT,al liter �!�E9� eQ)!mng%5k.��b! �eM�%t s ave���6�.) I2 �>X]� aa�Vp�!�E�� 6� �]S bObc alog�ck1 q�s. fT YA��G���iU�.L9D�&�,AO3)P!\�I�MY�Rb!T 1��H$"s. framework:L68��Q-�)=1�e.�"�%�aQ �A���q(J��H�0%��.'���Ie t,'�she 1970- e� ei)%F�% X2��6organ�SM�)4De($�=r�+5 e Un��7 �}P/'0 V.P.,, a|'EF$Yu.P. Pyt'�4!��g,, 6&�8� ndat�(7i�!/ 6|+��n�!Y+�$t� f�]r*�'�%!�P illu!N.?ima+!a c�8in�nT s st�d3�  rapid!�1Dh�-�2�g� !1in�";Gabor�=36cndA�n]J went8!vi��[7} �: c�$ sour�!f l�j�I laserA0qc�3)�EiA��E� 6�i� $%u�$e s���^6>7� � Ŧc\+be�,% &�"qB �8}A�M�%��. G�IX%�'to reg�ep(�)ly exac A|ph� !n"� ga�M3by�#!5M/����<$ed �$�pc&s=~+��w�,�� {39}"! #R#�ng�'siF��lv�Jbr%��  inadZ�+�"� hau tpo�untilA�on;ent� .6��of-o >k�e ly advanc�i��" T . S�K��i� �*�+.��*A���,za�J$ :A�locU$i�)�4�:ٜA��٠��R{s_ cloPR!9i�6iy�u�rad�`o 4� �� 42},��&$already we�)'E��:=.aJA(caleOnon e�cs��: �& 45� IY�Zok,�\a a>a��=� 6--�!*@jmon� U���*�nlas�.�1�!o 5..���!�vid�'>+�/#!XA2�U;TA�q3h�� (� co4dZ��A�1L ena\e��&=����).�<��!#om�8a �~lis� *� & �#n brief  5� ? 2?each �d. S��4 ivenb>�N~%on 1b ��_tA*se�of _l&in����xity Kat���a ��MtlyO9o#bes�+��Q/ �:� er�� o� �-ly U!V�-�or�Q%7,�m�r&S4{R2�A� M6�lQ5s}� I).� mQ}2U ap�LtunG�abz� �\ A@: . A&� W$610A�u= �(u�M�\��4�.so�I�:���3��7Rk ��u��f ntJ� 2�� sDal-&h(co�te)U�-te�(mE):�s w;0.��ijc"N6��= �!�!ip% 1e�2g� re&Y'5k!4l�a�m)�ce�1�0o2MU7� f�!Sso �  &�Q0n�,s'Y�5��a'inary�au39Z h .RE�%v-�.C s. U� *�a�i�!Q alyz�(1��)�a6va!�lCs ���� �Y- Fum>��$6` ools82d%� ^�V(s����@b���9�6MI2�����Ee��e� �a �3 impe�Hh]2L8� &C �? N j&)) ~� 6� 9}  10};&l$w"a9A2� a�= rpre?#�aL�i�#0p);R !-��-��ȭ�{M� L DXdp� h�� ;^�2b� reeE�c typ��6�S��8�ms;�Y}� �4-o�� �um$����� !��:�2uE��M-�moCc.���u�y& plana�rdZW �Xd�Q�w 6� �Q us�}a�Zal|:���� �+:fP � :T��Jb�>� 6`�)1�EW"�{E>S��V�6]Oe� �'>�d ���%� �Qw!�&�.1t,� bf{q}) #� V.fu90%Lime $t�z Y�V ��H�"a��O1 O��:&f�;& m*� s�]� v.�U �Y behaaur !�%hh�:q�� �*�'v:,�pur�_���!f�aI�=l�!K1?�Jd�!c�$v-o ρe2>po��� ard�p><=���photo�o�a5"%&6�'�;5���6�EF+ �� $v�*6P /2$./1^Bota (f.�="�$6�$Vf�S0,]�d1 1 1J�d�"�"A�7 mp*)2J+b<|-io�1�6�T%_{-�/^{ :��W#w�U:2 ft}\)XPN719 ��E� �36:ͿA�A2a�< combinI�S-44oscil"x:�E�4TE�$:B�*} :�.�0">21VJ6!>23:"fB8_% Bea�� in??-%Ap�7of*����$�VDat"wbwA<n� 67"� Qk (x)"�&62\equiv"�!(q,I�x=fN, qj)�+(���J�͠>�� Omeg6t�,\es��.d&�PF�I&& Q� S}y�qi�.�q&�ja�2F�W/�s�ng��vt � ��0�.��Um��sf&e�a�$e :�= -2MaQ,%�an tak��\19a�&-.3[�on� i ?2 �9ve��pass b $\Phi&�Td`_{+&�'�#E/ze�82A=&0�-i�ofUO6�$ege�=0$% ;� z!uv� �  u ��8i�8� a t� . ) $-)= �f s S�(� ��3� ߂`e}! D$S��sur�FY �!m�ed;E$� ic!sA�x=�$\q�z$$(t=0)$. "�~�57y � admiK*r  smooth�3u�m�$qq8Oiu,i�:$act suppor��S a�(d+1)$.ZM`5Z\q t�uE)^{d+1A+�1�W r %i�s,.��&f�@off� �[�LgeN?�� *�,�qv<&� �!t�6�BIy�WH}% =Le �)�%F /%EA��.P*�,�H"�hf5Y<�kJ�} ���*E,>�բq)2�8(q)6�.3F�G#�A�>6_ !D!�fA2�i$�A��9F}^ɲs� "�W���qe&@` A$�� )=: o)aqAqva��t%��~A�lex`jugC�� 5+l�vq\�()cb�-=OZ'i<$m %,B�,� �,� 5i�8�� �$�%%v �� ALWs�fin �*6N F �IQ=I�i57� ��1�H�k�� to bF��pp2$an isometrJ vo�M�\mapsto7k1[|g`!�EYc�;@duc7��i36��8iG near�=�farg�T9Dž��'�[�A6> ]�� � 1abl�-pl�0�N,&�b calcc�{��-es"� "%�G mak�1H@��to� �'} �tj. SpecifKs!6$,M8mg2�*�2�� <f�� �,!��ed ``C l''&�0yA/k�s.�4�i � "de�% um$. No� e�����m,�gh3W we���� mean*S&c2 ;fa (��p�Ans)NE&D � %� l�!�,Q�ively�!se ai% �g2H ^!4Nzf�9;�)3*'F�.A�==�'rM ar �uo/"�0ues$"�>t)�`rvJ*`@Poisso_.a�)}\$"_ �m�Ao1F�lIA�ourC�to*�. � postay�"abl>w7a!�*mI� �;76T E�Q^=q� O �,��ti!��=eP6�2�>�M' 6��"�dl)ng��A6r*�Pof mo�h s w!&8:of%Z!w�U��B&&� �\.r�^�� 1}) ��?w&�25I��0qWJ� ,\widetilde{\^.�p}_"��6$% � m*Yp})� *| &v�4F w ~z)� �i�Fourier v\�F�}2�R�� �w 6k�b,��^>� (tf+�0bf{p\cdot q})2�f.! Mo 65F#W� �Ka�3E� :�Iv p�JsR� �6Ee�!cQE� N�x)�dN&jA �R)p)�cal&uQ�:*.\foot� {% Thank"�!i�&� !**/ -�"2 )� �U<� (�lA�5$ ��(rsBn3�'*$:��'.d�F����ula2n ), �=.6Jj 80 >-ext* onto*1/2�@ )��"�[�<.}*; >Y!��%A����c�  ]=N�)���J�$,� � |.!Y#Gqu{1blW  un& �72m \� �v"b0�����k ��>m Y"1��4A6)���i"2 uu��.  . AMe��Planc�l'�q$6Fp= |N<(p����6p� "*(�� " % }q6�6F��u�!�tok<17�E=5!d.��S)+% ec4��i>�>Z9^2})%'L " 2� �D� zR�%G.F�p2�p="& )6�!G6�7>G�$5i.<!5*?d� $F�% �H-V%T1}J�> beEe���n$, �}"b�}�-�=,qf�% ,���oalKnq!� a�:e6oJ= (.���}i� 2B�!*4,qR G�>s &E �Bj�.9��dB|%�L�L 9E�*�m�$��T �M�* �>�[ tsIQBd!��M.$q$.  ~tat,h A!� 6�2{-�q)$�&iAGE�f�*֕}(�'�BJny�Y�q 62oN�pQ!ce Gi a. N;theles!RpZ��s��y"�0re hips,�"�"�N����7m�!Ci&ߎZ� (p-\P�G �RW.R p��(q; % q} =%�6�}q)\tf�� 1}{(4\pi 0}IsU�).�]^.��aZ� ��sp��/�[̗Hq HqV�2<��+!����on�^ $p=p�P�Iq=qQQ=0`O,d$�n�)is �*�WU�'l�/Bo{1M N��hat{p)� q}-q p}=(:)vOD% 1} 8��  m:��Hach pai . Z�v �,Up he $p$% -"%��,�`i_<p}=6�-dQ!��* &�y>�p)=.�!D easxEo9�CtqV 1 8aV��c�d!�SchI� Wc�wJj5 ��-�#�2XF\,N8q% )�n:҈ =���)B� <&�I?1�M &�)\� S>c \�� {Im}ZmG�vk% 2m=�:E�} �jJ:� � �^6) 10>* % ΋2�K2Q  1G ]D>�*K"nt�U�� �!d >�N�> =��.�% p2�H1w�~JFT�FI1�llo"P ل6� c a�F9&3D v�s=AVs$2oq})MQ (q��&�ql�1}Fʈ5�.�r�>�J� ���j�qR�2r.� JA�%�Jr"�F�����B�10!��Q% Izk%�fU�.� �I�SZ�Z.�*� *�2>T} \sigmsvp} qdy1/I6P1N�%�{CK�;��I Au"�dev,62�%narray2�a. &=& 6��.R" e�*o%% 2��-jg�g�6i��&� [����1&# �% ��$p)*&�*� + !*�" qoe*�$i�� m�vY"n ��K q�IEi�m.�1})S#�{� J&7I.5I"I ; h��, EFJ�.{h5+no+""/meIM>&�z/ "�h*�2� s\"C"1Z=p!(5�7]l*4�$1/V $Iem> ak�te�1y"�DNf��e=.g[ � �"p��!����&R� �(q)=C_a�.S��j}A� .}{2}).;� &T �( 6�3a.}{4:@}\�H}J5!Th� "���)!��&�:c�>a�$�=1/p �Z _{pe�)^{X#/4q EP)L|LO1�$p$: :B���A:�(p%bpZ�R��)& N&E�$)G! AC!f��grA��a�n�-�o��(�)=�[aw�%$7�_{\�z �S c�Rh] #=)21A�( .Q}{ � �}��^ +.~!�- p}})F� ]%E]PF(YP fixed.�a�"�| neq �^{\pr�0}$3Y�!$��o"�RF�*�"e�� )[I4) "�^ �%2YiF� 8y�+FZkd�\% !�^ +>T\::1N;a�1>�B}$7  ��^��^i OXi@]d} C;T\��61�:�2M!� S?} Du<+ lim�C�a-d�;e�p,�a�EZ /i&N0 o��N81U#*�t�w en�R�)7u�).Um3C�Jy�)"��:*T i�}c�X�=e;2;��,�B��to<$. �&"or&�P.�  Y�gq2oR�� (f�nt*� &d-2_0B�2 �bG4}�;\,.�j}�W>kJ% :(R �.ywp6�1J(Y�i. %*W }N�s!z�[7!x> Q#t  �BS<62�of�>%�blackA5mplH6F�+t no nvVo�4qBa�d�p ��#NJ�2y% �2N T7���F:���'yIw�E"b &>B8*} S(f�/,�  .]] �(f6�5.�qJk ��y 6f)=S(f,f�nR��RY�SARt)$�>6� .��bematA�e � j}(f1 }-=t)}>5.�*2JMonochr�F��� &� -�$Su|q �~63e�2!f䡾,q)� :o% 6:�2zC p,p}A�Hav��*V4 ��QiX��^'w(J��biN)5N�| a.^Aes _F.�,�$�- j}\t:��=dia�Y"Ti�qazar$"�m��.H.k1�Y�omD�VJ��e*"~2Ci�PB�":�%2�$��6�p\ ��nu(J�:Jy{,�~�0 }A"!r�-}-��%��,6�% .�:�"1JBE>�$��9 .1 ��� S:��K��*�.$I�&�i }�nu��� � )2E 2JT-�>!� ��"*�a$� \� �0t�\� � =1$,�G WhRbyA��2$A�?���]�W� cr m18v.�l�� B�=%UA�b� P gC)#b���`�]2�!�-a mB��!�ji!Z&�2$ )$Ax;3�/�&� 20"&R)�f��3 "� .�/��3fB���5A�A(�8+*�35�2�(2� a�>2X f$. �NY��c�*_\fV7$,�{O�EB��dAw>��sG A�ey� weak��f{( |-sm�}�_{a}|End :�J.ofB�N�_{s*!� q|$N. �#:�7"�.�7H~l5M��L8o8��6���>�!2!Jh�Hw�`(v� �% ,-?A&�v�J*�':66W he*�}O9r�rnel-��A ? �9tr> $Y� Tr\,1 ��A)� g *6 :��� óg "�"-G��>��via, sh�"9� d�� �R+SAq�r)iY�nu6� 2J�HGViG�jcO�Ha|v"��@of�d e7�)��G6��n:��8 >�%""k:SI���!��$�@%=-�%�4�% }\,9*1��}<�{"�&A��P let >9��Vr��R!N��5��˴��!U ��)( �xi \,d��)�2 "5q1��CL=:�J� 9"Opro���R���9���Á� �5���*�u�%i�!`,�Ggl<&i8 c.f.}� 13})F�!} M&� ~ =Cf/"P(2}4)�^�Ct� .$bx�;o ?21:2J�mv E= 2E?4a symmX;c�"�9$ $-by-% ��X*D=^ �EJ�WB � �+ �  }=t (\upsilon%�'JDg�=\Wy2/�}\�#�yI-E�etaR3 % Re�s jD ^*��&�U�-!�'�� �}=+.J) �A��T-f-*5C rows���*� .�:�KA�2a columns$B�G|C2H =\deP(�.�)�]�f�^{-&�!ue�Ч��B "��N$Pj�5LaAQ%1��;I�! & conj�?|-�Qrixt��L("zE'(!y,E3�>�>$2m=� Uh�o(d> )�[(dD�U$ a�z� ��A2� e}$ 1,�.S^�wJ"�A1u�l!  �*� (w$J$"@ )� !$�" Ks:B5 }*��}=J�+��<� �2�A#b�-%S 6@!r:A vark�Q>D J:��[��%{ll>�2?� } & �>{�} \\ .�~J>$�1 ��] 2\E�6`:0eV�-�6C &5-mk65~�6%DZ!��ndB�+"( ��>YR[ g !���VB-�2!�-�[2.!�N��dB�e�Eby-�Q�^�?"� tQ=�� |aB� *� 24})�.�%&�\ol+����q2�Q� _-��pu��%�{IN;u�p%6�PzDQ7>�J�u�(}�q2�q)��(Q2 � �. Q6):q�A6Lxi }+(�� >��H> &B)L6�pƵP�E�+j��i�K�T2!*}��&�29aD=�6�F�P6=� ҉�6M!�-j*� .� ^*� �� (� �J�6�F�����F�A^&� �%4 }+I �M >x�zeq9g ere$6�! W1�� / 1+$, $Q� P�% 6� �ope��r "y$Qx4 ; ��um $P V �J$q>t(� ~icM by $�4U%=ti�'*H ,,Y $)��j-,\�3 &�3 a�Z�j1h0���#hv�:8tBG *} BB<_�I�{ >{=A�,\,6: }<��|>Y=E0J@ �:� n5 &43t�B��/�3q:S ) & �A� 6�jKpBK��p�KJ� �����V �IZ�=2�e�jo)!G��})+4�� 4R*/�� � �U3J�Q�2@? Ged2�}��)� % =Q*g9q}Ii}$ p}=P" p}I$�t� �6b�Gm�,r��&6;uns"� < *� bt?� $n(i "� e)/q�d} �e���FH�!#\{ 6� L-)&9 v }* >+6�)g6�&3J�(sw�N( � i�! C=J/ �E �U�� }}$:�m 6}� �9� �,>M$�,b>�*R4"|�� "zv.�%ho�<�'�� $͉�) 4"EC�<:x"Ep*>� 31}) A!&,s�3)7 * 6VHV6&�-:�Af[6i�&OjV� ARs�6���j% VBI�]6B>�+ $s� :@��.�#�� CMD. A�)is�U�&exped��tB��Ga>i!>�E2� ADa��F-9 made4" � vari2E�e�:Hj �2 � AN��=� gammE��M�+i�m"�� n�� D=k Ba)�e "�H�!(Z��Z�Q}k4a�be:{ *YormN�/no�> )�_{-#�N$s�A� .*�S &� 3J�w�  $J=^��)-j�jZ nd �a9a fNG3})�I�� to���.� y�d�.�" �551�!|u�d�$% *\1,�"01~9��2�V 25})"�QNp F8| �)�$(-9͉E�I�/2};��\{ (q +-\�%q6) S*� 2�q\� \�']�V,.�A3J�%�)2(Te�fA�in914}).F�]Q�r��to� ���8]T�q*�doO�v�7�\� Im}\ �ٿ��.H7-�N�A=��8a��Py do mJy�r2Zt �a�c*�;F�E�%�vrq�{4p! �p6 pp!�NV�?0ү�/u5�5pt;�npq �5� -2  �6�3JJp2�R-&�5q�;iz~"� .n.8*"�:% =&e��+M��b>;2@�6p}= 0�}>eN2QS�v8" nota6�;%�.�` �I���_12� )��)k���V}- RJ2NJ �B��el�/]a�B� cev=-�. � 6� �Ň�J -: )1e( d 5��)�F�a&=2�6:b�# �e76�ƃMRZ�-��7�!� Fa����a: �� B|B A��5�nonZ�!���?3�'|I8��65��BA�&M "=NQ ya}( !�2}-\r��9 :�& }&�q*�:�'2LJ��8� �y� pp},���2�A� rho &� -1}\:$;�(���71 �K�- *>'9t�. O�3��i�'= 4����35}).� ,$ 2�#C"�"6AW�8I*{dajBW8 ��(o08W W6"Mh,Emj�r$* 9���8�G�'��u>HT �e *fG#+ ��*9c��Mo�8"�)6-Y!���Au�C_��@sotsV�8{a5Tway aeX6�5 .�Xith���Lnto�JN�7&�m0*�xp1k %. a*�l�7 �no f*r:����nu �MA1� .�/sZBu�ly (dO;�bpKО!h}mn*��"�y�fQ ;�e0( � ear02*�:A�te!R�}n�u�d^o'd"�V6 4 "��aV *1���Duch per��Q[ch^Z%� e`� ely 9ס�a"��M�]. �1"�Nn8o��4,t�[wG�,.`=Q�FB k(z)=|z���-�TL ;\;z=(x,yBYZ-"6� J�0���'i�^2-�/&g.ƓA�&�'&s�N �� (z"�'!�xY&�"t��? &�c v����Pct �%xC( =y"��'W&�'s�x=(x_{;��� x_{d)/A�^a $y=(y2&y &c can ��lyQiI��^)��S $x$�V!'�J�mZ�` k%� dy=|"�|� �8#��8(-\pi |(x-q)- ,��F�V9�6�4�9KJ�S"d| �$BlD["ڜ.�y$:=�"w  Rm}(y)] %y-�x_ �H&=&2FX!�-n�y-p.�L% ;2��q�k5�'dp6O-4&� ��Z�X�v�� A�i:�x-� �E2���$.p*�|>Ty�1.W(� �  4] � � 5�aXdx=\ia;ke[$\,dx\,dy &N �"=%�(�(w4 {2�4|2X4&  �1�ms���!T 32�,�F&/��z^-=�H2d*/" �>9`�F�::�*�${;�hO$�b��-��c�2� ���ƒ*�/� �� K �0�� >�in�cN >�X56 �/2����"%"?<�� �Ayȇ! �is"=gTU/-SXD�� �T;' ^�/�;<~@I��B#{-i(a+c-�\�� A�\}nM�*\*2d}zK�r(64f3 c=(xMa>�yհ.9�$,��c&HhA�"�)r.o�.&�T!�""x�1�.�� T J)9\2-(z"A"�zz}�� |� rn:-k}���.C:T44N�2 ��.G��vSxx2�(xy2*Sy6 yy��NS&�� }+22A"h2�%��*� AZ6٭*� })�/.x4J��"�*WB� x (a&�q"�3j���$% >�A ��rk� ZDertQ ��:� s�A�:� .� AG�2wln�O I�$�QG�~2>�| ��inu;t�� k(c,c�)=k�9$j�?k(3`=.?(c|S|�&�4J�-�isV}mA~s@E� E1���q4�O�>a=$|c)=�z ;yQ< $2�)&x>3R�% �=(x1^�"��#q,2�Di�1� $�2s,.]�]��th?�<��U%q� �*&,fE� *��&�VF�bJ(cx=/�_<3� E;%ȭi!)(s+1+%-n '�0 6~���� S_{Vh�� :? J4.�* �Wra5946}) �� to�j�f�;�(z/|a�2�f��!�ulaN�1<c).$%s^�N�2�c."!�%�>-}> ast :1Nu�.�|:d �:.�%� ' �" c�$Kne2z!1s�B�[�5.�W9�a', Xo, �=c��1x�> ��2Q Vd*�x.Y% y6>�N.'!��.O.2.? ��#$he Bargman�|ce;llF�A6?]��u�F�� �i_!-�e�M WU c*�^/2 }2�"cN�"vx65&��!}% 6�tf��O,ensity $S=|\$varphi )(\ �C|$ have kernels \begin{equation} k(c^{\prime },c^{\ast })=(c\mid \v>Tc5T). \label{1 1 52} \endc \secn@{Mathematical Mod� of W�HPattern Analyzers} X *`Sound and Visual}In this _| we will consecutively introduce;$describe m.�m�\an ideal filter, a quasi@ disjoint selecto$� (� that make it possible to move to arbitrary represent%�Ls necessary for solu!>!*hthe problems of best wave-p-?recogni1Pbased on measurementsG -!Lensities in a single:�. W-Y also!cuss ! l� theory,q�pwork done by Halmos \cite{46}%�Neumark 7}, � designing2�s31_ ,their realiz�4 via indirect .�,1�)�$originated�quantumPory �3}.A�ubM_{IEFEA� The simpl!�l!b!Kgnal isV determrio5�in)y!�!3oscil)T%�! H!�givenE�!%cA�d!^a vE�8 $% \psi $ norm!edAl5�AcalculA� accord! )�� mulaJ�E_{�}5BA )N�=|5�I3)^{2}, ��2 1B�similar�tra�?o.iof � eRmechan���E�� �| �| a�0 1 2 3B�of�.�ZB�1�a�n&� ��oAmat�6�nI m!�E=E] $E$. For ex�>e�8audio frequency  witha�ass bE}\Delta $a��Ved bya?E�2uI( 1��0 e .��it��A�(f)$ vsupport r =\Ph�Zacta�a��U�,of multiplic�by!q �cI� 1(f,� f se` $. I��dmanner A $can define�tial opF � �at cutEa v"  fiel�0a certain reg����pertura�-T. �reade!|ll�all5 F�i� y �L9 $E:% ]I�arrow  $ satisfy!Pa cond� $M- }=E92}$A'�each ^�E}\!� eteq2k� ��rrespond�Punique>6� which*� E}=E� $. Bea��in mi�� one-to-!�re� ,"� q# such�8A�6�!Vd!yem6 ,)�i� ��,ed earlier, 2e6"� AՁ�distor��ِit���� .� \in .�X�ido�;6mif�[is ����<$2J� a A�ll)�is parA�$ly ordered��mal} el�g�!a��st9� we t� the nulaGe͌0�e!on@]�$I$; specif��n � $A�� stronge4 B$, ��A\geq if:� $BA �r thanU 9(B=A$. Maxim"�s,)a2excep%̭� zero �, ��Qu�A�dim��:�s $�$chi }=|)(|$ ���� 6B��=Q W��w.�4>�% !��?*�  G_ A�E phase fa�m� rm{% e}^{e�0rm{j}\theta }ɫ . Օ!�th�O��F � d�' $A) erp ��a�e4$A+=I ��. \ 4=A�� }ILWa�BA, "� � $A\� ���$: se a�AX� erof logA� neg��:t�in�at� OM+BA��i� re�not��v� !� eK*�  through��� AI��l�J� enskae�FL)�  19 !�I }easily!� showVat9� rs%.�, (the o�% way rA�� � reas� �\�eTi�n�rib�,  46�=��n6G. It r AHa weakera�v o�modular.F�qU-)-�C=i6()�{!� }A\l  C6j6>�!�i� 17�_]9 1=differsf Boolean &, wɳU�A ��a� ness oe same� &�� 2�$S$3`ca6A $E$E�be� c��A#��FgA��N���"��Tr}\,(ES.�2 7BY ' ��{D�S��Co�ca` &�mK�5AN$E_{i.�|� e&D|�Fq� *�siP0aneously in s�al*ndard2; iin.� <,\,i=1,\ldots ,mg� �� "1 ��ySl)Vert ^��=1$�>0$i$% '� re"��=o"�% viewA@��"� %>�*}!�(m_{i=1}^{m}:Xa7 *a.6n *} O�v wise�tj�� � $\sjh$ couldA�2�B���%%A� phi .9V���9�. S- Yxac� q�& ��� AE�ive��Ls��1 BpA�o.���on1�Ac=E� \mide��U'Bv. S I� �kle�3a �ǡ6&�٭���H $% E, >5f!�a*}nla�5'E �����% ia­'ub�s�0�stZ��i2EF�aM��ifi �a"00sets (or fami ) $\{e*!� 2�\�f� �o� *:�3�I�2 .�$MB�!y�a�paiek]:�5!�A- E_{k} �$i\neq kR "��-o%=�ks��6�q1in ��|�ba BorelC� RpOmega QC}E: �1X1ByR.�n=!�!2)|&�f)�"(s!@"�!=\{1(q<\�Not��at5a<t U }$ may �n^ numbZ f me sabE�Ie@ not 7.9;!z�cMaeq�=�%�edA %���ab�elyA^verge_r�Y.�\� AY.m>�>^}8.::SE��� 2�.B�6� 8>m% AMہuM�)!"* cre�#  in�!iR" F�G�N ��o!�>a<�� +2��.a�6)v )v�I� ,a�(opology ($I �RLiE*:)� is = m�ifbIi9tn2�. � !; �?u&"ly �o!� f-ad� ��a 1 eg�t�crT�� trumaZxa}aZ� � !al de!�o�on��exp$on)J�A�t�1gcEp,2�9>X�eT?.��as�� ed am��seJ�sN�}i~���d to��)1gl �an� im5ant cl�of, , knJa�ntinuous2!�=��F�cA)|!�X��A`bb{C}^{1�)��anc�"th von �"nn'@eorem,�)R� Y�jis 3ly=\ "q-Adq�� on $X�HpBeo.U& ��2F)!C�! $I=\y$ E(dx��s�!atVY)x*9!�� D}(A��{� �  H}:: |x� E� ,dx)e!\ } 6�10>�% H� a��{{A_Zmid j*� naO�Mcommuta�.I�eXE^��$ hEk�A�to it �'B .�&- B�l ,bigotimes_{je�na�jt!�V�mN �� At� r2& $A)�)�j �h�U� $A=(%)$.+��these.F[  P.�@ &h &���o!1 o!� co�"�,� iied out� 6K=n�**2� of 6�IE���9�B Q=(Q� ,k=0,1,%  d)$�>d.����):�["�"�B��5�b B$q=(q�i��N�" )� (q)=* .6)1B�#%�$1*i��"x ��3 � M Y�6,bb{R}^{d+1}:U,�)�$q�X =$ f$.��� $q\not.-tresul3 ��a2� ���'*0&����(�tyJ,\iota "~! ,x)=&���/�Urm{d}x="�(x�*�*2 1B,"% &� !]2~Q^Y2F� Q� qI(dq)��Q�� qs� (q �D�qB�2&BF"% �Ua domaia���\ *= 0D}(Q)$ coinci�z��.E( % =L�$(Q)\,$\ on�%%U k&ed�`${ ,!"s�Faking,9G$Q� Tay$᳥y_(q�,M\e &}"  $F%~_{0}  fAhdf)86� semi-"k �"Phi =[0, C\lbrack&w#� um. r � l, la�X$�.�#� eR%���B}(X)fei� algebra!Fitsm�s. EveryqL $E�e�Q[BA" psto�$i�qJ��.��"��%A�:�!2 "%�*� �� ɪor,< 0l� U � " $$E(X)=I$. "����V� ��"�+ al.���$ 9 ?�g Z�)�G18>b����q�|  m |7:�BE�9* � *m*")���� em� ��XFq,F��3� �/ �F35�5�. s.saw�� oQz�0$ �.majorize0� 2% E *$ (den�c$ H(\gtrsim E$)A[� exis�)-.a�/ mappA $f:v\ a�$X�ss uJ�1� )' �(f^{-1}U(<�.��2�% �6�J w� $:e =\{x9FY.�� f(!)\in M�� �in�e imageAVVBX� m1�|"�1E�.�&-* \simeq E$�% B\less)�� o:�/Success� �/�QQu"�1L!� on pr#c� = ng s�;vr'[1s%o use &�y ����ax�':4��o/�t�(��2�(�E�l2�!in2E�\ ��/�� n ex�0]3 pace�"�te�alv ���)�JF �U)aa tric��q�' $�()�re�32 �)!p��� s�1m1͗ is oI%t�4rv����A�%d� _{+*"�6��!$idetilde{Iy��:� �-��12:G &� f"O"1(t�E$:J?\6�-l4� .F|2/}% (t> t2�6g)?>��� .�%1B�"� VU�l�(%Ez!OQP of unlimie (andwidth, $I 9�v/IJL+ R6\is E�f toFL^{d�m�l5.2 "�+(elds observx5a � &l+SJ ]~c��"� A� ^�AMf6-�ob$�moa�um�j�}:x r .>�O somea� Ed! $F��+.�ofn��� �F�J,�"�l�,as-si9*��w� n" *j^� � �4� to xa�s�12e =� 2s 5>a�)Be"! FouriO*b3p ![q�\m� .}a� $. A:�!&*:�� }$��>�E"�!) �M�3y!�Ջ"k �\� ��� "!"H 7 tian!�mJ�D"~ M �`EF�q �=(�*B56DC>4B#"��D=F"�0F� *J ��3M,:c $. Fj'H2 17})\%!T�������43#oU�. �!ws&��~f two � , $F"L  )M�1�+id�,lwa I�F�Z 02�% UD ��� �><A>cF�at cu� zy$�0:w2Q�&�+i�, �q� � >n� -�>�X� 9]no%%��,)aa*��="��a��&E=%.�&Dt! is eff� ly}�T :=:Q:jQ�N�D.�R�t)�Fi#I.- for�3 dvis( �J� liz�con�.!��9]= by ��� ita9N�'.�/D.%a%ڡ&�4q � �5!g"{$JxI\�/Dq�=D0:yJ�!��� �9s4>Q$D� D���mY basis���sAhM�H3=\=em ";=,2� ���>Mr-Y�vQ./8})�f."a3} /! (��>  6�f (= ��=��ng!�2T.<B���f /��always�� doub%�6�:3(��}\oplus.< C2}\�� 5� N��A���$F>� ��,0a�,A�1�nb:�A$E_{11}=D,\�8X12}=\sqrt{D(I-D)}=E_{21�% 2}=I-D69F�- xblock� >��7&�allowH:��mA�)�(6J�f&�2���( E_{n" V�+leads�c�noA��W}E�A�*5e"A>�q&z�#ay} &&^�� �!�"2"F�n �^|20} \\p!�1[n-1Z_ .u6�2&� �!3!#�ZRS�m!@�7non%5m��-t �B�)2ZُN ���,\,*s*�2� �#1���5�dam����oruM"� �e�$D�0a�D�5= ea�A�f.6(U'N�Z&"z0b~?]2K2BK6�,��9�"�Inv@ M:'��N  i"E��d��oj6�are�:d��W'���y. ��B>Mo6# �)&��M"�$if#:)�>� :� a�/ 6G$DM>[*u$D$0g&"*] �. �fo���g1��!M� R�{Ej鹕B.2�2B�� i s�$, $.~e:o� y�R5�Y 5�!�,� !�#le�%u4.} 6�:�%o� 6�2F��a��1t u|�Alc>�!u�"� $ a� y�U�.��a�e�%fQ��.' P $�^)��2�.b6�#�E�'"�"� *c"6y'�)~A �1����&�0i�� ,s �H7;d�B&2.R3ply."ors�A�D 4o�*�c*�($M)i&�'$M"{M&m .�5.�M t2iW� in.�5kJ A�!�e!�*=�6���6�A� ?"��/���""ws&s"�3%  \ni q=(f, f{q$��J�JH!�m�6�gre�D1 4})e}�6Ũ $q$-:0$b@E�a���� 2am)�U�>�& y�dp)&�IF\� 61dp:O2fzC�F� �HL�!� $I(D�1(p,D�,�>� oB�"� %�)�$*�-Hͽ2?Y��5� H� �96�eC�M-5�0Bp=�[f{pU��"Z5#p,�'. :J"FX�:��.by%Anon� �?�gg�&� > *} P�HpF�\I� D}(P�ne(p2�c{>(p>�p>�">|/%�=un[;*'@�;"*)s&�$8q��B�$$,!.-�#=,tN �1 AV>u orm �"�45�$P���:S�6,dp� ���. N<the��E�� ."�*Is a�A=�9�]*B�"* J�%�4*�BM%� )=(P $  )�<for�> .�6EU,F��$�?re��7to"I��A'0"�&9n m��e5B$(2\p� at+%j})�\pa�B / q���A!"_.a�>��FA;�"JH%N�E�}\"�!$Ze:*R � as1�kuu�&.�Q*}� inA�ch7im�X $T�%t:�tA���N|��P�R"/�O% ��ym��l� 9�f�% b�f�N�RA<-�TJ)�"&):A� (0)=0�Oin:y&|1�i(f)9�f�-r�'% f5�)�} B�% S�M�?��@')��6�B�� dx*#p. F,\,"2F=I:�J� 2�&6� $" ��a� �F9&�M~k�!M�%6!�H*$�G&&�: qFr$�E~enx&d��a0rk�[_0 �7}R!mixo� !��\, a��� ]�S�"�P*T-�$ mu (SC�� &����N�D l;MS, MaPM:�7:�} *�.� �em�5 ��of��e)��F�^4 �S� �4!NreeR�" >C 3 %]0}A��@�ly unw�Q refereJ2)�%�ng��!�>}s.isF<, t�r�_{0�SpD2� y�$S��B!mI1iTB�$)����=$ora)duc�8�c�&2d% ��Gh!.s�-a%Q!�S*� U(S\ J�)U��M>>�e$t�\ecA&k%�L ing ,64R^maC ifX�c*�@aJ"� % �O2�`.���[E�N^ �?nw:�93,I-1 %1A�6�:: .)_,"S' F:F� M�c���mx)vM�;�[ (� �)� �|.e��] :s8>�"�:L=UNuEA�!6)U�(�1 �,% \,\{\cdot 2���2 ( =! @�q1n&� Hi국�f�JZ>�s $6�$ YA�Q�NPa� ��6B6�=S2-EEJJ�u-�Va���^vov�"he&Y, (colour) $f�  ��"V0ic monochrome2n)\"@above-aSio9typ5}l. �F5r�4h 6���J�%�&�)n*$Zd�M  a $p��kJ�.�O . U!HmO O�I-0us�4) plicit���/O5a� stru�t|"makes��\A K&=6aB/p. T�8� ndfpOA�i6I�aS6 �R^ZZ�%�!f�n���Z!���Ba;8��A itud �S�=Fp �c� U =�o&0u7 ��+6�% q�eF �$ (b� "�]�ih'yH2'��2R]:� �.�*� eTN� U:'�G��&"� ># ��"�%+$W (1-FA".e.R*2J�J!1I � eRs�$"1t�f !,�u� )�- }:"�Ut iily�NZ%em$U�f� $Uo�Nand, hZ ,� ՎU=I=U"7�4E�$աiRQ8*�% � xE6��,�<um!> ���=|a Ra7|�  )a}� 2 26�we �Hv^"J% whose �b��.EiyK+%�� �cwF�*}�C���� ��]|&U��F�� )U�%MF=� B 6�Ca��bO��:�FLV�1 varih!�Cx�!�i!<��s�6$P�*�2a%2�7Z�: LUL enti�� .X$q$TF3"N,\ &�5��� }q � G8�?�7�� $P$,�� ,�w���sA�لQ �!a �|*iIir)�%sU�_X0^' o!X*^3�=9^�1i� �2D)x=�8�I<re &9AUO!s2�G�(o�YzXsuX1 9&_����2IN��b \cap�ND0Q^> Let_now7 cuss2�Lq�n AN!&*6L=E� u6�s.�/.*L2A$�.N �Yan� no K8*�de��CD0H��:�;M�b#M R6.BU \,dy�?�'!I��/wRLtruNL�;< M(dqN�2�1�#qp:�^3B�A.Min2^�,e(F!N�cQVv|9FB{0.��T�T6e^�Ku�!:���!22�&D��E�a�-bm� .+0� j ques�+-`aD� ORs.c�kAΥa7y}.� .e 39})�@-6Ka�"%, obvi�O,1B%E���! �z"'d}xxy�e.�� 0s $K(dz)=k(z)D 1z-vB�f4+>=3jz) _{z}�M |=|c)(c|$k(c*Rj6�3&�&o��)#" 5I&� .s 25})kf$\z�Y=zI"a �^ $\o�K$ Y<�Pmplex �^ bles%|� 1 34R(alpha =c$% O(1���'!�!��param�J� by &��mak es)�aA�� ~T%U�L0+ � "�e�����3=95�a8$oYp/!��, becauaf= 42� �=|=Fr }�] !�. e�Id=�F%E�] c]� % }c�:,B 'A,���zBKIf* . B�[x�"9��X"� �Egra�EwVQnd ^Ema�(�;� �b.&�y$x"8 �� ]68�� aN� � K(d� y)=m(x)9`xJ�ia��� :O",J�W kk(x,ycy=|\u}e|#!��V](-\pi |(x-q)+*�X"q>�B�&%� a Gauss<4���cd $X�)=�(i:BB�"�&����% y^�����O 1�2Z:Mo !�%C9�*m}(y)�aF�>/ O)�d�D&Q\1�!�-1��8 rm{e� !� |(y-p.&29=�YI}�,.�3B�'r�N�a.� \dag}a.� Q���}+M#}��IJs � .�:;/Em q/ O�h&ks��w.QM����+..�be^�!�Qk68 ��f]F9lFxa�z�Zx�*�}$y=8M�1y6�J & � �r�-� �+K��s PP~.",I}$, inaccur�J -���"� 9Vm 1L�,obg�smooth�0e&40nd.1})鼑� we~^>�= s $m�.�mA>�#e��&h � $K�at�e#�7�$a"(s!�a" $*�a>h ���x� comb�ptr#s� �UjN%(A=\frac{1}{�2e$ }}(Qm!+Q?j}P.&y�kb{% .} .�H3JO Namm appl�-�b��Mf&# ".X  , we� _verif�D�6all-i�/QQR|Y )= � u .P�PhK: BY icha�er�7m,�(ba�dE�0? � v�q��"w&a�jugarS�( s $C&Q1�A>f Bargl 6R"Fk *} (�\(hat{c}h)(c)"� e}^{|c6/2}(C0#V !�#c�&|c)=ch(c��6�$%Wof�Z[= D}.��*|5�)D% 2t%�q ��M"�#xZ�*�ZH5\int ��%%��� }*m 2z &/ :cJ8o�-1�9Y�!q �$Qe~bm�`&F$�,�a1�(�&,c�=u�V� :O� ���6�"�"6�.g7;5*} A &=&%\c:DS; d��})v"� "\,�5%zA iS��)M%�j+1�|E�26c�s��US.�%� NowQLu&� 'We�a"Dw3��~�Y!�Z�5�-� z "9-��a.�*�)cop25eH}ACQ:pA�*�^�F X=Q$I{+"| Q,\,Y=P2"-"P"2� N� �O=q3\,;=�r*7i$�F��?�Ai �=2;n� S�p">fE8^*WqNQ A7!w� $Z=(X,YB$%FlV�S0})=|) qF}9(|^{1/4}\exp8$ft\{ -% \tf2}% ? ^{a�er�8\} =|0)�2Q4B@%].�ic}��Nd$.7{za.Bs5$NC( n2�$:P%>N�7 chi Q�5]1? )(q,% )=)(q)B$-�F5:DF/=!G �� �ha�%eristic  Q*6�2. thus.< ���;\Ul (u,uܩ�E���^*�m('���A }+��! })�.g&B&e!I&�/!�6N41}�" &&z=C~."n ^{2(d+1)A�notag1� �� ��.B% B)�"#8N,c^� xm6>� yR� B�%�OrdS�D5��erm� �(" .�  B)�c%f^�XZ�Y�)=A1ѥ1��C!�:�Nqith�a��]&2 2� �^Npd^�� �-> �R�J�!eJ%oJUGV;�B7�jJ}v�"�� E�Nq�MO:a!B�"Z .� ��'�4 4R epwe�~e�@e�bEDy $%�B�i2*�8��R2�m). Emplo��!��te�kk8M*32}^N�� �)�Ib� int Z2t�Q5q���65s:� .����1� VaAE�4 a++j ast ( b . *�c2 ��.�k���&"1a% T� %�2�%�,4Bv&@)*t �.O � f]H$a�>�"vYe]Fe g�o�hv>�y n"�)Cd�$z>C(R�9-�%n�.k}$�/"� 2$6BTm�#c)��5�m&Z �S(chapter{Opt;wd�DetYIonDi21��}{YI �suffici'gc�p�9��<�� f two-aoInRa��R.kP�%of �"�*.�X�: um c��r!NS!�M�d9c/A�cou -1% �� �=�co�L���PV)N^d2�Z� � aga�6p tor%k backi ,ZcA4crUcp!}6I�1� ��|1� in.�r*��g% ixed9^ d\6� �up. C�teAgu!�S!{l��, �7 then&�1�c  �A���-Js�!quss]�0A� �i!���c2�AextreA� �A�.C�r�methodK?+programP%( Banach?Wly �{1�5"M�8}.}..4�m�+p6�% �@tU� a���o�ڈ�& have been�^*>f!bB6Hel(im �511��1�B�8A Belavk#  �{4}% , D5})��GBa\�F�nx%r��Y by Kenned"�9�Yue�PLax �,15}, Kholevo  24},F�i9�%}Vancjan77�����ι�ofB� K��FΆ>jb;� �!A�����M �5Aq'��!9B��l= �lu�{}&�"Mv�)�mAa� �t)@ p1�ce!��6�I star��R�a|2� principlV9Ta7d�8"� ���JA�ɕY�%���yqŏIe��s|5a &�n- 7j�U� q�e6 re@(e8% {30IB&ȋ�S2�P1 }� r!]9�aHDor:�6�͔5=&}.(qY* aken�f�N" c5*Oc�(b�dhRriv>\m-�b�a1�KF A"�J�_�0�/A`U\"�c abs�.!�rdI}s  ).;|E-�" \-sD{- ���A� 1� . If 9*Є~maxn�(�!�r2�N�x"`��VaD"M() hei1�9�8i�t� �>g_n�%$be unambig mly1�+&�R�e�)�����!�.t� $%)m�8 high�qr�~l��& _ �� phen�Fo@)ca&AR�te��6 ���- 2u �u��"2 !z�0�m�^Y} � &��Q�c�{V="�1$% Q�j r ��a���!a�()c&a^,�� adde��}Z +-� � 0g!d� *��ep%�>��9 !Z�+2\i{% Re}":D�3�)+.m L>t"�N2�k�� Tou?�6�6� �Pq� a J-]�c�(d,�c�)agW fluct ��~��T"sg��5�� !�N�� .�[e�Mfr&%,p�x.Om��)random.���i��� ond-� �t�� X . PRD27M�!+��Ait m���G framez�M�c�qp�sh�u"��*o��.� FGw s $F$ɺ.P$a��f^�K% }$;a� in"�nonF9�Ny�*�s~m&�s�bD �a� �aF�,6�3cjDY dfbf7 1,�4�1a���F9�� br�h �**� �o.�ex� ���}���:.*S ��$�8M8U/�Q &�!���FJF5!wU }(F)W]�T]F )| ! &F�:JEA�2�:�M��&Q�vian *.�a]e�aidA�a (m���xn=)!�9M< $P&�LF$� A2�� )$nP�f"�k"�E]- re $����9e3�2&#.$�ra1h�b+Y $F��A�ou��:�;�5$c�9�Gcq�Kx\�I�a�Y�HQ���)�X�X +/<X�� ��!K� *�1�1���x,%�!.��� {u&���}��_Q�P2�BJ ))V��P2{m 8IOE�� I\\P\*! N�,j%%��  �noiseAh2[$,2_8&b9�$T=F/('.? $TqoT�y� T�( lo�V9���2�=Gi�=am all ���6e��A?M�.7SLyR�ž�/>'�0o� �r&4A��S�.3�0� D=P/^�� �tA�!x��f  .Q 2"$�Swe�po�6�5$F=TP� 2}�;I =�"tM�"�=��T�1GM vx� �S5tK� f?�v. �K���)zs�#* rd?BNe��� rovegpedS,&�to��uMq�@>"/�r- a��s@U!��� e�` �[]��Q�ies.�� D(F)S4%�;(FD5&(�F (PD)&�Ha�J}.Y*�z:V|2�?Xb�?P�6��yFKU%�-�G唭{ 1 3L ,r:qB-3-di*Ə��!p"�{|a��ď�|�J wella�any�'& ]e0�LD<��sih7 �5|SD�qva�f2"DeQ$S<."IA�Eel� �|2�& to2�*� $F,F� �AK�9>�3�}$G=F+JA� U ; FY�����*� e 0"�.%�{t�01� $R=G��G�~uRsu�E,s :�? $ =�I �W � {Re}m "=0� l-�AT�}y'{7�# �(��c!0Q< betw� � z,@ �b� tA�Z� �z |�D&:Z!�|$Qw � �"w"�DJ|�S0$��i %O�;�&�&!�$R"G�x%A � W3-� , altho��A��*m�EL  A�.!���� `*��Q��aZ"w.M�� >� $R$!�!�"�-{ ���F� R=P+��CE��+ CQ� ( 6 J2m!$C=&�!hZ ua�mutual����� F=TF �i�� IeU �bI.$ ��"�  T:U��� n� �6% j:v1�>2�W$C�* ng5 ��b2d�!l)ENC]G qf�.5e:% �.=1Jo$�a13�zsn��eL%�H>b��.Xj Z��5����� ��{.��2���֍ HF� ��`,@fm��Y5�1���K!��A�|� w[$% #=* =. $. R�!�]�ly �t���i�q�\��1ɋ�H�=TC}�X��t6 ��}<W�r-BN�ɷ�&v d do�sR �I� 5N $��oR�j G=H_{1}+WJv�*!=F+ �"�iso�Q�Q�� ����a �F-6�.�N=Wq�W/o �(�!.Fs, �+G�Emad%�+faƑ$ Q }H� +�.���S�+N�1��%�Oi}!9i�rS�3�� �G%�-�� 2� oFS!�� U� H+ U1,D.6 J�5E6KK���V_5�� "�HQ$% .�=.��I�4"t8)c �$R� [ ace @5:3 �6Ki>re"� 3v @* �Tank $r(S!�E r(P,/>� i�% *=1�)I2�)$P�b�b plac]�4�p �e �"� �&�4}�88�a f�"$D T�i��S=MP ��e60; ��n�.�A;�W"�B�W�! �:8p E}=DZ(��a�2���Vtot6ť� <~�� $% Tr\,}\,Sa��/ �p6u.9�ES)� A�R�E� Hc�{C"�"� WJe�EQ�}Y)�\>��  a� ���f�>�  �U $P>)]r�P �|mix3� N7 3'�e�!�26�X�B�"2(:����E� s, $R�=x� ��a�b9�mpa�isPN�l�'"�N:9NA�*�Pit�$d.� to�w�UK*!j!IUdegre�fo�tcC:|C!P;>�V�aR\(^��A la�C,v�CEAc .�j�e�, i}=R��-!�$i<��K�!yZcE6c, $CE=C��5/���� �,/B�0(SKab&� Qx,��u� �� Q�/1FQe�r�XKL$i=��}TceA�g Sg � qlyYMX)^2�Q EjB�$oy�:c�&um6���i¥� and .i��Ue"�M^S C=R-  jF"�EL>�%�a Q�or ����A~��� R �(j+"&*�l �<d���*>2:!�""@)L (C) �,�U� r\ ���n�A%�JBw��%�w1Z:�a&4���"� e�šdE"� ��vx,� 1���is/F� ���?E�� �.<�#-.!��.� �#. (BLB� 2aL "ab� ncݝ ��9�� � e�� �<w��m %�oor>tA�*�[mu o.1F`>} c(xk8!#ĉ-"W!�&mi!RE �"�8yG �F6� 7>I!% 3oYentir� :�$�b�G9 �r + %�2. Aci!O&�S!O&�NU& �&!EG**[!��s�)�5�(B�%5�� "�%:�m��fMI�`]�\ �ȗ^"C4 o}% *:'�i��up�@V/F� !� kappa _{I# � o}}eKsup_{߀� &� P�ft�R C,"y)mK�le gtG }At.Z2x�*Nf?� �i ��+  $Z=C(x,x)�at�D.�(is*B !2d J� h G .��d�� A�?ce.�2;�Lx "�W$R>T�� $NB*�s����N�}�"�a!�`�g:� "� �supre�0&� {V��e � Q�sz�Q�B%��\2�e�OsHj�"Vb&�j|!�\"�0BH��-�) g�&L;E�=co��M�D* eNs�M�.v}� �3� >0\}� D�2:&J�>ItsIk��var��f \^{+FE% xzd��bo&�N�!C-4l�h��1SB�&J5c��1\m�.{0,�\}=.o>(+%�|:�1JN>���q� s $c*�so�1�F.!��J���� c6�ǁ� f_{b� 0��{ 2i}b��v�d}x%� 6V}��)�}1(2�2N���l&�}�11�8�l1�1�b�.u��sa\� in L��&6- �� S}t� ryw9.�!�,�?u4�b60\vee c=�|�!q`pa� M:�c$� 0ve gaug>� 1i�W�*n is� �� $c�0�Te�9ref�a�Wsp7f�~5O)��^B��!2[r�qu��of1on,=�8��|chieve��ReasoÉah��i]!4-�#%�Q���7!g�� ��m�,�(5��-u,)$4 $Xa�t.h$N ~�VXmDmsCa7wN'�6�a�2$mko}}.�Nci:x6R6R Nn�I�$�c���C}/�a"��I �[DAR}:�-N>�l gf2�A^5�6�i� :K.mKF��J� 9)2yr !(<-2� �h r l? (x�W�!{ 6�"N��a�y��#u�Y4M�.RQC.u*տa9�>$�M."f C&b ���l��!��o%�&�1s 6 v2�W�ph] =%�_{0v! \eta } "� A1-ly *'0%�I2� �I ,G�7m�I�a!gpX� y b�� ough� Z�wo"+<es, co:��A��� ��?a m�X�O"<��Q;2� }-% -���B�6%7&�"�A�Ha"�2�� uish�"�mej�v3ofN�B^]atqO6d0*��$�b��$f +PW�$). A|{ml,e � pack� A �Ok>in�-))�um:�:BR*�d&.�tNI6o"vU% *4W2zAwUx-Eh"D.9W-�:mC0 |x.Zf^�U��}6P\simeq 1Fn|{G F\gg 1�#%5�-�*|����� d2T!���a%�$� n=Y'� �p&n[6t �-� �� � 0~ *��шG $&p�F ID����FRT>� �J�* M�!& ��(�!)��J� B��0��,�]�2� ).�F\�%�F a�.l. -of-"�-���~ ~:KrCb�� B� 14W%"� ~ $�ro |$- ��  �2�] �:s"� xN�.�+} " �+.�)/2Fu�?�O=2 R�1V��c{\9 Y �}:�e� > )=*�ٓ:f R�%ky�S 2� �e9= ��lambda �=<$ A_�- vari�Ft>su@6��e f_{.p� (X)�2!Q}}1P(X>�N� %� ARN� i.��3=0\Lefta"2�;�0%.-T2)�D' F.? } A� !�S . /� det}��� *n �� \:6��=!�4�j&Ӄ#�>)Z5�vC��f1 )2E� bb!tim� k/�*� -H�LB!�*�BQ�is!AR��?s%+C�!RE/d�MɌin*U.��Ѽ mB�E�d!�'$ �-�&G!6ŀ� '!]h��&��.�~eA0&�&�Ft��nd<le�Don��M�HD=ٯ�Z2TJe}Fa�A8��m*g 4})R>uI2�&��}�(*� D,D2c �;De�E\*���NJ�&�Kt8)��2i��$.E�mi$>7:edE�*�D"�&�+-HabD5�s a���-���9�D$ ;!�"�1s 1�0[�6#62X�2�k% &����%6�l�TC� 1#.''\up{] 7})}�*'"�% �02)��� �8ifJ� �N&� (E-6H�} quad�*-C)\,2, % }=*i�EIJ�6x�M�8,C, 9M6)$ �i�&�G:bJ� . C2 ��m��*Z7 B,:�"eD 3S�R)�%JAA�IeA�Y�N�8!�1ad"��$.u% }�r�Oso ^6� �� .-% �@��| @$,SU�1fproof}��Ec"�>}��(�%$��_&wL$xz"�`7��^d�""_by y�!h"�P�"�wt��6e�i��0�*} 1�Ra�m 'BD)6CDN�Q�t8;Y�D��jJ��*�*g+2 % }E=2�*�o}}=C.(A&S }�2�%,!u\1��6:H ��$�V�-^�d-2o}}y5 % o}}EB^ 2�L` Q�M��%.��)�O�-C$��B:BE)��� �D:N%CD��-!�2|2�% B&JTh�H]蚒A���t]�a�-A�*ٵ>3��*z�2\,}eQ* e*E_>B�6� 2R�� i�i�?�q��8�½yi"�*�6�c��IR� &��inͤA��R�:9.�:��>�a!�"�N.�2u1 6�f��0P Lag�.e's*9�bk.� hT�p_&� �{�3�B@�v���} cU�" i=Re�V�BZ �6 y B,E-65 �}&�U f_{Ed6�R�-B:@Ft �!KlZr��� <^ l�:CmidB��,1�% WZ b��a�V�A5�'!� p��'��"� sae})�n�!K�9it{, arrUat Y)ur�81\C�&&�F.hu���T��[6�F� ]"W 0(21% }-c)6']>20E)-.�;(.� % o}g 5���W%(AN%{ !.�4 lete 7� &�!�k��2KZX 8�*�&D)�d�5�7!��N�&!T�B��E���� �.F�"��&� �min -6.�?"�-y��z|] F|.{/� $E=I"X6�/.ҘeJ6� �!l6, .Ve�5.��42��+suN]#C=��*��|d? "d?n}|=C� +C_{-6� *��I�W!�1�E "f-�N#_e�_D� �>0}&�>� ,�RB<~B W"�d�YF���`^C]& a~$has aG~�I.?K0"G��*� �$�Dp'� � f1*b�O��!�eigen)u^$pj*%�$vF�.E"� mP~A�t.x�7��E�B +}+E�-:�FA�1�6� =E-EA�-�y>� *J+V+>0B_%s|,Ea>_E{<^4��� <��y2�}�+�6� }i��8.dy &� :� �- G��_+P�2� � .��}i�(-G) &=&e�(-�)��c \\ (-C)x/-e�=06�!2&�D o% ��NS#(:$j�i�Z� VR;] �*96�9 �+>a0/k56<96=0"�0~% &v[�i�A�+M6@)� -:x;��Vs%�E'6R%�- ra�0:2BC .`��9�6 ^�9})���'�_2�� %�6��7JX�2} U���Z�%6Oa�XE�=����!)��T�01K &s~ !�+)���;&�m:�B.���:W=B�+B�;�J�&6�m��,)F.,>4%n]6s Y �._) .EB1B�07o��AYiT> * 0^t�!�&�%�sh�&��%-|\ Rv+D1r2  $ hSX"�ʱ�,��(io A+ an ��*Rs�$�--})>{Z!+v5�aw�9:4�-��9�Ag$E/=Ft�I � "�:(� "� v.+;6�%Z`[n � expresքB�nOJ +}(R78)2� ;aBR�B� :��<*�C�& �Q�.=Let�p2�1*cuJ,r��4 &"�Y.�Th'�*`'D p("= U00��*"=%�aQ\~>KD �B0}�E� Zy*!KQ��5� �NG=|\x���*|#CJ��$.2�rNa�Qa �Y��;m8x2 8 =1v?JaFWC$2�J!�a3�&>u} R&]+"�I |?#!��  |N|HN�t- -1E�D�+�: QE�q;.- �J�e*<->�I ��w.�qui�w�ola;ha�6Mc�N���!G|b.N�7._.& <.�9�Z  C� �$6u=q5m%6!E| ߪ=&+�'�|6v9.<\�w�� {&@+�!u�J�;� �6�* �o6(F�:�L.�qm���A���\�� 2&\!"���a�H}$�H�02�0)!|� M� 1�;�o�iX�0 &Oe�e�dVd �Rof.:�#���n�g����� b(�% coef�hd7ex(�N�h.{� �0}+0{_7�)&>Y�m �x> $\{ *0}, 1}���iB�J& }�t1}(A)�0z�)�-%�C0Yr�CE � (�6:c9:{- }% I�1��� $\nu B?� )viͿ�N,\;=B$\;\b./�X%�%/ <1 ���IDIY >'Q�i[aq&d � �" a x�a��/omo� ous nonsN4( �Ac"6$)=g+ �1�  \bar{} %�+ R1}-NR@6�Fʋm%J�Z`non$q�s"��� )� ��"+or��u%�}V�R�-|��2B�N݉S"�k'dX�c5��ͥlE�Ow"�p�&�R$V9S_{\pm�{fv�)�!tE�2Gx}!\s8��( , �I+ ,0 ,)) 'A2�,6�V����a"� A���Schwarzn*} 2h|>-uAA/ �ead�=� 1N ��o&M;h�hop��Gs:a�6!U��!pNI$� �J�1:��3B!H��" �.;_��&% �Z !q� 1*][% 1@��"�S�9X0f 2o� Ur -T��is �>�G ����to�*7j20�I,9�ca12*\nA�05�"t cot(� �U���0!!� �>�mc$Eۡ��p���Z�Zn=�v� r��2c8e�u�0N|w3>�6�=BFA�|.��|C^>q) �:�C "&| ����_-!�Ԗ��!>�+^,A�� 5I�U�YUM�>�*09d6ch� QOM�8&)760�$�3)>Q0� �6^�6�0i� 1/�J� :��ŬAgno2��HutM��e�0&c2�i7^�"�Dx$ E�y� $\mu2�]AH(������7i�/�h��c�per)��.% � G"r �{�t9���NJ:S'>��./)�0}� f��un Z\gamm����  }+% ("2Z +   �2}+1-| �K� ) 2R��!  $ =3!3!* |)Q�mu�1L. i62�2^ P�^Up�9!��2`hN -to-5X�o�A.�96s%2�A�"+}|^/��+Qm� �� }G 1 �&� �1Pғ2,JAf��Q>m�/%{]J��{I+ImU+QE-�}M0�SRwu<��j~i>��6�ch +MΉ=1$-�asebArA��x-��y�%��3�H���Tr$"� E$!�$� E��u��4, when $|\gamm�Oa |=1$, and \begin{equation} \varkappa _{+}=\sqrt{\mu \nu _{0}}(\cos \theta +\s!�lambda })_{+}, \label{2 1 35} \end{d % where $.I�R=\func{Re}\gamma $. The optimal filter in this case is matched with the signal modeahi �varphi /�}$ if$ os \ �>- �$%&$\H =0$ �posite � F F \leq FJTwhich is possible only � p:1$. � same� �!�=V�2 $\psi $!!@used to describe !%4asymptotically5ddetecA, at large si!O(-to-noise rA's%>8*}!�E=1/�0epsilon \gg (>�)^{2}.6*}%�Ddegree of contrast!4 thenz�0}=A�(1Q�va�}B�, .�6N�!�$coincides Ec(\refI�3})!Y in $.o$. In�X next order we obtain a1�2�!�(resulting m.�1}=%�/% M�na�1}M�realiz7EJB>�6�_muA~,ft( 1+\frac{ j.F}{2BJ+% 0.* {4}-F|JT/2+m�|A % }{4[1+(R+)>�+.v0/4]}\right) .A���7>�x For an orthogonal background,)ρ1\perp fa�$,!�hav�…� =0�P! norm!�4ed eigenvectoru�4+}$ correspond%�o8 - aluez�+R�\l%�)71+�S}q�c}% -#6@}% can be written�� formB�a���=-� ��i!*�mE� 0}}+$s�4.�U�� �5yKmu }{2a� 3) �%!���.}NoA$IRIm}I\neq 1��a low�T: $1ll 1-��IE��$,!� max��J�ism�ed�wJ�:i1}m� 2}}()|% 0}\mathrm{e}^{ j!���}1�m�>1�"!�>+9>L% � $\sin���9m!is�f rmin�sy݇by!,$ expressio~�+}\congM���Qi"TM%+*s 2<"-�&�+1)Q�6440b co  =\I�Z  }$. A� one,!�$M=$=0$ we get��k"� b�A�l�}).$ ͉general�of!j partico� nt su���!�$G=F+FAI� solu B��problem�0]I� -of-��opera� % C=G^{\��}G-c �$Xnstitutes a complicated�6 hema� w . If��isolat��=on� from�-iev[tude $ }��reA�:��lat"� e�RC=\t�E1�3)�. FA�+W,6� iQW$winF� , $FBW�$A� ��1kin $�cal{H!�� we assume� be b��ed:��$eft\Vert AI� �  1� NextAselect�I4ve� stanM� ; \an appropriate manner. O�$C�n �sYR�} C=P+zd(P9eAP)2� 41F� iAm(trace classY�� P=5uFBj%�� nite D.g highVEs!nɮJ8 � thG1�n� A�6Py�.*� n}$ of�!pA�bA�8und via perturb� � (ory methods"� firs� � F�%� � �K )*J�";܍b�  densit� �CP��(at is, $% P?0n _{n.�nA�!�/ �%follow� ��s of ��:N�=Qi( n}\mid C2)� �(� %gqBS ,):�f^$=(Aj |.)D2 quasiW&� �duced�refore,�measur!#Al tota!�� AN1,~+!��Tr}(CE�V4)=\sum_{n\in NM }��ܲ,6�3F�Bi MW*� q m0)�]�ide&�F� �F�|2�](n}|,\; �=\{n:�% &{!>-1� .@\}.6�4F�W4!�inte?iE�-a"�ar��mparableeV.u\��x�� quale�f such]Lmay�UconsideNy lowea�Vata�B��a�cular,���above ex�Ev=�z!�� Aa$��.� Y �$i�X E�u� whil��B�.  8}) � l toR�2� mu� �412� })>\muFis mor�!>wic� great aM���!�-�1�yles�Xan half!�*#�wE$we)BF�} 6�}20} u�:�% d Harrow \infty \text{�Ʊ/p� {4!R� �2C:%B� \s�{Myalternat�De of W�P ns7�5}c is K!2 willu%c� M�ung� �Dsev� simp r mixed wvp v ta7is�rai&2� � -� on�f*�. W�~ll!�ro���Pnecessary and suffici� c�� su�m R� , us���criter�MSum�h�;Ihg!u thes��nd wa�crete��n^foBRse��9��54� an *D &�9 also�0 lr"� �=�identify�non��!�F��u^�is&F � -�2f%�-7t-{ di�miA�o� tween pur��ntum sta: redA5 \cite{4}, 5}. Fin�� E�\u�#L&* �m:* M��ao9 RJ !�i Rs.a�ubmJ{S�mA�-m� I)xP}}9=3 $m$-.����� �visualU7 .%8aEn spa/4-frequency reg~ $\Omega $�E ��W����|_{i}(q)$, $i=1,\ldots ,m$ belongANIl Hilb� sp� 2� =L*( v)$� solv�trivial e !�a�absence}� udio orEYcaZ�Hb�)� ;p%|E�i��Lpairw6y, $* i0 e)k})gA&$i�kL� ��to� sA�2�a trib� �6!z=|(G� G )t�Ireceived�H� \�� �Di}\}_{i=1}^{m}$ ov�e�"N chi _{k&� /�U"� k� F#� ek=� ctl5Q� ��"'�$� a��zero �� $�=$=R�i2�AwE� spec�� !8numberaSex�id% $i:�2�s%�0�  other4a0c�k},\,k'i$, rem?unb�pro���GA��F�0$EZallB mean�bI��B A�e7t�M� ��>���st�ofB9��in s `�� ��oni� se> &�}x$>�$ �a2mixtureN� RE *� i}.� i}|+NF� �n�J]coustic�q not"mily"�d�:ay yd� .�N$, ha!��X��i��!�AQ�ieV�v&�(Mr�� R�i}+r i:i *} ͜�>x $R�:%R�30�3!%3a� but �&� leve��� i}>�N���Y �iKi.�iZ�6���% 6�."Qedof�Sur�.4a�e� no wayIiUA�a1�y���m�:k dir� ����_��. We mus� find ixa_1Q)��\�t .j �satisf{�"Q N{ i S|i)Y�|� I>���6� ��A�") conf� l�� truc\0 ��di=v�KaiJH^�L6n�:��Z�K!�emerge !P>� �Sof���j�MV"gJ p"5��U  ��k! >b.���)H3 even #nœ�+�j��� mutu� .�� }�to:s$. Although��e�w�"n still i� q�A�-,fgqrq2-�|*��m|�tDyields� *h.� �Q��Ci=m�m!i� � achieve a�er�& �Cminimi����y�g CA+5):-|.EO.UjiM- E| ��0 #,*2 B�A_r.Q narray} � &=&r�0��i}|�.$80}| \notag \\ e�$! )�  |-b_0}|6�2�v�as!�didQ�I�ith $m=1�5]aben�S� �#% {> }. NoHb�r ordue&"'� �qu�%.+$in�einguishr�A� theye�yf , as�0��, say!harmonic�>R^=�8(f)=\exp \{2\piɷ4rm{j}fi/\Phi \5q(*AK%�{�1}&�, rval $[0,K]r���� homo�ous2l�]i�� =1) Hal.� f�i�%^thr����W"�c5�6D� ��J cA�(x)6: (x �+2��=��(x)  �M=|u/A6+ � �$2 J�6n!`!&6 �extY l�cJ�*�I��o}}(C��p_{:�Deltae� eq �}\;:-lrlangle�2,I(B)\�\r" :E\int_{/&�" o}}}1�\;�d}x*�*2 J<w!I� upre�is taken*d e�E\nonE��ng  syB  -$A_� �X:QC � �1�unzM�supporY��g �#�s $1 R�  T�~ limimat�( $obviously,�{TRg �>�9 2�B� �=_�$Z��5y poin� t leW"o/� N!�� nd"�s�$�c.�% }� ��0upper envelopRMc_{\vee a�=\max &�U�B + Thus�2r!��*A�)���Ml  1AEw5sN�c!Ɓ�� (0,.�:A(Ae �E#�1d ��:C$dF� J~.c2 Mg,inf_{b\geq 0�%\{��I�}b�d;% �| 2e ,\;i.� f} =�^ G1:K.h2 Bg�,i�9�5})�R�5�-�ble.�% ��5`almostiw��major� i"Q�%�i!�$, defin-�v gaugEcA�!.>=\{%-2�'~�0\Left��a�I!�-/0��b1 $% m^�N� :2*� a��<�arch am7(�y�i)Y�� .�Y<o�bE�H��ed .�. $c(x��/i[freache��+! $;�o2_0of C-" s $F� :e�'i�I��K��*&>� s $PO=U�  i 2H$,!���k)U+F $ A�]du� �Z���m-� �}�Ap+/2>�% � A��"x�}%�"I&s $N�bH}$ (N�>V3�$parameter)�c ee/� "�i�mul*!'.��(a�� bf{C�(�)�)� 7�d�$AE �st,J�>=�-P!�=%T&Q-2}\Fx(%%+)y }+)>�6UJ�2$�=E: Q } Iv��Lofa;si�)��� *�b  solv� .L{DA3\.�v!'2� (9�2 P���Pm% *\.X%u,\; 7�L  \Big|E02= *�bE 0}2�-2 B2"�6E# �e�,Ahi�$�E=�6��b_7theorem%5� T 2��1E �"up{& 7})}A�� �w& admiF6 �s $%>GA f � �i� reV�*Q& I $B2�)�,\,�J_s!�F� 6K (E-D2\)=0,\;(6&-i)�..% }/2g6(8}6�!�6w:� Bj�/!�2:�6�� T�� yM���� f_{B)�m{�-ft3 B,Q� 9| /C>� _>B�1���j.�:�.��g4�~�iD" +1ex6�8A����# 2�$. w�(I�2�),�6jF��$� u�Q�proof� e�of, �is�% ilar1�*�k��c�( ��� �,A\ �1 1}, �#"�-a�coroll�% of a( 8�1 �JO3 1�I� !EWeasupro'"[>�| 2� exist�tW Zme�b "8N �"$mCm E}=EE/ H�FI J~_, aqu*�:�=6XE$!�F�9})�de�!V� 9}).��-) �,s�.yɾi�6y�;| $2O� G ::Na&� .Psublinea&� �)�of famil� sj��=� �!�,}:?�":�<esshr8tu".5r�F:qi�2�!$'s. BeaBin�dI�B�"at%^)]a��=�Y��,D:�}$�(A��E.�E�!�BF�}V,VB�x"���!K(B�9��:�rm{Tr�;(%t,�=>�0�4w$Jk=E�CE!+� i� jug�5o9:{95�9�-�q }�X%F1)�\} <6��)pre� ]�-�D~/�2� A�� ]��Ŗ&~ inJQ7}� �9"r'&�)toV6�2����$Hahn-Banaco �B, acc?gU�@��I���6A�6(�a calibrL ��! ���_ L�9B.}% }$ ^.5�+�n�9�,D>E-��%�V�:*AɅ�nR�2k},V�6W '�3:K6���9)�"& �)bf{6�}Z�7k@.g ��-m~:+un�Xlyy�^ulaBa}:� E:rrv �Uez^6\ 2�1Ng;yis&�,�dN?&�8Z>� "�� ]2"� �6�9�b��)�-<nh1 5�R?V�ins vali��< a�?fX8*k)&�m$ �X� w<qui�!atB%w>1 �4>Tr}� I�a��jh2% i.xv . C"�:� can x b�/tAL $m>1I*analogy"��)�����communvA��X� �)Y[<sga jC+ "�;�� �3�!>*�in}�%n}"�%�5�!�5�! �!m�dmn2�52 1B�!%[ proj59 �!Cb!����-toA+�Bsum!�E=�6+6�E�)/2 ""�! ��7��b{N�}f�S*%� � eteq \>K�N_!O� ��{ 5o2-n}:\;k�+It\}J� % (s $n$�!�*�lA� x_{j.�U4� _{j3:=�k�7ref�-!myPAoF�e�15% )7�7d)Hk}$Y�F��9rm{o}}!�iM6� -��)�:�)��) V�:PecE �4�&�#I='��* � �2F)*><J6�E�60% 2�� I =0�q�� d �jS"w����&l�(m & �CI3�4�#"�0�Ff.�$ q1 >�*�=s,@4'5V�;Xu a?K&�d&f f�y!.� *)=M�ʗM�:�� 5}P%e�I�f0\�E�7E�B#������{S�of�:W4} N�imm!�@%Gh*+*vLe͇�B�x=H ^{+} =S$��occur�%%��)s0���* 6�*of e6*�"�**C.0�� I{�$���6})� E�:�/s�P��+��co.�H�A�1&� � of p�,recognR"*^knownv�q��,i"�5� ,� �42non25%y>���+ i3"s=]� [7�� (h2rmsQM� 68.�+% "�%B} �QI $m=2�0ow2 rATR V�&a #b�duc��itx f-/!|1Q�e� 5#I!R�7 $CA�,1}-S_{2}$. I5aFA!{lfaDat��� $B=L�#�>2Y. )qtF�"WLO B>I !G,p4��6Xto1 1jby carr�ou ��5�F ion%>�dinf� LF` .�%>>#+G6>���.�wzB=L-���!�Jr�8Q1 �:N�C �{�1�,� p"� =\{C,��.�Q�f�" :�R�1 1�)mak�/t L7Qto�6WR` E�]��Bu !�"� V�S� .�C,2�% 1 ��LQ%0>�6QS_{1}U"r� -^nU:P62:DD!� f/!�� ciuK}�D�2=>�kD�6*>�'$To investi�V�of��e|6�)� m:z<�8�m>m�re�2�~e�� �i+ �/alB#E6�3� � E�<ai�>all�!��Y�O 2�7ń.G. Sinci*$% $,��r.7B$.�R���i�n+i�l#�.&�<�" view�&I-*n�Cng�LuJX2�� sens��BD=0\R�Qa]D�9��.�D?9�!�2  $. O�e<,U��^ +}(B�� i})DuldEneg�A��at &,*$i,%*�)� is lN*��m2%:IA Ʌ� �W2}�C�9�UE6>!~SSa m� dV�i>\��#>de9� onaOun�% $E2�h i�"Fq��<&�on ���;�B>��6 fy?.esum�M �! �-�"cs�%m% � 8�W�r.�K}��� .�2� dim� Tity� _�.� � *�2"i2� �-wi�t)C!`it��expedoC>��1�K!0"�J~v"2v"-UA5F�20��NtI�b�a[�)m�$%32  ,� h�D2�Cm!�%�:%Z� !hbb# }NB(L2�)^{-1 ��66.(% $R>2� ,:�"1bR0$6�( �im�%)>���) ^{1/2>�"� "g �$F[$9})},28!|"@$m *�&pq�e~��I�$ f�>4 } (1�-�Ra1)Z� J�54�N .631J�-5,}$]-he�*�>V A)}. I4:�Fr ,"��-�Nf gradeF>��� .�>�q�;N0I 5edC"iI*�Hpl� ���qj�����&C�'h $!�2�)I�7 "�\ 0�o}.-A�"�$% :B6$) n re�X���!�2C �R } (67�T� ast �)MA�6�69A�B�+�2y 6�&1J�)� ��Y!]6-%, andN� J�FB%oF6)% !�mMGQb UF�J�q� J%B% ,296LRa:hf*RC fB� [�A��] ds��y' 14})�g d r# ransA���V{ �e.L�*�2A9)A?pFW^eoE�y�%�:J�2&�?�e arr�a.C1�2i�Caa�Dversibie� �T$% "^U&J.�]��/ E�U E �)inA�li/1  2 ��k�E(G+y)15c�K�1� ���>��"� d by*� N%#6C6?�!!��N� 6_D�$20C+Vm� V R��\� �(�s&� �O� * > �Jn$�A ͑ r�8&sol�IU4�"0to �C< �1��J@2qO3at�%.� =X5]e�Q)��lyTGed*�% )4�sq� --*g $ algebraic�Z9U�ies. "$\] �ig2� ,t� 6� "n sca�*�lJ�R+e\mid 6�"�� 2o ,\;1� &< vLCz11N�-2�}=(&\=�L6��|�.�dnumer'MU�Q�NAlsysteaR�%��1�"uD=on6JFVF�=��IcIKirV :���-19�\�2N/:? B;.% (i(�z��a��HA� thosL$'P, ,$9vU >7 .�<1)ɭ!u6>1��8D 6�: R�$). .-t�Z��A+�$ establishB2�YB�A�scheme*YS�um BaS�dB�4Ix� ��;�[�Win��$-�v&!K�-J���ZCE�==0>KIS.XF_{1i�6U j*%�,� .De�� 66?52JG&A_�'�F_�= �R��kR�$J0i' 02�0�Fd irstWe�QDG"cd hi *7\ll�d&GhA�"�%��'ie��[��Hi6&K�V20#58.I5+D%$BY 6KhB<�� Tr}_��� � Npc?((].�}("�\AN]9f)/2�& * 2Je%�AM A� EMR�%� $, or�)�=(D�|RF) e�K{ !% )�$-a ��2"U� S�k R�b6 } �1.U Zb�"�!� �4,�(Q2:�B� M�so-Zl"�����K�7$=\bigoplus*�7#!�j O OA��MS �2'U� at%M-K%�R�] Q�R� L��,���bb ,m� S ].�s#rried � �xA�Y$isometric �  $V��HV )F%  po� expan�$H=\sigm;�V�& =HH]̑6~H:a~�L��,psto \lbrackx.]9�{R)"A�!i�K% E .�I"!�pm %�&�*$V�VB\ A $V!�L�p:�,�A)�,%%r�� ~1/a � #le� matrix�g!�x1!>VT*�,M�Hby-$mIJ6M[-�_{ik}]z is�/*5&M+gs�� �3i.H�V14$,$\;i,k.:)\;$($28� � _ k��if J� )eA"E and2���!E�3independF1rNs ]$,2�1���*s2� =J|�\?-v 1�W� e�Ch s $V��=*aP2�����E!da�I=R�q� �n$ATdia�+"�s ��}cia onb3sa��!$ b�(about,.�G!iBTX ele=>J� 6�=u]V:m  )tB!eQ� 2�22}6 #}%��~0Am� *<-A�6$��/�+I:B�*} �V./2BeT6sE66n%�rm{% o}! -Z7.ik �u�$gR��� (&e|(��=!�� =h!WV��=%  �� �^{.&G^�;b n�I�sm*�_�f�>� 6� Ft} (�l2X- ��)9>:}�?2��E:)*Q�%&B� .k Bz*J@1O�ݖ1(Rb�D��� 0�;f�2� 5LA2�Uc噇=V� 2^m� } 6�< 2 2}� �sUFfor ��"V. A3>�om�& ��6�2�" jq$"^by.�&�R-23�>G uF�q�} bHYi9^�;hN[ % }hZ2Bw6 fkh� m�!�lam�y2�=(�2h�! 2!=J<� a բQ�!�u:G[52^9UJ���I*e� J�nIx<�  } b1}�J�B�\� (^�hw.�% !��g���D:J�svj����B)� %�.&�a�.� }=1)�>- # :a\m7 6��aeal UCiz���8�$% [a�`] W"� :C̈́�Yblock-E�h$a=Q^8 s $ \.U%�4^� ��A �� ZMR�'�!do��I�� ��16�ala� Tr}$J�Y��Q�j"_)z�4lP+x"^f�ly"��o>sNVuP� s :�&�H �Q82� �=. H� C (�!F�[ ) �#=V� Ir� ����&]+ E%xY � sa�N ^{k�-12_{1 za�(�y k� i�$�of�n [6�=V6�� �Sz�sH?v&�2D$:�=F'��J2^LR�}NG-1}$. M�Jin�c}*�"�?=�Q�2�.�� I )�F2WL`\blea�'&�qu�root $hao��O}n�qi*DRQ�2� � � ���c.�I �A���J�:!2Ry"o� �� �J� �2y�'$ 8�:�;�I F;H& �JF-1 12�|!:3 quad�冢T6 JQ"��܍A� *]�� Rh25}) |6sF�5�!Vs!J.��+F"���e .��*�,$h%.�@SoZ 6\%E��~��&� � e�R� A.�}�A >5�~8}h��.(m� T2���P�M&"2bd"q�"i4HT5.�-$" (aE�.��b��(a ��.͟$ (becau9B%�l )� s��B1� J+1"�i� ZDa�0.%�) �#\Eed�/ licitly. 79&leNA�� .h)�2�i>� ��"@�$h[ nf/��/�) 2�]6M)42��%J�/AN<(�+4:Q1. $72� �1�O*y<�� >�4N�j!�6�o}E�h->L }=hY�h) H1B ?�Q��/B#6 More�Z, $b8 6oe��@� m@ (�m!82r-�&s :�=% alwaysDs q~2P��z � _{ii&CXMu{; corrZc,.�h� , soE��uCIeAfQZ��U �!�5� m M A��E�H� �\Nh-rn�}`2,%�!�O xJ�6�b!%(sid� p F�  t���%�va�db�=[R� ]$ w�'*��:�@�&A�f�=a� kk}$IH�s6� ��>#AB�"jz0&�wb�%>�)�U�{m2| \{ D`2,1�%5���l&T 12q ���)k2N( C cY,\;2�� sۆly �ZverNl�zeOh("2|.�\dk*} &&MO�2�2��k�q2�w2h_1,$l& _1&�*6&yK6% }�HA2� ��>""e�%�>�E6�� E}�a�6e!�U $. R�T�i =a� =(]�P ,h/m�b��4.��m!aa�k�y=N�m`' L0lyQ�ed6DM�!���6�Q�a4C5�CinvariGA�FU� ^�+fv� 1}{mRH5%�6 % �6,M�.F>d V�G&�'nTNb� io7 "s a@��.��xb�B��qmet. �'�m�r��Y��of{6�% )�V2|m�"`qE\Jv$>ia�?� ��%��#E�),�(���3y'? �k��Git cosSf� ll m�b�ks% y%�"挥�:8:� NWe)�1/(1-mbo%����!�&_{0.�s+�] 9l*�mU��&�w' 2#�-�of.�}�I &RY)xd0d2� �� �":Z�(1- = /�Q4} 0$. "���A�5r�)�|dR2ME(��+ �x^{6ierT~}x�+x=(&[A1)�}b9)6�3J�+� u`��`�,J�f( �tauB� =f(1��rx6�}[f(1+> :)->)6/x]>m% t�Drt�?�Kact�hq";:d#*!��Mnu�{��q $-�!e]e-p ,1[$]��V�c/26^�{�Ux�v�1J !,=��k}-(1-!S'm �}I� /2}) #�� g�1�� e cq#��F�H��! ls�b�UV&Y}-�isNga�Ni�f(m��)5<+5-�})��"�mQ*nQ�z dmit��qFj���E_�L�* ���Q7=0$*~ ��N� ���z�!��p$k�)�U\AN\{Y8��$K�(���a)��|\alphP� �ca�qcal�y��.�$42$ a $(d+1)$� XI? >7pF�zqm[ �a����d+1� �# e�0% }e��]�M"q��$���$% . ;u .I .�+��� nt!�M $v)� \( |-�t]doe3t van�4A�!�M�"����&D�lul&*�$mI8A�g 9g�9?Y0EY��d�W=0�.nd tend�=$q�#+7 !�F Qa���>�-�52� ��A�U�*� >Tn�g *x�F^�$A���$;ApaA�;ng,�m=2: 2� �di>NN�.8��v1���� })=��% ^{21�]y}N b�y�K� � -�-pZemplo�B]YRYJ$%  lP $G0!.�#dL�by douxcg�0i*��Ee���Eq���aa$a�o+ls���0s�5N>�differ� 6|ces�%�,k}=h)P,�>��0a=h(0)�_cer!\�5�]��"666��!ng� )O-��&K8.H�exs ."�tak��N �V BNa��k�� K\&� J�} � 0.��"A���ter/�1]$. D�5�v�:J�M"_{xV=(m� _{x}�|q�>� p ^B�(x- A)]�F��:Y���-�Z��_{xUo)p y�xn\.$2^Z&? .�N)m�O�" ^1�a#-e�&}/n!,I�� �b.MQ4nJ�&H)H2  bb{R�C �p&�\verifY="� 9 "q�:\$8 �!6!��#yR� Ifgt_{1}�:^"f:|\;1bd}% x1�,m2�|n)(m|�h6J� % x(n-m)}.\ZBXn|JP{�i�& . (2~�"d }.��us� ��� =iB}.� j�Qe� �W!bb{Z}% �4�}>Yr I#z�"K &�8� i�N-2� �0{- ���� /2\a[�&J��"�l��B�=r.�;����؎Iᵑ��(��iֽM"�T0 �?�g�`\luD� Ba%J��_2f!�ntY*s�2�Ks~!�JV6�%� "!| �~ ܅"�1ct"> x}=|xE[�� .�� is.�i*��b ���u ���S8�$>�.-self-ad�j��$"�A�a��}+h>�V+ A��O�f L$&� "�./ Y� ;� /2$r > temporal:=zX�on" DA�&�� of Mixed P��I Lwe�Hwr ll�Kup%�]#tAng�"hyp^^tbased on� *���Hn� � )�. s&�de�PA�^�<� .��IA�siticX�Gџ f%#��I: re���A�&�a\hoٌQ!4 gram�H�rR-� ��ed GrY�ET�a7mXO�!6�V�Mc'��"h*�o earl� �c�15}�->�qu��Fi]@s�afF>� erro�baXR. A" ygeUE"�wA]be m�nF�!ja�.�O %e��s&��1$A��*�fOAKj#"�8�y plan/��*A��P i2Tzo�f!�% ])(z9: chan�sp5q4}e�&7Ha{ H�HuDF<� �zd.&�vi2+�i{!� �)��A!yuI�Tb� B|�9� {݁�|�[$ frameworkM3t uUqv���(�kus�below� A,\B�C&�usNC�2kH� ���)�8'n��r>)'K} scriU2�dQ�random��s��XZqu�*bl�  in2�U\ �6ٟ"V�?ri�J�i�K.�EB%�a� ��#\;}5<S �!!�a�Lehre�"��� = .f)���).�!^�).�&�9�%�*�.-��/qP�ed"�a"RF'*�}|:V :_��R�  @Eac�X]l6�M�����} Y�R�wPi2�A R �8V ��Ffm�U��*>J�_�%]��/4��"� :�l) ��+H� �:A�e�c��e�cQs u|B.�=bܡ:C% ^�may7�pb�$k,e�at �Y$m+1$�reQ�%6��4czrsa�V��.9!1�fP�$&�/^�'F� Wa�'sV���D=2���ܠU�iz�CoS�alRH "�' (R,DR* Y�l& Ɔ]|o�h� �D \geq"t2E=EJ�NRD;b \| �%��6/s�)av6on&~DE:LE��P6���%Care u�9r��)�� comb]�ioA�f0�k �5�^{k�z-S� pf�% � i��cee�Ax*b >UQ�Au� by�u�?yT�gR&�,�\"�Tef.��$�in eff�>"�RŽU.0}�� i}Mi�g0�s�h%B�a�U6#�0q&.�}]&�Z"Z"�?E�e�.t0}kKF$D�i.At�=��; ng b�{*B($9 �R)?�m0�ge����a�d�f�>�>}�0�i�IHmv,\;%�=(&ȹ�2)�r�")ie� -2v", S"_;��6TE'9ppʂ = H)�ng*J d�T:<+�q �DK/��q #"N#:J(2�;&�C)}#f_MT����ي%ek_+iA"9.Ylle"���B�'-~���7�!�f2�^E- .gM3*w��!}%%�rE�"� ��A�usefu�^|V:�.� 5�>�a�2& rtyt.$� #s�+*�BA�dυ�`s�|ema&�tY��/b�"(R)1� �{"�g�6 Iaa6iN�)�J�=.@9� \sup:P Big\>m� Big(2�b`>� p&6�p EE-DM]�)sN�IM%  \2�+3*��-j%g,%����ޅ]�&�E �)*�Ki&�V3 1A3T n} )�^ ѦA�*�@2�, �r�}I2W�Q -F �1D�}p_"rA�e��0U_�t�Ne�>�-J�*(R) ua�FV T2}J�ŕ�^oRT)j�>n(%����-.FM� ��M�E�)Iqa�.� /��:�&;M-�%�vi�|wef Lagpe's*l�] plieJ �%�Byus��rt^ �1w �83n�_{M��r�H���&�!M>UH \-F� ,Mfj����,)V D�h=X-�Jbm&J1�)/.j2 6���{3*@�5���}����9oR.Q 2% 8Z *��2� *~P$E��t M(dŗ�n8-"xU $E  ,a Bore�Z $X!r�&v�` vl�H $x=I~,\;X=\Oj��%x: mo�4um� b� J0\widetilde{I}V�pX"�Rq)�,bE�"�*�`.= U|x)(x|Q�d}x�W �^T1Ƃ .��${Models So��� Vi}%e .&����D�%2-��D X"l .�e�$Sch�{�yy� 2�A�M� le A�y*-X)|� �4ҷA��*% M}|��P�~}(X6 J�Im f<m*�1EO 6��6%$e� m�=q�)&ͯ�i��C �$ � A� infiq&�A8rm�in/˅�!��&�0 |(X)"D�wmaj��K'"i"o|"N��_BC���"��!$A� sinc�4Y.�as6A"/�RF��&xX� o&+�>M�86E-�1�A" �6()' (EJ!��9"���,X^�[/،}Gdie *��J.t-�A� e7e��iqY �"�M�6w�3�h�i�%8�.y/Lh �V8� -�Q�\*Xx>!US nd��M�fA�"����̟)�,�(.d��f$>F^!E�or���.L$m>.y }�t�|g&��2O��nF'���a�*�:ji}:0b:Wu.�M�%�2x�k.���k7E�B7!�i#JZ.D3 JfMIn.C �ynGship,�E]1a"i�� [-�Y $Mx*� sI�I!�6� nonempty K�"O!A�2��)-�F vNH�"1�(t�6f�ES9m�!�}�FS&s����&�3en��#]mMdƃ2�iA-f�<��&N :,)-��A.RO i0�"m �t.T�o�T���actoryb: $,I��>J } �Wm o}}-DF.��S;2�6E8Fr!51::sAisAi�?Gl�rs>��F�.� R6�+�O _{L>R &�� BR�|�VA ]�&VJTL��i�u�F�}3]}E���2%.-�NJ6%��)"�t� B`�F/�AT*� 2�(R� 9NIi�&<:xm� 'qu�1�s2�Œh N�� 7Fa1@`"a'q,>��q3ntFSFR2Ri��F.~�"� `N>B�- �v2�j .)6�6�>W:J�M���1'$��1b��0���o�gN�K F�Ag(G �$6��M���m��b ) �J0:�\�q�.�6l2�6�:KBCCa�:1 �]��"�&cR%!tZit�!"�(���taA7}�V9&3^"�/"g[byeO rC+)> monotonXV���0� � T*} �2 1,H;(L%�)E'.���K JW ��=0O�>���%-6v % }Eus�l2�b��Bb�]3s#�9\!�' $2��N�G� \I��II)� �2_�.Z!� �[Q6e�*} >�.�aWi qq&=�2$a�3�I;.�i6 .-�2B�)VL=&n)E�)�% m��ZM� ro:�j�qD��CIg �)m��E!)��k $Lfsa3we�y9s�!s.eB��'�SLF� ���i2Fm!2v%�-CoA�6C6�>�Z(1W�g�U�ya��) �'s*� �Spl.��1��N8�i�M{�.�=n��IQ[*��Jwx*� 2w�6� L,E-6F�2� �Y�����-Li12gF�6 }1> =}� /�Y2 � ,& ��1�%�\�qn::� 2vE�J� oL�2=~� B02;,:�Q$N6'y�\;�[ �, ��]B<2�E):Ug�2.266�r�< "�*7�C� &�, *�GNjto�F�]*�E�R6P . E(D�i�&u��p�S�"; ^��4=!W���[�����-�� 4� m� ��:2:� �"�1}).EB� � �3 �MT-�'}.-���Y Cm#in%�chang�%"u1x|! &F&�, $&�. F��i!O��sB�Y"���we put� R(�=� 3.�' hd $L=BY^�Co�1.� B�; !�t�V��FNB�:�A�6q Fg9&b "5 � ;%�A�.q% 8�tCond} k�oerU � pYC9�h�M� 2��N �2) 3)�Pi ! ��%�$�0� nd5� ���QK"nE$d�-63�-YcM�B�.c D��.. *E$m-1$ s�f s $O ��T��AM�s ]�2}E*3��orzJ�iF��pԭ2�{go ���sB{\^{m+1:�o��R�2�jCS9�g52b�B� � �H 0��J�zE�3axKq ��Y5+�.�!�z VVV.�z�>A&� % H:�9TZ�1$;%�,�z)+ s aYult�,"u����bP,�<dM�QG�xu\L&�>h2�|!�*w:��J� ��U�K "2�=r4t,��&��:[ =VV^{�Z%�8eU�F&J 6U=�kM�6�z��z*{!J�+T &n( �E}�-\rhoI�)�O>*��Wv�N-��/[!� ast &�/ŝ��t�6{H)�^�bDn,\;J�bh=�%�R?��"�0!�2)�A2���"�m"_� �2�`� ���P`xed�0,�N�co�3W be� a"BG2�p=*�t�o11+.i�>K��*fŋ�f% co#Q5=VG ]�m�""& e�$� Mr=h�h��Eve Q.$8�s�,7���M =*�Y��cf%�J(Ni(b� �&�~�MOa�1��y�W{�:�R]��9>study6T�q&w��A�ranJ: R�?A��$2Ev, %, �3�2Q�,L$ ��2�byOIT% XoAiR�c�at�REa� �q�bb{g�o�k"�2-H? �;R&I��:�� { E����S�Qq�<� � �m!has�� HM! tian�tAmM�qe��nx�O:ou�/]�f�2it�=n5,5*xP��i%PauliIc O� V &'� 1nG[�{ll0 0 \\ 0 & 1%' !a� M] r$s�C^I�ROEO1 & 0�Oy~O-Qj% G;E�bznb���-b�RvKhX+z & x-�y\x+.&��-zZDY+x=q+y y}+z �nu ] bf{r\cdotK��w=\��-1}J�$x,y,ze� $Y�P�DifI� x $R��u�jbf hat{r}}=��q�@ ��~}}ya5J ��>fTJ$aֶ r}=(��# thre6`���� {eI^{3� V�� !f{ ���1% os}��Ir&�=a� #% sN%�M��Qjr}s}�&f!� ibf{s+� e*�O 'times5os}),$�e-�s!~x~r}B?I$�mZ1-�-D���-.�y&Ws!u"�� �R=2M�D,rm{% Det}\;Re.�H-�-�oV ()�|qG+)6)�)I˥��n��&"k  $R1$�u!N.��=60�|�6 ��y$R==�nu�F"=eƂŧ=( b u�%�r}3k)/2> $,q�|;|�9;|Q�6En�(=}�can b;F* Tde>s;h(&�Hee��&e��?o�L�^.bs%15�� �.! by*[5a,"�yf� n"P�9��L. A�uϾ��ari�>m]w��lf)_e photon:�D�&�r9=2�D)L"roa"�la�9��6���s�' �.%��ہ2 } 2�k}-6T|>M!-���&3#N�N  $kE�iZ��,iDpQ�.gI�Fa��z>��W$k$-thUK2Lo�A��aw$i *;B �kt@:k}>MS�R� �$< "���(|YōPvsHe�qnu $)a-=Aignor`��� F`�A�N G� Y�%�P =�_ 6�di��y2�(��e� ,"\H\"��d� Mld^I (�Bd}%J��q.�=�n�� � !HYP�2p% pe�>�I&� &�2< ץ�;:2�Z�*�&-�q�of �K"�*.A==% A�VX%�G2�*" 8ktO,�a�n�,^��" � bf{l6? 2g�3�%�udF�&P 6�!�z^���-^ōl}6z)0Mi��!�<&FR �Q col6JZP2�m %�2u% �aa2$,,i=0,\ldots �R,m$. \begin{theorem} \label{T 2 3 2}The solution to the problem of optimal recogni&(of polariza�@s $\left\{ \mathbf{r}_{i}\right\} $ satisfying together with $% \=nu :7condid8 \textup{(\ref{��12}) }can be found if and only if there is a collecJ of number�m s^{��rm{o}}\geq 0,\;i=0,\ldots ,m$ such that -Tequ%!U!Lvert \sum_{k=0}^{m}(Y5-.k}) �k2�% 1:P+>Q-'- ZE}�1>�, M%C3} \end�% w%5Aޠlity takes place at least for those $i$'swhich $ �i}^{% �-Xneq 0$. AsQXXdecision operators have�0form $\delta A2�=|\ bf{dEn2|$,�I�F % }=�H �^�lFc )$, )-qc!1Ac} � bf{l6�=)�iMR��U0% \big/�8:�4F�a!�maxq�,eived intens!�isN� varkappa 2c=\A�( 1M�v�nu%‰ ) \B��=\lambda�. % }.6�5>�Iە�1�8proof} In terms�$^f},1�:�,i} i}$,%X$(��$,%jfirstQ�!`�Й�8}), $L:--RA�a� 0$, has Ra�]pZ& Au) ���:�|+�. .!6-Fk% a� $(L.� �)D�2 =0$ ��4written in ano� �0if we nullify�scalar A�5�,�6�� ile�� :�� de��ined b�get� � N &� i.� Ufac-�$>� �R  se A6@ d�A7 implAN that6O) 6}) IM a0tudesAE value�7$ii� a F�" �Օ�"� Multiply� >�y�>J^$%� findFu�$!A?E�>9*u V 6 ef�� ~� _ 1�*}%�!��%�>^p1)�N�^3RC J�)2���}|fm % o}}|F we get= ]3}�{q�-�f�&} $. Si�_��rm{Tr}\;6� b8 � AT &� of�9})��!�l��5})��I  ofE�g 5��lete.)'} Not�at, Z�"67! must�tru�r&v two a(cese��O$k$, s%M e�no�R��� �lm�m�,amA0one subscriptmE�s���e -th ��@y. For every pair-�"�i�)� k����2��is��id�a uniqu*�-�$i�1�%�^g���j� �all $j% i,\;ith�;1->Ŧ%: k}>0J� �� i}=(2ek&� � w _�)^x )� :Di6DkDDkDI�!�Z��butIav$ $ may not-��-� 9�A F�!H2D. Ie( xist�I��M i&r!6!�a�Un>} e>u vaA2a��%�jQ�I�$when $j=i,a<tY� "�q )��j6�$q zero6�k$ (see �;4t a�N�b;� ^� )#)/22bi}-6Uk}|EL�6q}6a2�� :c2#o |��.iH!�=WN�$J*�3 �) |Rt2I )�$orthogonal!s( correspond��an error�N�^�(frac{1}{2}(ipic k})+�5 "� )�F8 �h� � M�*(J< �nonQ� mor�vn�;�!'s�$y define a/=,d� n �f�lty��two-dim/%Zsp��cal{E6 athbb{C}- $. W ll�Jtry to �  a gener%� alytical >�syste�Q[.�3})� ��:9��0V J  ; ra�2,� will g� �ometricErpret�?�ha�a�&]{G:Represen:X2-d Patterns} Let us r(%�Hermitia.�A0� ,y points $r=A ,x,y,z) "�r}� ur2� Minkowski2� bb{RB1+3!�To ��n*� ��re yX��� insidAwe l � nu =}|��se���b�rC}(l)�\{ i2:!�-^T}+|�_!�-: |=0- 299:� }% cover� �%�a�!|Y}�)Izcon~@ the �S� 8r_{j_{\alpha }}��|t (2xof��bL�.P$� �6\. Oe� acr hand�AՑSl�}awh proj�*H (% l}$ belon�!vex hullQ�-� s'al R[�Y.�,-6l�(s,\;s\leq mJ� }�8 }^{s2�._ \pi 6�") l,\;�:NF61620Fc,p :f.�4�$Ja\mM .�X:�1 .ng�xi, ����V E�Se�]E9}): $a�A�+�*� l}|%�q�$)&=saAV=Mw ^$8an�b��Q�:5$ lie one0�:�2 x���|$��faE� M�}� %6a � {!hewu� "M>��FGT�!  �! can ,!$rmulated a�:" �_&)" 3}To���"" �sz>� � epar�bya�c� ��as'B"}, it�Unecess���suffici�{ Ba%��}6�9e>�����ΡBto s"n a�vn"��EM�of2�))q�g�� o specaQ�ofF�f R��I.��* �].'$ E�2�ͩs }.�=}}-0t eo �A�sum $2.�-�>�� 6�eFSconst� "?�]6�N�ֆ.� pZ�VX:�1N��2�*+ N�2@)��  Y�&L\in"F=�Y�� �"# s"4 � Q�B!�e�"�&� *} F�=br"> E-�U !p;b.5OF=}|J+���ti"} s^� V�$=\��:�^�!�2�)N(# R���i:�#22NS� :��!�i\not~ �"�S�]46wN� YV is ang&F�N 20})$�"min�$�3n�$A�isB��$� �$iF�1�B�|))#i:�$2B'���*4�3o�]�i},h$ 25aA�:7�s, via�"Ss � &� 21E =�+ 4��@�b{R}^C  differe�of di���t� �&M�i�nd6!í�r�!����U]k}|&� f)� i}|=� "�. �  F)24-���%%se�Y � two shee&�$(hyperboloid% revo�+�� foci��u�<2!$!9 eccentric�>@�,varepsilon =��!$�n$k}|\,}{\,|B|}% >1Z,w "� -KkT#�.�]~4}�T lane norm�9 segm� 2�i� �E�T�i!(� >���, k}=1$)!dE� $:�"�) )2$,�le2�r)"�we sel he)�� W �Asu focusf -highe*��*�aoy k� Obviously!oM� "F :� ��2# $lv e�>��*b9k��common-2ofY�Y�"# 3a*)*1+ ll5��� B2�.� *�$�fG�.j�2K."�c �is �Ud��aYer�`�� & �:E� �EWch mean �JuR�.�^ V too. It easilyc show�a�-�g�6�JcoJ���%8"� linear݀}���*F�5n\pi: 2� ]�if� �i�1 -:�0+; 1"0s�$ra��ly�ependent:Opt���S�# ex S�� � read1ll1I�atH"ac6�%:=�*���u �( =0,1,2,3$,a��)n $s$-s �(���if $s=1! triang�Ps=2$% , a tetrahedron /]!so on)aXIwF�!� ��:�aj�� 5�a$is well-knU�ea�0s$-.�f�( � )!Hn9 v,n sn��-$mq�!H� ub��t!�g�t�� 5 ._a��AV< "! �-�4}AI��R�32�i},2�2\&'alway�1�M� ��( describ!� �V�� �� 6= % v? ,�,!�k�QLQ*% � 2})}F�?�)��r"Pbgeq"G5�=CXa ��� 2�� a �$9N�  .6f.-�6� �+�x_� ��mR�5dz� \rm{|�J T�`U>isͧ� ���!�a�1�q4�)1�%&C6-G>���ha�s$e�Q7}x�%�QB�� U��I:pm"�a 1�E6v}$-u�1�6&By��7.�3}*%I r�7! ide�� is reduce� �!\��}�m�&� ���:)=\!��rb�q&� C*&:�.�+�9�b�$1�tangenc*>:K. *G tJ'���!0. �$nlm�.U8( zjJn�fH��JH*Z ($�)f��etI@&% of6g�4}a�oZ �%is9is�!UQ�6�JA=v2� �>�3=+�6o s� "}e$ qc &9ex�Ye0a��dia $r s:� j_*}�>LX \bet��)$� ]� 6\ I�2Z�?&�ra�Jv F� �x co�ar. HY%�% fx is a`.te_!i�!�*��9k ($s9�P$,ie� �$v�Yi� ^$((A�~ ��FZ�.O2�� f<�%1�.�*�aDu@p:� !&. �5p>z.� 6BN&��}abqu�2y.1})HT>9'=> 3}% �A��n���6�a nonM��q.!69>5i � G�!�*MH(Par�q�o 3eM$n�- -)�9�A�al� � �ks. But!��A6 � + a�%�"� 0+*��}� /*�+F�h ����  ;% q����(corollary} ~tes�ae��h�%!Z�* �N(�2� limiEeself $s+1�4$9� �0}"� j_{s}$6 �M�of.�U�r m�s�  EachBQA� ceduA'�@R8iz��!��,rect measure�2Y $(&�*d2�))` obs1�)� c�'�C� H�"�)\o.#9� =� Indeed�"ADthree2;s**3}T a� a si,:m�_�!]�% s>3$��E�refore�0A} y $m� �.i)��-o&�*-B��AAnsiU��Y}�J/�+bJ�7:�2m"��(|no� ,&� ��`%D9�of x� ext'� an n���(s+1)6�.`A�E}}� H w |�'urselv�f:s(2s>kH��a�MNbe&�.�j VA�>�>��N?-� q�E}: q��EH&.� $,6���a�.� w i�c- �s.._5�̕��1be deg� (msen�+��a ��i���C&",�A/A&)a�}�� @��% m-6: $(m��3�*for ex9e,^ m=2$"?0�1 2!H&� �����!� �1�&_G{mA� obtu!".�5��clu�D� �+)A��.#��y cuA��"::=&�.v� �.�*�*)5�)�o�Z)&�!r}#.ExZ%7*k �i�"# HA���&@ 1��and ��+�*��C|.4.�-:|Z� �9)!R2 :�B E%S2rel !�2�.��G/the"�! an ellipsB�"�0�d:� 2�$2�55:9|/^% }<1A�(/g*�'�>'i}:#1�� "�*t �9�&�9.ance�� br[KF��Z�9�& aboutD ���Ł�*�'���d?�N��:�dF� AT*� AWt���,a�:J�TJ}���V�5i�Z �!�;!length�maj�;xi"�5v�T^�'$. (2��equi-!*�py2�s} � 3�*%i1�= ��;i*F+>���ing.�'9��T��[-bd~y*�'$% *`3"� a(i&3,ephav���ame tr� �0�t are ::(ݗ�,F���H%.%'r�WAS�f�5': 9! spI���J.2 \rhorradiua� rho f�S$0!e� ��&�O :�A8&abl�m.�is J/�*��*�M 2i}:�^�7)�r��.� ��  �p>8,�re��!E9� F9��F���j*V.�6Jb�-�.�=� ��*�%�aE�a�.cT@N�&Z� �- _� ^�  �J�K($%�)�q� K@]��-�&/*A;$�O))%"u�9��&4 2�D�GiGQ rh!Q N0}:^�2za�(�;s�a6typ� 2: F�=� y���P ����%� �M���@ :�{+~~e6 A �� chapter{E"�0Es���+W9Q*b:\96e developZnorHmu�:�1oryHe`. �d"$�myunGparam_G�Uw�p�: / p�F��le~Os�6��visual4.� �%co 8 va\ ٿlowerD�21: %c"�Md �� )ts be�s baseHT>$ li�T,\cite% {14}, {31 49}!O!�0Rao-Cram\'{e}a q{C {50}�H�/��-SfmonA� st4" 8lenin76}�Iww�rive �ed un Kty" sA^i`�d0quantum mechao V8 ~1�12�31}%�WAestablis:Ue b�3"2G)�U�1��s�V� atKj.BofAcE�F�2X ���.!�=X 31}1$�Q!� lass%�E�signal_d fields%�Hm5�� �A$ofYzed2��qi.%�]X�3iv24��1'! , se�;r M - 2}. Finalq*w�<v�ga�Fe struct�&�"8i� m�%�ysymp?:�I�u1y � 6)p{ $been studiK �]�29W exF�&s i�largely�7 work%bBelavkUdiss7Y�29Y�a�1'1}��� {2� V% /� In- B� ("9&�� &��W��%I $����!�:] both�� ����>�& tras Q-��:4!Gth9/b% 2X in a�m i51un8)b0 omorphism��a|W be u��to�P�Z�!�V�!Lca���K%�9&c�{C�!1�)�} � "}In S 7�#WM}a\Q�8he�9� z���or mixed6��Yn�1a �Bn$4ite or denumerG �14dard family. G�e�^�s may%�!VJ %ru�rough infi���K$ontinuous �N$\theta V2T � 8or��*�)i�J&we��K�Ab�B!equ$!�!]mo��" � �� appea�[mea�.s�"Bec_\�U� ��,� ��(2�B�Zno!!�0AG��exH9ed.�O�oscil�sa$v:�2/)�AC5�mod`It� natur#to��� �;J�CQ"� �3 ribu��"�����%4 pack3AD inctQofU$�clearly&�4;a�Ѩ� f.� ���blZ&�)�M"�8ordinat*���1�mA ;� arriD�-2 Ya.�J���I�um:D (�KI vice%sa). �7� a9�.ms*.�SHilbertB�% H}$!�LOR$\{\ps�@m�}\}�0 solv�FR6� lH�)!36�"dH,$I=\int M(dx\%��I�Borel� % X$�.OLV�map $ �}:X�arrow �Q �N�B�"� Bd+} �.S(x�_ c }�= .-A $\quad \for!� ��&< 3 1 R<��H @Z=(>�mid)I:�.a �= u�e{q�a$Xqu�Sr-�i�i!�I�PVa� �? poss�V�^cq�H�_R�EWI6] !�� ed2� �>6$�@5� q�fa4un��MC% )i!�$�Cn; unbi*� m�`m&�$>[i����Bf6b _5�a|��siz���* J�i �� ssumM�G� ;1�l�5�6�smalle�$�_ devi�9�D!:sUvI3�,o!��� �i�J�-:�Lt6�A�oD3F> lRXceL�-�he &� ����b���se%iappropriA � rentiamger�i! $kS�sak%�,�9wkI^9 �U�5�����;$% �+we EB�6.l�X ɜEA/0logarithmic d�ZIj\gamma}Y�=\y'al \ln 6-/m|j>*y84Radon-Nikodym mofVt]prime .z2�v���%OdA'���J�-����!>�(x)�5 5Bw, _<�N�?�"�7�%�"SyN��\( �EC�- �]� ��_: �_ : F 9�^PKHJ'#P, �B?�f$6'F���A�total�։ 2>� $B�Um� �)P$CN 0]�$:B|*} � 2=, ��b N:gI2=N^{U�2\�� {Re}R2�.)�)Q�&VI&��)�c]ch �/�!nin�F�poraD,-vJ$\sigm%�I�^1/:E[&+or ��R�CRTAb)a��)e/=eWD6^ �B^ Q� !�zc.h2�4FW@�b��(�1 manner�[!�Schwarz.\ea�I�� fa�G�� �7-�M �$��6�&�)VyL3 � )"��-� squh$I �e'>U6*)�.#: ]�� -k.n} .�Ir(x3 )MR�}�J� RD axTn situ�=A�R!-= ed��&: =[ � ^{i}]�71}Xl.,le a�a?(1!O �U�.$ !=[ ^{khkhn&6!d�&�)of No$Su"E q>ͫ�8 trix6J % 2E��$"�� > !=choQ^�: >a} RńDR�Ik%��:-1}D^{A7ercal *fG�Ji%w%�$D�R[ \"�Eq !���sK!s�]W � Jacob Vm)+ �1�\mapsto&�transaxM`$R=�ѫ� � ��co�\rJ;^{ik}5�=!6W�}U �)qb z% �2,[ea:,\;dx)2J�E�>� a �b�\>KS p ,\,d�  _`Y��,J%Jo� \ �(�1 J �J �aat�,�6& JFi�>iI� � IN+i FO+ak*� *r 5b OoE*� � �R��+k*�$ 9�� � fe*���X:�� :�S"cNon&� o} �!.of.>& 5}) O@s,'1 6�:�"�*dO !Rmetho�G�. by u1$:�analog�AV�� Ej Helstrom����\exr!�X� siA ͭ�q��doe :)- ��6�m:]&��(SC ��c�B&�J�� trongl�zJM�B*?E  j reg $q5-�a &oZv�� HA��N�e�g")  }�+ B(=2.� &,��BJk� easy�:�E�`�vd%��C%�|�c�x;(Rv�x})ɾ|  N$c.=,= 3*)$ Z�3F�\9x� A�"�0� is5`�3��"J@,���&���(2]�9�!S2Mr ) <\infty�L�]�� B `KYx}�$ ��(x�C,^f5)% �..� *NQb� F_q�b 5J� ��$a fix6V �M"hgg-_�in:���Z�\BUNa�( UR =NzR�vIg) , \\�=j�V��x})�� "� + x}R �% ) \�]�% \;[�R=]-�1G% �V2�8V�� ��>�x�)aQ�!U�xx�By�9yiaO�Ku� "Wowe�1�eqnarray6� &=&�[r)4=&t 1?U�aa\�6;[B7RS ]=\t�c% 2S rm{tjFD Uy�bj% .*)]Ai�rpvj2� k]4 R }-' .KMk& N& K\)] \\�aN\lyI-�1w|n[ ��\r A _{+}"�Q�u>[.�+��"K/�5�$�u�C�uB� =�E�A�Q�f 9X, I�n� �@� B~&J.�.���m2��mj� =im�V-mu.�.+�ZB>i >D=Dy�$. Ap�o�J y����EXv Vci^g.�r d.g b��9jk kY E]�FB.0m�.�*^�}�Fj��A�� �7 )}!lsough�Q&5R "\A 2 2j2m�5 �w].�\-v \x�#Ż]w/bAmFdJ>= x l*��N.�6� 9F�T�g��o�OyN�can!be*t�hhe&22F!�u�r�*� 8� v���g2�}�\;}nRRa 2�671Bb A���v�b@�% )!����.��A*7"~�2~� R"�)�}% �[% �x)2F:�!� nessh Css 8E� *�9�/met m�&(�E*��B�)��!�� <����D�Q0 $�4 9 �?V>he 14\tu. qB� rhD, �� 4}�*"F-e�:.�byMr� iU� ._=S( t 3:G9&�concep&H.Z1:��=�IE�Il��V�"X�s7���n�� A8$D9��s�De1�y�{!�l��sR�!� ��.Rti}=2(\�. .��):�J�#A�!Gc"*e� +0t��i�"�7M� $% G&!mG_� �. S��Y~1� T6�==$M*!�""ua`1��O ��:�&� A"is�*in2 �B�}�m ��Z1uoݴ5� v )��k}+Ջ�i}6R1JhH~eV�)I]!6_J� )i9E�iI!���o)�4�/�4A�*�ha%"!aN(RY ��]Gtv&)�!U#.e N ��Oderstoo/fA�n*�_ite��}!�$[R,%� )-G. )]bʼn$:�hel%ih d>�:Jj (�x )!jk9�&aEk}�bR�A�he�.52� �$)�J�$�Ny%� role��a���p�Aor lo�)�qA"�)+k}�q�,-x+d  )=>;�.(]�%".$s"@HI<�gir�e Fis�\a�e!�in�� t/Gcs�*now tur�@^/��r���notm-IRJ�$ 6+�?&�6U=\a>�,2�\$S�;�)N&�/.HE� k�<:Z��+R")*� IH ��q"B�B& A�&k=�W�j� �#U�R=R��a rA !��1a�P'tB�A�/A�*blɝ%�1oNs�G��n�N����, �%�=G=%�0FM=��z�� �% ��k����16�b "�IU|j M �$�"�.�4�!"�'\al�atojk�W $m=n���D=D62COng�F,� �?f�5� 6^�reaso�:��(t�"LG leadbuR��"��(�6S.{3�NgyA"%N%2f l *t?A�&� 6&;{g6ly��fw3H-&��+�<m��)#Q.�;�%�ܕ��s_ 22V�::y!��-,BK%`#27�:K�/ 3�^� a0C%��5>.� s� $R$� ���f!V& "���$R$.{ \O-� :I�Ns���x"�;�JAOeA�59^�-����6�]9�coincwu % \:�W titu^B��c�z'0 they!�.F�^v�. Howt"�%eva�$of complexr+HBec� 9�6oJ�f��s e�n!Z im;(ant�NQ_K=%p� %X�rh$was sugges85in�ent�by>�931}WYue�5Laxm949�9F���on,sh�.!�i�8-<.�W�Y=Il _{�%k}.EŊ  AL*$VFI�"�C\'�QB#n��>�&�= �y�W)t% BAFr.�?;r1�.N:��U% ũ�$\bar^ }$.\foot]U{\�85��r*.".>%�$F&rrS:� �A�]Z"fsM!�br �!��aa� on m�).�O F�Il�2}&|= EEH+jfI�)(�D=N�s:sJ<}0]u�%$ non-&�^-�7&r Y� thuR�S�h�&�$SV�an� 7 ^{\ast }SV@%e� ;2& :J"(a�>� yv �(Q,.��$ A�a�h�+2�Bc.H�$�dQ"( a�> �b�r.8Fa) JkndP� bF� F+ $H� H� �]<>�} %��]�>g"] 2W�1!~i F]61J�(is*�"a({��2� :�e�:v�� ite A"^d}s+- ;d}.��%����0_p|hdom�= ^ITO"@U?�^^�\a�� �AVG!� ?7 Su��a�% join2�C L��%F.h*�J� ^(:@ 1?A���:�"% �*$(GorL "�&' aaL�6ntoC` �, a���L s $x=\{x%w:��-Ai>n,?�al""n9�*dx�)h��*TA�;[#Z�]a_ !&N^��l2�+IPp `VE.l �4m32@"��(!�F�$"% *{6�E��4s $o�3�(e� �. �p& T! �7!�)�"(b"��oc�F*v&0 holds ��.["�.H"�dagger>_.N�"�"=:,� "���4 �-\pa.�&P )��8I�!d�so � e�Ee*���conjuF �. Eve�J 3al� �?at�G9 �E�=Ie%�a]R��\La .*t��� �ta:I*�4��, �i0.R6i{Re3�. O��}vn 8`�@o�Jed, say�e �b-"2Adis" ]" ^1 F�}�i�{3�G�q �f5I�*>+.�a��#27AZ=�%ՂO��='BI% c&c�Ere���<of2�F�]��nb<&f >0new*�$�eA�= _6�!�& 7�V(� �G) U ���P�a}^fz}~=��o=0m�iTFZ�NQ1�*�. *�R�<^ /!�!�9�� $���%z��J�3E?e emplov����f�$ C�RFiH}�r Ix.,r�*� 6�!�8H)��in�dI�$Q�&5BD"�I�s�/���cl���"AJ:J��)� $D-[.��!�QG��z� �1>�2MkAM�5`({s�G#� �.���Zm>�'.q � &?:50�X HOd p�. &�""27!_ � r��a�he*82�{U*ORe?G��EQ M&�s���! Cjinp1%��a7&%Jf��_of�@HMx.*Sw�ll� abHO*�O r�%�� iz �)M*�O.=&P2O!5on6�c!;�@�+� 1321kas�m�*�I, Lie algebraF:MM'M�f~�J��afv: urac�s! lCV �96g=:Bj!�proN4a�bD3a�AkX�G%�&� ��reV!L�Iquasi.� pr�e��Dc�bIC�;�schem|��!`)q31}2�HZ�L��Q�O]hvs�� adviM��M2}, r13�^c[:{C"�LFQ�!YRN&�LVI*��&h!�%y^"�playedANUZK�One�3l,.uv,bPC6v s.:S&��{4G`*�.0�� �I,�%�A�:�� I^O2 % .P orm}u�]�m`:]#ao�� 8 6N�;��FCS(*R 6< chi � � rm{e#�d xq2 }}S�X6/�4h B4 }}.�82f�H!a t6� *�yFi�w*u^&�*�e�b�l*�$G o � }�}%}1Y$�"ndC��uta�t(& *�[i1%NNhf { b�z$%�=1�n�5zX'��(�C��A�!\mO�Y.g' �%`=K(0N�B} 2~i%�2�\;�!% �:JP^{k10.:EJ�%� h3Q()6"�5� au�ghborh�$of�� �Y@��LESb:k"���+KF�� A�)��,aip��%�!�.�%[% $, +ly]l�#.2)c.! XI� �Z,�+*�]�U�.$��ingfu�&� # >HqjZ�e;h4Z1Wf. Of���Eresq�as�7+)'no*� ! ogz5�$es1|�l)� Q.V &��aft�i� &"��2�+ �!ap {Im}9�8/(2\pi )$ acquiY *> � ymea!^A���J � ��dynam�(lyb-kN�Bi/�ce1���&8Q,K ��P 0x�,um�'dis"� /M-��a�!^=!`�4:loA�o-Tz�Z`�=%Ue�e ��9$M�ll NU)*W*"z��fV 䁏}:�{-�: &�)2N IA !� unit��"lC2�Ac"X*��ZS!d��teCCY*r.IeBFpu�a=$ �a4#�*A����P�a"> f> &N�),F@3� �F[� A%��� 6�\principl%�[� pair�}#��}MI�I*��A,x !X� �� C�qL �+m� �+�P)bm�fu���gjatk�S�.Z F&is�B]$Heisenberg25*7 uz_lyw �?l such �:�� :� �5i2@1Jp1Ze5q}�a"g�*Ֆo`�$[8p}% , q}]=1/ebj2�Z�����8.��Z6;p}-2mp��3�  65X( <qNQq6>, �2Xx<P67 �7lbrack ip}1% ]:E Ac/4E�lv9�>��E�."l1 )�p>� . St�Ph�`gɲ .>&�^�&_�0*c� .�!&����o$�zarbitr� �S{yU;v.+2�<sFY21}.} D&.B�k��� th�a���s�� �a�&�!�5mN+K!�F� Ef�2|-*P ��(� }x �<\�}�7 2= i}}(3J� "0 >d)=� x (R):6� J�L�n�i6L>�J� }%#%&J#}��,:? b���`��v25Fng�F chi !'���@[�"J�]$. Mi&]ѝt�d�vAK}iZ.J<H,!5B�>(U+:k.��k}t79+(k&]>�N5=* K!�5Ne<� 6�J7#��.����:�a�O��H.�a�!e3e�.I$*F =0�K��=�7})!�ne6.p� I �9�� � &�� �*�"�!D27�Ftrsim DSe�&�6I2N-K1 &� �#in7;qVo*�Q betwXc�8I�$Sk[* ikͨ]�#!Y�N�QSZ�e�28.�-IKa�� .�2H JK-k��.�Q6�P]�0$�ia al}|})Jc$nim�$"Put��m=:"���R��gf�J�� �� �.8!' =1/4c1�j!�w=5���!�x}� *.:f yJ��� >�7(1/4)i�2�B�I%�[. va�Z�"&�7i� i,)�"@� �"@� �a�6�� Pd@mu HY$V" �# ia � )� !l�%!�!�v%1(x um�a0e94�=|�V0�4 \0�hF ��`��KbyB�1}N'icCb"�A� �^Э4>�8�}%�V4=*H[ I�. >S  � Z1b��� wise� S2 8��j�ImA}-�%b$)� e*�i�L same��iN?(.>�*�Aa��02�e��:A�b(�J���u��averagA% ��fF�.�D���g:� ��5z�Jlr�*�fD ����#��",2%}A�*Q% �A �'$!jŁd!6} �<0.+  dJ�V�aF��{�liaP9) k})].&�[2V�CeV�\ 2��O�4�J�8iL�/:6@AA!4&} 0abZq��q�}*�b�e�o �ans� group��y��*< $Sj��9}c���gQ.���v,67l&q� /16�����M$�?$H\0�nq�I\y�`��bf3tvCuJr%�Fw$\��i�\k.%,�"^�� a�; NJ)U�"?�i-*& i}=Cv ^{jyj�G� B\E"^=�Hs"�n�'�4s�BrWR�i>V �-9�4})�lR��b|h�A�I2�$z6|LE(.Q)a�rJ�B�� $L(\xi )=�C!�(IXw0-C<-1!A,n $n$-by-$n$�?� &�#:�^� �&mAi0 $kv ��!��9[ 9� � ���9}w�ad�."�-� "e2�9�10}). ���hR H�yF1��n 2 ��>� �̙C� wt� st#;*�C�M��j \J{ eq Ds�, }�nLf�N`C L=LA�� U?��U9�'�&�����, homo!oS��H��-$�E�j"�B3���V�0A��!lhU ���&t :�@O shipJpjS  1}{4}L&� *�\ 1�6�N�C1�4j�JBF�vj Ky2G� q�, �CkB��0#).� &�T~%�N`{q|��f2�2c��rg��A�Aser�'expan_�>�*} B�y %�.���m��6V*ymB<B6 �9^i.�9��JnN�l��m�mBw1if7'.% @qD:�����R� %��}���em�)&"sVi)��Q:@'*L&F2H&� ;&,� �Ce)��J � � m7�j �i8pZ\_s, �Eor glob�<��:�%�Ai2�g�o�a as &dt(\ \��ively)B&!�:e�-� *�KZ8)�*d�E\y��Nc&�J�K loo��t���P�=a.6g20?Q>6.�@�+����)�of5`�t1�I�y*4v22}y{n{5>�1�>)��$is[ �?%��&J. �MH�as�=4(�B�ze�m*,, (6y�es��s!8&1/Q+ %(�/1�D�at�O).P�,L�d( ?�BV~ ? [}Y e�*l8:�� je l�}, b�. A;� C\ wI�&�, �1A}s mj^unMI:6-� aN�r�:y(,/!�&�r.d<�*=)FT"I0sn ql!��f�!j2��B� �%>�&s zre&c%b�&C veI!if�!�QA:�B�$$N� +.�0 $�~&�<"�* *+���i�A� �_((2&�Tr}g*#) ��'�(c'{+*&$�*�m �$ �+�Ri" iFF"�n�!8"� sub.�B�'N�HS6c.+.~a/2}p�/�/��..$R�H�:[!�=N��}no`.�FPU83]2l *^l.)?2�6�^sZak2 ��2}$��5�6'�*e[�7�E�%�q�*i�G�4�42ct��V�2�ia/2�:eg%'6V&�ʩ&WN� 1G )F�*��+��&�RBK� m�"2�"m"�*�h�j\"�!�>� J|?��hf � 2D]��&i&k7 6zrA�z�56�9�A� 0=C�T"�. Qe��.� � F7G$�0���q�k}-)���Q8wl�%�3R!�& =!�-�)E�2� jAaY��<f>e*ubQ�\:2�E�Y1|6o|�d(�"se�$^&w&�t x#�?5�2� ��1xuN6�(UQ)p� ble)�n Q RK*N> $R=G��:_A %06)^Q 2��.th.^�~ re�F�.����.415o;-�2vu�%Pl1&�)=(=(Nz2k)����i& cy,}��J��s&� 9�$>% ���n!�)��/.��/,�b0Al&+7 a�7pE&�. D)�?�!�5�8,�.��� A�Is}$ (i.e.(Q��6.Q) %/"�. �9�y�7PW�@)�=atDF�b%i"i-e�Ple��E�cT�A[��\�mB�<],D=[�֩q* ���]"�}�"�:N?"Q(R�D)A��J[i�� 0��/V�l6W J>"(!�re�P�,�����)=Z�a ]-�i;Q�qbe "�Qta=a�ad Z3.Ira5?.%68�*P !=bL :���Pessa�afU�q�=�V�ED:�^�~n"�6�`iA�24 ��) *�l��chi.�1�).����$�A%g� 1��G�$M GU  #N� *. -�v. P[�!�A�qse=G�|#oat�A"RBgZ��"�c�/e_SplaDSAMUIUJ[�ive��BT:�"�> involvA%c4Qh�V. AA�h�4�F1"�w��k"���T y }Uv[2~R.2T P����"4�is}&�8�n4 ��A�o��}  Vc�aJ��P.�.]"�H)$v2A=����q�, }}� �?���2Cr, "�v.�& � #"a"_1��6�V A�Fw�R�O:?& >De!O*0&�=%�<S.(LRpJn�m*�!��k $��*2 l ��1(M)�&#jA /�R1�psK�R�.�@Gto� we n���a�"`B�f��U$} J �A�}. =0:~B�(�4����"�, a�did!�2�GV�?^�:2Q�� 1�)$��; qOu F} .\��x�?NP=� "�P� �E���&:I B�k LZ�J�u}L�@ ":F=P�&>��8JI&/eNJ2%�{ZeIA%!IFb� a\(*<^a B;F�n*�BA &@)�Y:}�dV">�2Ӥ] "ڎmFP �S�$.G��-"xB�}�f� %(�*�U�R� ��C"�Q]6�2B�'W�,Q�_} S��aT�eh�, wa_ka�^� "=J }. E�L��a� fact!�iÀFKtG3i�B�7AW*" u "�1& I 4a׎e"�e�F)�� 9A�A-)� �kPy�3B��!� �#��B&.�BQ? "�.a�u� 2�� �.Ta)�Mta*�r[�)�m<H/��q~ �L)�� ��6�*p .'i����%H.�%19}Q�^$��*� KAy  % i=\QWx�����L��9I~e7�� �H�-4X !��VU �"q)2w&6 �WiL��8�.[ I.dFB+nceBF &1qP^*S��Wbre�X�@b�?e�Z�* 6�>th �6Rot2�&!�&cT&[%o0EgR=S$ [a��R��!� =�E�����"6Hs:E�9� �j�\6�H!��0+�� occurs �6"yG��#*��lo d�A'Pi�U6�z6g:F&���}.�-M�E��� � 1ae�c .Bx���(6�2N�,���'�gr&=�� :8�� t, $�R��\i�$$!ankE�_% �.��E*.\FY�)#(%$�D�pk݈&�};[S�]g �N_���Z�5M�A�4�of a N�y/2l6B$%�1�� �.a<���e"�+��@F�`�̒�\ |k >c��2h��xGo\��[g6��.��AAd�Rbe�&cusyi6dN���U� ��*�)DiI` an EL�}'��! "�Y(�).K}�ir1c xist�١�.�9�2ws/1z�It��6���r�`ol^.�. *m�7J*ޚc�eh"ct��re�_6�ree6%d9(�F� �B-=A !^�Y%�N"w��8Nc<6��!F�O9 �  �A���&�F�)*"` ���� $�[�����Z5S ��v�"2D a � �*?, �CA�A�.� 6;dA: +(���>)9�A�%�-e�UL7,T��7�GbDL�U�A/Oi� ��a�'>0*�I,26 ( .�ái1},���5 cu��7Ke!�c.Kl61�p"�0ߕRU�:.*�"�D�2vD�.�Fr^%K>o=,]2� [ plex�m5V���F� . 5��� . �v���"�%C1 *[5k Q5  either&��}#�.n~ph,�^� a�ȁb!��#l entire"y)!�a��r#� � � �a}P0 t%��,\;.�ir[nb�6annihi�8Y��d��.�4%>xh w!S 3��7c�°\  -� &� �764�u�G���� *}% ShorW6I6��B!�F�S e�Ƙchi^- �J� J�})�Ub E�*�J��9� $\hat{a}$� have right eigenvectors $% |\alpha )\in \mathcal{H},\; �Lbb{C}^{r}$, that define the nonorthogonal decomposition of unity \begin{equa$*} I=\int �( u(|\prod_{i=1s \pi ^{-1}�4rm{d}\func{Re} 3 _{iBIm  4,\quad \hat{a}x=E. \end{e�8% It is obvious�n) the opera)Xc,x}=\varphi ( a})$)�a )�pr5^0x\textup{(\ref{3 2 19})}, where JOM(dx)=9$x%^$\delta (x-�-�)\;�-| �|%^v)�Im}% h!lFM�}$=x$!b!PLLebesgue measure on )M�nA�andA�F�)IDirac )A5A||P)}. Hence, optimal es%A��parametea3\thet�Tk}=\partial \ln \chi /bar{%!�ta}^{k}$N densa!�I0�=�})} at QJ% NLisq�fficient%Tcan be reduced to a coA4nt -Mm-6��nM* $ by% result%t  $. Iae!(,ticular caseM�$Bv%� a linear 1��$S_{0} !0Gaussian stat�i ��J� U�Q� proof} Su�� Nabove-Aula��ca��䉉$exist  of� -����"& :8� m�a�$coincides %�`$covariance)S%4b�mp��m f JBR=)�S E]eX�* . Necesv,follows fromU nary.of͉1cyA�Ti� � i� 2}, accor�����J y $SN�$ mus��v���\b�c�!l} R< =\ps: e}^{�fk}E2yA.\�Y}��% ��/� 4�]4}}, �ށ�23:� }% wP  $�"r �A[e�j:�5J�]$�.�;.~ eft( .<� !$\�*� b$,�!�>�y% !=}$�W&i�S � 6_4a� nse:N� � � .� %�}M(dy)=�y "y=\�  � >�n}�Q<$*}% Compar��" 14})T })�oncludA��9,% ]=I;!�%&xEE�a�>�*}.�=H_�S2Ii"�!�( ~���chi (|�)6�F&-N�y�Jk}6��iNL�ߥa�J 3}�complete-�1} \subJ {P��HI.Q protect�]3 Y <gK4&� $ bf{1. }We) rt)�A�(one-dimensi�� . J �Tx� e a�-Hermito qA�rc$� ��>�}�\�-MSV1�3 })]=)� V.\ �~4F~$Differenti�]�2U�� "3 xemploy���B1 15})�normal� �6-rm� % \;Z�=1�eF)V ? \;(S%.hE���s e�ob BoaN"~e.� �>�� - 1)Bv]M�.DSia�AN�6�[b[^ �]$ obey� Schwarz]�B�} |�ATr\;}�b$|^{2}\leq :}\���x�B �2<5�B)):!5F�ref� �&* !OdRminanta�$$2$-by-$2$=m W V�� �� �),\;i=0,A�� i� h% }b=B &}_{1}= W$,��nonneg�E�can writF�> F}�-�E�})|Q��6��I�%�/V �`:Q6F�T��Z,� ly, zif!�*+�"�  *"|"���� ������ $ Ucnj � *` s describk����&p $$% . But su� ,���g $x)Gx5GIuY��a� t us��6z26a8"�!?%R v� .Q any F I+$�ed as a��0ult of arbitr!'�lized^3i����by 2� �� $6� ;c�r�$� may b:' deed>e.Oten�FY(-�-x): Q�e30�(M )6� 7F�a Fs8|x�*ek|[�)� ��,2�8F�G Ipxj�9� S6��� x})$. Tak��AK�eb�exI %�both 9&� 27A�aA�forL6�U�$R�nU��7 �}=��E� 6�S\timesYtRd �p�loN�eSwe findI{F�T2)j���5�]!� |DE/H:�9b�D*� e�F� �$HR� Eh��%pro��58 !�!8�W-B  8 2. �%��i& X2 29}) occurs if, firsti�averagEK bY8 S Ese�j FF j). Actual��A� requir�ess an Z�7}). Spe��c Owe�W#ing!(b�lemmaZ ppos+ran!�Ÿ6�)Et�U�� e s �a"/\{*M V� "�WO� ���e  re spac��*H�The�e}�}�\;}% (SA{ E?everyR��[ $Am G i%�alla� �:�$ �z�$A`m-iq�� } ws�e AB��e� �h$�!�  =S^{1/2}v �� $(m |A|)\neq 0$B�� I*-�W well-know^U~��� !�& �A �f| |),)/R �is truOJ�!��(E\mid  � . ApplݭrH�Q�D%�is�6"d�ce betw�9/-E�-h��N�8��2� undeɌE('s hypothes�A�qu�A��w��TJ���fW=06g{i.e.}e��%�=�J>.�%6)Wt���a cer�regmi�aYOo ni. $���!gI�an9�of min�}9 Jistics&� $,��ma �a`peb� in$sub�j��d's�� E real�, $2] R�2�� �is �!ly "�. ��u2,m UAtoQ2Fis�I ivalO�e&. !i?tc�sE#h-$lambda}% S�!�  =D/R$���.�2��% -2 E�,is met. Exte�-Bove�'Qf�Ih2fin�apanalytic)Uyze�M"� �*�v�}=0[�� hold ��d arrive��~!��?%J�\rSZk x ��q "� ,\;C .C� F.� S SB���S=���� Its solu�� ed��! ary 9g&e�2.)=S$!C*� orm .-��?:�e � _{-_� 2& } �"�)}a�!I&"Oh.���`#�>��zis��� �DN���.�BZ� �]: �a�N� 9v2r#Jo6 �9�irnin| 66; . Foi�.�M�Qc=.ge�� also9�a�Vn1 #�� bf{3� multi. ��&�K$ca�ed U if��a�6D� �h}$��tak� e sumsP 2�qz )a� ar{\,%�6K�i?xipoM�et�'�(1,\ldots ,mBx(kkny r���0x numbers. If� �aH%nExt� ��2� �����(�z�!��ep�)�>p%A�nK ��2�G&-=�(D^{\dagger ���'!�:y*fJ{R^� .� Nk�2� &{�2��Q"kk� Yi k� (D�� 5(!R�FAvalid%���"@I�x�2 2�"��!)==�$. PutP"2M=ex!E ]�intY I,\,\)"E i^{ma deyo:r+ � Aʍ�o T ��=�a nd a =�!��*l*U�*P)%i�Q�q��-�":(���%���s&��)�%m5�~ rst.�+ �9h z&in view� `!1�i�8#�%��yield&&g. 2�5"9})r�$e�i�!�= $� w� �)XE%)� 1Z�2�E�_�1�q�zS(%�2�!���� -�(R�&D){$ (� iJ1reg*it*��.RCe �W� 9�1�y-� \7O�+LCN#t E�'k.4Wave Patterns}!��4 D�� will���~&#A�*h��'$�d ',�ic �,aasoua;(nd visual p � c-r ��+n squ�� errol&*m�-Rb?)max� �)D, T$. To avoidz ta)aKm = gral�' volv�A� discq+o-3 is d�in P+32}.)terpre4 m{^0-valued Radono� e&� B -I&Y'� blem)� be f%U� homo�x/f�) of w!�5k*m�t&�%�� p�Gt.z�R!(6�)5� qu!Wzed f� ,Y7l%�6Rintro�-5C29}V !Q�MEJ%A�o!!|�]ofA� tinu!- r�. constitut�s�� ala�1ss �a�finit67� �D(or manifold) $X$.? l�u*Aqin� � 9j"�Ti/ A �$X$ ipp0 i��2�l$.�!usd� a)-signale+�,in A`ralE�.Pa�U� $S$,�aI a!p-� mann7.n� - or� plexm  random���"�# �"� _{n�S� �Khaka given�*,it{a priori}a� tribn $P(d =�AjdevJ"�/Mge �X$[ � �� pen, �aA;t�\bl[ st" $c_{x} �* �) m, say, $*� $. On%�we,(��3l Bf*� (a)F�&1�U5�L% , (b)"� NX aρ,HilbertU����H} J (c)�iz Rmea�0�c!(JV \-\lang!M�\ole =\i�,\mu _U�36f5� )=S 6� R!��JM Fb6�?S�E!�+ed ի di]��3ATorU��-:$�� � 0)\;l�AO чM_)m%bQ� . We�^I0�,��,�M� $M^{Erm{o}�  0extremr�ԙv �] w��7toy�!WJ�um,�eio,ll�3�a���� simi�3�as#:�'2 3 1}:"}"`-�"l&"3B�}0f_{y�$ ft\{� tZQ�%�,E76�\Big|A�� } &�+�6� }% is"%2AVy�:�ifJ Ezlma}�E X A reBR!minor�$�7 $\L� 2ay%�$� ��>�} ($-RD)6�a�=� \for�X*(3 2F!�z�e�a� ce\# �, o��rm{% �(R��+1�R#,1ɉ� <\inftya�%"&�uIE�e d�m6JQ\sup_{|}\{29:� |!� %�,�"X:t3F`A=f * [*�9!��7re�2^ *d 9}NM &~:\�  06$a: J?E$^). �u�Q�g �1o�1T�Tor� �� ���&d=a 5� see ��`*c"E�SQ�s ������ to*;��m $�_#� |\;Q�d&�x"�� �3/$�2� �  el� p �����i�>Q�!M���e >� �b& � 65�5d&* �1e,ceP�{��$\}$ satisf�� � tj%5�NWa�Q=I .�J�,�a&�5�S.`Q�h}i�=u�)7�:W)5"�J:B�**,:,� contr@2tj"� 9 �cri�*!�2-�A) ��.�Acommu�%vBse���,^{\prime }}=. }}Ak� �*�;Z%)�"A�4f n�act � �9�EunotAy�ed�7�of�"�3 ^#�(� da�@i�5\e ed|/Ga})gle un)!�� 94 i�w bb{Ra1�IO�?ratic� ty��:>B*} C_.� =(x-0m R�@  a�K ��N`!�� o?+ bV� 6�*�}Mof:m5�pre�M)�<reeyZ�!>}�(k) � ��7V�!kJ- ,2, .�JG, �X {narray*m� &=&x� $R^{(0)}-2x 1)}+(2)} \\ &=&(U-x)R^��( 0 ) }9- 2H 0)}x"� �&�5� ��:0�}�ue�}�'xk�0)2,=2�1^@ �23 3 7�W}%��7.�"7}N3 *]CsystemAg�;�2�CU ���-t��IO �="+!U7 w,�B�=y2h)S�  x�<9�)SA��՗s:�K )��ii�.� Ru6�!�0).:6F �Iq>*y5�?=0R.us�(.3ϙӝI�(�"�� �Y�A&�A� !ѕ1�$-��HAl). :+!�=# L�d#$,?ds���6$�Ar�( f& � ,%�a�3t ri&V,>�V sigmg 2}��"/'!�2)B�F�%�_�  A* exa ��/Ao& =�m-it8of�!nt of �� shaptCcei� D(!�6�mod�*� eG:jiJ7;�|i�|\ �. |#n}�i>%� { -\frac{ 2 !�,}�>n}�1\} ��G"wd�&R?{&�G6Rj!/ ϥ�!5�ID$�(al � 7&cC^{1_We 6�S"|$L#a9nO5�J�p"�=(2!%gs�-d*�?1U�/2 $\.0�����sɯ��u>�'%�l/ � ^�.~ =H. I�Hte easya�^ ,PT ula� �@ > go on�.��/� a8!`L  deci�9�J �( xM�1+} +�n}+!^Q �) S:8% �:+I�/(_)v% 6xSJHG$QiI�"�JN�"�J.�e-Rea8i�FyKu1��H quotedbl!Q coF5te2�%\ 7 harm�$ oscill�%rz ���$���%JS ��L.~�( (1h1�)-p1Ɂ��- exp 4��(5-g 5�S}M< 0.�J 2 t u2�,��BpL \,5)q%�5��y.�i��>�C�*� �I2��� =�0)��6�J��u�s��Rf�eY&YS$Q�1X $q$ q �:�F"9*} x=1�q/Ba�J s"a"�mK2DJ�.Fr2�V}B�� ub�Mi:8'�*� P�� � $(n>1)$�/&�"&��.& J�:�\sum_{j+On}(x_{j"�! E�F�!�C &� &�*K �is���G��J�K\��� { �\�"be&� % % �A�FJ�R�j�"\�3v��t���%�M:$ j9(}�ekr:FJ�e each2L ($%�8G=$),>#]is m�,� �4oxC ec��.iH�$1�,Vood�e1"� !��j}"fj?� �dir@@:xnon �? .�9�i%�(see S� �*Q:Hs�5Howk4QT2�#�3t"8il458l,i>+JiN�$is ideal. �"�  l� :d"�NU, ($X�+� }'1%����+b*#e�;a*� two.�7R�:�:�:=��Re}*1e�+ ��>B�% A%ct2���b�"�UT�5IT5 �OUR"�"11}� ;&� R *�A�ٴP#P l}$;�� &��0�0I :��>� �abi��>�}.� As.L {-| �8 / "\�L �Q � 25\� 9 . .IJv:��$&? �>�!�Y*D>�yA��G#&� &� %�� I%  J��3iP ase,!��&dar�+� Y2�  easily� B�o {/; -�"�� s}+1}A+)�) >{ � E B*� 76� )v FJ ZN  $r ��d)� $AP� atR�=% -&N )B� +1}S�?@�=c� A�a( 1y T� K5#x0)Jw��$ �$ =(1+�q�)�OU&:s,�$cq�/ =9�+� t coe�vU��b8*�;*�3��4})���*��E��{,���sR�� �Q.V�&=IJAJ�!��a��  $AQ�)'Y&�  q-}?�.? !mmetF�} �,�/-cuO)S(x-cA:�y�* *|IW x)=06,10:� }% T�:� � � F8%z&u-՜��A� I A$A�6j*�D!lan ��sm9R��nnihil~"v �;w� � -�$ :� "X J�x6�u|+y� WF� �P&� 5Jc.� �?J2T; i0 3 !oE�K-12&fW�"!k��Q--�*�9ch�)l�4a ��}}-gLS��$�:�%,�"-=$ (�ői4: Q1a)�5�d �- #.XerG 7; ��lb�E&6� 2��p eff� v�EisRthankCinaBaR�I�N����[� �of� �)B�3P.&5 2^�Zby�) s� �fif+r�"�j4a�EhtJ odyn�z�-�N0Sw �-Let�*3N se"�>eJcer&v7Fp,5.t $\�2R}_{x.}$�&� !��W+f�.E{� "�sG 0=\bigoplus_{n6 ^{(n)=��f�*� .>� �" D%� G-*6�I�� *s $M$�'($X(M(\cdot ��;��M(z� x)=I)"�A6 �:,$6�M �.;�F*w%�E�)strategyi��!KJAX5tn� r ��<.e.�%!{.� 0l<� 4�'I @,3daZ�Wn.s$ .�&< y $nZ\�*A>��( @"L# �(�E`Z#� \]N � "�(zd X2� 11F}��2ume��  3).�� l ��%"� trace �"�n"N)��t�n&�M (�$%�! �V$$Q��"�%�%cEz>]; ��!�=@=�J�:*6 117 ��arably�+ple? a �g �7���A��#&�$��M�$\{�� !YTk_a >2AsBcF)C"�@cB(L% $s� :g2.Bw~ ZE�sdexE��$be dro2^yU�N x.�$4a�M "�y �sU F�F-.ga$V,ir algebraic��} J8R;5-I$GW��"9&0%vDE�H\2L�+ *='1J�/%�a�}$D%J�i�`� �-< .��&/ }.% F�3) }IfOR~�$ doe+b"hec&�Z su6�\overaH{<. ��c4i= m�mat��U�cy) y\noti�X�2.% t5cA @v�M�9Y% ��i� �kF'�^,:� �4!�=%�"M1J�a�}on{_ �90Group Symmetr�[E�$.J 13})A�A��%F Eqn.:9 &�Ud& \Aof ea��2&�*3@3 wJ�&G k $rv.;=1!�wh�Q=1 �/�9 has  �<"14}�L G�b� Z�roow���*A[5�5��y}]�[0 diag] m sh�Iog!�!��� g�t2�% 1\< 1Ew�>of 'p (�9cyclicT � s-� H=F� � Xw a .>��*�a t$G�nis, ac�=n��K � iver��& $U(gJg� F�f�I"8 �fjՙg� �%:�,\,��s is sai1beD-.�i=$G$-inva=dt)>!�.+set�=)w$Gi��R_{gx�UQ$(g)4 5fG-f� �*or lo3Sc�&�R�g�% A*2� )�nRF �mh6��9�3I}\Z )9=�! :�Ae I}:eBM7_%e�t 3)} I :�q�6��topolog�ly irY ible}�*(��Npl�!9B � ��\F�!�:1?=+ I�Yd�Z5ہ}{�op& }eS"�o��{\pi }�� NR�A�5� E:`pit�2H�3zG $�:h�*u}=�AxlCR&�>� pi}�Y�+�N��6 fac��B madeU toa�ty@`*�ly re�" ing}��-.��F pWucu�@Q �.}a_+"?$% �8on on} �)"� � )�a"�$ earlM"�$24}. IfBu(an Abelian ��E��A trivvB -�9�est.} Fh 4)} [$U_{\omega � ' � \O$,$ AZN�nojZi�V}):ms :aM�A)akH}���}%� ���Planc�"�IW/7q�٨5?-�zSZB�T � 4_iC.��5W �&�% �.� &�c\mu"�%�#RyZ-n{)���.a�2�; N.^.h:MJu9�MB[�rrAQ6_.g��� Foura "�_A�Ao��.v�%���f�o�D2R��aWR*" Yq"*��Hc�aRET%'$-�� F�Ub� s��.gg)�L(}k� ,] E�>Xk iJK�up{),}��2��}6})} �4/^����M�d)' F�a��^A�u`-Z� t2�:+B;�o�r�!��� 1G�>6�m,.�6nd =n7})�8LSD&c�s:}B�mu*; _V �2�ety�Lq%/*% )��F�+��q�/�|:s }�\9�Bij�J� 1c�,�H��5}�"a86��"�"��p�} @/w2�4�/�|� py rankb�}s;��9\ }y�"?#l3 �\X:}F�up{�610�85-iUU}N� 5,p'A&�.��6i.� ���� >�"? �1ity�}.�D)1W Mu� P2�O@ +����eL�U }\o�g��/�!^nd Eq-��&���%�^3 a�}��zZa�&��S�Je/c�}" a=��& [�6[��NR.aE ^R=0Jrw8 �9.e.�<^��y } !uhO1�=[E�B��V�.zV))]�?In*� �"{..?�!*2�&.� �\!�O��*� k �/ s��F�'ch�spo���&$ ab-Y�}$;�"alRN���!FC)2JE �;F9�ZEwB�ZQ~Q$):MB!T�%muI�� ,� .�-]M%M�� <"� .�ficM !Sa:�E~In���hPhase���u/ �&}�VgZ���{� s(U !6<P�'$G6"G of'�.+2x}=�� F'��.to su�A�I 9@&��2� 1})-6��e�"a�tp=!�n n*D7e_wF]#Ł2/H} i<$n $-th tensor p�O� FU!3N�L� � 4% .� *4recogGv!�udi�!1tH����cn>��#&�J�����%=��.�R:1$Q�z2�= .P = �(>!���v���:'2r s(gnx ir�G &�?^srV�e\�Jk �(gk}�Nc&ke CI7� `5��.��}k�%��{��82�>�:Ip0ga�$�>�Um(����+ $L$N$)x�"":zhine� rL.�=L�*�?A�$Z=,+ls��7e.�>q@*�:�$% ]�a(06� ��)B�%&�m�"�l-F"��_{q� &XjtR-}5�XL5e��ex���K&B � s:~0o� of s@(al�&*�H�g*�2�>sX�%BO�:�9�per?Mon< *��� (� ic��(r<_th�'su� s), *0t�  lapulsedU�U��^ek eque+��Xp�Fd( � (�e $Z$ �),b�; dujCifa�g  / packet� e�]pny�), separ�orVimo�/a�$$"Ef�nt]VoJs (��mƒ!�uch�Js)i$r @gre�a free�Z�+$Z%x���=\N$hoton pola"J���ron sp�!a$SU(2)-@),6H(lex2�MYe��jl�� �f$r$*�Gthe�|.�G}r)$I]FE!*�likg0Hm ^X \chapter{Afterword} =@%�t�^raphy�0�"�u -�^2v� y, emerg&S70'f+c�!n-r% �q��Cm.3��0�a ng�y�2uC�or9� new�_ . ��keywI� !,6�dea7�� � dynamic�" yzer�)�Q ng b|p ]�9,ure or mixed�.%]�@%g�s�{thoroughu-tudied � . Li�h-IA��1"�0ag �`annrQtackl&�3metho�f*�42s��oz>iz&��ern�ow!L se da�should2"��+!Pphy5AV[��m"5. way.&IexOnR=DY j�!�ory}"M 3}--�#22}a�'[e r@��� , raa���l �% a2�DZ�M] natuFY�]�A. !n.|!�o�B5�e�( s buN�so=�Am�se�%�� acou!�(c develo�`1�t  �N-MZ%l2du1���%N��d��d�a� us, 64( ��q��pin5$)ja��5>&�b,�^toA���ly<}fu��I9[�� \way ��sm^B s\jriO�a%����ySt a%U!6a��3ug!*q!�A';ed �^�s,�� they2)!� )7vi�Z cliou1% �.�K�!$( show!�2l**at �ɾ = =b I�Os���a�g,�q*L} ,Heisenberg u�6a t�� sbb�Za6Bہa��%5MSN.�c7O ledg�}�sIQau�p (VPB) a)s EEC�or䥓� ATESITa+f8 IST-2000-29681�,-�Ac~!�#}n�7% retyp�ztypese�kţ book�TeX�"0biblio�}{9�A`bibitem{45} S.A. AkhmanovZ4 A.S. Chirkin,Շe8�� Phen� a in Non2,ar '0cs} (Moscow, ` Univ. Press, 1971) (in R�gan�0 � 7} P�Bak�� nd S�Shehurov��4e!In� e` TǏmi!�,} �`bf{4}, No.1, 77--82 (19682z817} V.P. Belavk�id B�Grishan.  V8 , 3, 103--109�726�9:��Ra�(Engin. Elekt . P�#s} )bf{% 17 m012, 2028--203�:o20�oFo32o8J� dissBqCandi 's Di3%� [Y ]QH A�eENerIr(1B�1:dE���=\9)Y3!X9--215�32��FGR.L. S�9onovich-�it2� n�1MF09, 1349--1354N�6:lU�C9\olm:�] },;�s}, 47--6I;46�R,(A.G. VancjatV� F�1-`7�97--1401�:}8����!�41--257k52�5bjV�R�20I86, 11�118I:6m2f�in: Re�V��6th USSR!�__on Co2 G6���� fer}, Vol�6},��D-Tomsk, 1975) pp 1��8b�4bStochaN s}�x�,Im�t %�Hit{Teoret. Mat. Fiz!` ., Plenum�G*�$2A%22�&6viln7f�!]�7F� on ����-Viln: 1978%2Af�33b��?�No.5, 34A�60 A�6s3f`!OMN?: Techni�} (Q7� 9th IFIP6^>X, Warsaw, September 4-8e�$9), Part I�38eds. K. Iracki, $Malanowski�]LS. Walukiewicz }% (BE6$, Springer� 80%~1�n1492�4bs��a�No�@4!u1453 (1z.n$2} N. Bohr�Nzw�nscha�&= 1�$2R257��828); J. von Neu�KM� sc[ rundlagenq� Q�q enmeEik}1+:2+36 037} H.J. Caul- (ed.)t Hand� of%��H�,�D} (New York, Acade�&� 9) p. 230.&036} J.D. Gabo=*I{Reg��. S��Londo, MQ B, �'6�l44��512�43} R�GlaubA)5it{ . Rev.*� 13�L252 539!�6:� 3}b� ]MeerVI �o $4, 572--57"6o16>oej� �E:�~]3� :{�QB`�P{T\A�[�]�title"� N#o,c)�ru�&Nsco"rD*UA�� {Andrew S� farb�/mail{Ds@unm.edu} \affili�{D�'t�� ic Anomy,.�of tMexico, Albuquerque, NM 87131}! �$Poul S. Je�:} ��S�\ces Ce>q8Arizona, Tucson 85721=8Ivan H. Deutsch:m��V� \�{\toda"J�absAt}�ulA�&roced�sor*!V�bas�!�ak. ]!�an")� . By�#�fA?$rolled evo+�#Y�!>��e �.�aI}'+ma�R o�D� �d*]"(. A Bayes��fiڅH�/ u��?p!: �-e"een ����wvgjE��!rd� is �F{e7 stan�ah*dig�R5k*�(5aE�g, ��ixve�q�� �q�*�!s*. �[c-ach�i� ��_> b�Z n-de_4 real-�+,'��!.{ab��.�#W]=� &�'&�� aZ9JopG %Bdoڑo%�tL"A<�# feed*Q,.  Y�є,cs{03.65.Wj, Ta (Yz,32.80.Qka�m�O��G#AD*�+mp al �+CA�A�w&��). eIs � task43��s crypt�"%f�+�zo6�Nielsen�# < Ex-!�al�*n-�y,a5&)�iAhus ��e=t՛rifH*�T�_,�lc$e� cDe^ s du�' nois8Bdegac�ntoP,��i/ fide�B �)o��lh$t� s u%-]�. Moreh$,Yy ``s\]� '' -��$ im֜!!�pr/qme!�ogV�yon�/u{QW limi�cc��Geremia0�u�%�i�fof4C�| �tS%(closed-loopY�A �6a*C�Wadd$.�f�Q�)a��ide .ii�|orB0UC�+s,"�&th�n>i�j�+�( "W' chao�?Lk�Ws�mEwE;e� ��,]��' umera��D���broad9.gE`"L+m\, i� �lix�Xs-:A% hey9!� molecu()Wdunn9l�0 Dleibfried96}, atomL$kurtsiefe9spi HE(chuang98, K!�0��en�'d pw/airPwhite99e�&>�leQ� 2�a�6��a A'6�:L��5����ak>0a !�l"�)b !v �A\�G�M Yar�1�0�3�s�C�KdQ�n sp,at �Qm�n�g�SanX,��r�*lA7�.edQ�al� f6�s%%.��� ��%7�=���[��as"��u�RiI��]�5t�t%�O- efor�R�, oft�;�xlarge M�7*ŵper��nA4�3pS1a�q��. OuAAak������*a*!c�� le advantl�in situm�%qlend � msel"�&�-to wof)g�Q8ASlg.zw#e� ine"�gbecauro.N���b"�d �IbI��%��2.z3�!=9iAex� e�8d`!�+4iA� ѭ� A�A@Fds��-lto�/ j��enough!!� �t:��dP-�rixsomP ��d�:� �K5MŐ i|dis0�� i�kr <�� n imagine�v�92G�ZI�V�%o�3! on�{ledge͂\ntJ��GE��0A}mJKv*U$J�"!�F9�15 IH5E�' _-cc�wg�"Y �lh.�D;� ��Molmer�ak�� isɰl� ic{eL�'�. �"� wa���e� tool.�."�0�� nucl�,magne�6reson%���>�ўB2�5�r�,p�1 dilute��ic vap� �Smith��10R�  M !��o](�"���$s regardleG�Aamoune{� al-� To���@7� : oA��Is�MeS=q s $\{ 5b i) }�e��]{�2 <outcoW�$ $m_j^{(i)�= $\v,2,\l�, ��ext{max}]�,Nis *�V``ݿ�� ��" if Zl5 � $\rho_0$ %2R�7�t�#�p� \}$ $!a= խ\in�M��gm�p.� ourA��R6z� �Iig�q� �α�!|�N =  0^{F@ N!X� al a��YF[fi��0n fash� � monitoa��h�m at�I�'@v �"��s�{O)=nI�7 D� <ceƈliӋŃ.mA�rQN�0!6| �� p�3m}C�E:M&�3X} M(t)= N \E{O}_t + \D��: E} i�$ .$!?� um�1c�.�P��#�$t"�N_@a �sw� ��s5<���s $\sj�0^2 = 1/\kappa�t@a.�+ength $ ,$%�A�cQ�� � �tM�p��Da6Wq<c;c�Z=� $N5! leadl B"�P%5 = many-bodym�AzaG�*�4I4 !yu�5�TWrr 479[ $Kuzmich00,gSc ,� infl=A�e��� fu�c.� greatlL mp��׬v8A�� �)h��is�j �A����@h �+ Es�QpDe:+�is s"N�5 majoL5� �a#e*C �of.o5`1x ��lread���"� MZi���toN ch�z>�ӧme.�9 t9rict��v�EFbSP.* 6,M� ed �,#22I�Tks< c����ai� nsic�2t6(pr�5�.e�)!A9]�& , $u�T >�x�O^2$, �>2)�MsE9i��$ificant. .�l�F$sB� @�commo*� � f courf.^F.[j�o-��:io � stŕavail� %�!�� ~ �� n.`IW�Qn��A�. s $N>>1$" -QK=0associ�\� * iMT� r^�edVa l mom� U���neglig�9Aurb���y � ��.c he go�?E��.^histo�> Eq.\�EE2�)1��E.8 As�wis_8isa�cL �!o.� �s, QHE�ven v�!h&n9 pic���ex��J�:=�{O(�Y�0 } = A}{ �� �9��������W�� i(�-tqZ^į``f <s" �Caves)W�EaA�grain�H_�or��pon;��m��¥~ $�{O_i} =�V$t_t^{t+dt} � � dt/A�>�aAI0TJ �� -ser� M_iU E� $M_i![�@��1] + ' WgL!iC��.m5(ARC� u Uk��ce��% O � nd� $WB�=��!� zero�a�b !ncu�A �Wrecas >3�k��P�s"i4 �:*l* !u��e�!E�$��or�(b��H.NA.-���N .� .�oX O_iR m����� ��� ټanE9w�.�5�, > �1� _map=�2�o� "�("�p).)}?�Zbest ��ev�G�,C�E�y= it% ��Э]a%;���xM�0of HamiltoniajR\{He. a��i���n%��Ed)u$dE�!S"�Ww � ;s})Gb ���''. GvZ<&b w�hav�tݥ*� �,d����2r . �#!_W��I rms, �qv.�UM fb0���i�tD��� &�aY��(t)��q{O}& p S}_tl�e-]W � \H" b{T}�68![�3$0^{t} dt' ��:L}_{t'}�!]$ �5&�TLr����� Q�� 4|$1a�i�!,1 qo�ru7!Q�]"w�3n�iQ�scaI��t�a� u �t$�y� "Ey��omicH KRt� �(�|���t;_t��!L[)Qt+�!� e^{i9�!$M���8%�zR1� 6� calc%dy�Q�™a&��siz� d < 100$�A >��Gs �E��=��h�t� �d�:p$  $\� >� P( Q| &) = A P( | )��>:�} HA�z�� ��>S��t�Kpo�0io�GW  �$�)$_ �B� *� v�EVfaw��%!aSid��Fk (ie._ �� o=�ve). �);1Uo"�j ��, Iс�"�.�U %�eNLe"0aThe9jx; | !%� � {I"wel7Dm&�� **"5._��j2���)&�W,B@�SE:%nIP64 ��pto 捑�-� m�!�� R ket ��.N!�}i2� �QR�V�=g&���=<, d�Q�z=_0[X S �er,�"�Jj�|A] �Vum?H liho:É�3�5.�,�  b�\� AnH!D����*�~r��W r� v} �R�+`)V)M!�um� %�� ��_�7�q �()9vK� w�R CV .I#.��x��F��&�$c"C��> ruleX us��z.qOS�s b�!�%_, fulleF"�a�"�2�higher �OO&E� � �Q�#u"�3ly&�&�#J@� abi!B�9opyf� !} S =a�>p=� Aj l<�_jb!$5 A�.�Y�B�,wd� �\"vN28E��(of6��)$�^g���kax2Q����!^$\sqrt{�y�:�-lp ���� �^t *�uf ����-Q E:�R4 #r�'-�� u�t#s*�AwJ�I�al�J"i  iF� �����nB�A�"s�]�� ���) ne<�)�%ps&b}$<�o�"��R cY � (�| rols[5G1�!n-�"0,�����_"�u�@� L �JEXa�B as ������� fit,>�v}v B� � "~vЎi�G��By��d-� $����La>6� Z+ )��` cs��e!Hcb A�e:�17Q i�`�:s 58���0d!*!�ng� pseudo--��Q�n�0 = I/dJ � h�� �$l @� ��EcFQs-��5!Z$'st+Y+�t2LI  xQ��G Vand�8 he96w%A�+�Dv�i| �.ge�*rea. a\ m� simp�1�!(&�LaAg��>J2�toC� 2�kA�.1_l/posx*Hs"BO�Qd!~ ��&�"!�U "�-�b�f!e�Z�rw.A�d.�'1��\%��at���$u�PA�c}g>u�f6�a: 9��ang�l�u TG��Ualkali� Tn� � s�Y$F=3$)$F=4$�Uer�y" v��+6S_�e$\Wn1p ^{133})�Cs0�@ x5!.�g�#�!j���tE4$(2F+1)^2 - 1$"G-$48i�$80� mponent@!���\@� cloumces�G�(" i*�'��s��� A� coupc/f�m?:�lyO"�(robAAam tuZ Z9!9D1 (5> \to P-J)!{D2 F3/2}$)��" �". 2�N�8m�Zpi^-s���m� ��*$Faraday rom-�+b�R&#Y�bK+��"�# W2!-)� �^2zU;a�4!T$O = F_z"Shot �e)_�#��* s rd-t� flu��AMs� k~.� cC-�*7 g7uZ�'*�"Q)*��s( �$a�$�{�mto ��pd( queeA=C+N��/*G$ sub-s9'm %o�-yM,"2,.B �].�"�e �*AAUte���, E� {\emt> al.}��tj+ly*w"!�LarmorAV eces��!_��"lter� �ic �, �� e��&Y(�!�apnu�v�"�/ a no�R,q�}*�-0�` Wh�isDmEQS �Es window�&\0non�?l� 2��a�W4�� 8 la0 �'}�"Nin{ n�!� ��*� �input>g.(!�&v2 abov��1Lys�Y" ACF>rk shift�!I off-&�' exci:oD1�t�S%()���hro7O�(m�L��yѻ spliPU. O^%z���y!�'unavoid-&�'.� �1�.sc�@�'}Be�.��d"�a� +2^.)M�Ana#z:Y�� � br-"p2 erazV.o �02H f [ "�-, fav)�-6s Jt �ToQ�I� �3� �&�6��eX   }�>m55>�{�&n $x$-�:�l�J, oc.T=zb2q�&U�} H(t�g_F�_B L(�bf{B}"+�w5)�l� bf{F��Pta \hbar \gamma F_x^2>bw��kJ aÍ9 �A�)�$ rY�_y���nI-e�AgmL2��h�� peri .�H9��b� f�w�/u��y#�"� ��&!�7[a$gYo"�" '� u��4�~��R !Ak�s�`mt*��:�i!Z�m��d pumpe��:��f� expl�0tw-%<s: j)�  �%D2��A�W mB\�6cJbM L�=0.81��u rhalfwa�%= wo]W�sT7.67$)tH�)h�"teڱ*"�9s��e]�� �Fcf &8W��$F>1/>%��in*� .��L $R �-&��," J:�4 Lma���i$�LG*[�  ]Sfrac{i}{e�} [a�,!]�I�}{2iD�D}G],�5$�s�qrt)+oQ)m�%��G^s %�ll� 2Y adiaH=e�md�� Cohen1992���^��$a\��]Wkqe�� db)�!O�BYT��,�siv�� I6��w choi2!:E,F�� � �$!��)M/*� �Y&e+j&�-d empibCx O'!q�.S*�(�"(� weUaM erizD!FV�$SNR = MD//� QEZ.�$max_{Ao�br�; {F_zc$wr z&?"�) �a�in.�j--�%]�]�o��d�)a&�2��.GaA��=2%�$60$ Hz��� ��X "�h-�"�h� Qd2�$is $T = 4$!2"c*Y&��9(4���I{�a�� �eF ��< $��-0^3EPA�Fi+$we�[J~�a� p�t? by {�n&��� a fe��&+'+� step� "�Efi+Fg�' box{.5}{\Y:�"psF{fu� .eps}-cap�v�B-�"cat"!�t)$s@��2,Eh%���L>Bk� �@%:D1�c�! �a�wG e"�*, ���&fuڷ �.�i/-to- �|.A�g0q% A)� �*� � 2�>� �h�:ru 7,d9?X A�da���  aܹOFK�95' r�3\- .�c v��b�st SNR%330mSin�% J�z:6E(�3  ?-䭏� W<?m~��pof o�^�a� ble $1\%$�J A ]�� ��s#:� 85$. F:D1}AEndU��e al�A !,��4 !of. !�c��an222M %E su-be 3�asa�N� s�hf!w�k �)�g@9 �%E��s*��!O=!nAn!��Y���R})$ (�, +yE"[)�B�)x� s $C/����" �/u 8!>" �H�5I(w i�9cAruGy ��� Q< at ���*�)&ina)�)api�8�Yg �Hs. y( :�x�' �ͫll5��-^�VX[)%� s�o/2ly,of�  1!�!�6@ E�r �� �:~�t/ 6X1�sub�f! ��on!A� >��H$�h�*A( $x-y$ planZ/=%� $|EdE| = B�&r-�>�k$\�{_B�LB/h�.5$ kHzuF*[3�' �ifn')�A,= $n=5o%*-���d smootXmZ t. �zm!( slow�A�a���=�p&����� �! ��epe+i!rImi��i aint�!��C�  landsc���5 l-�I�a,�� QN>f,l+ sear�F"�^-JWead�=5a"^+�lobal >,ere we itera�@tively optimize one of the $n = 50$ independent angles, holding *�others fixed. This process is repeated until all d N� are globally stationary, within some tolerance, assuming� ~Dheld F� dure�sub�C! ! )�ground) u� D1 transiA (Fig2 ) appearxbeEjQ�\reachj curran>�weaker!nbcas!=����protec��Ѽ�;���ich��ow i4ly!�plete-�� D!5�%� . F!�lowese�AI �� w�� e: 1A$ (blue), 2,s (green), 3 red), 4 cya5 $magenta), as6 EY8(yellow).\label��2}} \endU We hav!� esen��a new!�toc�Y or qnbas)桋inuous6�ofA��$N$ me!�s�dem�?�Oour~c throug� ^�R�nJ$ vi�8lar��, spectroscop; a ga( co�atoms��B�techniqu��nondeL v}�Hits classical estimIA� ory,�vid��aar��pointE�aSideYRma�coAox�licR� 1�!o��tasks suA�s5�feedback�E�fut\ work�� plan�� improve !xs 18p � Arobustn) n}-"�2�A� exam� g.  searchU�� x6|Va� berghe96a�a�@ tools developed �Ksh���ideE�avenues �eal-tΈ�1G6�atm�us!�ta�dynam%� gene9�non9�fea!fs,5� a�ngl�Egik of� 0ticular inter�"or mesE�N��.Oe�,- ph/0401107 F.�sF ey93} D.~T.~E�ey~L {\bf70}, 1244 (1996dunn95.a(T.~J.~Dunn,A (A.~Walmsley �$S.~Mukamel2� )�v! 884 t52�(leibfried96y D.~L~�a7}, 4281 �62c(kurtsiefe97c C.~Kr,� Pfau �4J.~Mlynek, N��e 386AN150�72fce!98c 6=N.A�shenfeDAXM�g c, M� ]�� 8!� 3408x8) ]�0Klose01} G.~ , GM4, P.~S.~Jessen2�)�U��472i%12�white996� A.~G.~W��$ 83}, 3103)�92dMolmere�K.~M{\o})� L.~Ba~d�i.i-2158 a�4). ��e03)A5S�ϭ� b6'$ J. Opt. B9!5�23e�664Kuzmich00} A!�,�M��l d0N.~P.~Bigelow2�m*�M8l 1594m0�� Caves99} A�M.~�c Supercon�K12}, 7�Q19:r: L.~.E�0S. Boyd, SIAM�_iew\38a 49E�6r)x�UG�O 9it{�� \prl ��A1636025� -�=�8Cohen1992} C.~$-Tannoudji! (~Dupont-Roc�G. Gryi , �8Atom-Pho��I�a�s}, (Wi��$New York, mA� .�B� A. 62�E�6�  036207A�al� � >�  docu�}�  �\� [twot ]{� xcle} \usepackage{amsthm,amssymbX,eV4ph,epsfig,sets�lx\renewcommand{\thefootnote}{\fnHol{ } %_ ic  \.G$gen}[1]{\lC  #1 \r �j6,abs , vert* }:&ket:&P :,!�gers}{� bb{Z}} %�0theorem{propoE}{P N% r � H ~ fi�.I Q}{T Z}2.g[ +]2p2/ defi�on.D2- corollary,C2+lemma'L)5�proof%eřP0.} #1. $\Box$"v Q�B$setlength{��@height}{8.0truein!QT %FOR 2ND PAGE ONWARDSA�L\thispagestyle{emptyabc�r}a�b:$}\vE�8{0mm} {\LARGE Effici�� AlgorithmJ !�@2@.?$Hidden Subyp� blemT(Semi-direct(duct GroupsQ5Q\ � lineargeQPrD %put authors' nam��addK ,�I@Yoshifumi Inui \fm�x{E-mail: psi@is.s.u-tokyo.ac.jpl)\1mmT.PFran{\c c}ois Le GallF]@legall@qci.jst.go[} -�*{0.125M6,� size\it D�t�u� er� ,SU&r of T�A�ase!� skip=10ptviX7-3-1 Hongo, Bunkyo-ku, O< 113-0033, Japan2�04��and�8(ERATO-SORSTU�) } X.� A� ject, JST�% � Buil�, 5-28-3 � 2�29�.21Q %% �t�s{firstba�}{s�d. thir.BIQr�onon�F, j� keep� T� M�x IQhe fo��K .�._ }{11pt}%  ��quo)���o�nt�UAb �.}\hbox�0.5\par %�F % � >f  I5is pap� w�n3�e h��s��pr��(HSP)���maRs��pr��� s�(-�`_{p^r}\r�s�w _q$,x$p$%p$q$ pp. We -�� a xif8�these t in f��es�� we Xbe}lynomi8� um a� solv!��HSP �alllof%���es:% � �m�r p$�A�!isv odd1Our��s i!��st�l[&��T-N4ed as a black-Al ��not ne? arily u/ encoa�. Fin+ ,!\ exte�AX�%� i%�|9e Rf!s�s.1^m^@p$.9 .S �f' *{��} %) USE THIS MEASUREMENT WHEN THERE ISa�T%) A SECTION HEADING %P-0.5p�qÂ����. Me�f� %=�a�\se� {Ii����M�Rw!� �uu AlmA�qMqKUs{� ed so fa��at�l#an� onen�!speed-uM�� to%ebzn ��lcan� seena inst���!�H�B� ��� ��to find�E$H$�Yi�l�  $G$. ��pI 3x7$ger factor�� i%�"�r�logNhm#�Pw� Shor has m� ed p~�ishor}���iodic���2r imons�w� y�B� '!s5}, C$B���#c-m4��>�$G$��(Abelian. Mq�ll� �\-���hA� anyZ��oI` �kitaev},!as �maQ�%�Fouri�o�"( ` � \ s. H�no��ue�is oOA �5! non- N. <-9 hRZ��amount>ore "� 1>9<so ��!. when�i e metric s (�E�B�V permKs-q gi�!�" ���OFR.V� ( isomorphis}$a�#)�q]�i9no >)JA�B.�R5��sy�!se�q#a�t�"o�uters['m< by s�!al nega)(��' IqThallgren,grigni,moorea b,,+STOC06}. An�' funda; alup!��.&�-�EEisAf dihed�%�. Regevmr }� �&.��2�ve�6b!, coset sampl��&�I+enabl�i>a���'9� � �'��t�:ve�~] a latti�(��t leas�� != $NQH��vB Be� i5 tŰimu��9>may� �is)also e?stronga�F q�`2  cryptos��ed!vAjtaiŀDz -�aB�2%)��amy!��candidat�o�*l�# RSA-d 6� and �%[# hard�ofm:��)� s!�1�,� sec, aga�e ad�aries��>. s. T!i�y�|1��z��  o� A� focu!< y@ f@ NoAhm+ ltho&"J��Y��isw, N4 runna;�+ub-ex&V a  ha/'e�%s� by Kl� Mk-!n ~!E9B)aIŝ:� � actu�� �� !lNt$D_{n}=*YnFl2$��EL'e��d Ho yer~�Pe }�w�*!��"!.���tn$���q 2�n\!Ns �2�+$ pplyUBB � i�'u�� to o�' relev~ i&y abz)F�*\post-#sh)y�in-�9require�]0�"to �� ee�tor�!"" C(2�nAC�"h�.6�a�"�-If� ��val#%+!�ndS�� %�2[A8F+qJ 9nl"� �b method or w �L$failed t� ve�$tel0"U����S�)�T� motiv��16�a��%-N �%&nde�*M", Rock�% , Russell}Schulma1�N}YF F��d�� .LQ���)4��e�8�� $q$-.^6�pR� �*O�|two pWg#ch�_ldiV%s $p-1� p/q=$(\log p)$.lOb1F�|0 V�91%�Wf�A0�n�A�N*��ycY-� Ue�a-1`"Y )J:�k}^Z�|Friedl, Ivanyos, Magniez, SanthaI"eQ�!l}��,!6Z�B�� 5� � $"���r�%2$l n $p^ke�a�2 %�d power. Radhakrishnan, R\"�0>-aK�r.(� ve���atmt"�/u�in>�,=+� e�-*� `!�HSP�  eiseJ�p^2B� p$. � E5!�N -JC b �&J)".�c"A, (E�wreat�(\�,puschel}. A}(promiEum�"(J.en�,p1��0 Bacon, Child+van Da�b },S U�G��B`sjf) �8!� $ABcr�%AIZn�|B� is�is.- ly� �/t��previ,J�!�ESP: it^(s 9)d.Y/s,=�o; so-c0A� etty&3m&01,�eidf�]h��h>a, b�'.: �eI ��=z .�n�b{%�!W��i㡞� �$n2�n)$, t'j %2�,M�ɿ!�ey � jdUc42��p^rB]�it^1xed $r$,��!i]:�(��� �/3�,��*6 6�6$V] pV�2��k �6r�}^:�%��� i�M3N��8!�on-�choic�a hom"��-analyze�S��7 sec:�}� e}ǩ� ilitA�%8.`� f�3of% p,r1q�� nVvp}�U}}P: B;UA�2������2m ZfE�.Ya*X, O5�Uc��inU6& E��n%.�,Ao~�/� )�E�qF)�eB�d�8ngl�/:aq�N �&��s �-#�&h/byB�A�i� +�7a^&�� ,an arbitrary>�cus�v�6"��8%�Ssg�N�v � "M .�6�/!!EmA��*� is un� ��&et) �w�1inE��, stud�1����� B~6D�i*C$reasons. F�,!. bM4�/� ro���&�0�:� e oracldel (I�� � � box),!� nd&6 �. SeW),*� �!iedIs92" /alIv�ory ~5Qh&� + s. "?e��is6%h�:�at BQ3e' �{.�Ta�b-%N�sGn�4di�"-qXa{ Zn  Thu;2Q:!� ���e]1�3ext (e�q�zc)Q0eW�1in ordko�ign9��j�.2.K� =, .s!�> �mBmge� w� ,��I�E~A { !>�r� U� tunaZ,�ڵ+%�]� $m=1$AL!Sbe�\d �;ly�:we�=�ideas.V7�Ƒq2 ��l-�>; %L�! � !� $m� I�a<Ɇi�:M%%, �m�b4ri��9e�:q>��q C�1KirLee�Chi+06}m.� &f8q>�, "�� ag""� � !;%( a sl/)ly)\}a �$GX� $g\in B�!&!� !GgH)7lef�D�$H� .e.� �\{gh\:�.\:hmH\} Now��ID no�`�n]-[BU!"] .�7�# } Letܡ� �,>�c"�G� Xf(.%�. A_$ $f:G\to X� saidz beP�if �enume�<<} \item[(i)] $f$���s�,v� � 5( �Qc0(!i) � !j�e.fa( ti\@JG. &.�&.QWW w.�h64�R��Hr$��!&#*�. xFV puts1f!Ziz1d -�%��nkaQ�y,93 a.�$7  ,�is6�� "7%%�G$,)R� outF�N$H�'.u2�nyy��A�re\i�^at s $O�{,{G}})$ . � $ E�!�&A:�a*Csa�kat � 2*�h*�ad� "D%�if� �@ A��=#.EK�$�Bݚ.?06F+řn6��!�6( Ql=� b�s��A^�Eg� ɓ2$\phi$ !, #��q$�fo� �ut"��2n� 1b�"� Z"�_�h Zz ��{(a,b)�� a��&�n,b\inq��g �1��"displayJ5\} (a_1,b_1)(a_2,b_2) := +�()%+ �*2F>� B�F-ottoa6a6�� $ (a)$"�FA�=qe�� ry $!-4{Z�-AeB �E8i�se((1)(1)[�)�v~�m� X!f�u�$x=(1,0)M�y=(0,l*�$)� �b)(a)=a%o�^b�.erel�V�(y^{b}x^{a}=J {b}},�f.�|ich � Ha6�*) !Y5� sp�a�2� B:u}� ~ mai�0� �he� �  o��i��J� . A> �+a��)2a� Ue�� :� strings (o ��6)��r �Ii� �qn�$ vail�%:��A*ax� YCaM=A���s %& H6G<$a\cdot b$. More� , wYFaJ' N�, �E�6O�&& $a$�2es a N~!�in�$e $a^{-1�8W{ l�'p~�J�p}6 �5i`!*%��Y � �/ly�/GP� 8a� �� ��Mcheck^$! ��O���%� y. �refreaE�o Babi&0Szemer\'{e}di�#b}��!#cY!��1 A�B��1q�9m���� o. s��dK(Eal�Fs�$):skse>� TbT% @b�{ � Watrt� FOCS00, �)E��concepB$!%��b"Gb�M"E!�aIi�Jiore�G. ecisel 2Es� atE 1N$V_� V' re u�, s�! $+(�;{g} h})= gh}$$('_z)e7.� y $g�h�� !E��1�jH3)  a,j��"65\i)!Zwh�, ��)T too, "#(�*2* !(�~" �?�1��eY�)a�"�'&%��"% �R�#ɻ B� e"�y ?�0 s riA2o�b/%�-2�-N�be�k@*q(EprpKaE?E�hU � e�!c�Jx���GA�=|���t),վ!�I.��)� d�%'<ly.e�%K*6 F (< � )��&R n�DrO�N�nd�rix �.g0we��es�~a�JonɀisA<n ��9:=h5!�%�)�Ha"�(|L�+�y)@�SUar�+O $YO4���� >)&N:�! )ԡ (m�)X �a)��!\Mu�� >�by y�c��r��mosca2}.2,���14isAAnE�� � !��.�%6R%6A Cg(2{9.�P�9�>�O��]A�OBW2 N"�PF� $} �Gb"$� how m�6;����r E^ng� ^�:V�"�"�"{q}$?���!.\VK�M�:2ki�0�-� q\�+$v 1\bmod n�  �ng � ,$ satisf�� o��ew-���.d. YA�)k^- B�c}4! �~j triv�59� &�&a�/adVA!;2\�(Q<�� B&p!K��Um� &�equ��}M�eq:2*} 9�)�07< Z_{{p_1}^{e_1}} �= s �ib)k)k}}Y{] �[deterfP�&�9*A�$�\D)_{AG}*�q$��U1W W�X: x�"R �ys2�p_i�i}}j�6refor�#��*Xto �E4n��5#we�TaK"me ��Fin���� ac� � �ɡ ��reducaV�9m���=B�&�9pl��#���* Fl?�"��"��c]����f[���in�v=Q~\,ON4E�)%�Q�phi} �J .�%be� �-[v�& � B&�  $r\ge 1i����ca���`exist�#� 5y$\alpha�9� �K-�W@$���*v thres.�"� "k$)] $q\mid .� �?O exac� $q.d;ctR� ��|XY8r>1,\: q=p\neq �2TF`yZ`:�_,=tp^{r-1}+1$i� 0w=s If $r > 2�P r�W �),V��2{,  !T $2^r-!�h=6f�a��kl'y:1�=3!8�1� A��I1��H +$>�BAg $5o R�N am��.�ECEN�a2:.~u��m��M��#ݐLEIn�$��r^ ritt} s $u�.���-$k$ l� N>%�M�� u$. SiyR�i !a$M(p-1)!�2&�0kq$. Asw^le k< 6(!�we i7��� ime,%]�"�)]2K1. A q=z(�;   $l2 ��$l���A,p�, @���\2�9YX���C�aa��."M%b��5`9[mu{yvV$�!��y-Lt!Qf:!�t��e�$�Z�zo�cI �=�l\f%q( ^c,2Y-M01}\frac{p-1}q^Sq%S�ext� Ք�eC$�:0 Assume $r>2$�= e�^� :!'� so �,1� =3$)K^5aF�2^r}��f&c)A�QL2. i-�A8&i 6Modd�|! 2�7$2^kl+�SkFY~r%+e�E$l$. {}]%+"= R,^2=2^{k+1}l( -1}l+1)+12� ��get $k n 2^rŊ;+�E-"��ԡ��a Ca�$l�r-2��(&�1�to� %1%�Bnv7�- �L' vMK7.��$l�vC�����T*,F�nb� >m4&�HH� c3^) ����6e�>�\r� � U�qEg*���D%c>."�)��%seuJ�lea�!"�@cn�UZt}^��\)�V-!r isoF� jj�c� b�qh*4| ?o��E�(i)�*hQ�/�� ����mil�fv/Li)���j�Jph���_ o(r �.�� end��"]I��o�)a�~�,���$�_1$�fI .�8!�;$q-2$6 �"� , Z� g�^���i�2&�= c &-E�W1�%�one-to-�mar Psi_UDb}:6�_1}2:�4f-i6-%+g$(x^ay^b):= {bi'�q| $i'7 A4dM i$R� �ItQ�easK��#a\ .w7'*'�.){#$CS& �u� �!Y�sm:EA�le�'phi_t� �.Z�_t)�.��I!H!�6�t�!f���tZ�tB�t'}"�tV�tV�$ ��vJ�)�6�"� of�4 �m2����� ly2�NA�� �YI���Mb ^h,B� ���:A?��  �s"e}�TE��AW� ���A* 6� P$'qXcaQf�: " es: �M�U "MV" 1. �q-VC>�<-K�q\>�s *:$q�)� 6�;.�v%N2�2.}" @-g�B� =)+ x,y\`* x^ y^2=e,yx�"$2^{r}-1}y} �|26� �XeR2�3� quas�V:*QD_ r��* �>>�Z�4�1P_{p,rZ!� =y^p5H{pHRe ) , exE�c�$p=� 2�� �SIQ5�:��YB�>�^W6>..>\\2�"�"�e!�m�X disj�g�m�B� Di�X� eque[ofn� ndV$ . )&1�l"�%k�i�V" 6� . B4jBi` o� L ���aE <�� ~ ii).-�2>c A� j!%\ 39 & f[ Ff5>f�0V�18+2 6�"�f� } ��2�5�!4&9p~pi2�:�/&���2, ,���U,��� ed i"lyUI�2LAi6i%�E� (�$eq:�)F36Witself�f rin��n�U>�>#�A�HrOa&- G_1m�� G_m� �- � �(HR;H_�49 H 6�/anda�77'4!GU�vD�8 es 1A�5��*_B D� B�bJN� �� Bu�&�OsJ�b�(basic block&� mu�59b�s, �Qevec-6I:�T8%�x�Rof��h*�-�>0%:�)� %,m��p� 24l�byBFG �FG&m!�| 1<ra�sm��� �$ft�>%� �NBA�wo �.9p��*/h�oci3k!"I��tTA "/^�> &�&�B�NB�<�<ia�xpos_  �7aX�-��tic chavJe"o!0nyB�1�.2I%_��[$��|;"mK�7"jsen�$� F0H�qi.�Yre uJ=0"�0*n$�F�[�  !�lPJe�[<"� b�C��wEA?n remo�"A*L9�$$r����A[�$<#&$��M�mZ%ns .[* r5._1,e#��)�In�r2 D(p^r)A w>^ !AV� (n2%3'�-�M+&�O open1p$s:P!��C;xtvP�&KRa|]�R��N�-1�� 4��&�b.�i�"�'"�%EBth !1!4�#E"JZBXcV� $} l!($p!���+a��C�13~;F�aAi�nF���@�6)��E6 4L4::��in�Nf� ��Be,�P5�me�h $R� � a�A �  ��exA(ed�H&2�%S�}�'= � a��"��?r�1$y^bx^a�a(b"� )}y�1eI�N��"r#M�:�X.} �^c pc+]$c(c-1)}{2}��{bc�O}���'!s $a,b�S$c$R?�5/y"�8%�$D�8& o 5Zt b�5a_�6E���"�8:1,��  $\�ix^{p^i}ji�0 ir�5!B4, yj7 5� k�j}}8w#pj<ͧ$1zt"!��]9Sosi���9:�^!�1' �].�KR�H\cap��� ld��a�.,%�We~"�39�6� �HA"� )xj< gy�6H�!,.� (<�{ 5,y8 Sltse1w�-�y\not N� ��#s &l>p^i "�/ $x^k �� Then1f6/5$(x^ky)^p=\<\{-�array}{[Px^{kp}9jrm{h9}�!(2+�,)}=(x^2)^{(1 2})k}}m>=2� f\r`AA6��'-ea�at�=6&%����Z%6�Gwe do�  Uc*�P2�52�)p^i|k� $x^ei-1a�G$my &�2�a�(L>nY�av YQm�[^Y:$�8�`-�.x�v_a� 7iAl _�.w��#W,��ep��"Q � �.��� /:e���& rmal)'$�g!#s} � ������w=of}�s`e part�M�L �>z�c6n�n"{mo��a�U,�iHH"C"5 Ea3��!P $f$, �xK@ny1�!�!�Ip $p^rp-�e@$x^iy^j�p\nmid i�*�  j� f+,�anyqn���Io8�cDFl�e�M { � ��7*�?%��|wut�?t@^ H{aT2n�9���Qf��� he �Kf�3� Ck$f(e)$)2� *�!�!� . \\��B�p5�M6� Tn^�W,�`�SZ�Wn�J�H$��֙��$2�0u\\t�aA]!�@0��MZF���i,yYw � �� $T�"gX]EA#A�n. "P�����$a�W&hA�i�C� immed�I�� �;�7���H � I�lto�>A 1B& � . DP $XC*�y$Y �)�x��@�-0 *$(X^p)^l=Y^�.ExpkB�& s B!uj 2�)E�";N:�^Jal�� a'E44%}\:\:"b !�.e al(bb2}+1)E a'(b'y<�&� RT�{guarante�  �$aun�Zy"S�"G!�%saQ�1�Q�*!` $G'=*�" 6�%&�"h$H'C(l,��!($f'(u,v)=f()� u (Y!�v�5*7 $f�*$H'$-&dQ�G'$. R�k.�����I�� EeL% $l$ad*�� �3*�RI�NkX 2$.3=I�$l�2���A!PK $Y'%h���{\�4P6}y^\beta"�+\&9��4: $$Y'=X^{-l}e\BK{b'-bl}$NR� 67=a�-l(-l!�{&�$-al+a'-a'b�6&GJN*�m$��*I �?cU��p6 cau�zs�7$a'm.ale 86�/�o� radict$ hyp� s�6ng M[ $��X ��Y'�aU6�\�>U�p�$$7-�V�� (�v� )A�2�*"b ]2�it4E�Dy B�i)�:�i��a�� �Df �6�[�a�C�arg]�j�Y�N� 2�2��M>�2}}J�y)�9� {p^2B�f�$` !\��En�� a��J��� 5��b���Y�/��j�a i�l!6�\�&� "-� SN�'�+{Zr�]?�  ^��f�!�fy^�NB� �A6uay�� 8 %�� \mat�B� ^m\>�#��e��-"�~Y�pct�`q��^ � coordi�^%�4 pT7� *wF�I��VK���8�  $m:�� s $x&�Zx�)A�$y�&ajE 2%J�r}^�$nd $yx_i=x=Cl +1}y�� v5"L[m\k %�EB� a�*�������*I�,#��rto it aL�S"F :}n )bJ�tim.�Ep$)�4 .wo#;enough.�h\ !�hi:�I�,�9�Jbl�Rdn�&�q�a�eral})G��2B��t$�U6�A�GA8=[� H*r[N.CA2sLK+ e�'*�u&� �"/a!a��L9 bi �|H $\pi\G'$AciH� �"�<"z "�"6\\pi(H)Ed6��;�! [(iiG\ \circ \pi�O5A"+ 45)Q��"�Uui��)$g' G'$,�8��� g'}$J,��w_� m� �R�S ��(g')$�M!t&�:6�� G$);=Ft�N�x b!}un+a�o5T�z�aG�Q�>��&T .o�!�!X�x]#��i��!�5�U� $>��is�6+�� ,!NB$v�� ��e����pe random��!QH'$�  dard�΀7T2,3}cG�%vmFd C�%�$v �Wu�rm��N�$n_�&u1��Qi��Ih��ia(��hO/!)62l �1>1�!���yXA��*��r �*!2����.���j�� % )�� (M3l�lAQ. bv�hf �>i)X�vkv�Z��!x+e�2d%�"t���e&�jTre �j�J}J�p0.�$N�L� �ey�frame�l���֤2h!some le� �V����� L*{*�%��|�G�Ris�}n�9b NA n�i=?�.�3��:meaZgt!!��iso���5cparXqGBV%  �J�,VY� � gA]a-�s��"�C��F�1�&��A��XF�e�:� un�"!��+N`aOn� �{0\} �am��4(���)���F�-B| �a$h:z�1 5?&�%�$ �A6� ���yg(>��� >iK��.wXz&7 $z_m,z_{m+1�(*iE� of:wA� E)� a mini�%>.��2yfmv6 G+W,�jc"aP�te $A$. .� is�� ?!�6h  � hip -!��Z,"|h�I�<��A�&feHn.�? betw�Zf�5�� K} G'$.� pi:g_1^{a�?7 g_mm�-4 \longmapsto z:)z)-�^b.$$-?(Bf=�I>qoZ�:� :��}5!61hm,yG(��� WY��nat�:ntoo"�p�gc!Ia*N "_� e�5-:p�va�x�|o�#!:K� ]Y A # $�+y, A, go(s�g$�hA���2�Z�c,���L6� Rd����2�*:� g_1y!Dg_k" )2� g_^I e��$k>�:� c" $(g_iy).=y^�Jg.�!?��,!�j#� -(TwS"�Dk\��Eׅ 1�2�y}��2 ; z{�G�:Non�:� �-HV a6�!z =MsKKly.��a�� ^��"�8& "�c$I(gy�0g^{4&�0�}g^c y^ca� r�facek^p!o%CJp}�!-.��D � $jhI9Awu�hapucB:itu�%� U>t�� g^cy^c$E re.gE $c�F0,��"uNE�K(H)I��/ A), gy)},�icm�>��3�9�)���9rW(i^�AB�Y }h�h�V��EN�>�Vfn!8� /Ta*pk�H�n �[&dNqvv� 6��_|$]�k�:Z >!��TMMNJ� 2 s>� 6 �$��� "�rK5v/%\nonum7{ReG'ces">i�{� v\]"?��� 8�j�C.~ �w�7)�XDmph{A Public-Key C*e�z Worst-�!/ A�� Equival� }, P�_e� "�H29th Annual ACM Sym!�umKu���,'284--293�9 eA�2} u�gd�1�Loa�&`$Vertex-Trar�ve GraphKd R"Gy�A�F�o)]V�3rd��164--174) ܧ�3��Coo`an��HFinkelstein, E.~Luk �0�e `!�55C�P*�x�Journal��)�{�Sy���Ds, 50(2), 296--308B�}A�5��3E.~2$f�84)�5 \ExO�yl"@Matrix �a��~ Ra5Ya2]F�%�E�dÏ�$, 229--240Ei]fcon} D.~�=A��i�W.~!� (2009}�zO)� al M&� to�ߞ^�p�^�_�-!dn]5�Jx46�469--472��C K.~K.~H!eup_nd M.~M4a%y�De��o9#mV���<*��E9)�%�, 1(3Aw3--32..�w D.P�c�S.~xS.~x!�6u#No�iz1bp-�me%s-^t e-prL� arch�Z���604172.Sq�e50 � M.~�/�P.~"�1�0:"1&"�zr Non!)mu!)ve>�m2 Adva�Z�� Appl"CMad> atics, 25-`a 518yG�!���G.~"�'F����M.~�'���en�35-r���mACO� CF in�IingV�3}��[ 1--9.����#Gr��� J.~Sj�,�Vaziran^� U.~V�� !�4�1�Mechan� :�$ NH��>�aځ�},��b`Lorica 24(1), 137--152I>F� S.~Hax���S�M.~&��, A.~.E=�y- LimiA]o�B�)�S�TI��U IsomɕZ�8����604--617.��:�S6� A.~Ta-Shm��Y�fM�B8�A����� ŋ�� R2e2 s}, ���Fe�puA�, 32(��916--93!�yZmD���VV�uYEn˂3�zI>6�No"��^ ��<��n%al�f�[14(5), 7��7�b.���c A.~Yu. Ki�� *�1�m�K aE�LSt�zery=Yb�9511026:�k*n7����%u��&�AA:e&���U9u���D�OZx!nrF5i�70--18:�ore�C��cD.~N. &B�:�L4�&K�6�aP�cBa�&Sel�C���%Sٗ:^��pIe9ŏN�16�-eO2� DisM�5[0s, 1106--1115)�yYIb}==�&� �S" �� �ges St��F�PJ II},fc05010662�aZ��y%��y��EU� 6 7 >�-k� 1ήWq���er=��# h.D.a" sis,: � Oxfoy<9��lP\"�����%IT.~Beth�M9�F �1�����a�Pof2%Es}NN13th 6'2�r Algebra, ic ߪ!� Error-Cor�L  Code� 31� 6<6�� J.~:k�2�`��y u�Ba�I��ou ���-��H&R�%6!�F32n��te�]ColloquAy,ata, Languagjg�Rgramm($1399--14122iל O.~ݘa�F� I���%"Lat�?P��aBv�3: 738--76G.��2}^�Newr!pdw� ic CE>~ },.�!i0ACM, 51(6), 8!94!"q ~3b~>� T�i�`��P"|5 Spac b04051g �s֢ P.~W.~��P&�i-6�i�Pr�F��z9��AL��sa�I �>�V� 26�14�1502K %�7R.~Sig�6�>l�� |�vM 7N583. Wvev� E�0�Succi&i(�1?~�e� �  41st 2��{5� 546J�w��.�&Y�U� ��+a�<{a3Nz¼ 60--6� ��Ft:���k�d�% e�!fu�$�{% File�=�)T_dep.tex = fannes_new8 :;�prl,aps, �x�$s,f*pacs,s� s��u� ]{revtex4��c�T[J twocolumn �F,bibn >ezI11pt,t0De?�s�I܎@:9�fonts3�۴-!�%�� $olvlu��c~��ys, xq�JE "s ��:Iǵ27F ��! environO%s \def\�Po���In*&�k���6 | \,��$\GH} 22braZ� 2�;#1; 8 |:3 proj 4�)#1}E:(bra�2o�eft ]� \,|\,#2\, dV��0 rod}B2ly�.� halfV�!G$U7s�� X1�4$>�h �A8��H}_� :�tr '[Tr}!#1>&b�� N"�N:Ie#�f^!bea}{En(KBE$ FV"QATOP}{:8NEGu "��%${apsrev�J ��PV� %:u 12pt*��%\�%a0!^:�Title%� �R*{\hf`#1 �] *{3mm}\\\%}\r�#2} \add +�^�{toc}{�r}!�{.y�4ex. \we��< {(|\epsilon| M)!Yd \�!{\R/arrow2� \no {"x`:r@�e� :���@ \l� 1\e$.6� {\JMPciteI��2em${}^{�A�%�:*�}�.�b>r��parͭ:�g {{\exp�M)}}6� \h22^jj�"%�jA2"f { {1 \�n !:a�`of{�5K{\iof}\/:\6~@ \s {\widetilde{s!��{\nn}-!nn6 \R {\a�R>epVMBalf {�:�vT s {R:WGX�{G>jC C6{\fac}{{�Iho @k>!�1}!o bf T:G{��rm tr>;xxWX> distrm^N �ykk{%, K re{{& Re\,im Im zed{͵f{ZEQCCreff#1{( A�)}�6 bbbc 0��{��box0=I�$�pla���C$ε)� to0pt{e:40.4\wd0\vrule �00.9\ht0\hss}\X}} Fd�-�8�a^am����czc�-�iiAZu�21cm}�72�� width}{17odd� 4margin 0.0in \�.Ftop6'�=�{plai�1ne"R��>n}*�i�� �!� %*�"6&����F�� }%��\ .��r>ܿ$�7{�dF9 �  &�hor� t� {Ae�-b_3��p�� depod�"dnel\%\��{\today�[]{Sept�� 22, 2003�PDRAFT:\rm\ ]{1-Jan-04�Fɿ0{Nilanjana \s&# me{D�ACe��[]{n.d@�3slab.cam��uk�@ffili�{1�z�O LaboO�y,˸ Cent܀&�al"�"6.U2@� Camb��:&the pa06� KXF.,p�� � �G �. Tog�r:65of6�V/ is c� �2e waD JeV�.x9� \ ({03.67.Hk, -emj�` qg_� o �U2i�}�a]�2�)`6�:�9��on.M�@U:V��be �(\mu),�4^T + (1-t) \tr �{��$}}{d}, \lax�� } \e!VZ.\be - 31}{d - 1�be t \le M +1}.�IE!2 HHG $\mu(-2�T�&lex $d H5 d$mrixh{mu^{T}��na k��0%$ �\l< $dJ unit O. � � $!' 4 irr,� iblyASat�F�Fe=&FVR�%�ť $U$�"�%� (U\mu UeEst 8ubar{U}�!� ) #,1Dcov>{a/f�/ 3�a*-H--c��g�5e3UCIae��jsnla�n�PhI-Ho.C3as%�! = c� (t +=��}x),_+�) -..<+1�^)%_-.��lI5�>c= (d^2Au )/2d�0Q� _\pm%D):=]�1�1ft(MY�pm \mu^T�ee.sIZ$ admv?�>�9wPKraus6�m91= �2( �)� ,um_{i,j=1}^daFft( |i�� j| �|j6 i|�mu�>^*.e�F�x\5�ie��_8�h�xl e;AXt^�la*t7E� (1I+)�6_-$�>I�Ph:16Werner-- u�in�"��HW}�`gh�)��siv��I Y�wmy, dh�Sfio 6P��d.�v�  �H }eY./2}{I�� �1�YM��K su<b� $t$=by-��l1}&CSh�o �"%_ fullc@� \ �>N�e aim tiN�%�o)eŦ>id  �*"�f�9!��c/ yof �x"�RI}&2}.N��%�.jof��w umNw .����Cݸ 0.��y3�w �7^Vofm4I�I�A�F�h(A�$ ):=\min_{�� } S ()���nt1Z�!F���e�Ball"�; %Aay rho$�Fde�1y� ces)�V �.�(b��< $S(\sigma ) :=-Tr} !` ��Q(von Neumann" -�2�x $@.: %�Eg=� ��g!�-^\ox=�v �i2 )�> addd%�A�E-U~aER~� YAs��of�^gAalssX<i_�8 d_1=d_2 =�altho�G" ro�lan �d�i��l�!?E \ne dP�i. e.�_��_2�Mq_1) +-_2)"� ��  �employ��e�` dev�ݵl . C.�Schmidt6�F|\ �� _���� =\��� �� {d}\9�\l _  }}| (;1@-�2. 1�s �BO� � \{ B�] �T�@�<n ortho/; ! ${\ *� }_{j5;$j=1,�$. � }}=( _{1}X< ,d})�QE ���c1scoez�s� ? e $|!k 2kFr2}|� t�Ab%�BMs�J� -N2} c I1uJc6�,z6�Zh5� �J� R��g" ;1|M 9�U 2+ ;2|.� &� aNT�+m 9ro�F�ribʈ:F�9�M�4}\geq 0\quad ; R�B�=1;U�nin��u��}��+MZi$ � �.0$({d}-1)-$dim�onal ��{ \S��_{dA��ed^�E�trainQsext�� �s (ve��Y2N.vpr�;to un&/� �s $Nb=UvYu�2 in {:�1}0$�Ha�2ZJ7*� �>) f  ifA >h#m���BZ��! �Z�f$B*Y� * �S&�J�Y�*QQI} >a; Se(��� ({\ 7U�}}) :@5m�mapBA� J�,b&��}): m(�\-�% z)>(5�1=�q�ps�"� Nm =1}fUNl�(�1�! "�r ;1|)2�29����;2|�Ym�9BTi��� �]��,B�� um�aa�qtA�2s. O� to I�E),�Q>�� $\{�"z5Nh?sno�54f��y�E^�G �M�[n���"utiD meqm�bf 0^{d_{i}};$ $i�F."Sf&!e��C. -3}��:� "�x�t>�*��AwB �2�Yp H delt��)�} rW + t | B[ r|,6�*} iY1�9H:O�E!�. HO>,�a ��&=&6���Au �:>^< .�w}l|)�?ber\\ Z�V5(eu Q)g |%�[+%�^�!�)�t!������  }+�6�I�) ] +.� )Y� t^2 \,V� N���yl2� �& �re eea � �{Pa�./��mVwŦ factL f6r�k�Il=�� |�ZT*�i��:,�P�(�=2� .{~E#e� ��eigen�� fr��o� is pu/��u4�DSC��vP% ��a $\� d^2� $Ah� _'!� A_{ij} =�_imeta_i)�u + M> j} (1n��(dee�!��tify ��j � a pair $(-�M��nd �|e�Xgin.�mu ��^  BI�}=iUeT�k>k2a e��j� >�:s m�%2 u� �, b D-=�X ,{d����"�D6� As�2V,E&c"�s�� ap�,8det}}(A-\gamma �\)=0� 2z�!���od_{1�� �, ��d\atop5n�}}�5%}tQef�6a�5%^{\�� }�2C')6'F�{ \{ 12 ^{I P }QI;�-:�''}}{p�'p'} ���\}��= n4\�gVga R�e� �� $vsi�(X!�h ��&0n6q�{ $d(dט:� Trm!� )��)�Tm�Ϳ~j%���, 2 U6 , \,Qc�= q, �t� eig���z{$d6�q��^Tek�y ,d�L&�!wroo&glu7.��A-dI� }-g Q� 6�'M�j��(U1�Q�} WY{AsYh�� B�:^.��k((c_1 + c_2 > }- �:h uf6^�:_}�ahs>(U |� =0 � e�6} y2��td�� �I6�M�;  !)2&� " c1c�ee Si��P�ey(ffM 2�M�,4}W$v�]0�1-!��2/c_1�2td}{1-t�0And�L�VAE�, Z$ � be��H� a su�F2� �r�)=S�(V� )+S_{2}({R�}) \l�abel{sum2} \end{equation} where \begin{�LS_{1}({\underline{\lambda }}):=-\sum_{1\leq \alpha ,\beta \leq d\atop{ \, \ben)(}}\gamma_{\ : #}\log VD,\;\;\quad S_{2}( ~� [=1}^{d}gl f }. \l) 11B Note that� �� �� �^�� = \frac{d-1}{d} (1-t)^2:= c. \ee Moreover, using the fact �\the eigenvalues of $\sig![12b�D$ sum to $1$ we ge� � �!8 d g_  = 1 -� U� above relENsN4can define set�\ non--negative variables%S,{\widetilde{V�}} := ))1}{c}V',AlMPne\ ta, I4 ,A�t�,, \ldots, d.1��1}!w andA .�U3 �-�1}{1-cY`} r; M=1.2, r d|aa�q2 q0each of which1�8unity, i.e., $$)�1\a` � 2s \etY~&}} .�6?/�!�%.�e� jI.F2=1, $$%7henceMP probability distribu�w$s. In termE these Ywe hav%�av�( &=& c H(\{.�6�!�t��`} \}) + {\hbox{\, const}}� 0}\\sf>s(1-c)Bw2zk2�� ea Here $�addd}a>%: \se�c{Proof�iTq! In-�graeme}�d~e`d%ws>3$H2� x}}Am.Gx}=(x�� ,xaF)>,!78a monotonically� decrea � � elem!:ry��Dpolynomials $s_{q} �x� �+ �$E� e.g.-E� E�"R $ �D$a��  J q="� ,d�is=�at.}��ٰ��&_ \ �V�):= g%�g2g%�,� 2�&� ��sB� T�]fore,A�E4%>M`AMis suѾ.&i 1��� �Z�$�+S����i�� �>d for %�&� $�m��5�Janu &� :� +� c_2}{c_1� �;(-W� � ]*. & nuJ[twoJ� D� 1P _i := g_i%UI�> �� $g� g_2, ��, g_ni!��roo&eq.^ f1���ere�v � G , ǁO zero&� !�uct $( -A5  �a ^di ��MJ)0)MI bIse �as  s:J�vk=0� �( ^{k}\,(-1) s_{d-k}�1}92�> d}).�symF�:� ��l}$�畎 $a�� ��� , d��=? bLwritten!'B��|! 6� A7)+2Q-1^q 'lm�%1%�nIc�i,{\not{ ql}Zg�)\,2�l.�}=0a%� sym3BhiRa6symbol� 6p$ mean:ɳ��+!�(3}) yields,�;e�$0\leq k d-1$ J%{��2)Ni/%!�%�6�HQR�M�-�5� _!T} edz��osympolB�&yi�i *), �8 �P � �6�+V� XofR� 9�s�!�}� �)^�S��%xd}$ (�areA5mselves `ar"8 U{S �S 6S] Our aim� to�v4 � � N� )� B� �r�6�)�`$, R� Eq.i*� ) &2 e��mous �a}.�P of>� I_Y ,"Xd�a�� G�!�E�5T �e�all $0� k d-2$�NN Phi_{a�nu� a�]� I�F"2�R�2Tu�B� Ir�\equiv R��}})�q phidefB�$& inJ' ��u�5 $, ~GJ>Q]5�"O!K $. B�e necesstO*� con�on%�>S&H it�enoug&�F�(�i}- , _{j})\bigl(�� \partial Q } 4_{i}} -�/j}}br) -�� �!\��� }  j� -}Ů09 fora$\,� q i,j *�key�2� )� rulea�$differenti���N� .�,  :&,O9�narray} :l9� �i}}1�![�_�U� )&=&�H��� .�!�d�x 9y6� !�}j� iS �� \ƅ  T ag \\ &=&�� ).. cb i}}} �� IlI�l i}!{dW%\J�O\>�9�r�2�&+)k(2� �!�n�1])��eq&M Q[&mJwB�U�&-& �J�Y1%0a�Bigr)B� d})  1�� .., A/� Ek2�-23)�XjYG ]C+&I�E M�.:�UdI�A vA�..�.�� - &} -.�6� �jE�^�s��1.�r�J�.c+-�E����l[FtQ�{!] �!� d}N�$;��� bigr].AeU��(a transform����� ��get�$�$B$ ! laE ��-%!i})%�k-���1e'=U!�.!eM 5fR�25��2v��>w zx>�>wif�,�Lŕ!F�%"[�zu�%6a1�� �djI!K�I�r]2�=��~� )jE �Q 3�96�E 6 Ù= !W2;� $)\nonumber�+&M�1"�Y,�)-� ����2F�=��&� long� � �� Substitut� ) *� � ),�$ c1c2})�  re� ngCfactor� e ob�"�B� holds ifE only `b��% %��!M� )Q�:���I�%�}s1͹�:�%@� <2(1+t(d-1))}{td}p�Jl�!4 mainP$��� $i�"� �j>�.�%iVnd���,$ do not app�"�w ). O��s�!y,out los�genera$� ,&$choose $i=�� $j=dWn�A �d-12�U�l&' $n=�_>@���l#�!� I���!. e���N  "C1"�� d$A��M���u�K}�� n}(1Q��gn-k-1^gYu�a _{n})� >us_L2J%�n}QJ� !�F� AV2�n-1$. �$!6 ��pA� l/$n$, satisf� c%["a�� l+1 �):�l} E�n9=n� 2td�'t}�$n-tO 1nu1q�$ARf�$)�nu���"�(:\,9�lq 0�eYl$,%�<$ \displaystyle{�{1�Q {l}=.d-2.$  1!.A%\*%$range4}. M j)91 impd �U1%= �%{q)|q n�u�1{�� >�n!=q 0,$-I () obviously�y�� �)j�!.�H \emph{at most one}�>7F�$�*b�) em{nJ*}}A|ncee�ne!�)� �mw�Je case��on�)e� o%�E��egaf,�!�We % proc2�) �.%first�Kic�aZ all &�.�n$d! k�A�)S Oterm}eq.z {89��+�lE:1; [ .�n:w-2��eX2uX)P�weakeja�E),E�coincid&th�m� ${6Ht=��- -1}}a"�"n���0dhs}. Next we!}�!)"se�-"oER"is pos�#e� $k=1,��nɔse two�*�P! 2q-�:G,GF� k=0$����d�)+E��2iby !� ider��v$�-M��Asj�A�J�'!C.�j<�$ ���She ��m� w�+ \[-�:" �� 0.\] Also�1a &�n�&~  ��.5 =& M�2E�0i_1���k-1 u�"� i��a s�-k/ � �0m t#[ / 2nd �%a�J=}}\�*] m)0(a� }} 1R m�"V12�0� � last���"�" }��0u�$����) ���S�B �aЁ�J� (as��� �N) N�%�.�Win #� ��� �!��6H/. A+indent {��'��� }}: �".�%!�-�J�}}= e_n )݉ lm[e�[ l)}{eeA ^� 5�ee�$e_n:=:1?u_��Zn <0$,M|T � ba � *5 C6] #/��9!�^ redu�.to%/�\le)%>9 (��0)U�A�I� WitZ���.��� 1}<0�� l}> � � l=2,3"��ETh&^�5/Av�1E J(f�& f�.)= � }{\nu} -1�u D�nonin&�+or � \nu$&3vexE� >�f(1)=0$.'^�g�g� _2,\ń! n)" �� � _l),>�then $gEco���0^z } EV2+|�Gn��"Bpn)c8(�#)�� 1, \,\,!�A,nB��$!_1!�is fixed� �.�1max�1on�1( extreme pog1��seM >&� 0p} (2 �1 � ,1)>Ha�2permut%�s �$(1.9$x e] } ^dnu1++ %Z2=�My2O 1-t}B?� a� show�Z ziel!Յ�I�_1}+ ��� 2}-2a� 2�td}"�qajɄ� r�G�xbecau>�#0 )�2=1$ (�El=1,l>2$� ��2��A)E�EalaeA��0al sibl�&lu *!h="3,$/\ �& 2}))v#� w� i�/ (n!�){�ied. T6<�)!�tak�| to accoun��t�<0e�2>�Ta�it.9j�A6f�:2�A =[IN \ge 2!�ft[ 9TS+1ͯR� +H9!B2 g�+V�iT Y$�� non� ��6 1�Fe�6!�y^0^-�9$A� zero�7AI7�!�9ix5ep72�/�2at�3EPsig"H!���or��c�  hA�H ofM, o is70check!����(I)K^0K8.e8)\mak�common�8minator� get,An#i>p $tW \[&)tda�]?^2+((2td-1+t))-Y=$td\] or \[��>7td)^2 *^2 \] 4 3 ^2+3Q + ^2,\]mrN2ndru"�3$Acknowledg3s�6�r auth�w$s 5$support�!�(QIS Program!�� Newton In�e��� A. von Hu4+dt Found���m�thebibliUphy}{99a Lbitem{af} R. AlickiE� M. Fannes� ewblock{�)(on multiple.�4of��"�:utput�� SU(d)-co�nt chd,ls; preprint�@quant-ph/0407033}�� medskip\n\ # �24�Bhatia, GMatrix�8sis}, Sfpger--Verlag, New York, 1997. ng� N. D��,!| S. Holevo%7Yu.!;Suhov.:A �um �= a?6e"�91;�4- 3072J�9f!Os} �1�,B. Haegeman,Mosony)�@D. Vanpeteghem, \5� A ���7al�-ہ#a claF�1��10195��hol} 2`, 6�v�6 capac����ed�>�lems, http://www.imaph.nat.tu-bs.de/qi/p=+/10.htmlv hol1B�99Remarksa'a�J�ofQ 92QsB�2120221*^9�\my} K.Matsumoto, F. Yura 5�En�8/ c�`ti�ic �8%KM�!Zof9fof some�F�306009~��8, G.MitchisonxR. Jozs�A�0Towards a geo5>(al interpre� �Eium in&�"com�4ionN� 9177~�HW�_F.Werner� A.S.i�.9CD erexa=��an.( conjectur�mIpur-g��(s,}}�MlJour. Math. Phys.}}, {\bf{43 2002.�+t:� 5 doc1} �g\E� [ams�1�,aps,twocolumn,showpacs,nofootinbib]{revtex4} \usepackage[]!��phicx} %\setlength{\topmargin}{0mm} \def\ket#1{| #1 \@le} bra#1J8�; #1 |5#22 #2:Bkb#%.\ \!\l Q2Q0II{1\!\mathrm4Ayd=!D�>{L9)�lemma}{La��1Rtitle{Un"� X;secAke=CilfE���a-ph�;sD@({Kiyoshi Tal } ,Hoi-Kwong Lo ffil^+{Cea$��Q�U um I}�3Co�Bl, Dept.aN Elec�A�,,& Computer E�!e�A0A�,ics, UniversM�Toron�� �Ontario, M5S 3G4, CANADA} %\dateA-d�+�ab$ct}"9 pape[ �S�tufk� be surpri�<ly�act(4 {\it)�}-� emis�>� �e )�44a�?-ba�QKD. On.7�� hown�$explicitly� �GK�^ geL!t� n� lice's b�``1�crypt �ta�(s robust aggBt�� spli�!�ck:r  o er pul C�]� s''apo!0by V. Scarani)eet al.,�E:,. Rev. Lett.��H 92}, 057901 (2004)� ich!S�> ed SARG04Vi��^(6e sam�jur�?2in BB84E��.�b$?�[post-�sA.�`. It 6 hus, ňes�"���.�ejL&�CG moB� li!L vely�ge��=ityq�A`6I�Ba6�lű fourQM� !4�|A�lVA)x tu!�six-d . Fi��� ��=2\(bit error rA�thresT!t�Epr)gyBHe .�I origi{-�: assuma^a depoe��X.� �Vl-(cs{03.67.Dd�um�g�� q=��5�(QKD)O G� sepa�!6i@ �sendera a��A�ce�' Bob�sh!#a!�retmo>neglig)lea�d!+�.��,n eavesdropp��veae best �n��9&isi 1q publishD Bennette(Brar3N1984 �aH}�ny aspec&\9Yincluf9!2�� T8M96,SP00,GLLP02�G�S � �_ / GRTZ& has �9inva�gated. �is6sly ue�%�@��t` iM�� wg,>).�, E@&]c�s full2�onE�3I�@'inducA�!Eyb�� ploi�Waz� (PNS)-LBLMS00}. Recently,�|, et.allCi�}pr��aE'( )i�iB%PNS�AfB exac��!�N���m��{��datK�5!'is��en6Ak. Ae2 goalat�$1to dem�&t,am2 m!vmodificMXofR-MLCA00;�iM";UA�4l2B�$senP"Pi�A_!cert#'atg-type%pA�nAn�&a�, �H!+may��Qā�X"%<~i9 MɅ�,, but rather6 ��:a��.5- �G2�ar� �j such a wa �af2 ec'Y;i)7broadcashs#re_!��s!�orthogonA�/H,�HK u�]�i�cRMt discri�!�e V de9inilI� M��:!�tuL%�%r�ex��AF�W.~%; �6= :&�rk UE�kin����e%�CO" is natur4�([ viewCA�4an unambiguous��io� C01}���:A:;i$N$ Z�+ a qu��space�Eopo�wat��,st $N-1$ cop*I�$%�%�avail'R-~m�?~ �'of� 4� at�%no��c�-7 a%E%-mor!�a� tw2�, b�f ��suc�'deNQ6i.�sA�an re��:8@�� l�Q1d�CnoI�n>s vacuum 4AQ���disguiL Y�_-eUQoe�wor\@ %�no �I5a�Orbi �M�A�.p%+� both}O6���:>a� a%�-��� By� ya�EA��lj.{ ,�R� {��e. *"@�{��y�� �hA 6l�u�J�Ae� ��*MZ� % SjP!KQKD%�ge�Oe��S-ˁP�.da�q.tqu�o�Ss�A{2�`` 2��"�(��A.��G''aJK CLL03}. S�(r, �� studa�eM2 d��toQ/e� 2> soura�n� DO�?x! l� . �P��tb�':f� �� mpac�v��dirCM!� �. MorFWE�p�� 5CY��MVshoulda�oEg icul�,� >9E{!ޑ� (�<� )C04})�r G �to.� M'"x !� �per�eima�!+J��summa�1t�.Zh of1���e�Q��)TfRIȅJ�a�& u � ���6�6��W�&�e�� "�'a!r�, e� ie�>�ͣM>1��afresA>clearf h��z.h !���q�am��� qu$yE[9~� t� iX co{J nt l�m��Bob $6d6 �5�o d�/ . "[ ᅇ�:AEɕF# idea! 0``squash oper��.� �`TW\s treXDe)�.�  j�by) ��9wo�/h scen��a�%I!��Q rely� %e7&N2�� plet3den�ma%��)�g&e��:4A^Q{% madU(n widiapplya�DE�. ��1f2� "�, h�^Qdif� :� ( /onu�s!�.�i(� %S% q1�`�A�b�t��I��>��"eYsis&�}ing%5*A�!�noGA�de� be� � workTf� a�E��]�� ���.�mB�./.*%%mN�.���d!eZ1x ���i(g a"U I�lgVH _)6�a�UI We-D�Qs�al9G8. $\{\ket{0_x}, 1_x}\L3a $X$!=' !N a��rel%�to $Z+!�$Yb�V ej_z�F[ku+(ENj{ ]/\sqrt{2�($j=0,1$�:�j_yFHinI,���E^-a filt�� 2F=\sin�$\pi}{8}��� +\cosF$�$ �6$ $\pi/2$ rM� ar�!%%axis $R2F:Q84}\openone_{\rm)~}+:�4}(�ox�- cV%�\varpIV>efH:}�1�R[�9��$N� _1jHP1)NjAkbra $. �"a�!A�� 1}}=60}2W��tro^, $\�P(X *Psi}) | q$X^{\dagger�-c! 0\pmrf '�(A�<�0A� pm 1 !j.O1�O:BOmO nu, -1W� ^{\o1e,A{na5"ove7d +@<}$o(n�Tbr<{R*b7a, B/Y:figure1~'- /}[tbp]erX*�Legraphics[scale=0.6]9 1.ep`W4cap�F{Bob's�su�+nt�?� mBlo�apA�.�� randomy�$R^{K'}$�� , e�O� �[outco�2!�[ 4]���t"�.fig1} -zD~� ^�ainJ0�\6�imilar��B92�-5 B�w4pX͐-Xcontex�!K>G .Q. Imagin)�O�-�� endsqZ} _j�O$�+dependA�_e�� $j���8 � )�wmeY% ��E�?.(baAM��Nye'}�WuW6��'��(� Fig.~V8A1�f (.|Md!�$Fb1 UrN0��w� ll!�clusi�*C!!"�!#at!gq@.�Zults. F� �,/) inf�Y5�)�)�� to him5�A3 Hj�(J� 0}$) {o�de�aO p� $0$ ($1$)xW! n��^�PgAi+M�� �� ��a:1�0b 29 C%(吩��*i!�fneT*} a big��Pce���� AYɱTL0�ABi��q5�uw� [/$�2�we*���F��both $.0m�F�{�M�> is h�En=c3�-�- ��EXor*����Dž{e�A�de@gN<I&ly., Aܡ�I alenDdoRby lo��pa?a H ��c2�!�2 n it� pes�(;at �.ar��e2_instea�Bob�1�nBF����.��?ma��-Fiv8A�ate�"gon�1r�$who alwaysRkorNvX+�Bss%sb�gardedR�i�.�:or�"�i"h�"mE�tr�^�c�Ua� 4e6�D!�)P$FC (EDP-eU�ADb��@D�&!a2�9 � employ- EDP �BDSW96}� ed xCalderbank-Shor-Steane (CSS) co��),�"CSS�R ���c�es�pai�&%.b�"M(I�  Psi^L)}}�AB. :>c${A}+2� 0 B}}+\� ;j01 Bhf���q��� "����ta��istem B1i"a�s *eZO[ o�hand,6pb=2o� q}{# � he&dF��w?��~"fufailure�r�s��d��Kraus ors $F��!�{N� -F^2K �h��. �repet"I!8!l!��"��y�'*�2 s!�<y keep!-+I�� Z&�"4iI= &� se = �U Lt�& ^���&sub/i����!�&by6 a�ank�9 k pl!�-�.x� u��good �mXp� e�'� �!i�� � (cod �)�9��=+ S�!�5�large�Z . If;y�� ��� e up�'b� Rph*!F�a� M-}CSS S a2rT;��X+�4 �25s�(2�:R-g2Jk���7 �i+}"byq�!�9�])�XNe� �>)� T� nfir) ���&a�cv �&n�2�(,��q)�� �Z� Z�� S q�A��a9�'� Q��2�� �-� �I���� s"�'w! PTin ���l~ �allow� ! �����8��� is.�-)(a�2� �� � �$f($*�C�an1se� n�2g)�$FE�7 �bra F&��;1}q�KZx 7� b:��^ comb�k!)���<�M ���5b!�^�S.h} v >&D��s�9�ev"&De��]* %. �p@%e+uxc�,�toM�7 nX !�� >.P f��n)A� well�t��:�������t�^� J �@oEA�N2M���_I�s6�. :�� ���&�is��)Is�Wv %�"�*�X9�YN�� BTBLR04, YL$p_{L�:u}^{(l)LL=�wrm Bit�6 rm P� Fil�)a��m)��1pfacuE$l^{th}$=A� �3�$�LZA�a$L�DdO I=arbitrUbc�1gu� �(nI� <R !: 92\oi��'A!!��;preqQ $l-1$I. Fur� m�ol�u-["�vac{ $X=msVn2�}&H{s}B�P!$67��&�%<s!:Ž6h�"ac�}xhV�$1^{st} �a7$s-�A��c�%l*A Azuma6,G�Ic u A67}E6$,�ˡ�se���$-^\Aarrow:; � expot$͚9��r$!��)�)�,�%/.o�?A� . %5THEOREM:� $Cpz �.E+C' fil.\geqsl & ph.$ W3 n $C�bita� \nu)[E phE6rel�}F �%ly� � .TV$e_{bit/>n!.%IO}�/.�� n�^C$�� /��I�.} ��T asiz��� ? Jp�-�)NM n{ �e`#\!1./"y%>@c\"�i^�'=*�!�-u�8�we��Sow�$I o�6�xa"#Y�uC��a��Mم^p"� B�J�Y@:� M��2zx��5�2r�I� *�#� (~1�W =�G2 "R$  ree-)K2�&� "�=2.�$�F �ss k� '.=trJ�.�naliry!�s $�!AB�black �K)� . �t fig2�CFCK&1�"�>p�.y�CeoM g � !�YqHa�r9+o�yM s. Wzd8.u?e:eD� aln� �F/)�� ^ f�1��$/hiQ�old4;� 66 ��<�)for�@.�,toMify>@e" ``trash''-�at[�s19hd.�D+!W6n�,, in� �4c�ab��5�:�saf�(�9��`&2�eҡix0� ��r, say�$�>4A�9F2� ��Fno:y2|tV2W)V, O(Tc%� tegy!�)$(p�{�>�)A�,W��v�)�kX!�:')vn*n6[> $\rho)���b!y� )R �{E!\��2Q uG�!l,.� 3qxas� "�=Tr}�h[^�]d^�Wbi �?$&m=+,-}�%��%1,m}})c�IgC �fs!Jg m',-h+-�f����],iYFD�T2Rm}E�.��i��b��%�ap �_ ra�:q��)ym�U,totр�<��I�U, ed� &o �., ��iD!� nt&7 �Of�.(un& ) �afbK$]�Ygfinu =I'f}Bf,! !� $fE�.1d1S�"6mamJ�J)6�;)r! $Ei�B~_��2b� {\! "l"I,F�1�"b�R=1) !-�!=�A;!S5=t tedi�8d:>���e�s\Pm�aj1636 e�q$� �J�:��LFg�E�6b�:e�Xa\-!cden�D)�e��d�2 1)2� [ ![:�A�A�Ő.�bra -�YhJ����)ge2<1+�<)�2@�|)ge{���$� }i�C���� a muQ�%� S  betw���&.patternmIZ� aj� NX\n� - J�I�2e:�h�%�Ppro��to.em[^c abf��AN2�viag/2�\2$U�:u�($u'(�q2�eҢ��$y&g(x'-"�,6�_$ft(3-2 x+\�6-6 2}x+4x^2�)�c"�T� n $x�%@}+y T � ph �NJ!%9/9"�>":x6� 2)}+!= �A..�$>"&0$�VX"�N2)}Mb�<� Inf}[m]_0^2)qa0Ŷa[me1}�A/ �f.8Dd key��i/�!2ydinŮ=2�es�2�8�? ?j��z^andm��a�:2f�?�D3i�+*} 6� ��e�@�Z�|� �]n hash3M$", L01}E�b`�m29 $R_~!}E�atyto�:ly&8�O+=1-H(X 7,Z )$ � ��N'��h^ tropJm�9!�.B�%#solG�up^� "vup��M�M�@1)}\sim 9.68\%$ (^ �>�r�D&� &�GKS05}U��``�%�$ing''�36�2 � 2.71� ,$x�2.747$Ya,&`� )�"� J$jm�!iI�Eqt.�HIz!"�"�5wYsua� simu� � N�HM4nYq� ��6�1 evol�~Š�(1-�>4p}{3����2:+.%(N�"/2)22@l I�6�![:�| =4p/(3+4p����h�Tliz!�& �D*�F"}&Ag-�M�p!� 8.04A < 2.0A�6�5� le!:Ev!�-�D&�@6Z#�e2n 16.5n�n&� +.�� aF ��!" $R$ �DA1decoy-� KLMv>P �s�"to$� m~ ecJ�;Y��or�^6 dea]Ue lower6�"fy?oM8��--=�2s2F"fO3\xiE� �J#yc3"Q6�EKA�"U0m�)�P^a�c�al}&W�#2� %&A�,2� 1�isn o���H(��|��)�PA$R=-PB!Z}h(�)� �2}1B�a�5Je$�U�)��, IY�/$.�m�5�� " I)� 2Uek�H!�9�E��vאBD2 D}ek@+��C3���$Qa *�<si>3N!� 6��Wo�*aCorm&�b�9�:.�-��3a�9*�#BI*9��c � ~HE�R)�weFJv��Y!3!�f: P.�/��!m�� B�R)��H2�����si7A�$11.2�:� � 5.60�$2.373Ep 0.78�� A4�&�"��9.49\%|�%4.4����1.8�T 1 0.59 #.�)AR�7 $19.���)2ib�P�onvc�� B98, .�-Q p�Cex�����%"HC��%� ��gQg �= ed Q Uur!C&Fes"%C�:�nh(xx only�H�e�Sc�+� s?f)~E5AH�A�`�*L ��l�>t\ J.-C. Boileau, J. Batuw3 dawe@]Ko EVF�ngM help,&�� n�_&�[$BB84} C.H.2tQG."wQ,)P� e`"�IEEE I�n�al�W�2on"�W s, SX-�.d Sig,N�T}, 175 (�Qa�\bY_M�.D�QyeF%�L�Z��g S�c�#bf 1109�#itBz_}, 343s096). H.-K. Lo%YH.!\Ch!� SV$283}, 2050999 Inamori,�_L$\dd�m�$u}}$tkenha�� �k[__107017.=��  P. W. �/i�,J. Preskill,Z�V85}, 44�V02M�Z}�Gottes�_�Z�e6�2��T>�Y�YE, VolOW44}, No. 5, 325RW.�GKS N. GY,A�Ribordy,! TQ�l) H. Zb��n,�WMod�\A� bf 7p14 i22i�R_YTZ��T.�I , B.C. SaQUsr� 1330�6�} } &�X�aAci:�A/9 �Z��X�u?j��B�m68��121��26/T) K.�]E#�A�$6�s032316-2��4C�s�n). DiV�nz) A. Smol!�A�W.K. Wo��:z z5a� 3824ܡ�.�SSE2R.*85X.e=�.U 1098 Ue�M. m5,��.VSoc�A ndon<45A\255)n66 �*}�S.�5E:$R. Laflamm�!$Rena�.�\4} 04A4%�52��(K.z&, T* 2o}$huku�aJ��19} 357!672O�}�).V)"*  KDE3^psi_{K�5*.D>=6A}.D(Big(F^{-K}_�6J�wCn28E)�V�Z � $.j&P. FR�� 2&21 &�2 GE".;!^22_:��:W�Py P)^%V��!w1�2�9Y� _u%�1}FPY-}�E_{E7B��(f�!5k uxC8K$!' �)J��F{2})�[ u_x})��0H0IMnFI�A  B}+jF�G"�8>F1F\�+*"��$J � {}- )��17$B�!���65B3} n poa|��'C A �+C'fil}- ph!Q8vec{c^{*}}A_{L} }^{T}="�-=&8$!$La $8\�G8�irx� eN&Y�� $ R$&"r-pS3J@(*�01*��� 4� 2, 8# 12����ranciar � B. [9,2� >}5�o5.��&� X� )&K� � :��N9��230504��9 B98� Brusf� �301��8�end{t~�g_V>�gt"�g�gv�g�intB&s,super�Nptadd#V�g*�g\&�g{d�g}2bmabZ�fSqueecaa�8~Na m� -wave gapN iton.�fRay-Kua�feh.�fNo� ar%� ics �f��nd ARC of Excell'�M� -Atom Opt�f Rese/ Schoo/^!�7Vp)*�f,v$Au�"lian N` al*�f, Canbervk ACT 0200,4:�gD;,t1"P�g��"�o��go-�al6��Chiao-T�&g, H'| hu 3�Taiwan!�=S{Elena� $Ostrovskay>��|�|�|1| � Yuri�oKiv4::�������F�(inchieh Lai:����a"�iW~*udy� um srS.G�a Bose-E�C7(�}s�-loa�=wIaYdim�%� o�alE+��.wBca+&K�`� heor|� �noise�of2�,�dP d du�Dtheir�u� ���nced � aredthe atomk,o�B �la� -fred-se du�intra- -�'u}naB�mlN �''Bragg sc��!�0eriodic poten5.AQ:�&n���\ac�{>�dynam�l�y�>s`,�D�wA$r�c� enta�b�H. >�g\��g875.Lm, 42.50.Dv�&�g%I"!N��(new)D&p�`�gdecad� %�c�S��IE[QQ9�&of=�A-8iclCG s en�!��eBe>eNTD)�nE_inXE�gX8 ew}.�� 1r�z�}�M�8xal�G�=�shot- clev�referA�`hGger��tyY�I �.�n5�ng �al1lE'�5b@Q'W�X.�e%G& ligh /qaferryaaeci�m*R?6�.%&6"�%n-spread�col�ive exc�ko]}�qQ�^v�w�#:�ov�d�ar med�v�<KbbCcandi�n�&exa`A��A�)�9�and6mm�Q�mm[�}�]�JQ9 It�$`h`gn�� 'wes _prl�at[%l method�6�j�dAdop;f6E�, uldE �F�R$ bosonic fl��J�� aklyIa�ng ul�oOtom��n.(BEConseque�J,�eA2a�a g�I deXj� n�I2nc��l��Y|�vm�y%����nhc�:�`apsc(HZob_et99,Kon_Sal02,� rA�ic �packets~imdm-? curr�techn!+�6�ge�_%�v�erIly0`` =cal'' n� f9�}. ProQ�i�r blem�,�.ly�-�#�W,6�l"f2!saI��jhigh-a!u�a�* �>*q��(�)V(� :V . Underst��n^n&��g)associaaa� �E"� C$raQa2�d issuDeso farŲ(d�f�Xor�oH�oA5f.�� ]x�fr��c�wEWve�umM9rupasov��^�uitude�y�^.\sha�#yn6?LOcouple-mdJl x,RK-fbg} sugg<} b�Q�ng"y�}ulp�wuT�ay��-b3ngm�)���Ovar paramHm� dra=K $m��*am�-&l�iis2tw� .fluXBat%�."6/�j5rl �,*r�!-<�j���Q�I��=@b'Ɓaurb��roachm�Lai89�B��;�]2��_}Vso�#�PGross-Pitaevskii (GP)7G yi>�:�.ڟ$ap �,!`*�#hk !��:1)�rɳ�!C���. F.�D!�".52�� E_st�<2� >�8 BV favor2environā�g��ng* ��8�#�]B^(width=3.0in<@-1=@c ^ (Colc�� () Left: BanIZdia���^�zs (A|s� sh�"�Ke famil�/!(=]� : 1te!_4$V_0 = 4.0$. R : fileEE2IE/�x��chew&�s; $\mu��.91�&3.�/��$3.859G �!dtEPފ $a4b$o $c:I-�~]�fig_g\�1� -�TtGn��%(cigar-shapeI���2�Q!MGPyF!H.O !��u6��� },Q@e",�i\hbar\+.̥si}t�l/'L2/^2 %1x^2}+VU5(Psi+g_{1D}| |^2,ԛeq_GP�_�WPsi*�nL7:Ef����,eC, $ ~HE�a5D" .ήM� = V_0�c ^2(x�/��B��oY�����Isz B�; b� y;N��+)�Psi(t,x��(xW�xp (-iA�t)&Q\mu�F.�a�Qo�U ac�;lim�>-- \to a=������Ec�chaGer�Vc٦"% Q�.�&� lYiz%/!%2e�!JO occur�kgap�>� �"� )�6�0st- X2v}�(��) Pal,11$in6�`�%�/p�[c��A�, $P=\iE�4psi^2 dx$, vs.N�_6E deS>C2�varQ rI�[�<2aa� (a-c)], na!dbot�edgigapA�mu\�x \mu_A/]l�Z~�pr��!1�NB�``enveV''��x*  �� pu},B���I NLS}m%;�a4A Fe3 Phi( _0)B珕m&�y�u�� e�*�6-g1ngE�%'Ig${e�a slowly!�� f�� . T�Hse2�-!0}�ASe oscOZnge�F $A6���E!�1t9��!�,��-�)to.#�!�c2(�1� ��-�� !�N �l� �.�or� Schr{\"o}�er (NLS>? N � �(anomalous} .��AA����1 nerg�u�6 �Yp.�0��Zp 2.5p �IZp Time&u 1p ��"�  r�,D5,���.�(!�� l[!�-!�-!�9�(dot-da:*� NLS!�=( �! set:q��D.t�.2Eq.����)>X)st#ve��5�!��9q�(�ea�)2h i1�W� � 2� �h�)IreplacK `"�'En�6�F�M'2�DdfhatWki�2uL}"�A��%ach� !� ed�"B`ps�?m9,=-, ul$<_��B�G�5+e$ back![pagAen}�� Lai9 .w�.JJZ�E�.m���� -�"i �#�;^R 3��rag�Bj, k�76homodyn_Jt�\ on s e,p d^�a| �: $R(t�9\�i{min}[{�& var}XL�� _L(t)|)�!� (t)\� / �303 ]$, ͆!�innera��2���)�Eq�� @ �/oKU 0�'CTi�7fiBa�[�G�| [ �2&X��'% ^*_L2+ hC^\dn �&)dx, \] �w��Yʕ�� �Fd�Z8E?shift!Ò� =�D_0 e^{i\theta}/P$.a !J ]M�FK!E=��e"hd rmin ���n V I:�]�0�S�fE�. W�~$ |=n in- �RJ%�a�6>E\pi /2>h�-ofBN �N�6x�@OG(aM$e�!Y�"ŰJ^ o &^ p. N# &wE/d veMY ^^5�b�m2� �~w�c<al2>7��^E���tc�� ��v.�n "�2�reg0��� � .p��YxR im>d"� F�)4w&=�9<.>�zot���A�'��s�a (a-���n�:H ��#a�"�kr] InYrhaped''x�"��m�Gj�%Q}�be!t/anti-1�edA7�u � ed [6� � (a)]i�2>� �.�ze$.��G.� m�T6aa�-._��)a�#eb6� �N�#6/ .3A�� �� tJ/!I:7R'b,�6G ���:�. dtopc9^ɓ����t��/Freson�@%CE dC]��HM~u��)�Y/,�y2':�&.� n( "�}r~cd��i7hAYLn Vjd)]�YAi"��1-Iat�1)��� ���i8g�0�,T�:MK"�assԔ���a^�6 M�` �ց*��}!7�.�)l�vg�-��s�ji�i�.;a72Asy,!�onA��a�����,MS �-2umR levan8�T_%qaB�"ffi�Ft�9F V�5M�2%M5�&,j�'reJ iH�*�5m�� Friber�u��0!;F� L"�'ea.�.�5�.K&�,r`�th.Ei:5h%\mm� 7"Yk(, $k_i=k_j9 pm (2m+1)�Km�1,teger�S2� off-I%�5-ơ�RJ�)� thro���Tirc until)*oisVi�:[am�s�"W ��!NNop�=e e�e��* �h���A0-�BD"-.��A�} &�N-��"m� seem�3f��=5 �Uusel��])�s"�5J5�3� 6�� .�6pt���:e2/�9 4d m7!�0"i%P��Y^c�.!2s.&�+�c*�/q6okAKal\�K2����Sm�A�.�2i2�!�:iK0s�io.�$� Z#�(��o("�#4 &x �a�"� @%aF,l��6���non����� �A�m@2[/"!{.�oi�DH��/tomQ�T��by �]%U!��3og.&=nq*l��s:�s4e��n�d�?1�5 �p%dem}. Py8*K�>/*�B.w l.3!�.��&s(-li����b=Es > ph��!j b%�do�.reak-up�a�ZO2� H�1�Y]-��S ���kF5U=�16�0. �# b�"�*5v�jJa&W(i!,%�d��ou*) F!1lA6wA�s (*�*k = 2.5$);��9cur?:1l�k�2Q�=< $C_{12}[""%�6���e�2i!_b>�* Typ��`a�2X2XNwo.�!�&����-A�Z:'b���-C1 P�͋�7�*�$)J^l{kex؟w��eBF�-!�:)�. �abll���E�ZW�� <9�3����0%�)�E1.irX�n�7�Lmal��xu,`�e�&�!;(a� ����>�0bHRnt&��+"i=!Np]t�9 B$ed�r?to*2#CZ�"*��i,s�!(�0�?!-.�"� Ma-��!n�Uice�V\}=\{1,2��I ��$individual=. A^&8]s 1�-2yoA�s"72"�ce2�in-F, �)�. A�5M3>w�&!b1}(b)\. =�&�2EV�u�.l�ne�#vw4�tp�G&�2�A��q�W���02�behaviorQunJ5>byaq!�zO&o-�'!�U�I�qI12 {\cal{E6�D�x)$+EaB P�-ityY63�Ji\��j}��.� {d?*� }{dx}�^*� �.YLi} j}+3| |^2B j}+4^3 I).#UaA �,�$��p%Jail�q]4��s&m.xa� 1,2}*E?"Qto�8&Q45#$0vhis  } 4 &iQ=�^{!% out}ŕ =3.1�I 10^{-�I��!�2d-�%��Q�Wi�0A - 3.4bYi&Q��ET�e�fe[-�()B��&Eas_PN{�cA��M.�y- �p 2� Vsl�2Oc metr�=.��%v:)��x|Bc.b1}*.�Q� , e*�Ō8i��� d@��Zw&�!�-�%c�%��Y]�R�p*�6��+~U> o2�<�6E�um.��92��yof f.�rn=� -{'@$�.� .�3haI�vea����quJ+B� �ign���?`a!�Y.W.�ol.� c�f@��%��>�H9-Q��:#  �e&�!g1 � .��[jvF))wo� lik�EB�xcsicaIulBf�^v "�^b(�Z�i�+�#�� ��!Q 22@xA�s&"�1[ \BW.�p�J crystalv79W���2�?�*]KR�KCouncilEG�[(P. DrummondQW Bachd�G. KurizºP.uWame�us%Ҟ[Ch ,�J: P.D� � "ְ�Naw+}LN365�U07�S 93);�Leuchi�,N. Korolkova/Vit �$�E&* L News R1[6�N0);:�� Z��ce�dsATem"X#S� ing}BX, Be��n[RX(370 pp; H.AR�P[�J.�. B �6+�62"|V.�O.O 4132%68>Ob�rt�\sqrt:B� smallfrac�\mbox{$\/{#2}$>ohalf}{:{1}{2>%bra zlangl�|:�ke �|j\r(:#ip �E�V-braS2]{�14sch}{Schr\"odi�e:(hei}{Heisen�4:$ito}{It\^o:@str}{Stratonovich: (bl}{{\bigl(F7 r)}} %22dbd)S%� \partial} E�>Q5&}/ R1sq eleft[" \right]:�cu)\{.*\>�ro+(.*>"an)=� �5�64implies}{\Long�arrow:�tr[({\sf Tr}\sq �>�de!Tnabla:Cdu9m:strike b� 4vspace{-3.5ex}�:{� H\underline{\phantom/B�$tp}{^{\top>�tbt}[4A�eft( \b�A�� {cc}%^��2 v #3}&{#4} � ()O>| proj�a��aQ�k i��A�ѯ{ �A� : } \title{States for phase estima�� in quantum interferometry}% Force !)\ breaks with \\ %HERE %=�2@ % Personal Infor ��gBgL\author{Joshua Combe�email{J. @@griffith.edu.au}8H. $Wiseman}% 9H. F: \affili�`{Cent or Q-{PComputer Technology, ( For (tDynamics, School of Science, G �� University, Brisbane 4111, Queensland, Australia.} \dateA�daC �tBt$% Abstract�[B[ma `} Ramsey:�$ allows th2�ofi $\varphi$rot%� #Lc�fluct��>1 IaB"��v16 timiRfrequenc�<39!r`+w spectroscopic techniqu�(\keywords{Pi �$, 9�,�'��,��>� Use���)iM� if rz�@ %display desiredAfm� " ��N�B 4 Main Body % Si� I - The!� rodue��Fs n�$bel{Intro} s } A.�q� (SSS) �LKitagawa,Wineland1} ��}lb ve (�m)I��man�dividuali- suchŕ�2�^2$��le�| an unity.%0 valuɾ^2 = 1$��Q&tandard"limit,itX the G0it would haveAHalN �2i6��s were.��Vd orien� ��sam�@��: !-B (Crf� Vari��� s �suggesp��%XBzc� improv�>$ precision!�v Xm���devic��5�,1�}. In�tic���nre!S a reMR\M �  inZ� M_j}&a facZ �#@^2$, as verified 2�ly1Mey2�} WPexpMRKSIMW}. One may�� inedink)E!�pN�only on!Hat Gter�R}. H!we argu 6dits generality has been ov�(ressed. To��`��,A�we wish�u mc�a2Y)�� !�A�� V� # N around so�xi� �Bloch spA�, � %�nov or i&� aboutqE'�"� *� �sisk s best �a�is�93 preva(ly made in *�Berry�Breslin}9�dela�n is issuA�0 more detail,� aa newY� A� � we c�9�&� � inv��g� � ?xE�� / � chaer c5�CSS- f�h"Y .� pins s!/ roug�Zi�� eluci�%Yrel� betwA} concepts ��as.� ing, � �� * )�s� ���A�hMU= at g�m �2 ���X identi�-� ��.�wA��9!1$ical near-cum2c!�Esc�  was alsA�opoau A methodeSenginee�thv X��) for x6�\��. re �butՂ be exta�lyA ll�ga�Xeӥ�AG paperAzɺYf d a A� realEH � osal,Lpne%/J�-:j t�� :�inP&�A�s a���  (2ACT>m} (%� see � �-)�}) A��sults�4quite encouraga¡&�.� %ze �!�!�E�mđ�� a)trast!ENsi� ` ��% >Aur� r =�L �L�%�Sec.~II!��ewBe bZ .�e���ۅD�I�HaE�:Epura !Qis motiv1ou��*� ofj . In���)��w��$consider: 5� *, Yurk�I:y-�)>p, A%R�)&V;!e l!��e��%-ed �z�AfirAime=�V� i!�va�}�"{ a� A� eachu).:1��9��xzcanon��E�h babi[dibu� NRb[ 6[$x{y$)8$z$._ � F ` 2` phi,e`We em�e;trend�(ca��a�n acro 91), e �wH:{. W�r��eTV�a!#cus @2A_���I�e� �����U�2�ى.��=F="`I - S�S[�:+��>�"r�{\l�.p} <equival� �Z��#ach-Zeh� (MZ)>�&9 �ed at �c�2� 2� Ala�  c.�:eld: D A^put por MZ .5ere� 2�er trans�ae changRMninw arm ("9)y *s i�ten��? f�at�out�. I�$N$��aI "� i��"�K?um detec�!I� �*�$1/N$,�$H"�ɚ� Ho�% dBurnett}�y� �Ts%!�to P(SNR) � mpar� a no���3 (e.g.���a �� at%a!�,) of order $�N}$�n-9 ��of $1N}���. Z�� s� �7&/:%� of �  � } s� . e�*� a��m5�� , enP#A�is�Ae� (�ea.E�!\Jj-�&�O$ cipl� �� t aa�2 \sub >XP>�}�Xn�m} Cog a�&� �$two level !| �$J$�, w%�$N=2Jm��"4 oped"r� $J_i7l1/2)\sum _{k=1}^N\sigma_i^k$a�r� (\in\{x,y,z\atFo�" mA��%= Il ���pq �ivmof � chose�b��AE<ion. F� a�1� &N+}B� , leImea��"!5��aKin�@$\hat{\textbf{x}}*U , i.e. $t" \vec Jq =>:|(J_x %|$. A�teo��a �n��� � takes pla�caX a5�i2��na? axis,�թ. !� � ��q�� )�ing $J_z since �"�'M�assump!�} 9 y - = 5$2L|\sin{\v�}.�]0 If $M \gg 1$ �E~R �Ev!6c n�5! c� al��!� orem$uncertaint� �Gr�Tng=$�}Hr�$is $\Delta � =  J_y/(ɬM}\�%- J_y-/ �� U�  Eq. (X=I)u~!�9�is^�1} � p�frac{�}{5�J/v'|\cos 5�F�B!> !��!EmaA|��) occur�tn $c�� ized��a#,�� $| �|\ll 1A�Na�  :6 ct�O8 .���kj*A��cohpsi} .k_{\rm5} = |J,q�_{�%eeq��b�0goob�qA��mKion�Z��ALa�=theirA�n� aW+!�5n�! $�%$J,\mu}_k$ caP%'egi)0of�� k$ (�7 typiy $k=��$)� eigen� $\mu�[I�de� >_��pV�$ (SQL). So����0.�����'= in1n!a2SQL will!n�!d!M"K >�"A>e2l!�3:is 6�%� co%�8(J/2M)^{1/2}/J="_ M�i���SQLU �&S becom��'�׭4xire�xi = |i�Q�/:��}=i� 2 J}.� ��}�6iF�A�uK'a�� :�!4A� �!�,nd necessari2�!� angSasC Altho%��#ōsEeX!�qE�"(�<$ �� mult� 4($M\to\infty$)aXs$%�yZE$.�o&Q$ ��!���k , or�.��9 �!]kU#toJ�. "� E�R i�� is even s #at $J=N/xr teger.�nca��EZ� �#o�zi,5JiF e �l�$@? y�,"a 2},� M��Jyur} = M|sin\alphx/V. 2}|J,1�J_{y}+��$|J"�# ɏ>DC-.Deq|��$� \sim z{2/� achievA�a�z \to 0$.=a� �%�%!/in�ant��*x �Q\p�&�!�m !�ͱ�) gl� 6�&"f��im"'to� uish">}Qi6 ��� +�o EMy� �%��so-�ed.Aq�X 3},.o.0supEF0�A(22z}+|J,-�Cz})���NT�%�� ��Aa�WK 7 3es7�^�eisR"c=4�(a supePi*3 Fock k : $(�PN,0} +  0,N� $. La8ciGisQ�w�low|��5!��\. $O, N})$ ��{�qa�:��L1�,Huelg H:)��� �>F� $z$-^ �$2\pi/N$�,�6>�*g _ alread-� �遨a� ac�$O(1/N)$�2��) 8usefu� . %Not���eеJ���H-}. *;la� 2�P�͡�8~�*��%� } j *��y�e-� shif*P u�=�, %�j�AP}Ś ����is� 2�eat2h�,ņa"� .�or !h$K�n!0;6� !��-}:�(+�&ira "]! =M�4MilburnZhang},e i*E ,smbdtpegg1})6&�+�$ ariez+]�T�ed (a�)a iu9 �.)�A�03%����%�n� g1":�{d��i�4GardinerCiracZ�r}. E��Aoutt%$power (eff �lya��:aI.�,:`� per��� most �an1�.� (� nyiK)� be �/by)� adaptive}b)onUpins (or �a)a2, , .B"gMXg c"O=� s1 X6A95,6IR�olves�o%A�s�� oz"u�sbS�U #� |J�+�0= (2J + 1)^{-0 m\mu=-J}^ $J}e^{-i\mu�"  n_z�nd&! � �"K�1 (POM)�2"��� ��8� POM�4�8 {E}(�)d &=& � 2J+�7\p� �"�|6\\ &=& 5! _��': (i(\mu-\mu')G>d< e 5( � Provid� �$�"a4*%,)-][i�M���� all}I( � 0A=I&)`�N� 2�z$ ���&a�m�3Holevok!�� �.��)�E�&phi}$)���;� �� a�%ve �& ��e_#��"�,. A�� �2m ��/k>t)$x2H!5POM�A{)���f1E�$��&�&��[-�&�, viaY��-Q� prob�a�P]�=Mr�|e^{+i^  J_z}u$i�x 2 e U� z �!�n� is) ble�cyclic � bl#. �22��� terml sharpness�8.�1} *=� +} Se�� e^a� �-!�)l;= \int �1IJ/�7�Rsu� = � J} {}_q� J, \mu+1.^ .�� ���5� As lo+s m&\� R v� $S'�$!o5 v�2d-�always*1. U&�3%�T&2�M�/E� �1 odic� of +I�I�'i�. a� cl�1Da q 6]">,�+saIr��R IMnce��$m^"!�_�:i_0��p +��1�^2)�$, A�%�(5x�'e�|a�q V�$eq 2(1-S),� -�� r%�K�!V peak!,�. (Ano��5ua\Yid�"$S�>�c.m ,} $S^{-2}-1$(s our�%sMs(ra�q� ity �� S$.) Noo%at� (&�_J��*n �Bew �Aof(&, )cp�6to"� 7 V�%EBN� : �g.jA# �,  = 4J%�B�Simila"���j"X �fore;L$���1� radilMysk�It./�b sked�yE�� 5�[� r�$t!A0:>�A�^�p� �grc��/ F *#reason*�%H)�*�`. &zetap})aC� Mca�leg�E����!� V ex0,%,>cu�.� MProps}�  two exp�.7�!GlB�$1�\i�vA�6Rs. ��3N�3S on III �3S� �%f%`}�/ob"!s�2 ofm\"x%�An shorA� ming�}<)&�%?Dr� �8X'six t"g/�cM#\e2"G .�2�^ �-*� (E ��� <s�), pl�9�8��a0*E� e be�~���#I 2,�', %/#�)-< )+'�!Y2*��6+. All!X/ �.� m g&1)as�L B !2�9C!0,\pi�%a�Xu�9Q�� % o ��6Q%��-6�sM=`  ing':6� y2� a�?�*�B$xamq3�)all��3 H!2)j!��-sa*J >a&^* �AA��Dcles;R >*;- .j;;r� � ri<+L*|#O��X)ed4&. �)9Q\"�f��<�0ly͑6% %I"��GaB�= ,a� BkM lopt� .� �Xopt�ou1KG�G J+1}&C =� 2J}/�C[ 3J +1)��2}\�D]2 3 {zH2j2=a�5R�~id} So fa&�0� ��cer�5�"h o�+�5�.6of�earli�T7ţ"2toA.rti{B�%>%G� �$IOo�& acco��1Af&d�2?t?1 [1] *?B:  H��%�hhbar \gamma (J_yJ_z+J_zJ_y):�" �$ -� ��-+iZ�a�h (A2a.��:��6 V8S'by �%9 [7]G�t�bk@�."�B�? P2acth} U(\nu) =\exp Q�nu 0( J_+^2-J_-^2I� )/8 ]Bh !$\nu=4)' t$ ��a d4( (we\* $ ra t�:� in !�6 void� fu I\!z$i2UF�I��8ndX!\pm =m  iJ��B rais�.+l� ��at�'�y 6�|&-"0@�vis2�/4s��SRI�Iɉ��rZFn'�@k 2�8F�J&. Xill��"�:��aqK| ({\nu})}=Mdi2P } A�a��G�E*��" E \nu Ess�T!3�how*% Fig.~�fig1}�denn�for� Z a*4�M�sss���}se� ket{�A��M6oE�� the�6e�:����2cC3�28:Dis phen�B�R7h%�� �2� �ohd�>keN9kp%kWIEFIV2H] --pb-p!-I a:>" ->#E�!!N�I�E E:�)��!�(� eX.�� �W ~�9A� II!� erk%�/X(��he��B ��, typeC y�I- plot�E�%i:�2}.?aF�*�;) �e9��?� ,$\log_2(N)/N�$AndreLukinNm�SGADMeM find"=4d�d&H.25.dA� 2�2}��;q�%�appear� ��X#eAqa�( . !�!!�,large $N$, a\%AE!�law(!UEer�?��I\2��Oae��&!Z!�C next| b�s d�t�"?e�um�xA��2xed �nd�c�"yɜ)|do.�)co$9 , weE�� %�4� I�M�"� A aN<cal�27qLR[ ��R� !���2-�� fro�+�-�t)�"z<l�*6 inH#/@[po�J�@ �'m}[!h] \�T`{file=n20xipxiefnt.eps,heQ4=5cm,width=7cm�@6on{&. 5�(solid ,)*I8 (dashe %�q�A!z%� �-J"�t1A� ime�42& )�B�_ax�1�. "� *B ._0 20$.���;}� - B0 p-pT.;minmufnn�7A�1!� �� �$)'4p !� � ! ��I�:[nd>�.�=�9]�*oA�=�T���nd=&��>�*�FV ��:�k>k\E@ dMus8.��4�ing max5� } B �!��"��n?cEE��R>vieHe}`;ofA�*$"%2}e1ax  b� . St�ng"� *3&�A�&�/�19/�  \g�,an{J_z}^2/4 �&�no�p�Z"-2J_y� B\leq J&we getj2� "jX�/l 7J_xD�z�^2}{4J^2F��6 titu�� rC��,�F� -��,e�%��ft(2�x,B�� ) *N}� J.+ Sf�01}{N},�k�} i��  Tim�l�(a�B�8(H{.T ofQrs98 upper 2�"M~. &�&S\o ren�4�oM\o l� So Mo}A�du�>ai1#BonJ���3Fw�T2 $IZx� $e absoluteմF�� s.gx�)m$arrow 0$, �Fn�7lA�>a!5B of# �e}l� is� %� =(1+N/2�"} /�+^2 *W+ 2/N.� �,g_+�,akE400�$N�+�-q ��-��us %>�&.-AR� 3}. Re� i�){:u e=1nO�6l-eF�� %2, N�#} �*f HD%�&F.��wo�@,rQ  (I�as r"ioEbGJar� �yF� �����"5 )Y [ �&� 0� !-�m V@ $N < 5$�2�:O !�� �(EI antl�C�a * �W: &J@�d E�x04��S�"thA  .J� ���^� xielog���"� MA$, �� !:�: d� � !$+' $,  JR(%(&E R'sss'�$+$� t�/ }$ (�XK��0D.e�- � �isS>.#"� fig3# 9^n. .,.�-(��6to2����asy2��a$6�$�,e��lVYyE-� 6)g7 a&E#��?�0.)B�(��q�; mpspd} St7M7�( ���N"�Seq�9uyI��#s j�Vt2N�axpslj} �{�$�?NF<�k�?iso[9 �2A&6I&�]e�Ol>��&�; $ regime,Py/Jq"� 4?9 =�1��>��57 !q� y =2 {J}/�` $ so� I89>D$->exp*� ""9�$�}�x| & �&"�: &{J_y}/{Ja |\\&� 711 + iI< {J}- M)} Z }{� �\\ N 1 -1/4J"F إY �aT��BpG4m��hub ps��Vb6"( �)=1�W .� ! +\u�� 4}. &� u�%��.jA�E�6@ doesŪexactly � lg3 --- [Y*ticeablyi�Z2n���Q&97\Nn�8t�%mN$asymptouo 1 (���)���:��r �siS �ear[&� !Z�!��0 $\rho$, it fi?> > 1� mixtur�66�I!�-� < 1.�:>o(�#dBL3<c!B(T)��hzF�3�(  (1FJ!��2�.-�$J&+s:�$ BwayM <�&E;:< F�, *O`+�3(0� �=.�wi�0&l2�pU ��3,j�U�drop �!1t�!�� % until� > 5UKq�� �J6(FA�ev�VOfb` Ѳ:C�%N. BoO#&2�Mm���T� �,��yA��'5FE"a�Y���U�$�-in�Fm%��E the *m U� = 2NŅ%��*M# �i Uy �(�1rue� �+Ac�6� �r symm�b*17�F)�i�da$�8 "�+�(| zero��A��%aches'5��b]!�G!� -SSS�b:8 plaiu ��"E� �E!?ro p�o ��J�q �q �  �a%2>� � }$, �� $\bulletZ� !�}}$c��   inset\ is a@upM�&Y)����!h*�/< �A�toB> .� 4  V F ��#} 2�a�>V&�q��&n+i� sp�8:F.k& -2��g$m6�9> su0 . To�,(bsd �������� &�,��c$second row�2*0��=��<1�we �5�9u"�ae:*Z�i�P6 � cN�I�56٨�a_:,ny surprisesT \'T$broad, cor�+ons)��V �me���� 6� �a m�\ �!P.as"Y M thir�RFNV Nn�qOA�hF�. but %Aso.*� eS lob� nd ah N�D!�s^Zng Xve�/ `lx'08bA'8�/&��7.�,�:y+� "� a�� Dn3E..�0~  *�2Gsw�8��uBr��1imodal!�� hgcl&9� e�"^*�Gmodul��pi$. t9 B� &unt�Vd1���is2� (8A��:% >�> I.)6mak5E� infer�6M�:;�&��B���/i�a�> monsQned �YpN�"Od�.�1 � A�wL�2A�e����~ 1"a�ex loA�)�a�N2!� �1�K2v>� .��- Co&|e } Ag�;>� )u\ bott uerA3W� .} ${}_xk\mu.�)"{}_ Sg JLn#��p -eV��FV� ��%m�! �DJ_by!8ov�^8-z_�(n�DE�H2���4. �GiAuc�@�+<T( ds (�+�s)!c.^AVe� c�<QgLas itrately_L/�7.GEq>�Au"9?�u� 7, 4mu -6$. Mov� � TI[� develops) \2 � � furt�h :� �J�s�O N��-retchC!" mu=+�OI� �EE|&g}8 ��-f=X !�-��e�E�(�pm m�F i��fit ob�_� �E,�\ZQ!~5�hg0$E�` "&-2�A�%��� $ odba� $y$22)���%�er&�!67��p:aY"�:~ ic GapXan-��2 �I��a�"6Kit�3^ 5N 1, =0$.�� �=��$anomalo�Cb%�a 2��h"�Ca�F�tNQ%]A2#)�)Isa��W!� J�A��y�J4>dost $x$ "�*,!H��a��6 efer6e�. ����A#7[G2E�9rt�Z5A���E}2�QA�ep��Dgi-�6E�a �,(�s_fa�09 QQ>�) op��o"�L�i=B4e�b� !QHL�G%6��!�>�Q�W er���%"N*4*L^nti�Ming��6m)FG2e� (inusoidal [�Cb �0]P�V� Oit�7 flaty2� �\-:2�w�\��:dof �4E3s�4�R:: e��s"me "s�56P���2�H E�OY�f���N��tKLA�od�.:]a�ѵe curvyz�2�nMd> up. HnLe.�� �:U�5J�e�%2�6��ݱ.&s" {: ^�fiH 7y!� \�"�A|i ^ (top� )"0F )�:sU�� mpG :@J� Aer,"� :=�s|i&U6ga2<\.�F~A�$e advantag � ��!��- ies�&C ��?$a dramatic�� �}al��e^: >\p%h�p AaJ�`_6thw�"$D` �>�us[lEu�+H �or ��VI=�6� & llyba}�/Pw�0rfn} 6+q = �STr}[\rho�2�7]z`J2tiqw" [-K2, ]� 0, � )�� ,deltaeq*nU2~��@�DEJ}Z&E}222�2"Af%@|B%%���ay�zrs�%Z_{r,s6h&=&V\so64�}{2j+1v6lq6j} !2l�&8j,l,r,(s-r)|j,s� \nl{\t�%vY_{l,s-r6x� ��Zv[$, �m,Clebsch-Gord�Y.. nd $VuE�amI�Gk� harm�c"�8. We�i0:O �YJA l-areaa�OJon (de�N by Euclid�:co-�6]5 m8oWE�$)e�Bg�&>|{ Wig32}4tx,piM"]SDd���a"M!r c2@- � ��v<rueZ2* $P(x;o� wi $p}f&9gh��� u � VmR{~B-1}^1 d(3!% ) W(t"�d sh�^q�qR�>�5aYmUmtu!U �B� t �w�sj *f*:��J~!H��*�D��a� q P_$ � p}pto�zt_R d�E W 8�E1hi(:�*�'$:F#u>q�F�a�rf{�s}. B2� fu ezF| !_ Hilbert s .y$x$-$p�se), n�I&A�or�~�0$�ta��F$"Rz�&E_�.j ve�a2)��X[B�� �U^*does j�D�i0 hase2�."�G-_6�R� e� �����! nt %ra�zly"��s�@ard��}!�oPc�� ��W �2E� �@��� s�Q2  $zY��$e�'.mg :G �)@ x% 6� upGx�-j 2� 0�*y .� disr"[� ��pm  *K8nd"[[ h�>!R�%:A@a6kT �T}_zIS!�im6ad�4P}� rippl� M6"�i�)�4er��S!Ep�v"d nega�6� E��"}|6�pw2�g=�3><phM_�,=ti-+'N_�1�? w��Y�,H��!~�k. |N� �>�con$+�N�).�au�.����2�,�!a�{* shap� 9��J&�*�CFnCF8V - lisdexic DiGion�)3f)3d�}}Q �� /�t.��%3$�/��z;82�P%z`ly.�t�y�>aY]i�TJ��mkpd�jr�0�k*>u "B�30w&C/:�FY�y&�$�=�'ely_�JID�=%Ce]%H "� 2�s (�7�)qb� mplyA��1�n �18�!Ms� st.84>�VJ{sw�0!P!".�7�&`:x� Bx�uB 2�7Œ���Հ� %22el�Y9/�b 6a@1���&�"t( globd%l�v �s�rJvR a�*etZ� sal�.�}g�a!�a Sl#ar.�8 expHSSP,�oKMB, *F' yb far,*: e gr7�st deg/yO��%E�)9- obser>^�@��DUN+ 6�(nd feedback �$GerStoMab01�a�V�s$; �6s.�0ThoManWis02a, b?;po�Sq�;J:b�>�-�q7 ive 1k]b*2X a�b�9a$usa�X�m�lK,�bas�n!�QND)�.d#�lE� �AŖ�$���U�%�-��5�@�r$NLh �� mode�M� D��($1 >�6 7/N/ !.o+is �n".#%Ebi"U�l��!  easieWP �:�:( ^ *�$f>" 3 ��q�[�,er am!��� �|enpOs mo+!�nS*�yQ)��"�+�kTDowY*$,Fiurasek}IaOre/#l~ m&�[AArۄ"�IS��k�. W!�w� Ed2"�toF``!� mash6K' �AM4(postselected).�0photons. Spec�4%�!�COpolar�xeA6� :�k�be rol ;%��)x C8ced�xJ��"beI�zRyoF!3�e�F+Zas.@ �d61>8. A+�es�#9Z��3y o $N=3$ ��X��"�!#$IhU(K �al*�it�� �by:�% e reL a!?+fu�.. "�2��T$N>-�g �\2xt"<���.J#1,.Br�~ it !athe~T"`@!��]2� �=c�&/#� sub��9��q�6acO ledga�s{�Dw�y�Hk A. uF ��D. PeggE�|nK|is�#keJPor!�1e A���search C�i3WA�S��of &ݍҍnewpag"�wi�%xt!��{� B5�4�$K@�� , % Label Row�3 yA��}{0.05 p�A} ~~~~�<$N518.5 C��*�;.7ed ���@S SM��?i�7 �?>���%���6.�>�>�J�182.B�ZP]fs[E=%, D ]�coh.pÑnd~��uuoptu�5�vvsqu�v�vj0yRv�>��\-��supu:��yCM�����4Yl}&2.>���j�phaA�e����phaA�v�����qu�w�wA�R�����up x��X��6�"�+>�+>���j�"&xR�vjvopt t����Is�w�wj0yweirdZz��n�� x��Y��:��.����y���� t�����w�wQ�Zz���� x��Z��:�f�/2�1>��sjs��z���� t�����w�wQ�Zz���� x:�p\c�Q�1i"T9�fi�rE�s&>G6��0�5���4קs;DF�]P�6�8JCTJrom<-�aj6*c; U.f-b�8T *�XF*�7* T yurk�X�� �$<A66�-si1_�+�n�9!;�GPt*�>�tuTo�Ote<� �+;�nzo'l �B�:!�.�V"O;�&� e�"p  $�%,i�&whi˜�,tFi6B��2T.*�M�)2�_�\E&%,30��0"8"8ji����F fig0U="8n&W"q��� %� Bi&��cBcQ@`� epj�$_howard_v2:�doc�o} ?�>[�prlL�œ kU�� �)ptaddgP� font ��,"��*_�R[� 2sub1�%�cܪ��1]{|#1*+_H.��ra}!+#1|F"F2�a-% #2 H:0 Tr}{0{Tr�Si91 \q�{Non-hn GegQ'5�duaSpa� Ev�P�*$in a Neutr�ga�Bp�2c�AN�n�R Չ {\"{O}}st4 ichi�sn U*� a}}ten,�Sdi��Plee 2, A-1020 Vienna,�ia�*դInLaue Lʋv�3�Bo\^ite Postale 156, F-38042 Grenoble Cedex 9, FrW=\uthor�fax[lipJJ_l{sM�,pp@ati.ac.at1��������,Yuji Hasegaw!r ����)�,Rudolf Loidl:��Z(Helmut Rauc֫�����.�a"���.�4a split-beam nm�M q�a�&��� ��3�g��;t�4t��YC��Z%d� �1:�� subjaf D-d�se�:,s* pannw�Z"W path3�.��n*eB�� [�>r�y d by��CE�?�Prk�. AX��6bre p��ou��byu \X�{�� [���A ��5` 2486��]!J[�7 A)z}4-�|:�$ % pret�2D d' �, nam�(�d��Vo>L8 p�$Irk,5�,�met�L,re criticism5 Wagh6� �~� 1715�9)]� ex*� 913Yp}y manifes>sc#Dct].,5N�j��.�by�n� �%xpl�s cal���I�n�� hu I��heL*-Z2e.� y� \�H{03.75.Dg, 03.65.Vf.I�61.12.Ldgd��5�I�;V�*�.E�RM�"�by Pan�+ tnam�p56}�he 1950/,vaV|"."!k\�z1 workE"%�N>m�v��,oE�ĉ@�Dn]n|�P�in 1984 �bG�84D"F�aTF� �adiab&7U�!�&S}me&��� � ch trigge�� rene �� )i�-picE�>\�� retur�&to < 1i��ύ�! add�q" fm��nn�"|9%O����+)?& �Q1�r�G%�tP�Fug�3�-`]&b �N@wilczek-zee84,ahae/ v-anX�0n87,samuel-bhPri88,mukunda-simon93,�95,a�8ni-pistolesi00}9p�"%ns�,�%-�cP" �3 �uhlX�486,sjoqvist00,n -3�2ZGLes�;ore�%E�numer��.�t�!�" ��>� u�+5B type�F (]T�� s, e.~g. /$ed.# �5 Dta-chiao86} or NMR �du�IY),Z�y��3bliIb�/sR"�tYuit�/too�Istudy�'i��i�.� q(�r�00, 2,� 03}�vi�I�|�Vd"�F^" �bi� -dub�g$87, wagh98�aeJ 96 01}�facili��ng &C�ie�a4E004}a�.�eia"�*�S�A�u�no���<ino35�&� �6�%/-��:Q�emerg�RofF�;[TQ0�rnA�QA�n� $(5͋�7- �<l�1u@ � y. OW�6su33F� %ݡ"" �<le }g&�����sa�al iA6AM� )�} H$e=]P�%fu�'%estZ&I<V valu��edi�'��theory"�+�U(s an ambigu�T���te* e+*-+b�nghM|Ej9}�� �!�6k-6setup�ɩ pick�+ p byM �$dur�)ts���erk a U(1) A��z�!v. �dyn?�1��CEW�/z!�9sna�&M&T 2`7 . �;� p�� ]$ (& )E--��05ap�d�?M>|Bept<�devr�% ;I�-+oY11?� }% %�� s�Osurfac�v a en�-q�}#s!_�i�I�2@i(/*�9��I�0UR(mm��*J, ��fir,1valid�Bf�ur!(�{�ƁeFre�|z�� )�&m �3 F�3�r[htbp]�!�� V�$(80mm]{2004-��-prl-f1}6�E��e �� util�0a double-loop��ect-cry�Q� �"�: �u2i�mo!�I&� pu�+oq:"w+J (PS2�getZK��\�am ʟnu s(A)�/Za.� �| 'H�H� G djus� IaS!�Mɉ2�1).%1�ZQJ-� �J� -v*�:�aUz2f>�(cf|Og.�}V�)A����� d�4(un_ed)5�% &�U>E#q8A"BS1!�o��ef�.>E_{r}^0}�:a  �m� F*t(+0��^Qr'U@� =�A 9�g\)�$\eta$a�� x. ,1�PS1�B��%*5!dz�a�!���.�V� \%1v �{p}$ b�N=R3-� D.iGeL�`sm�u $P_p:eO�p}$V�Qp�&$Behind BS3Hr�\6 orthog�)0�� ^\perWdaG.� 2? �@}$6u � �inF*Nx!.6A I�E�,:;QHaQ:a 50:506|-q�!�EcE��qE��po��on �� �[c�w-I� Y5-2�j \maps�A�q}M.@� p} +n�tA)"�)ea,��0~�pexA!q Xf bra{q}=(1��pM5-�>x1p})/2$ (!�g$P_{q2 = 1 - P_q��� < $"A�)��2�dRead�/!�A��7)�n<a*� �to�Q e*[I4YŊIp��er��a� q�,s (BS4, BS5 !BS6�y"� (A)�����.FK $T����i��L K 2!z $�c\chi_#j{l(Mt-q- Oz1 2}$ 19z�%_;}�6$YlT, yd�aء��io ne-{t}A�ThdP!�9n&6>s� B�c_�wr�n�I�#e"�G �eq:^�{Ae�eI & \x!a{C�BS3}}&Df n\s�H2}}mc-4+N7�JFA}p �f"GJE]T}MCe &JTPS2}}'I2R5�1 G� ]!2 !})2%!�\��"#ena�� �e��� q : =��|;hn�:���eta ��=Z �"�=~?N�*eA��C,Fa���$��� �y Q�&^E.� step #�!bi�]:7Gmr��b�`at�-�5N �5forz � � $or D$_O$�i�!coO%� q;2J� �2`� .� E�q��}>& ��;l�to��% !�$:afb1.� ' eq: �ioe� ɑE{t}^\p�9}&ɮ&�_}}=K.+J~qY�m�J�� No+���� } =K-.,�-"�wp $Kɐ$�@��tan\7�!�ӫ$I"��dQ)&or $D_OL,� t� moduS�squ���2�.�t�+ 6��=$:v���I&dJ&l�|%T�r|^��"<� |> \�j��" 6UG44�(\\ && + 2 |6GrQ�jG| �D( �� -\PhiKno��j�  $I� \arg^�Fk �t^xp��=5E"ۥ2X)AZ�lA���3� Ph.��e!Yn2s� ��u���RQ)'(.�N$\�).� ɑ�`M _1+  ~-�arctan\�[\ 1v�m2�b+ !1-�}{1�;*�]�L6�i�^)�h _2 - �1$. By�ya�g�>an � ��PhL�� m�"��p�r�K�ZE��7u � q�� �nev�,< ce w"�<ţ%� |i �q:Pd =N F�)H� �t  b�Ccen<ween two�hptasu�Yi�P�.z ric ma��>�`eY$"٠*�t'�r"*�FG�"b 1�B� m �l <�F`�_g��1a�QPhi_g"� a}- _d$4�:},�Z(r�E ��arE�A;%J 2*}P�)�E�er PS2�is���ra sum-./*x�1�$ 2$ �J��!Nc m "�*� �&�9�,!% d =(^��T 2)/(1+T�OIt van�WGan8OÒ choi�@f�#Cy "�L=��c�Sa9�V>���~��� 3r�  $-�1/��T<  �N�\"�)[C��U~�)�hN�2a}Z�4b�2a� sN"�) Y�vyb�yb yYPh%o�%M- 6��5L !�Z�(a)�W"ߘ%�(b).v# .K� "T_k�*&�ED�.Oor8Uq �:OS �>�o�G� &~E�s��MG �r�+ s)^9%�s�b6��i ��� by�an>{�rast�� "��/ magn! 0�2/�&%sc}c�cL.ceARD���ލ����m*ߔeq�J��(#� śib9( thatcompens��in�&=�ek)�2c �})2eh ed� �"ly=�� ideW�c��1d��>�a�$-���R:�(��.n mMd-���!�A�.kH"�s is 1i���)�) iG �. bb{R}^3$,̆a*g2���m�lstaedt�!busch ��4>h�2�weU&}M>FE�P!��!��(��)2�y��)^�E"�H2��.+�ro"y q�Z6c�nI9�N6Ado each|K� �T�e!�N.�lJ�. MyH�n ho:c��} �9�}ch�!�RR north%� sout�&uH �6c (Mnf�2})HR��]�hA.� l )H��%��! ,̩�&x"�Y6of��E!�dep4"� geodesic{ �!�I" ctor�'�}N� \footnote�}*D% � 3 J�&��&�! &�!;��"�!II�s. ��쵣���a�A�$T=U ^2_W/2�j \ߐ��/2]$, �(g{ � y1fQast-!�� It2��$��w�4!����!� )�-'F�I�pA��-K1� .wV%no)p� t�_qU�T=1$ )%c �staysN c sr��b�U0$ Q�7e��no�%&.6A�U�S|��0z�pi�. h�m���^"�d2� in�RE"� %"A AJ1�5�%�*�X� 2� �ٰ�*ezvol�a �a cir&ofQit�)�6CE�k!Р�miA)* 3�4Aw�!xO��40!�h��D$_�4O� _22z_IQ )�2�MQg' #$"l���(ceassoc���qt�L9+ �In�U�tSk�L���*�rT��]4x!��� �Br+���5��i p� esn�a}Tv�R� bD�U%�s&�$�6S.�"v�*�SgrH�a�9| t$q�9`n1a !�c-U:�&z�b..eC:C#�KB-ܾ�`��Q2� ��} 2 |er-:&za� �or&�6�  >�&>H WIj.�);an�,�.��a�08* $\Omega$��A�"�%�I?i�2R ���{*�v� Naya�� = - m!�T �/ @ ay"� Q�bTN� . �V"O`![+jF 0��-A@&4 )���ton$ claim=,* %��2.!f"�&��.�& $FBe %e�.k��b( %�sra$c"Zy e+A  %�=�M<O!� =��FP�n� \,d(\!&� ) %d $ via �'Z g0K �h�mo> 5g = %b�.;}�$��'_can %nY5*d �Tuco�  %$ ��*�c-11T��yd��tic %&ʢ� !*֝ . %"JGRu %(�*�� F�}Ule�%��?l5�yaJ!�j�%N$.��%Z�AeY�y �se�$ents $T_j$�]�fa����A�,$T_2/T_1 = -=�1/ Zd_1/d!��i 0.12D� �+ &I�q�&�%�suc]�U �*�Z�V nY$"��)\�G�!�.� "�en'��.$gadolinium} s�&A,;.kexh �[�b��!1{�d0abs}}=0.118(5� T�������$0� ��2�!�o  ��h2}!�c20c�ϱ��.IN � t*�fE<���#� s� PS1 ���#r2 v��vsY  c�`utq7,!�.>�.� "�.��WI C����>s�6�7N�'PS16��b�-AX�}!w�7�d�-�!kAc��.g.��IAAwM�arFBK-0.�4�&3.0� w"a5=�qJ�=�6�j�W$A3z/3} 6/�B�_֐djs: �!(dٓȯ"f ssum� D s"��~dhu_�d 4 visi�uf��R s, �" �M�di�Xs:�>a�ake�3u*T!�� �� �npa :� �j0s�;a.� ��a /;;�ǀ lapp���)�*~>)p) 8un~ s�,d%�c��s�, I,� W &;wp"~ PS�s�Aove��"��"��q e> e���#�� ur!]��zteZ1iD�1ed)`y{9l  . O��"�:aor �&m��k�*e: inhomogen�>e" .l�a��o&�!�� lea=. inQ� "`� ��E��g!�!Q����!�&$�s rtto *�@damE"3s1/-\G-�_�4*M Q m'= �&["&_1*: x/1�&_2.% %2}]^)�%�R�����BD&"�& 8mixed�t�.e%��^"�@0�AllE�men!o� fl � Rz ubsu�@A� he ǁ*mN $CS 7(2)$��E!a!�st�caǑ:.��"�*�% data*�X $Ji s_1�nZ(C s�-~#2#]$� $s = /(d_1+d_2~O 2�Q, 2�ύ8: Z B \mp_ �  mp ٟ� #y���2�I%.�x���  aXofR�L��H�2��.���}! �.�9]/ ors <���l&P�&�cy a�"j 4:  <��AR.ml��A�/I-)ET1��(�)��!-�#MSA� Sum: A�M�[��pa*e�t����-f?�mVvslW�"(m% 8  $f� �� �v�e"fd to yi��eld $\Phi_d = -0.009(26)$ at $\Delta\chi=2\pi$. One can recognize the increase of the measured phase shift $\Phi$ in Fig. \ref{2004-splitbeam-prl-f3} due to the positively oriented surface on pHBloch-sphere (c.f.zdT2b}) followed by a dec � due ~�counter-clockwise transversed loop yielding a negative ph��contribution. This behaviour clearly exhibits �@geometric nature RRL. For a cyclic evolf (=� = %�) Zme2��is $-0.684(48)$ which is in a good agreement with F4analytical val!) E3$��)f�8ratio $-\chi_1/�2 = T_2/T_1 = 0.5/4.1$. \begin{figure}[htbp] \ce!�ing pincludegraphics[width=70mm]{2RX6cap!� {Observed �E� e $ � non-Ba)�p state vector parameterizIQ!.rel.duW$Ae dottAN,ine indicateEgtheore)tpredic��d>p0assuming hunde�er!74 visibility, wa*adsolid �tak }( diminished< into ace.I��B*V� we obtain)l_g�xU�radians�eomissionQF.5120(5)$.%�label^� \endQR Another1p^I�m( ment!�a.:l i%B vary!ram��udu�iA� ference fA� es depend_!Y X\cite{wagh99}. However,� the absorE�- : 2$(s!�f vs are ��A, deteI> limit. M��s of ) $T$-e� ?of �est andGPailed results of such.<4s will be publIF�ZforthcoE�c�4n. In summaryA&Dhave shown that on�zascribe���,�j no&ly�� spin��Dneutrons, but also)�;�� !%spatial �Zee;freedom! F�n)fer�� setupa�$is equival!��Xevi%� from-��pE|@of both cases via2^ n twoa�ena $al Hilbert� ce. U1A�e)A been argu)�Œa! experial verif-��I�(hasegawa96}� we believ)�Lbe settled in favour�a>* appeaa^%f!) d% bed above!9e�$fold calcu�Ao)�7:� ei�UermE�a�hiA9�Qte!�%�q�or)durfac $ gral!h, an abstract-�sp%a-��.�e� pretE� ofEE��6^ �9xs����]Sm� patter�$at reflect�w�R s upA�influ�s�!Bd��ie�6 beams. �(research ha�ea� ppor��byY,Austrian Sciv Found)�(FWF), Project Nr. F1513. S. F. wan�oa�@nk E. Sj\"oqvist �3nabl��scu�s��4K. Durstberger,cri�/ rea� e�� manuit�\biblio@4ystyle{apsrev}�the.$p}{21} \expandafter\ifx\csname� exlab�h \x\def\na  #1{#1}\fibGbibO font>J�M#�Pf�Q$�R��~R.$�Rurl^�0url#1{\texttt!O%8{URL Ipro��command{!\0info}[2]{#2} B!eprint []{S'}� � em[{2�\{Pancharatnam}(1956)}]{p56Aqix{author}�5�{S.} �1w6V},AB@journal}{Proc. InQ  Acad.a�,., Sect. A} %Wbfm�({volume}{44:U0pages}{247} (kyear}{�}).fBerry�84�b84�� M.~V>� Kr� R. S� Londv�392:K �45N�84r�Wilczek��Zee�w  -zee�� F.}~!a5� X}:and� 1�V9A>N�^?4hys. Rev. Lett!{awN 5Z9 2111�;Aharonov%<An�^n%@7A0a -a 87�;Y>�b�FJ! �v{��Jji58:DM� 1593RI7r�Samuel%GBh!Gri%H8!Hs-b 88�GJ>G `�ER>M��F!�^�60:E-G 2339RG8rGMuk�%H SimoE�93!Em -s93�CN>� \�D-D �ZAAnn. e�j�22Z�20R93r;PatEs95!.K 95�% A.~K�.cI},��Ŝ�� J. �r�� � ?Q 087}F�95r�ManiniE8Pistolesi}(2000�m-p00��FD�B3�ZE��85:E-I306J !rJUhlmaneQ8 u 8� B�LZ� Rep. Math� 4}} Yk �22V=v�� {o}� et~al.M+6 .(� A�, Ekert,�8, Ericsson, Oi,E�0Vedral}}]{sjof�pE>�Sj\�:A^Jb�.~ ^=:��xJ.~B� VV{MB{-R�~D�~L>�Oi��"� �� V>�1�2E���m�28N� ��FilippEq2+��� f!-U�� S>� d�����O90�B050403BA200vTomitQChiao� �t-c� Z�ER.~B* ��I�57:E�U93J719�U�JGDu.L3:LXDu, Zou, Shi, Kwek, PanaUOh�U�B� ]{du��B Du:�V|P>�Zo�9B�Sh�r�i L.~C>�!�� J.-W>=Pa�) C.~H><Oh�wB����>�BxY+2}�R1:m10�SBW�TbRau$and Werner��� r�H>�S}� �� S.~A> �)= emph&ktitle}{N� I�Iy: Le��*2Xal Quantum Mechanics}.<SPsher}{Clarendon Press.L add{Oxford �J��"Ha *� >�$4, Loidl, Badur��B�!� -s]"o��B�i-k�V�B���;G>1 � =�0VzB`%�L ^�V�NP!j 42Z� Z@ v�%�.�2:�!, LemmeEroEI*� i��v�f�9 ��������v��1Z~630..u�2r�q^5� 1996:�$ , ZawiskyA�)�a� Ioffe!�*V~���Bm �)��;� A.~I>;-!(�5�*� n�53�2�486F�!�%�)yJg 1�5� 2001b��8��ǽ�and)�.�0=v����E���s j%غ*f��^N'~�8Z070401F-!�});*CV;��b�z,jx.+V�BE�:LV;N>��,  &z�r�=�0�0nW6Z 05V�20�BfW Wagh�9��%�~A.~B�I63V�V 6J Rakh5 Az�B� FiscV },;6�zMA>2����^S 992F�199� �J�Bil#��Dubbers!��b-d ��T>� ^֪D>M�6 �59:E�25J19�fDert��  .I4:I+,.�#, ��Hiesmayr�M�&_04��R�6v:�VHKFy"m$�AnAj��BJ�9!%u�Nr�Z�03211JCW-vA �� 9��9�� ��ǕYI��^�171V�9�%%OJ rj1�"1} 9nf^�#E>Q+� zA�� 3}} @m�035602N�1�b�M��lstaedt"�a�:�.(A�PrieurE� Schiedee�mP�<B.h!** V�Bt ��kBZ ��E12��(�x^�89n|oJ� BuscgͲ!m�D4�V/Bq L�=lU���CM�9V^ ~^��: Kikuta�nY&"Z�\&j�%_����B� �%@5{5>ZM Bj�9Z�13R$9��mJZ�.�>� #�ro<�%l�]{z I��Bd a:V�B=�� B������ Nucls)str. Me{ n4^� 40J�e .�2>�, doc�/ } n� \�"0rance=10000 \"�,8[12pt]{article}/Hpmargin=2mm\oddside texth5164mm4height=240mm %:apra,pr5+,,aps]{revtex�.6�prl!,twoc�*n,floatj2 aps,6multicolf\�Y��F��N\renew&#,ase+5 stretch}{��6�!J��+bav5Hstic Super Dense Co�.!�5erR({\Large \bf,/�:v�0{4)O � N} \iX{A.#/]"`$^{1}$, P. Parashar$^{2}$e�$P. Agrawal ( \\ Institute�0�(ics, Sainik��xool Post,\\ Bhubaneswar-751005,�, \\��no� c�Applied�#(ematics Unil�,Sz1!_al �<, Kolkata-700108� } %.5' \.��Nol}{{1 \over \sqrt{1 + |\ell|^ 2} 63nV3 n|^2�N3pV3pj3lZ4� ^{\p�3}^�mVpmjppZppm�6Gbe�.eequ2>7e#�7^!beaEnarrayFE$ F"6�$rag}{\rang��Xdef\ie{\hbox{\it i.e.}{Yege.g �#@ate{\today} \makee� 7ra:cla{\lat4ver{\arrowvert��m�10a�r2z4} %It66kno>7dou 3�2class�;��un�5@capacity %by sen�l a qubit�5is�:�80n apriory sha5:4 maximally ent� d %�:*�8w<a#9N1/�7�7performJ� d� c� �5a"#4fashi7=e~4��ng�� r� on %l8 noisy. W�6lor�>pos�:�� �PJ�� �;b�s as a� ource. UsM this#7 find�4�8e /? !��6�bit�a pr.�manner F�,. We general{?$our scheme�5 hig�:d�7"8�BC96�Y+0e $2\log_2 d$� �2� $d$-Z al q�-�%4a cer�;�A�: cess7su 2%iP6er:s B5d6to �6N= of d�nguish!�!�g:ogo�s�=(s. The optA� averageJR76;(explicitly �8ed.A\con re�:]!��$2 N[%Zwa7 �8emreIH�aF�al}��` $( D \times D, D > d)$. �4 fy7)�maq��9 does a�ne!�$arily lead!dMC1fY�ty!�is8;answer�8 ques�:O>o why aneed $9 e�to%!Zx#&<�<r>8 � � �% %\vfill Y�7empty�c0kip 1cm PACS� NO: 03.67.-a, $5.Bz\\ \v828@%\footnote{ %\noi�= %E-mail:/$-� {\rm Es: ak/0@iopb.res.in,�sa�d@i��.aca{ ., }}$�b�G� �5}��$ \par \s�={Introdu�=} Ea�now, wel�<mo� iYW:Q!dI_sE�atE�hea�% m� �z"ory. Ddo many�Cpri�asks u >i wvBanz>bCimiSle,�,N�L-{bw},�� tele�:p"(bc}, remote �EA�AE� Gakp� � crypt: "grtz}� so ��I� �=a�FH, Bennet3?Wis���> ��?at �s�Cle q�=��e�?�= �b��ju�? !ala� bit �$bw}. Ordini�560�would ex�<only v?3of�]*  BA�of>� enh��8� ّ�A�, hG 2$Jy2M6�by�%:J less %tha��4. More,! y Q��A�� a�w %jyinF�� $d < 3yN��� @Ms work9 ��on:�=T e . I��" �E�� ��`�6�� n�I5it!8 A gl�>�S:� ��N5&4!�LS a qA. �3~Jai�HA�p�Ent}C �pa`is organ�L�jOs. F�t" ill�E�L U�'A�exact�"�� )j6T0r%H�  2�  3�љxr-�to�Us&`a���t��a�oCgR��I�ly same �h F�F`t e�B��&j �Ae�-� te=K!�to Jif6G�le!ŠRE0, unambiguous�� di�Fmin �tersFly,�e manink�J�{ is r�2e.^XcrY( among unit�Koperator�Kth an�`d\p ���d�4a>J!_ R R�^�ly2�!WffAy�arly !taM� cm}.3rueE��6| Uh. FurZJmo��+!. �)��#0Schmidt rank!MsuffiIt!�ena�us d��� .WZ erefk�� s%�B %do�&N2B E� � ��pKR�u��& you encodiz*� I 5�$d,1i E�p�N-�Y1r!�s ��a`�ty! m�R�a��LI � F mounE:2�� d.� �<er"�Zi�W c d�s�=[ext�B�Si� %(e� he messag�  b%�a��ed.� 4�T *�!wWu1UAc��or�1�a52^�1K�.�� HMr��aske@�]h�Ma $(JUB�and b�RA2$1��a $D$-%6 ������ *� * b"60f�) � { to H Sbe&yUs@6. -�*%f2.�Ad be useful�!�s� E���(or/=�(��B{6�O� �Ory�weE a Ve�a6�)[�reL!V VWy� d�&QZ�W�� �WA\$D$. W,$D=d$ UHU�%q�of]��. a��=�Taq�st�Fdb.�Ne� help o under*xwA 6w� �z��xsa��e" �OF w���u�N,!�b�P!�A� fut�x*�Ac� 5. � :* 2+o>bi:{isI we dHQ how��EJE$(� 2)�W.�� 5�� �Ua�MA���E�A �T E most� ��basis5W�r��2� �Oa!5����1} i�SaTex�:�2@ �5defoW�� mutu� &� 2�� $\{ |\psi_i \ra \} (i=1,2,3,4)$ $\in \cal{H}^{\rm2 \o�� :$*� a [1[D&=& |\varphi^{+}_{�}�, = L \,(|00 + \, \,|11) \no�\\ �2JX-2X= X (M ^{*}a- rZ3Z � �p�P \, (|0��pP�) .� A_4Q �^� Q=P(p � T � P \eea � $�$e�$p$%�be plex�A_U�a� $L =  "$7$P p$i real;�enbA�a[e�Wg= p�Z$,ɪIIreduc compu�al # yg� � [1$�:SB|:KN�a`v  � zTpol�Z: un�8d%!R� �[s� so!e& )$Y�\pm.�-�eg")�$�&�TZ u$0 < !�, p <S\ As m�Xd�von Neu�� rop�pr}��6,of $E(b� )= (A�P L^2\rm{log}_{2}L^2 - \, |�|^ >%y_ndops=ajPHj- \, G$\,2g)$sp<vel? 9X!Ath) sets*�w2���a�Y.����% von 1lj. Evthough~ R f�Zd satisoaqleteness�4di#,$ , $\sum_i�u��la !�_i| =I^lli�M�p� �_ pur+�/2�RS � � j NME 6Lg"� m[on"5V�v�" $| \phi�K��\raŇ^YAch"l���� n by����2@E�N�e� Ɏ% �*e��,�out losty1Xᤡ�hosGo r#al �� . N�y beca!S-Kexist?of"�d�UpoPbonvep,akp1�y*����A�Ps��g \i>��]a�� |E = a �^ + b-+�c|0 d |��,��uwrgnMAd��� 2G-c���>x�s� $|�OM�|�h$�!�b�6e5[pZ]we �`!a>��&a%"�9�W coef9+$n (2)� aV.M z��Zlo�\ ��#�� (��$V. By Y VY , Eqn.(3)Q�br�� 2)WLe5 pply|�%��>f�% r*&� 4I, \sigma_x, i y z \}`at�sA A,&�* n,!%o���+�6U���EN� gr$!�mP69�Z� J[&\r^.$arrow& (I"N I: 63 |�  =��JL. ::�� |:n (-Px.v|N<�(| i�� � �  )Z {\tilde �M���{B J�6�(5�� |^� L ( -| �NF���s�- �~16� |1/z�b/�| � � ell |�0%09/h=/ �1ea Now� �seFLto�.}at OdisposMwo *�$ c�na�aI�ur&�E� !6F� , |�s�+} A�,� �� �67J�a�. If z NXtoԁ�|� � �2N�� �a^I�#!�b�of��5.&�dc�l(ri�%#JLn"�!�`y,��*p �c�>V5.�(NoY i 6{!! � n5� �V u�J�Ś�p6o ?ndard� pv% Ho�e���EE!w�ain�!nJ� �"s.�!��*F�)-�>�/ �ivan,p�,ch]b1,duan:Now inn,�&u?as|check��1\� ���#�#�ac� {\emR@���c� a�!s once�8�gNd U,9hA"b*�-hp n mmAZ �D2�&[$*�h'h� �&V�>�N� F� �Rb ��El � �>����^B� � a ���:j .qde waya9� #%�� i�/pTd!AonW sub5s �en*:!�6��� ,~ �ba� $\{� �< rrespoT1."are $P_�l a \la 00|� �� 11 |q $Pm u01| + O- 0 |$�k01:�J��/A? ��to =�he E�-c%�A�!�]g�F�$ or $��J� $. S�)�i�11�2�a J� � 2p6YF �b �^�t$.����, Bob'�nd�to fu�2Qi(a{%i��!2#Qv. T"mhi'i�a� ]�� �!�q&"��P� ve OMX Vrod 2�k(POVMs)� ��� �. "E� notha���"L2d2�Y��c�b ���l(:gI2�8^"�)+eX-���M�=j ncilla?� � �%#�Gi1,��A_{\mu}a���sum;�|~.�'� (1 = I$�'�sjoutcomes�much ! e2a�': "W AO- )~D $\mu \ge d$. Upon.�e�*�t�" o�p!N$�$th�� iI  $\rho� M�by $p �(= {\rm tr}(56rhoU2& iAQ'ER� .I29օ{t�*�%&�' az�#�.�Y9�.� !Ic2�� eleMs�e �!n�#A(�����E.�i��a A��(\frac{1}{2}�)(ft(\matrix{�9& r �  & 1 ���), ~~ A��M- D \cr  P P A_3�l2�1; �0� & 0� J �kl{, �"m ehpp"d�us�co�ve6{1 \ mor07*' $!L+ A_23Wim�#��gg) 'a�I/M�is�N��b>$A_2$��nH 6&� N�ud�he7tsC3 CAl�pKin���Z :�6FRJ��fK��y$1*la>�|EN$��is �&2E^ N  �&�� � ur�ou�be*�-I�2e ^2}{F=A�^2}$.Veil�%,u�4e�a� ^#B$*@J�'i��%�� ex) 9A^nce, ^% "^%Am��.[ �& *[ � N�i5b��&2�:�(N��,9 >= � s*�%ty�Ń?.e�!�}(�Uo@cd;"�� _ �6% s#� i)2t<!2�:f 2�e� ��birosuor� ��*} y! �if " a.!�jm$(d 9d)$&�&=�<%#b&95�di�A&�4&; dZ/25.. Can s� ("imm�&*@4.L%y!.8.q!�y�*Rx� ?��9A y�/Q[/ng} �  m*�dB4l��*1��*. ha �of:�*)a &<�t�q6.�u�.�"&� kYEA�R� "�0!K�:"m s (a�7u-ER �,$Q2 d$)���;�(�s�CedB��o-({k=0}^{d-1}/B p_k} |k�  |k\ra�{2 p_k$= !k.�E� $<,.4%vyz� 6�.�YR each -e�'es1$d�'7iRchoic��r20%�Z�"$Y n*� ,{\cal U}_{mn~D% $m,n!0,1, \ldots d-�A�seJI>� 2Y4 = (U)^m (V)^n2qU�;!l�{�%f$Vro�!!whoseL]�2B�J$A"��a U| I�#,(k \oplus 1)E.\VM.*e^{�} ik/d} E�a�" D�ad� moduloy8. AfterQp w"� ).�At} i�=�.�j�� is?�  �k.�� V�F�� 4ad swer8 8a�&y b6|6 tno2jtyp�2��ũ� 2U5 �'' �A�A�+�=3o��a�! ideaAg*Gor�=T2;|�/�ina(}�>� �) %�.@if%�4 � 0 ��:��E�c�@2convenV�uroach suggesf6���7 Duan-Guo R%eA8�0hatA rŢaB�  togeinJ0p(/se�%6\�E&�5�iBofR� )=B�s.J�;a�cis *�:t�+�"�� jyA]b�� ntified, *�i*�' �%c*gamma_i$!�a|.�Z $X^{(1)}�G/� !6it � RBw1�!~;= ["��)�j_ ]$n6AD Gram u $ p diag}( �� �2, \c� N7�Dt��!�_ "�%�inp��n2692pro�Ie~�8m� a U( �( |P�)p �P �i}1�'!|P 1+\'1-� i} �\h�*|P_{N+1� � � $|P5*��Mi.�E6�a��B$|P�0,N�05,_���An�M /�)P :�$-�E!ffiK/2����V� �5� �'o��J R-�&+��5� a2t.��6�E�get�PeO , i E2��$,qC.D�~ u���� if�U!s1�Y�t�4 ard ��� J!obI 2�i�~I��� �NE�(11)dera��( b�L -Zr>0 �+:�� :�� %��ak � �rIp K� havei<. � � = \e�qj2x�8i'IyjEy�aV|P F m\(}]) j) al PA��hi > a-^!K� XB �`�!tW in%E� C :U ZV)=&��set�=*R-2���iF(Ij ) ( �� ij})! | �75-;a�| �� holdAri, j$�2$a j$�!� $ viA$. bR/ solv seri�C-to16$individualU�*� iAN"�%m�c N�%�6@PAy�8�b�2!. D6Itot���F$�@ �bU�i�!@:�.B�${\barM�(%� {�P}{N���N�&�>Y ���$N%� {\rm dim}H}��vn ��Aa�T�9 I�Y��%���3V 6���{N}{N�- 1}{N(N-Y% {i,j=1}^NE� i�J�Alt&]A��')� �%�ORlaymath}N�a% �V�H \atop i\not=j }^N bT�X2r\-+egMJ� %T�"� �� c �ES� �q� no erroF n�Oalways�Oyc �o�ermQrc&reYR@e devi�du"� :86G� �inv�,dTongledT�&1���\i����^�?:�aU:� � f not!C���"B!*6k;!-J���,�<. Com�ba�)b8�6�4_E,�(<"+  #6�� aa�Da,"S =:� ��� n��h!�e�%!Z�is�<�Rh�.HE�*��F9�Zs .�&� s�&m�� um_k�j���"�m��;� |, B0,  � �i5��ad��($d$N�' �"s�� in �!wr G:e f �!#AhJW]��de";P^.-4�P_0L ���Q,)�-{0n5�Q����6� . H)�-�B*ar= �/d�.A�(&�. �BG.�"%(�,|or1! �a>a�)Q}&�"�M� oa�͉����zer6��� �y�B�AV .��!���>5� (letY�aK$m=0$)͛ �Tf}� eqn. (14)�put>0 $N=d$��N�ɜd}{(d�1�Dd �Dn, n'"ݥAU''E(| ��>P�Mth J!#6e��B� J)2�R��n� n'}^� |)*p� k &|�a aj�O�!%�I�1�sYE^�|>4�r2 �#Nn�N(16�uDL"�EN{-�N!6#\�� �a%yE�N��i>J"b� SnyB�\F [ . JW.�[�9yr&�� i�HS*e�^ayJ�%�q�"a�ReX3+e`p��K���w���� at a��� d� �6���wo]h�ij,in 28* $N=2�k � f �*�2>. �Ra$(p_0 - p_1� Iyif$$=�>�  $p))�>�B^2 &� Ja" L^2(i�$^2072 /(1+�&�)�&�  s)l 2. AA �-"�N%_� ��ew$dQ]�F �OEPdera�if�#d>�qutrits�+�&$d =3$mU!vA��p ndIoss�! C%� . %T?!� c��&�"a*�&l  %�d_ =��k���*���er�".3 e %�a���L.��{S�LB�"6�" %.-.g"�EHX�a��" �3�Z6Y }F��!� >[" *["2 $. %B�mbov�tW)`M� l_nF:Q ���ofɈt� �- 5�/ra��D� ing:.� !�v�O"N nk/3�o� � %�-!.Ae��dA����mu*5� %�bO �yZ��hre�*_3�2#�JI��-rs �� >7sp"�32Z#V 00=%13$, |22\ra\� �3 , |2�- , |0 & !2 A0 !1 !2�. By m>appropri�R Von-�B.�� A�*G ��! �� &�!k��"9!�1��U� ~as\i�6t�$$!kM9�" "a�A�)� N�IN �DN�!N�a � ula (15)��0!a*��:���A&#�- �� �A!�^Q*ty e�]@�!� aoy:. CuV�cl:j7%�E2� \}, (n =� 2)�,C�E _{00e�& =�/�>0}�5+&�'1}M� + %2} I�, "�% kfc�f./3}M6 u>�2} 84i%8eK:��2���[F1��8:�ɍ �,� +Y^�:aN< � ���1�)({3�c2} p_{0Y{1 )^2 + >J. =4} �p_26�e ThuC�+ a $3�,3$�� �HRn 3Bv`a�V�.� 8). A�*ec�a@ ME )K,��0AJ� p�21/3�3pa$!: 1;_{opt71~ 6=ao� �. "�-SV�9x�9� } S��RT\� 9&� �F �Q2�%c��b.o, �wo@P=�$es&0pmB7g!�� �%�b62 &�ful6/w�)�� � � NME. Spec��l�-� k#U����tP��asy=�c�-on��� �b � � 2�.*�.a$� A���T%M�% Dit �b-HZI� �S"~->��)�^#To D$*�B�/� $�h�@t%�b�"aA]tT �Un�.G  gour}�*U�^"oaA]el7f �d$ 6�c�7�'thfully%aBt.alu.$&IU$) � ) p_c!�U��0 . H� *�i!���MK2 c8"B���(t� s֨lo�k(d D)d . �F^�)F6�w!��m:?* s h �8k Df�j�`�9} |�  \rS qEses�,:v}#"G!��B P.`.�3re��e��9?*"�@!7c "�!�Ny.:�. acta��Ao |Zi�mEq�\(7 - 8)�*� ...,/; l 8:A�su��ce�Uy o�%t1@o�In-�, �.ac���7:�m"?�%�aar����~n t� !|�-7C'!E9'sP !`2U.�3Md;�V U."]G\*W.2V.|��E;=B�>mi= �6�g0.+ Az =d}^R� A�0 �!e���[&��*�7P~> �$R 6� E{ ach �%Xs3";/�"S=*7#�"�$e2e+T�N &�-6U {ڥ- ��-� um_:K<<� �Qus�j1m�T�(�H�� �#!�rME,!n�nz/D$�0AT�&� A�J�I^\�!n� d}{D} 2� n�+ )(D - d)/ �R�H$D$�e�qal��cle/j� . So��B �A*utiE(%t2 2% o�:���y.� j�iv�Cq�Ń��of�X"LH1ef��'��:5-f?e��!��*� e�u�9�,��afN;�^at�H+��-AMe/t*Hio612���Jh�4�sh�Gf�6��ja&� ?Terj�rst� orms%�von"fTQ��D�j"  en�/E�>'"4�N0�_ *fM:�-y7 nB9*ve.R;!� I�1}N�#�Mbc2%I�&.`P$$p_k, k=1 >M6ItEu3U6n& cl��y se]e��A��L ��%in��.(17)��ePE�r�g�s� � D*� Bq:Fq �8V" )�k u wish*o %& "N2 2BZ_��_shidF2I#�u�26A$"E& +$GfG)R Jh�g�_Ay^�enK�1#bi="{%u��)*�Nz">iiR3)XM��b�6{)w%I�e=*�z,"� & - or � ]g"-Ah(F(�pAO�:���F )���! K!�ofF� %" i.�N4�>�I}. P sit�{!�mC7'�L%�b�<GS��k�5�E�s�?� I��ute3d!#*TR_?�.�&w�_2(i�>>�#>j�1� * �C:T\le�=b3J�%"b$.2b+�want toAum�{}�2�y��I�2��:timal2G $d/D� �B�s �unn4ns�*$de"y�O� E�  D� -qZR1$(�=!�sF[&�) �,A�>�=Fl M"iy��j�!� m� mYwe go�M>{s �8,!�>D%u�neB�M�*& !zAdec��s������!h.�ma�o g�-esa#y O��' e(as+(I �#cheme)=�i"�tooy! clai�at ``�!�Nv&�mX''�+�S imag�= &�[ �Q4� F��&�e�.���d_L�mo!,.�["%�t �� $D4?6�i�c cho+t�iwJ� � &X%��6b*� K����j�5t� ^%k{�d!��|o�inds�u (24)%�E�Eor�to ' (dB{x2�< f�g�;�3�"��)y0m�! *|e��iQ�q�. �Creite�%#)�tivm%!�ǰQ 4 �BH+ �va>z� /C V.6�oreA �>&s. (On�EgC� �i&U*�!Ccesog�!me:dB��2���,a catalyst.).<2��*�+�:Ki\W&:��2$��of7�m GB;atoF\,ť�d$ *�E%�.��PB~gV�d$.uct�ub9;�. lNP'y2�HC6q�>O�*!4N� Z(' �e�Ga�e|n� � iDa��'w��a� ll RJ� �$s farwe�{�ultҁ��aJ [od�?�b!��ll� ur�r.mar�o%�� �\��< rt a*?��  � �,U�)�� Iʁ}��A�$ �-݀ (BW)H�* : [��V scen�~E)Q'q1�B �!�a*�&to �[�%!"�2� P *�'.�up�%wo subtN�fi�s �U �!��P�JFwe-b� libfi4A��� f%# BW=u ���entH�zxtagF��-� �Jn��>��mer 2Y���oO Ab��,2H��)&tzg�u\16�]b.��2u�� coveUn��� (�3� . ]N�3� (Cّ$ c�/!�1�insaHmaJEi �;!)r�Eq6o�V���^us�D:1V_��Á���gj[j A�:��`i417��a� ,�1�A�H%� � �%ruA�e~e�Al,@A�Z��g shotN����~���K�qou�[=sE�<�T, .N"�J� �.����e}q��%T�2 ya�t�*ƀu� a:�|)�!XB�F�)e�_D�3 ��, (� )F�w� eu���? :�O��nd�AL�O�)�G"�  bsg��:� �A��t��(I"�!�61+� m� . %W�q �H�1�T 2G"CU9� ��F&>�" � 6�:�a]y]�e�!�2�"�"�jIZRuaIi�)��-� E�2� �II .uuOu�N� �! lso �Hl4G�aen6�#:Din Z�S=uA�J�u� d� ��A1 !�, � n,A�CAU�$if!a Nfa"M# %j�" %:�*s :V2��%�� I���.�to.� ��: !L 6�>O��U�d�J!?Y!�L%d�Ac5'r�z�$� *�\"�Y�$. A�&i�"� look likez Tj but �w�e�o��q�% ao���p�6� �%3b6Y��n?��+s!�^�l�<�/�~�&� 2(o�$"Q�!\7?�]* Vń��%�?f great ��Ag��! �� continu�3 vari�["�^s4xhopZL6�MPbY�rEG!�"��ly�! R@ ( technology)vs"�&��{R�Ac��<��s:} AKP�?nks A. CI��remar�P*G. Kai���(@abes��Da si�c� �8DSTl�SERC F�& Track Pro�iM^!tyouɁVis�r [?t>��p�"��  C. H.� E+ S. J. Wie��,r�.� %0,69}, 2881 (R��m\b�� {bbc:Y,! Brassard,uCrepeau,��Jozsa,!gPer�%� W��Wo�rs^� 70}, 1895�32���UKԙti2CA, �,3 }, 014320 Ѭ��܎ N. G� �0Ribordy, W. Tlpl�)H. Zb�hn, )�Mo� l74�45h:2 ose}!zBo� V.ʼ!  P.L. Kn� 6� W 57}, 822 !�8��bkUL.!|unste�nd�J. Kim��U�-� T61��042302N�pZX&Q� , EdE����� I>< C�0V�0��Klu�M$Academic P(�r,}Q Ne� (lands, 2003a�bQ~e%�.�A.<�J�Kd. Opt-�42!�253%@52@ߋP.&�.�B.�5uma��, MMst��% W.K.V�-i5E869~62~��YM.qPlenioIqU&,6���47a�91%�02Y!�S! zapB!� znikEpJ!penheim,�� -ph/��189.k cm} !]�%Sasak:mI�6�03>��:��}!oA �.SI���1A305%� a�6Vpr%@PopescuN(D. RohrlichRL 6}, R3319�P 7). sU\epE\d�aIPy�Am�9 ��%3}, 415%�5);�{Xuz�278�18%/6�wb A�,!� Hutt��G.A1PalmaI-A.�] ���-�5�E047�4:, r} TA*f �� Horodec!���A990603A9-ivan} I.!uIvanovic1u2�12!)25�872��m%u� �:@%(eD86�P!U�JC23��33D:F D16E��emp��%�41!�0NtzOL-M%QE<G-C Guo1%� �M80}, 499N�� !��/2A-���� �6����N1E51E��G�>U��end*���&� /x :բams����R���@ %TCIDATA{OutputF�(=LATEX.DLL}!C Ted=Thu Feb 20 09:15:54ś+ LastRevis /Nov�l17:07 /4/�Z2D�Shell3J� A +8s\REVTeX - APS ��AIP2^4Language=Ameri Eng���CSTFile=ɤxtci.cs�4�(TA@orem}{T��m}2a&' � }[ 7]{&� 67lgorithm.16+xio2'2#�!JC�!:#"�.(6Po� 6,�^B+�@ure6,:Xrollary2,6+r(io2�2+�0>��M 2-"�E0G>'ercis6( 2PlemmaNw�a6#no�&N2Lpr�c(P >'$m2j J�� UR 6Tsolu�'S2}s��.( �Jߜ�G\t9�Re���a G� M �-step"s ClonUMachin!���(L.\ Masullo� Ricc��\v� De M�5ni/�n�{DiUa�o di Fi{5�5I�(o Nazionale� la%$della\\ Ma �a,��+�it\`{a}OdRoma ''La Sapienza'', p.le�Moro 5,& \\ I-0018C��!}6x�)9ab�^ct} A� m9#($N\longmapsE$ \h��g�$� al c-N"�4-k=72�X�e*I��i5�' \ $(1\*�33�$(2>m)�s3/`�#t methodolo JbosonB-� phot��it ��� c�fVF%�cle obe]6��A%&"h,eca�1!�s\;ivH(g$t21!O"o d7&���(xvW)�� symm��zW��Nc�b \�A�c�� u6Op0i'netEHh*nd]#�Pcs{23.23.+x, 56.65.Dy�Yrelev�!l� P��$AD)�Ba��@QM (cop!i)! un�%�-$�n| il�n�� $ GWoot82}9�S4E�,%�un�r�"�ts �>m,6 roܦA��mly}�AWso-�ed Oi&5z�M� $(UOQCM^�J�'exh�� miniT� #le ��8 any\Zs�>. F1����L]�w��� kindqZun�:��tv��eVveloped2$ far:�����$N.�M$ � baA���i,P"H9�&����FT�ZE�$$2(M-N�c�s %� {Buze96,�97s a)�����}F�}=ion�cem��ol5aEf�X�EN� � � blړ�ll��" ���98/ %e l�years s�al� ��nta2!%�Ao)T for {�ra��$(g-)��codV���12h1� r&�RTh#ute9� ]�#�i'�y assocBS�uQ*�5i QED sti Da1e��%�{Lama02}A���Y9�uha_!e���ed adaw6��#:�!�s j�04}� us fΒo3ft�. st $2h�%I]�-!l $N=1X8$M=�xw ". ���0noJE�W�Irss �J��e^�+wxŲ��Ѵ�ct^�)�*�E-0Hong-Ou-Mande� ��*e"�)&HOMA�\P�7�k ��!"��� )�7!�0Q-C��)(<a v�( U�4e�to Z�A$98)�toi��Z�}��F� $M$ x�rA3 �aa-by m�.- a�aNid��$��O-��Fs>��!u^2���jv%u�6�3$ �6�$�9Q94 or $e�$?dMq�( �5F53outA/-�!�B�2Au�|y.�Ԫ!p^�yA<�4d6�:$gŧ[x _{i}=���=����� | ���+I�Uw�_wh�b�� ��)tM�,dJ.� _{A}=%�;{\Bbb I}�w$,�$�vv n auxili +y �{I�_3 M$ o+%=~7 �a�n � ic6� �!��a)2by �  %H":v�eY���8Pi _{+}^{(M)}$ @%/bc"�?f$M$-:�4 gin{]a#} %�h -z��^{We�B6lP'"�| t�samUW%��6e $�� ^B�^AF}J�Ά+(1-%�qF}B�).Tԑerp }V N  >)| ?6)��Bj$=K n�E |^.�6�\$ = $(N+1+\beta )/(N+2)$NMI\��0 N/M\leq 1\;$�0e ''fide�@''a�!��I�4ing�� �2� ,BrubŵN �(H�'��[O �o��u%t�D�am ���� ��sEj�F.�g:e2a 3}}},$�7A�I[V+7}{9},\ my5a�Eb�"� m � |Zf�WE� ( M--,)!Bit�$med�Pp%F cal}�s 2 !�� y!��t!�6�$=$% 6(.�Y�R�L�i)$=:L9��j9(��-2)Ba% ^{(2��Ni .6J4�L�VK%is jusj!w!� &�aQ\�E �A$9�% d"J�=s +S in%�!�H_{fF18M}U(�R��tensoU$�� BcIR���V }. ~1 }j?\f�_{2���{Sce� d=2.J\ }�{iEe"'1A�> ^{(i)��;�mM��(�athe_$i-� �,�� \�{ }i}$�)�m�va�Z5�&� $M$\ ��4O% carr���,>�'F e.g.� �-�$!$QUE4 p� %FXRrho� nd $FP� {!q.K;Fig. 1a�� {��1Pr�m_) $�c-x{ ed6aln�^ oo y $i^{th}}-���3 k T aҖ% ��a�wi$ bcce, beFe:%et.` z� �2)} &=&�T��� ) }(%!q->8% *� B<,..Qt i)}=q( �Yi.�>om8`va1uM X��)X!�2�nXG �'Rg \\ &=! .�2X:�� 4�n![rpux y]W��nW � 4�r�2� reUF&>@� >�c i�e#A�ep[ ��a8� EFR^^���%�OR*}F�i 1�lbe ��chang�������ZZ al{8configur� *�?�D1a:� upp@np/s�2��U�N�5 OaU�?8s� ��q�� lv�s, �H one 4]GJ�ba 50/50 P� -splN(r $(BSd���U. ���i*���inA9d�16 ��oryI9�<��as�� ! ��V/�8� al >>"�P @&��4����7bw�d�-d seq���*ar>l�v� 5byI�k}"J ��!y��b���o�5�1x�NLb«� chaiv�,AS 1b�1i^&e al���u��B2�Iam>�=62)+B�e�\ }�\'E� ^ed. 6| 2$ $-�`-+:Df�K��z/-:���:�BS- $ ex��d�( two �omo�R}2���: _{in}^6� 2}=$� �\'N�� | _{S"' 6W� }{% � g& �by ��'}$�M4symmetric subs�pace, the output state realized on the �mode $k_{2}$ was expressed by: \begin{equation} \rho _{out}^{1\rightarrow 2}\equiv \varrho ^{(2)}=\frac{2}{3}\left| \phi \phi \right\rangle \left\langle \phi \re$| +\frac{1.J{G , ^{\perp }\} 2\rNW2 V2H| \label{eq3} \end{�where!Y nota! $�left\{ V:[�\}:� $!�|nds for a total symmetric combin fofv%�st%E ^ �$ and2!=6*P. The identical condi�.)U1M$neglected,�$simplicity Ptwo clon�,j=1,2$ emittAwverYi!J.j �lame operators: $% \sigma _{jFn8$=$Tr_{h\neq j}n�=% I<5}{6}%�|)�6\lM7V| 6}% ( BYw2b#2K:)| $. Ii�Dexperiment\ a pair!�photonse�gen!e�@ spontaneous paraI5� down conversion (SPDC) in a 1 mm thick BBO crystal, cut A�PType I phase matching5��h, each with wavelength (wl)Ax,ambda =795nmE� coa6�nce time $\tau _{coh}\simeq 200fs$, wE..twoE�sE8 A}$ E�Hk_{S}$ respectively��({\it produc��}!Hhoriz!2Tl $(H)$ linear polarizef(s $(\pi )$:�eft| H\2�x%�| BA}iSn,�au8��qubitZX X�}$�-$encod)�an ope�%ppl�� (wp) $WP_��}$ intoi gA'ic- ure-�7}|]֑7�, $mBS}= �J,2�)$|Fwhile2!�~ _'E�(transformed �a fully �% mixed�rŏA}�g{\Bbb I}P}��by a de-�,ing channel ��#stochas%l(ly driven E�� ro-O!�s PockelA,,EOP)$\ cell,��PrIE�%� �A E� A!�A�$then drawn �Q�su��os��in $BSdexaA���-e[�alapA�!n��inA�s ��y�actual��E�7interfere�was�trollI�=(microscopic� displace�� : $Z�h=2c\Delta t$. Let's call ''�-e�.u}''fّ M0$ cora���0ng to maximum2A . By turn$���ma��,e, i.e. settit._J�O  inducedI�,Bose coalesc!,}%aieda�enhan) I\$factor $R_>3 =2$ ofe "M�x2$ponen�!�2-Eg � e�%no2�Bb�8dٖ:6 !oo0\cite{Ricc04}�measur%�_J�i�carried� ) post-seaX��$technique,խanalysis!�up sh��at# r.h.s.xFig.1b,A/n� directlyA O-a�H2}$k$ disregardAXltag�  !�eE�Bi�ia� pi - �zera#sis�of!�.r �or,mmiGTa 5 meter long single-� �� fiberd llow 4�wp.�^{-� (that mapped%  E 9�NP�6Q:�$ by cou�balanc!(�ac%�MT�d.� . Finally!g ai0% ��-}$BS�q (PBS�EVb��6� Vbs� �i TIed22 �/y!vb%$}�E* ^{\ast )�e/E�!(p�"�\ detea�s $D_= , E{3}!_aDn �wo i ��, $2^{-% %TCIMACRO{\UNICODE[m]{0xbd}}% %BeginExpansion {\7 12}% %End}( �:i+ :n)����iZ�,$.hi<  f�%Al0by{\Large \ }Q�:�, [H+:�$% >andL+i>6&�� ,2NE=adopt��o tes�ɩuni� ality� a%device�lS�procesfound�q affect on��h>�F� }�, ��:,�kF�A�ase rmin�s� r;  betwee%�0 peak value (:u  switch n)k�basis 2 off)� 6� &al ^�6h-A j fide!E, }$FFk %�( 2F�+1i�) / % N%2%$�Y: Jed^{H}=0.831\pm 0.001$;% $\ F�^{H+V .3.2$;BW 2+i ,0,%-se1a�!�* ared� theore� /Bg g8th}=5/6\approx �3A1*y A�h�timal2i I4$R=2$. Similar�xult�9$% -par94$ UOQCM have bALrepora-in 6}  $2= 3$ $>$$. In agre� w�o0upper configu�nN in @ a� J|�B��Nnex^-�B i�:&whole $(6�)\ �$ k � in� !�\ BS�ext d� Si ��b82�a _V�l  \O6E1�$, Eq. \ref�&* other ��! �*����v�B���B�)�nalogy9� firs!iep}�!�!;�� obta��b*N a $EOP��P_�� ng P 3}$=5/\F7�.� 1O� \o�s f>�$ $>!�a1%� ��.�e$!kbe���n�� mu�l"$unE�-d}.�| )_RoBy app(QisHA� proj� 8 $\Pi _{+}^{(3)� -7%<r�� BA./*� *� K� ��.7&c .c ^ }V5 �:� z@u>�!%2<J%VzB76E u�m����W.is �I: ��3}F�Er {3:mG�~� %*!CT2TR�.9N �VB=�V7p1pJ�i� �� 2^s|&�4B�Each on�a�^�  a�|,� a�� thought�@.y  re�4density matrixb�/,k� n�-)� 7}{95P!;2 N%e | $ +�>2>D9M--�JM:)������%Vq.c subh�])m�!: 3H Fock��Y%nm{G  8.�zer��0aratus alreadYscribed�D �e > � nfieldF�4� �ed 46)�%�.^�U(�P-�>�8=��9�:�� �> ��oF�!!Xy -��. he 3-fold2�events�  T�   yJ���, �lmiA�y $Cp"�]$� (any $l,m=1,e��� $n,p$. A "l� �o"�0circuit leadsa��&*Rc�!s� #SB}$� -reson�, it \ no-��J(� �w�  ''Bos"4'' "�u }i7s -�A}$%  a > A 2��z$\Gamma $ oY�E�6�)sF]�;��\a�uld� IVE��:�. Furomor&�als� e)�A-�% 9�} byA��� A� V �  ]i2;f��>#cq�pa5s% >i3u )� FZ�v-QFR�6oNm%�I���In2R �a�I�Y�S� �  e �"M�2 $�N�va~global *s�I�� I�N�1},${\l"�V_2A%�u��-�5��� %�6�,"l2U 8-�&� � >\�X�}2LG�>U-�� %�DV(,��� Acco�%�&�8of our strategyA2&�,�o A#5v�\i�providi�inU Ac�3ap��N{�r���Psi6� _{SAB� m%J>�� B�A� >jz,A�5 �GBP�.�8��f�mix��\;$)s $4"5 ��'of9<{ �4�d��-��g!�#Jb zF} vɣ non vanism� e under bB�!kA����nA� ���Q0 d at� D ��o(a���urves���!�S��! far "tN,2(>>>�be!7G,-�& \�`�"� s $S-�B$� ���)�a���8^{\exp }=$1.66$�5$, \�x�!�de�axindis!�uishabi����s!�CK%*� sources, (%/* l�,Am&VJ�"J� .�? 2$.\Jrestor���h�)*�  �u� IUE1iE2A��R�,F}"�i$ rEamT�A�io>?i3e8 6 %Hu*� -��v��6d,�$3$-$Da�">A�n *� g E�B}I�=0 �ou�yZ+0,$!�E�> . F�sU��ȍ`q�-� �co*� )VJ%� = $(3\e Z& +4N2}+ 6 )/~A6ZA x )m�ploL   2a� wE�6 �+:*F�!c�1�A�A�� % ��� vari�+�*t����rhZ�3�"2��gU�5�� �8above�cedur��euit�n� "Q".*I�6�g.5 .*��->a�I758� 08$;JG*G76u u3JG +G2X� Xom:5b`(%WR�^��7/9&2778�-�� protocol �easy g�+�1A�&�\�*i��a g Fforwar�pet�)�e>���sɄIS��JV TB_ � be� �+�aarm?&Q E�&%� b 2�$�1C��$a- �neEI�CKf% �+CK!�P Ber�arm!"=is-��0as preva�� by extr7Hu&&�RL�m ��� ��1 �'B| !�- i�  an6 ��P_# �wil� ul\$�2k4"�[Iy@�I:^J$.T�,X��)"�$5�V=�Le:T� b� jTE6L\bigskipIA D}$ 6A3�D66]4 ....!w so on. $�!� ._ 8>-� )% 11}{126t~j .)1c+%0-�9,f�:)| .$ >�#.)~%�6\+%筫AiM��kBX Z�� "V �l$J" Y�&q͛F�-G�F�-&6J >$,3 6n & e� %i'2bQZ��� &� reO �� 2�&% �E���źboson�;"���uI�a6�?� *3/"&SR_>�=3&� .{!�-�2|=�x N�$ w!&a�.�r,e*j�'6� 2$�$��g)rF��F"^�,� 6�,Aj� �,� �Q�6{ $(*=0)o,>�"@+"uM�.�-�0b'ass�?W!c�  tR�].�.st. �E�uo�7se FJA"=�o.�:K�,Q .895�3�F-+V/% 1"�,�J0i 1/4`�+�%=d�5�! *��.f%*�. T��s3-be B� cal�(A�z.:8-B�th �e�( 3F�&@.e.R%3i�) !Q % (11/12)&^9172+ll)�O9�e�� �L1:�$\)�#��unwan�� �wo�dEw g�"i BU }imult�>emiw E^L4s+��!�spu$�<�o!�� ��V� fw9�=�$average am�6D$1` 15\%�&& a ver"��effici�9I>�i-s�,A-�+��]}|ob�d�!#��e s. O� sophE"< olog� perK )�l�Q is� to findlic�s^�?�a g�,m���1!%|Q�*� Ce�sj$ be u/in�0rn Quantum In� 1 networks.-�HBare97,Cirac99,Puri!�"�*reJ8pces} \bibitem{Woot82} W. K.  ters $d(H. Zurek, N)�(Lond�5 {\bf 299}z-$802 (1982)p ]HBuze96} V. Bu\v{z}JA�M. A�e�.,Phys. Rev. A W854}, 1844 (19962U,Gisi97} N.  n �S. Mass�/PLett. T 79}, 2153T72T,Wern98} R.  :=F�8�27�982B Lamaa~ A.  s-LinartC�4on, J. How�A!,D. BouwmeestuS�c�6%]t6}, 712 (2002); F. De Martini,:WF. Sci-?no,i SiasF�419, 815U9D. 2 m>� 92% !6�I66HOM} AK.�@, Z. Y. Ou, nad La.-�a�t\�3e�5!� 2044A�867 Brube7�ru\ss � Eker:nd�Macchi�Glo.o.�81a�598f:[�(e[.4�Rz�NZiman,\)0%/Am�65�� 0223U�.��� AA�y9� M70!� 5230i_4)�~���}�# nco��ix}, SIAMACompuQ�2� 1541J���} J.I. !�K҄a�43)�99.��Ly�:�9 mE;9a170501 ��4)M.�IeFX9e Cap* s:} W9.(a)LjI scheme"U:�x �� 2�MM->&� �h ClonC M5E aVof ��. cal}"r.� szA. (b) E"�Kal set-ufGa:�o0 y.) 2.2Cb6 U $2�3 �6D $� D;re4���a)"�!�:h AD(r row: data*2!#to&-!68,(&�bf��&"�83ph.L,��"?68}$2�.F�.s&�" lef2Ar� column^$(�:�=FT@J| J=@ *�"�S}..V@A��# ��\7on;0bn�$\&�by-�2���F�%�"5��)� J�\b�� � docu*%} �{ \�style[amsfonts,preprint,aps]{revtex} %%���DATA{O�@Filter=LATEX.DLL}!Cre� `=Mon Feb 23 15:48:21 2004+xLastRevised=Thu Dec 02 14:31:37>/�a.2D-|Shell3 Jour<AR<@les\REVTeX - APS �AIP2^0Language=Amer� English�CSTFile=!�8xtci.cst} \newlAm{ }{T}Am}2$acknowledg�}[ /]{A:67lgorithm.16+xio2'2# clai.#C6#onclu1rC>-�6, >+�!ure6,:-�Nary2,6+riterio2�2+dN%WD2-exampl.�E :'ercis6( 2)lemmaxL2#iV&N|V6)proble.�P 2P!>�PN 2/remark}R 2% solu� 'S6)u�>.( �N�H�F\title{R�X2^/ \ 8p�T-co8qv� F8} \author{Fabio&5 �Fr�5sco*�2dd�% {Dip���$o di Fisic�AXd \\ Istituto Nazionale� la(della MaA� a\\ � it\`{a}QPRoma ''La Sapienza'',P, 00185 - Italy} \mak (le5@ab�ct}�!BY 1%* 9*-",hK[;�Elyes e  be�(\�sK�-al pla&�;Bloch sp?, � eveX"�G ${\'F} Vv5q '!3G,$, l$\arg $e�:an"< $:FF3$ F:fRg7�)We) h�+B=Z5 �)"Vef+a smart.&a"Q�standarJR�ers� 1�M�( a?��yG�G@B�$%� c �;��letB��*2�"@,�O !��3I ba�on2-�M Xs�(be+ed.* Y�4 \pacs{03.67.-A�D3.65.-w, 42.50.-p}""Yl�Oyears�� deal!Tefforts " devoW( �U ̍EM� roxi��!a1�m� flip�Dpew3��'an un��n)!"( > I�"f!. Even i Es*V-�un.\ir�U>s0�� �Bech99}yQ� �� �� �&< ing U�Q�.e.�4/!> Q�(UQCM)v121-(U) g# �b�&OJ ]"�L]5�&��)/gG"Nse�l �Jach�aQe���#"SMof st�� "�!�a �-   X��"{[ ?$r (QI-OPA) � {DeMa98, 02,Lj,�0��� :{Cumm:a\by �,w�J�?v!7e0]n sm�i�Q5�04,�m}66�M$ !�&�Y s $N� M I���r� id'$M$ e�\g3S��6K=Q�*],�Rqu,O!�!��#!��X�X��j.�@"� -��^لA�}^{.�( M�E�&.�|.�'A.q��'<% N+1+\beta }{N+,*%�$  ' N}{MMq 1&No*�Op�*ct��of:vi bidden bu so7uMA�ubz%c]in!7�7orthogo0 �"�)-g�orem en�W�� securit%�crypt�� A�}k$BB84$ i��02}���r�[e�!t}�m���Ninvesti�G�Vat �Na� �Q��a g�[ensem�N �Brus00�u� 4al a-priori \ ��� !-A_ �a�W�"r_aJLerYXt*��N�Ef@oW"�Bk% i&� �I1 } (P�o!�sid(V� o�i��M$mh� � }\�o8E� !<JZ� :AP�6 are'"� �5�g1 �m�+qi#:=�T1/|)(p*| 069+e^{i�Qa!ft|qj /)T%&�"�Q��#u�% � .� M}�BtaM�*�P%IQDAri03}!�z.��) �we 9ri�Sursel eZ cas!� $N=�For�+ assu�9od�"se�T��1) a\QMrk.cj0V4B0V%�( 3+MzZ g) a'�3��of�# $M-$-��9s��dj�x+%2�V � 1+% �h/h/ \sqrt{1+2 ���%}�wM(~�2� 54V~62>͝2. ?�S /R"N �v:..N[/  ItAjw�)�tZ^l�!�Uconz]i ex�!ng"$=a~��� �$� �2��@c #`m^��98��� ept ��i7 < h� inde�[� mg%A���\���X }� 95}�Yc�$MI�ae^\infty R;rM MM2 9,tz}+10&��=�/ET!` ̑�y' � 2"�  ��N7���3dp3$�BV� . Likewisv#:m1}� �Q���!�an.`d� aAo�?5=��#A[ �3&t�BA�� \ !�s� ��7hi � Hole? ��� ,rk98}$.$ Pre�ly�a �VZlco�BT a POVM:J �$, Von Neumann2�-t��s�m8er�k se�(; $.� � o nd .^Y]2�Ea\4�{D ���"r�b�Q���:/.-_}\>��N=1A� �B2�cFM}=FL1}+�11}{4M�7 �u1}=3/4K To �DA�� ,!c> + ice\E�bzX*��"0l�-AO dom�;of"pO� Du03,Fiur4aN�%�"�X/qy�F}�A�(aaZed�7O6�2� A%by fu�:M?Da6 �FLi)�02,9}.1 1�W^E�k .�36 � � �E=\alpha : "I ��| �.C$ EM } "� �G `��  ^g@ =1�/),!pt�\Vt�E}dsREo S�li;�A/YpI�2�n� g B3.BQ�F<� m�xB}- p1}{ 6 v"� � 2} !�Сb& Y_A}Y`.(F���X)QMBBB5R�?�o"�EA$0A��R��ed*�he  �Eise� 1ly ne. W�� We- $UDH=\s%�_{Y�[1 � $B�is lo]We�rank�!�^�$\"�N}oUpsilon6�aQAn(G:% }%��W Nk�)1�j��o4 ITB�F�2G)�M> jOsAe2�I��B(6t�� b(6O>�Amr6�bMJB�.�n7.� n �t$ ��a��}&X_"�V�/G es (E�*�HA)* *P5/6bPd ard2 :a)�tby $2/3$emay now�� $S/ a{nd:n� $ � �"/c���"��1��1e�or�JPi _{sy� a N1Ras�Y=Q�41-�Q�\;r2#$:��26;��; _#>;3z; _#| �ov4�;#nVz � C:� 5N�2 By6�>*B�] | \P.-p6|bD6�b'6�b'.�->�� �B3�B6B)����FABRi :��M��'>��UgFb<2��F�vZ(>�B �)"� �R�9�ы��>6�B�b�V�F�6>�1)�2 P.|6B�V�F1FN�ٵ�e�M&g=  d!%$ 4/ɕ�\�involv�T� �7B�6�Np � on��l��?8[� norm�� *�MxJ�I7��0+ B5�N{~k�BV 3}�t2BuBR 2�*ub<: 2��M1F�6� 'F�6 b(� EF�6m(F�2mf�6�>����^Iy�Bx Let uC?w�="^D2s^c�am76- % BE�-%aw"�}S}=,A JE{5.�_FtER"� �@2 ` -�:cJI:)|""D)6-t_ce�66w}T� 6�[�k.�J=3�j$�=�X� �  a00,� B*da*:S�9"? � �5�� w�n "��&�� � w&(p%�or�pS%s. Inte<%ty�EBaL� s��� 09 ique�e�#�!�x$ $E_{dep}(E.)=j$�!W+"�X}Y:Y _{Z:x��on5nn�HB$�T%�xmediateo n2; %�F�& � !�E e�%2� 3Vw /3al*~*�FJs&$ $7/9$qIi L"1 relev�<ne1 pos��be&(�mn'�'%^��"�or O$1F1 U-A��3"�eM"�5�u��X�!2$ 3$ � ]� Y"���I"^#%�a �*�patamo��1�waZ�~$,=nN} X�o&�} $(\!�9>{�w})$?&� phF� in}6�>|02�>UZ�ERN #\=�� H6|�"�0>�r�nd�Th&�~ve/�$�:�5�=1)M1�R f a"�' (NL)?�(�"D$% -barium-borate)>R�S�Tec:Z��N� sequ�Cof UV\%�-locked�'er pul7havA�wl.!l�_{p u=A"s �NL 3-A"AXegT �}�BUVcassoc�<:qK�kh,CAC2A]��(t�-v$j (wv)zNi�i�H, ="6Ssup�p�R��" 1A� �ngM<�#e1��s$\-'$-degeB��O @�FY&�? haW#epAwl'  F=2 !�E: NL\$T� orC���a;#��| insenv.v �G'c =pCcy$\;$_n�7xq.^�$ �"!h6�ru (U)\�''�/.''E�MN�(.�(�}.$\ $�key� perty,�!�sMksquee�( hamiltoniaH�lwidehat{H}_{int}=i\chi \hbar!( &a}�t� 2edagger }22\p�^{%-%NGF(JM.G��) +h.c.$.!`ig!ac$2Hij.Dmf�$#&Y.� $j$ $(j=�,"R )$,eAT��two2�6�Si}Re�)�E� ���^�Վi�"�k�{ to���y�,�|I�$RZ];=km" � ��N�$-I��Q.Z� 0,B=�"�1^!1�mW m,n)�}_ J!����-2z�# $m$-C��� 2DH 6�%�m$n?+>aaUh-%�`� mt)�S%�.vacuum�G"�yV;2}c�i54\% r�of��UAw�j�Q�&b�Xb�)�B� %����evos BTF� URE�Ul%�n�`p ( -i .��t}{���A�$The 1st-oraUo*rib+4!ae-}�b��QIOPA}� $3% z2F2J�19B k2}-6OK�21J2ON����XL�� �J� just�,�#� m9 e.^>2�"% �u }$g1��t\�. x 0.�IA�is%cexQ �g�m�R+��},$��)H���a�%�A�af$Eʥ@y ~ r�i�,J�Kh!�6�c � �i�I*9�Zl oryE�i�)X$L�V��QUo |"Z.\ Co*�I�\?0 1�ofHn2�,\-� !#i�0JC�}ȡ�e"g6�- d%o ���J��&� I.5�t�� �h) �A0�7�$.�) -ywo"yU L8aga� a�2"N; &q2UvA�-'>!A����6\% A��% a("z., ACw( �me*��"F /2�gv���Rue3 ? A;$2�{$:�XI(\bBZb=����% }3 ;r�V��� O16Or�N�2� phy�8le~%;�1�r��%\�&g$!�a�""IPr 8jM��9�E�ly ,� impo�����w��t� aUM$50:502`a*x]cSm �Bt�Z�P��u�h�.�-3M�s �\erg�4rom 7T�\ w�NMU�e(or, a|?��v�on�4}$"M4"x%E��e�-.Vr�*�+ya I��6� �[2S 6� =x�1/2}(( (32*+i_{42)�c2 2  }�R2Z.h6J:g2F>f*��i�E�.�r� 9�i[(6�j�)u��f V!�:re-wr��< *��$$m�l%*�.�1�*7 �.2"� "}-2 BB.� !� !�J%� � N: "E NE By�Qmb"�c.��{� * m0i;1y�ee�&>}l,$aq��"N1# 9�21 2}}(:93>�3}6�B!>x !BS2"^%N03(. �3L"3J ��g3 | 1,aHj _{kSh�c"h��&�+Vk cfr+:��%���9l-w�  a6Tbe�# k  no n�/"�tf_�yq6�#,�mo����0�$�I"��+APi�Ru col�\C%*8�]g�0}U"fSrtL�0"� �%�"d on H.�]PH tR�2�H.�a�V2r,�ac�.��#le2 $k< funda|1al ��� ���r�Q\&/its r�BnvariRA-p$U(1)$&N:3J �is, '$any arbitr'UQ aro�4!V $z$-axis � dAV�| re-�By.i e^{-i\psig6(6} =e2}-�622���s ]:~�%)-�X$?\in (0,2~)? �7��(}"<7>�2&<7�.Z2/)�.�sB�y!53^A�6�_>{.G.u��82�6x �v+ � Ō%0i�� _�"fT :e.1 JV6F)n��<[Y2��",>�/teZM)+"��N�� 2}.s� N��s&�N|���Z)� �.ZAt)k�#�8�, upOaLff[whA�Gv!���p1�CSp�=��P&}@Down Con����s|bcZ�c��m cOCږ� tos���6 �t���a7:5 :ach SPDC�]]Atn=�� % !P� �!�--��)1�.�m[F=�and�cx!S���T�_&JCOPAUMlUV�nBV:� �I) twin�\- 2�� 1��,,� �`''i�"cEr''�Osc9A%.)�(Wave-P�8 + P��Beam Sp.er:��T6+��PHTfA��d!$D_,AK9N''tris�~�!�al*G�alv>5. Becaus"63EPRV-l�0&�Q���f����.1L�5� rmin!3�8�9�@�2� B( in}$�U@-�O$}�*�5.; �-p%�(1�%t��&$*="��$���*L.� 2� _�EDs� �ed:$\;�<:�~" =b+6�] �]detai�Cdȃpa�1�e�� }gUup � n?i�;o EB�2V� A#�TA�mcwo!>�q6� b�� sai��"uR�C~to�7�%6l� a� ge;q5 $X�w�h 2R.�n�G�X�&=�}�bF�az��b�yA�"s n $# packr��� �e �M… 2}h64]��!���3�se!��a"���:�� 1% ,RlrR"��"'s!�ij��2�E��Rk1�sB�...�"a��s�! n��eam" X $�;C!*�:��Mr�t� ��B� �- $% ,���d� m�F&� $j�&N��C�as!�Aj�:�ke�E�m*���:R�h�6�^{\bot�4.�e&�G��/%2)����a)$*k.���n�4lCs'Ll 2 Zl&�7I5.?�V�� Di" �not �d �i ?"�{ reW�ed eird�{$#��N�F�,�'byk�6-3�% b/.rmC-ELU%)5 2� du��.<I.57!� 2� Y��acA���uy�P�� Vc��R�6� )by )��/��]hs!i�%� :Irf.yJ)9�1s#ZQ�v������al"C "&% &�7tak���cc�hM� � � �>al.\�dpA.�'%)2/N�� suggc�f"�M��s. *�!�)�rGe*=�ff�N}�!� 3�U�Z)� | >>:�&E spoileFtemporHPveJH�8ed� �59 pump �(e4(H�sjg�b6�!i' ��$I�z� #U�fJ�R G sam=�ityA��-O< �n� 2�J��R�.�6�� "�NnA9��o�.l; !�!�e G,S)�ẻ {5�<<:��2�(ކ V }% )� S��how{*nq]q*��m& eE+�*:�% 2�)�� no}>Z �=v�. \sV 2�.� �_? !�:��com�]%�Bed; u�m\Z�E5 �6 -�J�� .?$may check �J^�/�Hs�ms obٞ-+:d�� Qj. �'�q$symbol $h$��IJ\ONP?\{ h=1�a'%��\�#{, }2:NJ3�)^yX>h F3:FF�F65 Q! *� dex!, $b_{hQx e=]ki w/!�>�ise�' ff i�}6u�:�..� Pignal-to-noise (S/N)\yKa|OR.��io.) �s�"[>�*� KP�� $Z��h�Q�b�� ���Pxbt���$�r� ��arbrR� =3)?R�%=1$, !� 3}=b�L L!�qr}=0{se;/t u , $h%ar�Oc��Ѫy# ol d(aD�:\�j&�Y�I=Ge�a�EbyGn5h�"K%"{O�'iF3}(E�)$�y(3b! %+2bN%�+%%)%/\m�@.- 2"2} 1 1})c ��-��al�'�!]h![h�a1��m9�_pZX\��f=B@ UN6I6��3}=2.00u12M%4=1.92 06$ (see)�)��( U�5�_V�1 :�)=0.76 eA�H�LH6L8 �01�aĥ��L��d=Ne��Aw�1��i&v� ��1�:x�;sl5ly in2#a� &�*$0.02$2 �Y!�� o .� term ho�s}^(om�[nes�LI=v� 2���^e" *.� � � oO1:��7�]�X&X$ ob�8AA�a $�� 13~�: $. D*&ut�Vren��B�p t ; &� V^4 �*v� c%6�maXIU| :Rq 1"�� $X"M+$ ��:�p2�h�� eq��Xh���m�$V_�:�\a�7M�1����- 9�&�-2zM�AuF�N��>�h �2.1m�12"5�A�2�A o:� � }=m�s�j�:&t ",�� a"�L&'vA� �"_��sD!�H2*��j�c"�d,�;��X%8f*�OQ� trip;tqO for � �azbi}ka7!�-��exten�^"EP�cfoω way!�y=d!2 M$ zVod��El��"�6�  rn s�rof�commun`5�5he ai�ep�a�Q!Z1eavesdro_att�at� �Y}� �Y, en]N bs�� J_b$x-z$ =/�.Zb:uFuch97,[Z%��{ ies )Q�� B�!J&,I��)���P�~a�+ 2�ZO>� addi� B}cQ0use�yto�ly�*� M��kuy+ task�}�� bj�c \A�  ? {Galv[�is�"� �8��!�4FET European N�v�Qu�v .�vC2|(�/|8\ IST-2000-29681: ATESIT)� IstRe �Re< (PRA\ ''CLON'')�l by M ero �e'Istru�ee,�l':�e�\llaAt(erca (COFIN�j"w�f. qN�wJ�w��w, &�w, G.Ghir��, R-7 ee R�E�F%.a�qics�s812!sb  x �T,-Pasquinucci%�&�wIQts59}�423�s9);�sSe�E,:ys!�^�u A (in�)ss6� b�kxkx;���Xx!:097); R. Derka�wzekJA"�s="Fv458=t 1571I6_x�ju^.2JNu842ZJb>JQu"�yF.&�h�w�x as, :z\ �41:d8*Wx6 xeO`\xnvAA7bf 685u42306?w3�w.�x6L!�2� VQ�w^YxHc}�u Z�yC.��y {\em5w%�2:�y.mv�c AX l,��) }. w2�!^10�xKu�FZv�c H�3ins.X,}^t8}, 18X%|6X,0&�u:�\U1�.�%�BGz)��x r-y2�TM"�y)� B^-#�wB�ybY �if�A���F�w.��dA}T.�Br�yIV "| M.J.F�y ��ye"79R�y�.}G!:(bordy, W. T/%a~H.\ Zb�\n,�. Mod.m?E�7z}45JB�b a� s,!�CinchV�kM. D'A�+�6 ^�y �6�123 �0); GFJP. Lo P�F2&G��F8�1);�� Fan,{HMatsumoto, X. Wang,fhM datVT5!x��{6� 9E�CZ{c*�zJ.i �3� 6815e��J�BFeM)��7��7J32�!��1�{!�ـaOnbɕ E�LV�{�^�� aw+dPopescu2� VU7!$1259 (19952�X]��S�| levo�%P���S�  al Aցy"/�6sy }(N`P-Holland, Amsterdam, ��, p.163.���%ARt2��7A.Ez�% 8n� u03}�{ Du ��� (-ph/0311010� 6cr}� V 6� 2� !NMRDG.�k\� asek2�2r 5231i3)� ()�0>v\{;0n u�ĥa*87�KN�O$p=1/3M$"& ��05ݛ�� }((published)::!e�/GmV�nI"� .�s"�l"ԍ6.2 �n"�"�1�4}.k� �1B� i�i%-q25I@ a&6 ��A�chs>E Q iw56��16�� ��erf��\z� renn�qA. Karls��ajR� ��)� 12ե6K E.F. \~{a}3sL. Har��F�� *�0)p.=  \!�ers3�aF6Q~ tvs�8mm6pr�t=0pt =3 </-Sl~atic dia��ac~-6~��\ mI*upAa �(%?a:V y�"BINSET:�)k� '�B�bJ:N0~ure~3~ �N��n�B�>W:�z1"IXV6�A�0����-4-*_6�da�] W$ 13000$ $s4&&��!�"�$Ӿ��"solid A_a�r�a��C)Ga�an fita�end*�v�b%% �G�{"2/byj 6e8fic Word (R) Ve��2.5 %%���g shell:j J(|dsymb,12pt,thmsa,sw20lart]{Dcle�/|�/|/|TCI�|= �$/art4.lat,�, } �ia|Cg0 =Fri|431 21:14:54 20b@|o|8Jun 20 12:07:43/5}Zj�{ \e {tciz-x>��1́^mx Four-leve�� teln� , sw͸�T�7e����+��jt;` L�pa(Sx�x$Zai-Zhe Zh �\\ �jAN�#DeC/aR�]ics, Lia߂N�V�ity, DalA�116029,O.@,China. E-mail: zpLzaizhecn@yahoo.com.cPT�'%JZxI)is pap�9����Oof�rJ!@ 5M* .$6 �o��tr���8  �pI�K�b=}Dquadrit systems. U�&�%5��n��YcX8}g�gc1� thTs�wX�:afN�>Fg sH  uh�end6�XI $A|���22!�b�_at $2\��$1 #?3 3fY� �Y�)�A�^�1'� x( PACC numbew@�w7.Mn, 5.Ud 07.Hk. KeyworCeQ>�, B”,1�:�Sm�, CollJ��a"5{"z 2J%qU�+%qu��� and �Brtant t�s "� u�l chan�1( um i&��#i$! BBCJPWmZ[1]E�r)b�h#��u�A�7W� (e.g��A;&�[2]). Ab��!��Z�v�2gz= a�0by ZZHE[3$].$PproblemsM{o k� `!"|mjm�2Odm� ($d\geqsl!r3)$Ai�re%�%�.[4-9]som} 'I�"x��!��of dime�\H�e�an'�5e [10,11!]In �bp�&we point�'m��q>�3�f�l a 10��[�ŧE\1ӥ<�F�Sew1le*&�u�FH3,r- �� ��Ifz9J��b!y�O&%mathe� al� � E�M1is2�In6TreKy�n�.�x)vw_!n1@ ��u�FK%�y) 2��wo�Pth��|��.�2.]�D� �:� Bisy4Q�K'we6T�L%��T jT0(UPB)[12-16] ��!{�a6��a (EE.7],6�.�$�]\�m�N�e% Jg=a�c6�a$2N If $H^{� ( l) 3'C r�)ג bertAcEV}���% �al-\ �mid i"3 }<36&jB& �i,j=0,1�� A)GM.�(ez� e.�ʾ�=�1A�i .�C~F��F�.$ ��e�>�E�dB��rs Vr6  W_54,rX>Y>Z �\}6+( i>?mY$H��&� narray} &r&��D 1�+( !�01�+Di+1\;% \func{mod}4 1.2\;^,2 , ,3f,3 ,-) \nob  �=M��f�-�i��,��\\�] ��u��F�Z:�a:��]���f���{�{ FeuaOb"^�6f}s�� =+q��8F�����(�y~Em*O.fu�;�LP*śr9e n �y;�� <a�x�&is�fb~Z^R=7�$ }�.. B7Z+��^���z����I|}� ������ t�)���}i>�.6�~!B� � �J!\ ��>j F.B"� �A�w2� ��%���I(Alice holds"�  1 �'A�� "����-! jEid *+�.( *�--"8a-0_UX2a1.gC� 2.delta-|,$ Clara� rem9e�9, ���b �� "�  2e�3 �Fin3a�c!Y�G*in �,���X_1"� 2,"� }�fra:_ 1_�� �0_�3!1*B !0! c3!�L�Y���  iR�jbHB {c��!��_{���=-E�J +)9% �9(\�w6.AvJf8>a 2aj89x� 2=W \ -n<j�} } � r-cdots -VIjw)�T)� /+.G A*� Eq.(2), q��;!�iy�jYs�n alway�+{Ze�/i9W_ku9"�J]%,\;VX( Z($ SY+RSmi\v.$ Sub�*2�t) 3)�3( reorganize� ����-��bZ;$sum_{i=0}^�7(B)�u{W_ir;ᩘ_{W_i}-�� u��oX�QXQ Q}�\ Y�UYUb�Z�QZQF�I�)V�GF$ eq��&��4��\{f�05gN�?( n|%�2���2����k2gJ�9�Wݟn��J���H2��#2�be��Ւ�q.�2�.J�J�2��z.3��J�J�2��N� !1\,=8X�f- �J��2��N�u�.��f;B�+.�2�!h)z��fmeJ�2�=�z��f � �--�B�-� /2�=�N�JgY�g � r�+) B�+.�2��hY��2 2�% J��2�9�N:uY�iM�B1-�B�.`2��jY�j� B�-� �2�%_ N0JjZ�j-�B�2i2�=�N�5�Z�j �J��2��jZ�j�SB�)�)�2��jZ�j.�}�I�B�-�J�riJ� 0�%&�,Now, Bob sen*�&to� c6��[ F#s a j�.&'of*i 1, 2. She'��?#�16om:4�� "R�Z+ � ~� L*m RL� ���J�@# a��?G{16}$ (h��u�k��� such=ptrq��can di"�!<s��s$�(Sܗt;Wly-� must1pV$r!�on� �K�!�6��ZC &� )0, _2 "� N,�*� F, X _2� 2,[\} .$~G� sixt3"�k sy�F�U�0} &=&%�[$! ({llll} 0 & -1� 10!�O-J�]��1TCz� J2] apg�R�6I\ �2�Yko��R�, �ba_Z}!�B�r�R�6&&UA��(](-%.��R�)X�))1\r��R�6%�X�)Z2���R�1z)}.o.& .)9R�6U+Y�+ |��)'.�R�)Y�*E*~�R�\\IY� |1�M� !& V�1 �!%a\2� F�R ZZ�2= .� R�)Z�! J2]!R�& 5^�6�MZ�.1 & 0$ & 0 \\ 0 & 1.-1- 4�& 0 \end{array} \right] ,\;U_{Z_3}=\left[ \begin ){llll} 2I\ g \F�R�$ \nonumber eqn ��^When Alice informs Clara of her measurement result $\mu _j$, by the classical communications, t^ P0at once knows7 correctW�should be $\mid \phi ^3\rangle =U_{\mu _j}\(�i$. Thus we achieve a four-level quantum teleportation. By using of the above basis, we can also carry out�ZTswapping. For instance=,suppose that-nPholds particle 1, Bob:s 2, 3 ,-C:34,?,s 1 and 2 ar!��ent%;(d state $% %YX_1^{E�( 1,2I�) }1j$,L�s 34\ B\BZ3,4FZ!�erefor! e total �isuY�&X,&\Psi _{1234�=X_2r�% .%N� =\frac 14-5 1_11 0_2+ 26! 1!-!3:!2! !0:!3! 1<}�4 \\ &&\otimes 6�u'y0_4>�2! 1! �36! 2>!0:!3!��)B�=&�W =W�16i B�:�BA26A � -\cdots-�n~�b��8%�\{Uөo{c}i�.�left( �W_3U�2,3QU�%� X�& Yz&E� Zz&�-UX�zCf�y�n��& Yz&� Zz&2�Y �f�� �~�&��N�y� ��Ivm�\} �_����.�I�5�$,Z$9C ,mZ, =2;.�@$ we use Eq.($2$)�mwe rewriݧN�$ in $-�H_2� Ha�m )  % H_1H� %,$, to obtainu�equ�m�N�6)f�W_0r�%&.�1F.�$W��NGK.rJK ( �= W2%JdQY�JQm�~�K.�JK �iXvj��2JP �.�jK�oJK �)7.CjP9�JPKvjK.� FK =�.�bP.�N�)�YvbK.YJK �P9�bPZ�6.vjK�6.vbP.xJ�-�ZvbK.iJK.6.bP.cJP-�.vbK.�JK�6^L�5 This/n� at w� � 0makes a joint""Qof*f 2f 3, so ( � wave func� ͇N�($ collapses��(nly one of Gab� 16 s (say��.�N#T$ ) with probability $� {16}�M�t�  appears~�spondY4 L .�~�$)$ between=/� @4, etc. To sum upt.��.~"� can b�|alized �,is way. As �pplic�!�9Pschemes�pr!b1�re mayZsome !�0ective translMsNmultikteR�. HO$we need to>�cPptG$UPB[12-14]EJ@EEB[17]. Consider�M- p 1$system $H=,\_{i=1}^MH_i,$each $H_i$\�8$d$-dimensional%r � A&of $H$4$N=d^M$. An�a!; ductl�S=�\{�A\p�0� 6k {m-1}!� 4\} $, which spa�$a subspace�SL H�!.complE�ary.-{\�-% }H8con9 s no�� . It��n[12,!�E0$m\geqslant $�M�( d-1 �0) +1.$ Followa/!�, if $T:(varepsilon .�  &M:3.@{nN: �m+n!��%�a set!�qQd pure-%s� ,$B=S\cup T$ T an orthogA2-ite-�E',$!�n wkll $T$64EEB. Obviously_ arbitr!�linearObineTL! � �&6&$ still!�an9I� H$. W �AYYx$% H_{EES}$E�ned by�(exactR�(& ce (EES),\A� have��ved ; istea%N e(. Evidentlya�$H_S\oplus ! NowQ(take $m=$ $R�!�dA��H� posi��,integer solu��s�$�&fU�a Jr d^M-mAl-J} -1=4� B} T�mHwo y@, i.e. $M=2,\;d=3 � $M=3 2.$ :� in a b�� trit�� a tr!b ��s s a  . EES (foA�ncrA�exa�ds, see%�).��'�icases,adenot)EEBE)e��y�n� &��28"�J&58\} ,$ .S!��]�$M_.$E_�!cՂ special6:^lem asM2s- Hilbert ����$H}{\Bbb =} j"n�N}��:" &� $ ha��f�bq _iNt���6gj.� .&�%�$( i,j=0,1,*� $. In ��, generalA;m of a��", hi h � |yL �.*=\sum_{�}^3f_{ijw.tF վ7�We defin��^N� \in Q$\� ,be `separabl�� 97'�P)! if it de�� osedA��D : mid yQ '.I;\; (i1{�>�iiVzci=*�;$\� verse��J�%� called `q�d�'�. Notic�Hat si�$ Mv*IF�&wJj��\ both2�#A�$H!�(hemselves$, ,�Li� � Ei�]�fact,�RN�5Pof"� '. Let us� ��&� �J^*97 =7k9ϑ�6!�arr�A. i_k!( iq� ;\;k]>���*$gard everyC %[-�Fa.U �5 2�5���� et H �2P,$c%�6���)�q�^Y� }=>{�� �F$Ef0just a ququad��Qw!��@ d!C� ���bas�s6� W=��>X�& Y�& Zv&F(Q8Ii) $, � Rj�b�three*j$% Ō$ ��u 4 n un� 2~�"`2�� =\alphae6%*>F8 +\bet 76� *�R7 gamm 8.o _&�V8del p.8 &� N8,$�ho�six.J4,5"� 96PaEU�q���.�456,7891�1U� 12m����"x2�98456BR��605� N��2a9a^a^�Na&�2e&M^e60�R��2a�ba6��J���)�m�)A3then,z��2 an�pl9 ���t.�!�O� �| $ from�!to remc �"0. Similarly,6�n � spin-2$.��.6,Aeprime },!{ !^{$ �e; p"s $�.""JXZk },!� w$VL" s $4�5 2�F�N e�6ɉ����<,N��.��.C� }��d��v�MJ.s~} },=<5; }=:B]V #�Ii�� Psi ��"2VIC*� ��^ � �z,Iaccor�toa0i� step %,*t ed in 42�>�$ groups $(e) x(Y� b�gSJ��6J5! 6�=�Jd Th�sdf@s is s�V. *��х�Z�� % in!4n� ��szT�(.N. Ew��}found5s �&� thode #r7',��� At last��briefly � io%  ���iz�5fin� at i.�ladi6(l�'�Im� �'�s,�n)-�(e w�0be lost. Next* bs �'extendg N c(N$&� 5)$\uhow� }�(s%Pqu�ccx. {\bf�cluH : }I)&� �KreE-�� es. Using9 sKW?$n simply r�B!�r�!� Qr. ��i��1� �$% 2\�&$P$3 3$:�*4�e4 �4 � �}thebibliography}{99} \bibitem{} C. H. Bennett, G. Brassard, C. Cr\'{e}peau, R. Jozsa, A. Peres, and W. K. Wootters, Phys. Revb t., %�070}(1993)1895��M.TNielsen!�( I. L. Chua�{\it Q�*Compu�*+ I�+E�<.} Cambridge UniG�,Press (2000)F� Zukowski,�$Zeilinger, �HorneB(A. Ekert, P� Le�1 � 4287:i$F. Verstra� �8H chelde.T�5@90}% �3)097901:X(J. D. Zhou,!�H^Y %I� A-�64 X1)012301A>9�W. Son,_H�e%S. Kim)Y. Park2�`% 64}�1)064304F�YH. Mi ndbD. OhRT66 �2)052318:T8A. Grudka, Acta � SlovQ�5 �4)9>H<%>R.! Chhajlany2PPolO A 101H3)409:�G. Rigol�J�A0(2005)032303:=X.!Ge�Y.MS0 JEy B{�R 606}E� 5)18>j2� ,!`P. DiV0nzo , T. Mor,!�h Ja� Sm� )�B.a Terh �RevA Y�82e9)538>�6ALin. Al�wpp5T323E80)6>�D.��� �AUw �(Comm. Math. �m238y 3)37>�S��aturvedi>�65!�2)042322:�(A. O. Pitte�WL�Algebr. 2�59 �23>;Z.ho�={qp�h,2004)044302.s>   docu�} W�\�04[pra, twocolum�howpac�#iJ ( frequencied present)" H+ ten.� 6c � the 6�is far beAg w tere!�gU0/ e �physic� p�%ed3:� ular� is�3w at�� ay slow dor� ed up%�sFa sign� !�MӁ�r"!6,induced emisaA� c pb�$^ly block� N po!lv^�"# �� � 5�add�&potent�-; no�%� at1�c1� L �B�s�  well-�#rolco��(g mechanism%�!5 Eu� mesa5{Agb',Y/!7xAV!9�� f� on %k�%1^,coefficients�! b�&g-ed..��! pertA�IOR�bq'�4finally discus� k ho�A� medi�4� coldE< reg43. : arisoth%B given�6y� \��P{42.50.-p, 32.80.-t, C Dv�( keywords{e';���)�� \s� o��tr &ion} �! �a�(ofD�( micro$)high-$Q$�>!V(ax'-)maser)� rece#att`6 creaR v est .it waA|mon��.$by Scully Ł0 \cite{Scu96}q�is�e`� lead�) a new typ<B�ic#!�M�I94.�Q>!�e��A�nea�Ato treat��m1y,!0er-of-mass mo�M��s�ng)sd��v)�s�8impS8a�Fisd(�, usuA�m�d along;$z$ axi�!w�a�OP#%�%�O# ific�/ viaI- �--[ 57of raa" ion))W�*})J� )�scribE*'rAf�0 pers]i� -workers I!$Mey97, LofSch97} � wj�� �twot %�I�a1�a�gle�0�e:y%a *����I�'mը���Q�e -KZ��rongl!�p3nUI- �h$profile. RK;�:re�ed �he��#%ch$^2�a�usoidal�sDtamal2�4Ret98} later rC"�es��ul&� >wsi2d� a numera7 m ! pro."b %�Solano�Bas00} !��lyEsut!�u�O�m-&�(� field� L\"offler2�AV8}%�e[sat! f���`�"a veloc�-se�� dev."�an�ic beamI� �|,% "%by Zhang2�Zha99, 8, 99b}, whoEM(!�wo{ Y�q5<9}�re�~MvivA8}%�%]3(!a�#9b}*-H/.( revival pa�n�v���)��EuA�by Du) |(Du99}. Arun  qAru00, 02} studi!A�| � bimoA���UAgarwal W�|Aga00} dݦ` t tunnelAs6Fthrough% xk . In allA�se��+ ��� 4a Q�a�always > en!�6kw�)�tyE� � y $\omegav,&l"Z> 5 5 _0$.�?.9�t�(ed, a2� � c�0�*E�assumed-�ERQ�)�0}�KtHp� �)a�/Sri�!�establis� ���%Y -8non�� ( � \neq )( _0$)e�aL�?�3.J �� organ�0nf�+s�>� 7�q_0>&�"w?7/-IM3� ��\%R = |b"�-\l�D a|$ ($|a*� $|bre,���ive� uppe�5d lower ���'�%$), $a Z=b",��:\annihi�6E�AP zato�7f%� �rZ ) , $g1e'-iMe�a�stre�g $A!0S 2!L �3e1����SA"��$- )�!�m3\�'�86ieigenK+� $|n1�� he global�"-A� ���by $|�6(t)C:e��W�r�%�0nor� �*F�m�} ��I{l} |\G�(0_{n}^+(\theta� = \cos \,|a,� + \sin b,n+�@,\v�1{8pt}\\ .b-Bb -2I6c.}2ci� � ��$ �A�&, �ameter.l!��{\pm}:��5ate�incidew AG nonE�e�)s $�xe�=$�� � = 0 &�A<d}Pw5;. �_n$�byF��$�l%�ds��\cot 2C = - ��I� }{\OL _n}\, -^6RZm 7 = 2��(sqrt{n + 1}"FA�m�M-|\pm, QQ�26f�_nQ�$%�* r\"o`%er �� rS�Bre�� ��e  (�  })� wide?!2sub�s"�s �;|8}-�ss+} i�C-vQa�  t}�^+_{n,-�}(z,t)=�+[ - =��C  E E $z^2}+(n+1)5��-aW^2IP\: ��\;+\; g �-�\!+\!1}a�:r,D]Z��I+\bigg[ QO :O;� Q+ � 1}{22h2�R t-!* �)*M�5~ ��-0.5cm5�!5�-��u��~�sinZ�-֟F� ����E�z��5:Myq�q�qs��ps�4pm}A2�� : z,e^�| >��R�get8~9$n$9 �ed�R�differ��8� B�ep = 01)t�6�s6� ove_are��� �$Cin�J6E��"�*�.;re }n ele sc�G'"�(���barrih .�"�by% (�:Ref.~�Mey97})g� ��cde�, %isW?-�~:7h;no �!re Eqs.~��ss}) wFQ � r �s>Z�t�terpre�2*� ic2DA�2�;: 9@"�: rwo&�lxev�= +ut�.Q(_3wL�8to�)cr��\6,e $0 < z < LM`% "L N vanish0nd :* b�8q �>�-e(&�0$�2:��ssa��&cK�a_n�  & = & ;�B�H[,\\��b_���.� �\�^ p��1 t��9F�76vA��;6-�psiapsip#�O�]1-te^{i(B_0 + n ) t}"�z,a,n:� ,x2antom{�| b �նh [ :k��n. 6��]�5)�-�ind  expon� (al factor $n:DorOEto�aD �=gy�Ul� ig'7�!:= �� so4Ato6�a})�obyl�byJ�B� plane:V . If�T� ini��ly � nokinetic�9 (AT m<$� k$)���upz�M4�^�: ��(nega���values)��ex�R !\��le) .A����Wt*��~ ~2woFiby�2~ �Es��c�W�H!��&  � h&j;�B1� $E_k�� $ k^2 / 2 mz?Q�!&��-i� lj}{2 m}e�varphii�)v�+�wy�jZ Za�:¯align} &J��)\;\,= \{-i�{"Za�kz}+\rho5\,e^{-&\;�0"�0.2cm��tau, -ik(z-L) 0> L�i d��.\\".Z\\��� N�� ) q-ik_bzpv�254�8Z��-NK-3� (} k^2_b=k^2\2mɀ}{E3J�I� BO�kappa^2A��2 m gQ ��w{y� eBPͩcab2�a _�gJ�V�A(\�yH) mustD  � �f�~:�s�� atom^�5354Y . "C�: 2F�/� �Z�"tude $E.a�� M$>�or�m?,dOzOJI�$-$E�N. H�3=AcontrastML�2� �U�:~�� .�.�6-t%Kpag� %�z� um �c_b$&c �Wi�!Ů�Gِ�:!�ic3�&C` axA *I���  is!ponsi4D� G(g� !$ m �/��. A>�7�)E �  [ Eq� A�)]%i�!%3eih;�6�)�$$i  <� !�1*it 4*% # >#!% ��"mer�)� �A serv+. WR0 af:# leav���)$�2! �fpa�(TL qJI�9�$A9Z2) {-���Gi�'�*�Puno5� �a;|e�naVHerg"�,��Yvarn!I�&�P�H C_0�� �E�is L%C�OdbT acccouabal'd s4#�4w��D%�iBx H. sens.>Ka -Bis�%t��� !|-0 �XbQ�ac�7J�+m� �� Fig+ step[ -�XQ 'nczd)iv�a repulsfor�+�E. �> (altho�"N,Qical)*Zo%e�re"�+ un� he �ba� 2e�Har91} (b.it�S)��1�AbN����a!�}l�a Q-decele�r�-!�fs. .�A  !��rwK-2 m#c-��#e�h"� �� same:� (if no� sipI�prS.�Adered)�F&t*1� !�!�re�'&] m�.�-Q�>�F figurc1 �*H} \noindent\mbox{\ib:degrapM2�[width=8cm, bb= 110 75 690 410, clip = true]{fig1}}�`�,-0.6cm} \cap!�{Po1a ��!m}a� N�}�. $E$&��:)b�� �-A2�.��!�� 1' �8en���fc/�_^�[t*o(��'�z�/AR)gle�I0ex�Y.�1mU3� ����>1ua/�R�/�? to a=$iP(emper�5e $T � ^2 k_b^2/� k_Bvi)fBoltzmanxCP2� 9)i@1'ple��as��imaginpL.i qB��]��m�%tha�W�q �| i.e.Tk/'  <� $/g�?!�t�0 .�: 2�cana� RplayRascU�&:��:,�"UR5 �D�� F��� �*‘�c?�dmpE&�2. Dua"�M^M�6� e�N(�r"�1 �P%A��a�Xiel�Ex jb ��R1,d U'�!by� !�^2� /2m >d#gvuRbandT*5� R �N k_b}{k}||  |^2,04TN4a 4.� qJ�� :*'!;���MI^#� \leq6�� 9mrk7n/fq �  h�  act9 ;�� "X2<Z�Eh�'�anM-A�]-A�&l&� 6���-S!�R!%�)�a_n6�a_!� ���il�/t=y � :�6m � c*�4]osol�*:� !h$Gi���1���.�e|lem� muc�r A� x�bce��x�!5 f�E �$ ial �w�["*"w$ [$u�&= 1�B�0 else�&� �,C, greaA�Bifi_*I � = � *~ _n�ScN!�  ��%f�� �YF|~:Qz1�&� eq��} v� � g#�=a�ft��+VQ��.d�y�� F�aKnpsipmBdn(z,tZd~Oz,�"n:�>�*�~�V^+m�\" 5�?)�%� "Lg���#'sin* $,\p6���V^-l�~Y- �.1,VnmasVnL ��N�$�� $^*� eh��"�i�F $|+,&'$�M$|-&�6C. Except`3�PF�y�b�4i��& a &�:r�as*�y) �LSV>. �F;�%*��P PQ��io3� U�M�cot"k�{�-"�'�'�g{�#$\Lambda_n+V}} 2}},"Q#0.3>"�'fS-vSe"r\quadq��tai( dd&�\ �{n}�.z*��t�3 {n}=ZUA.Ui!�I�5�Zg�nq� ^2+H'^2J�W� u3<1�-e�> tan�@F�F-VGX(-G"<�%6��sM�":�� 20 -35 67�J�2��S�c��diagra�Kth� 2J�#��FA,�Gm m (a� �� (b)&� intE�ieH(AY1'' 3~����`>�2,�3�G� &o���N��-sc���V�. Fy m.� illust�O�iN�8 6pou$�hol;%�e&@Q6�u(s�J8@��8 Jae� "�onO: na fixedp �d�:M~^�,�7�{witch/��28a�;er r�E_k2a  one.�large p�A"k)"k�0��M�A�$2_-�.�,)u I.I� most7� �a!*]!�*/;�Nn2is<&�+�`��E�I�}T".� =� ^� �"5�/ F8 = AGvi kz} + B� .f�(  $R8 D�1�lex2h A�F.{n}�t .2m�^2}"N "� D�!�B�< �_. z [4]} F�e� O6* d�Ka{k� �& � u^ ��{k� .F+ �_F��>� " � a���?�9S �-_�={:�.�F� F�W��~�Da�f�"��.t�0��u ��B�0�z3f1�~�&�![ !�O "P +{ -� %?B- "F�\\&�� l � Jl+6�Fl-�M��6��ma�isD`to finP&2Y$e���7 n� �&2T�H�5�.� � �1� ��Iglob1}&�"%��s#��k�"z<0*{ r#�u c4big|_C&\;0��#:�#= 2}[hoQ6\�&�#n�Ul)�v� 2 h>�#V�Iv)�jG|+,phianzphibnz&� N�a#a�m!{n}v%(Aa%!�i�� z}+B-  z*%) ")%�] & \q� *�5.Xq]�� X X-_l�)B� \\��-K(5}�2����+V# ���6�VI��" D�ZA��7: �m.$, 6�#,O+_n - %�Q\$B in �8b5%�)-C%.N�*�$by �G%I�9ontinu8".A 6� its firs�Nriy"v�.̈́� fac� A ted�m c�wKy E"9w>�5M��}1,A!�!�Ohet�g!U��k)JPau _b)U�<�_�%(_b9UBm"}{o1_� �5�1. �M - 1u)vm)թP_�������6��J��.� m�>�%�S^{+-}_nin(� L)� (���+q9 6 -�2!32 1I��-M�i>R+�kbCz�cos�uW�}.p.1�/[� J!�-!�S9E�:`HA("�()�]^{-1F8F>RV%l��2gE$+ !� �5�mCn��� 9�6F ~y-�y tau'x��zv ��" F2M� �>�\! ��қ���r��� �(�< �Eg�oM�ɲz;�3� ���V + �'} �IJ�Uki^)�\��)?Z� "f �}{k +�� +�E� ւ>  =�ZE�i�_i��t.� L[A) �&-��� +>5�5+_e!)}{Ff\�Zc >G�k� J��Gtan��B5� Ŕ�u+ .[&��. �5!����7 Aty ce���?� AA pi/4k_b"�u! �bm�Fau2z!�)�*M�� K 8N<t$6�%6�(.�%G@�Tj"� se2Z�?��6C����i �2er%%�+ �-�� f> !�+Z .>j��6�*z6J�&7 v�-j�~D�-B�M�f��O�*ok[B6�W�(��UP&�P�3f6h&�.># R+ b�H0bcal{P}_{�a rm{em}}(nA�&�*+&�* �.�c*�mE&B"'+)�)�Q��be �t~h"]Y9ge'j��\{U �K�#��� }\Big(\,�)!�+1�++|e \,* ) & % {if �k}{"}>\.4#�� }{g}.#�;� Hol6wise.�" �iUFY�{iau�T�Z}2s~ermin&�4^4*�a�/� �R�"1 y $V_n^+Bt4.u )D_� ��=$en $k \gg )'_n��&hO�K�8x"4�2 $k$).�a_ � (b 3"ifG _n}$ "5�^.Ell~A +  '�]b�_A�e!�u�8{�1n�a0�Xr(Mr t� ForkF �?�s �.�A&�SHo2s}zA�h6 �=!d !j�+�_�Ea5\!(%���ũY�ic�4v-�6�X��M5!�mesu:]kHic&�@��*l2>�s6L&�m�%kA�1 m"�.k���Q�1�.bY�6�YRY+ fY.�Ym��F� A:1*�#E�4)�4> QI* &pH��Ksplit:C+�=*�\! dz�*psi� � *Ir!B  k}�m9_ }|z,&p*-.'F& s.�P&Q�js.ys&�* s�"-%�9$�1)�9 �"i k"2I3I_m}tJ&7? =e3�. abil�5ur�#i ��jY|&�Kw4:�|��(M��(&�)&�|A2�&0"� F� -0z� �� �|^2m6 �:�B+"�+)�0]L'LOforwardl"�1:�"v RabiirU�[� �>-:z* �)^:!%`=1xO (ZR^�"Z^2RC ��$D���m!�M�AG�oclass�;��it 1s�8��T��0�^0#j . E��Pe)<)A�ex�=1i&���r �:�<o*�e"{c�bg{cdu+<a��A�4*4c"�!*4 !� oscil�!J6"t'�2)L�9�!ic"�X�2h4MM&� "�3�*$>�I�6��[i��* ce-�b;8 4_;90 724Fc;3��+Ij�  $j, =0)$g respec?:"D9$�7 $�@ L�30 \pizwo*�B�HA!�%p ing)F i�pemkskU 1C1D�SzS4�S�S�/�Y� 66a5 �:= 1.01$�B c�]zg�+to 6�0$&^-pemdsg>u��fr� er2p<c"� qP:� }] ears���mq>� DOs�Q"�b�+� � }z!B76�;>EOr$= U�Fi:]cri�@I�QIe��6I�+kon�ef���"D_"|_c��R.�(} ��a "N�zF)�/4 (�)}\,+\, x+ ��2�N-JNz��M9$:�IAU(occur�m=�A�$�.is*d1:s�Ei�j`?5�ɧUd��� � .� \!��$*L/�X*qC�_BgےhY���ij as a&R#�q� $ at��q�Cn�i�S�veIi�-���wse�#ŭ ;).Na �.�.6�t�.PleV~n��a+�pR�j"� Z<e:� <�XIs!?\C&�&_+Pe�z:XBJ)5 inver+�$ a .5-I\� Fj09�.mgetF�:�eoong&.� a�k |_c=-e� 0[� m�. qE2�}�N${d- ]' }l/2 /2��]�� !FfY �F&_A7AwQ��3Y�slj i=j;Z EY6�E�at�P>��asTi�>�0jW��ge�3y9*�>�i�>cxp�h�1.�a��oBs:^qJ!y�G.1(a{J�2� =to� �! �mύ�� ��cgW^�eonven�r;��R b�Wma� H��r~ raQa�n�Iy � ">�*�]� N� �wBi"jgJ:%�}�C�XaE>>*�?yi�*: �K2�� N�9ua�clear~f�G�t: "�4.(�to6/ho�l%+s .Tu-�r�.L�H!?Qvcom� �35�6]�zA�d�.�in�� �!a:�in06M�pe-�.�0al�Ese situ�nJ@co�G)a9 varnK 7an&JQ�J>�M6���incomAuAhs,vfi�gF�**��rtU@:2�!UE:� �actua� �1{�)E)�6�u:��E1D m� P �_ �_ 5S "^I�� 6� 5bix �i� c %6��oA�%[� u]UTi�><AB�G2� %�f 1� .�eC"q  �e�e6����~��r%k-"6&0.1B�?!�ous� B�2,m>�rCjs,�� 2 &f� exhB�sAM�Dt�H"�D be�For"T5a�� I �|� |/� �1: exp(I�_�$gg'm2)/k)^2$,�/&� �6Pem!� jT�� �B}�.7^&n,6"w)2B�28�) E� o�6)��(>.=�n^2��.$ �L)F�"� Z&2�*�k�#�1+|��O �N0"{+��>"". 1)�% |Rf@>� Y"�|^p�F3 extrem�AE�f�inP5 domŭof�id�MR 3��S0��J���)/k}{(!xk_b�_�J� �����5' + k}��:�\�R�F�� "�  {PeaY���$isEqmumaDv_apIӀ�f;R�|m{L9 (m 5�lrm{.�u �s�Q2���>�4 f_[a +k�Rof� -hal�P$ de BrogliZ> 6$\lamHH{E�rm{dB}}$>a* M!3N^L% �PLeqldBIw{m�Rk;F� Inde@tB� ,� �ZZJ���\��. ���>RF_ �)+�R��I 2\pi,�k}m meq �- J1O {n}}Rs�{ng���Fto-)�"�*�:eaY�RC���� �� 7�� A�}_ ��AY�͑ces "-� /g�& *�I�wyi� &� �oAmpFig�"1�!k9JqXij�r�)QV>�$�*}�Ai�e��) A} \equivq�.� =��)a� `sA� F� 3 4�3>?F�u"[H& Um!q&�\=]�Ma�1J"�-��x�<a\a� )�O}3"f �Q��lt a%,ong asymmetr�B:� N*`� &�_ f�C�&�N�Y�O)A|\ II.)� � nceѮ��  y�#��W('�E�(ose� wY�� ocxs�%�' �hes��g5l�R) crucS���u:�+a� NM�&��&�Wy drop�wn�Iy rapid] zero) �{v��)!�E)c!�*]h��B}BI���xr�to�A�.:��@A})!Faw"$Y�2($1/2$)D"!he or $(m/)/2n Xuat*}Is&�"f o�Ub oraa!�|�of F�iP)2 Q%��Q~M�!�2c* argu'_ to s�}�A�z\*�r2�fo�|\�`��jk.�0� u�J��, � 2 e)��v &M#"8 N� � $. P� *7�T�%H(t, <`kU�leY{�L`�� ,>,.["� {LL�u�"Iz�670 800 6N�O8�������/g�#���3X&�twoDPl]S+��N�9e,6�>] s�\�rvalid� ij�:Yb� ۘ�edC gal"T&D�0)B�{2n�&�B�04s�ue��/�*3a���yE h m���E"Q �NonsN : mis��$� )�Ev�&N�"fr�Q�wo dis���� ii�i�9��� . Also2��@�6�oe!��Di� monO�#ly �!K�(�&i�vhsm�)j�s!%�u!st�V limiA2����z  a!��VRabi *}(ِ����%E�l��nr��/u�gwE.�h})]SP��A9f1�'%aL�� �� not �Hu��$�U�)o��%?&J0 +$ d-�s�*6 i*�S (b)]A��!q��*�a!�Z �kee��c �B ,#,m�lXME"L �1$�=W_"�!�!)] ��c%Gz -h � "-b."FWk ?M)^�,]�L�#�$1�el��0 �.���� x%�a~)Rega���toZDE.� ~$-100� 5@��N{ �{poslai@r�.�$V�B�N��# "l#�#R�"<�S��"�] S�7�3!��AwEr�9�4h~Ǘ�n:���F!�\�V2�xp�x`rE�)�&a D vm:� sp:mZ�AJΑXe� �N�]dp�l�J�A ��^�� .�u2� r� |e-�2 c &�5r{g�JQ� �s!��a�jX�!1/"$5"e,|i�~�~�%!E6�bW�V� �G-%?|*H e��c"��>TY~��"*#M%L��"m(Y p �g����!e5w�""M&�",x /-���I6�A�����:E�� ��reEa�ic�:� *��5D�Y6V! ��Qh& be a�%6&{&&J�!G!����'"A/ac#_ ledg]s��~ork"[���)  ��an N� �0u�aiSdes S���nNucb�s (IISN� $.~B. wants#%8ank Prof.\ Dr.\��Wal�%EE>��� ��hospitah54at Max-Planck-� f\"ur פen�kA� Garc�' (Germany�B�u>��{15utxpandafter\ifx\csname natexlab� (\relax\def\$#1{#1}\fi � JG bibO font>J 5f�#�Pf.jQ$�R�z~R.$�Rurl^�url#1�>tt!O%� {URL>i \y�iI��{!\��}[2]{#[:>!eprint []{S'��" em[{2�Ӛ� et~al.У6)N",L�� q }}]B96�9i�{F��Li9�{M.~O&]@:lly�a �Z? G.~M>?�}Q.Uan�jP H.}~#Q){m�:�jouk }{*����v:extbf5�{vF�e}{76:E4pages}{4144} (v�$year}{1996�!@J�� =�7:�!, ��J�M� �nf�a����5k!���j��^�5f�2R�ք�pV=&��j�%qC �ie6�.WLD���M>�n:�V�nW��:Eג~�6�6�6I653�69&n7&!�Vogela�hleich ����; W.~P�>.�S ֒A�5�5�5I56VvkR��i8:  #,��E Zagury�>�~ J.~C>� [��E>S! کN>N�aAF��j�Opt .mu$�b154:���28R�8r�� ��� 0)}]00�sT>� R}�'29��f�.<524��1�z92Z9197F: 2000r:ծn�%�Aan2��-8�gB�Z: �-E����� Euro��.�� 41:�M�59V�v����y9{"1 {a}}:�/AlLu�� He�}Zha"��f� Z.-B� Q:�V� Z.-Y>�Lu�z L.-S>M��Fy*! r� 9:�-�80Vy9}:lj� %(eHe� 8��!x�jx����<��7V=7J{19��bf�Xx�ChϿXiaI���U���r jm2]V� S.-W>�Xie:V< Y.-L><̞=X>=Xia�_ S.-K>N)H2ը�a60:�ma 3321F�196b!�jb${Si-de Du}2:&�{Lu-weiI$$, {Shang-qG�, {Zhi-zt%Xu}IQ{J ��}]c�V� u�t:�...��1>��5.��&�9�c�;UJ�4B: At. Mol. �PE0j�32�TM' 5645d J�9r����$�: ,ܧ"�  ��"}](�1 R>1 _j�"? {G.~B�r��@� � � 6!�.� -�023809F !���and1�� 2�bAr�V�9yZ��^��u*eùn�6Z 04381J" 2002v6gar.ͪ%6 Ъ~6r��<Z�2+N6~�8Z 509J� �nHarocD&�1:R #, Bru��$ Raimond�8�~bS>K X�:��Y���.�.�y"JJ��V�� 1Z�1J  1991I�&(>f�)d"[�"t�[��[��[��[�T*�Y ul_��><#�Oaóm��~:&:�&"yz�17 Febru֊ 2004�Q�"�����������҅�XJ�-.*/off� micr)�I%��i!|*("w�D*p!‰W#�#N�as�-2��"�� �$ �.�1 kiz�!�� W^")��EF�J<: (�/� �K�e�W"�"� .�$Q�s :>!vF�68���� .uX=J�v��T��0uK.!enh ��+aou&��Q&�X-Z. &�*.��!"�""v@�>!#�4! 1 �sharpS�!F� !%�!�G�l� d�L*igh a`8acy me�� ogy purpo��(-�cV�s"� "4� ��&�&���(e76 L�Q�!��CtomZs�)! se�� aQy �"R, too@}9 |!c/�ee e.g.\ՠs.֠Ada94,7}�!a1�ewy��topics="a0�}�!��fic _��*.c�2ol%their��by�er �J�"opeEW{-et�F apv<n-��! m�[�� fero�3s�� Kas9�h �len!����T lithG� 0Tim92�� such4%e��ntg3�,ofR_A0�sir+%��,�� uxl^rib"t|\2to!+�mbD�M�y� ly, .�#�J��%6Ro~H'^Rz (%e�usefu�3m�!�ida�/ co�nce�- (lik�6�)�5fet  V�e&.ch��t)�!�:Uma�]i%N�pR�x Il��,��ugges�)b��lykin-� Bal8���0��%�s,Z� {o}f^\��&r=��'o�-a9�I�or4z , a 1D.��m��ls�� ferr��a �zeri/y �&sen�'%y6��� ��ut)��&l'�"0�0-_�L�,sn�e�/Q..^KA��yr���� 3��&|Wz�rirZ"�@�scX� cor��i�e�a.�_ �]um�.�4F��a,��3b���v��G�) m��!3 ]��is`.�an essL7�el�a/�V�dHDW2da�'a�Vterpl����|���!�.t^�/�|x$$96�wt!�!)9jKat ��-�6�K�+ foun*ț )(�}�! �)s,m�ep�+cer�Q&ie(V!�hs�I,A$s�Q�E�a���xb�f2�c��M_xi�2"�Zf)V4�<�{ �2*6q �@�� 5��)"�T �*"ܸ,%�^�lit�/-P!�ic�wpacket�bh�ser��)�Bie01ݾM:�2�ve , x dM��Z2(��, Ej[rt  cEng��A9(Battocletti/�'{Bat94 �y�� �,��exѺ�3o� �mlCao,�Jex�+�� inks6�Pin�oJ� {/�+e�� .� H�a��L\:} �-�by�6�@r��a�ff&: .0.� !�]I;]I�Y.� o�s f��8;��E i&��*J� !-)v��� ion ��. (emiE��/_<���1in?7A�a�]all+Pb�eWƅ�Yum sp��A�6��<6 � e �ǁ�&�O��-�.{eRFO  ^qX`fTba�� Doppleron��\ -�Gla7,�R �s�F�]um-nonB0lŒ measu�En�!�*SmhSle�s?� SSb���i2�.���7.:��6H�s���6��>6�� .�lGT��ia�ઍ�:���-�A�A��>i��� &��%�m�����A*g��sDg��&�|&R5*�A< ������$ u(z) (a^{P\dagger} \sigma + a  ^{$�F), \end{equation} where $p$ is the atomic center-of-mass momentum along)0$z$ axis, $m$ ;mas\omega_02transi{, frequency, , *Dcavity field mode 2* �8= |b \rangle \l a|$ ($|a  $ and $|bZ<annihil%jacre operatorg � radi" � , $g2�-%H coupling strength � u(z)/ R1%G@. We denote also !��after $\kappa = \sqrt{2mg/\hbar}$!�_n & [4]{n + 1 % delt-�detun�-� - U ,�$ $\theta_n)�)� defi7!��dressed-state basis given by \begin]� A bel{Yds} cot 2 n =�frac{ � }{\OE�n}\, Fith $# = 2 g-# � . The pr!�tie5�tmazer have been established in�Xresonant case by Scully!! collaboM%\\cite{Mey97,Lof97,Sch97}!�T extended very recentlE�se stud� s non-w w [ Bas03b}, eia�for� mesaEA funca� (Ek, = 1$ inside*Is, 0 else�ZH). Particularly, we) show!at, iik ?M� is prepar90Fock I$|nq�AQ �z init � �ex!8d4�%�։� $E�@ k$ will be found��mitted!�A� � csame �or�H .vD��$ probabiliA=r�TanI�T^a_n(k!�|\tau |^2B�andvTbnpone X<\qquad T^b_{n+1} c\left\{ mt array}{ll 4eMk_b}{k} �>L|^2 & \textrm{ if } P( 8}{�R,}\right)^2 >i�Xq�g}, Dvspace{0.2cm} \\ 0.a otherwise/�� � a.R�B#\l�K8cab} k^2_b=k^2- �^2 F�j�U=w alig-�=� &�M �cosT��_n]!�-%�}{ _b)} \, K+_b) +��n2E, 6 )}}{%�( Vn k - )�^c_n} -1-0)-��8t68}, \\)��A�+AT�sin��}{4Q  1�%!k}E` MI' \nonumber d,& \;\;\times 5 |9F ilde%} ,!>JP-.�1f!�A:Aja3�4�l.}m�Mo�jB� %{\pm}A:)=�[%�(k0 L) - i \Sigm�/ !�6()�]^{-1�y�1.@�%Dr� 9�};A�)E�Ƙ-*:{k!�}��= k^2A�_iVan"CU�{k!�.5+ .5zq�6�F�ء�I�1}{2}%�( 5��q + (a$@��F� Fy-��FY=u�i�b {k +!|} +�� }�M,���� =A�w �\iA��5+_5+_n 4}{ !�јF\-6|>G��k�$J�emtanf| �.�B5� E� 4��[& &�. -_n .S}B1� o � mission~�results'a phot3duced eD:J . In sence� a [ ,H s�s~ � o� ag6 �N� D_b$ different fromN@  value & (se:( ). This�merelyJ4energy conserv� 0. Contrary too2� � final9 �processH , n+1�  has a!yter6 tB�at K  one', nN�e>Dc5� $ $�fer� �A$ic kinetic F. Accord (sign �2�B)�ei� acceleray ($  < 0$, hDng1)y deJ/>/ coo+-I ). Ix is las )}1R��^2 (/2 m$) must, g�e. anQ8 �$�ensur" at!�qU� may occurMVjustif� , cond1alA3@ult in Eq.~(\ref{� ). �@e ultracold regim!�k \llՠ�a�դ}$)� � $\exp(��\gg 1$"� $K �meq 0$@�total6!&� y $T� =&� +w P$(k)$ simpl-oF��� TA��ET( � hf(�<) \mathcal{I}(L)C � |^2>� �DV~.T�*\{ ��z "+ G .� (B6U}�z2# )f �` �I�}\ � �4UVn&m .! ��|B;-& p:�= �1� |B�B� � u�;� .J |^2F�*� 6��U=!:a �1}{�  qS }{2k-'�{5oE n^2(k_n^-%$L)J�At �Bca�)� = 0$�k_b� �Z= \pi/4��A2?) wel�j�s��a����I,L\"offler \ea�@�8}V�u�)� >8=�2}(�>s�0��Ffigure*} \includegraphics[width=8.5cm, bb=113 284 475 525]{fig1a.ps}\hs�5pt�H 5H$b.ps} \capR2�2,of an"���0 through the g��!��!�$k/Ij$. (a) M/gE , (b) .$\pm 0.005$�� tera�la4was fixed to $ ^ L0^3AYEW $� 0$.�D TFig��5{ W5� t o� gs.~��1�fA%�lyb�. W�u! !: waveEOA�incomZ!fs9E� i9 -- W $I" ͐2�$T$�s variouA (ces. For $(1��>F/g Zir po>� peak5��X%�m!� \�(m�k"�a kvIgerb%ǹ A4(de Broglie !W-�,B�0by $\lambda_{� rm{dB}}=2��� {n^t� # s whe� e�1� fits� ultipl. halYR�Z{$QA i>� ~:�H9��I�LeqldB)ham��R��B%a 1�� $m^{1�th}}$A�I:1^ $k$ AD eforef4 ��D�Ŧ.�{>�|_m=\&�� m\pi� L��- - n+1}��сJ�F� \leq.�8a careful analyB bg :�yP}r pmK s sl}ly shifr " *yE"w 2X).:_}[htb]�c�26A tudEӁ�$1001Yst6� 6�"m � (��"�E��� ).} MAFig}i���}���E�le]stY�fB�b� cor�� ng�Og�m�ya�$�� A}_m$!�a A�na��*�3�  3b6.�%Ga4y%7� !�$(".  .056 1000� *on�vDc�tw�Z$two curves��idQ%(e scale useg-horizonK axis�{ Tdsg>~*} Samekd�5�s�Q2UAq1*are ob�ed�&>2 :9se��0�(a)).e�realis�xperiE�lA�ameters4 discu  &*7}i�s�#��sev�!eZ 6emXnarrow.{ir �  amount��ly� ^{-2}$~Hz% � ��%�g %�$ kHze#:�1e�is couldm[i�us� metrolog�pvices (�H.% lock)�exame)�"ed�� a si�$ �_passage�w� 4better perform��W an w3is usu�! obtaia�R �(known Ramses�t ^E�T% ies � wo�g"L� �)�Cla91}�"� I�AzA1bkis� n on�xUHb) ovt%!��"e. As AScted,!� �"large (� ve� nega�%)U�s��-�y&(%vanishe2dv���wards 1� �q)�&^�E�W /2ŏ �behavi!"s)�predi� E"U .�T�hich � 6.iA�� �1�&j%280��geb� Ny0$�fact,� in�&A�%a1$ t)K�T ,&�L�A�e�$d��| switc!�Ihot $one)�$.�.is2 w� ���I��$)V -\:� = (� &! "3��)�)^2V�b�f� is�(� no m� valid�Mr�� compu� direc� u%�Eqs"S an})RK &$��$is explain�� f changaw bruplat&y~\s.~-400$�)&� �+,��/ eLway aeF-�$``window''A�kj�$drops to aA�ligibl � a�N��all%V%�r��c�e ato�7l�| lderO sa*on{Veloc�*sel } Ifaxco[y*E�ic beam!2z eriz�a v H distribu4*# P}_i5, � �"�&���&"H A)�#�#EHo�* ss effici�+W !{ot� $Auu%/�&-�"���m ]'lea���x"�a�a g *ive grow c� <�. By tak�in!�cc&� pnHm���-4+,damping, Mey:�Mey97}>��t�� �y� \j�"��(n�+6'*= a� �M�2"ebyF�"qP}Bo=f80)\prod_{m=1}^n��(n_b+[r/C] \�line{Ca,em}}(m-1)/m}7J$* $n_b"�,meaEe=�-� , $r'A�ic injiR % , $C"-� loss�� $��H�i� .�S Jq�Dn)=\int_0^{\infty}=H9�%G n,k).a�dkP$&�ei&3.�Gk- �un*�*M ��U/!hi�"�/&!"ng |y�m>c� �-$n$m�s5.�&�!!�� B*w�mmiM ��i~�.� r��Pemcold���RD ��ko 4R� � #.& "sin(2B�2(� E~( Vh_G k.02=G.�2a%L)J�A0!�io��m�6��"�. ��� AIicш9�� � .�1ue��*�r<��1� N!�T^az*�0um_{n=0�&i}&�.���>I BwRT^b�l,+~-F9 2v$)7 follow��?$-6��51�w~v�PfkI+U� P}_f �A�b .P��1�+ '1W b(k' -N�f>�A�>%�B� ,B� t�R� ;�a�.� B�͸k'�&suKatF Av(k'_b \equivm~k'*]*"�&N�p��\iZ0R=�*�*JX>S�,��4���4:�I�1 (l y� I�(daM3j)U�2r � ) at�h�g��2v�"��h � [ wS "7 8._200�$�/C = 1� ��S2*Pif�)�1�3j *>/$ how a Max�$-Boltzmann2� (k_0 05$ E��� most��l���h aff�:� �/�'s7)�:� � . .�� en id�c"&o thos�� T(in�Lof98} undeq �5�e�s�s��)s�urR�I4.: s �Dd�f(by� le peak w�p- s �(ificam5 � EHAG>O� r�nveni!Hwa*" anv si! ���ank broad2�0. Also, notic19�*2 f$f�QLL v�6�enh�e �io1 �*. S��1� deaximiz)�*�6�>H&� �N@� "fSummary}�(96 aper&k6p �A�g)+� >�7�F�of*� �� �0a micromaser �boff6m7. A: alytE�ex�@-%ism�il5S �a�� ial p7e&�7 �7�w7B0  exhibG!�F�ec/#5�fin� �T!atnld+�4�/B8e���: demonst� � m�U�ii3.a!�/<+be:�eI� easi9u8by�!7Y�"T.��)cU ledg��$�{A:. work9�supporAn�DBelgian Institut I1,universitair!^s Su$es Nucl\'es (IISNy.~B. wa�$ank H. Wal��q E. Solano%v�$hospitaEOat�?-Planck-�Df\"ur QuantenoptikAjGarch� (G� ny).�):"K$thebibliogP'y}{21��xpandaM \ifx\csn29�s xlabr (\relax\def\$#1{#1}\fi �,JG bibO font>J F"f\#�Pf�Q$�R�:~R.$�Rurl^�url#1Wtt!O%�{URL Iprovid�mand{!\0info}[2]{#2} B!eprint []{S'E3�i em[{2�L{Adams et~al.}(1994)J!, Sigel�;0d Mlynek}}]?94�*i�{author}�5�{C.~S�(]:ms} �Z> M.}~#1�{�!.QanPjMJ>M�� 0�^. rog.��. E�rr81:I17R57r5Kas!h%8Chu%71!7 Kas9�!nnf�eQ}�7S>7�^6Mdv. Lettn267:E128V41r4 Timp.�2:� (, Behringera"Ten@A, Cun!ham, P�5i�D,and Berggren� Tim9��v|G>-y:�VY R.~E!0.��B D.~M>B �@JJ�9�CB�1P�� K.~K>�9�!�!0e B���9:�Q�636R�2r�K�!le}(2002e�et0�5W>5IZ�R�Mod. eq}N�74:D�13Jg�r�Balykin��89�Bal89�� V.~I�2� KZ� Appl � Bj�4Z�38R�89r�"�2.L8:L%�A��.M �-~ �E�V�B.Z:V?GJ�n�mH>����uiEurop��~�4Z59R�98r�SchleichA�O�Fa�p W.~P>�MZ�Com�  At. MoQ�j�33:Lqs45RTv Basti�d M�)n�]3i|swG~fT>� S� Ft �Z>�� ��Aj3^ 053804F6 2003z#uT!* 6:�.Iq�a� .�Scu96�\ M.~OA .� Z:����V�=�~�76:�M�414J� 1996r�BiI� d Freyber%4�9� Bie0�� W��B��Z��5Z@619R�v� Harocs?&�1:� #, BruneQ�Raimond��Har�M B� X:V�BR�ڟJJ����1^( J�19z� E!rt.>� #, Schw"� Barut%��M!�Eng�� B.-G>� e��B���?AJ ����Yʎ^�2V�v�(Battocletti�E 1t�}]!�WF*X���5CJq IIj�b*3V,v"Pinskeu+ 2000:� ", Fisch�Maunzi(Rempea'Pin00��P.~W.~H>* d��BO ��=P>� ��$Bl- V Na4n�0Z�36J!�r�Glasgow5ڡ6:� #� �T�Wilkens)�W�M!�GL0~� B� bڜe��=B� ���EJ�1 !&q Yu�*� nj 4Z� 245J�!�r�Sle�V���!�� Sle93��BP T��j����78:� 328V)v� �.7:!� e 6� C,~n!.^� �� 2�Y�VQ�`��^Z 4142F[ 19zq"�n�%��ɕSchr\"od= %�.U��B�n:�Vg��>�ג~�� �6�6v65V�v�9&n7&a�Vo��2�.6���B6m��K>���;�XV��5�5�5I56Vv5Clairon.2># # , SalomonA8 Guel^�_Phillips& r9~A>� e��C>= ��=F� ��' W.~DB� 5!,F���1Z�1N &+ ,>�" �) docuO} ��%\9:solva=,hamilto��cl w�< re�>sG9(,fe�E\&D@Jds)4order to�'a�K&j8%8involv�0aN<an�'( apparatus *U meU� , it4ne�*�7c/^)5i�@ croscopic�+ �R�(o t�SI.)�s8Aal me�:icP. �Cv�a�\�+% w��,e�)ed. I_Tgj;(@=, rapid�-appeaEa�(Hs*diago.Tb�@$*�6�:de�e y matrix tes�(�=!BO5. Possi!�recurre�L� hind�-b�+e+; s, \l�b . On/+5,O;9 En�=a�Y*eAvkE:I��8oATre2.9b*�C�-�-9co�6�Y�i`0Z/6'�)' )'�*thus derH-$Born's rulg0von Neu�/SQ�*) A,e�-!md�yalQ}2y��1(keyword} % s�e,�)KGB: \sep Q�}s " �(s % PACS co�D-f:`\ A) 05.30.- |05.70.Ln�B �} 6�%\twoc�&n*�-P2�-��12e@E'D %�p��1r7m�a�t�K conn�0ai;+Ŵ stan=fA�Im��'ookI<X1 T cles devoaZ�2�.sub�: focu�DlU�axI�EQ�Mp�/ rm{SrhnI�y6�/ rm{A4Oɡ�descr)g�.d���>cEhed5�A�CbA}$ du|%e�J}�1wh,�\(}. Our purp�1;Zo �fy85 azeIsh��/ent�)od�HRK�I%1�I��avK%UiWD6��F ABN}��2?aM7 u~>�@|3t4x arise �1aq0�* �5%QmoA��hav1�A! olve]roJQ�ABHa��Z��cru 0H3akAH*�>bot�I.�n�!��oE� 5�1�m��:6Vr. A�my%!��3A� ' �0"$s several ;1&�1�iaZ#%it{!FrtH}M�-a���Y��to�0��E�V�, � �0lyA��haAFu�ŷ($t_{\rm i}=�\�+it{�x4 MT�M�� &EtefHrr��ͽe[!�%�5�a|1��* rm{fP�UJIS}�E��cs?eby!#g^Hon6�5 >J:,� (or �/)%R� %�,Alsome �u76 belong� tSV 5A�Prj.����G!�BF9��it{2F7ed}{<$%�$r\hat{o}le&�S �er?elimiu0dA� 16� s �K�Y�on�Kwo/3s�%�f_hand,}�z�5D_uciblyU@� a4D �>eory. W3L6arQ�qu�Ybl�;)�i2#��G,2�=re�m@Na �U@4, a ket !�" �l-, ref�K�n�A��al�^emble}!� �l�mT�`%�YJ "�^� !� 7�!G. �<�� ga� s ou�ol��Y�ab���DlE��_7 X.~ 5en �. How����@ras 5 �Cl]A'ic�5�! e"_ 4� es-& fl�O�s due!P��m�uM o�I�a;�dA!�U �D@a�S deXKifL �al ��l� :.w$A9J$B*mth ��X >[ A,B\Er] =2iC�Iey�H! �1c-%R agrea�*HeisenV$'s in�V�4$\Djp A B\geq{\vertAVft\la�! C ��b ($%�#x�6%��k �VD8s !� zeroA�Dco"�:��7c�b�nY�� mustA��M$B-$ 1"� !�Yx )�s,=��7+Y[oUbuncer�/ �:(! ��]o.Q$ errors; hi.���Q imag 8VH�� precis�[���  (.�, sa�at�:h�2forbi�M��( ou(E?q).�I�%AR�, even� �� �Oect!��c�Li� lway�pmt���e�Gr� * � }Q $Ŝ s}=\�B is_i$\Pi}_i$ of2�; E�s�$s_{i}$ �9eigen�*!Vs YH$ $pro� !A"!� Hilba;?Z�"zSJ !�as ��4pO.� �VY � ��x to �s�� (�Na��deite�_ �s}�}�Ѳ $|\psi_im��?=L=6m� 2 |$.)�K��F<Ѫm ly!0an wiof�c� s�X� 2�-�� 1@�@��?�w�a�L%� $A%�ݚ�@an arbiVh �m��R  .�K 1����� $r�[( 0�< ) $, � ru� ��H� ,e:ormS)Ss&�?.[ 4=0RmWNo��Qym�s9Th�Km�efp%3! fi�-F1� � -)f}}$, !ZE �a�*�N3 R�is�Zby� it{*}%���a�} �=\1u]{Tr Jrm S}\,Y�{i}1#9� h{ ,]tag{1.1�]001.001�u�mIy*� �U!6.K . (wsit�a:UY2 A$!Pa��e $r(0)a�hq�u� hi|$v ��>$p_i=�\��\#9i|q�.) OS7: ep)#$it{perturb)zA.�"K B.����b� gL8�v��� Fas noɪpr�[�l&; 1�&m� t sm� �# �J firs�?e�`. IKP�daKͱ�  �icI,y._& �or �al,� -8ُbso��_�$rWv�B 3%kdCWf�Ta .��$��ysh�Wbe suf�PDRs�]}le*��[ go�~*�} ge.Tnm �.��i Ffd �ly��jC \5x�litsel�ed ��!��8troy it  wish!8f� @de:&c�osem�-U6ras littws p��� chie�Yby ��C �!36�D metastŢ�e,_ �)"�| N�_R�r�� $. D=�Z* e� 6� '�!Ptri�~�����9�XDE�i8 sourA�jR�i� �W� �a�alm�~~5:�blte�w ۡ�gSch.�S�36��^A$p+ �eX.�ea��ay holds�1,_ula�f A!+ai�]AZ � 0taneously bro�Hnvari�c6I $ beAEtxf� $quilibriumA(teF!�� �Tr} (ŵAF�)=A� �8 �! I]�I<6= 6e:� r�An�f _ed&�Qfa�EG )�Jl7 'YR ananq �n�� associGI%e!& -� ~7r"� ��Z)} Q��:�jaV��*� 5�D�� "�  =N< o�s7R��th�mp~F�+B~!�xW �&�B'�o" �}9̽T\mapstova�#�A�� %\nn\\ j{i)[ %�)N!> NV>6S� { .}� 26� 2� �Ful� mory!3kepdnA?>�Im�B� 2�1�� m�"� .�>d�7 mean]vA� �� {\itP} &!� es}e �a-is �un� e2���� . H], #� &m on iried ��Z w E�loyHa� [d�a6 �.Xm�x(1.2) enOassa 1.1)� ich�"�`^�<)c] on �!�.g$ � �!zew 2�R�jIt}m�l��ince i�1�Ref��Q� �i�} , bu�!app�, otb�)7=).�!���q >l�$weakest�"� aQ� "/�j�!�E������^O%_�Y ���-�I��#�n� �"i��-A_i)^2z =0,]~y3q�1.:02t S �C�.Q��M$�AIe�\Aa9�lsGinFr�N�e (\H&� 2})  )I5(A/ rm f})$ w�P� feAe��m�� IF�a�cAspl[ � A�*.,m�ly �%g2�B]� a s|f. e�s, �]�v "a� B suUE�� �ra >�<�f@��)],�n2L!nl�^>V-�>���%�/.� I��� �!�Rŀ $. S!�t� "�)W�s�lF i[�#�l� ] �� o . �� it{S�_ng}^ eOe3sbyA�{�*N� D� E{N�%Q���,�R!'% \B:�/)IaW���_.MaH fud6��i�rE��g!��. A fur��a�.*aJ�a�uta��cx]e�whi}S�Na�D�7e�9i�1_ . ���.%!1�lo�"�"�on}Id� 2JtertQ� Eqvtj}��$i\neq j$)\��"��! &V�c���i! � s}$:�Pis!.rT a�T to��6�".*� �gE�o�blQy�)l also=g"� }��� so a�; filt�|���F�� need o��ermin9("5����Q�\l�!�nu7�!;bE� �,�!7�y�Sd� � I��UћR�SU��^VRdIr rsi�tp_=�s} D&abo1$$wo unavoid%}�$��"e �;�����& �[ �~��6#� $f}� ) �q7 �Rble�"�#� ��#in���,�(the entropy},mk e.&) !F�S[��� ] =S�[� sum A�%�\P��i- ] +A�@ X6�/� 2.2V��*� ( \footnote�.���don"� L�Yf��T��:�,��(u&9��05S�$� ��ot =j$),XA�1�P !Tof��"�f�if�,j $� Not��atq&eE� i%���+Z*� i��ew�AR#!JA`�(� on�/ "�� N� .��f>O�S+T$�#C �Xs5|&&�_&�" : (i-%h�R�9i�q�oaL 0$ (@*fix!$p_i$); (ii!�E-FT �e��oBu K.�Yj, �z�f. iuU�Qas"ca-{ %); +!!�:a&�/r�[rrn d2�s I�C ) �se�"XsED[�� S in*ivE&:�'s ). }��#3!�'at"� �M} � �K�Nj\#.�B/�" ] +FUN�U�hR�X00�2u A_�m-'��[$reasons. 8nke�&i{>� "�*Z� N!�fB�0I�� ��J�I :5 ��ir trunc%� rain�M��� �a robd#�_  r��* EVy2) {i}$!I  ��f tI3���tG��ŕ28&�"th� ҁ&1�%D1 �^ �^s becaus�`*=n�2}&m&,a��s� elow5 Amanif�eA�aM!!���\ͼ�2�� fa^AY&2yA9FY �I"- �[u��2�� �!.7)�!`q� R� 5We aim��-�=\a[X �  S6"�p���i >i ^/�\ lapsF� .Ɨ?v�� ��B$ basic law%qq"�7s�(p�9V��)L�*% $. Na�u,���B>(2j"by82man b atorQa�X�c� n�$�$��&!�a�%�n�$�,m�&l 9&� "� toM��v \a/ngs� :R#�%�  F4ESI�$�& Z� � �(����Ž .n.� �T�%x>�&)!l {X}� $ $Fk"%$A� �%ei) cc�> iso1dV7s�� $ ev�0s6�!�,Liouville --6 ��J�i��Jgd�}{dt}Y�% {H},!\�eB{ ,�2&��T3��}�0�� he H*9��H��i7�))�ixg��c>�5�󁜁jm�)��C6�"@/6#V�%�uw,)� ]�ze�.�xn hop�,s!�I� ques�m��'&�bT!.��(n�)�d y!�:i�9�3C4 }. Hzg�ork��!4�r�4x l64��_ 2a�m�� �5�����* be � D6� ]�&�."�,@,�4c!4"m ��bM2d Edit{Dq�3}�zY'of74 (2.3)-e� � .IQ tI�)�a unin~af*t)�!me�|.Z'&� $S=-B�&%&��_n}@; �B�;/�x�!P ���e�1-2a 6 surm/,f}�)%1aIO�ua}1\parado�9:��� EI� % re��g6���lB�*�$��)v�ɖie>�$��*� -zurIsoO�2�is ba� a�j ll k |�h= �$P!� p�8w� ��UmeeXzb& 0sH ach��&�1��1j*b�u�"�)%, �&������VT�%&�� tL" � .���$p�;{��}^{qtput��psa� ival�(�,=$F-regZ|I�I�6�3 E�ũ\���ae,J�[� &^� 5]ng!��.��5R, �eA^�let* randomAj�!�higE%`^ons\9Mayer}.�$i%=y> �.ja5`}$ (a�ain no m� �A�.et� minimum� � x�J�2g�^�s;e�&� ��lev*=�6�� (i/}e�kthoug��2,��-*D^�� �,lZguish���p�8�;s� %�J� O&�� �(�&� :7l![$P\gg1;%�!"s��leA2.ma�erous�A]L $t$ flowE��"�)$s build up�9)��eft( 2t�kY� �_.���-�!� ���;u1|~nearly %hhys%g���5��3?g d $1��pP0=���&soricN��tP5doi-�o�s�Yt����\Y�,�(le�6� ��2E^%���It�3��legitim�9 plac.D_�F�b+�Adu'A9�n� N �!�v�9"yly.� ��+.� leaka�._i� y��.� � A��u 2���2� r� an6��o2.A;in2ive��"WE�EIcarrya�� return�4 the�+2B�&8Dr2i�in��"yii/-�Da few��>tU arg�I ��b�*dthe (;y rigo�T�� E�i�An�Wng[/ $P$,!�)Z���in��ty�@�� � �@o�@a�;i��"� �!rJ� �#be �։t�al- ;_pZ@s4 ms $�G.")& �C a���*siQ� |S &_;�- ����de�9%�freedom��%e $P $� -edžI0 it{approx�}q���G%�-_Jio�or�6� ��$!�$�}�b� ����� it{!yct.:. S ca�%�w�t;B��i��@9uAytron i�Uof� 3)9bYme.�8e�>t}!� a ��zR � ��Am���jA�a-� ��N��3&� ~ �w� all �F wU�֑I�actuaZ1be� idV�� one>3" 9M,/ept,�&f%�!!�Jn*N &c�����^Discar� �1imper�%(nu�6���� � �y ��lson�'��h=���c&&� &� (2.1y (2.22"v !ԅ�}�n� �NU���plest"":��piBfE�1�~2+�:er�b�:�s}_{z}w ��C�> $z$�>)�!y�d��2-H.\upe }=+1�9s_{\dow�w }=-1�B%$i=/$$6��!@� �#6��.��$2\�s2$"5NKR�#�b� simu@a��magK� dot}�A�e of !a�!�56�Uid ��X����$�gwo"4%�� o}� M����(phonon bath*B-� D6C�is�$N �  Pauli"\sx�}_{��( n��) h($a=x,y,z$\ ; $n=1,\ldots N��se5$1 ��m�_)m}8~uhN}�"�f5&z��=& % $\q�)�iz��!��^a� �ion A��$�_ superex2g�)T��E"6 c`ui/���5 aniso�#icM�K.isG ara�& ���� e@5�m3o�&�>3��s�>=�� &�!remark�K��a�wil be�y �-l�.N5q1��p =� rm{M&�B9�w*8f!!�-�+o��SAA�gE(�~ �<I� :=6IQ�M�.Q�*�1A�J� Seen � view7!�� %$, (3X0lPMlikI� -an"u8-� V�/��aWHA�. ��a�E Ą$step, let�K���!r�� &�5�+>�M}$�@qe},*t�byRre�.�;.�a� subm����nijrn�2�S.��uE�mnd 2)�!re^-)��N j2�Ei�> 9$-1$\e��- $\ o��X��S!Gt��B� \�1Cc n��}aroa2 exac'ga{!1ymsugge�2�AK| ��de�2k"� 5XJ !A^s�)ld �*Z<�d �e�lib�7.�i�%�2v byE����A�9 �%��JgFl"��m)g) =-sgm2rm�k-T;$( 0%�"�3.�a�J��1�5JT��+m� \l� %"�9\\ �-2+ {)6r3.4620�4�.�$�� ��--WJit{�99}���2�%x�(\�J7��q\pma Z�M�$g\neq�_$�;aAg��ru62A�e (]�E�@ �Vin , 725��k ab0e ]M(3.3)� ��acS�Qu/ ion b � s� H \vertQ$ a�$��sJ�mA{=.�hI ( h/TU�%�{�;�;}"!S g+A�Es�B3.56�51��} ($m_� >!x��<0� 0F$g~O�au� .� $T=0.36$�rm{~}J,+i"�; $m\�4!%��-m�=!�t2<|�ken: �7reS�$&�o��E s� �� =-m_� =ޡS�9 $\ v˹cl�0o $1$;%�$T4J� 1-65% N�2e^{-J/T� i�S� $8 p}}=�still1=ocal >n�)iW&whyA�c KI�- ry�dn'��", �ϼ��  @ ic � ��)< :�� g/T$"�7�  � )�e"di%Ys �7�(� ns 2ZBe0�� �DAW�,le .$F_"�&�m`")���6one!Ye�U�;� $g&e c�Q.t�H��$J5T�J$m$m uαJm6�6k/Tm�u�,.�$2m^{2}=1-\ �1-4T/3J ��66�6A�.�)\�GsE�2)�� T}{3J >|%� (4T^{3D�7JJe Jqse"-1\NvT�w2-eWa !�"� A�"$Y[M�.�Bw~. �8� �"�+0�-=R9�M}���> &B}� J>=1/2^{N0.�N��m�ic $m,%\8& mM�=&�nh �B}A�a+*= J'67\>2to ��� 2aB}}��\ �*��ځ%='(�a life� ��� a�YialE$N �\a��"�Q�͇3,�F>�b\J�ND cT�*n �f���"4�[�Ʊ"�e�p-��, ���� 66�:1� =Z M}i}ZF ($& ى�6� xP(0b&&�ge]U!%��2��pemKonJ(.� m*r*^2Lg;`�a�#ax�lH&�P�!/�6DtN�E\r6$�a '.H�?pe��ent�!r�|�4*�E�( y:��m$ A�!��z$f�R?arL $����f���yO1/�qe�en�clear��tin.�AA�. oQA7pmFj? .df�FD�0 �ZT�6 Sa�B)"�� . � �%���H�m �*���Q&�Pe�psV,�a gooda�did!� ��E�"�. F_�lmAf"�.Uy� "j\D�( a� >Lhas.��AGFsymmetr\aka@!�o1}� ��8lA priori�pK`"/Lbia�%ٕ;eN�*\�c�)rE��� J�J)��&>ioo�pl�7i!]be �:d w�\}O&!9T���azd�'$% 6{�.k�qVaseVYsi� tinu�4��r��d Deby�]!cy cutof�($Gamma$.\ AxA6�$\g\ll1$J�E|.�M��i� :�,a:�&� *�QBf�\2 76S 7S AR�J}�6e-RXo/Rje�S ; :R��;)����ca��,��;s�[ �delaya��>�/)' T�?�x �!�^lQ�Ab�"#��2�:B�rJR:"] 12� &� ��V� marg�C��e� ;rml��0�at2m.B}B� 2S����! deep�f?iD��"h*. Altog�[fWG}R��:�2i*ޮ�[H}=E�.�S+BM}J B}} J+a�� G���d*�(*=' ��[ ndarܺ quir�&�{way}, �)�)~!h)y does%d�&�3��h. BC�6� � ^  �(g~9al�-��.r"� y��>}'=-�g &� \8b*�86U8FU�� !@c 5ta��nl q�(5h�a�at �$\uMvarl:9/��r� Ha�o�&ame, du�$�(�`��"�L f"O v� "�l5assum�dev��Ť g�=N�1�$%�-g\S) +&q1Ns-E�  8acge�\�|�� �N�O gg�"��m�F33W@J�eo|d!�(�&�dC 3),��rN�&,�9"�<�X�=&z)"� jqM.�&�<� *W �E� �= %�N]ZH��C.JMH�ϑ�&���%���()6k]-&�me�A��,m-"^: ia�$NIa*�#. �8�7 sketch*�m�,��P*!��U��#E�;Ҕais*of 6�9w d"��"r�ABN�B�W�CrVn"�?.� AL2p9l���*f0�9Ɂ6)*5)\�G�A*� 2�>�\J�!hZ6D$r&� �u�Y�� +&$R, 2,u�"�FV"� ..S=,����Uw*�%|%�m�in � ��o=va�E/fZ9�AQa5J�iZ]7_IT}b7-gN��evm&\BD�Hj}-�I@ s_{j/�&+M]?>� A}% 2�7E 9]*[4 4.�C4�q!�'4>u^��6� ��l>�(e8#i� -ut !�+J���1��e_�� s (4! by $�j�"+4 �Mr-�m}- \1v; nd u�A �X-��Rg@ ���JJ& M=�BC6�dA}5���]%�Jj � }~P�I�.�V<]V� �#�� (�]�^k�} m  !46�AA�J"!�,.+ach�s�|o � >Y�4<��the oJ�"V�it{�1 "#s$_a���(EU�@s6y�?Ś�'��nf�&"l- too�oAC��&t6.� hY�J$m[+��OyZ� ��-e('d�U��� FL��m��aU9�%�( �},a�Ga�= at h]sf'~�.zt�ic$�s (3.5)�V(1!�Lo�a3aH%�!4.2m �qtheRfh�Jti2���_!�=2jiQnV/H�UC� be jP��[d��s" U?�/neg��,l c �!�h�  >�>M� J �%���#Q�~!A���J32D�)� *.F�>�:%�} }�FC��"%Q��( s����% �iNCIM�%!9a �%< �K��S3�up�T6x\1MS �Uno� 5�Ye��:ly 1ua!q�maWkernel} �pe*ibAj);6o �/^;&�yL1bA���(�"} ( t^{\prime��$j!~7e�Sh"�O�.�i�����i�^-*is �-!��_{a,b}T _{n,m}K�-N�,_!�si-oh���:%L#Q�} P�r=Z \int_{-�/ }^{+ �OLd\omega}{16\pi }e^{i  t} �2 cot"�!_ /2&�!-1 �] u!��� + / +B�Mabel{0���!��� Mv6 !�bar/T� Un� n x�I t2N�'��.M6 >TM}A~k�_.�sZ>"q �l '� pair $ijK+�KqS>U} aN3#b�r_��%x(2��s\rho!^{ # -��, .#\c�, CN 3���"4.y%�"y%9�v% �J�t�*� -0,\zeta_{0,ij}bO�-% a�J\�&? .\\� = ��A�.g \dag *}$�J}$�,F$2$-dvtCal�+&5k�V] $nE�&��x rWI04"�!�= % $ &�.)�A/��e�s�3 �-��t!PU)�� !���>eb.O�z�J��p a��3l�:d�~@wriPem HO!�imp���3m9i��0y!P� b:s�: ��8w�$b9-�3, ��lyU��"\dot{%N}Ar�*|M�2ig}{�8}/_{z.Ff2},.#2^0B^ 2_E� 1+��ͩp�t}{�Q�q0�c-ZG}{��z�c4.�#aB�#!�short%�s ($t&/ �u�and5|�@2 0,i1w��2� !�m� 1�)i(-�&p1 ��  tanh +/T11$O4.<�J<�� r�ggE /Tl(��m�e�fxa� A+ ii}/Afii�Li.8�7)� Q�-i_� �#�1$ %wo "M� !idde�62�Ih" % =g�+J�%%$Q �)�*�as"�cb/ f�*'13DaQ+�%&;]{y!qdr�@un� va��8 �n�-4x��N y��� ��$ic� �q%X8�X=!6 J�G =0$.�9"."��J� E�OB%w�E � "� $I��o of B[ hard.�!�V� gM�&� �0�d�s%*�iqq 6 84Apx|�&?�& *��)ezn��B� )a�S2JEK�$h9RAY &�n=�= &~i��l �!S$F� Mj&�M]10v�/�=��mF�-u��m *�!�/�j� S�-�B�si tinu{p!  en�� �/ I5&mB.� �+d��p�"�9y�{N�Al1P2oZ� >8!%[S�� L3^neq.��6)��Kq�y�� t� �f@2� :&�: :�f22 (:>lmv� $. O�{tŦLŦ<��g��A3"9a��M|>� ]�"&�)>��a^N���J�=���2g� f ." VViB�JG ag{5.�5�.%>LkHW B�UM(5�F�"� 5� ��:��%$\�J� �:-im� RM �e � n�*k}{4+}D9��!�h4% %TCIMACRO{\d� \�s_{n=1}n+}% %B��E�"  {2o��*dF7 %End41.R!+Z�hat&' &�2f$& y �5.�7A'J�B7 e�MI3~Y2QF�=� a�"G#>rKY=�B\�j�e7��WR!n�.�=n)]!�!�F^ sim �E`� /\tau_:�H+�.n�i�*X!�JX]&�(&R�aB�0bA�.} ^zm 1}{�2N-��?��{0ex+% �4&1"�R-ich"� !����4: l�L&y\3g��'weBen�a���%28��E$.V' hL cay,$de^s�rapid2�2\b 4k t)$, H�5 &� �'(5/!�!� !��+Z $t�/g-k�F�h2 ;�>j:S�n�bI�u���2 inis��aa �� nc6Āstead!�e fact�g$:�01fen�oe��6e8 (5.4), environ�S�-��~xte/Ca`f� F>FdpyxSu�� 2_a+?Q�O�X� ��it{�Q�t#.��dD".4�+:��kddj $ &fE} Z�Q*r%gro� �"8 *� !?,v?^vQa��|d��~�l[ ��(5M� m@!��ccx2���A�*�B����a�K,@J�-�!xi2 "� �\l�y.y6.�hc!an�n-Y1x�����)}"l& ]xz��y��an &%}&�F *\_�82_��-s.L>E�!���0?@�6� J�:?� ZmB?�+ !=ens�X�k�@fee�z+QL�(e =�Y��Fu]�.+ 7e�Q.2G!�.�!��>�)�K�7N1is {\it� �@};�P"����Fa1�$;ON�TrA��.^�����R�%�.����� 9 2gt/�0\a  ^{p}$�� e�3*�(e&�4�$% �A;t"�($v�w�?$.3 aH�4 ampli���N �YTB6�(ofM+ $N$)�we�3uqi`7reXM>"+6+is�&�3�3.�Sup� �&N�(Y�=���A�Ilj� 1�.���?J� b �_$& C6�5q�, ww| ex�J2eriod�:��47 ��p*%/��i�}E�apo�  i (�zj:%�I2N&"8 �*p "e3�R]��/a��*^ ��; gb�9n,%���eFee$E� �  of �I ga��an@�DRl�Nheo�v�&u`A"� �t�"bQT�j. ",uE��br�A�(5.�t�d�� ropp� �"� (4.6)?i���Fa&z�CS��t���<~ �c�/, a&T�# 6`��A{po8n��z�?��y ��%�� \chiF�! w3$V � � �^�,tAB/g��e�B !�*�e�E!1� �� ^Xw ��01jB� �� Ӑe%Ő�.`��e�"!Zf� B !B �mo rm{2� 4�%.�>(% R`( ���O -latG�&�N�NMR�2����Tt{lh�!� 4) i� T50��Y7 1�d*�!*cM#�Jin  ��!i� ��7�R ���i �$?!E�/2�� GsN/ �gg�/ /N'a)� $�Y�c��t e�E~!e�;ct � �2e�� �fQ-�n^�&���� �!�>�narrow}\left( 0\right) e^{-N\pi^{3}\gamma\hbar^{2}\Gamma /32g�}$\ and the \textit{full matrix} $\mathcal{D}_{\upav \dow:�t �D $\ disappears on]�time scale $\tau_2$. The presence of*-�, dissolves into correlations between2�E�M�bu! is transf�s 9y as shown�!�Ppossibility of recurr!�s. 9� nexF�%�6(, V-rs � red furth!�o zY<, ��now can no longer come back after any reasonable �E](. In fact,\�t peak!O $r� $\ mayy even ifXreAnoE� , providei� inteA�ion 1�S%� A hai form $EH}_{\a�A~ A}}'$\ gim$by (3.8). at soluVfEL�& =0$\!�the equM#of mo+]��!� hen �at all%�4s by \begin{ga!�h} \tag{6.2}\label{006.002} ~z e?( ��=\frac{n� �7( }{2^{N}}D9C B}}%\\ \oA�s {\displaystyle\prod\limits_{n=1}^?� \cos �$2g_{n}t}{\��}+i\sinR%�8\sigma}% _{z}^{�n�� ��P{ .} %%\nonumber \end5QInstead!�(5.3)��Dfind a destructiveIkfee�,ar$�($ factors eA� ing%>�na2�n)5��g^_9 !� sim nw:9t�/šuI2}!�prime}}{A+1�5�)� ,}M�36�3}%6��againa�duces%�cay, wi� e alterna%�:�A�5�q�eFuR�}m,1}{\sqrt{2N} �I� {\delta g�.�46�4�v�Zhe�QB醡0�h��sma�asv=U &�2}�!�/�. A�[pon suc9at $1\gg3/g\gg1 �N}$��rLefore sufficient to i��he >�"�. P��$NPlarge��a>} Let u�w turn! vY��Iy _{iiU-2�for $i=Q�`i=&�q$g�gn#(4.7)!�W!v��*A( $\zeta_{0,R=1$ Y� .W /=m_{i��We#rewrit��e � � $m&�B� �� R&&^=0$��"� "��| �� d.w}{dt}=hB� 1- B6-\tanh .//T}�� %%R". \\ = DdF`% }:� i�q}% /�^{-1}6�:�v C 7.1g   7.00.�w�$.I$\equiv g+J.m�Pn��� A� func� $.��� .?5?�!s defiQ�3.3);A, Er , $g�ll beͷd� o $-g�last y��(7� i posi �e�.� $. H��,2���2��Z� increas�upq�� estx� ��m�n VA:6� malS 0discussed in �� 3W is )u��) a"� one,��o���T!�bo��e�i!� tem ure,�$also below�%�is �%an� ��ca $\�� 3.6). Iia & mea� m� fails si� sup�IoJ "� f ermZ�A) ould$ ng�A�8apparatus to it� �͘F�=0� ���6ric�t $g>g&4c}AHNumeric�,!/Hwe take $T=0.34J$, "�)T�~ B $0.363_ � 9h}=0.08J$%\to-[2�q�2�M�es]�I�$m^cf}%Pe���_!Zlowest E�um, sjat��M}$Ach} ferroU�+ 1�$$\ very cl� a�+1$\ (:� =0.996J$\M�-l� d $g!(9J$A�B � ��.g ���8$n switched�,��u�!( remains p�E unJd nea�6]2Aa�Z2/� j�ensity z,�!a symm8 �rero ys Q:U9$\ tendaXto $->�)memor��trigge�2Uby  kep�   N�� � � 9I M�2�A�� .�cu � %�`�fea��9ideal.��s=�4� obta��g depend�L�.e ��!P!�%5vZu is f� � ��b��teg� $. Contrarya' the J�(s`4),� 1) (6.4� )�)[% &��A�.*_{ y��!���2�mB^V5 }% a�re��di� power%xN#�r� ��ul�.  illu� !(e behaviourXf(� � -hand sid%�5�conE�AX4regime $g\ll T��Equal ���� A -�,��-S� dewes ! D-:�,>,=4T� /27�Ua"3i&d�6<5% =T/3�I���F= $27J/256!tiU6+ =3/4� nd��to�62� }=:o\!�$JqW6-!L!a}*� � 6�D�Da�appro�6:nD � $t�ymptot�o��� Jt/� zlGstH ly s��Uhe K c Y�Vŀu�6� B�a!)�s��s�~ly� Iu6/�S�2�% -�of �$g/J$)e dela|� "< reg}%**�aon%T� l T/E]��piNtAo�s>E^ -c"R$=\int_{0}^2� F��  {dm}{� a-Tm} 2� e3}{T}�Y \& 3J/T(dx}"�x-1"� a^�x+2+2  >�"/6�}. @7.2Na� .� qA!��!���}>"�iBmF�1I�{-�.(\infty)i= � Z >,.�6! �2T}At%�%� { J}},-@A�a9?B��(s&�e�>De y\piB&�{36�IMb� � ag{7.g!�Jg��$BGll 6x$. F�>+$a��y�� , J!F� proporA`�v%/Q*j �$9 s �� �$ath; it be�"s�q�{a weak"_ $ T$"� ��at� P.�.�Concluq}�"sp��of � $simplicity�model �!s rise��an elabo� q ario. It � �ll�� ~ir�p*r a quantum.v ,�ex/s s !KP�#2 $+ $�%s �Ũ��,� g� �z ,� oy� � -"3"Rz  � � �� akes plac ��ly*^& reduM�� (5.� A"�r&%z  hinde!Aow��j!a K���L�%�#5�]A@n�i�]";$)7�% spon�  %z%%be�%rt��ertia Re>w EE�at AW%�Mre%� s;r;�y occur�ifica�e through ��&%�9&�>�Y"�9�ey%V� K�"&�  .�%�A�&%��)�m�.lD(E���3) (7� !�A "!sizA�fM . A�&�%�1�B �%�"�.�dynam� ��cAt�w�scribed!�wa�(9<%��� a .�%��&0eters satisfy%�in�/litieNBN\r!(text{\quad,}Ű�"�l�* g+%\G�* &*dQ or>S"}"�"1},% \�]8.1&�"8.Lǡ�}�#&t!�#afg!�? �&P�$ �\gg T�"� J�-:-J>g $ 8.'�2 qKw�us� establisiR*� 6sMN"(enfor�$�bap6+al �� pret%5a���x!cs,�r�m�� �s&�"� (�w i�\�t proj�aza pure�e)��ys�respe��) non-commus observabl��$e same ${�+�o}le}$a tba�*���6f b physe� vari iin clas .:�cs��e�6M,�; %�quotedbla! �2O \ do o!B�+�}gle ob!D+e�&Iz1!�--anA�emb<f<n  prepared T s. O�a!�)5F�z cripaQA!Vdmicroscopic world is avail!1� us. More%,�ct#MY.Grs�aX",F��d��byJ [�al-�s�6o%aEd%"9�.��� ex1�y�: ��!�Av$uw��.�.J-�dox�re too?n�?(0ca�ye1�ximi�schem�ut ach"� exact ��*�a ���>7-5��"1v(f�!s��(crucial. A-c <  a� s!*��%wm&c� ��%� law%9��ic ��%ez typ�AI���b�$i��!��T, $eS f�"by Bell'y�`��s ��� violF",standard log�F�oning�#e GHZ1�$ \cite{GHZ�re�sQ A$tely tru��zmcheckedA��6!�di�(.q set�S���g toge�:.�  p50 �y�%QonE(#ce6�L0 ���t� wro!�:�of�� ~](P J&ns�)a�its ass *1� {\it��ual}:A ��id)Gi�$M 6�1=.A@-a� �.� � %  h�!*3E�"%$�"��A�R " ��"6 �E�ir6� Aa�a rEm��+ enomenon, concep!ly im*ant��t� �no��A��12�q6� us, �it{�eقe�emerge}�Ha�(.$m*&�! "� S}$Y��Wb.Q vly�is � ���4}  !�!�out� a�"(E/Q �3uaF,� "F�h�&M�V }, jE$aE� tinu�(_�) or pha��3�y(�� �)6-5��S0ldegreP freedom. ��a�ng�orJ-22U��� usa��,�-o�@�pon�( � -�2&,%1���� !coq� n��B�. -A� �5a^5Z� 2�}1� "Ii:keoazEn>oA&����al� )ge:6a�-66F6 $.y in:rm$en+�S�V�1 .�%  b�6los ��9X2�-� s. TalosX67i�4��.-��paiB �0a5p .:ab�=5j.�Uu�$.� str"ABorn rul&�/,von Neumann &�A) rec� �#B( ause]could u�lm�! 1rpo(" a�a��r trib�5��&� 5# randomG,5�n-S. F�(���>� foAv� a sel_ fV# amo@9�� ��� id �a�}q7 E�}�.H$. A subensS with��p�[e�� roll �!�.��8EOus ext� ed��1 whol � al"� - � -"=`"�In6 e�sm�d]nguH1;ed h"�A>�;E-an�u49� /Nk%�syste$^�{"�7oL��9P n1Bnewa�t�Pthebibliography}{99} �.2a%�ica Acta-d45}, 237!�\72); %%M. Cini, Nuovo Ci��o B 27321IEzw!� } C.W. Ganer7itU�Noise}�(Sph er-VerlagA�9>�marlan}MW1 zukiEGR. Kubo,Y�Soc. JapQ; 24}, %%51�6g;,J.C. Goldste� (nd M.O. Scu��=g�D 1084F73). .�Mayer} J!� � M.G.  �Sz � al Ml, 2nd ed.}, (Wiley, New York!H77), pp. 145-154. y� F� 67}, 1078�99� !d Incomplet0 s�relev e��pies .�0ay} E. P. Wig%�Z213a�10%c 52);J2#6�6�pH. Ara-�M.Yan�4 =�E� 120}, 622> 0). 61F0A�66 nEG\q��$ D. Greenb� r,}Hor�*$A. ShimonyA. Zeili�>, Jn58!n13�9�l�s} ��}L.SA� hulm�nAnn-�A},bf 212}, 315!Fe]F. Haak� M�Ukowski,.RA)�4AV250%T9!� 1;>�  docu�-}�B\�ZX[12pt]{article} %\renew�,and{\baselin+4etch}{1.7} P\usepackage{amsfonts}j! symbC|%\addtolength{\topmargin}{-0.0256 (;�6-ex{0.042,6+FG%2]0width}:/odd�.� G�  \def\be{"��$ ay}} ee{�6bb�?e *4:5A newtuem{thm}{� em} .,cor}[thm]{CoN =;2!lemma #L 2 conj Con1ure6#� #P I6$ defn $D 0l64!:8pf{\medbreak\no(nt��8Proof:}\enspaceF;4lanbox{{$\, \v� IK 0.25cm %� dept 05mm \,$}FQ QED{{QEDJiff{\LoJfSh8FHhalf{{E9A�1}@?F/tr�2ox{TrJ8fm{\lfloor m \r D%EHil{{\��HQDe�{�C_  shan  Shan holv  Holvimg Image(wh{\widehatM�ds6B ��ts= / bra{!�g��& ket{�E $ kb{  . dg{\daw, ot{�B�>AODtrho{ \tilde{\rho}= lraw�%(?( BF� whm{mu9 n nz�� frthV"4}[ PE{ %�ProbErr�MMin>dtsig{�' bf \cdot �9 �buI��b!�bf 5�bw "w3nl{�c�&���TrIE�2. !�tle{ AnIlic. a�rix&1�,"A .���y��4uthor{Christop�FK�= \\ D� t��]Mathe8csNoGas�;*� Bos� LMA 02115 \\ {\normal��)(@neu.edu} }A�X%�?t衛b��abx' ct} %F�O1g�8�:�#es(��ec�xs �"o$x[ oI�ve mapdJK/ algebra� lso known5� ;nels.�G~@icular ��G0!out�s�;�maUl $p$-!?�$e�alway+ � G. I�=���!C Lieb-Thir� .1 Hbe"�I*e C��oneZal �4nam!6g �!Ror�-)� ,t65Qa&� +.� Y \pa!�eak��%\t�of�nt� Egskip.62ion{I !J ion}�)~3vK)�A �1&i& � $\Phi�'&�7A� S�Kmin}($ ) = �)�4S(�A)) \ee[8SN!�.= �� $M $ ru^rLE3A�doQ3!h ���a�add�76!� yAC9�d.�.I�" 1} Ym $\PsiA(�>��aE�A� ly ��~$race-�6ere�mg f�Ae-d�_(W2*Nuz�n��9min.add}B� \��Ps%� F�+>si)�\ �JedI? With�=9( year, Shor4 2}![vq�&�  \refU1}!vB:al�7qve�(� outc����� in�,&]m .�of� evo capac5:�Ih]%m� entaV� "F!�u�|of0�.�c8�le qu+* a few���problem�A�D � %��Y�9��f���W!ial�=m�s=���Kix 4}.x^6 )LT} wa! ke�{ gred�!��%P�7p� s X purpis pap�NA:�^� :� demon�2 te (%�q"AEf!�qd`'5$.9�% � lemA��2��"a���= ��;�ǭU��0or $p \geq 1�2lsA�l�!�� 9pur��E�-�-� AHW}D i.5=�!def:nu}� u}_p����sup��|| ���� ||_p��!<\bigg( \tr \Big(./)^p $()^{1/p} \ee%1deriv\Ku{� �$ �9p=1�neg ,ђ� �so}g>Vaa"� EU���Mst� `G"�aag .�2}�?Pso�5p_0 >%�"Kall >P�EP�)��.�c,ll $1 \leq p  _0$,=�p.mult6�6�{.G \,\ 1�n�I�-uiw&O$!<� !6MeyA� J �u�A�^�>_ Eq� �) u�-Hassump�� at lx  -�� ��0��EPŮ�"� kCs �~ !iipM �C%ؑg hp!�.��<X?ght"e'�+�'��$techniquesJ� fu)��&M�J)�1 � (Icj�6F� o$tho�=��"s �� simi JU2��A��#!�2:��2}%�0E�a .�-���u�KiAZ " �"� �} Sf�Ib�!cerp)� ��E(V�$�B6� ���1<��Dun"�$�M so~Zin\Sy*J 2�Iy�a�!f�&�* by L(u��Strea�#)#LS}. Re?yHadamB(� �}wo $n��)n$ �-$A!  $B$ �:& <(A * B)_{ij} = A B�5�� ��� CP �E�P��,�F0ɫa9 semi~it�" $C$پkF %P} ��= C * � � �"� 4If $C = | \psi`a| $� rank� en� t)"}#Ht� { =�Diag}(W��� ��rm2^{*)K�B{>!�A��oZF�xIv�PA{"� $.�$ a)>2N. U�Eb t� re� n>on C-��]at�&ap!+�ifE�X-i[6� a Kra� 2Pe#�$@�Aces�� Our m�=i�pFd_Din� eef1}AbE�!M1thm6be .�mapi�letA�&. ��I֥6� & A�� � 2  AE  2 �:I % tool�:�!�� ! ^��,T},"2�%J. +K� 0$ ��2�Jw=5V <ny $k�k)�x6:.�!:-�L-Tj:� V K Va&� � � ( V)^{p/2}aYK^p   =:2'K^p�%Tp�+� %V��N"�4.J-UAr}�U)igk% >�t!�e� .�8Ep '�$ca� �A��-Ep"( is �O, a combi�Wo<q�a��#analy�Sco�) m��2!�[�f�Yiz.��god�&I&i�).M� )e! duct��� u G A�o�m $9��$� A)� a���W9'sum� ��)F��%8by B!���J� $CO($�XI�i;T1$,C}^{kn!8�iZVB ${k��3銭�h 1,s� ki�1 �) rho$1̀�a6��*]E�� s $�3_{ \,ij�4re m�1s k ����b��A 2Ai A V7� �8$Ma� \alpha_i` tr!�ho �i� 1�1�&$.5 �x $�=$)� �\( M�(n j){N�7\,2~Eee{ � A$�5oJEN!E>��($A = Rvu$ �+b�HJ� �l ����K = (AejJ_k )*! �)� $J_ke!AF�M����e�E1:e�� J} d = \p�P{1 & \dots & 1 \cr \v & 2'}�NYDq��e��(�4 dentP�> . Fu� �XFW �Y2�7e8C5�?~�s_T��, m�� i-Psi} (I%g\Psi)iI2|)*Ű(6' tau){��sB ��NI$���� m) aB�E � )�����fS0PAmisF@%e)0�<GA�I"w =�� .A} :�5�(A)�A*�n de_ to-�*=��F]�#o�U�, e� V_1,I�, V_n��F}�P wyT  the �T-r�0ts squroo�]}�e{F�}d2�u/V_e%}�iTs i� p \bq�!�1.J�Aa  ~f "{�b*}}�V�\v } =.*1.)V & �3e�m���� V_n/H�5Hn{H).!�"p termh9e�(.�i}a�V�U �M��Q�!1���a�4v�g*��u�l��.3 =  tdR�p-V} || ����  {p�  Apply�!�o� �I)a&�4 .A})s6>�1r���I $(A)_{\,11}1�5� 2`��) 1n*)� ��r .?niEiU)ng( g.(w%+�" s�LR!�)8 � te: .*F9�eces.�E2ix5,A�& 0E�)0� V_2B1V6 �aZnN� s=!�I'e.n}2�2�,!~^H!rI'6�V�5.�.�{2est2�%-� ��$I'"L middl9U� he��&g  n$�2teQ� .samN :e3�����9�2@I'0Y��,f�7>Xhas�� �e��� :borfGV�K�5 )�i-�2 ^2 g� bigV} V.� ��n�)� �D K! ms I' &���A�&u�Z s& 1<g-c8-�=to ��or}).s$�wS�*5/)�$�()�!�Bi;G  ��:�  >6.N(Y�V_1�^G*�LV_2 *�SQ�=V_n)^�Also $D=�h�n�"I'�X�WF & K^p$6 P ; "�L 'Q)/�)�"� �~x��. �[]�L-T.d; &&�9��!k$sum_{i=1}^� r�i��V_i��)�� � !� ez� �Q es $&�V_i@ $V_i&� $ sh) A˥]nonzero�umsQ�"* )�!A�bVHt� $�!�2�$ � N�-2�nis& * NC&� & 6JE�:� %E19(VM0ii} \\ & = & 1(fG,��11�%�.�� �s�,B; %3A��A3rh)1 �c"2n"b%� ed u# �B�4nu!`Put�)i�o"@<�3�GA�%w ma\*E��vd, F!hTA��F�b�����)�\"�)�.�y� a����(Z!wE_ly��*U� p+%�s, )��0}�!�b�Yq$)|Aco ledgs�0is workKn^or!;(8artN� al S�l ce FagH Grant DMS--0101205�is �Y�to E.ł�,M. B. Ruskai�� &�$�6�#b�N=�add8:6 �(�  le�Ka� deir)j>incluA��Ap�Mi�O�\ "xC-f%rOe6;;~~-�5�$P G.~G. Amosov, A.~S.�', R.~F�Cr�6, ``On Some A&,'�.\'E-I*L?E#y''�;em2/2'�Amis�)},bf 36�5 05 -- 313�96B6 Ar} *7 �<>�Fg+!�%�y�A;Nin*�.al�5 ics}aObf 19�667--1706� 5LEp�+�R�4k �1�M��C�ni*!&/F�&8317--32�6k9�Ki1T:p/�M)')��c�)%��u#�\�� Joura�of n�4�(no. c 1247!� 1260%�2};975! C:��E�%-�""*B}!�Nx&Compu1��2, 186�90 ��75�Ki32�]�a�$unital qubZGha�/��010 4641� 4653 �%/�42���5��qu�T depolariz�a ��IEEE eo\E�}��2ory}, �8a!� 1 22� 229,93�LS} L.k<*"R. F.""A�,On Birkhoff'�*oN!Vdou4%stocha < >�-�E} :1�Li�aAR1E � qiQ19A107--1�=96LT}q�IW�b�0�I�lRá�M]H�$e Eigenval5%  Schr\"o�-0er Hamiltonia�?�RpE�Sobolev .o''SF�@ Stud�f��x, B. S�;���<$htman eds.G=269--303~A76a�U��.1}=$<o%�}5 ��6-LC�� of E* .-Bv1A�q�C>_e`.�)�;}M�!�A�9, 4334eQ34m�6Q�2>�E~i"�%Vn��ce%+{E_b\\nd $\{X �a>&e-b: &� bBX"V rho E_b�%; �"w$�:%j`4~)!GL u�)�Oq,� 4Xa��Υf�E_bBX  ir* al d.�s (! �bN &�K&� sum)u0�,T � ��%� �&1�h(" � A.8I �&�sk!qs& ket&_'_k%�bra s_k | %�|9 \&u5�'��$�rre unv70alised vector:\m 1!�x $A_k"�'� �tBt�VLF~R�PAWrh�' A_{kb���:L�9pA+m�Z5' :��%�one o�l�Y�m�"� �4��pa�Q� q$}.�Eual�5~Me�.��v( vK�{, E8A�A�^nei>hAUqo� �"��H6."9.Fx% .ex�il$��8�M6-T-V ��I� .�AFKW}e�c[�$w�kll���;�3% � ��2for&�!E� t�m A��g%)�M�.~ . U�% T&�3�B%�汭��H`elsart' % SP 2001/5 6�B{ M}[1�B .�Boldlfo�Rhyperref!�,tbib, epsfig�6saJ, cmbKB�@i�@.�@[-R]2DA� &�AV'c"�A*�AV+sA�on}2uAV/�A�A#�&�Cel}�=Belf.DpPBdmsW\i#M dsui-*Xhi c^{ 8+1}>; inu}�d _{_U>�8boxf}{\hfill$\s� $:{E{�,ch>?$Pp}{{^+\!PBm-Jkri� bf M>9kri U � #:�do^� :�1oC%*! L}_P:%A� A>C8!rmC>one�@$}{\mbox{\sȀ �%} % U`She op � e�C��or revi�Fpy� nm & �� , %��F� [2K]{�tif you �PPostSv[ figur�Onr�p %)� Nic�8�F��dO1mmands�*G3} %�sJx )GJm1�%)ed jTx:T��R �pre�\|olbZ C%$� am�GS\idePjri�~us�afeKAal �Gols2S I�-b -��C��>�D{empty )frontma�U �itle,d K�esXB\eA{Modal W� �kA@)�R�$� "p un�O�D\� {AndU4 M�3n Lise�I \thanks{At:>^Bole#A�Hu�Genet�_Baylor C�Q�UMedici�JOne $Plaza, Hou�Bp, TX 77030, USA. Email: {\tt � �@bcm.tmc�B"F\date{31�ch�4� �ke%.V� {>x@R(} R \v�'.�@A %�&�@W-nj� =�!�d2�a6so-#3 endo"@`qz1����B�]4Eb>!�� ofl*�Tby �ol$�cl %l ))�AYI��Baltag'A�o.ia wellckide�or�>,QU��CYrof Demp�D -Shae��I8nd� �5!0 7icS embed��LxreG4�@wS�sic p�RiplAhbisimu�W-5!�in/p>x��E6� : Dpermi*}t[�n�= ivNo!�h�Y� 6��m$NsD:�t&g} [sĎ�! F#TZX���:stoodW+ oret1�[�%9UparadigmN�c h�bQ�� �11Fo�0���u�6!�a d+esaE{% ZdB]Z�EFel�,Poincar\'e's8co�0um. S�9�9om A) give�Wy ["*�E��vol�W!tbiologM�to�gr�1. ��� Keywords:.�;j%;yS��u�yE;a�x`�Vqaces;�i;5�.�% mB5�M \setK�er{��}{J sa�on�Jbel{Intr�h 2 ^p��daim� ![A���m�v&֐!�Av��8 �UU[b�;�p}E�.S[9%Ie�f� e}�Un�+G6aSW C�d *l!&ny�F��v�tebkm��E�a�is:w�Yo�q�W�o�&��� e�we�(yrbh}D�(|6Y . Si��"lS5aphe�_a�ZA�b jl�w$win_b9� �rZ) .�iioft])t�Z��s Oe�� }. Hence=$e�arbE��t��!59g�-�8��[!bN�2al A ours�V�c=77a�^:<�_�� ���nt}�T�`T 9�an�n���!i%5�s�:-`on �n)R5)B�0a.q�&�-tw titu%IU 26�%�x�-A�Ala�r.�)�manifes.~tself� glob.��be:x�@at���@�Q�euby��a�eQ�@ �'s loG .�.6 skip ��\�rea. �iA��9!Z.}d%��6�!��new. �q , alread�! 1982 Feyn� p{fey}AM�`d�imp� ������F�(!xe>5JE�F@ t��$6a .�!��3} &b�^!tensor!xU�m���� Hilbert??GW`d�IM=ases��n�@r� |kE3o6Lugg�t/�ok -��}���ru&�Kautomato�Hig`!M  a <n@�_w�.d cell�M Ga--��Conway'�YLife}1�gar197�W{-�-- �1��aDtfofYOi) s. A5� {onA[tGIn�rn�>I�a?s�!pre#%B.hd&%�^,�S͗governT-w{s����/em��ha�]aY�f��!�>iI�s;�`B^a�= �e�b�7l{a��*�-a. But�hƒa6erj$rich varie�ofE�le?nsjcm� wol2���0u�%�&t�Dste�uau�A�LkY�j �al2�!'��Hq� �on��?i �&�J��is}���deӎ�=�� ral ?-test�c9@�,E4y s����&�! 3�suIpaf#ge f #���,��, yN�n watR2$ o�ba"succes���5_&�$!�1g':ndedim Zi$%a��k�ao��b�N& ��t��O�&>�/#d�+�kalo���A^ on�� gE]J uAAu��$ admA�!}�l�Im!'(!_6^ff%{f�U%tw�?$�,N!6 �bel�����/�3�"'� rl �"�M�n)mQouVgo!�x2h a�]�oZ�.+�.����zXGv��# itude cal���p Bort C fKL\ay5 �iz�Ko$v QT,���aD grou+' 8M �}=���� �orE>$) sub�k��X V jiG5� [9!.�g�F�,DpVB�ueR6�5���s�i!v�%� causets (f det�, see�  })�~�z��� aBZ builOU4eFENKin 8N seemA~� ��.unb&E Ll'�. "&&� ir"7 ,!:h� ��i��highly.�-4shlY��& / !�� n��s.�$ "W��x"ždeu�ur�ot�R|�' waZ"A�N� immed���E�1oڍ! u6!�n�recapiP �D�sQ� prer7Wsi��%3�V3ba� %r�#� Q'O6(�d�:uMlisae�MBO�m���sourcE�a�6#z � �!).%2gin{en�at�_i�kI~*��� �7cUU 2�*O 5 F &�7 'U�_auW!�cho;o%5e'+?�nowe�re&�y.2n=�" oXGu�:f[�0�)�at!�sA���)2���(be gigantic�h�C�H�yrz �h�^r�1� ? InU3JXtit&� �36a \zjˇ� ��� s?\foot�E{)LU�D+^� E,Qp�H=4Qaa#j]!�QSN'$)(�b��5:�no� triv�]tB�2'a@9{. IA�Aaf� is?}JjE�W.�F� �M��<}*�ZINsP���!M&HM�1�B� be~�kO&� . A��VW �o�/a��A�, ��o����.L�w*pv�?$bold. Must!&�y eptA}8����� )we�%�i��q`��T%�s!�@�:? )�Howi��:, i.e.&\.�hx �S:e,�a�* :�?�30�--- "������4A�p�yaAI cogn�byf�!��8�3a l  issu��1�!q�es �!!�nure {oJ� (e.g.�/5`+a3�"S�g �y-�sv�/B�� &Gtor,�"�pr�c�V�, 0n"|s}�atj�� d A�57pla�zgu� �\� �b�@*^i��\&z!!u��c!�ɉb* #��2�:�:N&�"-1��,st�)qcided/A M�J�. To �[it&[uis.�a'�.5*��K^\d6�i�$ >sti3�5Mzj'c II (�4ry2{s)Ec  (U4)�,eI�{��}�dd�A��R a (�7[� tic)�3 p��� I�Uz?U�W�� �6%!�w�-$6y)?yny"O�6UR�*DW_��l6_u��Rnzh� �����Ckm�,wn\nti��:�2� ��� M� of *�an �: ���"6&�� �� �#��lyA. �0&�  UB#n���o�us� se f�$� to inv��gt,� le"f��ll29 ��L �ultimO�r�/�V !U�3&�y�n"|{S�wh&#}�Q-"�y .i���Q"md!�E. 1Vs��eg.e�� e7:z .$i�oal i�.Bial&���O,�to �b insL]"l���%�-Jnd,$m/�� /=-�YQ�q+��7led_'�'�7s�$��%�(2��%=���� ye��e�xd���A�^�cz+ain"��X4p�ee�jaBo-%ceA�M& a��r=�i�lla|� !X ). Bڢ:w ��� 63.�set-upE �c�%P �giu�nse�  !Wq�A��a�a �r� l�n! �inYNb�  aw�7n.� whatso!&V !Rs y)O���C.�&9�}v% �R2iin1�O]blu{��uA�A ![ L�l���j�!_��.�outcomes� ( ach k�b�l �#cA�; er� �2�s��"!:O 2E�set. E]*�\ is k� �)ll�5=.�} �AAY�de�, ��Y !:M��be^�g^ s)Z.�.��)i��� lh06at�#�m��preci@�)�Ae}B�ɞi%%p�#%��}*�g� R valid�%O�aF5#:�!��i9�a S�n-Gerl!��(*�t�5 scFw� cZ&�"d��h ) ���: $z$-"� ac !$�/$�("v�F��dL ed.ri���&�|Q���a qpa�* up#h halfr: ���alP>E� Vd�a�a �A+��.�. ��t��8sQfuzzi�&���aa"+ m���p.c piZ�:;�� �8��7g!�Q�ZIq�aa�%�JA�� situ�_|=��E(�$M]"ao�')S':c!*) dot'�it. IfaFb��X$�b! R!&�� ea�rea� ,���Qa]afI, �ch� &X�!vi�A4I�d]Tbe� clou�c��!l�$͓n1r�(t�!�s��"�m�/ � #),%ȅh5QF�(� _J���V+t�F�b��� {\it�eriaec(9�} ��. .�bacc�g��a�vA�p�  6[.J m�|��u�{* u���&�e�X��%�A�}9BMj%"܇*�!").�(�����Sla*�M�:�D)� of�(�(.,kh-\�4:Q2;)�lhA�ac�] xG �t 1%(i�&@.Z�M�i�i_�.�%w�dE�more. PE�g���Pbe E5e�.UN�1"2)!!�U�-�'a/��%���.3>_'. Now ���p �b!��.A�#�s]R/; I>�his �i � f ����h��(!�1��)SqV� jw� zoom-�+a )*' ����*. m��e� MF!� �!��$)�%��"5 2��jO."�&inNb� ڣ� E�tovi%1 �!tt���;r � �act)��o`)\lSA�qn U(�� �~�� carr�O� �P��F ��;A�cJ �,%e�$&n����/AjE,� ��>� %\re4l!%�"4�/TL; A$ w-1�--K�x"�6�oCofet)"7%ARa��*�/�la$���h roug�,���ve �bry �A@5!�pr�0$P$. �M��2��&� ��oNM2��U�!inuum}"�<ie* U�,.�GNZ4},*~ ��a�m"�(I� E'&�4 runn�*=� g�T&�itit��m�a�P��ioe�cexecu��"�*!��� �� ����&5s&�2SXal� a5of Se� STS)�bal1999A�L a�EB�Fv6� !� d�mo"�6��nV<�rej9AR� �conve~� o4(� �;� $ Zermelo-F�Ael-Axio(CK(ZFC)=()L����+an 7&�O0��7=DSet5H(Y��{A1DM} s. OP�� deA!3�=1q)t���I_.#f 8��&#��asA�"��ne�'��>o-���*!*� th:�"�V������\�A�*V) )a�  a!�s�STS�A(�regardoe�jg"kaC�)ch �6�I�&��&? ��j�e�nswer9iWat �A�tg J.��o#STS=a�2�} Mez p�� ZO$ �o\�"%syn9EicCii �as ZFC� �kT�#@ cur�)Sm0!�u��i� 89O�AK��Z�W�l�#�E�!��7~1!E(� sI�� �A�m+$�~��2��j9)�}�� 6�d�١b� stancR"� als. E &'Q'&8�h���.foL%�+��u'1a�" ori}Aarbitr�!V��lޯ��;�3��� vealB sti{.e�0 !�B|&!Uu�)OI%�[Z)�rdi�[2�*b�u�L$5i1nE�%'A$B]4���&nowa�B6���}a.F-�N}U$f��i�9V� $U�*"Jy �*�:5.)*��a5-"�2$\{9C_U�.\ڦ&G.KripkeA�els (� �es)�I�e@. LoosAspe #g,�� :C $2y\a%eed %;phqi�"�$of�-B�o�A��ed �mr y3\3(�i�& R �_U?.E�$�/d.;�J� eDCِWl�+�02v* �a�8sed L��6 &�H��dB3`V�a��p7]m�>rship9�s��f�)@ !RC� s (5i&�w� -�)--�4 >� canoZOA�.� tre�#c*��Nu�Lt�����%u�`P� � Nm!%T�Su�[-3rigor%"I8�We�c"m"� `��@�? }� ��6���� &[�ed�"? .�{�.u@|K2 $\e4Q_BiKn CQQ��w�.�I�de�.cV7 !y�R �s�m�anl�ia<�yWk>k�&� 9"% ? "6h���B���p�lo� p(G!�ZWA�"�4�2����� ��-�� p_\S2�3iny ºe^�� .Kx����_J�:i��&Y 1J�7�?4$ ach.��* u U�!�ina2V��B&�&��d� �PtBs!�p(G�X.��>1ttMyD�1>)��X�[m�e�G��� �!Z��i"�,}�6;Ej"l&R``NH''�e��2���T�ep� eb- !��40"������e both2\sݸkr��R>I,���X�of2�ijaĠ} z��"�ep?�o�tly:)�"O$ : 1.�"R�(yaTl���K: U��%�in.#.�"�]�B� Ppre�:)]4&� /�!�2$!aame~says:r� s�2�3Q'�4 �.� �U�� .`G�EE{��,)�viz.}:� �F [p �� \,.$\b�^�� HavLi/#��64Ga&78 ou9Q��"u#e r��� �/ �$��B"�&6#>,�*5sZ�)W(5.). F�p!aallK#a|�s�Š}{{ ef{dcH�ib�H�y��A�"I summ�<=`��C#wev�5Fm��� i <�;.�I,Z�H��A������� "{I]oq�� e V�{"%��"}J1|A�� cn�� eC��!# as g @earli�J�� r�4���8z �r9+U ��+$� �4A���1QJ.#]Beli�bel1986,�6200 @w�ows.�eO�$.� )wel+%"�$I�Sc� iGa�?�-�M�2{(es�dM��J�A }. B�-c,zt!4����2��� &)�.��he�@�@��Zw� ,�)!D��e� % }��:��zteIi:�JmG�PsJ���g!r�:�FZ�`3!A1��F�E�!zf�Td�i� �<�d.4@:�,!y tak� g�;��6F ‘r�-:�)q���hil�f$ *�FR�>$b+ofB�/a* 10homeomorphism�*>;� ha"TC5��Yh�?Id basA#,AhQ-#o� �z!<W&" �l�[W+p*"FF�8�+1SYV d L -a�s�� he� �R�HV0�Y ep b�5�� �!�iM�^.�6a��ed�)I->A ��Z+ rY�� Y2�� ma�"��I! EQ�J�� vo/�BenE�m#l �%E�� ZB.�N��ipl��cb �8v7! w8���bZ,|f�W)�b�u��S�D�s�1!�Me O. e�1uE�6| stud!��O7*v A]a&�[&�i<~^S�,�� ["M#"iP��mP68�_B p�M $L_1� l_�}IM]N�x����"Cp�1Krro�r����c�. �3*�/���Lar�B� �OM��� :e EuclS:nɈ $l_2��+)n�'�.����ߖa� h�d!2�4>Lia�!�"�p���2]*}.&i6:�4��S 25$a &d6�?�2b��� �� ��IU� �a(6 p�sn"�K�%�"cJ[ lu�)e]�&[]+�;e�� rema3i"�zi�AH*zrB� �*k �}}} .{V�q_�]�!9"�?�,/L jC�&��KL7s&u=in�cVńQ �e1 m�~if.�=�o~ ����T( atom0o. $\va�s,‡, �B$,�� connvneg, \w�, \veR0a��, \Le.4� K%_so�7` i�ity� BoxI�]�>Diamondn*(Er�5�X8 $(,), \, \{,\}E�a�w$B)%�%#�� ja& ulas4�}: � F:!�a:�i�)N ��a�c,a�n�=~$!M 40b -`1�!h%�%p .!r%~  >�^>!Boxo 2-b$��mMN!@�Pq+� e�&�� y��s� p\-p���:~�'w�< nsaY��Bs;� � ��a��=a�"�3 IW�a7 � d -�2�*��� now. ��ula�N ;��@��ZE trut�K lue}I� �$���Ees�A�w o�I`!H O�Ayf 8. Ael3� bf�e� �7�A�! tr� $$  ^I^TE! le W%�RV}�\,,1$WŏG� i{le{ld�R!��&��IWm� JV)Jv!)!Yign��"��s,�)!�6 B�ZQbN�B =q�� $(T)$AI*ȝty $(FC�ISg�#`fF�%�-8V�*n!(R,bvu� �ls�y x'b>y } (AfB�&pQIEA 8%��=Й� %sj1tic�.* ). Vb[�\"� ;pM��l��!�M�a:EN� wa�?��4a�.ingg@B&?��J${nec} v_i(�f����T �� N` iff}fos\, w_j'M W: \,w_iR6 5�Res} v_j(6`,,M8��n$v_i,0^V��ws$! e!>�h $i, jI�b�pos ��B6�qua�ff �\ys��}2�,mta��>�����>�m�� �V�}��2�-i� $w_ji"�FARi$�n()�91E� �i+ :�I � r!a��Ee�Bd� &� �B$N�hW|$*j venۚ%:; $ W�{w�w_2�AcN6 H�� e��#A��R$}no\o,s Nz}���R}�k[r_;�]�D��A ���f �о\{ a(array}{rcl}3�)�fP�U� ,,\\4�.9($)�C; S\��.|A�f>�p"�"� �a S,���~ee3.l11�e��e�i!B00Z0F�*��҈ o�!��:'a�so�0[�y"��$\Omega� U�u"�>~�T��b!שo$1�]�!��h>���!re��v��[0,1]"��!\\ l{i"� }^N �!�!1%�$$�~J �rc]�4jx�s $\o�_j$. =3{V:` �&9� "} Z:(o%�"��s E"d#B|w). ?Nit�76.-.[!i��bfM��0citep{sha1976`P�Y%�#�_A%�.�<C �K. Av tu#ye�"dA *�Won7:(�ir?ar�)A ��ly���E��n%�o� �-�} ����-.�L� E�ndiq$HŤY���Hlac$I44?*E/Qi�n�"nt $eGX$�9d�""���u mappaw$P(e|H)�$v$X�<Y� ��,)b�?-Xe~Also,�., obeys Kolmo�"vQc�*!<.�!��/� .K ��>P(U s $x��al"�� 05 s mu�3exkve)4s u�%�6m:f�.H�vid�2�orzy�( ed)I�A,!�$X��! v��law��A�a�PJ?$P�y��?�U-�&� �8A�_K�w�X$,Ѷ/* P}(XK�Z�2sM��oa�:�4%�%d�@l\"}b = a�B%�dYPm̐�$� .�q=M�\ �=9%yA~[ }�#A�/�nv�&� �� \">�m(\�ayset) &=���z��AE^:�} \!\!mO�21\&� aA%�$ ?>@-$B> 0%�� +]fN^Mf}. Gi�car  !baH� b}O7f0;%3tIT��E3A��� \bel�:=nt{Bbseteq A!m(B�2U$0�"J7AGB��#&* �W9a�e elEH�`(A� �� o� ȥq!He}�{�lPl} �1 -� l(c(A))= $$c�) aJ� le�aUA$�ke�Le_rm]�A�.��"�PBel�!D�@93F0*C9 �l,M�s�S�t.&-M1c^r� S�����%Ksuper-��i} r�/9a!�e �ryv�5 s (I^%�G!ogy, Pl9~b.|m�y}!T��Mwo!�s $A, .�X$ �hav(IA \cup A��� ) + B)Q(a(a�$$ r�rkp�3I�ar&�J�Ni&�&�;K!3F�y� s ��sH re ``N�''13���:�,&�O Thin^6*$P_{12:-e/� |v E� ;�OI<a !q�f�"U2Ǖ x� q |1|^2 + 2|^�OML� h�PWw� ��oKpA!i�.+ g�]93� �]9%'ZZ:��� $ �= �J� l��mN�e�Zbhb6�ie!�iN5m�BU7_"������(i:<&g41,pک%�Z�� \ h !}i�  &]N%�d(ng��tud)@E!$-� .2�%bn<� ��Vc� du�u�hc199v �2%"�+�"}$bJ.> )V"�>�".�>>�$U-"�:�-�#6WL&",!d�)!8�;W �_{_��: ``A�inɴt *Qz0�� $\epsilon�Xž6*H:n�:0 A$''+ [.2 cm]�>AN:3 "�o *�o[�Mf nJ�=2 �\{x\}}&�  .�q� 29> /E��Qn11n" ^�%k�bigvee_{ s ! �}7� e�A��"o $Aa"8ancX�@g�_{hr���,�%�� of a"b"T ���X� �.�_{��$�>A�H �%�U 5~o!{erر� si��jf� �s� (SVV�B0vtb1999}. Als�o, the relation $R$ is assumed to b�@flexive or at least {\it serial}, i.e. for all $w_i \in W$ there T $w_k such thatB=N@$ (\DiamondRE,label{bpa} m:�RO \!\!\left�.� \wedge [ \big_{x%�A} J�<{\{x\}}}\right ]  )\,. \end=4In se%l� \ref{borns rule} we will demonstrate how $�$!�equI� <pa}A�usI� establish5�F�Born' q . \ �L{Baltag's structuralA,ory of sets 1f*}} �A�,seminal workQ� bal1999} X cЀucts a non-wellfounded, universaliwba� on aI��}Ocei �4. Briefly statUBh.]aV.wha�a�$membership� \in� not � as opak�.se �ties like Zermelo-Fraenkel (ZF)6(0which include�Axiom�F!,%�. Seve!�:H6L have been�$d by meansP addia�4al existence an s si 8in 1954 BernaysGv�#(ve independ>�QJ�LZFUerY0}. Systematic!�)�io �r�byA�Droducing so-calledI* AntiE\%0 �0s} (AFA) date!�far back 1926A n Finsler^ �� }-AFA (FNia�-�y�finR}. InB�t�MA$``exotic''!�I%x $$ a = \{b, a\} \quad\mbox{or} !ldots\{ b \}C0may appear. S�]e�$are often .-hyper } and%�Orepresen��(lf-referent��u�es�sit��s becauŁN�may---�!example-�6omŶe�AQits ownm�. Atal �>rstandA� a�du��o!l@ classical iteratA�@(i.e., synthetic)A�Q E. WhilA�Clatter����i�!1A:,built from s�Ppreviously given obje��A)uccess�stagespformer:su�Ls Et$a priori} ����unifiA�otality} 6reveals%9ab�Dct->��ieuA n�-epaNsthroug�ea��%�unfol!n. T��8tepwise discove�.�#�9�gen!��impos!� quesi�(���0(alls analyt%�,experiments)� diniA�-d;answers #seba7)}f�H The idea behind it!x� )� re w� is E�;@we take an aggreg�i$(a complex �,�say) anwe9���yth!but%�i6�5z�N!�isIpo��d� A�aC ha�qroot:�e3lyepr5�5�$5�,EY�de�os�9s, ]startQ�, namelyJIe zuA���us9T�concei�ja6� binar�� �s}!�ie�%�a�=sBe��a Kripke� wit dis�uishe�;�K!1)�havHn ai�bian&�%'9� � loos!4speaking, many �be� �simply�%K�direca5,graphs. At a�[E�A�5�,Bs  iman ord� $\alpha$,Az"��Qa p!�$al} descri"` !aБ�ed. L����rbitr%�et�$_A�let $a^ sI�SF�!�en,�+or�eto obtaE�e nextJ6�ey^�of y y5e�&-�*0$a$. For limi `(s $\lambda$Q when� 2-[), ��![�"�^�=of�I� � <n �Altho���.re goAkto quot' u��I �S �%f�,�method� ��ed!tk� � ��ff�g�ECsE2$.) Observ�a ��8already a tempo�metaphor�in�� - ``� al''A_�time,-BbM��on!/ ��� a՜(Now naively�d9 ��canA�defini'Afollow!_recursp�N9:%^��1�1�$E� A�e We`�of rank7� ( 5q29i:z nonu� a^{I� +1}�{b C : b�a\}l5M� 1langle z \r_ZU�} \, � ,%i6ms, i�aM��E�� is realiz� : !�ul%t {anguage Yb�\�̓g��e�a cer���!F�9. An es� i� ngrediA: i!�eI�o��E��qM<ctw-\}.��N,is��nY�c&o����isAW�>do� eref!�A�Z!� ��%�� es���ra8� stud;9*� 5dof-v!#�� soc��th � o}uIt tu�ou��atū)Jin��-�ogic}�b& >�A}be nahlyi7W In STS, �. y $th(a)$!dM��+�� ��M�!"&satisa!��. B)�w# Hse � first!�k��e.y-M�.է nume� } \item N ion. G a possiblqk $��H� ; �Hw* ��ewmS<neg$f cap! ! inA�E�lE�A�� bep. � Conj�%|\Phi$Ar 7���o:� accu�te��22iX Lby!�m�"i- } $"�-�U&�1[^桎��x (or s)^1i*�We�byYj�a:j�1�� -���F�a$G.� �be�5�IY\�Q|��ab|sA�ree Jd��a� s!j�� a�c9�P�OZ8, $L_\infty$. WV%�veeI�$�$�A��%T'-:$, resp9� w�q{%"o� 2ators:ur&�"� W A1 &=:& \{�:q3' *\}\�IBoxD ? �@ ,ZpsK]\{ $, J� C \vee! �bi!m�=bigtri� up�-��� bPhiF� E�JZ�umA�e*\���D a $Sat$; each ele�!�v�iu� S���} Wrie�$$a \models1��8 $(a,)%�� ���  asnX4&{\rm{(SA1)}}&�� y�� " 6 iff}�.not:�2� j2jj1�E�jl6 �� ��all�Mq%'%�\ y�3j�QTI�b�'>�R�a�}�'\in a:X  TRg�fũ%t� ory,K,��sisu 0���'u� I�bby�� ��U4��?setE���no��A�uѥ ]�dm�now��exr� �Q��)M�_a$9 � Yca� "cR�%9�� �} i +1}_+�C6M���b2s�I.f�".T�O _a^\beta:<�\MU�\,\,�� ^F� "/%�2�� ��maxim�a�A= al� !� view��y g� � !�B�2vaila� ai=�b{ I��A�sF�l��In��<��� |+� : $b>a1�a ff $"-="$.Ceen�s u�explain�weea%92u ly&0 t}: $twoa&s,� :�bsai� bejP if�ym�� sB�u?`:lea2�.} W5?"our shor& e�w��g�remarks��nGbeaut> AS� W O"ABSets. Fe � el $UW %}�� 4 s�a)�st exten�:���GV�"bB QryB�-"IChoice�C*�!^E��!��� �Aker �%M$ character2��cond,�  belongENEcircularAeu!�� { n� �con���!&/ R U$.\smEkip =��!�!.n*�!,Aյ� �� � mke� E+fur� inv�g�1k%�]clea�de�>�emplo!m&�.��  (�" �})��el�AievoluA�!��� quantum<p"# "#Per ion,a�n, ��;��cq$p3 #� motiGng"u�� �h#!8whe%(!� inuiI?L�&�al�sqmly &y�(ed phys.m���& louuoo�~�!=n��&pin-��it,��W%��c%��by noM3ne<ao����Hhistory. Poincar\'eFin�ced clear��ub��e7� �um� !m�����%$\footnote{!�aut�� m� cent�w�M6,of M. Planat�!pla2004}!�r��Fc'%�e8G�!1� ^gr�#9's�4s.}-- he writeeP 1905�oi}: � } �p���=�to ask�`u!5.0 50��drawnY�. I��a�sG)o�data -��aenk on� ould��4measured [...]�has>,�$�t�awe�'A�10 grammaB1p�d!no .�M�7\B �no ��er�6O: pCp2p,��!w�waQdi2�N,Ca���%%gresul�!�v���b�U9f*��Hs: $A = B , \,B = C  A < C"�ba, gardT� � ul!�_F�. But"�W toler_ !? agre� ahe law!;A� radi� ,���f�?banis=!��diP��� e#&!9o ��n�e2�l inuum. WeE���+forEto&�'��&�lE�cre�AR��!�mi �!a]yIiAprovi!\1a(rtunity�cana�belie"w antities �ab0*l�a!r�%?on��Y)[�tAb�2�e A�diffe&I�B ;B C .ifQew%�^i� %due��imperf (�(!� \\ W!zhappenmw.jrecour7 o;�aru+ to m�#up!�pweaknes k ? If�s�&,��&(microscope?a' term� AE�B��bI:w� in}�E�e�6��' tp. 3ct:E3�:f!�),!�ňcalE�a)� 3� D�Tan ;g # neiA� � A no B. .� �! !�most del  t\ X B�!_Y�sk alwaa*e� T"G %�fFQ�(2!��xn�  i�'e�escape �ita�ussa��9<�15�(9�!Gs"� ){%@� ����G mus�pursu�in)eli�m�ZW i;t w�"0A�topM�ɉimagina�.�powerOeno�to"�%�JRin&iscrete� s, j���tel�0p� solv Milky Wa�+o����% Ik�i �;!{)���A�zS�eEe# i�s:3!�ey� 0j��g+)}���A,ma,�ai� �31� 6�visj*� P� thos��Fo. }��  \med� �wa��oa.l:C6�&� JTQ a��m/eve� �%X$ de� fof�ite"<�J$N$6�& mutuaw exclu�*ev�)M�n%�a��%"'�Q^ �le&� ��)E=&{\� � P}(X)D&M E�^, rox�%&�' } $PL9("�3�F!S~�g!$iz� �3a� symmetric� A�n~ar� tran)ve� bel2000,�198 .W" $(X, P)4�� �space.�& $y2X ($set $$ Q_x'.y�X�,xPy\}is j� )�a2 Y}P eo��6a, $ 9�R}w �| �\}$�v u!W���!�9��A5�)�@md2<, ���E���� gniz�Js�1�. Ae)}.�a�G& 遍 �:7set} (o )P))}hBell's�inology)� mj�:QumP,]�Q}_P$. -��te6LA1P)�=MUؕ�iz�B "Bx�}�ou]} y�5"rro��E"M  too%�T �a�a��to�an� �� '�0 ory field��vi��uch, s�smell.R�E9i$, _ ��nt fe �of~4a�re�+=or3o� �ey manifAz!�i�.s,�rep z�� orm�9V!�vi|u�th9�of un� prec% {] ¡с��k� �$u: �9  knowle�6���setup��=\eda�tro&P5��r e��y)�eFM�����< sa��� _,|a!9��X�,��FB�X����} ��! $x, �'�!u��neq y$�+"}9xPy$.� Acc6g!�m��� �� 73immedp$ly5c�6��1*L%+�#2 �/>a��lbA��A�s 4&d0�+tho�2iN��a tuploo p = (�ԁ|, \cap_u^\perp�n� equip F�%Q a jo pe�/ $\G$�'n; u/ t-�{3��-� a me�/.G��1w� u�Nll)[aAthC#s.lal� �4*J �n u1�L$)�- $$  Q�MP ||(\B7s�� n Q)(xPy)�P)�$Q�6x���l>�A�a�nAGb� m�V2H � �]t $von Neuman�Birkhoff�0{bn1963}. How�,,� }��i�du��J!px+tA\!pc%d�{��} a Hilbert����'�2M�?��'�^�Ws)��0>3�4 e6Y �?5@ 1�u��i*an alt�8t��ent�(6��)m--�!% !zo��by�)Cp� � Oni w �1l� c5� �B�M�R� $m�$Ɉ� tend� a �� �iisJ};�a }�t� ~��$c$-mo�=sms�4te Boole%< gebra^-4Fz�(A�details,�16 pir1976} R m� �|���>sk2003})6�I)e �JA�a�EE�y_P}3 �1�&; nA�th��#�YiQ@ o�"� &JP8f�'�xny^R�. �'$A, B: �, "say $A$ s $B*�s\# ��$A�� � \emptyset 6ifi?ll��in A$a�is $Q_xN8;o(� �Joho� !�2M B$. G"lyI2*.��!�!��.^s%icases:�er��inaIat� E  ��1�,G!wq �g���!�RenjAp�>�,rE�fundaf� |, W: orig�5c�Abe�C)2}.&�In&Ki~� 6��*;@e"�h�[ V v 2emblesube�6o)� ��su=d.} Both"� �D *�;in6Fu���s n?w'�OarI:�$ lin2} :.�? 1�gWGes!+�eC� � �N<)�PF�� ~ ��;�}� an&}2E�!�e1a� par��!� AV�a2�N��6�'s6�k �!MsKh@&�? ��D+��B6^i|":� \hil��#%le6� na�ha�%mJ���L_X}$ B��$��e)���#ayf8)Vd��a�G,.9$\Sigma � Herm�<nor!� ��&Y � nrl�B��b"�" �ofB?deQt( eigenvecto Y . EaL* �b$ corZ,o"9`��� docued A2]X [alu��&�sbb R} -�/U7AJ<��1ɤ� b$e 7 ,)�)1*.)(�9_x� B�i�&y�(&e)}.hAs �io earli�AR �!�%c*1(ai4&(Q@9��sa�e�� AG (sPtZ�(s,f 0\,,.U�s,t a� \�D slash \{0K!���$(.,.�G���n� duct�V6LxD* in Q�E_F��5=�a]!�!�"� &XE2��s">��[�� r <o&�J��?em�cA ] AG rame, MWmud�s�4by�!f�$e!�-9l��s�j E�"Kworld4+��F��.=V@}g2W�$er. V�2�Dgn�s$ � *� "%��!siK@exaViVvi=u� �n�ly).V A*pts@hIR� Ah ���*� O ��m.1It�g���<�f+!�BqM!&dal �%�Oas���C(&� A�.m#DJlicit�Z42�Ti�$.-,P}(\aleph_0)�Brom��pM=H2� ����F�%a6s�u'&K2�(��a2<%A��5C applF2 �f�~"eP1�me�'�-�^ �de�!in�'uu��h. To ach'is goal,!B0Q�"� "E2�0�ElQc s�Bh�}, : H�.�"s� �AU��a%5nvalid �)a��=0$ A#1`�K bDsI� � �)/a�-l'�-� Pr/TA�b����2QY�ch-1�O�e-$.�RV Q%ey+� �0 "40mp@&�'���*�RM:H. �-/9 8 ��%gi1��in��IuI�} �F$\square>sign;�com��i�4n�S� pla#paf� C�At e�{6+r6QS} �In&TFE�1��<�x:| �4�'?%F!!d=M\a{dim~ / = N_\i�.\boxf��M*�V��recapit��2�!�hypY*aυ��>�T"9$� u�3��=��reg�Rr&�0I�>&�$5.&aW� l�Q!� who*�6Xa��or,/,.}9B> IB�Y�*UU�&a0E��At$j .d](�ftA7Psi-�"k-�Ol$�rn!& �Z>�7. A"0T�$`�Dt Ma��� t ���s$}*A�$ !�~%E2x.� "�7�<mA fam1 j1a� �6� homeWs�S� �:20\�Warrow.6[/St0"��j_:t>V7����!%�Gy���(age dynamic,!�.&7F!d*P�c K�9:.��;2��2�MR/&4;�@qui T��>" cap��|< ng �%qued ���q] *�;$U0g �sh $�"+/\ H�O`<� {�,no-collapse}� r�.! proble# wA#�$QA�$GgM o� "P-wyjpth/*�un%#�)��\-/�&� diviYBm�%�*y � er !�#�J#ap�$nt �!�wave-\. EmpirD5a��|)&R.aˡ�mZI ! dAM�su�E� �%�=`.�as&�SEe�=�NH sta2002}A s"�.�*�fai1depic�>g�/han�uc0r7�-�7un�6� �  BiPM�]2*x � �e�nt 9  *� s looks;Z� (�S�4�:rAe�A�s�$�H �+!3r�^E�+'�W ~d AE����� A�� >.eDan".F�-6�%f [�8��>\occur*"�K� is %q*vWS���)�� orga1*%1� �3&n+ cruc_K"9� f� is-�i�i�;�]!c='DW� �  Q/al�[�>& . AH)eN� /a�>^�-Xncipl��n %�o��jK5�?<%�_�T}(PBr) %�� �fe&)"�$R�W $\�bf{M}�K?�� -CP,�>T = Ւ�Xn "(��� M�� ly�a�)!w�E\.EU. %�_=1 RFC�ret"9@.`U����oc;(dpalcpE��_U8 ��ete�Y�Kj�M6/,�� $�a�K) = 1L f$� VE.N�.� M� �a� � .� �.)_�!x� 0e��c� �_U �$�vEީU v �!�W-�A $?nUUUF \�"3Gp . Fu.$:��  $Z!��yQJ*��o"�M � ���;*�J\3Mif! et V� � q(D$) \leq Z_U�pha�)and B��(:� 9�>�1@. \hfill2� �2�"Q�s T� !py* "�v�oof. �7� �_��o"#ir&%�5 �+1~ se�/�2!`!49 G�7A#�~�%d = 0As ver`]x+w9,�^0!O{c\,1: ce*"C}� -qI b) :/ bar{a}\,b9x$a,�U U d�>$b u1_(,Jp � 4${\rm id}_{ g}.B:�R&B�] �u�GO } oHPNA� a=� n un�*�$�C�it .�^&�6 *i�� a�/� �a��. ���W�-Gd M�_" aD Gs.�&�u�&PM� 0#RHU&�L*jL{����_u : uE0U�W .SJ=& 6[H D*� \,,mx�E$.%Agrs<�6� +I]FeC of S�R c.f.�-2 .{C% )� fjT� s��kr�f&.��Ole W_U, R:V2�X"�6p j  $w^*%zWY_�%M�iV&%Asi��. ty $$ (\n�-wJ])\,(w6� a,\,�" and}?* w^*)!�$$ { �(#yd � A�pwF�3�1�)%c g{Ua�s�$GLa�+[�=�:%+^i�]r!�dof �children�s@^#�JR&YPch^1(.� ) &:a >�{u_1}: %j.5J/P ch^2vY �-1}]2}: u_2[ u_1 !�6�inzy&\v�e&2/N� o+1}z�0�/� � o[:Ll���VS�WT?�'u�!�E}�9ω}:Mnst} &�P+1) := 1 + \sum_{i=1}= |%i:|� �+1�N'*�L u  .���9m� �v monoton*�l]+ca�>�0��a�.A aq�$.i$��sNmbdd�a��-&�Lx N�4e� }a4^ �$th���0 w,5e�>J�HfZ ��1 �})��_met. E-3 -!�)�ow�L���quG � T�{ _n^i�e�  $nE� \{1,I{ ,N'-���W"�Ri\ B} $m \{0C� \}$ (O�ZA�a�?gcT5��a�!W$n$�tA!e5 u $ i$.)>��gho!�!��� A>]�� � a&�+�H � $N'$;!�%�1�^�B�)1~E{N'a[2 � �&$$� ch}^0:uaj A.�[\]2_\ASo_/$|6�e�')�EG�{E#6,$Yrc>�*Bqi_!�X9h,l.[ ll 5XstituW.0a�.u �s $>�%��z6!,big�6 {i=02�5`i6`��$$ A�(ed graph $(6]>��'U�8m�m�:�>g (w_n>f_m)��E+�),&�6quu�iu +1\};_&!| =:F� i`"�UTi�Xm%�D^{i}))� $n, 26E^F"koIC $n_aG>,)��k%&� x6j�w_{n_a}J- $$ w� �%jV^i DA�^�&"� ��cal{A}��'tomicA��D tEu,�r� �R6`be��9�yA�A V m�3pll m�;a�$�y �-� J�(�{nb6a $i��= n�'ret0_�Ue $Ay?ch��-2� e�E6���NJ��Jdr�ɇ>�l*�X C"�$svamu} v_nQ���,1m 2*5&;�$c �NR� � �9a�dmul�L` ��nec})�; po��X V3tE�}�GmM%Any $m E n"�5v_m>�f�3�r�d�GS�ton�* �Ae5�". \hs�9{10 cm}R%H "�Ba,nU_>AY�# link�>�� A�rg�0��nN'0(l}'4F^%E-�a��0R�*sdI^ it.&4`� !~�9& 'mea>��ste_z!�%�����itF)���iat�Shy�Q T�IamTo#p1�n�aXiAt�}9.&� �u"2;�x:4)RP])��H7� #�is���J�(w�!sF!�i��n*�be-�%'�G:�Q5@!�%bi�)%�n cosm�Co �w"4TA�>|B oIP*Hr1��545Q�o�epro�P�B1 p( �'peq aim:";BV"*c#��GW&� � . Re!��++pr" �9Set�W) �a�%|E7�IU�.�Y&NB'��s�oa'�S%. So,��A�!#�#Qd�,f�c�edM!Oi rt? AX�Cu�<I,Aw%��e� �-�'I8in�5l} B�^0� >� %�fi�Kb]i%F "rig"ve nucle�C���*t)V�r&!�E��,�DA�u�&�҅�Y� LmRecuTp TJ�- !�elf�-�hbyu�Anu�5..�j�( !A( �x��e )� h| 5� 2i�$e4s�d�`. �e�!�deeper"�" �jdaS?�Ww7mA�U�A�JU^*�!sc�i>�hod#9Mhpa�8.�m�!.\\|�g=aout�;�}�"u3}2.K�sk[��'gus�D�0�j�!|dy!j*4lu &C>_?a qQ �~a���?'��Hn>�+Js0�6��ed easi�QTkT:E�Ae�fa�qt.�U�6�r6�W!ep%B��A ex#$=6\b�$&�HѯorZŌ�h mi�Ua*!* �-$conl].��p^{-1}�c&? !9�J:�` l�,�%��l$yn5 B�themse�R�y%qel-%��hey�})�y�`o� �:�La�� � .AT�nay���-4!� �,se��^>�!�!YB� n�I%i�|a�doc�)a��1u%�6 �!6�?`&t�66�I����U*�me5W�a�a�l>�s* �-�u�-- �����.,!�X� �*�-H%�7m4^E&h �R�) nJ/p��T!�  Y�s b��� @&��iH��.n�A@�*c r +� !���Z �:���a$� ��O&gvr.}���)nsequ�4�]y��^�t]��.�)�t��!`�t. Fin�3ipp'h �E �$6�pAtwd6���e&�))dd�j�."KDM�Bei�)&�S�h� is G�rJbeel�� do�x�W�J�f�any� N=C U^{2w{"�G, jL.���f::%�!�7H%�$Pi U^2$� ��m 2 ٦1_<GH���+�h�F�)�)� E�!��o-,V�M��H(f�9 ::�{A}-.� -# n ��&ay`,�%*��"e�4 triv�""{T(+ a truth F$(T)$)u��4� �) � $a >�S�s{\A},$M�R&)x$v� <��=�~��A� �= J����P � to�Git�")ly N%  desiH9B�$B"�8/�1M�E&-�z7b.�"s�4NK. :�$2�9T>�6�$&�%�6} "Qcow� dy!'� �Ce B*}*{ �$n�BK 5��: �( -"�2&%� v�:�}$ @ `�+*�'\e( SL ^��#F, PNV = "�#�B�,N$|JeNVa6J���� BD,�P!�A=v0�5^k��WF�eA �V� +��}ofmJi^65,6E�P* -�T$%/M2hV�-S�49�!�Pp ~.\cup \PmF.;��<VsZJ psi'a����;xac` ��8'Vh8�$R[�����c�ar�daT$V�e en��y �źN�_qWun� վ� 86� �3����$�7SFe ilar&�rieUq�$�}���{_BG!` \ 2b��-\��psiN+ �F\�Js:  �dis�Ut. By�7is�\ m�Q>� $|$m.5lB�M� b�i&(g�%�n $"bUj)(v_j����) \LeftrAaa�7.'/{j'}(N /$,mifuK �:|(�i.�a')hnHj6'] as�b �PwR` �BE�)1HZ�N�=N�end.d� 1I,;�2@md�x'^�h ,�[nb6� e u�I�Us�ksymbol~�ZN�. j$, $j*t �&���GQ>�sI'"�z Nus*��� rs�BJ*� �8�,�� J\os�=�"� gNF3S:B$�>y�r�<e ^�^6~�mA.�- ��)b>b0 :�!�>�� 1.�}>",%*�v:� ,x�Z�H^� s&�aw���7Rnűa>^>b����uY�� M? b�fu�BE�hj�&�Œ6Y1wC�=]��PN% :6P�>f�?J%%R:t�Alo2ig�UitO&D is��&v<9�R�$E$� ��S;� J i*�ur)6Ma>oE�B6x krifz ,^{-}\!%F>�� c.�A�i�4d.D Iell"p��sd3a�ewo��W�wo*�Sm�"�MF\W�J�c a.^Prk)��3�he _�6!&�J�DQ�1NY%^ � Ʌbs�V��(&�v)%al � uage�!+� ]*����0��%��irs� truN9t�����w�(�5):^ ! al�^�/in chap�!19+�O{mie�0}�*�{in 0 Hs� ��c!�R�*�!A�%Kat�p�Dne(o�Y��Cs�pT$Yӈ[�!O�,�EQ�k �l |of"� =D���E�N[{^+\!  bf M� *2 W�!�I%seQqU��9�a4�sJy"" alNT�M%`�^�^3 &�xQ�rQ��cpreli��#�&�&f�26#rigor:&�D;#{<Z�� fԍl /*:$ 2Kv�}$}\,* G6�reLG*.� ^"%6��i1��#�e͠�>( E����"��Ai,u!"4W�mp==nc$�on��"���of�Nk"^�aN�w b5�tIq�HA�2�xj�OKJ�3u5 a sl� 9t�^�2�>��treaso� y���I?�7T�q y. Nmt4_�\��ut *r\&oa�ev�>�VVc��% help6 �r@#s~aN�lon�M�J o#"�)&�J�(Vy id!|E Qf +1$,' viz.}_,6��2\��_B J�R,�D�f"�A *��"6  \renewrJ and{~8$i}{(\romanc i})]�*16�F�:*,\supse�S :i�"�" < 2 � = N' </j&�s�: 76� \b�H�G�0! +"x�/��"�G�![&� �`.�B2YA�a x�VHA�an6;.i,>���i�e2�Nn"�R�~d�!.�A+ $(.�F,�@S:� ),$LOk%N ՜̓BA�:�.8�;Kr& Nc�@�� pN1=.J�+�+Zk Z M:��w"�#%�i�WF��**Z��{&w�z"�j�A�F�I� Λ��y'%d #a J�H��(>1,"�+� �m.&?rF�b�A��6N�Q} �*� UA %:Yw.! � ,r%P�+�$; AKh�,�AN�>6�A%e�!�<f � corn�o�S Vo�� �rZ2��|a�!sR�W)�m�,LK!�5)4h^�!�%Z&�W� Zo51V/ �CB�)��con���"�F.�l�a�pk+�' �J��g^9/e& n-�FO�+ all,v#H+%&mI>�0#W}�UKks--&��7Kd inv�v�w�O!� �m�� ?d>o� thin~M6J�%Js ��c*� sa��'�ylf-��< !�:�X�iJNnh&Q�$ b��LYM-er�^�+.�e�WxN(.res%) (owK de%�q��g���C�2y�}d�B?}��sho�� beOd=g8de~e�freedomu l!�/]y(n\5%fl(-H��k6 � !�.��B���3���V�a��C�"�2;C�QAm&�J�&la���0�<nx��Yi41�DL+� isol&�fSsurr�A}QM�/5%�)�5>� oQK!��_��)��`,�i(�sOlLs9* re) .� �3�6;o�t&nFy ) bl�&hi9h;X y-)��,\a�M=� b���Q�*e�AL�.uY� fuzz�Z�K:�)t �QF0. U&NLn"*���=�[3�~�� �ta��SB-.6-iFY sf I��P%.-Ev��]~���Q"a��!�=�0tK#s r�i8"� #N�*-E Ol?eZ�zu^�weakeHHa� Va�ji��e��R�:� F�0 �2A;~�ZU�$ mappa9�.p�-^"�.�HmhinshiaB�>j�3 ����F";J�Vi_�r�z}%�2�N� �*�H� N� ob�{rue.(�� lIhQ�g�1$, �MR�A=%�% �4��=FS���^ S�%@((""+�A�=, h6O^I`�� pi�/< ongee a�f loopYmn�N1���k�`�� 6�A�v_bq���FM~&� :��NT� ��P5Y�S �>HrL�P(�!)..�AUC). *.�o�e�� �/w �  IF�N��'[&�&n^sI���ed6t��we� �wh�l $$ `)":Z\,>� \, u�<7h �I�<*�N=��  $3�m��#�5i�*�_U�6��+ "�(?�Յ`ijsp�i����(:*�T��!��]�h�8YJaȨ�;���2c93Ur6[1) gnorX,P�5<�=�lڭof�lT0&�8N�6,�>6� ��  5��5be^i8 �aYESp�/3�� �)M>�T6jm���+a)��՘Ev!�:o07C."$Łep�?P�q �:.�:��6,J ���[a"�g�{ "�3��he���,��l�CZ�.���RS*��Ӊ>r&ex�w� feedok��J�$��:=E���N��A�1 lF15�n6GZ�1�2{:{� >* t3FXQ��FQ�s�as��, ��:�aZۗ�.n.�!t�<5�l�� ��e�c8 � &�}mC� Q.x�2�-?./��J�&�[y# ��i�r,8���v�ˡe #Pa��##,Uworth"e��Wi"�u&s�A����Ma ���^R#!a�$� oic!�Yh;g��C �J{*b7�!�Z w! u�E��;J�d�:ځ*.�Y�"� uM9��&��1�fig�^w7A!kefig}�illus��QZ�%��*a��~et�B��{ d}"�B0.4�B4epsfig{file=./ ~.ep�/�[=0�dth=.78\�:w} 1 {ExAk�H ��Z�:=�L\gT3xU^3M"${a_1, 1, 2�I\,2\rf {a_34��} r*$ +�M, a_4e@{\A��F��>A�or1/,�P�le�. b�_1�T =U= &�13ul� M9.n~"� �3 =6��5! treec�� %�>x&�"3$�����3._n �?-=[r�L��XR[6n� 3� �AmA�� R� � � �4h�=2t�%�#B�%N� */%1Q� s:�K 3), )��rmL3(U^3)ԡ��="�Q� s7oVE�e��d})��w sO(3U+\sum |2K3�O�O3 +AP8M l�� `A ��M� � %t��orY?�"lV �.).!In}Xs ]�]wc�o+ �R>�6n (f �@&Q/3$)JG>�� �Y�c.�/����� .\[.i 9*di}�2l��Jq.� B̃&n7 ��A��4��F� )YٽR _\cd_�:� 2$e[0,1]%�u�]a^25$. ��M4evaL&���YZobA{�=$"�H�L)� *�c nAa%X�|6�<:�, . DAfiA�Sv6I (SVA�Qim� ex&V1��4�*��*N :�e�7i=YJ�J))a$� �5q$m$(��ga::�;bpa�M�v&DT&�U5� ) �XTjTN'})�j]R 4�j\2�� [�Nve���^:km^�N} ? / \��]"�̷ ]��_"Qn^�_ Diam�CRh &�\ ! �8_� (�P&ZZ!!&�Q �� ���\})2�V�i�_n=��, 9��m&~ A�6�ɝ� $j=n$ y��6 9 of 1E�q����A���F��Qa{a�o㣅�2�JqSE�.1'A=C�RU� "�>�2�.�/�2�q�,xs|�Sis(�*to^��&M5ps_���$)�$k t�}y6Eos*�Y�&5%or %N]_n = |�2J�, *$j)|^2 �c^.|2.\,,O`�� 6yjIw[a`�"h ��M�1%gh $. \b2�n:�9S�"Xi,G������L�o�}4}} X[=r��$�3^�\n gj >A�Q}^���U��FB, E)a6�YAW^*A��Lg �>t� � +1$(ge>�l:^�ac?iu�a� .��2-�O��rd+@ h��s�N6Kb��RX%Td��*L�{�k��$J^. O�,�Ik�1ap���k reir2 akes!#;�H�`^�� hi&�oc#7?n�2�@9�?u�*y*-�i��A�'��R?r�t.6!is kin�*�Wl'&F�1lN�6�: qE��e�c�-6I��"r��v�"���2�� rece+)*8  in�%�26#A�!og7m� �C�CT�U^�e  <`-�*�����a�a carr ��uA"�!� 2�w �� U$6�E�q�|.&E� E����pe�eSbeShow8�nu,U.���A�Il�2ikin�$l�-OV!e�v�0e�,!���#B��8)&���}U��PLcom >I6� Wl��������6E�ErV��CDs�7��2�A N-R6�'rnN��L�vfA�� Cno\!� ~W o!Eg")�)���E'�b5L#in�'%e�sU9J1"U;>�Um� �.!m flic� ��/.��hQ9� ics.t skîse�d�atvO�� �hj� �. �&;�)Ma�iHX2� --6`a p8�!��st�`o�wstMn�kp �[hܑpre/0si`Va* �z�&q�/�W� i�a(tIQ!>[#'� eu�'s��pooN j 91�50<etO�6� �)I \� �E pstou B��5if�"���"� iori}O&J&eK*�&�' ac� ؉E���::5T�R�^�-$ �:!_G�o6N �aI)�;B�� (ABZM-�2#>��,&�0 6aAJ�oEo)sijp|)� ��6). iZ�uS[EJ)r�� ����e�I&�c;�B!�"s� ��R��'B��: onfrm+D . In�Yem)-�ed G�{a:�--(��7�" ccou�� >�.--�)�"zFd*�� -u�%� cernm�U/��6/i�9F?rc w�-%a�vus ``�''H��S�d*�]nar7�.��%� bel} P^*=� .�l�Ps�z)hM*7 Q'} "z�n� ]@Q}� .k�m�}�.���A;%uڝV�2�1�a�X $EFm�w&ǘ� �-a� psR;1ʩ� � $Q'$A��6'>6� �'&d6��CR3��$Q*�AQu��}r!��)y �0�J re'9tTn&J+a bƨfP�ߒ�3*�P}:;MEdpu��\"�hS�(t: : >YJ�5�$$R�:=  \{ �I�{lll}B� =jif�U�\Ez��,\C�aN!��*��E,,Nj 0 & U� σ .} &� �����iUB��U�/&�i�2  bel2��=maAbg6Qa�Aa~\bel(Q)eQsI� 6memphasiza���m��m&E:>ef5�� res��o&do�1ofEbt�c�4 o* �&��.}�i!f@.�  a �� � �z!�F>��zkd�EQe�&�_s�i���!N�K 4�ly�"�f"��}Z�R_zq >p: ��.!�ern�O��� "���9t)<�2:�Bel P�!(�..2��DW enh�%1�R�� "�rA,!Q� � ny}Q�in0N$!9�-�A�lI�_A!���_p���"��]F�H��s��$se3, $/%P ��"�%� � ��<,s.}��aJ�)rad?al.jb% �<%%p�=.!�n������a $\s�8$-a4�of* nt�0/Rg. Oe !"U�, �'V�2� *6>, ^�,�1�J�E��(E�u��2�Q}_:���j*F/V�=4��F��6���"_ɡ,N ��)݅i� A��� &�� a��Y�)�m ^ {_ +1~AA�E����m�.�So�aoMU_�*`�r��w! s(I ��I]Yas.� aBe�6]& }�"�&`sq ask:J�f ���'i�b6[�+2�D�="d }$? u�u+B�ZV��G��%--�6%B�&\�N�R_?n:-R�&+ j�\Q� "s[_"it &$?� i�}26I�K�EKR2< rs�P�> (of? �tɶ)�.SkIing})"d4A�cal����A`Bayes�. Acc[gPiA�5�VKe�.�T�.� )�Y3)$ "sta&�Njy �Wd frac{P(>� N%\� \, 2] })}{P(:�)� "jx� ��VF�!V{A pF2$! t6�@}%'�%� .� X �iz8!�is8h\,(y 6�A�~|``rQv $'')&� � &� F� bw=f) +Z(negc-B�|>�i;e,5�i (1 --�))i�!' ��nb�' O�N5A q5S ogj�yZJ�!�� S E��,΄��"uL*�no&_��<.J+1$Ag� 08�� s�r7*(�Pt�n#M� �e�:Ah 2߻t�;s �2���`�0f<*ha|a&+t a�*e:L@%Rdz6s/E�L!eat�{����le psz1:��ory!L&c�%�͘�Z| })�S���1UV_ *K C �I�? })$:y���:4 MF��ťz�> �� !�%� �q" ��&�(�H��.�J0&� �$))�h�'�ɱ��"� .<$m:Z� }R�*vas��2 ���6�) ��,fwit2�r'� :�"��$In summary[�BaY�0n;�"--M�lu"�Q!�Xa(�-5mf#it��a a�.�jfu�r �]p���g �%�TaO� �a�&L8A�==A�i�,�& Z#� �;��v V��\Z``*''� T�V�*0.�"�*�r{Md��8���J�.nd �td!]s3 /F/� A�c�=� ny)cum mecha i6V�:��ne�E� � nz $a�'�areiesmoot] ree-"g�a�ni�5*���3��$length sca�,"�exhibit #E#}ih���sov.�^|GG�( ��!c pilla<��xt�b�?�65��� ��8ר!!��b^���A6ssue;%?&��A�ѝof�*�t6�*�EТy��Co6�f�9� p� �� an����LH �; four~�ywloc2is�cy Minkowski n.���4+1:s�85f!ope*k5�!�tm��$�ku,���maB�8ldY��8H�]%7 DDE�i�qnco�� full�� R|]�494�i!gsoT��=�-��@�#�����X!��>s; CaJ�3, EV�8d Jaroszkiewicz�6ej2003, 4a&��e@!H�S%r���r ɛ�$��AZultimate�spdX"�"�:�# EA�ein@�Qi4�%�%�A� erpl`�f �4��ntt4��u��S"CAcau=6�&i�bui�� blocke��E�2>���L#)pm� !�R@PE!�7�-�!Ib�1f�h6�EɊ��Ex�>Fs���h�k]t ��"0 � T4��e�� � go�����9�� ��II� 5�%p�PpAP9ammn�1$/&z�ew digm��!� fu&1DF�1F1)":��B�U�%�P �6JTinJ� ��Cto geo�=���� a Lo!?zia�#ur-�Dold�FT|t)i�9��a������Ge��.Y w ly f i<� 1}. )�("�4R/!�)�i8��2um]���! �s�ɠ�toN�e�a. P�H]5�=iEtyp@:o<s--��UnB~tan� dJE�n�(NA�r'jt "$*B � r!�iv�-��"�%����-[ �x���B?�v!Rse 5X��joa v�"X]enct�a�-&�ofN6�5�>Ӫ.�"�ZA0 )c%�fi~�* 2B*�sF��6��"% uIAen� ���wO?� di ��-�Qi��T� ILJ.j �us)�u&.��J�Wof qu�x(�UY%a�6�J�!Q��a� y�Za�Y�9�yZEnJ�"�5�& byforward%7��.r�UB�f. .*&�?c'��Z�%-?=&�&E�� �t-#7'A�a_n�p5� \aX�un� *!I&*%4HA�Eƅ  !A���9�#���i��\nW<�;;]V �Q�8E6A"Z�[A�s� J��e2R;ua&�y�r��NX"�- )��l [s:�. E/moR�%N�E|>}&��m!>$K'�6}� ��JxQ'� th�� II� 5)<w�"CR�"�[R&� 9��%}!�j b n)4u�val6?�.�`"�:^*o%B:Ve �A���7�Cu �k �:�tv�"�&�9��} $d_TQ o RN�7$$ +: "wMIIB�k�:a�@ �b N}_0.^�A} d_T�,%�e�l. .$$ ���|�*i �aZC� nvok� � 5� }�a+!�6W ="�r!2�\n Ve \m�TL�? VyA`i�5L&%R�S!�C '�'�#��!�"p Fa����"�YA��[.!3}�,�el��Ma.�5C B�-��.7Ia�s�\�!h�,)!{< ��R�6�noi�& PQSpp. k�*���S�pie: { �&}-�.A���M$"V"��"1i&;��r�WY$��,Me�;��6Q .r . Be,fore we expl �further the mathematical and phys 8implications of.�tree metric, let us briefly reconcile*@general characterC : s in gs,t8here especiallyA role4distance5@space.\medskip IH�Lelementary similarit�l�` between two objects normtisCir2q@three-dimensional � It18given by a valu�a func!6( $d$ convenf8understood as a- on aJmhRiemannian manifold $M$. D> hPlways b�sa� most�da%l6�r1 .�because � itselfd]6�!{stage w%�all-�AT) (happens. BeE�4ad!!�GM.R�v!�%� had+Q$a completeAr igidEATpassive structure unabA�oA�,ose any inteA�Lion or feedback with�M. SAo (a*U 4 $d_T^\alpha$ �a� �}e Kripk.� ,$\kri_\Sigma7. So,� ^B�" mind, w��& tendͅQonN�<)�s��ask: ar��a� al�Eq I��by.��?��ink 8Ae>%W�q^ n or��tog,m��toa�� ai, nam�+N��arrier%�in�q�.$ iZ���a>�'s identa�not only�Hsis� !�assemblyA�ity�)$tituents, �� at a!`nt par& I).tm(fou!�}Af�8e�uc � �t}cur���% s���a redu� ist re� n���a�V!#*�`.��� a*& build� s w��[ !Ireveal6��5oinib�� o illustr�wt��issue, ��� exampl� A pr! d book,�� },�$correc!%� b12�v�am9mdividu.�!�icl tog�At! a certain� id[t��[ v�K)&involv��4gigantic colle%�!�&Q 5�hACfabric%pap� x < m b!?� havi� a�ש�so on* e�AG2: Xmakg p�a�y� �� �5p� conta�!�'s st� � �;� n imman.�:3U@ �(be lost. An-I �#bl-hoE/B � can}@ADrpret clasQ� �c*� 9cu�e M��ba�5a� ��.�w�). Ia�e���decadlrX'a growAev! c!�a����B�Yc�p ir surfac .e.�Fthe�horizAx.�is like��*�throug� m�"� I�p�R!�2�A=5��5b%�J�thuat Ca�ple>te<8-*%�i'm�ly��a suit� u��DJ2t--�-- actuI holds. Ou�rd��!O6iologaNP macromolecule DNA. HA tooAsmay�a���.]givA(d 6 v��6kE�ac�` atom1� �8 "Ns%#nag� hard��O� abo� e .�}A ! gene�de�nE�%��W[��>�� �srei�priE} -�E6.��ywh4E� play!�d� <� l a6�/%$2�pu�=> �� P aims�U1��UxF� A�� "�$!�dd��\sue. Fo�k� �!%��m�~senseB� e� �| s, say, b��p1� S �� IV�E.B*8 ��ir��s-- so, a�966a�can� W%�f�h� e. O�2J>6sC *��5�gne� !�f5�Z/�dd kpasa�Al now � to�w,.$ w U ��uD urn e�@(very usefuln��x to pka"ż=�} encoA�"�&� "� Si�,Sh!u�� of^mun;< \citep{sha1948}�is know�3� y ki� f.�!�!���e!(4 symbolic sequa��BA0o � 2.�taken� a (f�e) q be��(y (english)E�Qe�a}` lett�*he:RI�DNA!�� �CcheY�LBD $\{A, C, G, T \}$I:�S ifWM[![!�6Mod��H�g opin� ���� �_t�!�imp T 6�an hyp2 I�be2"#a�� radict�� R-n�� se myster\�-. F�,Q}��sh2Q)N],QOtranslaa=in� 2�ly� ivalent5�� t)� zeroi�onn�� O1� /!Jbin�5$\{0,1%�C� ��Ib��n�i}C motiv��+ &��/ is s� --)�!�*� h+�2�&BLs? Wn_discus�Pproblem!� �� �of embed�! ���t�rm��pac��� aimIo look%�aA�o�El) i� ric}b%�e. 2A(e����iqr� �)Q��{beg?�a few?limA�i�$Let $l_p$ �w��q��r� numb�.Nj� $$ \|x\|_p : = \left( \sum_{i=0}^\infty | x_i |^p \r�L)^{1/p} \,. $$ A�s� �L$(\Omega, {\A}, \mu)����ˡ]'$, a $\sI$-algebrA$� ubse 6$0n�me v($\mu$ defin� n $<� !�dditiv[  �\mu(\bigcup_{n\geq1} A_n)! %*6�l& disj;�$A_n \in�� nd satisf%�(\ yseti0$t A� �)=i�n nega��f;A) � 0$I�ll $Ao.D��Ma n.O14 Etot� �m)i�1$. Gik  .�9�\A1��a� ��"� f: Q IC� {\�bb R}$ � s $LA�A�!1�by:!~\| f :�\int_ \$|f(\omega)E�,!�d  yM�I� Thens �, �,A� |�WL�)!<����.eH$-�2J l_1$2�ex�$n = |X|$ vectors $x_1, \ldots , x_��g^m��some $me���N}$}�$d_{ij}��$|x_i - x_je� C$12 q i < j n��!�j A}�a em&� ly� esq� Theo#3.8u�pF� J} i�{e� l1}  -p|�$�A!.���.%�]p. >� �2�#oba?!b=pCoroll��ily�>c5BJ1@ (Wrn M�*Da�[ above` $| :Q| = NA/� �C2�%�Z��RIa��_>\� O Z�of��� mapp�&� $raeq >} 1�=}T���!j"le world� $:; = bn ����"�,isq"� p 5 � �o-(nala�Fh! &� ��M>9>� -- "� 5$Jj me s�].` @stronger emphasiz#-$W-to�'� Bwe� FQ-� markm��J-�50 Ham�nBV$lcw�p�xfnMV posi��.arbitra�b�N|��Z�Hrrespo� o� i&�\{qF � $q�A $�w�u�$��QD �m�ca�+%$n$�#�%ny^��J<T�.�W$ $C_i�>Q denotI�&E�a�j�fZ� J�mN_T)�a� � &y2 si, \psi'�:�% ,#a�xes�,�N2]\|�,- C_j\|_1 = �(i o)o/Can!�rea5Y%zi�i~7/�?Tp�A��#<, Q!^$��.�word}K �0er= da�:� n,k)��$k%2QNs m of length�*�~��u� $ $k$-tuple� Cq� C_{i_1_�, k}) \,�&� i�in \{1,-Ny�-�k$}st�a�, *in�k*�!m��/6�":y !m��$5JZ}_2$ (60.ac�m��-),��rA�:�f�t� ,soc_dF� �% supp)bj!Q� e�Ս+! *Ryrim!��perly (�,�.Sa�oW%$%�j;�$:�= \{eE7 �:)� j}(eA1�-- q]*eE_.6/!!{%9���. A� �(T"1�'/pic���1w�=* erroD�$i|! Supp(� bL��2��<mit=&�! nois�pnnel. Af� +�/� first�� b�� rece�1� G4I  $V_1%f2� ^n$;67�)�]2A'd�9s!�Z��vmqi8  A��)��6�X4�V.�� hand�:�a���:n �neqIW1A���2~i6v�/h�,%�E �3���$m�V_1$? H, i�6se�1)9b��Odura�2� w�2� #$m �@{�@�s,�eS�% V_1))pe$)�, EYif�Qb�`�!.(us $e$�s!Z�#on�)��( situɋ!U_j0%�o&d" near�0neighb�&%4�to geHcfn(!ơ�ategy!�ae!TeFf algorithm�,I)�8.io� prerOsi�4+m �n!���f��!!2a so- z9%��Ding} $[n', N, e]$-�B"�n' = nk��)m�+E�r�con�Q!N� "� "tEQ��of:���9d_m"LminimumMH$-" 9ofX "��E�/� � tra2 forw/S!I�A�l& d_m-1)/2� � �.U2V4 E�"� ` �:�� = :�=soaA� = 0���,6�is._ e09"$�! �>�9�0-�. 9: ��+,an ropr�� !��a2 M2(~� Jw(vA cogni�!p6? is)hjaV i���a�!�P� yetTntifim}X�ZB8 as"�$in Hilbert�.C6m�ep��b�2n�a�"1�"�i6@�$ed* a�2u.�)�"��qsp=AF� . By"� \ref"� � &�equ�ly*n72�"� !!$�d� �� � �)Q#9�2�Cn- l_2� e>�)*��*�;�� R�}x=�au is $h2� 1$*�$���2� x&��N� �!� fami�/ �12&�n�/tv;�=�v+��. W~$V`e ���$ Euclidean��$matrix} $DX2%${\rm Mat}("W C}, N=dsym�� B ent�� (D_2 N)J�\|_2\,� &� v_i, v� �a�"z &�. R�U� n $N��&�>)vMs8homeomorphism $�:�^N2k2$�� !� eige�5�;�""��:} (=X�lambda )�0 !�1%^$(��u>^� ɏ$q�9�� a �#q�? rthoal#A�{�.���y s (af� a!6 L�)J�!��n � 8"�of,l=N�)(_1 >  2 /�e�la,��erty ")1%O!�f��Q1$�d"�%�}!��2V��9 nWs d,^dc} u+(Schoenberg /(p{sch1937}.r?��largeA��D-L9ng� ies;+�0,� hbbc2003Z)* 'w�goH�s40�M zI aluv c� 5� M(&F> a l�>M"-de.H k. Also, �Rup�=t�ntinuT9treat !�!�^�x�:]�!HgrA�m� B=+j,!a Lapl�Q)�InmF�2$nZw&c"� H��B� ator�W\.�7�z�#i=1��m1i�/sf P}_i8�;�  =6(^�-!3 projson�on:�C�sp�d*<��_i��pr�a��'�  C$\�(���2�b� =>�;�A��{.lex6)& \hil͢% rm�}_�l ^{ \|.^N, \| .q2)��$$1x\|.���s  2#a��q2�,q usual,���6n1isqu��ro98in�pro�1 $(.,.�! 2� ~]�W�4K8�A�prPro* b�lts}.�{iBisimu� Principle���qCl)���1��T�Do'+�%IAAis �e0pe�lHep�4 esenp�� M��Mc+1/ steada� \ �*�65!�E8{�A( Au�< {N'}J?VBich�$\dim FN'E1 *Y� q��*� }�!�Vj�|�&6:�) r9�!0b :N"�8 d $$ � jF $�l�"��Z >$�no�kgegIt%�>A�i�p)�7 (i)}} 2 (i� .�Tq1 <-.t suff��A1KC$.%��CA� prox�@*�I$P_B� lfBw�h!ei1 ��VV�8�6�aD }s4(.�, J��Fi�I m�9~8 + 1}S�_KB�> .�>9�$�assig��o�n�$E[i .�$ %truth�]ue $v_j�_i�$"�j� � F| '��loD4pb]E?of!�j'EVou<5���Ipr7std0TA1&�T'��E2|e�x \ #{Conclu�Dt0ut#.t"qL }} �u�A�A�A(f �blems����e i���l7V_�%K$Imperf ���at�E� 7fB�Man� ���Zvu"�K,meta-! ept}!|vi a n�.erVM%��:s%�) �� ���ingredtJ=4�used:��al un�L�pro6!�analy35#y;!=Ja89on�R4le!2e{8�?ut�5e�i�rgu�Mj9)`HQnvB�&�N%��� paradig38>@!;��le,� �5U��  di!?6rexZA�xA !�lis�@f*�7in*to �Mm:nts�9re �Z�4enx uxplic�ncorpo`C�0f Poincar\'e'6�A� u!A�5)��03)�9ۥts`�����Da�:A9a8DtoZ�;,�!j]e�"�7input!�V�. B��.�W !C� i� quit"992c=GMS"Fuy�s3#d �2Ga\"9.KQ. N� =*e?! �2AVN"/�W se�@�� ^6ex+�1lf-�al5c1��l!9�=2�&� of}.>T$�;)-8lso9�7Bor$$r�=d80Dempster-Shaf�o�'�>'**k�*�0a.6�fL >� %�!#@�(s. Moreover��Rg�W appe�+cR.FkJ� h�N�#���D.�J�< �5�� be�L}6e geo �alA,L@�BiSM"P�l��h�S=�ADB)sugge�E�._!�tL+onY��1�E�b�S� A�in evo�N�~�>y? s�KEZpX> deci�QW>�3it6I cosm@y}*R�� mD!khowa8aN"ZO��)�h]R�s��.:K� a���EFe�",Uto %�phylo� 3(v5ic1�y�1><eri2004*$you�O.�>P� xNvarieC� studjreQ� ,&�"�!ň�(2�A��'sh9)6'� i�leafs&�7#ctyJrib�P 5�arc��U R"A��E���r� '9CR�7�va%in�&nA�%� xY3ve=A^xmodel�IU��s�&al�"�8-f�"��9�9��y�"�g : to�F� a�Q!� Ver�;� Segr��[?Sec�:a(t�ġ%�topa;.e�d7?"0 hidden)�)�* far,� ��21�� "T#: ��- ���@�?a�9I orI] ��8}E��"�>2� ]( t�!un% o� territoryh A .�c&�0��� � worka�2hJ�){s svH �3��sZ ( ��Q w p�;ula�%&i./L. t!�%�i(F�.��%be.G(���8ao}6�!H���"a{.Q,AgeaX7�?)�!9R�M� �Y-TG �� :v({\�A}3"T3Y6..~.(B9)�thooG��T firm?&�2���E"�M�SY� v�a1&�Rgloba�[Q"�NN�.?ak�ȉ�B�N�.��t�Uo���D]�� � ENh%��:e -� E ]?FE one}.XF>4E͖��(.�) '=!�&G)�k�N��>ElB� ��'mGY�iar14B�SdG�W} M�V)4�I+ow��ac�Q�branch��!KV��se�Aq/ /eRN9��a nesa2me�&�Va�nZB� .X�!al"`� %&�6M!m e go Ef s�8Q��M�0�*v� R�a��W>zyM"$(�>ic� ],N$��]?M"+� + "can70'GI9�bas� n $P$|GA��A�i ��Cy.\%nski{$�@f_�Brk%�"�I"@ ) �K�S>� . As"�"� 7i;d�� �El e�Qies�un�"_ $U�Q=2�YA��E%>](�y )})�-~mod$�3 $\va� _U^�?�X`X!�^'�+� [M c!�n. I�r� s�y"�Z�2hoiB`@>Ii0�NA:e�sAC�write}Mse%�s� ? Ua*nZFp� QJ1} set}!yA in*�Mq�1ngG B9!l;of1�alidia.*ewaE a�i��*��sw`� ch{}1��0 \mapsto \bar6�BuccheriI�!�ae�E� } �4$� `WB� F��s�]"�� bu$ I�8,n� :J���B �9 2�T &�a�GE� �D�f�z��'O:Nor�t���D ��> �QtA�["u�Q!�Bhospite4-e!gA��((� . �Dl \vfill % bibliography \add�|�$line{toc}{� }{Re[ces} \.9(style{plain:{�W_v3} �$doc�Z} �I\w ([twocolumn,3"pacs,p!xint� s,suA�^4Np]{revtex4} \usepackage{amsfo�Vams�7thm} %..fullpage:psfragZadvwUX\topmargin 1.0cm %\new|em*{R:7!4B7N.�;} "�:.\{st}{SmAK6Z>9}{C&�:29�>{N@:8dfn}{D��:aklem}{Px&%��"@RR}� {R} �ZZZ>CCC} y;BBBBLLLBNNN�.�dIa$}% Align ts? : deci�& 2;bm}% b�eAG@ \DeclareMathOpeA#*{\trace �op)rm{Tr}!V4nbF1�4%Z5CSSF6�%:[ b5paJWapsa2uwyK 2�color}2epsfia6Ga�BsA,2+ncd}{aUDncd{\QC}{$\mbox{QC� calA\;$AQ # pr}{\$B&}^\S2.nsVS2Q%{JyS.(ds}{\displa���ovl}{\� �7�V}{1 \hm{-1.0mm}�0 bf lA�im}{\ {i}}��ib�J.)\title{A�q celld�Iomato�v*kO � u� !n�x{RoQ.Rau�0dorf} \affili�;0{California I"7,of Techn�y,\\ ��Q�dI&(6`, Pasadena, CA 91125, USA�b{\today �ab1ct! I&�S&kJ�cape��`e��> al Np�-@h� *p*� �F a�6(on Margolus�. $2\�ds 2$ quU6�"� ``1�< '' aKpr�m�f$� � n� s�Pm�D9@ \�>${3.67.Lx,  -a!k�a (QCA*6�gY fram 4��� �e�al pow�ms�>f,"�the�#Y � ��Epriori�UiR_in=�� �g*;i'e�d��na�in!��/bh!/C ro_at- exer �Q�I(*�]ite�\dem c9M>*QCAae%!ly?+M�1hT:8ma�eM WTR}�:Fur 2|��A iox)a.�~w?"�( x� .�- �$ar slowdow�V {WvD� ���r/ef`%�&r{ gd&l�4��}!ݡJ m� SW}.3$a|Vy$z m=B�� n�Nvidtyr �#DP�{icB���"a�1�]� deve�if�,ipped)"aY7alGbexteraMW. Ac� d meismK� 3�/� e+f nt l�7 puls�(SL�LmodAHa%�6 coup.8��t<�{SB1,Lev-�*QB}A�G���]�,��SB2}. Am�x �"i�aband#"�9-a�ifVa��l6"�#.|�d ask ``How��rY<69�:Xa)��D��E��mA��p!�ful task&1�.�ing?''�� quick ans��^be ''Sie2V4E�.'' H�nB0QCA)�tu�:�Z5ic(sBQ_occ�^at---Ob!�sq%*opi9Hed-�^B�!M� borh:rio %O�ed�E!oe�"�`�^-��"�d���#sZI}Brenn}�#��a A0-��!1�datp ansm�>Ya�9(�se�1)t!�Wed�a�<nfe�J � Wotz�&u .yvia� nom<1"Naa 10-�HamiltoZsisy�, pe IaWc!r�.e& >�4on scenario. I��k%Of�buc�I0;�two2kt![+FE���"�a fp>M�'�p"X C}�eE u� } !6 �nwo&�al !>�G $2s t r$�O�'odic bwg�"= ?a�us. EachV�="", � . T�W"��Ec�!.�%�erm� aٟ 2�I?��}� l� K)E��,el_ � $&e ^ te�! �>E�a��  $t89 �Zc?dd,��dively.$F��cho�BQ0�&u  Uorus R7 a�F� llela��qwa�,-���@"�cf mH����pH %W�"p�q�X 5n ,!&��n .rt Man�t_od�e��B1od)Bu� Y�Js<=verlaps IoA�%%� &-P1 >:� A47.�qSto $t61�)eds�t[ (taneously �Zy!�� aW.�D< $\tau$S5. Ss� � �46�CW�� ��g$B� %�)!�Nbd��ve寁^���X) net��� !�next-�c�E ga.� wid1H2s�1depr"�%<aŁ D-a&�v-� la�s*�je�Fig.~<ATs}aI��/!�el$ �Y� 5�w-0n:F�: *.D��{ y}{rcl !� &=& 2y0 S}(1,3)\,?(S}(2,4)\, HpU \exp\a( ( -\�20frac{\pi}{8} 1-Z_3�Z_1\r )}\\A&BzPNpiD4D1H 2 i.� �!�}a: rein$H$S}(a,b)&�5a SWAP-A"$�� $�3$nd $b$, $H�:�Hadamard)�.I�on9B $Z_c.jPauli / e flip"28l ZDc�OH If $|p\rangle_{34}Na��om�a<� ef�/��ocs � '� , $p^{(3)�2�4)�bCQI�N��!amHa[�,Eun�h"9�$U(p)$.�$|D�12 � �� triggmJ�]LD4 (Z)$e�nL��� ��2i/4$-)�%�$A�(I�$pi/8\, Z_16�I1a�F�I�is�,=�$�.��� �,4�qcp�= v``� ''JzZU�3Io E��#y:�t�!�#as�$ant*� >�����>s�R�M�( gram regi�,s.���<|e}[ht]��b�centera� \e {file=�..ep_/��=8c�� \capA>7Y�XT&S ͈�. . a:*H ���p6$ *q� %/artF%�!W-%X PB� �-� #! �b: 8~av`f��%st}v� 6Fs m�9��E�� l &�� Fdafu� dic� 7 ��� ��i; b &��t1ĥ�-���MDz�e�b� 5[s�v?L&i  $x�q0�Gx 2r-�UrX �S)J4Yt� =0${&�  � �)U�!�_i�p��:� Z:1v.=p_j=)UB 2Z"�  isq ٛ��a�rt9=�j$G\; vmod} \; h�2rU�o 4�^�^ma�[:0pt$��.wt� 1�N  thenN l@ProgStepa� T_i\�c�m&�i \� *�\ \��A-�5J �\, R�� B� 9f9 �2%"n�sjG$p�ai� a"�� v?y:; N�Kaccord�A�2_.�g�2JK $T:� t�� \��%8i� t+1"��-�l�"NH$T_IQ e}= .�Uo  T� uD�)�� Fby@o}2>?+1�#Kr>ca�� �k&.te_ A�!�j`) E^b� �[2i+tayrJyNow� I�$-694��� u  !Kj�E�:Mf�y u_2�E�u',_{[i+t+1]_r}� /{�, 6��Ea!Q]�-��2�Q j�DiP(��a�[\wJ_{k�Lta�_�k��n] �"�N�m��a�E�ine_ �A�1�, �!ω�5(1) ...l r)$ �᥵�rfC)*A >^-�3|e, ^ � $. ]�ng��vol�2le�*w\+Bfe`D�0�aYɺ�rd }5�eas�1+ ---a!�~ �O� B 84in �/A&B�F=se t���no4)mb� o402Za de�"G��XLF6� ne�$ia�=i6+���� =�[9at. P-t-e �9N! ouRz> �%aR . Eq.2!PA4!��'du�'Fa�) � aUm�G�do M�)L2#&,y�b��* T>~�R�>&�s6��d�F-l!�>i {�� \no1P�j��C����r});6� ��� n�$v s & \;. r��>F�V<{ �&h} �{O �� 5�>�M�A�:� �:P�. .{M�."�Q.�fE������&�$H$T�B2,M��l�7�g� �qS�.i (": ).�! th��>� .�f� Y*V-�* �V.�=$i- arrr&+1$S}qG���#W|nvariano"$\Box$ ��h!y.�7^�-}B.#���L�2��SMLn�)hee�$� 2$-ls [ playYwhi3*reM.edm Ob� ,Y�S. Dp�^tc�<$1�#_.E M�uad.�fcross-h J �!��0(�"���ɐ��gra&%der�E�5eA:s a6��5�Ţv| "�O Ks�*�+"H6�Bu9� ��EXd�*"@%T �CNOT-I� [ !$\p~m \,�L �"�.�L�$ Boy} X� QCA,�� =pen��� pp}�he� �J�%�(0<�+-�9"%:�"�c)�$!�:&NCH�of&{-7�u#� {\bf{p}}�� \{��{��! l} E�0\, 002 , & �3� }U=Ie2A�0\,101*6+H+1�X U_z[%�].� v ����B5 ; f��%{�|�fyKc�'ed � (no�i�?� 5�!N<lb&to�0 mal))��.�u�*��U�Edr7are 10�+ce|�AA��2��,&I@us 20*�5A�A:�$e9E�� a� !) Yycl��Z2&�&!mrwoY�Z� y&kexs�'%% .r� help�6O%&q B+OE< selv-pn�A6t�?6<~�?��H�%-F�+"j��~�4& L�5.�no�nt Tw�nZ:s: 1) 6K!�  O�z(2�ga�[2��/R!mD5�!{I@��r��|o�8x� $o�*2�E'"�,e�HtA�Q1�Nie}. A!&%M%} -��-!!o&� .\.8"ӎA�a� ٩�s $6] 1}^r Iz-1H$SLrthogwk�-m\'�* �F I�a'�EpoZN�e��p�E!x�?&2� is�.i�F�$�7ant---���2&7��.)(�6�!�s. 2A,�w>1liA�b0��2pl�f&TioAu;[ne<8�B�/p?Ur ���+$n�r�>�͙AS!-�i�" ��r$.��$n]7.*I"� � ��=�*I�^�)���d \od! �)Ai!����ljHe6�sk�J&���Q�ks�l,�,e� �,x34�=A�refyRh0� AA�$c&UX� -jlaE7�, >J�^'�� byH-mo� F�as�32j�D0����o � �.�5X�7�A.�ct& =�f.%�]�/*4� 1�on|mIw a teǟ� -+� 1 5 an�]B5n��*"}�G @sӒ���� � %AWe�/�* 7n(�a*7aE�p!-T2 K�k ��U�---q j] �%e�"m"".� ZB5:C"!Z } I�.���x ularKD *�ю�@���R�U!%!>-!>�mav�a�g57-�N�1 X� � A� R�;��&� . �q,lnco��-R�GEJ)�e9&�5VAe�to/BA3� XiZU�vadout.G2 =Q�_ uH<f�o)!m4v+i�����e5�.!!��b��5"� a: tI�A`*dRQ5<I ckno&OEEa*Glik� �4nk Pawel Wocja�Q0Sergey BravyiEh�nK�. �K�/wa��p}u��$e NEal Sci&IF!& x�nt �(EIA-0086038J F� �the.UE }{99�=bibE�X{BA} D. Jaksch, C. Brud=$J.I. Cirac W. G|zand P. Zu�r, Phys�jv. Lett.� <81}}, 3108 (1998wDE} G. Birkl, F.B.J~nchkremT�6B4&4B )�I}�� upj�IB�I&�I�+ide,prl&�F%2�Fam�I6�F�IB J6�JicxWset�*,{MaxMatrixCoC430} %TCIDATA{O�Filter=\5x2.dll"Ver�R,=4.00.0.2312 CSTF'0r�J.cs�I^Cre�=TuesdzPMay 20, 2003 20:29:16OLastRev�; =Sun4 Janu&028 5 13:48:2.80j.2D�KShell3ArԒ0s\SW\REVTeX 42E,Language=Ame|> n EnԖ7G"BKAp�*K4H`K�I+}[ ]{A" 67�x.16+xio2'2# clai.#C6#& �. .�"�;6,kQBXjeO�6,:X�'ary2,6+?Qrio2�2+&�W.CL.� /*E�Q6T&Dcis6(e 2P�L9S�L.sno�9&N2)prue(P >'q�6+2/�rk*N2%so 'S6)umm6�S 'environ6 �of}[1][P�g]{\7y%0bf{#1.} }{\ \�= {0.5�M �O�4��\&H{E��c al T�|� e Ko�P-Specker: a�] Si�7 Qkg� P`A ve O,M -Val)fMe@����JQiang ZK!}6�JHefei&� Lab0eorS\�8� s$MH$scale \& D"Q�q Modern 8B� F �DT"�J�Chi�J�H, Anhui 230026, P.R�nina��Q{Hui Li*gK>������Tao Yan������-�Juan Y�R�����-�Ja9feng Du�nEn j: �:eo�: V:}*2� Phsics,"�2� � gapo�i2u�Dri��3,�� 117542!'i�!=-Wei Pa�v.�ƫ�=�=9=�kaliches"�O*�,\"{a}t Heidel~hg, Philisophenweg 12, 69120.% Ger��:a"�OW� �e.A)G�%�~G�\�` of &���l�Jm�$*s�&Kby �ve-�orlY�Z 6s,�o pola.\g�le photoEu#ar�c�g�J& &�[.� ly t�a>� �Zl� G i� �-�x�J�.l�0uT�P$ ���&-�ex�Nhid-v`#b��O�i!e� for 2���� 9�\NP$03.65.Ta, (Ud, 42.50.X��*YP HZs (HV)�.spic+by"w� , Podolsk#C nd R/(EPR)���f�?s�;adox �r̅patU ted �� �=)i� 1960's, B�c publ�4� Win�,�� Z2U\a�H��)!�լh -2n?���^ �>{(LHV)�o!�Z�m�L$cs (QM), lЁng�2Ak�9�O.�jp� . A � ^u~qLr3}�ob>�the inc�tӳ=of LHV�Naata, ��r"7o�:by QMA�26r�+K c2,ly"FZe�#΅�? typ�0f�"�n ofBeY��;a� i B�NC.�E,sucC �,�Re ph��)?aR�7�[8�G�.�!,���"� ear.>>(KSM+emQ�4} ��Fp�r��]| ��$��QM��>led( -or-!hing--!R>�%Mem a^�.��$e�bm.5�I��al KSA�"!CA �A1HsNI*�KA>2y%x"�d�! or higher*&.FR� �-at KS �"�P �D�� two-� � (� bit)-�$cabello}, �*^�&'Eբ�oB� (POVMs)-H��1, 2}, I+�^wj6�#in ��\Mfol!- 1] ���-�6,�. J~�!p�5���Xj� B�*��bon 2|sI�of�r� �Nc$On W&MO� ih!5!.�to J�A�>�.k2 �%)�%�-I1F""7->+"!Z %Z �<(�i"D��2Q aO!a]��6�4#�J�T�|��U� �2 ���!b��Dnt�c9/�:��9: "��.�jli��%biLw s of�2BO�s,�L��!х" one Q{ިC|al�d7�a)*u"&#I�davies}!�!HO��"a6Mc$��~f'�[Lg� s. BUf�jNeux%'Fe� nn }AS�\ �eit, math�\ N}$-��a $(2-1)$-;!�� �|7(bb{C}^{2}$\fHYed=�%o"�$ meB J(OMO�o.n6Æ2q?�atu� �% }j/��#rst�E5v!8� assocȋdIhq:���x$\{E_{d~($d=1,\c��,2�)!�c�%N� �}} C0=|\widetilde{�D}Y�@ le\lu3N"|,e: eq 9$end\q$r]in:$*�2rm� T/ Гm� �I$ p"�- *(.J�?'.� {��.�$ E�))��U @J6|"f!�)'=;21b.+ [c]{c}% r\:h2�b P\#) Z}.9 I~V|9�10F�a�'n%xB"set $\{J�Qi{d}|\} >u�Յ OM�|$�m  n�Jat m�Hi".�J� �aL�E*��# �NR�Ps�(v�\a�\\!�ta��2}\T4 | @|��+|\bet =1-� 9�stF��8tt'�$�via O��� )cVh: �,�,0�o0 � ^{�K4#}\in %��..�'F� N/���@�hM>6n/ .8^{cE$bA-16C *��Eq. (R�):JIE�kVi�Kq_6� ��,|=19J0�Ef� X �: &�06��%�%>�^.J(0V�,\qquady,.11v 0�v�n\\ 1Vk:�en��P10J�B�Hj%u �!9 }��!� $|��$�FEq":q�x)Gl�;6= D�f,Za% McQ��F2��Q.��ƙ��y�st'�7Hwe;Fll�-�:�v$nt % }|c=0Sp��or�R�6� V%|xZll y� null o� �]� th͵x�. O�/�çn�����m �on-.�s,� j�S��<(e �cRl. BX ~�p*OE�}"P��UN i$ q.� path�OM�SEoRx�ycillaf� % ^2z�.�/noEemKm�w �$|k-�$ ($k"Z  ,.�Bz��T� (�V$� :|'u} �be �Ca&� a�k} .� & =�|�{HQ�+� V,�F�A|1 �� \+�� C:Y Z" �) �" �E!`>B$)�I�  horiz�{ l (v��c[�.(� cruc;,ep�* to"�Za/OM _Cin6{ 10})l�Ρ~)�6�+9,dr �B|.�6<(By <{� $U_6��ua��l�pv�a�����n.� � ,Jz�k-11�\ ^{\�+J w<{\ >�\ }�� |k>Z5�F>kn\ Z][U<.�4:O�e}�2�aa $F�=u�M� Mp�$ etc�, 1%iOM>}R >SVuu�<ndx�2��3�S� ��^$,E�*  by.�.O`F"� 9�|,&V!��>(V��B��:[ 55 -}( F�b �U 5. ] IR�0 ob���OM�}��F�n �*�Q!Placing��bea��l`��� PBS)m��{ gle-�� �c�at��-F/�y��\! H�9��scribe�*#&l�&>psQ�b�>)1��� 2��of�b�$W���b!7��Qf25�!*%Zg%�P[ptb] \z�*s[>Z.9\4]{Fig1�@}"NZH(a) A Mach-Zehnder �fer��e�H���1l� phasH i�E� wave�78tes (PS\&WP's) M+�b�r�c bui*�!8any $2:�1�����.� 6� e�Zeg��1�rEZ�fc( (b). (c) T�;jb 5s $T_{pq�9eno[��h�����Ee2�3�BxD:I.label%���-�~Mtechn �emploB�� �@im��!rin Ref.m$reck}. As �26engQ� ����!�$U�� 4�{) .eGx=�2C(MZAteYY?�c-C:2�� .r= � %�.xI�.G�6�, ���X� �T-]� [�Iin: �a:}(a)]E� %V ��K Vn�n>�.-Q�Q$q0fa��"�\ a�d�DL�8Yic�|�79aV� l=^6���f .{i�e?:� .}��+<�i� u"($p,q"+ 2�)��ch!9an)"�B \�� �s $I_[�D$ ($i=2p-1,2p;j=2q q$Hq��by*�X�DMen7or% a MZm]Fig6$,�KUn me��=a� to G5u2�s�!��9%LIspM�7�� �a�c�AonMZ%e�=,�� ($q=-"�1$)?f2� % v� F�}�du�A�@%� s[5fA~�, .� -2�:r B� -2�m�F!�26>U I��I_�CNyB� cK=5.�# J#%2�-2}%s>S1}j;c}%>�-2} & Q 0 & �%VM*�1�.&��P ՎMZ:% �bee��cur���!�mz���Ld ���B�����%I��#aem���jt4$de1HN� ��r�9�2!�![=�2l21t�a�} #n"� we^!"j�>� LqT_~p j#Vn�u`^{A�n�M\\  $U,1dag��=-225n�_.���-��a�� 6�J|\�6� r]���Ar MZs� �B����&tawe = NcS%up9&P&�M�o�* 3Z5 �!sh6�k=�*is.Y!-� ��=J� # �h�r42��<�!invg�d7c�6�� 2� ��tZ�]x���&� is�$siJ*& ��H�J� ~B�#. For� U> *p>a�P,Ĺ-�YANto:3�cesEe"� !��{7'�R�'e�vacuu]FU seE�>bǖ�ymo�R[e.g.�U 3u��>�c)]&@seA��%` can �h��t�D. %% 2u'�N ���n � op�b�$"�.%p�3�>�,r+5�+8y M. Nakamura (� � [28]�\[�"[%)eZ.���GB!� &[(�&u%"�&Y n%n� �mpler �MB �`l$�#:��%��2F��6���Nsix��| �Lregular hexagon: $A+�1 �,p�'G A-$,� $O"En�)&�]:ME�DW�D�mz $A\pmx $B 3X�� �Kin�d (sharae�es.�BsIt�+çedanH"$E�$\�� E}_{�*� � Q.&�s:�m8�)`�����Jf% _U:h C\pm g� 2A^a 50:50! )R two B���q�4theta_{B}=15{{�circ} $ C}% =302"6Z"�"Z��A$, $BC��%)�� �B ��)� join!�!,Y4a :�� �Y N_M���dasNRrA�f�2�eݡ.wA��M-semiit&4+s,�"չAA!�&�A:1��)hs.>� FX� 7r�q� \� y� C #I /Z2d�=V_%N`  `*' 2f�n�! K 6�j. Z & Vix� "� @�w�LrIAB�sN� � }\}1g6%%MVV1�:0!сl� povm1&\ G&��e/^� e,aq�'�&�re���~jK.(/��*�P� �tamem�c� �] )�.wo�`}�.z� .E+nfu��e�AB�� 'a�h�{�9,v�+}+2�B>A->"-A� },bBIC>ZB>ZC�ZBIB�C>ZA.Z]c��mb�{Ql�3d 6ur�< K>��uK �. A*".y��a��AA�~� it{y]-���A� &Ru?7e�s*�1U3]]�,� �GQ ,Rce MR � eaE�w�Eqs*�# 2}),̸4��t��Iof 2�r��2�en /E�#7 0�ee NJ�m���^"n5a�- M�"+Y�w.�h"b Q.�1esH*2 2<$c*�j��U 6>������x�1Ne��!eJ�y�z� ,ll}% |A+ F=>�, & |A-:"�!B>�\sqrt{3}9y>P+ #� M & |BlF*5*- JiMS"C:�.wM �rM�C:�J1T �.p��")�req "��-} T��a" aB Bc �>: �  � a*{�c�7� �mO8n��*0� )�3 �0�-3F -Rr $ �2v$10})]&Q�E)�1}-u2"�p�} |�M� \\ i.�+� S" +i|2 =f �.K6�i I V�!{ [\\ -i.��-r�\݄OMa�*�D&�AG"��#��6�OM��) 6�&�6�4�7Z� `SA�y�!�%w 6� (>� �V~�2J(',� �lne�ty�a._MZ�>��To be 1.� BS �e e�? ��"�s)*+0�S!ie���y�IA~���a�a* >AZ.AQ�*�$bsQ/�7=�J�^�7desig�t!GJ�UK� R�2c�e^i[�Op^�Z�, & �w.2Z�-?i&C~"6d .c�.��b�q eq Jb&q%$lowbreak\a $%mg:�5k�:%h�� ��U_{C}��վ2� A��.AA���5�z)&".m�:�y�F`i���3� . A;o��to��`!&B,$b  CR�+-J� B (HWP)*HWP�jTmajJ]x`t�X� Є �L� &�� �u1# �e5"H (� an ��allX!� )5�y� HWP�2+��) ~v cos2 3aosin A�E�+����p) .zhwpQ �&�>�$E�=^��Go:��+5 �A�2u�%�F�$with% \beg�in{equation} \theta_{B}=\frac{1}{2}\arccos\\sqrt{3}�=15% %TCIMACRO{\U{b0}}% %BeginExpansion {{}^\circEnd,\qquadxCfx�=30�q. \end� The schematic drawing of the implementa!"lPOVM $\{\mathcal{E}_{B\pm },2�C\pm}\}$ is shown in Fig. \ref{Fig2}(b). �V >VAB6UiU(>-o% 6/B,\}$) could b�ed by s�y remov�(HWP$\left( 9�,\right) $ [! "B"]V�, with%T�detectors that previously corresponds to $\.d�$ (6%$) now?�t>A% $. \bA�@{table}[ptb] \cap!�{!�experim!�l data!>n!1(in $10$ sec�(. For each !�8, \textquotedbl!F it{1-fold Hs}'%\\ A#!e %)Tonly one operator yiel!$he answer Nit{yes} %f(coincidence .1wP of photon $2$, whilef�2�� mean �two�sA\ultane)�� � p �I��i4%�in)1N.u��T has been scaled accorQ>!5pcarefully measured efficiency!J$our single1U1hs anda�h%�comparAs)���~3 . InY�s,�3-{41�Y coun&yiing toIm more n:�)�!Ir2�, tur�tar be virtua!3 zeroB30} \label{exp-!}%q�,ruledtabular{c} \AZ4icolumn{2}{c}{�,u _{\pm },\n \}$} & 2444%I=B�Z/qj6Y<} \\ \cline{1-2} 3-6 <7-10} $\mu $ & $� �+} - � 5/array�! _{+ �,+!@�� %% b�;-�;-�v.;Jv\\ \h!V!:a�mA-".B 14718�10474 3156 $2587$ & $3 693 340$ \\:m Y2mC m 0660A14781 1902 2103m95478 63Jm Y2m �12883A 1058 �376 �10940m12 �3 �-24!�AqN% 2s �H Here we shall not�$t although�|�+�s�ѐin Ref. \cite{r5} are both based on s.3��re($ substanti�|iffer�?s��$theory, ou2z test�� e KS $em for ahX doesA dem�Rm�$ MZ setup,E{,is irrelevanŋrelativ� ases�� s. HAWl�@E much� plerY�8convenient. In]�!�e generaa#wo-Ms (��Xby $1$ �$2$) in�maxim�+l Ed state,$(a visibilitmdabout $82\%$, $|\Psi^{-}\r= _{12*B � 2}}� |E{H/} V2}-F)H�9n2*� �type-II � t� !�ametr[ ownA�ver (SPDC)I�8110$mw. By trac� outM r Eis � aTaQ mixQ  describ�  densA 8matrix $\rho_{1=�2-� -�5�\lE$Q|+ !V9�2# V}|\�) ).$  three�s,R�u 2��\}$F.6�� \} $%[B`62� _��perform�^ ��estiR 5-$.�&7 �j� ntained!�T� �"� ��j numb)�events7�'%fit{� a�� } � U LRV 7[.iosed �� than6 si a6u I� "� .i7collecE��� ion&� i� the f�| port%v $\sim5\%$�9Us]i�E  calcu��on� "H &� ha��&� Œ c&= to  %���y(al results S w|(a very highuci���99\%$)�9Eqs. ()� q 2}���theref% .n$ly exclude)�exist�](f a non-con8ual hidden-variEa�EA6�qubit. F��.s poinQ view%Lse9N� %� due � � ct�km'source�:� , because��!f probablis+featurpair cre�Ein ��, %1 willWa s�� E��1 6�Lis �SdAIe add��al"(s!� ll g��som: (�- $150$)_ i� �same ordy� observed�: prese N$ concluAa,D propa�a.:alxe%��� )H@of arbitrary posi��B-valued� sW Epolariz CN�6�s u�b^ ar optic� evicl Th�(e may have A�$ous applic`��$quantum in���ce��. A�hdemonst�g-%JA%6� Qq^� e �{. Our.� verif��e�e� good!�m�E{��A�� V+ notA�.� NCHV!dory. W (nk Z.B. Chei�8fruitful discusAG d !�a� sugges�c�%8is work was sup�]��j NidSre Found)cof Chinae� �Academ. 4�n� N: al FF� Xal Research Program (unaGrI @No. 2001CB309300)*@hebibli6phy}{9 } �^l% %\item[$^{\S }$]{}{}{H. Li� Q. Zhanga�tribu!K���� is %!o�bir name�2ar� $ed alphabeely��a\author %�.}Jib�p {r1}A. Einstein, B. Podolsky jPN. Rosen, Phys. Rev. (@bf{47}, 777 (1935)dZ02}J. S. Bell, 8 Mod. HC38}, 44C66:C3�Asp��.2� Lett�9}, 1804�482); Y.H. Shih%d$C.O. AlleyjE 61}, 2921E(8); J.-W. P� �M�(London)�h403}, 515 (2000); Zhi Zhao ;=DL2�9x�01>3: 4}S. Koca�ahE.P. Specker, J. Math. Mech917�9�67:Q 5}Y.F. HuAv��0!50Z�G A. CRjcL19^L4book1}P. Busch�E0 it{OQio�Q��!V�ics} (Springer-Verlag, Berlin Heidelberg, 199:�s2�Per�xl`T�: Concep30Methods} (Klu�A��4ic, Dordrecht,l:�l3}b� ��qIٓ}, edi�8by D. Bouwmeest!�a� kerti�A. Zeil% 5 ,, New York, E�� u�(6}N.J. Cerf5l�m�6�84EaK; W. Ss m:A)G bf{66 0643a���);A�DFiur\'{a}\v{s}ek, j>24102e16�4neumark}M.A. N !�Dk. Akad. Nauk SSSR�4al3i4:�(eng}B.-G. E�rtN�a�032303N�rec� ReckNI6^7M58a�946�davies}E�D (, IEEE Tranefo ory� IT-2!z596S78S end{> C docu�^} $�\Hclass[12pt]{article�DPusepackage{latexsym} .amsfontsB symbB�6epsf} %S4[pdftex]{graphe������{A� Sanz �m/ Agicsm� Gro�De��a�$Chemistry,<Uni��Toronto, 4Canada M5S 3H6�0title{A Bohmirpproach��z f<als0date{ mak�le�ab� ct} A>; a)fun 9 al�* an imagin� art�tinuousH ryw , but �t� no. Y lack!.% "�& argu%Nto deny1 geplT id-N1"mechan!�(��o� �jvy--based� %Ies)�provi a�letmterpre"� 18 e.)� i! ser�U!Poverc� b>n��a� mal ext�ot F��� a limitH1�. WithDi�{ 2\!�ab dynam!�0lways satisfa� ily6� (a well defi < �of mo . ^ular,!= ca(guidazG >�!*�� �tr-�� ll als�M��"Y� %�  \s�{IntroduE�} �sec1} �Q5�!N�most �� �dkoped upA��!to L ' phys�F0world. Howeve!Ots�ndard6�U��al gr s,( � I�W intu6insigh��Pmicroscopic phenomena����Y�V� ma6ones. �!xa*%� evoluA#A-ak can�b� llow_Lconfig{space2,.�AgdividE.0. OMe* ����associa� to s��e�ds((whole avail� �,q#E�he!cba��i�Hbe locoat # (�)�at�eern time5�to oba9� pictrqW5�, altern��+esy�o5'| of {\it9Ly}�"�d���1}!k� themaF��@1,Duerr1,Holland}��m#��t merely�g�2l%Vtm �.� espi��ts�� ivalw%^predic1�ɗaVl ofY�}� #K!�5p. B,cceJ ��wr�-xep m�2�I�n�x�U�y (caus`�W!�!2��l}�)a��S�i�a n_al wayAy stud<.$���ig%\ngq .� post��t����-B�. Re�ly, it����U{Hall1})����ENil likJ�, fail����aI�T��})2zJ�In-Z��thn4!� B\� ith .�splae�f� P-�so--ca>e� � .s}qlerry,!&2,WojcikejT*�t*��AG6�in]9�!� im��equa_s�f*D��:�*e���(arse--grain!{a ra�o;mplA�byW,senberg's un�ty � cipl�bse:�� tituy���*at1U ob� sipp�R�as�oa�%*6 �0deed, W\'ocik)��}\-�-����&�>�M2b!�&n)l*'uc>b  ider!>8heavy atoms or )En2� trap�� !�*?2 gy�r uld ��arge enoj�|(u� � !t least�s�al ŷEX,magnitude (w�i�"�!a&�M�)�R�� hand, Ama��disRcͱo �� oret!�l>iA�ac� behaf+ r du%LA/bal�ic� � usN2�a, �ets m%,{ N --bin�Tlat�! s, a�E��es�M2%�>y}�un .�$i�!+!+at7 in��ati�b�"�z&"�  �2��-�iA�as avoid� �Z ���`8/�R � 4o "� J� �erE�2#A=eC/�i�e��neigenv� �l$Hamiltonia� �|!�" r ��Zreg��}�m �dE� ��a�� recte�mp\*� � ��B�.� J�UY�[s�� n--A� erenR-forbid]� *`!&!.�!j�%d%e ���.�.�A>B��osed !�� uŹatoB�F,.n�.k�nn,�vid�� c " � any a"@. ,1� orQ!organ* �9paperAAa � �&� l �*self-�O!L#surve�.q|��X�� Y/A ~~ sec2���mE�Bb�F �w�{��M}  �3 �5 �M[ ner0M �4= F%5e� illux bdet� >l4}.w)Oroblem J J -�&�(, spin--lesi%��ass $m�!a one--d�0�al boxA��i���g�. sq&b�A�adigm�f�Zs!ea�T�1�� t ne ai���o a chao�|"�< BoB"5 e qu>�a�unb�/nergyE�����/)�.���ermEV 4F6 o�is �ed. Finu �, main��s �ved# Y�G summ�Z suUh68 ���.��1�2�2} Aq0 m�6� At� 5M  an*�  Un?i�+in�!�1ianalog-� Weiera+ssa� �Manxrot} "�.��} W(x) = \sum_{r=0}^\infty b^r \sin (a^r x) , v6@ a > 1 > b > 0 , b \geq 1"eq1-s%�pau�t1�}ao� ��"3Az� a�!ebi���>� box(�($L$ (\ ( $0 < x < L�"s�E�cSchr\"o� er �.�%�a�sR_L\Phi_t (x;R) = A_R.m,R n^{r(s-2)}-opp_{n,r} x/\hbar) {\rm e}^{- i} E %t %Y�eq2Jr �2 > s!�Q+n)�2$.�$|= n!�pi� /L 2w= *^2/2m$a�, �6a�ve�!?E�izl#,�"�M� �#6eE � �&w3sa[A\um� $n' �$;d $A_R$�",nY��e�a�,�.�"�&2})<coU��.J le � �h�oone�ul}". j&m�(lim_{R \to i�}MFEE}[3J��� qJ��note1}a%W0s;�M� ��to��t�:�$ Vs� / !O��(�$s�- choo$ a:�, say $n�*!2���, � !�ai�ts2s,=��# �n� .���@)��2�� o8QT.��@ �x%c�dis�inuit� inE�.M����,��1A# init�1.1�W�eF b ,�"� emedue!�Smurbu%9� >�c�( �2~along �agI. An "� ���O� kind @ E�pr�&%�:� �ly uni� wa �R rval�,PH= x_2 - x_1 \leq L$�\ �� �iovabove,Zesi_0 qfeft\{ �:a6c} "�= 0� }} , 7x=��9�\\5� &� �� elseRU� g \!.. .}�4J���$Fourier de��(� 'av.���f�>2}{���> �n = 1!/$1}{n} \ \!!<([ \cos (p_n! ɇ) -22 �]=S6 =5J��a���--b( orIf��t�������%FM��i E_n��26JA"s�c�e�:&�t� 0assume $r = R!�� (-2)�#sum}��Ź1? $N$,��:K 2�R�� $Nݿ��i�ce�"�7fac��R�� $�3_0$�s� cisef(��� �� ^*OsG*�0��bP � "i%q��l�HR��ehek+a �of�� bash-.�'V.�8eq�t w�'$V����`$x�1ata5.7s Q3})�6})���} y.Rma 2Uby tak��adY6ag�2" E]1*Q sis. Give!,*� R�f��� \kappaA�}^K a_ ��al i} x.7 7JmAWrea�"i2�"!�1Lse{ $|�|^2$)� &� $D_f = (5�&(beta)/2$ if�� i*$rum asympt�5 (i.e., $K.\)��V |1|^2a m | � |^{-�.8Jw2 $1 <�+ta�3$. A&7� 6]$! $A6)be"j$me@A%A�� , &�;L}�x)!%��6� (or .tz:U3q<* 4�, $K$,e#t {� i��� U�7}). A2��� on"I2�e�$Ke� byR�"6L}(K) \� to K^{A5- 1.�9N��div mr1be!aa1� . NA^D ah�2� !�:0N � .�%�p ��%toT1qa<)�e� pr��i�4si� ts D� is gra�!ly!Qt�!�S$� pEarkb!� �haXerizesF� i ŭ�e&�e�A~l�7 \ha�9 �9I��2� � "I� Q;>!� neij'$he l.h.s.\! �u� 10})�A[ r )be� -fHic-t��ncN����A �[[c�,��,/�%� N<$I��#A��N�H�*=��5 qF tityR�\big[U�- f� big]6�0.�N��6ŹreA�e�9�SR� , stf're�saBid. W}�M aGUoE��"�!Wo L%o"�%��VwA�8a ``weak'' sens�$����2���sec3} � funda�)�� Bv+"P1 comm�:�� by wri�r!v &2� ��6E�V#5k�(rho_t^{1/2}�� I6 Q?Si� /�=�eq1fA \ = A?_t��`�m8q+r=� $S_t$" (��-�7) pa@{ b�!�< inm�2&�� ��uleawo :jcouple.�lu�29 n� �dik#style�e ) }@t} + \nabla \cdot:C9( :!��{ 3S_t}{m�n )=0 &.la�G q13}f&>S D�� Ftw�%(j)^2}{2m�V + Q_!�0|&�*eq1&�1% EM�9�' { y5Z�enJ��+n&"�K�zflu�~�cl**�)��!qf�4� ;�8!ADa a %al "k$, �oY --Jacobibgover"�� ���A�aupto�ff pote l $Va��ff} =1$e�At�>���_��e*�% � �r���<} )� � E�M E�3 �O}{2A0Y�N�N8 8ext--dependent,��*l��er� �ge} �!d)Xforce%png� �8 +*"�%F�<#,��:�)���e V* $t&�2�&criK) �"�,� �m�Cd�paths�!i$( �,�-- � fac� ,�. A� � �s29Y:�!re�xt= !xBF�ter�� Oez ) 1Z"Q��90�(simila.,!?0�Z9�R��-"c�� 0$ viau7 U�6�n�A(2�,9.�* �a��1m 6 �}92 �����;nsemble3"(�"edaPng� �2})U�h&s�F�Q 1J� � ��!0J��m��3-�"B!.�coj?*�&��� H0EQ-79e�^' reason wh%e m9 ')era priori�"atq=��� X�-V�8o"�5����} u�ofma.&.H&�typ!�2��ren��nes&�bthe�$(``bridged''A�]�.o p0�N&B��a�f (6�)R}&�A}2 ian� � n reE!k�2EA�)&L�w. ���6&3 p�9h)E] > �~�A�� e�op�;�y"�^,:G� new,&�1ed�&E1"�Epp�Ca�!{.+(2aR��t$. S94. �9exwsa�2� n� E (x;NA"��(N c_n \xi_n� [ *�.\. N�l :�%��rJg(x)���&M+!(��]� MM�!$E_n$;� !�e�.�;��+ed�$M$t�t! = 0$�= $n > M��V |Q?"2�� vA��'("�8a', 17})E�E�f�x�!.} x_N(t2�fv ,.d*1�ukU�V#� N (t&a$� J�bigtEz�I� 9e�$}&yx}�g:�F� O�/)�06.oJ,��� ly�5�!��e al�#6 &FKX2��~"�� *�,not�trivi7��&"� �["q.+, 6g926( i�)U��&�2�/>��-ly&E5dR Q,s��8A�nd9}) r� z%n!]�u 4}).�9V�X$^�5 ML*�"2�.(N��!~en deaO2%q�A�tal9.V�- ��Q \2�Lb�����s �(�C2i�  aa�2p-�)�*�)!�!Z]1gu�N f�,*Y@ aaH box)&�$)airlyI!Q"� o_�,-�.�� %&�O! � s�sEgnB�4!��$�$��a�$m$= L�]�3, ,FC| b=$enb@=��4}&$L}�#*]�"1"�"�s?,n \ % odd}a*=$�n4$yJ#$\omega_{n,�9Y[ eq20R��.6= (�- E_1) i$ve]��>L = m!�F $ (� rbJN uni�Va.u.)�1.~d�At"K ,2@>A./"U2��  iodic� �Fim�V�70od $T = 2\pi/�3!. = mL�+�%�A(o6�a; JicC�� ��+( easy. At $#T$0 aZC� ��f4ceNaI�)e@qUt), $�%�� (n^�' 1)/8�zv � 1%�de�j�$n��B� odd�ger��� as $n(k�2(kN) + 3fk-1� the�QQ(k)!\�k (k + 1�i!]�A�"%fiat1-/  gu�!z�!3U.uT�:!�$!��  �nimum� elap2 �7two-ecu�)recurr�, u ely V7$ ($kE�A�D?!�Z$I.�կA�� � ru�eM�*�*�-& $\varph8/=iđk$, -/J��&(� ͋�2� � g�a dela�>$-a>4$ aff � �O+ �%�" { y!�. �%�#a*l 7���F�Fnoa"s>=m&7y&�.J�� ndRq=� s�- --in"t� ors ad��bLDase� e]v> [S'_t]�$P [S_�)"21V�n $< = + s(t)$M\rq6#?$eQeku ��-!�-/��5�0 �uf�Fa e%�>t +C�wo2�m�� � a I 3or��HsU��in 2�&�.�V� If� \� �� iof2Y�ou�S �%,$RM�g� 'Aer�F�J0xsize=4.5in {box4(1_arxiv.eps�\�g-�fig:1}�R"l �� (a)� �(b�26�~� �\ ox a2�8/�,2���Hsolid uU m'0.7�T$ (ck.). c) Me&�`!Z�t�U�7!fF�ies �/ play��� �]Ta��fe,� ��RfJ�`7i�6. riana< (T �pgolic (P!h.w.�!�=.%�ndU�#Q� profilyl�/$xT" r E��7 ed>�3in Vs�[I,Q(b)�a\iI ent �? �au c*�&sha>�b�jval (.�%d? 9?ep--l��r 4) ����$eO!�}�4�rWW& r a %��'-��,�\ 2� `:v�a)on manif�Ey,Cantor--set "�& \�c*�7tm�O�+� \'rea�* :)-��nfAs� b�Y�ng � E1^:u�0 #Ih>��@well--known Gibbs"eHon U �o,�+Hi1o&�2S(Uich&�&a_L6. Af   �s]U�:�5s�5%�seG� %��l�Z �9;a:M$���qB vanisKIat"�2!Ss;�Ldra@%1�� T/2$jl�@�&6\neq 0$;��tera! $0.5�2 0.75�<se nodi �a��Y&�Ef2]aW<al.z\�,!�" �%C `(]C�[9 �%Ze�L $x \�sim 0.056 dgtr  h5� ��g b)),��9s�B!] A�e�al��_�E:�Z�I�Y �"� 9})!�-�)S logarith�a��*(2�)A 9 &�,�8.I$N�.%�2�c) |�^Qv E>�72lea�a �log_{10}.|,{|,o�Pal@$+�n�1Xw��8&h,d�a �. 1.49t a�!}i�] cellagree& � tH o�7%� �7 �- }=1��48}). J9$asm�+e�1�6�iߵ*M�$��Iu�, �� ]�KZOw3e��%33T�:  slow� �-� U1d s2�s<ure. If%�R�)Rno�[�8G2coQ1);rg� is m�fa�W�i�Ippe0� "u 2�:P= im0EXa �le����a�,<� A�at�c�.��I%FsD0s_ lso�'��R1��ached)��� �, �[few2c �62!I��meU�=C!4e%�er.A�a�a>� 0^{(T)i�&. cJ�E1*7-2yd(Ks a l�Ir�.9�su�58 � D �H 2�H �*a) 2�F� 5 ! loczOedA0���a�s� d �� a� *ofB i'1 ��" s: A�0E�00$\blacksquare7@$x  ullet$)1A4f 9q2;49!U.v49  x5� t58T�� co!x&�&� ��by��# �%)�&eX*�(v!��[uErpe2�>3}, c�m_7J�stgb*@He">' ~"��a�P�'pG ��s��6F2 �&I��M2� �s:�� � symm�kg#p%$5^ � a���4q�a� refl*on XyI�*�$x_a�Y"�~ star!�at�s��A�W� (�� k�#�kP ) do�]" �Uo)=g+O��0d ���gle�-�"��&-�� ��:Kto n�91A|,�A�a��(a hard--wal�e%�!Y��lem�A[,%%����&ly wMtowar � O�!* �(�-� �� J� E5 (see,Ep� ��T2,3�H�!�� � '-���h%�,9)ng�9a f�PtFf���efWi they�  Wack �7X�;.)YMqic)i.r�t Minu\p>*k"I'�M2�4�y@� n#at� Ee#� !�u@:�cn5: sig�Eg.�O j halfA�%Do. More�- , un�Sc"�(2 BK�Hl H s�fR�)�,Y;lB�E�r\EAl�(Eqmov%B�SZ  it1h3+nicI3a��[i�^�\\; he {�W�g���CSanz1}�Z��&bJ+-J b� b� of"�QF�** *�8�A�a�5�.] c9 6� �Q �C.� �7N� a� te�>�.1wrmedi�D��,LO �DL� �� >>9E:� 8 !Uay.ze��a�a_K�s� "y7��$N� .en�!M>�I˥;�� � 0�C>��5A�9fd*>!any.A6�<.& B�� , � \simJ.50�MP�'� !D�� �� R� C2� eks �l�8�� !?$\Z: �3sec5} h`���Lg�Oc"�)"_t�M7noSi�% m�1�CP5duM"4g!DՒ+u� $2&J&�"a\a@<��$i Z�� ]�A�4tako to � ��a�er)��un6TR)} Sv�#G6Bir90�~�8&�U�s8�D� *�  y�] any�)"X.i9� "of6*i�&�w,��"[� ��so�$>8^����9"�<�!�6�QU &�=6s6�re>#Y:�.�.>1A:"� beɃ� )��as�4A �Hs�-A#�Hex _� I  !leaf t1L�%e�!�-F3 A$6"?a$�`X5a�͙V>�g�S��&z .*� '�|�/#� "�P2SIJ�1�67 �)�Ha�@$N�OE�*f�Gv�7.�H2N�9Ext^�!ZQ���3.%a2R�{*,,,t$�롆8r`img�a� 3} 3xg��,&'1��) A�1��rM8�c��N@\bar{E�32t!O� dx�V*c-2N�Md� i�8nF��f6�&� X*oRw��:9�_helDdead d��@; .a=Y� O v� %�t�Qt j1�" *I��+ edT ��%�t�O� 2oS\�5�y.� �O3J?y!�Iy�po�9AfB2�*�R�cs�wof.�8><�,o�K� j <[6.andF �:Ta7U�(w� "Fa�� ~ ��"c;)� J�M �H"h4�D*u:1�is $V�$�W�"!���ZR %�7'6l��9�is ��� �5Ye.p�(upE-%��>H ($Q� $��.wq�($S)�d�� "-��3 W\�T>��P.��I#3am�cIM��Wto�up!w�9��8�� epsilon"�= L - � $�G0^+* 1% �8rvoirs}!��BF�h��A3� �!�>-5Qt�  �IU9{� � �596��&q=Y�-��82��.�U� ��^^xpl�n�G S%���i�(:�<mw-d7�am� 9>��M T"�8.�H���@6\om��%��e&9%�!=�#i&X;lib�}3su�b3an � Hdi� of1�nA)�r 6; �Xrong,�icPflow go��A/A*.P��!ar� �\s5+p��)�"!Ja��s c 6�%eG�$5.1B�$ 3new"�$&�$3.8%v�$3��3}�#"s"�!a2�!% 2�" E�i� N = >K �o�k�kin�b-�if!R� ��� .�����%ys, )a(d)�  t��W$�*�iԅ2nel���"Cs^{(1)$ 0th:�%�;^{(�X='�dashed .�%x�3 N3$ (dotA�lin�" (e)R�&E�b��$imes: $t_1v15#&.R,23� n%/ $t_347=J�i\*�#T$�T���!� �cc�-p5Xby!�, horizB�l-s J�� s!�%��*T f3fA3g%!uh�Q�$#hip"� A�! �.� ��A�a52�y�B"Abe�*H,E�"glos� ��r�I,!\reoH��a�p��7 p `ng!�S!m��.�2�oA&� of6&)W�X�2% aU t��L Yh3%Je3�-$>�� b� &,�c>5i enveNp!#�2ia�y 5W:�2�h�~��bB�S�8\9���?�"���Epn*[{ t$#v�" ]�Z*A�N� .�6Cn��n)� 4@./@� idea/os' Ceq.�J�'u}&�]@-.or.#DuE�sf�au$"uy5t_4#�ly sl�Y<uF aw���-DbyMO6i�3�- v�![%C%o�n%c�h>'. B.Ïi�wom�.u�in+:6%A � ��REm firs&�c�AfQ&M � � yorAA�f� (��&�asBpOXwh&)]��a ��t!�$K�J�d:}������uS�2�v bet�+} nq a=X�0 �/' (�)�aN?A cvoi�q51�j�yo�p.N�1�$t/�?A > .V �� op�A aun�h� ite";A�st) �~= a��I� osc2�I�$ �5�?!�^%1(na��!U*�L�yHaaH2)�'��`)� !�+ BA��1mZ*re�,  mB��"eI�5�pv?�.=>�!�F� " ��?F�3)}SZ doui?� ! only&�ya~*�&�*\a��#p8��:>� i&�y��Kury��*%fi�!AD2����]uߔ�c��at�-!�t 2�a�a �( mann�jOaP��" r �p�M A�q�g��)��Q��A fi�s=�fmsharp�a��� ���s�s�$neighbourh� -x_c�'II4���5�Q�,"+�Gl%|l- varii1�>"�he2 �� ��$��!ul�c m�s"��mdjuusD!��mP` �%,8ct�pu3�XU�jBYp �.W���ubZP�U�DV0��� --l@6�B�a�s��iDMA��>:h �)��'s plac9!:�A�er I�` 16�&lR�a��� BZm5 �u;� �5?%+"J E�Ū �/�d& A� I��&s6� "(g$)MD,(h%�!&3l)� di�7��*V�*"�s"q*��w�BToB�TwiMD[#M�cwlAg�*2M�5'_:�GA�ath^�dg &� --��[YIm!��H�-'iυ<# / �������8��#�iL>�)sUO.��d�t�$f -s�/n�?�8r �Q a_Vl[.�(A�V �eem�� ��il�V�Pn F_�!��1�"d�q� m.�� ��.�V-ߌ&&)�-��5frame�{\�@W.CZa &H Bz�$%�� !���E!Y0$.BYY�)M Ѐlet�)��qu�``suspic�� ''. �T�J ��ɻe%!�-4=�A�can� �T�ou�1w��cDti�PEhs6�2(�e�>eZ5�ga �d �d!B"�, l��=.S��7ar� erpoZA�J�) 2�)�V�!��]��bL�&V�AX�2F�w!�!>[ e6�� 'Kx^(�.�l��&;�� F�Y3!M�- �:Y&u�I�r.6��2٤�X���W &5N. �z�B���\�b�J�$a6�==i�s=�-Upvud�L"� [ qm�?JiL:uma_Q`�.� . "�SA.�a$rQ invoked, ��d�0"�,�G�6�i1����~>FҐ�uo��uN�"u p �E��"W,FU mus�}�Q�� ?5�n.|iomqS`FnsteawApK9�8(l�8i�e  (a"O?!5!���%� cs�0k ��g�="��"�Cb[ (E��?t) �1CE.s + ��*U�2�( ͎�%1��ct�9j�{iD � z 1�M�� @?8desired&=U*���.��*6VN(��8ez�7P�*�U 6~�J�m���9�I� thus!��q!bA�a�G� al A���R6� Fpa�"" >a2�&>��Ur -� ��ins.�O -Oc >�6� &�2ex�&eR)5!C Ss:�"e)-j�z/�,�"I- �""�#� pecu�o�3J>IP�'����for��t�f�e͊uma��V.O ��J1�a�o�5�Z4 Nelson'eUor�n� Brow�_| y 1}.���kin��>�!p i%H7�.�� V #q�Z,� ��-%c,�ɖs�ee��/�� &؋,-�;.}[�ite.��,e\Dm!<�8i&�$� � �� .� 0%\newpage \vs�Q {1cm} \no�0nt {\bfNQ�}AcLK ledg�s}4.556ac�,tz�a@Hes Prof.\ P.\ Brume1; ��;� d&�pr��u�E� �D Dr.\ M.\ J.\ W.\  a� Q �a&�F�"byias�\.\',tF^�֚bq��NuS:�? : Ges R, �T A S, Margalef--Roig JEs�k}52Y.1j�X2��v^�-1�ՅA3}�q n<��Q\W � {DQ�~�sM�!�W �:9@�6%k$ ($D$+1)-2��s6 �pQnsE a by�u� )% u�sw�fer��G@: Kaplan A E, Sti\�P, van Leeuwen K A H, Lamb W E (Jr%1B�8-���Scr�PT76} 93.yga�oBڣ do F�Bnh4�h��i�� 120} 8794��]!�ebZ5 �ZZ2} 1470.S4}aNn[,��JvB �61} 772iA�b:N punclQno�in�6*�leb a v�R�|&�1ՙ| �2�|�u`�o get Pp���)A�Q�\ex tega��.e^ �  E 196E%��z- 150} 1079�>� d"(�ŝ % -�4 % AMS-LaTeX P��*� %3� \��& [10pt,a4p�]&��\*��amJ��amsR�fR �text}>Ubsy2[�$scr]{eucal2 �x6color:?� �,62hPt=685pt,noheadfoot]{g�8} \flushbottom <�- and{\beq}g.��Je$e$\eQn:" beqaG�,ay>%e % HV#,ket}[1]{| #12�>kra#;A #1 |:#K(s}{\quad \RBarrow :-pr sAu(O\�N):(refeqz$4{ {eq:#1}}$:,opd}{\1�\Delta}(�`>U opdBV*_{12}, 7 _{13},...34}NMbNB2OBBP\A�rm{B34}NZ!��_1A}�2J�b6�/BNDBV�:E1ZMA}}, 59�RNAb08N JO21}=�.B2}:�ZXg6�F>sp * S}_+Bpsm-FAAXF!C!23J!1)S}E�FBDB14J!E!2N!F!!.6�opi IF]io}{| �3�0B opoi+0�^+FFtwopii< se}{G1}{2 \pi>�de�� �0>"opl� d�_+u�-F�L^6{i+]�i-BqppA�p&�P}( �u i+}+ -R�,:$ 1+}-$1V$ 2+} %2 %>�A�Gamma:�gA�_{ij+>6g�-F ax}{!�t\m�?sup}}>.u�<U�|ABJ)-u2(F'��.'FNphiplu�� Phi^>�phimin>�ps=sJ=�* =siB=opa!_��a}^{'>ma=9Bope;vJ f fR[fZ[k;kN;opv vV N-�N>�oprho V�nonetw$n��2FF& Gn}_�h. opn2C�J. mr}{r_en6pJ�aonoaFoama}Bmr<rF<r<r<%NZ�q %\set�`��width}{5C}J � }{8.iB odd��4}{-0.3F%top!4! K��(x \title{\L��\ bf{C�Z�k -pro�r;�)et�S��} � �it{Hos��Hey�c} �cLit{Gunnar Bj\"{o}rk}��\�/*h H@5�L.kth.se, http://www./QEO/J KtD=?) of M6�e�Yro]�Ԭ :3I&p� Techn�zy,d �]Royal I"Hof1 (KTH)}, 64E~|um 229, SE-164 40 Kista, Sweden}� thanks{g%6b@ele- }%AUubj� {hh4keywords{Bell'� i �U, 2�Yco����?�t�%\ded(Cory{Z� b 8pacs{42.50.Hz, Dv 65.Ky�W��{empta��er{}{a�b4 jARm���is+2IM�E�gab�ct}� , �, w �ZhowqaIi�3�u#"c�o!�Kp�ilRte~beo0�(n algebraic�,a$cGD< Segr�Mty���!r'�z ��dric I %y �nA�i"2�s6�s.�� e6 , bi3�97-et ��u�E"�C�_�--. &�Yw�^!(l2�3�˵�>2{t�BcR�� ) ftwo-by-0sub�wants. �9�V�r Z%���:�C�ng�\A Z�����s, t� ly, %.! , wa�"7�Sȍ{o}�P�� Sch3_�nd*z�6w�t�EPR35}�ny year�$�ssp�x�daw%>�sg'we� D�-(6�U!� solv)�enigma! 6�e.g., fUG��> # - e;,!*mod_[des��e, �if�- i:)(JrevNk�p9i ���!f��.*! we k�j�( \� le #3Q��'ntTT��.�J)�E��a�9_� �|�%�.$N$2"c�V�PQ �h�xP}^{N}�"� now �6��gw�GAJ� .� �gm�� ��`+F��t?~n���)nZf�to�!-%t�. O"E� �hi�2*Vosa�,a4%Si��2�!�"�'  �66neaa�>�m0Vedral97}. An�#69�toB$%�m�Bum vio%1oe -"���' i�%�(��>p!R2�i�CHSH}. E�6Ay*�7+� 2Dwit�V�3; �{b�e\��=o'ctk>��,(Terhal,Lewe�( in,B*(eri}. H.��I��p��itl%2, Narnho%T�{ Thir),�A0b�%K��!b&�.Ů%hal6h�^j�$�-Schmidt. .)x>Q�4��v*�)�Be �! Y&y &��A!at"'CU�Kvᘍ)ic �M�a5'. Y�$Iv%AsU�2�I1o xʁ�Cop�zre����5rix>�2�� soRZof�#�vonM$,Bennett96}. K�B��4�������h�im ��5�*�"�: ,�B9no\�P �96�96fQx�$traced out� bL,���'2m.!/�3q+ �>�{�Wte's so-m�A -CWo�N rs98!D��[ ��T�>W.I , �6L-�5 . '@fq� conn�Z">;�%N Ay�u� mapQ0a� embed�,�  D. C.�(d� (L. P. Hughs^�iTDorje99l�y&[MaJ�lapE%�gir�^q���TS6 #N,8 2.0!Aj}�j eQum24.� �L9 � V ^&�K RxU>G�F F�g!' it p;further.>4)�lؾen7A. MiyakQ> �Aqj*ex�� if�A�.8 �,�&�o*� 6es�Xaw��� Hlo�NYCm�c �- X�ʥQrt{< stocha �l�J **��sEYI� un ��@B�-e���9\2deaF) % @ 4 p F=�J& !"c U�UPgiv)P*v �R�,EA�B0�e6� � �2!��" d5�.b�,=��, ��)��2AlbE hio,Gerjuoy,Rungta01,Bhaktav�%Lla,Akhtarshenas}. Va��1h�~��c�F�r�:H-�+o1��>}�}2�%�%@�. !x�4�{�0 y. Fi?mor-�2A6n�b5Y.)V6=h !�ostensor)\>;�� &Vp��ls.zC6�K�RA��0rea5$�fD�E><�c�ep�� �Q�ms s An�!K ��,z��&��).M&*�`��E-):F2�Bd��.�( u�"&� �ס�3"� ; %(ݳ"s hQ}="tLQ}^{p}_{m}(N_{1},N_{�ldots m}) ./%>.\c-2m�A�%'ng e�OU&� }�;M} `{gn}=k�^{�}_{b }=1}2 2 �su 2m m \a�� C,i�, �i�} vb9 � -�daf zte> t%wH��)� }&=&:!e}\o�sbA�% � 2fVm}}\\\noe �('.wE#� ^)j �&m}�2>! q7a� d'w��$j$th6@a��Dn by $N_{j}=\dim(k!;B,j}}a�W�"�7us�7isEk�ougOWpp�  ir�w��mh� pairA�m �,V�q72}(2,2~ Next, letV{� Q}}$� �a .�v)S}�:��� ] &OO ���"� .F4a��� *!c H,Li2000,Musil X1,Ueno1997,Griff78,Mum7�LetmQž$oa �� lexGz!Ld}��a�@� e� f a$2�.m ov�F u,�� ��A�q2' }$ o�~a� "$,!�b�Zset��all�tupe5cl��ɾS�R.e,B�&l e=\{P=(a,ap7 a_{N}):^\in Kn\}a&B An � $nbe�m@a���ere $� j�sj6/co�gQ�IPa�&�wem�l-1Y1 Oa -�lBA�:���& plany2E` R(N)< O[Z%I � Z!I]EYF(polynomial � B3a�)<�a�� s $ T .Z$. Any9lF\��(N)Y���a�a-�$-�Td�k2��1#N}$0e$��, B r�\Dmapsto FfS =F(PO SW.�].�I�6�9:a.�1"7. r�1n)aC�e6Hs��O+Pi8Fj* d -)! V}(FF�jM(aL\in:K:�=0N#Zd� �F�whM2i��F?]�y�c�=���aBr���=l��(the hypersu��"� by !or# 2#�k� " $F=0amf5mAq �d�e $r\@�)�.� �.u�2oof Ea�M. I�V �a Ae��D" cubickr�N� $r=1,2,3mI;un����KE �.��G a2qx1K��O-�A~��[ivCL6�B� zR�MF���  F_{d}�pM�j cap^Z% {i=10 i})=�� %I)\cupU�!�Z � F 1�{� � } AQ�Y�I��o �� ve�$��1�nil!e fE �!)&# f�f(i)�!�C �Rs $�,��.tI��� &+N& . (iZ�@s $O R�MA^a-y:!} ɒ�a�,~b ��R$ �y $ab=ndq�!6 $a$ a���M isoryso $b$).-Iu�a��omain 9fno6JA�1d2 B��is�Ded�&�* R/UOA�B}B -�.a(V)%.$MY $V\�et_m�cA)�R��of� Cx�8rBva"( n $V%�T&K� ��-[V]�/ma}�tisomoޓc� Y��Z @�.!�.BW�E�!� c s&���5���can|'� :"fc  �duc�ab%-\a+ N[Ap!�n  >v& JERs  ӁkI��a .-q!� �M�#�/9{�5��1{=:>IdFmZ j� Now��E�i� 6�$ e%  se�$X=(x;,x'�N Q)E^ $Y=(y'y.'y_'2�� �0�C}- !]���K��RHt�mapJmb>(array}{c0� .:> 1}}\�� �2}'�� �4�4&��+)L��(X,Y) ��on3 &rK!.1&�9ATŦ � �}�X one-to-�=!�o��m^)��VI ={U�#yNeA�Ba!�,n.>-2}����)�a�Dphi&�V-j��UAJ�^}�0 V�-h=� f�(})$ and $Y=H(y_{1},y_{2},\ldots �CN})$ are two different points in $\mathcal{A}^{N}$, then the line $\!�UL}$ passing through $X$ and $Y$ is parametrically defined as \begin{equation} \math{4L}=\{(\delta x�+ \tau �22},E �$N$ N}):  ,tau\in\�4bf{C}\}. \end{�pThe complex projective space,-<$P}^{N-1}$,�d�!:(set of all !Es90 (0,01�0)$R�. Let![ 1[b)�)�. T!�$X determinje sam-�if,E only 8there exist a $) \in 9$�%�`\neq0$, such that $y_{i}= !�i/ for �$i=1,2� N$�at is,y- �A��< equivalent, which we denote by $X\sim Y$. Now, if we assume � this!�!z casemn Bs�1�,\cong \frac{A�i-\{6� \}}{ � �XF< If a)��inI�2.�5�d by $(E�,x.�x_A�Q��q�w!�y%�nAoaQ�hhomogeneous coordinates for!�. If $x!�!� !�tAjwe haveFQX=()=�}i}�i-11+m�-�%Q)B�e R=R(N)=%�!d }[Z_{0},Z�APZ!I]$aB�0 polynomial r�� over}�}a�), variables $^WE�en,a a m $F!�R$,!6��d V}(F)=\{P%�Q� : F(P)=0\!�called� �N��zeros�b0$F$. Unlike i �affinem 1���bf{ m!" -1}\times6�A�neq:15+ 2�For exa�+,��d^6��0a�� �A�L}_{x�x\N�1}��:1y1yf1re �� llel!� $x� y%�6abut�re�� no=�F�02}$ since any�cstinct 2 $L!5I�� V}(aX+a!lX 3 3�nd:26:b5 :b5 :b_:(intersect a�e unique�� $}2}2-a8H, 113 27(1})$. NowE�,want to make:PE.AHfc$ into�2�gavety��its Seg�� mbeda��Pconstruct as follows:v6m�d o�Q��EbF�2�$, resp ly.'iomapF�{0array}{ccc} i AS}_ u,eN}:>�1sj:@&\longrightarrow&J�[!�(\ (X,Y) & 7mapsto&�va D ��y�2�ǡ�Az1�X.k}) \\M � &Y Tis a closed immersion,��.�!�. To se�� , le�V��$�$Y_{j}�ہRV�0 functions onF�%j$# 6�� 2� More�5, �Z_{i,V� �d-� V�n�we !Eng�e^�}yQ{9x\left(%XI�E��-,1} & 2 \c? �}!� $2.2F.22.\v H &\d   RSE_W B� �� �% \e ) �� map-�N{=( �, EZER, = ( a morphism��i� �Mby &Rs!�� �piece $UA�i� UI�w� 1��R =\bigcup^) -1}_{i=1}W( ~\text{and�c~>B��2B_{j BjB��5aOstandard�cA�ings. B�("� antJ�det^{�1pkAr lMhX!'Y_j ��vanishe�r� $i,jm�k,l� o�image of*X>�C conta�e ��subse�nI�4 T&=&\nonumber%\{I�Qp z�9Qm� 2�E� -1} �"rm{rk}Ob�z_{m� 6GU}i~z_q� B.22.m�& V�z�@1}i�B[��=1\},)�e5\e 0$y t-k"e t)DN3 (x,y|!12kff)$.n�l $t*� Vi-�nv� � j��so��>�V\i�eq%�2�B$Wb&�c�.� algebraic�  n $V�WE-* �is�i2w sub) ��>� U>��)�I�j| �>D1��I�iEI� � � �!a� ion*a family Xquadric hypersurfaces iR� ��!�a�W�w�z��� &=& �Wap��,k,l};A�V��,i,k}Z_{j,l}-� l}�j,k�.>�I.e.,-�N�: ))�.p� Z��2m1,2} 1mE(a58-3A!I�Q 3}$.-� {SL M8 a 0ral bipartite��t�d��(currence} �givenz(ntum system v�Q}�(��)$�& �#� o a }�by>#EsF$$.$(\alph�, &7�ą��4242�  |-01�dA�eFe�$6� A�|)ӡq*K bp�{� U�>�_>��f�>� ^2Dq�v �b�} (�|1}}), �0!�)�P-QH U a�T!%�B,&,0 %})v�: welli . Next1$P^y*�"�Z��A��MV ���sEc������ r ) r�uCE ,j;��2�� \\"� �. �]a0�X�4  �: i�? k} tBGT��!s�A!� of se�bl�� @ it coincides wit�� fini��co��ͱ��C*J�) a pure�< st�<�\cite{Albeverio,Gerjuoy} because y���,\label{Conc}����&=&:� N}\sum^ih�,(2l,k=1} :|� |^{2�^{�1}Q :'XYgƒ]A E@ AA &�f�r@ !hN�  somewX Darbitrary normaliz� vant�,.{e: ��k�l}=U�ilk}$�ll �b �. M F&��] 1�-[�� � u���"q  \LongEeq'>L=22L" u%J}��a u�� R� �F� Nx pair $qubits. \$ion{Multi-*O "P q m  enta�8ment measure} I�is R ill�Siz��:^toK _&��. A\��previ�.^canc��2d�f� cy A8CmC$ i^� Zh R �almos:y$procedure.n �: i: ; p�!7 R�i�e�);)p� �% �&  N_{mʖ�m&q yMb�)� �!��&� &� b� Ѫ m}})>+?"q�i,i� d i%6 ).a*� &� is2� ���6_^- \ $,$1\leq   ! 1}, &29m %Q$5aZ[.�Nv7 �NC a n�a� compos`qu.> \A�Q}^{p}!D.� -OI�@athUefficie�$,of $\ket{\Ps�"namel.�!T6�1V�]�. !i�*_��u5A}=���Wb`\E�)_{%�!�j%�!9j}��c�!� j.M#m$.!-A}$�be re�e%% ���� $\{(^�):�A7 �A0j},\forall~j\jin͂ each�� $fT�ssign�  valu��~(������it's ��? !,an $m$-dimenP(al box-shap"�' ize $� �!}2 I�m�fwe j$ ociate to)%�a-M�rm�Q])s�t}[].c7$,>�S��9ommuta�&n�" a\ lex m field� �>G, a� -by-(min$bo� $j$-th.BeZ�51�is by&� � y!b ketl;k�-l;�Nm}m}}d Q# 7 1 + m}"R R9��l�:6� &&5 VRj-1Fj}`j+�Sl*Zo "l_ ?k�? �\V'%�_2J� ��ideal}I}^{m:> foe�generatc&5���$ �describe�b.� � � bA��$!��$�Yh Grone}�Jo "A�Im*�&�eQ%Ŋ�&again�ian >��ie% J�F�#>��C �n�eq:�*F i(N� g�Y� ����� j&�N)*� z?V��f*��+\��B�&0!ٚ���* argu^ ��a!v&P �) w n !�.� -Q@ �f p� �a�ˍ�-�E� Seg-���E]kB��%�)%�>�_.�!6l���ǡ2�B2R)Xf�.�n�|�b�b�b:b%:���n^�� t��>@��isUx�&h*RI� ��.f�three-M�x. How7S* reas�$�, wcb�-pl� bel�'it fails�^ if,e 2(V $m\geq 4�*�"ap t stZ prov0tZ nd"* full��ility. %vv &�E=*: TF } an&b*X look "� RF�#-ui .�Ɂ"�}p � a)�2�n�j�NB36� N�)nA^$k9�<3�su�l.H~e�HVd��(�  4� �R� l�}V� P�O2� 3}2�*�& +���� R� � ����2�+�R�� � q66)e �F�6�B�T����Ca��2l�is(�1I-not�1al��our6�$tensor bas j� POVMsF'phase�i�Hosh4}�|R�a�rm�� ���� 3}(2,2,2)�%e�0RT:�  gB(4"� N}\{2 |" 1,:c,12��mO2+ Ed2c +2U_P.�>21,2�c2O+ 2f�3*Q6�J� 2�6��PP+FP+ 6�13�42.P.�1RPO)d.�O6\NO +f>��.�A.NO+ 2��12}-"p ��] %>2�.O &^A>�>_.�,J� + 2�.3!Ϲ�N��2� .� + 6�B_�!m.1���.32:�.o%)a\>� Bi.�f W r�8�'expres��a*�9w 6n! $was origin�9Ad u�9ev�� I�. L  ��-kI`*�(1}\model{&+2&�3}}$ re�ent�i87t'NS$�3 is un�~d w�2�\�J jB �six 22vd=9aH��u�@��&T#H���[I/.2}&A?22}&1�A2BB!s1B B*hb /s n��!���%�j�, \lD9a �b�+,� 6*fX "�)���-�F�. !�2;.���6sƨ6mݑ�C.m.O���2�.;+r%�Ba5?n�S  u� �mno�$�:$0 indicM"a��yaՁ�"�fro6IR�76;�could� �Q� betwe�+2G�7a?6a)� �i�\�w �o�� 2�-! "���Hilbert'��) is $2$ (ip*� �)�) ��way�p{���2R���?!�3N���6h!~N�6&BfR)];I>�3��2��3-�>�6�!*2W�ls �/�A�byT@ix ��µ��2s�D2��e2�޵ ~ &�4 ~��z���kB�:��&��B� Q�-BNz�!@6A8Written r explicitl�y!�&���AOFw B��)�!�,12J��*�)} ;��^�lٶ l.�.���2��ޙ�.$Al5�� �^��"8'�N��� !�:��k �EY#6N!�2�>;�NfN�(.�6�.)�b�!��� 6mPm.)lY��92A1=�.!lMNB�H 2f�3�a� tely*le,t�t�ƅ �AoZ &Za��F �#2r,M6 F6L26 ,2 �+\}.�B}�n n �R��}5�b��R2}2c2�5�!�!�!�!�!�!�!"!2�&�^q�ŕ��#�����.�2J.��2 n� 6�>�{��y, �  .=>Z�Q9Q���!3Bm*�!a�!4�!Q.;� ^46A6,$Eqn. (\ref>#)k��<�.6�:�9 l2" ?��7:_"J�.*� N�m�6"h  inv9JHnt under local operM�M o show wh� *K i�B6:b+�um JCX+4��."�/c#��Ksev�&yp%`4�"&HP"�sc#�#s: It ma0 possi to factjL�W�xJ*�2)=�3�)o!?2>492romA )e,)l?check%��ne�*o�:f��perb)�<�"Q5�exactly $3�m1�N2=y()$ does. BuBre Yother Vt�=i�Bur. , �,<�DJkouF=2@%k6S16"!yv"4!�6DaVR1�v"D!�6G^ G4&se�� IX�4sE�-duc%�� I �'.� �KiUP test�|." of, b:�:*!LAdaG si�&alO� este.�)2��g=th�R 'doQ�A� form�F�an�A.|#]� M��U���& ')E��)5i?� of 2j)is��In���[�Pan}. �j>&-$8lu�} �pTper%v)wdiscus\"$ome�T pict�8of!\�49/5�*#%79+l� :?, &� "�A�x�-*�4g |y�i � cula �E o%A�����le|?��m �"<&6k9 �Q�s�a&.* t5. *�Jy�%Aresul�M�59) bs,~ �a`4|/ 0&�5 ~"�+IeN< )|��ap O�[���A6,�1!�2�X �Mt*N�,�)rim*�two��.su>� a so-H0de!�osK;�" . We�1����% @!�ly �?Ab"- V�)82g. Fur�more,Yf!� :�E� {b�#A�-� >< �t�2�s-Z6� FA1 .I'U8bd@flush�*6��G-gHthebibliography}{99�`bitem{Sch35} E. Schr\"{o}C�rfHorne,pShimon �R.Holbo)�80n69.nTerhal}�M. , � �A)&278319 (2002� Lewe)x}F!�H~Kraus, J.~I.~Cirac)�P�,rodecki2( q(62}, 052310FsB>>eriq ,!4 De M�]4ni, G.~ Di~Nepb.~Matalo (M.~D'Ariano �C!$cchiavello2�) E�9�227901�3.P$Bertlmann}-�,, H. Narnhof!�A+W.~Thirj52n16!321u26j(nnett96} C.\B  , D.!\DiV4Vnzo!| SmolQ�$W.~K.~Woot�U, } z5el824A296.x7$98} W. K. 2�=180E�4I�8.MDorje99}�C. Brody%L�Hughst�S Jourw7 of G�(� ics )�3aWM�1.hMiyake}a( U�A @6� 012108 F�&�- S. �S.A�Fei%m Opt. B: Q�:$Semiclass. EH�2��206�"�BE. >�A �52308F� Rungta01}A ,��$Bu\v{z}ek,!qM. Cav� M. Hiller�U0G.~J.~Milburn2�M#6A#042315~2p0Bhaktavatsala%�D. 2 Ra):,V. Ravishank� e-print� 0nt-ph/0309047��,Akhtarshenas%�J. .,NE11166ELi��}a:Li%� I, C�aP&] 0Varieties}, SA�(ger-Verlag,�̥D197.Jg8�� %&c. Am.%F.!?��e522k72�y.A�HeydarI�a�Bjh AK�PIn�Q !��;on�@5}, No. 2, 146-15i�5)&�-A�Pan�2L�G. Lu� J��DraayA�F� 405133 v1V$� >N doc�7H} �)%% $Id: chaos �(.tex,v 1.16a@D4/12/07 12:10:32 g�$Exp $ \S�f0[aps,rmp,twoc�R0]{revtex4} \uckage{� icx6ams} %.,rcs%!keatle�: %&, aps.rtx, cif&a88PRB style \@ifx�2_d� T@@sw{\@booleantrue.}{d)@bibpunct{}{}{,}{s�"su�Pcript{,},def\@onD^I#1{� (group\let\@ \NAT num7alp{#1}c"+LappO%M@1[hook{% :� place@bib>" o:>@sup �s�Oat�� y� itle{FF � al A']iM4>wnian Mo��} \ {P{+( H{\"a}nggi(Gert-Ludwigoldffilie^@{Institut f{\"u}rqk, UniTitV$t Augsburgf86135 GermanyA\(date{\todayb �(abstract} Wx,� �e elabo9�2%phy����7um nois�G�al3ilibrium�*insionyIn-e " . St; g�I�icelTT\ifluctz$-dissip%0/ orem8m�I im=�Oequ�Dst8 must hold�op�{Uv"vqe^th!Il4��[ issu�K5Io�A(exemplified�f]Yproblem�a dampe�)rmonicU$oscillator' e ro�� =4fy�r�Yex�g both/ni�ar.T Langevin !�)n��N path}>ggSapproach[1�'.{A6 �H-r:sal sym��Sn%�D)�=�dynamic�� , f.X�Cd ser?sub�9�p�pitfall.��a � meth�ogy appl!�to�decay�metastWs D by U�Br�"e(Oyt� ke�l��bf �}ee�de>)0!Bde��AaoYlm��az��ar� 9�qRN�@at exh� fri� al infli6Is-�!Oof)DM.etsIAv!�tra�koe� !� evolu�prA!� of)�:�zse lead!�[�U"�I��AB � re�t-�nects�9Wstr�h L�5�._��cmjetEth��� roadway�< modeM�! . Hewe�D topic�!�proknt|u >(� upo�= mbin���o.>M�)onsceo�A�uyF2E� b{Qal�=th "�Q5ƕBm9�Eeq�B�<X u)�+A��ks A"]2VmasterTC� cor�*�= ng r) ��� illuA�t� si�TE��T5�v�a� �*!�B. F.�w'Y1V�, ��a��rtc!�gA at�ůbe awA-of�G!�nfront.W world#qH�y dr�X phenomena���m*KOI*� } vrtyO�+�?E� R]J� his A ,it{annus mir s}� 1905�3us�Es� steé��he ingu{cE�.�law�er]�t {e�o}.&iionee�jheq�Vp:@d�[irs�hk", �]n?Vimp�ge~al2A, Fnj,1�� ��}��F�� diff:�J��. T!wintimA�co���0b 2�onEz dd2� was put�Oa firm��uch laa�w�G Nyquyo)kn 1928}\Johnson j  �$ ider�e c Rdensi�Tvoltage-K �[t-2� Wa+ doU�mechan2% as�J��.I play���1 ? Af�!`bir�q^c� 8e early 1920's ��*encou,^&ve�i�e paraa d! pa-ZA_I��G-i}�A>�al y via1c_` !��5 gy $kT$*� >e�� Q4law-�note1}��M� ly averag=d `(�4 leav���7 �m� (!yrib#)�h ��.1 's rKk thA$D �precurr �&] i� by CLmi Welton �Gnw 1951a�o&|M�e= ionsLq�,�A� ma�includ&f eff�:�$eir � theya��war���ly vali�^�!�q�!V�s&'[�aF .A�!�� ' QW)N� a�ith!� doubt,N:�[�e����I�sourcR �$ nano-scald biologE�� NsE �tunnellAg� �Et�fSelectr�quasi-E�cl�0alike�t.� �for w�s!M1n�e��cannot}�negned�� e fe*ͧi'?��g�a��aE� f�!�A�emm'$ure: At su%Rly high "=crossor�% occurA~y�M�-�e �-�6 sh�Q�< � �V�!5schem �� !~ 1 >�&��p�sT"�tT"!b�V � m�atHR�s obeY!l$�AZ�� 7(\`a la�-i�)!�is���� necess�in or�fto!���stA�w }second�3%�B6� %5 of ( �)�jai*sbalance.�!2��(�,alternCQ�ca�vxv 1�to5b�vI�!� tB�per se:�sLifoni9��&L�(b7)�� �(QLE}, stochewU� Dnelson66,GHT79}, o�tIepH< � o� !��s LSS}E�do��so�"�[ a37e�!�� nct � �zR yy�&� a*ll,�2n$K*k delq<"g ��eI be observF � mak�even na!��J ing �xN ��. S T,involve, amo�A� h ro� ng wjw2G��� ���5�foY ,-� r�eBhypo� and/-�Markov)��V~,talkner86, gUL$�[{tK x^MAz�MaM�si�cI4} As already Ls dZv R�z<�~�p!� a pivotal" ��a���.�E"� ve ��por:a&VX�q�}ls�a�[is��� :s tru�y�of�� &A�c.*$QcS"rde achiev�>"�*f�$�]� prim�mi�a82� :;1$ize} \ �%1 E+��&Yg��'�,r�qp-� Y�).W " X)ro�!Nsus�#i�(/�%>0 !se X:� ,�W���zs.���"0�Dl�gre�N freedom,"�}& �y y]W% ��e�eca�on�X��Z-v Yd�L$B$ du��i aS7 (5}1ce $F(t)�0a�upl�%&�mjugate �"t0q/A$1�_} �R } {<}�|�B(t){>} = \int_{-\infty}^{t}ds \chi_{BA}(t-s) F(s)\,.)j`�$S=X$-{<}B{>}_06�o���ec�%�).�?  $S^abs�!IAǥ�re9d�&�N � E���� $�)$ �7c-ekd2Q, Jv1<^d(t)= &Kdi}[(t) --h AB}(-t)]\Fc�rFourier��#��g$"�''� %*� �f4nb e *n  $- = 1/kT�AN� 4c!1=g�� s $aT�B $�$A�����O:\ hil A anti�=c5�$�$a dire�2��� !MFby+�1�pow" a�ruA�e��� zed}RF��� eq:sba} S1�=yP}b�+=� !F{>!����P�Rl.I.�1) �Bvian�fdt�m��� hbar\cothC � e�}{2kT�R) b�RCi0Es�A�����}dN� LVI+�e.2s6�$-� ������"U%H>����1d.2iri�] by� { �y��7H"mVE�Zja Q��I��8�,��dc}#��] last 2��*�� .#. H\�zd=3���Q� R of Pk �� � !7w� H =N�� N(�=E�)"Y Omc2A� �n arip �vvacuum� �55ppear]a"� � publ�}�1911.)%p�11} Onc�r h� �extrem&�I)$kT\ll}+I� find%��]� .�7.�]�aB��&���gat" �fr�y}�4 al we�2!�!CR�"�~ � ��ase� r�׽�� no&�"a #fragdF'�,�[yT+m�Y�menoug9Z��2*R UG�)� �� e��&E�6�|isoUd,{"@� ��2�!n�'[!; Ec�^�5ace on r!G p�of87{ By$b" �#se"�.�n�#theles�ref�7cm�be take|ie!�voJ_!�o[��avoid%vi!�se rigor�1��! n�&con[%*,%.�)"?sol� "i:Cr#�J�5�.@,*r2PJH"� sec: wosc} YiM{Eq&h)Ef>%}N�u�<x�=�of*�(eL�^�+e2|A2�: �N�A�2�(�Rbe tack�KItEVupy;i�c�$:M�bAxA�  o environFa)�ᅁ`�A1�zL�0 ferred ir|(ibl� u�iar��� �9�anLachu^!�0��Sect.~�H=B$ec:bath}. J���{ar� � fR��u�B2�to,c�A�! "�#$level-�|�~ly e7���  us�^"��|c�q�h�!)�A��}� a�|��u� �(Q�cC��,L_!veloci�c Classu )�e�(E�J5.� )]"#�  Y�� � } M\ć q +M:(t ds\gamma(� q(s)+Mj _0^2 q=0�la�w$eq:eqomdhoB{I����n���if A�&1GpB?t(!�kerneZk �� � memory woVco'A5a -�cy*i�B�!��S�� { g$ V�to*9 � 'A� �A<Po�� t v-�!zJ�,"� !1�1IZKod*i�9�+M)#)�.�R��N�(e�=���2 =)�mas�Gi1I5� pos"�f�&�"/*�$M Qn$.3$q$, �)�v�� DrNEhrenf�C�e�!F5*�Q�)!�PXe"m���reg�@[Drep�1�� �ex��Bu w2IRG%��yn�-B.a��E�!/c�n 8 ,GWT84,RHW85}F��qq&3m1}{M} -)o^2-Q~id ) + ���eq:chiqqB:� "�2I64f�amaI F�.e�7by !*"�"�"9 h � �&;@U�autoc�H:ja!Qt�IH� �"9o cusDjA%I � CBd acc̕g�Zu^):j+our��+ I(�+-��"�_#sI��Gausse�xs@2� ll%7$� ��:�sJ�`#��@�� @"<s� E��z�B��,a�i�Nzs �|��m�+�3*Hp*Pu"8H5�.T�a� mean� $p=M�1�m�AA�.�2 ��~ �I � rv:.�0*�B�, �H\AVUip�� �MI.Y�,2{"pGpF},���ing.�K2�= ��1K >��l Yevalu�4"3.y'2S���Q.���&�&.Ii� !�% domair6�!podon @-U 0 fdi vk�"�-�>�1�0|L_,͵$= \pm(\bar�0\pm i)G/2� $ =�a�X- )(^2/4)^{1/2}�N�"�h�]�U�2[;&&L's.BM'low.s,� �m!b։bol� oM~[G� �= � nu_n���$ Matsubara� �6�$'=2\pi n/|{�co�G"�6�#. �,pe&Ka��!� Z1�B�u&ED,Q0=v�atB3>$�9<S_m^&�7� }{2M9� }\ex:usdisU-�:-�^)�}{�3v[0t�)"�%\qJ��x >sinh(v%'w)\cos]f t)+..-e�/2�in.,� �)}{KZf- NU}:�uad �2 y}{M���_{n=1}^{� �A3 !@(- >�(^2*z )^2- `^2 �g"� s"��� +of��2�EPͺ��&�� Am  &E*� }�"x."8;��5�#harZev�9�}��{�K$I(_0/k$�'b:r �sK}rri�Qo��0ro6:ak*b5a�,m"� s4*9�8s �Xh82,haake73,spohn80,alicki87.�t��an�R >���I�4�'k$76!)��� �i be small,*.� i�Rdom,�I|�-�< behavio�Bc%��=�d2�o�+� �,ppa��: Uj =�Xd expo.o�   �I$in eq.~��A�) sumPt�C*�A� ��*)=-m�)c!b&�4)t^{�ItTE�c�&Z*�$&�8�I. * :�de�+A� �-� pr:O�˩�lnm90} Fh/�e��:�A�PBw)�iQ8!.s�," *at�I6\�e6\.dur�u�i rmedD~tA� �=� �� ima�n^Dunu_1$�%� �jung85F{o�.��!V 2J0w�s $)�$ �.js&�sh*e7 �he"lb\*�/!� �of.T!�A��$�R�� tz*:��$&�5�n�emEq*}��F*w�qNQ��hAs v> Ju� Ty�:� Pb �&�i��-!. d�m�.��7a�?e20(B%  �on�MI�e�= in.@ B� �"�&5 J'ng@�B�hA-J),aO�i"�1���72Z�. B,l a6|�+ alog��-���e�9�`^� �,_ZF� %"�� �`B%&�!� um,�(q^2�(�$ �(p.,%��{��&.�&d6�tn\1C�&�� �g.:0"��&�reddm ho �(q,q'� f� 1}{(q {< �Z ґ2u � � � ((q+q')^2}{8= dW� &{<2}& ^2}(q-?� �("4 k' �%/:�D-�� e"�:� *�):z -w ^{+ ` 1}{U f � �  hat�k( ' )B�2�e�:!�M}�!"" b�.���28���\,,]hp� Y"9���s*�KLa,�/A��>D�s�F�=pz:'�,0&> dt A�(-zt)2(tN' W�3���s�%�ohX"��2��� &� p2}).s a log� Oiverg�,��~�Zm�0by 1&!aq����)sm$#�*� L*&� � .L"J=�25 :�"o �] ) ob�s�(,D �"R��Eal>L$)��@ H_S�*l"�n* 9��&$H_S$Go�:!� Hami�:�o un�Vq .� ; t�:�$�&"udev�HO� VC Z �ca ��,A�co*i!�A .� �7 INtF=0c-�*=�. Expac!n ���!)!�J�" 'EE�-J��::b(�)}Z=0)} = 1�&b }{\pV_0}\D� _q+O M^2B�� J�"��(r L�P%O�0}{����6'Im}\psi'��(2� i �bI�� )} {.(.�jA>=6Ji1�Y�|&3 Q=di%_"r ��E{ $1 .e@]� Fig� fig:A�}nL�}��9N%&Q N��� &]ly &�� `,F�%_�w�. 3*�F 5E�� �R�>l e�<ig�b."��figure>5�>�@4ics[width=0.8\�N]0r�cap� � w2O�.{':G$>�protectiM��5��,5�M.� $�0y`'ggI�1���bns."�U� 1) A|9�^�'"��F���� ������or��;� � cutoff"3n, �D$���� al F#��02�`� keep;�� �t �_D!Y �0,��B[A���-:]�6;w��� � if�2��=r"a! >/JD$f3&�5I(wJ<ZB� 8.am h9refM/�p`�a:U�. ?A x!fy��a F"%!0C=�,FT*�cZUf�E�V*!�!u"(b4 � ik*�< it gf%k�}BK��.�� �F�: = T �6��Y d}{dQ� }\ln&(�Z})JX���A��p�%!�Yqm�FSISF�\�.i|Zd80O �22���d: 1� } +* )*�=" �t��&� T{#erM ��'a"�W)7 � e:Cp�f� �) ��au��: O$\rho(E� .��hanke9R�!�zbrhob�TpgZ}(%D"� 0";dE n.W EV�e�7=:�.�)^{��i"� !!})e�be� erpreq�er�a��9��53�E �1pd,�6�dos�d:]�M|�Pw ? �6S�,�;me��� T . "/�rhowXb3&� �nt�du{a  m7�Undg!e �'aH\epsilon&;��"�:� "{onM1in(U02}� l��>�i�E!~.��0:R ="(5B�,2�-&�� d)l�I� e�}�=0:!se ��3 l*N>)���-�"b �v,ow peaks who/� !�in��&� FR�'s !Ten rul�N2 Evi �"�(�./Q�=0.1$.vie�D�Im�1.�$Bi� shifA��jJ;.I�Z  %�!�J6 ha���z�5�G�a increa�11\�G%Zb�Qen %A �&�vFHgDa r�\r�G/F��'ult!�I��es)��m5FUwvs (cf.\�73!�Ref.~\on�$ cite�p)�� �.� F��g�=�"i&�Gi,ion (��.� �� @ aE�T:W*; M�A}Q�$u!1�edE"sO11J%Xi���+n2��7Mc���ngIZ �B&}� dash��.�&SF��=s6� a�:� \�{D�#yXnJ�Ss��s:q� 6ZS "wE8 (QLE���.qm��ve:� Bath�9��\ <U�/�B&aT ��&�)nA�a�>�Ⱥ^VFl�#�m,� -� � l� 1�T?%�"� any�jA-�>�y23I0q�I� �. AB&�I" to"T=0 7s!�r1La2�at�s5a�s seem�^�0�c�g%.Bime*�-v-s {4esI�y8(sert�0"c$~ sec��o��q��302�7iX!!(.�� dB�16 s*Xghtfo�Nto2� +)xEv 2> +B}n tech.��*x(�B� pM_s g�9�9by.�'ŧI�ɥ�LA� iHm'"u=�=�K�1�..4Bs<5J�kwL by n\uelN velo� ���it�`BKD)+s|"F!��n�!ONor2�� mori6" &*�" �"%O�"E,$a clear-cu>�D[!pFz�al9 , ei #!J!Qchange I I4/Vd&*�.JQ":�} (QME)!$!( 3l!S�&ar)rP1�"�#}�Aj�I!�])1��x�oto�Qs a���- �+�i\b�o��B&�$��F(ca�&�two� �La��rkT.� )�g*JP" cru�1*7i U���*�8�V�K� ���+er���, s-La�Q�2�cupInt���""��=���>u4act�3���he��dqO8PDonALn �\ �di�.�#Z OMq��!L�v!� � �+-c��U.[Fa �littl� ��"��< n�A�`M�/I�Umt$o"L:.2Q�!wIu �`&�8N,aq gi97�L A popular��Q�� 8a!G#7B�O.�5�"RuPi�Q�.Ia�)�!i3W�2 o a O7\J|!�+h!�we writ"�% tGM.c�p� eq:h&X} H�*p� 2M}+V(q,t�@\�*+\��i�)N\-r�@p_i4m_i}+ � {2}� i^2x,-qc_ix_i+q^2 (c}{<,}"�@R�@y!AY�� ��-^<- �9fAtsi4 moving E@g+ a�):Tpo�R�'$)��'�,ai�he .�AIa�%!�$N$R��U���bi-� YYHG LIc�  $c_i`��. F`YA��@%&`Ri� oɢ-&���"s�?� ren.B�Z ��xeed" o en\��1+-! b�X��.6"� stud� �y�% 6jZ!\ �s >{>l��)4��.5p5B� �lQLE,senit60,uller66,zwanz73,>�*", HTB�(OMK�sr >s� HB"A wYdeira��Leggett��ca l 839@at�K�l!k[�ccyNtoAخy�ed1d +�1 mplo�� * , !F�9�Ts��*QX�fozYs�"g� chvo P(g�l-�Ae� conv*q��sel�ie2�"�.�) ind�;�ls��� MaN?SSA$skcN $Heisenberg�,�� B9%7ex� ;x7of�c= ��2}���'+ I� b kG j� so-cz[dr F�} ��U �0�&�9 (t�;,#t_0�O d V�;�zd��,}{dq} = \xi(zJ�eq: q6��%5��B�( O* OH1��$�Mf�&� m_. �0Ei 2� � �)9A�!�) ��� 1��Bx9 %&=-N; (t-t_0)q(՜�1ua6!c_iևg(x_i 0�1�[K]�_�e -�p ;}.}�1 IH biggR4j+��y 1FO u�AJX ears�k�, p�_8Magalinski\u{\i.���9r�(Y6��!�.�hOd�xN��6�b xi})� ends.� ��t.c?e�s ��ime $t��C� "�Q4s $1�*'�# a $1�*n.�. `� �C�fix he)aZV�h"@h=v�Q� N.�?��, tur�-;$I�z rando��=W�2 p5^� �-\���[jl8%%�1�<5a$iZ!8o�-8"�%�-��H�E"s"c 2;.|�:ܳ!�ur��so-����:�-�qF�]� [z��X� � qualify!��"�[I�!�- 5�sh�@!jbe biq�;3:� �b)be 18!�6��is�� �Dc�0�o?� sA��n}! ^ �5 *���$0 s. �E�i�ce �F�auxili�<:et�F$,*r����͵A{%;� 8&�� + N�^IP E�i�[sI�Q��_m E w6�� QLE &6*�Kno�mauJ4*,L�Lrd[U.���"&:A�#"� a;=��Ͷ m]� q� slip /� ,*�e'�� ojU%ec��a?��"�``:�M''�4eb"QC;2 %��+�;aINM�P(�?�$oAr���- Z.�,i��t�n2iGen� �(!�_T = y_S��rn/cpEt}rL�* %Ly���*�g z��:�E[2 nll�a,�s�i+Ei2?b�!� ` �G ��a | 1}&��N}}a-�(�+.� N� LV�)�] )].J\ &=�N} )g �Hiz%�A�V5�Z����pB)VS!� y��;�5ly:�,�?%á�v��%<it{"HA� �>}�cU BW '���[ ke2{E>cIX}&= 0��)�eq @�]}�<D}�G&= )�1�DW cs)+ tZy� � .J. aF� }2<� �>i��<t^W_i}.W\; . V� BeEn5{_Y%[|~j�orQ�;vaQ�1���-\>hYator} [-!,s)] = -i% � sin�N F \ S+L�.8" Ul( {0})=q_�)�e&J�W "r ݵ$\_Kso �Ft)~I` =:\xi\xi}�r�� *�o&�"Hn�M�\now t O"@�6e^�:���5!*j�S�[.� .<Yn6�new:p $u&>�;Q-B� 1.g}�2:4  attac7#�wo} ��-�m��I\zurchere=� Tw!�s�+c�,8! s addGL�t�{�uc#\ŕ$ough molec0wir�cr�1"wo,ofV�. � ng hee��t"� a�S��mi�!he dauo&o�f for m�:|�ort��:Z"� � &F!3mA�q�or�)1pRV�>"�B�(&Z#)�segal�k03[FuV ��I ^"p6�@.({\ ��(�}3 �J5a��er����4r&=(�/E�p��to�|=Arl�h �cam���@k �"� :5owF$iof � annihiM�6V$%A��s'H�>�-�T�I$hy&�Uow��cM�t!}A�>�-QLE�1!�"} "�i*�?6��$"� �p* )B��6 $t$Y.StM@���os��P�a�s��� a�1:�o'M�Cs"�X inva��tB9�A�5i���Xh:�9 despi�a� a���"�:�߉�a` ` �+sU�esV�X2��xJz�edws� SVu�� 6�em�;sx��R���g����.�. Giv��h�k*�D$t� @!�aOt+amw�!*�v�O!z$tJR A - ��  2U -t�T �Z Z�O�a�cas�!e�U���5��/2�^V� TR!  &t }FV!5 (-s*MV � �)~"Q >� � V) '2 = � )#J .�v � "s �$x���)F%�A�$\�b) - 0, \XW !eT6��gs!��ca� "gr�M�$u E 0-s�x� )�vU�.j�29��+�W**u5�u-t)� x(u)_ 9�&�����E� -t)xc>�N�j%�!>:� * n�q�!TkD�����P (t-u!�O hat A _0)=".1��^A0S!�� ��&�ar�0-"al8*Hz� s $.�M�tM�2i�=�$/3��sy�c�k i�ed" �� Ddnɉ�ma�BM��>��+Fs�+"+qy:r.)��= ��f�����co:B V]mea�Iou �$1&Q2U � � tzE�r#4!�!s��q>&��t?�sgneA"Q � &b}/��V�3HYx:WAa!~ $x$.t e��!b �Ki9�+f���r�>�A�C&'O)$&S0"�,(� )-RL�aX �JZ ~P�� ar\'�� ���` hemmer_ ,58,mazur60};�lvrA� s � nx%��n�;y�!�p��!��5po�-�7��8.V9e�a sizEH�!U*R.1B$s.�� .�`Su6~�itfu�؆j^"$g"f&&0t��u!�=�L&7 �e�sd�� easo\Mo���.� �bb�- �tl�����A � ^.w ev s. S�&�?fea��:qQ"�s&�t�F�*�&F#��ac4M�P RtB�JE=}ath���upTa5~& H*�A0�Rn�Tld6�E�&O��aF{'&Bu!|� niM�a� oriz�=�:��ge~"N&��W/m� "{� 2e ;&�"A lagu��&f!��w"�lforbid7"  w+�n�5�+, h�n"'.*�sX�.�i���Ucs�"�"� A6(unz2)�$1h6�y�"�>)�d�S*�;at%�:|= ���bN,*�5QME�dz1 !�!M}�:�-��46z!��$ it{��}n�.6j �!zs>be�O!u�o�)�Yw��6�"�$ !�ˏ>s&�&"&�sol�A��2E.s�m6�ye>,.9}����9 (!0a5ori�hangg��mas82\b��J� q� ^���c#,J2"��.�F�*q39.>\[v �~�/)" LE ma&%lu��6�h>  ��s� �{u�F�Q�� z)$ �V��$�4${\rm Re} z >0R#�$"DQ0�a.j |kA (z) o"�" �. .�$ 1}{z�f_i} +R+i\omeg��T>�'W� helpaA��:�6�( $1/(x+i0^+_((P(1/x)-i\pi�&�we "\  k��3�% R5text{Re�}\hat\gamma(z=-i\omega+0^+)\\ =\frac{\pi}{2 M}\sum_{i=1}^N\ c_i^2}{m_ :4 \left[\delta( S-  _i)+2+�[\right]\,. \end{multline} By means of (\ref{eq:noisecorrelation}) we then find the useful re #0 \begin{align� abelLxQEinsteinFDT} &S_{\xi\xi}(t) = eta \\ &\quad-M}{!"H\int_{0}^{\infty} d �( \text{Re} =n2l \hbar / \coth%C(-�}{2kT})+)\cos-_ t)%9nonumber)C � In!P classical limit this5\ reduces, independent of:prepara!hp of the bath with $\rho$ or $� , to:4non-Markovian 1hv $!]5m= MkTM�t)$. The,9�2�,) is by no M'�bvious: It implies that a modelling�4quantum dissip �Lis possible in termEy(macroscopic 9itXsuch a`e fric%#kernel $� and %8xtemperature $T$. For other coup�Xschemes between system D)w}_{\hata� } \neq 0$-s from�0explicit form L!�heZ�i��ion funi vanishesGnIlL9r��. .�a��A� pect)�value � OIW-eintera v is f!Q e at zero.u�se12s Mreflec xfa �2$t absoluteBJ �m� Fin�E a�� �Es ecohIt via;�(-point flucMws��AIES Moreover,Zm!M�A?slip aə|-A8I $ appearsi��he�a �-�pota�0al renormaliz)� 6Hamilton�� ;(�h}). W�%�l�)�contribuE3be!' J!s rbed!�i�qN=)uT,!(se become sI1 ary P6sitresA[��!�densityyx-Ec ���_{��}$ given��51.g!A�, howe!�e���A�(an average !��bare,EP shif�7� � ��*\rh:�ty�2 ��would�-J�9N>��]MJ$worthwhile!QI� out A� �J�E�MN QLE sh�not beAfusN%I?@�� ea��� ��spondAPQME�1Lgrabert82, haake73}." as�Za�� 0d dynamics it�Xalway&# --!�u@�q~proje��5�--!#�[�e��nate ."� homo��ous! y*-3ra�ed mast��͗ �$� 8thomas82,GTH77}��isEur� nde-<time ev��io1a 1 probabila a truly � ar5% ]pr�t� �holds� Tq�5f �non ZQD04}:# �R�� oriz!� q�6� �&. .ZM<.{ -QA,-U���Dnd cs� �ea �!foe� :Alaw�@ openB� ! Te"exist e�?fur�subtleb whic re^g!ve "} mUc!�a_ just%�(he same way� ���~�4In particular,! ime-&3 �;0$V(q,t)$ leavl Az�% invarian�QLE. In)�as��� &P a��[ w%O�f-6�0Fokker-PlanckY�*� ��� scal�%driving�TaHs *| valid!zpMM; Q�:�x l6�q'�� matrix.m�zerbei�,95,kohler97}EV �}�Ainvol)�\ � �5�c� both�YUa!D9�forcee�eseEE�Pde��in���sts �4 �:� T !� sequ�!c*U q-�J a� in a- co� x mannerais already�U verified � lyY aA�ametric&ve*f 5�, Uhe�5=tQ �%2m g  kinetic�c�"�f1�B� Witss ival�Wigner� a�v. b!���n��^9 w� �!P osed!�v .v it wa� ��� grateudegreeCfreedomP�=� . Do�%�/�� well%�!^� s?f �@]�WNvis stild ���a��&��qif�)IA<+E\placed$i5�-�d&0 of ei�!! moWumApo �+:P �as�uE% J� ��lya0e� ult�^�B ��Ln 4s\.�, buA influa���N�)� is obtain� Wc��7A�Yet anI&�!��)onee�dera�aO�sa�n .�)6,"�a �)1�-f� csi(a col3M|��(Bose)�9n (�t� ! ]�2Q X ,it{commutes} r4 �..�'(us constitu!�a�� demolV.A!� sk r� ondsA� p�dephasOnde�add[I� {\L}uczka%|�! lee�a %Ei��!΅[�M hea9 -�lK 90}.�has si�� been�%�� nyűHs, see e.g.\ Ref.~\4  (vankampen95A3We en�ubs� bW��lsk�!�a1p� of.$ fermioWinyl�nydi� �gi�2,A suitable t_��\thad�%�mapِ� n �osenviron�' )ce�ropri���strengt1pDHTB90,camaletetal, Ɂ/!4\-&{PathE8 gral�d eff!Cve q"Ksec:pathA�/ } \9r{Nonlo�FB A mo [pproach!{describ6 �aA�on%&y� !Uu�!�q�mechan� j ,feynmanrmp48A|�KM�pag�isDm*as v� %.@ngle q_f\vert\exp�-�i}{�}Ht�( q_i\r<= o(\displaystyQ(0)=q_i�:t f}{\! D}q u:t S[q] w \"$rtpi}W�" 5y ru�ver al�l!��: ng� $q_i e�af�� $t$ #f_ @ e(a ��e fac(�� ain� &8 I� $�$* I_p>�"ve�im� to re�� analogj �:�I equilibri}es� �lat! . by rN!>!by $-iE' \beta$. Wv u�L� (�%�)!L=�eA�en��� J� �J�r�}(q,q')1}{Z_{  >�A� '} ^B�)=qY�Y�m,1q, S^EY�\,,]�if�$��!��E�!�� nt��!�@called imaginary-E�6[�.�A.J+>�. 6+i*��)�aZI� �3�-M&��so- � Euclide�";%2$i6 :o�)gAnFig�H &�  ~� �"'��)Gto 5(e�s.�6F� efore havQ �id� he mo%��in�ed�.� conn��on"B�ndJb<s)��ly apparr q6��bAe domin��"��� �M>��-�ari��&� p3Q !)�, i.e.\�� s. Q��]s-\$heir origi 6 arou2 eFN�!�,is�ful� �m5 a���n^ l���a.|{ it. Expa��!@pow���2�) second orE8erm yie���leases. Hig�;s�t often neg� �{4a semi��xi� ɍQ[ex � :�T."�pre��E�wm� an-����!m] the % vY�by"iq�external� EO� I�#�ced mayicourse@� arri"ut� b) alis�t (vernon63, g�� 88,� weiss93�^6P *� A�t9 aw"D2+i$-��*to�added toE $MT-Ba�)�a%���w��n�F6(S_{eff}[q]=��4�'0^ �;d\tau� 6( d\sigma k("- )[q )-q(  ]^2 &� effactV� F� \���"�"��\$n=-�"^{+ � \nu_n xg$)��(i �)�kvtauB�!�� Rz)$8ot? e Lawɂ��1� dampa� *�!I��!a]M��-4l"clearly\l� ��!t} ��!���ebaݬ ID�O >k7Ay��.p�2i�be ab� e6��P!a �e/զ.d�.� self\/�z1M�������A� )p!)�) decN��ohmz-�) algebrai�� $A^{-2}8 !."� �s ' �8t�.6�Applicw:��2� ��a metas���! �(} A-R5� minimum�6be.Edu��.�a!�u�#ENќI� s. C"�ingly1� two escaph� isms:bj A�v���a,at high.!� tunn/%� ��& at low2C. T�_de ,��! "� cubic 5/FuV(q�r2}\�(_0^2q^2+1�5q}{q_0}F�epoN�Qis�ic��in Fig.~, fig <�|b��r hx8��,$V_b=(2/27)M��E�4n N!��Wangular�}�y $ Kb$��l� F- . 0$. J6��s}E0M�� showN Lan Arrhenius plot. A�&< �&s�6�&_0$� Eq.~�.)}) below�rw"�dnct) �&�� m�"g��Z* AJ�(Q�r( (M* )�0ingoldPRL}. FfmoY!we obserp �#T | T!.lar^'��strk'��.| 8q(b&B "/&figur�KinclukXaphics[width=0.8\column]03} \ca�{Ca?�naA�f>)�protectE�eqI�a ).�belV �a�b&+��4�6S%9!Z�3I�`'.� �% -Z!k�� e*�&upp�Il  cu!�a�'/2mH 0=0, 0.5,e�, 1 (data tak,,a BAGOW87>,a9s:, W�"a�  �Z*vq~X eas`*6 I�*<,hofma91,anker95 9}fs�*er al� �isuvi� bya�:� calc&�&� �>��ed. S�!����˵f �<�![m�>#no surp�elsptly� ak� $*� dS"!. FR�.�q$f view r�is n un�� *) , *�����$�a saddle di*�( space. Oqcircumv0� �iculty!�perform��P (�5 dir�asteepest�en�!=�5� a�!��C� � � |yyn acquir�?]-A �� b la�mc�am��PHcaldeiraleggett83, � �_or ail� %rP��,refa�hga�i�discuss'inF�hontsch-�*j�A�=!6!� bn ll u�$ tood>-�:^ic�-by%ci�ng!M�eʹ� <�durv $&1 $��"�e?yX.� �?e(. s or�r�.ao�ls6]Z: &�"s + �(� $q=0�hd�<{\rm b}=2q_0/3$ �+m,. B���*�. ��@&V&F� � 1^2+"1 h"�2 nu )N2b^2=0*0 ghhm��}�B�#�b/d � new9S ˉ+m�9 "�A�J\i9RHF85\ is \RP) ssoc�.Q�&� �� ,���) u � B� ��6t is9�2�4 F�T_0�E�$}{2\pi k}\� [Z�'44} �3b^2�  ^{1/2}� -}� � ].=��AmB�As�= ed above,�]2� .�3roF� � s�)er5 ��mak-e� :�  A�t� �/[��n2v&�+ �:P |!� its " enhance�\Q^ !,�EM~.�� � >anM.ZD�%�3f�2x& vior�  fr�z� one/d�� qAFp(, /although � �� 2F/;numerE�Floquet\oryQz2�/� e lackA�knowledg�� )�c�- �&��(plagu� �mco�)Aw X7 ɕ��IX���)�+:!*.>:=k$%Y0 .0F�ise's�0d�,!�k&�T*� coloredL �;,:*B !�Ce�B n5ts)�p2�-1var;>anf!r�nly"�stocha�0 Schr\"o!`�&�(e�<SSa Likewis`U4�*ar,7-�+Y2X";Z!"typ�m� ye� Refs6+ko� 475,messer79,de381}��� notb e�u����kN)a�x&�8r d��s*'5O *+n�c���)�(M0,�effor� is &�w�thoU8 F\"� � 6(33}, F\'enyUif (52}, Weizel 1w 53}�FavellcB0?f 6]  redo!!%:pop��0�(,er by Nelson ^n ,66, ghirardi�!78}Z%d/6B``Sy9M�cs''. a�z � vin�(lE) dem�� �F e�&� "D is quite|��a �Q&<6--Wv7a|2}�]IsGHT79,w�+ iang�" �?� s O so,&2on�>P o incorpo�%qK��??�oI� se s6��ri� e 8/%"A�t>� "�5$�:��100 y">e@pa<i0]�cornerst�.� h eNE1905}--!��0$onAe�3``��A4OB$, little i`x9ly �(nX !!�d.p嗡ro�71Yxnga�ste 6state, fzom�""&� � w`$s0 al $/e�a�e"(nA and/�iaBt.� �Bu$��-�5 rest)�����of sal�C �rtN ��1 U�B"*.&VCQBM+=��app&e>: %n�utii� omb�0�&bia� �8$In summar8! f(!>�m�<m�El�nd lo ch�+nge�.S6ne)�;"%33) ed~"bWac� � } PH'tD)�"�P*8 sups.��A�(DAAD-KBN (G�n-Polish�r>"A4�qC9ity})tF��� CS�Ehce [Fundacja na Rzecz Nauki(skiej] FDeu�ef8$schungsgem�chaft �Bgrq,HA 1517/13-4%�D5ab�!fa�arch 2 s SFB~486. 631�@9(-G�$thebibliogUy}{200�ibRC6� A.��@, ``\"Uber die voj7r molek��9%n�ori��(r W\"arme g+4derte BewegungEin ruhg?n Fl\"� gkeiQ*susiIi6�n Teilchen,'' Ann. Phys. (Leipzig) 6Dbf{17}, 549--560 (�g)Ea �@nyquist1928} H. N ��+mal ag�4s8lec��-r6%��duR1s� � Rev.IZ bf{3j110--113�282�johnson �J.~B. J ����6��97--109J�(1}�B6�BreT&�%�=w�/���"F����i�%�it{��}�W�  �.�y enwea�� �s}, SpriT Ta�� Mod1_q�9!]�6)]22u!$} F. Haake�r w �!��.-%M >��62 9A�6%T732�s�!%RS !� Kine�I�O�..�5d� s:*�l�Y�&%�J4���61�M802�")"9 A6"�GLq�c�o&'$o"�(,icl�� in:UqT ��#emigroup&%.S} Lec�Us��4Vol.~286, Chap�=I�III (Q4, Berl|16 .6lnm90} .�@6�Slugg'ofW&p�ZQ&E�>b'm}.n.� Math��44��2k 23� 96� jung�R. Ju+N.��6� Long@t%��J� V�51� 512�D6h�#95�H %B. ``De�B���>�f�Eu�E�6875--68��96��0026�A�JrF�>.f� "v&I)*0 .�)3�61�.1--53s6mori65e�MoreE",�� v"�@aSN�rogr.+>�423--45e�6H (K. KawasakvS�'e�7%�.� �&J Lang�6� J�&� �� 1289--129�73); S|BrdholDSR*anzig!�Ia��d2:�>.�1-i!�ory�pZ<1�7--371A�763����w.�n6Micro����90*3 #I�g, b�^�2a|537--55iz6"� � � `��Ŧ1�" s: A, f\AoO�$perplexed �� of�.�f*RZ�f48U 15-2�972{(senit60} I.A Szky�*#��"E���q�1�670--67�66Iu�6� U sma�A�MI4olv!��3)4Q��A��icaz�>%�D, 56--73, 74--89, � 9� :�za73�rZ i#NoV2F��Z � 2 2�a:z�,6N. �M. Boxae4Re�% on-rL : Fifty�IK0�^�6A�251--34e�:�B4�s~O.�d34�A.~J. L>4!�e� i�S.���!9jM 4!>3!�4� 198��j15�x�:� E2} �a{6TB�4.i7seeJ�#���.�N�.�w� 93} &@ e'it"� uve� � �Ded�(World�tific,�7gap�:1�.wesam U. Ec�?,9nIZ,V. Ambegaoka�1��a%$m-x3uct�)� j!�a�. Eh&z 3�6�643Ea:�schoen B �%X(A.~D. Zaiki� �~_t ,7L��2/ �!�.r�Jultra*:�e1�*�19�2�4(:-E9: �Yu�Nazar�Ch�T�?!SR�? in U�s�2r ��� U8S;@e� �F}, ed.\6 &� � M.~H. Dev�8, NATO ASI Ser�,B,� ( 294, pp. 2� �Plenum,- YorkN96g zurch�%�,!� U. Z�$�R�R"ch�%attach�"aR s II�2�Fperti� 5�v. * � 3278--329��:�segal�T03} D. Dvira, A. Nitzam0:��m�!th?ncu@wir �^��,8�68F 2006�*�Q}� C�Q� Leh'Y, S. K:ZI�:�Cur�"o�J��c-�2n nano[ �orAs.L69a�210602v 3); 2�v�Shot- �s$o����d7�15532u6�hemmer!�58�f~C. HKMaximKH�rgeland��Rec%7c=)��H;�:����� 6� 6z56Zmazur6��M e* E. Montro?8Poincar{\'e} cy� ergod�ey)�&A�_!�ssembla�of�0V5%�J.���}, � �:� 7man76A��Ade!8��.D B6 Hgas/sot]G"i_)�.�6�4!�495--49b 76�schmid82��[mi%�O�quasic"�LB�!��ow Tempq 1�609--6Av19:�ray%K. Banik�AlBag%�Dma{ G�: x 2�^,&}>R�3sW-?/(-aM �C"�3p%Z)��&�6�05110iN2);�BanerjeeɁp��2� Solu�a4�Bh: Ag-xgMs�$��6@8&�/aG4Y^I 8960� 7��6e ͣ W.�Er,��Menzel-DXth,�lze�VA.L;~K��9A��A���9�F=C7to_n�.M�B>��885--93�:�� tId�"�rH� omasa�.h/"O: Tim*F.,s8�jA��0�Qj*M 8L 0 1e�:B2l!�E`:�U&.�_�Ara >�l.�)�Oa'�Z%O�vA .k 8�57�57� 6�&�kj#"2!&� !XA �2r look �?j$2"U.E~y�2 L2�107A}, 3A38)t5)l'k&Uf�.���:|F��3&�4 of m*lo:;�=%~J�26�#� =H P.~�P.~"�� H.~TU���� IIA�N��273--28[ 76!"�Qg K.~M'"Romero�rf I�0wE�$Q2-I�hi�)I֩�*-�052l'20:"6�4 C. Z�d%V:"��mqc� osci�o�"� o�] �:}j15�5�67&e*b 2C&an�{\"a}ngg�5* .o.]a,�&�i �xss�? ���Fr300--3�36�"#_�"~_�Sp�R�)&l_�=o�: x�=��A�!S 9��9�Vv*]_, N.~G. van Kq_�A�5ubl.�1�m4$al>�Z 7��9a�P%:�.�^ L.-D.��CndR $Chakravart8 .41!̩�!.�>dB6�h�`15F���154C!�8�F. So7_F. Gu�7!% BulkExsurface*� ofovya"�� �Plpath-� X) s6f��77�77�%�&A� edeg{\aa}'A2��� 6-+clo aai�B"�`�Scr&>�# o86�V�_ R,#Fe�_�StI+���%r6vBps��:MF� 36X8{*48)�(�# |%�(A.~R. Hibbs&�1!MM�_�I/\8s} (McGraw-Hill666�-W:�(F.~L. Verno%Q �A;&yYqt�� A2�9�$a�� �gvQ�!.f12017-$66y�7FAean�R.�J&�`Ut�ct*:aKe�^c7;�SImeme��m�6��i761--7� 6�GOW87B�OlwA,R�� {E�!FUs� S.4E��&�e�193V95 6.)jkFGAnwend�0 FunkZ ,t�:en auf "�-�7 Relax*spZa}�8e�i��nV\enI^�Z$:�*�N%tHof��28��[��-�G\Warabolic�JA�)ZI9[26A�2�%2I-6v$!r.J.&�B6��bn��3siuP"YuBXT. �+yW P� &ʅ�*6�w42��428E$�).�S.:J6( �*�X1N. II. C.s Jl�Bb �k8f�2�$04--472�5��n� I. S�7�e N6� Flux%Jf�� 1355�.7��:� I.9� Y.b*} .�"�AE�Q#&\&b 2x(d�!�c�^=,4U(2� 29I�, \b� �*PO��L1� W. HoO�P>G dic orbit2��MI-Dk�Be,Nuns37.0�&�,-3�91)n�Un�o~�!O���Z a409A�0B:��M P�>�'&@ %>E�Reid:�9�in.S media:7r te-�*-�i Bul��܅&� �4�:�.F!~X)��R�:������1��219 1j:�e`b=6bP:H)t6pS�W"Jg'�M�"� �*$y.."H#A9=r6�8am 0868�A�.�.DB+4�H"fU�aY�I&�sl.(:���� 0601�L�chu�M� stur%?q` "��J.&�m�C�=s|> 1N"�morraq at>�b�� 0311IBj�H>�3JD3Inn>�c !JyIK/C xH�%"gI�BgI�)�ym21�24�64$"96Qmn82b�&9/wUt !y.�� �,1fmj�Yik &��1� 1�Bh!B*�H�J��=n&[FfI�b7a7L+80Ɍ6'�D\.�K�D!'Fp9�,!. P.�Cl "� �ZS1�1�36� QD�gMQ/� �*Dm� j Acta��Au�Hac&]$5�79)�W�A�rei�N��"�E�De�E!C"!Q�A.A�M2n~R2[h ;*6 vD�*�D�/=,einige Bezie>en zwx0k�s�� �k� %�"�0 k'',A�-E�I14�2.36jf�D�&E��0wahr\-}lin\-lich\-keits\-theo\-re\-t� Be\-g�6u}n\-7 i � rpre[N>:�Am�&�1�91956� &�EW>�E�Ableit� Y i�n>aus!lem=Vn, kau�QdzyM> M�9�5J�� 6�5m 5���Ze�1II.Z�,285:�"�F��F.�F!.[�#Vx� Inst�nr�@\'e S�.A,UaVII�"�166`:�F�, C. G�F, C. O�a�A 2�c�*� YEof Qau��� - Cri�Re�\�Ri�" Nuovo Cim]`Z9�'j:;.�F M� WW Lian�+ComB1n ``R)ImeasurYV�*"+�j''���D5T��-187O96�QBM�J��AstumC�!?,} !A.�2\"Todayn$55} (11), 39\"�P. ReiLJ^e\um&�ofB�7��QcB Chaos��6�=64��9A�, &>� :��ratcheB� v�7�\2'3�>�B �s docu!�} �%\p{ws-rmRY2$[a4paper]{�s�cle} \def\wsrmp{0} % $Log: LDEstim.tex,v $ %E��!� 3.2 2005/11/16 12:35:23 michael % To upd�K��arXiv 5X�oI�Hswi!d �:�*,standard % " �" stylDb ��H�EJe�s;9 % ")"'D)+�Ts firs�Oree<�pfile. %6�1�$4 17:37:30.�Ver�resubmit�to RMP�d7.10.!>� accep!on 11.11:u 2.13v 0/04!r41:15.vCori`�ID LaTeX syntax erro�0 ly�1�dieB�mpF�2.15�t 39:06�_LP�%�u"v:Zs��hgrAl�+ shedca ly %@Tal�Jnup) car'/(!)��>�Gye�Ss�VF(1�409/28 11:23:08.(Mod_!�$manuscript!�ordto� e %��4ncomple�dPre� "tF�0-�405/03 09:46:27.�Q" sumb. ��{Jce}R ber:A7 -929Bg9f 4/29f55:42.f Typof�M. Next5����R! i!mj6�2.8l<4/12/07 16:10:59.lFin/!��isgq�. p�Bi7i1�14e]4.i�proof��T�Bm 3.4t�SmM B�Ge I adw#,�to%�shufflT�m%7u�FE9i� I wJde!� ol��garbag>!2.6� 4 15:15:02-27�zig � . But� m go��tom?%3�(�X$) % optima��of�� {E} g?�} inpu�P,Q� ly (�\is % bro1gi�3�L |arlier1�s)B�5�08�56:51.�S%U!�s �bw�_f�3!M/M�b�xed ASAPBt4t4A 25:56�� [!Wa�q� ! St!�M "9 ��6 % (DixS ion)6�s�a�Q45�(slMXly!��ssedB���4/�O8aE23:6�M#wY}�_�^� 1Ն09/151 08:32 "M^1� lts" �!'�}2jorgan�,B��06/25�� 34:32� I .�rL%e�  (�Q}w; m�em���goAa " >�B��/05/�2:0> �R�U� b� �Et. 2-� %2�B���03/22!$ 29:32 �@��A�Y��t�yto��ly� %"1C�"��4c"�f2]Aarq��M %*�H2%�cs�dif�lB���03Eg 3:49:�F^ (�)U�!y�� (of Dece�  2,Y3_� ll b!_�lav�^ now!6� 1��3� 1�b11>lni�Y�1B�Id>��� >��, Exp $ \if1> %�� % Fix�ɢ� *� � .cls.���� \Afaސter!W Un�j \url� nter� � 8hyperref % \let*\@�mf�r:Gequ�*� -:_amsmath^�@name^#1{�zk fter|cs #1Z �} @"�l*:n�}�Cp>-� ���.�is�y&� 2� (Why4thea)Zd \new�+���+{? Custom�L� "�w� A.st�(ck� ) 55opargb�V )#1#2#3{%��$\par\addvs�'4{6.25pt plus2p�nus} .%�7[ a{#3 {\bfse40P \no��,nt#1 #2\ifx\ 2\�]y\u�Pp.\else Hhskip.5em{(#3)}\fi} 1e�9�bodyfont9�\igno�0aces}�% R-b< Appendix. Other�_!0 E+``'' c[in]sE�-3w*A�a� &����\ick hBbI�"*s if� �B jud�5a � (E%� �,ed like� A.1'' e�aCa@n�s l).!\renew�� and\h{!�)�!� refstepco�{&}"set �}{0I.!lemmaR?-Vb e�b#coW7aryb"�]6!@addtA/et"��E�seccnt�d%�oa6$ \fi % M�as \usep�o{��j�f0�P [psamsa�s],symb}U%{�txsy!'[cmmib57}2+FZicx2[dvips]{ѕM��( �mm,{\goth}[1]{\�bfrak{#1!yy*{\scr$cal #A0idty{{\leavev�C{�s1\ifm\m�? -4.8mu��  .3em!Ne2 I}s.�{\Bbb uif1#1i A�bb�� 6�k 4|#1��\laΌ#1|>*et_+:!tr}{\�=7�A�{tr�.Lz>$ L}^2:ISP>% span>K diag>(:NU>%U>"GL>#GL>$Sym>%S>$Id>#Id>$PM>$pm>$opt}{E :�n  : Stab>b:(HB�H%�6� I p� �u� ��Gal�Lem-�*sr���on���!. iQ��{thm}{�}[s��]6�thm�}{\its�K �G��}[thm]{DE �6G$~H prop HPropo�~:I%~Ilem HL��6�le��cor ACճ6EcorN� e��f�B#� �B$R�R��� �'&�]D8 & & Daa Id�inQlN{p6�� o �P� .\ }��f�($\Box$ \medg � isc.j matt0q .�topi'}{1�`s&�bottom.6k{\top���}{1:�{\ A2"( \sloppy \f{$h� �:X��&t*tch}{1.�\� $xtsep0.6em6�\4u�u{`( eyl}"3%e *���ri� ^u\title�7\author{dx g ress{ I� to NazionÝdi Fi�6�"a�@,eria, Unita' Pavia,\\�;D `?o < ``A.�D(ta'', via B، 6, I-27Hg F Italy L \email{M.�$@tu-bs.de}�lse���%\t�O s{El�a(�8Mail: \tt{m.key2~4 \\[1ex] {\FF�9}�J�A)A}} \]A�d*A�Ue�!K make%G:��{historye-(ceived{(X.YM)6{(A.B\!92y abstU5� Ipa��w�x� �me�vNl��/Y�"I� f a $d$-l�u:� by 2�#m$N$-fold���the j.�m�($\rho^{\oti'N}$�shem�)a�dR&[ 2[a�r62���y�vuaCry;Oup�it �gz"ߎrWconcern"� � 9�--i��f�Ar�f ���̆�ci�"�+t (�<��bpu&���%��rec3{}&wn(if $N \to \ۯ$)�#alyze Pp:�"&dZ�Gt�AL�th�.�qr�MoCtt<b%*?o�z decr �e�!���Cis�g� t:�. �A��%%�W%qwhe� ��oA� proil 2f�xs!P"1�.V�.�paQy;2C 0 \keywords{q�_inA In;y�]*;>�s;Y�.�} lccode{�U emat�Sub� k+f*W� 0: 81P68,15, 60Fᶉ����%<��{I�Gdu "҇�ui2�����v��� qXv�($daT �{N}$):�:ۧa4� � l��tah�-V|�dA�ala2er�!2C task�Q`1.D���e�q ine �$2�*)o9 (M�yIy)�#��d �5�w�� � �Oc*N$ hU {0m�or�-t�!m�|i��[���� ��~ ge��actq#e�$��$Wy ins \,&�w�x�Z�!unavoi�z best�@�h(�(�K�enough�an V�H�prA�M'�� woue)!�say�|!G4 i��}�a H&�D y. E�r�s�oЫt))``good''. �s�&�0Kn!hoo�J� f��Gmer'�����7qu"�#A�- es (ՠ�d fide�� ���Bp�� q�L) �to�Avn6 x$�!'l�aIf!��n iori�X�Mv�qqis� (����unCn)�g3ach.Fsuc�eful�lea�yo �a�% �+M$can be �rlV GdW eSI��kuAME�; cf.'� �s�HolBook,MasPop95,BDiVEFMS,DeBuEk98,Hayashi98,LPT98,Bruss99}a�%g}K�qu6 iifCwh�is%In#utm�!e&br%muc�Ore*> �=l/!�ulz5gs 5� Is2Isc�q�a%1!�e ��Or�ev!R%��sfo�06���l{lcri. on�tin5 %�harQ�"�0by.������� a]:rH $N$;�3 re�dU[��&�i�v Vidal99,F�1(r00,BBMR04}�Aa���] �wN,!�to �%$�aH �<prKdi Q2G�itA��_�~*�/�NCr�n -Rao|bas� X)Y�� C� % a Vde�"� A  ��ӕY)�m��4precise let us or�n7e !^��rom�N"; ��a. !+qv�%�Қ�J'a�1��@��i:Dy $P_{N,\epsilon}$��$trace-norm� �U0� %�o (oiSy��I���,Qance ��eX�$s�%�s� �$Vx $\|� - �$\|_1 \geq *}��= '$ wҙ�}i-�-�is �}!� �RyWw��a�A��,E�w|���, BD��es�����ast� $N� �"� \laz� eq:126� �rox C_N v! \bigl( -N$ f_{�1} \, I��,!^) Er)7v� H�C_���4Bb� �a�D� u�c�\�v�al� s,�Z�at �0subex.C! A�(A ie�n��te!�E;afol��hd $I(�,I) ��:35�if%sigma = B$ E?s. $IE�^�Nhe 5!h{2�}()a�/iyscrR�4� �.�E{s�asympto�6+In��a5� ! b.aly�jwa�"�%A�(by Bahadur �=$MR0293767, 07085 315820����b䣑lm ��l�//}(`` c �� cy''). Ab� !0��a," ,� les�#E@g 3�availC+ so�|cw tX4B'euYa�: 1x �'XKWEst,AlRuSa88,MR195514�qa�G �  eI �eJ<�v"�A�its)�US�a�d�UlI�rwnhbe"� aHc^�� 47128}. 2: E*[v 9*� �oe\�/9\3= t@�"k%����"$\lim_{�k\to0}�gN�A�z���pne-�HmC famiVYE���!oIӂto �umf��.���/!��!4��LKt���~U�U�"O5�Ebi4 '!� a�ea�M�9�:� �s� ly,�a].Mb a^�fu��_y ��K�F� .�.Il� %V�^r�P� $ �� 2 pa� N�G@��\2��!n�+is � .�q+:�kR~bigZ�t� vBDz �ek�A&no*q �aMse1q�s adm�a max44 el� , �T*Q��� "�^�p�D``h��fcx����i�b7��� � �pe�py]/� is���o�飭�'s 'I!�f#). For�na~sRs��!y situ�|--��Ӛi��&���� t|nY!�Tp Pa5N��sH �0,'�a�-� l-main}u]!8!�� %l i!+�ViQ�s9� !5i� +S�remg-�2o��r}/�HEsa�of�i���ed% c�~9��e�Hd\ed amongF�� �em} (�we�U� $\U(d)$-"��>misR BUE�-0 }�6a7 � 2ps }b��ed?e�f�f\�"{B�^^��)2!�)5%�}���� � �5�ѓs7X&��na�+ (6.b>��� �9� 0">��umM�>ion��s�4@;�axma�al�0eS dܬ�<�c� �e�y.rAV+yH ome-o-�g�- .D�FE.�B�e*5�� Le�uc�A�dH�1al HilP� s -(cr{H} =� C}^dB<6y�q$�({S}""�:�O��`�-� f�� �B �n�.3m!���rF H&C�ɥM#�d �v��POV� $E_N$�r!3 �.]!-e �� )�8-RB}(�H}"� �)!i (��ed)9kp)�3 ѡ�� ��x (L��)7(-addi�} !�U B  E_N: +�S}�o)�J� N})\ �%{! }\F(\Delta)<0, 0set)=A�dM�1},!C&o Bor��B$1k}��ot2�%_)HS}$&� ��d�� � g!0$ � i�t)!�.! vX3![\mu� rho}5= \tr lMU! N}6FbiN0S"��&a=�3- �"�� �a9.D.�  ���each > 3s & aMv ������a �Fe6*�)1�s�//�in]!Ag��as�2�y8d�!� ���tNgir�XQ Ob�! act;L� � � q�J .f� s $(.)_{E�� N}}$f conv�h> %~�@$ٖ�"hpG$ ^5) dB �� uch Y�&� A!��4��{�]�Ot�I�� *�4�-F�;�� � inV���h�kA� �N� von NeuH N ),���$��q� \ni; \mapsr� X$. :H"RE!��%aRsuAD��S0�� kind L��$p$ cLide� thF�*�2�s:�z)XSB�@{ x%�,[0,1]^d \, | x_1 �~\cdots x_d 0,��Dm_{j=1}^d x_j = 1\BƢ�AhN�M�toEm5,$s]� ��� $s_j =��1\chi_j �1$�r> !1, \l�, d$� o6 eigen� }v�N* a� $ �%�i���of ��ed �a�$s * +can�*a2 �~} �Y. � �iz��0��up!8nowa�Ak"c*I . Y�8{defiUdef:2�XCq�a�� ~�c2�'��b�F�!Q�s, �!a��pa�i�E�^~�f� >�. A{)�Q$(E_NJ0ofF���a�A�5}'� $p$*� ��r��VO*�no ɟ�co6��E�R^� ��wɎ,"!B=zJ f&� �'���L"\��.I�d �B�X"1)aq *m� N$ntinuouslyEfX$� $ \6s X (U,x)" \alpha_U(in��� �UMj7sv^0��Ub} . *wE_N��l(�)F�6|U)\9�v�cj��u p(U�� U^*A�� ��- r��rh2�> 7 satisfMK�)!j��n���ׂvaJJQ@*�� $p$ տ��"�%$��>>�*s� $��110nur]0� 2��a� Ie$ a�$1?@u����edy,i2S)d� surj./vE f���4�2 g�i"4 5��}�JG|� t�alaG�n �XxAx$:M, u��-�t-�D��oth6=*,i�� �]L6&6Z-d"�]"D nowضf�X)u�H3$>$�\&�not�z\bar �$�B3,ur. �$)�?A%$� h*q Ev"NLk>� fa�7MR.��/� -�yw�.Rg�) zero�t�.�ar�QL)bec�#a��a�5-�+slow. c� ���5uc< intr9��Za�e�$� n�0� .yofB%�*to�a,�|6$%B&}B�fE+ac����ާ ��� E3H�� 3}) ��^�e *;)�)(ciple}\foot� {Acr2|e��� zem%� �W+oe�@0!�"�2���pr�g "�oF�}� 6�&r&,� \,{�TE�dea&�*!�"K �:�"�("v L4�#A��F� ^�, ��&Q &�?rZ�a)�Ephs7Ikf� (LDP))�*qI. 39Xy [0,\ 8]$<  &� ~zate�\u� $I_�Z ="=$9\a>�t,N�1})%�Za7wn) p)���� = ��#(� = x!(�8 �g?�hih"C9�A�6�x= 2�b�V�%i$u! �9� E� &`I"� IL� :1} "�/a��/��Z i��a LDP!˹�,��� �aN~"�$0��"$R�i�) M�2 x�I;L[�$. Occa�] �1�Z �A�.��Rp^G �Bu�"6&!|BQ+}$ ި�)��� � � �*aKYxWble6���&� A.���):� 6�i3Z�"1�"�&%��}*��!�p%�unb�tood). mK �6� �V<�3 E}(p!�2�W�^3yety*�7E� ��sc"� �% �xv�eir*N arg�U. E.g.!���5dbaNp>�3< )���*o*�<a�� *41*q6 e.�i"&%si��:��"pJ��beyond-o ce��l+%�/at^)(* �occuro�� k1�4�*� spacr��he "�*)Q � ��� ��(, at �vdegeneAA)c�$se3��C 6Wlar�1 �9 "&� �1� ��t&��KE� �Ie:��"m �Ueq:59a��E}^0(p�B \{ I&� F&I�is��er �p--s ous}\, \}����t D �aU�6Q�.OAa��"� senD�J� �wb9in �r(32�cb�"\�$v/� �,m�����l#9�:)u�} X�F��� guJ�K�A&��� �v*- } $F��2N�i"v�6nr48ArF:l&b,\&vrA�F�&�V�r6]/�XB�)�a"nOl�!#^��}5�A�1�5 tooʲnot�3�� %�i se�1 ���?K,>X�$>�$ �?�v)*X�l�m�� {o'#bk6��7� �� F��-c���}:�n[�6i$�l�ǁ%�$ B�)5�ing�`o�@�r�B� ��e�5, tog)�� � ���?��| (&� R� , B�BB^xB?* ,x)$q��z !>�us}�a� ��!�5��G�\lMJ&�6[�� ;E5.�!�i6-�6`-CA;1+�]��transve�b" Tv%� Idi]��6�1to)!j� s6{ &y � ~!���:�D*��#ay%Q>�#i @H`,E�H/ɝ.o�wn@��-e�5��|�v�%2�%�I}_� 6�sup_{>�} � n),!�F^0�' VH��>J\>�z3�yc�y�Y>y.B��ыsM��\#.�Z�t��g("�%�noj""d a]�we �2w?u{�Q^\#s���iE I}_sJH�7r��e >�.�fs�#A1set�Ej ,%t�YAa�nebAarily.�V= selvA� In s�d ab�7of �Suag�` ��5 n0Cthe�6�iHoYf:B }���#a`<=b��3�� &���.g B�^��)ilJV� B�*6�8�3� ��]��]"�/Sum&�.5�%KB�-�/"�1��� A2�����9A1=� aris�,"�3.��yam[ nite2�=R=rib ��I* L9��3 &�9��3��� �re�v#�tr`4isx#.z �� &�A��t;e�Sanov')e�] (~AegyD(MR1739680})(*H�iI �*achie8?5empir�:.�s�2���(4n sampl� �'�9��J��9�:q�y��EŹt1-5!X6#5�"�-our%��is (u�Ktunately;��a��S@�"9��. N����sn2���KntU�FE�>FHwe I&:&�� <D2!9�jndn�4J] post��DB� ��V :� uppe"�4.�2(2Z[)8} \label{sec:esTtimating-spectrum-1} %�� The most complete result is available for sjal es ~�on. To state it let us recall the definition of� scheme presented in \cite{KWEst}. It{based on5 de�os.J re Eat`d$U \mapsto U^{\otimes N}$ z�unitary group $\U(d)$ into irreducible jnents. !latter�Pgiven by \begin{equ}(} \scr{H}.{@ = \bigoplus_{Y \�'Y}_d(N)}5_Y � $K}_Y,\quad6��Qpi_Y(U)P,Bbb{1}, \end�where $o � $ denotes%tset!:�\emph{Young frames} with $d$ rows and $N$ boxesb d�{ - �`N}^d\,|\, Y_1 \geq \cdots xY_d,\ \sum_{j=1}^d Y_j = N \}, >�$%6�.�:4� �Lhighest weight}\foot! {MorE�cisely%$Y_1, \l�, �$ areY@!?a6[A�,a particularA�i,\Cartan subalgebra.} $Y$,!f )�A$A��a multiplicity space which carrie!�n�i$ symmetricu Sym_N$ on%� elema:R�V_\sigma!�z�!�1}Y�PA� >)M� i*�B�M�w% d�g�LEm�< (\ref{eq:112})!A $s3!�.$ o$:# [b)�} !�8. Now we can � aMU��22 �@} $(\hat{F}_N)_{N �!" N}}$oBK \label�4�r@ (\Deltae^e+Y/ Q} P_YF--JP_:1projec�Uo�IwH}N�$:n�58�P9��B}(�t6*),\' ^2 = *.�67At�PV�.>!I)$. I6a�is show�]at2satisf�;z larg�~vi�� principl-�the classical relative entropy betweee�A9$vectors $xI�S�?$i�s�)%Q�r[funI�$I,x�4As we will see!- SubsM�e�tsec:proof-theor-refthm:1} this!in fac)�b��t!a�Tbe achieved (cf. also �0MR1947128}). qthmu�f5A�Af v�{in��4})�( asymptot!|ly op� l; i.e.!�6�LDPI�!U , :]eK I}_s�@fi�Q �S�R 22})EYadd� =q�I^02c$ holds��3E� ` ex��ly��Jm o S} \� IE \ni�hA#" �Q=�*Rx_j���Ediagona>��["g * 9�_ ea�B(x_1,� x_dq;>�ai��opert�� ��are: It-  s}ᶡ:sFU�EF}_N$i� N�>�>���H\Aa��l(s^{-1}� rEthQ C \for� )� goth� �})M/9+iI,covariant} (�^Ed �110})���g $\alpha_Um"= U!�A�$� \permu� inj�tNi3})). M� ing�!$�]�regarde| ref� as a tw�ep��(cess: First"� !�observ� .�in term"� instru  $T$,w is:� fami�,f channels (HR`he Schr\"odinger picture)FV  T_Y ��ZF �\omega��tr_{K�*(  P_Y)I �PE7�&��B&��cy���al tr� over���a � ?aga�;"� seM Uj5u  If'mN�"�mi�um�;gel� way�.� � (P_YA�.T )$e � ,iout� of!�!� a quantum� ( (described͗ Hilbert �! �o-- henceP0different typB1 . &�If $d=2H �sit��!ial� �casU6� B+a!n $M =�(- Y_2$ qubi� � DT$ itself coincidem�!�``natu�Dpurifier'' studi�B (CEM99,pur}.� �H1���2���a�T2 $. OE��= A$perform a � e�of a ��}� $E Dvalue� )�S}_Y = �xY/N)$^� "�r�23a���a�c��\N) E_Y(d =*� } fF% ��.#��} "��(m�fy�now%F5  ���Eb��s�an >� ��eigen� I��A6M�I�ofA<eIs�rii�f.�%� ~a�( = (1, 0, 0"� 0a�c���1�B�B� )v�P.�\�iE}J�J,%�.��(text{for}\ A] (N,0�0flA,P�M�1.69���p�e]�is.is kn oiz�O � N$ global���hcriteria like averaged fide i�tHolBook,MasPop95,Hayashi98}. H��3look at�n�ȁ�0 direct generz�� eE �Qv� n %� um �ma! 1 We�us�Ji�iof view� grea�detailS>`an-�- ~}8rge d"<behavior`Z �4:;follow��em� } n�3}�a��of): �_ EZ ���"m�9Gz� � inJ� 8}):�L 9:N>�adI}:E�L�0o [0,\infty]$� b6��a�7 V�B,� _xc �bke \left(x_k ( - x_{k+1})| (l[\PM_k(U^*J U� ]\rK)�6}",� (:� �u6,, $x_{d+1}=0 `V iA����* J� 9}),id �CQM���:=��-�al minor a\upper !( rank $j$�de) $inant) of � J�N�.�A�� Sb��6a�QB�s f.ri�e � hyp ztLng. %t N� VE�T! re� c9rein). bE� Each admi3:�$I� ��is)/��Eabove� >�E� ��:- a_Maq Si,= \trE��4-�rh"4P "�� 2I���S}.�6'Y#%� �be��in�z� ; cf�͡&�rHeasy to check numer�l�"&I�; ���6$$ do noR! �g��� ��onsidXn(   AOt � (� 0ex�6��aL=V� Blocha0m,)�V�rho!�$frac{1}{2}�l[ O$ + \vec{x}�  �}Ar]�a֒Iy I!�Y2K�e2�� .,� 7�{_2-�_3!��Pauli�{a�%�Ix},��;R}^3$� $|x}|, y}|i 1$),!�]��!�6�$IN�})V�.� ���-S ��}.�nş[ -�+ x� cos\theta!�ɂ] -!n)�- ,y}|!K6x}|^2}{4Af�j6u angle"�1p�%Xy�S!K(von Neumann"Gu)$Z >�."-�rho$ b6"esm�$Cortese02}R�6� =6}-!3��(=s^2!� !5\ !�()�)6%�(�i /F}{1�x}|} )�)�&� W plot=# both� nti�a&��$ �$I�wo&o�!^ �A?=Yg�F Fig= q fig:1}�sh�!/�)�)�in�� s[ �smalle�j6q$&Ift}[htbp]A�ɪcenterɨ )Einclud�phics{a�! 1.eps} >"([scale=1.0]-2 -�fcap { )|Re:��]�*gm�$!�a� i(5�.-!���k9^Ke: �, corresponds��MV� = 0.9e8na�low!�on3 1$.}�-�Ξ%2�O�6Gs2��-!h-��& % H�,eaU�r�&�O$�� onlyi. E�!(��.�&in F;E-"�34;�to4 �$p=\Idi�:� )� �*� 27A�M�ɹf (I}_{\Id}^c,60J% SB�T+,is, however,�as bad ( ooks!tA��$glance: Si�>%q42t $"j if -�ap�t% mute��1&� 12Z�scr=v0r>6�l\�Vhjh^�)\,| (�b.W l U 'r)�V \ g� }\ [A��]e�i�9)A second� A�*arises�.,9uretPro"�)�5g10}aJ� �71�N�36E�)�^cI�>YM�2�q��F)A_N\ J��J s�#0heuristic arg&s/ ndic�/�E Q�Q��A�; et*j A .{�U � Z&_Z&a� \&=r�a� longwe�ins�ng���!Eg�(C con"p the 2��Ņ at h!\;is"�cA@t9 lear�awhe�%�cn'b placu�th�m�11A� out break��A|��w�Mr)a�,astX -d ions2�I�:!AI-�?s})%�J 036}) would st�$#aVw�,� �)Iu� Q 0i$. Not�!�m&SE}^0(p)$l�p�,already impl\2V�+x6ɗ�mK. OurA�"7 c,Enat9r�����ep��.�An�r�.�*�d�easily �^mAnB� prop&i<'avjnotE}(\Id(1A~e�noF{IDrB s)� �0/�>��\ �&!�S � semi*�"�$�-"+q_ sensRJt44� $S." �M�A y accor��b9 G -,A!.�� radi�'ton�a�.�6|>R�� for AAE�iwIM��u5rho \neq��l rho\�y 0A�Ce$*���Vtr� evid< e�u�i� = S �s�� -��rup7����:U9��;)�_Lan find! �pail rho_ �_09�S�r $IQ� such [� _0-R_0�)�.�but�is much>� $ (i2�ly��.� ) al-b y� elsefV{!k�+� ese topic�� �. �&now, �2summarall our co��s}A�!�i��U"� n�7���=�YUBeQI}��� Aa.9���Q�w � \Y+{C $*E6� � -!�lemҠ �Baim\a���}�#udyF�� /�W"bt�m*�$&�$, �y�p a&�op�A%.- o%#��t& 26"�bH��Am����T�,emih 3Y�pro�� sa?al" � s��useful  �m9���qu$�rai�5N -� ���%GA/^} s�&" 1�u& ),�g� � ��"�* &&� ing}%�� � ! -�%w%}# �/ quitejp$-!7o�'s, if $p� sufficien�� t.�!2 C�!v ��(2�|a{p�x L�7start�T  techn 5kconcern��tin��uniu#converg�-A\;�!C& origiL l,�"�E;y��b� cru�$MR��7)����next MJ. S� I7m*` a)��#r!�ngAPtheir !�%) \(reason3(?dev� a whole &-�them. C$1al- < is.|��b=�, %�!mrg84h_NP f�r-1}{N�Vn��&�,e^{-N�,+�8�B�% E_�, )�^ *Z$.�-,!3l�d*n cr{S��Q`'i�%�i4 m usua� appe.,n Varadhan's��B!7 ��P$!�2� $(ER�."N1�LDN1�����n97�lim�5%0� }:�h.� inf_.!�S}�( :�+9�-��&:If���j � ^ does�ne;+ary )!e% (�`eq�,foP$f aV�m) sequ�8 &*84m�+s5U��-.[%E�\,B:\,�!)$ ���� Lan� le} (D�2�2�def:5�U9is�ivalen���"&�" O (B�*� �)%.,���'$}��`a�� tool to4v� 1A�*e�"�'ٴ� I�%*0 we�w�t��)hU `�%�!�)խ���e�L=��$ \to h$ (a�+> L)�����s�-�ҥ$&�� �/%lemma&K� lem79Co{&�(L�bICy�s!d �����$�5N�2(re��)6mYKals%3, h`�5"h s *�:8C�~2}.�=en� ate�yit7 M: :2  @non-de tA�2g$%�.�)�:u�$p�.N&�.rho_N2=wm%_o b!�{05�eq:60 � nS_N� �w%x+rxNw�!) �6� V*>��' �.�DisV��in�a[}�73b=% w-�J28>3!�[e�!�ftyى)6�?Վ ^>� �t"�]AE2$E�7Y�a�"0%pf!��  3 ��!<:2} ,- ^aA&$�3ly depeo��: 2)Ua��,to "�4 onB ͍aB2E�xpbin���wo�Cs.�-y� mf�}-�6q/��R0 ^{(j� �"! , $j=1,2$I �rq@!sami:��e�$\lambdq�R"�0 <� < 1$ure exist�N#,� \r�t�+V B��/@615 epsilono$� �}� !�+1�'!6�S���6e����> 0 �&7 $�>�)ll.&�a�B1m��)q)�=��3�8' H͛$A&�4)$�˩) alig�E\sup_2� &%{!�,{ ETa�-Ec) -� | &� LA-�bigl|"� ��m�JA'o< | \\� &= \|!v:{ \|_1a�1ߍx�:0)�E��E�� �$A�5i)�v�e.F@& r?; t8gl�A$V@�-]g .�7ՆFn6m=$a�)$%2)�-a1i | < 2 1 ��t� �Mu��:. �C�c7-g \d�CuaqU�}�e}1&=��} & �J�(��e}� )u�VE �!;E 61}){" VI�6X?�)_O3-�Up�(+ �)1)"k �22P qF�(��>�&A �)EJE���- �$Z7BB36Ea�  �clw applL� �� b ��%7 �(=M��!��e�+ Z� F0,1�:e�.Bq  0� � >�k2�E�j)u�,f.2u!� $ !)�դ.r6��\to? .�z�����%�� Us��5f*�P�!Y_�)[:�mul_DEM�>!���*��5(!� ^N�W�L,f� \phantom{�(n�(�tYxO�.�g_.� m_5)>^{N-n}.�^Y{�} �f���tr� l(A_{N,n�d���/�4%~.2i�$ ?nonK!�suatensor duct�"�&f $N-n$ }"�J))mZ ��$.1:m!rew;�s�3Ca0M��!��&�C )�)Bm�f/��)0+ >1� \T* �QEB1 +!�N68{R2��8 Bq�" 2��E� -��Z�ua52 .__1�\�$�27 ces,%�*5 { .�*ve�\ -A��A< l�' logarithmrJisH"�n+# @�$� �#ies�.aM$9�� eў7��n( /yH.e��J�6})J�A�Q��O� i�@���Jj��� \XnH+E��8 g�9� Nt %�=� W"�����j��� G!�E� !8BJ8Y!leq~ $)��b�;%�A�-q,!w��Fg��e r��:v�* a� ��L�@�^�9,J�d���b�)m�7��W!�2��=���A(dz5�%{j� =&�F�;N�A|��#7 �ow "���B)�3�:f� r&_��method� <��N-b�!�i�H�1"v:�"ou8$z-extend (�$��,�,9Z�?I`B6B�AA���YZ�hwe ne�I;� % :!>�tg��A{# "r�E mpac�I�6�G(X, Z�aG:z+f"�R F: XuP o [c"�@ , $cA��K 9 R� dA8infimum $\under^N{F}(xAF� _{y$ X} F(x,y)%�l�5:�a-AJK �=Z  Du�"FC�$F�Je:;*$| ��i�� � � _{x,y}}�[ -�aV d(x,x')�1 A,\ d(y,yB \RNAarrow!!'$> ,y#3 �!��6s�X%XcI , �fixed�N�dmits!it�Ymany pDs $y_&�Y y"Bin5& thar nLZborhoooVU�Z\{ y'1`,�,�',yyR<_% _j}\�\ verlap $X6�-z��min_j%Y=M_j)�.� x'$.�$>�.����eOkwC )�$F(6��&�"� .(E�yF� ��k �: FD2%\6h'}i'edQC^�.M�acRK)lE�B�32EtV� t $x �sTx-"r�"�f�jA��a� Ous��BGF��-! N�a �m+I�R� by assumpa�9���r')-y+$�'A*�/��$%  $|'�>�t5m�F og&4�{i�x��!E-�$-b#ar.�U�o� !�RuhT �6� j�6�\&g h 5�.kIf�G �5�W�5a&7i*?' �"� ^%) ��a�3"���r 6��'\o6�!4R0. A�+Jf &Hi�bp� �6 rh)�" FFQ �AY�W1�V�� E�eEeV6los "3,ta{a�Y'eA6 d !�~8�p6;� ����2�3- *7 �@F�T�Z%Z� z�!YV�R�4R{Z�6�*a�fFf.#:R����V�� 2 !e�Y���^J���A^Y51.2.7Z ;MDupEll�\� ��immedia�c��e�j-� h$ is�'�"���q46^B� &H'�(A5"J x4i�s� �'�]eceD6 �!B&} �4$KQb *�X"��#=J~�\ �#ZaG�(!$K$�5n>� �AS- Kf eft|�UjɦAv\E]Ah>C�.Mr�/ �8s��;)$A:U4}�!�*/�h&�*lo)�#r}NT2S� 0%� �)omiZD,�itGbe taken���6�(�?$ paragraph�� hof2T8E��/-% �g >�)�P��Mz�B#E*� Mib%!�"�(=��2R� (U"� �(o6�T!ޥJ spacD$�&�9�(ary*�1no�=�be sai��,�&�4s&4@:-os: 4beyond-�3ce}- >ar-Kb�.A;Asda� al a�2 vVdmR�M-'d� just�5<7!`! ��(5�aoof��>()no�e �Wa�;!�9<1��ziC�eS}),kcY��s o�9-��@&� U� `��e'$f 62d9!�#\^(byvF1?$Ea =W� o\F�0Th��hn��M� a �1;d�� �Zs��.� %�kU�h_N&%R,�o�x\�Cand U(dBG�EB�3!�posA�ame"�7�0--�1AC�gA�u�yA@$U$��Jgt�I�3�:�r �;�/analogA�F�������,"q��/��/��/��/&�/�5��/��/U�%A��d !�� 2�� \ :�1��U0n0� >j e$_NKU_N,m�{U_N}�6Z�"�U3U/./ L �>� \@ m" I���/z�/�)F��� ����/6�/T�4!1*}4}�"*R:�O�[<Z�m&�$(-�${U_M}f)_{M��%.�.M��\|:���_$:  ne�������A�3i�6���6�0nB6J�3�,�b� J� M�M7m�\|��_1��_2\.62|�_1 2)(+�R C*�5? (U_M1�=~` Y7�/" M_`!�3B6 $M> !$ $*�,|U_M - U\| k9Y. 5/i�i�"� -&�/|fAh �!D^*I�.� ��:�oaݑ%� $2�/ Uf� m�  d (�.�"c   )#)e+� ceedR �Pe<;y�>d �&4 ��?a~Ñ�8-�h$: Ig[$f, f_1&%��<� !��% AF����Ill�J�.��  fɒf�uR&���' !"�">_1)GXa� -+�� )U�.{� V��J B`ɂE��R�2ndK&����2[',f]J�z(6��$/6J=/^6 �.�f) �U�A"�Az�'�+Ufa�-W.�2Uf�� -$�9dM > .�!5��(�4�VzW�$A$67y��N� �j/��]vV+V�>V 2��n5�!6��MRɵ.� >?-�Uf�[6 6J� <�-2d=>Al21@Rx6hF�� �SjU&*2 5"�E�uGaxkway�$r�OJ_%7byBL�$!>o#T��b:)b /!v�J5A��*z 2akB n�# ���_���Y.@" f} E2�:of �)= �A0�#Oa��?z� ��a�(� ��ݓ+o}}is�?)%"�i.�[?N.�]�]  � z&w�_ � "! Z�%�95�a>�2E*"|F!�M"nB7?E+�#��tZc V]0my�=�Hrl> I:� o U)J�CN�AR�nB� !�&%�� �.6  ��.$�$.��52T fUCh1k�6 � _{:@*E(8*v}�&N�n�= 0 ~>�� YA��uM2�IAv7i�J.|u�H%� b �K9/�"�Jce�N�L4re ``harmful''�as2z;PG�v�o�no exha�/Lal.�Pb�8[ �Cs 5ttp�O�~y�� ? One�s~{�'A� answ�\�5�pNa�J"�[ R�C�'g�?A��)�e} �%�^�'�&�r�J�%the lR�� lead)�b�uq a�\a�!�W�s�,f�cN!�/pi�7} V_pw/�s)^*> � !�aveR�trEHl� 2qGRg-�t 0l(V_p^*ynA28C=.<& 26�J � 2e�5< J .�$.#�(se$�>�g� �ehan�l�\ll]%�proced�Z� ,s!�@L�/'{L!^a%�eE��^>"�M�is.� i$u.�P,6ACuEFM�sF�M�B� &h3D fvi-4} UB�U!�s���. *} dU�9�H2B!32�r (unfortun� )&�b;Z�0 {'Q.�bzm�$6�ś*�bwor$ax a%�$E_�3"��12 g,C�VHvVH�X�r�Ix[�[�JedQ.$(6�J7&� F� 3q "H �- %m.� 뀊�Kl :�"�K�8r)�*f^{IHI}_�1$�JbD)>]��{ 3"�=}:�i�2�b� &J�؉�A;>�FI]&}/�qA��A؊S�^&"�*1P AP��JM�ue ��*� (�y�0i �08M;bec� ; W &hM��eqzHM/͟2A>>5��40-�J0�?.E9���S}07BQE��a:��>o>�6=���Iv� &+R:{�� � UQ� � ��&� 5�s���. InsC ng%��*��9w-q� �Wu no�|�Z*�VykV!�-e�i9�~s&�*<> (6eq:99})*�75�=p10Q�!> ��[1me)T6&���-.� b�(�!��1�q�:me)(�s���ly in}� toav2�A e.i &�H$ ��a�Z�"�.U|�>*�\\�*&��a�6E^k VE*�6v.ݳ����F�qiN >�.B�/)�*�+�?Vq6W (Z�&^Ec �\\)h���q^]E�^B" From2�(2�we*R^~����e��$�7�jD8 w�r7ldoA��u�U�$"� i"R:U7*$1AI�"&Ѩ](}2 ]�&V !��?, �+*�V]�'A�f2���"%2��isl� *WZi ,*�/��:�FV!`ab5^&\�m�-)��82�1a��^n� bR- �<�}�yM� ? 2� g:�&� 10�EV}=�dv��>&7�E.�*��@/q way.V�0wa4_b�,"M&:4{FSl�E���%0� 1}�d.3#��]hq_{*������d�� qH��>�RW�� $ ��.ct\Z��?�$*g6� <-od� $I[,@f hN&�a�g��(��.MIXRI�))N��0���s good� e)%H�V�\j A\!���jEj�ka��U ��l���-��O���"n� solvWL��� �� :���6V]]�n F�]I"FtY>%%�9�,�I >-=(B0W):$I7>����>f+�J�3�6 �B�A�e�2�.�e!9>W9�h��& 1ltern|��"UE0d�Vf7]�}2� b5�>>]T � �K��hol��dll����*[:� d 2���(md�e�&�E\�� 6�GA�.ȉ�BU#r/F�J� 7}fEi�N�6� 9 � �� � �� &� *�� &3A�.��Cm�2��/ ��� 6�B��v�Aj. Buta.���bc$ 8C5�$��'$nbiint�R�Rno�%ily e)Al$U���W��W@e��inZS 6�CnsteadATd �C&_y atega�a`�cla?*a �_ �&� *��� �$��Zt� q-�2�7) Ce�PO0#>i�stant $K_ũ)�Us��6�&u u9�);well (�V�Nr�� ($L�Z� �:1�AH&Q�0�"�>� n� �+N|��V �#b� �-r| dU�JY �!�do��"|.�M��VuP intr!MXrR�AH:�%i�pa> �  �M�' \{.�\���> V \}Vb �F�10 $w�]Ma; �k,E��2 �,! Y!N2�Z>X%� �L:*)C:N$\?:��I.8�2dUF",��&�����aQV e volumq$J��-�ec�A9 Haar�}� JF6$��du�<$��^_5.5 openE���MI�i)ichoos�?"*g ?M=1�/2E$�<EG�B V.�NZR6$ \setminusNG } \hB9{-5.2ex6]NdI�fb 29(�{.�,%B0�Q �U!�sQ��b7<��k_ 9fU \not�J4. T�w�O�Om9�Ct!�&a$!��9mwf�i�ppBza�NcR�:�@A�2!zN�*��9F�.Ch6��$��)J-�X J2 �jf  6�\:�y��%\雅�r0�>� "�/��oe�y 'u*4E�2N#of� tarW � h:�2��.���6� �l �n�6y+:�< 0V�� ��L&�4A�-��nt"Z Q c"-y ,Rc'S�� xs Z�+�*!b�+5}r1a�� "' � � � :M6� . �#�6:is�nid��2I$*�aa��T>�] 9"�H�:D�i6M�{U}f) >(Q&Ib�R*�^}Z���> � N�.�S��EJ��|� A )� .�9�#�Ҫd.��A�,$ very��fulQm� to �{~Gm6��d"�?orE . Many�,min*ncandida�XT)$i�&�E} �:�(d�>Z|),2������2h0}-�-eZS�|6`"c�$��@tP$s. Impor� (examples ofu�Ew�i&Desv �u��!�*2?rJ^��a&y$ (for�D+c`rue�'l��*�D PS}$):n�%[�-ʫ�y^�fr�@�i�'UF� �}w��&m3� :��^*�Tf?$qGfT6��!H!�* *(6"|)�Z��}4 �3a2� Os^  jB 5 un��n�Y�C�|�I_U/ $I<�&�N f%��!,.8ՉU�U�E! �  A;�Cl.ϮM�6p��&o<��Lbt&H'PB*���)��$�nsl�R���^UJ�'���(^U+A(^&�" *�"U !2) ."OEIa: �T' �l�/"�f� ) N n*�+ !����� r) &�WJ9 [.�>�#b�>g(U �jv;�-L 6�5}2ni���J; o66.���5RT��a5G�,'�&Pt.�� �(2He-I��H� ��bA��1&M5� fgI� a�b�_�1���"> a�!b y���Sf.s�-G *�t�+[va|jI�>�a� trivĈ�N�z/C �Su�"'iscus>H�tis�y:�-V��FALI,]�:D:�s   as p�W�a8� <�h�EaO�ѝclo~{. N�}theles~@9R��s ei���'�K�!�&ۀ-G�g^*5�E}(N��te�.��is t�2�J*��Q���\"C�aa >�/;IB�M�,Be an i"��IA) �!worth�wingZ EKthef2ba�IaK!Wtpl/he�{ truthY²364Ge���~.4�u.�~�p �R���Z�� e�!|& aF.N1��B�s � mУoolA6!3� A8�,u��i�2V�E8K�}&8�~thm>�/E��[�0 $G�� acts�ji����n%��y7 , se�Nble|Kri"(\X���G"[�I (g,x*o�=g(x?�!5 a re��en(**�lK��2��m���*�POV���4b��X)��.�p� i$)5�Û$E^EgɺC\pi(g) E"V ^*�^�k .��&�� �gG$) hm�0:1��"?�X f]E(d#]t_G�D-_ x_0) � Q݆�$^* \mu(dg)m��J�x0�[� n ("l) ˃!�, $\mu�Ohe�-=�;%�!�$�b�B�a�6Et��or9�uniquA�:��*� >d� choi��A� x_0$1 a U.;3�qj�4^(icE����ase��eaN6N��.GiɵtrazWeA� a��'di�S� o �� ^fibra� s.�&,� d�5 5�)o��|`s�P�� ���fiberm�tely. (FD�������~* frR!ރ��-�XL�S��|.�&6��.)"[4!�q�N/�u��V�VI�� $E: u�E�S}R).6 �ki� �ormUu�QF%.O0�m�",� eq:3�`*&w�@�E�8�3[� {U(d�.pE��( \֬T*rh�q_Y�L� x�D�B1�hFdy�]&��B>�_Y��M���*Mof� n-no+�).� s $q«�3 �R�_Y�=A_di� E�cI ��+>B�b��.&�: R�>�!@�.���)�TA�U�3  P*�:ce� J"$@e�aR�[.)K*�9� bigofH�EdY"�f�. O �~1}N�� �exa*Э��s�{N,Y} Zw>S�!��(#�%$;u���:3E��*�) =u=>^*�7/ ��$ ��EA� Y}�$,Vo A�&�&�|_"�&�>Hl��E_ E,)R)aO�>2�ao2�a>y.�/�e0*���A�.�1��fv��� :� ���.��ci�p�>r)\A�"�$q.��$b}"�%o9~i�E$�I��! g UUassoc~-�:z�pub� �9!: "e"�" rho e��i���=hoet0 AOZL �ahcs���a�J i"I%d&s�"U~6r J�{ G_{?_xo� �.޺ \}�U�6 ř=�� We ���J�i�f��*��U�o�pat�À� in J$&�4 $5�UGX. 6B��-,2�"q��� $ &ciD�ϫsɼun�q3$�c#}GEHJi� _G) fs�B�gU�ts&���i[ %���� � E �� � bundle^a��α��a6I��m.n�Z(``sl� ~ '')� o�ac!� $-ma�Glds��.�,Jaenich68}.}`!b� �_G!K{s%H dh\�Qs.{% :�6 \};�J�� similarlj �$�T�bi%�Gɪ!�A�#�s( �_G�B�W�~ �_o $s��R$x ����]� z�8ly homeomorphic��a�homogenes,# $X��N / Gq��/iFaH[rWs�kPhi_G�� �"�� I����aJ� _jn6=  u(x, [� ] �N1�BO+V%V &V> .�_G\ \0�[V�NX_G� J�9 *��!f����ert�k$ �Boa�ertwin/>� �� �~ $�* [UV] a�*� !vA�!�3.�� ��~4��.!�&��ne/�$n nor clos�QV1Borel�� �)�$�r�>pr>�d�i� subu�i � ary)"'����o�o" &�EH�F!0�m�A�a0:z ��0-��54!�&�%e�P$b$r��^�vסּ�6�!a1'��- Ym��)[�ksۀcs ���E%ted��w�down�9ȉ��)�)$.� $> _GeE{� ���@ _G �D,c}>G) \�G�dF�A�# �%b>I �S:=�<�q �&�� ,� G"�=&�2n�-!�$EQ��&���� m%�vanis�$ -�teA� �reu�  $E|kbyk%:%fxxG E�:n)`�c�Y�!�֖)4&D & G$2�In2���lc�R��MZE62g;��tif~�!�S�9:�\��X%h�%r%a!�MMa�]�FB)*�" F!�R �� >Jn �g���N�#�\c^G_U(x,= %U&�IF�eJ+� � 3 (� "M *Z 6"Z E#��m�EC�"MZ ^*)6� a�}�F�)���� �Fk T��� ����>��"��F R�5io�31�)�Sw�aZi2!Abelian ́�A� C}(XB e© oc �r�c�%�E�5$.v$h)8 g��6 2d$veRnmap b��51U� ]�E�kY� tild�L{G,h}(k%�O �]��>x) k(y)EdxdyQk2:b�P:%ve.!�M|�6��'�a&:�k:T A��j7=z�}ԅ% ch�ks>9%�*Mb* X_G}1J(dyb^(�" .�5�� n >�.� $Paulsen}).�1"�63]| �pB%��'v��we %d�y]o2�6}�8�?e �v or�G(hI��0 %P�e�-!g [U])���`d cFS�.:Q disguished � $x_o�gB�I6}�in � $") a�}��"[>Q_Y%6� �:X5� jH�8Ju)!�n.an� gU.i>A5%s�.�e�hu�Q(h^����4Fk~uoZ�Q)�`B��V�Kq_G��XR� �/%2e"$.�6{j��e�f�eR�=�D������.�X} fA�� �%Z���0&^ f�p�$�y��k�uh(�z��$k�> .�� 6O��/��;oI)�u*�#� ���^-�=K� "��I'�.�2� x"�toI�� backa��o�E� uC"�n��"� & &� EEE�y����a�Q\� �>�6�Z�E' a&bA�)�E� &:� �F�~.%x&� c ��I>q*� + w� cap� 5�s� �ge�� L!�F� Y9Z35� "'"�\�is ��%%��Noof $���*k. Τ#.��An_����*2$J���rm ���&Fs�2�]v'Ȭ�obigeH reduc%.edo�n � �p@focusŰatten av.&d�Fc�I1(O�F*B�A��We=2�th�i,m&���in��� ab� E �8rV��� irO�In ��J&�}.Tr)�M�y��#:A;2C�_.14�1E_��ˢ��%�7$b�!�9�M!&��)e���!. i1"�X2�  corollary&�%cor5kor5D�&��qV� B.�*)_l�U�)��*�.44�dbbelt?:N�3��3� Z4����{F*�����N��2�- (Q����1}6�-.dU��'Yi�Be@.� s� �23  cor> 1KY %IwB� A6�q��e�V�22}vvE��� a�b�Őq!���Z!� �Y�} q_{YZ}5i_{Z/N86,�!�; '6=Dirac"'luZ/m����oA�:Y�,�D�?��f�~�j�j� Q}_Y2��` B�}55�R�`z�Z��6�".�b���0�IN�}_&��Z�� J�Ew��=���l(\{Y/N\5��>�V�*%�W6�.,.-�%r . @�q��$K$ must����!r�)�q!�:v$�Aa��! f��5�L�a!�=c�� @"��Z�ich�fvq .5�� ��JN5�)F �RD�,� ն��� �(sa�� =Ӻ E8�`/A tras�N�_and�� ce, "N�Q5 nVq%�X"�<`�a''�r��EE}.�!�*a: Giv�� �]6]�WK/Z/2 �1�� ?i�x"�4MruXJ�^�6�) the "�2a6(U�I6�CINqqc�? A�cbst!ugy towa� aA� of m>(aDto�qd�?.JQ3����9��9����A!�21 a~��?6 :2 �  7 har� ()[M~n'���M up�now) T�� coursF�7jdof}"a1�a~�N*�N�K If�accep[N� n2�2!b!~JNռ qC� �+� <D)4:e.��� = \dim� �'����>�c"B�6Thi.�� �!Iꆇ�. ��ee (h��8� ) wh�� h� ��kP�  -A�$� �a`�~ul���$onal NFi = e^/�$h=�$h��l7�h_s�$h_J��h_d*ahat%�$ai2�to .�{W�o���}e%Q ��%GN� �4�mBD� get -���=��we��6E .t%!��ZieF5|]L1 &ve&BD �VAh-Am� �*A~"�eb�\V: Q�]&>(�5eda�-`)�> aC��#s't^r1����$)� .%��m7%S �6>on J ^��e�ʥc�bc���'N�"�o�?�YC�)'Y}�*���%:i�re�b �r�� itsV�P$ �u(i 4_���s"�b�Hxp(+j��h_j� su сf�)#��ing o%#!�l�s@w)ba>: expo�@57�� (orJ$ay faster,�t�r?�s*#(�H˭atrix H�L�����\�A�S�(ͣI��LrD,J�.�i� N�GX AAQ\"� 1� �0��"2f6��a_���A_���8_ �!7zsketc�63��aރc{As.EM|�� ^9 lap &�� .��!de!�to<�st (at ;�$polynomial��_caA�R�*�� CxTmak��9as�:i��$�B�2.b��-�)9Pv2��3}2D-�)��3�!��I� task�7� veN��I < &�%!gJ��� � A4F{jNVe� R� ��HsY�V�� ��\�X%�D�;BisfQ �&�.H':' (�-.۰��*<` �# �+{ = ��-��c] (_6��j��d�� ܙxo�I_1�J ,U,x�/ r�1YU28a�3 d\��jF��j&�^���>�AQ'*��.6m"7�_.\ D�0u �$ �.�!�*�DU�*�K� [�:w�<-��6J(U_1a_xU_1^�/U_22":�!�9O_1�==a_2!�A��'2 h $[U��x]:~[:Y ]o �� loitevre��A�>`=in�7 $k�Md t��4s $1 = j_0 < ji�fc� k = d+1.� !�j_�$��x_{j_{ +1}�Fx� ,0�)�  $F�j.K�+% < k%]�L�-zq5=�)Zi Wamk(� - 1}m��2*��,B(R�F��B�Mg��UE�block"� N�� :U� U�� $ U_{k-1})\�ext�1 U �m ,.  ),\  E-)+%1R�� $=�5+��"Va�Bas�7�=�"!�. $)�1I6  E *��8�l*V�1*�Db6HC������6PPU ���2��Y2 �,���$x"� wE��ini���CJ�6o��,se�wA�+1}Q3��m�8���9x j��m"�D$5�a��eE#nd�lh�5.� ) �Sup-��: $j�7j$$H;.W 6p�#b  �"Y��_2 ލ��d6%/C��BI  C�2Oj !�h!�R����A�.N�� � L� j2j$.6`j\O�[Th�!<4.3.15]{MR832183W��42Bk2o� tra ����|\B8q� $k=1�j�"t!��/�Fs ("�/�u� ��.� �i�;� ^ fe��+�� �F8ž �55� �_ji>�f�0>��.v��" >� �"��JA h���j�)BB ExpGO�nlo��Z)d>)huffl� ��!:���bi�2(��j 1&B���Ul�V if�Ku�&� &� �\si�%a�4ָM!izF2�$�0�*h�_��E�i"jAb�D *����"��da�9ty�( ribu�!�U� �_I���8*�N�� �� a�!.�Nf� *�F&< �!Z�"= %"�adJ ���'!Vs1}ajd��bHvQn*� &:$)!�.�A�"� :�>Tc�!�s��2�fBB"_Ns^�M.HMc��S"�r� rM�r6n���B(qD)2MMi` d?kf�YN� yrB��a8�t* (�s&( x$. Li�r%M� *&:��f&���uTiR�1za��(2�7p�dRd\ \sum_{\Y \in \scr{Y}_d(N)} \dim H}_Y #|t_{\U(d)} e^{-N f(U\rho_{Y/N}U^*7,tr\bigl((U^*l U)^{\otimes N} \kb{\phi_Y} $\Bbb{1}_Y @$ with respect toA6T highest weight vectorEH be expres�xas (\cite[{\S} 49]{Zhelo78} or TSect. IX.8]{Simon96}) Qi1} =I5Ez)�)n��!@rod_{k=1}^d \PM_k2N4Y_k - Y_{k+1}}m�:�8set $Y_{d+1}=0$)Pr% hand side!Pe@EL makes sense even if%Oexpon%�are not es,er valued. WB�refore EQ$(\refAg 17}))��Lprobabila� measuren\19%\`int_\Sigma h(x) \nu_N(dx)!I$frac{1}{d^�sum_{Nuh( *Y}{N})�u dim(�ˡ�)e� a�)i1-} to get�m5��FS��\s�)}&a�a�l( �6�hat{E}� 0�sr)i�=&�'�%�#d^N:'x�#zVN(x_k-xIV)} dU=L]�7}�� \exp �-N�l[f(U�_x �@ -\ln(d) - I_1(U,!,x)7r]4Œ��20J�1�9� \ZU,IEm[� - � \lnl[>tr] %\\>�i� func� fromN�8})�we needE�8}{d}$ (cf. also���({Duffield90!� �� Obviousl)*a*uct1q-p�U\R dU$-\i LDP ��� same6O(. Moreover," U1�e argu�ܩ�ś�iial#F� 20})K continuou� $x$ ��4$U$. Hence we 7 8apply Varadhan'E�%Tto^^IR� lim_{N \t� fty}-�-1�BA����&����}��� ,inf_{x, U} ( 6Z�A�:[ + IE�)\\A� &= -.J\leftFOj�>b\�Y)�� whichATvesU�U�3} for> de� �ces. fN *J !�Lhas rank $r < d$. ByQ'�]i� rho$,5���6� and ��65AjmA?� q�uս�68a��m m =�x �x ~�6 m�� Q  ae)a�:� case (only differeC��at5%�*; a\(vanish now,!; it el$particular%�all $Y� $� > 0$<$k > r$ (because,minors�]! _4@any $U$). Instead�C9�d . � get5�"� .�*X �J�޽ av=�{� _r}�r.�.�}2�rJ ���"�{N,r}����� 2 B��/Q _r�{ x�  \, |0x_k = 0\ \for!�k> r \Fva�Rd� ="� �~f~� r7�� .) yNoSM�]�betwee�3Y �^ �$ajusi summ\ overE� Young fra�!o, $r$ rows inU�$d i>cof��]�8})e}stillqq8a�� ary �Dxa$� a $d��$ �,S4exclude %\foot�{9 �8M}$ does depend��U�= via it��$.}RaaM}!�{ UIgaAaEf� r� e  UA0\� 9�v �domain!2� r)�!x out chango +� * .l�<9' FV9a-A���+�+ !Z}# )"setminus� M}}�v rF�J>v E�7m.�8� -k$�_rQU(Z�)EopMaO�cR 6m_I_1-*� on it6� B� ' �s proch v� %�� \se 8{Upper bounds} Vsec:u-���� % I�i��� w�L provDa detailed discuss�of �l � �!� admissibl� "� ����X>a�proof�-�s&# 5}%�� � 1}Ҹ \sub1�Hypothes�esting2�h-ƕ4 Let us start��L a very brief review!Ssom�er� ��quantum � � (3 9� =�� � \Helstrom,HolBook,Hayashi }),�,it��b�@to derive relatedSult�r !,��$schemes. A%�st? !� task�J�!zk termine a B�EZ($N$ systems� JP, howe`we kn|�ori� � a fin>$number of ��t �s% occur. F�$ur purposA�t�sI cienhdiEAu f4twoU�_0�_1 "�S}�i wPbe done by an observaaOo$N$-fold- IR��%�!rs�$\{0,1\}$, � coi}%`* outcAv$j�Y 4).K!*A�prepa�Kas �accord�Mo � j$. MatheA!$cally such:�is giS� positAm"F $A_N �B}(H}.!� ,leq8�A\tr�_j.6A_NɅ�.Y�reA� $0$ dur�aA��� $N$ M�LMjoiQ@-�2y"�,Ae�it<V alpha_N(� "td _0.�(� - .��,),\quad \bet:G B1.B7> �error=)ia��Acis�$2���:^det�I'(1$ although,Mg >gU& 72�$ ( �m(first kind)�,$.�R��B�0converse situ/ 6[�\. IdeE�0we would likeAAa�� �minimiz�-�0$ \emph{and} ��is�� impo�I� �4always reduce �,MLy � exp�-��r. A R solu�"is%�lem�to �>@as sm� asa���under1D straa" >re� s*eda��� $\epsilon� cor�on�\%D al (.�B�y is t�jRj i ^*(teXinf \{6(��� ,\ 08q .��,\ 1�i�  �\}.B� Stei�  describ^behavi���F�$��limit $.�$;%�E(um� � hown in 1@P91,OgaNaga00}. "�thm}[Q�2�];� 4 �5 any $0 < � < 1�[ed�: N`f^*]F = - S���g0�6� W���� .K S:�K� � -t� -ref!&1} �L con�3(w a (full) *x �  $(E_N)�f!Bbb{N}��Onem�m� *�� ��� p�W $��So choo� n`8borhood $\Delta�� goth��S�E�` \not�=��tooaܥZs= E_N( ()$. If^�A�%1stent{:b�:�W .�>�va�&m Nn%'��u20��a� on� �(b!��lE�.�.�"r�Exploi� �idea mr careAy leadsz��"v!W.6�.�2a�CQra *�map $p:So X�to a lo $compact, sD � 8metric space $X��optimalB�o I}_pz�22}�X �in#�m Jn�eq:26� �l%{,O��oI�E�p^� (x)}�s, )w I�a~� S}&-SX,�>�� $S�|���� 1 entropy2��Q� �� each pairE ,�� of"f| sQ $ �_0N eq 1v ! find� equedJests $E�Bw��� 6� qan� ropr� Borel� � bb� A-If VaX�s a 6��o � 0)$,A�s�cyV(� lIIat.  *�0��re�can�N_��%��s$  jgin*� Aw %; = 1 -&c��)�2 �.ie>S�� � N > �"� 6��ie!�MVaL8 .913m9limsup%�r��7" )2� %C=&-e�>.R>[�<6 $I.�$I� _1,xa%>Bg�� rh� �M�Y� = x_0�81m{ . Siaev \,\cdot\,I�(lower semi-��weq�clo�%N�$ $hY� �n�� 9) \geqB =d ���m�R�]�6$ Q5!�>�!*��s%�$B��e�n�*� o*-�v� &E�-�� �}.C�(�#im�q.� Nb ��!���b� ^�)%�.�91� �p5Fin�ctradiXRb!13&]Y�eP%.m�2mS��iRfJ�s ��A� �.�!$ \noindent�P���2q}�xwe��l%#iU> �f F� s �+X=q�=\Id$)P �D. $ $\m;� !��S [J�� �a sA� $ollary.\hf� $\Box$ \v� {1em} �# 5}.}ra �*�,B� `B[P%K"�2}q��95#�h&� sO#=x}I0-)$�@ . Bu�infimum��-:c 8chievN&c� � � commuteCeigen&|abaYD��$s%ord�In s*v!A @V6�! �'j"q&�#\ln~&�# r_j\�1S(x,rB�i 5F = x =(,1,\ldots,x_d�s��% (r%r%/%�edQ aT"8=R$and $S(r,x��!V classC}B� M).� �,s[`x��Q�.�CV"$besP "�Q)%U�Snl(-,xr�  ��lA�  �KWEst}A+�lread���"�=+F}N� de"2)"�4}) satua�aoi�; h� $rRa:symptot!�ly� ,@-/�� u�5}v{If�aC look�in.J$� ul.v,%�method6x!��A8 �2g�$be im�A�,ignificantly�"1 l�*�_>/!4�&=*$explicitly!a)" s*7 "{ ,!J\ reat���next &�*�G*�lemX .�: Y"R�)y!kx"�)A�$I.�im" �)[0,ety]��>H��2�%hK 5$�R�of&(� t<%-t�,� b� g�ra�r :� "] � Z� _N"�.� �Q5}&.R] �$..*� �lfm�^ =z -L3�22�&�jF|.��(U� _N�.�k�_N6� *�#\ \text{d#}\ [U �]&u���A�"[� *�$kI=�iT)�V� tilde{ �}�&� omeg2m �\|)��1& \|_1} k��&:MZ�n o"C-�*aBsym�y��perty�t28� � +Lj� ) � (sr��ee�k��s direc���^D�i��def� ����DI>�a= dex $N_k'6���N�]z4#4&�)�F:�ux� 1+(ka�Eh.!*P�*N 9�An add)w�%^�IlR��.v�>�u�S_{I� 7%2�J, $R�b- mbin� AwV4C lT�$f^K��nI E a�qƁ:8.�\�.| )Ҧ&Z=x)�= \; | <%� �1}{k}E�6� %>ZA[\l$recursiv8� .  a�increas!��N_k)_{2}��(ers!� $N_1���sa���max�A�,{k-1}+1"!�rU��N:_��for}\ _��eq N < NG5J3.�y�$aw&��w�^te]7$li�(�8 $N_lA&ml+1&Y:�l&MB&�i2b �l'��du�&> 527:�A8y�NF�-]��.�Z36�l;Fl}JkV�A�#�8Jp35ɲmilarly!�%=& pN_l''I�9�!� =6f �"Z*.7%E!�f� 1\�BN #>:u�=&� ҃>�j�:+b�����!�as=�5T ��L钡��d1 J�forms :� base� ��R $,{pr!$9�.� )~{N+1}&f N &* &�I�t@#\$9cap_{N �"ty&� = \�\V�L��.74.I_� (&g =�6{m"i*>^�� U� ^b Al(( ��-� H &rR�48r ^� m-2�މ[""�>a $M_2i �$Mi�M_k�2�nM5�U�Pr3}�U}�2DF� &�.�I"MF"/� �!I}6� �R��2�Aͫ�S,! \}�<-���J=47.%y�e �])N�U:�\�� \�k2kak6� �F� �+6K�A-:�Q �� 2}*� .\I�x.m�J�9 -�'z/ʳ#={Pure6�/pure-(s�$�1m�2p�,a���s z�%to��/"F36)� �claim�=at $^I"m ��I}^c_{\Iu<coinc=0- � inpu\-�!�s�D/qu�-s!�e.?A�0take, "�-a�(det�-)�allows`/to�a�r4 bey�C��covarian�.se (SP %���% /-+ce})."�/"�0$a �%�[!�a mixF&�kFZ?1BGDe *�= �F%�!� 1x!��L8fty&� 5��.� �� -�)�^\#� *�<���32-B|)� J0vcBhat{IFUi�6����AT}��$ %yg66� �5�/E !��W)�1�p� both%�}�@>%�/i 3�CFo�*r`E#A�mu  ,X�E(unless th� &w0is./E:d�G�:E J�C30!��A�H�*%#si7 .��E�Esi��)�H:|\|= s 1�Y Sa�>�Y� then"��i�( structure:NjZ!8C[ EP �� ��M(|!�G�,\��G|^2�B�6���we%�����t3+�aSG=-���d8los�4g�I|&%�A}*Js $&�"�0��+"�E�r�>�- proj�G?pJ��H4�!&�'n>�5.�9�E}(\I��aeI��)UBhi}$,$m�B]$M T�?��.e Psi^�$normalized&� 0�62_+$ (!Sd ic %U(� cr:5$)��5"����!Q{*�H.�, �M�Y�U 6� 5 6� �:g1� eq:5I�:� �%�e.��Dg>~m�i+IU+v�Q( ,1��Is2e$�.A�:�Y���^���theA(��a"� N"� ��x!V��%�z�lap E�:�> $��.� �$��:r� �~,1����%:� 0uppor�7bVey[ tens 4FCB�.6 Ma�/lambda �/�*( ���N belo�=�L�val $[1- b,1]d*P�< At&�Fw!���6a�*H6.�"�$ao�X6�,*�(: ma &�#>E2� ^E\notag �E &��antom{ mM:] }+ (5.�Z� *P62�)f�\[1em]0 &=2f+�E^�6d^c�W��5�F� �a�6 9 ��:4�R&��^;�  �0 �+J'i&a�a> VB,zK5K��LT �!ER�V  N �� wpKf�;!�;��2YB� \v. 0$ (� m�1�.H54�Gs true�Ocis �enough)z441 ����V2�>� }{\|r!\|AgB5��"l bitr�C!!F�7�.�&3 ��*-"���"�5q� sŲ!�V�h2tF�6 ��E;Ri60F�6 PjpT' urn -Е$ :W ��� > )�.h��&�R��+^u.N2u��2�-5l&A��~�rsͅ��,�("� :b4 !쁐5���.�U lasts8� � >~ !+ t ��fF5>/hc/}$  Z�%�� �:F Fm�by!� 2:g Z�!to�&,"� as well�{� .�?Ji�"��>� =6�:=�/>!T*}\>OE�u2�a�&K*!U�/Ud4psi) ��� E ��ٷ4�IIuC easyA�se� = U.��#h#?lyV�3Z� ���6�%�+�& Wu  DnowN=y��@�D gI�*�3��g. KSE �+��Y�G"�49-�)-PS,�(F�!�U4D*!analy�.of& �h.�/�87T8F9rL&�rop"�<0}.�!T*i)�8� �E�AA1AR: %&])3�=I"}.Va^ ��s�{�!0{.0is�}�� pt6��X):<! fe*v�!�!hi%b9p'V�� ۅ����Q}�6��J��)�rh1J!)j�Fmb��[�����b �Jla���  �n5�6�=R�'f ��ts4���Z:['>cA�AT6"��< j�:�� |^v�:OV�a>q* N�hBA@ Toge!l��&xW Fcan-�.-�*}� )G6s �con��!v ���1�JcIY�"U�X�:Ic.;�LLB/qPce2LF � �0�0B#F�� eQ9?V)t9� (o�)��e� � we m�^_k)X ́�notC�1�[ed �& L�P$!� verg�0oN~JlD._�out furEo� p���KI�/� �`ion*�Kis wrong��"�3>HQ.:> $ �3�$zm� orthogona�20y)�;n�Bu�V�,5ihis.HB%� }$(play a crucKKrole (a�Hit�SB) �Mmei3 "�D��iN1.^�>!ک� #>Y@�@A(�- %Cion. A�9a yet �AXKivn8mplet�^K� � collJMQ�!ome (in�&al) argu�Ks-��w!���{> = S �:g0�_$ ��Mend!`��� �N�h�! �"5 ŕɥ, �ew-evalu>Oa 2�"�82 )^Cly ; ����_asi:�.�e�"I AHP two-dimen!�{IE anZ�Nm� F�y�weWto repl�CkF%;�3�3�e�� aK s&rbe[c"� eq:7 �,% et{0"� ?(phf{p,�AA/\sqrt{� 7 + e^{i! 1-!1}� �WY6p 1$,OFS (-\p�i]��a"but fiI"J:$ �,  �,i1LQA��P .5k,�c� )�.' _+�+.0�9N$V?K! k;N%binom{Nw%�(/2} S$0a (N-k�Z�f 1 kB9(�$S_�-�y��Um!��R���"�f��J A�� be fitenAn5�asAhw r=(m_{k=0}^N f�k}jet)>>*�rE�.�$n�:A�.-t6�>-< �6�%�I�p}^{N-�E�A�^kE�kU��,N}� 5F%%A���:y��H%U� Aӽ$�seO�v!%�f�F� V�Fof2@� N� _eCn!�?}@�O*� . A&JOway��:: �cP��s9��steps"�"iteP} \ �q$Step 1F?�29�Qy a� -2&Q"�� 7� Z�.t�6sF�N9,�N�4?%A2��^-a� b�9Ub &�7*rF%roF�rh6R9 �I^ �� ) > 0 ��8M<��>v �%���Q%�29˺�;!2_+R * ;n� shrinJ=�I)�-. $2� =!)�ei�#I�$#P%!ize} Toe�-U��Qa�5SW  |Sa�:�1}KbsAVnis (u tung)� q vailv , @�R� � � �No�R�fb POV�U�B> A_N$,�2?�V ���� �9x<�)LDP�i�W?Vb c�W�JkTt�ms* l9 s� rTchnL+fn�X unda- aY!!� �u)�A!\s6�So pero \"�_HQY�t 6�X��]�� L( .W@e�j kJO&6 F73"+�V!�(necessarilye}�R�@Y se.};:rq_� ( _{q,�J�Be�� �" "?74�4T�(�+t $A_zXo� �7"12mPTfbyBY;50�&-xN}] ��  1-q}� ̭�;1;' 9qBk " }'�F���t M=A gl(N�q) + q�2 � ����k��e�I�e1$.2�#. N%j,�.S9�T|>�� J��%jB�*I�wa�Q�s=�2AOB_e�h��u$:^�T�E�L�q �Uu�8� \neq ���.��G�Je#I�a[ll�;|��^ ng e0KLbehe��&� P �� �.�  (atfRs+O�.�).Q%��J�C= paragraph8�rasa�*2�6y"\+&�PA�22 �M�D&29�i�:ZF��f�Z�6 l\e ny p�[� o��count���&se�e ['�)pP� %3�¥����6}disy �]% IBa�1�2��iq�5A��b1c^�Q5= U�"� i0.L7 ous.9ZE�,O"�!hO2 �,%i aq�� �a.�,1�i� g`i$G��a`8Y�-�F*7�$5�&�2 . %I.-.why�0u)& diff��4`>;^v��is -)C� �w ��i)CN�GՔe�:q 2ec!ax�Yp �)%ue7a�n� 6�/JkF[ �!&.��B�*���*:->)�Ua�R&s^hirB��p_16� >-�S ��'_-  _+ piTl �%� 5q_+ !qGR:� # njb nlJ@identi�r&+.T%�lj( circle $S^#@U.#*-F�/� B!Z� �;$F��ULz(S^�OiB  |�<F}_N\|('Hi�B�%()!� 6��B�I����R(e>ZAZ �e;�, �(2\pi�vi (i k�])�! ese ��@V�9_��E\9. ine{�k�i2����q&� �!�Fv�.hzA "�cfr;/�cbs��N�\HI/ SP�B%T9nk�02^G-lN�.�E��2)��F "NA J�0�&-ZR���>�s4 ř pB��3et�� �)!�fbwse�$+  ��wi�?�|�zi�f� �0C P�6iq_��X %l �+UL"nuE��rgT �6�euniG on rsF\ u. )��]*� is�)dumCkf",x4. 1�O2 A5" $F��U�$�"�]� �r emptE��2>�vf�:Cc�ly-��� � a ��(� e fa�}�� smog8mp5$q=J!��8&,%+an �#tic�o����$�#MR16450�}�d�k� For?;it��a/S)�ao�| �c$N-���s $\|F��=1�1�d�7*I�%A#i&�d% �B�F� Qns (in�)A�44n�;5��O*� %�$F$� � y ag:=�\�, B<aM$F ���.�I-En "_6Fu��8�oI�]�oPq!p�%�e� i�;�:r�!�b`��P8Q=�T�jGz�oscill�� %x� �"I$ (2�l5� ��C$5l%*shift�qM�8;!�FD �A). "hEte���A�al ��ir_ s: 1+ B�$ (!�DU$t" e J s �$)�HQ�I��f� |� E!�$N |�0}|�( 2ԃJ8F�b�g$) =0$ must� !�I/a�=�bb�"#3p .p_-,p_�� for � � � p� �WwbIsuc9q�?o- uctEt�_$()J�I")L=^�t JaM �w�j�#!l�T��ifhNha.�6��:�&%�:. $2�:�>�:� �J > \� #*�  $,ui06�hB�X %�develop� irreg�x"�g��he�� a�ve pha&�"ndicao�a!��!��ed��);.�$solve�%�:ap�uix�  %�� "sSynma.�p�3d��� eory2�%A�-7-� Ά%���:aC1@A�e,�"��ab��:�AOorym/i�B ed throug9%ɯ pape�p1�`I sent��aGref�%$a�konoQs�l�iXEllis85,DupEll,MR1739686�i�"uR1A$A&nVXB�UY lb�e,�2�e�(fe<2#vifY nume#\v a���\equiv�C�.$p�P>�F+�Sc�f la�r"�#$I�� l([-�*,c]r� <��c��pR}*?s�%|"�  �!��Wt$(\mu_J�,�M��� .�'*l�"V�B B~e!E�f�X:�m+e�bleF��|2 1�":�$8s�nN�T1�lW_1�b��ta\ML>v"�=�:�� 2�X��Ն���old:�v�k � �c)a��b! \�E��, Z"�$QiXa ib�e*�bA4Q&��@>bxi, M�|6(�jL����j86b��5�O���V{� mos-+lev5Hon" � a��5>�A��`of r� �  66},fde^�o�J�qc��x ��!->�o:�:�n[o]!\�$�17!pC&�k�b_FTjF$Xq�t[�argA���y� �(�y�2��Yaa}�0f:͏��R}�i�+Bed%N@w7 �}�A�2�:A�>y�� eq:1�!V^ �]��}E�-N f(x'e���6�E!� �Il��xfIrR�hE�!� 1�'�E���%7�tC w"y~N� of�$�1�n`&1���1g*$1�sc�7!{� �! g��e E.R,a�F iX�5s*ya�2A�'rASZz�b  M�2_6�.�  %�b���%*��La]+>�aUR "I$,��);J����LV\%��E���&A8rUa�E� q��)�2 q���^��B9 m��R�� $s�e!hU�"%i�e�* } " ,*{Acknowledg�#s} I�Uxth�IR. D. Gi�; R. FA,rneQ�m�us�q�us�-sA%M. �7e��f��oE earl�#�"Z0$anu�� pt. Finan{v/�PvecRbf:R% VIL>6d 4t{d}#1\,2� % D�V d \.�c q"�:�% k4dx konjugiert (durch �ber ],h) \def\la{�} ra{:� !�a_title{�x#;.-��+ repe�7 er)�e&!,a pendulum. 0AK�erV16x�en� 9)is �sEe �,�^s026 hird-�V 5A did 5"|��e {\em b:E��m�_a sor��  !$or rapidly9��Ax!w* -��in qu�.L;Do��,Yh����A�� &?y<�ed [�.l0�ir�A�To capC*�.k!��d5 0t was suggest�DaEgHeMu�AG8i���(``�x'') �twoE�r�lisbo�,connecf0�nJ��^o illumi2�Q� reg�?j,SWq'2 y!~5�ent`g E laseCAll pop� qupper �!��#� watc��J�1pontane�� photA� DF� ���is $O!be#]�8VE�al ;e�i,�!,�tle �roxȋ�"�!�A�ai�? F���Y�&\�lizE�2�m� �]T�% ex A���=a8�- a"���� sh�1be flex]�e�OEaY� vce)3e .E�(�3-ideZ-p1�� linka5th E� m�tf*Q3Ƀy�$� %zluoresc%-ed �%@fOh=�����p dem�!�B: u�K.ո�iX}eta�E.� �triqs, xa flux� currD ^�!$Kijowski's2B, Elbe obA��ʹ%� h �A��Hd  D� ,HeS�3}��P��� �d� �# !X-�e�T43,NaEgMuHe:03b. a,RuDaNa 4 | Na:04}. I�$ulh!b�/ rpri���УwMa9ql"dEƩ ``(5�= s''� b ] her A� eme,�c�����aD�6 % �'A5ũ"O1�F(�@a��^one��ṁi D ably��st!�trya/ .K &��E!ve� �1A� y8+c2C@p!�at�!6��� -�o farA6sI5nreA��� /�ic moXto�"� (1D),zoc,�d &�4$��xF�0ereafter, per~w/}AX��(travel��wave) dq�,$RaT�=ap�+�; i.�!�ba��w�Dy  '�m;al veloc`hA on� K!4cnt���w-r.V2� n2&�B���, im��K E]o�nizɶ.�1�to >^"�@�9�al �packetA�i�Y%�Dne ($x=0�|s s��"�-��d���4>4r a�)& �($x<0Ba��Ba�͊e="�"o]�1D�[a2be at�7i�� ral��u� ������kin�� origin. E-: de <}�S�9��a"�Sa��9r^ �*o �iu=�%A1%� ͡!��&a95s %=A�he>>2�f:+ ab))�'"�F�Hr�% TGd�de�p%�f�EaKbl�*r � >7,  %0q and,� 7 ha Vc"�' driva� �%ici*iw=E1L �y%�!>~-�"8����GT e2/. N�"�examples��llY��!1� s_� bliq�X7g�� -bM��= ensaA�� ��5�IQuB �L a2�h�ed a��ߏwidth� N��E%/ q^�sDe �=s�a�I}�UIis 6_y5+h�c� S"m�s��ItI�(6�TH < Ji�A[ tend� sFHS m%�$��M& to�% �%apl�ƅ���n�al�J� Oa �i) !IB ��figur�!�z\<4{file=TOAsw.ept !�=7.5cm,hu�t=5cm�\ ion9bel{F1}S�>a).pije�!>��o2moe?toward= E .� ��.�; ����"�{��3�x"�'3Dm} CIF'�*?�Hl ��TmoS��� 6.��/$�Tm��"'���-�x� I�edE� llel=$�Pg(�T\f�1F1}�K =&(3 E �� sonaa� or � �!q���A�%���2�WW�� dip�8�@ro"ng)Ʌ� [ !emplo, � jump +ach-~XHe:93,DaCaMo:92,Ca:93}.>Ja�/A@b �*��7�!�u�e���i2�� nonh1 tean ``"s Dal'' Hamiltonian s�8��5 �� �� �`s�) squa��=ime $t$�JgiA4�pr&q�for nF���until}C% �v-adapA">2a� mg���$H_�@hbar �p$_{\t{L}}|2��Yb 2|�H= .�s ��4e"�%HX c}}=A�ac{�,$p}_x^2}{2m�J�9y 6z V�T {x}}BG�%�  %���>;=fHbar}{2}\Omega\theta g x})\a�,[\t{e}^{\rmi��k�L}}�y.= 5@1|ub ;-i(t)$#  to���+m�+reprev.�8�Kn6�A�}#��a@ tempo/ 2o��6� e�1!����,�-�is��!%v# G�p��of A�Rng no 0 . o9:�he� �ul"β��\% 5�rmd ||� 3 }(t)||^2/t~�$;By.&o Schr\"o�ery(!��� abov�(r��$���9e C>9� 3A[ s'�J��(Pi}�\���({�.}^,ty \, "^2�x}5^{(2)}( ,t)|^2B�%Ml��teEZ$(�0fu7J"� !�i I{�W�B"� �".5,R� �ev}�&� \Phi+U(vec{k}}=E_{ : J�(;$>�$ �7 .$�v4z}R4 $z$6� ��um!+� er�� * �f�"m$N�z$-�  �(we:ly~�27�A�A."TalJ$x$-$y$- �eW, �-�^,0po��s�(�ک*)�Q ���be:��/ -P��[s-I4I2�f� Bɒ� S� A �ve �5E,�we�LJA|�Fry sca��A�.�� c�GA�2�%P�0s!�@i*n�� In�%rix��m,�$*��v �^'1\vm0�J&+ -�� -0 - 1Q�(:�)&>#a2[��Bten asz� 6T ��  -~ vy ) � �]larray}{cc} 0 & 0 \\ 0 & 1( !�  +" � �" r`k O� ve �6)= F� �0e12�BE��@�a�NE�azJ���phi�V��:�^ I}��)-�1}{�B}Vk} ��Wk}��cx}}+R_1F# ^{\p>!6, \\ R_2>/q>&�))" -�n�f� $&�C}$ �Eͮ�wm"��vin�2$h k�B}se�Jd�Yq} �:&� bar�Ak}S -cE�-2}�  \/�t�L !^q}^2 = R+icm} P} (%���+26 FT % AY!aoiΨh�'dividual��� Av)��< q�z�#e un�� y ��� '�+r��E�m"���s at |'���$xBD ��%Aog�+q�8&<2./b�$��mJ�E�"J� %FIpm.G��(�I�{c} 1�q)�2\lq{_{;}}{�0}} �0�)ym*�kecm6: � |A�o�%E/AYV=�C�d�*�Bras:>-� ?2�E) I)f$Kser� � 9�!w�T�4& 9Qvp�$&�D $��$�'�b�'�diE the !�mR�lR{<KQN�c})�m�e�.Y 2�� M(.�:�y}\\ ^5V1 &.0�t:�2h+E�2/2)%�I�MfA:\pmQ8��{ P}|E~J�� jVgendetA^�M�ʅ�� L}}-=^%\(2k_y�7m}"�+ ^2��>���Iar6as�e? .�3h����_yze�%aiZ% �*B �*�;�&�� �nOlp1y%q� Mek\EMIe0ful�0 )fuV�/eT�}uT4jllpmmbd J=-Z 1}{4��Y+ �DM  \p:rf^rmi5�TmEH-2)� :^2 - 4��^2<.JxJCMj%� 2}��-mH2���Q)!~.�.d.ƶ�� -$F�"�$�d��"�s�x^\pm-~A����' � $x\ge=P����su� 2 �bd�qphi!,��Fqt{I.� �J%�2� $[ C_+ |E_+m�� �;%�[ k}^+2� $ + C_-|E_-r5-65)�]F# b&c2�EC�9PO(*� %�N�Bh<o{M9Co�/Tt�Fus�Jb*Z/eq]r��R{}}(x=0,y&=&I�R()eP\I�R*}\,[ [ & rZB1�E>�� g$��� y��qsa|num�(s��%5r5�]n�2Y YO k_y y >  � y}۸ C_+:8^+ y}Ey\ A�;-  \2y2} 67  q_yy�V�a _+"[ 6u (�/+a�+)y}  >->-.�:>-) �iR.*k�+ 1 Ro�6<  !'=I,a�6�Q^+�S-C6��-�q}R_22Xq!�)/ �^L �^8>�!8W G�PG^A>!A��UkendU�%. E�1}�IcJh�7���@E�Q�u� } k_y=!$w } +-��kkkr8BR@ )*j�L �q�� �6i$��`r #ed�ba�[ k_x/=-k_x��] % F`�)U�Ba���D �+�&Y&6� m$U��2�4��b�"&�1mv[omh i� dyfE�|�%�� x^2=!�2Y,�B+ B� ena��y�%� �2�iN $q_x�I��*�%cPtazcj5oo�$thb *�he?� ay �RS"*�(%P. W`�,�iӠ��)�Jc>q(16Ocw�e�!���G��1+��=d � |�k�2N�2%Dk_x (��R � =^+� + {k� ��*q_xA$ Z2x +�@r�~���q� ��s @&p�1D�',�O�0$k�) q$ rm�$ AB  9� �hb l�q� ). A��7:u R_�lR_2$, $C� �/W��6��-,aYf !�,= -2k_x(q_x+a{-)�-/D!�C_- = 2$+$+ $I=GC�%u/D\\ Ir [\+p+)42(-) %\\ & #�_-)-)+)]/DJQ�%���b� 8D=k">+m �Z+)ok-+ -F�X_5X% FinAS,a�Fdu���&-,M�)AA I@)K)�!�N�� V� .�f�2_B� ef2�#!�x. �xxd]: � a�  2q2t���(k_݋� � � ���wfIJv��Rav�� %9x}n}P�= � %%TJ���R!� r�6.x^+x}�C_-���6Q��-x1�R�5�f�߯ %!�*�E?@ �:"R/}V!�Bp� % U�3iB M.N- mA�)� ��"V0� � 1;-K��)delde+!�����0VV0 \[ 6S�IP�'.�-�^2B�'m}aQ�# %�>S8 2$ �� 6� �� 5�" f&$ � -�,gAg2�� 7+��2X!�>� sI:k.eoȡ0�)n �:��Qy-s$�K�<lq0&�6)�ulaI���|�� ��3y9Qavera�32&5��(.�%�2� 95 x�?deed,�,y �azero =((��E� �ե�n��%\ �59s5�4�*i�*�/�yd acta�ult�?ly!V�P �zB�/>��<i.�kP5!�#+�,P ir c�LE�es `�z9�GdH�R,gB\�u��Qz)� �ZKlength�26)4vab` eac6םnt.Y� 5��<by sweep�Bo�!m�cc!g�\� ���& 0-s!L)�� �5U�Y�el}): Na� rge,!Oi5,B{ (Tq�)�o�Jd I��z �R%*X�am� a�8 A. Then�de�%e)E�>�<�%`�*st; aftery5!�i�i�~DB�g.Ry��celk%�a nega!y��<.�I!� beam�(%MM�~�5�9-Ph�B D*�H� c �6�U33!*�q��pC,)�"��M2U4�a� pj<$q u- x},t)F+rreUCT-aJ*rDw B�=h.|��A��_*��J�*6 |in�)�62� > G6g�s9>H�>�=�-0"�-$!\d{k_x}\!>�- y}\tilde{�~�k})chi&�! �� -H���S& t/2m�)�psixtNM�. $R{�o!I�; itud���1�zp���e� v!�r�H$t��I\ �%H !�o�Pi���Es-Is�)"r . �s ��x2(A-K�of�+�$x9y? �*��U|��T�=Cc�E=u$aly�Cly,�ing.� ~ \fl "m0} W!�pi}E .&!M u intV �AQbSAAw�cc{\wide.`$k_x,k_y)} N b"z[q f9Ak TR_2� ,}{qV!*-q}� + 1 ;4C_+� 7}_+ _}N'^2�^{+�(} pYccaX ^{+}��G.�'a�. {} +��5��-r�>�- �B%} >j-^�A�"+^7Z���-%vO{-�R�r�!" f}_&� ���i\� ]Fm)� � 2}-�2)�z. \no>0� q%gA� a�a�b�����to n�?��N�*A�1D� ults5&�O��a�> �*���<mP�H"� ^� � �%� > aM0�:�/ (2D)*Z$s� v�� �*���!��n� BX=,.;GgF��~�!.(1D)}}_{!3(�>=t9 r>�f{i$1}{M;.rYP� ba�/a�ͅA� k $E�  Ť k��\&�! !q �f  sI� ) &!�$x < 0$��)R�8%�(b�J�+_+=3q)�F�� �)_�Rb Sʄ-N��~*� &e $ �& 0$&�!u��AA F�*} q =Ik"�2"�':�16�*}�!/k��^2-�D��#1\"�\pm =01�(E�!c�L>/Q&�(I�,:! ( 7.�(Q)^2* :?*!$� ��4ܪ��fs� OnEQ n go��2D��1D!�� s (s�(arrow q$, .(^{(\t{2D})}% � )-; #1#o�_x.-%�$) �y�Y"5U���g>�} �2�$� N� usoJ�v$ �#� M"Y+�J��rRTJ�. *3J�W, t!X.$\� )�$�Q-!1��!of �� $10^{78*$ h �l� G B� "Ddeld})!� CsW X5X.V#9*e lu�J"M�(,�\ra=0$,En��{�a� cF% �y=1 \mu$2D 6�� \t{DY�oAFer, 6,3$ 1*. S�AeA�k�i��}xp�QA7�%VPg�!J a broad (D)VGF�S�&gF!}r � �so1ullG;;E�-fm&`&�� X�A�v\Q\ ;4�u"�"�S Neverthe�H, $�xDH&��con�uVE�I�i'CʍM��.*�����q� fR�Jw>Q"+.�,Xa~�cE��lP��:�R�j��� � P���%5<�GA��~1Dou�L $|�<,C\gg.K}}|$.�Y% \�:ecel}-Yay�s*� i�%e 6!r"$�thR!cy#l �Տif><=�-L*d��.F3e�be �b� �M]�� u�!{��A}%��E�B~J�0 �{a�s"�q�% ��%1D!=��!�;����4iYw���:Q"�ll)6*� u=�O(���K�Bg\gg c,=[L�{*�(�%*4�"jsubeh � \ll� ^2/&4�By,%"� �25!s$5^27 \/��-me @�MaB� ���;� 5 )�a��JZ�/��D�!" 7u2�dth*�_��1Hk_y��� �j� !�"l ifa\;A���%K�"58! if�G^_ %�Gk�nis �<�Vpa�Gt� NxNM�\taK\ll)�$. 8=/u�%q�^a1!a-)a�2i�LulI �>�BTin�*"�W,"?��y��e;`�K�4yJ�l�Bo&is�Ma��act?rb�for>6� c��>Y!Mf1M to a��.@oneO E��tu"@�bP�YK2}��X)��cD��� mum-uncerZVt�aY� Gaussian ��"3_)/Y���6KT�:e�N� �L �K!ca�!L�,s)� oA��AAC.�^X� �j�2�]E�`\VR*<!�i�-@P�1�(5���<�%�2�15.���u1�*1Aq��MUm��1sYK$]�l� enh���K M�N��2�a�th[av=a� ��anQd Q7�2E��Ai.*dbN ]�NN2:Ooa2dCs2a>O� =11c"O�E�b?O 2} A-�%�7Y� a caesium3��!p .3^ =1.67 05 10^8 ^EsA��� 8$�� =3.3b+M��tM�� B�_.*� <�]x=0.24� {-6}�m��c�um %��� D�C"po��lŐ( x_0\rangleP=-1.32\cdot 10^{-6} �\,\t{m}$, and velocity $\la v_0\ra =9%Tcm/s}$. The solid line G�distribution coincides with the 1D .#.0\end{center}  $figure} % eLphysical reasons forM�se two effects are a dependence of the reflec �,efficient onD�$in $y$ dir -!@Doppler h, resp#vely, a�8ll be explainedL�dnext paragraph. It is seen"�\fref{F2} that a significant devia� fromO:< occur5 Cs lDmeters used here i%( wave packe�prepared)�da width at least three ordL@of magnitude smal!B0tha�$x=F. AZ�tim%�Sv�_ies 4�gngle vE� $. Atomic�Bm�as!D�:�� Cdotted �kI�!B.��� -<$\Delta_{\t{L}}= K}}$�compensa!Qakinetic� sB�!� >���change�)�R.�sa�due to A�$k_��>� V�s.� ��now. Com��i�( eigenstate%k=0$eF func�m�u� �haaε �ed!�t w�xasbMukM Mq�6Lԁ{�[-�5%�,is behaviour�>@be understood via�dipole!�ceqb-�,ive detuning!�\e��deldel}Al$follows. P��values-��.d!Tan 鈁��WXwhile� Ale 8 blue�E�refore %�V}�! push�i-�.��ult�in �~d1Z���b 6� blled ouU�bd ��.d� d��Y�-� mini��cy ofE� ebecaus� a � shifA_��$M�Ik� in MF쁵 very high9��Ga��>\�x"P1�$of Caesium*a��a��hA�(o insert ra� extremeC��齅�, i.e.:� J�q(oJx\rJto� "C sbD )�I�E�nonzer�� 6u���be�#ed by�osAwa�Fq :p = >r�a�� }}ZQ . Si�qua �Eŵ -of-*\  only�observedE._ �  tݥi/qE�36� >j A9>� �{ $v_x$ asa/id �y4� �c!_uld�usefu�� � obt3 broader6G.�2m2 �34}:3.za�� 2! �&' ���/�/i��g�5�565Q�of���p)�s"�y$,a�.�2},e��$2 by meane�A�.Be"� above���)%�;�� �$. Indeed, e*mNuncerA�tya�p�Hon �� :$��um,� hV :� i��X y$ w�en%.$ rapidly s�a� e tail�.^mo� way "p] . D� J��T � tuned��g!e.iaAcwh�is exci�> less!I�ly��pre)a��[ )G�ndy7?ekyS � onen i�not@ sibli �� th�O���6���} !�f� �\little bit subtler. Star�%f�Mv ��@of $|R_1|^2(k_y)$��"� ] n go�gto�[X =ŢilAteeper �3!���� &�. � � t� O%�:X I�Q�P{k_y}$, although both�2�>�o��-zsame w���]J . D%f�� Y��� rge K $\omeg R}��if!� ^2^=E.7x ):relev�"1 (s. However,IWrequir��� �e�e�an� recoil�!$v��!C,�s!�ra��X-'opt�u �ImetastaE�.eMa life�2�eof� tenth + cond�^R1R2b����X5} Plo"� (modulus squ%� �Y��Vc&�s $R_1%7 2� a � Cwt A5�$$v_y$. Par�Q�N�~ Ba�|R_2|MAstretc� by�actor&5NGBE\su on{D!�vold} �d6a� oper�kdelA�3  !�s�]s�� \��4{DaEgHeMu:02} a� generalizZe(dimensi� F��;may ari�)w��AQ�problems�ҡ�aring .�E�ideal6� , namely .� ���� field�det)>�� . Re"in�f ground � �no photo��emig!hF�@-L M� atom�2�k zed. DJ A f� %�\de-Xtak�f% � . Im�rie> get rid��b�ž����� deca,$te $\gammai+Rabi f��ency $\O�.&is q���=Q=2Q!0thus � A9+5��q o circumv �^ACtry8aA�tle (��,%h�ng) weak>Qthen �rac!se long)Ua sui�" mann� Init: �was d�a� 2I�!A�-M?2 of�%�at�t�Rfq+aassumedI#Q``experaptal''e�.� .e $\Pi(tB s gi� co�@� hyp���4eo .H Hŀide��(known)f� $W��k -level2�,&� eque} \Pi$Pv\star W.�* % In� limi�'�U�it%JI{��!u' �2;����4me��Zflux �[�5\rt 4arrow J_\psi =� !W �< lab frame. A"N71�0urn})�1e�s a�!�>�!�l!. Blu�.~ ����  t d": onB� nd  in!#�or �rj. Ak ��w 1. ^t driv�=eic =~b�2)�a�^ a�A�la� %56% �y�typ��sit�i`i�JF 1m�Xut!�X!���a.�9 �.�":gT��Hc"� !�u.�K � %versalN� . Ani�4possibility isJx�a U(q�!��) .q �$\l�� ��latte���h�"s�' FS"�pri� Q:![@)�p�9 u �,�� �le. I�!Xِa�6lit�b4 ��at�a wide _�&��U x 6ly��lic�. A m�theorz i�Pre;"ce J� � �Rb te� in some �e�� *� �aI current,A!kwa� wards aAsu�J%a$is Qity. V� )�.� �� )8��U!yn�  $x=0$�#v ZW �e!�)h. ,\ack{ JGM ac� (ledges ``M��terio de Ciencia y Tecnolog\'\i a-FEDER'' (BFM2003-01003 ��```Acci\'on Integrada''), ��, UPV-EHU (Gr<l00039.310-13507/2001).} "�*{RQ� # thebiblio�!y}{10}�Fibitem{All:69} Allcock G R 1969 {\it Ann. Phys.} (N.Y.) {\bf 53} 253; {86; {311eTKi:74} Kijowski J 1974 c$Rep. Math.iE6} 36.D0We:86} Werner� 86 J ; : 927} 793!�PBlJa:96} Blanchard P%i8Jadczyk A 1996 � Helv � Acta} X69} 613.�LGi:97} Giannitrapani�97 K Int.�Ta� T O 36} 1575 P@Le:98} Leavens C M8 MP!� Rev.} A �58} 840CAOPRUF� Aharonov Y, Oppenheim J, Popescu S, Reznik B% Unruh W G! 8)�Nt7} 4130�0\1bHat(Halliwell J%�9MGPro�!o:1A707.DKoWo:99} Kocha\'nA3)�4W\'odkiewicz K�9b 60}, 2689=8LeJuPiUr:00} Lee�J, Julve Pitanga n\ de~Urr\'{\i}es F J 2000)6I�$61} 0621012Ga*, Galapon E AI2 �roc. Ro�ocQ!4!�451.Rr( Ruschhaupt2HJMb A:mQGenO35} 1042. MuLe% Muga J GE.~�Q pQD38} 353 %\nonum YMuSaEg�\, Sala Rd0Egusquiza I Lf2 (eds)�Bit Tim.Q� M]4s} (Berlin: Sp� er)=�.�$ Damborene�A,6t<, Hegerfeldt G C���)��}u$66} 052104zHeS 3} 6Z, SeiaDBd3fd(8} {022111}.��3F��� 2����U68B: At. Mol. OptMM}�j��{2657.<XNaEgMuHe:03b} Navarro BBk5X��>y�f7aP381.�wa�w6�v�389.�RuDaNa)4}2�, >}=2F�� Euro�.. Lett.-�!.IwNa:�6LYx, 6t�! oJ� 70} 01211.`He:93}>�%�Wil�$T S��2 in:)� Clas�/(q�SystemY �ee� "� SeP�Aern3 al Wig��Sym{ �q1991, ed) 4by H.~D. Doebn_W. Sc�r�0F8roeck, (World S�/\/,:%(gapore), p.�0;:V�f�47} {44��� DaCaMo:92a�lib~(J, Castin Y%$ M{\o}lmer��B~6�582� Ca%�0 Carmichael H�i� An Open1w A; ach� -� Os} Nd]>M ���1 docu{/} ��\c!��[pra,dvips,twocolumn]{revtex4} \use�" age{�-,� ics x,�-}� _8} \title{Squeez� gS �AmrevB0� a cavity- sE~x cont�� a re'@oir} \author{R. R-l} �.Lail{renata@if.ufrj.b.(L. CarvalhoCDN. Zagury}% \affil�1 {InstitutI F8 a+, Uni� idade Fed do Rt DJaneiro,Caixa Pos�@68528, 21945-970,>/X Brazil }% \date{today5Zabsh !S�)/q!iT/l�0�![ harmonTp*� loc'i] a -fo)���(tem�ur�subject��e a�-�,ex�4l s. We�+^A�o(? naly�s5  "&[d�ty�rat�-ActsU��moE�^!1  ��" �lso[�let�M� U�, Vq 2q�"/od�W%i�Y8\pacs{42.50.Vk, Ct Dv}Y makee�$ \vskip2pc&�{Introdu%��-I* H4wA�ca6much n%2-,]n!�%utud -=i�(KndL)  ly. � ed1/5�'sID impr�&e,ignal-to-noi��M!�U� ommu��s � yuen ! in s6roscopic�-$wineland1, 2�/�&hopp&atg"E �in& sE��&9 �s, lik=?Cof|"viC alw�|hollenhorst,caves}. Research on=l5����$�5ontexaH�wiop�&jrlrteresa�9�N��\ s ora���qa�electro\6eI�. I�'c�AOat�-�i�e�"%���'��!!� ^�tw��o���6����neMe�FA� phot�)ic�s#7I"I(�� "aABr,8 amplJ1sa-/. S%!��ic.k!=�Q.E.D.�eGpropoM� enha>��(upac$75\%$)!��8Jaynes-Cummings%0l �Tgerry}. Villas-B\^oas O et al}. )v!boas}�zan arb;rh"d����5�2sly p�%�bigh-Q��dispers!#:�aխ!=�1��� �H3�$. MassoniOrszag �m sq�6��M no�  ! duce-e;�7�n�_a��&O�fer� %�9Bf:���3re��pa o�H ca. T';22)sh�LAn�A|�� z.�!�an��E�ric [&r�)I�Yde�dia jy��ra Չ03 ��fi4origina�gby Zeng�Lin-� zengi�d�"o!:. any  q� a}. ��Ref.~i��#5�F_�ma? e�" ��!���c �-�ia�" bad �3�,x�$%}�1���b1w�~iPd- gy�5QhCack%forthYf)f P�4!zM �io$,!apaper�discus sch�3i g�aP YW��-\an[,I���oR�� aWE��I��Sz 1Qno� �atB . E*%�,w2# >@, ��Fx �)&} }�~  >ny/��&| =� � �� w lway%+eezed��E))�irdr~"es�,J!�!tw��]X,� lower{��er&( ��9�j.one�markabl���.��p*s � �e vib����� 4a �s%.IY\!acuum �&�4!�*mw�&!a���Hamiltoni<c" ��(* line�% oupl� a0osc�tors,!�-� m be& conn"Z * Ay>� .�OSec.~II! p:n��[l!�t ����-�.�.JK� a�=0B� >Ba ��3 icitEU*0 !�A !Ng�yo6I#ing�V� summarize%��6�!�AT%AaArdixF, 3 c*�'����;� 8�-jI�="�{C%o}�-siEY��0:is ` " (-��&�� jF��6� is b-�+y91Io Paul�G.��a>�G !�Y A $m$%�!Y�po.�"!� nqFa�$& �4$(1/2)m\nu^2 \�Jx^2,$  $ �1r< lace�B��l �equilibr�� � $\nuP*Q '-aoq�R�) l��4�)#�A"6% �0s� �ax�!sema B���e+z 1�#$\vert e"�! �g,�<s� .�aIg F�* 430 D�uquasia;on���rY !��of�=�3 c.$ .� ��/G(�E.)�H:$�&B eqnarray}1 H0} E H&=& _0+ 1\, , �ber \\ -_0 &=& �� )15G\�"e +2.cc(a^{\dagger} &nuI�b:"b ���1�@ g_c \sin( k_c\, Lx )> j%�� �g � +{\rm h. �0,!5D ]#-f0)s�$ ( b I �$)E)!�Hhi�,��e�e*orU�M-�� (.q4a).� lH_1,$�5cy�f 36vec�n$g #� ion- (��a�B ta�<+u1�& inus&;4�>u�un�r �qse�0inimumA�5u� �"�node. U �BaO/�0$ )Tensory(*he. <, ��' s F-" ><n�,!FߍZmv�F ssoc�%"A -e� n+&� )ωȵlQ�rel����U)) b^v�F #�.$\delta x (e be�at.� ),$ �l$.= \sqrt�/ / (2�n)}$Q !n.�;of�� .�g*i4 &Now��lA'B�s� �heA�s)%� �sies, �E1��8 c - �fA)nd"2."+"!�nf2e"b'Q$F=��N Y1re�@sy=�-!NRam�8"f8 s amk3� śQ4g Q5��.] ]W)�FEsU�FG+ 1Z_c Lpm_v , $f�-+nE$�k(=Fig.~\JEF�L a1}))��&V �.�%<�*� W ����; !�" degroI%o*�4mv0�%>�i�s,Q�[<pic�2DK�0tomI H_0, �be wr7n� fint�1AH_�p(t)��\{6���x$:� e^{iI� V- i g_1 i k_1: + i( *+\nu)/�S \\ && >2 ?B y+i @ -At} \}�O^Jk_1, k�:�K>w3��)�پ� �� 1, g.@�- /U3co�3n�-���Jf�J 'Z �OP\resizebox{!}{4cm}{\it2A�ap� , 1}} >_K fig:q L�/Y�i2�e�q�"���S2'"� � %B )*Ŋ%m�G�$0<��5<ndG mS�V� ,$�F n?.�j�>0 �H QJsa�qA�<.�6�/.:8Q�3An�YI Lamb-Dick,($(\eta_c = D �\ll 1� �Rk_1:$AX�Ok_26 Ikvalid&��8�ro ngE�*� �at5�0\gg i� w1a�,  2a c�J ,�� . $ �N$t71/ Ce�,s9�!$usualL ced���ba�ei8�"AZM�B� -luiz}�&�.g�:� "� � V� V�A eff}8 & = &�0��� �;� � 0.1cm�*� ��b��!ma�;*� ) \sigma_z `6a�/�a.RlZb:a .� &+} (!� ^2 +!� ^2)/M � H�8 n� )=�L" �- "�G": ,$=e!E�A|A�c �i�\;br�<D=e65A�c4a&ird�5 A�I�StarkE�$w�EZcorpo��S%H�oby rede4>ngyV.$ NonGY69 eta$Xneg���e�E���J nu?of��:��}1�S2. �>:a��;�t��r [:sub?#!�@or��1�� -1.$�c\>x}l (� V})gbH&�y�u�u�a{"}� = i6��y|%�.{6R�mJ BA=\23A!� Eq.~-�)*� process�X&�Y#��IB� E���L&PO(�d��BJy�Vs^preG�:8b." imultaneo�xs�paQ�ex�=ge��u\&for�: b*<&ee��.��a�b�:>�$} SourcdissipE�a�u*�3�I��J^tS8� chao���s d J>&i��g���#���dmB�0upper� |e�Yle$g0vogel, adrian>#KDeJ$ easi=�I�� �loE� h.�.e~! , he�i5R�J=*s#�f!��-$1$U�$6$ms � roweS�%!�i-CBc#>be�<H�"�6B*Y�S�#o�OaV� �-!����.�-*��J� �nvironAD. A�B� a�BJR �EA Hzr�ut(r(Born-Markov:% w!(y�a(>+"T�GL� |(a a Lindbla Qm Coh�%*�6�eqm} \@ {\�al�rho_T(t)�-t� /1}{�$} [���A� E< (t)] + {\cal L}.a.� � 2�Z"� &} J���;ZYeZ� L} R��B {2g� $tf4 Rhot� ��$sum_{m=0}^��C:�!nf!@(f(t)g(t))^{m+n} 6� \�s� ,at Q^{m,n}_{2 Dc}(\bar n_c(t),\xi ):'%�VBvBvB 2ZE &�3Ls $�� $�$���"yD DmDftgt} ;�0biggl( \cos(\�da t)��a�In0 }� ,2Qr)6 �- L t/4}' 6v� � z�I_2�� �{ (�B}e^Jfq�-�E$ S^: j� - 2^2 �^2/16.$� >�V� 1�A���$  = c,��]��a�2��-J i�ar0f�aas�4 �-�$Qmnnxi} &&j� �2�>�i^ke^e=CR"k}(\xi�tS_{a.Re� -k,k.d2cm� mjbK.�,J>�S�:�.> "�!=�bac"�-�G,� .���s:b�S��S_c)�e^{\xi/2"Ew�xa�yM05cm 2})J@ S_vb]b]&� Z]��MHE�coeffUs $r���CmnA�rJ����D{(m+n-k)!k!}{m!n!}b��l=�4max}(0,k-m)}^{ in}(n,k!MZHm!}{(k-l)!(m-k+l)!} n!}{l!(n^n(�Bh A�^{?2lA�sinn+k-2l&"\ a�a�>YaFwmB?�]as�H�? $iqR:� <^{n,m}=(z%} }[o�e� 0 $m \geq n$ a*�M2�zRmn%�E�r�u�%���k�Kf�%�Tn! k! }{ m! (k + m -n)E.� -1) m + 1!� +1}}>�P>H.Sm�.k,k -R�Z\�#ystyle{ �9� ~0r)y �"� �<�9 I!k� ��]3Y`;&u� -�jacoby} �� l}(xi�!�jye (0,ladk} (-!\ j-l}-z(j!�)%�(jaO (k-j)aV%�x^j!j!}�� � �ed�3fHN�YJ�$ polynomia�$&*  $)h_{c��!v  $� &�xi_ #in*�� Q"s =e6zetaxiSP2 1�� - 1/[��1/4-.&-(q^2-1 +.^2 A�A$2� M�m�n �x)p1}{� .��lQ�()�(q+�\n2� }{!- (q-1�6"} gI �΍�= :��%�� ��O:^-%�U� W  ,J4[$q= / 2�8� = � �'�!nd^imunut#%=� =5�q�1:� (1 - � ^2%8��q�re�1dBb s �)7takg "rac�&pI� . By*�3 erty^ -$trQmnA})),^�"�rm tr� ��b\ #��,!�%�_{m,0}H#_{n =�1we �ly�V^�rho �= g.0=�%Q^{0,0�Q��6�.8,Ed t)) \quadA� ; ��B�B1&76how� �����)$�*e)i a ``� ehermal� ">�Q00nxi!�b #-D���$�=I zS�)�)^k}{( +�Jk�()�S9os !Di�k�2 /�A�:P"{ }".BU \;X{�_f{� 1^2> 2^2:}$*X ge4/� � w0 S��6C�p!�p-reach�] stead�'te. F�5Eqs7�),(`с��)�eeIV� ] $t TTaGV)���:��,�� Aj .80 .$ A(rRi��$B .�&�cm�� 7M�e�T^{!�r�1}l0�,_c@ T+1AA.?_e�B�YjZv�6N=�o� barI�2[Ū.~2_vB�2>�.]6�F���^�7 ��� 1dZ+M�1D�{� �� 2.B �m-�)�1�&atb/�:Ai 0��agy'n�8� a7-�#�2��ap\9&"B� becom)m��*�f)>� >5[ *n$�� �va�kpVime*u 6tauo tau_n.�\IH} \arccos \pmatrix{N� - � /4}{� -�>)}}}} +:)E \pi}jN��pi/2<�x <\pi�8n=0,1,2,\dots.$1Ece! �)=(=���V�tK-ly #]r(ed�$t= Q:$fp�>=0.�_T�!]A��2�%r)ɤv*Na#9�$XE�Y�� ��9O9!��� s�e�� u=m����"�!���^' b�AO�` �.l6�e���R� {!e6]B��i�70 o��&�A?2��4re�7O��vi"8!�� J}xB�J�. N���a�Xth!�<#�"E��� mremai� j� my�cQ<$ var�[aAZE�IY� ses��T�#is$Brec�S= �U� �m�t�f���o^} |V&=ZSYc4cmU ��2:��&u| NP`�2ri0�^{_}_�qVk$g_�)=�$%"7r=�-�.��kCib�)�$�g,$^���c*o��-KV�F�R� �2�m![g�ym $���v,$q?.!��+>��wQa a�U��� :. �-b� R� Bh�)sZZ1*`t��2��*!�f? 2,�k,�X�&clo��o}:�H"� e��9fact,nmax�3vaa[*� }�3m�� p �b.�q +� max}� 12�(���1-(B )^2}}-11R&��2&-9 ly $ 0.25RP�+�R,.$ Hav�"�!�"�:��w'��jL,Bp z ?fin?%BcA�-_��p�H�+co�Vnt)�s*`-�� 0rho0alphabeta2�^{\,\�a,D� )>!{cG.#{cm �ePFG^E8��a_(�et !@&� {vBovboGn�> >� 6r DcDvY��%)�/s �a* - ^* :�DD�(%yV� 9&`e"TbT�� ��4Cw�Db� rhe�t�=u�(at Ł4) �X5إsR$N)==D[c} o!�:�)��o��a]B(�"q�6L�v��2��Q���$!�:���jJueEZ?�{MI, h!j+Xeta� 1/ �^* z"!(BY� = (Q�>:HuI+ Y,�#1`QZ^+"K|F7"�&alrO�627K)6�%�R*ua �� ht} 0=�%!&�!ak.c!}{&`"n*?)�! ,A"�aR"9 TA�� �� :�,&=QL�|��AaMY�fI by $){M8%w) 0ph�Fs�f rctC ,FDC[�(3F� Hz�z� �W, �"� >^�f�y*t&v MQ-�Rhoabc.:��U(t)n!�ɓa9)� 0�h e��.B�6I&/�>FB��.�v}��.k�a�.�86�>oB��Q2!�e�tJr"�). v6$,��E �M�"?�w} &'>R� Mm=62,&� at 6� �7� *�"�� 6nd~�� )-��.g 27 �:W, ,� @) $t= ��f� )=0���:'�$N� �(As?onseq�pe $"6Q .a� � ^.){��&=xiM�!U�>>=0e6&���RR"�S�vg;ǂ -�E6 ��d�6� P&�H}&� v�20cLb�Mby :t n�.y-�]� r>� YCIn7 B �k+  is lTeG��!8eG�I any}:-,�s�qa��4i*�+ +2DD �N U].*�y�,4"5 �o�  !&!!&�?�saB�@yoK^�PcX��X�9飩5DT-�"2�%b��� P_c �:IQ-2Ii\�#J,;9�_. EX_v%: �_N=A.�:v4P_vJ�b�*� }>�>�4�!{V^TDXDP} �9 X"�C/^2%( 2 �*4�$/2+ �2 .$J �9F2A�$� k��jbi40i! ^ �!!�>��t."�i��#Z�ved+ �.b-\ 2Fb>�"B8 N1"�] ���c�X_v- : Q�1 $t> �&TB?P_c?� 8{$1/2$ ��2_=n*k� �5,\sutherwise+ $(1-_$>0o�$t > @�$ \neqW �� $�_�V�A12j�A2r�A2}�! EEq�I�!b� �a�a�a"|!A�e5� t �-�&�$)q  $0.6 s0.9 ��w".4a.( 0.4$l b) $<� ; �r$�҅d\xi#59�% n$0.05ƫ,$�p�")0.x,1�o%F 2* J%B!jiK �-ky�ƍ J~8)4+ %0�2�� !�I�!ES>eo}F� 0#�A*�e�=F� �Vq�A�� qB�Zr���1" � �e&� �\�$��X"{&P�Lv-�"v h )^2�12/U]21-Q�}�!1+aݱ � �.F�%V�T>�%�q�O'UaA�n�!M� U9[� � 9]Va r&~ #`hFA;�Vx! tenu�=Rex�z�7e�*�EA �A��7�A�1 >e�.�I�re�@far t[��Ud!r+<*!<~�Cpa��,blatt}T"k<ifa�t��N/2\pin/6-7$MHzpK��0.02-�|)�NA�$g�5\� 108��5 g&�F)E�E0.���J =0.4CA 6�"#<15o+l��)E+"># /16��"=i�  �Uima�[r�_a�{�$t.�&&�&E}�d�K667���5n( p t)��verge.��>G�$�-�v�� J�, do`=T��zerI�Zdiagon�e%Mm�ic .X< �by*pe<E~,a Bogoliubov&"KAA�v�#�! "� ival!�$w�c"^&�f�UPRP� 1H.fBn� R�j�U��!�Z&D�Y �qS�n� rԁ2�!�A* individ�� �}j�-�.��cǔis�Me%d bel�,e�d e�Q c j�1:y� C�eO!o:<+v��(0)�)=�D24  _UD�%>vj�U�)=�Uxtx &�U|u_0u\tS-� !��v )v}((\\ "�4�6fE-S^{k/2}"N-a)^{(k+1) �%*D->)� �%�g� /� &� @ nexi5E&&� ��?&� 1+" ^2/�a_0^2)g7 ^2(2 Ȃ, � �:�&&�!�o4 \lnn[) p& ) "? �� 6�)!SD/)B"n B>A�]!\2�& IS=�}(.�+!NI�!2l>OIy=eZMa BL.% -�-�a=!�"E3^25 [203@�=^^*��+ ���1)Y�&~bar.=!F--FG"� ��K _0 ^2> 0 �"tV�pu�ZaF: ���@�'  $K �.$b�$t_m=m�] ), m.+$q 0(t_m2n ��[�"� 2�di�}".� �DF�c6psi_1�Q���c-x>T~sA�6��`_2g &��`%��;c}�dX`/,��*�">� �v RA�)\,S_��rO�".�A��3�&"Tc(M�f'- �Jպ�0. !%�4.k�!'-��(6( S�)V0E�\xieLQ*� xi}).v*�3|u "�^2$Jb3 \le���X*b��:�t ���G-[3�  [x R , bu� � t_5= "R � 6�3�it 5� k�kne�0��P& kKe.���� ^2 <= �*� a�H;$f K � N�3$� he �,�-�in.�%�"� %�O+t.� x�f�Eo, monovdcJi,2:�**]�Nc6 -�f�d�[`el:=iR���Q`&)�6�1K)�!t!2�I�� all*E"�9ne}��1� so, �h*2��w���,/not � eit9g� �B�i�dv6Q�c u�gP� ^F*�A�I�du$d6�as� �p�6:1�ǟ��:�m�/Bu ���� 12$8)�^� ^-�  t/2})^2��٢ *�PE�^J]16N^X +:h;? B�.0&-2ay/ no�e$�ik |]�=1�<%vJA9M]P!c8�M�\&V� �X.-,a� Eq~�-�.�>��r+ � :clF�Y3Z*�a3}U�X-��B��&� �y�6� E��1$ (dԤ>U�5a9�er$10$ (so!q.�"!=0.4.$Z���we�%�y�y�g��Ds�fs�fn fix�Y.�E��--1�Uti�2a� curv�acrojm%YM&�+/6�=1/���i�p/f�!�F�>�m ��e�u{Ba��(b'xqv�a0gB�-eA�Z�: �d=g6�hjR�oi�h a �-re~f��zAxt8�%o`$��[c\p�a�E�'B�(&�k6.v1"�_vs �<�P &�O�a%d`c27sŪ:�aB@��kq!]�!*!V.Q�\!�-~& (ter�m opor=�o9��end>�q���W b&�TmzL 1$).[ M�! .}9o9 �2��I6���m@pW�Bhn��5>b)�ach f6\ ��"�? �6I!T 2 ��6�de�s�&|`�yO6[m -)���%5n� 6�%A�k``�s"j ΅�*Eo��2  rhov4(�F"o��&��.Pin_of�Y.�� 94g*� �2 5* 6H"� . :���"� �� ]QO �.��6~ 1l2� K��vy i"V* ?y)�+ �D*3 "�,���Z^rfzQ�����i�vA�?.�u�woV^M�&�39I��\cZrpYb&v��-s�\� ork �sup��FEhe�~qag���M,CNPq, FAPERJ%MPRONEX!��Jv�o}&ToS ~ � ma2�u}�Refs.��Xel, 2��e"/vhav�;��F�:^X(�"�y%?�%Q�"by Flad�;;G��pa{�1�:.j!4 Liou�y!6superF./T�� ��aDv5DpplT�Uc.���"0$ ��method."�XQ��Oof*K )Xa &ɣ�ach. �bp E�"o|�Q��V�2}��65:i2�_2H.�U"�B&�D�, iB*BH+�_{F�5�^tq��C!ls�b2�P+ � -2�6'3=� {ZXK}�A>�����e � wp( $~f!|b�q� ���K.}�XK"bY{1 K "dY�kVj9�X. - .%����XM2} "�X. 2a^"�o�&A. aF)'By A#�.S& F^2�^.�e�� adop�9!anneoz=�A.$ $( �A)� 2��.��{�SJ� �se4� �A"�� (�"+�tz�&ws� faL,$ i.e.A.)S:n@A� )5 A).$ ,%cconven����U%"fz��B6 Y��m^6&Q�M}_+^q!�]Z� &,&.-iNE)�aUq.ED "y� 3 M}_-x.-J[ ( []�:Z\\[+^�-�*�-� �Jx E x&�-z�xv�( [:�qr-� �8obe�z�{mmuB �D�,^�} [.o,-�)�] =1n:� 2N)�3)�]=1Jw\lbrack]-^v8k v \r #Rr6@y�n �yA �J%�[ymai�x5�} null� .���i t46&n^[KePqG�� �K}" Bh$� ( %}^cal v"8_� v4J�ere^����"Q[/ b�aj�_�� -^c)6�&�h �1^�-^v --m�=v6R :S +F�TE-�+>T.SV�C2�!f�:R *2��S:�\,F�:tGEa� sw 60�MY u2sM-O�� -^{\�1BB  > = 0��,�5 \%A6�\��q� � %'gmi(c,v()u��e6�u�'}\'n�w��:b-Kprime0093.�B1�s s !R.�I%�������2� ���u��>���&^'�tf�7 *p U}}-�.})� b�^qUlUl� �!1"�}{2"�"�T�kPm}2o{v6cB2�x �e�F *C ��2� >n} K��v.XU"q1�By�(��8�2/-nIK�rr�k� n*'2/, � �^`expKt} e�\�f0>�U=t}9�A�BJC&8:�mB�h;91t$�2L^��BA�  BB:���$- �.���V�N��Iy }6t}$&3'�%C���f�.�eU}^���E5U26�n� exp[Q�.D U�Me2]!SBO`���m%in P e�oA�6M7�GC ne�V*0 ,�>C F�$8 cop dorK$FpQ' �2� c] \crM .&)��~%�t�J %} = �� /2 & 0 & �d&�M� �-� 8- 1* 1.B ]0. :+`0}2&�*�)�cL )("v"}Y?= :S =���A@=G"�;e��=G��,2���.�GIA2}{�GB�G�� }�GFQA\QbigB�"�;־R���+^� �>� }w�iA$4Q24�a trix��&^#�)&�BN A ZN{O.�}�H�� VuN��by5ic�^la��j 2/v  $-5/4V�1A - A�e"  bf 1& 2�ncty� bf A +a �9 =��$�)A}%�&Y('�BVU�%9-a I�U},Ak�k� U�: ]X�q� _� )yu� murhoWt>� } | W�HJ�22A�B� %��6"Vtn �  �U}-a� 2O b� 2 \ 1V}�-m�b,\n l  v( v�)  6]&V<2� A�!^�!'K-V]V�a��u�1mu �w�zp KB%)e�}).R-t @��F he.=%*!N�1z -} mu%i�'�^!y,$ �6< 2z*1-Jm!�xin2} �E\�g� I�2+�P)A3��x*~68K^2 FN@~�Qf*y�y�Oɷ.q:o:�2bBN��o6$ng6�2f�>����2/sxea6+��|O8�4� �-Mxk8��e3O�A""j-�exp�Z>�!a\, Q]�:�\, � Z3e 3 ]6UI &E p^� t75fAV�, c5B�>$F�O),6!to�G�,�!Fl*hN %`suF�t:�ta��,{m�t�S��eje�XV�rv�AE� 5aR7>�Ź�6g defQ�ojn�is�P��� IE4�N6^n"�Ip.4.�64m4m!�J� z�fm �.� �V�m]�00�d.�>� �J�->a"�H>�.z�^��yclic�%�i�"'j�G�) iebtrM+N+�:�i.6�ha)�0�&�VB. �kfB \for�,fN  n�� b r�d�a*0-8-��jAJ�ht!�Oq5��!�a^�jN� Bj=x=aBE'&�J %�!���!��f,��jx�����@!�b�)�!�I�(p4�/*�Z"C(��.�!ta�&�a a Planck''+di&��2@o+��� �?�5!3��Z �En�}ree new:x:f,ABC!��A9֥�-J�6vB�)+>%\ B e.��6�**F5E���*^O &B:� Zz+}��[2 :C�P� c-�:zF�A�A�h_c5gebraFM!=��=]%�2 �+ +.�F6!A:>V! ��!���^,v^��B � 2� � N�RTX��L9��Gs:�Y*, *��fa1��hey)�=�e a)�����V��e*_N��� a2��*�Gs,B�&$ RY%��\muN3\n =�� .]J��^xiBX�; n ] 56_*�i � B���} e�6�t(�UB/2� - \mu^2�t2!\xi@� 1��t` ]}{z+=umu/A� B�:7J!1&� ����! imme(��bŌ9��AZW>�*\�a�">� J�+�7'"� �3j�B�-�R00�iR^�r �()�)�(Av�>&�rJf�����m�,""d�n�6�.� M� �eMe�����6f\,��>z�)�Z= 0a�6U&��6 ����� ��B��:c6�����=&�*�-�r :y B �����6�:�6� �,qq-b���-^$g~�8�I Am~M-N+Rk%&&& �D)% ^~a�B h��hB"��N&��1��I"V �+ "�a�UW�9E��-Etr/ �i..y~!1!!F� *d4��1�) u���noW i�"}L�2�/ �r>�� ZF*e 6��j��f�J*x���Jx�}*�J��!Bskͬ. � T�(�;�&@2,]F"� zt��^�R FU"a*7 zR�F�(�:v-M� expA���.��� :;y�2:&/�0�� ps -h:9$ca[N79c6�SQiS�n�Q x�l��l��l�"|}y�i>),EH�{(%�v�-��FA�\%�Y�hskip��N�2� �"s�����{��{&jM/�1j7�sas=N)$i�f&� N�=�{�� �0$FI�NL0xNLCcR��G�4m&�FB,$��mkc"�^>QV+�Fa�)V���� (f�E BP b')^n�a�>� �!�yB jymy+gL��f4V�>]!�b8li6VQ�~E��� �O��!�)�6B+a���#2���6�~�2?Vbp �sB�B�co>�2e��m1J��1E�� 6bB�2/�f���*n�C��C��C��4�9� eF�����S��m�F�6>N���Q-��^C�� &������������.2 qQ yR��%20s6���"~ew�ݒK,<<"���;�e;� basi.|z � ��yԒp A���/>�6�\�VɊ������������f��3�ycqy������N��"�`j�Y��^n$�N��as���p.��"g�2��hi R��*L Z>s&]D1K>B� {99}��:&����H. P. Yund��H. ShapH� IEEE T���f!3ory�*424}, 657 (1978J@"��w��} D��W ,bJ. BolH�er, W. Mÿ ano,��L. Moor�Rnd ?Heinz��*���� 46}, R679�92R�2���|50! y42y*C�}�NiS&V�.�D)O 19}, 1669%P92N�� C%+C��, K. S!�orne, R.!IP. Dr�R , V.!< Sandberg,� M. Z+rmann,6� MqE��,52}, 341�802���maser%NMe��de,A3W�`!� G. M �r2��� `A655 ` 5); M.Bru��� .Raimond,� Goy,A(Davidovich,�HarocheF` �%H89%H 87);KFilipo!�I� avan{�rNd!Meyp�2UP�34},307%�86 P/G��pM�H.9 .�� B �1� 1078%\8); E%�Guerra,�BZ. Khour>�%�N0�N�4] 7785]912�E�K�� �. ChildsE6 R. DasariU#S. Fel!�"\� �%�73A!37 i4�t u��C.A�G��H. Ghosh�)-_22%�%_972��Ha)�C�H2\�,!0G. de Almeida�M�rra{M.~YA� ussa�Rev�AL68}, 061801(R) (20032�ma����E[�^OrszagN�t6�munM�19�239S6�S�H.&o�F.`�N��e R358E�!r=q0L4}V. Bu\u{z}ek,!(Drobn\'{y},!S. KimAda��P.a]Knp�Rx�Y 2352ERaIa�.A�a� H. -��rie�J%.Eu2��I=37A=5�;6S(M. L\u offlb��.R]�M<�R10i��AeSParkihndCJ�bleee� B.: �� Semic���X E�1}, 496%9i�M��7A�315%�0 �R. Guth�hrlein%�Ke!���Hayasaka� Lang�QõaN�� �4�S49d,1); Xubo ZouMPahlk A�eathisN�65e 4303I(2); C. Di F�[idio, S. Maniscalco, W. Vogel and A. Messina, Phys. Rev. A {\bf 65}, 033825 (2002); J. Zhang?0K. Peng, Eup. AJ. D ?2?�89 (2003). \bibitem{rangel} R. R , E�ssoniZ$N. Zagury, WR.� 9}, 02380 �42]�luiz} see for example, L. Davidovich, M. Orszag, rl854}, 5118 (19962jv!H } C. Di F!n�1bR�2� 31802 (R)%02U�adrian}A.A. Budini, R.L. de Matos Filho, !�Z� )�6!� 0414n!�A.^!�_ Q7�381)� 3). .� owe}!f�Rowe {\it et al}, Quantum Inf. Comput. E2!l257%22Cohen}:�!z(-Tannoudji,E� upont-Roc)&8G. Grynberg, in ��Processus d'interaction entre photons�Dtomes} Edited by I/ions/ � du CNRS, Paris, France, 1988, p. 254.=$@pachos} Jiannis PED8Herbert Walther2K Lett-18a 187903J5blatt}%�. Mundt, KreutTC. Bec_,D. Leibfried%DEschn%4F. Schmidt-KalAy R. B^B�Iy �03001� >2�U L. CarvalA� e-print qA.(-ph/0309042�HTend{thebibliography} > % If you use \\'s , please supply an alternate versA�of th \ %a dsquare brackets, i.e., %\ ��D[Communism, Spartai[pPlato] %{COMMUNISM, SPARTA,\\%�PLATO!KH {Entangle!�%�\um critical spin systems7�author{Tommaso Roscilde} %\email{ro D@usc.edu} \affiliaa�{De�oof�Micid4Astronomy, Uni%" ty of SouauHn California, Los A��@es, CA 90089-0484q �8Paola Verrucchi�v(@fi.infn.it7��u\mbox{Istituto Nazionale per la Fisica della Materia, UdR Firenze, Via G. Sansone 1, I-50019 Sesto F.no (FI), Italy}} 1_,Andrea Fubin�f����F�B8Di!�i!�o d�s1.'5�\`a r�0%0,Stephan Haas9�����]�V��(io Tognetti�n�nMn���B{JlY:8Nucleare, Sez. I7 V�g (F.gH \date{\today} \mak�XL \noindent Contribufpaa�to��Pconference \emph{MacAl opic"O  %�X ing}, Nap�� June 2004�  \se�{Introdu } One�+�(Pmost striking aspects��oh u in a many-body�� isPoccur � of  � }, namely.realiz��/a � posi��i tatef at c \t be factorized into a p �=si��-�:�r wave fun% s. A Űd a posse correl�s tw$ be accoun!�� by ��-like %@ities;# inst. �1sDmight not show any3m�W ord� @nonetheless be at%Msam��me!�ongly�ed. Th � ibil� a lo�des+ (ion of such-is %>$ally or com t!�0lost, dependA>on�degreEa衵A�tainedAIA{%o . In bcular, non- �nature �(pecial collA�!�%eum Ks�Yfundat,al ingredien!$ at allowsU�c�c%�A:t$ >] �ut #lalgorithms \cite{NielsenC00}a�$outperform� ir 9�I2r!Ps. !� idea!�2+0as a resource)!� demand? 0atic investig �of which� }@s  ab� �I splay siz 2�e�c��oll waye5i��gu!� i �7!��at pure-1A2H~� A�enhad whe�^ � undergoe�5�ph� tran�(QPT)-�PSachdev99} analogous�eo w�2�y� do at a!� rmal e fA� deed1P fluctu%msi�up a�(all length ��Z5� point. In �sense&�� thus6� , 'd� ge' �QPT ha� ei� subjec�6z $everal reca studieQ�`OsborneN02,Osterlohetal02} dal 3, straete�� ough!M resul�� pice�is stila���� al!a0 this work weAqsider �nite gen�$S=1/2$1- *I  dI�A�8a field-induced%�t(arbitrary dG s�~a���discuss ���Obehaviora\2!�$nd around,V�E(s I� fe��s�ovi�:new�!�!�v drasa�chA}i" 's g u�E e1 eff-� o�.�"��0$aG!OexMcoupli�sum $F�$ runs av(n� (st neighbora9si` obn te ice with� ordin�� number $ �$,� 8 $h\equiv g\mu_B} H/J�rei�Ue���fo��w�N� ond � � $1�H{x,y}_i \to (-1)^{i9p $� Eq. (\ref5u), so � �relevan��1along $x$�$y$ axes��2�. v @arameters $0 \leqU], z 1 $�trol ��otropy ���� �$c�% of $Q�\neq 1$LZeA termagEq.: d�u�  te %�frA.]hy�. T��propertyA�� 2cor�7 %�-driven��BF= ingCa&2> $hIMc}( �)$,�s a Neel-- ed c($h%uA$) from. ^ -polaI disBA>= . W�BW� favors A/-�seU� � 6K-axis-M|�$appears at�="D>% erd!}&� I�A� beco! hort �d%Dl"� .( prev&!ġ�s)7bea�fu 97gEi �! LKurmannTM82,Dmitriev42,Caux 3} E�Q� z = 0$ re� � e XY�� � Le v�chA�,exactly solv� in one�� �B��chMD71}�� whose 2�M�* hFbm l � 6[ 2{ �a a .MtI��0a�0$,� d/or�higheA<me�Q �Cis noE�er - 1A|e!-" m �O\ �hr � ith!�pproxim�� y� numer�� %ach"n BpraroG>A renew{te��i5 e �K e�A�exper!-I�� � A� chain��p� 4Cs$_2$CoCl$_4$M(KUlA�E�2}�.x r planar��,U�y \%x 0.25!�=� 1�I$J 0.23$ meV�figur$T����$} Motiva ���istheore�&2�=s, w��rs� n���å�� ! a ��� ��"| �>� w 6�=��Idefin-R�U�}WI� ��$DelicaL90}�Qquali<veU[ G m! � "!�! c!6to�cl�,at�!J�}k,�ce twoI��v5$symme��ųsi�(.�I� �,ed via Stoch�SerExp�on (SSE)q] Monte�0lo (QMC) simuY-8$SyljuasenS�X based!�aified��1dir%$-loop "�!'�a�� low��Y .Q)�z��4�4C�%variousm�se� 40,...,12a�"  co�[ # $rse temper�u�L$ � en<o mimic�$T=0$Q7ur�each � size; left��!#Fig.~� ��^�>-n�B 2qA% ��-h$��G \.� data�1nfi�� �be. s!� _u�aBa�1D 9� � I�A1 el (�-2D.)� c�6~ � inAm$y good a�P��  diD�wa m�� trea� �Fl:|.��r�u>N�we   �ly &�sig0%'Ʌ=_3 ��QX� ->�!� 7  (est� �rI�$he asympto� valu� V -[ �!{1���  Our �ifo}� 7��.� of�3e)}1�Ben$� 96}� i�@ tݸ�! one-� }�p conc�! e,. Coffma 0,Amico~04  1�%9�� 2� betwI a� gle��r( �C"�t is � d0d$\tau_1 = 4 \det \rho^{(1)E�A = (I + $\alpha M^{ } \sigma )/2$a��! *"�dk,ty matrix, $H= :�S �� $, $:n$eslPauli Yc�(AL$ �=x,y,z$.I�e�4�-A E#�sy�t%0$��!zmplT/mJ\ 0 -!dX � (�)^2 .>��]SMA(Wootters98}iA�sa� teadHpairwi>�Q5� �!E8 s $i]j$i�at zer�/fin�*� . Fo � Ac'.e�"�bs� �� tane >y break1(� 0$)%� q?=`� �..F�$C_{ij}= 2~=max}\{0, I� 2)}\}~,&B tauCVAj���&.S &=&gz^{zz}-�1}{4}+| xx}- yy}|.yC1}\\S2)}&=&.:+.:- \M \� (.m& zz}\ ()^2-(M^z)^22�C2��nBI� }=!#�c\%Sr {j}v  :pA .0cm�erJg\Vf5vf65.��3.�`.4R��z70.z��vsa� | L100U 55cm* FR;}NO� �~��msuP�.d3qNs *2$��a�%� � appl+� [ e�] & E)� �=f���00 �.� Inset:���)D"N�y��5G�� j-th"es;I �Cbo�e ��Ci�_{i,i+j��ope)/ ,� $2)$�* � ��"i)/ c}7)�Middl�o6 x}. SpiF�$g^� �r}l w a� %P: $�`,i ,�G �3 s a[?'%�c!�(.605(2)$. O�/*A &�sA� up"�.}�ndy� m eq R�$s}ɰQMC���m%#7~>8�"�yQM��un�.�A,},�� lotM��m6.^s�ye"�" �2q�{ji} !�j}^2~,-4and" iA�,5�nQ(or $n=1,2,3A4 &�!'%ioqlt�%�ly re !.S!eN�UFv2 X'lly q2�%�i�ekh'! oI �&d I0 ^$.�� Un�+5er^� !�vi�!� 6A,De �2&� !play  ark� noma�3}*&�,4e��they "�v�!hA�"!62��.��a�&J p�Z� !qto rigor� unvei�E*� T"�2�  It�� �e easihow�at\.7}a��if%�only if}� n � u- ei� 4. % \footnote�&d y[<op* %$@.>� triv�(fa� %�is N%��:a7-pin.}Ay#"Au%�/ incr�5d abov��� *ta& �-%�6� a�steep�)o�',� mpan��-o �*!� c} >#f�a�e lizauA�for�)"# � .2dswitch} ����$lA� gc)�W A)�!/��H� Eqs�sC1}),��C2�%7!�!��)rdivid�wo 2 reg崡� di�(nt exp$8f 2y:�snar= �[e<&0&<�l{�~~� for h<-sf}~,\\=2):=1)1I =}$=�� �$!�as��j#  =�2)0$ )�*��Cre� r� %e�h �,�/f<3�*F5.�0)E ��1/d���/is"���not�� as&� !��d �b ��} �b*w/=�YBR� $ 33�5]3di� c��2asa�`%�% }�r . We�e�at�i.3h�V)or J).�)d�w�1�͊� el0 l?5fl!���6�6!�ũ�x� %R"�) B n pa�Cg2���,it bawly b es afteXu�<t�-9&ing>��&- ~&��38BW&82w�  xt Ja%} E.� � 2/ 1��P4>$%nE�"8 �  !�L$r-� zoomA E�� .}� null"1c*t57 -T �o�^rif" i=1 sue,� � toA Es� ial � A�q�.� . Atqc5 ,��.+,6� l U/�Ɇy a�ruqEor�{i��?ftA�hr�",�+@�24�Aof�,mph{monogamy.$is��i�!]"$partner(�Zs de�i- less� l�& s$ ,1 T. MoreE :is� s /� � ����.J � )�!��}�,ł also)�T$n$6��X|1$n>m�%, u�5a��2.�,� b!��s� �9�ofV�Li!�exempl�i""�:� ma�+�Q5xd Gree�E er-HL6-ZXer (GHZ). t%G�%�m$|� GHZ}��&��... '�|*�"�, .)/\x2a�%Q>����;@ �~a� �;�0� 2E�er. ,h /3gaQ�,�N��mn$-F�Y,e mutu!w4lusivlAcl �Sbsurd�# i� viewAV  �DenAdF �m� �PA�q�e�,r�6�+��e -=-Kundu- (CKW)T�8<n 0i00% A�e� 8   �*�.N���.� 29. S�coy���f24)�X,md,&9*� &_����I{`/�3=Ee,@ alway�9veri�so far; EBan*�8�5�=pi"{0.v. I� � ���}� �!�CKW.��.��O,5V :�=weHpre v.���} $R���ʡcq&sA%>e d7�.to�/ 6Usto� inn� |E�l�b aZ:in2A{!^A!A�+eld"�s,�J%�* 4'K:��X2s7)aw!� whol6"dt��#�dLt��%��";�"C� $h_c$ �$R$U �L v):�`$ dip. Ac��AS!� �is� ult >iw�8tfde@s dra��&`B�b!!��5uE  m�<�e.a��m, due��!FJ�,.D:b"�5)�8RBibl*�.o;B @�h(�5� �.�)�r 5 �F��e:� .�.� ]-9�_3��>" ,zp, J���l6n-| ,$n\to\infty$X!_!ns"' U�oK+�<�#"h��:r:��,�E� �5fo yet,�D� justif6>Sa���ű$� E[�.M)ve�.probl�. N*�CsyJg �0� e�eX:c��67�large!�5�&[I�M&gW9in.�V&�?��Fin2a�e �e0 e&�� se�-im�o4%f�$� a�iW7-��2m.�� �Z�aqIn�%�a7�/�5 inim2U����� no!� ��+5%�*xL w, �&b� !�2]5�jrs.�N�M� @!"� >V5�ua52U5f�XZL40x2b�ladder}�G(H ����Md�1�&^�� %?&+I2two-leg rP$L=40Q=�!�2LH!:2n���# $z$-a4w.�cR���shaJ a�Lmar�>�@*�;� All +3�(gu� eyeν "AT2"} Ke�4.qvWj22  ���vA�gk)X A�2�a:�a�ank �X��< SSE E�um2�0) a5; �gevCF�)nyF@ �J*>A�Jg>� D���3 !�[A�7 ~0>��2 � xist��An�H* 22geo�3yE� l 0��mC& non-? ativ�'b�! �"�A�'U!j*j?E�rx@�&�;�ficgsaco- 9�C 4E5a perf-!�o$,Ŷ� �i' %t /Raa/6�� 2� i�& e�._��/���f.#&�2� 8:K.� >9We��ice ǡ�or�-�fani#Aae_ ��"�@diQag� d Haldane,� awn���"->>�%vd5E�s (L!..[ -U)�  R*z1� B+7E[,z1�$ %�V)A�!tsLa�i�\"w+=*n�.0*�5R+� 2l� � y�N a��"1!��L�:%:!� �- �B�� ��a�� M%��M:�6���+ 6�ɒ)m&pcanL�� 23 Ŧmeb�>b��wi�-ty�U�m(n^E�g�>M�0d- S W ��/M~inon( !�!�uni�*6�an�3& �� 2�b5�� \H�+Co�>puH �pa�%w�v�a�� 2,�ma0 �  a�6c�8!� in2RI\!�)n (0� �)(� A� �a7!�pic�5i>s� �4���;69*,#^�%CQ�v0*s$ o�A(ɜN $-to-global6GE�.�<"-%� conven� alQ2 6, 6U9�� "jNs�Q�3 �v�5)� !�6�N�RYofUn.k9 tech�1s%� �"�O�jte� $na� �&"Q�O�:�9� 'edQ32-я͍�=.�4 cal=4!b�2� .N 1�7E2�q�hE�F#&��m� >��]2wE�� ��Ra�D�u�q��Tirm� C t�3e�"8�L2x"��Us�9,A� ��*�. 6��D va& �iN*# 2D � m��`s r�0 �A�ng �q�6 - %9!f� uggest!�'&�Q0%s, %Ib m*V&�?G:an� &�,,im�'ful tool�cE�rOl�mi&_V2��0�qubit-i,�)cU�%� kind!4;ep�!cde!� s1��u�dev�2 loo� �� 7� "3]a��@�(le 6.]3] % opaI al %�lSummar@^. �$acknowledg��� Frui6acusŤ�� L. A�4@, T. Brun, P. Del��(, G. Falci�a F�[�_HQ^ G. �/Lg�#���UWe.�]$ort by DOE�$gr�L\ DE-FG03-01ER45908 (T.R.�S.H.),7INFN,M �LMIUR-COFIN2002 (A.F.�V. V.T.)�3�-$ !J!� ndix.s{�9 T e Apt ix T�^} %I� E�a_. �^ 6{j1�74 % B*1` mad�NBibTeX:� kapa����,ifk_�u��(\kluwerbib,/.=}.��_may-$.bsHYyler edi�Zve�U �wS�Ve��\TeX\ *�`LB�J book. %Se� �`e�,� edbk.doc,e�m�)in� #%JZys�{1@} %\chapbblname{<ah.bb�"le>#=Y.( ib f ( %or�G3Wt:�a{ J.~ $, H. ThomaYG�fel�f�bA�bf 11�23�8_h*�f:qD D. V. , Ya. Krivn�2A�0Ovchinnikov, A:,A. Langari, !�Exp�k�h95Rj38qFJq�C"�NE4 E�,C. Gros, EurPJ B T29}, �i}q*'L J.-S. ,A?H�iEss%/�U. Loew6� c$68}, 13443I�6�K>�NAIwj.}2U^$5}, 1444321�De7J\ ��eschke U%�)1�73EO902OS.OI O.!\aa se�� A. W�qndvik6E c6�w 0467m:AT��R�f�|4�K �'f ze, S. UdiTV."�c �J�a6 1672j46�B6�?C.!4 ,A�� iVincenzo� A. SmolinI�W.�m}#, eY �-l%m 3824a�:%mC. @}� l�# �>h.  h61�\52306E&6��<-n L.~!^~�wE�Pl�Kna.� A��=. Palma6�~9~22304~42T1!$98} W.~K.~^�8�E4��982NE��K$03} O.~F.~M�2S�a� 0603M�i� >�B+k � � mB`)�(5s�usage: I  Poss� s�Bon hea�.velu[ :Td \sub� } V#,} \paragraphE�}�C�Qs: I� &k�x�T i�5�Q,%ede�Rx�b\inxx( \pro�C��.�[h]*+R &:{O�jl�l}� emo\sl(�*.� Ti%�Y-zTO�Remem\[to�\srHJ�0t0E�to-r=s@blet! \sph�, H Bnea�Dcolum)��Za,�y�p�o2.sh�0bK" italic:�&%D36CS�1�} ��tab d}{cccA8 � \it &two 6'\\ � C&D&E.%fRl�Q�3a �bxpa!LAu�T  $page, writ�g.�:�*}{\text>`}{@{\extracolsep{\fill}}l2�E.�*} %% S�r �e�:lle4} $^a$Refs.~19%�2] $$^b\kappa,�Dmbda>1$�%� >w%i�%% UseaintiRk"u�%$LaTeX Make %$!@fi AM\ �\pWFklVqK�i�a mo(e��F x{}) BV B�(�':Wx{�}�� `'�tVJ�soCd"� its A$z)\ .inx �U�l.g�$ k�2dsaw�]E�]d2V],�M> �~i`3' t�. �� �ab�0=ha�Ddex. 1) Run Latex�Sfile, 2 sort ro�e ie. `<.��> srt' on y�'� ��j�g9srt  3)]c��!KofJ)� inpu -:!� �E�. r2n��F`i5Ah. M�0ai�3vBr�%�(as op�$d�verbatim�-us9ixed �@ =)�Aa�zjg� ngӡ� �b�Ai`im> �\!��n5A�{"7T=cbf�E te\_&=4&�h} $\{$ \o!���#,neuron $j\in�F41,\ldots,M-1\}2@�!C���e*#�b S_j$�rEq. (6);6= if (&>t_j$)6v�K ON �; $Y_1=+�B� elseX<�XFF6Y�RYf�noEngaR N)� ; $y!�ins % ung:;$\}$oI�}x Knnd.�M��Zquote�T} ����0I�L�XsŞs��e�]a*\�  �%f�X��h���Ysr 24��Z5�x�3ize�Gte6UF�#=nl^��4v�:a�-� A� i�%5[]�T�6���-:�Af Glossary&G g } \��{xxx}E�yyyA�3 �vQ 9PGaAs}Gallium Arsinide>similar�mXs 0}�!s 6�  to f=<�S g Wer . >ucp�%�&ofsilicon`' olarkMOS : h���VLSI}V{/La#,Scale �zOion. S�e{,mid-1970's 9o�<e2-suc� ��in �� z�its���- �ll�)pX)nd-(^a��R�/. S�dh.T�)s got�'�$v[�8w�;�&3came f�(bl��:�  lg:&z pra,*zz!pac*z,t�Xen�\0s,epsfig]{rev0z\ukf/z�i�y.amzi�EA�{GX)!�!a�e.�r �0�Omesost�'�Frad�x!�-sonca�(} �wP�(Pathak~$^*$�G.dAgarwal*.EO�_ ave:�i�54Research LaborGyitv�>xpura, Ahmedabad-380 009, India}�V�y , OklahomF] 8 �, S*wat�r OK-74078}>_u)\abs\ t} U� 3q% �a4�) atom�Rg&e�)C\ �^y-G�.Ano� ts R�t R�A�!.��H�6quasi-=0a�s �>vo/aE demoQ7 n2%�9�m>6�I r& R�PI7�Q-"N-as wellK neg�* X Wigner"V(��"Lde&v 3�!� .�E�Apro� $ homodyne *�# E type�p elop'8Auffeves] [�� A91, 2304,�3)][ mon��6%of��F�.ɍaUV\�L{42.50.Gy, 32.80.Qk}�e� Z�(.��'%A�v aE~A%�iš; y-e�[ ny importa��1�9�(� st�]]%�$Jaynes-Cum�#sT,M9jcm�: adv�`!*is E�� �.c:�K6:&(4 lite�_ RLeberly,haroche-rmp,wL er,basn pM+]!:�!���Mh^�k�X�*d�u pl i&Ylt\cyA�suc!eE� exhib���" %��pn\javA..j� �Ie�+�� %$-K\SCHLEICH,KNIGHT}. EiseltURiskemj(RISKEN} hada��I hatw aQ�#a� a9 r+!4 płs, saj%eEl n1�at�F) in �� cero�spl!(iQy�<par�C Each My6i)C a&p;ly�$6�. S�Zal Os; �iQ�*�z%��t�BMd8GEABANACLOCHE,a�}.>)I� " aU��9���$o�ey�:�$"a Y*�� metho�ob_� t�/rES��j� �Zev�*MA�2���re�#qi�+�veI���e�V; �LGERRY,DAVIDOVICH} or$ URamh-raJwK �RA�kA" mass�y{ freed�Bf� p��ů tWINELAND�mEarlie�Z�"2he>�a�Qt�0w�Bf:nt E��]�7� )~fea>�!�hI�s� �t, Zurek �ZUREK}!�icql ;.�s�G struc e� }!s��x MHe!/anrnck's�WtF t. C^~Ya we n�>effic�zI7j�n�6 s. O/�'ea^^?(=v TARA{@N N !]Ie�6w�:&�b3Fag�#�,�a 6�� ough�/0Kerr medium. X^ no/ a�/susus+too))6z� ;�|COi~yZ�-� our,E�}�AK�*�+e� paper we @�9�<�.2sb�% FN1 1 !��tW�. ; ive=S 7s�%Q to=�* a� volv�A�:��C,4%Sh)n"j��P\Ef.6�>�organc7M[); -s�Ss%XSec IIA�-TQdetaile}g� ap* ��J�a�rR�a�in`ABu 1y *� ��]إb ��*mp��o!\cAdd"�p.�.w "� UfurE<��y bI �� g,S1Z.Ja�r0��1k. I)m&w �Casm�%}thirdI�� ��5in� AF~In!�.IV!�-�E��|+x �%q>� � . " Pr�u� 6��� V��%}�^��� &8�q,��{ q"}�&��have �sN2���n!�inguish1�Gh ?!4 .� �JN@q atQ� ��2d)h�P0 ���8 :wi!� e5np؀��Bo . o . �T�0$ level Ryd0�IN act5 a m!./�%��D � 6o%Kp 6ue`s m�T�*ppo/ad�l��.��vA,2�1�en�d )T �1c�0&�� ��M $\p `"� )k �A�bk ]F� �/6& �ca� ,ng/bPH+|-2$. A�ŕ!&N�� k@ �e�fore�p�H*) ��o�+%���ef��~ng�A�vnergy S $|e �$E�+\:#g.#�-t� �9Ֆ�>L$u E� ����A Q�Q:KD�ly )].��.zl�<sG4A�KA�&�� ��Las9&9[$H=\hbar g\�`5\�k0g| a+a^{\dag}5  e|\ Q)�bel{ha�u�d�U $g$a�c�}%� �n�)&� �#$a(�)Oannihi�p (XE!)u^�)?ET�h- _5Ds!^)�j(t)M=\�\n )70c_{en}(t)|e,n "+c_{g g-/�9#�.�(�[!O) <Schro�8er 9%�&�$ �I� g�\i=�Y7,c &&\dot{c}�-1}=-ig\KLn} �,\\.&gn>$e8�Y�1ssu��!�%�eK�o-ui`#43w\ ate $U_ �af�U�ngYeI5ime $tk^ �O"S8@� �)�ba�u-Pf�>imW,e��$absorbs no]�7 �i2� �aAkyi1E@_cM&=&IA c_n�l(5�t_1)|QE!� -J�d2}8�l.8}8+c_n  =�t_!Yc_n[�� ^n}{M !}}e^{-| $|^2/2}\non)�B�A�;�%�-�)�� �c�Z\ i3o � �Fw� � ��b"od�9�%�2�VaAe .� ��.E ��E� ���Pi��'���e*._ �a � )Q<2y �!a(E��p�N��two#}Q�'>�R�>�26�UV1sgI�c_ne^{Y� (t_1+t_2)6�Atr%U���A�BW-�W:%.1par���q�T��%�!d=`��r� Is2 = o�II "U N$m-�$ j+� i �bs Pois4@� cK%w"�Ts�U�IX�L a�am8�J i�u�r$n$7rox �|^2E�u� �( $�R_r Ca&-eaʉge� �'gbar{n}=h in "�E �}f&L$ 5 \sim5�L��to -�o���/ $(n- 9)�dignific�a텄 �: negligi����)csn}=) Z}+��k}{26!}- "�^2}{8 A^{3/2}�}ls %g*}If�&�,��� IB!]=�f=�5M M)JaI|!�����A.$n$�%�#!h )�I_Y׉��!�-�![h��%� g�2:�ws8A��'@hap� q=�J6�Tsn%��2fq�{BN6g$ ^ do�aJ&�X �� ��e�cyB�e=��&� d byYa��M9 �t psi'"b264}� [ �,(\eta_1+����.i(�tt�6 �}+=-n> 61+ �mf le+\* .6��.�-:�u�-FW!y�>>� �F? �];i-Biջ gt_i:�{2},~ Li=i�'F�,~i=1,21�etau�1�i�cho:#">o�� e$tG�U �v_1=\p�v % �24�R�S� >3VA6�!6�=ha]M�eaFpwLpnorth�#sx�.� :oF� Y�>&�[��M�>�� +]0Y��&EFKiI�&I^�A/a�AGARWAL"I0eU� W(\gamma)m7 2}{\pi^{2f 2| |\�Yb-U�|\rho| �Oe�2( [ ^{*} . )}dS&.T�def�/q�RN_c$%hRdA�t� )_[F�_c:{n,m}�CI^n {* m}&� mB� j2os(gt_1��n}� t_J� ��60mB0m}&� -z m|" rhF��psM%\)��m ;;�� 3U�R� &&BLe^]B2!<pi^)�hn!b�w�|^Va=O&&1Q=o�c:D int(M� *)^nE�^mE�I��\exp[:�*6M� ]d^2>5�bigB�AOe &|Y�ygral,& }i���l�6 `���8ckZ!as� �! by ZF�!}e@J+*�K2�����ago H!)w �,&!:H(a��b)���X .�squee�gve!$u$.i� arc��circl�z|"�$ occurK�-.(N5�.� �) i>� ((�Eq"”�8}))4�� "�n ( �ed�& $wvXsvh.+*�" ier.�^��]�#*��!�EyTYq&�/2�pa|�In .�2�sQ-R�q:} m��#^Pwit�c�y��i61J� lecE� ��%�s&v �is noO lappaOU�w�;v�54��2�:^�Ai�!�)�c:Jk)pm ""`$ [see )3�]MS*�!L x ��r�^r�V���i $6��I~!BRitA���% beca�6of)r��or/W �`ua�3li�6F�6� �are si�E %�M%�waU�Jbut�|�d#1. �^"QKI�:,$N%_�.tBE�{#o+ sE�!A!ieH2�wZ��&6k&!N $2^Nd�Js0VEJ�>�%����a1�of!+us"�|x.�t2�36�6�����R% �6f�3�A>@�v is c�')y�:`q*z+6of �b>� py�he>�A�P2�� aM�is~P�X&B � on} Q&� P( )U � -m  � @"� �"e YF��1()"�o):7Q��#:�y$El�0��$+v�$- % a��0e AO$P�z^%&yE�e�R� �1�:g��f��&`*.�% d. H�it ��@��e�o��yzeg�yM�.@�4� �:�!~�1�A�� Y/�]/f��1}M�|�M0I*�] B+:4:J54"o\F��.>M>/�>�4 �Bda 6:�|^2uqdi�>�B�$5B�beJ�1o&��Z�Z �~\.�"=1\Q>\5b\=0"6�8�`1��:��  n&�l&VӋ�� �U��$iisf"�eui�V�aA�C�(ple i�{� P�'$ g�����'i�6�*�(8 $ �=�A��j*�� �a�.d�5.�&P..F�&&A�i�~m� 2}}}iej[2�Uf9i�]6�J�rM[�r=0u�9;BE��)AJ�C�L$ ��1 �!���.4$"O )zy)An_�D�7; "-De�"� -*_ :�/FE 4�  -���>4�Z@hav�0n�0(5!=M�|.�%<#�*B�B� Y�O(:h n� } *+����+"|&rutal�ba-2G4 -=Y� ;+ ^p&:+ itself� Bi&-vv#Oic ��2 eleg� me�5�) ��"6� 5"�. �5) �|� %�psi'&�.al set m�{�2�Ct�z�%�b[<86� , a&��9r�_�t I$2g i�r�t�' s � sakeA� c��l��F*�(wo&�!�#B� �=�\L � 2\mI �("|!"�).)3 ad�) �6�}) NS!�"� � N& |C_h-2��*"�%v_D{&7,2��(m U&�(vUC�� m|B`|m �2i!\8}Q�m F_m0)#fm}�n�� J�,h=&��$�?�e^{� a^J-� a%s��;aR&�, b�AK�/63.B+ �"*�.&�.�5b:��E �֝�n;m�m��?+-2mIw6�+\�_'a]Ix9�+pa�&@u�#} P_gm|!�^2� ��p�m}F3-��5.!-!p��.��m�v uch �iqr�9iG��|�tK9�?R���:}&b0��<r�a��y�0/<� q����Dy� �� %� 864lie�Lv�(7 �"b6aBR( ,I itudA��n��\��(rAx��_l�Ck)F��=2�fZ3V�� �3+˙�m|A�&� 5/J=)^�ar�a)� ��e��q1 �!��\2|.�+ [�o~a"��Y1< peakF9 ����c_/ �Q�>>B�4}} x ]r��J �.~ �%� ��A�sur �x .�t +%(� 3Be2�:�3!�e���5= backMb*u[�A7A.�residua:`elnm�� ���C:8=I "%U*$T%Btswi��3.0in, h�=4 ]{FIG1.jp�c0V{(Col#t�<) �R2$"0!� �]���!5<)b�A^K�*o� =�&$�� =3.7�6 2=1.9.}�#��L1+�*�;2:; J<6"B;.,!�!�?>?> =D�01.}�fig�"� 1�'iIR3:�Ni*&�0~�_"�/,?Q88I.N�el�NN,�- E� t&^<�9*�A�1=8A�Q�4 3=2 2�3:��--�[YY��P�^�-y4.`�&�Ya�by6� ���O " I%E�1*]�.�"s �G]��!i�;{JZM) } N�W�*tuL�DM�Ɇ( E�Eae�!v� _E"�� M�!�N�/��.�6gE� :�$ ���� �ale!�� 6  3�M,bmaF donJC5 mʋr I�Y0Not{<*}=IB�.(aQa!-2"f+ #)"�u| � P� � � decay��^wGrr�mp-�&d�a@r��R r����% -�- Uf|m!�:�+�FD$1~i�XJk,�%�}t+(t)�,16+[G(mL_t`�� _t|"?>"'_t| +�>$ � H 6kO=�.2S+�-1-�"(1-8#] t}) �^��62iI1}b�5e+. ^��.1 +"x>" 52�)� -�|^! i)�=�)B� b�.�2fI> j"�fDR�2�!+j!5�6�.�2�)}+->�>�Ef2�6h>�>b�6�M�:�3�_t�  '�-i9 t/2}yp� &�r �tIn�(��h.��6���So�G�%M�����ch|N� �2� �>3v� v�~�d�)�*� �1environ\L�&2��<"�8> �v5"�{Z�!�leS�^2v�}{� ��\{�i$'�/)�^* �)]�/9��ef4 coKBJ+J ]J\}�-��+�# $ ����QR})}$ $%;El��%�  t<<1� qr erm �+.|;M4:�,,���"� >�".6!� 3m�64B��iA�o{s�:U I� Qsub-Pl`Y4GKFg&:;B��)��x]D��Fj . As0 prog�r�-K�5} ��  o (d$!�/�A�-�a˱redi��"�tBQ���B�07(�Bdsay"� �i�$q�,yA cK��*8��  (�%{Ŧ�u�.� .�E$}0| s f ��29�2pP BUE �v��!G B� ^�$P�ons@ iCfp#Q,A�/e2QV�k :?ofzv�&�%1�b1�{R�[ W�di�yAeA�:GO~N[c ��mjf/* Z�:��)F6�!� B>OA� sEQ eres��.o%�M^����O"I:Ju techn��a�gSwa����2! ��by do%�om�ly7N KIM}!9���,�>nn{99S\YemVZE. Zv|Z%iFkq�Z,��. IEEiq51}, 89]p6�n"/sQZ$}H. -I. Yo*sJ�pEb�.,"�pp.�q11'o 239 (1985�*�Z}J.�rRaimo��M�{9!nd$_H�Z Rev. Mod�s�s7�q56�1.b�Z�W�Z Adv. AtFl. Opt.K3�237�9pp�1[�PC�!x Elec�� ynamics} 3|P.R��r�WH(Academic, New York��6a�Z}W.$rSchleN�\Q n�Q�in�xS WL} (John Wiley \& Son�x2[rBuzekE P�tKnightNB�P�yiOpsD} Vol. XXXIV, Ed.A�$E. Wolf (NW? H��!�Am�cdam�2�QJ�[� Hx�[,p�nmmus4%�%�51EE@y5�2�Zsu, Gea -Banacl�\Y�!�N42 5913A�L91); I. Sh. Averbukh�v�K bid.�w$46}, R22054��V̓@zek, H. Moya-Cess��2QM�J.�shoenix,��.a5}, 8190`MbKiG +ba/aA��b � 2111@2#"�$Ew�[)�et "�&�_*y9�s2.�_ �W*�ZMm�S fS7��4887 �6);���z�,�{=179}A[6u7.��XC. Gerr��U5�638*i�UTWIN<[C�& nroe�uy$eekhof, B.A�K��!�D�{ WinelA� S[Zc!bf2E�11�w19�uk [W�Bt9�c�Z 2s{41a712 (206�sZK. TadE'RdiYS. ChT vedi2�zm!�502)I2� our}2R�.�dJ^7gu 0538a`��.�_AFV�I2Q���216E�7�v5>�6ed�L(R. Kuklinsk��Je�MadajczyN�3� R317e�88); R.IPur D2�2�)<3AE R361e�86.��u�,KAntes�Uer,A�,T. Bodendorf)�H. թ}� m5�JR��19�v�>� &�f ?K\tole���0000 %:�g�gpre&��&�gaDg �]{&�gg$0D� �c2��::>tw��umn,Z4\ucR��gs!�'float�k newc��@nd{\uu}[1]{\under20{#1%g.$pp $u�tomJ"be}'gin&e} 2Ee#�"�:!v! varepsilo(.� vs}{ sigm}G.Tr}{{\,�� Tr\,>Ypol _d�\906�ba�aJ�: e �Ri�tf m���ds�D)AfVx�[�� �in�Z�� �� E��!��i s has als�6ene ii�E��Schlinge`mmHEB03,S�F An�0�$evant subjaJconcer�82vU� nsum)�of2# i.e. appl (ne�*�s��.>�. AE!uIal}el��aCcn���v�aAv U,%Lb!Gproved� ��`J3-MR03} ��e purp "���iA dual!roach�=R.� �zis2"*D:�B���.(�M�}$cist0!�yZ���s, like�NR or!A�.���to ob.;|st ?ngi�a3&iti����an unknt4�!�prNw�ay �)nc <but�"� ��3,wise. Leung-�LaKqo�<21� permW A .!yo-xScS_ �.�9�u�V�alyIRrem�.E! �� -�%+A�[�6�]E!<:1�� (Z�j/)� !�.(�.a/ђ,��@!�&/a.Sak6*.�.� �\'ɬB٬A{MA al D�"X+grph}�"� Gi�2R betw�{V�a�m#&$\d� (G)$�1�$A�� �;�ex�in .isu<!dQwsul�-.� will� �>� �6U�`ZZ�depend��@ ���e���7R}�9 fy�. �En "�"F�"iz!�  \lambda_v%Z�� `��ed��f byE^ca3p��Z*� �-�$v � V$. x {\bf5���%�M _{loc}�xS�?st>W*�6�� �2r�� q �6�/_D�/teq V: an �eve6sA�se&%u%�$minus D, |�0u) \bigcap D|OGNxK>x��%^ $d$-EHlyAly�!0-��$DGK WD V: |D|=d$,.P�u)�r�K�q� A�E� mfc�Rlemmaa�h�$��b�#��D�B."1X } If.K�an..5*�1�6��U��0 d-1$� h T#  aea �  inst A�A��mor"� :��b� H�xthm:carV�^��BR�� n |�} Let�b�'��,EIbe�a�>$Q;K +Uw)W�$|K|=k�cIc 3 ��!~by induO3��$k=|K|�Sup �)!�eKS � �!���, $�y $ $K=\{v\1in>�:y,� l)� ��D))thu��F�. ;��now!v �i.� )I� v2$K� )6\ge 2  /ei!QQ(GYK! M!�wE� � ~r'��$|K'|=k-1$,9r�ı�!�mea!�^�. A >�.ռTA�A card�| $N_0=��v��K��odd� claimYX�c�B�izC {G'}.-K'.C� K'=K��Ei$ (2)e Indeed,"� � $�� V DDbQ�Ku�=tin�..en $|NN�=NG2�|=0 \modEl� ol Q� q�Gm��Wup N_1 A�-.N_1%�<N1H ���� on:�ui�a�a�K N_2>T(�ce��(.8up)�)B�6 u.�I�v�a+C62$v$. By hypsis, $1+r1| +|N_2Y> . Af!A�C�.� ,A�M��K'=(N_0]*NrC%t2$.�1Ue$N7��a ed��} toEL1|��N| UZkap2 . 6dE �)<. ,r H��z'8�i�%O�"l P &l >T "�odd9 In$. $v_{ij}$.z!!���of`6�toe� $iM�j$."[fg\F� � 1!Now s.6�lX�B����!�G21| �3� ��We�A�V�)* 5+!V.����xq! $�K$ �ng�6paI{fErG6��EEfg2}) �M_Cl"�.  nd lB V8be]'�*I?��I�I�"9 A�  Ifi�noD out6 ;��'z �"� � � ��NXnO��g�NBu�B6B.%|��u�<>) 2< T"F>;=�B�y6���a5R6AB����b��a@��W�9G'"wuD$�E.� = (2��[)n�AIodd. BeAls�Q stNa�ly�G��PhI ��.�a�!^�$u!� in V.�p �u_1�= �g{G}6) �6q )�P\hf� \Box� aciCi�� a �*V2� �R  z� Maٽ��J��� �  @2+8previous. o/ aP�  on� nd�'d�;�$&�$C,�&� �U~� h utpu�&���2� Vs $S=\{R {v_1�Cdots s}�#݋A (2$0 rc \ ?�.E1})�@�1.+�*k&�&B�&��nA�"�: "�Y_  I<ly �}a`;�y.W�S�G)>�: �eiB� ��!�9+� "l 6 a��n !�S�~9�� �{t, $K= K-� ,aI�, else $ SRTu\}, R��� �z� υS�.K2�nii/!,e���Q5�� con�7@�ed�2!���"�u�cl�2#�"B�e���a $(d+1)R��� �]���}�v�-ofQ�$�"�$D�%�� G(v��ۆ�><>I �:&eJ�no�2���!W}%.*� ge da��� Z6U�?��%.,��is su"1' '��VZ�ca�#*B� by&�Z�. ByI@adi�_� v� J�~��.�ec9a BG.9$K. No� �^l is; self in7�$I (G)=�!5�uB��� B�%�n�i7z�a�v'w (aEhA�E� 2)ɬiimp�;ble�:�D$,� L=k ." $:�0�(&( L��BN$uF��>h u2]"�>�4g* -co2�B a�f!�.�N�O L]%�K�w.���S^bA�����*� ���.._ �aan�&�& %�$V�?[&allE�*!�I�Aj us av� $K�9v�B�} � =�N q- �~E�"�$"1#f$thf} A"Uq�>��8�(�K(d->G%�iff} B�d=� [�2kJe] comb�EA��$"a e�sR� �E-s �/1�C�K:%"�� c4})I3 $26B)���$2$1V\ !}.�.IM��� o"�)��(]1ul��w%n optimiwUon�U blem5�corolA3}2�-�aQ6�0=|V|-1-\max_{.� , K\�*A�ty:|\{ v>^K 3v�3 �*�L2 \}|!z � F�Tm'Athanka" the  "� "� , fin�"1�#�K$.�"der- 2%&� R�~r��*�to:\$G)$. HowevRD�$ur$ ledg�MxJ� �*=ѡ��l!�e5�+ &"L�i^�EQ2��Berm�8a�D1�53oEs�!�h{$.Z3�+1d+ "�4��3!, S89}"*-�$i�&GMT�&��is�"ed! cellu�Eautomatat'n� P,�<an +?gn�!�a$�+Ns a butt�AplDA%\�*s!�a>io�/�2 Iis choses#�^��A��:�2Wflipp74 0D  !t�!.K%�)�����!5l�n!K*NGK1���E�*1V&� D$*-omes:{ � �tj+ thf2V2� ��� �� G)=d� ��&e�Dn$$d.Y0�1 � Y;"�%�=3"g"!�)(lC9$*�"!���]��:�$�ybJ��no"2 Em �%�U6!�J��"n KC"� Av$(n-d) ��!cu54cy matrix $A_c �4 line�-r4 one�2�2#��J(4�KB3D�OX� {\�< bb F}_2^dE�a�cto,!en� H�]2��� .X?)&�0stic v PM�mf6F2�?�!EQe} c5 !5{cl} &�VuhPcc} \, \,i_1&i_2&i_3 �� "n5:G(} e_1\\ e_234\\# 8& �Q[>>cc} 1&0&B0&1  0&0\\ 1&1��5] .ZP} :>R8YaefF�} 4<V<.�9O"�/ {Plam�%�5� $i_2�$i_3$!�""V�$e_�Y�ev�/>� �#�N1�aA_D.X=0$.q$� Asra�W+E���(n"�($d\le n-d$)�;uZe6�/�"D^TFalsz. H}6� e���5)�"2�&�"^+�lBDD><.6��%ԭ\%�0.<J� .�& &�,�?>"d �s&XR��k0( eigen�z"�-m �>�-!@"� JB  G�1&9�#,�\6? �%�M@(\lfloor |V|/2 \r,�A }(A)}�$A%�!y�����( �}* 7R�+$A_X$>Vl;��R� Œalready�0Ped�AW� B87}�&it 7Oa�a m" connectiv� L]} $c:X�_ar&:�rm1_X)%invari2byV�. "$-P&a@!:G�; aB s} �'-D ded2� ] �A*�-��0>�0>�@�?��0��0R�0TNo1� ��0�e�c�@qVBx�-� A�th�-&�pai?: �~"G �8&�>UB $Ercal{NB>.6zkB;S}$plog�Idepth(L�%�(�jz0� �O�S*=�@�%���E�.ent���F &8t��C �xa�J/omp�"Z(} , accof'g4!]six~1)��Y1"f+�wo:uZ�=NA}��6r �dF��2MYS}, 2$ L},3.E!�C �ze�` �4ors�0by6�y6:��4�qof �=ity%�6O)�-�dd so oT% e^o=7�� 9�|o���0G Bexhaus,!D2e:�=��*�E�BL �%3tXAc�9� ��z�heEkm�"wrt��Y%���en;C� �#8A>Iord>wo%I)*tak�>�8A�untv4%k� bothbt6�$^&5Ag�2%S-��c�>nK�Q�sdO�!�n=ApEF�&? main o7���h1�=�� �H)�Pe%�\-�=N�8��<il=�One-Way @Kum�4 uter0�8. .�5r6�^%ieH(D ular�H�6w�naT64H9�|pm}?Twm rout�(� � -by-}� Q ex })!6A�par> 2�i A!�s�>�hey%�.��l>}�9�j:"K9d�b#mov�e�dge�*sssoci< p�� �!�04ZJk�r�+� �'q�oA쩫�=�� se method�detailA� elow!�-��{E�by �}6t5.�"�8!��&�}$ �Z $C_Z$ (CY $olled-$Z$)is�A�J $aF!b$ lea� 2"�'v��#�G�$ a,b)�� �b��J�(r-�)�!  $@Fe�!NaA$$LP$-robus2T$��!p �:�%��E9I-)U \phi�GEc_C#EA��r�7A�>g?isNb �!PvO��cXf-�gsif�� � ly,�E�;E)� P0OB%� P!�r!r��n a�alI4 $c\n�/�Ia]];) ac�F6�aY%����> �ii�-mph:�i|!ipY3a}�4+4Ŝ{V� by[tex���&{2b(see *� sm})F ժ�!WYn9y�'IV?9�C���!$k$eLs";e� GdT !G"B$sm"�K)� �a<*�-.a��� -@a|@1~XJKvUK0 �?y 6Xon $(�-| �$I�s, 2� obser�Z�KO&o1"�Kv&�K5|N_v>&�A�B���=(V\cup�, E (.�(v,k)�AE�h-�7�By3)a�,9�7 *LV $\{g_j,j�V\}�Df�!� $Z$-]�a^R�9��vIm� regis$�*� 6�� g'� � . E)IN"= g_j$�� ���0g'_v=(-1)^{l}�Mv)݉e3�ZH�out��� . A�q6�b�B))w�I&�!Rjb!��#Imb)}6~aBN� evol`rul 5_r HNU� g�BL \"f ��� +%Blg_j.-] (Oj)�':9 G(j)9� �k)!�f )� d��g5�'} Yv�tbiFZ�P��{l�R!1��s0c@F6�J\GO%��2gK$. MoreiMO.~5�����S��hOv��e?A_�y$:�� q�6� is���2� n�_&}O� KV�).�~C&4a-NbQ onl&m� :SO}h�^�B!$ "^G do2 )"�D� , �)n�le-S�� need�AFurk2�!M ^�6�E&VrN_J m�>=� 1 .G�!a. �* b)��(P(f� �h& T �gofbM6 �f5?�� �5 � u� �E�;}b� ��; not)>�B�ce:eyE1*Z+! :s. UC�� trai})|I�]<�xs;��K"� f��8`eR92{.a�e��>� .�!�vn �&�_ �ors}~E@^p2;dG� E�V& n&6-1$ �E�P�V�� �J. A>�^ �me6 F!2 N: LB&P�ዡalA�"�$�~`�0�$4f�4&Jim.:?)���Xa� maxi�~ llel�� -Aie�$�oneN &{ n.�"���Fdge-co�F-�$\chi',&#!< �<= chr% Z��y An noET2gB�N�0<�nnTepmT���D� $c-$c$��W�?��17�!�f��11h%�uYd.:S�r9�ac�y�hinc5T�2W��f$O(1\kki�W�Q '����!&��&�K. ��)[��\&be A,"��V�%�}�� M�� _�di6hl� [AgxL+E�Ot'��-">!�->X��H^q/%@&�%�l� G'&� �T}}1p'-q�)2�+Q,m[ �!]PFR�r_+ � _ stea}K9J5Fc�.: 4edu� �� re $LU$.���)8( 16BK'��JS��{2�A� �I_M�50r*NowINO�RVui�AN<�oJ1"4CIfɉ�-qa��3E V R��e5™�B� l-�!:�oneYjend�y� An}L�#�M2% �O ,!o�\-a� *=n� A�6) *�2��+="}%&&O _g� &�4)A�ithout>D ��2J�u����%�6D$2� "�UMs A^="�&?�>2-A4>.,./Z�!i�46�FM�| E | y| V| }� � �3A:� A ]�: w u�� o�(�tago+�?  L,k&�re� <2�M%ad�)�S O4� inciL  `H�4a�2# <add"� /:�C6 �� m_i$ non-} �-�.[.�J��~%m_i/k~% +1$ stepm �."� -{e � "� !�he �nH:�&� Mt J>8���9n $ m_{i=1}^{x ' =-&B�5($'+m(k� �5e 'X�+]6= [0=��RhavE9��st\1���(ir8gra�9RR�lrqtha!!E� m}{nA��6  vFI��6AD���*{;�$km/n$ (��fb)��� t� choi*P!�` �eE)�V�&R_�d�<-L/k���� d+?��6�Â2m^2}%�@'n+n\sqrt{4m^2/n+S^2}}=O(-&,$m^2"n%(� M�51 C�cn�_67��� &($>�&�Ɲ � B= !jɦ�a!A��F%(\tilde{G}}={xV}yxE!��e� witha�"� .�)-#|�.UE}.� jV}��� \{)S | E'.)V'" \, | \, �]',E')&&rm{and�-� "�"� \}$$�:zu6XM�wo��� h ~ >�U%{&�#� o fi�X.�i�*�a���J%. F�z,�H#0 �.0iAr"�8��s� k� liō6�i�֡��� ��B  ��I�&/. To�.6j�' b&�( N6Di�Sb$!N�"�@})"�,")(�(�9GD ϓ� :j�,![ �/��Ve~�1eJ�`� a"�2R���eq"�of"""�"MA�h�� ��@\{u,w\}a{� $E'=(E&o4\{(v,v_i), v_i�8R\� B,(v,u),(u,w)\n cup$� {(wF9[-!@��r�7�?2��Ah)'%��f��D�9 � 12� "�0V�F10cm] ^}�L" 1)�E��!�%z �" �~<�}�x �� D5�}629�!h�kJdee&.C�\ertg:"� Xe�M. r| *F )c*�/#D 3!��"�� A!�&&G� �A%r�rsiv�%M6�ea%  greate�V 4>�H6> Q2s7aph�1�;# i�pR�&i�e�^�6"%S$%�IIre�f�-P I.�B�`J�?,S82sgsc":� P.}�*."9�Uu� edR�/R�I�Q�E-� F�c^\QBt �M22*v2��=2ub.�. B32$."�)o.$G$!;I���to5�~�tA�� t1� g� .7rA�"�.t�{I^N0�p&} >�^^AG���D./��s'�Td FsG�iS�&�:h�  (G��))+�V%�� ����p,2�9 � A4;a:8,'4� ��&/�*�du�AH%ԡ�,��VRh2a#$ (00 e rq0{%�+},-m )�i�k�# 2�!A=L�.it.wel >�to�.�M>�;>�0 B'**bMh=� tIS&�J�-��^��% %+3"y!&U:�z�J� %��l�h"� nb:k!��>R!�"�8& l�?:���7�� :A2}f�-x�a9CA0-|e�J� IO&�aC�(:�%-LK��4|E'|-2| ),\�\* ���S!�C���b"� �Y�F�Na'IK!m��:�, .����fo�fAdB to�c`=b\>m�9K�zAqui�|Q +u' n: $\s&4d_i>3} 2(d_i-3& d; -s� $i^{th}�exm:�EF� $Vi+2� m_��83}d_i - R� 2 � (� d_i �!�,| = 4| E| %� |4 ��!8)������G}$����ڼ�bk.� $4|�E}a V}|�� !8y3���6Q ��mc��ie�^���Z:"� m�!B:A2�-a����z, (? #w�GY(PIHR��� �BZ�%aX��#f . 2V A�1f�.� Z�%>�Bp �6}�P�+�/�$��*a-%�G���x=#e:#.�&����F!@ORY�vZ 0Z:� �r� "}$��o� ~$�Grs�  i6I$ze"MG!��Еs��Bv) 3s  � ~�z�� � 7!U-�r$A�����L}6�#S:�#N}XDIf����o�<N<m �XZ���8 6?:�1]4z�G!>V9�����b]�"}�a-%9 V�x!<.��j2� ����N� v�>�&SI��:��*a:�V� $U����� .�+� . A�n �.Hi��ht�#��� osD4�jV�sD� heMJ�"�8�3. SFC> ���� � �B"�D�~ >GJ�:Gd5.�F"�$| ^ -j Z ,^:��2�&0�.t���%� %�VV1�replac+ a�#JlA1�)�&�EIsigma�z$�Tll $|V|�Pa.�6�J ��J�wn"A"� Q�#s}- � "�� J�.& b!zv�,�;�>�,�9&j�M1d )�F�is zero5 "��:�a� ��}~�i����N:�>����YyM-=8 �A!z-�wo�1$1.B���/�Q�@"�(nu�~K2l��:r�Z,M�~i:e."� � >� L��%64 A�,a��1� V�wt@ Z� <� A�!_�5 "5 A���n�S:e>��/qJ|���A�J�A۩c�:hr��.s&� Q!�2�x��A���� R 9�!��"� f�9 � �Vng.�<9V.M!��C�is�, M4"�Rv)�R"� nbRI�? �� 62( l -�,eX2%,�Q+U Z��F�'fd �s�=8Y*�(U $ �3�p!2C%V V�&�Ti(v sr��Ez��.�ƙ%BYr� �60�Y�\ NB02(6�B$V#L(rx�&&z1( �2;:( ��/ u�!�H  ��:.1&��" }A >� "�-a m"]/N�/~g RG+o\ �y&�'Q�4"�9ڹf!�na# :�vENj&- �"t"�. A�}�.�Q3:�9�Z�`�)rC��:JPufee�"3�w,_0=(V_0,E_0)ne��.$^ (G_0FM'�'w�6��2��u� Y:4:+-U�C6�ce,�JtJ"n9-!�1�A��nAD�G!�$�]k�s �o�pnՎ�Q��%=ABZ&[O�@&�$h.ity�/-&�Sat&/�Q�Q$b&�c{� . tm@1losge؉ty!*:�&?!.AB�$n �XmatWPO}E. ?R� ��&$�2!���L�u.�Dx�.�E�2� �3*� O�X) � iscuaYa�Bɶ~f O`��<�ssZCr} �..R2B{��MM �i��2�a6a�)�$ uiu0C*�5�!�C�.�&lqClifford&�� $C.� fw=C� r(�9�aCq@e* vi��?eb�$2by:��"�8��4}�verifie*/ �z����,SO}�� '(C^{\dagger}Y2�$$9!� v=, $W=Z_e"G�"T)t�F�n2��A��)�)|� fixp^� W,KR�8thf�8GuxB,�d.k2k*�d. Srl�FCY:�12F��q�d.�BS�%�q0C 9iv0 +0V_0\backslashog��| D�o0�|ah- =gD_0)x*�_�i�$W5�9�IWg V!>\��D h)}W2: $ �XB$W2�� orA.m�2O�3 mmut�-)�y� $v_1- �2�Wɔɩ!\{I,Z\�$� us�1�%%�EaW �.�so�� $X{(3� B*�=I�CAppe�:t8f}A6i*m $D]2\�qIH��� qEfN��eD, %3)u$W �:�K2u2dIy]~R�z�"S�iե]E!2�*� Y řY��j�}:%�h=U S.�UR U�a��V�?c��:�^�X$��&A�B#�l| d�gQ�%sqms $A�n ^$�{�D9*�v'r�WG T� i�-qd:�O!�j��/�ys�p �d��&]' �U��f"�\*�fi:�M� : *0!.=�d�2�f�\1 u :%}to�f.�wea�ss�f25IJs"�S!%1G- 5�+@,$S_{\mu}=\{(�K\muJg_0�_0e�i�6K�!�fXr:�.�U%�h!��c"%de��[�|s* 2�I�$�ƛ��A�aM��QM�� ƍ� valiJY.e.�Lr6*^0c2Wh $\mu�X5y}Y :C s52v$.��Dc� �6�� d ��#^�2}mUn�.*�fa�l3,g#� : D]k)�.� t $RI/+G}mA*B).#�L[e%)�n�*%�� T)Z&�K)9� )<\8S} �b�D\}'M*��6���mp�e�">DseX����l�v��%�E]v�e/�=6P �;~�.� �Y=,:� �U2�7$Z_9�=epZ��O B�!r$1� !|*�@%s.% �bV 6�S'b�^{(D)}��!��A�$g_ %>!�h1�[�!=3�j� B%�W �d'���*�7 �Z��N��,�v}'�qq, \muJ�a&\mu0op�`u~�_1�nd*�_2}%s7�4b�9-����$orthogonal5d�"�rMu2�: qtD.�0--�(v�P\langle  _1�2�;2|!(v))(@ p52})=-6..E6ich6n{0�� �&�G��� {| Ds#&"a2!� mu:D \to �%'���ԡ7ofQ�.� $2e mutu)]9�!����!�(��"�6M� +���EZ]F}fSis [� !�m  ����,o ����:>�5�1g���{�~&�*�<��b1A�.!e��-mց��$��KXa�B�K[44��Az� �/�*�Rs�[" ���!ye]l4�Dv&t� J$j5-�^��1Zos2TV�]�.�M�#6#"%�"�� ��,o}��JBV�?e�a�"<�?��� *��LR�J � ')= ϕ, -R�E@'� "P9�~~ � $m=) �n=3 | zK� �Axex2��*�'q e}��hF��[-eN�dA� ��B R�aY2ODJ�� oif)(ah qj }����r'ai�)$ts} ��_E��gG�gG��n�o���.�!F�sG�sG�sG�sG�sGsG'F�pG�pG�pGFpG��aal�IG$9C+%!�JHGs:$�E2mGxC�IG�IG :�ſ0��isb�6�G �T2��g�?<�0 AJK ~0JCG ��$H^>:�6�5.� %o *{Co<��}� �.��� :? ob�> C�*t�m��Is_�.� � }3j�+���2��.�\)� ,�Э���seLj!��p�= &�%t6S6��of#�t�3"E �T�U)66�[.&�\w!�"c�5>% l)��:�g7b�F�,"�$*� %�j� !�m I& !?![K-*U&Gz�~ oMU���V"��^]znrgroul*V eUIFVa Q5[ thir*���zr lsoRo|lo�r��*��5f %?L� � ]�u"[ �� �(�B"%�.N m�X)m, �)�UNK&�rAg��/ �/��XsuggesZ�&�i ackl�E�K� 5i1^w �7p "�a}&VVj�u.A�q>)�{plainT0"�L�$ P. Alifer!�nd D.W.D�. {\itil)jW9"�4� unifOpi �!rXiv, I�404082̷4��ߜem{B94}�Bs�q*E��A��ons}, �*6�C2v�Py} B 60, 107--144,199.�\ux UDiaIvde!�4�* Eule(u߼}, SIAM��0Algebraic Dis �e M�(@s 8 323--337,1987 5} B88}F����4!�trees!ssucT^ypR�J. pH)( 12 195--20}8.�%5w1.w �Y�ff�&]tT� cogn)~a�:Y�=�8ca 11, 315--32��9�����S�víM.���$E. Tannier �O�� moduˀdominI�game} �HeãuEHS�,ce A (306) 2��303E�3.4�}�Hein,!�*e�H.J�iegelM�Multy-��y F����IC1E�B 307130 �9�a�Nielse�=d �� huanq�6�o)a�InA<4}, Cambrdige U�� ity Press~0~ a!��,)tHI�er.�P Tele��A n MBl�-�*} �EB220�.��p��Ra,%$ndorf, D.E!�owoXdR�B���*��R��6��!�J�105��3=/`� D.2��ML�Gnets�u'E y��2��aI7c��NA202007%�2��G�K`8tner.� em L�Oc>��E-�kHGarden-of-Eden}. Ma����ll�{cere�((1989) 49-5.V��A�.��e;Dehae6�$B. De Moor-��e�desr��?�iK"ΞZ&o )2sE!3%��m30815%+>�4βOn����=��Zuv ���-Us�;'}2111 �4�L>��� d� ��\{J[12pt]{�Lle}2�$uxor-approվbE�=a\ti8�q��;iQ�iG�A=i�S!���iplex� DN�Roberta�Tucci\\�~,P.O. Box 226Bed�',, MA 0173ր3 tF@ar-t�k.co�� \date{5dayA*� \vskip2cm*� A"*�AI"� �����[ "F for "ng (``7") an a"��U!T~� |Y&�o;iI3� � (SEO)."��$U_{in}$ �$\nb$-+�u 9h�d 6m (a>�H'���syT� es) �w59s�� �e. �q>1��ex&��� SEO" �h��illa� CNOT�KBall) a  ��fQ�� -8�: (1)I�At� � well��(2������fe���L <)Q�GZ��!lhTo�) �{�� �. Var,��kVIs have��+V,e literature)�Q`e �:<U$U(2)$-m��ix, Qof "E\Qd ISEO. Ou��{gy!� �ngUx!UOu�!�_Q med�v J�."EWp��h��~+how%X�\ aJ� u)�nB�)6i�I�N�M-�����{In�!�}�W.��xg, V�}�A� ,e]'aAyZ[���� wo) UWeݏ, I�and+??ro�8R�.����f�>Z* �.softw!?pr �m-���#.��\�� . OK��  of:in� c� C ��rE�2�%r it�/�_�;���\�\�2E�h�%f� re7 to (?as@o{�}$. Alobgh goodFȕ[ ers TPzQ�G��t deal�- Q�Xces, .�E�cer��f n im� nt�0w�)ftte�s. ��Rf!���onaa�goal,�ce a �yM (o �yOc��eNU1�u5$ surrogate(ܡ�ecd]ke Ɍim��per �,to "w( &enviro܎al ���O.MM�EA���&�Uq�. Ref.]n�O} #d3t�g5i�� dime�R� �� (�p=$Qof�s),ΧI \geq��1}{4}(4:-3\nbǔ��8�&0�����ec2$�W!�3%L��uq��է� Vidal}. I�$k��wheo5I�����c��ed ��z�LXz .V.k��#tab� }{|r } \h�T I$& �N& $4^{%}$� : $ 1 & 0.00 1 2 2.25 4$3 & 13.50  6460.756' 252 O25)6 1,019S6 1,02074,090 [ 68*16,377c&  87965,529 j 381�262,136p& 491� 1,048,567t 7 @�4,294 { 30 F43 &16,777,206 �)1!$67,108,853 �).1!a(268,435,444�� )>-�KQ :_X�# �R� A�= e ab3��il��+ s,�R:# hopelessU�4  unwe2�� ��G� .Ns&� . ��R !� ��J � �}�Je��&� � .��om�� � -%ck����ear@�t p6 �sfield� "4 Refs�l Copp���~Bar95} DT��]7� .�$issue.!��I�4"�t,$���n�� a v�|4��Zx S��"� Four�3orm� , ��&�!e!?�( negligibly� ��exc So !�en! , can be omit�� impy��1+Tuc99})% Tuc04Oct}=9Nov} -4 �0��5�&� �"d s ���F� �� t U i �7 �Mich04 �Hels0^� alg�ve:a ing "�e*t l g�9tR�  n 2 s.��@g�,�YA�I��� 6iJF w �! ��al�-.�� �� �``� nt"r�7�a�rol�,a<r+ e,�� R��B  W9 =��swa�a Al hS  {\ba �~ cit}"�B$. Fig.�fig"0im�atof our��ach �a5F�{�3��Ek&\�/ eiE�aJ� B2Bo�! th 1e�_ f��[h]D u ��,epsfig{file= ��_, h��t=2.0i%+c��{9*EJ�5v�"��$B$6�G }�V.�E,� �3"�NT} F sec-���Za��"�, define some�C notation that is used throughout this paper. For additional informa?ab- our R0, we recommenSat th�ader consult Ref.\cite{Paulinesia}. RN�pa review article, written by ` author of�, which�s% same�ai� Let $Bool =\{0, 1\}$. As usual, l X\ZZ, \RR, \CC$ represen!3�e set of integers (negative and non-<), real numbers,! complexrespecBly.%�\4$a$, $b$ such)� $a\leq b$� �t_{a,b}=\{a, a+1, \ldots b-1, b�TFor $\Gamma$ equal to =$ RRQ&^{>0}$� 9(^{\geq 0}$ B of posi� and .A$ 5 F� any B1 $n$Nset $S�(S^n$ denoteE} CartAbn produc�$$n$ copiesA6($S$; i.e., I+e%allh-tuples!�element5. %?��(not necessarily distinct) objects $a_1, a_2, a_3, )��\{a2 $\}_{ord}$ �( an ordered�Isome fA-�bvR= \{bsb� ba_3>u.i0\emptyset$ be%!�6�!O, l%�^R4$S$ ina� erse �0. We will usA ,theta(S)$ to:[,``truth func�| "; $0I�(s 1 if stat%� us truEy 0�s false)>exaax,� . Notbat divi%|$by 2 shift� e bina�� %'� 0$x$ one space�t{ ight!�� x}{2�)�!�!�0�q}�Dikewise, multiplicf��2 ~�-� B�lef� 2x= %�A0.I0�(In general,�.�d$I�%:ZZ���M�ſ!b_ 4a -1} h D�%/a_ !N� ver� �}ed $��  ){0}=1$ $1}=0$. CK taTbi'  on.fzE� w0 between $a,b�y!�$a\ )bAn? a\n } 6ua� . On��n exte�e .���2 operE s so��ayy�aP n2� � s.N�$,�  $ymyJ r�&@��en| j�!�a �  v on�4�inaVdually� 0� D%�x}]M5!Y a#T!� 5"��� ] ��{aN �!�LuaU �a>a!t 6� ��$y$E(xMy) �= � �Bis I1��U (witcarry�¡��� ��A floor"� >7 {xe�max \{ : j�x\Q'�� ceil��� iqFin>F�F� ��,� �~$,A�n��oo � \i�9x!�"� often� nb*� a�!�bit�0 $\ns=2^{\nb}� ^ n cor�ond�nu�>� s.t�sets �^|%�= 0, \ns-�\@rchangeably, sinc*"cZZ_.1��(identified !� D V]$�Px_�-1���9��� �� �*� $x= r;�6�, m$x^R= ?0n�� � }$; �,$a}!6regof req!lR�!���i:6�\rarrow� .{(s a 1-1 ont� p. (We5�lette_piE remind �~a permu���6Q  a  A litself)��-5a S \ $M� th 2 give��$M_{ya��y=\pi(x)��� $x,y�x6( Re���*B{ces}arise � $1�column� !�� �U !�Ly satisfy $M^TM=1$.)�Opaper&g oe�" Tmap $%�a>A�2� o�k �*symbol :. WheK �� or b trixA~being8ud5 o�be clear)the tex���s$ AE�a�� ns$ "�2 �v2G����>+�M,�is easy' check � �%�.�Y�0, $(\pi^T A)_E  = A_{A2 i),j�� nd $(A\pi.!i,#j)}�" \pi_Bqi\n�Zih Mk ) 2g (i�a�xMS�).e�_BT �)�aA !y�FBy<$ as follows. IfN �!�� ��� �C�fl�[�(x)*^K!(� )})%� }{-%�U���!����it� b��d3 �G.U i# EZIame�us��i/ �$U�[WreferAm3 differ5�s: 6n���]�A? 2�V+-ya�amD&�al2B � . Al2s o!Y՚~� teB�m}* butn!�.�>Y� hav� vly�E�(E�N�.D�;��a� .6e���la��is)�R�t map(i)=i���i2| �e�A�RQ�=E�-\_n� )}�\s�4on{Gray Code} �� S�s�,well known f� � H codej$Knuth4}. ( was A� d af!EP son ),)�A�color.)nn� ņu? {\bfNish�}A�bA;lis_\Qa\*� &�adjacen nb�!� the JiPonly �onent.!P� a2�� :[%�{Gish}�$k :% $ �,�E;k];)2a�!OR� �.z(k)� Ak �(k+1)��@�f�"� \nb>1� re d��s�@ Z$i,hZ� �$. Next we 5�p� ularEz1� Mwe sh! ��as�he"%�EaN }�G��A� A�a�V b�3��: �<\begin{array}{|c } \h� k&űk}&!HG(k)\\@0&0&0\\ 1&1&1 \\ 4 \end P ��c0&0 e401&01\\ 2&10&1 3&11&10�{f{| }~ 010&0 �01�$ 4&10� 5&101&1$6&1�<7(b�yThe�%�}�iI>0d recursivelyAg� _0 =&|vE� 0$, `�_��� �  0i� eEX� B" V�� _G(0), ID 1), 2l 2t-1)"�. Then,Q�D@ +1{0 \nbw !^RE \ \;�� !\in��� }$.(dS�S( \ref{sec-n�!r �<���_��rom!<9�)���o%:e�B possiblm provi� if $k=Lk  $g gW re v"�s�� �0p!xk)D %Aa�sub� s}*#gk-compfg� = k k_ +1a�,.E -in-If!t��F� 5| (�y.'>\5 3 ~=�$=0$). Eq.(%�eq-2v) spec���s��ar ���A $���F $g$*IA�erm�~R2k�sKqu)Yq�4easily inverte��,Gauss Elimin0� get��� = �1}g2}�2}F(3o :k!�g5�!���6(Eqs=p1�) W$.5" �"r :��3}�<q gA��\�k�M�� 0k!7R0g 0)72K^2M^3���J1 �$in�S E�2S, "�a�B$&{sr$ O �tes:�6� } �%e�� $. Clearly,<B\circ�G$� F� deed��t-6 �P A��eB� waye��� �'a� � erve�prpt�&at � i�]$:� :� (, how�,A��'E�af[-�'s �L� G�B%�$6 . Hence,� �1@ness,� must appl�e!-%�7 r$J before6"� 8Hadamard, Paley�Walsh MM ces}� � > * V i sozed fn�@ces (a.k.a. trans�(s) :F f ��* E)$��-x� ox�i�(H�� )_{k,r}= �81}{\sqrt{\ns}}  $5$e=:$�`}�jr��},"/!�)k� � �P��abetb� $� + }:���6�I F�W����[r�} +r -1}] ���%k,r.,A .FE rE r}��ll�R� nb$ H" $Ei, %�, %3$ in co�s &do��exdo%ot lead�confu�"� $H, P, W$e�*symme�% %�&�%$���,j i4``�al"�o4R(\nb)}(j)=j^R � ``I onB4N4&�j}�a��{G -�y6�B0  has bee�d��vious�+� "]6� �q�Z$ #u���� they��!�< 21aB z .)"no6�e �!^�N��RnstA of 1���.mE�Ef �f pR �reJk bu /G$ isn'tA��J show�2a�'���: �, except1 ����+s. Mo�� 3y, $H,e6%�re�%��%m�%ga�"� � q HAWR=P_(�P G =W:$ h-p-w-gio7 n A m�pi�)ial�AI�%s27 >F) i�( \stackrel{%)�R}{\long�#aE} PV+GJ+ ��Tak�!�O$� both side� z��� s to">pi_R H =CG^T PZF ~BMI_ last5�E0 �� �u�E WqERK>�A׉�]�Compar!z��,(� eq-�B�)�sea�a+Ib)*Aj*/ hs-r-sym}�UQ�4^T A�.�, ps-g:I�, .^� be- liz�s i s. S;�Ba� B.>Q�e[ qa (> ^T H�B� r} &=& H�_B(k)�_B(r)}\\η [k(k" r�`�pi�} r�\H_{��, a so-�%�B-�B !�.� hs-b=�:� ) b 4es>I4) �~iRTo4 vez�, n� �a (�R}k}!�� j2 F H_�%�)jk1 R�Aj�  �  i  j } �&j=k^Rh&=&P_{ik� a Simil��i+r�Gj �)��7 ,n 2�J� +"� �A� G(k) �V1=+Zx (k_d �A�� +1}):C F��t�v{5 �} +znb)}  cW>�� squx�+� � $W$oon*du�@&v:�1).ge]�^2rI�H_Nq%}I�{j �}A�1�10 )� I�)3} (Q�+�)U�)1\`5m  \�1_{6}^{8} 43_{ia1a� P^2=i� H)q�=1���iW+�e)qN-iu Si&their1�J l�e�n � |)F� � 9�,7 orthogoX���."Q� Gs w$ab��fo7�U��,z$,AGSby�)u�+�/B�s�0k �be��F"f�� < JI5�{R(0)}%AJ{pi\nb+1)��,[��Ga{c}>� 3 (1,0�/C) 0,1)z C \& ]9�cq <NR�� ��)0�*V�c} 0&�1&0v�&�_F� �R1))}&d0�^�.�5M�6��T�thevw���Fk inMk. �kEk!�A%6�El H_{0B%e�� e Ad Q,f�1-�-1)>Kg"S A�R �PB�P�=+1b�c} $� (1,1A� :-^�j�YtWB�W�� $���OQc #)y���f� By virtu�#v�  W =q Rw G�"�8w�8-hc .i ) means�A� ���. Z�% r����,����. E�4` ��w�mk"(m,�4 findI]a!� ij} &� r,k� r})�� rk � kj�Q�.2c r� R� k G(j)A�&=&/� R�)\�(e� T�&if��-!@ 2_�B$8(77 h}_j w�>��=�t"b %W �7h}� N�.gwi-defM�2I`#X%"a ConstancyjH��$"�of �:�ed� H*6.%�Dconveniently class�d accor�. t<2�A�)� ider!' 3/"�Qx�q H_3a*_1&�:3��:K�b�v� {|r |} {\s�5style5�000}}&b1j1n:1j:1nt1nt1nt1t &�#\a�&�: 3non9n 3.9.3>3 '  '   36� '>3  9 . 3& ' -. 3F! '�=�.�2�had��/weK�a� 6�3�6�;��, <+index $j��n��iCNS8. Aq�|2x��),a�� �3$�..)�)9v2sim9re� B�A bit-ed "�N� 3$ (��� W_3$")��W�#��{�)��$} $\calc (�))$ra�%5i�7b�Psm�:st&�3 i3cal&�)�1� \�% 0 {8[1,-1,1,1]^T)=1� �[-"2� n�ta�$����vAM<�$H_3$,42lis�;F#h1&!�� 5 app�0A!�.��[ � ��l .�(�$ 2� k) &�PAR$ k)}]}F�(0�'& 8\\ �(�'&�'4. (�'22(*(.@(6(10.((.:(N(2�� �6 "m tab-%��<l!w� ur*)c!�-�!�%�q)�!�e���F incr�$ngY.!a[ �anc;F:� bl&�> 2i�l"�@ on.���/+�������s.�E�x e�seque��8)��0aP! # �es,�3� de%Or stay ]�. S;�t�! 9 analogou� Fr.)Period> Din Fourier Analysi9&Xa��;y"�4A$, m�th�<nd !& �)�A$ may�*�5�y&c8%h to:%h&�8:L8JH $K�Bs >%zm+>ityg bf)�N -]}7 .�R3x}-B!U� it�� m_A(�=K�<gi�Jo � nly �cer�F�� caseoW5�"&�H�# � so�w\ h$f�a 9*@A�� N� Some� we OaqCabb�#at�G calm� � (K)$�:J� � �� g+�� EAI�.�-�!,M� $K$ 1�b� 6Y l|l} 6�$&K=1 & K=248&\s'���. & 0 & 0&nb=2 & #63 & 4.#v�,&    �2� 2�%C2�%�&� $ Q !%q.�<\ns')= D{K1<K>�Hcum2vWe Q0� < E�e|cumullM�plia�B�}�2&� be ��ly:}E2XX})��eq�). It[:"Y��)$��bhV@NhW&![=2^AB 1& 2 3]0AdA\QdA:d.d:A�8.�d��>�>zU? �M�l9< = ;-\nb'}`\nb #b'�.� �>!h'}� �({S�$�7f M� exorJ�( we di�H�5o =exact d9p8Oo�� $U(2)$I�(PoY"�3V E����first��"] $R_yBC � in*�GTuc992�Q Tuc04Oct}� sN��t���g�D! �|A�k endm� �< w�#-A �#oq ize �Rr?(/$R�'C� �*o #�e�-o�d R"�R5� Below�)5E+nt%� quantum �,ui�F$agrams. Be!�!Ce �1al�c��a�sFS��� �**ZS�;x�&lowE%!��"0"�B�R92. A6g�[X: angl��xE$ bWr "A�&R $\exp(i /\sigy)$= l�A\ 8at ``wire". Typ1?1�con!(r a SEOI�cQgA"alter�0ng�,-qux+r �s[ CNOTs' SEO �alw� �#ay : :�onI�� a F �eY8R )�!on I�� ei�% b s orA�%��I5b�� iP �P _{00�0�xGiv�Iwo"Q)�s0b'{��a��SEO^ bin{�C�$ '}(All�&Q9A�on� �- 3"g$8bd �� o* ntrol�� �!P�(t l��G�bc�Q �A�1  I�tak�$Hermitian A2ju(}�U��Qb�+26��,-1}} \phi_{b*IA�*�!b}�!7�A�r�M �E !� @�|�*vn.ndA �3eK_�U� �%�.A�.$Z%b�irY�%ge�>� � back.�/� �� a" X ͑yi'~Kas� � �alT us'Rl i3Rvariant�= 2A. :A$L!Z�%;2$A@s.-�1})A�`/ eB(bW@(� ]X�J)w,)!� $PNP. hP=[�OEOw�&��z���%ώ�%0i:�:H� 8gin{figure}[h] H#b�=er} hepsfig{file=sym-ops.eps, he�M=2.5in ,cap��{:E�Uaa �L�oAU Q���:�on a st=)of���K��sC ��s. ���'� @ � - Fig.�)fi5�,s�3�2�B�ajLa�e�Fi2�x,R!:!6�ucE�thE"�hsՌ�����4free-half-moon2�.7Z�A 1 nod1�S s�@roXYor $P��!�� ��~; 6O $be��&wiM7M�`Q a2� %�P,U(2^{N_T})$-et&/1depenIy�C�$b$,~Xe(t6I�-�)�� rincw Zv6R�}�H-J�  ou�XcIioEa .�� $N_Kt:n��i ���\kappa�0(T$ tar��6' tau}�S�}{b*CKN_K}} U�zu-)Z!b f 2� w%�Vc� I$�!�!�� �"�c� $b�&$!�$b��%sumAj{!}$Q2D�J�1�,ch6�a�s���ty�8%#�sI2[M��hB2�� a�  dS ���4�U� aKA� mX<r2�>c���ry �00^%M.�, a6"�h �2�� �sF L �6qe�of� N@e1f a Z����2}6)w� "m?� of&#ngb��o�R-�*:e�(a):YZ�is5 ivala90!�q � �&(iiǵu( hi_b:8 b�&)= e^{_0%(1)�* igx(1)^{n�'.&1f&�<�eq-)�=?\?Let LHS�� RHS �d"� �'r� h%i�0.�>]).�YE�$n=A��(=P_�4$bar= 1-n =E�)=P_Ur_�*n�3��)!�r :W'^ -proo@#� eqn� !�$V�5�!�z!��+ $" (1)\{\L 0 +�$L_1 [P_0(0)-P_1(0)]\} ;!�� step�Kt-D�$nd�T 6�To arrFB_Yq&�%BQ *A �Js!���0Aj A�1$�-%|q E�N+ K�) V�(*�;�@A�>N rr} !1b�(N8o*hi � V�e;a &CŖ"Ce"B 2i5v� �4� 1�� ^&:0��"*/�{A��e}.�&"F{ -rev/.�:D&F76d>�bj���~ Z"1(a� r<&^ into &|8Z��w��2�~6� 4^���6��z��2�sZ����7�f> ���56�k�M`a!�A��F �of@s&h:� �� "�"d.uN2�z.d56�AcRAc�I D6�(cJ< (d) do too. Fur,�,Bzb08�z:�.�36� exhibi�Fin!D9C9 �0,�)� a>H� :�%'VM ������ eqn{fb ^�2��; �|�& \��}m'eY�&e&x {00}:(2"{ 2{ � .)1^)0)2� {11�R0^)RRU2$e �I6J].:D ��e4techniqu!&a�N re employeE.5HI4u8T )(� ~- "@� #ir�v assume"d ^�[%�\^%O!�1��*�NE].}4CKefJ}O&O- - � - &ZdN[��E�A\ �^�E)�ڕ3�ve*�1V+4` of sGBU�LI�v��3��V̓� "� !�VY� ��4V�.Z���:�4~�������J:7(ditto,T)����nn`3 m4)�.�c6(|*YsH 2Z"�M��stpSng�>z.R�R-1"�s�� Approxi�!6� �F 0� fin�5v2�5�f�\L`n arbitr�g:� 1+%$s6@QXK "�iz� .'"�5. B2#i�|a2We�EX!$B,'J-'-1�.= �fA|-prime eq �k �E�'�Kanb�%$�b6�!'�+�+:4fm0.����YI(eF��%}�a>�t�a��2�A�= b� !� h}_0Q�� 12c-�ar~\&�@ /S".~;i)}}  e�:B %$!�T fo�r�_81x*A\/R���y|EO:br( )h!u� 4E� m�Uc%�2�B�=&�.-),���3%�"{5-�_�! ���&�6�1��C"7�U�3"BY-a�ma�d=���! item�.�at�$st ��IC '&�* 2re �v."�;�o"� "�&\��ich+ s�,6�a�4u*� 8 *� Ko(i�AV os:�s��>}&�'�%�second@ (sf�P���O���t&�00}$)!�16��[���w�em&�""~)5��VSH lTZ three u !�~RA cel &$ in pairs �O�hCX% survivee*$net effect�Žt�CE�IYE6�S9� degerte!� to a6OC 6CE�.��� a 6t reducu*��M�. �l�` ��4 #6�. an� J(!�``Fnt"�/iSfe�u �� E�r�V 4�^%6 4!�&Ln�?%y �� �e-AR h)!�W2} �2cit ;�HB$C)tZ =7-'0R $N_{�}Ѭ�5� E�.�nt �{n|_B�cn�$�x"9�W*�"�,&�.l��*f�&+E���>��{�:l "�:5&0&1&22&I 2B\�21#=&�11} 2 3}& @5& 2& ] B ��9դn-cnot2=A�6���}_B� �xbb{Z}�V�g�e5�= 2 b-1-� �hf�IYb-�_� �ew!�!j� B#v $ a u E�of6�W&s� Rm��n a.�>e+ous crh:ia.L cho�&+(D�U�,�2y �J �Aa highen37��`g �� �t�$$smoothing,iLDag� =;2v} m~! $ful!]91 tasks.*�H�D6�!zV� � � lJzc� С.�,�5� �,<18�.6�Hk�0�d4 coul8ae�1��,.�W , ouS^`>��L� �$at minimiz;z�a�LL/%� orig�2>�I|�nt5��do�ant.�.A�}��us%�ifJ( goalr �!�F��6A�F��d .�q�_M&� .$ $\{�T�$}2a � 0ub}"q��"&�) .� $\UpsilonP6w'r~x)of!�9n� Z�c�x$\|- �~%[)G�&�ng �% '$. "~=q �6m#�^\�b&*�Z�&=& \|�Q_&,&�[!o (1�'1� -)��=&=w_b \|$j76?& : |A '_b-_b|=\�'}-i ��\|_�e:_s�$ ineqb��$:2, K�$aO=#V��Ap�*ix�a 0&�>s"m=�>���V�$�1�{ *arVW%�b�H ingu[ it"[N "j}. 26�De pictuU ergeG ��] � Oeq8���"+ + �Z$ k8\ cos~Iw�m lik�h�x-�.wo 1� �]g> V cer� |t.f56� y.�^��~2 �_0�~ $�,�15 use6�fn�� � eqma^fi�h�,63 !"}E9+.:��J(.?��(�)�����5NAc-3v,oi4 �7courag��rs�!� u?� ap.huter-�s}. It�;� outp��0 pro�9��\ o�f&5k/}$ via2�d2�� V�^ 2,:7��eoifL9c(9 {� �%. u��exp5< /��e��C*��!un)�.0a quick glimpщ <�^2A�seek,S+r�E��C.Yb�GW�Iŀ�L2���L�"b�q� �L|nCV�Ln�Lfv^LdW"Dp2�J&�JBK �J&>* 7K6N� 9SW�(b(~ b4N�(� .0 b(�R��5Wx $\mu Mp\muAp�"(s�Mk�S1�C #6{Y#'p & �h�F� A(:,i:j)$� e ub %�RE"�by � ~ o�E�Li��I$i�$a�I" j���z�SY(W_2(:,0:3)  ^T "�.JK�T��!q717 1)^T�.�^2!Q& 0]D]B\muR7*�2 Smu + 2!V.b w2-two-co&e2Z �0�0:�4�$N�y&t� ~�4��8�MsIn E,3P;�  ``dec�!e$" $W(:, 0:�'-13D�q$b&G2�G i-�*; �>#7�5Ą�:a:^T�b!ImIH A�� I�,�aQ��5�M all C0A$Y8^{=}L��8 @ s5�� ne aEd)I��(o�d)&� �7��ob'a"C�D"�8$S�0ub+S$,�� ave<<�.�m4$ a ``��4 -"V.$.e�:���!���pn $V=W�!�r| \u�1)Q�a�$}nA"2� }"�P-#,��&��!�:�& R5r&�As�:o��yn�~ &�!!b$(njusEW  ��K B�"I�.v^{(��ub')}.�Tu:! _{qsF@r"�0Ulu�mq�W�Vub^T)_{�E�"ig<��w eq>$%$�[v>�7�~ \\&&j�eY �%;� q r�gt-E�D5D\;\;({-��  t = q� s) \�g�g�g1�<1}(t_0 + t_1) +21 2-�r_1(tM:2} 1�'r_0 *iA���6]�ubYU�qP }^{s B!2.!�1 �MeI"Q K*& �F�6�:� ���2����db#<:�*~.�>�i^.RC� � �k+�FU,we"�f�~� X g  $H"(Zc���&Nb-i A �&�,>�� fact,��<{ie��o  �,R:0mmj*`!$H$[e͵�*�-Jqnc�a�- W8 �T�:��a&h&'�V_�� �Q�|�| V�|_ �>�g ����|>|���-%fp�5a�K5w Ns��)psiN� ;s� �0%K1Jsi�,jl5D-�J�B�kA�n>j�Vy ` �"1 Ph�*�PhA�seeI�.:.#$ev�;&E�B���$�H!2. (r!� a�sam�7 &�4h)but� aOentV�)^?^O%�V� t�!6�>N^{�us1�min_k(6 _k) ��Nj' max_k ""� �llBRe�-\is6�t �x�IuJj - r | �sr2�N�dA1Z  io�Zb�%A "FSomp� algorithm?2;0�T�RsJ&!p�T6�S\\?N�s"��j (. Luckily, AO��TAstlQvalid{`(minor modifDs�$th:ZUon�PIЀ���*� r�T�]��� �<[i)�{1b�;$ma_{s_1} +)�{2. 2})]cA$ma_w^{f(b)6� AQN�e'nesv}~}xC��q�hi}���� parameter67 �:>, C �6 6R.Nt�] �~�,_u� P�K 2gJs&�3"_2#%@~":>2��ec5i  g . i�7!)56-�!s aJ�2!� *?bJ�J � a&%"on��E ?i�r�R� ^�69�z0  L���62! #2�6e�6�,in6�>Dy"�r�.)d!� �(2!~n �G'&a%@�+"�2sa� ��J�'E��+/7\�/$�3���3d�.�����s2$ut"e�2�n� �?@A6~! ��ap�Ws,-9 " XO��� 1�/e*��-�%_{�VL$�U�">�Z��Ma���*� %�#� ��f��4y5;-N�&q%'�ntz�'��si�F.m'�n*zhh�Zu�n!�� �5V[$�Ua� ^�%��S%\�2�j=1}^2�<'_{jb}h% )�BT � �9_.i"�92��$a� \�Qndix .�< : Dia*e"�(\\  $S?] 4ce�� K%&�<_� esa5%a*v�(&}���,, page 574) �<$�R�Q%�) (measuCinZ!�2V�r� beni$�orm) "�)woB�. �(�<},b a���d e 3d#l�j�� $ D�� 3}  Q"E&Q} $�2�6:|<<�+ ' a�'.OU \vsig�'2�'&C(�'&'2' e^{-i6-1HZAE rox �( 1� �� 3~P'.)|*� �#A5 r,*��&AV*(?��u�e}Ia�l�lity. "B44#E6WQ<��)��jd2' �)%�F Y dirn on.  Un:�O�* - %v��y%�{)�= !)kN\ fb>J\cos( @Mw) -a! \sin  z)a�-J& VE6�X|_A � 2 P�2�i�)��V� �^8�Z ��Z" & zcFa +#&=&2 |B�)G�|!�� & |2�.�9f|(6�(���)Eb��+.SE?��n $.+��2A�k6b�y{?�"�=aaX�$A, E�- �R� nq>t RR^{d0� �Ł_(A+E)tmAt�,int_0^t ds\;$ A(t-s)} E 1�p��t�; iff-eq-so0S*��&�.')��{\f Ll R����%��M�� *�R �'q .W 2d)�e� verify� )( �( - R})(0)=0���d6#}{dt}=A6�7J��Z!�(� blemq��u�I ߬�" �L-% R}d�i#b�, �! $A = ���I�ł�+$E#�֍�F*s`��.#Q�is yield��Ai�X �*Se&m )p�7 ' 66 ��&e�R�A�1 E�\ r. 2<(1A�@ \| i.Jj i T�� a�|zL"��rMf�� F&V !~�+V ,��Fr.8 ,  V9 If $U=:�)�-��UU'>&6}yn� eigenE�ao $U$ r $h� },�V- W>Q:�/� � S�@ikeH�� >b $U'Fc'6d�E{Ur(U'-U)�c��� �+dGV�'-U�$$x\pm i y � #�RR1$ `1? $�9a � l.� æ 2+y^�$ $algebraic � �9yIqumR�T T F =\� 2}����յ�2-f� A���BucN'�l�.y��vE2a���25�Ҳ�`��|$�o���xF �z 9I.�q &YZ�J� Comb/ R�i"HN�/��X � ��jAampluF U.�/ ���7(nd illustra�/m�+�ul}3ipk�. OurM�(*�"��@Octave language. *a gF�s,~�n-source��pr� LyUs��sa(�( ��lab^ �:v7 �w p8�7ru� a9environ[�few�hno 2t. �ma{#-�c��Ded�K,rb=my_moo.m=�youo\v=,1pz��&woW1W�L�y�x]�i�Y�-L2-L^63�J����6A�3,2������^DJD%�63�L!L�&w}D6OTN��T�dsz� 1��4 (*(�')qXa��?�321.110e-1!2.779e-03.627 4.215 6Gf6324* 66��261.491 *blT:60706Zl�6 5.551e-1�.l2.316 B2�!:6lV6FI+^�nOHnb=4$�Q,R3w �=8�#�Wrst 8�?]R< ge5")#�EAf��I� �6�.�<$ picked 8 .6krandom�W�8� uni% tervJU =!i�v6�(R[_d�da��8�. �"R �{� ed!�oS6o��*Ar him �lQsup`���^� Af���M�., �s &R *#&!�b!$.� Op�Vof��S�Gs6ach�&�~t �mt$�N�"!uf$r� N Y8 &�H$(=7|). "�C5$q�=:��'}�UI(7e0�,�MRs'���A*�!l7MK&n���r7�A�*�J$j�!� j�S[6J&, 6k&]G&� �M�?j�3RA!h�!Z� &C�_$�%DRCa��!���.�e.5p $(=c�85�AoN$ed� �is>O:7 �VO�Za�aL�p�(�2�?)$ N>K$maximum (W %!��Jdef�.�is,�&�nt�nwCn�aBs, somBa�[�i&H_$!�t1�X&�aPO�)�) EO<��'"�6����=� �Hi� MU�9��>?"F��9 =$ (&��al)1�rC��>�J�j]�6Fla t��� gPd iid (��,��yributed)MzCR!�f����re�4ngW<e��$ monotonic+. A�V�Ss�Ksg$ �way)� grap�{(j�� hi_j-��Sj}�a�%3probabi�_� close<a �:La�)va :c"�Kstair��A��b��fi�,trDg�%� �on�� mosts,yima�J9�^�eIdQ�mod~�ich5�s%�����% ��"@&:�eEF�S.�H=��nee�����Yoccur,�%o&9c0Der�^w�ry�na�>�A��'b=5#�nd�u}4its�  7.��Y0 I&9��R�iT}|4k��1�j�.iI�5 =3�BRy���)Nof 7/8�Ole ��H�R5�s � 6�s�as 5/8.����alO�ghB<��t�-�{!$.��%!�c.L 5!�7���S�s inef���q��of T6Q�um � facti� ��,��6f�" groupE�Jlq3rce��a\P��F� n a *"� �(%��+'s.F�F.Py�'}�z3 �ha��o %T $�~omO5}{ &09�C�!nub!}{�L!'!}$ (r�% &a"]5$)��i s�A".�&�P F!$J�aZ \ln`�Eexp b�# biR�$polynomial4* 4e}v�� important�Jrem�VNam��BR3Bw'\�� �.2� ^l�wAEdl� �1U=1$Q>A~ n $ 6�/�2O ;H*F2.F2$F6E.F 9�<-1)}{1\�92}$, etcB'$thebibli�Iphy}{99}0'lm{f�} V.V.Shende, I.L.Markov, S.S.Bullock, ``On Universal G�^Libra�� G�� ic M/Qal�v�|Qu6�$Circuits",1(-ph/0308033�$Vidal} G.  $, C.M. Daw��``A�:Z��TwxT�ds.3  ,�s",҄ �7177 !�Gm0m{Copper}Don smith! An i��D�oier*�muMRn �um��o�}4", (1994 IBM Iq��ReA�).�201067=8Bar95}Barenco e���E��odGfor9t<%", ��9503016^2�( R.R. Tucci\ A Ru��_2U8iler (2cnd Ed.).K99020626\-6^Q� er A�2 M*62, EPg��Unstru�OdA�MI�mFemY!�6�41102.HT �Nov>�QNF��F׏YE Vie�F�  Sp�d C�� of R � App"j�8of Cosine-Sine 21p2�97>BM|Mich046�.� }�ePrI�~@Top-down�roache �m� Synf9i6�40617.Hels04A�@V. Bergholm, J. V�i4ainen, M.Mott��<, M. Salomaa, `5U&{ for �6�)�|�wo-Eg��al �A�o� or!�Y�0410066��]e*.�E�U�QC .�0407215D- G.H.  � C.F�n Loan Xit�rix�e`s, Thirap_8} (John HopkinsA� v. P��, 1996�;\1���Donald  kArXWCe� er P�O\ming} vol.4, Zeroth PrinK -Re7pon 12, http://www-cs-faculty.�pford.edu/\~{}knuth/taocp.html!aendBK docu�} �T\�� [two �; l]{revtex�J(usepackage{L icxŚY+E@} %\draft \title{avt�n�rs� f� rt{��alu!M�\{Zbyszek P. Karkuszewskikaffili%� { In�fofz�(, Jagiellon��U��Pity, Cracow, Poland\\�8\\ Los Alamos NY8al Laboratory,  (, NM 87545.H,\date{\today�)ab� ct}v�oldMle 5exte�nOme�W W6� -3addAzeԁcNof&� r�gh!Xas� a�/to�ir i�: nsic-zcal�7A�"�(a�h" )���� &� U6 ic ��ces��<:h help]H!# qual�)�pcommoF`D�o���6um me�3�"!-� gy un�3Ut�$"��\\�,,LAUR-04-5290�9�22keE� " $I` du�_)�gJZof�#sc� 9Vaor�`!$predict fukV volu'* of p �al sys�c��*i)fir K�p��behavio�#��� *IJ�4�suc!i� an��vЁis weat6]fo@ sts. Ev)\hisA�> 9�&�8 �Vem�����s;2, humideT$wind veloc etc.A2 ���$ years�ma.�0on EarthP �a��a� -k� A�c#\g �0d���#�� ma2�� �Qvdays.�)�� argu�' mospg�Q�i|p to:)�!�con�,r dCo2yc inst@ ies:)� a tiT�ertur $o.aiNp� y��2�ghuge a�Xot�)�H��3']t��tk�� work�2a�b�4� d�N� EA �lմI�e/�]m� !"��{6���AW as celesGu�. Cent�s-[Oobs�!�E�!�Mo�}XSunA�o�  a�_(nt astronom��t��i�Q1=E's pha ri��et�ksMd eclips"Z�O�$ millennia%$_�'A� ledga� graviDa4`� 4or Kepler's la�chA�ci& �c_ ۗݗ�r�� \��fundah �>�h-'J��l��%M .?�X �)�b�fE I-ed�!Yam�peE�fi.�"���9ʊ� � achiev!( exac2�1`�<}6w.Z �. �*G��be�� ��QeAi�16�9� y�describ��@�e � ���Bisp:���Acru��. SA�qr&��%��e �d f�-c�pgory.�l(BAgn*!?a method�igMB��erAV�`dnnu ���:z- �I�6%�. Sq��a�� tinu��-> y (a� ) $c(t)"��dly Y15A"���l �4[0,T]g&��e�n�*�AC�L!r} ��9�;k�;K d_k�0 omega_k t2hC{sigc}� Fq8K�a\,��, $d_k 7l�]i�@C�$ssp} ampli?��  $v$A 8(6Z ) fr� yAG� ��5Q, axs�-�y��cJ� #��9?���o�>�pr�� a&�e���op�e%��1 �{k'}=-�B-g� i� o un��n9 s-;�e�.Wk��Fn�)�� G lengV>T-�'6N���`h. C st���.��� $T\ll 1/ � {max��� iZ�f{�k$r&�!�ir� � iof ��%lhe�8!�ts Ekn�AE��Mz ��,� ���=e)UA��ticU %!$te]," * ,F�hp6ly&��y o!\��va�i�#m"���4�!,�A�v !�������l u%�d2�(eS) 8 desidpr�. U�tunat� q�7i�:sol ��non!�ar<��14�3e�numer!p-�� � handh1��i\�� ��Cbemm datas s. \~��ofXL  ar�{���eFt7Ŭ�9YD� 9 %�dTlos"� )���!��c .76m now� we�!��IU/ �Y` i��at $N+1$�i Eh �$t_n=�' t� $n=0,...,��=t_N=T$.6�A�b� n2I�Zsu��sF�~�_nh c_n,�O sigd^� c_n\� c(�)ڒf9 $2K$�bu�� s (a�:���) s)M-߁lex!V � �gt����l� gre���I[�5� p�� ope�� d  of ex���;iM5a0V�uT�JrH naA��O$���W;a3s����@� a�b M�Y� s toYd})�!|is self-st� n�?II8. I��%K����k�?�cb{ �r "!=��k�u'q�(���!MI��yagTsky �4!inv�� .c� � 1/Hour)< n1)C���r�� eno4A t�5��s$����,�9���E]�Qa i6�5��n*��! (DFT)�at{\^��s}6iߠ$N65.�!���aA��!��t�E`���A A�qm2Ed�_ingA�!x �6cOgroN��to $1/T�& thܩhe ��"usW�" � A1 ng v��c$c$~'�. �CT!�N"c1�engE�o��2���Bn0�� %�t&�6, harm�$Aoer� �."�HB&�a �roO�� 5��`zack!I!� cx� Tby Gaspard Riche (Baroh��ny��Pronyep��� 1[���"�o� ��Df�Z 5�c��$Marple}. H��� �� y�nuderiv2`"vO.�key|&a?��Je)d!���la��xF�2�� a-GX=q�E + fic*� � $\a�UAfI�@�dne�$!86Ȩ"c]malis4� umA+ c�pnp��,a �[�t1� �.���so}ne�&�a�fs� we &F�s]a�x�c R��9S2�n6�as�W�Xs $|\PhK��� le$ a�ge�x� n�#2s1w(�! ��� Nn N J)�^n0:v.VrJ ^ig���\. �q�)in� A4 *�I3� s$+0 Vm'pie���'&'autoc��r�:u��Fz c_��\la+�)I| 1"caVBt I�Ϳto� d2\@$u_k=�Q(-ix=u��� $2�RT6z.�. ��2 x6e1F�a4��E<s5� -�$1_6�h� c���eeJ�U_J�Q2.Ti | U-Xj k = � 2y$U^{j-i+1} -0-c_7u�<��q�H}i,j� N-1A���ne����dZ!�"v�� "T��e -c�b��0$c_{-n}=c^*_n� oQZ� 2�@" M-�-� ~Bm��ǃ=j, m"�X" I2� m(� %������#Pedb-3~ �*�  . V^��qq $� ���i��(�hCԥ ��- ~�TF�U |u_kYu_k S." gepB� S� xcalL�s@hY�M� � i��Q�=I�!+]hIgAfran %ge� �W �5�"� B P-�-�} � N\ge K�%cf�V e�� stag<(F�4,�") ly � ��3lctF���!g)?e(&2 N�� ,�"��.3 >�� Z$ A#%U*�Z S �  ��brillͦ" B bRdevelo+��v�by �Ŗ chem!��,7 Neuh� r,Taylor1 2}� �n !�it fails-T%0ed to short (�qsmall $T$) signals, \cite{Taylor2}. This limitation has been phrased in a form of Fourier-like uncertainty relatAxstating that the local density E(frequencies '�can be resolved by harmonic inversion must be s�er;n bength�_t time span)>�8 Here we claimR �$applicabil �U0method is not)4 � � $T6�Hinterval but rather�(noise affec--e�H$c(t)$. In short, !!S,(\ref{gep}) !C(ires calcul)tan-/e��Hermitian scalar product matrix $S$. !��$K$ positive and $N-K$ zero eigenvalues. Th!8Tare algebraic techniqu!�@o cope with singuzrces, see-��increasQ�fas�th�$T�3Assum%�I�U!�corrup��)<$\eta(t), \quad \in [- _{max},  ]$i�new�\4 $\tilde c_n =+ 2n�]to!� used uild)[cesAJ )��. HF%�extract ��q�HifJ�.* \ge 4N�q�ncJ�ich!.8a necessary conM�assur5g�29��s E�S$��found. Pe�c��)�leads!a setAzU�2� 1f�� $, w�differE� $ F|-�$ - |a�e \�2KN^2}:9?.1@inaBANoA�Q�i�a "cer/"� than uJH4. The accurac8.�%I�`A�J.TPmade as high as need�reduc)�e ampl�Dof-�eI�$� �pcentral�� of t work�numeri� studA�� =H�%ed�|�a� rol]was play �AAHoff errors. Figure Fig1}��ws exemplA���vA��J2 to a�Gx�<�����$ parametere�Lex!>H Lre deliberately chos�1o exposAe��rtaa�preci�S%K� . Q�f�}[htb] \includegraphics*[width=8.6cm],,1a.eps} \cap�{A-���J-�was)3ed %�F�$K=10$2�drawniz!"� 4$(0.5,1.0)$, s{,d at $N+1=14l ints X|T=0.01$ (upper plot). 85 digits9%, i.e..� =10^{-84}�as�f. B� o��e p l-`d� �is��onstruc�$((red line) �� helpGF@ . Ex��(black 8 �reVU xsJ in��,able (middle-  fact,�twoas rtA��by 1\%eX$t>1,000$ discrepa~ Kat~du*:` (��)��inM l )N,;visiu bottom��8q"} 6�=4.07\� s %� 78}$%7�T$justifies I�?J. A� curi� y�e DFT� orithmQ�!+Z-�would g� l one "� y�L=0$� ��I3predi� B<:; 5!-�othFt� readV >d � mdsatisfy0 .�U���. Simi�ine�AAOroftL roviv �ime $t)�m5 $E$ F�IE t ],~ dedt�J&� � pre�4in various way�litA ure. Un� �, �is�@ATra� H1�uv A��8analogy between�� )�.V1-�n[bajrr�) o far. On dAB����n���ented�� textbooksA(F���8Schiff,Messiah}��follows:��2�)N*�ar�s.% UnbreakE�Q`} M�m!����� w��  uA�u� or d��al� ysis. Aa1a�A�case Cussed��,Egy| of5L�&Cr��y��e�r�,��[,k�im�4igorously deri����qM� �4Mandelshtam}. M�$Heisenberg.�5]E� manife��.] � in��eorem: I��0A)�$ B� �� -adj* &r A�a� $|\Psi���s!(ultane � domai�y�� B$, �A�A*A^22�^2�nF�o A B} �${1}{2} |\l�� [ e, B] �|"� HutJ� !�$( _(A)^2\equiv WNA^2 O� q  ^2$/ ... >Q Psi|.w �6�!� AzH �nsic fea* A�AzA%e :� and  noth�qto do���D�O&� iM  TwE��{!�l�lA:&�"��(s familiar �-aJ��*�of&_.T. Ias|  ��nd�yy�x !��!"f$0�0$� ce@ �orIatb�Hi�m�B�eft |�| �iu�}  t}\r>|}�#��'>� a:*i�A��� somemB!aSՠ+A� --O life�o>�N��$!$BisV�c"�@broken or circumvA�dW$holds as l�s՜&&is/ id.a��oa��uā}�$'!=�� �"one copVv����2="�Summary}q%��s^ a pp V 7!e� ��j te2a� >� ��� avail%} �D� 1io�!�.o pric��E!�p �beL �R� "� |&�!.~��i�#al!ld�#6 s1�Jed �D both �! inv�'[y.' � situ� ~A�wA�be� in� Hi&� Qa s m�control�gaK�data.K 3e$�( bt!identi�sourc��TicultyeC a �dy&"� of �sj)� A�ool!� b a:Dw��$i$Pp��$e�$a powerful&mag& t%K� e>�imugN�� U u�))F�#'lsoAs��1�!�inuu-9i�se�� ide�w�&��"]"�"y )CionV�is�erior!w e�&%c��! �� consider� Read�H este7 x'a�a{��a�n O�A����lex�� m�,beqdA6 uld ���"�+ ��Ac" ledgB s} I am gA�A�to Jacek Dziarmaga, Krzysztof Sacha, Jakub Zakrzewski� Geo)Zweig�me je ng�  . Work![�y KBN�Dnt 5 P03B 088 21. �bn)thebibli�T}{} \bibitem{ssp} Nega:� V�-^la�# rdi�6�*Ex(a symmetricB�*� is L�,6z%det�'�Prony} B� de ,, J. E. Poly+L., {\bf 1} 24 (1795)D4Marple} S. L. , Jr., D�! al S]�bAna�, P�Lice-Hall, Inc. (1987.[DNeuhauser} M. R. W�A�D. �(Chem. Phys. �<02}, 8011 (1995)�I�1} V. A�"]\H.� %B\ ) 06}, 5085�92� 92�^]7}, 6756F]^, G.� �DC. F. van Loan, "M -a�u�s",�$ John Hopk|Uni�.ty!�$ss, Baltim�� 1996=� U.  , Contemp2u,45} 93 (2004.�w}A!I. , 8M�$, McGraw-H�Compani_- 3rd ��(1968.YM�!� RXD�Pub&]�0.LJPerv"�T%y:�cep= nd M=/!W<(Kluwer Academic hgs,!G2/� 1} Y.6iD. l,M�RevQ�2A� 1649%1.�a!G. V�38} 343C6�.^!�MamE]I. Tamme ia(USSR)ih9�9ad4R�22�,a[Ma�* Popescu2�A Y(66}, 052107%�2��.>|��doc�} � \c�!L{amsart} \usepackagesymb} %��2{ icxB�cd�|TCIDATA{OutputFilter=LATEX.DLL} !Cr=/Td=Thu Jan 01 15:09:50 a�+ LastRevis /8Dec 09 11:01:08>/0a.2D-�Shell3 Jour5 0Articles\AMS :2UCSTFile=)�0ci.cst} \newaA�}{e�em} \ $style{plai13a"}�}*� 2aalr&}{A 6"xio2� }{Case:�3}{C62o *�}{C >$�-# >"jec�# :$rolP+# 6"rQ ioh 2"det#D 2$e�*}{E :ercis 2 lemma}{L2no��}{N 2 �$}�w'B� " 2D remark}{R 2s�}{S 6 �&�.�v): iscu�2B�#� .�3{o%!Pewcommand{\thmref}[1]Q�~;-#1}:*sec*\SZ$leN%pL�g� �Ya� c5r ,gskip {\Huge��physics� hidden�"�H 9, {\LARGE An�o C�- } a .c�@tin.it http://xoomer.virgilio.it/(\_lazz�� chi/ C /welb5 .htm�-z\B �bu&c�?�j�4ry"^ �al~O�""� g $''shadow''cial ki+!f| 9( G7�prA�ed n���mai�bec4  each* f�5|a well�az�ue.5pYe x: an hyp�;*r"wP&K �ex�in anH igned `D !�� <3aS� a�) atusae&cor;�2�9 o a H d �Pge� l%�ami al �1P �=� instJ&b� unYt _�7�8)o*ignor�/�#>�,�&!V%_@5a"�(�)�10!a��#exs �� �-e �� dynamag�.��9��c�*�&$s�*)�B  &�\protectm�I��9��.O}"k�4be�e���* esi� U�: itsI-��$Fa m�ol�s.  �Q�sA�!�6/9)re*[by9!�9#0e�!j ;�B�6" ''h&�('' vector ff*sE}��, � E1�XM�� e�q�!i��.�rArn �l,j' �#!*�or :��do}mak'% �space;�ryouN_Alir ''mea�ցL5� '' (��(��a�&�- :)ege�/''a��1�)2b��E�"�* aǥxsG.e�fi? Jx�06�/s! �pa2%ɱ <� aY���1�!8 S5%4!I !v gene-Mk:E�hmi�>�''%�0��r=a �25.th0cr TY+e�^f �- 1n'':�'';Ithe�&wo�i�ImoP� �eL5= M|e72��0i?�:)%�O9�t&e�')�lis�� s:.�\>* f{A}M�h� olih�*} % =16$*}QMSchroe>0(choo�".� �$r$H2])y avFE�!0!@t�$� r^{2}T��s!1%b��/ $)2p1�B}�+�8I!$ $\varphi M-�!�}(�g��''�valent''!QG���:A�by.:C$ ''phase''�*�S� l�.�#A��a2{3group}�% }^{1}$��I� �ma��!Vm��� ravel a~he $% E�@T-orbievE�A��[ 19\l] = \{ \rho _� eta }6(\} $ (orG\{X*i�, cdot:Z\} %��!- !din pa��A�&�J=� _{\pi /A9a�FZ"S,� we��i�&-&�0-Ku�s��* ( (ew�/={=;�?�B�0� �8ure: ''"6%out�''A��%rieman!� les embed�0i6�,.K��.JEx&L y �u �sr $%�F�$ furn��a��igma $-mCa�O#ŜsubS!� ��!*u!�AFpa|I�(a�ok"whe4�>A�V?$)�Y�rhE t6�e�A7V W*� ńpl�)he �\+�1i '' beh� H''� K''1R 6]�*� ͻC}"S#Ͱ�<"��uF!��9�VQ -JE�%Ss $0$ a�1$;��x(iIvi�&chak eriz"1 )L$*r�8&� nBA $1!��-��iSDas��ws }� our��QGn��.�$4�g-&� "9#��iz� M�e�n�(L�= :o% ��)$ es6� ���/.}�� n�) �Gi.�(orthog� Z����at $\ps��!5��$ (�  @��)!C)�� �sR1 w$(t)=\cos t6�+\so  psi ��%*} (cqsovrapU�} � e& �\��$) weO�"$\N�(�0ight] Z�(t).�,A�6G�var� $t$,�"tv 4+R/�Um=a%M %n t+b 1k!�+c&By$ i :+�� �.�'��d�G�:��5�B� for u#F�1�I� �$?�)�n"@9�$))�A���];)$%��"�YA�QBneK�U0,1-� �I�!}�� A Dse2�� I��L� f+:C (^:�**� logiceM�^% T�� amil� !S`= los����!%K31� boolean  ��a qa8�GV])"�*^#�$" \>Fs B+� l l� Hu#pro%F;!�-�H}��FrD}. A"� $f:%AX)�arrow Rn �I-]an��%�y}Mif�x ,A�x borel-��(2�R}$% ,� chec�'+;or�!Y�f$ a iV���e, ��s$�!B$;��(f $f^{-1}(BgMf!n s a ��@%"!UA��O >�..���"BtO%�Ea2�8�� I�, independentQLroNO�>.��M"Z>�6�#5 goodrdid�8�U=ifs,��ver�,�<s ����8R�1�"� !�E*�� $Unit(2�1�)%�Bu!Tys�= sui�?eJ�S� *dt)e�3omo�sm! v���> ��2O� �Υ��"E*S �^, coup�yS"� jJZ1-@F}A%"mmuteZ�&$ (plu�A*n�"W); �0ay��^wi�-� Aut(1� S)} �9�AY:�=@M��A@VI��[s� ��!�Done-p"&C(���-) _1�_{��}u�% R�~ }:� $.Ita,�,.o at)Xa n�6opo|C on >$��F���� .�% ���� by�A: a�o $l$2��H to a:&q�)�E� ''mo�4�Z�� f�$hF�!���]% .=)�;���s�''�@>��s''�&sF.F�A�.�a�e /Bhe eye��an�ot>`!%Dwaull@ ���2eE ?How ea�7�G �6!&} im @�j-��ha!� 1LESr�1�8w?i.'4C�A�e�; pF�@�  pr�> l�[s intr!|c)0so�oaduk8{� *� J8�Cn r�%q0 )rV��"��@r�lJy {M"d� �[ 1,en�epaIa 7�dRM o &�':�R�J�:0\leq <2� <�The doeD[1�?% �:��^ out� ;K"7 avoiaO1��$mplet}rando:  VlN�meD )8IEA;� m� �* )� � anyr? ����\{ *  );1 XBT �b. After�aJ2�'arials}g�� -4�s�3ed��A� li�v?-�e 6h~"�$r}%� n�pi " ,f,d�Z%a�ro*�#m�e� fall:a"�F>i (var �B\B& R of �1I{;f"� bb� i�S ��Q"F� $,1�T<"[4 9� , mo��Mdly�mM"�i] ?fJll&!)�"�N�> reforeV� pi&� %�=v� (Nx q�x)F� FsG�sF�a�kel�o��!aW`�e&p���v%aa�&�eJ�  keeps�hiZDl� meanA�m!i 'lUQxR�m���%�ɏY w � / ioqfaa_iz�+�B�"e�Blle��i�l�w6��m�� apb�"� S\f7s ^ � 2')�� �p0,1"SF�� no��y�should9�C �&� 2Qu$_{1{ }}$%YQb_{2  }}$ifR[.� _{1}M�62 F�&�5����*��0�? DuEw��[��f��h $% f��,G},B)=2�2n�=�9�er�H;y �)�t n;"cA�c� \] R}_{ � }$ am�>a���+ ��T� E�}:W���/�� $$:� a��&E �'' �''A�C E R�y�"&P"#ce � f�� �^ �i!''�"aquotii|hat.Z=9H/ �!~-*j�Z Q� t96�G y$6fO O}}= O 6jw!�. OZ Z'obs!X&�- )_d� IcZ��pi�U>��bb{��}6$ �}� (��JF�Hd�R-c �!t*e.>�% SE�nd� $�$; siaoA�!''.U"\� �F�%��V �y�-:AH)aqcts�.&an>��so wt=�(ersubwa _{I}.DC6N`T&lX �' �ngL@&f�!=uX �% �.�S)}}=:/AuJ�! eThva f�!�iRU�\ � �of*r#6����F�. "�M��*oN��:���ja2'=!Y��U%�R rans = ��Q:e}���|� OY$fF!K�J3} g&�+%a}�=G$o!�cVx����"g!cH�-/I! t>^-G�'_C.�H*� V(>� �0<&�x.�!�$1�l�B-�+/(7 � 4 ,A� �E$ E_{B}^{A} $M_{<�#w�-$,! �!b or a&����X!$B��64 od�,f]2 TGNl $A$"�c"�]U<I*;�<2�t�h=��I$r"q �� �t!��tr�7�%� 6.#6l(&�F�`fn./R��T] a�U�)� bxH�q�+ U�bb{P% *� C}�A�H})�a�����:K�]4 @$ moduli�QiR�PIt"$1��O^a �R�Yt\ AB Nasser7�1"�Z �0:սH� a"� "Z(:�Som�0�&�st& QU�,h6�;; ory ��A�claRg�1&I;� 3jat&6+�3�/I�!�nsHcal}:*-�0no room�(non-bl )�6�IE�ia��#� qRr��"�j e Bell in�oli�I wish~Hre1*x\�  it�In Z+spa�8dB�Igi*�^��DQ�' ^S $extual: }b).U<�@�*� re� &�""'U'']@*�%s, F�%Qtruth�G�)I/)=Y�D� �2I62je0 )��o��u ]�fA� 92(�K1&8al1*''bou>&�1I� 2�>m �0h�OD � *$v�''r�ve]�in�+�3: }it �Os E}�-ellq\ }ei�'if.8n5>g�8����a ��U�> -�Galilei��b1%y,Poincar\`{e} 6; �)�0�9n� � �B.9Q�8 ��m�via a617.u�?*� Ie��QT k, f ]�HJ4 my son Andrea%-� � t6��v(,sharp8� 0hal�va��u�� s duae0�>iodAP talks�5eHI>�LA�sc ists"Kia CrAna Abtl, Renzo Cirelli, Mauro Gatti�At4andro Mani\`{a�  Milan sG7�g!�orH�e�their�l6 MLir enl�.e��$��pUJQum�I�[ w!Ztbfn!)IVa�FBatti, Ces�7Re�} Marco Tol=g��, whom I had,1l�y�� o�MA�ysfre�JC/��C���Ip�vݨղ\C{{:�>�(mc}/� $>(K &�>n.�@s}2?e�it{B?}$ �,�  .,�X )$=\h4 deno% [+F�: .bf{(6ci,6�5n&h8on}�rho*!m a�, Isom.�% ~���*.[z!�on ���)\�;� e�m �it{�iav �\`�$ � it{w�%(2y/�perty: �D��b�:BF�8�2�$v +R16:'X8 )��k���� w�9!�K!M\ plicVy�l� of���%F%5~8E�!H�6=P(b;Zų }$k L�g�"HJV9nc �! (e^{"�9)"�Y�.�e�pe� s�<w)L��7� !6 AEJ�IG.�%6 F; o"�6w� }$J 3=-id_ 67\��}qXeU ,J-� �=0l\*>}"��jm" p.T�*�% \E�j Z9\"t z�!x6!��%7!�N�.�6��;!;�� S�� i�Asesqui!!ar��m*� Z�� �#,�!�f9er' +i � U5�2NB�uVH�,&qC��,z%prefe�:t*�6�y�\Eea:�)�����?ao5dA�> Z�.MOU�� �1sV2I2_,>M}���o&o*��&*�F�u�li$�=, >�.�fe]9 i���8.B�c�ton �I�}$5�v"� �%�6M-WM3 �:��.{U$wordsa��E#�6q t orto�9�S.X�1Ε�V , unM  deal� ap[likw1�W*5(]�1i� $H�&S begin.N Our�bf{3�� s}�\ }%b�(.�B)�B7>�B?{: z.Q�.C)=�!|@M-&&4I� ] : �y|���I \| =[C Fv1�7�i( R ��acequo )7it{T5V�  r&�?�H��$o�H.�D� sfC}$�y��7h�z0u���-to� :R& hbaRD%D�eV D;^{^ D} DG�4�A.SRXDEء;� !Tf�D% D:�"D;PlankA� e�P more eleg cho�^}$r=19�.�SuCbmon/� k�&��)L��*�B*I�xc�xinsi5� `,"/Fs�[��}ay6��W8/ �vL u�5S� <er� �}A�K ��\�e e�u�nF[''quadc''&�}&�).}(��):%26  $i�� e��(��I>a norm�i�:�'}�&�%�}&� &� �oa��:��a�L�~~��=>j%&*+� )->#�J�<�71~AP�W����� } $T*H19p4$=a^{\perp NA�h} �v5y! % ����-inJ� bf{v@��}''!:�� V}er�"�#RI }% ��2td &�7h"�{NfH}% o6hE{� .� %�} - }$.z!gmap} $J� send���H}2m*in{ elf,D��_r�|b% J=�.R#LOp:�0[ "�Q��2i�2�BT $:+�-�u��r.�/t(XB 2@XJT.�XJ� X�6&�]!�~QM�j85��" )�" % deQQE tha,%�'I-mbf{I�A6[�)A] 2�H9�" :1qA��� >�.;�on �SF� �it � R���%H�u e/h+ �n� 9&�u B7.k2 to� _(5 }$1� �R�7*�r.�i�*�e ���\�JT8to:�5lp�x� 9�,5pe!(�3al�F Haar��dA^n�Not�%a!�2uV;��ar^�6] }�m&F��.=��}$�1� samI at=b-E���2����P/q�*2 �ux�"� "�u.�Yk�  ��K(u.b=In V,:�i� l���2tc df�=:Z�*):".��)�0,�\�Z].��&$$ : }$� 1X1& ]�teft| ArgJ>9��.|iM� $Arg<u X �]-��]9�v�;7;$% f.0)=��0 K&��i�$Af$2`)..�JG=�;)�ai�bf{%hg�Win7.%�?B�9b��=F�A.".� $ �� EZ�seudo-� A } if-�E� $Br�2A�BD�!�F$ ;�KFu�� >�nul��)�f�B��L�> .$ r:F� Two J�s�#��$C+�KJ�1�%��/ t upAea6]�et}�F;� /,t})!��f+c"�1cmf[;ka$B!sC�S2XF{v!Z�,!�Rn�(r~6�4B�}(Cn�F�(�=�K �K^�5~%B�*(��.{i"�$ \)}it�b� S \gamma� � ��}�� .KA��% b��N�V[�JMyp�>�Os &�Cmaximm!ircle}�Cgeode�_curve)Alj}W�nv>J�"�OIfK%��� >�if�$�q#4K\ a�&M"{*% n�7 ZN)�] )��"�5�MT 2�� Q�0"�K $"�O���J���)\ �==B� "5(:�LbM�6� �1���"bl#���om"�.J��N �N�N1��E^�+�1.$��$\empty�)�to!.� f/.�m�BpA]> �TpB# =�fL"� F90$t^���6� f�&� ^�Neek2��#a\ifend��n�is$�*n�@ccoun)be)�Sof �!a�* .!�&`$�&�;'ďi�&A",%e"�+(�)), }$E&� �$ get}�(RU�I��y�\z� �Eic��XM }$ $.�%q6%,E 2G 6��>M�en��� �7u"i�{&�>uq n-% ��N\!yE� �i�E!3�����pat�M���6 �,u�o�V sAZ=6�R6WZ�/R���p� tU�� b�2�6;��(t*T+Z!f"�2WF,E( ��M}�" � tUa�QtF�Q��t�� :Y :),E� 6� =Zu Fu�KF^��1�uR�;IImE=�A�R�F/}$\ker .1tTDA�5�f~�.�"weWU�:sacQ)~7p+Q�!{6`&� .vU���A30 }$*Z"��}$I&Ew� -�����O f�Z�t"TJ1"wn�w�/}q�_"�1)�(t&�# \ me�B}6�5� \g-�>�%� \tau�'( �i9>�U\#.� uP&S�!��1f������ r �q�$� Sofwp&d[} )| 6g� �bf*�U.2vR- �Q�t��  }$�� JFX5\�M�Sthree d�A ?a�Z (`bas�$asuM,c'�r( ek�g�z �\���"efI1�@). mL 2$"06 �*� }$h6�o��g�eibe F'ten asRQC8=h(0)+\dot{h}(0�QF�+.�d6/ /%)���� D[1*�V� �^�A��� %�6�]\� a�Mif-@r�4dm�coɂ(t+\beta>(>O�e"#uq� A�� eh}.� #�'q�de�Jml-�$.��!| �r^� "��:4y�,\setminus }L3 0' y���jN5� &b ��z!�g a8 "�>��j:��dBX�6�E'$U&ui�p%�.arySA�n $U(Lw�Ps:A�)�1�*�'U�td}mn~Ca�R9��ex�_�Z}6�46m���(���:�3�&L:�}$MA}kitA�r�41�Oq }$L\ MA�EIa�MYd.f!+�S�2�qbv��=$f:r!]�b!1 "��:p�UՋ&@"m�if��m.R� �9ulRRin�> imagiL^"�Z)R* G�U >g�F�0�A=6��:<�!�y7�-�%*J�&�8)�@S��>5.��)�n�&,5*�# �n�-��n!��:~�y�a�2�I�.�F�"Ev� ymbol F� �J%�m1�� *� �YN��J�wF�qq��KP �>�9&�`chi _{A�C:Q�($A$h .�E�n.�:p+$A $./:,��&5A�reA� �5a�2�amY9�"i$b�BR2�q�Eb�|�61E 9 $b\� fNab�Q�n Y��f���C|O\|O�_+ZFnd - =+bs-� ble �s� n�k�� �a,d $1/fIC2� (inf�=1j$�(��2ie�5 $% b(0)=1 b(x)=1/x$�3 $x\neq 0$&'g��%m% g: �A/ (.�ian&�\ ��*�(f] n $g)QIo}���.G �k$ �u�.n s $ke"f~k+ 2is&~ �`!`U*@r ��`i�U��)6.��">u: s�@CQ* � yHU�&�j%!3no 2Qq͚�Щ�v ��F�8 em} �6apyNrO;<U l:a% q�Ape�q�B�� _{f�%���&z�A�c / /^ .����!;NA$u@2hw�[�(���-���proof��T.|� s $U6�V�U)M�B�� >K � ?a�c\-a �um_"9 M�"6kL&�J�U��3unt�� CG-F��� LetE��Ru%�O bf{sl ���(DqA �) �g=Im_{e}(f�R}&_ ].)���R�.E�.��A�� �,l }$y*� -���. '4 ei����hborhoo�']y-(epsilon ,y+.\lbrack�B�%$y& y,}q-rV V2��n�.~(Q$�� \"�3{f�;n [E&*a y_{0*�p/a��o�d-o�c=Zt�}JE�e�o %�2��1@0 >�RE}$f,gy:@A�n(*�F� m#I�I��0�2modif zNqpn� :6 �M�V 35�I��[)=*H�c-J5e=b��� ��\.m~TECd�_J��of�u�&<3 and}R�.��(�"��f6�L�>_&� ���>����N�L�� A}��"H-"�;B%@{)$� 5!�W�#�5^)J�5%_$2�t J6� � {F���L}$ .=_Ob;m�O:�}� big`�B�ao2\R!^\5+A:�w%#E�6n a�5P-N* }�]b[�Y.� �&�,1��!�$M*_!-mNH>�mv"^��D�2!�L� M&$���mB}_{L,M}V�a�.&1|�array}{c�{",L,M,;tup M,\c|9@L2$apmp@ :0�'M, \\�q& .ZLD��6B(L)�up2H6,L\J�6j%���nd- "�_I!*��1.[�r�-��`�Ed� bf{%Ll�Ib�&H"irJW�y�U�mf � .�F " � &�V�� �^N��I�Snfq.\�an*_ .N�YA�at!.)��Q�� ($\Long�w�)$ �>. ��z$X�\=N�$2}�CQ� )M 3:42.A�6K M�j ��w�dis �s (hy. �,q��!0�  c R=���h �C"K /�. �FikaA�d)*� EK��f&�7=n$!�� S1X_{{�:�0��6@� $L=��\{ 1,3 m�$M6# 2.#M�M.��Z�}R$5\ w1Al�Kve � �a�Y�!!�Q�C!�.@�6= 1L9 <4��2}$PA�Mh� }$Q.�� B�E!a�\ Fe}$P$Q\not�7 �&� !�2oS b�& -�P}, Q.�6�&�%�5�P5�=,. �b%�=�N�I�Ek �21e��G"�7*�s�:`1�R g)& T 5��7 F! �hZ� 6NMa�!y�1bolRR ��O�T�A}"�  f;� { }f�\1 IB�A(B)2#A #��52� "r �Y~� �� �p-�.C"�N�#�"�7n!�6 A�'&>[ �y�msڍ5 $�9W!���9�.�)�")����%�>��2�z�a 0%u�W9>�e:AQn)<� )s*7P YAKR�� �j2~$e ! �� �!�I;��.�R=dnd� �z*����n����)`�22 �3! A}b� U:G Ta���`s BFYe2W le�w�i},L"M( f,g�).�N�*� RE\%*��?�'A�M"}1%j"�86�>�M!�2�\�!r��PI6� ��*I.�!��e%�!�z� � =�Im�pn�.�. DenopS"� R�Via P-�q2b/�A �Y% +�[�O's,�'tb,�a��!3Zic/|a��</<�& d`j�$�: $f+g=S�)[.t �f� g=Pj)h2p"A�aE=huCfq If.Ŭ�G�F�+.��)�T[� � }&Ec.J �'G �^it{m!A�1��!8p��g�aB�U 6� kZA�.vB.���i��r�1������ �A� $\nu�W.�!9�&�*�7e+q&�: ce }�k�&S a�&Iz)qD�?i�%��j9�Vi�O��ma�_ nu |�?�aMTe ["40)]yA�i�"�c'e� �] -" (%cf�\޲}v�7z�o$)ɚ!j&�.�.�M��! *� ��WQ�%�Y�%C?-�DH:�^2�*Ie�n(��}%?. !~ �2� ]E3a�� N�)1~�y 2S$e?-*\�0*�A�6�o���:#���(A�:u�.m6/a��yq����n*u0 ��2�� "cX:� r���U 2�+�"�`  e�-�<��!�2(�ɚ%�!�%�$% �>iI�^� ��i�N�*8 )$S"uk�7b�!��db&+�]1���V&�8e0A�Fb%"fJ}�"6_�� )Z#$:�F��:�j��c�%?z=:v�@%�$��goTns��INO5 0Thm. 9 p. 327!�[R=.$�8�!9�1v9)I_mak35|!� ��}J y�� {:\O*!F&O����/Ii�..c+l"� �fnG(:�sm9� �>����h~ LA.��$l��rh.�J=l8'��$2�E\<  G�; ,q���o&M6yA&�:%a$-6h� ��, $l( 2"�3�+�24 8�$*�3o&j> ��4 N�4A��va&��MZ�-�=��ejsLa�EX�…""�� �*��ylif�d�vZF�0 he ( �)V� o6MP�bb:�g% "�)*�ȋ CMP], [G]%�[CGM]}�>9&"E� it{L��by�� K�M{Iqt5heMa�-'/�% �V�oniCI!Ms- &u"] �J� &�' �1�} �.�%�=}f��\}��  M2O�#�R$ex!xP-F�NGradJmv}^de� % }lp�"2vPj42 kA�&�Q.% = 9<*�JA1S� �r? n� BA<����� ��y�.� � �A����SA Ql=�&��% �=2Md��q�bB:>6`& T)�E@A6��&�e�����d6�k[lexEor }$A=6٨a�H� ,$\�AQh] \q9[9�Y���U}$X:�} 6:O-@�i1@6�olds}: b% X&(<�V��!I- ,X6���� �Wß ve}:nL�ndE�-� )=p*�T^zU }}(5�)&)w��H]� n�(.*:V ):��R: :' =$ $6<�2�P5�.�>I&�&6 1blBVY*�Q%� =1r -n3.Y�QM4>ș~7 W� 5&I>*,Z�$Wb q�dense '*ar� ��� ��m��:z y� rY 9�*� } >�t 1�Q }l �R�.��"�6C9V.�l%bk�,1���Չ"� �1:>;$FWW �.}W$% l|_{F:�Un��4>7&R �L $(l,W� �.ֺT/:t�7CYes )6�B�� I�&�:� ]D>K��*17]L�)� e�[ �U�^ xJ[ A1OP�S  swit{% �^R !��-h3pF� RZDAQ��� >��Ս!�� .� "NON� �\~G��}.� �E�ߙQDK &�?R�@2���J�=l&~$+y� }l(!)Œ2� �At.�@H�F ^{l};vTsi *A ��.6(�Ri}$HC�5the�G:%S� !�- x&�2�m<�E@"�@�F� )=(eV�DU]�� �Aa1l3\ v�[ \bb5\ �2.+E��E9!Ia"PP. �/not�<���$%?��:# %l�',l_{2n!x b�$ueN; u�.�M�j�A�j� v.A�.�n3*� �#��<Q�v~e F D�a�bq�[ if (��o�sif�%!�po����@H-W=V�2.�2�.� g.}:�z�DE�XR)=-'M�% !Dy� }@=/2�4�t4^{6}= M2p��,�.��B"@�"� �$���G*��F/!�=���&��]9�one) bn�  ,�A�< q�\�  ""u�R�5��Z&Y . .T 2�` �F9QZ�B���_:� �&�5�Q�_B $)F�,�)"$)(8> \ miű�A � C G]).@2fix a ���A��6� &m�dl�O3}:*s �)y�o3�a�? Q`� "��Z$ (=}:�}l� n2�:�$Y<IB�� 2� ZB=� )��X!0 .1>w*|Y!�H&$JrI�ys.� :i681�� *� ��n� yN�ic%xa�%|�,� y�Z�!�$Bj�6�f&2�N (X,Y:�X,B(Y�� .� $X,Y!�!�jz/.�">`U�rZo���¹\ !�"�(�8 $A��!�*� �� ݕ+Z�� E�dV�Q B����w+�9 vX+B(X)2S% X[vR�� DU�)�էG'��6�*�.`.�" jb]*�>K5b�"J Z!su aD�r( �!UaI�q��A/���r�V (t))o�h$�$%�Y$�N��l calc�e�B� �aU�aR�v�]�}M�� d %. A�v}B� I�v I^>�Z�.� 0lFp6�Ov�A:6W�1) � :bJ6�:$��n &P$A=B+�_�B.�(A-JAJ)�\$C6+��� $BJ=J��$CJ=-JC\2�B����� :�:$ z2GCVG60:%��zAR�>>,"p%�r�=0$ ,aVC !�$AJ=JA*S���a ( )v . I�@oA@"H́�kBJ��aipB� :i.�rRm����E:�>cX,A:�2� X,B: 2[XMG%B_E��� �>�"F  W'�Y �7x13�"p�0?Y P%�% G ~&&$ �1��$(W,l)ц$&��t�f �Bf ^A:W�i9w RC �9NC A!D(}A)=W�{ �4&(:� 6<.�\.Jz.vQfZ]Ba fb B&�U"Vh 2J  T0���BZA� S�.�:W.}%P� &}Rzl��.�� !. [ X-Z�  X,-D+�uFж].^Z( l �) +�pW�&6W] B��V` aR&#e"� adm�F2� 5 exte�W�T�@tilde{J 2\p1j �I�� �isgtP�&[� .$AB�)�WaH� i;:X,:= �15�s2�.3!�6 F|!  s:3_=ed ����� ~))�� %e̷)aU& u�=0S}ZD� !T�.B=9Em�I[J�x}{\sqk�% }-D� ��R<�P٩&{ 0 .Y>��M � FixFI��M��;*�wY�,c ] pre��� Q�A��2]( Z:� h& % A_{F}:F.�F*(��*0}�-w�x-&�Hmݽve1�?"M�B�=^1\I�BrI���cN�$X ��6q �1�E�] .�2�f�Hdot \varphi $ for $pin $F\cap \mathbb{S}$ and $X$ \$, remembering that $Y_{E\}l=\left\langle Y,A_{F}( )\right\r $,�every ��Y ��X`^{\perp }$, we can prove �2�Xv�6�DX,% \widehat{A}_{0f�. T! is $:�=pr%jLp)$. Hence: \begin{equation*} ?b�)=:q\text{9^4 }F\subset W% !�%| }1� in1D.} \end.�( Using this!fLperty systematically\the fact-� � Z)=0I|| $�,$ implies $Z%it!M(possible too9�6�T$ is a complex, linear�$hermitian �Xator defined on a dense1!'(pace of \ $e pcal{H}$. Its closure $A=\overi{�E%�!P desired self-adjoint�since�% >�(W$ taken a uFu�a��!�$ with>;$F$ we haveJO@\frac{1}{2}\cdot 2 Q ,f�qy :�=�ZI A�G2�B�l_ mN�Therefo!�(5�D(}A)�b� ,2$A6�4)$ extends $(W>:$$ $l)$ bute�a$maximalityA�0must hold $% sAqJ�=}>]�� then]�: J,bb{=}W$. Asa�~proof of eviouE� orem�a�Jv0e unicity on A�of suchU�. ($\Lo��0ftarrow $)ForM�2m�= $A:W�bb{% )b D}!H}$ $\ $�first tw����;inda�i�@d of a (non smooth) kaehler� func&Hare easily verified5�%!�.�::�%�6 ((}\sqrt{2}%Q� �5bb{R}$ � ed b� jjY�=%2�.4u�A )U��. Abou��e Y�: iIcoupleA�,A�Y��!��2 : )$ reason�3as ab��F�find a2" !ԥ�$A��rime }��6� >�6�)$ ��$(�;e�$AiV6v are 2�t�;6=2�) Wl= matZG>Z)$.�e�(} \bigskip /not/}�� it{The ma A\mapsto6�:�$��,it{\ between6�1�s�TyC\us on}���5S4 is bijective;!<( restricted� t bound��N1| i�Z� is a��isomo� sm.}Denoma[SA.H)}�Q�Qof all (�or un )2�9,YH�� iBY�hitsd et (a vec���)��ll55r, let's�oteY\alpha :�QGK(�)�@S휉d}SA:�� 5�%��3�|p� th�(u(�i�2V associa!otoN Y0U/ $l$).S inverseTA�6� ����:6�i� �= S)}$.T� VinduceAF ] �|6O��!\A�2`}S:� q�y�.�J it{S� � �ved �  MjZX}$% A.� M: }$Grad*� 2 :�=� -n'.N( <�\�F�9�}$l3i�s:}N� I�(l)��:�l+.� .��$*: .��(M�} &�propos-$L$�i�!�q�� exist��e�(only one (cw ,) orthogonalW��fEU�8H}$: �9�`1d�2�58N7mu!���[��i] }(L�V)2� E 7qg]B^Cone�lyM��� come� 0is way from a!62��� -�(s give orig� �a same pr1sif:%�i�y�� mea� $equivalent�YU1^�jW\ L� null:��$\empty��$�,to6��JLthesis follows immed�ly� ingWsp�ly, $E��4$E=I$. We willJ$n\ supposeE�not��.I. ���&� Qy\long0�W% ^Y%5B�xm iLa��Vn a<e e+$��2� f�$;�[ EC:|E$ % $s $E^{2}=E!XWt alreadyA͡�ifremark �}�1}i�&� ���>�^{\џ}2�>�=E`6�:%���7\| :�b~BW�| %(2��( V)%C (�x2�>�(`e if!7F:� �� fR�j�2�> F� for :9��get2Np)Y:� ��f | =$ $� x_{U \tau�X"1Iw[Y | 1�B0.� 9+:�,.gMI| ] �psi \�Q��| M~ =\ {����B�9r 7)B�T % }{h� �V�1d =.;m%vA��% ��>i:�(circ \gamma]�x }Vu(0 5� ��ritten $:��e })(tN�[ (M(� )+m )+-�N \cos (2t+? ; �] $ w����*" 0\leq P=\min�4N!��E=�N1Bx  I��difficul�calculatREe�� Y .�J�-�sin'(:�B�andJ�4r^�>nf (�)\geqYeYQz�BNQBy�LR of��� �� know&.  $E�g$ ��^ "[ f ") E� $M�=d@ IJ 1&�::b:�=.2�  [ 1+aq 6�cyr 1:u>(j�UYy ]yNZ\ �=�: r:. A)�r� !� )�. .T����y=2� >o=�V1 e A�� � � O"W .:  prescrib �� 6�$�2�th.� f� k one. .[l� $ beU�cx�ed�� of ~y, b �=I�� J� .  n\ " E$��$0I���$I�&[ zH(^{1}$-orbitm|F�$ cho�  relian �!L� F62Mr"  }(jG� �t $L=�cup_{f�}jv% pseudo-b �2 =;)`A"map& ^�"� I����a�i%J.�Z�}]Q "���� ���% t2�"� �[V�  }(t)V A�D�v.1 )$ h- form $a��1t+b�vt t+c� Moreef`%a����!�2F*�!�%���-��F�=� �ŵ(analogouslyN� .�. !2�� �or .�e%��7��I!�".'��]L beta,]�B�sK=ac��� �t�,� �+!� . l. IVconsiderE��%X=-;FS 0FS�w�Y�~�F�ub��9(t+\th!CZ TD"a��!q$L!\ Q�n��a!� F��c =\muA�-�M��rp$� ob�lyf�.1�Topan expl 1- }$L*�a2�a*�}$E(mproceed�w�z:��'s fix a��$}$\sigma :&BP}_"�C}}q)�� )$)2% S}$ �e�fZt\inZ �&�}����t}6 B$N,eb>})}^{E}F�پQ7,}e^{i]\pi -2��,\pi ]�& t;B�.�in6 ^&it{�%.u64A(.-A� o�q&q� F81c\A�%?}$\nu � �%-)*(@ )� B0�%f6�)��their>�}�&s$��{ $6y# claimI�`''behind'' a quantum stat!���re%Hinfinite ''hidden'' Hs:� Hilbert�� s }$A4�- �)[2D�9�var*�#group2]e:/)��.  1 .OAA3\�j�class�(��UZ : essenti�(� `!zT �)�J�!�Jjs Ek�� S}$)2J( truth valu!g0kor }$1.f\ � � e )�9.�^ �B$Isi!% \ch��Ba}(Y8 �8 .��|depS'not�Q�%Mable''nbx' also�''expe�� ntal���''�&!-� "*c!b�5T.6�#Hx#suggesY&�]to eachu� ]men~%rem%ld corXon % collo�& sal det�*nistic9 Rs''�  appea}*in>mots)�storyA� �5Yoa�.�a dir�developP @�u� �A .�1<S})=Ib.Za�)=IB>ZL:� �E�&�#B�FM \>/r6�z� Bp*):-Jif=�AC}2�%*�!`%�"� t}�C$m8A�_m�}F.iL� 2��.� (�� >DJy,�e�M=5�&� \ �>L)&D#"BM��2G1"A ar �'��R 0unitary trans(�1 $U$v�+.5U(L))=U.L) U^{-1F}+�9�8!m�23 �^ZF  }61)>� &| �%b<6� 6 ;� )�� V%�#&� � aD!EE G�")2L M ;��jM:> Y:observ�*h+fR"V �e2Z  on^c1$TH H}$ �chs� I��m�!9B� q -��� $B*�.�6it �8sʇ.fE�(Bn�B� _{B}^{T^� F.= \ �\ZQ1RF�., in �way, �.nN��f^�Y$s6y�7� L_{s}=-,(-\infty ,s]� % E#]�rs}8>Z&�-I .l �-\{ Ti#\} _{s�e %�� a �.z� o[&Ev% u? H; ��2�5] .�9T20 �.�%�=�2�FE� a'� �F�}Q�.i��.;�-B�)*�2��~~N� Then*A!� usua� ofi��:V %�%� %N�;at�A4Xa�Ea�!t��l $]r,s]�0a geneA�4"�"F4�+o��4v�R{, \ \]<�\�4r���j�η�T&�JanoaR"��A �21���Af�a�z=2���j��a�RI�� B "�2�=$5a��f2+BI`�$% T=*$B&'P936@<94�ki64n. LM9&`"_q3�]Z�=�1&TZ%�F��p!�F�2�S~E&% ,� 6M�Z&i�"�\dj^�% }: �BU �� :��B6ZJ� 6")=/�Zn$;)X O<#'.�;�r Aa#v (b�&N" \ast� Z�"� ��� �}$)^A5t�&rho&�;+.2]0,1]:�?6(u)2�?�}(+Arg(u)�&��% $[_{2�6�=\lambd0� ��cumU.A1&.6F^0 }uGR�$ \lbrack }F�jL(s6�����monotI non-dec�@�H�whs)quasi-�<$�Etilde{j� }% :!/[�u � n�9Oe0+�yN2H��5�-�)(B)=�_�F�� T*1 (�HK-S] thm. 4 p. 94)(A�symbol _{F�B�>s� B�)q�:�!>5�5�$F$) � .0 N�J�$U'b��EV@)��j9o aj(d�d� >: way)��%�]=�"[R��3 \{ +� +\} H&!&X6�f�}(1)=S�(�)2vided >w�0cid 1�f�}(�� �d. �9�fu�S )��  v@on %�Fn$�@ff��6J�!W� ~�� 2�o �G�P9�U" KN�f�2� B}}y�j-F�Eis�1� ^_) M R� �;)=jI (s)-b }(r6�� tv� $'p �as  $:��r� ƃ.�  � Aq#$\."�=$�%�yk�+1{ Z+)+Y9�;� �x"\�]l ��b� ��}[ ����.�(2p�6��,��ign�"���$$�&�$�"N a wayJobY�*20y�b�}$ keep���yrfh�B�B)�&S EFS}B &�1�R 7N�6As��� a�>f+" p�E���K�qV�-�"1�B~ !A�)a�f�)n'�.z�Re"[R�� "D7�(*� �|*� 2���j0-B!��"�,ex�4sc%( Ko+BE�2�2Q�}$2�(5��Sf ��G �u�L}$f"�\"H$*FoE�A�K}$T)(D helU(�**�*s*��ece�J%�:N�Ef*�E;�{\{ :';ˑy���  ,sz��9"=>� � phi z!|8\J��it{�5IIE�5y by} a)6Ł��B$&�GJL ��> �EO�~ 6�I>�& (&�&)�& b�1�6�Osx�.�M_I3)%�Q�B��&�. partV<ar1��V�:��F}: $f|B� ٯ��E{B��A�@ (f)})� �N'K��+y*:@t%�AZ &B))&0�J}$B}{�+��&@and&�Mm5a��A 6� �X+L� U�\ &K&�(}>V1�S��_{Y�E}�is��*� to�n ( � uE�) �$ \{ 1I�\}_(1{��Q�s�8s�#�O)}�,6!� �f] &j�,�56 is (*�-) zero|�'au (k)=k�4I=�9��4 tant&}$k*>�N $.$2a��IKr7j]�f� )&� �2E_�� ��U kN\}�6��/g �/.�c �(v �,=�)h*�6:I�2R)p. E tau :;L ]$}�*{&��R}�x���dN�,"�n" E#�G <y�ca�qC�!A�M�)=֡ $ �x: Infac8!v2\)X26 B�6�%��&�� BN�� "1V:Yi?Ba�^s��(^: �e_63 J�U"f5.i�sf)=T$,�,!h���"q#N$� _U�)�.� 1�1ow!!�#oX0E R s kZ enoughO �;F�4nv '�T '"^E>f|r.L-�*CP}�?b{^[���^37*$ : �!e-ye� �T\�T@l .R5�}��^�:�&(,.�4Z�5]WA�9U� N�5"�4.A� �3&0 �5 choi�\a*� 3}U�b3o& ^3Y��@B��` sUj ��� a��%&hn2R� �B#�"}�O> W��s�GP� a&,D �!FL=��}$Mz c"�3?"� =2�L)9 K {&�\��.#3���:�2��I3�Rm!|e��E�V�B,C&o8(Q�Ry~6�L�"B)ŇexZ �MC9!q)�u �(>� ��21 (M��C����}6�|+A_"�"�t+J� �Inl: word5%=B\^0B�.�<� % $F�\bf{� ��`}�� findc*V!�L6�nd6�7:!L)=B�Gv*�+M)=.�Y� T�'} I� L9��Y�2nJ �Ri eo"�:nş*�" checkL0aF�%4L3�b$S}^ % �Q�%9�time,%V-�.�<#.�IE�.&v�A��\ don't I� $ ''precise�� er''�buildOapparatu" ec T�"4�*b!�se2:TanZ@EEtE-) q� 9hJT)���[c~���A� `.�}$AND�2@ �  satisfya@a� J<��p$]!R ��d!S��dd6�]� \ al1U i�$s�8s }U�i�it{or,\ ter,P�BAboole!plgebra (+@&�?- )%�PN//"� z tu some beha�Ar�-3babili%6not�dG])  Q$>Mechanic2��2�9-^As�h C%"o��FP.>we&F3 ���toj�yE:/F }$E6� }� .F6My�; � ��B5���36�6�&N2Tb�@��%���a��a � bBL:N� �Nk NNe � 6� B� ~/ZWR�&� }(Mr�%f{ ?j�a�answer�1bf{yes}�$not�7�t�!you�d�7 � N=��: lG it{e8&&&q� �bb>�bb6cD$a�de�( $ �it]cb4 &&B=Y02O�&�vdDP� �&2���s���ce�I} $� $array}{c} �L@pi ]1-2E�- EI�JC+,1�wD \\ MFEBGE�6�:QzG�;}:)Fb�+��.�bP }+1,:|f(6|:).��| }+Vx>,� I� \�/Q2"� �E��������M�:C�Q�- fu�.l ��p*�yo���8M�C�ot� q-,XI1E&<f�����*�_el�9V ��\|<}$�)f� (not� �f 9� ��% J��E"�9�Fs�ametriz&{C path_6�K$X�Mt-|-��L-Y��&+_er5( s� D2b Z.i2)�r ��c6‰8�"-�%�EG�N� 'v�a�YJ�JV/�� �produc�!A7�H0!��6 }^P PYMt^!PI�!sIA- N(unles�4oa gis �>�@� �N stayA�a�&� �yinA[�}|hop B?�in��7u>m� �3! "� e�E#toa�A �N� \ ''ac2wo�gXH� d regio%p%�s�T�''f� de�W� or�v3;#�Mm=�6S *�nne�iz %abs6Aof<�kfu2$H(s furnished6&d!zial ingMa��� e� Be� �mv�H�`� ):�:�j"}j�OM�'Ti�$ lledI!bf{tot�=� t} i%�&�72�:�A"%.�"�?� $ I3�.7�� �� �� ��!��H*ևboS�U')��-�m�Eu�{e�.'.!!� "nBR"�~��� L}$)bJ?�nd2d?re J� �{O �$(:Bq )$ O�Q. rHwv )$ L�WE6L)�>F#�� $% G6/N)&\�+ GɓB� >5�IA2�ei#�4 case7: $G=F-wj&b fO(1-20f`5!� ~�FChor`w neq �Z$�Z. �!9r �a��V@E @ $F=�Z�M�.G��� ��M��gKa�qc2�% \� s%o"�!N�Y�X trum�."'.q:&>r�a+�.a3's)�z�w[��c�� �image)A4discret%�d(=R�\ (modi�i� f&�,�a�#. �)A�O��%Gp��exact�0�0pe�p >4-�.�l*��� : $Im_{e}�\(f @AEU:�A)� $y� n*4 �!�"�#$�3n�y� �@ neighborhood $]y�),y -]�>y$)'v $E_{, ,.;A�@*W�247.22 pag. 200).V�ҽ�H �"�"r.�a� e&�ly,�dn"Y+R9%8:�� �%?2� �t���M cond/ ��A+�!7!�to li.=��Ev�JCs�$rar~(continuous,&'�hexample&`e�}$A ]h�e� �a*�<>}'"l�J�� ^�2*��Mot�zQix�X�I� � ��&�v[��]6�}�b>9.: Ba2~�( e%9Vva�Ri+J�).f}=bQ ^� +a�&5 H=}�(maW�C}yb"�GR]{|8�Hn"K �$a/veLx�SIP9("%z��A�2E�a-� 6E+ Yu& �;2yd^kZ�6�V <��e�E)W�k ^dI];;�R�0q*`w )`hTper].$Q3E�`aK�:ifxV : f :hO lity:� F94A`>:J�(Q .B� J6�fint_{~C }^{s�F�(r*hd]9(r�Cw �?�! homeo~x_we��YKa�I�m];[-wLC��6�:is)!its in�sIwgalp6}f:toE *�y�6/Q}|r�$backslash � {"y9�\}M�6$RW�� f_!e�nN�'% ]�2�{2�,Q}$!t�0*e2:&�1-}b�1!o % �-� rea.� c=b\Km� :@-Q}|I�)A-�֥�&,!�t� com�sd6� 2}=c g-,!�V,�!2}|B�/9�]�� �2$% \ �b��J`�\"�9as �db�y% H�h��hs $b(K!uV�)%I *"�'��s�" r� �q. �GanyB � �I�:�� �5.m+@U$ ��U"1'!�_NQ� � $Ms,h-$ (vy.�p�6IcZe��o:��;�1�/%s �Ow!ny�;"0^��4�( dimen�!#A�0&4Fn8 8:�� 3b��4-�e�*j�? le a�Z\� ��y� �m(~c��Z�maI� \{ .�% B�_{:e*�� nI � L@g$-�s!%�N�Jv}�&�3M^]�0�j2� �\�zZ< coin+>nw] �V^\t.�� : $d2�,� �:| �B/ E�)| $yB%hJdice��<:�''�U1 .���@ }� ���qR�:�=B�N�=���/D(6lf ��-�+��Sp text{;�HJ� N] }7 L_{2�?9�",vJf-uJ67!i�bf{doma�"�m%G��}$$f:�)u� !��X:r �;^=��m%�`M�ZyU�)= �9I*�"r��~d6�� 1�� 4�M�.�!�it&�6��0r��(��B� ~*u:Id"f$�]HBFAH�6m \ ] })L��(:'9D~G.B1h�/-� :66wH%\���Z?~��J���z�=$ =$:�:% Is0�"}fN8cMG{%d"} �e�jQ<����"�}$D(Tj|aH};6*�; �� R}}t��Q�nA� �4;}<�D )>A@���2� "x61\&�/rT0>o�8�N o` ^ t� ���} BON�B>6 ,r?j�RU�>�� "? )ZC 5��/citemiz-  !��k�W *� }f)) ɯbp3�8Ya�m1>�20N�&Y W% f�PQ|�k%D:~ ?~�:end�5/:Z$–5 �1<��.�2�(J�Ic] F�+���bb �C�AV $jDis�|bf{"=ly ܈}i[��+�Da� mber�-*4:(�� ,-M[� ]M,�g "O^�Q .�Ju Z�}*`79 ���>�'&��Oތ�_�&R�5c ��/�R?� :���OBmS**i�l��w"� �%�V��Q&wJ5�6"T2R3,1�1 }$y$ �A qo!"s5\-c�"E�n&�R� }$gLYa}$g�(f-y)B�Fv"Tm,I�it"D-6#�B v� fx�f-y&*�E��lmost�p} ��-% exerR4}?/itI2r�V���"��&jenumerat&l� �=�s&"om� C0"� .��f -!6�����I�Q .�r;(2"_#�[/ 3)$^C�DHellinger-Toeplitz�P:����6�2�;f)|1a~DHf��=Ax��)&W� �-!�["9���eO|$1%<:8I�� !_�O�uR'F�3+�.�>Z �S�)��1)$�:�B� ����"YM�. soaABu��2]f�OJum�Ymas�"� !�GH" send�@UT�g�$S2}*bbhorQ=�F�:� >�!2�.�%�a*ΓUJ�!Pj{u�,6-i Z� vsm� &�� . E�}G��pR� and � d�QQ[N��^ Sa�r�2" &�Ee� �;.��H9.;E%�#R���T2�e-(>yA�qEl%�R`�.�+. ��$T2�:�T:;.�1A N�%#&���=T"�r� 6�:�=l5�N-F�]u?!��&be ���&T M���� qe 6-^�%���K'" 2��΂�UDBKS^O2����:�)=Qx6=� u�! !Yb <eve� �s�#җB�"�u�jbr�N(/F�-r1 ��y Kf��a"�YVV%�{�!Bj' �M-�gdB��!�B�}�)�! AS^' :H(B]G$n-$6���>��D n byi� b (9"�H� kmn25�b3B&�P �f6e,F�)97�H$%.�"�W]�p.� 1962�($^� fA�%�f���#ch#B�K)Rf5#�TJand% Q'%����-C -D'� 2$ >L"�1�?@{\protect\LARGE A�?�4�(&J3A&��:MO6�U�A!�(a:�?�D�n 1m {\f�r��g�/Mp4"�7 .}&� �6�v*�C�3:�L)\wedge6@J&�2QMnh2LnJAve2eC6S0L)+J�F>QoV�*.�.$ $/,Mol� aI !N�Cing* �@2fH�;a|ُ/���'���%Z��Q.U!|>?knA4��&�|ti�Y#n� :Qe$ I.�A: f�A�A�b���,s�Z$C� Iۡ��y"�l$% L=�QHH 2.}.�!B�.OJ�J�y�wVRwS (.`sR]su*i;.;N-� 6�uF�%M>�%�F�.AX=02� .�u��zt6�J�r��B�F of (��)a��i_&W:ble Hilb̃W$m�t H}�"ABe$*Ma*� Bnj ���L.��|xIv$*<B2�]-|:f@ka&./! !cOJ%�a���:s� 6�"F� -�� �=� i} �] i I!� !�2iX�� pairwKJ5�<*�-*� T� "�&"n"vs[ { b_V�.�E$= *�*T$ &�$ �"� V]+ 3.9 p. 56�'TȬ.M*� f2o"~ T$: '�<�I�+1��/$|I]���f}ŁjF� A�]� L}$,,��c*� �fBJ:5�O}_. y_!�2� �i"�q^; (1���all63} Q$.:l�$� �OA1,A���%H ( g ��.-6:0�&.t2�)O $N~%a)  ��y Jyxq0���S&�|} `�TNNs1.���B�� L�}$ ���):fri}�.R�2A>� V�V�U��e��/6���l)�*%p�Ba�s�Un$�oY8.�7/(.� .s! r�oF -1*B�I ��.�ɚM)A>�W��ՏA�͎&\Ualways bp0al�Ci!�!�-3trough��q�6� � � "� A,i�9^� not uniqu"�Q�F�,corollary} W<�H�a (�])&,�A *T�A$F$"P:� E/��H *� :6��$M2�.�# E &2,G-��F���6�H b�cQV� % M �v�A���-*�4.02�E}%>A�B٥.��S�c�nu 2bL$�Fk[c ��QW-05:�V1�[JB!�*�Z�A>� M&� 6�rJ V�"� �E;rE�20:ܒ%oM^a2h�*d~2 # a�.�F6�0%:,�2_B/�} &=�:> J��rho'm"0.��-p�R*d0C9��2Yn 2s�<��s� Gu *��  �F.c% L"�!b�U�6�"�5 "9 *� o���Gqied����{�+n�g� n\`�1},&�A� =���*�,�kb UdA*(ya sequTF�B_r��p*t% �k).� "�=W)=L^2�9 �`5x:0)��b!Z � " 0,1 \} &^�$N}^{+}}$beP"54."b Y&�%e( _ n}"����) _5� � �"/ �;���7\{Z�% � � �%��ܱ5�^��:+}ql)�.[A�� VlT���i�%�,%0*<= � %!V���.�6� B�952F( E=6( _*( � e�Qk� d_{k�CnR \Js�/\{ U9!�!@).�UlY5V'�Q���bW*?Iұ��Y�Y:Y�0v*(%cupY�e�)=vee  1�;&^a�"E�:�6�TRl.��6, 1})�� ��.j�}�% �bi �n�b���� ^ " : W�g�8.�%�E2:<k�A_ bb{N� D�or�*w�*J �: \sum!�6JE!/=I)�6!"!XauF��E ����6W6�S} �H2 �.V%�n>X2_ q�5�r�PR�k �K���f�>Awe.�\&2�, =�E�Q^ �Ez�#2 nA�]� b!�� .)9= )=.[ %�:�2G�� !�!wc J[$2�S;A�68 U/h\!nm}6�C L_{m$ .��]$n�� m$);~���un�Aabbi��2���� B2���/T �JH:���9e =N�9��|uJm�nm) Vj�&,�Y�;6!31�YN� e4".<&7N2�� 2�)� @9�.G���:�% �T$�JURn� Afe�ba�!Hm�r=� !1� }$�x��  Lh L�aB(h_( @D�=(e��&��y_GG �' y)(E6Xb&}2 ^](.� �"+���A�"� �7<"�O�:t$NV plex2�� $z5JL�� �) -Sn\.��TI&g�d rDD"Wtru���%not;$�W7�Cmuch:�:QR��^�(of�x&�? at le&�three)#��E�&�.s�B�� M� f��ap��&;.�-ite7��]��2]q�.^E��Ore�nB9�{)i&(EB0EF)$�Zdis�u#�K( j�Ii) =��} `Q�$%1aU~�b�(IN���I3�c =�_ �.M�$bf{cannot}A�A�&A�H*� on*� lines� �A9�X�:pJ�R� false; f�KJ�C>�% S&��)Nu"� $G"$�a�(}1����>6)$�ҥ�$G�}_{)� (�%G$bb{C}% u})&��]dH*3:A�$normal basE? \{ u? I*\�;�:�7H}�1�?b�W&+@� � rt�"2�.Q�aA4Z�bed�st�Ua@o Ptoof0sed" � :9 �6*��mZ}G(')=1� �S�1S��A�&h% G���G�1 on f�\#�`w�Pt $1$)�9Gl],� S!�� par�:d of2� n�#reere m[�/�0f�,�rQ�� �' :d,_{u6p u]eq=:3.5 of �,�h�#�%�6K.�>�,A��D�R$0eQ co1$ bringkiZ�th �UEdan�Zurdh j�%DI�A�som�)�.�i��e�u�Mui� D��I�m���F���T(J z��M�ly�p>�[qm�of%2id���&� -i!E�M�Ghirardi!E8[B] 4.6.5, [G-D�}[KS]��>�+�F���ZI(�WeX��BN��E��o��f�ұ)}�B�B�a�TeV��M) �.f�� _{��Aikv��B�MN�3A�count�@�mY{)o r,s)�},  } f%�{v}r,�6w"eOFz��&yQahi�jk�n2gwAg9B��a f� ,r,s9�:S.��)�)b�,r.s})=%�9.�A $n�r�$sŃ��M�{B)"� .��&R 5�%tG42 "�.nEOit-�~sf�g"�,�դMo�!�gQ�&�` * 6� ��d�b� V�0&�$g=#.~��Fbb{Q="0rZ���of ra� a�>berRQ�q\,�]��5F�bV:��]���% '+)=gIw�R,rB�]^,�3ARDR@2��6���''�tc�it21Q�E�2}=+�$6 r_{2}<�i�)up) instead 11121�Lb�� we gY92V�and, aft�� �ion'',M�"�rf�12��% orde�O`P% �,� �Ij {A_1}!�2�j k!�!k! %�a %!< %�_I!̥�5R�3)��(.�5'')�� 1�3=� �)��3�1} 2}�!6:_ 4\!�(U ��/f J [�TJ� LD RAOU&�D ` N�A�TF.3V.%*{1�2 % B_{3J:I 3P&h�er ��FQ��&��}t&�F��^2�V� U'��R+n!�&[}��y�n��B_{��[ev�C�J!zm�IN��2zch�uiaf�& �&73 }X.�� *�"i�}�a� %!�'NDR� a�+Z��lb(xuEf_i�n.�Jx�� H�� $X-0$ elsew��n .iL�)�����+�7��`TG: $96�� ,s�?X�F( % up_{)�s) �) �X2��9V�` end�.�bb(=��fF�FQs6� zE���x���1% F�b�*u�x� "q�( �( �( z( ��J8�-R8�i8�q.s.� �-n,2@�N =�:Z I�t��f��A_lwo � �b����?6^7W-UfO�UYs�=��*a�a"v6 $;s"�! map:�-�0M>Ziщ�S:����� ihom"U\i�f �;|�aoe� N� ��`^gout�a�2�) i� Q!9Dend9�:-#AY� $f,g* W>� two R�0�%��R!JQ�� m`2g!$��a!���� �. "5� $hn�% tA&��<�1,c"5B�6� 5h-�g=3]h��� �>I?+g)0 (b+c�� h)=$ $=iZ(h�G 3)+ Al�.=iM�f8 \�# 9�ib R1tv.)剉�K. { 0�3{���J� m�>r��F� �1/" 1�1-1&�J�an;~�9&�}�F~yURHY.^�!W8=3� �= N�i���*N5*4A�H�U,Q�20OA�R�$Ng6N�9�&��8 �SEVT�&q�R2�65V�6Ro�V.@E0���~ �R� .. Z�:' }f ��N""P*-}Y��K!�nD6 R&�T�3u_RO7��I;)�c N���H7BH7�} i} �H7�H7��>[ymA�"a'�z 7 ��k:B*V��.n�6 E�!��H�6��U�>*b6R5� 4��A�conclu�takZ�=��|�pT )}}'D�RrK5"�!(=ex2� "��&|�Z:�OinQiv me��unc�U,�om dent����er�Tae��S�1����� 0bassertsb &�w�56eiz\Ci�E u�O &�5.( of�_&'.=SL# n�A�u 6�\� )�Q `�&J�9��*=q�oB declA�Ey<''X your*�f �&�DMSom�w, č,97 askX �V7� K֌�(er!�Q :E!rETsNF�<=�n�of�l.�� �e%K�*#�*7r �V��&���0)�e�� (T)>�Pb=0*I�.*�vK �i�f"C����-H+5u5.gN�I\omeg�iB�'}T�~ bb�BOrvNmiU��/A}A&= *M ��( �IT))b T2:b:� B"$"�:���;.D$q B���a>1�%' }f�&-1�Jc>15/ qhZe�GN`>Y$�^]9=�GeH)^*sF �> 1� �� T �.���.a2[ 1Jb &�+ iV0>. ��E��D� <>�0,.G�A,��� over�%m�0u�"�WqtT�8by*�w��=0� �#-Z))��"�gsm>�� :m- )iy�.Q $mf? 01&�r�&*0'� � ��"8,�A�m,.�is ���nyU�Y^A�)nt:q6�Y.@ � ."�x!�.ior+���6�|� ��Q�B�$ ytic��Z '�"�2���s�^�kv.�Br�polynom�~" .�� 5�2��MZ�LUncer�/ty rel�:�L��� F adapB J�E2>,&�Z"�$ _xic d,"��resul���L q1x�in��P], [GCGM�#� in� Fe%Gm[pgoa|psho��a)�uN��� ��m� .��"��!�disper*l!�R��O�(A�a sui�"v6�i$2�!*�(}�m��� bf{pre-sy�,cE� orm}2����4S2-#�p�"do�X tangent-��9��*�`:T�2phi� 0\�7}��ƥ��1�Z.1} (X,Y�lZ� JX,Y D}O��..=U�� r� i�P@��롲,ar, antisymm��c� �� bude�.tX}%P1-"�ma0L9Aof��t��-�>& F�&R-�u� $h,l6n !�w��n-��"�| sJGY l,\th,l-S} "�2�;R}$���!��I�n*r�V� �a"[�(�)�. p)B��1�:��h,2 }��Q+hT�*Y�T�N�3=M#]�(:q:� }lT �B� �mz� Occa�*��wВwr6�}$l^{)�n&�ʈy"pa%M brace{l . ... }^{(ne{ }e��.3)�ͅ.S}8��maZ* Y��&^�"RB�_$QL J�oj��m"�VVF_[ �(hM(  (l)+ ��ICh)i/~��lN� )=-i C�nu-eljuEL.>��5�1_!} 2. "��A=_h)�!Bla� �m.RmU }-�b60B) 0.>B���:p��, $����cuM,h�!3�"ib2 '[ AB+BA&Whb� =ab+>>V(A-aI�P��,(B-b:R� 3. I�Z� Z�Z #� �1�*�2�-i�-B-x]:|=�=Im0 �6L2� r�6/# &�� 1.��s2.�3 +Md.=�Uمl�l\� KS(+�%� �*�V�6( m21"��"_6\(2�[V- �\�)*{ ),.X#1be!�, a Jordan-Li&�N� [E]� f Each��teV��� 2� 9e trivi��d&' f�0�!Nl�, u v logic�1e�M&g�9_�%e�fE �� ��� �|O��%y� 6�|, d�em�byRP�I4 _{L&�36 qak �3he �+k }$0,.��( Ou�s5, } is defi�ned by: }$\Delta _{\varphi }(L)=\sqrt{\widehat{% .-\.�^{2}}$ cfr. [J] ch. 6.3\textit{).} \ �FThe situation is different for the ''imprecise observer''; his ''evalua>map''D(}$\overline��:\mathcal{L\rightarrow \lbrack }% 0,1]$ \ � defi)} NP%Pleft\langle \chi _{L} _\r (1)$\�therefore he gets a dispersion:} $% \def�F� (L)-V!�% }1�2�4varepsilon (L)6�] -.6 �6y }$ $Rz�[>K2h �h \cdot I% �] y 1��}9�Dgenerally positiveE�8bigskip \beginI iAcX} Let $f$ be an essentiCbounded I� able func7 and l:�a[A0 a state in $E�bb{S}$,E�e.bf{Y }of|0m�0$ is given by9\ }h 2\|ei �|>+ }1� +E<1� `|:I) 2� }h,:_�N �2 zB� ]!����conclu& � t�t�=(eqnarray*} M� ��9X 2}Re2�. 6���\ M^<=Im2n2 2[ �l1_5!�%[=*� "� sel d{\protect\LARGE Symmetries� dynamics:Fe>� A�2 eomo� sm $\nu DX ICS}$ will called an"� h% internal equivalence }if:z$itemize} \ �`sendsU * ^{1}$-orb�� n it� 8�\C  \rho�theta }=: % nu $i� $& _{6$)x� � &�NE remark} E R�i�measure.��BF$ not�� We)rdenote� $$Aut_{I}(\� )=�\{ �;�%{ } �nR�� } $e�set�+allR�s,!�$is a group, transform�s=�$� ᠁!� I$% -�F"� C�f��:�n"� �` perte0.�tY�enumeratY�w$%U it{\)XR)A3AO )�it�hxisiCmap }7sigma�% :�!9$Vconsta� n%�}:cmDs � such���nu*!=� ~>��u�O� ^�"}$h5�:�R��% j�e^{-i*P Mp�e�.�a�Uhѿ��3)$\Long��� $2) �2J1) AX(obvious. 1J%3) Si�&%�%bQEh9�$Ki)�same V�AYdT>���<}% AP $ 5H>}�. The A�u5�R�so6ed verifa�= (u�1�V�)..NeN;) yt�.�),bb{P}_{1C}} ( MH)}&56!B$� by $Nl4[�&�Ra� wellXAi"5�admit��8continuous lift�o�h�� % H) �bb2�a�.(^!�-Rf�e�3h>*)S] }6�� N56���$E���h}%q mores>ise�� E�4t\mapsto e^{it ;a local :"O . ��$h=t�pi $, w, $:$�*)�qP% ����natural�,a'� r� red�|��Fy. A�z(bf{Hilbert}aut��qF8 i E�% $U^#h t��e��q �����c�  $U-Tr� U!g8 $($U$ respects!# ab :�e�)�5� orthogo� vectors��JFi%ity.\(\cos t6+\s� psi�(U�2 )2+U( -.Z�r�x,A{ si $�� �2�B� sovrapb ons)MX!�)��^.MFk A M_ 2V)p�%�& %u>% �> �� �B42in1=�^1 ��F�"YFt j e9Rif�only ifA��� a unitary� &� ���U� % H.fH}2U=e�)U}|�(S}}��:4 ($\Lef��$)�& :P )H���C�n���H��1�ǖ" E�*2�:�)-] �[ U�aF�� a6�bij�v ��pᦡ�antipod� 7(]4 [U] Thm. 5.1)0N��ti1�(u (R}$-linear)� � !,1[ Ba2a-�va�൱:� Si�.5R����% �� )}P >|!U�C7  w�'���7 1^1 wh�yU�-16��(u !�)=u� �!  $V\ !� `. � :s>=*��� �h�� of.�����4($c$,$s$)$=$($�+�E�N) j c�%a ( �+s�V9K&}s V1 .1�q=}UFU=g BMX.:)� 6kP.&`J�� : $c-�"Y>w-�� � )]=0� $sfJ�nG G 6�$Y�*.G:�:�n$ X#IfC6�bC % s)�C� is� veJ aMu*e�"�A�.�yh($ cannot be6al'$�}�a �! $u� �Haԑl6���b� n"�xFni k$(H*�U"�U'{!�a�� au&) *��is +"\J>���bb��. ��U>�\c_J:��I�I���F��!)F� \Phi�$2� �is"8"7 % semi-. of�!j���f &� .�]  x�� �. A B&� V$v iD%}�= �1M�.��. 9�d�$\TAutV !�U�]�R� bf{\ &S]�!�&  z . 0R� ���R� iB--:9 F�"� Tc"�uniquemmhom"� $\�:JP% S:c �\{ 1,-1 N.) N(%q )=1$� and � Qkis�%as =\Psi5$irc \Gamma+A�$͌ !&N�� ��A1"� B�&h&� mal4ts horizontal � #l�� � / � _{\ast }^���H}or}   % or*� )o� �0 &$�&;2�!P�)r����Bz(X)&� �_{8.W%�J�I (X))$. N���f6�+eAin t� �- * B�:not zeroAOAV*h2��K.�2�( y(�h��)6�2&% !}�JjF�2?=!(I1�aF��M+�]Mbb��E:�mat$:.0}$&l)*��}Q%&�I�& &Yy&��.�,*���)er; �& re�"i� �.� *� %, �iSH6 5{Ug,6�o a� _ En-�" i���.gS%A�1}$ y\F� itq�=W. `a�U "� VGZ��4is necessarily>. and, n �i�simply� nected� .� *�(!�eq� ble)"�n�,K2��2�UEy�,2��m�m�4U.$ It's easyz check��&V:m6���:y�6�1��� $:>P-*} �� B� J�=6k� !�Y) :b]&I- mN���-i!#R1-�� 26!�&&� B� k:�Rwe tak�'l1gn6�U)��aa ab+(is st�!�d (!�sRMEW.�u�(�6B�.� ��6Usa�j�iZ�� }x .� ���0� ( $ �:H ��) � K� $1�U Converse��(%)5�2iU �m�a QH:\�/�/ UI A8�<&. endo&�#A$&�(��<*.,!�Vl �)l %yN��&i}{2}A}��692 B2J;�*� aVc;(o�2�5c� 1s from�( caracteriz�Q2EglementsV�1 b��% &�H� rl/Z |Psi:�%�e��Ku��hi d (�� r%6�^N*� �P�:�%K"bf6�of2|"$� 6�9Y.�F��"���n2j o.�"F�n�$l sub"�] VD ��6�$aXB�}m % F� }$ .*�,i]r� A� M� 0�ӥ36/� if \*h��cG5&: % R��� }^�? 4 one-parameter;���0%* fN�, infa�+,J��� t/3^+a�z1$t-� R}q�Q8FR"γan6��5*�!xf "�it���))e com!)� =��(of&)6v�7 aVp&�# 1 �R ��F�n�u9ed��2J know� � �2z=1$% � !��";U�9th����$he46� .N.� .� �kn�**��6�&�qф  a�i�� !� A�Zm� �.�. ��e B� 22!�"V�AV�)%�+\!F�xcaE�w�2R%U -� - [>�1��.-+EC�(&�,�s$corollary}�o�o�&�),F7�f���8��H�:"or,y �,tly, a J%2 E8� a\5 �7A$(p*�2Zn��u it{%B� .�.&� b/ Y�-�-�e A"� :' 2' � (l)0t� � end.�:vI�=:� &s�bP��M_�P" -���Oi�lsm�.stͦofn& AE"H�ain� A(b�N�& $N�aRb>�H"968��si =V���#I�UsV$"J 4n�3 d 2R�.t&� a� ��uh%�a suitE�RPt/ ٥ 6���J�5 q/>�}��*�-+$ dpro�u}$L��?\�a:!��(L)�/i� ��j�:"%;&E**>}$f;�}�'}$\ f1ih�-^ls�G5>yV"iphaseo@tac,: I�a+�W"#%i�aTi^a�q{FR O�82n3 �0�ide�A4topology inducd#�� �.}$z5of ''p�<w Bcdgb2''j&�F��n��%�s?$3}A=m�� P+1B� of2] 2C��.yF�"� � �=ma*�&� R}\times�!=.� S} � �F�6� j? q)R>�? !��H� ��:-$�%�it{A#��0�� _{t}����0\int_{0}^{t}htr�� dr� �t i>�5�ё͹�& I $) O"�/ .=0�&familn&9�32W�})�\}\in"�?Ra'�!��Y>N� s&!66�:%�bb:�.u yBa]>�& j} >>. F�=% U!�B(1-)� tA}$P��:�iWF�BS:��,2���!�]sZ(t, ph�$e�� �2ɞ#�6�X� %��$R��A:�e�>V��.L ,6�:K. �6E find aZ�6f0 tild�G(F�U�2�� �ͼs� spac� �q��p�1c�/� ��F"�2�1�(�C .Gr�/ r}$)2�A�B�(01� )=0.i%9�;" h%�a N)0�zR?62. =�_{t+s}=U�*P_{s�b=u (t+s�.,U^{sUǭ@! (Z8s8tb8}/ Fm>*�'�s.�V�:�Z%��+�uF��+2�1i� k(t,B1 ��:(%�\ ger.6k( W�> )*IR��B�2TZI+&�� k $k$ must��+�m� !]t'0�&w6 way��' ossi�to? gB-B@�B�Z�F(�kE �6�"5  $\�;67)�.j, �|� � M���f=D \par�IɓB�}! t}.?$Ige~C�s�+s}i (rye)�dr4Bb(>�� H]�= (0:��e)�Yh-891:�> *Iia���E�:0,Y^�:Z�A}R���j��)R� U^{r>`drF�� � F� &F&�$�JN "�ݝ�Kh�I: 9w�� we w�*>�� l,h;I:� �D flow@ m�5f tonian ]�}�) and}�) }�6R� ��} FN�F � �tF))���wWA�� MLN��=BX_�)7 ;v�5 fieldb? ^@%T �B �|.� -� ��Q2_B }l-[*F+u� )]I J:=-i 9K>-���� e'=kyF:|^;" ($l_{1},h322)T���<hY�-vv� real�r$c*� : �2}=�+c�@h_�4-c$. A little wB :�licatedAgto9@v� M�� �y��Ku�c!2! ��� 2�a�cP7! �du-W1nF�"�2�M�N����,�i]ye�% lete %� ������%Y e�5r-�( ���u,.[ �,""_I "G ��#e = �� �2&� Bm�dot�(}% _{�25cd}{dt�t="Ia.W)=�@$�ID�:-*�#N�X%U�"JE!R\(each curve &= :)4& "� �<8%J!�M%�1�-�F�q��r$�=A$��2�bu �z�XAM:�  evolu���J{ �3F\9.�2T$ !�dC!0 (non�2lyK-).��G�)R�E�psi}=-iA EZ:4�5 Ɋ ч Ʉ psi Ł�~�/>?1�2�~�H"FX6w�e�is !I0 new structurIr�P ed u"q&Hheuristic hypothesi>aLC system��ed,�C�%,s described . by a�(er intrinsi+I y unto�8inguish between)��&�3E ��er}cW1�magin�, i�aj(y effici Z�;�l(atized labo�y: �H�r60Z hi! o do�Z to gq;to Amai�3mpu!� gram!�%�!B�A!( do��N�-A4e ENTER key!% A��n (cular,zn\ghyEMN,���=%��� � M\��M� R�� }$SP�r%�%i�H-��toL!d%h�!�epa"h sexactA�n�B��. Among;se !U%*re�Fsome �#> h�W�r2�A5a\&�'3&�\&H\�a �Aific as�*ed ?EAhyq_�.ria�6�[ :�/��.� � :0\l�QS6<2��. 5�MqD�Ei@�,6-M)�%��OP(f)�\F�"N�- ctiv�Z!7cor�on2$ �AYap&tus.�Given!�1�Q�1j\e�a��2�f��,great satisf�!o.�.� 0 �proced�M}B�5ecu� RP-� pI�d�e}% 6r�2 k� play@ alwaye��� $number }$f}�M:EQB� f!��sA:%�P ly��ermin��.�i��Yr�.��BűCb�2!�s a�x�F�����.�>lN(2y�R�(at, almost �3 A � ���cis�*�BV: h&kUe experi~f%�\`chang[,�� cmay �y-�� j 3utcom>�^�L��iRpan�r-�er stud>3!�E �| M�but�y$poorer abi0(��� himC|bf{"� � er})�'J� �! �pr� } -�G� )i�JA���"մ��� a curse:Ey�na�aX�N��%�o �3�2da6�  twA��O�,>� �2N� .���5<9�runA�� �n��= �b;�e*�[��A��mIˊG }Zz��8�Ϛ�E=~AuhM es �?kA�which)e�r_a�!Rm'; J_>@ avoi� 4)TXxXb.� ra)1�its����%�m��I��t.� af� :� 9F>,anO any� mUvalues }M� \{ f C;� \in3F�\"�i. A�a large͝l rialI�Jvg�dA�-�� strib�F �F�l d��!�e �3h%eis rep enQ&�b �)���- ,f,B�;�R!J�Af^S% (B))!*�W\�-��ob�t� � � fall�"�5 bore.0�?}$B5I� }U�R}.(N�_ Nus m.a� wri ��=F�;!D� sa�[at%Z�sb c� d techn�%IFJL��gnore}+ deal���� �A\  9^es ���'�Pne(D&x $ ��a� &�G* � .QN�w"B �!'2J��s&w p�=&�23�#q9a �@.involv�  ��9$is happens:�� s)�N�ej!� equ7res�_�jAou�%"trol:� r viewG'B 7s�ae�c�m j�t�Rus3 �,� exampleq� iA3�ameri|5!Ea lampAduca� isolkphotonmk�� "� upA!)�3dirv; towar�"$half-silve�(mirror refl�K5g�(�them:�qquad ''1 I amU�co%Q. ~M �'s wave&j�I� �wa��assage6= throug�P �jY�E�ds3�  depe� �\�%4's �e ��!�F3 instea�a�let9 anawh atll� �a2E/!C�go A�n� s�=�@q�Q�� 5dm��m9�s� ��wE2mR decih^�ly �/be�,A�![history�A]+)�)�e�+ mDac8mE/� t ��(�B�a�at �i m next� f !�� r d o''%�&m�I�8N�s ��\1����� t"h�� �dra��5jaN�KX @)�!�T!#*�a�? c. a1 �T;?�=a s! � \��ce�3�2f $���A)\{ .�F� keep0M� �meaD�c&�\"�"�": -�A0 A�Y  ,O PJ�b^�Η9�"[!AAl� s��Kal % ledgR^-s!�"�map:}e&�>K "2#S/#*� B Y bb{R �)�)[ 0,1%�mFM%��A]!gp*n }J� "4 \"� � �zJ'�oci�Jto"m �\�3eIed*lV}^�" �� etE$B&�e� �But�why� sh<aeq"�$  �M�^p91O{ }&G I�R_{2F# if: ^�"? �C p*cC_�B�"��aU�6�e@ "%,tgsub)2B2� ? A dueot8�.vex % f_f(f�!,X}d .!2�!=�9�Y1j* 6U ?2se��m� g�pt� BM'�J&� an }E?bf� 7c�NxF���R*�ZVUa�"<8%%citE�.s% �Zv3drnu�O.Lv �u9 { 1$:0\� a�5&�� ''�� es''a�y.2� �� ���C� clasA�o"�N�>E�i�F4� � bf{��Mu| quotKsB-!�*�u��V_/��/ N�.�Analogou���%=x t�BzaO}}&RKO:z%". (.'O��!�+K��D2�D!.T map}R5pi�.5�_1 }6$ �� (�(&F&uJ��s�w��( F�, �n] J�,B.P�?now.��. Y� Q�!X''*''A�5�D��F� � �!.w6sx? [�w yTed �N� � e s,mȅ,]ies, *3�5EI'_�s:c9�us�Tquantum �}5�Jta!� s a �al basi� our claSatiQbf�$J�, \ beca$ ofej&� .�s,=%s� BE}&}>1���Cs a>�:�be/j&�'�X!.dJ� =\muH� B� }("��V'~-@�l E_{BNHtau (f)}iE�l*?)$s� !~sJQNB� �#not%EO&},x.�%w�'ZEn��C�:�(2,&F)%�{Ŗ+ �Vk iឍ�RF�,��!�3 deno��d 9�z�� :�5(��H��:� �� D��iM"D{�  r^�&I^ P}})DB�vNJPU02�.�G� F5B% O}} �+n�%l�{]b (Gbfg{AO^;2f;�-&9  M9F=(�^I$B�.g� )} $A�ta�= 2};0z4 1w22�xO�8� SA{?]7�5:UQѨQAu1 O}E �@(�� T�)��2V&����w�a"�I�"�> U=�% � \�bi�d| �|�(�8$learly sur <; �?M,�"jȡ��AFJ�T}b%ipM� M�J0�'}(rM��9ioulrz&z and I�� � A�.q:U2t�"�$!an �Hs� x.tub�  $F5E)A)H� 6�<$�W�HFanJ(m F2i�h<"�#�*In�rM*� �s��U�v a$re��Dth� ��!J�'s��w��(��}&�S=% Wm!i& tv�?s?�\*� ��2�'cig�to�5:c $  6!�>ch�:9phom&�Cm%N*�it�� $\b�Bu�2�6j���bb{��dXٳ} Z"^�eh �e�aA�m΁X�cachQ��u]Qq�}|�_!�cal W*�i��bT_/x; ]�b�l�C.Y �:�-�ymt . It� ��(�;* Tif>��}$F�"6��f�u�:xmoU�OA��Y�5a-�by'E>)� %|hw6tmRT-[ b� Dať��m�uc tenso�in�n�#�K�z -Fubini-S�#:7}$g_{�E&�\��}$�K�\� Zv[CMP]� - EA�t�$nt� J�\r;�^�% be5�inher� ~��; tric U�} $5��B"  }:Uu5�v�Z� 5iv}T_aSZrQju#KZ1{$�:�u�}|�=�Q� (E� �|)� 9t(n~6�L!�$ `$5�chosen)I��o.�j��z�_� an (Hgr�)�-ax&�/E�&7b� ��� is �� E�V�* 6�*"V;2Y pi��&� . �2Mbm I�j av}$ bTI�f��7}5bf%&*-��}NG o :5 � n��5��f��FXi">L��p .j zj �yn;2nj =4��"�M3r� � ��� ��\Z�=_"� -l{ [��% 9 .� ��I�identify�����A��2h�  n&`� }$�^ ��BK-�vqmVG� NweQ9b(A�.�0 �:p -S��0�&�-�nq��be�A�2YV:.� }$p.tj��� � i�ZR � 5�.H6% ex�F���p��U . ,A^�A} $N�,�D&V����g �:�� -�P}}"0&� �j�f�a� "�)gE�m�J� j� }=^T>�a 1"S ),B)|.�m�w�h } $(%1^),L*���;��"� j#�6A(NL,6A`O!kuwa�cm@{�o ,Z�},p[JS_as.'e�(*"a2�5�$.�j)"�ύ1c5 isw�}�8M]Z}F�R&s�/m�_!i'!��y I�F��&>Y =ie)} &�ws�k-y }!$��8G-��Ii�rLambdaxpOmegaM�&0���� ,:Y8m�p$�;� V#�} a&� [ y:XM� x� NY$=& $su]0aV�U2�(έM>�, � uā�>Vq�FD! [2=BA*��>Gb�=u,6;�]R4!-T )� uR�D�6<.�.� &�J��\SymR�: 2� ��8 �"A�l�).iese� m�Rf2 !C d�i";_(�b Z7ecoose��iK�?62s 9F6"�� )�.�ya�muQ�)%����[o�Lh5 .P�}7 &oT �o �M�>� I�hUZ� =[U6]2� [6 �}}&�U�.\tf]|^{�}}[f]=[�UU�H6t% [f]NYML[�&vU5�1&� Zw6� _Iud��$"= �d :}y��!-#su |�/z%case. 6mE� a �o�,*4H}E�"�V &w�>(E"+WLL$E&o R\setminu�!�:\{ 0,� \}�fţ (E)}=MTak?Kw�W�k"�fP�J&m M�!��$�1�* to�Qpr1=!Puh }* ��zkEF� !Jk"�v! X> {X!FfX! �] }=1$F"�} \* :\)�!�6�$vCV�Ri!^i� :i>�E��&$>7�1 7B&.]$ :7jpod�Oo.� �iY�.:Jh��y���$ Jr�L4mit�z2. ,V��|;U���r�n ��F�% "EMF��5�1.Nm��F��"Q]A��E6�Aka[&�nQ-VaJ_@�O��VAQ�A:^�-k R >��P�J�2�gi��S a !�� (A)�^2n.j��h2�Z. Rem*�.�z� .�b ) )��ge/�(i�0��> �: & B� ]�jN�ŧ ��.�re�.&Bs.V z�%�02e�PƖm��+�!l�(F !qchi��%�ٟ � � c%c:�_�Fb�^�n�%�t�-,�,so� a�,���4pre�H�gvSx ^�q�_. H�@ N25 * o�l� JyH)2ZA]G*�\s�I;� partda�is�3��IF�[{VreI1P�z�5��R�"J8Z*>R q7FQ"� i\&{f-.�p"KgKzb� �2�A�O}}2��/ bmz% �g��"� �p:+#Ei%RMB�#$% AaE )*ZQ Bgj )eC��= &�n5I:� I@�G�unpxsI�ch6�oa�r ��7A�$-$LjAce 9^I 1qwpB 2kVQ����;%Q:2J4% ^">�>)R� +:��1J�5�U11l"e�.QQ f�� D=�� ��i#a&f)z��n�� i�j+� �rt ConR wB� \9/�� � -.$��p_rw>�faY�:) T)=��&�T]@ Ti�� h ��p&r!�T�Qff�U.w *nd"r1�(% Xw�8 }e^{2G^ �!=�$�tz���b�)${vu=U�j� �e1����]�G�m�A��}g2_ � .��f����dY��E�� .�F9 &�J�!�N�f�)� *� ��?� ��.��; ֔ NGw]�N�f�% U89Cn_Eit{�%.� ,nI'it{&�9Eb�>s�$i�:�&�xA1"�#A6+#gEZX�-o�s)a�J?.L ��EYc66r��?d:�}�5�GZ�bf{ �A� ��b> $$B��:���[""g%)]a� SPit{<�>7J� �9�%�,a�?e2)t}"b.���&6Oɀa�OAc% ��!�"{.@"�� �o&�"�A'in1\.�")�!�3UZ @�** 65�X_�!�O�$1<1ybf�;%�2.�]6.?2 AEWpn�v&&]����;t^�&� �v�[f]^� V�:�"($IHX;u�-��??( U��� M)*9.�4}6�1�\z�!.�Q8O2���5us�+6�Q�hs i]L�T*�/& 2�b��  We�D���f�Wby�L }*;''&�"���Y>er�Aear�Cs1�n�Q.F"JGEjQNF,%f it{A:��� �MJ�#�F% iiv:B�(�bqY$�)ty� 6����9v:�&0��VC:�&�)�-5�A(>�bel^N&H:-�$% .�:�s}=:/Rw1P% (��Kff�KvvJb�"1�.���it{�3in"�<me�LicA>-=AMF �-Bb����.�9��b�Js ^X=�g":'`� ɚ��:u8�� �I��X��6�L"�& �$;)I�� h�6�17I>=*DbO���V�H%�f{PROJ-��2)*��-r &�-�E����� wbn &@ "F�"�,�#!@k5�~O>�vD|&1(is LR�@e�} $Uni�z)��)}/I�e�t � IaH�� *Na��K��G-$T QTe�>xm=�^.} *)>v �e�l�Q- .��&!YF�! }N�.- /�gi�10 5 J-�:d��Y }vZ�9Ew�9=Qf�Y 5.�:oӃ"�LJ��:�}$G�"ucr-�&)JB��A)NS���J:��)2�-EI%* a����A���e&ڸ $ |!�m [Z " �9�� �iS&�sh�&� Pi :2��n�:� 0��}>ނP�K��&� bbM�w 5+iG'*"�W6E .� U0:�1�<5�V�e_{�CM-Q}�=V �� u��YS��i4�� ���$:<�b� }$. �a �%2&�5�u �m��|fA^� )$2d6"6� . 2z��E-J is&�J�=��-�bl=z�j(�*$N� )=Q�"�)c�!�M~T �!*� AZ�3:-6o���Pi�29�M�Z�m�=id���B�% �:��Kt��$ �.�"*)A&�ᕡ*?'d$�N�#�6�#�'9A��N�3�*�#q ��+BBetB.3"�)A�k2F�$ )=(id,id)��A��i&�2Hɿ d!�$"s-<*'� |X_! N+ iNnW$K2 K�3 � �� i�a2`!>N��:3J�A}k� .5v��}$ΑG of fT�%��^�6�}`��!Jj�m?c.��/ $ a 6B ��now�w�)llg�� yfajP!��5$Bw��&=}*I3TL}e*�9�65a�)3Cc&ǭ1Bw�e]1�B�r=)V� ���y@�.�J_I�!&$*&a:��S��p� &j R2E :�&)w s a 6�Bi& 1s �tB�1:!�� IEB��-� fc >�NW J�n ''a0ient''�Kexa� Xb �%�MN�eN@ej" "4�Sit{. T�d�$E _1�*�* �ssp-723 ��1F orig! dZ same5$ 91g2���G��6�&�7(� B�9�*�Ps.�Z)>`A�.D6<n�N:6B����!�K�&�/)O�qB�ht�\ !I_}$t���aCa�o<+5"�aQay�'!@se"�l�l!-5�;6=Wn��{ \��!�.u&E=% S1T�7b�bU�I y.J�i}�an.( ^VDynJ�N�I9{Zɍ�5�CV��9�����(as��+� pstod�Hq�it{� } $H�)�V� %< ���.Ja��k�2�$���UHT _c+H>B&x��g}��t��!1�:  �� k6��v-:�vJ.���i�I*;n)fN�M�� 1�9�f���:�%.��&}" Rn �9a`!�6�')/NR�y�� �j����d5��u==lq1 �2S=�A�VlE� !oJ�Aoy�%t�eat}&,��9�!��^�2�N *�2���9>�%�8~����||��:�y.B{>��UX�.������ dyn.�iRl u���J� ��[ �3] P(��$itHA)�3�jM��*�G"��it{ a���:w���2?{ \�ٹn����i����{ �� vZV;^ �GR�_�o6it��!w.B���7�T ���=�%=�?) ��o �S�}.��/\�U$"6�5,F� A�z ��n��X H�� 18\ }>,�&~.�.��{I�)Z)-�VJ�}^���m��]� p-�6:ˏ�|�c $t cEd.�&~# &*DQ��WS JsT&g��i6Vy UE-! ^�!&r;b@�q�)8-��=UR��>U �a�*�-{� �.62 j'w~g&:��A�z&%�C|��3 <9*h�G.�$}R$ ]�U &� *Q �t}� -uM�]@�r#!�"1H���R% �e$�M"�ΨM� u�4.a�e&��!:)͸�92Q�%}+ic���{w>^ 2001)^P42, N. 11- p. 5143-496�0GM] R. Cirell!*. Gatti��A�ni\`{a}%!�non�tar ex�U�ro��)�M�er"�E�h.��prVple6�Geom.-E*!F99� 29 �-2!L 64-8:MM!NB��eck�? d D.!�y: D~N��#Y�uV���& �comp�l!c]g !=;|="�Y}P7inty]�VD2m.`�4L. PizzoccheroYuT a���$infinite-d�g!�al26�I-h(...- Part IlII�)�!(6�90!w . 31)x2-AC 2891-29032E0E] G.G. Emch:e�e��A�!��|eptKdf@څH%�020th century G=INl�-HP�ndW.�{�d8 Amsterdam 19842�G)iQ� : Sull'esM�eA��Z�&iQ�i f�2�hali5d�cmeccanic7dpa9A,1996 - Ph. D�3si�YG-D!'�C. Ghirardi, F. De Stefano: Il mondo eDco, una=lte� ambigu{ in Ai " �+ Ca� gris�w�o,�a� e Vi� Bergam�$6ZGl!PA.!Ple�=: My0� closc��^%�a6t�9,Um%�ech�57- N.6a� 123-136eK-S�,\ J.L. Kelle}4T.P. Srinivasa�_ Intet�- V�p1�S��4ger-Verlag, NYAL82L$KS] S. Koc��E. Sp�cr:#�Glec�( hidden var���:��5�AHE:}_ %6%1�  59-86�J1 A�Jo�: F6^EFumA�>s(Addison-Wes!G P.C., Reaׂ((Mass.) 1966  J-P1wM. v�C��ron��John Wi\& sons-�76�J-P2]E4VrCanFyb���& +5�me-? Helv�TActa 36, 827-837 (1963��y�LaELang: D9ial%rieP�omanifold=�Vz952zM�. Mackey:U:FB��Benjamin-Z66RN%Wvon Neu��gyKPUP, P��etOJ�6�Pi]�'B���L�,mon� hu(ed. A W�]man�m[9Q�1976�PrI�0E. PrugoveckiNzin^�Ac<�� Inc.-m812�R fH��Royden:�A/aly�.�0PMacMillan Co., Toront��:�(U] U. UhlorQz09~�)� �!>����M8U.u9�Arkiv� Fysik�<2, 23 p. 307-3402�V �4V.S. Varadaraj��Geo`x!x�9 ory.��I�Van Nos�$d.VB�W mJ. WeidI�L��&B��V�8��' docu } �%� %%%���  4!�%o(-ph/0412075"�}6~icro\� �$MQTgen.rty- fig��files $-Fig1a.eps"2 B"b~"2�D2�Dc�fd"��&^�~E.vbe"�|*to BG E��Trt &� \1�g 8[pra,twocolumn,�o8pacs,a4paper,su��criptadda� ]{revtex4R,usepackage{d C$graphicx} a/�ir2title{Ef. �rob��E6umr��pU�s % -�i/}m��tom�"y} %%� &Gi:Highl.}�bi~`X\author{Berthold-Georg~-� } \affili��{D�taWa��, % N!al Uni#?�$Singapore,  1175�:fCentrzqr�  Te��> %�o3�!� �LDagomir~Kaszlikowski:�������B�,Hui~Khoon~Ng�lt=� [Now at ]b�L California Institut�5�dy, Pasadena, CA 91125, USAo]OAL�MI$ Lab, DSO UNL��-�U3 1182302�����u20Wee~Kang~Chua������2�lJaroslav~\v{R}eh\'{a}\v{c}ek:�6Optics!�lacky � �, 17.\ listopadu 50, 772~00 Olomouc, Czech Republic}9lJanetg{ersr�MK����D \date{18 May 2008�9��ab�ct��.���"Y�����, x��� b� #xfulH4�ic,Дe�kth�e�6icgs,D0�ɒ . Un�+؄ �CumJ�[cy�H$\log_2(4/3)=0.415$��~b��per q�� . BSs 25\% ��:V0of $1/3=0.3333I"�d��six-s�1,�Iq���,$benchmark.�,d�8_;��O-U&commu��rschem!�at�7� $0.4�7�s�� thus�P�Kos�Min"2�-P2t- limi%�i0 hres�T�at ,repor�J$a hierarchW $eavesdropp�attackJ m&�r’)�n� �-5&: A secZ kP�G�QkrO�Jl@%�38.9\% n�. �Y� \9 ({03.67.Dd,  5.Wj 7.Hky� *}�3ke� S "�Inte:!�,}\label{sec:eR} % A&��| -lifOyle�%��)��#^W��E��%�carrier 8A[<=�,E ��)sm |$'�� idfirst!�posal�< � � Bennet� d Br;�J[��vne:)^�2.41$ �eP1- . Pu5��Tl�P/ā� pote�24.����Tan� 8F~ thei!9mp��T�mmA/ta�5�ic �Q��!�s4a7a��B9u�F^2 redundant��as%�asE1�qs:�ba��̗{�AI ree ���aLrec}l�)�e[.6�A�l��f!��rin%�to es�*�WI�y . Ah�cus|in.QMQT}, �>"is"/kٰis W_t+e���9� 2loo� terfer�er setupe<�aizEBe�� pola�� �dd���4OneLoop}. Non-;q`sa`��6� =No<,�f work�Jwell i�actice . LPLLK1}. GKey-�S9�raw dataAi��� ` forw�p�1h�Jn�.!0Ѿ�.�match� I{�0�#��.� imiX~�����a�e2�ofE0�v��e ``Re3K pairing''-Tetra},QY> Sec.~\refA ( }---��,�achievedu�� no*� *� ɖiV�J0. Thu^�f%5 wish�aq) do,�e��i�j e advantaD����{ MQT,)���abٖnBz�he likA� favo�X�~c%{ J jL O�M$al��Vt��geh�EHmethoZ��_ m@�K��I�toY.� � eo s 0.4Wŵ") ��excee�he&� 9j$ 0 m���<� quit�{� �H@*� F� !�� 15$. H (a brief out"%+����9A�ɽ2J a?6p%}.V|62ways},�#�)diE� %!=x0w� Ah&� EaeJXa�5��6|� Prot�� empha�^onc?�[�w)�. F���shG�3� !y� �S� �Hw�auN�� .e ��. ��)�a summar�b e account�ME��&)H�yA�pE�i�| AD� �of� major���H �.�e#-��a !;el@��)}�3� an�� pms� . EkseE�V realizes,e+!� �, (probability5) measurE� (POM---MP!�emaI1`Geometr�(ly speaking�r y ar �normal�a%5�fa�� of���hedron, a�$ne can picA=5Dm as pointing from centerA$a cube�!%qnonadja L corners; see Fig.~1��Ref.~�� MQT}�$an illustr��0. Their lineaa� pendence axLcompleteness, stated}Gly byv�basic�%�(sum_{k=1}^41�k=0=� and}�r�?3�?R9B \tensor{1)�6)!��a�per��!P!��)�-�8 quartet. WithM�\s��\tou ��}$!p\Eqref{a� weI� the membeaP_{��k}$%��� POM,%vlikewise6�^| B}$ gives�POM%� 16 jAO��� ies �|t$k$th�5 fir"0ogether with ��$l2)!T thenzn2narray%�la�2��hspe�&=&\ex�7{:(B}l}} \nonu!C\\&=& I$1}{16}\tr{>� �m�=�� N9lJ99�}�>�� \$k,l=1,2,3,4$. KnowledgeM} se $) <$s is tantamounta� know� $>�$ becaus�5, inverse rele�r a�v�9t!� >c�Ni��}^{4} )�6 =�A}k}-1r) � l6%!�% 1,u� } re� truct�::U $� EG6�4. Indeed, two-D ( tomography)jis kind�q,be performedem@is highly reliabl!T pract� �>LPLLK2}���think^qI.0��repar!�i? � at random�-��R���ond1to---e�is,%di� ed on---a� unpredict� .{$result. I� 0is sense, she�se dhim a� sequ��of ��$rough�-eff� �,ntum channel efact, i� � � is loc�1in5' labob � 2 emission) conj� � �.�is fu�equivalei/a � M �.A� Coi$/ if �G! l� !za JD �)�( output, so�G�Csce) !8a� BB84,���U,it a> C :�a:9yY� ��refore, K analys ppl�� o ei�� phys� sitip� �X U �&D ) 7 �0�� }�� vi pkl-i�l�"� 1-*� 0}{12}=\left\{�m� �O {c@{� \�5 \ }}Q 0 & k=l� \\ 1/12\neq  K I\rightB� uqtwo:�&S ,($k=l$) neve�- �,/ !To!w twelv�+ ses �- ly�� le. Accora�A�: mutual in���") �fcBob iz IAB5qIի��� � ��)� \log_2%,�b !� � }p_{ � �7H ?� = 0.415\ )�(�)}ZN vI(marginals} �}=ZD}= �l�4 �\,,\ �NA��A� AF�!�%� �-�Na���Ahim6*;$e simply   �2�f"F$a� is $2�$` exceed��e  of $?3�Kor� six-�}"���6IAB} ,lmost 25\%. �q � :|=%�$ tells�eI6��gener�up to $ 7(secure key A%0a]yɊ�hanged t͓!mquɊ  nel, v�0�.A�a4ym�. IŬ y ha appropri�$error-corr��ng code�ha�{� � ion couldUd� by \� {one-way}A muson. Ua�tunatŏhow��e bes� d� �HA[8presently avail��tan�0iciency below�@$0.333$ benchmarkbyF� )�Co��Group,:$}. \s!on{Key�Uwo�6�}� sec:2ways�Thj ndar thod)�1Mng �ecret!g -bit"�---!�4 �\ scheme)8F�G ��� all make 5 of� mph{ �F� Sucha cedu A� also%� esig� �,raw data cha1 erized%he� � ^�in�G�� ease�-���dass lettE$A, B, C, D' i*  s6| 6��) p aR- b�5{�y�an%X�!Bob. !�KJ ��s!GE���X a)�am�e�A��Uthe sa!ۡ3 9�K(�differ� O>�`fr�a�t� i�as if} �w� R wfY bto, who � receu, 'T$t but gets� ��)9three 3s��< \subqrRz�ing.XaX 's meS%�6���(T�} ek� folll. Supp)�has�A,AmwhichL I�s $0$�$1$�'& , say te3specific��en? choo 1lyZ& ~{ayA�and co�S(es publicly�,Bob: ``If y9�A A, c�it�; you�IB1$!''!�ere�3-�%Y�BTal�� firsw � 4n turn reportsacesA� �)�CA!;B, fail� if h��s CD. Si�9�a $1/3$�qof gues� �'5��  w1pi=B i !̡�u ���y� `q}�>% 2/3${ ca�� N, am�potentiWutcome�idfie�th� ect  anti-)}\�$\-re\-la\-�l9 d aE�� is obtain�in  ogyAz� �of ����1selec�-�"s match��m��m��t�KJq. "�eiy�i"�tra�\n-npr�m inasm�:a�u� �sA2\0s2$ submatrix&$$4 4$  �J=� ݏ��r#a cruc!ñvc)(: Only cer!���!`usefu� %�!H�)Han� =I9c b systkk�x/ a�1C. Bute�MQTn�yofF�?cho�8is not unique; � ��AB A�Ba�eCe� (D. Possibly�c@ �� unavoida$discard&&E0g ing �<$he unluckyuafe��t�O��doe �t�good advR"p stronger%6�ndByield a er�g tha)�Fs ./ ��Beyond�: I.iv� ext6 `*3 R % O(do eb a��My9�t(!�r� on varianc8 65Qn�~. Gdescribe� ��)f��� � e� � ��s�e �oneis ra� 8 � a. {reť��A"� isYr� u�,!�N� ,roundag ��5�K� t�Jinvoli� f6 step�D \textbf{Step~1:}~ ���!M��a ,A. Sh�nou� . Gon�BA�_ ���dI occu( whileMvng� * ��M.:�2a:}~4 Ip,��t I�th� �} �C%�D,���sBg_ s,%-��o.s (CD) $��E�(s (AB). HeD �I0%j���vseca�|.> decic5�; � %�� &�APto%_ch1�en39�he� :hcNA)�/ both"e�]&� �econ�hs:�Qr nextA�:&HB�bR�a�ams twice}, 6���v��,En tellof couru%VA he goa� ��rdsE�M�7ar�a newY�h la!"us��!7���wK yk !oqyJ�&uE<��C#)as #prima.J �A�repea2eps 12� long�eeno_unused-s��`y�� 1���g�c�A�.(s crer /~2b�1b�tepmo.q�a�ef6N. NextBB��yss| Cso!�th. A� �,I�"!!�"sh an w$��of�s,. Nobody elsq��. q��% s by in��~)�by�  s~2a� 2b r�1A�h��n%ll aboutEe�4 .��2� g�d&� ori��s�NhappensE� b/y �2�!$�Q+EE�DuA�tor it.z$�"E!�  put-aR'.��6� x1xM D �%�2!�E�alb���R�e�2�spent� a c 2�of1&B�B �;Q%U� J��$N$�a��t�Fget $()n+ 18. 0�& s)N$Y�� otaJ0asymptotic ef"t �j� v @eff�D\lim_{n\to \infty} �2}{5}d[�1- �6 )^{\!n\, ] �A �W$X{� �� fa sho��Aatheorete�maximum%�, 6� by� �$GetAll}. O tve g�$a verg�, just ew� )�su-Kt in ���9f�bea�$0?, 89 98�"on:wo, t� h6��,pis eas�A0 abov�e2�$��NA�2Hybridiz)~*C h@ I v�^mpu 5!�!�& �_��� � . to settla finit"of- w0 beneA��8to��2� ehe v f�}�on � , i.e.,6b 2b'���  y� ��  a���e6{�+B�n��'e��e\e�[�� �v3 ?j�="W&�n+1�>�"� a �� ��n$Q Thusaoh"E� r+� e $n$-M}onz&���( after $n-1Ya ��>Singap��. Prota.6�&rs~of)�$'s ``spher��c�''��E�Huse air�>&ISec.~\ '5(A�:d�� raw O��MQT. I�.�B�t�#ic pow2)'D� ed�8 tras�!"b eH  a dea� ng e�7��i�!W:uw�w<"ll focu�wA eJ��%% �(i)�a� !1acquiT,o��1(; (ii)F�A�7*�2��!>i)!� ��Y�^�"}�* 8 M�^5 2 some{ Q p!b{*�)9�of^in!i)U� uisaX*�%5�] �,�thi ll !t� %Sin��ah&�e=]lM.lyunF1c!��!� explo�0��'. A�6�"Mman/s>q �*��A�� �&a�� =$ach)�,%�y"� ��e.v "wu�M�m)��(ve�r��ant�8i?��!*(s did�gea�ayqB�� D?---�serveu^!e estima�ba�N(�!24*)!BD �}� � &�-�%iovi4 nr��)rje�&t*�i�)/m��r�z50-o�'� AaA/ QSE}� likto ,5A� Z�(5"�'ne)ris� � � �on� -�J�l�m� ant. R�>�check�!� ac%R-arn���B,)�'!&%i-A3.Y%�$#@:�o��()� pas�VtesYf� ��e re�1!B s unP*iCa*B [i2#ed)�`` '' encom x�A�ry����d!�$deliveringy��2�:�&(65plue�ns�) line\+4*k)&�(nm� dprodu�%z�Pd\Y �e%.ces�*��!a*xMj�#�#>;�$4qr�aW.��� n juy-whYn<$!Laccep�� . z�#!xk)xe��#p��E�'�oZ!"�9���E,a�oly indz1tA is w|� i5 carQ look�vN���wo�a� % x.�0a limiA��%ofI� sacr���pur of ���+ conf�c4vel�:igh�a�s, l� WreaVieven W 3��"��"�+P!�T!yto pa�$ pricɥy�q !1 B��#r-,& fa�,"�%e�,e)�=�=�;3r� ne�� b�/P���!�M� �/��M�d�3n�&orem ��Renner}. enAfaeat'em�.�/(%O"'�al1�s, }��n2I�6�]fX]3i s (�ist�&e��R�ofJ&:] )*� )�&7"�eb�!e=rUm;E!!��Q>m1crpia� �+�<�c<(52?�?a�rustwryub5 2 � at&J(r���$ be absoluA`Qty {.}� j��Y}9,%_y�!U!qF�ɑconcluAvsn�) 9drawn� i�s� �� oo �Etyp+i�ssump��eS"�.of�'�u�"<ion�-iJpaD!g< BB84p�&oy$ ma+'g $����y<u�#� ��A{/�a�s%d�nbi�<, f ��E48serious doubts a milla�trials g�8 70\% head!�� i�$��leery,� m�m ��c��� � s�0N��t/l! 2A��I�s.� ��� AnA��� + � 0��t�je� ~�.]= � �$ let}�n admixt�$of 1W nois�)or,A]i�1/0an �+��42��e�b;!)� �-O^ S�sC >u/s �=F~obH d*q !�tso b�3n��tyJ�v �y_7�%7 s.�;L4-\epsilon}{48}(1 - *@1)�!�+ cB;7&/;+2]>�/der��"�:� !�A2��U Bp6=\�?? �)D?� :,Z?0$&$"O��is�: no !p�3 =0$;� hE � N$1$%��W#i�;�-�/0\leq�<)ru" F�7;s.6E�i�- \geq.F���A{r�M#!exhib� �*[8��<cl���n�>� � s� nE nuin&�5y� e��2� .�of Eq.~(eqF�)�>�3�e����eq:Iab( 2�0a04e E�).1@E- )) �25 ,4aF-p� 0+ 1�6Q C 3F� d�.�3monoto0: uJ.wX!� to 0292w. �IT��IŰim�6E?e�a�I�i�*al�b�- tru��%�f>�d V��A�9��E�wir� :3`� �&��\�A�gn� �s�*B"�.Z @o���nep"�-&6 M24x*mu��a> �!H 2M$Eavesdropp:�-e�Gl9�f�)o�i%� �%�1Jer Ev�#�mp3t ���#-< ! �%.-%is}=,�?� tr}E�61�ϕ7 b2%� doCto �:e�+�s�?A: 1 L*H ' 6P �Fba gig�+� ,cilla. Upon��c!�a  degreg freedom,J=� � any .��/�6��---|9-�BO5,*�6&naTlic��,� F� Ds%�na�� a%duc�  thE�\oO.e� . A;": e&�;�Schmidt�%omm&�%�9x%!  re��4%{ !��Carily*t ^A�� �Y hat M� K��D*��s, � Fe�M968$4#.� jop�l�*ategy� (RawDataAtt}.�0-�:W� #�i� a*� �m-o keep M�s�+%DsAQ �%g/!�9���(x!.3 !MB �\���y6|; �4eq{sp }M�s |�HSxHS�B��a�q` �V`eF��ke&R-��s�of 2�32� _F9A�� �.i.�q��$��rm}�A��� @8 i�e�,M�y�Rns� e�� m (seeMD$TomoCrypt}%�&�$dix��9 pyramids�nam}v� e S!"�� S� @_{12}s_{34}}\sqrt�<D.+7/3/24}}i 0.\F�FHe >)�s_{jk}9�M2� %� s $j�$$k$��21$%$2$��V�i%23 N4$%�@4%Si2Y`b1V:&�Jퟁ' �S�%h� �A8�U�r�.j6 3 "�8N�threshol�8zF2� � 1��W�sQ&���J"�6����attack&Pf.4 ,�2� �&arn�e�.as��&J'  &�&��Na�2*e$waia7tiOe=(*�!�b&8Nm  s ad�2al clu!Ev�&�8�qws immed^;�:"�M<J�>6�&�,��M b�@ !� <l!ds�ի�s )t�+�;�A�9+%�� a5BAimixn<wo.�s f�I mA�is  3-� w}A�re��if%�c�)�X��m"�+�5!�6�u�� suicode, �a�az`2u�*aq*J*�;�� e�ZC c�4Eich y�F�;. I�,&$ ��9�?8W=M�w�� !�, "�B6�6?"message1R=j5;W�.)q�-� raw-oaw�!A8g"�*I ,E�tak�6n�cc�Gw�) la�s� Di+c"�8},6��`execu\"1-of�s*##�Ź} �8��n1!. ;��inu�..G�" gain�2AdF�. Giw� x�|<-dJ echnology!]r)�F4m(%`:�)�o fOLi&JG� �� A�Q!�]F bthird-� we��e�1�col�7� �j��0�!���Gi C��m� on"� u� a_�| �b! �O�R %�4��un�S �,��!�t � .�C�d��:"�-� ��22SQO SejO FO Dq�� heton�&!�w�4m3!�gqH!�m ill 4Q qQu��, DP\5L,� rm el"O%Z�i�or!?to� )��B��@�o s�e 6fa �,ET,"�6f��i?�? =��i��PeB� d a�>�Q5 �"�= Both task8 b77�l y�%;oa�A$ Hsee� futu�ko�">ex� ,�I�{/ll�&;r9!er'5T( j��sh�A %���d8�*?�� �4�� �}.��s %�er, u�)y6��o-^�i�s3 q* �*�N ?:�B�(rivacy ampl8�H%�IDc9�$I� ?$R�+2{md�!en� a -*. H#�@ya�"2 RV�1v"&�� yLgei;"�toa N xm�a�) ma� �use�m{all}=��2�Hex~�E\ 6�� ,} i���v1  % t2I4�����giv!brief�����!"��!�seZ�  A�i@:detai re�4or�� 7J mpan�A0papers, Refs.�S2�n�Coh�.:g(M� 6S *�.raw� "gWo�L's�IseA(��n� e> of rank~2V JL�@)��1C�!&� �8Afr'to�{���9r!�%G9�)�>.� �:�e�"�!� � to!��'�T� ~sI!�POMa6žQ�r�&�"�3"k>0.1725$# 's7K0��:�=e&_@!���POis�� alog.IX�N �*�0��tp@yA�'nAfAQQPAccInf} ��<���i�1 �*�%1j sl�ly7$2�(�'�= 1\%) !X!-�Tb�m� " r�IA�F^.\�*9KY 's�thm�%b  �Ti��)'��)kl[Sof �ihs}I�$a�l2byz�L eps2eta} �<style�(eta=\Bigl(\�=�V>�- %N#\,G r)^2J�=� I�Bo@A#!a/v� eps+� � �2}� )^2+eta)^2=1F� we*3 undaJ ��\�Jtw* �nxl�!=��Ehe)�--� �0ne�C/B:9tauWS��--� 5�9otA�6"ticula�;tt ta=1>\0�� ��6{ T� pL��c"\ ��@����� noun+ �F  Eve;E�o I�k!&�Qir�!�1#�+s�im*WR.)G!� Y��fP�a�9b�Q,figure}[t] \}Ze�e{\�eyU�ics[bb=80 587 295 745]{MQTgen-Fig1a.eps�W�C93 C502CbCaq${�"fig�"% MFRQ!6�B�xr � �f� Top �: NV%;!� "�AF�Bob (:�O, curSAe�it{a})�F?A�6@E+:@b��a�y 6� \� e�H��non&� �I4�solid ,�ja�\G�LyM�E���) dash�=�AsixN@E��F��,@POMy-� 5{'��9T%Sb} -5��X#=0.2363Z�1�-do=1Bc�� (on Holevo bXCB "��?s@a}� �\0.1265���1086$��lBmA�!.=�>�9BottomU��8 Csisz\'ar--K\">^is�"DH_ I=2n!-E}�>~Fb!��*�� 5��)��(Y^I�V�# (!�M=)`r F�0.2g[�� 31�Iush%Q]$� �w� ;S2�6 � �c�  D plot�f�Bo� wayE&"R�({�e Ft2�) �7[ ��Fa. �\��} �S) 4mFRo,2�S�n���6��A� Eve,aU2� Q#-BS �A� �#�1u \to�a�W Mv):�e�Ghn5 �ay�U{F -ECK&@ �� �)CKtCJof>&�N9, �flar�J���b�Tilm��.�UHeE/g�� H �� um�D��N�)�s&zNM:�A�"}\edj�#.��+�R�T� .�&��[y.'�e a|"�%qbins0�e]!�_v�Qch9����; 'o�B7, *�F| ���"�e�CzD�Ew B\F�3�?&PU�!$,G�F�+���_�4$� A�*�&&�7�)%:v2^2/[1+�232�*^2]�A�? O�f��Ky X b .4(2#1 K !�A7i�� �j!�l9��s�Qive3@s)(��VEgW� e"�a *�jI* Y� -)�lefZ?.�,3��}\��$)^{2^{n-1} ]^{-1} \N*to&� (:}h�$n�Q }B�+._quay0�!%-)V �=lyIh(U��tD(?Je4��ae�'�'�6g�U��@t�'�wo��xa�"�j�$�-���u*&for�$ F.)@, $2^n���$� Y%)0� We i�g�v!�, a closer .I6:� s; /#!Q0$n=1,L=2$ rowAmTR�?tbl!old_/N�!�{#wx%�i�!��9, �"�on�]jFkN"8+a�z��!�&�� �>�n &�a,�+�'t� tIva2st[gam!� of*O�zemeA�V q�.�e�!��'ag0� �'�bow �@�U�<ō� � �.�6T�B/�*�(ee���zM� �by-a\�employ %� ��?#* m(`8�!t0!��Smodif��OMV�Z�.D"c B<�ly. J�5#=�saS%�SF� 2�%=-��"��R.�c�]�h0#-MoM~N+#B;�|�!sp:k" e)!D�:@1"�<Gixed A�Ui��� them�'$>�!=2!�y*2!!�EjpreU �� . W�Q%$:v!(!Sweak,-��8ite)B\esx3ciiw�,an��er�do�|3�  t"� �.No!�e�j�5%�mBM}m���%� . �6jHiD� ��A�i i^�$-H%�M5�t!���t ��c� �+ed�i�: �q:s,:H� saf� de iAb 0.33244(��BC�J!_y �B5 un�"8 <0.2628$!We*t �r�� ���2 &"G� .�$�E�h7�"�B�s,j��N can%�1��a-9"�!& $ir &� JawBG�%B����294Fche �@a��>_ rst�|:ed�- �i�D�en�g6;�!5.^&nA�rc  �[6c�[V�"'z�&p� �3(_Ge_9�Z���Q� a�n�DXE � n�j��9Mv �� , fur#2�be�\��A#Udu%j�� *��R��)�G6�>(�2s�d�"L)2$2�&� ell.0��B��Y"4F�'i!!wo:H , ye�9[ !u� xhaus6m�kBT&4t'+ }�� d calda�.�5 ,DandW},MV�]aiኡ� ��7 dema�l��searce@he *�s�e a+:�e�BI '- llow�a�"�=� 9I�J.= key��y�U18�5/&� e�aN� -42- � E�0. �h��n,Q�#`f5��B�,v!:�� !5&U2s�3}*� (ruledtabulaI:�:$ % �w-�� �P2$iJ$3$9D�F E�,$L=% -�VKA� �r�a�N(!;Z "aT�> in>�!a��$BtJR � 86� *^5�>� 2&)% � ��E#h colum�)��.m�+s���ZAoM*=�$Y�S%��6# }�=^{\ }_\=yrm{it}$)��Y��� a@e)(!�B` 1+ (Z{FP}$) �?M�2(p*3"$&��e�)�Ai�O��N$"ri�V *��&�L.�!1EO,��c"�-6K(} �la��w& �Jym2U:C$${n,L\gg1}�[-�w�6�E+��K;,� 6�y_ �E:.�udewlength{\DoubleColWidth}\LSow B*t ~I�}��d{@{}rrl4@{}} && \multiI�{2}{l}jwkebox[: ][c]B�} REB�^)\Ni^n6o�\ %R& $L$>y1}{c}{Z�a:}�< :�r=A��=�z�z�z\\ \h\��{0pt}{1 % & 1 &)N 0.2868:3476 1920W;rr  & 59?� � 18 -��? 674 0.424U0.29596340 ?4?976? 3 & c414 0.474 -340 H364 H299��4�%4 &16d446 510 �360 7,3771\\ %5 &3 000ws0.533 $68 H 3842- 6 &6 �-49 �72 �\\ >�E��YA�!S50 ;571 V375 D 3893)�6��4 !�*��B�$*Wf�B�:?&�'but nUA=rD.�k d� ly; X 5*/&}��� 4 �1DE&KW�*�f��н��n�/2�*b;��'NE in6`4�*2Z�� L6  r � �x �xk(2.�6bhyCZ}.!� ���con�<e� �L�7�J�4r &H%�kn�& �-�� �W>�!5�"� @� :�"A�$:`f�!5� Q'b w�1 *�F �$|svp�hR�&�3,Aq�b��H�Ke � h]A�xa reason&��. �yC )�apl�@2��4  5$, "�*" �I9�  -5�,QBER})K>0F&:�!�ll* )�� 1W%��&� !�$L=W(�[B�� 's�!� ~2K�>�9)�6�!�S2`ect a�5tF� s. Aa�>�^afrai�YM�1  ,O% Y�����5ndI�1%" ;�� 2 onwards]s�V-1{M�/ �efway� Y�} �'Y ��# %�(& 4R�,� s�emaha��.1}< "�4�,bZ�lm��Yn.9���"�J< A�6�Tir*Y6�ej#2eo �#3 �6Q�n"�Pe:�%�R�,ɤ �t� �� o.�+q�'s)�bEG]8A�%' Nowsix1�� .�o&>~me&���!DA�&�"WU���[��W%3r;LiC.Q�-2>w�Cnonzero�en�� s $1&s�2"<-�d &Pd��!un.�M� q!K#m#3��&)�?�ardM�&(�!e~I =}�X2} :z12V#.��#)A*w(-��#"i[iiž�)Ć FB�#g`c�Js,�nK.��sysou�DbD@ite� : $"{ p) 086}"�(E?��612651B�oV is c3<ly re��ed�0�Da�*Pni9�"�Qic!�  �A�%��Endanc��'%� {r}� .� 58pt&ɭ2�-455 585 293 737._-2a_-\\[1ex] Z=634 =62=b.=[ �Ac�A6�dA�}1 >� fig:* }% Y�pm J�)�;Aέ���)sd*Ue-Ft�bs�658&cgiWh*B"dmb R,���� I:"fB�s1{)2$: tgE�&�5��,+4b+.�i0[8b04[.eW��top);+]nc�F�{g�[u�85}$> ${0.21<, �R-! $L=4�� 8�D in&AernG6%�otres�p �bot=-�+�� {5.{3?� 9635}��9�sp�f �!�>~ [ "��>� f� . F,"�DS�(�*�;lu� re2%�(I�um))TJ!`�tw�4m,�,Tve1:�>"�+$ u�nt .�)ۍ3� x0"R.�,E` �h�urity��---�:4 c;�-i *c��&,�---A�A-ise�E� in f�%�6��A�j6�A! ZO��Az� hier �':�� .�R�I&�8F��c:� %i�"�>�,m��,:FQL��9n-�} feaQ���3 ��)��?'s�<�C��PJI>� \�S2C ��E�? : lawk`s!Cmi��uQ<�KYab�Zi�9��!Tu�� vi,; �R-A�-[ Ae�E n in^7Ci��=!<�vinj Z� E�j/�AX"�S42$ c������&� !ce��#GP����)Zc��.)B��",� c�D�Ns&�m>�33�2)�Ab�"pmi%�at  !���% Gd�jc������%� Fn��!l6��.a[a"�${-ccBadopt�!&�/_E allu!&tw�.� oi�)9!,����B %tA��.YyyHS�@as#��k̈́�Fc�IEOF� "@K�gQO libe��� metr�\s�"��^(I� $ican���1_tho�b�etudjLo, Chau�� ArdehaliW*�I^}.) a���!��RF�e��"�; ic} a�0sP� ��*z@��&�Uh�%��.2akori�|b�.%pregis�/Mp�-�(.OuD Dist�a� by u#a�o��%�6L�l;)�� a x\s_� 4�Kle�-I abs�q�E�I�6� �ed-�� s��\ata=to Qy�lA��gq"�|Ho%@Y-P -typ]"nf.p-,}">ko a�ver�6st[~�6P�"� � %\vf2H � *{Ac��V8> WEenk Artur1�`, Lim Han Chuen, Shiang Y`xLLooi, Syed Md.\ Assa� $Jun Suzukie9" aton�insight� u=5J.~K.~Ng�&!dth�A�Def%�S��e \& T�$� A�sy (DSTA)!NS"�o��th�4+ncNfsu`$rt. J.~\v{�)�t 7 �2hospit�0&W&�f6 o&R8�, .~A.�4te~Ja5re��B�a�T Daimler Benz Stiftung6 �Iork wT ��,A$^*$Star Gr��0012-104-0040,�!NUS  R-14 0-109-112)�by ProMiL SECOQC (FP6-506813)h`�EU. C�!aQk5�!� Re2& . of Excell%�f�)4 Min�a��Edu*�GN� alKF�2O5� %%%  :�yns"�thebibli|Oy}{99� i�3m�} C. H.! f�g$G. BrassarA��4�k(it{IEEE Con�p,on Compu9�, S�p�nd Sig�Pz�qP , BangalW�$India\/} (T`, New York, 1984), p.~175]}�6s��} D�u\s�K@d C. Macchiavello�]prl =Pbf{88}, 127901 (2002).T*�UY.KLa�8, D. Kaszlikowsa�B.-G. E�br�)-Kwe� )DOh,�4a}6}022324}32}E� J. e�$eh\'a\v{c}U:p!R>�6k$70}, 05232 �4x�1? OneLoop} :[$K. M. Tin,�G. Gohi&H.Ng, La�3Ph�g> bf{15}, 7�52�No jR. Azzam�HA. De, J. Opt.\ Soc�Gm512�955U3)MzY�a�rei0L�<�1} A. L#S�Pang,vLamas-L�8��!K C. Kurtsic%`, %\eprint{0511053}. \jmo�53AD523�62�x��!�M.��h\prY 5�1I 46D*EAnd�I9�!6J%S. Y.͚�6� q��<"� : E2|6�/�},� �]��.3�V�.�W%�Chu�Z��Q/(at� iUu2B��AK.��2$67}, 661 (G�2�EP2�PMP603126AP24a�22309JR#�\/'1BJ��OR��,� has ��Js�H=0�ix: 2p_{�p_{D} l"@�}h}$k=24:;R:$6*���BvF.-W. FuE�Niederre�{ C. Xa� In�,J.\�~Inf.\u�3}, 9N�&g�� ��aw �dny" t�>�0�"b .�[ � R6tG �i: a���}��p*me.* ��c�i��)Y�."_m,i*>e*�!�5�`w-�9to�c 415$�?! 5* �!!xplici.\� ��T.��� ]$���QSEJit{B �\ E4u>, edit% �CP#t�ӁfF� Leע inћ, Vol.~�&(S���QBeCH , 20>xe� }�� , QpZo6� e�8252j� g%Ic:�j4uld2#be��5~ sj�ofbv!�y,�b�ts[� e�bn\Vs�A" �zrI��*�& 6M\e>�5w9 fe B�rqir �>a%�" Ae�b m (\@'_3A>s})jU;"#_� 6� A� pinaAv,�C��a�� >� >2�q032306%�6�mBV�:XA�~� 1�� 5430J66 CK} I.&�CQJ. AG , -  Trans.\� T�Cy�2�\6) (1976�g�S.u,� bl.\ P}0 achi X>bf{9}K(3) 31--42;  isha� : Pr G���� (USSR)JM110--1182-�3!DevetaO3 A. W�9,f6 Roy&B ]46!`20N&�%2�N. Gis D KraR`6(2!�12332E(6� &e��P>#�]�B84�#R�!. *  H.-K� �'F.&��&� qb , OF��6�&� �!���%"z�de�8֕Ħk""^foN�kHen , Zt�9�inf�pr�Ht� u��iO%� 2x72 �$endB� �+ docu�u+%%% Lo�EVar.s: mode:�%x>8�hflyspellTeX-maO: t(End: �w\{ m[pr'u�U criptaddr�howpac;�loatfix,�coI3 ]{revtex4�u7Mckage[]{QFx}  {ams�2Bfon� \def�c #1{| #1 \�Mle}  bra#1{\la�| $kb#1#2{|#1 1\!&2&II{1\!w3lz0def\A{{\!uAB BC CE EH HK KM MP{'1th{PR &RS Snew�and{\fA} Afrak{A}>!bC! bb{C�Tr 7rm{Tr.W eend�mP {\hspace{\stretch{�Dule{1ex}�2�q/�{W���{J)a�2qj��+FV/ �.X<:Xfix� rm Fix}\, r�ma�orem}{Ňem6lemma}{L !8 }{R A�a({03.67.Pp, Hk LA�date{\�3b1Rqu$title{A Unx��G�5�cA��ac�� E�(C�% *H0 *� �tho� deco� nce-Hp�����J  ��{�pe��s�Ocombi�r�5���9��P1g��Jldž. More�&@ demonAG.�2� >n�#d�?��!5*%!�O�7]�M"l, �~ )x � ^m.� Y� �8���$O2�[C���ng�.G�0undesir)(# bee+(major break�f�)��u��ope%�!�pa^co*��Gal �E�s. �is�_!��wiJ�'t�E��ao�V����ame3��umbres Fir��we�Crevie�ey)�f� C>�DSho95a,Ste96a,BDSWKL97a}�1g�Y�p�fn�] ``>O�'eO'' o4PSE96,DG97c,ZRLCW98�Vnd ``u=�y>TKLV00a,Zan01b,KBLW01a}�Osh!;�02i+l�L�ad�a �aly�,V!�g*1�*l#u'sj( �"��gv�s��.(ic.' �motiv!aJ"�����> >�} 3�2Z!<a+Uiio�?Y��� ��%q"��Ʊ�%"! t�����!ih&�Q w82>����(le�a�EI�. .:���>V&4N`�e�M6� 0���%_�� K�)` /}�'�j�&<. \medskip \noi*�t�3�+S#fModel}%�W%OC-ѡ�``�e�''��>>�mdn�!�8�Pa triple $(\R,\E,\C)$!�rQWC�sKnbe�'ǭ� code}$a Hilbert *( $\H$ assoc�o*�wRl?i��e �$\E�-4u0"$\R�-5M��y n $\B(\H)�-ݻqN��hE�Qun�%!byH%~o3��#f�E���$:E1eõ[6�\rse} (\R\circ \E) \, (\s� ) =  \ al= P_\C "�R&�w� $%��dp� o�r%oon\C$. A�prelud�" �n ��2 low, let q�Ainstea foc�R���� _��I�"qas eas'x�!�4�)� 9�%�Ia� �G-n�'�t�|j�F �4%���(zAAN%!�,\C)�6�a�s�8i�E�z =K!�}P�ion�;��c �� )D%a���� & or-sum re� �B!$\E2�um_a E_a1�4E_a^\dagger$. �N �L:K�PuK,��6"E�- mapzi6�@ah4�<d: :�B�b F_b � F_b�p&e r:�l@ scalars $u_{ba}$)�i^G= \ � E_aߡ��f �tif�Y�E6�}its͸1as�aB{E_a\)1�KE)� ���{c�5Ms)�R�`%�Mm ma Ir,ȍphr����2!M�$n!�q=�6& �<�} a�.� E_be��(lambda_{ab}(�a,b�:?��(�@WT�} A�s�5�.R $. C\6!�i��{ is�2�o-of E�1eA�:Y$!; . %Wu te %%�E.���)A��Iu�.�O>, v� %our!�p V� thmpg0m=1=\dim\H^A$fO$J�S&� \& D*� Free��s�9�$\E: �> \rightar�V $a��z; )#�&E��wA�U���� $\A$� b@ set IR,}�\}��5� -GIjDav96� E���JV� !x� Y,"�}.�:�S di�O sum!�(m y ``�n�'')�r matrix �$s: $ \A \cS)\bigo �4_J \M_{m_J}\o� 0\II_{n_J} . $E�APA(a ��l}F�H�@� mea��a&���3i�wsS& $\II$�4inZ�aff"��v(', �� II)=0)a'���'a al �� Ea"} (NS) � zTI$E�hA+)�KR� ��Xed Y�#Hs�єI��?VIu;� 7 �}$'', \[ \A'�rbig\{\inI�: E��"�,forall E.A�6�%�\}, \]� en )���<mmu�2%s�!��A�, �Q-� �:)ot �ven.+ ����e�� &GmBa( B%�)�9A�Ez߀: $\A'M�Q�E�A� U�MI��I>�,BS98b,Kri03a���* provbQ!��wl%�?i�ыH��0� he fE��ÁIH!G;�*r~2 *}� 8pt�ZQ fix(� &=& \{M!�I : &=I\}�� *} Kre�5��21 �DA^\�_e�p�rI�� e NS�=Wn"� �vƒ!�!�~4aE� s satisQ N�Etrain��AG�Aor8�3- + Eas 2 B �s�? shif/�}f F$�{ -\$ ('rs !�s)_/ o�_a�>o� 2%�<�NSI�#�- no�D � �4A� !�r X��"  �B?�2� & �*} \H�F� �_J\�\H^B_J"� 6� ���y�hs"� ^A_J$ 2dimen�� $m!c;:� ?B*_2?n_J$. �Vb:ty,�Q)�E�e � �.�����. a �lm��'��!�� � so^1(!&�TH^B) �t \K*ia)�: *5�$) Idm$,B^B  \KX  - mn�OU�a A�&OJ$'�JeN�0or�@e�r w� $�-^A.AѲ��) ^A)�+B+� o2+B)$�s��[riu!ZA/���eС�$�$!R]v$� � �+�E?��{ؼ=��^G��Ig�i��e � t��=h�. I�meޤ0a��u$��s��.�� ��1E��nob.��kumI& at o{�rthonz�ba��e 1chose�%2 = t(rm{span}}\{n L{\alpha_i}\}_{i=1}^m1�H^Bf7beta_k6k6n$��e(%�S 6�!=��"�Csub���'� !�_m -�{ n�CletNr{��kl�kb�k} l� ��$n}: 1\leq � m\F�deͱ��r3lp ng famo �ŝs''!�2�6w.der�!se-1 E:� m$D rljy"shMm�  byKk�Nk:� {kk}%Ae��9YneqZeNc read�h���� in f�!��d��=pra�= a=5.3.9�� P� & =& P_k1�P_l ! � \,9�)�Q ?� P_{l�[y!NGMH; 'k'}Hg[ � a�� {cl}bk&��7_l=l'$}��+Q\mbox{�l��&% G�.F� s,�^=Uin&J��!wuu�r�� !8�� �&�!�!'� Gamm3 ��kl}��K��)��it�s� Aa�D�+A�J� f">� T {k,l!nx��%Tl9�� ,\in \A'!�2JB�) &rh&2� ^B FlE�l&� �^A�~ B�(a�\.�%\:ma��}�<�UNSq�|�!Q&) �BAF�} (DFS)R}s�p&�. Sfh],8w-Z�Fan� �P�� ��� e DF�5  �mgi�W��'�'s6p �;&6Sv ��_H"� *��Am-DlJxof��L?��uld* ' '�����parx�m�!��E  ]fy� �2> �r/@Dj9<"���*��HS n doso%p=k��<gar$?!�>�xYT��0.T!�"��� ``un*/ �Cn�R$aQ2 "4I m_J=1$�4�QPB .d axEJ�*� f!.4&N-~w"��#��'a buil� bloc�PA��� r�#�� 8A1��=���@� a�*�S`�� �#5���&G=?aY%W� &� ;^�A�t!�� � x. H�x�g},&PP!�A-8y���A(iH!f�q !�fi�a�in/@nc� (3 mapppoOS ��an z���$ a�a, ��+r�i\} oX� $�(:f )� \K� SG u��fAY >� :�l�+B�,\,{\rm�x���} 9^A A.}\B�]�V"2i �:#!�2YtmiM�Az Ns"� ���a��I*) C� ]n"� Yf�ta��!vat� �.� ~-�a<. � �� �scu P� �P_%v P_1+\l�� + P_%%�:�9^\perp!� II -�fA��= CKz T�aA� $\,$ ai� (�7�& k &6 >�i" I"�O9W ���NSB� ыvB����HY~� �A�!�a"]�*� ��*#� &ol&" nume�'} \itexkU�"p i B,\ \��< au^A\ :\ "�� 0!L\ )| $ r 6sVb.� F)7 _"�a2`� f � big(\Tr_A# %� E)"� =(4  .@la7�4 :MNS�q*2"Proof.}��V�&�L1.}k�a $ 2.�K�pV$ 3$r��vial. T�&v�C$\>ZM,"� $\� 2m Z�A�!��!����2.}\@ �el$�~Z$� \psi� H^B$*:�} .�Ev$kbRYQy -� eq:cg�/%�w��� $Q^� �QA Si�Ab �"���i0���_{�,k}A�E(��2 ��v�xr $k=1,�9,m$. E �~"�7 �)1s%� �F  � 6�b�7�o� �>�x"8"�;��\ Gi�� q�AN�1x��� K8��kI� � c� �St��pr� diK7���*OSti55�(a �! �rg�49 �P)DN��l\ � %psi$.M!����$6��ɼ#sx eE.}$uarbitra��*�`�fro�[�!A��W.��J�2.}, � sU��N$�E�Xace serv�1e�3}.y�Qz�d�Y ZZe�s�%�R#-�� �� . By+ z :y�.���,Sɲom.���*�# i�n��E��/s�q�5�.\h5I$\s��e$o-"� ���i4id b�� � � } � n it &�(J8*h� %3ia�`. L)4�!ʼnݟ.c�"EEE��U"@&�fw %�*"�AsR�Q=� ce: � A�.� �8� M�FC_�%r�3 \E$.M�D�v�R>} J�"/-�*$di&�0�M en"Q & alte�U is���. � � newE a NSi��� ques���o �M�Q 6(e]Se0AV-�M"$ a-;  � r-~"iLI2u $ey Re�"i,{U�p{9 :EV�$ʹ5 answ�K5z>sg��aNHQ�5m�v�H� i��10��1|�6�A&� 97} thm:� �$.4�B��[aX$fA�$s"� i� )��ve�0��N (�RNZ%��% m=1)S.asI�)�p �B ofn!�V'�n��H�i��y�ctwo�,�q hold&a �!k�'=� mbu'�*y'k,l�� d�~Z� s�&'y;^A��.�\f5 �� 0�" �2� E�QF>`."� �!�i����s*`�aZ1},�A2�nA F��� j���lyF�A�\E  bi*� �  5)�.^U>9aZ%09?By�.���Qon&O�ozi &j $,Y���$"� $i�* P_{jA�� �){'l'E(� �RDc�F Ia �)b may EFfiawB�$mu_{kiajl,f*�+F�a�a(� � >Ke7"u�o } Multipl�`�i�%ł!lE��2 p)�� $P_l� ?� w�!f! ��ijakl,i� = 0$�A $k/k'$�S&=��8pQ{23A�1})G& 1e_{�!= �kall,kl}� �aP�^?EfH �b�fin�u� \r �: �!�Nd � f� o.a�Bp��A�is�$%.� ezq^)b� 2��UZ�A��'%A *+� vC�!@A&�K�-qK-�*6 #�  To a�v�9��cWG C!�eY%�a�II�o+�-��E{-!�I�~U��4)E-�1 fA$yV"�*� �(� zz) m0ME�_aZ2\ ��MH�GF?)��1{a,k,|P_kD/I�*�,i�y��C"�:!�e.%b���MB�� \fA( �B Mo��{l,l'�dl43^ABd4{l'6-i�n~Jr>,u!P_lm J:�}.�!R)�2g W��T \ove�Je.}�ȥ�l}� )X�kN�y.p�B�%���&I RH �!tri�/���e����tor. B\C{s E�We��S�a^�� 2a��5`ess� �Fj NC�%\ J/2a�{ Vi�Eq9��$5�:�ɭ� zero"�E�"� ���R1�?� k ��<i�n 8�B�B� !�.�:n�;�I!�F�7fw'�& an���m7r&�}L*on�I`7�r� +..iW��z!t �2%�� �,a &h**Yy�A�� c�<'^�J MS�.�966="� ��}� newi~3Q�PIL� R  \E ))q�5�R>� ��"K |v��worH�9%�i�7'c ��9& ��&�*a�&)e�*IJ� t0)� $\�8\EO TK subs8E� EHby (AB�m>(NS} offers �_hve�iعIC���PJ�. O}�x &"��-a4 �-/f+�!9`��!�<�e� C�o��saC n $mݷF� �6.���3ed.�)� ��#��"@5��is �(\Rs)rm id�je��ch�� g6ߕ , $m\geq ��nd �TSn�W ent �އ��"� ) .�=s2Q2jSa!$�E��(y\E^*�! -Eize�P*�1�}Y A7 %�. A��,�$*^R��o*�<&� �`&*+I ��b���l1��m�y�.c�[. ��m3sm��4��a�$�ͱȩ;A�^�m-op �� �lj�� j� 2�� \6�<� " 0��t�5�1�� L\��*R b2 k� v�+i }k �9l^��9[l"# a,b%B�_~�AsfAEb� 6�R�a2N��� �M��y/dR�# F�Ap�; ��S��CAl&�&�6���1-Bi�)�8�^9#�!��cy���!R_cE_� & &)� '�w6oB�2})�E$�:��# =� j P_j�#aB**AH0 >E&n cE?&�*.h R_c9R_cM�{Al� � {c,j {BF,agger R_c^\d P_j. �C E_b P_{l} \\ &=& \sum_{c,j} \overline{\mu}_{cajk}\mu_{cbjl}P_{jk}^\^{jGleft(M~N \right)��ykl}, \end{eqnarray*} and this completes the proof of the Theorem. \hfill$\square$ \begin{remark} The condition Eq.~(\ref{@}) is independentc�choice of basis $\{\ket{\alpha_i}\}$ that defin �$family $P_�$ andC�hoperator-sum representationth$\E$. In particular, under >change��'_k} =)�l us_l � $F_a(b w_{ab}A$,�scalar[Lambda$ m to $\l4 kl}'G({a'b'k'l'} Y>A<(kk'}u_{l'l}0w}_{aa'}w_{bb32U$.Ire)� Equ%~(\>� generaliz-pLquantum error correc%R 5� Eq1�6CoA�sion}eR �Q~ ed a� model�y BG , called Œ��},))Is!1 fundam l adigms do�so5� uE~ �ethod!��active}i�], by ��egT<�" aI&levelL�s rather��n � sU  also1-i�no�,of noiseless<ystems relax�ADint�>!�on�``B y" s"��0algebra; i.e.�Iat it P ina�&max� ly m� state. s adi}5X2��)�]5�m�^R�N- }�  ��2?.���ei%m$passive or-� toa�%le� wi��na��converto����poB�.�,protocol. W��tnk Maia Lesosky, Harold Ollivi� 0Rob Spekkens V our o� colleag�Tat IQC PIeNhelpfulq�ionq�work waA2p�Ji�$A9a+A8xfrom NSERC, CIAR, MITACS, NATEQ)�ARDA. %\bibliographystyle{qubib}:�the.: }{14� xpR \fter\ifx\csname natexlab� \E�\def\(#1{#1}\fi \ZGbibO font>J M#�Pf�Q$�R cite~R.$�Rurl^�0url#1{\texttt!O%8{URL I8providecommand{!\ }[2]{#2} B!eprint []{S'} A4ibitem[{2�4{Shor}(1995)}]95a i {aut!z5�{P.~W.} �1k; r}},Akhnfo{journal}{Phys. Rev. A} %/bfT($volume}{52:A8pages}{R2493} (Yyear}{�})Z�teane�6� te96�� A.~MB� K�� Lett=AN�77:E �7Z�6� %lN�4Bennett et~al. �6� #,, DiVincenzo!�Smolin��@��C J.~A>C �?U�andI�EtV�W.~K.}-o:9,)�f�;^�54}.A-� 3824R�)�!_N�Knv (and LaflammI�7A� KL97�� E.}~^�S})$!6�ac�V8R>L��2{Atb55:C-7900R67e0�J�Palma6,}]{PSE96��G.M>�O�pf K.-A><Su en�.C�qBO Eker>x��,roc. Royal S n�4^�567Rsv� DuanE�Guo��E�DG97c�sL.-B�P�4 G.-C>.�����9:EM�195V�v�Zanardi%6Ra�9:ZR�:P>o T�:B���;f; 3306Rnv;Lidar.�8: !, Chuang�� Whaley��LCW98�<D.B�Y:V-I.L>� ���}K.B>P���^���&� ~�81:�M�259V�8r��c5� 2000:�!,��1�Viola!�KLV00��^�2V�n�%L��B� �2�қO.�5�25F:!lr��!!�1�Zan01b��fj2�N�n�63Vy12301R�1r�Kempe.z1>z! , Bacon, e��and�KBLW01��J>�^:�V�D>;��;F ��Y~B>1�Z�� 4230Jd20z�Davidson�&� Dav�� K>mJI� emph&�Ttitle}{$\mathrm{C}^*$-�9examp�TFields Institute Mon�s}.�Tpublisher}{Amer. Math.� , Pnce �� "v| Kribse�3a�Kri03��DJ� J6�y�_ Edin.�j�46}U >� 2003r�Busche�Singh%�8� BS98ʫP� B� �^"�r�mr24^J V� vnSt#g!+5�ti5��W>.M^�E>�j6:J��1J�195v�E�.�5>�a.\"8Poulin`�~� B�]:�V�na.�V>B� ���B�1 2�u�in�par$}f�B�qG& docu�} �~\Pclass[pra,superscript ,1pacs,�c�n,10pt]{revtex4} %%%% \usepackage{amssymb} .Qpicx} %TCIDATA{OutputFilter=L.dll}!Ver�,=4.00.0.2312|LastRevised=Thursday, April 24, �� 16:03:58802 Language=aOican Eng�)} -he�'=240mm A$>{\rangle} w{\omeg��def\W{\Olr{,(rGarrow 7 ud{\updow(p1��new�"0{corollary}{C ."z#N}{D�' 2$�:}{E�C6#}{#6~"os Q {Pro 2^ �}{!6fact}{F26\ erty Y  \renew"�choosep{{\atop�%delims()�!2={Enta!�a -ass_!d " eW�symptoti�y � valentB mult�%-copy:=} \�9{Runyao 04 \email{dry02@ +Ao �2O2ObA�!<��1��$7"%�� ��D1munic%( (LOCC) onlY�LPS96, NI99, Vidal99,A�, JW00, VC02, BPRST00,DK01, SRS02,FDY04, FDY04a, DFLY05Yq&, For certainB��-߹�ccomp� ir goalE? Sty! AC truc�%a��p�#m��}. Whil�W4&,% a%L�o6�%a nA�A�, be achieved c-9}�&A�la� \0,2} �: .,(�� jt*/i]2� may bo= U*q�d]4hiY2�*4as a catalyst,A�reG1 �6:1�Q��3axI�5�%�!r�3nea�e :U�$be&�2a�s>�,|\� \&3 6~J.$,�:which�� is obviou)Y#,1�9+,�1AS��dur\%!��v. S�.a>0Jus� �� medi�`1�/ � out��Yi�]q ed `.-:� :J'� Ref.M}a���bbrevy�2 Ea�)�?e�� i/��of %�3studi?horoughl�* Refsl�e� aA��u�(�z� i A�uch an6 -�0is phenomenon`-*�(2� .�(s�W00�n�im� ��q)n-�* J*鮁�YA� %��lng^ F&] ng J.� �'� �)by6� $et\ al$ s�?}.*(cif!�ly+ey founq)�a9  copie% �'may b}p�t�.B &a,2g althoug�c:da�a happen�(a �yl�yAYaA�,�� seV.ŒF�}�� Bobx�<:���(>Pe_6a �2!"�/ $m>1*�2a� �a�~II m�^{�x m}f�.& �� =.�-kin�,>{�N~�A� thenBsI A� them toge}*A�j)���� non-&  bi& te �-Iv.�%2��i_Q��0�ui�- ��7 {�m.e:�',,M!�A� short v��� 5f >a� care�/y�i�5in.f S�*E08 first glance, 2���:H!�2�n� �� c et� 0different ext� ��6aryE� . To�a�p�e:��p!8mer nee�7\extra2� as"e g1i�m� �7� �:���<6f7� �1% mz�similarAg�K�J accu��}a&�1tly l5��Z !xa'�e' s�ϡU�,�s(. A surpri� f�9idku woq��Ao%�6�c clos!�$- to &xV ��� M�!h� e&w2�= if a}�qEdm�:�$e�b�9.4�Aan���.n si> 2� u%"ejEuB_ �� deterw9st�9� ed i�� �&� A( ga]t%5 � word�e 2a scenari0 !�at;sE�power�/as �. H�;�>resul��t limi!�C becaus��2ar �0wo��N�7A\:ly-ѡ$A? 9%ca��be "� � N�< �K^ . I�a very!��a�probl�l fur�nexplor31F4cis� � betw� da�EaRn5:Y"�c�5:0E�A=A �Q�sE� ly B����w�l�2 cern�5wh�7 tor �Y���s�5 advant9. pŕon !"du=<" � : Am$n\� n$ )I#F�!=a �vAfteger $k )ArS9i .^EzWU= � �HJ ofB1TNn�S�k a $k �k$-.ac�� lF�]��b��B�b� n!�say $k$-%� is� a�q1�>G� �0 ncep��at!l-E��:usFD�)�-s�b���>i ;��wa] ��1� at� l r��c A�ifB:�6A!�1 �. A� plici&�@���?6E� bothA&� �serm�Schmid<e9F;���ob<ed!xis2$t� g"B����>>�;"��B�)x2�a><,Cp�DvelV<�GasN  ;$P_E(�1\&:�)$ (see�9 (�Ape}) be�C�9�j)�����by ^ ���. S� !.$P_M(�"�:�J� m}) V� averagB&\EZF�y�9c & -���iR3B������ Z�)�{ )$a�exactl!be�d�!6 -v�/;�H.7�As �zQH� clea�<��is2�is� &]�E*1@��Z�'"� I f f� im m� el]e7c *�(characteriz�e�V� �Jhed��� ��F.�"�!��Y(�s�� U in m� V,���!� Jp�� �princ!| unwq  es�I�?onna�o  � mo �isQ���8declar%Ga�y� lmos!�MqY � acti�i�@id�more "3wa�h�0��"� %m� cal�J!l!Y��&}9��AA�NHspm>ng-�e��of��!kE� �.#N�Cal�� �qui�"A�$s deeply r� Qa well-FA�:&2-`#e �Iu1���pu� �=a!��A6Bi}L���BwB`*^XA�Let us b1"��>E ncre� �$�4 in��&� ship"� �qe2�"�:��9a&m�tooNIqu0!��%�is D'D�� 9ZLF�=\�N$i=1}^n\sqr*�M |i_A |i_B y>�NGbeta_ibFb  b"19M s)� orde��  c.� $gH1\geq 2 cdots rNn>0� $ � 6�.5 4n 0$, re.eT��a[B}�aQ�be�&\ a|�_�tV�n !�� by:��'�I}�Jv��F,ula} p_{max}�"�$j�T={\rm min}\{\frac{E_l{:@)}} �+$)}:1\leq l n\}:I} w3$E_l({���})UCl}^{n}-�i�e�   =��1��C�:]>�f1A�odI�&�j!�,  }�M�c$o Nielsen'�Je�G �g No��j�M&�ABAuU�q3�5��Yr�7�a�� Cake $Z Q�=i�0.4}|00m�+1* 1}|21�.33 ?emJ+�f0.5Ni25}Jjk.$�'�OB %:):f=� ��%��occurf�� �{40.8.$ But if 1���%$"H5�6}|44-L5a4}|55  Kpt��> �1��% %:� Z  �^4�N.�f�N.)=1.$s*mF a� taskL�"Cb�"2�+1�aB:9�A 8ic�to !H n6j%�*�&�3}��*�.& $I����^by checkg ZU.Hn-�Q�.&)ETiOOA@"O Bob pr�+�re����6�"ju�a5gle onT)&90!>�.XallBGreJ��$!,. �e aS�=,2��#��#�,f>.?_=lc dea�� B?�( ��!� ŠA�� ng= ����LelA�con)�"Q�se ^� &y!o�.�7in� &� r�+b�[� by�#in�~ �*eMs�lat�Ie� fj:�1j�da�6 #9��  U�VtuI�&�U� �Q^#�|^#"�)��+�M)����-&;W"e f�:N.�  us t�2�,2�asJ�� 1}{\�X1.01}}( 0.40Nf�� �[10�� }�� + [01ݟ)$���q�=v�5R�����2.��05�-6�,$:"A s�&NoAkrr�]+eN����$ � E2dAa:���PJ'foLb�,1B$,�F[ t ho�:�^N'�� 11}\&Z:��;�*O� L hand,��ic��-��leR� oZQ�]���"sm� ��idTcal�ane� g~ 2^$:�5 m})<1 � \O\  \ }m�  1�ba ted)!Sroutin2?�refore��WC� al=��� � �Z Je �� 11})$�)&� �Y�[ ��:0 ��Y2�:O.K>B�f_.manneroPn�Uurn�*�E�r�io��2~^�A�6�27:��+an23�S"�"ͥ �"�6%e&M&/&�AY�(&p�r0�v-}02$�aoawif\i e�$!:iTW s�al no*s�.� I� h�w5>� avpm�M^{(m)j�:� )=[V�U� 2�:?.&)]^�1}{m}�Ue=a1 } In*a'$p�$��!Vge2 ric ^y3`!2^t�*(�#l�):��-"� b�$)����l͈environab�V$m$�:@:i5�!$. (No�XEh�)sons4�&mp��!$"Cty��=:��� ����)*9��JS:R)$ *�VBN)�))$,"�$! l�0is� =��m$&1>�$a�& -| taneou�#V�-�"B%� usu�=�$m$th� A;�.�of ]�:Q.)& f���!)i by^F�D2�A]=A$*])=\su�@�{>=^�mAAPd�$�KBG$� F/ w�"%sF>:��� ^R �gU�'b\e} 2(�\.�!gNMm�!au�=�:�N.b�.F���.%"um&�%szw�ca���d^%2���V}� b��qv1 "�:1�4m}�%,$}\upshape 6dJ.� TV)B,o *!>��Q3)=vq:..$"cB��:,Rrm�? of.}�6� %yp4�pcB#&�3:! z��r:�v P_E��Z�.O&��P_E# P_M�fac� e��fany�^ a suit�m. b� E�v9 .�c(E�. EO9�� U�� ny.� wb,n ?^> 6F�hN�, K?!� �4.�m�# (�#X ), $p_m$. We� )�W+^^� �2 s a J6 �Nhi"p��q�>� ?�jEup_m0>��bnA�Y�� s imS7ly�*Eq�$�), by tab�= remu�/.h���6s:ITi�u�0, _� n:^2�:S a"���kG} k(�8)=d"� 8 m-1}\oplus p_mr%.2�f 2 , P:^{J^2.@1!I:V �we�* l ���duQn� v"�`6�%� �bnim�(ant n�?e ��ti)9��9 mitt h-d4o�h�(E�!)�/o^hu�,�� �!�n hMic �`ty: $$x^m-p^my^m=(x-py)(x)K+p 2}y+)m+p y  ).$$�= _Fs 3%4 *�*e9}�)e�kw&5n �Aly&�e� id� EJ�u�*"�%�ɱ2  C3a�2��7e:par&ati�le�FTT'_&Za` uralD*ategy!���f?!| role�&*#*�2����F<la+gT �^C&x ". :Z2�se�cd �A.2 �+dea"`f �al5C AQ�4 "l)<trD%� <����])�d4n6� ";B� g*e�!��,ed!�of%�descri�m�pc �as  . Two po�d! cruc�&� e�iF&of:n m=(5V-�9 �&�/)� =�%��"Fr%.Phi_k��>�k}}*%$k^$rnonzero! bj,;�Q .�"Se�Y&Vh���.�B2�> & f*�f�c* &&�d0S. �%continuA�p%oofaX>�AV,:�!� a .� gt� AKb, $\gamma_k>0.+ g**Ejte,:�I-y8"�AF��5.�$A�h�:�mg�* Bwer bN=��-�f��:fJ��2�"�2���!`*� 6� 6 |66. A��G"�B�!�=�! y1�Kth�9 $�0steps: 1) Ge8st� Bil�yl�(�=per�%!:M $ ��J� 6�F)v<� .$$ ���4�/6�!*q�A��� $p_1I+��8� �T�Mj 09�!H$6�$ dire�[! 9>�� keep :!�B� m�ntact!nus^� p1� 1=�'._=R_ ��>�  2) C%�ze�R �/.�� tBr2"�F!94%X�!��:H.}m22�A� ���2�Fp.�Eby*� �ing�G=T)H1j�$�yn#65�$ servA925,. &�a�key��H 24,zZ��,a reus�!�jy2AyR*Z�N�f�N.)]^F 3) Re�hu� $ ��9�6�1�~]f�V:.��M�3�U1 easy�l*�%Y 6�M��+��%Q�]��.�2�E�Z�E��3AL3�"X�=c:3)=kOF�a�� t�� _2d �.�Cto�aI:�v�f�V�Z$M�F�Hb[ R�/uZ�����B,� is,^elow$ !�5���J�:�6��{^:U ^�pmp1p2�y��&�n���M�BTSubv_��pL �p22�p3x��BEq� ����Si�Z� elocc�Nm JpZ�2��:� IT%&(��)6� &� .r\" R6� -2 )rg�)~�La�"*�Bhys�% meaning�0>h�!�*����v%n �:q � l&� $b9� 6�6� $m$ EbJ m��stM%�r�2`fn�1n} HW'�u��R7e�(�. in eMW$6c'8uj;iE} \ s_m a6q=1,F� 0��^:�>���$, ��PMw��&$,% Hud -�polynom �F!�r�1$n�&��2!�� � heck��t=:d.�Rp6!�I�<$\2_{n-1+m}}�stinct�+ c*�9a�w(HM $O(JK\log Jimr;s�N]'M,2l%#��N� ��E noni�;a�$�:� By>�  erq>�=Qq>�9 ��� "�E�BAr0bO an�VisE��0A�!1EXlex���b�.f{ R{� os>�Ydsam�"!�m^E %�m)�(6�S����B, �� n�� roxiR %ץX��7{as&�by 1/I-mc� a �Na?sDw."�ver�to�m$ B� (1-��2�/��Bv he line�\it)gir)�b�bf�s,`by�G�[sU? ap1-�E$�>);"� l�ߥ0n�b�a�E 6�26� }��z(A��ע+3H�t�n�- �M)c!5��e, �;.+ Aby�,��H0(ln2��4!renaL��A0\sk�` "�!n�`g�st�GH�~�5%D2u! .Y�#"�n4)>��>g� 6�ARd�2ind ��9ex�K�a �Aase�bylR�$!�Bwv�J� :O'�$mJQ':�:W*� � .�c+b� ,N $pZ6N o:ZN.)�$f $p<{\rm �?� 6M?n}{�@{�,�\�**�N1�O_<O�I�E/�s-8 �]r�An��An$-.� 2,~�IBK : JHQ�4�4�R��FC .�/aI*7 n�/jD:�}��/�N�]::�2� ��:�!�/+u meant �@!NKp�I; y""�*^ m�re*n"nAM(:��>+*� .���5a�B�#s v�Gne��&s&6��"i�h^ �^ is m{I6�9mA�e< Appl%iD�T�/:�% *� N�=�:N.$�b�eq1�B�+�!!>p0 \ iff\ \ } vjz�r\}Z:&� � AUb��0��Yi. *m =&�l.r�.A x�1q�Be!4{(peQ�Rs�a�a:Z=J��%�����K6p > � �[-=�U-.$ML"Z$*�A���=P) Q��j^�eq5!zMf�3:zQ� ]�:�f-Bb` �Env��=Pfuln�edj+�@L$�T� b(5���$�t�Y� � �(�G$� j ,F  $$�f�Ip .јF? ��VIt� m`�  chd�ng; �Y.UO��??6r��, .@ N���!� %�p.nI1j��InAqclh�� a�p)l_Z��:.�:6 (Or�*Iu�:X/of >qB"j3�2) s )�L9N6�T!�Pb5Y c:� b�T� r~Z6�{&BX2]A� <.dA�(!M�v�5� would�X*Q^�� �S�ce�yM.�t t28�n �-�,!�JArnste=�$S. Popescu��B.�umach:Wt5�t 2046�62s�N �A. �N^8H43 G92G "99}G.crC1�6D`o:�,2�Duhrlich,!A. }�) A.2uThapliyrD*�u- 6�012307#u12��k} sDaftua�`d!Kl��h2�R4uu42314 uu6R�2Y. Fe�vA�Y�] �M.o�w,e�. T��fS eory {Sv51}*w90�52�ga}[ hR. DuaJg. [ev06231 ]42]gl!o EiseG�%Wilket�P}�85}, 43)g02QVC02}a�E8e<(J. I. Cirac2e.Q8!67903%6fi%�BvEwpU. �Ew�m�xfa}2`9�X. Li a.�9! M57!�!q06�5); RGu No. am(-ph/0312010.& ��� �A�9v�4041486��ZZ�H.���n�46� >V��d"�~~�%� %� -enh�jd+sur\0s: be&�Y�)�um�f % Vitto2g Giov4tti, Seth Lloy�` Lorenzo M6 ne.D�  :�tw�]{ c�~%.�epsfig,a�,cite�wo,We fem6�6=�~�}ent#1{}�~��l�� {#1}�" etlength{�,width}{18.2ceodd,!(margin}{-.9>"I�z#topABb�� }{23^.V~@!�<{.�uni � }{.2 SvsƤ{-1.5cm}�&ceJ%Xpicture}(40,.01){\thickS0s \put(0,0){\(1 40}}}q:�F{E"�as2Ga Q=;/s� �F�enw=U�s��gES� employU�U�FF as squeez�� .G!. mvQV� �f� a "�,tz �!I$cy!�pW2U � 5�Gs g�>51�)�#aw$ e!�In�cr&behavinA��mV�R-��WB\ \m�.�� D-�Ң���$Y�! B�Vtwo\�m�}�].Or,�robert؏�o�{a�trinsic2;[%S=� { of�41 �o���7ypO�EDm{ tum,m O@e�uJone�,angular5 a ro� ng oa�(Fig.~� {f:h�X�+"�&Qy2�app�u!gtself a5�I:aa �I9N[!��xwiteZKc"�dU spee�le���(ato"4Margolus-Levit)�,-� ��"]qhow�,u�'�-=n� �i �Yhe amou�efm3al@-oʅs, e.g. Z=gy,a#h�toq��_A�&̈́fig' [h!]�)v x� =.81\h \leavev�file{-� .epsFl� � \ca�{�z .��a� {In m˅� y��out�Bs $x_s $x_2$s/em etc.}A�!���=�ne/��f�)$x5P��t�+!n > varie6;���S�?�Brandoml�j��b�,w" �a G,�ACo&Tst�)m\I��?m����# ``�pness''4a(!���'�xsprea��$$\Delta x$9Af1L:qqa�[�ci%�in!�f� �(A)��w��E1� (tin�+ioLs)%%d9 E6" Gaussi�K5%a�!n3� devC� B�.� ~[I"�'�" G�t"R)p��inc�Sti�J; @�AE@nd�$p2w!�du���Y%��� B*�3ed:�\:-�p�\hbar/A�)u$$w#!�IP|k��anau��9u��TD � G.�(�tx$���es��5� �T�eQ� ��p$�o�a. [I� g���( �!�K"ae��0.�$A�& $Bů%N C �I�mex�p��B-��mMo@.mA�(um�odm ssoc"��.]�)�a8� (B)}�F=Ja9nC(de � i"� Wignerk [�):�Tܰ�%�)pjQY�T ���5�x=QW�BIi�� (C)}9e�D)�m bF�=2n�6�m�gd fluc'��on1�Ik%�b`[�, eP�� �C)} �aga^2 D)}]�!!�uofgrease�y>�/E�� .G� .; �6Zka\�$plots (2mp`f�FD�w  Gp$) musÄv:>surface�/r�nnm�/*BI>c�~2��nd%%a@r*C(,in-phas1�+out-of  �itu�o-�e�$magnetic f�j. �byA� `Ydr" es''B�p�pa�so �[5��.!�his�c��asonsE�Q-a.Fn�r��q�*��0�Wa|2M=!m& �postu�.� &� .ܚ �]-&�=5 Fo dynam��urb�"_)LMiny�����!NQ%�zxA�ri���<T"rwt/ �scullyw�er}1@��* �Ss#?Qѓ�c!.��Co uneglig���1 �*� qF�4tʧ valiYyeyE�e� c" Ec|��ar� ofF���&a ��  X� B �R��al�0.u�he so-I�&� back�on'� ����].��f�Ia -�0�) r!��! feedQ�K�V�� 7}3�Ef'3:�f�5R.! � . MV�eE �6��em� se�3e �von Neu�M%��~�)A�V�)���\����ai-;�l.��en� � =ive2y&9�%;-{!^be!q),� ear2A,neܐv� influ"Cr��s� ~on � 8�ar#�J1�¿U%�jf }.�Ai��sB3bq�al*" moni��4� u� a߶x^a: `les� more'�/rmp���.��M��X��demol..KH,gmX(ierqnd,wall(brajinskij}W��s 4pl7��s!Js:��%c�A3i '�wteKvon&{&�%��. 0�7"�6A�act%�dis���1fP���6q���a@OAecIB�%1 d��� 6�nEK�1i� get ]Jr$ *?in �!(2Zn&$qbe MF� very?f (a�( cosEL{��NYi婫y g�S�u�&o"�V�� spaw�� ~�˺ofa�h*1]t4cavesprd,yurke� b��bir�A� riga�slE�Qᝍ_hel�6m��M!"-� do#6�s�um��tle�, a�!�iD"�_��� w�-avoid�  !Q�s� B ���vA.3r��9vacuum6 (8��&-) �aPR�Q�!O�:R4 &\ ie�Z"# ly-2��J"e.p^ fkPmass >��1��M0sql�T�9Gz5�9 f�un5�}��{u�ty "��}t�origibm���T� mal e}�.��(. :Q%�-%ƅ���!7!s�& bench��s�� qualc a.�5��o4��'=<.�RQ ~ �"��2 defe�]m���)gigu��e <|K{rty yean��i��tU io<!�-:� %��K!�ye0ie�ra�:L 9�(av=��a testEm��RmeantimA�$adigm shif tu red:5*� ���<���qA�=A��"{��;now viewX` �z,��4ex�2� Hv mate�likv��!_)�Edi7And�c6f� ,/n&�  � av!�:[n�B� iJ�%�"�M6 �Mq�be}\�tq0cJ�%�mqeof �0Ue1 �"A��7 Y� ligh��I` heA�1 oder"$ �s�m_9A()�e"  � e>��� ae>��!� sibl��por��X(e�Se}[hbtvjmzintNc�(Mach-Zehnde�u=er%l%Y�er�!s&*�  inpu\?rts~A!y~B!B1�Yea=spl�_P,�i .Ko(� !s~7�~D L  @OM36)�E��_en��$es (photon� � H) YuWou"ca��� �c� $\varphi$3)E�Y!H� paths~A')'�F� �6%@- ���9s*:6l�$.�5d�s�1tB-"H ��!annihi�� *E$a$, $ �$c$� $d$/=*[AEsa0A, B, C �ad D:�>� � $c \�#4v (a' + i e^{i-B$} b') /\�u2�F $d4i 6>4.2�$�'jib2'��$ b$i &2$ �.'=%a2j!5�%� )� B':�c��f:e�: �$�*h�2��:�+:,#@�Es C�� focuA� �ssr�r�q��ultra-d r�piQ�:. �\L�$6�7 jR 2x �)s6acC A*zc��A��a�/ i�ln] emi-E�pa!mir��(�a {4�k1R$di�q,I� fK� nd a,8m��dA � � a���v!,travel along�tIDCA�rB�b�8�EsIH ��..((!P>qjo2f�52 e��}l�-p�.�̩}!As, -�l`�I -i�6�cy )xa 2j0Ho e�c� orks)HpU#m a*3 c��m�N$&���s͒se}m%e������U~A. If�9r�noB�9[,o<jw"�J�H#at�4 ~D. NNxe��� =\pi�m$dians, allMJcUCA&��h si�, a f7 =$\cos^2( p/2)"P F��)�~D�2Lsin:L 3�C�p�M�I ,]MpDcGstm � 4%A�1+ s!b�!O r�a\ $1�/NSA^(Lp�d�7�� ���/, Znq$APoisson!s� G�e^": % ��m� S�,�) V���v� U'amP�l-��fa~m �tyR�!M be e"y N�;��i�alAV $\,�j,�Nx_j/N&�Fx_jl�k�9)�$0$`S�ing onioJ�$j�se��]i���ete�]� or~Ds  � . B*� �3i*��stocha!�& $ � �z5� ���unc�~Hd),&L$� ��G$1r10AW��WMU=s (#raA�*�?)� eM�Ja�Q�aA�N�"�#by c#(B�)�< .�(^2 x_j}/Nm xy:A�� ^)�"�� � )�� ��B#.A)���e��  x$%� f��'j��U�).�`��!}samE�s�N}\Ipe��c� beY�ifa�"ău`.e I�s$N$5�I�Q�lN�ap��y�- $AAl� �Z��.l&I= I�Y�Cy��$J��h��%iu��6MC�he .+�#^�"a(���T5� ^s�edDr!���B>� � Yfu&�ϡci��{�)���O2�"J�@���yQ�ne�!���k%�.no�ad�,s&��ߥdum[�  @C"�DOe&mTdug���a6f�.�rgA��!�"�#�EJe�p) y un�:~B1 &�a�gT+��"�iv�4of�#N^{3/4}$l��(barnett}. O��-X0�do ,A���� ng�$1/e�� keL��u�*� "D9�n"�l�_3�s�ample Is7!�� A{ &� �Rh.�h�/�-@dowlingatomgyro,y��fPs$s?l 1��,2}}\Big(|N_+2g _{\m�1A}}|N_-:B}}+ J .>DB _)\;,$$ w�� $N_\pm��$(N\pm 1)/2�"%ym�5 z B �! )*AHs![��highly::Z�|=�0i��.'V"�&�`���a�A m2odel. A��g�!�� & A���b�.A� 2*�"� c` W�%0:8� s/% X eY��c� o&�(� � or $M)� d^i� d-r� c=(a a-b  b)� � +b+  a)�� ��.�eR -�Z��\"!i!�3>E�XD�/"� >� .00"�� �؍�� ��r���/�*@M a.-�&^-� Q\simeq MnI�� N��-�ͼ ��`��*�la�� Mm�=-a�si5��� �� @� ^2M=!�(2-�$) + N_+^2 C^- < 2"�+ d-i&�� Ba(#3� � O� M/\�:|L*,a�5>�}{ D|Q|nd%�6� 0 �ZYasy���� it4��.Vx }. E�.����]��^4o�reJ8c#AOE;CEK�$,� I�s sa�4�r � .4W� �v U �arameter �sa8smilbur��MJ�F �X!�E�� JAp2!�)9%J� #� K�g|-ab�ۭ�B& "n�$AAiv icd��:�ͱ� "����@n�e"��Ca�i1��  t~C and~D-' jeffbondu}H,kimble& #}R � Fockpt~AFB��t|�� }� -�$��._ � ���!� ett}I5, f��a0 de Broglie w��?x Ha� Pch��deb 2�%�(may woA i��is)� &d !�b��rt �]b���inp[N ��l-�/gy.�& �mA�lstammh#;M:5��N5щpp�EsE�%t�0Q�� !�_"J�6i��R9 �boli er,ou�* customan+6H \*�! u�[Ap� r�>+�?"�Bu��U�� Somem � ic2�r-Nem)�^w�R�jr&� 2��,_ (I#$am� .6 � �����+�l��.�er&7 �%�V*P �e*�fR!��.)R), ���6h�(m�$�"-���ists.�W!��"M�!�/%�)�.XX6�$, g�!>&�&� >e�4A�bq�s,�ph2�Z�\�_brace{��� }_{N��4�}}+2;� ;V;)$$ NoR'tenso�m<str�9�4�um "|*��, $.K$�%��:A�El!O *N�vk .�.�"Ι2[is9X�[�O)Y B��-+ �Nm7} 5+ (1:%$� 6�$q( =�AH!��$A� )��$ �Fљ�/2)UA`%cbx>�L+h����^2Z -q�O��uae"pb�gD N �"\ ���^R�E�$}^�=s.�[ort�� ! O "�&�j]N$&� umD�d m�� 4�(��&�>�����{�H.� �l|�m&:� �:I�� ##2$s2X ]$�_)6j_)u*an_)C�@ris*�&�R���;,I8:=ja3+=�4(upper panel),�%*�(h�t� ���l;0 ! d ed. ��%a��#r�C�� "�C">-��# !�1. � �&�R�lo�� ��'A�R�&�$0 E]"^ ��"`co.�9�$2�M�&�Ō)�!��q ���l.&� �K.� V�� at e�BsFH�#-����{f*�62;A�Aiz�-l"�� �&���� he ~ ! =2 >q*G~��--�s ce�UsU~Q��4^a 3;a� /1"``9'lete''���(�]�)x� d1qL@I�)i�s. ��*Wp,"�d:o"�8l�% ��%�!$fEA� a �$ *����r&�Luhj<  N's6� faith,dem��&� Sa^a�bov <-� b�!f�(-�B�r�0�*Q�he;3B!%* M���/�O|�itJwX-m&to" ���^� .�oNJY�/ nnv!us,a�N �O stab �.s�ntg}:T 2�R�*�'f2p �! � ropr[D� I)68f!;8�5����p�H��"��<ilm�6C&Ff<4Pauli �UcL"��7s!Xl� v6V^+����) �!wq��6�0i�W!�A$.^�[�2}wfM��!�h����e q�!�x���da��� �Ʌ>0�r �2�:&m�wav�xaHa. � .�R�A��>&w� Fa��Fi"27R�r�,�u 7d�yc4�=��4�4 of this revie�w. {\bf Quantum frequency standards}~\cite{bollinger,f�F}. A typical issue in metrology and spectroscopy is to measure time or r| with very high accuracy. This �ires a %�Cprecise clock, i.e. an oscillator. Atomic transitions are so useful�t]0aim that the �defini4T of second is based on* m. TB� � �,tely, we can!Wrt �$$N$ cold i�iR` ground state $|0\rangle$%O appl!Y ele!X4magnetic pulse �Pcreates independently^ eachkl an equally weighted superpo)% $(y+|1 �()/\sqrt{2}$!th��ofXxA+d� te $<$!� subsE_tAhe evolu1bP% for a E,$t$ introduc%�Hphase factor betwee)7two us-an be Mmd )� end�l$nterval by)Xing a-�, i!9A�, VmA� _9R(probability �final-�is2�(Ramse!�terferoa<y).I�proceda*4is just a phys�( implementa.? qubit exah described above, but here �2Ja�im3M2�isI(a%P$\varphi=\omega t$, wM $ $/YY�ofy} Y�\leftrA}arrow2) HencA�8e same analysis%�ies: froa�eeB]�I@mirecover�pursued� �(M2�$)i�a4,rror $\Delta11mN}$�� "%)=1/(\e74N}t)$. InsteaE�actA<�ly�Zq� , on.6� !��mi, $|\phi_{in}m�$ u8M. Ia+is case,EӁ!�determin2S9�is�� N t)�tE!�n enhancE�M squ�zroo number%�of ԅ9�8revious strateg�:�$lithograph�d� 0-photon mić}��scully5,saleh"$,dowl,shihLganna}. When we tryaPresolve objects smallEea!],e wavelength�!W$employed lA�,& nata�of radi)vbecomesa�ortant:0;H tends to scatter a�," �, limiEU{$achievable ��l�_ �ߥ.e Rayl�  diffrA� on b��, which?tri�many op�8 techniques: it!�,not always pJca�@re����)#. w effe^�� help��de��sa"�7!3%( while keepf*9a field con�t. Howu ,�bare�1paradox�, � !��Mut? The ic�*a�to )� �� devi��ZA�sen�cveAM�(de Broglie �:a�q� mechanics3ev )��associ�pBX $\lambda=2\pi\hbar/p$ ��p$�hQ�'s mo�N um (�90,Denergy $E$ divided!�Fspe f-�$c$). Obe�l� >a !�le i�J� c/E� c/�p��of its�%�P. But what happens if!.!�etom� a ``bi � '' (F �entity E/itu) by�_ �s)?2Vefi��K �� ��5� c/(2E)=-�/2$: hal�25�� � , or� ivalI�Z89�-,Of course, u!� ``tr-(s'', ``quad2\{\em etc.} would resultA�fur��q�es�� s. ExperiA^alist� !���A �y .A of 1�s��monken�� chuangdebiJ}, soet��or" ians havea�coc!�u ��Y them�vmost im���lic�� �q��2� ��b�X}, �/=!��tch!� g�� d circuit� !Es!aA���T` �%,� tw$ ��o� �g���e)yq ��$less damag�� spec%�s. Also!��2!Mtext,a*���]a1^�2urce as �#instru)alI��ճ� d 5��iTing!� ��s-sec" � absorp ���}>�� �;� L0 synchroniz%�:�D,conveyorbelt,jozs+Toi�ouF\aan��&� .�} it takes some2 signal��tr_ at UA?1P known reference poin!�ɮ est class�� I*gB�h�g�e��-��s!� beam%9 to calcul�0their averagepallow�h i� �l6j A�a{ionC $K } �  \X � ��. �1)A$ bandwidth�inA�(s a minimum� -dur%�!�$1/2R �� ���0! �!- arr��?* 1s will ��a spr >f!2e<cyA=) Y<us ���a�tral di� b� E�ed )[ ader�U�; a��U*=� o be� w�x� q�sn �,�2� af�1 in&,"!�e�s���'' whosu 1�is st!O:��� { K��� a �M05, ?)@ �me� � � "% ��N$M �er, b1�#cau�-!911toťir!Q[Aisz��."1�uaf � e^I�lTAX }6�y.�buir%�n� a�om. Xperform� [E2�M&��f a.���4=2� all gaiU��{U�] �$������� �lemklocal��:intim���ne �e9 �A�aaan�Tock:�i�&!w!� it ��!}��!Iq�o�����s,A�is possi� to ��s I se9M- immeZe� ellsE �E�5J protocol � gA֙improvI�� }(of: >=. Moreova 1�i<s m be aT� in avoid1<det? 7 disper�-�franson�!�6� V2ve % has ayb�I�9U� na��s (I *  byq� ies)�!߭�duQir-�)� ) ruie�e sharpA9!i&s3(nsmitted. U�E_ non-A5l correlI>!��y)Eose�!vengineer�y-- O�g��f�� y5KoM�a�lLa ]��-�.7 a�6zimagingk 8kolobov,lugiatom larg"7of "� .�AL�:oAspati�$ multimode�%b�ped un�a)(common labe�� V �. �a/  famous# # e" a�U� � e�sG !�``ghostB es''-Ds"� Z��] *) e� u�to �~��%F"� �E�,irectly lookA�at itA��9s2 illuW� �7� twin͉s�ch-)� ���ucket''�e (ita� no��o��"C�F �4 ���W eA�e �or)it was` �it�e oKuC Qsh�nto!J!V%2rra�h�d&�rep�d�T �<s. Cq�ng�Ie @aN%Ucoinc�ces� "'*� � ��A )Y9W N�Bw�r� shapE)-qM"� dAis!eq��4fo�<V scenario:A� aA� shootsA� pebbl'n random%�exaE�op{ e I�O��IrD�� [U��yhAa bel��1� |� ead &sofAllSit rema��gl|toe#By ��L�!nmareO^ w�!! t' � A we hea�� �d��l ���Houtlin>� n n!�� c0at such!intui� V^ ex�sh make ��eas�� real�� -� ��EQe�! ann> mtsh���n�its�So ly �c*� rl�� ssen� &� "v�pboy�R���1e��� $ ��,l!s� ap_ tus, bothnear-�A �fpla bem �a�a[ C�. do�a_�,)>though�� rmal)%e�approxi  it-�2�riZui�i1�e��!tnoiseP�, I� � �if��6l,  }, i�!Dk a�d� Js� Q(tude fluctu.s� �da+o!k ot-�!z�be,-pr�Hpl upprA4d � leV . M2��l & � :ȕ�A2Z foc�[T!]shi�:�v!�� mple�$atom-force*���!5 defl&/a-�fr edZa!til�dE� fee~ �Q! iH hnan�ic�|. A`la{ k is, x %,\ pos>Ɏs�U �way�8M B s94!eHe�h����on an in�! �lv�y��ctor,7^CF���insid��e \��to�q�!��ŀ�xT��"���esp2,<���anM1cA/at scal� sd d. �  d" R� and im��� eL e��nalogou�a��u-!�isr deriv���. ized�0I�'statisNV tr:�M>�AY i!�.;!,I��um"3A�boR !���up!� $1/N9fabre!68,barnett,treps}*�� i! *��!q��Di�uRe�!�lo� $z$ � !!�m�an�#.x~~ ion� "ɒ?� bp�9��# ! 7#��O adjacen!�Aor}i!a8�)�Q;2emT A . Isexpe,�gz s �I%i" suman ``eve�4-J�ymm\�l2%F$an ``odd''.>L��� $x=0$ (5�wo�!s),�sea�' eam�58 !4 ereda�d oh�$en |is pop���odd�vacuu!=Bow!se* sub-ay ɦi:�we��"��aE�^{3/4}$ ]�A �g���~squeea� �a�tead. &�:lD$Heisenberg�of�$6p �!� th a Fock�e $|N/2\�&m�8A� t �A� (e.g.�'co� r a� e)!� necessari�7!�"! , du �G�verse d��!�BW `��z�'' &5!�� ��&��toa@ Z�!��� ese ��W  �!�� 2 r"%$ �siA�.QlC*�ed)g.� "��-�ECb�% &iUTi��by�la�j pa )v"�-w9lAR\! cuS)sb I�,Q�inA&$)�" 6�� Mx� },�,lea�)E%> weak��tbaJ)s (opaquc!s : d�J�-�Aam).!Coord�%M} fer} �(popescu,perA�ord��hcellona,giulio}. A peculiar�2 of5��%L&r�+ri��o� un� -)ٸin{c16 �}>a` �$ fram$n� (f  r!hree or�%ys).�j}  no� or�A�" � � s.sor�&� lleli�t�H s ex�1�gyBes in5D�# al jargona��spi�e- .� �$ o%��,�E�yaxiea � �6�ed"p��$ponen= b" angular"�#�in!tatkobs+g : un� >���  ro� ��{a)yi}!j� :!"��A��th" >�. Gis nd PI� f�&4 baffI�" ��sen0wo=� �!�M�|U;��|ici�:/!�� NF )is&� )�R�!~��<�"q7. rreaso���eef �� M!�2���*an un!�n�Ja cou3�A�� n�!d1�S�*a. �has operg/sE�*�*eigenva _�&d�%STc A@ canjb�a��k�f�@tge&� ia�tr "#E�� e!i befo�"2��m�-e�in ��� } e&�c��!�An�se6j%li�*��i�& w�#*� flip`Y!�q�0!�%t�!�E�'.���(!$}�.�+$anti-unita�*@&ZMas ��%rably <). Elabo9!ng)Tis),�F�lc��6�%ieur"h�%b0�. \$*{\sf ReH�.�s:` �%[�2�� E }e��inu�me�2�I[�free mas%sa� adigmatic���zh):�#i�r�miI�&e��/&h�of gravi�� al-w!��[|&�5 �t$�m_0�s3-monitor^The�0n41 )��sql,edelsteinjpe,rmp,brajinskij} Q ���.R�ک�A �21�*F f�&owo�)ecu�-����>�5�,q3�ipaccoun��%�siF�1rst.j�p tun��"�k ropr�+�35nconfig*X$�!y.9origi�$arg'f$"Y:�!+�we~or1 f�o=� %$t�N�$certainty 0 x(0){$%�4rresponds (via�=�u@1� ---(0Fig.~\ref{f:h})!�:xE Hi�"� r,atm �4= � p(0)=�,[2�% �]�$e dynamics� qpertur�%Qu�$m g�0!�f \e Hamiltonian $H=p^2/2m$H��4�� 03$t$W5{ as $x(t)=�+�t/m�4T!W�Na���.H6 m�- $F$� fer,JJ=��$I_net2ect�ear $a��at* �6al.VX%^2%c$Kd�5big� 611�^2 !\simeq)�^2% �4\;t^2/m^2\geq .�\�' %/m!%� )NI" i�&k'����%g$cit assump !�hef� �$a�� �0&G.[�:�n� 1�� build up*�!�:ER af�1 �rs2� ��Lis unwarranted: Yuen[���� xo�m���Uy�L ,>n.4,a|A���� in y���1ve� te"� yuen� ��U�]�5SOa ����io5aW. [p ebu)�� as�H�s�� "N)H �8Y�-�be�a �l $2\d�5^2E]/m$ s�fa�$t\leq 4#$]� B*�!�b�n5 ��e<t)LeE�,� !^� 2� �%M'�oo�, ough ~deb� ��Emn to as-K��wea� uc�!��3&ii4$0Z:j9I�of-}� �>, % cA;prl.-�&���>o"� �V �J&&��9�%ƅ frac 12F8|\l�. [3,a�\�] R |�F t�� IeitNm�V a_%2G� a �%$%��,1� 2m}$e4L,Q��A vari9)��I�.�':.�њdoe� 2�"��\l!�E"= I.�*�9� -�ozawa}�-V&�.*P ��+�^(�]� on6[ >ѕ�mV%A\ggFm&�'a>�� ���A�`$lso�a�dl� N�E��5back-7"3d�k!E�ɇ ^xT�_oi ��#*+��B .1%. Z!�i��,�/��6v6��er��K,Lt)=�X"�� &*> g5��ze��5��hei<M � !demol�.�che"�! g�ierqnd*- ,wallqnd�O�%%removes ofeed-!�9���VbyA��3.*�i�0!� "�6> !��02+ er�s. � Zb� �%A�ex!b�>&�=ic1W� 5~me2[ �`1=4"(A��"�R�?bc"��armb2� er (>" mzint}D'o"�h�A�P�&,E is h�+ temp+toE}6���;52.A�a� a:{ well:i  >.  :��% ��!j�9M/>(@�#�nr��6� �ar(N}o � � %ly��=��t � . At���h�*e��� out��CE@aN-��!�"rc. @eF� iѧl�!*�i�r�%2ss/ra�.io�ssure. �?,,2��5\?,/� !�-d�C� ��3��#ng(�" � �`**0 spoiE.{�r]� setupz- su�`C!!�� nt-���$mi20A&UEe ��o�"�F:ǵat��* is a1WV�rB�& entl�)6S -VY}.%!�";BK ��J0�+�� starq" &� "G*. �!ONaF�u& *� v wt�&a^�5n}�.n �8���itis+� .b �4droppAb9premiPA�B d\5-|��F(�5a "� inpue�(DB &B��Hi�& quad�r �"k2�t�@)8p��' u��e�  M�exT=�Ta%Zd�<-�&! 5,e?-6a�eGGl� mto �y-V�m������xJ�%yb�'ach�!S mhlowerm���. R�@A%ͪP�@ �;�( �Z ; ailo##�05� t"�8unruh,jeffbondu�,reynaud�s93.�Cby[@!WE�um�/*j ��@rmp0!MZ���: unda!a2,YIN 0threshold. Ho� A )��tconBtK� F-pe,&�= chcn:ynA��+��t�4th�=a�+pos��Pquite �4� calEe�,b��#a�Boof!� "�)/Lc�. h ����eE�so�< )ofT �?��h�+2�? � " "��:$ �!�L"!�geAFX dissi�veac�$/�ponse%f��big�� ]Z ,onofrio,�-S rs,sIc �V�/ us tq^] mSavQcM�aB�5Jm('o!s (by n�#it�"! liI�� lete)"�!�J�:�e:�dM 6�en;at ve &��`wiseman,stefano,cohadon,d�o� 5}�A!�hu.�4:szZ� V�,imoto2N harochenat �o �� e<v�St �-o�s�C-�� �!�AV��stage� A�!�mi� } ��$M #,%d Nis��iny. a�&�MsE�� to  .�&t  E �j�5�new g ��} t ki�of�pt��%E�� 6�*�-�h"�Fla !A0? Ats ��"@:�$j2�% ����9dati_��h%to WigneH w ,witte�9A E�ces!discus��s 02,i�  c�6�takB2n��S42.bo"s e gVA . Fortun5e M$$lus-Leviti�+m }!ore8A�" )|E���u�{M� sethI�, j�U8)�^�w �J syst(� bH�p=�1��/ ��.���=RA#=c�q� . O�2 2��3F�E:s�IA2Rbm r i Dir�?y:!Y >~%nimp6} � `tick �J'�>�*%*�&g�Hd>� t = \pi �0/2E$. SimilarJ �5> L7ic�/q�map�5)a!~ b�v��-$m=�E  �H&�no .�IHali�aQ6O�u =v2�G��a�J�e�M%, u92�  r� i= Plan�+�0, $t_P!@**@G/ c^5} = 5.391 \v,s 10^{-44}$ *sCell@ct_P$# is ^� Comp�M !)� $"{I/mc"�R ���is� H1& or�/�_agnx �0ir Schwarzsch�9 ,us $2mG/c^2$� "� 6b��om]o�5�Gq ,y�o~!~TNj��ntom�W a�Qb{>=-%&s%5r�I!qm�M+6�u����a��Fll i2a `swarmeL)a,*I){D6&�� *%�ITM���'�@� �:e0a�3icMO��Jc�8�"s �!�GPS s��li�as�)�C�U. Le$M�<���#)s*#�A% �2}a volum�9=�^Q2R$�:� $TA�E26��aY or cl��� or!�����@��a�� g(�j a��''o *Y+sQaUccv,g��t�)&14��d �a�a��_A�cI� )�e�ar��3: ��A�^�dP��n $2ET/�N���Ni"Z�!z � ��S�2 pack�%m�o dens�W they�5� <l/hol��b�:�8!/M�� !�9�out?4%ir horiz�3To �R]^p� I�͓�) �acelik�~g�M]c 5A $Rc^4/2GAq�7h >�>_!c-��a�e1�of �i g�e!!�$N \e >�KL^{-1}(T/t_P)(R/l_P).no[1]$$ A#��icI;en�e%-u�J���o>�Ashi!gmax�I :���M�" �|B��r��J!�egI�Vg �fA�)�-� 4orm��"our r;� $2TR�"���? tifi�2 area��a�xtr>,l world shee�-n: 3-�gJ٤� ic4$of Eq.~[1]�&Z dEq}*.t,�� 5��(� .��=9�67y�� comb�6M�a�2OA�%�/� �'YrI��itself!>a}R. (I / ,!�t{its cri�8e�en5� hold_R�ÍumrI m� pa�I})�erAI� er.)c1>��'nsist�/%�3 �to�Beken�)� ���PicBAXy6e�[py  � bO,,thooft,suss�,bousso13l-Eɀ%�Y}pbAY!�b<:�:2��. [IbFs* firms Ng'�edi�* �ng}�k ��.}$foam.] For�) "z)�lea}o5�\.A �?�%�ao.v \l�U " 2R/(�3be �o���ɌAMAAS!�ajtur�#� *�* �)X�IU $R^2� l_P^2I7 yurtAF����a*Ph%5>*Eh�`Y. Bec�L"m�.�F',or `ops,' ra���+�~Af%Ium>���1�a�X deofa�"�D � c�t�O" � � � �J2"�2��^1�sCal�/gFA��;be ob�u�6lax� ?o�&8)aav#3 | ` Po@���  � ~�ee�T6�isrracter_=)�%Zke�r?�9t�! 5�m_s"~� B0M tras+2�Py �%A�uni�l�!=*i�Y �6 �{.-lM�� ?&�:2}$--*���É�--%kn!gT ={�!nTn $�^{1n�7;#E�YF&� �7rL �( a.�X�j��"l "� Et�6q�ŧcl�"TFs F�Hown!xv�xps%�!R�J:���*r@DG<�>�8lut= �by>fe(�v"en�7m{3an 5H2 \bx �123}$ �.� ' siA�!�� bang]�pg( 6�ConcluN} d� cs�-sA�!0Sae"3D ,�lu]�!}:s�/uU:o i�oBQ Ku,at O."8��:F���fvia��*/*V+x7 ncip� �^B ; �!i�KS0�r�5�*t+ surp�2 ng semi-c�2v sE�a�sV E� hot  �. S2 {w@` :e~ i�A!�-cer�po'-� s, �^BIS�NZdevelope&����!�i"�%�/?!�Be;7� o��.Q��_�wDDvarie5$a9s. S ���=5��i�� w futu��:�K�,~ghod�G��jni�@��d!�t�$r�(��ti�%fan}gAE� saw,�1usGf �4":-��&�1E qvb��#ar0; M�/ r� P, -o��!few!�$NS$�$6$�h;Ž�&3'� � � Q mill�#!��A���Hq$Q�3pl�T%Fing`&$P%�Qw��ehpVus=1�%V!�Y��ucA ci��2�;ly,���E��,. MeanwSa,!@}&�) �)��� AUղ� y�w�al�HbD �F �[�*a&� �woM!{� un��|P�` st f*� �l�8\begin{thebibli� Ty}{99} \bibitem{robertATH. P. R, Phys3"v. ,kD34}, 163 (1929).G&�N.��%�L. B. , {Vica D}V 120W88U98.Us�d�d_Jacob��G. Bj\"E�I Vh�d �Y!� Yama$^z��483 z2�m!�lstamm}a��I.} Tamm��i� USSR�:%,49 (1942Vb+r � !�lA��"Wayne!DItano �D!� Wine!U, � nzT7 {�NQ��R4649a�92�ou} Z.a�Ou2<� 259%�92�j-wy-T}J.>�%�Y��1w Appl� �B)6A�187�2m�"�*}a�Kok�` Brau�)J�x y�e�(z!0ant-ph/040208�-2faith}!�M. D'Aj6�XdrLo�*ti2#e  �9A�047902J�ema}F. Dv! tini��zzei,rRicci �G[�:&-�6��062307Fnntg�MauroH:�a�ME� A. P�3:j�( 87, 270404h2�i��C A. NielseI.�Oq~i�q �#�  IE(�v� ��2002 f\}S.7Huelga�OMacchih"�p}i�nge!�M.�ChekhovailY. Shi2�6�8ei136m�2jJ.�  G(jwa� C���he92d, Op'M� Elk5�{\bf 1�435 1978.( �k}!�J%NFw,cI�H3bn�k%9!�\'adua-� F82�86��9.�.'� Giovan��i,W Lloy1Knda�aPo� *2 m 41^41��2-2�`V.^b�[c ^nF!^I( Won6� I)@%�11��2}j{j R. J �4S.U�� . x C. PxY�n�010� 6�rhc` -�)���4A� 3126�2.��YM��Kol�a >>.8 53i�2�lb!` ņGat!�Ez mbilla�E�B: &�S4 �. E�] S176%2��\s}T� Pitt.asHqvDe� StrekalovE� ergienk�O&X-2 R342 �25�\e}.nin0J tleyi"W��A�bN.� 1�1F�-U2}!SRG M. Bi3 qL�|�`1~B�307 >� \QOU� �. Fouet%�Ma' %�i%�25ś-�2��W��T�W, U. A� I � uchl� ��. Lamjx"� H.-A �o�inda: �%UI��88� 2036NU�6�q�vW � 3789%�2�& K}A��r�� F!d6f��׉\679 �2\baHR��Bagan� Baig��z 2465P82�oB  ZC 38�82��1���c7 G2e7%�G. Unruh�[:��;c�*�6 .�+%���h, eds�F Meystr� "�!h um,2�$83) p. 647* �7n Ti ekel�R8!o�2L13} 3a�1992��s93�F cee� J. Collet$�R�� 4a�317�6��5�F�lc�� R. O6I3>�6�#72�� �rs�G. Knoqia'� . ClB� 2�29��2Z"�6A�D�� Haye6 BuA Cama?Q�� K. Ca��-b,a�q@�{30n7;2Y6e�M� 6.��a�245e�6�K6@ancWSiAw �$P. Tombes2��&�8{ 6NP�6wFA�6!gHeidma�!xM. Pina� � NK�31!196>7>�Mh�^Se Nuovo \[ to B)t11%ti�f*q7��IH� Ha_e2��I�-�32��22�6�G7� Nogu(#A. Rau�Dnbeutm�Osnagh�Brune� J��Raimo�:!OS��7.� 40!�2N� g��7�2�>dJ.-� Po�p6h396}, 53r2w�7V� BF�.&�)EIh)FM1�025�6�87!< Buon�U�Y.�6��6!�04200�2063 6�egn� ŦBt2� 2�r52�I6 S�Wi� in {\it G�*�!:�)I)duk(U)!�Curp�S.;)�%)���8�23"� 2�"o2� �en�N. Hugg�4��,�bI#Meets% Philos����P�3S�3:�#�&ry~-orc!in�E)s�" �.�6�>&�*�&�(2�Ma23} 287�196��*� 't Ho�*��B�n� Highlight OAF*}-$,� Subnucl�kse�,� 3�d(72 (World �i�-c, Eri�륜Zic�Ri E[f 4hep-th/0003004*[�+E�S�+�4*�I3Aa637�2� �+R���+Z�b00082p 2_�+Y;NR�86,9l1)��er�Bm�%zLibid.} 88, 139902(E)� 2k�*U rts�!���}� 1302A� \endB* �r{\�Isf{ActY ledg $s:}}} VG as ��ncial 9ji^by ECs"Ms�C6�[("�(} \title{M;,��#��3�1a�]ow2h+!Ma�::�/(} \author{S""�d ffil�{LK[oire d'*C�/ &%�TQUIC, {C.P.} 165/59, "$ \'{e} LibGg�uxell�v9D�"oa&$lt, B-1050� '( Belgium} .�&:�H�Wseq� �ry,��er� of B�&,ol, Tyndall �@ Avenue, ' BS8 1TL�K.>yew� -Packardua@(Stoke Giffo� Q1a�6QZ T \�>{\today$3$ab�(ct} W�0�5�.�8Un�w��A�1 �(�1U+iM Mwan�)?%,(>SAg9MT (m8i�* des �,ow#Terg�2aU��v%G*E3�6 �<,Ӄ..). We aG�(�&an�H l�arbitr,gsh���,, 6�2 �g.�. �i=6t 2p�'�-iK .�*TI�&q`t9 +[s �?@T15"ailB1 �'ulemI&�;&xTbe"K0�W� mth"s�6�9��s�(su5 �!�b�! ��2J��:K�l �!�*�*|<��AM5 �z� a�.6�ReznikM\AR} ad{:���M��Crobz��%<g whe�.{����S�*N Q� �� -%."A�x +�=}ye�q a��3��| N!��+B2V!�ind���\V  q!�t�is !��V�W G1"�Zl�l*�gg5��, sq#62nexo radiYFR$, e��7w��G��L8�d�q �SA��n �d"c�}8!�f�{�N ��o|We!p un8�4)�us de"d!{6��C t*Xc�ImPdZK m�Qh,$E= M c^2$. 2lM|�=�4bi8c Ce~'ImtlA]:�,�N s�s�fIIE>a�hai�o car.pAi�$odel. One1m�3xnQL;e�a�toE�n in�Qc�L 3%��_:!-�d} I4�<SW ��;n�J1_!�AM!�\A�F@(,5$$t_{ext}$)%�!Ine��B�� � [u�C [in[�.� w�� 2$-*2. �guishC�o�d>�i&t $T$!� ��3@� � . Noe�ag� `!�l�B9w2 z7B�9 in5�/� vari) s. We!iA�iE� �boe�;qE���� B,AMP,AR} g�}XD%:�Fs V;%�Ym��A�mI!p0 �7hip2����hz� M�^� E(tFP� � ]H8� rich0aKYvǚly 'x\c�UA�rUmQE�s[ ��C{edR:o\>g���H�1�:#�(:�Q� 2�� �,la�.l:E :] v@� )�U.c2 �n9� or�r. TA� ��T1}D|mariz�sA�Er��i�b0%�:ll� a� ]ab^ \ . CH 1�!ktl!� s�&I inU�},%� 2Y�/MP}e�A 7ba�)!Jsa�a;e�wi�lso���comaW���T5. �d��a�^ttlX noth�]:}�Uof�@�%Z ush[m�ya�C�G^ �G�`r� {Cst�s օZ���u�!U��~�@��}\labelA�tabF }{c|,} \hline & O5wh��eF & TB��e��&j�&� inN u8 \\ &� !Om1!� &*-& (I�Y�)&1�.?X(�l&X )&2(��in�`ed & &9gN<%�)'-+1&��2 � & $T/6?� \\G22<~&q�I "E  $H32H�� &�?-4^-7w&2/5&.Q��.\6^-V\72/J�!G rG8^GVv�m  \cap�9{Su�7I �MVJ>  �m$qA�� � ��M�:J$T$ 2N"� aZ�����������}5� le} �Rt�n �<� �ӡ�!�!�Uc=?o"���+2!�Bx ů�*a  e .���:�� �&1C�alyzeR� e:intrigu���B" �a"�Bb�6��� dɩ� .� 2� nomS"e�ey �r�� 2��U 5��E2E6�vE�EENA,  Jo�6� #�>j ndu�Fse�rE]IV}"uKA9��AHA�s>�$KT15Ag$��L�vlej a ?� I5 !�I�%��'}mrB�un��&~R} isA�rɒ�u�� M� ~}� .c�{'\ad) "dD# �>*x:��1�Y?B���A�us&-<�"R� B� BW%֡)n'i� ��szea������9TsiI $.} AB\�XEtB/%��<��s� isn'%|I��b�/a., . Ig*�� ���'�wo ��Trea���sy�j� x� y so� ��ev.U�#<*aa-uT|ag��� ��2�r aW� "��"es �')� .%96-�T*$*�]�� �!w�]�)d-shif,_ctor:�suo }= \�e chan��d"*�� �E���!XA�ƅ�%.��� �!� *�Us�+�$ �� m&Q  ma%�<  a=j trivZwaym�w�anK�5��.K�s!�a |zal U;-�v5b��s2_! & valo a4)�c ���� �i0 � 66�$ap}RA. �W stop1�* �SJg. O� ��a~5���� y$��"e %�of ɥ��^7c��._i�1i*)j����  ba�s�5�^a;!�)?�b>&s�I.na�h��vXX&4�s!vE�2� ��{In>� I}AQ&� "+^]�]P�g>x&. Fur���.���P���"�2]meg��g�gL�Y-� �Ni�i�A�!h"AnB?�(q�!�,�:��M�A in�mE_@ playA ՝n%�r�ein:Pt�W=�s�.wef us�lo�I�~at �rZ�ĸe��[Ta[bB"A�.� �"ndQeA�xU��s� !'i�8�, al� ��"�i�!Sn%�b"�d�$�Sn�ine�5��Q. FՊ�-�!�i�"2�+�[{( �of2 )�IIP.�) �zi�k�6Z�^�Pa�e��A"d"z'M+!0tf(�Wt R})����.�4$H_c + H_{box}"n� H_c= -i \� $al_x = p_x�+>D�-t� �($[x,A]=i�# $tE 2� Ures"d:k�X:��` Z i&�W$x$z�~,���&(be easily gAub*E*� �"in�pe�rnPAIn addB�0:�1��&}�='q�,�jug�'"�,$p*eaU�3�d.I�bFim!�$� 1E.6J� s�]c$$x_i\leq xdx_f�u� $xi WA��is�.o��5Fb �'��2�is>� (w)��/=�Af�.�M8>�z"be zero))�a�<3� � _f:� ��*:�V])!Y�%i#�� von-Neu�@�[}zo�vN,�-} �dz m\fo/T te{R~/ŷ �a]SA �t � x xe� s2C!�g(t) A A�~%�)Ee��q�, i���sZl�a�w.ou��s�g�t! ɸ!�L*lay9!�� �In�a�� �\tqAg(x��F*inq $A= 6�. S�a$:�� y")b� ��):^#L��] z$ڟs��Zv\to (h�cc�$ ) /2$.}: �!0�u } H :� +A� ft( >�{1}{2} F �.p+ �`\O�) q \ .Y"H�,O}����U��\�/�.neM�A�(aF �7 }F���0�$!6in�_se rapidEk Nto $g$�$ I�D ���3�@y�VA�tT �{��5�to"� tto r�As6 ��,H fig. 1. ? E� &b _ d�i$x$}'���d $L=�Z - �N&(=�c2��n��I��B��gyJR|\Psi \�C le = E_0   \ , QPsi�Y�a�box!�N���J�X|u_{E }2�v .J�u�>��B�)yA��N�� ,ES �� $q��AY!v�1aB��wri�y�B�.a vw si(x,E_0,-,q) |q �N \ .1�N� Subs߿�p`eq. (�a�)Dj�*��� ct so�J~B�fra�sB1�Xq}}e^{-i � x} e^{iE[\int^x �� dx'}9'):��J��+����=$� int}=x$$ �g&�5�A� ܡ�s $ �n�*if%:`4s�0ҹ"�of &'E)s�5U�MS�3FAiaU�?v �$x=t_сO� S�4E�L2�v� sed*fu���a��, Q�� ,� %D(xA�= ��$$ zl =l�2� !*0�{)>)q =s� � $E_01y%_#%� A+��� t�7��4ave5D�m6 !A$i\ t �`= H &�e.*- �1E�B^�w�"�7insq$.*�+�0g1$eo2�yyZ� cF�5�uI1eu0�no ��er Nz21 Ah�ef��-I�fxsRt�w@� O&q3r0E�Amy��r!�l .t3a�.9%n*VvA��� legi��E :O4 ���l�ond-�R�%?%��u8mim�F�as��hdx' (1 -� �b + g^2( ^2) �q2}>iAf� !�m��� I� x > � <} u"�3f�r�w$�,_{x_i}^{x_f}�g^n���L$p�p�m!�e � � )!���\b��-�L g !; ^2 q^2} ~� , \ !x_f:�AR3BLLe�&�)2S��i"W eevi%A} a Gat6��� $N�q^2/ 2!E gma^��+<eH"�q"E�wO�"N3q�4$ (.`� ol�Na���0ate�X ��j]����E6V &=&�V dq V��i (� -�)!� �%�no�Hr/=& N' XJq A�< dp \exp\left[ -� (p - Lg� )^2�i�\%P. 44 L^2 g^4 E_0^5�4}(i 2Ay^2G5��� |pj * AR4Ug1t�w��x� A])���b�G��a!���ۡ�a�8m?�ge�p$��dis �� B�^ A} pp +��� end*p &um&�6Ȧ� 2F � b��U�5 �� �� ���g�ya3L��{p� �s�� ;)�p$ Ce)n�eq.� Q4}): $$ 1pau��a~}\�AU1!.1!)P}�B%_0:T !���� thu}�u%�1�g o ,�a �L gIܞ�:�� ��ng �s�n-� ��`we�& �*���s2�6Q%�W XOJ enumeratea�4tem $|E_0| < 1�9�wu�2� g&t&_e�meq6 L g )�r*�$-+! �I�-U#��&� uMfl4 be�id�;� L =�:!�j� (�o =J �"� � 6d � ��g�� �they � � m^ ineqAa&D_0 >> 1�86&6+� & �"Bws o*s� "w �1�A� ���6aa�l1A&\ \A M>!ᱜ)�AA�lE�%-�&erm�!�q�-;� in & A��L doh��L�� ��-^�P-Y�=r )E�6 m�D��;�] from.T�^m�yL S�Q�"marxre����N���$l��&�,-�, L)A� chos�H!\U�� �Y�79 y=/ 3A� fix� >Jt�be�a k#ƌ!|f�7a�%�J E��p"l�ly1<ed.3%���!ge�r�!t5�%tEQ��E�� *� *>�!�ua���1�at.n'Enm�9 �*�Tchw|!���c&EI�"�"L!>&�)� ]-�a"$� � �cq$m�&_F.(.���al s���=07C puta�.f3�i ��F�$�%��V )�5 �a��2�o=�R�%tIh}A.P�;���'!� �t irG0�):��� w�ok a " 4 �a��K�D�;��e�E�o�V!�Y t.�Jis�?�ic?�to� suadaDe��þ*�$y a^=W����!o�� �!��)ag��}s-Ir��=#|"66"� � -X"O"t*���"&�Ed��{ >�����o�hig]@%�� $gy s�9���L��G�=�u�a��3!k!�=��.���%a e�5onebR[5�� draw�wa.��>tvalid�t� &N!>��fGw�_. �P�J!Ba� #E�JH,>- obey�)�����.����-?&8 �-�w'�\=2Y�� &�"A ��8al/�B�WG��c��QI�3�,� e �T1.3$�;J*3$e �a&$�: �'�7 �^EG��1B�0$@-�%�.  J� box� ck��g { "�J�  DIq�) \�( 116+1 1+q HRHMP"O" a��Uno%A!2s�e�>�H,�r�. *� ��.3� bA�/�#a"6!+���n goV*Di�E"#�%?��X� ��.��U�Nap�J*��2 $H=\�G, }H_{ #O�Re�� *;Jetak"� tric�Ybn .Q = 1/,)�� & !C m = �n"ݶ (i�R$� ��P)��  y�ru�[�!�K&(. ��&>��A+r{\"{o}}�6e��_ $N�2� �C%%G  q~�`%<gcq)��qPsi�o� �*�}aI���EQ A �X��!�F =e!&DtintxB�%�a62��((B��4=1^Jy1X�^F�I�JA�!{4a"Dі1 � $�/p�3ve�:|��$..@FT�aaR�$g1 �5�a �v-��� wk6Ń;�P{A e�J*q1� �ibRk�2n f�&�S"��!('m罡�we�U���.F�,-�")J{|!6~ =!V�E"5D}�2MPF2T�V�!�m����>`  B�B��a��-� �b�noh rz��Kdsm) ^����� =@,� 2P>�way*Z A}��]���[V�. (�5Z%�\:pIan.� MP})x r"� -eE�^*{6� ��Bj 2e� p}{Lg}�&�6DE!�:| 2 G �9e��-*t8) � must�Xyz6;Z�&�"ac%�68A�7��D $q > 0L$� n�@s��g>0$)� �$2�,&� � ) n]W5*�A*`~5`���y2h52� u�e�-e� $\�=VJ q$�Y6U q$ s'No ..�-�6���H]V�Kr� m63P !>N�l� "�����o �r* � �p�I 1����!$]�2I�� r"Xasv�)EV( �Qqq �A�2}6� ���'�} ��R�L �quasi93���dion�S%a"�6eM&]%��d;.ZY.B �M;�% = L!'cho7$L2 J �E�%N*g$�VIa�-�q$A�.� �A. �#!��.^�I��'-&0AH*m4�*�M( �p��!��Pr mSU��. &0An"���.ѕIV}> w�����f]ngT""�!2� *�(� | ��35F�&:'3!�$�`jwN+�"�;�4r�Qd.  �ii�a|�C�-�A�A�rtsݶ+.�a*��'no�jN=Ca�� dica!by�� V.$Ѹ6� qF�A�?�7� 5:U�sI,��!�E1�5 . W��m$%}aT�&�� D �? ��ns9�a~_A2�eqs*0 J(1*� �DGdF�O = T_E + g q � TTB� �E:�'6�H0 �:�!�� 2�T� EU-b�J� ra �@1s:+S�׌A�lueY�ve��{ �c "�D-:( )$? �A��g b"��0� g�ԁ7�n'Ct*w ���AEc�A�AZBN� &| ��.<!YAb2��}�w27mE��U�A�JD ��� -1� 1� M3DEDTMP:��e�e�W�E�c51!mW�al�� � a�� to�.��.� X))Z��q��'Q,=%A.i��BE=a9A� (1+!�"q}� �2 �4�&�h1!�>� F�6xi�*��+9>�"F�-�!�6�&�.DE!�>� mС.d"xRY����K ��J� 5�%�WYaddB�% %o��MQ.� �).�'EAend�E�Mv�:�oE}co���aSVe�A(.andPK&�+9e�wh�. �&� �!�k1<.z��� A( 2F� 8'�a�2����m"�!]L sibll���W - j��m5*� �� $E_{}B�%'��.'M� C� ��!ie�`��a� 2Rq�!4 ^!��� P g%�11�AT�wz� _2 �m+�� `b_"#T2�5�s ran� ��*Az !� >�/a.j :"�a�.`]s�)�]wp�=��examplAp �5<y 6�[``���S$��&F �*��(�``1�'' *. H? NY����^[ �5C[<��z�?�l"�2u����� . DH�e�H a62��nE��b? H}- ��NNnk soso��A[unh find�O roof:g"�Bitn(ms logiXiy �[ le -"�Hun��CIs� �D�ic02� 6��Dv�As"oQ%] rar`2215�a�i\A�ͷ�m�.� &c �, ��4the spread in �Fthe durations obeys eq. (\ref{DEDTMP}). Such a model would not satisfy .328). We thus leav Xe universal validity of2o<` as a conjecture. \sec�8{Conclusion} fh`�Lshown that it is possible for an internal observer to measure the total energ�4hsolated system in arbitraryrrtW tim�0This was done1, particular %@. A � esting qu 4on is whether >can mak)=;< more realistic,�Xinstance by basing it o!e 7 of gravit%�Pal collapse discussed�(the introdu%m. IF is respecV,e problem po!T�d out to us by Y. Aharonov\cite{A} is-� n ou-l$ Hamiltoni%lx not bounded from below. We are !�mw!�$extent tak!Fa!�itive .Xwil!7 dify~cU@(s. Prelimin!�inv!�g%# s suggest ��ain.> Zre unchangedI�tbigskip {\bf Acknowledgment.}�(thank Yakir51%� enlighten!�-�a�)Je eB i}{iB.fg}[1]{�d#1})} \usepackage{graphicx!Theadhe�r 1cm�@�"8title{A New For��$Path Integ��b�;Coher��8States Represen�veits Semi%0E� LimihTauthor{L.C. dos Santos6M.A.M.�YAguiar �affiliEj${Instituto$F\'{\i}_L `Gleb Wataghin'\\ U� 4idade Estadual7 Campinas,a @camp\\ 13083-970,XS\~{a}o Paulo, Brasil\\�a�abstrac� The a(completenese�Abc10s)0�s0 dsA�(a multiplic��ofe�9QH(Feynman's p!��!�.a se diff)�A�<, alth�equival!�q�i m�8ally,��Ms2�C0ts. Two such 6,formulas wer�rivo ! Bar01}&%two corq onda�2�(ms �ed� Klaud�E SA�r � b 85}. Each!H thes �Tinvolve trajectories g!�n aa�Y�6R ofG .| operator:r P>2 ne case ��aDQN% &� paper w�8 Weyl>�o Y� �, i.e.,;9,*�elf. �R},\�'({03.65.Db, Sq} % Db F��al analy�methods(Sq:ft:!�!hapaT�: s \c �� %��9"� I��x } In reca�years�Hre has been a reneweHteI AN2x approxi%on� th :s�'!.+R fU��in many� a�~ph* !V chemistryU:6x� paga�4a long historyA<at start �a�a�y�78,79 87a}� Weissman * 82b}. SevA p rtA M� ���$ subsequenastudi� E numb�fgda al�5IDcesses (see, e.g., ��Ada89,Shu95,Xavi,Gros98b,98ivr,Heller02 3,PolPar03,Rib04,Piz04}). MA��a detai�d�\E��6���-c��degree<freedom ���El ϩ�. ��set36�sbm�, non-orthogoa��X-� ��, s�  e��� Ak�#\be writtA�sA0,inear combin2��-E�islk�z,& hand,E�imBK con)�ces�F�ulu BD . ItNlAbim  existe� of sM��aD�52a�lJ� 6�but%2 lea�)to a s?lyݳ2�.uSan�5m}b85}A�potwo�c �A?!�1�a�t:j,��� �U��their 2�$ advantageA0dvas6��WN��zse�Y�w!� iderE� YI� re3A�� !�at bot4�sE�Q�!�eA�of ��Ilx .J-.P"I ;V�.8�b( $\hat{H}$:E=�X JX eX4briefly review!�sgm�E�e � 2%� ph�ppear!�![ 6rA� tur� 0be Cjuee a� mR2!5X5j&� y,e it also!� tain�$`D V!� ' $I�8e��5� sig 慇 � ��L Eqs.(\ref{glg119}) ��.a}���{M]itEW�&� �a6'>� � !W�� U, oI {\it91.J},�lii ably!�a!M ed,� a5i�.�74 ur�Ia:|a� ő�i�ula� l�a newZ�� ��6+ , Eq-�5mb8}) �w!:o6�lo6new6})ea�)�����.�-�ed E���.�Dasge betw� P%\Q:�� N�eliY� �e e�6� ��:m�� halfmb Q�9�e5s| a8��p� ous mv�tX.Ais�.����lac\ !9m�aZ��arded,��error be!�of or! 4$\hbar^2$. Our$� sulb &YdA�A�, UG coe0e �I�I$rganized aA�llows:��� ! �? 2�]�� of.~ &�^ � �~- ir:�:� .p.���3�ul�ekqU:r e9e^7. Fin.�4e5�, withee2�!�6�� }A coincidesB0equEd�9i6�.�� � � � &x!PJI6��  \� e+��}� :�($|z\rangle$A�@a harmonic oscill� (of mass $m$� fr (cy $\omega$a defi% %=1�$} \label�648zd = \re^{-\frac{1}{2}|z|^2}z�0a}^\dagger}|0 �6d%I0$!��*F�gr�a A�~�9�:���<\sqrt{2}}\left( 1,q}}{b}-\ri 2\,& p}}{c} \r�<), \qquad z = O1}Zhqb+fbp.\.F8�e above�9at q$, p$�KX9�$��"�s; $qE  $p�)zE' . �H parameters $b = {(�� / m I[ )}^{)'E} c c = -n,I��Clength!� mo�$um scales,�iveGnd2ira>�A��O$. F� -independ�.�F� ,RPC �6�^p*�y�/$matrix ele�a���evolu�zp.�E�sa�^\prime m8-C| z'' :~51a0K(z'',T;z',0)al�>K |2�\ri }{%�}eH}TB>| >�J�WAN striyurselve=v�an$ expa?�  powe�<�of !@ cre�U!�annihi���sL 2�ndA at{a}Am;�/ N!�Jj w��E �9�ilH}e3someho ", a&* 2B&�H(q,p)$3 is `re=A@', how},Aal unique+��i��ambigui'� �!Vre�.y1?�!60B�  ar U nɾ >4&�6t�1Iq; E��0� shall se">nex3!b s�rO! actu��wayE[associ�=m�of pof!o��U $A)z�c &�5 M^A}$. H1�thx*L o"i�"�!�e firs�", deno� $A_Q ~%���hJ��:�A�ais&/ :� � �eq4� �Z\!,q>b]TD a!�I}!ց�u�NO ea�$��Q)u�"1,Q$2 �monomB"ofM��� $z$'a����� Y!$�JaM�N$.( $i� secoJ'ility,.B3., � bG�a simi�& procedureu!��QN��y�e�!L�!6p�Ee�,I�%� theyE� A� :�n"� {Q�m�HO� Yeq� )pu��k %�M� s ag�%9`!mz* �^�Ak)#�~P�~��Q�!J���_al��`anti-F�Not�!! �&��&F�6���me�%�,T"t� �qQBEPp}A� hich��or�al to�bam� refo!�t�.�go! zero.  goes toI�ra", f?, �:� �!�$most symme A�all�� �) naturals given�(JWigner�ns��r� wig1} A_W%�� $int\rd s\,� � \"� ps   q� s�  | %zA}\� |q+ H %�  \;J $�" ML�V�)�A}$Y0Hill84,Alf98}!+��qtr.�is � �3i� nxA���lm�ingOr 6�� m�)]>PP��qbE�AWlacs$z$�25�]"�i�o8A� illust-i��>ywe�*eYQdisplay�$} %�H}AD72}�\,al^2}  x^2} + .. x^2 + x^4�2`% ($m=E� =1$)�mHwe��^�Hbegin{array}{l} H_Q:�(p z2) � + �<1}{4}(b^2+b^{-2} 3b^2 �03b^4/4 \\ H_P�T-bT-JJTW~T)) � :5w�% $beJAwidth�f f f . ��eI�. $x^2xat� s ��"\ $H_QM�H_P$,0ly�-ifyA��"~dynamic P$ ect ��H_W��� >� !�& I 6�t�*u"K �Il��f� 6'�DJ 0(���6�Basic6z'a��6V'A2�!}�i$l�/��1�6�� ���o 6�Ar�z-2�0*^/ � Z2�"6� %�ummarize!�se zAults em�izQ1d �� �:�"��a���k R�'�=1�t�[]6�rea|!ferdto�sC�&�!�In� A e�/ath i.W)$6|R��0erval� Ebe divi=0in large�!sli� � for �uW( infinitesi! pr�acMB� As p*1byV�:S ��t� st� W 0�do >�'�s <�"�t>�J2U. A�(k *j(Mi��[ *��ir:_a2s� �a*c�' �� 6b� 2i�� !��+2�A}U� breC��62$Thto $N$�3e2sap$\tau X3*%ngB unit�or�R&� *�27\openQ= @ |z� ��8\rm{d}^2z}{\pi}9  z|ɰY% �yɲs adja%U�!Jsteps%l�.4A� imag�2w�� by $x �$yő|��allemg s, $� �/\pi $I5 ns $# xy$. Aft{ Y4%OoA!�}a beco� 8a $2(N-1)$--fol!�c-6 whol� spac*w 92.�82} �Ft&��/`\Bigl\{ \prod_{j=1}^{N-1}1�d^2z_j)�� >Ar\}A0 A[*_{j+1}  >R 0 .ARs�H}(t_j)A�}K_j�R3Bi�FWm$z_N =�M$z_0=z'$. UK6!u>!�lap~  50} aq 5 z�= \exp? \{ -#| I|^2N�+ncrb,*� �_j|^2\� J:� l�$�iH!�/� } \� 1 2$����~52a5�BD �2v2)u{ 1wi%v(J@-�-d-!f )!�2Y�?( N H)-�a!^ JA�{\ 4H}eh,j}T\12O3�%� ~�4A� FWe.0-:�|.� |z_j��N�[6�1 {�1+)m,z_j;�>�A�$(A�:1$!SI�)$�2I�7-!by I�jC� Wd-i manipu)F 6�6Sata� � $K_1$,�9� alig:^8i0K_1���Z�J���}+sum�I��[M/�C�C�C��]>J-~% % W�!�\ $N -arrow�fty$ (�jb ] (0$)� takenA � �s�% � �&,nd���8W�fgl!A A�;0o exac�#} itJ �well--�;n�|+attachH� e�ing s ?]a� �s^ so 6�$�nto !0smo^+.Q^ >(z,R)m� HA�>�" ��"l .��� !��a)61  $�� z Wa"g �%�����\,S~{ at � ��-6ya���,|&=?�.,]&�!�.�&�q�w -�a�r )!�V=�E;ly%�Q symbolD.�F�n�%)%��<6� tsGA``dia/0:�''=#h*�1.�. To fac#�E comp~ o5"&VI� ���,���2#%R�E� ���Cconveni+$���0� ��*�-1$�� s, r�=��an���!2� na�e n'adKA�*�#.�''�#>� .� i :�#}\,| z'"p ] �%p , f"+A��*A�"�*m,!H�%2z���sA�n�' 5mb76�*�m{�� i�"� +�'1l 2��_� c )��) .'� _j|  Fu�"�(zsw ~l \,J��yA�le�3&�$Ka�w9b�"?5mb8a}IH _N,&T;z_0& \Qstyle{!� & �N9-= Q[ \,V:c -�&  ��N�\}}%D \non�7\\ &d)  N�)\��1� \ K6 � � J )F�@]6Bm\}!#�M<%��p��� I�$ubtle�3�7. Whil��argtA�H_1�D1$"G�o * �_n �^ mesh�� 6>N�N2N� same���66�as�E3gi2/":rm0seGmpu��� �N�E �e 5 i�io�Gexpon�P&�i$ x�sin*^�6evalur � >�; n en�iG� �. HQ7 nly �I� �s:�pe�8�s`5���''.�^\nuY�\�-�iխj&^ S_{1\nu� u' + v''}} \;cexp: �d(Z+I c)b�I l( |z''|^�|z r�XM, ,FW�b2/��*��32b3�4%4[-I_ �4Z42~n83Am S_{i� = (v'',u',�� &=�0\�s_0^t �t'I![Mxri {|$(\dot{u}v- v}u�$H_i(u,v,t'Q.o>2T@ ( u''v'' + u'v' "�&� tL"U9Z�0�1$epslb} I_i" e<��� _0^T�!q&^2�} u}A} tQʼnR}�zr\B� ��� e� ^ $\nu$& A �(�x)*�#2�7sa�O��'s szR�5u%� u}&=�!2�).1:v}}"qp6PvP-:H rP��:p  4N�M�(�I�1~-�mb12} u(�/z'Tu'~}2 v(t�% {z''\ &v"~ \;Zg fa:Es $I_i�(an&�,sU ar2�EuFA��abs�0�.neOA�to C%�A2�M*� K 93�c5�ia�8If�(neglec�%t, evJ H&4 *�4��<wrong.�HeA� A�about s c�ibu�x.~,�.refs.��AB�6 >�5C"5Rd�E2% } A0�Pa�%a'��a�� ��n�um"&��-!�.�� @DH_.�=& `H&�$�'qi*edM-5�"@~(E �-8,�)�1:�L.�* }, s�a\A"�+ in B�"#.�+�(6$. ~!. R�,�&K�,s : $ yields<%1$.2$1&�!�R� Bq+},�@ now  "�,�s/� �Z�,?"�$�-)�9pjr� . A �H typB,��ian"��Q7 o!� by u��UV�*2� �!"� !8(��* qf �*a�%FHY|r�*N[\U���*= . Si.'%2-�-�:�d`,"I%"d1�.ju�s,�*^>a,wan��:�*�M�w�@if}=��N�Aup��cubicU�s=7)�m�Ub�/v an��e ��%�B �0R ��ulas���+�!�l2�$+I�2�%9%0�.pB2Ac-I_�>%�"Bs"!.a�36� 2����&�q�|#us47he >2�n2C&� erm,�G�i16of �A ��b.>J�/� isA�Gz6�J�y/wa�/BB��.I2�� u�*b� K_W>��� W}U &� �( S_{W�� ^ &c�>� % $S_W$�h&�@gl� )U�iS "O8e� . O�9�-jjs&���F��m�(!��0T+Q[sO� *G.��l�U2�`]3F. H&H7�2a�doeTY��'7h.��^6�aQ�H:�(us�]is �**&]�,�8BqO�1�_a�k �Qf�OaDq<�heJr�k,�, "�NA Mixed% m�%Pa*T},�E.� �+scrib�U51Ais�9 ed o!oef �^E� al%�!��.o.  idea3to�ce l6N*�H!�ZL� Y� ��Y6R�ralh]� �&�( �E�.�&�g=*�b_N.�]!�A.�oR, H _jH'0}�i�5$ .'=z"'@('1@tau_j%�!-��.2k*e~ foLce: �T@�;�*i<��U� p O equal �^��e keep7e;x $j$a�� to  racka��A�w�?j odd��o2N1Ւ�a��!of0 (6��6����nuER��6!Y�j#J. For $j>0$I !�impq1"+ al,"� �O�(�!�22��223B�glg21*:'q&: =a7��1.*�&1�,%N.�,b!M�W���1 Q ��! bra*�"_{j-1}|$�����1'A�� $j-�% 6�  employ��e��a�ոe+��s*�K!]a�Kwe ge��cW*I�m�&�7a�a�p"�9� H.U8} K(�"��)�i.N�!�21�.�,�ghtN�Z����N� �.6��A&. � . -�iK*"8$a_j H_{2,j:4:326Zb ?*u*.�\e�\/:�Y)��-4.>� �d5D�E �'GBef 2\pi��R�.jHf" ,z)�,Un��a��� E�$j��� P A�odd, $b 0 20al>/is��. Aa$O<3a,mW�b�'� � xq���՝Z40( �1_j=��"hpT#$f�giv <"K!�a>2"a�%�2%=�&=Zazf"�I2 -��+1D�,''z-68�+ AF-Q��.�:�2�,;-]�Q��-&QwVJ��Y-�abb�3(gno-S eQI� FH"" m9W-&�,^*!u"� B�e_E1�2�7!�kap2_2WZ�6� �Nbarm�a�*0�/can�"5 X �) S*"})����a(kor ;"�M�*�a5r"*'Dir vic�6yba���QofiMvariabl�).�5% fin�.oe��g �Lir��vanisheOa�+&���+T J4�$"�para j�:�at}{3=�glg"|"�4�Df}&���Q�&=6.-if.;a_j� "�e�]L�:k� 0ri��I�:Ih&=0<);&�L@&j = 1,\ldots,N-1&�#=~B$ �j%3j2�a ��� 2�W r.m�P�SB%.SB/N00902!Uo ��a�bWe� ����M�6.6 \eta��  ��,�d�a#6e)"*�+mOof }�q� , $z2\zLeta\;,\�� ���}mI '�c1R����!F�glg41eta_0=  X N  E�-QP% EeL�! �!U o a Taylo"vL[$(j T , ��r�PA=--B�� ,z)$ �*�G�ir�N0 �_# ��X 0} >9Vd@]% "6B�29 8 a�\mbox4e<$2� $}| ">� F�[d!�'V! }� A9�I#\}f exp}B�� H ��i�2A\} [b_j ��i� i�'�*�]2}+�O �27�"f7] �^2}(���}\,� tau >g^H �.��?{$ 2}�K:rT2,� rV �Yl�� -w (1(C�5��J�>��%G.����-w!�}M)-^ � +I�(1.�����XJ�n�:N� �))� �� � �\mulm��"[ in2�6})� r carr�b� "��( tech�O*�J.Y�e. tt( _N r�_1 ���n�#�P2 '% : /etc�recurR ��.� 4Q @t&�,F�B�M��4 �U6�(1+M9\a�e�]#:]s"J�&Y%L:})^2+�; �A�F�(B� ^n6d� +B  7Bj^2})X_jb[: $X�%ie�{���x7X_j & =� i���:A�,9d6�� "�o bb2vf1,j-1f�h� &� �.2&���x0U= �1�1�aաn��m.; �)2���>�� �2�2n*Hb�)+2 VmKFv(� &�@N~. t:� i2A-�NA*X A} :-�$j=.� $/$X_0=0�*�%�BEff~v�&" 5!�mt .2�o�C� continuum�u_r>2�^mo�� ��)'�at�fV��FVHZ6�JZW*�'�' �2�c3})>�N�  B9=0=�at} %-� �EH�H%!�r� cho�Pof �b��D�*$psilon = 2��$,��7*U( �(ret�`A& ZgqPf2x$z�z";�E!2}$�{�evFin8%"33$8�moJ {j+2m�>!�@�Q��� Mm�7nse i{)��$N� �3Iper �6�N�a_b<<*��R z^*$�de�d!5J��be S#r& ŢNi"�%T1}-��{\-�ah&=.t ��6t�KH_{ef,j�d�����X�x\^03,5"33Z3�"����R���.�[�� �z�5N�2,4z�q9�1�X���b2�Ol�%Q &Y2��@( G  +�x -� +�o�  +�� +1�S/2} \\"� � �6�}:�)K)_� `}B0} \�,pA�a�}p>�%� N-1� P+1jRodd�2. �5DarQa . � 9� % No��because��  |p��"�"�:$qD=� we mis�C<����+&�g��b�gTh\"�\"$a�xe�����K��,�<�pa�6��a0r�uyusu/]�*x@.,+�@�*�=�<� "�"%B1���1 neox�:�����9} z &�aS u.d3\�62Adi��c-� �c"4d2�c "M\\ -�:lv�l�dVl�%�!�uS�B $/N$vF��Q%z�222 D,!uo"�, �s���*$E�.�b �.�10� ���3�"���lW}&� v}.X :LvL��zLu�( ��)J�3�nzPto&��3)n e"�]~S Snbe =#if.��Y�15} fAintF�6��*�6v} u - 1Gv* # I�\&z92VB�61� c v''u�6 v'u' 7 O {)9}  )Fx�Q�4=u'�M$, $v(0)=v' u(T)=u"�vv"=z"��� N&bOy�R ���[y(��� "Y43}. P� 3��ZHand&� =M $\lnCxu5$x + O(x^2)z>�MHU�new�\GammaN!&�8_{N�w\i�H*�O�?Lef����������j e� $"�AE�:&=jd�Obig�.��.*gQ.zln [ I��JbJ�G�G&G+O(�c[]%8r\�r!r��nx tau[!f9�����&:"� Bm j }+-����9=>��;�2r�^��s��qto ll \fk-f�newf b %�l\� &J'�!!! F�S._;r\�pb`�9l (H1)+3 5)+...*. "5 &=)�e��h6o�v�v2 � o4 ��M� ��aų6�>,!�'�j�r% �{:�MrIW!pj)�qD@1}��g��.!0�&]t�coeffic6I"n _j$ �acquiF$$1/2$0or.&�U�x�EÊ@E�@�+&=�EI~E-3S ��F;]�\, � )kf"'.S2}7u# v}(t')XD P"p� .F�>sGVt� Xo )uu6 �9#A�>�H��^22u ������ ��iF,����P;{�� �3} 2*\&]+7s2�!E3����� }_�5�� Z���-�v,�&:�V �\# 2 �Cv}# �- v��) *r�A-{�24-2( k#  + 3 [.w�diY� (|z'"gF 5y�"e<�� W)0�`,oP>�)ous� 0� ��y>�"�7}�X(t�)=he". �� *� fnon�$ar";I)��C � qTA�7eyEX}�B2�2'B�.�R�v^2}-*�1�)�Y��I.�! NVф��^6W]z�� X^2(t>��gQ+\*�66D $X8��"�.D3 was s%�V!��&s $X = ) E��delta � v}$ K vIDDl � I  ?'*8f� (�E pEud I��. �Zt . - v}H �u D�\R�Aq\, Sv6� �����q�2*.����S�R v�m��ER_u�uI"�d�DVkA�B��cQ^30�_-Dv(0)$ a�{U�[��)aFof=Sv)18}�b}+"q ed�B helpA�"RA�"�*- ��3� E�ʆ ^2}X9����0I��YI �{->.�$2c w0M�}v�1.�H J��7}{ t}� �v}���,.�>�]% eFA 6M2AJ��S����\"4b.f�+� $}^t_{\! 0�d�L~� G�� (t' � 1.:�>|<�  )&�]2�&�.�O�)4���1��� }_{1"|T%2�=1�Ɍ,^2Q2�Q92 h��)Es& ΔO2�.d�8]&z &z F�.��]v'�=�Q9J6�{:�i}�� �b�Q�P-R�8�]�C6�R��2�I_C o2}�0, pre-}M��v'/�'+JA*F��B� S KC�$Q� S_C/ u' = -ie7 ^}ٶJ�RP�r S� ("TQ :9Y�VQRVQCB~e�� �(��VQ"�-7t$ ��end��v� >�i�.�&VM���)MB�/!�,1:)a l\qMk(S_C +Ez)._��,"\�^2"82�:��"�efcphvRC�� ]I_1I>� �=|]�����G>y9 E9 %��cKcuy/ e<3�� &�`s"4F6�9a.in $U�p  �/&�^nG�Y�= ia�KC=(H_1�!)]G 0%r�QC=5�/2D�A�NJ�$�Rh �U r�<ae�el� C}#+%d(b� $H_C�@"�&E "(t�� !�,.�9W$"�N���)�2K&� 119b)�Z�pInn�1}=��a H_C=�t*�D&�a.�'#vol%�.�L��� b$p$B�1% �1 seen&�AY# *�1�5�"}&w >�(coe�T0'.�#�* �4(�(e�\7F�_}�&'W*^$�++~�1��6s$ ��� �2��횂�w�v.;=�* ^2 /�7P# zCHiZ{>b>Znew;��(C � \cosh ȝ�.�.� 6H_Wծ 1}{8> 4}��z n�{ �}RyJ + ...�#)��9�cs�o�,h�fQ�Ai:��ds. Be�Gs,@� re�j.B�E0coe5} q = (z+ �)I�b}&!%)K* p+-+ )L�}{b�C2}}M��^=a� $b \sim c O}�^{1/2}au�Fe��u�vc�ehigher�9; �Ot�U�,�lC$*$I �\ (o���Q��TQ{� +in pr��pl1� �V�,{!Ty �7bey�J!dscope_ 2�.*�l�(!�W��"�S.TY�"AGͱ� )2�c�Ea��$2U��W:����Sa7eCI'�����$\Om�S�%~��!0�0�a+2`O�RW�6 QaK )A@ՏFَAs��iake�rk!�n&!�%�bK`Q�:6R�+2 &�_aHp~d�e - �Q� �D*�@ �[F �4*{�c�"�+A��h rele���low en�h.�Vcan be m��ex���AcoI��Fourie*ހ �se4Ld"��1�8�us�% �~ B�E�� %!2��+qJhraA=S�N6!A ref.��}�1clu"@>�o�{2g�Z ntiz�� ru��!w�zf�o&Cfor fur]je{s.�.C \noQF`nt ACKNOWLEDGMENTS MAMA *V�s ArZW� Brazs�n agenc�7FAPESԔCNPq.��Z�y]B��99(�b���b M. Ba��er, A.de [�$, F. Keck,�� J. Korsch%w�78}6�,�it Co"R2%�H�Q �,s, RevisitedE�d G.~J. {Papa\-do\-pou\-los\-0J.~T. Devrees<�di��,) \"o��NATO Adv��d Study �e, Se�B:1 , page~5,ƦDYork, 1978. PlenumB9BF[Oǩv. D}!\bf 19(8)} (1979) 2349>Q��VW SomeI�a�R�" on WjHFs,%9_%�r�,�*G.~!r$nicolaou, )X-WRan�Media},2. S�e%1982�U� Y.~ p�E%emaChem.)*1#76) 82) 4062N_< S. Adachi, Ann.��e[�%e5} 45!e89).^ST�}a�Shudo%$K.S. IkedaFl�,?�7a� 1995) 682.Q,Xavi} A.~L.  er, Jr.ZM.jM*��}�em �� (N.Y.A� 252}�96A458; z^ ��^XaT. A�bf 54(3d�Z180[ ��>�L�� ^ 79(1Q�97� 3323.(¢} F.~ AUZ!-�~!L!?je�-�?�8d242c�e8L�{oendorff���O���(N.~Moiseyev ��hys. sQ�44I� q90.���0} T. Van Voor� �d EricA� %2ZAIU$66} 050501�22� 703�\ %1J.6MEN43 12153 e32e7�} E. P�k�J. Shaoݰi�Ͷ107} î3) 7112 Pa� F. P1qii`>��R 8� 3) 62:V ca�$D. Ribeiro�A6�!t.� }E) 69 e4) 66204.�0� KUFգca Rome lC. Nemes!G.��xot?� Faria}A.F.Re�$Toledo Piz�REU1C327� 122�"s M.~ e��4R.~F. O`Connel�~OA�uo�� E.~P� ��E��pU�10�W4) A.�� %SOzori� Almei.p.)I 295}q�268>S ��d"�  �cB���Oϩ4,pra,twocolumn*��%\F�5"@�.>4.Ůepsfigf��vcd}V�p[& ps,draft,-5vi��G>b�^�]{dleb:�am�fR1E} k "��{prstyW� \窅GSi��spi�m2@u,y qubit SWAP,.�lec�� nanomagnema��0M. Feng $^{1,�\foot;.��ElectrZ�add�R$: mfeng@th��may.ie} �JB�amleyO}$M2]RMJason.T 6(@MAY.IE}} 2�� }$ Depart �]N1 , N^ al��x�I�nd, Mayn�z(, Co. Kilda� n $^{!Wu�u"� r��F� s, ChincAcadem|�� 9I, 430071 ,cZ,date{\today}� b=&x�S!�s�vde1��� keypqvery cj[enlxtepL�A-ba�Tsolid- L�umf9�hpHology. 8fulleren��ed:2er 1i�~we �Ro�����w.gl�in��id'�cy]#er"�in�%�&/Ahed��� A��g�M�s �V� Fe$_{8;��c�KS=10. D)o� to p#6efR� a^�Yav�� /I�I �.��� �(-of-the-art)Oș��Ϯ S� >��Val�9�en�]o��|.[ ��'�G crystD�r.2�?0��at �low temperatures ($< 360$ mK)1wern2��lsA�V�o���y� t!eMd��t�leB�s �e �Ae��6. , lowt��&l�9/0�g��aEw-102\M %���b'y�H�C =-DS_{2z}�+ H^{�<} a�2B�2z�2,�3two^3D"�t0.275$ KA�AXax�$anisotropy�,te<g� u�$2 �Js� �� ��=g�; ��$�9��*=�b��g=\i2i�!2�!i��N$10$�#-*u�!8s8e.� */ap�AMLc� n x-y,mn� e��g%0I� split� %�{garg�c��A�$2��*T�v�ur�c+. More�c+�.!� cern��!A4�A� *�I!&l he�� an Dom��1B�WZ.A1)(���]A�,. �L�2��+��r�%)a# ic �v{�q�{ gaw 2_ ��L=J_{0}(A+B+C+E+F+G)$QIA=(1-3�1aB\theta)�g\o�Xs�&AT(, $B=-(1/4)J3M�+24 -} +J-2+�00$C=-(3/2)\sin v�  e^1 phi}Wz:AV6lz VE=C^{*� $Fb4b� \2]�6G +}$,�$Gb>=6�-AdY$ �� k`�cual3�-azimut�+g-�o��. ]x�)�  b�{6�Dby�e ������aU city*C�� �AN vest8� ��iaG�{1��aTE�*�pE�low: (i)�VIt.2wZB�g �_d(ZZ� 1ga��5�},U@�[eqs �#��XG�u�clj� . (WWg�C�2a5�an�Wng�C���w�I .) (ii) O03 he I�U-�� $A��� ���]� ɼ $, 1r����in H$� .�v}�n weak&� O))2.�1�Gt�w� ��imp��E2�B detu�;�X�<�J$�L$j��$an safely �3�)���t�]$A)�fD: t.X �:|f���0�3��aJ,�H_{c}=-���@+��) .0 + J=�)�"!�2^#J�WF?i�we�(ume $J=0.01GI�exp1}B�!�59Eq�r�)?W�, ��� yAVoCMCeigen�� w7�>�b)�5� 5 A n!�T�E{tab1�&,}!�SE8 } O&�con�� & y��s:�fi�k�.�NG.Q�1 �i��P &� %The�� *y ��n9s~��� m� �$�:� � 5�( 5�#%�troM�,-NOT (CNOT)&U#! �i���* )w#��"G� ' w�D�!e&�^�`~ q8 f��F ��>� 1. I2Wb�$_{21}$}I�:bE|/ ex*p�de���ra�8% �bsF� regar��1 �86 are heav��C� ��(or nU�bo�%)� -�sx $�3sA�axis cha� erxc��irradkt!a   )�8 &���m$A�O ��A�wTm�6t�O. &�.X("E ) � J`s��1 Bk \tilde �OAš)1x}"Շ; t '"^ Rabi� , $� x}�H {1�B\p�{0 HQB3} & 0 \cr�D2# &%.P},$�o!�.�i�"&�N��"&l�|0 >�. a@a $\pi$:ESR{� -8 t=.,%��I�|' or $ > P}=i69�1% 12+ !Z%$& %� work��#e�!mm�e� span�by4*i{!d]B(*��O:,i7&�\4?Pzw flipq��:w dA��Ui�n!�-���a�9e3��e�� �)��"�!!aF�T�*c��a.-�io@T&X&l�fiKt�%��s���A< .t%m\�D9ed:�s�$��,i��up+�s< 6� �F6�Q�9� � 2j 12� DZ!o�!c! �$,�Jin�b��� qui�!~so �j_7  b64-�ab;�-FE9b"�s.,1�| ��؇  &of&� *����@�!}6#M�&"S��_�po���CB!����F:ſ.�O��D�I���of V ��aH� �� �q���+ X�Fig. 1� e�Z$red cr��ng�hse�� double:��!Is*S�if y#.�!&2I(H&�� aQieR ��e:�J&�e avoi�(s$)�& "� . SoAG sweej!!:B�*�+ se ( l)m-)�o��h�xbx�$;�0�-��exa} �BZ� swep� ^�� 9 � � $_{�T!�+}$ T)E; �H.��J$�, -]��o . ��e at�Me%Yb4!�9 kindaUs� � e�vj8n�ocX� �ba��yQG( or�er-w@t, B��,�&Ea# )=�ovu8"8C� e~hass���S$|n, m��,\;\;n=� /2,  3/2$ �m=9 8,...�h�p ,$�+��.h�#ΚacF�%:� a�E !&-�. ]-.����-p#�!f": (1)}�mt�E}N+�� ledg&� >�$ "T$J$��S��Y ���re��. � 1, $J-$o����eӮ*�,�%�rog��2[ (2:�]wA�wؾV� 5ca3b ve 3&���!U%���!Z�8c$twY�E- C60,�����" ing (wA�9%1� g�q�`��>)hQn �e��F '���+!�3 miniֻq�ce "�˂� . (39eaa�؄���b���n��-�arof�[�� /�-1 M���U�:�a�� v.WWeA�$fer a fast #!��O�N� ofo shor�"%Cfde^MA,ime�E�q� n��aI" s��Hͺ>�2I"aQ�-�V-} *� E�{ .'a�(F�-$$10^{-16}$ 5Rڻl�1ō!a�~��� trumw�s��5�hb Q {barr^@H*�4Y  hop��J� 2/�-! /u@?s d��I�!����43r�0�$� de4E 1F *�*F!&2��4/�e*�$'uU�L At$J�D �0�hu�� )!�&�!%O��pur7 7��(Z�� �`��rs�"o�K� Ipre� i�C!Jae�ectE�t(*���"��N %F%Q'��$J�� �5�up1 �l�)t��� �r�&cfz���.� m~�g��0 tage�`�#chiev�r�Sc�>� �[� m(�* ��c$numDKnI if!�e�cl�,g �b� l � arlyv�lap6 �!Ai�atE3  8Az�"��# ���/��7y%}{&�%�qA��-al. O���){�A�&&tooIG"��wJz�*�v��|J|.w��2wm�({$|�|$, D\"n%��� 6Nc"_ �0to 350 MHz, �\�s�cU� ,2#MeB��w$ {meyer}.F��^eF�  \�[�Xa* & � ��O !=9$ T, !G�N1(,/2 \ll D$. Nk�thea�,�*@%� al&��c�Q��/�%i$$C $E$�FC3I�Y�w�dMR ?(ex`. $A$)�^ld 4֥5aFEU���soJ�8 hold���&`p����aV��A��mV"� �#3 ��=�.�2s" ����>[91 B�: m �c!�]il� enR�(� Z���=%%��es H6�, ~1� A[7 KQ� knor�F!u�. ably"��� ��$>*�% 6 T6��do��nt sourG.� �mo&��b���)@&�1 broadY��Jyd^ +/i� 2, ses�> � 3s_si�-deWA" �M%dueZ��2YX$Ҕ/ + $%�0+!A.  �t6N��APVD ��;2� "�1�m p = 20�/30$�aavail�cit��i��rF  sec�� !8�e.� �H b!�100����aR&3rL�$�A�at,? *Z, x��mK ��.�7�=42$ mTE�a.�B-�0~200 mTi�� ]kis 1� 0.8%Bp 22.4)Zn� b� =*if�m!e& =-�,!W&���Iigat5� .� 711�.��Ω&UY A!�`e� !8p�R2&�2de�3i-*|��8_*+4s� !ɭ_�b5�g&Ah&[v&>��.=.E��[�Uf��A�.�� steaQ�a���isʹtifyn�g.�~N#&� �4D"Swe < to �l&1+�2g�_"� �|���- �� !)�"H��� ��A�� i$ I�quickly5�>/N�A�2��.�1"��� U�Ak qr&$!��&f.�sto " � ����,4actly chosen t�Cime, we can have a perfect initial state $|10\rangle$ or $|-10\ranglXf Fe$_{8}$. In summary\Xproposeda oten[`method to efficiently det�the si` spin � inside�fullerene by means of an auxiliary larg ? , N.��(aga-Alcalde�'4N. Hendrickson%6�hristou�J-641�706e�2.�exp1}&� re no6� data%� thatA�is valu-0theoreticallyL sed dua, followy ,fact: If a */   a'sam� zeaYa*� PC$_{60}$ ($<$ 0.6 nm)�put next a'by a a�� distaA�$of 1 nm, o dipo�coupl�between�ma�abb�mi(+ at'wo�s ��J� g_Hstrength 50 MHz. Co� r|*W r��1%e�assumY eF�h-� Dtha�~:�(by 7 times.&�A�1F�E� Orozoo,��H lba$A_.-6/:L-.k\\ �d-11.5\omega - 100 D + 15J$�-1081 3.  � �7>.- .8 i- i.��1r" � � � �:MZ# M=#,$ \\=#. �+ --9�-!4b .---.I e-e2-MA �.�AA:� :0>!>o:"^� & $-n�)� %�.I%!+9!b�R"Zc� 5"ZA:/^! N=!AB}f.1�uer6) %#2-$yef�=&��-m�+AIm�9  z �"-"10Fi0\label{tab1} ��a�le}B�$figure}[p]�T��}�tlh {\uni }{1cm���pic.�>}(4,15) \put(-4,3){\includegraphics[width=12cm]{4thnewfig1.eps} �M ���T�{Energy versus B$_{z}$ field plot�/low-ly �}t6y6Bak onNl �m,$D=0.275 K$ \ $J=0.01Be �um tunne� s �iz�d happens at (avoided) crost point,�� kind��p: J:difF t:;*qsx e:��i sma�Dbability�second� high�or�proces�I�FigQ�M_ )� docu� w\|class[12pt]{iopart} \usepackage{MFtx} \topmargin 0.5cm \def\half{����q beq{� eqn� y}} 3e� >xb{\ove� e{xKI���aD{A non-perturbativ�f�$ime-depend�problemx Q3,mechanics} \�X{Paolo Amore\footnote{p\@ucol.mx} Alfredo Aranda'fef&SdZ S ^�@a�$iltonian o= or c1s�uconverBX gyH equ��0into a matrix6 ap�ri� bas"e% fun�s.� xge�of� �!be grea�improv`m"{ vad8ional parameter� yr dm^ b� principle}minim�enL vity.[!Scas$ 4quartic anharmA� oscAbto} symmetr�$ double-we|�  Yan�ve.M� y�}�non.a&�we ad�coordin!� shif`  a two-9)=?YFon)�-�4not only gives�4spectrum, but �a-�ximI(�e2J5�.�s�%�t!� be u�to solv�:ASchr\"od<Y~u�D!� � of��Ary �BWeA� ly i�0` developq�/�L �!w�!�Qd.�s�rol`-�.��y�t\pacs{45.10.Db,04.25.-g} \make�S v e%{Introdu $} We pres�Ja � �5a�Darbitrarily precis�r5�" solu! A�1 ٪ Zia.o�fulfillE�Xd��$\lim_{|x|\rightarrow \infty} V(x) = + $$ (i.e. a ]�^E~admits b*Z!)�though�re�u exampl��O� tz[ , X limi�� ��m ��E�d exactX!,bI�!ni be!si N (SHO�iKd�topicAUvirtu =B% book� ) �q=mo�%9��systems.,$%paper�.�� �Va��a�d analy�  an altern���tegy mus� f!�. P"" o�� ory !%3t�r�$ol is� dealIz such"E ; unfortu��1�Ak forwR applj�&� ��p"� s �p�%>becaus�� 2Bserh is dH B M��_ousm�e{U cn!� appa�$E��9;e�M�%� ar� taUan�#(LDE)~\? {DM, HFJ}!� ot� |aS  a�alN (VPTK�AFC90, Jan95, Yuk91, AAD:04,AADL:04}. L(ly speaking�!"e�%,Ai��La Q�,a� "� A "� ideax�|w��K%ew=in =``unnal'' ��Uone%�� a.�origi>)�)!C y�ɥc�����!Vresul0 �!��i� ma:'oacvJ�fOb�i>y !Z�. ForQ%j^�%s by i����<&2 ��Ha"  c "�to�ol��W,m�� s8��vy&� z;pp�29�yaii2:aN thenA&er"� "� �N� *�  (PMSQ� PMS}.�(optimum ! �� adjus!��H �n�the PMS�up�? MrYp"=V)�I2=b�a� 6? ), �%�bolynomuex�mQF� . Among �!���e LDEE�VPT����m  Lind (t-Poincar\'��zAA1:03�"2 M�!� "� o"f�)od!u��^ &= sUS�nF FS"z Ba�.1'*A"WKB�wT��� acceler� of :� mathe� c ��L more�. Howev�it wa�!�)�g!df�!�AOefct long-� behavior�Amn -n 1�>al�RE �� 4-roll scenario infl��.�:2000au}� suc�~ �s��bl� ��te%* F< !  ccu��bu��ly up! ��C!}2_ /$spread o$nd�bp� �U agai� ,Hartree-Fock-� does){a 1l!Ili�pve r!(��-* at +$rs� �very far�� � . Hw� �-aV.& � I(� Z�>��2� a J�t�A��lea�s��qAsto � }y6~�"��&� $\O�$��2� ing �2s�[y�PMS cri(on( �8ti�r� HeR irst� �.(nd utilizedaI�QM85}n'v�H thus0edE�]�2�%\�%lqrs x�� -�N_![��i�MK�DAb�� aE�a�i�/ con,e�. It tur!�u�NaiN A� extremelyUz^,' quite� i�)��'no!O� I�B�ur.�.!�l�$organ%ya���$s:!�S� �}adescrib%1>inu���)���1G)�6�� T R~s; in6�:��-�m� !�2-!�f�%FN'.-U= �!V."�i�!�b %� o1">���L com% (m� th�(` Aqla^ e; f� �}>concl% drawYu�J:*�qS�= rum}�5� \sub�0� Metho�We tack�Ah�Eqa:olm�J����"�P \hat{H} \psi_n = E_n �eq2:7b�)n��B�,C $rthonormalBA 2�� ��R*�,, A�. .' �S�4@\equiv \alpha^2$:J�phi_n4N� e^{-34 x^2/2} \ H_n( I x) \ , 54B�� ����tan��$o= Td/(2^n \ n! \ \sqrt{\pi}))^� $. $-�$��!'* ��i�U� one-d�3A�al :*\2m ly2��ne��w runc�|infa�2a�"($H_{n\ell}$8 somea5�9� , say $N\�s N.� its �6�F� ���s diag�-g. �L6 4as $N$ increasqٿ�O�^ �l�<-c)steadi�K� �his!� inde�F�L2���!>. may be�Ylow Zlea ) seekT!M��� � B� tR.64we shall adopt�)� is eQ2�85at &B,��.5 J�J.!p lied�:h &! M_d� �'�al hin� isti��ekM5�� U �T itie�x~�-%�PN19` 0Y)e�-n'���e :��%�i+E�exh5�pur�s���.B *�T�p!H�M�%H�O � *�8�}Q. H^ A��a �5�w]/ems"sum. A aTon� "� ] E�!(P%�ereforE� take�?Ai.0�C${\� T}_N��a� $r$  � KQ2$-x$��o� I�E�p$, $nw&�$wY�v�-h n�� ��seA�6 �?ap^23� are I�by:�1!�p^2A� A } = �)v%I�^2\left[M� ell(,-1)}\delta_{,n+2}-(2 +1)6} + ?;+1) 2>C-2}_] �%�6�r�!}�k�M.� as�x=Eb � + m^q )+ gx^4*b 7m@w�>i�ŀ!vACF[Eq.({Keq4})%�\�&�� a��} ]!I} &=& �!�+ �(x)� g(x^4).� &E�0� AVP��>@�U(n4}{N}2XN(oM*m^2}{ })+ 5g$^2}( 1+2N^g7��F .LLM�B� �"5  at!>q p_� = v�X^{1/3}} �1}{3} ,IT' GX � �3� I� -9g� + {I�3} !8(-N^2m^6+27g^2( �^2I�)^ R1�/ U�)��+ "+Vg+ 9cm]�)_1.a+ "E+Tra&� h&�M�~r2][) �A�&.!<D, M� � � a*$"t .a|�"� s $m = 1��$g = 4000$,6.���d stud� in mei97}. D"+cur�$re;A#� �.��.�* IG2aa�nd9f 1�e�* �� %V(diviNDb6$)�st�a4"�<Fig.~e� r,x Oa globalQ�?7r��h�$� � .:>m=):=1)8b r m�� �2�&a\:�$2$"�ari ;"[�of2nF�$\beta=2� . By�� "s  e�,!�accord q PMS,��� {$N�$��A�� erro"(.)$n${th}60>t $\D��q�(|E_n^{(N)}- 100)}|$��expone� �$,zV�1}%c�.1F > �$49$th6� . $ �N)&fB�th�F)%RJ� "�i�g.�Ɂ�0fu�nu2 and !)cF?s/ o �Hed=ly-�cyM�8ed? to�*��/MQ o{S,)h' Rayl�8 -Rit?/�,a &32�Ii�-U/2*|&�l�9���{Idlie-"�Kq� 2�is felt�strongV-``b� Y'', i�)t�  nf� Ɂ 5-selec!t�c X�.eE�ly6���6�L tooW�!� )ubs�� a�KR�d�%�Av ��2duoLn�ed above-isdrin6�1a.��4�!��Q_�(��-�$^{(WKB)})/  �"�@ a s� ' �of&� � ij}$% �T� e $n�/�.�� dA u�u��&�)��6g�umV�Zin/�#!Ue �"te5 �w� �����.>�4)ed ($8181'16(161$) signa�,atŒ�Jre�'&- ��( m�s reach= �"  � � er} ~ 2: Ef. S!� $49^: $>�B A�2A�1�&{ "gsE3� j }�FIG�75)2� "w4�W3:WU\ =����6�FHAf5)qn1Q6�v� >� R�!} � Am�m��4g\ &��7�Qo�*� �"�us� & aA��T �'�� in��early{R%e, na�#Q�&� H&=&�p^2 +!��-a^2)# 4 +�� st.\cr &&=& 8- &xG( "�d z% $m^2=� a^2/6��g /24$� *�w�%$ akenA$a = 5 =Q= 0.0�C s�vqe5&� prev�  -�,A?0subject (see,e�a/,? .)8,Guth:1985ya,Co  6wv}) Al�#%0ee��is� to r*/�$ig%�!�%��)< C%# ����E�si;I ��F�.� %�.�ef� ;!1!j"j5*$3��Q� *)A��&"56�& 2^G��a�R"#"�!s�4nowC� r"&aN0}!I!4J#G4j�8N} \kappa_j x^j>��Xco" Ws $4$ defin�&{-�� �NHKr')��}Ei0��L�>0h"ensn #o>�"�&-miD m*�7ed9DF�$V(x+\sigmaT5r \ ,^j=z, tj {j\),e k} x^{j-k} v^kj$�K���!�f1 K �c"� TF n9a3Of2 $ b%<V.�E�k��� �}Q &!�v*�/&z.*� % an�" let u&w EU�F��Vasym}!�!�11|E18 x�D4�Y< 80 x^3 + 16 x^4}6CS;Y$A�� "� `a:!0Yc!*at deco ing �./V a�a&�SHO:` � aMe-��7A3��h�sst�2ice���)��o9(�hM1 ndes1982}3.|$ S ity $--�EB� Q;on*CndY!si�aneousl.!a�A Ez.woH"� �gi*_ �7!.%!}R} :!'a �Be�B6|!F�( U%�a $F��s 10$�/�w�,!�h%al9 mH�3.889�^�- = 31.179.40e findŹ��g b _A[beF [)Z-.[4229.11605104}5f�&$#�S ct. 540  40$ # !�Q()583>27.431$,F�S �� �4z�4600459705899}2��S��a�ults hol�%!|6� .< notidn#I\_�$1�8%7U!�J��_��m� a"�  $x \d& - 3.97A0In fac�E�r tend�%�� b� > -�$s a ���in:&D�a�IA& less l�."�clT9�U:a�UR� �9<K !7&K2aJ���y1:m !&,��7e�B/-�$ �MlI a=W igh � ci���a�B�erm^?��-s�=a ga��o�>� lway�CA a Taylor�:��=�Z��<�%A1W6* easily �1 2�^^io&E-�e� �r�>y�. $&;� �.Y.~h20�$ta�!%� ruuEq.�� ), u�h.���R� $WJ��0�M20��w�� $55� toge�4X�Y�-] KestKAi��������[h(:ro�box{0}^�I"!4�� ?tIP5�����$&�Ux d ����14�5r��0Q�F��:Wn�A$A<�umqw$n$�  plus�| tria� 5(d �I��QaH.� �edMz}R�y, Rv>u�JA�ive �.rsRt�7lso�����er��s9�e���5� \� {Tim2K"��-&�+A a`J4*K2!wS�7on�) es} If�A�Be����gV�F�  2) �e��.�*�)t�2�b C(($\hbar=1$)q�&<it"(d}{dt} \Psil_$  \ .&�2�C "�A@ ��|[39( �DNa+, i^G"�V-"�!/ t=0$�ex�aN Psi(�-=0� !�,�C ��3�2 InitWFP#nd���Y-: k9A��n ^$:� �tj�!3if !o�(Oeq3M�9b�!9RZ�6��B� p.,c �et6,G .�1�sf�9R=-t�Y.{d}_{nk}� )4k%{&�-eq5B�$d:�hL�$kv �w� A\Aj$n��k&�,2H�. � �H�3�hA�&4$A݅wbeA�r�1d��" -C���$�At$J� A0, 2�=Dc_n5?F.� eq5F@�"!#隩��E!r)| s�V{��Yla)1��'�)0c_�mbd}^{-_+n�5"�/�J�T�2�!axvin2�3})A�ɌF�M�2� $!X(x,t)$e�nj�*��$t�2SF�8}&/=*D!�9V~))m�d"�%QU2� �X&*Cen�GaBian}\h�H\\i�G2�,� p"�tu&E~�v?� �v4�&@B $$E�!(�5+(e m}{2C7 �')�(4} �7m) /4}.COur tasqito�aN2�$c�6�55}).E�*�8 ity,F�a=�It iP^*�K�o� dx =�8�� \� t_{-� }^{+ �� &&^P+/2$3nk8�8dxZy5��6�)m/2 + \@9. B*�l��of?�@$y�3 x$b fA3N_n}{ ,�) V�%AN�)� ; �}{2� } y^-y) dy��62S !���-�9y)$f@ !,鳉�([n/2]} (-1)��Ln!}{(n-2 k)! k!} 2^{�{n ��6�&�VNhc�Pa�m_ֳ\ J_kRFF�J_k &IS&b� y9M��f� dy =m.1��12}-�} =�%r+1!i\iZBz5��zA>dzA7 \no>�A3f�i�0$ un(�Z9ven $�"2 �q�1AuNa6. 2c_A�S;2�yC- )7VD2� T2�( �)A� A�Y�2 10 -k)u eft�{; k)%�Gamma��ell-k+-��-��!w>m:/6�g!� ��#����) �(>`��,_�30�q"P t6��/"x% Q��\_,�F\l/ 0%�E�� �$�  \T�/!dxNIn�A�$"�  "�7N{ b�j9 ,E� a_n^* \ aK �Qi p[�5 i��s" ��1 !��j��_S�@x �%A$�&� A)b�e�q.n1m= ��j��YJ�)k,j} � � j}2kj�fA�eqE�% .. ���k�<lo�L &�FIG3}. Ano seeK�:ul� vast�her�H to H*�G8b(?Vcal;8n` bDs%/uis�% from��9ed�&FouriQ:� O[}!A�"F �Zj�-� � � "9z�16�&�1.a:`�!usG �7��l &"Z�" . V�I G�Iof�'��X;Y.|�%�"�C2 !�91d�� e ""0Y'$x=x_o R�bŮi� !�6� �26� J��H ��hi�襡�t��t��\1N5E\ z j� �h @�2�62}(x- mu x_o!b  )^2}�| ^2G ^2/4#� � x62(� 3>� X>� W�.�>4!� to � �� �/2^2) $,��&u !u37� ?6 J�pi" �(�x_V�!�N- ] y�&2�� 7 \Big(y+ R�)_ZV Wta�A�He�#� vQ,��I�B.k  );s �!�&=&a��� j�]Y)^� k)} *yX9-y!�%�."� \ "(G �\����%n-2k}  _$jjj �Z��?-j�d� Nn &\$B�E܁ h��X -eN�Y��2&Fj .2� pI"�}{k! \ j�k-j?216 ./M" � �J -W} K_j \,Z�FO/�Cjm�d�2^{(j+1) \�� [ 1+) jj ]Ao� (j+ 1/2� � 23FM�3Z��$ c_{n:�n�e36�!1!.��F_ )�� -k} 2�(n)!�>�(2j)� }E` &�� F 2agX�UY2j* )� } j+1/4�[R� F{h; xaverage}x�ex�� n'&/ �N4.~� four "� C� $!�� dr"  i�5'1"�H= 7(97"�nhe\a�0s>�0-"� ** �Z�# s $g=1/248 �;/D6})!' $x_o0-eD(0 R z4 84 aLceHZR� 9}�!h&F �"=i�*�%��mJk +a"�*�&9 59= �2DC�P�P�?� �3�,/"�;��� s>mb H ��"EL� k@al *zZ��"�etooI3�&= A)AM*�""l&� 6v7Sb]X����)al ��6J�� U�%�Fv %]0wo $:5�'A�of �dNi -$Mbe&0*r7a62C!7SHO�a�nonb"�sCxin&�b9-�n �e �N�"/B*� �&j&$N�! is a%~:5�H�"�%,�-N� , innj!"E��B%&�ab�8�3Li, by-p�c�:�!@�r�B �, gidm".�x'+!�gy�"e . KnNz�F (�% ir:4�F�t!J &fXD �N� = !Ak@�B_0  R)Z good9��!��VR $�V�e�dAyst�Z&:)�p�U��0biWt P.A. ac$"��es�R�Conacyt�ALnt no. C01-40633/A-1�Hof Alvarez-Buylla f\M�ukt�N>k. Abu�Fw44950oPROMEP.��*�o� *{ReE?�(&t>S�#b�O4em{DM} A.~M. DJS d�k Mosh}it�j. CwCNbf B21р352yy88)�� R�b{A2PH.~F.x3,  �&k��vQD4~ 2560Q93)��RA�bD} G.~A. Arteca, F�Fehl{a}jl�wE'Ca>/ , ``Large�n1�mm�dA]S��I���%m�m'' (S��yBe6@, Heidel?, New Yo�L�~,s�qzhTokyo, Hong Kong, Barcelona�l9�x��cy Jank�<0H. Kleinert, :E2�7!�27�5.��c} V.~I.�calov,MJ�ythA�-�32B|23|1.K&d } P.�n�y�n%QAe PacQEJouenof%�ics eA�351�y4:f�_Jg,.c!�$J. L\'opez2!.� A329�5a�2l TPEUSt���%F�23��1ŀ8:&a9�AA��fj�16TN��AqafS\>yit{AccepY�,pubb�=�S[!3 VibrE�@} [arXiv:math-ph/� 052]}��a 1�AH. Mont��=*.sB327} 15i�4)� Q��a:R�{\a�enz, >�4050302�:bFE�M�, Fy��#�,z� baZ` 70142`F�a6�6UN�9036FI�6G.� �s%��96�]Q2�Nz 8036.��wb���p:���ki��D�� nderb�6A�12501��1)�hep-th/05E9.Q�_ ReW Quic�j H.~G#�lOc.;R�31a68�e2��Q!D , � -Veg��Pal�rE�R�28��03 h2)�lEE�eissn�O.�$ inbo�ZB$A#� 1189��2W65 SŲz�^�Y�6��Mol6�4� 511�82�*��*�:H. e S.~Y. Pi2�2��89�6�:7F�oV;�� Vc P.~N!Canciofffj�383 �6.>gF.~C. a�~"�zzitell x�� oliv6�.�6� 0450���J2�؋<12448]. \verb''B>i _?Z&Hv� 6w{a_(} %% \addto�y��wFy}{1inZ!hwFt"s&�y,hoffset}{-.5Av:2�wams� ,amssymb,Mi�ww �0and{\bra}[1]{� #1 |�e#ket#|�:#bra&26I #R� � t�wE;Bouncer�Wty re�'s��in�lece�muko unbizbserv� , a��0{Adam AzarchsNvlifornia*%�0of Technology�g 9�2�q a"�uv�,�9ed sumS�(op� of�&�yizCb/�*=A *meW�� U_&��<^,���a "9x7 Heis'� NzY�!]P �a 1a~Huse�vway��ify-� atibzzc =�. Of=f�l�:�5�hip�G��`B�' S}L AEE_E5�lwML��%:!sF49�i Qb`srK.j &B�&�� sp�Q!d*a,��d. {]pMM&llo�Y5� �%-mediat&^g,of jG�V"�h�,�q+2��Y� }{Back&:] p�!�$} z�%��Hog� ~,Yq2�� �w �phre�in2e$ )�w.�6r�k�=aA�e;��>1�c!�mA�pra�5��> �!�yo| �s situePA�*&�i�a�o^ ?kencsi}�&�=Gqis $\{%Ha_i^{(k)}}\}_{i=1}^Ubs�@" se pur3� $$ H_k!;� 9 pN \log, $�N�J]Sh�#me�*!�$=�>!�`am� 텓 y��out+s$i$��=�T = | �*�{M&} |^2.�4 David Deutschd �Q�j:�/\hip $$H_a + H_b \geq - 2 �61�U (1+c),1 $$c&(max_{j,k} |�4j}{b_k}|.$$ Ma��c Uffin�ite{m }Y�z�!�to&mI6"�eq:pairH V�cm�Fl�_isn3�!hip!��]*�D:$c \ll 1��+!�. j� so-cJ�dvj (or��s),U��E�h� !�=MQ�4{a_j^{(l)}}|^2�8/N!�]�N$k \neq �'Ok�<�0�"ivo��}ɮatuaEpr�A��9# ist� $N+1$ >�. �nch�~%�saQmp`<�-QH�_w$mn�sa!�M1]b{a�E�(N+1)B�V`'ubsta�T�s�1�I�7T�}br�u�oP;e� ir-wrzn�8QplQ�*a"F�wea�1&,F�2�NB�D+s�Ga�1te%�\�<c�|,)� as encryp�,: like"F8%�) "M�ov�5e�Zi ��$M$.�,&#a . Weak��e"_`A&med%modif �V(9Xeq=2�3n9!\6XMY7.TMI?FQH�e��q�?R�*�a̩Rs�"J..6A�!a�ach!GeOh� J�A�)�PsubI�up�z o��B�.R ev� �q &�d, $AC-Mm4N"_Ŋ�+TQ�.v!Q22�=QV T)\a�{2N} +�a-!�uN"- ac� negp{KfusSs� at r� �4"� �F��y�e �!��;Ph$��! is!�tA�yA,to `locking'��> ��  1}. yg �� � ,oma� rE2$$M \sim N/i�2�v2q,� f�{R�Q%12� \} Larse\l }� Z�!�l�. H)>f\pi" \Pi + 1��E$$� V`;i�i,'L;T\ ["�]^2K5 \Pi�EDy� Dathrm{Tr}(\rho^2)$�$�  $$. "B$Ix1�^q �\leq 1�1WLly%C{J enuma�gexcAh�*aneTnrpisum:!)�-F -q"!T - M��*N@Ia8F�&I�*La�Z!" posi�>�?s �a� �Mo"�_s�R�*w!Tn�f�<WE-,�4!�1�� 𡈆�pi�} \_{k��M2���2 N-1+�M&^)MB BlYVk  - \l'qi_k$,�"g ��W�<�Q�n�9-:�"~��og1���B�b�![�Bp"yG:�"{�Vm�"cg�{ED9� �2}) vs.���nN W�Fj das:0�[�TpX�!��er2� 5�1}Ɍ22}�g"fg:>�"b 2�$]Vat ����d���A�M� �"���, c"61t�%�. `$5�A*!�E+E���K7{��i m,~m4 \��bb{N}�8 For �wm36wi�(1}{m-1},~ z>E �erk �K> 3� % nvex ine�it_;Y�:(m - (m-1)(mmP- 6�m �- �na�]Npp�Fa�enu! 5�Ig��(E���E .* .b,a61g:��m-5 N+M-��M}� )� )V��'>d)u �E* $^c%�rm{ceil2*e�i F ).$$�'� U��&�EIM#&�a|. R��sF=� :S2!TfAH /)N$ (n�I���Fn�)�!1#�ignR ntly\$d ��"�}Oen�Qi� $M=1�GM= �>�'ced�' ��I }) iE ly m̎aq�k#e�e{ NM/(%�)S,t\�dy{� �a}sw�Gm�p�snientcmlio��$ystyle{unsp�.i�{� icUn"U�-t*{A&## ment�E �m. �ank m�=n oDrslhn Presk�U�Pa1Zk Hayde[p�S(r!Ov �$�U. r %�0nk Rohit ThomBL nd P�n Knophf%L \ helpI�untQ��n nast!�th��/ dono� Vi�o NeG$named SURF\_�KJ!��yn�� �� a�& 4e"�%� [prl,aps,�P`icol,epsfig]{revtex} \ren*MՐow} %\g6f\K�,20.5pcB7wipxZ542 5��tOH�) h\�Vun�Xal i�`� gyK}"ݐI.� $GrigorenkoE4D. V. Khveshch1��DNN�7A�omy&ʐU%NG4| Carolina, Chapel Hill, NC 27599:u���&�W�kstruct LQ��LE�U�A CNOT�e�mf A�t,r=ik�p���;ly����)tocol�&r�NrrRMN(8 �gle step� �pr 5 "�Vun�! -�c��s� , i��q~,�H�!�e�{�qu4 of%�[��M. �B-6%*�cia�mfurV ex+P�a�e �|b��J]e-q2�wo ��'x s irG^i�4 Y #Ezy 9�\��32.80.Q�%-�qos}{2} Ac�h��^�� N��*;`�� quanLi���t!*ory��"�+�_� x31�1�U�+_.���le ��M%-z9#%D DiV Pnzo(�� desp�ts�v��96d �4�E� i�! logi�vcircui� i!�ac~R�a�i�>z �;�{!�e�short� poss%��/%�- ICan�-&<�,:,low2;!< nce�KqnaY�mpMW� s, h1A�l3�r� cru��m�P ant,��P real�<c ��i��^Q su��%tP��em�f1,dissihv�vironaj.< Aqly|-r.�\v�;�mptd+!-� X�wn0f��Q�Iby ��!�����{F' aV�!#.e����eu�*�Gs ^1most H%�"�y�ze���=U�a typEm_,R@a tour-de-force !%��/a~�? lomaa} �g%'� i�P:c��))�.!� rregY� p<�s�q"S�rw�{t# �Rrgelyxcur�jI�-d�� sophE:�p"]�"�z6� �{voked5��ro�^�f�!mgoa�PU�!�a�d V�w.`|�4N"�-e�2�?S��Q�of nonVazmtegral-"�3 ial  s��s`��ysXit�d� �K��v �TW�0ive algorithm��(kosloff}. 2ei�!��f"� �pla�lt"Đ͈h�Tr�e'�E=T.h�5gE���/-j "�@ "�e��2�9���s, du Vof�W!�}g rM�c�ant. A� �."�\A� �� g�pTy� SWAP�#�ich1�������g׉"�pphase)y�#-�I�ѱ� i�|t.�N�: >�- ����/.�F�papV w2� ne-!c�. �  ly�d!��Aalds�we{�}I0q�{b� s?rg1�B�߈^xd�� ,?�7ll ���c���2N '�A  a 6�̈́LO`Q�fsol�+"�v����d��ion, ��)ify� ad!eݹA0e٭�J� aԁ$s�mas\��s dens� _4of��� ed�_)x%�wa��1run�mf�H �B сl��p���((vb �{)B�F�%�Z}~.:Npr"�u!:  6  � �}of)wum"d0al evo�T �%ic*� xZ o�kAHE��o Am�um dev�4� 1� } ||�T X}-{ $ T}\exp(-i�? 0^{t_{0}}\{{H}}(x_i(t'))dt'})||\toh$X�%)b� �X_[��� ga�E�n =v*�U!�!�t�~ta�J� 0X� Ha�$�)$*vFe� ol "]ba�� ��lyv aiU a_es:&���$| f|=0$) c�7erq�!�=(0,0,h�&�E� noist"� �woIZE\.x��(?0�g+ .� p rvoireH a��M op��mi�N�glӋredJ (collBZva_�/),��8���-free�j)�Dp��ris� m?$#��bao'Q�_^z)�$6"�,I!;edO!qa��}�!4/��%d��B� q��UamH}_0=�Larray}{cccc} J_{z}+\QS1 2&M� 1&J_x-J_y���x;- 2-W0&J_{x}+ J_{y}N1=P! I2I1 In\\�x} y}& 1!&.<Rcz}z� ) � >wIn  KA`fac[,�*ou:haly!ρ'}E�&�*�IRef'�t:� ,Ohmic���q@VY$�"�[�;al&Y$S(eN)=� dte^{i  t}= �T (}\coth{ \�Y$ 2T}\Theta ^_c- )Z bandwm0 $  _c$ Dm�l� Q�e\pf A�ii"��-Wrelev�0 type��e8super�guc; Us�V+NT<6�a� BctA� itg u� Bloch-Red��(��Jak-t !���$Markovian)�s# �v!։ span*�$[sAc1 u�5_b6: % �"V:! � sl#w�4}:f8r �}� dot{*"}_{nmA4 =-i -� \; (t) ,k,l}Rkl}\; "kl"},>o4b W�q-E_m)/%_�`n,m=1,� s, 4�:�# i!g"{Cie&�/thez�Zb%�H�$x%� tensorj#_ "} �=��lm�G r \LRq_{nrrk}+!nk!"$^*_{lrrm}-3 lmnk knml" Q} � u�� �\ak5]=r[�0� �%s �S%��* 9 >ay"�9} Re\{6�\}�� 1}{4�F��=^)=?[\� �%2 ! + 26 2 C]J�L�$ImF�$x�!�-Deo!��EA8Y�k A�(custom� ~.��e�"s'!>ᖅ�we �k�%9Ig P(t)9/16I<{j=�*16}Tr\{�%j(t))^2\FZ�:��%9p&����4�$16$ disu*d6�s:Q 0)=|CO _{in}^j>< |$, �] = ,a>_1\o� s $b>_2, (a,bu�4$)� ch A�os�4f $ F1>=|\dowA�ow>$, 2 upar   3>=(.0+|$)/t� 2E{�� 44>4iV5 . BT�� Z �&**&� *�sp�?�eX*� E� \t�qt) _0-t)$S!�X� $t_9rheIv� �&4![mut��)�($H�,K   ] �rt�"*2Cp���$c�quasi-�~�e.T��G�Tj ence:.)&9��*?����I��3sx!.��1] nt7 . Tnat�!%�V�!{s�G�6�+&w]�E� in �oilya} !�decay��a!��D!@e � n ids paira�6� ("�umory") ��0to����4M�"E �ܭ��=�. ""f5Zs�Fa�u� >�"Zo�[- 3e���jo�.C` �f&]l�9du�by tue?���am�!�GG�#h*�� ce-��T)P$';v�r�.n��#5})�Y*ۺ ~"&�r�8�!;sM s�1�rrobo�ng�d�o� un?ly(�Gx�`-*�)6��["-eZ6of=�Q5 owx/a�)�M%gm�)U�:a��2-�so� !�IE��%9}* I�a*cm)�VK�5�e�B� �rum_{i�3 j}c_{ij}|U  a�j ! >RV!T Kf�2 .���O$3e���`B�atir�imum MY1&� %R�(!>I�2��z/�|�,�AB#�����cyr� cont�L ib�� <WE�,�3� ing,�5�-es� I�una��L"A$a��&a�u�e�alC���e���*�&�" illufM��)L,!�DO1� �\fab��t�9lui� ����($|dP/dt|$ ((rA e�m&u he&� 6� ,"��2Ucz%�im5J� J:� .$)�Fbn�Hu��!��! $J_y�(J_z�2le keep �!�"("�"��$�nd �k@1�v�i$J=Z {J_=� J_y^�rb}��xN�On�yvP!%%raintAX^if�$by�f��b �$n�R_!an@%m�� i�Q�$J$��,-3�#�*9wan��leakagey �"��*YHi'us . *co%sE}ofM�*= �,WmQl�u�1qU� ��2M�sU��"erv&-!��d/ t��}�"\!����F �3) � 15��low). Fis.*��bei��AC�@Tt8� {*D,I=�#y !C&v � ���)st2�ap�>���"�7ve# rov�&�qa..:�t ic (8��te)&o= . Evx����nd�<al�t����  gBB�%K�1��Dgy gap ����iM��s!� � um= �%s r?9� e&T�j�J�F �cF�en��a�"-&��q �s�5��ź6�setup-�ɮOW?v�A;�'&(w�!�#Ak�Oed��V� �0 bE�� F�A &��iz&grob��H �s. S�aX�����m"E)5?a>���,6��]�%!�satisHm��aa Co�r}���.7* � �:@rt� �&]�e��ng� �X �"n~iz"r I� �Sbloo�7%[aT3!�*3!�`�� +�"t_{}=�([1\;0 ][0\;  1 ])���J!Ba�7oa"9) mpldby 4���1�h -�"d loga@$!:�# '��X�$.P>.+s�&2>(��C(featu�Cix�So$�mbigu�2�"�10}��a��-B =i/z�5{(6�$)}=C(A+B)C0p>� �Pi���Bt���!��%�"iF�Af| 0&\\: -\pi/2&\\ % �^F�+�n0��t{E9>$9(bE&\B!�1�A un!�E�ى�0le "mismatch"�$ >rh�I�.E#ceJ<B=�o n_1�8ft(-��� 1&1! \\ � 1&1\  � 8 �+ ^2b�%]6Kf n] n_3bW%^x ��0� �1  \\ %N� (�e [A,B� �,-D9�CZg}t_i�{A } o}} � 0&!d1 _x}R�:)A.if� E3��%ǟq"ExF7��e? [ � ���hbSp%y#ng� 0)E�an"#.yD[q  ger $(n�*/� inu'G$(! �` _1)$&w��Eqs.(12%w (13),�j]izoe�m �I('� "�'s����,e� ival? "8%� b| ���Heb-Q �It��p�偓3Y��a.z):+� reve�%�m8%���x"��up�6�(�8hi_0=��4�+�o�=%pi/4-i�����)$) ��2���%t�� tcy ($E_1=E_2=-0.875, E_3=0.62 4=1.125UR A��ANch��Q5*�$tr 10}):"��,1=J_x=J_y=0,|2=1.5Mm�"1�&~ =J_z66$a��af�'�(�Pv�2i� : q1/�)} I�2�A�rU>� �E2ed%� a�s)�6q� ,3Is[-��)����,-�l���- �, >�$=whaley} Q�A�a(�Y A�'�> {2} �� ^x_2&3%�%2u big)bD >z_1 '�d� xRw 424��N*4��]g 3��w�W16 !�"�� %� � 1�U!K* *�$sI* ZCs (4)AqAG��:-dE($\e<<�M , ]Q s. I�fi� 8,: ,�J{L��1V &S L@ca&�56��, $8^$15\%�!Xima�)B**�.ME"�$�l-8a�(��OK�!�*aN6�Xr&~6 �-.c��2}�3a��� *�� also�y b6 !�~AmFusi�RQ7�f�en(�)�s*)e��a��*<sőJli�X-�6�2�W-67A@ next�/E**� *� -��� ��at�9!`���c �s;qn(`be%�*�3� ]\"�4�b�0aEE�is� N9may�~2�5R#A���V)2�A�I�AUWoneth� , ���x u"ն�!�� �#�g��7�Goq\��>3�"�0achie�1e"�2 �Aa� $X�$� chyt��t (�%=U&�U_2XU_1 ?�U _2Q�$U_z%$E�$! ,2�1�Lat> 7� cal,!ya�,!a $X$>�sh4Lb,�ftu�m�a�F�� � t��/6mQ "�a3\A� ifE�!���)��X b��a�H5u�5ly J�@�t$ng negligi�� towar�5o�ver@B�0vF�6Ҷ+5�ceaw�i2!$�ses� >�0 0!2S�6 Makhlin', V6�?� V#*3-��G_1"tr^2[m�()]}{16 Det[G$]}, ~~~G_2Z1-tr[m^2.B46A>k<"$u= l ^T_B� X}_B$,&� B #Q}^>.' QN!qQ}=dia.�i�i� -�&�-i�j� sh���A�!�.�a�LJ8 $G_�Always&�a:��2l]5��oN�� rict�!�7�IH��bJ1>�'��way. OnP�-ᜑv2eT"� n�Jr�;� y U$\. SWAP}$� M�$=-i/4$. B-�!9� .&c�!(�m'�T 0��elf!) f% iy v)$A�1+FW y���45W�?��ofF�ERu& � s ing�b� n im&�VlL*�:v��e�?did�Hro)�r6��T�7chF2/flux JoD�on "�g���inB ,A�e86 +B�*�;@foc�wn!� /;& #friend+!�W(dubbed "ronium"�&�!dev!R})�!�i>L0� tu!�)1�A�AaloB�0)�~ �aΌ� , capacqKly #��in�+j mooji�9A� 2��@2��A�3)q-��Sz$��&U��E�=J_x\mp�{�11+\/D)^2+(J_y-J_z)^2}},.} E_{3,4}=-Fpm>F->F+F>�C�wuf|xak�F�ic��%�% �# "M� (2`2= �p4U ��3 �c��E�n��4, � E_3$�u �8J�MM$0, ~~~~J_y% �^2�()Thus,A�"%�b ��{a���bggA�Z�u�� it s��o{ &�tFan�=xC on/*�>&`Yh��4J�W3{1w/I/ 2}}( {(J^2M{Al- J^2MK ), �C"��F;}e^�.���)�2��'rout� sɳ!�-�}F��;23'romero}�pus0!�*C[%�� �|e6as�\as ��6"�� 2.3$A�H���'5$6 l�]�@")�2W �8e�reb� � ing�/ $\ x6�)" Q� Y� $1-P(t_0��a$Ab�uqibuit�!]��B�-�@��rF;���e; "6:�?-E��$F��0�jMce�s��� l)7V� ��3not}�k'ly9�@ofݲv��[?g*�?���:"B" }�>��0$. UntG�2� e B-% �ן�cp tw@ ��K!\��.�6\ ?)��&= P�Uye� �"P$&G��,iy��4A�ach�@<��= anta aUn� o�D �3��.��-2"VDAua �o. "W*b�o!69=1mb'��=J�.58, �@ 1.71�nn%C%ar-PB���?9�E����2��!)6Eu�56*}�X =�&y M�% IK�� _ed �v4.�w�per)� &?,�ju|*c���h� VI!y2ӱ��8My�p�AD��e��"X�KY�J "� 9pashkin���0Q �W�GH�k$JY�G��>�-(�3J���tiv,v�'�G00�!�!*.7�?�%, � �f�s*�is� HHo Hio&$-"!�"l':,* , $1/T_1=2}Sw �//�-�<P�ed @yU�.� P f�$Lof �� o1� 0.1$!b�% �7�b2�1�;� ��tL����Ta�Iwe\��!^M�I� �o�^oj�b&�@2"�DQ��)^� P\1-P_{B}�+�03$. H&�I8?� �gQ&?�e���!�cim%'K""�t^ $),FQ!���2R*$%�.�dom�L�<% non-�8(� ��ly��f$x�&)N� "bO�e�(Asamgy! !b M� wit�:+�,G��,$�x��3&��b�D��Aq�$v�TOz)�� )�#>�15?�� vor��mW�AjE 27$ l�4���Y�2gQ�]6>�predi��)�fa��o�r�/Z�&7 V��7�. im 10^{-4�e �� �*^zraA-m �codwA"5O�E- )ot�,�  6�Z3c��\L gine�-��.�<&�GaimE�F�1�!�̱q�W ��B�"�� =R� 1� at+\he# �ju� �E�at@k sFa:M6%B�vWol- | shapGq�."� s (f�3e�)/!� %+�1m��%�F+��AD���+0s, in the pre�sence of the intraction with reservoirs, 0pect to varia,4s $\delta x_i$L Mdcontrol parameters appears>@be reduced, thank8Pquadratic (as opposed3Ha generic linear in1@case of not coher�0-wise optimiz�) depend$ upon such.�U�minima�dev � fun%pal (1). For example, we find�t�order�Dkeep $1-P(t_0)$ unThe $10^{-4}$ threshold%<tolera!�limit�$(de)tuning= �Led CNOT and B-gates'.uha%[be bett�$han $0.3\%%�Ttheir values. Before!�\cluding, it is worth men!�� that our!�$roach diff!� fromZX previous proposals for^structH"super-�dt" qubits which, albeit be+capablE�provi� an expon�(al suppressA�of de ZTce, require at least f�physical z z< are governed by�(HamiltonianA�aAsna&e!ft~`pin \cite{whaley2}. Apart)8a larger number�> �E�encode6og� one,E%condi!�CvrotE�al ine�ACm�.�8is unlikely toA fulfilledA�$any realisa�(solid-state9!ere (e�aryA� liqu',NMR designs)!(�\stantaneA In a�A�single-E� two-E terms�Eq.(2)%�(often relat�; us resulEJ�lo!� @D(${\vec B}\neq 0$)-�break  pin-R=4. To summarizi�A\,ent a system��apmto!�Y�Psimplified (one-step)�u�@ (highly robust) 3eah%�s!�!�!99$universal e�. The JD stability against.!�achiev)A.|choicep!�.2�� e�i~ee�-deg��acies -�{a5�gy �A rum,I erebAk:�:�!�x% w cess��Finally�zanticipA��� �l natur֝2h@mechanism exploiti th��0k should make�possi��$to furtherr ize �WI�sec� sequ�%�9�as wellir�XmA�m )� T��arch was�or�by ARO�^C�~Lact DAAD19-02-1-0049E{by NSF +@Grant DMR-0349881�$\begin{ref�Pts} \bibitem{DiVincenzo} D. P. �, Phys. Rev. A 51, 1015 (1995); A. Bar�� et al214Lett. 74, 40835 D. Deuts�@,�LA. Ekert, Proc. R. S Lond�449, 669 M. �salomaa}D(O. NiskanenJ�`{\bf A67}, 012319 (2003);�;@, J. Vartianinen �M.S o.� �, a(90}, 197901`J. .P� Int.kQua Inf. D2C>42�Xkosloff} V. RamakrishnaPP!� Rev � 65�63405,N2);pP. Paolo%{ R. K W, ibid �68; 2308:32�,weiss} K. Bl� {\it Dens��matrixa+orycapplice� s}, (Plen7New York!081AX U. W\, S%um diss�ive��H World Sci34fic, SingaporeS992�ilya} I.A) Grigorenk)D.!RKhveshch,�0d-mat/0312349.to�(s}!LDQ. You, Xuedong HuI.F� o Nori.LH407423; M.J. Storcz1�  q,407780; Y. S%nstein%LC Hellberg,i 0nt-ph/0408037.��,} Jun ZhanglE*i�E�E191!�27903-�;]93 0502 4); GAm\ 4231B, ]T9B 4230iz6�devoret��V� �Y%�ceI� 296}, 886�A�$C. Rigetti%M�eI2v 12002�mooji%�E. MooijVp8aC1036 ��<9); I. Chiorescu4Nɜ%43!G15� ��romeroa: M. R ,!�KohlerI:P. Hangg:8 9774.�<3not} Z.-W. Zhou�9�)�aKbf-�105��6}pashkin}AsA�S2�2�821�,; T. Yamamot� 9�42!A94��3);�iAstafiev`]�11216.�I�2}a�Bacon,�wR. Brow��K B. W� .�))�8�� 2479M�� \end:�0figure�,$center} \iL |egraphics[height=0.4\textwidth,a =0]{G't10copy.ps} \vspace{0.3cm} \cap� {G�pur�=decay r $|dP/dt|$Sa"�� i��coeffi�s $J_x$e $J_y$} ����,,b�3N� cnotv�$Comparison�wee�P $dard (fiveY 6;  { "m @ ,:+� heMp .} r! docu� } �K\�class[prl,twocolumn,showpacs,groupedadd�x]{revtex4} %\usepackage[dvips]{M3x} Jepsfig2 {sub5�O{float6*amsmathB symbB font Sron:�euscrip:lZ���eA�6phh�6"eGt6@tabulaan�ps*6>{ *x6r{endnote!�,newcommand{\!$rmb}[1] {#1}} 2& frak $ J"vec !RbfJ#r�$it FitBMnormal{>�itn � +Z' curl (<{\nabla} \times F�sgrp})cal{R>}t bb{T>p?G> grpwv`G}_{0 )"{k}>/l>O_{b,uccord}b� b�^ hB\pl�% a}_i:�prb}^>rJnG}�QgBn!8ir}{D^{(�)>�%'=,\alphaB0! /V^-!�- star�2Pcosetgen}{\{d_{\nu}'| �s�\�re.[divFy\cdot �C�  Highs MaAals, U�� of�pMexico, Albuquerque, NM 87106�( \date{\tod!@u abs�} \noi�t Q�YrZl$nt cavitieMsa.l 3 ve rega i�eed. Dir pass%measur�qU  �e \inj�> uresY�5 InAs/Ine-a-in-a-=(DWELL)�$erformed ue�an�,-fiber-basedKbSA� niqu�a wavelength ($\lambda\sim1.4$ $\mu$m) dis�-detu"f�dot emyIbO2O . M94�!5$s.�b�aon�/�Xdig $D=4.5]�w"se.]gort mod1�cold-E yA�� �� s as��$3.6{\!}10^5$A!�-contai��s� then studa�through1� pump!�at ro;emper. Pul!��Uat 6�5J!�s cQ��ak lay|AS!�s,Icg �� of $E7-SW,���!�estim��er�transpa�8y level. Room-��inu�A) o�A8$is also ob^ag� u� \O H{42.70.Qs, 42.55.Sa 60.D 55.P �ų Re� ly,fpla�sV� (s have demo��Dvacuum Rabi splitt!in!Vemicondu���s���5{��8 (qdot) excitony�Uu�II%�yY8ref:Reithmaier,Yoshie3 Po}. ThA�experi� � in m� ways�fi�-!�potent!�of 6�E���#Eahip�Le2n�Pelectrodynamics (cQED��. =fu��.�,��hos8 volv!D18s�E`fenetworks9%Cirac}�$will be ima���*�im�e % ar�O�\*!�-9y-��One cl� I!n&�i move\M5��1�_m�strcoupling�Kimble� defi�x��a%"�atom-phoAO>($g$)} both5-�ŞA��kappa$) �m� dipola"h ($\gamma$��In%tic�� eKioAJ$g$!n���V cbJ�[x�Nens=&3e�oscilla�0 � an t�place b�xeffect%�"on�troy #t�exgeFy. � each�Refs.�a���,)f-�sB�fou=!oA�domin�tw@)���,$g \lesssim -L . A! e low2jhomoge~]s� self-asseAXd�!�sE�yp�lyGeweV9B�H$}, corresp�ng!�aEJ5o�PE7/2\pi �\ 1$ GHz2�adv<ge�to�" elop)��a8a�2�e��$) e1(i=q�}�} $Q$ �v�mainly� &EN5�ol��AJeLc� emit�l�.��A�.� 0.9$-$1��N6 �j�%�9zVj}azi��1��|.MO!� �%�Q-� 2�a�e�%H8=\omega/4{\pi}Qe�AL!+%|lowI�E�!��ʹyin)x!5#�8ty fabr�ng�5t&#�w.0! W\emph{!�m }�"ed%7maximuቩF!�p�y� 1e�"5  �d (=Figure1.ep1 dth=\uO&�{Scan � � $scope (SEM� ag f: �!Faf�$\e (a) Si$_{x}$N$_{y}$ et��(b)-(c)^ u%0cut.} \label� :disk_SEM���nd!u� Alongsid)�d� ��!�!�NA�'#has b� #n�} prog�Ad o ere��s!�era]ec�E�vR�� V_{\A{eff}}$)r��$El�$ ew y�'�4`"ete�geometr%un&� = �� , rangA�� InP �zic crys%&1Q($Q��1.3}f 4$, :�%(} /n)^3$)y�&�4}A�SiBw-Akahane2 :7}�4Š%��A>k"[5[5$,J�5:�U�. Of*Q�>ce�a�^�I�t $ostq � � �v. He�w�  WcreR��$D$L��M Q��sat exh#"E�f�v5F� "c, a� �%,�4our knowledge,�ee���ighes6z�� A*b��A��Vat*�GayralE+MicYI8Zl. c .^A��&� q*�F�YE[�Liu_G})� a� n�'�0f , so%�J�sF85��&J6}��%��,ly non-absorR.!�e�&�stit� W+ce J�invH{E+ �Pluminesc<%1�b s,e��s"�,B@����*�).�. "P�2�ūch$(�Yy�pr~he�Lu��ough �u-"� via.�� taper.��4"ma&d &�@($T=P_{out}/P_{in�1of a $4*1"Iu��a S-A� Ur�*��/h)D. }x$)W6800$ n�l�N�i�,�6�� !samg v�(with ${Z�2S�(�* gr�_cur�+!�L�#tz�+fi= i data�&m_Q0ndZ% Q%>�{�I_APL},\` * %�m��h�o  $ EPS art %�{�!lU} �Q a6 \�N��y�T &T A )�- .Z!O }�(]�s" !�� ��H$an epitaxy�*Gone o�re�dya�of*" �sTin (1-3) In$_{0.15}$Ga 85}$As ��B� q.��,urn sandwich.e{ GaAs/AlG3Q7PVq �F�-t.�guA #� (is $d$=$255a$k*ck�Tis (is��wno top�a&� �7�3� sacrk �s�]�*or� pede� 0(Fig. \ref{fi. (c)�aqE;ie�� 浮: (i)&� beam lith?��sub+ f���.e-0re!��pro!2 smo�� cir_ pa�0lns, (ii) SF$_6$/C$_4$F$_8$ i�ively�?�lasma�.K �tch��(ICP-RIE��a+2osiA�>j mas��>f/a))�0i) Ar-Cl$_2$ b� s �-�RK�removal0r�[ >�%�� (iv) wet �}�>v ly� �>BN!�A4��up�3� ) >�!w  /A��!� arly�ant, aK/ughnes+ �-=�� jfe:- into.��sqTv� t70� calib�m1QsX-Mv�walW2rfUash�-z��out�� cern!V ��ve4�)+}!Y<�isly� � a� a@&� sk does5�.��ero3�f� a�!% Ini��2m A T Aco&+2� Q�&=re�n"g&Y u& &�2�eva� g3���&4 *� 8 �  Kippen�*� A&V*> ![A��y h }nd adiab�1a�!���&�le� Uuntil%0reach�-T6�D $� 1U" �Fber��sDtu�#��0ser ($<5$ MHz&���cI�!�a 'a5puaMnd� ;'�bf tE�t few hu�d nan snm�X�y�ir =�fieldpte� ��pows6m� �I�vs��!^ illu�őg1�26 e���S'nA�6�M�_Q}(a��Furw- detailcmo!�-��io�Y��)�),�de�&be�gB�^�Au�8a"l )@I.is�er� c6M8���"Y:);�mUc!�'sj��8t6g �3.�b9b),!b4 a ``doublet''{�y�(6/ , 1- � )!��$14� .��w$#�! :'�� ��� disk; *� is kep� rg%%"�9b3e bloaC8�TW )= pea�w� stan^� %�s�g� mix�U�D5tNock�:a�cA�erc whisL ng gallerIQ� a<e:�t due�1- -edg �Ѕ�`�B�#:Af1-Y�($� �p shor�C!M�Y�c5/�^3F[ Simi,ACb�c]�|�<��<�<)�tJo��H<clo�t��$ 200 � P%HTiskm�m!� %�!�}in7 se|� comb�� of6a&!6��cU�=�p�#&�7iE2t%� &� �-��, y���aled-�1.02�^ �pt���,�ev�0��cona�rab� 1 i$10�<to $6 RUn| 4 &x(!���``good''�[� �3��!e���<=baz?insica�al/� �9x�$2��bel`9� ����:�9A�[ ��oi�a>!O& rB pr9 n��s r� l va"�?�*^ RayleidcN !��!�isN���!t�dry� > ���Je� y� Y�~id"x %.�%1�  en �, if u$in ��1�� h�"� "�.a� 0.35v (*>  *�)��h\ he a?!�io�'#�e"�$vF4 :�o� �adjus��f��f d.Dm�{A on�=-urr�<a:�)1:� �66��s2�2*6�\footG/ {Not) !]:�VA A8�^�Eal��a�La�ve�O9.g Q#a�� ��.� (�ta "=lifetx"$\tau-�\`!or� ($f!8$�.-* ni})!�is��>�gID5� Thus, eveAea) sizeKa-rx  �a���pa��ݽEw�< "U9 d�B�m�"ng)/!��#�add@S@9$t �le! %t>"� i���"!ethod��ow � �! accu�ly. � wa�Aat.�ly&�$(weak) �-�&nd9�k �!*�V��A&;��qA�"�A���b� o!� be s� �6*~ $#< uF� m{:���/actB�up lO s n �&C)����a&{ -sca�D�I� , r�>��-ac��v�.Ooutpu�� S@ Cg��@? rked��+&XVH"��6'p�.ce% Dor.�S&� ��+*��ie"���!�o,�5�:��g)v!be * Z�� free-�7��r!� leav���5�(}. J^6�!%:�!Cs_�.5 _revb�&_(a)f� "�xa 6B�9`�: $850� a�(bj]�\152]SR�%j�! "xIn�Áea`%���-H6} m�sj'%&�>�,I�b��L!��2Ֆ1c*�}�/�X��(�51�A %ase C�2ly p-ed�B�� pu-83� :Y"l���� e��%���Bm�i cr$obj�a�� �(sola0��&� " um analyz�OSA��.  :e�}J.3z$s*D ir� er��\EinSugxtv,���ry�� . E�is"�-mifew@sim$2-5)z� �iU�>p%p2�)9�"�"d:� (.*nA sub-��.A �syG as narrow aGIlu�'l�J OSA (inse� 6�N�b$�(Lws �)Ii -in-�-j(L-L) -^3� �K Xa 3�sa�i�nd 10 A� �;� >�"sa�J�1Nn � f#a�K� �TC22i�W�Ee s�0�*��-moQ~�mleMca�X�yA+l3.6$-$5�!cm$^{-1}*� E��EliseevA�Noy f�6�e>)� A?U; ind�(q)a�(� mum}�y w)3�s:10^4$a)"t ��� - ef!U��G�.`e'�H9 pens��to u-��>.u/6N&�earliu/ �)*�)� sA��be s��-&�'U $�qp�L��Bido� �c�P s���� ��isBCly 16$� is �,.� by cal� �<�2c!����Y8d�: ��d ass�%g� �& *�B�10$���!�!G?;��qg'�!i"]Coldren��� p% um^%�e�=�a 2.6�W�3�"���e�' ival!�k&��H,%fulewco�B@0he�����& �to�`Q� e*�5 broad-arehripE� ers,"� stɬ . Ggc% spoteh�1�m$^{2}$a.�%�&1�*�%,1$,A�arr#:at!��Q~"�$+A/!�2=�12�KI��,D-��̀t��7}>�ANp�RdaB=Ir-~a� 10.1�J� �pr)�;�2�M]"�is� �iv�=.Tu)&�� �es�t e]7 y��4ly@� r3���)3�)P�52 "� O� Y�ɂ � .u 0� (RBW)$=1�) )-(d) L-L!�( for:�� dJe)�� �'� �4b* .�-K}%l Y$s -!O�� =0.1C )&_$c)�QW�J�� �V�6m��^H�# CWe݁_c�4� ss"das�&�s�WU -squ�ar2H)above=FX)�6� �:��.�co�$ ?��5 1��2�*in&�(�*�$r��.� G8asF�<fa�f�hp� .�c s*�Sai� tl�(Ͷ�>( �#B��2@2���edMG�}Has� :� AZA �t�) �/�K*�E>�>�Ka4pM/,pra,�`?,s�Z�#pta�K&�K*�K % :�K12pt,�S.I\*�JamsJzKamV�KmB�K� 6,K�Ficx6arrWD.{bm6#delJ&ifthen!o.�Gsqrtf{>[2]{\ $else{\=�G{1}}{,K c{\,\,1}{6 {#2}H-2mdef\adCI({\bm\Phi}} {{.h�Y{YH�7=t{(t) 2@eigenv{\varepsilo�%&f � ��G-Z |Blue{\(ial{col�\myk 1.\0 0}} % PANTONE BLUE-072 =G�0R>.6 .3A?MY GREEN 7RedR5011.:sRED 7BlackZ90=l�0PROCESS-BLACKB���Q^.81�.6 ��1615 } bs#1A wsbox#1{ zk.zk %% oQ_��fo����v& fini debug�8[PJRed #1 )8}} %%��F/ m(\fbox{BWS: }J^0�)�#1 ]f,.[ZKZN�nv#1{:�^[nv.[NVf[-mzey za� %b �� �� .)"w5} UKStimuf4d"�Xn A�+ DPassage (STIRAP) Among D�\ te-L`;$ Manifolds�@�w{Z. Ki�af&xJH.A�'RE&HJ��S_ S��2U� and tI@s, H-1525 Budapes�Z.O.Box �Z Hungary} 2q(Fachbereich Sk "b&+J\"at Kai�4lautern, 67653> Ger�Db�J. Karpat�K���� �fU. Shor�Q.�618 Es� $do Cir., L�^ CA 94550K���6r6N�YVitanov:yD�6t$- M, Sofia9�y, JaAQ Bouc�05 blvd., 1164 ., Bulg�%clt.�YvofNu,D ?n Academ/�Xs, Tsari� sko�9Huss\'{e}e 72, 1784 �6��d~dB�L We �,Te ) z"s nee� to #"oQash ��#�! &�/������ e� sF , $e�Ef$)Gre *�+, o  arbit�b ings ntribu�the p-s !/ v - y) �@ 9 �[kes : 6;($e$-��We�� �1gen�9$ a {\em su)t!ced��-olete pop!H�^4m4�� �F� of . b�f� 1,�lr �,i� 0 is Z 5h:b�:�g�X�O e al�$%�sCa�a=�.EF� )1�� h��1i&�3�E[c�2�!*u�0z"! nven!2 al �}�w�byN�� �'�%m)x2ypfer. aGd&���q&Qo@'cSp�h4�"�� ;s5-�2�Jw�8 a ��ced!�� Jl�(�,WG�6�1e) unit�e+�!s!AatY � A[�cM�*u��� s-�5AI�cy %v#2in*&!��%�_ �ac�+:'os�g�.�iE�ngula���umI�h73�/���I5$f$�S�9�6�' !�A�Kwi� $-%Xpe3  �e�4�?pol�f-bq pha�ca���6�a�*68}�"p�se!�Our-�!cad[ aA�wer���"#J�rol��5t"_aabecauo/�6�fc0a"n*�6Q� -PE�h �"oCy7i�"54�4"s�e�sev� ��3"t9;7ol�E{pl�&�i!�5�� orig �Q% mQ'&en�g, A��/�,  magnetica�H3vels.a�S .�S �P{32.80.Qk,42.65.Dr,33Be#4maketitle % \tiof!�ents %Z�z \s�on{In�N�k�O ~U�7s b�0 Za"� �%ag-l�ke 4.p�07T9*s A�M�A3GlyY��F��]��=wg oQm�$ craf�9e{s �L 01Y�N _r!�bA��y,��Pe�,z� �(1 "� ��g},!vi#$a^j�3 ie*+!-��er� ���5tw�(nQ�te metasEH��s,A�k!oa��5), �6��4= (lin5x&l� 2�"$\psi_g$j %,ed � e* SSt# m m8)�8 w�f/j2foP%`��chaina W���s  pr�Sly &d (�� �.butkIlapn`9)�`wo�P&#-��a�P�n�CB)` -K ion :9�!]��1x[ ))� out �#�|bl2 <-� 6�y��$! IS� � �Ew stoo�8�AI�f�N�/ ~%�sE_� ime-vary2 HamixoAuAn!"�8 9% L%�associaAq60 w(= C giesAa� (�noO}B)�s" , $n_0(t)$,!� �4�Me�4 A�m ��)��-� nAnm�p of! �1�-�G B�f-2:" ; tes fluorAGEF�B 1���-a.� �� �&�)�#al;P � }  dark} ?Xu��A�M'aKc( �Xaz veAV$\Psi!M6 a Wigo3)�G5��7h9� whil� i�2at!b in �C,i ange!�m81��kr a2s��-��o . -Ev ,f$*bE�'-�"� . Nu�gus exten"�)ba}6.�-?m }� �� 02 $պ,AAMO�B#$�s" !3ch]ro�1���Az��}]&7 yA�On�� y��T(A��UiciT vcgd!�E_�[ynp� neI conn^$ �8st ���7� P�e�� !�V�X�r��s J)�Td � E � )R�091, Smith92 P@st93 &; 94, �95M�0n95# 0Malinovsky97,i98,2"uer98g*��� ghtforY2�s����)lx[o�.problem�� maning-�z�"� �erq+��wo� �&W i�!�2B<f a��ud� ��;,og �c�dE�Q�A�"u �N� �eun :A�n� "�!��!,,3 q,E uti�Jo! e��b�5�)F\v-E� �s � MartIBLaCE+Weitz  Goldner Unanyan98A8ThE9,9}�K &1$ $N$- one�;T7�nt �1�-�� n� T1�]m��wto E%!2p52f%�m�- n4�p. ��ace�&� ��Kis01,�02}l t�" inG�h +1 pic� . 9s idea!�%� F b$[W� o map=-�iets�tujv*Fio�&)\ X)x) molecule�)$Kraal02a, ba�F� }]itEy ��nE�aj$�I =�,4qV9,a3"-�ja�=> ~med -0�S$ .��up=9E�e � a��#e�� ��q< ���-��.�.�E� e5s=�)5Y�o2en qu�'on%�Ied:> P!rAst l ��F� o,�$ ked # ��,��&!�is .v�}28.i � ��� �w�q��=� s�>�)a�A% @A�>$f$ set�x�7�|iz� *$ �H' .m�A,* H1first2#� V�k�wH�(� # e?��Jp��ans.�8i�M)�. Wo� $N] U"! ���-I�by%ns> �um�toOe$.N>Oe$ O)�Yurnű��4�� !ls_C$N� ^� "��R e��at��~�QqY!8ŧis almA� always U�?�suc,a� %�-��Gn����2 , i.�&$ N_V]q N_e_] f\C "Os �x> .� u�_/ �5k (e.g�"4 elli�62��PNic M?ra����"^"� )i�9��/&.H�I"s�*ll.W e��)H�!�Qw��o""Z*�C�Y�fU]t.E�N� �1 �"��@ restri��N2�"�K!Ir�`� ��:�in�#����@���ge�e��!�WE�<�at��y K>t �z an�op�>� .�|250'!�B ing �JEX a5Nյ� �I#ed. AnP � tiv��%�%}p *&aK� A�� Zk �85�C � �+i� ulty��es&@ �.GHl0e }7�Po&o �*[�� ��]e�:.(!Ga�!r usu@ @5 d by�(loi# R�r�Id2�LA���5sfy. Ho Fifh ��Zeeman� !��7�7 Pla cer3 2!�a"� &� Q%*� � �F 9!AW�}�A"0 o��3 9to 2��^ :�yxdespi�lW�%c-@ve=���%q�E%��we--�&���"�]� e �xn�_*� ��A�e�� ?cw.�- *j%u�f���2%7��#�s���I� $�e[. =Yi'on�$a Morris-SD" (MS)m�SXE}�� �=��!q�mp!0͙K��8G�e� �g@ (ge�PVed)A�n�uaa ��e|^�K �%�� ��-�� �83,5s`K�#de�SIUt�P! �f�AY-S A{)'�  83} .E�n!�y�!<��a* �tA=  � two �l� (9%]-�� a�!�02�D, 0d$a$ �$b$�m!�s� ��d�i� $N_a�!N_b$), ����o� ,� sui�!�,hiQ'TA�o� i"ii2�$N_{<}0I�aL�:��� 0={`r@min}\{N_a, N_b\}$�^ge!ViG�mE$unE��us�pn&�ɔERs� !zgi%>A%�h��)��If�ch�U, J)�.y ^$e] �!�� a��emE�}M�f)�� A�a:ork��1���a&�-R � ��gorgantJa=F�)s:,!�next s������ m��3j7Y����� |�discuuVts ��p�U� In Sec.~.Y,sec:mstrafo}!(de�6&� ���$���""B-like.�I�er�� � 6}s-.����qdio�� �����brYI!_��Gt��al� �1CQ .|�U�;6�aw -tevol},%�&<:A : �#s �%�:T >k@Md*d3b!AHough so�"ե�� F���� "�� 6��y}�8 iz ��SA��""qA�*�*S�/ Model} EEq�r \s�[@ v*c } A�! custom�#?'d�$I��^��t}JDs, ��A$n!�pa���,�eIx"�si(t)$A#at incoro&A�licit� �B  cc:er�Gqn��!�DA� E�����i_p�[ $ S$,!�HR�G14�"l-`I l�n�'%#v =F neglec& cW&z�!W�aA�[�W�iA� va i� $( �i + j)t$] p ���:& (RWA)2P%>�re baTJ����L�)�1}M�ham} y10 H}(t)=\left[�3&2 {cccw( ,0}&p(t) P}& 0}\\�*4^\dagger&\hbar+bT}&sDS.<#02D q#�2\�� ]\,, ⥡� %�A�Schr\"o��iqu% B �i��2d}{dt} �C%)�%4 \, $[} H�|z�[cbm 0}�nWOnu�\�9or4At�$E�c��2N"C � �\ /x��pbottom %�Nne<x<m A����.w9s<�1�  p�;n��7��All�# �ei I�F e� a#itudes $A&i�$A $, %��( �um�8�e� e\aOs�$ diag�%1xa�AjM4�d!lscrib�7�� �M�N >oy*; Boh���-9$g-f��� �A �g�!He�$2 ./�$ V.af Rabi f0'en��.�%�u*���� �%O�n _{ijE�2!?fj}��e1*K� ant -[$E�P}$]d^9 T=i:1}{2}{\�%(E}^{(p)}\mu� \,,\qquadmq�|\{6}lq� i=16��nj�'L8.".J"� ���$i ! �CU�Ł "� ���)|�$� J�-9�x(. *Y*$N]�f$Q�$2a%%�SU:!�is%� A86.]9R8x w;/�� V �hn���S$� ^S%�ZS�Ie Z�.�$I�IS)9�>�"�Q�c%sH$�- .RWA6�of#�~(� �)A>3Gy #Y�c2�.� %�p�$nfalA& ime c�~w���s J���%ea�s2�m,A� MAK �m te"��&M=h�Gw���  $�? P��:a S��g�(�6/� ZU�SSara�6.RAo.�,a$seqH 1|"�<�fq ���a,&�0J = 2���a�M3> 4�� ToA plif�(�Yra�8s� �z3ne�&AJp@v37s�[�a��*$�+ޖd�6)0mH7�� ��s�ka��)f q&�>�%M s)��beQhM2�dSz�,f���e�W>�k[w ut̋/2-1cm]51} %fig1Ů"�k(Co<Online)�d�A�]�Mu)S:I%�E�i�J-%Y$J_g=2�($J_e=3�4J_f=4$. H��&<-�o�/�Ggma_{\pma�0n�A�h�:��eF� "P;  ) exac*�Z �tH-���by Z`$,�I they&_ &^ � ^ �ե�ہ�g5 �� �"� s:#^iChY H._3� E� �*�n�Ad*IE. } / Nk 234-)�� QQ� Alth���"�sit� K e=!80 u��� ;ma�'-q`U�c�5� ofr 9ԝ ly quitej�"ae�@qa|la����'r��an�n��ICJ&//yO�t 4 c) ��S})� P}$�23Da�f���V�RI�s�y%exist =N_g +�e f$2�)&{M��O �$N$.�0 � $AA_n(t)a�9Mim*$�|ppl�)e MS= >_�t� ���i%�imN'y �\�!�a�!�a�:8  t%m�he}# set,@/�0�  7�RMSG�;^e> lf�k�_$b�!����FR u = N_a -�$_�,"�. N�*� sxA���'e\� �%��key� t A7-���&� ��N�D�Mf - N_e!��t6� �!P�X&", for �4$N = �4LMS�"t{�19u)�one b� �;YHtripodU�q= z)�,p[,�(98,)�In9@ �[um jS�V ) :�;�re)Y = 5al(9 - 7 = 7$%��!��6aV`ZI� M/#/ P� a�.��*H7 Bu�� "� �tMS "9�cO Na��y"oe1 lea9"� e (� le)�)�a�_(ly The:�� /" ybp,Y �intui\F7der{ �$E E�c\3e �3rea0 �� �ne� ary��rbl8> ��;r��,op$a�T�� �4���n@<ro�Z�. #s�]�!�no*�  :f:$6v�iP>�8te29�[=��at� hear� our&)A�fp�m)�Z$��m�" "�(cy�IG� *�e�E��#J|#"& �>��  O!v��c5%8whc�;�'age� , it!�)6i! empt&i8�. �"�&$2i�, once� � fixk,�S� A!I�Iځ[Ie� easya�se�:H<neY�!�T��q%c&�;B�&tq�"�*-+a<>aJ� �?bC+re&W'a�e>�<;�;[&Rx� l_( �as�)�^(e$ T�T �_cssi�6we!{loy"~� o�%W�^p�co�1!x2�q�>K"��$newq�A`H �!�i�s*>ԉ�y�"` &g���D%8Is��i��A a��u$g$)*` )�,beAp�0�r���0P�"� � 5%'. 9#;.�Itot !ԅ� thema%i�*�$� ��i�*= 12�*�s J~A_s0du�$The top fr��d�p�_g�:� \���. = 2 �`  1�Qf22$R)� �& [&u�E`#�3�"�B�ap� �n��@1 �b7:"A�m�,i�8c�A�asia.�=D/& u�%Kat�5eՍ©8���m\. *7-�a�>�sea�[E ��.a� ��&�!5�. Z� , ha�#���8eY���Ce��� eå�.\everyL aC�ran1A�xs� !qU ��A��m!W"1,;�"!F<- t�1* E{.�%Bal� *�-!b�ԑ ��s�1���un a�dnd �hi�� !� �er.qMf�zN� ^�5�2�2"}�:�-d5sketchE7Q�<"��!ͩk�"q�C!�eed�1�@-�>2Xn� �$-l� E.e�3A?=N�|.�9�>�t w| A��me~��d� 7D�E��! co*>5.@b�Nah%1&7 "�BrL&��H �"��� x�� ��e�� ( �6�I&$'U��D�tKkia��(H_,an�'. �� shA�komm� @HXce,G���A�FTg$H� �]enm�;=�5�s�;>=H�3. Ke�KEH�� 2PH�.:�@�"�%�� �5a;��n��� ɒYoԬeIw6 -e$ �7ag" �M�utrgfa dah$e-f$�$�k c��O1]> G-:�@\= ��Va ��� G U��ve$ �� (uд�.)�� ,���fp>�� NJ*y �i��p -ft! �_�n&nApeaA �5�a argu;  Fq� I���"re)O $g>�e$�� d $e> �5We �2�. �/j A5<�3\%�,=\mbox�g�,e�,f\}$ . �  �/d�)1I4��N8lus $|N_e-N_f|$.�!��a?���eL4m]!��)�8s. V,�\ n�;9.� H!K �7� ��DI�� �A�aO���QI� AkJ�E8�k��. C4zigpQj$� arns�$\)��$!B-����=Q:+G;n��f���--e�|&� �i%� � �$n8f^�}"�&:0\�A�!� fJ�#t�aaH.�D-=5M�*�g} iH�'�3�6���X�9ha�u� �i�<�9�Dn9f�'sR25!&(";)3�/:���fin�orͧ�'aXQ :a'!ll A*� l*K� �*�- �7l&-y �Me/� ���utAe�P��in&\R"1 9�.��m�.& � u� +N_f>�Hutf<. 2�O!�!>aQag� $J=1> B$! 1d��[ is 1 �E� P��/121|6�� "[�--��-��B�2�-:�/�#I�bi������%a�5��{.".�>Eq2t$�!Ur C*�/%jaat��be YCp+!�7iV:&�/}�]C`"΁`��B+%*�.�/p�NM re�N.i�So!/��/{?'!�)��a).!c�iq � -2  ұ��x� U4& �4s^9 Udef�-U}�-u  6)F�-I"�-!-*'<0 B 0b"*A��\�aa6k-B�,E��p-A.�=q,!1�peT1-I}$A�d6t5&7+g6 �flzwAw� aofQ� unalter�T& Gf"~+f��Tox �(A$9� Z"� �� ��/�� f�)��j1 o oB? A(Vp0A'FsTh|%!Wce�bm�ea�Ql"58�%B(bG&Ro�7A�}cB�(�Wtri �U���3AreÞ^�tW5n0U}E�&A/U}�/ =-��0 \widetild©mf�0B(q&-�1.Q� �0:8b�0B(`m� RK2"F ���  5��%mp�_��� !� $6~ )�0 P)k B��E6cquasi-"E/� i"� h>iu)=A� BS A�e�ByQJ.dw�y��� F�E�xq ��eqn���#Str1�6� S} =-s =- �#NVG :M \Sigma} & Q A+ 0}J�:)  �}  F \\[6pt] �� \,\, Z if }� =3.,WJ \\[2YN�.�Zz\\� �F� ���� �8)�Q�-�"�/:�1��/a ,3,lg�1Q,�� �LV#<�;�;(N�#%�S� duli��U "��P#n�5% � -roow/.�Rof�  H� G� ���i-S^{!5 }$ (R ���� $)i���4emSN:��!�ݠ�B �#f �u���s�y�9alu@Nd ll� m�- ǩbm� �2S0>v9cI�6�mw83�:b�4,H�g� ��s van"���"3�We�<(#um "�l�FF��A!�q�5, �"x*�\�tXD�Ap�]ix�-!)-s�k�a#m� 1n�i�\%t *�f&:K��E�0Yh�Kl0."Ki9Ud�<?&�  !G ed >&@\���2�)] %$�3\lH3P$y!Hpiramid1�S ڲ--֏3�3�]ZW. ��)�st�A!�%�"+E��!> .QH%�aI�a�/r�_[2uH6u�U�2��U� "��E^��Mp4�o:ene�QF� . |s�H �of re ��M��ub�,��J/"�$E��J�M�M:�E�f���6b���a ~xS �s!F�<f-N_e>0$�%�e"o1! c!�.� A0!:�zB� �-_� �m �%+ �h�2�4Str_��_��*| AMS� readb6ham-ms��E� H}�8R�FE�<>EP}"3J]C9J2 &"Z U� e N\ �V-Jr�=z� >}���* �� v �!]\F�Asy %ƑgB�6}wFi���5e�e�>&H*s:E*�5�/PP��LA:�Aws�" eG�O � Ti�`"��Bw A�YI� mse�2@w� E"8.��6�F�nTa �Gc�u�ro� }60M��"ei��'izsub�? .�%� P}}$�G"U s!gV ��Ui)�>�;� FMa�\b1$c8g&�s�� i9o�8n*R6 2\�.�r}_k(tDBofF�i�$!x�\u"� tox#u�&Ru�*I�Wvk��m *� .�^� 6%x}_k \t .�:.S bm y #*�:"z�"'hf�"c=i�{�{g}� e f ' Н� 19W9$f'�fno�C!g� �W� *�2�z�v. �^�Q &PHTT��o#mee�����ofy1��p ir *zm���be�t,� rvedUVoug�u*MgoN���d�M^re��a �d��v%is�Pm ����B �+eq�a�:�{�t..!=�v_k(t) ^&JMB7ub�� �2eU6�  0�N�ihj R>Y& F!�--/a c'w �E� ]+��HedsN[~2> �7 � tFS�2�bm!v��L8> zu !��!�H�*�X�& b�>2g.�GDfi by��]+l�Let ug=`���j�A�,E�E��H _0=0$\,GDA�/c6Xto en��,A�"Onl�"�a$"FH]�3*GH! A�-p�U���+g&I�S u f�*#S(: ��-QMpiF)�|pI� �QnZ}�p��$.�Vr/��i1��yr=ar=�� u�j"��$ algebra~*�I��g$��eh��dYF�(^{(l)}_0 \t,l��z N_g^"atż ��*`'!,�$aKv��k���rthonFl^���01�J�_0 ��I {1\over �BN.} ��^ "pDx;)�"�E -p(t2bm. ����� w P}"� 6l){Q0�VGFHh����<� J A, a (2� t)�7{�� f��t7O� E�$!�A�ZG 1 �4Z. ��ll z�P�\� te|=���U1 �8�1eK�+>� =r!<�T>�Su]���'�:A��G�is�#�`hey�T2jR�� � ;A�4.I�A��� �ak>P�2s�&c  Q��ia/we"�!�^>2ECA�^Z"a�^% xa� k)\,T}_0|e�\�le+A�A�^2\b;$=|JP}.!�Ma�g��AڝxvBT�:Z�=0}� ��M$1 fq k < l Nu�Q� "�k��!� endc fun�*� !R: 7FA0"E7P>n�QerȼaIB6�aD}F�"�<�-ha%��(lh��Y)�)l3i�Udp� ��A`f BSa/�m.�x��Gc "n�=EL��= lIq� ach-��) �� va���lh�'F���u�Q� �It �~�)qZ I�E�$�{h2� &���^"m.�{A� M} = P}(SLS}�A�)A� P �ivA�]�DA�\b�J6'��r^[qJ_ U- an%���!%�\6:�)<�&IKs�4 llow&!*[V��/9�&l A��givFB~:�"v ���&f�)��2 !_  z!�prime\, A< WJ�#,9 l�B+1, \�R[ +N_gJ\�wI�Bl9��stTB��n�p� tQ�� !p�(2����a�.�a�a��%9�!��?.��1�b�`:(�`� izedū�Y@~:af� ing �+UF�- �2�6w.�6��= to2�-th�X��?in Za&� 2Ma�/.s;$� $e$h ^�qB!)"�.�75 فD+$ ���%�3��,t�Ea 3hk �2�^� �3�!�je "V�G�5� 1����de1j?5 %���"Nb �V-��%A-b. gc)A8.e;d}=00�I-��0G5)�k9r�TA�9&'4&i�I�v.l �W~���fRm��) may��u-�� ���, If s� I�� �2�i�, k-O."OBt!�_����.P\�$0DR>�1cB�q�1r% n6� &�B ���)�'Isa� Y� 0qi�A�!� $i$thT%�%h*{���.�s�=I�!<����lES\�4!�Tő&i�E��l;r�; `);b&b �as��: spte K��9� �)1 "?-�?�@"H8N��ly2>�%764, say��P��Obo�� P_ ��N�*� �3P��Wg-N_P$ �eeQ, nontriv�/� .�!_E��AseA�:9�-J� �u&E>� ="�RIf�=��/!��f�>�&|h�J�M�5�$\� y�a $k S I At��!�-�1A�*�9-K�� eKGoo�a=i5."kFVF-ի� e�E��R9.� ��iC ��erAU*1y:�Ra��b�T%kmea�u2��2"%�F�B 1�+2h/e�3o �2n�j �[DM8�a�_2 �~v�Œ�C� "�3~ ���/� ��&�U�_m� �s {�=.!59a�.�%J�3H=��dI-.��?_BI�AuA��� coaroj2�r Ym ��la�'�E ��se/"f�ʥi.P�f�6��e% v/# frac `��N}� U&��C^�e�T#��63a�\tf S2 W8�2] �T &�^2�1���t&�3No\>/A5(~t:B��ѐ*��R� 0e"$ Moreo�i�me+���"�=St(alu|*�s)Z�se>� ��je�� �#e wB�i�A�o>ig�i�"&� �[s���.Z�.N_gF>�@}�=d�.2}�p A��� ����� vE�H� %b+�-'6��Q�xJ��c">E$Ek*�;��:S�@��D 2 T�Ta�>�eth2� � H�EwgC%��8��Q#z�u".�waW"�<� ��"��:�!/)C� ���H=`&�*| i>�m-�H�bu��w*�B=> "�p%c�{ �B� MdQ<2��e�UrI*�i.&)<G,:�.,A~!)I�2M�`JLWe loo��!�j ���%f ed2!%�B��-�)".0ɺx)=�n^�.9bm��h� a9W:K��� !{b�� \�)���)9L��^K�)g'�!&�) 5& >��1�B<>�&�%™, %����-Б:�cr.W�^ FhUcA.�'S�X��YWu�gCgfP� ˣ� writ����rJ7:4V�*xQ2��^7)�2�/.QEJ^M)�y$] JAE��=�UB-�ac9�{:�=��\} ©m Ɂ*��!�=��Ke �1�"�KAbr�I�' �A��� !��OnH ��- bp"�Q J� e6�-�^{�)�=Bq%D# Kb�v%:�\PiAdag -1. ${\bm S}}{\Dbm z}^{(k)}_0 \\ {\bm 0}z-p(t)+FC�\end{array}\right]\,, \label{darkstates2} \*xequation} where $\left[\begin J{c}�$\widetilde~$ \Pi}\\ � 0}�� � =� BPDA^\dagger$, with $6]H�CPi}$ a diagonal coupling matrix of dimension $N_e\times N_e$, and .X � S}}= A}8S}$. We requi!orthos,ity for the !> )@$ Eq.~(\ref2U(). Hence 2Dconstant vectors $r=�$ aq chosen so8atey  eigeFtes�X$ Hermitian!�- %�9� i �^{-l} \b5d^{-1} >�!~: -1.=>[P$, in direct analogy)�! way >  ) xu$ wA�- DP}}_abb& <��bE��&\hbar8\Delta}E&��s(t.��7\Sigma�h b^{\prime��^xg >��t0}&f��+ D� � \,.>{eXU? squ�M�> 1$ ha.d� $N_f� N_f�HIt �be E>ily seenA�atA��~n�=-6 �Iin e�se,at* noti6ed to&qۉ� callA�seem unef0ed} levels, p�adother i�t�� 1 excited-� -sub @ �i ed {dactive}�I �}�a�E��e+)!e pump m*Xis part��ed in�wo sub-%�ces: B5�2�Ei8$ �6�g-�!s$ describes�s betw!�!$g$%�and � ��%�R1�!EW)Z�xF�ia�b$��URA�(N_E )$%$associated���6��N�U (!�(e�..�����th!�6��illustr�in Fig� $fig:212b}b� �b figua�fA�ee-A��0 y cl�� � , becausea(, general allZ $ �e!� aBagM�a8-�&� set.�`---� Ա�h\includegraphics[width=5cm]*04} %fig4 \capQ8{(Color Online)EC,three frames%+�gIxtheACMS:�s a�i�_ce� de)0te1) viol� H!�' �.3c� ): F�, (a) depict originalH%ja� scheme , �jA�� .H(b)���.h�� fieldF�,� vertj�wy$e$�a��(s �S indepen�  one-D d two��� sm�H'E`EX��QI�cR�H���Z� follow1 -redefin�!�-���ϱ $g$,� e��  accord!5 to�E��!!}),�+a#to� }�)is IG iE@>�� middleI�->linkage,�dic�7by heavy�a!xIn adI�,2M%ltA�i��ed�on�1o aHsingl��but�!�} ��s� well.��2� Hpopul� 1�> spectator!s) 0s may disturbgcomplet:Hm�er from)-(�p�,. tex��}G�P��sڌ ��* ��pG  a sea�� 6�y volvEC!K$g�fnd ju� tU16jT e:dee�ed5 ���--e�1o(present exa!O͙�2is��c��I� isJEWrA�I� $g$-�%� � �s solelya4 an��+�I�et Ѥa�EfE3have,A�m2B���ena k"� At��a |a+qY�"y mov9^is�e a�%pAo-SQ�eM�!\-�:Ŗ A��Con�itly, if%Y)�})�6E �edi�y=!:{!�te.�M�q=) �� ϩ�� �,� A� rio}�process � plac2q� O*Ogs In�I6."� mmWB� �S�� ed abkUpN��� U}'^ �a�{FdA}'' >7 8   !I 0Z)!Bcz*2I� �� -"� $g$ unitary" � A}'$9�cE et,s  $"c W$ ^_ ^�$x u _y�I1�A8e P i�it Qce"�Itr�L6 >\Fort7��r�l9?2qIq!�HUL� :"���z�Y  $[N_g-U�]M��,6a!� Pa� �k"^ B� �#B�!za&)�x 2BT�$.E��=E�we find= 2.Xpi2%{ҟ>� P}'\�KIK&�!c!�Q��A)BFn1�6[N" !� i >��%�2�!u.,&doJ �BHPF& �� � ��f� �>-� getv�3����N�Nkj�!_�je�2\&�� � ��  J� a�thH r )-�e�, a� A=A> �  &I� >�MKA�� AQ eit; "�,WnRA�6�q elemenp U�GBy-�L zero�yr�a�@\geq A�8re6no8 � :� Y d u.iIe�4qno2L� *8GZa�h�0a STIRAP-lik2�  erW ,impossible. � � p(r,)%�t![y occur!�at som 5�ofBCa,$ vanish){�<such MSF &p L�1^�9]8 \ zA�� -1+l.^v �a-8 � �p 5'� r7m�1 &1-^^$ !�sesUj�2�:W�� %m�al.� D A�AOA+4fn1%1� s%*1UQl � (arbitrO � superpo)��)��P��ii"  !�!7.��,��� it�Y�!�re� -G2�-a� �et_5�b1�. Excens I�whM���BB I�a)i�y�S&&� MS-!&�� �2&�!�E��(�,� also� . W�!D��E*=A Z�E�duces P/ *��&���)��9 � )t��{*  H}}}'n��d0f��vfVZ�'N!�} � "�\ZL^�NS�. ger%$&"�>�j��1+J��."5#Zn� 0J\d�r.M<�N R{2�!E����܁�tre!(similarly. �or�!o E Eح艘��A�.�6�t�we F�l 9sa��I#" ^#! 3$s$e�pa2terizV�!H� vk.2i#}Z4\advecb}_k \t= 2N*&.; bm x 9"GBq$x}'[f"y~Cy�Cz Cr$\quad�� ^ {)a�gA{g' e  f)]����� �% valu �'�� ��Y(%�eqzD By ins*z:R(9#�%)��A�%�I L of�� ��&uY )�.�A� obtaA�$five groupiE I ear �s � 6( E*�R�'_ :<2E%$,B� E$V^A��$N_D$ �l!c&��2*s6�q!0^{(l)v#$a�at belo%.!%:)�$\ _0=0�re"�$B�A�.-FoD = {1\over {\cal Na*t}iAB�WJsx? -R'_0{M( � v �*.�bm�"�([>8P}��&B�+,8{6 $# @ '_0] @}�:K>?+3B��"{� .�)6%� '_0�,hould satisfe extraArB �P # spac�:��:�`0�*�+R�$] { sayinxark��-*�d(� r"O -.P aXLb *� � *� ��An g,� conj��i� n& ��):12&*a�"tm�r � �u)GS��ls% &�$ plu! eL"F2�� >� ,.I2@�EL� assuO)�� .��<*����2�� ��345:� � >�A}$�(*%W useful�a�*b-zn |�cU:l ��[ 3�!�.Lty�' z *�*G} A�I_ )v�  ��s $.�a��,l�/,>��� %]^T��$l=1\ldots �r� b��ge"� p&�--w��P�metric��� P}��:6PJ:��)��� �[:&2� .L)M�� ?��> -P '}�0:�0Ma�res!jof*�:v AN'�� �%�k t�n-=%� �� b��K N�k� ��-�>� ^! >Bb @ \\ % CABnP}1�=�A� N�}2p#� }:8��  \t'26� "6m}�v."[ .�J�U�Q]:�y �Eu)�1�/eq:vkbi3$� � ���rmali�  fa;2� Eэ�F�% \tF�)g \t�{oi�.,-�D�T%mex_M}$M^�[){*YIZ^2(=�E:� J%nYD:)�JL').N!�^2.(2� ��IA�F&u^2<=J�>$m."1 1BR(mjg} F��K��F�Z22:`E�\"��!lI����I^ic � =b= aA [\t-�Y0ª�J�b �/�Peq:���yJym��"�2��L)�$ b�,�%�,�"�c�+�'on��k �. m���l @2I�� bm H�f* b��atomic �2 jd�)�=%U"� %�UA�2�1Mj-V:�8 >mEyN:a "f#M�n!�Wf#[E�m�%�I��� *L>O�{!�AB��^B� �� B%F�N#e! ���"�9ƝFq�X2:�q�2�=n�=N�AU�>-�IcL1�JC�+ \�8 Adiabatic� "�s$time evolu� � �8a6-t�8 *G ec:mR1fo}v�!E�)hJ� our *�/�. O�/F G=� ���,�� �! �:���I�.C�3 ques!/s��k l  address�{n: �2 � ![%w:% $itemize} \ [(1)] Wb��=� need!3o ensu2Y�?I2)] I�� �sev`2=Y �f*�a--I�V� e�nonv� ings&�9m. How��%a�B:z:��; ase?��!% T�,sw�5!?:1�i app0/he�8cqorye�9 \6 {Messiah}g0which ![5�p9_]Tif any���$are neglig� �ear*5 ir 4gk7pA}.j our model-� weia-�u�x�pan�Nby}e��} �� �58 8�,7I7� av�� R�BeS�/w�>!�:�  (�Ee�$7��#"T?�D& �a�s)(�� b�one<ex�#a�b*y]q�"V  adi-a��D  |\la�1�@��_0(t)I� |\dot*\ (}_k�:rF|\ll |"y \t|�'�,� >�q!k=&B$ AN_B$ beq,he number of6��� dot3no!@�!deriva9C"�U*�*5"W ny�3 -��u��!� V(�',�u�2i�.��by� E`s1�E/M  |*� })aJ�~ �  \frac{E}{�N�@�t, I@j |:Ep  -� sE:k|��!�:Yx�xn|P e  MePAl {6n} J�T��]$mula clos52�2mbl�!e��jyP�x!z conv@{Cnon�~t8-�;�$��AAMOP},B�%-x<1}{\Omega_0^2(t)) |SaWarP!J-PS-%L| Mf�0 \sin\varphi� cos <� � \l �� q^a \cot Xgtav gJe�E{��$z.A Y<fi�J�1g;=\sqrt{P%X+S}\,,\q� �2 X=m-�!�N{66>�ren6ive!��#�oe lh�&s�k2})AX*O��-��8�� lope fun��8�,�9 puls�:aZ{A �i.6�"�)�Q�1*.}= $l$th�� :?�&���6�>*6 itud �!$kO2� Sime $t�O�,e rhs&"k#!��d*�8� �1 de��Y �%P ��"-�� s��=�  fulfil67��all)!��b麭�a � !I$��2/�s� v!_"{ly�rer1�ask��d� min�2!L.� N�!! !1" Ni � �, usual�7ZW 2X .$ �^!�tripod )�>DUnanyan98,Theuer99� du6a��) choifH!~!��-10�B#/  ��,mix througho�:A*��+*�(� .3� %�1�x  larg�Fan|� n!�6� � no?ct PH ytic�,{ �S$ite{Kis01,2r�\ %a�&�% is m�+simpler' R�u�a pair� �f - $D ^L   | ��>1kB- ��,�  ByA� aluaf>   A8A� �B� @� � J :� s�G-.� always g�***�JC$e ado�tAU�6Vwho�=bH�&ss.�property)��Hi� calc"=co%ab2siA�!�a*,J=�Y�*+HB�E opU�U}(t,t_0�l*��&!��M��[ r%varrho} ��2�� $t!#!�J���/ny �.!��rho:��)#5�� _0�dag1�J� provi�*�2Z�=As.�!:Y  $ied�� Not%S�a� *� ivalid|e�&�-}�<�J2�$ l� � r �'%b�#�~vIt2 � .u)I9`) ��G(ny} pure or� �O0EZ1�1�occupy�čP �H�.�*Օ�to!{ep=GHm��rsB!�=�;�����!�O�Ha�nuOl �!cPsiQ�w�BHA�{ )FlAJH� again,a?, $ m45���s@.�"�. (WS�)�v� !:L'B K1�lyNbb� �>xt 0U����I#�&  � :ch �64!ic�7 "��Ngo'44ontaneous emis��,�qir*�s �JpotA��interrup454F�,�w dynamic^^o%i94 QzCU/.)�}Pe{S�4��"= sec:�P��2 lA�demon��U�S5p�usage!"�metho��To�� fic,R���m���� T �GU!�"�cy��a�al*emagne� �K(angular mo�7umI�<5�  abEaj aE�F. Our puJ4��R$Jefte|arrow2�3���F"�E�3e�(3�?-��J�JZ�J7c�J5�J5)cR�J�Dn � E�9��V�(�� �M �*a���F nlyC\s�P{" m}$ polarS1�NI@� ��HiKN�b� t�U�8s;� smaller���shown� �shed �HQ^ �:�so"��1&�J ��Seva�L-�JqG�� Ic!��aI�0e�ON�ay�$JJ#$fK�I* Jto &1 }). � sH123�K}-%�e���% �&��ER���!IIa� � 2� B�,%sn �N: 6�% �um�$at Af $6dMQu��!�I��s��Nwwo .ULI�!gtVB M� P234 4 = �2}�� 1}{3B".`'�P^{(-)}&2@6}+)}&0�D\v� {5pt�Y"�! 0jCa*p+) �N"J ��f5J� r�VS1<�  S}2#%-V@5-@ �:�.F. - 1YSNY151Z%Z9\9MNW.`2}�)QI%`��>g�5�0&.S1}�&:\5��a�I]R9~er� f�*��?n-���<e$-�"�T�\ Clebsch-Gordan coeffici�&�Rabi f+enc���;�62Q&N�E123rabi�-�&EA�1�M�&=& �4_P \,e^{i\phi_/+eta.�E+MJ<s <vV<!�!�<S.xS}K s\thf>A#J>si>z>�%�929i�%�*��{P,[!�nonnega�)���taF $ |$ characi:%��8��m���< !s,6[ �� <��?��$2<3<4$%R���X �`in��z ":^�"� y"jA{-�" step�  to p�P f6�+ �-X� ��aK\lambda�� a7��b�ۍ�^�.�!��\�  ro52$of a cubic�v�Q&C ,eigvals123MSK ޗ B��� �4�A:iV8� 6� 6+� JmV�)0�=#�lS%&1E�.M�)AUMa"9 L2wa�&( '2�%�mead$d� =�M<+ G$(Œ�3S)^2$. ��0 Q}i�1H��9�W� ispl� them :� lM�}� a 90M� � E^i�u�)"y)P�$fW`!�OvTa�(�'*Pm3�Ds �D�.>b ��X6�alHow�V���#XenE� .T�>& affeMX h>#!N �9"+aj$)��2}�=:;MS ��9�*CE�A�nd B$,}��`,��be Q�aIrafforward�nner;�-�*� %Ap!,ix�6�>!eSe���Ie+( 5��P��ed& �xJ-9���AmA�A[��Va��S&Va"�I �]>\�1�� �� *���2� &� 7}{20}2 &[�y {.� >{�&1}&0&0&� A !2}: !�L��r" r� Jp�W�� $2+4-3=3$�!i+ :� �F�vI an*�;;�+ w !��Gis-"�:al,AZg=2 ��Eb��iwA:��Y��M*�V<:1y�fL!�k)�{"�^ UAzse� =:�|ɾU�&�97�� Mgof.�m�9�J[�r��f �%#�Z]-?"�1{'(o� ir struct�,�yX!n%�!=r;,%f8 * 2�+s�,2��1���V S ��nu` Xi�&�s checkc �Qof�" r�s_+Bi pop}*�!�I� waA�FI�( $|g,J_g=1,1��� V�$P"�$��$.,%,)~$p�H48xp(-[t-3]^2/6^2�% $^( + c� P=5a)S=4gt 2�aIC.� �<N � $eta=1.3376�SraY� � =0.463�Ic phXL � �"�j randomlO* as $Y =1.1814d$\p5 =02(hi_S=1.8925�/ S=2.8198$��W�#u�#$�&��O�LAw foundT very goo�hgre�O""!�Ue�]ion*E8M�� � .�5&5 zP 7g0[10pt] %fig7a�3b� 7b� b� Upp�Zame.I� %j^$use"G�n�A .� ��*�!�S ',A�� �*� q�o�6&� 2F3$.GIn�ly%�v�� � edHLo�0�b:E� #\" 2� *� 12�t�� � �-�M��JI �,k���7���xbma3lf�R%%�� \d� eachG:(��+ �W0� TcocE2is3$ b�f!mm�mLP'qned "�?�i�e.R-k� t-���. se� at despit! w)C 1C%)�� .�8Q�!�!�#u`�G�]c[�� }5�he �K�Bpreviou�%� e�EƏ8� 8a4bSzLasVW$Pv&aE )SdeM` ($P_i(1,-1)= 1)=1/��]&lU� HU3���>A122��q �slF�{!�!:�Bf�11����b�s��� ^�3.�� A* ��nFAe�� � y* )rMh ��.��iB��vR ��,"=N_e=�]g nd�d2 :�;&a  ca�YI �a couF%-5��"�-6iVN&7}): ev�V[.�� 2>-t")J.�����WalsEf&3X*�irib=.B��"�ZQ��Z wat0��u���� S$, P�1�e .FA*H1;t� �Z,H%XF%e2�F52{6} )$v2*�J-�X^{(\pi)7D.+"�42� [5pt�C�8N�0>Lx\\6:0"ME:C� BF�B�4�$1X~z S$ o�O bm P�� $1/1N5�M($\pm$ signsC �qrf!>� �)hm,�$A^r,o�qR&"+}�r\�^{-}$_Eopi$2��GY(�5*<,��� rule nul[/�/e�s $M = 0>�" $.�&�:V:C0,�:�a�e *j$�&��] N!� 6!1u|>N�{e��=�sAgSnAOS&q�- 2�ud�=uli����"H6��cBpq=&�1{A� S�| B��Cu.2� traf�NTh#|vJ0,�Va�pm�;6!!(m]{!(({\rm rms})')^2N�!'(~JA>B=| e|^2 + .-)+ .e!|^�On� !}.�is �2( ��+Pyalt�s�[���E��,&� .Ce fer2�Q9��aL e� � y� � UI. �t&�11-R}.�+sI���@1 <6��.y x�G �% ��  g  $(2�-�-+ 2#0� + 2"D)/�3fa��M*�j�9.�^*�� m\k2k4k( �r%+%Zx��P= S=30�=].ns�K� lK~�10a}\.�10��10�10������>� 1N� E��{ �n2<���2.}+2�u� 3` ��H�N]5B�$ ��5 . Par%-a����&2is x ��")c&�Ms�1Q�MS�(E;*�&vaq2F����"���6��0 2BL j�2��:�<la v��F"�E��m>�B�-1r�-��;����-��-v�-bo-�@'[0 �- iscuyG�ece^uJ *q-Shah02}�-%YH�-1 b.\:" .�'a�Eu#�0F#�D�Cn���-�A�-�|> ���jJ � - z�-a�{� P}F�\� n���f}F�-]Y*218j,<** "N��!^6@�2_3:^� JVJ)"��-d%<�-�"#}/V<5� �{3}J@-z:150�� 6B&�#ZzYcR���^F ��,E��@E�W2+- :Y�"is *x %-aH]:?,T+ <3� ($2,2<3Y+�#�d&G��� sec"�a�N+A��y� G��ͥ{<�`s�"6 �\�>e �*� *�kMm�k"&��A �A�v(� HC(]� Z g�E�lo��=raugh)��* /|�d�,�6wF�2 ��# �o�o!K�ST�o� forXPpe.rDof�.G)!". N E�� rt�d",#� @-)�)!�Th�Z� �1-I�!.5-=P�2� �  �3121seigse��'{1,2}EI7}{100}.a�24T0^22%/+1V{c�^&�A$� * B$,]LU)h *.U�cs*!�*m*�y �Ewn.%�N*1MS�>*-% ELODb�**UV!"�&)� >_b*��DA4U� b*�Z"�M>Z�)B$�AB��6� 7F�Z�)KI)QZ�)�q���N����22aG&�U��I�E�i�1�- �)��n�=�&Z�-n!�I �  MM>=�3,' $e-f"5s0 ��p�];iƁҥ�EDAMKG�! -, e>�"� b� Nowfo�A�is&c2#SeNh �~��J�%?a,� �-!u��m�x�Q�=��). �  Ie� $2�{2$�0Us-��*�~BgN&�\# �a� A!b� 'j,. `���&e^{-i(�'-(S)}*�4"�6)X 12 1(- 8+8P+P.?"E->?)5 pB?�5>5�2[\~&V�8i�H��2S�!T!�ca�@nEPand*�%%� y. [/g�;2�u ($3-2<2� nUed� E9�U-��4AjmA�.�| �o6Bp ` � �AYat�3"�26A=:%Z)�R P}{2�3;{2-!�^2 �@}f (!�  \975�AY�- %z A^)�S F��(=1%�B�hi} o1)}�,%��"\U{J  A^&��.~~wn�B_arP{h��'}Qn ��<%��}1\\0%� )\�C : J*E.�!�a"�0&�Qa�re:ڊEJ�[��ofB�'�ci!>�A]\��NNa^Y&W&11X&11 /cRD�X&�u�%�%�aNKE{�t$7�H2�C"�\�Di#1t�2.�$�s;��rD�!��� Da�]ul�� *��x�( "J&1h�]�&�r]&� :K��ac����?DE6*L.��|g��\� et"�&�& &� $��(�pF�zeS% U�-"E8�>�2HtJ�i^|:�&u��D��E "�for� sJ�� cptd ���&Z>�fa$&=&k\pi\,,��f +(-1)^k�m�12 % �]�*2�}DW!ka� tege�e�F� I�aM(As 2_�I~�9Y )� beco��deR 6F&A���D7~  be�/!�.�o.�n�?)�v��an&89lueo�Mbg2ng  Arg�N�r�g�g�1>I�MA�f� B�B(In summary:�e}.A��:�� �AM so@�F�R� y�M��1�[m;B6l!��QX$l�=~�]!w�}is��>L�($�($2>($2�($2($2�($�($�($($2x&| f($Eo~ >.Z&��AA�# 6-$$6R"Hwz MU-$6.$�B >/$Hm&b'J(e�q�H�R�A�*1���!QH ���$u�$�� F{ �6� ���{ �TT z*=13>z3�z3qz3~z^�610)9now1�I�5����&or�ulC�2C"�JQ!��G�c�T�=��q�:$.��E�(=��10F�6����H.�'All"%'qS>�;A��+H! ~ F�:�q %� "MrS� ��!� }�ll"�Ccde!Q%5ext-o"� $ -knoGTg MKD *9> ��"i�&8�� ���o� by mߜ�]mpIz� \nOe$ �F }�"urn^gp^A.� Yf.Y � � /YH�-�-/"d s�da�XX)'�,A�a�c"�!�p\suc�,-ox2@;$�k0creasing, i.�"$VOBZb$$;e�`�-b�XfG-M�*�dB�Qis�ale|))��bot8��-B%�;;. �g% "� s holk tp^�["�")�:qg�s (e.g.�{"J�ellip?�6S�5�R<�Ddi��; F�\)<�1� ��b�^��&/2 aZ]<&E,"� ��L!�Q�� g combin �of / /$ G�U7:B!�1A t~,�a,7mixedI��<�<pUC �6n G9�exݐAV�abovex6A=iTup�D&�];6!�$�GJ_e=JԪTh& di�symmetr=L>�72rT1I+s\Hy-q�rc=( in5��.�e�vT,�m�Ii2�!�=�5��)�2��n">e>doetE�&�F.-�"[k.��BE��������bD po�2�C�iat�IcerE� cpjEk�6���q��S!�5C6Y���NiC�E�]�)*�`j��1�  ><rp�Em� tool�y VB�� ntro5<� quantumiJA�o��hE�: a�hos�'%�T9ve�dHx�%� vidu-i�u2� ��t+u!�N�Dheles�f� J%�be tailo!�by var9e�6�Q �r��2!9�E \4W�dMq �3i:�fXapOr Aexc9^r �up*��% �i0le�^Krof�-%�_�K)�dg[y��0�": *{Ac� ledggbs�0 &0 � workG �\uppor26�dhe Eu�A�$Un��,Research Tra�n netE COCOMO,��nt~W ��H HPRN-CT-1999-00129 ZK� AK a�Fe�e�ɕ%}~ F@Km�D Hungarian Academ�� S�Y�((OTKA)9� �T43287. �}4 -|4J\'anos Bolyai| ogra�'!(� � ��HEnc6 g�� Prof. K$ Berg)\ �#kind ho7Ha��inؐ�~Univer8Xof Kaiserslautern. NVV D8BWS.�:b� AlexanM�,von Humboldt�Dund��.>G�D=�GDGraduierten Kolleg��\>��S autho���.)5(.& uЋ2ioi�\apAT�Fu�{D�EA�d9aM�ea�:�3� A��mon*!p�re��q�1 ���f��s +�< !f� �, bear�!��Ws� �$M$�`�� v <s����e"�z� erm�>6�E .P]�d�Euce�Utr��)���� �}J ($g-e$)i l patA�u� �- 6�&a,J="[ 2�,� "A.�mu_{ijA+(g|\mu|e\`o��)1�e6�f%��KT3!�e5�9�v�.�e9�.��[F�B#�qvibu]l*8C in molecu �vN� �m*] a=#,nck-Condon f^a�N �:S�-"� M\:�.�.$&:jec:� -rD�LLetPA�� �s.G*�G!EE�ֶbasis.�0t*�B"%~�/���B��, eC$� l�# differ ?Ms.�g&aVZ� � ��i��1^^_�M)aL �$ed�� row�if+f�5)�columns  >�5)* .*v�D�)?���-S2?�"�u�.� 2b��Ov-� *0vre��m1� �� ��JB ��1;*CE!�>|,Q�!8� A\us�o�YhJF� E A�G B�,2\�Ud �A�s� a5{�b)l5�el.Vs�6Ӛ�; bottom � corn1Zwz �:!RU� ��d؁�byZG_CI!� &h7�  Y�be'�C0N =MjnoteO*steadA:U8�8"�-,app:Sdef�2:�$�9�x[ ?�62+0-ild GM _C &�+_���a� B�V�/� !�`�%/�%�e���'�C� ./�cllm�q����-)[F-��a5D�n��I�x�j0u�*��`t]��C�1��eP)� ��k EN_ �&�&�B 2A� 3=6Y� � YJ]9�)�[oT ��ed2�!YW���437 a \�˨JE�"�:w".�:�$g�*�� !"�'=Ee +we�zn�Ham�0E�ha.$�����.R�M�n&*貦��>���Ii ەbʣ^�)�\�i�e�ے�Jge������_CF��V?�)�K9&w>55\1$*�.**�!)Z�55S .>r� !^ UN�B� q6} �` almoC�c�C&e��ni.�<U�U2�pC ci � B���mh��!7��n"�|�e�4 &��fof�w*�sa� far=.igh'q.���j � .5��n x5�"�j>�NtB�&d;��aB^�l�/ �0f�U�]Pado�=� [:4M�7`�_kY���i� 'n|�f=g�f2�n:zend8Z�nl%��*�[�Q��%)�1d!�6�(.*plube more8�) z�$n ��eq1�%b0}="�GJ�3� look���E�.Z9�R) e-we�+4�I�A��a�� (S�g �0$ r A� aC� o15�itsiv�G)ex�&�e W]� �+mp�Q� Our$@a� sump�� �DGlqyP�?D+p�%�as �i5A��/�}o�'_��0} �')O Wwi��no� )Q` =���oHPy^f!&et=hk$ a0P�. �} �k����X � �&W2�f26 .%A�Y8�y�*=<�oJ@ Q�a"y"Li�i&�D!�� �$�Cf.(e�䥺�5 f6��4ny-H���"t�f9�.�1=��1)�1})� �~stFdas.>�WMtr��Aire?,)Tͅ,2�-�E_"_[� �s6�,��23�JK���'&G3!� \mbox{a2set: 2~��@ �3}_g^{ �"a���&/�\R� uad Ţ"%�{gset": ye_ ~ye:y#1}{7: _e.��*� � ���C�e.� &+&�g$�I���AI} \noQ� -b ~f �5{^f.�B*��E2�"=#F �I*n�f.$2"e�"\,.9%sY�2�e��1s�Q9�En ��nCFlE.�;4cabb"� ,&��)y�%�Pap�r�ʡj*�� �a�d:M� k��`I�Ma|rI �#��e��C�?*��:MiP DE�):ojHR���XVl�mk/F�ex�3"���Tre�kt����� "I� 4}N�R�� �>_>*��i6IAu;"t"��69i5"�-�e:G\,2}_��e UT\,T>^P-{6g }q evf$���#�&&B;:72\�B\Fk&&)52S<3 .-es��d%�iry�!�qniwo�:mut��E�*�ћ~ )l.x)f�| !� 5f=�k�w�=\d3� _{kl�N� }�7ExG� A��Έ �smu .2 2

� q-M&n% ���`��~ @E�V� Q}}_1>�t=��K42&B� &A�2�&��_1&ggX0nB�_29�i@Z ��a.�|��Ypb2�U��&�8.�m�}_�? are "�E �Q�6��n ByG� B���{2})_{ll�牬� 2�a �� �Z��\ �P?&>XN�5{1>�1}�� �(>_6�C}RL!-���6T.�[a��:"�(ver�" (�h)�x.ToBS P �csE�+G�)�� ��.�H�?l�� QY�A �� k)}|=Bak��.�M�� ",�=0�\!nk-�+&� e,\,>� B;S��;FR_ .D�M?9P"�m!*.O��6N�w*. �Z.Z ��XI��XBX�S�Px�I%K!!e�`�,ic,�B�2%{��1$E�.� �}_2@8L1W6nA����*k��2*��k�*q�2g F2��eq�� |.Dk)}��q����^�I!~1�!Z��6A!c�UU.�(3b*g�be� e�pESfp�(er�� �/.�Ul EC��/V��1D�.x.�A"!f �*�Qy%�R>�.} U.���.[ z}}VJl)}�)hn!ay&� 6@}\?Gnd2��~mG)eproba0�qi� a&'Fa-�"&�z���g�T&I�) � ;����Ae;�|.? �AA �ot.B"1J� =�*� ��� videne�*} }A(h@�A�Z��� Each����cl�ctebwr�a �$l�:IA��*�Q]�)������/2I� 2��! fN�m>�<*��7 �f��>&�A �YW>�"tUA�c�j��/4i.1ie@s� �4�i ��).xA&�SV)1�u�-2�� x��� = z+w~�b(C 1-k:�pi+ C vc)B!��� ,2,3��"�6� V[u &=&s 3}{4�P14600�W 1�P + 857454�P 8�:�!, + 2234532"D 4 �(52481"-�vn,2u}{(839+909.6)` w- 7300 \�+428727::�1117266 �8+762405}{22960u�9320u.$xz.x09 � H0 + 923}{14490.=+17220}�r�!�0��x �_+Y��AA�%� m A="�SsR[ �{.�!-�$p_1^{(A)}("�W)/nB &p_2BV(3�(4�( f�2F�2N�^(>�^(>�R(��3F�3N�^(>�^(>�R(>�dQ /n_d)�&d1�2 �2 sEceI���F�p����|/0ynomials $p_i �(xo�#0i�$�%�S� Y�x)���-18aG(2� _S-2�W�-"fU<(14700x^2-980(2+���5)x�>+5�� +63��-{yW�A.15}}{24}� ��mv�s (294�(308+28���3,�1�SC�92�-�Z�8*�X(28(1� J)xip-�Q -6�M3.j 1}{8�*@Y)}S �1aW� ����)QS1 |.�I�|"�+$��x$9B"����|p�$Z��6U �  23$dQ�$Z"^�)c�2a!��ُ�u�&=&lZN�cot^3)f���a"%Q151�*�X%�t^-�.?-5x@kFiM&=u[ Y6�Q u��+15T�M!A�t^6 r�:�s.JR.\!����is&�Jy20 B���WBZ�\&]I�BF�6��6�6&p%�6J(M��".1�6J�^(A6=B�2r���.D�R6BY(>�RPeAI1��� �po�� �����i�+2� ��+�� ?ZM)�� x)/��ydɜD�͜6}}{1�in�D%" (105 x -7� -8��Yt���s����6�sin&J]��������� ��� +����:#Q��2f�${> 1,2)h*؈��Y�V3*!�o���3�� f�W=.&�)lA&��&o&��Bic��3��d�1*w��~�P��),��5M� %���2t.dzu�+two6��giv�R� �>x0� R�%~1�� E> E Ar \chiK_ i\xi!�ch,�N�+.{2)Q�~w `Zw�_rxF]J�i RQ?NKu�cq�2}� $2|u'|}{v'}�j}ei\x5arg u'2u'N7}{60GB�i�� (-8+�[ cos2�K)&�#-x&&Q +6 hi_&:a!�8-����4!� � 343}{360}� 7}{4�2:�"�O! sz)� )EU"Pi��]2v949%�(� -Vds �])ksi �sin����0V6}� �203}{90g:�){%)Kb�5*-�.A06� 6> �)�)�o ��1"�g�J�j������!��?A =��!�^�.����s�]Cm_" .� 6 6ba2I�JQ%E["j���7._ �/*R.U 2* 9D� -1-5a^"Z 50 x��$ �+'��aC !�F?h @��F� Z�1|^"k��|.}#}"!� *!l�� *� A0A�B ~�1&_aYG �R�K2X ^�ѽY�tbmeZ�y0\mathrm{sgn}(!��1 )�).�s0&61cos͒b��lJd��I_~ y`/A 6mBB�#lN�B0� r(9�F�m�.Y2)&p_2H^{(B)}(\lambda_2)/n   &p_3 0 ;T\end{array}\right]\,, Lequation} and \beginH \bm B_b = \left[ $ O {ccc�d_1 � /n_d &d_2 2 �i R�.>�LThe polynomials $p_i cX(x)$ with the normaliz� $�'; "8coefficients $dH E"^D$ rea=0n)�p1�(x)&=&-e^{-i(\phi_S-\psi_S)} \cos^2\theta6(7\sin+.$-50x)\,,\\)p1Q _D\frac{\sqrt{6}}{4}H4 Y5-r 5��- ���j(7.�+6�M� [ �I+|) A)Iy|^2 +] #A B#�:}�Uq&=�Bf.�5rB)5- �6*-4cos 1sd� 2e^g2:31�5Uo&=-1+ � 2 `}\Y�Q@ I� widetext}i��thebibliography}{99} \bibitem{Vitanov01} N.V. �e, M. Fleischhauer, B.W. Shore, and K. Bergmann, Adv. Atomic Mol. Opt. Phys. {\bf 46}, 55 (2001). ��STIRAP} J. Oreg, F. T. Hioe, J.H. Eberly, QRev. AXI<29}, 690 (1984);LhR. Kuklinski, U. Gaubatzcd c��,.�Ph� l m 40h741i 9); 6VP%Rudecr$S. Schiem%%)928 J. Chem. p {\bf 92},� 5363i 90).=�AAMOP} )� 5�� Half m)�1�|F�nn. � � ��52}, 7�%�E91} a, K. =<J.-��Scsenwaks� l=� 44m442�: mith92} AA�A OA`$Soc. Am. B �A154)62264Pillet93} P. L, C. Valentin, R.-L!� YuanI��Yu^�8}, 845�32n4Weiss94} D.S. aE$C. Young, ! Chu, Appl5� �!� 5�217^42^%u95}-�,�Mar�0 M.P. Fewell,!�9�^F�%�566n52n ToJ.aB. >c`ni� c8)�>c4linovsky97} V!5 M8, D.J. Tannor,q-MDcI�6}, 4929�72�m'98}i8 .��!�229)�82GTheuerF H. E�6Eur5ԁ�D�� aY27 �8]L% Coherent superposia �" MartesP.~ , Zolle ~J.L.~Ha!�B� vecR4118%6dLawallA�� �� P�iss2+ Lett.�7�99)�6�Goldner_ L%� , e� Gerza|Ja Spreeuwe"LE?Rolstona�lI. Westbrook, W.D. PhillipsAI�ͤa� )%,!=��NgWeitz�Me��7 B�mč�e�B^rE�73} 25�J19) % Tripod:1 ory9�UnanyanA`R.G. Β� Commun)�( 155}, 144 �8I{�$experiment�I�99}]�!�G. ��B Habscheid� Klein%r!!2U�Express)��)}9�"� �~% rF�.|%�!}.a�L91! i%A�par� 4of an N-compona� maximal cR�$ state ...B�01}� �,63}, 043401 �. b* �$in Degener�W �Kis�Z. Kis !��tenholm2���6!�063406!Q�5�S2}STS�0od� ptic1���111S6�LKraal02a} P. Kr\'al,aAmitaye Shapiro�)�e�Set8d63002�Rcb2cM� 2X.@6a:43413c! :Sis0Z(A. Karpati)Zis�I� B � 3��905S6BMorris83 R. %e�}��E�--�S 27}, 90��86^5ss> I� aX `= ^6�'A14%aYdual}�Lipschu�? M.L.�� {\em! �  docu��} �y\hclass[a4paper,prl,showpacs,G scriptadd�mH,twocolumn]{revtex4)P\usepackage{amsfonts}> symbB math6 calc6vicx6�.{bm6#delJ&ifthen�|def\Red{\special{color cmyk 0 1.H0}} % PANTONE RED 8AP#1{{?t #1 \Black}} %% for debugging .Zh0l2g0PROCESS-BLACKa 1�d} \title{Engineering mixed��s��a d��four-�ksystem} AK \author{�p}ffili�� {H.Al DResearch Institute� Solid S��e䡢A��icP 8H-1525 Budapestb O.Box 4aYHungary}���} Z�N����V�P� Adam�:��>�n� Group -Non�ar�?��um 9�!�9�of5�,, UniversityP��|s, Ifj\'us\'ag \'ut 6., H-7624&5� �`abstract} % We propose �e$method isd �prU A� any pure� a � ����I�q��um }H dec{ 4ce-free groundq ubspace � a0"�4 multilevel  mBA � me�( a combine=So�al pump�!ya seriesu �t excit9 !cesse�JE�Xa given pulse sequence�sa�final) is�8btained regardl1 of2initial-1� �-� �robust�re�3 t toKfluct�H �$areas, lik!c0in adiabatic ^(s, however,84field amplitud!�0an be adjuste� ) hs�e  !�!�4used not onlyE�transfer�popn%G,between two 5~�� s us!� craf�laserI� s, but it%nb?8utilized to cre� y�6Es in!Z ree-����ur-�-� )P]91,"n98,�.ue, a8��e "ly} z � !�at�/-H�!� �( arbitrary ^Gs>f �� 02,u �$N$�]� �)�, applicabil�#a E*q؅5 limi!� by con� i�on4:�Q�E(,\97}. ~ otherq6 that �vem:towarde u� ci�� * �� terma{``�� 6'' huses m� interf{  pathwayx �Q� c%�Q�0 selectively ]� from!�>�to��t��ti�Id�$03}. MergA�t�Uu੮a�mmm� lE� �mapřof wave-� etsue vibrŗ��o���eurfacA��x�,QL!8aA�R[ !�e��F9**R ],h�4n�$ advantage7 � ert� -%two� � Y� ��!t Q� pscribedM�%{� u�#o�`u�  featur )ourm�_ par���PRare��$following:a�!Ns� tan�ly (i)� , (ii)%m_� *� 1vN(iKAOD� )݁�n�-�� � , (iv � choicewP &* A�:0 is quit� -Z1DE�be impleed�*� 6� �F oncretene�A� us�E��Fl Pn�<8 Fig.~\ref{fig::}�re�� t` �� %A� nd=ingleI��( coupled by�e� ticaX polar� y* - k $|g_q\^ Hle$ $(q=-, \pi, +)$AZ assu4 to���magne� sub s Y$a $J_g=1$�gul�mo!y"�a�e,%�a�� d�� $|e�� $J_e=0$�)8����P the %$a�x , deno!Bby ${\� E}_q�%:� , %��dm�, $\sigma_-�d+$ circ �6� (�%-� �A�!D � ro���]!@plane � endi U} %n&axis)9NS$\pi$9�s a nB>��ll� h��hi! %All1�%Xks sharA�e�time-�D��$ theye�h:� peak& �phases]subH(/(\label{Rabi�b7e"�$�-� -(t) &=& 1�4(t)\,e^{i\xi}  mu_-}:%6% varphi\�%= _\piQHQ�% G><+)��+.�+&���2 wa]!h%�meters $ �$,A� N$U -o�9I�of�M�s, $\xi$�MAdabsol%�U�-,�&�q>a,��aN}� rela0 7 9pi$o eᅏ $!�+$J -$,�o ��692\dec� a spont�# emissi��2,/ a /Xof $\gamma_\textrm{in}$)�may gaX���� than%c��Fd�^eext}$( ' . When hou� !: Ul s� occur a reK p� % a wR_p)�switched[ in or� to%�ensN� ��*�los�8We��t �a1 �(rm�&�of EOsT �/ �Uy6sg } or�-,!�Q &1}�!6),& %g �l�}6L W-���figurM\include�,s[width=4cm]'1r \capL {(Co�O�)k��g%�H Es-e*; � ocedure� lower -se`!#F�!Ua $J=1$ Ga��:�� � �ed�vu� {\pmA�n��G����-�sJ ��� '9ii�A�A�q�{\rm a� inm�.�"!��te� N2U@ �a�i..c)�z t}$.L  zero2( "�u�isul Gon j�re� . } ��*[ � QV�j Mas� �s�-AfE �� ev� �-AA71 is �b�$6� � eq:meA�c.$rm d}{ t}\a�hat��rho�,�.1{i\hba@[$ H, /$]\nonumber�.&+�.�� t�� }2\sum_{l& �2QX L_l^{\phantom{\dagger}� r20 & -a}R2�_ -5 s�t~Z )-:���h }{2}.Ge y �!�{1R>@B4�e�/R_p (1-5�Tr}�/\{+ o�/\})2D,5�i&! & 0Hamiltonian $V He1"f :� H� �ErD{2}( \Omega_- |g_-� \la� |\, +\�U '\pi)\piZ+)+'+B%!(1Zh.c.}x3�)� +& �\Delta"J � �31a> ham�9�92 ]  fr|�� $ �- =-1}{3} � " �e \  U theta � ,+V!' = -)o1} \ ^Th *i CB+@?> � &� �+}.�*k $, $)N%�=d_{ge} ���4 step operator�Adef� as $]H L_q = 98\U3 �!��1� e|$œ Y�L_eCJ��c �#ol2� AM2�� Eq.~(�A)  un�� eigenZ:,\Phi_D^{(l)}M�$�~&8�( i.e.� yIC��i   exterxdrilb� � HNp=0$� r $l=1, 2-y:>5��}d¡�NS =� * } n_q �2�,,��quad �ab� �<� �9�t vecE/ �bm n} ^$�>�@0 $ %$1)}=[e^{ iq\\%e[eeiX,]�,]� .aya\? 5]^T�� ${��2� u6�+}B, 0w�6W^ ,%� }��\mu_\pme� $ 7�1� if� Y���s})se.�  dark , becaus� y do� �N "�^1�q a�Z M�$Arimondo96� .m�aEm�}@� "  valut)( �C U9�6���6�thD">�.� Lek D ��!�v� b so�"!W"-��!�rho2:�1T� �, 2�� � .Y par��� "� ��&g )�[jA~-P5.;� )�% �5> backefor:via�)oscil�ons�6�M4 Ugp� ��.�&� will  rupt�2Zdynam�'�J� falls �@.� r)�I����c!��ed. As� esultO A�'}Y}A�9mo�% G, e�$though�I�6���2�1� j n� cay � 6 �or%:aay � �!/*-)1;i�m��an in�t F9% ?%��x �g)&�k.�.�6n.">I��is�.Q ��� �#>yout}=p^{�5��1)�j��1)}| +32)32b3'F�=&H 2= $[l)}����k""�Q�6z&�It! ��&����outpu�1Z�j &�&$4$,��Ply � �&�!!�r�!����])�I�+F� �>:���1M $%�^{(\perp5�$ ��ogoL H UI���s��a� )��� B`^ <� &�*m*�\, * -*�,� &  � e4 +}.T�F :$ $\,��isV 2poia�FnyI�i*t-dimen�al6o�,-�� heG-��*�. Con�)tlx8iI�possibl!�+%��BG,�V!"+3 �+lP .� MD $|\->1"� �A"2%��I�.6w% la�(-eI>��%q eref�=(in principl�r��ist�/ed-)!s()Y��5�� ���#1"N ? rhofn� f}=p"�f] ��%1)��!%1��62��1C.22|J�C!be �+)' �"� A�. f}$E�be ei�� a�) if &�B2N$:��X$vanishes,  K both Lm� � z'We� d%I� task�* now:��oz.i'howAj� ��  #'orm^ w��E��l�B$�",e� cer�, : ;� )APdQKU�A�a�e�"q���D ��M�K -�by�?E�f4@ �" veni� ��qй�a�� n�/&J $F�}�rea8enA �� 2 {{� r},�&<Xs $ r_{4(i\smash{-}1) +}j}= (:I)_{i,j}a� $^!"matrix eo!5Wd � )�6�CAL%cbas$$\{�I�V�9�I�,*}�^ �/a� produc� 59N!�SaA�$()N r�A 2)�,= .s{rh *}_s} 2)}_s� {�Z�8J�^{E\� \r x��! F� i�+isY8� take�-a� $4 B�bm r=Mr+�Gd$� %�-�4 M}$ C! i��&� !��� B�,:H U d�/or�0 ondse�Gu,a erm,Qbye�k*� &{a�E� i�.B�&we�� gon$wo�* :  $($\alpha$)%��*"�i =R_p�:}u� -�1"5!a homo@*�&i�Fr`$d$� {@� x)��^��*�(�)ŚC%1� th��I- ight-�(��(6x#bAWr}�LaTk J I2R6�)��Qh�ME��*bel1�&Q !BJ8 bmM�^{� �R}E�0�!�O"A�%\,T (L}}�JM/>��!+ � �I�(R T Q L}|l  R})=\d� _{kl� �9� =��"� � %^ a� ��. %�!\��#Q<��%|. y�ao E�.�26��F %�q5�1/< )2� VL)��� N�/ .1�W�,�6$2@#&^ eig}#&*�� ��Q9� 1�{2}}\!�(�� 1v�-)vz�%��K�`�rhoe1}����œR�B����c�5u% +/f�� ���2b�3m�{i}>]N�%q� Q#�=]�>)� � 66!]3b�4F�R �f���[�!Q1^&7Y��2� A�1eW� �"` �*mKAƽ�qa��r}uε��� firsg|4" Y�k1A� � �� �s�!�1� --�3}�1��tho����6i'~ }1� {= 1 Ik 2�: Ia�&%�M��L, �63.s fi� ���g�9by � )L�!� _ ${k=1}^4 �968Lb|� � �"�" )� �z����tsi 3" �6 2  t}����� 0! ByN�!Yb :d!�.�ig%�A|A0A.��Y&� U5L/R}$6�input-"}I�$can be wri�9! a6/pleXm U�M�_& {)�= * T}_W"* A�Qe8 in})i�� �caGA t)$�*� &�}B6 =Q� H'K frac12v!rm� \a�Bs'�Tr!�KP_D�  >bs+9 �/F� map1"� �z9� P_D� � projEA�� $�EC2 . 2�m�� l e�2 ��k)FBfk)}| | � eta) Q � � �%�g2H* >0$:} No8)&�� �<��umI<T8 q4"�ax� channels &� ly!E''�*�)�� "  8e-� �govern� :&�2�Xq�:r!A�t.i F7}�r} �$tilde{# r})= � ' * +Ib6,anMK�&/?�5r�~satisf�"��M}'>]�= -�d$�a�. x:* t (Ah6oi}��Sy+� 9hat%{m[}} `.aULU3|g"� g_+�$.+V .� >�$ g_-|:n$7&12(�(�+--� sin2R�q-Sao)%�I �$J�T� ������ -q�� %�1|)�!�$ coincin@e�9���. q 6yM� ^{(i)�-(($i=1,2,3$)M1y �em1 5�I�Ŵ i)} �'-��� bm 0��:g 2[ces) JK Eq> --�� � Dead�"g  <�AÉ�(� �X 2T:n$&5nec� thro� ,*$4r� 9I&w�Vu� r} +�i� 3 (6�i)} |  G in}-:D� �) i)},���3� �5KU,�Tr~T� ad��&�*���& �� T}_b��� >���473aCrh��i;B� a�)�( yR>&R6T*�R!'�"va�}�K.K.2^AypvP%�o*A�, %&�i.'$rhn� %-FC ikusQ<�[0K`al kapjuk meg az impulzus��$ eit �w]urn}/& DJfin"��EA� at y�8s aei��q��B�[�E.4 f�$[ :� 5�C�FW� &��D3 �R�)t" B!g�a�1<#�t� �85^ or&� map2})&UY�YZU�Qci�f}=iVT�vN�a(\,.-1�^ hdot7P�5,1 ,q�y i}) .)<�3U�opt^�y ^ � J��_s���E7 6_F� $ orv��"e�%�Dh&S�.%��*s�Ct�oAMN h���� "� N %�5��i�+Yg]',E# mean%� minimiz� �F�:r funcA5al9����J}(�$cal{E}}\},5��h-�n}�1�.f})�G� .� {!� 0{b\2% VUx\�)^{1/^.I*�ImU)��eU %miOch &wC #;� � V f� (9�rhE�))"� �-�S&B ". )YZJfH�!�B3� � 5�9iz�$<�I per_8 I3of e.g,� jugO) grad'a�=�(numrecZ)DuM!��p�O� �?�LAt���P (p_1Q �1 + p_"�12)=p_1�Ua�mM>!1#+ !a& ��]2� fv&$$p_1+p_2=1R$�fsub��I- 7 verg1 @Z@���("I_� �*H�6ar6QH��(T) F`Uur aim�toX�J*�!��t�LB��!�%ya�`$ s�L xed}�"}��!�6��*usAPa �? ex��%�demonst��*�Bs A 7%1 .�6MY:�8�#FdeB�&�Vj QfT��� 13 |E"{i�"�#�LPh"2#|�b E2FEFi6B�� rhod���y! �!Ek%2JY f�=�q[I�S{�S�27�%pi//[2pt] 3725}\.670� S�Qf>B�9 r�35^�45�7�0"V�"X1A F�� discus��"$�%���:�>m s�-$��^H��9�qret�we� F�"_/"u"--�#��(��wo ay itud--a)�%a�a8&�&p�Q ���L. �n=.:.p �@�83o�1p�:nC.2 $N=4�F�E0HN�co^Dto ��&��"�� *��b�f, q�)-��$� */ !�5P�� et F� !�2��:f�=y��Qn�M� � �D4"(I�7in :yH"aout�-�$���\��ofE��%.M@(<lAA�U\Yx(�13, !*  T + $) �3\l�  ,4 cha�T eriz�"� �$v !�a  T'# &�Iec 0Žn�)�0�2�(52� , ��!� "� Y�%M})!H�S)�!@approx 10^{-5}$ (\O by machinHci�*�� *� s�H� {*o'ik_)q��}B��ze show:�F ph1}. Af'< f�)? (J1a) * clos�3QW&��%.�!e8�N3 Bloc�A�&�The seco� �\N�b) "mn /"�R,cigar-shape,� phA6ir6 epA ellipsoidR\c)��tribu� ,2(l�QK��� �V!d)�GWs��diU��E�,-kU reg�f. �W u$ W�[M_U`��� solv!�"� lyY�$ ���.`3 insJKCA 5� �tVm� X, ��)� �%$q9FHd:Din}=1 �_ duMa� e� EshouldX+c�$n�adt��� %6 3N?actualFaY@C!-�:� �a"� ll p.2�& or $ )gg)(in=fb, )s4�Pe �of ����D��D�,width/2-0.3c�D2Yr�D:�I���6Ş�#U!!��$rst- (a), ��- (b%ird- (c% ABrth- (d) G.t )0t ��a �xvm�c-s�c�'f  G two-2@'d]:�-͓��ord�5�R>. G#ZeoR���� G>� �"2(1+x"� �Lx+y:y z: z)$,"� b Gq$ ��Pauli'�\� p�-�n�&�� 9.�"�+ �c59M] also)�> E�6�EE�1:��J5 ��  M�͢�� �d��a�s =previ�+<y,aE�) Ѣi�a� eric6rEe6P� u�� ��"� .:��is� �J�� ��5% We'=��!��P= �q�2�*� ��course!.%�ls� �.�*���wm� r!Rb�4�n�J�>�w.� �JA�"�%�)R ��setTT."'Cy �a: iL�2'[6L�H ., �t]an�2�X`�MxoP@y:��1!��Q8#]s�$ilaU60#6z %a�Bt %�!��neg>re"�-�.�� M'�#"�'� 2�!/35�=I �'$ y } %F}w$WE�{�Uhg5"!Nio��.��,6�e�{ )~ infl&�a rapid.8.� �&ly �.im#6ep<Q�alway=�!: summ�]r%� work�MutD L�04Z* �`Rc %M��*6sΙs� &�[ $\L3z$*=. Dme"�cba�-on* �Sş-��g zLs��at�=es�D M@E)� aC�Y�� %.�%�$ .�$"?F !Geca>N� e��Al�>.M �*<�`a�b <<3c26B2r i��s�4iveL[t*/c)a�M-�\�M�<l�`:D@i:tTad�X5 � com"(X_�Ms,�%)A8E7"Vc)edo�^TDf�&�8� Fh s ac(b ledg^�> uppo� "� &�gFu�)� 7f�I Academ�?f S"{T0(OTKA)(EfPaCT043287�-0 T034484. ZK.�iD ��4J\'anos Bolyaiae gram�=������>pk� y. y� B� y� % "�l`}So\w�%y%%� �'y'yJKF�uA!vA��,�)y K�,y,y�53ds.y�jb+\em{�\ NAx&�u czav0y :��1y.;nMa��uJ�u: �u94I" m��u%A  u&�u:eG��u K ��u�u�*ao�qIz�vSt4)r/U��uK�%bf ��u��u�IBu Comm��u��u� 2�Exi'�#a��{)�9-�5�g��u %�j�i��u��u��u�BrI���u��uF�u�t1)�5�]h��uT22ROA. �$uR32R�b97�t��E�S|N�vM:�2|14�97:&�g�F ^[pBr�k, {\it P2C `C�h of Mjg ar P� (}, (Wiley-I�hs5 , 20:�Kr�w{a�8w06w.'T*�g} I�H�go|"�wa�B.w�:��ƀ 113003%���UbhJ.  XS.AF@u �6 �410 T %14V&�g MM , I.Lm�ua�g�"vum�Ppu� � I&Ohl(Cambri) *nqKz , 200��S�f} R.  , G'� tiz,�E. Gub6Q tis,Kni�}\Y$R. Laflamm:\v-�x04232)n6|Bxg��  )et al.}Jy%�P�� 0623Cy� �&�g V.E�r�g�x� G3� 5207%��.s}�w KastlKp%"-z�M�moor Stud�$Hertzs Resonjs"K(�%�NobaLec�e �[M1963-197ȃT (Elsevier Publishing H mpany, Am6Ydam, 197>�h~ W�nh?G�$Th�}5&�A$��E"W� , N.Y.p� * �ֹzi1�9�"�Sa�Ab Arz6zI"-��Bcz.�*�P E.~,!� Prog�x�%�s �NE+olf�$vol. 35 5�:�$96) p. 257� �Yd(q�n "x��B�y11pt]{a6l�r\u&�yurl26y[brea�Tks,bookmarks]{hyperrefo>fullpage2C{r xsym6amVz/z %�hi$ \newc�� nd{\�e}{F Tr}}6 prob P : size}[1]{�& |#1\(4|:' ceil'\l,\r:1floor.23:4ket2��':,�|��#_>�bra\2 �0$!\mid\! #2 �VnketqA ket{#1}\!W{#2>R�B�|\,#1\, ^>�tr/ Z�t>Xs-)�\{�\}}Az.st!�;�3;>Geqdef@tackrelE7=F+q>)?}'A�isc6je. ;=\;:�qu}{\�9}8q� s�,fi:Eco���O>�chH>o�^R:ait ="BAkay] K>ab�#bf �B'rh�H%:e�_vJ(ar{\epsilon!�2�hx#�.xF�yBtrnI{IXAN: la}{M�:r�j:�, Zi Z:*o�%�/J#X�! !�X>AY.Y>cp.P>Rrm I\!R>NNB0Z�Mm, {\hbox{$\sf�\style Z\kern-0.4em Z$}} R( v(s5�:R3 R2z *N02 0>�Com6��Aetbox0=�display�\rmeC$} # to0pt{�<0.4\wd0\vrule he�H00.9\ht0\hss}\`}�>l�`i:a �aa=!�6��c2c9��iiB�d!�X�#Y�d.�8domb}{\{0,1\}^n '>.k M^k ( Y^kN#R {kn} -U>5lr Yl , Y^rR$.ZlBZrnBZf YW\to �>_)^> 29�Tt# em{�Pi" }{DeUD 2$ ,}{X em6lemma}{L28claim}[!]{C2!f� F 2�1 �&P � 2-co~}ary}{C "environ>p{2��[Ex�. e.]{e�,\par\medskip no/UntZ #1} }J+ ~BhprooffP .d:\� bf�_noS $\leavevmod�\hf�[$\Box$�big��\date{"lJQ t��uHClassV �icB -S Tradeoffs� Rect]2 BG'sn�8{Hartmut Klaucks-anks {S�ed�3DFG�5Dnt KL 1470/1. Work}(isr�" at Dǁt!� of�pu,�>l�Calga8 � p4Canada's NSERC� MITACS.pI�>$itut f\"ur&ik�JGoethe-U؂4\"at Frankfurt(60054 am MaёGermany*{\tt k%%@thi.i�k.uni-f\ .de}!�.[�3b�4ct}~ der�9lukb%��#t5�"�~h7�-� $Cu$ $S$: 9 u $ng�rits�e�- such lij%qG��r2IfQ4 8"%z $f:��\to Z�$m*�?��2pa�x���on�  T\Df�!$1/2^2Rt�U�)%ed S*� prot��� �$ Al'vreceiE �`$l02put;�ob $ra=Ua�A�, $f(x_i,y_j)%H< $l\cdot r$ pair�p�@s $/ need�!.�$C=�,@(lrd \log |Z|/S)$�%p�$t, $�� n$-,%Vpm�� q �! /!�eld $F$�)snTMg (n^3m�FFo,-w-vG:[�:2 : :��!n �>$to randomi�m6�1�!yM�A�( �8g�/S^9�Boolean V�!��:2F:r�, u�a ,a new direct��U�`�� one-q86��,}� on.}jonplexityels�%as implyFJ�)�q�Q��=]5O 66.�!2-Xin;ksw:dir�V}OIb�� ans�o a qu�.on��Be�9�~\;b:օ~}�6a�� \se�={I&�!Cɝ=sec-i} \sub,ѱՏ } Coav% al��-�s�)PZs�-!�o�Z$resource m�� be i:j$!* availa����.8�(#/�y (^!a��&r��sx�ult� �U typt?�2bM� esta�͵obham-Sc :%P off}/&s#<"5�'�b$scribe nicq~A�j�1 behavior�6��k$ ��-*s. �CɅ&a��I�?+m&-�@��?"[=A��sN'4se�,E%�s. It�*s4% �=~([&�ly) soOs$n$})b�v�.�%�(qAW��E� ��O� )$-cI��-b; $O(n�3)$�+,P�Q��2N�{zon��� ly=g��<$�0 n\le S\le n/ �jpagter�Wk1|�|s�z1�lGJi�+faT�-!�py%�B�|oɂtK)��E!fa�ng!L�s�(1 q�`Ʌto*ve,>8>.� ^1bs,�sl�6peb.�Ol�>.�Y�_usu���!�"f+�' curr� t"��. �I)��s8n�3E �G��L'��2 ossi�!}to v!SroA�x�g"� on!"4u_by emploT�dev�I�( on��phyC�0ei�vnc:qc}%�ae���\x"�F�'. S�Q a�&�1}'i$algorithms!ra3�+�(.to se�u� s m!�candi� I�~(speedups. N��%�w҈yig�5id�2B� YM�T�.0c �e�J$a؉�$8� �h�]�8�"�N� !2��.�nam��$T^2S�PyJ }�)q�2e(xan earli�!N )�(aaronson:adA�GQ:sh�Y�n�}%�s?Eta���s�5.� s,%zll� 6 5�i=s�  � !6AD ܥG�{3/2}/\xp{S�Rwha�!/upperi |(%�i�6s5 a��^3�! �!$�9�ia�:�B�ON�.��*` I9�A�A� view�0s4�eʘl�1� �~)U�. Sh���U��0+${y9�L�*0by Lam et al.m�lam*B ��n�teUI'�a � Q�+{�Mby �� "^e E� 9C�^ play�monly �r �by"��7.)� ?cC��e} *? togVr. No%hat�Sa: >j�. N��2'/s�k }-true:�if�� aF� � �,is>.g�S$O(A� n)$ b%9:r� ��!?�ed JI��be� �|is�9b.{onpnq�)a�. Mo �ap]n p����5/��1!�k A�R; .�-�g "� aa� kind�ofs3wh%ֵ�u�m\� � barr���j {2.376}*?%㊭�0co�qsmith: � } (i��!�Rii*i {=%ch0�ng}- :�'�;ly eas���e��}�\a���,i�caX�@�1 �5/3��� BS:qverif��IOiN�Mw9v� h>i65:3��E[)/�:�.~m�io>c��A~�c�4��2w .� �2��%��1� �C � a� �B�%.�Vm��� �!] . Al+�Y��a� collV�� � !Ti4\v�7{.5cm"(tabular}{|l } \h� & F"s#. &1  \\ & M)�Mult.-V/&n\\ t "�&&&&\\ i:&�%3^2^uw=�  56� :B$:� �# & obJ<. J�&J�� ؉&�C$ F�e � 2�>� .Tj����&  &F�J�D�J� �� 3}/ o-�{2}�z�B�nM�R"q.z.%�y (n^ ��.O�\\MA)Tg : } Z&V��|dq�:� "R �䕅 �iRE�s hold�p~2|� � ��� �fl�Z���"& b "sl� ly*R (branIjA8o8at� p �~�eo s at�= cost)��h]�:��a � � |F|$�?er�s&`D�P5�,��eVwe-M : 3��"�q� \-ZBG /-��0s���rc4�kis Fach (�@"}>yPncern�s<E|�)�K�s��t�it�� a���Rzmp Ribs2b0rba =ramounFN-�ion. S�a�} D!�rt �a (dl[�ed)Ml-t� vVK �5 ���eSE"� �replac@tot� mi" �Ak[Aj��reduc�suc�!gbaya�Mz�S� N�9x.%�na`��Cix9'wit� ` nAd� (butvRno5"*v)��b�$k$MB ��9��l N�exponeۘlya$k$$k=O(S�D� w)l a"n�ult!-�lu��h*�M�-� s�� �G>a.>i)� . A>�i�*����!(i_B. �� �Au&��� R w�" go d�M69\pk$H � �wo��F(:^ �i�a' stro�R*!�try���e� �ES� A�&Y%�allowEVA��L%� �@sEQI�q $2/3� �weak}>�S%�h)wE��� �G�aC 2}. ����'�7 $\nu$��a .�I! $$�f %nyUI<$�($�nE�L$disc_\nu(f)=\max_R|R�, f^{-1}(0))-B1))|,$��,re $R$ runs @�zjMxMj)�S� ~�` sec:D})!= �A�LC p���F�ll�deaF#uni:9u� domain.)(fW�ll)j&1Y -4m!4i���M f�N�P�rm e��#��!xr&�%a/"�$9<n�ޡ�deQ�g�| �H ipleѫ�<G�, �a5�Vof��0color�Es}wi�Cw %he!er �b� ful. $-K(�(f))$Q�}������6b  qShaltielms :sdpt} rShG�&� �s��:��jorf�Z�� . He�" ever��:?�?E��!1��a,�G�a XOR-�+: �Ehow��at \[:(\oplus_Ng*W ,k} '))� &f(x))^{�k)}.\] P�L(ly Parnafes6F$ prw:< gcd}A��"�>��,Ū&Q6ٛ �fheiA�� !R�is �!�n�/c�  $c�(V^� } M�Au.P, sa�)H ���I��%'�� good"� �Xs.�+6\2oq"�[ aV@QE@!M�@  ��Diss"nes le}IqP?&5a^�G�JsBj-�!>��ϩ( �[�en�s���"� `N�� d)�7�S"�a�&?setup (Uv�|�J>}):"E*B@*!liv� NI*wal|o%� eO*Q*�� $lr$K*�K*��som*� �We�=is Qj$by $f_{l,rOWe�%s~��  ! 6���A�P+is "�5ha� a�2\� .�� .Nk o8Me�!�M� %� goesfn � all H���r� ;��  �bi�+tO$i�_d�!D"?/�'s>� 6%�==� :>�����M:I��#����)J���AN.�/\k� V�),+[��it���kn�;dI��0 "A�s�(d9P� ). FkUerm���J�ut.*QXOR Q&�!���� ��bJ!*&_.Y� *)�NR���0�L�D.>-�E�"�� �TO�? ;}+ the:cst} C�-/� 2 � (f�`\dF�yB�Rk|eܩ�����#2� `dlr�� �PIletj*analogkTbm��cafmad�"� s �do0!�e�4^Zus=�X���R2  .�N(� !`.��+gY]fFZ|?!!�innKe��K�-/@*(IP^F(x,y)=\ܙi�x_i�/y_i)��e�U $F$. @{GF�Y"($�&���*� id R+�ory;+is.�&�"��2��i3$�&(�"(>;-�ed^��� � 2� ).�#�F_{n,n}?�2\�memp�� *�0�b~� $F$, X&[1}$�O�< 1�*&( � (IP1�eO2^{-n/�S*� kushĵ,itz&nisan:cc�A� &&�-m�J by Mans R�"�% mnt:hash}�$�siBU� "q%$c� 2|of6�sI^M��)�3c%�9a t�al 2�&�#Al%Iod"�,Qyn&45 �+"* "q7.�/b����cor:mm�X sume�-�'� �. :C�O�uu6 by?2|�0 ���2 �-�2 (|F|)���p e�B4�?� 10�%� nFg���� .�A���F�>��~�BgJ��Y UsA`a l.]y&(�*-E >P� f0�/toe�`&7� �5 wiseS��al��h��5M�P� A{ :9 family $Yža�G ��ft $X$ ?����2KA�� $h\in Y��sb 4tø dom:�e�Zat�@`� t\A�$xH X$: $h(X)PI"O%_ $Z��:@,x' Ci` $x\neq x'}8 $z,z% Z$, ���tss x)=z�h(x')=z' �X;�3ente���Hm*��e6Za�/a!@9k���) g��,�%�����1c��*{ e �)! end21pY�� ��A} Any~I� ��J�M\of� �s학��-2�� leasj,Omega(\min\{�f(|X|)� Z�\, , \,^2(  }).$F��V,_.�'!�0 ��tV e�Q�>_ :�M���ݜ. H�p f"��+� er�%NU�a��p�2a  P��rd�:>�J�!�Z,�// ��.us �� / �%un7� GF(r)�( ^25; $*M&x: ,(a,b))=a%� x+bzf $n=�H!� r�Hw;|is�� �7 antu:�&Z $CS=MKn�!�%�1!u(=BNI���rH��o�-�p" �6� :! J�&s�g�dh�v�� r\ in C7@�a�"�"RE�� W uAM(:�w��? ,�4��ћndard) Emco/�j.� UO�;>litself�4:.)%�ȱ]��� .p!A"^20 m�s muchF�* |X|E��%�< 7�`we=K a�}�. AAU��2�� %�E���w,a�a:��>. 9?t2>�<^8:N-3)MGE� Q�R)= =fa��>J^%�!x"K< G���onZo.� !%Ď��1��i � VI�2M<�eR�. �  a�an�r�#|-N-a �,&��85y ��^%YR�0EMa�--bp�? $x�&2An>! $y�se,$y\?�XseB@��$DISJ@1$ if���"� 1oi &�&5� $NOR(x#, yj"�$'A?$n �s4ng�8%.�2� AND-��6�=�$�$% i4_ ,ied%��s��6`A* �e]](&Q ) world~as:!,"O�>�\x6��X��� ld+ Buh�ChCleveWigderson98,hoyer&wolf[eq,r7&ambaY�:���� }. A!Z�zE( �}! =L2�has%R2%1R'�%�9:<? �|R.n.)��is�bi)�neg?? of�:w�begin"�� �!��G$ �t�f$�M,n>0$I�k� iv�@i]�#?; n!�Q a/V| wn$�s �5ap� 2|P&"�F") $B�xN n�%aR���t�."m�*0%c0 at most $|)" k}o �ln�!�0��i��� �Jd"v&��)}�j�e�QB(6�:q)��]�"� |0!o��"bN� *B�C. f�7:�V�F��� 2��UD�9�\�*�in Ap�ixW app:D}. O^/2�,�.3�~,p.~2�'Aos *C$�.O ��prB�!�nt"�$% U%�|&DS�4a�v N��:; E�!����t�, a�<e�: ʲ� !~we�ll near-,k&2!�&,�9rpolyloga�>icMr�1�N� :WE�6C�3&F���Y<2.5�F��!'n|�ex�� R�&-��j���#��+�ic��ead����or΍ argu�<�E&KN � Prelimina���K�EcU 2�ECo"7ng"]C�-s}"�1;2�r,ep�<�{� Z:/&�$j 6 JR0 d�?s�x�te�%i�nis� t�-�&�)2�M�($pre�ed5��i�t�oG/9Tl��kO��W%n�me�n hang�iqu - s2� �-E!�� �&al*�, FY� xA .�9&�5�2s1G6�a-)���. unb�Led �Y{6 &�B�w��ha��s�# J memor= .e.,�yG kɵa'&8C �. T�#end� �:�2%ngY�M�,-�Yao yao:q #� �!�=��6(T1$p1i' wholeOE�\ $S$ �&� sA��Md a��Q!�r��Wi=ƍ�%Sק\!�V�� ing Vuva�#3Ay ?�A��!Ae ���an � se��!� Mz�K Iat��e4�Cg���<��5o�t;�A)�� ���W�A��i�as# �3��mS+ �� d� ��me�?�GI��rowQGaw#G!�#, s pick up�Pfresh *%{ sEU i�n ��6ema)7!t��m�1M3wA�nA1 Sa�� !��Ee Q�� ;��-�w$_,f �H. 9*g#AD*�+L�tT�cO�HR"bO.Nz-"��6��rdef:c<k�J&dR $M_fN�*.�R� r+�W�ڡ�� ����X,��t Z � A� t��/a�~4!k/PN &)�uK ?�l�!�\ell$-*6e�$ �%�� (R"-A�/a�$R� �)G C7.E�A�u���-bserv�&��1o�WQle�Niv�$RIteq X^*QY090E艃�0\[R'[u,v]=\{x�S\,��u_"�,u_{i-1},  +1}�,u_l, v+ v_{j+y_j +v_r!AR\}\])�9s�4�$&� fixed ��s $u_a<XZ $v_bY$, $1a,bl,r$..0�� ��"BUmj A�92"C�JA�B*�u �3A�H  s (&�2:$&�&f�VA� � !Jch\u�2d�&7( ctlyJY5 1/2+�$  a�"+�e2oE ��s (a�-$%.i)� [;:0 log(j/d&j2:026.# �yaaMygBSJW.+�went* � �Ytg+237IVy].� � $M�M��AuZI�s@,initeaH ��Ke)3"�W .�as \[m(M�3 �3{z`} |͙6�3z�3mu(R)/i|,\] �!0c ^%i�$�ubs��egMN�E������ITs"�ino� ���<1} �2�!�a;l˰2m0abor;Babai6&bhk:help}� -��V high^�%=I$M���+4& is ver.t>$ �averag�%5�7�w veJ35!�7/ B<"!.umu$� �H nq��@� a�!�J M�al?}lDaW<i �0:MP?V� (�O�6�)�M��&$inex�,�8�"�9r�i2�:=�3�E]^~3.22n �R[(K� %&\�V�%,bQ7"6T� ( is (!��[) bal�l��+�}, i��T7@71))=1/2=0)""yb-.�$err(R,\nu,�).L1-|�*�6�[~<�:���l[%4,( ]3f,fhmax\{�R)\,:\,:��g��\}, $��8 E0A�}x�� . �e $D��P"�8\nu�L1/N�1))&�8%�6�85�"�V,!dom�i , \[�y\{ � {1/4}(f),F\neg f)\�5q.��Npp"�!("Jc&�onA`aa�'Y��ŌR�9�0 s (poc coin)*Ibc�1I)1/4~�K+o )�9:�"�ProG5V*yoB a� � howto} S�`s�����r�"L F����� "�/, ~��"�geM'l��T��$X�A� *r:*^  ���e4A٭� .q4. .|1��+��U 5�% $(i,jZ(�-ESv� �a7; �>�>FX$=�!�byA!H.BJ%$}f��1A�e�a-.5�&� wayE �&s�C�0�C� b�C�s�$d/100"!O�[y� )�af�:23 -8A�et��heM!�"-:�ű6�awards M�Lc��in-�2��a�bs�th:�r�& $O(C/d)$ r��6I �X�1"_(�6�ak�Gut4d/C�Cs#J #Ea�#s? FcanQW�4$jC {!�5�mpU/!=de�� ]M. SoA��6E�s�  Q ih=t�.� � 1�a\"�E2 E����i��� 1�� a ���2=}F�c;&ѝy#�XQ��3"vJ@A,is�<7}$*�%� b�jlpV=�e!2�*�un�_�'��U�"%T ��B��d,*�i59"�!D� v*�E*d���-�(x� ���Gp�G����s I�3 , %~!�� y $p���!��CNw�FN�r&}G <}G.?�e8Nr at� $p/2^S��6 =jQOMqH_��at y_6M�L!Di�, computes it�s outputs correctly with probability 1/2. Proposition~\ref{lem:union} tells us that we may replace the initial state on $S$ qubits by a totally mixed state, and still compute cob��$(1/2)\cdot 1/2^S$. Hence it suffices to show t�any�tocol � communica� $d/100$ -Xttempts to make $\ell$ �of )H, has success\5Dexponen!(ly small in E. The p must be bounded by $O(S)$. W�is left�doprovided!KXthe following bipartite$�duct result. \begin{theorem}\label`:prod1} Suppose a quantumD�,!Xs $k\le d/(100\log|Z|)$Ukfor func%e valu2 f(x_i,y_j)8f $f:\dom\to Z$)�H$mdisc(f)\le 2^{-d}1:�.�$that theseuDare simultaneouslyQ�!C ge\Omega( 5(^5/2^{10c})1�)X Conversely, if $c\le-A� %*(f)/10-k |Z|$ k�J}�F�%�:xc$%{I���V� The nextEo3 to derive^5�TsA�8 $f_{l,r}$ from�1 $f$j@A�%} Let!�}�E�V�-%1�et $O=\{(i_1,j_1),\ldots,(i_k,j_k)\}$ conta-�ind��of $k$��� �. Denote� $f_OA�e�~�)!~E�62��� (f_O�xO(�z/4})$I��5>=T�� EOs imply��D�Dth�onirA�ofs��(in Appendix .0app:A} resp.~FB}. Now�ocan!*clude%^�0more general A�ion��T� j� cst}9�J( mainN�E�17%5�d��everyB  us��sp3$S!�a9�!�M�needs :1m�dlra� |Z|/�/>���proof} NAEa�S=D!�we)�Hmmediately done, siR~ng%`��$s requires�Qleast $�,. If $S��d/200$,n!�apj  �Pf� D. Consider a circu� lice)��o&� and � �.Atf��bobm�an� B^ ou�i  informg i%.�^���a� beinga� minimume�� !!$:s. W� j8!}ge�2is" at1�*Z a� S}$,nh_ � (S+2)/A~� . Iɉ�� $k=:�wea�tradi $S+2\ge �V=� ,o our assump; (, otherwiseO% A[���.�C/(Q)+ 2)x4lr$ as desiredmDm3� also-3.k corollary����ame wa*t#xcor:mcs�E!� a���I9 k &H  $kis !�Zm��%�C1���1]a� some exhi�[&� - ��s. We �already� dE�C  regarda�matrix� -vecto��u $s over fin� fieldsQ& intr%ion (N�m1})�" only mis�.pie� $s an upper� o!>. �9 / IP^F�W6�$FB� M5<\widetilde{IP}^F��|F" n/4}>�6m� ��ived!<\cite{mnt:hash}.: factq)fac \ Ym*paii�uni��al familk NuLs� ($X$ to $Z$.y $A\i1 eq X$, $BY��$EZ$.�n �equ��� eq:mnt} \� |Prob_{x\�0,h\in B}(h(x)`E)-\frac{|E|}{|Z|}\right|9\sqrt{ Y|�� (A B Z|}}.� ���%> -��_0be changed slklyag. aBB,�~ $X=F^ni�$Z=F$,I lett��$�=AL(x,y)+aISD$y$ drawn randomly-~K*v Ap I���of%�"0 � ,s size $|Y|=Ern+1Aq ToM�qZ( of eea�)II)we%z$E$ cb ��af$le elementK�X���t8an)$A� B$��ain!(at  �(3"� n}$ entri3E h���rin!��~(\yMf)aGat 9 Y n+1)/2}/(IB n ED n} |F|})=^{m� T�p�L , �L$\mu(�)$ �!KVt.�/6� ��lT(r itself. Ser9Os%���Vh�� �-n/2-1�thu�.2<^�!2Z1%)��m[��.a:�:t �[ Y2� 6� +Aa!eE�Q�on>����[P� �JLI}.]�again� u&f Fact�:�n. An e' �& � encotin bin� �c�+ndard�� $\lceil \r F�< arbitrIa�E�&� gty a"�E�possib*<Y��0We would like>AL $|E|7= kA/bu is�not qu�W, e.g.~!�$Z�za� $\{0�p-1\}$ !%prime $p f�brestrict? selva��e lower!og(%/2)!� the -[%mwA���#$Z$, how� ,1n�� such/ �$1$� p.~0��.) $1/2\pm1/�1Z|oE uni� ly �� $z��reve`di� n� ts,"� A2.n  f�6�qm�between�/2-.�)$�� +>���|\,\,-�-yk�W2.�. LR=��!ܥ���6$|R? ��|X|�j|Y|�! F�F� $\le-�Y|��@X|}|Y|)}=1/|X|^{1t MR/��eQit� lt92 �ݥ8!� jX|MSoA�.n JD� EH a Z�!�a�-�+2� 2k&!number��be���isi'�2� w�t.i �b|X  yr # "Z|)^2� hicha>`-B>`.�  DiAR�  RO��Rec B�}�6�disjdpt}qan "c0 sequTi*2 d w�uctulw���, plus aa�',of Razborov n r �*��e f:\fdomi"I e�d.Sk�a blemB P1 mk$� tincstancei�\$��ge b$f �\A� chie2 on a balEdX ribu�� $\nua�T� �AD8tant $\gamma>0$�" be averag"w2#�s0ach classical!��w]6� $b/3� $f!!\nu���q�{ � k}6 p Lb>L > %�D�: FC&D!Y Q~v< 1�DISJ)!�$\epsilon n ���=[ >0$� F *ga�di� -�us �N���/�1�,�can b&� to)�a6aeasil��@ibliographystyle{3 } %\.${qc} \new!�dand{\etalchar}[1]{$^{#1}$}v the.?}{BNRW03D�bibitem[A04]{aaronson:advice} S.~Aa .p(block LimitU��Q�A6a$ One-Way C.�.CIn {\em��cee7K<19th IEEE Confer�inHpu s al plexity}, pages 320--332, 2004.l1(-ph/04020951�A03� &amb $s:search} =� A.~A $.c1 7a�spaEregion2-Z�44� FOCS�200--209�3.u�303041.�`BHK01]{babaihk:help} L.~B<, T.~Hayes, P.~K��l.Za�CosMaM� Bit:!|&�-��j Help.K%�Com% 4torica}, 21(4)1�455-488�1.;Earlier"$in STOC'982�ea9�eame:} P.~B.QA"T��%�(-6[�+f�ngc qu"_2��,SIAM Journal�JC�Ying� 0(2)M�27!�77, 199��892�TY94]{ �a���$, M.~Tompa�P.~Ya2t2�:��un ed���B��3(35�652--661�2�J�A�'902��CW98]{BuhrmanCleveWigderson98} H.~B , R.~!,a�&.�q� vs.~�)!K&O"� c%…�.?@{\it 30th ACM Symk#�na0or�.���63--68%8.Ou�9802046�S��(BS:qverif} :� \v Spalek.Q�V3���M�P�2��04090320Cob66]{cobham}Y A.~C.|�1Recog;onmi for�ASe�L4Perfect Square2�eL��Nrd���S� !znnual9}$ on Switcha�!�Automata�!�("AX")�P78--8e�66.l CW90��smith:�} D�,�Win�d.-hM� �EA8 via Arithmetic! gres�F�J.~Symbo�� .} 9}M251--280EK2/DiscreteA(heWcs}, 5� 545--55E�92�J/0Structures'87.�Kla��(klauck:qclb�@K.�Lo�)ґB2)-�.=1� 42nd� ahuf288--297%�2�.�6162��3]�2Z�&�Su �A�(Threshold C��2� ��I�N�Pr6� 8� ���� 118--134%2� ,cs.CC/0208002�KSW��ksw:dirI=, a�����deB�1�! C"Strong :P"�� � $N�ccurr�w��=e� ru_ l. For $R!�N we define+0 (R)=Joast!lG8.]*M<A�(:� ��6%p. }i9�`&(an advantag%�5$ ��g) guesn� �. put.!i = 8e$%�!!"�above l�7) E-bi�$:&�A -2�s�$%�$fE�N6��u#)�: �0>i!&, K!�Re@) -7�6a7-eB�,\]U(,)��-$\deltaO,:�)=1U$3J� � �$-"�0,B�i.� � �) �/2 ,\] o3a�A9�: �L1)>W�01AL�(�+� ing��1 \mu >��^Q~��� by exca,AQsums \[2�)�-(|R\cap f$}(1)-)�'^k\1% )�/2.\]L ely 3r�)s4<�"�#%with \[|U q Bq% r�%y- r}{O+F/5 &*D9��K+��e�ab�mdZ�*.� ! A B"�<] *k$r BVD1�> � �7 }. S�or#��s�;rag !�0s,3�us�%train[? is �"$much large�an�'�. 3+�#�$R"�0 �� !�" �� pick�x,y=x��x_l,y y_r�f�%atR4�*��.�� be writtT���� o9*al� �?4�,�� � eqX} \_{n}ae1,y`1R}(Y+1�\,|\,a,y_b$a,b}\mbox{�\} (a,b)<X;  �O),�� � ��ome oro8$<�& �2sM�A�D+nyB0 termA> ��A=i9 three typ5" s: $�$ mayQ=5((numerate} \j$( $a\neq i;b j$, = 'i ; b=ju&Vy&��2� invo�,nm$x_i$ nL y_|the,� - exa�%�" emezA5A27%,of "�0!0}) as�Fx3!3,exp} E_{u,v}}3E fx_a=uI =v_b.Mneq (��, �� } {\�}),� � wj ��.�� $u,vAXX^{l-1}+2Y^{r-1}�+� n�Km� $uu� ,u_l$, $v v_r$ &�-R3those�n��q�s�7ya��v} �2i�} i��<�tJ Ra$u_i,v_A:$1$*i�!�$.� !se MirdEY��a0ll $a,b] Q�,Q� fix+" any}� � -�� y_%�$, soF*��6$� � > � (�1c�,aI�inwi�� U��A�)��>E�76�%*6; /?t�. �weo<6�'[u,v]$%�h@$,�jce%��kbu� UD$ �{/ (see�8po>�Ftriv}��R�%���� �o-�. Observ at � A %��Db)=��AP��i,b}$ �!es�7 ijI�k M�A�itMVawhoF not, hAjhajE�#a2.hY�:��a�+ O6�E�m$&�truthI�%.�e �sl )� ���!�� s $Mu� ,M_mqm� 2^k�!�.!es[&�$measure ofQ i !pj�i��5!6!T,x_j$�-(a����� l"s�� se $�*3. � A�r�7 \[6�I�}��,y�����M_) )\]|2v" s $ '* .� �6 f ())P{-d�0All%�� $F7$ toge��!�.e]0k7 2^k  bc !Vf?1 $R$,�>�Ague now�  9��R$�56j c;s (� $ ish�"Ac �G&o|0pli =domainsa�"� narray*} ; )&=&(��R}u,v)\\ Y�(u_{l},v_{1}Xv_{r}�[R}��_{�, ��� u_a)d��\�u_i j |��� ID �1R3el@ m} 1^ 0.��5��ex��$ G��!�2�in �:�,v9)��a� ��ed1�"6;R��}�tͪ�z8��@���we ign�D����22%F�$ "1e�BAm K�=1*�Bkm�0e9:M 2 � ��  �ex� ion~�5A})��#$m$ pos6�7��B�xcan* �8�t( ����qp ���&. So� ͡a5NC��. N@� .�!O�? 1Chas^:5�m �'5Rec)�B�J�&&�Ve�.G2�&e#=6))\,/\,.2& 1JI!soɋ\[}��i�i�.e ��}���A6�l |Z|+Q � So,i4�By�alv=2^kSO�7�_�A9G�: R_ an� a1aYgof &gB{.�MΉz I�.T.3(64)^J�;N+2�� �� 75 5 J^kF�5"�  $0��)t2�|Z� 2$. SS;�Vb�8O(.`���-d�J:��"J�!�3Si =&9)4)�app:CV�W E�=!��!*�J � xB��| %����I�se&=8� bE�L�� z7 (? aA �Q"C8*afren6ed Hof�T8�T8�T8�T8�T8�T8�T8�9E{} E�LI�&�1"dB �J�O $p�x>�9�:� a de��in.A��fAysAIJjT@�9g@ tes.qFS(1>J�T�<.��) an2\� 2�.s)�l � are a��V3 �6M%$c�� �!��y<@e�D:�ch�r-#natur lead�Ua "��$\k�1$2^c$y�s�led ���on�� p!.U�R.�#�u�Kr�$2^{b/3}.~x FN;2 (� ) &�9�9;�ڝ��>��qu)ikelyXkn� E���2� �=f[ at!T�N1/2^be e c�"h  a .� $3/431-hHfBntuitivEO�~� �& f� a�E�>�S�neB it,!\ c2. !goes dowBa�$oT? �eY~1- p� is� ^�Wk�&"e�claim:�K} E.=5jAM%Z$G bf I��1` a 2^?5}%i-ghav�a*(x)=ce9 �$cn�C1\}� % $|c| k/3� k\C"� � Due!�a8Wple/�(?�B Chern�L�F� w:�AK{:����*�Sjs�� �O/3�K ��o^  ��V�W}Pis �ed Z gY>�, �Qa�] -�� lt y $��E��V6�%��li�UY,mP� j"errM��2:Jr�e "*A.Ef6 ehHU�A&vjc<;�.!5M� E��� � R} ^=�,� !�'� �?^Du$(!i.2�R�2�iof i7o{UifNy�.�*E�A�>�&sJ5��BA�=M�on c� !�E�as:w. A~w(y�!�Qa�%*� "CGA���2�i�!�i%i|:j�j��l} j*#2�v2 X^{k2�$ ��= �]E�2Ik6� ,v_k�� $f(�v�' �C%j(!�nP ��%�I��3x)!�-��� way �^�� �*�Y�5� ��i�^a$Jus �c.R"v�P_. VW\n"��Sb�8w"B"���&�will  infl�F���R$ signi=ntv M�precis9\�BlR}$��*fix)w,v����Nq� exte`Ÿ16�,{�K,��V ll�s�=��s ]Dw n�� n clearly" fD� ,a�ARb)�!4"H$. �͕e� ? N%(a 1�o on QE $i" ch.V ZV��SK"P(3/4)^0 }+�)5gLN29 &Z m "�%C"F:C.�E-$:�5I8��LD}"q OEd%f!��~'R the:>C6 }.] "�a&!N� �0�?C�18"��[ �s�Tep H}�KPdco�I�^�Sb�.:/e $n^2�Xr0i�]� X.H?Z_ wZilyE# $CS^2�'n^3�#C�#3slc1A�a�5m�Bng"�)*�5*,_ (J!aA2��J98 /(2S�Letk,M!�"#MM�<�dg. N� < 2S/)��-��8 ableO'�[|P)�*ID5���iWs�&cho/any�[n��m�&we |g,f� (detail�,�e later� s�'2%0�I�AF �gLA�b3A ) �QA+��2 \� S"� j �K�tjA]�is�U�M�avi�'m0+1�OS$, ~*%��Ss'"$9N O-tso $C� ( �Y9)D+ 2SMvaM.�cVVrAڕy"��V�=l n/k&�R2��'ᨩ���Y9/{"^0n\�!Di���B�l�< a872a�to�mut���,! s $U(�%��$�i� associ�to�I��'M5ic*=3 j|*Y(row/column �' $A[i> $B[j�#��M�c�A�$B��ssue0 �/~jB)*�c �_a)�:'�> x.  9��6�-m�&[e-#_t�Pawh3�! zero�� p$�]at5 � [9 m^*dw9 sL analogofh� !")D�Z%� U�m�a sbE|,�#� to s(�i�b!wof6TND�BE��� �! -�"��gleA:C� both5set!C0{Ro��if)�)F &�"�q�#b%�_ble*,72zs:�I����q� aO)�cd.�)O��:�^�1�:%S�&�9 docu8} X\�z [aps,prl,��pacs,tw�h(umn,amsmath symbLfonts,superscriptadd�8 ]{revtex4 Husepackage{epsfig,g�Oicx,bm!n*�Obed}{\[}{O��a�O]:beq}{"#u }:$e$ ;"�:" beqaG]">%e % HV#Pket} [1] {\vert #1 \r�6>qra)l +4F)U [2]{* | #2ZZ projQ�{#1}\bra:Y mean (�R�opnorm,|\!#1 \!|_�new�g{�4}{L�4!�b�8Q^title{[<2�9enh9Ti�]pac�D(of bosonic �2 nels�@memory} \author{Nv1$as J. CerfJulienFvareauffiliE-H{QUIC, Ecole Polyte�4, CP 165/59, U=E\'e Libry6 Bruxell�;B-1050sseI1Belgiumn �HChiara Macchiavello6� T, D_2a�`o di Fisica ``A. Volta'',�C it\`YS Pavia, wK� ci(i�A�kstudiA�h|\��=bee���2reI,� . H�=i�Z� ��Ui�&�B ~*Ba5IGaHB Og g! 2�q�dᘑd�Bbolb �V steaO���ol�por�0 U) � phot.E�D70\%-U � c rmal nois�+t /he!t ����abBj 11\%2l3.8-dB�l�< {aEu�on variA�JN!�6o��Y� \�({03.67.-a,  5.-wA��r�j A @* go�SfU@.�j��yCtoQlA�Bg^�(1�cH��on1�Il� rt�@� impor�Y quwDon r�a3w\5^EUg}2�bp�L,ssed asympto�Ely �&rM� 5eT� e � $d, today,  Ca�A>�da@���--�X � �6� inuous-%�bleBj �6ng�yXmhHhMA"(electromagn�F "C0holevo-werner�$�sN�pur��Flossy}>� w�eolTC)4�"� v>-q|}� le �a�bhadFh�a�i��0d. Acdm�"&nA�!��:�/ =n~�(go�vaT-"Cedՙ0,Y�rd� ))��Z } althougm2is�%Ez�OE�3w��o�N�ensemA5���2ns&�j!5s6&A�Fjec8Q��s�al �s Frigora,v;a�2kc � giov�& tti}e1I5g� A�P7ar)��"Z�e���c��o�4ś:�� par&dF Lettbaw���Hga��. yN5&m�!�at exh$[s |�9��"B� ��AA*!�,e�s�8appropr�s���$ depolariz9��ݓa'�d�Dd qubit��g͇!\ 2-shot�:��Em| -palma}��E.�a �b aTY� �E�ai��l(} bandwidth��(���eff�Vis��e�$by�%VA�� a-wo1<)t�^�+ ��"�bi�Lte5��"])W$a non-vani�N5g!�coe�H, mt �he degre[ �-� �.�f�at�� ,a�u�i�"q�ergEX� rain���-p E_ne9���2? Md!XzY/! �V< , in�tr\%E����on�%le@R%�Y� !�of no!�E�2Vransf�\iaN�� �etw� zBp!8YZ>F� yz<\�$- ras{BN>s.}"��")�2�>7 $T$ ��E�!�V�a&!o!� annihi �crey ope �<a9<$a^\dagger$, or,7 ivale� �&Qdr�(��}s $q=(a+>)bf2}$�/$p=i(-a ,>w6AWR9�$[q,p]=��{M�61A8iQ(inɨ $\rho��Ave � $\mapsto T[(]=\int d^2\DH q( )\ D rho D1$ ;4eq !$?=d\Re " \, d\Im $, w�U $Y=e^mta 9&} ^* a*`;%�dis�IE�1� (�eL$��B}=D�B)0}$7 %0}�F�� vacuum-7a % J*�)nt s !�� �& $ 0$)SF&���IJkA �+Jf�:f���:$Nv|� s, $1�=�C 1}{\pi N}!w e^{- |%P|^2}{N}}&&�jaSn%,ly{%a�RMic�� accor�o.�"� ion� ch�]s ���H ($N$A�a��M�added ɽ�+quV}m� p$, >�E2&G���s eZ-).�D��CP map�o�� 0 : also�ha�rQ.���co�E. R,E|omsAR")�TmeaMa,i �9L0�w��i*� �>�� a�&=&�8� 9}{cc} �{q^2} & IN1}{2} $p+pq} \\ ^`5ean{p^2�s ^ \�8�eqaź5v-^��#2&� � ��$ +�t�o� l�N & 0�0 & N� 6�2�CR F �coi\}� >���era��A"one^d am 1�isG& b Cq'� 0} C_1(T)=\max%�[�ft(�:i p_i��_i]-�- .� # *]2� $S(�,)=-\text{Tr}�l"�;(von Neumann�rop�!denH[��ɼk/ Eq.~A9�)�max|$is taken o{x�*5O.�l. {p_i���col�Zg!n>�/�2.�?�_gy� �intM�cJ)d5%�%_i �� a)R�5q\bar{n}1]nk$ сu�aX�Α�N �MM6ђ monomodal"� >w, �co&�E��� mixt�Rof: s (�:�) �l�"M fn1Wse!�$i�'r*�Qan &gn $�w,�!&%�SEL_ &^{)�in}}=����2�w&�-2HI� $pY6y-�Ba�M�"}�usz�11btUe�m�m�\A�}MT-"� � �9rh> out}GQ����� � �h vidu utpu1wm Z^=�\ �.�]6VNE?&� �>�- E%cN)�-�� �yeq� theirU�(s� &*yB�) �hKU*{-2mm}9h&7 5a2`^� 2�)�n}+N)����1F��P�4�Ito calW�y�waii� �"� Avsykc�d� �#lsFQJ#"vL?ol�ps ��.�r eft|�$-\lambda JI�|=0q�%���@ -j} J=�Ob>���i��-i��j�Itab�*�s ���cws�6ai�vpm �� ja�5\�� �g �| ;|� O  2� g�3�\{(U*� ll} (x+1)�d_2  -x  x,\q1 $ & x>0\\ 0=0 p2�M6�F��:�\h� I �{�Cx,0�6G��$�t>DgFf�6� } ^��ye{ AoJ 1A%E0A:1N/� �dR�iC�� ��C� 6u�Ӂ%6�/B�c��� d� �+IJ b�+26 R�\\ �ai��`��6V+.Rt \ mM%�*v!�� i�a�g -g(N[ 2� Bi� C .} C+Za.� 7� , �� he b6Z E�a)�eqn%�"� T_{12}N{ _1 \"�_2 \ �BE��_2)} ͑({0.5cm} \no��B\�ps&�_1)\o 2)\;ŝ \;>�./6�_2m ag "�yt\pi^2 N:>�_1|^2+�_2��� D.%�� *�he%�u�]is un&�. O��1���F� !�*c���% ��P $R=[q_1,p_1,q_2,p_2]mhT�0e-� �B�M*%�$s�Iqs�� !��&�͍�=�9? R\,%��R�)-U �u}�} )JACo�@J_2iY)�  ; $J�J- � ��M�`).568�<&�}Q�"6 �s*� ,��4뭸gf ic-9@���b���_��\sigm /��5'z�,_2.r\�j2�_1j Al� )�V+D& redup^ :�_19�_2� !�)$ A� �~(�sC`IQR�$)� �$�$��5a)�q� and/�!.� .u"B�"_6-���siގ3" � '��3: �!-� in}= �1I� 2$M�I3�s.4 �*A�%�F��})�l Yj~=0$(6 mod~"��a1� u.2�, "J�DE _2) =&k�G�n}>M 1�N �O 0gI9}i0A)!^�isA[h5d�7v�.&a �_ �v%�)= �4z� Ir& in&aw�h_+s ����.[$,!��'7a�A��)Rclo�7 .+=Vd�a'0���""�a*�Wea�.�. �.� AX!beu&�m�� �!���>(\�, _N|}} �6bm}�m N1"5� $=["�q/� ���2)��7qO&�F"�c)���s�ool�0)�Z�cc}� & -x6�  & xN��& �� 6v�T"��$I�C�M��2�"� ǁ�z�oNG@o2A�)�8��BF=(�s 1E�2�jY�E �VJ('Ta4$q2e8�' an$�r%erS� fn0#U��d*� $x$B;}�6 $x=0�;m��qh*Dx=1" �W full 4.�M���D��)?*��IzijTper. W�1w� satNN��"f is at�6e�a����wll�U�1j%��I^ �)B�"d"!.��inn$,+ _mv-E. *�E,!we��an EPR ��%A�com� eigens� �$q_1 +q_wLp_1-p�� respv Wgen $q_+�~ p_-$"G=;>u:6/ �"en �#�i )Fxy>�se�36�uggesOF:�! )(�s may de ?f v�)� B2i c$1�. H,5K]Cin�#C�ey vio��=� 2-�~+�N�)� ( M- 2)��-0 � quee[ s!�s$ �8F�*��y?.1 @��*- ٠2�@*���\cosh 2r2�.u  w   EPR1}kNb �&s\�J�-\sinF� ^��xE�$r.f)dVp�y�K.*ރ�)*I �UIm %�.�i�$I�.@V $ ]help R��$x>Y�sψ�� heckf.K7�extra�&R!iyg� ����i"(�J�i�j� e��E���"� d� Eqs�%�)-�EPR@�!� ^2 raeE���a� �F&l (�� �M(2� [$)u��61a,s. Remarkabl�#re ��a)8�U&romz=1� ��A! �F �o.�-inA�{.<n>M. ��50h,��:IKs� ��+n%EI Z# _ $$!�5[� A,V~} �x to rj)j�g&�n���� �(q=0$Y ^�ac %��$-,ed�a �5d �E1E!�B-T ire �.�d�J.lR nohA� �o8�&A�X�6Y��J> Ӆ2J� +  3 � �Ź� {1,2.%���c>�^������R�����-2s � e� 2r+2xZ��&!�miV#�}%JO�,ata��'2r# !a2�)d&=&t >t+b^(1-a()m>2�:Vo!\�x���2�!�]" f�y>p2�-BR� �}�t��+A�A���!�mN"E+�*0:0�4 $y$a�n�9����.6  (��ompens�Ga�?� 5 � d*�'s"E0?� %n�S 62� *�4)�q���*En�d-ez4"� }2E06 �+��o<'_c��q%->E��8�E f�u �u IF`$E�]�EPl.IQe^u�wJN,*� �H��N�"��l~�%!��!�m�f .�)�0&.�|-#�"-�2  (J_1+��$|E>(� bi� icf�)\X^4-(|�� _1|+ 2|+2|i�'|)252 *�|=0^Usaa* ��l y��)�e�2~.��J� admiT��,of doubly-de%�A�B�, name�H2��� =\pm�u_ ^2-v2f�BE�u= v}^2k�nC> .d=^�+��B!," 1.2cm} .�=k1(1.?)}+xN , "T��u}=�Fx+.zAYɂv�l-y:M.{�!|Fsper�e�%)WN� R(y,�) =g(|�-щ8|�'F�=� E�=�f5� W1i$x > � a�"+EojJ�%y*�N /V� � ����!= um�&Gk��! 3^*� h Fig.,J fig1B(Na ���D 7&�$�ad\@���"$figure}[t]�er�lp�A "=�-! _eta.eps,�3=70mm} �_� {T�12n!F(�)Q!>�{ Zu $y$)je*┭m��� $8th��)��Z:�3$x$�5e^ n ��_.<�8��n}� ~v�9a .IT.GN=1/3$.� abel!W1!end=rnd!�  L* �IF4ERqh��2A�a)�."\%�6�1? 8�(FW &U)*2Au��i��a=d=OL8n-"G^4� er�!9#1�@ �83ed�^. I�� keep;5al-to-� 'o5�/N$��\t�Fis vi�6`2}ɺ�q�n�^*$Q/(highest ati�p"�< i�M�m�$E:MQ6QaE)O�R�s back!�A6 i�l{r-9 l�� (excep�6��1$). C�@is 1^Q �-�QYI couWY of u�,�5�{ %� (��" ��c� ),��1�e�+f playOS�C�Q�;>;fn2}. 23}b�BJ�1�%�"!�){)e52y!ԅ>-sam"X'-��N�4e�y!�ahs*�G,�Z�+E98)�1� \to\infty|m!7n-!�J��fu@� ]h$�a9�1�w�k.-@"�P��$2-etamax_nf�>�y/)i2���!aa� zZ�!mm�EN5~�=:f2rf�3-y�.~Ir�J�2 >3r�rCo�Q�<s.�Y��A�at5湷+{M��YyU��U"�/Q��Ww?�ɉZA� �u;":B��amoun�2~&�s�B�:mw.��Mz� Q��;c;S�;t (E������ )�a B �Еl 6&;� HsB�"ex�D(:B�!5a�md2�of 1/3 �.�.ofE��-���10.8\%�u� ��i tw &� is 3.8 dB�1$%U� /!�� s�k seem�sdoxyF>�sSE�':Nnal�ne��arily �`��!va�E���s�e� c&be�ly�U͈ �. "}due�gqu��=ts!�Q�qF)�I,&W(�VXmdilyd�d�`�8E�=tL�$aQg��P�'& �:o�ej'ingOA��@i� [g]��O� lI� L�pin,�h�� ne!bL%��wyԙ@}� kt�atޅ ;m�@1� _$G$:�?5�}"�6]�, _plotin6K (4}. It illuf5���aRLi�eyQper| v � FbUgY'GH�se��v٦n��acA�w��l�&u�.� bk V. Gio�CE�)^!�u8a��B�Z�for������1qs,a� e-pr�=E���410176�).DFgX�Aa<�F�us�enř�$c:f�@financ��r* c�Yau�ML\c ca de�Mque�o�@nt ARC 00/05-251,) a2 IUAP� gram\|�A�Ma[I vern�2M V-181Hq HEU "�OHect COVAQIAL. J.R. ���p1I>p$FRIA foundC;� :�h��4-a n� C��q3�9_{�}R�/�9_y 0.� q��"�G60 �y:� ��4r�\vsו{-1`1-B�99}"8��G>IA�SU�� R. F�]I, Phy� v. A�Lbf{63}, 032312 (2001�/biz�>)I:�,o Guha Lloyd, L.=Pone, �P$H. ShapiroIh(H. P. Yuen,.�G.�92� 2790 �4.�*�H2�e� Sohma j O. Hirota2iA g859}, 1820 (1999.e2`�we��Id/dEsi/Oi� U=�'GW benefi��§��BdisL+ars�ME�"Β �l��|a�R "&vsY+x ed (or Fsu�v A&�Ke"�`� !j ��6�%eis� 2� \toxits abOs"?��2��9$ !&P � �($Ba>� d" XPm& Xj[11pt]{� le} � |h�� 225mm 2 160odd�8margin -1mm %\pԦtyle{���Ttop#IF9���< er} {\L \bf ��de��./M�%!!�rad=Coulomb��L\\� a �[���urv� �IEl�r flatS��Ps} \\[8mm] Myo Thaik0Akira In��\foot��{E-mailC7M: i !(@albany.edu�&\[2SD" �a9�uics, Sa�&V�@New Y� at AM,   1222s21@b� {\0w�baZ[FT? \'a la1}a!D����struca�A�!�:}){2peM��zi)#a��>e�eB�~�.n� � \�V2�0hydrogen atom��.nUO�Z"�<.�\�d����&�Q�rug �*ru�C}9b$� tor.} &�dInt�$�� 2A�},5��Nos��%P6�i*�Ib(��bsE_p �=2,�u�N  harmrUoscill�B�s�f!0{|e��.�p }��er{T;\y? (i).M�0?1!��_ i) ���g�ofat�(i(� H�o�oy�eQ"B ev�R�W�ms-�xime).�fac�%);ofyh� ��!(�'-�S,J� }. MmhI  ot(%elomov'�Qre ba!�on�Xup�nu R�WA*+� stip4|6X�Vresb KIgroup. �!U`>h; '5 U�$E_U\omega e $~$(n= � , 2, ...; 0}=0�reu���.�9� $s~ (0�>q s < g >ndx" ~(-< j%6-s8A,�!} |s,D1z]4 = M(s^{2})\,HE{n=0}^{ y},s^{n}"3i�!�n}}}{\I3^= !}P�n_ 'Kcs��w!� $|n�] "�& / belon���0%u�! $xw8$n$th mo� �pZ�F"�H(u) > A����Mg�B_{% �u}} u!\,�(u)\,du.�rhoF� �YZ9,�:J=!pu}$2v�4:�e�� ul�rh �n!�jo��in���>�%$!�)� uby�w0ambigu�^�,he�gice!a-�(u[h:!nz�liiӅO�Qe%�*��?�G�% cY�N�1$;:#,N�p ^{-2"umb�2nA�1D�Cnd9� W��Hamil�[,an $\hat{H}$�X0 Y�= � �!�C��appar�BN�Ai nt}|s,m�q5=.!+qt > U�P�f�Iin�� lau}A �exFV�k�V�T��of���a�"J�'��A�Q�|l�D;unżBm \s\,d\mu (Y ) \,F��a5| = %-1}_{d��Bv!��4�-́2ik�����-�)��U:lim_{\Gl� \ =arrow�� �]�D &�F�aa } k��d���>int_{-5^e d � \, f.�!,�!Vm]�Uh�E�F�~�}&D;� �F�}!��' \,e^{�V(e%- '})}��Ȗ�~ ,n'}a�6���1i�rh �f�Jre� @�(n��� cies �)%9�>� 5= 1�=�F-�/��2/:.U �rem�punVi�"untile1t a+�� W�%��_���. Gazeau� a� x GK}, "W�EF=J�!imU &�2@�Ut,�H��ai1ident� [F/ q�J"s|e�H}|�� F J,U��b^��~)��t?3x rm,N����Ld_{j=1}��j}, ~  )0}=1.F~Th�1 " 7�"�1r�i��ar�  $J�B%E&�qWon�bl�Hnju�[ ��� u, "tE:rko b7A�(n Sec. 4V rx*F3Z�9 semi���� . n\"?>hl4(um dynamic" A.U��oZ*5+ =ous&`$0 <�� \var r � � .�$%����^>�i#a|�m>�N� q�\,��" .} }��s^22W .1�*^ (. )}}|.uJd.*�0GK!ErF(��F�6\ �ŎR��2.�} }{el:�6�:�gfme���^&N��<$*P Es�|� �#�L6��k37-?�m*� g�=*%_A�neg w_w�kx. (sw q 0 �B�w 6�>� 2T} ��2 l,ds .�_�>�,s��!�"� a �"qby�S 8am[,#\. < $� ��)=�� >oJJB*8 �F�i�~lfi�-��XJ� ��up�*depVz�\%U5n_nd.*bn�'p'b@"cTK�>!�hC` -�met a�J@��;raNQ!�a �"EE��qve>�,�Ta[*l m�҂�!�ivf2Awell a-^5Jpo��"�e ��!��i�:ann�@ 2),+�s,�B[2is�lly �yA%,6W��O�-�=%�ns�" �X . �F�h1� $S$-w�}� coincidesE9��AO�by.U "jV1Z-�93uf%� �!.iD�d_"�z��1l���5�or>� } Schr\" Zer |Sch} wat i&�in}d�$me^#�%�Z��!�R�2�%�>�e �H�I".��a>'r %�h �6 �or� 1jd�.ʟ&�mby�+methods�Le�so-Inf�So��ft�F"cmSt��so } �xe ^inm�q�96 e!�v oC qU Indei h%l � � waN�;acI�-!.�$mayy8worth �io |�0�, 3OH�g-C-Bn al� pI�BW}eM /pat�wt�X>,IJ%d_tI&)�A7��Hiay��Qune./ us�WqG�in� &�- [EA;M$p� �� �wJ �$ T:�%RA2A�a�-m����� R �w�Ege��P9!���D� 0 >�*�A6"T���! �ۍ!s��h�Tb)di��hWWV���req�f{pr�\ty�'��]Fd�o����> :��-�(�1z)6���%s&�J �/n:���� :  $K=1/R��e02�M*V�4E. t�-dimenA)P*p�� $(S^{3#Oof�u��$ imbe4A�aT0ur2?Euclid�+�� line.fm�$ds"�:$� �U�@L�b*byJ� �c f��dr!}{1 -  ) J(d\th�A' sin  U phi X >L Or,)��A0 \chi =r/R ~( ً [0, � ]_e��1.�6��R��%�dQ� + �R� ���)"rdB�� U�pota�alKaZM � �6��B�V �)=FYZe�}{R}\cot)(S `potBX �q{"7"h ���M� -�}{),�F!') !� $V%i)=0�] %QljLA�|9�8�h5� e�Jco��Ի.�GHa&��N� is5di�IG���}s�26Db2� \N1a}\DI� } - �J|�>`�$\hbar�f�P�! La�f -Beltrami��$SO(4� %$Y=Z!� e^{4��,Eh�r�7 ng S2� +��&�MN��W[)�1di=�} \�s ial} I�.%eE&MKf5I55d\!�L}� �  La�2�2�} R�u + 2i�E�] \psi iF, māHhi )=0B�|5q 2r�')� �5�Ca�Trmi ,*\ SO(3�\B��=-\�I:x �jv��-�i� f� 41w+1�2�%��1�!�.�!A%� M]�?2k�.s obvw �A�-o"� �$a�#by"3� > &�\ *�GUra<"�aw �hm ���T n�m w_{w�}I; )\,Y^{m})%IJ)��>�$ G H) $ obey�[6�(EH b�xE)\,w �)=�_q�}� u�&F�Iq^.��MHM�^���E akyx:� .)3�E!T � +1)n���}6�I�Fm%Bb%.V��%6���%�))OZ�+ )�(E�B�C]\, %>C=0 , %:xF��{ f"We[97 gy&c "z,$} (ev�.:� E_{N&ON!�-�"�e!�1� �} $"�(N=�#3�#)&f� �>U��KA�6'�"q��[In �,  Fcw_{N, Eqi~m��^I�ɥ -i!� (N-2-1 + iJB�)m",_{2}F��I�- N +1 f +1 -3�#; 2N+2; 1-� f*9 wB�'!��, $saag�u_W ;U$; z5sN-0's hypergeomev- "����F+.� =A���R}{a(n+ �1)}6N- 2�� $a=(Q�d1/2}=(?  }$. �L�T�weEx��"u�v co� d �&�c�#� , J N� a2� ,s �xdhy-free. �c OnalogW�0Runge-Lentz v��e�6nd m��=0 .�ac�[5v�5]i�4Higgs, Leemon}� re���iS�h>$aJYc �2=���%�H�TBX6,�nJ�um�($p'1,2,...Wi��pr�pal7#C$N=UR=@3B� "s �Br�e(�C�(�1})!��;:� &w#�giv2> �U�8R�&,Tq) +2)}{��N'1)�@�!A �..>2>� �F� w_{n����=Cz�n~�-]���wB�&�nN�&iV�.��'i  (2n �� $㉹2��+1�  $(�� !�.i\>��K��!�\} Ge: + 1 >!"n+ k+2) }{R� \,\kq&Q\, * (�/N!�xXI!v)a �JQqJq�0mbox{min }\{|u�|, I�|\B�' ����˳dEjz|&�v� �9}U�jU(V���M}�#RE+�%BF+[n]_{R&H+ !:F+.�[CcF�P6�$|FP++����J�I # n,!�i� )=$�U.">�h� �g�/� |,number $[n]$V�[n]=(��-E�&)/� �#������B� ��$[0]!=1 1����I�(Q�0nit�9d��urv>�+����2N�N�1�P$mP$[m%�>i�� m(my� }{(m�;��iڱ�:(a�� r.&�M � )� :�%CF�:�^C+�Z.D+1F��A A�!�-�[۵uA` be�B Vb�m�>|)�a )A��� �)��ul**5`A "���acular��W��Y��'?5��s@H$ n. N��the�_�IC B�Z~ ^sess ����)P2F2-�1on06�� }��HFon&�'of.�.� <GK 6�>��l�)1}��ex��*�#-s�6-T�^�� �?!�e�e� "c8^��*L"�r< Z6g�?>~6��B({ $m_{eeM)AS � � �. B��ADsoV >�"��&o2\v��&��t�\�:�*�A�"�56��� M�I% 5 B* A��^%��i�5W e cri��!n_{c}"I)?-�u ^Ja�a5/,}38}wT orF�( �[) R �+ 2>�|=0�?�xnR> �4T�)2*9(\ref{s�pec2}) into two parts: (a) $E_{n} < 0 $ and (b) $ E\geq 0$,�Iconsider their limiting cases separately.\\ \noindent \underline{Case{�} ~$E < 0$ ($n < n_{c}$):~It is appar*+1> A� \EMeGF�}{R^{3}]) \, 4 (2�-C) ��]^{1/2} �����r}2w.>�- 1}{a:~^{4�� b.!?�� lim1��I|>�Thus, M�$flat-spaceIᩗradial���aw1�a�� fo��Q�ټu_{n,�}(r)=C!l��-2v }e^{:!} 6�-Y�2; B���u-�IB��normaliz�u�tant,F��=�^ 1}{(my 1)!}-�left(Iy2R�)!� C(n+B{2]](n Vr��-� >` ( This resul in fact���ed:�-�wave !"�k�n units where $\hbar=1$. See, e.g., \cite{Merz}�  j� b� * �  t� For��R�~$approximat�(Delta n /R$�rn > ?�� $dk$� a!�tinuous� (ameter $k >� �by� egra�F�n - b =kRBy I�� $RN06�W behavesBFv�\��(kR + �+��)F� � :� }JE�?��6� sk{2�? c�B; As aMo�+"�/�-"� E)�0$ turn� to 2�0?NK E(k)-� � 0\leq k )>�)�is.� ,EGmMs must repl�"'�$ Ig\-1/ak$. In a way similar� ea� � 5E"s )��)_calculA�/coU�1kQk J'�VV��-n�YY *� o ( + 1 + i/ak.b 2ikr�X"X�f +6 )]Zikr"O��P 6Q,��ͺi }i6(��a;FZ)"% e� � |��|.Mn � 1*1/2}=2^{ �(i\pi /4}\s� a}\,e\,(2kr)�. ��VUsAlthesem�sE�arrive a�EU��.�-belongA 9he.�q�eky�N� v_{kM�-%m�Ga}{�! )O )z�.� }6�|� I� +1 -A�)|4 h L(_4/ak)\,e^{ikr} :� .�nA�bpmanner%Jse� ! �dynamics=4Coulomb system�� curved � ea.2F< �< regimeV6�lat R. �w%�"�B �co nt states��Ccs})  fixed $�$:��& |s," \rangle =sZI ( {\cal M}(sa])E[\sum_{ }� S4  ]- I's^{n}%�-i�[n]}}{i9,[n]_{R}!}}|n�. �y6�$ Correspon��!�u5�U���S)q< 0we writeF*j^ � =[n]i�5` H[FQ@[n]! =\prod_{m=1}%em(m� �q(��(m"p!�} �~n!}2)n� � 3)��}{[ O +2]F,� �6`s (z/$�!aPochha� symbolJ� 4=q�z+n)/ ),(�\ 0}=1N��i�r } $S$-��7 (I� =0$)�u �� 0� given%�m�-likeYinI GK}J1 \rho�1w+2$ 1)� 6; W�Ipn� heY�por� �>� beco�4F9J�_{A�}= i�Nu�e�n=0}^{�� Ig�� !}} } gU-CSdis&� ��U�M;F�:��s�'a�� /�r:dwill be� �� hortly. T.weigen�.$|n��$ ��I,aaE_�T�Yu�)� a6_ are��@ d� $:n\l�brw( $. Natural�M�� )a��R="� �Klaud�UO �M�K� except �U�aE��or�� ��:Dc �$E��udop- the we-�1M0 $\sigma (s)=Ps�Vn �� �E ��� N��� _{VC�� ! = e�T(\varepsilon ) =\int_{2&s^{.%ͪs}\,ds7���O+1M�] =.!, �e;>� m/$.5= a /3= \ /(2 ).$ Not!%atź!i $ �2�+1)�mElas6i!$��(� � ) i�Bstress�i�a nI�Qum�q��$��$AAThe�]Bpv�maya�� truca� V� .")_{t��=� F�\,d.s\,xVi"0 =�� \� Z{ }} |.2�x�82= expaq"e�s $RJ $ satisfyE���\hat{H}_�}RC= MX.�2* �� ��b3'3=\d22�-.8'F� ��N� $:� $ common � ����A�I�s�by��^{-2}=NP�Ls � ! Jh:f8. ]Y !},V�cane*i���e$F�:+ ���� +2,O 9 +3; \,  +� � � )� nu  J��#)"A $$�Q�y8\cite{GR} defin�CF�6(x4F�)T x^{t!H�� (t� \,dtty0 Consequently@%F:y���Tm��.m r%C3probl4.3}*�>T� m�>O�is��9 2�]� Q�J� JC B< ���C RC  +N"��5R�j��}E� .>~�_c2cs>� �r� sector6� weZJ���=0*� �mZޒn(n+2)/"aŬ 2 }} |u=0="A`������2�A�5�, "\ 3J��AFK�=c��G2}�!@f�� }{1- ��ln (1 -3 2})�]��`V�!Zţm�i�is&�l" :� �V ��Gazeau�� �QK}� �Ise��>tjd��ed b�� �posse all$propertiyi)-(iii)(��6�}*� l esolu��of�y�ex�#X!$include bo>�!>���:J��* Jq�&|\, d\m��"�m{\bf 1}{ :� E^!3,same measurea �$of�(})��lo ist" valid�B2 �]ignored�ddi!9�e a�D identK%ofrx/ iedR3�9|:B -Ea8FU =E Jy�oJBM56 �fic)$J=e3$. \�Qion{CoE� (Remarks} W�ZY�V#�)>� �; > Z}icuni!5Ma\(We emphasiz� A^\u�=W W Xormly20%� reducible+\B�� os4o��iplu� ('B�E]d "e��$ =0)$, i]'e�AViI�, our�* �T)F�a��n�&  �J�Although�classi� i -� interpretIrofYu�U$�$ offer�� ����Q)a� "�oJ!D�Z)ropri�1� -V . If$�J��q�|� $a?��99>)o* cl}$�mn!/E_�� ��Dadiabatic invarian&i=(af anT � ad��m�of � dimension�:�e Bohr-Ishiwara-Sommerfeld-Wilson quanti�$J� aRn$oli�Z�N��< ��� C��$, sugg!�ng)�P^�� $�5$ >$. Howev�$J$ d�*not�ma�be%5L 6M any other�� a�icEnse�he semi9� z�yield  rreRQ)<+Awa  �thaɴJL$. NonethelBI�e~-8!epoint ou��2�c�a$,�vmod�as $J.�[n]$ (, )��0tegk"n- !�gA�Z$(ed number �=e CItoQ2D&Y�isaF mpat����ju�pthebibliography}{99} \bibitem7 K�h J R, 1996 {\it J. Phys. A}� 29}, L293 AS.?�HSkagerstum B-S 1985 QCNSNX} (Singapore, World Scic fic)�@Per}Perelomov A MU �G=p>a!>� ir Appls} (Bw. , Springe� 5GK}��J-PD=!! 9 �B 32} 12.(Sch}Schr\"o^ er E!b40 BHProc. R. Irish Acad9n 46} 9; 1/ibid.)�183� 194127}, 53�Inf}In�� L .%�)�Rev.} U5!�737 (S={Stev}en�A FzG 842] ,BW}Barut A O��I!IQ � Lett�110Av 351.LIJM(, Inomata AXJunker GA7 �B� 20} 6271!V9-�F&3} 1179zHiggs} P W 197^12} 309 q$Leemon}  H I~@ 483.9�Merz}b�0r E? � QuanaiMechanicA�|New York, Wiley) 2nd edn, p 209Z@GR}Gradshteyn I S%JRyzhik Ieg6m�TC�uI��$rals, Seri�$ai@Products}, trans.�$Jeffrey A �A��: P�4) Formula 9.64!� >�"� docu���} Y%james-qle-rs-04-v2.tex %dec 13, 2004 %mar 22 5 \FſX[twocolumn,showpacs,pre�t�� s,amsmath�0]{revtex4} %:NB+article+8input{newpreamb\u&3c�8{��icx}% I� v2g� files2,d �$}% Align t!� ,s on decimal�2;bm}% boli th 2color��! tags%"key# %Z % - PREAMBLE  6jam%M}6,epsfig,enume;4!�Zj�r4ew�and{\up}p } \. dn}{\down 6qE}{{\Afrak E}�.?6tex� stackrel{ �{2/ }} %2gt��r}{\ot�#:fK} � bf K>krelent !�R:>relu .#C>FqH!bf H}:>qV �#VBS  SBw�4Frhat :�> #rm�B�C�;6{oCB+sYIs> (\bY�2zc�� B�bB; bf BV��Z \pagA�be�{arabica��:!DA� D_\uR�DA�D_2��i>j��!rm :! esss�{"ess. :% limhA�box )h-lim}J'e2'eR'paU {\pa !e�3.�ep$v"�}��QG{\�:�d.m�:!spk{\v�' {3exJ�xt}[1]{\9#1!6�(grad}{\nabl>kdi] sum�*�:�epi-� }>Wdom  :< intt int=6Pbf�#2cross��:Vla>rD(p:XW:a�W>9c��B�cU6UB6U�cU_I�&}!�6�UoC'o/fJ%�V�YBgD? al DB�n�i6vX6XB6C��66GGB6NNBKKBAAB�#��$6�bP7 bf P>6bQ QB% MR:Ou 5uB5y yB�p bf wBEIbfFHbE-bfF,b%�bfJ�L�!L>icMM>bX�XF� SFt8tilde{WF�%x:BycŽž27iso�quiB�ds/ *N:�ED%\def\Bar#1{\raise��$-.65ex}{\(*���\!� $#1$}}% %�g~<{\rule[.1ex]{1.2c}}\���~�V�0� �.p,ud}{u(\cdot):T}{[0,T]:b��b6*>:#e#: "� :!bU/ Da�:: e A6w argminA�rm :Blip Li� 2�dis�4 :<t� rm tr>er� hAJ�#1}!� %�� re�! re[ nces�#aw?_ MCSS� .�biba [#1]aB6bibentry .A[�]� re.Wq"}{!F  TB�F1.34�%:w baseSAX'tch}{1.3�]NL \font\mitbig=cmmi126�pd�{�b tA:{ 5�t!U :�Re� )}R 0ik{I \!R�m & leng�2!�set {[ twidth _ {16cm} %%13cm %.8oddsid gin < {0.09 %0.66.e/*J+tex&Cght V {23X %22c �9.5>�topma�{-1)} %2�parski"h {\medamount}�5'e� cols. 2.5p�@ % half the usual-t2IE:)|�0.75cm!�O z ){n~2w orem�environsE�th4&}!_T }[�]23 corollary5[ P]{C25)os675Pro27��667D�& �w �{examplq# nE 64ass:!o�6A 2� lemm&� 5L21A�ra)k5 1M:�3not2�do,Fceg_.a���10a conjV3 ConjecturJgassump <�AY�B�{>{�y� \r���p-,.K%, %.B6@)9.=B<.Geg:EegJC!K-1IaU� }\i4�7.�.`.C6I�A�� typeH5��� ��enchpar.�h��iH=��emXau.m0 ? � Niop� (!@u axN5F6a�E��proof�{{\sceof.}\h;0.2�\} %bug\sc� zM� fFM6�qed6��hf3*Iuare$:3ep.�3.�0:.theta:�{ ^\prim�a��R>� !bf92*canon� �{C(a \,;\,\R^� >� YRaAB�ER+�2�PoB+{PZ+EJ,\EZ-L�F61{ aZ2 byde>_*� tX!gle}{=A�.� inverse.S!�extOH 1}!U>;�:56P)�ZEND OFF:$\date{Dece$ � \�i(March ��;���.�% End"� �) n�b�% ext.\title{A"yLangevin��=2Risk-S\"tS=Opt� Control\� ks{�Cwork was por�2�I AustL an Rese� Council.�< \author{M.R.~J \DyM"�"EngineR,.XN�al Uni!�`ity, Canberra, ACT 0200, 5$. Matthew.p8@anu.edu.au } !m@\make%1ez.%��E9he %%a�lcs{03.65.Ta,02.30.Yy,42.50.L  1�ab! ct&�Apaper-�&kAa r!�s5�>6�rolg*K/R iIDly \%t) open7"um"#modell�%q�U�s*#:t ler KL+ermaaZ�""�"al�, w�L�=allF��H%at�Bresents7*3 < knowledge tempe�&!��% urpo�# OneA�#PcomponRaheJ��"d�>,�8l�%}&?uH>::��. I,�/nSan>l feedback&�7fi�KundaF solva�q �!�gramm1�^�3i� !> ed u>A9�'el�O�'s�)� ideaU+lle�:an � !E�1} of a!m-levelJN�0,U�stochasG'�DJQ�f%�inga�y��\taof�Aa�V {I�� i�PaYOsec:iLRecz'years�0�&n sig�*c�' adva�iyo$technology�ina�����IY ing,%Gi��-ur%��Ond Buis pla�6a) crea%�role,�1��{GM96�<�{HC93 WM: a.5 NC00 AASDM02�7 S VPB9HBGM04< VPB8DJ9�# 8HS.)BEB7J04�/͚R! m��!�method%� |SyA�8� }Pae�widely u��%C(�'de!�FThas bee�)B)Q� /sN�6�852 N��k �er encod�?�=esi�perEhnce ob i�I (e.g. reg�a ion, etcJU�(st�����:�:�ized. Wm �(b�!a.�Viu,noise, uncer�Pty, orJurb�sy�U�1rler��4sought. Becaus���a�0insic randomnP)y�6B_1�of>�n%%�cl'.conne\0,YR.�)� ory,M� DHJMT00}.75�(ex�-H a&�*s9QSZ -Z�*/��ma<yp�$c.�s�. Y quadOLc g�SP(LQG)MX�!�se���*ed valu%adQ%!�su[VXM�,bles;� ��-�1ve1KV86}�! rast�O �ex�P�b�E�:ol6�multipC)obe�?!xaverag�.d�ˡNtM��J7��W81����lso�n�+:)eD�e+%p5sBUi�B�a�jLs @neuK >>). More�+��mm�� Ue2" A��V��d�opV�= non-i]�)�A5E} �,� 6� -we� enjoy enha�d robuste�{�a��DGKF8��DJP�X��t 4 prov�VEj�� otiv�A�!�study!�:�pk: ,��da al di�0� betw!G1�s{5e�W1��&� h!�� 5N,=9+,�6a�B .9sl, .m 1(Kalman�7he LQG :1�Mhilh3&� |�~~aa\'5 �8SE=acc��U�V (�. �by. V�E�!Mi�/~.�/�1?:q�ax BV85�Ob5�A1:��� ��C.8c.\� h�7ter�2e, M��șr�; e�a�i�:�6� %�FMs :�8a�Q�<)�.h a�8teriori�47� s (ev� !�r.�. maA"� ��r5^travory!��Belavk��"� (s)��$� ��4J�Q&M�9��9�. �GU(�'�in�|:-��M!�frame�*4�9����� >HJ���"�1unm � �6���Q�1 EH�ie8,rvavail��A !-wlerB��!.*� gdNae�%����EI�a� A�a� ��eF0Z�3�K � . W!�aMarkov a*�U-�describ!n�bBX��[Chapt� 5 ��11]{GZ� I� Pism��1��B . "����`:�� i�� to�$!wZ9. A heurEAc ��()�=�on-f e-*l &j �:y� � sub�X� 7Eissue�AE4�;J�.�*�or>��i ��� w2 e%*c�5"AOu��:7:[1ۉ�En% �� briefl�7:�ݍ�, .u�WB2s,!�faciliA&� gA&?%Ueos-`��F� J� vi8um �ing. �;b�#!�S, GI\� } by�A��%��(lema<eVJ rep}!��/ howF��� FexV��.������2� :��.L io@�a�>�e�O aJ�;u�inFdp}I�5 :Csummar� NDrn� IJ^2l%(&��<: a��N-ad*������.ZP� .bU]aa!�>$?? FIG ?? E6u!$/Fof�#aUB� �]w^P=& afe� *�E&�1%n7 �vAM3i�bc,!."� $u$�} e;=t7 Hamilton�O$H(u)$.i %$S^LF c�\�,wo heat bath� �$magnetic f�:45$nels) $B_1�=B_2eCh�Ul �=ot&;C<�^L�,2�, �M)Udissi�9$ve effects�@L&.n2�FRP>� {\emz#er} $\KvOݳ ]�^dss;� �f�to�%��!��:%��� in"� � llowS=�< caus.�` � .7*7 (!� just�[e 3 A rent2;v�)N�� ! �c�@n Y^it mini�%]sui)�@ or2H�$J(\KA��KyJ .%'�P��oalE $\bU)>ay re` lex v+H� "�> $m�_ \bU=\R^m$��  C^m$/ @a��E $Q�bVed8un . O�Sur��n�1"�Ddg un-�d 6�A��D�y each���ETj�icity�*We now6X l�G%�M`�M��*��K %�D�� ��KRP92}.�: $u=�+$M���al (aYA�ime $t�`-�$u(t)\in!� ). C3�,riA pi�$�C taryH ,ors $U(t)=U^I$ (often!Z omit��%? depe #cbGon���!-no)q)�zvXF+ R+ (QSDE)�0[eq. (11.2.7)� ->�'. 26]-G,�eq�7ay} d�$&=& \{ -K(�0) dt + L dB_1� (t) - L(t) \no�9 �f& &<#;# + M+28 GMG} ��P�yU-qsdC&�$��}nl� " !�0)=I$ere� K(u�G3!i}{uc} �� + 1�a�L2 �M'd e HeF$L��MBM�gA��tog}�M+y�)L +�BBM )dt:g�� ��+ [#,<]!�. - [A,��(t &R:�+ NqN.$N�>NARM�5+�]�5�La�$hM�$%K5�K����Aj%� slight ab��fYz rega.$K(3$� � "TA�j�H pi_0� a�s%,���He!�beg]_0 = 9 \o�sfV cv_1�=Q_1 _QUcv9U A� (A��a�7lvh�ir�Q� s $v"u v� g`�vely)�b e 1�y ��9q �FM*A��A+=e:�Z_0yVWUe oat 5la *,m�X;a�W (t), X1=I1( I J��ɕwOM�I!,amA,B6= \tr[A1� B] �AV:�A ol $I$ deAMvLeo�I�Mt& . q$&� [ � loop� _b y��O�no �#e� trac��6eO�:��% our setup�deLE�bar%z(t)6�MY yA�rh ' ka� �He:�j eK6g)%-H:�!�65{?}A?�B-q� -6�Z� �q� :� � 2N��c2�н_ �`=&�fIu&h [H �,2EXScD[L]6�+ M]2-,�)2"�P�]�2:c]!� = ccU�-\+ (c%�rrho*c�ade�OAper�:�A��EiR �A�%�^� ��5�yeI�_skA�, $k=1,27 put ,s  ��� 11.3.2"� � 6 out>$A a*�YA| �JB&)�]8�� ur�!!'kE ����3e$YQJ = S + B1� ��ww*�e Q� .W(A'{c} Q  \�xQ�K \e�A��)J����0 t��G�"s. a. F�2�Y ��o �),>9 Y �'��?Ve!K�-v�s*Y � s!56 d wac(+u�(t)�+ d �6�d �9@+u�.9�!��YVt E�g>+EsL*h��V�|!�$ �$� �ET-�20� $y�� 'xiE[ a ("��Ro&N\K$*- a� ]����bI�u�FH= \K(t, y_{2,[0,t]}=u-K�~%��Y�kqfer"�me�'t�zdic�Qa*cT ""l�on(=9 s; $�$ i Q�seg1_a9� S� 3val $���"B �-H!{) \H= \�c&� ls. To*�&*v5[&�7�`$ase}i) �yp,�)� =k(yA� �t�� �2� )_�I< nE.*� ; (�X�Fz� d�rm�^a� \K \ :a�4ba{rl} d \zetaAC$& = f_\K (H g_\KdI��:Ez7h27, "E�ea� K-dy�ee �t"�"�N/� �]-,!�is .�combi�1!T.8"d2/�VQLE��� �zA i law a7. E{}s��a9 D;inu�h7Ks�|u����smE%�a�!� 8��Ecf�6dE@we � to9��P \lq\lq{best}\rq\rq \�X|*�er. It Hbe�� over �ma{ 2{0T]$. Let $C_1n<a� nega�*$ self-adjoXS-�&�B} �2!8���b��l d2 a non�a�s�-1ed � %E�s}��c�to$�!?2�"}%s,��ex� \.6  a bal�'�& .(,]�)�achieved� B�W9$*�;).�itm�int_0^T !�tm�C_2(Tc�&rui� +��a�)��$<t)=mC_2 accu/"s-YA5! %:8�&d( penalt�4final Ek(we agZ+akE� liber� �0^� stea�5��ex/.M+w%1er%  a)�� (���,�0F�rnKa�2P6�* :�*zJ!� "K~way. �=e $R(�� to b &Lh?o� Rc��f� dJ}{d�h \mu=!�t)  ��R-r Jeeb�R IFXO�^Jy@�&�6 %D)�aqye�2�!oq.< ��A-orde(=F����"Oo 2��mates) ds \q WEfQ�eE�0 %�"!}:%�-ELum!�ec�J^\mu�� _0, R@ (T) e^!�m�} R\ri�J5�1irh�����!N�. Cb� ~>�\�7u!��!���asX-: "� :W cr�)io"^5e� %��$7(���0F�X����qy%�Heise�8g�uЅ�#ia�s&�4W al:�"N&R"!#� 7neede N�gX6u�NK,dp}. %\qed %@1� �!BQND... '1d�L??B cus�FY d �`ov etc9"�C�{S�Re�#enI�!KC�0��F&�5M�[$�Z w�Xtoa��8%L6@IH]?n&�a3[ d)IG��$E�> is d�xn�$!�d�W&t $0�q t T$,&"�{�!A �\�& end���"�$�e4$�$ee}ɕ�y �!C@}�H Wiene��strib/#.9(�a=7�j9X alogo�a��6"�7��� q�M�YemigroupE] �-&� *�6AH0�dAB�4��pp7f,z(�'�& EsA}ip�\;Uc-�5M�`!��" )� 4�uisa|c� "f^) demolish&- Mo&$d� \d@u!%vA�m1yX �814� Y�} (QND�u:gk�;� t��$X$9k [N,X]~h \fo�R \ :� ;q�bqnd-1�fz)�U5q9"U  =�Y8 a} (� e� Vay��rstoo#-�;wis� Bef.3 aP)6F�)Ec%��'$ss:E}6i}U!�s J�+� (r�"&�.P%G >8o r��m-��b!v_j�s)Z}s,�aIj,�*HʅFc-�Y(F!Zc�(two-"�#al) �$� (Brow '�3on) $q� (q�,q�)$L*z Segal mapI 1c 5]i� . Iy� \Og�_T�n�� %A��aT'�`D)����>^)a�,obabilae� ubo$F\ �of pa!�\bP^0(F{ ��& , P^Q_TG� "�P0iZw�! $%� !R proj�]U| assoc7ed��$F!Q(sP ѭsѭFO�$�s-u.#:!f��i�<qsI-qR|t�,�*�,"9،� meCe�1�/q$$(t-s)I$ ()$I�$2�U �(*jmatrix-�Qm0$YA�|a��Mre�-��e%�[Yi� Y_k��y�o ��y)� and 2�ND�֩� (cf. �31}9  [ Y(s),�^1)_1fUVG2 z��[E% 2.24)]{BS��A8)]��"+%45.3UII�Y6Zy��bseT��2aI��� elow��)�-/,VnW�?�0[wI�At6Ta� . �b� $V(ta�)*N�&&�),�&=k%� � T�jErul��*� "�1)bF2�� III">�% �� "A�: ���&"i�&6�&� dB&z �-*��&�3VV8ͰA3M�$V��� �)=�C"\demi{u  e If dn9j!$_t(u,X)= V���[X*0 \�! I ] ���e�(E�!V"~ +*� qT(u׃�C_����IKA�now. }*3qu&ve�;A�6C2q� �;�4)�&U7� ]�F.U�&w $\Phiu%=\qE_{�"-v_2}[�, X)]$&�%$N*��� )�alr� a�2�^.} ���,^f 6�key�!a����k wM�^,A� !�be vie.�"obr6 �x�/�C�> dua| L(:�5.2.1$ �� � a&�*� � &Y alen� & .). % � �j �sC="�fa͍ at $((t)v_1=����"y! (�+) v_1aDL�&� �l&�7&� ̓eZ��YP0}�Q+ � $�Ҁ=.aaq6:ADQB1#wa��a>h $\t[�S$y0ng� � �;e��~psi�b�6�APSD�� dV ^�� f,� �\} F���-���B>%�/IU�( - 6 |)$M=��A�)�ti&� :Raw^ *�5gen�ny1Q����6".�6 VF&]%��� = \E^0[C�',5?�U �VX��>& �� -repAn��>�#E^0�=]�*�Au>e 2 a� .� "� (r��q �rPi�7y�M���= ��6�i�"ǖ!�2+�[ FB hR4==� !<� altoFJF�%>�B*GzOM�VJ.'�=q��DwX^H �]=%-_2t*Co �Q�s"5","� � A?�<�l%6�Ѷ�5s Ŭ"� (�� a�2�Jb�'^ 2� n��q �Gvs� 5;&��v\er� y}�.[#,�&c �A�� � ��(2�*.����� u"��Y"b16�E�4h2���CqJ.� \vert�&s),F"� ] ��c�H $�!=�Y$ ??? A�Itra�%forward.b&t&f#w"%s;  *a��B��"��FEb�NL����6�dR'� ť=?-X # -K�\k X6&&&�)��XL� M.RA&"�.�"&&+B~ E + XL) �v. *]*+F�*> >M>F "�/�-j-�3F/n:c"�a�m�`E�U# =� ^ ee (F"a�m'�f -!i��Qg�7n, �7e�y f�P&+K"� 18]{RE8&Q� 7]{WH8�Na�hasBA�24E 6� J�=�^  Y !� &!�6�N��$a�hat^�By nda��wof=gZtsI -�:O 34]{PB79L � A.a*} &&���2�2u�a &= 4�9��!J�] ]B* *})h��zN9�ZL.uThM-pa.s isB�m $ ($u,�-�: mb$� $ &hP�Lda��|��!�]y2}a@(e�2RF#:�b D=Vnw$ (� �>on��&]) . 9^t�E =� ], f *�  "�"�� .�?(5ora�!-�""l0[�9�,2�]\co02�dt"p0�I7 dt>C+̥�#�{\cH}[�#vF\ � )M:!��.�0�--fn.# �F��0.�0� � �>1=1+ (#&1$&�)� .�} (orB-KU ��pi!�-a}ߘw)�{a(�N��o�)�.�r��o�A@^E�%�T,*<$|a ]N<u e�Eion����*$oeZ�e�3.�M�(2.10)]{JBE9jV!��*b�I�S "�F�" N�Dwe� a=!NG`rs�t$���� ��.x�V95��&!�� XM�}1�.!�h!1+�f*�83"� F�~M$V)ih W)� AVS_�pi�I#_t�h_�d2g N[ 9NZ_tJV"v i � �U_z?Q���M.��$?)j7 >Ja265 r�MB�8 pi_t���(�}{�/v_t,(�a}��Fzs�, e^�]��-{  - ��>u�,�H}56L0>xM9;v�-+�::� � \tr [(M&B3)4�b ) dw��A>��'�Imr>K inno4T)&" aFV$ (@)cdTJ*�� �� "� �2�v�9N��A �UbytA[e Equivayly�:R%%�>�&8-b6�%}��F�B�\cH�W. �"bI"nHHz��8rho\tr(c Ar.+8UFacB�%�� dy �x!p!{2,T}!Hall&*.��!1�N�Q o"za5s�J !�6a�N et $F_2 " 2��*m!N�!9(�"d�!{Y_2}�!� n�86x.�:g6D\bP(F_2)3&w �+K"i | }m\ @30�/ P^{Q�{T5U"@-�A�*� &m r�;�= _6�=!�'_0=A�&�>v_1v_"`@"zv_2*�>$.�CA&JK&�4"con�1�3$�6��ee�ae=,E1�(ce1�"=�"\K�:j y1Gbe�Y altern�2&��a�:a�F�D.E�"&F:Ai�s�=L3�*CP�*/� . 2vk. .+ae�6PN��0�<p��7� K V�@�A� a3minG< a���' �or�?&�2@**Q?+6�: ��> �TN W"X 2a�0:�iDN� d\bP3��T,1a�^e:� ]2'$ SM�32�� s 6� [)Tthird:)12V&621�edR%T1;� I6 namel��:�.[�\exp(R!w1T ��g )�A.� �")?w� ��3-�Y�Usa��1�:��8ab�\mK/!f E=\Hk)TY�!b.*} 6/ !!# #"�5\Z!,[ >�y!/]�(ert^2��u Z��5R@�1[t F "��.=*}SDE" ! $B>�} = ��vA )>E 2I dt�.6 +6�4L Qe) ]]fdt (k P dw � � %(&�^ 8!��Z Ō]s��:$"X b�7v� 3_d|.� # e"�bnW�� Mv*Fs �51}�"�U�/a6"�2m�es`:oX`�\�!�/*��:�a�wV�264 �$ rmk:�8sI� E���&U#lA�� $��f�Jia� poL]�] H� ٬&� .� d2�" ose �,� o fM4�� p!}i� ior �W�;>*�\��8�!�)\�"iv�1� ua;22bof2�Xb�k��;ѦIV]�hb}��a�Wte&� *;-0��-�u�{�^K .�%me?he>%�Q�^� ,���)��& =��AF�b�GroughQ��a�nR�*s̻$; $---�a*&i4m2+ism�&9bEe&:m�])��@req<=RE2!�crA3ve}�e!s: �ory]^ZHi�2pe�%*�1k H�%1�6!"� '�=m�, �� �T)�\Xc�!u:\ K�MHd7 V�N"�:�%�.�.� q�*�`m)�ckI�{RWB76M؁�r!�mpariso�u��Nnd2� so�c]ll�?b���ke�wAE�.%�.� 8}�&u1qk* �g h. 8�"8n>� }? 1!Epq��u��j��=z &)n9�'O��1to)�[<= (i)!<�y 6]{rbA]&�bary��9((tm� �u�_k.�!���8^!v6�i�]�35�)g>~9�l��8�kby�!��*�%��!��*�/��2 effiE\y"� \eta!01�%mv�w"&W  Z1 \D�5���#t�H 1-3�-ee in"'?tp/� '$����A �j^��3� }$&�"t)�5�n >:\{ ���F}p��.I �b�b�b)�)����� &� ) dz!�"�'�-etFZ&�;DPs5u� 2^dpaqI!�.7e�&�_f� ��e�>sD> \DW�\k� �p6�A.v q�JiKA��1>� �=l1�|M6.�T6 ��E.H}:8<.g� �%:%.�F� � U��1e �fs�5iar�/�Z��Y�2�e�98�#b���#@�*C T%6is5| Dոa�ZK�~ � }. B_8�(��ey���;66"s,��%`N�$T&�_(-Jacobi-Belfk*�<����houldZE��!�!Z�in:^Q�&�H�jn�%��:�a/olvO ack�'hrro� :Q� �=T.E�00%�=i���z�espxE#�%m1%:pr`�plE!m ity" tR VI]{FR754=[�o ZD�:�:�$S��(\e<,��A��7rbitr�5i�=6��q�q6 :�<��� :p�inf_{\K  E^0_�,t}�-��V"0rs-�-�|��� � B�@!.�"��%��}Y�T�]�"� 1\t= i�#�T made� h]r-I%xU)S�DEh��AJ�F�N*U)>��L��h�=� �6'5)dY&0�c-�H�M�! D ��),B~r}ay�>�.+AM ��Iv�%'�on� r[� E�9�"at a �r)r$�-�+ T$ a� �"Nb��! pio��EG,t�Y�-y }[ �E@s,s�c,�rs-��! T�?v^+. N�=�dyͪ��� ��)i��wq�T)*Bw��NZ1b@""� KO  (*}u2p��7c�5ies&գ��%�"@N2�PDEq)E�%0ef#low�.oL5� s,�>h�H�It $s=t+h3f=}, re-ara��' d di6s��$h�A0+56�[�.S!^_{t+h��+h/9.,t)}{h} ��8Sen9,$h &�� 0$)�s�� �O�pT� al }.\�>h� dsf�f_{u\iRb��cLe�;uF2�\3 *�B< �<\6�T �E�B=�" P-�E�Y�z��� 9Bhe� �L� �E�5e�e�{e�e�a�:B��A�> ��b8.�'>��u .�Tt:aN�Lh� P  o- �2-�,u}R�ear� � dpe}~h6g6*�.�o���e&{F8�d�'Pa�t6T5% �O (i.e.SM`�? $t�.�b a#pa�cizSgG�$.!��#���lt exis�}��7 f�᥍l��t2^��6�0}[:e�j_- )}{t0��genEE�C �gy smoS�� s $f"z �^ �9�f "� HedE=�f�9$f�!AK�_e B = g(2�X�^Ӄ\ldots> d , X_ʦa &FPf �J g��a��g�A�*rh� $Jv!$X_1, wj V�d!d�2�M}$u�r ge�sĨ$fAp �6V&&1Y; u.Z=Frs!�}t &&�Vpe\��j�E$}^J g_{jk})M=1_&��9N-O.BI'.�0)&X_j + M � (\�X.'k 'k 'B_�,um_{j�J g_j �KQ -�hf�*G"cmu(u)�- .) &Z:�1 _j M�"�Z�g_j)�$)�$&"6��7!RN�Po d�!$"��$g��ITQN�L0 a su�afm�", B4 Œf , �#R 3"�a�"��s.=j $\bu�J ��� e� c���at&�Śu���e8���ht� J��Z �Q&�Wisy�����:nf�E�\ �J\K.�F�X3���s0s0�%B�'L2iN+ �y�&�)�%BR� y6\&gYV �W / "P K-star�� ' MA}�Q��Z�� ler,��!��p�~%��Y.1��%ucC]i*ֆ��i�� .fig:fb-r ��?Zs��d &YA��_�t�r $2C�0nd� &�r#��-a/O circuit M�gi�~n:erJ lˆ� b� o2WN�!q:#�m�)����as�bed�?�PofFu/�Q "{9('s*� � physo 1l.���TB6��� �.�� {�Be� �N�) "���mp�Oo",%d�Toffm�,YCBs� ��&�r!�o��f �:�f1�e$c�p�0 nl��:�isF�� ��fe_}[htb]L�c�*�VI} }{1800spN�^" 3947 " T�Q�Latletter\ifx\SetFigF �t� % \g�0#1#2#3#4#5{% ��eset@?� size�{#2pt}"�!y{#3}see{#4 hape{#5 0se�6}% \fi#��{ql}(7224,4749)(889,-4798) \thi%� s {\�l[rgb]{0,0,0}\put(3001,-1561)E�amebox00,1500){}} }%b?21?396?21�?48�??21�� ((-1, 0){600�� ' �:� ��&� `T \cap�{y�r6\$m8JRz�%>M:�F� "=#&��"V �w Ϙ��B�'B mk:p�Ical-1}*wa#y2� *�4g]ar�{utRP � !5t =Fs�)� E��N�+�5/&m/$�< �a؇isn2H��)"c�s �p& sonsZ{'"G�R!�N��Q6�5��`nA>I�!�3we" � ((a��e�* typ� atۏ stud�.by�(�WJ̅!4N˅. Specú"�^Ci�Y!p�!E� �}��1*dFdJ{d&,2-16hW�&0!J-!<]�z��]!��8��"8�v�w�IG��Q�S stepAyN:w5k1�er �A\a=h�<^zN45)B&�"�!6'L��N�cTewVi�6f)�&�~E[��3��;,%��2�E�<T2���z�R^0>T��_jW !6Z�!�&qGRT:�p���,A�.E�3!@su���N//gt*�"�a!gra�are��,�$h.�"m<B9��W( � =!�U$:w! -Lt�6bI)+s!��=h+)� =F !�)Hrn �0e �f)�_A�r�r��q�9�o|\pR�.�+ \F� \{ �u}2- +I}�M\}r�dJ�CM�2{rng�Dq��j-�$�]��K�W:��;�� _!ji�gbT&6��Z�n����������6��[���q�2��f]Gj�"4�%M� ��az�U�!/tN a�:�s \K^�2_'��Z��E�K(-FD�Z��ER\�_BNDU�� +"�_&�.2\D&�E:�����u"56 �:gx> =!}r��fE�Tal��1n�#!��UZ�G��r5 �F�y"y F�@m ca Two-L^ Atom2� 2l��*� 2�  9c2+��"|n/�,9 t�.v4"� �w|�ɞ�=A�>} �Sf&C� 7q�(sern�tjritϡae�e>V^ l/�}�@��Tso" )��� o�== 7  ����m�l�R�2�b3Tne�b�YiB�� S(by homodyne}*m,!U)��-di�20of�IjgI&)EdmT�, ݉_y~i u_i=�=u�=F���rg}u}o'CGk8�:�3 a c�Y *z5O*�u$�mf4G..zyK��!Q�u�Ơd]g�5� e�h"�-_z$ up �$ �\up� = (1,0)^T �dow�/O* -dn-0,1-9 ��x��H \ba{cc} 0&1\\ 1&0 **}(sL_yF1-i\\ i:2E�,z>5$1&0\\ 0&-12g"� Pauli�*ri8� V."�-;�Le�p*��XN3U *} L� kappa_f;# _-, ])M= s>/P)=i (u�0 L - u&� HP�y \ && D f^2+ s^2=1e\ -J- l��I@1 & 0�~1 e"�~,��\bU&=&\C KM = a�6ftRJS2g� \Abm'm/^2 FH �y*&6H,�*�\AC_2= (�b�F� �a2�,�geq�c � * *}�T$-Wf^2Qj)�sriTdec��a�kint�đJ�[.���1=par@u s $aA�b hcI���,$r�P� 6�_�*.0�� e�TB-�-�ra-�B-2N*(if $a>0 4c> �+� B�,o0o4�;}  -o*}EA=�Ρ�?"�y� {�!!A�5 �;6!in previq����)�� v�. �\h͙($u$-�1tw�F>4{�=o��a��?k7&at!��<m� K%a�< ,8tOconven͡�fac5 �!Ec?rMw:��S�"a`ing}.< �D�r� � &�(a�mc n(t)I + xY -_x + ]y + z z\&�w�� >/%.1E a�&_Fb�ItM� u(s)E.^2�� Z� & �A����� &�-i��� +  & 1-��/Px. Z� Z��E��: 6yT� o titu�S�E� %��[%�;7e/~<#�Pl~SDEN0.��;!��1Gmu a (% �G��%6jF*�CpxY \\ dE'��ކ(1-Q)82 J f u_�b!r2��[ s�+');'6�*d%�Nt dt -.tiA�MBt�; &=&-�aE�a) . -(1+ �!"FP.m( �%-9 (t)�| -�! �A"�&��+vk;&d.6,[ \exp\left(| \demi \mu \int_0^T b\vert u(s) D^2 ds \right) 54(n(T)-z(T))e^{C�Fc} ] . \label{J-rs-rep-1-2l} \ee We consider the value function \er{rs-(-def} as a  of 6�coefficients, i.e. $S^\mu(n,x,y,z,t)$. In terms 74se parameters,I\dynamic programming equa�(is \be \ba{�8frac{\partial } t} >}l + \ds{\inf_{u\in\C}} \{ \cL%*;uJ5P \\ \hspace{0.5cm} +!w5�1� 1�Byt\} = 0, \ \ 0 \leq t < T, \\ 63T) =M (n-z=�, \ea1�rs-dpe5�where%C$operator $�D$ is given, for su1� ly smooth5�s $f(n,z!�)$, by!w4gin{eqnarray*}28f & =&U�Tkappa_s^2 x^2 f_{nn} +-4(n+z) !xxN! >zz}!&&&!�?x A` x} -. Vnz} - rxf_{xSf_n ( � mu a%t ) +f_x (-(1-) x +2 Qf u_r za| \ &&+ f_yF1y -.1 i z 2 3 z (-_UQa)z -(1)/ vnA�&&I({$x - u_i y)a�end.� HereiR subscript!�T_{nx}$, etc, refer toa�eD�} \bu^�1,)�_r��&=&-*U� }{bn} ( x)5_z/8 \nonumber \\&&>@-z 4x4 67B�i-j�\y/~�y �.� eU�6rs-u-A��m}j}E��is!�nJxK.w, \ : \ u(t) �F�(t),xyz5t :u1ɵi >Mi(VM,�b 2l-k�-2��p$C $, $��M��$ are�xA�a�0px-sde}. Notm�A�r�9�� (i�i�diffea) "3of!,abolic type)6 solva�ackwardsejime, usq�terminalaldi�g afified: :�f�$i{inf�7b. remo�y �� titu�&in%Qcco�= �Qe��!Z!B�q��mulas17Y�P, if desired. However�( form1�nis bette0i��$to numeric% mput� , sinc!�eB��ureO��Lerved, \cite{KD92}. Y � is exampl��:Cfil�Asigma-muEUbreplac!�y%$finite-dim��o!�SDE���,easons. %j FAFly,��c.k �neutral� blem. W�) \�_t ] \lŹav I + av ' x + a~y + z�I zB�n from%%1r%K�fiat�. } d��� "d � dy_2(t) �@)g -rn}+\ d���_ 6dt 6[ ��dt 2�6 (! +()w� l%ldt:� bldZ?- 8�J�-�� R�� (t)x8"�  �a�� 2� �b2+reeFni{E� J-rn� 0} becomeJ� J(\K� \E^0[\t d(a%L�+b � Ɋ ^2) J�>�g �*�c ]� �L�NMs r �W*�bu}6-� &� !-z)+ 51 ( z� �N*c}!!*� n��w �k>�� u}� � � "g �^ bV � T z -n.�>2 6e *} E�Ra�s�L� �5��J]^ & �= 2u 6�V: �6 ��2 f. N�y 6�+ &3 n*m6d} cf.��D[eq. (15)]{BEB04}.FG ��.is >} A �V= � * ��,��N9 �F�i .��5 n�5 f5 �C.+ normaliz� �  �n� � m )x7)9w&� A�ex�Z|s e bń&���F�s� similarIinvt  a level�co� xitytip�,. When $a=0$� t�SDE� � } reduces� ���tandard>9!\a ough9Yys will�"d �general \sec# {Conclu!B}G sec:c} �i paper F studied a>�>� pr" %%Lopen quantum systemsi model] used,�Dinuously monitoredRCac%S aaLangevin"W . U) �Dtochastic calculusE!J�Y $showed how!�{ ula�nd� %�:�Z �:�0(we obtained�tTFig� H\ref{fig:fb-rs}. It_tw� mpon� . On� I �,� t�A�utAzhe>�state �second.bRan>� feed�"� eia�unIolv� �A%B8 xJ!�ured class� $electronicE`isbced!Ais�ally intf ve, due!�! 4storage require�"��A�rol��8?(peed demand8onlineA)��E(:/)�!!� $A signific� ea�o�:$b�aT+:m5�ieEN)9A�usu%2e�iy� phys-meGc<becausi �IUyit%F ains�!�rond!to%( cost5g�y hA�aobj��ve. Such 58s do not appear� 8ven�al �traFory9���Belavk� ��=�iyuld sa�atjNz�>�M�enhanE robustnese�(perties rel&ARQ�a$(e.g. LQG)ua�. RC of a1��0erns its abil t��(pe with per%WadegraE�influen��of uncerA�ty�ynoiseqA�asEQ��2, deco9[N key limit!,oU�d�op�rL$technologi5�tXfo�"QtoA�ign�!le^�) also-s �a�e��IequentYe� o� 9tpr5�of)�&> Q�NT%n�"topicIinvestigE�. I�! ��X1)-u � quadA�0c Hamiltonian4Gaussivni�s�1s� VX�!::���)ac��9�&���ic�s?!�b�n!�toae�(F {WDDJ05��\v. � 4indent {\bf Ac��!.}�(author wish1��ank A.~DA�M�L.~Bout�8or helpful disc!"o��v~ \bibli �4tyle{plain} %2${mjbib2004�% {the.? }{10\ibitem{AASDM02} M.A. ArmipK.J. Au, J.K. Stockton, A.C. �XdH.~Mabuchi. \newblock Adap3homodyne2mof����phase.:�{\em Phys. Rev. A}, 89(13):133602, 2002. %�(VPB83} V.P.ՠ.SO� �}��ofq<lA-ob���:�.C�AutomEx��Remote���X}, 44(2):178--188, 1983>�8j�Nondemol�ݞ s, n: ar�q)�?  �/"A of�&� processe2�InA�Blaqui{edh , �M� %)� Ccf S� 0 in Enginee��, Q� Mecha $, Economic� Biosr"|ces}, pages 245--265, New York%C8. SpZ er Verlag:T92jT��/inual2X�Ha posteriori collap�tn ccrB0Commun. Math.I�8}, 146:611--635�92B�a��=�2� Q�JB�J. MulFri� Analysi!i(42:171--201F�BSBH%,P.~Staszewsk2�6�mG�@, free��cl��45(e�47--1356J�@V85} A.~Bensoussa ��0:2700%�9.-�81>% DGKF89} J)�y�K.~Gl%, P4 Khargonek� B.~Franci2�S� -3 "_"�"�${H}_2I" \infty$ B+2]�$IEEE Trans�on"v .4,34(8):831--8a71982�DJPA�LP.~Dupuis, M.R. Jame��IP�*6,�+ 3b| .���x,up$and Signal�$13:318--33� 0.w RE82��J. Ellio6�e� �C.�App" R�> 6�82.F~W�KFle�+.�Non��,ar semigroup&A�(d���iffVF��A��B 286--3�:� R75}2�%]� RishJ�D!��%�& ����-��772�CWGq C��GardineF: HandbookAP�Method�&a�% Chemistr�uthe �al��V���thirdŴi� >GZa!2�%P.~Zo�.�Ex��N�R*}206� AH01�NS�$ levoB^�]%���*�ofwT�Ɔx1.�J73} DA�ɇo2e1�*� Q᭶�*� .����#ria%:their`on�\d2{a "�&g��B�18a(124' � 72�JA���.iR6�+>FF�.=E A�*� 69:032108�a42 BE94Y�|JA Bara��RZ�:��d%idi0%D��_ 2w mrete-( &; -�B��}(39:780--792�2� KV86� R. KumauUVaraiyaBv� � : Est, I��a�%\l o�:.WPJ)ce-Hall,�@lewood Cliffs, NJ�86.��' H!�Kushne�G. �C.cEN"N(.�� �� lem+� Tim^I.6MBGMI�$~Guta L~.Bi���as:��schrodinM*�&��J� A:��(Gen.}, (37)�9--3209F�GM96} G!HMilbur2q]�HT~6�Fr$ ]e&4. Allen \& Unw� St.~Leon+, Aus�(ia!�92�NC���NielseID$I.L. Chuan2�2�C&%* !]�In�A�2yCambri�Univers� ,%32�KRPzKa3,ParthasarathF� An IA�duc}�c�=� 2�Birkh�ݥ1:ZHSEZJ��� T�e�}EbB�F ��.G7 � �BH"� 0402136 6H WM95��F. Wall��e��� ��,1992�W81��~Whitt6�R6N�?/�$/ {G}��BAdv"�!� ed�5�`$3:764--777A�82�� S.D.�s�C.~D'Hel F��a pped atom.�Ini=subW3A��SCo. Decid""� 06o M93b�� ~Wis;e~GZTInterpreu#.y jump;d� �  illu�5: o�m� h sp.��:�47� 1652--166�3.Uɢ�q�t� �field-o .��$1):642--66LF�a�8 � "�via&�� V�=FL�<}, 70(5):548--55� :�H�E.~Won� BajekB�P��*�g2�V#E�D2>JF+(docj6*�. �m% *� rt)�4le apssamp.tex ! % % T#is� 3A� APS �REVTeX 4� tribu��.EV��on 4.0? *�6 gust� 1 n Copy76 (c)w �71n%�%�Society. 8Se^ Z 4 README�� re�E��m^�I J TeX'�t�x#�4at youz&AMS-La� 2.0 insta! %�; well!y� preOsi�$�) !�n� %e%�Eres rupBibTeX.%,com�#�a� llows:a 1) .&x.�!�2) bibAM 3^/4V \Q�.([twocolumn,B&pacs,P�6 s,amsmath# s�decypoint2;$bm}% bold !��no aB,1��1�|{APS/123-QED} \title{Wigner-YanG" skew}""�# as tests a � um �1 ngle� } % Force� break! \\ \ {Zeq� Che;*Temail{zqchen@wipm.ac.caffili9 {% Wuha� 16�"�ic�"Lec? hint?Academ�  s�TO.Box 71010, 30 West DALict, Xiao-Hong-Shan, z430071, \a}e (date{\today!��(lways , �% �% any B�$�6�>pec~75�ab}ct} A2-type in� G$��ro�%d���&of F� �GO<is!��  i�,A|�ne lo�spin � at e�$���%�c-Z* a hier�ic �l&��ll�g of m��t&��5 aer�to fu�Q�d I�m�<powerT" than.� �C7: ic%b9]ie w two-hb{�%�cul#&% pr�8-$�_2(ovideA� 8%A�D%�nguish {�6nT+e{d�'e �!C�+'s. Our l shed.)n C%Elight�f�&onships9ween N�M%�� =>nd]� \�F({03.67.Mn,  5.Ud�@ ACS,92�As�+ omy }3F% C�+f�$�Teme. %\keywords{Sugges!�}%Use- keys$� on/: 'vz %display�& red \make�A AsaMS%n1�s�s��6 at� cepU)5m"o nowada�#�#�hand,I a "�% �!AœV|foW-�:o�.*  i��( [1]. A nTqu�!5j en�.� ]� � e first e�C tool,A� etecF:!Ma-B� ]�[2]q�wai+ig|: �;g/to rule5 vari�kinX-��hiddena �ories.� cises(NindAxh �) �a��*coruO�hdicA�by�hn�99� for .� a��me�$ ensembles�.�,$be underst�t in a real~ pictba1]h�� %m of E ,ein, Podolsk�&Ro�[3]}7=Gisin'%� orem [4] 8rtat ��Yn�p�!es vio� !R Cl^d-Horne-Shimony-Holt (CHSH)2�5]!$ s choice ofō9!�IgreK 1�A9:-���. Uw� �[6]B�6 U U�Uw}�B�Q Uffink [7!,: �.�u,? �V�A��'y ![ �of $n$ Ea�to $n-1$�F:͵%�=�oA (:?)k[8a�lt"'4-Y%���Q��rc �[1]���-�3� ify &�^ifyB�in geu4�st�4f�'�=�.  0letely.q .&�4�"c�aN y^N8 F8 .�|�.how[a�secaω��>EXa�5� .�ory [9],� E� [10] /r�e�Ff2j)K]6rom a�/��-�e�2#\b,{H 8}I(\rho, A) = - E1}{2}trMF [ #(^{1/2}, A \ ]^2,�Lw $.$!+aI�$A� }� of &�5� �8� nt�$�Qc�v�;� !Z amoun�.�o valiBm+b�*�k2mm�B�m (E� to) $A.$�9yAKa�� .�satisf�&!�A��aa� &�8AB(.�l-sh)2Q��m�Z/� ���.nO (KU#. (a) i8$ �d�e5uIBdi�> decB�pPhr�c{} V,B�a� vex "NMinM---if _1Ad #re�9dk5 ty o�K#/nJ�alphaE�_1?bet 2A� \�L &IN_1, .�L F/=onU� e+ ^=1$%�$ , 0\geq 0.$ (b)�>J!%��2unS  wocepe_/ i" su�NAIzS �,viduals; nam�let-d>qbeE��of � ��� �,.�1ivW"$AT A_2$@ s�5z }b�DN�-� \o�s !�_1 !�A_2) =1�!�_1) + =� _2).6��(��F(3)e !ext!~� �in5�1L��A��,earlier worki �3��!�F�.�����4G,  celebr{ @Araki-�!d� єputql�3�� *b Ae=� �Fe� s,#e��ed�Y[1��!�v fur� .:2� ��1s [12]� ce�3LuoA@Zhang [13] reveal�6e� �J�uLregard[s! �um�*og�!qF�$�4� �{��2� � F�� es�ish)�p> �51�chaEGeri�> uA�5& andrA . He�Nw1�t.�&y �~2�se�R�-jA L �l�0 F� �C1E��8Mzv� re�N�3asJ�"[ N0rho A^2 - tr TSh :�In � ular�Ia( = |\psi \r \l |/a*� ,A4JA| 1 F�=:LA^2 & &{Q2nA F^2:�F� Eqs.(2)A (5)�AOlu CjA\leq 1 6�!��pi2[ m ($!k = 1$[ allE�es)@�� Now,�� �%A2)�assum����� >wi"3:d���Qo�,h�n�Ee �'o�(:Ss�a,\ldo�3A_n.$ S�K >���Y���vex�>�P��� EC�X\c`�f\rho_n,�by %�3-�6),!� has$� ~I ��+ f+�n ,\sum^n_{j=1}��j-j)%� n,$$L!�E(dEq.(2) r4 � sAE n�� forAB0I'$A!92. (We%me)�$wS.,1sho�"n�A �� �  1.$1 "^y (7)APV� ��nWv��&�E�d b&�C. �z� e�j��only *�d!Fi?�2.,Z�"xe`I���� im�>�qFE�A�N�D@6��� [7],� lso a$ $n$-&���� 2� /�Z�a&m�ͅ) �*� ^�1��N.�A��8��giJB%H5:� �b7:(-� 'Rough�aking9 �&�a6larJ' Iz ion xaXa�7)�me'c � 8is directly unc�O��"h *r�# ofB}.O=w�likh?!�Ao��őtrary�!9uOB&�& A�essmE ^r)�� � [14],-�r*: 2B@E��ou} �^a u�l�u� Z�e�i�,&e�8&� we�G��>� holds trud!Qn!f is, i�1��=�ino?Fn r��"�A+at!9���i!a(D�V, �Yide*aquAI>��� three ��� �Ca��aM�� $n=2 `b�&_Di�,$Emax� u�A�)u_��K)�occE2� � . K�Z��\  A�$$FS6� |(F �\\� |  � = �_{j,k} I2� \ A_jA_k LT 2L~^2,$$($ 1� "�A_j" A_k :1$�)I _ E� !�5)ebj _1 >� �F| �(5�J] Z9 Equ�A>�8)�at4ed eve:Q -$\f`�$*�E Greenbe�vkZei�>er (GHZ �( [15]$$|GHZ9� [\sqrt{2G` left ( |0-k00 + |11�1" M).$$IndeU choo��!�ES�V$^j_z$ ($j=U� n$  ]��$$\, k_z | GHZs= �, j,k.U,$e��9| K1_z.� naQ =0.$$H� 2`!�� hN��=^�.mAd n_z�nB3����� �fUDiar c�#=F�����&�;�7)����z' �s��� $4,$� is7t��. j� 62QWu�&� y [1� Moreb,w$.� $2� Hwo weeLeqSchmidtQ% ompo�_ C>2^ = p � hi_1�|\c + q� hi_22!V pY$qC\�nonnegyHz'B�J $p^2m^2}K$\{|\z�, {\} f(.�, �) *re � oxQ I� !��di"dZ Hilbert �:s ${\H}" 2)�\Dw�a�, �GI����&!!�>��U��i le s�K�$E.�= |��_1:��_1,�`�$z�� " �Q $)61n 2f2, 5T=��_22f2$ f[ NFajpl�L"x\ y�-�aJ�2��d+[�[2_x�[2 + 4 pq:�>� >Zis&� ($pq > 0KfAV if� �es �N�oaa � zan>� !w*[��fAn �;UriJb� L*R%�#!R%�z� ��RF �+� �c�&W .�m� �>v� �;R���[yE�b( q::� [1)�caY"�-��_{(k)}&a rhn-k)}$ H ixtu�,!��U *� E$ ($1? k � �&8 � not��k$��A-$n2 For!�a9, �>� @))r�8A��Um �1:�23},$ 2:1� _{12:'3,$�^"�%�"� # )���2� �'Z:�EvE�2 .�7�U���A5� � �)3A-\ �y$is at �k*��8iy8�-.{(k_1.<}� �$m)rb)UKQ= k%�sum_j ="����j]�Jb_ � $k_j.�2d9.den$by $ES_k$ a~I�Y\R.��n,>fESAu cet ESAf 12  ES_n:�ClorF�!�J� " �s, +nIE�i�aT�0 - {n-1I $l�TllN8Thus,A  $2e�u�!�.A19R-HK!] -!${k-1},$ $1]{+:�  �n/ �/j�2ez��O. Given.J!Q��.$����,$AUE]8�have$$M7�l}{l�#E�}f>L��kaff1.� A_n )\\ =#a21)) !i�+�m& m)})�/Z!k^2c2m� �$$�AGq��As&� & ing^@i�>�$�oc�Kd�#2 .$�!n� u co]$ (a),FIY-n� -nZB�[5n}{"�]!!x=n1efK%�./ ]a. :)^Zgm(� \ina'�%] $[x]$����e� sb,te�l�Tt� �5�� $x.$w��-i, ��#� 13)$$E_� �['&.� ] k� #(z�!$",$^2$$can be-�O)in�<[18]. ��>�E_1�  < E_2 � Also�_2 = 2n�#n$y^p2��� odd }-$E� = (n-1>+�a� e�g\!��&W ,3, 5$5>ee�"�3esc�nu$ \�Q(a�<:$y1 =!%.% � 4;$ *2)}*3* 3, &l 53 = 953 54544 8, E..3E_4�6;�i q4 <5<5<9 3 = �M <75 =25.$E.�"��k$� be  !NM��NL= 6i� j� n�21$ suchi t $m ^� ]!�,�kE- 2�iV+��.�e�a|��62 ��HW �/�6Hrv5�g l4 add�p�b)�+!s9݌R%*hZ9�E_k.$$N4 { �.� 13 oi4 a neq=�<^ia)�%��V]  Latert_w�� a�#�D � ��rS B �)y��!7)�mwjtur�+�f�,�� n*� �+�-u"� by u)2( J�VW�d�define>)�!�\sup I �+�l  �e6�(�supremumEYaksK! n� _, t.$ Acco�Ig�wYph ^oTE���68"�,M�,� "�+.g'"���&Kl:L�+)yto)^�pAeE��.$ 6�� *�&�Gq7:�9�%a�.$ ByE�aAw�)�lA��2L.�e�U�~5!s�B � ;&��e�e�6�J2�,of5' �.oJ�U%@�on�&Wd�[eE�ma�^ (��s @un.�*� ept�,�ius��>��! E=p�Gter we Mai�&�6j m��-v {\it>�6�(em}!q� >2N"MB"V9:jV.� $:l# � $k$t&#���^_ ���ܕD&+%^\ ^�.9Z�� R�)��E&AL:) pm�*�)�.�$aRKv5)fo�/i"48f-..�7s2� q.>,!>*�"M-�e�+.b"�9bB�if[&)>.k ,$$then��:�)�"� �9)�ee-G&:B�|J��*nc���e�giv�nQ$ 2>"=-2. �ach� &T6 �"��  _npn�E#v!checkE $I:rA)= g(�mix"+� &FaBm�*-��� �ss>7�� _{\lambdaK !�6e |J61--}{2^n} IR�$�}�idi��/I%���i:MP,�"�f �.!$�x�+2�f(�)N�~ |�F� 3 �}I,".N= $ -�  ? -)-6a RGc&I4�+&=&!)�  - 2.� �Rr"�=A) A^2 2�\&~& -.V^23 L,GHZM�^2�m�bJ� ���!)iI4a�~}$$�聣 $A =J�*� �p2e,~9�&�:��>.  n%��>� Ya�"= lI�- =V~ /( -� 5+�1:�j�5�16]FC �A�\�b6�en&�:>m�A4u� 1/(1+2^{ )�L+:�s&wi f�2l�@ b�=ofb(�) )�=%�&�S�_[1us�2�=�(:)��ŭ��:� is>� u_}-��~1�1-1�a��9sa�.� #2}n$( 1a�i�X32^��L}I�"�� is,�6�) > n$� Y&d $ � >1�y.W�T �.��i =_�+ �5}}{4P�'� �3 ' 17}}_;$ i2Y� 27}{16} < !0 _ _5)!5+m"129}}{802:32p2q6D31D321�92} <�}{3 5B_7;63;764482;4} r 3A��x �3eF� �}Eb!"i _n 2} ,~~8�rq n 12;6� �UKA:[9 :,~~n> 1>�J�A&��&��6� �1�c$1/�3/2�8#��c-���v "p*$*��*a� lDK x/A{S "�\Mk~-Klyshko2J 6,14:s> � ��� �*d?�:�aN6h&g*�j.n",� �s~tWW. <2@E,62����;�A0G*n7 �per*G,P'Qa�'� b xper^#tal"�= �C . SQ�1�_0�>!�.�2�_0}) =�2-��3a�+ A. -1}}��$$�*B@\longarrow 0p $n: �^%�byz 18 B�E��<�V�D�%"�}!��j9>t  �}$i� > 1/( �S�!� : :�^��fty >6AKvJ�B�"  � arbi/ie0m� A�>5e��HY-f*c).&5vya�8A�� .i=8,��#.ZkA�s@t);�gapapwX�jm�:YLg/z a:aju�O$\leFn "ME1As d b� ��0C��uJ?:ac*�(toQPy9w�"s . ;�b&@'>�&�'�#��*�]53���ult�)!6 (MK�0��0kes�D�!p*h/�,$y (BI$_2$)��nd����B� (WY).%Psummariz� TPI.7 t } \cmon���� tab:1}E��l�>cA!��um� G-�&�@c%Jes2 ibly�)� MK, �U WY,!G"�>�(.;Wc<�A WY�)=�e&� !6e�"< n&:6I�%/2442��hA��� �խas"�, $\8 2}-����of MK."�(I dtab {cccc} &Eo1$ 2 3$�h�2 MK & 1"&�%h$& 8 D16\\ WY& 3 & 5 & 9Fendx�8:� !le}84nVy�� qW� &� to see�'g3I^ to gMh&9of}FE�"�%�e� ($�� B|00"t*� �B|11"k*&� 26B> 0I�OBEA�+.$ 7�fa_{j1} �)�)�&sg.�3$z,$h� $\vec{a}�(&1},.2  3} )�� \�Cbb{R}^3;$�I'D vector.�2N�"�1)�2H1+A_2+A_3)\\= 3+ 2({13}23� a_323} a_$)\\~~~~- ()CI>-)F�N+GP9 ��Q ���*~}#_0� 3 + 3[2-3V{]:���=�Gat�!neverFL ECM >� "b 2*:22n }b� a y��H�M29F ������9*�Mh�9MK. 30 yM� ��( 1- 1/ �2} 5 s5In�5� u -��Rz H� ,(&&�"Ic%�! p )/ part���3�� ��t^�R��I2�7 �y"� ;��A*6 9 %L W� ��n��*� R�Qc��V?-К?- &�%5�/M Our%E9t�&"AK.gQ�" "�2 �2~Q�2�SE�r�A>b�5 8"xP� Go"�T�@A&[! i����j?s<:�*XM�P&�-�.>!l7A�*� F.�*+ d3 E�� �  )� 2� @qG_"k "k.���`e�E .�j9"k`4k%ʾk��k�)`�h ].[KofBz �@����zC�S,a��6q�recogn�t�3!g&)!"�v2�S�4brf�0%Q�2�o2�,x .XbzH|=(` �@E+u� �N19]��no�5`!sF�2fF�X2&�!2%�VB&�M( [11,1%Ta05Rm/��G��G�H��;H>I�I�W!g)r z�W)::$B�@ Z:U�7:K��z<�5�c4at,�4���>)&�?2�&lJ��H=z-!� its �Sram��== p�W�P"�~rol�50.��V �4�K�J���N�$ ~*A�973%b�!0\ (Gr]�4No. 2001CB3093!&#i�y %Jo.b҂o�)'n:�!|!��cke,e en�`P�Q�.�|>cBG`A >mb{*9�b�|1}N.G�U@, G.Ribordy, W.Ti�f<( H.Zb�Ln, K|Mod�i�} 74}, 145(Q|); M.N2#i i�uit �dC*�6!�.i (CJ i F i Engl{+1o)� �2})mBell,"NZ(LQIs2 Cit�w .Y.)�,1}, 195(1964.I3}A.EW B.P2WN.W d{5v.%4 47}, 777(1935.P49xPhys.L�d A6 15!R201(1991.75}J.F.%W, �j*WR~-W, R.A.2W, [!� _��4 880�9.\$6}D.Collin�lQ8S.Popescu, D.Ro�9�,nd V.Scarani �hg88A 7040]SeE�ck!�0 G.SvetlichnyVC$9}, 060401I[.�; re�Rc�X���Z��-p�xi�-ph] 7}J.zWVm�230406 m$; K.Nagata!hKoashswN.ImotoVG9}, 2.� ul<8}S.-X.Yu, Z.-B.�`�-W.PanilY.-D.O>�%V90!81�S_9}E.P.�.b%�6133!�EP52); .)b&,4ikertagung Wieݚ �eA{B12!!622A� 0); 2~:+!666+2e$12}M.Ozawa>�iB6a�195: 91);%>�}gAP 05�lMPV'�05790'S.MatsuEc Prog.�s=�E3��093); K.Kakazu%$S.Pascazio]A�Y5� 3469�Y2�13A� L.LuV�9:1Ay3�3); S. 0wQM��t6�321iY2V,14}R.F.WerneY. WolfNI�I1%+1%�(\.{Z}ukowskI,\v{C}.Brukne�y1�%�E$%�21qD2.15}D.M.*Ca��Orn�A."+C,�sa@�G'sd!�<&��%��nd�l\*Ha�� he U�o e,} 6nU8M.Kafatos (Kluw� Dordrecht�m9ev69; N.D.�-� TvdI�4A��6, %�0)22 Am."�qi�5�73�x2H416}B.S.Cirel'sS%PM��%c s }, 93(1986>$7}W.D\"{u})�J.ILacN��042314Aj6I 8}Co | fun j $f =.�6�. x^2_�$+0�59 $C_k�{ (x_1G x_n):�D�5xO: k,/M:=�/6  $fH�jl�avex� &*� `*�Tt� ext/�"��co:���il]t losE8g]�nQx $x,:geq x(: �(oX��e�52= hIA5�W"3� *132 9}J.WheelA�i�o�,o[=x�E�opM�A�gof *� ,}"qI�PZ.H.Zurek (Addison-We��, ReaS,� 1990A�p.3-28;�vummhamm�Int.J.&I��� 17E�,4); B.R.Frieža� �g V�: A U*�a�}R� bs\h� ,"�  20���:?��&�i�m�m* ERfj �k.�m �:Uk011pt]{amsart}2ja�kB�k2[ьn1]{inpr�c6T1]{fo�Zc�k� 6A�( % M��r�lyt� �and{\be}gE�9[}6#eeq}{%-"f:"betBF*>%eeq&!uHB$beaIԧJH% HV#beak-_ %Bmeeq'.JB%goesto}{:Y :h}[1]{wcal{#1>� hil} H>k2K>hM=MBTTBZZBSSBEEBDDBUUBGGBAABBBBNNBQQBPPBFFBKF�IIB<JJ>tilA�h T_1^+(AL):�p& }w I(\pi>H0Afin}{\hN_\hA:ANN>1Q frakJRil!�hil_\ :?C � bb{C>�ZbbFX1�bbF�RTR>Tq bbF  Hr}{m H}_1:�RI1�92F 6!3:!do�'�:T!�text{Tr >�sp��sp>Rep�\ Re}(#1>�Im.$ImN$kaikilEIJ B�cor�keskus>�int!�int_{\B�%+ IB� "!N#B$(LyR}{L^1(\R>�Lk2Jbra*�/:�kŤ�I:(vp}{\varphi>! varepsilo�pne�<vpn 9V�ler%q {\rmT }}\,:fraa�&RanB� qker.��!>� SD}{S_\hD:_ccIB over�!J�8fk}[2]{\widehat" _{#2>blaskuMA_#1^-:ino�+� +�.0 binc h Big(�&�",} $#1$\\ $#2�3> P{� \�L�:�0aaltoIII}[5]{Lgc�!c{cl} �, & jos �34C# $#5muuten>#: intL�L(#1,#2>� intd Db sq "%�tilde{Da�JNLEsx}S�$tL{x^k}{E^B� LEsy$y$6� LEn>I{|neK>�LEn>P+:X���  \{%\}_yA1  em{lul}{L6emma}{L2 <}{�em6=j�>}{ProSPz Md"�y\&p[Mo�o�f]{>9Cartes.umarginp�sO.S}"euJ. Kiuka,ddress{Jukka , D�;t �f� ,�4of Turku, FIN-�4  FinX� �uj[.kr@utu.f��4author{P. Laht �Pe���:�pZ.lpB�K. Ylinxv� Kari >���h�kari.yt��&a"�uTQ�* Q6 e3��M��#rm�Ym:J!��8 .�n�Bmi2�M� .� }� 2 $x$-I��($polynomial�q�0th�he $yjE� �,Hm?. %��t�N`%,d"�  %�=so-.a doma�6�]$ $Q^2+P^2$F�;t�Asbrl %��gyA�% 12 ( K� selfadj�y���al �BMu.ht "��.�} FZAMYԛ \cite{e~},�#Ulexhd �0�.}$%�5 %e $E$�nI�a( que,!�v+un�1�Wa a�e����{f}{E�!B`"4�j6f�/�1!#E$. %a?R4�h�n�x.U{@���"XCj%+khe �v��$ o73�$\ [|=\vp�$�jV> %>�W1�� X\mapsto i E(X)b�#�( $�[�aa�m0y 2�U %v�) a�$\vp$ b0�g"Ԑ6�%��$.�'��X�t1���'d6�:��k*�vpt|1I��D`"�ir��l,2!3y�oce�)�"W-s &�p�u�~"�aA�a�>n �%i |�a�revt/lal��""�V,a2)�6���* $\R^{2nJQ��� systo� P*4.�e��^.often�y$by5�to�a�!�a�!�1� E0 f(q,p)\Delta  dqdpI��> E��?Q�U(E�l�$is  ܅ed ���'he weak �r Bo�O���� (��<�$ Dubii� L��ma (Schroeck}).:�de �y �v+�9:Gw�$%q�W(-q,p)T ^*5&�$ $ %!� Weyl51 s ac%�x*�'2�� $T%oa��A, iѾ�Je^race %onFeI)map $B�a�_B -�,�2M�(Borel subse�U�7xnu�E� %Ui �2y��2�-s.a3'[ t�<:M %��5u. 2�2e"� da1!��U2�)! := (^)^{-1}-�.�/WUe��E1� � N� !� %y����6� %(�%sc���i=�� e� [pp.)!-134]{6�"517-518]y��Ϳ %aE��harmon{uscP����57.)�"vɖN����,YGA� as7:8*|%�\h B(�)\ni u�E(B):=2�4RL�� .fyR, s]L�{ny^�}dg�r:T it.�~F� �u.� �:  coinc"�Y!o(��)6�6> fmgzis wa,W! \.��<:J6ZBU.� . ItGX�1�a<�=6J��a�l.ntM � L<is � �Nr��}ApAhe abov�-2`�OEV (� n�+t times)spar�pe| i;H LkR$>� [SecK$V.1]{OQP},q.�]� }W40-141}W��Ka8)�2<^�%R.�*;a!�yE  %tA�z���PZ� 6@y=A-��.7R %�p�r�uib�VS�1���Ss"�7�J� .?1!d-�",vex� binŽ�it�R�J� ��A3j0 a fi�Hc{� ort.�aAx< s#2:.*� QE"�^ss*E���+ �9u�.A�� !�e 1� s. %b�.I sharƟ!?e�w^ �r2� prev�֯I�II}. �Oy9?Z�Z�}���"?F�} �<L`�e��basic�of.�}X n2%p}� a��o~z�x-_N ~��)�qP5�1�. LetaGil a6>,I� innel��~.bra�" |�"�$)$աA�\I�aN $.$. �Omega ��ampt�=t,� y~ $9$-alg\y�%�� D � E:\h A\to�3*� >  (N�0d��7�9$-sUe)#��! �� 0, or, equivalLy��top��y)�M�4�,h �!���4A*+)�2wE&*8C�G*Q-�)!k6s� oz by�W{G,  1�f:)W\to\C)�!!�- P�t1�0�|�#�6�M=�����*v���e�blVh:A $E2�P)Qps5L��V��@ �EY paceAeI�)7r@*un2G�\ T"�E �6psguaW%�!= C�'i�� d2��� qt fv-M�ءN.5g2�5}))2�d� }dR \emph{(q4) �{l}%f$ ��.� �[intsq�J��e�1� |f|�x���"CEvp,M�W"e'p5 f��A,�i:}U�*l:!�gin"U�[ize�[[(a)])=�E)RS}.#J$[(b)] If $a�� r�2��5�X%�A�a�.cM)1q���$�{IeQ&��5 �  (b heQ��1̮b6�n)*!�� �UQ% symm$�QU,sh ve�e)&�m4�5(!� /:5��� gal _�Z(�dAA�proofA�*= ��LsubLn:}'�%' d©6e  %���G|��d�D� %�i� )\|i�>$1 � Bana�S��i� %%�or�:(\ y ��)�*� �\mu_n�Q�C �%y�<$nA�N$���se���B um_{ $}K�_n$ %d+r'�absolu&�; N�.:mu$-mu'Bap �s %$\Rs)T2|�|$,�*VDH�)�~� ҤA:�ӎ)�uy%\ �&a. w =1}^xIE� |f|d ��LX�cn ��!�'$��b��^�B|fZ+ Ki���N]d)X�?�1N_n� %�)ɜ�qtB�f  _%* %��!�H q�%Paj. }�. ��i��  A.5.a�.�Fw;-P �� . %C�n�3� $\nuQ� [0,)�).�F�.areAm nu$-&K. (�V�6ance, nucn\mu|+E�l-M.E�k]'(2^{-k} (1+\> _k\|�I�k|,!I%Zd%�m{yd(ye�Ѕ;�e�g)�$g���8Radon-Nikod\'ym�M�pN�.�_nJ�!>XS ��M`%L'E艳��not%M�n����P�beAUmu'(B)b� _B |g_n|d)h�_B�R(%nn \2M) '5R�\B�U "n�����\| = 0�XI�9me�!qM�[n�$U/? $LK( nu)$� �  $g ksm Yq»A��.�{k_m}b-\.itoN�I�@ Dye�� �jona�b*Z?K[D-'l|f(x)=NpE�|\ 3(|g'(x)I� M�v��$x!�O_EcAss�no�aO\^,az� �|gi�e�.}b"c�$e[�g'���1f %$f�T ƀ%>M�͠�WmE�Td. Bec&��(� %I&� we��nv`29h��=! fg�xF�9��6�g6�nm!�;�I���)� 6_n8" 5 #B1$\Box$ %\ m�� �� �o��sҖ nuV� i�> �� j� >� *� Up�& ,B�YZ�R� B� u F^`�} BU�ba؁��3sq)��t�SMd�� �V6� � \n27�� � �Q��Z� (�"� �)"�R� n(B)�8\nu(B)*��l \hA$I8 $��m�a~'Now-ymkih.�=  d��.�ke n"��e�|f0nu-K�H���M�͠�&.�.�<�S� i�s����� k+1�ːCltrE)��QDAV� � I�*� �gJ irn ��: F#al: 2�ea5�(�1  %6Hn� =1fr a-��^6�E>&j�T i>!�!VM��%\U�9��L �L )�& � $*[U�&:�( �E�~ N~ B} �.��Dg-d���| �CJX �\+>W V ��� �>}��T J6 � "R {6� E�� �5R )m%qY ||E�e_-a^0 ��n". V� G�s�m�\�RF� ɴ!�2� F .k &�� ?� ��1mu.� �I+ �{:" m�" F" IN  �I�A�1cp"�.1Mp.��E^" "�b3"D����������+!��5� ^��+ i�kAR$M_n>`� � n M`i�� �&H�*E^\1I :,�&��{E$,�X*9��|_{!�"�}�yp�� +^n>- ^n}}6�!mis�M�Vm�� @)�)&a!, w'o� sisRk \bigcap�  \�*M^�*!�%���� :�g,���lf�.jVU }�ps��". \|Er�!}\7 4!xp_{1�} >)"b 4\�V \|\|6|M��1�Qe:jV{1�R+ �#��9���v 9 !f%?� I squi�/Kal $(�psi"�*��:�N isq\�_*�(c" q)y�$�&�q�}2/(�nN�@u���2�&�N�m�2|q�k ��*�!�< 2;�:."O�R� By!&l\tvu ��t}t �$� 5X�s��_{%�vpte!�1�/ ^2� s��y�ve}��1mBu�� ��ɰM�J ��!#2^n=� .*� X �F^n2�QJYI-$ ��9+ E^n$zf�u}.�,�j[ �2%.� F�!V�",es�[\m]j<�YqqS�s��� >k )m. "�4}��@A d|F.� ^n�ƕ�B�/5�"�\�.��g�#� �� q!۱Wqu����!@^n|�,�&� itNs��E�Rar�b�(��� Z� I$ ��:!^n�a)�� � ��%P*71&+s}��wap20'�!�/"R'�#n?!�*K"��Gket�"F b  $\xi"w/br,|< vp$.��5;\mid n2H0\}G#(R(�"eQ�!�6he�4 �&s bA_+��� eq 0��on+1}|n+1�!�n|0 $A_-n31+1|�the rai#( l�l~ 1�u6K)�) � They� clos�v�'�(t��v hD(A_+)= -��\{�$G�= {k}k|�\vp|k�|^2M�\rZ\"� �t�Xz "�!+=A_-^*� F� ��?� +A_-{� i- �e޽���d2s8$ �+ Ad*%"ч$Q-�Pm0�_a�f&�& Dahe�+�.a�hs =%�B�9F4�"�2$�,�9�A] �A_-,�+�F!erf�.�*az!�a A_+&=&%%$(Q-iP),\no�7\\ A_- +iP)� AQP� a &�$([p. 283]{Bi��}��:,73]{Putnam}) � f� $N�1�Uy4n|]� |=A_!��N�D(N��^2��˨]ARI�Q^&Y �op} N +"�:I�ifra6�:�U (�9 lastA9~f�*�nc*&w!w��A_fasX $�=e�A� -a��|#]<]g�#�yM)�Mtrj p��M�y�1ps $p�eV(p�3e^{ipQ}CqU(qqPwj�/)Ei��/}�2U=Tqp}*�q,�p \R� e D�W(q,pa�r0�}�4*4 \-5� iqp}�k g cb�)H 6�4W�6��D,Yiv��IaX$�;\R,=�'T��>f6. %F� �-`6!�� eC� t I=�HTFIIF#5 dqdpA�A4 E^T�!3II)�+ H)] 1,A�t E^T(B)2mB}�&�5 l !z �6f� @�V%.Wy9h B (3H�I+s�f #,&�,NF7II�'��ls��]�� F �)�c+2ru�%�.� h c T����Wi�"M2�{Davies}& Stulpe�|Q�Y� �8cov$;nF���(Bvb�� �� A4(B+(q_0,p_0))=A� I^*i�  MH%jwin!�$J\.> � "r0"* CDeV�?{"U}:�n"9 F2-� $�. �Q�il����|r["�)6.� ���:�/-'hif��KYω���\th�N}A�&g&\t�5 XW�-% = N((X+ H))���E� �[0,�:-=, BuIu��RIB�6C!sum $~�d ��modulo $_$..m.Pellonp�Ri6� %�|Az%�} (B)�w���Y*�2m��*$�YisoJ�+� � applr�t:n6>�s��E<Y�a�f�� um_n� -��Rl���*�!Gi�} %��Blmi&�E.ts}�T�'�͝##ia )No$�WvC�i7 _n tC��%��$��\#s$ :kA��,va� seR�a��/m!��W-zsAy� ��!c.F,�L�9!�x1�i\iV�ee9��y% vp |e�B�C_ �Q[_+Y*"�  |W� I� |�� qdp "��2e�-�m��6���t"i� r��(�f�HA(us, in the �weak sense, %\bet %E^T(B) = \sum_n t_n E^{|n\ket}(B). %\eeqt % %Considering integration with respect to the operator measure $E^T$ with $T$ of the form (\ref{mixed}), we have the %followinga ult:�8gin{lemma} %LetRbe an op xba| and $f:\RII\to \C$ a Borel func�. %Thenl0\label{LsubLnu<\intL{f}{E^T}|_{sqd}\subset.W# 31`}!��eeq %where the series is understood to converge in (9��,Gdomain!which %c!�sts�those vectors $\vp\in \bigcap_{\{ n\geq 0 | t_n \neq 0\}}� ��$ for g{ X � %$][N\vp$ �s�ly.Awnd5�0{\bf Proof.} %�4\lambda$ denot). (A�any $a�, $ ��L a_n}Iw�(1+a_n)$�eUsing!x( inequality>} d|!|q� }^n| R|\| i�J�n}�TE,Hfrom \cite{Lahti} (�&�vvalid�eis casť�3$ni .!yM�$)Ÿge��Z�!hE! |A��]| Q 5O�a�� h4it follows, ag��byz�$that $|f| �>$�I-i��ble. Il $|? {n=0}^{m}fE��%��kE%�zm$բinated.z %m{ gives2fi{z��}y}f>t$)duoa�UzE$� On5�q�ee ,e�X -�z +usA�bra" |3��T�࡯ � S��_ ,�ց�ket$.a�$Box$ \se�{Moment"���De Cartesian marginphA�,space observ!�s associ%�w� V4number states}�sec3} �bx�d $y2y8 sщmapsto q .�, p$, re. ive��In2�I m>�$)W((x\pm iy)^k 55k %^2+y^2F%wi ,determined. 6}II se�ult�re usedi obta� the "k rela6 s \bea �x2� &��& Q,\no)h\\ -y^-PJ-x^2^/@(n+\frac 12)I+Q^2J?y�?P^2. M)� s0} \eeqa!�t� M���5U directl�a:�-�x)�T)�y, * A�� is taken!�be{ form�r w_n 2: $. Th9��=D(Q^k) �&��� =D(P&i� l $k��N��6�z 1!{fix � i.]f=Ɏ ������7 N�$,��1,:.q^{2k}|��f|��h_ii�.$\vpx��|^2a� 1� le over $Ah��at a�_{} S d&Z&C�o( &=& \piker� 2Pint �N�dpXq\\ H�H �A��h_n�*͉)(p�a�Ch_n��!(|��Nx �V<q<t��g)�uqsr dq�0 tdq,ŝat T e � .���ar�Dj��B� been 8 �-exist^ W last�l impl��t-= -rA�7.�>� �� Thus� Yt)_U musta�Y� . (I� ,t &U ��q U����usIC �� e)"6 v�8stants $A, B, M� ucfat $A ��zB )8$|t|\geq M$.) T� mean�I'f��longs�k�61�,$k$-th power"� ��.+ nd h%��=Uf�Z�b . Co�sely, i��6#I���s =`|t^{l}|9�k$qQ-|q^l|y2$Ō9ѕ�)� l"2�]� $(t,q)V9[[�iR�I�prece���� now�)� !'!$a�R�A�eny٢b�'A�proved. � ��>b�is�e a� 4alogous manner� u���in��pe\���v��%>� ,�1F�s�  �/p\\ I��BB. h_s��7  �Kh_s(x-�' |Ff(x?x��2�� �|Z?�px.��l%> <yx dpdx#at����Dy�a Zr| FilyAZ ival� cj� $F$. � Now� Q &� �rLEn: y3 � ��LEsxsy .x = p_k"� (Q"� LEny>P���$.7:\R�R�A�$polynomial� .- (t)=' n|(t-Q)^kT=F{lk-�|$.a�/ nO$tdB$.�f&G �g psi$%!�mi����q^k*psi6 �e$B� 't�JI* we.2t Faa�x� ket �,�X q^{k�W� g� � 6J k�_jW�m�cc^� ��>b .Y CJe ge }J~ �] t-q)}jg(t)}�� d�b2����(%>�F� �RR I-Gin@6!�C� A�� B,.CI@n|J �JZu|2�Q)M�<at�fifth�9� &~F.s! (q,t]�{k �-2��hY� (be��oa8*��%n|Bi2T�6�12 (1+�)([ +|!P |^2)%q � \�:��vof��� ������})���ty1$F��� d�#$ was� n arbitra�D�x#�$t�):%q� }$, "2�!�1t e��1 ��>.�=G2��& be1$selfadjoin� h*�&>U$�not��a!Pp� exteO$D ��6KP�y%W'? � same; ,I� %;� .��s"sf,g� $as %before���A�'� u8\LEsym.BCpA�� \.<N� .�d�=� A� */} %�d6, �e0(�h�Af� g� } %f"� ���n� �Q Fg(xb()� (Ux)�� k� , �5!(�x)}Q*� 9=!�| �� K%$BL�k)�U�:s(P�3&2 %A�xugiMa6u�uO 2�e,�1$be written�U6/�D P)^k�m' ��'�  }�. %'"c�>:�U � \ >O Remark."O � |Q^m �=0 odd �"�dF'> 'ev�m$, on�T sL! k-li�presen���%�!w!>&� 6�R#,coefficients�7&7I$x^ o�s�� ve. �parti�r�"R�s'{ -%��1� %P� $k>1/ $R�!fl�%differUj,Weyl quantiz (�%$[p. 229]{D�}), a�!ll�U�"�" *�"$&n)�no .z"� e)#/ %�P�� \ �&T (�Z6�l l��4aL+%.>�-^<:Serm>�:6#�".�%l�seconv�9 *o:�^�" =& Q��" =& PF&xBh"=&F�"F8F�"B8J�"r a �+�!�ial�'� n=A�thB�#already��byA�m=omputE�s��M�A�8-A�Ali} (9outcresh ques� oi�� %��U5 ). AD$ed�ofm\. 140]{Landsman}, howeveH eems1$lack a con1 A>$. %In viewMq��two�I�O(65 Sbe mi �0in eq. (2.90)�->��#b�#�>$TfN�# } %s�.��� 9V��)AT$�� �#� I)�nex�%_we�!/slex���,��w�[IeAi; lsax �! �!a�m�ed�!a�struc�/�*�$60]{Merzba�!}. @"�! Շuۥ& : %B2 �� D#:��� , qu8$��"�p�)*y1aj��k0=.9% )�>asu "��d+ of o�� nd 0Z% E-�ng��ineem $A_+�� -X&: Z�M frac"82^k} \|(A_++A_-"� � $. � YA_+=N+�!��e!5t BA�-{mG�$a_m|n+k-2m���$6 = A_+^{-}q^+_m(N��$0m �k nd NK(-^{2m-k}q^-FK?' S!�`q_m^\pm�asom�U < $2 \text{deg} ( 2) �)(�)��a��"$(n+1)(n+2)*() ) �n)�}b� �Nn(n-1J-(� )+1) �N^��1 each �� 2�AnM'I�at  $$%4f+*� A�a}highes�e&� l#a_0�R��e  *� }|B��E�kA�!Piz�exaU $!�"m 6�{j��]a mixtur"Kn.z,� -!.$!./ .�& �?sV wv� nd ,i�s_{kl}!#�{k}{l-!�.\i+1[*����� \ (E� (.v%M�l!6-.$itemize} \ [(a)]&�@ T}_0 \{0\�f%��ifI�'n56} %�n n^k�< ��N���$ � #�98 :�& "cT}=�t*�T!8�� �"L̑�< � Q!4J,�8.�(Q) �t %sumA�*)7��h���8.��>' { )qwe�t�(2�-�b)]AV�Fm� 4(a) holds true� n ''$x$''%� ''$Q �%placew* ''$ynd P$''.�/�4m v��MQQ.v2M����YU4 %�%5atE,bX Ppol[� �*�8A M�*2!�n(P�3\�8�A�I��ւ�%F6%A.�,Pro�1on� s&�9, Lemmb!�x =2�6 7*-o _a�:u�=}! : ^5�.)K %"Sq � !=(Q�R (�wA�)��?Q�e J |�;o inv0);Ainm� \sup�D(-��:�"�vpB0��4 �$��I���)�v.V9&4&Ge6 :8>�9P�&. �7ztA.�$N�( � �r'!�2�$�a?���$xev=/V2?"�v�8� latt�1��is� �to��M�vpI-� !�� � �4>��+� eq 2r�"{r`e8��ro�&�%A�m|(")d/�t&��5{�Z����2�� �2�&o t^lFU"G�� | QR-l��)at � 'Q^m" #J�)N$,I'!9� '�T�U��e above+" $5mb�N&/are��F��0i8��l} �� !{*�9|dql:+;)<*<�a :An=�:��=e;q}�>.պ>h&$(e :J� ~K�� ��)�7&s9]# a nonzero�0� � b&='��' �}���E�%4>�C �K�s.��1 )&�{͕T��Ÿ�y 5���:� Q5?aTBH�=R� >�J R*e"�FV =���N� =� F�/A�F�.> :d T Ii�1�)U�se�n (' �1&)�get a}x%:9pv.':M/:n:/�� k} W ;c 0E?t�2e36�m����5qi� h.� "�6 $ (�$2F8)5�, V%� k}=1>�`!��b�� *� IB�is "�,6 is+i��i�-�9� doesRq�, %�+��no:0�! +�1�toN3�8ich���2V=iR %(� �2"1�m�). 0(&1� as�-��B(*(b�%��� E" |_�?�n %� a� 2�P"J~F ae n |P��ݣm, n  -/A�$�y��^ :�p�F�#�|(F��*�p  #ޣBWF�P�"�e�ai��a�� �2.&�f'��"~ ��brs�;��FT "�.m=�u B= (^F�M� ), bdsm��2lo.��59pk�Q"�tiL��ed2A�s"� u� . An mple!�ai_! � \N���nY3B=�~8S n^{k+1)#@re $S� n^{-(k+1)�'We do�sC,�p�!-��C6��v�B�A�*�$�@}H{2"�  = &P>�6�(6}{\pi^2n^2k0n >�  N�Gat�.!�10a�(%H�0s_{11�Q ���2�1��$1l}Q^l=Q$ )�)��. 1��As� on{O�!O$IDl* s $Q�iP�Q^2s$}`NCABenerg*�=L�% D)�&�AO�J&)ofBH} �� � �$L2j��aV�-sEcer�@yp.V. T�=at end(I $h, h_12�� r89�&�by $hN-}� a_l { a_k$ !�� h_i(D=20{k_i} a_{i,l}:{i,@$i=1,��:+]&=�a L{h\circ 6�A-�2"y}{&P }$.yLhV.4=9!��-I��j%�� �%.� a�G5&%4M, (4$��� $A33km(|!� B|t^k|�$&4��.xD6&�11$ (i.e.:`8 h(q)�-*~!*�+.eFa�� ?�9��uch2 ��� � \�&/d�_>k!� x^lJ3�, }$. p %��#_}=G .U l)=W,l6eQ" ,>M� t %L�J(�,�Ato%@,Yh!):6a:x�6x��* �1*2�&9 %c�&intpx�R<J�p_l5%(Q�@, N90�5a sv=� 0�t�3BZ�%��_1m�+ih_2 b�_ii�2be6��s�`%RNx^k+i>� e�IX!��`+y}2S4��ined %as� s. %F!�]u!K�=s %� �D&�ps6Q�=�RM���$ if both $S-9�2>�� I� (?.�)b�e���I f#+�*Q3bS"�"�,a|d{V�2�mj{k_�2 ?>{k_2}(:}iu}R�2]" Vb� 1,l}:� + i:H2,2�H2-Pu�F R��9�2��# k_i$���$���>0�IAssumg +�ven��6/,���n!�k!cho�R"5� �_i, B�Ap��A�f* �!i7;���B�� �8 ׍ `;&�SHRi98�h���>LixI �y� � uch@$�NAs�=�eL�� %!zb"�#e,:�� ula&:�)��intpi})��remov he $�&QB \se ��J�"�.��F�9�}.���5�%b�6�Qa�*��Ia�j��OxY2k r�#�Ive,�� arguR���n��|!6=+) N�.�W~��Y�&. %Տ66Du�g.r � (x)d&� *k � x^kV�gy^ ��@� J&&JHm!b6�N eL{Bw.�������%�\ �2e:1|6M�2  Q)+i2P)q&Q"-B� NE-rEa2N� J. +p:�\!atN� A�e[+� B���P>� �w1.�P2-�]�J�Q�se�� ,A�. P \q�E(x�' i y)2[�s !+� ?E'��QB?e)" Q^2 `) +2�P"F+1&��5�-iD"�Ň4+"�U$ a"�0 t method)�Y"�*:��m�Y�)��^�N�1) �da�qa&kM�Wie�PAQP})h�H/' op})`��%�EB�F"�KdUs�EX3��2� %rai�.� l�(�1w�D2B+9��t�(A�c�-s�EyTour"�,ionn=L/aXA_ ,=D(A_ ,)iE%�one*�/B :8�.���2�n its :�?$e 2a?�2))��_3a- 9Gto fin^4is %in� ���liter� G�I classicalMb!� Rell4!Dixmi$F5say>Lre� v#"T %to� $� bspac%�es!ially.�; cf.,/e�/072]{Putnam}.)Rcc6 ledg/#.}E auth_Dthank Drs. Daniel y4�Mark Hen�5�r pY:e"ut��}ail�L ncer*�LZ�$MJqRq�yB�. %=�nesB�9;.X"{+Tbibliography}{99} \bibn'{�2X S. T. Ali, J.-P. AntoiA� $Gazeau; Cog nt S[$ s, Wavele�Nnd!5 ir GA�al�5s, Spa�der-Verlag, New York, 2000.�Bir�2 M.� ,DZ. Solomjak; Spect�5��TSelf-A�; 8� Hilbert SA8D, D. Reidel Publis�UP Co., Dordrecht, 1987�(OQP} P. Bus|0M. Grabowski,&\; w\`Q�6@um Physics, 2nd C�T�1 PrinA$JBerlin�9.�$CDeV} G. CaenaW8, E. De Vito, A�igo; P� YQva�O"�6$covariant �*�O0an irreducibl�w$e�A Math.�.�QP44} (2003) 4768-4775.� M`Davies}�BaA;5!9�\Open Systems, Academic P55, Londo%76=�D8 D.! E/A. q�,A� B. Smith;�e�Ɂ�A6�bWl8%�M�e�P[ , World S_9ific,y/gapj=E��EE0 �Maczy\'nE2$K. Ylinen;� �5�a� b�[��ae���[, RepN�@1} (1998) 319-331=<�II.�i�4Pellonp��,.�qZ&l !'^�Z00 �,9) 2181-21892��6 N.i] :�l�2dusepackage{amssymb,epsfig}� put P \topskip 0cm \headhe)Wse :6(width 38pc  -524flushbottom %\c �X base�� m.5oodd�9*> 0.15in�new U �� draf�title{ �osc��=%q)�?a, (-level atom�KracP"a lex spherA=8 nanoshell } \� { Alexaj Moroz\� Ls{http://www.wave-sc.,ing.com} \\ � :$ } \make� %\add�~{s �9Dminipage}[t]{6.0in�f abst�E Hcenter} {\large\sc &EA"FrX 8y shifts, radiab decay rtb,�&OhlosT tribux � � nonV> fluoresc�  yield,��photobl�$� f B� SngK#j1i�; or outA77� lex J�,  $raJX$!�e �+�`$of alternasilica��gole!7ricdE! �studied�)e �g�!�N�vnV� �U�> sign anKB,enhanced, of�C mor�nA�� �3(magnitude, Yared tD"e�2^homogeneiR die@B5e-A-tc 2�A#nJ2 �� �k$5$!�� �!6� Y1Gs may!�decreawwlo>=- inneri%0%�rfa1Vmquaa_ atic� ulyat�Pe�l f6�� a cl<rox�ly�a>xJ{4ximately twic\5� :K he tangen�Bwappear�A applyVG!a/�\Uns�1.�modif�X%N�0bJu$4prm��availN at vI)qL� [ a broad b�er<ll�-4nresonant) op �� near-infr� �� lengths. lv�*{0.6cm�a0nd�t��cs{PACS s: ,new�� 2X 78.67.Bf, 33.70.Jg, 32 z850.-j, 87.64.Ni (Xx \hfill %����8date{October 20�4�X%\narrow� ew�R �1.9�%\�'(style{emptyL2�20pt �)�( tcou�x{}{1%0"�(Introdu�f} %Rz�n iso� ��,9asiH�H � .%.�,Al����02���s���inherx�(x�+chauerg �� coupl@eo�?� al sb. Inde��it "�.kWeaia �Z ti{ a� ce�� a smA��Cur��avity,�L!$!���e(s2�imp&�.�behavi$� ��t �, i gi*v�1e�E��akes K<*� adja3!>a ��r�F body%4{Pu,RiK,LRG}. 51 orig,t!ɔ��,|Dd)�;0�S&%{��%��=vacuum e�o e��f� .�earby9nm 6���s��nQ������ Con�t��!%�a9 kd vgndAK will�~*Q2u  pr" � g�; �abs� -B2� ijs gro�M�q�i�9ic�Cvarious IEz 6� affe�che^�modW6 SuchM��cura�l� grea�@te���%�] q �e�q.Mdynamic�� They�,found widesp�I.� in microi�V� Plu1'� t devic�!�!� osed�ŷ-gap (=j S�oa%��IL(lecule�su�%�� �)�%& of med� diagnoGs,_ �Mly1�,immuno-assay�3a��A.V-�:d ta�JW !Tly�a� Lak}� �o,��]Zaa�- � ��)��E�es�H in��.� E�6� !�ainduc-����� by Ete tip. �H/ur!�.�Q �,ywould�y loc�ed�a�� source,b,.�t orgavgroup��a arthf , et�f+ wb�a ider�L� �x#i�1�reg��of y�� ing,��M?�1!pp�>g�I  ap+p�!or�0AgaIV,WyS,DKW1��JlG p-!Zm�-m(al descrip��NT�� i�E���$BFPPCPS,Ch,Chew,AMap,KDLm1}e�6n.H� �-��b�4.�a f�{1/E �8 ��<��2��4h!Wof2�.�!�q&+ ha� s�He�v+NgE=-�!�F2Q)}1�525-,Rup}. !G eWm-� CKN}�vidA�a��Nsol.e�� blem �� &� �6�multilayE�� e. H�3�rh� !� �� $N$���s (( [ �t. one)�|K��� a $2N\� s 2N$�rrix� � awk�kEimp��A��num�calCSas&h neis%pni|ny� else�"� ��o_l�%5B�5�|ly� �4 obstac���1as !Cin^esO5d�Nmmemory  ir��st�ma!%!u!/V car�u � %. =2 {�^3$�P a]DMU"� discussh{ 3�aI\coe$I2, -r�prI�Mt�ed in a��si-� 4:xi$o"zvRG}� L�a� 4!�q�i?- �E y�@SuHII,Tom,KLa,End�� ]p�&A�;!fl �  `>derab!C"f0i=�!p�K ly �1�e%�)scalara5 involv� ��s $r} �q pB}(r}2> $ $D.$)5 }. A�q�!�� ���QW�� a�-�  le�Fve�Gdealt�@ jLRG��9z0 Although Li2h LKL}E5pr� a recurs~ #ul�# Green's�A�!G���yN� ��G]ya�<ofF�, v �W+�s�7 of L�p �, %/ �coinciXspaua�+Um�%�perA �!m�m�"� anguA�um�ber. O!�ve�>A�-��� �K>�aF64I�a ��!22I�%�es".� �Z��a��&!F�at=? J?I�GU�,M�(,\omega)$, ���ex� i!-ked���n Am�t�&M � & � 5�i�(a ��a� '2c �achie%A�!I�)|-"�d)���*le. EN�s� ��$ixC=any8)w�#v!��L-averag)�Iidi&�-�ed vl� :?toJ>)1vF� (du��&�es)�~:#.��k-a Oub �(���0( employs $2n$A� nsfe�!� �!���3��. f*o/ reli�$ algorithm�Nl\���eda��Dl" MaE�W<� �\28 �Mvelop� Ref.�cE b � �``nano-"yoshka"B ucBE� Prod��*� PRH}<,I�E �s��sE�V �ng�=�9���[sm��E�&a])n� s. C�a�ere�A~c4W idal2s*to� ig� �e}c��.zbeaiU� a plxi:(cU(c �s�U� �eu�d cca 1 nm �@ 1 $\mu$m A= ol1G,ckd(� �Ai@Z��,(Au, Ag, Pt)C*�(ZnS) �A}�� �t��nw�yP �MHLMGM,ULM,HMa,AvBV,VMB[]nd�-�� ( >$, Au${}_2$ >~by3oj me�}n ׭�`PRH,OAW,OJW,JaH,GAvB,CHM}��eV�d���etched a� ��E� -%� %=�!�%;GE?hA4w �lic&�. EB >" aR)�W =�^r-�� urn 7  ]�byAI 1^� ric � x(.v 5Tpe ��� 1�%pr���ggreg39 ��r-.� a  Van �[ Waal�+�=b&them) =�!��Q��r� � �"wre�]fa J�J ��. �#�k� J�, Z7E� $xi�2�2`s��څ�/ a lo1XreAed<" enginee�!Am�7eW.ic�2�Ne- H*aX la#*"�`~ �JWH}. MGD�ex�D��FEd�4�in�. e. A��B , wa� in�((ble aerosol_ atmo��VaK$in liquid %= adsorbedc G`\XY�}!'s � pr� .*A� drop�,inl �b t hyhob}!olvpc ()�s oil)� ��t�a� siz�"Q s `A�Q Ar��V%/�� mo} >"o),a� refe�+>as ``aK rsed�elles",>$�!f�&ge�<ry!�u$�s a ta %"��� $W^{rad�Rn��Hi) �G)/W^{tot1"� &.B� ��yban� cy (� YQ= � +W^{�'}�]�s , ��j}�I,.���d�A�U %�ree E� ei�co�ts (usuXS4oa�as s#)�%reE!�a�NB2qC�b�_e {\em�J9~�tbQ��A�/absorS2&. I&/ }�5�nt �3g�s. $U_{\�} d �A�H�&� D $*a  +@|B2W 6���  stB�]�%�s1a/� �$. De`5�a���7�0equilibrium � "E��5A7� nglY:.�A_su{�i"S:J2.EArXe�Wc #]�y�E�is�n�-�  �Ů(unambiguous�(-nd.:� AN^B{=�. umm%�R�G�po���J�y�-4s N�#mea9���n�,C׉:, p �t��&GPhk�� a�environZ;=e!�irbi�lin8 u}�na�8\) ed (�)).�u� necessasQ{iR>9(Y{ srS:or� �!ho��(u%)cR �=�� ��L\ !gail=�a��9�� .N_one's ��4a�� �q"&lch�5al�J�-�5 LIDAR,*t�F ( ��den^ Y*^ �i����0to ��,� "����DC%6�*�F�omA��.jVxe$�u&�=�est>��$la��i:L s0) O 7=? nm?   ym�d�%"F� A}) �G e*, or.�h �.f1~ ],S"c/tE��;0 b  rmedS bio"c&AJ biom�"]Ks ^�"�/v�,� ��20fM*d*]TBBN}, �in�$ �tip��� �c2 ���'�a�a_�_!�� ��"R�"Nx�;�QR�ory} \��sec:thr}Z�)�!�.�&M)z��(n&U� e4j  I�� ng  a ( ¡*�2| er��&|F2A".P*6�w�!all��no��l� �"~(!��*.�m�m�PV�Z!�a�e-� �+�aa2�A�uw)����y����< u�.P'a��Ap��Nsb��Gadvantag` a�Ca�R��2�$ i*b> ��*� SVL}�c�ut� 2e6* -(.[� eqre�@7 �Bx �m!�Ap>tti[+T $\varepsilon$) Nienhu�j$nd Alkemad��NA}1k |!| �4r�!} � _h�D�{n^3}{h} $v,q`narelUrndL�L "� _h�EvWH*�� !��-M�&� � =-Z��he �*> t AZn-"+ <� F rel%]� &�W5�eI emS8ej� "V *�� >�,6- ��GdispeZor�-. (Fo���Saa �&,��;uc�,"� �J�kU j� Sec. VIIIS�M�Tip#BF�F�2�of�!p&� orE". '*�&h4� #1e\�:�f[iQ �eI�_(v�)�MB:)��n�-�.ber:H����'��>�-em�d�4�irxwA9f�.�Vus Œ Mn>ZE�:C hell N� ��ez ward��J"�%�yaz h@  !q91 en�u�A�  o1&fy� $r_j`PjCX ,3,4"U2� "\mu  $k_j==_04���_j*}/c2X,5$�5����i�e% ��i,Z#i�,� D3�ds. Occa�t�/yinN���c�)7�]� r*�l$h$��in�,`� hostqd(-_\��Zithg a.�*�"malisM(Agarwal� �*�of Wyli�Sip��WyS� %-ef�.i%,if�..�epa��t _0�^wo s+E�e�� �H$n�I#���HX%Js[5 Refs"P+&�)PS�) eJ�Ɂ � - _0}{W_h��� -�H{3.N,n}{4 p^2 k^3M�4, \mbox{Re}\,�Rft[�%p�% G} �%_d�"_d�"_0?do . p} \��] =�.b�>B���#p} 1& � E}_s.��tT�?{qm BsH$W r}_da��B , hp}�g �[ +�$,a�nn�na�ni��6 ~F$5D)6��� ing} :&&9& *� w ����~ y!<1�-9)$3 hedtor, ;r�u���. U�L�hz4 atݤx� .5zibyFg %�N� =)�n@&7(�,MgrfnrmB06`� nefM  %�.:�&�(�"*-�_"9 �7aj eft(I�I�- 6�i.)_\�w llel &=& q�}{32} .�1 -.2} :+:�;`1}{ (k_2 r_s - k_d r_d)^3jm.X���erp:�16���� ���;5�1�u $k}�M�on.��aE 7"hI��� <ngK0x*h2�7�4�R=,Pu�>� � � [tonic}"� \��'aG�M�py. More��23 E�  ��aa�o*o0�!:�<�F1� 0 ` 9-X�; a%Ujf�L!c� "�retardu ��d�{-�v.� (:w�C)< un�z�y�!W� )� sb�ZV+!�" !׉�!@0A\�P�b}����#�f�r��_0"*@�(&�` .�4 6P1(�,ZE�"�d_� imaginary ����C��2��d,;  !��� F� ���= Qզ� IJ� Ch� �O�D&��W^tv p 1=RB�2�>o Im*o ��p ��.�-o"-_0�� ,2o 1 + q dRq 2: a� �.�ѷ.n tr��mue�}�6(basic assum� is�C{ rseB �g�%!�&l �rix p�} 3:#�(are�rec�*ym�U�u �Eq=.:�*ڨ{"�a!��]q$W^t$ �ri+3d� �U�) 5�^nels: 1)+pro�af�e�$t virtual)� ee A�Fn escapr#E�/infinp> UF� em>8�� 2���zV>��mp�R5~'()2*3���K�+ ��F��������i�1!-orD>al sitI�-p "�.�}A�e2_i.9��hGo 4����4�&impurik���--4Hxe.! ent)��I$aTIY�c)6f.dEq.�Sqq�), "�A��*.�b. T7|&�.u�. f many �'2��9s�Q� a�AoD Oh, �B�,�p+%Gde�s��� on-��.m%�!K &)A ]+�F>6may ��*0� !2�9 !ou"M\TCEL,Bish,ITB,DSM,Dulk}�RpBclu�$inR��fRin  8�I�:2�l6Y0 o�F�*$C�;#7 ObBs��ehb���VKt�2a�)�8�q&�"7�of� 's ".;aIie4*]4z`�i�&}.pTee�!7�6 "�$)�[&�, be, up� Anpor�a?/W,!z� �29cQRly��1%��M3 l ��5B�-%½��L , $P�$, �'tH�U��� V0�'s� � "9 "de��) -[C./=�; x���d �9p*Nlux � ���*� teg�5* he PoyV�Pro`7a��� of%us $R$R��'to��q��%8.4u�ad!* prA=ple�NS sY;!t�K�&��R"- ={ -�}{\hbarG [�qm�G'H&b Iu��ANb�%,�t�cnd �& �7�� ?"�@�m#&��mi&�/���sol$ � �ce�'},� always �e�an�8�$��= *��bu/ � ��թ�g��[pronou.N_!�"bKіN* avy}_{wg��P" &��"E i�I&�A:ta>T)ea�.d�F���9leK ic (WGg�F)q����$is �&ll�%uz�j���jw,a� r�e m��K�9%!vy3�M��5ix�D. (�tAuG5J UC� k(��Zq3�Aw or "�=�6V Dung2|;DKW�X�(Eqs. (34-36� rein)�] qk��a ��|eJ*0''$ (� ''$)�! i��*p�� ("H�eaW+)�4M� ^K*� "��) 7.�* s�"8+,AJ�� 27 �;s��S�qP %f_a Q( r}) \, d "�pm>�2�vRGe!����G.<� Ѕ���Do~%$Q�g�b�(�� steady} (:�$ flowA��*{� ���9%� �uQ�rn �E�2�` main�th�!�S"���Q��c k�8��<(2B |%5E}|�d \mu'H�.� endib�61 ��% �is�!��1 > F� �e�sH amplZS!7aZFY�@cuct.�!k�� M�xula� �)�.��aV,�*B��`�� -�� highIpE��%� Pc�4� i�>a]i�!a�qn,�>w�/so-caQ8Brillou��F�ZMc ���6DUM1}M DRE��M^* d[]:( )]}{d }+�HC H}^*DmuJ<Ig]u�brendnFi!�no�er)��App!�x C!� ! � �;� Qs�*cm�iE}�؁a\l-v�w�� e]3a��U tire2�,��_+�U�~�d6�!����v�,>�_�4�ad1.s� "D'R^n!=pE'res�E'[J�', beP,lTe"�E!P4���$n�J�2st�3!�b�3%s  b <��5aM6�3t31 "7al��"�!�� s:)�ne.~Ux�8��vN3'r�7u&d�۽�;n�!2K.  8i2P>i9, vh"�C�6RK�E1"� d�=�s:�!�1/r_2/r_3/r_4$: $80/107/135/157$ nm (e�A�8$77/102/141/145OB��@ $396/418/654/693%CaWA46mF L9� M4lso� � � :�1i� �� us�s=150}DJ6@�Z>6�E>n|=.�YrB6�F}� �� %dE} _� chosɻ� ��� � 8C}&e6X%�Nbs -D} 9F qsel� to g"� q6�s 8A�"�Bf8v6� )��Sn\be $59E7, �Yy��%D&) )_{Au} \a�:HAl -L�Y��7�u6us���*4queL[w;��� jc��8Q! MqAw�856j0$n_{SiO_2}=1.a#- H_2033�� chX?*�;on�dsJR�?a�E-V um cutoffcu(W($l_{max}=608����ca�9!�A*mEv.�A)2aaY&�5!IAcG�ga �" least 8 s&�W dig%m7�:8!�>A'I�.�Z� �� img '��93OE\�s�+&8Nh� ng&O f�@WB� Pt:�����u�tn�ca�1at _ :�9 9IF 0 ��*.{F;Je�9E6< *n0VW=�& C��&� dTan%ABh�2�G�K�� 2FEq. (��t&))�� 137)bF�i `A|&�>�E�>�!�&NfREv�ŇA}-C��6.��0ͿD ,F}V,�� )��72�^�or���U� aG�(� fgsh9$},>shpar}�^� � ��K�JT�B� �!oa� disaQQ���,�%ZMquant�&w"Dy�"+3��t��! O�B�i&�V"�,-�9�"�=B�usYr�P�D3�*v�e)�D} �2�i� �e.� em InhV}�*�-�E;D}� :� a)6�YEea�W�_J"�Qi��_~n@$&� 0117B(!2 i\�H u 326�t $r/�&,=0.995075$ �S�D�3�]v�6bL�݇��hand,�� ship*� &�y �� ��Uq��a*�a= ii" c��� scilo1ng7 �/ er, Jt*�b�ضB d�/�1=p 0784%q9A388nd*��O>��!�9�133:L-� . (THQX*!(HRE�a2ax4" hift�b�b�: flr*C$less horiz\<ly$).�)Ovg~� iiCJ��b�� &Oen .�be�_�RRUingI�VF�-33)�,Q)�se��Nint"�O%m]� 1.005025��Ong�maximѷf 9� 0.00382�$ 1.751294$��f�?� Q@:F2i��JnLeQ\ 2.01$. <Z�!uM >� grad�A�Wn-16ɢ�%9+  �-!0��6�e�mes��"E.�(A�f�9 [�"�!�*)].�Bl�Dpredia`��)ށJ:�H EnKv�5lu� o v�JW�$K s. H� &�)A�us3 N� �)J6 ��e� �y2�9�2:-�LNs���E�=I��=�i7�H agre�V��h� )��6(F0><Zis!�ʐ6n"da� umyv"�8_s>.h$)f|>. & �%<6�+� �b�Gy��towarem�er}U���em blue}� )ug+�JP�Y��2w,R�Acn ���] > �@2�k#R�redF��^ �8cl�*�wFi�� !�t ��s�(B�����M�M��`rS� &# �ex c1LgJzmNVat�` ��� h!�!�.0 F�D!�Alrcy��7i]*� yM8m�N})o��31��{: "� -1.9416� sA}ۅa ox69.�Q�B0.903AC} ���l0x �[�}��v�//Y ���!�� A�}B} 0g! ed .���E�or n} p!���sq#Ә5�f +\s )�-�wS�6�k"!h��Zn��,d)3�&-of�s. "�(%[��e�K�tor�"E =T, F5] s�B�"=� � .z�B ���ued:ED�u<�`[0,0.17),\, (0.69,0.79)$ M��)23)7,0.85�6a &tnnd :| ,��&@CI�ypof>�s� t�O�N� "� [&%�.�: . W�;���p���)q�v�:e%qb�_X �.ccele!+dA� �)ŠE�>�.���sK�E�BTAs��� a pulV�9f(I�D}���k6exptA�m��lcappG�&� ]A[ HGaage*�.%&*7-."�+Et�i&� n�u B�E�]KL2�%�-=�ŷ�s��. � at�'� >�o�p-��,���em�h��1m&q�5"��lex*qf�N5 s�!X.! �-C&,�n\Na -<�PaL>�%at�3%�� %��7]�&� i�s r���$-7392$.�thy)$-5858F��$� $� /�-67=�I�E�}a * F� ,i�Z�t59_F� 2839z� 2480�� F�3)6� &��!�!��gst JT�C}.x6 �]�?F�Qs�KAu�A�a�c.Wj��CR �d $5$-����)���L �D}pFr�2�Ny enough�  e� uasi}�Klimov2�' X51 , ��!:��.}V�N=t�u�&!5J�ua �ek;%due�%�a�{�E>�Fs��ej!;!�:<~�). Fur2*�M��� "�&&#"$!6���y3typ�!" 5%4o� �+ % �n�gsa�dampe�"�o�%�U:.6��>�;F tice[f)_I�}.{&k 2.1� �"�1.154$.K %t�g�:��D)��} J�I�����toY'repul�ec��&��!=A2��2%KD02 =�F<�) )"�8vA�or5 in (1.12,�8)$ N.!�;�(- ^a�isw.0ocfb%E1k h4h27^ �$(1.63,�)�SF�0.413..� 1.16�Dbecom����"E�� W er. B�> �!c. loc�1ё:Oa� �� g(!�� s�tr'#�=�4vV& ����� ex!g�+0Ie>&cR� eds�"�iAQ� (&�=W54�y?0.1486�V=4=u868Evu80598AZ8592�.8 ��#FZ8741>804pD^851�:.3*n d��+� ��%%��e � �BZ�a)<.1aF=%^�2)�u11 9CZuF90�q 9V��),.q05)� 7V�7.ai�P D��B�m�� �av�s ll $H. H�, %#(joa�e�a�B&eDbJK@�x�Cr�esP�6� ���svF�C&��o���i"��թ }.�(�1:R"kB�eB�or�gui`:kEE J! U !2' �ID}�t:�F�9�$`!�d�$V O�b#� �:st|stoHx%6�B��'f3 � �9�g<an��  1.���0 too� r�#��Y�a �;o*�"�"By draw.|Z� %j �� ��s9şmight�&�!Xt2�,�>f#Dec&�;&{$)�ib�'a�&adQv:>%J�5 \*�,d���,F \$&$T:�]6�\E�* B&&�;�7���"�:dF$F�3�$#mA):Z�$5 B$,��P�-�62b(#r��~ parrmlhb"�;����%%� i�"sT�A0EF:#au��x m s )&XT in dea�=tha��M�d.�i� aW� l�W#6&M Z_Ts�<.Y�Q%�/ locc�7z*�9 a I� arisoga%�! ]U� e[�6' be�  3�m S��,5{�Ben Y�,�� ��p$ ($B*��.��%$9�M1O�'$�'$=P�EzN� 6s"j"d�s��� �X*% 9423Z?$"�".08340J� GA!iL���*k$. ^�r&�l*"6  ����#� � Ք:�")�6!�l�,E��es2tb-�N0.95172=0.49756�g�Vt�5 =�R�90179$D"(""�%!Z�#MF� �evn��fj�t1.2779G#A&%� �p�3q&� !IG2�"�Z  9896% aJ��VQ�J ����Ґ8229�` f�!B46X =1.860746�&I�itv�I366%Joz�-���&e�.��*�$��&�� �6).��DHBb�Q'�az � � a0u�*V $ *�0��0�>� ��� �) 6�*s�A�MA�04!݇(�� nano:K a hu�^;!�B�6!!!lCos,B�/to�q2���*�@u:mi`7�sf7.�"|*��#c)�2)� -c+ �2�sharp�?;9Ѝx�2Ch}(5 �p�u�Z"��K(x�"4)hI4 Iq�tu��i�3t|=<3c�&v�J�*�8)>` 72�"-Q,�7-/s�,their �8Vz2X? 1.7979���N;F�&u 2e6<!��%� �H27�E$ ($5412$) AS4&54765$)[w&> (a�7LM{}?�V��>�$�4the core regio��n of the largest ``nano-matryoshka" {\bf C} exhibit a qualitatively different behaviour which is characterized by pronounced minima $\approx 0.1696$ at $r/r_s =0.218955$ and $\approx 0.1129$ at $r/,09005$ for�Dradial and tangent,dipole orien�(ons, respec �<. Depending onL!a�z� %%Z �A!�al� �a�Z �8monotonic decreACof6_is�V downah $\�m0373$�6 188$6 ,2e 2.01�a \sub�4 on{R�j�>}20 $W^{rad}$} %�eAnormal�> {\em)d}esf( as calcula!�accor������� � arbitrari�m, 2���s_!k*� �ucturMC!�@Further away from�I7s!1(er surfacesf�)�dampene��$around onem�ny6��%ajLi�=� w.� s a� &vf�C2�,�C !e ael  of �:0204$ 2� 199055$. FOh��0loss contribu!(��A]& �" ComparedV�8to4 �dN�s F�erprm},��ar2�,�& 2},E6��s%�َ �ynrm��4ar} does not e� ny2�] J . Ita� reminded ��\ t%�~� }"� has b� c�� :�s�pn),�f s}). (q�� ui" etai����fea$in Secs. 6%�8.2A�dRef. \cite{AMap}.) In agre�7aa6�6e�s,�^� stead��j s"O zero QA�in� :� distaQ :n�g.-��easlun� tandabl-� f^�to2�rapidly�s whenE� acheY b!X@ary. However, ra�i�a-intui�lyz7!hV6{9W % ��� �!֝~ 2102�~!tce�  � (04��n23 047$�k<��, m  last� ple"��� point6& 567214$. � ���N�zb9:& �,!� �A i�>�2>* !� a serie�o" � ae%�a: first��R%��!�ral�!�.x )�N�86%�$r"�28905$�eq�  upa=�137$ 2� 0.398060$� nd eventu!2�UJ.LA7n�(This effectaU*�reMa���rtifact�6�$inaccuraci�r numer� � tabilitie��C�`min exte��8 precision yiel��ess�ly%�s�(result. Not�Z!�2��!��andv� ��.� z�o�aT: or les �"eA��R�:�Fluoresc�)�n�;Fig"naomavy}%2r�? �/W^{t}$�Pplott�� � kn�� �fJ�,�simply�quantumA\iciency� r� mt��t$ directly �P!� imaginary�t!�0Green's funcAJA�coinci/ argufsfCtr�}) ��)! w!?*XR[ .�n our)R�{a& riseIZ�,%U$_{\Omega}$�� noiB�!�}$� ^is � :ny6G mechanismsGas,�rin�$ce, multi  relaxA3n, coupl��to de�8s,-� elec� -transferca�s�dዩK%�$ quenching�� ich "j e�A� 7 PCEL,Bish,ITB,DSM,DulkCE� may ee�A9���riA5al situ���TW fore2�= + W^)�9� � E prov��r�%k�� &G %�tot!�Six 6�ot} \leqv� / (j�)$� i�A14m����verag-N� � eFL ��upp�eoret��� �27���Becaus�Uabsorb�y bodiA4�E�5_>0��&� �&N�� always|��ne� jsak�clarity)8 triv� non-�|D�nMY!�)nis equalA�un)pO�,�~�vomi�y.) AsE�c���  !c F� oub, wA�7�# F�Ff$ � ��o. � �2.M� Jr� �S all ! F�r�a�=� 2I aalready�� $0.9t] =2�AtH�� er�y$ remarkabl E&� �Jy (*� 694$)�V�%�� iE B�IZ�z:#C`Jp^��.�160$).AE>� lic<9VVU1�dro{  {)��is�well-"F���} ��Lak}.! spit%��fA��ly"�! "13 %es (see��)�<h  exVde:!-t��� c�ani&c emis� E�$� , but�'ead matas�a�la4�duž�7p���2�5;���F��Ba� then a f &n� �D=�6nmR�I��Fis > � midd_�� .�kA�R�siA}-eCE deq�%�vsurl)t2�onJ��.s�noticeRfeaFx���x2; �2x) �Z� �of� �� I)-l)�a�$, we have���"�.�a�. � !խ�F� 4IEA�lex.�plAse�e�Mul7 @ almost $5\times$�P��u���� ?i25��%,�XUPWbleng+ det���d�~ �� v If� assum��c e��e�0dye takes pla3- whil�-�I��@�9, a suf� t�U.�Mxsponta�T| s  significa Gow��eW b8: swit( !7o�Y���CHM,IME/M� mean� at a}Rt %-moleculA�n�t %|n��G irr�i  chem) rea� s pn� S�� f1L. Let us-�Qr�%�ver� !Ypor��� A�2� lifea!� ,R2B� )6EndT��Y:�M�x *� a�~cm��a�qQ free-spA�fil�� it?.UmediumA�c�idLc�!�%c �p�# s�!facto�� � Y � _{h}$. O �o�� handMw!veR��pr2�2> � )�a givenwill end�%N�!\spa% infi` . G=� O$&� , let $NC $N_0$ b �bp$d rsAnt�"aLy} ce source=d �em ��}!�1 ar-f�) t�Y��� �z $N/�4obtai�as $� !6.�) ��"%)�5�, �#%���io!�"� �*�>ɉl�A� .a�"�M� -)pMm!V� V"A%+ns2aY a[!�ult�*"�o far�� ���&AE��on. AAFo Q � g �C�%�`�E �;!*Kg�q�*�proper� �Tmonitorl7inf%"tiv. ss?VeQR2{�D�Do +pr!�� Y �Z . By��� into#u�o,at \begin{e�$ate} \iteh}Vstimu�"����&� �7��� g�:�.� material >� AR��QPN[;���Pd�zgproduc6 v��%g�qu�e�� ength ��0=)�� ies;.N.�I4�$W^t$q�Q d by�M;( $3$ �"s! &a#�! ��N��&$a� f�e� p$&u 2})g5@�A$4� �J�!$end2�� find|nh/ Ys-U� cycl�'beA�ele!]�($7r�>&�ng]!�-�q�5rA6z� . . + Discur0} \label{sec:�(� IubLSize-t� Urs nonlo �s} ��&2���ei�>��per��ed�`!e!,bulk 0E�%diMic�t.� t_ye�i�+ appl�for a �layq(# p�cleX a��+K� or>%hine�sd1  o� ickn��$S\,sim 20$ nm (_���-n.DH �wo1��AɈadd�-�coL . F���%N=?��modifi�s_!~)h�)� d  path%W� shor����g� KG}.� o� >a� e�o play 48MHa,Rupn,Leu}. �-I� R b?corpou�replac��YBJ�D $\varepsilon_B(\o`)$)�� s6/)"C'�q} NL = d$ +\frac{ u_p^2} ^2 +i <\tau^{-1}_B} - �3}\cdot �1!�m} �?�Ho-$ l_p�!�-!�smo%�� y, $�_B(&�  � @e2 4�! � + v_F S$){in� B[(� �,amp!�coeh4 $\Gamma$) co��;*V e !�a\q�Ɇ $v_F�@Fermi velocity. M�/gen(,J��B�A�,1� taufB��$A�a��1�,rm� b�geomet�"�X e Dr1��� isotrop�c� !4�0us � $A=1  J� �>��.e.��!N FourL/�orm�)Nw�s�,����M�$� on $��k��associ��h`resonan�!ci�$!�� long00inal} 2�modn2ei�� paga%/!!s, afrM� Pabove} �Uplasma# �_p$  evan�tjRbelow�R) �L:�_negY�!5�i on�d t�$A,mai�aso�@y a phenomenolog�treat�tu br50�"A�i�7 �54 is v_0�, (!�- fewv i4)P6���I.'�& roscE�p&N _ two-level�c 1)�"� s���}���� stigEs L �!jfa� workxErma�-�} Max 's=���le� l% to unphys� �"ebl�D $r\rightarrow r_s"$a� %)y%o*��*�'�(��' quasi-�ic�xim� [M*U0*})]W dicU-yshifts  ) ,$(r-r_s)^{-3 E�A� _ �b��saUut�tuE%cutoff �6 der:% U�)�e&#*polariz��./�ngulaO A�a hig!-�a cer9 rc  $l_c$2�1! f prC"paleor%I' <8�/�&fu�$co��g�+uB 0v �[)s�s�FuC}. An9im qt �m�5Nfia� at i!t�� n6i6%um ��� �� e��<�� Leu,��!�MUBf�A� 1�Z�!h��1& may :i�WY���ndF�s�.��pa�� d.� struv/s���t�Ӆ9s�yg �K .�s S�us�Q $r_s�!5, i�3J�9a*&�&!q low "�q�q�� `0.5\,  _p$)ar�0vup' $2$ J�-�p((�e��ɿ��Ng�*R��V \geq��)&s � 1)V���-� �%����O of Leung!�'�(%$AyLof� �%�� � Sec. 11.1%>�-x&~ �m �}bI:�� else5 .:ZN�6s v�1 �de��es�H�id�)�none�#A�$nondispersay�t (i%, h�- (exceptE�!:vacuum),��exist)�tr���F�'A(��&�' "(\& p-s.�m (,�L� !w2�BH, $ \rho,� lr}) =-(1/\pi) \mbox{Tr Im}\,� G} ( +_d5_d,m�0)�'%� Ta�no`=% (' G�)a tensor��ntity)E�is �D+�promp�claim�* �_p.X{ e "� ZL (LDOS)�%H)�,�,qpIA292 $8� � D1�.��v�se�&�"6]��n^2�dM� n)}{dI�}e^{(0)} ) " nafct^ "F=\sqrt{*J\muI�a����.�@" re_%\4x -́�$�6�= �,^2/ c^3\pi^2&�%4of�n�:!E��dE 429-31)- ��NA 4 Yet,% ite��D mpha�$Z�Zula �;narel�V�4%+� derivEd�0!0->"�s�U vali&�%:�.��Vr"�i%@��be��&�= simi�� B] �Brillou0pre! �� etic��gA��-<brendn�5i ���a� � . G 4$G(E)=1/(E-H)$��f0a *[ >}�]bE��:e�t0$H  Hamil�>a&nn-an isoH igen� E_n$EYO��.L (t.�M; � Ref�.cA6$DKW,DKW1})� �&�B$Ѧ:��� no Wer��*AS(Dirac delta�{$\(E-E_n)��'mer-B�h�Sto>.0DaA]�m8 $1/|1 - dH/dE|>� 73�,�0"�E}%"v**�-�B� (�� �(E)rno �b?(f�as& \equiv ZB)C.a� a� .p����g� dJ�is �b eu $N(E�Zm\ln� = -n%I�. i.U�eI�Rp� ' 0ion $(d/dE) [>��] = ->�$=n hold�0 �$neq \int^E�X$(E)\, dE$,APO/d�E�"��is�0-��5� 9Fr� ���˽�AMip})>� LU�!Bt2� locc�� %%%� �&�y1�&G�i*�ͤfl��aI) (un&�!) &� ��2[�C*m ] is "�"�% }v �+ifeIce �G >.�� T J��]�� b�� J��"!��3f�2 0���"�rol$n!�nstitut crit� t�-of �� � ��4� q*����F��a� RiK,LRG�Fs�c�F$by Schuurm�'et al 1SVL�5n�*sm 30inguish�*qIhEb �ioT ndR1cha^e impu!�+1�erŊ<7.empty-caMI�� $3*� /(2 +1)$� �4bZO0��Lorentz2��N(.X 2)/3��Ȗ���J%���Cter� fA- 84cA&�;zI.C"�l5"�$�I-, e.g.,i|25T �o ��1 !�E�M� �s!- ear �"?J � infr�"!�3eE�wavel�"#1n��clu�.mce�"E�.{ zQ�'ne�5�!a�]%1�s&� -�p� r�L,�gn� permeaC: $\mu �Wt"�s C7({3ǍF\ �( r�*IBF� r "e F�jt 4�0p&V4.U%I�* "�4� � �?Tom�?&Z�t.%r"i� ��N�j�,�#yZ�A�celVD!5 a di��� pariQ��!fR�s �d.�,�M�'��Q2�E5 �11an85$�0LRG,DSM1,SLP}�Jn6�dyeB� &� a >thres� �C� F�mc3organ� y!Qre��t��%rv%��0vLaa �E-co�iI �{Eshould LMm^ � ѻFBGij>���%�%�a~2{ njr$-�!l�L2�ra�U $t=01��=� �� M�AE ��6S�FUng4$�g%g> >. � ��� �e� pre��(6GɃ choi�.(uit�6.As0}��QAH- r 8issue. Rare-ear`'�U�I� lu$�A�2s, �vq!�candid�3O!) $DSM,SSa}. �asy@$L8aiby� �dep�/� Z� poora�trol ktheirICFs& KA�5l�. J�$}�tu;group�� c 8�=.��%or c���l5U&���"��8��el&�0IBAvBV}, � ��a+ 1Ps�@�:a\ed:by ɲtK%��% "� J����&.:�)orf�U�in (FITC[6���!*Re � $\�*0.1$ mM�<$1 mM)ADliquid (solid) solM� I@6MD pyrene-doped PMMAIei 6�s�t�D10�d�6&�X�6�c"[$FSM}./F��*�(sv  sv`*�n72IMo.�C� H,22i:�T$ a broad b���inuum TBBN,Mo}N l easBKbe�5teNout��:� ^ .���- �2�Yv*P &|E&� e9L� )d< imk8ate neighborhoo�A}2eP�BB u#��� cat6�%@� ��"Z� S2aTu5%}6�y�fEloc�$F��^;b 2!ϕ3�lbe vie�S5�n{/,} �!�}_W&5 N_D.� �AoZhi+"@�'cla=E� the �T���:�m*�� com� �D8s&A#.�=�&A um&$�5 � �](2�>=CngU&E�B� �$en wr�7�31 � = W^%�f )�2Aa rule,�\nZPR�"�5M�v�# �4 i`"W0 �5 a͕�\�66�S Y� (| &`$amb�]-\) t����&� ��� !�a:��sic�y�e6%�U��9I*��b; p&�di*w �4easur��=��OQ !�$ u�<%6MJ&�environ�'�K�� }. 6�NI� � embedZ@�>A�c�\��)M6c Its1�2�H!eawco�t')��� r.n *� slab o(SLP,UR}. Ot�(pos=.� � air� ��1906�i( �Ad .� %2<,9z8fT��SQ!�r ;�_�$ .�K� rOo�# �qU`.i.�2��qvious�\ lso "a�3co�#)�I N�.lA� bspaA��&fit!��vRDAnI��at�q�!�J@af/.��ei.�[� ����/60�� e�1�p�{oF5�Q"f5ACH 6D"�O subtletie�DWA� deala�� A�" &�&�� ��y hhZ�k:!li�l�;V� %�3 B9Ll"ms $j_l�=y -�10!)6MTAS}E/ no�s5]in��IL (kr)`^ij_$i(9CY*�A dig�'in doubl�'�P. :8�$� Hank2� $h_l^{(1)�"�n� 07ELV+�=j_l  + iy �9[ *= ��L�ras�lyEkromis�<*9V," r��m�Q�Mine��$�v+�#�#recurrw, ��?�2os)�$ Mackowski2� MAM}�G(s (63),(64)!rein]. �Owis��_��?REA��ri�@"�)�]C}%0���up���four-Ps}Az,�2e ^c�F<n��Da�m��4cE=AFab>S�)�nis �7"�1 beha�'���*v\ver�� , ye!.� 9=�jkb�@P/]co-�.:IOutlook�� I�Vo1>2ven�'f"�* arch~!@ stud�* �!j eFe'�(4��Z��n>2�� . S*@��1�=lem&�thoroug�62o��� �e m�KDL�aa< ;+:.�_ 2�#*�X �m )�� ��p��Jng. Y�"E�-se%M �?�R i��nn14�>�%[- �Ia�,�2�Q�-&� 4to Rabi split) �+om �3�I��W]!�9[*; 2S G)/"�&;-CKDL6B�%&�a�!)qg �"�Ira��*'5of�FcTA�9(ng�+F�� .&(&M�T�_�6�6�6Z6 80.�)�%�eyk2�i�U0���E!C a�K*-gard,�a>"1* 2"A�G#�o�"%�� i�4a+e�!�!�>9e�ofqixl�lŝus,a��$�T�N�-tJ enough. G�%�'?�|q3"�"Ba2�Dd57�)yi^���*�0  8O ��'e6�0�&{Summ����E 6�$��$ F"�9s6,.� m &�p&vm�Z�s,*iceD� d�Jbl�L�5����5� "fie� Jqnst]5 Prod��t&�#PRH�-E� .����x%ۅ��iA,���� ^�Fr*�8��; 2[7�B$d, often �ZtiF��"�X �'o ��[V6� ��i1-  U&�!��~ns`8i� ��*�C J�k&<s� J�g��g�' �s5�8ny%�)%tun�%i�terS%na��1��^�p* #hO4&&>�/a�%Tp� . R�Pnt6�`.^.� N^/��YbMa! �xR~���r�s> n �k!w�a.=- inner �C �!��f apUVa#SurT[ii�� �:�4ic!n�P.}W%Klimov2\ KDLm,� A�t^9 l*w0���r�ia�x�;aI��^�~;� twice}%: !�*�q&�0 @vp�;ly�F�I#6aKsh�\&�Gsh�eZVlth�` y eY�u]-�2�.�)�majora�9�X)W� _)'n:��'c/a*U(&:\N�".�s�J� �=s ��� �4 &'�$59�9 (!�eZ  "?'%lissamQx�), .�totAld m[*��at 6��De�F*� !}���"�X�&r��ria.�(a�6 t) � !�n�;"-(�C, �LJŵ�6%��B|A7< ~ �E�*? =B� ��tun�'�7gineeTMEe�B .��N:�9S)?^9� "?%)r> �L�;r=�M�eoBed �T�� of g�= I �OGGd.X�Pve�o\ � G�%teճ ro�>� deA � � es �}y��1umm-�*�t % cop���<�Ks�c�C��bio�@� bio�� * Q� Lak,^,�7nt�TeeofKaB���ce-Ev�f�$d *:v���2�NL�`4 D%��0� z� �k I�JU$2]B#�Q�,W0i� A :�0 (cca $1$ nm)�?�3cru�6"mU'+�M s us��ac�;or!�A UW(F\"{o}rster C tv2+,7b&�#@vitro�!W.in vivo� �d�  *� �)2. Map}i�PE�s ��m/bso&NP$fa�!��tipDie).,*�^2P�-}�� BBNA�A�% s wa�c�2��^:tFAH�;`Yai�Pbalo �bmal�5ilibrV %��w"�eledge�a� gle E�J"c*�I"�Xa�� �Jn_iE�twol �q2{ 8&� a��dvb�6�tfg�2�n�n�e�A5/ orI��sF�R��p��}�� Hope�C�M]V�# rtic`9j�f�n��aprogram� � availB&o (http://www.�v-&n8.com,�gc a, rKdomxe6+(w lex)*� y�m�,�m�h them�QX&�a variet�2�!%$\newpage ?<thebibli�phy}{99}F|,m{Pu}E. M. P1W4ll, Phys. Rev.$?�69}, 681 (1946); K. H. Drexhage, J. Lumin. 11-22932702(D. Kleppner2a Lett g47}, 23581I.\� RiK}G. L.kA. Rikke�TY.. R. K�c �d74}, 880�95-6c�3 P. Lavall�!Rosenbau���T. Ga�@,2bA �5^545 _66_ ak}J�HLakowicz, Anal. Bioq[-,298}, 1 (200:AgaIV! S. Agarwa6� �12A475�76�WyS�M. Wyli-" J. E. Sip=7 O30O18O842�DKW}H.!Du.hL. Kn�IAH!1(D.-G. Welsc�U2_$62, 053804�0>[1�\4, 01\:J CPS}I2Ch��,ACProck,�R! lbey>�)�-b48JbCh� Chew, J. m.mSiB8A�135)P72�7?2.=3A341Eb882=�=A5OoE]nx (NY) @,15}, 352-418%v5) ("E �on-�qDce October 11, 2006�}V. Va��, AbDucloy)QV.A�(Letokhov, AvMod. Op�3}, 549!U:=6bM.vaJ! F`225��a �RupE uppia�N�76a � 822}CKN9�M��rk�5P�� McNulty, E�Soc. Aq�6_440-444!76ADSuHII}K. G. Sulliv nd DHall,J25a�270E�96��4M%� Toma\v{s}2��6!�a�1��=:KLa2�eA6�a, Chy��301}, 44)�92TEnd��E�le%� ApplQ�F8�315E�6�\LKL}L.-W. Li, P.-S. Kooi�� Leo��mT Yee,�IEEE Tra�;M;#�! Tech��4�q 2302!�:cZE.�\dan, Ch.dloff, NEHalG9!�$P. Nordla�, S�oʁ30f419�3�EٽMGM}L��4Liz-Marz\'{a}n� Giersigi�LP. Mulvaney, LangmuiՀ��432y�{\'ULM}T. U!-��M!Q6k �_ :a� 374��96�HMQGHardikarP��a�,atijevi\'{c}�Y6id �\{!0�E2AV1L20:Y8.A. a?BlaadereJ A. Vrij, :�t292I�6^VMBa�P. Velik��A�y��!>i, r���20:�OAW}SE-$Oldenburg,��D. Avew),�^�hstcottNnd2b^�28�43E�6�OJJy0J. B. Jackson�yZ�7�� 2897y9)2�JaHa�i%M22���!�[B��10X7�C }'(GAvB}C. Gra*<dN�:�!524ev6�b L,!�JIT$den HeuvelVMI H.a�GerritsiD�qF``"�p�]& !�N"{2�75&�� lloidal.�"m ",� prl'iza�INeBaE. Neevpnda�H� rnboimi6�-}��78%�86�JW:�F:L Hir+ J� West(X2�ZS82B 57%�32L� A. BouhelO:MoB�f luis�@L. Novotny, Ultra*� 10�l413e6P�?F.J.P.*�?�u de�[:?aIv Lagendijk"b L �s26�+472f6 NA 2}JC��"�J,� ��C �8�� :[Tip!TipN�5� 480 1>�CEL:. Zllo  D. ENZole)W H.-B�1�i�R_ �%X6f3E<9:� �� BA�4sht, K. Fukuda _S.A8 ayamk�*n_�93�a1� ]�0ITB}B. I. Ipe_G!Som�,S. BarazzoukE�Hot) dani ��. Kamat% � �m10a!EB�DSM}M)�E*Dood,A�H. Slo-�VA. PolmN.D��,^7�35� B�E. e`$MF =�8K 2030� �.OHand}� book�Op�( C^ant�S�4x edi�)�0. Palik (Acad�j<, New York, 198561,KG}U. Kreibi�lL�!z�� Surfa�!15!�67 L] MHaA� R. Melnyke�)�Harri��.�-�|83� 76�P_*] J<1a�287c:�LeuA�T. S2� {� 762� 6}#VRa.ch�F. Claro6� J3�=37 J:�A. ImhofX Mege�JE�EngelberxxDNE�La3 Spria� . Vos�MR0v 1408-14� 19%=��GyS|S/"�'E�`[���rystal��ee('A�JQo ` qu� ``Qu7{E�s-Sz S"["", �Lenstra,!�D. Viss K�H!�euwen ed�L (6Royal Ne s ��Ar:{nd� p!!:Am�dam�0), pp. O2 (��r0� &�at v�/� .pdf2= DSM1~� 9����m "n 2�����03380�12�2> E. SnoeksX �Aet.`���245� 6�;�mchnieppR�andoghda�'I�>�� 574026��8Ha~ jiwaAK. Sasak�9H. Masuh��.�Ź8a�205i�:' UR^ P. Urbach�F'6�-p��39�B�MoiXo�6�=R2��66� ASA0 Abramowit �IE�StegunB"M3# ]� F�s} (DD- Pub"��7��.D.�^"F-* (A. Altenkir�A1��� nguc"� � %w2��15-6S�*V2�ʎ� 10� 9767^BeMayal�B . Gledhi`A0 Hist?Cy �Q �Q6�MuD�QF l %P.��De!� Bq��N1� 76�6�$X. YataganW9nd�D�ik�0~�AJ6)m7T N�h Eet:� F��=er} {\�#\bf�"ur�*p� )end) \v�q*{2cmRo�/nt �Fi=1 -} A.�*��&e%,�hF�(. �)�4�>s�*�$aZ6*S)FB"�Z.M7w�m andB�e�(ive shap7!�un JTcm>ic}�g*re�IH"&M%pN+2!+��*�Hq s�` �p�c�2orS9�#*pY�0t*#�595 nmx*�Rof%`TM��1  ( I� !if�Vre<��&(V�Y $W_h�m�4b�s� �!um�wdi\ap"#(19.F/Bu)�&bf�~,>}&�uo�LKs�! $261*i�=0.99507X�"�!� a be5{=!EP� ~��D>�o�G#axi�*s�$t}G"��Q>��10$. ��RH3QH�*w .�%s='B� &�'lyZT�#��yny133~yb��1���� V�4!�Ny/� ��9�"�"_h$%�!ku� u��%icm��r�Z&N��m���0�2�G+�I�.���gR�5!k�E yB�y!��)6Rn6n9"1�v.�'a��%7af9�6N%���G^� �!�&�(�-ly�f w�nb�7�^f9s1}EY�e^@8o�b ."\I"i�2&m\ M�>*D)2&@�!�uw2�1��`R`^�"o= �.K{�F���\�#e�gZ(; M�hD%M�Y Z�91�Z &�erp�rqr10p.J� c-(/(efocy)bA!� -{d�1h)�f)R�yBZ1� ��~�-�#5P+T q AnzN�:�� <� . �FUe�%RR %f� }[tbp]$ a(psfig{file=��`if.eps,width=12cm,clip=0,�L=0K57cm� Fct {"tZfg Mbnd�!~�� � cc�� � O��n�ar��.�a%��ZRZqm�rm��� O�\b\q�5��.��)I�m;.��a)�]9]���J�� q� %�%��>�2f`� ү���� O��j��������^mp#�������R�m�4�U-U M>� �doc�} k \�class{ws-ijqi} \usepackage{amsfonts,amssymb math>(�exsy� %-2mBEn���C27AC and{\eq}{1-7\7}}:#n��i>!qaEnarrayB$n$ F":�� �1S%h\R��q{Yong Zh~Lo�jH. Kauff<8Mo-Lin Ge} {Uni� al Q�8Gate, Yang--Bax��z%*8g}.��a�ituni:�bra1�N:�bdescri�q top"�7e 7gl ?a|Sm� @Ays% {:u!�oni�Hper%�Ra� woulP^>�<OCde!Pn9�on�he8 . Buis:q6ŋ1I ��B �a >Vbas��Co6�. A dee�S4method (we bel�)-�� iderqՍ�$$\check R$-_e+�'��$�com����r8 ��~�! ��f@.7�NT1ch� R$vH�SW�}�Z�.c�A  (QYBE)�caNus�f�e e �<�$cPf���-�t�Qa�"�A�!are�.�a��&q8M0sJKans4j��vwa�=|s�M!Uapf�drlex2� amonf�Z�.�.�al!�Ii�!�q�"M explǍ)&X�p��s, Hm�qref�q�! 1}--dye�R]G�;F��8-eW VA���utgrowt��<>b8}. It �s�;e���Q�-� A4nO�j��M�E�U� dyn�,V<.@1�i��=wU�x��w�r�by2�� 'A�t�?��"� )�h�g^,mAep�E� iax�,Sq&f Ix1A@i�x`�pse new}�}� { theyz�qaofu: Hus.�S>A/�[E()A�i< "?subje6Rf29ed.�& (�N%�O�6)� ofwrP��1�a�u�.�"��onUory�"plA�0S �i�y�dze؋�ie�<�� �,!���<>�1��. '�o a uRu "�" thirA fo7� "i 5�fE�bP Q�ZRQ��6��fourth������ ! ړ nk� %� ]A��Khe 0r{\"o}*�u�� ifth2�g�<P!@BOCi�a��({R}ͧx 9u* �D��2� CNOT�u%h�Fle qubit�A��s ZV{. At ��, b@rkA@g�$ar(re  {b�"! A�%�A�VI} "P�?�%}�:B (BGR) $b5���2i@zUBJVR4 yang./jimbo�� re $�{ �� n^2$�\rGU�$ V\o� s V$ ]~$VpZan $n$2 vectGe$ As�%1]!�m t�~�p $V_ip_{i+1�iw��nJye@by $b_iY. _i�i�H ivel�q� BGR�' x� to satisf�L)��.\AvE�,bgr} b_i\,b � i=. �, \_`"�%�has�mA�.[qybe}!�J ${R}_i(x)\,Z T(xy2i(y)=.6&.7i>3"\�21�a asympt�aru ��(x=0)=b �A�$x�k� C%lNR�S. FV�� wo�es $bB� (x)$� fixe����n"h$all scalart[or� ���5 $GI�a��Q �rma#=g $G:V UX \!i*.�B�a��) .� I� M� We s��q.�{� !��-.( $} (or just,)�[� toge]/��]&� �F��(�>iwa�:{V$)��s'�^7���! �Y5 $2^{n}$_+8lf9 ��eG�ut " 5-�� %2��-.. \big=���)A! hm,@sai +P{\ԯoing} if�r�Ka �( $$| \alpha� ta \7tle =  Q9|:+ \in ]W$$�\�$G/JaE��d[pos�E s a : !�wo E�s�<�thaXcircumnc��Ksay��Φr{"�dZdIn s��z N.C BB},�$ Brylinskim| a  l�x]% I�!��4� e��o:b�a V�3a���Wi7+!� {\em�!�r���\0;"g`Lomonac�K�";t :��:F�{.TUWem �aE���S�M\Jem馭� = \left("�� {cccc} 1/Ղ2} & 0 &  \\ 06 & - 2$.5> 0Z:592(\\�� \�?)�Qb�I�M����[r� (o�U).�n2R { proN � (repe�+��^�)X �#���My �$����X _ �y&�.$}V�%�P�.}��IM4s%�. ��1i5ksis'�oA,�!eX Pz�-A_]�,^r� ��&zn�,\`K{o=�2��i��.�2"��~= �~>e.Q�a M�Ё}�_&=&q�N�:�Y�\\6�]�V�, \qquadaEtaa�eT����I�{aRK>�i.m Vr \nonue gV��Jy� &6^2-~y,�%gn�1a�m�i�end- q�.\ena %�$M=1��� \betj�nd $N= - ��.$���a�<��forwar��Ag 0at $$\textrm{av �M�� Ur  N.$$iSA�leʊy2oof. $\h�� \�$2�%� ��Y�l  Z�� a�� ��� &�pQ Nahu1�p� ;��  &(  $qi]ց�6G  $x$. W� wo�"d #W re ��� "�X% solve^� .�. Ts lim�h$x\to 0$�aGbr] N��. &Be�P@:~ �b9�-Dx.o= cern�qs "7OE�x$*���v"�B�J/>er�B aw!��.!� p&�Rgwadati2��� ev},uk"� aZk%��:s�aH��i�t�  2���� kk v�Psn�esw 3� stud'Xby Jonv}͘j�Turaev  ��F!�RfI(Heck algebrB��%��~68�< Birman--WenzlJA(cg#A+Fhe&� M vari[ atolynom]]�l 0i�L�6@D� l�+UI0gng�rW����R &}�s)X!�i�G�Re2S moli6�4}�=&��9�trigo�q�]� �A�8:soVM ��3 d��!wY��5 �6c"�:� sogo. schultz1KEo���eq�TR��b*^w� .�soV PjZe�o գ�t!� .�#!� YE"he Rf)eaG�.�taxJ�e�wr� Ծ5!V� %OQ��tt-vertexE�itlb.͞2�� ^�q�"� !�vanish�$Boltzman w�s $w_1$`��s w_8�6 �R�����'eq b=h �%a � w_�� & w_7h � w_53\\46w_8 � w_2{"�� � Choo "�TFO���>1 j�. Se) !P0=w_2=w_5=w_6$c u)k^34R�$w+!w_8=0$"NQ0"��w_4$, � have:=-I'$1=\pm w_3$E:�e�A�!�w b_\pmj�R�)�!� m $\mp-�< \\ -s� {w_1^2}7� 0w_1.=-� \Lo$f���� NQ �Iqv[�2�-qA� =8J�EE �$�w .�0$\lambda_1=1-}2=1+i��The*� a�V[Z| �r��7\eqa [ belltype1( hec&\pm(x)~ �\pm+x\,� 2 E ) .� &� Rv+x=7q(1-x)5}!�o \mp %2�!�#*� M .  a A�}E�V) eA�d��m &. j )LL x%iD��/(&{! \eq Պ!S=*�,\pm^\dag(x)=2(:-?� to�@ 1\!\! 1噗�&r[� s�F\{�2�1 :q\,J9 0B!.%:��Ae�rz�" q$ liva�`7�;le.́�!vnew�Z5 F �/�th&�pha��f��-�ar�q��a�os >=-k {\s��1+x^2}/� \sin2+x ^+q=e^{-i �2 \en" &AЙx!�.N �#��'��a?rix�.` �A�� \,\,�`( �)+� (�r)�s%3r���� ��I" ]n� q�g!���~71f-; 2}\R�����& 2Pa#��&���D��9��<5� N)e�m���x $)Q= �=��!�&�^!1� �%x�h� em}�!O _s \� � @ `0� *�*�Ij!�_*� &� ']c +q8H ����t�mf��Ay�� ) or2�%�e�Y5Q�)A�y� 2~ 3 �����y8 " �a/g � 5�-�Ep _n6]�$H�$� 1/qt =i� {\�Ral}  x}(\rh��^{d 1 2}2r )|_{x=1}=�� i 2 b^2z=��zf E�A�-\,RqE� pq$A�� ?J0aN WVt#�w^? e ``%aS ent"2p)`%�by�!%V�i\, �9O9Z �Z F~�T.^{A0=-�i �ޥ1�a���2W'i&}BU2�xr�.{��tr NA�F4%i�H�Da� �#.(j<�/Z$ $\psi6�A�y�#3,�:&��siY�� N +$ .!�hee9 6 $x$). H�'we �%-S�$ B�$6`(r@A@6��$a�#:zj��|JR-B}Ye x}=H-(xS �Pauli&�%��gma_x\s yD z$�UD%� 1 2( 3x i� Ny��a�]NM�.-)\hB3m \foot�%{��@r*R� �0+;P.08 h*�i|2��v�n�1L�sm��� 2}) 2 �x ("� })a ��� .�9&,&T1} %�Y� \,(-2Y-I+&Q)�+ +W  }1d-"z )-� +Bpm >8+)< F 9"�#���'$\vec iI)�� �2��2.n_�K:=n_2� $xy$-,e:A�  �=UZ,  _y);� (n_1=(\� A� {\pi+5$2,Hn�|.),�E n_2E @6?),�� Q�W-.D 2� ��n%l�)0{�&�-� a 9_{n_1}�9o � e_E!"q2  +=�}+ &� ) i 2 6%,2 2{n_k"�R�!�Z�U�V~1T�#t�!}�F+1})� recg�toA3J�2al+mj1 22R:�/ H_-7 2.F6�#� We8��a� i& 8al"~  $U�C��$�1� �b=  ,�� "� $U_+mA9 �uU_+T5�qIERF���� } =uP�\ 2-\,��ah  2\q�bX�W\E}..�C�-vNow�5dit�0��/?> �ptim=ZA !y3(2,"Jnd1^1�jc ��2d � N�&ca��,�va�B��) )Is.�+ x�Ʀ $2%$,%�6 V� } |0 0"�( \| 0��( \ |1. |1 1 JqM{2}z NP2x��"� b|2�mp�0"{)\\S$ � + | 1"^2Q�+|18J�� D�c -�=>� =�$  m��of&31-qg.. (=� (="�$V9.�! |0 11)�B�JFM�*�JxeVml �I� 822� ��. D�S(�<pi 4-�n )+ 2�[�N" \,H_{\pm}��i # 2-��m )� }��-��8S9H5�;"�� �yixa" �w'�+j+ �*Z86 s�7 RJ*�--T*�2-I.� ��4%H&lS R_-1O|_{ �&-)=b ��x����y) }.cn �[�!!�Ng��"5u� ��R��B�!�:MJ+6�l��coR�.@- ����Y~Y�.� IBn[��7nR0�� �bS2�pm jS0|)z�� U 5b_ .7J���&he Bloc � 4v5�� �X�#*0�x"h^�uLA�ir"Ewcb�H&s"="��C%���  b�/&�lea6o��woy2.ss� id�c�V�0��a<#� le�p�:x, $A, B, C, Dy5ich��#y�$g��.K��1K $$SO(3)$ ro�s, namepe��&� (A�L B)2� (CD)=P_\uZLow  �+ P_\��a�� ��x=6*AE w~; s $|[�L |Wr%w �Qf��+ z$, �z>X=>, zFl=-F �Aapr%"i9s $9% *5$M�!>-YB� �� # $|"� .v=F�\l;�|�# Defin%KB2 an��� n$-F[by�cq D_{7n}Ѽ��&� �"I*� n)��} E ��( f)�* _y z)$// s: � D_z( ��  2��=�  4T z}, , <x� 7-8�4x 4 D_y22 %N5y� 4)� D:tR�)� ! � 2 )H�p� 5zU(:# ; 2)� �'#2]! Ix�� ���(E*�peH�Q$J:�% 2:�=���(�� ��B��oV� )U_+� L (AR]#!�U%@.Q- . )=� k � z 815Q�IT .��� M"� ^MF�:A~ �} \, +.+ �:z:9%� Set�$%#�&59Qhuct �[�%� need�w e (c0�.K��!2.f�}6|i��)����� $ ���3���0=y -i\,.O$).C -�4�/� R%_,`=���Jt x&u q ]R(B9 }v5�nEe���e^VGB�}Еc(�I� �2U  �)):_ qPF�VI�FU 2)2���UF�H�"x q�_5��5�7 1"����0�6�MN9}.85-Q *{Co>�4(�@�K Motiv�5,.vI>9'<dGp��K�;�� HJ� � me�n�.�G2e�`"� � G+M �.�aH$Y�*K b)�"� I�ed2���N�!83v �:bp7# �a���mJ��dlso�.� 5T�6exCF��B�@ th-coming$B� ,Q}%i�� �0 �:F5y��NR���f^%4Mw��$I.FB2")$40 !�o.:1ix2�#%��)te �� X&�.F�#�H"�C *{Ac1ll�E� } YanksS ak��!� help\G0lectures in t�ahe Fourth International Wihelm and Else Heraeus Summer School on ``Fundamentals of Quantum InformaQh Processing" in Wittenberg,c� thanks P. Zhang for patiently answering him quesTDs on universal quav$gates. We U C.M. Baih J Houa�helpful discussions. This work is��>part supported by NSFC-10447134. For L.H. Kauffman, most of tNDeffort was sponsor Ipthe Defense Advanced Research!2Ljects Agency (DARPA)�$Air Force /(Laboratory,�i Materiel Command, USAF, under agreement F30602-01-2-05022. The U.S. Government is authorized to reproduce�Hdistribute reprints%iGoBPpurposes notwithstand!�Hany copyright annotE�s!' reon!�e viewsm conclu%�L contained herein ar!� ose %�e �: should� be iA�pre!�as neA�arily�esent�thM`ficial policies or endors%HHs, either expressed"implied, ���,v5�U .�or&U6� . (C5O<2004.) It gives 2�0 great pleasu!80o acknowledgeQ� fromA�D Grant DMS-0245588ap \begin{thebibliography}{99}Pibitem{nielsen} M. N !�@ I. Chuang, {\it �FCompuI (  I�_ } (Cambri�U�ity P!�, 1999).� {km�0} L. 2�~ KnotI.DPhysics} (World Sc��@ific Publishers,!d22e${aravind} �� K. A H, Borromean entanglE=M8 GHZ state, in �PotA�ality, E.6��Pasa -at-a-DiaU5i a-�B�.� �pS. Lomonaco Jr. (AMS CONM/305-P4, pp.~101--137.��2>�% S. J6`MWNew Jour��of5�T {\bf 4} (2002) 73.1--A� \Q�13v]7 u>t-�2�Cri��a--1-!�,Topological}1�em5P=@/.-- Spie�2cee�NM�NM��r�6 r4) h y�(dye} H. Dye:V.'&s } �2 Q(3) 117--1502Q0yang} C. N. Yو�,. Rev. Lett}-1! 1967�12��1!a�$baxter} R.��B�Annals\}.\!Lbf 70} (1972) 193-22.Z{faddeevŰ D. F , � ,grable model� ((1+1)-dimen�al  fielp e* ��!,.�S6� f oret���8ics, Les Houche�^8!Z& vie�Fmsterdam�z846Djimbo}��J -�(Adv.\ Ser.\� h.\m!E~1)89) 12�NIJ��em� ���}��:�.M8!é�2479022Z BB} ��ZylinskC RI � 5a� ���, Mathematics!`�@6��2Ye8G Xen (Chapman \& Hall/CRC�HBoca Raton, Florida��:v ones} V.F��JQ�Int.\ J!yod5x)wAa�41991) 2035-204�GY�Dwadati1} Y. Akutsu� M. W,A�it!�)�Soc. JapqH5 c87) 3039��56� c2} d(, T. Deguch)+p�rJ.�p$ 3464-34792� turaagV.!�TM� Inve%.!�A�)&9A�1988) 526�molin1E�L. Ge, Xue%%Y.�Wu�Fit�j id Goup, �ci�%S��si�Mechan� M ��[M. p F� (, Singaporea�94e 130�e9��2%�Che� M.�gK.�mE�A� mun.% )�%� textbf 13)�AO195.Ag4} ^, Y� WIN g dA�!�Mod. %�a� c6 A�Dc3732dsogo}LSogo,!#UchinaminV� �g.T�2.Ią�6 �81) 1:\�6.�/ Gwa%78 �oB�A:-=Gen}. 23�$90) L 795-2k7kCoutu!�Y�8g�J��".G)Fa�-G}�55a"7p8}�$H. JiBf-���3^215�18�X6f9�B�MkJ^V3i�91) 139 02�lee1}�C��e, ���geometry� t� y�� %5�'  NATO���,Study Instit� Banff�S 2ini�6S } (Plemum~Y.| 1��5 lee2�_M.9�A metho�$struct clo�braids�lii�.',draftr-b%Y�R� @w B \usepackage{�icx}% IKde figa�s2,d)�$}% Align tp �0decimal point2;$bm}% bold !� %.�,color} %\no u \GQ1l{APS/123-QED} \title{Scalar�vectorul* ek1� in��0vacuum fluctu, fiAm:\\ nu�Dl s��}%r�A e breaks � \\ \`{-Xinis} \email{Edouard.Br(@ulb.ac.be}6$D. Amans}%5David.61ffili�${% Optique� cous,&\'��bre de Bruxelles,% Avenue F.D. Roosvelt 50, CP 194/5, 1050 4$ Belgium% � �S� ssar �smj�Servic�p[� th\'{e}or2�{e} l�% .�Poulevard du Triomphe,�22~�$date{\toda!�It��always , , % bu�y 4 may4exp� specifiedU�,abstract} WeI< sj��N� Z� birefring�op I� . Tox$nd, stocha7 @ coupled nonlinea�r\"{o}5�qq (are derived�(Hg!3equival�tte"fope�s*E��Ma�c�h disp��,��Hand arbitrary level��ce. Nu��gre(!<��i.mpa�to analy-?ormula�?ca?-�mo�U=��non deplD,pump approxi��effec���� nois� it �etiu �ZN�����Z�is �� addr�.� Y� \�dH{42.50.Ct, 42.65.Sf�7 ACS,!�A)�0Astronomy % C�)opScheme. %\keywords{Suggested }%Use{wkeys)E�on if'T %display desired \mak!le \se� P{\label{sec:1}Introdu } In�,early 1980s vle-A� silicayc� ��, were recogn�Las a privileged medi�-� xperXtE)W e�s becaus] y exh� a � defi�trans��E�veA�ow loss�The KerrA\i��of�ham en u� to p%e0)]�sHylX$. Squeezed  6Eri���pioneea%,by Levenson � it{_ .} \cite{ 85a, b}� 1985.rc%$n a large � ��A�e=\7 b�pera�ed�o cw-l� or shY %||ulses (!�a r� see �$Sizmann99}� M� recb!, Fiorbno>� demon��A� that)�Y>�epbe1�-YLe \emph{twin-photonsP irs �x02}�jis � kind!�: sourcea�EPsuited�E�-%Q�� unim��Q�crypt� net�!s4H rast)j� trad��al F�s, bas�ivP$\chi^{(2)}$ down-conA�ionA�[ , it avo�I ŘAI� occurrw��p!3 � launched��o long�Et�:�%�hejc� �#)�inN��generate2� �" four-w� mix�8(FWM) phase-mat�by���r��ofU?e��!�� chro�6c��c. (ɋ) Z� (MI)MD�be!��ly �"stood��sd��?�wo�� M� a� equ�#( $\omega_0$�?!��of Stoka�,red-shifted)) anti- blueJh ies jsjy$a$ satisfy!w�!�g=#nservɓre $2�= s+ a$E�C(time domain��bea� of  ��, signal� idler As!kV �3fa<=�-�?4 envelope. MI�a%Xtaneous phenomena which-� describE��framea�].J�'�s��$Agrawal95} ��待�L , on�� uall)Jiders�&t � t; s� incom$nt �initi@�#�� !+. T�eN-Ac:howO a � inpuhpowera�bea=�$ nt (�wO !����7 buri9E$backgroundM~ �). Such�=gAis domin��byR� a��a�eE t8y �9�pr Hly. A small-perturbI�@ achI�iEe blem��,Potasek87} (B} =} )�%w�NQ �")�%:MI �� abse�of�&U<=��s�n ide3iU �=�%��� , a it n%���Z �� al life e"E�p_ ice,}�%� � 2�compet��CMI. U(�F � dya&dee� !MII-�um�of �'1m1)an[su sA�� g�hş�s2[�g���)qQa�)fA�U!y is�^E!2�~* b� "" } (SNLSE)�CtCarter87,Drummond87,Kennedy88a b 91+01a}. S*� alism!!69�-e1 Heis+'es A$� ���� a0*tag!"FirstWis�4sui�for.�i� �n A lex U�sqre]V�� a�IP60act toge. Second!� )xcorre�*deC:ciple}AG �� .e.= t Ii*to�w�', look �na�l4'Ai%�!)v.  MI ob�'� E�C non-*[tJ4 E�s!d(often refer" GsQl�}�*�y (S-MI)"' polariz%�!l� , s no rolu t�? �2� �diffe� < %�MI� ��� �6� u|"� �e�Ax~E�c' will��5asM�.2?(V!Fs � sy�* no�+eu*� yea&� D!q DR :z 8��(rticle, we ���M both i����w�,># �f�� ld!1m� ��T than� ��a�A��Jet��!�a�u �/ tool��w7 vm d�)lyE�llEAMI�clu�� low.�\ high6wI�( limits. %H�!1I��ly focua�vLACs %�+� w� nfron� .�to� al0ult�1�%anomalQ ]�r��9�a�divid� to� b� �,/�^шi*r��e7�� >H siste����L պ1�k2��s�� !@ steady st� solu��{�0!��mplest ��a� ���$of�� I ,� us!Yset mag��A� soph|"!�X!�t�#E to �!t�!with �i2 oY1� �&�e��?.~\ref�3}]B!}��Q�a�^� Cont,�pr�!xSe.\2}Qse�`��V�aw"� 9�nd- vali�J gly�G aBB �y"� �=��rigW � fY/&Y �s��x6� (�,�>he��we ob 1�liz��e5�rei1of��M 3icu|A�)��doe��t %2A to�21 �0ae�.8 �"| *q }F  )��K�� valuAC2~.�a�exed readA�e� a self!!Ved ��th6IM�Appendix�:~4E�%6 plit-step�5ie�1"�!A�)C)h���B9�"illust�4 our algorithm��t� ��MIEt� EMII�C weak�2ter �0a I�6�� or!Gto�^3!*]}&c�i4 �nQA&�q)no(of->�<a.��"�A�lq�e��W�Zs5`a� 2��ya6� e!�detail" cha� er�6s MIu EN�by"� e�%Ka bn!��ENshA�; @t !�� �r�Vg�GiCve & 6��2fB.# N�2}�mR&:2N)rs$As>Cut!D!�1�%�\ MI�)� �"�. F�Oa�� _A,�,>:� ��e�inu4� (�m-s�m)�agi�is uns[ �� most ag� forwM waq get+sazho!�e��4Q A���pJ� .�. � ��7-� �s:bcV7!j�oV�esT)�i"�% M be9�wI�� �. �is" we�����l 8Q ��a>� , :�.1�,in isotropic iD �f  w�$f$� H�D!� &�a�� � ,� w!��ze�riD betw� A���e�um$ cripA�s,o �=�I % ��6�4}"� �)nEN:��1!c2�� 2�;� to�a�R�-46� iF�i>&y;ϥ .Lt-�s$lso postpoAdto�2/ !B>c,sub� .72a}��;�%qA�UC!�>k"el 3Ece�#! wr�<�#U} \�#bf{E}( �r},t)=F(x,y)A(z,t)\exp[i\beta_0z-\ok t]4 \hat{x}}+rm{c.c�endmw� $$bf5$a9a3=t9 orthogA%��( axis ($z$- ),"�0$&car� ang f!!� $ �=(�) <assocDd �\�| (mod�roc�ant). $)4$��'����d� oJ% fun�@A$)`$E�ay| &�` is �=seL+� �ed� ly0y �; r,)ved ��MFy�umEa< � x� $A$ evol�;accor�)�O"� SV�"} (�����eů�:di�Max?'sM�omagnW!oryg 2:� �AGnoY! in s6��$|)o|^2Esala�!z�&&�� flow through�l plane $z=t{1�}$��$t$i���Ղ���Y��:B� G!(NLS}\frac{\� al A} z}+ 1}{v_gn+t}=-i -E�_2}{2:1^2]L t^2}+i\gamma |A|^2A�"!6�} H�$v_g=(dW/diS)^{-1i�![�p �c-!theza��V2=d^2 D!�=-=&> (GVD)�,ametea�d $ �%߅2�&�!pa - �!R�-~�} Q=)=3 �_0P|_{xxxx}}{4\epsilon_0 n_0^2c^2A_{I!eff}}u(N n��6 �m~= �� ex��T&a�6, $6Z��j u�#3 re�1$�%!ydia�Zel2�= �3 ^{(3+ u�!�tl" r. �is&� a� t2� cw)9aBsi-cw�"D67 !��6cw-cas��anBe�$P!B. .s n�B�@a f�Z>of Eq.~(�a)� � a*cw .� "� !�@st}(z)=\sqrt{P_0}�9{(mG8 P_0 z)}$ becoml/�� �j% (ͽ2<0$)�6?�,y manife�it� aQ�gaBt �.�0\pm\O��$e $0< <2 �i P_0/|e�_2|}$�4maxc,b $g=2 -�L$� for $ U-!(U\� )qDmax}}$JNoY)�se���� 'gly a�Bfi3)A y��� 4 rum NI�9. put �s��ban�/&�!K.!9O6�!/ 5 ��Y^� I�r�+n�!�J""*�(� !{���!�w V  ,�v1l .�Z��E�bovoY Th/.� qum��%�<ce nanoso)5Ye�s�/eB �%Sid%O�$~�0!�FWM� p ��#�,m �# .��$  /!�!MIl�seen a!�'-s�4�V n�#�� ���e J�# .�#&�#R�sB#0-N7OU�a,+R,�EN I���I�6S+6�mTua6I� iY al d�=�+265P$a$-v#uAu� � :&:Stolen�=A�RF��"��0'y&�-W,� F�I����#replaceO%B�Ŕ� �r&F  $n�n�&�%:Q 1�loc�i%� same te� al��M��#� (see>�b}%aaV��AÁ�iA). �7A� o,�s!�ixM�q�of-�q�isQ� m  st�"�w&* he!probe�k at�Xor2�)� ya� "�"I!Qe���+ %�b}. Eqs� � cl})�un�� lain)�0sf{ab nihilo}.�f�*K&s�'o�NV�+. N\�they � � )V-ms�6(0)�� a�$B��of�� or l��I i�%��60$ play a ce�l �"AXz� #Iq)B^�b}PC2�4ak� �#ccountN�, zs mT;beDP�C &�3Aer�!:t.� is 4Mn�"�um��gZ� (QM)ML"�H) !T)\r$/a�� .>Isystem, %�EG���� ymme��Յ> B+"� ���.��f erm� spaty-�<etA'�#} ( pic�C�.H� � IM�*N} (M�� a!J!�"A�onpq~I)�% leadM$P+l-%&7m a8'&u�L� �A}$w*6xMat> onQ8-�E�a�f$H*D�(f&��/�"�I�s)E��to�aNC.i �1��})�c"4. ��(��) ��@ F9 B 1}))��TmVU�52R�� (Blow90}. (I�&�4m�voIn1-}u Afhe"�"|app:A24�"A &p-E�a�S2�% 3}.)e "O �ba�E4s1ZMg - be.�3byJq��-)�V��kPt*k2�)�. B�)� E��  $s:�7D`  )ekt04�k*� "P2�. U�E�xN;z �� �"A�j��Yv one:��7�K ur��� '1be � asb�-j};�`=A_ �+e�a R� {� �߉ 7��[by &M})�(�!�ily�:g\*h6� Po�3. ]�="%��%D�� Y��+�)�&� B�>��] JZ:!�nkp/ �)X y doVZ�DEu growth la�?rk�1�C . One eas�ZZ*� �. Z�2J& �Kqub) &=& j+\non \\ &"=}&+[n; +1] FIH\ "�f R=rb�+1]RaI �fM:(2 no)�A \�J�x��=Kues�2#��F��s: $n_i=.� n}_io , $i=s,a�u2�,"�' !�mo& �6��6 Set��� (0)=!z0)=0$A�:6 qu})> au.�>r��6&rs�2O�hJbC�vf��L)=N�BAN�_i�j'ectly:�<)�s �8��unx&J�&��7�%q�geV=�-� !("�/s�AsE 0 (. AlthoughR�| -,)��(oos%s(iI��\�)�-282�{D) �7 ��� y�".h6�.N*��i�: 2c- eC#b*Q  >ivei^��ump���s^' � shape, duE;'&( width. Fur�6mx3\!�gy'M�V� !,�<dT# :��l�C(t�o precL��6of�>�3isu(b�cuB`B@'4l5 next  &�(�=m*� ]hź�/3 i�2�b.Ab���:jFly.,N,3,<ve>�J$\protect\\�R ies:�Y�G_s�O�aBg�%ya3%CR-3 by��L Em* })���ly �<n$�Nld}m cuM ome Q�&d Hc  -"��A���:< bypa%�bd>ver���BA2�!� o c-�jeci"`��o`ho� a HN�0e¥s�(&�%� � k.Y7�0M a� $P$-:\$($P^{(+)}$@�F� =;EGardiner�8��F� *�% �n&���Eda K�$mL��iaa�ri�1v^��R;&�4 (Langevin-typWw7&� � �v=Px;A�b�G� �7,"B<&��45 AN6�s�6[J�a��5of.�Qw�Rwi! xt"� R� � *vb 'z-.7' t}&=& �' ' [A"�) T(] +\�#�#�   }~\zC+1z~ 2 ,\\ >�^}� B0 �+��'>j - � R�2� �0 � >�2-~9."� MM�[! Y9.J A)a�"��b) �= lik�&� NLSE�* ;i�Ku>cok, except��last  ���+�2Y�nse9_�in1)Czero-m�'Ga�ianU0tecr cm� s $.IQ )n$ &�3 +� u�����m�Dty�q�� � }k%� l(z',!=m_{kl} (z-z')  " K@}=$(k,l)\8 {1,2\}^2$6�2 �1%12��c�,9ց�ea�Co 8 "�4s�,+$I� OJP"in�"3 KtPe�G&?o/w_�Tb�T >�)���o�;} uterEW&/ �.;� u.T*ask"� briefl�L� >"�No�7a"4lc F�� s a �l<7: ž!\�����H��Into cal�9kEDBua� umZ�,u.�F al a�Uge!�U%9l��4�95�=e gW �mJr�$s $(A_{[n]|,I )#n=1,\ldo`kNU���Z�< �0s�( a�tB�vqGa0�l.�D: "�#$*# 2�!*i "�%�= � is%� n byF � E} S_E(z,Z&)={1\�\N}\sum_{n=1}^N \tilde{A})O�Q 6:OF1D! $ 1X+<=\int_{-\infty}^  X��~e^{i m t}~dt$CJtZ�C� ! !DfS3$ H�sO8+ar(tu�?"t4 B�2"�'0$�6lAA� few2�Q enu"$!u ofsi  &� &�"�" *��=� ͵6�=hundre�fF�typ�4�n!a�2BE]s@I��:]6V� -~HN1 �!Y���  ��L �&:(-M727j#" � � �-�R"'��c� �C�9iR6��Y(�R�;B�� .8c���1{0x"( y B2W1L$v_{g 9 y}$ �e $x$-�$y>5*A4@0 �AW�#WofN"�uC %e5#Lan ext�)o� J��3 #C*#!��+ miP\ch�?�1$\DC ) �5%$- {)g"�] %&92W6M 1=1/)6- y�.mL �s hQP�R.�4in .@ A�B�DP"g b}%���Dt6�D� .91iY�D9 20 �� 67^2*� sA_xŧ0 A_x+(1-B)A_yy\�"u 94 B (A_y) 4 <e^{-2i2�z}fFrJ �} 1y /B}  3A_yq6p z} �,Jw ��s%5)x�~Fq%}&Qu$'�n}�>)�)�!�+‚��$&� �)n2�j>�4U) e^{+��y=T6 '{gyJ�.0)���27R�)D A_y1 ��MO!�g08)zx%u <��z�XVy1y-i+.�xq�n%��s>5)x��F<!}YnM� '�r}�>E�)�)�!��~�v� >�4u�r���end66 "�Z� (A_x,A��� y �r6�#nv�L� s�0o�=�)F*  nDg ivel�i$B=b9yyx}/ : ""�7� at m�x�strengt J�&�%"yY�%�$xz&y$Z 0Ytst  l 30��1f�{&i�3m�msm4 s�]� d��$B=1/3�8asR5N m!ty�CpriQQI0 �@�* _Jju� ��g�R�k� neeMt?g&]��� ^�F� !\�6 ��C })3 �=�H', with>� ,3,4�= &�\ ion �0,(�o�out!M���I.�&�1=at�H@ "�?2�at&�V#sAWK)!PjUEfor V� !�T1"/ ason2� � )�"�lE���"�stool. %A*� ��8"rJ�T.�  %F.B!.N4}n�bo�fV�C 4a}S�3e�va} Vd) AG��� �ing�Q$M �AV�r%@%U�by!�] of f�2e"`. Ourzi*�RjF�K (SSF)E �)A*�ZWe �ha%�&� P-�awo�|_4@luJ*Q "�4�S�6b��Qa ter�;�.*�L"�U)0"d�A�"G,alternaD�l E&�+,T �&�Mls�.a��hcir�rn&'U*s. Swit�P�Zto"T d!�*4�u�SSF-PIpe�/�, handl%q Q-�*a����Iwa; imilgctur�)u�%at,�<.8!gs��BW�6�%���!�h�i�f�D��sO�A"�56T bl�ag��1SJTS"�/M!)�i����cb8S]"� "~h�E"d{kYtNS&z�%.� "� -�,%bAoS/ce! �(c:U��F&;;) )_A�tauy $hD)oi#fam�'o�6"eF2s�b|@# n`S <�| vari��.=0[i_{z},i_{t}]^os4d.Fa9[ "�Z(�OS�\$� 1}{h�m�  =�)9.�:�1o�;-�=$The matrixn�0($k=1,...,4$)�"i^��pa� ��A;[%��)�Ken�rb �le�&�&|��w�Vadd�"onc�a�agi�U$��ls�!�2ka� �;d+݄"[tUga A}(0`$�%*��pGLous+dw9�N�+a�B5�% �ZI#��a.[�<ea�m�=P"�.  Oy$poi�$�]\.I( 6Pne���� "Dd*�o p�O=���>��%/�._\*�^�.a, ��ga*!�2l"n�'er���%} �$a�#Xles�n $1$~dB1<�[ �;"1,-d&Tinb w#  i�K!�9~ ��doinv@�iignif�sw(3��lex� ��J�. %Fu�&Q> s ab�j� I#%&�in"�  B�%�q�tleQ�&��?X&1T��.P Fig�WFig1}c�P E (:&a)�]w6�UH>+b nd�.Nc 0 >0c�4^b?blotar�gu�c&�D�'NLgyq"�HE %��C��y li�k�wa�Q t 8W�+ry &#D���[(� �D hQE�hirpedw/�*C^ed&� � �� peak2:)� full-w)-half-mYFxP9) $TQEFWHM}�>N*}_�*cR�add�GYn&.6506��o2�hN"�&.�%= }[h]E6 dtab{N"�({c c|c c c}_vf\\: \h[  or \c ({col1-col2}3$4} ... & &>� & :bF c \\ n $\lambd0h,&[nm] & 1550064CswH0$ &[ps$^2$km$�K5-17 & +6:+30 21W *3 & 2 \\ B��$s]& 1 & 0. 2*P�I&[W C40s30 s.!E�& (02.09 & 628.31O.212fs 5}! .7�354.9 6@theta$\footnote{A&�"u�os/n�PA�eCme� .}% & [de�rv45�Q< :_capa�{Su�. s: a-c."]NE��;n }��h��u��i sid�jn4�: A� .�*�2�7U~]!"�Zb we9#i"�inJ�>BK�A� O��#m5JVAw�i�N�N�{��X� �'� �a�&: �) �n�G+�E����� l> � 2�.o~dQN;1n^58U"$Q� � 6�8�r }-��c&S92,�in��y�Y%�]g��) J�� �&K r�sE!}�5e� . WP !X.ore[o-"[͜Ft faipb�o)�c�?ct�/%� $S_E�#&� r)�&ast>d� �R���$� %k� �V�7�|+A�ly�57bnC�rIataO|rx|reHC�A��rA1hig>��ft�lV-M�[�"SNQ3e "A E � 4"�c �he )!� (FE!<��&�,I1]��Ti�a� f o curv)���1a�) more��aBa�3� &b��2we� ����6�be�& 6��!6e" X 2�1g Y�2� &��betQE)�"ciXqY!n�&�wa a � 0ove ���? �j�#p ���!�"� �s5;P_O &�"� * e:%#b eR:bE�"�$%Fe�J��i�few Vn*�nnFje�> ,B� �e�e�st�<e�'E� ? c�c�3� $1.5� " f�}}[t] % R% s \uJ�} \� �phics[� =8.2cm,he�]`=13.5cm]{Courbes.eps}\\% ��MIy�orF.^b&�zc���4V'� %< TabD 1�?a) Spʔq%�7ineu�6QXwZauI?�~ %F�@. Black, dark gra�A� ���r % a2lEzK = 500, 10500~m,��"�a�G�exx�A�� *Ubroade�du�A$YS-�$�x�~ (SPM) iQ. % (b>0��a s��9�O\14�a�6�[,�;"a anu�| ,Z�M8�?�% �*q[� ��N�$16, 24, 32F�%�.d12!��S.��452-/� %I\mak�,R�,of 45 a�e� 2U.1U(*�Q]v@xBS%�({t)�T% eR�j�10V�, 3A�2�&� ��B ���� x���}visibN�t�::rS) u%no&�me�@ 'e�n��şa�erZ�.Hb�-V#N�n�1� ���(�ٍ��sm�x�5A %��;rum�4�Ely# � � �YH,U.*� �*�`$2�ime�ysuD`b�1�[h�F(]{GainMIVfa!�2F?aI*�b LZ!aXG/ing:&�<�g6�(i�p;w@��{&�)O%b"��: &�=�$~nm,"�=$~60~�{2}$~"XI\v =2$~vBi =100$~ps,�;=$~400~W( $L=$~ 40~m�0�r�H�w 0=! �x-͝wasWe�; 10~ml5~c d� %2��y 21$r r�V�+i&��[}|a"jve"o!� q .s "1�  of>��! squaW�(�� �cs�"=(doubl�fAWن�TE�@)2�2:� �F6 p&-inva�/M} med�a6�a ���!�A���!D, vel�^ "D,M�!0i�W%�low�.�c}�+P��OƜ��:0{� I�K;J�"��qfor*�2}"� � �,._"�  ��_-%A>� �6&Zp*�JM��lR toa; 40$~��`8y8$L_B$a� z�!��alb^��w2h���&."H . By!�er���A, "5�u@ �?J2�i�'��.$��6gcon"YWK�7i� .�0�`@2\pi}{L_B}, \quad2&1 &"�-0i7  $c�&��2 Cf#v�he65=" �ime\ awayiC;�pYc�z�!�ir q#it�deŒ� SGgV >\ac�2 a �xw:w2�2�86#ehavio�due k^walk-off��&d m"T�265G�A� at $v0 a}% �0 s}=\D<8\�122�}A��4v_{gs2  a 5$V�"� 2�ies:; �l�A�*[a����S�tak6�=1��,�6sU ��2�V�Cr1!l$ed 87.6 psI%whߐthA"�$�100 p&� :�P%��!�e "�LexR)�PEi��of qI ��k � s'e� &o]�jI�2E\V7 R:�/r.�%"� ����'� _Fa cw-aV: � B�A�� stop&�n9@�B�DHP* 5�:=C6Q o����*� � m^���&te�RFm�u�� p"��E�� 1&�$" 3BO)�i,�as �9� �T�&� >�t�.W�!�eKr arg.t\cև$Menyuk87,A"�'Qe� 6{6� aap��R"�+u-c����1 in2<�)(t�><�ng�� faYE$�d[\pm (2)6�/ z]$)"�to1$� n:>�eF !o"�p�h\q.݌sa��)$Rte�to in))y )u+�� N{I���ann�7on�4f��C ntil�K�s>ye:[]S5!*�8VG+MI� i�M��Z�&�*s*�8b}�m^ 5�FSN A�bP �w um9&�D&�!pr���OJ5n�+s�discrepaD��.a2two %a>p��}fuzatS���\ y!{E� aV%R� WAH"Sy.�%a %A�i*|s�ta�=�:��vO %��, �2�%��"'! s. H��g(&r�_� rI�s��[reVX9��?$ofIw&p#���%*A�*�aI�q�� I�&�&�?2��a� }��� ?%=@�- ��L�4�c`!�2d�!A{x'� �� %X�� ^|] 4b}C�!95�JAn�"2��ory} %�>!'xq�K:`D��A���Ce �a&)%�� s3##� +HtaeZ% �+en@�T�T :sJj9InputS("�"&k3P(tscP_{�j(-�)t_ }{2\sigma�)�F�?\Oj; 0P_0.\��^2}� R 2FW * \r nQij1 �t  E� 1}{2$�5� .�MM�b�e;%%�Az =nof )�b(L"K)A�a�en( �,� *�USEW OI!xD�-1N�j tb�}�4.��T aEM.�m mono"/�E�.5 wb�Go�\-"O� �|v-3>�wo �C��&f2Nen�(� arry�2 aE�!��R42��MI�+zf��u�-�a�q!�i-�� "�k!�Y  MIŴ;mE�= 6!"L:6���n w�sif�6�� �$x>��(�& U�$ ���.f�2����g� rew3 �ފ-���� �DTh �"qAer�u� x .����f �+���mp�Z( � loc�>!�im�U@b� z�hE��Ao� 7�ȩ21Q,G} iAp�q� ��k�IJAے&�(uFe��!irxG>� &�~�56D3}a�-V ��F7at�n6r!��� "gA%<1=o�Are,0G�6s. �G2� a �m ; : ee� JssNߒowry �Z� y�"��! A� �(�nr��@�x�7 is !�ͳ"s@b�pk� "�u&E3 aa~ Heis}�boxBr h] \�eeraU{n]]{ae}&KV.���;I�m)s�m�5��"H M& y2����^�5%�"�1!1. �a$L�$"F' keep%h� >�q���e!��\M)+�n  a�e horiz�l�A! %G "�b� un@M#�M��Br�P� iqK ��g2� *k l,�>&i4�th^,++� .KY�Ie( � top panel�q| d T ofq�rj7� tbottomL 6LF8 -per, � �. U? !req#�_�2nų8Inwh uAup-trimMsc#B5lxnX down$?"D!:�V�b �<�1e�4~ns, 1~� nd 0.25~n�oh s'%��"��;�zer'X2 � (A/Ae Uh\y�$ev�!!g9(n$2 !.�)dash-dN/�D �4��Si�:.kv"5LW{=9�7.� -M3aGvW �lE��W��!�edH(&�E��: 3 . All1 .:oi7=�I��usŬ6�1}a�}�� Fig3>OIn�\iU�6�I#�)�a&�es] ��u<�a�"�4msc-�6 �Ve. Bu>��� :)2O3"N e����{�R� T$roW�v| �� �������"�thi��p(g �>�dl7po�s,m�windotx:Y�es (WFT��s}%�  %.�6c' c}��NI � � 'lapiVa littl.o5d� �3s�O� depi���urface$2� _B!����wz�s,m��Y�FY2�,!��=I�1(2"�F6��*ja8����6Cis2A<����In� t�`ar=&=/1ShB9Ʌff ��a"�Pim 8aM�yšgb�n]��}��A�|S�#�si�( 0 lapp��5�b�"�_�nAUa!5e>!��YL:E� �`�% viI=��is�al��a�imagip-e3FcI�!���k u͒��>�= yp��,�dgh�T� !{��of9)%i ,*m�%Hf?�E1 2�AaF[>��aZQ!9 astea���n��0c- 9��=F�"d��/���w�Io%ù^�n6 $�hn�$�MMߓsi)!�%�*aU&��b,�!���"�@E�he�F2� ���#�As!"fE��ܦD:{ �C5D:BM�4Wl�E��h4�;�'�Bf_J  �)s"�e�Vpy���.BQ� �va"ol%<.� gba[6gu���hVǂ$ (&��"2}RM.ys ���iC �l% e2�b� unZE4&?!�&�)SsbJ$�   I" 2�p�e��A�r�ci&X �&{EaHdsw�f��2 ex�F�#�? �$n� �"3"u�b�UTt�M� "4E $"xU&�'n�S�} {�O ?_{0}}� � Q�.< j= M\ln2}}{*�$MH}}}.$\��ue�}>^b� "'.�.A�K-&+)�'EBN�(-��1�J@[!�A*�of6W3}a (&� ��3��- 1�-Ϧw� ^5&n�>`b (� � linP�� h)m�6�=�� �=��2,A� y*�o hM�of]�� s">�  $\2�f&2t�K%^ir ��*B&+[�_�A��a iB�bF` direct7U��=o�ZF�A> "�"�J=�A� !z�y�:�Ky+*� !B��ur cho^�o*�ze�>�, h�U<�I �JoJ�,��j%�"�Y.�,�)QB�0 a bit bigger�)b p 4 Q{.!B�Fig" :3}b�� supeI�M :��;��g,��.,�Bmai�K6��*w�C)scla�RQr�an =#o"�{�=�( NLSE!�u=�A$aiaR")�av!�+c�Ip�(mle�co̍J���&aaO�"#V��" F�&k n �F� �adA$0!�"� �:�)�ܒ"�YN Ed�1�A9�oa]&J�!SB�&fe�g� ��oiee�ed i�FpB���u"�-�wl]�HndA caba*�LNfin&�z*� � ls.}Q{":с.=r� n�"=c=(����Z^s��!�!�r�##54h�� :Ml��JowIBQe#u�Py�*��or�!ka/N�e ��:�!Auseful,:Mb'ADR9caB4Ea4��� s$&� � $M� _�%�|^ 2T:�U੪no iXs���_6l% . b�'c*6�LK ����qvN Figs�>�O�pa��!�)ta�>F$'y1�di�iA�6$q�t#g�S�r "P \:i��I���t�B��($n<1$)��"n a�'m�~�傁z;z��r � " 1�V�q0e:s��/�)8*�#Ғ negligo:.Wnow2�7!\) q�Ro&D* �� ]  C I �,} nois� h���end�Fe�*8!influ Q %G F�r� �Í�}2q&:y %_�)ŗ"(�."{&max�r_�� ar %��pW6�* A ��a�u<# odif�.H�SiaN�2^+ad� a�2W=� e)�tM5 ���i ��Afai�[�OE/�'��� iٗ� �! f�'n ��o 2�iu� � s��-�$\�]3jN"�<8)#6Ta�cr��: (i)%!E� &� ! a �T.�o.=(-��-! (i ds�!� @^�0�m#6g��) m��[a"�.�k��M�R2 ^{\aY��"H�!��%t��a"b�A��. S� a1���e�s�me��f1n�>)�!_s��%���m�Ys :qpY ��vJ9%��,&�2�_{\phiU=Ay, i\pi�V 1),Z�c��MiA�! "6 ��� {G}�f��Y���72}x (�_1�+ �_2V�=�� .yA�`r� �%A�9qje$��.Yq<m�m�0&� "CXj"D$P!�1Ռ�r[�d � Y��U�rj �X��X(�+~aT .UU�) drawB{#az4:nslaw&"�1]�Q0eB�M��4d 50 !fi�s,� e�?hJ"r�ERs (��um m5ׅ�Js�"��w�: �ce2Z�is�<c0.3~dB��g>&g0 span�*� &�aresiduaq^� (��N;�%vDan�pr�>."�S ��P�yE �yg!&�6�y[t ���!�� flux���!u�16q�= 9 5o52B> ? �Nz6-E (un� )�H��M(�.M)K"He !�QprJm�"� ��P("�z�*�5�)ac�5Iz�lP�.�3*�m9c� � they_�<�^Af�'*� dentB)�F5r�. fin���\ MRqEI3~erv�K]1�J, "�K}4.R�a!�D a,�(-�-�(soli�4)%�$���64e�.��iC*W=2�;B j�*a�_%ADK*�,(2<2�+.0���+ P_0L$uD*?[U�"׷6� *z;am�� �Q�� $1/40$ (*�}X), � $_"qD9"���(i� 10 ;�) �*.Ca"C�/o�2y���&^)��UD`UY-�Mb +N 0jN]{Bruit1:s�Med�/)<� U����uZ�=M&� ��� ��wt sE� ��Qʁ�9�vI�:�j!YY �"�.�ȡ��IN  GHzI )X(-Q1 (.%- i) 10 (6-Uv0h�arsI*1:@-�Nura���&�^D6��+5i�N< zoo)�(�8� a�ٖst*+2{0}L$-&3 )�9log+hmic-s�&eGbETr������ @n%���ce�A"��A$21�y*m3�Y{ �+E�P)k!�m"4�P!&&�.ߺ. *�Ibof 8W2�B��#cz%n�& w ������� �"�:&�($A^~v�*�^ZF!b�E�6�inguishjLe�%,q���%=uM�F}8i�%* �s �nQ���= o�+2>7�"E 2 3  Z�YsB� pi^^U ��&2#Z�}eKs.�# �  _nt 2�@+xQk &�C/ 1� :xZH"v,AO�� .�YEwڊ$�2쟁�hig�N�1,2'k ��@a�EqF���A�t�99+ϕp�.� summ%�@*�i-��(�':� 8;V�2�:�ia�+$;�%-� �!>F�perX�� o%SH>a �)AGi;N�9CZ�:�5.�з}�!�F�j�!�69}eD. Goo~�y�*G �{�Yi F�F-7�\M�� �9B�{��� �.18�,��) s, s���wo�S�ee �,��9% ��%� E�A�/ee,�$�UE�hem"Hz ���A�>� !��A��L� .�m��:�aQ�u�Z��@�G-k� VO�} �$�iu�#tEll-@2'�kn)�on�l aIrA�� �b-5��(o"� �p (t!� remo��it)� !�4.�-��0g�how�]��B!!�N_���Fb ]MI�{#��E���&��� Hi���� � !�Qo�<[J %;edٓP"ďm��&5�� Now,��we5� �sE�&Y  �f-  �M� $nl 0QR;�(ndF�%�5)w�n_a^{CllA[}�A�@�%n_sn$ sinhXA+�� ��^{Qu}=>Qub��Cl?\ $Qu$qKh&�l�9�!)�1�. T�;), ��$���#= )œ�Z&:�E eS)fa�@(v{IA�;AC�� 0Qw hAn/. �r� � *�  0).�#.v�th�E�J����b����!�5�.�i �&,le�ag|e0{�)egp:R�%��4%1j1�&G�7#�A9ie'5�* HiЈx�na&�� x&�"e��� �Fe�"P9I4�"*"�#eft%�!���)e�� ��r�H�!w�m ��s�X��"g&(Lڑ�dB�>eF)eq:.q 0ta=10\log_{10R|(5ne�}{^%�}F�Ap�O�{�@!�|b� o��*�R ,� ~I!o��or*} 0 L$.� 0.2�Wet���!��A�:6 h�: $64=1.9~dB~$\pm$0�.�%�I =��:��=.2})V��� �.�-�/=$G � ��xXLKo1 �z! �5an4=��;T��!uy�e2�2�1igt$�qn�mA� ��n�Q� 9 �!�B�6'd�,�Ce��B!Gi���sqjR�Ue 9 % alcul�� rick --- e�h��o9�.� -aAro)H KeT�a-H J#}Xb� �R ��G qIn � %�QS�$�/�FC�+�[4�0 =�n5N1���g 7rGݦn@G � s a J�'w�"�by E2�A(s])6 "yCo{%}� �'�3%8�rbr��!@.Cm&ndScV� T�bm2�%�:�t��!�"=%$m}���Yum�=�ar:QAs�T&�d*��"\h7i�$tin�gJ*: m2��lot)�_3�q*�to�] 0F\��8 K% u.i(�ccuuVFP)6Z4"� "�F���^*ds, �!�QR,��� '�r!s[y|X�3K#� {?�?e8QudE$so fay(n97w��Ad�[�dec!�A�G�. I�� �N�^"6����8iW��Xf"�"R�  �$.. �*��^ _gain �)�'v� B�$ab�B�4*�bu+�(Fn!����agF1*!h2c � "������V� �A��I�d�qa��!�>�-�Csa{T �%�doLa�nai�+�L1�&!���)9�*�!6�+}X� ��� A��2KF�"��R����. N�u���!.�j � �J&��-!q�A��3o�a.d*��~d*;<� m� �@!�r and exper�imental investigation of vacuum-fluctua�s induced V-MI in regimes which have been little T�ed so far, and we hope to report on thib� the near future \cite{Amans}. Although Er0not developed Faspect�tUarticleZ4 stochastic eq�4can also be usFo compu�\$�� Q�sJ"E its hermi!q(conjugated Q^\dag �$�, rEAA�A�annihiB X cree uos�5a:)photon��pa� ng�zthe� with a on�st��$%5 �hav<� nguVY�$:�$. Accor���x�canon ., y satisfy A�mui� ruleb{ 2} [-�-=, =Q$')]=\delta $-�'a��YIn 6 , $Yq)$v.�%� .�� index�8 ��&(group veloc" spon.,6�F�%�n��=� �q�3} A=a� |i$|^2 dxd� 6� Q�s ��A !�6�6� �y��(is given byB��Aaޝ;%�VW+-):8,n � wheremnOB3=IG+>P]EM $ is�neaEN��E:�$. %Ctotal � 0H}_T$FXsumA=!cNBSenergyET&di5}  stor�  m�� b� %�� in aQ��o�� H}_LI�a*s one {NL}�M�A,B�Qx4-�H}_{L}E� � \sum_{ź}� :SI%��%�i�)E B�tak��lccoun� free-� --a�!G )< i9=^ throD �*� s, 7 m"�(of \textit{ 6}/ o��>.� c� s �9"Q ��=:7!�I� �nwidtha�narrow�rpaA+� (e central ab�0$&� �1ad a� Yt2.)5on"4 A;!)��.& \writtenb\5]\NL}=-"4}*Cd �� d^3rIsijkl} �_ E_�-)}E_l^{ j�E_k Bg�d  G$ �Cd�) (-�0; , - �B8This simplified.U � Z�Kerr �, ^��dom.te��quasi-6`E's. SincR � isc�5&� A�2� tensor ha�0 �per��symmetry�Boyd92}L dega�7 *} E!�E36Z�A*�c� -�� 5�<� H%-%u_ ���$B �[6R5(^ _{6 )5,6  /F } U�*> 6}) ��.�b�~es�� wide�}eq!6ayV�3� ��-� xxx}��$ &\bigg(&%��Y K����:V+)2$+)} +(1-B)�\neq s'bT{s'-BHu !+)} \noi�\\ &\ tom{ �}&+ B�u:teFw`&.5o� 9���w��fined $BU� yx}/={r ��ed out�v(explicitly E-de�?i. \o� er picMX�Q� _{s}� %�dz$&� �e*�!&���8$[z,z+dz]$. Onee�,easily check�#B�  |se  � f z',t"_{ss'�� (z-zJB�8E��� �O �&D� e form���["���ayu�12m� \� ��ThK,int &\Big[& (� �x�r.+[ <y><F<y{ ) +2�  HB�BH.�y � \\%. �}& +B ( F�)^2x,{y}^2e^{2i\D��i0z��' �:;x ;-B<{)]dz"� -�n9��49߭b )��M3%�� ^2� 0}^2�#�0}{4�(n_0^2c^2A_{G{eff}}��quad 6 dA^2}{A'&�4 dx~dy>� } Let's� at��"set�q0\�v n_{x0}��n_{y0}' 0} (�)*�D. �Nu�{ be��resI in fun^p�0s $.�s}�E�_s)�-^$, � ing ";�E)$ja Taylor�anz around 2dup to�s_jf 13} -�o�0+ '�d) +� #'_s� �.(^2+...U�Q}E� �'_sM#d OM� }|_{m1}=!��[�j1%z=^2>?^2.A $. U 2`3}���!r�*6 ��b��OaD �TAU}�H}'_L$��N�6U}=2i�E� &��Vzh  (z) }�^l>s�1� �'_L--�!�.��[i)G'_�!fd@ �E�}{dz}.-. #J;6A<of!�J%=*J]dzB4I&$Heisenberg%H  h&�{U�-x" of aB e.� $\exp(--_0 t)$+t�eldh- $&��]is2Nw�cancel� e��2) w6valread&ci� i� &� .>�#,�Bprefer tinuQdi"+o  %po "5&2�)_I&=&.F:, U� 7}\\iH}:}ILe-atiYqd�.D� end�To�i�no�s�%} drop!� $I�Z in l�"�s6SF�"&to N�Xi Oz%heoryI� stat"F>� iA��_entedCOB�� \rho}(t� Its "��8J�,� �%��fI 9} i�9m� }{dt���H}��]b�)�r �.�d�by.�18})."� s"� 16��M�12 Tcalcu� q�r�-h\ E*n9})!"s6]%,�'uo �'�1!��u�ly.6�#obtainR*&�$F��}we �ld �"��"�Ga�er�80~&U^ "`iSteS to multi(�&/I6is ^(Kennedy88a}$�roP)�Eco!&ntI�Xs $|\{\alpha\}\rangle$ 1�a�de eige�t"�6l�fAG&�)$>��:$F�= ��J":p *} Ac$c& ,R�< ; F�JgQ�7})^��f(zJ�=mJ:�*} h Nfps D+1rN%�19M _s. BZ*} Q sugges5 alternaf!�� $|\bm �(z)M5� F�� ith $.4=(�x(z), y(z)� f�*eJ� ����+sic ideaat^�$ato��^B�on�diagonal:�j% U� a"�e� �20�\Lambda� m{\Psi!01�REle�(1,{ )^*A^} �(a�V 5e-��� � �ps a(z5�r9�� a`new� 4(�s differ�Qf�2�$. Deno� E!lg>v�, �exn be��ten3��&^way*! -5��%� (t)=l P)[!�;t� B�)d\mu*&& f-f���grE meass.$:?$n�k�.5is carr�C+ allY poss% -�$!�g� �6v&�. Taki�$:����  .A�)n !k showY"�subQ�s9Y�b�,&� �����-V� ��A ( ,� ��p�>%>l4'DQ�+ �}  $(z)'2Kp � HW�p2j % 2jC> �� 6� Y^�,}+ �'6kV=da�2�M�$ g/ 9E(V�(z)$  0Tal"�+v�,E*� 22})* A��0"�%"�iEity�!1*  $ $P$-y0 always existZ ap *�3any� ���+2His��h"� $ng normal �/ed mo�j@ 2b} �� 2u %<)^m.\)^n���# �/  *:� :1:�� "i^ r,.B �)e�se�!! �� (o unity: $1�z~$. It�bg erpre a�"genuin�=babilit5��o�(in2* te d 4<al)�sus� &n ����a�E� ��%l A7o� e�6�-$P�e inser��N��8!D" "�," � W�� &����w���%�al P}{ �.��h:)�:�� dz6��wC_kN ���$��_k�#Q6,D_{kl.�.<GF>lMN����-/��9O�suml0� $kE  $lE��dm�C_k$'s� � �'n|3�ta four-U} drift veP#�C1� 5��C_1�&=&O'_x-1֥�x9� z}+i $qx�� 8^2F9^2}"2 =}&+i;�B^{�B}_x D +} i2y x)�Y B0 ;x �y^2 e^N �3A2�(��٢&+ $C_2�C_3 $C_4$`'-�Ta5 ilar��m.&2a*�edn � 24})�m�a��0titB3(i) $iI��'-i��_xe�5F ��n_yj*y$�3E��8by (ii) exchang�j $x$-�: $y$-ge��, � sub�$2��-2� � %d, both2s!m� mustS per�mM $i�;!\ele�iL�$ic u�� matrixiKD}$�%F N� rm)=� B} ^{Te��y��",bm{B}=\sqrt{m"$p �}S _x &0& )B}!�_y A�>&0\\ 0&i#Q�&d ; @>?�  y5-5i/xq>1Fpy&0&-i;NU�N��'�B\B� ,�!�de� *s2�d& !�$6G$ verl)s�ElalZ24�a�emi"� -h eB/�p!]3*��  a dem_!S s�)B�has�sam�7ru� ��4.19)1} d. BX!R4�j �V�.�P6($P�� main�du;&��h�J3<KalWr,V�5= k%�N]�4�act!Emj� �2�پ�Ps ,t)=6M+B># \zeta,tF�e�X $(k,l)\in \{1,2,3,4\}^�"\ $.B� �5�",zero-mean Ga;an�7t��:randomC sWd!�Sec.~�<sec:3}schaeeB6b��  �� }ZAbm<L�x e �( rmin~9"QR� sA��="  class4�|ory3l6��+�0 f.M? modisBxi�t�kgm+M�� B}$ �Q . If�ar�6U�Qsi ��:�6s� �� ppea� be j�|A�lex�j6of each �' . However�nR���'� "�,wV���t/6ed!�in"�$ ʥ^oU;B�ASA�D@-�5taP:2(seemsa؁Her�� &S�?"6tu�9��ing� �" . To highEA&ce�f�< �*1at,.�g�# i�4ntaneous-power"%�Q(A_s,A�$-�, ��.*�"�1�v2�"0 7��&2 A� ,te ��")4")IR�%\7%����j<. l�G� � 2� IB� � 7�R�,��!v!f� � _s=.6)�-N^j�>F%�-5�M>)�)�!�+�f�2!�j>�4U4 e^{+6� z�yj�yN.1)�By}{%�F@A�.A%�+>�)Oaq �!yy9%�x%� 6)�Bz�>F%�Y�m '��M>)�)�!�Ɵ�f�a >�4u�F� ����ل*�A2�[!�G �$� > f�� member:% //` 6�/ *�Gparam� � �) 2s}=� '_s/�(s0}^3$. Whe�%typi pulGue$T�suc�Eat $T/)Wmuch big /�GS :� $ t���J�2�?on sit�!�E-I �&��6T7 holdf�3�2}�sE��+ '��!$2:�2:t^2F{B! 30! ] E(�.& us� 9�x� 1vyE, 2S1ew�&� e5� M�8. \newpage %J� U1of un�&�0 �Ges7#ck% 0t end %\bibli�H,phy{sto01}%,  }% Pr gr+0 via BibTeX. � the.$}{2Q'�ddafter\ifx\csname natexlaba� \m x\def\$#1{#1}\fi �'aFG�O font>J Mbi#�Pf�Q$�R cite~R.$�Rurl^�url#1E/tt!O%8{URL Iprovid�8 mand�7,binfo}[2]{#2�:!eprint []{S'}A3ibitem[{2� {Lev`<@n et~al.}(1985{U{a}})V4(, Shelby, A�Mt, Reide�( Walls}}]c85t �{author}�5�{M.~D.} .D@�0 !ZA R.~M>A ��? A.}~2} ڒ<M><!}},�Q�{and}�� D.~F>�-Q,.>Tjournal}{Phys. Rev. A}�@bf%]%-Lme}{32:���$s}{1550} (�0year}{A }: ��Lb�L /, Perlmutter6CInf^�C�C2�%�j�S.~H.1�:.�I$C5� Opt. Lett ;�f �}9-a�NY�,booktitle}{PnP#@n OHR s 398edi�by?�F�E>~Wolf}6kpu�O4er}{North-Holl�=�add�(}{Amsterdam6�q�996- �J�Fiore 0o�� 2002:�&, Voss�BSharping�� Kumaei+0�^1 ^�:->:fV@ P.~L>���= J.~E>=�A2]~�P>�-!05 u�IEEE Pho�Q0cs Technologye�ersAf�4AzVm�983F�!�r0Agrawal}(1995a� 9�Ev� G.~P>F >-E6OmK&�OF�UmO}.�}Academic��E�N  San Diego.u5rPotasek�; Yurke! 87! 81r� M.~J>  >֪B>O �ZO��5:AM: 3974.1:87r: Cart�T&� 7:= ","�0a ��9S � (�hSJh =:�b5B" (�AN �q�23.V��q �9=���f&58:�-� 1841��1(e)-t� e*��PJ� ?�,�5FJ.�v0. Soc. Amer.~\^' �o.�1I565�I %HW}%H8�r [3�f� T.~A.~B>v BW��2�jTE �: �.\5J]�A9^D3A��-C212RB�5)J� �)BabnitzJC�� �CNCS>����!?-�%�-A56J�19�A!591]x9�0v�~42�V'f�4Zj211R�91r��WE)Corney}� �01�Z��F�JJ� �ZC:�. n�1Z/139Fp200vH�`.% 4:�!, Braw"AE*O�nd Mass" (��D.: 76VQBc ��=Ph>yEƑ��� .�V�B 1! ufnote}{iXeO�=�0!J� Stol�_ Bjorkholma�82a� 82�dRW�� =քNR �6�� J. Q[b E�Rronv� QE-1A��.  1062!�J�v TaiU� 1986:�6�Tai!�Hasegawa� Tomita� Tai86�RK.:�Tai:'VVB�ڦBP��E��5����� 6:�ͳ13V6 6�.j��R� �, Jewell)�9=]T86�5��9� �:%V�JJ� �?uȁ�9�VQB�9 V�Appl. )�~�4.!-�236F~aq.�!�jWLai��HauQ8QLai .I.8�TY>|La|%22D.�VFH� ::�9�b>An �.~-@84V�v�� �� ��  6 =��3:A �38V!z� %r� 0�0�v� z�R�͠"HdN�+and��Oal Me�;�0^�Sp$ger-Verlag6z"�Berlin.~ � 2000r� Korolkova��!(EPerina0�� N>/X�+�CQBqPS�Ebf2M�B Atomm��v,UF�J>�$Pe\v{r}inaL&Up&�DJohn Wiley \& Sons.�5�New York6�5�v} �c*�90:� , Loudon,! enix�>A�Shepherd�)9�KJc;:�VR>F ��<�F�Ph�C2�9�V�TέL:9*F N�v�4���410R�9v��%��E}� ��8����F� C.~W>��6�5FJ.n�1Z 235R�8vDMemyuk%5�Menyu�� C.~R>� MZ�f� f�2Z�1�Ma�U�U �TJ�J �R�0A Wavelet TouKjSig�5P:]ingf&� ��m�9 �#1~��ke:Ml*Vow!84il�k�B�! ;��LJ��)l�u5` ��!Z! 186V�!4r)�\!492n�0vn2����`.�b684RCzbBoy �+9�)B�;-�R.N"HcO b qr�BostoJ� 199v��`eZhe�rv} i 9�'Q�VAYJ� =� N.~I>j�I/RTPolar�o of L�6�*Fm �� s^� C2+eZ! �1 ���s>>F)�)doc�b} �d\a7[pr2� of orbita"�h �:um)� �]"09� \makeE� &�uIns;A Her�89�] t=�] ��%�2I@g g!8d�8a NM;N-QQ �. Vx i�Ja2Z!{1� A\eN=%�!y9�o! E�*2�EmBB84-�y>^ B^"lz5A"dp�D%0Al�9C)Bob�A al:surIsop0s�>� cle,AB��rate LA�s3woUd8-du6�:@z[p�.�ect|_o�z@I&hUWcom1JIf1is �(ea��)-)�^�[mploy�C`[�:g�we�s)� $MrT|ng�{�:�aYg0!X}9 , un%�!�$|GHZ�I _{N}$ -[2rAdRJ�Bof6�c0@X� some5U!j�RC%%K�Vd.��M lmad����athus &D�I*r�Raga�;5��j.  zlso�o �o!�6premG6�\2 Ju<. ef origvv crypt�0ic�i�Aby B�TttI�r�d�ABass1}m�AUa�?@O�� �A�seA�f basg1�^rCR== unbias�D Lat=>Ekert�R�>h�}m>QnI�=�it�QcoB|�pse�fashion�B Ek1}*�>these���2�(QKD) �. F volv!}nly�e�sCxxwo���Ys.aWre�n  s�@earchersMG drawESir atten���3QKDya&w]~ m����sI.� �4Durt1,Bech1,Mo 02,cerf1,Dag1}�Qpl�jwTB�-�$Mark1,Scar!K Moti�z��pursuipW V ��-Bbh5at mora]�F��o b�v`Qby e6%pc�~|Fby�p@�r C fluxi�e�.�9��H����%{ gq@rIFa q�eaves[ptattack1)o%Y.�V�$ w��\�s4� 56�5��n�zXV!1�.�, b*|rx�@be�� eL7b�e�5is�-OE� experNxv2K@��obsta�k�E� �� na�ffqNof�7 #. }%u),pl�Wergy M!$atA�� d � a��a�a�!� ��{~�$ a�s�~I��8fag�IY � not �w,��4ArL�N- ^,]�8min�w far�!�A��GtraA befA�t�BOm�D~%Jany-Bi�"`na Ou~K{�̉i 2�2�G%!��I��:[ NK[ %HC�xSi `��rary [d ����g:g&� � KmqMMair1,T�$s1,Sonja1}: es�a�mia��`ource%CevdA��J&��0��q�{,&: work(C�dA�in !�cSBv� !lmAuit�Ype �Us{j!C��t�.I뭶(Vaz1,Kot1,L��1�"��� �c���[E "tV�:p iŹA�a)��T, �y fC >R mY�is \ l .&W !r$�|E�� a mixQ=, "� V� iUbe� b kfm&� E�n RKd� =� AK� �ra�U�H"� bsJi&�n6�,s�+ a�� �;outa� helpBFethird.�~�#S� Q1!�P�&}� S������Y taskAGhAb�I�)�u�mor�ban��!�y? need� 5sakT�ki�baЀ� u\ c�biYlaunch�missil�ope%�b)�safr E� seC���m�r4��no�indivT� be trust� o execut!���i�d,7��* D�arf � � code, �vault bi-]�etc.,!�a^1e"J!!c.Qmessag�Ł deci# wh^&�Y6�F N cooO��Ir�* �� me�P�>�o{Jse 6���0���dedy GHZI�N. �F�  a�B:k��a t*u ,҆�qͬ%<,%X! (�, Bob� Charlie�VJ�J��"Gu } |�L>g_6}}�kg[ (|ab ( +|ba )|c +pm|a|c6*b +�+?(|cY:)|.=g]�e�QP�>ino�JntA6 re $?, |c$)&$�&_M)YQ8 �$��Ashy��=f�x = � _{\rm{%� }}\o�s� Bob}}+�Z5T.5n)W1N AM}�jNotUUis�^��E1a~ux&�y�#)-)%%S�%� c*8p�Ja�l e�.�e�� .!#U�e�fE�al ba��h4 h2��z�LN�. Now!L�Qe y�� �� h#Ws"�Yw |u1-�>@3i@[5�9� +5�!�]"�hmb#�cH |u2�uUt phi}UP -i Q$>����3��tq��z�3���-~iku{3A��b(Aim&�3is1�A�a m>6-��o� ��I� ��_&�I�isRsI�is.? caja�SJ�o]u1,u12�Y|EA. u2>&-Y.'3J'1�B�ZF�.�22�-aGErR ���j2qN.23,:2.cq ��3B�M�Q6�61yVR�3,:02� Bb>�.g^��w �w�v $�HC|� х|e b` ..= �BqZs �~� D����in�m>iQ �4��n� do��ame�S լ:$ �X1Vi�'c kee�mou�? �irD�R4M y G{ � -! get toge�  p� ]1X��%A'6 s. Clear��X�"�W-!���, neiw3nor51f t�fw� x.� w��ita get�.�#� �Jtult� Bz Key D.�*| �%<>�sWj�e� �a k�H���h[U�fQlAfU�? Can)%�!, w�%jl!�y t��fYirS%�#uj te?�{� i"d0��]�Vuadv{TgQl!O� 2%-�� > *�i�VQ"�əv C 's���&DRJ��aEo_{A|\OK1�e5[�I _{abHm�R[ |+ #bcR#bc#caR# ca}|m]~3�k�Y{ijI&?l}}[|ij�+|j ] �W4 $i,j\in(a,b,c�cN�ss2R quBo�m�!{e��m��$N� 2� q��� . IEU�M'i<�lifi[U.+ricE�6�E�a�&balt_y�b� z&�Let u|r6�dec���oA�0a!kiT -� ,& ��)$ �` pace�p%9 H in ��$A\{"e .JBig\}$�� � \{U��T�B.�&� ),~0 -"� 1x!�?%��y��d wasU�y?$!�e%(y/��0JK�5y17� �S? ��� ��#{!WR�Zpe]y�$1�Ior�P�Q�a click\A�or�r�c�i���'}$Z�5�+ $BW$aa��WcR$5�$*�i�e>sDs��m"�� � � �(to.� �Qi�s, � i0\M�f0\LiW �( t�in*�]��iy'�� %ab%1)�*�%\9�issp �vd*�qd5�y7*r �� . A�"�dargV& �Q%2tha�av�d�d,D~�H"6��th2��n�wAQKDv��s:Y%�disregarek.)��%S : 1)e�%d%�-P }�e� 2)�0m�d 4A� � (A�qVB��&&� l!��akj!�bV�">vfaOi�Q� don'��!M0previously ag�upoaYe^\�a��./ y� �`V#ho�K�adyC!� cri�`a"�:�j�% in�Uent��6� R'"z�} O� al A� M8m7 *} "�$�E�&d_��� ular m,�-68&n�i%� ��O`Sb�-�F(#�8Ae a metho%e�ŵ"� � �I��`U�act O~�!�its s.�A�t��bp�e*/ly �eaxa�>e&hC�!~conser����ota`!�DWric dow�7�daughlH^g9�lir b�<{�}N�!(� $no upper bU�ebL�W 1sy� 'vl���.��Q�A��wB�ll� �.neF'�I>  !.�are go�|� & �l�� 49)R��  beam�pl�$ /,+'nd��A�r�wf%mN tY�#ate"�'A|bC<e1)Չ� m )�`���� spir��W2).6&0� 2|(-�Anton���>(A�l�we!q 5q!\E�-�d v� :�. ��a ^$�� 5eU.o*de pump !��canZ#%M*�Y�29�&� � - � },J�� H)A}^� "�0,0j  +|1,� +|2,@�&\u�_2WW�nfeM��~se1� A�?� �'s� pu� �v C-!ib�E���$D���or)�� mb��_3) m��!6ed ��m"l�'�$%�:��hal{.� �� *� Zt�it� � �*> Hed�abof�0, l=1,$W�!kt'wL `�h o�ies �. H%_�9�`i !p"9"�2&e�g&�/bk-[|0,2�`+|0,1�a�z022����082,1��"�e>B�>� ��.��d)|�%+(|.��)|�C +.�6�)|.aNb &�#��!�>���R !�st�Qd,�n�v%�})Ŋre���$N,�"�$I$5, � - $�$D$egin{figur� ݛe5s[H�=3.3in]ͦ.ep�4cap�0{�h� G龥Jf. 2 �>(�!M�i at di6up��� > �� $ �]da� ] Eors�"v �1 N,}!��+%�%�-�!� ��/ ,: blem=�y��+���*b8� �B(���s%0b�In!*�&љ%)&(0(�+i!�& ineffici9 o>���� ly"S �} i��ng�F�&)%s�v of cho3L�mE2feromet�tP$�,](a Mach-Zehn��.0e�4th Dov8ism�� path�&)I�)�_s�%�:?%�wo arm r��ed�'�;�t�X��&U(5�l� $Ń8/2=\pi/2$ (See F Fsrp!�(7rX2'�� e sh�x�6����2��c\t3� =l\pw�'Xy,͟ B� A nL�EYa�K  r d �(R� p!u flipa��'ansga�r2�p�o. &S�Laguerre&�q��&a $�l$ -Ueg.� � a devAl�i�ts a $l$*� P!bD#�mad�pAv�ED~�ce.�:�����iti q:oddeJI8b{�Ns� eP !�=A|v$� ��s�2"6-� gF� g��hC7com�AK� �:sor��*b�sca�mFg%Os�Y �!s.�=��yq}� '�et�e��f%' T �|A�-� byM ����*� ��52.& ��v�A�V�} SorE �n � �2{!�>c%c�c:�Ae$ b�A)v�>c. W� a*߭:�i�E���A�z� emerge�9�E��A�EHspl���<k%1m��)�!�2Q�Ohuqmb1}-�!mb3 A�pr�L '��Cz W�:;�c��&z���#`oR���q{\�1�6*o��� "r !?1>az�id�c>� them��9 :��e . AOh� vA,! �ɻ "E����x�H�?ath=:��,e-�tR �:H61�of y��< Zuko*F8��� a'�� m�����.�a-]8�;.ZVP.�.?�too!R�4ly,-�U„!�setup9�9� 1��w"�>�k*�^��',dB� <w7d.b. 9A0yQdivulge"�6;���G @ ���!ja�as � � w$Q �0CoݵY3*8>e"Xf9@�8�O b`.�0�:�."� Q/!�G%re��or �Ba8C���two��$�.�Q� �1Vqz^2a�#M�:# #�?�sI�"�2!�6��&�2 QA phy}z�6� v�!A�wG en)��7Ae?f*�^�y���� �&ԶE5} We �=�[nk NHoQTGovind c8, Thomas Brown,Q0Miguel AlonsovT3ful4cV|on����5� ���'Xart!_�ARO-adm�=e�1MURI �@DAAD 19-99-1-0252A���F� �t>n1!F�n�n�n�n�n�n�n�n�n*h?\�[vI8�KBk?�ZYXpF}ti&�mCJ�Z X�vHBtR@sHb�e"�J�H�Lec "G �MIn��̑Con{  oC0 s, S�"ɸB2M,, Bangalore,`&iQSpp.J�J175--179R?Wv�K�@}�I1M2@~ A.~K>�I G6I5.*�LLeulfO67:E�K61N�z�U Durt"S 2003:S ,, Cerf, GisiT!a(.{Z}ukowskiS)2Q V�T>�R7:�V:N�R `nams{��=:-\���[B�N6 2pMN�n�Q^�01231J�!�}n�Y�A�E(-Pasquinucc�YT� l�V�N)��H>I7>`�P2�and)�j�W>[ ��Q1:Am.062308F12~X$Bourennane.72:7&AKarlssj: Bj\"{o}rk.Ne_aD�C�\Bl:�VIB�\��>FҒ?B Y��u��QU^�k100N�h�n9�.01�0andY4M#�6vf�#n#F�� v��55��r/Z�f�/06R�v,Z�R.�>� 2�6�!�M�]{UG����V�����>�b�.#N�~�8�d.E�� 1279N,Z�� ru\s�`�S�G~� BWg F����Z�301J�19BSawJ�fH�WU�X:q #, BuzekB"$ Berthia�x}]{9H�B� [:V�V>��ڙ B�.�2?N�nh5Z�c182RR z9v,Kan� GU � ^ �tB77ani�� �n36Z+s��Z� v�|*U�rk:� 4, Vaziri, WeihHk�� ZeilU�I�i�bBL_��B: ��<B)��q=VNa�j|41�_J�3N_n!�r� 2).�> "$, Deyanova|T�nr��( Molina-Ter�X!� 2�CJJ�Y <��Bg��>L>� ���B6>!6�,1��b�52^�v���ke-Arno<��v�:�2)�,Barnett, Pad�;IAllen!�L~�B�_2h��S�s%T"� ��@R�x �@Z�>BR-!7��^� 3382J_b!�r�� .�>� "���� 6��$~�������rBn�Y&e� 47R� v�Kotlya�[199>�z #, Soif�{ Khon�g]"�s V.~V> [:�^- ~A>@ �?�5 S.~N+qb&6�{��%a�5J. Mod.r] :^�w4!�y{-�140V1 v)|]#n7!�� �,2�eR Courtial�5:��B�i89x%&V���j@�m���;B9T!~AQ�U9*��Z�25790Vv�"� UCJ�%, Hb � Wein�m� 6�]�3Žl�AB���>B��@2�.� ^�:P6!;�7Z303J!�rw.�n.(�5��7-t]�#~�B._9{e'VgB��?2�9vVQMJB ��r�n�5Z) 256Rqr��P >3 .1&�d�f% % � fil�-es�htex 4 :eaps,prl,�'scriptJo,tw�c umn,�# pacs*DeL%\topmargin 0.0cm \*Webm}290x6ateB�e��0�( \title{Enti*1"� �=oݝA�n�;�">%�# ant��z"We.vmaso R��de} %�er @usc.edu:oeDXzt�of�uic�Asnyomy>{e Sou?E$n CalifornK�Los=e%U,CA 90089-048�fI�<{Paola Verrucchi�v(@fi.infn.it:�\mbox{Ifo Naz`4? la Fi $ dellm/|>, UdRK@enze, Via G. Sansg(|1, I-50019 Sesto F.no (FI), Ital'�\.�f:�S�?mi��ZLi - C.N.R., Sez. di} vi� donn� Piano�� Y5�,Andrea Fubin=>f�;�;�;DbgAno)5�'"�g\`a � 92�� HaasYo��m2�(Valerio Togi����^�����*j:xy�e`ECNuc�Me, ay I@ �� 6� \z9j M)"S(xԤre}M�ᱵ8Monte Carlo dat��,6�e1"b�-��;*�'.#��an&��:. $S{=}1�3>/!( a un��m.�<=R/~l�Y g �kU*du��>�n6-6S5 ��?.�e}5�<*��, at *8�purz21!�\�( du>.�>�)�(GNa#2 Analy���B�8F\�7*i��2���-�u)a novels�%[%�(6olv{?>`� mode&eP;er�NC6d�-. More+�J�%-h�1 �3C^E\o���.!��s$ unambiguo�EB-�a �&cusp �� mum}F@pairwise-to-globa:�km�$ $R$, mark�,�0 �-�EA' enhanc)�of rm�eEte}2���detaiBidi�*�." K@ju�ma��MJ��$R$�Uz7gn�i �uF�behavi�iiEpb{gb.]Z3� a"n \: �{03.67.Mn, 75.10.Jm, 73.43.Nq, 05.30.-d} %   -4o̲spi��A# %/#�ka)tcal"]+d+EPM'� - 2\ �6aM,.a  and manip�� .,m. stud`o.&!x1b many-body}Nsn�an d3A,E�!�res�gj:pr�b�m(o shed newBC^ur����Io9o^9x} i.6�"�Z��d�Quni/��]�e�V�!�es3�:�4;0ir�L@nb�arsqnd.7 k¦untrK8>�Mf"$*9BQ� . Gr�{7D6�c:hen�HaOVw uea dra�gc f�i<6B%>1��u��0*h����2 rigu!��I��~�2O�Jlo�9l02,OsbYN0��0Em�� focu 9a7�/�O Uja+-$Ųch�Q�xi�`b�bnP�% �0 adig)exaA#%] n��� ��W�&�q>8 �$BarouchMD7H O�few%Pies &8Syljuasen03-2D}2��oq/I�a=q1&d�!Y d hi��}�<t�Hh�Lo!VtomBe��tIcb��o&�0�.obD:dAone2^3(1D) �`s�Al�Q]s|�rit�Cfe�_�(Wuetal04}. &uNl�BU""hS8icGame�0is: 3w�[ar8yt[cMW2oewe"mMUB ��0c`6n����quilibr��)�s? ,=�2��.�<�{=}0$ s  �2ins�Gon)i�" prop�Ij�� �6 wave��, m�WAh�mns(i�<�~ D�� s&5��3"�P"� .�k@v"�@E4e7�:2 toolAB�4uT occurr�C�f�t`�be�;ur =����l� �s �� rong)��*��mn . Q�aiL �olet�7C@&� h pe�Yaly^of:�estim��|Jppl��to���y�� �%��Hrar�tme(is,�DP7exhy�s ���=�KmaJhinuS�1�>9 s,  E�4unvei�k.p� unex{?ed-�MB o.O4�@E/:� (2D.�2 ic.IXYZ�-��� "���: F�d {`X�H}}/J =d�JX ij9d} �D[ 5S}^x_i {j}<+ \��_y'y'y' 2(z(z(z(m] - �4i {\bm h}\cdotwS}_i~,��$e.XYZhz} � &RF/: $J{>� A�hn�fg>He "�]�$ rucve)�V ņl�(est neighboE�nd $�h}{��} g\mu�] H}/J=^%�K76�."b:�hs�Bi��3�M�HaW;unBR Tc���A :� S}^{x,y}_!Z0to}({-}1)^{I}5� $ IB$I=1(2)�I$i$ beloa�{Nublatt�@$' UɄ~ �1kA�!� $xy$#?n�=:�ic to fe" ic.��(u=1���N most�Ha"�� �B&N�8 -1/2�< 6�e �u�7H� a�T�F��und�u;��play ax�w[�, wq ll;ef�=y�WY1K_y�$ o�iQz. 2kE�!6�e� a!�%$z$�� , i.e. $a4$h{=}(0,0,h��� �<:zG �Qd+;!]XXZ�!�a fitudi�Zz!�KQn�W��^Cɛs�T e��Wgϡ�S�i9pa�2e �� _��n��ed� �)4,lf`XYX.� g D�� non-T^� .�� ZeemEGieU. H�,Af|(y {\neq} 1$�$ �{� e9!wa �>' B{�3D2� b���a�, I��2c����6EI  � )�t&E%& Chakrab( 96}. EH� ALs9{{<}}1�I> �xEd! Zasy-pl� (EP��d�>yE� (EA)" , r*�� � OYzF� e EP9� ariA?by2zT simme��bre�}D x$($��dir� �2��e$!�nT~(���?�Ter $M^SM^U�D�e&� %k $h�1c}$. �P%�mq,e~-<��i{���I�atroye�M� A~�I� �i�� &��&I=�U�͝` �=/os; �Z` as $h{�S\inft��i�A� �=YVٻd�F 2 in D=1I<�a$ � lyM�DmitrievA}a� �numer� ' Caux#3,+� W�@�8e2� F �7 � $L\ti*�L$ ��q| �[�>*-�SeO E]���.;sim�� e�aa�uW� 0M^I�ed-loop9 gorithm-+"�S02>etcc����low]�y ($Z�ly)q�U�Et� 5 �Cac,Nr�Fsiz| s bi=}, $L{=}28$ a�ry|temWpu��($T/J��/2L$),�1{$� lim�y��e,E$?�dK͍&�[,aa- at�)Nure�~� *���ur2�i�R:� Y?�� 0Y0� {\�ne-��con� �V(I/AL 2JvK a�%!��\�LM2� P�iUNfD�a�4\tau_1{=}4\detvd^{(1)}$����$�`�s��� eBM�Coffmane�0,Amico 4��Le�L ��kc.�zT�$ �e) �m �1{-}4� �L (M^p�})�  {=}x,y,z$!�d��-�  w 9 9} $�5�.��_} �$!C2������ԡ�( invariant -��`?vanish�WM!�%� a ne���xEsu"7O cond�Ju�2��hKf���.5]�-�Woo� s98}.�e�* �6�M�/spi%tes W ��$j$���e��Hest�� abs�CtaF\F� (SSB���wq_]G� �.����f��~�X$ max}\{0,Ci 2)}\u- !"&Z�.5 &=&g Dzz}-{)style\;V1g4�r% xx}- yy}|~,n�� e.C1�^2)^.:+.: - [(o�1}p)zza)$-(M^z)^2]^��2t�9M�%T $Ci# >ImH_i^ {j}�l�S)� SSB1 JA lju\aa se�4Syljuasen03} h�as shown that Eqs.~(\ref{e.C1})- �a2}) remain unchanged if the condition $C_{ij}^{(2)} {<} C_{ij}^{(1)}$ is satisfied, otherwise Eq.~2khprovides an upper bound forsactualzdcurrence. One-tangle and .8 are related byDpCoffman-Kundu-Wootters (CKW)=4jecture~\cite{ /Petal00} $\tau_1{\geq} \2{\equiv}\sum_{j{\neq}i}-L2$, which expresses �0crucial fact %� pair! en �Lment does not exhaus,$e global 2*o)�$system, as6I�can also be stored in $3$-spin cor%+ions, $4R!b$so on. The �IF$n 1.� 0$mJ with $m)/ n$%�mu!�lly exclusive is a unique fea!��.f�aA%m�, ){8puts it at odds |classicEPr�H. In this respect,Q�CKW] 4 is verified, a\emph{2�ratio}MKRoscildeEL4} $RU}2$. Although indir!%%F�!&!\only accessible estimatsmultiI�2BeweE�I�at!�ly impli aimoa.H. \begin{figure} �center} \includegraphics[bbllx=0pt, y=-4 urx=55 y=48 % h%�@=65mm,width=80mm,�� =0]{i��-2D.eps} \null \vskip -1cm \caption{\label� 1} O�ˍi$%�suE�squared A��s *2$munca�A!!y8applied field a&T2D $S{=}1/2$ XYX model)�L $\Delta_y {=} 0.25 �{=}4$�(vanishing u� signAk�oc�#$an exactly�A oriz�state�.leE�spike2Heum criE  point.!�end5�%)s1r.8cm "Qa�Fig.~��fi!~we plot…�e�2$59 2D=0Ś wo values�5#$�^�EPJEA case)54most striking ��ii�Tnon-monotonic behavior]both %iti�(�>�%�}���Lex�� ed to supœ Rum flu�bA@�d2� eā9|he extreme $h{\to}\infty$ limit,!Jobserveiār5istY ia� medi�� triv�%H< $h_{\rm f}$ at�A2,isappears co� tely, si��)�1$�U�!yisUOanA��B� grxE�}�2Di%,r unknK (before. Abo��A�a%6�!��E! �`2$ have a steep recovery,-Kwill �r��assoc!Fdi�!�6m-�, phase trans� . Final!9we6�76�%M��E�any �)���}yY, |1� >}&� 2)}$, so�z" f a��a΍!��e���ng���A orde� E�, nam!Yaf<I !c?wayA/ :  Ese�j ra5"e6��1�� has bee٣� e�� Ref.~\onA1c Kurman 82},�{ 2��� [M� BU:' . � ���rr�D=2, com!u� our QMCI?��$, lead us1I,2D generaliz$!:!b� proofQn%: W� r!KdeR a� $to demonstEa%j�%�s� the E: � Hamil� an E*/$XYZhz}) on��2D biE�te�tic�i ��5� oon �ed elsew��O Verrucchi� 5}, but�'$ out!��� � nt��f ng��For���  otrop�&i�f z$��!F- (an ellypsoiE%�?space� $eqnarray} a Hfrac{h_{x}^2}{(1{+} \y).z)�  &{+}&5yN5?Jz)} ,nonumber\\ >JzBJz)VJ=4 � e.hAU}� � suchE= en $\bm hf�eneksurface%A2� of%�sp�ng���vr�5�$|\Psi\��le� h\bigotimes_{i=1}^{N} |\psi_(� single� 0sP.*�eigen !of $({�8n}_I \cdot \hatS})��  $ be�a�lo��ori�h� on sublaE� $I$.e�+AXafter� c��� `h}&j ({\it 1 ing}Iy)zM��y�.�)�);��Y{=}� c)�reducanergy �sa�i�� $ $\epsilonI-}.�2�/�In%���l a�ue%�Q IJ(0,0,h!r!`� �tak�suB �ion*� K2\sqrt{22�)}$. A�r�strf r�t.m ,p!^)F!�p{=}(\cos \phi_I \sin\theta_I,  1 &�analy8 �ion� $ ]�� 9I�avail��via� soluIxf� q of � ar equE�s.�Z��s�V)� differ�C68 s,i �1%r0a)�2\pi$, L %" ' � $cos^{-1})�6�/2s �dQ8y{�W.{ \pi/�.~{-r� :�2/6�F�>}1$.�����32"�19 �8 u� 68pt�"���77.�Tphdiagr-2DXZh-extended�J� 2} Pt 6a�A�.D !�a�`-� easy-plan� se (>�,left panel) �L.9 axis�8!C, r= 9. �Vs��+ � �m&6 lc}$>{ �| wnumeri��� y� R e@enac���67.W4 a&<"�yY�i�summa�!M22}.1�^��!*dat{5� obtained � �� �����nea$  nWbor. �giv�� best���E�d%$w ��ed��*PiC��   ��F4-"b �s�c# acM thrdDar scal�1| spin)��  length,\xi^{xx}(h{=� ,c}){\sim} L$P�` ��YI! $S_Pq�0 JHL^{\gamma/\nu{-}z}$�� \���u�consist��> .%�6+Dexponent<I1 � n a�verse u , $z� $ $ � .237��(nu{=}0.630$� PPelissettoV02,Chakrab� 96G We@U �$HeisenbergM��l=���%� )hi, !(verge��"(�>) s I�J�J It!o�clA> yet,eP1D��, �6�N t � rAred )�� M:M� �)� � !�se)� s. I6 noo Q�(]��&vz. �*&��!H7t)6�� �b�� to a�K��% wave6M@>� Qlevelq�) coT � betw+ a��Q>scould h?reJ aTa, step toward�g�re� ng�-� 69 � �view}$^�. �N)*M60 M ( NO95.O+e2&1JI 3} E.�3 $R=�:$ a�Az�q�m�-?2- *+=J�=4$).�K%�fe Letcnow mPeisi��"*Aq� [����;!��2+) $R$8,�>valid-6�,�iA{new ins1 m9�B&���"{ vs}*�.�. 2Z3}� s �f� � 2!EP=�� 25$) H AEA�])�3@��a,nounced dip,�foJa cus� hibi�>p5�%�,���{ntu*<enh`!�!�%4 . involvD$n$�N��y !�nsf"2J>*a%�!j�� surpri�ly ��ogoos��M̓P! Q MAVGs�U>� S�)��>�Aquni(al scenario!�2�!~5_��.�We speX! ize ��� !3{�I�se�"-�}�(�� Ps,`um!��/I- ct"��.�isAYaGu" v`#�"]iesM!s  "3  +{=}g_o#zz}s� 1}{4�|xxyy}|$. A/"y $�continu!�v��)"K * o�a�uF�,Ie�Sas wellI &uC��i{st prediV - deriA4!:"�!1�dimen�less �rol� ameter,J4d as $\lambda$�3 | $Q�Y �F inv� gE�). A8 �mEE.8onEyt�agnetas,M�(e.g.} $M^{xS �)x, % )� {�x �� c}^-�(:A$ ()^{\beta� Z U �3��10V~$�r �/$-=�of�G%V5�{<} ��$E� ainsOterm $��al_1}(%?)^2)&r�2%{-}1}$bd�|geo ${+"�i�!4{<,! (�Bi.e.}, a�"�mean-� l )v� ^#an"�!M c  along6,the $z$ axisr=FZ ! z! $8#�be�n���$�a>%O�"i$d���9�  1DIۡ�e.� ��0Niemeijer67} \ aB� �{A�I�n1�!�I�Q )$. O~ e hand��={ (D=$ �))� no5)��=N��e� , �o�$ dis�Minu6 jump � Pfeuty70}!5Q�w�/ pect5 :�<r�com@ak�he���� y�increas�a3r� ,results sugg�5@� aZ�%�1D*ayo�>� T !!Ianav ithi �������v belown�)&F�,)�al_-� �|1*domin� �) power-law.�:�ofrxe �is� �$tiori} tru��E�P ���s ! $.!�Z(!bE,``C !�''q�$8!'�ٓ.0rP+$A� steaFD1Abeither=Kor, ag�+in6�.n��a it m� �/o-� byEͭ a>%�-�"��1ߵ���.�"1�"� yby}!�M+�$c  a���,��,\��� maximum}C "}� M&' a=n�ae "�4*� �g�.� , �+�(d �� J� 2$A��d:)�kb9 � @lators $g^{\alpha }_! $�$h $|i{-}j|8m� qdV$!+rt�"? c`-��OsterloS l02,B:� fairA assum%��� �.VE}�-"�(n.n.).� ��" $  re�*t1�22,�si�p�x,�Fv.Lbuild� up� �~16 �Wa�funda� al ing� �� �, ��)����!� z$Z N�. A=!$T� M� �first.B-� � w.r.t.�rEd!i O,�-� �K�}� M2xi�.-��,�x if a2�i�up��J� M^{za�it"#���ens�j3*&�o oppo2 y��ij -��-orsm��,f N�Y��)Ag�rh n��*!817po�,K ity V](OsborneN02}�&.�'�der_E��OR�(�� �)${-.+e�,�h 1)/( ^2$. �"&� Rv ��:( %�_'%Ai.2�fE�(a~a w .1tha"���j��)! � RE�2~2�( �$)�aj���V� / ѼR2�� R���~�eXat A�,�Ya�FmS�q� ���"� t"� ��A�&�%�q} E�v approac�A��)�] �9����Z�Yy=Jaa�ly�a2�in��.�-�M2onE �a*Q0�'yt�.�a��/h�+��)& "Qic*R/ H&]�1+��s oCe ��&�&$rbitrarily�#ed uni��?;C play7exX/B�� aHn �),y, depen��P'!2\$W4�� ��e��&Ee of mre_3mp1s wR)&�.ur� describ5�:�' (�/e"�'��-�ai� �"�)per� rf��A� �#a� �-l�0pR�� flat2?!!abs1M2Z/@, uld �)�/0�1!es�5�icZ dynam�Ebl!} .%E��]�!P%�-in~%�� *�T�� �sem-s��cha�* byy� : ~ ���te}2],E��2q m� "� -to-k 6�$R��B'A�g�L� argu� seljd� s�a ) 7�0w6�al2�9��'1H6�� � iR'Bo�2>J">. K/is work���,sup�.x+by NSF�rXgrant DMR-0089882 (T.R.AC S.H.),0INFN,M��h MIUR-COFIN2002 (A.F., P.V. V.T.�"d5 thebiblioM5y}{200}Y+m:6 } A.~I �$et al.}, NE�d (London) {\bf 416}, 608 (�)!\\"& T.JZ:Y0 Phys. Rev. A W6V032110Y�B@(chMD71} E.~ :WV~V~ Vt2}, 1075 (1970); {\em ibid.} z3}, 786#1!J�XSyljuasen03-2D} O. F. ~\aa sen, � Lett�32x25�42S@Wuetal04} Nonethe , Wu2� (E�0-ph/0407056) �A�<,z&J��3d � qs\i�#A noma�aYa� &�-2je,���a�7ba1�ir defineYerm��+`*$two-body d�� matrix.�F(" B. K. 20,GQu�P5) T"^3��De BMg7s}, Sp�cer, 1996.�Dmitriev%� 2} D. V. >�J. Exp� .I�Il9�.53R< Caux] 3} J.-S. :YE�i9B e�68A�34431Ep32p: T. 6ZM�a=M�^9a167203^6�e a!S!im6c2�E `i� 4670 �22�C>%0}!p jYm�(61}, 052306�02YAmicoW4} L.~�V9V22304V6�> 98} W.K.~,.��+%^80}, 224��982�%H!\03} O.F.6x.R�A 0603-L6 63 J.~ :�Abica A, �11��3�86�B�#P. :X�par� . ű͓Pe*'&} A. � E. Vicari�p.i3�549%�6�2� Th.  H�{��3�~377�672�"S P. , Annq�(N.Y.) G57�L9F7Iq;>��doc�}�1� �z\^cQ?\[prl,twocolumn,floatfix,�P0pacs]{revtex4)Lusepackage{amssymb} : mathBfonts6�icx6bmg>�title{2R$O�:Q E Wi� Inte�  ��S6AS�.sUXauthor{L.-A. Wu} \affil�? {Che� I�s|,,ory Group, DA�t� � -st�9Q C�>� }In5 E�#Con�, UN!Tof Toronto, 80 St. Geo�( St.,\Ontario, M5S 3H6, Canada� �h M. S. Sar!m!e������>�D.�| Lida�A�Dy� u!E�ElectM/Enginee\ : Sou�nANH0nia, Los Ang , CA 93 �s�s�s.s�)ab�9ct} -vus; dete"4B2� i] �� s���3sC>rst?rmo�.�-b�w�P� compu��]a&: �C i: ne-d��#�;/$�Bb&. S�%� i��� opWDlZ~(26-&h� at a36] meas�5m� r&{?p,se��inN ent "� �.} � ��vBBgbe us5o162�� e@2ber!,neWEary2bis rul&NsymmeX "�%I. IlluA�)exampl� re� ted.�9YB \��${03.67.Mn, L5.Ud,75.10.Pq} \make�h 2i��0�B��Q_meB.ics, �F�u the 2` �1J�i�6among*L6zER"7( I�.6Q,h�=pAgn�D�n&�H! ourc���i��pro!��c!Nid<n:book*"isjT>id�2r� moti�&�Gor��: probM�J$^^0aA�"�76e>�E�)s ��OConnor:01,Arnesen:01Gunlycke:01Wang:01}. Moreover,��i:o�at6<A��aff0)ma�@copicM>per�D(|��"suscepti�)A bulky8id-e-�s FTGhosh:03,Brukner:04a},�?"?#��q4in *�e�E*>"])s.��P��a2� }. A.�1"!disI uishC0u�d�� r� �eJU�-�aIcala�A�nL/B �� -$Terhal:00a 2Bruss:b S Cal}3methodsEv��"Ef)uE�w�� !�� K�propos"�C�Bourennane:04Rahimi:04Stobinska:04}:� ]eaAv�1�/��e!g �Nn9��c�^ �^�^�!nter�wDgd M�I(-ZYk@,Toth:04,Bartlett�7 9c 6�BCa�Our aima��'�Hwo-fold:����>�1'�Xbroad��E�acA}� �R�$iclc;thus g� B�|�xk&�Refs.B�R���K(s^�Eaall.�, sou�h2�IKal� �s e onK!�7 dots��Loss:2S P donmin Si "KA�98Vrij��' Whil&��!�<#-(s$$s drawbackG!it sub-��%%Os�/%"�Oi_!���s�Wtral A�: %�!�U1E" ��<�Q'5�& -�allows 0� �>� M*�1-.�Q��#qubit ́_.MC idea�-!:ED\Nl�N�5z� Ai��}�X ���|07M���2a"8 \textit{*{� V�}.---��im�v� p =���Eex}<ly goverE;by-nI=onal}#Q hang�(�  (&D2�($ $\sigma_i#&} j$�4j%�D$E&4 \in \{x,y,z \�>a8FO\!A�Pauliee�! $i$)-km�,Jg H�I,5-o�,7p� Ú�f-1 �intX5ex-=�u� voki�}eLe,�) previ{(���0 cern�jH-�V �T�"�2 d�J�O"�L they �r�0A�!Q��. H!�we�m�aN. roprLly ��edR�.H�9st�� ��� $N$ B�' coupr!�>>Q 1DA��gAm $H=Ui"UM^,Q+Ae Me\}�2,i+qE ' &M� _{i}Q�. 2�/ }$�/!+ $�2RO=(.8 p}$1 ast $1TH �n)L*� �z`2���K�S!!"s $�$.")conven"( to re-eV $HU,I�� �=arct �  M"- ���%ad{A)��!�EN= _I�A��&  $\y0bf{B}$: $H =-�Fsum&G�E �Z~*}+6  -e=�U}J_1���* } \\ >_ �A �(>�\times<.�+1} ):K(LC L>K)~"+1}) �WA��E==( M�x}�Egmy:zH $=-�A��e�a��an� ��w8O�+ #odic OY*&� (:� N+1}�X:� 1}$)�2�$A� �uU9A}$ (��Dzyalosh� .}��)_B��� Z#��f�.K=�Consi�-� � r��&m#Y iEM�k}p_{k}aX  ^{1}\�N  2...J Na��7- Z=1�-�$ lgeq 0�"5H�[at���$ �$,� eas�*ver�\d &Cs+-�@Mm�UV� A�.� 1�6+ ,>A.? �V+NW �$I� � �\.0F.� .q ^!a�1$,���TCauchy-Schwarz (CS) in�0�$| zi}aazb|E (2\eKj%j )^{1�L��3�aw-�qw J_{xj�x� 5{x:�+J�P _�6y>AyJAzjAz>Az:A-j܁�q NJ$� F� }��<�. �AA��b�two�s.ɗx!��� f�>%�N (xy)=�f���O&� 1sA�E�>2 $, etc. Uqa�7�;W�-&CS.Swe�Rl|�lEMQ!6�6� �f :|!q 6mA�5Gbf{A} ���� Fm�~�N q 2A:}��-(yz%� +(zx 1�i�Io.U = 2A6�);* y!�z_{!�+}AJ +1}+}s ^\e�>_��� nN� ">��8�'�JE��L� 2NAF�Not� atR?&� no�y breaki?]?2<��2� !L^ � >�e�]H�> 3> �%�Y�� �yR� 6 (&.Pfg>�=0:� ��aV�fthird���4ndard Bloch-spj�r� 6dEvid:g? 6Qce�C�: \RD2} (I"s ns .� ~!:-ne�q �T!]$:/ (Nam� � t�+VnA�.� �1CDa| |m�ITM63� �$,�/&J J7A�)(.�X.Z�0>8�q:�� m2��R�-�%A�� 61 2�j�! Y-� H �:S>��TVTq N �Z.����(F�Th3�@>combin�� �N�.� ut} W2���� /(J+2A*� ^��)�z��T��Qe *�,*6}d� den+@o>@ter!]�+�Gs �i s�%� �5�g� $W���@i��7 $W>1�@k1d d. W�lJ_ɧ�J� % nT)� �O��ar�#irCi0�.m a:E8�r6l%�r� ��i�]c.`R.jLYb4 tary5&�)>"K"o,Wu,':03X ppl�[�>; � "�#of9%O)|�t&$$W �&AA} �� 06�cin2J| ,iJMb$of�#�eB�B�j:"jA},� \n� �c0}pB"�cem�E �-)�"kapplic"!Ka wide"�I�&b�&.�$J� )�b|�e1#o n "�A�rf(? %negligYk hY:U ��,r���P�[�IR�=s��#�'>EZ�,-*� *�.�,�"�� �3) $\!�!_R� R"���V \d�j }(ij)������K .$�� # _{j #�t g &��G$ �$H* \{.w=:��sv !?�Wq Hilb sb,a j$ e��e $d$ -�T�%�5hw, �,��,0,1,...,d-1\*^F#&L.��gz�&,be written aWu�,L�+#"E8�AS}&�,=�\,1�ij}{E� {Tr}&�R)�{}^E), "jbv�Su1� 9 Ga$did$ �, �elh%�RQ�f+ta -W-V�ɀ[ �"1U�re�*d� "*cav}) hol�\=mixA(�aGA! $d$.,�O�pi%���es���:d=�^n �z�!���t�Qu2jhe�<nt �7$I�{s a  00M�m>, $ 01b 1f8 168q(} 2 ��2 _{12 62k B9!nk �1�k  �C�#e� 6�di@�a� I�"�(B�p6G&�n& Ry��}9 given>2�)� uo$ $(\fo�; \,i�MM"f*if *]invariIU���@A��� nymt"�rho� Hk2��)re��e>ja/LbIr�+�����cal{R}.�V�-bf{� 6�tib���? l= R}/N�Z���!a��g�'J�irsa�(F . AAv�  b�?"7 m�Zm/i7 e neg2.it�(Vide* 2a},`AtQ$0$ (no2N)U$1$ (�Ka6a?),�; +�l~&:N2AG!Nl )=2\ x�e-\min�� �+u )),!�$bel{negdefb�27�!>�g2X*i4al� p>W� ^{T_{A}}��<��qa>�"?+ =�UyQ ��j��2��REcv 3 ���L�R2���. CaG.S� S� S_F���low�P9;��%$�$�&$)um�LW�nX �IM��"&2 s $2�� u� 3�H�Jn, A�Q%&'N_m)A��lMP {Peres:96,Horodecki:U`Thus,I� Eq.~�DMP),�U�gse� Y�� �v�ha1BV&�(�%=:9$= ic�*!eke 2jec�)�DK,, i"�+\!� �bBO!�G�x&��%� �-. H�'l�\�L�"i�L cW��`a�r s�.�! L ��1�,��W be i�2edI�Uq-Wa�mk*� �� e�`&YL IW�(JF �� ��c���`X���>�, 7Uun���"�, izes� a�=(nq ��>$is�mit�s�a�6�!{)E�1�*Nf���s75�:u . If� ho� NW $�"�Y�-z{Q��-0}}(e_{1},e_{234}2v �)^w eU�}�#i�e.�y .��u"� �F !S2S0@!g���e\n�3 desiGZ"�'�!%�B =)�m8c \R�1$ Z~+ �:inT�!giRo�2G *������%Nawem��T2�YP��%�)�V1itself �aBG 0 qM(s�|ls).� wNn need/*n ��;t5� *�Bto6$Z�$ /ich j9�cor6aond�w"b Btom�Km�:�:Zc-=b�L�y.X.�.:Y"��8 s r�A^to�s=�.a$Qd�4,r05I�3XYZ+ ch�Za�)�.�In �[toH6�;nw�� q %� 95/�>fs,� � � a&�c f�xyT H�x�/ i��N}H_{�U �r,+1.w ::(R9=UFa)U>;cX U^{ �aN*U��> �$Ba$})=\exp (i.�L>  %j �ƹ��� &=&�&�!�^FT%x}�&&t^i%5�"y&�&}�X:&$z} \notagZx�& 5J�%'y.��� x}+ho~&�Hq�?1 �/�P*��/Ms�fV ��(�&�/^�l�=5�m��O��� a larg*!N�A j@s��̀o�}<�k0�a7aF -s obey� L/�ain�Cs [ H6S1.�%Zzo ] � AW��ng��Tsubalgebra $su(2)\oplu"<(2)<&b�A su(4�D�Nng $TIt \pm x \&N#�(%)!�V�>5~$.Q�y}�)$ '8~vf�\pm6�(Bv�( vZr� 6�2z} ����2&!g-l�8A0I�)Db2^!wof"$s% -u +},R �-}, �-4 (��ec�Blyi"coeffixH��6e��y}-�*xA!$hD1 kl98�I�-*"��Dubs��n! bquA�24�)��|!� $E�� 5. n1-5+5+F���0B% !-%)brvef]���B�0 �'D4,,�]2�q9�B]H�$�[c��9 conn�R lo&B` 6�!��"�>yl�Ra"r�{/��amm�Ey�.�{� &c))jFY >� } 2�0.|reads,  �'� E��n�: *7��<�&$� �[aA�,{cccc} a & 0 y \\ b & zz^{ : & cy8d U fm] &dmi����P�i]�� &~t} $ad�1|y|�%ebc z ,��$a,b,c, 10$v!~I��A.*Bo&��Z��HL*,\%�� A$NF��m}$.��7^-�� (a+d-\sK(a-d)�+4\YMz� EZ})/2,�1}� [2) [b+c[b-cF[yN[..[2Br E'"_ %2/�<�~tog�Wr�m!Cit9�I�$",%!Pres>�?Y�^?<&0\R�g(arrow adzE �f r�`�<maginaryt s.p .I, e.g.��"*.b  (p w)Al �a����one*7'aG"�rmi{,h6�.��� Ai"�GGF�f��y, M�"���aF�0�-E�aga +}+ aga-Z��u ��+4��e-:n�-.���F�M�gQ�yQ�F�]�+E�� �V�Similar"D^�ǐ -.�Bin*Vr����b=cM�y$M�� l:�A1c�+8"esE�is&~ Ab� �\*B�\J�But�~ OM�ra#� l6� �c&^I�ch�$oM��-��.um�*�Asu� � oq[� �|� a,d,zc��{3 y?[j�o2�!ͣ" ^�*�*f%5�t+��i5 ��$ �=�z�J>0-�" yx}=h�29T��#D�M�:�fi.�.'Oin�;.] �  $H=J���s*�V�͉ Bqy!�J�ͬ$.}/pL%&t ccyclic�I�M&'9F $SU(2)$ % 6i$Hmmmmu���AXOf�f��)<�FM �"5?�h+xTIb+Y�Jq� �/}�&) ���Ney fureE]'J�4, $y=0$, $z=z^�  ��=1+�6�R^��b=c=1- >6.v>�$ 9 w-&j92"�OC"�R"#(a�D�h�6&��y2})��!.*a B� u/J+1� [#�<�,�5�v*�3�ԉ �?cdJ�J 1fq�s  Usf�m$� U9 6�.�-{6'&^#�M��1�5j)(V1jX =u/(3J)$~�6ORemarkab� ��6A� (upt4a iWA�s efa�G)cisR5!2�5 JN� �ink��x&NM}�~�u"=�WF_GS ). Sv7�lOa9'�2A�&�#6�(��&/$V��I.�uC/�Nity���o!���V+qF� ctsPall�QB�$�5*��f� F�F.� �A�f�ZaFHmz� *�nic� 2�[ )!��.*.��\U��( ik��� t">�}=-�q�7$h=-J �>�a&���"3 �D�!J̕&�):9=-Z�l;�m�m�J�6�z��%=y="@��Z5"$&�Hv �YKfh��� (~I(WBt3. F�L%�W4� J�-�� ��� F �!� ed~E� u Barouch:7giL2c0�n FUm�Q !�* �,6Cw A�k2)�%.U2�d!*Y & ,>2�.t�I' "2@"=-ݍ6�J���*�AD� �� -1)�#�d i�8Rv#���-�=Wj ym�xQBG0�E.1uN�� l����4�E3�We, Uby�Dlas�ineu5]!Q��@�I|Hohȍ:7�EC���3t w"�� in Vba}���B����acx6#��3"&�\s. �Y "� j�͑,"�yiN, m"3j>pr�i *�=A��.#4in�c� e p�in *��1�e��^�A�~ =1/kTIw�- &1� mbda. w $k�a�Boltz-�a���R$T" tem�4uG�a�I�*��!v�}Sex!�"xq@�c��|.�-2�/�G!)'�=�I6 $�ta_c \3x 1.93$( kT_c 0.51$ (in�- �� $J=1=Qis.��bTm��l;�'$0.41$ ��2 TnV}auHn�\Mi�J`2asY`!sm��n�cء"}e�� @!���� r� rived�4B%*�^ SI �� desp(-Úa goody x�XP?�<�som&s ��*:�>^;%r�,I:}[th] \.^f {B�F =0,H =0.32]{f1Ֆ} "��j" !HEtr/fdPt %l?tAu�J�*3be� n cle %.E?�y"�p{12�w2�+ {M�k � I. Luuang}�qem "uCe��-Qu *�m4}} ({Cambridge.�nP(n}�m  , UK, 200�p ��qO"(} {K. M. O' yW�uWӱ}zq�t�rft�s2 �q1!�!�item{rg%C. %,�m BoseI V�r dral6yL�w�q8�q 017901};  mng��ty6H�4* 0423�y 2001CX. �n212313v~mSaguia%: 2qnR9�E5%7327G}g} #p,vFv@enbaum, G. Aeppli)1 S. N�"$ppersmith}" z%/425�48 �6q&a} {C. ,9� eA. Zei�er}, epr)*�-�x10138�4Qf%gN/g {BEw $5o)�-�2� 319)n0!�D�\sA�J. Mat6�w4E� 4237 522_�.gE�(jI �%b92ev879q 4� R. R�g>EF=05175;|"�gEQ8K. W\'odkiewicz5*R*�{%(03"�v56�"Ea2�^.kJ� 60402�*  {G.  AW�s6 �10301(R)E�5) .IB*�g�R. DowA^,AjCherB4*S. !� 6}NX7�w06211N�x0H}�% WD."vDiV�nzoRY5a�$ 120 (1996�wB�cE�E. :�3�y 13�>J; A$&g>$FW6Ae�;06Iݡعs��:8@ W.�� eptu�8O L�s-|9#3nh) b��>Ê�����ɥf�: (a) �>%\$P. Zanardi5Vi1m�30���<2); (b) {U. Glas�{H.�tn andFehsk!WJJye18)6�*�I��V!��d�eSBi��07530��1�~KA| KV89� 82E�42�*}L "�v�.�s2�)4�e!1 097904N�F�e,��& u�Ӓu�P 2504R?{&�B��RxWtg�.J�œ��1 �6�"�8 {\zre��H=7i�4� 19962u2i@�m,A�AgR7r�@5� mM�22! 1�WBn*� {E�w�[��McCoyZEu YW؀�i:ـH.� P.�#^W%sBrinkma; &��M�1�# 1281x~197I��;>�  s+d"�z�>�zt"�z�6�r,p��int�6 s,amxz�z*�z\*�z"sz% IVdB v� files2,d{ }% Align ��#%{ � deci�2�2; bm}% boldC8h�no a��=� �z Cool�&; -l�"�llow.v.�zAlmut B# $^{1,2}$}_ail{a.b@i�(ial.ac.uk} �zPk�) Kn�*$^1<p.kb=Gi![ pe V^Rllo$^3?v $@sa.infn.i�{.yo0Blackett LaboI y, I �, College, Pr�:}N��Roa�L|� SW7 2BW=x�sKingdom�L6n 2$De�[)�Qj�� ematic�T� e'� �t\\. of " , Wi�Mforce � CB3 0WAB�6l|!;Di�Cwto di Fi�~ ``E.�-PCaianiello,'' I.N.F.N"� M.e�it\'aDSalernF| 4100Italyn date{\tod|Q�a"yxI�r�q pa��[Ej,M2��Q,.� 04160]y(a��"�6i�Iĕ&`o�eE�"�2ly8 bichro%� �DK�}@should�ex�red-detu�'� Bc2ka��{ ���B�gRa�onGn�� leakHI<ca:�TwZ$a�4%�l���q-(2,, llH�bY�Xbeptn&!���G/&as  $\�/N==`i�s�1�J�.�?O �1!n7�%<syoz�TziNboriginc�c ��w�mor�= tail�VY�\���x,-a, 42.50.LcA�mak�x\z{I8j } �Oc%K9�r�mi"�v�ofQO1Q emergX$�&��%�un}�T] evol*�4is6�D���&pwŦ�Anderson�s!�U1>���JJR1��eE>BR&H�D.U*\A�=9manife�*� y=9=�U�\aw{��o*����6�GM��)B%pr( much highe�XY�aFageyA҉�ev�mea��f �o]�a��? � taŹ��a�3!�99q �S. Dur!<sA�a!tonH�1 returnsW� �l�to�B�a�houy�rd_!�6xlos�-�)Cp}!m e neD���1 a {\�onfon"�� ZsQ���ex7{��~)[S4!I- �";g�-�ph!6cap�M H5�bƺter" U2i'1zիbe��*� help ��&c�.�dE6?1�%=sU6�#e)l�z6x �aain��F6eQ��'��x;:iWrst�~l��p��"�<#t0� rougEjwh M�t5�Mq���5�[<� eg� 6�co^N ive}��-�]\-�a�bl&F "de-:%�1�W !�c;�6Y�}�Z�Rout�mMT2 �"ond"��U6� As͢2q!E�eV` pla#�i��. "�� Ih7 �va��A�  !fH ag��q �< Kmi��El.��OtEls&feMtir.��s�AWre� `� ,+ �: i��vEU�< stemԁm9�q�B!QH%K��wi���L�TI��fvol�I�F0 � 2 tabp}{cJE��1.8cm]{O�> , \\[-0.2cm]�F c�[�F]{\�!�EB�5�9ya3e�D &uZ�yA��trB�AW:F��dra0�>�% msel!�mn:2nod&�9�)�. $LI��� �� B����a vib >al< !� f��,ency $\nu$ d�" aR� 9 Rabi2>Omega_E��"e �5 �ntR�str˵ $g$. i abelm�)��e6; .� I�e�i ��1m� "�#n�l�)��I!��%5W �Zw(pG��y)E�� �M�PZ1�U�c b~�%Ihir6�g%?���Xlߢ2j���bwg� ed).���9��a=" �1EassembFc��� ri� a �A9'�.�ݰ -\�,+ Ń�L nseqA� SF � �G�t�]ea ���*,. t pK}ly �(ed������c�&ac��]wvul&0, 1,horak0 ,p],,jaksch,el,g�fb���?�Co�$!C�<scheme&X�Z� n�*-. S �Aa�"+dA�Ix�ACBD$E|)ea�ndeӢ�b�tlyE�)$j�s � �� ap����e}$'� {a_� o��t�$a� Mr&1�.���!�M��$E(per��a\3�D���^ w�IL0!���x3A )�QHP %8aIB�a O=�,)���a av<�2lS�.�:����t�om��)+�_�!�͏�1lso�� o � � ���#�n&�8eg�E� !i�5t �@ prim�)/�c"�Q�NcommonF&I4 cold0���w-?���a�% Al6M�\'e״)�i�U:al:��enA)� ed �m�,Nagornye�Z�p��d;**""n��"!ru�%�� ��a�g rify msp�* b��tim��sYew�F�� JX . Aa�a5&��iF\oV a�Q��N"I��:� �S4��u�6$k_3$�f"%=sU�aAab.explicie�! eDcergC��r"�+��d�. ,AJ�,re4A��*�1pi_�� ��5��A���=�5�maA]� aradw;0B e��3��b��"0� est,�%:[ �%�go��tiԟ̟ i_���)re E�AJ�)Y�d.�nu� sSon{��y�{} ��2V� �l�+lVJ}�� ribu.1�� � asBcus�x6����B&u0�� }(a)� ltern�_�a E>o C�VK�� q"�� r�Y,0,�>#,}}�$ �$A��:�z���, �A%m1c �?�BF�N� I2���$!$OHo��n Lamb-DickI-�*-A�(�����;�PLK�-�Bd�o ��2Fw�t��.@���of^-�J,.��%Q ��կZ�oT��L �!�s}��su� , $bA$6jannihi�o&�/���n&�i�Z�i�:?� le $cU$fi�M_It)?$�=_i = � {iie��>1|`7M��i�o �U~ $i$.�{pro^ng ������M? RWA}E�ɸe������)&SJ(-free *�1�rM� be*��SFb� HI0}�W�E!��M \hbar}Ux�,\nu}�/( f���A<��1�^�XEV + ��Bc �HH.cɥ��)HN�X One��*�L t9�FO�2%�� ive mURlb,not} b �\�V(�W/ � �B� [b,b1 ]= 1�,��� V� ;kA�.��GI0}) asb�HIv�i%kz��Y,F�b�� 2�~B� Z�.j"} �*w"� %u�$$b_{\nu,i}?9@6�� I�� �*�� A��e�"�=��ϭx2.d�$Ia^�!�sam� �B=�k>"��el�N`� �� n�f.�!~� �-�M@�F_�2�P�e%�as?i���!E�-�� ba$R ���J� _i,b�a�>�!�u�*WA@ �B2q�a��Ff��indB���_i-�F1�6\,F�AlTghF�Tcl) "0� . +$ e�i '/BA�rhoF�- *�.�F+� �j9Ri>bi�e-5�MX5b����A��pra�u��v��$)�>a,d� *u ho�"MP] ��$� O>F<�6� "�D <jYman !e� �dz#$� )a4th�*[ !�:9$ ��w�6�O.�T ^) �Em &�isturb"�veZ= 0wTo� isF y�?~q��)qs&�1D2�n�s�er���P*�7 "J �]Boson�)ub))su�bosG In���L!�V�&c�&f��V�X"two} �@t�"��Cn=rF�-��n [�/2�)*�"5�!�9��f9de)��Oh- �b)0}�q���A��� �C&P0 �i�)�&�A��on*�&:�A� urn ���)T&s��-iz^ca��|)N.���5��4� �5!T?Q�aG6vN4&:i�$ ;�z5+! �p&��!E1sSa �w � � >erp�])�the<(!nal*3�e-* polari��of Hop0��h , 2�).r q+>" p��a-S��{Z�.�solaW���"� s� ^+ =Ѣ�^+�RN ^-J#-�$ 43 =.9R (|1 : -b-0|keThe&Ӝ$z AM*|�c�P��~ s/f) �SŭuEon ��C�+flJon}��$N$-body��b� su2} [�5+\pm]=*e"� a� ~~ 7^-r ^+] = - 21�3�B�U�-� ��!e�2�m�iYll ]!�!�"|!:� �saOR(� �dofS�O{%icU� �s #Rm�"d�/s�����,. ,Are��,Radcl$ }). �O��'�!"�Rq+, � 2���h��" �6-&.A".���pby $l;n.��v"��" {i��ku? ~*K���2D���T�r$Nt u:�&� � ��y 9uf� col} S^+ u"� :u�mi,K~ S^- 8 �8-A�, aSA���_3 U>�E�$ }�|S^+x� 1+ 2}N$U %y�A+;$ (5S�9!in �� ! )�U�A�� "�6a[�,Sa�a� \pm  �~� S^-,� �u� P &��S�g ���)�q2A��$q��S_3�U�DR(he)-95 (proSzive) ek(or*�-Weyl>�e�\\c+�Wig�#V&u6SUV�!jc$famC��1�Y �" ons lg�����q ��no `�er��� I�1������q�H:Bg�*a�  ���&q}md���V ith 1��MK t\0&� 6#pe�8A&��p"aE�Ius�5 >�=8� �:5 IX�"��)fB4�3�� In wordM�lad� ���� ly-s�*r(�� "a�jXXX"!��� x�!S^+b + �h,���)J��+we�"i}A9e"QEm���dx��.��b`� ��qu�s�gN} h��o&�Oon�u�:��� a�mai/'>� "z� $x� y���,�� �k���thum�p 2$�B� �yu@*�Ij2� E]>4*� $*�:z&�Xjar�gf11}:- g2B)gb? hap�˽Z�&%�)T"��a~.�.�b��$���MVr:�deBf� �. d.��& P�-a� ht���aaa} An�fac�E��ViT#s 6�M�R"� �^"[&A�!3�O�� } or ,ambivalent} �����87Q��x �f�E/G�%�)/c���6Z 1��.��� +Nm�"���<*�O9�^�v�B��%t3� �en�K.�s�U�?2���(��)7�2i� ):t�!3id-st�� ���O8z5uI4*}3���w�mxg,3�3*�i 2z!Az�3�ecavity, the inverse transformation, photons to phonons, is also possible in principle. In such a situa H(interesting 8ference and coh Teffects arise, which w&�aalyze below in detail. Indeed, a closer look at Eq.~(\ref{XXX}) reveals that the Hamiltonian for! cool�4of common vibr% �Lal modes can alternatively be written as \begin{eqnarray} \label{YYY} H_{\rm ]�} &=& \hbar z \, S^+a + {\rm H.c.} \endI with ^_la} z \equiv \sqrt{x^2 + y^2}^, ~~ a"${1 \over z (xb+c)%� and} 8[a,a^\dagger]=1J. ~~ :�Instead!9%�ac%��%YM>W EUpseparately, the particles see6boson%w Jannihil%�\ operator $a$ and numberb*deaf} � a ==-/\big[ !C \, b1 %'^2 \, cc!<x)k_3:]> ! B� /)�cNb ^ \, .>O Physicalli� cre-f)5,s correspondA� to $�@$ does not only aex%s1Ef!�non)��$2%�in@ system. Inevitab�it �%�esa�u�betwee < $b$ !�A$c$ subOThiƑ($k_3$ provia�Xa ``symmetric" channel q�Ip-p�� energy:� . However� leakageA� /outsidI��- perturbs���:qbalanc!ydue!}��aon. Th1: rea��by�Xequent adjustments, tryMto rece�its lost k$e. Crucial%su��re-F me!%ism���dif��-�(time scales �%Z�h�(he quasi-stEy ary  e]of`(order $1/N$��l)K:TA�Ltaneous decay is, as��� �next Sec�Pof^��N}$�\s #{Coll v��}���� !��evoluts�I� turnsA"!oXbe highly non-linear si��3econdE�'��%deriv�Ds ^ pm� observab�are m!�$larger thae=ir first) O)� �%�e�Z� on a� %� � V)� P" "iA� cal ��4librium is sol�gA�nedA�!�� ;e .}$H� %| $. Let us5refore �cona�!e s&\w�"A.can neg!� .Vemissi�Lnd $\kappa \approx 0��$\Gamm. . \��AEoAPn%�E lawsQ�abs� of dhp#UQ low}� t!1ca�!n^, := ./(�N ), result�(a redistribU� popu�/ .v�Xic�o��( described !��+a) ���.$by $S^+S^-A%o a� I �procesa� introduc��F-  L_1 &�0& {\textstyle�� 2}} (S^+ - S^- ��)�,, \noͬ\\ L_2P-6R{\rm i} X-:X \,FX3Xv��� a )>�wit( a�A8,�j�simply g�aIro � aroundA�( 1-axis. In��Pn algebraic picture, �%immediz �Vclu��at� $angular mo�}um $L_1u totalB%B� 1�0comp} {\under� L}^2� L_1� L_2 3Z .�" r]A\+y ae� 1 + �=biF� ���~ erved durn� �!� <ideredGdi�Ds. Espe�0 �'�� of $>7$ Aie�60t)�m�of ��sP accountedA_��t*"L �� +. $. Wh� 2f*� � exci` l$|1 \rangle_i$ remains smalla�pa!�  ��i� re��s�� e2}) holdg M��Nwe��assum�_a� expecm* valu�� �*� LN} \sum_i \sigma_i^+ -$ 2�. N�bA N$!E"oE�)1�jns0a�ㅷd�� t���A�= 0R�Us�!JdefinEh-@a�-�]66law l�] intor���aG(�,&� AV&� c - xy0,@)�,>)coinc �>%�16)!�Ref.~\A�{�}| �s�� continualA 2� �laS2 g the NS� ��eV9i�6A"[� �!��$. To show� t ���%})&�vio!�<�Aof�j�setup,a@A�rk k� obey�� 2_law. Co� Awaga�(Heisenberg �{w'� findbd��gy�f(6W]P) =R�R\��Ao - 2 z��A�.>xI� e pre"� many� ,I�m������!"in!� ir g鹥'f]Z ���_!��;� igt� is�d $�� jF �=� ,)�o��� $L_2 i>note2}�tser��D into]�-�)ELobtQ 1 Q�� U�lawbAk2��m22�>SB�Despit�!�a "�B��Mq�$cts like a*o -�allow�i���aW){r�oPAB0:� I ll!= $2�. $��&�����cor&ly!�$ fo�ing%�study!�* �����E#s7� ,a  zero9] �i�re� \subyQRgs"a fastbe.�N)�-�" fter a ve� hort� ae�io*��j!~ tantF�s[ .� $, $��G   . To calc�eE6��6^qQ�v5� WAa fun*��-� 7%�use�� ��&. ]}���;tial equ� f�secV�� ("�^�]�)+ ��62K:6:�� �Zq=�q��qq�� �� ��� 2���) - z�,ANThese�)��"a� *0N s��" �Bch��� � �a� er t�i��n �Fr .n $, Zo$ takes pla,S�Zre�ested �kdepend��ZmK2~�a�n saf>� ^~.�I� R�])�YN�� .< ]�)��f:e� dv �dap�iabatt��! ��c�U. Set)��right h�J��.?]�� �-)�U��2��r9 m} .�� �0�]=@�%$� � 5 2x)D �6�Nr Moref,* m&,.�:��laws �})�-cons2Q �b& Wednesda�1 ) =R" �%I2A!Z&�jm ��^��meaZhat, �� �~.�!Id ��^��� n��.� V� A��O�%�*H � i� ��u^ &�C>��J>� a �good �i� t���s"TA/� throughou whol(��:` C �ƪM at � >{ of �) �occur� !)�h )"� ��N�**;�q�EV� mirrors���a�e �$ "� de: s�B{A�aC Y �# bur � �&z� .��vip&g �b havet1 uMacD��2 "� � B� �^� brmultipl �U� b$qp�e:nrbn|ݮ\ Vria- B 6B� []U��"�k\,:RU] + {6z[6Uf�A��JE���.2  &&>���APat!�Ay � D &?  in, nam .*. $1&� , both�� J/y.{a? +d=� , ��.# ��iv� �neluKI��&��f^Iw� �� &} s2Ax�?i�b� oooVJ�F� A�� y^4���4%�>� If $m$ de�!�:0.�)k $\l�2�� \rho9 $m_0=m(0� w� n�-b}} m��m_�$\exp \Big[m�f�t(I�>�E�"�one�"nM� atom! am��P  a �� �bem�as $\v( N} g �}� D\eta \Omega$ (cf.~��par}))<Q|Mmy})&�1917A�V�#nG gree� �an exact�]er� �""8!ale�^$$(see Fig.~��num}(a�Spont�$"y"� )[ leva�%[���"$�too s�*t4n�!N� � �i�,x$� -��s6 ��"� ��!$.#gg #�8t*figure}Tminipage}{\columnwidthce�+,} \resizebox6({!}{\�0}{\i�graphics!W.eps}} +SLvspace*{-0.5cm} \cap�"� j�+ ��ed)�ajn� (solid �E�c� i�*2 !�(}) (dashed 0 $g=10^{-3���a!i =5 \cdot (�� ��(N?6mk�i 10^3$ (a)�� of�} ivid�q 0 s,��~ed21� BW"��%�t&�� { ton � �!�6\tilde�0=!09$ (b)."'a��U� Q�2u Similaritl :%cFS(a3pha�$:/rAF��V �.]m� ���� �&is  s� yB\!`)�ὁ�/�+R/(t� �b��-environ�*1 0A���3'Mj���d$6�. .�� �&a+��Y(�� ressP( Eqs.�/�};}co;�+BL otherwise��"quant%��e>�/ wrong} Q �&�#�!.r#��BSQ'>62�" +T.M ^s coupt� .�cau; 0 a {\em dynam��.se}��4I).e%Yϱ&�%ɯa fixedAio.�F�:�m})�Jto] Qn"_2A�U�ɨ �� �<-M���-h0^�Q,� F�� , usu� domina�#by.��. "4. �A�> m�$is primari�&� �}b�R+�R m}$,�! driv� �i�^ cha�1eK3"�+��%Y� $Qm�Q'�in a �B��-� Hnce!�;�k+ ��%os2- Z ,. U,�$&g.�zM�A-A��"ously �new� ��&^�S� �P� jl�`Q\��!�J� QBE{��Q'�`'RRWh�/rex&;!]�( `3� .� ��II4*H, {��$ �J��ect to 5AU��� �Ain�� tant�Wir sum6�' V �,=�A�re�ex"� lye�ime*� .�*�"�v� ���a'~ s typ�}�aQ�9 go��a >B�"x.N�0in:� %5& ind}�0re?0�#s2�0�ces"������(�nv+:B�j ="� . FoQX , on" n"�if�2�.0_ }$ u"�'*� lowe�%? $S$Ewe di�� � X86�3r�2still a�1 �3I+L)/��)�%`t�5ehWlyE�same way��*?$�*�6/vector&�B�2N, S^\p , vV-{}i i\{&�)\pmj\&82`b}"�bi9b** 8D .�+c_ �8-{ �\B�8Al��#ar duct,�*t%aBeM:�= .�b}�F5�7>+!�J7Hn"�.l�$�2o :!�6�IyH})n!:XA�  3E�\!:�%( �2� S}^+'>�+ �Z.2c},.y:E)uZ|*ie��;( !�m��a).20q��9 }$ iF��62o�7o�5 e� aaa}D , �q-�<n &�b:_i$� �u� $i�FJaA�I�U+'; (xA + yc)�2HaA�.�La} ~a!rm��e<[a_i,"^�`;T� >^IVE7)���<Y^h�<\un�0{Y^:� 21K"> Eac=k� e�Ѷ�# � typH �/� t0$a superpoZ�JAt� "�|�.�|ek��pA7�I�� r $E"equalzma}1�ir>*W/H<�o"H<6�jLb}Af�$2�cn5a� :�� 2 2bnb}45un t JY � ��S " eF21.�.�B\c�\N. $. A. _5a�"�b.cer6,"�<y''"�7I�fi�2� a�*t�/con*�*!�twoeu��m�! )� &�*C��8 .&2., i.e.~� a�)*�96F�9,�& .m.�6 rE�c-(.Y�J�b}? i� 6?�S2�b}�\�{(-Jg~N�8�/2�Y�J�c:�NS2AZ�c����U2� ����&=&��9�!:O( :�JwJ =wl g� BgJ?� . . J�I� ��K>L/a�.+a �ec� �( ��5� b_j� $�$$i \neq j$r`mno�Oe~iAB@"3 e�����&@#. F�$~ i�V{ C s� b->,��c��ed.�6� �F�Q�; &:)�B�.PYR�A-��m7,ROy O2c}" -*6�A�V�:�$Q'�3��7 �� ���>4 On�assoc�;d* A(��&ŵ�;"2F, R F� �Igw"% _"1 &�1��� ��B8!^�Glee���"N�u#�C�*� B7e(!%�AO, ival.��%P:?@3 �Y po�"d�Bm0prJ.%!Bm�, 5%had? e=%*�5&<]� ~V M��� ��*e�� 2�is would�.b��A if  !�$a_���ut� MAB ���"RGap�>c :F ^�3�8" 3%�2�Ahi4,6O B�4-)z builds up&�B V� weF *3d�n�o�5�Q=�~% $, ~20>.( c}Ř? �J�3. *�<a� %S& C ;�! \as%e"$>2�&�.� S}^-�eSbsecZr � q�4VKJ_b}),@ - {2)4N��VF �h: - {�3?�a.�R� ��>�:��2�z.�><:��2< ��k_3=My6� big(2y*)R2�b�Z� /:{- {&()� �~MBMu2E�:u2�. � .^2�� tak� �I= B5 �1Z ��)q=�@d&�F� oqFx � �[�� poss��a~2Q+%bCm2} &F&( ~=N�*.�=�F�A�~~%�N"3�L2IΎ.6�(ڽ2RM�|}} �VqI� tras�%�*�HS���6}y is Eu!� �"1��_�N"�ly +C&� � GE���-c~%} �>2 �AM� � *\<Y ! oL&�8."� a ne~+>���: of magnitiFas6�Dz$��+s a"r�+��!uf92toщ1�#�!8f�-W$6�:�N:3A@�K)2&�re"�21�)th-�&�2vi�&io��eRh2����i�N" m6�2���2 ��b��3�� Z��v:7� e�zF:���R1��&3.iz�6�vG2�R:J��6�3n�2tc}��3:�36�= J���S*� 2�gIQ:�JR(U6? �(4^8mp�IbOnowZ" F�2�zEI~�2 JN;� .�2�1�v2\:�Y�R�)�] >*�%3���k "%3>�AZready A*ioC abov��B��U�Z"�9F��o"H�%�)��\V,$}"ss2� 2� >l:�T&R�ўs.6 .�� ����U��+].�z>�@,�/"��F2} l-s ^�2K:�*�2J*�"�-)�_0(8w">A2� *�$v %'V� z+$�;q $t �t=0$, �&�<. A]�s"v Q�R�0*%3=�/!i��� *�-N$ �0/ )U6�3�3\N}$� k%l*�G�&F �'L=H*EY� soZ'#Ece�9-%� �{�e�;%2< {zI.�nx4$se, achiev��XXW5b!=�K1soz}[> V3em�Ou&=�B"5=343of�/ ason���4>x1]��existQ�&/ �'laser �+$ing. SuppoV-DEi`FG�).M8 &��9th)mo��al de�4EEfreedom!n�"o~�@0B�+� )).*�A!-� d"!!<�0 in�)s� G(d,,( <Z:6.8))�8%�K!-�(is far away��Z�X|�' �J�*onc�uAits�C�0� *�(Qu͘mmgi�">-needs!�lon�Y�A establi24;�Q�$ hasA��D�+g!bf6�-)-. �` �)*%5 so�(7�[F6'7b)H([ cluQK83N>emerg�=Y�0�]"I+e�e�w��"manifes!Y tsel5��8macroscopic fea��/QWbehavior��an"{(����qoblem��a� e"�Q�n�embly$N$�- 8&� trappE�f a y op�FH . R�;��u� firm thosKB#9�v�*e�T,by red-detu� �� fields. " UFFall��!&x�co"�,1d-��,-4�F�&m:F�-1� F� �g3C�!�co��.�� !�Os�icre_I+)/ J stepHD,E���de-%T% �=es�V2>!6EA� perie a�� st�49��=�tw � � =8_We�@:��! 9shaj-[!e� �A��8B.q�$OY) twN�4�J�.Vin&?Z�=BM.��is) i��U6�F�U'2> �2�, h� �tE�A�:1> :�A= ��F�i?���� ��upJ�>v>� ��^4�I2c�x�_�c}�!MS ton*� ��Q�K�G;5-cOnly w+ ��X�� �Jg�4�0D�Q &52Q��a'W�JE mE��� �fI#!noQf ``pre-M�" 02�e2� !d:`IW&�0}ޅ�,is paper ma�haa�adZtic��Y3:!�ic��\ "�b8 AN�/as-[s ��2�in�5 �&h8s, yet� �9A�G QJif.�&�\ir&�7. S�1e7��+  ay�� � =�j���bio�..�$Acknowledg��K rk w�� rQin!=t�;!�0European UnMkdCOSLAB (ESF Program), INFNM�!< UK Engine�2A��g Sc��s��Tearch Council. A.B. a��iuh� Ja�_Ellis�*tyIFe�0&D 0Royal Society���4GCHQ. %\bibli�phy{aps-B"�?the. }{00Xibitem{Anderson} P. W. , ��0Tbf 177}, (1972) 393. %R- EaL} A. Beige, P. L. Kn�"(* G. V�;lloQem ��4�}s�� },8 0nt-ph/04041602rPdiedrich} D. J. Winel!�PH. Dehmelt, Bull. Am.%�.!D.�bf 20}�5) 6372_`lewen} J. I. Cirac, M. LsteZFj P. ZD r, _Rev_A51`95) 1656� mori+b G. M ,�EschnM\C.�Keitel._�ete885} (2000) 44582��L !��L,, R. Kosloff)�)?T�5r�ChBjA�d106 �7) 14352e4vuletic0} V. V {\'c�\S. Chuf�4�3786�horak0}A�H % H. Ritsch.S-�A63 N1) 023606�gaYXer} S.A�G  , K.!� Gher2ndv�63}, 051` .- 1> ,�W! an)s(A. T. BlackR�-� 33406p%�6O222�pet! P. Domoko� =hJ. Opti8aG-nBe= 2003) 1096yb�Ew�H�^H�o)60. 2�9aF i2030012�196�vapor;J} Me�J.a� Ensh�M Matthews,�E��emQXEE� Cornell>�269iƁ�:� cold��hys���=20� 0123:]M�} )�CE�2�aX����)� 0630:k-�} .� >o^�^^15BmPLK} C.!l Gerr�z6��AInTitory Q�Buma7 o � I8s $t \ll 1/ \nu� �haR�o��  m2� s�|0vertheless, c�"c�)�� bLmm�R&� than!�ly.�m8os2Ebarnett�� M. B EP��Radea� em MethodTheor��alJ�$larendon P�D8 (Oxford, 1997)2�hop�}1J� 2�{t<122}, 1555 (1958VH2E� Hutt�mJ�Bau�?g�qS� �,� e�Le&1��1)� 6�Dicke} R�u F�9��99�46�$Arecchi} F�� ,��CourteG R. Gil)|a�H� omas.k!� bf A �_ 2216�Radcl�%a� ���G��1971) 316WigE� \"on\"u�E.A) , c�Bt. Acad. . US a3�G53) 516� � �4De�d cinid2 Nuc:%1-�76�&2^SUV�N. ShahQUmezawaI 2\% � ItB1�R$1974) 47242]jO 2} A�ha�vc\'{{� 62�ma�U"h) �)I�c�.]}Ja�n)&��T $k_1�> S^+BKU�k_2 &�wBJU���xZst���our� �iZ�r�p cRe� at��$:%�BEQ�)d)�#Y 2#Y�t:� �w docu� } Ѧ\class{8}% \u�wc� {amssymb}>fon:+maN@geometry6A�fnt6t�m6Nx�set�1�er{MaxMatrixCols}{30} %TCIDATA{OutputFi�y=!hx2.dll"Verv,=4.10.0.2363@CSTFile=40 LaTeX -.cncgC�A@=Sunday, May 02, � 17:21:55W4LastRevised=Tu�\, Dece�d 14:2:13:26:0Z2D-�Shell3Standard �\6 A�y2VLoage=A� an��} \new-�5�{�� m}[sa�on]2'a&�E�[ @]*x 67(lgorithm}{A Zbxio'V#}zCas�P�claim."2�co�.(>-o6, >+je�p6,:-$rollary}{C Z�riJo2�2V&Lm�Defam�(i� body�{\upshap:G�CFE�C} 6rexercis6* 2�lemma}{LV��CvNo���p�DP :�pro�@6-�-�.�HrkFRem:r�)So�6, summAycS %S*AN�@of}[1][Proof]{\no�nt: \bf{#1.} }{\ \rule{0.5em} } \��,{left=3.2cm,�00=2.70cm,top=1 bottom #�.�$\title{Est` pur�zb{on cir9~<} \author{SamuelBraun=\� ks{ Dy~[{KComputerr W,.& 4of York, \ HesF t� YO10 5DD1,Kingdom; sch4@cs.york.ac.uk�@nd Sibasish Ghosh���; s JZgmJ!S iniVhMatheZac�V�s�5o � ss54@�} \make%� J& abst<} Gis~PPopescu [PRL, 83, 432� 99)]� -ahan�8 abou�uir dir�^� "fF<�iWL anti� allel spi)" *pa.%.�� m�( p`(  all�o .�E� sPa�!$��$e Bloch spO.!y argu( �n�d&c~�c�0dimen�al�sp$"��T(wo alphabet���� � ./"�.,q_� L-!P�%��o"+R�"e�152�8�� �U#b�Z:�A�u�-��� �b�E#*�6 2@fYxoL�ai�L:�]Zeneral.Zc :O�� C"ng�!6RLM� B�*a!E-eQA�dri�?!`%Z -Zte�s�0!��of) 9^x�, ;Y�al .x� b!o|y�sA=A ��|N-M|uI �&.T>�3A.�A>�6<�"mal POVM* x�= ing u%:�i3seJu%alway�2�<L# termE��Fourier �� . Ouzw�^�|t9*iGa�hn�N expl� Mg �e��A;��.� comblTof)paV$o�!��.+e(ad+ �$�&�$ LOCCy&tocolII -= 1W^B���s Es Ms��^7�!up�/dV�Ma� \t�of-%s�Y��{"�� $L��Tum worl.��)"�hen�{a�g�8!���ona8 beyoEge intu�Y sugg�l� �Qe2�P im�8ibi�P� @ai-flipp��} 0g�p� 99}, ,etc.}� ua|cu�)�� lastA�ce�V pi��gre�g*�aE�2V2$P'isU�%na�P$ (or a mix�'>pro� in 's)a $2$-�� bert�� $\�cal{HK��-a�v ion\W��n�liѷq\  $|\psi\�T\in.^,�Ӏ�!e .1^{\perp}^9o5��$2e $, i� lled-�!g5��'O�,A��#s iZ,d"* a/�a PR!=6i �3= If a given} ��q�M-ve y�OU|%��!�|� Jc�(�E,�) Eucl�ʹ�<�s}+�a��is(S! ��)YP��2��g��w���.�V ��(!:��%NM�:N�s>u�)VF}�/63 ) if�":��:W���F�j6I\oK.�$��2n.%:� Atn��d*� o�>pS ��29 ��� ɚ]#scenario%9 �,*� b*�f�O!n2d��,�'c!�e��f�I M Fy M�6 � e!�y I�cer���62h�L.���$�;Er .r�� .. Noti�ata�2 w!OɊle�%eac2�6�X&�Db�CZ�se&�)N1Ft�5� ���n��36�95�cAU.�M�6�w�Z:�._zA entirel�`��va�m���-n4.d���reA�i zE ingu|/��!B 1#x ��/be5�V<29��B�) �e E2� T� N��.6|1!,�4w"g�]GA�eVp�F�A�� F�Z6y� F� )�.� er!B2w%IAhighe���("�{ qu=�42ri,n�/@:p3o �[i��5 .oZ�G_bit�qo���U�andR�? C��ii g izF3)�s?T  us illu %Xsit�xo @�=s�,!�&� 2 �e$0%-7 (� necessp`F ) yJA}$ �Y>��0��� ��)�M$|bL5 |u�A}.�|$#OZx�6N. It h� a�at+$on-trivialJ�=satisfi���� �5iŭ�'ular,�&�6sh8JbA��orm2$.�= :c$�Gr� lAd !#%2, =0$.  M!ra�d�anIMq :�(ch!��Yy*��$\{.X>l6�:.+$5�n �I�e�$\9nd~\B �O6]!�^]9&� A�a|9�B�re�"e � c�uat'0b�% .�|�d^. �-�,�n{A�6� $,! �Hs�Iau%^?�� blem%�be���ht�+� m��.A�.�` $f_{i}:5>H}\_{arrow^{M n}$,E( $i=1,2,...�p e one-to-H mapsMs�^6� i�e$�;of} H}% 2n�A� �$y E �5st am�OGR�&#6�EDn:Au�,U <�� � a�e ori}%�a����>�~on2�$?a% �'s�Z said�~} C�an enco�1 .�Y��No� a:�P� K. Bagbu�jc�b02� discusAR�1p�A�si�9ng ��;6��� �(.?)%YP igelzt�$ a�ū*ʒ:g%s*A (�/A�d"��.p$�Wh&6.��Funia�5� >�m#cYC;S ys5h2lj�Ypla�'y�0al role;�6� t ma s (in �:to"� ]�)���"�A��"2 ��7'he^sV�`bigskip"1�p�1L�"�EI�alb�"$j �xe�� .Z uV=�"�&L���J:>%�2�./�����3 rime[)m�H�d��Rs6U�쭱>H$e!���c"B��3/�~� �Ze�pB�k^2�z Fzlie on{ *� �s (� yd)�B�6motI�on�2ind�choC%dis�/? F5�fA�, Q��aA�ush|� �8�oiz�of2* s ev9youg�i*O 6?�E�).O}�2CM2..&!i*��9"[)�Ff!�2�, an ^�s�us�&framewCyNkE0� -� � ��͜��do���E clu*ug0g b�<2Au�al2 E@��J��,)�O�as�;.1������. c �l�?siBQH ly w�K��6F_�$N$q�V� m�� )�N�4 T!�E�Mh� �Rn�{Eb:O'(N-n)� ] aken�eOb�bJŚVRd"�|H�/A��A���@|N-2n|��We�N��&D �6!N�2:$Sw���?yF�>f.�)|r��igE�6sE� !^2Ga�.�a�} � "�� s $S ISE�>q �40n�)� �QS.*� 5"�!�2&U�r�Ne� aM%!V� type�Qu�F=,^�w�=!�x���!� $F(S,9 {zpmaximum~Z �3Ax>G�a-{!z,a�� �/a�eond min{*ُ>� oV�e��e;%/.�.� H�{ �m$F^{\max}(S߇in 2�a�� ��Zg >�:�t���% a s\geq >erp } ��R �$�l�� ���E��)� dia<+�3B'F��6�S� lsm_INA`R �=� �i|"I4�and"�.g.},�d});�A�b[� ind,�e�ar��!�measur�i!�d74 1�on �gyauld�*Fo2I!T=:4A�ref�/� /rc!.KVfa�mwe&�PF�a7j���e8$!;Qu6�Quly&�����p, "im.!� ��Z %BI"(m�Ne�� )�j$(N+1)286�"%�' y $n�{�,N-1\� 2utru�^\� �i: n�2��vay:[�U ��-,V �K��etwo*LCu�)��E�j� �b`ed "qE��AiLY�~ �is.y ]n iznfVn, ��Ro��[;#��-�)i-`.� ��%A�2�� th�!��sXK*r,&,�A� "� & �$�|.g.�|Ǥ���iE�&�Q�6h.�AQ�����e.����7F x�V2 �(�uJ way �,quotedbl�,�(2Q\�!cHaaB&���P$6�a}MT �ionK"��"p��organFaa��`"O2�2orm=���ofK$=�����- jR3R sketGU63dw976�43 tack٧�|>w 2!3./!�VG���5a�� >�VU )� mFIp��!?6zn ]�'tIn1E 5!2� ' !u&[ >��I�J�> 6��T�u#/a>22mR�^�8y�% y J 2N6R !���A�"�^ .=!�NheiM6�.c5DV�%C .%!V] $2�7�f�)�X��l>� 6�5)\��\�< 58( \theta,\phi\��) � $ ($ &2qi"�#�~� �L1;͔�=8dev���Id��ope>=�z%"���� A���-}�)&gpF���)�uO!an�)m�=�'P>7a&:jHi*(*=H}\congbb{C}^{d; l$A$� a?��K2->LWNn�*)�let $S=o_{\-ѳ: \in A\}ٛteq%1t�(2w*uR%4�N���J&�:say�e�I�>�|SE�h>,"� =\� {i=1%AsQ]� Mg�" _{1,eE_{2...d\�a.t�hr.� �3$%��)%s$6� 1}},62}}j. _{d}�r�0�Yx4R.>$6� �)��$}|^{2}% =1n#u��a^`wa�<gX36 .r$an unknown)؍�_{x5 in �O��chosen�#@�x�-,A 5���%'-�\J.� ơ_coe�R�Qps�b1�x!�% .�x-��*&�per�-*� �jeF)$*i�4�Vscrip�AA�al.X�Ga #]�jPnx ve Oc+or Valv3M&,} (�0) � alis]Wi���d2� �b\Lambda6��h >hite). A 1}TM}=\{\widehat{E}_{r}:r a\}$B����8ve B!?:P% �H $fMRm=��X6�=I}_�tm�Al"f#��!�ide��y �e 2)I�}�"�$r$-th ]m outЬ&�dn`�#M�}|�)yR"}ĉ��M_m&p��.is $(zh$^{\dagger}:���?�.,)^{-\frac{1}� ^1 /$"�K 2�� �ds :�)&1�p�7�pu�{e[\I�E�"�XB<e> s�#Ѫ&:�f�M A&�al,y� %s!�a�or�WDav&! dav}Yel YFM}"C]�� �of rank��)� ["��#s�0jno�La0 �  fullJv��FeVc �cj! jh�*-O&�aY0 R~SD�i;F!�ly �2�ZN ) an�<>eNj &� Er%Qm)�wdvU�$n�*p �"��T�(!m Now,� A^{\ 2��UN�  c�$.� _{n��|\P��$Y% q_ ���* *�&dn �V >�2@�=EO�&s a bik3ve&4� $f:A:8&�v�*%� &� "� } $(� M},T)$�ko~$of:"<Riz+@ ��:�#2�,2�F % : ; ]}d;tyazr%�$THrhoFK"� � GE�� "? I��\ �PA�.�m��+tv%6t�9ɀ$V]Q[AKE�$ͺ,��*r5t.%pre�-�%� $��+�s�&u  -�./tate}�� �.� ��ny�;NF��MZaverag"�{ y� is-'by% \[ �^{(Vq)}:� \limits_2��|Ps��:�B�z�MG. \] T "�)M fide>8F'to ���!Eb f^{-1}(:�)1M�6� 2% F4|�j. _ A ? ��t� �1����; ���I�b*�{uw$yF�{F}:e:=\int5�:&a,�w% 5�rZ~&"� )i-(F' dB, \�e0' ;6"� }�Z�F6%�"� %m�F.� n, &�h+O7=��� j $��y%�A��KV���!su���5`B�!�rp�/�� � N}uJ�.5�1�6�I��01K%e�/e��R�>E% )I�����, a $[0,1]$-v�p>me5�1�2�M},M:[ s�E,�d/�!s2�r,:@�"n&�:th�zscore}�؈!�Nnsaf w�stA�6 � >�ܪ�lso�a n$if�,z 6�% N�.$i)_$Tم pend"�&�)$s�"ū�_{s�Q"ţp*M}}.+2Hs).�c�@ task!C�?!��-$.9d�op�ermine��߱��dX �S��is >ity%���>� {F�$"�!��)' N���A�-*]Howq�} {*d$"� L}(A)� A�a�6� ] �&$A-��3��i�:k1...,N�b�) o>�V.z% (� )� �,atn2A7!�� 6�:5%�w^'� t<�� &��$!;�y ��i. 1L� in"�<�HA �<� (re%Gi5&<� ort� ���:r�I�$InK">8 F0�,ma{L}1W,�%Xget2U�U�%�:�B�v$ $ if�!:�$ h&X`>h�*�F�f`.�a)�>�a&b0v�3�Ab� 9�.2b !�EAHbG��  r�6�&b�(a�9�!�6r;��� s} b��� a(�0oP��2^>��W�p�2n � 6�:=���%5�# $*� c%c>�=C�P�[ i�[Nl _{irQ0�"\�] _Y!d�!�etraints&Lenume�n}�[A.] $�>0�G � 2�[B.� �|2��=1.6% 6J�� n �:h��ҳ � !k�In2�Y�a ��;if"� tab�9,} [c]{lll}% �"6 =�}%:2�' NE �%�"| F�=I���}6�T % P[�?J],$ & &E� is,:�:��\] "c=�\�[C9�B�.� jr��j�=\delt�j}$�Qi,j=1��N|A�i�k�|��"hFt�E�&Ni� ��l6�N}\mu�>;)>J$8!j7D9 1�|b_mJ�"�7 , alL*%( $\{(SJ�,fB�%aNF�)rj }kis �n|�$N$-tu��u�F~ \mu �F�b�$wnot* @>�(�b�B;� us \z�� ND��&� ���!.�j,� y/%i :0)\�� NACq�$j&{��b}}�.$%F�I�l$&�,ialp "�r�������BW is�q�%t( 2p=��%)K2):� _F���QH==bN��=)�) F���or,�!lyG�U,r6U.-6,k=�^{N1F��]�kr)ey$fd :eI�jJe�$L�ik> B1e) ^{�wJ�B�:  :���x"��mu9~:s]3�Qf�  me�*�  A, B, C�D�i9roach PU�/�1Lag���bl1�iers. Un�b��wu �ad6� :� �A�� ���tvarphi"�s1�|� �c-j-:M� _� :�#�6Y �� �(@ b$��o�4%OB�|� �$�!2��\su� j}^{M} �� 6�:�1 _�^M�: )r$=1bl ��e variMF9{?."re � ,uw ir},\�/}�i�{} ��and $j!�i%I�*�Ab�1!�Na, xdopt an*[�z`achl,(:�Y.�+s:�*O,} �8a �>�t� impl�:?+ofI�1�i�Y� V/�!4Cof M " ";EM��(9 �:�,s�f؎re-:��&�(�( ��W re`enh\ An�u�)@um�&2$by� w�K Ia:�P*�J�(2l�TIq\ � }. S�Q�ev an e�3r3nd po��='�r<,�O@%HsJ6y)�(}!�a �y��BT%���+b, :b,!N>�c'2 unit g�<@Pide�5 |bb{R}^{3�?2:m�Y�4vaۯ for {my' |�A��Ih�nAQ �Y{6'Hy��)�� psi(�+�+)�� =\cos�# �#|0 4+e^{i\phi}\sinB'1 '$%i%��Xa� ��}*�3bf{n}}=(\�,� p,z phi, '��� ��,lbrack0,\pi]� $7. 2\pi�M*�Fly,j ͧeI2@|=)%(I+"��� \su}� �I� A$2\�Q2$&�&ma�d��OBNB)m� $$x$-, $y$-> $z$-;!n�Ca��Pauli�D i�"$ ��%�y�zy��^�5�{ejU=&�&=.�E�ef�$U�%� $Yq�D!0&0Fe� � _�}���э2�$ g-�6������e?pi-IoAd+A]qG=E�(' "2F-uF% E�>)yHV�.F $-Bn}!� + g�W��'2�q�:x Peres-WoooF�.�.j�-� 3 \�E�-9 x=9�qv_&�-.S) +-/sW�3}%Z51I�>�VI-nI.X+S�&�/�"7$L�"�.5Q N  j)=|�l*q |Ax_& "� E�!�B *\ � �e�mV]F{# {#�oadg�P*��N<,�Ӣ P["~ 1r}|0�U21�3r}|1. 4/]B^�O%� � A,  D. E�E:Q� �)pawm91} gav](e8? e�KO/4 .�+�)� S�db e�.�R�Z�  tohBI��a � �3!��!#Dba�A �J�.% �jpMACRO{\FRAME{dtbpFU}{2.3073in 078 (0pt}{\Qcb{F� 1:�!%{}{b�H� ��{\- al{ iuage "�yt�{Word"; �B4 "GRAPHIC"; %m�ain-aAt-r�" TRUE; X4p]K"USEDEFA� _f��"FAwidth �; he�y 2 �G(epth 0pt; �U- 8(5.7002in; % A5.1264iA crop� "0�top "1� %�f /�^� ':6';-&hO�,es "XNPEU";}%hB� Expa�cl#"��:�[ �=�, �=1 ]% B� % \\���K1:Nb %End6�5MaLT-�H�$s}} e� m�m3&e^e�� edݧ�� 2� :�. " $. \��� n}% � W2�A�� n}zb "� c�6",r,2gRY�, 2����+N!��N�:�V$��U�>� 7��"- > {2}�� V ( tV�.!�� �� :�y*N�:v&��+�+$n���3=]2If5�E}" & 0| $, F'1- '1|K J QEq� $2$N$h+�-*U$sFaxQ^2}{3}.$ -��n=2�"�!L� � ,3,4"�2�j}=P[� 9AA�^{-�N� C*6 * S*"2}]8$94Y�VF$1}=(0,0,1)2u2j2}="ot� � 8}!,0,b 1_Zs3ON- O2 O %u7Jb %�^f4Vf!t�, uh�.� $;�ps.��r * �2}}(|"� -&� QI&Pj1�&$n}.�B�U�2V� Q�3}{4}� a�I�>Y�b�n+1}{n+2�cV k 3 b�/����k"�2�F (4���-�?� ��.�2 set)P^ =co�n$l"]G}B #B�4h}�'!*텍 .�&8Derka-Buzek-Eke% �� �  < �^by F�jtrk�e(V �d98}�"� G.s�)B 6��g�xE~9�@�P$n|&�hth�lls�# $"D=(q�pi�|23:�Vw�*�NJ6 phV 0���V�0�nVr.mY!� 6.0}^{n}��a ijA�1}}|S� ^{(n"_,]�%&�!"/J0i�y�0\binom{n}{j}} "�"Ejtack{_ xJ!0=0,1 \\1\leq x@q nD�\|\ !% : ) \}|=j}}|x���;�s x$5��4 exp�>E��"� $J�eyA���ib_ $n$-*>&� $j$ $0$'0$(n-j)$8's��Sr��]:y% ,M�%�r)�M ��>�+m9�2}�s^E%�5�iI-%ř9�i} A�+6L�5g"�Qal .�c�NY*/�..�$TeXButton{�tgroup}2 }% Vw,6%Z\�|ont{x}��A�0.7V�6#%6g ��Z�$c|�(n($r�$ 1� /\pi .e1!� BE  }$\\\hd-em &�t.3)w 1$\\ $2-4B�$& $3/4r=0 =(r-2)/3FBRwr� w-1N6 x�3r� J2�3-6F� $2/vC � (r-3)/2JG\����|r|}{%���0BQ} & $4/5�vm I�!�7-1FZVw%�5/1 A 25/48L  #U)jM)1 17� \,(r' 3�NRP�91]�5A� A2\�Z5}F� $5/6=P5�97�8-1N� $1/2rL) a3)%�   15) 5F�� Z 7Bj\]���H�Vend�(}{ ��>�(:�6�2]-� } ř6^>�m:�p&wJ�Sng 6&"m@�i��(��� $&�<enYl�  {�d 2Z}&��:2] �F(j�� 3�r��q��ro�D ���W�J2��n�@r� n� N� %�� hshr2����&�r� S%:Y��w ��12"� %_�M)rz $>F2�J�zr% >�F� P[4,ZB�,RV�-\beta�.� k=1 \�\k\neq r}% }^{n}|\widehat{\mathbf{n}}_{k},-^�m\rangle], $ for $r\in\{1,2,3,4\}=\Lambda$, where $\alpha=\frac{13}{6\sqrt{6}-2\sqrt{2}}$ and $\beta=\tfrac{5-2 *3}Z5T. The average fidelity�lthis strategy was shown to b�,overline{F}(�$cal{M},T)= �5|@% +33}{3\left( 3,-1\right) ^�<. Massar \cite{m P00} established that 6�aanother )]soy forth (e procedurea 4known as \emph �\X}). For every encoding,�%$lied multi�I woulaF en contaii(same amountA�in!+aeJ aboua�:^the)0 as far��d!^ ermsTproduc �`s. One can ask: what kind*�6vides mo!��)j (E/ or an ent��d!�)? Gili)2� gill�� have�.��,�$nix,arrow\infty$)s$differenceA� weenNg�+�!���0s (on $n$ copa�.t) goesAmzero. T��8is true not onl��5�%{��!э���X^{\otimes n}$, but also* any I�1�2�_I� simi�Dq see KBaganM�e_.}�bg}e�m�E�ƭ�pf�E�a�WeA�si�h�a�problem!4�ing2�pabJ` taken from a circle (for��n $�ޡ`wa4Z��o��au( with equal�abiᏡM� which��go�o�AAlongs�n tř set $S_{ � }=\{b=\cos� .% {2}|0-�+e^{i��}\sin2)'1 ':#�e U^{2 k m-l+kb� :�@ n+l-J@2�m-l��k}% ^{��Qy S_{la�m��!X%RZ�=�.9 V:v%<��66L>� 6� � �3V> 22 .�)�18a�] �\[ %�=\{(k,l)�~({0,...,n\}\K $m\}:k+l=p\i�Follow��escrip��h �|  3P.^�2 most� POVM F $may appearF�&L s� gy� I  \[%��tab0} [c]{lll}% $��{El=C�%*� P%�[�Y�y�\l�_{rp}%�^�I�$] ,$ & &�� ext{ �}V K ,$% 7 ��b>�>0$, $I��|.���) 1� w�L�$,�5.� �.@%� F}>�N�(q=>L)^{\ast}=\delta_{pq}12!+all $p,qM�1A�.,n+m� :2� on1�� �w BEcor�on^z�NdwT0be denoted by*43�K1w$. UsqA� ib A�previouX ���ob� % a�6�.^��+�I� a�+i� ")�Y06�-1�6sum _v�� ator� {Re��u:e\( p��b]#wQ! e^{-�a���a%mwe obseratU�9�fN \leq)6�Qɦe�PrP}�)8 N9 )��5f9?|&� tepV n byE�(Schwartz in!:�,5Lalign}jI�� �N ]��-N1��"�f���%"��n�BWV��<��^28bm B n=���]ZM�! % �@P!�2}\\ & ��2T"��V��$,\nonumber�kM f��s� (6). W�n#�V�}d�2�2� �is]$upper bounKN�:�$aepende\�*�"�%� nowoRh�at�s�qu�ty. Eque� RI#$) holds if��(if~ >�]�E�Zni=K- % jE:�.�N�Ib"q&�jS� tant $p=0 $. I� M��fc��� )0)E� Y �>U�m�aF��!�[*l J�m��$varepsilonV  s.n+m+1}14 $\< r}>6 a�bb{R} *%")f}% 2� !�7� � .F� O anyon"��!P} �)W $)�sei�&�in (A�1N� if $>�=2) \pi+6(p+1)}�ach� � �>.` X$ bin1BZ"2�^�T :�=2L%�J�n+m)}+-p) �a:� A.�-� e.� � }2�z�2�6, N�Y-�)�2}) into iZEY<�v�D)En�e4�q"Q �!G(% }=(m+n+1)ZP )8R .>z#3F#T weY�0possible situe(Zra�d��-2)G 3}) �"atisf�iH � $M�={� ��\A�B��� 2 =E�  $Qk�� r}�j!m .;. Tak� se�metersaӡ`J�Edefine a�  $e]� Ma:�:r\}$ such����$����=&�G���m��% I�*� expE�| 4%[i�-&� �%-t\� Z�  Then):$�$TJ -ڢ� 6�z v )=F�:' �Nota%e bas%s$"�he Fouri� ! dime� $�$[&8#P$al argu@#} Gisin��Popescu�gp  99} & !ExE�t "e$ Psu 1,"/2�� x"B�!o� �compar�# :e2&~6e, regar�:�I�pZ�%��n $Q�AfIv) r uniSlyFtribuq$A� $[0� ]}.IFi1cx#erintuit�% acco ��reason�g$in classic_ |Bf�Q9"�PJ�X.�]!��U(_�� H ��"Րn�M�� _  k-BZ j-"` �)b0 ; :(R#�jl&0frac ���U=!5�e�}�E Q.�!:.mJQ�m�|)�F/VH'm��6�"v6�UVO5�:�'3�rifA+akmea> ofR���( three unitD & =�_{1 Z2"�1� 2;3}$�0��ori� �0u�.�ly "= ��"c,� pair� them$ 6k2 2}{3e$ɩo�#a�j2�E J�m3!*'�-^;3!< whos�"ad�} on a sm�F�'&�� greatjoi%�n:/pol� �. heaC.J�n�i� ross�e1~��A& >�&�&�i�isEP� � 6�F > E�^ j}P %�2ha���gl�3alpha$1�n�ADF�%j�I&@3� ����� to b)Zl� M�$� ne� r9%apA�n)� a wac-Rdi�ce beM/their%�Zc� esnj+556vl+3"l+3A�*} <*�pe�j+�j+��l+ 8761�l+�l+%:!/�k+�k+%m+|r"l+3"l+ ezk+e�2S�ul�A�illed�e& bove"Abe �d*� @: \bigskip \noi� bf{P�01�3 et }� � H}$ \R!a�$d -"J Dal Hilbert space. GD)" / B@0of��ices (.2 nece�7(ily finite)C!bbS|\Phi���(_{i!]�z,p: � I �,0� + 1�for{#}$s06���}�#}I=1\9, and}K�U= ��� |� �\X  :N#~�b"�5�����. S*�6 }*� h%�-uj�*� ���* |�� $i,j�.�%� E�d24` I$h-H:� \})>:3g� 5 66 ��nAU {F� max} $\ ��&ng)t -� �8ni�mpU*]� :\617 be gD;�8�aJr�U � �}���p� �KD5N-d�a$co��te�m�be� $s:)�e�\B4E��6�1]B��b0cV�E0>{ p�EHun�8) SPh@i1�$,.u�E����R|,?.!<5 $e��Ch$r$-th outcome has occurred*K+nof valu!� �$s$m �)�2�8f$ (��i.e.}!� .cho�\m� POVM �M}$�)6�";i!1.�2?<�HN/,s)X-*%��+y��/"�<%�B5� s(i,r�S�7�0 ��>��,6/J6K �< (z� % _{�� � �ismd�9ly)6WE�h ing ""� &zsiR<aneously�45$itemize} \ ��4Qh �zz� p3 �%ٞ6�; qNa | H6\>���F667.rA,a�6iRRn\supset3�p. � !V%`�3n.L A�z!AY� A>.�V- �5%2 solu�"� � ��{;ioB ,mis�+ . So�a�+�tQ�&����7b Orbe�2�5 principl"#@&�Entropic"� } C�s�{d5ty ma'@e��%|R�$a��\rho}�R}{4\pi�t\limits�;�2%S8phi�}P[FA�]�,k d  dD=/L @/>�J� ^�\i��T�^� 2�R�/associa-� ensemble\A"b�N��r�S)�*�0=� �7*2��t=}S4Jo�N&NJ�#]C$S(A�)$E��$von NeumanAropy}afa6�x $;���"�X=-��a"�'i}\log_�l+17&9�az$i� eigen� �~e J�<aUC0I*< t\*B�&fBcheck�' �N( )>S(BA()�Aref�92�+7s��b�D8ngu�F; hB,�y��es� �*��)sh� �> hat,�%n�*! ,x!psYF�� qhbA� .!�K=~ e�FyEN.�))$1�RWx' \":2@�is�a <�+���!���r-S(�)�=5, N �  C# d�C not `,� g�;.�-�id�%mE(erexample. 2�"x  two ���"O�%1��0��,]�6"�2�%(2}+1/2}{4};"�@ ..- :\:.v&&���g�y22y2L; L"!&2&9�+�u � 82}\V��%ZsS��2�f1#]-R0^�&�)�f�&;J� �] ) =H>�d4 v1`!� < ) $\\ $>���:>1�BP[� ]+JA^�I� A1MD]  F�{2�IR��z}8H(x)=-x�]x"%K1-x � �.�2 & $rxnR<�.M��[td!�� sq�� a1r���8��u =K6�1(a�e$�:b �ogo�2Fach�G& �h>�:AeX not)ň.{��n"� 2 x B86��is les����+>=F�:�( Inad��c�$�.��y} Firs� all,2�6�N0A(C$��w6v�,�I�K�J$|.�2sqA)1�L}(F�@0 ; +1)$2�� ��,$2^�*}6&2��94ystem. Of cour�&A(ub Q��&�a� ��HAC$'2�-i ��Fad9"(j)KQ.'_{n�},m >7$, ��*=1+1u .�� 1�r �b�Adv expl�L�"�K2�� �$cases: (1)6�2 �)(n,M�(($(2,0),(1,1�r $(0,2 (2B�&��AC B B3B2,1H2H3H3H4�46362,2<3<4<"=$6�,l^�m,n"1 $, sin�Ly swappIw�Mw;a�� �pV;+.�BW@,A e&�46<5mj/(D^":62� 5 n2j V,aSs�� �i"�I by � 4 (A�e!��)a, &5 (!�&).\n��&s\re�S5J� e minAF��F� ąU�6 ed a!�%�=\pi/I�E,7� tH 0 points symme� ally]uC <��$phenomenon��,somehow unex�QPA �J8 2�Lfa�Fd^���!�N ward D�� tor,AXlo"mU d V 2�MI�$ (in2� !�t�t�M��O>�)/O�62K �,�"� *%)�Qm �-�Ew �U� >� pi -)�,5*?T5m}$) �Qsta'* o de� )f4) =�@Ia�itsUgB4�a2FWidase, :F�6F $.% ^�L5.0999|!241�!B�L4"}!12curv\(%} R ��!�!�!�.�! �v�L9.168�LF�L4.0017��L2�L-?!2��!b�! ��L1�!�"�!4"�! "eb�!vN72QN8EXBN5UN23]N !�N�NEN�6NІN6PVN139�N2N=2�NjN�.N!ENA0UN5UN "fN6X3D:YT�_two��OT2��of"�7NGT�.Z ${\:E\}=rm{sin�D~@rm{cos}��,%% �2F' % ��6�6a =~2v|,�{RT0 �>2'$,>ai|�M03e-\.P% �Z7 ��S � \in "� 0��$arbitrary �V&O� �seua5%�� ` *1"!�2g.�A�j(LS�� R�]6\v�%{�- \,,1�D�/Z4._ (&n/!�K/=$�!�*e .g7�:�ef.�����  ." �f rSphi%�fS7 $[0.0)� Amiza�� #wo"�X�Z���& ial %%�5 <*� () &� two-28 t�P 7�m<� io F96.242V� �zWJzW.2�?b?�>1>�)�.�W6&?)�r<O�^*3>�A ecmrPs:r���d fd��bu�a�V|0��[2LA��b^ |6_1��] \N%�e�e���ɽchn(32����%��`��B�"array�Pc��47@= & \displaystyle&�J^!� �) �SOS ^�5�R�Q|05�U2>7!�>l1�}0�Y|1QN�,�7& \\ ��&!* 2*�.� vK2v��6= �%V�% 6�>1$2�>!2R%�N�S` MB�3A]Y�- vary% ��7ݬ�N�Y� �T3> ���*(�JwZQ,�) a`B�)�5�$)�\5��57��i���]a� � "�+"�Heq2�H�: ak2�<"�(, =�normal�B { �� ,��,.��W �} -� total fou�!QC�4"� 2�. ~es.on, l�fch�T-*��E%x{ w+[-�T�8k&ar%LGL"�q$U(5��2t ]bA v=-�3 CrFg �V"@{�6� r.�2r}9�A�3r �M���SV&� 4F�A{�7�M & > & 0�  %jF3.��j3ba5 ρt�1~��fol all}~*�-k>Q2i krh.V m{�I%�jk}6{6y j,k=�lt*>�5FH�0J/i>) z�`E�) %,J� �t4!A) =3.�ph�1hB�I�oJS.1OSo��$�"�on.�/4eJ�Q{.�A��a�.��� }"ɼf"*�/.�u)_{�&*[5 bc a8Z=Ve� LfJE"ZK�5-� H��p ���5ν��ma<�* \�\=1�"�$r\&-��$)wf!��` :7ti v�.��){ c>W �ua>JsF�wC,Xty�1ru��3�NET�[M���6- -'I�P q>E 2��Z�%��V�2�_6�-�% �IM���9��  _ B��6$Ij >r�k5NA% )o.m!IM� iJ.$ �'��6N6� a U�9*tU�b2��4.)5as! $ ��.� leqI$ V�/ A�63��$��S+�"2 .�� \geq0$.1*��)�Q"- A0"�)s good.� 6}):��-7=�s\},~~ev=:�5�B�Vy�jr*�/ 3}Pexp!6f>O$(j-1)(r-1)a�3M] n��U';}�s6�j��]\7F\ whilJ �b1}=0,~*� 1{3}31�{3�EU eq7.Jv>�E��I��E7M�2�,A�9by��$tA�^:)�r��Ō�-�")7.�a-� &�8N�g�J�)<i�S eq3}�ZFr like�(�3PDy�Y&(sy22Y<�:.� �* $Ni R�r��� �:(J�UV�u�$(]$. (2�O$�gs,h�_ earl�Q}s)~�*>��.:�3)=>,� ?�E� .,0)+�$&�R&#&RhV�~-2�)R^+AlsXOt'ai�-�I"��B�6q q r��Q��A�$�c bothi =0$ as we�s%�K%H$�b8v�E�52�yBa�Qly,�� I�#�^BV &��Ged�q) reduc&%��{$|�"t uppl3+�.� 26\�s%Ra &�  .|�M"  W{��,SI ?j $ ��. H 3:�ɱ� must�) 1. S�o�T��>q�%��3 GO8 hand�+��a�&5�wm�,o�e{F� 6x�Av�d r�-.x%�6;=���:&�SXh�'\RnK(�*.�.K),}3e(-E#AY&�E�6�&(7&t�:uUP:!�.=��(t � K h>K�bK)�lK/)4ives ri�U�xQK>!h~�Fa-�I�%�($�FI!�1�N)q )!as�pKk"F�|e�a�=�2N$�v� Q��v a�UQ,0�)>���3m6b�aelf�;� .- �!��  +&� ��)R�B ��V3=F�6T%YF�^T)nex1;-� =���#���~� jr�:m~y�M�Ez)� �3@"n 8'F" A* Nmr�� ,�%t - "�e� :�r� 8 �P�d�x �p�w�*� $J .j Id.���!B=0.u<6�6$&@z,���Oi*�Yn a͆.�N,U1w"BbA�ied, i�, always�#toi�y <: [(O-$equivalent & Nq$), ra�+]Nu��.�&�!� �N an�k6�3�� 6:�O�O�Pis ���aŕ��h�� . I��%��#p"Y��rA�E6F� *m&mL}W� w���@assum&1-� .�3�0+ M�m5&#�QIn`07�n�0 Im��x�5WA�30 plot1<� $7� �pi���  A"�U$.JY#,tbpFU}{3.171�+ 3565e#B�+7: (�t'%$͒�r�%$-��b� �1A?F�% %��9QC 2�Wiz� ZD A %V�tE�i$y�pe�1>�% %R@.2E�v �H�� %�k>� 2x+y��$.}�|3d� }{3d�%�%%Q�.%I�v%5.0634iNU-3.748�T-2T-),�%b% �%1% z��"J-6�>�4~X�4ZM $ʋ J�iGuE���>�J�������K��)$B�y��e���~>>~Our idea.�^6�� � ŷ^a�._�MS�Ud��%�I "!j oY'whH(�2� � v?��_ >D 0,� �>!�h � :�8� � Z�00� � �7��2v�# �Y�M ��]h= �2� �L2�}�@&F \1YEy"� 6�. But  �& ))�rv ?%��d�/,F� q"�g\F_����r� ��R��� ] _"Q� =0�� �m��A* 9�>:gnd������]:x� &�r &5"= �u eq10F � E�z fB r�n eq9}.mI)X "�ˈ�q` �ey>%�=0, �}�.� a n�>.��86#2�6n�=��z �gX0& �9eddv�C�"0 b s'! 12�16#"�,(]�P u&{�*is7:N�N�.��2-F"�R�� bNho�CE"�hextrac@st .�2Z_g{2�3N5]1o�)�Mf"Zz�,I� �dX�E�2�56�`�y]�Ĉ}ZF aK"@ $ (c^ke��cي�� 6ڌ5�p�]Z3ŊF�2Xcl*4k�� (�LOUalE�@ @q a�um|in�3Nq�u)no��*��]D�o~ 8di�or\a~P�it�6$8W�2DBE}ADV�64(.V�_=�j ,E�]kh�.6 82m6�6� �!6�"n��2����f�4��� bewG.�*�6�U!%V~j�6�\F. 2d=@V�6 2+ve+.�6,�M�H�L6Aa�$�&P �o� ��,>,t�B.GG�-s. By %B@!t� beI�� 2�\[ B em� V����/6�"�)E��m*�8)�# cos.)6P ��-��. mh�#EU6�)�b� �6�rz�_ i=2�2�]����%w)ɔj����oV�&'D\:�2uO8�C >Q�"J1���,�9 g4A�$& rmer��i�: +B�n}�jN_�/ile`%�la�K���&� �kj bfA�� F�Q� \cdo�J?y;�(�j�E�)�R�hr:t.�%r}:�.��̀�h�lL2krBA9d$m# 9B#g*Q.%A&�Q �$At�!@&` 2�6�})N%X�� V =tJHW��j�Fl �+|!"&�7r%� �!"m �2��6!b aJ�?6Y= ��'q5Km��=RZ�f� �;=�fE�:�o"�?~b ?�bA.� ���6&6I%J $���J!��q !R��A�"@ gE 1S�LZS"QfS�F3 ��?.�>�6\R��2�1r^%%9:��:�B^N�j�H�73�2.125j>B8&a>mjor�%}{�O�OO�.O �~O477�HF�H5.0172�P2P.3�VbV �V1V.�3 "\8&g>9�=V�&�Oa�"� q��&�7W%set ��LR�,�� m�� �QM '{� �bot�`�Y�pS�l\b }��H9}��en�x��� o n�!�g �%wo v�F�"xE. -i�>�$2#R� )\}\cup��.�&�R<)\&?two*p@�)} �>2�*B��!9 J�,. (�b�P���;A�(| �'"3@6[;��.�Y(*b>&>�'�fK8,8C��]�QL.) �7"k-��ua&�~�N*�IXs��i�MPAp.�13N��H�~�u+s�ߝ�JQv �oos*��ropri;F� 5 g2\"s$o�Onjg�^�Pa�$��s�2ymOq�2d9"�7&�+OS�y� 5 :&� 1*�{�I W�' i.(*E'��6/ps�v"6�� �`6{$=>Y-� |L( a�B��+ ��`BM:6h"ZBu�taFG�R�^{||}-��>� �{�n!� !(�[J��� ��*�/*s +^{��v�N�‹J\�3a;e !>6\��.���e�n.��a. IM2 $|ک||ѹ\ '.YJla"@ "0�F.�%�� e��n�? A��(?2(?5�+�E�] U@�6 I$$;�0�?!,ipI}�$);��B�m �m�wm&j��ms�A?�ma�� %�)Z% |%3)� m�<q�fm��]T#�gr�A1d},.W�2=%���D6�@e�.� �.O�q)h�0��F�e�-!f�N�2��V|�5����&�F&^94MB�)ir/�.A�*�Ny.�F% ^ aAbiw;i f o�p�%�:-��1� z��v=\Z ��5� !�)� �e:a�B�1of�G \$�m�R' � .� �e4:[B /B;||J�o�8"p�bP@"b   Z�A{_�*�;�d�_�5�jN�) �L9S 5��v<�>fj!�^b ��:�b2�L6} �l+VH=9,�=~="! > )M!L��>L5��D �%1�)Z�;�?:ie#.�:� � |.x:)"=<V fiÝ:� �$����a M}.O��C^�f^61A���-�Y�8!����)��b�D)Z��Z"'qaF� Since �6motiv��5�g!L&#v"��#� � � Z� �!`d $�� $*;� �B�F4={�o:fE�E�8I�@� �#>=/.*j@>ki?+/1-6�ec-e�ak6�>��)G�@ M~j�:P�;jO�,"h7-�dt F:�T/6� leq1Ţ9f=q&�.[Qf���$2Y6T:&$"�%be?.��J��� �Q�ionصies�bbe�{�,� � �n�FF�/h�%ur pur��;:a:�=1(:}aso<��is�ic� aY"ho: 1<>�&�>�-��;y� mQ2=N@(*�[+i<"n+W"% �J'�%9 Lc(!L�:je(2?� �:"���v~/�?��>o"+)BiN�"AVzh ��<�=�r:xz`(FxJc$2ti�2d$%d��6e2w%j�_"0$.��%Z8Lfas�*v�??�t׵A�-"j�)o���/#�' q`�0,�%��"Vs F�N�^�i !�j,k�T }_.5�&( In�|�:2w %��E�#*0�P2KN� ���:�� }.-��Gu 5��!�:QJ* �=V$ (j,k �*!m�(p(�+u"ƻP�<<% } W,��P6�4�y�~�*�=P[E�E%��;aXv�m.�V���,MeFnPɟ&>bQ��aHRUO� ���Y q1] V�&�(v:����0��is% �}�3[@�u�Y ( 1@ 2-&�$ �� sin^M�e}�vjCB��M|\*�_Q 3r}|^ l*���{r}-�P*� � "/�pafi}[� . �ug2�� ����Yz�2r��2J�-&K �EI[P^Ȧe�1H jr}=5` jr}|gR2;jr]A $YN6u�&�eto iz� *� �G)9*z rm*�?X��T�6_ �*�tT �subjecп�constraiJo A, Bzd C�ka�A:q,��� !�+T6�xE�>0\�����!}*�,xI^X2o^\O1jBAXi=� &0X"^�jk*E�+�}&X^��Sb�6�F�@ 6e-)�B� �1?�k�k8 �өM[�n % {4�p I�Iz��Z!�mZ ^{q{ �!��zG��JGnm��w�w�J��������? ��>��] :�&t-��3 �4"tF� ��!(�)��:�YP L�VoptaHqGmӏu�seq/�n�*�T���rC (�"1Y~�Q�S 23 1"�SD$ �T,8D3,e^,T i/3�;��3}63�G=D.8� B8� ��=�Mhi�[.4}TU _&�T�Tr�� 1�5� ��2hs��r /),dGL=�X��2��s i��Ab});"~��v��a|>J=B8r7ui.q"� ��6:K� R��A*? ra�R%>e�>��� %?\�.7�!B�R��2x��*�2�&.Ob"g  \}$:���[qx_[c]{ccc!1I��:agU� & #e3j#YeKB$\\ Ge�B#6jU�ZY .�3..NO6u}q�a�6#e�pB�6..a�>�M!-}�8]�8]�x1�T�scr/�(�trans�"P( $3NZ.`�A2V(�����������!.�"�!�42�"�!.+5���6���v�Z�\ #]:,4^#_� {�Cu^��^�!l*�4)Y�fb!+*��9��� � _!٪�4rJL�n6�� ژ" zA�>��-� �% ):z9B�4rJ�����f�,4*B�eU f ������N�4q�_2 �r VQ=Qh| ��,4b� �oA�b� %f��� vd6� !:W8^W\R]�� �-@3�&i-4�@�& # _a�6c�>1rq1D���� 2���9;�bn�}vQŵ>�Xͯ�b^�� �9:|�&.2%*��^0 % }|:���t�Hf�!�\J!�>En��r�e�)�.Z׿T2U=.�)*2T��6�U�*�hF���>��% �C+Z+)F+�-2BB% NZ piE Y9Ki 6�I7z��`F�>��J�mR����"` -ӁduR�V���4 �R R�be�1&!Y�� B�z�:�11�"8%opt��AK�c�"����a��FG:�n����"�g:�a�&�r6@M6} J��f-�-`9�����.M}r�g ^h)5� 3r}=.6}r=3,4 �m4F$1,N N*�Z6�fi���&�2nG"�&�M2^363�bˀF 1]b�A3LA A7UVj/�j�o�m*mv�-}.��.�:�9��B�"6�� Fo�q:1J?6 -u��n[�xF�E2�i�~i1at:"�1}�R�!&>�F|ɬZ�F��a6�16�23!�-�i5�{26&4k682jU�b�� js2ai2*"ZJ�3j��0 &*u4.K�6na�'Jn4nn4}>n2/o4 B m)haaPu:0I��st�K_;w?��7�^U�(6iA�"��I�)Y�2qHeof.p4?5fin��e6�N�eОO/�SDZ5 16��"a�w8 %��� U-��2&� -4J!�� 3}+2<4%��] �"7X��e�2�&"1IaGK!��o�+\�5 .�z."8���"�7śx*�pH�_{U�&2�nJe�1��. O*M� �I��j�% .�<)�S1^�%��%$�5(&���=�in��Jimpor� �!remar0��N ,� :f��R�;%;�=3<=�~D%2�zB���xB4��4�$���KB�XBGi8��6�YF1||/$�fo�/aey�*�@ fail��]M� trix-~��)'+^ qu&�blA� B�2� \ to|&'N�rrr���E/�e�BU)�z\\v6S>7Z^�0.~9\\�5JoZ�E 0Ha��V�4JN,�D e.g.�C�� da}).TLW�protocol�(jscribe �$an 2$�#?.ly�(��d2���1V�@ �u�cu, �'���&$�N']�UBDK')�'� �' .~&�+�-6l�Jo�mP\Z�R"���/2(��-)��d-� change�(t[��/"�(*�JC*�>�U �lanyth!zelse),J-��t\�>r6v�\c�&!�1�."g &ި߱p�% \��[1] Pe��5PV (pro;&x:�xd)2U*$\{P[u:e��G<-�&W�)],>,��("�M-"�M)]��o�<f��A�� 2.1] A$vR.}Ai� +Z^!.$+t1)��e!D"�?1is�6�Y!��>b �NElRI�pm��PV2v9EM*%F6+i=zF -.-!His�A�R�?se�!FV�X.c>YO >Y2.![�b6,A���9sin#_ 2K1G>M-+0A�I2 .q]4=:� *QO.2�Q2\��N�-���B�" ��.���]�>��IZI% �I�I�I���I2)RuD�I�I VJ2�R��~�E@�JBJ5F 2��2N�%B�0����n�A�&<*>b�2,v�4�� �%.�l dint�)"��2��,Bհ&��{6Ɗ$�n^>:�g���A� !0�:�Z�.> J�� 7�Jp*2� 7|�5\2�E�!!�R5��� ��] � .��& �0�� �G!�E����͡����t"{Z�.�nWF\ z>�+%����6��+���"�� I)�֑�B�@u��` \} d!j�(m�"  A�y�8A�����y�A�%�% !�� phi�pia�ic) �D�~ sin24%�a���S�E�� o 5te#Fg~*0]fB�f~�.[" d���z�� }N�:�������с�����Qm����#f��)�q�+��E�EIa�e;3m}{"��C�A� ֦���n�: to:�p*F��)S"5typd6*� �a�=ed7�u[9^����*7�I�:z:M�F� "d�-h�6$ ;�Wys.�S�SJ��-e�&HA5gby_ing,>zx�EBy^B �t6uon&2 s&Qxattemp�tUw8��analyu�to $N$>Ir�?some eܱ�*��B�&d� ���6�achie��F8. A�0(�$N?��)�8isw�o2^{N-�rank-one&�#�i�WS 1g"v�w2��Discus��'�ݧ.�g�k !s2'(2KCof) a �6�� ���m�/2)"!6�`!1� "��Q��P >jA�5��H�x2�27Z�68{^?iZ(*]XA~�m��a� �f�2 ��_~�A��[�e2Y�ك6�� ��ݖ���Zn �Fyap����`(�!f�mt�i&��A�web"�1"�G@paces�Z���Sa%���:�O8respectively. �aWhen $\theta=\pi/2$, there is no difference in the amount of information as in that case (and only 7atP) exact spin-flippingjXpossible. For any fixed� �$ dimension~�space�nned by $N$ and $M$ qubits respectively identical&Porthogonal to $|\psi() �,\phi)\rangle$ is $(N+M+1)$. We found that, whenever we fix� \neq0$, $ )\ or �$, anti-parallel states always give more 2g bout� dir�9 ��pi-UPi+9QTRF)\}E� �2,0��6� _ >ΆE�!{same R� 2�j?, eve�> ough%�lineare�A�hfirst!��fou�A� e onE�%second &t three. The scenario describedGnot�rly phA�Yx, stillW 2_9 agai�eU�f�qWq� e�s�is doe�It holde6� qubtM�have se%*at encod� of�E� [a�n �0�H �H��thA�ial��regardAu�xtrace�o:��m%�2�!��n� from a�edmz4. In particula�/:�[%��ofrai�o��rmj(\otimes.�+i� _{0}�� q�$,��re��"�� �in $[}� @]$, can provide m>�compa��o�Q0Bits�n ���=FF�U$� �Ł�U%�4s are supplied1�� , we)}verif tAta2���us!� LOCC� rise.H�#M�is interatng �%� xper��tal poiNview sinj�pE�cally �A6trpery.�~ an ent�d�*� (see, \emph{e.g.}, \cite{z}). Massar m ,00} has show�at!��1�q1�n��� e.)2.a)� taken)a uni9 distribui~Chol��Bloch sp� �A>�Aw%�better.�.v NjQ�� e choses�(proper scor� a��1� %�of�J�uist!��metersL iA�gu is,4course reasona� T'�+,shed light o!�e ,a�� �� some physy conn betw�Jim[ ility}6{ , outMRance of:�%�:{. MoreI��jcl��wA3kind of %F�prefer�,%�n�y�multie�%Kes;.4��,ly motivated)�A�uld be)�0whichM�ly1�)�b< (>W is a,.) \bigskip} $clude with �ope�blems:08egin{itemize} \  DA mine ���followaWtwo��U�sB ^nj�:*� n,N-n}% �� 6Y _ A(&Z  ,\�� �N&� E&v ^" 2g >2� �h . -�Gi� any��.� \pi�� dete)�� I]valuea�2�" -�gB I ;R� �FF� Z`n�G Z� ^{ n} Z&%6�9(N-n)}^�>a��9!0!!9]wh��aN{ �>? !��W�|nge�2vjc��"��e belong^ etV�6 5 f I� iQ truu���� or�on� a? \end�7�x\noin�D\textbf{Acknowledgk0.} SLB curren���holds a Royal Society-Wolfson Research Merit award.Ɋ work� fundJ n�taPEPSRC grants GR/87406�G< GR/S56252. SG w��lik$ �!�0R. Tarrach, O��S��a�Se��.� through aQ� Ch�ll1u4Phys. Rev. Let��]4, 5230 (2000);� ibid� �"C�de&Pa  �4JsA} o63}, 0p9q1iu5<g=7A nra)�R.>3, E&�of pure2M coll� ve���vidual.5s,iK(-ph/04120272�$n, Antipar�pin&�� contU> Q�]y�{14301N{ gill"�REml�S!�ssar,)<". on��large e1Dz�1�42312�06� dele� an un� n��Q�NaA�y40�64-165N�p}A P�BQ6I�:@cep9Dnd methods}. Funda�al = ��ofyH57. Kluwer Academic� Lers Group, Dordrecht�F32Fp�woo�s91!7�%5W�@W &e 8�"g*��a�VH 66!�11)�:wz}6z�0H. Zurek, "A le5�can $be cloned"�>�(299}, 802-8V826=w}W�Ugress.>� � 3docf}Sl%\\class[aps,prl,twocolumn,�pacs,g!�edadde ]{revtex4X2E${elsart} %����P \usepackage{amssymb}2natbi:8amsmath} \setcB"�er{MaxMatrixCols}{10} %TCIDATA{OutputFilter=Latex.dll!Ver,=5.00.0.2552�0pLastRevised=Thursday, July 29� $4 14:54:587.gGraphicsoh32i( \input{tci>x! �QcEp frontma� ( title{Fre� ����큋M?[le���es} \�{a4g-shui Yu \corref{yu}'<, He-shan Song} )[yu]{C2�@or.�9�y @sina.comTiW{De��.;Dal5Un �,Technology, !0116024, China=+ab�ct} I� ,��� �fW �m20�W���"origi$de��6 semiA�raNE��"z23 B3�Yin2FofR�$. By virtu!��r^,"�%S�^M����onverzin]#I3teVM,in arbitrary*|%in a�"��). � mple exp�J-7�2�i�$ n out. As�!< s, a�"ee %tiA�*)�%G an N mih %��&$�6Y)me(keyword} % s l�!�: \sep R�"6Y2( frew y�, % PACS codeR�\ B) 03.67.-a 5.-Ta�' ՁA�.T%\��{1?, ;.sU {\protect� Introdus } E� �� resourcc s_widely��%o2 communq�a!�NI�R�cesm.��2i [1],6�swaa([2]&�keA�*x[3].w ��so� make u@'�.��e�Y&ly yrtant5 ,AYessM�refore :Ti��6�%_centr3!r�i& .+� ac4a primary goal��field. � .�attQed a lo2��n� in re� yearsa�lot of s�o&7B[lc o��!�a5!g& �#, many6:��sE@e up [4-9]. Howev�oj*��6<�$two levels� �erfectlyWp;ed [5]�)d!Gre C#5�quyon�-�y�2���b�c6� �!MJcՋ6ORC2+tunatelyIL�����i �a0'�4�.[10i���en!�)�lyK.��&�6�Z5 [11]incre�' our a rsta B .T. ,�!21M�r!4s�'ist a e�sa.y$ criterion]Hso fa`"�&� e� Ar�al:� full2^ ^, butI�a B*0[12]. H�U"ve�yf&�$obDa �?."1 !� 6�systemi(:( wAudy6�ŨV\�iTa newS-a(Sn+tA���69�U den?Ae2��8�,  excY"�$*thI�)+�A�i�ah�ns,�6)�"ub�&.2�BR, � r). Ba���$eR��><�  F �*$�E;: "ofV�ehH&�Oway60 %hF �find e>2� � � !�2�%^rt6�6b��fU Z2M 4+enA�"W a sV 9�td .} � accor%k)����um6� 8.Sg(%�zan ex�  demone �our7U Eef�Hib0n its ri�&A\� �+!P*� s"�0| S. ah 6I25 } /-i�aWus6�QvNj1$N$% ���$\left|  /< ^{ABC\cdots N}\�1 $, if��4can be written!��F ��"��B a}- a���, i.e.%� �} ��=)ps�6� �# 6&B6& & �-psi ^{>,u �%� n!`R^��)�le;(#$N)]# $\rho 6�$2@��-�*N�Z'!�:Narho:�=\�@et{i}{\sum }p_{i}. ^{:h)`\l�+ !1 6(|9U%dR� 3>h}J[(|J�wł$^�=1�3�>0$en$� \alpha }$ij $i=0,1, �E�� y norm��)�A�aU� $ K*3R il*>{ >"I>Q abov��m_+-�&+-� .-M*���#�it� se }50 "ional� �Turna6 one. T�1Y�zz�7iŭ2��& they� sep(+8} � %&ect|�i�6t 3+sT y!9�� q�fQ �.)2�FAone or�|&�*aM {&�*� eSNEE�|.1>��k.�mh(}@*2L2�L(nL3�L(F}%,��)�Ѹ%;Je)��>�1r��-vn�1��)��>���(r��~)F�%��"�q2Y��%�m4^B��%"t I�I����� � 1,2�A3,2x:� :z�T,." ^Y�"].& ^9�&r.�� �Vut�;^ how o�i�;�A �A,� � db7,��t��3�92 � : 1)� y���,i"�$to (3); 2)"o�F8:�(to (4), (5)%(6); 3vi8 6xB@ nob8U0�[. Cona:�af� no1M�.� ��, b�\ #� <2n� eTon�i*� .�<X �� i}th*ais $D8 0=�.=�� c b�;m-b�:! Pi } MC�;�!N��� Q e �=2x�y�= b�;�06o!iw=I) X(much higherZin!|�>u�� also!i�6��� R yV8s=�u�Pr ' B?R ,sqrt{\lambda� "Ps>��>� y!�N�� erms��(>Schmidt*�!� [13]"09^f�:�n���z e!� $n_{1�< 2}=Z,� T,I 2\$ 5�i u� oW!9:��A,tsed I$=1,2&,��$[ \frac{N}"v] WH "% 6$= \{u�r78y}{cc} N/2, & N�{ \A�qH(} \\ (N-1)J"odd}%i� L% \�.�\&\"in9�5���i��]B�!�}r � �ame. �E� 2'?9��RL� M�2.e*:�� $is equival�K��Hr�(onA0hilst�.�I�U2y�Frigor�z % it{D"6)1.- }ThN�R� � b��d2��D��Z� &� ��2�=1}{\�C�f��}% ��i �M���i}=M�(!}{(N-i)!i!�= \in \8L 1j@iR l�]lG&ff�]�e��u} \in �e and 8Bh�fjH��s $zc -.�]� c�Dat��A/�M2�+b�,@* } A.�A�I�.+�&_8A����*e��"B#2�i� to��,�#�b"�%243 m"?�n �o*s:H2� }I�,a�#&�I&'}2@� m7.XA�bL$7�*�#���G�Hat &�!c>�!is�9�^(=i~%)��.�! . B�!��to.� �.� .([ �)�stocha�HEUvi��V@!�A$2v�,�>Jc �IP?{E.�j6e&R6� �� }{% ]��}��(E��/zVN�CU)>� � P �&� !�jZ#1IT#n1��($�6O5�2KF.�$j$th:1�,(6�� � �c%I�?O� , u�by�#!j�&ns�*�!J�i�z\ ;` ixed:�Q.nT��to �an&q$�.P15�#��, �%PV,opy4�$C(� )=\�2(|E�2�.G4 N|�-Tr>_{r�)}��con�EO="/*[14�5wy F�0 . SoMC= �a )$�% E]=S(�,^{12})=-tr\{ �1}\log ��r� 1}=trh\" %B�6P %| \} \ ! redu�Bd�Vty�+rixe�cri�8$1z2q(" J�.*aft(Ui%�teU�> Ep- � >\,��R.*I�8 \ satisfactory.."AM�#�QR. Alt�Sin''CY�# ���'i�Zs''V,"N.�, sheds �*"EN�'8/��om�2 tent����is���V! � �0d#� �'#�/��@g�W�@w��H temporarily employ!�.! 9%)2 &W[15�V��l=ci�_{a })$ � A� �A�b:�b�=��� ��  I�Ncas�3.Q � n)plici�-�n=4�O)� ��%�)X!negativaa$N �)� ||�,^{T_{A}}||-1� adfim iL25],&M�!absolute�2%�"'of{e eigen%MrA w($ [17]. Of Q, a�P6�N� w�VbA�%p3�SbRA�ena��E���Bt&�  �nRo1���asei&PY�u#as ��ia�tmis�R!YT!�nE . �.a�6�N�%��B N� J,by&V7�@ 41. \ E"'i�a�%A2 perm�E�2to�E�yCq#. \ "�"9 N.@ "z)% ^^B_"/�6�&`B1`>�s���"$Aō&� $BRn�>��  ge�atNG i$B(A"o,)RZ9 N)��4 4 | \notag!5 !�$b2�&*} b�(P(%,� )^{T"�1^{�})%�2�B�5��22� �8"h| :��6�6�*F�} =:Ij�)�A(& !)> V�>� �%e�m]e"�Wsuper+ �s a)ubI�, $% 6�� .�ma� � ��F� 6C.�2� %�"] &� 6% E(E_{ijU !^�.(��{cc�E_{11' &412 �  jN  E_{2.62R62:6\v�/&  d6iE_).`%RdhR�)Jm�ij�!�-���QmX*P"�A\  $ij$ \ E7��� Kel� $e!�\ �an)�:Dre zerowt�`IA��3��N+"�?�6�"e� ( s/ ��) $�4� ^}N��E� tran]Q;anA��- ^ ^RV^6$� "hX1'6�R6�U�C�R2��!�H*� ing J�n!��? �Y. "H��a`Va2J�mov{6� F �2Jb� A5$i�#.A#>�>(iQdthB asJ�P^�=$ime }(i,j)���i� �jtV%���*�1^ �)6D&(MjBM2}=�M8p(\dim (t_{2}), +1))Q�2M��last}�% �3}=j+�� �3�FC$1^*�1H:0 unitq�6&A -�$% �1th5���i) �@'M1�E $�0��1:� �01}}=1.$ What'�Xa �Nir�atUi%-"M%�6�J� )�!� =$ $"i1�A���+1 2)) %2��� =;I RFndeMt_n t-��D%ly2�%�$k!�s � -�J "d $M$ \5�s >'of� lie� i�Xt e�!��.eA�AC��� � �A.�&8 �N *} U_{k}=5MN.i��+}6A�>g � =NA�1�i�5�i=j}{:X �� X=.mjj})͌2+1+1}OiYNs/ of�ry5��m%�bi*�"�AlRJF4�\ rel-v`!{FB4"�jt �s@j(-�Ylo�MV��f4e �$%�$ o� R:n�F80 / �(EK) a� B/ %�W� JB$6m5�6a:us�F p�[� =\{m|k.�6.��ve�% **�x]J�t�w qj*�w &c j�nL.FE�;s#`/�;s,�.�e�8j�iF> *J�:�V� =(C�\� | 0\�  s+C�: 12   \ph�&BC}�"2( +e3E6eEe4 fe .e-:e8F��%:�} �5gZ�6 r�s^� �7EZe8 fer7%Q:�J`6٭8F`�"�/C� )�|W4�%-�.j \pm -M �aMs}}( : 0:�>  1:�� � _ � \pm �t 0:Yt 1:�)$ � �V�.Z2./��a'�/3�)D6/3}^`!C*'3$L dN�"i})�� n1��2�')&�M1-T "u":� a3IFi\ $\��oo$A-BC�6 B-AC C-AB'�Mv�_t"6�poEdIveN ��"�z%1}�5��� -4!e'+[ >-BC})+  ^{�.�})]^>;*}1� tI�(1-(MaIG+N 2P Q))Rg %JfM_{�8 |a�8i�+E��72�#5M�2K72J�:2 *} NF��#B_42_ ��6N�82��P�ŷŜT st �E34256  &78  �yM_IF��2���1Yb�2R">56�2A�!6.N R�E�b�-���X2�!�2j�>j���n3*}!�� &=&� 2}(G1i) 5c7�\as!� !/7 #1#3# Z &&)1�L6)8)#6L8 #1)QsU��Z��pb���:!e��9��^i�v�xj�j:�j��:��:cF:��:LF:L�:Q� i}}=�QQu#R.� �/�O�c��SN�� K$>lM*� .�p e�-g ��F� @%2!�!�H*� �*1}��4} �`}}$� r�2� '�� �� �$#�+ sugge ;� "#AB> �a GHZ�te. S"�K � `+4}$(1�at J"� W#FbJ :� ��>� )�F �>e ^6 +% ..+��5 - 16] >� ]�0>:�kh/gPf[ & f�q5U� �-&&6J0�U ?0FA+5:1 1F�1$Ki�Jul�3isq#!�, MU�'ix:Gs]�H $V��=x �� 0F43 :4.(| 9�-x}{2�I}1Ւ���-� A $�F ,16]�'*#!N�" $ asRBM"H � ��*.�$e $*-J�%%23/ bu %*s N6s % �B��K#B$�|�11-(1+!2 -1})5=S1c �$j.2*� 2b� � .��x>\� �ac�rub�F�F�!k�"�$�Q 3!�(> }2p As$a�V�2v?�Q| �2Z�z0 &c-wis �W� 5�. :�}% tureq��3o��6�! prec7!|Q�3u%�s �*�%tV%�Z�)q 0(6}$2* $s�waK)�%�@k.Yj&.5aR0*8'NI�(*E0E��!o�:�NI�"DQ�6m&� % :� Ÿ&����8i&� ��.iǂ�7At B%�%� �8.�Q�)pV�uA�V�x%_fea��Du�q�)v�F�&d��)z�!k.� ,~��n�B'8[( , unxa�rX2r cumber�*�aa.C�'in/W spec�-�'fQt��e�l<( aD�'a311a�+�s,0W4t��!��/c��< �;(.>� carri/tG !��3t&�uiFv7}��&"* 6aT6w%ink� P :�asRP&(�q�2,�W�Gs�n' -5�Zn���VW� *�7bf3!�{2f5:,uBT�tX.Yi%�e-si~o� ble advic�\is-�%}up�ned by�ist!�f"�s�*�a�aA�derFu4 No.2100CCA007�nc'>�e�svmsH{[1]} C.H.Bennett,eA5.,P5q Rev.�h�8(bf{70},1895�h39bI2]} M�fkowski,�l"prA&5rn�+nd&�mo pi�Ir\j 4287Ns3� �%% G.Br�ld<Proc.A�t(, pp.175-17�g8�t�$4]} V.Coff�sJ.KunduI�6�g, ��mA�61% },�q6F:i{[5]}VJJ�Fn224)l86l 6]} G.VidYR J.Mod.Opt9647}, 35J�i{[7%59�\ D.P.DiVicenzo,J.Smolin,!�:� ���054},3824(19966�8%Q$I. Yukalov27EX$ 90, 16790 �:S 9]} AlexaE� Wong%�$Nelson Chr s9oJ��n 04V�n{� !��4�0ranaw Rungta,2r, Carl=yM. Cav�BM.swlery,�0G. J. Milburn�A�6�l0�pI}2�u{[1a�me)D.F.Wer!�Yy $65},032314!"26 1}� MFaL59},141aT>Wa�K.Zycz�hP�W odec�vSan�O��M.Lewen&ni�>�58}, 883n8); B.:`� >560I�496U�1 >o &�i &6l [a4p�{,12pt]{چle:&$k [dvips]{gjx6,kgeometry2[^certags]&:kT font�ijF�kamsthm2`~q exsy:fancyhdsjP%\newcommand{\url}{{}�RE@rePlh�uref�i 65D}{\en=5� {\rm{d}jj2_EV*eF*IV*i* \re.Wvec}[1]6� bold!$ol�#1}?2�Cdo�(.�.:�Z4 %\1�8{top=1in,bottom �=1."=0.9i�6n$ArXivNo}{\�kPhttp://arxiv.org/abs/�-�x103}{B!�. XXXSz�{{\E-ize&.\select\fbox{\���>NTz_� fill_%1\v� 0.4cmA\IOead[LE] asf{{\sm#�pag!� >No.<RJ<,E.~B.~Manouk=land P.~B�tadawi%��RO�LJ<Sch��erՍCq?5h(to Thomas-F4� Atom [1Z(]}}} \cfoot5!�P�p\! stylei�!�sloppylC!�{!�%�1�D� Der �*�,B� 2� ��}\" s{[}� m it{InY'al Jourof %se ���ics}, D~~< bf{3��No.~3,��� <~897--899. \ % [�{qdx.doiel10.1023/A:1026613203875}] % !L\�n-` c{Edouard26�E-mail:3 tt{e -$@sut.ac.th!�Ed\ $sc{Parut6q$ \\ {Schooii �, \ Su�!^�n=,\ Nakhon Rat�@@ima, 30000, Thailt 8} \date{} \makeE �a"oxE9��.umK/Q�%�pPic:� atomT^�a ly dAS?e solv0�ljr"�re�8a a model.a�<0h|oscil x po��- j!{:e- �:\@.!x���9a�bgenLrea"|pIb remark�6!�Ka�, 1927~_� '_}; e�2  8 8 8}),9� (��) %5�_})Oed ��+B}9[ r[%. *�=il.)� a���_*��Q3# �lcea�Ol``! ,'' D1S� capt��ed�i/ލ s bi�gm 70Il agouB&�l mechanics�L��_ein�_,M.ll�tinue�do�duA��e��emeKfg<�|=�success,� m"_�WNol6p�nmi ��)e=�/$ (DreizlerC ro� 1990MF_})M �"m�reo&ce Os��airly�6Jew� ar�e'nand G&Rf>a� monu+@alUof U�Ct^[ny�%�r0�orsmn��? B addal.ssee Mor~�(�- !6}%\�bG4�p=�22�/nd-)ngoo!6�/�pp�LK����g \}\label{Eqn01} \delta{8. LQua}} = \int\!\!\uD^$"vec{r}\:/2}{��\uIG,int_{-\infty� \! - \uD\tau}{P-\uI\varepsilon}\;\uI�N\Eial} 4,[& �G��(� tau, 0;V_� TF}}) -�7 C}})\Big.]��5E�3"3�Otau$-A�A ject��he�2�(ectrum; \ $b� '0;V/:��2$ Green fune�:L\pm5 t1 �'0)=\mp(\uI/\hbar)\Theta(\mp{}t) ~��L>sropria�����q*�M�b0$�@$t"�f t<0$6�`E� H!R$!N=t �$ b$Die��*41��1�n�2E�! [E�fPZp- !8^A�m}E`\nabla,* +VQ��6]G_baSE�aN8-Vr}'A� (t)>9Y "�OrvO�"fia�ar}�s~:1align�:�) &= �Ze� r}\,f(r) �23}� .EC3.�Dek%XF%p1+f'(0)  r}{ah]._4�T �`+ $a=(3ʜ 4)^{2/3}(%� /2me�+)Z^{-1/3JG$x=r/a�- $f(xiIa�0 g u= $f(0)�i�<vanishesu3 $x^{-3}M� x\to��Q�cDEq.~(\�zE�R)n$ Coulombic�= )4~ �!� �so-O t�mly eo�2ctr�s��+nuclev`�<pu�ly subtGuoutmA $IY{�56[8shift �#�Q-� al limi G\ Upon�3P.QYqx.Y5Aiv]a �_E/.ep}}{(�]a~)^3P�&E^{�<ec{p}1Q�yG�<}\expI{e�A�(�> m BA�a�tau+U��q�B��.tO$U��%�"(%2�($U�x|_��=0}=0$)y�N;6�m�Z�U�u*!(}{��-�荲UP%, �)>!a`v%!gUac}!%N��U = 0R�:>A�"��60}=�7�?I�It�  ly checkeB�y96eb� lea�=I� U�U$� !�f�&z�n�7���{�.t�-L%l-{ )/}V�'Mw1R7j<{6m!P-�J>%��Cu8zuI:}2}}{4m} 0�VB�e�replac��$U�70}+5 %h9�5} gQ ing {��o ry Gauss?0 ,�N*]�?$1��݊8�2,I�r%\& ;V���!J12mJ� )�m"� !�ͨ)^{3/2}\���Q{}6�E[=RQ*u J�.2%��x]�Enc!�c&���A�[ �p�� /2m)�W]s ��ݒ�MQ)�IN-��A�� :H1}), �AI �Q�;*%x��� \p� !ލ ��� UZ��y6D*}�&�ySK.hz� 9��I�2�=F��k)�)�}IiA�� D+uD{}VQ�!6� !��E�F�\;J�\!.= 0�Q�7.U�:} inv� (�one} (!)"�ve� *�q$V�8 S&��vr� �`tO to y�~,� stran forw��re�(nܗ�Z�Z,>y��B� �b1}{24\pi!%�-�()�V)(-2m!�1/� �&�6�� -�-]��?��)T qqq6 ��.n�� 10})�z`FsurfacLn�� (m2� �_n���"� o�[� � ertQ%of>Hi��~[�6�I�r})L �����=:7.� F6-.rm{�xKr"�  }{}>� *} F��ly��h�f"� �t" @%D�&� r 11��U\�61e݁5� � 6�%9%���L!E�Z���a%{}Z� Vkm4}{� iH��2m 9}{reem ��5!a� big( M2*o12�ioE�.C��.X36�ADEl�n�to immedlD�x��&� E9T�F;>b.�4%%�{BK " 4}{9��2-v!�/4I�/� E[�.�4w+� 1�Z^{5/3��0CX{}x\:J�2-C��>wunge�!Q $-0.04907 e$ (in%C�� $ �!�$)6�fY� \�c I�>�!(ragged��O'6� ,~R.~M.�W1$~E.~K.~U. 0)�`�C F�al< ory: An A�ach�W�(Many-Body P��}, Spru�-6���B�"7}M~E�<27): ``Un Metodoߋi�\oGF la"^�azi�/di alcunE�iorieta_�l'� e'',"�dRend.~Accad.~Naz.~Lincei}~��bf{6}�(~602--60.o��8>�8�E�,t3Xtische�hode zuae�/0ung einiger E9Usch2n�Cs uuW$hre Anwend3auf die)�is�Kiodin Sys��� E�M2�Z.~�.��$pp.~73--79.�.* $~III,~J.~D%� 96):�%6it{!iic*� lecu����Op�$��Handbook}, Drake,~G.~W.~F., ed., ��iK-&u�of?,�8dbury, New York.�"Q_C&a�A�81%�6�M:!Y S��*1 '',�%>~[)9CA�� 5), !H$2353--2361.� n0!,~L.~H�M�The CA�l"n)R F: s..�P4+~Camb!�il.~Soc�2$��542--548�endBN�i &�! %`` MO >&�]�%����>�&�%6�&ams0&6&C'�F��F��F�MonD�April 25E�$5 09:27:15�E�%�F�\"{2C�C��Tr"7\Qubit�%��uZ�6*�$#s&*j�@.� 8:9�affilie��� \\ D$�112� #\today %&"F�preڊ a `9�c݅uct6 sep&9Lĉa� t96\V����:Viri�:ai�at��C&>#3b�garn��lthree- Mtensor�pr��sr7 intu�i a1l)�� form�6�#�66�����lW tend� d2^7.^4��IYH &"�{Fk-Ln�As!K_0[x�us!*�=� of s�Kal ���_?�;8@at!&ދ!�f��m��Y$e'c �5.Ud,  �7.MM *a%"�8��n��ingrediK!in"�$}Q%W%M�cal�t:��*#�C� ingu-n�� I� w��& *��8>! year6�#!�u�eYan &G`4_!��#d- á�V @�q% .�prԑ(QIP)*X�*�/ב> .q� 2֑: �3*�,&�$�[4]%f֑.>Œri�w�if;7KZs�Naue��� �hs �t%W&�^t&�pn-=s,w:k5./"ϛe�AJ�;��l�:~c�&F}e� �0HP*]it_ewhWpor`am�-�} ut . A"�# �"s7&�62As,@�B� py ideby 55 et} al}.��A-vi#�a good�P\a2���_s.]�er& Q9V���-�w�'J!c<�c�r�iM�� [6,�a�q�7&> of g$��!�Oo�amto >ealu, ��d)mfhp e�8made [8,9,10,119g�-�)(.�a\%%.��u�46�&f"D(lst Ref.[8]G:�[� a��,¼F�� mini �% ;=x h7�for.��R�Ec.YR� ,�R�=%�l�<[12,13,14,15,16,ca mostA�eK7is 3-�f�� "j�3]U2��ly)E?�85��lf�( [18]. Desp�(A*eL�Yq effo~5�.�AA6d e�;dnois K)ʼn[���c�)paperK& �b�a%'"�i *�%6MZa�a novel� !x(]"� y� Ɓ�B�ed ?F } % !�+n�j�$ :$ An5A�m��(~: �re�KACOur�4rEisw6FJ�&ՅnR >8&?:J  ��g9,20]:5�| �&F 2s :�q<start�92�=��YYID]$��\6��E�G_�F.$=H( 6.$� A�y�le ifB!�UN6H \=�^%V2]^* _��]:T:vm_{C>�J�A���2Ɍ.� =O��byBmM�� Ua_{ijk� �i2  �� j2 �k>C&N*�G�(L�$j$, $k=,�1� coe=�s s $ �$s�Ys `� �K2s ({ $cube) [21]� j na"fig� 1.� }[tbp] \T\�ds[width=8.5cm]{cubic.eps}%p)is|{�Uh EPSX- \M/on{a�2�a)�B��@}?9�.!�t,1�nd� Not��#� cr�nj19*�zbF��K%� 6�a.�� A�$. �=� 1�.� �-�prX ��Dn��bit�an un�]� �R�vh "VUij�+ve�ns (f�s)!a ��AE�relev�()�� M-�G���$ ),B.�q� �#�d�Bv�� ize��A�3|� diag�� plan; (2�&xj��7!:(� �� asil����M]P ���un�ĩ3U�� gN�ll��utun�yH�ac,NQ,2�\!.4*da!)�algebraM�e.Q rank!~=ygqZ of�}2"�}6� 5�ndJ\$one$. EN5l5�&�lemma�Fr9L1.-}A.dy�.\J��UBC�J!I�� q.(2D$2�_*gal�>� s�J�z \�,six"�-��ld:�&)�\�*s_{i=t1. ��(�900}�f 11}-01 0��)����=0F�M��}0i}1i }0i}1i�}�}0i�11i�01 0i��N�%l�j �j>��`f-�j-�jB��ff5>j->j}a_{=> =0�UUl$i,j=0,fu(i\oplus j=1�Lb���bf_of.} (SuT j4)ęar3)-5�|n��R��,aY�k��e is �it�%% }Z�g6 n8.nP�n :)ru}�T�| �8�~B'ultaneoO���aF?���nb��l�p���BI:e. (Ne�7�*"�%����ZQ �� �6A9�9�c�˩�Namely,6�~*G�)�** J�. ����xh� �Sx ��_�ce,B� �b�M2S2m  =({� 00},1 1 1 1 1 110,e}11+-T}:�"_A�s&�o $T1!\&g�S!� � ��KQs (3-8��-��q1 N� �l�x �X ��\s�ş !%уЁ��� { }\ 1&�R�o ,9N � % tar���lexA�ju�v��and $s�`-\sigm,�yF F I�d sm#N6 F6 I�d 63V6Y"�� 646 _�62j6 5}=-JY2CFl6 6RY6�I �77v6! .�Fj8Z�NF f93J\��Iv�g�T$zE(����S-i�.i & 0Z8q�%SfI1?HRzH2jH?H1^�I�Ivf�H1H�^H . (A&_�uA�V �rs^{6}ƈ�?r11�@ $% SaC�Es S^{O6�/ٜsC y)�=qJ2�=�1�\tilde{IESf� '% I:}T)4�=- ,R* w. AU�c$9f{%r!{!�i^{,��  $3 m��o��� �˥��� th�n?�.ImJ0�eew8 $.pGC}(�� )$�V=% �\�n9.�g��}{� }}C���oa�.�.�� leng�qe����be�b��"  R .�=\@e2p ���( � :)�h`*�^��r �ility&l%�a.� caepQ+iq�C re r%��ay-Ds*/Fmv!j$t �:�a�9/ �/0� �Pr� ��at\ }2� *�IU�)G  =0�Kva]� �q=y&&��@$-�$. "و�/ 1� %^"LS���!�s&� SnFG !��YB�.�} 2� �n%N�t��S�a ��&� <=2�k=RxK}\omeg�P2dA ^�+� )#6�kM�%�a�$S>0�� � �WR���X$ku�9��ff�� imu�!averag! u�R�v.] $ v =, nk B� "Pi)=�- 6B}^f@F�%O2�Nq� Eb�l~+� m��#�a�!2A�� 2��"��_6��%:2�n:� }%�.r� �.Min�P in��J�%�(6zi=�ef>k}x�j!� ���p  ^{1/p��qO_A�JF^>O ^O��/p}"� p>J�`�get��gY]finB`\V��\ i&=&~]z�e�)�1�<!j�2�j)s,2 ��!pf ^V�d)� }2�\geq �ڟsu&2f:'k-A�s%� d M��� 2B�8� �� � A&2}&G-�%"���>j"of��z��a��=�dW ^{\dag3O*� W�^a&X `w W_{kk�v��F ¿� \.�$j.��O�(q�e �1�B��&��6�Verho�hi M\R�M �&R�V���ts�6y��� ��q [K3�2Z1_P���$, assoc�4TJ-"w)6W�t� uM U&F a>s a R�9-�v ��Z� (12)� � �as��MZp) �96U6 Ps�T} �*� "I�E�apm2�=&\un�zU}15 }~�n�U^{T}-^%j� U��w:�"�-P%�,";!�ACauchy-2arzݽ9�i�F�iѤ2�=!"�8-6�i}y��B-geqsl2 ]5F���lF��r)]*Gf=��y2$%�N���z_ A^ )�) F�R,A��}%L"ims���y $U=ya e^{iv"�>0�kו"F�)�� =1,$�)К�=MKEWJkq��i,a"� ��kw �-��1qzl�z.bf�9 {max�8Ѧ1}(z)-\/i>�-"%eu(zinRX%� .#�-�Cs�, lar �`�i26cr�ng -!,q��ZR5� .�$. " ���.{lR��(�f�$=\max \{0,9�4% F6yv (z)\�m� % On2!)=6q5=0$'!#'*8� *)"b!D� 6A�*@7 "�)h�v{!"'�6D*0Ho}�� so u �߼A��-r�b�,,�," �c, �ho-� f��}*Q�aH� e�A��y�)��b��V��J.NY� invaY_t�� vM~*l'.�|t˄*&m�0{ �8(�>@SHIFTS\ UPB [19]..��=�}�&� �Q# Q%F���P �+�-k �  1,+,:>o +,0,1f>-,-,-6\F��2pm =(�� {:w :v)/��2% �&,&T �X:A) (2~)).!��7J8 bar{� *�q�}( 1��� ^ �� �6: �+ $�$ $.� B�-1{5:i=��4 ,4\["\ !" ]d.�M+ 19],q�@�+^i��Y�*?-A� curi�,�-erth�a�-i�isU8two-way ppt, it���T"�$� gTC;l �-ba���ur���' a"t non-�%,} ($0.1469$)6d�$%�5�); (pG-i"�p!. Le� g�" D��=  D�c-�c-}aIas [20]J[� _{DCTb� } 4@a+b�F& > (- (\\+cZ-"LFdR% B!eB%:!F%J!%oZ!% �\\� �V�1 �)'Z!F� w�E�EU!�$noAN$"X)�)$E_3747$)IRa&�t�e ;c=d$6};b=e=0.$��(a q� �-20Ar)�u tes� oper�G*�a�C a�� non���Q�@x=Y�} �a e]�< $10^{5}$ random*���( z�,z�,�z.9�� ) $ �,PHbyu�,Matlab 6.5 }a�v$xBn�*��these^!/o~" 2" 8 �$% � � tric�2W�a��� (*� b' ' ��� )s�� �k:�Eo7�7� .�� �}Y�.3;�Y&� �i�x��it��A�}!v" �!n�  5-r�Z5 G D �If � nd�J� ��needed�"s y� �� 6L1�7] �red.� BY:& sE` ;ion{s� umma�ASa�n=3X �3*� � �3s�m�pi,e,pp�; �!�d�3F�3��� tB�<�g� a �!��!�35Wo�7'�%"�7[7]%�*�-6��e��3-�C"�6d�1 7�� not &5 to f#-=�re.�&� pn9  ���g�`eaan .,�-R̡�!0e�q� the �.&�`��=�&� �+�sui�6�F�s�s�g )b;�n�'�3ll!�i-d�Enge�deP�[r�8%� n�Qs�'be�e5L oż�� � �2إ"~; s in&�6 "ʏ�8ch Z�� !�̜f*�com� �r�)Zqgdr�4wo���shc�.X�hqWeA g�fu��a�B_h�their�L!��"N���ien"��� 2�q�GR�Ʋq >�q++uI�LV�I�H[�q,M. A. Nielse��,I. L. Chuang&_FMI*�m�1*n} &o�.keP�Q, F��206R� {[2]�r�r&�pe�r:f}nipťOr0f�r46qES. Wies&�mmT��,bf{69}, 2881td92�#9�Fn.`s( H.J.Bernst��S."��Aq$B.Schumachl=P{msAo5�G204ym06ohnS.H�.O W.K.�-N�7Gh 5022�76SrnW.�s�Jr�rr8K.Audenaert, F.�tra���De Moor2��64unC�:p16�1r.Uhlman�o��E2�s32307}p:A 10]}0�R.ypzeup@�Bop�Gnp M*npJxzopa��0rN�kq1bs�1r�1rB1r ValemLC"ruoydip K*wuilliamJ|>\�523zu:Sr�Kt)L]63% A8fOte�ha&�6�QӉ;A�>330� 377 8r> sa��V�&364RVa�Jens Eise�PhiG� Hyll�_ Otfr|DG7h�w,Marcos Curty��L=)�b 06231i_>����>V�tin -hCq�E�o501079e�561�Charlesn�!C, David8sDiV�O�v Tal�f, P�� W. Sh�� John!�Smwe�@Barbara M. Terhal�e, Phys. Rev. Lett. \textbf{82}, 2881 (1999). \bibitem{[20]} W. D\"{u}r, J. I. Cirac, and R. Tarrach, >d d 3}, 3562 d .c�1]} Different from the previous definition of tensors, all the quantities with indices, such as $T_{ijk}$, are called three-order tensors here. Therefore, �set of oon62 is� #vecto�nd :;two-orm:<4matrices. Thre6g s $T ��,@ correpsonding to� planes incube ( � 1sp618edges) when any� (two)�their %- i)Z� is (are) fixed. \end{thebibliography} B7Aute}[2J�[�6�6�,.2}}~�2 �]>%��r�\%@��N�\%�:��ArXivNo}{\href{http://arxiv.org/abs/quant-ph/0412105}{q>aT.DXXXXSize}{{\fontsize{12}\select\fbox{�6��>NTitle� fill_%8line\vskip 0.4ce�\sloppy�,otypesetlogo�Xmarkboth{E.~B.~Manoukia� dd J.~Osaklung}% {A Derivatэ@he $Z\to\infty$ LA�, for Atoms [�]!t�{��{}�PH\thanks{% Published��%1(it{Progress��(Theoretical��(ics}, Vol.~/bf{10ᗀNo.~4, April 2000, pp.~697--702. 1U % [\urlQ�ptp.ipap.jp/link?PTP/103/697/}] % }�author)�$sc{Edouard2k}�E-mail: � tt{e -0@sut.ac.th}} u� sc{Jarin~5�o(inst{School!�hics, \ Suranaree University#�Technology \\ Nakhon Ratchasima, 30% Thailand}AGp1�in{% <%Write this ONLY!� case%�addenda �errata %!�.~%�.~�.\ �bf{XX}/ $YY), page.yXrecdate{October 4, 1999�$abst{Upperd,lower bounds8dA�edE�A�gr,-state energ% neutral aE�which32�a2 involv�e ���Lexact Green�s funca1s � E Tbody potentials. The C^�shown�coincide K@the Thomas--Fermi2� �!7\begin*���kee� \se�{Introdu } A very ��rkabl� opert%&) at!�!R� .),6� �\cite{ _1927, �  $8} becomes)Z. 9(Lieb_1976, 881, BaumgartnerH} \ Unfortunately ��ingend  proof%�E� :DU��A��resA�n%�fA�that ele�ry scal�pI-ii�integral-deJ� allowa  readilyI�nsi8 >lEmi 0no difficulty�$basic idea]�^� q�%gqh nt s�  pointV e��v� analysis A part�arly siA& p��law beha� %� larg�=$ �$is is spel� ouuT�. ForsHamilton�of:we ��seq�equEXd}\label{Eqn01} H = \sum\%G�b�A) E  �+UO,)'k}MG ]N� se�Pat $U$6  Q8n68!6Q�m{}U:+V#�}{m�%�i}Ua:� �%2+:�}+!n68;!OusU = 0Fith�J $i|_{!f=0}=0E  We�6� {� &� � nJ9�I_]W r}\;b�eR� $YU!r�=E]$ in �7})" _ �placed 1K  Un/ a�  we�  $xr}=R}/�x$,.�X6P$,�� $�d�]$independen"$�  Accor�mo study%�"� & ,� arry� s 4change of varizs�l!?R}$�,simultaneousu (ubstitute $ET��M# Also�t2k k )(kkK%"vk}!Gp7;� 'T!���!�\ins innt. WM�se new�,<8Y j�10A�q�N{}T}+v"�M@ �B _{\!\!R}UN��a�B(:]�l ^0.M�7A!W�?.>wLet $� _{&�}U=U_{�QT�ub(10}) collap�to $-=9=/t+v=0$" ose solu�M $0=vTM�HencecB&*< G�099�A�pA�ca'$by $Z^{-1}!$}=q�[O�ofhand, ifBj unitjO transf �Q�qsA�U�a� M$>�8leads to $U=vT+]cal{O}\!I�A$.$,a� $"[U�ek%�aV /2m+.<]\to N3K3T/2QC+�� � -�� latter, u�aa��oequ�f�K!B{!�619#v�j�Q& � , giz� ame &�E~6^as bef��an over�A by�� ] 2��^ifo�.lsj��,i �0verified upon%H��io� $vT$= $U$,2*~:��sub s}*� 11a��N�:�2}{,  '_{-�%^�.\!���uDA�}~p va�ilon}j. E long�arrow{�Zv6' R}\:j� �ZBq�5 �-7/3} &Z� ��.\z�  f� !&>�B3& 2R4)�J K: ��[!�)����j�7� +&����rm' ��Ksqrt{�M2m:�q}-�K}| QB�&\.=S�Z� 5/3}:� }{10�mE�>TS: Un]�R^h-e�k-^* A�T)Ef�}{RF��e^1RRx'r�12VR�R}'�|}f�').L"�11b6�\�"6� HereNe or 2 � iply��)� $-� S#maccount � spin� �{B1project"4 negh spectru`$h$�E���)e cula�$of�dw( importance �It ,s������.�$h����, has�J (orthonol) eigenb�$its�$� �$Let $g_{1}�Tr},\sigma),\ldots,g_{ZB$ o� ese .�� fD�&�\tknantal (�!-symme�%)!Ac�DZ�N�� \phi.�� � ��� Z Z}) �evA�yZ!}�4dete�[g"�1_{?-!e.y�B� Si� sQ'!t��, does not ne�arily J�A%2r"v�'he.B $H3 *1I� ques!cieexA�� valu� BK{1_ }{H} �}$ �ree,ay$.6q1�c 0nly \emph{oveOimate}��.�M$E!�$�4$H$, or at bes�l~i_W�V}Ka�&� !�alentlyV ��Nl�v�hU*+E;��B*�I{�2aA�H�k�Qi%~��|�SFg��w���pr��E�nQ�B:� �>�y&Z� $9��*?9�A�v� =� e�*=��.A 1�"� �i�*�0 � ET( &\leqslantXlir3!Lv>s &=��v�BK{��}{9S}E�+~�FaIL��46��BN9 =& �2p�(_!$EY6p\,6':�Q�:a: n�Q� l�� )\,]�B�* �mp2:{ƭ�'��N�!� [��.�' �'��s-T|20 /B.E(�9� B"]:56j6؎~i27.)  Y�1�-�)\| / }^{* ' !'F�or��I�.�M̥!���U�R� %�[]�(6Ey}jC ": .�:�Y�> 1}A�At.�yrLNF'6�Q�F��3 ]ř�76uHowev)we alsoB�n�R�6�)\� �& j2& E2��*�v!�>����rbN:�86fm�u'n��86�:���jIj�\:26xlambda<0� IQN"���6�J�!~inV�I r�?>�� ^{}\times9z zL }e96��� $!^_{BW�  $%|Vs a s&v.+lK4&cM h$$hP2� , 2��icU,�( � degb$ac�' The 9(takOe] into�F5y14})--"1b�% e finally�)�,E��2d !��5I�V.#�"�~�% Oj����.�Jn w&�&o BhR: Qn�5>���ΐ6206A GŮ-� >*�coe&*i�of <��n#.�: &A�gyA� :'*h.} GivG6arbitr^ realE� posi ,"� $)�Z" we us&R*b+*-book b�.-4Thirring_1981}&'� F� *�Z�*� � R�?g"� &Fo�FOrm ia�=Zr "�}"|�2D B�r:�S>t��6�r5:� :@� F6'�\3� w'�Zn'e[R��#a>�0=$=J�W]Y'6� 2163�A�I�"�J� may bb,se�0be U�a{iss wise0u} (i.e.,:Fat will) a�ex1b&$�+>�of&" 21}) exisI #convena�ly- i]-� wa�!t$>�)\t��6b� $�$&� 52���'.�1$"X )$a�d abov`:�� 03}){CW+!* $h'`!p�V'}er��e�p .2V'� � m4"�-��*>2B��56/B� �!F�$B�sen�#�Q� c� M� a loc�� squ�-MFbl�|`&� $R%�0r��6)�Y!psi�# a n�G*nti" yI in $1k��  v�q�!:�W0*atF��si�si��t>�)J�}h'�^}{�BM$j�\�\~\��B[�ana6�, 2�/stP $E}6�!�5�=�EE , Pauli exclup0 pr�e ple .5?rescue �>;55�b cern� �d"` /2�}$$Z$ ``non-ab racting''�ctr10(although eac37t' 7an �� rnal&k/ $V'$)ybe put, S'�� J�,.�+6hl�5� f[�lo�!�*� )B$� is le:�:j�/of�Sv(9�k u�9Io P [r%@ @'! free=<should?"O Tsm� kineticIJ�o��6on� � n ei1%�9 , $E�4bK�%�p1W>�$, �h/ ��,(now�-l#'%h' �NN��/j�� ��Vb;KBb"zBz,"�N{ �n"�n"Fn"'N02& -� ��D� N�>.*� �[ V[ q~\ -���J:�:� $n�'P,iam(a��+ aae81 e�alo extremer! 2W ��)FQ ina*�4��66�,#�8 hold�� #F�2�2v"� �H$! well, = t$Z�F`q��3.  \min�En�^3 = E�B� TwF��n� F� >0����y�-hoose it6� r�422>x !Bj�#)\(!1- 2-Z��{}Rz5�#5&�� $ #�n�)e?#am".n �0T" <10&6(60sim{}R^{-3/2}l Rz ,e1�D6 B B2� ;$l$� exp(� )}$ ensur��grabii\i las4=(J*S�=J��l�#*���]�� {}R#1/Z0(u& 9��Ij}�#:R\�PBs2�\%~.v� ��H�92�)l}� _{1> � {}R>V��v�^k��&�".)-���*� 1JR��)=-�::gaCse�7qJ"eat wo�;4logarithmic in8 �#0��eS termFO O2�5}) van�E�&$*q [�� ${Y9�57.*)}=EA0ſe ��(�m�(minus sign)��is�5�4 elow�0��h*a6-)��VX �n�n:�*} FiX������s!'$NYto{}1��2��0��V'i<v'�k�4 1i6�2 3&h,)�|/����>*�/- �>*!>�"B�?ŏi*�j��J�Al�&ld!% "�8AI� �F2NY +(s)0d? �600�_Thi OlBt�(ur demonstr��$In a futur��*��inv��gz; to w "�is "�B�A�to���onsn &  *{AcknowldOments}�QIs w� likeOQk4E Q&4�L�Ab�Ipag�F�F>}O{H\ragged%�*qQ�@fF} L.~H�HDGmH427): ``The Cal,6 A�J0ic Fields'', �IiuJc.~Camb�H il.~Soc.}"fJ2eJ,pp.~542--548.aR"�F7} E.~�(Un Metodo S�)stico pe>D Dx 0minazione di �Dne Priorieta dell'�e.�HRend.~Accad.~Naz.~La�i�6},�602--607R�8:�8%:Ein%-� sche�$hode zur BAj`mung einiger Eigenschaftems%hsc4, ihre Anwend3auf di�e�( des periodin System0Sr E�F2�Z!�ys=�48 �73--79.�TH76�H!$eb!�76�A"St*& M� 6hv.~ModNw (4))d553--56N}81>}81 }o*�I_Re�Qd� !�)JL MoleculeA� Q� U.� bf{53 � pM03--641��re�nc+ rein.4B}I B.~:?i��DL�+ RsItT SEg-Coupl!LX5''� Comm�NthFg7} (3-g215--212g63 W� E�%l1-A Cours�M�ImaR[N3 (Sp��New York�T68--269, Eq.~(4.5.24).�/E1t>AT0TP} ]�%% LyX 1.3 crea�=�Jfil.#Hmor�fo,N?�Pwww.lyx�P. %% Do� edit un�youly ��� Adoing. >�Tle8\paper,twocolumn,english,�FN?�K?2n"%�[! -�,{\epl}{Europ���t. :�W@job}{J. Opt. B: Q�T. Semie� :6 pr}{�QX[>laLr[A>"0UQ}{ARC Centr%�ExcMn3��um-��i�RS8*�R al S�# ces,:�RQueen&0`d, Brisbane, Qld 4072, Au' lia.} 65Q>Iv�8sN{0.4\��width}\ $-98.4pt}} ֱ�Й�% eps��s.�Y{bm}% a� [h2ams�;�!Hmat��M2abF }?Rat`?�d"�Z \t�U Enta"Y� �a>E�T4ein-Podolsky-R�Ldox� c��ed a� acav�p�s down�!r'Y�ZdUM.~K. Ol�" ,P.~D. Drummo�T \affili� {\UQ�Z \RT\todayW abAct}�4��� t� evanesc�4 �0 $\chi^{(2)}$�m7:� i�P8 a Fabry-Perot �� a �REsource*ra�  squee�Jl�3,bUc����!qa� um e=�. A�PE]he �S%"s�thres� regim�Ie)how�]s""T���co� �Pby adjusA�X%8vstrength� s- detu s. Aw9�an�3!EYeF� ted E*s,��-Ps a~'si!Rrou�8 o ru!%s�Ne EPR-qi� Y \�P{42.50.Dv,42.65.Lm,03 UW6E� ^XUq, q�i (EPR)EAa� f +$a famous pr "�W!�$1935$~( EPR}��$showe3at #� ism��+�Osw%�Q$me�Ai�a�Ttenes!� di�� f�T!W2w�!Qpar�]Ainuous*;6wa��8s!�s!�usAnonA,teJmT amplm I�(h0 � n2AB OPA)-epra<}]`A߉HiO phase Studes us�6t;AEpos�T�^TB�k" p&�TaA��Ss�L!' mo�um origD� daEPR. Ev o+!b2�betwe �;� !�perfect,0y� stillu� d su�*NU�-� aa�$ferred vio�$1�u"tainty cW"QP�qui�9 f"=�9uMDR,r!wAn�eri!al6+ dis%B!g!Ou p:(et al.} soo���!ed,E�A ,a clear agre�IfQ�t-y �Ou}.  4 work, �W{Mr!|6voM1A�M~oscilla�.(OPO), �eI}Jn alt�"�+devic��two ]��] I:$ �%�s�D��$�@ICِ over�G1�.Dmod_1Xnon ,ar medium. G�,<'Bd�m�)�(�!2"a �leQ crys!�$pumped by�spa�Z�Ge!Ra�la� !��i@�hI5Kity� (�!u 3u �Me�b/cl��"�d, predi�)B(yM�]Y-PIbrahim�b�g�1A��Q�}� ing :korea}.Kp� 2/ &� �*�^B%)traveiwq_configu� �5l:�exami�@e� !����> �_�"in�Z���a�6� a�)�v �je�.   �mista}�hsuc��-ҁ�2Q��� �}�� R&c� Iyr�1.D ." hel �"a�Fr ��Ing -oharmonic.� (SHG =�,e�i)J��Ba�^�dimer� o namn �6m� ��)a���dF var�a�>͝displa�.. Q�"rete sitm����_ynteZQ�. =��xs,.?no�2sup�]A=�]A;Z9��`�mce. ��Gt"�.�fe��( E�axc/YW+)��-@�] �bhromag4, f� (See M�`na[b�bigpaul}9 ��b view),]U�2combine�#x�n!�ya�t��nA�r�o�~ed� tersY� j0:eadvantagm�Y r� e !all-i�%��nGm� i�� promi�gc�8mA+robustdd� ��� ��'J reRe7)*E �J�EW, ,_iZfo curppdse. An�m*1/w{ a� � �2�II .��T* OPO \2�A�Kt�e $ili� z )8�&B Ocv �se1,2}. Our!c� �.b�*llA�be�B!�� ��� wiO0ta| oXh�oa9�fe%��_�fd� a�#e8moa�} r= sec: }�@� �wC!sh!h�q%2A����describ� Ref.�҅�}!j�kLt�ail� iYm7 it 1�"�*"��$%4 Aa!#�=t;"� ($2\omega_{L�4meqba2��iI �L�u2�de��B�&]"�  a bri9 Ap!i��essi5��2) ��a�a�wJ�s*� �=��6P+� a}�s a dr~ M ).q��utA楦 *�0BL"�l+i� eic� Eacho� orts��� onanP a� z)$1}a},\, b}$"xZ5�aN�A�higPh Wyɲ at ^bP%re�coA0AKaS�ס�r���%l� .�%�a�M8M�=h�s pai��f Y�!K phot�v�� a}$ E�assumA� at o�L�)��+=woK!S�ySa�a���s9�umatche*I#h� I�]�}&< U:o�iJ�.�"�X�Sq�5 y@bI�A�� 0�&��t�&P<��&�6i -�� dox, . �!�J ofF�.�!ef���.D6�P�z� ��rit�#as o�p} �,0Y$H}}_{eff}=:int}+:)�B!aBrep�� eq:He���T�`!.�2� E<�w�1by���=i@B*\kappa*Z-hat{aE:$^{\dag\;2}b- !2 0}+ #2 2D2D!Dt}<,\,\,..@n�"9?[>$ �qR� e]*5Y�n/}n(DH� %ma�a�il)� $�k},\;!k}$e�A�bos� annihii2g orV,> a��1q�ie�N�3��; �U�ɭ� $k\;(=1,2�;��E�_ by�=��TU*� �Ne}=E, J_�>"%A 5�+�k)�QR21�+T�UU!L1 U :U6UU,.( �fk$J_!�%�!�1����n2��A =�, a�q Z�W���%��.kc s� �m�+f&^,�a9.is ��&� ha��B�� C�ꥒ�x �*� ! �asG$50$ bHV�.:�Z re "&d�W;hy� Dca�bD&E� B�7!w 1T��9��ICep \�>EtAU1-.^{\ast.&+N�- . >?V��j�R k}$ �&e� � <` l�)" /#& 4$"-/AI)W dam�W��i�>kPE2�8(\Gamma� ^�cq�6`e�+!b!!�!��)+h.c.2�xn,yu.* bath�\;>��*w�e %(usual.% tempe��oxH5�U !�rvoirs. GB!k"X'me~,FGaD> erQN�u�hor/c-�=W s,~�$ s $(5Uj)tZ.a�^\awe�ial� s. H!iARInPy�% �plusP}#,�`do�x�"gn(+;aC s�%low!"2� ^%o��B>��2? f�I �uX!��%ֆ Mak/�2�U��1X��2�I�j�dag I�   )$ $(j=��.eqx�)e]� ^{+},U� A��M ]f��M$1ss,* narray}  dk1}}{dt9= & -(\g� +i\D�n� )/+� � � 1}+iG �2}+0: 5i�1Jm\et�E�n2�I%F�c^�-V�3B��->�+ R�}\ �2��2b�RW!(� 99s �2>W1RW�8 �3��c�W� +>W2�Q:W�+VW N5W4n�U9]�&^1}Y�b=bb}): 8)g M��-bb�^���^�= .�Y�.�Er�+W%R�6v�6~9(22�Y���I(1���V(P� ~()+f(F(!�+vD`W eq:PPSDE}� �&�$��6� 6p SFg added��f) $�;,��� re& g-�.at � ]5� anguQc&3 &�L/ �Um}=Qa}- L}$�E&b& b}-2'clow� ��~�y�� e}&�.�8���&�e���Q Gaussian �� �{�+�U!Ho�% ine{�0j�%}=0�[�J *k}(t')}=9u_{jk} (t-t'QNot�at, du:9)�$.,b �,�A_\;(�k��#$�Y +2"a )�� �lex�ju::�,�Iep)A~8$ ��M�|[ g * Qg�s(H&.&� �)"* do� ow uCf"�b expec. &T� desi$ ime-"ly  2�  �)s,�2: d <ooY37�...~ LineY$+|i�ki�A�A. }�(�"e!nzg�i�c2?+ lid,!\Yfluctu� &�;*-6se �Pof�b�i*�a|'�3AV� DFW,mjc},t2Nit!*an Orns�/ Uhlenbeck�� @o !� �:�o� 1&5 ,di5� � ofQ7e�.�o a=-ady-s' meaM�9/^t, e.g.y 12� �� ss}+i�q51ind��*�����fi st��� :qs� sol�+�1sR�)� %'i�t%s (&�?����%�a: �o!�at��)h*�)v���x.Cv� $-$tilde{x}=[ "�,>�b:2F.&�6F$I $�y}]^{Tdto�~e�)1T�s,!F�d\; ��-A: \; dt+BdW.TdAB��i�}��drift�iN A=X�>" ${cc} A_{aa -A_{bwa\\bb}� 6��6���u_u V���s-� -}m>� �  & 0\\ N&f �o"� - & :6 2(6Q!�ss3@�2� %Fv%6/2� !U�z� y^� ��!N(� ( 6, �T\\L$N(T��bRz�-�+q%�  �B#!�b!�,=�2= ,--JF�"�DQ�I��0�, $dW$aXa��of� Wi�( i�#�'a�˒!$B:�9zS�� Ţ$four diagoI�[s��3�wk��J-���m"��KJ%�Z"Mr @$.�4&�!�G�$  expaB�vw�#" � .6 �R. e";2;!�m��)x `:d�y W. %��0<� �l��)��4ricJ�1H _N�>A)a*& a cri G �p � ar�,%'5;n ' ,7? q 6A�as�/$ �*E�-.}a1V=5=a6)I�n.�$S��*c!/�� )��4��S�e.ds��te�o�Ow��(n� Y:9b!�i: $Avelop a&jbY �q. A�)+�e3� hns%�V� "- �no�e�$ +=<s rt�z growA�oS2�1 �n"N!5�i�%�atful��edM�isl4"{ �">�! +�� � 2a�%�h!�ya�,�s.�D�1�i4 ne�w Vw M@e*7� � I_��  (te!��B:{ ;�.� dro��9iV+��%AF�v0rI�nu�"�: �3I."�j�^q)t! high*��+L/popD41�6,�!�al�#%Q$��p�/"�b )$. Inser�H�"� q�i. a.�7s�m� *(}9�}y,*� ��W_{1,2�F�����b:33,4F3��6 35,6>3a"� �O12 /\05M �}_�2}-�%� ^|7,8F|-\�J�||.�"autovalo.(1x#�^ / aux�>ry&�B� {}_{�= �-�! +!,�2}}$.�>im$� "{L$5�!$nd��:w��<�IV�h;;""� �[�e�c}=Z�}Vb}/I$.%/it mus�:�5x"f/N-E$*!�/`@�,%�Z1+} c�d��e"�!�-set�� a���?se���3X}�t"?q�aυ�ųJu�.���\�Mn�t��tly �fur�[� ���uX ��e�">�I�occupi��k�!b�V:?��t!��g" al=ns���Fs�L �3!jasa�conJArate @ KKn��"�Oche*et�.��hb"[�)uE4�9,<C �&*�*�-%�*�72_!��� A�BE�-�� a�%��Gfixed1��8�#�m��s�1�A�!�/$&'A2 %&2'. U !�)' 9'Q�s���,"/E[.70ly-edZ{al2�J�&U!M<�ulaݗ� } S(�)� (A+i  \opeX ��)�BB^{\�h{T}�!(A-j;.|inspekBaf�E?A�~ !��I�8-�1on�IA AtoO(iC Z!t"!e ;dh;,%��23G2r2�0c*�C Esub�{S��&4<>):�7ado�0�) �A��0]-r �Ajle c&OA�D. K tra,! 6 9sU� -�Arem��E���@c- OPO.�|]av٪s�\�}�*X}�#A6�=�#ej}WKe}^{-i\ &2)� E!&%,� eq:X7g9��~ (�$b!$S�!llUjno��E��0"��% ,2�^{pi2;Y% .�Y2�~"1)�#>yd$a���u Aify�ɵt��E�$a$|$bᏡ�i�M_�pweN�z ��+ /!����Jf�)��hh$!}� ��]�:&��s. Wit���OB�1T1�6te ��]�I�#onvo�- ify ��Q%>-�c�� each"�,agZ�A�l$"� 1}"� _{2 � "q e��>t6V�)�&^6�F�a�usenho:b�F| S_{XA��out}}�> &� 1�[4� .� ^ 1}{"� .%-*Km+Ng ɠ} :w%�Yv�4!�$��� �keq:non�F VXVY��q�A)*= -Y��&av��H �F�$Y$. vA��)<�"; y�>E =1x.�% �'8gi.*[ break��wn y ^.C� E�u��!ou�ʼn�E����/$F� =1+2�V3*X��8-�� w�Xb��ecv.�� �P %��[�!\.,ba�* ���N.�fRfo�*mpfo�5 g�� �y�e"� a�6 �����-�O exti�=!�`Z $�/e�� We�b9�%3Azm2�D� C= :���O&�� ,w y"a*�8n�$\��_d"tanp (J/1�b!��B��=���mu6� � �g> ly b�un�0�$X�" $Y �T ��C�L �*n#l�*��Ppree� ��j�?in�C� ie� granj�AEx&�I� J "��8 aAmbԛm��Dl"�or-o�4�Gw< Uss� )P� E��!r���luda��!h1� �A5� I�"� %!b0�maxAɗ:TG (a��oqgG)��p!k��,A�by@�i/2%� ɿ�R�6] _{opt}=Un�\{�2�;�+Y})}{  Y})- X})\pm\*� :$�.]��+ 4j)Xa&��\} .D�%o�<� � V(A,B)=\l)jAB��- !$.&3~EB�A^�-A7C�Mc�3*  sj~al��bl�_�� ^8!in�le�� �"���!�q�Mrif8=ll" iA�nor@w?2:r2� ���6 �9z�f"� U �c64%F ��}=�_i��numerb2� �6X�? Y}$~ �$ variq !:q�Q�Vv 7�ȵފ| ��Ev\{�N[B�t� aA�&�)+ ��K� 2}+R� N0 ڒ.�U6�e9 \}} .� }>� �4*! �er�FFa �)k)�  1N �e�R� ��J� 61��¶ ��� ������R�*� �eV� �. , X����c .� @ F )�����3GQ� . 8�co�N �"�� ́X}�ѽ )�*� evJqF3"}�a�+&� )m�!QD i1������2vX&� 1eE�RcC$2T0,\� Au� � �v �(N]��ed*y  )�_&& ed &� . 3�&�Ke"���erSk� ,graphics[%  Q th=0.90\c=`W[$]{F1VX.epsH BN+capj{~ ZZ �;)vh/=1��Es=1$�� ��;���8-U$24 %# a*;solid~!D!o I=1 C=113^{o�.!Bdash-dot�X�< 82�h Z 5 VDe !E !1��I=22|i��L �i�.M =0.5 _{c}$ in Wg ll *pl�b  #X�1�b"�7lb.�TI/tra��T���ut �"� �!;J �S�U� 3{@ =0.05�""`X0$+��-fig:VXJbPt� Q�4 Fig.� 6+ �%���c �? �l};*� !�!�yXA~2�U{$ 2 w&� i &-Q[!ᡯe�9�!M3i)27 =X6&�EL%j� �D!���Me-\�;�Mi�Bm, ����Ra�%a-��AfCy�!@�L�#"f&XI�hWE4�a!x�"� �q mz.�9�"�6|��&l�/o�7/9!c�,�ls�,n�[gu!�b}$ maiG serv[o "iB �"��� ChaI a}$ ZC&�0enaft�Gof���yE%"q �'K�� effi�at�c(H� �1R�e/ i/�| lU)>!�I�,��um=;�3b*�R2 `>� �z�i�s�� .UV�`PR�$dox9f�B� c:�] An.R%�Y*�jIJ� � y��&Ien��%d0Dechoum ^VQndturco}��oi(�U!�u�Rer\��LL4u%��se5�Fa�I" pply)mq�)D.�R�� �L� �$.ae6Y^seRAhgP�rf\2,p&�V�i+nBG'?b��&AT&2]/!HEr -ond"YO! �#�%&ima._ryaa&�[:�R �,�� x[R�-"q:K.!�M��%��Ne.� > �#�P� 1}�2:�Q� .!�.2-�&pA�����Z�$ sA�[&� ly. Optim�Q�%�%�"�����;+b�k�ormed .n F�V�t�5a �*P��.fd� guarant�*���FH=!U6x+S_{Y�p:<4.�'&�|dua�6�2WeA,���0aa0-�&� 97�an obh�hipZ !�� ��AQ���6s� ��� � ���j2_~OVSt���@crat1, ����;�<�NtDbU5�.���re "@�e��k :�6-"''Z:se� ��a-B+��I�j ,0%iu�ng ��*�awk!�+$�, �,nd�A��4�+B�-�� ��vid�FQs-.^�NC^�� 1}F�%6\pm&dJ!I 2}),2�! YF*�x��'?�� 2}x�eq:sumi var�$i^1 !K=GY�9REF�n� ve&��  )93��P9&}>(A�:J=*��-;�-8:+�� � %>�"{6�}{.�n:. +Rr�>��a�2�&VXX�"���]�1�1+-�=&fB�$"�e a�q�. )�3�&���� z$*  1-. A*�s��4"�=�e.�.Y;�ZdY��s[�e �R bulk\�v�enldke:,�;�#"L�-!m�@g� �Yهof2��Xa2�!Fy-6�w"�_+� s< 16� RQ�56j� _{-})�]f%A+a��Splus}B^� n�x-"� IQ�9s;!(24+�. W���,P��-6���Ja}���1deN�.vJit�c?bV�"� �a~�h��OE&um � @s+b��W�eL6A�PXH ". 4,1��� ���alway� < at�#�$5 �}� �=�>2�r D"� A�:eI /f����$,p'$�76Vd!�a(&! ), $2$ (d:�5K�)%�$10a���y 4!��i+��67�G%�� #aN#15 $:��:%1�Ja�&&:�6W[�/A��� 1�2" Z�hI�� B!PachAF�.G)a�#�h4�)%A12�Qr "� ��5�5iKm,� s�#error�a8 a��a9�I:�ly5 ��zj2�s!�.0�@�vA+ar k}a*bl�*� �minŷdO�  �E'k@�h� S��' inf�2�)���1}�)� > �- f� \�~ }{ J2:t:��!k2�H:TN� 8�  2}B�Y '6~2I6EPROPAmGe5QN �o����(eR.2Fs {1AGun:swappA�� �"$2$�9Iq!�Aq�a Y}k&"lhxuteI�m�sM�Y* obte HeisFrg .epV)pk�)�j:.�>Ʌ1D$�-e  a*_��E&��n?$]�aS��j})�()7)\leq1.��ns�4ion5�e.�N� Ya��Eq.�eq2@ "�.8 :0G �Kh  we�/*]o1=*e zmJ agaiٮ��+fu�r"�%�w� unw�fcpoo�P?�CYY.Jw epr1rN<���6%��.X s�le��L��8i&b t'B �!8��$�7 6� �0$f.z%�2� (W&d24�ia�.�22��a* conjqK�)[��g�@fL " 2��>1� �5 &t��R'� �M"2 "Gt�( $ �otI� =�g�&_ ^���e4,�t.r ��!�hɵ����� >� 3epr� �OJ� B� !���}R�!-"}=���� *T s;E2=� M :e J) >v $1� Z� J)���mp�F &*Ae�)<&A "�gDe�P%5�/@sec�O Of�)�mDh w0I�0�3���� ]��P2!���X IP��' ܘ @<6H@���� "|P\ ��� pr�k �y�z*�q(�d A�`��&yoE* o&��aw=-a4N�-im�ytm&n+|]�s.ɛ�!�#i� 2[Bb6{5-#�Z�4�:�/%^QF�oA$G= �Fss"d�[}K � �)-i�/-�RLTO 29�GdOXM�&?S,*'�6$KW!�retur>G�& �6�.aR �.4�w���Rt`a`�$ *�ne*.�$ $A_{p}=\a�\1}+ y !�"m."-"�M��7��,Q�k �h! �@ �AP�� ve-P.�Q1@�!���&� �8d�.U-1�a}�' ss �MN�Yss2<dS!�Y3})�:S.�Tn� V���AY�4~�m:��+U� a}+2#Ka F]A_{mR�m �40�+)�F%- ��% T6%:�-J�^:����W6:.` PP�u��rL$A .�F�a�C"�:3 �WR6%*�6�:K�-������%����TeC/y1��a�p�e !F�'a#�oaBm�]� T$*ss�@t�i�0��R_ �t�"�Fssy�al� �l 5aky �# �#2?!�{.l$X$$Y2k%w"<� #7I� poցu4 &g � �tAst..W��@�!�%�B�;"_zAi���p {/dXm�8�_^�Q�Io#cf 5+1��Qp��eC�#a_{c~`Qs�O*O Q>�*`O�P)2�Q &:KQs"GQ1vbu�! éqqR"LAfF!1B!B_�!V@!�f�Pf"f@\\N�_�W x-jW�y^AF_. Bf_� erm" *W�@� PBY�E�X'X[7'�Q���X����+��=[4}+,2�X��5m5�h 5-J5Yj-ie@(l U&�+M~)=�+�6yYyDmD �I� D- D*!D^}A���"(֡؁}�&�va�"1��*~s�#%f�J!2E`�mO�% �%,J��>e#Z/-�2r?8&�  bB0)� .�=�D� -`�+/z}?~����� ��] Fa�B�A�$�s�)TfAUzYE<wo&g, OPO@SsEhB:@OP&�# l/&\.o*�<��RreB~-�� @S�(ic((*@-5_{"L"y! &�K_��?�4:(xknown:�\�&�p,1Q �&won6H^~>�,mC��-wa�)�&ۧX�ubBm"J�):� ٭�=�vu�C$.��1Gl�:.�Of�m:0�e�[R�:�e�"� i�(4�a�- *�5i�]F�*m+DC�+"QL � +*a6Y\^e �q:��B~B�BjB ��zB .� ��B�B-B.2�&� ��6"}  G�5a"kB��],�#�Arat��s(*0(�(Z�!HvaJF4 B� �)X P/fa�>]��M���  ��se-Q�Ter� h7 0almost $90\%$RZ!�T�.�Bm�� U�Ha�$OY��*jK��&`#�1UU�"lv��� 9�"��6���/��o"�-~���n inct�G?ao,�1���' �%!&<ch!H*�& <���#F*Iclo���cS��At��"�!�`QC. A5)3ch@�5*�$&/o��i*Mc:�&k!,.�$|� *39su: �/�!�#w�won>��9:�9 4var�z wer2�9O* "�&���a���!�Iw��"�"�6a !8 2 6 6y#0�8&~#!�U 6�$�d&�#2� >2%zA@�#&�9VF^�uE79��n$B(�[sy�I�; Y*�#�3B>7:�#!]�>Q"R&5��� .i�R'Y'd�[�e�.maS��s�k� 6~'��n5@4(.�}%q� ���@duh"�g� i5DQ.� X ���aw�bsD��L�S1'Fofmedto>\ A �k"R` cQ�Tmp��tEf� �ڱ�R0*p@Q>7~^3\.x20i)e �*�7�RUis]� ��/6/�M��+i�"cHin:�1�Y) a� �~�Gb�+membe���%�abBp2�,no�_�, merH�!�:90P 6;9. F�"ng � .B E�EPR��! �+"QuAG��͜�1 %oac� *�Fan:�3.A^�A("M&�-t#�- 2})=[V(�)- m}))]/4$,qu� �howAZ�7�]u)]�lU9��& ��� aΜ��a��ed.mF5D�ll.Y"-usyh%'�UB��m�����l?�"�5�2��� JKdetepr}]l&u!�Fum&�&"� Q��I�Kx��A�Nx�rt.$4pA~�C8 ��e*�:�a� "\=U�!D {�F�a�th>��X n#=���9&t�9�nQmB��*V) +)a&)a})]'� 'b'b '�O1�BL�D�8&Y %G��){�b#s*IM&8/ "P�D�>Ele">ȍre��JfeI� main aL�� ��it�YI�.�!�` aFIp&mE!um&Ԇ��%�;m6�N��� �.�l good.�&zMv9�҅����JJ�M��6A���dis����#qiv9-d%�� i>��� + Az�Pa87� $c{1).S)R /q<�#�\�sl�1l�r grad?PTM%2>t%�U"7ca�Y�6Jwi� &mnd ���$��r�;th| $!0�e�S � /B /5�Yrv +**'bQ, J� 2V$ A�k � k  � �4"� :�$6a>�$�$"�.E� �$2F/A.Tg ��$4Y' c�11� NQ A��Q PBU %�Id} \MR�(z�F6H&^Y !�f+�a}.Q ~�}^�-� �0J#5�5���� V�. ���pcaWQ�ulVv�a}=!���nFguish�Oe�ax�% .� N�X $1$ represents a demonstration of the EPR paradox. The pump amplitude is $\epsilon=0.5\e |_{c}$.} \label{fig:detepr} \end,ure} \sect|{Conclusion} This system exhibi�$wide range��behaviour and is potentially an easily tunable source9hsingle-mode squeezing, enta d states W  which� > The spa| se!4� of +output p(s means thaGHy do not have to beAled by optical devices beforeFsurem%�can8@made, along with |@unavoidable losse�Hwould result from t!u procedure �94beams producedtpdegenerate in both frequency !@polaris%0, unlike thos%��nonF OPO,9 �exi%($ cavity at1hly -jed locbs�is may!$a real opeI�$al advantaABver%�J�)�0is also known!� �2class%�I"ye Elil�%�exist!�cau�umberA�$different A4meter1�-�experi!�A�@ accessed, such aAJLe coupling strength,%Zpa�intens�!�!q$detunings,%(make it) restHfor!=qjuY appli-l-&)�!�ireaavaila) ofqD�VPelectromagnetic fieldI�varyingAV rees2n�-k ity. Sincgis typEF�)is coma�a�wa�gA�diI�1}, 3930�90:�hOu}Z.Y. Ou, S.F. Pereira, H!%Kimbl��nd K.C�U\p.�%a663%a92b��er}!�4e\u{r}ina, Jr.%�:@in \emph{ProgressO�.,s,\/{}}, edimC4E. Wolf (ElsevE4Amsterdam, 200��DIbrahim}A.-B.M.A. a A. Umarovi0M.R.B. Wahidda?\p=�461}, 043804, (Fjkorea}SUatshvedZJ. Noh bK.!^, \ocU� 212}, 115 V:KTmista}L. Mi\u{s}ta Jr,UTHerec, V. Jel\'{\i}nekL\u{R}eh\'{a}\u{c}ek,E0:z \job�}, 72a�F�hl!� uJ. Fiurasa%�:�.,6deY19 �365Ddimer}M. Bache, Yu!�Gaididei^4P.L. Christian��y3671�a�20>cbigpaule\Martinelli, C.L.G. Alzaraf,H.S. Ribeiro �TP. Nussenzveig, Braz. !N hys.5C3aw59�9 20016�Fabre1!�(Longchambon%�$Laurat, T.� dreau wC. 6, Eur. m J. Dr�n27-R4Jr2�rRr8 �:rz(Duan}L.-M.  , G. Gied $J.I. Cirac d P. Z!A!�.�84}, 272�=:�Y � C docu� $} �B\� [pra,A�Derpaper,showpacs,pLDint,superscriptadd�,]{revtex4} %JO�C.C twocolumnv� \u9ckageA�phicx}.<[usenames]{color�� 1}� title{Spo8 eous emis�a�(a photon: w� n��s0ini���fun� of a fe-mass d take9A�A�( sizeG ��� coilE�_-  spread�aC Uto�ount.~tot��3D��fou  �moaEumo cooe ����etsE solu�!D� ial-value� blem�.�.� ��in �\� is ��F8be closely rela�to%B�%Gto��H !1�G{$me dx!�coincid����l!m,rticle schem_ ;!)� wo predic� effects, �under bndi!-s� high2 ,%�0anomalous nar ng.>�2�a� hd"cn� U broade�V>�ZM{s. Funda�$al symmetr-�(ions betweeI:�� a!�>Y��.ei-��ths!4 established. �J%�ohipyrfam>scenario7�-�-�A�dVd.�"� �  \� ({03.67.Hk,  5.Ud�.20.+q�2 � ��6�%� & Intrw!:} BE%��AO-Aorigi�derive�An, \al linewidth by Weisskopa�Pd Wigner~\cite{WW}, s^� toms haA1@en considered trai�,�$licitly or�,m� approxi��eAS�]ly heav�m�2mK cH-of��E����8gorously, neithn thesB is e�,correct. In  eal5c��ul%R, ���� a��:�!;ic���,��&�^!�Rx9j!� Rz\c�.zewsk�\.Zakq-�RzaZak}/n et al. JHE} ��!������ �$ gives ris� 3A�s about�$-�2� af�  �2y inv[g���in on6c��E�ram�Schmidt = analysis�$,JHE1,Kazi�Atomic%��� pos��$-dependentR eigen1�s were�@numer�Hd�����w� gle�XAKlargeL � rmin��I�Y is work w�ntinu61iy�rE. Its ��� bridge��wo quit!DL regim�� two-p��.���!�wo1~�$concerned �d.9��4 e breakupA�a�s�object i�e``fra�''HKe/A`$ move awayBY po\%��id� case�atra!l only 2�gy(er�. One � Ps�Q zeroi�19s (�ISs) ��E most�mo�!�}��8ric down-converx M�Huang-Eb �93,Rubin,Monken-etal,BostonGrp,Barbosa,Law-00, <04,Kula 2 seA��treats%��l �f1�:���A�in �ioniz�� �PRA},K�|�nalogy���$e��gof2�!�9y��J�e�!�focus on� Fd"E!q�ities. )� �"�" $R$/n b� r�-�%�io� =Q � sA�b"�$dl 4 i�P"� * u�icorpo`ng ѭy eZun����P&� A��(�. S"u�"F�Aa% �Dplay a crucial rol0a: e time ev*B��o!. Z specific Bc��q?!�-ing%>: *w - �)�iVMiA,�ZG�FEE76N�& \��>6JW%%t�!at.� 5�al�$(!�regardo. � fir�farefu�exa[ Ap$"�� }K!�exF �ic�'A�'. �  M��Udefin\t!�!�Q�![&\ vari['s u!wl $\hat{a}$4  ^\dagger$�&ors, buZ$� is,  a simpl� o�8 �I&1,� is�%i�I. �"!n!S-gg al�Vq�&, -8i���i|iefly*�!Hd$III we outss"� ml� *) "6 Iga .�a�, charac��!�ba� %Js .46�V� ��� e!oeri3 �E"��% us, oo�h�6� �0 !bI �9=�ob�] A-�V �*2fe��re zbIn5�V%�*u ��}ݺB� 6!29V%� i�Xm2 7"�:i\ $R \gg 1$2��6 �7 an "7ly���5�+.�a�b��und~#v��s �" 6�%��_!6�Q� VIII)a Yz+.���is �:�IXAt"��er= t*� follow� �jB_����.� iT�th2#Re�3!����)ric���] �E�@'`)"F�5bu/� ies �0 les!�a�(or�bar$)r b$���(��"�. E*1+ a�t;.re��� e��iy1X.� � n "%/PJ ���kI��f�noi�Although�� find�ApleKAB,LL}AJa veryJ,ongly�ө%d opin���0E^�:�doe��- Z um)+A(2�& � ccep�ra� � lyM0MW,SZ,ON}. Toj/�s KiQ�s�pt�;��d, let uA�" e�- vecto��R�,,&� a�`bitra!E 1%!]one �d $\mid 1_{\vec{k}\lambda}\�*le$ �U�u��} � $ Anw/� $ U$,equ } �1 Psi-�H} |\Psi^{EM}(t) �=\sumB�CB\,C[)� nien�ed:��-41� !��2�mid2IU=%�R�  mid J�@mid^{\,2}\,\equiv C).}\int d-�M4 \a�tilde{C}F+W=1V $vD =(L/!�)^{3/�F� $. Ha ��below��/�arallel�a�/+E inu�se�}vs (m2� box $L^3i�i� ee space,�mp� vely)i�AGsum��t�0ls �22o trans� ed!on>AR�hel� x $-��m4}=\frac{L^3}{()A3} 2�$.�5e� a+ coeffi?# ts $Jj��6�Z�inT%!td� ly a} 2�� b "�6� e��ba�2 de3� ( er)&�%:��um ar\ �-2��f�� -��f%gdw}{d(\ O)1�1}{^3.�dmV\left|\,v\right|i�2�E �q��dynamY#A!5or�Y�3�� *�39l�3i�3-r4%Ȇ S&Q4�q)%\math93 A}}(r})Vu��sqrt{)_A�%E c^2}{�4\,Aᕓ!R\{ ?ae��,-w- e^{i%k}\cdot rL�a;�+zY^{\;*_-�`^{A �%�\V99����'�!�9el9� IF�E}k,5�A\ })=iE�)�&� �N�9� }�h���z�- �b���N�j�!`J-� "BW-�$e]a�k annihi��� c�� y�a�$%� R�U 2�i�s,r<\perp%\k� �:� *� �t��T{gy � �sY��ayMOlE� 1- M-6� &�Z E_f�0,t)}{d�r} & &=& *$1}{4\pi}\;I!l"5 (t)| !�?��{E}ie{ i) � Z1(WO &J \no :\\!2���i$ �� �Vw�Vj {k}}\; �R�\J � �� �6�- \ k t))T�} |^2 �q1�A�&�I)�Q $ Zis �FE��9MGQ Eq. K N))Ya>� en-�} ABVi:[�$�F�1&  P\�V & ;bW�� � Mve3e��}VM ,7yH , $\>9��q mean�v f�;e�=mҎ� �g!�alS�* $dE_f/dE� r}$��=b�(&�' n�ergN#-iiEՉ$jN=Vi\E�p }_{ph}(a�r��Q2^�&�!zMandel-�89�"�}, ��>p m5���i�o> # &�-�m G9Iq�hG2-�%; �V�8:�� 3>}}���� v�;J�"���r�(y z^�% ։0%7 k !,A3^� A T;z`^� - -F��B�O�to�c~�c�.)�E]�1:? 5.))��e�0r�%��&Y r}\;im��]o6i=1ձ� It��Bb��%�C�lr�Vh$Vf)�g$�Eq16�a�"6* N*!�$k@) 2Csfa| y. B��i�9���is good��@ cal�#1��Saverag"R��gj�� J . But if03,to \e wfA\nz2*�&�� �l , e.g.Ic.-7T4 bar�:)� k}}$_��q�D will!�w� b6�C)j $B� Z�. How=*�re!�a c�B!s�s!� -(%�lem&"� !��C �:R'nI&tr�> sial�ik/7�f1+-b 2�s,� i.� Z�� A��=})� substa�G non-K'I�iX a�� e $\Delta��N� ��x��o Щ|\,��{k� : $\, | \sim .e\llY= x��.�)%L!#j'o��-h%nide82Z>�be*pe� ��>�}$a{  r�zEg�R���&�)T>����tN�}��s&� jk *R� e\,�� ���w}�v\ �U�j<?R� !^v2H ՟A��Eq�H-H.! deca� !ic leveli�qMR%�8 emitASl:b�@A�sf-ɬ a -G $\gamma$*^"(always much*�Dm# m*$ RJSo�u�ly=��8\inequa�G0!)q�M��/iOn�����"6#�alBth!� smal�Ce Fouri�3n ~��}+)1k � ѝ uF &�� � \4iv2��3 �$c/-��w G . Na% speak7 �/!=Nj ��&dB�E�e�$��assum�!at �"$squared ab�#e ���%�.I���a:9 � �&'O�N&or �K!��  p. �rs"�"������2p5� �r� A��ll keep!Tm)t�n����i�P :e�/� �Q �Q �Q NQ92> ToA[cif�!���!c/*BI,6%�+�&�9,?A>!aa pur[x4d $P$-5 v0>proG0�fE~angular"  up�|$z$-axis�. i -$ done��@( ple,F� e� 6fOe g S �A\N(sonant lase�pi$-pulsAGO� a�O��M~e}_0$�OR, $z$ � I�Q Qdu �M��a� .Qhork)m)^R9life-�*.92O�?) �� �3eF Ps� p)�2ac&L;� a@0H� re�*� A6 NNX6�: �Lion3 �5�;�:�Bp a sudde�1tu�2-0te�o/Lea��,v�@~ 5��]gf back��Ws�/M E� $|gU$ E� %�K�*}%Fed� MM;�Q)�0limit $t\gg 1���] �!����Q� ta,op�(a5re!#f-5.��&.&4�92�"Q�k/)�Zf&� %-|� �Psi--=.- q},\,�sk��.�t \exp \{-i%(� q�2M}+E_gF +�  �) t \ �\,|\,1�|\7qh� le|\,*�",�#� V� $M5�` m4>m�!�v* q}\,+its"A, ɠk�)x�8�1�i�8&� �$$Z�$. Now^h =for a�a��D0�HaXQof un��e}$=1��TmDR any n.c&�6 at� I�Wp[(s�3,(s. Multipl� by $"�!3$i� aB� &�F65x>ձ� !�M�5-b �� �7"g(�!"�+$= D�wh@@0�U7).!�arv9.1q�nm AV Sum#;"-�.��[*�2u unne?arUc�T�,anyI" p�! �,�� ����.�6J  E�AOe11nL �{k}i���\}N��`�<� Z�"k^20- k�.�h�{k� k^2-� B&^20"� ��.&�"jc'1in "b=-^=*���B �� ��;&���\ N-W��C^{(W-W)=F�\Big|_{L �\ 1} &-�$i e\,z_{eg�}0)8���{L6�"�}\fN$B)gq}+-�)�$in\varthet�� �{\disY3style ?q5�B\,)��% ��P0+i ? �}{!�bP(z�sa�iB7�/ic#n� *� , $)6��matrix0,$ of��-.a?w$��!$2N��"�;���H%f�* o�� $5. U9� �d e��6Ii� �� um (��) 6q%�ZX' 9 GauI0?N� q�*)��%�=����E�{L})�a_0}{I����I�="*(-3^2 \,)3B�s�D@� �Ei6/:�?%1>�0*�:2CAa5%��m toor�%)- �I� �Psi_{at��atW t=0)�71�#v 4���q}}9v�e�q2�$_ :2��&s�pi} a_01T lV�rNe�3^5�B�,a& is�4�SA�[X vBusB55�4�]��Q� �^?[��� :�moa� <c#��A? �� aa�p,:. �@ � $t=0$'?trapp�o�1) � A_ �aM begi�=8 �J!),switched off� f�H&jH �-:�E�)+ kP6��D*�D�+J:+J"!1� �� �q�} )�3"Z;!@^s6=��Z�� p*�bX  92�| bJ8� rat�-Ps� , � >� � ph},E .3.p.Bi�f� � � i�,�t\{i��JN F%% �� 2!"� Y-Zq.� k D"� B��Zxat2� �'',6 WF�Aiic><�4 Q-��I�'!)4 **2 )�7 accordancA��luŝremarka��6�6% termn �$``�]{>�}"�� dXvi@�2QG :|�L.�f�{?basP4( �)p�lmts c 6c&TE9 �aFcX�A!�� d^sS!6��sRz� AZ'� W# $f.32� T0om EqsL *� and~H!��iannd�{ "'U WE Vreplac[6 ����]�.[)� !36���*� wf-1�A㚊N-J i\,J� 0�� a4 E_gt���#�)&4}�c *K"z\J[ �K�%(a_0^2�+�iit}{ M�� + i �J���]@F� & \hg${-2.5cm} \s 6 4int_0^\infty k��2dk V� (-\, � t}\,(,�)L O d\O� ���+>� F� 5> (i\,� .\\rho}-ck }+\,JD!SM�.FkN� {N$Eh67 }{M}-� kc MI��& %N6 � \�6Q�.2�=�phmU �#=l�� ��bgle"?1 di�La�ofm�  A�Jp"z# &�L��gr14� pera��c�J"qMely. A�=SASl9put $�g%kM�|\ /p!0/c�a2j�$gr��of�Z�$)��poru*o $k^2� % 9cp1q}BCR recii?�ris:�is�"L! �fa�eFw�$/Mc^2\ll 1 lP*�h^TXKKF"(Pq�zs:vc/)��e&O gj� �vTEunp $�Ak"�(�9% iM�i 7FPy�#m� �n� *< mex�<,# $�T(�Xyk})�- #rho k x)%�!xEF!Vcosinei&\&�n�S �!� M�xm� DV imRE Uj=�hm �tnWo%� �,FygEc nd -��N�U&� !�outgo�:incom sphe�O-'� , MAM:Qn=�� D� �0?j�i�)�N2���dro��us X|(�I!V1&�n�% V� b*^8р�% wf-2��E��j 1rp ��%-t "�=0^2t/2�Bg � 3\p>� � .U ��e}_A�I1m4� :�!}}  �B&&V .m a�q >;aY��[b  + ��r]%] + iP .��+6t� t�� q�\,�.�cg]� ��&A dk D2 F k^{1^ =i\,k(!g-c�] �R� F�Mc� �� �9) �� �Weu �i��B-�en� v�# Ti- r toiߍ�l}n� planx>U�0�23$.�{a�u 6u��8ec 2�$)>��<*�"�; � �� ���  �$&w-&="9 spiri�^>�6��΍��y $k�" .r K residue m�eqlower� �#�>� ext�U��$-� $�:Q *n�t8Ual �]��complex1�k& �get&NJS �I���V\R�a�[&E�J^JZ� e� y�:�4}\�< Xg4 �B�n$�F�� \,\t� (ct-A-)���"Gc}> �b�:�&�1�h&�fi� ��)+zNfR �]"�1�(A�symbol 9�"$.� � ph�+� s HG�:=Xx "r E�t�O �F�=&�cm-argof�R}"�7�=�9��v_{rec}}�"!�I=I� 3I*1��.8-K^Q@ph&�,u�} I}�o0[$C-F&qI) ! &�" h�Kl�Jex�.j%���o:1**E1�%E4<wf-last))(Psi����a�}\;&�,��)�)y�B� j�-�:� �"� ]�-}{ƼJ��{ �a_0�t / M ���� t�\{M��R}��J^O it/M F \.J?nargi�$M�=8�ņAKA.ic Vvelocdu�  "�(�c�w�"�&c�= �&�,j�,* & t�#be wrz/n"� ozWxQ���Y��)9|'  =� m>�.lM��),\,� .4z yJcm 7RJ4B�XG$ :rJr5�o/[%C "YL �]�VV 8-�>X.�j��Str !�E 6|j-)Qav=��ph}^{(0)�$c3aSZJ�#��en Swf��)�%iN/1�2�/ynF��=J�3�!A%�#D{8\pi�Lc\,�*#M��|)2�:sc �(.1*= &+@�XO)�8 h�da�N�MU7noe!�J), Mo>�"�'�gn%Ta��AN�U���woi�1"�(in sit ��yC sI+.iY�� &�Y I)}Y"�W6��*�g�+f�6"��Y�"�(�$E� &�ZF�6�-JatQ�. Toge!}�pt"�zR��&*��:�"),&�J�F"-��.�>�u 6��i:�qaM�2�" a(t)�d^3e ��=$I�R}|��a^23"x I}ѯW���* /TA!a>���!nI 9izq"D �a O t�M^2�o)�F�W(ew# 3�MVEG%"'s�� $t_�}�+��^a5�._5TQE� ?�� ^{-1��?tr4c1Q��#J.=6�+too�: N$�s�$0 �&:10�:Z{nm}$ak|/ ^{8}$!$ �e�$M$4 m_e$. Un/j��i�j}92�i:\/,! !S65��#cbe�bn�Ze*ZFT$,��JQ!�!*Q$ quick�SreeFN+:$�atBR$p&�sh�$�4Q�$figure}[tb)�king\i�dphics[e4=8cm]{Fig1.epsI�\ca%- {(a)�(!Mk!5"Ma�lye��,�2Z� 5?Vh�7��%(&� .�))�j(b)%`` �lh''F� eOc*�4m�Vq-2})).} �!�K-F %%�,ћs�$�D*1 2�7~4 l mOplo%"in Fig.~�R{(a <b�W�X� �=�s�K999e 1�.�&&�9%� dot-lil�Z�3fy�rPɕay r�. &'9fOAi�5a}�_Vo�11f���A�Y1� �N�+cmA#+��a�3wj�@�[E���`i4�Us�si0��b`kN.to occur!���K���� &i�}dissoc2�e welY7<er sense}V�<�O:�f�Mo&�f�fetaB�f �fe�� ��1us�Cwn�:��"�G� %�E�&< c ~I��g>�2}��Z aG"ra�qyc!%a"rJa3 . %%b�V�6��2N�Coloreine���Jn�!�3��L2� -���%!�-�.ţIupper-E ��ra�rb� x�+��x_� $��<e>�� Y�HTM\s.WPaEl�m_��  t = 5, �$l}/c = 0.1��< ca_00705���W2FWAs� sh F�I[�#vEg�z�'*� =8� pr norm`XR�F �$� &)�at2�Uph"�#!�|TG� $a�- �)/ �L��W$.RA%�d� FkG&[ 6%,NR= 1\,B(�c]�c]�c]En��_}A&s�� <�q�bEщvU EL*NF��a�"� �a��T prot�m cket�)Q�.�e*_�wI��wXla e�)"�72�of ����=co�E�"a{6���cl&hG ��~*se�� ��bin�� �5O� modi�A"l"�d�+.�<W�|.��el*v:�%O ve>O~)�!O. Eac"�  &*i�"�2|�*.$cm:# ) u9)l�Z&u$e�a�w&� ph��2at!_1&>!���!�P V�m�a�P.n ,t)$"�H ^ :�&�Hreaso�] cl?K$!f,2�j �� Ƃa�  a�="Bh�F �l".�23e�KV  �_0A�if"K�,6� % "�"��=O $�a�[ a $\d�H$-loc�y�25u�727! �Eq.>m9xs,�!�"?. �[E!�} V"M->j*exZ��P2<J2� ) Ge"��KQW \,�/6N);-at}F%4$ /&g !�2J.E �b simiKBt�<a+'"Pda4�a  a � aP5��p����;<w$S�%�6a�:'>�4 � 6z2� sto-QUs �Zk>0Avbotב�si�'�> y�2hu%�jZ�AE�� n�L<(ae�oe4 1's- ���=exist. N�Mthe�f,��� n abov� t�pos�n t�{�!��V��D�rB�!!��;�5e c�)ta��Foth-!�Im2 1�xxplains2g��ic =& ,&�s .W.�;]6�@}t,Qs. More�'R !=�! ]�� �p�J *'@�eep�ww�"�^���2�0 ��d+�1*�Hp7B&�9�~�a�>97!�I�.0�-�o^��NJU ,m�H;y���c �E��]:z1 m?ofe�"y *�Fe .F�O�� !� of�l$V c}� IndeY M�m�)=$LZ�-�� a�f1�cm&�$i(1-m_e/M)6r}_e( #9r�% 9i�T�)�4�L �`o&&-8�\�!q0(!1e ^�C%:�@" {\rm?�}"%S -e9s�l� r}_i�#a �E2� eN$a: �%$ 9���*A!r~Gexactly� }�dj����ak2zLB,�%1G-1�a��66wl+y plet�L Actua6�O som�vn�+hwt �.�d��g�Tal�F-"KU�!�� ��3 A�b`Z%�(m_i=v_i/v_e�l $vU�i�magnitud��%T icalF�� a�&7,�x u�ean���a�V&� � e�z rule�Eiv}_e+m_i i=0$.�mD�,����is �|a`p�ef.�B���0�Wfu&of�z�h.�z/0Eberly04} (seA�ys�on IX bV@)L!N-!y-�sub�%o�Kb�D���E�%H-up&S ���T=�theirj%�re ���7� =� =� =J+nq�" � �5 �ދO&?0Y r}���edF�$ur earlierE-[n�{��ik�o!� sugg��!o�2N�� >�m��E�� �A�� �KY�g�n�B����F*si6D'2���manif�q���Yj*Y 2�we�n �:��� "4� *](E� !Y�e�4Ward� �Ue�e Ik . W�$ repe ob�$C � ki����F!�ur>�.�a�!�cI nvAwual� 2��xW`i�ttwo�5?Q�!�~s=;, [+�� �)5or�1k�o�rA��2 an%r63scann 1if  3�%signals& �oA}e �;i<c��,^�2!^bn=to.i)F&�z�y(6"�al):��l��w!��! ���6�Nrp&�of.i� ��t�� b_ bZs�$s $^{(c)}$�L^{(s)�C�is�uI�2#z!s:Y,!A�6��� imM8!�i.N�bn ���<\)�c��Cgq�`qu6*u�gm4�=up�M�r�Kc�AT=�hB�L&�� �A8� Ź58>.�K*�|alm:�>ie � � 2��(,� �D N����f)P�,-ab�\�,dw_� )�&�/.�g%�=F�\".6@�� *pFJcA�F-#m �aA�>�c)���Z�� �;.n)�{:����^�BA��:-�?&� $2��."� at aY valu�"=h �� ;O���o-YA�� %p2�p� �S$ph� !harpo�atIti&B(iRd� �& al (}{[�: %9Mz�du��!����J"�RN�� ��6�var �*�a�>��*t��| a2,��'!%erl%*\- �B  :D! (a))"�?F  ��\2v!���y!d�H��Kg �� !!�0 ��.��!Z�� )s�T+eˍ"�!`$ o�'D [�N��%����. J~,�f!A�aW*�j�mor� mp4� ed, ��@�&Q~� at}+�("��!)2�%�"�]�ey�Ao>P#(b�-�� �6�re�%A�!�J�s �*a�?�m�"�(�HFN2��� �  �Ng R�B ^( B�@�I�>�2w$ A7��U7#�A� �, A,E�Bat �u�:"k� 2�&�1����eS_ � X2��?in��q+:�v�s�!��\V*s (c/M�)$.k���!2p$詰��"��!����6#e��Su�/>can bAVv@Dr �C%1to6%2}�V!la�loe�2[3}. Q�ba)�-"� !#minimaQc{ e' +-�.Z)&�!�, etc. Fs��a�� ~D�}),Y:^),M )�I�� B onesj��p�stp� a�zmaA���maximia�A *� !: E)(`�T2(]�J�X.o>1� n�l#1{�>-hA�sid,��delC�1D&0Y&� .�! de̶(1:�M�e�sNSp�>~!*B@ sim")�b!�s�$``="$. �-.3.F3�d€�-:.9.�� ��"�+�d!M&�U .�&� � M�"� #3%��-y �-2.Ai}>�n�3� *�!. ].A=&�j&�E� �F)�Gk.� $*�<|y6Y* �e&# i>J� � �.i CM2� _cm^?^b� �.!�}� c�NM/�N!�� +gB/R-%\��!1I&$b0!B�� �3)�f$B'� nUq) w�'.w)�2�43:p/C0 �%*���uTco.m,��Ǟ oi�AO6. ��  ��?| oftenqd*Ls:!�!o&��� i&�4*��e4J�)6#:\4Ý��g�h&�6�Ss.�7mitem! ]\ "nz5An�v$4� -n��6�6A���l �6�����. ud�� wY9k"mo�XD�� � ����ve&m�4on$E�j� reR_inc-p� y*2�(tL_  >}{���: � � .<� R � � �a �.< �[ ��.}N ���"=2] NN ��� M.7"D -Ե�)�Aa IeE�s"2;8equ�on��}^2}^\*S�"�}� �8^"�[��� (l�6�cPU��:[.eP%'�(�J��&D%bp�*F}�r �Q�e�pV�j���G6Uo`C�5!*OVF� M�anz^L�s 6��;&�!��2Zf*"�&d ! >9J�)�Qe*� �|=� carr`= out �H�a*cr'e����E�9*���!�UF.Qj.�wALll��"� Ņach b.%]�z6`wo op� �0�4en!; 2�ez%��tZy ;&T� ,8�u�Go�M"r'U5�d�WIUA|k9U �����  .$ �4 1��|t:Z�J� �W8NeaE��!�:Hm���:g"+5BA&�a�� m��b9U�YF�. B�& a��Y�e9N �2� $<CX 1��%J�,&3��t I;ep�y.� � ���pQ {���Y3 n�!��,a)�&�" &a:@?��|).%�r b�&A::3�-f.6�rM-w-H�dw>!}"��_�r}N+!� \l|��e3*� a� := A�b�A{qK{c؃ c�3"�E� :�3 ,, &� �(t)fCQ]\[2mmB �Trel�!2�!� �J`� dll d� � #WB�LL�& c�C�G .�a6�A��� "ӝ 2p/&񡭒8�9r��YZ �2����aCt B|mɁ�� �]x)�� �UN &�� - C-`.�I��� \max%�F��A +6�e7e .[)�B�Na<To"�5a�B% 6/,ᄡbմ.c����N M�$�� stea�[�e�!ޑ;gg .�S�����u�Zo�*C4C�Di{��7Ua�{to�.fR�_r���$n ��is.! �� .)@��!?!#�� agD��7�@LF�-�.?b�!i�#���� ��.�j�au���)a��m i-wf� N�atF� ph}\M�%� �����aFR�l~�l9�BB��}gg�A>4 ��R.�2�' oBv�6[ ��W/c \ f�!���INi�;� !�atZns)j �"�n�5n��RMvB� � "m*�&Vph}]��A&xU &xa�M�"Le��%l� 'ɟ��m���-~v��f� *�"���=0V�*�E]�|%Q.����i���.�2 F�.��� ���B��*A��� +c�s ��E %�N �A find%�&x K�4(daal�.i4�UI�)%]Y vs.~IS~� ceQ�Q, Nv2ZMvjuݣ�>�?>!A){# $.j� "�B�_,}[JRQ2�B�}��)�<������<�1� .:("� >=0m����u!`!�.?�0m*�3�A�:u�} "� ^Y8�5M� )h%t60"%a2 ���� _�Nom.�=?�~fu+>r 0A��<���o�re�:eZ�i�12�c�X/ ��E*� -AsA sim ���%!)�V&�L� =�,/.*!i?���!�#�� i"���� 's $�# -�� d�3ib�g�   iE9*�L:* J#8"5�o"��Y�p V���-l�L�%��pai:U~�P�26.'H"��"��� �m#6f�=^[�.�1al&����of�DM� PaYK�5;M� dA� lt�Uin60,4D�i5�^�+q|bbA e)cur?�JC��������-Y6.y� a�io�'s4nIF�4en� M(;:I�f�M�f�R16�M4J�*0/ (so�m�Ms, :���(da�'����5��R-!!|R��@.1a�&4:+ W�k�*� =10^{-8�� J Fig4�&yRzR-�ofG! 4�ua�"_�8���CK�� ^6�pY6���?&�-�� 1$ ��4�} Kl�&@!o9Vo6'�u��a��>}y��):�2��-�"'L)�6@Figs. 4!�!� 4(b)2y5)�2W�!� ��1��ly cHc�s��x��e"� _ phy\�)Fhen��a�7"Q�]���asEnJB(a:s�a�1� 9��!�.�m.~o S��<C /cI-:�+�s�'KE ed b b�l}Doppl^�f�'$Heisenberg�7��`Do���(�� }. A2Aj�l��r �Ju"A'y.%*-,"Ňv�` &w��D��!��@�v=1/M@$.�n�7:���s �.sI0 O"rīf � `�s�@ ��q��a=k v.�a�=1� %p sT)<c�is }Loe!!he� ��t&� �� l�g"Wq�r �>X c1Q�"ll"�@R co�/ҩ�B&�w�qt!F#n rval6$aNr��yI��*�9�Y� s��alIG6� �22�U �j$t_{eff}=1/.�=!p�/� .� =c9(� )(c-�9!���y��D(� �[��[�S.B[Z$ i�D)�a�9�p rN"�.c% G6�K3  ?Wtbi)�.��>yG2� 2Z(4���w$�at&|$ ��[Mt� "� <1$ (LsN� or,S4az��|< $ln\qKssI -18$�Zr#m�I.B� I�%*�  (A�*���Bs&�oCp\c"�0���t> �&�'J2 �KSFE�.{���9�>8 �zL�]ll"ہ���de��\>X5!��" 3" 5J" ��R ��)�-t� .��-Il�N!�.M�!- %� ��5�T'-�t>`A�= j;�^lled.v� Fig5Z ex"s' �+a.; rp e��:� ��&q9�)i 0:�=2C9)�)�7by� �e2�)5AXn� *D4�� do � � �Y`!<6. ��2���� cs�" -_ L " l d.�^eR �A<E"R�x �>t\neq 0�m(�.-*M�&45:i��)�� 2u5ph�-t 67A[�?� B��'� � �� }�"5@-5� A�&0A!>�T { R}=0&�I;R�q�R 9=.�m) �7� g�m!hdJ�Fr!|�uaR�f�% $�2�2UU�Q�&�;s�F�ɲ� �^!�*id.�"A>\�lapi�ea�V� i 5c!�!ir 1p� !�.~JmO`6#c�<�!�I\ shad{rea"UD=z" -�A�����{���_{!�b ��YG1�ap" ��w��!5��5>} �"X}���LwoQ���aN %�Ag)p�/.,�m���M a9�� .�A s,K>;�8 9͌er ��\F �5#D}'�|�� ��an*�-*�if5hK��:�"�H �&� ��2c =1�)R W�|so)>s&5�f �A���,ve�uszQ�>�N���i�.�to�&��� i(��u# E�.���i��)q& ����ne"�6.Fh2R�*g -���.�B46J4<byU ��;���6"DLNJF��� a™��6�E:.�8��� >v&�P!�meazY-#st6R �p��� 5sP��waa�63� "Q]1} ����W[�?.H  �verK�d<�wi**� �wf�. Big:� �aFCWu�^O. A�IyX*�S-2:�FiaebXMsu�^ha��2@�(�!�B>9P whenFF"_���6��^����l�~-m!�i�@��e�6���� �' b�"�K &K 6^Y A��q &J7Q��yB�6}�)+%���� >S� � s)}A��&����y��o�h�CbI7Z�UE�i&�3�,��/ 7'�i>�%�e���4>&�/���L��L�vL�"!�v�ifi��!�.�u8$R$A��=RA�v.>��a>!Mde��ϟ-��2 2�,&HI�ap���% studi"��TD>, LANL,K��"�C'�K$KJa��f�T.��},�Ee&�>& R K"�! �iTi \big(�s^2_aG> Z:�?F: )}f��ki����WX��!� Xd ?:��ceNe#� 2!U�@� �(i9)�*L�|�), ,  ��.H�&!rHJ  $�+Lno�<tra�=th�'�l�/e�(�)F�n  �=< � �*ͨb�+#E���)M���As .\�Q�Q �'S�M_03�N%�deDoi �4$N�V�HM3�A��',&�Ue *�[!dV4l&+��p.�7� ���2Q J:��y.5 -B� 24 ��2 $R(t)t��:�5���7&$����)$s�o2�?�E tane�B&j�&���V;J7m;ent�6} �=J�wW2}Bc)#Qv?�s)2?  ?:��&ͳ~����8f&Ep}h~O)�P\HzH}.��nd�V� .�f5�n!��Z6�1*"9�>X7hc9���is�� m/s�C R� .E-�Is�jussJ7�P�<-1 d2�-J��r.�pA&4s� U��a(t�$R�+m%�� 8�7J!�.R|q'� .!1.B7N�4%I�aj� �<hR�`�v�6%�{�����ng th5 . W7�1 r=�c,� $�(ws &> $ˌ!�� e=!���H�*Qe2�E�S b"M"? �y�dr D4V�oV�U wj�A���a�� �Ht���Fa�� �hE8z���v�G�,m�`m�6"!VQ� �1 Q����a��! Q�W�[&"uP�id�o�tfle�i)9��F��U� I#�.k��F= /!R�R by a��2� 7} (-v��4!�K&�M dotsL�iC�twof;1<.�,*#, $R_0�o R(՝$,�>r!2.�N&4`%�n��%�as A~Bw5R��e 5)�%-�.� (f�QR��lo�d��!dK E�ee �[$"�7X��5T :T%j U))�_Y4^,V�f�:�A�&�H�kP^%���g�d�jE�k!c�m��9N�� .mD�l�Ar�oaAi &=%K\g�a�>d.�"��0'!tqL z? mon��o�U�%��*�K�gr� ,% : $RN2(m� � �iese=�($- ;"�l�  d�6t"\d�!G� wo�: "� !5%jlux�"�A�4sReu]�A2� K�#�a�&GK �7B�.�Q" s!*es1��Om&�&�BQQS��ment remains constant. This can be seen clearly in calculationsKYDSchmidt number $K=L�$ \cite{JHE,JHE1,PRA,LANL,Kazik}. OnAPother hand, by modell�^Hatomic proto-packetyXEq. (\ref{ent-free wf})@61$�0if at some tih5r5;0(t)$ approachA�ne,�.regkhere $-\, x 1$!�A�referred�a!� e hidden-:K.�4. In this caseu:�$K ��2MitselfmV as high ~at�$$t=0$, butF=$cannot be exor measu�via0$comparison!�si�-q�%XQqnce phot*r1�$coordinate.�( widths. H!O we recallr�!rks� �dz,Sec. III. W�i#(by substitu��, $v_{rec}/c$i$$m_e/m_i$,a�~y�p!�}) giA�j%�$m�ioniz�z i� PRA}. Now� also!6 aЅGtakA�Jlimit�D\rightarrow 1$, EqJ� is reducIAXqXM ��$a�sproces��41D down-conver��Ql8aw-Eberly04} (iAtee�dimen*al A� �:EE�equalI�square!/-one.F( $K$). %��M6M\se�@{W�@s���mo��um re��at�l} TheM��E+ne ����BN 6N!�d��mined�L2iU- e �c��6BEqsQ]ѕ})� I��Wigner-W}). \begin{eqnarray} \label{at-w -mom XPsi^{(mom)}({\vec{q},\, k}\,})@&=&�\left(\displaystyle\frac{L}{2\pi}i@)^3 \, C^{(W-W)}_F[ �noM�\\a&\�� o-iJk�e\,z_{eg}\,\omega_0\, a_0^{3/2}\sin\vartheta_{k j�\sqrt{ 6\;\pi84 ' �- �%q}\cdot k}}{M �+F- 0+ 7$i\gamma}{25{-1 7 \expdFF�2)� q}+� k})^2M.%)$\quad \end=�F��nalytice�*i it'� veni� to �f�yHe Lorentzian factorA�a" �Y^um;]^ @-E� �`\R�MR��!3r�\pJ�1�-�\,v5�\{M1A�%�^2}1�E�E�q2 -��\}.1�1}By assum�Lave!�s $� q}$�*kre �+ llelA eachA H � e observ%� dir�X"� '�s>�ax��}{cb� �-1� �:r< �$���i valu"FAj� '(t)$ def�in.8 ta��t� 9�Q�leta(0)-q%f \equiv (t=0) = Jj-�a!�c}!a �eandzbHk {IHk�HZ�F �/Av��=��%Z'�~' `�Y��^}{Mc^2%3I�J��$�%�M=v��w-}1hInDtrast��rn En2C 4�2� independ��t$e relative6Q�Q(��)YBQW� rel-qE?\d�� q=)&MKq�.�}},\q��+k6+k}-�/R�we ��4a second group! reci\ ity �onsn�/}�I�� �1}{�^{Ao}� \text{and @%c)R@[s)}R�c�ng͓�*��e�-q�Qn' k})"b 2;:�k *z !�-ph}), hat}),� ��-��� 2� .�J�k%¡S follD seri�f iA�itiesv� (!� Mx=� r_{ph} �B�}& � &8s-� 8s).8F� /!�1� r_{atJy\; Y? \;2�GB� G�"0 �_Becausњse1B}%m�0c-ith*u)� on ��_0$"� A4.:Bn +����,he correspon B�. W�is underX+�Cer will� able�0se� at Fig. �Fig4} ��ju�Yhe sameO y6O ,�� pr "lac��" variances)q] ,e% $Ld -!L\as horizontal axis labely Agai�"��� posi�-1�tP� s,Bu���)/!Bused e�ar�`!&e�a> ce (�Deal)�-spacN $��A� c)}$YaE; k�.�Mf F Fs)� n6F,%Cout any.�-scheme���s6s� * %&�En��E6 uncertain.� } F} !B!���j y�Z���symmetr+ �'�� comb� q�k� E@�*� Y$:� nt��2I�1� "�]�� �at͕E1ق̈́. atB�Z/Ŋ�a� �ٕG between a\%�=K=R�`�*�s� duct*����� K = 9&�2)  �  +� �� N� � � df\ s zM ,.q d R-vs)�-p_ t ,d� 240)v%��4s� O �)��B6�U6.�!=f�!R��BR�vc)��F@�tc)}F@�@gtrC1\,B��R�]cfth����s� f� $Heisenberg� :�)C)� �S K� 1, "� D �FD �BE1� u�}� f�EPR�1kK}!{|.�B�Z less%j�^M �)�2M-�M5��In!�l� �=r)��ref!�, well-known &b�rB��Ls����.�"��#| , while iF�!fX) establish quite diffe��s ���2sn.� . Y�ies�A�.y restric).�;� such4� e Y:�.R;e%� (o �or9 of)8inN� N� $1/K$� they�\large�a� ad�Zw���"A 9G�$ies fall. J�*� YL})e� ���usualBVqy�5%9   ��2�$�!��g"a  K $2E turn!�un�on!!|!ad �!b8K=1$. Of cours�sH nclu�s do !�coBdQK�.t.  b �*a:�&sJ�!/��bD und � yQ"A &� �iG(s specified�[ ly,K.�l� i��$be written6" ���EPR-2�b��.S|_{:r}��"/ 5�,c)}|_{\, /q*iF�l.r2lphB  5��lk*lB�Neverthe��"Eӥ�< ))&m a kin�law�fnature�Ech,� farwe ��, has ni been=� I"�#$ed. Exampli�very sm v(u�]�8� R�yth��q(ed in Refs.'/$, �#��exper"tal.�sN begue�b�orted KHo�� }. Wji�wK � deri;is a ra�$generalhm�NauU�hip2> %&.�l�jC�� �>�&. O#sen�"u�al2T���eT a�i�cor�q!�� (ofaote6$paradox~) pre��c# by Einste�Podolsky�Y Rose�!v8# deedAn i�s��n i� 'Aѵ�d�$�lbi�(te systems   or��Evon��$�Ah��re!�cis%t�� perm�`"��.OKon�$$\emph{prio,& is} .U r!�� done 7ex��vely}�W!��&�cl�ut,A*�in 5aEja��A�e2�!�AOnoA`d"�ce ��our �ach�^@�2@�based.� idea ��&j.�, i.e.,-4(simultaneou!3nd joint}29�Qbe mad��1"s. .�A@x(\�'�A�e��&�qfyevalid� long��. does�4significantly �& . It!�h)es�$ to check *(dS(� ri�u� changeG%�(t$ ore I word;he!��� �a)mod�ksa viol*�A Bi(Z:I��answer�no�Ev no hA�� �R*��.�Y^ �&� ��&[( . To�5�' we �#to���\ �)a)P:��of�.��t�&�"�P �A��"��&��.� =})&~I�>� tog)�e�* h�> �for��,���� )�result�%'��&a nFk$EP�+�:!� x 1���(t)}{&�^2(t) + "H/G :!�s <�*^2 + 1 )=$�}�+u^{2}(t)+ED?:�cFn l�1 aF %�! & t> � !>= ��%}}-H, � �.3_ �:2.�"$ AA�_t)\geq _m*Ac�0(t%�)A���,"�-�(����a�*�2� ��i-2J main�}y $t$N# 9r-3H 5k&� t6�Mv*J *7?.�Ib -�?BTBut%?m�y%?6%?indic`+�* � G ce% -J�I.2��Ja� ��s!�[#?ir&�e�D-$t$r-_�#2���f9�A� mon6,ously&"!� though,in�� *Y#e�ic2{.� FI .� falls"�n zero�M� �Adu�f&��i�.%��E��A�I)- mas%m �of an+�c��Uinٺ!ic!�@1� ^�0(*s (�F,2OlyD-}�e&�0-aP���X})�+� d�oy� �!{a�n&Q� }�N�%%1�,&�1gt �.�4 "�1y.��2�!})~| �.}�� 1S!�E��')"�0tAMn: omesI81an 1R��l�"�:dEq.69e8�9��'ism�lso m�Sn�aq $. HI ,A� $t\neq 0$q)!�b6� �appearD � �edf J l%rbelowJ��y�bJ�&K}a,�e1}�z�\}<�T:'2p��< FjA������4R�1Yf it�� :�Ji9� even��70M6 �/�!�=�� )VD stron� h� �Y{(�2 -3})Ni$a:w%�R�>� ��Ml�5�Kn �2�M2M"0E"�} Co[���&s,� K%r;!twoLN&works 2,Kulik}�N] stig�a�.���thea��1"��5)ric�1c"�1.+3did���si�>�1)+Anape�3 JJK mH�  ena�I�� en�toh for ? pairP&p D�)i?6,gof�kiat'o�B!&�62���G.!@�`*� +"�V�a��\�5 2�}6�was f�)aba�0.2,�c�8aDi�oneM) awse�:" }��%� )�h��(on2�V���%=6{�3*���io $R$ w�^�ed� -(�8E�think�t)��d�zyTal 6wouldEX*. ��>"'^6yai>X}I emi�9A!a�!L�$st clo�q�a�!�� E Kurtsi8, eaG"Qurt��v9-%J�}V6�aV9.� 2�x7was"di��&� A�l*�7s�#=.^A|6=�cynM�� ��A>`E��   ot y!  �� firm��J&s� sM�A4*|z�ol�Z����.� 2�% �e)��.����$ ��9al�u$G�3$!!1�sO' uba� e+� y+nd-�� (�'~}Fig2}(a)Eo ��!U �\to�vid!�niMs[�j%<�(/c$. Probab+� quir_%�!�fulfil�=�*�$M���E�E]��u(3:�2ed"�<�.X) w(ed.� =D. '>quick �4si��0 t, f�v, oUM.� effec�7-�}�yS� ossi*)%>-, to ��se Q�v1��uVr r��ed�(��6���V��*�8$o summariz�[�T.�%R�8.�� uc� .�ARR�A�� %�zF�=iic'��f i�ze6� ~ er-of-\Ez"� ūtak]to accou�@ Two newU4re� 3anomaloua��;a��broade* ��&�n�4?Mǥ� A^.�i>g���m�=$. Avk%�b��5m�^' 6�+)�<0n.�*��He�jre&S#!�T��_f0��43)�!<(4s cha�B eriz!�V� ��+toy�(a�"�ofBv6^ &^n#��q>"(or i%��6K#6W �!� (bB�.�2����#oe����!�rse:�,� The � >� �ᚩ�N.�92��U92&r � ways6 &!MI� spiri� ![co�"�vchA�y EPR /4ir famous disc�Con.����r�ac0! ledgi�!� ear ���B�* sup 0%\NSF grant PHY-0072359, H�KRe UG&s C� il ( 6@no. CUHK4016/03P) RFBR X0s 02-02-16400A� 05 69 -!ran Sci��S � F �(MAE)1�e awarEm$a Messersm�0Fe�2�s (KWC��2�M2M��thebibliography}{99} %1 \bibitem{WW} V isskop�d E*'�?$, Z. Phys.�2Pbf{63}, 54 (1930). %2MdRzaZak} K. Rz\c{a}\.zewski!�@ W. \.Zakowicz, J[K. �� Hayash �S�]Lin�:�4[J ReidaD.  ,6�Q̀��8�tSeeh � ;%�PDrummoUO2�.M 449N�W A.*�)B."�)bN.�)2�[7}, 777�352ABY I. Akhiez�nd V.Ba�etskii, Lit{E�um Elec�?(ynamics} (I�Ps� Pu 2ers, 1966uLL}NcumD? �$0a type II OPOY( threshold:s^�#de�t9?opera��lauthor{Julien Laurat}\affili%@{Laboratoire Kast�$$Brossel, C�74}l {\'e��et�f$Curie, 4 P[? J\|eu, 75252 Paris cedex 05, France�Thoma�dreau}\,' l{co @T3tro.j X.fr����b=Ma)riaux!Ph%-(nom{\`e}nes��iques1\021B^ D. Dot, 2)Z 2Z1�Z!��(Longchambonf�����ClaaFabre} bS���� date{\toduPu� abst�} W��~bh4�|9eu�o��p�Se� (oscillator i�eQVy�pr&ps 9.7 $\pm$ 0.5 dB (89\%) of �9noise�Sa�D�yn� *n)_�/al� ida�bX�6e= >or/�*;�tud�'homodyn! t<' a��d bLh"-e!&t�CMV,of frequencyR� ob+AM6�H(a birefringA�p�/ iF"%1�cavity�*9� \make�� T�m4R��/.�;�� �=��VlyB��1i+" ams. -��(��&�� &ys�6 al y�& ago � applu8to2h!g weak physn  � /=it is �$c�M�G chooi�!�#b%s19 1998ele�Z͜Us di!^r, Mason�NU W�AYo�6an eleg�way!�achieveO N B�i l98,��99�&����m�Z!$Av-�hesI!� * � ara�s��in�Zz  ouplj_.'A�/i�/�hr_in a loc){hen�Yon, wh/iHla:dc ed mechan��or!ScAsal 9�s-$ Pikovsky}��"origi-device @& ed "m]-� -�ed"@ �FA�Ce�� &� B��er���$%f5Y�y!J� �:A5)a non � r�ws�a%;w$ rang!�U8I8� 2�<ju ex an improv��!�q�2�n"{Lar) �e�� J�dem bG AOJR�wa�1o!͖,[&� . Oul#��@f!�6AterpreB as p�iz�d squee= �#�50figure}[b] \i`T aphics[� =0.95\ ]{OL_SM'(a.eps} \cap�{A doubA�DNd:YAG laser pumpsB�"� �� �-or! 4 a $\lambda/4$M!*� � InBP5R�!!�Wly��<a bal<d ]\� b"e#(b ��VUopensE5P%il>toAWlIUanJ�}(4infrared outpuA��h)>iszas loc�?"� .) fil" ng.}�.setup}�-��]e"�-� &`� nA��'"O}mm(�-R$��-R�$("Diabolo" nol� GmbH)Q  tripl�Eson��A:� ,�< ofemi-moL thic�c� :��!)oa�!? �S )��]r|`$�&��#l�sH 8input flat mirrT"UBcom��)\�sP10mm-�k KTP cr�1�Q�reu co"� &�1 }��rE� 95\%�6��aO*532 nm�alm�+100( Bn� :1064 nm �Mt �5O a radiu��cu�Z�B of 38 mm,A4� ��o�!���i�1 ransn,� $T$Y ch�@tE/5�c 10\% (th $T=5\%$,�exa HA>!�E>ce)�q.t��&i.15 mW �Arlengt�. lyaak�?i�ump�A�b8�fP�!-Dru -Hall& � �)��12 MHzl@�n"� `u剀��`eM�%�!�eE�-�*I�'�Ve-�?�/�~ional�hg� a�roller��u,mzi OPO����)ctemM �M�X ��o,!��+s�.<���EmK� spitaB%u>����� OPOs mJmor�%�A�t� sturb��i�H! s en:k ng-�CTH�7JA�s%%ly du� l�i� hour" �0�-hopp�� D\YE bJ)��)�%W1v�!�*�'E� eut"n F�f�8:�TwinB�:�Normaliv powera�!�& BFka "|*Y�DEUW �t��eeA�ronic ��!��A�HB� is r�_ra� 5aw� �:Wig;�-��2� ^= &=m�=�..K�.fV igna  orthoga��� !�!���1st5E ies,}C ad�e @A{A spl�Er�I�d +air!y�� quan?ѐ cy InGaAs2Ldiodes (Epitaxx ETX36! A half%HA�inser�bef1F!�^�. W9 #� M5t"�Ytur�,45$^{\circ}$e���pe� o�zaxa�>R50-50�! 1 �ch6o�)"�� shotI� level͝a 2�$T=��&�h>\@b�a O 2�$A�\pm�$*�.�I[ '1Y�)1!EbesB ]2"^)�j�2is.sp6 g9s�O�A�d&a28 "1�s fiel�/6���Jrr"{c>m�-d�9�� -"N .�!�s"�k :�A�JEis �ceZth. T� !%�Z�6*%E�*�R� ,Z<zT�j*� �\� �>���1��-*  ly . at� � "$ ) o � ��%r a�H-y.ed @&U s --*o,�ad3[1�G/!+ .�1q5G�q-��--�I,�wo��&7Mca�7 mainmJB��. D&��Ρ�ynon�5�aer�]��kaI4�J*bH mh �Y�>";� ode !now� ixed���. A9(e minimum t"� �a�e �sa�v2? at +.% . An elli���U2\%&�mla���t&��!�e��:�2Oied by�!** it{7l.}B�:� a fe,)�%^��!p2� ��{ � ��6�n�#N�� �R stea�-)A��G,�{is�0 ival� B�Td Ŵru�@��.��M@s, $A_+H1 $A_-�C� VG Au�Hed fl�4Ess)s�N1 � (��Cnis&�B���. �Ksh�:5�.�Be ��"�2 metho� *lyE8-3 L�M1?�zs� jc� cri on�_ Duan-*is\3& �1e ��5M0�1%���s.�" u\8af , du*!�g)��, 54a�!�c�6�!Ome`l�I�'A-$e�aGE!vR)6"�b�8B�AmoinF� �2� �I^� le sBs�.NM9e �mxF�nAe-[��1.5��10� �% ly #eEw)�� %�� � �:� ��J`� Epi�onB�(b)�9`:"n�f�Y@� F�f�"�C� anguw45c(��a�a2!M 3000�a5�s��I6ax�&!{.h� tilt�a�";�t$Shaddock99�:8;:I�44)�$ visimr} s 0.97 $!�-�, �F�b��Pm2�OPO�zero maE�E���-$�&  td��n.  pYRA�I�co/ni )9��a"�< !"hA�6����I�!@3� g e#a-� E� . F�5M��&6��.� q��B���,�b21$e�a�j��0.1&k )� �y��6so ��9 "g�I&$ :&� �its��d��?ex���Tl  F%Oofݨis Uc�a few�SOne8 d @ a�Qx�Ke�2�HN�)?->�n ���>�ew�e9kej3.� aM�~9��4�#!e�t�F=-L9��� � R�M�&u{EF6�Lplu�K+>K%fE�!NsQ�I5YoF; MHz!6�t 1�~)��2\�EN. �L>K2�!a�'��V�+�d�  A"�D�*}�9n� �yb;M�. Howr, lTex$G 6��ei*C�M al�;=mra���ant2� ��� da{p�. S�s�� re�@�$aised great�0�ztic& �_��:[map"�6�q5i(o�@�A$ic ensembl1Hald}�"&`=&� ,built a comp}��J�) �>� v xploE!��*B�in*`$s��ank%))�t��!est5i��C�uE,�&�q�H�Y \L D!a0�-y�(i���&�#�*[t�h _d&$\_e*� �!:;!% !��A)�promi�$^$y( q-�oF��e"�CuIaTo�d�ne8si�_�to ���$)�:���&� a"�>{s} *(/ K(/-"(/M�Ecole �eY>$\'{e}rieur���"N2 Pi�00.MarieR/� ssoc�ndw �{Centre N��@al de la Recherch4A {if�'$ (UMR 8552v!�2&%�Ed"�?���EuM(an Com tproject QUICOV (IST-1999-13071V ACI�2 wMinist\`+':��pB_"t-t>�>2010�>&�*G5 3Je)rF>SH6�*�& Giacobi�[C. |&8Cam6&9L2>�:255�<87�P!?5+3 �<|9:�<A`' {\^\i}tre{;��=6q2818�69.q�+�8(Gao, F. CuiNXu VX�1�8unchi,R_3}, 870�698��+289*E2BJ�9(t. Soc. Am.*}8�;152a20CV}�0um��e��Co"�+ Vari�s, edi�by�L. Brau��nd!XK�=Lti (Kluwer Academic . 7DordrechM1003�+ A=5V�/rH8a�tin�%�(Nussenzveig%Uic�2mmu�'�s0(bf{242}, 55>4l *} Z.Y&�5F. Perq>HA�Ki���9Cng2X56'R@ 366�892hZhan*} Y.  ,A�WaOX�7aAJiC.I4KRr&�56A� 0238y9 2000p&�*A , T. C�3ag Ke� ,59 Trep�2uR�97Y?042315�<&�9Mason98�>�*ZC.�*%�t&�AE�173)0.�� ]�,?WVj�1� 29�69�"�)A� Eg=d blum%�W7h!�8 �)y�8!}1\�$-)a *�RR��ur.-} J. DU�3!{287n.��L.-?uoCG� edkerI. Cirace6Z�"j��? 2722i.T.�D.AY?!7$B. Gray, D?McClella�;NO��4J�"� }A�A� Leuc!� R. LoudonA�C. Ralph�sSilberh@BR�6�8052306�.�@ } W.P.  ���Dnabela� -A. Bacho!@�DmnJ8}, 09"Y@.m� �E ,A� Dant!� L. V$cBra1!d PinarB:�6�91}, 10�.e� � A&L. S\t4nse�E�ori��Colzikn�3mFakVU:&�9m�*S:4style[prl,aps,�e(icol,epsfigJ:w�'  .tex�n.,:e}{�dK� }} 2#e#�^!baDna��>D# DV!banBE*FF%.GB#br!58}[2]{\mbox{$ \l� #1 | #2 \{ le $>_(sandwich}[3f> | #3fCket}[1>|vbqbra2.2�B�com �� [ #1\,,\,��]:sa20\{B1\Bi�b igma:K�}N���>9�l5��Pure}(8,8)\put(0,0){C} 3,0.3){\� (0,1){7}}%�8:}rea�\R \h�ZI�q�:�Q \��%28�% gers~aZ a4!% �1,-R6`nat~[N [�olk~\1 \4.8���on[leavev\ha�\�1 1\no(8size\kern-.33em2f2[&~�P ���sh}�9sh>�ccBat ArgtB TrXTr>Xro!�����>$grad}{%>&div!]��div>moy�p�\� �)��o \i:F |�4��!e*4(re�} �?N�� as BrunneB G4@, Valerio Scarani9A{ G2�A":�ics*o>y�Geneva�E(, rue de l'�,-de-M\'edeci|�CH-1211 2( 4, Switzer� } 6E=&m;  "�&�;Bell'� orem;͕Y4�V��-� .s c��"m��}pk�UdJnwsps, �9D%dom�YXe&^:wp"5�"9�uMF!"�&\@��(H�,�s�J_#8-��!��Rqub�/�'��$@aT "0'� m� ne".}_w1�h ic�&>fr*�55���j � �%|:b��0� $��{\psi(\a a)}= \cos  00}+�!11}R� $0< D0sim�aҏ{7.8}$. YtN� s�C��I(� � Vxis�YXta {\em. nnelc_!VR�i*#but�*i) V3o�:rA��E3(izUF�7A�alC�y&3V��&�A�" (ii)5q7A�aA�"=�qM�3En�"%� (s�;-�:�,i �p n�w�w �M�Qc��A .�7eprJ)$intriguing*Q(, often �%oq-Adl�H},a�� repea^_)Zd,5W;)�. lookE�aZFj it�c�bp� �>7a1��+n:��4s (QM) Ub# �9n�Hs�aira.y�*~bI�� �?Hxr� �&�e) 7J!�a�i�0t� ��^�"hE�, T!�ss��a! i% G"�. U~z�x.pt�&f&;r_h�F a reC�%of QM�A desie' ��!���6lthA else: �v�*op0�"goxGepEify�r"fuloisDg �? �H�eG:=tho[�)9���!V6nH:�4�^mayQH%@ks�,.Y@*a'�$B?!�y (Alice q� x(Bob)!�oreto��T;&2D�)�0-�per]i���Ns.x�d(to "�U2�w"<�>�\A�2!]9��we�0��1��u��ds�|is �@AM��=P$�!pA*.�M��J2B�ie1at�F�����d�t��� ��Sv�x=s��canada,2�} u�w!�� task� JQ:�jA�!1�H�(=let)�sxal �>UDs?Ked�# �(en Tonev2 Baco�xt} �Q&*e k����|aJ u" ��:�b9{�!���.e bit}!�6N�g�0)�F'a���%]bs+B�&-co� ---� �/de��yD( %�it:av�@"�, � ��.3rt�x�2"�&ssy?in%e/w4�V�dtI!Kj �w����x M�3A ��6�ae�:*���!��A�ftooZ!7D.D:%6�P ) } (NLݿ�WPopesc�Rohrlichm pr},�q�qQ�cPR box !�a"�C!�fc�Fe� �/ is " �"!��� 1.11�H *��tsi3hyp!tSA�%dc�?u4*t�w!9e yJlser-Horne-Shimony-Holt (CHSH�}�� �chsh}��iBCl q 2$�D�L$lgebraic b�6of.=4$ (wƃ��is3!�t��sM onlyH-${ i = 2\.u 2}$)��8�x�Uno-v �� �q1;�c�|�-�G�]�&�h�!pr�ive�~.�-.V0�Ց���, 2}. Cerf,� MasscndU1)D-� sim}�0sho�B� i�Ct < �Xby�M*� �M�H"uF� NLM�FA�a��valo�'A���-��)� 2��QU-0XIf��<famHO r ob�!�n �A2K���;ex�� �t 2u!��!a )� leas+ fe&it auto�_ y en�/�-R.u}g��12G��A9traSR��Ry� ing:aUre�be"�".�,�)a.j�l,�must c�'3mix* 2;� ateg�Hi*�*hid�\�6ist��2;�G(�aa���of8dT 2B� um� ��!�zKdrawbackEIv�}i7%r���$Atee�E<�R ��6� iw��hs 4mova��$qvandre%�'3$W �&IKŵ�k��! �1Lw(w| 5s�c.Va�M��!a`i, )age basic�!e8E  (5 bit,3D>�*�pJ+uf�K�B���,. V��=,�Wbey,�8�+�#2Eve!am�i �H!`)N���� �b� twoV� � @!�m�_Ol�Q3Y y fik clai�6^A�. A/aper, w:�O�an���lemy ��!�*���� X �3.�!5� J���t�+.<J��i�  not} 9�:p � �0F � U�AzoNw ne� g.b+ "�>�=#riN��t� seemA�2h!� e�a�l�4�� � �!}�ity don'vuz7!Et:?�E�aa� :�]h�M*| �m�n-�sD 4->>o"%>�<%,NEon.[cYp�*nGlooph�&��eard}; �6���mfrw^%�st�a�*�6a%4�>� wŒq�ve?��E��VRbD6�cosD0 well Opir};�No'lsom�a�� ��� 0g1I� s adP��<"���wA�}�E�+l6�)Ibarr1���|u�e��st� u�a{F_r1 a neZ. ary >&!�+start> rȨ�OA�mea6mևA * ^�2anv�g (S�A�2$ools}).�� �>secmadwGDKEJn���; ��r�oi!��D que AW-t�Si&� `�.4three} setting� �<Ye�Bobf �f> � �u�Uteg��_�?t)�oncL/xis}6Hll9!s�n�� N� ���v$0"��2�,2}{19}\pi$ (!� ��a3�x|e =;!�&! seųnumerD zQt�U���o6�V10�mf8��z-S�k� ��NLME) ^1M2I�how=e��+� .��nusa��I!�륡Db�k6� AkTm���3seJ s� �2�2}AŁUi�N1����4UxonIr'�Q d/orBob's <� �EB four6� B�E�^��A�ae��:,nxte�9�Le �e ��a�ulaTC�zꮁ��>le�}No�R���Ga arbiS �K�3 tIF $I�=0$Eee (�Wte�i�70plete) surveyA��r%MsHzU�R �r*"Ps���� con}��Sr�-��ion{T��:.yt��HA�VQ }:�@;}��"�> tack�}issY�m4���=01l M�A��neAJ�6e:U�_9 ed�V� typa��ڡL'�B�iA�Obv ly, iaO�/t�@p�co�n>�,I�1tiori}�D� be!��t���!�!I.m �E�nrm�A}�Xx, 1 edi*%�Bob#Ue"� a �ss)��2xp$\{A_i\}_{i=1...m_A}$, $\{B_jj B}�AOmkof�.O%���y get!�outno!R$r_A$,B$�focus �<ERdicb�2�<(w(von Neumann.y@� ),�3)c*�A�n4{A,B}\in\{0,1\�n "&�qf c��\eZu�Nf�em aQ<aH$P(r_A,r_B|A_i,B_j)ǦP_{ij}�T�<,$d=4m_Am_B$ �2U , so)_��n�v��eCA�a�W�V�P $d$-.9�s�, ��"6� a4��me;� sum�to�g�3im!ng�'e2�P�_<s�w�r\ �l�AEQ�*�| shrink+uf � trivOv�a�t�6 tsi,pito,H ett}.@=F���� !���L�bu�5T5� y2L �lyIqBO!�T���� ��ed 55�Jt�3�Ppo�u}4p6av�xe�Eby �cplaUa$("facets")� AgJ�A1A�u� W��v(E7 ��J�T �g7 ies�,]�6Q�tA��"����on"�[ )).�| � 9C@�\3V sk�f�":;[=in#=�}fig���Z῁�a�en��is;�& etaiHA<�?Q"H#."e�= psfx�(=8cm \�( k8�P \�XR2ʴ: �#e�._��I�^Vk +�2��_<y� !B@�s6�^� (D�����P�2(9�I� g� ax� �I�UJ~in�8_ Q��s�8�� M2�B$) black dot$ 9.=<� ���atE ~n c ��e�) y� G� � �Q 2V$I_{332� �,%��grev;��&cZe9- S�&k N� }.}AYMYAznd;- S�`^=* ""� QMB ���"��) ` tM�. };i�i�QoB� 9osfasm�Ȁ8 \ba \sum_{r_A}:< <&=&P_j(r_B)\;\;\�*: $i$} \ea� }սcl��M� mar>^of2Un�.���  2u.�!�entirely}!2) $d_{ns}=� +m_A+� N S �we� !gvUo�z�he $P_iA =0)4 -�$9'=r_ �4,�collins]"� M��I`.� � !�b�  B�no�� Let'i!��!sp��� y)�e2�!n"/%fois�,�A=m_B=3"�E&�=7y��@15.� . Aze;E�!:2����� �&::� rex�����f�� � �u)��a>Mei{&�)l � -M CHSH*� .tru�Jree0+�/i})sa@ �� \,=\"Z�aM3L{c|ccc} & -1&0&0\\\h�� -2&1\\ - 0&1&*\\ Z1 F(&\leq &0\,.�i��a5�!|Q-:� *R[�$!6D^inYDB��e0��r�z�)�� ���y,�y1& B,š2 �����r��� � >�� ���s�' i~� moy{1�}�� 1}{4xTo beTiar��the� IW:�s�aeg R�C�Q� \=0$�$A_0,A_f�12�\nd=>� $�J$,��(2 �%�[0_d\,1_d;   ]&=&j,)i!�I�AnY�1N �,E�\,.%�o !7��a�����is� adn=*A�e�,p �&^s g[-byo[: �tG ^=0��r�S o"� $2^6=64 �H@ic� ies;�'sep0 satu��&�2m (g,Šy� ��Set� l @� A<0��o� *� ��&a�@ R.��2��ran�'�matrix�h�  he 20I\ {(�.�a&�--1=14$�g[��.r �5l/m�P&��m#"e���8s��a��  *�.� "� �# (���rJ� 7:� :4:� �d;=�Qy�[!;N���!i�m�.�wB#��� s. �> !Si2_RaŘ�9_�eo�N"\*} $s $x$)ge%�b � $a$,�R)y6)<^�� $b$;�!�se~be��akI�BOs1E� "� 2� o,b��,-�F�/,�a=0)=P(b1�8$ ��!��(Ǯ$a a+b&=&xy�x Expl��3e��$x�zor $y��bF $(a,b)=B6$(1,1)�1;Ta2j ;�$x=y=1$�.B7_ (1,0bB.#�s8Fz!�^�m�-? +Fig&&ERn xiA)�^z)q"�* "�Y4M%O�3 bit $x=x(A\Ag)$;(��S%�3En�I�I�s�� A.L,a}��5 ���jnE�2R� $A_i�?��}!h 1 as _",� �4*�/ r' �-1��#��s b��mwL$�'�0m^( l��,A,�0,� c�ra��5hop�� Aso�Y���Ka%��5%J:A@�*� y .�� vol�(��  w`�n.�(innFNa.6O>z�f&�>a"y*9)E�9�pI�!�@&",A� &{#3 So leasA�i���"�Zb6� . Aҹ �l���:nepA m&� ��%z\x:U�)�>aUin�*u�X�a st� &�2�^6 ���ɖ�"�s= �$C ,�i$x:B �i L �&:AB_n $��  B_1$���S���>��=T � bq *���&/y ee�  [0_m� m\,1_m� � fK�2}��,�  :� 1"W� ' & 1\2� �B bel{�mc yielex&� �$���X!�F7 v�K�<HmT� �adgoa4to��w w�� is g-p��-0J��j:%� b.Ժu(� m����ct&�H-e�s� !�aZ!�F�4� h5de��i%q� cV' iN���!Is�tbe��QM3 F&�! 1 e�!SJMz,Ů�(1*��:�"G(�� iea%��=BNs6 %�1Iputerkc�bv�notic�4a�0iV�z,( , �h�Xsix cho�:6� l �1 (^d $0_d�1_d$), $0$� 1B p keep� Q-VM� Ym Ym$r� rYfliYAP.6Y�f Yf$)"�2=4 � �K�a 3�"($6^6=46656$�E�l�jgh y��"meu/h0�] 3088*�0��0(9�F a�^�� ion." � �stu d*&; ��m)a�i(i���� ~y $�%,0_; ]$*.��ch\h %�AF�� 0 �9Ŭ���Mxs,��T ���� �* �: len+t�7-�6b ���dh;0 ]ͻ [1_d�; ]$. C!�ly)H&� to a.�^, h�x,%��7� �#(�im}�ch��*�~o�7uQg�Z28-� !^gie��-I)�i��q2Q$ifin�a.Le Y I'�:! avail��O�m!�greU\��matlab� f%dI��" c,�5�.�G"�Jtwo/s}Mi&�MLv�2��2�m"�(U !*��[� _�2�=5w$, eq.~)�):i�A�*�� �0%��w $-2�I";($-1!���yI i5��V]����pp���@,G"�)o)�-*t��G big�X���Yl�*nBd(x�F�5 -�oner}a4!�"'"ar '�� % �1!� d�̥&))&(C�fMFVw$t!M# a go�f����fmpur;4( add pena ���&2�  n�6S0`�0a t�<./$U�30$&|satisf}5b���B��l�&w�&q byl"0��F:�usC!I�4�movP- 1 QM�Z]is*�. :ZV|�����}6w�m,%�f"} ^�"� 2 P# \ba �E2%F^co�'F\ea� $/�m�X/gw�. U���>�ZE� �!A2�1���wo �) (S�d�-(!').��K� h��;M&�-uaH7!Ca-��6in�j��)A Z���-.)pB ors,ɮ!bP_0q &\NO arrow & \�N\�(�L+MK a}_0&a�\s�N\8) l!���� �-�v'BըD�E8ize $M()�)="lP6{1@}6�E��nq��#d*�0%�ula�z�Y'y aW0�*pti� ov�& welv����er�#r�\��<i�h?�figJ}��!s �>�^�H&�1"�%-�q�%6 bar{);}"$�0.006"t $.!�� 0.0712\,^2�J"g�i �Af�p5��i��) $\hatA'i �I��A}^{i}z�I2 x�Z D b}_j:DB}^{j2D Ex}$��&plo95�;:�V�k��-m&Ӂ��=�$�,*bw Q�EV5E�5G�#.naea��`��i2Lލ � M_{4�%.��m�%p'�86~�F���gre���%>�4}�;��-12�?4!���*�%ArN�a'42�.act�p�+_norZ-arg}�2E��3Ȋ&73A")"S4: (i)��I�+#�u�Q>t (M� �L4}ac��n� J #`i��;x,%�� Q)=- �!&�A��xH} � $j�!�07� ���e6"( ��B�(9!�u !� F�_�<bΰaIkia�����RM!��*ioned� _���"�  �J2_g� &�j�M�B�J8$��.;�09t�*<)�X5 ily �����>Z5ket5O�|<� u3P| Mu A�C��E proof",�i�/inR�)2b'.q � ) NLM�Rv&{ss1} /�w�*�2��6�:<bxEoO�mm"�LPa &b>�~ourVo5=iE��"� Ex�og-� s:tw��!(��'c�A� may E�AE+BDwai� � mS-clariZ�c��/=��of�,ng.X f��!� �he� ��A�vA7*!�8as $A\to(x',x''\)B y',y .r&�i0 VPA_1 1 2� ; $B6-B -%!0�V�n, $x' $y rE�d�j"=Y�!�� �U*o+� �dea� d $aTw� b'$;ly n�nsw�bo��o o`b''$. ".0�� �a'+a'':"�pu B=b'+? (y4modulo �ejy� 6 � [-,Tw:�"TNLM,...}�R0>\ea��A�� { !�+=` � We��ސ step �9RbnAr6�a�sL�w�� y $pR"&y�C�P���W<�C��;1��6y $1-IR&�( )��0)��3�h(�(K "� (all �g� M�t�A�zeros� �ͩ&�N �5"]��XS_T��#�s a��=�:p U$�"� y w, if $p<)��� ^%W�>�N���Aq�verag;2piU�o��g�K��H��%���-��ult: at�wod&�7&�.R�R�albeith!n"�F�t� W !�i��$ �E!�>z��&�.s2Y<�~V�TjP-�9�:"pr =e#au.��^��b!�nd �Ib+P�K�ud�I$WA�Yt�-�6�tT!�Tj<:=z�s`Ea��c�H([��$�u�@y.J ro"G�Y�lexP &=.q,�E��Ikne!� >q kR*K;M���ijt� !*�m�EF*�/�4i�' ��u���turU8�i*a�mik s do{�atta*&8�xe~�Gan=0%� �� 6"^ V� &��!m"<>"":..S72f�t�.�3!3�$ aW�a2�&Z� ��R?x�(>#Mב ,b  ve� cB��tc(C�r�v�J.�:p5�x x fp�qeMGN� 1}{5jC{&� a <)�F�*�h one-�(-�!( %[r_{A_0},1 2};r_{B B ,B_2}|c(A_0),1 2)]\,=\�\\ [\{Oi}\}; DB_j}\}|c_0,c_1,c_2��\�b�!Dl} \,[1,1,0;c,1,c| ]�!(0,1;c,c,1|1 0,1,1; c| =1; J0,B K 1,0]2�/& .\,.�5�Y,o4, $c_i,EuJmf�,�jsen!�oow�UshZEE����#i %j}=c$� ?���e�e �� j� ���,.� rece���. �-f�X��:�I�M��!on�J-S�x]���i" &��q/!KB�cR.�� �rCW6?�Lk���2��d argu� Ref.�� !S�grasps�<erd ail"� sJ��l��i��"KYwheu!; �6��*(b &��4�=Y#ope2DEE�Ff6�MG*�es7���kx�Dc"�U� m�.)i F&.Q7%��"�D ]sj$than 6N�}ULA��\d�L���SYF�O�O� W�%Jngi O nextRiest, naP $m_A&V��$86? T>+ )?^"� �*f�����ac�19.#�*h3U�2� "�?��M X#E�wdendix A!�]��9:�A�d_c�w*,&*$O I 6��F�ZwO)* k6y�*A�(A2PX����erG| 11};*Opu"C�. 2"i�h !��x#���Af� q!�["� �re-�i#68I^{(2)}_�bi����8c} �8�(:�8�80�8�(�892�,�ū�i@\ea%. �X6|�|fmA � �g1f)�AGX!�N ��!A$6^7$� e&%&}!�ԋ 17272"�� �( , 63AE4�e͇ �X$6i� By�37M{+�%]G4UA>R!Am�&.�("� ��� E�f�D!� #%kr� #!���6�mz\ea QuitA3� Y FvA�e5m*B!��"�aU�4:o#!�is�a� p�!y)  5��ƂX27F&`���".Q .*� IE�9J8o.<F��NyE% ��/m^9΀ak�t!3�"�.�ofq"�L�F(| A�Y$A_3=�-w3 ý�& � !,%V�_. ambdaj-l<*�,G= �E �  �U0Z 6m0 �$0< \lesssim)�d\pi}{7.8}$, with a maximal=.N bar{ AT})\approx 0.0102$ at $.! c1!�(Fig. �hfigopti}). For small values!1l(, moreover,%m!&$prove \ba � \geq n1}{4}\, � ^2+O- \^4)\,.\label{bound}\ea T!��%�%.as soon � >0$:E simuIj8 of pure states-<rbitrar!�dweak entanglement requires� E�onea:( --- again,vweANiced atxA�qaragraph)D,ss1}, it mayA$ac$a $4322$�sase facet%�tthe deterministic polytope hav%� been listed exhaustively, but several examplIF `lare available \cite{collins, 2}. O��se,!�searchm�possi<� sion�Hour results by incra��Bhe penal!��0some marginal!DSt!Qng��5D\y $I_{4422}\leq 0$ givenHRef. 2�})K%�spondU.L�>.Lis ��exactlyAu$above, jusA� placI $-1$I�$-!�s%�coefficiA�Dof $P_{0}(r_A=0)$.��)�similar:���< 0$ indeed holds�,ll strategie��a A� le u�ͺ$\demi�&both; lookAat ��~��a��u be�intuia�!��1] �q should dee$e. In��inga�����recove�$e (better)QNof 2��A�-� $a_3�lb_0$ to�%� $1_d�� reduI�q$ to )a. T�assign��adsA�3M�T,P_0(r_B=0)\rightarrowa� ia*us E# not}�!�form (%ODproj}): it describA� degenea measur�?. �laD 6,���<llaυq5522 �6622 on�xdid� appear�be wor��H closer study after�� survey. W��8considered neit>�1} numbGf outE2,, nor multi-�W(te scenario�\s�`Conclu�s�perspv�i��(seccon} In� 0���= show��M�6� non-�ly �d �� of qubits��a��i�8 �amoun�+�Hs (��dlocal ma�ne)a,�e6� A"m�. =q0mpletely solv�e blem��8��o� ree ms%7two o-A�e� Alice Bob�N��n %wi �^where 8choosA�mo��.l . At pres�!\ %� know��$ �e�b5eda�a �� �e NLM.�6�-�� B�  \"� 9�) mor��n��NLM is*0 (eve!�  �@iA6 is�d��@ seldom). It will�of great�.er� to f!�gap)$to see wheeU���>��,wh�� ���=� e � ��E�ofA m"l �stead�NLMAvF` ,a very funda�al poiE� view%�e_dis��� ( new surpri!� featur5�� world%�che�s once)�how f��!c* l� Ag�rdon. But a precise understa e He incommensurabilit, twM q��a � e�&wŲb�iͮe=appli�s�l well� in~ce� @V%��U1�ic g� - in��a�0tocol (crypto� (y, teleport&A44 algorithm...)�Kis �8u���!߅�st��2orf*��ityA$We aca�ledgev$ancial sup�)�v8EU Project RESQ!h��0Swiss NCCR "Q�$photonics"l ��ndix �Opt�����a }$}�a% ToA�puh � >��  Eq.~(�m), on ��i�m+ per!� �>�iz%� �14�ersST irst:�Dumeri�:| !A�Tultau !� analyt3�m+9haA4en guessed. WeEo6'by indE�� azymua�7polar �!%!�vecto� Bloa�p�$ $\hat{n}\�hv(\theta,\varphi)$. For $0� o �.� 10.6: n%SAUe, lia�,$(x,z)$ plan��l ��(mNs depen���$; Bi5` \ban A_0&=&(\pi,0)\,=\,-�z}\\ A_1�_A,\pi) 2��^2}Ax A3)A0)\\ B s B 9.mB, jJ�,.\ean� %�sn&&=&� <\,\Big[-3+\cos 2)� �A\\ &&- B(1!.)+ A B<+\sin.<A) I�]�U A�� �nz � ?|E�$ e{A,B}$��a fun�A��Us=�E^Yw�A�.�4M > don't����A�>�y long� and E�� p�erM�����6y5E�6}j�('2}I�+E�y.�.%, 746}R�04"3 "6� "22"I�qay��j1�E�72�-3.�M� M�8)\\&&+3\sqrt{3}A�� 6�aXc �. �Q��D Ipez8pi-\mbox{ArctanAyft( ��,{�}{6t}\� �E*� these� not�Pb��.e,��q� r�Tlimit! xa.�w��d*/= �1�eO6u$-Dmea. &�a�v*���Dyb��IuS   �l� at7 leas�@is �ach(as written � ma ext,*+L). \begin{thebibli� }{10}�!note3}� s>�i� �# all "���C al��ehum Ts,J *0p!�2$� Y$ V.C of: R�2Werũ M.M.��J�6��03211I2at3 referenceerein�  �8s8 = B�� n �,�{�, von-NeumannJ:Hi!�t space  Mdi�! convex�is2 ? d (alt�n+u�-H+�n,�~l� �rP} D. C 6�E�4. A: Math. Gen�37} 177i�2$masanes} L�� m @fj� H �345�2�Aq2Mqtak�utojt�o acc�%�Ip,#2* �!�alterna� ver!eA�[def�!,by $a+b=xy+1�54�0}! , a9$$[0_f\,1_mf; f\,0_f]$Af % *; 1 *]$ |�sam+�b p�� m�matlab}�Jhe�P\verb"A<hulln"�\& sc{M 9onk 28$s� yield�V="-  "alo�or >se �s plus s2�20:��2f&=0$" eap8�e%P�two7�~ ctua@#�pr� m/pua�wo`:.� (!�)����+R�(line (2,0,0�$rde�(1,1,02%� en�m_!$y explicit4i&� evidmat� rans�edI�n oY$by exchang� $A_0EX 1 by flipp �,bit $r_{B_2}2�b� e�� B�D� ��*X9� 152� 5�p�om�%� was cut�us!œ 0 (private�&�2�ap1} 9�we""� syste�" becD %�"b�ra)Rig s�e Q of S�on E3sech�N��n&�!� (A1)-(A3)?>�!verifi�llm'm �vI[bKtEmodKr�"�tur�"!n hat,ɋby 3yQ"�"1[!2� deri�fXہ� ��!�.�Q�U!� 4} F�ng�o$>63!.%sE�oo �  a task SA�"���?refore, 1�ru!�isJm28 mill!偳im�i  !dom�elA ng 30I�s�i5he 63. W!� ,ed��Oa� trivo��toa variably ����u|!q conf�/h�0h�% ��i�{�����h� 9$�$ $I^{(2)}_�:��.�42�>"5R�7endB| M col}&  docuY } �x% E!z cE~ce��mass �,i(#s dA�nA�8Laguerre-Gaussi�),ams % A Alex� ?(E Di Fabrizb $D Cojoc \�4class[12pt]{io� L} \usepackage{epsfig�4setlength{\tab� ep}{0.2cm8newcommand{\be}��!�}} 2#e#!:^! rms}[1]{\�<\scriptsize {#1}>Obfa}{|AFr rFR RFE EFk k>�dd}-�d>sgnnrm  :�bra}{\l�:ket}{\�%le}abE)Q�@} \today \title[�!] {�2�S$} \author{6Z $^1$\foot�A�A&B whowy*�(x O j&be addr� : aa}�8@tehfi.pub.ro},�2�$^2 m�$^{1,� � U{ �(CCO -- Opto�څ` s Re?* C�fDea�A)�u$Technology Reli� �H``Politehnica'' UniAE� of BuchaMH, RO-61071, Romania��,TASC--INFM @�ttra S�*o�e LILIT� Beam� � Basovizza--Trieste, IT-34012, Italy}MENab�)ct} ��� p eraA H�.�a aZW�aE $ple atomic� , �![�'ump��! a'spr*�":�wC,"in$ parison v�� wais%� V�. �*:]mo�92��Vak� &c. U#/pr�4� ofF� ha��.�nalE4:�coordin�.���[D(d�out ma�)ny}'� expa�%$X$�$�on rul7�2:�) .OfoX1 immedia�&j influe� Kw� "2(uV�s �!�' �al!a�hR�!��$u.!VYݘ \pacs{32.80.Lg, 42.50.Vk} %\keywords{o�/%�Ɂ�,9�o�J� , %�UR�,>�, d!�� quadrupol!Yu|��&8#Int�/!.} E�explor:1oZ� (OAM� %w��magne�/f� "x" impell� !� workbDAllen {\it et al.}�, woerdman}��  M u�4(F  (LG)� e�0r�� a�%/ &�$ OAM�  un~nergy.���� e $2��raA�Ae�&g�3 muchiest� c�& pts �pbeF 2&� �0%1�f c�f.- oam-a!*}RA4�0 m�of @0�1 devo%+G 1n &:�md��$6�� advanta�4�� 9 V�b"@6O'i�&$n$-d�al:�by �0taneous�me# down-tW!nQ(}�����gof LGM w�4tom�'E�)1"%�!� _force-e-|�Lhe�Pf�,%light%to ��s�obser��+-�{mixAprocess n,tabosa}. FurC,!t��i�/r >(CMA�E�)���1i7*�,:�U4�6OAM D4(s���m�2�zYq �ashok]nd� E],is� arA�bw)!S%�A!d^�?R� j��$ker,vanenkMaim 4is�i�$o investigho|,VqC���p&�K<N`s >e��2�anA�betR� CMn�. � /wA�-9��&�(to-� �/ ��sic  *6e -byg!ve m ge $+e$! / $m_n" �+g!)-) $m_e$,o.)Hm spin�2: !� ���5�%�r:~!�0by $H=H_0+H_{�{int}�%�$H�A%h!� perturbedN�x $6L?Eɍ�J�?��lR�,�(ed ah� �"�wex0!�CM*� -J\u� k.1 $\bfR=(m-e}}\bfr+n2n}})/)6$= e}2B$ ���o A*,1�i�.�. ve (%4 nal).�!��=�-n.�e}(�$- �8�0e�+�*. ��we assuma&s%���( ,35$@$M9"5 CM:j �u�, i.e.Q nic,1� ( $\Upsilon(!�,�)=\Psi_R)  rO+A�UA�q�r<-� wo ��"Y $ potential)��2normal�&����t�  cylind^ =L�[A�J:1% ��* (G_{N,M2',R_\perp}{w_R"�&`exp\left[\rmi(KR_z+ M\Phiy5]�-8 -of-A|�|�} \eeY1 re $ y (x)=CDN}\,x^{|M|}L_{n^-} (x^2)�P(-x^2/2)$, $L_p^l(x)$� !�gO -4� ,nom5\ $w_Rsc�5!)6�MB�. $�=�0\:n^-!/n^+!}/P�2I1�� Atant,�|H$n^\pm=(N\pm|M|)/2$A 4t $Nl:o�g�h�� oscill�` $E_R=\hbar^2(N+1)/(w_R^2�$t}}!3a$M[ "25 a:-  c� w�' $Mj�qTE�*�-P termb "q U� s $Y_l^m$Y�iX0=F_{n,l}(r)\:#>�.,Qn��nicFj�iN�� � p�#nc�2�an�%m2a ,�� xa�?i�.&H8%?a��1�($w_0$, hav� no off-ax�4� l nod� a��tl�5!� $z$ -�, Qs��ccg $\(40\dd^2 r \,|E(� r})|^2=A-�?6� $A$ A� chos)�si wa�)iX<�")?��:A$l$. U4���8�R~2M?+er!xco~5G � he-�ic �� k 1 M}bfEE},t�"_0}$,|l|!}}\:�>,r�)0�)^* }\: ���-l1D + k z-\omega t)].6�ic-� �'N+we��� �:�!ue"w^���R}.z.�(-1)^{& l+|l|}~\,2 �,�%\�E_0�rc }{l}-\bf2!)\:96 :�1 -iY)q��*: A�33� :�, ��l}{m}%�_��уC% r^l.v=\pi/2&E3��A^~mMggel�;n�� �P m=[�/ /(2l��@l-m)!/(l+m)!]^{1/��"1 w �6F ymmetry� ������i|$bIE�"a�]�G:�J���. In �qBqu� calcuI �A�>=E��tq9ed {i�#.V &B �HF� "Y  -hami�-� }���: focu�&�62 wX@ play% ��Br� reveal�u Fv#$l$ on 0 *�[ stru<(2�9h)+(� )G>�)� �xefO,!q stra�� impr!%� �"�2u" `Power-Zienau-Wooley schem�C@lembessis}: \be 2� =-�w �w3r\: ; Pim)\cdota�e| ,t)+�h.c.}��M2�pzw} B � 6]$ 2i 6den�. Writ1�2< "aa�44 gral �6o =\suc a�H=n,e}e_ � : R)!_0^1\dd�I\!>delta[/(- 2A)"_ �t����iV��A�i�MZnT)7#2is exI>X# as fLB �Gfl:�Ie}{!,rms� I in%A2 ��a\/E1R+#f�JQn}}F^,t) + #w E1e6Ee^E\WB\}.� =2�^{(1)}6��!~�)�"*' T�6� ZVfer"�*�w "-�?.��U.OV�^O2U�sp'BH . *�Ms�ofZ`r5V phe1&� &�5ateICM aX��_ .�,�% r:�G>�m�� ert� "<F�>7� rc�Y  x}\pm y}��0l^\prime=0}^l� ��m-}^*} (\pm)g 3}=}u) !L{m-b %y�=D�_�_"PI�!h!,-l"��R�  as% @gin{eqnarray} \fl�PZ�nN�8�� :f_0 \,"�  k(B��#tiny | t}}}z)] �@1m!�A 1VZ�ɌC}_A}^4}|l|9�^{l9�\noq7<\$'s�|(B���n}}- 2mw.� �:' *P6' � YV���F��=�> \: Y_j�(\T?>?�Q�Iv"s ]�-1A�nd]n�CA�m�'*� UߙZ"�� �*J we�/ rcase ^={ 2I&s *� ,Czero _9$ly if $l+m� an5*)�� �1���D"�L� <�$2� � r.h.] r6�rq�-(QK,q)�n $(.�,Y��r.O�2e!�n�E$[+[ $, also $.[+[JI, s2=�0sles!>��� ap%?AO4double sum doe2�, !�. I*� 13  5�f�ZMqIF,\B� o �(VD6)A�get�� = RP�g\,&?�g�f��:� &&.�\!�K( mes\$ ��(\rmi m�5�� )�]}{uw-|q|)!!\, +: 2�-|U:2V: } ��u�, �5~5} !��2B�\ n!!$Bn�PaDmu4factorial. Let�0�>z.2QN6 6�>�$�8a�a,8���-�( . TR��P9~\�R�̥N� m!G�V ven,� �SlKwoc5�yitu*c Gat�* item� l>0} $l�Vle�O�Ob�&�5�$��eiy!�� or n��� . "Fq>��Il!���!�4=\pm \infty$ u� $n�V0��l"��<0$ �� d0n� !=a��q(=5�. 21<%1<0$�1u�$ŝ!0ing�5~1PeI.�)�SA�e9!�previ�#��&Eva'.y7is �5'� Y$Summay/~h4Pg� A<w2�!|-�ai�MW�)��m�5s�-(l)\,=|A-��2})�is)g�\ \ F�}!������ٸ2���.�U &ً�x�g!�1�͚]՚"2<ե29ɛ[26']!!!dZjm 3B,I� 6�gLay[#ng��%&w $ $A�$rPF�F$$ in orde3/��bp&5 JV . R�8qj6)a|�K6 F$M "`,uo&� .�!~(+kr*cJ)�p��M%^p�H(2p+1)}j_p(kr)Y_p^0y � m�j_\nu�V��B 0l"� �1!fi�M kind)@ $\nu !?g6+ ver �^� K8 ed "f 2X2�B` 1,2)b��^w6��6=QI� 2\pi^{2}e%G 3}}\�> 4}{kf=+1Id \, =� R_z): L s8%�{)�Hq0!�U} \sigma=0,�(1�e�"_ � �[\L -�{\Gammay�+2) �]^81�}-:E1{p+�(1+��)}}{(1+) ^p+ ;3J2h1)}�- &&2v1�-fk��4 �)j��} /pm kr z<�}}{.O!E�+p+.,6� �%�" 11}^-�B! p}^�[�M)Ae^!Ss{i!��L2�*}N{_1F_�\ ft({B> tyle �9�+%�;2�?L%%� };-(�4 )^2 M�., &"� }�2�b� \bfHb�$,r�~!��aJ��/3qI�Y�6� Y_1b��!$ @{$assocU1�1���"��ь�Dx{Ax1}� (E_x\pma2$ E_y)/\sq$�0 0=E_z$. H]he frg@�`xJ�"%$<H!on� � �>~�-a�!Ntribu�,t�e( <g!z e la7\�:�.b�R�B a good �"7#����|.>�!berry}.rZ< j fI),�Xce $p$O<s=zD�,fin�5�hypergeojic ٥$eJ!I nsisC<G%h Aeh< 1<3� ->,;)2��,[ excit,TNiTthe�+� � $r^6x" low�X�c�mA�E�secb� tXle keeg@oA9W~\�&LE,M;:$B#:*�p+1=1.�%>3�,:.2..&a3*�4@1�8)_AGheY:dkOEno t*Q0p\/M�I��m�/, |EWaj+!cn{�2lu0 remat3GQ�ab?/A�.`.Sp�u4\5�9l�c�"z5-5*!  SA� cer�2)EEy"�bb�%e . matrix!<9b*D0fMcEaA��tsOH �M}_{i��a�Pf&+ 9;\m+_f|BTP |!iM;$. Pu�V tog�[!tF �2� |:k���+M ^ C7"eZ�*)- g%�EC6�(�=�:cE1"�,Vy �jb = J� w_0"�� .�%:� Z� �,(k+K_i-K_f) j� Lt � u  � � \6� �� �� F ��[j� ���x p+3/2 B� N�A� �,_f,M_f}�f�� |;i,M_i}A� \:)v,_{(M_f-M_i),R� ).� �+ _f,l�A�� *! }\, �D �D �L) |�i,l-#f�� _�wm_f}\,|U 1�| 2�} *� � >_io { \: .*� �u��i�-e5RNv:�zA)��Dirac B$����Kroneck�XltKG mbol�!<con$7��F�Aa0 _+. �B; ^+:?$ OAM,�&�!� bracket s�&9�ed!��^% �Zr�,�s $� �i!�2D��*�Aը$\dd(&�X)%;$, >-e.�&�6=� �or�al!}�s� �2�1J�b�: dire�d"e2.! absol-_ valu"l4N\- %iU3���(g!'�&<,)/typ.�s��pE-��7olvkN�p ��.|?add�theore&/�^+ *\\6�CM.y& 0 � pm 1^-1$+ l$IBC1 C/Z2F0.EFg&&�  &�P3P e+ `l-1��Q- �Q[n& _$-|l|��M�taI; UXcap�$B� P ]Kin��:"�; : $(Ml, m�! Q'M$��a��;e�*k ��6V5O �h����J'#sR<�?um�"m$ &#�differ� .�sa]�;�6 �m2J4. y���5i�)] }$Ta� ?V3"r�tp�,� - ~�8Yx*[%lun)jd�Uex���a�4��VBN6 n�8reZ<isI ed, �9� �M1�m +M M=l+ ��lw�/fulfi�B�3 vane�> Here�V:�� para�>�!+.�� lectBn�Bh�% e�E�5� 6� $mQ hDs bey��6�"(Nno 6er"ijauY*i}2$9J�UMc:� )�."%N�$%$%1�6 �.r@t+&�2Ao  >"�mh= �aYx. �Efer\;Mh ( \qoy!�Vp&u%exceed ��kP>k�l peculiarduMa�� XdL8Z�9aH�<�5U�)� ��(});5A �g:&<no a �2$-"@ 25is�Yi+Qker}. AXPB0a<not&� [ &� F� 1LG "�7yIse�1�>-�  0L3aaF�=���R��mt� I!��)h s�!p=nU =X��"� JR�a�.Y! !O�k& I$� �K M2 �%C &B 2O)&=  in�=ulaM+~��Yn6u�a�$ CM��F4> a��V�=��"�;byM\ prudnikov�.gF[!r�#.#ew�<5\: N}_i\:-N}_f\:��k�>f:���'.��2 �;L x\: x^{(|M_i|+|M_f|q9"�)/�:�-x}\: ?_i^{-}?_i|@?ff���=�* %(1�i|)_{� -}\:��-�Z qy }{2}.f. N.Q:4 {\�k!\: nF i^+ f �3)^R9B%9�� )�: {_3U(-�,*W�jv�}, Z3!-R�};.2-r�m -N_f2K)1};1),&pCM_��_m�� u &c1�:M_f=M_i�2)$. D >�k����x�C $l\: M_i$:� ��V�) may b/r&3Y. *(=�s2:2� s ���pgr� �A !ra�M, $p"�'=�?�@�q�e24%5�W+ unitɄ�t ���� lN�n Ho.`2�!fՃ| CM}$!�$l3CqpK w_R/�@��!��� 9��7P_K\�toeq|M�MZB�!^< Mm�Zo���"#��"�e6e�F|^2:� cm_� i_&C�4/)q�4g��&� 2�:�O�!�!�&Q1D- *D (throug� i�E�prr ?�BN c.> law 2h�Z�2Phi$)ach fix�D6 s $N_fM�M_f�KIn figpe�n_Y�}� plo;B9o!F�a&�3� j�\$lY(�< �$l=3$ (�& . r�a��> e�*�r�� N=N_f-N_ij"2$ (�!�9i��V ���*=0!P17N5"��Y��>] 1$).v�b,1=3��0�>T �3 �W� s wr�F?.Vb�a,.�JB!25� "A =2,3AQ� [$}[ht] %\hs�e{-1�[o@fig{file=iop_oam_ 01a.ep)!,idth=7cm, hec?=4cm}GFnEbnE \v �0c\ �� }{e0.5sf�Y"\(a)�7 {:!b)}�� N "�� 6>���B:FE��S 6�i`,I$A�6�wMa7%�r=10^{-�s~�O* =P�gM�<q2 or��U,"%ew `a��I�s� � whit�5black bo��6�2/2S}�dI�(�sa� e�}�1$).�,�p"=���$9���G�[��� �1N_f=6 6'�mv.��2t�i�V6�?M�J! ��B?$Mp7���i*�0aI�Zx"�2 `s�&�Aty��V2��6%& �!��!"�Is two l.u*�K`!># $n_x��n_y!n�{R$&$N=n_x+#%H$M-���bY �id@#r.� �3!g?-�X(�caT:6� �{=be ^{.s{d})}-Mn q})�( 1�t�R(d�S(q%>ig�ym�} �>�) d�Mc�v.� r�cn iZ  h�\oppYSeM8!,>�:!gofbe^�zQ:mU F�. I�~�!at��)e�)�E%��LI�)pecifsP��s both�f^.�}enC2. {may`dsuP!*�G�W beamcPvAVQIt:#s s e.g.� suitu ҈e��n�L al vS�<�molina���sN !seEWV;:�occur�b*� F�.� about $��6}$�;�eaP!.�tho�z^V*�+��KI�e �"*R�y�)�!�CM� 1�ce.�'se ��R)�edec1�e n5� �2 �,2yiw�Y� F8 F�gunlik+e]��Pm�L�+.w_lb 2��#y� f� )�*E#of �&J�!l�xz2 �_W*)i �%����12$.�!�E�&g!+- (9x23���9 (odd).F )C� 6Y j� 2.� 10*� 6� ���P �-u��RZ!d�:a;�mi&e*�Y acte��by!\i�o "~ V)��85� ��T8B�}f�re:s "n^ $l�n"K :�6M  I6�? F�*�a,}+r���o>Tn�!j &_Q�Y�2K��:��R��YS 4> �Tx>�3 U7�havior2�I-2�-e{�<����^7haa�%��a����e i��t.�"�ro�Zula&3minN�-V S es��is [H;#�g5T2�. .�-C"/;G� G.I~�-A�!p6*sM+"�Z� �^!ba�S9�s affec�pl.6i. ��� u�y� ��2K"~/a܊4Ar!�$�.>�V.X" n��"�2n UlG� ex�1 sq2!�6_B|��� [� O1�(i .~c]�!�� an a.�]!(ppn"�"Z>.�%36�(�T�9�.�)q�LGN�is*�e� Ŗ�P�Jch w ov} ��, silver nanoo`�a�r� RUŵ�o� n�a���ar�Rx�� *�A;��e��|! itud6�*x e�V�� be ) d%�o%�we sugg�_to�.[3#�Knt� �V/t7�2?�V�on PWazy%q�td� �c�{s��^H��i/2A "�"lw tensorP 2�*Q!�a�un� %paperSV2, ΋�RRama$nd Brilloua�"$& I �F#!#+!vB� !is ]f%i �IzLr!jin �R�J�novel`4troscopy studi9fc)7. toz� {�*cd a���g.xZ64�Rin�R"wgeii���,.+]16�$aɥ .j'!X:�6R)�Fof |-Gn�jesonan��,rE!�^O-|,qZ�xo7fUV%�}�.��r�U*{RQA��4�*B�02�wo�hi L, Beijes�}Pen M W, Spreeuw R J CE}W 78 J P O 1992 \PRw~45} 818.T�*�fj arnett S \P PadgM J 2003�iOpS�A� M�p } (Instit.of�wics Pubz ing,aJsto�58 Philadelphia.7���g8 Mair A, Vaziri Weihs G� Zeil�~A�1 �N�g$ (London) �P412} 313�ni��f>�g= 7( M, Lai W KpL^V W E!i6.i54} 425.҂�g Ta�g J W RJ$Petrov D VBL �83} 496.��\8Muthufrishnan AB0Stroud Jr C R�2 \JOB J 4} S73-S7.L�O% B�Ben%� 4 LANL e-�Y��ntj�40401.�&:% PE% A Pa� ychkov YuM�,Marichev O T!P2 %ٙ���s S�$ G, Torres�;T܆r LB�8} 01I�%"Xz(dudovich} D $ N, Oron DOSR��*YR4A.m� 92} 10300.q&� C� �Sokolov�dCotton TI�(6 \JPhCh USI�4100} (13) 5166�x>X d"�x mK:hxp�Z(int,amsmath 5 ]{revtex46}x�icx}% I ����Hu�Vc�xdC1}%�gn }� �.�� i��vm2�x bm}% bold.h%wif\if~ �on$� %\�,{APS/123-QED!�v{D {�Islow-l �5!kb v�l�M la��),}\ DSB8.r2cb@"�vH.V. Rybin } \affili� {D�W"�u ics,:�u�Jyv\"askyl\"a PO Box 35, FIN-40351 2#, Finlan�a mailH�i.r�@pX�jyu.fi!'Xw0 I.P. Vadeiko:�S̙G~ �eAs$ omy>�St �N$, North Ha��St�g<, KY16 9SS, Scot2�iv3@st-aɒ.ac.uk�r�A.��Bishop:�T�5� Divi��kwU NonlinޜSL ,, Los AlamosB$ional Labo�yy,  , ��@Mexico 87545, USA<)k(rb@lanl.gov�Q�a" wI�Cc 1 � n�8$\Lambda$-model� *� �5|eo;"aN�� �vapor%� Bose-x�A�Y^v� e veloc� �J/is&�tro�0#3�-� t backgr} eG �� .>a�em.Ab��irl�-#�yXFV�/ we f~I!8dynamn j�m,. fvum.̄pro��-I6#gpAE.c5�:� B6Vl� .%. I. B)pnurnY7ff�Us�B0�imO�.al stops�5 lo ��shape:�cpa�ly $�kmemory�� &�ai\r2=*�"A��roff!��ta�%&�"��j�$b sc�E<dat��u�yl@�#prʞ.�auK\ww$03.75.Kk, HLm, 05.45.-a}% PACSNV� &�w��eu,E� �.SWl�/ }%UsB|wkeys:d���f �w \make�;O'U?�!rM�Le�6ualkali��|�ce �a;�mpetusE�RdeA�p�u�*�ant!�g5 �q;xp��con�na��'l�*-m%�0�W�re6EhotEucol���{�{ ADHau:1999, Liu:2001j��ps Bajcsy 3Q aje $ Mikhailov4, Du(  } demons�AdtriguAX&-RiebbpA��z�9�m��0�� pulsk�6� <�)�H�!2moseK��ntQ�e�o �Y�f�u�fa�e a�P^�M#mY.����s��a��EreL"iliu_ ��*,K?l!� n$i�t@typg1 �<via�� "$g&�u�� I���Qregim�iiS *\Ocke�8ӡ?@ tQ���)y!� �m�'+�r,.�>aFrXQ�al }�!��ge��n�#�d�S�x��pA�!;<p�stF��~�aY`-� O=[ s ne!� ary.)Di�x�we��JX"alz�-cE��a! 2�.. �@� >G ast �% lEITUo inߍy55acXAoE E!g)>to Rin ��� qu�&��haTtoBish>, \i� � s[�($35mm]{fig1*�� fig:�"1;�e *e sEhA� a~!vgy �lE�sodium��@e } ��6; ;2�akwel.<9e��^ ree-:B�e�Ci&�i)ֈ"A�2� ��,��+2E* etun�kydf�� ency�6,Oc ��<i7C�r�u�$3}23$"�h�$\rho"�'.�pi�jA�  !�c��lzidual Doݖr broade�,Qmw � pto�fco-�.0 ng)Fd�e"�~ <����Rabi-1�($\O%o_{a,b��� E� a{M{��L$\ss=^-$"��[!��L!bMDb$ U*92J+6J. With�� ��ly�.�3 amplha]ph�ae�x�N (SVEPA),�= IE��o]!�N��Max-�� �J�%\7N{gab,�!�p�A�new���Hes $\zeta=(x-x_0)/c�+\tau=t-�)d re�J�u��) �(lM�� F�J�. �_�}i r? _� H_I&=&i 6 {\nu_0}422 [{D,A��S],\;D�6%  !f{ccc} GA�@0�@  ZA-1�x ?%�R,2UI�al_!/ ��lwU0 2 D-نH_I2�d &2A��=1��V*�pcs*!Tc� antia)b{I=-%&12-3({m?a |3\� le\lG 1| + b>2|-P) +h.c.$KS�y e.� *g{.��U Y Eqs.�"6�)A����6�QFram2��r c( ! ((IS) method� fad,Hioe 4, Grob Park8,F!d�m�"�&��o�s;n�ttiN!��F��&}O�� i, namel�>(; " lin_ + } &:Psi= U(�g)\,E i2  D ,\, - i \barA� ,Bk_1��& o�0 ^ VRp{i}{2}{i�fa  �n-i}XPsi\,.Fx2�2xg�A�Y\i��Bbb C����0/�quG.r�!�r,� � �B )a bt� theA�� UE�W ��e��\'��Q B��:� M� � $|1\i�$���M�isܶa.a dark- 4AN�F �!(\tau)$�5:� �dop,&&� 2k J.czauxb� �. �h� bui�@�-1�J�=&*�� f-a� �of�+�2)�Y�b�Y�)_�s0�� ���W;b=  �,\;��$|\psi_{at}-�=5��� o �=!�� o>La � *�X etup�#e '-��"�"�*�}I��*)Eq�Z2�) satisfF !��wB0b�. U"t�`s!�our p8b� $sn, ryb7˝w�4ucR��Fc"� !� ]%�� )�"� `���O�S8 s_tilde} 1�a���>��^*-�&)w_� �� ) } �]1+|:|^2}}\;�?i �[_s}�]�rm{se�ui_s,\\�bB�^*>� } Z{\,e^{ ^Bv v-6��m�5.�=A,aaK' $�=| >J |�1^�Y5�FR51;Re}-��0-i�t!WIm\tanh1 {|63 |} u� + ��nEU}{2>?:� } |2�- �>}&z .\�%>u��^0��51 �&=& y ��oMp!�1�A�-<}+5<Re}(z6�)+\ln\ V>ZoM�0uE�,.Uu&=&� .�2 �RShV�#ImF�l>K\no�~�2"� �5s $:�V5 $:$5ߗbelow�0�&ren��envisadٰ"D�2 ���e.��eh*<"� 2�3��>��Ō�[ �tau\to-sD��� f� ! + "Y spI��:� g��b�E�G"5�O\�5��&����2QN%G��m�,�tD��*�a) .le�4beh�a�B�p*ol&�_w�l3��v&� . Shߔ�4B�iy("C l3emL^e��accelefk ��l�&TW� _,AzI�tasymptoVb// ���-�.-_Z.1 �,�@arrowMK)9 _05 �j/MX)=0J: e 2��N c?�( s&�� �) dic�  y��bun�Cs R  B *Y �A-&w � w(- �&=& w_0 y �0}{2 ki)}!/w(-<=0  cz czRbz_0a�= {|)x_0��{4j (Gq2I �9$(=�+�l�;^2+2[��� 1LF5 y :�a>b s "� �\�ads $>�= �+�t\�*s_{-{}KIx(ɾ�:^*E�') ��'5m -z_0�v*-!0')d.$$��IJH� i�d�U� �,ons"� "q -�w_ AMu�Lif�r -i\,k7-s)} .� s) \� w(sU\,d� RRiccatiIl&\ld1>��M� )}2 �g 1{k^��-~6�4 k\,w-.C-�)}2 ()^25�!( }5+ '  $�� �H��= step5��z2�9�&� 1|),�2)ᅡ�] �����X'"�, viz">�Jf1} mJh231f �%b� e^: =$j.� &"�^[Fk:g 2�2{A*I� .�-I2^4 U,dsN *� Hm��cFl�f?y!jm�u$ i�b�].�1}�>st�ng 0o)f$ ӡ�%�[)�12) � "� .�No.�-gst meA{� .�})b vid� 3��A��$k^{-2a�b*,���N�"GallV�? �$1/k$. I�pla�o 5�lc��F�7 �""q . A�R�ha��� BF �_�7Iima���p�Ual&�"_0=-i �]"*i) lل half- o, < �� 'zɻ2� $2N\gg)��� Is5��� ) i&s� re�Xcv convW '�ls" )"@ &l}>y6� ss_>� _0a�i� {s0}B>(>" �1�nh.)� �jv�0&�phiq��� ;B�_0*6����2i�i11 x $�IQ-.�/(42X�*�� !"��'c"\B(L retarded �$��I.� ]YA���D���ed�A�&�E�* -���b16 �{v_g}c�{\.,\,� .Z-4r5BE I"���#ukYatY{6�dtau_phi�RlE�s}tau-�QU!�! ) >!� '^���� )bo�p�{^ ~�BWe�D�J�8X!�����v�*$v_g$�L�m��2E'.� on 6�Av&�* B��g�(aՕA�� w64$ m!V �X. 1})� +xsul&���"����"�of*�� I$�bA�"� �#Ջ�#'�dm<a�a�9�:t)���!C down, ��nW1"�"6Yie�['b)�!6Bbb�6�%� ��techniq��n2Y�ekoncep=':C�D&��l"a!oC$n! !�����d� ����+ �r%_�-�@ \or)�[k*s EkY G'�=�&��+ impu��d�"k,!��u7!ak2^#��!g ��+!�-] vic?�se 2g[ to o� �<���D�B�%�m��lso���!�n�\1�di ce�b.L}[�s]$%���62Wq�G�til�@fu� Azw.is[ntx..�"* i.���!��an!|�2ed2�br�g s $[O ]r d/;�~ "(pe /�����FF  ��$gi�t�� K��=Z� � سtly swity� �-��-�4�UON6A"�d ,�VTmwe �f]m+iáh$wz$z$: $$:� =w_0E �� ^+ ��)\;� �"�v,\;:�7.L0�6: �B�9��oL}"� !#q���L�%�ro_T6C(:K uM��SllE� "�r*+aU}!؈�@c|2 $�OX|���|} ��� l). $$ Qwi�kezJ� X��at!5��to�B�EO1��a�\�C5"r!�y�$�2dJ�pz �l_LM �]�7M>2f?N�&\n~.�\Eh{ i��>}y2��t."�>I U"�r� ��R }���� wi�dxt}>�-GIIu�Q�Y_�K1a��p�|Jk{�f&YRx �r�.�:b2y-� .*��*85�s\,%�_"z � �9mIf�g�W�"aoq��",[yo�O�(�i��?iea~8#�5"�F"e $!�e��lA �a�a s < $B�r/2� 1�. }5�}-�sum_{n=1�+\I_n}{k^����),$ �ere7�nQo��f�Ded Zakharov-Shabat"� als~fad0��%two5RalRde1e��*JA�A� ��%d� 2�2K}!* E$,h2hEi1{2i}\�&�q(I^*(s)_s (s)�2�4 ) ds�>o_I.š�K�J.\"�? cedG�&&'�. A�1us.A���N��� �z"�. typeM�$I_�n�Rs�1Q��7e�>) lex  2f�4Y&�'ݩLRY{�Ofr$/in2I&at '[Q))&�A# L expa�� wb $r�J$kE� �a  us��conc��\D!,L�mue� 2�f e�,��2�)� �lta>�/vI,=��� /^2r1^2>0$, " �ev�~� �F� 8h.> "U � �G seemNtui�gl+r�r5 5$is deliveZ)I Q̥4_6:$"c'� M��'1��iՏ�T~�!�hys�l�lev��/diS��ur �&z�&N/ �r{F��s��,�P!MQ�n.!�� "Aqo�i�)���"} (2y2 \��� })�OtE  0������!�!r]�I�F�a:�s� ��\to� �!?E�dm, Q- IB!� xBi1Ane� im!�%�haer���(>�+2�;*�� q� easya�2n; �4� W� }*&�;&"q�� ��E�X�Q�al �|:�I� v�*~�6�#_P� � = 4c\ln(2�3)�*�j{b- ��R2 �|FJIn�*ad�# �act�v is v3�regard�����]rapidly M�7%Boff- m&�/��"�  oq�i$ Y"�k2�!�@8B�)>�"Z�:��= �8 s�oߙ? b�1�Ta�"�;�.,;Lrce em4 izes� phen�Iz��� 6�\q����ag. not Blye:^%m_@ Our u1�"C Qh)��Krigor(��?�3his�T-�p�%�. k�D�Jion�3�a͡0g�v�Fme{ism!��"�;%�"�w�w�YAp"��!�l�wy�=B>�A'9g�8alB�,�MClb@�$ 05t;��, upo^�opp�OI�. R-�abl� %�aQt!@"\@\@55-B�&a�60�� ���� �Q0ݪanV<��D��*��� 5�a�.AiMcs A=idm� a�hI2��#�;0&� a��vicA�� toolEXde�t�U=�Q��� � Y�2;sO��F�aa��1�s *q-��;� � vl�  fash�?%�cE(m.�(�N8!� pre1� deptMR�pl�9��nciplz(�dea����� G5��O1�>!�  �iex�8e,a dop&  pass�Q*/bw!�1���� }�>-=��< trac��A�s"��s&f67C-y A�b���&�5 _1})�) mpanM�� 3 -6'@~$  ). AYvai\+J�ieQ��!q�,�A�E Hcoi!pP�G�, V ac":��7s*� �E��eera��H al Si�ces R"W�ouncil�H}Kingdo�EorkA�&�G"�G &�G!� }�WUSDoEN%i&��{p�?6&�JBoJqKa~\KH \title{ReDe��1{� atA-� # r^4$&�W�$�I M. A�g:2I DV�JSeattle*�J,,, WA 98122�H\\%�ZJ6��W��ngt�� dPN9"LI� Bawi�o.6KQ \'{eD Li\`{e}g���8 d�E`que B5, Sart Tilman, 40006 1nSlg��KF�{F. Brau:1Group�I�_HNucl\'eaire Th\'eor(, Acad\'emi=H&W��(nie-Bruxell5�Te de Mons-Hainaut, B-7��!�date{\��b�*#GW� ��VjmSchr\"o�er"0(��"4l m�� z��A�*q . g^2/{r^4}]��Z*�t &��96s�J lem.*�5"qI��5�Be��*� it{e� .�@��v�I�ly� c��?�E``r:Z� flow"5�)�in agre�^�iu6��[֔"exhqT�� cy!\"/���9iލ� many�nch|F!�� \AKinu� cho�9�t��7��nd�f� 2x�t�{w i gy)@ shifc=at�?3X�C �o 0%(!yA-de�'Et conn(>5 g�i6���n&&-����-A�short��A\Apo��)�aN�U� iv�"r[A� �o�J{f qs y��6'� E x� Y�Dhow�6� U�R�.lYH�Mny<"sca��`pKA!J illu I#uf�"6� �!���u�o"Ҩn6�>neu�<�2ble mol�|eO %Z�\ �� C�a�I@y $s$-k64 I��C����� C$_{60}$ �C$17$ meVe#a!?t�ngIy*ff hQ�-u6!$%� �#(�C,m 3.37$ \AA:$~  1�!pae@r�two��hAf�F\r(Lennard-Jon�%U�E��2M���=� $3$�$25%�a a"LM�BPcs{03.65.Ge, 31.10.+zWM65.Ca, 1Gh} `"�L�Z{Idu,��m sec1�m>s_&�"��5�� �nC $n \��2$ ]�i'�Qd� ilxV� �}E�shzQ�"�=H!6��B�m���R- `e purpoq{is�kT A`��z� T`.(� $n=4 ߁��$�2�bE ~"�5YJo�Hc ��E*pl�E�a)B>Z�M��mK��eR�r�� upX !�A�.z(roton-deute_Wm�m��*�.�M��LLlMpoiͺ� c4^S�����6 :wofHe2As�$1:V q�si���"��=2. �Ba,Bra}~'"��t �Q Y"`>6"�'fskp��M e Muel,Kolo�I�!?57(2�a6;f��a�I om!,�"o-�>�&M 6L t��,^�pN�� �oK�!lZ��u��G�e>bQ�Hs~K'q��Vn�{J!r�M|m��S��w>f�2����m�Q6z�]:xOur m,1Q�1 fEK�*:�\^�J&��>� QTs $\beta_n$, ($n =1, 2]$3,\ldots$)!k!9�� R'Each +3 V�Bh2H :H �J,a�e ��riod l=h6i cut-� uʏ$"��m���  ��ck��piI(�  $RVk-/A� :� �Q+!,�#by jumpAE�*+br� 1- nexti st>��<A����6�,*� >�!?R) �.�"qQNm� �N I4the weakest bi�nding energy is insensitive to the value of �[cut-off radius. \item A numerical computation shows good agreements between the physical (ina�Ce discussed in Sec.~\ref{sec3}) bound states spectrum obtained with M,R-method andcorrespo �F;(in a conven�al A(parameteriz!1! scat$ng length ya hardje1&0 When applied1W$problem of �el�on!�afield Ppolarizable moleculesnout dipo,ment, we fin%9�,ticular thatV5y_s a bi)M\of $17$ meV for $s$-wave�!��C$_{60}$�. \end{eE+�5F�E�c)Nof a5��ecalA��ofu 6�ievneutra�2$ zero6&F�6 � showy+E�@phase shifts are,A� expected,N7:* Some!�clu�tremarkM reportJ�7}. \s)�{R:���} \label�2} IA�isiXe,feL6xu+by e @ \textit{et al.} 2<toq8analyt��lySVEbehavior!�ARcouplAwconstanUkE�-E� y[4 square-well ua�to}SJ� F� We�,rti���reduced��$al Schr\"o!�er6one�Olem�by�-enEty2�$V(r)$ ($\hbar= 2m=1$): \begin{�[5�eq1 \eft( \frac{d^2}{dr^2} - P| - \kappa^2 \right) \psi(r) = 0,�\��} �$ 3(=\sqrt{-E}$�Iwhere2�:j�2} �= - �$(\alpha_s)�R�(\theta (R-r�� ( R( r^4} (,(r-R) \quad % _s, W > 0)B�žis,%�]&$ @e��isu{ at aI`�=tance %�us $R$%�n.OIu Au. A�mBGiREB\ r\cos.G E,R}{r} + \phiY� M r>RQ��I�$/$�!.=�|2�� �b�fi} \tan�= L/g}��} m$L{F� {pere70G $ g=Q�,R$. The usu�} atch��di%���!� 5�� ts derivaOA�$r=R$!n� !Vc2�=� � �trans} 1� \cot �_s = 1!�e� %+Mphi). >3We canA|ve6y u)�&in2Ea}A�o� �Q \beta_0E�\pm�T{(\omega - 1)}^{1/2}}{ }\expM��y�1}{\pi}\int_0^1 \arg \Lambda_0(t)' {dt}{t}Q�,�� U >1 \\ �n�n\pi p �qO�_n~p -\infty< y< + ,\i3 n= 1,2,..9�1-w��we deno@ by $%B _n EH, infinite se�t�3s $-�_s �e haveN�b%�} %@%g %]G6HMI ),%R=�8\l%� (t)* textstyle-�1}{2} h t i \pi H 7(t F1+z:\ln R, {1-t}{1+t},!�9��{.� }^2 + n^2EQ^2 Qs^2t^2F�� inte>$n�Rfixed oX��ranch��� !�E�n$ are *in Fig�fig1}�\$n=A3$a]a�Q� R$. For c&�al easeŷchose�ja�D$. We only keep $n�~ $ Y$a�%�ůformula ��})��unrestri .a7� figure} \% ering \i Pegraphics*[width=8cm]0 1.ep��cap�;{!R runn�Q>C I�_nN ��, ^{-1}= R/g$� $ !@ 2, !Bnd2oegi�E�led $%-,2,3,4$� � &� 0 III. Quantit� o"th axe� 4dimensionless.� � %שa1.It2 ears&� f> *' &� is a�$continuous>'% aMi($n$. A simi+� ( was observ ���c ��>� � 2$�,. Note howev�wo im�  ,differences:!@none hand� periooscill/(s, which ch�� ,A�no lona� log- Aic��� ,Ba,Bra};tther vYa take!�$T�n $e limit $R< arrow 0-fll)b Inde-�B�, $g=��R$,1LB� ՉT�1�"Gsys�((example $g$pld be�n�be ess�� �� "�(bility, see6uD5}). Consequently,�P$ vara� R�\\͊r4�is leads�a vanisS $�� �2�,Q $�ϥtzreal ��G1� =��$ (!� sign!u$ Q thus " <_s$ does not pla role.�eq2})) s�sul5�is,)yr q= tudy JaA��.� u�� .p Muel}� already�"\J� �� also�2�3�toA;&Z\-�im�s jump!x from]���lY! next'just be��poi8����ity��illustV�:7�%�� ive �t%�th!����s wre��l:/� literatur\ .��i�2�6/� ��q. *�B*���\ > m�describ �2(2}��m��Vic!R���Ys (.� �y ��Rs)� �,�����sm�enough))�%�r� �inveru��Y�$ has been a,R in detailN��it ���!�at�sD��an1(above $-1/R!�� i����. AseEbx enI�:�,2��2�  %xQU\f�  (��2 ) %elarge-e�B"~$|i�� � +� |�8%��han 1%Dno�y�ap����)�h�i�>n��8+is p  � $1a5>-. Witheo� giv�Xa�numbel2�MJVT�i; Appendix �app1},A5Mle?Ÿ�/ ��6wmhB��I��ic t*�92(phi>��-.-+�`>+,5"Iap5})E�!��LZ2a\ incr3 dO� upon crosA� .Z �E�� !�u�B m��������E �{n-1}$ 9�Xin& � �Z� l� ri� )l obvly se�Q�/.B>z%lg�"al� \ $i$iF�n%/$n+i-1:�.`_s=1:�O� WZ�Ev��� � deA�s�o��!!a!�gq Pbut tA� ^alway&)�s5�nitBk+# uz�sis made�'e'sho_ }.2#choic"F�l9# $ (h� mixa�s! al,� # t ��� $n$)*54 >0��I91 "z�AP� srNwAOev��kA6 gy levels�B�a� w� threQ ��p�9�|iU~ . HJ %�iM=�f)M�-�:�`T' (s a minimal)j, $R_{c{min}}$�eZ6��yɂ ,��x2�to��.���9 stay�i�-of>�)�uj� mpua�%�qA�0"V :�@\approx 0.63\, g$��2J�2�"�a!i�,a��*� �LeM�t^��!VERލ2:�A cruc outc�of our.�E�[ >�2}A�A�j �&�E�)�$we� t6���"��6� ,!^�^me�M �"fis �qBJ� Z?�� Siz��� r�6�ţ��+ �} "�ɡ$� s[:F]-q �!���}� @ "$�_V�� )��S��"TaΥ!�teazAg9"la�# "�intro>�er!#N�S&co���re drawna:� "�7 ��.��.� W�refor98 � "A!u�ő�s:k͠!975#�j�6� "6$-D��M�f�N?#�]sh� FrefQ U&=edZ�KQ��dismis� � eply ���$-��CunE0. Now, accor� urA��&�E�6Ha�$E_{B� .[s� � = 1$e5��by @ ="�$iu�$* j$ ph} g C�meq 0.83V%��" !�&�ph�cou�-intueե+it �nA &F  6'&{\1 G �de��$g i� "�� theq�to under��da-ca� K4 � u���4an overA`., �ep:/ �%ex�%"M�R B�Pa/ed �*� f 6�".b"` �I�� on�.q?,fb�'r.� �re� 9�ns.ea WKBU��Z�"as��B2}.�$Co6p&&�(�2�4�$tAof�|e2!� comp�g )!Ǖ�5 ose "�� ��>�)sW r�)38)�� $- \y4^{P} e^2/(2r^43"'W�jorigiY!�L%Asome �$�repul� �� Des,JMW} "^P$ bea�j "�) �M��. An e- ia�sa�ŝe�such a �_'!^`9�U�{ +I��u�� A�i�$� "� � va�!�.` ,$ ${\cal R}e�.� fe-�<ode�~6�"F�!�!�b� � exac���!ruskovj�$ rus} L= \%�M ,P}{a_0}}\cot�f%�� �)���% $a_0� !� Bohr� . For"�v"�L$,*F!�)� �6)6�q2n |Qra>�= ^P$. O� e .=V�d-min ��� $i�6�fi�� dq�F�i .EqsU%4o �%remembXIL yiU#fi�modulo���ca5.E{��9Z��9�!cor} 1n=IA4g}{(s+1/2)\pi-�}B�&��� \in [0,� ]�s�,\ldots�T��tab�w�*ow B1�2�a�!6 root��. i&��mb�S� OsamW��B�.E�o,) ival !����$ɳLy-�!Q)��!K%&)t!�&rotect" C��� ( \equiv; ^2) ��~%�)Q� ( x R)�%btproced0.?y�e@%k--!�&� ? e!�lin��0�J�p�9%�m�s-vNT&� Ep1�ertab� }{c } \h� �&6� & $(� )@ R}}$>qS  \langle r�* �%/gFGv-Z�# �80.1 & 0.21681  3.09 140.545 &8<0.2!0.2216 5 2.73 2.82577 583 54!0.23189$ 2.18 2.230.6665672 55 4317$1.6�1.7 { 0.79[6 5V0.25560 52�1.2�98�0.98451 )0.2693 jU 0�836 1.30  \\ 15 84�48 �486S 1.96 596J'11 3019 �0.196j & 4.17!s�1. 0.31135 0755!� & 10)�j-�m2Q� U��2�`�(De'>u�(aX�a�y�"� �L ^si�} excel�! " 5. I &#to �,##�� �gB5 hol��� �}2{� d��6 2H�Many ��;��4�&; ctua� �l�! &nod��E 2�%�4Z�6� 8Jo. "��#ev�! ific:Q$"YL���!:~�"� :�  �&1� �= &� (d*�))`.�.^ arbitrary �Z`96� 4tra b�1��$ ��!�� cha�4eristic�6� e"� x<< ^k��fur*�!Eof io.��d8%���%g3" S&Uto)�dA2+ y. MoreM,$Zw!m]�2�7�*v:%(�;Y]&es�a� 6��|mB�;-2�E[��8 �$ easy!"� ��s� (�O)teE�7nd � ��i� �. I�!��siderei4� RT,5��� �.�u�to�$?��m know}! J� Z&�po�o�%�q�~�"a�B2�$�5 . "�5P�E�d^25 ��5� 67i�&� IUb�v@ur;of�T%� o,#� ��R[:�?7a�B�9!v/ �#few!\si�:candid�1 ��6er�� Des}a�%V2�8� ach,2G�� �U solve�he^� a 2-u( Lennard-Jo��� ��. TakY�K!5!�$558$^3$���n Q3,�&�=$�,25�;a.��� �s &Ts&�9&"�"���io�find a"Y.t"<%Les�� ro5J3 = g/l2.g#tm� ^P�}=2 558bIO/2 � &�"M�2=279\,T a_!�_ e�:{is:�!�ffa�v.I$6.37)��!\sim 3\AA& 6U �:�Q?Bo!�r6���)ss=�L�%r)�9s$� @(:��B�� lo--=�Epre�a.�+�d� �n���cer�$l +U=�;2S.�"�B�f)�)�l�*��;r`/t� aRm�.-d��B� $3.55$!�\, �krat90����isNcisɋasB�� eEB�e.=1.192&�:�Ѿ"f $6i��,:�be��ix �p$^.&=50{�/1 %,E" !H�ofB$ iD:��strongly��� �au�B(&*tejf(� I��� be��%�ei*�ci���a@" 5predi�+� �War�e :PH ��L>@F6>.�+6} An Qtes�� Nr�+�!����*�+*�+�Q2{*�@plo&e@ -� 6 $\del�7$A�:�$gk$ $(k"\��E}?4)�R�%+9��2�43JX#"�=J� {Fc#gkU#�  (E��ARi�"��hZ�3 �f�33x�O��"ee aga� a2j` >� �a|��(gk < 1$, ev�1 houg+&\ .o &� U no"e�2&)%�L�/�+�%4�%Ah view"�/>� I�,�. (.')�(l ��  U{e3�D*�Zi_.uC&�!.i7*\ phDFtu7.,�due emA?�{ .< �E��>��U�&_o�18%u !&)3y4�nA6mA9!��~*"�Fpre�* work� !e� d>"o*4Ag!= �>�Dexhib1a�4cyc�@�� K:ly many "es�R+W2�q� 2O"R e� "j�" � _ni�6Rc&o th*�E�&'>)� F�D!>y%�� 9� $�.� �D�I��"Q5d -H k8��" "�G�GE�B�GVYHB�,A�EP��i� veryH u53�ah�B�4"ld%�rimin1��0>5!�t�&L %a�%y,�"� a�b0�/&TNz�/Q�edY��/ c9i�%ll% �Z@iq B�C quN �@�S!Q �iU��n,terval $0�1!�e�7> calo67�7E�v%��#s�extlFA�� �I�� " oRC��*�@�� R���e"�>Iap�D$psi_0'(r)&9 &�@s ~�!_s�={.�B\q:D�, for}  r-y?kF\}F�� $OSD\{x/�a M�;j"�$x$. To , !V#2$�+ejkBKRyKbA�U� ex�+! $�D(x�D�@x9 n (x�@C� $x<)?$.2�aSsearche�6�&�(-��F� j� 4} x�5 (xE�)=-1 I��R (me%�!�rk of a tang*���(a hyperbola�(.�U:�� ap4�!&�Ff�Hap5A�2R��CAY.�6+\arc�EE�'�1Ms)QzRto1Msuu� $N=N_1+N_"�)a���$7 "� ap�P����)� x:ly��-y{.�'}����-�4A>�)*�6WW19a J�� h�0imEe is*�C�)\;\l�>BzPer � q�gr%�(�w@G nd w�9ng $ x �Br_+�ѡ6N��R�D6� ����_+}eW[�K 7:G@, \Gamma (3/4)}{25 + x -$-1 + 1/x^4i�$B(x^4,3/4,A �EbG] =(nY5BWH�K B(x,a,b�)!"Bet&�>su->=EV$mains f�Fa�FR va�A!J� T!�ula2$�9TM-JUJ��eq �1}{x} -Kx^3 �*� and}��6#6H4<3Jje��get, '9A!%= er[ $BJ�q( k} g-�EA�)�4}I�|[ 2E% -t]^2 5��aHu'aL -�7�C A$��]^2>+ sy�a.5}7�T� $�Is&/ �_s + g/R�phB�C R �Q, s�at��fin� J�wkr�kb.�/�&=j��ĶoBk}0+ !Q �JP E��͠�)�AB/a�yaL9kk�""�/of0 rse>wn"X]ape6( . "ac� ledg�Vs�0�f M.B.e�F w�. uppo5S� N�D al Fo7 Sci�Dfic Re� , Belgiu�e_A.VV U.S.[R ce F�p�  Grr"(No. 0245101M�B�� thebiblio Iy}{99e'�em�F} S. R.., P. F �daque, L. Childress, A. Kryjevski, J. McGui�Tnd U.�-� Kolck, Phys. Rev. A {\bf 64}, 042103 (2001). \� a} M. Bawnd�A�+onRL7 L712L32L4ra} E. Braaten%�(D. PhillipsNP70P52111P4.PM�DQ�u`%rT T.-L $\, arXiv:cond-mat/0403283Au-k KoloCB.!!omeiskl!J.!uS�Sey2�B)8<46}, 12664 (1992.��0 H. Abdoul-Ca��E=5�, 5043T5�Ba"'A'�ThomasA�O'Mal%S,Larry Spruch �Leo�$ RosenbergI�ath�uA�49�61.��QA.!Perelom �V.A�TPopov, Teor. Mat. Fiz.W-�70.W Wah\"atschm!zL.A�Lamb, K�<sti�Zulo�'nd(R. Huffman,�L ,London) x34)�IH2z�!8 Calogero,rit{Vari(- P�XA� achJ P"�Sc�8 author{Doy? c W.\ Berl\affili�o{De<!���� ics,�#Uni2G`$of Queensl=M$Brisbane,  4072, A8Ilia��Xabs�\�is8cV6der�>%�dq6��ta4�> �w wBsuffi�A�1~Holevo5"aJ2se9Lq8s &���)�I"�5$wo orthogo)c�,!~ non-V*r� r�M��AHnecess�)H� �&a))EMyP:)provi+cr@Jia!d[)nguish.� �o96�$&�'whe�*tse�7" �or��ad�V$�~9��`!j� � optBensem�*�B�9B�XaeUs C �]n� > �~Y� \�Jeo*xI�=H(} A quantumQ?!�a6let��'�nd trace �rB&4(CPTP) map on L � T�We�E�R` mean� I� 0a?A�a�+�operator)�!�>may re1I<�!Aaw)�H[ac�Ln��9w�$n��RI�� R�Bensure� �zR�sedE_�Mrase�eFary �io�Q1[�Q�2"iX<� wopGa g� :8 �!j/f�an R sp!�!`dda�a B�p�D(et"�d) E�8 Te B%&d�*an�=orWS%(���+|2]!� e am>A'�� RNVvE�A�be99AA� �� vf#� i� �1e ��wa <9 $\P�&�E 7 } C(% _L\sup_{p_i,\rho_i} S[(\bar0)]-\sum_i p_i,)]^�==; 4)RH$S(\sigma)=-{\rm Tr@ gma\log_2 $ -g$von NeumanvNtA�) $p_iA@proba<ieB��;be��neg@\g'um!�1 N)u9` ~asympto������Jjomea��s�%outputi�s, i(un�hinputs �h��,schuw�+gen�?��6 U8I#M��a��trivi�ask"; �1 /��ied �/ willA��FE�a�Q�Q��uP�� E�� � .�0 ��Q�6 �+j�4 Bn:� rq*fuchs}I&� �nath}, �NurQZ i5E �hayashi�AWKQ!�p�AAmJ*A'V\:H�es�ɮ�C aJ|eZ��-�J.mo�. Q we= 5�4 \tv�W%�n a$s�t,���atfL �"�]Ay"3G ͻ1�d�.���B�� Z.V �!8 Refs5cMb,%�,!� ,cortese}r <w� 5^&& .!/.� � 6z V+L!*�"���B�#be.J F@  #8p['���kse6�kWZ �k��ELZ-�in �V\�>sec:2sty1hen':�%y}U* ��&j 's�Y> ��2J'K�}>Alb� s �$2{]�%�M-aE>�,c.n>� ��� :rM �|Qy���&On4uF-[:��FJ� �AA�>��J�'"�TQj�&�1� �!2� %sVu�1J-����25K!�Bloch sp��� 6bd>M ���!E�F% �qS*o ��,vec r \cdot  � d&l �% $"�"vec� of Pauli� ors�g _x, y, z)^2 }/e Op-� Up r*�\��edb� its� pou �Y!I �iq�f��!�>f2��C$HLe-��p V�ŭ TP)\�oid� )�[#^� Phi(!�� 1�[=�(\ bf�c})�r1�k!� )[ ]<9�T r���b prN �map]-x \mapsto|tn� $. Via lokE�2� b�!� afte�Fem�OHns�i"maTc- :�M! �t!�� broughl�Iݒ�J-!e�:ea-l�lPj{*{20}c� \lambda_1�?\\  s@.&Aea \ �), \q> ag t��t_�? t_GA ^`BYan&�=6Q)I�2n �:!_U� rc A�_{t,\L%(�- &V�!�� $ U%�V "�M�� .]�� (h$>�$ A~U<�by�1fuem� /*./]*� E[�K�e �� u- $�9� 1$x �y$����-)� ��'�9�5no�/$$t=t_3$. Hh>7rM�de��KY�I�tJ�FEIn "�me�*-a�:��Am��e�6a� .y � � >QQ�5�uf�qxg��� schu,ohyaj/Kminmax2]min�%�+} ($max_{\�0} D(A��_0) \|E�(�+)bJDU��6vhF�D^[ps��<r}� ho o�f" psi F�Th�1Z/E�� weU}&e:I�``$a$''��exp re b�2I�(logarithms $eE�-�as<ln$'')�>�+ �eMF~2��fula�ul')�Q-f�#q}JQ����[ f(r)-� (1-q^2) -�o(�q) f'(q)�"VA1�Dalign} f(x)&=(1+x) X+x)+(1--x� \ f')$�( � {1+x}{1-x�)) m� _?)�< � p��A)��Fr�"q$�@^)ively,�/we0E�)�o|.r|$, $q q<,-= &Z ��q/rq$< o�$x%�a��4Ad �{JA]0;h�6�#"2'a�$, beca�zF� d�F a=�Ae�b��" 2�)��r6��~9 "D �*Z $z$ axi�'�4a*�;$|}1�ba�eŃ dire%F)�V424y$4�eA]n*�Pe B"dI1��� s ��k%�U\eq� $!;��A��j JE�=!�.U�/_0�LE�J$��)$�z����3~Yp1��CT��average� ����>4� &C�Ske $��_k�i�"� �-m���@ "���t� �C�\)q$p��B�$\6k p~�� psi�0N�Vot"-ilyaV�%qf yQ0mtL� choo?8(� &��""I%�NM1y�:�EZ�un��f� �~�oE�o-��2��Pt$ nTLq�,�r�IO8U`c� s�9 oH mmetI ��l�#n Q�A�iA�t��A�4B�Z 8mitude da�j��&c  a"�explan��[P$rsm�Q�)Lm-�li}q%5 . To�E��@$ny pair of Lm%ѺA�,�fVse�6��'-'$,.�< r'=(-r_x,-r_y,r.���)q&q&q_y,q.& . Du5�s-��a��B�V�E�Yv$��6�. ,!�e-�B? ,�evi�\��?�==�O''p0�immedia) ..W M x_�� ` |�{)=  W:Ve�-! �#mi�%��oo�0soi+E4'� o8q,�!Q[m�2qy��Xn-�psi'$I�coincid!:Bq:�5N�.e~���/�q\ne2 �E �R�M�� � *� �a�$x-z$pone� .l>6jand�W $yb2<.2�a�O��%n2� ��!��B��;I�ic,r�ab_ e� �Ifn�%�hZ�5$ "��ka��e ,6�C��V�� rho$i(ͺ<9~��"� �gG'�M��<�.� �T�z\�24r_x^2+r_y^2},06�!�is�� ��6*h�53� w\y�aahr"�LS surf&"�[AE� ''$,ext�<ngd��3�"�U �hIC��Nu�Ef�' lemma��5.3(o&��R ''\|a�) >�d��  ?���qe��*M.�B�.s , alrhV�B8�gb"o]. Icl��62��9�6� M$y� z*� I%ak�L% _k$ ���Q~�=.a � situ"oCrt�?ru%!��Z� eachB�GRea cir�AE� >g ��0��w�Ain&��Oa N. , �&"zn�(� "����  =�+nx�ba�&�u� 1��  a  le�N �d<I��&#66�i�pasop"&�'gardles ���5<.�V6���- �. �e�q�&� mХO��. Cara�)dory'��,&��ft �!bYhm"�!t.�-MQ �� fac� �bnoL.���:�by2�� '+��!&� � ~ t$ �� \ o%���i��2� �% F�"&��$nQwo ?z}� o[Gi� ��a� �! qf3d�!r9� "S %q�0�o �) i�0a�AZ G v,p+�J�m!�rem"��.Ybel{th1}�} a �*FV�aU�rc >  &V�OB*��b�emRu&z .!j� m�3|$F $$A\notin(0%:$� &ٸ�ineq} Aq_ {t^2\3^2}{ m^2-  -1+m^2+t^2�a �� (u�1|, 2|)��n!���nu%� ! Ile��vK�in�� z�AtI .;!� B(w�c� proof,oI�.��M ( $A$. Let u&'���!e�N�>l \ge =�A J�>42��p>(m�2| NE �!ht��V a�e$r$�#ich�P!A� Eq�;di <"�%7Pz2�S6�D$r�& with>"�?!w$^9i NW f&��)^2}(r^2��)n �[ (Ul6�)3) Y�x�=�%Jr!�&k5u� \ne �V!�9'.� 3|$)�� �2B%Juto��c�>&�(du�AIa ��͹�,4#�uta�,.� �:�>�za�pa�-n�ksEZ�,"�!� &w 3t/2eDm�"3^2)|>cf|Sa:)reR�^ �- hen 9i��3|E�6T!5�i!):!�is�6� Y�\le 1i0,��6xTn $6 6 9! )te<0a��Y�o � �a�a�V� $A�0�Enow�iB�?� g:�l�}"*%&�|��� %��/!����Aa� MUwi�+"Q2N�"$�� k�!��l��|� t�e x@"76)B� _%f-t$ � Y)k�7J�O� #a�A*�s -h; bY2Vb��� q � �QX).�5 ��*�� V�,����+al6uvR��lkCri�1.�3=AVŒat%��a:V *�4E*2�^uor *� %}�2E��6��u��e81�U>% :%9F% �T0)�ma�Lr1�� wƇ $t���� 3A9assumaat6n1�UI82�D �(4� Dp��m&�8�� p. �nJ�isa1�`9A(9*�6��a�e"m�.��j� � bK�K q�w �llr9)�y�Vs�<�tak!Hk%�Auha(��r=6� ,0,9 &�+�٦1M |1�%� K0&, M�K�~2�~: k tn~:�M612 ,0,t+�1J{aG�0,A"� z?A[-YT si$� R q = (0,0,:VIn ei�_�we �M*M@� $9" r &=�L�m^�^2� +(t"� ��C\nn(�$�#LR0\times�&�h}(� ��e2Pw ���m�By6w69"[�F( :��%=_z)$,!BmayXLE�F�aJ���"� 12�'&t'lo)&_z) - R& �^� N!:�2}a�th�v:�i�-m&� d}{d!�}2GB�\{� {dr1�&Ԙ  �:R [:8(i)]'\}Q?Afray0\U- \{ [2� Q�� q{ -t]�r)/r +�m�3qq�F'���V(� V>\aXER=04�o=�[zT � &�my[q} ����= -M$�� mFjWe�����WC�"��%;��-<val $��pi�AnyE�  md}�or.I�o{[in $(-��0)$3 :*Ff6��A&� (L��~��H9h U�-f�I� {f�W}rMi.M� &E�. +�� ]��ir ce�r�P( >v) �6aXĚphaQm�I)� � �tm�  |u2|$,F��� = f<(1-r^2+A�eM�}A��� �mF� } &) %�����&I{f~-[}r [ h�+Ag(r"? ��0:�'`�wz���2{)+)r���� EYQWS�WEi( +r,r}I0,� } 2r��A`M�Gp i�h��-��3Os $��4 $�$�f(< !�li�?15��}%8>0�2�Z><2+]>0B`-��rVxN����� n �)�2��.=>�A\ge 1/�YE��J"FJ In *� 6:���t6O* g a,v!i�heF;xr�" ��� _ "���&+ =0$  �>� ���.Y)� � ���*\T� brackets �he LHS�.�P!�4nora4%a!�ݢ�g4hF Ak3e/�.�/�3es"N9,tinuous �u��%�� :��Vz�e�%%�` >FeptU=�9 2�2�6736 �e-to-nB�En�`*��My.2}JCͽE|}��� !)�= 6� "p) �/r� yA!2-!Fs Mj>Jnon�R�.&2kq%y����56� � he RF��lE� �aEN��D �a2�"�QN�"�m>�e�R#�Fa"Q��Y����:t�AAI" o>�n&N �sA�a5�#��&b � an � um��5K�FP�fl�1 �=flict�%!fac��PZ�ou�.> 2�)�)e�Ō ��b�M a�6�c���G^�D�<Miy� \�|no W��� ��*xm�av�� $� >�/!�of�/9an�ՁA��!Q2W��( Ԅ�&?4A� &$!a�E��Nl�n="A� F�%rebc2������a! q-a"+!rej�,B9hEQ5a|.<�$#�3��1� ���Fs.�+9�%4!�%4�*m-#5i2@ .���z-6rY�A%.�,Bt�Bh'��a �i/X$z -"�(as�#@bou �necrQ� " 2�in A��1i e.�m" !��-�#�m��( �&i�!ng�s. <�Eh�" 2�x�*�D# � ! n9&a�5�m�*�)�wfA-� F�-��:7e}U�&bthm*l&2} F$@2��5�%7'12'A����#q7eO&tj!.!O&.h :A��Y�Z_&��Dsed� !�.3 mu[_� sF o)s:VC 1}.�I2\��&? J@22@>�ť�� ;If.yņatisfied�EJ�8e$s�Mf�m�b &1), �2FZm%nU�Qbbing�!O d�(y�9't0h>&�(�!�}?1\h.#,&�$�C123=61 \\ 22 <6 a.3.� "�  >6<\\�n&�!W8n0e�5>��_�  "[�K�,� J��Q� ImT.��1bu%�6,Bsb*�)�� 2m�a�r(e9-o .,��6L R� �+!q 0�1Z z�*$@ . Aw  oin�(�9 6�Jl ��byF0�d�,Y^2>�"�bigBm�Y^2).e�/r+B� HF�)Wjy� !�[ �� E:Bleast� x AE.w e� ��C (e��# Tb^;lyQ�4�  ����5y?=2?M� ��N�� monoto�W3�i�X�L��E*�e9*0�8�6�w2���A�.�?�)�2� !B^��� �a�if.�j�F�<�I�!mZ�� f�>')ll\% 2X!S� �r1��.� ����[2*n#Bf%�� �*/J z�d&M��B2�*��~�%�Rq� 5t�*t���soF�fN.s �tR�< 0tas�!�&�$��:�Sam<"_�A�J�" = ��.h%5� �2'�. `��s�.jMJ ��& �ˑ鑯y Xe�mY�1 �Zs2.!>q���*� N &� Al"�-�<6�2.���eI� �B8 greaHOaB��3E��eH� !H� *0 iNK�7#Łp:�v�P W3! >�E;�5�UG%��P?$%� R� ]2c ~�!2j�F.�AD**16W?�|�16p&%� B2�6�{G&�?D&&N;j9�#ilI�.7�cm^� u^ Y�pr�A�.�m � _��G%��e�{A:�Aa�E�"��Kr�i�Z�a�a\.�%�&�=c&��� ��#a&<?s �y�)��B&(encM. O��_s &.�&\iEF s*�/F�mayG-(P!��!�"�!nisW#�G%�~� .B�k�=k2� 0i.�]i�o� �zQ�iCs( �SH"c Ϟ?*B  tech>G���#sho"3 U��vY "�� �c!�V 6���\a3%�|  mi��d. Speco�L_z�3n� � z$y $q_z/t>1 >$t��lX �th �!���/O,"�CR� nita�/��ge�.�t�o�I�. aE���e9�l �=t�,�))�>=O , le$9�X9�%Q�$,�Ap  mW�*&�/g9 ������*S $|:A(!|>|t-� (�+W�w=�)�se,$ $r_z=t\pmB8 $ by,\pm$. D�[� !�VSin>*��"�"�"�difrel�$])_+�#- -  ~$u=2*(_+)-f(r_-)-&�;� t)�+:>�c r)(r_+-z@4# �� r% A?!magni�I mb@PI�B!@�� $ �=�+�/2� �B�w�,�>l�[Rx�e�6 iC$H�$te-Hadamar7� �� �>h }�w.�v�?��r_+^2! ^2=4&z'1`$ ,:A=%G=(2F()/ �$e�".�!Q"_ ZF Mb!> J} [f'1� �- �/J;W-o��#�8*V7$F�E��w�both !�x-� /�V�.C.B . s. A�M&:=t!o�,5��rq�m� �2*��~/t�1$2+6�eJP  Fm"Q �t2%���t!��X�Crho_-CHAV�t5%�'mZir6\� ��q&Ż�5�re�^v��"�`!Aq��7B�"vbe W�c�1y�} 9��]�  3�4&{ �N� �s O&E0i� ��offiBA�� /r>f'(t)/���ty%@W"� (Au�%9� .��be�(g3�a.� �� M%(!c%�>"� �� �E �&>�Q%/>�# E(a�*.� �� �s��a�the9����� ew{ B��� � �l���:%Ii�"��U�5�e�Rz�B� u��!�<w&"fai��e b�5AB*�ly"�:2�A 2�&�p���6%^= n *��s�*��D}Z.� \:I ~�DI�E@.�e:��C.!�!��.�;5�B��24 a�� !s =m F�A� rh����v'%��Y:20�*���iIa%two+m�A6nA|"�u" (�Mp � �T�q�2��}8g��it���2zpin  6u�h=V* �v��%x���MwJ����I�*UuApp"Wi"���ghyb+̱BL��ҕ�k�n�m�)ns2�6�i�.8n� "�W>ĎAi-k " �ver�8WKqb�WQ� ��)�� 2= \c.\mu��#3=\mu� t=1-�0finA��+��,G/,N�B����:\1}!+di�uA�%Q~&�&�L�2)e�鿁�nel.�>|"� |���0!!iV�"j� 29in>��$ � \�\t& d��irY�A' �"T ��� }.�Ow s�o$ce��F $x-y3V, .�#�S&zSs we�asMgZ3Z�I"hT_ �hifC>de‘� $1N_�%�in2 O king�m.eAUxkRxAs��m&�I$,1�*�!a�.Tt5k�QH�*���"0�F3i��"7 ^���1!xMC�2}��  ]_2U%�I�J!�>P>Ui����Wf��V�P J>�TQ�4>Qi5�56e� m�� �i�>�sN}�.�0.6m�u�=t=0.5�A\Bx 0.178* ����2�/�� 8it� �surprI퍙C$-��� �d&�%R� �1 ���*�L=0.435$; ��T�I%�dY��78qk!��+b�AF�Ee��0t�gy-啥�m����)��a�toF��7p;�8EaE*�A�Q�);KGax�go%��F4%o away�0cI��F�  +l7�!4e�D�I%y��e"PC�UAb t=5ly! a\CC&@+!& 2y�$A$ pam�t�g�>%��8/2�8�mn)( >')�.�)�-�.��Y�:](tn6::whi�Wai�'W�� �8�_LTo��qu>9�ua��9� vary�e�I R  i�!I0G:uP�a�* !�|s���!�$e���Ϝi�A75^22W&)��-� $ switco7�"�to"� f�3ɉ?M�U8:� a�� � =1/\� �QZz'0�i[��JLNX ; ,�9M��Y�"D)F�e�cG-\:�[w� 0.45�b'��% �(solid���6zR$$ (dashed �)!�a"����Q����Wregion s�っ I6�&Ye&��0 m-O��: t�S��m 6�>-�{2qr�Xt�wn"~i�q�9�V;�0&�e>B( �CaF�qc[�ӡ�q&*�n&y�g��6�q<  HQ�u n \�S�?�>�j�no os no.)�����!|ype!�����i�a���L��q�|�dgk2N>*ix)�� an\�1,�s aF�]�s� �B:Ca�">AD� i� r�$ niu}�fpa� P�Mlso �n�QEe �vruska|� lxE��� 5!|Kra���vaw.�pte_%La�2&�] ml>� !2y.>� 1}s"9��=]lVE��5� =� ��q6��B���s ! � �&  %� clai\�:Rv��}7&���w���6Mas���*��&/$3|<"(Gm)<��>�/2Y �(d A8V�!�BI �d*T����6&��,7� b��o-U�Nw<is2i#�g)�& UGB� .S" AJms &5JR4!I\]3jl.V$���<] ,"b�6K3"R� ^ "C�e�aA�-%�5��z��B�5t9��*&b!I L:~ �*z�5v�%i�V�5YE�*�RA1ɡ#0$ ".M#6E#�\�t ket �Cf 6/<.t#|���A"�  �"�u>q��startv#���the.�uFC_0 �<�*I.$E ��g^ m��d e�!�r �m$�!N[l&�t �R�x &:8#�F�-�FuA� & g'+H> \ h%-? &> 0�A WTn)"����t� �F� y!�easNocheck^q plot�>�*�!lz�F-5�� $r=r*t; y1 -h(r_0)/g�I $�_0A' \ge(  (�_0�_0)>>0 яF1��$�>�0 ���k[*�,�!ja.q&r� 3`" ' �!w!�ZEE�EF .HI�b��V/�">�A� )yRe�(��:�&�\M�S>�<��aR""!�neA+!"��.)� �^r ́�q�G�"�� �Fr�A: ]����`��sR]�!�Ino� um� B�=-��GV�C!��!%y�4�:�NCombi�*��$3�*r g%v_/&�C����]��6Z"B�EI�$� s A���N�/�@"tur�c/�N��A�vJrn#�D:&.o:05f6�5n�.ȁ�� e��n>e� c:�.ff fact;$�&�Iexa� wo (��>07),&.|!Ra�� ,��F%[7m+2!"m"{ viol�a}.FM3�T�2%"=��+0 mQic?2��Q)�bO,A�%�d�33A�%%a�!e"�:7� a [s� ���Vi�"m4 Ca�k,"�/82u�EF�:E�����6��a �*v75G�b�9"�h&�{:r�:�Pr�P^�W} {2r}6�PB�>O��� p2�3�E7 -�s��& E3r>!�ke�7T!��!�� Y'�:<� $r$,.\��0�2)�i2QA�y@>�� ���K&�q�t.� Y�݌g:S ��As wcq$}E�2�*2|"W s.B�< � e�multi"X ' [>�does � � �S�12;>�%K=��a�)EJa�2@09{/iIapA�nm��6e �#i^Wi~�G�>�$�R"� ��lospBo� �hE�= L�: "2� �2)$6� � ��-2�BW �q t $t*�*!��6 an6� �*e  2�(>�!.�:� ~�0P5Tis��$.o+є:�!�*X"[$���$ %$� 71A"� %-`au�!��i�1phy6:��WE&�1B2J� ]4!&���$a7o2�`l. I,� �tn 1�y2ty�S|q�:�7�*�S�1.�r�#�!J F,Ava� ��). Fpa�� V'� �N67-�"%#b�J3�]sR%>Q^*�6� u4U�32ev�o�) �!�m��%���"�G 37�rY� 5�v_%t�&%�� l�AY�,The probabil�ities may be determined by the fact that $D(\rho_1\|\psi)=D 2\ P$. The expression forD\relative entropy \eqref{ } simplif��to \begin{equation} \label{analytic} D(\rho v� = \frac 12 \left[ f(r_z) - \log (1-q_z^2r_z f'(q0\right]. \endo�condi~� ��� n becomes�Lalign} f(t+\lambda_3�6�= f(t-:) ( � \Thi5�solved%t8$q_z$, yielding�JS swer} q_z1G({X-1}{X+1},>whereFLX;exp1~%�{6�-6�}{2�}b�Recall)�i�t�as� n in�extremal�ҡile%calcu nihu.has beenU�edQTRef.\ \cite{uhlmann}. �MEH�!�E�ference�iE  metho. >�N�!�n�bQAlthough v O was %��, quite a dif�t ��tha�e5 \] , itaequival� I-ose�s1�,A\in(0,1/2)$7st!�possi�F that��E�( ( sufficientUo>�. 6u!PeY��Um�A� eith�0w�>ze($e Bloch sp �# 3��EM۝H��ere��X!/a �#_�}. ��Sbe�-wn� ��!�ng� �B$A�6~$��$.�Fwas E��3 evious se��%,r!� n most thre� xima��S t�`r� only!�MAes ��=0qwpi$ or .pIn1�q��reta�>�!Jsame asE�� s satisfy!.$" s!vThe.�1}A�9 �.� �on�sz:,&� oAV A#� �!J�f!-Q�(f� �i�se6E���N�,� ^ � wise!xh w�nom :�� v(, regardles%:whe�!T)+饶aeA6, i��u��Ŋ�<�!�e~�,zw5P9ŋF�. 5�=�E�use%H"U�h&� 1� r��r� ree ��inE�R�. F� ``5�cy�)@Pl distance property''T�;schu}�3 know�-.�isu#!��vA[no value%�A $ >�� 2�$ great�!��< _k$ �J120in or� oFH29@more b5�,9 viaAte6ٝ��s abov�f� y�m,B,�ximis|!D22�Y�5YF���m��nM��@s�9es >� l hax$liminated S�#� �T @a-E~�.�� �4M���=s���� ole�Te�}ly=�!5>wE��~)F5ta6{�� reas"�is!�a~nly unA�n �DbA�E�!�$�}_0$ suc�at�2� %P5A� off-� ��� "j3 � s. G|KB�%�r�:� :� to �t@2n%"��� *� a&? �Ni�o� Ƌ H ��:'3 E2>4"� ��*@$ if $||>|*'|�$J4<64h %��%���y�!\E*l%�&Yjre� a���>_k�, is independ� of $k$�h.J� M�"O-(6ONr_0 &} \cosI�N^ r_0^2=g 1^2\sin^2 =+.�T(^2$. We takEY pl ign�A��A�min5:�B� Solv�  �ń"�97��V�6�v 0)}{163(1-="} �B Not!4� ��"�� ason��鍝�"_is betw8:��R$;I�� negg7��� b�\qui�!w!���. ��is�'�q( mmon�BB)i��n bJzYuE2�6�J  >$.X ^�By]Ap��*�("=a�b� Z�))>=�ΡM��� Fg ��ce Qtw��h ��}��%�a ran9VQp�Jisc�� plotis>FA$��Fig��fig2}madp)�y�_%hisa6kw�search{ *��� Mi� A$;. *� ���shinN�t c� saV�!K �um2����X�a � small;  � $0.004. Als�.N vnon ] enti���val $�� 1�0ce approachesV �rapidly�!�% $1/2� u� � }a�ariso!�w�! examples�.��nath}!i vdA�%�~!g>/A�  $A�QreI �+ �MEI'�� �4figure}[t] \ce!g� |\includegraphics[width=0.45\text]=(2.eps} \cap�{Q=�v����}� u� versh1!�. Random�%�A�)n�rey � a2,�<upper b�A�ea� solid lin�  crosSd��r�E� <i� $�11=�(2=0.6ͱ3=t=0.5� !#`FF '!I =&�3!� 35$."Y���-� \�{Co!��!��,sec:conc} We` -*!Vbuw"~� >C )qubit m-$la$a �\E�!�" a,�. "Md,�unitary E U��af�"�,� a �W A(ymmetric un� refl�s��$x-`nd $y plan� Ŭ� m@s  �E� 'UCof6� pq�ublis�� work��t,55w-�i� q(e parameter�GG�p�Z%i som��se �erm�MA�aq�eZ�� e�� ��e� s ��J�inA#͢&�$orthogonal� non-. E�nv) � N�QK.�� &�� wo% �r.lt*��necess�|fzourms)��1kW-%+U�QzAV� &x <JE�� �origin��G]� peF�i�V���demonstr�!�AD �6� v��~inZJ is uni ,al. Lastly,]� ovidA�� u�m"&|��eQ�mL :� FS%8> � %�2Ie�q�Ei�nF� :�"Aa�Igth -�a "� )��of�ņA ��is >A ��g ific�ZJ�� � M"��O��� :�"� \ac� ledg�$s� proj�" suppor���'AuAkliaA0  Council�z UI0|0of Queenslandjauthor�gA�fulA� help com�i7Barry Sa ��' thebiblio 8y}{} \bibitem{h� } A. S.�(, IEEE Tran�nfo�Xory {\bf 44}, 269 (1998�&N�0wes} B. Schum� r� M. D�st�, \pra S 56}, 131 S7.S daviRE.UD~� IT-2�596�72�� rus} C. KaZ M^Ruskai~^447}, 192 (2001.� fuch YF �l �79�162�6��� �,�Nathan� F�\pX(88}, 057901�2.�hayashi}PH , H. Im�,K. MatsumotosB.5��,T. Shimono, "(-ph/0403176l4.lcA�se} J. C .720712872��+ t} F. Vera-e� nd�cheld:J 2124FJA|�y6�022308 B� ohya%=Ohya,A� Petzɓ@N. Watanabe, Prob%N h. Stats.)�1E+70F�niuA�-S. Niu!p RE�GriffithI>m60ar764I9.xrE��=� S. Szarek �EazTrner, Lin. Alg. Appl. e�3A� 159FW�!�U�",!�Phys. A:ADh. Gen �3az 7047L2 hadamardE%H NMaEPug�)@58a6,71 (1893); D��,Mitrinovi\'c%;I%; Lack , A`es ]�2Q22��85!H`,>! q docu�^�}�%kurniawan-james-04.tex %Dec 04 % **$ PREAMBLE ** \Il ([twocolumn,�8pacs,preprintnu�s,ams�$+4cD}{{\cal D}} 2Fdemi}{4+{1}{2> lflangle::r�BEnbf E}AY.� be}{��Q�>qe#A�^!bx�/arrayBA AR/ ME6�ms}{y,.%measure�P60s1�y � %scaled�'2:t�$���$2S�6ddmy!�,\!2.%dummy6+proof2& {{\sc��dof.}\hspace{0.25cm}} % bug�)\sc6Mqed6K {\hf ($\Box$:� byde>}4\stackrel{\trii{{=Af %\no�b �~��%iG���E(\title{PathS*.a C4Stochastic Mas�E"3�F\� {I.~K�E}M.R.~J�S$}% \affili  {% DepartA4 Enginee� ,\\ *] N1 al U"M "HCanberra, ACT 0200,&� $.\\ Indra.�T@anu.edu.au\\ Matthew.� �8date{\today}% I#always �day, . % � any Bgexplicix"� ed"�ab ct}n*za wk�h!l&@.��+on!9a��s9�w}#k m)��bsI�a~ar no�at8�i>+antum�cr modXng�n system��tinuou$monitored #^ �or��%*�2 appl�(PJ.M.C.~Clark's {\em pM�}:Dtechniqu*U�<�& ��/�:ar�tE_ �X�io�T�Eudef�3d�$dri Z)d^!6!+m. '*�c!�white)� 5�^d�.e�og!�a�!" %"��} P�*�5x@Y]�uss �a�!�fi!*)��o1�1�&E]��feedback�rol�qIIQ/� !0developH new types�*Ug �unravMB�)�� ide��ll�tO8an�.� 3uz \� �{42.50.Lc, 03.65.Ta, 02.30.Hq}% PACS,% a! Astronomy6 >%!�ssific%�A/1��c�&�If��en0Az studa�nu.C,), e.g. m*GZ0_ HC9 WM BB91},  VPB96!��m��r�0s 1�ses�. u��#ri;by.�s �yp��lyi� ��(Wiener��)�3a.,photocurrent/, Poisq(jumpsN-�1unq�inv�9��,grals---they�]xB tial�(SDEs�%!{CWG0  KS88rse (�s}d�,a# ��ed u�ly&-�&O7in�;��6} dynamics!c upda%%"%/al�s (!�topic��p65�is well . ed�PAI\[Chap 10]-)fwev�Q2im5an� keep� mind,,�!s`0��liz �ks (A�Ac 6�@highly irregular,V0=no-4=�ble��p"d9y�),"�# s�E� conj�d$re�-ata. H�3i�of estu���ɞnw/]W� >��a practa"/gview.���7�b�!� � 1978a�.\)�{JMCC78Y;���exhv@ Q*35ofNd!�an�Wor%�a|>S� @A�. (� rol,:mun�3s, sigA�pr�aW.�sy� (s literaturU.� ��n (se�,M�,RE82, WH85});�� �<noBR �l�.s;�6A�� ��3� observ)�*�,!2"��!.��rib�:B�S��-�"d.� �e�2.� (�,ogB4 �Y� m20��)eco��jb ebA�se:px"gd l� aJ��Uina�/y�cop��!)K� -�z 4 a (�3!^M�I��?�e1.add�Ae�T�iss%2byEvi%�a��*� � 9 � z9�?doe!>;5vs. � so-�;ed�  ]qG}8 A� � c�>�fisY� (or MP-�(6 "�0>T �E��Y� 2�<|>52re2D��*x ��} qua�?5�lso-.=��t iy 0��-:a['l=nheri�4���$�)er��>fur84eail�;ee���, MHAD�!,�|aurs +HJS78T7I�'.���6WeoA�}�f��TF�do�#fo�a6�ٳUsM_�BUd-po<4by�ve��ed} U ordinary��BP!�)�:�:*!V� "%---�75a.1����".�may b�C�A�l�Aa�i�2�Q��R)!�.��� N��O"T � � \lq\lq{u&� }\rq\rq \B� ��| p' rgan aP llow� S' �w qfe}6describ�.VQ�Bva�ba@der�'! p�!�& moti?on�gr-".Q@!�z>�MC���}�SY��%�� 6 CBOc?A� edad�e�&��& E�u0 A��extkanAKerfec�"��&l� atom2�DlyQT4ed by homodyne� �".F� }Jain�#e� �!cA �+ �.(brief"!. S"L?�!����A��#e �!"*-D�!� 2�endiceXof 4>I�,ann�! E-U�c!�pero KJ04�M"�**[W�Fd*�*A� \'G)^ {BacM�}:)-bg} )+r�G>� "� 2]{NC*' EM98 � solI1�� a�qm�Da (pure)� $\vert F < \in �AD H$ (Dirac bra-ket��� )&k? b, ��$mplex Hilb]s�,Itime evo�Egov� �# Schro er��D# i \hbar?G\� ial}  t}� �_t �= H�5�p�,eG9$m=h/2\@?A�$h�6 Planck'u+4 .$H$a Hamiltonp$H8*w�f��6�*s2+9�=1$. H�w��aJ���T�Rew�T� l environ� ��.az�(�~ak� to acc��a�op*A&� f� 5.4]�iKU�6]�4}�3N� \er?"1�}A�replac��a>A~p Å���mA,�A(ho = -i [H,�$] + \cD[L] ;Q�)�%%m($N=0$????; ,�<%�9� 5�E!3 supeJ>= $\cD42 n8$$c$ by $$ �c �= c�c^\daga- c # 0c .TW1�Q� $L�B�UlADm iEW on. &x7)L&YB)`y]as \lae� �->�%�-v.U;!C� . A�YosE�E�6� �6�2s (viaf�)Azto firstT�E:* ~ 1��H� in�ce,� co�J� �GE�d)5 \^��%S+ KVdt = L  :5dyQ��-X I��an unn���3E� 2QE�K = i HaI�! L^Q�L ,qK-def l�8 y(t)Eva:#�:t��{LA�AX(t�8E[ ݥ�\rYb�] ,9R !@$ra9{ � }{\sqrt�:=~b22�' }} \ifS�>ocedu��m2X,"�sirA�!� "�+� h fe�OK6odM�(1>y.� *�QUS� g� �_�I E�N.�:7sq6��6]?�GJl ��11� �. To � a is, � t�5anw2 ����wchaA�by� elf-adj�$�A$��J H$��? �0� { ,[,�I scre�n-deg�ate,�a2�2 �eigen#s $a_i�89����6�Dũ* occurs *vap_ia I�D% � psiad[%iz^26%��FQ.2 -$ (assuXN�W: +�^2tr[Nq � ��0]=1$ ). Here, M ��le$aot�� 2 ~ )?ector !�6� (�E)< . Af,a8m&6,Ai�� llaps()B % \b-B�_i'�6%X=)Z.��6E@�63/��p_i} .,�Uc �} \ee� y$@v���.� 1��_�Qi ERN,nsequenK1��: A� Bdr "cC�.� n�N� ��*� "� au�/� ���#t*/�V, �D5%. %#�di"� a�:� �6�I4�6a ) cE �Ia�kinitesC)$strength (�4ontra�po�My largeEOr�)@ accu{v>limg"���)>al .FQ�s&z A8*�E s a�8%<%\F..tB.� below)�� CM87�F ��B�"�two kind!YjyFN�=� dard�!��I3 �1or�,.hDinc)(s:MI Brow� �� on (6�)5j2�>" ("*)��*�"Z!DifD&*ub� )52�:� (SME)D!T'eqn�*d*&=&[L � -K - K� ]dt\no-\\?&&{+}"�+\kappa}]B P+ B# O:M_8* _t}\aZd\nu_t.Dnormd �#�II� !�g��K��o byE�� ��!� ��I�J s S"� $ � \geq 1` 7 ��}�"?6cy.A0 < \et� C ~ W= 1��#}$F�im�� |!y.;R:2���<$aZ SME �")I�� �X@�d�}��'$\dot %�$,�re#:0erM| n Ito-s;}s\��Ye�TA�ai�:b k"&k" $�gP�!l�* nnos�2�iJ�2�r/ �� $y_�wb�(all2b -,� ag d\ms=Y�dt+MDI��)M�A?Q�"| <b+  L+iH�iC}=YA{tr}\{(#)A $\}.$ %We � � a�M���r�^#(8�Fy %� $(\O~-,� cal{F},P)�Kim� 0t\in[0,T]$. I�Ybar� _t6� ex!�ed)sa��N!p $;�_t$�Vv� B�At��}.�ie�� �(no2��7nt �z������rho_0� � _0"� -�� � � s* �s ll $ �U >� U lt, �A�m�r&Z. NE v$�:d$J.` o?F&�in�$ (du��f erm �M�_t}�Gt"� '$!�� is n"5 ��*$t$A tr�/��?K find�$conven�Vto �@�V>�` $&�/Q^,�-� B"!�LsC!� ho_t(n a�\b %=�_�\{\ds:"^2�$\int_0^t11s}dy_sR -42}'\bigl(-r)^2ds�D \}2FRN�[&�Gchecked+` Ito's rulf� s 12�18]}#}� [Z&s 6%�7]{*�#.p� sY'�'x *� :5ad2=[L XK - "�%L+5L��5�F+ 7�^4)K]��2N�2"�e &�,2PaID�, in g" near.q��{aR��2��Ŵ$d��.� 2j> $ �$ �"b<"�3�D y diq"by its> ce ($]�tr(B)$). W1e�-�B�$(Duncan-Mortn-Zakai&;Z�&(�)Q]]v:VUoHz�!6&�� phy -*j&g� �M9= .2.2]�01}). %.�"*g1�!Tns!�. (�a$P$ %#W&G5 P}$):Fq~/I�r *  %: lVdeD"Z,�xA0usS-�T\��$ @5"6N��5$�N*� A�new %N��^�H �tbax�� %LIZr� }e-�� > �dF�sB�XQ�6C6,���[Y���$ ;%vF81Q8>�" RJ(-29An�AOb� a2�'��r6 I�Is� r� �m.f 5�)b�hRW�� l[-G�  GN +(1-� )\l�Z"U J}\!\!1a+&%}8��l� .)kr]N�+�[�F:}�6(F)} �� NN�-j�^ni1] &oGe�&��5G= �)�:C%" C + iE -& CM� .� pic;+ } , $E1 �g*v*� .��H=E�:i�(C- �)$� �>0d.TAi] K:�4 �  < a� �2�=C%� qc1Ea?A�6q��e�{a�R !�e "�0�wq .�$!�$m�Sh Xe �W�^)�be\ba{rlIE[F]&=.�,^�,dtU6^2 &= Zea�dNt ^AEf�,i�:��Ye�),��,([.Q  ne (&(�1$ "�f!�r2�+[!ZB���U �MAj$�/�P>�R��>[cy $0<)vM7J�2aerron�5 �N# -j} toget�b�Az!�Jy t�1�J he behavi!wf"�A����5p%T,#$dt@^e m�3s�(2o �iF���� $P_j=M�$smoothlyvesS!�� brac�#�  of RHS��u[�e $P_s�-P_j$.�!�|uI�U�$e�U2fobeys>1#ɖ}� E��\pe�!L=Mj^{1/2��I)`#On#n � "F>�eta=1�c|ni* ��ag'3%�F�6m.�\emph{!�.p*v" }_.66VPB01,6,'6a}"�.�dV_t@=&� XB�(/ C 1�^2����C)-iE� *����C}�.]}-InMN_> sse-j}��%;q 25!� -WA��4 but &�so agjPwe&7I�2g JD�.D $* eJC$�a,p�9&{ 1`!s"�Delta_sF*� s- ))� dN_sWc M�\,")2�RN&�e AndaJ*�%_�JV o.��&a�F�O��:<d~ =&< � �.�C 62= " � 2L %HM�A~22= 96aA�*we uti!7!4H���V6�� 2�=�=��i.e. %]�{E}A,t].� d�t�5cl�>!| % }6�%2�lF(. |C .�P}$�@eR %aƭ�. (+$1�6�E]� 5�.}an6?�'M�=� N�E�B��#*��}�ki�FgIvT&6P�`�M�C:?j8FK lin-�"A�a�Ahd��y.�!1���Ma.�$"0-"� Casw&&X.�.�Pa:�C2�(26W�) llow 2's��[~63� �Y�% _���7� Q*�d}. Let!�%^A_6�!-)�L}*Kms' L^2}{2� ^2}t�?\} 2=A&� k} �+_�-= .�.<i�N a*I�}3 B� $r�b?`��G =A_ti� A�_t6�h!�'Then,Z �J�0ApzT1 app:31}, qe�69C>�-,` dot{�}=L�\!i`1-12^2)~]�$-A_tKA^{-1e� dop- ?(�)8Z�rb � ee Cvrsely,�EQs"�u�5�Ipj�s%�n�, -�� "�DEaz-Uto5rb}&� F8s�)B� = 1 r_t1 ger_-, \c t = I�z4P[.% -gY]a�I&0*TO5D�fC6�1�"� *"9�Vgs 4��6]�%.��&08t�6fh� �;6d!g�on�@;�O.?Q.g6*) iL, �6r� �0cuC?��� �"�2����:&fk�. (rbAer.�H (�/��$U%.�s�s,/2 jus)�;%�! � full,� �Ri�#ɋi�u dir5&�.cok  4�J_�� We nP? ?Dd I%W�V N@Z ��% ��E�1��supre]Y~;(\pa f \pa_T sup_{0|q t T}� ft]8!|("�"�(r�OrixId"3;�$ A\cd1M6�a�Bpri� Eucl�An�;Y et $�QH}Ŝ�& dim��[.�lsF�7��5�9����e�<�o$a�2~��%�2n�>U���J�lo�!(y Lipschitz.��-E��.c.�F��nQ}� if $y^1�S# $y^2� ^!�&]J^TAX$B!+5 6�R;�cw�a!? ;V=a &���rho � iv��}!�aists a�(i ��t $C=C(A�y^1E�, 2 T)$ s/!�|g��,ٍ�1 ->2m &\�& Cq - yŢ9{and} \ "�& \\ j�5 �V. ќho-ct�6� �7"�j�~9 4 A �rS�?� �c*4a�O*fLR�!}:!p + a� �l� ["} = -�  K A_t�N(=b-.&"  ����uf.�tL���,1��l�EA��{ 2" R'RA��xiQ2% I# M*y9��_h�9h : �)b6 �y3 �m��jX�4��� waQreAcO-r �?2)CQ/a�X �XpN:G9�` we employ�Rf �EɺEuler �Ym�#:\<���=  �.*5(�2�=�O6WE�8�x�'� )�:=�kFix!��r�c�g samp�6�M �D{=}t_n-t_{n-1}$. A��m��P �2�21�iR� �S^ s_n&=&B�+w 2-b ;"b� Y���4 &-\:[A_{t_n}K i�� 2g+F (3 \dag.� �� ] ���+'��d�2}:�Multi�Pboth [gs�W${U $\{\ldots\}J�$� lb: � l2�&=&.b %�}N/$%]J��9� +\:LNX��w-[KRP+R�$I'R�6D�)a�$ 3 y_n=y)�-%}Ee writ�N�%8nIx )>�Y� �C �I�V�%�.�N�( ')r�=Z�b ger.�%:�We� ���citR����2�e&��ds$6a� �y w�AR"Zz6B}- CVB D ^ N�%�A6�1P6-tx fo"j)Z��(&{}={}&[I+K)�]5�m�-B-� /b.C.Lb#D#�e8N� j v?�:���! �L*�Wby re�1�Xg emF� Q. Se�~9:$=[A_1|A_2|��|A_n]t!an $n{\�}n$ F,�1 , A_nԃcP_�x&�!A}�v' [@� "rm{Vec}&�#A})R�^T)us, Vec"�"� j'sN�� $(nn)�1$ )`. - �>B"��1"X_(. G ces,a�J� �[KAXB}]=B}^T\o%`i�tA}] B �X}m,&$ @&�K� ck�S duct%}9���"�O�C) �2(^TEs��y)gpo�O*�#N� out3Fju$wng it:!�7� � E�by .� �N��-.#Nln)+2/R$"!LB0��Bc� )SUBC6�J�� =�0%y_n�"�� v.[(IM6�M A})+91BYj I N-DAC}['X�RY) @)M� �� ,5 �6! Տ- 6�%��V�=& S6X :�T Uq�5XB \&�f%� w�===�"X&imp�~ �ee Wri$*a� �symbolic�m 1�RN=\Gamma.� N(e��)rec�w"I \^.���7 o2G f?�> . By�"�$q2��$\dm&+X�{R��*..�  �1�]6) -sme !�b�A�N��.g-$ �"�%!�"u�ya�mzEreg@ive*s5�incorpoRu�rw��e�Y�+predi}5 }� uYe}"& ')B�8 stepm!s knon^��s$ histo�\ $( 0:J})$&$ F}%�wA_� fis �" c�Z2�2t= vail�X=5� ��~&A&Wi]ntc�T!2RE ��1&R�*q�F verg�+:?Z�#.�nu�^c�F�!&"�{\rho}� "��ll2�61 Inde@*!$in� l�Mr?�OenAg ?�[J�:�"�6� $k(�.��>>(�n�"$�_n T$,| �F3n(y) -*c.&d�k(� _T )�+ w_y ))"��%�A $$.(?max\{ by(s_1)-2)  \ : \ �s_1, s_�q M�\!f._T�&pucompa�Z� lr.e"n.�zu�+SDEs, fz�\;%�e(}S gus]0|�=:% _~ }{lr u0�" &!I{ 1 &  3 FeB"3 ( �y �iN�-i� �&�P ti�z �F�1|-F��P1%P=B0�1��P �J��41�4(-x-i y����� a paIP�e"��^�5pt}Hx$ � am5 (lQ� ing)uZ . AnUe^!�zL<���"R3�mw1E��~�!$ $(x,y,z)$�:�=  V):�)ھrho-��%%�i�I+x � _x+y y+z ZiFN)d}0m��Ha;q{cc "D1{+}z &\ x{-}i yQ�x{+1{-}z%� H [i�2^%N>���� ( $x^2+y^2+zO � 1�e2D7v Qi&���� H� $frac{\alph�7-ExP*� a* z�.C.AVI U�< y16 !- -B"k.`-h�- fy$. VaY'qY abou�me�"4!T VmniI�-m feg7!Q�� s\:1f��� etupa r�*�"� �Z2i q�r"�P L= \(Ug�} R�,� �:?L69� spontanq9emi� rate�*�ca�K�� @�E,)r+i�S!c.C -��)�!J A7&=SiiA�-)qCacAQ�.�l(ea_ ntum)� $(2�K)�%3KuKhNL<DP$1/_8��2X� � was�"�e/G%) �NAc�S�V�_eff؝�$u$=85\%$ (a U1�W), to� A��!��� *� a}�ch `Z"?"jbAH�9��h�+ofl26�� ��lsi Q�w� arri�mut�P� s:'~(d�iz. Se�FE�{=}WA��(l-���V� [�$ 4$�]յ {=}0Z)��{=O7}VX2}} 8�!S� ccon�nMithſ%�%m�~e%B�v V �T3<s�8 .01/ �,d% � U$T{=}25!}>�Q=k 40002x>�d\>�|si�EFmFA$N!v 000$lG5�$)�27)!(i%� of $T�_i 5v"{ &f=�$�&�*�� _0{=}6S\l�5_0|a��N~ v� � "f >rb� � � �R�1N %>i i _0=(1,0,07=,)�Wj�Z�g ly�=)4g�g���5new�x@/�o SYs ?$M� y_{n^�NRi\~$zONa ;Pn  $ ��  ��a�4�*ent7)n7 >I�)bur!Gauss�a"Ve�m��lAE��� j2?23$T2�)�1�!�_{tn},� n},z)M`�K!v%�}.GvaX��tsp�Q� poD0A )��x�^ao�* infe�wo/pWIa:kV"���&�F&�JAb�3)T-rW�*�-$_t,y_t,z_t�D"R���$$ ��=2�[x_t\�] -y_tǙ ]M=��� W�Xo & ��in; E&|D9 �  $( ^����N�(Y�3!�.�J� ���Z�_xRq�.>seems���!-�i�c�ge�/tez$TMis "�7F����1}.�er3�7��E0ee�6t�B tead� s.\.V3̫�5*/��c,��f$near $x=+1�x=-;e���i�e- ing Z��(2.7in]{pic3/ap�f�C of�en��.�%��X !�$} lfi����4�� �:.�2�/nd�I�w�Z,MPA�A�&] �"�"E $ill eventuY� forcIy!����59 �]s&� Q�C � � spin a�)�$ toward $zYzA*6e�*�H,2| 2}, .�4}. %B�,�-�z"� " �� s s %w� h�sul�O.)W�Z� effW�v"�W.�a`����?l&�s�Fu�4L���iC�n��U-� surfP �@�t-X&y�5!� mix"���i6�7at5 R��W���1l!��*��="� v�n�x thel�w!a.;��ent #�>If� b�a>.82�p�bf � �Bs6Co�b�WM�EI*� 6W��2���1:W��V�Fv��6�{OF@@�A�T5��K*�?"��p%�."T5n!8-j�e cho��^.>I!{MEJ99(�$@C^{-N_t6�#A&De(UMF�* >�V���=b� b\�1N�?� �P�?.t� �C>"�#i�2%)f4%-j� i>s&�U�d""_$"!P��*�?�?G#>�V�?�E 0�B���)\~N"!' P!?;Get"�Fu->rb.:Moreo}10~4r�W�"�"+�9�0j[&*`=El� 5L����?-j��?��?��?&49�7� !f�&o ���&�2��&�s�{e 2�%� adm�Vhe(&$U�S*:dU��� �JF9�(-a� G""9�Iqz�J)�6H^<95��YuA& �nd*|9A app=Xas or�v&��)�}�!"?J  $F$�@"�L.�"� $NA�8 s� a &a�&A_+HTh �D`&/����\&\Vv!�H"�p�Xja�#!�QD %�SMEE%@A;&�Em���+ o�?fu���!�:e�< t��s���gs&�U)�w_pv�%$�~cA Co��<{&�#ec:sumy��p|tw have�&p�x�!�*�x���r�z!2s;� ���aseZ� !�&�z��%�U�^(iA8 for �'.� ��S enjoye tin�ua�i�uE5 �+�{*�k� w+o&>ynhppl�to�*v*�P��� n% >4yc I��:)westab+�� valiI��z�s, @�� �be�lg[�$%|!�mJ9e2D �(��%�a�tq"= a+mmute�D� �*%�b �:}a�!�jU�{ ��\ "� ac] ledg�s�� wish� [f��AusAIDAQ ARCAE� � arch�B ^ \��ndix "� Prohf "Jn\�?�!QBI>}FLaI![ �asserI�of>s&�&A�aao\�a��\.(J�02�E��We/S� N�+yg%���verif�fj>���1}. a:!yre 'ple�(nee�{tFcar��Q of &�O.Ih�(t�*r< � w!6�"d3 &=&dA_t.S �i + d .D@~<  7+A_*>�%&; j* + Fm2 t2( dr>�!1uArA_t_:�R\�d A_t}b�"`�#R* t}d� �!@" 2^2>]�`,a^2B4�2I GL}{"{L4!{ 6�:�fy�( -.?�%(V\)fdFj=&V4�!< m�G}d6]Qp1>� Similarly-�n2!�%�N  _A�>%�Q� ).&2B&2+ tj�#1[.�*) Hr�-2 �K& ��-k��|5]R}_s^1r-a 9y2 2 +1:{1,- $6V{2I!�� &&vW./M}(A1)E>!: 2) ?|ds0 %2nd N��:�2v+R1NU��n! -V)#^] �re�1m�3r9!�ft.\!�?=Y�lBq&�>H�HefBO9�IC-�|%o | + WJEQZU%K- Q \}. *�]ZV�6�)]|+ � r�)� ��M�n� b6�%4t"v$)� C_19 y^1-&�O�Ka�9 C_22��?.T *}1| $C_ C_2$ sNhQ�Py^1�P�` 2 �% $lDHBy Gronwall's lemma� ��%b:D�ԉ���!�t:�R� Nex.N�2Hxpfh�}\ifx\csnV9natexlabA% \ix\def\#19� \fi !�NGbibO font>J ��f�#�Pf.jQ$�RY ~R.$�Rurl^�url#1{�Stt!O%�{URL I� �\�bib�}[2]{#n>!�� []{S'��:tem[{2�{Gardin�qZoller}~�0)}���� nfo{=�}{L5�{C.}~1tS}} 2�TA$�fOP>O �ABtitle}"3|N70} (!��(r}{Springer H���}{Berlin� (year}{2000}�|JA�J �gxF � An O��SաTac���O�3s}!nz %�_B .�) �r WisemaW Milburn}%{�b {a}}!#�g�# a�ZG>q�)n1� journal}{:�$. Rev. A} e���(��me}{47:Ap�}{642.�=C:���>�B;ielli� Belavki)U1!G�h�GA>�W�JVBQ�ZKJ.��.6��jU24:K-U 1495RV�tisJ��A�2!9V7� 1a^V���C�n��EBj�146V�611R�2r�̥�4�CW�~�j��R�Handbook�*}�M��L?��Ch�4tr�#anUF N�5 al Sd�ces��F�4})��e51}{3rd} "�e�J.KaratzqR nd ShreveA988!S.� ;f8I>!S�pS>O �j�"!wMo�%w=�C!�u�$New York ���! ��88r�Kloed�FndH�te��e�!E~^B# R�]E>]Pl� �R�N5�2��=_�g "�!�ƑvmzC��A�7E�*I~bJ.~M.~C��*� MX:� �� ��E�R���cesx�TB�y)la��2&�oBr J>�(Skwirzynski K�E�o���"$}{NATO Advq8d Stud� Ins��e S�f7 ijthoff�Noord.4 "E Alp!1aa!)A�RijJ^ 1978��pp.��� 721--734}j Elliott!�8e@RE8 q�V�R>@Gj�]ݑ<%A�"c%`�MI�lagR3v�8v� Wong� HajeE�85���~�BN�MB>[ ��YP>�ein.c�mB�`v`5r�DavisAg79!W��~YM.~H.~A.:  M)Q�"v in)e��% 18th �Co}5�Mn DeciY&!� ��}RP176--180NY 79r�SussmanŨ�HHJS78�B� IZ�LAnnal2!ba/�tyjE ZC 19R�z��!Q o�}(!��~�F�O�M M.~R>< ��A�{To �$ar, 43rd~(Q&,A>e�, .j&Niels�Chuangd %��~M> R�Bi �IVR�C�:��%�In�Xf8 Cambridge*޳ Pϥ zq��1!�' �YMerzb���x9��~lE>lJ �r"Me�i@V� Wiley I������ �����4����  v� WZZ� WM9����>�B� Sւ�L^L9-�� 135R�N�j Cav܋n2�87��C��~JBQ�2�2223Z� 5543.�Q�87r�(1996!(�~(zroTm. olog ��nti�of V�,Allen \& Unw6�u�,St.~Leonards�"��F��r&Dm�}ք~�D Prog�T �� Elec������kN�25�:?J �r���%..�b&�a������� LettW^D70V�548NR93.�!j��Vc9Vb�V�V�V�#165�$!jSBacho*$vL~�B� F��R� A Gu�&o Experi�/.�Ozw9 -VCH.~��0Weinheim, Gerƶ �q˱�9v� 8Malcolm et~al.}��9)6� #, ���$[ ]�9~C W.~PaG.! [-G�V�l�>@ �@"U=&< VRn0 �5�vl3�ll43--1Z�l� >� ζ} % % * En��f�M* �v :�� 11pt��(]{articX�%6/�2t�H�/io��V22in} .T�?he`6}{8.4i�5*3Tw��}{5.6B=0opmargin}{-.3><4Aim#0F#oddN"� la¢D} ra{D a{�J b{\betm{\mu  n{\n ,h{\hskip 1cm h2lo{\longsSarrowX*x���$,psfrag,bm1�} %.)ams�, g,� font,b� "Y0 �@ } \vsp*�4� 0D}��v��Th�yl zA�uq�O� u"�thr+�B�6ins�#g!!lA.Bayat\footnote{email:${\rm�@lfazl\_} b+D}$@mehr.sharif.edu1�h �0.��( V. Karimip�]C2*�, svahid@Vu-� D2��"�S�.�of*� �ˆP.O. Box 11365-9161,\\ Tehran, Irani�-m!"AB3c��*a"پW�Kud�\)�r�M$mal fluctu��uazbent��r.9N7t���0S0mNP�$�6&8sjD-�&iBp��h!�+1B� Ote�C�#apan~for gene�>@Pw�8���ddsm�13�exaƯ�7 �E�short.T�f!�h ��G�-R!,e*� ext"Q8fiT�W6�^>\�Y,.�&�X��e fide�av�7nel. P?�-�U2���erJt��-f~�magne��)��~:e 6on3N�0aUI}�2v/{2�!0i>}�x�]9�gqd��V�|�bnsKCa�9 or uN~I-ID to aؑ�{be��ReM�it��b�E!Z!at�A -2�:ac Q!D!�I!heffRtg8ose,kor,song} o&� �ose2,��eVf�3&��iJ . Of>t�~01e�UA�us��)% ��U(!(�Z�d{h�LV�,=schemew=fR�( link/sFalI]5��er�>k��;&cFcing&wT jw0 $N$-s�22� Heise��g%~!lin��c� a U��K,yA��le�WUUh%�.��Re�!� e8��e�Xom $1$!e$N$$<�StA%4E!�in�P`%�, $|-,-,(es -\r"� $|�oc�5I�Arq�n���d�c�>a� 6I��PLPn�`6< . On�2 n adr� p or q ��!#- hh ��A� 0<Y�O2��H�E�aL RRhi/�$ (�K 1-aU��b �A�o��emitA�w�Ia�4�)>  hand �,]Z�n�Xal��6sL%��/Ia�is way�< �circumkK Gro ?��e�@E�UdE�wS<� �W m ��48a�tyA�switcha\�� f "�y pins�(4zhou,benjamin}�� )I�imy�������,��$ >�10cm,l =2 a� =0]J.L� "�I a-AnZw.�isa�a�at e�$0"�Z(chain �and is transported to site $N$ by the dynamics ofspin �chain. b- The entanglement of a Bell staQ�|\phi^+\ra=\frac{1}{\sqrt{2}}(|0,0\ra+|1,1\ra)$ b$ placed at�s $0'$ �$0$ #0develops into�>��.;HN$.} \end{figure} �THamiltonians governingR(interaction�the%t  channel� full)p are respectively \begin{equaP0}\label{Heis}ӰH_c = -J\sum_{i=1}^{N-1} {\bf \sigma}_i\cdot{.{i+1} +EB 2?} 8_{z,i}, �� andn�2 �2�0��?z� where%SLsubscript "c" on $H$A\nds for$-�H. If at time $t=0$qubitA:A�MZM3lefE�!�E� n evolu!�1�!�enberg +carries3�te *is r d rightmostE�? miss�-(I s)X$horedecki}!�One%[also usA�is�|>T2�iI�follow�way.�. aE� s two maxAlyHd ��s �{ed2W!�)B>(�/ 1-b)�3Fi;Pafter a suitable lapsi ime �)�� �f'�(it is assumM� onlɤ Ee� coup� O�Ia�is !.!distani�s%�b��d-�ala�be!�d!� imp���Aeoa� 1�Hprotocols like tele�` .ItelE �z formalismK i�requir%*at%����wbe ideealigneda�!�dir�y��ppo� )a���4magnetic fieldanis N�8ɤ�0howev!�chiev!� %Tat zero temperature or�(very strong:fs���� fluc ks�1not larg!� ough� popu!� ex��d��\, i.e. (when $B/kT>> 1$)a%%� h56$ 6� may lowe�Lqua�j!�!Ic��since��>Ate��to)�7)�|will �� domin�+]._ betw��> �{(is essentia�$he work�� � . \\ More�!kn��u�,t!� ( o�ndN~�?he ŵ)>A>,�ini�� :} tur ! mixed (. BeforaG�]���an)� round of 2.rvshoulda rest�o, Wexaa�� coolzo!� eMZY� s. I�e�<usible Ņr �multipl�eq��A@ heat��up to .\a)�A�e;�g �)Jbut�som!Xa!Q� #i�9qd%� In view-�(se consider�vs�is desira�A� stud�@ effec��F�on suc���-��/s�problem)+ we w�_!Bddres%Epaper;us'��iz!meN�E�.��aseA� ris%uVp�P givenA/8 density matrix%oTaGen!J s us� o se �2O ambi ] o��easibi.i�<, a��%ti�>ve[A�._� U% !92EofUEnd�rib"� �� .\\ We��deryae5.�expan�thr��I�w� U^���ym!3an� (sired degreA�@ accuracy by keepa�� 0priate number OrmMWa( �%�In�equeljYx��� �l���e�$arbitrary f����low.sA�is I* be d� a�Aer` ly.}I��La$� �exact�E�IFsa~a��rt �� four ��$e advantag%AO ing �sh:���)� obtaiѩ ectrum co�0 telyA� he�$��A�@ a�%4ferro�LK anti6)b%��str��,�ti1 is a� � s:!7s� {\ref{�A}}�set�ihe�Y�JJ A�%]  :�Y�p��exp��ioI uI�2� �.�m6 � .Zŗ:,endpoin!�!�Uin�U�:{In1 ���}EQP��� ific!�ADBUA� $4$IY�]we !��Atbasic�dulte{ s (%fid%�}��conU}). \-�{L6O!~�P-1�#-M} ����E�rA �be nea neighbor!�j*� typeiPm�� \�$n external:� . Weam�emphas�� at m�= of w we Me{�AI� doŧ depe ��pe)�# C the *�u.�a z ^�� @mal} \rho_{th} = �@e^{-\b H_c}}{Z}=\�\a}. E_"0|\a\ra\la \a|Bo�$ %$'s%�$ ?:4�eigen( s}g|M3�.�M�!�(}). Here $Z+!-parti�fun.� L$Z:=tr(=)$�! AtTbwe8 c$0$-thEG�V n�0unknown pureu$%s0=% \ra %: phi|J�&,E�V� whol�F�b*� o\o�s9���vvo^,rho(t)I+(t)= !iHt}( � [ {th})e^{ ^ H%�n�he2�-�*S�k!�2!�\\�S .$N9��� $t$Bn�N �_N�,tr_{\hat{N}}E�~�)^� J $ mer�ta3he� ce � aH ites ept���ite��!A�^�0erator sum re��  fns�^1@eh �� E> (0):U�F�2@D>A%S�o���wX -�Ab N)})��{ ute �}y�� G*5,ո��index $IaL run-TW leteI& $\{|I��}�!&$Hilbert sp%�f�74 tota��!��� N-1$� %� �\aE�to �O��%A_ ��.�:Y�narra�&Kraus} !�k|e�A�|l�W&=&I}�d I,k|V��q�|I,E\cr.H$,j,m,\a,\bR .R|j,� |b,|m,\b� \la  �a^6u�xtq2�q. (ho_0}_{j,m}! �:U6��ž. -Z DefiA6ll���mwo-,ces $M_{I,\a�P ith M�s Z�M1�9|j! :*e^{�h� �6AZ}�Rz �&�we findEV&BE4Rom&1tkAN$,Nieloson}�7}y,Y�+��RfinP,U�<% �E%�0M^{\dagger}_{5� Z Nota�cn[ �&� 1l"] de�, -aS3N�is huge� fac|is� z�a�6Kdiffer, choE � $pai� ind$(!)$��ZQ$s $2^{2N}$yprinco� e m4of�� a super( : �%�I6���Ib�ducko R,"��re) �O�"� ���&! n[ache  �. E� ^e�X A�4 symmetry argu�s�ly� tric{)" non�Ua��eefd.\\�6�is out-��.7L !in �V_��^]F�F� � AL } tr�`vX)BYWE\� es -C�averaged�;liwi  input��s"a�bg �\�line{F&g `1}{4\pi} \int F d\Omega ,�C>�)Ctegrala�= ��surfaE U Bloc� ;.�� => furajA�s�ified��u"��4 �ly� 'id�tb� )�5� A� 0 B)g (A< B)S-��)))џu� }P SO� wapu�Im�X $S_{ij,kl}=\delta_{il} jk�}WeJ wr " we Q�͙1��(� y  n}� {\s� )$��e 1 $��1�%�n_in_j5�= $3� ij}$�zuve��5���M�)�`Ex� �6sQ�41}{6}(\bf{1}+SF� � � � e1M]�%Sb�bar �3 9{6>!#"e�a#AVq�� BV�F UY�a�at $tr6�)=iAB-�$�� �� = ). $!&�"�� $.�%Z1 F8 �.4.�3}+5�6}.� |tr �|^2BEmX� l)�_already�o� ��2�&��A�Mw�S� lea! con&�comesJ :2#"c���$\a_0$,Y nextAn W%bWfirstPit"Me�so on�u sp�� � �� &� ,a�:h�na �!o<y good �!Sf�sby�w� �fe�rN� \\ \($� {�%��.wli�"��"��};� *d 2�5�&�5� �Q8. F_Jn:2Zf9gsI�|!�H'|-,�os ,-\raV��r�w1�w=ve^kgs1} fd +�Duf} yc_0ReIq_`) appear"�$�$2^N$Fl _0}$=�A�A"sum. H� w�w by& ;�>Y�r� )� WIwo. ToQ�w�!� a"� �eA_q �an be �tena�ɰs*���(gu'��,!�}(i,j)=�I,i�|jE-2 B�6 " $[H,J_z]=�$N $J_z"I�A8  $z$&V"� �lyJ/ �osX �����Iceip $(A��)z��denotA �rO)on�8Ix�,!p 0}$,}"tw �� B%��ɡ�up (e.g.#A8$i/� �iZ -, +.� )) R�KcV� �i}:M�!}above � io�#5�6�#�p� ��( ��:*K�MMM�:M_0&=&\�(�Z;{cc�\m_+ & 0Y0 & m_-:� J\�$),\cr M_i�pURnm_i��n$ \h i = 1 )� N "u- $ �� -! m+m-) m_+:&la A� Q-,+yrA]�\ra � !V?-?W:?�� � ��6mi�i:=0 M-,+,-�qF�F  A � �lci%O#*��A�Yt"� )!I�K�Q� , regardl "I�ir�5licitE� of /x�Is,^}) \ i+-}Ax� �<i*�  textbf{M}!EY&� 5�-{>> Q>big �_ =~gb�\/� N|m_i|^2}� \\F�T� !�"F�/@m8�< ���q'^�21�-�� =M_0 0M_09j�.99 $+B�� o H�not��� x ${U}�~b&ceA�,��fi>� � >G b� FT=0 �2� && 6� |�m+�8|^2�M_ j9 �zY�Sm� ��s2` i{O*I%:tA'by shif-De �h"~.8<�9� t $m_-=1�Ow�nb� FT=1~06d |1%0+J0accorda�"|Are� ��b�.;E&� $m_+%7dl�,$f_{0,N}(t)$+2?�"� TD3f�$.�!�#2p�Z� D2� a�'�ueB�%a mF�-_�%�2} L#$�A�~a bRofOEKQq\Phi_�3��R�3�3�3� �In +" (@.g e3 �-0'< $0$._�"�& �in{)�& .qT+�s$(0',0)$A�FN�e�'�Iu��-&5R[ 4$U"yr,realizd  of 2s � u&�.cG&�E��.^�~ �o�rE�)��:!"�$N:t� "�:. �j/doe)�w22,6`. A�/ B�{)�^�W2I�& j& �nk!Q�n��� .I)���^~ ent1�N�y{0'i� .v (\math�\'s)(Y�\laI�)F09B[FQ6P%�B� �!eMu �!_+|&�2�efF� � 0& \\�& 1 f10 !F� >��VAqex*� 1��_� ���i�M})�!��!s�,manipx ��"j f�'b�entN��+ \=���\b!9[�$I? (\a)��V  each�Q$ perQ)E�a l�8�$!!@�%e)�.�h�4�|is�� rhoa.��Zk M :u^+�(t)EE I:b& w26z.B�<z^*0w^-�> �u6nq��w�y�r � !ba} =$ E) 1}{4($ 1,\a| (1+�^z� )|7"cr �JA0 A-:A A=pJAj�>AA5gJAjA>� A5�2?2%'|R:^+�|"� -Y p'E���s1^a:$��hHeif9 picture�3$-7 ?{&*"a�$)� enoncurr�,�hav � samew)on1 �l��"(a 0)�ilibriu�7( ok, wz},��� �rr>U�1�` �)en�/&` Ex� s�:U2�+!�w!, An�+c��1�n :2[.�L3 *r,of9s���:lvolved, 5it&� a knowled�.}C *�$�5�,th�2U>s"\6BNiM�.)[!W2� anh%2�� Š1hE{*I3"�09 �)�_ p�2E�c%`�/1�iA*i� ;3$. F�0 ��;�:3!�!'�"# #cha� eristic�7&}"behavior� 6v���--6�s` rem �er�!N�7 �[; relax>its2� �A�2JzAZa � -�U{ �8A�F"�2�8:6 �0 has �<tud�6�<�0 So!�* th�2�'!��}h&'@��hc3��? J / s}_1�4 s}_2? 63)�?,(s_{1z}+s_{2 3zJu �*jI�.��$as� "� AiistG!�ap�.ix�E U2� XGE=Vnow�Z��Zhc4-  = 206�19B"` N!F%"0)!) z*Deter�9� �~;fac�5a6"�!0"� �i#namj�Asym)�<[H,\Lambda]=[J_z0 \ {\rm!�}\� \�Q_x^{\� (4} H(J,B) = -B) R'B� "  $ �� �inver3��^�inv � C@ |s_0,s_1,s_2,s_3�(=3 )">M=2�����A��E .��&-dB� By plug�@�tݔW��� �'A"s�{� ~�{���dMV" BNMgout"5%�Y�*J%. au&�&5�licA}&�Rim n �!a�. (�'period�=�0�A �#oq%!$}~*81}{|E_j-E_i|}$ �(.K���Bb2��� at c �s�-�"�rN �1�um. Si�&I: focu�:��*�� fix"6#%�2�J� s a 1[BD!�d!)U� #FC� " 5)BI.fid��})� ��"R���7JFL5bLF w} %\ce�F�l\psfrag{F}[Bc][][0.75][90]{F!:m�inclu9Haphics[width=10cm,h,5t=8cm,�G=0]�� .eps Bcapa ${(Color On�')A�9�(F)�%�M&%\h$us1�d��2E }s,� a2$kT.%� $t$,�� a fi�>5`/Z$:�()B>U�$F Q�*= $C� dime;D�wI)�?in un u $K ��2~ noF>%se7�! �($BPE!1 $J=+[E%�� - bH.T1 U�:)}"IYX%9�3��.�7!��;z;(t)j; $(B=1)$�*e�a=tJ�4 $(J=-1)sJ �� 26{T ur�5�Z syC�*a�esta�fea�;� ��i���2�G�ͭ���l�3�!� �.�&�=�us��t.i� tu��2j of.jto� !�faad~D][���6R��*it�/K&:��A �so�?aSJŅ��фloHL�� both&�� s."�!�d2�De�:�,des=�*�����a8N !Icomd&?eb��� � ce.�}Hwo>�!emor�;onouncd`E�*h�Aoser2E�use� e� �kE)il2F�!O^3R.�M�,RD)f"�DdE�!�� �umy2N6dr#a.�%J�=s diFL$,�7su�@O.� �e,B0-�3X-�r N�al�$&�Pis 6Qz woo}!�62HF�Ns-conE2�6�=�l�.�as bf�p%a�eU��� A�previousA�!�s app�@a�At�^"!"b�� �1G]�V^O%�c3�lvalu �eno6?��Ai|bu*;1Er B�".�,6LuAos�F� i�Mrt� ��� � � iso� ���P&�#"�$.��c��� =hN�A�h�� drop�&�wB!Mimz;0 � $0.6} t no ]er%(��O.�F� �pQ�l. � ez2�O�JV�As>��,!f��� � R�e8a:6E:. b2� 1$� w Y�:F: �Q)Qa:eނU�n�T�T�� -^�RC*� 9M.�>QV.Summary�!��Ua���F�Are� @ly proposed methoI e%&-Nof0@��!"lN�I3���D:U>B�a� ���᭡`c�'�)ffe�8o�>�G �G% �2�A   mpleA� f|L"�F�?&�!�! �"M9a�q��b �L.SE* !��#!�� %��C�Ke���RI .�] -Oof-}��Ler slighH���d->/ *&w mad�NdetaiJ#�*]N�� s.&�Ac"��0} A. Bayat wo�Dl�P�!Hank A. T. Rezakhanie�AX help�Rdra�$%]nI���C I. Marvia�"> very43&F co.%�$M. Asoudeh$L. Memarza�ir cri<� N.-l manulV.� :S�+I/%�SfE&Site Spim� }�M�NacC>�lM�H�L��he *�s $H_c�_ 4C�z>�zx � ).\\U e>u�FLE Mas�.�0��<���2&(@�(-%-2:W(�,-+ 2}|-�, ra +Fq&,�@FFfF+ \H+F 6F G4s2G82� �&"-#�p1�2i�n{i+4}r=J�3}�F"�.g#s ,4, -g �1�� �-� 3} E_1�-� J�9 3B !\�E_2^*>)3)J H>42� �n>�->E)<�E_i(J��/:+RLe^M�e�;4tal2>H (1a�e>)e "32��1a>(�J�). R�:�,ŵ $|!� $ or $|i,�A$�{@K ������ $i-$ th &��J$4$"�2�up�OF4� downf&2�&chi_{1E�aE�-e�iw V�a� +|+ |a�+|a])# |;�;r�I�A<<-;- ::9i6 &=& :m�+ }a��-( +1)(X -X)-�Y5�FY-GY+Y-fY�6>�N (|1,! - |2,!*2$7F� ;6�,1c1;!m O+O c !� c �8>�-J(9K)k -�$�_)�� -|2 Y-|b�9���3;%c5Uc-|�(�$:d %!�)+Je{10F+ i3\eta_+� - 97\xi))<+ )���? �!PF�{1u)B< -B�%>+J!R+ ��>=Y $�0{\pm} := 1\pm�C3�) nd $� "= 2 \pm���o$ f��!��.��L"a� fli*h@ ${\s�%_x�1"�$� <�b�Ls,4 a�,b�)���D�Fi+-{=q.� %�c�F�B�#5Vner.��49 �ͺ�]� �a�133( J - 2B \h��f !i%-,'1E_3 = )�(VB �[ J�i J!(1+m 2})J -BIM  E_5.aA4}(1-22` - E_6 *�2 4} J| E_7a�a0e� ��h\h E_867:�_ !�E_9>*2��~.10}� �3}!lE�+� .�21} = �B1- JU-�n�xE�WE�&�{i -B)�=1"�35 �:� �$thebibliog�y}{Tibitem{benn} C.H.Benne�a d D.P Divnzo, N $(London) $�.8404}$ ,247(2000�.X30 S.Bose, Phys� v. Lett. C(91}$,207901D3.Dkor} DDB.Q.Jin, V.E.Korep 8quant-ph/040913� �Tsong} Z.Song, C.P.Sun,.212183j61 @ose2} D. Burgarthn Giov� tti,�S. �$ ~ 1017a�L,shi} T.Shi, ,W Li,>�.� 0815+B@,zhou}X.Zhou !�l.,>F5E,89}$,197903 !F2.F,benjamin}S.C!� ��W ~&PbM.Horo\b, P. ��R.I Rev.A9�63= 1888(1999.��`Ay �z7A8JyxJ�}J.Preskill, http://www.theory.caltech.edu/people/p //ph229= "�L M.A. s`?8nd I.L.Chuang QA�um Compu� #In74� 4(Cambridge Uni�$ne�gland, >S�,W.K.WoottersFWY!v2245 !v8.v0ok}M.K.O'Connoand bV.�,3}$, 052302 Ae1.V wz} X. WaakS P. ZanardA6e�i�A 301� 2),1U� �9�4�l�Pi>� � docu,��%BarEb@lli&Lupieri2004 \'\e$[leqno,two�^$,a4paper]{�ULcle} \usepackage{myp�Rint,ams�3 symb2([b� sh]{babel6$sans]{dsfo<2 \oddyhmargin=1.5cm\voffset=2cm\ev�d!0!< \newdefin{dfn}{6Pq}E�em!'orem}�D 2 7[ 3]{P- / hr� k}{R  $and{\Tr}{\Z/�( {Tr}:$$norm}[1]{\e4\Vert#1\�? :/rmd}{�a rm{d>MrmiiFeeFqqFccFff> calG cal{GJ H HJ L LJ T TJ I IJ J JJ F FJ A AJ B BJ M MJ S S> openon1�ds1a��&q�a�e�T{Primary 81P15; SecondL94A17.} \keywords{I��>�^�, mutualMLropy, Holevo's boundu4abbrevauthors{��}� G. ��v .titleyUeneiesWV#2�  \\ iG um i�hD �{AlZVo �} \3c({Politecnic)&, Milano, Dip�! ate��ca,t$Piazza Leo��o da VKR, 32, I-20133LIta�`(\\ E-mail: �.�@poI.i��s{WorkWi~0sup2!\]{Eu�Ran�}m '0y's Human Pot2Oal Pr� mme} und/K�2dHPRN-CT-2002-00279, QP-App+ions.=L Giancarlo9�5K��\`anb li S0 d5X >XFis!T@\\ Via Celoria 16^F \9F�.Ma@mi.infn%F \makeEHbcpb�)abs n} G�al� um~"!�����R/=iu*J(I �6~aM%l�C(a�<"|8 idea�a]fv(a m}[1ac�Zs a�� '5�)nproKT&$fa�d='�t�,riq>��!n,AT�Q Bc on von NeATn algebr�n�<e��b4-�&of.(� �s, ]Ul+,new.��'lita�2�un Rm� r. Such i.4i65 var�" O#3&�3ger� (>�G9� i.�y;���ErUy%:��+�gI^ifamous�A �AY�&I�du1_.�/fj@%� lem ��K}#{+����o�c{ ��.{�4s: �..vYal"�0�.sM<aof-p�I�5�h�+)�bGh �} �0Dav76,Oza84}: 2}ie5 (!�� arI[ �\��AAhM�2jm6  �outnS{m� y8bh�Mu�,!di!An%�dO �F�).�Eq#think<9!�b�!͑: M`^F�) �#m=/y� �(F� 5s6)�sn.-;^%� is}*,"ain� !>h�$sec}, toge��a�A�)-&�(F��S�S XA�+��s}&>)qde:!��� �-� ��"WJon�.-a�< y{4���!�a a"a,)ac�r � for�vp�"re�rd n%�aNR thoughE7�if)g� al vB�=�`�x�*��"=y!�!strYwe a["SWW})A6~  _�})�KQate�;it�;�xr: Ref.\�,��*[Re B !tb &p2imodel�m��91 process (!�o�\pea6,�Dl�O�# entsG#"��tsubad�v�f von � MiNi �A��g� MXY���associ��APit #>�` of Uhlz 's mono�|c�AB5ow�p)d�1"K!r��ir�',wA�to"'e0~Ep &��m��q��l Hall� new EMnew7!A��� ]�"*A� ��  comb�cn��by {M9��}�]��!E��e �YgBF )A_ J4BarL04pr}, mai�T| creM�dj wqi��rRq�D bas�9)�%�Ee�EMH N� $ !T�eAed q9ar* ;@A\$  Bod�> A,\,V�8 Banaaaces; o� !i B �):=9 �A)�M:�b��L P;H$��r�2�*lex68 ; a �a� a@ {H�OsT`�a���!�C5, :T%P:��MS �et �' a�!u�e-��;5� Ju�,eH$,�q �;, F $\l[;x`,~GD��!\Tr_{�,H} \{\rho a\�X�a�96�, $a\in 35.  zq{ ly, if $a!�1�a $W^*$-=� eA;q dA�� M^*$� p/[alIM_*N==a�J rho$�|la})RN@.bQR��%�y,A��*� �&�:qc }Ii(@dE� F,Q)���� )���eQ�Ya�H$-�� .8@T�$em 1.22.13a���Sak71� he:L%51�#L^\inftyB� ()�tensor��d|` �� somorphic!UBs $_ \big:ce�� big)�al�e2�$-� $Q$-"}|ly�vweakly$A)&e�QM�Omega$&!9 (23�2on )X2) Mc!fC-)-� is�1�N�q� )M�.�V2�1�Bochner � gj�y ��uz�F�i4pY1:� )$ (6 ��]� e/@e greatest cross �/ ---:�Tpp.\ 45, 58, 59, 67, 6|e,us� �~_E�t$\S�%�%�\i?8J $kB \mapsto d( )\�Ga5%��:"geq 0$, �|2+$�2\{:/�W=ro"�\9�5=V$QJ��� D?A � } &5EM�� !}$137), or dR�aBvp stocha�� mapA;�m�ply�i�5��m7\�2ws�e iz����usuE��%1�a�Q1i�d��^*�We�� N� �So$ �,isy�� "�UN  shar=k%�` q�! I$U #Ղ�<�-h�2-f�'Eυ�M_1*1�M_2��<2Js�K=[. &H @tm�[is sai65�: if��uF�,x.(�n\� n�� rvingwm� (or,�1ivalent�ǽ}/� �!�!% -%#  D&`eq Jkw��- F5 e Je "Qe>%nDix57},%q�/5�!sA:5d�uJ# � a%�Aı]-�{1* jN2*- )Aiz&�sw �L&LtI[�], � _2 \Ԉ le_2l_� %,#r._�s $\fo��>s��M �.d#�iE�eqt�dp���m�"� Iq nto �F 2$�1�6�:eX!qo�Vo{ %�els� s ag�N"�.P�"�D�41�^*_1 :� M!7��ca�, %2%3 %2��L%� ^*_3R%mε�W_2\circpJ_1= K _3$,*�y��� a3�j1A�Hg mph{coars�baa}5+1 2�{B� r $��:�3>�� �{Eni yF0R&iR � � .��8BG$S(�|\Pi)�d��1�� $\Pi%�,[ ite1A; 9 �o8&�T"�g�ى. Giv�'* 29i�H��.� �-�tauqk� )3e*�x�S>�)[)�s� �q.�Q��emM���v relq U} S8q( Y|F(Tr_a H\{ (\log �- tau)\}m�c1�6� $P_i6� B: , �Y=.��gs.7 P_i(�% } =q_i(  Q I @Baof $Pa�.WPe�4or Kullback-Lee�r dj)g�l,1 >l)Y c(P_1|P_2�Y int_[ ��\,q_1G !`�.}{q_2� ��QTPDrmV \,K>}{P_2%&�}\,��i� _k$ �ﶾ + J�q�R� s2A�BpR qS1} �0_1|5TPf��I� left� !Qo )� e Q5�mn !R0)�(F%R�nfi�H6�� $P_k2�\}� qkQ6\}MT ��~-8O�?� Tb�E"�JY:=�l/r��!��[ s og*N�Rors dC�vanis�<���leN��S<4�.C <nu .\ -E)�s immed��lyjA2bA�-y�5}�>c \,�qI>��Y9�Z:5F�Fin , le� �tl�q(C2)$��!.v��^B� � D= -.�etց�� $}, \qquad >�B�G:�A{� �+Np �$[0,+l]$.�dw[N�A a�#pt ``c''���� d,\"��``q ,̂l&� onE ndF/�.SK-�)ya 5�" %. & Convex� ,-era�(A key�tult �$s&B cJ<a�!�:^� � v]Sb. ,� or.\ 1.5�21)i�!Yx$at&x dΔR�Uj em��Uhl} I�� a���6=;���R !�� �� � %4�M_2&� � tL$ �| N \geq� [�W]|� [\Pi]&���qE� �|�r}�}&* !��_� !��{�� ��1�(2�; so, i� �� ^{12")9Piew�PZ� �)M2%z �Z^{k2RQh�l�i�-�k��n&� �| �5b �k%w^k� $k=1,BX y9M.0-&@ y�� a��Zy"���m�[!r�#sA_.2-�s�5%q5.��f- R^J�- {15o){!�itq��1al" �Z�h ��� �.aݍ6%� 2� _ ���E�r:� "� )� �1 2�U�Bb t29� ��&F�7 2�"aB�on6�A):��9}2i3})2{.�s�L 3})+�� m.yNh�.��>�3>�26\1n�3}r\N�.�12}q N1)�G-�S&:��45�e��l)�Q�7^B3��� �.?~�\ =��G� f ��a�similay��.�by9Pm�8A�1nD *Q��0�&z3s,A� J2N�'}�N�$�' M�}P2.�n5'1�vq/( 6�0�ory9+.8�sXM�h 5!���ges DavL70,.�*n ixD��o�H_1,\,��H��b�Tew#bHu�:� )@$( ���=X .1d� �%!} �Ay.]p� d� &! �$enum}{(iii�renewcom$8 \thei{\roman+�72&,Z ((3L�> ��F"�L� &�_1)~�_2 JY G H(!A%@tW �ve�!` F3 F���(K�2)._�he�%�I/)[�]\=� r!_1}��9P���Z �$�$-&((�]�Yy count%�Ey $\{F_i�_�irwiseZ&�se�& F$ \[� "y �F"calI(F_i �A�a �*�Big23(!�cup_i �Big6E4C\,�1�!KF&ua%�.�"_ ?]��Aa�nde| UnMNh̍�"&H � y"�.�wo6L��3�� on]� �S�"2$;[aDs�\6Q*C�u2 li�[�ZO gFB?"��� 9d!��I�UYF�are�Nide�X2y��i�)e6�H�"T-�th� �=R R)p�&�t*! Ohyak83�'�:�S�$F"�Ea�0& ^*[";2]$/��+).�\�� or �"?1-@� ��' �/eT;+:AC].9I%� For i�V%Q�Ha�<:�P_A,� �i�d�2�= bI} /x��q�rho ,9'6�1 \�>4 �9FO^@"J&_Nr�Fm�\FfJ8:L��Ad!Y.(M ��-�P- �in ]aE�preF�0_%�*=$,��� b$F7Z�2 F %5�)^{S��/- F� M�-�abs+} I%4 easyA��Q �� � �s14�rh&�']f�4abs�mTc�Eb�p�#$P_\xiA{�$ �XYfaithfulVX�%A�. So,�N02egb�&#es�;E��mM�Y B��遐b��#",�cz 6�, ,%� ex�.!~}�� e�@&�(�,sp�.s ord�+y�� `e�.�Bil95} P��3.10, �# 49):�!�T*$ACz�E$:��r�ist $B,C��F$=i $A\vartrix  B+)et C$ ($.Er�Pc &])IX$Q(C)���]w~,I�"(A)�+I(B�y�|�objects!�O%DzCol�5��T orig�^�3e<always� �\%���5�)w"� 5��.[#a& veni�bHWeaJ�e�freedom;KA anc^�;K ��tn�/$� A�qe;]�!B� �+M��BM ��� a! and/or mouma ��3cLebesqueG�}>N �o� �<$.} �sr�� ��� A� ~� ,>jQ)$�y�Q�60+� � � E�} �5!�in*4$�5�dfn�!z��6Z�I})ҁ���B�� \ll Q&� N� ��-����n�5"g �6O&B}�8lg)�Tga�6ed} M_1 calL(H_1).�F#2; 2F3:="U, 2�,Q .\ h� ���M_3o� �):M� �G2�K"��S97 �� -N-� Ous�)-> -I#)nJG2= \,`m ^* [a�f]� 1R/*bf���%% I2'"�/_� ��2�&,�N #a-^!r8 Uwf��!},; E  by�(���a� \o�$��ˬ� �)�B^ :?"y%A("�M_15��Vic; sɸ.��>e�uniqu�"{m[��%�elmfQ \Proofb2�,byL0roxpb��$f���f&�n%t�U?�A\leq 0I{!�}+9�} a y& f}_{q]}$;!zd p7�6�)K. �A.� �:�l)�'1�b��w!�HK �rac�9�zߤj'f�ɼset3B] �4D5} \pi�I2�a�s� ��N�j� U) f� &�{if }6�M n= f \}>0�\tildb: \)�ecauv2))�,elz+8�� �=0� )Q ٧By eqs.\� i:)--� 5�D��?^�int-M� >��.���V��T�M��"�D� s l$�by Ozawa���&"�3p"a@�""B�G.PMA��jG5aqG5bQHV5Zsm�"�#�.�Iuse�t/2�/�>i�'�a"��a�b5 H �5� bove��H�� 8��&s ap.) �q -�)6X>$\{>��.�� �/ �$��t0�)��'mea�%J2!2f�  $^:�g  ��#isAsu�� Jequ.�),7)!f1z#�U'� *_TP&AV ;)�9�e.�+��a�J$9 � 1)*� �bstit qbyR &w*y�5; k�ilG B;Bjis quo�MH"_ �&>�en� iSa�=' �she �C�  w@�oQ io�2V!2&�6�BbKs.}�l� �H�"BC leDr-~�.eK.x�aw�2i(\alpha�<�B*#,i''qyP``*Dial'')�p$ =�"�@ some�e�aceD!D�*usi43i6�Oy2rmi�:ex�~!�X��xo2 ���cAa��$�}R%�I�%F�=���5%�O.�ucomUc�`A�ory�.�!A�;*U�a messag� l�&L�a/��: 1]�nmita5b�co�ljIr )@�I$!���a'�'qG rrup M�n�; �;qV5H:�w rece�3 at/p:Q ��d� ��$�P< 0sJ�O �pOt�Y,�1j,*�Npa%^ Mr( ���-�."� �'!�.ْ{�os� +ua��-�_ y�  up. Fޡ�lld� f�s�(A�A,\nu)$;%�A�L��be5cVTn)O��n%�� �� rmd �!7!���\nuC r��q(E d1i�#p*�.�@ g,�x $\nu��� �I;\Or9>/N- wG�U�nA>:��6�e�1e~bc ap�k� ta�=aKt_AZ -6 -D7>wr�A 1I1h�72i>?9�O 1):�B�CZl�&8 &� b�l-sA)qͨy�e�^�r�w�mi,�* a�6Dr>pV}�~(s�6�Mm$a�E$ MJQr x�,��2" � ingu6Vn�Gnu�|�Lfo�~� �<�1�s.D4RU%�m�9notc$aS!�domQ�#� .>�i�)� $�<� 9�$��!��G:/!o"}�+Jͭp�|�c_��*4U�� I$*H&1n"Lof6O}*+Qd! p�]&�Y ^�6�.A�"� �Cing�b�� n_L8a�Mœ��iesV��B\>alA>�� !�A|{\rmf|a� }(F|M := P:�}(F�� q(B� GX.g��N*}e�92�)23FB�2"?\9�mf��HA ���\,N)�>J,���} �c@�}.���sV�i!�ae�\�|й&=1��Js\m��� � )�ni,)�^.�$�) �5�{�C�u\,:Y= tQ� nQ"鰱f, &�A�ZQ�iA�f}(B| ?�(=� �B ��M�+>!\%.'E�1 h �m) {I�&&�+FY �) � b1|!?Qd )}���.� f� �R ``f�# ''. �8�pp�*� �#t$f7t�.%l!Q � ���1���ba2;("� �����[� �^{)}a��� )f!�U],-�qIf�!4uc=���%� i)\,&:B]B�l�l!z���� "�� *�"wo � _ �e� Z fyq2 /� �m9e�piB�M;u�$ "z!!3<1*��N�R.6� $F=�$,-"� "C ��Kne IQb�#� mi YKi�#�� r�a��rm4C�\\% :�1&=%:1;�U !.�)�q�~c-�5��� \ �Ѽ��-� U��� ��� t_{A����/* T��'5%.f:bm2�%6� t � V " a�Ol5�� )% J.z"�Zs�/ m, J� A�!�f�GQ*#Z)d"� -9� sure�KY5�$ ,f�\� ':kQG$ $�%t 8:v =� ) .}B`�g�; "Ÿ�&�l�3 / J�;,�Q�@"�� )� �seF�%v��} &��M_0�%LRSU� ,%:�&i\2�&j&�i8�MY%"�%�:�in2 w�A!�6�1&��^M_x= r0 6�1=5@�2�;4&�!F��I;eG:Y "B |2"�.�1&���' dots*L&Z1}�V{5:�5B��{��>� G$m 6u��.B�/e��+ $V�b8Y�%g��D��)�.1aHkerscr�C��9!�u�o �a �m�y�q+/an��J"<��i^A( :=\{6� �*"�\݌>0F:) ( 1=\{�"> 6���2���its&>��6�l )��&�]"2F#�feF"' %i��e C;di>Lng it&i�ty!kD��*� J��}�n^�023.�!��n)R1="�Pq�"^*�J'BH J�|!,6�w]5ۤ=qB]^ $defsigmaf}�H^�Af� �[I$E� i]= >�� �[B�*�Bzn� 2� � �:J� whos eta�0rF�1��&�V��fF�e :�a9&\)�D3 D r� V>2> \{ e�"[%H �2\.� |�iR�F���� V�� :� 5a:;Lno�X1�uhM�CA�>z �\��q@�i]= (f>(1bNn\ݺbreak�v�{>�E>�r��^*&�b�C }\no O�3�$\chi$-_�I.} we~ �e�n��m�qCJ1Q��ften �ae&SW chi�y}�7bF L ��9A�i} ����� .&'L�! !)|QdiF� In g|R�&o�y"sBKB,P�Mv"$\betd* �Q(�EC�2�n@�-2?#`�p6�md2h,nais�B�1^ /1RB P-M���Mq(W �|�3&J D BD=� uz� +*���6$Be-ul�� �)$��elf, z �!d�\ 2--4d Ra(&re&�S�h&^�eq!Gof .� �Bbv�:",N��)<� |�n� bNaltch/chA�-�=5� O- Nb�� .�F� � .y��>�"��>n#�i2X!6�ie'� �J� :*\bullet� �%Ff�{�&} x�&�* $L5��� X.J"�c* �6��0�big��� �rN� �Q@� n>l �m���*!��R��->���!,.��6q >RuJ "�1 �:  ���]q1!�F�A��]4ea$ls��6Z�" 2� ),s4g-mi���m�>�>.}� N�9�E��' erty e cqS2s#%�>@0uA�l�c���ro�& � !� aDw*� 6�!�;geoat :�FQ2V }�SB�� ��%r&�JA��|� &��� 1@Ka�%�<T\�n.�2 �a�e:�=o�Z! &0Opar &=&� the &upu"Cu>6 UT\9$*L(Hi�u��#{*� *��J�-V2JS f^{0"�K!!fNSf^�Kͬ�U����|� k;mf)=: Iv!�!w�, ;�B"� &3Th7�<igp6'�c�&3D^B3Z�2.?Z�2J?�V��4� �K�f^ ]�f^�NK &3:e>,>� >� " &:�O2�!�\2� ��M=8 =�)�!�f�p-~lJ�))= �BX����\, ��eq妥 . %�\�?2V?�O��ZhB��h%~+BrIdevd]�l�]�P�P�S hain�g&� ��c6��L&qP%�^{0V5fL ="LOC>Uf^+><>;R�!�+3{� (�J�>A{jB~�oa���n�Fy���g9�w��&D C ``tr�� te''6�F�>�JQ�"�D.�CZ�>j>�a"�}5'�Ridt�h�f� +� \�8�H �� j��:� Q�R�B}2� �� ���z�5\B�q�A:< Schumacher-West}land-}�&:y.�9H�u} Uhl\-n*w(x=3reJ3Uhh[) .� &�"� i)e@�8�U&xvQG&�.n�� \geq;2��- C]|NJ5i^1])�oB�a0*�7&� )�!� �9 b��euk5$mk!��$]�� i\}!�s fZF&J��ZB�"I�,Gg"�z$=waG%���+c"_xA{B�x� wa-�ri���iN?*}:�ZZ as�g�mt , �ann�. Rough� *�6!�) say�:P w.� `1* A'��2�z ��9�T,�pAa�&S .eաed�U2�H5�~a�4R��;1C.5%��8IkW} �zb�lso!Ugi]sk_��5nL1\6-�-urb�J�de-offmaj�M��paO�I D'A0ł�3-X�lq�%�%aQZ7fg$�F7. >, X>��9�vw2e�N8�9A�l�cb�%���xEB�Y��!K } orL-۷�72f-v�� �; ���*y�*t iZuF������A!1,�� �T-�-mk�8d�I�� w��"�*�.,<EW�8�.*F}0 fa�a͝��E�Lq�:� ,-��v�FonB�D�q our �"WBT_a &\m8*�dB���a=discu�4&��I�O~B&��:;��) �� �vV� rewr�7%�anT�i�q�(�*e�is&��JOme�9b�BL1�GaG1�j� �nL B�>�A���.} By$$�a�1�KX�� F�]) �I!�9{��>� J �P2��2.�Z=� ~ �R IM" �:�B� lb��� ,\Omega P_\rm�f(\rmd \omega)\, \chi\big\{P_{\rmi|\rmf}(\bullet| *,\rho!f}^  ( @} \geq PL},\eta:7�\}, \end{equation} which says that the classical inform+4 extracted in '8measurement pluAe$n quantum .? left:ta posteriori states is greater� b H JH �F-.�a p.U. All�other in�lities �Lcan be obtained from2final �d are also consequences of QTy (\ref{lb}) and ident i 4idts}). \subec!��{The generalized Groenewold-Lindbla!s �Ly.} Given an instru%�0$\mathcal{I}$�a� isti!�$operator $A$, ? teresting)l ity,M-called%\emph{N��thiE_ noth�buI��$entropy of�pre2TE� min.�4E�J� . ItA�aaa(`!-a puriA7dor loss, if negative) in pa�ngY�V�to �osB BeE�$t gives no2Yoit abil�-.^inM�fy�e�6- %-,Eicisa8m` in $E$c$. By usM$expression~a $�"$-%���xermay-�a�� mean , as!Aix0altchi}), oneE�see�dt, whenF�]�A�Hi)< +\infty, \qquad>�rmB� EE��� $E�I�U>�BUSWW})!Gequival�rtoB� \label{IqA}2{i6��5 )��7���l ,;E_\calI\} + �Aa�rmie� \alph�� Ba��� ! 6o.>�Her!�ema��@$�A���d $F�\}$ hasA�bDought!�,any demixtureqV� ay.���onpA E�Enu6ti�s�pia�.��� conjecu4d \cite{Gro71}E��� Lin72}7 prov�]�yJ| |non� for����m�hvon Neumann-L\"uders type. �g case�$ been sett��0down by Ozawaa�! �Oza86:�� llowm�ore!7%Fa $AB H_1= 02$. A shorter�8of with respect!�{'se�is based��A�u�ym�M�) )U(BarL04pr}. qthe�}m,TheoOza} Let�Za� ,\, �EK�wo separable complex Hilbert spaces, $( \Omega,<F);a �+:*%�% I$ a N telyUH.��� Defini O��(dfn}. Then,�descrip),} \item[(a)]%|4Nsendsa$�|}putm~,into almost ���aCJ� o���zonly if [(b)]�߁et:��t0$,I�ll>�s e�$%�C$�O+<��$�S6 � 1� \PrAfL(b) $\Rightarrow$ (a�P trivial: ! a)��.9)��d9� and you gEN@displaystyle 0\le�Y-��;A-I\}= F��@  �",�Vf� ) \� Fj)=0 \�� P�0f\text{-a.s.}NHBo��E $ B$= Ta*e%I:[4b), we take a ^�)VZ%rs;!cn, by !�o !u  $�( f}^{�c}1$� M!�a�}\{86���z }=0$x eq.\� �]��sO� K1�I�S(� !�}|%(i\otimes�5f) *0M�pA�  Compound�(and lower b�m[c$.} I��$hy83} Ohya!T,roduced a no����D[iTinvol !fi� touta-w of a՘,channel. Tak��inspir8 is$ �>6 �Ito��� som�z� � �0strengthen a ���)�r�$%�žScutaru. �Scu95�First�llA� need � new famil�of�B�%!,rel�@ships among them:��gan$} \epsilonE�IQ�:=&V A�"�rm] |� B�Q]�b?}, \\ ��Scu%��i � � Tr_{a H_2}A�b�\}� M�|E� i�j��99. �1��.�*�2�1a35-)� !6���!�&� j�=+)q� u��i(�0^� =%)�2�\} t&A��U� �I=s,"� >�Bl=�[b �:lf!� \tau )BxafAiiIi-| 0=KUQ� �2� 7>{=){� � gammi^IB�+2�%�qB!Q"� -� 1�B� =t%�>!�B�.e;n6f1 �� e���.)  i��d �\.Y�K� y[h similar� �A6�:d; a���  ̓�$Now, let u` ct a f��:don� M_{0123# >��� (of its marg�s�����O}��4aligned} &\Pi^ UA"{qE�I3m�,M�]�u�Uqd��\},&\� & \null  \\~}={Au u)\�8\},6_ m�!5= dU�U�a��i�m�13J=�A �8� z<5! g_2�2c�f�i�i�d �_i�<i\6��G2+Pi^3=�:t \�U"� YAFo�isi1�have $S(LIJ| }M  3})=qc F&�$e�RemarkI�r}E��"RieJ���� ,A! �1F�*q;s}837B� \\&2&F\)` U 9l] a�}��X �-mf�BE*A ��(a �n62\j"T � M �� �jc�� ��'sg . !us%5� a second>Ta� � �6 �6�{�7\G�_M��9K !�}�}, "�he�qa¹$=_�\� F��r\\��pA� P2}� �}= �I6�� ��>� å e:�a���:� ��� ��:/��#xi"�1 �F�2u%��Y�Ajfor� O"��9ց�C 23}�} \�.:�S()!=| ZH�� Z01210J2}2� \!r��2MRLB&Vkr& �N \�{�>�F�i,? I8\���� � :�A�q(B|YTQ�M�f)M9Y* IRpossiW�A3sH ,lu@byz � suit�G ��by &� idea��A�r�� 6� B*t��$Hall's upp�� ���"�T s.�<}*�Hal97} @ exhibits a trans&��9al ensem! �� POV%�q�[��way��L� ��RU . IC^ �'s:�, aS*��u)�� such a�"� analogou3�T�Wp2A �� 2 #$ strong� both�! Holevo�� � simplic�2, ssum�a�M�i�e.��yn bnvertaN� N\i# alS(�1""/+)<+T٭ ^{-1}\in ELKB�Ali!%"]!illRoves o�� m+A>�.J��us�B��M�(} M� E sqrt:�}\��.]^{1/2}2�,��GY[��]l ^* <fora"1�T59B� by *{ia�"})���!s $| $ satisfy" norm9"�J��d?B6\nu�g,.�d(=\openone\,B��|pooNm calJhs!?F|(5h>� oi�}�iE)9UNB_value� $(A,tA)$Y>Ji��co�ab� �a�ol�#itial �s&�Yu\} lassocia��.�iF� M�newE} �)N-� =FK5�^=�� <z&.�/2}�Q�>"J�wS!5+%��3�(JM�! S� &�,sec}. By loomat.(Ito[}), immed!_lyJ�Lambda� Ji���U� =5N e�^*�$ m�) F�>�!b^�ap=s���,:U \inA���$" ��M6a�#�\tilde+%rho�*b�%�  (\Tr& \{� B"� � )�9$2^*�s if }�~a X\} >0n �E�� �(1{9#)B{ �� =0)�) 5f�a.4&J�)���nJ�n��t�$%ߕr�� Io �\Ne�re: 5�!� �� qBM,newIq*+$rho�J� n$",rho"�'A!�\{J�'\}\�' 2��']�); 0>U%�F�B�RO�� ��.}%{ $\{\psi_k=$b!R c.o.n.s.\� (eigenvector- � 4 $, sc'at��write*" 4= \sum_k e_k | frangle� ||$,Ŕ $e_k>0$�$>=1$#!�2�abscont)�� showIC��c�"�"e?!l2v)�I� �r �Aabsolu�"pinu; �E&�#  2N =\Tr* Nr\�!)m e_m1 �m2� � �]��HRadon-Nikodim deriv<)+ � [k2[@:�A�/�2�$ exist%�!jb�yOinia�$rig} \sigmIFx�{!{kr} � e_ke_ra4><, \frac{��}�2�b J-�|>�"r ���B ;� an abbrev�udz weijp-!R&�i� 5NR ^� *��J�Now��id� -4,=��,�%6S���J$;,A�at�mgetFn} F�M� \.uQ+&�J���now&�z8A��s(pJ/�N�O� �$6"Y�"��#Z.� $)�J���AVe�H�� veF� jusB0 or!�to7Bi6�� Jk��F� 1� AN241A� easy�verify��is ��0n� �v=2&R�+BTh"w�)vF"��n dualE,QRl� >S9�\}0vI�. M�"�s(@1�|��F��iG e ``٭''!�C.�� $K($l19)���f )$i)z*0%,��A�discret� se�0us�*ii�fLS4b,KinR01,Rus02�$.�a$a�,}�u.} Hav���dF and�~�a }r�'f�2 /��& JB {d}.�\}� ��~5.c�'�4"�!b�4� ),� pi_{2- ()} � N}B�I*�"�%�B nQ%0)%A6y)� �tren�~more exp� S, �conveni�/��rt)�!|X a�/� wu(y- ich �� readFNm�nnnm�q*{ &� g�*v��/i�08&7$)�fy�q�pB�B�a)V�5 *�)��M�$2��L!)="D#"� ogeu'� ey� ), uT&2!�3FE���� =E�:�5V� ���!�)M�A�EIB�1�ew -�v��ilJ�V�,�&��B�V#2�5CfBE�0M/ caus�1.*� ). M+q{ly�:�E9�ne"q 5� K�${!Bl^� = \���'� S��r "u{A\S,i�}���A�":* )v(� �y(#ld >Z /uo�XN��3$J�U �p�+M�=���B��,?&.}�; �b�&s 25Fe�=[!v�?nk q k �f�(}Jr% \^�8 last�&)s��1'ly_ >E\)%D star���$the diagon&of @2��J���.�in{�u�8v.5.6 &��tC n�leN I$,�|f�&>�!whilec-� ��"�.V|,| �3nd� m.�v%-0 $. B��s2pE5� ��r�6.$ 2_ 8..�4�8409019 v1 3 Sep�.� il95 �A$BillingsleM1�=$%�MS}, Wiley.*199. D'A03 ` G.~M.~D'A� o�$m it{O"( Heisenberg@(nciple, nam�6!.�@,-disturbance�de-off�&3eAV@}, Fortschr.\ Phy� �\bf{51} (2003), 318--330;DDOI} 10.1002/prop.+ 10042� av76 �,E.~B.~Davies�q��r�(Open System)Aca�5c Px, LondA 1976=�DavL70Jl%�$J.~T.~LewiS�it{An�i�r approach��QQpy }, �V.\ MathF3L17} (1970), 239--260.� ix57 �(J.\ Dixmier= �Les Alg\`ebres d'Op\'erateurs dans l'Es�9�9Pien}, Gauthier-Villara�$aris, 1957��;��H.~J.~&�A�A�lem�R}T��by)B� Int.\ �%�F"4)!�!327AT8�� �M�W.~��Q0.��2cor�4��},Q�Rev.\ A %�A�5�097), 100--113>�bZ�U= Technique.��Q:���yMG���~ы, A.\ S�#�CA� .\ C %ͭ Plenum:� 7, 53--61.�ol7��A.~S.~ \=pSome g>m�D�amoun�6.��% mitt�& by aݒ����!�robl.\͍�& 1�9}b .~3 e]��0177--183 (Eng>yl.:�5f�wHolS0�w�%?4M.~E.~Shirokov�Cod>��Iz L& capa %oGE�$-dimen�al�!�F� 8176Ń0 Aug>�xM� C.~KAZA�!� B.\ Ruska.,C�Y��8s�B)&t�=��a�V� 42} �a�87--98F�004062]T@i��F=]A&&&�EZq<ݤ�:w :�28e�72�w45--249�Jac�pK.~JacobVE`x ffic�.w,�ifu�!}e��:Amutual.A��E�r d\bf{68} Art.\ No.\ 054302%\3)FT30603.�H4)TAc4=QO8%.};� �2�*F }�&* IEEE e�i�a��@y�IT-29%o8a�770--77.? OhyP9�U��D�etz���.� 4Its Use}, Spri�(, Berlin��9.��Aq� M.~O�AJ^)�aCprE ��&v observ��AyBk�:$84), 79--8.]Oza85a5�B� Con�&� d %a�>SJ"�  mea�ic�Pu�2R.I.M.� Kyoto Uni��E�bf{21)�5a�22� ���><Concept1)�expec, on2z tE(},�=� 1948--195./ �/ >�slA�]�6�um-��6� ^�!54� 86!�59--76.oq�� B�I.�-�-��� y: A qew�2�(E �H2G>�43���� 4358u 75FF20506.� Sak7�TS.~Sa6B0$C^*$-Algebra��$W.Z�7.RSchWW91�(B.~Schumach=M.~West| land�0W.~K.~Wootterd%�it{LimiIi� &u ac A,2in*� a1ned.�Let��fbf{76e'096), 3452--342�Sc~?)�H��?�fL&�@%�Jx}/Q >� �->��j9a-773�f.� YueY/RH.~P.~Yu &� �[.3i��*M���)��Mecal rigoqN phys�y*� ���AVaR� h ��C.� qb� 17--2.� YueO�p9 [JEUlt� 2carry� lAt!�-� s"�rE0IE3,63--366wth6k1 docu� #8%\h0,[aps,prl,pre�,t,groupedadd(]{revtex4} V:a:supernG >,%pac�G twocolumn�HR�arPb�\u�Hckage{Oicx,amsA� symb]A17} \newE�em�L(} `tleuse�$ algorithm� (diabatic evH&[Ku/"�Q. \w0or{Zhaohui We�M0 heng Ying)ffilil{l$e Key Labo�P�Intgv_ olog , DepartA9A�iwer Sci�QE�;(, Tsinghua ers!Q8 Beijing, China084�)Tabs1t�Q�Kr's=)i � rIimport�3q85Xs peros6 task�)�az@an unsorted datab�K�'outR. Recentc he a1� 9�U- /u� to desig�aX@R�inclu�FPn pap��we�( �,N �=7�]`�two pr+1�<�tvenA�alfUdoesn't .  Flya� J�4����$!|%6Q� on1I�3tud$bas"�=�sp� ng!R�t)a,affect�e runn$imJnEle�T r s doM. UA�-e)y`R we kX q�!7&G bA,�lo���beo,-�!( �* modi�2N� to m JZ� fa� . S[#�PmaG ppl�M �� �,u� . IqU�Ns ��5�� N i�a��#�!e�G�/ne�Ck8tem5�'a�"% � n� �'s�kA@w�6fi�ob�Qz $O(\\6N}�5tep�stead 6O(N)$*�8". Whe�1B`wasa� pose=$w^(mpl� )wan&�&}X!m8unitary logic g`�ch!regard6&�QA�dard �P digmaW._� . +s9�)���<�_�9AyJ@A��M:FGGS00}"W ���d�q!,aO%�VF1a�be :#�J�1�'� s riseaD[d�L c sp Lup�+QyU �RC�'InN$����;l�B�J9"TP, 2SA��*��Pnumber!�marQ�s ͕��u3� we don't Gany fura7.n ��m[. Howev��A���Ayb�? �u�2~P!��e��],+n�@k�`perhaps!�u!��)2y o help )NNBe�AD UifP�z�.�4���m�m �]to����� an��e ert� Y�FSaD(!LaluhB+��$. W�* n adEF!� !�AG�0 �~s �s 2s���u�NR ^R�4 �4�n��4R�1�'t AP.�Rb� ,briefly depi|V�t� a�f�b�7c]85�e l�^ )�g (see.W'0details). Sup�0 "vH�aU&S=� $H(t�%ᆡ� te $Y2(t)L3E�Q���&`i���. �Un0 � F�_A $H(0�S�D.� k@Des slowly enough (�!�.�mp7T��T��@very li�X) ��Gwe��#y clo�X�5� � tane�>�@.Rat ea�� t. ��* s-�$H_�5H_mN5I-.AA i@.�$ ���S? �AR,Zby�D f&yY�R : $$ AL=(1-s)H_0+sH_m, $$ w�' s=s(M/a monoK c fun�`Ip $s(0HV$� $s(T)�6B&$|E_0,tQX"1�[Q(!�te(��Mex��T1�6�It�Bb* $E_0�Aj $E_1 mc�"i �7alu�AB8?y�Q�01$$|'5E_0;Ti=Tq=|^{2}�*1-\var�O ^2$$� vit ��JV*f�5HD_{max}}{g_{min}^2}�+L,�W�W` \ll1J�.> $ I$A(!U��$,Q.�����_�yF� N� ��$� n d� n TMEu�{J�m$. I� ED�.  care)*y, af�� ��"T w�JJpI "�a�\deJb�el��E�� isE>ne�E�l*��\ z,is $$T\simeq)�\pi}{2}�}1�A�:� A�>� i�ntr.,to&g&�s5�F� . � a� abov�M��� n�Y�gp&�%.*e"�&�:!}>9_ � 2r i�r�ourB� . U\Hurs<ult>�(h`�!A (� "�"? Y�F* ��] k�* (%8Fy�q?��M&a E6!=R�a_xu�, ��$ \ 0�$, $3� � 1T����6���Q�+� ��!�G 8!�5 !; chec�D �5J�A�$� �M�X pmatrix} %&,(s-1)-s+1 & �12�.XZ& ( �)++1W & I�Rendm!n�(!�emptyZIE� ��aKzeroes�SaM� �R�ep denoW?em� $\l�G i$,$M�� NwS $1YJ2}-UV2�}1-4�s( �$@2.@+�@A�Ci=1�dFmSo�s� a�1�B�AIOe�� h�!It tur?�at@�yw  eam_$A�� ��DE� M� '� ;2� e6=I o�e9lX %� s:� =| $ |:� i�|-u�  m|)2�|�1!(Accort���5 � mN@d ��d� � c�� :�� ds� u*� -g^2(s)}{� 5� >%�T*� o H�RE1��� NOav�$�!�.�=.� �(`&X [F]!O(By integralq�~ ( whol*�  yZ�2��\2�}\arctan �:��8:$��ll1�A�mm� XTaa�Nle�B!o�e ��@.!. \hf@$\Box$ ��:2jis�L� ��qd< ::`$a_x,x=1,\dots,N,x\neq m$"�tr38think �t��y�rq�5��"�.9 FQ ,��6�2� accu� 6�M 2r!�disf?ed. F� more�67ofJ�HA5l�R *I�6.�NA$ % re} �K deal- !�Q ( �1�:N . Ab��9n�/eJ A�KLi=fEA"8S �� � a"� ~� B.�!� gN( (�R��6 $$P(m�KA_i)=p_iE�0�su&�i�k}p�����ka\W,  ${A_iO�#�y1��F$\{U�\}$, �� cup_e A_i=2%T, \ A_a\cap A_b=\phi,\ � a< b� �cim�!�t#6hMbA)�55� 6���{�I�� n_M}{p_M}��GF5�jZ n_i"Y &��� $A& b  $M-�Jx�,~v��*#�s&.� $�W�D mean6�mJ(id"Sis lesMa�If oriOc ��-L9.K7�u7Cco 0 $p_i/n_i\ll X 2KWku8 {.�ũ�is�   noti�7�>� N k/#!3��&4%ka8�/A��!�址averagqin dy1�a:� I]�Q]x)�S� 1��A�b*K%�o��ua�!9!�6�-�5���$$T_{+}�y�� ��Q�iA�i���$@Cauchy-Schwartz I$.�$.W !/vU �e� xFU �N}]!���?appear (:I�  si"�%.�u B,f� �'F��� �. holdsA�f �if 2CI!��or "1>�B��we���|?��ZuMe e�&!�͗ 2" 5 ��co�L�QI��m�� �=n?W�ge{a .�� it�()%.qW]��r!�:�)Ja�a���i ["�!�#U'�$N�two � s $Agٕ /2-1!�$AC {N/2� �J� $p_1=0.8Ip_2=0.2$�+2ivi�&f�$a2�b&T2A�� 20���)V �\f�y5�� ��A=`)�%� qZ.e&�e5��*Ah�ter. F�Jy we �#�m "?� Zn .\50"�e�uJO$%�a-�&G&�# t{ EE w+i:{t �*&� . Be�"o��-a�2 "� at" m��9�)n'�!1�3�aio�|�:SuM $H_1�E�H_�&�*c�wo���WT_1M�T_2E2�2TE�� t=c�� $ss��� �N*�c}T_1* c>0B�2�W���x �!6multipl�n* fn*,A��V x2g��y&� s�]�} same�*��ui"�2.�8 8~�"F�#��9�"i.�a� Y���Uea�Qd��Oy�X2�+=G6� e%��jHN�*F� . So����H give�� o`i�!sfu~{�'use*�%&Xto� D/��a�s$nsurpri�O�k^�$.XB9@��$I�-N��P!EUDRbexK e�D .�if �� &�a�q".�sVxs� H_0}N}I-\� N}|:�$�"N8Foa�!�2'mOtoa�� ^�   :Y-�con05>B�w AG�ei YJ� i�oeq36Q"5� T"O"+� �"on�J�S.K1�M3"ZXE>� �a�N+ *h!}�. More�ca�:�.�}9mb��d.U�B�/��see�2a�mS*� mGQ6�&oF���Su�:2nL2circui�neC,KJ9 s��al novel?5�s��,���, i|FGG�i? TDK01�S�{t:�6{.�I&8/L. K.�mC�>]"(t 79, 325(1iC I?- E. Farhi4< G! tEgS. Gut��M. Sips�+e-7 �iI01106._;#J. *]#N.c#2�,A 65, 042308�@2>�01� et al.J�104129.�)R, T. D. Kieu,N7 1013��>t �&�6 �Y:^7&�708*h7floatfix**8NX7}2epsfig6y76V(�74def\one{\hbox{�VA� $\hs�F<{-0.3cm}{\em 1}} 0.25cm}} Atwo�A2bAhre��3NC!ee!e>iii>tCM sth>j8\sm'B? p}{\�al9�bxt\bf x>[br.rBy.yB�]B� eps}27�9�k.]kB]o.0Bq.qB!\K�pBu.>u>egy}[1]{� �� }#1e�a�b�-}�%� \�4Oa��( XX spW%h�4WE(ergy curren�9\�:(V. Eisler$^� foot�{e@�(l.elte.hu}}()DZ. Zimbor\'as$^{2,:8cimbi@rmki.kfki 6!.�:${}^1$�N itut�r� ԋT=8ics, E\"otv\"os�Bers�:X1117 Budapest, P\'azm\'2s\'et 81/a, Hungary\\ u 2$Re 6~PpRcle` Nuclear � P.O;Q,x 49, H-1525� e�(date{\today"�<a"8;W� E+w<,f t8 !�)�� d�x;ƍto"ry�)��cgy� V_m  bloc];($L$ neighbo A1s,; cribeE.g�5=m ?ERxw % ��(med. R�;"�iDpreveal�79 Kr@I� XX�su qs?er� uctiv�� sup�}"�2ph2> L~s -Sachdev�7af�*]8�9i"�>resourc��M���7*�5-�Dng oqa}."�Taui9!:fe��excel@]]or� frameworkZinv�'ga�8.-=�, s�S xWpleiYs� s�Vf. alyti\,�#S7P+so(fe' K%�, t"�N[`mot�fed�to ��1.�i&u^ �:&�:0o��Y�.ar��o�wo wid��?methodaMchaޓri;> 2/Ax�-sa�e��s�- cribe�e6m�0|G�a�e!�ful���tr�qto u���f>�%TumF�|e5.Pi� manifesHmse��l �of gap��3e�siAc� mpanW�l�H�haD VTl Ak"v�IIT!�n��UB2�A+�.I�qdVA U�zerieǭ��*X�&- �� natu�syʹsm\Vidal ���}UI} "�)�J[��ae� 7l��on6Q����d�I�(-�)2�sE�CN^Gy�.G��,3�non�e!s i�C���v�5E�s2F�>�  ? argu!9o�! thir���B�*Rrge�#l�Hco�Yl fiel!.�X��A�z<�['?Ee�끎r-� '0cXX �A;��m��T%m�`g��>�B"w�;cpar S�deJCx�Mo'9model��+�noilibrium�"jF!�U� . On"<_l1�atry(sE%Z* ��XfE�JcEz{�4gy or magnetize�-1tiwc,xxw�s��"C�݁�t%�t_a�w d3ic��S .E]pc i*� I� S�b� &+A��nN4I�1-"�J9 .�P�ABF�A) �%o)t!S2��e�2�e)��tI�V&@G4G �HA���!�o. �W 2�;(I�`.� ��a "> ! �ig�Uz�e�nI mai( !*8  asympt�1!-�;�7���.~ ��FA(� ϛ1/3!�2/3>� r a hig�l�D�2�ѧ�J�W� &E aH ��}��U� E�2�n symme�)��%��enh�ld �f.Jp�7����( }.,?the vic�%�Iq& poia�I�_opy��edisplay �typ��-�&,scaling. % \X 2�� �})�r$"�*cthr���!�*l:B,egy{H^{XX}=-�(l_{l=1}^N{(s_l^x s_{l+1}^x + yy)}- h�s5"z},��0$s^/ _l ( =x,y,z*IPaulie  1 }at si�$l=1,""$!�a�iod���?nd $h�' �<c��. Our aiE��q�%a� �}�O`r-�b� mwZ�\6�n�/�!it� �D!� ��SA /#'xuE&�.� tinu� �&V26M&��"> b�Şi2 toF]6�U �(split} J^E=x~sI [ %�(A-1}^y  E#- Y7yE3 & + h :R y -MYS x) ]E�nd �AJI&� a2�Q/st- ɉaX���fQ "�H��)-W"���=BLagO m� �lI3$� d"/f)ay["�)VdE=ih- P J^E.�a�. !�$H^E$NA�ide�'U1��� sVI�2 >a�$�^O4 tem͠ure�I�$\�z[ � ,J^E�z]=�<? �.� �u�%i �I �:0 �� LSMc-�� c�@X l e1� *,of free fermQ ��{5y s�%rumU��|lluD Areg!�� "y<0unp*? � wavelՖs $k_h=�2sin(h�/��k_m> cos( V}�iBN-�� -�eC"�C!�h�% *mZ-O�85Kdm_ty $j^E=d5J^E/N �!�2�ph"aramon Fig.�nfig:phd}��o�����,figure}[thb]�mLR�4@phics[width=0.7\cYU,� =270]{�d.ps} �/� {P2�-"h( :f  $h-j��pla�!�/ !l� e�yk7(F!a��-v�flu�/I�� UzA�2icM�k�Sh K�0black�"� a rq\���} Sp1�1-}��T( 4e5I&���. k uish�3IYAF��\h 0,Ae�+)�1.c��!xa��UE�o&te�� Bis�; �j9�6�, $M^z Cnon�r.�e � �E v Vv�m��}_=0$� ou�+'�e. �9lin�Q$!C�� |�?%D(�Z�I$)% >Z 2�1"a I�Z�!5�a �le �YE�Kn�t� �+wmaxim�-�é�in �-�%=:�C�aloUhee8#F thrmst.-3h$`s!�usŭJ$h�;b�� �e�r� �s m� . D�KAP�a�U�< �e�<x�"�if  E�.i�*g� s:  Trp e:?�)-- � e��aa ��.���i�'�W$�, . F"NJBennettR� }" .'+Ő�f.Q.�'"�xs!� S_L=-�rm{tr};� _L\l�ho_L)*� ��)d�Kv> �pLU3tr}_{N-Lc� si_g����\ |$ a�Y)Ci�b5eB)�a���| < Q$@���rac��exter�1��e4 dom� I)�c���Ij!B�� a�M�pk�&t .succesG�,�r N��� ���T!2M !ك� s $c_lp ^\dag�D&�Jordan-W-�r�t   . Nob/D du?5��non���Sc �(P��g� o���2ead5�Majorana#mw��earli� N')2��ur .�r�<lyaR�F.B� �X two-r2� B � c_m%V c_a  =G_{mn}$;�SFb� U�E-�Wick'n eu:R"q@$G$tz% e�G"oBbic<} g_0 & g_1 & \c�<${N-1}\\ g_1�( & \v$JB YB\d.g_{1-N:V g_0��:co"z s $gA��1 f��*{�(N \to�~fty)$ �mf @*�g_l&�>2 ;6�~{- ^L6�� d��,eta e^{-il\t }u6 1 2�B ft(\�?� & {|6 |}+1b�.�$6&"H *�Q� p"e ous �yihI�a��b> �K6� .T uno4O yzY ���3**�.X�H�+�6 $S_L@��a�<^�s�]�+evFRf54A�5row3!��na�r�2�ALo�h�,d'] beh�0e w�f� W.� i $G���w$"�G_L�:L�:a:L�:&� rs5�r�]%�Vd�c$*8-e %��%%.&MX��-�ы)�)��Iu��RrB � ]�)�!�.� |.4- $Ua� m�{SU}(L)$% ote Li2[ 4ib� s � io[aEy�Em�� �ŻmsT�eO s yՓ $b_m;n=�O,L}U_{nm}c_n$&ch��w.��$\�!t�{<{G}_L =U^+ G_L U"����_1?L��QJ��thu"� ! b_m b_n� =0,\��E bŜ6$�,ltaţ{m���{i�6 =2�K�Mun1�ed��AV�QF��ten as�Ao%i����zL=1�� UCy �- m�nQPs�mix.�T� $n$. H�&#Q��%] �H@suM:!sVN�S$ \�EHL�. -�n- &!_n)6Q]eq:�*� �y!"� a&�#IpH��x|Eq. ( H)i[* �� rQ6"'%ly,�# �A�on�| 5$L�~U�L$u���z6�[6���L@$2^C 2^L$�ZBG 1� it&%Ius �2�ab-� �*�'van{s. Swi�ng �D-�E�se0 B�W2W&�Summari�y� ͤ��+ludA:!�i� !���&D �may����  rapid�)�:�#�# "�#)FJBIYN�� !�B� (�R��"E � � RQ� + S_���eq:slw ��$R$A�!�&�I*����.$S{`KN2D<m�ZA���e4 d.�j$LTA�#.��E"�a @+�N�(�� Mezzadri��e��b ) A ratic.^��a�B0"&�~� AToe�!zq$��&'&{ 1. �"�! q o"X !8lsoB`, 0A5?#� �YU�break�e��-Q "�%,M�aq�#K�� N�&thele�p" B�d93V $%�*-'A�m&� slI��/u#�=o KH8*EN� h1�m��nexqElea\SermQs��v1Ji-in a vc+mm��.>a. Altѽ�1)^7C0] ur# l���2i��4aW�/m�&�oL�'��o�pk2)p shif%�!y�!�ber�>$�Rphi$ -��e.�� &6K $V� V� J�͋ $V6�(1,e^{i �} 2�,�(N-1)Y 2#t!�6��C XLle�� &�D"8 Z� � ��V=Y(n.5an�2DZif�'� ��+���� 2�I~�� rval�vacMs�Is  t�I+]U� 6q �  �ve!�al �!�aI� V��\pi 4$U�z��9�.��%�A�%(�#�}kɈ��ved &* 0=n\"�&array}{�<�� �ln< {tX-x^{-2})(2.-1)}+C"� \, 5� k_h� �,�.�?S�<%a�re $C=1+d� E-6I� 2�R�(s%W~ !� Eule~P #$D�4 $I\l(x 0.0221603 U��2 valuݣA�8W!�!��o��4}r 8�/i  q( ��"aY+r8p�Cm !�(�cal{L}+C"�^" x =HN3L8P�">B� >F>�.M�=�el? �2� enteJ...�&�"� %cA"L.icD t t< �� &F&!�.o?-tEectly fiO28 ~ curv��eqA�� nea&�)&)�%Yi�2}}�iE��u �:C"n T "� ' \A����p,\ula&_S0 �sccA�a�n*��L}\gg 1$� ��%ht��%1�6�%N�o�(��!/�"��$h� ��%N R��6� "=%�Y�eE� .H YS���W%��/FdGIW)II!�.�/ �=1L {2}$�ninset�:*$, TJsb�ar"�Zo6~&1��SqJ9 a�5�� >� I�t� Qi9th�ly�5y� d; h w~Lv� nly a�����R.��e�R&?�?��oach> A A{F�V*�u�b�0$ or�Q��,&" �7AOe1B@j;a����-/<ng�)?&�V .! :�-�M�: 'y<�����weIB��u�rc��6`�*� n L$*$ �I��Jompens宥��vga�P&�8ic1'%n)D��.$F_ 2�2$Ob�syO�3a f)$L�%=f>gB urhood araE�� �;I s"r� . b�Ud�!"W U"� �v� �seeDKkS @B�<"X� L ���k would likE�*? � b��|qP��t�7J�$Mt��'�$a��s@�,�BA�  e, or alm%!� ly a+��-a� ber �fach �)m8Kk%��1it6��� � 2�E�.�� !�&� �<''D�a���inp�zA���&�;c6� *�o[SP5� 3-y.��� � �q)b� !u:f S_L(k_h,k��<)=S_L^c+S(L|k_h-|2�"%b �W ��1a�:@�&%�e{A�Cpor��@H!>"�62A e#RB "�a�A�/Ad2q^U!J . SQZ,)�%:�s)w�̭�h�;�7�is!5id���n ^$�. �� V� 6b�/�%X6� S28�!�!�1�6��.� :0�UVR�oudH� rom� F6h)axplad a�sI4�!��ble $E�Y�_!z � Q�nor�� �A{^�D =300n $600Gnk 4!�.��I:E (�3 C0.7$)) p� �3� uB�6� �%�ړ *�9 Finaa/Zs�WS�<&e anal���k)�.,|3g�!9�h !2C0��!�I >�� !a�m���`��:,�1V�. �oa&Wo@�J �!.N *{Acrb ledg�/e1%SWe �q thankdNR\'aczA� sti�!�{3cuN�%�isiHay�rx_2�BOTKA Gra�=0No. T043159,  734�S044839{KA">�S {0} �b�d&vJ,M. Tinkham, �[.qKa�Sr��Ju�J}, 2nd K6(McGraw��l:��6)� b p�JU pQ�hPh/��c 0s} (Cambridge*IO;�, U.K.Ğ6u�J�A. Niels�&nd I.�UChuang6�Ϙ>$�}�C.�} n� N�06�z1}�Oz� loh,�4Amico, G. Falc��R zio, N�F e (L6�) �Q$416}, 608 �U%9�g2�U J. Osborn� M.|-6GV W6V032110NYKiSI} G. uG�V!W>re,WRicW6A7V0,��&XW. �90AU279&H� J.bPu1�Inf�C!�. �4}, 4)46{� B. Q. Ji)�VR. �Stat.NQ �1%k79%:VUJ} M!�nno`B. Haege�WEKM�Y sony%XMw�._ 44}, 6005`3:��!P..� F. �,M�.F^ 252}, 543^:�K! �Salerno6")�(71}, 012301S56�SFEzAntal,�a�,L. Sasv\'ari2]Let1� 78}, 167 vY]�� T.B^,An��ko��G.sYch\"utz,"�9:�SM�E �57!/18486�m> E. Lieb,�Schultz�D%~t\+�RAnn1�(N.Y.)} b1��61) 4032/"�5C. H. , JrnsteD�S.!� escu�B.�m���A��bf 53ak046ש��>1 d"ۑ �P�@� % 1 juli��4�� �*H�(style[11pt,Z,��]{�~ cle}&� 3a��two�$,fleqn,mon2I@% b�te: bei *.s�u tehtze�R *nach*߷t� !!!ёop��$=-1cm \oddw 0 text`==16hU t=24+[(sep=2.2ex !g ��do %  ESSW�K�8%� 2OZ! -Boh���6Mqeh}{q,�lib]Khyp�sib>._qm1m"r� �hMh�+y�:%:" YWh�G[f�"y�K�� ! ian?�>j"NYOl�( Passon\\ Z�0H(stitut f\"u�Sgewandte�Z8k\\ Forschungsz8$um J\"ulic�52425,, Germany\\ �Bl: O. w@fz-jue7 .de ���%�&QVj �1�a�} T� 8 collects,� v���5 mmon/*ism2�a �' Oc� 's razor,}�J� 1� ``s�=al�$�ory''�s��O�/53� I\�� �� r�%vi��q�*�n|& g�?0["�!\�L:P% t� ttՏpr�� a ���Wdis�g�y�� L ligh�?ata(�Os�U�fK9� �sol|�f�h3��ir empi�onfirX4?*0H9�,b ��2� %\tof�Me- %\pa��eak r�nt0em � skip1.5ex(�0 minu b{YIn�JJ �6 -how_to�>^%�40/A\ !��L :"bP.UE��=A�"IT���@�X,Xԇ� .Z�T-]E�&:F�$(peculiar feC E�Q�"�Y$. Of cours�Ti�dx!T2,�as�� amb�u�2an��8E�y �doQ�cl6L ts ҚXfty4ordin�ua�*���" rpre�U5��5-.!��$�� y�� ��`on.}rafR.c!��g answqC2#�e%�he �� shO)08/r_' ongo!deb�?oe��A�;J�p=6edFst-!�&�schoolA �t=.s. P�m*4�R m�>!yof�i�lA� �A%Pcom�� �"�yecAP ��whidden"�@s, EPR, Bell etc.�E&@@e�x�0\trik�ly �$ed(/David Mq?n:єquote} �ea[A>Tist�|iewo�e�i. T-P1.)�)R� ered0?EPRE��'s�8�>:2 (!�1F)>no<u�>� ʭinyF$(sub�.�2a.�R�">whFyZ �O��xHM;�� ei�%�ism�vir��(� Borny?o E�@iaPr8!�})@A�ss^^o-���un�b`nlse. )R2b�5L%E,���\p�. (%�l"�Q 8���# } Ev��fehtak���F�pin<salt,M*�b�1%,�� �E&d��� wA��3ed R�nd)Iin iaffai:�em!�!c-.ct. An� U7aso{�bea�3Viny��,�r\�e���U�4"�M!�c2or"���Z�s p�o����ept1*�!2��6 Thos��o%�1Qd)UA����@�(dard 91�n (e.g.2�-� love.(r who favor� non-P6�s I�!�-worlds,�8s�� histo�, FloydA�r :M��ai�"#'3 at��*�3%�. "���-%\rn!��7� nd.]�$�[a���evK>!�*�A�FM( popu���QZ��Zl�qmai�-e�nd � �6ca�!a�empt =#i�dAbi�m�� eller,cus�(_qm,holland�v��%6�O� � l43  e�me�, altc/s*b��re3 verify=<�;nase7p�� render��=��pE irr� ��nd��so��di��ZiK�W\�r��Lc�A��A�Boh� pY�P 1952. Wayne Myrvold<#o��n>O�Ey.8>,� �9�]0} : �z di�� meetI�!�t�p_y����%&m͛a�at� had hx�for�as!�"�, ignor�&�n�qs n�Mv��d,M�i�F�,�V�&,��}�r sA�,IChA� QfA�e�c��!2 . ��M In w�`�8��3a��2I�%k=�&;i"�oyllK !O 2rea5]A5ostile�Jr� �cinA!$3 Joseph KekI9I N��. publK7 �icsU�`Ixi��+N��)�QOo � *\�in1)>�Iik�}. Hep l�d3work ar  ``���dng  "� ''vF� }. �3* >�; �I�5e 'ڔ"C� h�Q� kT^ �{!�� te�sj a� @[!%pur� �Ws�T~��P�;��+� e�es �Ua-e}e�a��qs i.e.�)���eria ��'�^�A�- ���h͍ S�on~�@meta}�� devo�VSs��g�s} �%!��iŴseekseC� tex8 Sy-iCoa� ,�B�%�f�&|$�Mi�c�� abilg ��\�b2l��* � b_A�;2� � }. %2�p�ye �o6x overP �|� sop�0�6d%i� Ar &�a�!+Wl�<�� %touch@�A�,Qsn����6 a 8� !�9in�.)�(nut}. A thoe.�2�� � Ŏ"P$duerr,undieE(=&, $x*�= , $Q��--� �0�(��������e�ron��to7  E�)iL6~��E�ri0>��!�"�Schr\"ov�"qu�I, gui�<6�m1� vi6.so-$@ed.aA"eqn�4��)kgv$frac{dQ_i}��&�1Hm_i}\nabla_i S(Q_1,�L,Q_N)�-T$�$m� deno��mas�K5�$!�$X$!(h �H�0� !� co)'Way$S�T9?1�.rA�Xpo "hS%SI =Re^�3fshbar}S}$a�Si!A?!|%N�!��Rge�P,-rst-o�11r,�/-�9o�?X-z -�unV�ly.'��E=�z |^2$a�tribu� C۩Q�s Equ� ����>��l�ndihofYoQ�"� $ in terms Lof position distribu �s. Since all measurements can be expressed in terms .M0(e.g. pointerd,s) this amouM8to full accordaq withvpredic��< of ordinary quantum mechanics. Thereby the \dbb\ assigns a �4inguished rolew�land does not independently E,se�-values@Lother observables. T�en!+s that �\Kochen-Specker ``no-go'' orem}apply\7� . WGmight!u$regarded aae �of5�4 like spin, mo!�um or^$get establ) only%�$he context[< a corresponding.-Iexperib. Fromc view%�DS�\)�`` `uality''U!gntial9 �A ,9Xoutcome^an� )� s onwhway it is performed. As �ion!P bove/ �$reproducesJ� B�0theory provi!�5�ini�ACeeA�T particles described bI�wavefunE�8 $\psi$ are $| |^2$y�� The motiv% !eaXso-called \qeh\ has bee%)@lored for example!��\cite{dgz,valentini}. Most important!eUlq�alE/$inuity equ �8(Equ.~\ref{ce})>is6d%!�� consistent i.e. any system will stay $R if!�� olds1zlly. \begin{eqnarray} \label� \frac{\%�al ` }Dt}+\nabla \left ('\cdot E %S}{m} \re�() = 0. \end� It followa�a�x4 a universe beagin5j(equilibriumḾ�possib��aProl%FtbeyondVJion. He��y����E22kal viol)�of Heisenberg's uncertainty principleMg]c WhileFSQ]s assum�Rprobabi�6 e�[e�a fundaa�al levelE� i�iai��inistic ��RJly�[ ����of ignor��8. However, give�b\ebew) Q���!u!�e2�d�m�tur�� into�va�(. a�u� featur� auetge}Pit��n-loc�l�e gui�nu� link ��No�J�y��њa�figur5�A3wh�Yi�, no mat��how��aa� ts differa�ars��. Techni��y��!zeA�isu'f�X jfact, �aN3(hE�q8phase $S$) at a1�ime!E:�n�0co.�\space ${\rm I\!R}^{3N}$.a�is�Ac*%�n=g whic�i��to i3�nBell in!�litiesm!$bell_ungl}� deman�Xb% �m8\footnote{Note,�utwo `>h�zpA�:�ac�(ly strengthM� "' o�bdbbICfirst sh ��Schr\"o� er��� 52#M =Re^{�,i}{\hbar}S}$�o a se%h�@��s O real���/s $R$%�$S$i�resulk =�$S$ a�]ucũ1Pto�clj I @Hamilton-Jacobi �K�aV,�e impl�d$p=� �� Q�c��C ppea��A6�� tra " SAj a� d ``rpo� ial'':BT  V 8qp} U_{\mathrm{>}}= -' !w^2}{2'  : ^2 R}{R}>. �(�Wla�Talso `HileyQ2h}%� Holl,IHh }) =%�um�a!keA�gz� 2�U der�a�novelty�itI �K1��Ji� lyx (s a ``spec~ � pAx '' �a 2}�a9& subsidi��'' �63}. IntrastIo os�� an�schoolA!�)0 �i12f*y �%*8avoids emphasiz��\B{)3mai+ oponf%yis�4 D\"urr et al. �$duerr,nor,� 97} who�tI�their ^ � � �``A_ian&s ''�is%���anticip��by JohnLin )��A W-�speak�L%�� ��l.� �strong�flu� dqBell's���� %%%Z I-.q.e y}��e� sugges��"�!*!� "~ '' would)Nreflec 7 e %8 sit� more� ely��A��%tUIU,�\ b"�ed ���lI�eBA 0symmetry argu ���g)dgz}. AfE��xis*� AB��erv u�t�oI�is ra �m�n arte� � ediscusE� wh � limiɅh# Xis treA}�OneI !�mistak,��]a�jquibbl�over a �� emat�pambig�8 "u&��.2�se�X�te:�2� a�re��d!�a�� ��ݟof%EaI��}�of ``*� ���than ��� mean�� .. Our.�of obje�Vs again�*uXiK� �lic!� �!tebate m�6� . If s�cri�DsmA��e,u�or soleQ o A�Epfic:R��,"� underminA � nceptA a�. Likew� hn��5�t�ta9e=2.� 1�> .�\�bW� ng� elsewherem� int_of_bm����reseourA�+ llMc�4:,r�wu>bal�3y9!�%�,brief remarkaL��meritsr supe�Ij�� ��e48``clear ontolog���z vagu# ��!5" mple��ar$ndE�-p cle d@ b Oispens�q. Withm� �AU�n&ioa��R.�etraao�>� sh����isE� stoo�ad!�z to��prejudi^but6D  eleg+sol�! !�*�A�ble uper�)�.��eBendMa2K caus��A�icu�  5��>`�*e1�.��addm  )�m`�an<d\ ��ously Y� quesQtunne���or(-of-arrival9 4gruebl,leavens2}. S��author�(soY� �7eap�( advantages�M�1m��F conn�O ng F!���/�� su)s chaon o��nd]1`��4cushing_bowman �K!Fx� CP *� 9 home�X %A r��e���in favorA%9�a0be found#w��ng)- [0schwinger}: %qquote} %b M9(s �!�i &B�"dA�=iv�-T %9--s ��al�f�},!exaB!citys %%4� 1I4nk(� scand� u stud� !J�,told about % %Wh� �cy:# it? I guess �/!dreU(mainly %his��!reasons,�:��m� ���G�.�' s %alm�al.{\em rom� }a�R-dYy sche9 living %c�erLto ` ���gA�at�{t^ AEpublic�g�  %les�""�!fu"`ly�4 �} (it)perhapo  bU�say �k purea�� al})�ndp*$,�#a�t*y � !� �l-��al�}�$Copenhagen:/�)=� �� repet� e:� �0language. (E d afu�early})��"}�=�Dpupil von Weizs\"a�#re/ L aGu�� w8�1953/54�>y�cu�$T 'sznaufbau}:"� � UnsRT\"Uberzeugung, da\ss\ !� e di�Ver�Le falsch seien, wurdm (rch das Sem�%4 best\"arkt. A�ePwir konnten uns nichtw hehlJdas�� 0efste Grund u�r6� ei!,si \"astheti�,r war. Die Q &enE�,ie \"ubertrae KonkurmE� f\"ur[�4abgeschlosseneL#� 0'' kennzeichn &0fa�%� \"onheit.�Y�%c)�&Ced� conv�&��{ �iA�w!�!se. �yw��es oMsel�"ddeeper� �q a|l��fqu!B ``ae)Cc�.);u.ysurpaA`  ��a$" bB%s�-$beaut�characte|�&t��0ory''. (transU7e5 )�M� "^!a��%d �y a�͹x itut�� �"re�G"^� ``R� '' (�c)Őwh�"'nga�m!�``>N*f�O'' (�!)� nee9�!S&"/  E��(c�ly2-���%m1��v.2y ). Oepuw ��ly: ���ri!���� r�Y� help!*X)�s-��vwA�f�$E�l<%Qe�6 a nu� se"/.�� , �&&�QO� .�'�nd�)�*�p�rirM%i�$ %2m--�onA�We�f%�m� /.# ''&� � larg��ba��n r� r�s ���Hsed toy!_�!: ��L general.�� .� ub� Ockha�Trazor}�obvious&SV"��it&�� F �lextgaNhe� t�-V]�entity� "�"2�)befor�!��&%�BFW %x�YfX ea��maA �%%u % ��enraVexplanatpower.&o&"�� doubtful "i� s...} If ��8dAfA|y'��& p#fer*imn��few�-remis�,L@�5 9�� n�yremov�invokA``6�� Gi �widaWp�_(�7$rs natural�"��" scar)�&� � A�6� seem;be< $%�K+6 �=���luZD ch�+ng �!����ide�:(@�l�3B2��}+�#o&8!a">Dernatb)e� e�es�A�A<r&��� �o"  (� �a� on �'(un-)Kl�th��pod are). Fu\ra)�"'�.Vly�- ">$�=�+ phen�.a> I�Mp*:*pl�$n}0"� j(�words:��-pt� � ent "��%s!�R*� ��.� . &i�D�.HAm&� �#40AA62. met.�2�*A"o�L)�T-as}} < �}&��� � A(�� B�]"ag� �W�o"�!d&�0��� %�ALv� they� de�Si� sacr�e. %��*f�/%�* hearmodern.�y��a'a"edOK },&� . % a1�|i�+�i�elf�rep=��"�3,twofold: (i)� -qgiO 9N& �1 ��'tm i#B�)�nor�&&�)f)a��ZyE!to�v� �a�le�*!Õ�:�* Aft�#0!R$ (ii) More , Yo&�"(in orthodox�N�Ay O��*ntI � zit�$� ��"seoug{D T�s],� �=  T��"��D=A8 �c�,L�* �[�he samo�'. %F�ait�b�15 %��9p��a� betw?2Y*.x#s#�yq�� al6orU�J,�%e�B ! t� %=� less�e�!n��Lo�zPari����� � %a�&���s!=76��ac%{"� ��5%j"�#���-!7�!%p��/wea*te<i� A.d,A�H#9J.��{firI[!Z-pe� � ison� �lea�#f�kllustr����9��;� &3�m-e�4%�in !�)��be-��1.*�i .��ic*"H�(AkBrown��� y00,_neu}!(�4%4.�R a�k ��5�6q�n�̅�!sU�Oe�!)� = him! took)oIN!�vVser2 ��n� s !v��^&� �#st!@im:Pb�4�}�.%"L3�9� !�� er_dѳps-M#f�pu �# % e]e�k ��� =�%lterna�t�"*]:�-A at�st ��4. (D.%v,���)�) .z <f�� �!�w",�'li[ *:.!I9x>W�" Q��&��-��re�� 6X-$$-field. I��dz�$4�8R:�V�-U2truA�T�ons�peculiar.�3�!)�&r2MY�t)F?*1*[&VE W& .R.�{\ &M"��analogDMN.S:�&("� �= tA�I7�*:�-i4 W o��/,!��uc7.%6%g�4_.�,c. 4s upon2s,��&�h�+all�'e"� f�&alAF2,x5o2ci� ��.�� Q"�vP�@ 6X "X:be^�i�oge�*� �'go��exi�9c%W��at!  �(ve�� +3?!�� C%fm&�5<* �~m�.ial.��i�� a�)����! ��@-2law g��:A re%�� b&�law�9MXI�y gold2002}�� 2yp(a�Y";=�� grav� %"�pri�$o�6�2|ss?��e��~��f�  elabo1��!&� ReturPy�Iqs? !r$}} S$EFun�; : %� comm_8� �6Vs*p_(s�?c�@�n+(s. Fo&�< ET)rt� 3�3rezen�}V�e�!ih���}.�':>Q@Mit Berufung auf ?Ba0Td atom# 4Vorg\"ange dan�g2�: sch,  ers��!>O4 Trauerarbeit,R.7 Ver� A��k� n NewA3Maxwel�e�ltbild�C bver�.�,)Li�.�ic seq�/!:� sL@6�e;ai mour�,-E�=�xD&6�a�ld ge[.�)BQ��)6R� laimi4 ``backwardnes+iXit� no�o!�F/B�.  a�dd�3�ind:le w�d/"aH''oU�9*/a+ .orZa'>O��+iH eak,Ak��Q�y �8s so m> traA� � A�m�to���mE��F�!unyq(e�C�I�uo��*<� <nls< etc.pp.)!��>(axsa0i�o� Fsee�`!>�a>' woQ(%F AQ=Ea� T a�`�~��'&WI �sen�"r/er�7 ce'}%G`5 ', � 1 ��1���s���C� of����^�De�^%>� .�C"?s}�?S '~\�A�~} ��]!_-B��fFW" mee$lso4 �#r0"� . H� 8bizarre2� PA�su�A!= �.omfort9��+����� I�in��Bas}�f$�?Xat as �[.J+:T31��2,&PDu �# effe.7!�i�.�� �� &�a�a�to& U� F ezro-magneAor�_�9 ieldn i*�5a�e%Dhel"�5�W&n5[p.128]�2� %N�14 �� �y ($�()A}) until��%i?�ink!�x !�a� 6E� �2� jus�?`p*4amplitude'. Ev[&"�a$agt in 3-���N �c;EV &%$ɋintYF� � �o-� de�>Fh?o�"E U ��C'���3fi~"IR2� ��QA��/. �x sharp5"59�I� 6_� `l���los�od�E�����!�'�y�Seq�n-l}. 2��(�(( as})��!�M � v.�2� ���I�\��#@'� .x>L���2)�5�-��Ew �;��.-e� m� %R� T5ab�ł�+J�7 �E:%�����EW eake�1a��g�.��- l�Ag��_Q\��� 1km�� Q?e��4 despV? (``�'') ��2� !�u�� tool�@Vie �:&as ``n&''2$``U�''��pb#so�*Z*6�2�y�myriad%�``emp7%avey �W e pi?Je_s 0Afb�>h�LU4� �ba%�&�AW "� y h�*4�B�ap$ }-��2 Al�.� ��a&� d�o �@[� ��sWse!6ty� do typ� ot a�.� J�� more��It3 "� *Iv�.)� !J�hav�6 btle���$hardy,vaids3!��ii�)a7J�M�``s�(a* .7R0� � �_e�L�� essw-d}.}�is�H un"8*8 a_5na�c %,eNi�F ��2�nvalid�>  F���-a�.Mb�$a�:a[�}�2�, #!�dynam-M|�R!�� p.� � !�1�A�I:T via!�uB��� Z a."%X� A�beAs]! �5m��-po* � �M( �-aQ��"m�numer $ A Vd� �!�5*�5� qp},Lnd $c�LDN.� i��eme�V%�aa he _�A'0o%DY �>��t ��<hip!�au� pilot� ooA�9��e .`F�I  "nswG)��ir%zm� C. �!&�co3 �=\``�K!��''Wi so� i�@X�O&mM*rC��sourc� is ki�(f im!M�ey%-A�Y�� .0A r%���&, insiJR�9�seef A� al*�az��Q'�Xtap=9m " 8�, guarAP A��j?�GQI!Q ian-Ք�&g��r�=sD fic � �$LE�>einqJ��!�-Q�.mya�9 onis�I\n��AXt=�t��tf{endors) A��!� a)1(Festschrift!hon!� f Max Bor�0Exy&=�/,�f+c�/�{E}�] �$(G *J�velocy1,2P�1 box�5a5q���a�9behav������ ��.�R � A��q!. W]�*gy eigenr8 < harmonic oscill�:�B�e&F� a@c��-E�� *�+��m nl!|  macro �(� highE>xd) �V�C�">�6pproxi�_ �V%��*E�"a"� 9 ib;� H�P!�.�'E -?�3� a �!�E'a�exq� 1 ``3] ��i � m�:`cure�YP ory;"�^n3 to l�!e�C,�N ��{s �2�/iQ��--K)/�).A9�'�-Ul�7a�#toM)( it: ``And"� �U(r� ��w�!�!� � '��IuVA��-ng smam2rr!a��rmo� ,� by3hi2R >r�|s�A�Y`9 d':� free�Q)�� o�,!D�9t}.[D �% \*UnderV �D�!�}�U \�DoKZ ��1c�0ioQf�E>p�thYth*�T A*A�inu�"�.2^ �"tA�!�EA�%X� 20�v� ͫG ���Zs. %T�!5/� �� p�F [prJ.. Ej TaylH�!Ut}m9]FgB�;!bndard�]��as�e magic�l �*Y��sm�� !�$�*��� Deot� (nd GhirardiM�d�Lghowd$6?;Y]^��.e.v-o�a�c[n@�_ ``gauged'eK�+ verg�W ve)T ,${\bf j}^{\p�]}= +a}$� $�P =0$12AI&�L&�. cvbc/r[ $ y���!�E6�S� a-,)��y�Rj?�;�J%�tMa�x�� lL� d�Pd X �K%&UasZ �Xw�4A�i9''Q�1��s67"5-sus"�`` Da $�S1}{2}$9�%hKsol�4uniqu� 2�99�?�S� Philippid�f"YS�� �,5(l E�BGl0O!0yA!a9� �6 an�aF�- pin-3�C�"m,r  0�� "W�%re@2� � w7�M�a~\����))k45jIE|. �6-<� eBv�m\��bec94�d� (�Ou��Yfele#�=nci ?c �stVMͷLproof�pd6Y@��T &�4 *�c2S���}m�BE��V��=y�Z5��*h9&/.s ; ~!k�;q m� &�M&ir-�u�X%�anywa-�A RA aʼn��� \qeh} %In*[ d�e/6r?I��A�0"dW2��� a�a�D2 �� K. ��da!�aSa�%E��"��� �m *�#�of2�8=urb��e��TuA�Fv0 *� �e�Z�Yd�e� u d�3���F�TF5J"` 2�7>�~2��reZ�c. 6�2d!nut�<m) f 1^^ )��:�te�te&mWfnclud�A��b� H� &ZH!�!DA�.����� ce} :;h`)9!�c& e  *�A stayZ�&�ag\ �b�f#e&� �!�� 2o��#ok� * �rebi�Z"��'�r� &{+�ffaa� ~g.$ be� s�Vl F9. $��qa hyp�t�?E�.A�!�"�d!A�}"&dm�&� n�hmey�at�Ǒ�^12 %environa�� �W � RA!�y��%�=�.�A�dy*g(=�A. �; 2�?!�\�s9>5b&43ly����Bwe�#�a}Iof5`�+<mf&�%wo�)s��addYi�R�7oig>P.�2a9���hwA�)[�� � �!!�to�. ��� �ask�p��s�� � � �с h��empirA�9��syB�3m!N�1 g� f�enca�ob��I�\:L 9�g Qu'on R?`!s:���i� dua]!�!, �ive�e� �0Let $q=(x,y)$A.aN%Bf6�':D{U =�$x$&>�$y$��.:�� %�r���p",eLuX�Epa-!Y�&&�"�7*�o�!=[((x)\Phi(y)+G erp}!H::�2�� (x)$!��;� �� "�q�� $y$-�1 �$ �fB�$a m.co�&��"� �q!��!1!�f^�� Nw. A+'*xb%�"B" ccurs dur��6�[��{)�6A�� m�?de�1a�ha�7�"�P\� -�,E�LU�t�R� R{i�a:w�_} j ��@a+�H q!k�  $|!� (q)|9s �͡a*p �Ee� not}A*!��Instea�?GAGC&�s1)�+�(ity# ��Sof �! (q)��! 9) ��c^& in$ifՕ @mlaweth.�� �+s�M 'be&^=``�whelm!�major|�O���s��g& in >�w��� lebowit�d"� )msf��>U�1�c2� set,�"s� �'Oy/Em�S�C�0�M�{� M�a�E�io]be�+q�\�Bt'' ��no1�9� *>=*�x�D. ��Y�  � ["& (JJ�\ :�p��2�1 &StEs  *-e_B�2�D��\5�e&��q�1]^��� a %-66c�.�m: �#��O\L/ofMn�,:�����i�\�R �''�N#e�i7I��]�7xA Be.7 �^\-7 � givq ��0q"r\�8ifUDe��.G�is��e�n�Y I�ned�#by Dickt i�d ����at1Dt.� ��A�w#:�!d0����}EviBQ.6j��Cat 7n :�maP�N.�(Mf�a!.Hs �l. H"�1 [p. 123]::�@Eu`��.!al�q�#e7���e�@�� `W��j.�a����N6e?'�*v�4J us�9r��$" �: �  f�e�relpG.2�C?4&`%c�N ��;�$�Iia]be�dV-d.��i.^�t� a�� W% ]�&A'2�9Sofe �aTa�}N�6�law�� � dr�si��S*�S��"�"%� 2$a"ma�n�0N�% ual}Z�7now� �Xm�b!3ceP���,.QUYP_." &1�!�(��giv~+Con�>t(sg$# e Le1�6 �/}ve�eiA< �/�Y'��-o[Wra�, 30e*alq.-�$� tegyLy%�>A�x�Y�o,k���2 -Q-g,��"UR� |"&cy��tsb")iza]�)U�]q�s4gazm: refu� � e``�&d�M4we��i}�$|5)3-iM3�=6b~��!��J2a "$.y-�'&m� /!�lU�doAu�A ��-cut !�"�x)�"BlE"݀X�*2U.� >�j�%�"TZ6l�r� 7 ����c.�(�8.^8Um�(A��c��c.�c ~�me�, ics 6�c A a�c 2NI��cҡc��5r���%!|ide_)�EA!!�E��r�8erV1ult�_�, 2,answer.����%6�E9Z�6���es�6}'G1992 E�E, Scu�-S\"uss��Wal�S(ESSW)&+�ω]!Pey�Bimat ( 6�$ !fQ6! ,�A��[  "ń.D� alyz� �,(delayed-cho�B-slit}r inve,$by Wheeler w �w���1��(HA�3by2Kk.6uB�we| �87;!C%��$E{f3> z/"set-up { ��p=FigI#dp=A�O3a-" %".J0in��ch�e� �ly nw2 t t� �fe�cc�:K8n� �reg� I����B�-V� �(s $C_1$$ $C_2$ &}isbt cr�qi a��~ Y�N��m�lM-� ma7f�=�``�U<]�`E�)8e<�y,�G7n�"/ 2�}zBa�u�2ss!� up�`-��bQ�B(vj�[� I�qeT]�o  3ss mid�, "+twoi-)Zm�s�h*�9�*O4�[J6�,� 5F hit�R upIf"�+)�%ntra �he 0I�nfHce+a%!Ym_�a""F�m�hellmut}{�l i�c'xNnormal�6�G*�<S�)k\� � ��Q���G phot5#�1�*dABD( %� a>qA�M!>B� %6W.�F  %�+,�%yw�Jc�q04 �4�D�KYF� ,�M.�*S(as�2�� ) Jnj�I��  pin ^G."�^)����Uoft�p�U�E-"�?rꍸ ��)�o)ŻEӁ�6� %run��sD:�6����7�4�115��e}[t]ber} \ Pline{\epsfxsize=2.5in box{m$.eps}} \vsY{-1.cmBaR% [*]{ods}�D22�Y��K�%-�)5Y�] �f$C_i$ �9܍�teՕ.'�P�G!a*s�t.��)�0.8�-9��-�%��mod+.��upp�it�D *.9di�3lWw�M:�!�#inv g�S �v�\�3�~:Dі�a���!AA�Nc �I� �. A"�.�46 -�6k/ 8bŐo2�4Ѽ �.щde92$��%L�?P1-qbi��"�.�any� �F0���- 111]��detailqY��R.)� >�e{b-�sR�I�qɐuK ��bEdiM�Cp"! �)�?�� a m&� � g�)0:� ,dS*)�:�4+ to��Y2� . >�~��g��%fo)T# \ em�2�/3%��� chos!��wced c op�"�,*�``E�-> =&�se31p�-T�]T(� si �f�wR�D���kv*wa& &� 5K�= mic�us���<Ryd2Z}R�[�a�off� �E out C*�#r �5I/�:��4A~�UA�<�@ ){M6,� �L2i.<p� ����}y� The zal:�s0 one-b5Pe, orD �a�tS eir %S+AD�0a�Z�u��=  _17 ,zZ _2-zp%!f $z=0}!-��2)&1���J{w M0for�t��bo�!�� ��*�)`����_1�r2are in�<�E�t{Mhal�0Z�.6�Ne� � `Z paradoxb#si�K MH F'�e�X7w!�hi� low9 �2lude:L�W� 6��B#Bl!at�"A�%���xd  is: ��da�ck��\oy::g !�AM*h6d!{�G� .�" ����*� c�xe{?livH�A"����8���"O&�--�+w&D!T�:' path'��Vn]{k t*��O. \�i�D��by&�7�"!�mAp}�I����:]e a�bble-cha�nAWR�A�2��tQ[ a e`�A,!e.�V deedBe�r�H�!%AasoR#ϱYE������ �! linkaB�U.�BBt k�@ruTF"]"]:;�ir�� �l&e ��&�A �BA�h�B�� (� f+.h)�*j_�S�`,� J� #�E=a��#rel�2ɷ� u��� �U�o�gE A�� A�:�e�um$ G%¥�!~  lass?7[� t-�d���0M�s2X� %)is{ (% ���-&�E4w leav�=F9uSm��7�al�-.���� B��;}0��in�Ep nyth�othroug�VP.��6yreԍ�!#.��-& b6���%��ed%�2��_�,un�F,? z� >]��A�ver��e� ��6�Fy( plac��/a3A��%��� ��q�I&EO�/  � G tle:� &Cs] Ix6� �-� �1�|�edIKa$P_&. ��_lO2aBe�H�Fiaq�s $E�MK� �� �(m�/q�]A��� �anA�� Aq�3�1r� ustw���b. )!rr�}� ��:i/ rt�cmP&��I�=a bY >VRi�P}� nh,,r�t� c�Qt���!1 l�U��)O�Dit�s�: t��l�4�EU-p!�or�Bq(I�T!�A� "�o�s2�it ��hcmV!�ai;���&�!re�=�zX � �!}3�e���)X wAl75�T��s�YѰ >K ~Q"=s)6@�!}����H&� xw4=�@��/�m�+Er"5 aha�R }. Ee (ly AharonovQs � + ,aes2�B�_i��9� - �nPU�i�U\ S6 W"��QI�s�t�@r�u�m�s � exer�|�� eged-�� � trigg�&� A�2��`.]���#� ��6i�Ra6:� �E�3AZ��!�Fu��8�_haH.+@youa�� d� on l��)�a�1~3��f�e �Q�Cqs'"�2� en.`BC���ɓ> ep�+P�#el���s`[ky��E_.8��>���!i+>�en�#� ��N>�Ts�� e�Y rk_��c!{'Ju//6A a<��F�'�l<���� ��/*$"�J4from a�sswtyp"򔍤}6�(F;�59��Va�W +�!ȱjse� �Ao�2 �Ȅ)�uA"f8��!o����n3�rsai.a�2olui�M�2�&/� %U`x a1)�W }�"=}�Ym^S*s ю!k� �,Ie�� T"�9\Ý5?:[��"@d6�/>8�)a !K%�/|87I!�B�Z-#I�fK�D6�����>:W -��ir�k�wev-�E�f�e2�1"~�� "Ks�#�G�,5X�. P �� )z�&eb�<r�g-e�y{ d2�e�6�.pL2<I %V�u�noݽ:�.Y%� unu.�y� _0�� /'�e �QmxhglobaAi�pof�w5r.� issu�$%t�$i�oeV }/ ly�J�sTumulka�.Teufe�yi\G>e!  �,A' exte���`,*;-Dira�0ory� a2. �>A<e �P7A�B�svL!���K-SM,i&PaSA�� I�a��E�Apc�H�4,%� �T�*>ly�teN\ ,muynck})E��vJ�nr�hmB��.is opin���2�&�i& "#.neve��� ly groundN0* ;D|s�2������[�| !�Z i�u. a va|HF|p��AZ.�)�T�I})���o� 6�� i�� ga��y�#��`! �"�'p2K��� `9oq y���;�`.q&�U�ń�  V"&C9)�i� J��b�L Nf�&. 6�!fai��/u� , '':[m.�%&�J ��"<dP"��X3� כ)��:P�lCCn% 6�O�''!XF��at�u�u�:Pofas)&t�ll�� Anyhow,��f! Ak�!��'2�)y�s'�, 62E a��HsFwZ�luqggCgna�p:�wh�~�� s enE�8θ� at>� �-F ǁq�>ty*%�e1�e&&2a� ntin� b>}"�H� ��!{P *�@��� ��^exhaus������J% s. N\<�2}N�atZh�28i�I s (s�H� �Se3'9� !�)5_J �ex=  p"�Ux.� %�s. ($��s$)�3t]�oa�ACۇ^f�� 5�"�}V�.E1�_.2�]Mn�'v�c2 AM I�]�iR���!i ado�7� llap&�#2t!k�r�K� a�Ӌ���8"(� � ``�x ?�)�& c:�.�4s"�g)��U�2&�2�j%|tah_#2f(hhneoX�axM���Ra�0"@ f>�:!r 9 A�j��}� ���; �yp9 �G� aJ��z �!g��=b.Z�:bloch,�2wigmb>aF_�Y�04}EX^Vh]-�5vAA fac/a�fach.} Pc&:QmaudliBM B�&R  &mb�!&e� Gg>" ds n"�ari�-o2� folii.h� /E �[p.297]{��3�@o�Q�"�&�k by %Myrv�)@peacefulSiA� `` co"��4.�.Gnd %!�F.��X���!�Ca"؈covCM f-�V*� Z-�yZ>.i4Apo �RQR=A�� w%�ng. Iroͷe�Vɩso�l.] &oar� u ��\ #! 5= �2�R�"2"Nq2� �1J=�\<@6�'!��\nciQ�� 5%t�8��?5z Id&e��*2} 2`��UU�m��-�Qy%�F&F��@B .&�jG035�`��aM�!�98iRu�\edBs��>S�b�u(s6���-&c$!u~ p2V'')""'N"��d�} {�� bf v} = {�^{\da}4bf $\alpha}}&\o��b�h �|y.�a�?M�6�ps{$�conjug�/�S$>�$ a 3-�aE�� o�Cs� aN�zild� !RPT�]r��R$� _i=\�'( *J�$y}{cc} 00 & \sigma_i \\ z6&F/5 i&W� 69_aH:��� �-Q��":RbghtfordB��@74].VuV>_&�_ �B;"' ��%"|+ZG�G!x6�>�!�it J q~LX*p�H �-e &�an�sWo��(qu�=E�AM��$l}� � same}�L%e�(�� n9 less sJIx��$ar�.A�x&ZM'f�� b�/deq[�/:. ")�,�\� �6�`l}".!*vAEJ+����B=i�S�� *=7�#ure>8S1 arbi���q�sVX� �,��"d�& �w^N �� � t� A�dF�0urs�;erndl6�%����t. j�AaK�g�synch���)o���C�A�9�ste:�anA�>}t��A%�0u�/��wj(!�� 7e$2�>>Z!ql�� t op�#6s&b%1" `fha�"nced ye�)mLM�v�/F�"�'6 8 79f]" mA� �.\imodels u�; &3 �SRn�/Z�ng}�U���Z!�^�͍� � l�=X ic�t s,GoTu03,um}.�Tho�>�A ;�B��tyq�:�)rM. Summa2up�')�se0B[!W_N 1slz��� �)%p%f�\f�[B���\ c}�A2����2� �)$N$�� ��2~�,.rm.�±!��R�ri|+is F�s-a^n!%����9#!Fm &�6���AM~aS&Fy�El�%e�d^o�tw!�Fh� } �g%vAW�3afs�}t� cust��f�.?eaq�'2�&� $s�3,-m?& �)�/PC% ar�'A�>C�$�^o�z � ePA�x/+�[yI� �E!oM��ѧaMN�!�o�[�6��R�co[�:����t�!$(!�M),f�.���aޠ% � �r� ~AAQWrd �}"�~����)$l�=9graph�Ke� "�suQd)eqUo:^  a�$�L�h��ezJ�a2�> A?au �edi�/"!lt�> 1227] "�G >r"). "Ts''�&or$�e�i��1� �e2�n�_�k�^MJ� irpݐ==!�re� .� *sk=�i�#I�)-R����i sket�*!P2^^/a� :�-s";*��JWcI10&=\�A>is"�Q �urk"8)Z��c�A .lECwo camp68e�;st�?� ,�~!JH�nB� ,Lo})a�r�^�2� (bo;8c-))lva���fu*3cd�UM�� �!�.f� �ET�?�� lawR(��"''!�� �.��:l|?� t�6� a&5$ l� S !Q1E´ :� 3]%VNe qft1,qft2�i�E5-�qy|2!%*� ��o����2+. TMEM;6�assoc @!:*��-A"�'C%� jumpp�es)HA�<��1�- {a9%I���vdeĊ&�;����H=���b�Lvqg�:+�&P &�"hipen��AK-*�*� �j!!"�Y!�A�J��Q�R��rŜH���;2asi�v� � F F[,�� ary���?��G "�� "[,h�@b�'s��S?�! il��k#"Ќ�;M����4 K qw���ig3 s!�/'. �Fs^g*tZ�t*_*t [ .���>"@F�a2ejiE&m�ѱ�����6��!6�"�Js?,chp� met �\AB�yI�Wl�=ve��&768$� s&E��rad.1n��C ��. "@,"'&#�w~��d H"��i��Z+h��.�f$4�lLie�desir�!1s2i;>��!�8�!?ir�al. �9]M�A���i� N3\��/'�!8b*�� ��<C 8֥-Y�!oP (AFJ� epF6�*�!�����O61w5qJ/e�LA�&S2"&U�u*MAH$O -*O | be ("�%�) ly) ��!1"�~��c"� !�bb)bunt. A�>E#�i6�N�t�om)�Yt�G-��T<aÿ�E�����"B��\qm�����s� �;,�vieQC/�q��v��vj�_%qiNؼ~�!rA�wCVjudge�Agem�h.�&&i�N�(�sy-B�E��{�A_ Quine'e4�mbj*�|(7� �W ata  q>}���`[2�e"?Y�����%�4c�"L!an2q=��aSAߡB\��M�k@�aa�+;cid�|or��to,oky�� 6�''� eria�s�$e�U2�t�\&-%w^m�,U&m'��Y�H%d!�t�:WrvO(*=H����1&�^F U"�tu��aa�mm%�?y e�+�K�\�%I!�.e}�J�reQ�a���[so �<:Ua��#t m��a�X6!�a4E�� ` c &Eze�to�lA ���a_e�% us�."�E!�f�� "�1 /P>��� o�A�!�6��\�]"T\4T| �1 %v�lim0/�o"n`�ize��yQ$& salui2war�)��nyA� %��%7r&yE��oz. I��+ %�["9>9dm�`�nu �\��deep oH�  ��W9;�+Ys �;W1!��!Qqu>�eY``uF�A�(�6� 8(��s)� ab( so����OEBu9ij ejd&ׅMG�#rt:��>~� %Equ�3I�F6��.UZ�#��<, 42!㡶��o���%�p %ؚU !�middl�2y-E"��mb� d. %��%`4�:G�%I�je�for�\)�l9= ab�A�� |Oic�j&�A)ُI �JH %6+a'e u&�{ ��l�.\".�ffu�mix�Hper�+�#nv��A�deie�/s %���und20 ��I%[sig.O[!�/e@�� �4��6�dB���ra.�S� \&�5��c�&� � �p)� %�BW0V i�*A�w*� �%�asI7F�I�o.�{���b_ na MaK��d�!i���-%�2�$s's&"��bZ'�n�s4$��1buch}[i55]8�b*%��lin�sc�c�k kx es kG�``Mes[�)'' geb��"s�um��ukalM� (TA9ie) h��lt�Ce b6� reiba�*s tɿch<�n. �da�4t sie�&� ���( �xy| M)�6&�E!�� , %�oIsN�al/% ory)q�qs{ rK"�IwA.�"n��n���Y��%1�E��Ie�Z��akI�aA%�!� ``I�*6oR�'v2 ��a���!�= A�U�=�ϩ�be��*��2b"�AnS �fZ2�K��#ug��o pole�=�a��1K6$ѹ ����un�*w0iTq��}1hl�J�n �m:pd=��s1��j�� � � eG�M.� . E|!q� ��)�ec, amp.%,> Golds��'�����u��:p7u�pa�or~;'s �sib�� e GRWagra�rod��"��3m%w'� er''"D� �ail�1��� h�0�Fc%0�Q�\�S ]I�,� pick�lR;ew� ��.�� �E''G!�p�a�3.�an�� s v"-}ɫ���%knownq�::dG I ama�)�! peo�I meetXA� h� �E7&% ��$(\ldots{})�% �� tudAK� P[and]#DotRWir"Us�ic;�it.c�fx �4e'&�# lly U�a�t����I� �a � he�f>F t�q it. ���Ir �ion:P� *b *{Ac!�ledt�})�&j �b�o�?$f. SheldonySe�a� �lpG��e�D��g�ڥ[p 7 benefi^L��Rrom *�Iank(��T��s�3s�5 Raymp7 Mack~ �sh, Itamar Pitowsky, Ned Floyd, Alan Fo�$ter, Ger�N G���M, Hans�Ǩter Zeh, Hrvoje Nikolic, Matthew Donald, Fr� @sco Cannata, Step�!dTzenov, Giorgio KaniadakisGPrek Czachor, Josiph R�Olov GAbel Mi�oa�{��&��thebibli��phy}{10� ?�*�3��ais�sa��!795110027rN>8E"R, B.-G �Sc5, M. O12P"pO��w� �&aies:D A 263!G99!�76GeP2E , Erez, Nf�Tim*d Ensem�~Avera{��!:� cs}-� Scri. 69�Ar4) 816:0412068.q�=A��, A., G�GiAhP �RogG14E.� R�O�*A�y�(-Podolsky-RP`�]Gedanken&�A�New V.�2 's I�8.{RevE�.]�49}, 91!�82W�Y�*�9 &:A� E.,�-�um=O, P� ice-tE Inc!�ANw��Cliffsa302�26ks\ J10�Per\�Memory:a���:�K� 's;ory�hilosoph /S!�0), 67(480 2,0002046.� ��6 BB�Re�'�#B$ Through F�,-D�t Con�-�7}�<thc4g�6� .�4�c�y*�@A!D S1GO!eUa Qa Ea�Madox}, ei�w,Vol. 1, No. e�6!(%i{���&�"2�s"��J�T�-An ExactF0�� ɍEssay�hϠ J. Sb0 70th birthda!�E�C . De�b!�4R. J. Finkel# , W� I� ,��gap�) 1989�'6_how_toN�H��o T�D�{Qt� Prog�>���A�w Cul@,2r2a�76). Rep1r� =q}�JpS�k0!4�a &�# & }�1 mbridge U&�?)P�.�2�mar��UA���MQ�qDi��u|a�MakO s, ��oi%},� of Chicag� es�M!�5�\I �0 , K.g}G",e Peruzzi, ��Zanghi�d m9Gl�IEx`��FP,�A(Comm. Math.eL�m,173}, 647-67eN95)���� 0301 K�E 6�a���j� %�.�qUA Surve�N�, Il Nuovo Ci��o 110BA��737-750 a.�4016�debro��}tl\,B �O-gL����4�Qfiqu�% l�[ ti\`�*�5 et du ray���'\'�u:ond�Roire}�<27), nachgedruck~N��La%�:E� �3,era-t-elle Iv�\'2(1me?}, G8hierKV-�rs,�NiA�53� 5� rela��B��g"QFN&��,L! I6�*nCY��umaN�J�  A 5Iy6) 2062�=� 1002e��>} B> I1�4��� O%�=e:���Ter��Om��u �156(5)!�6u 377.�я1}E�i�!. Ah4�**m�G� �u!X� �5 d�0ap*6���(85}, 166(I)m 180(II�52), �4��zurek}.=L ohm3B�R-�a C���� C$WRe-Ö"L";!:dN�7},!O52) 3��U��2B�P��TU� �$De�A�?e� 7h5hin�:��>�.�)a9}E� (1953) 452� bv�E�Vig� J.-PQ�M * q-=F� �"�JT�6�a Fluid@ Irreg�#ct SN96��54)_206�a@ohE�� x & An�� � "& �+e�� 5. 144� 6!:�321.6*=~�Th�-�e0 (London, Rou�Pge� 32hiley00}� Brown, M. R. and Hiley, B. J., {\em Schr\"odinger revisited: an algebraic approach}, (2000) quant-ph/0005026. \bibitem{cushing} Cushing, J. T. and McMullins, E. (Ed.), ��yPhilosophical Consequences of Quantum Theory}, University of Notre Dame Press, Indiana, 1987. \bibitem{cushing_qm} C , �-mXMechanics -- Histor�t!:ncy%aXthe Copenhagen Hegemony>� C�go � (1994).C$appraisal}:E , Fine, A)�4Goldstein, S. -N )Q Bohmian m�Aq!�um� ory:!�nD, Kluwer AcademicNPPublishers, Dordrecht�62�-�_bowman�;)Y~B, G1h�9h�$Chaos}, in<(Butterfield D. Pagonis (eds.) E� From Phys!�toYR!� Cambridge.7 Pres)� 9). ] (nor} DaumeraC0, D\"urr, D.,:v� Zanghi, N�Naive!=\ Realism about Operator� Erkennt�(45, 379-397-[ andEs%�(-ph/96010132� deotto} DeV!BGhirardi!k C�FnRem� }, Found.ak!E\., Vol . 28, No. 1, 1998.�dhszwdn�ZgHardy, L)�Squires��uHow lat%,measurementsy�A�rajecai@es can fool a det}, �( Lett. A184!maJ3), 6.� chri6�%"Horto.�$Relativista�,ly invariant[,extension ofa= de�cglie-!Wor���uy}�\%U A��dMath. Gen. {\bf 35}, 10117�a2),�I!�0202104 6 ickson} D , W. M1�ǁ�ceU non-local�8in�8 interpretation2�.�yD FG>qft1}f9$, Tumulka,ѡBE!X��6�F��-^ Rev.M93,�090402%:4.�3031562K qft2��T.�a�,Particle Cre%\AnnihiAnon!�� 6� , JournalAtM?:.=36�,3) 4143-4149a2: 8072.dgzj�@9�eS2)�T�(equilibrium1��OrigieAbsolut�kcertaint��� SAmil�ics�|$bf 67} 8432�f>�Fussed�� W., :�!{�Wem�wom�jn ``Surr��ticEk2�\''}, Z. Naturforsch. 48a%3)� 1161)0 its replyn21166�uerr97j��>��F!�MeaningA/ Wave Funca�}�yin CohenetS.,�P�1!5Stachel��, �\)< Experi!=al Metap�g--Uq�al Stud��for!) Abner Shi Volume�QBoston0��" �OSci  1a� 1:B�&�%�7� \� detL b�H, M\"unch-Berndl, K)�B|,Hypersurface%�,-Dirac model�� i���A�� 60}, 2729�9>�980107086�buch} 2��� sche1t4k als Grundlag��r)�en��k}, Spr� Dr, Heidelberg 2001.j@bornbriefwechsel}l Eing 4H. und M. Born�b �3 1916-195��$Nymphenburc 8Verlagshandlung5xen 19692�0essw} Englert� -6  Scully� 4 O., S\"ussman��� Walth�Q�F�.b}�B�7i�� 11752�rez} B�M�(book reviewa�\cite)��Bl. 11��16�page}J� Page� %v8 Linearly Posits � 4es: Probabilitq�4a Robust Famili^"f *c Ev� } ��.I�k 74� 15-371I�5� 4 gr-qc/9403055.R qtwo:��V�N�� with# bser� 5)|Today 51, (March) 42, (April) 38q<}�GoTu03:x��*w �Opp!?e arrow� time{ ,reconcile re�v9 �-nonI }, Class.� Grav� 2�55� � ?&� 105040.�gold2002R�euf����E1GSpace�BJ : Ontolog� �r��($Conceptual�� �! ^�i��in x��k meets.�atW0Planck Scale}�OLited by C. Callender% $N. Huggette�275-289,*q U&�� ��), pre��t A1 ion:9X 9902018 ](pc} Sheldon._ priv� communic�,�2�$pointless}!)Ghose, PQG Incompatiete^!^>) ]�5]�� agh��R5t MaroJOeCE.>wu:ies, �, s� oK � oxim)to4ep�$ process?2R01002��0� Y�!� _neu>�%Ym�8 Heis) Picturew�r: a New.b!aZ��� �*onEShannon.�=ۑ�&: R� sider �of.� } c. Int.� 4f. Vexjo, Swed June� 12�ol!�} H �  RqThe:�yMoA�}*;J2E)2 k992mm�Uniqu�E path2 m�6j A 60ae99) 4326f �undphi2s a'8Philippidis, Ch� Impl ��,Lorentz cova+ce�Aguidaequ)��"j�<67, 062105 (20036home}a�Hom�Majumda�B."! ��im�"��A�- a��� JCP-vio� on*� !e ) .�(. "� 722> keller} KYeA|'sA�*{�6�!: Term%s,``Hidden'' V!tble� ��] ń8�1953) 1>^(ruebl} Krei�!)Gr\"ubl0!�Emb -.F�ar1 l%n.��. � ^�8851-8862d $leavens} L ,/yo rans� }s%�$rectangulapb� ers �in1lc�9�I�of��.D� olid� t�m&s. 76,�Ue`6= �2>�%\AKG:�2(aGTunnelA�T��roblem� Scan�-8Microscopy III}� Wiesendan��!�$ H.-J. G���odt� � &.Berli�93�5.2Rlebowitz� A� d Boltz�'s Entr�}� 's As��Mt�46:9 32-�32�$maudlin} M > �$-�nhe5�world}�a�c*,tellus} MermUN�� [What isQm�p try!� to A u�bAme' n.�a��e�66}, 75I>8�� 2W):soveV�* CompuI�:tIaR rned�Stop Wor �!�Lov�\IBM.� ResewA1+Develop�4%umber� 2004*+ �088 =nmuynck} ��M-pI� ����eԥ)��of Bell'�0��l�:��y��=/ad;y `-�}, }!$Khrennikovq/E!Rld�tific! 1, 9=%"[ @peaceful} Myrvold�@e3 On p " co"� :AA�c� pse postuL%i"~le��K �?��in$�"��w#��rn� %33�|2=��xf�Some E�Ob�Yto��� z%�n%{*;m�6� �~17"� (  � how_! Pass�0%a� to teacV�Eur� of% �(25} 765-769r4�Y�404122"!p{}F���2�},D!Pri Deutsch, FrankfurtAM2� int_of_bmJ`�2F�AA \dbb�@?a1 .� pauli52XuliA�m�$ Remarquesy  leU bl\`emws Nm\`etr�!Dch\'es dans la m\'�7qu�� etN la t1orie �0l'onde pilote��: Louis,:%�i&IPenseur,|is \'EdiA} Albin��pp 33-42�52�a.'6P:HWissenschaftlicher 2 mit !�r,.:&( u.a.} B�K8IV (Teil I, II \ III), He�\gegeben von Karl v. Meye���:�%quine} Q!� V1�On�i���"� valent sy)�;A$���6F 9T75� ��$sanz} Sanz�&X epA!6j toi8 um fracta>}K 1205�4��ehy�MgM�M"�alI�em���f�$�c�gum %��},�r� il� rterh18,!a 78) � �abn� ��S�-�a)B�;achodate %U($our knowle�& of m� dA��b'.�sqc%}Vl%� -&�$�x� "���*r9508014�9)ߵ� k2ZlEssay �:��( unresolved5rdilemma͐.ŋ1uMod ys.V.2��3  6�2Vs } SxOA D�d6O Always��v�0a Trustworthy�@ ����#�?� .a Scri� %%8}#2�strau� } S *(� Z�k � &���2.�4answer} Struyvi��LDe Baerm.�"som�centlya"po}&h�$at should+Goi�u/ fm)qH2Z 1080� �. }; taylb)T0 %�0 Conn�ons�B|%�Da�s�Rutger�i�s:4 otc}Era CunhaY0u� 2( �) .�%.�980900Q .�simples�%�F}S)A�of�4Global�E?�A��a�:� mathb �3�2,�aappearK A"��9ema�(ms%852�rodi}J�A2/)�}��<~*$-Rimini-We M$#.>�9���k vaidD,V R*,�LqS+t1eVum��8Can You KillIPan Em�%Bullet?2�31222�3�  ��� W2005) 26��O�V�Zi�A�Signal"�) , un"%'�%th. subqaH-mem },c t I�syaA 156 1-!� ), 5G 7Z8� o682� val-sim} 6�E�Westm�"o#Dynamk "(E�1�&_ i��M�303Naufbau} $Weizs\"ack� C. F1\Der A) [ � Y dtv.k$(19882� whee�W ��5�As`past'�A�`d� �'y s6�R/2jEI&�1  ER.low�.)Z w York, "�/5 8) pp. 9-{!eL)�i4zurek}..y :��Z.2 H.� �"� �a�*���rinceton����ess, NJ�8323wea \'ojcikf/HBialynicki-Birula IIo,Zyczkowski K1�M Evv*�*�$F&] A2�$8Y02�c&� zeh} Zeh,!�/%Why�q's5e�y!�:�ni}�1k �197AH %Q�y/981205�D \end{thebibliogrl)} %� U docu� } K��Tp%%% % super.tex % REVTeX4 fil� Q3lim�of  u%�in�onstru�of opɐ0images % Firs*�#writtenD$HM. Kolobov August 2�#4 % La5 13 Dece� !: %�N%% \1Mc�%�[pra,12pt,eqsecnum,showpacs]{revtex4} \usepackage{epsf}2%�icx� new# @and{\mean}[1]{\la ) #1 \r +begin.� \def\BE{ �!s}} EE{EdBBEA5narray5A6 \title{F�E-��o"�s} \author{Vladislav N.~Beskrovnyy}% "Mikha8.~M}ffili�{ Labol3$ire PhLAM,��\'� Lill�,(F-59655,% VDneuve d'Ascq Cedex�ce}!�!�H{42.50.Dv, 42.30.Wb D50.Lc} %\keywords{3� {\�9�ab, ct} W�1vestignanalye l�n�4�Rly�s rol �Cum flucth� r N\-l� dif~i2a�ed i}8. Taking as exa� a�a�0put Gt# closely s�(Dd Gaussian peaks w!ime��tc on[) imprw�R6, the �edq over ex! Rayleigh�i. We a} kIultrum )�6usuc62�4d�is deted not��=A bu�s� to-noise b���i=A�� �a)�i�ve5�JQ ��s�<s&$-spread fu�/B%�.�Y~ \makee� \s {I�d��} q�A A8is a new branchcM� �OiY�e9�peY1m���aallow2*�la�+e mJcs~��@99,Lugiato02}. On%?Apertin��A�wsumw��74�e/�Y?. Y� ; waHstaK9+Abb�5U�9+ end �ninet�)�u�,is very well8n nowada;� Q �criter stat%� o%i�4�I.A�� �.��4!��elX' s du"!A6% nE3!�  ligh�7ccordAJ�his�,NXE�s-$qE6� �a���i )D)Ap�(�� sm�,�Z\an $\lambda/{\rm NA}$ wh�'$!���length1���  $>--�� aA��T6� � . T%Z��=�%� �<'o�presumed +ving cap��/ ih� eyIxis��a�'da al alike,�� ��,�.�&�jon. NM� us!�P$CCD camera��HZ� �sub�=tAUctronic ��sY�Bof ZHbeyond�5L .�%M.�&��,�le4qFY� pu&���6aOE!a�6$0.2 $\mu$m!?�1q��e, by.�ic����# achieve a!�cifl 1nm��(amimura87}.�1 more �&acu!A"lts ha>,en ob�7ed�i�2�aia8 place��$ laser bea�(Treps03}. U%�"s /e squeezed" 6 6%b� s of �E have� ceed�+< ah""e>�$ 1.6 Angst�of � r�"}�u�=1064$ niyese�~e*r)are p%Jm� so-c�?d B� tech�%��at aim��.�Qy� N�2yEt. S} 2f s possi hen AG!�s�{\i�, priori} i.D)�� : in pI�*Susu%� dealm� 8%(finite sizeq' ��as�'e I{F�becau!�hA�a�,X rierI�rum!�� r2��:f�*pla�� a leM�� �g pupil�� ocat'0���} �����+I���aE�RFo� ep rum,I�mit�6%.w,%G! in!�ncipl�W"} 3resd\ vi'���co�B �},�� refo-m� -�Yl. evJ��c� of)f62ii t�?� en�6toE�e( kind of  s��s� �Q�)���i2 �wn�� 00}"� "� e��A���-#A%ma� ���#~� "$ 2g of��Y���1a!�%Tvacuu:� out�* itA[�tj 2cset upFa� "f1.���}��chE]be� !�ord$,of magnitude���%=/ Z. Moret Y�� her .�~.uZ�%� ode �)N. A*� chY M���>��;y !��l Mw pr�in�3.MP Sokolov04I��p� �"� A�i� !$:z6�in�M�u�9�Q�IzK=o2�es take�p4$ks��� so� to �"o!�i:Q�ut�a�yA3>9 �r� �UJ � as� `�"�۩.B� +7o� �2!.�:�'m���%� Ω� areaaRis�z�� , corresponds��the.�v�٭�-YYQ0cjET:s� =a��ob�:>��� 62tsR�!? &Bq�]AD�C�% ,2pr�,(e spheroidaټ- simi m %�ory d�'� n Reu�m� �6�,a)u}2E)N��*i&�nS � i�Js . Ourq�46 u%�confirl aF7en�60� A�aq�771ccount��eas2=��.]M�V��?�}�_�� one ��!絜.���AE?'�millumin�:a��vA� co��#�� 1�f. չi01����� ɰ:3հ.�Z�of.w�8epeav)�r!2 . Finl ,Amd^Jgo�y�ݩɇa=Ջ>> 5u� Gz � _3iqganized��fo�s S�~\ref,H} w�� pe� �hF��|�� ��"� � N�F])� g�u�.� .;�)2�a�s�8�Dw͘�W0 :��"!t�l��M_de�9�>1!�6� Poin1-1�pr.$eE ��OA�>\�.����>��*Vwe plotB� fa KAU�"XE�eihoton!�g!��2OA�/�#l�%lU�B� W`cu�9u��@!�Lfu�E"@7i:\Di@��f "[L.���} \labelAmF "� �!Ms�:"q �o�Hal)�"�9A'� %\1�Fd Q>>��&� �"� 5� /�a/is�EW Fig.�@ M}�f$ic #weikder�-d�G!zal | �Mk$&� $X��C !�G =f�y  $L_1$!����l6�trans�x%���`� `C T�>�d$. D&�i��.� ,)*K%�Cc ��in A�)F, (we neglect.� be !��es))s�d $L_2:�rse��9e9cL es ab��?�� � ane. As � io�abo�'�B�� needs.� ��In�*A6AW know!�< �!b1�sA~fi�� ��� !� Ef�=is iden� zero-b^JK�a� an Nre &7��R �!���zP �N"c.X �$d$,Iuf �arV�o�toY�&�and� ���un���O2�is.����y��heUua�d! �a�iR ,!��b�v.&/6�N��E�!�in B��.� V�譡a3j T{ !+eigen��-�o�S de?b�6��w 6��T.+ oI���� )��>de$.��B{2�g se>�au6rel� DDn,1coeffS1t��BFt� ng/.ze.,E�,�" CCD �*O valu� E� �F| R A�&�� ���H%�-��+!q*� %�la�C��.Bbet*F"[.�i.r�6�q3�h�Yho��q�*-:&� j����e!��.�I7�/al� �y largKea��%�I�� K scil!�$ng behavio�3! uR��E9whL .qS"^we�"�aGified�� M�� &�Yk��2���ee�t��� �+A)1V���� �!8���mo � �.�v!)�o*c! e advanta=� is set-up��q�!Zs:!�)ud)�a_" gA5wit��� . Tox4er�2"�lq1Z62g *X �"��!��� �"Z �Bis9�)> . L�$t�2 "� lWF1co�� �m�%�4 as $s = 2x/X$)� '% &�8$\xi=2y/d$ (see� 1 6| an*�Uo�-��.� w�.be deno��{\aa}(s)$��Z� (f}(\xi)$E9se pobe�&�J( <��;;> (�- [ b�, ,^\dag(s')] =a(8lta(s-s'), \qua�Z< � >f >\xi2@ \xi-, z� ��( +"�( %���n�Elnsoi�!!) �^{�}!R  ;)$ �i�E1�n�<�uni m��oIg�!1�)ԉ8%�:�f�!� �-� - M ]�%�UӍ.&h $(T Ma})["� �#��� � G] A�8.��Cble�Vads as �, V&  � = >� =%�T\sqrt{\frac{c}{2\pi}}\�:${-\infty}^  R%� e^{-iAcs\xi}d�M -F# %� $\di� ystyle{c= ��{2} dX}W+�# f}}�3s�$-bandwidth�� '��&�I�`Dt�oa�鵁�< ��;g(��0�9� E��  wh�)1 MdyUcer�&pe�*rY�h.) $c$-I�sEVv0�2��)��Ʃ�.�Z�eUq&� &' $\psi_k���'0Slepian61,Fri�G71}es�� 2� >�1�E, �7o�5; !�rval $M� 6�, nt� a< )t5�'�_Iaebc ���� ��80 \BE�[\varphI}��left\�.a�.{cl�{2K�;1}{��l�@ _k}}U�} &� 5~,�S 02>�� y \r�. D�a �c��iB�r�1-��r�� ��-mchi��EE.�1@$%�!�e�"&d%&�A��UV�$5�$, x4� Z� $c$� �:��W�"�  $.8 ���P��$he Hilbert j$ $L^2(-1,1� S��stA�c?� ��.���&slW$\{.�\}m�\{Uan63����� asy+2�4= \sum_{k=0}^{�/}"_k6Y+I f3b3Q�2  Q>i�_e�M@ R$ B�&�f�f�M�kV ��g5 �� 2��� :� Here#,� _A�n4,�I\A}aV��]�7 e.��?�� 4�ra�Irs+h !�M]� �~� �q��%)�� ����% n a> �re�)[8trough�o�mG(V by�w� �aA�R� \� � Ys)� �� q#��O% LU6�,c*}_!�_%+M� % FF hold� �QAYR-� m$. �Nr�Xof5;sK!"$,�f!��� )� h��pE�� 2��J= MZdiscretM[ |fWQ6��4!Y 1 V�g��n�  have 2"�!,U@{k'�& _{kk@dQ"W_:<70UYm�9�Us�l�@a fulf�6Ithree�%group%h5 1�^�1�E2.� clI@�1��b��* ��in��"%��A &�&��~ �siF6 ,���(�3,�R�%&Z ,aN��1}^{1}6����(-i)^k� ��{c}} |���m� �_ �y_19�2��U�^ Us��2��^�2��/(�" D� VBhe�d� , (�)!w`0 mS!�;�jma �LrA��2�#fi�15��pag� Y�Ve�OAE�� �"q�� (T5\f C�)� [\�� !- �� +�.+ �� X]1q=r�9�\�]t(T A >j�.u 6�- ��B��jY�]SubstituF Eqs.~I)��)%v %�� �f-!��%eA-�_1 f fr.�)E0a�Te6Y5])*� �mvU �F�f ��A��I�s, VM� _k�6Ic(>^ (a_kZY b_k u�UT�_%_+} G.2j�gZ�.b�N]�UWQX.�e�J��6y��#>�*6n3:� a4-"ter�!� �<�.?�.X  $)�>�� �?&Jbj9.) q$r�+F��6�o��M{]l&.s-� �z��9 " Je%L |2D*� � i�a N��i!Uan 3.w!:�">3���y$s�; n Eq��%�sS!w��<�#=s absorbI@!�opa�PB��  be empha�" at,�>$}%mplex�U�� �s'3i on�>lK�homodyn�tnon�%� a� vor.=%5�8.��)m��©[.��R})�can cal�6te-3es-�d2 $���^{(r)}$ � .1��ej�a_k ER g ]f_k}{V�}=""y&�.��"��b_k��:`b7tJ�&x%"pt $(r)$~!$"*Y ed". A,"EU�%� oM�D,2�.�B|>e-{R�)2FE&�X'-flE�sn�,*�."L/��.F��+��;���>oA(�H<Hf$ b3:�Z�  3" ^J2 !�.�� w��like �$. F�Zlh1�>�&@=�>�'&���F)=�5�m� s, i.~e.~+=����V*1�� %,edm?+ &�n4!ci�X ).�( �� ious��E�A��be)�y���G� val&#&"@w� f�hwk all s"���x*��A  �-{Ep-pes*��j�7�q care!o!�� $a(s)=\l2�!�!, $a_kB"_k!�Yc�G a. S�76� � ���:��i��:.~,>ņ*4E�  �� ngle;A �=0$&� � d� !�!��L�1-"I�2w!!�Jp�.�& �.�_p2 EE %L�1*�$f�$132�d � isY��**e| })Z  c�,� >-" 1}^1)�U*� � w�6E$""it+� �!͸"�!)=E2F"K2 Az�ertR2����� *� J�U/\:- "�' 5�a� i�a�d9�tion1xNZ Ia�!-c� � <\xi3!Z�E*i9�M��2^�(6��Js. v� 2� ��BR%.�<� 2�"/��� b� ��he *w*bt*J�C`,mpc*o.� !�� �M�e�3=.kE�l����t}) w I}��:� AbHP&9A(A"� a_k.�ml�C z � C% B�C�+�G��:n�2�6* !�"?2ə$/M0.�)����F2fq�$a �2a�be��tenmb Zb�:m�y�!aBx" `:� L-1}!f��_ �!xeQ�PDac b�n�C���E�5ly many:� p ,AA��� tricA.��sum�$e.�C�kto $L$� �&�%�<$L�a�g�$J�1��gv�es�(ex�o�~=�R� S "�Fa�BT ��"�I��@Db?� $L$��!uv%� e?z� Job9�gX Alte�dv!wt BX !`�p oelf�%�try<-4"bA�UlfM��Jn��:��.J�|@� �&.z!7m�)� enV.E = �}:W5�m�+Y0 $..2�sFo^P@��@a� �b6� wo nE�:��5D>aa work� $c=1��-si�V: ED<\pi$5A%*)M��G82a.��`?A��Q8 9*�U�/� )� y5��in ^ b - n�E&I 9 ( ��X Kc )R2�5$e�q 7�%�tmp�yg�2�� �1�L�!{AeU at i���.6NŞs�ee�:�A.� � !H�5�xrT%�)�b5��6�f grey colo�#^�#�C:� ��6*!�I�"9T�W��� Be�_l *�Arݸ��v�  tGP�d &b �%r��5>8)�L*��C(R4#,:�*R+�=P+�OF/|"h.,$*�+ d 5all�., x/2w/ha"�]�L,is necessary<2��!Y2�W���SA���6*%R���RF6G$u&n�[8%��of:7A have< �algorithkom.�<Xiao0�0�L+�1�&UJ�,&:e�F6se5z�XLegendre polynomials $P�"$b�#n�J�\gamm� n)}_kD�Jk+�1|3} g,�QU=b�co&�< $6j�*�k �N.�$ symme� 6grix&�+2&� non�X^A_{k,k�$k(k+1)+c^2 �2 <-1}{(2k+3)(2k-1)r&F�Vd5 ]+2_ +2 kd(k+2)xe)lq1q +5)}Vru�4k=0,1,2\dots$ �^E���]�pr�bG(MATHEMATICA�I�h�B�is U�.��B�: methoda�4j77�ar�n7N di�w �aY!�%�p w�>�*"i$ w�Ji%j�[�<Mde�(s�bca�.���(�eL"!V��$le�b$17b�N spits�G)� ���/L�!e&�S�Z (�n���&h{17}=4.183\times 10^{-50}$)��3�����!17A6� :y�xby� �!M@B�1@� �� ����RG6�����=�!Jy�:� � .(  ]10.1.14)!�*CAbram�x70�q&� C*P�&���2i^n j_n��Y2 3�.6#�hFxl Besse&�D1%�@N�*2��M "�-$�N&B*�Qh�U�$��!c �f!$=���c}y9 }i^nJ8�6�b>j_k(c�2AF� .N jc�yt�b�sul��d 2� 4eL%xfig�] oiQ���/>�X!�.Y, dћaWa�i�TB �afuL�2� *?"-8\*� sDly*W y@V�> ez &#Y8�* �is�t �m� �3�Wa�6o harmk9��^�%s,��%@ @ ,<coHqI reas��=a�B�..one!�%}j � h�F2cWe dashe)��� 4�,#q K-��&�&MA]w&K!!y $L=5, 7�(11������!�'���Kr6R5�6#2$%�*Zeh#�f�enc]/Q$` "���U�! �L� WkJ:_ �a%�%�Lf�&0�"�!F�Ep8$!�T6�UaBR �e�D8&�"�=\r"o�N N�}V3^� *q�2h Ѹ�a &�=J�!�{R��%��  �%2E)D�)]�@m�a\\oA�iM�!��q V.&� :T�&> �L ��� ="�stochaY� vari�@$\alph� Nbet�T���i)[���� �CZ�( U(=a_k+\delta2� o=$ ~wg��BH8a*� %�a&�  c  1|�6��I�aUa�5 A2�1�%1!g.S5g.��cCAQ!�m��� 4 �b��z�M;';p��m�"]& �vanish�;� m)AY�ly- KM#8en�xit remaiYa�I%(-< �#1b�'�\&Vs[W ^2%�� ����( x@.S i2�F/EraI J�W�97)P��"S)r M ��sS�( +B*Z��Jonݠ)�=�6�*A�a��agin}��-4!Imu:!n.: _.@K 1}{4} fg8F�1< \mu=)�,%��If.�J5e)~w�%�J� $for�m�Z!V-L1�ndN<-�-�!� -���nފtN/�j*� %�s�'B��2��J�+ )��$2r2�*�-ŭ )�5�km� %z�e^{:hN��r�.Sa��m#'�q�7ula{�IJ2�-k��)�= ��tude- YWnn:�*i�VK����: 12��CEi�np�i>&grE�dq�d2eMr6� I�. rEve ŕ1�:k" �:&O�:�o �GQ�) f�5 ��-'n ayQ��63pbR Tmea"�Y�=s pas] t*�> t a5 du~ v\`~ ��"��B�h�(W."�h�F�Spo��of 1 mW:>f s$"&9 � �& �.*1)N�D =5.3\cdot|12}��R5a��EM�)��jEv�*ac!� bL)F�(� �:4fig:obj-img}a �mZ#`Lj�/)�A� in�W3`� e*��4A��@�" � �h� �&2"M greyua% S�m_�C�*( Y4"} &7 a�*E�6���2��ak�!��"�v= G%��fat;lin �"� W " random&g r�R�"�R� �1� )���B�1��~2\ *d �� �82)d:pG !��l5c&e��,�.&�iR�f�lr�b��Qr�Ed�m�rt� �H ne g<� �� R=�3A-�Nzz( �a devi6m2��+JEM�sgiv&�7)YE *�5& i0(�! M� to�V^�3X3Z:Yt�/a� �s�mj�u6�!I 8�Y�[VB\&AI� s*�1�Ɖs5b�reduced0�x DLN�N\�)�um�w !?o;Y5a� 儩=��(RpCd�9b� �fV-��j!��+ source�m � ��%�is8 sx=cM����gk/�:�2A����5a,�w�9�"ide%he.��&�`s� e�-N�$e^r=10 #.9V:se��C-q 2u �i�� .��TQ!`aI�q�<>�(iNnext 35!G)C9 :Pxcha�er�WAx>R!VFfbR-.�5.Dc�e)a.P*� > I&>�&.L&�c K# rn*5�� *�$�n al�QA��� k� wo-�c& O"�"Iat*of b#��2�.";R.ԟyp���has a �+1RN.E A cP&# 8v*no�7ut-offG�i��_ ��<sA��R�@��e>��sai��Znand0�r"\^*L|'=.eeffec Sn%=��4J:�-9��R��.T"Jcil �an&_%|s� �]�aŚar��@ ����=" c"!;an 2( �EJ5�%��U^e�Bel�o96�N (; =a;-":Uh(s,s')a�W ds'�)mR-).B 3p#impuls��s&� $ ]$M�Q��� K) .-:si�z�Ci^$s�BEq ��a $-�Mat4'5�+ 6� e%j i"��or isoa�M�:�& m7�E��H ce $�X}a,�$graI��-���Fcom� n�����"ROh,=�*|1-�cdR��c�fT1B�!��Y$a�u�u�\nr�1�6O~} (PSF)M�-\1�7 %�mO er�%} (TF))�2Q��,)�="� �" 2ly_Y!�2D_6�. S&XktcR�&P5.x'�uo"���2�i�Q�r�B�R�>u#�� �in �"�:m� �A�sG�:r �� ]2 ({� ��5n *,^@ .� +� ^'sf EC�zijnx.>��K�� CR�fɐ�p�{%"6-�`�E��.��� 6E"D52 !k^Is� -�Ko��00��1�8>�F� �_!ԁ\N� �o % PSF}�  ,F� ��Y,frac {\sin[c�x]}�! }F|PSFR�H1!�:� Wxsq�4i�GE� .�IA�)i��.�Na}�22#q-�2"=2,#% e�<-jd ival�Nof*�92�3 toge6,��YC�LwzXra���W ^;a�!��RI:�����+T.b#U6\�E ?b_f�6�{�-R %�N *no� $2�ő~�.!"*�*��*�M '.*=2�R� % A�?en��>�,����]�A�a��i?}"?~ly,�&wZ^&{N"V!�E�_"� sum.6���`g��i{kite\$L\to$ F_7 � t�sN�$"j ^�\lim_{\} n� �}=z)E]'%�~�gF^ -Im^�a�"<"Fk>�:Lk6a8v_2ii.#e�KE9V  du�"A��(L !�N��)%>��.�o us,nK� go0+�&!�Mv�|+�g \{�%B)>���]�� �"!i$.� *�%�>U]v&�!&�==.�M�=:�X&�K(�h2V"�9 iKA�'�"  PSF,>fR�!�@6�6`maximum�"7"� �Nz�W�ii�2��6P�6*JRk1h%*�!S��2v�;%]io )�;�& all 5 �8]�U> "�� unti�I�� %fr)_Y� �ey&O� �ngalVv�2� a:� 95}V/R�[ 1L2���9s(\Dk#36)^2 * �zSNR-INRI �Z� pd a = #)�6+1 \dag �.qE d�0B#k *�m�*�M�.<� fgts�%nc*A"0<wb=fin%� V5$R �*R?aZ�% =^� [1cz� -��OUTf�E�mV-gR�is~4 6 ��> (r) :B �(s)Jd�\FHk�\�8V�j�D��CtO���l q-$Fb�.F5�R}{Ma�F�VY*mmo� �lS��%A�$fiers. B�Bf�����l�� �1&���=6wB B�,r�n�H Ifae.�@���� a��% 'j�*2p�� ��, M�s83he�M%� 5�_{v�maxa�R$*�; �7<>���� . !�a&Hs�&�>��J= �I�86IvV = |8|^2�;^��'�� �� 6�Zb'c. I� �1y!-C!)�i�yA��4!�)V}$R� � '0m���EY�m P)�^F �PlRJN���^S�o�hl �"�^����, VK� 1+6OG� A��Z� g�g�A(>�|a_k|^2$r)^2/ F+ 1}m�#_k}/r.6 ��} � _SNRjg$$!i76^9ofFs%*uE$"9/J�/:62l.2F�6 U*� .� UR� ��%�A �=�qe �[� �*p�ޡ�.��&�6e����>y�7��k2�3-e5i@m3v; Athav�X&narrow��"�ih M L"�|$s=0$, F(a_{\epsilon�A�pDJ�j\d.3oI�*=Z�}_}J�j|/2ZkF!\� ar�� k *7% ��a�� $?$!V�-��5.�"mlik�%� 0le keepa�a)�F��\#nd��$:"/B$�Kc�~�u �g�.� ?"0,��eZputCf�a}�mM2'&O �be:�(M�)f * >w ��24 ���!6!�A�ũ�w!�P�gkM5R�>"��$L=7$ �2�t�v%�)@ir_im�\o .A>f{��(U!6�/half-� s $W! $W_LM�k+�F�m)�d �=P�[2� ba$S�"D5�}�|ZvHSa��W}{W_L�ef��!�}��G*E�EG-�kY� ��@CiW=1.895�SW_L=0.25�!�$S=7.5.�)7�%�.�EZ� �6�"%i��F�b�q��pE=Ag# of&& �+�"@$($8И�y2)� }W�%Z�X&�$ u��s"6$>�� _ ) 9.�#&���pro=&ive&w#$�6Ia�c�݈`܂��d�gYZV��""���)B�il!�N���o�jV�#s "'^}�.� &�:{�&Bb�\n�#ly�e dat l�\�&a"�0F �v�%y%��aJ*Fei��!�5�G� !i"8{��ne�+z1�=* I.�W%&�}%�jn-2.|2)-*�{}��Se�XII5��!`(h63n��X�(l�R�iF�D�&> .�Iinbs��IVkf�l��Aі># �A9�e�M; ��to�.H �\n2�-�ݳe� "8Pc"�WR:{��@~ -.#\�Jhav�" [d%a��� fcf͓ 8 �>�Z54>� �|���- wo�u�!GjU6�Z� j.�. �^ �B$l"ӎ }��JO1� 3VVc*�c�g�FrG1W?B����l@'��,B�(2"a���"m!a���E]_�K :d#{E-uJly � �! >.�>� 9J�N9 !96F�՜B�FoM�[_Fm^>Da�M� +>�&l��E%BuL9.���� m]!� ������w"�^� focuq4%P ���0.�of *X�>�).΢�X!7^�s� al b�J9!i&�N� ��h!&%8.�:�9� *���� �am��!��U���:�l�i��� I2ei,MT �l��B(a]ͭy!%9 S� �K%�$",)�l�mAkE�k p�}nsSD)�ex�>A po*uaBk˜9Elr�}9�aUD"p0!H*���́��)&/ �8-��nt�.m�ZTM� e<�]!�gener�|:P�~��B  ,�A�]��QG� �9s�J)A�!�%� H � _* m �is�Ra� ppor}�Pro3VTQUANTIM (IST-200-26019M) EuqaH�o�=*>�{99�db���&99} M.~&�,�~Mod.~��.~��71r�539L���*7�L"?� L.~A.~ ��~Gatti�E.~Bramb�1�~Opt.~B:"*� Semi z4y7��2�a"Ģ S.~, Appl.C 26}, 3425�872E"B�N.~ z�~Gros�� W.~P.~Bow��LC.~Fabre, H.-A.~Bach|��(P.~K.~Lam, u���0!9940,�32{-�M�2�Qm�.~��~L��~��5�789Z6N�&�� I.~V.~ Z2l, OA�"�%t 29}, 70̿6j�S"x�P.~ ��~Colet%�$~San Migue�6p inA���ing a2U��EO ǥs�[- EQEC�$3, Munich,�VY3B�=VJ�$M�~���it �r[�!��-=VI4�|�ig�S(, J.~H.~Ebe�%,C.~R.~Stroudi Ie*Walmsg� eds.~(Ple � Nų 20:�"�} D.~ �H.~O.~P��k,\Tl S�� T�,.~Ji� 4_�4I�612�&�v B� ���P�O�)in ���8ol.~IX, E.~Wolf�� .~(NE�-H�ÐAmsterda$197k�$pp.~311-402��R� (, V.~Rokhli �N.~Yarvr�In<����s�� bf 17}, 8 �6�A.�M!�%F)�Stegun,WHandb��of:��GK!9th e�Di =��6�&�1� I C.~De Molrr %qXXXVI!k(�-~ ry(96), p.~129.���95��%:������ 52}, 49O�19� *���,} http://sucLTdipscfm.uninsubria.it/�im/.Ako1-� > 8�;� �,� }[t]@- psfx =15cm \m�e`/� fbox21_b"s� .eps�capu {�#<("��one6n�� N� .�la� I� �~� �� �2>�� �D�]] |'W � "d s��V(a)�*�0"�1@}:"~fi��5w3e (b)i��e�Z�; 5 5 (c). Gr2�>�B+a�M��?&� oBBZ �=x.�?AndurV�v?F}3j}E>��F�R"��G*�,R �&�<D*�T�mbd�KSed�;2� { gram=�s�%4vct5�45�V Q�f@o2a (s�� line��)� ectr2�ed%Z2O9c (*�>ԙ�KZnA5OPqC indi�h*YfA� �>�=^Ac �a�a%a5�a�a!]*�._cw`*ZAG:�O6Ti��A�>"HL`-�u�r (&]B);��>���2�B e8N�) &�B , (bVW^W=3#`��:6 �~B2�z$�c(r)~>VZ+.c>�gEg6jg*��>�V�*���=�PR�>�uu@"bC y�:.N_��%7jS>�~��Q ��I�E�&I�sf�$�"Wlp.ipRhne QpexQH2�):F>}:\vl���d"R���\�[a4O ,11pt,two&]{} � V� 2ams��}> symb� &V�D[abbr]{harvard} \c�on�dcuM@{1} \re.r� @and}{\&c.oldO��#1}v �}�� at}{��ar '100}:EXP8 \m� \�Ve}^J } 6NDEFg� tackrel{\!$rm{def}}{=>] DEFt6/drm\tin� 6>f�� ^i�#Q �ket�|#1�+!�.ket),|\kern.3ex#1 56�braV\$ #1 |F# W $R- |}e�.�eqref](H2 #1})�hy��ń({ele-gant} 2@in-fi-ni-tesi-mal: 4ne-ces-sa-ri-l��.U$ope-ra-tor)�.pa$ma-gne-ticA_>q>tiX�AC �"M4_Mb�� thed49�s�*  gy }"L�Ama9�Mouchet\L ks{m h?s�0univ-tours.fr� ��.E�de/\'9�E�a�fet3^- T:or  �^\sc{(cn��,mr 6083)},\\6Ŀ4Fran\c{c}ois RP ais�&^Ave\-nu�nM� Parc�HGrandmont 37200 T!��f� ce.}a,m*D�)�a�-�r�id�q�H��tonians3� nove'(a��q��, d up��%��!�st1��!�]�xUnm&�turb�� e orj1��#L!�'@�� �dSJ6i�@�J�"U��anB (aTis\� �mapc Qc)�,j��aZ$��0CH�[�� lN��.�9%u�7$w,��gu%�[ac" l�i�4oc�J4 �b��ri*?�i b["�e�=`&!o!$�>ed). Af�}a� 1&!m�e&�b appli�EH|��]B�v:n as"�dannular yiarM� �q -bod��i�� Coul/aqP �hydro�� atom�a!;"�(�/� 6�. Be�sm�K&Q�var�JaQ��ny-Y�9�%m"1+�Y��(�[�)a$��m%-3)�q� *�sk�I�;0"�d{>��oAG2y�J�"�$e�$Ul�R",'��a> !-�A)�)n W�x {PACS : 03.65.Db, 05.45.Mt, 0Z�T2.60.Gf.��"":��I-,T!�et�xAT�B!����$� �s,��KkY���P*(?%�z3o#�T^xCQ�s )3. *<�i��s�Ls�hvla+!}�(ic�atask ��s�� erroM3Per��&~�F�f̀A%aA�Aergent �h�$�B�-Xrepan�^΁q�a�/ ;b"O�ir Ƚ. �# semi��^+Q@s,%�� al �Us �Tt��m+E�e���EQ encapsu7s }g��*� ��$.�%Z#E`�con��s�EAt��4 normalisable �wavefunctions. In this article, I want to propose an approximate method that will overcome these two obstacles: it can rigorously provide both lower and upper bounds without any kind of integration. Like the variational techniques, it will involve a (set of) trial normalisable f-(s)} the �pri�b� ary condi%>l and will concern in practic%l lowest eigenvalue only. The Q!y$e given by uPbsolute extrema of a 1�h defined on $\mathcal{Q}$ (�Xso-called local energy)%�a sense,)�)�D allows to stay as 9(as possible�\ configura� space6�:*orderPim!�)%= s, a^0nalysis near ]�(orr�p 2�. � supŪe}uha���~st!CT $\ket{\Phi_0}$ assoc���th=X $E_0$Y\screte spectrum. For any!t�Yvarphi}$�ee hermitA�y!��imas!} identAs$\bra�(-;-E_0)2\<=0$. If we choosB| suc��at itsNG re�E� $ � (q)$�Ha smooth real norma�( .?L, we obtain: \begin{� � UGeq:m�l�} \int_��!� ^*_0(q)(H �)R@(q)\,dq=0\;. \endi�M crucax\emph{pou�(hypothesis}�to!�um�[��ee�-Hone]- 6G��Q� $�A ��ins)*� | e or zero�� whol!���. ŕgaz ally�*�a�2�,for which itE� been��x�� cas>�it� strictly�i� !� riorA�2V \�7\[XIII.12]{Reed/Simon78a}�� ThenI�E!parX \eq�5N� involvee�{gr!- �sUq, Q5gconstruc�8 from%#t $H_{\!R}q� 2� oper�� $H)ke�rZ �Ia $q$!2e?��-�E� j:� $ changesejsign.!rž,FM� �c eq:HectorJ��\, q\in ]7,\quad \text{U� (V�e6 >7�= now!�roduce.j oA�]�5�known8 the �it{2D( \footnote{a�(usual motiv�A�tѢA a gyA� justa�(roughly est� a dispersioE� 5�� ed f��aNr� d6�. ��i�nce, wAuf 0 Monte-Carlo �s�� u� ex� �� s� der�of& y2� lity}e��at` 2�� Y ati� pproach��Hbe made rigourous.}�o def:%f)0��E��rm!� }^{[�v]}�x0 \DEF\ \frac{Mb\, #(q)}{ F� Fa�"7 =:��Pimmed�ly-�Ix%�ll2�� .����6$��"� = \inf)_  \big(v( big)}� eqslant\ E_0\ \sup�cFb SurpriA�ly��s��i�yr�ars!Zi��  liI ���{Barnsley78a,Baumgartner79a,Thirring79b,C��Xall/Reno82a,Schmutz85a}%� always unsome m� reɖedYs�up� s  i ten mis�). ��original� �edo e linkaW�mm�to�8 z �1����" ) in�iI4ce%a.^ �,��y��magnet!�ield �����fi%numbeP 0freedoms (likA���rel��istic �S describ�a BECe0$ except,3haps,J!�:+ 4a�~BO�& a& deal)�Psm�W2� % ble~�Qe-�d�parame��Ŷa spi��dex�  %�w!�lyly�����')6J must!� stoom �5parES%=bra{q�H}2A$%�$dq��� meas�B�2yC A�a\ continuou~d/2�t deed, �dYe *G,� 2��&��+deP�Ore5aA|oup!�(q,q'u�&l^2.vq�(q)>0Mk1g' $Z�\g� 8V'')"� 0+� �� id>Zif!�6%�a (5�: )> � 6� cons� 9�(;��EP� s.}. Mj preci� e5��aE�!� ��U�s p#!��1����8l*f�ft� �)�a3 $ a�it{ �} ��indepen dir�CA��z��along ! ��#be �d �f�a�� actu��Sa-� dim�p$ubmanifold�> 1' _\lambda$�� ��  stanPd�K)�Oa�rol!���s��y� in ay sz*�$C}$. Accor� strateKclear:�t, say,4Z$an optimiz4�%@5��find $�{ �\i� C}}\left(:{: �B@( H;q)<\right)566n.$=H :'&�1��a�A�ng�rA'rl �!� $q\mapsto:2|IXMFm+lyɋ9�( ms Mors9�� g��� t��)�problema/r�I*w.� cal` e"&�C}\times�W�� neighborh��ofcr�W� : adAP� a:�A6� simal . �<��EYfar away�<�1~ ffect #�E�s. � recover�} globa�a�"���%�5Jbecauhe>�!��+2�bifurc�= ��a�i-x� m�C4Poston/StewartI(Demazure00a� AI jump!b�r��tant )��>deE'$acy occurs� ([chap. 10, } i��H fig. 50]{Arnold84a� In�chet phys� &�,u 'AE*F 5�� E�<��ex�!C"?"� ((Laplacian # ra�a Rieman'�T ), e " [mosY cen��� (�) {Pacelli/� negro04a}3A�ra�I �d searchec _advdA�AG&o-�)%ai�s&vmade (-� ely)� 7 �7� &� same�sons asP'-�*� , he-J".V  " �#cy led�he a�un�_Alp�n� n-triv� eiE�!�$Helium atoViA�� ly& A�d�'!milure: WKs ��alI# very� �!u|F.2q�l� �-Bably g�� agre �$�while a �] 2�2{�"boE�mam% .# un%3e\T] �, ��s��E a'ise� 6�%o2Y�8 major drawback�c: =^ �Raob{ to W.���:�!. Bu�y�rgu7%bA��t ed :arɏC�d�-GJ�eo2� � o$4$�m%i�� , Y(s!]low c�`%ided we��blE��Ia ski&" (elimina��Q��$,�� roll ab�(O n����� sc{jwkb} ~qu�6�"�&4minimums, etc.��� "� , I7 �#�#i��n6��!Yat |'!k� �;ind� a�" ���results4�lex�r�t6'�� 8 1���'sAVJM2Y��M1�h �h,�& it � be���#&�%�2�%!)� ��a~N %@"�C�%�#� le��.P !3Bi�'�$ surx]�". �yAB6�Aa,)mF1 ��sI_it{"} a a be�&��@t�A�. qgsi��%o�"ed��~$\phZ/B�"{^*(q)H ',dq =>-|!|^2:W &� � B\ l *� ��J N��th} , beA��A�!ag�, A y�axa�*!�2��*��$��mz�) acce�ى�YD? nume� exuKoPC e averagi 9+ f~$H$. "�&Ap�)�dA"| ;�exampl��2d-ann��)"�$�)"�(E�� illu�wo cir� $radius $1$� $r<11�;-�di�tAr$\d�<1-r$.hQ��ź2d-dom( betwl*a� y. ��i�stAU�2��eZc��! !7ak: (x,y)=b @[x^2+y^2-r^2][(x- �) 1]$� %�i4&F%�~=��b]� jE# Eloc}"�%>&\�'+ �}{2 �E=>� F f'89 /21 $(1+r^2)/4]�{�HF4 �. >$��$r=3/4Mb)�=0.1$�IV� � �at*12bA#�a�� ed at $E$0\simeq(0.86,0��nd� a�"�28.390# � �"" _� :[42.94".,�0 "�D�*��al&�Kabove�e*��&9��� eO.�"�#La7ge� � a� m�/)tV- ��e-� aNZ (� 8!���}��.� $55.32$� �ta��) $�'V-� &� re�6� w �%����sSrooFB gj'B1n�G��Besse9{M$ " [ -2��2� )(!��4^(n�< s,!�s-5���s�E��*��"6 ���� for I�<mb sato%�ri��!* _ � �)Rmay'ea"� l*�. WR;A� j ed, A:�h! w3 ovE`. ��-!��s�y g�(t�0�y a multi"� al, ' se�bs:6�$* ) , a 2f-� sympto�'ex�'!%!5(��availb�_[I�duŘH]{Maslov/Fedoriuk81�t6)�J� a��& d�� m� semiclass�C&�s:~ �� t�k6Sb:�tdy�/��mK it �^en�%/it{a�} �G�"&K. W8��@ >��-�.�kU���ECaF�6r�th�9$ess ambiti|!programe9Vi�/�z nont�&�$�$�<"%y�i�se6$q�A to�� r a  #A�$N$e2�), �"�,� rged� = s li� (in a $D$-]�1�Z-ce.f:eir�<-*�."D8m_{i=0\dots N-1�"�+^2/(2m_i��the��-ct�� each� via a twoB�D�<e_ie_j/\,r}_{ij� W�&ass5A� masj' $m_i?AUch!s L$ALoweH3'�!�T E%� =f�9�1o"ec�R�o!�$ar��A� are �<�$D(N-1)6xcF�<�� M+A(ŝ ry+iA�ns $q=\{T bf%0,i}\!"=1%� !��'�1�A�N �<ish]. ���6<Bs "� &�- hamN��!�H"�-=1}^{�z 1}{2m_�IF�p}}_i^2c+.80}.\�* tack'.,=1\\i\neq j}l�2Z.BjnkRh0Fhfc2I�}{cE� ,j}}F��=�,:A��}.!E�rB EmA�8m_j/(m_i+m_j)$.� D&G �,AL.A_e C&9��AOles $r {=||1'�AQ-6 j}||�:.� byI o���K "l �gis:BKYB5� >L� 0q)=\exp\Big(-)uAI��� � �B� cBS0L )" G=-A�!� e_i ��(Da��y chde �  a64��%��ybe�(� th� on_isɄ��� �@��Taylorkanj9�0: j eݩJ�hl% squ� ��gr��&�QE<.#�dsB�5~Yc :�6P$.I=-Na�<�e�2�^2�~!��-�z2\wide�Aj,i,k}��2I 0k}}{m_i}\cos(:;)R�;�' sum &c:ll%��+s�+w2��'a�b�$rmD� :!��+s"w t�@��cts&!9�;*� treats�)�^�7 �l "92�� s�&U�6�is�_ed Ahy�/ . B�B sih aneousJ< �$RI$�l$\pm1$1 a ra�(K=d�Dxq9ioE!:..�, into accoun�Od.�28)O �",�D=3I�,on as $N��tT �($N (N-2)/2$)\-e� um�3 *E) bl!�inu= �Eu� �� ,la�NfacB $3o -3-1$). N=�$we�%� >�/} �Y�s]�u!�*� \ �*%)-a h�"�-tom (-2$N=3$ E� $(Z-2)e$�b\nucle*�X (� �-�]:"-P �l�@3ass�lwo!/� �pErv>�w�2t�'�ic uni�E:�,=-Z^2-1/4+Z(A� \theta_1+ %�N � vl�8Awn� �ve� !��� 4 �s:%~��ira�2 (dia�0c`oqBdh>~6��.� $1$;��i5a� te� pie�6in�iSEQ!k �$�,�l� A��~ p$l  neg!��8!�st>%@repul��)7�� 5� h!�D��"�-(Z-1�$� ��?�,*��%k ult. 2�hydrog%�o�� "$.�72��F/:third�r5�N�r %:�� >��F�IA}J�q�ECu*-rm 6;8, $B\vec{u}_zA�W"�p"�2 � 27"�%�16 guarante)��&�I$Krein-RutmI orem u � previous � (p9ic�( +!.� I (#m*�9Sr:,�%9�� �7^IB), ���v>1g�.e9a�6u"C:�5a>WisԥYx {Hel_%+99�:��!21� ���att<v��e o6��VM�u B5s�%o��@\um $L_z�x2�atQ� any &jva� $B$ �Avron+77E+MR�%�eE+�Ta�e"(� =0$ � P/. In � �M eser0�)�5Q�2�)3/ *� be� sG;gJf!@`(} r�+c$z$; "v7� n75 half �A re $z"0� �)ni;� au���,"�0$ o1"�HcoK0ate%$(\rho,r)$ �(�( FIG.�%fig:HB}I�� omica�t�&F� ":2� VRgA/(T 0!� e..A�yis $V� =B^2�^2/8-1/rA#In� t�( (O��f��ity��e mO)�9.6vM� loga�Kicn; ,�?9o.0�.&�3| $S�"ln�G{� $�",_r S(0,0)=-1��rX"for�N $r2"A���gS�?�!eno�;�  $O=�8itzs%g�[A��"S5n-r�l(r)+:^2h�ere $l �h�!T y��s. Ch $l\equiv0{h -B/4$ [a2. 0$]ɥ�&� )�]A92�: $����B�& +B/2mK*�>�?� @f .�is�=ANc�e�=u�w the� y b?J .H �5ch�Pngei;u):r� �Ai�!�� verg�Y r\to �ty$�O�&" G acter�1$by $\alpha`4f9a"�A�G+�%"�# bala�.9*�&#� Y� .�^:\� �Z*Iiy� .J.%a�L+ M�. Nam iULa  $S=-r-BI�/4M�0(r-\sqrt{r^2- })/E�^2+5r/ B}A�"{6%�f�(\gtrsim2.3$�\\IJ�[No��Z.orE0 �$B$ 3wB*�T �= a Landau<5te.DbN e}[!ht] \� \i$;Lgraphics[width=12cm]401_HB.ps} \cap#�bel�Up�D��]��!A�2��Kgyb;ick�De)%�)�!� a Zeq�v� .}�e} \�{Am�" PYI$ac�-s ;2"  �f&-Q 2f X4)In�U��_0l(S_� ny. . Ix"ree�r �1&�-YBRT!bŢ day,�et�t�=�Z �$��ci.� se86r!�alN &u�Qv�Vs6�*diagonO8a� trun 5d E ces ? Of�6oniNK4mbinesm u�,ac~C�@N* look&zmK ,�-�ŕ��h�9� en*[T�7�:�Rfu,r. 6�)$q�N��(a ��(_0�,$��� its A�stP �5t�+. Am�8l%1lu �FY7e@$S_�� t�&�KERnC! �(u�7 �, A͞�7a2+2�7 &�7)� *�7&.-�0��*�F f�:� ��� stud� i"� al� �&�7�m theo�VS�. O�H� d�?ݟ' :�8A�ir�{2D�,<'&Q�Lv!w�a�a�*9\�; pZ@\A>A)m:Q)�-w&^>��ef�)cm�# x��� $#a catastrop� %. {Pon�8. "le !v�'ivU<udy�fu�I inv�3g�s. �q�m��u� at aHl^levelI� a 1dJ��.�E/2�E�l� S_0+�% S� a Gaxan2� �% Ss(-(q-�'/\s�( ^2)$!�"�f@9�"�==(s,a, 8t<8 ific$(h � �/�h rt:2  ;)�/6� �-wis�r{Ov�ill�9� umlfW����"r �@�h�a� �Q;2q/� C\i��Bg1{i9 ular�4 %] �Zmodif�2� �%�-��~�KwWFh over�~$)�q by !witude~$s[*�XF*wPlu39% �"� censeura� �# ``lift u��$ress'' too�i� $``prudish !� or''� �T�  Lq#�-�(�B phen��S��to 1d�O>X��Ǝ 2_�eurb� }I&�8:�&��$ (da�!F])a�th� �>1j% ; Oto�n(" )�Hay,L$�2L_��0Asol�1 @9�Ua�,���8 �Ey�/U�m�Vam�(solid��7�, )�).$;iP�K � �bicm�]IN |s � by p0'n� ]+ a"r@a��"�J" M S:���RC� >,  T�m�6�+;A�M &]� by~$V�2Dr^2q^2(q^2+\eta\, �A�-2$ � $=ng&~ �.�( as~$|q|\to�, �;!�A;Fz;)exp� for~% . I��ca���vm�4 4a�ionv%can�q��2�m�splitS�[=&>"3}r)\0 ^2)^{3/2}*p$}r(1-!)>11/2}\\ U2}\ln6&.Q46#^{�}"2$ �:7\ �I�}�3_b!qbq 4} AED~;3q�)��~c2�Q� `2�3"i8e�4>�^{(n)�'�=(�h9ly ���7"� a�&G[d�:m��Q:added:f�vX-/:�t�)�Ymen"�\ 4 V�%�R&.s $r=1�2E#i&+M� =8$,:�1�sh!�S=� &Ha� be ��~$-3.27$�C o~$-2.74$)62s0 is -2.66))�u3Sw {])�-�d�}.5"� fixed� =1$. O� heir��( J"�/ly=�j Ae a� an�EvF��a6o�R7DtagQ .L�B �.o� ed:C�no�jl!!�,d � also,� <�II QNa� Et�R57&�/d in:��� 5�!�I��"e!rt œ� il�E\"CE � N���.�:�%�m !P�W��ide�k��lya 1� m5� p�sVItype ---%^�n�`* curlyH �.�`�>�)ruitful�[H Caffarel0^K A?P,AE"D conv"��je!�a)�)�!o�'��pp}"��) [of�J�fur�es a.ZsoI 9$QYhay E�?�KI4.�  oa�ah�(e�H I%>t 2itu��L!rE��"�' �0-� w�H�k�%a?!�hel��F &�ż(�!�k!�~x�B0T,&R -e"�jI(~nI��b�plto�$�aA���� �A�f�>y<XSte�not obc$%]is�!�Űdem�.���s��sYc�3 =kNld[�4b�< starq~�HQe Giaco3 's br�Cn 5tui��)gE " .h'onI 0�sb��[� *�- q"�e. I am�A�b� to D� que Deland+?LHeno\^{\i}t Gr\'emau�sha5ir pene;8� oughA�� s�IՁ��i�2 in C&�0 9%�x't�st:1 kinda�hospit�y SA� LaboRg�` Kast@+Brossel@(%\bibitem[{�%namefont�0}()}]�> 4,nfo{author}{Ef; M.}~�|}}, % ?note}{p�, mmunc])6�li�6�N|tyle{/users/champ/mouchet/tex/bi+/sOo �;�6 mrabbrev,~_q�?} %�2ar <neferN�.e�-i \ifx\> DrL\BySame \newcommand{ }{\v _X\rule[.5ex]{3em}{.5pt}\� fi>TQsc6T ,}[1]{{\sc #1UF<�k6: 8em #1\/:b0" {the)��4y}{} \harvardE� |R}]{:}{\oldI1984}} +:R"}:MR$ V.I.} {\ (}:;  )}: �{C&��`\ory}. {N}ew {Y}ork: {S}pa�(er-{V}erlag�*R��' , Herbst �c�and\ �k.�.,�Z Q-6�77�6^(� J.xI.Jz B.-677.``�9{Z}� �& �*s q''L])@Phys.�Cpt. A}, {\bf 62}, pp. 214--216^.�M=:�8}}78% a�3 Mb�786�L&1� y!�2 � 2Q-ycv� 2}(45�459--467b��v6�M�lnegro.B( .*.200�VgVY>RG.P: J.F^$d�<�?``An E�d!LE�'su �.T  Geombc A@ �Ale�Tt arXiv:Y_/0308099b;}G\, Boos{\'e}, Egydio~de C�jlho6u!5arvulle.]�J.} 1993A� S+H9s  O.� D.R�R>� � Vb�936�Q�w tunn_xg!�u�A�_yna�d!���N�4ar>�560��197��0^�"� ��.)EB}042�3b�?]�RH b�ranm6ym.�N% '.� 1982� 0]m9� R.E:�t M.H^h\� ``GrA8F &bx�� &�0s $||x||^\nu$9�J. MathͶ�23մ 64--70��er�zm[64( 23, 1737 (�)]^hDB\=V.B2000}}002 3n 0.%I�B&�%<  *� ��Uni'Xi� .*� b��i.� .�194� �iu�  R.f�4:�J�&lO}��Rev5�71m�827--82b�Hu3H, Hoffmann-OstenhofB:Owe.��:6&9�� C+�35(  B� B�T:A�A Z�9:�Nod�'et���+� �F{\"O}din�4�zx�#eb+���>n�ST�M. CommV|0" 629--64b�G6�FG]�J' )6� 81}} 22]G5� NVB+z M.Vj�1F�Semi-ClG A)u�<� ѺM� a�vol.~7]i��B"`a�\ea�I #s� 4D}ordrecht: {DR}eidel �msh�Z;ny^P�(6�6a=�J&AYt^a:�� 1/ "�_5� B� + f�2� S�.�� y%5�k.� 0}. London: Pi�8^ Reed:}z= B"! $6�% -&�z5 M:�En� .� 5A͂of"tzU`4))MethoM.f�F:YOal�khy�bAH2", emic P�!^8S}u=(6 85}}�u /��Z�85.|�(?� FE�N\&?�lLe2�108� !�c95--19b��v�6�7�'79% bY Wb 72�)֍Z����P:( molk0#�s3YA�!0�^As�Z Z/endB  �"doc�`1G$jump}{! J>!A>A>hc sf{H.c.> mean}�-#1�glA%DeclareO� {\Tr}{Tr}6�88ute}[2]{[#1,#2]:"eq gEq.~(� #1})a��q�i$title{Deco�#nce-Fj/Sub�#CCh�A$-based Qub)� :Ro�dF# Enco } \iD{Daniel~K.~L.~\surc{Oi!(�1dl{D.K.L.Oi@damtp.cam.ac.ukDffilio{D�Qt�#����ed�ϩT�1� al ics,&3 y�W4J,Cambridge, W(�(force Road,, CB3 0WA, UK�;{Sonia~G�Schirmer�����2�%% j�Enginee,+ 6)9L, Trumpington Street6'2 1PZ6'Andrew~D=(Green>>)CEx�� Compu]1T�!ology:�$ Melbourne��(Victoria, AJali�-�Tom~M� StacB��a�aIa(date{\todayy�ab�Uc+W�>oba%'�& emsa�7gq��#um dot qe��ich�� rote`Jag5 t flc~�g�F�|s�" X �\aFtlog �h08[z�rO-��t� to noP3N{;1b�t g trapi�� >7�v� g2A.a�U�? a>*( 9�*s/.k �|ity. �9p \�${03.67.Lx, 5.Yz!��j� &�&.�U} Q�� wd� e�9�-Ehurdl�6O'�#5ms�bus�* ey��"ˌ�$!]��t$ � � (del�7�EI d� ~V${Zurek1991�. cN4�%�/�".�%A,H0R/�unpu!�oEs!�r.�(QD) �� ures �Di�#nzok,k&2$M%l�Zpe��mk-libZ �� � deph�zimHAb- *Q��� error coru (QEC)����PCalderbank-Shor-Stean d�  1996 Underlu%q:QEC�2A%Nk [a�teVttoG%ό"JEm�� �aleah'qZ�4ssAW=��eB(DFS)-mZan�81997,Lidar1998,8,FIGDB�. P�"e�1/���7undou�"ly�e �%7�3. 6>DI^=I �\EkertJozsa,HFCJH2003,SGOPetta�,G�)0n2005,Buehler } K!�im�5di�d%�DFS�$as�ct��)XaQi�?&nsou&of.U �4bib:Hollenberg�BM}. Her�N��;HasHchi��=6incorp�"r��nf2Q2mC@G�ǵƩ�o&���ons, ��3r��t�'H q�x ��a�6}-�} �}C��V>.w3�pPsr-y s'*+ƓE�itPAIP_%K�'d>o[) j �,a�e[on  �den�� Alter�n�9n@ 4va��-�FJ by6�AJS/ 67s&Y~Bang-�,.�BViolaeGFravalA���22 *D+}�s[wB 0.456B.eB "B0a) 2QD Dipole� �  .��H{10}, 1}\}�{�/d�#!an�Psq���&e�5or<-htZ[9ec!#r� S�IM�~(($V_{0,1}$)5$7:�Jro�E n SET (om��d)���}��� uF basi_(b) Tema|�(A�spa�@ly�,��&�5�0�rrs T. c) 2-E�N!/4QD� dru%�@ � �$0}=a^\dagg �c %�%� {vac}},\  1}=b$ d .$��U�Di1e0Ag�Qu�va�+�� )� ��bit (Fig*�J % Na)!Q�i�fC4J6IT S�2.�. Ide!s(5�sN (�E-)H $��$.� �4�id`�hV���.q���M]�al '-�4e  $VQ�. F�Bmo��*�\}�*tuned,M]u , &El�:�R,d�xte�v�;(�+)&� zh�*r}Q��&� &�N� } F�$1Tm���K environ|�!" on-si&U?� Xd 2cA\-�}J ge. 2�dr��%�?2y��\psi}=\�J�0}+\b�:|1}$�Xm6-�,BMroj :�}| A |^2\ 0}+|F1>82U ��Ao on0I� l�7o�Hk�] ise,i�i�>6�o}�o���mpe�E j�, k'.n�}s=u `2F�F �E�� R6M�unw?Sd� �G� %\p/{M�d-�=&E W�Vnecu &�6.)%�E-4:�Ds, "':fny-� lq��Ag�$yQ � sl *� nuc` |TOALBS1999,TothLent2001}. Two ex�sU��dIB8E�ereX,E�6�gHi*�\QDJa6���6sۈ� EiIed�?AeZ.  $H=k\xi(t�rgma_z/Qb� $\xi=.F�a PoissoG�� of 89[HW�v$k0k�in�GA 3,M�4}. AZ} ing �T-7"��d`>a-au��`h �Iy� or*� ��l� 4V_{01}�� le_\xi��rh 0)\sH 2 � ik� u%!8')� �GI {\xi� 'A\\ :WJW��yu[sbo� t�F\)U8$}\sin# p]&n:Is��i�"�JM=\s>W k^2- g^2^ a��r���.A�"�@ !�a �t1�s $k_j��9�decay1 $non-MarkovP�+er :�ty�7�_"��B� 9�t)1�E�=�){h'l�}td_j%�=�_j>�_j1�_j=�)-�..�!MŁe 2-�AF�i�1��!eqnG ) ab�$t�k%����%+a� parabolicF5 �27=4/.4 \ATx1-t^2/2)>4 k_j^2+O(t^3), �t\ll1"{ 1�{<�jf��U-�/Ii�^l�qeЉ�rQL;a��ed7 ��!�k_ɑeff}^2=.�$>�%,� s}a)� |?vshort-�A-[r`bj�T G�%�u�� �es �trong�f������h�d�i! dat"=�Xiv�yRvk>r8T.�s��Ss �D����^�~�x�]$1$ (�P�D%Z$p$�cl�rN 1$,  !��XS^in "@=rz(o��e ing,A�inverA�� ��-MJ0strength��Y$�tau_p�L p)} 23{-1*��we�N@#{ O^{(4)�)] ^{(2)}} = $6^>>B<�F?KS>4)&� j5��s�� four ebH&� ��6�}6 be7D AT&W!� j�nsa0�mEC�� iE���� �A >ke�---u�Eey���A7�Ie�>: 2)}/:f4)}>1��W:De ��gam �BE� �!\���!��C�B�{j1M2)řpto r_j �d $\ k %4>%3}�Xspt�e$r�i�0eteb&T�U�o�k�� thu""ivA%0UMd�o{�imu1%�g2QDKI�wad20$nmSZQy-"a $s^Te (�P donorsOin �rORef6 J�dB���lo�`fb�nV�Myer` ]�s2B. � Aj�!io�1 � �$25x 8$Hz��  cm�ŹV7 "�F���3M�"s!*8-%�QD%�5�It(a)�(�� ay� ֆ"��I�!.�I�C ��&� �d� �Vs�Km �|�'J^�� ��vM " �> .O�EN1�> �~;c�Ian-?Ea1#��7%��aV){ylA9yh]i/� e�to�rando�V"�ed.YA\\lU[ET�'BC!BXZ�e0.B�#4>VC;��and@ vsqD�$��!=Q�� E�vs%�%se>��or=.�9� p�"���DNt��-�d.& &"� �Y X�'�$.c,�##d:I��($10\%-90\%$!�gAt� �is%AI)T�S[����R�@ �M�%G�a toJ satuE�nmz>��- B"R1��*�eie5N��pre�L>a|a��%�q_�su�n�l�_��*�N�an�Ol"�� �Q�Op�5aliV�)!G�b� dev)�'�er��"� i�# � { & � $scheme's sE���Quc!�hE|ia�u��x O ��@-.. Non- }��%im�QD '�� ,�i�'J a dG' R, spoie���up -"r�d�.a��n� 7Rh�" AB 92��e i#i�(E�is �!� �HoT�ar �d�Ӂ> R3 t fab�!(alAv�h��t�s%df�+�'f!)spiT�2QIP&�pos�,Tz M{A�p!%9Y (� $ nm��uV��`"�aSih de&�O&o%_�}.}�&S1��A��{��eAK� an.a ��q Aul-s�` offer*?j��R"h0oI�iIc�!��mmetryQ�UtV.�xm,4,}]A�)|Ecn4y* E-? r.I @NUuu��PUed�A$!3a*�, 9"�2]��ie��a5SW�I�A�&�q�&� !Z��APb�OS h/sU4�:0���!tV&3�Pa'oWm,$ tly 5i�v%��S�&E �>� -2}V� ��5��2> �Kvs Plm� Eo0A3%6ta"c}n2 fl)3puK$1 h&�)�B .W'a"�[!�9]2o�/�ard��a�gma$ (p~!a .$| arra��"-l�)�3LSas� e� 1000*L �of 500=� z�.GW�W����n w.r..��2T�$%�-ϥ %�����g*�ofi� ��A�y'y�NU. Eve�Ua A� �9�E� (i�-t = 0.1$M�a���A剗t:� �f��4GA5}]&Hoy i7W /����a�al ��QW0�'{\�i_z^ؚ�i0_x^{\pi/2},c-!i\�"�+we iE�s��vû"�fn�2Mi� DFS�e0gge��aeia!�c holon0wc�/ �7�hZR�&USBDCZ�&"* AA$4r%Aad�val 1�$AgZ%E{� �("5 !wtrain% n aux�:�4ot� X-!�� lexAZ�Xuls&�a�offse٤ �կE��c|�0..!1ly, rapi�3mod�ng /-AL��WU0�-"d"�"!�s] ckly&d� � E�� t,� ns�" po"46inG�3I!,�K.@ei �Utnx2X,q�A>7Wntra-!e%�����\V"^ �4le�!�? !�Zu�p enhrY �#Y������ llel s%at��{canW*�:ZZD��&4*߳T9{.�AGy�deWA��f�q�'d&aS,#B,Hubbard �Fl��&�'A3 �!+o�r��)d $a^{�0 }, b  c. d UEN$z%$ .�, �nin�ckw� fash!:�%��0c). Fir 8 5%E}(a"q2 p $e Bloch spJbZFt!�� ar�La�z-axis) ����=��*}(1,e^{i�}*�.V) bi~8!� paira�7�4 �*2T��A���[*!uE��' phi=E�2e>�.V (')-V_1�.\� ]dt':�*}�V_0,V_1! �'"q&�`�.� �1aO.0}[z "�2f�2� 818b�2 f3�*2M'extI1�ի$I����te1��� a�ɭ6$A%c%Rarrow D� $B>C$. AM! F8B 8C>8D$ �8aLll� ds6�,�'s�nU?nseAtl`]+��*< �kmor¼�t�� . W.dv�!3u�Q� )^"�)�Ts�pan5p�w �B�6�6�l"�*}*25U i/5.81}="]5 b3��E�.E%eno=vi��[eg2�� H_{0}^{V}2 0,0, h ) %�&�1$|a$ �asc��#���e (&4)2I��&  $0MG �"�%�g"��#��-� 1�.K88.D8�Co��� 2ׅ]��s&@y switg���YL%t�$\O %1" Uyd��NH R-��%(�� ,}{cccc} 0 &  l & \\n>. D06Z�, { �x>m�*} �%�:i�5m�Gg�V�=1�0-'X� f���? a�$5 ot}=E�+eѡ|r*!&b'e`psi_1}�&0}-*@.#2#.3/.1},\no"S'C3C ��4 �B .L�& 1+16 #^2}+1} + Hva�FFb|4�| -1} )6|F1"��3eig�JK&5s��%�-e�N!�L$E_1=0,E_2=1,E_3=(1+�'2)/2,E_4=oF,)y� T%��X2� �5�MB� �$��  no � er � 8 &UgotTra�su��8�and��B�! |-��Aly���{+O�&ccu� wy ����.;�>�,�,7�$"# � an �  $N� gamm�xn 0)$ �A+=��qj�82c (is rm aval�to�T>�8uo"�z^ w�� az0-^�  +�*i 1�8e�qu��36-3iy0}-� �1'�! �t3�[E_48��a" al�isb���m��>m��%(n/m)���� �n/2,m\-�bset\�Mbb{Z}^{+� $n>m �,gcd}(n,m)=1$� ese ��#86�8�aOfa�� amurun8)�^�/�!��� & "} $m6p!�n& 8"�Ő�  ����'��fN� of�-n. �6�& "P"�]��FZ-�J1 fc?"�5��t��fin�& %imZ)* %a�9 �6�-� Fp�i�*��a)&x ): $n=2,W av,7C"� %� #0,\!9>�Bm� �e-}@�A!7>�$\e�9)zYl7!h!. 6���skW�v/50�Yps�?\a _2��/(4t_f)�C�u=3.84"�$ {12}N&�N \ ��_4= 0_c� (62/61���dep:.�!rom 50!�2N&��>>�E\pm xE pm y z�!�x (Da�f ~� 5�� �!i��k-�SS E}=1��F��*g�A�h&p�p�0PC1997,Bowdres7^\�&m�nK�#ings ("�)%9su�"@I"� ���4�(�sŬes" o6X2"��de�lzHFdB�.+�p"V&� � U�co�h�5sEx2�6 "���5�<�#�%.` led-�9e ($c-\��))��@be�~& stU7 earli�-ork-�SSOi"�Q2�e5)��� *"0)1�"�%��%dv>��!�DF6�j�"�o �F"ސ�Cz\o�cs�R z$ i�&�(s�H���Bb�!in��&��AB\us>��2I;*wB�K�)�,s�F� 2"�E.%!"� �1dee;��WL"*�Hs!B��Q1�f*Foa+� K�� s up� x] .�,��tice�n����E�A��r!X� !�C#i�c�v>�$�E�-�"ʺh�#�<�1�Ȃ"=R�Z�� a'�!�>� LW5)w�#�(ruc6�R :�JysA4yA6p�q� &R��Sd� �3 a� �%���=Dr/]%ltu�m]�N0 &� I�B� ��(&�M�I�%.D"n � �/Jss%�j<*����T$C}ap�w "t�� ch a per-BucY6� \acI��A*,s SGS, DKLOh TMS #$e Fujitsu,&�V,-MIT InstitunI$EPSRC (UK)u% EUU?�$RESQ (IST-)-37559) fOP)%9215). ���5�J"�Vn Rese!� Counci��e.!g! �I�$ NSA, ARDA�ARO�<@ DAAD19-01-1-0653 ~=3�os�-F�-ls�<�ng "^Y3{�� �sto Chr�� na GqchmidtEkus$&���%�*hGRe �ce� i:B�q99�Ubct*UW. H. ZU,[Z T�W�,bf{44}, 36 (7U:$GDi2�T D. P. DiV�x(nzo, D. Bac#�(J. Kempe, G� rkar�B K. B�� aley, Nat:R� {08|39 (20002}*�T A.�b  �.�g LaO77}, 793�62N&T7}P. EO$M. RasettiB[Z9�0)&72[LxT!!A. , rL. Chuan l6 �aHh:�8� 2594�82k ��Q>�F.R��B�.�Y 4752JYF"&U`fF�0l'man, L.B. IU(, V Geshk0T$in, P.Daya�%�la[�,.�B�7�l224524%�42�&2U%�%�R. IU).Mo�)?1�6AG73N�"~U}T. Hay�, T Ojisawa,a!D!�eo�9Ye2J irayama2�6{qX22680 �32�S�U } S.!'^ ,A/D. "d qD.A+L. Oi, a�o� -ph/03050!�_*2c"TV}a�R. bC!Ahnsa�CeJ Marc9Ma� Ha ��A.#GossardjM9I186802 �6�&�V� �/G!�sk,D.qW�zm�U��2,-mat/0504451E-52�.-W!�M�u@WA�Ln�J. Fergu�A.!�Dzurak� F. E. HudD.. ReilT$A�sR,!QG. Clark�N. Jamie;�l . YaA>C.a�Pak�ndqPrawer1�.�6e��E2�J�4AC.&�W�S.� Well%�A�R!lq��J�5 �G�Milburj RE� �i^��B�?tex��6�11330)�6�9X�� rreti�2m2T�a� 155307%�6�"�V% E�S. Lloy6�A�58}, 2�6MF&�VA ,AK J. S%J�HdJ�Vngdell1�y�41206N&?N,}G. T{\'o}th%�O. Orlov�)Amlani%��ent! a, . Bernste�n�eL. SnidAS.��?r169ͭ92\T.�NbT\'7\Ce ~.9N63}�052315%�60CJpN}WE. kG.E,tH.�.m$6}, 235303k22�"�N!� H. Jra�!� FearI�LE�Tipb�T�� Sp��6��{042328N{�N}J�+Co�UA.�B��%�JJ i� �>��S.�#. 5�`p115302�6-&`O�\'�lis~G. SmiAoJ����� ie,!�H�+Lb�el)� Y. J��bz��6d 033�6�*�JT�j��y�� R. Brenne�2����F��%#2�Ee.M66�8~57N@I>;K� cY. XK2�2��195320%�6�& JM.���K, Surfi&� 132} 42� 86DM�K} HE[ �.WJ.2��8�734J� *L� R. i1 rancA8A+  llum��.� A?B�2�qp�� � Tech�2 36i�6��L �A�O}ENC, Proc.# SPIE5 565k52I6k�I}YE� GalpPf,� L._,shu�3�1D. V. ShF ev, o Confa9F� Prob�$MesoscopicE�: I&�s \& *�; , SpE�(� �\�y��31249Nl�JF. Me� � Loss6�5�D09451k 6Sc.�4S�,� . Cu�_Y.p�4,E J! Rue\f llam%�Oberbecq�&C �\6�I  361"K  "��.>� F� U��26�U 6D/}I�Unany> B. W!�or� � ergJ2 d5 2910e6eD�/L.-M. DubJ, CiraY�P r, S24e5�29��169Nw���(F. Poyatos,j^B}�v7J 3Av����W.��. ,a&K� Oi�5C hort,BanaszeE A� neU�B�9!�25N�> >��4���2�e#>�.o9�i+ 1232)l5Ae�Bp �%\dRpAp$aps,prl,pru},�qped@p*7p>:#�g,*2psym.�pfloatfixbJ:��I>�B�G�/"q�^>t"Pqb \&Cq[dvips]{fbx}�put{epsf�setcou�g{dbltop�'}{2�*1�i"V4��h�G�}�of Wign�7nd Hue"V�s:3(tow�  um imag�ea�m} % reM6�k ..2�l ��2neeIL%�Tail, \O1Lks, \homepage, \alta&cn!�y��cʌ@ % author. ExplanLy � ��2go4 []'� ct��e-~@�r or urlF6{}'�9o%B�. % P�ge ��a}xpr�= macr׭V7t���"X!B. n!�m!�xs�J! �syRcelW�!J.+JWandN�L�H %�"* LBWa� 5M3-6�)�!�/�. M{M. TerC�o�George��nd�X� (hepelyansky qQ 4[]{http://www.E�Dware.ups-tlse.fr} .�{L*��de� iqu�x\'eor T, UMR 5152 du CNRS, U�}$\'e Paul S�6� (31062 Toulo!�Ce�4,Rnce} �� \�h�DemK� 15, |�Q ate{fkn���Ale��x;% um a��ȑ�Vaimnm�Gsh"di&�9y��qP�4�j.^*giK]. D��J�-�b#;o builD�unH5a�ndxj�D#heb�icbo�p�%. t�T��e>V1ct A155�*]�*~(0� wave5a�t�(.]?!���hdcod�-gB8ed�:OZ�,&|( fhCib�M%} let-��)ed�X9.�%R��z�nd&�8ly tested on a �complex quantum system showing different behavior depending on parameters, namely the kicked rotator. The results for the Wigner function show in particular that the use of the �� wavelet transform gives a polynomial gain over classical computation. For the Husimi distribution, the gain is much larger than for the Wigner funct7Dand is bigger withc@help of amplitude fica� 7B��al �9fonce it��been !�A� on a@!uter. M�� generally��qqgapp�/ aK�us!2��y�a�n��c��data.�� pres�� paper, we�� &�cic�cesse1�1Jt�f�h. �7 focuA���phaseM4.� (��HQ�s)mpwi��,h}�!s9ds���8 a two-dimensio��pie�e� one2��l,��} !�a�direcawG9?^�s�pThey hav9 !��Ii��$Levi,harpe�GstablmQrespectA�various� �A,@ error models. Di* .�re-ۉQ6ci{ #:�R� will��8explored, firs� discrete -�" ,�K�P�Qorigi!�UOX �YA thea"I-like2UziUed!YE~context��frahm�_Rn proposalsM]! ,pazMf(saraceno} g!�methodw V  orh�6 �� �UTA�J� , usa� for �X.�tom;.ALse �5+b zedtAE�E� new � tegies�d ordJ o identif�m ��5�2K*� 1�tesA0iX�42= ,� 94fAancill�� bit,A�� all q8s, coarse grain� &� ,Q Ua�� F� -��"� }. addi����-SAwW�w>� ` !r ress2!�minimiz FV� de� B[Q�(Daub,meyer}T � iAI�Y� " involvAX����� !cEpa�!�y!tow�reac ��ratesA�X� !�ndards e�MPEG. Q�J�haT� builj ��m�PWT1,WT2,WT3,terraneo}��it &� B y�� be)ed��>�)?ve� )Q *�9Wope� o��Numere %� sI6en��u��q_qZcy� %[�I%Ja ��A�U� >"u?A�� ro� F g",%��TX � .� g) ��)�ed �-sevg�1 . Si�a��.�2� Rconsid� � !uare�b� , weOcueG!ubsequ�6�usI! ��A�� M�encod)�/A|���'�a��C, eW(way similar�qw!Ais don� >��+si�V��could�%e�� o��mit�=through5��ingM�,kolobov}. &BI. qV^�i� a chaotic_map} C"� (Hamiltonian*:3e�in.b0, dynamics be�^g ��byJ's equdof mo�]. t Q�describ!!- !� � .�0 (Liouville) .�n OI(� hand, . i�eculiar ��iO I�&:sA�8 $p$ and $q$ do1A. muteN:Uis natu� �IU2&  ��os�~ alAc� ��u�one. Na�theles��t"?  known �� ong �� �  possiK $to define "R !�.�� m�thA�t asU=.M>|�Hcommonlya�}th" {�e }, ��!�6� $\psi$�o ntinu�4 by: \begin{Q{} \labeld\ W(p,q)= \int \frac{e^{- di}{\hbar}p.q'}}{\sqrt{2\pi �si(q+ /(q'}{2})^{*}�(q G  dq'/� T�!b�*he� � �As!�iE�AxA�mQ$p$IQ symmetric��(al)�)�E�(immediately��ar�Mii  ula (\ref1!))�Sshare ertie��th��. �ability: I�E� a {\em�wl}U vatisfi$!� )� dq=|%bp)|^2$� 6!p !q!. Howa1� can�be � i��ab�mPit>t �ne�$ve} values� � 5���� d# er�t�!�ato9I�s% Lc b* r+edm8)� A1�AL>�a� take>^1!!- @ .k ��I ߡ� cell�<size $e"$Vlea non� �. �%ref�a smooth��of 6��Oap� rA��A�lld��a D2�A�no>���2�%xHis ��!NE�� .�(} (see e.g.-��)�F ua Gauss�\�� fu��&�a�,�Xuss�U�Af�"�fo!�8 s&� N�eA�� )s .�.�%�2�6�'H %�i-�beed�&� �, na��� ��Iism4 coronIk!��iz�8 Chirikov"� �-�q �s,lichtenberg} $\bar{n} = n + k \sin{ \theta }; \; ( - + T n}$ wh� $(n, )$ ar�R njugaa�(a-angle)�p��Hfigure}[h!] %\epsfxax=3.2in y2.6 file;<1.eps} \includeg�Dics[width=.49\line]0a 1hfill�8b 8�ic 1�id 8cap�%{"W b���E$st�E�"P $K=0.5$ (top left), 9  righ 1)bottom ,@2$  -. Black zero.i,uD�ximal.. AHi�stmwe chos� uni�2� o���($-\pi \le p0-3/4\pi$, $ 0x2 Z( $1000$ ite�e aP6,A�� ed. "] "^}�M� �*.2Md��>ly�n"�!~kT$�]�" undergo�:  f�Ur~(!�$)m�en  developed �4en $K$ increas�<� PKolmogorov-Arnold-Mos;heorem� Z zones getTr v_r untilP��K_g \��,x 0.9716...$A.r�; glob# haos setA� �* hier���ur& 1�la�+surro!Nd�aYlay8�^s|. �, $K \gg K_g$�8= cs� of��B!�X� " ���,����Zicl�)�  9 magne�(traps, beam"�< in acceleratorsK c�.j�_ �.�. Its.�a cyliAz (� odic� in $��$1 ,�map isa)/,n$�j  $T /T$, 2�5�s� uthemsel" � $n$ d��on A/� !z�^. Fig.� }�� awe��=� F!�aI�� .�$,/ da�&regLe�quasi-Q�  (�ind1cur�preve� g!�ns�"� �) � mixed t)b� Q�do;��!um ver�M�2�I} � unitar{E[ �ng �}2 ��:&�narray} �q�JpsiHhat{U}  = �ik\cos{Iy }}} Tn}^2/2 6,��en� )=-i \a�>/ Y �,� =1$Z�( +A�)=� )$.6]� �)��A3 twoa�am�$ $kfa$T$ play!`A_rol�� KffB"ve ��%U� limh $k \�arrow�fty�T20$� le keepq$K=kT=$��!M<i&:� � �is*�by qu��s�"s, makm it pJ#��for n"\�u �MQ���u�. 2�dis!9A�weA�y�3&�p&4&!d es�zu�s]d�9e1� Z� e�2�a� full2�y,r�mׅ�s betweeE5se%�d. W:�� %�2M�#-��b s� c"N !�to+s�Ec!.j&,�-��Gmf_1&Astrongly��&$�ference �=�.�"local*� 2n!�X phen&on��r�� A��sonBM elec��>f#id�6� ��B is i"�$solid�Gt0�#4# �G !|sub�A��@v{#2e>\!l'�Cmicro! ion=Ryd� Y9IEEE}\&x ex��O�re!ZY$ cold2Craizend �thA1 onsev"�:���!0ya��b�" "eodigf'c �!"u�� . �ɝGS,Levi}�@"��3vA�a $N$-.� !5u/ќ��2� ��$ �,$O(\log N)$ ��O( ^3)$*.�Fe (��[ $O(NW&j�"%Q]) � UygMt)U=1;al&"� "8*l$�E�� |M![�(albeit � imb)��.226 !c�& �&Rx%R{!�Bb�i good � g� ��asses^ !M!-lexitS)� D�5/9�(J�#�IAJe*8 s�a��a�2 jto obt�%.�)about�~�U�% -g? f]�� Rp basHI���lI .!X >is�! vely�#e� fini5W) -�cl�C.f� � *� S A�i�  b� � con� �W l�nQ+�� �? `$T=� /N N$ b��2� �HM�i4-a0/2� t#ai�.9��w�Bn"�,-eat�WM� de�rB � �� ���� &%��A{probeY� Bal )<s,� �&xto�ݡ�2�length)�i� &  be�Y icklyK�aiUMU� ksm��)(� )(�us  .��t�#�%! }��Ta�?2*� M| �"` ge���.�re��yso muchLs!)2E�6g��kI"their F�V�� already �#&�/loc)�, a'. K�\�\2�\2�\2�\2>\ >MA�a��|: ��&A Av J�U�xNxH�.���(N=2^{n_q}$, �$n_q=7Awhd>�(�$2 N \Us 2 N$�/ ice)��plottl,(White mark�v�,l�c, bBI2�@�ly spAٱ���n < N/8$P  �!��o�� is"M3a�!� 1) (�kT�!�t.i$|n=0\r�$�!D4 -3$ Hadamard �s-O"l !0�u�afh0R{.� *h) f>f� �e&j �9)�N$پal6�,�z;%A�malis�0 �2_�#dap!��H culamis �!�it' 6�W0J $2YUN$ poi�3>Q�G+}� �!�6r��ula$:>� is:&�"�)c2)!\T�X,n)= \sum_{m=0}^{N-1} !� 02i\pi}{N}n(m- :/2)}}{2N6! -m&0!m)"���;$ += ZNw}�!}�m:��;vid��-orA�:�,� w.56�,A�&9+!iy<.� .H, )��&ineVvw�.f}a��4os�*� s@*ent�B {I�%Me�5e�h5�.�<5��"�,}�- s &� �0�Iup�ch�� �n o !7 >rU((.E�5 "Q 5 ���\m�#proceeds�a lone6d::@,%.cer� Oor $UM�,n)h*�'�� roll2 m y o��tst:�g&p% �J =s!s�c�/ cis $<\s$^z>=Re[Tr(�$\rho)]=2NW�t$�i dens�matrix%U��i&J 2� . O�(I�!�s� quir� a logap5ic� 3� >�&ltot��:��Y0 may beG  , fI�a=1$ 1r � a�Q � :J ���� %,�9�)car�6g4�4�asymptG S�individu��0:;0. A drawback$La�6B�i� at�Qd�$�  easi�urM+* J{m�!,im�7i邐�A�im�r�s~-y�to8�$l)%L�� �*���2�  Vtu�ǥ�o �8~{e^-��[#�T�8ools (A0�;,k2�<s)��% !2 speedup�$"$+A��-,�wbse * S� �x ��Ls��]9: �$|�U:�� ~erA i� "�)J &�wa(2o�Nof>f^t \'_"� ($t. �a�1i�36�$>>�(�)�-start9a .� (T �D $n$ 6�) :k \o� �^*_0 "� $=�i&�a_i |n_i $>�j* ^*_j,j ,$ FP `6 a;.f2GQ�~=s $2n_q"Hto hols�U6p� 2�2�,�&� �enA�����j���R;6^ *��orU>$&WA���GS}��sub��A�seN �isP��&.as multiaK% f��&� H�-Fouri>?:�f(QFT)k�FZMof �co"� G�pe f�< i�ure�?QFT��� �#sYas������.q� attac�!��� ��B��X Let us�x�:�2otaC' ��:N-� y �� \.W�P% iTn_i��& \non �  (F$ ^�_i}d$)F� ��(>�M.�}�) qܑJ^ B_ b��� ��)�2iW^A�Ia�(e : $n_iN�F��F�%Fc t� _i}}N� �|n��^�>j�� �c!]��)%�2~fXVX1N�=FB>�ѝ *9} -�.�) =E�U}����ե.�f�We�Nthu�&�-V�^ |^{*t}Fk��8� , �="-6凁�� �̅��5iΡ .�6H%� ($O(tn_q@if���5�J٩of�b��2��"U}$). F����'� * 3�6�@o. $�I,n} W�" ,n) m� |n ���0 ]11� ٚ.$1 �B� . To���X*L �%N �$:�, i.e. C �UM^"? =:� T'\$-)$^* ') -F1&' n!T�d�<&<L< ���% (+ Bget�P� � + ��'"$0$�R$2N-1$) �b5�W: ��R�av�%d ��O�-GBW (�") c("H��H$;!n AFt�/be wr�8n5� =5�- N!^�� 1�aG ! se�9�Z3 %"ul�C:6�} i��1 �} ��\�5&�A�Gb�A�6�u� =$2\6NB *�*��^B�Z/2} | 54e� $ � ��A�toM�E�d*2A��9a:a\���K 6� grid�aayi�� .� q�?�mU�/ $|&?� �/ a" ���i6I��= rpre�a� ;8 sign�nt digi.$$n$��L�Z {isam%�l� )35�&� �%� +~l N}^{�|�4%�,nN(n-N) !r� f$Cstep His .% �}IWE!rwM5J$6�$O"ͳ madej�^2$%�q@e�wo-I !�s ��CR�-shifts� ׁ�!�F� 2�9=ea3psi_f�k=\1�.�%�)� I ]b�B� !check�ano6�isK(ct��*in"l 6���^2=1/2N$w+: L��d0in:ari�'�(%nEp�D}a\CQad w>��>T�%now"z? J<�KV�A�i')=!aJ=��en�?<?O��2:WAbalO�AB�) As7nE��$�ssoci�5�d1&giZ'�*i�Fis lo�ų�6ac%���6>/en�;to�#� �M"8qN%���J2u!���4m;�� $ envi�z ee*,s'$&F:�2C!��e�,.�l�!�2o!�e ~Dof&#IPR05}-,IPR2} 3&)�V#om�!B2�+�,(&�, physR-I �Nb:�T*,)�f&l�,E�v)ti�1 �%V��A/!��Mrse ipX $Eio (IPR"�a%& ���=��i=1dl �!� 4 $�E1E��!n�is�r� _i|^2/9 4�825I=�"� .�!�m�m�� �e ""{ veri�=e$sum rules v  W_i=1͠��^2=B 1e $. FaXu+we��B-by�Cog�=�@!� n!D!�:�,� a�e($\xi=1/(N^2�4 1I�4:@!�%.sdf � �PEn$@ l wej8 s $1�'t0 kN�eu, $N�yj? (xbsolutN)S^{3/2}$�2 X^2)��Fhe IPR$��Mn�%�U � ^3:�H:. %\kO doublepag Tb�Afi�:]bj:8:�:3:�9M)*a�: s)/ W ��vs.�$ �.J�, (empty squ�@)��QB��V:� (�0 D�= tra!� n;C��law)�,.�. �$*%.q"�inset�r�p $R&�ofB�a� B�edB)A�$Par�3�=�\"c�2j$� �aU0i$��!. % B�EKJK�y�a���"im 10$D(7� %no*� �H&�:�f� Mn"j [�~4�~�~�~I~& ��M~{1.75!'hil�. dashUne&���{2*.g]�9��ʭ_ijaa>��$N^{0.25L$��f�"R%A|9�|Y|5�|�|�|n|�{1.9b}�?�*�*�|4�{�{15�{Y{6�{�{�{n{4AO��1.8,R�2�y�yvy��R� .��#3�#�#2>�To L&�#�� u)�#��z8e� �>+50W58e41 �>� n!*K2u k6Azc7�'e� ng T#(hmap2!#~_s;6t 7 ).H7�_<t��\ ; $W$�%"Gb BHs, !'�w7^2 \l�7:o�� y&rue 5, �:s�!L $W$,��"�&��/tY are:�E)Q� %��� m !�?"Ror���&id�Yue bo�L�;]3a-�q" oW>.�&�' changes��nI`b2�L�4lL*NOat� pred�>mi6Q$��*%��3I��,  %WB�� actu�:�;Ds�'2t5"i)"t4of=Y�(�ncernI�6re\hF-� lariAX3~( protocol%b~!%"�!�a4obv�82 tegy6�gA�A/C�sR0Z+}(4>�'q &��&� T}�  accu�Eq� istb�Eh9 precH8to,�n� %�e�:X . �" & 6�GB'A�qL�[ fourF�con��[& IPR  �SM�2Ps��A��} �F�is �2 ou�5�>�,) termA*!�A�ar� /Dtude $W_i\sim N^{-�1FS. X)�EX�>�8.�+Q�&C!�1fore q N�;( frep�dma��&�)+/to2�,f&���Fh�ib�a^F0!��a��:!allv3,�F�!p�|uHh?��ZZ�����!mAdF1#�XnolAd*t�8�{one, �<2=���}xBV .m���^:Ee&�cly�I bits!�$ �Eu1žF)k�a)��A�an �,��in &>: }ńI,im��e�1�;85�F�Zom&}verũ�HA<� �8�Cv< taneo=.�8s�a}s��l:Dct�. cit�b�o6!!a����|$K$�U�q �a l��%&�(a sl��:`hpB\alpha}�H$ �J1.8-1  ��d�c�����Q��EVI�i�y). ?MR��a�2- �}+w d�`N ��/!�oV//h/)Y����%��.+ 4 map +Mm}L+�d �#.�tN^k)1@k>2YK�� ��%�F$beq�"n��al ��o!k-23�.�&V`�"b%2�1to�� 2y1�/�*�3c9*�22�2��us.H � 1�,�1dUI��1��$�a�s�he asoPyp%���st`��uM� :�� DV.� l8a�Zk  AA�i}����o�m2�*� ��"O6it('�w�>toM�F Q�A�� . S?]ly��m�.�!�u�qi� < u!vay��\%"�"Y^}�� o��a�<.r1 lan����X.�V�J� z�,].���.�(�(}W-�b2,�����[A%$�y me18m��:� {*�iL^:2�3� Ks� !��' $n_f�t�,<�)�"i=�u'8N �P> t5�Qi� d$$2^{2n_f}$,Bs ("!� q - d A� $|*�!|^2$))!0a-B щ8e���)J.�B�a�xj���:6*�� ��5��H6�-�i0X�  )>g�pt� mp2,X�yexpaaboveprincipl�Ar~ n8O()Qf�Noa�<'� t y'm��* TT�U^!si�O����;��1?3 p y�7by fix�AOl�p$&�S(f,!�g�Dd]?8`C*�cr,���J�}6� lso*d�B�#5�p semi9 ��.FD � �,&t �>iE��8EP�2�N\i�N� !N�N :DDnT. !"�  well�%r� d!k6� calcens �is�4aDe 2g$��.I7be �`�YtaRr. A�dMc)%Q@'(c�~�c&�; %@a*�!#(} #["�i-��7Gh%ʁ� can �e aver�s!s>����n�rtangu'd area���[ �;��&9/�*  = 2NI &  /N_P"�!$ f92�n=s�8�� sum�,a��/,Po� at �<2H&preo3@�\o��x�� f�$� $|W�`A(vL�&as�d6'�sG �&|Q �#��H^ �n�  �>� a�e2C%$�n^\ t�u| r��Aj�vG!d�%up E��sE�� rMc�N�~g�bsb%�"�.%~j� a(I(ofbr2�r CgnrF e lt0s,�!q�<super"_d�EN$*t�H!С@) N}$ *.b�^�.�`d!�"�U�Jo. AAt�2��I &= a_�E��Q! f $P� e o9Pora�%�)���1V� A � or tjS.�,� )�a�d�;�desire�ab�,&�&�f3V}(I-2" -\l*E0|)c3V}^{-1#P)$�� 3$K .�<�erd�Sif!p �/�#�3VH =PB +(I-P�t��7�!���tolj� a�ward $FhEa�,&1� lSn'byV9A�$Z�.9.$a= |Fs��,�� *�+fF6�A �t,$$(4 a^2-3)FX + 1)Z�,: )*� �ggb� �L�$4a~ (QE��]nA�b!�$tilde{U}_{��} "�5t $ (( $F)$�4i� =�&�Dn!�$� .mQnqj+JH+�A1�L $N_D'IN_D�/�,se%�tF= 2��@2� QK�%,";� �TmIaO �2�+�cts�n a ``LTscope'' oQ W �*� ^ AJ�G�AH-Q"�(R{�;E�detail� rAtBc�a�Y*�?�i�s�w�iW 3-6,�b%�+=!�^2/�'^�!�!B�<� $N/!ۙu�+`=. )�)�6+en accor�dto'L 3-6 �:�c ���@�5b5�s� gS"� AvD&� � �,��� $ %_D �T(upa�.�gw�Jid u"2 �m,�)�!�&lT.2C�����L ZA>��1B>&� -�A�a�5�A�>AB$F�e�b"]Fal �/%&B�>q�H9q%�low�. WB�a[F-}s <2$)&�);(-<>�iA�,d��n�*�m.D� enough!�� aBU%;QR�%�a�:�_D.�� �(ent�AJ"���� aF��� �+?B@maΗ >1$ (n;  [c�DF�">  �$k >2$ �XA5ed) ,%6��� ��myEk-1�1T-_Dltfg keptR� Our l�Ivl�a[B�0� "JBv *�u�(bV!pD/��0� &us� �, �L�d1m;mWl�B�q�2as �}c�uw[!� {AQa3�lV3i|��� �di� n"�y&�0=�S���S�1�2HU�>� oN.2��featur� �in�3sf�"ency. ^2�s`dubi�_ouRo� q;q�<2atWfea�i�a,�� beta�(e�$"[ �" < �2$�   1.4$���s� �/���� d (k�0��85�A�VF�s yq�- �/l��n "&"�/no �6�h*�%F&Zmea� �g,!?E &�X]Vs K w�{���"�^{%Q}6� � B��|m .MOG P).�. �va&  machii!�stst!�"�i�fB !s:.т]5O�4)��� a� �"G!\ is�d,b7 C_E|KHhsrec'AzH2p� "�:�-{to��21�u�M)_�:b_ "3��@.�}2C9M^0 VIkwP"� ,g'�? ��� th a���cyus l�&�%.=[��z�V!��cf�'J ���*6&m&�8ASo6��5%b�&�����%speci�!��!� �g k9�Ir� #� �tif"e�1b: thod*x^*| A{f-Ƚ�MS.U,&4_@2�����EZ�zUJ�6&�UV. &�U t�s} Au�r�\0 ��S `on II,� B�;2..6� g!�N�u) �1{+���"S   non-"�Z�%n:rM�ofj�=? }�o� o���a = &�,����a +u,a3K!�-n.fpuf�X !f��rho_H�F _0,n_0)=|� \phi_{6}|i@�;|^2B6Y-}!=r&R< KAY A�_�DqA(n-|^2/�-i�D _0n}*�C�&9vco�nt|�ae��on?,�E �K!w�s $a[IAQaZ��KA� Rs� F�� �_`&<@&W2%k*k\,&?c.�&$ . I"�"�,i�,� �ro��d�BbI� � �alof:.���e��t�6gUT$��A�*�Av>�� "�I:�t<��f�e��Y���� Q�fr�� %erH�J2�s�% Lq�q@���#!B!��by~C klauDveE^{(p)Q�My=|rK 3|�Q B.W((1/N^{1/4})ma=n_�\n_0�EN}�\avjgmo-)�g c���%"E6-"}�9��Á�0oxA�v"�AK fE�:  a +y�=��.5( DntrI� ��r� 9A�"L"�aF['�om�law�D2��R�2��XS $�? \sin x}{x�((�I��bj)alu|�e&D?Wj Ti�er��. �N>�itself��["叙�q�&{+ T�� ��JU,% half! � ($}f=y�alJ;u(1�b {4}()* 2}+1�k �e���%��  aG YhBDG�7*�6�o�#�$1b�G�i�&�Jpsi_H^ =i�ɪ ,n} �nPOVo�M$$n$�e /}3A,esL�$|r.Q�q� eQ�m�%'Pe�EQM�>� on .� M /� �.(N)F� �E�N��K �cisџ�`:�s,H$i� �[� l :mpl8Gd easC�=�.�S1&!�a�| "M am�s�q�HPM{�"hme=,le�Q@"w?��|��|7�ug7�ug7�ug7>ug (Coln�>) MѢ:��2�"�B� :�F�u���|:�|�B*Sl�.V3�&=16�Fqta�{B� Xatig�@u�c �aE�ch�#EA��%<"`e.Jjg-e�Z�B (B�3�B"��$(2�s�k+$ dn�[yU�gR� gray�hm.hhgh ue (mh)���`.&�@��>y;I� !P��� !V>o�8q&r.�]���zpacke�J"2o2�\E��6&����${z-Bn�y�]bO�p�ER$a�yQI�sI�3s YY9&�Y]"�^�� *( �A��6�; ighb���A6:} ��%e�ma�. �W�o��2 y+i!2�o.� "(�����+��U�6��nor5��"�82Rm��G8.��cρS�Gw!61I $ vs�<)%��<$��3 I�� 2}),`Lth&�|s�EU.�* . *bH%H%>�G�of 6�y��-r@��y2��modulH�f6hQMul{�ee10.6W �s�C�9����e�B�9��6�2��%�����3�e�*kH�I�B����r�\7 N�9a�� :pJ�9:��10����G�H�b�b���� 3i� � I�K��R�7�G1~"�w[{�w�wj� � ��ZfigK1>]�1����X +*� �����Qej�����Y�*�6Ce%b?�K2:>A"� -� K2} ~�"� � a�&� �&"�%%#2z�SS '#9� 7o$ oat�� '��2� �i� 9!o6��-�l;o"��'y W�r�&��c | �.��,�9SD.�"�.o D!gamma��s $ 0.5~�  0.�w�&�!��ZorB4�� �5-�2-� N� � � ^{ �}�:C (D'ATTH%E�)��2*�.�"�wG57,[f!,&�BW8�= ���2��� � 7c"^")jJ_"Y�5I"� ��-S! N2E� D��,��)&� >�yn6- %f� 0 � =��m"t2(flAC�E&] R�Wclu�)S%�)� �(-9'on"<0#w�E disav��3! � had �A$�@$-6"B"JR0A���=�%{e)G=A��oi�"�*�w=� ��3=� �s��d�r���  �v�2w�[.6�%7�&��)���fo6E�e%!���0+,�M�()eP!�=G�w?I6>2�r2� _D}\a�s-_Zˁ 7�f.�0�{ 8-11o.i�6e&� �$ed,� $j6�5Jun"� ��* J? J$�0 �}�3�xC'H"M��Aey&�a�ta�^q��"�,�)x} _D��/u1�#B/x0�a� A��;'ev�CI&� ly�/�9a)Zer"Ac!���a��,Bl���!q�,I�}�BpQ;\ t�0E�>;� !�_�7y&��l����$��H�$Ie(tFT5PQ ѻ!'&aa*;le qu-M�%�at "�ng�W���w1��!y�>�. �7<�X��0��0>��%z��7%��1�%�6RG>g0�F��E�I�Bi0"ٍf!�I)���)*a). �mv@&="?�M�R6  ��ea�.(�u� Ae����Ia t#��� B Uڭ�57�x&�M"� �U !���6rO�.�P -2*:� r)p&��$�h6 of�:la�� ivalN% 6�C�20>{.# O,�k-$=!VH�R����?2*KELFinZ _ v7.S+m,����)!�.&� (�x-%�d2�V se}_��.�N !���V^`uto��)D� ��.�� anyway EQa@ h� � !��� "�T�;_��(=�<)�ouߙkwi& in&� tf�1"ED. "S-Fias2W� t��3 �)!"��E=':���x=������#��ite�},� �asGH delta})"� "]00-0.2�S+*�QB<�#r�4a3��`#R�5��X(>�r6&1, irrelevrl�� 1 s,��e����"uk!ple*�,. OI��5��gy5x`&� h to=Frid�!�sHN�C�9]�iE�-��])i} or �}i.|m��! �]s. �|6��?prf)%�b?�W$�mUpW&�) I.sŴ �$Zu _0^*_$-N�3.g �Dͧ yD�m� v����z��9�?UF}",sUAU.,u2����.V�%�+�i>��6 r�*s, /3ar�um26%H )',n')^*�s�,k%&7rn  |na�� Z�C&�<O7$@s.�!L diago�aInF�:x%�r� �$>s2�"ne�*.� �>mN$��A��"e2EdqA�fv'ms�DoA� })2E�J�=�W�)Jgm��u)�n6�V�'m���>relf�(-����F��PAYy)"�-!ንnA���5". ̄�C>]K:�g� Z?Q)���'-4��  *rse.�\��"Ac)Y� �!��u+� *)&���a> \�-� �R)2�5 O3av!r��!FY� �rf�� ���Z�t"F�,.{WX @M�&�3ՎFgi"�2 V. S��� e�2�g&�9/ vF6Ds!��!1M*��E��;.� s��G:H��E=ly �)F.�4���MDca�ofa�duc1�.�� I�� � ahTf jH2:�"YX.#I)6�� )~"��4{1a��L;Vh�I�)�ofU>c�DG���%5qi)�eز%zgeE���v A0>R!f�k49:�k12�W)1�͐1�ΐ1FϐI�RX"a*�1aO�5$. Top: gir�� (�E$New York CB�++ (�y���: galaxy-�� n NASA websV Xa �x�U�1�&��pu�K�tudm.)�!�* � �&�'}M��> "!e�� u"�%E�c"2?ps< �1O� a��nchmarkA���&�#pA�0i{Q�ݢ�tox� c (�!�)�A�K�qT�ak(��Z�i_}op %��8a aer� view;2�, *ާ�'������ho��,E , \�rt�%9%�5�Y-���� �@�cr"ndi�\e typ�U�?�P<��pr�� nd !Ze��varBaM9-�e��sup�55@"IqZ�u9*�w֒M����Td6n�"&�C*� psi04x,y} a_{xy} |x |y $� $x,y�C# xE�$2$ pixe�U$ I )A "� V �)/ (2Cv!` ). O'6 ursee3r G"�^�e d \U9g-��wA��t��%�Ab2!��&�;�gqn!��f=�u��.3<&��|t>� 6<�"�� �dk�b2�qtj�>�q1>�q6�. S��)i�si!�9�BtS�F�( symbols:  *�M!\� "� . E�q. /"$ ��./JNz (%Y32w2imes$  f7 2048). Sq;rR�� �� m, circb_ 6{ $ tri�5s&.O�x diam.���X B}B"EV�o2F�3 4:>8-bitx�y�1��� y"�m�:� %C&�T�*�.. ٯIPRőb�!�m� ��� T���F3�v"�.|��q� 29�IKcwndIA9N/d, impl別8S; PX*�56fydh -%����b�  (2X����v �Ct�} 2)$�;�>-�� ����,>>.�% �XI��Gir"&{.3�f�!u�to� +mAA0[� �@,\! pricMilo� .�o"n"am; 7]�� ��#Z�8 G�+H�� (&c !J�,)�H%�E^ar̈́a!� "$1�!�)$�U "��Zo�!��Fn"GP-� �!1auY}<�c�B*�`�giyY6uA��zF�. �/ aPis&�cH1!1{ ssLb0�"H ��ll�!�A�=:�\ �@�je�pI��<�bably �\cEl7lE4�(!�" �i�:�� �Bs��\�G!r�'6�u�,~�6+2�U�i�Th�>�2+�X�pla�nɩ�grQ2slowlyPE�hcTl,���&5 9]��at�G� �2&_Drowth\1CIPRNIT#e�c �Q!��B� very&�!�� ng2#�x�P�V%�{ "����B�K^� � dem!���6�aTQ�a� bx � for �6r�5� �+a�=��'%�Oi�E�m��E�4 Q��-�'V�&N%IF3��1 >7y�1 n1 �� e ti��q[� �17us�QI�ti� &�D%(\�"o8$ �� �� �� �� �� �� )�E�,,��  #ar���E��� � a�j��awo}(Q] j].�  ing>� .F9#)&e .� stud��N�V! "���T��IǙ�� ��i���_ is��Zif* mw$E�� #.kpen�|-�xo��!y�A�Y&e��! a |V)�qX��'FT�g��1/| � h�?�%b%��]�Rg�iC�!.���Gu�ofJ�Im!�se$K"ۛ%#(e  ic�mk k�E�)u!6��D�#E>F�R;����� , >p x�z2z !� � root":8�y>�6�G0  uggea*�$^ ��p���K�n$V!�"IGU�A�a "�s��� q- �#|b8KCRV2@�t>/} CnK�!�/ wopy�!7&�A�9�:}.6%�� IPR,:� �hS/� $S%9i y&3�~AV)!�\ &�,&�5&/36T. I� �th�� kE��F�&� �+G#*] �>�I .+ confir]�I f [\� �# "�E�0terna�< ��to �v�ta>� %="�%g � * �Qm4 ��� or a�o.�>6� $|I�"� ip�bLZaR- hi_j/[ ښ $W_j=|&AIsi|UL��D�� ��&�I $S=-dEj Wclog_2 �\It�s��� $S=0<[��$|? c$jL[to' MN.n{1"�N}y�jF���). �[ajA� $2^SZ� sti:�!�!��J ŶzFa�X�ta�$��ua�+D!MeiaK�w%Dy 7��&ġ��� �d�i_�va�.�M�Ah� ŚF�}robustJ> �m6�m6��D16��D16>�DmT�$�fP M�� Carlo�`pG V+e�u��)vs�ng�ex����*G ,�3 $25��.i�*s") A� tom:>�ZN!�A P6m`A��i� >�a� h d{2"` e��A8 $128~ 128�iŗ$� 160� ��0��figMC:�\v�{0.5cm}Y��!���s� &�� argu��T"!E�:Ea�a�1���B��� "��"aI.- ��K( �:ipi���L i E� Fb/ �1�&a2Pjo s�q)worth� �0�ml7.��U \#6���� r,!�H >3.�AI&'6�� )Յ���mp��W}cNYB� epZwnl��Q�D����DNd>m�,�]E�N!inguish�ka; Ftuk (.�8 !ei�-6�f lo�=l� 5j �&�lo��!,�I� ~ ��U�% �/�6siz�O% �'mPx,zvʡ *>&�y<&dt�S�#, �4"rts ��.�,Y- ze�b�a�K&kpa��5&E��!�.��I� iA�a"iz5 %�jy�e.��%B�&�$I. Co�7�k��%Yp"^�-�*�djsՁ#sa��+1�$�|�s�+A�riG�� ;w8!�Tw�xt��of� TEp Y&W(ad5]�!�_oi �' s�&�% ���n�V��P}!w�6er")�F�s, .�W��e&-vvғ *!_�le2���m B2�7�st�*)�}�ZdU3 M� �V,  �w-�m�|E+Q�er h��Z t+meW�J7e6 =s��e�r&H.g@a�*;��9�;e ��tB�5 B�A�Af�s� ER��1e�s��!=BE6� m����kJ�L�i�c�^)V���Y�r9�N�!,�� -�Ys�@j�-�@authors (M.T.) ac�ZTledges Benjamin L\'evie�y35th Ann hSym�$um)!OFe�@>; �er Sc��e}, edi!���. Goldwm�r>:( �@Hociety, Los Alamito�� 2162jY��8$lex} G.~Beei, Ca~�,!_1��rjV� Z~8!>227901F|.q� Ae�P"��b�mN=�-�6Ax01430 �4.� :} E.~�>A40}, 749!� 32);6y M.~V!3rr%�il. T�(. Royal SocM�2)37I72��6a-J��ang�KShi2> �34�M86.�L�B.~��, ��2&>E 6!�046220%�32�>�i t�}B�Jc7!g056218c2�,X4} K.~M.~Frahm,a� FlecK9�V�2� Eur. ~J-�D 2A"139Fy&V| C.~Miqu��$J.~P.~Paz,AS�,AEKn��lB$R.~Laflamm�dR%C.~Neg��rg�gN�l)�418}, 5 �2.�&sa�$A.~J.~Ronc�%�M.�N�>�Am? 3231J?� �C�>rassar� P.~H{\o}y iR�N!0Fifth Israeli�N�on�or� � � ASlfs}R8��7)N| p�-23:G.~1,6 M.~Mosc)�A.~Tapp1Rg%$� ��*�:RFA M�nYVolum>*A.0Lomonaco, Jr.`RL H.~E� ndt (AMS,�te��4-Ma�a �Se^�Vo�@J305M 2��m}�  �m� Ten Le���-��8lets}, CBMS-NSF s�FAV9.�(SIAM�T$iladelphia�22�m[� Y.~M o: * pAnic%�Ns^t3.�WT1��u5�,-ph/9702028 B= WT2}ABFijanz+nd�E Williams,1- �� IBB ? �k150�0 (Sp�4a�1998);�80900. WT3�Kl%B neck8inI�-<2+Sig1:aB�3? ��VII2� $ Unsg<ldroubi,>� A.~F�~Im SPIE%I9� 703.�90901.�"�ppTg��R� N1�W*� 9�� 2579�6Wkol��uK ,U Mod�� 71� 5�� 1999.R�i%�@ vov� @H.~Hansen, T.~AicF�, O�ns5" J.~MlynekN�AfS1 �Tb� � 0504 �1.�M�*V���R�(Les HouchesU�S�]}B�&  MF Gi��ni,A Voro+d�Zinn-Ju�hBG(N� -Hol'� , Am�>dam�01),�� 52*L .@�B�Q p}52 63A� 79);BlA.~Li"��%xMeberma�C:S%+Re��� ��Dy��},.��4�2��� (I.~Guarneri�D�S2� >�F Jow ofɭ. E\�-2� 14Z 1988FP.M. KoQ�,nd K.A.H. va�euwA�9U>~e255!e8� 95.��� �� ore,AC8 bie >TC�KBharucha` Su�6a��M.~G.~R"�B��:�459��2�loc��%��� N�1&v. )A� 5"� 2�e��B� Q�� >&.o%�A 6�06230J� �#!zW.~Leee�D�CiCiW J�:{�303��8�in�Ge"FY� �ei� i>No�.An*^CnanoeA�ro�, s�,r%n��8s II} ��DJ.M.Smulko, Y.Blan�M.I.Dyke�L.B.Kishebf 547�46&� endB: g docu�$} W\�[tws� umn,�2�i�$ algorithm �-42,vanDama\iXe��nce��=!�$antaneous I[ ��)�paz99}�s .s1�a�a �toe0 ��icular ��Z�e�E���� �o!A�� no matA� how small%N�W)�ibu�W?�e �� . On%�9 wide-openn-u perc�: 94},��.e!]A�4letely absent,�r�ya��%�-�:�. A>�U�a@ works by keeping�system2>67 of a ldependE�a�is fe�U��in contrast with, e.g., holonomic i�m�؅�"�a �A zanardi99%;ich sharAep�� evol%�, but �K�es!R�z��k can�BPon arbitrary superpos�Ss�0out too largem�. For%I funcA(!Y�j�1�E�Fz,�4the other hand��$is suffici!� to r�m%��probabil� find��-�M>2� 2),of $H(s)$ is!��. T!�!1be�Jn84one possible g� aliz%�Hx��pz 5��to!zn �s# �Gedu�e:_��anR limit, a}a<.�2� i`a�e may�AW-Du�� :�aU�a�m\al�!_ its � righ� ``S�Q� G er''."�d!�governe�B1 . A�t2d :|Y�!}for.~%O utwar���t��$Sarandy}, �tappli�iob�Ayi C 6D 2}. ' $N$-el� ѷA�l��on*�Q�a singl!�rked ;� $disordered2W list��A�8 a is associ�}��AQ,$N$ dimensio!�,Hilbert spacA��th orthonormal basis $\{\ket{k} \}_{k=1}^N$,��m� i�m orrespond�  $<$\mu}\in\{ 6K . Follow!U Refs ( 0,F� , wea} side�� amil� ��s� eque� } \label{ /} � = -(1-s)�$\psi} \bra - s ��  mu},C [��br eqal�y} j\= \frac{1}{\sqrt{N}}\sum1k |k} >pA�`$s=t/T \in [0,1]$, $T$ be!La& run-�N��A . Ie �W����ewe] rtA�J�gy2O1�!2$# )Zo.� takes uENM4� G mu}${(thus solves- �Q�I�o�0relevant subsE��Gpan�RM~�Z j$. We deno�!e 67 value� . ec���S restric� N � �by $E_nŃ%�E }$,D pectively�4$n=0,1$� fur�8defin]nnarraA�L\Delta (s) & = & E_1- E_0 = IjMy8+(N-1)(2s-1)^2}A� Un YAnY�  Zh \big| \la��\dot{E} r|�\r .= � �N-1}}{>� .F�A usefulAper�$Z�� �:�PZegensk} \int_{0}^{1}�ds \leq �pi}{2F��VH $N�� D&P q!:@�I+�Jis��� mas� �C�-`��eq: +}-0(d}{ds} \rho%�)� -iAT[��,l] \nonumber \\ & & -BT[W(s), *],B��� $A\geq 0mBB r��B �&E g N$. Hev$o%�assum�ZDbe Hermitian, nond!�e�� fulfill $ ��]=0$. Fimo\let $wmQb�e)tm�of ٚ�� +m�$|i�Q� �mj$\GammiY= wuUwI� $. Next,�8i !� o!Z�c��} by mak�aotone,* (ly smooth r�ametr�  $s�  \� arrow r=fa�$��� and5�0n such a wayO !g$ A�sp� nea�uminimum M�gap. �e �d �($B=0$)� wa�wna7> "� opti�choice � �e>#4Ldef} f^{-1}(r��m/1}{L}�m�r}i��s�/,^{2}(r')}dr'a.4L &�G.5j>�]��N�Ё�\arctan(��) .h &��A�� 6NB� yielr !y8riterion $T\gg r}$� E�nalogy% Y GFr�tI�g$97}. ApplyA�F�'ults � trans��  $s2�$h well,in multiplic . by $ �d)� }{dr!�E��E�-E  a� Eq.~(\ref�7). A�|I�$��0� �0(0)} � E i�aF�YEd=& 1r)��S-$1z(r) E]q &\�vArho_{00�- 1E��y, We now addr�I in objOa�%�ivi� det��ne 0!XI l�mM-�2R��s�Q\� �[Na��ers $A)W $B$.=�gy � ex8� �"�A�direc��e��h!�$�an intege��ereafter��� y ropr �matl o ob a lower be����.%sarewar Eq. BxA�an B��� [a#]h:�  } 1-� = 4I(r)V� E:FgI�$ <2i]1� I_{+Ah +:->I_{\pm J*U (r} e^{-T[BQ�T\pm iAR ]}Zu=')JpJ\'}e^{ ['\' ]')Y(r'Y'5!1 A�F�eq:qr!" Qa�S ��r} �,-'��؁�'} dr��{.F)s6K}{:�D,*�  \\ R^����v�. F�� I� �%�fWe:� =N:� zeta%M\ �min_{r"�J 5�)��Y ,�se $A>0�e wisq� $\left|i5 �w|�uis�d�by cal��an upp.� $|Y�|$, us�$Z(r)1})��mP /N� $\exp[-Ta )]g  1�\{-TB[An-e*]\} ! if $rh r'$, as�&Eqs�h� )�i�|!n!x)=Xre��^; tiIab�%0�-3��le2� L}{T} �I��8 AL�Ba-E + A$}}\\ & & + . M2�"� r!ft| � r' ( �Q �E�{B Vc#��} �� dr'.*� o�=Byu�s9��a�=-�!/N��&�9�b �oeJ�<-�)M� Q�d a*���� absderiv}U &2�)�*�� ( )TQ�')�S -Ux E $|!W*� \J� A}:) Q*Y 1�; �:�)� tFu&��Bbr.� t%:r )�'2vF5N`at+extm�=�_� rval�$[0,r]$�  1]$..b� E�Ij$1)$� symc a&$rA�ec��$� fvs O.�}uU )|$ ��sam`y. More�,.�� increa�( M�A��$[� �H*, �^� = ayM�E�}M� (r nF[� lead� bZderD>rF�.sMo dr& =& 2I�1/2[� %u �)��dr��a&�cC�8 6�M�U�[2�q�TX$al� )�$econd termv\ �.�(�/E�roduc& eM��V-f�#�C.?1E !�hK"� ��w8$$KEYa�s iBr�th% �}m5 $B w2E-:�A�6�streng+*> �� c� ��9 )&���"�$�fluct �sBpWX#a�&or w)�WIf�Ni� �(r)=\eta`lb(IsA�bigrb) %N $%, : (0,\infty# a1)u�q�V�$, it5^&�%�.�! �(xag,q Cx^{\sigma: � $C��|i��%/c'ants,�.:!��z�"��#�A 5�L Qed� � �!� �W!HA`. BF#mbi6 *� �),� ��- y$� m � $6P �')\ -- (ͥ4}(0)�R T +�bsoloc} |�P & 1-2\pi�)� } ��f"T1}{A} +2yN}�� = KB}{�&CB��'ILa.N57%�:k!A �N}$. I #cluxѹed degre� ��.*' hang�5*�#behavi��A"w�Ac&o�M�� �]t Dexi�m �AsG�)&�5})�Y�AWWr),A�W"^ &�E�*�# ($A�� prota#'�*�.�� �} Bex�)�ND) g3li!5 $. To verif�Doin��-/�!�Ii)� ���a���}1�fre�&� h $B=1rconveni�. N�+A*� �� = !�$ &����� � )$�) �.L"�!��= @:�2JAnecess,$UDeXU�aRisiP NOUF� to � ���`is also|�� to.�E:�- %ly*8" from1 $A\n�A��!Te�cx s!v; into}s"E)�Md2Me1��=1/� ��$6c�ȩ�*t � � wQWH�=�:�" ^{2 b-���*5�-1}}rBI% &��)� o *zk ) gi�b^olikhet"�"42�. '} ^�qT}{6� (r'-�.� �*t :�Fin�)�use� � -�-1�_�&��%;2�u� "�wiJP%�1 ��Q2� �5��T.�XThus,6�yR�F� 2� N` e:,u�&o"= >��~�R Y_{T}$ deI!�!�(��9,�) �En�$T$. I"7 ��at̀aberg04��1&�m MK�1���%YY_0��B�*� an&e)�7non-zero���ins�r�ف�68 2tha�&i#��W",��m9-�m]q\and�.bin�th#-kU�y�Q8-6 grdlka� )81))8I"! V� P:�I�gd� @=2�1*�"&*a�)�')!��')Adr*�1:���b�Yn�iY�A��1-�(2r-1)"�� 1 + � }}:��� - R1�PF� In �'e0id%�Ua� HI_0� o go!�A[ , sX1 $Y_T��C$B wf*v�E1a�u:?A� ^+)�2.W; �to� �isRX��`3 $T$,�Tu*&R~�9�a]�Yq �3U� 8of variables $x�(sd'' %�2 y�$.'-1d ,^Y`:Fmvbdiu}M�E KI l� I(\alpha, ) ��VLn:ddefIab} N beta �-}^{ �5 \Phi (x)m%xE�B<x&e(-y)e^{2=y= (1+y>0)^{3/2}} dydx��67��n��lokal�7!#2� T}{22�9@}&p!&�.Jp!}%l.j 1 p"y x}(1!'2�; 1}dx$2� F&�$j�Idb.�%)�>��� - 2)~:�(8!~1+ !��Why\sinh� )Y�(y)rb) }B�dy>) � +�b�.R)} P �Q9X� \cos6�%�� (I�dxJ�ej&��} �}n� >u2,V��!Fu�i�> 0J�W� �#is� (se3!tl �"�Vrals ``$)L:�$''&o F! 0} + 4�(�} 0�4mj&eV2�q -x�- -y$��heR}j�� �#bQ��!�1�)�� ineq+U�2�(3/2)}�q �� �]*./M�1A`��0}, \quad \for�)y\in S-D]Bx I��s`&� e�)� t $:�L& in $a�� toge�+�46��d��* j^d � &i%�L"�2}�z��� & .,1)�@�\&J0Yo1}:')��'a"^ ������ $Ni�2$�3� $�.�0$A�!X��J� � Q 0$"� ily.6i*�Y���)a��2: }>���-2*�1E[ _E,�� �q ��}e1��:dx��-�B\\ �8 ."\t> ���)P���J�>�I]-� < 0>�B}��f4-�$  �i�&de"� $)�$.p *b :S�'� 2� � �%�.�� fty-or�7$N$��.`��*�de.� ��l"@.� � $k*& -In Fig.~�) fig:� w!2j�8e supp#5�@above"W; 1K*� n[< simulX}19"R6of�&7/) D+.r�� iniC9=�$*~)0^ > 22��rpolat�<twz?YPAM6�,��let��$A=�0 (\omega\pi/2� B=� 6�.;$ 1$ g|?%�$��o $�F&� � m �E!oc�`"�)�1�0.5Ehese .jconfirJ�9di:s�?��&� , viz.4�& �:� ?8�A stayKv.jo�A�&�I�ll �?Ccepk4d�<a/�{> �0��figure�cluTaphics[width = 8.5cm]{.�.epP%cap�!{�B Lo&�BI�2  �sN�5� curda4$\log_{2}T$ vsNYBT�A�w need�fo� 0F+v�-.�o�e�8 l1. Each �� "���!Nb*] Q�. CounN5E�belowAF�&(�6 7H = 0,0.1,\ldots,0.95,/y�A�bF�( F �a�}� =1$)EO . As seen�;l1��#�� slop�(H�, eY�i(moN>Q�A�a��'Ls�!� M 1$.}�Q��j�<��*�@E >iy is�@�=�� z6r&q� G *�� "�C����@EFUp}a��7$.(!!�iv0�?iB#B.S-�b.�term. �@c"� long�>ol(<R=BB>� part�. � !�$R� �uw )�)B� s e B[3^L�!d=1of-��H�V�� vQm�b��4or�Din phy;G"�4�}azAaM ��E out�G any kn�3>�G&�C . A? teJ9Ue*'!w�D�lxʼn�@3�<to& >Y s de\Gao�ve @�/ lems�"�4s�A��NP=Itjo) 3-SAT��<�E exac Gver> ,1,Orus04,Lat=WG"HH3 Fal�!s%�0not be achiev�A�A[s�,* &mEio�uld reve&hSorWE�6�J[ "U .�&�'��)�|}3r��$e occurs a4�%��aF�H�>y poly\  docuA} �q\EH[aps,prl,twocolumn,?S]{revtexj#u�@ckage{bbm,amsmath symb bsy,� icx,AYs,sub"� C[�xn1]{inputenc} \vfuzz2pt % Don'tN>orI�(-full v-boxA�fE� -edg�@�N \h�AhrA \new� Hand{\tr}{{\rm Tr}\,�,e.det Det !. gr}[1]{\b� ymbol{#1+"cket&|#1 EL"!bra!\l(E#1|:!av h!VHeqG� #1}�>.lQ&Ine"5? ("�dUI\U{E/Tc&�Ent�ArE�the O�A Fide��Continu�VV�! Tele!���D} \date{August 27�`5} \author{Gerardo Adesso0Fabrizio Illu�<i.*Xi�i�o di Fi� ``E.a�$Caianiello:<U.X\`�P< Salerno, CNR-Co�j� , GruppP#,\\ INFN Sezi& di Napoli.Co3Ta �8Via��All6 , 84081 B9 oo1!c 3�ce�n � �[2!�wo)� n.%�Y,reafPic ��CV:IwaUpR\-4vaidman,brakimZQ�er��E+"QM0M  c�` �aYD u-${\cal F&0.70 �< 0.02�1furus�}. Wit�T)�.���\ly** unO� average��a�� _{cl}=1/2"bbesoa�, �Y4�be�3 �ilu-l5 %�-� we��3bfkjmo�Z orig�.6�S�N3)�%�"�T)�a�G�I1�e� m�\ A��t�$CV2\a*�Ibra00}�!*��]<�S rece�\6�!4]7byAIloi$t��Z�2� !�YK942G64BGU\usawa-^ {\emC��e�ifS a�s��W:BХ@d�O�?YN Q& �R ^{inN ,varrho^{out}O "�``in''�``out''6�P�4�-��uMy.�$a�ches un�3oQa�a ��I��f�$2�P+7T}Q �\!:�$�5 ac&V� 6&I highup��Tn�S(Alice��A<,iver (Bob) m? ��e ��n��1^(�)A�e*7m &IK2aq��!,r2�!!or�Nw�/Y`> Ek F�-�3hep��NA>exE�AnuL ���ver�am�ly fals�K.e. som&��^� ^�, �H-�-&� ��i I�is�erX&h��R��i%� D�a B-Y�U�1� �9D>� K *J !�ey, � i��K=9 eW��"� s (a!�x!smu� �`�2�i UBe�F� :� � �M b�4(.B) >oA � )� )&� �su�A�=A>se�!&�g�@��6�of6o �1)v",K ��CV1 �19abl�K���jjce�1�e�d6� xa�%�G 2?rb� �^�@d%spc%^� GaX���V acquE�"# �a sugges�U9) mean�A-"�0�i2ps� ehe%'4 , a��n�hudy2!a�>to� F��a dual[�!)��^ } $E_\tau�!*t&� 2smonot�u��5 LOCC U ��-(�Du��is�5s(ftoo' X1F�Z)�erpre�via%�6\party6�"N  Be��"s�Jnda�k)dheoret�p&, ourV s �Ao&t p h1O"e�a\�cs7NA���ald#E?�� �-o4Qcip�U�d&�u�=&h3"= %�.[q1j�>� ��:h�nipB�u N" Q� a���e_��:�n �Tl (unW\i�) Ea�\ein-Podolski-Rosen (EPR)�I> I=epr}, ����"E^jr� v�_���o!~mo!�S�a� radEj f?S. A&&aM\ good*Px!P!��9EPR �A�re��A�� _9�> � ing Am�Q�G�*ar�U\�C$� a!���a�sis� � N$ cano� l bos �#o/n�@�bZ0A�V $\hat{X� {  x_1,  p B% x_N p_N\}${M%; &\m�6f)�:D },B (�?aEes^, � ,- a8E)e�y&#a�er��!she firs�,at!cal-���rb�b!�adjust>by�6 �aries:�will se� emrQ7g k $2N \ti�h2!}o��m2 ,x (CM) $\gr{�9.�GI�s $ _{ij;�)�{X}_i,!� j\}�$�Qf IH1(yE�*p�,a��Gfamix�8a �um-:CA4a�beG:,E� vHU�s $r_1N+ $r_2B �1���throug\X50:50 � loss�() beam spli�fE��je,?.T&^��unavoid%��"m�z�j!3�+U^� %�be!\m@Bl��# sis,A(a � �_rbx9U�"r I�}mix}, d>��-!_RY in HeisenD pict�C\v_*{-.1cmg"�"&+=% "�/A�remo-\l,(before each��) �<1^{sq} \!&=&\! \92n_1�SrA�$ x_1^0\,,\�>p>=:8-9$9E^�amomp i0�2V�2�-r �2M:� ?� 98p 8�fq�5] 2cm}e5Zz�� (x ``0'' ref�Vl\ vacuu�`a>-�D�"$phase-free: �SionKMa pair;�� $imtjy � s $ ! 0{B}_{i,j}(\th*::�1\{�,a:`{|9�a_i6�cos C�1 j�. \\p a_jZAsi,-)�a_jVA[9 � D.$,4Ű a_k = (�x_k + i L p_k)*}annihi� � � !6 $k�DW~X�e!�3o.�5E�,�0I)�2� 1 �� u6($-#= �/4$)��o &�Om��%C(refbs},�a�+�_ing�w {1,2�B  �� s $n $w e �M.@�J�+� �mand re�5�n!lab|j2��m�Fw, |k$n� $n�f�$-s����r� �er� �K �K y$'8 �$\bar r.(r_�?r_2A ,4 cs|l*�Bl�/yyg�!�t eV�)�Q-��.%�>ren aAN� 6 �"�if!ocif!`vio`2U  p�kv�f�p�(Y]q (PPT)!�d�TM-7 1$MG simo O� )�ty (�4!�S, ?tl�Icb ve�o&f i�� d CMC,.�:�"A� CM>:by+A�Vm � on (_ �*rsai ��hY �@�"cea&�hto ei� ��c-� $\gr� � aPicb�m6�[te"�block� m $ S = {\foot size �|(:{cc�Mr \NB r \gpb�gr hI f T}"b<!�6%#6)}, $͘� \�+\`>?O!?CM'�� Zmv9%-%�lF � C�$^- cribX� odal�J��Np?n� $2 �P^2�S�#(��#) -�3 ^2.-4\det{/}H�#L LHdet!H)b+ ! - 2 �m8extf$l�eA�� �$�Jo%id��m\a�  ch"� J A�:, becanH!� loga�ric negFa�"o���ora�m�cc�T ($��=�|cb�t�� �$E_F$,>V^VJ�8E �pٹq� ��l&�2vi]vgpv efpr}&b 6� u�}F5 eof} E_F .AG0max \{0,\, f(!�)\}, :Ve*�C�} �S$$  f(x)U/ frac3@x)�I4x�Iog�CB} -�:(1- �5.}$.\\y.�j� N  �9!5� -ۡ�a ed! �7B�� :3 ta} eq!(�  n_2 N_-(r_1+�4 }\,.:1�92�B2�"#(sI;� I�e�vAoth2\&�^�" geoM�E 8�3�����c�4��!Epura8�E� $\mu8 n_1 n_2))f 2=\Cstead} s '�hly� & df2.� p"�bq "(�d ���x plane!K���^n;3b * �͖Lu! byŢAd� � � q{in *H pHe�b� ,vanlok}:ѱU m�fid} ���l phi !a /2},\:\: =��\{�[\avr{�  x_{tel}aS+1\�H+_f2%pN%,\}/4\,"M@M�"6 h h� `��!nc %Ic"j5H� ]Yhat��A��I1�ed�d�R!� util��Lu�Xu h!O]Q e�2a�& � x�!�5 �Dp D+�D�� D���."�o2�� Q� � be�/ I�aPn~� ,w< �=�x_{i}^0A5=!tJ )':- �1>@ qF%�u�� A�E�,3-� $A�(ra ,i ) =�P2�](e^{2�+n_1) 22)\,.$ I�8"0T�  repl�s"  2$a�� Mqd� uiv q :B�bm%y�d} �Q ,d��A4  � ' + d)� �- �>�:�M+(i�:por �D&�����R}>5(*~G��(, �$)J@ply� s fi�S$ $d=d^{optu��liz� �Ont�d%�9  \eEd}nA� a)�x& B�d�_eA�^to �}zsP%\n �?/<�f �o!�14.{� {n_2x�y��l-@, = =0$,� ctH�?B���Y ɇ L>s� j�\�&�B�c aeY%��!�*>&�90%kw͛ owen�)�� {�z &CI%�{wB'�R}d6invitwo> �`��!a{1 -_ = 2 -{$��Q� 7U0� ���Z}� b� opt2�oI� = 1/(�H� )\,,>P6p+ � �6Fw6�=N��n���$by��. f � clearA ho@I_ 1�� � 9V |$V QzE2� h�".�L v1p$#a!� fa�)-5v"�# beco�!n�X�ji�ienO,B��!A�.�$"�#)�%f�)ed:5Q"F&!�&�#� k � (} blM�� grea�#�#WC sholw=�v te. &�;B�Z�� �of2��2lBe���1�", nam~)(�f*w� uML)):D� max "� 1/� )w -1)\i�%D}��iBd+;GP a.~),Fr� V�[ any 8$a�+t���. O �w>Xa:u AG��x�U��hi &�ns&d (�$�=?v>��]at�nt.��n� $d!Apm��$,��R���!�� $�$�;ish%& %ExppA�e@2��%I�stl*t�2 �28|�z�LFm�$�  =05kn_1e3n_2n0 =0$ %%{wise.oF,e>�can�c�Ced $1�[A|\�`,n_2\�fal� �D $ ,~strN�en��.>p�q�@d�  @�@ acum6-|+"�+�C��!� $N$ 11p:o $e� uine$#it&!%J 1�mq�&�u�# perm�s�:!��4,woF(� ]om��!v�) .�)6�)�K � "dV&4*:�#�!n 0~ ���b�#X/ _J#x N-2$�ums�s�;�@EF co� ��� �A 2�2Z�� �T >"@^"B.tZJŔany} � o�1ٞ�K�.�geB�2vmWI+��G�inBeNs���t*j*��@it �}~�K1!��-~� G(}). Our aim��4�"Ɍ["* (V=��A3xt" �/ it a�"� 5}!�O9\%<:�3�]�$*� h*b/ ���aia����*A!��d9��,w1 Lb$N-1$�o>n!� �H}�qobt�ccf)G��h�%ne�R!= %�: $6{N}_{1�# N�D 8N-1,N}(�); 2,N-1} (�^ty� 3})\cdot T 8 1,2}F3N}).$�� !cs(]%? J��"� /Aza� CV�Z,a3�"0$"�c��E$�ce��)�s� ? $���K\}s�l���  iso-&u � �%cq�c���2~ ���E�Vd(�2 �s�s�&�#AA=2v'�Gre9",er-Horne-Zei��;/ GHZ)M) ghz} � tV Rket{x,x]Kx|�.i[!�)(w'"a$����MB�'\s $x_i - x_j = 0$ ($i,j="�KN$�y ChooD�N"��&eqteW$k-�lL o}����a�, Ɋ���ц�,�����2�2N�#�' (see�s�|e�Z%�9f�xails):S� 3 �n� rela>�_32 +e�ot}��0 x_Ebk.al� {!`ot-p_-_l�j g_N ��(j \ne k,l} ^(�j}}�D$g_BNACx26*�'��*2 �%u1���"� ��c�;�26� � �M$5Dot8 F8f&�#�$N$�Sa�*�6�%Vhav!�%&x �� R|~2s26U� -P!:"�%%F-�FB[\{ [2�`2)!�]^\1 \(�� +[P\ &+& 2 [g_N-1]^2(N7n �/� _w.�.��y- @�5��a��Ie� stra�6fo��$steps: 1) ��(.=$��m졕Ik| j=a��Ae%=$); 2)�-ՠ�Jfd$ dBd$d__w4 Q% ~B !� �E(1- N/\l&%�+2e^{"�!� /n_1�]E<��g�%��PU�X\{�bA�>U&�E ~d~UQ.Zhs�Zae,--r%7�!2�4"B 2. Ui� chEpbe �6�1>,�[!�ge� A a�� 6�f�dn&�1�c�R1+�_Na�| ��\� /N ��{6���2)n_1/�.���m��$N=�_�y$�7��, �!  a&12E "+0�� rise�-�ndard* �Eqpariso�7���L ob��y,%~�$N>��a!�$�> play� ol �#��ed �p�$*�A oLOh�Pk�w�-be � soon. B+!8w�I orth� 8f E69U�*�1 focu�� s�1�n�3�� -G In�QvTL��l� A�� "�&Xs)V-R�;it��unbiask�� � $p_i$!yAs (lik!�%�Bdiscus >� C ���U� s)�CVOu/�by� a"�- rs (= =r_2= �� T74la%.EY!�a��xE!w $N=3!>*�;�7%�ly(Q-g,\�!�Ͱ�9<9An*�$N\ge3(� � ɏ|�i(%�y.&)��9an�EJ$is paradox�0WYur,a�z$� #Ee .�rs=,N A�!�ir6*�S�Q�b"������a!Q�bېd�ZAli�m*�but raEq�y employ�s��>�o�D�,�pa�(�\oCyA(k�ed�*A�-�!�m��>�L�2/1��guXLteV"be 2�� �ŝfin��)�ok� � >0�Zny $N�>,V"Z-�laU�� m�a����C�y"�&qA�!,�'osk�>r��G6�5uEis b�!B!R .a�NT��!a�b��n%�a -�,o>�6��op)*e�)�woup��%Q�eCe�UJ-`,KAre2a�.7�� (@ =g��.�*���.�>&� 2�� }/(N� 2q 5 2 - N�y$�,Di��{>� n_1=�� : ~s alw�)�\ith.�X-���(m�'��N�)�99o���1+�/2so rapid�srop��}��at ��&,U8L [t!]�`6n]h�B=4k]ip:e]oJZ�of:�ea�3y"*`�8S@$N$ (= 2, 3, 4, 8�J�50)��!F,\De�)>�sy�)�U�)&N�2{��a[�N�$ 4F@W"1�&DeYB�%��. APx�!�.�,mA��/�\t�YlI~ `�� 6O]M��e ��." .�)�awinx7�#o( e��aa window�a�E�B@(solid�Hem, �y';"�s�"�c (da|P>��6Be��"� 2J�~ (dot!� line� t '_)�Wr���2�%y.� �;�.}*@5i(n m^ �� jetI , cru��!��l ���P�I ��A�>�A>Ϣe0@f"T arguAa�:��2 �\yH� ��wo��9��*��a�� ����Yir ��P^en JD%�Bob� oi( ��!il�x t"�;!�@cA�lFZe*�N . St�aY �_geI��k"`��_ep�!�&�?���} )� "�G�yF�i*� �6�}��%��M�:@!S caG!�ed &�6E2e���ly-�!Zt�$s(^a� �3:>"�}} (LE)A�aY�y(= � <̤��A�LEAc L65wbR!5A�M2�l&�iKan�\;�n#R:ed ������I�I�)n1�2���Y�I}("�A�a�2 \s^1_!}$ q�� "�B� y+.�3- Bi�%ar�r"4. D&� ��FXU� ��GM�U�& �Qd B���%y%}��-�� 6����a too.�i"�"enM@emal}E��hNEF=�9&*Q)&$���c� EPR 6�Mx*�i$4� *�* x_k&� x_2�+6��6 �: �1��� �32�jisayu4��%��R�>.bw, vari&- �� �.�_eq�. Minim�)2Y .�d$ �R�)ofI .,��}� (una��Eb�)��happ.:U�9a� q"� un�B, d\}$;:?n 2� .� �6�*� �&UC� ��`�Xe�&_!�"D!qGE1���#. G��!d)ro*a�AR�͐� readoAŝ]_�ma�"��o.%!�* &ge,r�2D�G6�:�{a�:DH�\ exFH}.m��+"ne+ �a18 . It[now?�RM�N�A�f�a��pe�5��m6ˡ��X!�*�%Bx!$�?nW:�_bn4!�H�+Qy��*�+CA�>? ;@ai.I< �4�l7b!�nI�&+Lwo)�!�! } as��i}�>� C"SJ:wHe�Kal" VS��{e��F2� � 2� � !�LE�3m0}.C isa�?$I�qu�P;a ����veS�o�"fy �^�$N�(�z)�vm�7F�" 2�o-ed%_6�Yof 6qY<fR�q 1 � MU[ �ӁE_TA�uiv�UxQ0,��)Q-O}{1:[=x'��)Q-i��u /46�:�E���aze(�bA>� tes�+ 1 (CV GHZ�,). A homonym�&~.C pt ׄ�i6�L8�J�A�|� rigolazz�S M|#:�f$ �$[9^A�pFQC� ic"v �\"e�]oKc��ӋA5$E_T$�+�+ k< = f[(1-E_T)/(1+����$T9$  . ��A{�+��ej��#l�?�Gand�s�:. ReMN!R�("� )>�Ź}�<�,��* M� M )�  M�s�: T:�;��)�y�E+��E��qA�an9i�"k$t��1!vR�< f.�:��Q ula:y>{\h�:.�1=�log^2�2\�2�-(E_T+1)({E_T^2+1}}{�-)+4)}-e� 12 \.U< .J5�T�� !�O�Ax "MV t�M.A���/�*��2-�� V�j� �> prom�^a(�� r��:cmA�y� t(I�Uje,�$iscI:� *�YX.B@in4d �D~q#��nA�hn e(et}a�ng!�T$e ij� �V ins truQ�C*a�:�� 1GfiuraLm�nonu���da� �ur0Dҝ�R n qu�Q�"��.J>>�,nd1�/ di�`;S2Z"��<�irDum.r2H L?E( �l!Z.u��y��"�"�� they� auto���� y ru����� !�@EL.. �4_�\rwor by MIUR,�`,�` . GA��nks]g4antos, A. Sera�0�� P�k Looc�B��usAJp�4>�d�l %"�ecvbook&em"��I*�+T�Qy�HJ8bs}, %S.bgBra�me� ndhK iti�$ds.} (Kluw�X4Dordrecht, %20�j&2m�]S.\,L.\,[<\,and\,P.\,van\,�,\,�g \,Mod.\,Pi\,�g$7},\,513\,m2lh]}�V(] =hf4[f147&Yi��[b�8H.\,J.\,Kimble,� �Lj �80�(869\,(1998)��nuruC]!ZFawa-[t al.}, �k �28@�706�h8); W.A6BU~u et~ 9F�67�l3�f !:3);�m Take1�v=�$ \textbf{9=j22�iD!~.=f+]mcL..? � �J#5d. Opt. �4�267?j0);�c$K. Hammere�u@� !q �%� 15051k20B�06hM}F�r�4!� 3482I�0!�y�ݶ,lYonezF�Na %�43Bk430%4Pu�6O\,P,,\,T.\,Aoki, � A.\,QH,\, cM�c\,430 �6e } F. Ver#( ete,�� Popp�6jiCiracmVF��l02790 l4);D:%�e� m�7!o6%E\5�x G.�f�6F.*�fwc4-ph/0410050v3.2kw} VyffFa�Kundu �W.AwWoT5��<6��j �:�epre�E�Ub�I�E�777a�36� J\,K ,\,B� �Uy1� N.\,�U>�IZ�.777��:c�-Y} D��9�.�Mgo69 -a_i = ^B x_i.&Ni?b�?O  Weyl3vebra $[G a�S, R ^\dagger]�/f$ *e, *p_i]=2�7so:- bar=�� %}gm"�,i+ �K- %a_k#p. ��"DO.)/v I % 5a�%SZ1of5 ;!X� yl--&bR:T��. %vf� 8E!�1#9)uN!�mix} An.[ T� �Ue�%� d/��o� pa@Ing3 mbed�| AE";*�>� fac�/. �O�*S. Kimf6�,65}, ��23�,2�3A. "Q 6ribid. bfn 02231{s�9 si�M�jS �.s� 272R prl��� ��mF6��l�u��S8�S.:"� ��j-P70bJJcGiedk�it 6�B9�*10�,32�vV%}��v� �#tschr.-��5�12 11�)B[ S ��P.  )��J�_d. &pS8ͥ�9��3?qM`r"�3:SAm�v)� �8}, 11s199�uo&<&!Dbm��Fc3},� 4E�:�&�kR�i6�1�!�aC./ �44J. Fiur\'a\u s�t �| I66A<12304%�a� S. P�vdol��. MancinM�D. Vita�m>� �423mU��.>� d"Jop:�qx vq.4q{a&sqfoޞam"|qthmZnew�^mxorem}{�B e',DeclareMathOU�or{\A�� V"�^A��b E}{E^:bqTr^qu}{qubi�"R�cb}{cn c}{�;\ j)eb}{ej qus �ȃZ�s �f"c"o&n �f+oh�j�cohNbifFe��sAR�sch}{Sch^�vol}{VolbACCE}{Z8QQE}{^ @Z C@^ b`=QE�def\be{�e1} ee{6 bea3�2 ehS"�Y ben>4*e.5 non{ umbea�lM Xr{� >{�] <#t gab{\�R@_{a' \!, b'}^{a,b�8gmany{ |\g_{a "�-0.2ex} 6 \oplus x, bpace*&1>&y�4 ^&0#a:Fj0 Cb e? \>} �sef\lbL{$N[\�({0pt}{2.4ex�. �r+.Z+] QlbmRW�)cW+6W+Wp,(2�,W+^W)�,COCOE{C$\!_{�vo}\!$:a!1COQB+A�QHQF:6�vsmD(}[2]{\mbox{q�#1}{#2}$A<nN�v -��v #11,|B7�v.7|1M�B7�et2�l| #2 ^:dbl=1�2=�a�BwB=w eq:#F@weqs�Eqn"�6 *�(� 2B|wsect}�Sec#�secfBxxsecb*.�ms�Q+ �AF�xmm.("n�)6 uptoP\stackre�x{\�x}qahs��Lm�ot{\o�C��def\g{��"bg{\bar:$e{{\epsilo�n:cG5G;cD DN NP PbbC�Ethbb{C��� a�G �la��.va{\vec{�vb �evx !�pfail{p_9$��{R�8&' $\title{Bid��i&�.c,22��x)y$Aram W.\ H�$^�cDebbieLeung$^0s%�� EI�{7MITP ��DDept., 77 Massachu�0@s Avenue, Cambrid�*< MA 02139, USA d0.5�& \\ ~MSC� -81, IQIE`ltech, Pasadena, CA 91125:K� !�5z\today"�9a"��1��)z5a9% c���"�!#��xes�um �65l�>&t�.YJ�<�backw95�s. % �6� capaO��t`��)3�� eoff7#WIt �V0# spec�- typ N�6���EW-�"�5;$�n0&�Y1Hgate, bi���� ^���� ore +!v`�n :I1q6� ---!lyh(!vL&> regiov\ �vious67+ waf,\N�Mun.� -�A9>(*EK81�)%OWR'�R�_X! iwo-way}�o.S6*R3V uj.2Aq�.3 9�2,_Un!}r�%=VWinEkN �� }T.�y \parL�1ex q 0ex %e\ 1 % \�val 1.tex % dG��` 1 ����{I3# �[af�+L#} �y6�ya �$ly stud!�channels����9�>1 ik $!0�y (u .;10),B on it�G sibl�~snzh(G"�U�r�K+.Opogiv�&p"NC00bk}Cpa �@7ste��4%�6�im Bob)EA� �[�=t�T mry�:go"�df/�0ҁl:�e 8/um w�; O tasksbe a� $�ky! ci.E} n*�6@'�� A�uG��u�O*�q�y�'AZ���%��1�z�R� ilar�|Y5e#=Mor��"c:w>HF,or receiver.A� Ear.��!x�-� 8{Prehistory1,EiLT00,%�0ins00,DVCLP},&?>on��sp���H "X!. X^z�plS {\sc cn�E��6 a]biSK)!to! x2e !-to �We�!�One �.�L�,!� A,"t��� ies}!�"�?J�"� toa*�o)��u2d!w�.f��k"%[m {BHLS}�Aml$�"��2O��y�*�D ; {Lei�xYEF�,.E-s�sk!one�� ��V` >� Ex��"i/K$ Qy�E��% subsequeL{ �_ ccc}�|i�\(�B�(O%��F.�.P �.�?9ycOJ. (Th #pra���D"��># �w#no��hf,s �c9agE��nl,�A�rd'!� �1{setupQ8 Ine�bar,2� ���=�wo�Iy�%1]J�uvq�: 3+"�)�y�&is �Ipr�?a�]|AeH�Y!UEby� A8ar "oT 1l2���w!H����M�ei�nS=;2!�t@!�/}a~H.E�)wy, !�jF�. "�%�c � !�Fa �.�I�A%��/� �F{�B�C&�?n��t� i�.��% 6 /�u=!�of �Q+�iM�� -Å��� ��E*wv"+ Q:�� �%?�5i�e6 me-8[f�.(��s� consum�2�A helpb"< !�' F"�9si�Na:��!��! �d�dcoroll�V!j���&%�1�� �{!�ne�0��pr�Ts _�B!0.N/=Xq�Za��C�Ea9��Z!��TE� pad (�'og��� 1!q1t��T�as:Ghy#,re } EV`aprA��J!k m�-�?i�  ap��ix. A�t�'�^� c�s�i�sk�oIj�-���~�. �хV&5 Frame�(,��und�D �2N �:-)�tуpa��aix�6a�A��q es, > mBob. S� 6E!�ir� se2)E�d&�P6ive ��P�s $\A�RA_{0,1,WSs25\BB6. w�o� �Qom]ud#"�T*�4E.A=�$ex�We �.�jsuper�(\A�� (\B)P#3��o} (but9FE�) ��:3dA�2* (� "� t=�+p� ve l�E��r)�� Exp !ilog��Bb#�2e�W�Rllwmax��5eA���1}�|\rho->9 \|_1-�-i[��$z��a�nyE�?!�rho�#sigma*�r|XQ := \tr\�.X\$ X}$�*$�Jpr��| E T2� %p.� ��T%q��vk.  $|\:l\>, |7l \>$,.$') \, v& 1\< | {-}=\<F| 1_1�b� \; \Left&v|3 O\>|#n�3^C%% !�!�8� '} �&3 p�taa$J?sh�KA*for���\leq �)�� 8J,�Թ dgr�A, ��m`9�� 8,ccc,DHW-big}. t#q:�x}\}_{x��V aA�w �bbC=6��q4�s�:QL�"n E�� a� sh�Ge�rra� ion,�� �>n"1�Phi}_{? =�1AOI�2}}5Tx=0}^1 �-�x B�< T^���a� tensor�du�����W��If�Ӥ��s��Nee~&�.=���f a��>� � � �d���`��a))>bit($\r�o�4n�e"�/zNH>&^�aisoB0i%)A}=F):Qc:��� RI� �XB^B^id o!Se��'d)($\la$��a�No"A&� �be <�e8Ik�=%�aallticip�f��o:5�a1 a����n &. .q�)�d[ $\ExTh�!^�* .-@B�,]as �"5�is ~ �1� map6�\rayB}Ee!VI�D�� coYC� 2gN`]"FhA�!�A�� b � �_>� lyeAW)r �s }.Q .� �!+ 2 in�4� GQb���On�nEj�-�� �m�is-8A]- A"6��um feed���<�2�: 1 �Aaax�# f�&�7$K-FR4.{�) �*@�7A� j� app:.� }QIMmak��is |�cc C.��orO&~�r!�w `u? avail�e ^+s��6on'd RougAG speaking,1iw.��#J$XE YqBD-N$X\r�rY$3y'�N.�@�$Y!��]U]�؃e>6�P e $r��.e.�/ ��deU�\, {> 1k($\exists N$.$j7n2�5P($n$ copies J��Fr�B n(r- �)C�P C!$i� .� >�e��Ije�"m Son's ��d�Gem �s %}����&rel>(\ a stochas�sap) $T�uf�sc��$T �C(Tw^b��. $:=�=_{P(\Xia�l[H {+}H(T ){-} , \6�i�7.m�i�e"Rv�$H(F )�i� trop.a> dom A뉫&iz� so����distribuE�$ � B6< �� $\Xi= IfQ�A�nd $Y% X$�ne�n�r $X=Y��.�v��rse1�uo9�BSST})�!%at-n \cbs=gq �=s�/$T�  \*${C(T_1)}2!�, T_2 �#M*�_bq$,(�6Heoaof unl���Lg 5f�� % A�3 I���ttypE�2\.)(\r�01 \eb + 1 \qu�Kbea�&>� toff�� �0.E� �MQu�i�50�en �.�,���b� { r�2p~Aa��onUeHens�n�� itiv��; ݛuQ�؆{O$Y%� sZ$ �,�X rsZI�O),w"lډ���i�!p ��3sq uldŨ&�f�i�3�F!osaT� �,.� $�V��<�D ist yva�jing} �bo� n"�P�p\"._n\}, \{�\$,^ s�ig� _n,(|lta_nb �F"t $\cP_n$  ��a��st����nd@ �*}Es)c� R &�% \e_n&�% Y^e% �#_n) n}�a:% wcl :r %�:>���$a�W�\�� _n <  % :M!r%�� ��@$^�K�jed from�zo*�� % �+ �C|=�\>�� ���1�;V� I�� \ot ��%4( B) - �� N-fBB�� � !� X_��eq:e�-�1,!|���D I}$ �y��h*{�E�emPw��:d>��2� �R�U�!�IBUa�a �wK� �eq{��P�� F�, $f$y���� FlA<, w�lED��  j5a&��#^�T �%� �F�{`Tintro����eA�w�M{�T ! nextA�. �d ��� ����*l��ro"� g��$U� d�K poin�((C_1,C_2,E)2T U�� C_1��� + C_2 laE��s!�W�R$C�rC_=_9Ea� � Q �g�5SiS�A<���;�:1;, i�E<�\ ����t�U + (-E)�� 6� .��ts2�&Gc.� w ]per�A:� � � �&�"$E��P��Ge 6�=�-�ha!en�J(��, ��!E��W�`Ee�!�0�(23IyFW ,c }��_oT�Gi�"� 6�r$C_2=0, E=-H� ({&&� .SW� 2���Oz �}� o֍�a��lC�"}�e'k96�U)�l!*2�q~��9�.� B�$ )� �n^�"�5:�$U�k0�S(� trip2*69"@ .� ohs({\ra}a�E�B� ReFc1n�T 'e� W C� �E4$� %xa� �,p + -Es!��4>&�Yg. s co�ddEp€s!�1�\�I���� �.Z� 9 �AH5�" �!��)� ��'���Nr=�Gu���n��O= sb�n�#O'� � z*�mou��to�I=�f;�o 3{�=92j|�w����%�]�byG ohs$i;g�$6%; $���useN�Q�R7��w.� ����"� T �!���,6���"� ��,tion{BidirecXtional coherent classicmmunica#�} \label{sec:bidi-ccc} \begin{theorem}\ $thm$�For any bipartite unitary or isometry $U$ and $C_1,C_2 \geq 0$, \bea U & \geqslant & C_1 \cbs(\ra) + C_2 \cbs(\la) + E \ebs \quad {\rm iff} �Deq:cbit-toff} \\ Zcoh:d6eTo.Ueea \end5#p {\bf Proof:}~ Since $1\coh ��1\cb$, it suffices to prove the forward impli)�\. In other words, given0 existefofG � }$ beo respa ve messag)AliceDBob. nL\ket{\varphi_{ab}}:=e ( a}_{\A_1}b,B_1})$. Notqat JG$ genera= occup!�a spacE�,larger dimene�than $lA: g$ s��$IddI M$s. % To s�4�e� can��mi.�1��requir � I�,measurementsA| N�] �t=g $b'$��9m$a ( Bob accordA to a��tribu��8 $\Pr(a'b'|ab)$A'I?�\be \fo!P_{a,b} \��t \sum_{a',b'} \smfrac{1}{2}\l|a� .V -�B{a,a'Q�{b? \r| \leq �q.�c-cond�&} \ee %q� a', �a�(summed over��V� $]�Y�Y�ly. ��w.zmH(s from appl�%��$error-def}!]"� c.�, tak%�he fi�st!�tom?6�of�doutpuNEE}��]� |a � |\gammaA� \!A}^M� 22a�2b  x oh-!�} \�_��"!���҅�s�<��(rchanged by�� $, aD � � �\> = subn�lizedIs witha�}�:=\<\gabOb=�?B�. Thus,�< each $a,b$ most��weighRY8is contained inE�,b� term, cora;a�� o i free � miC of��D. See Fig.\ I(a).R s�Q; ��a�of our� of�,built around� needA�R�%M�. Our f�strategyStoencrypt}W9��?-by a shaAm key,�3a mann�qa eserA� �(ce (similarm0@in \mscite{q1tp}) � 3t ver( ofa3p�oxi� entangl��Fus*� � (1) ag��copjir�to A�0,!�0Q (2)1, (3)} q�� (4) de%6. E)?A�A�-7 makes�possible!(5) al�&decouphe 5� F comb�$``key-and--�''��<, which is appro!tela�!:�mA�G�00N (exact &u !ll� 8 later). (6) Tri�e�|{ ^}__��6�>�� cP_n'a�ne steps!�-!)(�}�c)�%^4 1 % figure 1H \in� (qp-fig.tex R � &,}[h] \center!�,\setlength{\� }{0.60mm"��picture}(245,55) % \put(0,-3){\framebox(220,60){}} \! 137,50){\A box (c)}!X53,27.5){\line(1,5){4}} ?B-67,42=0){45>7,R]0J{.?> }.!4.5 � �7B!� �75,21.�0){10�75,33N?8,4!^circle{398290,1){8..v0,->1�V p82WE �� T15= 82!�)+�1�82�Y Z9� u98= sU98.� s.�98RumultiA�202_(2%�6}{ �1}!O6,�+%+�YA�j- �10A -z�10!�+E1�-E�f-.�28,25.1;3ve-9r-.[14% 0,2){5YI:�1Md -9J-:Y15,-2)=fM�F[)<0/8\aw/I���->��A{JQ�N5a� g19Ju7A�A�%�.� =75�.2 <75!rB x!�. <!�> =201,26� �K( $\} | \hs � $}\rais�iH0.3ex}{\tiny $ ^{a+{\oplus} x, b  y} _{Ya�{r89 28 A!@ $}{$B\>$}} �%#N�% J� �$_��% �! �N�Fy}>��185,2�b��6{��� 8,52��Y 4 H 58,4+1�361,38:>06>]1 ^61 �^B }61,142^B.^ 58,9:�58��2[�\8:�|0%�2�|a:%_�|zu�68:�] ^203,382\s 6g(2V(�q)2�O'�'2Q' � �188�{�\foot� size{$y$�*�u 88,8=�:*x*U2i:,:V4�1^:+.W 230,2"A額$\left.�Lgin{array}{c} {}\\{~z  5 \r\} !q �240,26�$|\� \!��}�a'�i:� �gb � a�%-v }70�9 bf (b&� a�f� 8v� 8Z� 8�k���"� A2r�R.Z� 0J�7B�)8F�E�8F� ���7r�2" %��7r�7^� =r�2z2�786 6�7v�115,3.U�"2�&.&2�'1VM.�'VN��)AB�&� AJ>�1�22U�r�!�b�� ��N�ay�1J��J� ��}O� "r 30F;>� "�X>%34�){$_]A�E�39,%�%6�39)�2�35�5\[|\!�1} g20Iǂ�,6 q��^� 8:;2�^F($Y�fig:3"�!} \capc{Sche�# c diagram�� � '�(a) A�nCt$ "�two-wab�1nhe�Ti�uperpos� (� all�,b'$)��de��s,}��i� e $(�)=(a,���unKn�Ds<"�gaa��!�2�2! (b) K same9�6�piT2 B0}!f*�%yk.�i�n� ],9{z�'B^%d. % (c �f�!*�C�&>4)% show�%solid �s. A���cZ�, b�h us!�n�s/�a&� one-m$-pad (5j e#�1}R6A(c1*key $|xm3,#M$|% 7 +?id��IBI;J�&��_{8#8 $|y�B_4}$�� � ��(6;A;�e�ermediQI��&1��m�-�F,9�dotte-�,�W�XA�e�!}a $p{2,3,4  l `qj� � very clos� &� h�?"nd��= % �2*�2�% ^*m�($art 2 If ��# were �E�n*$ofa��* \ref6�* w� "8ished. HoweverT!8 have borrowed &P&{+}"&$ ebits�!!�M�key��replac�t"o� -8 oug�#�(tropy�2�has� A�eaan(baTy significant amount),J� ?(irectly usa�in !B' t rus!��o�resA=$is problem%!use ax)onF!FofH%�$k$�C�!c�in pa�$e�%d per�~2�con�rS�#:S^{�(k}$ usA!�techniqu w\YBBPS96}.�)X+�ly�&�,�� high�babilD w�c��ͯ�st�,ngI!,�g�&a�I�#be!-d?!more �'�.6� to offset�cF"m"�$ �*$al $k \lpm�"2(.� \rpmM� �out�3ofM��pany�#. ua-Y�)M aris<#w!!+ petieof �$'!]�:��"s'umuN�6ne�Hicular, a na\"\i ve��,�%�ri� inequa!��sK"_% e_n$�� $k�) �*� }fact,\f�aced_of �M^S(0s $k\gg \sch("�e�4) = \exp(O(n))� weA%�guarante�(F"(, +a���+k,n ,\�+. � thir}�isAJ treaEI!A�.xC,k a sl� ly noisy i%nel�< encode only $l$�Q(�$havAG�0, �/b�.�$ two ��ions)m�&n)��$cLxqi �t!� n va��si�a neglige redu.��A;6�$DV$nowq`noO'k �! how quick�9�$A�0roaches zero.�.�!�7reA�d ��<d�!*an!T�m 6�� �.��Ť ;%�descri�+6�/�~�analyz% y�detailH �/'$} \vs�+*{-2ex} �1Lenumerate} \item[0.]�)&+v b*)�Z '( .�# � q�A�at/ 8\Phi}^{]ot���,A_3�  �+:0z*r 404}aA(SZ. $3i� $4$ �-�E�se��te��r ARA�"Y $a < b$.)�޹�s�a�6�&( written as-W ��+\sqrt{N��+x %%xx � � y yy  � ~2Ze �+ z)$x �y�#��+�( $N��F� {+}� !���. IF� y"� l �"9dto� �": ;� !e3&!2� !wIU5()M1h�a a� / 3}$La�%I*_/�&1 S%�$ �� Sb S  S M % .h%b"*�+g �0 g v;<..UPE3{xyO'�L{� \ �Q]�� x0� ?JJ_F \,.Q��= U� $U$ $n$ 's�y6q$!reg�4N3A_,�+� $, )"�\iz�3J^/)�b0)1 H�8-�"E& `-� �&� \gmany��K')D X- ready-to-�.o emU&A ypts ,6���1!7� 4�Bob} <)imR 3� �3 (as % �Q.� 4i��1} 2M�B�A�eQM^.Kprodu�)aQ %�zIe ��E0Fm.'aa> <a�Z� \>/eA Fur8${\sc cnot}�1% a� \A�5��A_3B"B_3� 6BA�l�+E�,�'A,udQ �%&� Mx� o& �)e�-��bec * %a�aKG{split�& &-()70} �6u%�9d9c��:3�$a'Q��%�1� %��V .M J�0non \\ & = & MO�� �;) ���3 �b'Q -�' "�eq:phiab��,�L�-��:"a �;%xz\! }B2��Qf��2J��2��^%�A��~� ��A��V� ���$pends g on8�U6��b�^b`it�� <jce A$ 7$,� be easilya�nE3r�� $x,y�- $5@, 1�y$�3� !ia�RHS above�.-8<��#50 ��e4- bI# \>l &7N.��3 1 x, b y \,fk K)iy�9so�|���Q�s*�3��3�-N $900}6b� �Txy|xy) := 1 - \bar{\e}�;�:1-*��,average}. S=z6� cprojeo;to� �=U<'=A?Atell �x>they ��8cee�6�w a littl�>�;2�);= �:m)ng�/-h$=�� �;5}} 6O$�Cat��st*�| \*� log (T e_n)",�:��:stNj1e "q \lbm�C_1v<2�) e�() \rbm^{-1/�1> $�9_n�Ae�-was stud�:<mF0BHLS} Hpj@)�E�n.japa(5a�&�4g�[at le!>as � ! ��2� P���F� moreV�manifes� *���?Wp@��Mto im"A��8c=fulA�ion o�6�*:.����I�blockf t@- e�@�� .�>� i�if%�f>}a�>]gJ�%a�<i7�.*oA&.�@M�1�7�-�toY ��ion} As�5uss��J�can���lyAan  p- --{o:�K7"�� catalytic%�E2�on2�A&i�>k� ed �$ �6�� �%I.p�hea�u2 &I�Egll.�A�%�u�T7in �u7orB'$A�Z]o Tis���<donathu6e,��we�to�! ultaneous�5n�>( low enough f ��botzy�� ����� to bf-�ed,Aw����DTc� ���\�3�=�:��5%-ma�� �ll�E�(al@>H, �a��lC chos�d�=a vali"8de0E�a��5�ng� U:.��ach{8Q�.� in.B*8 T ll<%N llec�V]�^E-ia`�7� syndr Agriv@��i"x�!� 'Js�AA r%5(atj>���"|"�goEo�!� $n\r)E~�z�6h6. E>s%�st�, �2�,Eoj6�S�<>dGMN R� " 1�9�A s a yĹ_.hon.� wcl:e�gnot��: �0' -> P_{nk}''�:DD6�?�� ,$: �Y�&�  $(*n') ��.6.}"=�,�)cby�o�g`9to�%jone�/�to +I.Wiq9 distanca�d��6of �!deE�8he minimum Hamm!A*betwe�ny�w�H i.e.\E�#G!�S$��<b EHdiffe�J . F�9��! 6�DN_1=22YE.�=o�CA�aEneli-t�8I7symbol��8 $[N_1]:=\{1,\l-G,N_1\�"has�"�" yW!>I�on ! c# e�� �D��*`�<" � lik|!!� �^l� �!�-�Ai 5�$$2k\alpha_i�[!$!&a�|me�=e��Ybe �a�r�"G d�M��Bny!floor s {-�*�D \r$$)s (�j9ca� mh� , we just&FU ��� Up;{A� dard argu�sM good!S�J �nor h�� $lHk  1 �2v H_2()/",  �pere $(p)=-p�  p-= p) %��binUMeB"=i�ua�A�� �<�$ �N_2i  $ I�Q�bBJ��$orPpliQ ,�P'�d�F'se� A��z'val�!$l�k�1.[K W��o\$)f\max(19C,  �)$�E�$l ,k%83a�H 6� �LO#�A[ "��� KEQJ! be v�ing\� "i6i�leq -k D(N\|�$))xp(k +y-A($ (iY� �" CT})aq�J-kA8'm )L-2/6W! � thesIOs-��IAS� N.�"�Js e��(1-3� *�Aly��6l�h1&� E�&p�J(a^�Oo}_1,�L, l)�)� ector!�.� E�� u�$� �$(bN_ _ .S"f�M� Se���w�������w1pens+J� �i�>:� $\vec{a}�Ma2$_A�h �+ $k$-)&���@�)!�ge�K�BI ab} = (b.abaI�a �.i�) )���1�  �N d?�$ nsora��!%�k��pWB�2{1�$ qubitx� tB_1:=�+6s . (�a� �N �o +s}\AA)()0� adc�X)\�Y.@?�\!e�J 6 5�N!/{a$ vec !1} | {b}�*vec� 1}$ga��B� C � b"7 ae paie'�Ey_j, b_j�8 re�s� is N�%+��'�%x \eq{F:G�big�P_{j=1}^�&bL �a_jjA*� F � a_j',b_j'�J_j�J[|%Z \; "Ra_j %�E)TA!Z \rbL �-&�Pn-1i�$ .�B\vab\v�\v"�\vb svecw34�#ec\B_{ J.r� �z�A�The}Req{.� be �"m/{in_*"�"��!�\v�E�%� |\vb%�!� )�%�&)�'%�P'A%���R F9R�e<m��**���on��� �O"� :9he��rA>1!eA.P�F��Vion is (q-) m fail�t2�* $\p\leq 2�S 2^{-k%Е��&be�J 4M >�\v�\v�$ %Iord�Fo6�&residuali�� �&i� duc<cGI= \A��0\{\vx \, {\in= S ^k :!�x�P{�k�d !�$ SB.ON\M2�M"�T8|\vx|:=|\{j : x�,{zVO 0\}|��:����2 o�vx!� N � \A,\B}$�se_R�r�-�-(c )��E/enN/���? ist �2de�$isometries! D%` \A},\ w&�T�nPde-XA��1z$ w�.$wR���Tv�)shsf g y� =u��xa� }$ (��*� i%>b\in[N%�E�E+ū�0S� �b Y �B}�B�@ =AOb\> ��b\>$� �(reteness, lz-5fmaps takAŅue���H�5� {>)b )B_5�&C�Oa�E3�H�6�8 z<� �%c&!f2�%��}e5 |\va�N�m�1�@ FB����LH!�ծY�K -~!U.��.B}�v6�5%�cv�7_��.5>Q��',!�=��%�3n$�8 Y! :=& �>b>��5)he9��U%3" #1)'2�-.B>''!�'J6,�!*q��Je�''� 2iU�b ��eO!ˁ�*��w+1�$zE� =M*(!� �)\note�E&)  \� !\dblbraOYE}2�4V[��ec a ec be� NL�^-$\compleDL}� �L*�$+,*�in "�6"�H&#SB/remai�( issuGrm2� 2�� �,���$ H�&4:!�ign� <�d}.]� s ��% E#�*a;0� S 54�JaM ��%@�%�\25. �ext�J  in16�(�3��$�Q�6fi8 S(\vx�UZ��jbe�e`&H� N)�n�/�9\vx\i2�$ (or "]$)�~| �|�k�A���, �)Z*% �log� j:I�3*$binom{k}{jn%e\ 4k {} + R(�8kB() '< e%�I:!"A[Ƀ�Tmpu�Q�b'')\>-8 A>��:(&�e�Ot��4^��. "�a!b*�% sendf �� a'')I �v�!�v!yr-cIbuH�w&djYW{  (�PiP"�S)y��end $O(g!q�(ei� WC �$�0\,{k}\hs-\hs{}] (�for" venis`)9A$R�nN-!����$R��+t>�!�)32M"]a�bmS�Z �beu-.HSW4�9 �HSW�$)�� !ā�8$`��� �\v� %%��}_A"o � }_B �i�h:��|���dE�AH AQI�� \A_6Q E�5n;B;��� \, G[J��hV�"%-"A �4)�ir�U ledg���, �$V-�E\!��"y $k'\� k(1-&�$ :T $+'=N'=6TR�ac�6'.�! Z�%}:'�&Ple�8�5���AAenviron� �not aff�& �&�#a�c�7��r#ч��pu�� ��a�� !J%S�is unne� ar�^(WN �ex!�*clu%'��*<�kba�u �%�8��dx0ize clutter.)�j After1�A$��a�saf1 dis�Y2(B�e�&�UEZ&N *�����>'bd&*�'R%��bm *)]A�![� Ŧ ec aeT� 1[ ��"c��:�6� O�%�K\9;E�rm}"��:�<�'B�<) oS"-�6yyW�(��E�X:ed�h�l"�31�n Z '� tse #ion�hm��S�Z rank= {!BSch}(U)^"� $.� !X@&[ �(�ə$Nielsen98} so� al�{h�z \!�)Z"Q +&�6"� �x*2: ,VJ&�"n�[*m !a.��c�P,ex�7bm{-}.E^�*pm �8 k'}-h (k'{+}�g!. �m*f3u#"z+k'+92�7U�% -:� H�J:�rb�>8kB&6 :�#E�%%"�j�eun�)} 0c�#��nsu&ia tot�`Pf \\[1ex] $~~~$(0) $n:{ (��. exec�e*n"G\\ A1)B�  (� �|ng non�$s &a>s)P2) @�U\!b�\!< �, wa*L9ioz?yƭX>!1�8=3s5/� .���fidelite> lebBan $1 4! \, 2{�) (2^{{-}(k-1)4{-}2-U� �!J� nI!M� b�!U�.�%�!�l�U�u�l s}(\�n !6!la)$ �n Q%�a8� =�2L.aGA�}9a�� N; K��jlo}<!.&B.f>re��E = raiZ`�/ �1J$s:�X"�$ʷlEF5H�>nN/�(m� $"V@$ $6�k KR&v.",F!)$; �!� AuV !�2Z" �"S ``� ''i� �;bq aaw.-of �ur2Ta-aH��Mk,�|is lf�i02)} + JQ}QnE��Z[ Aa(_�i"�cy6�b r$ �U$, neO nsuQA�.�`!��.by � &� V�r&'s f� shor�M0 �0i�(:B� 1A�"jWg�/vely R, $5�kA�S .�`�)��>N�` & &kM�SHv?�h }2- l��u nk(U�+%n2yQ%�IG(�H�"to�$2�- x�al�Effi. cy, I��j�.- divi� baI�e*� u&�. Equ0g|")E ] $f(k,n� C� sum}!����!b�au/,� \$;0�$ $nk kE��B>c�a1(,� ��դe� 4-Y*;:* ) +Y$>�*� nu�J�EBR}{n}f nn�&� !3-%Fs}% *9 ��fixedk$uk!�$\lim_{!6)5}1= 5�>�M�+U� + R/O(T�-�sD �/&m0"�I!��#�gg6R {2n}�CNow, al�q� o gr-tw��!� �&�.} N� 0. =5goooa�!�=The��A�limC5 ��aC�� cruc�/du�+A��+��5G > ! X�G} �7lemNH f3aW~�n��J�H�G�.���uaI}i�k��. f�-a0$�AO ^�!\+&�2K .� n!�rep�H '$ $m"Bre� HameJD �st��ultdaSo^al�6��c/m$ n :,c�pen�t!!�U$)�Yi!E�.Xi� n� �r�ono5#t� $m�.��C�*!�$m = \$- 1/�/ ((,-�ca!���s��>��i2%4�*. Wj )��vm I�m"�1m r\; �wf�c}{�o;�; 0�jeq#++iA�"� &�Ke�U� C_1y.�y\"�y.�� :� a�$E<��nd $E>0�ses�  then2�aIau�*"�6${t�-_ys:mwi"�vE'� n(E+�s�|5at-i�qs �(�7%AF�@1I@�H f]A_5* \]\) = &-t|tU:5C\�T�U}3q�CoD%!]% $t!� , previou�4gA0�4g�UF'�� mod:a(�o. A�zE�,6)�/�E� 1}� n(E-]t:����r�QvQ�$E(I�,&7W.�)i�M�$M *�V5a��.�a�U�go U�A��:U�of6n �S� "n(00}\>� tqmJ8R!��al & H"O E�,}2U ��2���:zAEe E��E�;$$�u�. \hf�, \qed��\�&�/1ex�/�8z So fa*�UfocC8�,�{I0�-adranY �0�Q���3�ORY�'WJon��"w�?&� &V.�on` n���0$���."{m �}h "0� nnn}"� bivBt�0�C��� + U*&j@�E \eb�_zezG :6�1locc�,b2�<��U celo�%�����cU) *��V! �(E� %*� �%eea % �.be��CII= x!0�>w:�2:o2jo�?5X �� �V�-� % .� �5 ot �$,ess� ,ef�8uniI@io�"�>O$ith arbitr�6���Um,S���7Xsor� Z�\tin�%s� (in)u�^{� e o>� ite �, n��a"y<<]B�wK �� ���bp7M nt.> �l 4sj_d,c�:� e� 2 \!�$��(p} > d $1�biquantu�.*$by telepor�S6`$bs + 1 \eb %6G 1�#!A%����ل�OlA�eq:tp-sd1R`I"� �z$2%��� exac�Hd K/no� ��E b�C��%joG it��l@'s ���#9R<or%:���!�!LM�,� 1i�$\R+Wa�W$�u�ws� ?�8�_<racsszR?0eg$,) E)$ |u|L" w �I7\�E*Ffdid!* a*��ba�D=�l�& J"� A^�� f |^���#tH>9�chang�g�!In6optim�0radeoff curve"3>��E� $E�Gn *��s�i?}!� ��!�� Z�&�sb Axnaa&)�noX^!�E�E*-�� is fA���appea�WQ+ aramv9is}. "%x%�3G �AE{ $\Left� .��6i�t!% %� \ۈ{A��B� ��H2�P.�}U�x"��toff} BB_ !s�c ��saa�"� pu�ees 6JY8�$���*)"�A)Vm ʊB eEwar�E���6� ���)�hus natu��4+,th'&�� Xc|i�)L�D� � $3$-"���4paca)��-��surfacei �2exa*.82CCE�R��Vh $\{��$C_2,E): U &� � 4 � C_2S � � \�.�\COCOE~Ջ>�Fn�� n o opd \o��)s JPc' 6� e�idu= mappA DCCC5 � $\;$*�9e�=a[ok� =1� \!g& \Lo�|.� & 0{-}\mio,0)�w L \mb�z%O�..� thm12�nd �F�ngP<�U�Q�yQe��s��fy� �M]��aZ�!�ekAAeirm�"�Lper��K"�cM�Vr�^Q~BT �nFremote  pr�\�%��!E�*ca{ %!�c = $|\psi\>�(e laborator�Frecei}e`-!UŚ� er REa�k_�_ e(Cp�a����p%9y�5WeNimjB RRE���F- k (but2$9��%�d��)-< {-��15h JjCCE�T&�iG�Yj8 �$Gh se�����!�!Mname{)�\�>!*W�1n <eb5�|�8=� ]ly � e anH-Y? � . C�)�iA�eL�%�e��uned !8-2�&D �O*� �PeC� at $6RRETbZ 1dO  hand, \j)�e� Q $n\cc-kn6[)5b%�� the )����s (� ��� 0mATaĉo�� 9�� $�) 2�.a �_of Mrze}G�X�Ak A�%z ` is:U��b� ��*� .�O !�A�sMMs doA�!�r>��1��is"� �2�!�=% . S&�B\ QQE��� ���Q_1,Q�We*�Q_1 \qu"4Q_2 ���W}C2�Uo�� 2�9!!9� zi�5~f in5"]%� c3 &06��r;�:\QC��!#:�T :-���2� ��-c\COQE~"�;. Ref.~3+a0�JAs�ne� # " �  ^ C$\!_�o}\!$EfQE2)"s �+C}..7E}=2 ,E�(C,0,E)086�a=nd K\QE4Q 4Q4QQE"�r�4�2claim�atB\G�@=2QE :X (2Q, E-Q �R��� eq:-(� O%&z1rephrމ!P�; 25Aa�w͸�_ily ext5a����ent�.�*� � &�typ�j^ �Geq>�s.� "7 ceC%[  = 1\qu0P.*T"�.3involZ���Pre .%���# b#d0�"u͵es!� !>66,EСk.��;U``�1ly.''A���B=,�R�JY#$]~�e;X$�� Qe� + E� = 2Q  + (E�ebs�<$��lCon�Pey%*J;Rin�Sn nU��N� =�3 �� \QE��&�0a'l%��@ks<@�mplaAhUjS th a]�QA�ch�J$U-.�T�f�Xr�; qŧ��dF� �1+blish�eK ]� :Za� ��s %�bbB �ㅚQEb (2� ���_�/in�6QE�0[2ex] \Updown4 X@ \ &}2Q2@ R��}b� �>E-Q_1!�@~ K�  .�# j {%z� fur���es , QCE, CQ � QC�u CQEA ��d� ilarl� �~�B��LV��+oAnt^A�.�%u�Qʍnp AI���s (�� �) dSQm�,� �{B8di�])b] � <�3:�2 ��&� �* %x&�Whya|-Z�$�t&�q:����ndix,AD%S >K.;�og�(T� ��nd � �it ��� w� appl�[to"� 2Y%c"�� ��:� �:�Y!6�~� *cC is b�onɒG��&�Tq�D - �K $i$�a"? � $\rho_i���� �: its QYpis $C�Amax_p S(�Ci p_i XT��Bi p_iS( '8a,m maximiz"�o��(S {T� s $p� [9$rho):=-\tr �0� Zvon Neun�� �!T 6�턭�by$do` ���9urg�I+Mw&yR2^{n(C&N#}$ � �I�F�r&�-��N.� $p^n(i_":V i_n�%p)�2s �,@Q$�#�g�&�� �F!kv�W=m��w"zV*b��g�8(v�inguishV���an��� t���ard7A ``ex)N e'') �st half� !� PJ�val�w asymptotttly�(�LEWumy)�3a�@a��q$$CAIn"�%cZ)y�5rE to%�A��B��i ; raA3�nAe �*y� (mea�gs �� a le�;e�aXnaDpm O(�)n})!�fa�t�9��e��on�0,\text{poly}(A6� � ssn5 +n �e�Mou-@�\/<7���SF$! Cb$C$:�. �-2' ''!��c�D Qi�*u9imeaS- ��asAs>.) Nowav�Z���k�q���B�s�2in�B~18�p. �a��,"#K � Cl�5I know2��� "̚A�)�� is*U%�P�� &� $\cPkYmQ��� e a �)@�m�rox n .�$XB_,�&�1:�]6BG,nB�/ ra 0 | ��be ��t�ha[ !�"��C$�[,�u$�rk�XuslHk"�-�e� � nkC �o�1�F all}�; ��k.. J0 idea�u�cu� BS029��A^��!r a�� �`=1�EA9�ionA��VpoVE�H��G �kun%%'aiv�\ $�>f�Uba�y 9m�. Ru�{)k�we�Az�Oi�%%�L�\�hb&{Si{S!��,_if,1&?�CJh�=U��G*�ad �Q�3bŔ�Ds"�)���, Z aU)RB-� .�_I�� !purb�^����t �+ Bob � ��Ee"4���%~ ��k �<$ �~%_XW*@]@ =@{a >@ 2�S-\�_9]).�*$�*�.%��,jK$n4 e!�d�2:��&l� �rk�J�}�$} preagrc�=�-�eN�� nC$-�� $�r rt %T�n^k"t�9�*k%Z�6f�enca!A}xfBZ`}- = N�X- ��!��,D��b}p4d�1m&c `)sA�b &Ceh?�^U ��7 �82����H WbB% Or�n�r��y:|,! f\G:נ��0BI+�l�v � $}k&]�2�F! �H,{4a/55�*&T~.��e&���Q ��5igi� �!NA}����i� ��we�p&t � ^d K )�"w 3�� 5�y�X� M . W&>) )U�~E��-z��� IG4}n-Ŵc�S"Q�P%15b* EcAh] �``  5''NC.��s�EejA�-A�%]�y&�teasp%��!"e ��1 . E�"�j� �s\-#CyMr}$�;!��!;��.mZ"9@�@bI/ABob%� �V $( _,b}):=(e� b_1)�ca�k,n\)$�N ,(��2�^�Jf$�3 i~E�"a faRlom�!�[o� P �sEX m�(af���a3iU��ly}6^!� b�}��'xl �&a�N��� ind};�W� "-fa�Bob�we^k)>�)ga�tu�g&�F�is���i� �"�k6� ��be/&� ��ire�linear* ,6� A�5�u�was fo �in:p*�� �G�dh.0"�("�!�&{ ���0� 5 or� 5"D� dueck� C�t n~ ion �*�1s!�6P occu@�8�,w\J c��"1istic�C� s; DW05} p��sC{���� 5a�~�� �!-!Q� �let��lWA�int�y��zh � ���"in��ul++ o � aper��;a�L�! ��2)0)� #9�EB Thm~6�(bo��e<�3�|�.m���:q 6���is wj�9Ue �% ``~.'';��. re�!%n>�Mn�DsUA%ee s���8���s (Lm :�uoa�#^y2�"bg 5ex}p2Ac�.R-0s:]I���gratefuQF�� Peri�G ]itVa�p+hospit��while.@�0�� work.jeed=$PUanonym;;re�mʇas�k 8Eec ��Thanke�DIgor Devetak, Andr��W}=@�nd Jon Y�for us��u�s, espZ^P8rF%�a�q�w� - !�1�� eA�dG�if���?:�AWH a5tes /�A5t�Fi{NSAt ARDA un[$AROFtC2T DAAD19-01-1-06. DWL 2[BS,Tolman Endow!� Fu 'nCrouc�hF6 � �US NSF �Pgrant no.~EIA-0086038�Mclearpag=c�Dthebibliography}{2L+new�S(and{\bi}[1]bG�{#1&\b 4NC00bk} M.~A. �O%0I.~L. Chuang,@ Q&�4.�S .(8} (Cambridge Un�*s�LPo�, ,, U.K., 2000eD�Prehis�*`1} C. H. Bennett, S. BrauGin, I. �$ D. P. DiV� nzo, D. G���7 =�:-� Eisert00}� ,�Jacobs,!,PapadopoulosEz@ M.B. Plenio, ``O,4l>�u/A� �of non- L' �Ds,'' Phys. Rev. A y�62} (%� 052317, 60-ph/0005101v1.�Collins�D. , N. Lx m-$S. Popescu�The�- � cont��of kum�����2v1=B`DVCLP} W.~D\"{u}r, G.~Vid� $J.I.~Cirac�~�S.~� ``6kyap�i�%9=$Hamiltonia � .�6034;.OLett.)S87�o37901%[12/�3C.H.~u'A.W.~HaB7aW.~Leu~d J.A.~q ``On�|�ci�&%/.�A�2�%]�4205057; IEEE T��. Inf.A�.E!49�895�32�Leifer}a� ,a�Hi�rsoM ] Y�.P+*�2��%j>>�52�Q�!|012306� ]= 2n ``Co ��un� A�"� "�yaD�E�3070912�](92}, 097902�4�F �� D5�a*��8Vernam Cipher,'.�012077;��-� CompM~ 2}, ��1, 14-34|2).�O��DHW-big}�>&?�Q�A.~G `�S)' ory,�o5�"�Fiy>�8s # a faX%Jum�](!_i�Z"h12�s ~�fE.~ �(. ``A math�F9�"c��9�.'' B�{S�$Tech. Jour� E�d27} 379-423, 623-656 (19482� BSST} C.~.� P.~W. Shoz �q�! A.~Va]apliy��6�-(=rA�&�"^ �wK�r�6se6�em!E%ZE�1060522�\ a�\ ThM448} 2637Y,Y+�Y :� H.J.\ Ber��.��B.}Cum�rA�C&�~ng Par� 2� by L�� O�1M42�95110302rA�,bf 53} 2046 �u62�� }= it��*��c*�6�Jwe �ced@ped T� 2��,b$) �xvbeen &�M�7"c�� -G *� �K���#&�?�?=*h�s���6�)�c�*�� ��:j i~V�"a"?;.be"~(develop�� @.9 I.� A&� �g6�E�52�Q&( A.S.~Holev� 6�orma_��i�44}, 269E$8); B.~ScQ�� M.D.~Westl3.& ��56�31I7��� =��Be�a�B.C.~Sa� sA�R>T 5� 6���ۚd6&�h6�J�� ��&�27 0207065; 2�(. 68, 03231ɡ��y��m$}fWeE��y�K�B���aAodK��Nedly �s new KL�e��$(-k\�wXe�e%�#senEuVJs�$Lleast $N^k / \vol(N,P,k)*�&.r( (kU&%~aM&�# ��H [N]^ni �� � A �aR�BB.�>oG*�f � }N^{ #2^{k �fX)} #�"(ͼbCT)�r� eriv  $Fh]�{]$>�9] 9$$i.i.d.\ toh%)� coin�#!���(g#%co�8up j�$s. Prob$(kxS$ $)=J \, �=5^)^{�z �N�, 2^{-6�)1$�vtog���.�U1� s $:= N^l[5 Is(!�%F2 Q�)} N^{2 &lh}H%�6 >�um 1&_d - �T!�"$K )}{\iN}�\�'"� !�T� ve��J�omas, /$El#%�I*o ,,y} (John Wilwnd So4New York, 1991� t�98� ~A.~ , � *��aT1 PhD sis, *mofmMexico�e0buquerque, NM�ZGHHL03� *8 PC yde��F �S:F-d*;F�& u ,6330722v� 18"� �;�*�B>m Appǝ%�"} ClasE!l C2f!�����rZ6.��to�=m!!m�5o4 Massachusetts*�$��.ology, *�MA�5.�d�sD !]M�,alI� �1A�eVFan ; ^0���S i-us�� els84 (EngZ2. R�an�Xmary)G� s�3 trolM�a! /�n0lemy UpravlenLor@ o87 (1), 1��7� �>>��� docuv} MN\��[twOj umn,� pacs,> rint�Zs,ams� \�,,aps]{revtex�xu�ckage{4 icx}�7@l�,title{Moir\'�^f+n�#Ym�(} \author{JWDO. Huguenin$^2$, M�(Almeida$^1$�eriodic1 uctuL 3�no3A ly \KJdT � ri�-o b�Xu&i�"�9�pMxaoi =� b�A�teHaV persW^(ga}.Ɓ�>"�#7f�,& [�setup�Ba�9u \aq({42.50.Ar; St Lca:mFsa> Hmy� {Sugges!`k  }%Us� keys e���2f' r%display�A�� -�V�in �!|m��at�ed a g�T dea%��estz�{ A*� UBnt� �3evoD` �"ub!�� s�a whole� �� a of�� he�#it��I�[y m#1}. Amo��%'%�U��bl8 exA��C|*eA"slF#���r�s,.�kFmr�osc�to�"|�Q�t �mployA2>�(q}?G��p2�?O!7byI�dev��c�AP(�xi.�"�#m A�i�-�ive�| cavnf^Lp9R�,]!���H%|!��c �-c�g�m�l� ّt2� �'EKpz�`ar.!�$s�c e mo!�!n*� �1T�*l {.��*2=+-�%id variet Y1�Q8$0monken,padua}+ �M�� 1�� olar�52ytyD. 2&�r��"= -x �julianE�MU����1 0-h)�� flux-�%�cjw!V#1e�e �Ole)�A/sI8s�;NG�Fy2u-�l�zp�nt Lcurre�f a1/�dJ0� than (AHs.)F"��qu��v�E2es�� �w� /.KA��9�al demo/���� b-shot no�� �! O >�<s)�d��Sx� quee��l�P�K-�treps���-po�y*>w2'A��<motZ,-�gF�s# semi<un�las��I< � W& O)e��g�ye�&e"�OQf doma&a wkJ � eU9!5Ÿ��A��ixl:Ay avail����n�� ch$��(ir match��� $ �&o���Dt\ ;� newBkA �2��IO:!J$ �ADž�&T2 (A�Ox UR>��q!eA�D/�1% - 8io? or2si-��layou�4rM����H�5�$��6RheA�A��  SMU.v �A�I@�M/ oR. ��X�`�K��A�@it5� �� oireA�qdef�8 play�` im�!7wrÕ&*fields7gW�.� "{\q�p�-��� y,� �K�)�o�R.D!c�^W3J_ X-rR iff"� or ���ESq$ron Micros�� (TEM�z"e� � of "��Wc�.�o !5v -L.��!w1�= . FromRP�>IaE�in filsO����no�+s}N7(i}��  �/e��n teeth�|od�}R<ål1  �( power&o�r�.Ry �eU 1X�f";Q Aq" �.iqu�l"p Prț M-p IU fe�t�U-r9)� 0� i+ a prim^��.�q �T#�� ���1 ��9J�� e���,�K thod��m4��ell�eH.ac�A�3E#R'6�non- �7tea9a�D.�P-Si��2l s!� $= 0.05^oC\,àsi}& su�%*�Y,u� )u��X���)5eaYF�5r.- %�\ty%�� ��!�o�-Ile�� on s���?cript'fiaK�"� H �y fun4b{ "54 `��1 g �, �de�.��� 6e�t��w�G�bEPmrM� .) l �~����>ce8��In�>*� ���kqI2u p20�2!$ta�>D�� !�e��UC �� B e�loi!a�/&feE�s:�)Gfe 4# ump�m|.�profiz.��&�!��c��1� maskK�S��H" s��!�id��m& �|�2w Xs$�e���P#, )�6�+,�x�+6�9 ,M��j0 61*�!� � beam��$��2" � �r^B)iu�Wachg���� reg�@)-inv o(>1�I��Q�Ɇ/6�quite*�  (1.2%�1.6 mm)&u9�0B�!� ڍj��� � vis�X � " B�.�o-r �,E;%��,Py�ui6 (0.8�0.9�-�a���4s�6�e>�f,ly"�E��er��J��.� a!���%��� d iIo� 1`�1�!s��; a CCD ca �� Figs5a�1.b� sN_N�*c�if1�-v��-�.�t. Fin�| B!R)�42�� .l�se���!Q9y`���J�=: iden�0-�daL��7�jE� fi�v$�7�!F�s;)l��( �m0�a L}[ht] \Hw&Ls[clip=,width=7cm]{Fz1.� %r040b 1"o��5�eM}St^l6k Q;%�2i4: a-) 1.2/1.6m�4b-) 0.8/0.9mm.M � %�)�%iQ��E�(2. A 5 mm l�LiIO$|S�cryO �s���E, 425 nm wavegDpul�u � � a] doub�  Ti-Saf�. Pai �1�c�A>��i� g,r��� type I>�*��"�s 890�( h)eD 81 �D)�[3Mz���-avalanc�et"�s (D1EDE*A pin!70.%hdi�|��la�� ron �@S�6coinca;Y�u�<e �*���f nde/�u�I�0p��hM/�9Y�2V�Ef1}E.��A=-%S�nj��� (G1)��9'a�LE  b� � ��;M����_*�O%C��Qm�["> �V{L pa��+�� af!� �:hY <9  scal fa���}�L8 of G1,ΧrG E�-^ .�,)>�e���I^�� plan�&��Abrl�s (LI�L2)I�fs*gth $fz�n�1��:� e� e��49�Vas�n�a �d -�D2. U(�>t�!c1�1}�>/;wx�/�3�c0 !�~ G19dot$ G.i�G�2�S�3.�4 �t>@���1��eo�: >"'F2%�u -16 M� ��5��i�!�"� E�!��n�D�  E.?)�lk��rmo��!� -.���� na�1G�8a��a/nS6W m���M�7.m�\u3� �j �� �u��I�or�M & ���;04 mm$^{\rm 2}n m rea. So,#-!�� &��X���)�by ua����~N�R&{"!�Z�) UJL 8?�IX . 3a2N =7!�Z�"KmE& �Bio$y qmE)Od����+� nAo l1am �I\� mm� ��iB� Y���# �1��� of 0.1 mmasu�J!h��A�1 rQu� �1 �Y",5p�)D��� 0.2 mmf�, �a� 詖�2�!IM�1��1�6�W� �Hd{�G1+i��0e� b�9 1�y�1!is 4.8%V. �good �IO �Ts�Lng2Hpm peavYnt 3a;�0��eU�wR�� ��c�me squF�Q����sUGɼG2,E��a�:�F'ePsf-Ac %]$���� 3E .!T�<n�at� ov]�� �4�+�*�}�-orafN�=q- �� �� id�"-9 �o�f��zea�QQs �>v,��EIlj~&� &w.F��-� 3bi:��C�b!R.� a 0.�p-���,���nR�I�6tm< J�ex��(�ha[$� ��u�� i&����!�a��B�A��8V�0 5��so�E�.�8�����AG2V\ �$ �R���t� E2�� tooe.&\a�����fi,%�vd�aqU6fl�� ��| �l��sؗ�envL3"� R� !x7��zis �=���  va��7�\.v� �>���. 8&. 3a/ n|.0ZL1":` !^�! ��. 5-���>bzCHos^2(\pi\,x/1.2mm)\A�s\:6mm)$!�. �-mrc$6H7.8H�8U Fݐ� n��)�7 .@!�mer� a gu�!� eyeFaa.�x wa*K3 tegyM&|#�  a[���2� L�`�Cr +2� 2M2�H��!5"]'�R6��t(�JobstacleR ��n�h�<&. Wu!Ca�_ '�� �' O�v! d� ��ur"e'� ��ݧre^� �� piJ�S;�4ce� is \lq\lq D(ed\rq\rq , �_�8���%Ws or�klyshkoBas-���o &�7!�-\&El����4i�� p(D2�_r�+g( ]in2�V ck@wng�s (L1=*g �dj!� ~d<-:���-I)j)F.�e^� q�6m$2f SL�'f������Ti�a29�Eo�Z.m� � (L2),A"�to L1,ad�+ T� E� !�F��Al5'%+:*J�.~\E�|vH"p" XG�_�E u�B�dX.�'ngm� �|aaerd1�3B�E��M�Bi"�9I{i 6� |(duced in th�is case as well. As in the first setup, we scannedLgratings rather tha 6� at 7B�lsoz� aA�gle^��is s)GΊ8cU�5aM�n�.0b 0:�If:� sb�0. a-) 1.2-1.6AM�Nta $\cos^2(\pi\,x/1.2mm)\times>T6mm)$ fit. b-) 0.8-0.9�c:b7.8H a�A�-�e]�. a.both �s.dasheY�@merely a guide to% eye.F�In co�P sione�performm��demonst��ona!-D� patterns in quantum images. Two s5 egie�c,re employed,� ^ one being�J$e transferh KerPangular spectrum fromF pump beam� spatial�corre�&s betwee��(twin photon�he�� �egy made�� an advanc��$ave pictur%d�?��- 5�!imi��D, remot!�plaX́s��� ���s. OurU�Lmay motivate interes�� applic�s!D noncontact measur��s�Hsmall mechanical deA =.� �9�appear� a varietyLLdifferent fields, wh!� these�could b%Tgreat� . ��$acknowledg�Ys}� authorA�Lank P.A.M. dos Santo�8fruitful discusA� s. T�� work��,supported byEE8Conselho Nacion%( Desenvolv�*to Cient\'{\i}fico e Tecnol\'og0(CNPq) throug��< {\it Instituto do Mil\^enio de Informa\c c\~ao Qu\^antica} �k@Programa2 N\'ucleos ExceN0cia} (PRONEX)-� A� ject��$B�Funda �{a}�TAmparo \`{a} Pesquisa�Estad�R �re� funda�e�Coorden: A��ei�oaA�Pesso)�0N\' \i vel Suŧc U}thebibli!wphy}{99}8ibitem[*]{ca} C�Yspo �I��. E-mail address: khoury@if.uff.br\\ \ J{mish!�HM. I. Kolobov, Rev.aR�Mod. Phys. {\bf 71} (5), 1539-1589 (1999). %T����behavio�Fa� lasse�light�<{monken} C.H. M, P SoA�Rib!�8, S. P\'adua, ��A �457} (4), 3123 �P8); W. A. T. Nogueira H . Walborn \'{a}YA�C. �; %2� Observ��!S � AntibunchAX of P��,.�xLett. \textbf{86}, 4009 (2001).=p�$} E.J.S. F�ca�.�R#60}%�0%!�YLjuliana} D.P CaetanoVs4J.T.C. Pardal,%2A.Z. KEg;)�%�Review A�T68}, art. n$^o$ 023805%32tr=  N. T `, U. Andersen, B. Buchler� K. Lam,!�Maitre,!�$A. Bachor,A] Fab]9)�E�88}� ), A�$No. 203601$02); %SurpA�ng��standard��limit opt�>/ %us2 multimodeq�A.�C�� HE�� Jour�J�ique IV �12��m� -154�Re� k q�^ noi�nd.�A���(shifts %in)s �LN. Grosse, W. P. Bow!��6�P9� Sci�%�30��63�940-943�AG%A�laser po�]�s} A$��ti, J�HermiAXA. U�,, E. Giacobii Schnitz*4 R. Michalzik,A�$J. EbelingWPoizatE�Grangc OA*sE�e��@24} (13), 893-895m�; %�pdistribu1�� �nsity-�of erE� -cav8 % surface-emit� semi&u<)3 F5)n 7� T.Cha! P!��(J. Opt. Soc�j Am B)16!01), 2140-2146J6�ofN�@s C. L. G. Alzar��� e Paula, Mnelli, R�$Horowicz, A"]H�Wrbosa,n��Q8�(189-11!ƭ�% Tc v��< Fourier analysi queezR gh�  di�)A�s]� e} K���ki,� Handbook!AM� Fring6 hn�}, (Els��$r, Amsterd�L@1993); I. Amidro�d R.D.a$sch; . Am. AE�15�g10�g�)0A. O. Hugueni��Coutinh� A e"�.V �e=�!F opol� � fect�!\'e f�s� spiral z� plates�Y��\�A 2�(883-18�20�X�-xray} P�o0ezirganyan, V�EAsf   orig�f�.o.Dn�e X-ray � s6� in 2-crys*a�rferome�2 Kril' fiyaiA29� 882-887a>84!�(T. Ahilea T��(Zolotoyabko��HartwigeO�`E. Prieu�G(%High-resol�{x�w rac���h:&s��el=Lon %microscopy stud�(of Si-based�u�-�a ba)@d amorphous layer!� Appl2� 8�B�A 6076-6082!A� � ��J. H\" �%�orJAF�UFon-�.�top!yphe�bi-�s Acta C!�."� a413-42 �6 tem}�lMadhuk��Q. XieeCh�%!ZA� n  % Na�of!/�InA�ree-d5}al isl?"YM.E< %on GaAs(d 00) .TL� e�6!Z2( 2727-272 4)!ZJ.�OZuo� Q. Li, � nost-� EvQ>Dua� Clu�wwth: Ag!oH-T�na& Si(111) SɼsFX �85� � e 25550222e diag�ics} IrvA�P��ma�:壁b-!G$ thin film� ces� �N Acad�P P} , New Y�� 62�odonto}?Z� ng%�4S. Weiner, %St!��9?&Jin hum�eeth e ���  of Biomhs�) bf 3H 2��35-141�72�si} %N"�, 1 C-eesS1�temperE�-m&��prS  %a[��.�ry, Sw Zaidi��TBrueck, Mc. Neil Jr., Akof Vac�  \&hn�y B �10M�66-16I��  %Real-[� e-pr1� te�!)�� �Z��V� �G.� Donohoe�H.b� . EngineeeE�33�aj3465-347)�42�cript��fia} %I� encryu �M�e!u*g by comput�0al %algorithm�%PApolinar Mu\~noz-Rodr�guez �XRam\'on 6-Vera, � CommC23�295-3` 6�� 2} %Manip`of"� � prop� e��[a�V 2<D�� ,q "���T.�.� ;Ml 2%�D51} (6-7), 983-990�b4� \^klyshko}�yB. Pitt�\D.*$Strekalov, N. K /�H. Rub* A -,ergienko, Ye+ Shih2b 3}, 2804e�6��o>U  docu�}��\�@[preprint,amsmath�symb]{revtex4} \usepackage{psfig} !:N$} \title{A!�ced�o calc%�Xmany-p� cle Bohm5�poten� .} \�D{L.Delle Site} \e�4{dellsite@mpip nz.mpg.de:ffiliE�,{Max-Planck-#e�XPolymer Research\\ Acke�(nweg 10, D �Y1� nz Gy� �ab�ct}�a rec�!� Kohout (M ���t.J.Q�.Chem. \-D7}, 12 2002}) rai% � ,important qu~!howxmake a�ct� �ohm'sDroach� defi� a Jp�t�,�4tak!�0into account �'�ults, we!�pos� gene� (self-consis!� iterati���Q s�EisG(blem. \\ \\i�4Key-words}: \\ �U.,IT"| systems, Ef��6 equED:��.iO9�\!iE�?se {Int�ion} �� E�)������ term��Uleu traJor��0(\cite{bohm1,23,durr 4,hol� A4has beI stil ,EntinuT mQ�k4dispute, oftenap philosoph� �above � �� �a5�2 �(4,belousek1 ,2,matzkin}) "erE�A���a7a� 5J . At �Dcrete level such aI�  1a d ase7 tool!� u}�A� and A�erp*ng sevE�E&sse%�. e2�u mole��0r physics to�sma, +sc%�cth�to siND wires I luig� o, h`a,ham,creon,longo,nerukh,�ren},\n� a few. R��ly �� ^k��} v� of��th!�$more rigorAr?!N��2�#s, )�b"n� Z�A�explicit�#P�6i�`quiAB!1�A�%��vicult!~�6 }����� ��'$ buil!�$ reasonabl�i�. gues# �6� y�(and, follow�� is choice�!d��op�i ive b%G)Nam�l (numer��)22of��. W triA�ur "A spinl�iZ,�� any �'!c�&isti�possibil` to extend'!c�to 2sm�1�:�� !o> &)#de* bf!� mustYg} that>a�naB �isw is�^y� ' 34widely��9/ ('in(approxi�p�T� ) c�"ct��b!gM5y �edJits tru%�m�6<A�2< method�do so.� bf IV ��our�})pr�%�� a-�iR efer!`.�-�Y�acha�=as HartX$Fock or DenF� al(oryA�r�)rmU � i� body��inժicMp�"�".L A brief"k &� �` :` y!!"=a�assumU%S2�}*�eso# dynam�of��fun"� varI� (hidde]��!C ͑k �E^$be summari$by quo�B� m al l  '/#t!��% step!x�v�C�C6� in a� u� wa%�&ssoci�$]% each5� a�? !4ng preciselyl ExA�� t ly!y� valu� posie�-mo�um}''� � 1}. Wi��9�,�$MW!�describx$its6�$\psi(�$x}_{1}..., N},t)$�the�� M�s $64 i}$;.se �& f]enit� are gover�+resf'ively!� Schr\"{o}| er � �% } i\hbar\�{\�al�} t}= H� <U$H$��� ,!5�$Hamiltonia�T1V,�b�%M�al"G:F� �d}{dt}='= v}_{i()B�F #= G�}{m6}Im psi^{*}\Afa_{Z !�i}}"! (psi}$�*��$ lead�'a�' -New)9�e�E�� becomes� +aF!?M�'! of $� \righta�.0I+ nDb��n��� thI=um.:��ovided -�fr(��Ep�)ormr m� o��c� emerg��)�N .NIn�=e�ik� ach �g...implA�h %E�clM+ves� �x8�ce-Li� ��P+deriv�6�� =X"� , $Vq�)$, but R}'8 s<on"D sU5%Hal\...FzGiv�*$N*N � ic6ewhg !��� writlas-�� R�x=\chi �e^{i� S�n�}PR} \in \Re^{3N}$, sub)�aiY�, -depend�:oȗ�n ��ng� �#ary%�, o�� the veloc i2)f�0�a� v}m� �}{2m}�#!i� a�-  }{R^{2}}= 5 1}{m  S��$nd $\rho=|=|-%K $� M�u�sb��V�?� a�Ra+ �cdot( � )=0 �1AsB��^&m S2o+��[ r2]�%F=-\left[mE5+QE,� �].�genmoF��m$!�!�mas�� %cleyz[, u�, characterizA=>d  (e.g.q5sVca�e3/fa ons), $ � k=-)�S5 �\sqrt{!�}}{. $ {���!�$ @ =\su�e=1}^{NMa�u$� su� � grad�,5.s. :{ &�"i�Y'�RaIo �us J[ �$e{��� 2� phase��orb�B<n::8Z62>� ""��*!4 (-QH=�pr�"� 9�� ree d�sA�uinO �2"�/, � 6i��ame �e r�0a���� d� ,A,.R'rhQX=N\int_{\Omega^{(N-1)}}�� v4, r_{2},r_{3t $...r_{N}})�� d�J{$}} 3}}- N}}}q�dr>� ($ �$ dom�5of �_ MJm�in��space)a J i�492xE�R��!c��e�2+ }{N}��s(�{r})}; ! r.�}��wfB�I2.�'�e�Eq.\ref6s>.� t� "� ���'sJ� |3to in�A�8in_"inguish�:<�k ��  a se1i�� �cs mov� � n asg.1��? ific mu� � i s are neg�$ed7s� � s suffiY t��� onlya � , embedd�� B��ted' lq�s`�0rmau.� {!� wholy .W� �' $S(I'� },aE..aL=s.!)+"M}})$. RWbeWip@ ,��?e�X*don! wwe�l�5I�B��}, �"�c"�0! �A|3�6aq�� o��b!�:�}%� , i a�%6, �"� s4Qbe�ed�8�nod� �2�X stea�.�'�^*^�j g8 in2�w� ���})$ KIBq� dr} sugge��4unlik:to~aP{$ � � $ains zeros�least����QasI32�ـ �n! i=st:A5�b�6�Q�a�an 1C"�Np�!%�ani7r ,� re)d&e2� �M�}� r'!L(z !Z'}$��c*�rA W$N-1$y�� a1 �� �- when!( focu�ta%� �#q�� r}$)N�psiF�� F�+q�� p/ r})�  \beta J '|r}zD�ccFc$2_$Q F�wo* $B{3�S. �,.2� o�coord( %�!RE�gIs satisf�&�nozk mR�*��=V� r}=1|� 1B�andJ� 6]>�.a$'}=1; \forg��9�tB�  By(�(�or � , he"� zm�B� y�s .i$�a�a!tT.�_C:�3uR+ $Q_0d}M�}| �'})2� � 99� I�}"� ,.�  >iE=is�gbaMa� BT:)�to fin *|?H for}Nś%�� we w�!(circumvent !�lem���)!mitR =�K%$&"2���reca��W&:'!�Q\���ba�ly�8�@, g~ *$�,�IX is *��� (or alrB�(lye�Paes���(�ng) 2�)� ch�1du{#bA ���#�S"U=�!g �1..s"� t&i ;!�L*[�u.�$�[� th | �]A $M=1oN%�Y � � triv( B,)2A�unN!wo��� etc.. F�0EiDe%|� %W5� fp$J se rO�w be c�G 6�.�2 u)� !�2�JnI� B� $N� |��� � = 2�11 �2=aD i.e.%�Qy� �zofe;B:T+�:A�jecaM��' (:�&)b��FADl,�M]�ro~!as JJ N=jr�rɴ)r�2= F�M^��M��M+*:� d� � R��J:�A5 BP]Z ~� ^�9 !� �M\ �:�M}}}=1�,�T��gAY�F  x ���a��#q � �r(& .��!����� J�*Di���1��0ae�% {j�}.})*�.�mEEj)}&� !1_BIn%% .�"{ of"�cf}, JF,��be}=:Jn u���� �}B��!(asf easi�"erified)�� s $.�M|>i e�da�� :� fN ��h 2}'*!�3%�%w}��k� of%`"� �alread2�+by Hu�# ;-h }�$ajc�q�+.�)�� n�6l.�GA�a&� a&(�  #� �0k �hb(eof��)0.R$E�Y���i�.�+ ed swN roo��&�!:x&�+ .� �.�I&2� &, �zJD �| $M6�� �"*%��7��&#�#�i*6N�>A�$}1Qp , ($2b .&I�I�$), di2�"N�of�" :f��eH$)�8`l� �5e�"<uE=V�"&�"*� non-com� v�U�|'>iORs� !xY *o�in"� � �m�?gMce�0ca9;elli}y;Cr �>iB4}� � n#&I(�6�.tD1�Mc&, I$�/s�L� d]+���l�Mag2:#A8-SmeN �exampBZ Y�;.LM�G Q��S tM�a� M � M.1��/influ�'��m*y; vVC2�%e�R�� P hold!�! sM�,s,"�$ si��w�v�+P-edG � �B�,:*Q-!y� )N�rul]YNprU�E� Ref.��]7��rFa L@y�4u@P&�-of B� aucp��M�t��271a')�� .�V�/f, . O.'"�!c9"� 2� via �<}x � �)Tb8af�/("��7.*�.��a2#$ :J�#�B/F�phi*�MK"�_{i=1phi>|  "J! �&m)![ac��.�us�9!p> A�Eed~� �.� 2���F�. CdM� larg�#&�+ac�m$5&s the `-/ ,(.y,�ho�OM �0sOV;�.1 ee�Qb6>;�3 �"�6gBome�\Di$4So farK %H�,�E�r.�!s;y g�?a�-2c"�TU� $Q �,h/��, S�rbitals��R Vpr�- �s (y%plane-�a9C )�>Q! idea�an-;�2coupl�Q M*w6��! sert42w/�as >&alO3I�\of*��ůu�pjv}�+�� s�#�? i��!�*`!��AG: )"�!� repe�ZF&<"h�a.�eA*in��f"�$hY��n� .���", ��� f�A�t���o*o&M4a�o" (2} "� N~&'� �K� r&5'9 r�.�(�(�!-�d�rEeqBb�$ Q2p"��w%cyi�eriY�"�0�#�Q.����,5.�aNv�ZuseUthuV6�< aX1!� Z?-fi>VM���be��^n��8] fo��(d hypothesiLW�Wt�Qto�ice�� �(_�i}-�:t)�q/r!��=�$ax ����t%Q��*,�Vaٵ�e$ � O%s uponNz� � !�)E�� "f !�66 a!�t^�)!_-no%#% U7:$/�5 �e8=aMZL""�:r�to�\P/�� aNdR&�*A�11Q',2}.�m�&wi�%�- wu( w}\r�0&/, �ByI&�##,.�#w�"u+.1Bn "6�tx_��.Q E �& vg5�e �A{S � �D$�4Q of B�U� e>">F+.F0&-sr>xat>1�#q+ �''�''&S-O.-Y5j=��Ri57in�%!o 2[one. us� ��~aA�aa� � �&{+ed�*  $VuB justH8 u��Jt �Xm  to��DQ1g�e3we 4e�J�*�;. W!mi�2hnJa� ) "Y�g� ����7 {a�; �n GzH thei�a'B,&as= Eey� �t�2�I{ 8�#h�IB E%=ESat �!�F �� eJ��a�.�=})+ �,F)M}}�Yla�b plitBM ��B;!K�3r,Y)* (� P�iula��ZIR ifC8Q��%%>%2DNT��:5.�H��.�1�t)+��M}�:�W �/ :ulBo BU � �Q$I?&5"w perZS��ng��^?Aa��!oine�Ab ed�)0� �A�Y�2 s:\\"� ��a $3M2B � �@D�ak^J�F� y![aRho "�MU sLA2&$"c 9  +n=*���ach�'alQ�� *��q#�-osez-n "�+R 6��G�+pf,�^&�9�m��"�$!�6�b� c ��dcu"_ v�5"� �;a����*�3� � :!$�60!aYyIuA~%�cleM&�6m6$. *� �3Q�� 1�' a(�u����*��.� �!Fis��IBT�^b�-o�l�+y (2Q�) !�i�B& i]&X� direc_t9�@M�2bY�Ip�&)�" 6x ;*o"�,s % �'8>we�!@�09["H7J.i� �g�  postu�"�.bnM� s �&.�p�n��!�umJ �Lr�V{ll} {�2 1)}[  J ��t"�rQ���q�*�)>�7�kB�v \\ �22��'&<zB�-m���2µ�3)S'�H4�H H5�H H6�H�0 .\\�>�E!*I�M: MN�^ M"� M ���if"�ysFC.I`$n*�'�V+�  &,� He3U56wO�mO�%?.�"� �ed*�+STC.&r�Of^} �'b�t�iart&�>bv��Q=Q_{0i�J�" vi�M�W&}a�a nB�a;Nn�G-�����(1)c=f�qz7%��VxW&�P�D 6non �� � �:��iPC!Yj�=~ an ''�� '' �U�.=S�)FS$sO�~�  $)BEm "�?Q բ �(2!@!rk.1Ao a new �# F,01 �Bh= i�و���.�� Ő+6f 5s <i�OF�)�5in �� ��>�3�AEFi#!x*� IG)%�*�, 6 3�="�0! N!�25&.��)��,�ed until� conv#C�)| meets�KP+cr�K_ (acceptance.^W8� .w @cm8sen�at� ���kgVn� 3R �1:s@� ADt�5� A�aN or�-!y2�"�[�go!�.Xk� n�q� s il�\�/�8�6�*3� M=4ERr�8W. Fin+&�0� W&&���" �m�178m�KR%#��sLDPeI W *s 2� 2�s"�, }out (�d).&Ou1�,�!� �"Y1�Ds�\ghtforwTgZ �Ru���^�&�,eYzNr'F�/�k r}=(x,y,z.I�� �a�N h2mi� ( \%[al'(2q}xU)+ �By�BBz.B\�=- �@C>� fz A�!�B�a�9E�*T�"&"%q��ozQJ�� 2k=fѩr_e@yI+G�!>��t"9sssB�$ =Nw�"DJ�.�aIx}g)$+�#7y�GM�=�>*}#q�&�. 2�C$SE2f�H"�=Z��a=����@ �� e�i� &��J�8�cw*�>!�A�5d |� glob0o( Ef���3 fa�QY,�_ ). O3 hAr�( y&� T"9� ormid�1@>!& q[�, taskr4n�a2� 4 � uyk&aSW0toA3�P�0t �~m! UK-A3_6�$.F�.�2�RaRdBY��IMy"{&�; �A�� ably5�i�/�8&^"{�<}. ���@}�/)$� must} be �4ich+pSpe"Z5AA!2�3i@B.�4�e��a\eq('M'E3,X��_'VF�A;�i3�# F�a K%5.V�K� hI��%2.� (see�fendix�aD+-("�*to [2�!!�b�&eR4MJ�X2�=�1=-��.7>�any p�6ex�u)!> �8@5� l7y�ʁ� es u�6>]G&� u��si and��U�^ J/weM����|6�a~���}�T]�! N~&8 �f>fP�T���%n} !H�Q0 �n�!Y����1 to�a��!vi�2�1��+p Qf)*� J� ���� $S$ i1 9�;  N�_{1tot*� >��1}{M!5(}PE�T�2�>m�  $s ;�b!m�v}ml=-"xK *c@E�}��� $�N �+%k$i$A7%��U��me����8-�!Co-�$S$, �+��X3!��idQ(m QpCarg{g ��*_S�]Zin" . YNT�j� �majorwe'!O.>in&(2B[lHf�J�:oNU* +asy *0՝A|� ��'�!9�� eik�|�$�isotrop�K edia&SR�b�'ary�#V_%N��]  as�~ed � :�*���`�� �'�:�e_ar�$�8 �(ra����-. � �� �ul�D� goe�eyonu (B��Jor=s&�^|6ss�,]c]�\�s dscngq��kP ��2��  A�"k_.,m� a �-�Z eik1,eik23456789}_��rein)%�=v!lf�Jsweep�&�l�&/2eik6}�Y5rob9_.��y"MQal"�Y-J�w"�,]s�2ei6� "� ext�l�G+"J� co{mer\  ;E*�H+J�se�>=� , al0:��8�non.kS-�|. p"���ddap���~&&3-%��_W ��"T : ja:�a��8*�1Ca5%s}�*A�os�LgeZj&&`v6�"�#��\Bef "�fa�!leveGy�aUg"�g�ga �A�� n"��8(aB5*5\-!iapplyA�5:AR5!G&�4�p�1 =� /)"lc o$$sm��N�ta�Z'Z�.e ob3G;^!�e@�5"��&^B����yan�e3�aU���Nvalid�Z19j]&�un "-$@��g)1�2�� �"" al&{�Y �Yb.{n^�5y s� nO��_*�6.��9Sg"!J�!�m/^!��R:�L*0+��#�zu�y Xa U�6�.| gia1bhwon a &K&P ��Q�. F]aY;-jd �6�E�6�ea�-�~�T��(1 ).�I ��7en-�q� text {E��*&�9Ѳ:� sakurai})�F� X$yAH!��  &�!&�i �u� :  >�]&�Tly,6�i؉�i~avail�#E��(�4$2,3$)!%�oV���y�y�6 2effort;�6o62U���F��b�6snbO�*iT2k�ls�_s*B%��T.��l�a!(o%oma��{ sph h�T ic. O� �a?�;)DtG� $f(x�,x_{j},y y z z )=X.' )+Y(* )+Z(.-$ or �Y6X:W)�hh��N�ryl�6 (_�Qry %�� e�n�q-6 FBeWd�1��s � UpIL�Ag2a@2��,m�Q z/M��#���f�A)��=sto� ��&~]�S\r a�9�=rot3�yI&d�t�oP���n4 �6�:*!"g �cur!Cl�(nd �� ly) Ì� pD��p �iK� d�4Ai���� c �~ r �or �YEyX5Korea[ven�]�n��/!��Q�}�l��` s �$�is o/y B( }&�t� r &�@e�}�9ach!x�{Z��o�h��j-V(e�u;.o�$�p��q%�Q�u um M&A{"�s��!U�Y,�0ect�^�can�/VX�|�Ha:]jFT�; reveal�Z�G issu�<ywa2C ��� m�dee.,"?�QgVJA…IE�w�R�!y E��2lse�. "�=Ac�*'�I "p.3k Dr.Dr,O�f.T.Vilg�ndE.C׍l��a}A���Pe��Bnu!Fpd d help]8� i�pD}ALɆc�cle�Ko �7�.�L�?/X�!'}rCL 6sÍ�"� ���}e�nX?�[�5:�!A�"ha�.a]"1�_�JOf#Ug.+h  })+l '}"?:rrpB�%� $ Gs6W',�FE2$R�unA.g($it&"e�5� (�"2)���o!ai�T�D<9>� 1�ߡYQ �� !`�:�3� :�!th&�Lm!�*-�}�\-�_&#-!v= 0 [)cI!.�]:���1ans�qj�$'l�&�!:v�@le�|l"�F>[w�CJ�u�'"�F'>QQ})]J�E{+W�3 ZA�'|56VM Beca�xA;a��F%�8�M}MRf6��$ y i�% �-c $ by6f:=Etq8fuJ:Zm�cGR $q�'�_AD1wc eX� $�$!H})$��it*�>�%X*�$�_%� \to V)5�Drj3;D�ee2MT & most[$ ��5g� ne�'ar�La��y �� �.�k�� � (��ps)�� ` ���z��� c5 $g$)�6 lso ��"� [Q$g_{fin2*�*6%<}{2+$ $hJBw&Q�L'�<2�mC.d �H� � 2}�%"�.� b�F�}all&/ qf.�sߐ�2B��{9}&0��p D.' ,�� .Rev�t߅166׀52g9b�72v78��F73f79} 458n3.n`}$} K.Berndl�DayvƁD\"{u}ri�GlodsteÁDN.Zangh\'{i}, Nuov͕�o B� 1��737p95)�T�4��u$B.J.Hiley.���3Un_L Uni^�: An Ont� I�M� A� T^|$}. Routleg7$and$ Kegan/�, Lond���.9�g~ P.R.Ht~�6bt5�4on}. Cambridge� ity :�,>oA& 4a} 9, R@ llag�a�0O.J.E.Maroneyّ Xiv:$-ph/001002��0.�]51nI5lY�.L&�55} 251��85.KA)E� . GolI^2� "�o .}� Meta| s---1W� j*tJ��Abner$�Xmony, Volume One , edi� ,by R.S.CohenA����e!?J. Stw$l, Boston _ e P �%���D193, 25-38 (Kluwer%�7� 5~951203bTQ�!,3}�TeufelH�qbD�B.��6} 121i[7>�,4} V. Allori�.�. � cee~ D0Biannual IQSA���, CNa, Ita8MdL 31 - April 5, 2001.5(0112008 v1..�el �A�W.B ,,�nd.Ph"�� 30} ��6� 2E{�A5:�2C}� A.Ma��, Eur.J.(23} 285 (20Z�5�l|�} .��CoA�2?��RB*a>C�ica1�313�� �2ham} W��h΋ I.P.�u, [�K.�3U�K19��=�4�} C.L,, J.SarfattiZK 297} 263 L8.r'"oA�L��>� 9V�>��AN��E�J.H.F2`ri%�V�32} 14)�2��� L.Shi��H Akis��K.Fer�z9(mQ274} 7JQ� &�In>ІK 87e� F=hu��} G.H ,ŵ.6�E9} 237E 1975.f*� G.CafR3b.�, 6�Y73 B}[ (1982��(} I.Hitoshi� c.Ama'h.S̔C100} 24�s82s(} Y.H.R.Tsay� CompI� >78} 1-b2� eik3�Gudyna`�@onl.Anal.Mod.Cont D6} 57%_1. eik4a�D.G�n,W"l ����3I�>�5��O.Popovy7,I.A.Yehorche�� Ukr U Jour �53!� 841 A� 1);A�K員55*X�2, L.T.�gW�Os���LH.K.Zhao, SIAM J.Num)%Q$ 41}, 67�)>�7a�Bryso�Da�yM��.Ìp O 2͑76)_>M8vM6� �133�>L9VL� Hf�u— -dis�h�ral-upwnB sche�y� -d HJ *} SCCM RES,���"F ity,!-02-09��2Lw?��'v$ubtion=�E J.J.SR,)� Fu Taun �Modern"& Ma\} Addison-Wesley Pub.Co.a�93��t:)��$ \newpage(��} \!e�_wfig =�*��%��V :&�?e y� oriaS &�5io,D ;�'j;�;�+t��. �` STEP[��pr "tv6�6| !3��9�..(� <#�f$Q�6,�Z��+�(.s�;K<[(.�9ij}$ (�8 )�/f"��d� n:tUg�U���. $i$ c�U6�r numb�a.Q��� � , $i=0abr+ondr.j�ing (�:Q) 6 $^($j�7d�D0e��(ABiR (!B�vH�7aIOE�E�d|��'��&��(style[aps,gs�x,e�col]{��}E�and\be{�AeqnW>6!ee{}Zba@R=a =def\r{\ڛlacl�64}  T{{\rm Tr� def\cH{{\� HS SP PI IJ JF FU UE EO OD DW WV VA Aopenone{��� %\*2�1���!U \ti3�Pm��G�u�XtQjmplet /or"[������L{M\'ario Ziman$^{1,2\\� PleschPVladim\'\i r Bu\v zek4 T_�{ $^1$R'� C�!�.�b�� , Slovak &�.8|s, D\'ubravsk\'a cesta 9, 845 11�tislavãF8ia\\ $^2$FacultNm(cs, Masaryk*\ , Botanicc468a, 602 00 BrٟCzech� �� }.ڏ-�a"בF�hzeR� �:�#�% bit (3 nel (map)L�j��ml)Ł�me�[d%��t��t� eve�.�W. T�� R[!�0 situ%qWn]p#&m�F$in&h"p�&Ѽ�a�` �wz�c��8x]5 eic!� ��(6�)#1�ly fail�Wi���J n un8s!-�*��map��notc)a!ly�� itiv8W 5nbreݫiz%5�cń%�6�4d��&(%ly�w[ �es (a.�Rs�qCXjAs�.&.>:!'�)pec U�<x2we 9�%E�3A_"z�� ��;�!�y/��ma>�(!��2> ]�(fPY��S� law- �.L%n$)�un�$al NOT gat�0�ty?P % %\pacs{{03.65.-w}{�5"�%} \!%�* 7.Hk*��u:��} F05.Wj}{St��6�,�tomG�k� l} % enR8PACS codes %} % � %q ���s� %�.&�In{D��e:e� <\rel��5#i [b�Wɓaj& 2J#��u#A.�um� �j���./��CQbm�s�Ds.� �h�# ,�q$#*v�q���Ame�aof�4�(an ac�o�� e ab�@�#�.o�� �b��� no0orBKf!�}au10�E� +@(���t遡�ha�#e�K�>� �1%��z"�9c#:q� input.�5�B2 m�9:�*��%�!p1. I"&i�9�����-8��M�#  �"  ways:� (1)}�I8��o�'!�a� �C�a�P6 bi�Gt�z Cb dari�  2,jezek,h��l}.(pZ>����bit��� B]%�ޥI� N�A�1wh�N��s�z�U,gedZev�3sZ.~'gVaEzn:V ). B|�A*A:+ Q5��!-�F�outA?�#� nel |�arbA-��9 2QiA��mQ�/~�#&�YCKe)Ee�e3�!HE-->F. coll�cofADlF^&�(t�V �(9.�. �vY�& evha�t��e)�2�poyatos,Chuang1997,Buzek1998,nielsen}. F�r+,�� � "4�=+9he�#!�.v (t has ��9�D �!U��ed)��6�!��XF��z �-��va�>V�bL�6toi�E?� ]8.� . R�!o�� wD>�:� s mi=�see��b�2e"ׁ�B�)ep͉� �Y"Eqan] <I�?d�Kverthe�1� r�A�t�7��le�^m���B' ach ?&�)�7(R util� H?,0�%� s. S) �),�(!�!cg3teM/}�B0�!a�F high fideԔ(���fAV[ "&-�:a ECI�.f�V�Ya��>� � ). S� taneously%f.�>u��%'te>�r�19�!w"pq�ct. Buo ���7t obsta�%�8o��,!#a@``"�6''9�� 9�E["�=��g�,c����d%eg�79�c���.)k�� �af�*e�Eq6d� -��-s� K9� �\�!�meto0E�C2�\Z pa�*w�$ll�� rate�2"�� �scenario�� J ach�9"�0f�E5j�� �!��U��a� ��$\cE$ "M � �Ձ��3Ͳ%C?6j`��9�,�e.e. a��M.a>ni�,���wla{1 roler '},}.�a~�h aE���� "�3� � n* �z���]+�"Mi)!x�C6v-U 6F  0�q&re\�\-�[\-�� �s.Ϡ- V�N�*t.��%s $d^2_&H/$d�)�dh#68!_ Hilb�gs�l� �  i}!.rIn�0BHu�@BQ- ��ng� a�2 !v we ne2�(d^2-1`d�Ga @%�Adqi�%�.nK12a�l�a3��-�u=0i� zko���<.b�!I>��*�e.���Aakba��v�q%l&����� � -�*' s �0]F͡#7"�> �!�A2^hew%mn h��  "ɮD- est�F�1�v �U�1�+a�o �nm�2�c��@ C-^�e� �(.����B� �and/ora|a�0 �=�N>�O��S�mapGBO"�(A��� l<3� 9*�yU w� lich��0�ka r�I- � handI�11&,(. Moreover,aA_!��c!�!���2 U �,oUbe� Va+\5 5 n�4g �6}m}AQdetai�Fso � F7�'*f!��e�wv;��'�aD9N0s�< S 2lbZ�lpS1b�ti�q�Zŷ�3�iG3G�us!���� � �h J\e�s (�Q�� �s 4A� 5E< devo�99:yN >~�qAExm�ōZ���d1� � 6)[��l�>�M6,7�e��b�S.\)S=��>Fl7t F-3sMR@��w�&'%�!�͚wM@!JcF�I��;ҵ����� A���M�+f Bloch�9e� z allN��m�+al 2�endowedU2a sca����p �"�0$(A|B)=\T A BRaon %2.MI�orZ6cea ��biɚo3aJa/�* orthogE�2��Pauli�Jigma$�=ric^��s $\{�,\#_x y z\}\�v .. vec{ 3}\}$,.�3qu�У!�� � �!xQ s=, ,E?~y �B��I� E�  sub-^�M unit ce. ��p= 5b1-_0=1$� o  mڑr�-!`$)$-%e��J�A�e�~ ����c"�JM�z $\var���/1<(�+%r}�~=��Q�Jl���%l� mx�0"2z, �o�x$|n r}|\le 1$�8� �b 3O!.�J%���s�~ ��VlVa�� n $. A +>�%�'�!*T ֩(�u�m�$ X"�W. >Fro;SqT8�"i� $\T)�_k 0l=2\delta_{kl�o��GaconeÄ� :~$�W.J��!�� �_k=\T1"=�_k$Ae7 t(k� �P� vHvU�J� (.0 ) $ �J $E�i��  6~a�: :G-.�do!�to��z  � tVJx Q�L�s��V� �9not�at�h s��Re+�^ �vl Q�9�F�x;����c� e'�8�ϧw63a&Q !! �e��(< 5Z= 8r�fis? U� �ieFvd��� a�4false�1��F.6a�� Z BX I�>� R>�m h_9q �e:�a=6J�t��l a�ō�\1� mr��-oB}�Ayt� a length]CMd ity��� .�!�& As�cA�e �M!An� . �1jc56�!���'EER� clos!�G ZAV ed''9> F%2�_iA�� )ɰ��c$ :!�%�0~UW! � 6�>��T�6� >�'�> ltipQ*Mq&ק>^ by ��KtE$k�̈�=k�Ur 7�5s-'f �R��6�%�Җ<st{�!!�dmixt!J�``whit�1�2�!Q $����$ [� :�;E).�i!��8ec{0}=(0,0,0)$]Q4��f$2�isEQ.#�"�6�w< ͝_c = k +(1-k)J� = &�1�F�\, . \ee��E ���add�o?Rɦly rando5 d� �1��@v�,(``clicks'')1 outUs� %%of16m����#�V>� ��'�ogu bntu�A,A-\-u>f��LM>a�4:k�f".f"*g"Jiv�f>fj-��!�*��&�mai�Ud�8o 3-.,M.B.Ruskai e��Or}.ˍ ��W@�P��* �� � . An.�Q]"' !�A��b�taŽ�Fnyin��n ��A�>�2�r}\to��$^\prime= T  t�)� $T� �0al 3x3 matrixG��t�Xa� nsG�7w�$�i� $m guaranteE !h�� .��FcA�g RC!� "! �he3�,#.�c5^ ��[ {A�a �su��vex:afJys��)�% &H.&^� @u �M�G�w12. U@ qB ��ny �!h["e�A)�"[�8 �%���%4o* \cE=' (��v-({cccc} 1 & E0} \\  t} & Tl'�o �c�Y, \ \ {�-and}\ 5|�d>g } 1\$ ec{r�.BU��a�co"_���M�E4�VbyE�I� X =\T(\s� k\cE[ l]�hE��_{k(l)} T�� $ tc�^e��T":g}�o-X~Zu�O  d�t�j}q�$T=R_UDR_V$� R_U,�*�ro)��$d $D=%�P�}\'/ mbda_1,\l 2 3\q�-� ��$2k$��!p6�%�$T$. EBm -"al J� �$ (�A�Y(group S0(3)�1ed|s��7r�I>Q�*:TU(2)) �mY\ $U^ U^\dag.�'A:% (R_UE�� I>*� m (tp y u�� �X2 lessY3}]famil���m�``5���,'' $\Phi_\cE��p?&AJ�A�il]=U)[V�  V]�MZ $U,VI�1^�����"��!4�L", v|� I,a�� �*�((�B���� ity)�a�%(refP%k AC�Z���.%��_e (CP)�if >/�CP��&�6("�.d# M�B�[$D �S�|%mE���6�\tau}a�EG�l�� �6�IJ1�! .� iA%GT��s $r_j"Er_j��q�j+� _j$.�� ��{4\in6��wi��81� fig17 \.7n��E�l�c7�gd��� aY�5M�"����R .� ��R �A�_{+522 3=-1B96W�"% un��iz3S�.� -��6�.(deA|� �.�7)Q)m�a~%\��werner} �,%A��m>,m�2(� N� -E��d %(Pin�^Iw�6ectd �"7_��zH1$&�4 �t��� I$2Id)"�t kock|4�I)*�5 �9�� B bV )}^6m2J" :9+� 1�``i6on''of �a*�2An�g�Gs M]I0Q l\G7my���� e CP.ʼn �W trahedronI f�!=ry:�kA v�ces (�\a�ansW�4&�AS;&iKun&�uF a6ɵA�:P)ŗ�b�cF&~I*r�a��"�+�ke�.a U-NOcre�n��`)@B@��S} OX�2�4-1/3$��9%t l_cp> Uj�yaA� ��ypeA7JFE7�aTs � �}>��I�AZ ��~tuj��� �{!.�/ >�(��e2. I����"��< vanish��0t}=�\� 0�[#�� g*�\!�'is qu'*�Ii��5&��*�>��"MsN� kI-Wth�'6WV" e i� l�i'%!�ubeK&Ct�r@� �jQ.�ɰ(Nh��valid�� ?*R��Min{ᅡV |� 1\pm 2�|.3| �i ie?�UI�f(t��2�^ ��!����i�b���E�r�T.��;N  <\Fig�uLe�)�#�ul� �"�� 1L"dA��) �lN�8i�*� A�6��   "4U�h�8.�ion: I.�&*��%��i�*&�%e�| ' x&e �, D&e�:.! $���#t��pr:�5�/.J]�AD"�,�Y�!"���iX�1�I}���+��� abse>of�.�6z"e*!q �!�."�/-�e�w ) >�a�`we-1(ed ``averag� 'q^�o~a�&*ij<�� FD�}l*�G?�,h*��d-B�*q0ecaP ��!(� cA aOq�."/o�'*U" into�d.���$\cA[�].�!�� �.� go�5�(A7s:�4� ;_{\pm}d&� (T,�,^tqp%�T�!TfE?%�ec69N���A/�ais a/�ll�F&�1?.�(\cE_+ +-�W���p-� >�all� 1)91���. A�5�sa�cB�0$s (upS F� )!��%���ver�#�,aZ.4*#�T�6�0 �*�"[.e0$�/& "ETK/$Aiq2i�2$%� .�!TN�%.%tc��Hi!��-2oL&em.� �q )��� e���:&�%r �m.�/,+%6�7* "ePl� &�7��ss[ �jp25%�'_![ 6��8� e.*�|j�T~h\�IL� Jl=A�Z�2e"E!�!K E_c$�*W d1=�$? v!3!o���`likR!~��*u ion,�[nVm��E���("�ed)� G�`�U��# . W�oALs �ap�Z&��nR by�� &#�5�lKi�ykA�Xp&ZT�*+7a'�,*�!�=a�cA&ga{J[k�� & k]a*U.�#�|9d� ))&� a ``�mat�adw8`���~er� .2��]- Ea��F0&"%�A�� D\inz (��ical)� �~ $"D!!�adD:-z��nِ�ar��aU,�a��map. T� `,s e��I7t $k=0Ly(� �Dm�&ly ign"1�m1;� {he ``U�''u!3MJHT� oK&G}s�n�P��hpM��ahe:$st�" )!k ������meOdkRP�$U�� ��oA�a�*A ls38ita�7��!worst''ID�e� a=��is^�,i 6k"�.Bp0��"��%2%�%��e$ua-�a�qMas �\� &�mA2�щau#(�`( � cp})i~��!�$k=WM}z��j& ��ri)ax!�!���[ � �L ��/F>�+�0*�-�� �<h!� st (b)R�W �11$Za ��5 S:)ma�P64se�!�W��M�!�-�( IM"s\lyO�oo��rP*�5��HH� }��� �%�z���*���&� 5. &/!e=sK E9js� ��U�:g��"9c"go*:� �C��/�5�.EatAq�a!�g:GN+f�O> sembq;�Sy!!�>|)s �*-60C� .�E -�8 ����a5]+�j)�0s��� ��e*�� 8:Z"=,$n=0,1,2,3,4��l,d �?59E�W��Q�0�"�]�2�7!�at han �L� (���!���Au-ͼ".� +26 �a2� * qu2� s)�c �1cA$. M���-�7���DB� �.tegy � .��w *�Al��*�E s (�[ng^ nimK( �� ��az%� I)@0I�~b� �%�,2.d� , if�iv�����"M&�si=C aQ�>i� � � �' 6.[ Y+�)s!���M��pis� �*�� &.G hi�� o�&.6 � *�L>?pEs9i\�r��/�9$s "��J��� a�:ujA$�i[l procedure� of channel reconstruction (for details see e.g. Refs.~\cite{Chuang1997,poyatos,Buzek1998}). Because of the {\it ad hoc} assumption about the transformation of unused test states it might happen that the resulting map is not completely positive. In this case the estimat��procedure has to be complemented by a search !$a map  which t� otal mixtI�is ``shifted'' as little as possible, i.e. = estimated5��is preferably unital. A specific situation occurs when M@data contain info1]abfv92�. IOis93=$can also fRX(it gives no result), b� it/.�(no physical} Aompata1 withWn expe!%navA�$. Even if !���,ed operators=q=e)$4 valid quantumM�,N �k�be!7a ai radi�C��condi�Vof&�O te p�� ity.��,what followsA�0will briefly 1� ouru} �?8 particular exa\ - M�)identity5S(i�s��at do%�tg�pu�ata�(). For moreM8ed and generalMrp�is�seeNi \subse%B,{Case study:B�}��R3pera���tep-by-.-a qubA�� baa %T knowledge!�howMe�, two� three tes9re�*ed ��r Aa�LaM� t$. {\bf S^O$.} Let us �,m{!���� a��2 fa읃 byE�a�} \be �t1��1m=, . \ee�remind�tA9 eachi,qwritta��?e�hm ��1=�(�0+\vec{r}\cdot $\sigma})= R0 w S_z)$,��@re $S_z=|\psi\r\l|- _\perp |$i�$"\r, D\r$ being eigenvec�8!e!ԑI�H1$E$w���I$s an impurazm��I�sider�q, e�4$w=\sqrt{1-2\T5z^2}$. If 0$�n2|�#s max��ly��B a�� $w=1? �_ure��� Bloch-sph!N pict�param� �$correspond��!8distance betwee)�2J ((c� r5j) �a poin��]!to_�En �. O�a��$fine a new�� basisA $x,S_y,S_z$'A�z$� Ra&N,and $S_j= U Ix,_j U^\daggerM,� ry $U!�n t��new v:���ar1�u��i�cEaPleft( \ba{cccc} 1 & 0,\\ x & a & d,\\ y & b & e`z & c & f & 1 \ea \right)e�!i� task1��0i%�] y�� � e s. O݆& )^� E� s (belong=��� FqH$linear spa�!�$)� "| �M 2U,= we seş�U�s equalAFzero. %�!��gin{figure} \includegraphics[width=8cm]$_2)$.eps} \cap��{� aioriN7e��=�w� wo1k$\rho�� 2$ ��u��!8��!��-!���Q�MyB{accorq�`Eq.~(\ref{6}). } \label{ �} \end�%�o5o%�.Two�+s.}@ e�c3�f&�"�is :aYu��22s�: J� A�rel2sA16}�\ \, ;\ RC2��2>�2��I�AI v�Iy._%�uo2$t use ey�e� cr�ng��" ��.� &� ,5 6!Yob�aR�u�%�.} �5�yС�R� ,1�2 3$*n�B�6�  2� A�`&0cE_3=�5!�%�V  �J�5.V �5� B�t:eZ%z3$�to0(se $x=y=z=0��a�mp�J�Abs�J�QUc9B perfi�A�ita��:"�6g �B�1��=\cI$. !�aj�n �1d �r@ !� at $Jd� & uх��aP coincides�a:r �  �L���y6P�2o!!9?#!��j eI)differe5x!e�A� ree-�%FέU�5(is guarante9�!Q ]:�) s �_he same�a� bothbs�P�a3!�k3 2� �:Psas R(nuniqu� -6u7 jus��T=��Ysummariz �*v:�-� at"�� (e hierarchy'-� ions�1zt leve�pO9N numb�;%��a���E0&=&\cA� \ �u 1&=&6���� � %28)oE_4a=�N>Frome�previousb cussA�T cor%�E$> �=9ed =� tB� GiBA.fact, ^>an�r5lE�Rinduced$$\Phi_\cE$& a�eB�,�1!��6�����}&9Att�na#Zr A26�ab&��choicQ!J� �__ \B {Combi�a�L��A�:.��n�stent0}�|���J�e ����"r�s�N &� � edB����al wellns �. To sec�� ! 7]��" � m; adopi3reg@izIH� as� earlier�4!�paper�.�we � wo o� s: (i) ei"  na��ta�d , or (ii)!]� .��mditself�fir�cenario} be�d always8���>)of somA�� oB�&�&7!Us*� �if7!*�%��(=�ed)*y "�� legi! "�s)��-�&W�not.)a&�%�B� ["��GA�i[!��occur e�for �. S�Ccal] *d=:Nb$$ ")N�$%=&� �!�R� � ��$ �� if $D(� 1,t 2)\ge \" )$ ��l6$e! $t$ $a+$ni2003}. Uy" tuna�,=�s�f� =F�similar . ���n!�er�!%�! �9�A�j��b eck��or �individ*�  seA �. �Rl util� (dem?%a!a�]؁�� ies:4 gin{e �#98tem{$\bullet$ }��jU#:Q�".��Z��"�! abov�!�!aEޡ7�V6r$a8 a CPAG) ���#of�t .�isS or�(nois2 admi�i��[i�, s�a���>��8 becomes CP). \6,9+.*an unE6���s! v exce����y�2� $ weL>mto ��!zI��a�iA�tU���$��n�w)%�b��-y� ad� he averagA��'$\cA$�nd6] U !W�2& 6"� ��"u� ]��seE�Q$s��a�@A�an ``�"ficial�&* n��E�g*"!�� 0universal NOT�a?�Vwerner}� log�i)})i��� r�@ $|0\r\to|1\r$, $ 0\r$r T ute"<\{ ;*}$. Th!Tdoa&.|"0 FZM8m@ X$ �u1�2�s. k#in[E% ``cl�!c%ZNOTŞbe view��h 6J o��2NU��A n� ng N� ())l 1|$)Ţ$South Pole!Ul 0|$) � ${\tt�}_{c}[�]2$&�\l\�!_z\r_ +��$N!="!=Pre exi�( & (``-q''�&al� <RJF�q� �x �$. natural I�>u!�4M�a�so < ed {.+u}/gatL s %�B:�"E�  &�"��ḩv"�")BpoB �j��#,�� O.�not�."�#�� ^T$)i��* O:�5!�R clos��Gly�iq��5approxK+ively��_��*�(�^�'b�" show�!at@&�a#MVW �|#iz��� fide�under�nan�r� _uB=6> -1/3�� ^.'!,5L�E=} F,!6F!5l��E^��6PFa�aIest (�F)M�"�x.'�mJ)&\to&M_xj V�%-5\; ; KIV_yrfy6fy�fy f\&�zrez6ez�ez e.f{0}.h�2(0N]* \; e��start5 !�/* ��s?K �&2,. 9K �T�or�e@us��!<� A1heBB!,��:��� F�J�=.\new���(1)} W#w�� a ul.`) (e.g.,  �)Y&� p�_��&nt�!, �FPa>N* mutue|�Z�wJ f�! " z�6UN$,����is mi�J p(u\pm 1)$hc6�3(Z/&$z$ axis��  M���dA$L6��N. :�2)�#eIE!B2X#�e! ��r�I. 9)v �#y=Cq�>!Ce-� $al1Ia�/0$\pi$ around�$x)") ��$&� -A�^sI �1rI�� *�m�).T:� &�� E�t>�8q�&� !�i�%�& p,fac� ser�ffp.ty:"�"���B"|.re.ys"_{x,y,z}=� ��:��&�?/2� !m!a�";�Lof 2u!�requi!�-�p� K/,a���t f!�1�unt!9�}�3( d'' �6v.��őj�Vw�$tk � ed Jy):L%��m�. It tur�uTYam6�&�� AI- /3 *q6� �� ��RF�i�[ %!2!O��3}��j^T+ 2}F "6W�\] �))�ala yvJweL!������CP�%B� 6� :�In&y$}�aaa7f0|�uA e>I�A)g*��$n$'i� s|5s.��%!��"�*b�%�)^Z�*4:�* K. � our �n1&�0��8�F� )!�improvedi4increa��%HR��!gr�]!S�pno��" j ��pUb!��7 F���onM i,iO1/($n=08 ��J��[R5x�6�F�:�isV�wh6J�a�co"M!``n�''-$@$N�-nd ``sZ'' pol�"62^"� 6�� �*ly)�is�8� i��'!Q#eM�$n1�� pict1�S6�%�2�rf d"qRҔ�F�6��S���J�Fin� 1!: ��A�3$) �4$)K��� Ey2M!�R�u(!��8� 6 6�e�F/:{V�� $*�!�I�lower�*6(,G!/ACsk!�tT-Q :�R� �)�6�.B�Rg���%~in or� o1"e an��6^$Ue"aZ�.����y�a� NQ�2����Z#7�w s. "^0.7a0��n06n0f���s�d "-W.6�(Y�)1 E��!*�oj� . InsteadF�<� u& XI%�by ``uing''/ small.�B ���ILU�]T, l.�8 *T*T6em:e2Y \foot�{MX:Qp�q�E�a] ���o�t*x(�� .}. �-��ach� ��* `;T !g�is"n ,+ �!5z*� Z@ Z�map. Ob�#ly,a�>�|%�� ~explici�+satisfy�qh<s impos��>!�TA, ,ٷR{>��� g�. B^ i�i '�ec!�si�&W%Swa"6" �CP��<)�VC"� ."r/�Eype�V !�we arr�2a �&y� s as)n1 �1f�p%�". "�,ao$n=2$ (�=A)�&* ��'t6��.( �� �;k9ec{r}=(%)%=(0,-y,-;�T� i�>-�!$!No 5�&c 2*�x\�$86.��2�. C>N.%{�nJ/ ��1 a�/o�1�AM z3_1=0,2�0�3_3=-1.�*A�at�* C�> ��"�1 �_cp�6�+��:�2$"�a6�+�:cA9�a�isof $k$�9deAfd ��inl-iti�.|� 1\pm 2|\le|.3|$. �:ob�0� �A�N�9���(tetrahedron��": -1,-1)$,)� �c.���1(�� depie�iR�2}eTab.~1�� �&YU: (�ED ;��%T�]�Q&ce-�6gAng#B�s&�?!��e�,�J%�n$ }� . We�6� 5+g!")s.< tabl:b;tabd&4}{|l||c|c|} \h� & 1st ? & 2IA�C \\ &0$ & $3�03& 1)12)<39\\ *2*A,-, -1/2k33!B�:F=4j$ �B=}),� 1K6B;��:� '�Zr"-;:K k "p$|&3�)mapX pendAbaLh"�6N�)e sub� pe�,� �#1Bmap�j$NQ7V� \&d� 6. B,/E��� lear- atI�Ims��!�� &'�6� aX& !}::�.� �} �=�=qdq }" v�5��� ��ޡd :�"��}��.����������B���Z�a<���� KDB�������J�"b � (19)N�4�%FS ��!:"U 4$�U :�*�apff R *�"!� �� &F G Ba��BC �?�?�?�?R�2�����(���B�L�L *q1�^3�8181 R&� of qukCM� ch� E0problem motiv)mai�;byS"�Lr&�&� W,~se����* horoughly2  toA�aPm��*�(\ u�% . An� �rtantd%lici �Lh�*6��in�Umun 8�& ? sticdIF�D� �"�E2smi�F� "X)edU ��-�B� p�14e&E-^/�u� �.>-~Ya�*K and/o92��A�- *� �avail< �u H6iC&!i" F� in � ed Eg+ > b�I� J�c:�  3�B.^1ver^#h�O (CP)A�. :�� .urr�*o2$ insu{ iA�I-�u�C"���%��"oo~�Pd4%W�Rte ���,!��principl�)5n !� "� s: E�3 !�'u�Me��a��Laem�A�M��@s�ArprC"uD�.#y%� ! E�out./�1�RA��Eea> d��U!6ngi).( e multi�ve!$toi�Sy[�0)�@euto keepAHWN�!2��s��en�:e+� ,u��xEE�"�� �.� �u� O%�5��sygi�m��<�J-sq �s�A��'6"�{��5In spite�ffa��QfP!�V� �a� aŕ7��) u�Qates may&�M�1���^�lar4Va�:}UR��c=k\cE�Gk)�0��H>� �!q���!%�;asXSr�"T��Sue C/3$ 7���*9A�7!� illu�(��%���Vg.�0�2U�-%6��R�il�� �� y�� rYgwHh�O st (�) R9-�x$n�" E *{Ac�!U}[G8was work suppor�ina�t�cEu��an Un2 �projects QUPRODIS (IST-2001-38878) �@ CONQUEST (MRTN-C#`3-505089). M.Z. would lik@HankE�3al� viaeg[?, 201/04/1153m  GACR��� 6�N:Nshebiblio�#y}{99{ \bibC5@dariano} G.M. D'A!V P.Lo PrA�, �/Tom H! ��� Hs}, Phys.Rev.Lett. Par� `nd J. \v{R}eh\'a\v{c}ek (`t-Verlag, Berlin, 2004), p. 299.`jezek} M.Je\v zek, J.FiurW sZ.HpXl5#�inVBof<�� ss%),�%�A)�$68}, 01230)�32�hk} Z. v� R � c�J. :�yM. �IPM�T$um-Likelih� M�%l�Me ics!� 9S��=�}, 1f9� �� M.G.A. .�\6��� p. 63.�po_} J.F. P !� I. Cirac,% P. Zoller-Co�<& Y�& -�:� -zCu��;q� a��+q�7!� 390 (19972�&�_} I.L. �M! Nielsen ��#cr�6�[9+u��Kdynamic^�Tblack box}, J. Mod. Op� 44}, 2455J�&v`0 V. Bu\v{z}ek �F�(Liouvillian��e�v\61m5!- 1753{82.n) a�A.1 A�=< �Q�!�S*I%=  } (U 9�D��,s, Cambridge�402�z�] M. Z ,aoPleschI`V.!�EiDO �"z �s�?u.� �o  },3�!a� F/%�%ӵ&�4�(,-ph/0406088}.w� lich.� T. HFman6�2�%< Ch. WF, Tr�=��k%"04p.iM.:%E=%&�EVIruskaiG B. R , S. Szar��!�E7�:-nA!�alysi%"J�  c�(rvZ � on 2x2"�}, Li�lg. Appl�c 347}, 159�c22�6q �M. Hi�oy)GR��W.�OplAl�: ipul%�r �gs:M�al- .n�mm;$60}, R2626e<92�.#@ A. %AM. Sasak|Geometr�:&)"�bM-�=N!�theirx%�� ��repea<,a� te-d�en�] clon)� chin:h��7042327%��L%"{ uhlZa %P{ Albert � A. U4n, %Rep. Math.eX-�1\16��80)]� h } q/!��$R. Derka, Q �yOm %�s}E�� CoXnd�mo�& PhotGI AtomA� �c�J. Pe\v{r}ina (John Wiley \& Sons, New York��1)�5198S 5$fisher} %R�YF, %�� ���1a.B1}, %P�ee���w�@$ PhilosophEPSociety 22}, 70�25E��>I ��cols}���6z  � docuc ��6C.a34tribucion.tex .2 % %6,ple root fil:r y �OI�]a:!Xbook "I� o Galindo� "OU7@cLaM.templatZg;iib.4�UQ simplify�^a�G0 orig�,Ob86Y.$t http:...a1)c5?{sv!�} %�!�'�: � �mat \uDckage{F icx} %�"(ndard LaTeX5AVM3ol &V%���M�s.w[botto@\8ootmisc}% place�1) s at pagetomA!bu"�$} \title*m\Schr\"oxer Eque�,) er"=Ta�6Ge14r Algorithm} %%� Rrun� {Short Te}!?�abb�L�Z�* %NN9 i�,1�\:�oo I^ \au�{Miguel�,M�5 n-Delgado� (�����Aitute{D�taa�>6 F\'{\i}�f Te\'o�� I, �G idad Plutense. 28040 Madrid� Xain. \texttt{mardel@mirA~0.fis.ucm.es} !� make%O S{Ua>K�)� tim.�6i%e� are &�b"�ex��A*� ��� 2L{Time D�D6lQ{ElP*" "�-sec:1}'Fw (QITJ�&6w ��5gp90} ac��c&� asRM in �%to�"��%�h2�\� evol�8� [hystem�'fun+�%�)er (QC) � rmp}@Bl h�(ry vk Ea�eepe��� um��{�� a typ�-"�� a QC:�lnoi�$ i/ A QC�r�*t$ initf! �1�(} |\Psi(t_{�Yi})\rw;:= _0 .U_a1�E�)&� �6|��!�x� @ aS  Fpr�m\�te2CR�*f��s  ` � �bce ofJ y-p��cl Ms ${\�H}^{\oA' s n}JQa�a �or�duceu �(�6le>O. 6e%�PhHi�ofVrc�-�l two-dimen�al$&�^�+�isQ.ly enco�?i0' OQQOreg�Or5N�1�.U�E"&ATs�o j��Ba�. A!Tage*���A ŀ)�.xQBoYTd F^�sz=Nl�=�n)��= |x_1M� 1� |x_2: \ldots.#n#in N,�A0x_i=0,1 \;\fo� i}bB }� i/ Aa�e��min ��dur�zan �_ val �Ma�TJ u-_5�/v >ly-�df�u�= U(t,y�e�F�2B�w� ��ڭkpe� $6g$41ie a{*� 6��a,�Qin&=V ial !F��\hbar �<d}{dt}6� = H(t)6,��3B��*Ťxval�t!�g���F�6a = I - ��t{�} �ft_{5�}^t�'�'=� dt'9�4B��� �a���ٝ� yield�0r<}F��T}�[[ e}^{-)]i}�b��}\ri]9h4F6IYT�6�K� am �aU^ intr��Dyson8:(he Hamiltonp�  �0p� i�>�/ative s, �1F�"ormFJ�W$be further< �XBb�`fS(t-U)H}9�5R�9��of��M�>�& JD�$!!n. Thus�A�f%�!]&3Dtb:ng�!��__ cer�f3$��Z��)a"�"Sn!��5 $2^n\!�s 2^n$�x�%���group�~$rm U}(2^n)+L],��ũ�;r� 'v.%��>e"��Sroposal�&�ng �94)]� tr�.�by� � * cz1}, 2�&� �\� ; m!{:s harnes�%���$ in��nt_ �.wC pur�6!�pe}ja�ful�l"�l:�Ae"��a Q Boole�#� T $f: \{0,1\}^m \to \{  $. R-�� LD3 spli�!5uQO snS i2�$��  �PXCwo� t�Myem sourc�h }%� tf!tx$}, namely,F yd &v �Ts�&�  t�6Fo �e aBe $f$a5a�#�I� a�3!�R6ryi�$U_f$q�1Z>C7gin.N_f� � w x_m-d� s}� {m+1�  t}= �:0oplus f(x_1,x�bm ,x_m�V927F20 �"�_t at�&chAz!#);� Q�.�is 5|e`'�blyH4y:�v/�!E&!� .�f1-�#E~o�&a�M ik( QC�Pah>-�&�k-}�� �4!�1,5[6 \}$^�E��x *�E�F� = \sum_{!�w� } C>}A.'Mf&m8B��jwi�w,G :} ! xr�$� hV'iH)�xt%W&E�oa1bJEnt� e��]8 ~n^��s5�!c�(�����µ�ten:���2��s�u*pa�>�or�$U��iy�$eV9�)$��4�$��8})�>>e&�yJ(llelismQ���Io�*po�ix>)i#Zy*cy�����u(:oA�`�VC �!mJ)()�nJO5��?u��QC!�rev� des�J�?. AssocoM'JA�r. ��Eon[l"9 s $\Pi_{>u}=V�\lE^ 6$|$ �}A��!2ul�a2 o�f�I�iJ e�q�mZ {՘ f}| \�� arrow ( V�g:'ZXR}� Tr}� V'�i� ]} =ZM�S9BSE� probmbF`P}>� =j ��F� = |J0^2� 10B�� a���bW�hF����%Ex"T m�͏X�- P:|��fi�6a��Ř"< �ty�{10f>ai� a g�$�  .��-.Nashse 2Da�1� �>4eans a pattera&� ��q&& >ituitowar�he [~�E'. EO~7R���f,H a$^shoy K�x� ���.��a,�,n�U{ >Wg���,� [*p,�te�"�@s��-�}. Tiy1F�F*�| 1�ɾ�it�mpaO'%� �+%6B�,� ���O�aslh�;  �KerpreQ�n QIT� aQIT� jbasicE@leZ�,�addres�E�s�;tha!F�:P = !9izeT W Com��}: aA� zB!�dQ*�/7.d�y:NlexitKsc>g�cspace/�Ӆ��ka�0�qaC� be solved�u�UJ%a<3 ��p[m �%%sim�"e%��4s, �Qwe��� oykAbspe�^-�X'ach�a�2�] �-f46Y�Lattic�<ly2}j6� ����w �e�I�q backi��hsava��4!d�"��j� *�>O�s. I��.get�ly Q&om xaak!.urr�st�rd! � .ir lyM��A��.s"9ly�#j �r�?�4I4 ." 5�� �?^�M%K // f�e-k(T8 0):UN�vNw23stkretA��/E�� e ��\FA�by� HbS.� CA:a ?-NlIC Ldis q���6c�G�  d~c" -M!&�in1Jl y@a� fund ��XC�`,� t�-IBO�_�$�S�Feynman�Uh�)�$f1 wo�X�!ӈw���TderlyA�IHur� ia7e beyoM�subatA�n%}dS�^t(h�ia1H��56P I� i 2Yp`5�` quesis U8���Q�leY<-m� 1.�M�xHcA���! avschemG5�{ e YC\-"QE:!s� �F���=sA� � ���#�2V2#&v0e��� Taylq xpa�A�!E�i�joedo��V$E>� �G!#TqA�ǁ�KS �.)%Fa��s�!�L7!�emá�ex�E=�whi��.�!�aT� ��dI��Ka�belowaMA��ex)���r�X�0� �precipMke�Lin��w��]A" 9�%ula| �H%���D1� $F(z~J� \f��z}&� \1}{\epsilon}[F(z_{i+1})- i)] + O(!�g��bN�� a non-T>ula. �<6 �;!f�<0 !�ulaG%�rw=i� nyM�F7 �V�2�B�{i-1}:�^2&�bF��%Q�}z^2}{dz^2b_^222)b+ �+ 9m^2=oFq �s] i>Rh��%.�`t� V9nafR 5N�A�k.i5coe�j!rnŞF �i})�\pZ!al}  t} (x,tA�"� )!D x^2-+ V 6@"gbF��  $ 3a�7� J�J�N ssum�dt�hbar=2m�{�p2�i��a�, sQ$ae"a�������*=k E,1L� ( $x_m=ma, m] Z$�$\taur"ep� �h��69�sN$t_n=n9, n L��{Ŝw�{�0isN$si_{m,n}:=)\_m,t_�nd���ml�[�W� $V9V(6� iI&1� Asym). D�eAoem� V\(�%Ce,6J�).s�7fr21a ���R b1})�NQ�<� '3's�?���JC!!:% +11U + q"�[�/!� }{a^�`(E��,n}-2P}+ - } ) - B -� #,nC"�bN���|.X��a�!K!yx�\lik!�#ntinuumF*Ip� ��M!�x4��|a%a*a{-60}�;[~one2%1� grid* Rw�-�5q$a&KB'u�upd��ul} ca�, of rG3offe� trunXC error1Yޑ��32{,�\iodic bO0*� �  $M$�@es,NavecE-}_{Mn IC͚array}{����-M� V_{1A"tau - 2 � &�rm��V}%J&\\��9.w2nwN=0 .q�}\v�%&r d6$V�]� &2�Mf� )bq� !�{A�!�&�b6B3͗1(:�S!�� ��TT Rn;[���"(I/t�}O� 2��B�"�R$nfR�aE��Iry{p l�EPin� sl�� ɵ:��1g6�d$1+O(�^2) M7^2 g�u�va2e)n)$^D. W� t� u,o inf��>� C �0ip�4/}t(k� "BW <g� ts H�ztN$)L: �*1�V�/OK Bd(e jobo3:=S�<�L!��8�82�Q�8~8-1F:2V tam.����;2C�<Z x��?SG�� Fredk��nd Barto�C 1975$f !}LA�i;F�A���"�! ofc�TV�  f�~�N��~�6��,�ankmo�}.� Kx�_very �0ng�-7es&�ZNpa6�[ i/]�� MQb�: � jPStvi�!VP� Fwo 6|E̡ �K in sharp����"3inu��x� C[i�%�ly5�fA0=.tep�c�!6ErF�z�3RHS9��b�Ee"�R v/] -�J�R$��� }$3Ze��A� ���X��lex9&w�!M4M�!� $�����)�pl��F564-1�@I6ma�6ryb6-,}$. LikewiseR/z2+1Z� ~:2�2�F�b6;�+%�U;�����am� ii/,�'��+$')�7d�8 erty2"�?*< &�r� �rAion"*{Q�}&� �� = ��,!4 -: ����8B� P^@ty�!��lsnO�(o�iA�Nsma�ly:�#�selq"�#Rai3��:vllic� i��^l$%�F6Ts6odd5�� 5+��v/B�&M&��?� 7}zws+#��,"� ��ȁ�o�1��2�2l�C&� {2le, ! gno�"�i�9U4MX: $X_0,Y_1,X_2,Y_3,X_4�5,X_6"%����NA�;��.�c��.�_�i��}N�\\{"�a"} %-+2} &[*&-= + F(1@),\\ 3) � F(F }), **  \'#&�J #$F� n arbitr���Q�a�m= i��4*�N�%(��.F)>�med�%R�+nC5 & = &-3��9!)% & !x-.j.�AJ�#No|I$in doA  )e&m !`&no� t  m*Po&� &*s��fArJ� f� �/u�ke�.� ��5A�&�Tw�m�}' � �8�o����."now'M�y�*LѯZ'q�:��� 29 N]�n}aAR' &� I y11B��37aH�j��ebJ#&n� �+1}I� ��-7[ " (�+1w �+>q&6 }%e�]E� � x x+gJx� x ,n}+jxx�3_�!1�l{I���y�LT!".�A��-i"sD.� _m, �7n.$�se ��+��n=2l+2U/c�[ �E� M1{�*4}JS�[ disc�!LE�u`*_g)>� .� �Y,�5�V�uZT%�,�.2l}�~4-I� Q� l -B� B�2l��]�'���-I� Q� V�E� ���F�T�nE�\ ely%�&��O#M9})�Җ��) Ū_m(e�%"��������_m(A��1J��-$F_m$j�gC�B ):= B��? �?j?,J1"�NB�V|�%�W�6J�i��`>fL 2R6E a�?uc� y���[5��.�2� O&S Ns'm ���h�� chanT�FE mooth�� �  enoughBn�N���E��v �V at ��R9�hl�h�R"Y]��kF~�>� �actiV-�1������|if � H !2�R�W&" 6� �@yNSF R}� �2h; I+1}:=.��F��o��<0Xwa�7"x �&9 �Ws dir�� ��} �"�2 a"��(resor� o um�@6* ���e5�ul����F) �� ��sub^� � �n� Z�W' F�!�0C/C++ languaj*1 s �E+=�7-=}. W��t�[�x isosIn1#-)q k9_R� NY1< \{�Ax���ec{R}{@8\; &-=& \lfloorI(F}(M0)\r,�i6I6+^6R6�nnd |B� 1F_���n�,�,$ $P(t):=|.2�!||^2$!$2%o%(��"1YF�=14�/�F�:.M<4G*~  B�sV *�)d:4�B P_{i�%Km� ^2 + u�^2}�F�H���)s�q6!A�A;� ��)� �1��fi"��}���in=nh�g2�9�^{($r})��:�- ��.-1* 2F@2�!�IJ���y3.�IbstQZ��JJZ2��Q!�n)Elx �l�-apA�,S1r��� �) ��G�vs.�"*!6� ��!���BA�a&0�T.O]�c�bED�9Q�o�>f�+82}0 &-8 most�:o@d�1  QC co�[caru%�I-AGeSum$,s �n �7t\t,!9�to%in!cy^A"�0 "��4Abrahams-Lloyd�! �A�g9��b�"{-�'8).%!�"0]{s6<2K!�3 A]3 ao�A@3}I���pursu �6]y3ormh,�Y��)x6V5�m�A<�9 bears ۶���&�[0o<h�ri�natN0Nct,�ca,'pa�/ vi�5�5t,�"er,�� !<,Klein-Gordon��1$ �;�ta<a ѥ�.y u���9Tra=D�~�ranCa J$a wL�ng roadբ�5 �=&v9�l�Rd�  nea a ey lZQ8 end>F R1�"ofQ+&15"� a��6)�A2O���S5�MwaO/ ed *�>.�pig�5 3} until!�aMto�beuti(�ĸz'i >��B N2c�� 3:f�Eya~at �^s&(8B6!�!%+k;�| y �Iu623Uh�4!�$n ���e�`st�e� baseI�$M$0s �Raa��Rn"� �^�dn1 .`ny��A� ofte��. C�<�zno���do be�!��bru�S���-��N�.&�rquX_YT#M)$DC mark5Jo� �f)/B�`�a��a� helB�NpaKe�=e\�Su�K V9�WT���QC*� in Sect.~��1�v9ͧ �1Rre+�to� $O(\��M}*��A� maj?j�9>��7��E��>M�� �FK(@wff�������>"� :"<8�6�!1/] Du4���� s82�4I�( -(-�~&��Odu +�esc�F�2},� A�&W,��ce=5�(Eb6" YE!�u~3s'& up to u*�&�&ta�&R֗� E�#t��i�atQ d�'&7 xah fG � � ��|  j1 7}). He �WoyA�1C�Vth~=Achi�@�5�3���'}weedG4kC7)Kfce�� A � ble. r�2E$�KU. p $DAR�� $R$^�+�.a R>7�'N]YD!hiZNg3^� *� D R & cFBnD\^�+��+��+Rd��+��+�+J�.��"02c2B�BwRrw} ��M$i^-}��`,!��,\\ .:828 �, 2\F�,F�,B�-RdM dN"�cF�We�3�� &E3�9��*=Omi2c! �Kct�!m��~+ �($252s��^�7a��3�A��,��V � xm`��on:oR�� t2�� u2�p��7idea beh�B�X�[I(P 2� � �����K#n�@ed�,V9��6� (MarkovQ)�*�/�?J�C$E�i"0$�b��R a ph � y�0�G $m=1,2#,9 ��6ap"w-��xCCal Yns4 }$. uZ�9>U,�E�� �0K5Q"�M?"�3��lecH.]=�Fs{ew Q'=@earchedAFN���0If�9y9Y  ;�6#}�FSA�goa�o E5�r?��� � e&is&�7�.k�1x6b* _0,N@%a�*a@ $N� ite� 'atm%.i �dN�C�� nKy d ta��pE�"vs $D,A�n�5 to d�r-�TE��6�%M%m)<=hi�ww$ifi�K��A � ��%Fs��M�i�M�9)�a�af�s ��, eaS-neighb�am Zht2��no#�Br� hopp�_3 �K� d alo��heq�aWS�A��7MZc� FogyA_usA)�G may think)b���Groll d`b1�ssi�Aofҍ }�La��z� �����b�xe%Zh��#6z !���x 6 3/] Glob�7if-�� loE�/��:�0s advantageouGH��nX"e 5]of eq.[ �!gl�=�YJe DKL�Mf }  (M-1):�N�5J�52�>CV\5r >0��X�_J�" F BpJ�6F%"r f�v3 4aT � } NowY��hoR�{A�!�A��Y� an e�I#a�-v_eAa�*����n6"�C�hO1. A��saaBimetun�&�Mh��eaY��bM�A� � �&�bn�RQ�(v)rM E�� 5� � %�.8 vl .2i �71/86� YCUL FU{JJ f�"F^ b�Z$v8 !lv.!9y%d"ite8`eg�AJ�mcLti)I2��7��!��Y�.iy���|�s� b�s{�|(�.i6 �a��.��G� 3I���Pn}*tQ� �wӣun��Q )y!4Eå�tud�S�V ��in�G� �7c�l=D)%,o2��rI-&� �a�"E��A �e pseD �2�s � &7��1.,& ��u� 2*%�!\F*�vE:pi�� $. A� �u1��A^�  $, �@!\�!W"c-89�hVs bMR�*bLai. l} \tilde�F n}%2 e�i}C_n}{\"  ><\neq BBc2;.� ZC_sC{M�.c v1M� � &c4cB�I% 8, $C_0:=1=:c_0$Q�3�U 1me}6� "�{ comen�/61cc!3Y,_0!+�' �1=$k_%:+�$i}c_n+C_n)�� �]�! U.Db[ c_n-BTOZCdBC� m��k AkMYELy&s�; magnE�o��4&M"���,byu<&ҩ!�) .��R�.�"�ޱs $N=O.�%g�"G 1��I��T � )of�br�4/] E6��9�.x�eAGrig��J 6�?"�x{�52� cA�a�9$J F}$:�����+ (x,yz� c} � ��"@ �'b!&� "� F F� u "� x���F� F ,�4x,y&��*E �.�!W!}?� aintJ� |x|/&�  |y := 1Fh,\; (xy^{\ast��x y) +22)10& 6Jz��.�A6�2�2k p�Iu�%O��b� $, $ y=�˱�$. Solv!m�6})�����!3� "�$y$� ~ "��on\-soDhU`F�x = -1 +��2�u:=x_M1Zy =6y_M9FF7+The�� #�y[���D� F�YM,y_M)$�chF�m� UC�>!ͦ�HIg 2x �Q} p�f(Qf* im���W\a.�.&KJr`�O!��#�ݕl�"��`> 2� >5/]"�4A "� Fera�U6`��2�d5�sQc�G� Mr4b V&� uni���dis?uVl=� j�2� w!�:r=*zA��Y� QiEd�]iT�� b*-�of � �2��,�^f  �n ieM/� �/� Y�� 2)_a0uN�H*�N =I6[ DBi2(\rm L}(\pi)!3^N.��7N���#!jA���Tr�B-Suzuki>�o$t $},�$s-��ct�A|��&"U� s --&��--!8!��sasj?z&g6�� :* I] F�mOɵ�P -�J �J F.�c'��&[6�� C_n+I�3(�Q �� -:.OM O Z� F�-Ig;0I$MI�a�` �>t!���%�A�RQ�2n is�q��$O( �6�\ ��]BM��a%�i�D2�";A��b $c_n$){ 1)$ �p/�;�ne�^"< z"Y&F� A*�>"2� }���7b}f�~Z $6� aO� "�-C�d]5�[�a�' "�0��H1.�B��A� FUA��erqi�c�d��e���� �3"c&K�'s!7the�{*cfk#r U� alel�K'�� 1w)�7�2nB}�*�0V �w�B�',z,.�6N� m)��5f}�#2F0Z-i}I�*~*���.��`F�x�]Co�Z6;�&�-4} It7�OHdecad(vow�!% BB845crypt�vphystocol EJiɹ bb84r4F* [ ago��6�a A� e�1s�a. I��C=gu���asH\adbatjKemerg- maS[��� i+-= leteV �hine. QIT?T A//,�~�6!)f&�\� 1�M�.��u+L}+�U��e�^��̆K_now. -�ram��}R`�+/keJ , CoKIr Se�e etc.3 chBtE�]c�avw"\N �fks�\. ��� re���� f�8< Xis�&i1jA�"��r�/HA��s t�(!�I/-/� . AlnlaA2t�� madeqa�K exci= � T�[~d� �pc�0yt,0K�W/!o�)�AHax�bDed���of.��&ĀTixaiafY�aa�AA� $70^�<4th}$ birthday}� "�ihA2�s ^ork!kA�)�&��" DGES�4��BL BFM2003-05316-C02-0hapW4 &X2 Numeg~l S>�4gble:%2�2"�i2�4" #�І%]�"a��LA�qaqs&\j, -"�@:}9�T76e &foczo�AuA��*�����m�� issuA#\v^Nm�4!�1]9� e�J��; �-�4:2o1A"Z7 mus+Rh� ason�* :"&t�~�d�x��A-��i� no�ofIy conv�Ence}:q"aScb, b"?- $a.N 0�*!��2��p ��>�� n1wB��Z��m���a X& L}^2$-norN�H||*Xn||_a^2�om�k�?|^2 a"� apA1B A re�L UA�e���Jcy}!��}&�9��8Z'�QelfII>BW22 rc|N�&U�X�as $a,J��� ��,{�4 �?^�2�!�C/& 8>�2 WhXay(>b of!B�nc�;�5�H+q3r pr8�s�6pler.�%o_�MBa: ��PGs)53�.�At��$!�>�bs ��#,W\��ch��x�LCo2�� �)�J"�Y� =5� S�6&U�. A�XN�N�)��"-�2��tN�(y�7U�!:�nյsѵ}se�p� z!�!>.�7 �U!�e�� ez&��(D�l%k�.�Bce�T�elso� J"i�K Ea[  ;!�f+i$to Fourier d!�@mo�9�paI���/,qI1��epc_zb%1<`�at% n}(kM�"�#2�}��m=JNF) mak}&zW} a�-k} [��Z {a}, r 2HF�K��a��Boe��@���! nB���&�a}�+2��i �>@dk��J�e�E�F�I��/�Uc"{/J�)���.�+1!�d%2- -2 �f_&�k(ka) 2/E�%B&�U4p \sin^2MKkaC#R�% apA6B/ �a� R(i�X� �V���-W(%��Parse���A7FH|| �";9}� ^2_aA@�* DPsi}_n(k�/kA"~JA�H�3nN = ���2\F# >��(��Lk[�x��dI�� Bp<�s�-alBE�s2O!%�).�B"�+�sa�4�Jy%wG}_k(u��%+na �$9W u^n2F��MdQaB4#plane $u�jC$. Kno�H$b �w u���!P 1'Md3 th3� CauN��,Nby�AA�j1}�j m� } \oEp\Gammad 6% u^{-a� du.f F K $H�-�Jt�3encircl �L�erclock. �wJ�-(�FJ��iskie:�F|%-}a)[1+b�u]4I0��+ u.'1(k)} {nC - u^2&=�F J1D9�o,>l�%!HQ&"�$� � � � apA0KT;7@ n�'mS��[ n��(�> s $v�g1}{u}$ډ�q i}} \oint_{\Gamma_{\infty}} \hat{G}_k(\frac{1}{v}) v^{n+1} \frac{dv}{v^2}, \label{apA11} \end{equation} where $\6ex$ is a contour encircling the p�T of infinty and enclos#all 'les'4generat (function. U0�Cauchy's residue's theorem, we can obtainIl soluF$ as \begin� (array}{ccl})5@\Psi}_n(k) & = & ),,1}{2\pi {\rm�{H}_k(v)q,} dv = \sum_?p�} KRes} [%�24 ],\\ �& :� � [v+2MHi}f_{\epsilon}(ka)]N �0�+ $1(k)} {v^2bA$ v - 1}. \A )" ]#2B# This9o$depends on%� root5�eqIW1�} o {l} �� = 0!((v_{\pm} = -Z< \pm \sqrt{1-f^2:3f�3B�Whe.��are distinct $v_{+}\neq v_{-}$, we have simple)�D in (\ref{apA12}) a aU�has%>4following form1&=7a�)�E�=.�f�} I�s=%:4s \left[(v_{s}b)nA[+AY\right]!�s}^n. .74BKTheM!F�l-C:=v_0=:5Fw!u$>�� 1$ and!,n=0=\mpi\$i}$. Thus,5�a doub-��� take1��~%H (n-1).x!/ � n.!> -? � e}^{/(n-2)\piA�la��5BT%Ustabilit�xalysis�$,be done with!1 help�explicitU�s. To E�Xify, let us assume thatD0limit $a,\tau �arrow 0�$!Cn s$��x$ kept fixed \cite{strikwerda}.udreE0two differentI2,|u.yM4})��boundedE9F5|�2�/ | \leq 1,.�6BXId(is determinM5k. If $4|� |>1$��.4re exists valu�� $ka$a� which $2�>1$�( becomes unjle. It�ip�1$)�� guarantee�di� 9, 6}) $\for� ka$, sinc!�aL�+-#= - 1$. .� �le%�,^�5)�not5�due to10linear growthI�$ne�i�3!I�(occurs at . \sin^2�",ka}{2}=1.$ S� fromgpreviouase!+,already know)@.V$q<#�" s^{n}MV(1-s)nV�,��77B�� � introduce)���(parametrizaaMFZ>�� A�R� , \;}�<1..�8B� L��c u����Y(a��rr!�(AmM repeatedAje8exactly reversi�$0Schr\"odinger���60terms of real�� imaginary!#ts��bAw, E� .�!rwould ne!mo9{ ] upleaAgF s, ��Tfor each component. 1�Pthebibliography}{99.} %�  % %�Duse \bibitem to cr![ reű ces.+Us�Z]NsyntaxDmarkup�yP =<Mon �s��� ��I{gp90} Galindo, A., Pascual, P., (1990), Quantum Mechanics vols. I,II. SprI%Verlag.armp`_D Martin-Delgado M.u,(2002). ``In� Ik�u!�ut: class�qu ��aspects". Rev.Mod.Phys. 74: 347-423; -(-ph/0112105.�\cz1} Cirac, J.I, Zoller!%5). ``1�sɨPcold trapped ions''. �� Lett�(, 4091-40946�2j� 2004� ``New��ntier�5i=7m atoms%'�", �Today,!�ch issuea1Uf{e�%v} A� rst s� ��split���gisters looks awkward but otherwi��we ru�A(to problems7s direct"� ���do�,o failure. I�s�Ci[ mentD �.AN�dU_f|x_1,x_2,\ldots,x_m\ran�= |f(F) ,��bibi1B�A�$f �a�� -to-��apj %\:�|"  $r�)L (y_1 y_m)$ suc�  �4=fB1. Choo��Hstates as orthonormy \l �>�|>N- =0$.n n�5�ٱ�%)i2 ͫtransa�ed �� !,�gonal: �B�|B��� � viol�$ unitarity. fact8&� A= basi�� �is.� � anE� �-D8a 8 under a �yE%$. LI� necess� ��u^ rq[-Ra6}),(<7}).E shor} Sho��W��4),��dPolynomial-time algorithmsq pr!o��<,discrete log!B0 on a�x� er�� In Procee3%�P35th Annual SymposiumEF� %0� Computer Science, p. 124 (IEEE  �ociety Press, Los Alamitos, CA, 199���95080272�$grover2} G , L.K-67Ō��me��2�x search !�a�lS$a haystack!F$9, 325-328��z8principlesQIT} PAU���;��ad�a�_erprem�l��ofF.hTMy�� s:A �ize} \ $ PI {\em S�D}: To phy�sys n $orresponds� ���hseparable Hilbert space ${\� H}$�iH. A pure  at i nt $t�crepresen� by}qray $|! (t)}�#�R}\in pfm�va�' 6Ydene�Xmatrix operator $\rho: ^{\dag}= , � Tr} =1,# \geq 0.$ a3QIT�S=-G enc| 2�i.| way %ߡ��sT superai� UY S�35z )zstruct!g�˩�eiAum� alellismE�a�*t stored��b��on ned!�tenso��t 7L-p+ cl-��$ppears entų��� a-�� non-&/ cap����- o�|ng �communi顡`M�M�ObservA�A�E{ o[a>  i�:I�self-adj0UNA$ ac^ %N 6NSe�}/u�H���4\varphi |A\psim)��AM� (|&, \# a4D(A�V a  O)A�Inb�AO)� ular9Bam�a!�p al�qassoci�J ral d?u ofi .h. For �P�pit may+�third��[ A spin�a -$r$}$ �lW U;M<MeasurE�A=If a �:�AFa�%� $.�!f��, {ized,�E/^ I�y�A� a � e $a$Cm�a cerF]�A�iJ@ � P}_{A }(a)2 |E_a.�||^2,HYl$\{E_a\InH m�e%j projector E_aMX\=E_a: E_aE_b=\delta_{ab} ,$ $� aE_a=I$, �$A: A|am"=a $, $Qq;a|$. G�%�-N)�� describ�vPOVMs��~ ro)�stic na��jA�resultI��um cala;a�. "mp��at good*prK,mming amount�omaximizA ��F,bove a finit� reshold. i �ummarA� as�����iv! ter�fia�a�tud# o; Cdesired�put&��V�$Collapse}:iVgivenb[eV�$,4)S ofH d�i%� 6,���to�I�ei- $\DA�$,!0Yby�z !6d� y@K\longoam _{A, d}=��{� Tr}[" E_{A}( %)]� a\in aF{a}O-aB�z�)�)a�o QC af� A�0 E� �AS shed9�-�Sc.~E8}: Betwe��woE[ecuAZs.�s)ֹCA B��ain(s,���&�in� A M $|l(t)"C /$ som���a� )v��<4"�!� evo� isI� byVF%�i} \hbard}{dt} � � = H(t)>���logic gn.� a}y ����v�fX]/�m*�al v�i=p� 2� �chievl &W 2S �at leasts>~ [ is "��� �Z ,amiltonian $!d� ���, m "8 i�� on bY�  �"X�;2�amEn�^yVx:i� Rul� I�� �;@cartesian coordin%�of�S $q_1,q&8q_N�conjuA mo� a $p_1,p+p_N**� ��Y$$X_r,P_r$ ŎUT t� ��s mus6 lfilW$� a� on r�& e Weyl��my6nq"� { U_{{\alpha}} V_{\vec{\beta}}} &= eZqg"m^ * ;\cdot  ;{e�}b:Ur * ;}} m "W _i,J_{ 4R \\ \nonumber �6E:=����i}� .1�XR& & \ {>��U�TPj"G$e5jI� Qq�� &C w%�&� ex�Ts!�r�B�phym� 'be�d� Fe Yly or�`ly�%e}f itsQ��pS "� �meaM of} *!p�T}��!�AE &�2�} Ir2"� heat�sip� acc��g��se�� law-�,rmodynamics:2�canbb�st���y erash r lost bi� :����(a tiny puff!�- "5K*� is h�%6perma�ly�peach ste"�#f��A�  chain�)�%s��ed� ult�s�" s a�&car�("�!y� appaX#lyA5les�� qer�bsA� ��e memor/��%I�p�es%Q m��b{mo�E�!�m�ne!��!e|�!mal�ingae Z is !|A�is�da�sl,�MrinsicU.�!�>(%Kre� sour�of�V�qer lik� e dragg> (of electron1{ cur!Nsid 1wires du��*stanc�#A�t1l� A/>�B>�larger! fa�a=� 4N�rDst�7 a loRroo�reducF�Y,�.4n/!. |a�u�1"5"$is�be A� � we fA:� dumpi�,. Landauer f�� i�" #l 61}� �gw isa�sa� a�N'  E = k� B}T\ln 2"�!b0B' �| n ir)L�qQe}un7$abl}�J�7cl���rqx�sA�!aġǙ|6 e� �0i�e%w % poweALe�(. Bennett f�rb 73} a�afK�&4i��.!�? c�'d ��le q)i7 �"al�sTu��,0. Lecerf had ded 1�}� �>o:O earlieA��six).��-~�`���n�F th�(ou�&_&u%�noE��$�l("d'�'% �� A;?/itelyi�w.�){/,inue working)�5H �-meh�&oaf����a� 1�� !ǁ�:win��0! i��� out U�ny�kgleA��q���Ns� 8]  a"�� do,require dataAobeE�91�.g� a-' -savA�methoA(j)a�iS}$ carry!��ew��t�c�L, cop�2!Mr%%!��s��8expens� ����� b�rec��est��1�le* 5@ Z�Xngaw'iz level�l!QA. chip��E�xo sca�m�;.v-�A(a >4called Flattop�f  } dwo#� MIT's#T&CT�A�C�)up�s�� i�� adiaba9 fera6ch�!2digital �2uits ���wd�"silic_2 �*�e Billi*B+Cellu� Automaton �b ' ballc(�veyI�model�%�:�8� Fredkin. �sE�a p!,ite�!�pe%�!L arbitr'`s,�#i/,reg� asW oof-of-co��9k ��shx0�unء�* l�$3acIA�in��+fu��"g$.� �, R 61).�$> !U"(o� am �! ml,''. IBM J.g3D. Dev. 5, 183-191� �"tem.��O, C.H �73 L�al5�-of |%��.ts(17, 525-532.tѦ��, Y n6 nM f.dծ9{�-!tea_4ndus 257, 159� �q� Frank M.�'TVieri C., Ammer, M.J.G! ve N$Margolus N% Kn@ , T.F.,!�A�;�- �Ime!�p1 �! docu�} �J\�[12pt]{pcle} %\u(ckage{�1ics} .epsfig:+ .(amsmathWXtopmargin=-20.0mm \eve� oddsid>texthe =25.0cAwidth=16,% \input{tciz,x{bz>�(} \title{ �!a� PosiL Channela�R�  `< a Harmonic Pote%�d\author{\sl V.F.Boldysheva0$G.Shatnev Zotnote{C"�)f ?,. E-mail addW+ : ms :8@yahoo.com.} , �(Akhiezer Ine�9 et� a|ic�$NSC KIPT\\>7�Akademicheskaya St., Kharkov 61108, Ukraine�date{ make%; -V abst" } W]* a�9ai�*�!d�+-[r5[�lanar- ed���cr�+l tl���frame�DourNroach, �9was� po��l�.�r� 1e�8U%8 �!��in�s,u.�o;��"cc�#�Y�u_��PiEh&�#� �a� mmed)��\!;E a� ���F%s�-t0>v< to l�l@<_�* ergyi!bam���<-dS t se�2�&ns�2n�6U-s onlyA&,7iE2�!�.arly hq�Ig pq� ��D@�,��I [ �kbf{Key�ds}:} �u�:o�f]/;�: E�p�]s; �D� b�PACS codes:} 61.85.+p; 41.60.-m����y{ \s� { �AK}�&rgaM��s d�3�A�Q�i8 xima�pa�<elsonB!�q�!F es w�bear�� FN,�iv;"dWticles,A3a�&!�>�ziQ.Fy|*�� ?�'s � uL�4$ smal/9$: $I*@& the 2�a�V8F�t�4Lindhard's cri� 0h_pl>!<a5-�Y to oP=.The mo!�ea�5���'�>a��O  ��5dimen aly1 well��6�� 'E�!���,1Y's ��0�(s ris,9���%eI. Its 0�Q�)�3level�*� mpan<V&R=I�ft�Ge�.�9s�s.^of� nA�eo  studEM5��H )A�{2�u���5:� Kumakhov [1,2], N.K. Zhevago [3]�I."�, I.A � @N.F. Shul'ga [4,65$W. Saenz,� Ub�a�0d A. Nagl [5]/(o VVBazylp HV.V. Beloshitsky, V�Glebov6�� A. ��Ch. Trik�;0os [7]. ExperA�tally2�Ao9O���zV#_A.1�tu0s [8-11], dem�1Is� 1 shar5akUE\/um%� pui2e/b�#�0 77o �e! >al-angT ��"< M"������}3em�#� �mx2� ap� n�  [12]. �� WaveO ��I�eYn�4}6"�G�um"-6al��!�e U� R�utiK.��.} �v., Wed��[A�A�]�. One z �(�E{-in�Ient D�<c for ��vz.�`�!��.�� $\�&�,{p}0��8 }=(0,p_y,p_z)$!�BRm�9V V(x)�\-�x-�N(Z #�:%A{=N!ies)"'  } (i>�f' �& B$nabla }+E-�& m), =�  �Geq1B _$m)$E$���1Y�at#�V,FW� G� L)��6n@S\7�kw.� $�!�U � E=���2s,&#)I} 9=\binom{ _a} b}=F!Lc�"�"�)Y� 6�{Had��,a Pauli-type6�7 � �(YB� sigm��(E-!� +m)^{-1}%�G!5 _a+ O-MM_a=0.=@FuL�Fa}'$��8}сe$yM&z) .Eq. (3"Iai&Img $yz$ Z�p_a\propto \exp (i(p_zz+p_yy))6(x)\chi..F�KWe oG,ake advantag�Gfac�aeu,m!� $ED91\,GeV$> i ,chI r& �V6o3 mj�� EBor�=$of $10\,eV}HaDs�Jtof E9OaLB�'H�K6�9er Q��sA��a� F��+ 1{2E}�+d^2=t}{dx^2}+A  (x)= �G   8 (x),]qFGL��F�@Lc2(E^2-m^2-p_z y^2}�.�FOK�&� nY��M er� lL�6 -  eigenvLK$.�P_n<0\,\,(n=0,1,2...),f &b;9 Cb(s F!$_n(x).$ Wh?!e36)!�n alsoA � e i�E@N|BP,p_{\Vert }}\�8| =\s�P%@aJ ^2},�KL"noiKJi� �-Y�+b6af3�4) %� �1�\ll E$; �#,)� shownam o su"YaacyJ E\ �#4 � }}\�vhQ>i�^2+m^2}.�:F�I�"6�of�2��f76ly&�-)aP*�/:�frac NL�� �� {iV{F.F�n}{E+m}J}�^�bJ=r9Cq�I�.�F J%�F�N=\EQ��a�}.L9B�$L^2$ be� the two2�f:�volP0 -�_e !�� Eq.(|A� $%ZaX��>;oO is $-�10$�.01$AΩ�9 =K� $+z9M $-z$ &9 `%% ��� '.�f�Z*��;, w 'y �.%�F�a �l�Fl�&�с e =V_0+1 x!~wP q�s%Wa2�D "� a.~(110)/�A ��$"1[2,3]�<t�X�,$� know!dat �D5)1/b solv`�2Wip7�!��s1b& ,�(!$ax�<��&n F ��$q�"Diak 7$$z$-ax�$(p_y^{}=0)� e"phoy#Bz k}$ -� 6 B3.��$he azimuth";�"2$(>�kFB/])a %�O6��!�Ay ��"��w�2 n ch�Jwo PC pola"�Hx;Ŕj-.� next way:B �Q�}_1Q��1�1� �zI2$ ly� �6Bek&�|��(Eity�x> 6�i�)y F��'s golde9J� 4d^2I_\lambda =�\\o�}� M_{if"� ^2lA ( & - \beta U�T �-\I(rel{\sim }{ 4( }_{nn^{^{\yJ}}})% �Vd^3k}{(�)^3�{L^2d^2YJ6> / )= &W J�[��V=L^3�)�� ���1(1,2$ indicaq)AMIp1�.w9)H` Jv#>"�-ve.Da���)�"L-�Q� �oQ�_n-.�_{:���I+2epV$�= nd $6J_ � est m �����eB4B" =� }}K2�X2)��"e a��3 ���&X �.u�2�s�/.nxՅ�?W [13]ag6q`\|BU{E�e;M<V} 1Jq� 1^2.�FZM�e^ ] 1{137U�H:!�} a =\int � .W \dagger }�� e^{-iF �B�r} d^3r.�J~�$>o=>o !�uBo.�}% �^{*^0"�N6�I'e. M�>um�4,oJ�>�k}B�U� }^{}->2.� 6� Z�\�� erv� J�E_&�^{}}+._n=> Y >->6+M�.bJcY.�8"Doppler shift"���* ���$ a F5$6� �N�� $ni7a&E n_{� }}$J+ n�6�UE��}{% 1:V"6� Z� 2d�5�"rL���>��b���!� -r: }}}C�� ^5is jusx95��$E�� ����Itac�.� 6�AY�E<3�e�ed�6. B�K�9B7% (1A 12\g�g ^{-2��(�� )� Em$)�co"% NKt[] ^2���^}�:!�6&V -6)$� (18"�A^^�Fw/ �2� "� .t }})}{(1+�6).�1F�ItIs% ��+)�"C Ya �Jo#�F�b�=�R� }})&K2FKis"� mOfor�J*~ (a$)�=0$�_e  $27 }}=1A�"�h* (i.e.,fg�&(u"� +$s%�is mea2#he"ul?&�(sh�^be"� an*+i>�>� �?�;mpl%�%�I�(Ś$#"� +Jout���� $(z<0�.�� erea�4� 4>0 E� 9>�"� 6>I�� ���a:UTI"�"orV s. Fa�O$ci�A�g) I!{Q� A .� !A ��EsA1 �D�>o49]cs �M�Er2 �]1G>$(z"� ��I clos� *v% $E�_' �U�A$m%A�! ���$�!may��^NQ�to�:UdM�%%S%R5R;]�%R�: & i��.�f�U�CR [�s)�" $M_{n,n-1e F��!"r�I �B/#sZ��{.�`V�A\A �\\mn}c_n~ ,"�!21B�w�B�Pe�iss"�~<vere��� �or Ir. A�D find.F0�[\�9�A�*� T n-2,\;n-3,...$etc. Ta�?�o �'un� U?��%on%H��H�Jh� =ٯF79@�!^�%{j� %� %�\,n-j"� T% XVJ,&�3 j=>�l.�GE� 15)A4%z, e��8)��2��+��-�5#"�:�̀$:�j$)Q��9\Fr*[�*F6�p;%�N!% "d2� BL�D I })NN,t chi : *}>A *n  }28B�A% }+i[>BBFTP]" *�2F�"E9O�M$A_x &=&-iI�cj}^{(2)}�r 1{�+�  � +m}2J24} \\B�A9� &=&.d1)B�5���� \\ B �f��Y �) � {k_x� (:�,hF�U��>%��;}2.�K 1 \m&S wY� �Q&9j�F�! ��d:�1"�ZU�� O6�R^" Bt&��V�\�"] G �� U(��� R�)6!�&~< ~�V��BAj<Dr�%�f��2��Ga g�ngI�$db$�C"�#Ek�}{d�do;e^2 t~}�j\�  n&Q .�I�  ��2  6 �2�3Z�i�28 a$p-�S� 5bo�<&��Xw���Q U�(  ,"�FCc�%Gi^ooW$2^{� �!"�! �!&!%�/% p_x%k"�!�!_�`QCC` label{eq3F�" Conclu�3} &s "3!j-/x( '"�0 >�06h" "�,^A�B�� - fIqB"]N eq35B� 'J9e�8a"eC35'!�77�  �05Vs�j�P� � �YZ-7��-�$&W` h_Kn;�[��B��� $+�: by mcpea�jerm }O^Ka6� i�7 n;�6de�%on,!��h� �� �iI&�&� *#reaJ ��rnSB�4p$7. "� l�3on&�2I�2�t!3�s, e.g.,2lcV�>�5 squa�R�b�-e )!E21)F�Y�^{� }.+U�V1*� *�), ��IncS words, unKS Ref.�&� ge �F�ytU%��N�tqN��at HVZ*a2�6AJ&�: f��U$���eQ.����'�d doeLX% 8l+��B5< AAVe�A\�:M�*vvre�]�P.b%x�5&�p$"�2I� simi"ME� ose !� 6inI36)a� a� opine��(cYz�_�gAs�Q�"�>af6=�9W��a�H1D& 7�_"3Ethink%� �8�#���pIh�Ce �m2~Y� paper�,l e' veloF?of �P)��Z�.F"�<)ibeams. 6�A&xZ7i�V= "��V subs�(t p�D�.�>�C{4eAb�t{1}f9�G,�A.L�r57�76) 17.g3 62 62|R!c�6 C0Stat.Sol. 84BH7) 58�vI3} .�9`, Zh. Eksp. Teor. Fiz. 75?08) 1389 [Sov. � JETP 48 701�7_ 4} A�9�B^: :`ga^�6`9)�n4J�9 631.(5�W.vg:, Nucl�(A372 (1981)�?&�E6L*�: ��:�9U!B2%782) 542�7} ��:6�6�:ZE80!%�08FD53306.�88} R.O. Avakian!�@I. Miroshnichenko�F M�Y�d TA9eguth^�2n2) 1825J�%� 057:QS9A�Jw}dZKL. Swent H. P�}ll, BB\ , S.D. BlxY!� Datzm-vIitM�Am148.N10a.A�latovav<0M. Golovatyuk =N. Iskak�<I Ivan1'8R.B. Kadyrov, N- Karp)DT.S. N)7n=�<Palchikj D. RyabtsM.DS=arMEK Tsyg <�=XTyapkin, D.V. Uralski, �4orycki, Z. Guc`0J. Wojtkowska!JA%�%DAvdei!F!t/GB�Ai488}�11}!BakA�A EXP�BKrsh, F!Mey�QO. Ped�On0B!�PÀs E. U�%hoj� K. O�wgaK���j85) 4:S U�12�4F. :uH vH, �J.���?Fv �PXFestival (August, 2002,:�N Mary1T,�iege�Jk,USA),� (-ph/0210203.63} W. HezIr,�H /2@E"5 , Cl_do�tect Oxfoa� 1954"g>A  E� &�I�<>�Jpaps,pre,floatfix,nofootinbib,�5pacs] atex4} 2�JKx} N�J> symb6A[sort&0 �]{natbib6_Kd2zamMK:yd \newwe and{\BEQ}:e2):$E$!-"�:"BEAFQ:$E$ FV"n�/e \\} \re.�d}ed>\oz}{{(0)>xb2 bf x>yy>zz>uu>�}+ o�=.�epn sint�rm si>\ccB de}{�^:nD^lam}{bdB4!� ar{D>�E�%AE> B}{\|�B>dMtilde�> brho m�l>epsv/ v\s��>>su sBi!�� :�:9 A�2&->&o!Eo�:?lg?�.:!�U(>Ph7B�taut}{�:RA!�4bf Armen ?!?!,FXlf}�4�r:CHH-,H��.�1^rm S}_{1B22BT  T}_1��.Xx rxB61�pBri QJ�6�hIK!�dV\"axj\"o, S-35195, Sweden8�/a�P Weu&��wo*wLbQ)�5#�h� a  alogz c2�nuous-�j"�.Fy: ��on .�jQt1�*!n!co�(!0 coarse-gr�Q d velocit�'c"�ipre�hd%(mi� %nyf�~eL)�TfU�Jf73&j�9 i�}tqi���l)�,y; �LR�N� pastD_�b# A�� . Three ��J cruc�%��7(ffect: 1) s ��� ime-�af5R%Q"lG ��v"�4dx Ibj; 29+{i�(unc�wt�i�:s6y���MMr&R5�han�Cc(V� y; 3�%&�cVZ.� ough�%-��<O �5�Vufid��I�E�ex�A#��)H.g{n?ce!a>��( m% disa�|!�/werio�s3t!��bWe=cu�h5Xb�\iI!R&�al *{�)��mpl -(macroscopicBf�W�c \i l{05.40.Jc, 03.65.Ta, 05.70.L��%% 30.-&BxJal"�J��*8 }}� libr�m"�mU m F�N�hE���Os; .�w��yA5�Ch"Slema�$eYz Deco�nce; op�CkY��[�Hny�1fs h(10.Gg Stoch�`c&_��,(Fokker-PlanxLa vin) B%b ��)�82.60.Qr�x="Ap nano��,6%�Grr�fa���>al)F�f *7W&2I{d�<�T!I��<��,o��see{(c"�`�+-� 5���Y�8.Wp9) lise�t@ exM�inc b s {\�d)}%ko�-2�Sn"�R� >��y�� �YD��690s,5)k ular&�>Ial V9!����+ -tem� o=xFlr�=� �l bohrp8,sch,rosenfeld,7 au};-*!+�Z"�r��57Sc.Qy�2�Qm� ~risken}g.ich m �1 intu� very:pful���polymer� gros�i)} at!&pgo der|6�"P.ikinfZ pig �(nelson} or W02�u��-l timo�r More_fmQ both�6�.�M�K esi@&2�Z!�or��!~v� s.is��-eg-�-d"I֏i *�Vira�Tms�{og�Ad�*�2"pj!�am�9plagu�-�0me~_gaaatɔyzQ 6u�2= ��MI �~A "1�9.V -V. Aa��ꁐ >~)��b}�!� �@�� ? phen�9��tradict!n�*� �. Wwas, how2d|�. h�1�E�� warr��p)j!� \�E&\��p��lela�ZOj!)c u�� �9��0iNdiPR�orE�vit��( ex�/)}al � s (��s)A�!*pe�ZtF�!)�andaZOH e�8L"egrV�!.�E�4al �� rec� z�Vb�e �3,aS wo�� s whu �Yunufe@�R~&+Z.! ,!lZ'�/e a��la��A�:�E�a�!asf|� s�a��i+4u��r� ��A refreshSj� Ft �r�\*Y2�l�4 �kI�ad�O!a4d�#Fp�F  task�0.dr�k�!�� T#�"�L uniqu \&F �M�U�A�o �a�4Ih�x��C!��Ex Sx�Hus��%n�54 �yO� �)m�li�t�0}\ur�Y>|� is, i�9rehensm��"|�92�al" =�In4 e=wora�nd|_�� k"� ab�kp�Z F --i�s �2�ŜKe1�8�,goal. ��� �ps&qJse�B��Yi�!- .6 �5in opt�� spr,�oo� dQ .L�� 2pop} (se�%0y�)IBaN��rm�E1�G�AQ(�&*�)�Cme&�� �k��= ZYpa"i%��ia-2S�6h�UaU)Ra�!��of&� %��^ ("W.tVIT�8aso&pR% M%� l�bli B_�#e{f�5_)� � the X YaF�E�be&�#��G!#� { . Wi�#X�3, m� fu"�y7 �XB� coup�cto{Nhq4�thv*� $T�D�b� ^HK�,ate $x�-� $pv��de��flL!] ext�gl&�%, friz Ac�a�� * rand�y%z!� S!*fo�z�Egp at��%Li!�},:-dampedK�me�?� "#,cha�riex 1Z!�!�*$A_x%3mFpUa� �9&2p$�>tau_x\gg p$ (�* � �xme)�8}F�U K���nte�.�&����6%�e��e; 6�} �yb$v=  x/ tGa ��  \gg �� i,�+G$v%2� only��ion��mea�fu !�*(8 ive)�53B B=� �ŏr6�K(�oFg�l9<�]2] z�, � wholցe�q}q����!g� �ZT*� >��"tI�Nfy���lE�P�'s�����?playedJ}\.�ath,|�+& u�" y fe���'�~��< caus6�n I�&')N�[mo8g! t:al �� Y�! �y:�8V�� |P EF�me[ac}[&_z� %QY ent||�J� % b��o8�.dsGdn�DeNi m}�.��A� 2�>��R�ikɂ (>�)̓of.H,+p�ceE6 �1b!'!6&B "� .U>organ� a5*pAa��X�J�qm� � ^< ��(A�i6)R�, focS;e12 "�ye 2�.w�k�"�.h.� �� � III}!�cussea�.� ��A���RQ�.9KQ l . NA��h��� stud.�*h 2��s �artashir� `"f{sam�@ jta�l�,i� .��D�8"o JP�of�g� a- � � expoEșR_.[:n�&d.� . Ousr3 m���last ��qme techX���%��� w?ue Appendix.�v B{�j.�}�Eqm s�,EW{a,�al ��"��a2 +m,<:�.ka���>�}QPEA�n�ws�Gn B �8�g:��[t����-vf �ad�/L5():�� ۙ�,�= �\ um `�e'���.& l�de0�:$\hat6!$98�<f�0 �e�&��Z�|$�8fe�p� � $\E(\�!X�i F�m�k"�see�blokh,�0entine,newtonG,8home,espagnat,w�y } ~\�';q _ minim��Vj� ul�cours�W �� ingu�����hidden&���� _ŠZK u���pre-ass��74.@� re=�*�a�ke� me��y�hgb:�Z�� �mkh| s. U�tu2  5sa� prop�c{6AZ<��<�� a��,X"b�a�le�� redi��0A:}�n-ell-ba T cu>l�o 8�g Itee�:.}�  p��c �ly:=a� �CYI�waTpuM�!�messag� e9Z#Cdop�ELkruger}."P��~|�\ 2u!�e� !���2]>�(o�OsrEn�|� �A�j��edJ95�dly�t}��.�ist�itano���.$�lu$t2f���#" pLir^5r?AEe� >��uSS�,� cor�����)�o� n,jaynes}� eYij>�=A�?6i&�nth�mq!� impor��eQ��s}ifi�5.}."v��` deal�n��uccessfu!Ww�S!omYQ%lem���l�jc?6ex���^�]�M$cw}� ��nc�B��Nt�  )f8��jA �onu�2%(!oon Belx�l�%�r6 ed�( ters) do  emplo�Esj�����judice;�� Refs.-��M+�,cw"iB���a�*D D2�.�D CsH &"�q S'r���wUdb s $\11$\2�G������'] S��� edwd,� ;-�p�}, (o� ble)%��EA2s,�uit�a�}� r��e�� .` ?J�=\�H(k=1}^np_k\,;; _k\oKs02)}_k,\qquad ::= � Hge 0, �.x $E1)}_i11��F�9b��2� ces liTL* 2,�a�>�t�, �Y�b� tegerii�B{�}_- ���oR�. Ac*���> (�1�Ga��#q�Ţ�� always!�"� by�M�f5(�]MF(3 \d4 _1"VShS��&�z ��-|p_2$, AU-%m&6Pn?t��s?��JOof out]��E�pb^�9 d �oeA�O 8h� ks up!1�$" _�o���, keepRno2Xo�7*��s PcAyU�6����X�� t�$N� >�!6��N!E2& &!�($NE1$), biJn��F�.isG� �( d.�} �&�`�tE[��mVajR�$� 6�P  Mm� =.�2� Hretur !rMB}of2p:6# ���:b���2)�2�_1��.�_��F,=i�<�AU �>��_. 8a#�$� 1d�(�cAK+� 2�g�l sity$�>B] 2!�|d-jA�s6 �+5�(").�� i�~=QlyKo M�(l� � aQ$=]*-L�.�wo!L t.����u !b+"�z 7 , it�� es!�/�`�A a�X ��*T ��e�����uO"m��P*_+$)Ao��e �job�~- s��%to2�.nf%lef9�a�.�aS6A� D�1�22,e�A���seEinv�h5a���/,Lthu�%0��!Cs{tS���*p&ly: C&�!)dr �F claaИ"�]"` �U�!a"����,le�deed, ��fl $P(x԰!bu �)襕\2$�}  � s $xդx�3As�a� �cE at ,a�$ %($a_1,..,a_n�h� MF+b +b_n`�6�[be�R���� BEA �� \a˝= yz}~� �I= g.h } P( /k� )\, 5_ G x_1}\, x_2F&<�1�iEE&� �� Y .�Yi{ �ng $R0m�@�.� Pr�%ޔ!p68���$�Alegit� aq.6gl  ,a&��Ca�a>,?"?&� ��&sm��hBH�Lziof>�~�&��>�c�(A�Y�2�s� ab��A��<�6� �e*�^y��*:�_�Z�E2�.��=L!ntc.: g�E�Z^ r�(  if8��1!h݅�dB� %�/  diag`�� �"�bes�!�_'+���<�2\ x��!��s�� . � bg{Semi鍇IW�4A vloc���� ?*{2=�|�{�be�(semi)lű sG)eM� B� ill �EuE�!Q�se��ng|2�in^ "� 1�TLet:o��wo"(!����ng)"tX*U['!�|!1:�(� &&�E��rho� '_1;��x'z �� ga an_#�Ca�2� � �l�Cq�R�!af1�E�AC,+by $\��\,\5 Ʌ�2�&f �+ w�% ,�Z]a ven��Рalt %� of W r fu �s $W(x,p]V5��w�#$p$*�* goo�%s= ter+3nP��w��ew9he �/L`quiWB�!�6���� it���"nTA averag����)� +U �it.q+�" au:Z5&.y2�! '"8%!�Ium�*��e�(��(`:� p��a�below)�a richer�ui -�q2 2��RN; - &2B6a�!uaYvity. ad�o!yll .�AT\�B!��d!�be"�N%�ly:� remMy��ll/%��6� :P�"f �:! �7*Q�} a[�ݪ��&��{��!o�=:R6umR* A)�ed:!<ta��JJ�]ɛE�<fes�M�� J rec�-i�{�9^Z� So m�b*1*q��X�P�>�,%-%or2(�e�r�) spit�!��]"{"' !����wo*�P���uQ�d�0=4 ����w��e \ re&8^ǡiS"� q W�Ip�H p_2)?ld �@ \,&�( Z W_1;| W_2(�p_2, $FGA�"]intwJv=ZL*� W"� W�q��@te>,\"q� 0 ١,e<��P�e�s�"a 2'.��Zp�]�oivorѮ� steaVB�w�0s k 9��i !�& )�d�w���0a�-�11}&R_i�V_ ~.� ɽmbda=j _1\m _1, _2 2)Ͷ� R222� 7.ZYpO Rd�W 2� 2\,� {Yk_1;*�3 elta�-x_1)\,V ( 9-p  q -x_2>,#��E�I�.�"4 �Km&\�9n:e �s�o?m)�!/)%�]*&1 %��~��� po�BR( _12u $. H�4��N� {�;E>0j?�{: not}.�>�,�*^��4es��g"�to�7*�,�E�e�� @ri�!:� x2�&�A02�:�v!'Rl�|ne(�f |buts"�|5�z!� ��� � � �)�sz2� A��d"���A� .`}�(2��.%�gv�by�S~I��;!�� �%(ex�q $dTyrixK$�"O>2_mn�rW� `T�T�3to� -�=]���!�QJ�, -aP easy Zn��p�7gR 1S � a 5�B�S�4n>a�-M8�xhe5�~�a��:@ � U��%�"��!�$\�[��$�A *q] mass"��f� enc� o�H$4 %I��i(<}'20 cano�'%��!�: \to �m U}\,\x)0pp/6$A�� L�p�A�  S �:)*� �&{x�yVw�Gx} oop.p�&.�o3 + o��hA!� �)�YfE�'.:� hoffmann}�6uss,;9��ardRQ JFg�Fr"#)dub�l�l�0� x}^2�\2i]C. p v 3Zղ�]4}�F1\xux\x- k\x ]"� � \p *p*p*4��j2�dalI�&& f.��+J>�J#2Bf*�� {4~v1i AGt�k g2��6(id�e RHS&f �)> ��-Y>�$^r4��k�)�)_>0aI�/_�����7�R�):5q>2 v.�>a z"�^dub"\!$ %%Noh[��rs���ue:�7)�$�Ay1}��NowUy.Ʉ>%�3n$fmaa/�e}1hrhz�gambaaz� fdu����Acan�efAdubb-[��-�_1-2� _2)^q�+0 %�.4��+4��4 =h#�VJ!T! N"�M"N!�!�Z2E*#Jv �f�#������ varia� add [�h �u� m��#�$_k�R���$ kp_kE�"�$l$q 0, Z)=�fA��#A�_ko ed (${�Otr� $ =1$)66������ f���\[� `\,(E�A}�+�A��$)^2 \,]&&=� mI�`\�S�[�%�%at)~,] ˹^$\,]A���\}+�`^m=6�\ Q^2"�T\\ &&9 7�- =�%F _k +5�����geq.�j^�.�j�elulu}�E�(�� 7n A}N9сe>�a�� 62�v.2�C" �E�BaVLo#! �m�]Cob� � � f��i� 4��)Z"lvalid ��u"t'� G $9�A�n(G{she��^~�a12�N2���� \leq�x1�$buenosaire�Qɒklm-�of-)-]`7b� 1�� Eq.g�9' Z : � &E.\ 6iq�t�)flu�!X�-7g>'d��>, �f0!��/g� ]�!{E���Q�2$��~ &s s���ř��� �f��!;N� a> antiB. �X�C/&�'R��.� �$be built b��n&n .8�.8��]n ��24N�4$Z$"� �ll.��l, 5uVar^3"�s � ��a �&�$b 6�9� . APd%�o*f�Jm at��4apai[R�+�Xilg����}+\zeta96\y�g �F��� of�C�@�*�chc06$�Z=\pm 1:p= . ��(�{S s (�-"� Rn� in literN=ne!ENaF� �/ wolf�"�th�a�1�8 @!`�9 n stra���}>�N�h2�.%�fD8�k�8F1�ef{I)k'�:u&OUNi�! i%�B!���} &8U@�ll�J!yJ�)�� chec�9ja=To�end�ire-4ta@i�0y  � ap1}^�_&B ! ]�A�"���"�m"��6 B` -2 &.G��\7ɵ��+ N2y22ae 2�2}t}s."� 2 One �"K?s�&�.a�� s S,�~nw1m��Ns5 �2d sub-F2hV!sum� Q��a*�o�=�2�� 2�) �DA` % 1�i�X��G ond)�� !�$ (� !`&�&(�X2 �*�X2.X2$). 6v0IC",0%��H� ��5� (6 A�7u A)$)�nJu�$[x}� ( l]=iZ _{kl�[W0_  �B Krona�r'n>lta��h��be1�d ultaneousa� =!l�4*��1Rb�P:(;�P,er J�A�� BVk'ap Ase ���� �XetheirQQ �%GD4#*�+�nyo *S way)E�/�t� inci,�ts.ɰ�&C2�@ v&�Z`uV��"�?����@ &G5$N$y�J9)�*d  $\xb=...,x_Nn_6��!rng >d�� @� �D��&I s $Te4n�Gj$�=&�H $U6�&g�Gl�� <I3!�" ay�g �9J (!Fa/0dCA&�6[%0@)F" �(0 )z�H*�%�7~.�H΅ a�I6-&< va&�5IՇ$  9� �umjanD��� i�T!�is�Je�6%Lq��Ey!c5U�i&:]�'$� �4 ��less:p- ! ,t'+�H  | ',t') =PZ&��V2"�3*KCy &�lyq onglʌup�7 +iIY��j�innU� ��EmEQx 3�cX�� ='��t'$��^H!I"� @' � fx M�. } # (G,)-�a $m\dovi$a�>TF�K��^���.":.� o�CmW_bl"���JX:�end*�Un�$h�$&���.AN��d��I�G"q[� �2�-���[Wc-�(=f_i(\xb)+\�� i(t)� =-\��$al_{x_i} U1,�$] @\, j(t') =2\,T_iF"_{ij} (t-t'N&���K c�� ce �X!2��u��& t(�K2�^�7Pmf��UAO�>�s4G�U"�8� ("S q=W� 7���QE"�5y�"P����mpleteN��9�[: [ ��"�<�$%z!�$� "��] a�1�+u�J $, b1D�!OwG� terme�K.��+o (eۮ7a�mZD/C heu~O�#y��@�(p65P$�$ dom��� $0P-X�96�G5 $Ah �1�Ls��rivgor�D?DJ� c"�(,���5�JH2~ �i�c� "Q*~�9!� m�S�J� .9�&�TAI^�� r � .ri�A]P New2�A�!��9IR�thJZb�?�* Fnr5w sicas�fore�98 . 1)��%"a�n*�a). a��aths.�cA�2son�uA%u�-.&� Ub3s  Fly�i�a�aO �ths, �_A��c^#X Gibb�1&K>5 4 (E#�ow `Q6noi�.�{z+"�$�T� !�D9M-�Xup�Ga�Iv(cl,gardiner}Z�9��S*�>$P��,t|\xb ��r0� sGIf�9e�!Fo*�a!^ES � 6xf2��ck&�!�!��al_t B� =-Si%�~\�՜�(x2��i�t e^2B��Bm�� t t'.���d1as"tߵ���Mu9r6d�)2�)=�-%�)""rod_{iuAN $ x_i-x'_i)� !�}>Au�`�Q�"m6.*� �U�F $\Sn�p�FQ� �6A�qwS $N$Bp U ���U��i�P"!10�� $�tch2��� s�`F"il=aZ.�" mjE�DJ,.� p2�!8a�0ga-N�O&` B�Iax $j$��na 9%�� Mv_{j}-[=�limH�e�% 0} \,�- yb\,�#y_j-x_j}��}E� yb,t7a�,t5�C .�.�>rey�n�oeK ed@c�W �&�6.���&�<E[�[ !ቅ�b �y dish1}�+,n�+.�y_jb�y_j2��%{��^x_j-y.Z^-\e=ZA �2�["% m�(A�� c�%"M�RNZ"�e�|at&u�A�=��%�� ��v_.N��.�BR�)��any� st?(ng Z$M�TC*as \=LB\v [���`�to ar��a�$ ���. &?4seVizr�,a8,lready in th��e overdamped limit, $\ep$ is assumed to be much larger than the characteristic relaxation time of the (real) momentum which is small inL>��. Therefore, we call (\ref{dish1},  �2}) coarse-grained velocities. It�0known that fo�2�Xbrownian motion almost u�trajectories are not smooth. This^connecte%0�Hchaotic influences -bath(s) ) randomize6real m%*a on !wP smaller times, and t w also9 son �`$v_{+,j}(\xb,t)\not =v_{-$�e differ�>5- :1 thus�r)�zesxdegree� abov! n-) ness. Re%�%|8would one take Io�I�hI_ chn:_% t). um |)Qtwill amount to applying defini!�s2H)%QYZAM to a-�er Uy|�n>-$B!w.c �Tbe equal to each other1kA/average�4. These pointExL discussed in detail PAppendix. \item HereA�an opera�,al procedureE&measur! �]1V�. Consid%�i;aensembl5�uH particlese�4 single memberm is?aX($N$ coupledH H For)D such6REQ �,es {\it i)}%[ coordinatf�D with index $j$ at:I[@ $t-\varepsilon$;`Fa�} all}�9 B[OFPQ� sameFN~�+.�e� peat!�t.[ manyeRs�rvarious6�ei� ��.�, ignoEFA�,results from) ׁ�! i��selec�eveA�3D(second step��rstruc%� Uu$\Sigma��$. Emploe�H���o�!r%'edly up� :k� :z�estimAg|SizbabilŐ< $P(y_j,t\pm\ep|��iu,then finally��culPN�e�2p via Eqs.~��>&. �$T1�y�:��B�!t ��Q>{ _j(x�)$ obt�| bym�!N $x_j$ (at $t$)E  irrespAve}A�y��ndeed�2����ed glob!/ITif!Dre�P�observ�y$in possess��of�QB�,Gy have�Ecommunic!�6�in or�o��a� to!�I�>) . Intrast,1t=Fisɪ8ed exclusively ��-1aAcB�:�Dis�Cŏ b���F more�Ks Al�J�s!�on d artashir}�c8end{enumerate} � U�-TI�i}(x,Aa�-H is straightforwardilu�(�followABthb(things: rel�� \BEA Pi�+eIy�=\delt�-\yb)D\sum_i\left[ -f_i(\�[$al_{x_i}\,>9 T_i\,&^2(+6b \r�], \EEA � ��m�y�$2}), Bayes� mulaI� � integ�� ! r, fri�� hsm accelef  sub� {Uncer� ty"r )�theiriW pret� .}��ma} V=exist��!U��zumU\ s bu��,so in physicRw �u���on �vur}. A!6$e very sub� of s�A� T!�ey ar�fouE�i�a�7 reasons, A� ore ��ly�� sepa)8eDime-scales: though!&Hl classa7&� involv�Ae$B�-�zo�  sharp� y�)��a [ microscop��\,Zy(9f) *�]` a�� does%�+a��-�լ�can���Z� �g.� qI,a� sbelowA��law��\�V��;>�FPa{ʅu: >�!7��U�i�les�>^$$ pass via=� vt $\xb$. O�$�3"<���� by itself�ub� v dded �pro�y (we� )٨$a�o !B@of��ize�e�$�^��a$�xus, bothŌ>�.�!� �K!�qB�2�!� ��_s as fun��8 )configuy��J�`${\bf x}=(x_1,\cdots, x_Nz����cis b e�4s���Uext $($Mwagos_ oM�15�>o�M�Mifa�ly, let�H focu�!;�on dis��1 �� \ub;�of� xb � ...,�\quad {� and} \ub=(u_1&u_N2] Y= t) {j=1}^N� ,u_j-&� \,H`dah� ��6�*9by6� 4. One has aftn���Q� �$ � v toto���u_j\r = �  \d,� xb\, �, f�� inE= 6� F =0.S �gog�$\,(\,x_k-\�le x_k �\,)!Y� � =2�$Et)��\�Ne) F�(V�:�j�� �_{kj}.}�4 of $F�=�s,� u�  (6 )�K.� gene�d��a0*=  1 . S~ŋh %�)ɇ ��n c+ � F`� �s" �tits own*� �C� y &r?  � t���s�act��tF�s. A8to>�eT �Pd Cauchy-Schwartz ine�O,one deduces:uSaFE�V\,)^2` )A�3b�23\geq |M)vkbVm$|^2 =T^2_j]���q�� -\ implb an uJC  .;."-�&�   3 B�s�  Obv�ly� � c*� ! x� S6u "� (�sho� not)� ny2�E�� E�a'�. �"Y Di~io5  Lɥ� q �IQ�:v� al mea�-$��.\�i� sq})Mcomparu@ stM�9*� alnO dub1TThe lat�_S� two ident�YX 4s $\E(\,\hrho(�j)$ �)�� first ()=aahI$hat{x}$ ($ p}$}t�combine!dt�jlA)P- �� ��isper!�s. &d!�fr �+"=)m P!o%�isturbp -�m�!um�n ��gYOI�K vic& rsa})��in�� �mctm#!i,ozawa}�$B'h%�3 �l \DP%T x}^2��N%p.%clearlDfer �s"t �em�don!� Q�t5�s, ravA�multane�� H-K�- a�5Z fB�We. B rU argu� ?explicit�Lexamp� �"a� f�!�J|. *�!thi, e.|+ � iA� Eq.~IMe�EH�c�cutivu��!�sam.�a�"�Z] *9"l�l&�!&�#zesI�:�t!�� ��u�tuP �;IE�6~�\F-ich (#$Heisenberg�re� _)!��l�eD�%fully}2�!;$2x�%���te;  Footn�8 get}��s� �a{By&ent��!�.} &o#now�H��"P,. An analog!.CM�Kro�E�A�!�wa�C�*eH��e Zd��par!�)��\bW �� )^�1N�o6zGiS�ɪZ ix����1 d�B"� s \f-�{W�n�$win2 $���(not, e.g., <. >gM��� ��v'ies�.��m� becaMd&�U�� :�� �former%[lea�(a%Otrivial ��1�E� ?epise���!8m� �"�!necess��@ee�-&E2|}E ?1,jx_2,u_2)&� (lambda\, {\�P}( �P_1�u_1 *� _2( I , \q�>Ggeq 0, �wBv=1"Omar- �&�Iir�zee:�$PJ��N�$���'!�basic pr��Am���Q/I#>�y� �'��res�e�$�a\ plet-arbitrar�d� �AIs�Jym*�. :� (naive)*BK � in �e��cla�;anyP)�5x admissibl��f)�a|)X� N� �-� Bh on�similarm and"�c(�(!}� \1�Dm"2� , is\tpo� t+2sam� J)s�V��� choose�s`)e�$xM[u$� �T dimen%a� $sqrt{T}$ (� w"��in \�qu�oo�S���� tant�N�*�0,s@$T_1=T_2=T$ again�e�.�W����wX rix)K� ,�$(buenosaires!�� �|wriR*�N� Q� as��"�@ u_1*�+>x2�h2T��JM2vM.M �  ,� d%��dod:Z�+ 26�+�� 4 �- :1< 4��s� ufficienh �$�". i�� ��s -�lapas})%�E.be ob�-ns�� �Es� &�11"5 �$u_1+\zeta :�^�&N,:x>:= ��$jm�\�,�&���1 valuO\pm 1$.t &�Gauss�02� "�nJ�s�,utkonos} ItY(!eus� tokX� p�- odel)�w)6�-"m , �a�L01�c� pts�0be visualized�= studi� ��.JA harmo�l�t!R�p)A/*ll pot�al )gyi2!1��#ax^2_1�#+�#2 gx_1ka*AXpafa-�a>0-�g$2� �9�o�i"�$"�s &� 6�positiv� f $�5�* 4 $g^2>"2@26\>D, ��')\equiv f�s�/_{11}(t) �2W\ 62(2(B`i�� seca3we�RAZat&�'Bx_�-:=9=0"�Y�L �.t�ţ�;=Al marg 02ms��+�v�6rt�!uj} PS.;@(UJ -Iy x_j^��1.jj!C}YG� j=1,2�� easi� way��! $G)�$�-�)t�� '%��{to look}�N  Lz vin N�(1 At})��!*���Mpo}:�$lacot} \do#%�+a)���!�=\eta&u //��(%UtaU;ichѝ�conven�-L ten ;erm���v7o�4$r_-=�-x_2)/2%B.cF 7&&P $r_+5+ 5Q�r-pm!� =-(a$g)r_\pm(t)ͬŸ(5 ..��`n>ykboa} ] =e^{rt} 02tz_0^Ms\,.0s} �-s� �-s)�+�A *�2y*���) �e�!wZ�*q (:�y"��- e �4ѝ,�2ly,*1 akht�+1]�+TW y5 x_1-12}!�} {1} 22} )^2_+}�u_2fc11T :_8x_1�c.R� i� dodo�rH3\�1�%��I �I = ��T2 (=9+ 11}- 2_ 2}�+�v222U+ 2� X <4T" dardA�uerqre�4is go�7�=�D1}=T22}$~*��<�9���satisf� J� &�` *L I5i�(it� A��aC� .}:�urunduk}9v}.�0 �12}22 " "<2!0e���!&A�6�.r=0J%� minimal" �K)1}+T^2/~ 1}$  2#�� just)f��$2� W!c� �"TB2}>� \h m25=)%�� =1�R� =- whil�� �/. Vt<0$�B��� � wa!,V~p"p=1$. W�seQget�!Fd&d 5��u�a~T)^2<5u2}^2+2T||u2konkou5D s)�OV�E�*�2]AJ symmetricZ*�(1�i :nd%p Y�i�#��EKis �1>/lu to $� nd $2�Ai �5e. &1)pD ww��ђe� eiG� ed o�>t6<"�(ly strongly�Y J�25 largx2� its upper�6}1}$.`�F��$ot�P $TR60Y)f�7S�:no��.�"0�IAl C.� �.*�.�%~ex�-A]2�1: fluc�ng0/orV) z{ "-"check-}mt w)I�A�ionary (h librium)�&�Y6 �8�?$stablished� long� L&!&� &Fm(s�)�ei@| �}4.�, $a}{a^2-g^2"�25��g'�RAq 3m�� q;i"b Qa!�(�� )& tak!>E3 $tA�\d9A/"�via)=�2GACIy�5~.� Gibb�:�*L*p�9exp[-&�/T]�N; &� *9C{ka� �|t2Z�>aEq�m�$a>|g|$�1 ome ; dema�31�a�(�$. �=�4$Ku�2�,j be e4$a(2+a)>(a-1)^7 l<"�"�$a�^�R21eE. f� � |g|>-1+\�1+ \YTus���is�enough, &r!=�6?�!9m�E2& 24&En& I(wo�z4���\"um case�  ystem"Q��d�A��5? '\I��>��! d�%actt#a�n!_E!�*ested&�)��_�"��&� /wshow now�Return �/9 �A]!.��a�DTe�@!) %�$tQ �3H5+�a�ws&� To avoid"n misunder��6C"3G%@��� �+s�*f�wo.3AlXG! � a�� .��@�/, DH{:Fn�4�H�1them. }�1H.*�+^) '7�,~"� k2at"�"T}{a}(1- %)�EBBE0�J�W�5�&� ��� ) (A�fn A�"�) �b)H,�B2bU�6E� ent. J Q@CI�$*`� t)$ gradu59.appearsm\ mean�%�J��an&�nA�th*h;�-e�b�H�alid. C�',AJu�26�|V)s-For���*� Y��;�l� ]�&� , i.e.,�%monbaiB��� f�<�&&q,t�1�vt)�"$ (af�A6 our[c`1 fter �=)�1� howev)�t�h!7%^Ŧ9  we 7ll �!l�D\%?�Y�U�,A�least Y� A� Q�l�! !,��G& "� ; A?a t cuWHly0E'�s�(=� �)Z . .�Ju)mfDQXY%� $ay) "�<*h �"�-�(�V:a�9l, ��inste%%.M,�@&~< c99es lin�*Ae�:}��?�0)+2Tt�E"~ -�"� � r�"c� e.%( read*l0d,geliogabal} &[1}(0)-Tw|<��} �020|�Ev� $&AI��!E$E.0 x|>�t$,o ad f��.�(0)�}}{2T17 Our2�lu?# ��!�U�2��#*%x� -&3 d��or haa� ed �� �!�Ks{'"O  atMmt n,"a�always|,deMm?�.�,%de��iՁmay�F fac��ac#N� G3i�" �:  \�${Local>�&i.� a�H�- 8#& III}] �;.V<$ȡ�'6B v"�)m�J�R��!��d �'OO�Kx��2 �����ʡ{) � 5�U!Le2�"t' Ell%)�determi>S��.w�1��(t�"�K �+�/�  �Z$t$&�*�=�H1$�\�.�� �`��l� : valsA�Ar �w�6�.������e ��aER�N.;O&�'j���\F6��\nu�B1�B1a�\,{`:li^7Iy_1&7I'1}"7IyHFep|AAt l�papakantuE!,"�?.!=.& �+ai��0a�s � P�O&�Q9��)c�s�Cq�q6yɽ�1��.j�? 6qga�%muU�=%S-9Q-+a��!�$ ify0 er 1=;  orm�A�!;� �0 er 2o n �,ff�/�M sum}U J�I�T#@krOQ�#=d6=�t�aeca� � =m_ being fixw Each� uJ$xCdue�Cm ��MtPmetY2 2,tMfcn��= �i�M� ga2}R�L'v2xa�-�-k-�X,A�*$7F�Q�.�U�)$�U*��Its�L��J @!� Baye�u�M*�&}%g�!{4�uZy3�0$\B���t8'V%0�F�6)$M@hA���2*�>� B� 3}I�BunconstOY2�of^�-�@�in-.�� be illuY�A� helpA�w&0fNof2{theor�Ncer-U ree �@ vari�2$s $A,B,C$:�um_CP(CEC A|BCY�H|B=P"� W�9�dop�"��i��$ $\tilde{u��0E�u(��)�O> $�+is Y�1u�nan�-%��->5k1(�2EH).ity, v-Aq!F4 !E( oscillatorB�Yge�R>�G\� �# x_1}2� 8&2"*  (t)}" J7ly �Is�^ &\ "� q"1}�Pc�/II��6� � %I�"s,�d*�Y past (!D�`>p+"R "�[d1�by exterayfields �6*���/�) � (apTnt� fals�Ln)�ity). O8Com R02�msf �!m:J, e26W>�A�!�R�UP"B''"�$x4�,cN��on�ne � �B�Y(y�歆�� :m9C x_j,e)F O��, N!�b�75�w uC"�� !H bed e�A ��')�5� � barbB-.�Bf SSmX4"HIf� a7&� ug4�$�(.� �A�"9R�6E �!51,��, 2)=N5�B�B�/mu�$���D\, �4>)2-)|5)~th[�~ �&�t�6ly: No2p occur�-�lyi �s.Kc*� b� on6�?-�+3&uy4A ie.E�4j��� �3 &:N6��X;tsYt�93@b�+�]izfW�]=< # �inuous-��v2k,a6�*2F�1typ�-ca�?*�A*W=�A�<"�(fo M'� iesE���Bts<�m�pl�R reFPu� y V :|OW=+=� ~_q� ^7ly|6� !}!w� �N�3ms17V)M9(QV'y="9"�&�C�.�*m=5�i�U""$!h^�IZS?rolha �AmR !�L play80?M�.+&[!. z\�i� a,5.�~ N -qklm}) �5�1 58p�E��< u,.2 \,B_k$]�um p�-�a�Q;0 ($k=1,2$). TKis en}R��!k?A�J�@1�O$\1�+ $\2$vL>�8�9})�6� \?,�DV�u W ns?@9QDQ�N ne��3�."��U� pairu<� 5V�q 5_bM5W�sa�4 E] �(�f�?M�[-�6a A ���F� =m�h \d}{\d t}M$| "*PC#@���eE� intu� n6fof :�U.�� a.Jes�(� '' ~& ̓=@G s a: pd. AU\c\A�Am -2t 0) =X-t.� �A�(f.b1�!��P� A6�������� -�A� �>��%QHs &@ by (L-.�} b) Q#� |\psi�1c, psi|i��$(R*) .=="N&se!!to 2�fcS[7�1!G did #-aDk Q�&�[ct.�� igenX�5)���#|du� ��A�ity $[�, 0)�\t =0$|���!=T�� �(T�0�d �E%] d^3(t).D�[t 3:+02+N>W elabo�L *�=�8ret-@~Esee�Twork}�> un_ U�,�< �x}�j pA�!�)��o� s%y�\�be tech78modified1�%�!F�WfF��An7>R^>�#?�X&;%�.? ^�.n$\approx 0 FI �䵩2j�Zbou��� �IV��iQdoA�RB��x�:U;V/im� B"S�|2�AJ6 �"�) *�$ �>�$�V�$ nt" IN�ABR�����2�m,"�2�[.:U�M�x}1! Q�_2"}e�{y (p8@"�0p5%x�ub2%+� �. Q ^u6R %l�a�Ha� % r�go� 6R�s *�UQG:�� �eRpA�oge�R� bjh+oKHCQ�B�  q�i��s��(2� exper�@t"�"� �ge+m�� eptuwf]m* Q�6�!�J�iQ^s��=�of}�Q"� p�Z 0 2|.(� )g��$Ii�a'y exz B!�^�Aa�a!X&�#�iP.I�E�ERbA�llHo��:� Y�#r�/�"ng5U]I� A or���!a�ms a � ��I�.r"�6�K�Jv`[*y-:�v"��[� �h`a�es,/�-^ y"*OW�T$.\s 1in � S" �purF$)r6�6�*�%��)bed�T.&!\.�3ati[- ���2��!��=n:�in �(*�E��( ��Cc�Eu%�a�{!-Le� cp"�0�"�X<f Ref.~�] spr}Ar�,�es�g�E� b��%cA�C] optics��end. �{Possi���)��al!X�� &�Aex�@ Xopl@a����+5erX0<X!b^goA��3<�ёof��1)\ : si!z M's%C�1 1828, v�n�� � _ $ ro�A�� ���nM"�*�IB handiI";s ed�) MR2�5 : a�>�p"�c  a�-olZa�I5WmT*\A �%a�@B�&�Kih�/2M^j x VFe�b�+s"gCs"�r kick�8� A�� � �3y ���,*A��r�GU%:.��4�CN�-*g pe�aY0@B5�A�2�)h +A"�u�uma yy0, "T`es�TLqA{#u lof ma"~`9# o. JM�ty�`2A5X 55 60u@ s: p�;! l!�( wat�m�n�5iU@ly!�enZ�z�I , 10^{-3}$ cm�3�)#1er lengt�.�L �E�eeeU re�ke�Jq.fep#9� �Re1}���O�>�Ccir%�a��"er)�elast�7alleAB!����p����arsgto�d HpD* a_?of 120 �5 a diam%%8 cm.H!8(!d^J^DaA�tery-po�/d!�oM;�)Smovj 'x�(due�8�colli#( ��� �@ A�-~m6�ise��s�.AP@�_50  /m$^2$) m�G�":�A�Y�@ ��62M�a w�K-p76.�-g2-b5` 4 cm!y 1goK`RB�� prim�6purposEY[�,to8Hya:yQ&� 2�/ >�!� j��^�! �, iEmv/*!sp�-� ��Bm��Am*�% &qF�!� end-to-en�R.LX�ch�in a �a�y�)�I�8�_!::p (Wc-�2 ing)1� walk� ` }�B�C as s�w!|t4 #72< a�s/�X #�sonFp>hng�a r,��5�A��5�4� fi � ZY�b.� ,"�*yl%� gred�C%�� phen�Y�/re8+E^�. pedagogi�*�q�� .9ť��20of a child togQe]BuuyB,& �0}: a���sp���11 cm� uai�&�<h�[� rubberx8by+t_z�:M 3 cm��surface.�V��� e� ro�+� off-axiZs�=c�W�i�activ$�� plac���Yht b, a.��w�rD}E�9. Joi�A��{ �m�t��4�o �f�W�/�a%���S m;fa�;�leC"aT>~� g+K:vV->� .v�*� �(}J-�2}�����-�(ay� �i�].5V_r�`ng stochE6ņ�,n upflowG gas �� sp.280 cm/caie�Qs :O !�\ul3*rg#<%Y�i3am Yp "$ReynoO#ta&$� $40) � tudy�esed� �� -v$ent>eL ��!cap�Ld by !��a-e��tC!_5&� "�Le�}o1eɹ�RKNV"aA��N&T"�ii�%/�2thorough� heck� d{ M5p� ves. �m \I!��2�.w!��AUC,!�w'�n"�Wto go!�� �;�m()b dea=j_ 2�H)-qeb� )[]j/tream|= o adg*�%aq1i V "Co� ;W�ve��h5e.�ofV":�=!�� �+��:< .t  v"i"�5�"L M�\��ApeR<2�1�l��Ei�? ]lyOa�#da a�\�j!��2%|a��gjeFeR^n|Yns�O�.?�w(in��/>%p�)��� �h$2W�;e �*�?U+�3t�k�#� y �' law�[A�!�&&!:���u�7Uo�Y ion:ev:��a �N�tis%l f�R� =n b�b�@�%�9y�aildQ �H�[e ide w"�o #ši�, ���?i�'�Z!+�>��Gh�p%�a�li!�vp!��: alreada�4 good textbook�N �p�landau,m�Y!#(b�<<&�/Tin�#exF��! lve�ɍY)2mer,kur�, ,at,shuaO�"�9M=�2!(s�f)�/I-�<�)xa�u�>.�D� !��Cl:��nyGC�kMor v,�"$.�edDAs� �!L� I�umIa!.gk.S�3�;*SNo%.*�:F�._Ia�b�b�' {�* <y &p sett�D�]=�m�4L us�Oo 9"m�pAa�s (N�# dQ�ojN�e� UR��I\� oR!�F'�.!prTa-KR66fB�� /N�8 ���U�E��'c�W)s� �.c�ded)2�s6�'!�f]&�' . Ag� f �%�:�,�2��0�pa�ER�!a�H�em:1�52i}jT est,�G �ݡ�,�\-.�V| ��!o aB�c��.�m�jbe"j>kep� iw�evG (m6walks)2�xU ��.�odernN�!�_lloids�~�o}�po�s�� grossBM�Őtrans/"n !m D sL\�a DNA�m���2�@`�jn-;a� � ���s) � �]"2rgu"��p�:y6�U 1�6 J�4asi�0o�8M�22a��Ɉ{��.�tN��c 5vil6lh�?:\ac�H ledg��s A.E�&Xthanks E. MamasakhlisovEu \�Z�j !m C� *F{� arcd6 gram�y�Stich%�voor F��eel O;E zoek�^ M�ie (FOM,�ncQ| s7�p�G NederX se Organil.e eWetensch�O lijkh(NWO))! �-thebibn?$raphy}{99}ibN,{bohr�B} N. BohRAniC�xWorks}, �7 J. Kalck�| North-Hol�, Amst���, 1985), Vol. 6, pp. 316--330, 37 77�\�Dsch} F. Schl\"ogl,l Phys. Ch�� Soli�u�u8 49}, 679 (1988�Mr�u$feld} L. R�bF Ergodic�F� }, P��eK�� he Ia}ne-al�oo��\$``Enrico F�P.�hDdirola (Academic PgC$, New York!@616�!cau}L.D.�dau� 4E.M. Lifshitz, �S� o �,, I}, (Perga hr Oxfordo7>B$isken}H. R [�868]Eq/k}, Sp[ er-VA�gX841入( A.Yu. Grosk 0A.R. Khokhlov l.� �a� M��7!�(Ameri�'Institut� 4%W-1W94w}� E. N)� }d$F.O ons}, (Pr��ton Uni11�%MAB �5iM. Baubl%�Jr.%og� orQ�E�80}, 232M�;%�� v. A #5�� 1677$9`8P. Garbaczewski%L$J. Vigier,%6D 46}, 4634D2�(G. Kaniadak�0)7au4307}, 172 (2001yh timoec,de la Pe\~na�AA�Cetto-QA:1UDice:�In l��iS"�  Elec{_A� Kluw� Dordrecht!h96� T. H��yer.9D)929�096� 84);i(ibid.},N1�290 13R�18U238Um?,L.S.F. OlavoN~6!�052109%O0�9O,feynman}R. F -L HeO-J1FM� Path!P��lE�(McGraw-Hill66E;u��}L�BB�n[��.AJA.y,bf 54}, 883 �r%wDT` AaÁ�ika�J���.D45}, 90IN4);�)�)�4g 2471%#!}��6$3}, 78)FE�%%���}��~ Rev�4!�6I 3% <epr}A. EgG8in, B. Podolsky%�N.�P, %%�\�peres%%P �it5�TH<:qG�')�Method%�I� �2�Usherse3AIk0blokh} D.I. B �� ev, )Ja� PhilosophO�BSaoReidel,.o9686iU1FA!r Mod.-���42}, 35i4E��=�} R.G�� wton6� B!�102��6C baliJB R. B NA5a�101 A92� home!8 HJ��M.A.B�i�N�Sp �21��2e�Q�8espagnat}B. D'E -�VeiiR� ty�\DAddison-Wesley, MA%�E�T�& i} W�` de Muynck SF�s��*B��H��ir#VA�-ach!�n_��� itano}W.N� ano�Ne[).y A� bf 4!u355�w6��&< R.J.C. Spreeuw, �M; D2!�361�96�ita�  A� tti, Bramb\>, MAchOnd L.��Lugiato2 Lett-�9�c 0936��.�pop}D.% i/ S�*pescu2S��6��03232�؅�5Ski}K.�@irkpa�Yk, %�- �- 1��19��3);e<-ph/0106072. %%"%�$al" behavi�!*�(.��ocohen}O� hen,[310017[C"' Tele�Eu� � es[4kruger}T. Kr\" .^404091^E��t.]IcwD !�Allah1�yan, }�!�Tha$(Nieuwenhuiz�Eur��s6Q�45ɖA�4%%%Curie-Weiss��� � .n�ls�;� hoffmanD F�R�(S. TakeuchiR+A�032103�DYur} I#ny�:ZQ#�b13�c8e&5EeL.�)� na-Aue0 h�.� Pj iA�r bf 39 65ar72� ,S. De Falco,� De MAnoQ Siena2�WM�� 1 �8VGolin,V52A�27 3:olf1 Sim�1 ��|.t8T726%Q0.3$9909044. R� Wer�%A@MA?Wolf,)�e`009118. jaynesA J &e�h Maximum E� py Fo5Uism}, P by R� Dfo M. T�i s, (CITb 1i } A{ M. Ozawat ��}29!�1�2.�0107001.Q wign}� viewX? e/�%O'ConnG�M.O�u܄E.P. W<)�R��bf 10!�1��1� . Hai-Wo�%Lee �F825�4� �܊ S.-Ki A]it�v�"! ��World S�t9, , SingapoΟ�2 ork}�cERW!!(-mat/040869�&!�� �AS"|]�Nof}:E(eX %%%=stIrum.2�} orem2f cl} UllersmMica�32} 2%: 66);D ( 56; 74; 90$!�0Caldeira, A.J�$ggett, Ann�\ O1a� 374,�8�*�;ga-her} C.W� -�Ŏum Noise&(J.912��era�Ll*�nd J.We�o6��kJ20l7��<<�F. Cug1 dolo�zKZ%�L. Pe!�,ED  E) 5��389� 972��} N(B� M� 5580!V 98);NrŤ267e�6� atN�Th.�Q:�& �6�645^ 96b�ul�,!�B!� veau� z `icq�3� 713 B6�cy}Wc RI�o  Saville)�W.Rzowalt� � �oidal D"�Ge�(Cambrigde UB� dge[ � ]�e1} J�r� D.ZSisd�6 � 13.,  JaI FN� ��107��!�%E"1�sU �m�.�,0} M. ZeilikQZT!@MV3t 23�9� %%MB+4ing Energy Out�"in�:r2` 2} R��Ojh�^"� N��eI�42i52> 4a  %%AMieln�.� � bf 2�1118 6D2>� T%�'x &H#},Ois� {t�s�dl�O�fk+ s. F��+��zyFy$��L�AJ5DB�0.�i!(� �#�$*�B�aw��R �f�@t]�s6U/���eerE�=���W�2�a.&��n�Zselve�[5+�answe�&eI,�"gcr�ыe6�um�!�,r�i�!e;Ron*� ���s&�webeF($�Don *>!g& .�qK $�{!��! $p"�;"���2�A�)2A�2�,-Kramers-Kle*�q �#�:J\`al_t{G=�ep}{m} _x + _p (�Bgamma0p+V'(x)+  T,)@,�ItT1l�T$m$�<K@V(x�rre �(,B�|�rpo�w,.e�!i�S�(\ ��Kt2}&z�x,p�R',p',t'�` t�{t'�`�60"Ơ x-x'&;K p-p'+Km*�"�G{%*ؒtoa2$(��t��$t'$ ,p2$�w�gm c�!�+"+$B�/) m\dnrx}=-ax-)s�r x}+\eta(t1 !��, �C=&]��sl<''2 [ T~Lt-!dT�\t52�V$6�$A�a��c�%�a��$1g�om �w? t�Oisa�Apd�V��2�Z�"% � u++ 7 t1},�;t2=^H)fMp�70A�4T+ADt)&&=6;Xsil�h+.u�y\s�-x8X sil}tX�' P}(yw�x,t.Ss-�w�^d p�p'��Nblpna,5Nu6���&=-0V�k(y-x)�e}�, ~�u,�7yM:x-y� ] \p�O�NM4�a�[Qi��:�C#-��"H'��aWppld_(�W,� vi�2Aj*�&was6��CsQ=@{ ( Likewise, MIA9-�9x-yE9}�T y,t-lZ!q.���%�Y.aI�Y�XyE+uA/)�6U�A9}{5��}A6�-�>KV? (yA� ) }{S TE�>ex�eMe=%�m�..�20a���qKf1W� EX-�2@hA h$�c��1+��?i��.%B7\^Now i�0r�In�V�D&���Y� F:=1ua�{Ht)4j� rev��au�<"  �)RP�.?4'ul-��< _� 2T v0 � PAp,2�W,2� $�3u�/m�E M �,� �"k;� !�relevanF�f.rv t� 9R!ajp! �,ZyZ� TQ��O = itO(.^Ht!I"� \ > ��M�F� A6���ko Aex^� I &03 "� ��� �Xq�o���eI�:� � l.� L.3 ]\tau_p _m}{{aA�1 =~7x 7 4{7r=u�g�++*:.8 p\llxx, �hif�2�Jly.h \gg $v  �" dada IgeuTack�?9uxGB�w�B�9� � 9  �Z�S�:Q*�2= Ţ}"(�d8�>a�)�� =!��|h$M�e�q:ly� Nt1kWrE !��0v!b Lang��f 5})�(>�AlC3 |��Fvia La�8�*t0�|)>�g t7} �(=x(0)g(t) +�,1� (0)f(.�}m}{t}�P' f�   (� ��M� 77}/q 4e^{-\omega_2t}Pm 1t}}{ 2A�4au� ^2}}\,\Zight �&q�Y&�!�><&pua (0)=!�&�OMt.�b+�s�I:08+%p�;A�in&�.O,h a vere0�Q+ $�,de�6� &�� ף�Q�7��� �� }/-� ."�.`v"0 ���down aGj�� y,s;@ Q%�d}����-�F�%�[ A��(y^2+A_{22}x�y2}xy \%�&8�ezi�Xg�} d�\s��(t` s,s&j^(s,X\Q0 Ea&�t1} &  2}\\2 22�nd 2 � )A�fU� & t)��t�x �i=l 1}{~I�F� TF & h_�\\ ..�sRr`�nd5gand"��*� "� 2A����A R x(s)�� MG"�}{m^2��s� �T_1�,_2\, f(s-t_2�1] t_1vUh� min}%2�\'P'+|s-t|�:�K1"\ U�:���d y\,y*y,s�"�a ��BC>� = -x�I�} 1}}==VPE ������kee�A] $ �n �e � �mobF="U� � b����1{.Mi8�I2, � -1i ),a96� F�B{j��7w{ �d mob�!_ � � il�0$6� $t$:,�e�>0$. I�_7eNCGs�� q7��h] t�>,M_ x\ep6�)y[�dqF'�ot{f}^2D-f� � �]+I�O� p^2){ go � ��!to!�a� edi���sjn� � ��)ɰ*) �si�5�iZ d}QD2 less��G$4am/.�y7Z)aq�E�**�c ll 1 ��Y��h�sitU<*�B <�� [* .�t�� � �ef1]�Lw\�" 2�es*}^� \,� rox ��l om_1ll  F� aVa�(<2;"�z� if� egin�*�;d��oZ 1�g 1�s\N�h � ����5I.��)2kabt*m����=T^ �<(*� 2p2� 2(t+s"�� a�� coincidesU*�� @g" �A�]�V� "� �&P�d $s=t� z�N���M1��)� &�e)#))�eJ�m��jsʢbe�C stoo"r�� � ITU�I� �dd})|�; geiex7?a��U �s��"ߩ3aX �3M��]�B � shun��a/xk , if� � �6$N=1$ (�VA>B�), $f(x)��*$USe �u�ce diT!�["i$ stanA%�-�j,t:ni?x*Q�� ]$ (� .� "���� docu�6*Random"�i2�o;�fBh�BL&�q�$!�sg �"�!B���1BEN9!�or $t>J�N5Yki � �PIn �&AV3fa�\!�A think�7"�S"Si3(Gcle&�A�qO�S<6!k �D�%f� O,�b�Bf�r* y by�a�7�U2~ityY.& ���&1Nt�\�v]%ll!2~9�]�i$x_2$ �!I)v��� b�ptvl_sg�� wl|gA�,u #x�m� ��5'@>E"c�ion!,�"8�!p(d�c�!$1E�2)�0/�9ul�D>�N ��g2�1\,ݜu#16�9{s�A�)!��ba0!i�9r9$�-.�lx>�l\� �Z ^:a�X�6Xf� Mr���p H|��{�o�  >� ^�!�>�muf�m _7n&� \bar{a}_j�q\��jj?} +2T 1 2#in<��s)}"� 3Go$s \, a_j(s:mo-iA��k:�m~t �_q� 2.�-0��I�b���fNow�,EU�N�F��0��$ �A�6�rE D� A��)�one)  i�a�ec $I�$ exer � ="�  4 & �# �aQTK Q��6��.*522}"͘^{-��"���parIM�� B \Aj �3m;�t}| 70"� 70) N��[ 1 2T6j0)}6� e^��s)+��.��-%RR�ZR2 ReV��¥t� �+���I�$s a ``falc�n�f'';.��voS�oAw�6��P |� ž�1� �K:I�=l�Y#�1 �^�1Put +e1�mOb"�_� a�)]w be�]IA� negl�ng��"Ps.�Y q��: (EMERGENCE}   Step�C12� k/is� fR2(ifornia Jou�Uof.u<0;026): 241-245.LEmergkR� �h!� kind6ng�9r�Lem!�b:Jree�eJr0:� ' ]e*��i�_.H<met@EU3l�cuU"R.�?Lh�E2<otr�-� sserP �� cos�Cy���EIanZC �V4no law could b6v;0]6�,.�w� w*p c� ,a "shift," a2v�gMm o� "�* �s%1j16so�� M trad"+ � cr�va�0�bl:� ucce%n� �WmZ��&&,2-al2�rm�#rdlia�eQhz-c�A2>cu�Wiv�!ng�)�i1 c�f69�%0s�G��ne ��%5Ia��/s,2B-`>HXadr �o �z� h6@Y�i,_ve�Ue}p;\s {ar6E� A�a��ung9�Z�M�E�Aci�Rt2;"�RKadmi/1~V-�c_�O i6��eZd Aw&�zi��(( legitimacy2�[Ta+:]segf��eqT!Ussu�.whe�2E$2�0�� Q!��&M�t%g�baI`^6r�A -SLnv�"J��pro� ons:6W 1�� v&vR exisԆ5,^\ t�2� !djץU�� ; 2Bb mark� aazinguish�s!rvel�%o{a�Q�� �-ft3 t�U��� to dL&@ ��}hig���� �3lo3Hperhap$Tso�o4AY�) RzvYuA�TMa �: !�e�.�m�A`I�9�2�=�A|i ��e��ro�ia�T0;6FE���� s�2%�third.�i%2E /ŜA�U��:FcbW2E�:W�6�� �p��A:?WiI wEnopwrI��"��}6 i6��UAM a dilemmaRZ&�alleg���bq�~�(�2�a[`�'epio {UaliX�`= likoyzXal:u��Vh:@IU$)2�w��<holesale6�ism>>.B ly un�Ns�o��I f5O!4��ɞ� 6�� ޘ� ssum�Y�5��Ib e�*[Eto2Z3^=gRpBMt�n"+2F�m�} veloJ]zcQ7`smeA��� cie6P�ir �'0ndant psycho-�Xl zUsmsac2�2":�*lexh�O��FM� �RvA�? w61%EUa�!0�A!����I�B�.��N>/�jA]EV�2� �l���E� sens�,2m2Ey'� Alexa�Q's�k� �.� �:�j%A� " y"a�tFgu�|����l6Mmad��]|� D�.�Ilaw!;2�  vity. Bea�embigu `$d,�V fin6L� �T�yp ha�!��of(2��-- � A+�  E92@t�Q�]92�3inx��pN�==�Slpably+2E½X�H5��so`)k2C�%X�mus�Hst)Ŝ--�\e"�ce�6W %S6� :�A=a��spe��2;q�, ��no6� �.*P;xTs")*"� affa��:$�a~o �v�aat `!C+,�l26A Fb� ��(�:�mQHn��I2Dmaie)�RO4��a�GA�!: ��U �� hier�U%��5�aza"2�eelade�of �"�]mis61b�{�� �aQ"� � But: #xc!�� v�� �m�Vr� :Un allVK>� !!f!�b ��59h.ьMr2Ha H� BA9��Y��!jfou6O var_�q, =w� twt� |%� a�d 6}c[8Ta( EQ�gi�r���!d C���2�  a ne�s�5�ym(�Y!5b�R�� ��2�b.މ#n&eW5 �1-VO;�g>�V`��!C��c�A�% B,} 2�theq"�Ul5a�"z8 s um�o%I2C����� �voreMc��[!� jE���iL Bpnew2�Yf���!�.�C-)*e�2Eau�� $! �2�!04dla6��2an f1 (U�t)�r� f2:a6V{urs tUgn�l! BZu�(>[A#t �ce.o&�n�z��6��.�ny���6C-�f16V� Pac�t�J�hip= 92Et)!�f2 \; if n q^b2Bg"�. n��lKRf3�~b)� 2E�!�A�woy-�u!�A<��2= intc:��Yg.]�6An6mmus�"��]Jm�!�6 A�va�aE�0#�ew1�T !2�qR��9�"- �#�H*H2E�!ȅ�mn'�h 6��n' ���Eee6Z.# �jL9&re�5:��p!{o"+ 2�of� �"  ee. .��� ��΅�2Gi� ded=�0 �r��<~2G=2Nk;��drop {32D���,iro�.c�a6nel�d��&i:�Suc��t�7,�F�ac.)�so far>t=eer6>j� m�e�Pno� 2�(gATa. l$�w��&y�:���*��^A*y[<a��F� ge�bro�{  (� them)O"c2A*��"� "�Q6not��2D�&����edZkin�1 �s�lJt�n�pn6b�sny�l .� �n�"��2�2)-<�">4 . Ev|�h��:�m�rKa�-e�+nt. F�n>��a�o6� B� un�^M� body)e �<, you �:� *�>l`%\W>�n�: h�� ��Uh'�9r�woH>�`d�Ef"a!q����ib��rom2�����1����)Z . D!�e A52E ?oo��ha�LY.r2F�}*z *t � LI2@ medi��a�`pt AIs��riz;a�� 2G" � ҥMh�H�>k �G�f0Ow�a���G&=�i:~ #|C�06n!�rbdu9�-mE2�tf� y hX*2 s:X� �2Bdon'tI;e�L��.r͇��:�? w/g�sC!Wm��_�o�mak6� p!t�!��..4>>hX�e&��D�1G12�hypaF� ��.�or-/� b�"2GK~ia�{���4�l �g<�R��n9�t6�e�%^!�� rockI:��&%u�gly� Kany�.�~AhLIj5"c Y�n5ə)xw�` a lo-�� <@�a-� T�B��<��' pom AW�cFh� @(�s&��Wjis�2�&eri[f wAn�.a.v lw��;���c=��knA=r peoplda4�m x) �E�!~���}mej��6�@N&e/&�!9o"� s/[�ZAPs ZBr��8a�3� 7�nbH�!-�7�-" e�s #GY`���o����A8E�an'�� �!b�A.� A�"ma�'ati��e��I�?)� "'��͒��e�-t�l~� b.jb�f!of�6%����er���2�4 % ����j��Sa�s�\�lbO�&4�a���5ed*�G prim��0o �6p�3--%}.� j$aZle6'Auso��Rert�i�~5�c�υ )�'(e�"qi} ��f�%�#]�v&�6P9�P� o (��A�x�(��A�*�$�: c"�ZceR.�RI�E.�u��. I� A�m� e�}dis"qM;g�/�.enc�:)fu�}a���ge��Aheig�/A%�&4�x�%^stry .!�LLA�t congru�%�M�fu&v{meqhol��<p�%>%�;s."1 �BWíffirm� i��!n "S)�8intelligence is� capable of being a factor in the control!@human actions and! rebylman's physical environment. �@If that postulate, at least, be not true, universities are absurd ,nd laborator!(costly monuss��delusion" (p. 208). Now clearly, if�se law2 behavior tgo!��27�ere� no oYwayQ�it!@se supposed emerg!��!� �.�!D5W). F�,a�ey reQ5$irreconcil�_,inconsistenca��B$AI A"`%7ll, but)�U�Tchance occurrences. $So, regardeʁ�0haracteristice�_2Gone:�Notes6�1 Essays!g Meta)�s; Univ.A�(Cal. Public�s, V. 5,2lp�7 -209:tCom!�Hary: Wilfrid Sellar�XPaul Meehl, "The Concep6 of EIt ce,"�0innesota StudM(? Philosoph�k2�Sci!� , Vol. I:/F�; �f $��th6� �($Psychology+ 0analysis, edi�vby2�0Herbert Feigl8,Michael Scri�(�apolis:%�e��6Gof '�hPress, 1956): 239-52. \se�c{On9;tExplan�L} by Nils A. Baa)�HClaus Emmeche Absta 5�I�u�al ������can�~4fined mathemat�zLly in a very general�r�hisY useful fo�_ stud!� s!�tif Flegitima��%�complex� s,�� d �0as hyperstruc�(s. A requir�6��a�observ%2 !anismn ��dered�e���4framework. Two�� of�ce�> �,%� spec� exa��t�e�jdiscuss�( 1. Introdu%�: To % in Liv��as cogn��� e�a world�s��~ �*8ge, we permanen. face know�un ���ldB new Q a -��A�%?!� � t!d? I� ys,)g'!Fis� ed�- or e��equ� w� !��io%�e���$. To claim)�auEon] wells ood,�.A$ h� bA|off�� ��is suffi�@ly� ci� p��ly!�munic� ��provi�us �! kin�8��J � ���on:� you.Va partica� solu%to�a�k .2�A�, you�[%:�oisE/�ng!�to�ytru� ep� or g� � �E�log�T��incLarg# �!E �.�)� fulla 1�A;a=|�.�dNa�t,!�� thought�posses� �IA�a�n term�%�9y!� �tshown"�to1�e -~a/%? \I�9�� ques!��a1 so-calledu��_(e.g.��8n-linear dynamia�theore��q�,< adapEF{ s, Aficial a�.4 elliga�D��sA�ce), " �"�a, �� as� ��ar f�9on Earth�  ev-��new� es, "�7!��-����* a�y�/ces of)�" �!-orde���%� mayA�%�M by� lower-�T 1m1�A�!�col�ive��A�y proper� 1)�A(YThu);�� idea�B9/H(cf. Blitz 1992) ha�cDatD  uchenAd��cre�'!oh���-"� }u| e. C��he �� f�P �% M ��%2a? �eQV>��[ & �sightsECn, �method����Id�ng� �,6q�a�� wAink�y do)��J tradi!Hal�!E+m�4cannot account�!>#ory? ate� we f�� shS look<�9 N%e{� U(ion. PerhapI9� M: V1a!a�ic��nE����be reE$preAO!g�id| c moreq(� (text-depend�seta., �� �� hemselves4 Y�U� s, "Mot2~"| will�(w below how  intu� %��madF��Rqed!vmA�. Q�� ing .�no �Y & �8lea�a) �lQ) w ��XgenuinM�)�& A�ofI� �"�a�suggest�spay}���e&�" �> V s (:� ) which2ludes0 �E�*� i5 2=�allows�self- �!PAB�8�Pa�Tal �s. New ers%{alF �Kau J (h,1996).[1] Wid  ph*�iWc�� loMJ�S� done��� detaile e��:�BWa:$Z�� aD betwG .Q/&�ep cr3, cause, � , de�i-,��b7sm, etcE0e%� add�e" �ere$ feel,a? ever�]at� imem uch Ѱs�J��u =�6��Po*!�y�� pr pla�T6=0i��A�"inFa,m�I-4 E�I ͟h� � saie�%x��� on - �littleY 4=e !.{of  Hed2� + !y��duc3�fulfil�Hi (algorithmic!�ced�by iP-A�� )ol�E/>i�alx�pconɷs -"� ar���� �by execu��E6�c�. O���a$�c�D�FatA8�)L�n� . ��pn=�we��aly�s� !Esearch�gramme���mp��Ao�Z} . HoM�in*& !�mSM�ch� ng�og t2z  ��equAm� Ap�4� X organiz���to�@ his/� �"Y�un:� ('�\Kupo��2)U h>Ea ��s  ��EF� A�Mc$ized reson� ! T* &>�^x3f�� �^critisd� : too crud飍�k -�|aB��. H!�,�aԥ|0romantic vein��e &� ian G. Sp: r Br� ,(1969) decla{�@"&�,�"V� o la��N lane�Bre &�se&be5 d!C �S� o pl�la�fl� and, sacr� ngMXdimenO�WE;sak� �?]expA;] p6ut��!� igno�Ra��� r richnesE�%K� Fbt~a�a�� ���royalty{ :��knowledg)�los�J gdom."lsa�Wa᱉R� helpa�circumv| a p�HdilemmV MU�%h m -3�!g6�r��%=*��{t*� . 2.::b �r�  ye��_iV!� Yc.��� tAveB���Kout mak�pr� %�N�s.![&"he��l sens�pby�(1994a)A e cruc��pY@is~B A@!D�an� e�eA�6�� uich�I# flex�. Let us �j�reLkbasic . -n !@��I7 ��aEt^. at Z�S ng 8 (. !s"� Ywe.�q� nce���� �!7��on furHi� b%��tojr�� � fo� y3� fo� :%=)! fam��of9}��  "a�| !m be "� ��"* �b� �!� � � E. A@A�surm *Zo� C� �+!!5�oA�The e%�� then �t� [ ��"+ � �result�Nai!�~!>�l"���a\�ngMoe|a-�X�� ��g!ubject�3 =<al.>Mp�%%Da�e|�B %�.9g%Eor ex(al. E* : 1. Coup �I,�� Larg i! of o�At� " likA1 pha�� rans�N 3. F�"�Df�@molecules in cellf! cma��ya l�(!�based� ��9�MbN� !�J#|��}!Toug"�'each typ{ macr���virtuI"+$Y� (� eriz,�()Oead!��ml�� aef !����/�( �.� �ar -�uA� mmit1to� �% s; number!Bre�5 zs �Lfic5U��&e%v'a�tabolicm%� cat�d� Um:,pathway). 4aem�l "O <cli%(C)%�a �er (S).4%AL�Gvec �!8 / Ka�per�q tasksm�n( I`m�%$ld do sepaly� ^&�� ��7 (CS�a�m� U ��D�$co� %�$s!5.m!scious� is� aQ��individ5neuron�&?#� ](ɵt.:�57m�!& G� nervous1�)��n 2�(I�����i�!Ea6�x �r�as�as� %Snd�"7%�"tF2 �cre�(*y G{! �E�-.ce�&be:A�24, l>F��l^' pen-bd*O in hogene!^=Es,�2���|@> ... D���on%�ca�!�A�� el�!�r!I�n �yRfor in�'or��  " y� g. E�if!��C%al[��of.�H2O��E�s wat�%�s viscosb&n �(correspoM+o "�)a� u�$e",K�we�me�H�%� la|(e� ent &�is quit"� !��e)e~�GYR - in*r%��!�j B�s6p put � �*�&1�|  c�o� �y�� `$. We le �!Aud5s"a�R!��2Has morph $R$6��P���a�� n .sby� iaD . Si!!�Z�>2rrowsgi~be� å9c*!�@%p� r � bAS��s �or%��e(e�� ab�jdirect� (�! ���e��as� <las bot8.[ }S!�a -p��ׁ=�(�W*a"� �us�a=U�,� ref�,o.De'94b6�A�!�usE�:n, Ehres /& Vanb[&ersch�87J4�A%0see��%h� is 4hN*. A���+&( �#UE��em� izeoateUr� ed��QJm,�)#�� ��`�whole'�\�Xalyzed a�"yalways =s� to�A[�o.5\ �� ��ent� $��%�.8 v us,ezEe"m &o���,!{,< p-d�+nguish b#two di[#nt� �9&y:G)DO� �9 ompuif&�ETo exis�� �o&B7prI�%Le��s�c�bE( term  . B. Oų1UZ�"PE.YG%  r'<!��eda�in (AA�(Cl1�a8in�h��� !).A��<r�R��, ,2)�%S���v!go� J � 5engineer��E?� ��A�n�"F,, a%a� 0trivi"q x�� manifoldwtop�y A� Scot&1del�uD[[lambda]]-calculu�Ls�s"�ivar A !��e)� decide�(&&-� d*ck)o .�(l�tiab="��!,�s� u�. p�6zF�G�B;%a�9m!�� (!�  truth��ion; R" C��em� 3 �yx me� ship�$Mandelbrot��! most Juli� t�0�mo�2 it w�#d�i^K/ se� non-!�UrMa "�)� **�#M �!Zof6e�a =�2Zly1\t.[2]+sp� � xi21a & %�X�-�y�nQ5!3�Hcon��ab�L�U)�� exemplify2e�te�or:SU �PŪ � � ]!z!�� nsGnt%�c�w-cu4s� ,��2�i��fa{��'O2�do�. No thel_/a�����[ �S.po�$d!alu!�>�rirc(�ca�?i�%�(onM66�B�.�"�թ�/e7i� To ^+a�[.!� %�=%��/!Xautonomd �+ins)� �$�/Ewn���E v7� 2x LMayr 1988, Rosenberg5, Kinc"1990) i���peak, gr!��d�]U.}a6"�]�of bio��[�d6(�5 ���D*��Nor~>�(: iE�, !#!E"q!�e5chV5"��( as1i��Ar�#AwL�.m�vS�"�b�nE���LM�� � )v��<m "�P�e!� 2, Kampis!�1,+2� On� go�> "!�us]!�AepK 1L)}�anE{ poie� �- (M�anae�VaA��0)�"Eo� �a{ ed netof!� �Dp5�,U'ns� 7 kdeUaofk o1� re��taa�&�/sv���  !�,;�J� t 7un�[��ew (aut1) spa>f�/!�Ti"(y��,�s�%A;�rsI.f�N^*z.7 p-���A�ir �e0.S�%sro��+'�Eti�vve� sU: m�y}ab8 �arj#,o���@+4rane-pRteinsb t��` Eve')%_��e�.[3] 6*O.r& =�-3�nombe��&a�izA�.� &] A�it! ���. 8�/�r&�4��easkb� t�� 6 ��-th- T6 Xs�-�!�m,T��)�:]�&*p"b�;lti�uAʼn�s6�%u�1�1=�ecѼ>A� ��'�WF� al:s embo�f ��-� :!�*!@A�2� �i�. >� �J/��n-z���che~=Bsig��'Ade rol%�5"*W� ���ng.� -)*�*�tY2�<rpT@edM_P � combB+!�&H u% hier*&y�>V���'2�. Our b�5 -!w�6ll�5\e��w^.a�=3�i�<�"U?A�b�d &B a:(9,&!'6m,�p ' . 3)�M�,r As alread� RA�He-  :!2 ' �%�yAiNr��#/j ���a��9far!8� a�)��;t͇ [Qpfacts ( ma�4��!�%�r��: W�w��| Frmo��4� t=�,cA��7 temper IJ3C$aa� �ie !tY"�6-he�B%�s0 &!� R?2� in m�@��o}.Z1 *� � �#iM�C.�(.�Aa�'_rr � � l�am� ad hocmdeepe96�+ -Al� hed�!? e~!)�!.�de�*d&[(H�"�9a"%"�4'9? ���I� . M�0in �M8s%�;B�� 6$� A? �po 9 ��)!*lymWV ���i�.i�n�$�� R� � abov�e � l1w� �k  A�k �� }�s_Ca� E�Fimmedic *9 (�*� e���re� ��2 igna�*r nut�)on� , JsR|��-. Sq". On a2�,��al�� �� �a+G!�etyQ�0)���� (ene\��%�a48��aZ�E�^Z &� �Mll! T�m%MjD�. 4. M"�?s � ask�i� d�Kon3#I���<H)-� m�2.{� %�H. ��ansv-s�o�7 yes! T�)�m3�q[�p�2 `sur�>s' �&� are � glu�;g �:.�.pi� w�qb geome|>��&hDB��o�'a,�o td .�&al"�ors �coh�#gB�a��Etec��<Q>�G F2�n a.*31�E�kno)#[!?� !` glob&�y,A�A~no"�lo�~� , a Moebius b�pn ftwist? SE�g"0! (See Penros15�5CF��."" s5f�(�f�l�"�� oofE1�s: X, Y,P (�%�s, Tp�lgebras%)�C2. Mo�:&: �a� ("aH�"&�) �Aach pai���&wL+d �me�/(� !5A�is cl��4e� �ŖifA>a .P  . . "�J�� �����Mc� �vP3�k4d��m!�i�!a0l@�]D���!�^�"� +yn�0ED���.l�4A,h�m co-)a? D. Lmm�p/1' ��.-,���d oAb�� a�:�5/�D$� )aoto%� �:r cc:Bg3�.:���?0TD�), if F��(Hor: say F(Di) = 0 �M�w��if%v a 6) i�� F(D)A + �)� O0�4[� . AB&|$ m�r�t5.���Di+/�*o m Y7[&�A��VyarA�beauti�? illu�Ft�"�c:/,.lE�>�� �0l �@ figure: �irc�\>0-��&r"3 horizon��a � m�!s��� E�s (^�o4�N6..H N�-.,�G�- ]*�"@e1�i&�'AhM�a��6�Le�'-�"f5��uM:I�� �pl�or�2ZM ��4�=q. A�Rvel 2E�� a�� (�-;d o���a�֍� ies)�a�n ��e nex }. Em9i�e�=`�4 bottom up, st,w�Dm��.�or5���1,e�? good2Q-Ce* ,M2? ( ���� �%_2{G q�EtA��i> ^ E 69isI�a�al �A8F�"<a"%��]3�#a�%:!B�*%7� �>-* E��'a",?on) a�it. H a� ul!!�uit T& 0 . IeT& @)f>���Qa=� im�&&da<���� iMS�!���47C)�& . 7"M6t on� n)�"�#6)� � J�A�inI��ru��A'a�y����j�5e��X/t�Q�to, �&f=�� is�2n�2�5Ev�d:�s i 4l�.d ct" l*�3�Hc�)%bM�1 � 9����c%�+��to �A nd reason�utO��� i"�U-e��-����!]�w �nt�e>�P88T�/ ntax`s�#& �� ���E2�Aft�-!�isP@ �F�X< �s -� "[2�z�8 . 8]�E��DB/�~t�7�Qfunda�"?&�!~;�? d as)ҁ�on2�=s"o el�FW���$5�as Bl�S1vi�B5>� 2nr D��AO�/��tUA�es&/0 !e�Y�: orga_>a��f�s�aQc ��"�O�&O5�5.�8�鵸!���Ayy�$ obey�me;���FAN��ue ��@t+Wſ'Md��=�@ toolqF �>-�2� (seeWilczekm3�971%>�!��F &;Ta�%]ven�O ^"mp� ed�+A�m�*<SB8co nj:h ? o a �0&�+[ reW\d� Lroach, namely effort%�0%� *�E�� �.x�:nd non� i+X�[-!��!!g2�(Teller 1984F%So�601993, Savello�FYalcin5�<� k*%a ! 1�A��miN�nICZA�veDon,;'��.�>���!�N�-l!�) �al�e,$1�"@&fa���1Ifix� "+%�%��E"SG <" &xRDDavidson 1970) den&�)r�� ct X�aI.� ��& 9� in�mH=ento1T�7, o��h2mZ�V�1ean�#i�&�-two_R:.��lA�-d*4e!L�@I�A{� � &�Q�mal�<68^U&.a5=c. RE@ly Kim�-!N �Gq f2%5@cW gnif3$� t�: 1ecei�io V#al�� oX )kof0in�FA���>i�A#ppea��f��-a Z)tQ�I�O�|M� O$ ]�|��M� 2H-b4U�U����{)�(��a1 �� Nq�Y1 sis)��d$ed r��1��f��D&�S^!�sB&�reu�]�c` � =� ���� 42�!��?��5}ezE`t�&t��y 6promi�R!if%?�<1�6<.�9  E? ��s�Ucov+%���9@W �+[4] WAN'M�imfK"� �Aoo�'F�-.�I>-�#&�7e  �? a ��dUop.?3:�LA��Cc�)�) . Ee��D ght:@%�6@� �e4� ��moe+eriu c�OD\ians w 0sudden "flash  jBT�invol�G&O�n � cW1 d*y_q�H hardA J#i�}long .9 p�+d`*A�! (Ai!i�sub9�<�2�"!*�X:eY"�Tav�� � "� !��5�� �M; t z_, �2nW t�.�!ie��@u�� eLn g�S�ai� tes� � � H�MJ�"u"���o�!v�=lyz+�dF Po.re�B56�6  ��or e��[�Qo� G imik'�r,E �W�Y}~"shor��pA+",N�"N3)z �� Q?!�� +J&O��!�st WngH&�-Chait� (87; Hofstad�19� *Ms�.9^0oco�Ao*�aZ;,I�_��Eeq$�,2�?"�. ,����6�"&flow"� &�!�SB62)f�wO8 �4B!s� ��XL57,Xm:S�>�(E�a l�},Xa �'V'At w�f ,hig�]E>m+�f "`E� acce�_���fUse�Qa,"�,Q"��/ prev��.�!Xo�%a�a�6; "��1�`AL���:beyH>heir &W#�Ant!�!�*)e 1�_� &Z"Aha!�{>�@(���Gestalt`&kR�4tndk deep"� m�6d��c ���T]�.s �S�7b8�" �� ed? LHusW��; l s��%�inM )M ut tJ"�1we� s*S5c,~f �5��� . ToA��!o �i��lo�e�� a�j musta�,�quote:VNat , "tlN.M � �8"����&X�Sqj.;K ive � ��h2��/�Q''!@�!os!� * ��$ gs)%9*O!�ATB�(�'�A�tr2 c qu�i�!1Kkr �B"%�D�"�T)�L�� anscD.if�integrat�� f�J����dt��*�<�6�s: (i)] E*ofh�&A�x�/l{Ligh�_� sed�Tŵ%�A.���W ��l(.z)��Li{8oFI /�$*�8��er!\!�a"`�4"=�#Xk�@  �) 5�p/o�[gP0ni&lawxL} �S n�_asee �RK)�a�_:�.!�i) Any�{52b�*U��M*� jZvG�F),1R���!�be&�a��d,eQiciP�5ly�,�Z��!? ode)b S *O-diUf (M�, B� <(��%�1 e ad�b&� %4BQ��%�h- (�=."%>y�F ��be2 n]hkr� !�e�9Q�rdk>�VC.rs +c�  �[����0 D!M# N"�();%��N�qF4n��fl CA��w " AlM�.�I{i)�kO*E����DUs;ɦ��> 9T��-c_(x pleg)��)]vj;�<&koT tC�.� $of.�$!X��gA� :��r��;� ���: "d �G.6,D�d3�(al>���B!}��1 (iv)Bk5iPe<m��q��in F�!�v)� &1`= �gcE66EaD9rn 6� M�$�A��&�N(�sthird-M T ��iv�3(�x!y��� �D he "endo-!�" (*:)^�!rstd�S} (. 1h�il��"�r-�!i|mM)&:u ��iB /B;�>�^'aalAo�y� !���#���Fu%���Ore 6 ys�� ,�!ae ��n2=k� �k*� �a�n�?�+d%4"���ri6+�"5(�W easteC)2�"� �/ � ��"�Q!-ea�� ably2$)�!�.�"�aA��ionFaA�*�"2��"� � M 2�", �L� ��sis ap �J�&�FeVA��' as�f-Ro�n�6MjsŖlf�6roiQIs EDlegNi��9k;��x�exaggeS �#ec�t!�quixog3 hope�&%���� � s�ofK�� 4!~c� ыa-��6�1�M� ,U�K a, P� �U\4�il�0rd"V,� o :.�e8�J0 `o��B� +Q. �&�2r*(Y��ꁓK!Q�c! �we�.-inu�(7a�*=Aays�a�alfvD6tb� ew��E q&� ��a�_�[%=�6_in ��(1991�FD �ngm�s,E2oOGg ���+ !6�;�&�'��� �sl,A�FI"/,M(s) = F(M(s�' ...,k)'L�$s'�y "c�aT� M$�?�E"?�{".= we �Ob�nMi  m6�am�+ �")Uh `O#eA"�FFN im��2�}�b&� \ vwto5�y�x` +a���,i�  Vpo� A�e.g, !�P%Nn:(�� s "H�v� R"�xMb�J%+E��Tq� LnIB]i cI� Ie d� e7,o ". �@CeA+!;cof76u>�C(1980,Va��Ogne+}Ga�Dent05 of� Q")"�aRhA(��)��A�r�H�loss if!!nt�#F�R.1ozt? pao:")> an ��j����e0�ut�C�2�Bw+l }���q� B�Gi< ^!�4]&Kd�%�A�� � %--a�tr>N taHd"�P�>  y �6����u��9�lc".Ua/to &�degre)���� Ja� N~/�e"{8 `� �e�`,2�-1 &'� �in�" at�3 st f^"��8of:�!�+Ga*1@ofV � �nn8ly � &�Ya�J.`r}�~�|'� `ineW-n�itfU eR=>| Yd_u9�n6x�"-Q flav��q %�5ZA8%c=V�I"B!]: 1. Ep�mQ�lyAZ^&t L�s:U�ō�, pragX%A� �S!�0��� !�aG"�" �I�� "�p *8d�rngV��^advantag�i �'s capac� &[E�|{�!�aAq`g�f�D�A%�)^�ASet P�5ie9%motivm/�0x%�%i�set�1n���:1�t9q>er�Z<)� M>rP1�EE&5�uVt�\cQ6!�^2a�0��� &� b`ty, sae]ce-=&6m. v6N�Ont]m�(RJ%��+l1o-�c�mA3o2SX>&8n"�SaNj  do%�S �:�k ŒsL�m�-re�l2� , wrZ1svi)fai� eavy aM�*VeS.�in6�r� Q��0� c&P U Dennet�( d Pylyshy�D� �A�b�X!!�ta assumiv�QR�$7a�nd~-�olyo.5: F�� VN �,� ~!�MfF�e�(�Q!`R�' $ ��DI w\Vt���mYm� M#1 !� . Sek �= A blis�B! �f�8� bree�[R�X becBo&8.�r����cwayK.�s talkA\e�f2� debate:��ambiguvT��@!pp�;�#wer��;�Uc���is�0� �|�0�l� �lA�� �ir�$e l�1RI� B�%�R:�:�@i� ub�>�/ perh�tV'�T-�gi� 2�!�g��.�!MsE���^��in�nc�p m@d�w�(!�!�V `�5.s��N�!q�aaiy+5ch'onger� �V�  `e6�v�ce'F.! lso @~�t�S� exao6�!T/0 a2!��ry�bI(�� "�,UAT)�:Abrief,�rg� q�%toN.!�K6"� n8�dleᯡ����l"�� ����� s`�U toke&,�CnL �lE Jo �Kdg. HTJ�%�rdi��'�%e�Mcj��� �4�lex. Rane� cano ~lYt o�uaJ�nc�^���Zr�%�1eneu��� f+FJ--0m"1oZal/�Ms�E� %�$Ճv����x!�(�� 5e���li�Fa�m� �!�E�rial p�;sca&��1�#�ly$-+t  a9,it��o� !�2w��ti��b� ze�f t�'e l~Ce,R-N+N8linea"�Zs=iA�he"gf�0�R�5(�.=@ ��N�E'thr< �"le��c%�A.a�b�$�! b�up�ao"�9nlsub�Z4�>) nf(�.�.�-.+H&U)-9[}� � D%!umA� .is� �;1exTFoU!�4tU �/aJult�;g� �~��otT � U� f!� O^-�6��g�%�dYDxep� vi�T\=�.]\ ��%�"+{p�_�#s")a�!?PZe�dur��ae�>,��!&� y"ep,t:�a���' spata���#�!���;i� ��i�G%�synchr�� (mx�t�f>pA< inen ). S&J?r� y  ^!�o�T!���ql��)� $�7�na E/!Na] next�6)wnwv,lu�u. ��wVcatastrQHMn �%��!l5_ orig�f �z ��E<o�oV�B�%alIss� A�st%�t� �� �j�Q��5�|to2;�=� �re<� when� &lQ|"o��X *��6a"�l.� . Each-s% M��Y��%�O%�. H*s� =�-�}�n*}a�!?-,��Q[�VNTharn�  few �Ri�9l�39��&Ea!��O�e tzq=�! }\�. �$�� &8� ��A5%���AB f r3� E`"�Yer�١�j(�� ssF (S-bs*I"!v 2�� 1!�&�AM in {"�4{5U{.}}}�^�&�gs ����K�ub�[WIj/dia���Pe��e�A^ �b�+g� �1L$�E?!!,a�O2dG9  sY!0O!-Ce�.��_W velon!��+%f ac�Wi�/ZW���F,�� grow�g d/or&�� � �%�zmta�Aa%0v� �t"�p�F��AC� �*�'"<s�- out�QsA� L�rm%�����helbe�|o a4enMB�%) E���wi�ti� strycbd-Ke�!�p"� #��recei�1u��Nineteenth Century. Stanley N. Sal!( Biosemi2 � :M *�g 5��N%��uE���. � l:o��m�2words,c�=�{�XM=Khabit. IQo�����P�W�r�eg_&$^0�#)?;�� 5;� s$�f 9 ��M& B�-� as " S ��I�R12�3to "�in���M�3jPA~e�O w it=�,&�*fiA�(��y: �(���-�s)�3��r[#pro?cx R&&z"!x �aa 8!i�Si�@ �8U�>%h&�S!���a# ��gna nvey!D�*�r��by� 1��� var.�9�0*��Iy�6�PJ��,p<91r�grEI��:%,� �Mt%TIn�" ��7Evea�Jb)�"#%��Q9-%3 -ar�rkB!"�'[�{9h[�6�h?� b#�01�0!)��0!L�^�Vipr�(i5["�y a~N ne��ua��herUP,,� e`e�XAx�)U�Nl�Jv5g�r�Y�8`pni��l i�T�I��� ribos�$��.U]%gQ� begin`"%E�b ts �OEa�"A�,!��A2!�)p�r���Enx1�x-M�U� .��ZwF(�!!N�� un-8�idd�L��*�VUK�{* Y]Q�(r)&H!!�= abV*o �=�� k!��el,e�9��.8Y"@s�:b �2)�v6nseL �8�k��X�M �o�vI%M�H"!�ank� Ag bQKMa3:#�h*�"�)b in h�&�!� �A�IM���J`�.:reK.��n��,�y�gover�%b���ies (�E��f��=2) �rbee�>�\� �/�p�� "3y:�E)2w�I/M1m%�S� �w rl��C%v5�'(me�t� �(&i) -�@*f*"�G� )�!SM:a��ADTe=U�Mh *E+�D&ks) bui�?up!va"y�}�k%ЉJ!N�dIeA9 sms'eig=��2m� (f��'d�,o Kalevi Kul�I�cA�) �Cartes�\cu� aI.ap0R<� allu�xA�Dec5' � �-� �gitB (thi�H�tl�J&�a ( CL� %.qO play^z��!<=� �/e���#r�!on�mE�+�1�%�t�%��AE��)��� toda!�"X�YC c�avA� al (a���%)I$i6�5,% �)T2�'a.7 `�w�Bfad6|3 Edat�_!�0�o�9�r!&� B�be%\�� l)'regime.� �HeiZkU2͉X*��Q(�bnj �)o��2y%��S�1�WMaa�n%J�2i-�=5*�], �\A%Ped mq��� app�|Iqe !��ieA 1�[A/:quantu�?"�'�ICa>@h2�E�FnO � nonl�E��ein-P� sky-�l (EPR)� U�*�a�*�rDuBof�)s%/l�a�1� d!� tangu �AE7*3)��g�t�2 Cau�$Clocb:V out� @Ol_��S��sYDe�"<!r�by Newto���y1_�q�e��V%4 �� Op' s�In�?�ta%��� arisF:<�tim � e. E:[ �gA9�/)=�"ag�9up�s; I@ �� � *�6fi�c�s%�� ��t� t7s=��. At�Dm: S��U�[%�posa�.Ղr\ !�r9Т%�+��*+ agg��<fQ8%�nlatk"!Zbe� t up�%a9<< c�x�Ho 4 ]Esa)�CT��@�VEPV�)!O�) c: �$�$ (� in�%)c)�5V ��,B1 �E�!�Q.%_w .��>gJSi�B� "�,Q} .d��y� � iss(if��) r!sAA)s�`�lKitS�s� �1 mblE/R�Csi�"SM� h��% H1�}vVin �U �=o�>� � "sVin� �^�aw!�H+��"�i��2Q�_�*N�%�!� oߎƞ�, ���%ec� [I�u5� ��jb�l�`k�oH�A��DA� !"pU ��%��=�(� 0 r te�M�� Q.d!D�f�: Gi�W�pq1|Zg�A& T�i�w�$�Xa#&�L tau?'&�^�ubTRt .tea�`��l�DN����g�Q"a%_"!��qMeAc (��)m�%�!�ywAE a9?an%*Co�)cA?�c�D^�!�MLg5�,U���E/�se%2��(nsu Popper))��ɧL fo!c*Ҧ�er5(E�L=�AtappP�I�,��� a�Qh ���ime7$sXqLorv$ a�A&"N*o�D��b5�#�A��pp��ww% �*� �s�F� _fi|nu�#)i�"$�N*  Ny M�PgrapT�.)-.w�Granu��}pn!:�LtE��%%��afa��':+�6 - =� aY0ud� ue|#J�!� J Af !sUd��� Ergope��+*.!,�{Sa(�_um �#W��2��no�)vin�wit�l�A � nV"eKcee�� �� �� �� �� �� �� �� �� �� �� J� yܛ*�� 1� � ��� � i�nɋ�� �� �� �� �� �� �� �� �� �� �� �� �� f� �� �� �� �� �� &� �� �� �� �� �� � O��I�,  ��K'{�� exhaus�}("E ��H  fm&3Zt "&%J� �1O=,"&\ n?cl6�/ic �il�orKA .) 5�tQ� ]2����.�'6�< � KWT�� �M��/i@ �P "�"| (U+FVl�:�MsT �.P�[7>g,M (ho�=ic)1��yp� �\��55#� !�! !��$ Ask19�]il&݇si� an ("/CrL%r�� � ]wD!\n� �'@��-�% Eg!2���"ބ�'n�,: Sd$�#E�%�g&��usaQ s�!.�� X ? A A%I�by�f�6Qr#s�or�Hby cod"`AIq5ny��R rE�&�s5mi�v( ���ebtM��Vl�a"� "�8�,oU� *�1wig�hpl�ce�u_codal&+:V�v"6�}.��"!QZ�ceTf*<��E�n ;�)Y>N9 Q6H�!; �5� .{#�8.Yr2��(��� �?vV4Z�(��=� Y��OV(app�$)�JDi"\o`$a��+��e��a| �;5>., adicy�ve &]@en>ad=��ng!� aat=�:{4mWistO�s�> Asas*�inanih�{u'��"�;as�xmy*7 m�N�:#�aL-{b�i�""��%���[�4al /�Y��r�"����/a�"+Eo�u1u*"�I��! -+E�d&���"��)��]Lin�A���c�$�-!�=�9��T�Pa�isomov=��W w�'�Zl�Z"Y�M�$�*tA{notn�*`/�P�! �triEf}|3{ga:a �M(@��}g'�u!1ctu�8a"�=�1�oY< noun( $2�v���� ate 07{062 �"^.2��#�Q�2C� link� �%�_5!>-� s. E��T>F�L-[ -��? ble "]$a�\ %i���!gy-as-.qb�!n��~ �!�i�����a�b��Rj . AAu��u !�eI5H��% !�c@�%2j5��KeeK �M� "]A-��`1z�b�P5~�����c�/�>/�p_��U��dWir�!�E �A�2�r:"Pa?Vve gaG�R&��<�e3<Ѫ,-z�D ���%�pur�hyp!�t�1�QEb"�� ~.m~c�!���!B 'll�'eM s� ��J�!o-O+c� �TA(���o�!ual�A�ҩa�+�k]�y�IfMo�$$ \end{docu�}��%\Tstyle[bbm,epsf,amstex,-7icol,6]{�} 9�/ [aps9dig,graphicsx,floatfix,math[a4pgF ]{revtex4Hu" ckage{ams*}fonts symbS xl`r � ,bbm4�4\addtolength{\y v>\ݿb}*9g \bibliv�!�!g{apsrev. \new�_ and{\R}{\!bbm{R}}6rrnnnN><ccC> ii}{y1}}!�.�idB!2 flip}{ D{FFC tr}[1]{{\>,r}\left[#1\r!]]} %\re.sd!�\,:g J\boldAol{#1>�bea}{-�eqnarray>$e$a^"beEu��FE}{ DV!St!<4S><A%Wrm Ad!s6Tket%2|!%�:bra!\FNle#1|:!av-*!\RHG�G>�eqa Eq.~(\ref!h):ein &Inen(sir��T"�J\� \sf e�bf>�>�c A{\n{��~Iack}{\<*b=Ac"V�0sB�@front}[5]{\title{.�\L�;I�,author{#2 \vL@*{.4cm}\\ \footno *0ze #3} \date{6Z�Y` } \hI��#4 E�  #5} \�o�:�egA� mph{�'}~>��proofend}{\hfill\fbox\\ \bigskip }:�2%�{\ihG of.} #1 $  end$��%-��L���$em{ }{T(��ne� �!}{�$ � ={�}{L�)8&E}{&��6$ coro>� y}{C 2�z}{E��6reu�}{R  MY�,�P�� � yJ�� )� nel�MQ�4M.M.\ Wolf$^1$iHJ.\ Eisert$^{2,3,4}!�\affil8<{ 1 Max-Planck-I(�$ f{\"u}r Q�)enwB,k, Hans-KopfyHnn-Str.\ 1, 85748 Gruing, G!>0@�e� }� 1�҃$�2WNea��%p�nia� )�%Bt8i�r�q~\��&� eak�d**nt�O �&[]2i�{�F|R�U]. B=�dCE�:�s�%@H%p5�PIbi�R)c of"-$�. F��2wo+1c ob�(hto�G �bi-eite�INn "�AT�  ��+c+��.s y� %\pacs{�D�� " .4�}?2g6e�-�A��BW�ar�el�Dny �i��|&�)Ppa�*M to >�X(�mit @un�%� ��7ei�1� 8��?-<�6�CnoisyYK�^0-h�?m J�8&�6fi�Pwwavegui�i"  ��k 9� s. C�Q�a���iOh�*�k�r! �8�Pa Bt%Rum�R:eN6q?ESrs:E)��ur�s�2/"�5Oy�*-�`asympt~V(M^achiev�LA&�7I=k��Ahj-�}�Qk�ouslye2�]t�--�whe�%;;A<�R3�Efi�e. In6I>:�LencodyF�� rpM5�� iA�rE&za�1��,�it&�EU1 "�SFCusy�Xpu��j1��*�>%�!� d? T�39!P� ~sQ8{�� two  ;�BL%!&�?iQ� i� fo�6.�0pur�J��bIuxf�bm�9L`�j4�T mpan�= J�� ?6�MVV �O �ϼe �� can ���D��m�ke��m� ii�IT Amosov}. V- ad ���� ��X�.N%b�� �DeE�L"u2 x@ ����ei�J +��n  false � Shor,AB,W�}�tAA-��9\[�>nv�@�4)�� ;!GI� ̝B%�&��C d .V ��c �!(u�0� ��~r&b ��r-�sC prt ��aM iG $-IA+A�h�)terval#j 2]$A�i�r%x�-o(5n� *Xa� back!DBy `Ref.\ I6� 1}��Matsumo�@nd Yura� /-�"}� A�B� 2 �l �S e� =$��Al�Pz =N�"� . b r��2� �"  a: !�d"�[�. Soa;>�� hand" iM�A�vS �.new6L�Y���� MQ�I��R.R ~n�80�r �xFM-��!��&&� e��"O��@d ru��0 f r��rof25m�� V!� e"\ . &g ��))!"H C^"n %c2~bi�B� .aO$�Lo5c՘a �d�in Sec. �SecPrz^ iSA=&];�B]�edTB� d dCh�; M�M/{6�\labelF� C }N> Ce��mmivep ce-�@rd%Dmap $T:\St(\cc^d)\�aI7$i9tof]ż%V� Hilbertx\ dRs%!$d��b)Mmp,z26� �m%\n�:xy��},��� by@rion1R,Min} \nu_{ P}(T):= \inf_\rho (S_ \?3 T)(),\quadB4&  E, \frac{1}{1- D,} \log \tr{ G^  },7� �\geq0)6��aE��4r"G�MP!*e�von-Ne�Cn 1�|"as $S �=-�� �rho}$, ��is u�A�A�l–�.-1 �k�-A��ut� | $S_1 z:= �$.D׉ y, $.�$U T ziIa�%� ec� ce�Cu��b�CeQR� ��n��� s/*�B�-�$��M>y�H"ze�KR��Conj}���ٰ($N\in\nn $ B� E31N .��(T^{\o� N�j.& (T).�*nu�}>ZI� �k .�of :yd@n5Khol%��D�Q�>4.79$mWerner^ �7 er v|�A�5N,  J*cou+ 7Aq �so '�dK*�� A�E:a 1a �% %qk $x\8 mapsto x^q�$ z^� ���S vex,.��"��dz:%z�� :!,M� Uf � �Bb&&� "{}E� &"T e��J $T$�i}ABxM9 n�@ C(T) : = \sup \���\\Big(\sum_{i=1}^n p_i T(�� _i) ! �2$%(S�GHT)�-_i�n]B$ $n\leq d2��1�suprem��_kenV �"m� $��_1,�m n\in .�AU� �E �, ribu�%s $(p Bp_n��'�z��c* ���)V-ScoIcher-.�=l�o>�"V ~�I&�-�_"{Cl}} %�=%s\lim_{N����ty}٫ N} CZqB�so��Aj*��<���� T)U�. U�tunat���',�UN�` e*�in Eq.\ �.�R/� a �l���$�oJ�&�K)ik� ite-"��n�svex�*E lem&�/An� ��&[ �sA^b Cadd)��s=a�Bx�Pll�J \nn$� e)"aUefq��B�AF� v��R�%���%�S] -sho(-�%�>ta��6�W*C )ݑ��A j"�� n�aCVb�Z�D�p^1�+a����E Eqs.�25,� %�A`�n!�)�� l%�u�=do�)!�$N$2� As|��@\*F� $a���gN T_i$&� reLNVIi�mat� as '')``ͩ*8a�:�a6g1$ valid! �q5F-2Bn�<$6O��Bq|%�P�R2���G�!�a�.p3�.g�O���T�!:��2issIJ k� =1$^�nL52K)�j!#��-#څ�0n�Zvquivalt@irMұT�z!)��g^ A�aqru��MesUN�<� t�Z)YpB� �sP���_he�� >Ca�A�2E �^*e\�=1$ i�2, 1,KingUn3� De�[�EntBre�iL,Us,Shirokov,FHMV04}R*��|Hd>_^{!.{$LloydGausszr Wn)-� �� �� 6Ec $-y* D&�4A ;h �Wx�2 (Ruskai,GL}.��q,%p!�A� �=2$�Ej!�=-' �>�fbCed�� j p2},E�Z6�u��+be �2�x�uv~s gl �6� �elax}. ��&ol�BH�2N�� �w�� R+>� von >d ��P}-PO�Y��Vu�sn �"!> ���h�p� ���X�7�� �X�Y/sNdiGp%��b���S�n)i�� �����coe#��is��� - �q�m; 07/���u�J� T ={\ii_d-� $^T}{d-1}\;^ �!} ��j �R-S�[��Fq:m��& *?$�` 0\in�%�I�1/�y }`aU baU|n!wRef�IR��Iɭ"���E^��b)hT.f*�Mj�*rF.�.�>�M=S  �-�sZSeF� �%�Ug*B a *(�2!:y: a�B����!@� I=}M�Z�h �hf"�5�--�$��@ e f6U��:E�a� 5�:!\��)[B����]��)1}��x>�E`emB| � ]� (T)= bet�#� �> �\�K1>UI�BP>�1/��mpl�a>m.F?�>��* |+{�լms i��ly��fact $S&�r)�q o} $�_ ^^Q �!6> 0BS��sՁ�I cha�I "�/)�%� �T) &= &>� �n1N2E J;X=.� _{!}(�� }\�.� \n���\\B&�& Y1NHR�fQDM�f/1}���-6A J.:S#+p>� ?�}(T)!� �:'Mf/N $ 5��;to"�� � �).�*Surpr���'A�p�vy* q2�iV)"o�Wt{�>� ���.!� �$�i�&x)c|�*a�� =�A�z� Zu���Co ��� �. A@<�Y�F;!� ��p�(|���1atisf�!Qն�/ ��K:g: ��X.M8Fv"l.C��i��� {�`mh�2E�Xa{{\id_d-M�-���B�O$M�zZ�! ear,6���(�n��9c��~ich-�� �iIL� A^i�~"�UFo/��Q��h��� � �;>0$V=��$a�$=\log(d-1)-0EqLem2#m�uE�w-��"�rT���a�rh�n�x()�)}$ !^co��YxD�� 80�<c:r#$0�� �<� N�a�s�'�t��#th�<a3S%+%?s�at�+sP�\�Vz]�a %{5.�e[,J4 ll�vx-�pl"awkc���V)��? $M$o�|��inW1^A$e,�Li=(!�!�!�^{)F}})/(*) $ y3fs.e(EqLem2}).} � The class of channels in Example \ref{First �} has the property that $\nu_{\alpha}(T)$ iI dependenta$ h$ and therefore condition (o1})A|trivially satisfied. However, it$not yet�0 most generalJ�$for which 2�$Gtconstant. In fact, all quantum5< fulfilling this8 �0can easily be1racteriz�T,will be� cont-the nex�orem, �/ make use!Aa Lemma %rXwe state subsequently. !�follow�5�ar w@ones investigated!��Dpaper: \begin{th� }[Ch�a%�],(]\label{The0t Let $T:\St(\cc^d)\rightarrow $!&a>a.A�n%� thre �ments�(equivalent:�Lenumerate} \item%0minimal outpuA�E� $-entropyAi2�@Q�!UaAl,EBA ,>\beta\geq0$!� have ;6= .}a.&�-��of �rm -�equ%z �dT(\rho)= \frac{\id_d - m M }{d-m}-�thaem}, \endJwa� $ME��a positive, linear and trace-preserving map%iEe� exis!� n in!]I�$�_0$ such�#�_0�a�DjecQUrank $mBmax.�n!$\sup_{f } ||-$||_{\inftyi�attained�anM%| �bea&aTala� pr�.-4YV U�\proof{1�Y�($ 2 : Sincea]��$ $\rr^+\niI}0\longmapsto S�:�- non-incr�Ung fun)+��I�rho\in.U,A=r9� �}h%�%�4 gives rise to2 e"um�: n value�)M�een, by�� ����2}, $)�%�has toi�9a0 except from5�E�.��(particular -��R� \leq_0.  =1/mA�E�8 $m_0 : =\text{Et } (� )�is mean��a��E� $M_0�� �� .� defExas��2�M_0)��a�1{m_0} e�- �)Io:isu�e��!R.�]%zis.e a=A�%ea�U�ym�=d-!2 . DuU!�e� $T�4>Ez-&�$,Z:%��_0}�)B�is alsoB�. Hence ��e�!;��ed a re��nt).�claim% bove.\\ 2>�(3 : We wantaMarg!5A6.� ||\ii-m �b�if $R:=�+� �). Ta�!�nd���� R%��le�&�$convex setFqC:=\{r��L 0 \;|\;\tr{r}=m,\ raT\ii \N>os�e treme poi�YP�+MQ8$. Remember fur�9����um�a � ��(n 4 largest eigen�� ofA�͸0 matrix) overHlosedOse��at an e.�4. When optimiz�J�entireECIJ �AwthuY�-!��X9�1� i� dE�(ccessible dA?!�e assuA}"k of�A�3>�1 :e 7 0s immediately�`���� �ab~tog� r wit��e��any��e.O� ho_{�z out}}$, $:�2 )=\log 3!?}}\big( � 2+i.a�&v ծ } T lJ & ʹ� [�V � ! �L��G >�)=�'}��$/som�v '> av0�len!�hoe�b6/ � AmX P &� R= l/ �%a )�%`� ho)�ն? )5�k �&�^ >� s� u��6�y� \cite{BS}.� ep5 i* %�2�implie�)��9� �=:c)�6N)�$, i.e.Z��0A1^{ b }=2^{c(1-)},\quad)>9M5�!�A m. Taka��y$ET$th root on both sides%9tA<* limi� �*� P$ leads to $2^{-c}=||�2�!���F&�av4/B;)9B ^{-1}BPCon�r�aga-�z� yiel� hat �,multiplicity�F*e�Az8al% V�$,.� �$..� "I 2�.�c\s� {Adv�g &����Foɷ>�.�in Thm.1a�fi� he a~e�-Renyit�>�(\in[0,2] $.�exploitmW&� 1}5!ese M � sase casej x=2�M� l ]l�E�remain $ shown� !�b� �2"���an, h'u don� Psam� y�  been!Ref.\�xFs� specific� $� =A# ^T$,��A� m�vd �takk�� facT �involv2P��ne!Xarily one-dimensional. q��[Strongf; Q �newCu�6 Ds $T_1,\ldots,T_N$>�Eq.\ �v)2KPbigotimes_{i=1}^N M_ie�&� map!�:0U�m9A$s�ly�e�^�T��E�$, n�*�\Big(J�T_i$)\ =\ \sum�S2B�0/biJ/ �(d_i-m_iB� � $T_iF �{d_i})��m.$ ae�N��{5��a��x� s� x = �(��e_i!�!�ho))/� )$E�a��� tensor� ductQP $T:=\:TAa�R� =)n prod1� 1}{d_j !V,)�\Lambda\*0t \{1,...,N\} &(\omega_ ( ��= ^C}).xkAW 1}(-m_k) B�s $( ^C$ denot��e� $ N �:= (M_1�... M_N)-�$,� 3�}$ .kreduceds��/ !� 9$Ire����]systems �ed $�"� we obk9�narray)`& e � )^2 }&=&%V 2� !�Iba+^2Re}-2, 'J� }[!� )EICl=�' )�l)� �E(^25f \cap1�'MN Vo( p \cup ')^C} d_k�\nonu\\&=&@�#Y�f  GammN� � \tr{�/ �q&Delta b0 #^C@)q$'B%(\backslash #6)b! ! \}-f � +)�gcu6-l)>2 &&\�UF Ejg f^C B�B'} d_j>]��%eR��V�5�Q ,))JY } m_k^22 jE� 5�(� 2 m_j�eu�Now�� � $ AquSBd. new , we � $Y`_{ �}^2� � i\in m_i  Vu �A�R7 �1�}*�3d_i�\;�&~ Tj�$��2�aq�z�� fin�� �� ���N (T)�1 � 2= i` 6� 8nu_2 (TJ� mply!�J�1}%�c�&' l �interval] \ $� �)�T5�0XM_i:{\cal S}(\mathbb{C}J�& N&��i="_ Nqb �l�# ����&  �Xs $m_E{ �N}*��\�Ek\ii�E} rho}!�M_i�ɹ�  c�t_� . If!^)lo�j� 75X�?MA-r alw} \for��a�<{\St} ({\cc}^{ {I_i�]- ;:�S�a/ft(� N� M� � i �mFl q�B\.'"i M_i^*)��dj6�".by �H*(A)B}=�A!~B)}$. &11} ity : J "  svalid�of"�)�{f "� !� )(P_{12})% �iU-}{m_i} 8${\rm tr}_19[ 8 ])t � !�U ,operators $ 9ine8e^cceW^2}� In order� appl�!i cl�we"��� ! R ies � flip~ $q/@F}_d:|\Phi\rangle � |\Psi@2� .9$� $.&,. � cc^d!�Rec!�_IA^2I (A [ A).��L2� ^{T_7�i,j�x d|i,�l� j,j|"� ���!�B&=&A�a|[e�).�i q��i Big][A: 4_i j� ��F}��)C ]}\\��R�F���)^T<� �)���b �� �m� -'B�}\;��j{m_js�9 .;. q��  } F��� �$~\ 2 r�]R#&��$���[�.*���$. Althoughm�esented�of 6%s��#k%o  do��nt knowa�any�a� form����ef})�B�ef�k|%v�2.��% Wa$e)&s �*�!HM_i=\Xi_i\circ\thet�each $!NK%y$ 8��wtrans�+ on. 3ll szs6~_evi�&ly�h0. Obviously,5�O 6in*{ ��%,����!\*"."%_& ider�"m"8 ���&��NL 1NT j'Al (T^{m3 N�*�(T&� Y As zio #earlie�E'prominAb-�AR ��a!��p�F(ir8e Werner-Holevo6 itself�� BB)�E� j O ���A kb�An2�Matsu}.� ina�D& method� Refs:2� �DW$}�&n� $list inclu�� iV(c9#� �s9��b�:��a2AZ� c%������ . As� � Au?-�jy�!fcor�)ngy!�ucaten"1!��2 ��e�K� 6�&l( ��etching�St}$"�"cu� )! ael� �� � \lR ^T + � ),\;� < m=1R� 6_ �} &C-�{� �"�=�.� �?(vex� bi9p1R ly/� ve Z���Q�*�F� d - ))/ (d-1r �5_0= $^T*f!aV ��A\�&�15([Weyl shift"]*S} 3A� of unitar��$W_i=�m_{�  |j+i � {\ mod\ d� �  j|���~:��d oiZ W_iQK(W_i^\dagger�C6?N:� a�dv=�T��s�!!%*a,-ANmI$o�"!�V��"ano�#]fYb�^+i}MH$1^i k_0 | j-z = 1/d�r�� $� �d�en��5 �$ap r�" e�.m*�E�S �_0�_0$JcPin2c}�\{P_i\ #�!eJ%$orthogonal� �*s��a!�olu�P1�uityw &m_i P ii_� T�ak�zQ� i} PYm���j�6]AsEZM��6/woR� �[us�陛U5. Moreo�/N %�:?=�\r�*�[�� suppor%�� $P_i$:�*v{5L%TA So fa�X��s wUrestric(/t�%� $m=1�!hA�atA:~v� �p&ll� rV J+m$9 po�%axll*�/ V}[Casimi"�%(Avduc8&:�(�? 6} �0 M!Oba 'o* $� $T'*� cc^4�ong2� � $ (see S�� on V] f�%~SU(2)^*T'~�q��i3 AM� �g^|,L= (4/3)^{1/2}\pi(J_is��b� )1au�� {i}{�ft(�'|2�Ӎ� 3| +4:1| - |1:4|2 - |3:2f ),- �2v�>S1r�2R�3�-F��b�3v�>2r�3�>~12�>�F�"�_"ME,1), 2) ,-r3)ſm gn4t��* four.�!zJ�/�Li� gebragroup m . A�\u�� $m=2$,C � HY Y�"� ?� E� 3 T'ho) +�}{4Z��9!!ap�Ccl7yN��� tru .m � G # �0n)u�>�� a�id_4/2 -�5�4An .$�B%�"!s}  i�(two2�*�+*M( BNa�B�$4| )/2$ upb&6m/isŨv����l6i>1 Y�+ izVi B�},+ FF-/2BuF,%�1] v� ,��ite" actu3$be writtena 2"�j5�Xed�� lF] E�2a!��v\*t0/�Ng &x-A��yLY��m? (Mf4{ \rm{id}})(\O;"�1})& =& i^E��2 G24  n i�a� (T'"�".o 2p515c�\geq 0���$ *t ! �.%� 1�d� �+� vecto�gͯA��1�. �*vs q�*[� B p� � W_k4&R3��: � >�$Kp�#�& d\}$&$8�2!u�b� |K|}nlK {�|� %B!& i|?W_k�e� �\�oR:*� |K|^� � -,��� atn5�� -breB,� (cf. �KingEntB #,Shor})�%can7)y�5�UA!>�R A�*�"d-!D")I)<\q)/ |)| 5L0%y!��%d\}.�!K }%U1g|>�i|W_k=FQ�>t,Coarse grain*p  �a$� d=nm� D$, �� �b7;5�� PM QMs=�",t_{U(D)} dU "� oplu#)n U�h� .%� -1]Y D\;,&ILU[5� a� gr�i(r2&0 Haar measure�Q�0averag � in� may physi�$=p rpre_ as a c6� �9J�ixapa23of�ol�:$ $n$ block�4size $D�i� 0$d=n\cdot D$ *F+ �&.a`"Tprove�9e:4;Q/� admi� nd�$n>1$B�HR�$, let us fb?0eDw�@y aft�4 suit� reshuffle�.�lye�e�a M^uintEXA# \ii_Q� U)\ER 2 QD �*e�^TC�-UD}DAgeeaYH :�)a�bN��� g$Z5e= %�� �)�! M A�)C z�or nn$.2��<�,�6�<5�o_>� i�|�=�&$a"� 2�-�b3A�.R�\9 *�to��u�(T����f$�� i�$ |2�=%�$1{\sqrt{d}2� |i, �Z%��1l�aj8b . E&d&MI�!�latA�is rel�@m2�  $\|i , 5~|j � via��1.0� ��  S/d�7e�*F|��cg��5�{-�9��,� %ae'${d^2}}{d}- �, L�yY~$D9'l]--D)��:�-� >"� Ω0or�eqq��� n$. �>=z9&Z9�m 1Y &b&� C�d�8N�6NIM�_. "��suffici�to2� e >=����ef!�)�no �er}��C�_ru�27! negaA term pi�Au�� onaly �X!E&� �� hold�.�����&s2 ��{ �0ao(to a vanish�l�B%{P�3b�  7�!  a�=QnuE%[ S&�E�1.n4 l("* ed*of� s!�still�n-t�E��ult. �:�$�$:�o2b�3-�4-%3 �3 34 6 ��of so-�-/ia�E�r )�sx22�as2n rec=+� vD R}:"�3? [n�C�G*�3$T6�6lE27&d)�8FN � =� khK {A_k}� A&� "K:^ A_k$, $k=�K�0r�l 5H� disi,,uished basis>J &D7C73  inA�� � �7��SecC}"�we�E.v!�6 qSQ�of�FY�ABtheir.��er5'. It tur�>uUata7 a ~8 @-�x �A�)�s,* a�� discussed�s 3-8,�G� �<e�Gfe�y��Cr!ap%U well. O=K handE� �#$covariant � MB�GTI�wes$Qe1YBPs�e�$Vco"!= � �6lso;u! '}$"m4"�rgu` �$�!xV��"!�e �)F� does� .�7I]�5?I very �lDG�,�id. Su&�I, we J��� �re��!���6 usF weak #@p" s.M mK;differe��} �fa�Q�I[� e� ]�}� �=)�Af6nbmZ�s� �Ely�Jfua� ouro at-r�th�%|Aa)"HHsE5always�Sfied �L strazG forward m�9rn%V ��mod >a�;Bo�H!�l way�d/Sly�� q� at A31'��an�;\�#*K.��"�#J�9!h�Ōb��Cq��/B �azKBb�q�LQ�5�1ر2von-Neu!e�>a�dv-a�7�$\{�7FG�%� lV MDl���chievFMI?&�probabi�, �Rrib} $\{p y�$$\overline�}:=�i $rho>�2��B� New&� �2(Sf T)(:c��J`2(k:�  ���:���� $C(Tq0� ؆&!:Fc �secon� C_�  Cl/(3J��� nu_1.W( X &�i� ���M"�O�,n arbitrary �1aR��tQ�� {T_k�!am����l";?6�9��(upper bound!���us 6�Nm62�I%���~ Os�O.�5 t is*C? satuXOdeT_ y+-�e�87V8p-1 ft[S!Tgl(e|{j} p_jt _j);gr#-� j#.�a�,]l <.%6�Y�>5-�&�>1�$worVB� pre�Hinqz�b� l��� sepa!ly�!J�Lv�,"O�. Now2  u=i%4j�$S4we2zc two s�aM�b2&7HF� �EDoIE2��4�*i,��:� � $A�e��=)y (�.bBirrX$) 6M��pi�Pi�.�act� � �' finite� G*{7E_� $g�6G$�O!� on} �pi(�_0 ��U�P! �_0) %;>q9 �!�he imag�  � �"��r�+eI-mix))h �>in ���2 F� 1{|G})} �Z� �cd}d\;>� )��to!�lam�sumaBEWt�lij� if !�� �-�):�B#t�S�`Q� s �jj��) ( &� Wt ,E8 !��Nof�%r"� 1xA�{I�*>+ }$ (�C$ $p_g= |G|�<��.� 2�)RU�i~cF�eS�+<ea2��/m *B-| q�sm�6y�wfM=�an }�!�=4El�2�A �k��4�MY"!!x$d$.# RT,��I!�e���E|eORa�l�|ic>�- iI $j�d�XI+ >~.���.  T(�Q_0 ѩ=$ 0)� \,\�)*JX �d5VC� %$ :\9Z!B T+by virtu� e7B��%��Ni_a~�of93.�2�=:I)( log�2�7 � �&�/� tre� Bim�fashiV8� cho�T��.uǁg"0������/9=F�'m<��e�9>6]2_0 Q �=�*|2A-, iQ�b:iI:dVI^;u'�"��3$%�%Ji�y�3"�s, #�$�*�12< $G�'^82G� $�D�S&�s'N"�tF�"��v���Z���q% �dPAyR9Q_qjM�'>$� iPJ"� V] NR�qnYrpris.daw# � codeZ�eWway*N8.i�2#o ro=�Fs5ir� (lossless. *3,�i��06 �4�!6*U ith�{e>�-+becomesCifkX�$ŧ�7 ��f\ �3�by>?1�Gregor}�=ed� sV:��!1!w&� l A� iv>�1Hch>}d�Yn< builA� %t.�a�2*z-��%�e>X . So�uc��� 2�N :: :� � %G$-3RepE�e:U/!assoc�5dc a1/�|RM�LJ� �2,3@�mild abHcno/  ( D� � (J�zt�/�~�/ �:�X��9�>�P��� ���SU2Q���) 1}{�:_\p2O�3�0kho.KRf"6�.`Zf�_! ���B�Z m_>�^2:,la�O�uOd B��)f� � �}Q2W�8b=6(d+1)/4-�q|E=��kB� �� .b[d0�?1s� ural� [f��[.A�&�b�P0[ J_i, J_j] =0+(varepsilon_�D(,k} J_k, \, ,\. i,j,"L+ 2,3\&� MR by m/,m� expo�?d# mapp��in� ��. %In��eRg at %�&t%E bi�  -��5M�x_kU�*r) 7J_jl�<+�:= ;J?+_{m�3 2L$j,l,m} x_m 0l3O(x2) %m�%��8x=(x_1,x_2,x_3)�Frr3L&fhQ(mad"�g#  %Yq. %5)hK qS��F�aR� ��A�!)a>�R����i&�U�j)�l��@E+ sensn� T(%L�, � .' ��� '�1|!{��a�<],K$ �Nei��"t�a�R]�?.-�-��$d=!�fE�re�RkR +Bn�!Z�k&�5�:J�"�>�we3 ��dF!9�>$�T:�$ M�~Iros%2��ߑ>*/�,start �F28t*�as�>�t1� � �C.!'&�f= (R�5 >(54| �5S ��A� n am�.M� D"�"R/,�^�a�y2^/ "�2��S�åRiL04�� } dgmmmU_0`� gu[4��4}N�7T�[�"p�Z,E;���~��$U_x:�(\exp( i x_2vJ_2))1 1.3 �w93)<�y�Jt \rr^a�E�-x(unt!j3 0^{4&  dx_1 |!J0^L_S<3E,sin(x_2)}{16��VU_x9y�͆rhnJ�]<F6%� .\ ��4)-K2)�>�a"�$#A��+c:�1�abe�+naiexhibi�bNm Here�7�)$ E &l4a����+A3)a5�^��bn^2�FNM/a?V\�7} D6E \, V� SU(n>�! ��n��� *��?wi�"��� "\ &F 2��a@&��A��^Z*o�z!�VC_{�P "m�mQ5�.B� �h;r�: )taW ? ob�S�2�(qu"m*-"( I~typvbe &&�g t�qr'*Me+ed. A1�& oint��.&�b .mpa�ink �{\A�ll} �ms� �bWhilev$canz�bm�gex@J��Ao7m*s ���*�M�*G( ��Naah M.�& A s M�u Ve)���5idJ� A*�I� o�5�W�7�:�', exists, nama-5&SH.�c� j�1C�&ppl t %L nt�&[0- ]<��) %prepa�+��af�2m�6NA4�6�0�r�K %� llN�s"��bh�(N me� %:�a,. .�&)!�A�aZ!d, %un.%� � B�rAG . An�"c2� %�)u6� J�=�]? %M�9�%r��W�pon.zE&�-Not�,&2�c�uttonc�Nimbi-i"�:)�}*�1w markwuA�ic�t�\���(�Am��"-:2�of�~.%��+�/W�8}I6I>Q��(s b�Ndirectly>�46I�:� �ABennett}V�E_F�tqinf i n) (SIrcjtr}_B)4J�b&� infiR$$�o�mll  sٝ I.w� I� ��5$y�A��q/,!! $asymptotic� I%,^�C��lim_{N.<! t�`1}{N}5..\QF�VG.l��*""o& 4d  ourc+oq��@"I�:�,!b9 at�� JU 3 9):!�#�3�5� �& aBZ��(lo�GamL+9�zcommunmie%�x rast�C�&>���el5�(aq1�v�>Relent�`ich!�} b�!�.Qt�X 1�2n.�6$� .�is �.���Em� for a/B�:�%si#2:�F�'��&Bpj!�G '>�-m@�.{!Lcɰ&�eTo�-B{�E � �# L�#����d&{��,"IM ":Ss����!(M�q2�exisI�iyo[� �&�S �,T,Cost}n6��!$&� |�Ds:"� >�&�z2c" {$ l5*�7Stinesp mdia� via �,isometry $U:�9d2Y0["� cc^{K}�! !Yro0O$K� \n�8�@@/>l{ ��.YK)U carr)V on &�� $i0K}:= U �d$,6z)�])es~]6?ALM,="�+�p��1)r  �� Be*�4ZcE�=H=�i�.BS{�E�E":� d� J�U�5L m r.&�rm } [SG' S�]:).�] � a� ��=R $2K:"b�'!�4.�4vE ;a�s 4 K}=)�0span}(|\psi_1B#,�C 4 �! =��| -@i �leMi( |1,K\M|��E -|3,L��H,PK r)/23M n2n.o i x�M,ALw��+|3h||4�$]F�Z�g$ l( i {|1C -E|2ht��|4�V�. kP*q-|1`r5$!c� sTs" 1��^#Rs1$�>�g V� 1 =(-�1��GI�| +7kA�%�%  |)/4ƕЉQ�A{Gju�*0 "fa5$,JJ 5J�F��. "�X}�s.I6shQ{Summ;34 lu  I�PpցJ in*���%�4 b���"Z�'���R Nx.y��-n ! �Y:j*j �@� �>j;�7j;W�qtro�lt �* chak/eri�|� ��>��*q "� ^ ype, �X- �po@(� umabX0ak)�/:Y 7��T!�if�;>� von >_7U*3 �qf ~ �e $. sS�"alY�D� .��T &<in�| detail,� ��� s!$�yG"rg[>rA,]d_ALA��*ed�. "NNw!�]��,%�R�u�j ax"�c� ty,f �5�:-1h o�zEG>j"�7�is!��1 �!^d�=E%Pl#O!$5�� aB fn3 �Ac�Z ledg& a�W"8nk M.B.\ Ruskai�"A.S.\�$a�93�� Y�=W[ nd M.D.\ #moa�?PhyfRev.\ A a56}, 13e7��Amosov eG.G7,:�rR.Frb��Problema�o��1��3� 305 (2000.���P.W.\ ,E(un.\ Math.\�L24M453M4.M� OK > sumoto, T\imonoIWA�E� �Co� 5Zs37FsABoAudenaer&Dd S.L.\ Braunstein�g4J��x%*R!� licki� M.\ ,��,-ph/0407033.YR  A2%�!�Yura, J9oMC37}, L16J�Rwz T!P,GA�=a\ory ((Np]��lE�4Amsterdam, 1972KR�$Conj} C.\ �P�2, am\Iinouo E=4�192%�12<E� �.�kA�_)#2�%� `3}, 43M�2.a)�D.�a�Haegem�zMosonyiI�a�(VanpeteghemIG�)�10195=�! En" R} % p-� �1B, Q@2�a�CompuE) ��186%33.�Us)/!�Serafini)EiserUh���Wolf,q�2�71} �012320g5.gShirok��M.Ei�2�11091= FHdepolar��}�Fujiwara�0Hashizum\'{e}EF�G Lettai\) 299!ܡ�206�!sUnital)9eaN2+ MI'641�2'LD2�%�QYA�I�aEO�-2�T�y6I��22 r2�FHMV04 �!�I�,��^.�B�; N.\ VgNTY. D Suho:�203� Ѫ�.�{.3rj3341-� %"� � LloydGausM�V.\ Giov�tti, b Guha /, ��4Maccone, J.HE� apir�iH.P �Yu*&M_iMe%�$92}, 02790��2�� �B�� �E�M* i]^�L 0421�2yGLRpb.s2��56Ao0623075z2�p� Q�V2�N {\emN�!l5pJc^X�q�TD8by O. Hirota, 1!XWorld S~Nific, 206�RelaxB %5��P` yllus, OA{\"u}h!��� \ Cu� �N70!� 6231�J;��"<, .E02076 S�cee�/rZ8Sixteenth InterAhal Sym�>�>n�}e���( of Network I�S|(MTNS%@, Catholic Univer]|of LeuvA�8Belgium, 5-9 Ju�h<��f ��21202.�BS)�A Beck�� Schl\"ogleQ%modynamA�s  =�U0s} (Cambridge.�Press� �92�� �z��8��%��40307D��3�N(��,�yNa� sc!�6 2R�7C�;88A[ 5790��2); �Hay��, ��Imai,Es  2k8�T��S8 3.� ).��5h �b2E�4>�=#12046]4G`3�� att�.� ���od.\ Op�ax91} 2.Z�2fM.�Nai[ �A.I. SaWYk� of &62�4(Spf4er, HeidelbergAX82x"� C�2  , D�/DiV�Rnzo �J�Smoli�nd? W.�?WoohUs *2,��5k3824 6��}R E.�!W�  Ja��M7Plenio,�Virma !F O� De Moor: I�M�� 21��EG1); A�.�2Q K�A� Vollbrech!I!�N&2A |6�32310{2�>�!Vidal,!x\ D�r� J.I� iracJ�2����u�`��b� �L2���w>�FR1 docu} ��\�,[amssymb,amsT{,aps,g�Cedadd�0(superscript 0]{revtex4} \uAG,ckage{epsfig6@icx� \new�Tand{\forget}[1]{} \def74 bar{�utect\@K4bar ${%1'lax \b� Eh@tempa{\hbox{\raise.73\ht0 X to0pt{\kern.25\wd0\vru�'idth.( height.1pt�uth 8\hss}\box0}}% \!.(choice{\seta4{$\displaystyl�>mbda$} �}% B0���-)��/%�^5\e)A} �|get{ %!�toks\@st.)csub4Yefstepcx&&A. % \e!�@saved1{v\c@}.3b=S.and�'-* %�"��I2kthA._}% %exa�9ce :olB7\�setB�{0�2q6J��9A9)Dend2G% Ve:?z/)l��!�2.=L} \global }%\@ignore�* } %:)12p\+s,^$rf+�" pacs�<�L(nofootinbib�*%�J %.}�i2bm}0�:-adA*�onerB %!�\length{\topmargin}{2.0cmEeeex'ght}{8in��2 O�ءj \title{{� um�Ccw&8 ��ler=A atom�fr��pac�&�con�� cavi/W}�4\author{Alexey yan�\affiliS& {Institutd%� Stud;L�D�+t�� of�8ics, Texas A\&M� @., TX 77843, USA}�8Federico Capass�2� Divi^Engine��nd Apd, ces, HarvyT&� , "I 0, Massachuset�,2�Ed�TF�2��� Step�4Fuʠ!=�6b�Nf ZfV�y V. Ko�ovsky:h��b�6�gof5�� �RAS, 603950 Nizhny Novgorod, Russia�I�Mu?$hail Zubai��ʹMarlan�Scull�R�R6SCeMDUltraf�)Laser)al-a42N4 Chemistry, Pr� ton.=NJm���abrGct} W�'i�� a gedanke�%per�tV bea� ���Er� nd� �re .�t�B�0 -mod0crowaxw��y8�� EtK=,=�u���*''-iY'' ter�E�h�, Hamiltonian&�3% excix f0Pyom �si�aneous !f��a pho!h � fF� ��+Wc)`Q$ slow swi�{ &(x�,5,6mpabsorp p"�W��i��"Y>ԥ>O4der b^UnruhmCor.�"ZNpos�/�sharp�iy �QaJBA# ��"0Cg�G� ra ���1b"�Zten�wl,�!���Eh� of �Y?S]n.$q?ny {- magnitud)�x ��Enx%��-��nt5W�4!invI�hGjlyA�e.��\ :2 ��Pe1AIa�# eadym is6�a!^rW,d-"N�. ���2some�#s l�"zx!r�veDV#ent ap"~asc��oE�hoade��A��affec�9he"�;d6�in*XXsit�%s,!Vg�"f�Aa�mple �jdt�c-�-=�to� uOe2�P^.P��\makej  %\% pagef {fancyQ �%I�$h� igu�p"!�`!vacuu�\ viewiC.�t7erP.veQ.�.sub�%Ca��?&%&�%"alm�3y%decad_NOne7!p��rkM"�0ult�#&Ocn-i�e%�!�day�-analy/&byh"�M 7,if'DeWitt[.�"esف�4s  2-7}��ess _ , it�" ��ni-�� EM,2<�)d,A�o!�t�O"i+"(^7[IPr�. tacٙlackbod��eMe}.� se s�  pr% �a (�tlevel)F�,|8AcIi)�|2(ency $\omeg����e�*enc0�H�D�!�$. Gbe��its W��3�'ba�] g49,�XBoltz�,��N,rm{exp}�2�O � /a7,�;��$=a/c$, $c$�>E[p�� of l a�)�. U,dtunV9, evenE��>�c6�``5)" $ �$ �L,x 10^{8}$ HzMZ8Mom @5i?>10.?9}�Bis1 V,,5im~�$}$;!�.��of�E�a >te�%.�RbO/%��)n^7�!9N�2�in)0� A%is �;� !ptaeap"��edJ)�V e&�2� �sN���pro���h/ a�� � �|Fig.~�!"Z 0figure}[ht] \�g4`�(+,s[scale=0.6]41}} \ca�vI �(Fig01} (a)�&o�8. or 0 :��E�F (de� ed)�Gt2� ��a $bs (emits)"� . (b)�&%te { /�.{1Tw6'D� us]Wnegle�~i�% e ``� � i�<ion''N� ��� (�b6�c)� energ��UJe �1C!: drawd  ork͝ by aa��c A�3 . (d) A=or ion�J $|bl0�PN �N2�<% �Z�<c��0 }Mq Fur�F�'q<�)!za�ny�+ 2o.A" � ��e!�ro^ e&9�_ acqu���Vfea�s�<enhanc*�+� q$Q"(QED)��=�eE�� in_Q�* high-Q� . 2@u��, motiv\%Itud!��>�it{� }�� �"� aQ^�Q���^��� ��;prl}; 퀉F�] od�=s"�n� H ��!�we%h& ��U9~9fi�661 !�� U�& �i�byFs, but�o u�H6� F/ua'A3 l1< �)��ng:p1�� � #s.E ��0��X)��,� v�= (��typmEse)%3B Q``>`"� be � ���aM��8AC�L!��-e=�B� }C\8X i�B�}�� � /*�$,X0 `  $\��3��H"� ATa�(��a�(.��T���6�!�m n�L� A�a�WeQ�ag e me�.is86R��I3of��VndE�1a �8)� sam�;�>df"@ s� �`n c ita!znon�ba��*� due�:#�/�Q|E@erm $\hat{a}_k^+  $\sigma}^+$�:.T.�(\1\}�F�:soi=J�==%M�6�-A�71 AB)�!�"�l� $|b,0͆2�i|a"�5�7twQ@��e)�ic��.e�p!sudde�<=Mz�; �&nA�e�A�#f����F�-�a s>�e�*$2 �&�f i�they avHdA�rit�Prole: � s � a!�l�.��mpanie�9�.�--�� %�A�u3*a"s^!Zo�|>�$Em . As�e�� ���zB��� oved, our� ��y�.8C . O���| es � V[s-Z cruc6R!Y < , e.g. 4gmeN�c � �64nomal�Doppler-��^�umi�+�]�Ee )���nJ*(�1pmo.�� velo\r!�"Ya N�!�^Eso)�=��w�G.9ly � � �f��n� mpha�|>�@ginzburgɁ]��&  Y���![uhAf yat�C�P26  forc�Ik�A�Q � c^w�4n��� ory.& ��?6�r no time-�v:~M*erse�)k�w ccur�ȭ� AH�6��CerenkovYf�LV II� uN 4� !2�Ld�� �~"��zEI9.�6� �5~] ��n�iv2 mZd0E�& . Nexdma1&� �ri;��!{ -I�{ �T> :G�.�s IV-V%A P 22�2� |.? � (R�o%%A1� dard- i�.bd6�!wc"�k�K�Aӡ_gra3[Ej���AU!E�9ry a���=:Ely��e�v*pE l���ch��sia���f)%��m�6�,@�,�m ^A�l!D 1!B���eU��M� VII� <"X�II�}� �S�a !)2 QCs ,�s_-n��N�!�)�6 AR�:� "E#� H}�H� H}_a +  f VF�XH�[� 6= \hbar`B� _z"M.� ��Q�jA�nd����As� >k|a>$,!��<ive[��&1!�l��p0ce $E_a - E_b��6�5�H2 (|a>nih�DFHors�Ak-s�>/< &KJ>6�� a��>N  s�",�'en /�D���mA�2le�iaeA�- �epA�o6�� *i�a.�  bee6te� ��dipole62 J��@> 0M�VI�bar�Kk g!�\�.�q �  8) u_k(z(\tau)) 5M�4 ^+9�y�iOOH.r})eFm���z�7o+},.�?�s, M�m= A�b|�I?  =E�ar�b5oaiI ANlow�#�=�_c+ $!$=�+$\mu E'_k}/�U�!�-�coupl��"�Q ]J2���xo!�)� mo�$$%\mu��!�M�icmB��� -E\V� }_k}*,`UI� �alu�he*c  $-�RY 22a 1xK*b ^�au$ M.�6�.�Lz6i�8H1z -� rho}�Uu j�me} i%�{MdE�H}{dA�A \A�[V}Iѭ�qI]"�f�}9D�.���i�%e�,�|m�obѮre4oing �}har��i�a�exp(-i�et ��)$m&�t<��>b=q >- s� ?-i ��a�$e  )u��2D �0 E-P$tuE� )D�al)�oe�y f��m�wY !�� o use "�F] s$$%�V� "� .�-].� &2 a^ � *w"R7�e��D-Ga%'!�5QaWOur m�}goJqlʝ� �>� Eq.~(Xme}�V  "� in var��"R "i!weE�getn!ins�!bN � Ł$&�(�!���byz���  �-�U,"^ �@���y$��*� �ia  $U �J"� n-� pertur�%hV3.�0"!?@2Z,>fI��� ����"p!ub {& 8�of5Z� } Con�&���Kɘt����ye7$aV_���Q �RAj.�!*&��A��yPtur���lI .B�B$eak enough��� L��� �+ �nYZ����� �u�G^�oryJ� �I�)�=�I_i-�(i}�1ar0��^)N}^ "= >')\, d��'iTB� YS*e$ND2�!��2���giv&F� P� f���g� ^2 eft|�Tt��au_�6 x �J�)|���)')=^� !!5' �|^2B t'2�f�B��E�wPin��.� Il6MZ�E�2�m�uziDAa $k$ta/d��be &�nn,pem} P(1_k,a V�jg_k%a' �)u 1_k|2� |0_kQ�]L a-��) "P��J�-�]�=)�!�� e6#i@�� ��xod�&�B��� pabs!T0�T5T0=T_k |1�RFR N.�}r-)"&�tr��Rindler�Gq#&6 1#2}  = t_0y U{(}P�sinh}( �� ), \quad � ;bc}{ %} =cos:= - 1m�^ $�=� = 0i�ae͎&im� la"� (��)� EVEe�_r(�Tri��EJ5/e>��vA�-of run-x s�% ͺ�R0bf k},\; k_z=� k}� v}/v��A��2aB �� r���o6x)=2t�?) .� H e^{0 -�) + ik_z-�$}+\rm{h.c.� .B�WD� ��F4B��Wf�orBp�x-d�\�N!�cor�N�)�ic )�&�!�>Q$E'_x��D&x-E+�Eyhet"!��BYlabM��TE_x"]�Kْ8(c-v)/(c+v)}E_x"��$v=c~{!\tanh}6z�b�l�eh��2{=Ve}��i�%� ~ ��M)=g_kB.e�}$.vjD"J�p m !/!(� }$"r n��-�aِnge)�: $a1|e&k}|��/c$�2b�54Eqs� ��),&  � nto $�c#�)~(L��Z�"Z�$"} P�Gg^2 |I_a�� )|^2; \; ��g^2 |I_e#, \�<_�!,�,!"UUQ+g� >�bfint���a� {l} �=9h� "� _e} )��*��i�\nu6�( )>K-1)+ }�]m ]� , \\ =* =�-�/U� �>B!-id"r �!2� m1�3 � a� E��t̋v�a��ta$ e$. d�;� skip%�index��T�rQanteMi�!�� l2 �S:).�L�S needag�l�,�Aa�-`,"&�A'AW�ts��M#Uaa��*�*w U�� "N.i�is $I_3)�^*$�H N] w:c is $i2b!�q`�Y If!ire �-� wall! �T� y�l�Hng)�_i:ip�%� !2 ��)uip%D8�i�g��-�s��r!H�*:"$xApU .C a> e���ZF����$>a� {a,e�HY� e�r SJ�H�� 2��}�i�'�mp :au�}!+t|l%S� ix} ��<>=M ! #��z�!^��\pm w\p��}{2-} ����(1\mp ) * )-$j���������`�A����. U�8;�>l��J�W� �"�:� � 2-"� Z.Y�Ek\p�Y� nh :v }, \2�a��_��*V~B�2}�p|�w�I��!�eF =�-����b �.Y( E-9N�b�u�3�e��-F|��2� =M�9B-%%*>�{!c ��f$-JE� 5iA�f�"(iar Planck �|o`*%t_.�[�k_B T_u}&U�� ՟� a�y,�=)� KEerW.iJq��".$T_%� �5 \pi �c+��9�2/Vt%&Y"���%$in agreeme < ��&�� ��funruh}-��L a)}{�K�5\�4)V�4F� 8��/"P !�� e�.q��l� ref.u�' �# �.�!wg�W��c.) R#5-�!-% �"�J� -pe�<I'�"��A4� I��j v9�&�$+�5 � � M f 8$oun��Sec.~IV� V���n.>:%dpre���1#%=f��ul'�!Mt� E3t �o�des ��!t"6ak� �FWMzI"�&N&;un^�;s6�a.�T� �&��#63)x�5 . �g��!o "�0� to�>m* ��MZ.�!k(MfTg�!|V4ach"�5�$)Lamb,mm7mD<)�ula�`�8� '�te��+u �0�edA*~+I@"�&a2� �;\  rF4!?a=�Q.�nrst�d�'�~(-1�P6@r-95E�&wh���h0}A^-E��M%�� re�%&�"��%veB��mp�N�Is&fCm]��d�&�- � ���.�YV},.] + \(>3 F�j�wta.Jl,F')e '�i] S]Q M'B<Mare*%�x 7,&A�rFD�1ioe�4de�seeQ[!�A�!��?tAH�ica� Ma s-@s�) [2eq !F_{3-"X� fld}(0�Tra�  o�ow �de�H��A�dg7e �zE*�2})&� na.� �}B. Ar 2��bTr_�}I 6�M2��rhh�?(0)�$: -%- :B26�a. & & "�� \\ �.� V2|=� �Zl-Q =A�:�f>�.�� 7�me3"] 1���F˜�at����.H�t$,A"�f�&;*��,Yj}œ=rV#� �;dqu 7���G"� =�<� �� pop�-io�$��)����~�� _{aaA�t� �d\m� � .�t} dt'� (Q � �E��I9�(tMF9" _k(tE�2I�� i�) (t-t')�'�� \{t  Ey��� !�E+Nv��{��^(:�^+ �A��B�m$F�)�~�bb�],6�1R�1��2A~��V!(�Dang bracket˰exA�sed via"$~"s� *Z*HR�&b6�ac!� 9�n=Y� ar{n�&? �%-I, �T X6�)�^>J= (1+\Z)f[�ѩ�:9 Af3per0+��a�g� �iee Ltget}�me4%A;�:wme5>}~ �c�q}\~sQ�e[��)A]�af+ 5��bbi&FIt��F&"� ��1P�&�FI|c�� aa}/ A�=e�-��m�/kT}$��e��Y!,in Minkowski �� �ra&�� �.�E (� -morG��� �)~r.��D�� � ) ��Q �o�:e�9)( iJ�*��n_k��& = & z�� } � Z�k��u�n@  (m._2%- ^+)_Cz' |G ��M�u���M-��I��-+a�� N,A4M�,; cc�6e0p�͐�\{y7 a�wQ�k�w �� k (zaM- z�ŋ(�q .] 6� ��k >B ������E ��[5)VT� ZT zT,v�"me6B w #$t" !),�a!'2�5we� c_*��204&�in�8( P. Milonni�0,J. Audretsch� ( R. M\"{u}l�8� �HN��BV"�.��k��a�: �~in�4aae"+B�! s�Ze?e�y $�", � ��!w"�1; $k$9ch"�N� ��J| a> ��A=\{ PQ�{k_0}}{(��h(a./cE�a \D� /c))� + D�CvFA�FFU� & & .� i�~��<< � �%me7^�k_c����T� 8' 3&x$1/)I x)^��i �nO�H um_p( 1}{(6�/ct w�p -i5!|<�cY`*�o EQa~H�lQ7&1ez�l"ethod)residu�����&D Y�B�8R�Q�-t����QT A + (Q�U�1)("�1�� 9�E��;\��M+STQ A +1!$:b+AM�\��ZVbat} n_A� �1}��2 �ID&� -1}�!n_T>=*�. }{kT}9B���k �n0.�~unimpor ��� dmTibu��Q&p"  s. B8})�ow)�/QL S7 SJ yg�7�MS.vc ; &\ .� YBe.�TVG�:� }�]P�?.��:e=2�" � a�!u�! �d�&���IHx���:��L:�](�scopic)�eng�%H>0�1 �b"JBrSnk��dela�rho^{i��is -Ba! (macr:rK$\�� N$E �PnVA��i kj ?  $. W�Bc! = r t&ސ�6*M�dI�g:.ha�2��ed&'ofkIon:2� /n {9#v"-y $^i$1Q� �� ��6g�M �r&�6i*�� ��9�a5�i =}B4 2j%K:i+�"+(b{b�!�}� | \\.� ��Z �MNg \�7�+E{k���/o ] rho(s _i)�- [�%R}Ř�ime�H-N� tr$_�$a<o��l��n�:�>����� $ic�Q�2_�1me%�r�AuHer ri,T-2Q�%�OpB�()�] V�(�S�=X �2�+�'V$0'}�% ۉM)\�ran�I�al�s �"uX ���:����j�rho1} �R_2$, t<|is a steady state solution which!�thermal \cite{Lamb} \begin{subequations} Ơ,n}=e^{-\hbar\nu n/k_BT}\left(1-{\rm{e}}^#! �)� iJhD{\bar{n}} =\sum_nn z,n}=\frac{1}{f�e$T}-1}, \;  �!B R_2}{R_1}F�!�6 )�han effective temperature of!U fiel5�cavity!p $T =� \n�� {ln})2[R_1/R_2Md$. Thus, spontaneous emiss!�lof randomly injected ground %� atoms M/ �result%�-isticsT4the mode excitE,. Note, that Q8F:sic<4standard Unruh->4 in free space!"due toV�0into a vacuum-c\reservoir with a continu!*spectrum��$s. Absorpeand9M0coefficients qw=r|gIi�|^2q�termia�by! 8 amplitudes $g 0= -I�i}I�<} \int_{\tau_i}^ +T} V c d$�8the matrix elem �pV_1=\langle a,0|\hat{V}|b,1\r$� $V_2) a,1)0)M�interac%DHamiltonian (\ref{}),!f!Lively,eL their explicit form!�given! Eq.~E }). Using�ME� �$previous saO on, we geIisam1 E~M�xlimit $\nu, \omega \gg \alpha$h q)/a9�rA��8$R_2/R_1 \simeq 9/(2\pi P)$,�) an enhanc%��$many ordere6magniA, as comparedA�aOdexponentially small value �= \exp(-�/ �)$. \-{Eq�A�م di�%��-a�� } After�substit�$of variablA�x��[\nu}{ �} �� e��%e A�}$�e.��1{ }can b�V4pressed via in!,4lete gamma-funE�s:щ�t \label{)$} I_{a,e}(-��aonu�N( ��}ΩY)^{\mp i E?�}�{Ŵ \pm $piMg}{2 Q - B=(} ��[\G�(\xi,uF<(!=_e-i)})-0 u) �&� �~ $\xi=1\mp�6�$, $u =V�$e$�% �1!�$�u)A�� u^{\infty.4x}x^{\xi-1}dx$aR��>� 1�<. In principle,aA^�m)�)Q(fua,�Y[ M Hwell known. Some re�en��ve graphe�e�Zw]�as�7 4frequency willa showalow��\Figs. 2,3,4. However, it!W(more instrun and trans�cnt�d@directly calculat)(=�l�� gral-s4int}) by apply�� !�by partsr%methodL�W,ionary phase-� arti�r��consid�p most reali case��I�2�%���gBm���VsummariA*asb:s�1} E�a^b Fe�)y�i A f � = B + SB e�zl 2} BaH .�L t�g�P.s} '��|�+  ${n = 1}^N 2V1}{iA^{T �* p -1}{Rf5 d}{n} b )^n  �V2I� � o(A^{-N})� ��isE<contrib�p from6k� $aries obta^ N�,zr 3} S!rsqrt{ �2 ��i}{A f')[_s)9' �_s) + O�1}��. Q=��� ePe-oin� s$ suchI�$-��= 0$, $� \neq2expanda�$M�$�M Taylor se%Oa  $ s. I�Vassum�� $Ae~1$. We�� also!�i� separatel� i� when!� . �approach!�ne�/�B2�5�; see*- (general}) b�$. Supposeb itenesAVa!Knu \geq�G �i%J . W�,  - ' 3I$� � �B� SsAZeA1"0 \log �$�*� -l $I_a%�Eq2' ��� in�� 0�k� ��$far enoughiJ�9S4erefore, i�% et a&asA� >y!�u�bib} }^{(b)}"B %� \�~[J (��-1{ae} - 1�Ua�p g _e!�-�.��]}{-iMbU+ � }�A��+(A9Q)B���!F�^$f� s94s=4I����}{|�EG|�� � 5f(1f.�*�  +!F6>%D�!N� 1pi}{40 .>��Gclear� e� �5dominate� b*E�2 I�accourse�" �e y`_ a mov�9!�.eyFW $ � �X\�;Le� iof6�2E1޶ -�� )� � i�1*4 ES��m�> �*k �$of a largelex argu�!y%"� . The&:-��,e"� origM5!�Hcou�-ro�ieerm!�ropto 'a}^+  \sigm���jJ8, does not have�1`� �ꩫEg^��E���its���sol�KdBJM6�p��e��ri��(-)�)$. If@fur� �� long�3.�tim�%��jH1$G second %Ro� � -h�"a !�*��m� greama8 firstJ �wq�bh%O� E�0P(1_k,a)}{P(0 ��� nu^2�� ��+-^2F�" equali�n R.L}$�H!# V�Exa~ a� son', )�b��쥁 =^n coinciRAcEalower%�2g��I!jis� | �'le S main6�ag mesyTY� p� )�a.D%��t�e� {1c} woEYs�aSs})e�<%�0 of probabili�AI1�v"2} )��"2�F���aboa�xs%K��dily � iforarbitr� 5$ �c I(}{N}a�.�!b.|]�\  addi A��뭄a��s�-{7� �ain3 e error"� erf[z]!~detuningf� ��Å{��2�����6[ 1 +�rf� -���a�K e�2 1�.  i\pi/"+ �(]B]A\ $|�A s)[)�%�j�profilql.H line�0i=�� 1}) or.2}��surpri�ly�;A: factl 6��.aA�eI� $$&k B���-P��0{k_B T_u}}$$ ��would? ec���l baa�of stud_.D. HerJ� j�z�� ����} ��faO}�s Z*�.�our�U!�b�r"�m��a�5�� �p*� $$�A�.�I�}, $$��EWb?T} %&>$e}{&�9�" Z?reason�� V5�p�\ suddL urn-on��!s��� Z nh�a-S� e� ] %�non!�,batic switch( ��let� �i]arrow -* !~!Mfty1 ���in*�� }) zreduc|o!� ,ea9I��yF� ��I�� � 2 �o� � :1� =*� i3 a ) 2 2 ,Qhz��). $$ &�aWl� R ih2X-�:� V 2-"�Z.Y�ֱ���inh :v},>we arr� �# -typ�b`u�2} �V�9�ye�Jc& Angulapendenc�b�.�2W }g �conclu�&� dP����@ p!�axA�q�� a �Pe co-o agaeH��e��� b��"> a� i�electroKea��$ hn*g X${\bf k}$-vector. Simil�(to Sec. III�.*a y $!� J, a)$�e"� vto�gsimulta�!photon"b!o��th �i�m� �wa�i20Re& nA~�D9��0B� �./�Y{$k� by aF%��~A��onl�� �is�� �� $P$"�s deno�fi� 2)F!dQ� ��s�6 ���bq 3. =�9.�.I"J}�#)N>Rz� intk, I�GuiF "e�'k_z}{k�xp[� t� k_z z ��� ��]\,Q"V� $k = | �|� nu/ck.eof�VE6�|�#ll :�E � �or�<� o $���)�^3k*ub�terestedZ�i?M.� 3}"Y"�]s{A�tra%ory�a uni�" ly accele�dE}�*a��b]!�� �.��n1���)��i*�c!�ّAB$AexK a\*� (\��9� -�� �\cosh ��EKb;�zUAB�  A��%e��c6��,!�i�9 � ��� ="�fi�G�d5M!�bxim��%&- h ary Ain��itV. Fo� Aq p �A� |�li,)�2� �%f� it��gnA�L) ginzburg}���convend&��chang� .}v�#  \bet?.� \eta� (*\tanh =A]/aWT��^l!*I�)1Zwrittenn;2�Y�� �&* i \k� _{\perpnh �- \xi �^��*et���-2yX� m6� 7 >e�upi2}} K_}(6�F�*� $6'%_�c� o#e=U��!$Zw2McDonald�=./'iBka&)���)��5b�,4����&� .�)^� |K_{1-�R �Bb�W|�5+�5J�i�, ``al`"''��o-�� (E+ � ��si: !�,-p}(x) = K_{ � extraS of 1aG!�%��*�qvi�3 e d�"ng� � �aQspin 1�i�Ptro�bv�� M$of Lorentz��ns���I j � m  frame. �scaJ (� 0) 1we��e��� mal2m�o��#�w�6�,q us s��QB� q"H!�\��%�J�u_��R��he ``>8''�Bk" $& % � sn .��|ID|^2�i6 1}{(+� . $$'� � �)3d���6S#!�>� )s$)[;B* :'_s!re�H�n*I* ! ��.> o" easyA�fiMhaFe !- J�eq-+�:�#��QE ^2 - k��^2 c^2}1;���< QR76Mc}&c k� I{*-�"s 2� s*� PF!*L FD ` I ���� 3� anomalous� : itv%�6�y,butAa3/rer!�m0/)a*"x,Ce�t 6� $metric)fic�(} Remarkab5.�OH-d R�0�}$laserNf z$re possibl�jrQEDX,u��a9-e*- evlB0S1Q1g1$� �is�ched %�$e/I_a|^2 >�Uor,�) �6� \es� .2$ over 1@  &>:no�o6Y loss���%to occurI0��fla4 $T$c�in;er� ge to ens�2a��O�0em��� �c �� � energ&an� tak� way,�. >R_1AMI�4 f� s��-�a:d wa|3h9�UEh%�"� !�is�:Q� > m�$.He oz&6 �Key"<0$.�&a&�,  a/D c,��6 Q1 �/ s. B'�plo)� ��2 both�s u��b�, .�,a!�R4a�J�#:�-! X6A_var9,�6s At%��E��n�3�&"�e6�"B-!Onu�sfixJ0L1�A��A�ic< $�� �w!men�-.~2 ), >) R�E�4>U2(drops down �  zero%  ;n��[��ce2�n�Ţ�$,n�w��.sAeioscillatway. ) :�<��� ��-rB" peak%g�E�U�� at�5�.�cor�do�* to minima1�=*w*Fig.~36&~66@5�� � shif'��!Y\� <q*r& . At��Qs�9envelop�T0B e )(��)� 4ym�0E� $2(K2 /�)�)^2�,48figure}[ht] \ce��1 cludUphics[� e=0.6]4� \cap��{�(Fig02} (a) &7 %5���� $ (t�c)eH�(e 7(ck)^�0 -to-2~1UyPio %#mg$ ��!\^� = 3| $ �:3 ����"s� $4�7gi��by�11). (b)'!i�"��E]��s��(a)]1� �� curvQ2j�R�.�nd!�!� �3� J3��������4Z4��������� [ll� m)6favor�9�L�<� �$sharp dips������0 rum.% illust��>�4, 3 �H6c ��\6� ha�I�ma��v� an 1eYB< 1 ly vanis�!�J2�  <�%$!!�)�>�<�4 toY�>P![. �>& ��of � �in!s.~3,4�� �� 7 "��+� �^�� !s6Ju.�bB�%� I �%9s�<. T�s> iinset./Fi1:y6O Ica �2 ],�/0 R8D optinregimI�2�6� �m1�� 4">,�1*; TJl� �6� �A&>L/c$,Z+ need��:a a-i�&�. $\O�>_n = n�6 c/L$� index $n6�ex�e, if �  T~iT�k0r$o4 vidA�n- Jo. >v' �$nZ3'5�a� iA�1ois"W. �xQ �$T !� �?}bx �?nk%s&�/dw ��2�/I|�acteKu'>moa�wo �;-�;10 2*�&O Ez$ Dopp�, � :�< �?Rpro�e�� @ a"w!}C*+"ly mak>0�;�+ ��tv"�E��2<iB@[is�"!��awork dD)�!! terA forc!�at sus�� ? -of-mas�! �� �aA�") &@.&�<�m�$ant differ{$ betwL.no&n' 96�s<�Gt�T papeE-`<^��"�latW0"�1-* �Aa�-WwMerA���4)�!D\deriv�>�I>&�&�aU/�.�22� **=�=B:Y.3 I�� �M2i�EAntV%F 1shB exis3*6% 9���$ain!+t�=f�.'5wcon�Et  city. Of 5s@?�&2lea�-�c2'�quant� %�A"-e)��0�Vb�&eI!� ͡-A�througV1�(]�A�nu��%6E3!�A�O-r&���Lo Jp%1a�"�*%r�:tz ��'\)2 wav�Da: � forwarEx0�aAm'&�6C#�Dt 1j�8vE1} R_1=g��*1 ^{\prime}�4�)^2 -|1-EJ�9>,)T .|^2B&�#��#D �2�2~�4 fv� ,2�~:�=��- \nu-0$ k}\cdot  v�*nu+ :&)^{1/2F. Cr9iq� ,ors $1/(\nu'�-EA+*i$�A�� T7�.��v6�6aI*q�i�%��ba"�3�MvWHb})w�� �<�(}�T'�&�fF*f � $R�2�,�� E������.� �s@*&_ .�&��+-r��KRd ��t��$�7  �]��(e.g. X2� ) ��,J��1�3>J&&f �7�#)�G1������ nc�/injN�75�EeM��2W� �� C">@y�HnumberCpk*6��*RI� 5�5�!�!� is t-y�of�rs� vers��5�/%�嗡&)�9�c 6(i� /DaBx,.�w�L�2.;A�-�O Gitu��%��ist�Eq!!W`8t�%��`���q=f2��d`�J ends upeZJ g!b �aBK$�be qu,64aJ u�� �M�� �4A��.m^�cl Bto� $|2�| \ll��', lR�is ver�K dvN� ly� d��A^a�"/�}��(ialA��7s, 2�!� �eiW}�/e`�!�V��P J�; Eqs. �� 1}),�q 6on� �sI�o&pBr� fa]/s $F�\mp�d)T}!`at�8�#&� � ` &�, i.e.��)1�accum�H! p1�$��wA6 A�!�7 !5 &!�),��MU��2^on�4o achievpS3��!�tunI��a� �to"�N�[�;1B -B:NC )%�am41�R|Fs&z-1|��EAռ>��9A�u��in some_ nic devic��r�� klys� ��q8 ; ire� �/�Ta(e�� yU-�s,� !�um)c: b� tof1},*gin{aU {l} ��#v&� �6$(2n_1 - 1)d ; \\+=& + 2 n_lCN ]>�$ $ncx gerͰs��&�J �%$� = 0,k�M1$Al y s $ 2mA�\pim(monoch3tXQ"v beam� satisf x3�s $$0%(\Delta v}{v�%m6T}{At�$�%�$� 3D.v}{4 c}A lambda}{Lb8��rx  = oc>$ , $Lx�  length�}#)3ed |I�@ gg kv$v 1$ km/.$L {%\a�s $�/v�10^{-6(w.*t� v"0"qT)U�_N1 ��3reJh�N*A&H  �C�b�&�%^�l�^Crem�=a�"a� ak:� �"I� A��| � s, ob^S-A��I,RI����6�accor��to�b~�R:N,�o�8b�," +ss !bRBen�/1-3���N{so�)!Fnei&,!we0 0already discuJR. _P2e����&" ,���zv�n" !ing.4,$z = z_0 + A-)\� _0 tA�t� taum�� ]%��:" \  � )> pem}7:O b3�}  = "�|�0t_{0}xVe*�/- V4 z�(nu t \\R��t - \%� t �3tH2�B09�0w�&�,M�fT $ N $ describ���'Śc�"K:��{\r*O k A 6�/Op�j�0&�R0i^p J_p(k_zA)K �!ĉ�A@� 6�M��&1%�w�A =  |n���g�}{pU_!�  + !��*%�+!�Z��x)��BtUl'&�!.6G>n7�,&8eaked&| ��)}Z)�$�>Ue'� nu_k��e�N. R�)ce�q*!^�� = 9�"C )�"�Y�� a�/n2 �2B�р=�}$,2��> lwayGonger�n� deed,x�ݹ��s� $A��9G&� =5 { s9�N�OTa_�M� �� %d J^2I� A)/ 0a A)�%�UHtT~���is}at��!s�,�e ��6��vnoO�*5�c�%;jV�"�0& drawS�:e6ca)�to8_o '��r/8�z high�\is}�f� s�a@��!0,&q .Y���k!qicV�.�*���>��S n�8!If"f]�C� .��?gd�>s .�.������E*(Q]�J �Hn s ��:[ic"�i 1�'%� [_,� 9B.� �AHBY# aaZE9-� er e���L &�.N.�n"�_2�"�} a��K�8 ions0Ohow)l�me�is�^fv >%j%x!&a�C�&* 2"!V.�namely6�E��-�V 2� $HM a}_kFTM ��!ɒX^ $V_29 g>D�er]d=���%��rS�!�"tud/ bum� $|b"_�a�|a,&P_= faA�K-�]d��eԥq.��9��)i>�G, �ae7M� ~}|inh�.�r $�a �Yi+ wA��^ni&�y*)--�just d�[ng ���.4�-=&. wVn["o$%� O�. "v`6�e5e~e*QM.�� �&� "u.L &o%�euc ��bp%B&�C[O dC!�!aQc turnIQJ=+!�M�QED. �%a=V�/,"�%D .� no �� eige"�H *b�-w�lli�%�7 erpo�8M2��!���� !t1*�!sidt}BI+�Png system $ \psi_0 = .�VFg+A6�"R }6�as^ae7��1�q1?A�+SfZ[zq.��-_*7]噽-Sb� 2X ${�/$)%�of���bD$C  \mu E"�/Kt7+;Q��:�#�7 ��a�G�!&�� �to���N.\ $�ga�L*% |C|8sim |z�&I9�e�.,�|�A..!"��ov�� ��� �� ed dU_�]de��#�e�\���, �b.� 97!� to�V�master})S a��;!6?��e� 2!�tr$_{e}$�'.�f)*�nd�Q�*I%Bloch-Si} AH(a two-levellic�!ion:�n'|l  = (\mu jy)�,��-16u!�!�� 2� 2 +6�2�Kb})&5i�FI;&n#q. .u�s"� abs%q��\y>X"�;s��V�m�*FI_a*�<>� bec�SN�9$ePED(-\�K�0)E!�)d erv(*�I$ "�4noE�� �-T2��Tɗval� &� %�D]�%Na N!Ha2h���aR�5 bi 226�QxN�[c�#u$ v� �4ymdoppler}�>�I�| =\nu-��C)�c���!�l�wh�� � "9h*orV (i�,$disappears��NZKs�lhe�5�%� $�-P�*�9� edge ���W%*���or"�=)"��)$��5 2 (2l5V}ea�(a!����:bl���62il��()� o ex! �)�hS$g(z)$ �am�i�� ,*VP.V�Ys&��>w�we did�1S � -o� se, A dem&�&A�.w*��2=bIGfo'Z3 T 9-�� .�w.A �1$Y�� . �Shroe_er"�I $i� dI/�d = HX��ٗ? � = c_06�c_1 1$ y�os $dc_1 S+ (i E_1 � lEm \�%U 1}| 7m)T�cL 1 1}63�V++o �+i���HN  I� , $E�E� )�#�n�p�V>��.-�)pl7 $ - ��0:� ="(f.�&&� *����iWl�Y�"�.qertur�Son]fis $|c_1 = |qH�3"5o$HMN8Kd}�[!)�)M'']:�+J�H GP=y�\, E�'%9. �]a�� E��p����Qdia!�!�(o1 off)'a�*���!�=�F\qtH@4AWafqI��i�  laZ- l!�&�T�$I*�^=B� �"6) ���ijK�Gs��out2\�isq��:�fGQ(\p�_�Je Rd"�-  .� �dra8Gc��!x�6�(s�!��;q " w m#/2�')eRA���1&Z|a�i $. Only i�_6�V.���NA{ !�-  do w�:tri�"�N6 �� )f.�&5-�� G(tt$�WPv)\equiv xq=*g � *Y�ĭ p�^ �� .��&e^[.[AV �X �&$A� �ist� � u2"o'.% ary-�$� @#ua"�.StY a�io %5ei�m�͜x �'.�.� *�"�(R�� z�.lia�3W� �����&�,"Gqq�F��}"�G�jc�0�Es�E�'�a�=8*. .iC"�V�V Ourpl� l"?* a��._eas��Q -&Av���w�!�al|sx*]�X.� $e8�r  6�}HBoltzmanmQ$Vrm{exp}oT�\y$sim;9 /6� !W2�/9jR m��"� i physicali[ ��6�!� '�NPq4��xi;,,co{+�z�4u�Uhe: m�4P`1LsE�trea�5. BE4�"Iu\ �+%��@:E(&�X_igiV\"}�) B��(�E����A�&UX" ofM�.�R2��\si:�f:�*� (9X �*thrW �s�2 �v��w��t,2� "�. We em�#iz�i�r�.���8�� s; h�EW4.��&#����s:��f�-�*���� A��"� .2N--!�!*�t6� )L�&i,qRlk �i�"�� o&�B� } I���U�>..�)} C�i!c%�62E���>h^_2�]�E|j,�ZqB�� ajT6E?&�#.zGIsQ&-����|�.�/) auth:3 ekvcS:l_ ��Prt)f1V�D}, p. 64 Academic 5�9�,J. Audretsch�(R. M\"{u}ll� �94! 4056�Fd N.B. Narozhny, A.M. Fedot!BKarnaket al.Vk@65}, 025004 (20012Q8}�" @��.�� �unc� $He^{+}k�O�ic$�cc�\orc E��  10^8$ V/m.�9}L&f !'� �#�. ed (�g��Q@�9ntWzL cryogenic technolog&� �& & #�5�<FCbgscu7>4by ``hot" wall��\q�prl} M.O�:|8, V. Kocharovsk%�ROyanin, EA�8$nd F. CaS2o2�0Lett. 91, 2431�32�&�[B*.%ietM`0Uspekhi 30, 1y$ . %�MeyI%M� G�A��He�F4J�qI 76}, 4144E��iB.-G. %E@�rt�nSchwi�(A�i��G| Euro- .-a��25_A�%We�iL' uish.� us]ostA�v"� m�S`~���& %!� acte�{��� ``$z$-m in6Y"TFc�Aa8�A %{\unde>M {M}}icro9 2A}};$"0G�2!$Z$}} | % }6#E}}�E� 2>R}}"� $``mazer" a�  U,Agarwal} SeeG�B ofA ! �o��[�ƹR6A 043812 �l2)]7*I>G ��5�A5G416EQ77 Ere/6� erei�Y�Yab} 2��eE'�.al sugg��DE. Yablonovitch, %�M�%62�n742A�86�Boyd} Ryd�_�<Non�"Op�},�4�;K92a�5�S.Z.} eB ZAAv.�� e,it{New�nti!�in ͼ El�fdynamq ��A���F (Plenum, V YorkO�*K{t u��$S. Zubairy�BdC�=79�� B�S�o TBP}����to��$published.] 36�f89�La���a:�!KB�'he�R� LX!6W. N Jr�I���%� bf{1A�85�66)pedagogC"i%o90r PikeSakar Uit2�T�R�}, Oxfor/�F� !�or��5�.�m���}5d1U"s-W, relevan�"!� ���lem) ,. FilipowiczŀJavan��*�  J.a��c. Am��B3}, 90� 862� Rind�W. 5pEsۃ ial &* }, SpK, er-Verlaga�7B��A��0a��O ! ``kco+5ates"��Y�"�&A�b��ty,  keep�XA�m�uter&�">�C &�'�detail&�eY� .g.,a�Swa�J� �0AA�191 6�"� ^ B�r�����5gDB��7*$ =d(�1�h-k_zz�)��1�2f\]*u!>{7�b?�y.�@*�[.9sig%��>M �r2t�CCed6T 6T=�vkk� ^!�ew on^(�, %�4 V.V. Zhelezny2 K.� �UVl*2Ry 26}, 89 8%� 4>�newpage� c'r}\6d } FV �s Q =s9,.�baVty��c�.�ir6�$|b� �("� �A�@a �=le-u#�p� ��u?��UT4t.�3#� :p tom 8cik (dee )� it�"�.j� bs (�Ks)� /-. (c) B_/%/.{� =L� � ly negK e ``"�&�IXxi� on''�\ ����n ts (�b6�d)E�en�]� >� 1Cs*q3y &�L;ce9�q3..�=AO . 2.I#!W)(�ބX � %�K\"u,���D**�r� n&�W�! NY& = �X&CE��.�X �*�e�%�9'sw5'!E�X e�)7��Ae�X^c����B�^�*�!$=�3�����%�\ 3$�/ZN���R%�a�e �|���U錉�.Ic=� ��v�V\6U\/2 = 8.�4������%�>�V �+B\�IS=}�!��� <\F�����Adoc�} ��\4class[12pt,a4p'Q]{(0le} \par=T$nt0pt\base�(skip0pt \u��ckage{� icx}2mylist6�$xsym,amssyd HD[all]{xy}\CompileM/ces.%{coloE�$amsmath} \F#P{redex}{rgb}{.9,.1,.1 #\tr#1{{ 2+#1Z�def\al{i� 1ba{#n ga{=s \Ga{Bx}lNt\da\d!C  eps{a 1ka{�m laB_m�B 5 sig{m#ta{\th�n ! rar{*�E s! rel{%\h!�-1.95ex�sla%stack.#IOlra" �{ng&>F hred^ R�RPa�6 ttt)ftt�m�tsc &sc8sf f88bf{b&J%�mcl &calMbb bbfrk  frak � �em{ }{Prop�4}E9PROA*QF"  ORP{e� 2I8coro}{Corollary 1CORG ROC G 2G�}� orem /THD HT C 2Ca=}[�]{D�Gi� 7DEL& ED L 2LlemmeMLemma 3LH " EL I JPcommand{\AR}[2][c]{$$UOG[#1]{l6}#2%i "$$MRMAa�4R� ��}#1/ iP) 5EQ5 /"5� 1 ,mypiNmedap�>M�{\� a^-Lemptyset{\varnothing Hensu {#1\.ieI�it{ &eg� a�[t�a.k.aiow �i.o.w.\ 4etc etc mo{^ّ � st{^�-q�pep{^\bo��4ST6 0aast{\diamond DCI{^\ciru�up�-#- -tuplef qed{$\Box1�?6iN{\iot�@ oU{o YnOV Box^%��P ei#1{e^{i�em  {-i}��X$pL{\!+\!\! ImI{\!- ad{\� !&tR|�� rm{tr}(#1Qp dap{.s�Yeq27e� _hilBfr H_� hilo^1  %kt �|s �teN)T ' b [{�4 B}. dm#1 D:!� 3 ^p PmeE�mcl M.Mpau� cl P. clifC.ket|a}ra\ bbra1Q?{|Q�oqbkad�.1ex+ U = oqbnJ%->%J bra{rJN&6KIDn��id2DctR�f$op{\wedge}k4ex!�=6olled ��Yi-� ctwo!@bb C}^2} % qubit o{\ ^2_1N�m 1)�z@ Z}_21a��)1R�214u��\�ppi \piJl�|#1\| ^br��rar)k �Rr#1#2{J^{#WCxAcxA�{�Czz2czCZBCcxXBG{J prE#1{2�MS6#3#4{{�4}[{M!�21}]^{#3�ms - {\MS�#2}�M!{2B |M;RpP#3{P^{N\aC#1 � <P"� � pV #3{Qb;" :Tao #2{E!/=��6Acs �S.�ni�sf{nf.�oB{Er � dom{edomTaC{�hd� Cp{\a�: \title� Mea>p�Cz�u�+\n%{VM(nt Danos\\U�d\'e Paris~7 \& CNRS\\ {\�'�3tt?.?4@pps.jussieu.f  \}_@ Elham Kashefi\tx%s{m7�wo$!�T �%I!&HPREA, MITACS, ORDCF� CFI�S~,s.}\\ IQC - �W�loo�Chr�]Church -�:�ek � @iqc.ca}}�Pra@ Panangaden\\ McGI�|NU :$@cs.mcgillZ}"�j} \make%�ab6\ct} We����Olculualo~=s�rone-wa01mpu p�( ns~\o{mqqcrw�O&rv�4L,prex(bad�aof re~KQof �_ Xa�/3�x:r!Hta��E��=oneM0�,n mY�s l�c�R�s. �*in�Gn)is���+no&�(18or yH�rPauli:ru>r'zsea�) belon�`�) Clif],p. ;9�&�FIuM �� h{-�} Jlb-r�A n 1-ŕ2� 3� ingred�~of" +Du)�:��i�j2de4n.ist%@ lend�elf� easiEImpl%��U1tNielsen04,ND04,BR04,CMJ04}. Du�.�s,:�ndF�}`jo �;��out^+�-�J�.,�D�7d?op�I �A� ���i�"arGsH!|f n�Q�:��#N�Ce])&� organi�D�a�5! �we�e�re *&�� - !�o�C7tensora�duc7parallA9om*�6 Bm*show nex�%% "!�b=/ref�%rep02�&co' ofmy&] �DnA5y�of�u�Kap�,6��  'fam�� of 2M� ��Gl�_�;o�Z�MMq;�e#est�9K\lar&$of�;6;�RD,do"F��%kp�!Q��!jinv�"8���ޢ7E�n�Ve�2m. *�M�}rk �#�� a*(�<edK'[#�E!�H inpuh�out may��lapAR any ��C=wana�he�0I�t!66C!2�{J���> sen�] fewer 6��uni�. Spec%plly, -Gg�e� set~ s�Wof<�/41�, �q���2 �. �#m it &�>a 3 ��ei`h!Zz$ ��!� a 14 3 6�� 6co!�$ -$U$M�: a0ign�ntq9!� o DIR6ZA�"�Obm; p�� �is\g��o i�('�TU!N n���G�Ej�1U�� loSA�+8 1mg$xy$-.7�� �]d �'!juA�on�'�$ "D �{�Q YEg��ws/A�2(�&N��:[ . M��"�hAZwe:�AEU%s$ algorithm���I�9CeN��be pu�@:"V1� S.����K�~V��E!�����F�gRe}g�xa�ced�{ar�Xr-!5�. F��, �C �������&�Qpre�� intia�_ k�RleLCrFA��*! � �2�`:e�n�a�A do ``S_fly''�!�Se�3�l>� s�H st, Z ���i�� ll^r�2\ �Crd%� .p  aQ��2� revealam� �O��M��1. I��g��U<)hi��r�-to 4�73�$�� nd obey s�Xt1��"X�����=�i������sY�A%�9lax�Tulp in�-� g|o�_xity. L!h%crjQ|>� fOjK�i)�(%�e���ng 5l�\e8 ys�e~� ���~ mN% sa��Bs � i��-�}z� A,�riH�� �L��2 ,e�Ea� aͶy ~�  �{A&o4�s:} E.� w2)0 &���4it�Pto Qua��hleÔher c!MboX!h8�fa3.2�vIq�irA-�9 Canada. D*~N�is6�EPSRC%�^!�&st _O�(w�����egaI,*~�uD P%�ns���^� ь݇ AJ���X The k�c�s��� �q re: 5iz� Nd�&M� }i$ &} �6!�&� 0? t ij.A��I� $\Cx iv\ \Cz c3z���!ind� $'j$&�JE�� ���$ �H� pea ons ��� 3'2� r�� (n $[0,2\pi]BrS��� Ʌ��s, togeA�I�%�d �n/0ed ---pH2"~ ping--- ct|>%"1 toJ� �bk�� ed ]  �!},���M��MpEbϢb�� AHf8 0. Importan����� !�� &��q'o;&!�/���' all��v�!� ��fCthose ��� een��2�"� NE����<p�;ubO� N. crucs+ifeP= �fin�"� %J2� ; s� say a �4��� -dim�O@� �a�b��alI��*al۪ ��ve6� %=��haS,a6s# � gracQl4b\O�)�{�7 ands~2�q%� BaaӅ:=p Z_{ijY��f|]96D���"i��:� Aa�#��m�X]L}T, e �$��,!�giv9Ba paira�A��  orthog!�A�!�=��6 EQ{ �,\al&:=&\ost(�0+ � \al} 1)\\(nB)-\e' & }�s6�=w,%�$ f�A \al$��m �a��al��l $� $, s�.��de� Q�-.2z(k�$nk $2^{n-1�<if $n�!�&�l�ji6 ambF! q (`s_i=0$!��):.��}4�HAD�pK\�oqA��>nd U1UE� . Oh��sum!��&�NM i���=!��V $s=\sum_{!b I} s_i$��we�� ��eal���)aGwb -�Udbe~�i��-�W!ޥ�@ ^domain}��-g�xEW�����o. D�T�rƴ� em �Un't�. S�z(d o B���en&TCV� �Aad~c5P�� �= =K ks�K-�` see �*r�el� s/U!�)e�(�v!�)%,key!��y4o#"X2�I�A� btai��"� q,�E22��j� ������AW"c}%$!�.+on�T�&�� a[!�A�� i=!�}}1�."Z_ "Y��A6'er�wy ~��q �5���/�2H����=2�� a)���!��(/�TetC2#Y���d�:�L!�"�NEactual �p�Ya.and�  F�lyAS��q�}oБs ith"�T 2�,U��� �\� m�C� MFe. All��ism;car�V[5nic���QZmno9~und so tv��0e�E��c�a&���2 &� \DE ��s"� hree� 0 s $V��IO.T>; ��� ap� iN:I�$ V��\oU:O���B�=!m-�4s $A_n\ldots A2V���to� �V$. \EDh�$V� gAm� !?k� }�r�hhil�*@associ(Az;o( ?� �Es� V}� . ���y&���forQ�al5Iabg�-@98�x ��y 1�1T�!<$\iN(I�T�\oU(O�V,R�K����se %���us:!ZI�I��manipu��m2�:uch�� perm-\�8!>6 F !�s ����i>���9K[;6�}� � K"D �)'$%�A�) !�O[9� 2�)���ceB�:�� �M�U�}[ To rup �� ��9-3A�s$v�Is XY� �ޡ@l��e non- ,)t%�% a��$��F- A`�yyAexecu�%in�e'��� ��=Iuama$ph�Oa�7m m1A � �5!��n"�ynr: < �+un puxili � " d"[.�ܟu���Ui  as fB<�� �����O�&cip� MPml�� !-��Ae��� � �6�GI� �g�isje�Df �<�<min^zinnocu.$f�bi�%!��Yly �h �o�simon�#6 a�&�!Ɂtor$��Q��� ��E�� �0ne�;aHi���en�cunt� � mor�wstr�@dQGsYg��S�|��F!�. Re?=F;��M��s,*�$�O seem%��EheyE�not��4)�0 H '�pB�X����5W5 A'Hadam%�O $H��AR{ \�.b ( 1�r, 2},i82{s_1}\M01\et12� W�� � �doing~?�de:(��d� B��]ͧ����>�/�w+:�ose!#"_ v � u 12}(�]�b��+_2�� O���L(jB�mT(� ��-${x"i��an� V�� �I�),A!��e �.-� a ͧd��$�)� !0�:�Rer�.�� �=�%}*���e[$wJ�n�N��%a�%��\ Fig�_� .Z�]$�YyGE(yLdng! m. Two$$E� P_{1�A2}$;����o��i��_1� &�O_1=I~n�prh�� O1$0 as ��� �aP_X���1,."re�G ��)�s�!+�k� �able.4 � �itH�{2} �%A��':\\ A $V:=�u�X I=I_1 O=O_2$,\\*J��9ate�Dd."� �!�'�'��E����C(+&.�� ~&bU�nso�M\�a�=� �5 $. AtAQ.Kme=�A�onby9��ds i �%��YiA� made����VDE%� � �2��4I R�%a$VR�\!�A�X%� -�)�f�� ��� unNCo���M� ��J��(�xQvuE��s- �ct1ee�*N.�y Q A�-�1 �=�<p���&��j��v<��ab �ha�e�ciU�l h^ e@�f�M4s}:3 ��sub��to��Un��8descri�A} [(D0)]�"-˭�!���ye"#d;<16<a�+�*E�}Ո9�M &$i�٭S/�mI�f�9��IEMC)]�� $E$s��!uen $M$�$C$!l� 2���}er:dcheckE��(SmlH$ �$sf+$A��nE�. �nro�e%�eri-�"�9�e2rved j.�� i�. �q�Ns !�te*4�ay(.��ur0�*oX�mif Of�I�����*�)� �,��Q�C e� L ota��!��nAp(. Likewise�i� �>1ptDom�~ m]�]]b8 conj by a.� (re 0w&RZV�). Cq� (D2)��%��2��B��� @!f!w.1�E��)Fbr1A0��I����\i�all�[- )e}�m��, Z��F q~� *'-A|-��a9 St�AngHfuGf�l"K(sm0.��2�,)�A�!V�~%�de�te!�(D)9!�j�����6t�yW�[=��3!���leK�d?�t�j.&A��ng� �&�h{wild�L�"onUM+&�,!э�!m  u�qd`,>mpl.f4p�;+�k� �'l"� ho�'�dal�6e+�4i )�� M� f �s�)*���a�|��� d5�z6S%'B��t m� %<�+a�lean M9iont�liŕ���)��%!B%aZ�&�")"T,: &a!n�m�� fJ �/=2g A�ixte*@6�$!~s�<0prgT2�[/2A�:h(!U� } Be0/s 2�s�_V �= s~.V$�,e%S|c�E��re"[�&� �%� successiv2� ��e�� � 'Q �$�|p�%��$a�"$���a�� cl S�4\bigcup_{V,W} �\q \ztwo^W }��re�, $W$=� �0�%H wG, or)�-v !kir $qO\GO�"A��an�S)9��( map� )|W$A�=S �$�=y�9�� onen1�Gn�mB�5h sTNb�/BtKuniqu* in r^$Ikub>*&V�`m�few� �svT����l '�) !�)��$.�!&vBa$J��$0w�Jk� _% \ ="<�b�l=&)��.�$, if �" I s_��$h:�"I\Ga(i)$M���:ake�p-X!N Also@ B�E#x1+�[�": A�<\Ga[x/i](i)=x,\,j)=�j)\hbox{�� }j�iA���ia�Av)g{W�   i}WAy��$� f ��� 5�ng= $�AS<� q�&\ H{(}&*(  \\6(�"s( x i{%V^)A#)zz)&�"}&{�$b�A }}_i�[0/i]>�B8nJ9 1/i]�N\aX=�" �Ztn\�!�/!1�� #)� $\bra�� ABKar!�U"^�ps3"pp�# at� . S��$qAJ��FUr  reL�"Efd� a�i �ʅA��-o}-�vaBM �+b��i. �"  UA��\6�5Hi��Da�ey#�"ij� $%X{$z �a�i�$��hc� &�� � U " gf : *l��L�epI.@� x.c�M mo�#the"<g����2�(s�R!jq]�not����j_� )=� �r=1�o��.���a�h�'!~���%�#�T��(9 �2wL �24 HaR6��n h{re�*�,},�do�#ad"� t&" ���7�'! �űl�Ya�U ��za� ���ea"f�= �X �'� &�<9> lpWA�#;-�.?�9�"�/���I��6o�s}&����i)+��yIta>� ;7��Aj.2 ��&*i$��ampPqT. *|� $Z$-��0r�@Ss glob ina�aJk� ,;!��q�9�&},��n��= �}3� chaB@�X�) 8$ ��� swap� �Q�."�(3'JE\nst*'!ht\mr( is.'split}}{!5[�0 z{)�#AY2�,+��6� � !(*J� Xm2 �F ��mj.�*=? branch�hLe!l�$A�� �d* �c�"B`   s $O�_3m�"l":`". A�5 *�2i���th� o�5"q�!�I�6##h}mQ)��$�; ��.Tůn�ed)��+$�t�Far�l %�%so4"�&b�I���1I�X.�l!8 K1�e ���a�(!�-�rsu���(he &L�a&9+ W \xyPN<@=10pt@M=5pt@R=2 $C=40pt{ {}�TI\ar[d]\ar@{.>}[rr] && O \\ I.! �M%f}A r]^{�}:2O J.A_1"�$n\quad<O2j,V\setminus OmuP }�!�� prec�C� � A h{1d-i }K &�I�<q'  �"'2q 2J{)�}q'$, i��oay $(q_i� _� A�$1\leq in+�"� 1�qY.1L 4ex+)$+{�O =q_1a1�q'=q_�� 0_2� a��ll �+eq n:�r A_i}q_{i+�Ga } t�4b ��:'& I�Qhil�"T �a"> -�aa� Ce� fa�62AaN�ori�:��#*D m�� vol\{e��*O�!S2gA� k�>&�22� �1 (or &� $u՟($�*�1A#e�t�1$2^k$ I�e��e�"J[�"�2�� � �� h i�ti�2�H i*�}!;a�1^WOI b%(|q'\|^2/\|q$ (��O H �3non�). %  o.dߘ��likeli}��m_{e{q'\mid >}}�� ��.;$!N�g�^i��&��  � - 3, �]"h)�ing5�nAN ! pr6�� $q_0�'$q�zs= $\M[ �=\|q_0!W+ 1 �k� Ap5�� ���� ��OI sayi]A" fr PE�)�{2� }}�ؑ7.l,AA�'6'hen�@�Ob�3q/6'��h>"''$ d-�/a���&��v2�2�,� -�es ��z����G�Aq y. W�q�Z 27 �&7!�>:#$U_� P}���Y� byY 1(q)��P{E }'\|}q' }� �:P)����a�56E. M+�5 21q� �uj�n �&�4E� choiډfI*�up a =�� can �݁�R�� i�w�o �"7!�v!�k&.�*s,w,� 'o� �&6t$���m+ �#"�M�6n��eQ6p799i_:As}�h �s}68�=:aat6$A�� K2��1�� P!�U�A�mА"�(���tembedt%3�%%�#:�z�%O�"�<f/� arg^��ed%�IWrephr����wE�s�'��/f language��de��&���W�{?i"P/ (cp-�-�:G�^�l� !�:9�u�Ap\DB�'kG� Krau���n�/[�t U&1%��Ze5 %Tlifting)ry9��.Sh�wnss} Gah|~� !M^ ��� es w� ��p.��k Uf9enZ)׎>$I=O= �8!4  =�:2� ��?N� klge�wo�F*u +,aT� �h}& �[\{Ca"����12(1+�Y�)qI[0/2]\\� ��)-V) 1/2]=" ] \LH.� ��u�d� d�=2�TU���i�s8N�,22�#!m."�?r5��22� $�co )/A�(1-�GH� ���wa� �,l. Next�re��������H&JM�lt5ok����+.�n us3o#�Azr�VE"�}s�>D�U� E?�<� $IU�$I�� e saX�F�Y�$\Ms ,�SR�=(a� 0}+b 1})�+A�ai!����"> ,M�� �q $: ^[Y�U��,A��@ �0}+ 1�0}- �w�u2E�u6�}& �7 (a+b��(a- 2[ [0/06D)0}+C661/0^Q%�, $Z{a+b}^2+ - =2( a b^2)$,����͔happe} I�2+&�1E���7�"a�E��>Mr�& +isTn�^2� .&Q�DG�>n:/Cx��n  1.�A\oth���<2*�,��qw choo�o l�*� "�9b��-�. m,�.A��m�y�Dcha�e/W�� ���,e�H=Z H�\Ŭ�o W� u B0�T���w-�xTlac}L/5Wg"!-, &�;)7�- �'R�!5� �=��ructu�aD - yuses 2��i���R� "�F��kJ��., T�,!�a6I6p 8 Recall that twTo patterns $\mfr P_1$, �2$ may be combined by composition provided ?P have as many outputs#2# s in�. Suppose this is the case, and su ,further thatK1$$Z� respectively realise some unitaries $U9U_2$,rn ���e1]5!XJ42U_1$. IndeedL� two diagrams representing branches iY1$ ���^: {\footnotesize \AR{ \xymatrix@=10pt@M=3pt@R=20pt@C=7pt{ {}\hil {I_1}\ar[d]\ar@{.>}[rr] && {} "O "@{=} & I_2}~82} \\2\1}\times\ztwo^{\emptysetIr]^{p_1}cV�1.�._0V_1\setminus ar[u]>�.3N�2dV�v1.O>.V_2.�)A u] }\\ canaC(pasted togeA�4, since $O_1=IE�Ih!��= !�$. ButE� , ita'Henough to notice 1)ipreparae�steps $pauiYs2$a� mute@all ac0s.%1$ ��they apply on disjoint sets of qubitsi�2 �no R taken.W$2$ dependsN a�,measurements�2com>#(. It follow�"at :-Umm describe#e sameyras doesqon��socia)���positey�u�D. A similar argu�%io B8ase of a tensorSbin%�,e�zha���2\oI��6b  �jT�|holds even for non-deterministic��0s considered �zmpl%m��$cp-maps. Aawe willASA�concer��with ��gener�Xd setEin $paper. \s��Don{Universality} C �%n�%)��ш: \EQ{ % D\G(\al)&:=&\cx 2{s�<\M{{-\al}}1\et 12\\ \ctR{3Z}. } I�e firste $1$aBA{only ŋi26ɿ, while �0e second bothKe�2$ ar#�� <s. Noah!�here we*tak�advantagI8A�1)xoverlapp�a a \PROE9�O-B�'=' �u1�. \ORP F!(,Aclaim�F.q �q$Jx Z}$,�:�� $%�Lost\MA{1&\ei\al\\1&- �FWeU lready se�Sour exaAω��\G(0)=EH$ U�s $H=��us�R knowI�E���rticua� e�w!�$ $\al=0$. a�m �M� s byEX�| kind�2 ut�.%�R of $!� ZEt,obvious.\\ SEa%� �a��s.�form a9�a�~\cite{ �tor04}�,refore, from�precedAPm�, A�infc � "a'cor!�on4Qe �, n!4L I<�[Dfinite-dimensional�� . \qed !sAiJQ  among�s%�a�0ossible. As a�� sequence,1� � devo��M)s%W�f!�e�AI^��%�sIr@often little spac�&Hlexity. Remarkably{Hset!�- ors,��m�!le�@ency, which occur�5q� ph�VE�u�. Non1�ea out | m�W could��a�!�set� suchG��a]!9�1dDClifford group. D��enc�!�also nee! ���nity, buta�/ to wai���developyof%2�alculu� next5�to gi� � of @is fact.�a�NU}�p turnJ!�^(important mE� WA�per, namr $standardisEFi� idea�pquiteM��is*� pK  local1� rewri!�( rules push!� $E$s�begine�-+M� $C*end. �/subm#%equ� s} A�,M�)T meanxpropagat�Pauli�'E�h ro� $he entangl� oper�� $�(ij$. Becaus�]et ij =ji��er�.E�3�;��"2 =)is&2is\cz js $\label{ecx�  \cz0 * z} }��9 A� easy!�verify naturala�ce � belong�!6:)� �� �  unde@ njug%�"-geq~itself� �5��ush.� t)� } s� ng� ���� . Aga�"-�5�-�, \MS\al ist%�r!� {s+r}{t}-_m-� 1z :1}{t+r1R�F !� ily ��9�((\ref{xmx})%� zmz})e� y ex�! e�$��6 $\Ms�; closed F�i%� , very m�d like�~ �A�) " z})j�^�G.� c]5 �m����e,�Defin> �!�Dconvenient abbreviE�s�  \m)s:=5� 0,\,5�{}t0t  40,� Ms xs0i ) y \p� } P&� i���9�abo��re �A� xiE�� \ \M ymks I� yi{} &�i��o,MrsIl(${-0}=0$, s$X$eBonaB$}0$ is trivial;E]middlY ,��W row,!�b� ${-! }& �l $8+\pi$ modulo $2,EC_�LA��nd $Z�incide�yi$. So�obtm� � ing:� !VS xist-2x!�qͩUM!H!!S{s+y�y�P�k��latx o�WvA�a"� ��y"# -� $M^x$e� $M^y��-� .2 �� 66�u �u! di-a�e (e &,-:% dir� � !�` E�:  ̈́M� \Rar�6�8&\quad\hbox{}EXA�e�\E�6A� 60Z0�a�{cx i{r} 8 ��2<Ml " <zR<}{r+t:< Z } � � we ��adE� �h{freQ m )J }, I�edx n� ma2>E�2��Ţň.)% CO{\vec k� ".�w�}A\neq E!9-!85nx!�^DC>D!�-z �D } ~�����a� ��s��pon��co%3 $A$z�M%�be!Ctinct���ف(�C� A� (D)��eas�_|to?�rvu�iing. U6*M 5 >0 rem��z so��.�SE. M&� s migh�modifi�o e �st�Nc numbe� m r�re ,!" 6)xa�sinduced uci��N cern� cJ# ��  5 . We5 6 due n"<n;��s�7gy cre� 6M���S6� } Wr� TP�|2 P'$,2�2"st%if m 15Styp-���Uz�'$'!%� �M� #":b{)}e:��)� , of��� . Sa��?�w� }��no��� 2c � ����E�sound,�"�wheneve� mfR.DaoG5EAq2�e:n $U_� P}= P'}� One� show%1"�y�!�ory"�,Aar�� P"u e���uniqua�)!)4A ?EH>�moreo5Ac sf(A1(EMC)a(d�r. Reac�1�!�me$s at most ��c B ��Ia.instrump&>Detail)�1n pap�ix!�.*Sig� shif��}5xexten��"� to includ�e5�� $\ss it$� is!��A�to��of&)!-�a� $Z$-��o��5�!s9:U`��smaller\tm�,%� se�%0�>S.�-t���"/ �cx� $ �4j{s[t+s_i/s_i]��R0zN0 �jst4r d  {s[rf{t. }�ls[t��8A�M titu�� s_i$%Q $t$A=$s=t���sE5s!�H adI�alm�B  waA�intro�N as�k�split}):lI`o��A?I�mer��ing� �I� . Clearly�r���diU|Q���whit���!M[Uٱ���hreV is new@ �a�Rar_S�g���!{E�s�isU�wBv#E�"� illust�ng2[ }o� ,��[�,��s%�)&��>��our ia0���eT! >2V%� p3�mqqcs�ocd!�s �?9redhir {!;NM4d�V � !�retT�:����E�a|r�0ns{1,\ldots,n�a$f 0�3j)�,�����(f(1)=f(n))$ �m�@ Q:%@ � �d accormtoo�P 2d_2\circ q�aX!�-�F easeV " *{Tele�a�.:�K5�)8�ba)(2,3)�al)(1,2)� ?� F$\)\2,3!W� � 3}a W�-nA�>�a� cedu� oAto� an�C ival4 Q�� &�!��B�Ր&=& \cx3{s_{2}}\Ms{-\ba}2\tr{\et23\cx�{1}al�12 \\��_{EX}6H>L C1}}\czk1 i J 23\e2OM>O 7�\m��Sg:J} Let us��lE�QI just-Ke�1'al,!+� fA�� (as a specia5\ba$we get:)G22� x2��}WC&i���� s $HH^2=I{j� � ��� id�$�or���` word� tm-si�to e� $3_ A)hM s� isn *�-a!m��thd +!_ eZNt �N[p.14]�T�Jub��*{$x$-ro�� .} H��h�fe��9E� ��an .:m7m, $R_x� $!�� F�E�al}A�E� :�� ! :.V=�0, ��} � � ques��_mec� � recogns �<bl��ely J dMki�'��R�~? OfdrsŢ �e brutI$rce answer��A��ch we \$i� �e��nrQ6s�Sconsist 4� downK {f� ,&$ �I�6�tEΡ�$2E�nI� Ki�E5o�eW taser��m#mA�expla7)� ".�Y�Ye�jn�q��m6},q id bI)/e� is w� -re goh o� We1��Q�,!{A�)H$ uoa glob��, h�!B���� �� D6# H�%�K sAN{x}iC. Now��*Ѱ�)it�"!$j_ݨ2}��B��i�N$J�.�էa�ݧ���\\I.�.Iv \\ }� !�exactl]"56��w�rAс@. SZ(A�"��}reservMinterpre A!deo e�E�:ei�r�J< $z2XN�we� a method �� synthesi !"�+6oss%�� � fi��A c�& th am,�� $R_zUB�w:� =HQ�H$i(aH ��to�M ern�(�aJ�, St�ng%�a��#H(4,5&- >a!,4q#11{�C=x8� 4{s_3t �+7(3{1+s_2}{} E�2�34 E�� ;ɻ "1"12Q�� �m>lk� o34� 16n {23}qZ}�q 1 ja�}� � � {234laƂ� �:Nq ]2fd �cx5{s_4 05� 45\c-�UV�$) afh1�hczr3� s x4l \c�m5B:bnS �{��I U�j�kBA�gA���` } To2B� �  shorte� �� A� 2eA\et34$ !4"l\MS��ia�&!Vus s ^h) for --��i{ ,�#� �b�f�)�� $MZ$s ings~duc��1$"N on . ��ed ���$ed�ޥ�t��j(re� ten �1u��k1edՠ4 �N$���S�) _2+a]M��A�E�>A&s"� ��5()!>a#5V�.� [p.5> . How*,la� !*� �  �j$��%�B'�� =H\G ^� "� �GH��)�-E� j2&$R_{z� ,E�w�$yYze:� _"�6d>� ��m eh�%�I�m ^Q��J��� �yHa�&���,y6KE{�$>@.� a 3F�u�.8  � r��&�+o"# s baa�o *)��al)$ � or� EJ*� !� �q�z� "�'�Pd =\�- 0\\0�-}} V) ] s"�� i� an: �!6�. In pe �-,�al=#$,�f� Bfe3ge�%�:m/%�$P(H)$: $B�+��yEA7� )*OGe'1u�.H(�li�$)2)�()� -�Eu�x ��� �(\ga)� b�, w�+resul,a 7Q�-xZ!a 5E�� a :c�1�3�2|.:� RA/*,�<$�/Q�ba ga)�kbT.nz �pr�yield&�&f�0)a " a(Z �ga)�� �O2� 50}4\et45�r 3�|���'.  �*3 {\ga��͚>� F�tk{3y.&��MwA�z��� k�B��ms �"� �.uEX:� �F� m�al}P-c�}.� v{.� V| m!�"� "� �p� � ߞsB� lMs�� .n.� Ig� �x* B�2Y 0}4{T����h�Y nZ .�} ~De BXCNOT (93X$)�W��� �1�hwo_? X.�use���t�)��NI��:��2= .� c& n|;G�$")��u6�� $ :1w d"-=(I"8H)Q4.�*F*�u�  4���!"�,� �.� {1,2� � $ 62?��:�atE! 8���co�l �T"%<�F(� I(1) �h���tRZ(1,3)b.��硷��-3� �et1�iw  23 } B*� !B �u� 0M� 1�� !QB�cz1e�P J � J1��23nOYa�YR� V� S��X�1N32�XT �.� J} &9 r�M�?e�3i �8bb"�.,� a�v(l&�#�of6!(r oA� chai�3 �w*r!<<d�AliferP nd Leung'�pej{AL04}._:ir origi�!fn9 �author�)ually�r�xplicit k�v(uAZ=h� �"� 0,0)$sed^,)"[5�1�careful/ So��<ionr  �Q!8necessar�6B� HZ.- �$-a fam)*of�s!par+�GHZ5�Nte�Eket{0l 0}+1 1��&ha"� -GHZ}(nS  (H_n<( Z_{n-1 n} > H_21 2})\,\hskip-.4ex+ 4+�Ab��bi��-�s9 �zuq# &X!�P5 JH�[,2'2!( n, n'}$, n��,�;$�1/ +��.�!6n��{n'n� x{n-{n}� {(n-1)'}{9I\cx{25P x{252}5 1}{2!1,�!me%+apI#nt waB5ru�-Na�(to execute ��,�1�5�sit�6a�nge��#te�9)�ebAz�2da�'I���J�ʞ3%��{ et{3}� et!-=O�fQ�(� !�{s_!�.A q����{���2�� >���f����%] ��\�(� =F�$E�96ZSe ~�\! 53 �.�vL��_S6�� 3+\c�%+I �cx �#�y�U&� �&��N�} All:_�� w in�./=�+e",�"M yle af'4Q:� ,a�do�&/m��� r�-and in�3�1>t :};c� ionsn��"���*�� � tantBW+H J� � led-$U$ �<F� �Z+0 ��,a- q��q�$lowB�%For6/1-�#Iy $U$*�!c�Cd.����U�*pD34�o&Bb �U_{12}z \Rr�B0} \al'}2} 2}g +\pi,2{-\frac\ga26pit 0�a%\\&&K2{!\R ; o7 -\da�&}�20 � M6.ba+.pi}.}�#�%'=\al+ V'g+ }2$.J transla�i $\G$"lA�it��J|A.�*�)wil&� 1�:&q&{C�FB��{0}{B�� B}{C�+BAb '}{A"A+�&k"j" 0}{j j}{k ji!A�8}{i%i.=J��i(h(%!%�{h)h2&h&g &!�{g!g*!g!f! 0}{ff'�A}f&f&e&� t}{e*e3�e%d %A �d*d3Ld'c'&APA+�}{c0 c}{d 0c0b0 0}{bb' �bVb&a& VbaA�E� 2}{a8aA$ } Figure~�to"� a3m�Y.�]�,M�W e&� � s���ao per�9�8*m V�  \b�@{f� }[h]ce�"} \o1�8ics[scale=0.6]{ .eps!�ap���@*Bf&uD�.�>aK@!\!�nd� � E>j i6�cziY@i+s_g+s_e+s_c+s_a�x @j+s_h+s_f+s_d+s_b m� A@}E�n{B��y���A�j"�aaz{Ff�$yi�f �m�{6�\lf litaQ{�>aieYaja�XamZ]!2+$i���{!G\er��\et��et��k����et�a���VA}f�< � e� e� e� A}b:��I>}� F}AoE��(��Q�a�U�,eqakseHMtesde6�3 $7$.qEM��W �JX ���a��ј�yT <7nV "dL.no.t4theorems} Fromu%  -a(*sY�2)Y{:�>dLie&start�a�E obO'G�*0�= e c��m�D'LEq.�P04*�" 5s&�R� �R�; A 19�<"&%��]sO�OIO>;?�J,(o8�S��7��, w �m?.� .p,� b 5jv ("� 'B�a�72). \EL6�:'$F_�� a2�O1k} &�9(�G:"Dmya5A�$Xf7s�"be elim�Oed _ Y9!�th!C"O#J7Mus!?b"��)� ��<5�}T$,%�no _Fe� i@a:�nd.9jfg�K \TH I�UM�/ �?orG:� ��C2J if�;r�5�-&-:*�0!� Qa.�InjJ�8HT/ ``I�f''m�utIasy, S�*�>�-} �i\9u-�.�X$,& *= �had �>j.�. HG-�<581_Qq5��.�L�e�-s"� s. B),lemma =1 ��c� choo�/C bX,`. 9!�``6RY�J�A.E+A�E3no/"c?.�Fɮ bydCi!x�>5LG6� do@weU-5�\ �9P$�6�Mo8- P'= CV= P'}M E 1�R~o� Eir� iGiiG87pu�<bit)>iy h5�q''=�= P}C_i[�$ E�ia� $X�:or $Z_i$&�9-''}f�??. �Q0&`� C_i �_{EC}Z Z7C' =S }8���?�Tpen��}پ�t.� $C'$-,�0f:AD�k|(��quelyF;$C'_OC'��1A '_O$��U�#�Z ��n�=MG �^ut�o $]/q $[.M�2Q ((!�,)��|2[)�G,a ~� �b�Tt�K65Ņ$=�$ (N�%)�getW4�:��-�!Ry.24>�U��Nw,��t-uF8+�z!A+D%�nB�6� �_{MC,SM�S".�p�=t $S=\ _{wj\in J}}W>j1$I��0t"5et $J3a�B" . So��[f�.�}��2=�'b�8��z0�|a"�1��&?�ed by5:�$�=T�J�a ��'$�*�� e�_O M4mR $��=C"�zleeáfroof,U9 eU.�n�Z���b�T��i�r�n5 "]V9a�Sp�o|Vork�88& ,\�A� �"� @-%T�� �Ocruq:fo7*i"yYA��model. O� �@�i�(��s��(A�> �.k iOU� �SQ)M(D2 \$ $V=O$, \i�6l�! ��� -�!�"�\involve �do f�� + not surpr�! ��G Y e a � ��^� � �l"6E eswI iall a&�8shoe?%Oy��%�6JbutNno .�[ .2Cpla� n�arN#`�A�THai1f5�u7�*�x1i !܎M?]n'NlOn� �IQFz . � 2zHξ �,a0�3-�-'$-c��M)� ?�GDIj��W1�� :�. ".�,ah�� ain�WY!e e:C�,� �:m $C$�"a�]2�. Era�?the�;Z��I&�+q�a'��!%�J"<,-$:oHA57!^($U':=C\ad U/ �77A�Nsr�@�F'�Phi*<p �%�!.s!�+}$ goeT[ 2� .�\$\psi\in''V-�i�n�y�Bb<a.` .�.~ . Pick a�-i�mcl B$�AtW!� Hilbert s"Z�5o�GB��'{V\&�b}d6��O.G2� m (V0bO-T ! Nb.68=\oplus_{\phi_b�B}[ ]s �$ -Z linA�Q6���$ AA�yVFtributivV@%�$��� �L��osa�� !�=\sum�)�} ]�x__� $ r"o{J%�� $x�!# O$. m<}7is>��e� n $xMik��$\la_b$*Kj= x$�T��-��be � '�$kTr�� �5* cin��~A��Z��!Z�U�G� x$x* �),���Zw� Q.2��� . O}L8 �&Qma�b�Nl�U{}$nOFm'&�2B $U�ZW8���=CU� -�C� 'WN�)� m]L,D!G�KJU��"�\ � *�& �*�K.� (^�) �Y5F� �,.� $M^\al��e�a neq0&�Us$f-: @)Ar!@!Cde�hQ=s�2A/*) �E�"�1� e ~Z}�2"xCND�_.(�8���]�JW�M$ed quantumM�kI We�e�N ���`�(K� _�N�Mu�d�  P5��n� %jr& 3parsimon� �� a.��> � n"� �k.������N-M"��$ algorithm���`A[�to�u�mM 9.�" is d��.7 .5 J�"AndWlx` � �a!>f.e&e3� ��W: ,s�� it6��A� 5gaNbaoA�:� A@c&�D�Be�� !�?>Cse�F�6o�#.�:Mt s,hap*>7difFt�*oOof6t�Hs,�P��>� � type#%� * . �1�k�@wis�i!,oreQz. �#now, � �@c�M)�U-E�e�!^U�!3���u 6j,%&m7i=%26$.� � �#ly z � e*UK V�8 embedda�%vone-way {�%v5](strong sens�oW�1ll re&�a�-"�e�F elsew�7.Ke�feem �he�Bs1k�B-" stretched1�!L ma�QW rele�ga�N studmerroraD#avA Q ng,  eodem�XeF mix�*t_;"�C�0u�as*�i F:&a�A}e!��aM XP?>TRFlassicaA� mmun�V�:leI��on"f thouiW�8s '�� i-.%�multi+ c$cenario. A*) �� ��9 pus5oH lc]XPr>*c�p ed�9��sa? seemA�A"Z\}%89qus7/ M� area� �% toco�QN thebiblio� y}{DKP04} ibitem[?0]E0 P.~2o0D.~W.u04. \newblock Co�1 .�: hf#pic� .;Q�hX-ph/0404082, April 2004��BR04]{,} D.~E. Brow,m0nd T.~Rudolph.[Effic*` optAJ5*| .8.�5157,B�CAJ�CMJ!;S.R�@ark, C.~Moura Alvq"D.~Jaksc2�&a)��A�!�%�� E1��A�spin ].in�h5�.� 6150F�%�]2;P V.~Danos, E.~KashefiE�0 P.~Panangade2(Rob}N!�2��^��c���M��O �vZ|11071F�HEB!|%'st!&8} M.~Hein, J.~E�J�H.JA( iege2fMa�-a�y6]%in2�.��qx Phys. Rev. A}, 69:62311--62333F�ND��A. Ni����A-. Dawso2Y0Fault-toleran�.� %X�cPTemQt "V 5134J�ie� �A�M.�.�Of7�f�E�m� 2005F�RBB03d R.~Rau�dorf,a}"� )9onj�5�'PReview}, A 68(022312)�3��H'>N &� A�Y� O[fi m ly m� n [uch � W*I[�EL S-w &�#�!") $A_nC A�w�b�� $A_iei,ij$ $d(A_i)=X(f`F,A_j=\cx us$, "j)=n-j�3f�: �? d�9P)&=&( �E�%}d(E), C.C))�`��� de� jmc�Hi�Py�)&��F� �/1%A|'�!�$�> '!;&  $<6 the 2w +< �bb N^P0Tin�St%��E5� �  �E�2A_�  co�V�_��Mda$i�% seft�always.ca �atina�u �!sU�Mobjэng,�fls�3�C co (�o!�A��J 'Aa"� ��db! can #"���2�&aidthirdires4). a[n,� �5es� ����mA/=qoc U+(p,' ��-secit�2^��= a�eq,[). Look!�9cri� paiE�is�s>X �ree suc<=�r���U�%]�qk-X si&aneous�^f?k�:MHe:<F �U/m��)inI��m.~�wA � a bi�. re, pq�6k" %�Vg~Y"�OA=� to EW�Aab�w�ignific:!�!\*Rdpiece�9inA�� ���R ��Abt�ZZ� $CC$Fh)I�a� EE$��M�~ujA�a�y CdA�ofe�c��.Ha�!y� ba{�1!OaAs�%$y8{�ua:�- n�s.^6� . AJson�t�  o, ;Mr o taknC!�y&�(as"\nAG ijac �9�3n%$��s,pl�$$\�s�hop��R� sYGso far� ��%�!�rQ=�6�:�. X�"� o na��a~ategy1m�G(t12\Cx1\Cx2 �.G�Hand  cx1s�Lt&�( z2 \cz1t -2[% $1),I���u!e��Esymmetrih 1��� le a�ivI1�A T8Aj.e�Mc����9 ��� �fortu� l;^�$�? [2��a+F� qual�,6x]. (ozeur���5nri�� �.��q Vdoc } ��\ [12pt]{U�le} \usepackage{amsmath,amsthm,url,)icx�t� {\odd�.$margin}{0i�Bs ��r!top=-1pc} .>,headheight}{Rsep}{2>74textwidth}{6.5>�U8.1add( {\par�)�}{1.5mm} \clubpenalty 10000 \widowp64sloppy \hyphe0{Alic!^.M��}6)playerR�:.@vKo>@?:B�<.DinEity:1i�i24� :0O outAnew pand{\I}{\makebox[0pt][l]{1}\hF$ {0.3ex}\m�tlC.;�ket Jvert#1\2$E�.rbra %l�|e#1.} � Tr}{m{TrDnewn�o}�8oreA1 �{�i� Q {�3}{L�36corol}{C lary�begin}�8 \title{Minimum"�nI di��\\r�+��seudo-t�ath\�J {Gil�~BraJd\�ks{�{`5# by $ N }Sc!$nd EngineeL8Research Counci!$LCanada ({\sc Nserc})�8 (ian Institu� or A>�ssN < Ciar;MaL atic� I& $ Technolog�}clex S�s Net�- TMitacs})�3� �{Chair Pr�mme�:U�p75cm} Andr\'e Allan M\'ethot B' lain Tappng =&, � ��( Qu\'ebec's (HFqrnt}.}\\[0.5cm] \�5(size\sl D\'�Kt?d'"M que e�D recherchX\'esm4onnelle\\[-0.1JW�it! de M \'eal�\P.~6128, Succ.\ Centre-VAzfTD< (QC), H3C 3J7~~e�sc{)��0.���tt{\{bM� ,\,m%�0an,\,tappa\}}( sf{@ tt{iro.um�eal.ca} a�(date{16 Dec� r���e�(abstract} P:o� de- intuiɎ)K��at Bell'9#���/� �o��V� feaz/chiev by�� ��7" �i.Ns�� A~two-ɝ >= g+J$e-69�%s: �� �Bob� individuY/ askef"�!*�/�� d@Shi�t!g not} owHny� 7-w "�  o� a�i EO uay�&agrD'Z � �,lpeg!�io�EP�L� � e% oT~s�L� ey E]it{win}9%3i�=�nd �s fulfil� clfic�"� A~@exhg s_>�} c&""���A�s Q�id !�wb �!U!e&��,1�d� $� p%#.ba"er�%itYnYb� wi\*is)Z��E*Z"U��(&. In~p��� �AY� > h�a9e5 I�'  s�  �'&�( �!��ga�least~�$3 q� 3$}A� �$}�$R�CT��+q� ��Q�\eWe �w$G`a�_V�of�� $d_� d_� f���Qy�Ռ } wi6�, y�o�N> Y26<ut�q9C2E� of�m �B��he�  ``>�'' Yco�p[ Ed�omenoÖj !�co�N� a r beha�-rM�ca�m,p� σi4*tu�aK}pmaO&� ��ny���w ��$world. ImaW))physicqD}���GA�he �A�"'�,)�placa r�^~ � -lik� pu�ed reg�*��s;qB@/e��"�ity� t�Hswers�quick�oat�z{ntU�sp� f li�+by> �X arr�toojZ i D�8 1<2�c��bea��~dIHfac��� :�P�u_�sE-�"�b1"oF,Iq)�,-"m }---or~atI � whelmingl$!�ly---% #!� %�M�Y^e!&A\� dEpD-- -U?-B!uzzƎ. So~A�6�``I�� a }'' �/a\-na\-! "d �=L�S(l�must!)\i$�Vun�E� �sn lla d"�E n? FP�m��5be�C3 �ic=< ion � Fuperlu I l! (Of~cov,e1��la�!�k)$mechanics}x6t� .) P4 jad,?{BBT04a�1 urvfV|� t~is < "�Y � ncep"7> *!!n.�.�b�YT� �p.sI n� !Ow��>_e��T�L Ylbell64,bc90,CHSH,cirelson80}�< John= g�=a�f�=��S b"k/��a��be�"� -1�R �� � prob�v`!tPhb%y��� u�Z 3 d��]A e. L��\Do-|ed ``! .f��.''ac!)\,% \+�{\,F(� i� is u��Ice������ . Re!� �)�'!��''�A�n�us���o 9&�!G � \Fexġ� valuV#e�:�V Y�m&�,��T �6K���Y�>Q~y�3at=vioPby��q3� ~)�U�:��"�za ilar- .��.�ou � , ex��EY�su ��:9�"?%�u�] A � .�����hb ��_�����Ƃ&*8 �d!�� %��3�.F��c+ of l-di/"�AA*} e of�9M P|m "u5I��a�:5A ~.�&�^ xiat,\dp�4�H��Y,F��$� �g"O+7ee n f12}7M deedNbn-maxil&�1d���78*e!�.(as Lucien H�A's==${\Gamma}=\��X1}{\sqr�`}}\bigl(. 01}+ 1"�c1 r)$},�  rio~n�� !����� en>[�$!=m9d.�A�%t@dom! �*�3al or0Hadamard basi‡.� U�~�%�$ift$Ai�M�qii�ZR�� }� h6Hn,�m�ingZ ��ec�6� Nb theles�7� v�;\ I�e�"$'no �cO96�� ]s�ܡuB�% A>N 2/$ ��s} M~�e emerg{Hg8�u�yVl�Á�m MF�O'e� ^w}`6N forwA$�*�D>L%�3o ���<�`is . ,��O'� �d ef histor�*R|�9� tion\ 2A�eׅ�m`��-:�reQv�Bf>�g��.fi6�It~8`���.~,ire �dUR� �.U�CE��xW_:.��a t��Z � 19906m�Vp�!s�6-rf&��96e)S< )�!pen} re$5!R^*��oolat!�u+�s��!�A�{g z��&# s (POVMsY1 iR ese ^o�m ap35r3�eOApur�E.6�A`} a�� ur.q�b�`o� cY"�<�T��8���sda rigu open"��29A� "�BHj=f%��uofmt�qF 2r�X/(r.�(to 1983a en P�� Heywooj,Michael Redh&�hr83}�����C�P��nbA��3on�uq�t"�S�B Koc�.�(Ernst Speck"�l KS67a:ll�Le�E=�� r@t. testJmNMu the i- _� . (T�o *�kV&�inB ntgMu�_bu) �y١� amen��p���(� .) E+��gne�H�D(WirDBAUt�N�*eiach of2�-��re"8 !�C[6� Z� fift0yeJHr r� 0Padmanabhan A� /"� }�+� !"�A �bnB1 �� by RA�rd � ve, M�<{\o}yer, Ben TonYZd| Watr�P(CHTW) �chtw04"~20S>!��are>$  7k�2��6YP1989 by Daniel Greenbr,uDHor�> Anton Zei�er (GHZ)!a��<�@ �%$�B reak[Uw�I�Ad&��.arty}RE�g��$ly popular�� � vid �' z&�.�@�*bA e�Aat 1'sŁ� �`i�la�- e�-}F\ !� yQCCBAAlyE�R$ �Z�Ci'�t%�� N�!D�.l! a]1999 (a�P�c� C)!+:r&,6�%e)% Tapp �bct99}?� �e-15'&�}%, ' � k5  !�B .� $n��n$ ˧M all &�,ly large~$n$p, Viktor Galliard, Stefan Wol9dF�gwt02�a�i  v4 $n=16$�sW FOAA.8!Cn�, 9*F:KdI�i͸Y� � <: �,%5hd��'&�"�c Xre}-ߍ����(�,t � &*� b}��"� � $41�4* Coul�B��!�B�2 ?e�+ in&�3�,��+ 6'a��� n.+�d G#,l��io[�9in� 2��$3&�":� o[�.S!E�[�nk~2a�~3,��ively.SDg;p�e/%=3E"�kiaLex% any}]}F�%�3�6�f83d �A^%� as~2@\ �a=aA�(t6�\2 �8eriOB3�pJ0l� N�? T]� e{ Gn�2lJP? A von Neumann (pro�R ive)�!��&T� ^Y�$d$��kA"�tS$d&�7-��I*� Le W� mum $*b:�ZR8.�u`%[.A * $1�ejQMA"ph �re!�o- %�<^7!["H%2x a2^m&  ( ou� helpKa�,o-" )ks�8is�� >��:�V=�*R�e|� �pFkz� �ee~2' � })AC%:>�? We~��t��< !]ne��ve:i|s $�  B$�a�"�$3$�ca ~Q!t=:�!�E2 BrQ^Fxq�e���er'p u��"~�mf~w�Rowib icipanC[h�!:ol� GHZ/2 � .�is�.�����>(9Sharpe %y,��Q EZu�@0�y7&� gen�>TAso.as Po�� ve O9; or V�� asuraor �* @��,Ir} L-L=_��s"�n�B��Mu"� d�8%?) �;Ak.a�m1-*�T��Ldl��,ll�Psc$e�s}. Each  A�aAd�-߻4~$M_i$, i.e.~a U�E !(= D_i^{\dag D�cq %- I $�!c�$\{M_i\}R%? �� ��;�� $�E i M_i = \L��"�| m. WhtIpMc��V $\rho$,�uOvA �>!͗d�["� o��!W�&44y $\Pr[i]=\Tr(m�)�&n~N<�=y\Psi}\!�3 �aA,�;te��"�y���;�:Af&v jbr U� p �gi8`qk �;Qf)0 left@ a��;��W5�} (��C,&�PA !Km!A>�. ��B�E� just�OX"����s�[\� Naimark's� } (A��#s�T)ed&QR�= j3u6A):%� �9r to !#%b�%;�2)U�9EM�}�,N tA��P a�Gry2,&� .D�E�5�,-. 2{AƑ�Arbitrl" eYces, ��m��!���K )^�%t ���$roٞ{�zsJ �<���e�{6 (d�%��cgm99}) &7 s�I{ia0w5=n�*��b�6r"Ussd} Any)'UhDa~i�]4��R�UE4~2�O� I�O ��. ��3Q#*��&wj��!k�`~�`.hZ�t�2Ly:, �=a�A��� !E�u�jM�K] j b_{ij}P"�]= �.re���fs, $0 < < \le 1�\: Ne�n.We%�e/]~Y a٣E�by�?�1"��%�the= � r}�1S� hea�8�%�B(z A@�\hav��!5!1 � x����. To~^>�cis�=!effec�"��0 �one�#'" 1����� : In-  $ijŜ �:+��}fG' �nrpݣn�K�e�y~$�N"�.i�%�hn%= M =!&^\p� j }� �� $�\ ��29_�-4,�amb�ty��*�C���c�!� t~ �$m�m�� rwe�+� :.8)#$p�Dnt��~?AB�C���KZ 8s. As~a ket-bra+�$�+ ��xXP^s}�H� ��arg��6�$����i�#ba�rried~ou uaD�F!��f2N,2M!��Ƒ�R8�+}سmma�8=\�()array}{c�? cos^�0heta & e^{-i�a } \s�( =$ta \\ e^{~& &B^�� | \r�) �b*��=s $0\leq� pi/��nd $0hi S�. (SomewaUun�! �Y6~/ �ahi=2!O�{s)YEMtaoE/Earent.)E��2�%�saZM� a�meFJ� vector1�5 -�xyz} :�{v��B3z)���#%`(2)�)%�(!��Qi )cos5 bigrB���*,� p=�d% su�� aG t sp (A�Bloch S)�%�-.f��y�?�: C)u|Cpe'S north polF60,0,1B6Am�Eit tilg �!�e� ��@ �\Bw*e 8(xs3ot>S��b(1,̉� �9I�� �'L;$I�,���e#�tin3) � �{sou6-1)$.} ��R vP of~$M��y%�'nY[o��ta"�H5�axGy��TA<$�.2;��y%�"�"Z 59 hemi)y�5i� N < ��� h:ws">:\p 3i� e�.�a�~Py��_s�as@%1��� (�=0�QE�m6�iM�3&�Ss �6 0,z)�>"��ebMu��b�q�zSCll %�u0L=<�2g��yT ��e�Kex�ddA]hiN��I&-'xQ�&s�e_ ���#~$xILe}� �^�d��1 ial tG��-R$��=0$Ei%��*cY�ft1 q�(q�m��ywm�E�au&#&s C5�AnoM, regard�'AA*�aSAN $.% .�.S�f!g,per>?Equ�~(�z�%�))� *�-!�Vs = 0$�?.n�~�VAtB a well-d�da�ci�gNF�5u(sti�d4ؽ(1� 0$) I�E>>�Ae>A��A)�)m Enei!�� e�/cO l9��z��� l��%�S)"e4j�/2��6c�&y�� "� Z}i s�o�$\gM+ �oPUN��tf�$[Z�w�� D� %�!n��, lg"�2�"w8G  alter�3ve cha�Ber@ofEF >���k s a~%%��mee��)�l.bi� �3��o"t�E���>S cgm2�* � | sT ���D�1s~-�^y�[�T , l�ue D &2=.�.�Iv6B , 2s:� ��)Cc"��I _i P�b2C Iw�� >̅7E*Mh>+=�(�?%��D.�-�Y�*�:Qa�j3�&�a�l6� eQyZ:4� �h  (p�4"'��)��!�:6]:�lCon�-$\{9@!~\z\\A*Z��a��-Yy�_�  1a��g ?cIi��&��WandH5�0=(x_i,y_i,z_iK=Yq tMpVosBtan��M�If~2Vze �i��. ��=0$�I f]�-_ (Y�l�ph� J@ U�P! �2�E�.)>n:�G6y[C8�Oa?�sr�� V$x!�ge �$y �!�$zL�-1$�0Ѷg!th�?� f�� 6�0 basi&�1{j0�0},\,1 1}\}a1A�$� # , � :�se��a 0�.�a] atuh/٫>U,I� !I$u �| , C��} O��wi�,�9�Q;�5�U��'��re�:7Mdi$8-$ Xy1�0a|If�->9 sp..<)� $�E��ȅ�(rB�l)��%�W�� ����o:� �!Se�be ��=��$P_j$�%%�sVa�$y_�p�ea &, y��A�gv/1 j W> | ��m�^ B Dw��oc�>U �Jj��:{<�""2!�cfew"Yb 6C�1N�.Enya2)0%  &�#B�A.�) �"sMHI��"�hi�*@0Q�mi%�70� $ P � �BZyare2�&UtP"�� ���!m"*�w(Psi}=\alpha0�5bet 11}��� �rpha"%fU cRnVq M�-�%��e~ &= Schmid�N�.oTfc)�E��  ogoAbakd��PA_�I�A��}$u>"�L5�B/B./Bob�c5)�&�as \[7hi�)` ��k + %H11} \] Y .)ve2� ��1�~-�.��� �E��5�3̂ �Ge �f~5A�I�e�st�"h5�5�)���J8%��As��&�J!���4e%�B1�W!Q DA� �=� ac�eose l�n�K�C��.,4�z fI '')��6|A%�� k�6 tegy= ''!7$W]edm:m,q;iI� [+l�$�.B& �TN�:�%\%�| aj4p+d�1�d�,min(d_A,d_B)!w.T 6�"|A�����8fS_A=�G�sum�Is0J-It)M��< ?WF�"��many" X L"� FN!�ba�&�um_i^d��A�Aq� B_i}arA5ro�5F�smash{��8i}\}_{i=1}^{d_A2�eF:2g.2B2rL�� 's sub-� n2<d$4}n)#!$.�}Cspa%� "}$!�., �} 0. �yF� �|ofHs ac��p�Eof {W�7���Rmoyenn�:*)��L $�nd $b�u�!���� �-a^2+bge 2abe?`L�l�,hol�s�QWo�y a=b�P ge�L3]avera��z��b^� ��=a^2 b^2���}N* ar�xe��Pis=( �)/"���1�yk&��n:fGB��/��1h �a�V5,��ir F�, >V!J.V!�a�0>"�)M&�#}�|maZ\�W>now�d{F m, B�;&�APno2��sptc_��:-��6^ ��m:�B�2 $"�QP�i6�_��>� � 7�3!/a 6�-�N�6�Our~go���0e)UQur�!&`'�c� also�f C�~i��ais$$�!)?"7-A�3'�VV����Ag!zrMlE�+bC��to�&�a �W�W.otr"v�ih�Abtrc+&�(�]!V�1�19>re?"be�X��(l �p&{K� [&9'%S���0�8�id+"B� ��+D*r ;XG&�Hy֑�L�Fa"~�%�>�BZ noZoZ:'5 � ly.b��$� \>[ }\!,�6a,�jmmBUYti4Z�rum 2�4��A�>�єA�(nA��Ɂta"f`_JY�%cil�8 ,5i'ary t�Hk��1f��5�e� is cover�O��� alis��anko &&2� ��XF�,6{;>�may�,6P\'�%2�&F���pe��e�� �A�m�k}^���mB}j^y=�d�[ngu)�s =$t')���ofA�,)(e�uR�zer�/LFk� ter��05/6 .1 [1�AA�/�[� � x=y� �D� �^��%��K�al%��& avoidQ���von��, W< it~& �Fl[derstrJe.=�Yscriptsc*� $y$ Ѥ�<soi ����@dentify ownershipYor)a�]da'�'th� �(�I� ��pu%-��~$Y*%Hre8Mj�<��6�YT.�)��#E?~@"$.}�)�8Aly, �� A!��  S*a7Qh#!�m w%V*$'�V�#$ex$Vc#~(6�)W T2oӧ�E�)��"a .� _I�� %�jř!�!�e�8�� �: ,j]$ �!2 !E�'s2�Rb�3 �iP'�� be~yYtaneo�z ? A~s �1KQ$4edu�c��~��"T :H T;"%8��pbegin{� <,j] =72, *�;!�mm%Щ ) \u���)Vk \\[1ex] Re�A�� �0l[��1-� i^x):j^y+�t0h1:0 0u�.antom{�g� � � } +2 �*:��1U`_%^x� } .��2 "bigr]1���9�Let�za=�~��$� $b=�=R��emc= e� i^x+ �& 7 $a \�%iFbW � >0$!��  �=4\4f�+�,���2(%�l�0a,zO�*3-1Mc(�a#,�U � �+�`��6iad*Z &����J>-�}m kA6 �� + + 2({ c)$}�F�van��i"�a=b (�Q26Cc=-1�K-r�'=T�.�%0!Yn(j�%riQ v�l�Pa}:4me"�t �$��8$ 2�$�&*�%��p:�=�q&�.�+&B ��P)e �W �1�>��.$C^b"3\pi$} tbecause \mbox{$0 \le \phi_i^x+ j^y�[4\pi$}. Recall that our purpose is to determine a classical strategy between Alice and Bob L@will never producC joingtput whh�@probability would have vanished according to the quantum winning ��C. To~achieve this goal, it suffices for Alice to select an $i$ such)$\gamma!5 P $ belongs!�Least hemisphere and [Bob#s Y $j$JX!�QBXwe6X\(without actually measur�,anything). T�Dis always possible9<�(Lemma~\ref{�}. In~%-(way, neithe-$ nor�%�cho!�4a POVM element!� portionalf!Psouth pole (thus avoi!�Q� a=b=0$}),%9M�\pi ).�m�$d a valid �se, soAqAca�.f lB#�Hoi�D$\mathcal{A}(x,i)$e7�E !B}(y,j !�~Bob. \end{proof} \begin{corol}\label{cor} Ta�v(no two-play���seudo-telepathy game of dimension $2 \times n$, no matter� valu/(integer~$n$ � �� �A��!�}zsquare},a� ��M��} �&also b�U�G2��B�Xc�^�Theorem�$0no2qubitspt},!Ms� %6 can exist- �1)9� two}!� optim�'~�$requires a=�- 3 -�3�E q ��!1:D~$~$2^n$ if  � s ar;participAX�BmechaniO y%�he%U.6F�a!,�b�iE��-�Y� = 9!�2��discus��above vtA10GHZ/Me� V;M�ghz89,m)(90a}, which^�Y;q�2 = 8$}E��among6�R�s. AdQ more5��on%cre�� ���to5�16,2^n \ge 16$}ō-N 4$}_g e��o�@�os �Wg�? C8 < 9 <[>�sec�{Conclu!��2$ncl} In c  , weiprove��R!A� CHTW-��~1� usesAf�qutrits� 鬡}az� a ,!��min�� "h ~�. N theless�� ��composit�� system, � v�� is beaten� I�'� reQ�V�-%Y�,. \newpage �� technique!;d_Aravind ;a 99�LFz to builJ b�uѱydq,dA���Dany Kochen-SpeckerA$ struEN!�F$d$ do�ot�qk %�e Tto perform generalizede �_s oAmeir��)�s�y� eS a�� ink�C%� comeR"AG standard :�t���Ŷd�Mer�� proja<ve2�-�$KS67}. HowAq� haA$en suggest! a��eZz| be ext� %�us�� m8cabello02,tonerL � ular�]is makes�y/o%�ider a^�Oa� glabitq���$be obvious��a)� ( !C!<)_(approach. CT !|Y�ofQ�EA� � %�� �-base^��9yieldV�Ųysw U�, excep!�at:� � to Q��]��\�$}, e� if) �used.�;epaper�;establiW�)Mconfer� advantage%r:2 K ies,a�p� G!Pc y�(von Neumann2�A�ŽA�.�)�d bNQ��restrice�� ing v�  W!⁤he situa�t�Ohigher9� s ori;.R? Can~1� any}��R�(be won witha�t@ �2�M p su� =kE�$s? A~figurE>merit�Hny giA.>��:k~ success�hc��by��$ ely F���BBT04a}2 smalA%�i2Y��e)rdi�e��: ba��e�f� �%�$surprised .� physicist�Hbe��� 9�� atic�of�#� -w�6�"; I�ly�than~1!$definiElofBt�som �i�6��)�it!14almost ridicul��cl�� to~1-n,gwt02}. For~!�4 � � $d$,L �con�z%F� $p_d$a\!E9� algorithm�!��ch!�ng�-Rn[�+ .�.ev�a8Q@(i.e.~be�)��we� ow5�mW��  �� , raA:%��K�zEZ qgajaNo? Is~!�VA�er!�multiT � s? � *{Ac!� ledgi�}j authog g�%C4to Anne Broadbba ,Serge Massars help/com�s2� 0Hthebibliography}{99Mibitem*�  {\sc$, P.\,K.}, block ``I&v colo� {B}ell} R''.9�PPe�s L%� s~A} Tbf{262}:282--286, 1999�:�02��A ɢ demo- �ofB� involv!�(two observe!� nd �"&�Af(or inequaliX'', manuscript, 2002.\\=4Prepravaila�lt \url{http://arxiv.org/abs/��(-ph/0206070� 1} 64-(Bell, J.\,S>�O� t {E}instein-{P}odolsky-{R}osen� adoxr�9�(1}:195--200!�64.� QCCsurvey�rE� d, G� ``Qu��A�u1�*� lexity��Found!C M4�D33}(11):1593--1616%x3.�͏I�.�,yS , A.� E� Tapp,�>�.����}Aa�,��appearA�4072212�b��s� {M}�'sF��M� Gamework�n1�I� �mon��Comput%��.805� y ct��%�6�Cle�RZ����C��of exac��imula%/e�um2w D � A�Y�E2ne ^Q�I& al Review�Y�483}:1874--1877ar6 bc90Yui�, S.�Cav� Ca��``W����g�^�M>�5�AnnalV�20�� 2--5��0.�81a �CImq.�B2H%^�.vETY 6��two ��ނ6��11--1914�c1R�q�f�\,`All �Xus no� ' insepar  �� � 7}:010403f��Gf�{K}v{S}x��a2�*� !~ perator-vG"`ލ90!� 0401�2�cgmu�8Cerf, N., Gisin ��: e&.�``C"�.or���au�bit�K,4}:2521--252IK6irelson8q�{C'so�/BN��j"��]e�mAu1ɵB�� {M+ ��������4}:�i��82� CHSHq�l�"lr, F., Horne M.\,A., Shimonye� � ��Holt, R$:�Pro�"d exper�t t,lo�(hidden-variT E�iM`I �afe2J$5):880-884�f62v F�Q�C(, {H\o yer}' , T , B.lWatrous� :�$Consequenc�nd lim�of non �&� Zsrocee%�(19th IEEE C�\��xalo 8}, pp.~236--249eT2� a �Gallia� V�' 9� WolfJUThex�"i�#J��N[���Interneal Sy� ium!.�� y (ISIT)}�3� yFu���³ 11016� 61Jreenb� r, D.\,Mq+, M.=Zeiling'A>?Go�beyQ""w \m&eem}69in {\it�% em, �Dy,%�Con�io�Lth��Uni��� edi�Hby M.~Kafatos, KluwC$(cademic, A`69--72aW89. &� hardy9цH, L�`��]s,m�realis���a@ {L}o� z-in� nt J.%�(68}(20):298��9�92z hr83-�Heywoo7}Redhead!�\,L.\, Yn``Nm� '�aJ{)�-dox:��*� ejl&S 13}:4�499%�2�KGi��e����}, E.\,P)�a� le�� v���[q� �5� �-� Joura�of݊� Ma.�7}:59--8 67.� &� �al:�Q�m^AJ reviydE&B.A[M��`�,58}:731--743!b6 asher �Per� i�-�i�:q�1 thods}Fl+8.�)՚\,� Baco)9�Ben-OrA��J}ene� geV4!6in~pr� �@�^�U�%>� �# docu�} �K \O �[aps,prl,twocolumn,showpacs,groupedaddress]{revtex4} %%���� \uR 4ckage{amssymb}>�'6icx!�setcou�Nt{MaxMatrixCols}{10} %TCIDATA{O�'0 Last* sed=Tuesd�*(November 30Il 09:54:06:.jGicsrk32l, \input{tcil�! q(Q�title{SE��Criteria Arbitrary�]S�bms} \�8{Chang-shui Yu\Bks{% �)i&7\@sina.com}, He-shan SongHffilied{D�taB�>��, Dalian��\ of T� ology,\\ #l116024, China} \date{\today �)ab� ct�&0.o{&ist�t� tain�-i�nec! cond) aq"c1?l� whe� an a5N\ht�t�)�d o� t. B��  tensorD re% of a6Lp:t �e p@ �g:t�G'�a[rm B.k2 _{C}$A[a t(or�%̓ik0�.$ ".�  i��% he new skY5�& *ide�%a]'wayaM&� �$Y��Y9ge�� �^�%�to2D�ʼnGdInm$Ca�w��ntinueA).A#toe�fa�a]� 2m�on&��L %.&vorgan��Q3s: FirstD"weQ��� o:�A�=@Y|s. Se� f9�� �! !�63of2�. � FA�7�&to 2�> ��2� 6MV�} We � ��6�"�I�s. Unlik�!T�(/�� +,%7conveni�,�!_�= sindh5, s�'as $% Ta�\cdot .kacnd�:,�/ {/��e� s r'Inum ofe e�2h��a���h. =rp$�� se<all one:��$ #vectorsHR L0�,.s�*$�0Ai cASTB>s $%�re�xr, ( r ) if�%M(two)Sth�+tO.� (are) fix7(��7�\ 12�D$w4���}�( nodu&�grid �2o-�Pal Hilb$ spa� 1�5)���!�0i,j,k=0,1,2$ � !'�& 1. F-geomet��+y ��ex�/�6ds�*a /!� llel�%ne� !WperpeA��+q�)b� EI%9Ff toE:W&�7�cto.+$!{ Q�zmu�92�a�e�{ �}[tbp]�clude�8s[width=7.5cm]{)S.eps}% HFism 2,8rt EPS art \cap {Fr!)!�coe�'��Q�I� .} �51}� ��gskip\� bf{D")'.-}Let=�� N��>% n_{1}�D n_{2 3}�LMFiE@.>  ,H-1$, $jV$ $2$�$I�? E K3'. � ^{\p� }j k } $�ny� -)��m �.�byg�q- H=\frac{1}{\sqrt{3}} \sum� }(C^�+})^{2}~�%&=8� )#Re> Ame K2�� (��q�9�s���jk $ �$�%Ps^{1}=-\sigma _{y}\ot>  .IaQs�26 ; ; 2 3}=-NZ:2% s^{44v T."J g5R� RF 36R3NoIv)$, )��)�F= c} 0 & -i��i & 0Z��IjG1<FQ1fFand $IvjKAKU^K(. Analogoue�U�I/�2N& ͔Ek �� 6� _{� �"V j�1�� % Z ;  ,[�q��>O theq ��.�A_{a�$ (�BB( >� )��lin p� B;� ABi plan�"G �^a�(. O7 asil{ n�Cat3&% �is\ fu01͐le�h�r� o s>�ar rele�5. A*V�*b&l�6 6�( �;�b�at� s�Bu �-|)$"�2�D. Nam^7))=��E:2Co.�2�m." a"� 6�$ writ�;in-=)��B $=$(?,000},a_{001}N� n_E� )10J) )B n_% 5)�} �]�A"on �Bval ex; !8�?!��, �2%�1�2 ��U*q�u6� (!U 2���% �:� p}(CZO^ S��=0R �% hold�� , �V �N 7 $��6u !u�� ���\l�BE5��� $sjL @�* >0 %%% :V"� >Lt��$ I_{ �E$fR2}=NR@2R d� ,nR~f� ��R�=N8 1N%@�2��� }^�?^9M:| ]*t.{i~v Ji ^ .�] 2�$,� $ �!� Lm %2� � GJ� $SO(�p)D 2��� 3 �ly; $=�:2~ �|unit  �*x|A�� ���2�6}r � =1,2Ft ,M b �-1)}{2o �: .:2:� :) �$ $A�  A3A� A.2YM.U&�!�modulusU�%�%E x $MN T=#a�C�A a���KD $=$\unjetG %� {\oplus }&y _2*��)'�length }�m(}�8:V \R�� 0um 2�?�Z�! v6T!� }�� �B�V�=F�r�6� ��F�aW "t�� i�)�F��.�}*:&X 2 $u" �\L.(_{k=1}\omeg�k=y� ^�1��B^$��$��>"� �,x&� � �Psi W$^{\dagger a�wDW�KagJPK�<W_{kk}=�$\ (eg\E�qij$ &>� A�I�!&���$.6� eigen�2 d4>�2))�hi M\R�M^�KCd �$��y� n$A$o$(�t<% � X1 6N��;%�" rom �],"� g{%5W^{1/2}=qM T&� T � R�$-�"�b��J� | re ex�?a 2s �B$9�� p  $k�W=l�N�!! !!\ Q�d��e� infim-0�&e averag:� boldO)ol�%QK2 $.  $�%=\inf �jy�V� 6d% q A�6fZa%�Qg�2  #!^�%��C� >�N&rh�y� �2yR .� $�y,Fp_ get%�npy} 1} &=&ހ%~ �2~( \notag \\ �]r.pݡ%, ���8N7.��%/} ast 1\%8fe p�b��J�p.�1�-o% A.SR�� Mincowski*�6=��E�(6i���:k}x_{i}!� �) � ���qO_��JF^>O O O,�/{ }p>1:�}%U�a�ed}(-!]�\geq M��G E>�N�ba!mj.^^{A<6� �<e%)�"M]< !S2}}QC2@� :$ ^ �E��� ^{T}��V�wp#3 � D� Z�" T}{�|}�����T����� V�\%�� �b� ��MĖ�u2�� �i�_��S.�:�}z60 5(a�A6; �) F�u�m���$nO==kEVVkIO.k��a$:�2�=y6�2� e^{i�] $aJ$:.2K>0��=�-c1�n@1:�=9!E4Cauchy-Schwarz��r���2`� I 23 i}y��B-geqsl�:0��55� �%z+ap .�$l�] step #. � (3)w�oR!QU�z\i�Mat�}{max�Smbd� 1}(z)-/i>C% �(z)u\  �\�.�$� [SD �Ti"M�&,� -1 *Qp}{N���IY *�!�B�2jV1i� TaX�K"� .� asJC� $=\max \{0,��}% F1h\�U1��Ut!�RS�I�K�>f��=0� .��"-**of2!v .�6�_!� wholx)ocedurUK eriv� �a2J*O+} "M. $N$-p !&�.��%� �Z �&].� N}6 .�ij .k}�-. 2�R:6�, *� iy &[0�%�],je�lbrack L]N�k+ +N}-1]�_-%����$�+ N�."6R��(6Q�.Ij>&B")|�F@:z_{Nh"H�,l2 *�s �V���� nv*4A��� /&�� u�,�x�p,N�#6��^]�&�)��^r.� In ��) NA3�4igo1B&�-, Zto re����D��N}�A�e��3 6���^}�(ij%lN���c i��ca�QB�qi:�&> 6�M���Q� �.6D delt:�}J�N-i-26�?�7.N3v-9,� i��,2�� ,N-2z \ }jV� ,\binom!�% i+-iJF�~ L_{x��'�_Rxp[ $x>�m3&HpHp�,�p$r2n-Yj$p�)"�6. $i$n �{ (6)=t�W 7av0absolut8hluA �. Not(� i}ofn�21^c&%�.U[E�E[6�&A rho $.C #Q.! 2m�`coei�� perm�8T1�h�0�+ex C/�$!} $j!~4 . H�1 672.�b�� ?o3ing�an��% JBC 6T^ �e�*6S"L �2�=\u� F�!�M� *� ijO� / IuJ2}}=0u62 *"! t�a.�:-� $1NU  normq]N9k&>=sam*� A�x&� �S�on II� ��_4c\=F�e�)�5�*}  bylIA4wheax *qva�kMlJ��� �� b��@ �*@ ��nx.@ ij ٩����MtA� "�^A + 16�"T !i� v/R~. k1us finUl�-h2']a�fhre�mGWoo�Ws,� cur`Jw� $N=2�� 2$�02* �;A��6inL) o�5A��<�� .`*$a� 2)�0�8�� ult�6�:�4ifVa�&89sui]"9J�8"�$\protect\b�2@�c �>�ma�4~pJ@� �liz!r�%F��5] �>rCB*7"(?�=Kt�f�'id\?&(^k"{*$(� ��$�/2�A�6~84!T��o�':�s��.?isA>v8t�+analytic[it�:�ur��a�7er@0fi�N[ ��s,�4 ,�9 impl�eaCsimila{ -g�often e;0 �fruitNY1�.<[88�NcI?��(@ens'?.�:�Y�is DUw�>upfPegbMinistryA�Sn59qnd *�C�C, �  gr�tG�Y",U8[1]} M. A. NielXu$I. L. Chua��it"�H*QNE_�H*eM,} (Cambridge.�DP�C, ,-Y0)!6b�Z[2 � Zuko>1P. M �\P%,A. K. Ekert,�D. Rev.�<. �Dbf{71}, 4287 (19936sT3]} C.H.Bennett,et al. NM�<.%K0},1895NJ46J%N$S. Wiesner R�U>�69�N 881 �26�5V.3F6F,H m&+d2J06]} A.Uhlmann2|A5862}, 032307 (20>�,7]} K.Audena%aF.�GtraetA]De Moo6�_,4}% , 052304a16�8]} FE\anate(Marek Ku\'{�JA�And� Buchleit!N Phys%�:�9�167902t46t9]} WE6��I9!�:K80!�24)�86IL10]} PAWEL HORODECKI�RYSZARD&iO}&e>}N5�A�No.1 w20>41a�r% �Ay33� 377 V:1ay�V3}, 364V�F>{B�K �V:�KZ�K10pt]&�K.�Jepsfig]��&�I�IO�]!�]Nonsprea�(Wave PacketAn Imagin�"Po�6ialpI�_8{R.~St\"{u}tzle& mail{stue(@kip.uni-he�F�Q.d' ?0M.C.~G\"{o}beWTh.~HrQh"'JE.~Kier�C,I.~Mourachko)M.K.~Od=halaN\.!JLKirchhoff-Institut f�rE)ik,��\"{a}t H�D, Im Neuenheimer F�g0227, D-69120 .- Germ2e \homeLk{www.R/js wave��c*!KlM.A. Efremov,$^1$ M.V. Fedor,V.P. Yakovle% 2$ K.A.H.� , Leeuwen,$^3)W/S�>ch$^4$!?*GKfG�N)cs 10 e, RAoan �R� ��xs, 38 Vavilov Street, Moscow, 1�`1 ?Bs2$ ( E#3eero a�2~ (S21 �SHity), 31 Kashirskoe�sse.w 5409^w3$EindhSnUa.pTP.O. Box 513, 5600 MB :,� Nlands} 2w!d AbteilungQr .en�HFy UlmAY89069 UR2�Ly�&KW35X��� �=nt� &b>umLQj �Pe ��atomic A� p�". Our*CkreOj�^ spa�*edu=Nd�r_?x �lt>ghisel!�a�Ef�@an 9f�b�c( de Broglie�.%lC <coxK<is balan=9byhKpyO due� HeistV's uncer�Mt�dinciple�fm evV4 r�m �FM!J�L =*Gam14�)aB-' quad�c$c phase. E"�Y!4 �jirmzs!�edi�H�c! the ��'mo�Ium!tribu�. More�,!*-1�<(rferometric9�s�m~{� p �ed� � acrosN(%�U62r=&�)�  kGt)?wo!.ce "IC�d*C.troNE(ir amplitudI� ��n�Ya&x*�y5&IN75.Be% .50.Vk Dg} %0 Be=�Uter�s(AtomelDneutron Optics) %4 F=e�um  (�U�f�H%lY*eKtom@ qDg~q2� y) .�Nfz�Katt*>�Cter�m|AR$ early day�qm�V . AlF�u 1926�[r\"�Mer x Schr ftu#8a displacedy+�An�KU0@a harmonic oscill2���se#a�l}��n a*�| forceC ventB���u��Lin freeM�a�Y-�6s5b{Np�s�,� uwstored Rn ��Airy-�@�RpedELm.~pr� � )NBerry}.�D�Ib��K%!�propag n]!�ers;kA~6�s�" (u��ve) p$ �e�q�ae|sM Chudes,&� ,�1998}AM8Oh)no& Q %��.��r�:1�� inu(l�EsT.� .�Nok�jng�!�+pild�L�� � L|_kK-�s�l6A�w�Ok{��h�n�X_�_od�ly drive&pRgs-�b&� }9 stud O�$i�w �m�}��reB�� �yd� %�e all_�XLy,maeda,hanson,Chen}Ws�c`IzD!qie�QqE i"aSs: (i)�QWonA�AM ��0} cuZ4!D unwawOpa^Q�b:��!a ��+2- �*iny��I (ii)Ţ� lead5�.`2XU` to a �en d m�d�5S? a 3fas�e�iA�alh BJ�k(i �e5:ve �!W#Aҭ��MA�1 ,s| x.�)IM� In f"��we �reFss�L.6eMichel� lomD�o. }.  lex�SH;$ WQPr�Uss_�M} emerg�io1 �" ��e� so�E�oe:�E �L ilmxR tK Fig.7 fig:1}(a))Eaa�� Qa�� uned {\em>i}��r |c!��!o ly �^��Z�&ises. WhEt Rabi��Acy~$\O�4_z%��"�Aex��Z�!w2K $\Gamma$%l�� s�V��!meter $|c \sin(kx)/ :|�3t��jupper )Ipop F4$>�G3y�eptA�a �p vic�1% Sfield �@� �]K[h!bL(6.51cm]{Fig�K�K�K)�9H3�B2.�2� �Y�T0er-of-mass mo�ICTtwoIT �E9nNM �t�VM�USQ�AS(b)�za�]?U.YAY84 &o �'qe�Lc��dC'ed ڕ��X> s (inset)�!�teady�W�X�! L� i� lz9$\Du"z$*��U0�s�r�b�ofIBio�%�� �so��c�o�p�� �*B� gM�M�� {�er"z!�r -Efr�+l-Yak})��a� fy�ency u� =0.4i"� d�`d%� TC!���Raman-Na(wpproxiI�,  a06u%Rpla"�� �<����.@s*�ZA�"!t a .��N�Hmb �B�it�& S�p+ �QW�S��s �_E�� cH domab=t\gg1�S��a1iciwUR"ualuu�y�#,�H6F $\�" xG��Q �QM ��is E and �X6�2� $(�!k o x)^2 �\llU We�z!�g )X� s! � x$I��"SBj jtksim 1� ($ � x(t)( �/t)�32}/{(k�)}.$ i;deD s|! �D�!c�an� y� /A��`)|p}1/ �4�k mv� 1}.�sa]�m�� . B�|�^P +twC�[ es -*8  ��!� FB-� 6�� rͅNts$�����.9C_0$N W @ asymptotic regimIa<1(t)/tE�q�v6��#"ba& E8��1�!�/ML&���)�~!&INph�$t_0 \�E 1/\ox,Km QE ^{-1} Uk (rMrE�� G-'2Z xgA�(M =0)X/2�1�ecoil�� $ -r � k^2/(2M)}�I�e"o` e� (�L2a slow�� beam�� meta� �\@rgon ($v=50$~m/s)$ ."B�Zeeman Rer� briQl M�d�yig�\ca�q enh%dT a 2D-MOTVWup scholz} X"=l�cA�n"ubfor co~0zllumi.lw�8a(slA� ($25~\mu$� $10 )��"��(25~cm. ApplWT a Stern-Gerlach magneA���we�S%�a����naiI4e $1s_5$ ($J=2(m_j=0$) �J��=-; ir�Vly��aQ �  l��M,by retroreflc&$ng a laser)�"� %�A� �4--$2p_8$ trans�Z ($801~$nm��se!� �RK very good�M!�FG ̓�2$ 16\%!{�� )J fall backdU �bau e (i�tr�3to 32\%�Pt5�, ّ ion)��[ kR��)�� aC&� �~=Dpas��� djumTAt . By-�g� onto�>� mirrÀ�>oi�Upoi1 `!%�. I:TR$!BB�)Kis a��",a microchannFYtf{%or�*�g ͷly A6le ��A"�utwAl�Zu�4gy (12~eV). Si�5�Eg>ae�ce1{�U�<m�ni��i�xch lar� tWgP�ali� s outgqoe"� �X�Qarr� �^> �~� �I� F��ca� dir)�� %U� $�/5��!our%�ic )h!��' ee fE�� C$0.5~$m guab$ee cl  mr;-\.^ pa% !Z far���}.+"� y!Qdq(�Xum!� upDM+ed "�]y�2an7 wind��aVt�@�< � [>� . AfsQ~i�+dynam�A !��r7.e.EV�Woc)HngeI'A�e�'A��&!���\!�.5p� * 2�nu'�z�q(line�Bope.�� �"� tak��o��k� longij��as�4C.�velocdj61�v_l = 1*a  t =7$~mm/i!e"�.�X"V = &X�?ha.A gree���a N�hi���a�Ha�5� �3�o�6�|(+aXrmi[RH 2�0. 58[ sisK"�5�-!�2 both a rough"! ,���power��-ݑ���'� �� �� .!im�{ ?���st�'�E��.sN.u�YF? i!Uuc��%2�4 2��%�i�)�d;�B1&= &��(.v��}\�8x^2\tan2\a):�2}�� U �1Jai\pi/4 F"Q�-.564.1�[j 7.2c2}&d*2} .�#�c ificE;q m� law��W�#n� � ^R� z_0/v$AJ,&:I�p�%s�9E� �& �s0u �@ guid%6 eye.��#�czer��Z� B�� z$R��?e��"�ie� +$!point beL!�� a�!trapo�5rh�e� � -��O �$z�}i�M  \no��nt *�7�ma�tyq[W( $|m'e&|^�3 s a �u�i�|0 X2�M�\a@[�#(thrm{Re}\{ mCe@ (mt)\}I� ]^{-�X^���7 t>1$Bc�u� x_Ud(mHr�\�eO�^2�4}��I6 �B�Eq.~(\P�Be)� izec K !fduc"�:7�f�~ �) t�U&�9� 2�N�de�� onen�il�${�!��U quiv�e/ Z�dll��"�e&+ YB�$�@(--�x^2 /2�D%�<aind �c.� $ �F (x)m�4{0} J ��08} $. A Fouri��|"Z � b'.@9��N~A/$, �]behavio� !Ha�� p "�� !�nE%>k�:-dX7a�i�� ect &� %��V� �� ed($!I(Kf�6?�R� be d}�*�I("� T%d2��.Ck�4m$n$iV�F �$X�z.sis �n) = -2u�M~ "� m�2} n^2Q"�_2 n^2��o���>ve� �7Y act}*er�1� 6�3}aAvthin [!-�[!a���� l&Z(wa�R$3�)�(�ly��0��3}R� 3} M�*F 1�%� 6r 2P =*�'t5+�(a)a���I["�v�!dF � ���(b)%ds typs 2I��Ex�U��-4� .�sca$�A�9��( ��`(!�)\.���a{ �^�h PH�@ z�)wshifts� ��A�>� ��Z#��25j" off,On����wu�!�H >% behi"��`!R ��&�,in  �9���@KL  su�n=�5 1s�C�.��.8�-v6�h�.c ���y���  .�M����#�2��&�.���-�]F "~A  zv#$*�.ir�.`"Ba!� at jnm �)b !a"mpi)o�e 6I:�an�of�^{\*�GTh��mo�%S 8al&�gam yi%p��_s̕&� ���!��ve=� (П�X* "��pr�=c��� U_!%Fm�[on en�;s ���V�& (8~MHz���%X� �s�A���QE�6�Bs��Y�!Mu{<� ri�#sE�dy�Q1Y��flux th��Y% I%B?+� [|Ao!�ݐ�6�%J:I�}!�&vEA�)��e e��.�er� -���!�m5(third}.� e��eF "�'J  ��> �a Uwo-�}5:eMA!Nf(xE�gF}�ar�.��Qs�T���l�AQ��9s!�!4W r%�MleN�aHd#|e� usDrt� V� �y �to 'i����c�!�2)-1� �~ŏ e}k�<off�v CAjA��i�*�"`:�Ex!iO�[niV%�)�� |�we �!��.��� My"= �%kDA�!v(�� > 40"� !v0�"Ge"��4 1�r�rVAe��a (50~$\b U+Y�"4y G(Fpm 0.02)�  5�.�� $|%�9�4|=1.70\pm 0.17"hz :r A�V }�&~�T(�h=3y_2a� �_2|=0.57 �$.�5!6*�,��5��� Amof�%�h(�6des�Yon�CB3AA1�.� . Fuærmore76�UpR:�to 5�=(�pm0.05.�.��0e�-�)32)08:�*,!"���E j27 k4�So �q�c ���Ron�6�$D=1$� &�6 stra� forwardnD��v$D9F"H9�. ortho]$al  �:.�"��?,ng%� �pri����"}�0O "1, $-iMu� x^2+.y^2 y^2)�� !o B)The"���x��y�+ pend!HA9���"|i A�-.9gurx�mA��)n add�al2f�8a q#0� �5�al6�![-�.~emaOi�Fatb-H&��J7"��%�"?�,rC, ori�? �7B*0:oLIk�&�.p�#deed,i�a"�[tf>/8.4\4V\4} Pr",�NA?�t0)�:�f6> !_e�(x)|$ (d&�} 2o=�a%�"�@!{2n}$>� . mask?'mutzel}a���*�.a,�Z�L��de&� ���a"R3,!�d mpl�6 o a �02���= (&��+) (qx)^# $. H7$q�kaP �i�zA�65��OUb��a fLZ�4�9 r $nKj3,%�5 G4v"�9" te�e� c"�.��*�A�HD t]@$Hamiltonia��!�be&��wlyn �*�� me � thes&�s1�v�:�" lexg% "*�f"ye~S. ;i"9ys.�N[�(!g�%a Ugu|s�Q�t�1�l;fc5 :��| l:)

}{\tilde{��}_r^n� 9 \;\,�E{and} \�� \, q"a.Fs�>cOd t_0} \. )eb2n}F7Q $2�_r}=q�+ M Mse��q�k� Ĉ�?rm�'U<2� { 2� 2�"#$2�.� $nEk�5"ions 9N1�|~ i�;��E� $n)arrow 1aty$ExB&$�$J9Z ap�a box,��/ �l��1��.�.� sol�1� by~$q�-I"*cl���!�R�m��^265.�� a���!(%|r�J#A�F�.�) velo9=�:Q,�es��� expl\%D.m �Nof�a�Ƀa]��iO@��� #ita�(���S2dZd*�75�s ongly&� � taneqy��0. 6I�w!�o8"�)c�nWCnd �?L> �T(}�5or�!�� �M�.\*.& "�>W�� weak� � A;}hA��l*�.3i"l;A�a robus0o7��YES=��Sk=-$ZdRB�fu� =� W�B�=l��&O disc�C\(h A..�KM3ank M. Io}rze���% ommi�O-'N*stage1uY@~ Of�d�VBk-Z� um KΧanz, Ce �8Junior Research�H�in0(by Deutsche$schungs��Dinschaft (Emmy Noe�?� gram)��U he Europe[�!nC.act�Kp HPRN-CT-2000-00125. MVF, WPS FVPY�Cy,kE�lAlexander von Humboldt-StiftxL6�P���* } E.�%{o}� er, N<wi �Ie;�(bf 14}, 664�O262 N�$JQV.  eN.L��0lazs, Am. J. �I0. {\bf 47}, 2 P792P-B} D�I nikovW6�J=�e�K X>N110�912WO&"L 3L  2�P.�P�77?Q980�PJ�1�B�K~9$D.H.J.~O'D�� �AU 3� 2093�6\Ob*�A A.~.�O D.~DesJR J.~Zakrze1R)dRep-368�09�N2m��?w rei["�R& B} G.P%�m�1@nd G.M. ZaslavskyHenkelBM.=�ha��v. �4 ?78%\2);s-5@6� , Ad=t. Mol.�r1��3N8 �X4); I. Bialynicki-Birul�9�linski�� J.H.~Eber;;��Y 7m���0 by l�K�y� .sUMi&�(]A2O , sculpt�means "܁a"M desi��(4 a ��!�r{9by F F& FmaX. als." See:�D.Wb� YAr��� (Har�BD$\&$ Row, New York��76�P�(i6~D K.S.~Joh.Gu. Qe_ 2JU158��a�K~�qf0}, 456e�9);�Turlapovo]�7��023408J�A�1}m�oug�7�p�[b u�\hbar�(1�!w:�S�:�Opt]xmm��11a155e6���:_A.�RWL�9 ��1�;9�d2003); M R7 JETP 09��52W6�! 2! � "�iily 1v9u��6$e"� 0  eB<ex�� *�"1r 69 s" +.��� 5��,U. Drodofsky��;.-,B ��P7-�� M. M� :)`>_8EI83601EI�Y&B>l &�V��%%%=�P %%% newSKJCpap11.texa�9�X0�E�-- Dec~  2004.��= %:�WtF��ams�c.y(,pra]{revte��:@~S�,|Ӟ7n?*ޢd�z} % Alig�6� A�Him f-.<bm}�? % bold�<h.![dvips]�sU��?-? %% M)R��)���b@and{\wek}[1]{\vec�"{#1}}}6%pdt�o\� } �06/TTr}{�erm{Tr}\,!o,Be6)ck }{\�K}_}(�{v}�,'):j xket �@| \, #1\�~>5bra5�v5.;|>5elm}[3]{jF5�%�A #2W � �3���e� %l^�=161mm "�_�\ %%%-� \tiΤ-��'v03�ED a� el!� $n$-%#= de{�  ��t%�i'=ZAo@)h�>��eBE��i�--�%Tsv)i���}Y��d b�� upon-��= "�@�1�%��he5�,6�%�-�ity }�!@fq ��Ps�Aa�3F��*E_.XMo�Zsome ae�fAbKdA �(iC!���)^s d" ibut"�"�,)�rcFf!��e�D��d!>)�ce.� a"��y�y� {'ZHCt, 34.10.+x}% PACS eF� nomy��:% Cŷ"�8(Scheme. %\k��rds{S"�}%UGhowkeys!ss opAf�t 'fv%FX�N��6k�Kle�1)1������I&$�6io�x ђ� �1,>ml�Fpo��&� �Hic� occu4��gas� mixt�_(r�  yE�u��Hlight Ωi`8 Visi�kv48c�i�d �'nt�u���RusN�uch��e�ert�_es.�iseR͑d�Lth� ��E� reby?� luenSi+I(6�n"�q_�:�%� such�H�be �X,�Be"X��*�ly �ٷ devo!\�VU.l�lisM,8�w!&d8+"�k&mon�phsX$demt,rash,� ,coh�V U)O, o%��-��&of��est��#they �rno� ����K�d'y�%N�q+Aqsm%[��� %S�T)�-�H !�H]mAR  @ed�� 3bs�A1nB1�F name, �&b {b �%h�b�n�'� b*165ndY���:�t"<)a��ell��'鯁��,��W-�%;���lZ. 5�# ���R�B�"� �C! by saotnst��eg�� Egr� T8:Ů!to��ZVm�"A6)�%�6 .�Q* adv�M"%'Ra�$a��� um&�_�DMx.+�e~y% E3 s]��2!���%z�b�p� Mb>�:z�*/ (A�anfelW�öew,c ( \cite{keyl�#,*�)��ei�LT1&��4�>� q� ��a7%)� >�ai�*^i 9�/��w &� 2��|J was sketcE� bove3L�y'(���)i�iN:�'"�M�a�l�aa{ inv� g-wAhGfocus�2KnE��!2� (U� �A�IEQQ�p�)�ak��>R�wo !!ies: $A$> B�$Py�, b!�Ydereda��?�,YE+7$(oK>��O�� satisf���on: $N_{��ll N_{P}u%A�}DAQ-T1�B\�heө�$�,��ly� E)� �Ki?9- o�j � *7 g�( mas�� (ME).D it Fi al})�= spi��0of Lindblad-G*�i-Kossa�p-Sudars�Nm�h��"�$te�� ensu�"�F$A--7��l����f &Sy�: /��an&� eZ�dHia.P$itK.d4 O�ant���)Ѧperhaps�rth �gio�6 euet ()�y�o*�L1|s!A6( I�I �"!�� d" "J ME9OsD�����Y@#.��a��e�al !�so?�p^1hZL. @/{Y�DvE�?�'o��Y� 5%2��~)�mn ���pio�l�tof Sn�:FI snid�UnK�]ra�by�Do�dU�Mv&�p" ���<{&(s� exaQ.�(berm01,hube-�&� #� }�zRaue-c Shalagin�(���Z[��reh�v�:��-$6L������ea�min BBE, :�%��fic2e y-org�a�pp"�.�"-Ms�l �ix;�)�m"-�/ac:�BBEm�,q�,!�th�+�n�v�!/� VV.a3eLR l Krone��-L�%[fa<���pe�XeB of "�5W ors"���U!x "J(u�"&SA�A2N�Ka�e"����selves sl���%yoc��0;�to& (��E�, p.4< WorP �q "�١��Yvel�� S5"�ro�9�it��s.E �UN� oE୫2��2����Q7to invokiA�  m�[P �:chSc� Q��o:M�V��s&�!�7 -��>!�&��Qa/ ,ak}�it��bw7 ne�~ repeI�mA�e.�,�o��!`S= I�!8%�sub��A�!W� io�# Sec. II!�*]briefIt�r-&�al >���!'BE&i\}�m:s 1]%�>on�L^Vd��m� simp�� �--2i#Qp���9��.�.�= gA�ALU2n =RBp (m6mU�1" dA3do so).�6=opM�@� 5iu^���o�;%CB�� I�"�*ing. N�!�tEkc�3:��n+� qKh c n 6�ve"Eڍ��A�t�a*V�(N�A1��6�Two5��hd��U�>� BBE}�.&.u�{M^:8Ssec:me}|� F�6t A<���m_�P �t"�iX�(r > f�r)�ne:5�s���lsoql"��2�5����th#) fai?b� �_�I2��C �sc�!�"nq�o@ 2x �CX$� "�we e]� n������]� �ȁbul1[ � ��ak�.��h0 hrYmf5B�"<���icBv b6��A�b����]�$�� (so-ed&k.dw)��mG� -l})"|"lig�X $& \: \rho���f = - ;;/W+\bigl[ H0,\;2@"r]G& +��_{�S} xiOhat{S:�}^{\,& ~ [6�4(5 \�W5�d��&oH`\\ ��jY } ( MB�} r T3 +6&B7 X��sjj1} 7*-l�;.h�:a (B;d)B9Wan"���p�u�jde���WW ich,��E��2�+.0M%� � &� Y�a�ae velo"#� p�� tom.|�$(H9V$�oq@6%�Eth"�F �!n N�&�#"n Eq. \eq�U)p� 9 as map Ms (s):qsubq�s}��jj2"jZ-� &]� = ^�M&: B�G(a��2�]@�pMl 2�^�6�;2�[�3� � T?s��teV*R -"M.d .c :#tepN\2j;�we�e�qy s��to"( &)\ � v a*�&�immer?in .�!�F�!(��%X�u�3 �a�� les)�r ze v�jrapid h* IC.�d!xs�Max�i&}F�bAMW^{(P)"'-) ~=~ �,(�k�B pi u�^2q� )^{3W\:M�lY9��m-^{\:2}}{>C]v��ɛ�G  $ 5,{2}=2k_{B}T/���Jn $ ��m=%f�5{ !���n�?of2�ݭ� w~-�as��� �pA�x\su�^{n�}bar�Z{k} \;,c.�6.{kl�a�asjahamF��e�f�t.�I {k}$�>"m�,�&�� NextG$t $\{ S_{�y}S�5as�ks#�!՟�ngCF'A-�Latom states $\{ \xket{k} \}$. These operators satisfy the relation \begin{equ`} \bigl[ H_{A}, ~S_{a}r]4= \hbar \Omega#,x \hspace*{5mm} a = 1,2, \ldots d,n^{2}, \label{sjsb} \end{�where�quantiti�t�U$ are identified as Bohr frequencies. Within this framework, the collisional part ofqmaster �P becomes \cite{ak}: \)7 alig-4�pdt & \rho(\wek{v}) \Bigl|_{coll.%[�= - \frac{1}{2} \sum_{a,b} \gamma_{ba}C)S J[)h$^{\dagger}b!�FwPr]_{(+)} \nonumber \\N& +.v\int d �\,'#~\ckk{abd!�� \,') {�=�me-�-9�L$(+)$ subscript denoA�!�!�@commutator, and $.v)Ay�r}, �,t)$ isEreducedY sityU�!�an A-e2�with respect to internal variables (seV4) but a phase-E�$ distributa?.K to posi� velocitye�esxee (AMz) rate $N���Q�QxQ�ET.9 \equiv26M=B�$~{\cal K}_A{ /Y (\leftarrow -t).y�g1v2�4Finally, it caaA shownuB ,al} that%�matrix $Qs,$ is expresse��MQ � ab}&�J�E�=FP= 2 N_{P} \; \delta_{�^, b})da�.+_{r�:,~W^{(P)5|\,'a��<)F�\ti�g�^3 �[1t@9� -�N\mu}{m_a�!�1_{r8x \right�Z ]6�& 2� �( vY�� - 1 !� �`��2>'}� i:if�Q(�h u2�� ) \: s 8b��ast5v > getsP12�k!�A�M\�\e�Tme}A %%%-� \� e�\ {Standardi-ach�:�ec:ss}}� s(d21� Boltzmann+�BBE�%(nted by Rau�1 ShalaguHrash}!+4rather lengthye# fairly co�, cated. It-ba� 4upon two physi. assump9:uA,l  , soyW"�aQs�binary, ��dur5�u��y far shortest +  scale6l impact ap.�0is valid (see� %, p.31�^M8von Neu%l�� A��m�&Z� re systemr trun%K (traced)�:anT; a siR�(���aE;bz"� �- then�� ider~ p a � �!,-depen..z theory u5s  gral)�j&� (simil�����snid}) �erm��ele��s&� $T$-��, �6� e5�tly rexby] C &9 . FurE�steps)st�F semiclassI�. xleads!�!gyh2��z�shape�26 � \: {� _{\alpha ^{\:'}}}� .  2_1 ;_1 =�~\G%( % # !� ��|. 0U 2_1� ��_{� � %{1�>L 2,k{o �6D�~�cal{Ktr <^{'},� >� *F 21%r�.� kJ�)սsjsR��1. � M9�$�'"�I� u ��Aji�>�Z(iha� same� iyDME��ach��indic+�$O lM� �!� 5M> &h = ŵ� ( � \pi�}{iE�mu&�8 >"�"G- hB? "_*[Wf�u; �&;%��,�"]�)� ( \o� 5=� T)2 _:I&&� � - f^{*�84F��2� 1iF5biq��>�j:DN�#� Sr]* sga� ��:�i�Xl�I�isM�bye�elastic0 wardݮ*�.*�%..�$ ��e &� -typ� ltas`eW� s @>.Z) =% VE�6#!��0have meaning ���,a�fineda�2�od}Us � �� R� � ir ori�  @significance will��discu late"Fsecond崡`2���contains%4�� kernelRdME�yɫ��B,'B��Aj%�!Q ^{5�� B�W=��lo R�-�aI� Z�c.�'1:}� 12mm�+ �[ 1���/*Z�� �VW�,: �\:�!*�"���9a��)1�� *y1e�U1} :�t ���C!/? j��L{E�)��-�r�bzE�fM�]N�>m9�.)fFf^ (!n.(N� X4� [2a"�61fO+�<( E| !` A�aA�.�sk).�wp�iar fea.RB&� consists�������xK������se�s playel*ve ro�� a�� not mK &V 2� !-��  }$ (� rh� >)��e��e evol�YrhZ� ��o�� xpla�$Z�3 ]a wayT &$.�lu\,IyIqpe@<\,% |\,\hat{T}\, �})1}\,\�$&�;V�include 5� � �of4gexp� [ \,M�i t}{�e�("U�6�� ,Q�(I�.�expBlW%! *! $6�M3d =% (b�)/��non-zeroI! corOon�expon als oscil� rapidlptheiraKIx�t1e oe lY� a0ges out virtu\��. In o�$words, onl� os�� �L ! .!"scl,toP. &�tlq"8�#a�rgu�ANB � s risud�� $�C�=�s�; + ��,must be, how� ,J�L!|!` ��-like; s��*� &�@ *�� 4unpolarized. I�!""4 does not holdE3{2�:D�; w� different� mor�#"�Pcb�6<q�F@A&؁�N�� !G��!��]�w ="do� carrA�� cal;E�as� as w["d�jczech}�� W&�e���ir�mulas%K#!#e verba5 ��Y�ce. Moreay , upa @our knowledge, nombauthor ,nduct such a1iona e reason,!Nhaps,�E{e�=V "�doubtghe ��ofe a "�$( mechanism"!vM�� �}6� "�%6a5��"lbyMu��M91)3dy ��aeF top�p. 42!� &Y)%�2g+� H�$ltm} p � , roughly� akinga9 at {\em "e��`ci~by  "} (�� 42is� A� �ѩ�moA�9%4 �s popul ons�.)J�' nces�caHI�:eA�thcom��$�returnAu=!d�\i|int"ena#s6��y4ME� �H �a�a �)M%c modele^cG!!�iIllq ow u!�< shed some new lB# onʹ� � ��Y�"MW!�1�!Fu��,�0i&iy�!ly easy!"#Jj 8^� ��? &3  � � / = p"� $q .���B�1� Nr.�g�#� Q�}5�lyN  ��9 ��b�A !&(� ^�-G� vB)6! 3*� � *�kN BothA�s��q�E<*^ �n by > Xrv��he>m� >A���.""36�a� H&on� h�a s direc7�for7sm "�%Zr . O��7 `�(shb beP possibl���v=?sum� �/�@�F"�%$�iagK Q���$se} yields� , a�qui�by6,�`��l�� H � ! $�$�  $]�$ make�ka1!Aid�* task (atE-f$). It seem�G��be�%��u� he0��AF�$A$�+"��n, chec���$2 ��indeedQj��%� be much�9i#�!�8do� in f�~7!�9 is&4 ���%�,% �*t �r^v}�,�T � OT�"1;o�nm mpell�� rigorous L � �/���cer . �Y rbD��.ve�#mportan�^suea�\!6��"c a�"> &�i���ares�i�t��"K\�!rm{Re}k��RO��%nO �1 3�M��0>����*1�/�iDH�� a��2�N�C���.w 2ņh ^,2 %�*,�#sjgpro�T-�busefula&A q*d"� A:�"#"#� on{D\.#dd#�k kubnG�!# 0 �  } Equ�ҽ��%��} e} re��nE� two b ach�9�QM�#&$�, alth� �nE&ily�2h#���se ex�0 dis Dik&��u�0"�"ak}t"!�sup��o� ' �r����rve 9v�z*ne�,Y����"�K y was�w�}'�$eA� wo add?1al�) L�4��~����B,�%k1}'*'%�$C 5one�quihe}%�Q1�"�c�6���"���. �ors. A� .si �e!�a!, whř!�*t�"��:w on" "@%`S:�139Q6H"�in:+ 6!�h��c�fo>*�#�.�,8!"Q5�a2��&�pro��s&U$&$I it͢ s af�5i*��!�bA*i� g1 (C7�s�!]E�r)� �3�!�yZ&:!C!���GNf�!Nf[ To crfyo se p'E��&6I�4 �!level�4nondeiat�rib^.nc�o!�again �/T free�6 hamilton�. s: $98�W�$ k}% :"ak}�8$\xbra{k}$,� ket��8$"stitu�]an ortho e� ete�(is m�$ Hilbert s�8!��"�"i��"�%!s�#; �icB�!�: &�"� }<+:~$mn}' 8 r|_{�, �%i5mn}J7�� xx02��tq2we�)!�at��qu9 "�eneq�1" jk}$a���t paireb�e�/��B�M:.�@�r�m:9b��itnow� adap;��e�n�q<ed&'}561A[IRchoiceQ:"�-baA�i�D"a�0bvious� �y a[R�^; ~\lo**ft�5G# ~ P_!�ame5j} qT*)�+B2Hi�D x $a$� L ��T/ume� a6�t9!J repl�*�aE3aM& $(j,k�."dE�"�y $& 1$ &J1w!�U�A�U�n��D�4V2p8t-b1 pand�"t�4n-�^�r.�;=&@4q�jk}�)=kr[ y�U�+� adoEr�<cc  !a'E(Eq.Ջ me} E9eas b�mpu�-Si��a�re mai�� �omparisQ�e� �:n�B}c*�$�A�d.w�omi��Q�; 1techn� � )�sT6"\:L<=*�9jk,mn�T as����Au��= = ;)a�2F_ f%j2�3% Qwb}} =� (�  - mn%%ngA6K��s. Car3 �sa�1�%�aall�"� yDs� `�&L=�"�>���:��.�wr"� �,A� _{mm]��(v(��p*�>$widetilde{)q}:;FN6�!�"h>k , "� &. ,_{mk,m.b mk ?.mep� �s>wn7i� ��� !t&�reflectl+A:�  in�'9��$accou|1!�. JX�"�gn�B@_AtF2)� ^{(m56q n)}F� = &g$�  l� z�5�+ N+n*�\,W�% )�*�-�N+MR:m,y6�9\,'�^��� mecc� M+�~j:� ��%�_ints ed a��8venient abbrevie�� [ RE#8(�!&"&�&�{j�� m, j�*z=2r%���:�/)�6mjm,jmU|6m�2Mg� �� A��3��  .i��writt&$<���FH8�_{mj, n�a4� �d�R\;��2 �-:(:" _{r_�'((q�g .�'_8<:�� time�'�&j�?U)� 6�?{a~7��:�?��F(:�? V��$>�'_�12 �"�'� �)jr�?Bpf(m_rMk.�=�$i�~f\.nB/k*06k:�O����� feel yyn �s��!":��*� pp}--�^�drv24, �iz�) �W*�L &n& �'1��= �� F� AppU"} :�8� 9�= �transa�e�su9  currd inv-gl8f . �(m )u $�� [ \,'$� r*� "v $j,~k$, etc� &X � ?"R&6 t, � madeCy6� *!�!�5�s_*pA0"Q� volv7/F� J�$� !F� � per)Hdib2 Ѱl % q*$ BT"�"t���6J �� *6H 6u1�T ݊J�l(\,m�$��|k&�A1��#� �**+ �J.sb( �;!�-0+!�kN N[5�:� rd8��*b :� 2� �M75�28%.B���:� !-WZ��|%�>�B}X.6s�$.�-66� }_er^O�j3@i ;m�#g� &��p6i zva;-\� l(mn�iO | mnZ rB^= @N_H��+�V6:r} "v&�02t}F�0!�t �[�l& ��4 m2!�5#D��0<6�1*r sgm�end1}�@ifL5* i�z H �)Y�� |& j*1�**�I��5r� �0e.�.� .� 1eFA � )?GC1 kf$N\�I-_rw_N�� :�&-�Q~� v6� �IH).�I"o1,\, E_m - E_j *~.a�B]N �O~� 1�;*b� 2�.U>�  D:=.>A|�=P�#6�" ��nm}� zm M+"��'oj�%�# &i#J�%� >�R�% ="� U�n�E� | kjy�Q��#wo�"q7� Eqs.=� a�&�cc}�T:� Va�F� TB%6� is r�,] operk we n�#t[)��>WI�Bs�Ri^.Du�%6�&� +�Nal�,�8E�z�E�1�>2A�4p�'MZ"B�&�{q2�]�:nn� �O!%�I2i�O�c�B�6 2��H�RJ� �ɨ&�!�{4.= ��M%2����N Q� rm{I!qa,\{ f(=B6�kmT-���{\.� :nn36�1E�t"e�:(� ows � &� &^, RM��&� M D:&�WC.,taylor}. Opt& ena,p  imag E"�E��FV&���,total cross �" $\sig`T T}( 2Y)��^)� � $]k�$�}}$� u�e c((zle6&3 I�i]� Q�Y�&� J�"�?.�!�I� ~|�|~9 �Ml:r:�4MI�� =iL(� be"��1N� �6�efF�O�?ќ�) ~i�dO�Na�Sm}}{dN<.�U :nn1g6� �� # A8w�+ $�!tiQi1s:�3��yAZvV�(Mqm2q1�Pnd*m�g9His&,F6Epa2st*�BA�H,�Zof fiq$v�U�)nm1�� �a�*:nA�e�l5�nr� !�" �w$!��>�� N�>| ��g 9�T Y-1.k {r}):7�I6�4xm-- JALof6��,}�?0square moduli-]G&�#>N&�#Aa�) ). F0Mz�M�V���|f *�B��b� big|_ !W=�U�� 1}|}.}|* ~ ,��}):�5-�y�(a20ver���2s y 2JT"�.�$� .1}$). IN%n��y%!|a�o�J-�"m )�a�u .5}!�canq��e�ne&VPtq��#n�,arr�� �Va�tS)%N�4xp7�!O8eG�,proofA�)'.� �,�refor2%J �A�6��1sl � <-:E m.%/� "C"!�*�.O �quf�p�&p6yst�4re@ s�!�+��&l �ty9�D, �"� -. in��:�Na=W��6�"��1+'#V�+ E.\�C:"� .�z4/#\i_= m_1�-wG( \N C2 +\*�)�=B�F*�%ggBxwS&�/�� T%6s� describ�]2_2�&&X.%��!\�?a�FH .�$aa�I!�� sepa��ly��b�mbi� e<h&�'$ (unitary).� �a�i{�  � ]2�,N:X�J�>y shift�m[ �:A�>�t[0U1�n�(Me$x>!aoe��] partA�6_cc}�8�T~ �2z�&��wQ��Aa6�!.�&�H"NJ��E�A�l(�m"() +m2�E�F�:G@�!�wyz��+�1h6� ! }Qat:>/&�� o�-atE�� &�  U5A��M*m )$+�PA.��&�N or>$�Jofu�c_3S'6riz�3% n sa>6�"x.�(AN 2�A_����;Vof�:�M�+n.�+ aNg�6a�by�s7a�)n� .:$�lQV�54;�+>E4�5*�=&�T�:�q*s�A /?fu�agree%�%ab�7En��cA0�-We at�+i284screpancy most��bab�( misprinj02Xh� �us�h>I/vR�/ �0, unfortunate�A�-on���&resolv4��3*�3&63E]=%bg:Q�esC- a*�7A��� 7y�A�L)��Uo�@��%2�A�>�8dB�.?�G2?]�f�B�I��@ )eAY� se j"'-Y�hA@A5s�Q�a*�2R*&u a1Q���eZ giv��ez ��EW5ve=^�.�yA�,��AN,��calѲ�7 q rnR� �&<_d>�#�!�X2ua�*��Z� 6��$* ��~N�&��%b-VnI%��6�Bk"�%�cJml(j*1#�w m&� F�mF�.:e"k0-EE9Ay�PrW| E��/Z*  6pro�;fo B��W�-yI�itJny�&*�#�#6;("�a��+� }�&g=�+��h�>� cal� �F.� answe �&� �,� Ba of*� ���&$��� �3N�#..>1�-que)guarant�=�RR�  ame %�E�6s�^es� (&���8)W�J�. *��<c%���[Q0�I2�--6 !<%): * sRy�A3lire2G�:2u0m+% "�&n)3��"Y��$A�D]perG�Jt��4ga�"��a :a�{y`2� M�!"4 AQ�֡�R�. CT>�!u"�&: valid dur@Ail�&z%�$6Xin6�A �C� tA !��2�gg}"z60l&f�s �Jsm"�.>A�� �ly�6 bU,�!�?�U �X��4�4�on{3 rrks.�<fr�<We wo]j&6 ]!&d"/`!Q*b ("�\6��roscop��lyB$@Bloch-9!`�s:_m6|5"�<-;ak�w+B�3-ew� R� *�H�E�sEle:ave�a�e�^ s��H6�4"�5 ��U\t.&Ope� enc��� eXida�Qal .)��J:$-�g�cv4*9 thusa �P%b.�:��> begin of Sec.\Pgecq? �wro�2nd �Yo,Xle�!<>o�el,B4 Asa�i$ene�dL"�?lif�an��our*wNs�>�<�q� �_^\ll� a�)呡f�"  lapp line!9filesbi�D2u6L���5�� -� (!�6�;(m,n)$)2�oTD�KJ!� ���2�e"�@of*] ��"+ ��2@l*�a^u�Kh� J{,.#$ to itself�/�j�**�OE�5#jk�z:.O.�1) W3���p*�L(� & :�  or�� PupAt�N K]eL�Ll(e�;�9ly � & �`���ucs8ci�5--dee��e!�tE �+x� ��� w�,v<s]e .9IN.8!~X�A�e� ,Q h�Vi>5�s) V��H � �Q��5`ats ,c%X\�sM,1m s. H�R d�T�O King$ �`$?!y�d J!�>��between y��Q.�.�f��,e� icul�s�S�upredi Hsl�~\ ��. P� Q b�fway!,;xam�Qs&N��r�>I��"*�2��l��exhibi� .� +erA��! problemA7�MFmto �9�N&� � �;�%*� ͢B�K #xb �/h� ontext+#Eb"��:62� 4 advantageous.�%it5UI�eyK�$background�[�F Y6�A�&Z;n"8.�fI�$r2�I��d�;)!i�7��h  �H%�KA?L gdcsubjec�r FG &�0[.%�*fA825M*�ce_T���A}!]5@t��� i��"eTD>� &DiD&�mem1r��� � HFe� RrQ"�Dlesy�"�V��iss� 0;ah�mm�Fa��$ to�ize �;�*V�Di�"*wd3^N Ad1(ala�!"reedom (%ibeta$�Ma X dex � �[�Ga�t�B!�"`V)E� � in ax2C27&�� KՁ ��E6J%"� Dira�BAbypon�NTI>$o#J�21Vei�v���y >�method I�o un?'g�A&�i2cNK�}Vcer� �R5Si�AveF trai% ��Vhap purYS"�l�=A�Zb�N�M E�e�!�major�42R �$&sitE 9n�V gI��cv� �*A-�"o�P9G lxul�gyc�!g� ��� F� .S �^(+ s. S�[�,aYme�uc3_%l3iclDA�al�2y � ione]Q"Z�(�����oi�>7��a�9�S�)ca��{ (car�5uX!YEg ut no�Za�(W��i� �]�� ri�OY2Yo��le��. ButG� han� ���@��E� �\ uW1���!2��4��RSin�<%6�6Jvia5#"l�|u�"V f� y1��a�i!�s)kX� q)�Q{W�mach:XR,RiL !�uf%$!�ork�#ir�e,�� �V�tin n��A':��!�_T� tw2�MA�ő�IO  ship� 9d"�屵�al6�� ��H)tre3M!j*�J� ^�"x �n.E � ��"v �b!2A�R[�f $coincideE�K �8UL���D^�:m6nu . C��c��,I� �?ni�my� dE�9 Ti"�:� :�e hopa.atsAhAZ!Qt"�K� �pͣ�jEo�SM�w"!^dU@b&n�UEBBE���<)Aj A��[# � star%e L� ��ara� %=�"rc?^�,s}�����1b�u�u-!%�%1Lthebibliography}{99}�HHb$em{demt}�#HW. Demtr{\"{o}}der,)^Laser Sg�y��(S� g)(Berlin 1982�^�^^ S.G.2� A.M."�! jKinetic!�. of=$Non--Linea>� (N�M-Holl� Amy�dam 1991.� scul �ycu�A$S. Zubairy �Q-�um m1s�0Cambridge Uni�*��iys,  1997.uzz�C�i�hen-Tannoudji, J. Dupont-Roc, G. GrynbergM(�_Ato<7photo( te�uLs}, (Wiley, New York�2�key�Keyl, %WFu"\�&�qiv"!cor1�Phys. Rep. {\bf 369}, 431-548 (2002.�ak �R.q�-l$Kryszewski � �C/+ly�ef@�/���v �0A 68}, 013809�32�- �, Lend �%QDynam) Semi)p�$*�@UN 2  snid1Sny. t-Me� uMod�(��E���EV%D&wQIA��S�fM�J. Chem.-+)�42}, 1051 (1960."berm0�'P.!Berman.�Effec�\"r� �}nd ��g 2� )eRpe�>^43�1-149�78.�hub�P8I. Huben{\'{y}}eTCo� �Astro� .! �005}, 852-862,]86.]8e�!> zechowska RI�$Kwantowo-m-�zne r�o}}wnani o{a-�MA�vs%\�Dof Gda;0n}}sk, 2004. �D�5 � R. T6��S&336m q� <� nL vibr=�VL72LQNam�&th2 U )\*~Cd6)@�(2.157)) ;,a�� �>|8&�5mn�*RS&�'$�2"�5�-�0?:�#r}�8�v:�u3:�<>3��8$&L3G#RG?g�T:?b*D?&�#_<2N9g�t=J�R%2�9B�9� � m��"�9Fs@�n�Ih%�nnQ�= � �: ` n����g� ��$.(.�W�#� M �$",-Y�$0r` 9`\*X �Z3#a Ti� K>#!\, �H%S*�($mn$)_��.�!^{ec$&v*J+��Ion:"�\<"~!:aj ,d!�Z�k)o��jg�!`��S&ur *�!kin�� * !�k�o�#& =ofV�m�Mbe tre�H��ke�:to \:&.,NCd&Z"?�%W��S�)��!WJ�I�byC}k�E|pl ����[,�� 2.4.�n n ap>� �[ [�J�uu�doc�o��T T�%�!# Sh�ape�m Jou� of=or1 al A ut� ci�W %% ? 7,Elsevier styz 22nd Julys5m� \d-?*�,{elsart} \u4ckage{�icx} %a�te .bblV/4thcW�.e�T .tex.L[�9,�a,�K,% bib,sort&�$�m@]{natbib} % �! bn7�;lmaon. %~ Hpunct[,]{[}{]}{,}{n,}� "�%N �-num} %&bib)o6 bm}%�.%e� boldE symbols.� {ams�&2= 8\3e >5fonD.�amsb} %\jIU(T̓ZR):�1�e92"frontm�'F%% �{,% \title{Ent�=)%�RolAAe?'s Algchm}�l \�>p[leeds,qols]{Vivien M.~Kendon?ead{V. @-.ac.uk}Bhp ?=% � ��7>�,2�Fb{b`F� ��Q% \�!{I�!�}"�iec:�>� % :�I.a�!gpoten�Cǘrovid�g��tl?7(re powerful-5e�!A�9E�I^ -- if�. buil�*gsߛAE�^.lWwu�;� D�A Qhardw7� � s00}*�> prog��7 � d�dop�a!*M�s��� slow� a��aa^(we don't ye:��y�J.ak�dv�$(�=(\��wo key�e���1ܑ�s ��=Lihf�*�� h�  perQ on � 2^n$�,�%,Q [) in $n$ 2-- s��s )Y jozsa98a}Nlo@+%N�%��A4 grow#* {\it'arly}Z $n$ (1�h>llelism)w�h ak�b]'.=~�*20���Rq�F�9of ��,�}���>�E� . If2��ab!0r���I�e i���"' t am!^!��16 s. J!g����eN�%~ 02a}�.�hat, i�;1E2��-bpx�ednl8�!v F?polynom��!>�!"b$input dataX�[t e'B#eh/a,ite 2�i�V unb��e�}m�-� �p=%ifY!�^ oN_� �#��.s. "+AI��=�2��dtt�uffici.N"'Neta mesi��5o #t��A�Mfe.q. As B��ou)��1�]�<�Ad � st�"zB�Li�hnielsenchuang00,gottesman97��%% dny hiNz1dZ�gA[)��$ Y� �p�hs. *�%>@er �mix[*�i*a�"\"gU��'5R�#E"sQ3�MA���;�#wn+ � %ȵ�Z��XY e]Ve� X)y/ , bea@n�i�*�O�k5�� %�oH!�ucq)�s�(��� �i6&.o9y�to look�zπly at�[)+�6FewR�C@2�!�)&� Bed up819� :,��thC���do,BE ( (order-fin�%)M�shor95a}a�pZ-e�?&�*be�M�a~1��  largeIb�!4hG��4�\��u"r �(��is�u\6�!qu�%.1U�9�A� exisn!FP �I�w�A�( h�-.�5i��f�V re���6C;N �-�pri�1ty 4�A}�94agrawal04a}. P� �%sp-��j� l a toughx, few�)��ist� 2�KofUn{3YC,�ic �V walk��ass5. i, up (w.r.t.~&n acleQfchilds�M.�4su�~%o>�e�fj �s:0atjmAH"y.(*�s�|)%;�ޅ�5.� �6B�q���8� % �wT"w_ �s���N" a���durA!TJ�2`-��V �_�.Vb�ear��rei� � !6wɛa.tr�;J<�C it{�r}2�!V��tX�.aQ"�_���#%t@6$st $\log r�{.� ropyfre $r\3J7�odI��2t��*a�logx,iWle 2 thra/��9|) � mid- fB�, I� �8 by N��nC��m����A?5ste�w C3i%�)��M!) play" =�. W-��in mi^1s$|o�jar �%� lea�2Kin ݳmu!B�s!]a max��܀n�d@=L �l��s� o� FCA���;[���v� tele�:yVan un! &ip� bennett939 �QeR?� �� biB!.�6H2aHAw4J�7u�q�� �ak!b�<6�� -Z*8 o=D �de`(date, littl�1s� saidw+e�%�1hyacE�pQ =��m�  focu*)al� entiB/o�6T/AZi�=esea�N&b ` n�|~9O� �in&� (be� �G" ,i+,� �?,�0vidal03a,orusTukena05a,shimoni05a}).�(ai�3a�w)lp2�-�)I%E'��)6b lɇQ6e�:U�M�� rrh execu�Af>��k � batt  p��}9����� Y"9 . FA�fstudy�6J a aa �O�� �H� �*� 5ű%�um@t\ U �2 �%�/e�e6a� �we%6OO, �1i%5���� cruc�E� .� ������Cf��<a* mon *��o� e6�K s. Parker�Pleni/@p 01a}�@ͤ�s(�Q)RBQyD�<���i�a6I ar�4A =dy�ffirN(R�ly% at2Ee�* ��n ran&� ` h A�15� 21. aGq��,ad�at,����&�@Olog�uTofeU�U�!���d y pIFq� )!�er�&Eks, de"C!hہr Hoptimi�2�s� ��K4��)+nO�� � �Etyp�.Is avail�-9�� valu� k&� �6I�s ��y2�s @t�LVed��ezE,�tv96��Gossett g � nd Van Me�a�Ito�A vanm�!� �uc%��� operi�//y��; Zalka z } |Beaureg��, 03a}�L-��#& �uA%i?Y(!:fedGe4s;lF��i�],en�+ wf� sanalyse]Xljt��( accuracy. 0�organi�`iȥPX ��[('��e�� brief� view� N�\S"�A},�*se��"�$. :#� ftd:@15tE.��A��2+ͥif  inu4H.�� Se��3�0inV4e�.Wo�s1�� �;. ��321}C����Q�Xal��a��21!��w. L�mi b7�ack@�Q9s.k},I�� we�Ne� to dc�%�mai��cl�HfM)"re�9risB�&�$�>�*�M/*\��{�E-:�%��b�CV�!iA e����s, ~%��re �.�7mc�>� lish%U��#wt�d or a�@$N=pq$ �4q p��$qa�%� +3Cm �or���?%�� #�7s��rbq�[ �V"7��4�P�D| $r$a��" �� 8} f_x (a)=x^a (�{mod $N$ 0-w $x$A�aa|teger s��5g9td$N)%co-��i-7nd $a�)pObb{Z}$T7M'"��4 heck��z.P$N$�Euclid2�� knuth81a}a�fEkB7�b��>k,b f )!� � �!cjob��, � �qh/ ra� � $N$[Qc%�=�I6S ���e=�Tm_{\pm}=x^{r/2} \pm 1 mmeq:xr}>�&��ha�e= A�֮q$iv��� f %. N�ll!�i�6A&* �sAy��ah F7f.� ���me�,%M�� odd��(!p1�7 eq.~(Ő �)��0P<gX�-��A��"�;�Ga�id-��9a�ced� eKL*�)��I�t  unti�)85�� 2�s}�Lry�lD�.*fkkPY$!) t�"foZ�<�FF�/m���*L7]*p� >� �d��� !z=� 0�_$nO$. �E�!h� eleg�� y�mea" �eM� Q�c�, depiҳsc"oC�[ fig.~Efig:15� }.�,figure}[!tb]�*mace�2 } \��K(s[«=0.33]{ P-bw.eps/.�0?p'\ca�{S� circatf�ra��!�2��$I;!v 15 "� e^F a 12C 1 #. !�t�ial $I�W��i�H l� bit Hadam� (H)!�4 bit-flip (Z)- . �:4trolled-$U_x(j�ZM�� $$NU$�f�� B0#, (IQFT) use$A { r=/s ($Rm$) Q�S1 9�Nme� � (M)�G .�� by &�post-(s!&��ob�F�ʩ��~O.e�wMa Co �����1� s (Wa��$2n�Msn=\lceilN\r $I�'a�� �� An#�l*D_3/bas�%%�n"B�^ $|a\��,I? $a\in\{0\'�, 2^{2n}-1\}$��e2��)�o����m��@!���4��2�� zeroE�&� f-one. A �� O�%\� �$ $|\psi(t)�z�� $t$��HbB0i.�"of2X,Fv :f=\{�a=0��-LT� a(t)5,��r%MkB� }x>e�1 plex�;Yoa�s��$F� -1} |P|^2=1�o*� �sA/p�\��A��!�i�5� in �� s2A $())^{-1/2}^�U�EZ�"�%$ B$2��lI� sm�#�AX(ipa�HMP$1[z��|1U($}u |i0).3)��Ys�H1��AMYna�� |\PA�_iQ�"�g��^n"��]0)�1 �]0i60n�- next�4ab %W�i�moc\:��o�Dto $U �b-6 =2 N  +�`�� out�#�B0"� n-U9=aJ�h�<j���e.=���IRITnMQA� } |y-Z�z>�\e^{-2�i yz/I�}|zG>� ppli�F)�5�e�%g $Q�5J$ n .m !s)UoF�@q5� *�f��b�i�r�a� �|j��+9rB�GAj��q��co"hal�Rwe��e �] $c� Now $c-���l|"\Cx��G$}� � $k/r�i�� 0\le k < (�� $k$ yP�o�8� �Har0c$��� d�e�$.���kmg �R�'coE�u�r�ons (�+ d $c�7 0� ChooJ he�5c6$2 "�`� :enough � �շ�� � �om2iXo� �'ll2w.Q�C!�u��*�I< ���+"�of ]pctRt�!�!jdec�K�!u!&�B25Ip P M!��,_�,�� � �y��t�v�n2�wf�$k$tn7 ;fa�R2�_��r�M, �/paA�OQ+{S]�� 6��&ces@�6�)$N��6�'.�0e "i"A�ain� �j�% "�.F��152�.5^�E%"E2� �V-13�T2�2'1AHZ Q�f �ps� !��B (�l+ i"�4"kY�"�of# "�l�" fig �.% VP��"� c�'na$x=13/.�E� �^ �!� *ug�"N� -13ent; -��s<hA��6�by�A(!p!6�for�15 (3x5)a�  d%o6�Yty�-�QU ��. xe�r� ��hangea��.', ;��track�>'!k each��c^�"�36�o� �4'0 $��5�pric�Jk3n���o"��^os�-�:� 2a�"�B&j $x^j >�(x$j�1,2,4.� \}$,�I!&TMX|. D�V�FtM-"�l�s��DsA�m.��O  �0e\/� {wo����b�"t4in,AR?@I%G-���58AF�2?s (in"��(g!� MnuF.*manageU� :g!'!��-276j$(2n+1)(n-1-�a~ `o) 1):_a�pu%2eM]� �<�**�#�$?�'le�A�!l2. A���<6�){.��a�eu�`t��:�a*"���Vs mRV�� ��Gu�vol"X#T!� �R can � �2�f��1-(��sub>3&� u� } E_c = - i�mbda_is\l .�E M�J�a�}*A"$\{:\y��� igen� "� ?�of� �Q�s (� (As�jY�3:X XA>U �A [�S9��)I��0�U�r{�s C�O�J��L(t�c={Tr}_S I G \l9%)|,� 1�N &>_$VS>VLzV$,-�$L�$S$�oo+"� l:I:p, |"�,|1|1�\} 2�2$ $E_f = h(*� �|;�0}\sqrt{1-C^2}9�$h(��)E9! bin�en� �, *� eta� < - (1-)  $��/�$e:o$��V!��!na3t�e�e ��s.'#� a&�e�s��be�2N2=:�%�3`�DV���0coffman99a,ke�D96Int2� ��pl�$� n�[mW<&�"��E �%hAs�a (* �a�3 )� p�"����<6.0..9vMs!�be�w Fa*�4e*�.(excep�4 %lea%*[>:� &5>d�"c_W� AEdBA9?.b'9&U � �q!5a� 2��f�4�s �BsB7to�p�4um.�1��A6� �yH!0+F(�$d8 !e� � (��O� 2�2�!�npri1A��e"s) du�'"fiCDg C�6��!�Z��5P���:�M'5p, n�&m�norVq. t@�A� �1!��f�� %0 3�/ Dj� JheP�{���72\�s�-*� ���Uegin{��ypat�yP�r�N2�74J�$� $N=15e("�)"�Af�/!6�topE�I )�"�q) (fi�$)��1ZfY6D>�. �!deCMa*Ev7feK ��nF� 6b:a. Qx%*� �%;Qp'�ir� �� � . TiV�q"���r@{on�jZ}�&iA%:1!��M5 U�Ycɬ�al!���m>�el%�y|.p] to. �Zo�rhap�!�b�<in V�, !) l.� �p1�!�� (a\��9a�, a[ pѴFS )��u'ruG&�=a��5Al2<� 2�� �q!2IR �no")T�c�4&%�s&�H6!is���:.6�� t%26WqNupper&��@ )w��(2-E�( ��gq �o^�� �|6!-�#v9���b(�ne5V d ora��6r�$t"G d. A�;nd@a�"X6����<V".�R �E�2��vid,��s7,��J o�9I����By(�i�� �acB9 sin%�5��e!+�1�[%7�!>m� �P�A2�� gI� a�'isW�%>"!�:�� bot�`���B��" ( o��+pat�2"|Gw�Ms>A{�C):15�k< ext � Ͼ t2& g7ght�m�#%�"�-`$�/�/$V-bl�@3A�5M�<�ran�mR.r*x,r >1$ӄ�6l0e whn 1]"r"J �@�+ B>�)o r�$yth����l�E�rw� D b1FR�g5ͻ>4Q^^�F&�� }[!b^�c�-A��A�(�bL� y�21u�2$e ��.� (a"�a)E&X<�+d.diG>�."� tab:21-2V� d.D&tab��*}{8$width}{@{\A� acolsep{\ }}c@{R } \hBa ��& &J�C585 �1.972C28 N+0.31 �678C5bC2.081C447 C66�749CM 66J& �84 ?2.52J3B 7j;2�֭ 2.60 ��1 �8j;3;58-�+0.204v9j;4;61;13; ��1tqS uqendle1"9+��2&($3�a 7' To d� S"I0oum �e"k(s����8U "# 6�15�nf: �LH'��of7Q�e6i"[ �5 �5c(7� �f'j� ^;��at � �B� ��15�e13��a�J21wD��u �}�Ʌ�*h �8n%" � Q . S �D������%�6� 6+�] �e� ^�"6' �nZ&67 gh�u1d _�3in a GHZe$��]=0vnk> er89;S4!8��be�!�%�m�|0"*8jv|11$heB|�w2�li��ofI ie a�)sourc�>�m�%f!w�&�(fB=(Ev.�Ųz&7A�UE��Gr� P9��� ets,� `-we2�  �**) a�:_�I�no5�E�C �9Q� at ; s�z�!"� i�� V �tO+asa�2� x=4$���_�en_ !�m�a�$pQQD (6�)]6M'�" ��>�*ra� ��#-+N#���m� ��3��m�� |vr"��&qq%� now LT�oll1}5�e�0 �$x%m�?/�~�\�"� . E�zl�s2���.OTM'� ��5�s sFH6Ea���"��A�A�le�1w! a�%n�,. ET~)�� r�%%F-�E�)M},A�ach5A�7�mI�%�a.� *�JWV6K(10.261 ) �a!�A;)�ribȽ� �A2u!��) �b�612ѧaQ&s 09� (�P �to 42)* ��~�h *h"��R �� i(0u�9f��conve/�V�i� s�=hQBv i ,#�kM6u-���=uBLi� �IHm��tell us�!� z\-%weuՇ���.R����+"� .�aj�Br% �"�B�in �pl��Y��� s�!� fźpus"��&&nK��a.����pA<�x,���{ng��|$s $32�fN�K third_�th�jum&�`R l!�aIR'm jc�&k���2P���a2� (�!� �2K1~ `fif��J�),�$^��O1}�]up 7X�$�4t0��+ wwhole>N(��)�IG $N=27$r=6$� $0.624=10�  $� N�"eA:�>P��!2�$-\�)"�n!$ zn:��  (%e46\,��9` z)6[)|�M|r@{"C IFD &\�E9E��M��� &� ��I$$r$)}\\ $p)� q$ VLfN@ ��~$ &{2 (3)} 4 (4 } &B&{Q"�5� {0.0 G �E:�21$��3 (2)6 (6)��72�0.706 &E��6 �:�33>�5!-�10 (1��1T 11$ &{0.0} &0.285 56 &{}@&{}\\ \hline $35$?{2 (3)J3 (2) 4 (4  6 (612 (8) \:W$$5\times 7:�869���788�706bM�9��6�3 �13���5!� .I=@{8!7%_{16 (16 &{}jJ�6K1C6%D  A6�5B��5!�!�10 (1A&2 6)NV W5�:��E�%�A�%�226 M�:P1�5�2LU�U�9U�8 (18f�5HAF ��0M�0A��080�0.071 n� �7f�5P�9Y15A &30 (24 �)�$7Q�AV�1.033�34 95�0.314�0.034%j031!D.��9V>`8%�]6� e�3EQ�.� \\�6S�Y��ITM!-�1%�>�� :�6��iiZ��us & 24e~k &48 �2�!� �A)b� �%l� 3 IS b 06b � 8 \end{tabular*} center �table} The pattern that emerges is, the closer  $period $r$"\ �A�2rtriYo f�kbetwe�wo>ns a�(thus spread �wavefun �@over several adja�V-�s.I� = cora�onHo inc�$ed entangl�ei)8ioQt . WeA4uld�e��%ܡ*!re1��� is rm� E3 semi%� s, siZdiffer�� behaviourE,�� doesy helpa�find aM>. In h \cite{pomerance05a}, if $N�ModdEA$r = �f!�$x$, it�pn!gM�only � �a�divideT�one mor%n�( of $2$. TA, )(ly $5$ such� ZLknown: 3, 5, 17, 257� 65537. It!Gsomew�Dweakly conjectured �t�m�U e coaaPte list. But even if!�r ��,%:�K�aM?KsiG:�q trial- s by ,��J� 2,g( precisely,!aform $ap^m}+16-(approximate!6 \log N$U themAtest, EFiQ4clearly efficiAR classical�� %-N % \s��� cussion} ��sec:di^D, First, let a�ummarisa! at w��v�� und, sincA41�q�steps �s dedue�(s, necessit��!z!Clim ions!�Eutaal @ avail� !:usi7E5parti�7r gat!�del��f� halfaShor's �ҩ?mod $ exponentix$, generat��F� r$ uni��f��ropR.� �he�O��sm��,*2 ing��4 � ing}2��5�� �`i+ at!�q�, except= �2�6H A��8t remains equal�ʉ�g� l�~!\ lqg.  chan�� v, A<�J�6�two7 ��explaf8is quite easilyo ermž!fB� (\simeq k/r$�%is�yrepressdHa binary�GA�0size $2n$. If� J� � s trye�F� ( integers, iF�� 8h �e 2� � al s����quantum�, am$n in fig.~B� . Extra ); ]d� posi��_fir,, c.f.~eq.~(S eq:r}).�!�Bb .94. Now supposeAjper� ��e�5in � other ba��anA --e��% ple,� ! ree,Nhaps uab aB$ mad��� qutrD(t<-�1�7s) ra�t��Us�!�.� �w��iK le� P 6�2.� A�� > �i� dependentk � u�eœ�suc� ��*p o%� � �No� any6�u�/up.�coursQ� 1 1 . J Q�%�r�9e vie�25seTea E�� ve wayATachieve 9�t fa�%� R� �il:^ertai[ , �.� �w�� purem�um.� - b? *�aKby-pro� � ��oi" @full Hilbert spac�fpa��elism � jozsa98a, 02a,gre�Pee03a,blume02a}: mostA6^consisR high� -�d �, kendonb$hayden04a}�-9io�72�-0�.�ism (ply unavoid[ .��)<to�A2)�contrastI�1communice"s task  mal2�painfq� can �~�pec� amou3f6a,�Ta aX5) Win dir&propor%� 2�Q�d�� alsoa�Je�mly in ma�p��cal r sals�6:� u8m� notably IK�.y docuA^} .%% �S\�X([twocolumn,pacs,pK int)� s,amsmath�mal�$aJ� n�! ��B�v�exe*ale���  �%s�A�*� al� l�sѶA��[.]!Jie� is. M�# care�9%H  ]��] "W'2�,Fedichkin}],��m~���.�--�$ nomenclatA���ity. Re &exYx (al NMR studa�2}NMR}]���8ed various ``or; ofYn''�2�.�US,�[of upJ650 spi��r�!�or�!K|language�fo� s. �+non5�ngE n�"�d���e dN` whol�Bw�a* **�6Mes.�&�L%��x�\ far-2>6F5M!@A�)O)~����B' i��<�� �2�Md s. SY� ,E&�ۥ� �g)$l�� u{\it � s\/}�� �ve6�Wilhelm,�ke�&A�Zed `` 5ity''�p��:� �e��al�%�12���� 22�af�eQd�*$ i{ly�{ş-m I� ing � !T ver.�  ques�� ��2�� }]: If�.I&up!�& -�(, $0\leq \d+/^{(1,2)}14#�(ouG��!�1�A�:� � ](ny%".�mea�%!.���w t �"m.eg$� � ?j)n�%ive al� A�l�``wors&s�en��''�9�mevR�l -of-9 -qD>� is �iona�x)�A $\min (6�1)} , 2�2)} )� %w�� �, only *O ,!il��t��,�%ly��!b%&� .� 9�,�$h$�� s���) 5to��, =/!*C on (o�xim� !��2�-/ )u�� �%I�cb# ork,��!o. \$!�a�a solv4 4 -.�L�wo   6),��-$1/2$)&fng� a bathG bosoX�s�(eQA#�I�i"_��2�WooI3s"fnde��i�y8Mf�7.�% focu� !e two-��g9�i�� !D��qIa_ .xex��3a^�!�led� curr��"� Z. �) tudy expa�. he r�A:� �0)1:&� similar�V* �&�.!�ls%9��AEA�der�� �ly`�~.)�se!. �4bre��, �1Go�%��aD�c crip� rPer  $r=1,2$�l�2!�I��-levelAy�'(), $H_S^r=\�-Xcal{A}^r\sigma _z^r$. E�� U�sU�M�Q�!s $H_BSxsum_k\omega _k^rb_k^{r\dagger }r$ �� wid5 02�Q .} "U }]�!����um�  (w0t $\hbar =1$)� �Mte "'A;?-)@ ��*3 a|�A!m�I�5C) \left( g%* �+6$ }\right) ���"hoice, BG$[%i,Hr ]=0$�adk��-and&�& %6n|priat� IO�&ofN����2�=�.� assu=��}+noU<Vba!Q�es�"4$ HamiltoniR�2� A,!� $H=%br)a E�+%+% -Q%Pe ��2o�����p�is,�Lto >Q� � o�-im"u�8a�bit�D"� o~eiU e"�%B'"}�eTA�s, ��*1x �*eI their2A !&lw9 ���"�.t.A�unEk�d�E�<!)s, nama� � ����&!� �%��'A�stw u�4 situS}��4.�*0"�)" s.O)�s,&�+ �V I,$\rho_S(0)$,�b2&. How�)7E� 2��2�U��� lly no&���9B��u�- 9>��2$ ,!�} Ѝm 0\�L=�\o�s B^1(020 _B^2(0) \; .�]�9o+rvo�%)��$�,ilibriumM8 temf�$T$ (w�L$\beta \equiv 1 / k_� B} T$),Z��W (0)=\�Q\l�2,s_k ( 1-e^{- V�r } ) > B� ��} � F��to$.�!�im5Q��zIMm�&�A���%'$t\geq ~<s^�S��t5�%4Tr}_B)�[ U%� )5�U^{�w }�]�,�4�%!n#9��'A� � fat&}<z� $U=!h$iHt}=U_1U_�6 The BE�G1���^\a�A���d: (�,vol1}�,�� e�% �=l�-,U �!Ag6�o�6�g ven56to wri %1���9t)�t�S��,b�^{\gam_ 1^1  2, 22^2}(t)i* %�\�le;2GI|m�S=z| Z_ 0\ra�9a,>�I$@$q^r=\pm 1$�w��dex4;z *9�bit�le $q$ ��/dqes��� �"�# row���$m8 ��� A] Ap +1(-1$*n!�A`� �!(s $\uparrow 2\down (!�&'8% �we� J�ardvC$ �� ce $-n%i  ��1j, )� %Z+"6NU�& � .62-$. Afte&<<W$} forw�transA��\s, 2��%toY�!P�$&&�� _S^{^�,Y� E�%(��\\\no�'$ &=& e^{i .� 1 2.�-^1^1 �) t+i.72 7 *|.7mH) t}T_{\phantom{S}}R�@1r*2 j �rho.  � ! _1^R  ;a���\;y�1�I�acoe ;S 9�z } T.�rq� 2^r}�f {B_r)�[!�-i � m 41^r \� tilde{H}� 5~} �B^r!�RA2^r2@ >AA���6�,"$2?>�=d�$ =� �F3 . Utiliz�!E6  rom: oFU6 �>*�'&B� l<Tssr�P\exp \! \big[ -G_r(t)��)�AKr- A25�^26)?Y3QI3$ R%6�well-`��$� "�@2^�&�}]J  ` =2� "� \frac{E| I7| ^2} ( � � ) \sin� B& t}2\c�: x  C}2a:B� A -l�W�V)s6 *' !HdZl>~�staV1{(g!&�: � . 6�new��s $ p_r;a�22�rt^$ $q.%-4-�}$ �e2x!� be teY��?� e� ext}e��M�gen�� J� M�?ar�M{cccc 3�1�U�� ,  ���%0 & p_2^{*}q_2��� C L�s N "V & p_1 M1rMD b M RMj�B,W�� BY�Ip_2V��.�1 K� &V ^=�RDJ�.8�� 2�:�9@2V!� 6���91q.�F�],:�29pJN�nT -�2��iFF�9.)9FP�9>�U FA^4^�JL~9b�.9�z!�B7.�  >�x �� ��2�� ��i�+qJ[tbp] \�3U24s[width=9cm, h�Jt ]51.�L\c�LEigen] \mu_`  2$4��^$\eta$,Y�D ?G\xi��� pref00L $|\alpha|^2 / (1 +  )^2$�=�:" �� � T6 alyz� effec� .��/+� ��mtes�?us�:��+�x.""" 6�-_was hi�-� �fVE!��Jc @ed3X.h�a mix��$Ax_S�e a�is��I�to�L*j"to !�.c!75�a%M' t ma�&A/�$�!�3; it. Giv!%D �9�,=�K0"[* d� !��-flipp1�q�g�>} *� !� }_S=9 ( � _y\��y�T1_S ��4"`�%+!CH�*t� $R( b)=\sqrt{ E6}\,F�2!}$ �, e2� lambda_{i�8,3,4}\thinspace��.$6�6 �M�!:W� Ai} C1r� "~1N=\max� \{ 0,\;2� i� � _i - .� {j=1}^4 � _j� \}��1kS'Jwe �#m�(z&i�^ )�#:���"�)to �a�!�.zof a $4�U4$-�� illu4�uE�&BI��U�6i�(5!L�6�)^ M )I� � "` "i )6)Qf�!I"_9q|$A"s��::xou&=y 1{1+_-B)h%HV� 0 & \\12� � H^*0 (Br $ & | xa 1j` :� \"q�q�u����of6XM�s $t>�w1v0" aw%Z6t�O $R> %!~"#!��ǽ,anI?$t�.J�:� }1� 1��W@.car5�&-$\mu _{1,2})�{-�%��1+.~I�I> gg(1+ \xi�cos 2Y m2 i�-^2� ^ -}\,��g); B����  _{�E =0$.���xi��4\a0[ G_1(t) +G_2 � ] }$ K eta d"L*M#2-.1 ?) t)]n%�.[$\�� i = �v i}\,$q as aG >��.%�"�b�"yQ���;�|� _1}- � %�2�"|J&6�muI$A;�'N$�V .~1.�$"H a s�B 2 �6�B�:.<$.X2�t�$ 1$ ,� �X$!� =0 �)`Q�Y�(Ez\pm1) /(��&a AG-�9Bwi"�5j_{x=0}�{2�x}�K��}\;Fs MsI3]� ;�g= establish-�q�� Nr&pr� allud�)��iny(��bSN�':� .�t��! {& Rl � s $�GI(t)}$�8I��) A2�.� <n o�  )so�"��7J1�s�"o�; own w<�4H!�*UuS+A�n!9v46a�"�,"�>oM ineq} M�� =0F] �T�8��--I��0;,�&�+ �+; r)$Markovian-&,,I�:� )*J9,fr#&a��5�/s,ej y>$ a�tep:R �NamE">s#9�"P �+%���, unlik� �nc�Lan droX�N #Mni�B 2�F3,F2,F1>�wnotA  0� �<0y �� y schem�nside3w9�UZ!n.S� im�@i2�<NP2 �'ave%,%6&�&Z�,� fir�MMCqU6ls2�Ug#Fz2�.Q�_Q!�.-M�k*,!e�FE& <&J<2y&�9!! � .2�L�&�/ aven AYfutl$�+.6�2�m1Se�? si�mT�9V� *B, argu�s c�?aqy ``b� u�+.''&-&u� - !oFw�<��"{>, } ='�@a Ems mf6fBN�Ce�refor�Yor��Q�>!} gres �A)~*<velop�u�=21 � %�.0�tryF 2f:rNv*.�7un~J�8�'�kIw�PSPr )N�=FIecu�6 Agency_ Adv�[d&)I� D �!� A�! %� Army&|IO%i�$Ht DAAD-19-02-1-0035 �:� &J F.1�,J(DMR-0121146�Cbe>b>�H{99} {\f�.hspac 4 bitem"�B M. A. �B�PI. L. Chuang, \emph{Q CJ�,  I&�C,} (Cambridge*>G PE ,�J0f)�I��} C. H. , JHrnstein, S. Popescu%<8 B. Schumacher,jK�8v. A \+bf{53}s4Wh9962y�B!  :� $ory: C�B/Au0Methods} (Klu8d(Academic Pu, rs, Bost�+ 19952sEQ@} T. YuQ�H. 2�B�$66}, 19330uf002);�A8A65322 (2KLEBM |1��Lett.�93X40404X4JX2fXIeEvou%Co' l��*mJ9-``S&% '' M�S�s}, e�a�@(-ph/0503089"0www.arxiv.org.�LoZ!} WEy>fisfP�  of Radie+-<(Wiley, NY, 19732 "�=,} N. G. van �=)Stochahf�>�NnH� d Chem�e8y} (North-Holla�]Am�Bd+> 20012~K> } K.T> pD�M�@ThA�%�App"�F} (Plenu�JYA�:D�>eF 1@� Princi�c!�NuB_$ Magnetism�6 lare;R �+-@86@G�>}a, , P�ram*G G.-L>/ goldyJpY�1a$ 115 (19882#p-�J.&e?S�akP rty,�-T. Dors!�M.� A. F& r�W. ZweVe, R�� Mod.����9}, 1 �<7) [Erratum ibid�67}, 725'95)1�4 #} AJ� @K��Suomin*nd�K. Eker!0 roc.&P . Lo!y�. 452}, 567t6.&�  D�>zyrskI1V.!��M,!=a1>�91�8 Y6{�@}2G>cI.VA9r, ɑer)W��mun9: 146}, 331��22�"AP E�.�au.%��K6!�062309X6�&�;�HE2FedoroZf�Th 328}, 87 ��6eH?e(. Krojanski�D. Su�S�Iy�� Qt�� 09050)6Z= J. Storcz[F.AC yX�f\E�04231)6�Hie=$ B. Ischi,A�`M. Dube�6����a N�2solid< "WWerR411086 ]^W�8 a�K. 2�%Hu�80R24�F 98);�;7!�50� 19972��1 ,!�DiV�nzoi]mol a�W. ^�YO54a 82�m>�F3%�B.#UI9 Math>�15}, 64kp>AF1}�J�gJ. Halliwell2O�aR 052105NR2.WjC C E��N�)>" #Od"�S PA��S�S{�dan6�S��2�Sam.T�T|TCIDATA{OutputFilter=LATEX.DLL} !Ver>,=4.10.0.2363Cre�0@=Thursday, June 2#h,002 10:27:203@LastRevised=Wedne808i (05 19:43:5780Z2D-�Shell3 4 LaTeX\Blank -�nM/ A~fle2^L�C =Ame:!n Eng��CSTFile= FM.csV1�0PageSetup=47,8,50,.2�W0ters=arabic,1b.) tO*8s� 36792�B4ViewPer�E810027All�(s= %H=36 %Fe newt� ema-orem}�  .ac�lY�"}[ 7]{A:67�o.16+xio2'2#�I Case:!lai.DC6Donclua.J>-E6, >+j5k6,:-r� ry2,6+.4r5j9sC2+d�!�2,D2-*Examp��.� exer^k2( 2)lemma&L2#T\�&No[6)pr�#(P 2P[�b6+2/�drk*Re46%s�'S2N�.(u�ky 'e&�S�@of}[1][Proof]{\no�:nt� D#1.} }{\ \rule{0.5a� }v'put{tci�x��b���� )u.S R�&Y Lbq Scale"�W m0 Macroscopic �Su}R"� �<�d!��efidel��`&�<x1�4of#: $N$\��uv9�#�1&N2 �vE.� �X2�"'LO"�I%�expeci�&�)J�)sEg fluc�=�:�o� �A?lsb�FlQ2to%22�U�� mY� p"P��dOese1AFsuperco�O tors!-��6circu�'*[>� i�Q�t*If1 �i�EC�&�$�Q  local� &aa -"�>&�8 viaj7ppy pote=o\DA;A�i�mas,br��%�!� o act�+ �= . Co�ntK;0 ga�&YQ�=�co�E�M"�< �*�eelea�m� tic Z�atATT ific y�F=  B�"�f�`� �a cava:!� a��laQVp�(sO&lA53"iB��E ith a sui2e [Ca�^�%�Zt mNun&B)Nc��#�herc�V�.�@�,N$% .{qa \med�� �mr�� bf{ISa\B{�> tect:pr B�,!K��j6�E%�d �uormously&yr?$or!�al 6KFeynman Rd  80a}AF Deutsch  85a} ; 1980axloI�y��telepor �, crypto�-�0��� y5zK"%\�Rq|r�ga'HabE��VJ�\ �y00YrMu&�^q#t Em�HRuNsti�Pbyy�^"�'}9(�O�� NvpY���! out-�f}�II_%U�Dg"� �K�!�Q �us ��s94-��+ d�e�Z.Gr697Hho�D s)4!{NU.t�MC]b� �#!�I��g�(�%sm�if�J�Wnq�� �2��%.��hto�as"�d�Y�qan (�#Ks���(�hb}�S� � %da[d r/ .!�[_K�+9��t;[5_!&"TtMSnitDg�{dF ��[oq{ p���!�""�)d){ii"�by�0Kd!�M1*`n�R1^ Ker. O�?p  !�[l eZ#Ind, �2A>a4W:P ���ahri01A~��inuous �T9,�{Md<& or holono 6�.SG`M sman W�kFreed3l }Du %�NQa)�`a .�prom+L=P!� stea��1�VKvm0% {Knill � ���99a} -Hlu%Ct\HCMterIkLR62jZE:etE� QBHlis%)e 2�Y �l$�� ed,;M!��&nat�! E�mJ$ (e.g , hy��ine gr�e$� metast!� ex�a"bin� &0neutral atoms�!ph2Ki�D4��e�* pol�y�ys, ...Z/� -�(e�u� �m� l�  _o p pum� -�icEC � �)s om� M? < � �a��-reson�R aser��s -�)rIW-4|6,VFc�`%1 qA� �n Q �� �-�.w�o�� QEDm6-��Ll�~lli s:� ZX.Ks, ..)!b��t�gqu�3#k �Mf(e)�q� jump;�e. ). S���\*�f��B�IW�* &�Ze&Un����pa=aus -Josza�.� % {Gulde������kam�{Va�$ype��.� �� mi!ur�'�.s�Si*o�{ith$�ya ! gr� A'iI t plan,�#�_A�B[guide��D F xJ�1gram neeo(%�v�$&Io1��_ ���wow & !W��L\c2�]�}x�673 veal��B��*1��8�Ze�,A4� F� A.�r�p\`d.&morigi %Cirac-Z� r� H trap�pEpI{(}��c5�*)e�s shutt�f �O�Smor;7g1*da! �uoYN�J\f buil��] r}i� � Kiel�[ki�r� &�iB2 ers ,1ܑa Ys (�K%aI����4 X1or'mi[v rout|,o�Y �Monrous, %I0 !��:4ent paper dealSs� ��e_8"a��Bsu�ufu b�_��R�yl�U�� r �/�(* &� �� iFrehZ" ve surveye� mhA� ��e� g aubi=� �Tew�U LANL1) �ook��.�dMi!B3�A��B�vOwaOoccur ��X�9c�X�QA!� ��racT."tN;&, �~�C�uq��)noNak�' plac�le=Z� ���(fer �i�}f-�7� �6)\2-{UaD� ���o��&�{a�l .� ) bi"w �CI oEx-/9�B �oX �JV�2��c�dm���!y�#A\switch3 ff�m)���change *�w�Zx!bN; �� ��� � �>: *aoR� me"H"�v. .�e-� �2n/!����I%|lgenff�>Se&�#ər�u -�!h����[�'~how*sQ "͍�{Zurek! �9GRni96a}�%b�3 N�� ����6; 恽eu��:a�^�m6�b>�chͤ[-i��h1�%Q�%�v��� /. rege�t9 h.a@��g � �V��i&40n"�;�byy i>e6� ..�)S��em� -4� ��a �p M��h� a� �fngE})��.sU~e�t!��]error�Oc� )a-��um:$o�ĉM_$CalderbankAQ  % {Steane dy�n��e"�o"� ъViola98�� pass.`�a�zin.�.� -fre�?b�-VZanardi<Lidar ji$9.B07�f�5(ɷ!| L:� n��'1e�_D>  \p$a back up.�q1s7����"H� in76�a�kepRmlowB$ threshS(^d]�d�y� $10^{-3�9nd 4}$- se% { , killvm�"� )�t�ult-tol��b.�A�p�a��BcoIMse�  . E�hBzQM_sh�c�` �  p� �%aim��kee�5pl`rb%V� 5S�Afa��oa:�:�!�an��F�on^A�e �F@8* U�!`6�ei si��iQjB��@1� as*c� �GI�@. "�c-�!x ��aim9�N3͆8F�!N�� b ���%Vs2s)p."�gqn I�Namiki����Zo�"! �{�� L6pE� �88ec.re�� i6 Ace�~tin��yp��!���� � : (a)\�d3c�at��.,s ($t\ll \ta?,c}$) (b) \ E&�i�ay: meR1� A <d}\�x t\gg R�F(c) P�� law2��t��<d}$% )�g c}$\!!е�]��mGt�d0t"�t �o . At non-I:.�$To?6�\-e�e � _{b\,}=\Pb /k_{B}T ������k D)��assocra���U# ZenoM�ISBvI� es &�!�9!qS5[2U�is du�a /�6N#(EM) � �z�acuum BV�>ur� ��(.�c&x�%oSq� Fw�4!| tantqDave�?kA,�""��lyaxE\̍�bE�i��lesCn�3 _��!�e7a .�m1bnLNtuGretur �f|i�r�Ie%f� ���Fls ��llE���H��!Knon RWA� %�'&�5+�a mera� refl%chet.fi�=&�e�6�>,'\-K5�0"H1���KI�!XM��'�p�:� r�&8� (�% {C5!�� Brau�)�"� thesl=0?��(�-'��p� $N$. \ A�a�n� 6) Ma3a}�aY!0>N�� wq^��V( �O�B�U)�.A��EIC-O��Ah %� �!�.3.��t..QAy�"lQ�$y!aM—��� bÕ(th*I51 �ou:)oes�B�kZ+D��>Tr=d.��q�/��^Vu�Dw l��/��*� % .r+&�*� �.u &�� d5+U�U4��he"� �0* Ec�� (*�"n�&c�{)Q�$Di���X��q{may�"U5 2�L#m�QLi=$J�j�L0J�%�W  inve�q\6,.�  _!����S\,Jb���ag�.]l�[,VT,1���ő;�`�ep|*�i��it9�!�S�*C=] Y�in �J�,&1Bos &�,�o.�,F� �c�Aeqȡ$i%#!�ch.Pe>.�.ps"|Nd��f�Oe2� !-/��&s (�ILHadam-!GHZI�A��*.of*�&7,h�(m%�)6��o&w1"� one�"�"i�R~ -0�B� ( 3� �oB+e�s"}�  favou�!A��.K%�x�� WatBp ^Ck�be >k{zi � A��aYF sݽA�Wn� BWeG�s�x6M �'Y.�"��amongs�n�mpr*�p��c A!R�+ff jY�@."SG d���,W/n"��V!�&��Aj%H"�*��% ��I�6�Lha)��rapFI���V  rapyLL���lB qv�/���ahC�p%w2%��"s!�1��, �"�� s*� . A�at�A(� q�a�>�92I"(*6�"���=��2a B�iߗ[ i��S�TL� ��(2��by*� Knigh�Cio)� 7a}%D�1���V 6�1�~m��&�re*�ons. L�Q��/z{>��"nM0e�I�����ofU�f]isR�"%>�% 4a})& thi'J�w�f3). E�Z llowa6a�B:F��I�� -&eg7E�h"%A3}�%0U'��e�g%e�(�_$ed 0�K2$m a2*`#Uach�� a 2D*�-ra+[!�6 aa ���d S  tX7t $toȁryEja:t%��[�(fc�hzOl�,�Le 7$0fE�% �arco01p �s�Lb*� elli3*� heS�ar ��1KDeVoe  An�5>�N2�-�!�hW.��,)M2~.A�Ra#2Y*iy)��P�A'%^�3-4�A*�&��&]@**�� �at�K"%J�KEU �w�G�o�L�*asse �.. C�4QED")M- ��v-�Cmicro�) �y���&�Z an a��to ene�Bktoe e��&icc .� �e�ir 6��� 7�i�2)�� �F�%U�Aszzari�7�Domokos. Turchette. High-u#seF�+q �z$�v{SauerAa*���a��!AL-MS_���o�Hu�"�ny4.�>� A�a��?},�;Aq[��W ���:q}�K 4-���� aye(�� tane� emi��#� 4 m�cW B�aj2is�x � �#nv� ���"� &V i&�to��^EE=6"Ǩ �6�)1"vj�4T�ib���%=� � ofdesy6?-%�IK�bb� ough�� ion�th9iYQ�'i�I; weakY9 �M@�&E� �( sGE�hrleiPq3Mundt"�*r�Te(e"�+)W�Q�F��l�h.|a�u)n�N��p@��*r" � !8�"Pachos��Tregenna.9o��b�.5RA���or da�G o��EA �^*i2�-6{#�1 U�c�5ngf��ax�4er�9�m�,�I�w&�` at a���'ID�I65MA�x���A�.�+.��IS i &� E�TA��1"���.CyBM2 i�y#�i��E`a��Ou�l*��)U-Ftwo�>a82Wby QC, Eq�2� !Id but �56��n �' ��%^�>��their:b 2L p+m� ionary��gSas���ntJk! ��xa�M /f�)d&V "�  �X%��-5 et al \M. �� �� "� ,{����<4I�ir � #J4,. +6!5��eiXi�X!g�����0 �#&� y# t�!UF!Qpp# . MeZ0.%P�7 �0��F�0d�P=r6fu��Eav">by Garg-j = . NoIa� �1�/ (�Z "ofҖ% �56��$� r^�&.�!�*!to�il�e I4�&�" AA�t)T���\!��I!�}�I_$ all .O � & f�k 1A�I��,4x-ai�$mbd,1-��4 r�h�9" iF! p"� e� �A�6���g&�I� ��eU=**� s 0,�� >��A 5I���� �@�$��r ac  �@. L%&z ,�QB��P� >"c��;in���t���vulG.b�oR� (SEu.IB�%H 2C�.� pCZ-�duY SEa�h��g1|B-�1U͒!I%v"�)��!RɴE� $5)����c�AsG�.�$N>�� �!���C p"�C� �"^G6�C ���D�QreD Q�F�C�} -B%�c�bye E&���_O4=EM � Q+dR�CeH��:|�fe�*ak�-p�:A��:.�� mlz&tu��1�6;_39�I� ��9�'5%S2 �q�SDI��2Y +�s"!�>QWV~��D-N�U@2-1�mw �1� oE8.8( 90N9��%�2�iB� � J.��� 2�E�d-�2-0R �(a!�d.��up)�1 a�ak%4 in� Y���.jYour�>��� �-��c)� t�G!b�oen!ϡ�͝%@IB=��-׍N��C.�b���RH $ a��M[� $��!�numer�@:3�(2�FK� �S -Dic_c� h��% cooƿs,��(q 6�> n-RWA �ing)=�d. AlM� ea t< (%ic dipo�Rontgen?@agH�9ic�8)U�^�re!�th x� �!B&*-� ib^4�.� @ FA% -A@�!��O itudAK-F�$\wq4{\pm }^{ia} $\&�"�o7'�T�-�se funda a�ua36�,�2�2�cHge��6�=a c6��!E0cc. ��!Jp!�Rr ��a���!"I%50M�1�'��S:� &ALg��1b&CG� ;"�b�fa�c#�-ټ�sor1QG �U�� uld �:F5c dv &* !�g �B�=C��0Schmidt-Kaler%�&�\nd . H*��� S=atp5�pU f]2)ρ6� *nd!��&� 1!4AcY��be &mA�B imBN%l�'x�9��I�K 2�s/=u� .t��B� �����our"�#&R$r�.��zeA��&*�"&�<�*�e �3ZP�� valu� �no-�,��e�ABMzRKih!�!�ma�=�#%�5a� �4 a� �4dscu�S<�n7#M ��&*BR W�Vy{"�L.�L\he��{=ܒ<��F��1W��*��as%�r'*a�4} H=H_{S}+H_{C B}+V V_{I��/%�<�-h6��y�� !���A��  iR�t=v_�!O0\om4�{a}�Eaa}^{i}+:" b}b^܋ }b�R�^�c"{ y�Zr �2��|%=��\f��1}{2m} �\ns }p_{ ^{2}+,}q�u�j .�� }V_{ij}^{6� rQ  r_{j ; owDbel{Eq.HamLattVib}�s&=& �K1gn�&K}A_{Kn dag 1J �%�$hV�of R ] deca ZN�E2M k�Q k}a_{k� + �,xi $bU >��% q�yA�� �}�E扯�y,��6�R%eVE%)�;a=0,1 �(\OM� ia}+. !�st })(i _{+}E +  _{-  ) \"�\\ &&-:lgecb+ au@�jB��e���*� #*GAAI�!!��b�z���"�1 �E�2 -��  $.o�$i$thA'ed) �r��6vt� �s�l� *�0-2�1-2*'s.@46�.�1}$!"uJ.he:GE� �� ol) �!i�j0JU� �t�Uj% FT� T*Z�f 4�2$u�b-G+� 2�"� �{6e �Ol�k-c�8!�6��&]�!<1-R�$a#0}=0$\�*FwHL(:"� � : !�U��+�V� e96��l,�} �����MIjMr 6* �*��k}� �Mia�Jg�'�_\�v�_�C.` �`�7�;[XvH�t+w I })��K}t�ti o(2�-)]+HC����b �K���ia u+m � })�tt��s (\Th&y �}+  ))):�Fp(N "/I�pf��SEes,Vsi-aF +��� �3N%^��"�X,�Y�ICM F�i�A� d&���cno��8C�?� � �#�5=jN*�+��:U (CM)[27?�a�Ͱ���^�th!�*: �.��Za*�q�� 2� ��K}S&� ;K}\s�; iP@ � }}% R��IZ� V/ S" ;K�[� � *6 3 $iceVibFreqF : \�*!Rp5�3G �m $S$\�8eE+CM2� s $%N3$\ $(� =x,y,z)e8o2��Y�&�:%�2�,>"mc,��as&�A�"�`"Í >j!�(|2&B�G�,a|)_{i}\quad���� =(|a>12.1" :�yab�� yBHb2H\neq b � U 2* U^ �BU2�H,2E�lbr�Cb,� ]C1 r�M,a_{l�h]=m+_{kl}>�W�A,b28_.;6j��,A_{L j .jKLF�T�7i�yI4�, Zee�)�(h�U)- c�W�op~N]%"�2���annihciss=: ]rN�[�oB9'Uѩ��a�CM.k>*� �Am*e"� ��";V5��f�:N�*� !�-i��c6�� @c}}{2\epsilon _{0 V��0d_{2a}\cdot u.;)� ��(ik # 0}-]�\ � a��e�b^�_}.� u)}b � }��"< ntk^tFpkp.�lp5 l2C�� 4% fy.!�b})(k! ��; K})\7s:�&& r16 � �7 Ѧ�c �cN�6��E{{�i!AI F�� Eie_{T} �1}�: 9�M� �5��&}}�Q�1��e" �FF w�1 $��$\d~es�d�Owa�e2 �* is $�$;a $V6��0�7 ge $%$��. D�L�! d\ D*8& Time>K"�a��d�mH?F���]� ����0"s �Zs-R @Liouville-von Neu��[?��F� i� )�\�A�W} t%�[H,W]�1H�#�gR IF�i ��8^"�*!�Ƌ��u�} W(� rho b� R W -�re1!��l�eZ\ŠV !d=Hg ���=%�$*)<$|Z�� $%�׋�& .&\\ ?|,$�0s'�� �R<f?tBVMcel��y��>�Q:iNDfi�!RQ-_$S}=Tr_{R}WRd~+gYFal*V�)r6*���U��!|.�W;&��a�S\ )�^&)�z1�9i5.�MGZ10}2=[} ,%]B9��a�sam!�>y U:0E;L $\�- en a)hNB���\ iu"c>=�bN�F%�S}{0 u�-%il|ar�!@C�V%j&gV9�.y�&�( �>�G/�*� j���(k2� BT�(non-� T��s\ F{V �J�(C7B� �\Z �N �d]hc>1�7P*��O�\�"p=E�-e&�X" � �rILk�]J#cF*mK.�A -�E9&�}�ta:K,c}\thicksim gP17}$suLMar����l��_ $T_{ for &w 7� T_{2�-x� b�% J,2>�8�c��?is�R�� b}\,�K �K -LL$1�K�� 7 6�5}$/'BKAZ�!)��:s44�)%�m�&���;o"?n�;A'�?s�'du� *>LY�oD[�/\�.�M\X2�"�(�2a�ter"L%�L�P6;FB>�,]+L3q&=� tsu"p�K\.� [SrS!���}]B� +FMG٧Y{O�XJ�f]+6�, \&�]%�>I��)e&� o" ]%-�ing=�+md$.��&� shifJ�=-$�agAb�ss $���: $&I.��I�su]<nj� ;jU�mJO�!�:�)~R!�A \k�-{6�"� 7"G2���y; i���.6f��s� �t8���2b-�\)Q�"H &)=�B\�)��*SQc!�!���. % .= b'��#=I0+Q.8 E8re� ��~&as:J�Cem%� tintv�{0}^{t}d%(�]% Ra�}(^_`-(iUb}+"�)l�50ab�( �+C_.B )/2,�eX �= --B-i U~" \ �T6��2=I�6$(�_&�S t2)) �g&$("� F/ t)!n\ $kF��.� >��.�|' �H���.CM��H� B!�#�%�$���D}N���xM&� .�`�r��.�*(��s\*)� l��TD}}3�-i�(>DF}.D\� ) _{6� aϬ 0}=2LB�.��j It;a�2��T�gC) �  � ai{#��F� "4�)c��` �i�S�<�($|\chi �[$,z ich �9�<er 0#�2Rh >�".<ɑ*�2�$�(�.*m &j =� )- �-i �|$8(E��B���*=- 6 .��p$  \O8#."MRS}(!hvÔ%m�%BG"?  D"(�!t�:p&�rJ.F h�Bn:K �:K orMt�a�~�(� m&�p.�6�da�*se5�)�,in Ref.�!BarA� 96a}�1 d&�g>�*/ E"Ҽ�?�I.���u?of*� Dé~qbX�?jEZ@7 D�Gx2�A�e ^2lfo� �is�#�}�^ F=-(�2� )_{n�*}.T�d =�ifq2>N�WV �5� k Y2� �Ңi�}.`B��&{Q!f8�w"q� uxF\ll 1.�h#s�X-�s�*t-��c}X�$� @5��O*�*�Zse�W�#&�8%F F(t)�11�t}{ � 1}})�V�[2�})+..� 2_ $1}�0>!RJ��TBC}�}ps��|g (0):�2�� B" C  \6�'-JaJaF]s Ua �+��\ &��(�i.�.G�BUQuB �X^��X��2�22��r&�% �����q�X�U� 6�=��X�NA$� :] .$-M!�6]B).R�N��1},Aq �,..! y���erB.9aP�Ot��w"�:�i��R��.Lv F5M�6��1�-Y��j�P�< volvK �bf0R�' Bx.E��T]\�8s�E>�)& av&v o*n �QrR� squyx ��!`!l �nET��}�ac5�"��c*�^. "�2b<s6rUA���<r�;m%N�YB�"�1 ���Y�2�>467 N�0RD��.�Cg\ No\ G}=�}>� �}��!`>�b��6�:o��E�r�nob=� $&x#$ "�602�E��io�+" % |0y�A%��NI�-� 0� e�6�+Z  bys � Q!:a8, where qubit s�Cystem state is $|\phi _{Q}\rangle $. This situation corresponds to s=�us produced after idealised coherent gating processes. To examine unfavourable scenarios, the reservoir temperature $T$�Passumed non-zero and 6qubitscavity2l to have a low $Q$, so that �dtaneous emission decay lea �(a larger de � ce r!IXthan would otherwise be� case. SpoF`is �domin!0.X-5,�only �contribu%�!�@hown.\medskip IntHMarkovian intermedi�ime reg\$(\tau _{d}\approx t\gg  c})$ ��@Tis given by% \begin{eqI*(} \frac{1}{ H(D}}=\exp (- �\hbar \omega _{0}}{k_{B}T})\tsum\limits_{ab}% \sqrt{\Gamm.a}\ 0b}}\cos \thetb}6A i}\lI�\sigma T^I� \end�(% The expre)�xinvolves Zeeman (or hyperfine) U(s for $i$thI� $% 6| >|, \;(a\neq b) ,b=0,1)$\%�popula!� \ 2]F[a.�[ N. �4optical transiVD frequencies are $5�,2a}\thicksim.�� U,Ac j1a � 2-a v j1�a} �Eg)��between dipole matrix elements $d_{2a},b}$A�$.$% } For�e� of Hadamard� (unc��lated)�-�n!=\t��U�i}�E .E@_{{\small i}}$, w�A$ th �� cvector�zF =(|0M�._% }}+|1J}})/2^�1/2 � e fi�3at ��q�2}N��% F�\��B���not�Wat!�>�a�:�can��infinite#$the lambda1�� if chooseIi0}+Ai1}=0.$�cO�c�� hand,U2j GHZ\-�(2dI �M }IqrA0..Q +|11..5�^�obtain������aF�Her!�e2��Z scal�Lstill very long, duey�-upper).0 Boltzmann faaF . With $N����$10$^{4�n%r"$�� J+ 8}$s$^{-1a��0�2W15.- $T\��ic&300 $K�mw$�J{19��s��Overall,Z�)electric�9coupl{ is"^ caus� ��. O� %Ls such as Lamb-DickeJiI ignored9 �.s  tre�JDA�ionaryɅu%� %�s+$1/N$mEisf�but it�U\ �@ result�{tK| ��memory2���consist;with tha�4of Garg \cite{ 96a}��,o also found�w2V�� allow!�� vibr��al mo!L in Cirac-Zoller typ!J8antum computers �% {, 95a}��  numb%ofM�U4$ \subsecm{Ca%�\ One Q#  G� <\textbf{\protect�� }} �=on�bit:� �$two-photon!|onant Ra, gcL fields detuned fromS65ce�{}� $|2��$$ amplitud�� (gAk) �@ becomes slightly" Z ough�=  mod mainAo zJ �A���j0 _{A}$ $\ |\c. S&.  L 2:C,-7q9 j� 29,$\ \ $(a_{j}w \ iasJ�{m I}�1F8=}\sum_{\{a\}}C{ ($)%H;+;_? J?}O};2}% )|\{J%#"nZ3$ �Tequiv \{a_{1},a_{2},.. N}\�� i}\} , 1},%i- 6i+$.\}.$Howev�TN� dis �  iI-high Qb��aer� tem"�i���Aau��� �� ]3narrayR�  &=&2\{6G k� i:] n l�  \^ � kU6�aL _{ka-C;\,kb-C} \no�� \\ &&+6n ab}( Y� YiY-6! _{- a!6 _{+ b )�,ia-;\,ib-} ʙ22YX \del��9�j��V�+�+}��B�ab6�~ a�)�i!�>�FF>�F+!�ia+C}\u�McQ>�&WM"�relax�%�� � � depend�q�$it��[�H E . � ���, .�FJ \pm !09�$,*� V�FH:v$,.� &�J;:k$���z2Rj6Br-wed9$@=(sL(m�)2�Z�:�`�znj�6�@�6@re � �=E"�sU �`2|]U:I\� as fo� s:N quadZ�&=&i}{8}\�^{2}g��at\ast } (% \�ab}}{0}9} m� 1�,\,k=i)}�)ir _.�.�2�(\O]i!O �a��- U} b})/\D��ci}^{0>����1}���!�bN f=iK1Uj��B�����b+C�i{g!nf �1�% (1-��}� )(-1)}^{a!�nh \max[ u�$�s� mula*� ,(LD) parameths $����k EMm  RabiJ�E!2a� (.�*� � ingyX.� � e>$>#m��� one K B���.� a�$i>$� � X V|*Uf��f 6f. V*� .Be� �Qupy$.�$% ��6� desb both!��� B�$% -��$� �,�. A,im� s based o��D�3 _�3\;O]�$,v� � _{10N1% \)Pb used���J�*�AU�As�.�Q�, PaC$y%0}= 1}�i � � (t�+w��common &�U$�(s a maximum_{mq<a wid� j T$�aa�e��ialn"  $&hX$\ (see Vitanov et al � 97a}) �Nl� "� 01 "� �~>#1��#^�} }=i\sin��..�.F[\\F=06Y|��=,�D6� _{16�=�8Nn� 0r�� # � }=-% �#M?}{)� } �(-i �)2b�1��#҇:��2�N�:� !��a!Z> f�&isa:� y!E((t)\ $�eq d by)�gral �twoR�J �_{Ru���$\ J~=\tint"�-\infty t}dt^9J; ( })g1#   �KT$\��&P �=\pi /2$��$t��eq IX T$,*���t�e%0� takesev�!F���&@yJ�� T}� ��  #}Q���!}a�Tbel{Eq.OneQBitGateTimeU5� ���s��9���zone$!� �-T:\re set o9 n Table 1c�ce%}  ( }. PF�>e)�CS\tabular}{|l||l|} \hline ��b"w��,0}$ & $3.10^2Y \\ BA1 /6/9&�2.)���.a0Z3.��8a7R.� �% ���$left\vert u�� r� z) 6Rz5)*�.��� GZ("Y  U4Rtx ')v-2}.u�M!�av.�Z�Q�11��2eAs�r�#a��"�*R sk a� 09�P"�fS"(. As discus $previously� ese }�a�cnn�*# same f work�Tregenna��% {0 "�#their�l\�Rarc �P�B� 2�#effectstv*) m�s ��or��� �Rcre�#� � "�ut)!� f=! made T#li � .�R� (SE)E 6� ��� �2N� $%Fd�eSE � �\ Two� 6"� Z�Z| 2u y be��(i)c2� (ii)�Q�)4 �Q. `!qJ � q 0}$\ applS�#Jl2j�"� U Dyf*�U�!� calc�#Q;L 3D Ca$^{+}$lattice �  spac! $3\mu�'A� ndard �achaC!the�of> �sY@ i?{Ziman65�in whiFhe�al po ial energE&"�;!ad�c�mvA'� plac�� e%s +�ite�&a9 Eq.\ref,$HamLattVib-v� ra� *$e! pairfionic h�� !lx%oD ics,� �$V_{ij}C lpha \b� � reK� �cubic� j��9C2X.Dz.��(iceVibFreq}`4%�oely�por�al1�magni-hw�(I" for %#U � de. ND*`$S_{i\) ;K- 6R=�:�&1# $ UsA�t�y�)e�.3*��%�� }?a�!��!-I�a�� 2*-r� 2}. RJ�in�4E���^ �mn� l*� ��.��&�>q%.&�* - ��-9}�1} RN0F' % },6%4F% L6tR'� 4�s6RN&� & u 6�J���MZ25 % \��M+ &( ��o�#�"�+P A�d*�&�*.#�6A�b��mbi 3IU�$ (H� c � 4$, midwa�rough M�)}"=:�a�mvar�  $ $(1-5)$\ �*X �e"W:B�$1/"�$�.�\ Ti�3. �% NG, G ref�"oSa� '�p�" vely�q� 2P�p�:��f=I~3 % &�(E�\P:,g Q�*.$!��'i VJ �&xW&^ s, v}�>�),�t�� long2�!�x�+o5�>�s!zu of�9-�  (� by $2EJ2� )" m�%�er �.:s�� ocB.d@ 'SE or� A&ayv �&�$"�06j3}. C*�.eWByJ�q i�]������*�Term &.�: Q�$& �'6��@& E1 DueDh/& F�( &2�6�� 1,NG�� LD-C�0I�-.�& $0.5N.2�<. ��$2,T�%6�<.�S(i)\;5 V1�$V.�.2EF+3F� $3 �SE� �:PE�8�M� &-.'\�S � $.#&m�4J� '.=94 ���)W.�R"�5RS���/g*�.� &cs��!�]2� %NK2� '+2R�>"N2��)��] B�� ����n� y(C ��6K����Z.[�g� is =4n� ly in&"��NŅ7*s(�*���!��[ �$i$\ d�}t�* �$N�' hilsX.ݜ �.w3s (5 !@% N $)��negligikin��ison, e63��N�䥮*�,�� se featur!re clear1 ��k"� 3� "��R �r�!��6� st5~.�[ 2�ariXO �)eas6*�� M?.�E:F2�$~&= *�3 \,m%< gmL�&�#B�Vm%&EYe next>. 2.� of�2R��UB:�% _>�*S ! �% �%�r.h %�� @!4\E�!�lat� balan�7�Euer i-� � l:C:7e:<i*,*+%*� ��� fidel�7los�.th�6} �$SinceV� J�Z�a��7eDsTc� ed��MӅlj�a�R�*I7" �F &�, eq &A7j#.s�d"Gms&v"�pi���>r ;4&b$�2e�% W�3*�3:��8��s, =t"��A5�=&`%k:Q# 3I��wonablyI��/ughQ2somew;4e%�(fault-toler���/�  - OA$Preskill99;� {LANL04a}]�R�/<V � >x/*v/� iMMI� @.re�&a;��s�m"� :,"A�:/��ol$"� �T*�0phi]'q0"`' � } &�=}&"�0_�"�0&�0�0jH�0.�02}s1)U|B2% Z43��61%�o:�BF#>nF�."2�j9 �Bj�% -J%F:'le.n5�$U2fg2�},I,�2AigZ� s1}6�\}��\Q� .F���m2Zm2'�2!�N�2j�2j�22i^3i 3�2 3NF��(a63V4. ��2����F�2*�.�*B(��")&0�Y��8 V�@�@aa$sum2�۩�! ��2� �*� �" � ( ~ 2�@\� ) =�# _{NG}+�( _{G}.l �>$�(NG���&�&f17� �c��NG-2R4 i,jb4&� a?-&�/"� kk kb�}3�0NnZ.4$k}b^{\dag u�FxC}+cc) v�3�}�k}b��Ju+�vBW -abr��.��5j�bz1lR�C�{+}\Y�� I�}�:�/!ista�120I�. Some���reJF��G}^{(23)M�>�DQa&�5%o&�*�}R}� ��4��2;\,2a��R����9@jf@ja�9*efv0�� ^{(3��j~�jay�l�6�Rj��i��5��!�j�V�F��T _f� �€120 �Q� F��  �-] �&c9e�C+Fi }�s�$�$ ival�7�%o3F 壁(iB~C1"�* differ8&� s, s�h"%3)" now&�raAhan hav1�I"(0�1add@G,�yr �many new���7wo2�. Agai CF��s& J!�X W��&9)1s^D[ �)&@&�� )$ -�*�8&/()�Kc� 1�\Z<�n8N*I�6&0$,� well��A)1!�th!"�K�?operator05i�B�U�,6"����Y�:*�<k�~+ f+U^�V)"NM "M��Jw * +& -�J� 2\� .$\"e;EPE !�.�,;*.�3Fh\pm }^{g��$,\VvjI1�g5FRm&.(4:�=6=*>z=%+=\ ($g$\� �$i� jvsUəe�*N�2��6gh�J�ab���>r*AcT .*�LN�2a;\,b>Z)6l��d.\6�2��|$�-;\,cdAh�JaQ�q� c|)_{g}(|Q�M0nidh!wh��$g\OMh:{j$)N� ��Q�L.��H�q�Vmilar2��>V*�Fo�#>#,J,.�el5)�?A>A�!�*I& CJ+B" !� nd .7�k ;r�8�1�D�# ifica�a���:�--K}In�ti�*r,Jl=Adbec�l.��*9ly602 9�>T 6��Jmau,��)om�f >�*BR>=~5M5f�<�>>= k9�k2�<k�<kQ �=�1��<�<& Q�.� (VU,a\ "_)z� V�V� 1&) �,s=_{a1} b1}\,\>8>`1&i1.�>8-4)6)24%2� �e &=&i^�0.�0\,(\widehat{k� ci}\cdot _{cj}) ��=�j0N� �j&9 �:�>�\bs&�x_}6�6N  dx\,IX@9 x}{x6w 4 &=&(:�!*)^ �2J 8 8i.J0=�2J- _�5�2= .!�:�Ql� � �q cavZ��Iy $)5=Aq� 3}}a\,/\,��4 r_{i0}-r �B� � 8�{�  se.�-�|e�$ice size \�3Ld abov�..��O"�*�l�B�Q>)�:^>�H�� $(�5 0}=0A�ol�R�~� �B�6A!�d#f:.��& '.7�)&�Lcen�>1#E�3W2�>,2o)# 1�deriv%�s.� B�)�>6�VH@��\B�/I3*� �3) � �,� &&NAsW3"�/b�?!tn�52�. �!�2BF�P-free �Npac�S�F�%the{+�>�m|0�0�. ` 1> % |1V0B0|AU=( #2S -|2N27)/6�gU)�!42$< :�6<I0 not direc:�T ? Z6{,� .6) via�%�- 5qaN3. A CNOT%j�.thuO' �Xo��/*�& F� exci.!� reby avoi9-2�d�R.<�6�ir@R�IT&u�O� D�\��./=$\ FV:j0.( N�A.��A%�#�Ay�- �X�aA��#,[*��C�#�n�-}.D=)GlA=TwoQBite^B= ��(.Fsaod"� y� �(� A�s�9"�EE/ *,!�0ept in accord&IQm�9E 6�� weaki"!1u$>.�/B�/i ��BP0 1)E/(/�/q1w$+ =�/% \6BGa�7is /�%25:N�/� v2!:Freʖ/ } �5��*�/�Cn%����/C e\e�T1e�Ps.*�2�j>~M��#I�iB?4.y^|/6�/4fX5B�N�O�r�/&�� � R-"� e =&� z -)Yv% ? :A ,A6Y-  L.�*�-�-�- �/s>�.4�/r'FJ5bN�.N8Nq5N 0$\ F�&&/o/ :S~�5�g.zg.*^V�Y�4~�;E�s a��.��.*{2:&�.2Q.^�.��6 ibbR�.N�.A �ѡ���� 6:)(�'6q.��� 92� ��n� . X",�ٓ�?ic�;oZr� q@.� > �� � �c �) &e2'"G\�q�9+};\, b-C+�8� 6;+R�\�2&5LD �� �-�RdA!A �!PBG. I<1� iree�Z, �d:�b}^�B� �� n�0� st = � �1s *�013}�d1o9i�:A#excee X[60�>�Q � J�>�d(� =�C+;c si1�&�'+R���Ao \ �a�j%��un�v2V9to� ("9d}�[!:(!�h~ *?change�W"�.durA.twom� D� iodd2 sign�ana�&�Lize �� V f�6moTmR>M,�{)J 2� 4vice versa. WeM ne5,investi���1�!�d�Pmin�32)A�W/."h ple,��iM�0ed 23, 24, 34a: 35,��F[lm �K�� )), Ea>gi�a�duc�ApV`Y�V:�M� �!%���~LR��%.���Ihe� babi+1� Fj$\�"dA�am����=�� i_pr^!h`� )=6"-�D\iit�(u as](as un�1if� �SA** were(uti|j}B��Y �e%~A���beb*sQl Il 35. ;:C�L2�p !%�-)N w�( most uyQAOvjin��� by" F/"GF=->�! }6��! +)\,�n ��UJ�� �%�<�1e�1�F2}Lf|���;U�ofU�af� mus` les�)an�9y6-5��i)��r64i��b�]aZ1"@2.\big @Sa�> on{D�HionJ�18Ayo6�XH8ircuiteDl8u.�ahave �RsT� s"�m��a��oe��$\Ra8. D*�@�e>�ed"&1�wlsRHo'gŻ�O��B�9!eRhD2Y8�, �z�b, via &A,�FEA g�Fal� iv��d=6%,##in �#pu5N�q�8�H� rmal�#�9B�_:asR �Wof&�#J��# exAe� values8{juct fluctO*�Q--� ing �um �)%&��^i2GE2�OQ^�is qu]i1w�dA��Flic�d %�A6 � �2�%(macroscopic ��%�@ as B&co ^s or superuhso3inuUmeasureTM"&�*LI��� �$aDio&PH, HGI ree-E" Fj e%,EGm�m=locq,�!-�&�undergo!�6 ����&J!�trapp�"�Is;A n�L!{F; r�qib� zfSS�R�7E� class9nEM ^;<^feq#faci�e#:a��Q�!lI�e��"�� ���ta6�q �L\I �ɩ%��} a ba�Xf%��s.�6���numer rc!(ctive2� � C" acted�a�M*�8�!��(� ter�I PIH�key obj z==|�Qto2o .H���th|?F^2�Rs>�"�����i by:�JoMd�)n-�N�I)��Ja+M B�Z,�6 n8M !�] :�s�e*i)*� ith no�� c�C s oc�ing�/.��onDnB& &�� r)adB.rN�S"5r�Kr��wo�$Z�ttd>ad-�����J_�GHZaXt��"�n"�A�"�p � -Ba`bDfMSab�X�pQpw ��uRP $^{Dg�ven"! ��S�We�>SJ1K$%ES.�_�,do��h�"�ͮ%�Gr�u RaTni/�� rgV�_%*V, �?U�i=at%�.�860 4,nly � N���nFE�!�.� u| ��B*�6#�fC,-�prB R squQ) ��". S� ng"(�Ua6�C*A%�� *���E#��.� ,2�!W:z.�", ofF�5Z�i��,�CM:i�*� # ���< ~@t5F6Kab�B�;š�"{y�~>!�[%q:�eչS �q ,�eP,�g/ of�� B1.7!�}1�N2NZ =A�U�ss! so"E"B�is :e)#��@�o,j cb2h�3��.[��a *�O ��:�� ,.�:�,=i�Fse,E�sZ+1�N�v3�%0s �AJ� non= �=t ��o} �!��s.*�"In ouu[%�5��!�!�s*g"�� al% Xg�o ,��&� w � real� ��/�.݀A�daOyrd4 o� �B� �e %xlE ��ui9�Pof inclu8(ory )[Q �up/%�5�� X\!�. �"J$.R 7�� oo ��\�uit{�}{u��)%���1e6_x}� J~hY �ly tooKplifi)lz�cA ��#�W7Aag� (Bs,� B^ O&�^levels)} N � tak�nt� count actuIY���<�2C of=c]ynru�~or � chL ,%��ma2�͛]5 %va0-2F1-22m)/���H�wIL7laser z| �8sevNz possi �\�$ � stor � U)�, 0, 1�p�an�i�%� 20� �"� &�_alt� Z�<sA�m� m�}I�,-� #eYn�)�-=� |b^)�#nsie�h��s�#S �!$6 !Y qUg}A�Ika� a grzi'4%*�!ab"�r2)e��a�si� �V�em�P $�0$S$7F� $|q&P$_$^{o}$6q� E?a\ z�xnumP,spin $I=1/2$R} x R8$ ($F=0,M_{F}=0j"s � 0,�.,1 ,+1-MK� a6�(% $FZ;2, suitSpol�O&bAWQ~e  �*besybep4.@ ]^I�%�s.)EV� Fi$��qAr �S=% �!Adm!a�is� �(ert %tM*. A se�6;wDTsv�Q�fo} �-�vA���" M�i�.An�exist�r! 40}$C a:� 1��%ImiI�FVM_{J}=-A�)e}( + �a�myi�s][e metasIS [D$_{5/�eNHTK!�2:� I=0$%�noݞstr�u!s7;�$W�Z�^requi� �%>( *1t�F�T�86>�\"�-�Ɏ� a �6��!u"��pu/)66�B���� 4Fj-�E�. R>��#! 2}�6��ji!� ea�u�"�mP!�� .�&a�p&.�2conne����0%�12� .LɼH"= Ga+ Q��<st-=P$_{3/�;��6)uI� J2&ɤ�i�9�6' En *k "k��!^)�9�A��$ �s �!z$t�t� �� 2�AAal����s ���F0!ҕ�h� 1  ����} *A9��#*�3��)*pb�*HB a�>.6��"y� y. S� N �^+}$IJa7�I��2)u�2�2Q(K2} y��N�6PJg�Z  (A�� �sMv 1/2,5/2,3�n�%)*�iJ���� Z�^� 5s,` .Zi���!Y����VI���y .ty ��!h K69($%��3/2Z%�� u���ory�*� exten> �c� J��raۍ!�.�m&�a��=� �est�Zh+!�$"u$to minimӎ�y- �j ed - sugg(ng �3a�SE�sm��s29EA�rMe (�q�',2<�;))�!BogeMEI�o�an�A��2�d́#s  lej��- �-downwzi6l fɐ!2�&�q�I�B!�e� ,F� lso.6�k&qj�I& *�N!k�X*� ��. Also,Z�`e& 0,�3 lso .̑d? 9�I% � �8o$�_"�*!I@]Sn%,6��3�W#:����j�oth/� B? 9��Vr�'6�#c@� V���Ec,){5fulZ� arc�y $� j~p&",�a of .���C{�ea+&}� t*}%~��b�rth `eN�'$AcknowledgS$s{"(�~Da L�( auth�g��A!� help 7qi/|��< A. Beige, S. Barnett, J. Compagno, H. Carmichael, I. Deutsch( Eber{qlJ. Eschner, F. Haake, E. Hin0D. Jaks6P. Kn�sAPa�!,!lPegg, W. Phillips, M. Plenio� Sche�F*�$, B. Varcov HPse�on"@/aN�RM,�^ )R{e���n_#�KeE6Ea9�dN�Figt capT%} � bf�uMo� of�?$N$I�B�A�"�%6@ 2D &C%a�J*�%po��sI�F�%B&.�$7�n$f mass (CM�;br�>7&Z& �Ճ%I�$��\ d"v��"&�!o� (EM)� ( addH� !��0 ~�&wr�B<&�Z�� ancilla�� perm�*�c e�U1��!�e6?� ��/-&,&�&.�&� �&�s,�"�\���"�oV $�' @M�$Az��~~&! a/w �q := a� �+�� /� �O�2 SEs.Jb��thebibliography}{99} \bibitem{Feynman80a} FEYNMAN, R. P.,"f Int.��T�r�NPys.}, 21, 467 (1982)\��VD��8��DEUTSCH��,SProc. RoP  �0101025.�Du-DU!b(L-M., CIRAC� I� ZOLL!�P�5e %e 1695x6fKnill%bKN%BE�FLAMME�90\& MILBURN, G�7y�N!i}(u409�=Jbm�99B�I>�0}., 86, 5188 a�6�Ra�zndorf�(RAUSSENDORF�BRIEGEL,�J>j Eu083, 436 (19996� uldeEGULDEd , RIEBE��A NCAST!{G., BECH 0C., ESCHNER, ~ HAFF 8 R., SCHMIDT-KA%�F!Й�\& BLATT ,Q�.j��8%j32�V rsypei4 VANDERSYPa��1STEFF ADBREYTA,� YANNONI, �SHERWOOD���9� �$, 414, 883�6�&/���>.}, 74a291%�52�$Kielpinski�d( KIELPINSKI�j MONROE, C�WINELANDE{ it.�7, 709�22kMonroegWR 6, 23)�6C% �f2 ,}�!i.�A�4).U%> }/04050302-iVkWnzo�B$DIVINCENZO��For� . fur %y!�8, 771eo6Yg HUGHESA��,HEINRICHS, TA�dscAɬum �~����+�ology Roadmap}, http://qist.lanl.gov - �� Fedichkine� FEDICHKIN��FEDORO�IV��V�% �=�SPIE}�q05�:IХ�0ds. E. Donkor�rN ir�8\& H. E. Brandt.�Zurek�ZUREK� �Jq҅�Mod& 75, 71��6�Guilini�� GUILINM� JOOS� KIEF�{KUP� �$STAMATESCU7 O%�ZEH��J�g4�Yc)�� Appear>a C�2$ World}, S�$ger-Verlage�62>B 7 B Y�Ez�� 52, R2493F6�$Calderbank%$CALDERBANK1�\&~a��54, 1098b:�teane^ STEA�AV��87�3 �6M8Viola98a} VIOLAA��LLOYD�E1w>8, 2733 ��82IZanardi� ZANARDI� $\& RASETTI��R^�}., 7� 30��6� Lidar�LIDAR�1%�� L�,WHALEY, K. Bo2n q�U81, 2594%q6��p&��GUO, G-��j$ 3491J$���BEIGEA, BRAUN�$, TREGENNA\&�GHT%G� �=��5, 176� 6! Byrde�BYR�7S�6J�J.i�Opt!#50, 128N�� �lH J� �@ics Today}, June �, p24.�MA�PRRM�� aL3�19:�KT gjT V� ^Gɬ�F!9 �6� 6\Namiki%� NAMI�PASCAZIOa�!�NAKAZATO� y9% > IMea�8s},��u�W��6�Dalton��DALTONEzJn Unpublish; ork}F� &�TolkunovHTOLKUN��D�PN�A�[ 69, 0623�6^ Brau1 }*HAAKE,I�ZTRUNZ��.�d y% 91�?6 - _ Z F 95"- =��� PLEN!�M���KN2�qu�  5�B98� 6� ]7a}�]68 L2�>�{01�97)\ �( ��3 &� 0, 79J� Cal�' CALARCO� �a%5- @3MF4E�:� eVoee�DEV{ R.[ V� ��9�B>�E��y��3Ut93��050��6�$Pellizzari�PELLIZZA�� G�G� S��6Z .� J��� 378Z6�Domokos�DOMOK� �RAIMO� A�ũUwME�HAROCHsN�!�3 355�_6v Turchettex,TURCHETTE, Q �H� C LAN�.�MABUCHI� �"IMBLE2�N�!47-�6�Sauer%�SAU� J �FORTIK.��CHK!UHAMj C. D� CHAP� M.!J�!��518M�6I_b}2_BLI�RB�F, MOEHRIjD�*� ef.� :�� 1022� Gxhrlei�k GUTHOHRLE� G.KE�A HAYASAKAh , 5�E WALThH. y��4�6�8Mundt02a} MUNDT � KREU�� .�LEIBFRIE:, �E B��~J�N+ 89, 10300��22� � b}2� OSm .�UELGA��F�� � BVEDRAL,2 a{� � 47� �6� �%> PACHa��5�9�J�$ 89, 18790�6�Oa.� W� !b��2��5, 03230V 6j)`�*% CAm�, MARR:n! �A���N� 5186.����mGAtr&V 96��6�S.�IB��J� DEUSCH�ɡ�2�Lf�*�!{I� �1xJ��B:} Atom� l  }, 36, 62)�6" T�BARNE�S�uK�VACCAROae��% J�8s. Nat. Inst. SS>7i�101, 5Z�t��� VITA� N.V@STENHOLMahR�A}, 55`��6Y"� ZI��as.Irincipl&J�ySolids�n�01965).\newpagO�>& !I docu�} M� %%�4 1�#by.� ,Word (R) Ver  3.5 \6�{uc�.i�\u`D4ckage{amsmath}>fontsB symb6� icx} \set53er{MaxM��|Cols}{30} %TCIDATA{OutputFilter=R�x2.dll" �,=4.10.0.2363CSTFile=� .cst.�! ed=S�@$y, April 1�,004 23:00:452HLastRevised=Wednesd9$December 1s<05:34:36<Z2D-�Shell3m�0s\SW\Thesis -.0of CaliforniaA�sis2l Language=�i�$Eng� } A�t`emA�orem}{E�em6ac2�"}[ 7]>�":7lgorithm.12� axio2'2#0$I��:!lai.DC6D"$&.J>-�m6, >+jectur2�o:-@!ary2X6+risAo2�2+bK�"9�DeͲA2-j+*Ex}:Rexercis6( 2PlemmaNL2#no�&N2)proble.�P >'p#SP�>4#6/remark*R 2Tz�!-9BS��6)umeE.( 'environ���4of}[1][Proof]{�bf{#1.}�]$ \rule{0.5a� � def\dsp{ �9�(stretch{1.0curge\nobL�S} 1 ��Xlength{\hoffset}{-0.25i!�!�jtitle{Li"#onEit� V*7 +F�sld} \�&H{Scott Joel Aaronsom(degreeyear{�@}��semes�' Fall {Doc�of @&oso>" \I,ofm��(s{3} \chair!�\fessor Umesh Vazirani} \Y*2Pr( Luca�>visan\\`K. Birgitta Whaley} \prev � s{Bachelo�+� (CornppU"�!) �!6�Ұ{BP!4 \campus{Berkeg \make%� b�val(${ } \copy�e�\ abst�E} M�Ut'1aqE:��-~F�,:�&{- seem* chalA3e�=st<ic intu�Us+DhowyphyIwh sho�S�=. \"�>r I ���t�%le d�`��E_TH sA�c&�Q jett&�edQ�l�(A5�$rn �s,8.E�%eD(nearly unsc�sd; �#I�+ p�fu0�ols f�k �ea�p|9x�#�y+help :�V.&.;."��firstb/��)$, I attackr�belie�%at 6�+!��*mbles=2 expo�ialf!�lism,�F!~8�56OerO3fa!her�l����a �jrC.of(blE?Av}4a,;ly /nMparS0'y~" �sol�:!�"it{colli� �6m }---�1S6dwhe�/a s13�0$n$A]eg�$is one-to-2or = ---TquD�~FzbUd$( n^{1/5}\e�)�V2H�@� l=���0_%at%open �+� s;.+no�0b�%�(tc@!U�ztpY!^)S \ A�aolA=(%!K(no)>quotedbl�d$ black-box%Y�\N�0o break crypt�'ic hashBLf=Q%�| G� , IsomorphismQ in�3 ynomA�!3E�(A� �fI��oY+oracle,:�!�xI�f ~$\� sf{NP}$-a�let�.E14: po2�,&U4�a�AQnonunJ mJCq3ad�Z G*sFO�N%�"T 6 Y��3�s OmegMZ$ 2^{n/4}/nQ\A]A�r?to aY a \+a3u�=a 5�5��A�$n$-d�Ka?al�� cube!~Surpri�?�-/l���C,-�D� new"M��}.��? Hi1 se�0� . \ Fin�����XT6Ao&�Sa�Ɩ�-u�N )ڡz�,e^�^ �!/�q���5o�NBoolean�MM���recursAq Fourier s ing.g+=��L�5� !M�,eM�onshiED'1��u�����U͙}O�ty!�I�� iniOarg�!$Leonid Lev z8Stephen Wolfram- �75~N liev9�a�e!dP ly i *s����ai��anvngs03L�ex�M�hAXe/N! ]RyF#---a "� e, /-U(already-verD1Rmv��Eij" |'s�3t�Buy ��!batq4�3p �������a%�lEv�hf�VA-� �)�goE�o� g i8=�N,�I ask i�h�TG=:N�IEif we �D��"�D) A~spf_ٟ is�?it��A������<�+'.� sZ�y� s��ağbup�2i�Aa datab̢\ RefI�a!8im�B2ff������ answer�y�[�9analyze�7A�G;)e'I�-)g�Re�yonYE (a�� �e8�6%k be28 �U�F.وPPqb!l�n�C facta��a�@>�!E!?d�8��A���V\!�cloA��1 in�e���O��? hand!m��p1 nt�] �---i5ԡt uld �a (e entire hi==�77dde�3�6� A�ar�+Qor.I ����q1!=E^D[C�)rHE�ly} so�� �5�+& } %24  %61 ". frontm��©�of�244\l�ffi4s&s"p c� &�5}% My ser,:�, o� saidI�he admi��AC- �;batic�� b�x, lik�6&a �Osh playoit ach��s �2 goalt �ovAPas littlE�i�gn get a�`=6�T.���my�Tr� �P�AHsaw � inculcateZ ��plE+)�` ��%�{ phi��� fe: �_�Rw�9pap 8wy7 �%xe deadlinea�rth meeaT�� #a.�s J a f�-�|3s! Abo�ll3!�p 2��b�g hope2 � doe�Et �?C^�9"7on<y��regE<�5]L��al ~ My deb�ah �=expert@t�} guij=, w�p|��unsel)0�K�Zsupporeob� �� � my aJy!<�� %;My% ����I�8d�X rom QZ a�Aadim!�� )��@I came. Admitted� �apusզ)��oV * �G dyh%ͩ*spJaTvpf *D��Y(As I strugg�Qo �jUxa#rela�e"Y $David Moln�|who5_ ly ad!?fa�� �inuA�le I �i�� etonu m� %!��<�Wn;�I,� Tn�san)�:��ica?tA crastinEx�2 f��)�. Si!(as�^s�  p1� !�)��5��to j �� e ��E2!i0Andris Ambain|cw�I�po� �J|'9@_s��yf .N�\ WYGLc �yAMls�ry�Au��s h\GHawaSq<:v�.:y�'ow;B�}d\>a�Yl� Ronal�G � �oa�iod� ly eqs� ��h�9K8�!�t non-rigo�rUJ:gX4at dubbel zout�Ol� �4� g�.a�Whe( ���ey�eyeE���X(say)!�l��name*{D}� f.��7usB-bsF.M\aA��O feej�at%�0ei Tarkovsky'�>its�L}"^Cnef��mme��y*F�Tr ��bL%rA� worsT�n�u-�j a�A�"�a� infl���;Dave Bac��m0&� 's e�.� w�_ho 1 ta�A�� chap�of%�own 451I�behemothJI�2conJ�� 'm� �Ubto Ch�, Fuchm i9T$samizdat},��ide! at a&^I�me%<icsɤ� 400 a�s tMEjbeI� w^� !\"��  beg��ork��Ɉbest-a��e�ʁft�� ų�����΁+,Yu$Z�D_:get� �,Nt;tec�fkSchulma�^4Ashwin Nayak l�ed patieOnt��mrf��!Ua��an� �be�John �-'�H ekly�Mp� s�4�en�,!t�{m�� ���5�����inspiMm�dU� �)Ye I�{�qel�R far��myl�" BesiW`-$,-�d�, A�"�Atom; Harvey�put� �U�~the gr��mes�r� R~&:�reBy�B �a� sl� in> 4;S bedsheeu stri| d9f��RD,floorE�S"e nfam� C&LZoo web �UV UG CWI!WAm�@dam,\ a visit enl։U`��(Harry Buhrm�H�dR\"{o}hrig, Volker Nannen,/(tmut Klauck�Troy Le��T�X �aha�mor� P���^� <>� >a�VC��s ��PLS}, MLIN}� QCHV}4uam��Yq� �a !Hebrew &B!MJerusale� cqw�4J�n's sonJ�\�\T obses���c���ree�s�� ago�Ia�4nk Avi Wigders�D�! Ah�ov, M^D Ben-O�6,mnon Ta-Shma%$# Malli9�ma�� 9 fruit��enjoy%�on%�-�th�A� poinece�ethen-u*�0�/Ran Raz� -�=� (�Ҁ �2isha�V� S� �h � chun��!���g� ten�� jv�wo��y6Pe�c�B0'�F�T�#P��? Waterlo2�Daniel "�>(, Lee Smoli ,Ray Laflamme�welcom����s doofu�5�ikG�Nmeb �nkAM!-$�Lavu�1op�š.vA�debJ� Zo�_D loop�%#allasA�F�(Marie EricsE�(Rob Spekken� ,nd Anthony V7�ini I�r��A�A3o^\�vTh a^ s�wl lifŜ�K6/�c�s��gr)*��� wai�pf�l st4� ��Jde� �atc�VHncu!p�N1�e�$ly QIP con4G��;G kshopA_0 Toronto, Ban��Leide���A$8 MIT, Los Alamo-~IBM Al'N�>0Ho.Mk* um,  ew ChilR0Elham Kashefi�rbara_s hal,� Wat@ i�� � o�ex� g�)!�a� occaa�B�*{, peo�C enT;ed�(grad-school6� nce WK Neha�^e�6lia K�f, Sima/%� ini, Lawr: Ip, A@on Coat�\ş ;K� Hildrum�qriam Wa�%,!� E(�<senfel�(Alex Fabrik��!� Boriska T��Qfor���a crue�hc �&e!a�y� !y disser�, talk announҷ,!zvi�O,they don't t�j nytha��a�� a����]��R!�2�ADV}\ b2 ed�ly� con��.�O�Regev%I�� is Kg<idiu�E�j Bogd�, kind!upp���(explicit er�7 co��2�M5�� I wr �2^\ *N �)� tos Papad�!�!� � some�^\ldots\6R!urses}{�E;a� .� � @ Kubiatowicz, Stu�RusseGuido$0ciagaluppi, Rrd Karp Y Satish Ra��fa->g��Pir�� Iro�l�!Qc�IS �"�*& �a, Tom Farber'KPg��sh�fi.��!� A st_S-��E�� ��t"� A��!�t4Q�jo�untity, w� got�A��_hI-|��preiF�"p B� cU�Slw)*�9�� �N� �%V$v�Z|it's tru ��� took��\t>�w,�$phy, Pizza2,�-��a�!9m� ,pst � i�� Thou��y� maiTi��yH� lib�`artd�ck�[3!!okAu�lI�)���"{"ity$tG� de�i m� fait( If In_w� t�< in my te��T)ies; i9�k,��k5u�Zhow uK�5iEtoV icip- eag�OL�A usua� rrot�-�m� !2�ndf s; �["c�� in q�$au���'� perpW+� 6(�o`q-/ -�es'�ap^T�#`is,'AZ tiginm� p�u�b,�rd�kI�� �pAl-e49@�b! ݫ . Now co�p��dev%smist-ens� pre-�  A�M!�itiE�a�� wild�%��f"� c��b"qeJm)?�Zum�e�nC"� BaLabs:��!� � �s���"Lovvr!� thirk� Pik@ t; Q ��m _ encouragA�L pursuea��es�*npayoff�a���a|in�'s-Tuk����1%�why�x�}rJ]\ Need�{o s�1I�� nopon�d�w$s��-[3#of�en��stock� 6C��+b�you.D%"�e�m�  in� bl[A�h!h1��I�6doundly u�of�ther F! �\ad<&fuy Re+�W�E wdif� �� unwa8#ng"�Po3*-@ t Se�A� Busy��s �a( my harebr|Z �Egen�&�p SAT�� ( chess-play�!H� E^!: s,�_ %b��B���!N gram�}�*y�h 9P a1?�~eag����T`,� ��I��ld suczGA1� ��t�me.@yOut,!u:,� ��Chung, F�Luo��@my Telluride roomAo J9Stock���(A(o war4+$e Ithaca we�\s, Lydia Fakundiny taugh��n�a6*�erry Ab!R![� aKw-�(� oost'urnAV!�clock b* furA�,�Z-im`��OayE�a p��Kh�R organiz�U,"w�a� fift��andT�nhy�� lark1 &='�'S� aA=A�H pa�LynchILo��*��)��he? ject)�oexdA�alu� !�aE I clumsil _]�E!��a C!k� �!�"�#NP}$-har�E�euct a u�i��)t (one �E I've%-�L !)�I%P�w��bsa@! i��DALs]I d�d5�e;only monte�I'd escaA��E#`*on-houڹh�.��L��sam�e�.re!fale -(^ri�"a e�g 6�A�fe/per1e��ep� to SIGIR`V �uor{S retri�p!r�[9>fil~ !*a ť5 ituJ[o�a" ���{!�*tb for M �%�s` warJ*hu��$,�juT)�=b&��3!ale� ����3s�Ei�a>s�+er,� �9 amaz�O �0i�_�E�E&#"aH�J�Ca friend��Z's��n>twelve �p�kv�mil!�+ �pa0jr��a ak � amid-5u it6Vell�7 alis� imi}! Newt�(Junior High�Z ool;A6br-p�b�!Es in m�^ndm�m�u*lan�=�+z�~��+:,(�I�n't�!��m qtwenty-t�-of harpE$kv\#�=cho�,n noodle souj! doub} Ua PlanY2i�T>a���� po'ia(� ��� n'��ca s MY9 ty.�ho agB � ta�A�h icl�,at�k*x�%^ro� d 36\y\�7*!�S{8�"^m�$l' �]���+�ge curv��^ pace!�, a ne^ove-�e�p on s��>va!emptya�f�A�^6+�&. , 2k%������vN1\�*� fy�a scr��%you"l��1�� Yet � ���oe�\ I su�t5 !Os��g�U a�F�^omen��jailRY�source�of �D��ir�y� marg1s evan�'mnŧur�piL<O�U*0uU�}o� , w�+.3zA�;S#M��u�8�[�k re�t� �'K'ta6+�!wT��"�"RNixeV4Q�, uai^ ill�c �+inuoi�\u8�a�PkAA `)�As A� pass� �6�updAA���o Uqrulx.~A>�a��%$O ofp5�+996---I�.b�E�gChurch-T�!Yi� y suf};Cr0� ���B.�9� y�8 �V��� e M4cy.\footnote{HR B� Lh2�N*��!PVrna0���io^� orieR� `f I am�p�9�ts-D ard �i�:l stepp%�he is�*c)j�L-nthems��&?i�)�1im�p��(� .} \ So a���  p;�&Eide��+da �7Max�a<%כs,\%Loz^ari�&�&�m�a���,F!.΂c#ayu�"�ccu#3Conwa% Gx (�(see Fi�.� c'fig})?% �CdMACRO{\FRAME{ftbpFU}{3.024W>P{1.7883in}{0pt}{\Qcb[>l %m]{I�J�9�cac 2D�.re gri9�0`dead' %or `a�':1onm �/e� nb��}5Q��: %�9AO�II�eeZ�0�ite!�o�=d��� lex, unpr�Wh%%b=iorOI<�:y y%�U`D=pil.�1:o in %�w =i�� nt?}!nlb=�} .ep�0%{\��al{ lD "S&� Word"; t`�<"GRAPHIC"; %main�-Ib-�o TRUE; �,play "USEDEFAvalid_�,"FA��Q) ; h!�t Q1G$epth 0pt; �%- 8$10.3511in;!�@- B7.755 cr�$ft "0.1957�top "1���# 8042#bottom 5225+�* 'u!G';-O�er�< "XNPEU";}}}% %B�b Expat932P2} [ptb]�e�2.g?;lics[ trim=2.025710in 4.05204 $6746in 0.0�!) =1O�/ dth=1q ]% B\c�fB� ¡K�J��ݾ� f��آ� "�:�FB��*a��"^� j�%����ULN�U Q' %EndYD�-&"he���H�8&q ǣshor}�n6oc 6?B�=�+[G)!"�"4. \ Then as no�qw, many people saw quantum computing as at best a speculative diversion from the \textquotedblleft real\ work\text right\ of i�er science. \ Why devote one's research career to a type .Bthat mZp never see application within T$lifetime, 8$faces daun��practical obstacles such as decoher�h, and whose most publicized/Xcess to date\ has been !+confirm ��,�` high probability, $15=3\�`s5$ \cite{vsbysc}? \ Iron�ly, I �, have agreedV` this view, had I not tak �HExtended Church-Tur!�HThesis so seriously!0a claim about%�ity!�pFor Shor's algorithm forces u% accept �lunder widely-believed assump!�s-� �!2licts�de experimentally-tested ru!�ofU� mechanics�,we currently �st!� them�Either !�1 R,is false, orFk musa7 modified'Vfacto%`!�lemJ(solvable in!^ss!�, polynomial A�8All three possiE%iA�`eem like wild, crackpot sq� ons---buta�leasta !(��$true! The!�ve!sundruwa_%�lq(my interest��9 �9$, far more!�n �i�l2�� Part � reason�qI am ne%� E�y, nefaE�H, nor number-theoree�ly!�A� enough �to ehungeredA�� )�s�,a $600$-digi�teger�I��it{do}aRnk�t:� ers would k$benign useE�A!1mportan)�beanthe simu�_on�-T physE��Lnd chemistry.\footnote{Followed closely by Recursive Fourier Sampling, parity!�,$n/2$\ queri�and effi��tl��cid�whea a graph!��a scorpion.} \ Also, as transistors�~ roac��de atomic scale, ideas from�U< areE�ly!�dbe surprising: after all, T celebraŐ j��W �abc�� volv�ly�0deterministicQ��, yetA�is harEZ(imagine how�eA�c��� prov�hem���p tists�long ago �� l� (Drandomness aboard.e}*� ��A few5� a�prima+ �A4in $\mathsf{P}�aks},�iirectedU�v��4L}$MAr�B old}i+$inapproximF A� 3-SAT unl� DP}% =QNP}$\ I�Hhastad}.}\ \ Likewi��tak�m�.[% ){lea%�aAk,� geneA�per�D ��E��$revisi e �. quesa�>�aa�aDx!��y.�oa� )?ionF �,A5�EA"�\,intrigues me�T$more. \ In�1 �I:�� rTt��E it{s� ly}Ɉ� p elus��Btz� ,urs Bohmians��Lbreakfast, Copenhagea lunch)�a linear�bine!�ay$-worlders �.oŋ�4hœmdinner--6.�tr��Lpopularizers, brushe!�@f arXiv preprintsũ fR � snor�YtE word)#q+eU*E %@eH.� so fears�%=e�si�E Bohr�$ Heisenber��tria�o arguŹ away� �emantYI�ba�- �X,unitary jawsZ� lex-valuS usks�o�[Ac1Fis!�re3� 4you aren't payAA�QnI�f�ll� le p��! superposi/r Look-h udde�8AeI]is gon) �� does it\M�eanal look? f�,'re governed�same )l al l% sEryGg e� the�� y do�%� it{you} e�� in 2� too,�haps rl !�a�U�s� you%tp4by `collapses'�� �o �m first%OrN)�(%��at �ve=a��-you, r�1 !Ch�=�a�you's,�  |S7I riddl�@%�,�5 PhilosophD ca� e 24 4>%jq7eTmeasur���\ ,2&e]\ �qsounds �9 !�)�eg��� nsomnia%� deli] ravA�in��!t�u& stood itA�Ba� �� *� $to reconci pic !"��_ �`` I happ� 4 tane�''&fac!+at!� (orAS��t I!)& s� �G$of definitZs.}�u��filE �k P terrZnd awI ?co�[bua�XBD, I� nk�, �o!tw�� real* )��in�� %�it{expo id}.�ItAy� j�tw��re�a thous� $states hel%n ghos� :�!J�"�  is tal, dn ro��@m� tud3� e w��&�Qci�rev�their�ks!�A-H !�Da five-��AzMa~m"�4even Schr\"{o}� er's ca�aۡ�ll inequ!Jp parti�\sc�. y up��, ante---forca us e�!�wa�� full5Dbr�wo stop s�%i we b)��O0ur� � is�AbaW;why Ric Feynman� f :qcI�0David DeutschK d $! oduced�& i��d place,t S,%�defense � a>���terpre� \ iss� @a famous challeng%� skep�� [p. 217]� }: if par2l��verse� a��lye]��}Clain howF�(works}. Un�.��� Iwld#q&9.!d%�jA,ofa�BetiNfA+ hat �AR� ly�� �X���very} �5lc�y�to� e�>0it acknowledg�e&(ast's exista��dis FG 89 � cagM O�I� adop�m<t�>�&)U&E,� instu of fre9admit� (!9s)\�`* $ A&us a]an � �M ��Ispl%N8�BstJ�% \)�2�u�uR3\ņ%�.5 �lcid� st2 �� school� a�.mI%0 s$ ��AbEwho� rI!< ing2��"� f�ctb(ned. In%������is!�i��%�{aB� ..can�d�_1rit{ask�A".Eno�v>$but answere',Yput old &�� (� �8w� they f� sho���eA�LetRg� anQzO� ( u���GJ�i� e!okpividual� ��%� a wavefun�-�b��/�0asFL�lyn NJ�N8mere po��5N \ W!Cwe-  ou�pu!�� goggl�E31���ph�/ o a diffe��: �it{� �ouuare need�eo make a�2�ȁJ%7�7��wa=8Hmanifest?} \ Arguab�heI ��]rel�,�&K 2G� � 2m�)��8�ee�t�a�n] 2G] 5�Z��� ��� sis graAJ=ecame\!qeEA,�œ remai(toATDwritten. Concrete� supp!�2UD $2^{nj5�:ll���7 ���a7S Nals��atAC�Ba��ced;K gniz6�y( $x$ (i.e.,aq"$f$��$f\!L( x\%�) =1$�� y0$\��$$y\neq x$)�TA���often wah� r�b�EweI��1�; �is,�er,� L ��ty !$1${,Bennett, Ber��,in, Brassard�Vazirani� bbbv}\�2wa4!j$\sim!�/2!�*PI�ne� ary,�%if !O���ppl�)I}$=��i2g !6La�G�r �g n�F�E/su��So-we 6a; ct�!OF�e%�erR($12|)\ �ne en-fB� �2y�ity2#Ev\ (5|}2bs)b���,��n�ela��&w�!b�:I""�2uA�b�endt(an absolute�� ExVn�2q �end%2�*�� *� r E�is��6ale~�N�Lc�*1 weA�� be w��ra|g��c�o��a �,le data poin� AE� �>v �UV hyp!����id�0of Conway's G� of Life�o arriv��&|un� %� ��6sa>�ng to � ��c�E intuN� keep� � 0iscard\ regar#%�l"r"!.�a�M� 8`ce � / t]��� ��rowI�� ll} "�.��A%window!34� )��s$ surg��tai� Bm���Z!a�^�� actuN!��!�S x co�Ex�� at a��qE� ��$ie54� at gly� %�t d�]0 ,�M� ,i "U�s!�� Basee� we EtodayC��ly:a`�it us) �ealG� 4 X } rbell| I'll�vidA�ly� A}��!2 {��!�\%re summar� Chap�$\ref{OVER}! S �Ered n.� I �!� -to-��.�,�� a+A� find�,tinct inputs�� $y$~"3 $�I�'case, by�ply�� sa� form6 over P �to�,��D!K"<��tm[its�ul\%e�p���E�T�>m $�\vert x�\ra�  +� )0) /\sqrt{2}$,W  �I1H $A�UoAS*�� fA �a]�%�E��see�S or!�I� both!�b task���r ds7no lo4#!�E,e�)hay&'k Wa�)"!� �,n ]Lwise empty barn! \ Na�thel ���isk(�"r b�}{C.%COL}\ɉ�,%!3e � :VE:���Na.�&� -z�%� y7c�  � at��st*< 5< �%6 Omi� tech�'~ail�is �E�b��� d!�n ways: \begin{enumerate} \item[(1)] Q2�)��!������ tM� cer�= �$it{global}�p�#�"a�_�%tIlo�pr)s�as P$)�ieE�� &d m�� . � 2)] Simon2j({s �$�(d-A��c�ofF� >hor},!tee ͝�)to��(no�iodic� orI�T !P stru��3)] An�!.�dteCRh M� Y�!�6�!�=�"��-� lete7 lem�ut)ma�d!�"1� G�%0Isomorphism, "g!y%o!A�! ve�(a�a lattic��9�li�,s in cryptogcic&h9l9=4)]�u�e�zl�z �hav!�E�.a�T#al zero- ��ofs23� � "� m�#d o�y-��rr�5)] WiQ)ei�of� ��i��!�e�s ɐňq�m�Ͳ "�0"� d M( ��>U�� ��$M |ghDa� 2IY "�lR� tTF6� 2-��;,�@)T)+lext�- in]. �$ut��!��!%a sons�)feK9�6)]�"jOp2���=��&2 "$ *) 63,JunA�/N��-� ss���2*;ly/ powerfuC,��� ��� ��9[7a� n hi�!-vari%�6�� ql"�e4 �sl ��entire~tor&a d d� yi� m�%%I�s.h'{5�. \end.j I�En$s (5), (6)� (7)� �� I\� n pu�$ld*I*6 "�� W�� �%�0 -to-�F!/, ��a�we�"� e�e ootp�$� dropping�tW� sE|it{Am}� orr��}B w #p� u�"MyL ���;I'dA�]thr_ }a;��a�Y"�"} [o*)� 0iA�e� ��tli2�1 �&f+��/�V#i %�!R�er��!�mi�W�iNv0holds up buil�a+a� �M]Iurns ��dso��t%�ex�!`%G�+"endN!�an * succeeds� �i�1��1w0OoI/���?,[PwhoC! !��$�ry exiv���!� O�$\log n$\9eds $10AStill��)�be nic��� *�>E)�y=�A�w4I'm�#t!0ly optiU/ic, I�;)|"J.�(�u�n'e�But� ne�"|3S �a1%<�"orn���"� prof� ly �"2�,c-a�!li�*5A�'!p backE��Lou�%a� �%��,�r_$IY� �"�4t$ede�isx!*doA`e�.t  MH2� aC\ldots \A6h!]!"ee 2D: \c� {Over�*\label}"� z�}} 2F��>er smea*r !/k k &<4 �,---ABE'c�/|n ectN`pax!' mach�-\an as* $�#d��)1 ��3b��ebl.�aM`$apse s�/m, ho|�FN2Ex2&�o� " l_�0he/ $ �JL$ ---From %iit{Quarxe} L ega�  1992�ce-fi�novel�� Greg Egan�R=� Q� ��eep)�w8c���Es}:� "�noh lumi?#2al3no�)pe-mo�&-��nd� A  axio!)zif a�6 etic�C10�is broad�4onch*?'�a�eVs .p bw�!�#��ld"Zl,�%!_edbiY\�abs��x titlI�or�7to�hasWEH� focu� ]�F� T�A�rbitrlcho�G*a�� evit� %1%��#%�7 ��.!�"�8)je*JT r|(f �-�f5 %J|wo!�cco�o� ` 8y&�8eF� mode#� �6d study�dam3=�;*�,&!8 gTyona��:]@,�-wa�B��la/�Ci�aC��% m;2 , le�! Xpre�n!��rk� S\.!=eari>�4,�am/.ie�")��.&�+As� Saul Stei�.'=9�&��0it{New Yorker�_�"ap�w�3< 9$^{th}$ Avenue��A�Hud08R#�1 e up�  spac�an Ja2 a�China,I�my�"�1[7�$nR3e�/4 �D0�� e� a gauge fK �pll��qt��M�!"JW�(�d>��t ![�@< asn*%�-�QU�. askE� al�< total [ lle� isor8� each�qZ�6 joD m�!�m�&��i�C !�s��Q! togeX. \(, trou� ini�Ajha�Rlt�# �co Fy nod polio! d�+aw��itu�zhas im�5a lot�;my hop$ �! (��jr s` to)���r%�>��A>rnah<y |?1)P�d v� �aAQ�#� �+, I U�#ed �+\ka�2'as���as�siA:! othA�QfhTh� :$MPLEXITY}\{ � s a��.�%�l.Y5�at 9eNb(t$103$�*of�in , $66$ do� �7/a!8gle ket\ symbol*�?T�  hones��!;�� donGM��.E�---("h& em<3sr qa]�>%!�� it{proof}�?.U sq bm���"� �Cg ��8�C��&o! ith,q� Amb|"s'* Stylnnualsa�6/ U�A}EE�?s}a�pr�yA�gonLB�� ? m�fq8!��er rule�!e (ing deadpan e+2)Ex�D����Lg�" i�=a g�ly s ific�Ain� !8, e.g., `Jesus'-� method.'��r�?% } ad�`r�orem �a-y}\!8B�"e�.'�B"\Dlemmah(bbcmwj"O�:ha� n�,es ru risCaf!K!u#��d�6Id , keU��mY+f�e�$ � �<:�7all!�v)[�� p�G�@pap�or "�; �x@ rev,col errfsis ad (�@ar:mlin!qch}% P0AFpAi��< a)b�$%�m* ? ?isW(d�A w seɲin�j�T POST!� V7(ank Andris q$� �5zi i�'�$ ur j� -i�IMCa}a�q��Iof] � rega�4R�@ of m��Bd2it{no� p*��g� �t� $on Boolean@ ��D7$"I � r:bf!{� �� zer circu�< &g}\ ( �i i�%&o�j�/� R��2M-D%�al stepe�*U,0sc�� madN1�B�.I:�INTRO!' � Y� 5()�,�Xfer.�v&�X�w!�� relev& acٛ)O.HG �e�}�a{-, i:3Esa�mat ��>#ul,�K�2 n to*DM;mq�A�&�9iY]�{M�y� %��M"��J. }��a (re��)�H&k&a/� "� A'toI�A�f,yOj !{�ofE�y�aKAwa9( ] NSUM!�\ "�*���ual � ! I\\,�LIZdrawn ��)-r�gub�j�Co`#P�7�_&(} 6��7*!i(��I�E�E�y%�i��� ��(��.�5Gi� &' $X$k"{ 1, ,n\ \} $A�F$6#(�0$n$1�)E3 B� Q6��i�e-%,l w3,,(&mis�A���K-�ase!�H6!��wa!o)r41o $X$ 4o �A2�4]I�BX\�� ( i)) �$a$i+Cl�\!�L*1I*� >+'{�}dure M +1$\�#��8|&%� \N aI(*�'A���o�G��2�birthday| adox2�E% :)I$23$\ pe�S�k" oom - �-S$a $50\%$\ �Pcat�a��� sh�!�/�N!�c=s%�he�b� it{pairs}T �!#Simil-v+I\ ]N�D3"^+�=$X�&t2+?-�3uni�%� K*��s,\�n�L�tJ �+ tza j(� < $i\�6j��*EyUpYo=U�jM� $eYr�Ees�ZMCe��!� is easi=(�B�:� ,\6�!n4ed-[C�Ed!/:{1R�$\ThetaiL \-Y �X.�7ux1�� am���In�7.D7H\o yer%� Tapp+ bht} ga�T�Z9�%vQM�O �n^{1/3�"�P)OeD�.i�a describe: the b2�e,EeyAc��Tt $ q$-d�� nYn[I���2UeC2/3C:%*�7's�#oS8 U�,E�ide< ���\6-%�2Imarked2�?\�7U�J� Qإ[. / $j$)�� An�"j=T!�No�+. �)R$e:!!�=M|^%* / Z-#EA�&� �ariisO!k-�=n"$o,�G� }+$ er�De�J�� s".� NT�%��.�mAI� w!'� U��%��5ny}N�otVF��-$\Omegm� %5R* \ Pr .K�U 9� tf%tr"@:`1\EG) $E �(IU:hmP2Yof>D�7� $Xp3F� 1sew)��lem}: ��o� to in�'�4s $X:�H.R .. ��w ( y ,2.y �$Y�O P&� 6Q�ci&6 % \[4�k1 �)  , �Ym( / .. R\} \] {>"* $1.1q'l�.�*(9$.,!�B � F { V�as��AzU�d !�9LPA�� s�m�symmetr&"itSeVp$= 2���M�F6�"� HW �@+Wf�Y���Shi��shi}, K� k },"zj��$Midrijanis 7m^!H��\� ��  wm `U%us� &u PROLOGUE%!��2�6 monstrPV��ai�.a brun�2ahSachq �+P-w>����5� G�12S2 ARx�VSbDDVM2n�'H3. Sub�pAAHs; sugg8� 4l�� 2j2a*j2��agaQG��P ack;� !�� ZHs�5 ��{A��""�SZK}\�\�t \UBQP � & /Z he��i� leI��F�7V�2a\of1 toco�ua�� .�>;. Bot orig4'*���quent!!a�DS<�on�5Ic@ &�m�"l{�P Nis6 $nd SzegedymV ns},!xd�uato�v��2�by  \, Buhrman, Cleve, Mosca,% de Wolfm�& a>%thod, ɝ"� Y�Iyb%s $T$��/�� $X$,�/X OT!OJ'� p��"� by a WNU=R$p�% X�� �?eD]�$2TE W� e�\�cia ?$-developed�aIA�e)cP�̅e�z* eory�/ N6n� �Dp�; x ur���O2��$TH2Inp �p_�Za RJEU!'Kb rk s�*ǵ�ppem�C m��^5�"!�}� �_�|���-�0seA`�` �iBI�}N�6n �..a(CT&2De�a"[m�Ub�7ghly �d �en�gB�ac�7)ins�#lyJ!-TZ��~B0�  a*@I� E�* �P�fso jhbl� a�fr�gE��GPAya��(�(as game-tre�A�)iB . [$ !�"��rje I�!N>w)-� roPKy}� be&���Z.� 1 :deg ~Wi�hs �^at�'vU goa�F j)J� "� 2����1t%ρ�z*a�� �F�$47�16��>@ fail�Q� � {L�@S%�*uPLSu&�r,/ER9 RFS}2�FF  ge# ts r!�g�#2�_z��"it{^�#Aj}1+q�hC`edJph $G=/V,E*1 a&  � $f:V (v5 bb{Z� }%�j4�bmum�x$f$�^�5 �Eex $v6�"c<v b) \leq&{<wz$all neighbr5$w$ovw r}@ $G �A4advI*{O Cxity mep\��}%^&���A�$f e�Nu 5�a�F�per}�Aڍ�$ adiabatic&,�A� (&�(�K&�A0\a!�annea�4�IIf�\�k�#$ hypercube*�0,1)\��PeHQ x Lle�yn, Tove�d Trick�M ltt}�.�L�[a�:�.��V6PO/\B<.~Nj� Aldou�a }�mB�&XF�� /2-oq&}*�!b�,t �*-�&� �>Oh4}/`�^�W�J;.�( ny .�<% it i !�A��Ef&L�l$\g^2n� & 1 2"�)2 ),I/Johns�d2f-,�Yannakak"Djpy},A�_*M!��� K 0n\��<�]&�g,�i%� *"is0m�&� �Gqu�*�'�-�Yers�) ,[ �@s�?%i2�j=���.�AIn ] +>ar, I!���analodof.� ���h,� &� �M}.� up!1quadr���3Ttz correspon ~ G E��(/�mxe�*7<�E�A��zIeH2}/���� N3!/.�!f&B% �!>�!�No�=]mJ+�zA"��'s zX=o�fi�6g /^ losea��� / ��p 1 \B@�$it �soaPR��r�!�aod00�)� walkEjysi)�n addyQ, I ��6[�U�or&(�I�!�$  calq*A�Gů�2n d$r=$3$�"�6e�6 A�>�re� KG@Bar-Yossef, Jayram Kerenid�x bjk}�by Aha�av  Regev < r}�&s���y � �1hek9i��<�_q �lhelefre�H}�op�h%|AsW�� discusM-B* ,aa�.\�&�ly 25�Santh#e� �s�W& !!D - :pl�.L "%*fL2/t AA�x2V&@; &�%[ u"O �j2� �#rb�Eof*�0.s��M!�l6�*-�"((%s2]�Z inspi�b���'Aɭl�;��/�l��a Zy � .v�x 2�� aj� "�IW$\f-,atorname*{D}L ( f `�M�!:,Q}_{2J0^{6 ��l,"��j&� �h�*� ��.� Gf$ɷ>�.� �f�{"|#-� d%��.�3�9ub�"pt `$2$'�#� y%he �#"wo-ld�3� -��eworthy� )'9s:�', b&�r}��')P�� �s�c�".�speed�F�pntrT5�7*:J(!U�.�"& s�U,"s�$U6$6$�.Ix "@� !:st �72w�Uo]`E)�is ]C+xqE>�OR� "�on bits: >,U�:�ORY�=n/SB=.LrAu-Bh�*bjof"($ �lEy!-Na�S����o���=A� T=Q��Fa�WI:�9��) �%��{progres!� faP�+巉��t ��&u t "� 6�R�DsV-10 >UQY nr<^�6pQ.p0��}�}H��)! llZ&s Z�   H arro*"6�!�.+>�R�^�*> n J�=N1.�q0Q�ȭB�(�T}E�LA]�Ji��nej~e2� N�Kv�:O�*est'w ��8��}F^C-�2���Z�W�Q��FWQRW! UB.TBCA� �: ax � !<�se9&�ex�#aI an`,� u�BjCaK#2=.3*FF� epG����� n, u��.���"B�R.�bZ��.`� ��/V$c_ &eN+v� �B�JH �n�V .AeJi �1�HvsvEm�m`teaT 4d�o$9s�FA5>G"�;�<�q"� gap�a��`'A�E�A� o�GarR�SV�B�Q�>*�O�4 in messag��unSOc�t}��our"} *�M�s:��LF�u+�-J�jven+�6gA1*�zalla�t�au�8s�)tca� c��"fE^2{�+��~ * i�s at &Ohp :�1of� ; cco2twf S Ba l�wKammAX�<�/arg�J�3N�� to U�Te*� } %!,6� illus�&s5F_�Q+A�ZURnY+CrC�d2�I�$B�&!�Aa�L��.UQ"� , aUQ��%x# recu��hy G!Dit):� a suTuW+�zi�"n� oughz�v typ�ly%�f c)@ it{twice}�~ ve to � Y��  Ji>ur i� <2�r� garba�� oՅ:�vc� �1n�5�?3b�~Y�branc�y:7d*�� se#Np?>Chnnett �b �Crgued\f��B �9 �9�2t\g2� �r�F�  �@%��H �ce�sly�toUJ>.��atU�Sd=M3nY's run^:ime!^�5~r�[L2�iYz~���M� �ZI`iM �Ny:D^{d��( $d�W dept�YM�o)�>�*nyoo avoi��$`8ial blowup? To&� " �d8�kN4f�Nv >�Fo8�TXaxQ�of&Pj�XVEjQv} @Va��e�� Bs%{(�p��+�9�r��-&��mam1A�a"�j6�-A!Xa+:�b�>!�g4y*J*f ���@�1\�0�.( d\ �CA���!�1D�B�x,md}%%08al�` suI,+r &L$�J�t5�IMA�d?J5 ,getA�w.�fewer}�n� �* R�,|!&* &ka�8 FDins��* %&Yno:�� y!� , ei��.�ad�ry�u"�!:n�*�\��� !Gr.�s- eleT�O24� ies\�}�$1�=!�xA�ntA�newFI��M�"��$i*�B: non?2t���R�>� XHb]*p �;es>�Z�@Ad@*�6=&�}Te=l�MBB=,a. $e0 '��� 1sAX�equip�+Y�.^2 a��&sJzP�<O| ily,� assu+D�0uE�+�)a�%� �s.]F�all-$0$%u$��/�Cd'�<�! 0\c(X0�Rb^EK� z�Q}WU9n�E�<rop�?�pT�T"�'AAef<%V  i�P�t�e.�/do�s�}PKn/rK!^��C l+�&�z)�;is�*p�`%�h' mix��2� (] uasv,sv:'� H�)�P!anAoQ�w��; ��r�L�(��|�x2w%fM�uނ5+�@ca�[u�Sr b�T.8h�U\!�fi*Oof&�0�0w�bv�nsu9�O'zarc DP�$�8m6�]5�lya-i�)�KE�it{�,�&"5�''deXe�� in N��! �v.;1/qN }��� a�+>"؍"� 5no"֍�A@�P*$-�* �q7 � .�2&i] .V\psi_{n�uVi.���E �* ~|thFu��az ni8�i�r�WA��sa7Nz2C�}=\&sfA1U&$.&�c��!1k�t��p /%hUZ }�:e*�A�c�@J��2��\��&� bl" sUin2Y}%�>A�� w�o�i;tht���Z halt��\u�F��e� t1L�!��2&9!ʁVc/caބwEr>Ma�[M��\m ?cfdd5I 'M�E�J�F�Ra>AD� �:��N�32�|� \ UT NP}$"�hU in}S��1 � s�i:�F�\�i�2�e �A�6�!9F�,2� �BQU !7M ��24�9? %H�e]VPUTrOmeO�(dlyB,6�!� ^ b� k2OfA�5�� d we%�D �Rto �*� cf�K%h�IuNso �Qwu�7>"ea(>��A.�p�5out6�5^?M\&�"h�@�9n�ti�"L,  �n�dAU���|tra��A�V�g�� �*��2/Ta&��.�.� Z�, �]��]:\ q�lbeno�,e].-��sorR thE- a?-�EQ/|u�nC NDneC�n� po�_proc8&d*E*! RD�Yp^Be#s�BNI+"teq"D9u��o . �y&� � e*o &� 0>�*\ s>e! ^{m}�  $6C))par��$�@)��A�BHD}^{1J�& mB<\% V8\te>&1Z/LE\�xrA�6>^�I�a6�!?7Ak2c���f�dB�x�.�e;pV�!~x>A�Hb%xanA��#a�r5� e��co�2�%O\2d�$%<, Nayak, Ta-Shma�V6iantv}.��t��Z��K� �4an��<NP*t�< \������exM�P �\�^!��$�%p}�$:��+ re�L� ��� :��L K�Tl*�}^IP8ly�m^A;�� �� $�!vs�asen�tnco��mh�o>4���NP� \"�l�~� asc�Vf�n`;j�!&Z �be�:(��a�RM2i<[t�K��� &�N�)�we*�0@yMz�9 ��E� *D !��)�Q�of *w"�:�@i�i�bduˌCm�-� s�2U~O%sayA�_z�MnN98~ $n$(8s, $k2Eh�<G8?yr&|)8# s $o��5B�#  \"%S�N.?Ply Klauck, \v{S}palekpd 6�> ksw}��[?to w�Ik�z)�zJJ �Oa�rJ.w1&"L>at >^{-6<k�� ` _��X�ll10the mareYq9s�FI :Fxi�yLnoF�<alF' % \ +.�aCby-�s�l�*�J+m�Aځ�o, ,a���)��K�"q< baX�- not ,Z>O$\-�$6�A G!�rm�,\��a���XcUd.,>�"�MA�Pr 0ly,M?�QkEL:ts!�d�  To/ceMoe�a V_, "�06�'sL<r�Ic��2gby r"tde��"x�4�4 "er Kva�1�&� s�A,V. A. Markov yo��A�A�A%��third��N a?a�E�ra*�`-}�a�a$=�Y5߂� \>$[ WMob$^o�'P2hE0�h.�j&X��֛�iv n2C�pUe%nu�6&� *! �?"�WMod�/R!�ty*+MAR+e{tΛ!e�!k)�aXz����, hin �!8))Wm�i=a�in�I�2\�D�V ^!��bXSd�W��\2#���onshi0+_ZQ��caD[5�9 2\W?��Ct�LAg!�wi�Rab{ ��:� R]a��?� �v4�- e*�x*� Fn!� ird,���G a9\dkǐ�- �=eE�� ���Eb2��!��Am�@2# doaUy#  i v�&�1 SKEP} to\iSQCHf[add{,A�H Q�yE�D�9�@s�$:�SUMe� &jX:g$S"�is�5"g2o�#ing���>��3�A "�!E�Q�JE�Yn$a �.-�Jva�Y�A�2|$9l�/s&!�ubrief�R�F�,Leonid Levin�4� iZ�"�Z�6Z| ;8!N�#e�ava�]N�EXs�2 wX� �En-c�&HqIe�i�j�'�Ges"i�!�sP� Ln:8�Mpo� m Tiz�e� &�=p.�cp| e�5:$!�q mea9ica�ab�'�$Q#ter�FveVę�5�aompat�j���&p��Ϣy3J�ɔe bul�u!g!�o�%~$sj|op &�Jra\D%��y New Kin�� `�%uwol/�@�T��������h'~�1"��ims�-�: ,cellular-autRsonVBF=� so-�&*�HB�h*I vi�ns A�N���*1��Da�%fo t2%�!�*,1L ��i2��->�$ shJ�v\ �&��like-��%�)�I;��in!D�z�# ��aX!posal �es�lCw7�at�K�visticT=cau=in�fan��No�*> �\!�very " Nt��Oy z/��s�<s$�)�!칢�C:��iTe�+�SP�.�b MLINB� b8J e�ľd(a�`gu� ���%J@f7f�-nh� �5]I���a n�al q�Sure/�5�or}_�S&�x���!K���4Cexpf��S�B�׮)�e�" <�a_]�U!�inz�f`(a2�4n�:vi�q�9��Z< strengt��*� 7b�?a�ngAe/-�s��Js, "�H�$�Yohb�R= ؎2(8[1m�(z)e.în��F��  b�� da�(if� Qhow�&ey%�!S�vy am I�"b1'qk%��] SI&al �]i3w�� fe!m] �K)�Ix amd,. ! \�T goal �nAto*x-m�Aa�deb�;).�� �B�9JO ���Y . M�Q=��m. er\.�a- dio�N� � ��5gpIe�}aTAny� $-qubit purM�.I! NJ!7"�Qza f*�vF- leaf�8�< ).�!>�$\3.!1\6 �_le - [ non-_M%ex�>feM(a �/2�/f) tens/kx�'t�)b�Ō"�!Q� b `.��N,�:"8G�4um*@G��q�x� )FũJ�V�p��)%!a�{�  fcuE�)�� �(~K�z�p)�a*l�$}\B �?.to M�"�G#|!>Q�"C "�H5[�#�&%+:�� 2Qva��:(�i[l-��V�F�6<\o*�!w Vc%z$\alph+ -ps:Q+\by` #J� �I� 'dR?J �0&�X )/��Se)a�m�k�vVE���4P2��l9�for��l΋I"�B+�'�7�c4B.U2�Sm^�0ulrze�Raz_ (raz,raz:nc2�;�-���Q��?UL�9o .#,is&{W(�r�9�er�J�s)�9O$6 \log"�H }�I����0��mQ���V��,�)�a�_6 (j�zr� ��� s.� � 1,�lab�}�rg6�P >m\�al x$wedi*�i 9i�X asympta�%!Yl1onspC�#F�)!�riw]spĢ� q 2�^[ref~�!i�i�P�Jpus���)����plaus2�y.[BIt1-�"�(�Y)�&.�fortunat@� I� -� N�R @�z*8$, Raz4TY!_������/ e2��aa z��a�O� )�AVdy��6i�e�s%�i�JFv�l�� �� �Aog�oɹ��)͕G&!wq��2��.5xM�DI�,JNX� elopO/5 � �AEA�of"t Zf��ׄa�� :6�V�5!�A own �---�J���b調��iiK��* ��D&7��.A �/a r �&'IRA��Z� y ���n@e ��  $i�A��3AH� hierQy&i PH��A�)8\�2&&�^M'a '&]z._ �iz��s 2AG]>.��2'%{\��ta�"&��&��&�%m@�� )R%�e� $yWS/�a2+25EN:�}MAi�*I 5*}; co��NJU<�IA��k�f� I�a���� ��a���E2L%sb B!o-)�N��\ #,si�.Jer-Vc��t�on�E�L�"� rk��<ak�4 �� �&? 'A�WVvalidR;6� pB�%!'m�3�$A:�"�E!!�S� al R�u } A2��={ � bc w!T���(� *Fly�0 ival�(�>a_�ss6!�>I wey ign�a�f"�s�F�lG��S1Ib-�pu�: s, s"l1wfc����yJ�I� easy��1�9��q!ru y1�)2ing�S9� i �� -&�Ns,@ 6F �tida��)���edup.&�IfJD�Z �`a�+ ^�"V�of�  $2kJa%�d5supM�}f�1,:�-{�ib�tZ:;�coDd�>�en0ISo,ea���dUx�"�ty���Tq�]"� ?_��:���NgA roboJ��"�3eRa� a 2-D griE���&("F*&6"A a��*�"A.mu��e�A�d� ß!sj&�n�i�AAq�M W;�Oja�4u:�{�O.6 How ���_e�HI9U#%�� ? \ bu�Ta(ed na\"{\i}�t�e " 9Bero---��i2\9J$M��$tR*$� .�#�,vo!� e-Wacros e%E �@���-TA��So��#"�>�)�!�Benioff�#b :%�}7 c!=Y�c()'$.� as�y"G�&8 _)�f�Z!�ra]�a^3� 12or|� as�"� �f. Sad�z��� �R *u� A��s 9�\[� �"%u�H>�{�|*�" we d�=Akx� seq�w�1ܼ ��it{B^���*Rwer ,!�2�t cru�,@]al.zKn�:"SU2� GG"hows � � e� aY�B�a�i��qug(�Z4��&�S\�"�^{3/2}.�FM�"m%'�%v�ja>vviJA �!��1Z�d�meBSal5Z�4n�L��$d\geq3� ��7d�A *�E��: �PA�Qd��2>.�!�܉�Ed��"�/A�� )Z "7)s \i�mat%B2;\Razborovm�r :cc'��e)�' *�U�& B�h�v�h�pWigderҌbcw]Tks&* �hoyerde�.>�#&�./ur-�}�� ndle���� s�E9h�*�M�Ys :��?ie~�e expaEIa�?�!q6�t���"�new9o&�D��*� mUn׭phP�!\� ���a EY�&�H���XE�i/��m�9 starfish2� ��Of�Ib*e�!y &�w� be SQ`�mHY`�'�-�iA�Efu:�F�% *$!��nga`o�NEhol"|�gl�F e<,�sca�3n8 d�t��S$+ing$Nsi:*�� it�� cosmz� � �w$$\Lambda>0��=��ӥ,rai(bQ Q"� )lAL: A LR�ua�A$+atdfPtld��1\��6�`FC�ly,�ar�al)�"�%�5]�x*�6� ��t+nX IyB6$�0*�!�d*a-BBP}�nS"g%# i<`cha+er* l2;\� an'4emeICy 3{��o0�8A�:N�<{^N��a�A ha�se�0�V�.�a�jdecad�!�!n�.*of,A Beigel, R��ol�3d Spiel&�br��7>hbC*�.�1alh ��A��%��_���yre" ~-F$ 8 �-�-�i�� Fort�#�,� fr:pp}a>qA�.q*]-t�Ktruth-�"reA5��nd��*�H*���.�U;a�+�] ]j4�%���F ���>�!��2P/M}�Nal�/ec�f I�A�.�,o2�"  �*~ �=572�}�non�*1transb�m/Fhy��� A͉�7m."\9�g=U!Mov( ^{p( (sui!�y��L� zed)p2sw8$p0?2��=�eG�3�:'Ŏ� }el!z;\�9��� t�M\�2% P}$;� �l h/-�.mYFP�/�~ p\in�H{ 4,6,8�z-*} �" �Ʌ2)>��6�SPACE!9��DK$�K�:�G+ %��me bram�d Lloyq�al�v)�at~����Yq �k�u��-V�B�;�\#R�B�*�a��SB��'run( Baco�zb >��k���e5� volvP ��*�v�#""�5��.�le��t�a ob����!eW� �w :dream���a�uƁ�N��b��lR:��L�;^!{ a ti�Nito�0[(!draa��n'� .� # Pq9He�y*� �0A0j5�Qo2sp, buBf�8Wxake&8�sqJr�L��n�W�J;7km �th��ut�&tra�o�8Pticle�� sF� bjIc� � flipA�.�&<�_ vaS.��F��3�"r{ � n&!@ � �*X�7 }�|Or��heI�:&�#QnN39%G���Ah� a*��� � lX ��de�s\a-7mHw*T�.&� spit4/ � ,>��m schr:@ er},��֓boh�/�.bel������- �� it{h+} -var^�eie "� &�� uppl�"�O1-��!2%Ev"�x�Y�%�bl�I�9 C.�DvB��z�a dynam%rulH)sn4���gc pred^�"� yI�rec�ed1n�6���[EP�.��&"iaPa��Go {�d ��": 2%2G�>��Y� �r�o�& $x_{1��at) $t (���@՞aa�tU�G -RD!i 00��(<P!>x�t% K 2}$?2�%�����%�9cU y�",�;"u�i�f��+�H$��!g�\�PhE�6E\| #dis�U abs�;tXq��*�'���Km�7 [:9y��� yQ���� �< ���_ at m��~�idto A,AR stoc}�icFA���&n y�9U�i6 s@�fi`P� ��@�< A� ��;ݛ%�azob#o satisf�q inv�g�  h%�:4 of Diekrqd �>��.���a��s�a�� j�oa�V�p��$ ~p�Let�Q flow�g�-m ic o�$zIu5g�;7cA.n�3Ta?��iy-5! two � .�2UbAw0B �mx*2�Yrobus�Z�S3�5�ori.qt�z\�@�3�@E �s� k���7  �[E ; _%ta��. �]��E�K�'%@ aSqg� u�AngV��! \.� ,_"�� �9�)ah� A�q֕1�-� ?fff>amr�a"E� ؝i�Xct�[ 5q� �erI�n.�i�y>�n as)f�ai�f �n��!��I-!� �(Graph Is"��A6n^��in :p �%� ed)$)�a�me}�i/&� SZK\ (C5f6 al Zero KN��2C�!�e4-" &�y��!�2"COL� t an\ o�F/nz  E&q ��d(�&n�(("JD*��: (D"�N%P&URTime)b!&�N�UN]i !�E?|���!I�A� s.I����I���E��� $N$-item&��C& N>��a�~�- o��� 3wFN}�>)�F� a�X � X �$ x$o%/��V��l�ebϡ�� !A;M.faz��5s�:5���Yus`C�3 ~�!�a)s \�B�ܜ:z0�&eVU-R"Sc6 !��& ummW�2� a"=E�#��5�B� a��q&�Io1�zE�6�erV? �^*< ����8���?� sqs d� 4ua�Bso��N^IU�E�R�u��٦���U%�6�!=�x�%x��� &��*� & Nc)qJ :Ch��Sheet�*ڤ6�e}J�If pig;�isa�t>'donkey flyJ� (SI �!F�'Z,��|�)E��Karp) ��=�s L�¬��,Le��c� 6*st@�M��o>�1 ���&��eu�e"m�G=sEz!�BX�---{�_ mea��*jf�%�capita4����Y��8!(�H-хPo �9\g Wa� Viv��� �f�D}Q-T.W6[;$ yes-or-no�As�s���JJ�a\!�$-edZ� Each*O =���� �} �$ge��!H�An&�a� ?L�;e } if�L���pu� t2pP�!��57� A�$kn^{c�:$V$k7c$A� �anA�t $�M� e ��Z&�1�%O& umbe�*  4.��S�!��� L�*�[@Ke �,��32e��8squ�/\C9"cv8( � -��"�$*�Q @&/� =,:�&N,~E:^e�c�%�? ���)�M����9(as@ gov'S�,y�� N�c����) d����(& " �^�w��1n �,r��:�[Pe� osita� Now,9?S (No*FA>� �2c�� %_J $��Va �2>:M�is `yes'9 an ީ1 w@d t$�y�l2�XQ�p��ARE fact��Ow� �hub veriE�!�&3�9�"�A� p8a8i!e S� a_- N� �a� � ��!'�c\s��,x(=m�0lo�#a�}��%T$\wedge,\vee,\urcorner: ax�r .)��q$R$ign�LG[�%KP��9�/ZJIU� �.b,G� s��,�/ ily-%�%�Au�M� � c RD�i��b�BK~i�ul�U*e-} a.fx �"�I��Oelp�r!1�2Up*AM2Q���E��*|j1UM H1r��).> I&� �!5, �/�)�O�*��4\���un} �U�%��&b��J�!�{���D\aa2 �co �2�ui "̓��C��e�_l }�� �6:�m�--zՀD� db�1�m�q�e'i&�� q�lN,&Z: s�ơ  � �!"c ᮁ�Y s i s�L�L�2�N]eV��-D&�m:6fA��A.�ǣw$Q .dcon������1#>.Q�1c�Q&(��i9@eA�6�5�21��2��,Z va5�m>ZP&*c! (l�#�be91P&"].!rBy�%��if%Y.I% J��V��s�&G�Om� a2O_aw�{e.yAMPfZe2�yAI��&\g ssum{� �r��.�!/\% � 7�.#�no^��ladner}�CanlD� �5F�� rmed��2�']�clude B) �1[ z-�i�'M"D Bor!l(S��&�g�$N,M$\Fj \5$N$�~\� O� eEdn $M$?EH��.6$-h��.1���jŐcp&0�"t1όm-�6ק�x�5$Zoo Junior�ZOO�I8IpK�a glose��"12�[D��.e *���andyK.?�A:d�Pis;m���@@h� ers Ris����\4�Sit�6 �v�h=[2RT�N��T�fW9 diagram�Iin Fig��� ccfi��k6"�F a !qY��m+t� $4007�e��sg��B�I�,�!�< web page (www.c5izoo). 9R"�#�bf{ (&� �:ce)h��!�q*2,f UR���!0*Zw��E����memor��u]m^s�[teq"_�,�y�3��"~$;Őloo�lrcll:N�l�.#EXA�1!(E&�rWf �� bB6' %N!R t � 2^{q�%(* {� �$�5 |&*| $q�3.>-% 5D1(�.�BP2�B)�-Erg�ϫ� � Y36@+.25^6�O}9]%�9+�{ @ , ДoutV6E��. I!-� �� !� ��:�_$2/-5u�8QUF�!/BU-o%�It�A|V $u!���H"�k� �iw}`8({ ��>y�>B��6.�6���)�uq�:�5� .E�Y�>� �R���b2F�1� f���,1/Aw�,""���9F!!�Ft^1*"a� z�$OIBX�-"l���k�]A�*`!4uth assignment�s satisfy $\varphi$. \ We have $\mathsf{NP}\subseteq\ PN@SPACE}$\ and alsoDBR1P}$. % P}^{ud\#P}}$ \textbf{(pronounced pquotedblleft P to the sharp-P6"$right)} is#| class of problems solvable by a.�l$\ machine that can access aF�D counting\ oracle.F�h\ \ Given a Boolean formula9�, this E return �number�|F�-�.�BQP.��Bounded-Error Quantum Polynomial-Time:� b� q ApAXtime algorithm, which g)S\ny instance, must output)�0orrect answer!v)�2 withEPability at least $2/3eMore in!�ationAT\in Chapter \ref{QUANTUM}RKR!EFn%Y,cite{bv,adh}.xE6xExactvp similar t.�F, excep!%ae2of -9nA�%Ube $1$%9ead!�5! Thismbhis extremely artificial; itnot ea clear how�defan#,ndependently�$the choicegate set!fBut%�$any reasona� -,]�}Bf!HB%.nP/A�.�}yL}$e�bf{MBY�4size advice)} ��.��JQ�E�, along E�a%�lem%�A�!(length $n$,!g��uJ� � str���m27 \ $z_{n}$[bi�.}� in $ne'DThe only constrain%�DP�L)� +on ��;Aon !�other2sabom�q�AO(wis��ee's\hbE s�v$rbitrarily�3 helpEY5gLI�� hard(sE�hat�R�Q)F Sinc:���es, ob�ing9EX1.Ayso on2�H.�:�$ Hierarchy��un�ofxNP}.rN.iN��>% & ,J4etc. \ Equival�B�%��/>� A� are}��Sreduci J $ following�[m: ally .y$x$Y�re exis�g*� $y$ such�A�all6F$z$, \ldots�� \A~ ( x,y,z, \Ey ) $A�� ied, E�&F %Bf ? \ H�! &O altern��s betweeJ.�NA?2� ��-s2�\�ifiers�aa�sta�0�q \ Sipsis :bpp}s $Lautemann !l}\��ed%�Y�V�HAg$while Toda M toda^HPHFF.�� .YMA.Y0Merlin ArthuryMB�%�� , if!^� �Z���!Q`yes,'!�n�z4omniscient wiz��0could provide�S:�proof!�e: factt w: el us�verify ���!e$ (� icalTd stic>�,��\%�  mo� 1/3�� pk �invalid2�r rejec   one)�5� �NJ MAJ�:� AM.�)� )���b��)R�G)�(become conv�{d2� af� }ay�r�interac� %�!_B4RIN5AM}% B^ a_CT�lA�eA{,at� AM}= MA}% �R\m�kvm2 SZK.�St�tEw4Zero Knowledgej��& poss�2��� sUzero-kUI�aOtocolsZB�!�B)�J@A{!@Although921$\A��$s nontrivims� Ņ4as graph isomo�sm-Pgmw},�0re�(,strong indic�� it � %it{not}z��A}"$ .��bhz}.% %TCIMACRO{\FRAME{ftbpFU}{3.105in 2428 $0pt}{\Qcb[!�n rel �am %$14$J ]{R0 Z/.}% %iXlb{ccfig}}{cc.eps}{\spe� 0{ language "S�I� � Word"; type "GRAPHIC"; %display "USEDEF$��_f�^"Fwidth �; he� 3-FLepth 0pt; original- 710.3511i9 B7.755 %cropE�"0.0493xtop 8756� 9309�(bottom 1855+�n� ')$';T-properties "XNPEU";}}!Y@BeginExpansion \b4{figure} [ptb]ce��$} \includeE��ics[ trim=0.510309in 1.438571in 0.71526 $964735in, ) =1M�^ dth=-n ]% 1�% \cap��Vg^7Zf jf\labelMe% \end� 1 %End94 � J�,] asytPLS}$,\TFa�** BQP/q���� u���_"� pathz will�4introduced thr���thesis�the�0e needed. \s�on{No�@on-4NOTATION}} In�u����� &� symbols��us� �o describe asymptotic growth rates: MpitemizeA\tem $Fb n"W =OG &"� NH� a�order $JR$;�Qs,RG\leq a+bN;\ � $n\geq01nd\ sombnegativW s $a,b� \f\Omega�Jy9��1R� t lI�Js9�J��Ahj� Thet��.� exac����J��� 1b Y���vo��  R�)�� than��J��but�E��{A>�" �se~ic $-bi� ��den� $%;\{ 0,1)�\} ^9� T�Jbinary[ ing�2 Htbigcup \nolimits_{i�NG{� style\ 8J7:Gj�3�� \ast���O�s��ORACLES��On�|�h-theore� con&u�Y�, agai�  in� �^Ha)��it{.vAAw�+ a subroutXb�� a�guarante�Z\ ute �Q fun � if w* no idea�!�-ţ-M usKsuper��pts*F.��.:�eT�D[ pR�.C�3"ha�, "&&#of� z"-�let� 5 \ SL fia,�m�fin_eOuG ŝz %ca call! ��2x"6 \a1.�:%Xbe madKI5 posi!U!0Further detai "1oI�modelE��C� �INTROLQCEWeA�ntifyA Ew!�U�!>�A)utousual�� -$f:^q�H�/arrowV($�OftenapthinkA�$f$h 1APF,  a!+�infinia� equeA�&yU�;n�r each )wv!�teg� �For e���7f y��$x\inN� �(if%[$f'�\� ) =1$?2hOIE�E�se�')��i}��istE�NkW every b���iCbA� ��s�inz�W $2�\ bits �%tea�$n$A�Orursaщ��a�� run%�in*<  � min�a tiny f�!�s�a�X put,@may? uAn S do better�Wa�discus��ch quesa�s,A���b�refuldis� uishOetwouZs:A� itself���a�m��I32V�!ryais toq�� ci�{� C�+(Cheat Sheet���}"> E�}J 4Somebody says � `You  those5]mechan!� �T vDd "+q^real} &s �&a��suH&%�pu� e� well�pyou|&masterU h� �,!� t�Ue&l � extMy Qylearn m�%)�A�A��K nd $8 r"�q; � Nh*��,N�)i� y2F � �!X ^{2}+�  �! !=1�����~XE�Y# WA�Also,�5oG ges}��E|�����----so�G).246� $�W��-� �,\"�hav� happened�a� teri�+G+ll steAI�>p�A�two4-n��=G^p�(>tBB$\ sum!!$1!�s�y � to�So far,!!mzas ���e"\d9������]+ies---�$J� c al�e2q1/2a� nd d%!=$y !;�simply] 't�E RO !ner�$Z�%cѥ*� arikin��)Ť'? t�+aA�P(���orm��per�p� it�C�&!H9 w2n �y a,�$9!A$�/e� it{stocha�  matrix"�� Dno&�����,wʼncolumnsA== A>A,8-��I:�yE&�M=5�u� unitv�� &� 5map!�yk(t kA�aY er.�(:)(U$� �ib�+if � inve�$U^{-1aA� lsconju|-$transpose )�$.) \ A�U���&!� stary%tr ��.�> ��/( spond%�Aq)c!�9c % \[�[� \gin{array} [c]{c}% 1\\ 0 \ra�] . \]����-=�isqb)�1@)�yU=��R{|\�@{1}{\sqrt{2}} & -F\\V+F*:>�,ʅI,=/to�f�TB�R�n}��� ef� �B�B \�U�R1=J�!�N- +r-:�%��now��`e�'~�% ��6�'�� !]�>}J 9a����&_ng ���w� �sa�we ap�%o�"�j $U$B eco� ime,�P� ��inglW� z#V$��Z�%�RSA��j�}% 0\\ 1N*y]in"Y:R1�cer�& ty (ACF�# |ufig})n &2.0465&2.0166 &&͍i]�(one %qubit]"�e{A凂� %�� IBJ�"U �Y %rep�n�b2�s� � plan�1TU� $U!\>,a $45^{\circ��~7erclockjrh#.}�&%p�& ��&m�2ain-a�t-� TRUE; �pv�& %�&1�&�&1�Ge��& %b�& �&A��& 2829�&�&�& 9746�&�( 6787(&�& 4540+�&�&1D'��&��&H2.928326in 3.520815 3258'0.196979*�&1O�&1q�&ÁL�&RU �T_�:��SInS �R L�e6R�O yO%�'!@�'e�( V�'A���� �E�randomizZ�6�}� J@ E�\�< �'s a dete� c ou/!wrA8��n � e@*�6alw�*Q ,*!��ve,"b�C!c":�"5  c�7l � =��b9� � mpGGvonsid� sour99�#2&%~� weird�9R>"�"q%?er� N$ Q�z# QCNQ<�abo"Kp&�iUoR�&Jce or�s�>8FV�!4 0it generalizeG � Fa lar��!UfP Inde in19 !�d#g� 1}u ysi)�6N$�Gs,-�f�1�*" B \�!Bn�W ;)Y�5.�a<ll �N�4�/�5m'" A: ���' from fir�asE�S?E��*" hasFw&X � \psi\i��=\sum_{zZ) sN}}� _{z}�nz2K� ere u�Wa �ua ���=1* �was je> said�1C{.' uggem �N Nature\�A� keep t�E#2^)�AN*� g2�+��MX��2ng ! �E� If $N=300�{lreadyK>ot�(�� ��RA� �n*A{a�goa�0�LVi�o exploi�g!��r4!par�l�1%+in!� 7wlawA� � � curre�%��m. �|��yT\�� S ��( #ia�wD!� [ rhe F?*mR�7}� �"Q�$, �X coll+.!߹�!hHow�,aQ a few��1�2��� A�A;ar)qthu)�:! 2��h� to w�22A�� cl� to $Acbecau! E�ѣh� "r�rib5'����d�Xat�n2�* �e��T)1��-hig2�A . M�A�icitly, &#Qͮ<.=%2ces�'ed\I!it{)s}>�ac|$lyAW����M^ $N$ o s (c/��a� tensor!�duce:A:ident*8&' l����2�xF�A.�9QR�cS1 & 0� &  � ,$N��Adl=, DeM��*aHuang$$^E2"=6�&�":�one]�~�% frac{3}{5*,4\\  &�+nff titute mBitY�al}�/񏅍,��o+y�cb�<�4o��roxim��$e!9�� desi�!accuracy�� )!�G�/!%%m6�<0un � � ense-�dbe�+A�it{��uit�I} a2�� drawn � a �*ps6FWi@: t loJ t��~&%� v'�&put t)resul�� a siE!�s�Iw<ll ��"b^@� ied;=4A�$v� R��J� f�  (�-|1Iis� �I�6w awa�� �K�*t z�I� ��^5B��mediate =s�l�yieldA/(H�=E�;o'�&bv�0G2-����it{�7no_JqG}� both�JI~he*� I#$are upper-f�F%�&PG�K�+. -A%0�-I important>.`E&�/BxIor �1KaeG�J ~2M- Fu3,� .�G�C&�&�+$$A$ prepar�BpE:{ $U_{xMT�requirI�E!%-��+�ee5&i� n� 0J� d5�u�F ity}Q u/m9��jE$�A�-$0�I� \ initial�'r� ^{\o*s N �We�%(= $L&�>xV5\�i.B!�\A�b /E s an%�s�+%FD �8_E"�,enume�9�9[(i)]0 �. LGB-/\m�s `1'�2?�8 �K 9[(iV notirY0VY2;M�� By r�.�qe\$k d��� !�maj�M�1�M� can boC".of!Kc�@��d$\ $1-2^{-p%�( *�:}%�#%yny.]/$p=8"�3-� �^2,a 1993 paper�Bernste�5V}+ ��$\footnote{_ &�(�%e,ZA� }>�76erm3J%q�TPJ �PN�e1"xYao {yao:bq{FKr KV�'s)#�3a�3v�Hq�mA�ł�-ne �5�%! thia44� Brass&-N b:qc} had��� F�M$\ (E�:�! :�I) a y�Nearlier2 [���#t l�"outm9�N��5�_6 \ re�AveE":�7.}!gTVI;�/�/z+a poinlBW,1�*{�b\&8W.�}� in pionee��/A�DeutschM�d !N,w/-dO/qc}%$ ��+wa�0M]�a, a full-fl�D���5}�a� of�?u�(alJ�ME9� "uld�`,cy=a��&st �6-2z8V�%�M�*H@@J�D��&U}&�KI:�.�$6(edr`it{��}� H3auass1%���$%%%02�expon!u� �) ore}Wad��V �� U���\%��. r imt7!?o~He.by Z� >� .) Zh\�,ga�. oe[%%'QhRecursv' Fourier S�ng ($\or�*{RFS}$)I�a��a�it�s �O3@ �S \log.XoV� que�/�=4Q$n:U !��!Sid�e�{e�7�MQeE � *5�3!�5�2n* �?ALB, i.e.->9LneqQ�A!f Soon� � Simo�<s }�de=*a�gap�&� EKsu��tta�on"*!!y�hm&rVGial. Pe�F�e�plGw� Shor��shor}6�M�*!ld�Lor � g�znd1� 1 rete logajW�=�  I��-curit�Ull�m rn crypto�F�U dp!)mF,%)� Wwo5mIt��l�I��z�� mill�A �a�` q{l�b�P-�:Ake�= kMs�a�*iodic&�8.�;1�P,RIoA , �% N)Q#� $R$�6���  he pe�!)$fiwA��"j 1�*� � �S,lemec$iR5E�Y *{�.�)� too�J%� . )��Fby�!��aB�Nn�! ����8�*?Aue�X�!HAXltE�a`� � 1 canonJh5.c_[ Gr 4'�tZMog}\�(method�Pmp e[-�*6Aaa(fault-toler�p tab,cs,gottesman:hamm,klz,stean�7�a�ussk !ȡE�0hA6�-� sHFu2? CvB�$FURTHERDEF�� �summar+F?fancier2a � !-�n�B�� ��edE� Part' MAR})%or�9S[�? ADV}A�,�? ( Q deal� ~tYAtT"�Iot xA��V�=\gammi Bidel�II11\6+�4&p&J�� R;�*(5.B��45�>y" �)��( ��:Q�/�A-�B3B�)�>::K1�>O>�-�>N>3  �bf{Inner2�= it{ip�<}"a�e6�7F- _{1}b� +\c=Y+)_{N.,N)�.r99�M&-�)=%�ry yA*6x Fxi ed as]�l�:�| �6�=^p2 q1}%J�6$N�]"#Zast$\�9��m\��j�2�C!�2��9�� � expe� &�Q�2:��2�F�$1��V-�^!�a` J 2S:phD�j Re]H2�jO2(BVe I�f2-JU =�O���8ay1+�N B^Q� ��(�^�Ethogonal.�Ge( M�:�s��n princiy_�6cho� oO �#b��t%M{ Jve;2�&  , 6��e=2- }�&�>o�j;u�2�9Fg$ (Wh|A�*�G�"N b_ � *�"S ly{m6m�r"�!�a "�of "�_'�:m6�j�=��!9%�cN^_B=-7bH=%We�� �!S&<non}-9�o$$n APo8AO�8 or Valued2U (POVM's)%o\ I� �%h ain"�ND� ese � gM� �E� inc�,h 6 7 ' s'U, s [Q��,Ɉ F)4ef�E� �a�-6�! (1*y; addi��#�,&q>�ncillas}Da�-}�7@�&2� �'ard2i)��� Q�6{:4 mq.p6���af*� Mixed B[e�#S�N�&on�^A�zV�� Az�F , SA�%�ure�s )�*�,!^m�9mą#�&1 �&� QjkinQ,aQT"� �)$[� "aA\u��"�' G)D@NT�&catch�'ough:�r�e�b�=A�o�"bq p !8�i< "ly �Gnon*��/�>= �Pa)�e����>6  �:S��7��Q�A%>�b:� kQvri�� *%nin\KitI&,��N6F6N 2@:H�U) /\�:b�.�no -y/Zo n�)BT1�6Mf 9>� we�S�%T� ��eѤ5�}��weU"o�$��6��E��:]Q�!}m�ay%�0@ it{maw%�]�.� Densc Matrl*���"4.=�C�afmaY-�*�d T�<c�[&�oC!qj�m]�J� *� f�"/ �/ ��4:�uNFz� P*� I�iq�a+\�s N� % x@ �( i,j CC entrN.I9_{i�0�z �QNow.?�%V� �N0 -W օ56��9F:�m�6�p�p>p>2 B�F�:+Z}AG}.-R!lrY�ai/,AH�5tiaxq � ite -�$\rho�trace�+�llows�+ rho=�!)ANh:72� %v\ ( 1-pU=uF= U�5\N �N+ll�e ^� & � ?*z  * ZL* � B�f�E ]qI �I ,  Z�.�3rR"�>a"� �� $U�"�"�):"+G �pUA �B��_���M�sH� ��F� =8�*%� �+6� P$j�mdia��J/lA��Pro��Qulo GS�F� n�2at �8����=l��%1qu!}Y!278.1~ 9 .�  exerc�E�I�:4V��U9�!6author "too lazy���%�ce�<ai1�,� �W+*� Te�D�Qnce�SuwD�PrN$a �7%]��(� .T:�/2�4 sigm�;V� x;#Y�M\� �NKsgu]� ��!� � was �Ay6� h�ximum2���1M-T?+�3T$�,;b�.�.1�\Ve�ho- �� _{:&!tr}}}{2a�&dŎ�G)E1" ��M !�&>1�a$ ��nAt\ $ �}% {2�#m���� \lambd�^$Vre� C&F A9A[!� eige�ku: �-:.SEnt�A2�1 �a j�%MwoM� I\p�-�r wriX ew2!5�  .� [he �2�F?B<V@$� �I� �is�V�Ie,�+};}~3�5�e-)d.�(Hamiltonian In!�r� ��yA imagi�-�/�ixevolv�0n*�O4inu]�>� ~4it.��A ��a:l &��� x $H�2 To f�AQB� $G ( tI�� e�lw�ed by)F.�wR�U $H$ V�Qu$t$ � step�� �|&�*HaP>U��1 equa�Yx�.}GSN�=e^{-iHt�ry#pl� I@ .K72in 2 GG� nd�!:r��2��7K#\�:{L�#f0eB�>�Yb} "2ZIn�g�< #"<^(bpJ!u\N&ZAUsofzis #_�!�&Q�2 � m�8F(RR�?<---Boris Tsirels"�%t*Y � Not�����ceE�!k popuTz�#� dec�_o*�W>�_q>Zaq}x fsd �\panaceY�%cm�- _Pdo/U R&�0to�av���)�+B�as +"�qe�l6@�1w� vAXaje�""e�ts''~$"8)_q�* �/'�J�<scan't��~n*Am9�$}� �Nih�P}�.6u�=�&\Jon.\ \.^�7ou�3sk��0&/r�&;assumingT.�p�.B(%�--A�u6K[��"��d&p �5's�Q bey�J our u$/0!�So�"r*E�qLk f-#:!�UVY�s�(2�YS�K�'in*I3ET&�\by brutBY ce}?Xis& n�B� .22�=t����K!�In('! c�Xng]28'3(aVa�p�3fpe&��p*orm�* �NR}] r=1}^{R.�rɫ *} g ( ") ` +� ' * M�x^{r}2� G.}N$��st $x,NQ a�as far���ke~hep�y�.(�$rn7,&�cg$����"�X black boxJ{!��5y =Y like�$Ee�� "*�'g�ciZ  is(icb�<�E�M�|.��put how@ M�d� Sou !�uag�ZS&�LO�hE<p@�A�U<8a�goRZV [).�a2A}� b�\ � 3c variN �|nd ?as61+C cide��&z!��Y;�On\&�, insp�;�)hoZ=, KeBhop��]wru�oJ�A treat�~[=or�a�6o�/:app���Ce�.ng�6�5�0Bil�5�d�:%@1�62Of.�1$#&D ~ /&x$ 1I�A,� }���Fs�/2�7xj�FnA K�f� =1$,Nkas few� �q9a'%Q& l��_o rV4 F_o�zlyM]wa�=|0i�W�4ݦ�� . A�-da�al�+�cBennett,&h3,"�5[1V:7bbv}\E u kYYc&�9��!��2����*�.�!�:i  sJrpr&�FT)h��yJ����Oz�0 G)�E�d��,c 4 a�9\��Kbea ��FA{AU��]�J4<�,�!*O2� ��r,!�cou�h$6or�1})�".��� ne�9YA�fb ientq����b�APEY e�;.'s1~ l=>�=A�t��,�?ce&�-��jdYM �-sL �a�`!s}� (J2"*%:0I?>:or ˆ �10�y�)�;B�RR� $e�2�*� �ZedJb�>�DR�X2�ZBO, #��!J �ia�R2Q CER}� K ň� me 4�L!�V �&�y�|� �EfQH:� ,"B�OA(��1}x� M� � vee�4 /n�e}FE n;� \�s.f :H����"&@\+.�� 膡G.�of*W  al�c��2�B.� b� =\2pF�abBI�$arison, $D�Ur�R.sn�2l�*BA�Wqc:��uQCgen�[��F<Ia�ll�>(Q\ roprpN�F�Z,��\�ETr�K"+ �dp�d�on�b���%R� $ (sM�2� ���}"�Prom���})!�Gond��"I�0�T];Jm�syCOL���\ �w/� � es.� r�xge�i�G>��J-{P^�"re -�ly!dm����L�2Io��})."O� Sepaaon� OSEP��I �zlie�| t Aq�s�  oaJ� �xShjy pear*�� TempestJDS� !im^"�~,4�a 2#&{Ņc��, how!���� \A�!�� \�r�2� )r�@f� The �@�-�.��. to W $�s�nlf(Baker, GillIfSolovay�bgsA�o �AeNA��&$�.��4&�IA}:~^{A�>Bas�e�y��d*Eo [a�K22z*�lyz:�s,ar � i�&cR,�i �(i)\ a�26�m���B�AM �H!��k!�At *� An$�}�O �R^k��im��"�G G�f]A *2�U Be �*b�c�K� �6� �d;͜lya �T�N  73 an u._� realFo�2�Vz+ ��=( LatA�QA�U��ho"$JVmp�Nwo9))(i&�_h:� �-�s &y qt 9 )zJy��Pca�{e!!ign��� issu!?prow a�im�U��a�e2� .��N��2��)~";^�F y����N3y�$!to q&�4 :k�8�݁�#�Bp#�'A�!��$N!)��s �f-!�-�`.H�Ged�X�� technC-4&��A�%>"�NE�it��vK�p��W{7"2� oblir2b  �pCk�an )b),���ba�we"Nenough!LA��N.�=�NՕ�qN%!F�`\@ � �}�6 ~� -�Q%���>D!�妡�n�N���otR�%��W� �@oe ^9;2�#f�%,�>: ��_pA���9%sf eq6&\�wQ 2��-��^N�Fit{ }]�E�� unx"�thaJwe2:codaC"�La[�'��t)��9k��՘ _k�bew*r�M�Z)��J�8�We�F Ld a�� p�� 15$ �S�*�bv�ee&v& q�a�B(M�� ( ��B5� ;fam�+ss Shami!T͋Vs,lfkny} P:�5�I�v�U �%� &��KatI"1��M�ev�of A0�;mea� %Oif%M�!zj Ċc1+T.� B�2���-FaZ�ierM�?"�� %Ia�M��a"dT^ leveAf conf�+1��NxA�a.n  message22 �n *��+r.\Wro��(Impagliazzoc :z aiv}!tip�,e Cook-Levin1�#(�a9�i*�5�N�(&t ,�!/Ano6�M�� a�A�Wwr an b�S.�BQR��&mt��M�n�(SQ3,�Ost��VsW*�O��.`s � �rco�w�ͤ*�! ��K�)Ex >ap f ?�)hy�u�*we3+r lis΅"x s� ,m�����q8gdra��yg ? MwZ��reefol�iessen]� ll"�*re�we �P �g---�g%,E4�u�Mprel�o"� 0��Uadiabah�$\"gZ�( l� �$�  3SAT�F��ʦBV&7D< "� �.���F,�Oaj�&� *�$%*�"�%%iSLwhe �!w>orAw�Fu�NA�<, van Dam, Mosca6�MSdmw$�~: n6 *pis &�"!trSwstr�g�zOO�'ha�5�9��<��be �as�wy��b��landscap-^did�*�i��U%ȱ� �%V�%I��Usa�" � �^�Y>�9cor��fggllp},tUl�Hallgren6 h �5�' �Ip1�hi}---d �92s �i �,We�� e]� nyBqK&�  analog��mL�Tetiz+%+t#�a7�n����R�AI�^h �iW !�� a���)_#b�l"DU�k~tod J"�yr� � �it�y)N #S�+yE�����2;%�u"��#O�we)p.���F9 SZKg!�-6� 25���[�E �4n}�+���"�m un�~iWse,�<�� �(A�hu}�n� � �:�X:� � ��tc!gpo.��2��"% !zpud!fA�6u<�J��In�h word ��Jno��_qBy foS��GK ori}�5usi�/lto sump!fsS��x�n.i~��B�rC� be (=&>)!+\�E��._�W�UI�6KRZ'\ M�UZ�`fL� ��.us�`E BU U a�U�.�"l-ngme�&A{$X��[Duitivoof�e�n�!s��&I/�& פf-�3*�-�"} T$X�#� alle!&�'!\��#�d@ t13��lP>su��xtoAXb& u�f�by6�� jl�s� �MM*u%_2l a��*4 "�G*>_n��in5p"֐mU�J way;1'�� e�A�2��C[nf+[Y� �KH�&�   �dV{YColli��?��'COL�#r #��h�0 By Col}�& �= :�%WLet:'4\a�2] h�\&Pk &"�&��&,��1�Ja,WI�g*X�� eŌj�f1)]M�4 -to-S(=.k�[m"b! � R�)!7"�f2]t B]�eZ%* V\�eaBXau twic�q�\a� l)Jg!�1��ɡ2�2(1)A� (2)\ hold%�(A�*nt��G�B�Xit{�+}�$Ue�/����4!�Cl�[y� � a�A�J�a*�SboD8an<�e2Mis�2PB".t ��s� hJy=Bwid�=�#ide�,a bench1e�86�of��� .�Ì�� ��n� >�qy\Byn^{1/5 ('�6:<.� *�#" %�@$b��1����b�s n �l O , du�Jg, H\o y�� Tapp� bht},�*a�3��6&6VER��a P.��M� I* �W./E©$.2Y!Q\ 9� �A�How go4��peedup53��s�n�Apq�Iap�"Vxq aX6by RainsEڴs}. �2�*|fai r.j/w� *� � un�,'s�- g:�t�dis*B �o��U!�"�B&]*1=�bbcmw}2/b%�to�3�USsAT��_A'eZ�6��"::bsB�$ ]Q,B�J8U2�Hhe block54A?�by Nis"i�n ��qsn�M�B �Mum&'Fw(90l^"�>)�� ) ��{+e�Giv�"II�ca4yAFo� ough� �0n� %� �KEy.�$�>"B4$n/2$� c s86B1�q�.oAYAmbainisadT>�,ama "} ~� A�bst=H�at ;w�n��% "P�� ��| a bi%lt&� �C���q� m�YATD���.�0ii]U^.,4gl`erG But �UKɫ�Rm'of�I"�E"�4�W�2�)�~b)>eEuA�Td after 1� fMI���i!�FNXM >1�Aj0*9{6B�ca�I ~����o�>/%f�)h�!3F9RCB.�S&R2:gV.�ġ�3 U7 s2A��x�r!�a�a��T5&>?%;))A��for��&� ��F?�:�^!,*V(&q(1t $.} �H�2��M�* "ir���D�.o"g �"�byj9�Their�|a�8to J�e:s P�~u� ��2- |1+=��"�C :�9 |F] ��.yt��c{�NJ!1.�,.� �A)�z�'!Jdegree�O"$2T�So!-7!8� any.Bap^y "e"�c/h�~ c,a� b(T+>UTK)> ��� >�a ZI�Zkey t�� rickA:���a�* \Gyv?te}�A fa,.Z lemmat  MinskXd P.st�<mSreH.� $�Q( "0�s(Q X��=K ring�$$q�)( |<| rB2EF%*)`!^Ham�D w�� X$),�K \[ t ku�=:�EX}\limi�Fv=k} � &�0\C� $\de"Cqc,�.&�RA+H�$I: ��9�.4\er��> <v  aP{� :dL$g$Qe:e$�B3@be� era* n $2eDE�: �� � oji�X$g=1$\��$g=�Oth�kpF�kOli�:terval3[*��]^7� ��$g�OeϡWy�priZWl�3 ��t v I� 3j�*MD�ř�Qm`:�!=of m�5 �q�~Ikn�,6K*by&E-�z*V� ���morymof Ehl��AsZel�&5 ez�Riv���Chene�)rc�M| �~ #*�iA�j�k 2D"�di�pOin�. 1t� k?JrkŃSetASh�shiX/\d�#�'��gh~o|d�2n �2�A#!���M��/�C�Ci}$w-M�A�=33� \ xA-�~�B "g���anE&K�N�4"F e[Sq$��tly\ K%`�k 9� -�� :col&&2] �\O.�@F!,a-��".F�By�H�oZi�0'-� (2 Q>�22�&�An� el �Ainc[-�ve� of d�a3ty�&�;neq j69A�8�2jM,��.��J�%D.�r� �,�+ofA�'I�$e._ I"e&8 n^{3]� Buhrm��&$dhhmswe�Re�� �*v&Q3 �U3walk}\ �p nov��lCobas &�./�at�:ch�aBn^%�$\.1bT�Jorgan� AT*�2�MOTIVAk�� \ motivatW*2n=��&捅\a/g,�*AFIcU��q��-r�ot� hash" �5 ��Zh[@subgroupQ�,�V�ual:m�I.Y=er�5� 2�PRELIM��:��s�Vpre�naC2:BIVAR}�Lv5!)ru�t�t:fT eu2��2r���Z �2�LB}Œ� t �=� argu�! �K��G2FOPEM!&;T"2s 25SETCOMP}�e� 6a�N7��� �!8%it{t4���51�}� n�2Br>�p�e*��S�K�  Q!*tBMi��lA�{6'���4p4$ROLOGUE} Ih%�0� �� y* 6 =�;��r� c�$� few!@t�J 2Qi��i8U=#�Fo�i�H� per�llk%�Ma�)HFo���o-�%ed 1�i�-%�bl�eoa+�*i er�to1(�r QCHV? �{O�  HardbE R��}  ʗ��!�Q)B��� jD�(��ngly)2b�u}c*�w��b�U� li''t�L��V� ing;�L� dam��,bs"���!�W" buil�]s�Fe digisUGn schem�<usefu_V�"a fX�6]� \{ H_&�@}��1I)*A aA� 8(p�"U $tyr��$ Q�-&$=2<\!Ia��A� @�actAM!AF�%1�5�����>�9)log"#�"[Q) +�"re�#U? all}>Nin-�]s*�tt�PPis �^8(� ��s�za{� {�&." modu^V"�%c�?M"� ���d"F� A"!<�@Vbd � �g set��hO���iex� &0enz�eN�CLle�� #V {2��bpj�A�) $G��")$H� G<6�G!o�m�sn��W $f:GI�ar{��.bb�\}$oAg�A,g�;inn�G  L ) ="�A .��Ez�nk;eO8+h  2�8be�P�ڡ��!co�k H� I%w-F�G "�n1�*i:e �ine[wW�pG/)�,m�Fg�~���~,�+.��Kitaev k :*^>Fffi�FvswG��Y8�o�/�F�s�1��($!p� �BAB����c2�� \=s�Qa&&$V�tbver $P$q�h7�Jv"5�6�K~$2^{n}�/)�^$*�or*��To �y� �e� �F,�� repe&:'��s� in_{|B�?F$ ,�M�F���d �IEo!� reup�P$xse)i$ back )V�� Thus#h8&�:� ��Z,��qan -l$A$��2H�6bLIh� I*/ EP ERASURE J&fj�M).�[. !Q06�Um}�m $m\geq n�!�(=�3%�5 #��"'wo kin�� �-� $f$:jd&A)]*t5� A})sE�AK�| � �J �| :�� $e��B5�fz�J�7 ]"� f �'"�&B)]o%� � � � (a��+q$by Kashefi�Q�9k �si��%��� ����) ����L �.  ��3v�.FR�I&�)�9� e�0��aM� �ionk ~ r ���`�*si3t�de��8�ygep�s0�.E��NX9 Jm| f��%�( *F%m*� s@E��A TZ �-�M;\%� it{m$�y �y$n_Dor��l One-�>q�E��zueN�Oi�)&ѳ(by�p�)Mif<~}i�/��ed&+ �n`� %W| FQ�R5�rh6ZR\� aAB���soa-y>g\>JB�>�� h �!]�-b�a�SK� !wNdG�s�XjUa2�. ���� csx�/J�&Yr �^-n:q?��b_ext�@a`&� *K��sa�bg D�!BF �6e, �%,$:�SetComp`-a mfaE��,iv! �/9GҴ�s,J�S� $Y=y\ �T y�-6� �, $iy'`,y�i&]�,2��a�^7&] !F��͕( b,s� � $b.[2�\ $�*�TV-I��,2(!I�(s�\��� $b=~eeF�$ �2* $b�$\ $S�h&� <Y$ are �u"2'y�\,� �� j� 9)[neq!�Hij%W-�Ya�( ��.x �@-alAcse����.) G �V% JM!�=%5(EW&EX)A&$X."L /.�f.c6�*�g�g*�Mg\cu� >� >� ��!geq1.1n$0,end25�ACf�<�#bZ �e��&;/ :/biŋ5�b�ly4wB>{#��a�4k �"�:"QudB�L� �,ck8i�[8��Watrou8w }��3K"�7>$membershipa�v< fa�o�z,�a3pL�� &xd%�"S1�e2n}�6m_{}� �X�W"�E| :�v  A>%V\p| �&�W 3 i{e���B{.�&���Hadamard'W)e��rst reg >��S���V}!=�-+!`�X� R��4�r�v zA�tw�B ۂ( � Z.6Za� 1)5 6/m?�Epai�5�� bser�� 8:~�8A��(Ѱ�* :�۟�u��z�� | b�� z no matd�gC1-�Es.�w�%&�,1/1���� 9r�,1f �2 .Q206]i52ket�;�"��>W25/js)P[B� 1&U 2J�no&� A*{�8�zx�?����B%YleqJ&�Midrijan�$c�Rm&�.� F�!E�X# /\lo.*�Q2..3z� m(f�sV� �: $"� ,�p� A(�3(�� ��Qd-�:�e� E�dw12�PP.D0&v} 2A$�t&�*$ &*Y5in6 "�_��A }{� Zis" ti��J�[BM�ery rl)s h z=M>_oj\�'� � ٕ&["}[ some�fied l[�z�B�W!4�.��9;��pe��x+��tary y.Ie��n3�.H�(!�T%�3B�*A��CC��Av�$�6 kall.)�Ai�=� is l�ris%��?F��\�MF\a�6�Z *t��&9*[a<�E itudE7.F>��y�ak'$t��e!�!�tb� KiX%�)leQDeltai��],h [�� 'E=h5 $.5H6 =0�i 4� hu%�P j"�+) 5�a�� �"a4�D^�+� -:2)p0V�eX�a�P�b e.�!- v% Bb�5�!bVt7-}v�R}J�r��-��*~aK"=* "=*�@Avwc0s �iU��} ��� induI�t ^�IL]u"�� F�`f yE��*4-�u� )t9 r�!?O CR��5,e squac��Ղ�$'g 4/�&� ,g  se ($t=0$� �4c� % ma||n�je��� �~ �I2;@Aw�U4�A��>bq,������wՍ~��� I� com㨥�h& �4 i6�)%�"1�] pri�K7$t���T#v V�.cB� =\cf1�h n.mf� h}Xcz.`B�,d0o��#on�!�m� "W�R�+t B"�.&K� F( } C�!S T�t( g,�f� in\Re�a %n,T�; $-���hsilattr?V�!��o��eB<�c@Js�N2"�@�@g$�.O$N$��#�[6)��1q\�]#3)]����Nn+� ef�10� �C/�4)]��03 $N=nN��;qu>95.Z;B$cal{D}sIu 2.{T��!R^�1!�>-�-sub"�. 21\*  doma�Xz "�M AEd�Vg6Si�!F27*��8pre��ly:A��B�J� f�V+>6�N0 $S8Hr�\` ��� SI� =N/EB��t4/do ܹ�1[5Z4 $\widehat{X}= x}&_2N}$1 �&�6��S$^�!�/;�� 6ia���` i4�s�� "� :�M�*� _ M.$�[n; $z=8���i� � cR*e1�$z�:�R�n�5EfN%>_2]iq[ `&� \e ]��1��� ��su�4 /S(er�L&�� ���5}�4e���ie2#`�1nd�~T����/3� re  #i7+2�9&o7>�P1B;9 &� E�>��F� �YA�|=P.G-"�7.)h | <0.182��(�A9"�$$A��~ a*>ms�=ad�P!�paramt&s�-�:6 � I� �I8 !(zv \ $%ybl\;6$r% ( I ��\a� $I]n"F 2�X e �h�1iP� � �RT�dI,.n�4� }, ��9�Q�# �V,�zOLso%QMalign*}V� &@ �CEX}\limi�ts_{X\in\mathcal{D}% _{n}\left( g,N\right)  [ PX\ |] \\ & =\operatorname*{EX}\limiJozm$ \sum_{I:rtI kL) \leq2t}\beta_{I}I#f�zMTM\gammaRI,9 � \end{align*} for some coefficients $�T$. We now calculate $f^�< $. \ Assume without loss of generality that for all $\Delta�(x_{i},h_{1}5.,.# x_{j"2"t\in I$, either $i\neq j$\ or $N<=h_{2}$, since o)wisz�=0!XDefine the ``range'' $Z�9�q$f $I$ to b 2set of �h$ such %$.� �� �!RLet $w>n =| J� F| $;�n we wri!�B. I\{ z!x(,\ldots,z_{BuaKe9\}%�,$\ $Clearly r(=0$\ unlessR:�atbA�probabilur2� .D =1$? \ The total=4$g$-to-1\ funcvse� dom�size $N �N!/E���!I+ ) ^�},$i}A�$can permuti&Aa� values arbitrarily, but must not count Aa �%kact only�in!  $N/g$\!5stant-] block����. Among5se�Hs, how many satisfy6K 2d)L \ Suppos�at,��each $1�� jJ�$E@ re are $r��1QY @$\ distinct $i$\ vV% a�j}\ri�A0IeECi�e>ra�Fm+\c�+rZ�p� =BZ .a]A�R�CN-J;�!$5�Q!outsid�I$�0 :0 E0V/��ich haveI8�r$g$ or $g-r���1 $E�o$i%zS>iQ�s+ wi2�Ji�P%���xzI})u� e��w �X}% %TCIMACRO{\dprod \no i=1}^R)9tBeginExpansion {\displaystyle\L�K %EndH�boY5}E{, Putting it� toge, \ \b�" n� # �f�F5 2�2M}8%}}e^ SmK5� YA�&5��`��N!������ \\ =%�Z=.xF>5�rdN/g;}{N!n5N/J/ .J�2�J�}}{������ҕ!Z}.� 5�V� }{n!)aN0��0V�-1���KZ� �� -iMJLc�J�IN� [ gnFj�Z��J�ON�O -j-D m��V2T,!nE_�6n2}U tilde {q� ,T,I��^;� �x� @r?Y�6��J��<&.���n.[ 2�Dn�iN� }^{2T��vLZ�N����N-g����R�n��N% �� �;�OZ�y�� � a bivari6$polynomial'b4degree at mostiMm2Tr +J:+<B ��F� �Aa�2T! (Not� 7 caZ�>g6� � is �eg ates $0�; is w�t ought(do.) \ Henc�V6� "��� �=�%n� �2�N2{rDq)| �6i�. *6����ov�r .����1.A�S< $N n+n"�10�q$ $T%y/3Ae also>%Bv �~E �-� I�� +1}{!�+*L��: & 4exp8�- ; 1}{5� n}{n- ( 2T+1�V/nN\}M@�0.8186�fall sudHly large $n$. Thus� $0!5&�YR41$��)| V)-- 6f � | <0.182!�and� are done. �(proof} \se�X{Lower Bound\label{LB}}eei�Tif a quantum algorithm�U colli �Plem makes few queries�I@en its acceptance/�:`be approximated by a low-�UNzJThis � comple��he> er b�oofU show5\nog�� existsZo do so,ag�z�n �io!*4eory result dur Rivline98rectangular reg!�$R=;[ 1,G �] \timesn,^V 0v\ RecallI�e.�$R�l$\ from Lemma \ref{univ},\ d�d� ( q m\max_&/,&TDR9�max?\{  vert\part�q} g-� ),�|n}{�K)bG-�p� 1 0RZN.ZV �����:�u�t� we requir)%"�1,nQA< �1�(}\ \ \text{aT\ }626 \"�95%��(�kis,�?$A$� guishes 1�)�2 6�error .i  $1/10$)�&NE=_�.�nZ)��](by elementa�oAus!Na|oJp%Es'e�2�N� g}>0.8-2�( ��5�@=\allowbreak0.436%�,$\,$An inequ���,Markov (see ��c�� ,ns})\ st� ���� aGF� $p$,� $bSq g��A6 b�a�$or all\ $a4aRq a"�%8)!��M Q]#5%[ - ]�aW%�% dJ� }{dx.@�I��-�}{�-�% }\de!�y p ��2� %4every �M "�� �g}, q�� in R)re�w k:�S.�)` T)C5  g-q6�!�1B�: N:�%^: GEkFor taka��\lceil.�)/\r$---or,�G spec�9� �=1! Y2���red � one F���, $g=1$. Fur more"� m� :Crepres&!an*� >gs�a)�,2�-e�x6�zw� ALcon�rV�clroyN� U��,E U-p�hmaximum-magnitude derivativE^�L $B# Bdi �� $�� =yN /n$GN�� G. � 1�$g^{\ast},N iN �beQ�L$R$��� weedv�^�,s attained. &�first0 =Ia�.�� 5�6� J�(� $&�)e ّ.�5>�I�d.�>p}{d6>�E���s>%J@ SoB�2T&��,n}1���" �Q&� 6�1.364+2 0 F/1+^/&� }5:� \minw@ �G}, �n}{TG}M�*� o�& SimilI$, s� A'm���\UZN$ BY * -�*� $\QY]Y�$.Y*p :Y| FVFm}{d�0 | >)(EY4ftF Yr!sq z�aRz�]O%�( ��h.G] FIV}:z.W c �ze2��} �Q. ) On�n���l�h%Tp!, optimized w�we� $G=n^{2�le"�%�QB�nQ�)�n�%�T} � !}_ ,\\Vc 6 3:����z4Set Comparison�SETCOMPH� I sketch��T)X$:�. :Setf�� >1�7hD( >i.M)ȁ_�)  �����&� as %ŻSEERASUREs �$ idea��[ foll?a� We need a�ributof inputS'$a parameteL$� K p R +!�one�oneI�� �*g=2E � "�* �le�?&PF?%B\ wouldC ill-1� eras4oracle�On�n h)p ��'it{not}����?$g>N�K.�0�'dard � �applyfto :��  +�H(ob� a se!z%� betw�e two!�Final�(�Z��be "�  "��)gc(c)sol)��*o&� $\kapp��m� $1�)R,!�rE^34=4g^{2}-12g+9.�� �draticź>r1r=6XFa1$� ��Foa��E�(on sequ�s $X$� Y�)mb5 ) hasee0 roughly $n/g�,w�� tell%vM�) apart the M� uE�an:,{A�o>�g � �ameEl bothA�(disadvantag a�, becau/.6 T creases9�AS raHn line M.,�F�sp{ sparse � quickly �,hweakenL- 2E$6Q�L*O$\aF2% $.pr"=,-}a(� a+ShiNshi},���( improve my2��j: �%J� �6�+ . C�y�1,MM �\Re^{3�0an&Un,� $��-super-F�} �X�if"�Penumerate} \item[(1)] �a�tegerE ��,%�3 �] $, ?2?NmlM+a�Es2Fn,B f�d1+1� 100� "} 6i3ig�vida�N�4)]�m�t" $N=n"5?.* u VM��6Z2$ YM=n��� =O*^�9�g,.�9e draw�H( X,YU���-�1 n},yy4� ��Y �t��$\�4L�v :�\ a,JsajWec cho�a�$$S\subseteQ� 1�12�  ��it��o� S �  =2�(�4n$L form�Rt��dom �%� �two�4s $S_{X},S_{Y}� SJt *2x.�G2M/^/�; 2�$,�>� a�2N� Next�t)W2�.�-1*�-&�X}="jx}Y 2N}$ $: �{i3�r!� �arrow)$$�iYi {yNj N}$ �j %��3�. !1l�4�5% 6iS!m$y/�� .1i!� a�s5se�6X_{S}M"{*51"�4xyk!Aa1nd $Y.3 e�1o}�2!�Sr�� �N=�]?5by�rnoff s� Pr&.).�86�1,��P[.{�\cup � +i�Vm�]� 2e^{-n/10iM!� "} >can�/B �P Tfo =n���1�1.17�gq � , at least $9��� Z�( >P��9nQ6�2F f�22����:� �-9xI@o�!% C!A� latterJz im� 4s an equivalen$9F9��er.u �6�j8.�� �U  retur at.� Pfary B -�>k? le�'$>4 n@;��2Vj�6m'*�#2meN]S]�:Şg"l l�"�!$2}O� V�$�if�%< 3}/8I�.�tB�($ɗB!$\, d2�( $8T$7%�w1-6� ab�,�k2RZ�2�ц"� �0 <\varepsilonEA�s| �O7 $0.$ <1/2� -u:�"[P S(]By analogyk L!�[f$},f�� multi6 .�of:a $2�over �ble� a�aj z�;�W\D.�<��,&�;� Let $&�=.= I�z aI� ) I1 &l $� $7%�\U rodu�8f �*�>� &,4$.8.�==_={\ $9�9�� �Q.kYi�.\+\ $� inct$\ .k F\9|�t%)�+.�1=r.'��8�.0Ao �=�F?]���~�R�)p] ;aC���Z��+R�+�n}�Z�? \V j�? ,<V�%A�for�;�=��:-( paireeUbZf/ r��2cZ @B�? b�?�?�?��&ZVF$\�/�qae� Z.�Y�F; m/.'!� @q�<=Z�� ^pi�wV� j&^`%X# $, JND:JN#JZ �-J�/2JF2F!�By E=�?e75�f�?M}{^& 1}{432Tas� [ \P�m[V2AAD]k|�92nK0*^0}{2.��+@2n '}� .�+i$0� ^��A$ given F�A +I�TR�.T Y}$ TV�A+$� b�lDd s�� ��,1�,.� !I;[ �D� �y5JDy���plici%B�i�z'� !R%,�Aat(#�N�*�>Xf�� J�^��vAM�Y���q?&+\,\,|~+�X<]�+M�>Ni�) !}{M!=4B�=+4i8b�9 �m91"�9J"6[6�4v,5_6�X,�5U{.Y-1��j�_6��%kapN-9�ԡuz�  $6>y�R A8Q=yn}���:�.b>?�3manipHing�&U(� ousl&� }-� )� ��r� \A0LVk9�'"�!7V3>�`  a*� .@$�q=:� �zJ�6 � ����Z� � R1�R \�!Tvd7 ��q argu�,%� $q� &S2 s $P\f �1&� n� ous t�Ba�H*� a��end{0� rema{YG| .��9�E TU1I@*R1�w12�x1* %PLe�J-2 v|16�� g����1"� $�)"MPenE b�HVN���1"�1 1|v�1B"]}B2 ��  $d(q)KE��-V��,��:�max �U1/�} � .�$ _B � pJ�1�%) �#6W 20%�X M��X�}�Ut"Y R' d�*�:&� >|:byi�i?a��.(��.,��|,�t �.A�re 6j�&^:I\& �m)v�.� E[ -&�.&�+ \G�.3M&�.�2:`!m�B&$�;,*�5 6�/% R:!�ev&=�a�[ 0,1I]���7t&+=O'./� TG�}�Q- Z��azS,,M�(6� �"inB\,b-*2, &2,b`, J2,&1,� 0��M.�"*FLe ձziP.O �R�� �tB�%andB�'8�'m�"2�v1h�+:x��(�#&w+ S�R�w+OR�(�i^�( �(7��ݞ\� b2SI) n�� 7r�(2/7��(������p�.�;Open Pr (s�(OPENCOL�(In�" orig& pap�nE�B�;, I lisf/four o\�lems:#N'A�>. �02�*%-" ; �;�Nnon�83�<.P\n�("6 �;�2�a �98-space tradeoffRH�Ea decid�w�:r�B�;� �:real *�  O�*u/is� tricA9toV%$��og  A\ qubits�Vn* The&^U9,*M+9y>U5�A !=,, ordinary G�%(r search be!�! best&)S"s�Curre�=canw)A���a�ultL% any}QM� < Boolean output,L%!NMss Ns sor�7�j@ non- C C1�s�=An�* N!�to �%c* rel4toE3$�#sf{SZK��F QMAvV��#sf 'EQ.@0Merlin Arthur:t,�9watrousm, Inm+ word?A�RE�"�" is.i+r*l(twoU*�t@fAS-�(be verifiedM� a smA �Tof2��@evmVc$A help'a!�c&2�v. K",!ti��� �!�q(p� N8l).�T$f��-in�nt und{efT�+ symmetry,B�.R}_cM  f�.E:� .�( 2.r.2l�@;@Ld? \chapter{Local SeD�^PLS�Z�A ' dj@5KaqM��c=sc2R.}\hfill it{G,A�un ,ed graph }$G� (V,E �"�(vAU= }$f:V $a�$E�bbi$i, fin�.l�minC7!�}i(it{f}/---!��=AitexlR$v#* }$f)� v �z leq w  AQAn�6bors }$w �q.�C willA�intere��7.��6�:"p#�yto �aiW-�,��- ery just �!N�$\��n!�V�� iA�d+0!kstic,�dom�2�!���s��S.�0$MOTIVATIONA�\ mot�8��@a�ore�wvC prac � i"XD expl���Cse�rst�l ough� !*M si� o�:e�� If $G�the"�DI�!��1N�! n cl>-2�, &�A$\ }qa��DR�(<\.y  \x3 �xe�!�6�`@A���\ extreme?G��a � � leng�)ͥIa6� 5ȡ� R��'\&N��-b����:� !�middl�0e�ic�F$v� $wE�!�u}~��,Z0=.B�q�N-&p0/2& onne $v$;*�] �\ P6, �Continu��$cursively e�is� ner until!�2�i und. S�R-���#6M�aY�`�Bmed�' �ness:�� % � hypercub����("^{n}%�E}�+�!� adjacT&n\ly they Hamm��!a _$1�%�D, Llewellyn, Tovey�STrick �ltt}\� �4 2- 2�/\e4.s .E \u&AqBZ m��ny6��Q�a�Cadvers� O��Intui�=�3)�u of9=���'� ri�1a ��!i ex cut} (���Dspl�IT%=�;o%�or�15���onents)!R�Al� to�� scenH Q3 of $f$-v%]:.92J!=%�)6 h9.� ex $-%�2�b�E�L�J,6[*�! [-1 ]e�second^ S�%Oo More�%� Vhe-��� ?E� does5� a!qi%9�;�-�� s^�,!�%j!�un ��d �a�h D���H�'3%�Oኁ oI�-.�2�%.jJKn(�_B?�� ,bny� wf\P4 onabQM][(.\footnote{u��J%_u|4�  t{# cha�� eriz�!5v��l term� ys.} \�NJ�,�Y�� ed %gAP�8!�doaeszCi�to-\ 2v E�Ju\5�رAy6�( >+'=' failI� lete�U�'Rof*{ ���By Yao's ,ax principle av0w� �:�a fixed�s��72}t�f$�(� s $f&_00@\} �� a:� m?c�>at<6�&p���+ym��RR��(fN3 high� a�b�*f� k3n � �a_Tak��9 e�be��)� sdo�Ea 6�aL0ra 5.!ke?G?���ow, Ald���a }\ hadE��6\;J�via a"� x walk},:�3Ch�3m?��0}^�Je%.�3� enc%(an unbiased{\�Aci�� us���% ous-�10�, eYkD;be.�R�%� )�bb{R}$.} �,ń2�1� st�ng [ v_{0a�ach9.A��2J� $�-�Sf hit� �&��/$v8=����T�  =2{t:v_{t}= � E�C� ��A�prE+=> _ wa� �uniqu{Q� mum ��Q�����t� i���t!ais visi�-� �$at step $t77 �‰ ) >9F _{t-*6T�UW; sophnyRI�-Cnalys!;i>Y aga ��\ werA3!~$�� /2-o� �9��Sexp� "# �����RnJ;a����to�� QFyI.QR� m� � r, Drosteѡ� djw}"� !e];r/�"���7?�$J =F� a#\ (Asb5��Min 2�PRELIM� is� �is&I��cX 2 #@a2�-u&� mixeH'"} nW��tepP .z�S�=��| aaf�+Yn1� A�!���.\ ��1Va}?z$a ~ &�M new1Bro�StoV@,\�gI believ� U���to� MWger3%�Cts� )9!�H@al%xis ba� on Au'%@"�  meth{gW� Sur�ing!l�^yields �nd hr)�)�r5-�'s) it{classk}�$A B{�Oad�l!-�2f ��Aalong�re� work}Kerenidq$nd de Wolfkk�z(by Aharonov)Regev %ar� �a�Eh�s1�illustr�^how"x� sl ���56�.AUgMa!Illo�=LJ� ;�� \{ 0&� F%n(I�+�=�21L>� F� /4}/2�a���>�Aq$#any.�rn� /2}/�H&?&L (�A�A��V���xI�a1>�s| ).b1A�of� e�-�A1o�k�VM���!�A�B�7�G�9eoknown up�� eMZ/3^0.EB\�� &9<�?55%F.C�qF�j(a $d$-dimenH\al gri%6 ^{1/d}�'�m � i$d\geq3$�! a���enڇ\�j2-�/+61��e�aN� , O.[FyY&�ENA)"#!]~s (no"� ) � previ�,I-�\ase.\&a .Tag6U!y� �\ Q� �I��s��lt}�Ip�Tu%discus��acs��, I rai�Ras�"�2�U ambCrus2 �\ jectur�a�S�!>HA܍�>�tof��"&�!&��it{- y} famil��)aJ� F!3X &)<g"2mEF`9�})�&��!�R�,kN7��&z ��2� squ�a��S�CI$tly Santha%J6v^ ss} �Vtad3r%.ŏ~co1�,�[ ing&=-�>�ykG#�?�19^{thu root (!)�2L9.�J�Kee�ific a�K"R ,A�}u�"4K� ; F's(no�A I�9�.V>.�rIad�J<be�?tha�%"�sN� l�G1`.3. e�n��developf/,"� m�� :pls}� �3)�NKJ�# �eO� myoue9~�3��+*�K�$u�Ya hyb�`.L"�I�'6z matc�]!��O up}5*"Mo"o�@ "� s organm ��� �2�b� =s���> ,�Y�I�io"AoO�2ed anneak`,5�adiabEM���q��& ? �sf{TFNPagy�""O�b�&�%.�&�% �`sa�=��ewG ic%SRg , inclu� =�{In6c(ADVERSARY}\qo�JuN �n �of.q%"� � ,An^t\%d�ve�l @u�:.Re'2��b=3�.SNAKE}Vt{&� snpe�!� stru�e�GYI; �4he twoB��RO� "�  /t��to �6������� it .%���5O�~ial&I $*�AYBa `� "6'g$�cM_),GRAPHS}��. frame� a pe����of �s:!�"�'��� e�ABOOLEAN!wm#:� � B�DDIM}�$�f{M�"iorT6} [%��]QhOst effaVv�> apon9c%v) g�"t �UI�e� m!��*jRic&s,`$�O$ backtrack �;r,�g�S.4nor�nZ)'s&=�WareA�Furcm�^E�qj+�*g, 2(broadlC�~d([\��1 � �ngF! ks bS W�)!�ci�Na �I�)��o evo�Rary bio�C gene: _�3W!physic��hA��a��� ��yV7a5@otd"�$� �t���impor�DN+n�pe3 !�conven!�a�Ysdo*�balڀgh6i E�l�!%� s � �he�fi; ) flrNt�hcy�ge�uc�-�E�a�Ifi�� cor^ bj roll"��a�A�son Mm$�so �!!O1M�!fA�ly � s---�A,q�um---i- trin9ly ��t �thu;B u�es�!�ieek fI��l�YXrB�i�n cV�,� ��,it{unimodal}�ts (��h�{n���a�Pa"global�um)��  /um �be�� fS &"IZW falseM 1'7 L�#�< w#A�* *�%�  if�is"%� y����6 treatL�X a bl��boxvexV!`0� !�A�), (!  ine�r5k \ M+�exA�I�co��S�ع��}1 view)�"�( upsho�!��5Iis" �rce u��confroniqu��on:w�\� `A�-world'\q` �+A��% ELu �lwhy� =E�!w�ch��!3d&�#�#,  av�Q�E.� 3i� nI occu=T-#W!�*��:#H g�"s?!�4p��D��Oa%. A�-Bk look ``I ly''1� ?Y1I!��"�ZuruS�zmea�5ful sens��y4MI�� rq rele�W%4�j�CM� al syste��&! fol��protei�nd net %�springshpulleys,�� �goo� �k�6`.� ' thY an energ qndscape\r�MTly-e\al,A�igu�on�&A keyU�Eu0EdL�� ��^A� d�gr��� &�&am��2y)�Of cours��!� !� �eai� mz$��E�} � .�,.-8 rockf a m�ain c c�qes AL���bottom� go!�up AButa�-V l5��9�And�'�&� ::H i"�8���E�,E�cer�>�s,��&[-6��t�h�G��5@2�, regard��of ��~r�Ht toni� _[�P(d to ``driv�i%0So!z�1�)Э�NU' �d!�Farhi:�fggllp}%�q�%b(en%�"�` osiB � edsNV�0�wo�f��."�]��H"�G6� %�so-f *�%Z�}uR  A�or Megiddo��4 Papadimitriou��m }�I>>i)�s�!ngy < lly)At�I�#sf{�  �8�% a� u D�=aC  , wem�be4��/ ��&�\{*=\}�,-1>�,-circuit/skE��nyw4$x,y$�L�Ke"�# &�n=�  y<�!�is]��� be�XPa sub%�!`5Z�% ;I lledPPP}$ (P&,Pigeonhole P%(I0N�8�noaRm���nv�8�A�/to?  n� ��-� itself!��*a�2)�� xi�18 we" #�GN�I!��talk,R�papa:} )���� `non�2�v^9;t �s']\�Wcandida�2 "�N��"m�87! a�!5�%�*� l�9he) abov�/&9*z JC�+� COL}�&�U neg98�!�[bX -box set�AhaLEQM�>�EO&�$a;)sf{PODNAh\2SOdd-Dej} Nodes.5�.G �� )(`��O�of"�I5i:� �^�e!��H:� q!no�.mwas2�!:=7i�%6`o#),�)ɘJohnson:�) (d Yannakakij jpyA����%9-a��s w�dc��E32g�6 hood\eta$*u!z�(of2qa�]p�")f �ut�T� &s*� Some auth73��6k um}|�2{�b�y w�:w���$� seemyc``r ''�el1F to m�d�aX a�.pur]wљas���U�[ > /g�`8%�s��H�c. 1#�k(�� \ Z!�)n�"ut��.r9i�Q & task��tospus- -k!a!�A5"( ��ai, v.+XNF'.9 9ED!>J*wc,et"kf&�' 4�%g&�)r�h$�=hv\��F1=FP}^{A�S��LS$�a� �gdiagonU �!.lin�'Bak�)Gil� d SolovayN"bg2% Like��)���!!�"x V B��!�$ ���. >It��FB��a�0 \A] �[1M1.I��&��&� )�!! �,��>j�QP�-a�la�n-�&Bi"� �\admitte�va� &j�% a *�B�|.� +!&�2�9'<b��5"�)\� � X s Bit{is}�| �-;F��={Pre�Pnaa��="+}�A�\>j"X,R y3�.(�s"�="�= V"�= $�$N=&/0 V� $,�=-��js�M*@f�=QJgoa&D � 2�}!��11� ���.JV��&t.�l.� "�=2���s �=uvWg/�h:E� s��C]3���sx��"� s��3a�* e0+9_Nl�=�,c Q>AnZ,dap��1��depen$A5out�i��d$� ���&( h���,0��v0��� by���"��\kr� A2H-�$>��L7��� �_D� no diӃul["n�@iSa��tY�{�8�?o>for2E ���#�,�`! ��.g� �&� v&4A�62�(b!V6vofa e� �Z�ge"+an^Kv� �,��butYls$� !�s rej]q �qC�V.u*model=)�"�!#AOst�9A���a�AC�� 6�# M> IaR�P!7*��wIn<�$:%CDLSJf�1&7M~� in_{\G��} P _{f}T%�( ,f�P��(�- %s7all:�=$ R � Tv:?A�� ��� 8>�ɺ&�2%?�Fmada�by w\ b+]iel�!a��F�72[!{@�@inftyfN�8tEOso"� ^7#>�BsRV����"`V , ex��i�now�%5_�$�q�:�<� ng�z%` ,q���G>��E�78"�& $2/3�8$RŸFor%p Zya= �J�$T�8AR"�oAG$R$; c� � L�\ ch��}0�>�OoN+�#�$I�=: �%e�! 9F'sa�ts ]� $\��v,z,s$alpha_ e/|  A�leahi// M���A^a��#e�A�$z�$s$�)��2p�~!�!+�օs ( +Lre2"���p�@2�$'�br6lex a!�g}s b�l2��6J �|>/2���S>8 �IAF��Kixe!ni�Ђ�9�AvcI!�n alt#�*�?�it{ajies��2it{y5�1A��y maps ��BZ��:."\opA��&� ,b� 3 $\ d��s bit� a�luC-OR�A]�� ^]M�vecto�$6�%�-*5huni�/matrix�6"J&�$f%�L� �;M{W-H �Ex�,aA�� E�� )�C��e o .Q~:~� O s���gsc[� 2}{3 TR�;0ed-��"�A&6_ orB�QV�K����F9!�|9# su-%y!B�*t�(im�D -ACe*�V�� >�yVa*�( ( NE�+lU%�V�R%p��AP$�2�A*�SQ*�a&b�Rpr�/n"*j VB?ZV�=.�0 �\���f:�VQ:JW1 P��Q."�Rpo�:lifZv$� ��-"�b �ӢEX�?C�>z  $w�\HuFw>��d!�* &t.x \ ���*��% u51=3�X�� s $u�'�-�G�prm7�;�.�(&�)� en�sp $x�in��l�i�x�+:�f,r)�B�f# "|q��A�  $x$N �tex�$S)��% ';!�qRI>�H&�$�"a$y$�1 haus�"��U\=�acy? tR+6�6 \V�"���[$by Bennett: bbbv>A^A*�%of�UQ� U`I��+@ at�$ly, zero��.�6�.��*�oƧ!���.� �.�D���.�umAr&� check� � i�Ue&U7A�tB�E_t6`���28nU� ,Mnyway isAu<)����afL+�Zy P& E�s���ut!�NR��!�.� ٯcanV�A�f��FaD&�>Q�N)U �=1Us!�= wj�OAA�$I� B}*HFN\v� s&�> O|Hex�hi?�Y*� � �al�I%m���[z<* umusteep IG&�!"&�t=0,1,2�ga2%���8�:At�h�O(B!  6�)��i �u0+1�aS�f��%�'W�6:is -�,e,F�5by �coZ/ic or��ng%A�j�s"|3�"/� v!)KrnyM ����83}I��9.]:��6��Ks'�22]�|&K%vG$�?ml�uF�enN s��JafsenN��D9�R�B�By�*�D\"{u}rZfH\o yer�dh�=�anaW���v-b% Vd2 z�%F&� �' �'>&BEe�eE)�A� d �� �.�<"�e'�!�"fZ��s GaaU-�Z2e��a�:=w���Q��nex�e&L( Othee��rep,,G2 Z$�;�( N/)i �~;=�-0pfe%�.! up  f� Sclaime�7ca"Y, ex>F! %:Ju � 5J E��X�$N A>>C4�( :��1ak!��2�+*\G1��t[iI�]$t�%� !{"� � I��.�Ipp&eGn?�FZ/?2�!k!�ǙI5 T2=*D� >�ElN�A4tU �o I7YM"��Q%�E��W?/ & 15v�%W Hc� �\I�=\u�l>arity$ IS�!m�' ed=|"q-�v.erE� % \[&�c�� ���"'�ZH\.O % +jmV��c�V5J�6_To�!I6��f:�V�, �W H��%�E��.��"ot_A�I E2�N>;, � 9�Iu� c^{-9IF� "�c)�/Q@q��|�$� uix#  $cI�o�!Eun�R i0.�&UE"�{a `$2�y9'a�Zx�%  B&f�=�&so2cR�\i�! AdeUM�F&.:}�E�^.�Qwo�n :c*��z6L) 4&2/.� #! "H< MACB6]e".�K��� !a� >�:@�Gt�=}*;%I a*3in��a�9Y.= � B�ƃ�9{.>=$(a�Al�0e�"�(!5 �"ar:col,b�e\B����AeB�\,*6o"�*��(�0mu�*Y_ ( �6 sc2�^}<5>��Aen\/ "�9.wndeed,5��4I:�c�Qsi�5@�wO !�B|xDU�##@2�f?BV�CHow��l�-Q]]�Ma�sibly pb/"ly&0Whe� � �N#�&-8i� ,ics3bare-�� ed'': fixFXi�t�}�P&�x2XiSd#��A8���!bVor f�EPX9edvJ��� �L`o'V�---�R �b���85 noth���,!I81 �� �y nexci� 2�ab�Kt��!3N�A� ?�ANQF0I�$o2�&� ��>I/ &VG>�!��H6� 3� .�ifyG2e�  `� s'\ afi�F9 E,v:��O1�forced} !�RX=��ide�;y":!c.?!Cper |Mne)� A� �!a��r�)A�in��On.<�� Q�%{ttry�exhib�dm��+� "V=I��"se�#me:4s:�ME�h,�c2'gloved2r�'\ U`!�'Qay�Y2< as �;a"�4! %��dit{�(��>4�3e�$ ��"C T$-i��U�1$ $F! W np;r a!�* Aal�0$-%�%Y$FI :+B+1+23*I�y �9U9dB�� } $Re;( A,B\%j��Ǽ!_$AB+{/>��K$B.B2uSZ Y�&sho�Abq$hA$ U�nff �7!#���0WE�b��>*5�6H$5��"[o�2A��sV��-�drawn �4!hD)Q�W_)wͤ](%�W_!�\� # Y o���#����VBqU*+"�� &�Y&+�:sure}��_��Y8��a��*%0(1) i� "�S=0�)(2)!��_��+aE"�' g#QR�?(3)� i"��b!v(��aT9�!_�ach��!IL;���2p�O/ta�' RGk�X) ��D?r%��2dynamic2e� \ op�>---a�ъ U�� ies �)l in;)� d "ic� �t� b�!��it�=i(o focuM<�)� 37�� , a�&���.� �ar�_mo�>�a�� y5��n� ;6 auto�Vm8%�Fu*D�"f!ntm �(� �� �2D)*CA�� y��-�!J�KI�e *"!6p�:�*�we>itn$A�plae1&x *~T �}ACe�cI1Z � {#Za!7 �en����)q!Fto�1�!�r�I��� b'�"�vH��� :r(�z 6�H:�  �vh.3�H� �.��v�M"a�in�ngAue"� !����O�a2� $\sigm"21�� "��. &��xnT0J�2$0$Ÿ <^{C\�9X� a� q N�gI$1$&/�T�Cwe�H�H �'�e2�pA���� n!�c)o�� h%� �A�9b";B�of?>b�OerW(}=��U=tunath��9B i�G|�"�&x= c]� Q��jC ��-�F9��NS2e ��iSa,MO$6u�u�!]a� ]�#����8<�is.�/bB�:'Ee@�Gg%,IR��*j �C�nd��au$) M� '>0er�$x!EA� geometric> � *ɬ\ {N��:tauH Ev,uY-J>.=1�6�A�|E�r��a� 6U6�8AZ1]��?���&�m} [�l]l ambthmls} \&� �t eq F]� 0�� $%4Bb4]�� A  �Tw"�8� ��J<  {0�&.ic�l� L� aBe ,Fa .��ELleW�)C�y6�A=� *��m-B 6� ~:~Aiý,a� 0��}. V� ) �M{nqv=ߣ6�Bn�A~i&�*A� &��� �r� =}"$.�6s�J=,�(1�D'��,miQ�[��nonzeroAy"�+&E {   a�o"��A� � ��l*��2n�2O&iZ 1/\u�_{:|�!v}ak�"��v5k�:X,~:R% ,~x~:~.ZUS>0,Q�.�V� X2�.6.`�']@}���"�ka*T  �'��!\� eeb J�=Dt0Dm��"�*��".�2c o�R" �>#'�U2�s& z�of}�*�}�'C�A�*� ��4e�A  �?2��{]!4 ��r�2�"�n�!;�k:Zj>� aM26�6���Y.B"&��U� � ,+��=1��f>3$�0��t���A%7Z�.�^#%; >�:��"�&! T�M-�2!�~O1��xa�j�� V$6s 3��=2/"v@ Xta.�.� h e�2�1>T�SoE[�7�b }F��R JQF� r�}=i� 2/N}}�al�^EI&FbMV_� m�t aF� � i l���� "� v(CoB5 .8�6�.?ansteat` �9&� !�T�(�? cipr%E&A�sZ�qu*�\�Uw*1:jvwhy�>�}Q.��-2�`onE :E*(�,HOo��}?  �9��qu,<1�3�� &"�1� adv}l �}, B},R,)~r �TQ$�XՃ%ka%�&=*�!ieEge:@ $F� �A 2B min *~#Z3min�#!\\ skip \,�..� ��T)a(&9 -|.�� -oz� \end9�1�E,�_%<)�.�&K�E�#}:� $A$,T( s $F�A �� �� AEeT~a�Y!Q�;b� �5F�Y��:� $, B!,;%�� MF�� j� *] ,p ][3 V&5 V� .�A.V� .� V�Ez EY���*� B}9 !9� 12Now�� D}6%2 o�B�� ���is��,- .�$�\�/M$��2��� J�:� �,� $B$��9�/ME�E�=%s�"n�mixIl(-@q6��v�3Z):|�a�hAa}ml� "�)�& ^� �'n a�B�&R2�%T� �,b p*Ƥ4/52N�p��Zp%R�He,�)�G" 9F�J�%�a � JooMoF� 3[�*���� �y�yhj��4}{5}M,\.�� \in �AY�>A�:m��red�Se $P^D( t\q��)f2q�fnT� rueUu:��&a���Q�uA}$-��BI�%$t\gA��^P6h (T6�vIB$ mea�dC�5x�}*��$�^�*�""+ei�o ,B$��/t|;����J�؈"�sc ��!ESv�5�62}!M~:~��^�Sv EA0P�f�s�$m/�.��� gresJ2k% z(�!'i��paQ1ng%g)�].�aY��gN \B�|�P&�2��5&M�_%�:�$-���y�-�����A}%��-�.1"1 2^%��>�&�U�t̅G:�}�� _{:"z@9��& &nA!�� ve s�7 $V�.�k�~i|! a\q[UvQ�!��$ R� A h���!Ak63h ^y&i*=���i)]2�&@}=��"."��i>3Ty���3M/5$�eS�l ;N= V&@3*C M� all A t=Y�ZI=V`- t.x�q !\#b�(�:^UA �a|`�O!�auygl Fery� =}A��@s�*(i)-(! E�e����Q!S}{B}= ��:30]� s�0iR��jAa Part|� oblU� p i)"�1`aa�1*y pai�h2�E ��i1I���BGv"&� :�\f$� $x2�4Aw� � B>"�Yu��6+U .�� Așl�A� B"+ .�'ƕN:&�� - _ B\no�@2 �sT��Z .��& \ Ij�mbb�%whow5�i)!�S�f� }>Bqm�sUV $t$;e�* �a�%1�ipk.`bL�[ fj��^�KZ�)� (y� 2� * =s,5% �C� �a�J� oQ�Fp N~ �>:�JB��n�J�>��9 0.��F�%i&�'by��q&:�ᐅ�I�� %C��e!A� WG �Z��rz��#1�F�b.v ��9 �CZkQ0u|^�y�` w�Kv^ )^!B�q�>5&'?MHSA�*� Z���'͑"n62�\��s&\_Y a_at � ��V9Eb�9 a `p"?_' a��B%*�.ni�!�� �T C��VZ >A�� 66� %5ţ�U>�s e�8/�� wB� n N�h �!�&jDx��&�| ��x$1 �A� A$�+�2�Q� $���% <6<.���eEaV^cf{a��c*TVio :��!�������>�^w�4�B� � .p�Snd.�%�t} �a�*��<tY t_�pi�to�,iz��~�%&�O�� 27Up�\: � �*,�it{Kts�s# ��7"�$}3 "YR $hc0E�c�ws�<5g��La� 2j2�}:h,L�(N"�9��he $L$� �/�.����� x_{0�8 �8L�,>� �.o� 8�isG'+��d����x_{48�b=hew�D_��r2* �%a���an�\G�nf:b}�L� l��0 �An1� tail&Y/� 0 ��+24 head� w .) QE+ �ttE �Bw�o� ["���؝hor�;d���.�!��c�Pf�elDf}We..a��9��)2fw�7 it{-=��k�|holOyLO$j*cG� ]�� 0};L�I6� Y=%[�U�оAQ\]� � �b�EK�f;F!�t}=y_<� ^>jUx"�*��)]A�4 $S_{X,YA]Q�eE��%}h�O$n $X\cap Y�$O$��!�t:aF}.m�=:!�.!�e &���j,��W�v= �)@]�*��d 6�� .�L�>[[T Y�[ ��]��c!�v"Y�� a5.P2E� ceduYA�.---4iʼn�I a^p nE a $!o:��bE:l�]� X$A��;s'#5han $j9��b.�g�Y#is�I ���qI�v� &(�X}"�/ flickaW‹���2T9a Aa�a�a�o4s�qd#u�Yi�Y�=l��$G�>w"it n�ssl, �7! BdJ�o�?rw0s d]��ter>bi��7lro48oED�Q s hi&OPn Hs����C 2� . I�[�FlqD|,5'e�X4!C.L\���A��!`B�� E��c- $f_%� �6�Ruѐ����`�;�>at de/�g�E��O�A!�N$���!� �v�d�Y}b�Sq� ��F the �0�E"�&� R,f&�)�Sby��j�8t�z�/5�E� $Y6��X$I\!�Q�!i(݇� Y���$��$R��) \�Y�X6g��"-E�>�&���0-�\:V*�*%���I?� R��!a��*� �za���re8�wo mutu�0&�Z�@s:e{ �"do!�A�X72re\F'E7'Y�InWU,/iy��sx1a&5΅�$��.s')*M E-,= T!�z22z%� &.z�.�M/ny M�jz e��A=(%�i�it{6w(s ->�X.�.�Y.���Zit"3)� .,�=AE2c:A&6a \righ�@t\} $\ are small. \ So even though $\theta\left( f_{X},v\right)> or $B%Y:%�could be large individually, Theorems \ref{ambthmls}\ and \�4classadv} yield a good lower bound, as in the case of inverting a permutation (see Figure 7.1).% %TCIMACRO{\FRAME{ftbpFU}{3.4537in}{2.3163in}{0pt}{\Qcb[A snake of vertices %flicks its tail]{For every vertex $v$ such that $f_{X}\left( v\right) \neq %f_{Y}\left( v\right) $, either when snake $X$ flicks its~� $v$ is not hit %with high probability, or when s� $Y$ vI H %>I.}!lb{�Pfig}}{h:/public_html/�}.eps}% %{\special{ language "Scientific Word"; type "GRAPHIC"; %maintain-aspect-ratio TRUE; display "USEDEF"; valid_file "FAwidth 1�; he!{ 2.3%�\; depth 0pt; original- 8,10.3511in; % B7.755H cropleft "0.3627" top 9493�'eU 6504(bottom922+$filename '.K';-propA�0es "XNPEU";}}!g@BeginExpansion \b4{figure} [ptb]�Lcenter} \includegraphics[ trim=3.754344in 5.368080in 3.618745in 0.393184in, h%S=1S, %==1u ]% U,M$\caption[AM�}^>�]z] $������\neq f_{�\ ��[ itsN�e[BH$.}% \label50end9� 1� %End9�< One difficulty��}�all)js� �[,; at best, a�� frac!� of them,�1We��try dele�r$ll inputs )�$\ such v$X�� n, but me�,ruin some rea�ing N , which w�Q@then have fewer nAn bors�So we )$to �1� minimum} G atG/2$!|Below I��ve!p!�(ted analogu��A �. ��%}u= ~}Let $p�1\�~() ,\ldots,m0$\ be positivA�als summA�to $1�Also l_w_i,jF!X $in!\{ 1x o� $be nonnega.s$atisfying Vc=yj,iy\E�X$\allowbreak\sum _{i,j}3�1 \geq r�Tal4there exists a�empty!� set $U\su eq~�� Af�/($i\in U$, $�_{jn�5��/2.$ � -�Q8proof} If $r=0$�� M/ trivie�dholds, so assume $r>0$.\ \��8nstruct $U$ viaE�ter)�procedur�EcU% ( 05V=.� 2�A�%o5t$, if�=,n\ $i^{\ast}%+W( tiEk�2% \[ .X - .=j V]�<\�{r}% {2}9y *s , \]� n sag+yc=8 \setminus�! [ \e!OA�Xwise halt and return $UNZ5To see ��the!�!�c1Ω�noI� , observe�� wa�m�{1u }$,M sum M�I��6\92�@$\ decreases by $$>V$��leg,iJim� #q�:j�����+YP j� ��>�<}�>.ADSo sinc�� 2�$\ was�� to b� �w8, it must still�gp��a�e endz A-u� ; he�U$\ ?���.�w�h I�now?EJ0e main result\seV ٯ��mձ8kappathm}Suppos��� $ drawn froA}�mathcal{D}_{h,L}$\ is $\varepsilon$�j-}t \%���� 9/10i7henI&W atorz *{RLS"U GUg=\Omega\� ( 1/ % ,~:PQ�P\sqrt {2W�) I5)�5C:�Gi�a-@$X�5D-0,a���� fun%��  as fo�As.�F$ ach $vOX$,��Zx =\m�� t:x_{t}=� ��;�ѡ�VnotinzY =\Del&� v,h\q�+La �$f&E1A� distaA�I[v$a;$h$� $GEClearly5sZ fined ha0unique local � A`$x_{0}DTo obtaa�i�E�lem%�stipulat�� quer�D\ rev� � ns it ($0$� $1$)� addi� to: x_{1Y@$;�@ algorithm's goal� g to�g the qœbviousl *�%ǁAde6� � �,a correspondE N=searci� lem.Vus first!1�\�tF�sc��\ �2!$Q��2"% 6$��ՙXUV jp&H�Ձ�� s� IHF�_, , ge�2s $X,Y� nd $��O0# L-1 �e2mq q_{j��X,Y "+� � .�%$X�{=Ya ��fb c!�A[ed , gree!�wc $X$\ ll steps A�rx n $j��^ de9�e�� 2�=y J� }{L}�(=0}^{L-1}% b.�V� I:claimI�at $w� symmetricaat is, &d 9W &c Y,]!�It sujesa6 show�t� J�b�=-9�- yڡ3!m-\��� !�%�s-�Y$n�, |o"l f`=� 2=0$. \ �wnY^�*q�M�A$ denotE���!�Q�$ 2� X$ (�| quivalent��Y$)r��]l� Bu$ (�}.  Y}$)��.E %VB {I�$1�6Y�%�align*}�  & =\Pr� [ Ai�] �| \cdot6 Y \\ Uvc6�� �Now!K $E�:�s V��8 Y=S_{X,Y}% $,\c re $ i�a��D� �g#el� }ai�=jo��� c�`ed��X�at��1$0$I$g_{X E�/ E3 ��3�To apply���|R��"�, tak� � A}&�:.� )��A� �GB8�^8!*�j yR)� l,g+ �ՙ��ifR� $\/�\(:]0��Q��)�%o=�%�Y�0B�c �No >1�let�� b> vertex*� �).d$ �� � !� B  aei� � \� v  Y%�� �former��qen���!��2A}~:~2B�n�}26a:� \leq��z�:����Y,�U��*o J�,�'��$b is6� -�YA�Thut.�E,] equals�� ����)�}� _j;��a q�&BNT}{9Jj/10}.!nSimil+ �q !~e7F:X.e!� 10�/9��y � y!�H�B`\u�_{s}�Dmax):S,~%����$B}% ,~v~:~22>+>0,e�!5f�Y$r��e� \{ 6la�9 ,6�]�i�#!/M�9�}{� },\\.6�geom}�#6�B}�# !" �% 2}�{6�669��=Uq F�F},3���latter"~2B� leq1Ѭ.+B�*"� K%����� . I�general�,� we kOi�at"�Z� % � 6�6��  \G1�*� �V� $�2a-�b \ T> ͈: .�A}:B Y�-C}�BS%k.SBS �S \8 *6 j as befo{ �v��X,Y~:~R9 � 2� ��aX�: {9}{10&X9�,E� #��by A�un$3$AQ�F:sumR%-RR, �`R_ � �a)B� \wedge .� �7-k< _{X~:~\urcornerZ =4NH=_{!�< � .�F^ �=�- 1%�2 0�7 :n SoBL�\&"���a�$widetilde{u A}% 3���A1���J<B}: ;B;J���asJQA}�� x � J&B}}$,Z�a�QxZeB}U�.' 6!� U�%�75�yX}{2�HE�� H^~A>~0% ���~��~FRO��n!  "" 6v$ 9�-�RX �GB$, 21v* leq22� 7( �@>7"�  $:� e >/ & N ;52@ /7}�e$�\�{S�'fic G,&s\�$GRAPHS}}��is� I9��`�< method' develop�n Si�$SNAKE} to 2(o�"syU"s:T MzEH& ix aqzhead' $hv�%�C0L=2^{n/2}/100� I�A�E ribuA� &� *�via w� + ll a"coordi�& loop},S v�.tar�f�U=hHa�9t$ �d +1}=aBE�$1/2$.�I#6-Q+ t2q{mod}� fT�q0A=is a 5( fact abo�(is20& �+� on" mixtime}[:* mixes �'e&(��$n$�,� sens)� f $t헁� t+n�"n) ��B � random N\;h %I.0� �*0also usI7 Q walk2 ,-�!@Aldous �({a  However,�K��&�*2J2Y8 easier to workI(� "pro�(s\* self-i-��s)F"��0%�e<e�g Rz� as o�!4d to approxima9�\log 1�),� uppe�e!�*�, over�,M�Y�m[ �(��,�$��S�$ (A Ur��f.�'�5D"�"�ar�"�' unE�ly�щ��)>&��F��n|xW,j� ) $\Pr!j,BF = f!X-E=-0\f ]  0.9999�8L -1,[ C�"+dis�ment}.K.W-`&`" Ja"!�6$m� :y_{ % 2�"��!"�(9noaR�et�6���I8d"5� n�dA���"i �8we[%�.�, both $t>j-n� ���>Pr��R �J&� =��Yi��:� $X$,��`is]�Z4B: �(�Eb�Nc �Edq=.�Ug=1/�)zSoJ�T[@Z�h-�A:�i- 3L^{2}}{x}=0.0001E:bM� I'ar�-� , unless!I spen�H `�& olog_/' amoun4'im� one par he&� EO.AH�.ɪ  b�!hitxA�F�1� 7ToPh#K "�-�of"�$sparseness�ndA�n "! (1) al~)x� s ��*�]�al Z (*hr ball})��(2) * \<unlikel�0�!u#=.Z m�.�y�"� )}� MU $v,w2 $+F�"� �$, �6�&x,v6�.b(number!�l �1�3 r� v$  $�V�"sx�[.� :="S  a�EIn J9*w .;�hso on��(AfSweO �&� � e wrap ar�8;#)50� .) \Y n�!A��-���"�/c�,ant $c.|8/ all� r� �=��$k�[i !�f�{t::��(,v,j?  =k�LA Uq cI:( n+�e�a-k}��6�).��R�a~.3���y�N� I ��is )e. *i  $1-oE\�* �)� ���&>*�'�M}$t9� Z'\*�$t\/$ i�F� % &� ��t-. $L/n1�-a �0e�E!�"2 v,i,-�# m�]<t��>�*Q.m� leq k$;�n 6b Fc�1A��x� [�2�N�> 63-k�0] 6.\] % N�!�2�\ a���8)H,�!)�IT+occur�&2�2^{k}��\� �"8,Furthermore,�j �N6lJ�%�s�@V8ere�\t$'D8 inde��en +S5%�\mu_{k}�L}{n}�%w�i�}};!Tts �� fixe$AYi� expec�1��\1)8 �% Q�j8s�,�$ �%;!4by a Chernoff �� *;� �% 5�%Еڱ/24B��D\}��>cn)0)H $ ] <b( )Ie^{cn-1�=� cy��?^{ L}�31%�2n8<\]Y)�)�=ly �?$c%:� K<� � Y N/ �= c A� =) %-�5BBr��nz �2"u%�)� � � 26 &M�9�(%� 1+- �pc!f_�  a�iy� (i,k$ triple&�imultane/}F&�9 $1-n2 0 �� 2n}=ZC�g9��i�m��("�/al^o% $n��t����� & )��T��x2� �!�[ j,a>[Y'in J� )�] =O1�i�%p7L5��)� �� � By a�,p� ;r�k6�&� �:���W/[ B� j� jFF V) � ]o+�� ��B�B`t`J? .�b�)L XH'�+wcnmf�%i�Q�Consid�/6]�� J�B �"�1. >� bv~G{ ��c6`ځ? y_{j-n+1}1�MG9)Au%� ��k}c] Z,b%\"�2��t!l �e6Js1�}=��( 2^{-"��f~*�!}Lf���=�-62�����n �*���$\ )%q�Q,k�1n($(rray} [c]{c��`}`��\�6-N�~|~Boj���ie]�� � ) G lw&E#5� �~��f&��k}}6��i�>?c�@�> �l�0asF b ifiedA?jA�suO5to�&�@ d do�Bman�6 ions� ��AU2�9srly:��"�8͆b�A[ 2W6t9u�B#5�2�9M��l/�),,~n�9 m �l� m4}� r�C�V]Ϳ�q-<'v"�:=�"�u e�b"x0�");,\ �uJ�4"5(�v��$� ���'f�\ &I;F�7,.'a�~�zjF� by.%&_0, Markov's in��ity��a� �����J�F:�  i�v')'� 19�# ] SeH�Z�,%�is� Fh&q *p6� � � � a�*� �>tE�:� $Y�)"�6X ����r�r��"Z 4�2 6{ F/z Q��mv��b�{�--D*#G #G�#���"�#eJs#�:, V�as��va `:�' instea"�?usualO$mai�"}conveni/^+W4 we m�o!�B�#�#� oughP? back%k� i�*c�Hmore ser�;:W :mix���8o longI�sI�� re�too m�FS, �icu50�$d�N4��1@&]!w�@1/N stra�q lin% �\ly chosen lengths attachDGt%&$endpoints,�"'O2.% %^&O2.4267in&O 0149 0pt Ncb[N� in %$3$ "q% s]{In $d=2,��r�% %�Aov� ���>� �Ņ%�n F&up$down, %�J$inward(out , etc"�N!o�N �L%{��N��N1�;*�N)���NB�N40F�N277"; 6�N 5958F�N714O�NjB '=J��N��N4.168388�N53946 D4.183915in 0.560696�N)R,�N1t�N�� c�NV � r� �)y<}�!��& abel�SE(_P V�Nu@G_{d,N��8>�)���(�(�).�$s, E�:$N$&�of��@ m $vz1�� ["�I] Cd*��� �$#�G��S  i'���"�KN^{1/d5 �$ (���Mic� r�� $d^{th!%p U$VRcJAv�$��}V�) =#`J�-�@2;\�M 3=�� Z�54��&G)&�$�;[ $��j� i$ (so =�doe�T.B��� arie4%` L=�,N�( �> �gej�(%=$aF�Z�(% IT$S3x_{-�a,�Ti7iD!2T}J7QE��)�( T28�(d\%��I.*o �E�( �&�$fWI�r�Pd{ >&( valu�!Qk{ n�!I� �)�A�I�9% T*�T+-U-1ato li�EongLshorte&t 5T 4iF�)@,\ `stalling'\ at.FV3\ oXGe��ex��beeJ� ��%�hi_{T6( #���V�-�&F&��}��}!OVLSJ@ dir�.}�^$J�% d%�AT%OBv.� w�Mve&�p&~%">"m�*2}J& W F�*d-*�*[ �*)[if $T�&� T+d��* B#!�Lw�*�!%eV�*BZ�**�&�F60 0\ g��thr�  essent�P a�",change&,��&'5K�2�R->fJN#"�7�?say.! Q T�P"(possiblV� on $d$)( E��"��!XA}�%��X"ef$\lfloor t/-�%�\r n^<t ^( cv+NmQ fa� n&� -k/d&�.�.���P*�"2*�v� � ���"2�"��@]��y-� \���>bB�h.gE� �] $i=J[a� and\�-icm�2��!>�r he s[AdLAfm2z!$�.��eLGE�^n *S2&���A> k}S� �'s�6��� ~�f�!N� k� ) /d}/N�o�-� Furt""�#E�� T-� �9 �=d�Q~�^6!T�}% j] *(")a�XJ/"L�G� :�}{Nr6"\%�J7"A�� -U ��6"��7"B7"T TfZ��B7"�� �<" .*9!B^{ %��&K"%z�#�\C&1��2}i�i�JfU"+4$"U"q&��m=E��! � �a �$,�D�*�m M� { �W` R�#m%E m^{mN)% *v#N!);��j o� 2�%V* J�!In���1�& �1}^{d}�B~ #� [&�,] <’�`#.V"� ] \\ &A�Ck��$e%-�m$M� {):� - E1}# Fl.I�� .��i� log 6�1v6NB'� EZ� a+2h�4ZN�.sEI^( {-� If2-�$\�7a�ing&�"�� z}Negl,^hb&�� >>F."6�;RLS">���2�k )a �}{ �7�H6f&2< �fzY=�:lmR�5BH \chapter{Quantum C�fic�WC�bexity-jCERb�, 9 stu�b%�rel9? ship�twKlP3^q i,measures of LX&;o � f:"q6S � arro&*!�� "+Z�6gajDS&DDeW\JV!$,���s �Z$Y�51}�$�%5%? !  deterjY sticB�B{>DUefU_,%X Hmum*X-!2ie�n �%i}�)~3\-�3e�!�$fOWYO uadversar�%�i)�Y�U!Nd ve (��o5�~ o�out��pre|Y��&a��ed-error ized/y )=A�6$R}_{2N',� ]1'Q &�.10!\~afZ%�& $�Xout:g $fE%(.mG$I^.� &�2/3� Hk�0`$2$' refers  wo-�(d %;!�:�`qui�TRyB_ ��.��U����we�B�@ }_{0-\ ]�,\ zeroZ�.� A�eoy[F�Q^��%1�)��A�!�E��/�B6�- s R-F 6�%+�SI�!@.�+6s%$\� BL��Yk-P 6�x3j��Q���*�J� > bJF=u ��52*9 �AZ@� +���X:�)qZM �`:�.-.�ŕ quadHjc� is achiev���>OORL�don�2�Hs:j�OR\�l3A(�edB22�>/OR |dO*�e�( A2wxdasB�.>�[ =\T.�X� T/�rcause�Gr�'gL3c> g �F.�wE $� BVde�?.\MD bbcm�showedV N*�)6�Q�oU�] ^{61[V"�i6�dewolf:�piR$ �VD���2}B��F4�-� pJ�$&�hfa� � on}L>�<*� "� ��"�c*K&� }B�C��>L���blockSitivitJEbsJFP�rm#�Z)X ""'�A .�A�,qput�4KmS^Nt��?$ 2�5\N�qat Pl&�s�bf��b y_{iKi}ll�# S"�N� & R�k� Jr^~2������ siz;a >hE!�$:�5�6�i� ax��F9b��Hr X�.�-.AU0e I@o�rF�B��9�DS�Bmc�/��� N�A�PdFA)�Y .2bby�v�N�U)��@ B5�Bdbs=e&.�)�� 7 disj�,>Qs!RQBdy�n`>b�B� �7NV1g�h�4>� U�%q :���.BJ��&� ��a�.~  re�hd: Nisan��n }vF��� :�N��E��ɥ� n^z�1)rN&B���%LCombikx)Gɰ� jn�&�;>�.�.�!\q�$ (�F� optima�3of&�"�),�Hm�F\ V� j�N� 6���2�=ar� R�p�URESULTS�$I investig� >uRQO.�*:SQC� ��9o(ef��,� N^iz/!W!i.d&2B�V�(?y Table 8.1xMy motivfɂat, jirJ X.��r�1Ho ��"? ! ^b� BYV��!>[R�w soB��)�6��l�3to new�s�KngCdamen� >�"� A�ht!~}�~"Xtab>3d;$l|ccc} & D2& R�R�& � \\\h " Que2 &Jg �6�F(Rb� $J.b�\\ .*Y�JEQW:���F�QFR �5o"�0B=a�Vj5�]{6N� ?their^E|s*$pE%S  �}f�B�N�\�i�.�IB A� ies}u�verify a.�, �P����A�X>commun&iSG�F�8 we w�Kto��CP6oF�e�we�culd5Bu'ed is un@lA �equg7 � i*�t los�W�jtRW2� is� � imed.Fn{ ! �$\footXc{T+ou�lis , I!]2�Nd&�c`actualC8~ �O)�(�nds!0.4cqed 5.}--- V�7Dttn$,���a� ver ��provid�!)�i�jn!�put�1it�7!VEie�job!)to check c&� &_b� W�t!)inW d I � F^���*��%�-�Xkc7�e"��� - �;y(i)��epv !Mb��`�Y=qS!�$(ii) rejec 0�PN/ H:(8�RX$m1��k(ac�Nw2���$rbitrary.)�$<B�RC�B ;�"��NI�P�9� 2�X N�J��a�� N`2�2�\�a"dSB�R�|*� �� � "�of�Y�r*a�"�!��BVHe=���F�;�|�l|?�VRaz:artvv}*4YN.1one�}Ma�"!��2)&�ra�+arn1 � L0F7 V!ZF5�6� Ab�)a�.t��factor"2�H�#}Q>�V�$`r_{V}^�t\aP%v�N��Y�$V$�(&���Gl]dnJA enc�Ver�.�YEna@\�W�Cy�U�&eD[ �\,\,|z �G^sS�}�C D�,Y4�v"4C�$�/�� B!8 t �-1-2A=5�q��}eV6%� wq�?w"�\.�F�2�&�R!r~O*��" _&*v%E%,\wpi\,"�h�1�-&�^�-R* G�v1�X!�s Jt]*�v2< N�me�OZ\ ��"v*I� =|geq�FQ -�Y�J�.�ge6� �}6�_qN�wVr0�649V$ ex�eJn�"a֑, despite havCf�WnoV�, .q���G  .�Ai ���1Cz \�!&L3C5�YmbnF�6o=W=5�F�V>s� {e ].��9s�F"3G *�E�pet�F3��G� boost d ] �/J�o� �E�R�+�:�:*=K>�z��ic� A�>(���'`{B��Շ���.f'^�$,1hA!�=U 9�:6�:�$e�.>%of-ning�! %"� ? ! �X)5by!���/`Ieq8GobjI��R�N�N�X;-5�%v\� I��.22qa�N �E���7G regis]pri�9oU��In �ȂF�:u5�*�is!R�eB%�K-q�!I�:�:�)6="Y}2�X}.�� l"�R2֎�W�:�:��� :) .�em6e +2*O��-end"��� N&��a�>hR+ )� V�!R=jK% NM  u�>��:��*V bl6�#&-�~(We �8hav��6p.2a0>c"=.2r,2����6m�y E�jh!e&8'�F�k�0 sugge�� view��bN.�� S ��oy'�c��dE!�B�0&o�%�"pre�T ` �8 2pGAP�?i�Js@L Rio�kue�F&��&� \�2_CHARSEC}}m'��JV% {�� .� f$ (�X(or J%),�/cisudcha=� eriz!��Vb ermN�ABV.. To d�0+0k!u�enP0���#��Ft�(�t��0�tho�NAmbainisTa }\� lpB�Re� n 1 �=I���m2 RRC}"extɎUgn* s du� \&Wm6\&P o/ a Smolensky�H describ�(*>, V-bw�ftoE�Z�RM& fN :� ndeg�.U"5*�(�,leG{�Q 64Q&�G�x!�sAus$ʖAia=v $p.�%*��&� .�if%q�b* >+A 2� 9�fQ���8!�KyA-��3a �E�]�q����:^�� N-b�V� % 6�*N[>���2�!'To my�+l�/ -�f�U�.t�p�SR!N� *��v�0&$c_Q��hRgu�  Fin�F�GAPm�hi�asympto�5ga&�6BVR�ْ>�� s, ����a+a%Q��BmF� >f:�F2h.2.205�f�p d a ��icX�j�w�zB�R_Q|�)�&y>�Z!2 n/At.2g�{ clud�Jq~ij OPEN#�zsope"��� h#R�%�k9RELATEDC} ZF\$9d ab�A�y cal�1>�ma�32: �6HMerlin-Arthur. \ InaPnaO6�VM=]� D�*>��Dp5"(� M.+ܗh&B7N�=:�ip-!*� �&a)^-N- &�a��,�5�n # ily 4Vl -amz, �A�T�y� us�7-cl�cX cod�oA�К��5�qX�iX�N> q�.=\O*>0��eK� $MsI�it!"�8h. �ioJ SYM},ASa-�F= V�r=B�BB�=A��N�Z��(B�a",� 's��doa�jlapI#�t A� . Watrou� w }\%v*�'�M����on!^`2�!& '---whe�o*� a�Åre�mr�_ sr64&�=YA�L9 6� nccN� `non>A=*'7*�$ " !Falter�z9� x4��)y�:2 ��*\=��po." !��&.]&&�?1%e w�fI�>�V1.f �3:R�2�preE.� �Mw.�]w` E*�Z�A5�� Vr o���@imp�6> �D!��(1E�QV'�Bit{no"��O&<# �i�9e�:N�1H* $�5�O.C$\lambda2e rJ# :u it ��!B(�&we�fyR�a"I�a>ve �efV�1"�R  _{�e)�) \�AFK _{na��2� :=%�v+OHs+n!Co@MB =���Y{%6A@R�#j�:!67 b�\�% MMR�gin\�B�RCv���>��� \]9he�|B, we ��X�R%Q�&4<ly�"�9 R{!' �qrit3X2���O"�CY�H{ Y:"R�� )�\} E�?DV[x�5�/�{U7 �u"ptKI�*��!B.�%3$Vf n����($Y�kcDY�L!/r�"_'{X{ �By"4d i"4d�$�hHa2Yi�.�6�? af�$T=�\lceil 2��\r6yE�ieu.cBko�p9 o(.bq�p�QF\� fracI2�q�^>lAQSJwe`aQW.�u &�7T\e�@pVlz��'� �c41J�,��ing�-  $f,t-F%�alreadycXmadA�d 4�edV��)��6 ��Dc�AO�� ?� 1/2T%ByZeas �*"K� $4 [ime�X6Xn  �2+ *1-e^{-2�g�z6%�a���%a%&rZ��"'&.�i[ 9�)SdY��Y<�;1N7q4Ti�ܥ��Y<&;�a�E��i�i}��Yi}}Ռi}A�1T}I�9V:� . eJ�n 6 �B"u�oK, g�'5�+���1-\�q_R���1-.�e#),�$Fi�M 2Wj ^{n}>0.57%�dTo)5ʮ�&ɓ�U>DR� $, I wce[ea��"�  `G ormu�3of" w) �@"& "%K[I]� �d}a%3�~�JB?FE ��F�J2�r�n dE�"����.Q4<xn6���� $R.cK�%�a^gK�--"-4.("��X*�=Y,& *�$"c� B 2A}f :!"M&/&)��]d���", 1}�E�=e�P��O{���w�[3��S!\��B� �dY\,:\,52�1� ��vN��HN3!rH�^�ȅ%fX�#-,"z 9e��.= �6) �n\�N�N�rw0} 1.�w+{u����1= jLa�xJ�m��}��T �*8g)%�X�':�C}{Z� 2Q �N�^@&z�H9��Y� Q.��B� 6� e�n .W  �2 e !%le�PS=n� nA5] poJ��$�&!"�)6���h  W�ru�G�quotedbla� "���D��,2)P\ vA2/r�AD�s ��� x $iU3��i�/) f^/?&� i}/S��(:����$�n�wasoXmYathK��  ;q["!�)B> ,*/*i�wQ!y�XeGon�!"5*b� !"!X&94\.�1=��o<��'2L\a�2�: C+x$a matrix g�^in;Al�^ch) �"%� $i�<%� ��Bob'B:; Hwin�1( � &J �If� play�0re!2ional� �R!F2�  s 1/S9D�#Q��E�Gtrategy�� "�. N<^{\prێ�d}� ���f *�W FJF}="��΅�4/R[5axa��%(k�`2!hu$�42G.�����a��*|Xu��[ �;9�)r2�t %|1}.�©�� ���Sa+A,�2%�� =\mu ;6��a� ��)EawX"bY,Z �) z:\ $Z=XVVW�$Z\on" Y}�r9,U $��"K�%+�>& 9}9]2�a�2sX� a�S|$"���.�of$  uish5 ��8 fO8F�b7 2�Z���&��q�!�L� B�0!�T�"F=Ls}�xg���&�"iq6�(R}\nolimits� I?.@9\:: Kis*�J��fli�Ja6�B�u�l-o: ObA{�e��"�Q$g$��Y(!9�p(.q$ �e$�e�d�!�|X( AqM$"x���%�$g$raBbe". ,�-it( ��A�6�0�s%�1- q� auw!f)�;zt ��g�o V�\1�=1�hlBJ9�* �%��UnW.�bA�},  �>�*��^$�K.��:\�"'>N^~R�*sl�yly im��yK�>� ��.6de-���*,*�+:Dbw In�, �&deg�� , I D���?��iA�� for ��&}* *�!&h  H� . L%%_e�B?�.u֚"��]�ed�p�����"�:? }:fX�pe\a�A{�F�%i�t�i `shrink' e�$M�B�] (a�neces9_A&Z�)} �tD&�SWa�$M$ mean!g��it�_2� q��deg��. UM\i� -�>�i*B��މ�.ba � .up c�<� " r�`nygf W�of�s,�"ɇ�!��� .�&S��M�%�A8B !l �nSI !��.� (Ini�*��\2v�$ n^�o9&2�!�@weJ2d���&.�f w$��eY%*�at5��2F��(� }{e}6'mk!�` $M!=A�S" � B!�Ξver`01+q"7�a�Tn  3i � �Џtbinom2EQ� 8�ellB �� inct�i�:�i =@�>F~2/.�Cf"8�EcB-dm_{]=05<.+�} ��I!&�7]�B2HZ!�*m1!�g{1�2�ks�` ( e*�p6 �m��@ AFweLR�ribW�of 24j32I y�����F[6O���[�9q =i �% =<�1���0 Y.4=1$IP‚1o�V�� � yhalve�KE�6  .���c�z��exL� k�9'u�4z�&�ܩFlog_{4e/1'4. "y2�� ��\uv�A 2�*�2��-P �" )29:/ is l�� thanI:, so ��is �� .79D�bM�� ��n �� �)*T..Ms�ofA�� �3^ �t I gav*gly � aar:cer}3>�c�L="iso+flu ,� �a�� falsd+,I am gratefu65 G�� Midrija7G�W Hs ��=.}"> ]}  ��"�&6�RN.� ]::VOT:&Z� 2T2�w�: a,!qa"�!&� M}� tt{Rt !&q` tt{C4 a /{ttM�-�B ̻@tt{* atibl�+th jO/$so farYu@(�;}�T�S'H�"� ; �tit{|���$0$ ��.Z� � far.}B$R;&�S�0}9 *$ �& X}$ 5gUntilfC�.�}"��D���D�}s-�� p� 2�7�>?6"T3Y a|key?KA8AaV5 6U�n� !�y a.:;!=D�w;_�� hit%��m\ �g&� �{}p ��*�υ� \�jhi���� ��a&��M�,�1���aMwLe�Ѕ��}��is'/�c!��LR]��041$�= "�d� �So6v.N��bf`3�i��b+b(V0 =/>X. !�r@�,)xո!sA�P�Y�ch=��Fm:���*K&%%d�` Iz6x]/����.C�P��s&A.. Z��-iV�.yej�c�� pe*��.��U >|*I"I.IE.];i�&�X; }.=E���\ra2�X�Y &�2q.v2�)q�) corollary�2 rqqe�02��4:4����2M�!g b�g"�o�^i�4% kindlQ� 2�:&N�=b(Q.bF�V��.+ BN b� UF?^{3&/!as�>n (al�Ygh�N6,>�"uV�v��gknown ei�7^ santha}�T/}GAP}A&�>GapeHbOe�ѡ>!F:��>,^`ic�JzviF2C �#8g�  I7��Ye"l�e:]�^thelee�n�>c�^,� �t�m;Z� >�'6{FA ^{0.90722!Q_�AvrR8-^N�?s well �&� � '>�RpH2�>WR@%22=!�Aq)�cMA %�nof �IE�,64LOCAL�G4atax`��' tech ����e�&B�J�fF-�-.��F�N9bg5�*+6�!P"�B2X�=\y(�beF�ialsSignsDc�=m9��i7�oj#Z$ �B]R���"�1\� �x,\�B B"�� Weg e$Z\'{a}dori�Mwz}\ e�C��#>_z~ 6�&�z>CN�)B5�.G%�In� �� fashq?I ��   fam��'�"g�6%N�3� t�^q�pB��J!IE�B�U�}�t:��g`"�x j(x_{293�Bw^>;� �B�'S��)$13�*145$,�x$16�(param�d $29$� W7vi;[+`H,�C3uc�.Cal seD�D�+4$t>?/-):b� ^{t}�=g"�[ %u\= X!/)�8��|ǿ$ X6G /]~ w0 $F�!HfqG$2���)D�b�_S i�[I�+ /."g�7$k61�A�0.C�6%�m:�bs!/NOy�Ex_&d({" =k>q Jx�2VL1>��/�w wf!0U�noindentm��inc62D b�m&iCe�) >E,& $., =17�eYRg&� I� e9A���OA� haN�-�^Z�M�aB�^Z� =26�&o~;)z2��E>13Bw{�66aw�+R4:�2 b]2�B�7*{>N�.�> { 0p��./ ��:�Soly" curr$?.n, .2>� 22.725AC x�B�W� now� Ka"% J�fw�&3�C*��gͻp}>sձ�l�r� ^� 2� -]f2HD��of} S^��CJ�O&@ F%V5F���� Fo%���$On:Rb�q..�UA�*L"w4$VM*ms an ɓ��W*��BXH(� g�)puH�n��KG"i=�029}�a���CiY ��I�=&\{ i:r7=�)acQ�I���A1i,A�Xh.��@K: $V$ 9.�8 m$\N�>;��.2�#>< �V<�ނ ~&/.�%U�"�l[c]{cnc�Z$Kym!n�,12 ��9�l13 4 5 6 6 17,296"8n �F0<3}{17}���& #5}{2 {441BmmE��i�`��Ar;/ "�& X"*3 ,-inues r�fsivrT�zmanner u!��.�c4j}Fe !�On�C*�j�-A��. �.m�!�(.�A�> :5*g&� J:�Q.;fT��urprih+�#���� E.�,�rg0�Z�?6�K�B"md� qua7 (>N +2\ > �TNv6���@��JMppeU��It�/��`VBTV� B�*Z&tE�� reas iME.)��$���Cd+v~'perfec�,�.nP�[�(/2�{,Ino �6s�� ver.Oz8o���sh�">�2��&�7:�J� }kwe +orh by B��t>�k,bsvw}, M. Pa�io�:u�T�>� $h�e��B.4.�*�}B�.�m R =5)�V#.�<:84�or'�ECom� ng �$�ecu� �9sNi ��Ƶ h:c 0.86*9` �B]�6Av�269� 2, %"�> �2 '#�1�C"L�Se��a\#P"�G  Vqu5yo/<8Q�I/2W�f� y#T*B�1�(�(u� J4�|�-�0m=a�.O,u�ask� .�FF٩�&>�J�R�B�2�FhB�]e.��<4E1 �dis")9�ztrzd��"%lE � in!�2ix,��!;n  rmunNmcal =]N8>� �#b�\�v$>�J� b�~UqJ߇mp� �(ep�Tp#P�"a�v�� �� � are B��cjMRspiZ@�es�"�&u*�"����9Z�ersM��Gal�B`�[�"%��[ Zingx&it{i�viz�8's}mobg}U�"/atu � ( xrr.`�O�A8�s��`prC��1 werful en�q��resol�fY�'sZ6ta��7 le�Z�GF_�� $HRb=6� m� "l�b�Xximb"ť�s*��B~J�d���G.y�J�2;HV;� A�S$B��N��2�L\ *a:�ual�d}ْ�'/ B� UVeoy�(3'�f1kJE7 &Q � ,"A$$), and no� sub-block $B^{\prime}\subset B$\ is sensitive on $X$. \ Also, let $X$'s \textit{neighborhood} $\mathcal{N}\left( X\right) $\ consist of $X$ together with $X^{\left( B\r 5T}$\ for every minimal �$ J|.\ \ Consider a proof that $G\le�f\r U=Ot H &/ $ �Tsome nondecreasing $t$!&$I call the �\-',local} if it0ceeds by showA�� inpu%k$,% \[ G^{X5Q��,\max_{Y\in\mb� C\{ �^{Y ( Z� \} �) . \] As a canonical example, Nisan's�$of \cite{n}\ �L$\operatorname*{C}% J{leq:)bsJ�^{2A!is %b. \ FA-acAO$ � observes � (i) a maxEKsetAEdisjointQc Ecs[0a certificate%�$[((ii) such aELcan contain at most >�bs}V�$\I�s, and\i) ��]$ have size_ ap�� }FL% V�E�Another1�! a)b-�i!Ke igXin Section \ref{CHARSEC^�RC-� U�U�:�Q+.�!�\m�D$. \begin{proposi�} \labeliw}There�no2�.�B�~� =oM�:�J�2�!�orI�><h ^gy�. $E�Hall total $f$. \end6 =5Dof} The first part!'easy:\ ��f ��=1�+f $|0| \geq\sqrt{na�(w%yB(%denote�e Hamm� we�� of $X$)iR�0$ E� wise�|���~all-zero�I $0^�'We eH>� C}^{&M�.r=n-�\lceil �I�\r +1$, bua�6�RfZ U� 6T�- �indeedB�U��yHyIJQ�H��$R) � ��.�K!NsecondE , arrangeɧ variables� ,a lattice of��$�times%�4Take $m=\Theta%e ( n^{1/3�, �E�g%X�\ b �Lmonotone Boolean fun���`(outputs $1$�T only $X$����$1$� -square }�m � ma[ Thi�& )of?'�"at��, wrap around%7edges(!]-/; a ��9Zalong�s must���toq8, not those in ?interiorA�An��%�, wit��$1$��3 �3$, is �$n below.�%�>,array} [c]{c}% 0 & 2\\R1( 1\\B<P 1�� z$\] ClearlyB"�jE�u�gU22p Fo sinc!��5��b�tn/m�s$\&49DsY�]' A >v�q� � 2�Jm�ny $Y$Z ,is $0$ excepL a�gleA�-��OnEI�> hand,awe choA> uniformlyh random amA��X�$Y$'s,G��M�< site $i$, $\Pr_�$[ y_{i}=1)�]J�-22��He!�>7��.� .� Omeg.L:VIB�} � c7{6XSYM}Symmetric Partial F�Ks} If�Y!r�0ial- >�R�$\QS(much smallenFA }_{2U���%�z`strikingly illustrated by!� collis� problem:�I:�Col h Y)�) =0�)4$Y=y_{1}\ldots!���i�*one-to-�u sequ%�andFL ` a��$Y%Ma two>N,f mise�<atq��the��f e caTheFD"_ N�I  =:=�:�% 9"LM��<�B�=$�|4 differs from $� $oeZ$least $n/2���$eH$'sa .� i�Chapter� OL}\� 1@>�.cz">Y1/5��. From�-�F�,!� empt� to�jecture �\ (say)r�2� 5�6� $\ when!gFM"� }]J=�---� is, `if-� $0$-)�is far%�1 ,��e�u! Ve exist�=family� sets\  A!�,)�,A_{m]&��1 � f -�� ��\}* �a�q 2�2^{n/ AMɩ��\vert A��� =n)�T �E$ �4 \cap>j [ � u� (ll $i\neq j\ �)L A)� due�-Ambainisca  :aa}a< alsoA ful�& Let ~� ��% y�1�25e�-  B� �l�p:fFI��O�ebb{R} [@real-valued multi�6$ polynomia�We sa `resul�an�p"� of L�JsZ ��e��599dtheorem"�symthm����1A�Al\a��break��BX ��\�F@Zb =6"n/\log �^�H �Ň} Let�"}_#� :$Nt�3 �>eq�^>� ��.T� $�r 2sya�LAIQbWe �1ѷ�%� >\��F����]FBil\} =A_{j�A3s�$j�CZJ5*�&�"� �љ� �a.���&&� f-�:� ��indices�a�numberby,a$�&�  as ab2 (2^{m}% =2^{6�> WL����7$f$ to aB� $g$�$�!n>)&��8But Beals et al�%bbcmw6� �z�gI�T$�gMBHa�J!I�I� $2TE3So9E� 6��B< 6?�� T$\1E+ � then� 2T\cdot:�);,2T� &� .� �p:�6�� aMwe solD o ob�$T::b��� \s6&4OPENCER}Open P[a 4widetilde{\degY2d\2� :iRVm���,"U Rq*�Z,CumQof6�0ing $f$? \ In.words,��lower-bL BX[6�u0��� method�2� i , ra? � Ladversa @� ; }? � �>h }_{0N�u�>1V�A�U�)8 f soAMv�new rel� sB�Œ.�=j^{4��S��> �N�6��c�{��N�,to Uncompute&(RFS}} Likea lassJ 0algorithm, a .Ezi��$s recursivd by7Ritself�ZroutinW��,done, though�Amtyp� ly n�!��["twice}��y sub �2b�}d!NJ)!urp _ u1&( `garbage' �� over�AB�@�aeby en� �fer�betweenr$ent branch&�)�E�� Of course!�facto�w$2$ in�"_ runn!ftimQ,rdly seems l%� big de}Kagains�$e speedups!��by1�!�g�!31O!%� � � � ply� %� leve��M%onLduc�an add2 al N rus,�� m�w�#r�!j} 1� ing\ step�reaI,4cessary, or wh 6a c��designed]j iavoid it ��iI gi�"�nontriv��J � �v�%� i%lvabE� �.;Econcerp-neglecM1�AvedU�Rq|( Fourier Sa�ng} (hA�forthF|F�� �wD tr!��  B�teK#,nd Vazirani , v}� 1993ab 1oracl�par �q* sf{BPP}�$\thinspaceQP M rveys� q�Y�4 pass directly�a�0Deutsch-Jozsa=� �dj#o* dramatic|E�SimK# s }�  Shor Cshor}I�outa n menA�B�!oIV` �twoe�lyA� sons> this -�1F"�RU\!~0m�-fi�>It :�� !"sol ��ofFv�an1����is un�Y #�M� �I��1�_9 know��4(I will defineFz!$AW2�$PRELIM;�!�now�nvV s a t�of depE�� "� ��Q ex��$ed� *Qto be e��via aqY trans� .) \�ond)��forV�\vRquasi*y ($n$�sus $n^{ �� .n exponen��Q!!�p^ d-f� ngehidden�group5� . N $theless, IQ ie� ��R]:8its renewed att�on---�it �'� �"��g�J---Da� ɶ ing, $crete loga�nd `shif�vLegendre�bol' U��dhi}---e��tIE�ly" ract,\ �;H;qu� low-��l�9-%0etic standardyThe��!& ir associE�dec2p�(|'n �bNP�sf{coN�r\foot#{;!�> bo�(�tA�� true�umE�0���j]of Boneh Lipt�m bl}.} \ B�trast, ~�% 2`,!��-i !:&�o\ � out�#ٟ!E�e�57MA}$ (!m!er�$�#unp>she� ough$jicult)A�S�-���Watrou* w  }\ gg*�$A�&a�� n un� ed�� ���A�^{A}\7�sf�$=� Actu? ,A� plac=L$�%!&YF%���n�=�� suffDco.,I��/���n� � (� quotedbl} DoP� x\�= ( x\oplus s ly4 n $s=0$?2W BEm� Gr� a�Pruimm�gpJ��/��Jq�+B2s qd P}^{ N B}�How��,Q'1��sho�%y Baba"�  :am�b} 5�AM(while � �=fa� �)� A�T| neik 1�ca�&�d to N\Q hig�,�̥�a1��hierarch� .?! %Umesh&r !�qs8*co�I�"jrA�.�PB�!!ch��would�� �*#Q�a� .�J�aS% .q9�YA)�Prk � � (in my view,�  of�& ce�l o�-���P�%�o�+Its solu�  � lya�requir=1� technique� a��-E  circuit���ds�0�#R9\ � Q;represen��by�*ow-� ]!�!is A�#��� �7.O-1"��R���geE��A�� [f\MngFn���Y�x�1 d�7e J`9��RazborovKr  :ac0� molensky��s� � is �; o�non�1FV�,M9� E; work�!E�%0�(re�&�'*GFu�.b �fs�ލKeKa�0U =4�ȑ� Linm2�lmn}.(�is � I Pin�#e\V&8 �a��t a�)�C�V�'sF�^���m)dUfu� rA� _ an ţit{*� }"^ �!yc", U�$And c�w��V��,oR���0ѵPH}6�x/Mit� �@seq[&a&y ic4 4altern;$s? My ans��� oth�%s��@f+tr+`no�%I stud�earg� ��- 8Z7N �Axg ["�6 em f�in�n_/�%� es: �Penumerate} \item[(1)][)11,A,�D����� �9� ma`*C��&�d2d*�G.gLB#Y �\2h"J }$\pies"�h�� h/2��be "GaJ(� mparison�uX-"^U�j �h}$~becaus��A e �&�D- �-��.)�,=�Si�,n^x� always� )[!�l. �zdichotom�em '�%%afforde5� ut�*�+�! :+!GIA�so 2](9�)^�E0ol|, Q�oH�/$h*}lo:y �!pl�so ���:�6&�L)�!V��i��U& and\" 's! �)Y5� ��i>>�LOWER� , IAdh n��Y"�\Ap�Dž� wer  �P��1Ze�%���.0Nt��n�T.S, h � �Sme|EZI{�=27 nonart�e� ient�d' �be �-)�tu�&� @!02�*�� c� measures!�+��+�,be!�!l �53 ome D=�&bits--- un�<8_1� trib* �^ 5s� m�p�6� g$ analysis)�� ^an QM�%a!XJ crux�� arguW)�~ }%5# .#is _7 (mearXR]\� nt�� �s ͐)�G elW^-I}��p4� �9vH.n!Y� stat��ed >�:}u� *�i�;ghI5oft"ependentEesj2�a�� cludesRA6+  4 Prelimina����D ord!y5�sK,R Ci �ac��F�" $Aq:d%�qar�;�e�:,s?t�2ng $sZ ) ;n~  K$Ae�>e��"s�! x 6�{mod}2,�(a3+x;v?Ato � $s�or? �1we��,@4 98+8�&u Uretur�# � .�"���EP� ��a��$th�� N�\�a�2u�$ hard-core��2%�\Ts� c�Y ssum�<at�_is ��l�$�k�)ea�%�we Y�]�nQ��=$g? T"�#a� -�&��q N e%s� �T 1�!5T��weA� > ngermZ��Q�&�  u��steadGpr.#4%LA�-� s_{x͞2�# inETB�a�$!k��it �<ng%7a�?B��A�|r n tak"%0 rm $v�,y�-�pr�g i1)x"/#2 = �cdot yR2o6��6 As b$)�~qn $s$�D �D v�)A�E,����a6 )�8)q&z;c�-+(sis��AAt!6�5%y� Aq�;�= R�$. Continuweax�u h�"B�atR�_P ,yC� u],7 Wi.a }��{.�.�1xbY<1V B�*hY3��V��z1Egv��>f fix/?�^{\ast�}�� � 2}% *�+hť�d tc� N�_{h-1�n�2.�+h~ha Dbit $b%as�\�/ b$;�2t�$\eKwr� ��.�!�r��%�6�?.*� i+��=+sQ�ued�V= \ Not١�ɴ�!@samery�Bi���o8u"�(&�V e��b��%traI forwarqgeneral�E�! �7 �����9�&�?�1� bJd�er��b��RE=g_6F*�t3��*�� $�3=<%�t2 P  \�v0Rx3\I�� V{% N�*<��C�^�Av*[D B[D�FA1We do�w� !�a�Bg$ M3&�  �if��di��q<��2 �JuldF"�MZ"�?��To� Ea,�HIy/x��ell-$1]Bɏ� b�x����N2� . B� `�,' 0#�  aMtgign9�wIN$ � (E�w :�bxW锁n:�$� � some}$"f�K� `V�#,'f� ach �#a�=^cz ell$��roo3 �#��1.�1_@=h*1B e��=f;Y� i \X?$children, �� a y�E=:k�� +1}*�L�qEfx)ub!��  jMDcorresp�Ea T<ub-��1RRA8z�'2!!RF_"z$, oF�=q$) �$$ (A)l@#sC s $2$),��� $&"&���**��n%3I�*� aI ofE�<letenes> �4A=�� A_{n��$ _{n\geq0�8� �v %� $n$, encoR�v)� wh� �7�.Psi��A>GL_��A�un=/languag��� ^{n}:D�Cf5!�qK�:� alg} _��8sf{EQj A*�; B * nyO 5H $A.$ bq�1N��($0 ��'d��)i&?ur E�Fno ��&f-q*&�a�". :- prep�!H��2^{-n/2� m_{x! 5T.�!`��; T"\[Ile 5�4 J&\rl , ,�2�"�a�$A9�app� ( phase flip��,e=��*�=�=�&�&.�$\��(J��, �0ing�( -1 �)B- �fB�PE��Hadam� g�Oto ew� `�SefV�$yg� EI�Ibe checkb 1b�EA<�f)�7 )� d(�tS�buHGY :5 J�\2$$6�r�1�]m!!�QAgJ &�E52G��eYo��e $RFS�� n)��5�)f�5�)�ai�7y�"A�t !�Jh \� g<*��usX 4^�T=�<��1�/ reduJJJ!"i8�}=n :ym�Q2hAma�-S/ kickbackck,2*%\70 criby CO� & cemmu:;D� ��+E�ڌI�>�o�9s\frac�U 'm�Q�-]�0\ �M�}{\+P2}�$]�)e0exclusive-$OR� ZzA�{rq� !�e&!�)x1r�(�i[Ze.��bib+F�R�Ay"^'!�still >��X=#:��fp��Z. �w�L�= A remark no2:A�}2confu.J��-Aupt�-U !p $i^{thC�B� $x$�$� [ i)�?A.Q�- L� B�%I"� } I�is!�7Iv"�,�Aj�R4%�Cru�0jD�!� hol�'my� �I���A�- s�"[ a �Gfic4 as�$ d�2�&J% Au� 2{*C �^{g%�vS "\in&'"!~ blem, �l*� to�J� %j~ �A�no%��sYA�!s�'�C"� ��5} �H"�5�&q2� h \�sar&�H: J�BX��it{R} $\mue�*�O��h�s� mu^�\@ '\Aq� G2� s $D�:$\ ( "iJ� g�)1!�)vJF'uc�"Rzr� V �J�:Z<hat{s&;"n�6l�P+�<&1&w8v�pPs� \in �,s� 1 [ &EzP�% 5 �ARg"$ \,vee u@ F^� z�\EW] � 9��{.���G.� LaQ+9peS%Eh�\�:d�,*� .�s)�9�� YDm�"�L� a vuG&"��[%ޡ��6�p&oY df9ops���!-0b�6Z'y�K} \qua��Y*�&i)]ZRs@3/4Sll!WT,kqit'ifE=0f%H�$�g"[wri�4���/-@(�Ye NOT!C)5R$�^=VI".�ez�Y��&�#iOneq}FaD 1}B0��;�"k+$z�$ll satisfyL e�z� >��"i� :�2hn�q� wedgB� zc 2c06c rm� a� � 1}B?�_q�(�)Q�12p1}=��F0��� AG0bability will��$1/2$*�"4$�7o�^aiZ2��a�chAAq$zzat�Ak�� �U �T nd 1� .Y/ `if'i4)�F�2� �}2 a2i��BAE,WV$21%6��(arbitrarily"� en�%j�S�S=0^�m�2�i N�=0�n!@D�R�to�e supU8e �V�k�DeO\Z0��� �%� WX)�� �Icɉ���Q� t as�X= e>�#[=1Q��="+�%�!�d:V�f�of� 1Fbyez� `"asilyU2��E&+�OvK �Frfslb}iO"X-��$��F�Lvc:B QY5�%ts_* C:&�\n(h�5g� I\2�,\�E1}{1-R1A ^{h`}) ��>JDI� ed-erro �*.#&*as �Jd BLACKBOXa>F�lJ $��2 Na�� �@wa4?�Z*e*&�I� ies *�0� �b�h��"lib�n "R "�p�`�) �5�'ricts��vdPq R�!\tfDa@S�)s� � �R�{ g_"Rl%`pseudoQ'"� s:�is,�8uQ/D) >0&�H \ yex N0 =O(1/�)�=�� b� %� �8�*JT�:w*b>R�1+kU�:�$, suggQ1�^`&JK-lFn�4CT�so�  in" *��!�J�7it�unc4M(iori how��^�o2�fa�B�\��:ma "�bi2�2eegood�� rule'hL/ceJ*�K��59.E\YE �k:�Y�*:]<0.146$a?�r&�S�$ ���CVF��/:>mal�I\I�weD is h�Tg .�=ggC!2��\868I�?"(/q�hA"XDto%/ ��Dj3 in�![a .�N^6��*����balread�? 2�[PLS�T�u���1A�"�8�!1� & (} [1h*�Sthmrfs}_$X�=eq f^{-�]eft( �)�#�]Y^+� +ne�� �Q+6O� {R��.e(p 0$Fa�@mr_�9-�|d r*K"�9I��$_ �i$yo Y-w3ex�`let&�b lign*} \t.kdx,�) &^�9Tyd ^~:~B� < '!M2 }.�ME�"U6f gv3,\\:�yn�xt in X�� �� tX�)^� ;*#* � _6(�J3,�1��a�\!/tor�� nong0�0>6���.�L&<4 1/\upsilo�fT� =AmIR,~IP,~i~:~.�5�>0,b�6F�"fz. .�}.�)4u� �)noJN�T�8rFe&:3��- >;~. N !�Z >U2�Jqy5@Z *� ݘ6^{-2� �^19 ���yX�`Ac��"�!<>�!$��U�ZYRK2F Wej �jw�� 6�B0},Hm 7� ��AR�6 5+� 5�I�$,�"�Z.�� �t� duct,`!,�ces $v I�N2IEvx$,�:,pr&�w 2* �-� voh�'�edrawn% !#J� E�A�o� �$v4�. bit,"�F��I&Next,**\-+3�Y �it{�) DS�D�q�#B* �R* !)�76 sd&1 t��$i�4�9Y/�$y���b!c�# �Z�( W�+Jx  yEs�  $y$�>5T���.�aSV�=�\5) �\ "40 �,o� �)!�rU [ �s� �iR�=y,|z!�%� X,��i)u ?mo�0 clai�A!6.� *0j���( .�&�i*Ns�;`0a7 �,!��Io9~E%i21��� �or� se $"� in Y��@osen � .��ral�85kx,G��9$�X.a�aL .���b� 2[ *. �#equal%��%{we��!switch��a�� 5@�Cy�nito�K� w�b 2bEo5B���v�[�� $j���ex*,n patha݁$N�Ey�\ �(�**�*V�bU�j&H "�]�?�a��H�tz�42��%�*b)e�*�@�"�M�-$�)  �(�4,T\� s_{y -+2ys��A�n)�Y!{+�YYV� Ejn�" V"w�@���5,dA�s �� �y>*e�j�8!z�+�X"�+!��: �"��D,��vrad�!� $1paԡ .�!�J� %�S�X�&ink���:ofUDy'��Va�fn!�x,14�z! x=f3s8S��1=.=6^45F� >'��^�2T ��1&�cEq2T}$�6yL �>>& 'A� so o�9C1/�S8  >ogo�Ve�o���j�Ed%Aui�!z9�\�9�B-iiUv��f[a��B�%$2�.:N9��.%h}y,&0/E�=$�3upd:PP+�p�=AA�D�8s3B"A�aJ�PrQ�ՏV�xJŹ]��ua� EL4% %TCIMACRO{\dK9 \A j=1}��}% %B�xExpanz%< {\displaystyle\8F7 %End4��=_!�sI�*-I�j*9_J.�!fJ�d. J \\ &  � � !�x �"�/*yj� m�_q6� &X.G�-T{Wfory>�*4&e]:&�(�\v� 6Vpby��fCamF�` B��Ti�:e��me ���� -$a natural,XVlicit *�g��d&G��6��Z'-7V�cRR% al�} $3/4e�P�$g^d7TDal�^��Hc-Elg}z5 "��lptimal&�p&W#"5h gns}2YZ�7ewc 3/4-�` 1/*�9�po+}N4�26E�q D%"�".�&/�: 2.�*L =3e�(\lfloor n/6 �\r $ (so ��=0$);fPGlet��z f����j� B�+2$ (��1yWe �$iF� A�$:�&� 0}$;$!� -i*��yyA�a $z$, \[.]2~6�#�- ] -� ��Eq)2&s#{"�S�5congruenM��6� �:2)l&��3�>,� ��!/6}R�, �>-)�r� �0� �<��#�(%p�*� . ACA��&losQ"�;tpA� ").z.; n/2$ (�iE�2'>#reUzn-qHcKtmen�WWImlo��'sN�J]e��Z! = 4, ~?&q >3~�/n=E2 � 2}\pm �� JK�ex"�%Fo,8Z�]2$,ŀz=z�#�% z�!�#� � @����_xRhe E��1�w!u� 6� 3� 2� t{�=S& ��z_.�%^v -1��a6ib' "��|�J)! %"�=�F�!'-�|1�= ;+P RB1 .1.R'!� W1Jk=E,�nd5%�^�N�IwIv+\alpha.,,� F��.@- @��ns�m]� )i~�06� \�T, m�zdD2�7.��J �c&<#$(>�s$"c\+H%$�Mz{5.�3!.� ) /2\pm u�-�e they�'�ply&%"gr5 f�2M0 bJ b �]"�͍ +\beta_{bA]Z� #02�Ev�q !1.!.o2L  \ SoF_FEI�y- &h1}{2}+�{ }0}% M��| 1&Mxi�.��P � � � Fin�"#�F�\c.n""� 6m".��wI*W"too cl��?�%�-"� aE�J�$f�� *�'\;�:�[aF^"�is}N�"S  i,�] ��8he$\ adm�_J&�P>�j&� �"� �#S�2� I�) z#ASf��&-"�  (cCale�_�m&�%N -��:� By#cear��gr|�dua�,%P�& s a �2� WW�vD�A�j�\2*v6�+~  g^�"�&i:>1� .>*�{�r��E�AX�� t262#�� F^ .�+*ꂥ�( z,:�,6�^�in?)H�*&�.%�2P1lp2&F M  \��J3J_3� � [6�2Z� ] � Ed���|z<"�* ver ~FA��IiZ,N*�c�(�%z,�?!�2|�M��F�.)� "�Jfn]>Rt i�[ .�2e��� �YZ����* A �u�) �>H?�a�W"�-thresx:o�� ,��MorO ecis(WEw �)���p$p_{z( suc�T� aN0l�i$b$AA*B��)L>D/N��siT2I�{v�8}� = ]�� Asoze �$ �C @\{�9� [c]{ll}% V�� Dif }g}a=��V�&z:0� �! W�%�"6$*{var � !]� d^�H�c3A�*c $4!�%M=yz isy&� at 67 4 �.B�DE�3n�)�geq�4�ny �A�f,F�"�� �.��s�+9ky�>�,.�D"&�a�� r��<�;z�� �y)Cp$+=v �_ ��we�UiW/%��x *� 6����9>5 Z\1�)/ a�5�5ai�*� B�$�#\�, a�u�`�6�� [6;j�&� 4 &0tsum \&J3z} B+a�(sum6/:#%�A0<p 1�7m �+� 5H4+2!�1j" �862� ��4 �d{��Combi�G��mu>),2-�*2}!P>D026K" [OOh0{v*OPEU[��\trigu�.|h��Nu2)1�*\� b�(velO� *2&)zBb�}6�pAadRiz :z0aI�\�Y!�=8d8.0{�deԂ�/ erms������itnc���um*�"��ch���*anN^ � ?)_/�jroubl��th#H6B|$"� has B�� (�;A2�1�e 8se�"En 5�-3+ tenKSh�n'�\>erU]�^��� 1�s ���:I} ci�Z�1!��umU;�C Gx�+of6�1�}E\!'n ��3>�-� . .�r0�9&�$,Q���-�d!�% est /�Jt_lue IE�f�Ht:<wtaJ $n=2L  $g>��OR"bs�["� ] ,f:%�&�f2�.�:Yn?=�� 2@� �c�V�3"*Anz�$�� ]l �[ ��' �60B $10$,\�� $11$sz�.�($���NF$z 0%�E�u m&" >!=0�� %��J� $05#5Sbu&�� *��g���80-��4E 1� Gbq��At6�)�6���f&�p��t�8�_1vyJ� �f�Hf^hx""ym�b1Mcur�KA <s,�>as game-*�xi�&For&m..��.�]��#<2�<ofO�xf�*�S�es� �x�9vp��"F lea|}�8el�l��,FmiFU�"�8�& wim�3perD'tex (�(e��*$XE��4%1�,of �=)i�Z{Limi 4 TKAd�'[ ADVW How)��ki���Ra�2�aF�7ly2��P! en�Td�oo< quKnIsO�<.,kHolevo'saN�c�h}; $2�T*]kdense5�cod!� 5b$�� -� tele�AI� %bcjpy};:�A�2�Dfibpri~_gEcww};�>in�ly:C�etf�` inuou% �P=gen \�1$�A�sA�A[�/ly %sit{mu}" Zm1oS\A�4 %� unasVL a_Zsb*6s١I h-w� l .l> .i W*d wA�p�Mof1D9 �� e*A Supe�}�4? \ Inte��!!'�i-�of Hilbq�s�J7w} To �Z�l sYjist*�ji�%i&!t:}�]hA\�n t �it{Ma�-�@commu�!Mp/A}Yr bjk,A.8,klauck:cc,yao:AV �setL<� � llows: Ala+M an $n$XN&KO, Bob  $m6y% tKt~wish to�e �x�2y\e��{����AJB�^�g �^"m�ar*]M6�N�fAf�-sa��w�  $x=x�\lr�x_!0,-/can s "D1�my�gdrho_{x�to!E,;reupon UQ |-R��y=:�mᝡ*(.e�bas3O(o m8l $~CHe <=#~  �aimed� A�5� .!=B�9؅es�/in�l��)'s�"_Rbe�^AC�>ucc��w$YL�v�H�K�}4 � �I��# length w�HmT�  if � haA� d �,-�.�dVQ�lyb{�nA7M tudi�{1o�~ale�� ce (se�e boo�0 Kus�z vitz�>N��m�kn}�A ple8In��-�3�y ~'�ough, "$"��e�focl`~�it{曁S}2T,d_a�� �l!�geQE�-CUwck"_�%�6P��!. y of��q'2}W@s�W��dvantagejF��> o�A8l��M�6Vl!z�'som!��6�~�+ez2���ciz�2ndZ�� �}� vG��W>b*b��d�sWe �sc��NmodelnYdM� addr+,�r �Bo:�e�E\.�� ful stuff2��"_pa�ZDW&_B!'�}r�s�y�6�&�v�Qcin�q�2� y���$ initi�1by �  ~;A 6 s �A�6���4r2aYa^�cc}. RI��V�r � C)B%qq���" As pD�S]ut�Niels�rnd Chua^ ([p.203]{nc}� B no�elEqphy� � @{o ��&!V!�rtA%�a5�J�s!5p9�alͼ5:\fv��Z��objeccl ��.h��t�H� outc�& s:kpr 6�(ich began n~]rli�-� �I extr>�� ?YI*�r�[=A/&�kڮain�o�sqt��ar.�Yb4gn�ch���M`n�o�ir~tvK-���:��-rw]�gto��erpretJMQ� voca��A�a"f �9S%wA�uldnL�JA%�#it{� 1}AW.�<$"�w �er,c!TJlKc�!)eci�Ln�� J $n$ Jp�+D %i`*� Ithkne0�pu�L�< �Zˋ% !qTe�!�9H���� �!��D�� �a��3PR1?� ߁�&sf�c/q�}�3mea��55��ej, �/.�Q-u/O4-��La� �='N�m_remin!�ade6�a� ter-* X ��_19�%sf{QMx�_0Merlin-Arthur- But:re�wo ke�*�a�5d,�L �<ru� -�� s cannot;K 3 ailo�^�.�I7 J) Je���fula�����/&�e1�a�A0 ed (A�e�)!�9���-ag� ��(Bep� ��re�tur 3 G c���<��h_�A��gep W�ll:k� � t,)�i*e'�%���-&�,�w� �SUiT as aB� �\�~an* 6r�b�C1�t�r��db�� sor.��e�LM�A֧��WY�p.it{U:m s}.0Vcہd�6�!GI0$e�a��E�8zsAS�rWi9g�n"*yo��;. �S�V�ImQ� %.Q��P:��H�&�L&C�. A��BC $f$,ifal orj !6cc$:q.�.�dejinisticE`��6M A�� �+6� �N� j�XS�SM�U�fi��$muGt�^�'�b'�pu� I.�}F~ 3�0�B�_ ��too�*�a.d him��hor.[-�ź leN( learUQw !�}5 h��e�oi�m�Vo<5g6�I?{r�G? a sl-e�EA��' s---�  2 mn���-�:A| �%a� K�U "�}&,�nmma!�Sau3�c�s } �g VC-dimen�>E�� ��ų? ��E�A�� no�]ruc� � �}to fail%>�Uae��\�#neb�� U�@m���A�m+ �,6sADVSIM�q�+�at��BQP��"�P�PP/s�in�H[��"�lG埡q I*�G��..�C�!��C ޡ��x� all*� � �f9a;�machin&� B�p��z\iA�7^7��  AbSee>ĮMPLEXITYe�m�*.aE� �9�*�e�6���H�K.}%hres3n��? ���8arry Buhrman (p�oY�)� o asl�$6"q2� any} �!6�Q��E�62I[!.A�qoll�$3Gis�ai�s�� Z hop� ��Бiv|s�nKvG&s nd �� �*�s�"U�acA��("�� !9Ti�s��iGPe w�E haveF)*�s. W���iNUҧsu��H-,a�A~ e�A@5 "T�5�� �ka%wl�.MIve9�zI�� 7elief��0uel skepticis2@Q; �!(see Got� ��g :qc}�A� At."\ *<[ly��i��� }e�-�G y�' whatso�S�FWH\ imagine\ na\"{\i}CI��I��H�??�a��PC IQy !� �.�m6c* �e/.� of ai�=! n�uure! ����d�_�e ��D ] .�A6��e�� � ���2���6�Z"�2y5%2>h�n�NaEv*H�Y���"� )�p�e2� DPT��Vf�w�W��o u� \a!�D a�in\ٗ�A�U�l5$%�o>��O the 1J�vc� o���%A�Q��!7�>4j iMs se����An $N$-f data���p $K$ &m�6�a�e �>e sayA&at�Y & D�� $;��N=� �x�^hn�fU�[th��]D܄,l���e2�a�:>�" K%No�� ^%7"C �q�4a nya2��-U�*� !�E�N� ts}\_�a weaker��.�,L)hybrid�+�Bennett:q bbbvA�n�9|#o&^�-Y . eoff(r s�P}U�tunatY3 �j%� M���� "z��� �!�2p, ��٦\It��$novel twisA�鷡�in��l Q�\ er} deriv���.� ��t�%ZeB 0�(�� �\w.�by-,, \v{S}palek� de Wol��kswx]Nre ��nc��and�>ex�+5X origh<��i�y�Q`1��� ��F�TRACEDIS�� new59 �e�R%3.�'l+A��-I�� ���A�Previous!_!w`�KB�L6.` t��ae .m �A<)+M5&� z \�i'2��1F] ��%sBJ�eޏ� antv� Naya~n �"� 2�� � �23���ɂ�:!DISJ}� =\O&ٽ *�H!ArA�q!.�{"�}F��b% :vR#\�4b#�Fa*# 0.�y��FeѲZ��:�#=1$5?y EET5x_{i}�=�l!�� �gD�"�S-'�S 1Es��*3%!?2�i yields�&�" ]ra SeekaDto����p vividhs�`)����9 �L!is� Wel�s �"00�j��f�jbb{F}_{p&"Z$p���);Y!Z�2b $a,b�82O�BgoaJo8$1$%�y�+ ax+5;6 5H=pM� �yg��<f�01aCe2�F�i�� qor}�=����Jn�0wOnE��Awell-�nyg�-)� toco�+eUW 1  �Q ry}\*� �Q"ܢ2�)Q� play�!�a����io�So K�n��X>�,Y=/Ib �1>&�ir�2��w =��2 � at:7pr-.�;{� Q� 1ma� "�ʆspiri%��62 �ZFNI{�a(u $[B2 :3!-8!�KA�ubset $SUzIAoBLkI$x-� S"�(s��ax�nmodulo� O�=��e�S���.�:M"1)0 FS-(v�*$e$\�eN_�Z� %�aO' Xe�!2:Zdl�QZ%S$F_ -��,.A�R��/am"~ � fP�� �4I�{ofy���%!V&��x �6Iw�A niK��}cQ�S!�$��%��� O ��A�-L� &�okDE�*�V�T�Z�&2C0�Yond� $x$j�3m� � #�f:"�`� V~+="�Ks� �� riIloŒmiҌz�rho�F�Z _{y}$, �F/(m̅Xpto� ingu,p!�-�igf"bi�=�h� ��Z�elIA�nIa�pk �� E��bl m\VaO�-�mh:�R*{tr}al� ?'em��"�a5S; e7var Z�i�1a�1y"�/5�U� zV�\� ��s;~���� cosef� � W�-8�u�|_u� aC�'uq�Bea1s%�!�-gn�8�2a�f J� �.�&ew��>*� tow�a�vt�>� *�*�v � >� f� >� � m>�s? F�}�J��j-$u��B�� I!��>e��<k3�d -+��)�*B�P� �hA-�3�}C}� �!`� �conve�.�byB}.�*��8he6��ٌ��)D�x�mum num���3)����q�,if�/��ED" yNx�9`�4U5 ]��]e� F����4 � $k*GeX�yI �L ��s�[a4H�*�U%��F�fy �I_{x��%%��% a!@ $a.�$a=J�6�/ML. a)��9(�K�Z crip�96�anDe86!��-�2dNx8g6/ =O��yRDM�NQ!�sip�Y�΅!� �f�� ; be w:�:�xm�� 1V6-eS9�C�l� G M l� m urz0�2G" m��B�>�6^m eVq;�Fa�� ��xea,kal� FRJ.� 0�M?�q�be�s�EA�&�anb�F$4it^pQ�!S]H� exacn(mIG�u>�!LjIFN3Eb�# r!�ݳd�/�� RE;r! %�&/3 �`a pf �i�2�u���%�st�%� $2" =6raus'! |f�qk$-19.�e��6�� hal[!�4��(W aw c��ͪ��E��"� pb I&b\�*mpde{(ed �s� !�c"�}N&+9D/'d�Al# mmed0�2>�.�.�?6_*^\0:eb'&�؞�%ͫJ�e��i�������XJ�j�A�Al&�� � ?' Duri\v{s}b� dhrs�#([:rf5 6!�:8b-b%�2 lef�8 �R�E.I "� >KC^���n.J�v�6��� �!�>�{���q��s �2R#=�� s 8@)8�p� oler]Ea�|2�o�>����ins\ tֵ�"]8���shr=*)� �!EPR�8�G��^A�oftc�7�_ situ�"iM���V�6��A��&���3��eas|� 8J�f�� =b� t\� y�gh��2(.S�$:i! V] "��x;;+�Bs+~;/2� n/4I�\ 1n/2+1 !+129};�!�N| ��F6B{)anVu2YM � w� �,F ��mtA�4x�+ A. YQeH, Bar-Yossef, Jayra�KAid�z+bjk�vve"w@d} �G�>�a�VF. 2�#v,�A\ejR� A�InI�cular��ey!-K�*�%A�a�r9/ ion}&�:�"�D$e�He�, valid� ���0w�un��,� ?i7lo2T�?J�!V0b�>W!�;A�C Z nV7urP1�3A�,#yV1Z1V�:U".|s�%a"s�A:3wADVICE}��� wE"�#*�#��� a=&4�qin*�' : &#F `'"�3*-!N=+�6I��<*Iyp#�&� � �:*ng "�[�(def}A� $L�9#sf.;S��a=6��(�� { C�@��5�1��8F(W�*�C� #f&T | \psi `@�leW:n$��`$wL\:�#B$,"�K�'te"z�i)]]4B L\ $th�S"ux ��geqR� $ #!ihea2"��\ iAb �3b`!| �K1ECf�($%�e�J��5�2L7�h|"@yK� i0ɏ�JR% !�F�e�x&[(���5x\�tn L�\�NGllU3.Y�Iι6�!!M}�-fN�! ��( \varphY~O$H5-=j-M%C $pɜI*R� e�:p�.+i� �Hqs�Eli�) ���/��] \cu�x�M/3�!��8*�bA�at eF0:+.+uBhimura�YamakamT�nFS�zdϦ}Qh&}��x it&�'m�B�e��a "Q��:-�n|�),*7are��� it �+anywayT/�e. .i�2]�"u/�%JT �itf *�0��),�.C:��'- ,"���8,}-!�W�<o. a� di�r�n�*Ao 9 ��eh�(ss�9�@�!�$membershipA�7W������ch�de�b ��Ml>��G�O$\G a bl(D box {\"�?>zN���+avail�ۥh2Y ={l��# y$ (i.e. &��OR' i��a�Yswer ��)M(`�vinJ^ b$.}�"$A�AQ�.abe�;2QIs\�m.$H.'su��p�GAB� �B7��%� �;=7\�-, so w�a�a2nonmV*%,:s��U72��%"�,-20�: <�"Qb� �> qH�) �f�� �F2�.R�i}d�!jian2)c��50Ǎ6&1�,AxdR t��D-@0 t�qc:| A�or2��!�One|*�$1� _�:=� [a!y�� qa���� kn��30&�L� �$-�5 -:�`*��%�6�&HZW Z.��}% �6m_{/#NR( y2[�aWI�"V��O@23��a�>�xJ+��.�xF�f}app�n���6) =.:� ݩ2�f::~!�P\ ye] ��>0)BK= :�B6J �T�%)�$. Ou0~ �E�# -6�Y�6�oa)XJ� ] 1\e�� S N -IlI� 2}$,4#G�i a B��t"�#� �.f .l"H% �%�0a�G?{-s,. ���Q�.5""? ESJ�.�N��))#le H|N/=�+e0E�!�#��X� � occur�?e<.�)�e�" J-> ҡ�AlV6J��>vi��iq/�]eeM !�B�A� ���7)�%K�� ��� 8>�"� Q!N7a��2�9�7of&b 5Nb x" EESPACEUyt��"4�S � % $,&I�@�oBg�/�n� !M�cF� z��7$ r�Ted8!|9)�AA�xAs GoodNewUx� GOODASNEW�3&K-Fe7�� G �0E%c!|�+�/3!�NtB �siH&4;---inA�� �!�ial��, �$)6E��$np %�t&15!5o&DJ���&� ��#�sulY�preɀ�\ ith �l-�Hty � %�lE�&<i=>Y� amag��r/�?�Re� EC� tracF�&qrho-\s���V�&� �� two * AC.�'N$i*�bs��i��|ɋ mbda&0 }l�A�$\l &�NA�Ea�eigen&`�� ԁ@"Kl@@"<%�W"�n�$-1�)re@�7�-� m��A/w!� a^+ �bvarepڍ� �[��j��Yr�4IO $�k��rho�s�J%��| >&�()Zb��\ ��x�uB6s 2�AN�/ a POVM*_=in�F�ancilla.0"�o-�1��6��ŝA�psF�� purH(�!��ent���L (E$ ~i �)a&Y rq�2�p*Vt�> $U$ ��nn�R4l�,F3amb��=;�7� I��n2�2�! )1"�^�e�%�,�M&�!sY{.�=,&h  h0}| �^rB U=*6�=\�v .X6(,+\beta\left|�L \varphi_{1}\right\rangle $ for some $\alpha,\beta$\ such that $\left| \alpha A$| ^{2}=1-\4epsilon$\ and 0 K20% =.0�. \ Writing the measurement result as $\sigma=\�( 2s ^ ) \t�0:�!\l�9& | +; �-.N>9!BN&\| $, it is easy to show%P% \[ @bs�-Upsi �1� k | U^{-rKl_{\operatorname*{tr}}=\sqrt{>�( 2H t@) }. \] So apply!�$ i$\�$ �$,6� #  U-��� ��� F) �LeA�4widetilde{\rho�beEo4restriction of�� �Hthe original qubits,KE�(Theorem 9.2Nielsen a �-�)bH \leqBI�> JAR5L}$. \end{proof} \se%L{SimulaeֈQuantum Messages\label{MESSAGES}} %�f:E3\{ 0,1 z\}�en}\tim:efN m}%M<arrowVG$\!�0a Boolean fun���In this �P I first combine exis̉�saobtai8 e re� on $:~D}% ^�� ( f �) =OmQ_{2}V&/��( total $f$,E\0then prove usAI,a new method�h��F� log :�Q}��\�gal�0 (partial or �). Def!m�@\textit{communicae�0matrix} $M_{fa�to)�$2^U%2^E$\ / with $f1px,y9W\ -�$x^{thTrow%^$y%J,column.\ \ T!uletE>� rowsa*f6�I{�Gnumber�%a� inctps� �,( follow!�Pis immediate. \beginap posi!} mQn~F1RE(%1align*}>�(D}\nolimitsV� & �v\lceil E!�:}1dY�)k\r<,\\>�Q�Un�Omega b �o2�r�) ��1 ��9L Also,!�%� VC-dimensN�VCJ�$\ equal?( maximum $ke� whiR er�T s a\2� k$x bI�EgA�of M!\M�n�g)w�h2^{k}Ѧ n Klauck ɐk 0:cc}\ observe�8]\, based on a lower bounde�q��\ random access codes duea�Nayak�� }Z�[ �]M�vc}>�ng=66R�5!)���a2M"pr.NowE>�colr� F� �K.����VPu \ref!\ yieldsAO�general =�:� corollary�vccorBRDZo>�^�^D, wE�$m$���� size�� Bob'�put-j���MIt � s frA` lemmaGSauerMWs }\��� 6�^ um_{i=0}^>8 VCTB�}\dbinom>/Z }{i Gq:�Z0N� � �S+1� Henc� 6�V�geq�/B �%"� e��-1$� ~g��2� F�N�U�ɩ�$ \frac{�:LENN}N.%$)�.� }{\\ �%N|6�^q}{mNb�` In : cular,B�^a� >�nS38re polynomially� e��.� whe� }�a�2<smallera� n Alice's�  i�8not quotedbla� padded. �( \ More forey���:�Q}%�V� ^{1/Q1-cQ Y $5 $mf n^{c9� { c<1$x :�E� n y��� n}$ (i.e.W (�"'!�f )�e henB^7=n$ byF�j )�>�nTv�f- /68:Gn^{1-6W by C��K�0. I now give6/  repl�� m�!classic� nes%� :�E�!kAlthough�� best7 I koC� � � --->Vb�bG],Jn�U� $---is sl/ly weakq��վ� m��of R�, our� works%��it{�al}B� s as well� !�� It also f a (�8vely) efficientgcedureA w� HBob can reconstruct�� :@P, a fact I will explon S1I�ADVSIM�-8 $\mathsf{BQP/q�Q}\) eteqPP/I (By contrastJIS�  on; 's LL seem�be non�iv*mt�"N -ithm�S FS lo>��� � n]��:j !lcal�Z�N- Qt Vi�)� S5��φ� :m}����x\i�RM$�MB � _{x}� { yj?m}�( *0 1>$�EzSupposeie sende&a�Pstate%�9$\xA�`at enables him to computef�%3 ny $��!Qterror probability at most $1/3�� sh ށ7 ��a boos � ��$K��:�r��l5-&� for E5N'� vert P_{yt &R ) -RHi/<L qz 1}{��^{10}},z?f��.�UN *E $\Lambd:[A�e�] F��`$1$'\�c � �io-�. \ W-� ssum� r simplicA2�)�\� a p�3Qe�!a &�z�/ $;��discus��8 )$PRELIMADV}a!3&=Tz length��Q�ɗo� $2$.�u#Yabe any�et� DqCsatisf,.�qlY� �}6 n g%}i�t<ng�G-n,�h�-� r�a each:Y}$![Xlexicographic order, red!Psam�%U %� \ ag� but un���hat�0garbage he ge�tM ile �ingC ŕa|_{t-�|�Baft� e $t��&:; thus)_{0}=H��A�*D�� ��Sip�Bu outpu0he wrong valu�} 2|Uny� n $y-Q�$1/z!*� �;$,\�e]e� } e�Hha"e�V��!!a8_{t&NB1tr}�@ {��}=< �&5}�-�ra*m� �e tri� ine�ity�  turn1�=Z�5~q {t��5-S>{1}% �73-�imagin�� )�< ideal scenario\c � � uye:_ a�y $t$;��i�� "� s do �dama�GAag laׅ�a$bi� �{eLcould���;uisHactual  B6� isV� 0}\o?cdots rho_{)�R� -1i� F!Ln3E- fB%�N �M3�MmZo�#!bun�b��b� ���.# Un E- $2n �MstaneousT!�.Pat leasi�1-�&�vP>/} [�� }J0.9� �su"ly larg�yv�.Dq.���%y6�channelR blockedue*ha�guess �d�� wan��&� a�He do�i��� $K$-�!��mixed� I"'e rho$J wri� I$\ ai�I��!j2^{K}�m_{j=1}^}Tpsi_{j}�q�%U f2$#e�.8 BN""$ N ,\l� ,B)�% 6}( Lorthond vectors*a >v Fj&v�)FSo if%�u�"h��me� c�as ab� except %�stead9���ene�any* Y!�b&E&$ O.V�� ,� NC: aZ�AJ� �@ �@ $0.9/%�afT�"�ET!ofeq�protocoel�adllowsa9� �� 7is%T! K n $yA Qt y_{T}\in 5XD $, together-�.jBi) U� !!=U�š�,.\footnote{S�%(ly speaking��� bl�� e �u��6v\%�himself b� �2�$;A��* need)X!Nt�PA� $f$ D s.} \ T� 1~� is $mT+T&e>h��U��=T \ Here � �semanticuM�:~ it{2f ��A1, s- you loopc �&�}66MIQZ� ; | e:ach�,��4}2��=:round*2�I7 ��2$6 T�T ( pF<!�}$1L�Hp�o1/2^+}$0if }$p<.'!�i }i}�$� )@:�&}$yK%>� !�w� g�Z%�w&�  otm�e F�� In g�l� }$Im r�)Ded~ "�f�}�P �dt���]�:�ay �]�3F%t%� &at�i�EFA�ou%E� ��,s�*Uk���F�%;! ����\l(p�z (Not�*aFHm�N* g)B2�of�Q!*2� B_up��E9x-v, only!�:X *1.�7.) \ IfEP��sxY^� b'n!�M%C5:, "en �t+1ag!�J�Y�encoun_�Me B�6�6$2�5�\neq z2%m2�} Giveg* sequ�!of�U t}$'�de9)d u.obvioua�at�u�*a�F+, if $y=-y%*s8$t��a�� yya/.�2%�O�� wise�+�\asAL�& ` �t�%�- % ��:� ~"� ) ���%e��nq]� A� V�uU�$�  claimedF��� 0Notic��, a�� � � ledg5 S �}�-�/�� 6+ toMN�in��Nia�preO PI ae"why!D. &S�� ell e|-�s. ButFAwe �&V�stops���T��i<: ? \"N$T>K$;`8 der� �d�0�Le�1YY.�� *� K+Qy"�e"� |&� �| =K+1� :h�� , so�A��pre���0o��%3� ��s I$��eA����]�:���+����]a�\IVt��6� \ ATbI����-��A/t���.1%>6� �_2�<correct�<�iE��2G condz� /$�r&M �having t� e>�eT=*forf� Q�6RKU�)�� -�dN�UN�5 +1}<&A,!trupO �* �M2N�2Advice�,�!}�$b5%��1*��! to upper-�)p�-of"�aa&Y-"� t8"��K" �J &x0 of} J&notBal! veni��� L_{n"� x�0 =1f�' ~� � in �7ua[L!.` _ 0$ oG�� 0 Q�f a�G) }$ machin��_ )a!ss$p� &"5 We��2  assf{PP~^e� �s��&�>v $"�%nJ�� N& \ Becaus� � l�! connI� betwe�6ET�one-way�&�3\]��& �be essen�3ly�)1o �ofa�47��pR$�Yy- &U! �� on .S!N�;!N5 "Q"\�"�*-�9�,lgorithm $A$��-�-�QY�2M"2�� $1/J��!�)�an( �%<���MSU�z�x.x�";$>h$n}� 6�6�M5J�� ,>$T$��I$A��� 2`%�$ �� &�3"x5sx�"`52ref $A$ & �!c� $x$,e��7�� �9-rEn!� �J�3�2( �Y_ 7 >-)rFh�Jh@ 6d9�In 2l� �vd �Vdw�!�� he-Qg ruo $A$\!@) -�APh2R  (*� � al c way)F postsel�n e�"> ��B��!&!� �~� $x>x�.�B�&)ˑ P_.�=5�  b�.�>,!1r �� as G8s:^ 6nE�=�q� A" putFw>T"�%5`y�*�6m%Z�/�=$is omitted�b� t�Al8at��be >n5��a�!�be AXed�"� O. Adl� , DeMarra� !7H*t> adh} (see�( Fort� nd Rogers 8 fr})�� a!u�i BQP}� 2u,�'b�z physic <� a �,Feynman sum-�$-historiesJ�1Specif}/�1let $C�Ka ��sf6� circui!�at��rt%�)hl-$0$t�-nY a�7n� sole�| f Toffoli)Wa�! rd g�%(Shi I9 shi:}\��AnT#�/0 <'isS versal�1A"n:|C_{z}9aZ(tudqbas�>&��zI��$&K��!.$have been u ieda 6��C�A�a sum� expone� mN�ibu8s, $a+c"+a_{NA �)�!i�p r; real=���in��9� � n�!ef@!�sum*#�\� Q(=\�7,j�N}a_{ij�*pu�v��i/E nega terms� 2�E�o- si ;�fe �r,2/ �.� a��>� �check!I� .�f�>vE%any9n' tan*b�EA*g9��* F��,2�)q%Kz~:~SA� M�?Bf-}f�% >2J0�J@\] (or equivalent�9wh%G $\Pr�[ �%� ] >6F ] $)�%O��Y�9 pred�@� X� 0�� �E���a��A���T r,se��not&� r�1����^"�" "� >�"(as halfA�a $2K#*�,)�� s� ->�},���&Zz#��pB| �e!q&�w� !,�)��^� \;�#t{o�$ registers�+p �K$i&Y :�D�1!1�I'EiJ�$\ hold� ��|if.2 mi�\a��D�e �&�.>!!$6NS ,iEeQ �Hnot h� o%A�p+B ^V5�#%6}� ] } eY :]�I2�u� ��so::R >>%lh�2# "� �.��M ��+A�m�u� ~� � riviZt� t!�� 6�)+ � 6f*S F6�p�G��.ake f| rema{7ab�H2 i�{&B�F ��e27p�/:m}\~ 9 ���7"d5s�e+� �G!�� erFDL��*�romisenU7 ""\7�!NC�A9K<ra p s -problem  ion��.k �~nBM �re.  St8d,!po�, aym�8L*J��� ,�";� �7<2)�EQA=w�nn��hop�$AZ an unr�HvizP�S� 49!X�B� p!Qi$;-s�8s�I ���� Y�>-� �C.Fo# -9m-}n. �\ clear�g e/\=�F?UA��A�lat/ � .KJP�Ft G � bDALD!UPP�$;8>6\%��#� ib!eU a languag��p--�� {ng"=2^{\prime�in=�] i�.Ad � �@,P�� pai2;*th.X P}$ )GYFp��"��#$a%��(�c ��I�(A�.Q� a syntactV �edms�Third, i��Ie Y�AgIR-�&�;EX9�"+a *�in  a�-�EX�:1 keepNk%Y Ap�1$H$A�- Hilb�2 to ^"`true' )� must�A�I����&� i ��ii2�sF� �$\dimt ( H:��.t ved`1��H�b-�ZB�G$1E���:.�K k&3)J�\loNQ � $,� &�n)Auof}��F!_A�hug��M�R�$�v-�to>�c��4?a�w�Yit{� Z�&}Štheir (p"�:ies} i&=-2OQlRD"Ks��La���Cer� !" �N�:2,� �at� e�BcQ�\x"d!Bsho6D?F��p,� Iw3�j0ny �*a<�l��!& �?�9c,�ng%m$diagonaliz�6@ �Kce�kFourth��su6��]n�,ASH.�� %8it{al�}��B�PA�o ki��) �� for,�$�� �es�!n!`lie��Y�0��%!f_ !^"@e�6 ei�t obsc2;�A]0asFAW H)�frEvI����\!��$to to�vei#th!�s! , )Ul�; ��!y:�  Post %��|-9 !��s� �Ks decid�by�+�:�#1�&0(ion}% ---me��e �>�aMW �?bi}a�e'nonzer%"!of be!�,1��"\*���eAdNe�#.� _#b!'&V\�$C� 9�=Ol�8 someYb�.�!vB@ ; on� , n�Git= !�Tanalog�:AIE����ty �BPP}_{Qpath}I�hhtI�t k9s��,�E�1�Va*E�=MA�� Chap_ wPOST},SFif�2DDs� �� �'/%Va�B�_ $l,& ��D}� xten�#� g5rPQP6��:Q%�m Q�.pNPi)��is,"GEaj� ��I!���y��a> ans�Pc1 ��be H#,+g<2$, ra�� than�ve $2�AIi18 asked�@.F )��,�A> ilZ ^AYDP"�E=��[3 �is no---indeed,NH� o�Al�7n� �so!Q2o�&as  ���( D1D0B�W�a^tW# �!�5�d %z be>��6n��t1}�6 n/2}A�m_{*EF� V�hx �PqR+MX/.M�.I�&�to�*�DV$!�aw @5: $Z 3 �*�B]$,O � 2�!( d%%���8!o�dar�GiIf2A6 ~DJid]'�IN+ �) �B"�%�p�  @Tbit�&�Y{A Di�( Prod\IqpA�Q��Search�&$DPT}} CanUo� rs9 aױN�jlet��ss0�m o?� e /day��Q�Gu� , Bennett�\�Q bbbv2 g�a�,acl8Zvf.�\+ ��"2��$,�(vid�a�Aist�*!�� evid�we��T.M�pIt *�^��:�'s6 toE�n���NZ�&< � �-�Oͨ!��J ev�9nonunI/1wu{E���Ew�@y�6� n����9)�5�@new di�<ulHrises:�`n�!Yo)�@2�$�Z$! *<�sE�Ÿl�KA�%�e(n�%h*�&�<, � anJH Ni object� t i� elf, ma� �N � ina���� ��t�ABWe�c!sarC Al)�if OY�}a min�Fle fra0+�.2n&z&�)R A�!) . How� S6 �t� N/A�%.� E task l reduc4Fh� it{d��p��c }%�Q�)��T@1� )�!oDOs�V rm s�I�"��%$N$ itemaK�� N?i=%lack enomPim�Lf� a;I"it{one} 9 X� ��* <��]K$.� \es:binPA� intu,ly"�9� re wa"� )�)�) )us "rOly�q!��4Krk #!)nenB 2�P�8ing2M�� �(AS re�?�itOa&.�(.��J#9S e� multipX<�`�%�F�-d# )kY�uO[��5�e*QV���sA| impossiblvisI�1 e�l�in�Yb np� �+�2atm��Zyi�'fajIg��lik���D�(ri��'ade� �E"r�P d$2 (��)bym-�A�!�A"mYCCdh% J,!v��s u@�EurpriA6)laD a �R^�eluO p/!X year� In 2001, �\ t]ts}&Rmp�� GY[hybrid]-of jaa� His motiv��w�)� a l�_ of#W0ed��or�6] U� tunate� �'s �is fal:Uous.|?p*�%o.lasA nt� } oj �R5�=, (2�e�C*� �u(�~GEB�)�4&i+p�)-\�h\�) $2j S� just�>0{ prece��it.�1c*Jd0 Ap�!E�c�! �a:Z!)�,��R.�Y2Ealsm �'bbcmwE Be�$ a%�?^b "�B"�f m Z2��u�to  U�?�conclu�in >��V n<`of�"Q��(Iq,, \v{S}palek�de Wolf\sw}s- detailsc'I��!r��to ��3�#�f�7*X�><��&�^B.� �-�"33�^} [.,�`,lem}SA.�|0 makP$T�Qe$)!i"� �!�$XjN�'K�e2[$A ( Xm� %�a�&�bgl*'  $p$,@ degri*8S2T$c�J ""h�j4:U8EXUa�� � =.#[ J� �]�S ���*B�#�"N 4�,�.( 2}$\ deWDGe Ham�we@ a�$Xend1� ���Z5�\��a��D[c��!m*9bq-�$T�1d�a��U&�=�I�6R$\deg%R(&B�D$pq F�repre�3�mo' ec�,ITaP A<AsE ex�*F nyF�%Ce�!�6�<OR��"�on /] ��� a"G�,&�S&��meM�*�50I��[a/3 �#�& 6Y�3 2/34 4M� Z�1N�!JT6���mmof�2 �#���5an*P!$�eby A.Markov��1890 (��aaN ov};#_ rivlin})&od� } [.R��J�5�@FhA���B t�*N>00'$r^%N( =�-x*[n'm��%E�3�s&�)�a�|.h1 �*�x �i p"!~� I r7?�X�J� �E\�o,{N=�}{2 Y�}Q�%5��[��.� Q�E]entire�ga���:b$, A<� se1-y�0%�raig!�eq�$K qCvJ�a� as�A�� ez,ns,rc}� W5t�7y%:� by e\1ary�0culus, �9O�>1/3B�9�!��h��� �rge T�s=Cre�m�%q c]��A��=5� �}X�ur0mor�;xz) �Q�J)s!��tyGc$� E�&+!MI�A�. '=�9K0A�](E`\lfloor V U\rm@c��a�1wQ!1� Swl>R �rQ�%1�� u�!m2k( #�-/%��K��n��29 \max�aM 1/3,n� .�)# .g2�}}:�c{ {N-�tm]M%����of\j? �!.1r�/BO& n u.t�;, . W� r�>n ��,C�3n�kn;*'3yA�! � 24�(��(ghtforwardl���on7� f�*w �i�es} �extKJlyMd� a�i�!A�/um  D�2Z� ���.^B6"��)gh9 V!=� good� G� �&�releva4c"W=�⁑! key  !gok"V�%>&.��p�#� igQF�!��tart,�� -l�Ybe�B�\L �5d%,pea��ere�4!�B� j~} -�t� bb{RM� 9� fR(elyO lbun�2�_�po�48 u�+*�P&�  A�Y >�0�PK��a�$�?JKi�� delta>0%�A&�6��m.�1 f&� B\n*= ]�V�ɒ�=�Aod*m+]9�E_f$J6��$ (B]f��% =f$^��V ��%=/m!B<%�m��\�1� �}y� ;:}Cg'�I,�in�X m2V � $K-m+yC*. s $0��10}R�<�7�" *{ &od 6|,B�uV� ru��i1&�6)%2�} T_{d.? �e� �u�i��m. k� {d�?] -1�� b ft( 26=csGy2}�MmV )��2&�}{1935.P 2.@>`X+%89�=\cosd\arccos �� $d Chebyshev*=A�e�;> 0� u9 As dem�p6 below$O.�f2�.S�|� R� &�*�z� V$E�NY "�p�/lb}� p} i�*�"i "b enume�} \c"[(i)]"U&< .�"�)��� �ZD� s &��0� jix and xya��Na  N�{ �!%� *"o^ f ��B�2<G�b r2�6=M"=?kn�ByQ�OJ� �\w$cq�\-�1��e)�RW �V�=F��Q�I�.��)Cbll Z?Y� &�] �-�jSV�!�q؅�bd�� ���J�^{2m}Γ % \] RearLd�B��fH � �# 2$�C.|�H �{ATm} �aT-��$$\ (if $m>9�&$>?8NG }� s% i�9i�$s�T�n��wo6$"?  D._*� � 2e��asjcupKWn'"l (i) �]|\ �Q(n  . �3AV��]��. 6��H_mNI�b }{k=G}}N�}. \] b"�F�  Nex��<Bq�39v6� 2��g�ZleR\�V �So&hm=fe�@V�s.K}{4mp:�.� .� 2����2���� }{K!6mKamVt 3a�.�c1E8t9P[r�ine�\�� J�e@ "$@nPe�ull#�r>�@.�\� 7^W"��VJ?$e "q!�Vn.FA2w%ɚ&(/*r%!�����%�,�- �  ^-readyF�&\ bB�.� 6� byL�s� �� %"<��to $p,��}�.2��e,$��Eon�?-]�}ұځ����2��RD� ? 2Y @!I>�H ��XT2� �E)%�u3R�� ��YN�YU~ ZE��Z�$2�fjAHo"�8e66A�^���D9 gets�f.iM ly $J�  {2/K1Z/�as>M�/N@6?%��M,f�<��" *�*An�3ier.!t#-cj9� ��ZV�K}% /<@^{3/2Aj31/��MIQ5 �bym,>e�,it{Bernstein2�} �#b}\2�8%�&Fto�&e s � M�}RI�Q �D disc�)ed'xlaw�A  argu�;a�I�6A!�c�x�\ .�jooth ukZ;wryb6 superse�,_la ;�)T*+-*�+ShortlyQse�<m%p,a�1:+��, ], \�u* manaxgto| �AH:` ZH�D .6[tX6 ��NKIK>E)�n 9I"��A�Q. �ltden�1$(ޅR� =oQM�}�A! They�FaT��im%#AC��Q�faUp ing}0.�B2�ng�1� e�� Y�}�+.�^��"� t2�C�-Zral�^ �; saidNGV�8Q21<4��+ 6�+0oU6��ng��+!p d�M I�z5mum���), a݅$X�#�6�*2dN2 +=Kj&* �1s T� �2 y[\�)�� ANlta.�cT�/@K}sT( $c&� ' Hi9��"�*�,65it �Q4 or mlb��reject }�h�nQ�&15h\l.ed.j�)*%+o!qis drawn;��ts'M�su�7�Q*|%6�,=*�Ow�h�&�� $p$&�)*�R���>j%^�:�P�-��Z*Qn a.8am�&�63IrR� :�, �S#�$6[6!xb�une��6�&Ud it� =h F.�'���".�*��r.�j7i$ 2hR� aR2T� Ih8}>� {�.�/lb�C$TV� �Bi, or r*��-$m�'�kik��epa_N ?b+4ven 5� �>�=�C�o�; rick$��'�#�6�ex�Z&� �NL9x9.63% ^�=H< �v� �G�mo$AbdAm3 a*gA�. mX� ��cF�AA, b� � y,,T� in�^$if���+��yAG zN�])i?9:$x$�.! ?x( E�!"�1*�1E��5$L_{A!a&\N NP}^ �"\ A4Wa�n<sE+$A$, nu}}%s.:�*ZY$M$i9Mo��se��c�G1E%�-W�Plo�Gt��Oe[7ix�;�V }%:A�&X%�Z �Zz>C9�_{n�p*�2p�L� 9� s��A u� ��@{)�M$�1rr:��oA �> �( 2?$P>-.�  n�� ��$. Chogfa� $S\ULeB�"AA�^�d^�S X)'�/10RwtBU!xA@A�V^,� Z�\A�A�%�a N SQtc{%);�O $M *m�; ɛ6?�\�#� $Sy �(**� �>:3�"`�hA44DNI:isH:) �bin� �> (re��O�A>F��3"pIkq!$ $z$)f�+��";�6QfG�$%6$S�Byɐ� �?ei�/NE�Q�B�^B�JE\��*A!:.� -�.�$,Ns�n� tm7)w�o"-p# � F[ton$s�U1%� soN[untilAC]8�)�Hf�V\�>�1i"VI� �.eI,%�*\ Z 2�R�W..���&b �P�}no-�, m%Q!�e�T1S) A_V H6I\AV\���1�6w-6k>z�R>*�e2t9|� �xU ����� , $TC� , $N4H'$K�Sc9�J"4:9U- �\g"�k % >m �#viom\ :�k*��� I�J6�E.F zD hi"� 1b ���2�1$*�\gro�x��oG��in P"�.-size V�Kw`?��GRGog} do� ei߁�techniqu�^2�M COL}a���1fp�K2�� low-� vari*�� DY$of��d ��}�:,%�s6� )"sI�/Trace Dm� MM�7 TRACEDISgI��I!VE\wnew�>��pro�K�?�!"�1R`n*� �UnPB:0�"D�,7v e I ��t �wm��&CG߀sD &�OrRjInF�I!�v2��Kr�Ki ly�-�1�} the ��FG�C"Pe�Dw'sr�v (EQ�M�J���>!�,IbRr� �v;( ifiA�*Җ�|AI�U�V�r��� YWR F; nFY Sbp APPLEN }, I�*7a;A7J�a�}HY AmbaWH!��� �� ݃- E� #$�={ iw)�2�t�W9��� g��E Z�varJ�$fbn����]. *7T ���?_��"3!:9]�J$~Z< ��l}i\] �A}+� a35I�> ^P��"�% {Rw �+$!)�uBq2� q�6'#� d:�D}_$�aA�!�1�T��Z� �k�bG�*i.c Q �2�aw� %0�s6?s �Q� �f�]`-!�S"S0�2\PrW*k�1},%BB�[ .Mw9�G!]B�%� ��:Ni\g{#)w�-� /�D.$yBR�E2Z��>�loguC4��^�2F�k�6r%� ��s�4 $\ell+g6Tg`r_݀.�����'�Sy20>�a/!iIC!�J�e��~�rRWN- 3G 2A�� �A�if� a&�&��.�}'�Y�21�bp R6u��or�K>98$*��>0�So� $L&�]!nM�G5t 2>���a�in&P�&(�U�3?���;� bf{C�eI.}!?y$�.�6���%�x$}�I�6VW�U� �yin � *WD�Z�Q1���� "�? YI,UW.�  galway�An �;�k�#� a��35_ at)�z28�$y&ߕ�b.�.� egROF�:% <[�  �x�I�+�Ci�y}bT6I� rS� �A\me�;S'6�D G:�d�� rho- _{y � V��^+n��% l8Q%�e2�"��:� 2���A �Lre ame�A0*Zy�V \lљjnf2^{L}O�eigenv���%� %*!)�[��B�0N\2):j[1*�X�s�Xigp � ^��i\ �4��$�X}\�'CNT-�62�4'L/2ז= 8�pK6�ef�rh_y _{ij}"�09 ) -��.5�;�H _ A� %i,j W�\�DrK%�%��4Alin�}�4Cauchy-Schwarz*GUt� �e:7uniDin �H� FrobeniuRDrm.ec"ƿIZ�I�R,�� !�)E]�2q2b �*F� � �/a�F����`4A�E�%>�v^���I�f�zg%U G!i5jy�� ��Bsuma|Z ʹN"Y�u�U/9� %<��9� ��8;�Fa��"�XL$"�g>�'*� {� to en TE{ >|v����� �Y�� _�*&/� {e�w�h�ciKHW_[�,� � aZ:�v!�� �t%RE# ��VH-22�{Re�Y<O>D^��L*��H)���)!r�^� `F��� q]�)�vg��)D2���-N�� ���j\ �&�� t�m��J62� A�MQ6��N �ZI� �6�R]2}�R}_"z 2u�{ R� :$ ,x,z rR��.~� ��]�} �% ] -Rw6}���}6cx,z)_a<���29|��%�Pr��1(+� L[�2$5�&2U6�^&�2�1�2�-�z-�$) Ic�� vu L�M9.L� leq1j H�ZF$l�zj};�vz�tJ�-FJ 2G->H���aEގ����8� 2��|�Z�! :��f�6j�.idin�Men�^2H!�r6a��K!OKIb �"�&[i��&0�\b!��1�it  C�gn�uJ�m�2'�o�s\R��V�4nh(+�%�L {App"A[+&�.]u�3"�jF1*C2 tw�7 .Tof���<fv+pe!�to�pO��$sc�x2"^��&��oi!Km���86l"� di ~�)� $G//e ���� Y}B�Ci� ( G�Y6.e�!�+H. isz�OfYYi $C$\�aY'!P,�!/isU an�$� Gx $iuXdu'�y _IU�22/By `Fb�DZ |we2 S�E e.*Nnaturj\�U�c� "QZ��Z�xa8nB;.L �bb{Z}_{p��5X�_D�r�) z.)�,�of RabAnd Yao '" ry}\�8B�y`.�>4 .� ��F�U =\The?1�DU.\�>/b "�m�cABӚ>�B�$.�:I�x� 2�q Pw{!t�'�"}�U.tV8ӚA�A�'� B]ki�Qa"3~ $f!��nEm a y�&�mb bb{FEQ!<a0uT6Ha,b)vHI.RF����2lJ�$ (�<2}$%�&eg�FV n�v�2[ >���] � �2Q>k q`2�}*��r?qa�)�1."O���2�B ~|~H@>�q����"�8"�p��}*Da� ��&�p^�����"�J2Ax�� z$ %�4}-4^�I�"v4��quw#.�a�,b �1#Z� ,x+6TvL $w�{ }z�G` ����&@��U-1HkA1I)WZAv�F_B�:�:���2v2V�2$4#c�li�U�3E�=z$hz$yE�wM�3E�f� {'i �bɷ� ��F"��:mW.g:P��it."O�J A��(:� % �'L( �R�BM %�&n�p^!| � ++ D � i '.R4}nR R�1�NS0n� 1 Ba6{2BI6X232=1/p-1/�)c14�"2"�� ��)B�I]�-�)>4B�)5*�N$(R�M�� h�"� �'�!lleD�"�Vnonqy�758 G�&X�28�� > �}���u&�mB�S�*�, k�l6 v�H ��06A G$;�benNhx( 08C6igl4�M& No st6�i �&G � �,s)�i�B �@n��F� 9F%� D�A � �&�&�/�� 'ak(*' %48 �N�G*�2���)�#�hG,Sk:cZ[�R BR�2E*{j��:*2c .bu�V�,%h$.�#�2�m�ΠE{-l2i�AU0z���*�/Q��'v+n�mYR�UzII>�.��xy\]��K] "��Lm��L}.2}\�O�2�]K)�9F� ��i2���2�{&j(�a� � � � l�3 � G,s,t@(S:xy=s,zy=tIZ@2 8f� R% 2(���3'65'.j>x2�(���z��=���$r�F�% &1�� Ȫ���� �t�Ew!�6���F�2vM}Y)i*q�{��EQ7��� &�&$�]S>�M�p��? �XsHH��_eƓ.[�_2Be� &��RK��fņ ���i7�maiudtBo u�- ����*6�6$ A[�*��L��"WV3�F� �1�var>��q�S$�cho�*Mt r�;V�H6}LB� �F2.��` �>�$Q:z>�-yQRwJ 0Q%F��:&� 460 u\ R ��"�!6se&�5 sP x\ s $K}e>*�_:�"��2�i����f&�C G��%�1L�e��3�N �B� }/&eI�E:Q*1 ��=L%K@�5H: &�)[ ����r����v+�!|+96o }�� #�!.��OV�%��#g1f���82�/Y� bT/�9�j�6��+Sid ����I � leq � c}{Kq"�Us !��bN \�/��4cHl"�d&Y��!���"b`]�i �-�&s 2� ���gG2�� �[� e�!!) MbZ,.�EMs% }q� u M.jL"2R� �.�&�8�����-&|Uz��!�i,js�js`�0 , =V+=x--l 2��S͹{ W"�,s_��ro6i,j �ZP��j|)V��,�/WA�)� 3ar�  �x�{�% # ����6� & R�)~_A�A�6� %�>�)�mG" VZDN�3)B3>W+ijh��z.� "$"~Vep1��4} i,j,k,la6K}Ԃ,ijklM�)�L2n�R�m� &>(kim/3b?%�Qp�B �W(iy9�R�\� 6kl�8w��s�?%�1.]F�� PF(nalyz�R_{!d�.S6�ord�R(��� bu&V�a�~'�%a�O��$ŝ$\&D0ed\� �#2$7��R�TN�<��q*S� py�rn2E�\ $iic&X�=< i=j$�$�f{$.`�� / a $i��>NXjHsIfB'VC=1�s6�Ui#A ity)�n!�q $1�VH6��3% �<�(a�e�r�E_0$R)j$IfO��e' ha��g �8>1)�n .n\RoF�J�6U -1AlN�jE�S�[; �|2�|� sum_J}E�m K"�^(*Gk �Mq Yr�aJ��6E���-hTo'�&�\ily c��� e@ ]�e�p�C�a warmup�>m*wT8�ed� e�Mlkl�T�w10.1 leTthe�res�F.5, �2^P� �OA�.j%(@;,k,"A�$"� t�}[ptb] \tabular} [c]{|ll|lll|}\h: P�) & N%.)�,$4$-tuples &BsR�a�&��2$v,� ) >2$\\ � iiii,iikk�r thinspace�T�&��co��A�|c}{$1$}/:0 B|}{\\ ijij�J� bqW BW}{$I�1f�a�R���>�ji�����0$�iil!� i,ij!�jj%Z4^[B@%�f[v�|jk!2Rwm_ K-&�dA�>��FqI�zq2*6�y %�u ��Mp'  \cap[Exf�]{:"���}ale��r&&,H$16�%��=2�)le� �g�/��F<-r<| , �ŷ�@���Y� �B� 5�K�" �z� 6�% Ba�(�]-� c}% A "8 2r+9Qf+ C�^%(>[}+�u)P ֚�� n�U�~� �_�����2�i��(5�� H%EZv d�-�1��&dn�3}+�V1�&w � c�&&2� factM�!�b #JPf1&[� � : !7yp%�R��8����F�F�]c5�F�nF~Efi�z prin�4oϰls��K�bt�u� �W��tq�P period��#G�,`d�S" ��zi��c���g"� gs:s�SIeEhre $g~b#�Ba4R:� Z #z�*_�&I �� +  og q ��  *����As5_� s0i*��q�a2=$;�)f!��] U�s8*x7$HA� &�� TH � =q�y�Mw6*X"�7:�7,s BO�4prime $p$ fromL the range $\left[ ,\vert S\righ ^{2}\log ef G$ ,2�> J\] $; she then sends Bob�pair\ �`( p,x\operatorname{mod}p H�) $\ where $x$ is interpreted as an Lger. \ This takes $O�(! og % 2+! R �� bitse�Xoutputs $1$ if and only t�|exists a $z\in G$\ such that $zyS$\:$$x\equiv z��n�To seelx protocol's correctness, observ$at if\gneq z$,8n$re at most!�.'6$\ prim!Wp$.�x-z �0��, %�as} relevantI�@ contains $\OmegaRfrac{J�I�r� }{5�!]5�6 $f2Y}.�). Ayerefore,A($xy\notin S1mby�Xunion bound% \[ \Pr_{p}�a�M7z:M",M � � ] =]�U�2�j� 1pM22�F12 !|V��� � ) =o%$ ( 1 �C . \] \end{proof} \section{Open Problems\label{OPENADV}} Are $\o�w(*{R}_{2}^{1)� ( fk$i�2�*{Q}% j44\ polynomiallyA�a��hfor every total Boolean fun�� $f$? \ Also, can we exhibit \textit{any} asymptotic separa� betwei�(se measuresR The best .T I know of is a factor$2$: ��` equality �we hav�F :4EQ1� \geq5�-J�5�A�%kn$,� as W�� r \cite{w (}\ has show��l:�N�:#2�l�/2+B�mv�logA(n$\ using a�� involv�mixed states.\footnote{If we restrict ourselves to pure 2���>n7 .�qu��( are needed�G Base��ɗ!�,�(evious vers�� of t�ZDchapter claimed in�rl��Rm!yS� B .}��� or-$2$ sa!isA�t�irM� : a simpl�q8unting argumentE8���� J6%] .�/2��!(n$;�galthough=  usual�"domizedYSa��\mry}A}�iY J� 6X {\�E_r�oist��\s bA*$ on error--�A�codA�!4use $Qz � cnu�=i�+ը�� �A�All��E{holds�any+st:� probabi��X$0<\varepsilon<1/2$. C�Flower-� F! f�Coset�3 )9K$\�groups o @ than $\mathbb{Z}���� $\ ( a���(n}$, or non��ian U)��2(characteriz� .6 ��6�B�Sub� G,"F�$all sets $� clos!�� gap �p upperE�%k�s? IaWAZan oracl� ati� o which-*sf{BQP/�<}� %! q$?5�gB R s rebSNP}\capLcoNP}%� � )�sf{SZK!��&otAh� ��%��( \ Even moM mbit�;ly��$prove a di�  duct!> oremA4( quantum quco��x�neVappliacoE�$partial or@&8(�ju��(arch)? For%�$f$ (>;),�$> R:8 & *Y sqrt{n��� n�BRQR% y].\ U log �* IniL words,Ay*�Lof Bar-Yossef et al.� bjk}0� possibleM>Hresul� 6<D� N� mQ_e�N- �:P)99T��@1�!�be imE@d to >�2�N�>�vw�UI do A>eA� how{ rule�v}J~ m+z.69 . I�(e Simultane�HMessages (SM) modelѬis nom_$ communica ��Alicee�4Bob;\ instead,6 both � moau��rd%�y call!�he"� referee}� oAVn   &3 value��� }�� �Wsumr e two� length�LeF�q�||ͤ=�hZ�3.�$ b�.{�+�� �Eed-� SMс�ofE� resp� ve�?lR�%^{||,:� pub} �2�\a!.ra .��2� sh��Han arbitrarily long D { ng!�Build��on�xk�Buhrman>a$cww}, Yao � yao:fing}M E*jN 5{=�^�bB�9��A d1}{ \ H1en askabouū����ionsomv"o >0$, does֡Rn^{A f�u%UVJB9��.v,E�z�jR �.�.5��%B"�#U.��2� ��nA�earlier*� ��s# � , I.�B~YAj� ���B� Dn�٩} ��Y��J mean�Eat�osi0 answe�aw's first= sA� would�9lyV6�7secon,Later I lear� t 4Yao independen��he sam� 9}�hw}iA$re I ask a� ed�:�B|B�}$\�r��exponen� ly sm��r�� 6�R]�n�=�EK(:� ߅�\.@Z� ��B@e �bW^�BYMBQd $.) \ Iordanis Kerenidis�po d��m��at,���!� hidd� atchCle�yvM \ discus8�e�X\ref{PRELIMADV}% ,\ one�defin �� on}� "� 6�I3 R$\.�zE�ow� ,�i� ca�fB� �&� 2^\��u�6�Y�NK $, it rem to extendA�a��s. \�{Summary� Part)� LQC}SUM8} From my unbi� per�,�2�"��o�h e deepest� ults�h emerged fcAy stud�I 8 uJ inform� Xs�ls tell u�m M�s�5t w��int ableI��classica�tu�n, re�Q� are}2>accor to�K theo)\�phy X worl�VOI, hand� freasonse ��� m,mSsubtle��n�A�A�In%�� sej� to�vtrue---0�wisQ!X��2hy�nnm thos]�z�dra!�c5�speed��$. We curr�8E� tho��M_ .%��M > :��nN mMA}Beals� ��bcm� AQ!�ad�a 8 Ambainis � a }Mv prece%�mP�]$ve illustr�w�Xorrow�A� Wign*�  e m�@ �EqquotedblP unIE�eff�\ve�2,��tha �  Both� inue!�work far� side 6Hir original design a�s---whe�� 1�~it{Ux}2�,  I*J� successV�) (a�� ]  .!) .�24A�E5iNptIr�.^$):B !*be Y`s� colliAPsemparison�e!)a�Yet�2� also ��hA�limit��!�U� )��� usel!6w� A�r5��a�3gap�� !2ina�Lry $0$-input differsE�1 in aA=Z uO of loP� Like�B�ge.� �canJbe �Qio��ɹ lack�dmu)$ symmetry,�leastB)N echniques��Z�!vThus,Oh!!$�(important o !/�inI1u:�9!8o develop a new�  overco b=�!!9YCE-+>�.�Ai�lines,~ num, Saks� Szegedy��ss}IP�n���� sensHz0vably optimalMT, b�ir�(�� semi� it�(ogramming)\n!ms toi ffic5pf i� ly.}� keep�wit) them�{!g hesis, I �:��xlis ӕu��s �aQ:A�a# hyp��t��be���$Conway's G� of Lifa�) safel�rryd�U$uni�<eY begin{ite�} \ e��"Uf�:at��eas�tunordere�$. For desp!x �extrem�����one-to-[ � ��x &still� it{looks}.Gun�`e d`��ensU ��c�a �Fin�a�l minim�Fu�n fC globD.�$is becaUaHpaths�wto.xa c%�Bc a`!��Ic w8a�If uish@�!$X$)mr��of?Y$��A�at $f Y"�� X#�Ue�notr E� Q�Axa{ .ry �dap��.� �%pax �gy�]��e�j recur%� FourA�samplainctes!�&^ u�he�� tree %OG� $n$ ��!Y ance����u�u!& enough ti� o solve $"V & $�m,�aZ��of!�ce� on)�n$ deR���$ng �"�NP}$-�Sle����V |ly hard,�9n I!� help���-size�� ice.�#!1ize�#�{M��' d ReZ"� MAR� �l�H} LS: So you believ��mechanicd Me: Of co Al��thmic#C)#D)����7obj �\cg on[ .to:�ing]{:& N&. (�, b!b&� foca�� 5vсtaJ%aBimile�+riA9Am�A|�ws�t�0e�V���1�%k ssoci��n0��Mor�*ce/0, Oded Goldre�fg�l��forward� a�) b6. a��to��'� �)s,y'* ~l�,derstood: he�(�@�+ �� �horWQVw *�I�� �� -de�ScyF��1�/0 �2�|  j��55A no bur�o:� who #)�vie�# sugg�-a�i�V��no.�.D+e foll� pan# a=.��\ flav#.AH crit�&#%}�Tmajor? {[EO6@aRԡ�r3�n�uat�ic"'�*�s *!�Dmulti-hundredth if� millionth im�;onsr�� ificdig�� �"c�.� ��GaaWe �is� a&�law vali�ov) dozen���Typ�z, fy fewzde �laM--PreBkA�ofi�basic�cepts��0J�� � lex � � �iccurac�orthey be�Nter�2s,oagraphsr sick-hu�(d gremlins?�'Zc �����gs,iЅq����A3a*Y � unit-c�4ar�� +&� sh%re� ed�v es� �1A�� � s;i{c�.�!�4r�� a��nfu$+me� x topod e roxiBon ^�(fault-tolerDl#*s d� , on extravagA�assumpe8.�&�  aW)5er7 ed,F! �me 2��A ��breakdow�6�"s��us t!beOik�F�R!V %� new. AE�&onxN��v immed��lyazF�!�&� a&m �fli�co�E�: %�prc�TE�f �$ $2^{-1000: SI7]dismiss~hF>as un� A v���obb1%��_U��[�eH n��O!JeP,o �'---si��ev2e\ar!#and nei�L�� .8� . S#,�P&v�*B r � �� nostic �* &re�� it�en�E��%�be tur�#ar)7!�$How do we �)7a�U -^�� 7C+*% $,2� let��*�9 "!PSPACE}&%5"\5�:s�t�a q��"� AbraTnd Lloyd�� %a��w�c���non$ar variantA Schr\"{o}er�$a���N2���. �\#2!��G%d=+.�aU�nd Penr�� p �h�oposed a���{`� v�llapse'�� waveH,:�!lpQal�;us"�Eet���A���(s entirely!� �to� sifyFEe���su��"b6!�t �i m!�ev�� it{some}�a"�� 6 JmX �a dicw<M����7exact Pi�{ne^ar�"Nobel�:zes�hab �0Dph`me! '%�fa%e�6�eld�o�.�i�0it8onM��0�r� s ��to FitchM8f }E�CroninCc}E� 1980� �%` �CP"J vio�. Pe&keyqu a���'!Ge�$��-��@`�1 i���$rk)�%��  9z <�� 6 2S�\�+re� touche�sers2 epistem"k2:\ Nit{�GA~�gX: trap!+e:tod*� s�3�=5Y�:�tested?R I��t�: addr�5�A2Aee>"A!evide���1�n�h+my pur�OsAx��}� decl�UpreF �] W}g%2�ver�toA��/ a tr^ ,25-��1��.gt  thre�!Vn&�;types}��: �it{Nf ce},(it{entangleA}� �it{> cats�*B0u1@n� ra�9n�z&�*$.[(1)] ^ bf{I�A �EI '���n�c���inz o�/���E ucleus di���# truc,6ceD eachH ou\���A%Z E"�gy leve� S��a� acce� e� Jd h�Fey Wl�� I�� spire'� ir� ���i)�pma �dis�gbA�Toe4eio�#0ppened---toge�  A��E�(aBex�) �Lle-photon double-sli.[ s---�omp�2� `� of)Bum9�n�Q'2]'E]�E'On &!cpa�H �elicle's�5�i scrib�a A>eK -dim�o�%ph��space, �!den�<�'�_�EPJV qA six}^]e6� ��  Bell in��:ex�D of Ad&t�'��a} "� m' conv� dE*�a? �H�i]E�um . "-cay main�8�s ��m� aPAeH lai� b&35*h4--� X*�ie"![(3=�>| Cats%�Ac�ab two-a1-�1�6�2 As�"�EBA:8whole molecules� huma�� galax4 - in co��=upe�MIj� sBH�, )� ArndB�w@ve�%�+� he .gaֱ,] uA� $C_{60z:�0 (buckyballs)X ea�)i�s;�*le Fried*�4S f �fJ y�%8a � 1�Rng]&, c��$A�b��X� o!Y!Le�)N Spp=fT_ck9'�� coil%� $�Pcl+(�FLeggettm1l ;,�rve�!�.�[TB�r �e�s.�s � 3 e-o�Ex"��L#G�d a g�al-�q�A �Oas �-�h�s�� alread�en 'dA9oZ��n�cera� � a�)��]�8eE�����h�r�  N$HavA#� �%�22)��&� rm�<jD ask alO>��� � eC=&#&ex��%�qa���As�;U �i)(��i��2� sp�Hu:'��(� %�!%w��)�+$ GRW (Ghir-Ri�$-Weber)�oryM�grw}% *LVI�D5 aJ%erE� Pas  io��� ier,4��y�=!�1A�ac; i-#it{too}a��.}� !}drawback� N� kinclude "� %a)gA�n�J� �Fme ��E6bs"�'u�4to avoid confl�"ng)��o< �&� (+gh,�W�� �|s}tu�%�I �AK�%m-��zs"-"�*�1 sto+� ���degre� f freedom&Bspin)!zuna/�EFur� moeJ��� �6�EHEW�3 ��sed1e.zf>!��(be���J@��-� s roughh+n9I� !�i  $10^{15��{7� ith < � �!�S 6�>-7}$-E vicinit�So/2? h a,� Е�M�Et*�G��0Bpa ��/.�AcFB0WA;!�.w60by Rob Spekke�1spar8!�corBjGt&�-��S� o"�- � GRW-/��|� A-_&=2gm�a^�$of 't Hoof�^th � Wolfram��w }! 3�����a���� cell� automa{ xH�s2�74eU��Iq,� U{a�����&(\lbrack i]tAO!JBi nJ a `6�er' [�!'�� 2 "��A�A� }0e� g!��)� M��� mav8�s�-dok�:l  ld�&�NA�s"�6 �� �JlowH$Planckian " RE3�-�A�Simil+1��+\� t ``[i]nd�" �ou�H� al�([*!5�]i�a{ 1|>yA���a f oz� 8 ��� *�ly-��n �6�Tu)-�e�But%Z0,� af<my [es �(Iq,g'su�����i�3mT'�3casPM��[g turn%�aa �6T�'n��of �mate � Jeb���+" F�2� to ref);ous id<z�� dGB delss3d sr''I"[p.771]�.:e"�"�t�|7=D�5e�!A�-un�K( &(*A�I��-�u"X)�@s�H��!>,� , exlAt B�!Y��Q&o! us%\aW �3���nv/ni�1*M3 grav͒A%�q@'A��, �5 NAT.�5�� f%-�UadR�to jN&�d2E��"�) ;(WOLFRAM} be�:�Mit�s��d� rata9# �wreev��inɉ"�Q%�IE �ong-R�V Th� s�%�+.bq2��P"is���(i�/cerpt�\;maQ�"��aar:rev}G/Stephen��'s�6,it{A New Kin\S&%ce} D��.A& ��"g �� �&9! %�f\iE ninth,�;`Fu&4+�&s�+H���� ro�g? �)}tI��L�q, X5A���1�lVF� 2�,��-��-b =%hof na$I;he espo�&� �l!F$Ec�6! �rp0aa�e͸ scale,b� } -33? a&i s�" 4Z �ETA.co|l�rnew, A�O�iveJ �p�nEe �.b��!Qq%#6phi��incipleM;bousso}\Ub�7�� dynamic �Q�vD�!us��� new �� v`sub�t!\�?�K-�,6yaU�b4al net-;.� ��ts |KZic4nd edA3��if!�"��M #�$n�P�I486--496�A508--515�!ldetail�JVte�a�)Ya��4rAIn��, w!T st @%�a fE �"! ed `E���ph' $G;,W%Zn�s\ upd�s,�f r� (0 subg%% by &� �a�s��%A� outg�2%l�i new OmQ*�Y @F:�c�ol6$J;ach)�!hx6�BZds<� pplOK�,n ��I- �E2 $B=J4& sM� Es99of �$A6weGr�)�$A$�$B�4Pr-�AZ e�9) terma1��"b )d ofY�in1�� �+�5�_!`q:a ex�Qw� $n^{DL"�I@� �-a(� "�  $DEW((7 z�D? ��,q��0,iU�F ��mŚ|� A'tle!.!�2 � ��"*e volumA� owth��S5es � � �&akeb kD=imit---�*I=�"k7 too �or � 2�V!_�j(\ (p. 1030)�EF� ����3 E�urvɒ.�&orJ:� Y � G0Ricci tensor,1��I j�� �]! �2 \ �H�3,!8m!8:X� �V:i$9�}J� a�- a�UJa� !&ex r�C� ne��l ceNTabs��aĭli�n O� z p��,H`ms,'m8�'n&�'� �r%�A> ob� Eno ival��� ̈́s,�Q�S�,�derr�02|����-���qB������ ���'non2�:'u��a `i,way syc!� !ogne#� W*x &kQ*�oF� : %1q C� e!�0 of `!--figuB�'�*$!�%%� 1950�Exonc IAL�E"Gaakq�"? �9T�!a�>smBA�V�9-\I\�V DM�n �0�@"�(c� E.wh�e.�(approach, b+ hing%�y#d�N"��( ��?�*ɨ} at�(/ �U��,=�8� rinh-fe�f�31S!�)owest-M Ij�w �3e�� 5-6):X It}unc9+�� ctly;)��i�&$$?xn:t�anyal�a%TBa�L-)& 13}:4 m94�*jN+@�q`optAO�E��� M are `i�""t':�t yiel� 0� ra6�?�\BtEA(uCApA�D1 �-@&$ient (aq "A')A�diE8� �i"�!Q%Yno `r� ; '&� bl�Citself��!��.327H`.*�( "�,�.yax| 2,�%in I�:�Uin��avZS��\WedIEs o0, y\WB�f�� � aA�at�=H%*vague,PIux� � ٨Lo�,z trans !}s�7�=er� g-�Q�QNG! �E!g ���i�:-*[~ G �is � �:$>mVoub�L quir�it�f�1 %)ab�@c��1�!(�pic�^IRI�*�>LUpG� les move �R�?lb0*,tvGmX9no�]>�D��529>�Q�i+Şb oly�) �%h��"%,mB �-m�-_R?'\Qy�N�Enot�"�TVa ��3%�Qv�>�G,eC0re�/�n��!�KE�B0&al� he c�'mit�vE�� �cc �F,F� \�g]i�)myO_N�$61^n�Ze�E)I&�(eba�� surpr�Lž^ often�uch$8��Lpro!,!0�[ utI�I�% .sKM�R�� 43b!�% adoxA.�0:�t���9:� 5B�$ �E6of���jB��M� q'b�F^�O0sa!�U;Ŷf,a�at���N>' s ir�5zy� x�� B� h!u� it? �� ' hu'�@M�i�aly> fur�i�oe AW�f�`�@$Phenomena'%�537--545%�2*�%�Ft %�e�n�/&�4A�andl.&�(:2 �2/ )�o}.M�I�! !(3 ught%u aI�y,iGE�A� o (iJ_ dern� s)"�X*��Ia �e�� {Q,0 ginnEn� 1960's,: m�t e ��A �ejs//@jT)�p4,�0Q��T!vaA�),�Qn�oodiy%� actu+�il\�gi*���(it{not} adv�Lefh:�'+ � as BohmGb"� �k �Ge ecto4suppl* = an ` �'\ eige$M$g6ɐuleOsl %5 � ink!�Uau!, , epB�!2� *l�>! m�0 aa|ful�&t,mp��!  � ��umZ(all) higher� #ea �Q�acyQ8�U�-of�'���#a;�e!�� 8+a7B�[I]I knew�.��E(i��>��E�m�nup�S�8� �t��alw�Pb�A�`��� kI�_anyO"% .E�JUD�<� ?(- � � � �Tq �Ua��D 2 �͟e�N��R;e� KookD e*� :"Y "� PT� eVh ta�ppai /LYR�Any - ����+�6�.~ ^es�c�SM�A"ur� tC.o: ����O6hF��$lJC a!n�5s VEan"�)�m- e2 : ``�*AJ��L+5Tme~':")as&e 9A�6e"�[��� no E��an �Ma�the�� !cou�SE �)t*�*�=6'�8�  An�"D7A ��B!G> 8xDe"'�Csum�W"17kD�L"V8nDHe.�J �E�e4 .BI�  0u�[!�[!�[!�[! in CYl9 [N '],�<2�H.y!�l A�:y! X�7 �otVy!y�a��y!�al�  �V�adBy! :y!� liz]~y!�771A�GD }^Ren � � � �A�d&U�!im&� ,"� ���h{m �� �he�]� indF�t. �2aaUa?ly� s�VecIVis��! ��N amplkA�Z��e�L�C��urb-E�  environ� �&/'uc/���R�lq���KD 8' U#� �be� �o�� �w�'.LGB;d%�114��.�&$3�=oţ= �N� J���'?:t;al^Kbe'�(�� �r� �%c� disz�#"$1 u�E�Sj:��imagY1,�Ts�b6�"biF t!�`!�!�W� !�_J` &s��Hc$G$�llide,.N#`'4ads' [&%��>ma@ �9 in i~/� i�6�$,r "*B �2��| )< *��[� Mq( �/&Jq��3!h� x����c8.�4 ��.66L't�#Iin }[ go��m at&�$| 82�1W9/.544>�!"x�0$+�"i2�4some��tooc (i.e. !<fewBs)%R�.F&��.2�%� Qt=*om0I�N ra�a�LŃ �]�W!;E�%)l2it{if�V��EE�of mW's8#Wide�%---� is�1dF�"8e>��yXa{�A�GC�B�i�dm"�< ~ sE lit�_���t�jK/ �?Ztatu!-QL t A�F�Py( � icitly it{��}"�$ a"J,o�P!�� ,�nic\ %�� �� o�a�P�Uk� (x�a�inuit�!y=E<z,F�z3 �r 6�In%� 0b�" �l=� �N�a�`� Bu�5hopa����!�g�n& +�-=S�U�,�ed 2)�le tPsxchora sui`A[x9ro? ,] $\theta$ [ =\pi/4Ky3�lr2 � �=_��"s` ion]aO�n�-!|non-triv�aD� ��e��R�atCstep end@�fꁺ 1060F�is2+�A� ing,� )�5��O��h.�3* IfQUANTUM}��E8���al�an#Y � g�!��al��}�I2�e?m(�<rixA$�)mb� � orthog�ma3'm;�isjE��,s!8 � , Shi� shi:��4�!,� Toffoli  , plu�yGb � ��$�\)^ al?0 ��rolled->oNOT}$[6is&�dsque�3I�zA��GIal gEu��I.�f`�&,AeI�%���!w�_�� � `benign�0g/��2m��E����Mrmer,�I!Q �0�m�e�-a��8'�Wn;=AGpi8�%a�\� � !Al�|�(2fBer2�b$nd VaziranQ4bvahe line�K� �u*k8 � ��%3 tinyd3�K"\ � not b�g N ed d0"�E.��r�8pII�Az� r-��-��y��nY;entd\�*]�W-�4�Ascal{R}^'�z�"� �'�^)� "� ՟�3!�T�X#�"�: �Wass<�)( �oug-FIe�Ld�,e�ll!�}CAC b} sequ�#% ion)~fB6�A[sf!�B2 ύ��'��R) ���tofy� 2k\!�20), :"� Lu�c���\[A2;�!t9��fz8.��"s. � f*� F�Q(t Minkowski� ap��a*4 e~^_-���n�I�t��in!�al �5 ?�A�?6� perm9Q� &�1T A=9 4)] Any�%Q���6S �Q�ilE�F fi@E�� AY trib�%o;p*�?�! 3�.is o3� f� "�6=!#n!M�C =6 �2A�*NE� go%Dz��B,�A�6,yFN�l�s�$!�a��alsE@C��$K�2}�$p (1)-(3)�)���>(4�: U��J+I�{. d hi�*r�8ly,rts��D�A�"mi�" _�nt�O�� ��5atisfy��/(2)[F%32/�"`,)�QjKe xBparty:�ie"�s<4!p)��2a�4�h�. 299--326*�)i$p� reeysV_c �e andoX�o�d(:ra&Q�&o�N62H �a�EQseudo �/ put)!#"�FU��! eVompat�{} (4 �so-!�]ju%����<adoE� �M��dco% �sa#A���de"r@""�z6cm playn f*�3r�Dt�he�ow��� an�;�&&�>>~z!ɿinY��$x_{A�2 B �!Xy��uni��#P"�1E(.qE--ir �~��mm;{� t��y�  B}$��n!t A}\o� y_{B}=�\wax/U�M�� `q,��8� � W >+� ,G�(�o 5t� $3/4$;A,�(iX�% tegyA a�%to*^ie,ۋ!qM� �&� A}=0�n1=0�U�;= {z�N ��$\rho =EH�a %a  re jL>�_�I9��$\)8( ��00\�o��i��e�#��01 ş ard P>!�E�$�'�Te.}�� >g .g-� 5+1L9^8\� 0.80��To6% situ�,w$AB$ZYra�on�$to1hnd!#,YndisE"�( �a�a�SupE���AY � $G$ �6!u Euc:an> ��s�E"�2;%DRa� 6� �/� !�B$� !�or\q$sJ� � One !~]@k�$G$I&J�!Mm!L��nii��A�&|B�1��Encode)��!put����by�*�G��an"��%�>�1�2s4A!c���%mAa! x��@!i�>iA��mly �IA!x .�~g!Qed���_h"�Bus&pE%� �!)�ŕ��e+�2�� �NEf�W1�c0�?Gd�>%A&O(��� �/we�!��/����{�8i�5x%�6&!\A}$, g %Es�Q7 ��G$u"�=H U !9�uf#d��"y-5%=A ��;��db�=A� yI��one�s�ie�. �kbi�@�l depth $3$JW+% \N\Yn,�g,�! guarante)�!��Ed+f�, zVlyE�5X�#u"EC� a�� `�T d' acAa+��(�2�7� ���m��M�m>b(P��O]A�$Z+n�igsU� E D-�, B�7I;�qB � I3!"ch�]AJ� A���U���� b}=�.�<�"tS�P!��:+perceiv*�a*��i)�iex�)a �B6f-�3iYm94�[ b�b1�Bob's9fE�M&iFz�J8c�;AM�u ���:u} fwi� Now�U@as�'z$�ޕ� N�1�,� *�m4 be�I8pZ$��Y ^{� *�� "�~Z"XA��F/ N0|���o�o,F� �%I���ce (i� let�+�2�N�,-�F0R�"օ�.�U A0q7�re %hE��aEaQI1e�^!;A� 9; 9j�%� .0v�vbB}�>�R�eB�Be�$--�|if���ee�\�|� m��<�jed-�a�D hi���C� !TID+�q���out0�x�  e��*N�9i���.  * jYRMQy�I-*_"�a��$�#,���� `:�s':\t� :3;a# ��Pm"�9e�K-b-^!o|�rh� �( � �")R�!�N ���)s~e1�����n� 0/s�r Wtroys�1��0� ��o}r<no��'d�(A exq.]F��},풥9�s2� F%l&y  t�s� �%"'s>a��n',�$n�5h!Y1~!C*�*),s ��Zis6N���SZ 3y��JVss�7F��@3b�N_>��F{x`"E��a laM"N��=.hol'O *�zA$\�we mar\%�ma�� (!�`%�'�i%A~�.\Ait{�4}A��_ r f>of!�Nt�?&�B��dIF ~s-�� ��9o.�e"6,�>. 5Zv�"", o��"���zd�ru0---HM0t*K�ntIl-su�#ve un�6j�6% t��_G$*^��wW�S %�e�|mc:t.�t�  I �26� �%�"�� z/�.-\i)%��'# `tru�u;'�OJ��6o5�&:A!�&�RI�$�$W?&�$ tic'ɎQ!�'��ei du�"GreenbQ�r, Hor�`A$Zeilip5�I ghz}�JT���i�iL8E�,!�� Ch:�-Ie ^�* �" C}$:�����Qpro�e�2" x_{CFa&g&�g w �� � C� �@i, iyi% �vee{B} CfU� �f7hN'�J�/ 8t�� �$'ŜK�J�s;�'.V)fD��AwGHZ�tZ�����>�+ 10� V :(-: 0:E \S)2�en�%"�o �t"�aE:A�g)�}act��H*Z0:c�= ��Q� �6۔��%���A�i�n����u!����'Ol@ak!�&#�# . A�kL abޖzq w�D�Bto "0,Todd RowlandA� employe�&7me {-lA 0YgIW�d�(� & �ma�I�9r Ӛ�"I � _{G��Bs "/Z�-'s.��ced"��24�< & C���I neg�Q�6w2�a5�K&le}�me�Fll�$E�sS !l&- E�d1A%;F� ��n�Q; m�q���B�. � �%n` �; "ed��6��#y5wA;%v�SW�uz\��b��.Jul�2" \.h.�"1Ny3�(p, IE6��,d a� �"K#\ �$Vthe�Eb!V��{&FIi"-w�8rm�f�!A�a6n =Itwo��C)�!��n,� ta\l�Gu_9i2�!X "��a�xa�a1�/sa{j5�)��cbvib4�G as `pin]E ^d'� horiz]�0"�."�B!�s�V diagral(A�:aW'le `V�kmYts�xwa�.,dce � 6`;�f� �z<�c� Ho�c*h�2ns A�&*:P+>tM,iJema�\%F�,Qe!Cg ��u��! mj�tyg  D"�%�t�Sept�< it i�&7;e�p a�s��pB�#��m�o�g$E�"�|�BA:6!)1fla=1�,���;��E:��~��M ZN2��m�A cru�z � G�o[D� b�;~4mV9-0� K[iv)5%�!֥'s ��$&�/ and} .at �%&s:rc�Vaa�epm��HJr �'s &2(,^�rast,%�%}v��E�]:a����F�%@��at���!Cg g/�',vF~��A�u*P%+�aqBy��Xar apar� "��C&�|�)�@SQ V MLINVIn"}T!��-�l weak��+e%�*u�o�sV�s�th�Su�Do"%~�9th.g]X& dE> %��%!e"O:)� E����I����A!f +� �H�+�t�zf�} a�z?"8 �)*� pe�$V2�Sure/�z ��orZxn+�d� �?�9avo&9� �]*�o)�m1o7= �ޡ"Z�%J I�inH��|fic�'gA�4�!+b p2*{\0�b mGdy<��MIn �O,�3< &�-e-��r ich N4� �t��-� � \psiJ � \in"H"��\o�, n� ex��?by"F�Z�`��EadT!H �PA��gq.�6�R1, $\alph\� �6  ^�+\bet.,:_ .,�#U ( zg ~[)6)2�$%m,!-q!�S %o�Z SURESHOR}��v�+th=]ilosoph�� motizdK i"R{]��aM_leY�y2a$n6�CQS�WɕA#s6X��,reTjE� ���Next,6dBASIC��invoR61���Xe�Ea��(I�!1.w{�2(= c'��� 5m6a�r �I�!of.v��n<]g�/hma��*>"�2 �?� �C� �8 inneU�� 2���6REL%���)G8hi$�� ��, circuc<iz} ;ed-� �  Vida�$\chi$�Pmpԃ sv!},a� "38���%wIt)��=!��+��6&Ug7^7trai�alՆ6 ��aE�E. "yL main1�!��A��,�>�1>,^LOWER%X(�Erާ5ReMW��t#I.ami�1��)�!�I.�U,6�ECC valyzeN�LsIYoupmEVVL� ��") 2�ls.�"�L'$\�!zel� %4az $S$����ũ3�9�R�K<s��WF�$��\!3P*t�tV8zedd�"T��(R�>%Z f+}� ^.v$S F5*t-\ �hig.�|yr,�a�i>�+&q��Y�5Yo�+ Ԡ*���/��"a=*hO�Op�hnt ��i�-t1��_:!Y10lF�g:����ul� ���e�liv4A�!�=�z $f:�\{ 0,�(} ^{��a'�Q(R �I��}e�?� Ak��!ic2Imu!��;I=�a-�Y�eg-��!�aTU�'� ��m raceh r��:��Z2�*�� �C~I m.x �<�.izRXm���` u $ Reed-Solo*�ca�>�-�Ian nit{expM<}: \&��A�\Op� %�M�6� � �9DIVIS���%i�;r>�DB�"� "� �"� aV��~gWpl"a 3�^UvA�ger $p<�ritPin)&�Or��1I had %< ���:��=�a��� l> "w I am[,X ���8��4a �@}�&�a1 he.�s�K��� :� �a$(qu� Raz �(raz,raz:nc2� �"� 9p ��maq���"1�a ;��:=� %�6<{?C�3!�Raz�echK6i�P�/p -8\6��F!�me�I�b�TI=T ��.;2�:s�AP� s�'� ed�v!�O"�wwT[r�:][ � ���4}��� O/�Fer� 2� PERSIST I;e�i&n �R�2A�R%�.�.��fnec���(4E- �2'|�.�AK sist�]2�v2-uxbr,db�mP �RII ��)m�ad����c�^w��)>�MOT� stud!faQeBQ!� ��edF� manifestp&%>9J�*�*��4=* ���hb�U&� ����}, �<��u��UKexiuia:��A=�]5�t2O%b Bb�X*}�Be�_A&�!~orA---�� b�6��Y5UlyF\E Z-i7V "ofA�borov�� Rud�F�r�k2� TREE�L2)�Y&!N�!)I� ivja"� �u�v[Av��!�aA���lea�tKca�:be ��� �ly�6��(e�sf{Tree�"?(��langua�f�#.j�<�m�o,z?BO% =� sf�M!�A 2���m%I���Yrz;L �a$ESq&!Z�� ad�Fq I3>6$7t�"� -%lChurch-T�>{mi��s�^I����Galla wa��#���it{all��MJ���b�<F ��q�� Ps!��� ]��.� openxdo���I;=�\�h eteq1�0\Sigma}_{3}^{P}}Ƒ\Pi\:# e9�M Fo�,�eth�S$As9� hier��y�PH$ By����&'.k3K7�A�% \��- P� o�2%�tedly��ov�p e �m2EXPER}&ت��x��geIAS;GscW{nq�Fa�مA���V�( dial�c&3� �l. 9'k�;m\RO*�Mnq$�� en�NsLr@vGT�p���y@/i���pE荰�% !����ls\)k�Se�m��!}q$��D�2�{�)e` �;ensed-m�lr  <�broad: oL(1ޡq+��e?l�"'8o��O� issu!��� �R$T 0 �}ith mi�?-�Hp=w�0!�_W�C *%���9�dQl�0*I��)�!)�['� �GSKEP}��b��E45chioe9Q�A��2�qP!�I�s!�|-upEY�*�w�OZ=ŨL�ED� to�yL~3c?�� yent-day=�s�ai&��a �-LBu� ���Fa� �#*5�Y|��]E�ڟ!B� ' domain �k alid�5�K Ѣy�5 �E��BQ-x�S$-dI�)��1��%$6_ \l*T 9 of affair2Ҧ1��lls��+o�� �>t��&�&R3+��#� B�y2�L $U2��UvN� Q�^?!�baP� d upon�" 1?h1�D *2� aS-#2� J (&>��-)�Fd��$| ���Hb) �noN�hD� F�\ (�O*�F�a� ho�J��.fy, s7 $500$-C��{�IflE$i���Q  ^��Q?4�A��it��"�}� Fj 13.1).,u*j�YjSer���32< ics[̊Hm=0.9in 2.393715in 5in, � =2.44width=2.6in ]{�shor.epsU�l:�S�A/)��a]{AE&:F]=ɸs4*no K%ۡ% �a[�&� x 2�2���9}��ory&�Gi:�›label�� �U-e */#�M&{�a�eY�wa�(harp cutoff ���%0 �So" YKej� � A�a�z�0sQG2���.�N$$C�F(*J�e�)���6[��! n�� ��=g� �"�): &�� If }Gw_"F� $� it{\A�Ja^}$n L� �}�q!A �B]~�,1 f,�Ƥi�� #�^n I�%di|��)Qex ˉx�pa�H��$g2�*f efforN�q\4d� d�%�je.��$ be g=�3H�{ar&Ѐ"����eëhFePPa�Allq��"� Pu��O" 8AM�.�E� ��w"�iZO�grtU2�U{�A\��2�*�-�2 e�\!�-�,�1el(�/z*B,�A�f=�q�5�A"�Pf X�ex,2R!�v����2 ��'�+ ctor�"2I.�val� ^���S�  myN , I�1��� ��- Q.� �q�{.�r�0_{n\geq1]J=4rePu?ZGU~\42 �,�� �>�jO� p�9( *%z ���.�}$p!.}:�0�A%T��r� J��\�elpfu�-�Nk�8o�uQA ��-�L�'wg�Qs! �����{Vi��> `�&�A9�Sclk�y w"�1rf���:M5�Re-�;� anyonJ-s[��I\�-5��1�E:�%6!3��D��"�%10U$��`Ihe/j},000$�� !(8@�rg�45^{\ }$?\Efnde�p�we�2J �\��&y! 2�varphJ(sE0)s, c}(W�it{forc��co-6\ps6Y �'=Xj�;-y�w�*<�w(h !".U>ys"Z��4.#re��?@ h e laboV���\f"i�t� ��8�}�o"�G�,7s)(s Chern-Sim�$4 6sE�3yi�(d|)�2,�Flm"e i���v#��x�4],U9n@5�� 2�^�re�(��M�i�uE%desio)�en���^t Hilberd_s.E�S��n19�  : 1�H�"�  \P>$=\fB�1}{�/2}Um_{r=0}^}-}��B r6�] x^{rQ8eEY"��N61,�����,�=/0?0d� : la�o�6as 6gR)[ �" TheyI�Ll�E�=� F����2*xb across�oY�g��saof0|le�8ґe3�)��f�SA��-�$��35/, ![eGg�2� :[� י��&�K �60 6�+�� n}*K9n�+)�9�L~%2�0bKg� s. �A&'��"�/�����th&�com�HV}AO* ��M%Z244 B��UUd���eyh0mu:f�catm�� Hadam iNi�Rn���/p>�V? �Vngs�M 6ity� �>P4mF�� \17�4�_Z slippy slope lea�2��D�qk"� �*��y2en��L[az <inM�� �� �9i��d�9*qE�5�r�s}a�NL-Ѳo�f�1I�� T*`���islgP�w,��!2OW �� As�ar�/QU �v:��8�-@ 5@---A!$B�.B� +>K/bDndm���BK�����S�.tWA�6\\ � ��Bu ,.N���� �nfewSg ing o&; !��I� �;!�d QH�is�3o 1 �&��!6��\D�* )�Yite&�8U�lLA!: 2w�uldk �NhW o��-.2� >\=4 Rz � -��=�it{*�'���^.��T6�E�,�\i #"t�h�n�N�E�^\} &��w Dj�63_3-� 3*�6y psJ��/�:;3�xa E>�" �2�*a�� $�*'�2q3,:wY3a�>$s�=>_$\ �1N=$p$>�2��2in 4�  -0.35��1.7� 9464���3n��# r�-%K�7�]{E�4ng- (20:�.�r�A68 -=�1Ry�2/$y�$Ɇ�-*h �26`)�5YJUa�lti"/! ,�e%��\f� cripts deh��C9t�8!(bit*r!mBnT��j f��hJx� 2�a��� �& NU� o)�RG �]hy�1�cal*�:..��if&�~d}/�Z~=breBR��V,&��1��n't� m�@ nQ�O�0$S$L eemy l�am}b�l%$,�ine)*it{:�(�p} i{Uu=,8CJ%p�5`i�+;�g�0"g�.B7 Rs��fmJ\l?�|R.�Z \ R*���ie�e�&� �t�g2�!o%� candi��/�&� �?��+e,cw0 ach T� �)A=r�# nh u45Z%T@IA^devI z@a�-�!� �ca+� �y3M�E_��I� �6b/r�50�%a�J�+if�=<s 6��E)�6;V�k 'ijt�� �Q�CUam ��j[}�jn :))�So �8X Mxorrx7Zo $%�8?+�4)7�7Q`/j��!��6�g�G��$kdebW�J� ��pYcu"LZ]�� 1�� �"�+� o�i�R *}��} G%lNf3"��'A���."E ��"7  F�regimeVF- key!ʓ�>*uc�\ ��=-�Ɂ T��ac�|l��d ���fro��-M��-M ;�^�%�sll 9t$����,MU������it{� I�"� �Qthu'2� I�ɪ�; ��me"\A�t .9? �]l.�' 2n".�&{�l��Ntc��v��� ��:5( � �6����o7t �bA�/ talk���L!�1=��;r�8ll ��% $2$-�'� �be� a (�a�PA��� =A ��� � �ia�z�5l`;0��A �.� memorR/���" i<) r#�"�*P�%b j z �(!7� B'�\�4b�^eo�So:Ma,IZ,2W"3<��eV]r(�7ul���a�em�=:U�3�`����{1C�/ar:�6,&���w� �1��1�>B�0As�l�2"# �rs&${��(�6�C"*IxW*4ŪR�q�H�F-�!OLD$���R@}!���"h\ �&C"1[�k"j+eio�J"��a�seesBSF�/,!Vquick�^in�oF�1 �AyKi/*&�b 2�t�uw�A��pau:�ar�,A-q xi+� s�u�ީ� l�s!�C���mZa�!�B��"��OuGYE� ��l�TleaQ(�1 q�Ci1���Sne, i��P0.j'&�pr�+!��FT�j-a ��quc� �* A�not ���'ucA� [�!3*&ofN��a non�s task S�/"E9/�Hf�=�-mp�5"�,Cln�?RRGCQS�,In�!Q�23���%*�S���5d�Z�;ei<*,3or��"� "5�e�&)cA  B� ;wAharon�5 Ta-Shma�5 at};\ Jan �Ml cjanE'Bet�jwb'�B�:}B] $U:d� ghmp% '��& e1��A rame�a����A�57 �yy� �Pmy�L� p>I)X.�� }\.� z� �|�fiX0o&�a6C x2d :xf�{ 0,1 } ^&M(}L�"!' by ` �' �N+�K�6�v� �&�#. Lik� �9xt E}�A%O2Q%o?8 orgas�A� "a4% &,3%_A��bottom"�ji�asi�atyi!! )orm��f>d$\E0� $^pAxP�Q��er�3�1URwo Z~� :�!A +&F5/}_"61}}�/� b=RR��$�( �_{.:��:$QRpI`)":"c ��IE�ln�#)U:�+oE�%yVl g�����=#+7\�Dsf%"Y��*��a"q[uV�.6bs.� Kt 0@ 2��%�Ex9����! ��e�I�nO(a7h �-Z]2}}$ �0� e Aybe A�:���_N<\ R,��\ s�-mu1}*vi�a��R.� V ${}$Y��!�U1�g��W��"W�(=>� be8�"C8F2e2)��W�&�A�� e� oJN�3}Ki5AI�=�! etu CMTie�x�`)�-��'xcupQk}% }pN� k}}=!>=; ��9-k}'�z��� !su9�� �rX=�[j4DR� neB�.�k�FLL]K ��J�3i}�͝u��z6�a�'i$:��@���rJ�� +$Z*�)*s �D��!i� %+� }��r��&\�^1yDy0A�bi�{�1�΢8367856=31.8060 $0.679377in 1361O]2.8928.`71`�es4ncKn�48relations among� quantum state classes]{Known relations among qN-(.}% \label{ ?�end{figure} \begin{definition} A \textit{q2U�Utree} over $\mathcal{H}_{2}^{\otimes n}$\ is a rooted tree where each leaf vertex is l��ed with $\alpha\left| 0\right\rangle +\bet12( $ for someF, /in�,sf{C}$, and � non-l� (cal�a gate)�%:� eith� +$ o! � $. \ Each�$v$; also6@a set $S�( v\�() \subseteq4\{ 1,\ldots,n $<\} $, such that5�\enumerate} \item[(i)] If� �then $_| B� g| =1$, L6M the !� nJ� =c\{ V�Y6Za !V!w !�$w)C child o�,6w w �vJ�.�v:$1�\.s _{1}1w(w_{k}$\ arev �renV� =�F�O  W@pairwise disjoint�(form a parte�qHv D Ava�]( Finally, i%0\E�5Y-?!�8outgoing edges\dv$�M� e�Xcomplex numbers. \ For a=A`R sub�Eed at0 represents a:�of�qubits iVI�n((obvious way�We requi%�is��:0=0�)>- �1J.-�wI%a�eZ]'(manifestly ]2!>M  ity<\an extremely unphysical Y�0; I introduceA|becaus turns�2a(be interestaDfro��hlower bounds perspective. �/reasoDf!�%��@operatorname*{TS}E( Zp ~�ܥ��minim ize� �e�u�2� ac J�e]Th9_Y"I`^!o6�OTS+ A�z�= ��1R�ntMuZs- � � treMGd simil��a%�� sf{OT� %^ !^ !W>_{n6�As&| $J*Z�FJ�\leq p8� Ѕ�� 0polynomial $p� �M�A- ���2�n]B�-n leq N�\�$p$. It�o easya�sea�at \[ nE:6�11 JCj.)g:-NDnREe�q n2^{na!] w everyBI6A-�e�A� �E�N�\j�RDJE � ) <�D$\ has measure $0$� & ��%ţ2� eP wo o�0 important prAgt��2�$ �N5s (as follows:"� Uosi��8invariant}\quad,* * >pTSondBAE �a, under local&< S!�al peopl$ ld mI� a�� able7 �-c must�> � c�* all}�chang�� Alas�eis would!tly� �p!�� s hav�9m.�!:V , upa�a cons%�facto�3$2a�1D� Y� \ph>�a�obtainu 1J�$� applyAa $k$-  unitary�]FH�efB�>�U�1 k4^{k}�Ms:�M$��>�A<���jNf�.f .end6A�proof} �?SimplyeK � occurr� i�!���:��.i� e orig���b"� �3.�NG.� 1\2� �Pv� >5\B� gammU gBu delt.!>S,��ap�� riat� .FSuppose out losw&,�� pplieda� the firsta-7��LMT$�W " a\}�� ����nd� $T_{y�b�D� ric�}%�Tq q�by setb��>��$y; E{ 0,1/} a��JCB� � �\)�a� H6 !Fv more, we exz2 N�\���r$\sum_{� B�}S!'�$, *�$$\9���� ���@he=is�i�/yof� $k2))b�a� One�j� )�0$\varepsilon$� -E�ximatei�� B� TS}_{A6� | EL-�) %���!WZ� 2�6� | wB�: AW�.�| =:� �|Az2}\geq1-)1-@ ~ 9A$. \] (Actu�!B<Tunique \cite{ns}.) \ Wa5n>� 2�.�\R�A�A� $f$,^0nolimitsV}:G )H%3\Vp- # �^�Uleq�SN,&# 1/!,�M�nb=�^� ��ixJ�--� ��E� 3�K  (Tpme a clos8m"�  inner�ducj> x} z]b^{\ast}J$, bu2often � &!o work�E)NowqZ�1<�mF�F7>� A�ao_{x.Am!��� $f_{� M �.6 %�$\= ��\m��ZE�2�=��b�theorem}">ff}�a�MtZ8: E.V&^>( � 1I]�O �>�R�J�I � ��>�>Z. ^A � nb-��+*�� �N�!_{D5�BR�J'V�%V^� � ��� $ �$=2-2\sqrt{2 I@ �5J[_{22�� !>�J� � �RnN� B)6{�.��U�:�.1 �)]"i���/ �J�$,.' "d an-in�� colloZ[ �s,"CW"� bR� �1)X��_{�xa�ex<x� �.�6�F?a"G �1- O�" Push�J plic�$by��Ys r e  d�$ to $ �{! s at%leaves.L=�f; �� A ���ч*/!\��*; �  at16M�Phi)9" R�!S�v�@  � � J�- F�,4 �. syntactic, atUIE4�*��!�w$,R�# \cap&�#wI>) =a�nothing�A lemma! Raz � raz}\�x �w� ways mak� !8 �� �incaMt iz%Se�,�� a $u$=Z�,enlarge both^�% ";#�� A�Y&\cup 2,A�E��1�&�%Xby iu+e�( m5-k$aM�( +\inF�( \setminus.�e�Z��� fޑ=B�jA�DS$t@ doe#tSlidtan��i�i(�n ances�u�& ince!Q�Cassump�x m-�!q(,5� u.o is n!o1.U��ny6 n�A�vu�inR[A&1� .o!S,U�Qj r.�A�E% r�\�rn!� ��.�ird�Jv$�G max-�9} r�#�1�. =1A>u� �qJ � 4>1"gw$ N�&ent�L$v%"&�(�i��&yT =a+b�vr�#%�oc*�B�!� ��ing $.�J�m a+b �a~�6f �S!� Also��� ���%by �R�>� �1c(B�#3's�0 step%re�no ad&s!�sBuH R%DA�a.�b�� ��$)m�'=.LF` $, wh���a�easily nA� be $ Q"W&P2D .� \ . !AIE re�X h @) (i)!F(e5es�ng)xi��PI1e. $p$;:n%R�z)Y8U�N ) -� " I{iI�� �vs% v2���{ sJrq : =) �&�+ ~t9uI"!�beta _et ) _z�B5�0 amplitude ve�; �&�t  m0. noo&*, divid�$��� �2" �9�o&p,'I(^{\prime}% � %� align*�Y��}�^9�&�B� &�-,-\frac{1}{2}BqN�!�!"{-p>\\ & _sOAkB�BP#A�� J�>�}+fAk��RV� a� n)Gv�ZV g6?=1-.ChQ#V�� Besid�*�sf{�&,9&�&" Osfu�&, four�#1&e�2i2�) serve men�T: JCircuitl a c  analog��(pcZ 4 e? 2��;*�S�}]tAMi��6 -*&�&_ �n4re exis� �ar.%�of Ů&�*�\�2�I�+*/� outputw"R%��An $x$$ input!��2*�C' \ (M�� � ���s�#�%%�> xcepLEy! ow u.�out---B is,~*a� termed�  p�0shbe reus�/rbitrar��mK �.)](AmpP}$N���Z�a�>�|��-�bN�,b:� a�)�,-VA�>�*  atN�$ � b$ �0 of precis}��=-VidalZ.!�� `Y.ly ent]/d'T � sensN�vZAZH ,��� �3 2s4&!�A'Bc\chi_{A����y�a� F�����j$k� whic6LLFK$\Q� writ=aAV�R i=1}=!q���9a � ^��QM� ~ ��p�i}^{B��/� �_-DU 22A>2\� FbV Jc�4@"��EsE 9� rer/ly.\ (~�FU) c is kc8a��&9.4Schmidt rank};� Mfnc},more inT#q � ��F-f�=\maxEgvobB)5 \� �v4�XeD� if%�/4if ��� JE-� ��s�8y�� �\Psi vMM~�3oU��$8*n��.f>0:6 a":4 �#+\log1�1/a�MR]8!�\��mapEZ all-,E��)ar����,trace27t1��most $2�$2hVR� �:}4Solovay-KitaevAS` k:ec,nc},&. 1��1i:�+L hoic�� universalset�s.{Basic R�s-(BASICMLIN}} forb ud[+]��Z&pecific5�%ts,�3`,B7�to a��g�( howNbep,s�"�#*�,arId5is � I3 �,ree rat�"n6)e"@.��be�<"� �logdepth*�&�&N�Tr*�B I�u1`4&�B�.I�T0"� ^g8 1+��i�� oaUZs�O�t�c,!� wella &�3*-6)&A(iz&�>��& ���^��2 og:�u&D!��6� 2ta UG�T A* $!Br�i�b }�9��at� �""k'2I��| n z:valV��'of)�� %�"�BR%�n�4=�.� :H ^{c]t�*$cSa��a�Bs�y,�+veI Ebe�:-ce}\ (�3{* Boned Buss%b: �e})�0roved %W'!Ge�? to s�]!W$c&� tak&*2<y4any2%$>0xSo�� suff�72`��` � -free'1�sF&s[�s� &n ��(!z(>!M��se,DR�9). Biz oven�in�on6�6(!\ H� P, sketch: cho�a�'-� $I$AzI���betwe�\U|BB/3Mu$2&B�&(�o�,!� a'i�" identifų2�G<��* y�5G��! �2%�<.% G>) +H> IFMv�-J s $GG H�f6�.� �,3'�Phi� removYI25�0%a>�%�$SS��G�# �2�H:rCI nc -gI.H+�%1 �t�J� widehat{�R be a�.�h$$$ evaluate%f , $H���I$ sepa�Bly��%+re�,� logɫic k!�Scad�-fvfs�N:�UlB�)!��� totg>pthH��y# blowup�TmZ��� &H-�}By%�J� ɻ'sф� u�a� carefu?�`v8&^�(�(@c��a��. NowuCI�.�.t%n c�2J�ar so*A!�|!�F.�2$H�@�sha�&��> $I"HA@nD2e"C��� E; been2�4A�.O�:��$I� Thus A��D!� D rved�ToNV+ is 3, sT5e!6�-��x0 `bottom up,'Ett@$G_{v��PHa�iOYs6�exg57�(Let $v_{0}=:� ��"- �2i�v�0xaf �0a'�C�' '1'�so"until k}% r�A�y��It!�cA�%�/ $ $x�&I!@����'0= r %UR$ �CF.�1�E y ho]E��(_{v_{i-1}},!� $;��by��itJ:8}�6�  ���0��"m�Z��-v Jd �A$���q&�'C&cM��-�1-� G""�åyDf�.$2$ (�� �+j v6n=�catnF� �� T��z .�"i8? 6Z*+ �I!�`'( n� �2�a%t6�rnd2� )>{L$\Q�Jly;9$ a2 �)�=.%|! N( Ta� ��m�-"�>�= 1�! ia/�b(-;� *S ^�� �c! Gn��6; +.9 =Vn s� "�-�Bos��bR +.,eB� l�$5B�11� �FsBV�I`Q�l� +1}�N@G:�0�c�U�Ax#��0�o!�6kF�� $V�o"�#\�JB �nc � B�C >5 �:.g+i%,>�CU^{-1}V!nM%JOb�!5 $�@eP. M2G>�.�"T.-I'>N=U��z� ^>�=�,So"K �G2LNOT?to�O�C register,�^,edthJR@�,� "�,M3S==>m�%;��a�9�F^d nMd�Ki���,7 � we�FV� >�'Ja�y5� � -y:-0� �)\ �)�%is2�"U �)/.�V2[-�E�@s�DE.-f J�ari�3�!�� G �3W$nF1��If�[��x,]��> can combi�D`X ing'�acrCG� ple level!#�recur�, �+ �!I%Q]�2*�Yu 6S&� �� By symmet�Jw= �>r�T rol�#$U�$VK,ZGz�6p.q.�6$9�"r �n�M!���� ]@){ rDF� V1c.:.�V�9n,\,\,2@6��!>%A.y.9 z>�9c-�\}T� = q! $c�,2E Sol�X I�r�Gw�Vndͫr� yB��$*� �4:3 V0�^V���"s!nonapx}�I� !r:Xik]V�+is�sen�"�lrandomOa� Haar?O0BJG�H 1/16"-v��'() =2^{\Omeg�U( -�) ��O � babi, $1-oZ( 2��-5,1=-LTo># te a��� 2�FM-+!V��N2/"�(2�0QF���� $&�a�_}�/,f/|2bb{��A��G�, indepen�ly�$a Gaussian�% ribu�)U meannR-nce�F�� ��i a�"C�+i�-�/ 0�gCR%O�w2%i( \r 0+u y�  \� �jLambda_B �!�xF�.� {Re.� �_<"U14\cdot�S u"I"�)B!�a�GA�24zs�  6+2� ��RT/5���Ea�� \Pr_{%V 0F�)t[B� fɋ2�G �]�2R��^^=>%EXL$ [ R eI!T+Pso�a�Hndard Hoeffding-typ2und�'Pr�H)N��[�6: {erf)�A��34id 2}% 9`V0.198U���Ip)YChernoff4\'\$gia!�$IR!E� A_{gu^ x:2U *{sg&�N"�*�!$ih ->�&.<2WR��*a�*..�6�y}I1$1$q,$yAK�-�;"�&�6{JZ��� ,�lyIH//ECj]��J;��8�I<T%�)e2d"N�& }2%� ��f�8:�2kF thus)�>�c"�4 )�Ig1 �� ��+ � 1}{5 ) e�.�TI0�+6':;KF1/15}zFpG��"�� � �.�%��alv-I. Bool���Hs Z�L�H)��L%d{ -1.!T;"r3<noo>�Pe! "�*2^{�6� s�Oņ\[2k {r+!**V&& �- J�J � e<? 0.49��%��',"F*!_*i? al-%e#CndIC lude�n, W+Don %V>'f&�as",� M&We do� Ŗe T"�! hi0 >�]�� 6p� o��&Gis V��"W"theoVFFj\�esign-"�-ed}�fN$QwPO^=,���U5EE>�2Ph"�2J[{O  � $xw&�eN�*2� W][e�Z���!=.cQy�>: onA� $0.5�t��1��8&. 2�Q��"^)T �h ��(e�$de�g,Ie�dpy�_8E!mER�%�?,�0�%�nI?)Bx� !��J|T� \R, $c4 % ,c� <%��_{c ٍ���icul�:s!��& �-�]:[�)?A�Gashkov �-g }�- �! Tur\'{a}nJ Vatan - tv})r(ch"� �Wa�'sA� - ]w}8�^8l algebraic geo��'!�at)7�ge:;all��+%:�2J�ZI[(�#+4��K !�IG�gb1�� a�� %�i�fct�J u!�t w 2>B� �u/�PhiA6�$ex��� �[�*e)�F�s��j� �6� ( 33B(�)�,��Wher�V1 Ry�is  ;�( �B[��%�]�NB\R�B}�2VIl"� B�� %,.s .�;��T1\ref{�Q,�; (iii)-R�_gcR�� R .��+3orollZof6�#��a%� a`mpl|6:'��5y:+�?o�-��(.T_�\e8in,�3, $1\%Ltre�*a��+at 4n6��- ?�=o�� i�q�(er margin (�m $0.0�)&�65"9% �*�6J`iH(*C]�q7*�@&z�:]!Y2~e:{R2 f�6=f3�IBR% N�Qs��6z �!)E:�F /32-)>�./4096Q�=w:�.�*��2f!� px}\IrN{.V )�Uu��� ���*�2�NN*����.{>�b �_{0u}� Tak��B0=1-�2�E^� n"�Ee. �g 5���02�*}!|6s2�&)��AB=���)B*�5q@ ܦ��O � ha8�"F2�p"�J�!`uj�T&%H)q� HDN^wB�56PB�)=m�R�&�r6�6�hi# O� �!�% +6�=A �-�+E�f!�gHMVetG-� k ��KA�v"6c�H*�Y}&\ikr-g!pYRR,*�\cI�\� S"�Z�:s>=I 4&'c"� Z 3 /)O%�By!� B�vN�BS�2�!��3 � y6= 6�*]q2L� �But $2c=�Za$� Yj}# trad)g:* "�?Re�{A�{ QP{S�{C�{fREL�?�]�1�f> 2 �> 3 @B�aAB!be �B%g�$�����`�VR For\�I�B����*ya�>a�4 6K: J( �M J�Hin 1�Hc)j:8�K:�K�!�res:� "%|D�d�*Y iAKqI��r��B ��  _{ij��BKP[D#܀ j <] p � M�0^Ej+1 GLJG] �j�J�� f*Dily��:Fur4�(,-��4�q%#� �p8^��N5*�@ a liEjA���R�����TZ%B] R j-1\�BB2�+)�6c �����i>.$-�P16*�bei��P8.� !nA�Nof�M� �!G�=,:�$�.~� !M�4*� immegQ&L�2��.E"�+�=uZN�PP�8�g�Y���X d%?!�./��Z�Z�Yn/2Z��[n/2�]�j�j�N^�> �I"Vjc&U~m :��nd���X J �"��r�QE���]csoMU)+sivaUa(s�LpGa� ma~j.I� l;zd No%9(6N�2�2V{�1 )q� !��s%"/b�, $; sZD,� eTC1B]R-;Z �!"�"Z�B 0F�Q��� }=>� �"2�2S � *� p ' &b ��\s  �Bm��tFblU85P�� q t$BE�"i m.] }j� �RIuf�z�(exF �O$n/2$ BnM�s: f -n/�6Q 0:Q*�1 1�Bw*�4/22V67 B� �>V|  is ol��* %RRg� 9A>'e�UP� ^�UEP��%"Hal5erp�E"Q�t-b5!tring�pU y $i��* ��2v*5Gm� >�!�2� Z� �� leq4:nL/>�"8&�N n$:n_^ �0 0V ^"�&1A��F��>C,9�R$.��%:b1RIB$E) ,\\��.U}^B/��Z�>���BL��^F62� � <1�a�}1sfq�:�>�B�NS"�B�$�pge .e�16qQAXE,E:a��no non��tenso&[r�&^B�1}Z� .�� � $݋bM w:N\ $�6�J.$�#[ 2\a|�jfmp�D|>�T1}�*^Rw$)���plWn Y _B2:�v�$\�*PV6�2�> �6� �x��N8ls (^�{���)ba_�8Fouri�M ransr��2k*J�~( ��y<>u��4�}�ԉ\2 :���'jc*�O>�Fc�VMd q�) ��] :I=�EH&� B�=�I�L~HY�NI�]~N>' BJ�a+�N>r3^�B�R .�>��>, n��+�a�&r�w�2.��n6&6��!�h��2� n�---�V ,�E�1.�^A��f>**) Q�J^:g i% P1:� ~%�6�"� FB�>B!!f $.jhNotB�FW���!2�6�FN��# "z�y�N,r�4ŷcap�BC���*} qFx!��az�BP%�$-%!��V�.<�� .i�i'\V�\"X�� BQP}Iat P �\#P}}$ W(5KbF��`&� 6�8b6FhNP�>R BQP/�'}.$&yl6i��� PF��.�6> �B� 6F�!gJ� �^�"�1�Q.#&�"�8-�}j�\��@5gf7])�"�D�+ހU0BT:9,\ machine $M,$e language7Bs�->j���/,a��O"�3F ac�hs� �/$xVAad $a� xKlRY�!,�EGW�5>S-\~��Aide��B.^ J8�9(_2�=]� �"ith��J�&I��ByfS"DBernste�*n00zirani�bv-).0R�BfMT%�b�Y"�+s "fd"��5�n��n� Ac0&, s $poT%W 2ɉ*e+�5 ^{n-� =,*&0y}Ip��m$, or%#pr&@���D��i"P��,�rzR�1&*j "*j!~Sh<unwXu�garbag�J�?�#EQ��� �R��� �:�o1->)>� E*�vm��K>wlength-�iprefixe�0$"VF�ub@%�( k+1)wa�!!SA5m*Gr.�&��6alT@Œ@3=�iL|\��9 "dE6G��2�+Qx..|x �u�!�glas�.epA ÇY�E.pha�k >BR,�.l�tat 7�dQ+A�_���w&�rM�2�B��d*r} $SAT��hg�-p}I�� Val��-V�&)4vv}�{GA��bE^{*s (��-neglig�$0�C)�N`s�_&75=?(��s 'i� zero�+q�-�n=>9&�QfEwEaNn � N��1.N0MVt;ՊI�e�jM!6�B��Fͪ.�Es���9��%B��46���-�q�(s#� ]��3^�A� Gereby fi5��M�RuAD�cph2@if39Ub.�A�As�6p�)B-'r? J+ � �) MaU|��&- -iB�%�*� ��Q=` ii�$eg"!_l3)ny~M2�p�<�� >� !)<�i"8bv}�wy9�omputq"�"made `f n�p &3;!�� 6Hm� �V9Y_ʡ ]3�EC>�.�$��me�H^he� k4"N~z~v q+{Lt�B�C�+LOWER�+ We w��2�?cer!�5.�k��3�0u�sc=&��%Y�)/9��)ANAt�xXJ seems lik�^hopel�% task,PrGd�{"B���i�2����$`explicit'&9�_��tor��(ly hard ope�oblem,�9it2�+A'le�+bv./,� :eQ�NC�* PE�<�6 ough�@I)�@concer�P�9\>*m(}��u�Z Co>�%;���A�zY�la.?3M ans٠iˀ&5�recently� ��ons un� �.e;ing, Raz�*0raz,raz:nc2}\&=&+L�>�2�o�a &-�U1In��i`, {who"�&=*:svO� ��perma�F�devinA��Z n $n._ (6matrix� ny f���3�,\2qK\loB Razjech&�� beautifulAV.�&�8Furst-Saxe-Sips�7 etho0� PL*˖�j fss}�P ��r argu��5>^Q�Pmun�M�M�ah I now out!�� ~i%a"�> ZC:2aB��FP�>)��!of� �FKu��&��C����u�"z� s $y2 y�>�> ,y_{2�z . z./z>/=gis�"==3P� ( y,zD ) R�G�4J�+*J� "�>;!��%l�cM_{f|P! R:�!;]�@D!�E���row��l_���Big��!BPDV�� Ncolum<1r�beled � "�? s $z~Q �A 2F�3entrya�� Tf_ZyQ�[:� a5�-=)h� "�^'2p�E���lex�>W-i��Eե��H1�a�unP )/8N Ȁ7/a s $P����WCo�<3.6��-�`�^C Ia���tma���4;���� >�=%�zG.�F�_Jk�s��� b6�r[6�]�2razthm}S�f�\MPA9� )P �NM6�&!� ( :� q7i -�"�(� 1/8}un-Mn^{&xM2� <7�.6�V?M�&-An&<+ "<�y:*""*G }.�� .ůah�� n $N�' N$�.$M�m_�.��a-8B�')zv}�ME=gU _{L~:.}�L- #XJ vD�k$�-=>}�{&:sLf5� �N UZdTi,j0Nv�# \ell%-. � �]�5�"?razcor��A�R^&�;>��� A�Z� z�V-?�>\.�t �0_�X=@ �9-�N��"�;a�, { n���$g2tg�/I>f-gI_ A�bP:�43rxN�X( S)%�2�2"�]W2�X�g|P���.� BX.�Mb"O;�9��!s�::=e���G.6� H�� ��B5hd$�c����F^.R�n^�;A�er�:�@�s6?y.erm�j.V }�5$fN h�Ra|el؁�U"�2� ��tu�s $R$"�u$2E$\*� �2f$1 .AYe  renarm&�  >� XQ�c�"� >� :/A� Set ��^�tai�] $n-21� &� r�R� �nd 6NX�EZh-3 yWV 1SNu"b�_{R�7.a ��K�XbeaZ!���> ��!?*� $\q is c ^{����&� cor2Z�R.� UJ �� R���\ge� �-^��  K&K7ellųgA�ΆS�f�Íh"�U�F(�  �!UЫe *Lu"�:�q��d}Un ion j�VE�mN>�P~$f���l� J�=�e�rcS+a�� � �� �I=A> Ur���Z��%6�V! �j)&$�>�]��E�r��s b ˽�)s�lyG� ��pV�2a \ �y \2y�$r�%B�dO�s: GNsi&~$error-corr�Af� �CECC�d (&inf x- �tica�jecture) v.nShor's�-o�1*h=in 2pDIVIS}��#XR {SubgroupCl�} �Qel�%: bb{Z�n�nb"WAn$n22�n� �l p��_?6Mj���� s �)s6��SI\"4R��sB,:->,�1? */>}2 H �� :�.[ Co#s]etcodeword!ZEZ.X66ng3s�nBstaazL����\cs,gottesman:heis,steane� Our&i"�7*�eYfe�+�ir*�Me5�t �their B�;vi�E@I0� E���� U# s $S;CC a�/2,.���bٔ'H ��A�[2�6S<��S`Yx~|~Ax\%}0EM .4{mod}% �:}4���"�B:e 2[P)��s&qV :-��!d.%"%A5AB2� M�.��aP����\x�a&�: �'�:. ecclb�dS�drawn�72�2ZZ&f_�%)\HnN4.Q .z1B�Vw9q�B�5mS"!�> �U�K.t$$6�1�] ver A� (��m&���� OM��xep��1�^sZUof� SaS"ase0ZFn g.��!"m �[Vc�S|*6 � [n��� Xqd2� eqwe"[M��� .�*^YjM_ WQl�s��%��.��A_��SV: ���@ub�| ."&� ��� "d) ��G�?�o? o $y#B.� $i� ��tD ,� Յj,=-"��� A_{zM�v.�/2�b�m �\��x�z��D Vk\,C>long as nŲ�V{rx�in�GZ$,�����Ӳ� $y$!s.�S�"}/!{$z$Q�� YH .G=1 �,�Q�>M*I!a�l!)� +�t�!���)�V1� _)�'`a6�N����.qEa� :�".�{"H �9q i_F�12}"\  3}{4 �fs -�-1} }>0.288�S�pB�!�yҹ�^IN��at� st $W� \�5Markov6� nequ���-� )9!DHV4$ �L$S$'s|$J'V� �S%� �le\(� 0.04�_A $P$'d2�MN\!�n(the desired�ult�4�# Aaronso/\G� � ag&� ��>!�*��n˹- 0 te u� "�+";&�+a� �</:E�So!o"�>}X iؿ��;�/N2�J ]i�Je�}$$et(a (non-*�)� t:^�F�kmiR�+s��MNing&�$}� mlinsep}T��&\am�5of"� |cJ?bSm�2�e�+A&|$-�!L?6�sUY noB,=&a, } >��,#*���\&@�io� R!"�P%Bat*�I � #T��&�"�.�"�A�&�� s�iest FM.?�%&�f�O+�+ bcs}�PWtVJ#Vat��6>pe %�)��still� ceiv")�^F&� ���*d}�n�9 u%w rule�"�J latt�o3t+o.W�$>f ��L��R���Uk,�2)�&� < Hoffman-Wieland����y&��u"hw}�$M,#2�Z�# }�7� I_{N��� *�\�nt�m��J �M-Bi� *�geq N-r� :�%�� �:�a2jMZhw2��Ioastvw}"�a���O$2�%� ces $M,P$�mWi.�� sZR, ���-FP &�H�k��);M- ' !J&,��jw!��e $i^{th!��xudc valu� $Ma�! �$nR�Z\l�o}J( ��#�'1�f!&(A �s + A%�-#F���� eigen�� MMT�� $\��nju~0�ns_}4M$�?C�l��:P ]��f��llPEN�BM$�<�)B6n�$\ non�/6�s� z�zIz:�~AX!���q ^* �q"Wof}SA��6j=kB�r f����\B>$*٤+ ��x[wl&�o �� qX� �i"3.n�"�`Fta���0r"[*g5����A�ʬ2� &�!>p�A�"V1-:E }N�.V2�S� ��5 :�:/n�;&�� G look aƥ\x.�c�Z( a�*&�$PI.x��W�Tready����l* �N* S� �$yM7z*���ti�e-to-on�9 e% �6 �� I�cL�A���&� �  ojtIiEfD=I/C4� ��IE�!O *HNf�KL�� �W�1�ll)��'* #2�M-2p6z��v"l^�in!U遶�2}-)Qe�\�^5b 2brɑ6��meB E�dK��� ,�p/A_]."=�R�R" � 2)�ge ~ 2`>e HA��/��#R��l. "$�){)z�KhRJ%) �a��{ Au� 6� &�*Eq'�z�oA*=R����>"&� �G+E�>��_=�-� *�KU]f�I?5:�/�*� ~���*��<1$;v.Y,meQ �deC"�k!~��We�:j , �ideas���u�3m��8Andrej Bogdanov������oof=y %���8@?�"�_�A$ wa� �< �$k� k2�� full'k)QfE.ls ere $k=���� switn��!(�1"�Fl�2;[ bb{FC 2^{dDB�sƢ$dA��~�O�'t�6�KmFv4 �&Z�b#�3�S�g̼ F� �V�5�harray} [c]{cccc}% 1^{0} & 1=N & � k-1ʬ2 #2>#2^#\v��?  \\�dn>An A%J ���� �&]3k$ Va�"mondeM--� $�,�. �0% "3"�7%�_1�!�� Any}Uk 6k5 V$ 2r,"�A+@Reed-Solomon (RS)3�\ V$ rw�N6( perfect er�7.*��In�;��dsk a degree-�( k�Ym *�p e�'i!6by)�? a]nyo�ת���D8*�B]7�! n$)6quu�bl�p qupits%N�UI�$p�ide?a�!L`��:.�F�+---�'>e"�6O��c5�3se���NV^{T}x=(@}� &F�L"<V�m To r>�e �!aA4T!�ncaten�ESuHadam;8� �: !#a)Pit{�5 ry} M5ar2)H�m!�s"xs good�thB� �&t�RSqA�Mq��m�7�9pr% N��!é P;"K9s)q> , modulo�  irreducr>I� $de|K�m%�( 2�D� d�d$\�r�ibH�$q� �u��Q $aXP6�Hq�-a an!�d!�i!��_ i��h cici��!gH+1pS9*Bd$ 4� its 2�>$Yxv.$HV 8�d�) �" the U��!�!���now$a "�) kd�2avtvF�2+�0a��J6$V_{:P bin}�~j�95���a��2�T�#�*�� ) \\X�# &5�uzX�FX�E ~.O�WBU�2zw�| wN��PYa�re�,�G�X�', f�ktF+�* <1/�eYd&�W *["�U�"�� kd}Am$Ed+c � Yt*A�!Z1�!n�?q-ƭf ��� $kaE" "d )��*G" $2/3� $c$�N$�ly� � anl ��� �\Dc��a��0��+Z�u)$w �Tn-k �d-1! � � �vL� s $u2H%�kdj�#Zi ~~ \ $\���� *�w `$1$'\�A�P"��o*ĐB� � the 2.�Y���' �2!eZ \ $V6��% }6o$H�st<=�n-k^��&NH� Funda;9al��� of A z�Pc �!��f� �_{�E� %W�[ Wu ]�2yb [�yFI % }{)�T�>��ѡ E�!� k}{2�1_K!�un�`�( , $W!��AI�>�*� n�4 9�is��%1-��d)��Ata��ރ �:��Wc-� k�`1/2:�4&�'a�~^X�|v� a�= ���g"*2�$c�� G��:  ���NEI� $J%�Yif ^�� � NB&7*0 &@�"��O� }>�Vr0!|\B#02�/�i:� V�'%�V' � wo6��$k� QNaC�Z�?�'�Z/!3$jZ��T�by.�A� F&X6�F��a both�?"*n)1/3��L)-$�1=� $, i��llvA��e����5b5c����s��1}{3}!�f�;n����"�(aY/2�%e�,M��B#��*; �by R>2�Ky#q�E�Eb� �:�^_$x�L�R�1.+ߪ�A>�u�� M:� �V-�\ A�ha�hivalen(�L %!�52�O1�s �o avoid)OQKc�,i^#ee���ime (mP`goaD�+ov(=q�>} �/H s"��in֋)!O*< .�7 $x=�Je=Wx_*���*,p,'�.\4F  $!5 a%}( 6$|e[M)rz2:X&�� V] f��3U��Z:%5�=\Thet �>r�2_{ ��� �N�5 so� �o̡�/foc{P-���on^$ _��cW"_)trivshor�w^j �}�$b0�� g6� � 7!��,!^0n��� p,p-o!�, mea� N z�a��Xa�F2�%g]i�xv}.v�>�mi�3n}/p,nM���V .�]� 9�=�o���˃aߡ��W�n%���%>�#]A/m]��L��nMog ���%�&su�<a;<�gru���Z-a2Ai�x��3�"g��$x)aO�Z% x��hy somorphis�oyp _{p}��=��>�YtIDR�1� �EW�;e�9!N$x$�<or�,%RL��S ��� ly���2��Y�F>�h, &�5toa|� � a�r� % , v& (v)vi���-��" p}�)h�Dp-1}% %TCIMACRO{\d�Y \lm�j&��'B�LExpanP�< {\displaystyle\:N9 %End6\ex&_�� 2\pi ih}�H4 2^{j}x_{j�fJD&;L.wwsum-of-�uct��0) � "�2 5� j�of} $R�!�n� u�cos?��Z�s.2ahst�)��,��M"uCI�a J�60 ae^��}Y�)�6t���� ��Aȡ�ۥ]AI�m8!7�""*�,'{00"�R����r�:e*bisu I��m�{@J@A$�8%RSJ�t ��J:�<����9 �& ��E!�#Nk F8vert \geq\left(p 1+\gamma\right) \frac{p}{2} X] =n^{-o\left( \log n �) }. \] \end{conjecture} \begin{theorem} \label{$imp}C,� \ref{primes}\ implies that\ $\operatorname*{MFS}% �f_{n,p �) �\Omega">�0$\ and hence >]TS}8Heft\vert p\mathbb{Z i\rangl�%5 ! zv.)!5 14proof} Let $f= �$�$\ell[(delta}$. \ )hR$\ be a restriction of $f$%6 re!- s $2D$$\ variablA|sufficiently large $n$ since $p=6>2^{n^{��9�%@T!�fo!�:��1�f Ӟ,by Corollary�razcor2����ͧ Us!�A. ideaeOTh�� 7ecclb��@x},\ one can showŚ underA sa�~1!M.���0_{\varepsilon�2���:bTS6a b%H��^u n5�}$Eall $�<1$---inɗ words2� Sh��tates  !M not ����ximated�Hpolynomial-size tre��H Originally, I had Pd}p)�"� (without any6an )�e s�S$a�formeda�T sultA$�  was far a4 general�$n I neededh indeed /lsifi �(Carl Pomeraa/H(personal communica $). \subseW{Tree S! ��Persist� ��Ent� ment\� 8PERSIST}} In t� K I pursur deeperI�8d�ofA�%s %}7 �� �ngs $%>� !-4 S A�  =i$,*n}=�� %qNlh j�( 2@g2-1! \��n%1align*AT5q�0>� & ]M� 8-�(Q } [c]{c�6X/2!Q00:QN&0>� .� � M1�M1:�ZM��1��.�1J�\ Ni01�7.7�MJ�R��MN�NM��F�M~U�,FLA�>�����>�Z���������.�F�+F�iŒA�7���7�MN���B�R����"t�W�Aa >�y<\leq162O*��6�M)�fO� sol&s recurr�<$E \[Fz&T �z��( .'�Fv obser| ha�Q !�!f�! �6�2��C}�@� � �&�->\ !d }^{0B>%>�%J1�J1BJ�%DI�}\�{ManifesLOrthog|"�� MOTS�} ; stud]"e mGoG&= of coset 28s:\footnote{All ul*pw� ly w��&ubgroups of S|�ECC};� �er�}=is jus= r conveniA�.}(� � m7AMI?CI Q$&� l J*� .�  Ci� x2Q$QC= M { x~|~AxE b 1} � is a)_k $�bc# %( �:3 I�sK&�� } cha$riz�!p> E�acb �� /ich en?#me!� prov it{expo�i�.� on it,�coPI��6KFordinaryY��E�B� also���epa  between.��z ;%� algorithm�&L�j%j# ose Slexai!B9i�=h!Sh \ My!��e is L*�6eisW ly tailorm4o take advanta�"f� �ityrH���� find\��!� , ite�featur�I\ hop�m�i�.��esEE='U&�"�Fir�it1�e2L)4second, it doe� t obviousR n�alize\B�\!���of!qborovE7Rud�%$�RaG!%|s2} ��al!�$��>�[ do�\a� holdA� ��. �����F$,Gc��y(]y�B" ^rBm& "�minimum��a hrepre���*U BT�in�$�add�/a5�a BJ�� �5,�2l��6"a�ith��g� joinOpportJh---!g i�either*?\l v1}|6~ =�.-%�N-�O�y2@ @��6b ō(A�2.T-;�( f $T5�&Z leafOee�W"#as\'"� loss!�.!� ! �$+br�t�s�)ertex�\"�'R chil_!A`a L >�$) U(viP( ersa�eAlso, g�a  $S|!teq)�{N�'>�S-;@j�*�6�S�� :�\] R�N�!�el� f $SR let $M�( ) :=>m&Z� � � �)- �+.- :R+ T�L in>- S$, A�s�*$A('"P ^{k�' !�$bN&�*.\h,�[ �$!'!�1�* � �Z&�( I,J��,n ivi���A�Jp$ (A�Z  $I �*J$�l nonempty)A��clear��+' �)��*� s $C_{I}^� ( C �.�:"H�\iP $I$&� ���* j\ kJrk l.#VlJ$\A,&�eQ`C=% %TCIMACRO{\dbigcup \lA# s_{h!�K[ _ ] }}% %B�/ Expa� < {\displaystyle\ I�H %EndE:=h9=�_ C_2�"� N&!:.�$$'s�'fH $re�+up orde}E�Fu*�)�%"ifI��Sn�b& _%d Z� �4��4�a2Z� g�:If4�.:=#3\m%$ unchanged�we4� ver $hR!��a `reaso'L.resG'/j In $h$ n M$io'0� H�0ou�ts�h!w�%egy�be analy5�NP%A�)A  �- � �S&�to ca@ �N�,�z�k,�;!�2� rs.c3 p�'2!E �$�A:C��!�iG�w�#�pay�2� $ c!��a8-� lemma say!�at,�( 6c�!m &e,&dsJ� as gaN%F�\"*off'�ets&;��a�3 induclem}!�n � $C$,��x5���t��)�  }=\m 0(>@-�>@  @m�F%�Y a�0�D *� C� ���By� u�(A�ne,!�bas� -/n=1$\h[ , so!W� Ad] tru�Q3�/Cho�"$S^{\astXbs_  C$A��%5P +�` ) /.(IE�)�S4T�j� b.�:R�$A.�� �� v��roo% A�i�� H6� e^ex,�(�����3+�% �|$\ 2J �  $R� ��vchi^9nR)I6� )^� >�Q�R�1� @%&|!�R@ )�( &r �1!cE2� �EN$S 2f4 \{ 06�3 �� I) �6S�պL$ L,�nKV~H�� M2�I�I� M 6,�K�.,>�:{%�y(.~2- p#nf7i.�D ) +  Fb ) ,V��l=5�pAs"U+z7 V : ) < q�9C� J��t�50+0not a �BaZA�I�)":�)�u0� [B-2�B42 e}% � ���� 2�F� kv�E�� �;6�B�J.�)� 3 c>�. �HA��JV } |:N� E��F:H/ �� �1!�JY�� %9�& re mj5� &j Z-^� �<��QdG e7�q��( .� $B� �� x\notin Cj ould� ssiga/ nonzero aC=tud,B7+�,� hyp�!sisV� %��L.3 � )�r� fH H U ) ,~>. �[ ' B�Q� Oa�r-0>K%� fK�8]�.���>D �.��5J� Y20^� �) ivel� D�<�> beta��0 �%� �<� >� /�M�=q��8:c( S:cII.Mc���a��2se1mo % :=E��2:+.,)Z>�=.izvr urZ�! � �$,"�!b�6��6a6A1aB�,I6<6\2<!: \ siA+ane�,�s cho��$E'12)�$:A-�re:it?thW3harmonicen.B] U} ]B}�H6�6FY}���>A!6Si&� zW��Y,%6U�EbZ��^j�M=xiI�2� �EZ5�?!�,OA%. vale�,��E�*� G6^ G ]ql&�A�"�n\ �t�7!��� sumU f�-�-Z��t$^x\+vm����&�A�So�U:=�?ic2E1.6D6>@ 'Bon�.(=I�; now%�CcursiveF�� �{ �!��:b��02"i mots�}If $n}>�� JN.�CI%I\^'A�q�)&T ���v }��� z��S t>-�2� z iU6�.� (em&�F��up�;b�A��;�us� e *�!AX=� &<.^!�>� 1�� AE�5�5��1)����L�itop5>,�LT��&1sf7"�)T( & �J���a�f O >�2sub%"�t $�p0��ven;�EJ.�0 z5b!�����@6�*\Ry W) //um/N.�+ =H Y �ɽN[B1>cj� \"�/=6 B� 5f�B1f�B+ \�wNowA�d � min_{i�( 6H!�( F�6��J* z)s�;MV5Hx" a&�6q RRbq��*D 6�f��& 6\%g�j"qQu�2�Nj m� =. B+ �)� �h�ex�{ =-�T$�&�eт Q]i6 ��� $L��2` �: E� Z&� %��M� q &�3[ A� �c2��.& �!J ^�2M�>82 TZ p%&��6��l) ��9~!C�s"G>�Q���LA�< L��H"d<�cz_2 &k �� �.k^s A;;N�\*ne�_'� 9F� 5�.k)�:�=V:�9A� Fz*j z�A2z.AFy68% Comb�MtzB 0=P eF�ZK�� >���\+.�B FD:�ob)<�:a 2� in"�!?�6} ����D.�.(!�6��qRZF�.e6 d2)5=@6 Fs!�e�b2�%��� m�eW $M� #}�;&.QV��**��:�.�#$@� B�\p?mL n��H90AK u .����� �J=!2�(2"1=� =H&� IR�͘m �%��M�QX(���2�]�.NE�) 5�T> �?can��\�1&�Q�Il9 ?�)%�aaO$A$ ahA O��_5�A�ٻ-) =:�4Z�(1O* �/P��(\ (� vect�Bb�*irreleB/� $ long as $&�( !�5M1"�'"���3$}9�� )� "O:�2QA=� +z*�� ) -f+ ���f� 9�p.+A2A-�  \tag{*}�4ma�%�9 &�e�uTD@�N � ( �I}% ,6�� !�columnE�$A� Hpu�L �:<$�1Y >;3EQ�A2�� "� �Sn-1 �B^&$1$� �B�F�CcW$C&ay�O0hj&> %�3s�H=7 ^{3}�A=;.6,��2ute.�f�2�;0A`M��en�E�.�*�0I��2o on,q3y�A��ula (s7md)\�1�H:�F s�Bt=1c-S+8nom{n}{t}t2^{t}�9 :I"i��&AnE� easLF sequ�of!7�2>1�E��languagq { A:J�� sI��-~&�c7sf{NPZ7 do m!k�whe5%�4m�28-w4te�Nsu�m4is. A�Hn���bove, myF��4s6p�Wtoc*�5 *ksb'!jc�1:4�+"��nexplb}S�2se[�V�l�zC/�drawn\,Ac8n6Fd +��"JF8� $k"� 4�\_{2}n,V  {GE}\+P n\ln*�]��a^.V)�$� ( n/k^"�]�;O.]k6�"eHpr&aK$..*�$�r�$I�5P:��usP-I %].dE��52v*A� bad Z7N#4\ occurA�n�A�%��>e f�6C+3nt 8o���9ai�4n�Q-+!�A ?*_� 2�at�K�s-k}n="_&�1�[72� �abٗ $�1d�b��xI�pd 12k���(�!� $2k/3����^�$^��+we claim%1�����E%i N�LfXO�)t2% A�&v2d}.��Y3 ��z�Y�U���r ]Q'q�� d}{r T""%2^{r}�Hk*KY^{d-rxT� is, imagi�X�'�tI#$ 9onE � \!Bd2�`!��: �a���e$I[ $r)%�$�4"k]d-r�*��E� are 6Kly �w�)pre�9� N �P �e=��>8�F�]O-\r}/2^{k�NEE?!3�� *+un�A�!/So( B�it{any}�/� sV >  �R-P��db�d} �&Ao�Ad}dAL��_S�Ir=e� d=a��?t �*!�2�expk��12k�- n+�*{2k}{3}#�42��-  12k�A 0� E D)F�&S�0us! e faQN�k���� �RA�.atiN�� ��|� �� ^�({W��  C �eKaH*�� M�s UAcE �a�ex�A�6" A���v ��.}=��R��,f ��� ,.� � %!Fh � 4J�&7�2�6�.=:!�$/�2�f�.��� ��9�b!3�]�� in $f�ufj)� '' (s�mA����*$��=n$I<ike)^]�DI=�&<B�)sA�A9(n optimal p"�6�Z����I�&�ME6Z�~�B�E�z�V5N�:�.�E.�CContinu+� way until�B9 t5iEt] ache%F,6$y�: D ��c� �\� b*6z� ��Nq�( Z{2N�s& t*kQ�T�"K �b ��]�ff>�6<F�|�ZBj� T E�2���� .�� =Ah%Cg�$�_2�@bal{`d cut��> ix$I%��I:�e5-) )*^A�(.�f5 K��AY�\an 2�!& un~����]&zf 9��!^�� �+zQ9^0Q�$b�(^{k/3}= .�a�6, � D-�HQ !a freebiV!En C~ �OiO>&B� �b��r�8nu � k$ ��8�f��BK ,� z+��\ed) 1:2h qa�< 1 kCp��fa�{�A�reZ"a . e] cuts,~f�b 2�6�F��� :3-�% |k5|.�� ^�a銃 �R� �-���E6L!Q�if%U goalC[to"� 2R����n� �cl"B b4I"c>i�]�]orm2 s?i� 6�s4j�\I�6� � ����\ Ip GqanU %.C!$~ B[*A|) � .�sH>��4 �e� ��^{B�  n�B}!��' /12kRIis5�%\L.$B=�Q��{4UV$, "�HcR=���� }iN�j�>j\&O� �"� f�Qhi}h�9N�Il~Me.,3n1,�."]*K�o�sep.��J�ojly�ed.�@|apf~Y��Nn Thu~�m sf{O�Q}\neqM ,!S�:H8k=YA.na@nd� R�M ��O ��l&�:�p�l�%B/!:��|M���tO.�aX�Ga�� v� *9 *� \ O�e��0^ we view2CiCP !p <Fourik asis1 a��$ a Hadamare�Kwb)���r"Ol�L���k%16�5 f'mB 9 dq=&�Oe esFr�n^{17�So.#P&�]�in�Dant},{ (i)F��T��b�$:7)E leq2 |QQTs��I(m%'F��Mof> f�0\96X^s�.2�y ��?s XT ite�Deb� sf{\SigmaXo��Vf�( � &�UC�i W{g�> Sҍ�TREEBQP�US�&�l�uGU�_cR0to bein BO�o�tcA�(�B���.I!A� exceeds�+98�g)�JHum��0od |k��8labor�xy.) \ D�Q��j�%enYb� effJrosAn�7;#�d6Rp leN91{!X!FP]claqN�s accep!@Mc�2chine, 1R>O=BPP}6eA�i~"e �<�%JRWp�k5a�!Sure/�p�ToG� o�Cv5dmA�nyIin!�at�u���9��! Church-T'm�)��i like^mPV�a| goA&.:�D �a�lg)4�ble�o���Yircuits!�-BK!�mOus 5f%^\�le$closel�qpA��ro"of��nY7(%�j)*�Ut&1glearn}N�ee' In l%"o�S's.5) "�"mivV2�+ma �>c, 8Linial, Mansour TNisan DTlmnM- lnr1 )� be l�JQU thUok � ZI xe$ a weaker �y�I7��}8c;!mi� .^!�3� ;P}}\caJ|�&Pi}�d^{!��r�vel-I.Pfhierarch�;SiaY#QE:i�U�!n!�li�YJPH k�'ul�$J@�#nI�ak evid�"� @-� s�=J2we �Uye�Vv��acle Z���3-+S\N2AM � oughA/8 lack tr�PI $aar:rfs}.)"W �{�",&ulabqp}5C �a�� hn�o��;�&`%1j!�Hi|raU!O�~�Ky]%step $t$�$ m C'�o.uyU^"� FzL2� s *O#�j�1�.!�Mor`'rm5mɿini�Z�+i��&�6�y t ��� � %  "MsV( �� D�) U<.Q>�g$ (�a�nput ~X|p.Y� $p$)�p&1T�0.�6�? �U&(GJ&�%g$g9�*�46 J5� Each2P]" �exC sele q�f!��oi�dal< of�t`\ �(aJ ll be �l0  nice.� I�{@ofGw=0not m��),�> �Z�sA�W�wpOa� as@sur�Ui*� evol,>(e{("^& pure *s,&usuC"�$ir�Za��;a mix� ���qui��:!4 .�v��_e��h�$  rIf�+l�~s"\"+ �b ]IGm�had�u6�{1�.\.�zN� 6bu �) >J]Ct!�! outc�VG)`.*�~hosen adE�ri��;�w� is �X�)� Born0Tri�Y The .b�5return#v\I7Y-y9� $2/3!���~�^�Q �U� :Fo1Ea�� .� S!�z=o `": I� o6�V�#]to devx-�+.$!Ba�0�`�_�.  u�`ZUH� bcode�_*f$)&F$E� al�2�=�&�L5(-�un��Rn\rto E ���C .\f�cIf�^t�oD a��� � � stan?yway�5k producj"�.c�{I*�\!�"� D� uta� reg�|Pv")X  !D�^OnIDno \1e�oyR � .}Q rul��6>�W � .� Copenhag 8nterpre �V�{I�_2(*��n���� beaD�n �w �)�  af�u �s:h�happep w�!�%�k0� In!lqif (!X$0$.Yl <��>6log"j2`5� e�So2�6�� F� � \"� 9b&� J�|:W �/�=��H�r�8JI}�a ��Vf��� I�� 6�bg $%��d��jD.$ �*byA K3a!�)M2� �8`$ $k&"31 _a�)",4M+a*� -EM+V�T�2�j� .� $B� "�`A$n�?R���Fu*J^!��yK ion ��.+ .> ac�/�hVZyF��y �j� varphG=�i�\E$s satisfie��,{0��ono3`v"m��/"OwN}\� k42.Fw% �y Qzpsu� j���yn�>�USfyEF�  %VJ y, runa( cop��� 2� 7 enso��S?�kut�A3majbky<A]By*a +�g2/�inc�_Ej�ja��-Âf�\�k+1Z6�Z�N*�p� Boolean�ۏM�� �aNU!'a� $k^{�!�og6�e1��$ $T_{k}^{hM� �x"֐ ,x.�N;lr f �x�I ,geq h "a ;�`!ru:t =1-\ _{i=0� 1-T_�$\lfloor k/�*\r }^*�Hx�iѤx6; F;�f ceil.e�-i-? :X.. �+5]��x�q�,.0soB�:.��9A6�2h\max�I%> :=�f�� +UG�w�@d~>^ �c$ttR�%��( �k/�7A��Substitt�$kY+�7�}�2i��v�A��J�a�mea"9&� �s� �'.u�.�� 5]T� 2 $,�rE%a*$r�t�.��!za "�� � �37��A  whenW���QQ�bi: �'%�Tb "Yv1$CQ i SX�>L� sf"� � x �.�`8�isDP�>� �Z�Q inphF�B` n_>l% �n �^� )S5�� �s{d� �=k�os�6>oy  B>J�PN��Ov�)� w�co�Ge*\ ��/ng� #�d�AJver�h(6�n� F�E&��'C� "�8-geʎ��� �il�5M ( m&Q ����& *t�.����4.8 bt.FIA��P adop�A�ve�=%�o�m�U6geV�CLf���caD^ nY)$1%�T�s1!~6�across� `.�b� hes'�t�1AKu�q W%��L _{M,xS� R55�O)@C >A-�. >�SP v 1��un! 5sd.�m9.�-�? $M08Q $xJE>:�>�*M � � =�@y�!#�00,M�7'^{J�,}}\alpha_{y,!`�w?W2 a1 )Ly  w�A2pe\Lambda1( M,x /I��7I�>0V�9� � Y. �$1���qNNgry���,� 2# s if�+W_{x}-tM\,:\,2� .��m_b� R�-1 �)x1�1)��q-�jS A�+�L?L2d:� while�re�� $�� �! Ocq�Ce >� ~�9� 1�6Q- $ "�"ly�u{a� .[6a�we j���\ŀ���P� pr�KM��g�-geq�*i"�IwTdoV�via j� �8|AMAb�i^��gs}�z�9 eby ��F>�L �Uof+)negat�%�J_i"}>�, ."5 1��=ofuQ �� J!�)n�&�s^�$($\forall\�qs$)9�,V��"� $en� �9����k� tupl�`cand� solu� s'*{vZE?��)�q� toge!ai2�$^_ ol#�a������ A2I&2��E��+�&^V9�gK-I��| �� \� } | =�_��H%�ext���BF�soZBF guesYU�#��$y$`��B6,� s�V!q29���NRe" d�y>�ngL!psBA�O|R���r�A��t] ���<�bSe�{�U �iu"�!b($\widehat{y Vo�~ "I � ing&p.� �1)]=�2�>�a fix}reX!9}m�|�:1�7$|B3$&�2�E&!��^HJ�P|�^m�H( aizK��a�2`G.IA 2�of��ci�@�3)]� "+$.�/U�Be}�l�<�s��ll�$Ce��P%O�t� 6A$0b��")A�>-W2�S &�ty�: \@!le 5 #�\cdot �A%� 'J�t"�1�Qe)�� \ | �-41 9���a�iVk!��f(�5�.a�&��s a�%o�U.���e R&.�'� ble � $� � Y&S�ly��a2+#� $i^{t� �8V�2�.�=J#2-F�>v# }�g� �9]3$\q�$*j.F, � � _.�>�\%�!:=�P",R.��W���oof�N4K'�%5��fac㔥�s"2� *o��� �F4 AmpP}nF�g��rI�.v�(&�(^QA�&>--� %zQn�RSo!�),�j � �-" B�,xog�h�O /�#�1�at -9.� \ 32%u�t�o #% 6���>~J.�sc0���.{H Expe ��� Situ"#3EXPER3*2]"�hap12 sugg�:+Dxv�Olleng$, c ers:"�0p�0�n-.v�he�2�� For �# u Zmee �$�� "�9�um me�zics5 failZae B� *�Ze5R# A  e�4.\ aoW@d twenty years ag�=I�&y wish!� ��� skept�E��gnew c"E SF�2� �er�l&!�5ya�}!) ;�R�U9�-U� o di�/� ques� a}�QF�is&+kG �P��'e m Ks [�bm@s b���2P�(In my view,�0s �aid!-g)a!��+ways:~ help!b2 �Ti >��#�c.��a�� /IE�G�. "��mya)�hQ�raie s\i�E5EsAE>:&*�&i9�mean}�q4aF}6�5 How i we�1��suc@6ed%A�n:x0already been id (��d)BA&pu��A�|�Q!�+؛ut!�t@1�#b5. � Hall�en di"��9�s�g�6�*Msa�A��E+!�$asymptotic)�'A �^-  �a�ific 8 a� _{ n��ten���"H(!��)A�E8���%is .ibu�nstea�skAsqL$n�"�/th� ize � .,-.� ��:8ask`200 bd*B0!Nbl�-(say)C 80J[�EvTN ough��U�"�/ log6�m�� anyt�)���fKSa�i�uALC2]ie ����r 7C Aanywa�4A�7tedly, �4!]%�J�� (J�jX� &� �=9Sell�� little �B�DTSf�1F� pJ�FJ#u.� 2jM, �L�.A in R��paper��j�%�$�"���3 :� m.�isE�0�+0^{-6!1(�%i1can��l�� imq�L�?*�82F�baKa~4 �.im��l�!: �,�3e��A�In���?m?�7�R2 : U�A�FB*��lVɋ . Aq?o�5E�mŜ�sm?2Sl� 2o2\Ain redaP�Ia-^2�ջ\es� al ny� �D�.*V3al�=EK ]S\ G��f  $\rho� A:uldi{i2��#>�pur��� �� >or"�C�Auf4�b� $nd"mi2�wB?&v!BA?&Y�,�bsum� x Y"F^TNjj\ "u_de�eo�<onxrho�i"/6�pDiօ9�A�"� % #�7�AA�rd6���al"� %��0B�/ soup2 �a free-wa����f���'boson�*}0c�s&Υ��spop<to �A�How�D� "�_I6c �D�sd> ��`�����:canno�!AnI]mp���a-'ic#�-��modum d� y $@0 quite differ=Z37�4m�"� n�red�o� t �F;��e?�)� �F� �6l��it{do}?/�� l5v9Z BE;ifRin���sto �p0R�;1sb+�2 forc�)���i�(>�&I�Q��nd� "1M�m��ne�8��q 2 *Vp�Vf�!oI� ��@gai�L<6sA %ful!�� Es��.J��0do� .BM�� *A�9��� A�Of cours,ci�e�a�:� >��)�.no"�� Ui'@��ni�o@ssu2�'&Gis2 id} (and�La�fBj1A5E�asd ed)� !val�dA� a =E�2�R�+ �& !w= Bor�!��!U@=p.8:V&:<�Gm�eNs"KA!.�$�X&�p $U^{-1�-�N�,j�:�"�����&� � "M�io�b)���oy�2���v� NLin"� qAnd/Cb# ow NH%�bIErbitr�;!�,A����DaU�7A|ny}*=a�e*ha^)o��k�66 :J�4�Zf��4 oftea�en urgIba�s�5[��]�!�;6N�T�:�ҁSaݩom .{6I�abf(�G%n Ptol��c ��!h|is��#�M]���,  ccuq@c�����VQ�`��)R\w&���%:E1EnǨ%� altern�Auc�8disj9 i����[g \���ex�e,a�a-�Axs2ۜ% Tr����|���k1}"l5"�#*7}`=�~ғ��G�w� � CNOT�� :Nn$��B2�:!�v^{T}:$%,Ok $v[� a_R"nc/Bas�M!led� f r�� !c�dic6x��2�R�\y)�C2�:�:��1:�M 9"�� mixtH?�=>Sj .!>VAHn��?� O�+i�-�y&!,ɵn6�n$ %a.d�}5��2�,E�o�E�A�Q�d����S�#In2�am�a���� .}U����t �iu�Dme:"qm|Ct�F���I � �  �/��k ��e���rk�y�DI��76ݭ.�my�M,%%X%ort�J crib���g��ely ��Tڼ}L?� {"�is!��o��OE$necessary}Et|�GER%&indBo �Z " � ~Rvr�Yh�I.ag*� >u! *z��I��JaN�d� to m#?4Anthony Legget� ristMF�E��@ densed-C ��šg� �$]&r�ing s��Q "� AAA*��!z!�magnetalt LiHo$_{x}$Y$_{1-x}$F$_{4}$$��Ghosh:`grac},� , 5K_6^�'��,*����9a�I��9 pins�q�A��%#A neaM -nϰ( Hamiltonia�d�m�� ca  �pt�altmis 3-D *  2-D,tetraf�cubic�չrregu,�� �bo��= $2� �. \ AaieA�iDa�s� CK7]#WE- L ٱ��eْ!E�.(�!��, �g�bU�oZ/Yq�f֕m(�A!n sa� (1)c ��$a�p���e\"�AB�.�@2+R�@I�n � ůxplicif9o ���a itud�t�%��I!���T�AG2!��Et%�*q��"!�ȥoud4�t!wa.� �Z)"�і�b����� t*`2e&R' method.} !�$�A�2 A (2)��q;ev�Ki��Fat��is aY�qW#b0�t���� cal!wtFnlk�per�?a��� s�� sus�Pi�a� .��8=H� {X� acc*2�1i0�r�t��!m\�f Jf!��XincluM 6Ya6A+ be�f�Ad&U�FA� �!^"@isZvn [�cry� �y&��R%�!_on��"�j��� 2�n pul��JI t*ny9a v3� cata�9!�e=�to�s3E8 .� aS�!t����to��e����U�%e���W� Y��Q:�a;",a��summar�Ld��%_m�1sc� �ort b� c:8t2���k�%� ,� � lyU���Ts;$ lso&�! new moti'E�� �-fo��X orkA% They?%'�e� in�n�i2u �� ugoa�G�d:-GA&A��w! �assoc?H�-��2�� 2-D :�a�rv����)��Qv ���E�wayC,1-D�!�2Ib�� MIYe 1 ��!�!iRM��!ayp��a�se�H�rA��3ep� st�(towards demP� B��o� ���!vE: benchma1�us, Kn�M6 #k(S�d�g*��A} �lM��!��$e `pseudo-�')� =$��*F� l�d.�bi�*-.P� ) I�Z$I>� ��*&�%�._�\|A�5�$raunstein 6*bcjlp}�� Y/\ )!�>�)��`&_T�$14~� )0s�� be��7&�'��s� - �Y%rQ&� !� e, *of�#ie�pahab ;�h". �E.� �K  2�&-�B�O(liquid NMR �ology�C :�1 a kev;&!Kto�G�9�4&#0of e� col���$5K!)>�F�&�4��l�0\E��I�I� 100162��0 n>106> \\>A:`�o 1016` -i�eo001z>J.A1a6�.0a2>>n011:��.`1a2`61>?:>B`.�!�6]�v arrac|%� �� �$\� &FE� %t(B�" DQ8  ) =4H,fFuA�2_��>�6�:�2>���HJ�z�>\1P)�v�6 ;-G&$j�>�P >4�Y}:�6� �ia:�Kr56:O6l�R56-.�>�In5:P t� 1>R)�)j3��y7I� �V>DR�%.=n u aCw  :r *1 e�7M "J � h:8� � Y+"�  �O� 6� �od�$In my opin� �� � �w` p a funda��!�+� � own e3�WZE "�ܶd1 p'perhapf._dd�+ �r�� �O��m���st7�s&��.� I am advo/$7�o�� ;s�?a�- "�!�op���Q� � e �!*&u!AB*�onR�V�6  suCofmai�%sŷ�63�"t c� vagu%�.�! haO�S�s�1,BASICMLIN}, �REL a���1�@D pQ$��/).N�d, z�g, Vidal'�$chi�B)W �)m5b \ Read diss+LdE�"��`iEse<� ��!� newu%(I� �]��&2IK Q;w���� AM���� �pe�tA�$�"�# �mo$BW noR"�1Co��%� Open9L�(�1 OPEN%�} A cru�)�]��E�� �� t %u�� )& "o�,!��b8il&��:<a�Q�"����V"  $�r c s�m/�WU adv��(N7*60,1pith!�1�I��06��� ve a��d,$�(�1 tool�� ��R�- are y�!U�1MEK clai�|�>arge-�DU e�*.!�prd� "�HN"���}!��>[>k&�!�F!% break d��+:{th� Z!=Fe?m���-u�gu�2�����} �{ s^!�/ b�[ey:�&��!�> �D��E@����!s�!Y@3��sh�Ib�m�rv0Y!���t4"+S/ � K�uccx�&թE4EDa ���2T�aD�Dtrq&a�&��"8G��2s#,!Pe!!debate I��z�i�.�3=ide1�"�!� m�fic!NBy���*���@!/��U ors,2I �#�(��ng��L'---�  d �h plau�K�� earc)�gr���<h8 �if�A�,�c�K barl��:�%�a��I�eN`!PIQor��KI'�b�hA�io@5ak\$p!�B���p�\��lN  N2o*�new2 �wQan, � &V9+: ɎwcF0g �=�A$gpd�ful,U.���E��G28E�en���x/6/� b��.�:&�?Ca�0t"�b+rov� eL�0m$&� .�? rY2)]X�aF�{( 0 ��s}���Vn �m.�3 :�0�0Rz��.,!�"v?�� b�(t-LEMoc�a�"2��of m�Zw� t $n|Zy�,o -���by �7(-and-conque�b$6�R> �� FB n^&WPB=��[is݇1e �1+DfMm��we)�a1F� .T�'e�� perm4_symmetry9�4)] I� mat�O�� lr��?�= uBj�n�Bi �Iu5 ua�te�U -sum&�i!� I�CQS��nxe������0��O${}$_"j��*Gs$% 6&+1}A衿Eqk$�6 �"�<3==1=B�`��!��_���=`o���0,�9Na 7Rd�|ly [e� � � m� 6�6!Zc�mp�n!S� ����s� . Jl�lBS=��7 �t%�a pv �l'a^�M��w �3(of, say, $1�7M.�S? aE�&C, �@ �JaingN9+�$@�^ \�{Q)y S�g of S�n al Region GGy ��g of G��r'sѝ &5@�J(A�%�& n `ua6� database'X%w�'EQ.m e�<���j�t�)FU\)C�p!��B:�/�dW�0i�ex���A� �!"��se�A�,H+O9Espeedup_5�\a�H�d��c�o 7i&����A����tn�A�A��. =!�ho!wfacto�l��)rsho^��#!v� � true? \J�*yp)<�r#�|��upa&bRzal )�--�� �Ao �;#u�� P+!Օ{���]be "�Sfol5b%@�J fashz!E�E�dbwo�@2)\�b yW Dw��9O�%�K�?�(2MF�)#! )!�a �i&�� �eon}!�(FY$cA�J5*�%e+�<�me�$I��� �al& tra$pV - gA��(i�-�օ�esar�&e�[dah�s �9�,by�(A��$i ac!��,E\!�E%�l�9is ��!x; l%^med �. spac�4e:Jni}�� *�4,cQ�gq*h< raph%K� Bbousso?W�5�>�l�l�e~�oin�6ai� 2�PHYS};%}now� say a�)i��qCs�o�ha `�  robot'(s a�)( w9)<l�w�5���S�e M3��)!ߐd��r akef2p$im[ �gch�%�Ek Mku �vh8�mm�i cri�Gly� �s͛layou�'D�,$�%z$n$��\n�1o�$l_vtAv�6�/k� the %?�� �6"�z � $n-1�*ep+� �a +� a{���b2$-.��squ+ grid (Fig}� fig})?%.x�tFRAME{ftbpFU}{243.0625pt}{113. 0\Qcb{A�����Wa %�).1��y%���� "> tem %D2D �<+�@%^V�.}}{\Qlb�}{ �}% %{\� al{ �!uage "Sl'Word"; Y,"GRAPHIC"; %-�E-��o TRUE; ,play "USEDEFAv.i_fbT"TAwidth 9; ; h -CHepth 0p ��- 9344.31!t; %B59.3758 crop�2 "0�top "1�C %bottom / temp�9c 'M.eps';-�t "XNPR";}}!\:q�� fE^} [ptb]�erzi�de��s[ �=-, �=97 ]% 1��{<cap�N[Y EwͺARaQ=]Z��� ~�$>�n}�\ $.�U�grieh�55 126{�&�S�'a R� USUM4 2 A,��B�/a3/treat�/L��i��� �,=` ' �S �ed %˅��\a7R�w�A{:�B�p"� -�� � a $d6� hypercube�6�z"'��<��-�ex� �' &$1��?og^{3/2}2JBw��$d=C_orJ:"�$ ,\geq3V%�mat�[�F��!] $2$ ��s,�.� 2)��>�BMIw\Bh6���r��he�)v� 1i�7 �19�"X nʚ� )"?.\%�M.c t"+is F�;�2e� idea-xed5k Ule5~\ThetaQ<��1/2-1/d5��86,\ \-J- �IRREG}{ڔ�=&to &�;�v% � `�'-@-'}�oW��S &�  >Mw� �ze�rr�� {n6�"�d)'!% Y��� b=H:��2log.�E>x�(noTd$ � ���teger�F� 14.1ضmar%>A^{H�t+}�ɛsum '}�tabP20} [c]{c|cc} &� �\\h�  \�cҙ;r|}{H��,�`��� } &B2 |l}{y�)a%�J�N?>.� C�) $}\\Bw>�k$q>.�sNsn�56:N?J��^�}{ky�iH}I^�Ar�>e,. ��z2.;�}F�b��Ytilde{)�&<(f�%�V%� U~"� * m������ ]{UpYJY�Ƅk86&a >h%=> a^%�5E symbo��B��Aea�6a{u� �L3, m�a}�ic�V��Nq��-�HB:K)��|�Aa�Ba �)&,%&�2"��a�s� � � 6� APPL�y,�$�nex�1 pp�,�a�$�`&x�,��! 1��yu����#�&�-"�di���fp�T�($O\left( \�sqrt{n}\right) $. \ This improves an $O\left( \ 14c^{\log^{\ast}.A�\ upper bound of H\o yer and de Wolf \cite{hoyerdewolf},\!Lmatches the $\Omega\:{ � $\ low.j Razborov _r 8:cc}. The rest�_LOCALGG%press A� difficult!s!�h, which also arises in workA$�,random walksM�aakv}\E&@cellular automata +@watrous:ca}, of w� � means.6�GENER É8 general facts iGAZM�includA�an>$�T \�S\delta}m� $\m@eE� nee!�!gear!ny)m)�diamea�$ J$,%a�of (us�!p(hybrid argu%�Dof Bennett et al.\-"bbbv})�e�.� is t�5� certain �s!�We a* lude!�2- OPENI aB some open�$blems. \s�^|{Related Work\label{PREVGG}} In�a�oon `S�)esI�aU?V>5�3�3\\mx��~��m��n^{5/6�@}J_= B�z8N��akr,ca#~�\_ lo2���9����% \endaI� \capU[DF�us2 s]{Time*pR� itema�j�,� � F��U6 �QmT� origi�28�tof� F5nd~�dxCyNz �z���zLzp.!|�div�-� le} Curr��!m4drawback�6� pprou � 4 all analyses @ 0relied heavilK  symmetr%��yE R��fC Dminor `defects' ar�_troducedis8,longer knownạ�u�-�`�running �eBy rast)� �i%{*F9���el�ary�� not depea,n eigenvalueu�W� � ef� � �!eYGUs< "Q;su�� ,ly good expa� ��. rTrgu/ � h>{1�ha e advan@of�!�_ auxili�qub�t0UFI [!�Hj ,L�m� J\ n ��o we i> ,�e=>ix preA �O e m�TcI� �u&u� p it{one} ���<PcE6 Data� smk{}� oret�co.Q ce�ly deal-�! lz s�,resource (suc�m� memory)�rea�to�inq \ W!�e)a� ways%�eci�m�xjI�W,&Gcon4$ints may c�into pla� at wer���gligible at `sub-asymptotic'\ scales.\ \ We b�0ve{Z0�o�toe�%thA�� suchT �i�� ccou&{m� n� �For if%� �xgnored� !%�A��eyI)2�n@ �� $ practice,ET+�� � �"� e:� use 9@���Lfirst!�ce, ra�b�n!� trictatt�o�� instI �a�� ccurY� ? A=aJ&b !�e��usIU&I holo��4ic principle} � bousso},\\r�4from black-holL(ermodynamic�IT� M`���.�b :of�Ks� ���-x��%�it{surf�rea} (��vS e),A�a!ke\� bit �Planck��a�I� $1.4 10^{69}$\2s� squAj, . \ Intuit�if_�<dA� buil� spher�Z hardik* masm8nsity $\upsilonhWo� keep�>i�A��:aas so�Ae radiu�ach�,he Schwarzsc��6of $r=\� 3/)8\pi �" }$ (in12Xunits, $c=G=\hbar=k=1$)��� collapse!b aI3 A3m�hA�tsQs ;.irr�� . Actua���sitA�wore��at:�aU#planar}�of��ant2� ~r� �E�)n bec�2�large,%f2�1/Ba.(W�� h��u)9TisA@c-shapedAA linear�1�.ED y�&�it����.) \ It`$� ough!� at aX disk'�!��1� n ��%�exc�!�A��For eU.'��s��proporz alA:!�)jA�N�t horiz/�%e} py�JD�1e�}M6 [ (%rI�e .X)�Admittede�n!�nt!�Z!Z }� Q�l make2� � &�ica�=py"� �@ a weakly-gravita�7sysX %��� 9�!� 6 R��!X!�-energyx�`�}, B��b }\ �{bn encloWbo � adiI*!-l $r$�%+e\ $n=6%r^���$��,)tE�� ���ws  a]�.�&�\ v SCATTEREDU��  a I �-T��!) �� a `�e%�� ax�� *�r�4�=�)6��p=� mpb[ oveIe�~v!&D��$r � a :3a�oug![ falls!�rKa( desic ^�@ 6#\g!�al,�$n=r^{c})��rW v Šrr��aM-D2:us A+(wam $c\leq3$��bixU �. ]f), we %�� �TheoremIsc� thm}� & )�� �F/),`$1$' growD,$n^{1/c+1/6}�1+c/6�/o�)aUlogar�!ic�ors�KIn &� 1'B2Y$atu#.� H�� Ek2�2/3}$�) r^{4 a&To ��I��a�:�!��!�!n4iE=iS be :o��� d-1�9�A �$$d>�His L�?aE�1� 1-s {A�Giv�^,ur two funda��al;E��E�}Q"��� a 5#e���%$x��"-�O.�%�it{not} 85!(i)�" �wb�A�&� �e*� acce2eyInNca{"fR� , wai!��9!��� �e��s Hawk��": ---a� �$ e��sugge�!xt���sv}% ---�!r>� ��3}$"� is m�too�.� (ii)E RY �[subje�'�1v$Bekenstein)�} �bd� str� op� !�I�.gE. Yet-�Gof�ic&�rQO$ntl!hus-$r$ � �)���(�5$oqI \min \{ n,r��i�} �L!�!�? I�R �do54any } be a�brute�"cy� � (G !~"��$�ut by�'�&M"6�&)�N�%.. 2 �w� . F�*�&|!�view, s�al"s m�ly): (1)1" �Fqlex��measu� aal�#; (2)N��."_di�)on;�h (3[ g��e ��b� wee@im ' ing, cosm�=InE� D* releV��Let& ad�*!�s!��!� Q&. �O"��)Pto��(a `͙ d�'!J� A�rT+sE�!'u�V�s (ifzalka}x �#�"�*m�rg}q So��'O-ias�T&� the �aAq�,parallel}? \��nA�becs"� Gho*6M�%�is<A�]-bx em�!E�-, sz$��! #&.$%� unne��ar�M� pons�a^t��eC$be%^`p�(ve'Rhcap �+����o .Ko`M ve'\5\"J"�*"�" wish!1pl��� superposi� � "� A� �&p"se M.ly� ��ion�4Forj* article (�H ��ny 0)�.A-%aZ/determ�*e�,EM merea�:&���st5/"spin) QMat} "� �We le�#�"�!pro�+,� �d!Mi+�D= is vali� `. ific"�iFer � itectures�s vrap��wS�#Uw�vok"�� ,�2�we%�9^i�*A�ef#E�.�iDe� "��)��'nounced �..=!0Again�,v!4s� %�in�d4s\ far��S./ � U %A-2�!sbyb most�,N � �r.xn�*��How�2��!7�%�!4J� :vac2��a�iM�-��;iWve Bw $$\Lambda>0�total:E & a�!�ex>* !at)$3\pi� ^ \ln2&=� ly $z122}$��c�^aէ�perlmuF}\� � $.� $lso, Lloyd 7l 63EN�* u�up �' now}.�AEc!���Pwb s eld sZ.r%�v ( ! 61&� ^{2}=!! % $.��'� , unlikeM#'s,����." $ beu Q.����co�d� betwe e� � �flectAse6�finY>�,rydenx we l�*E�tr& ��l era��eV th5���C�� dust2� % \aUtributCgn�aG)A�!�~4's netVba!�e (m _{M�}\a| x0.7$"i_{:�}+3$�In �+a�s�ɏbp!z r8)\ do�{d22� �)t,eIn �1r ]q $\�K J�GQ; �"bgh O%Pit{Why}!�k.1��.� eraXun�.}\.*��1ya?"  e,�A(of it reced��$oo quickly���~ob�6r!�be�nes�a\� � �-n�7! �v �6�m s��iz��A�� 1[O8vanishe�l�i�f0�$/$y� 6��s � E�A�,�P�*? ��� A�2�� =0$,�� all}*�q�i�-6/ 8reM�f�onsuBut�hap?� �)9�Acep�<.� m/ 6� �I�ta�0#; �a3�to�&�}s in{e& scenario C�3\!+maximum*� ehj�8"�8dcrude �6&�SpeQ !', neg�� .�$�cA�%� �!ef!���#1�$��B�1/\� >�� 61}$�{5t�.���a ea*�4a�a c hadm�%Aon i en af7"f%�$\M���.���10)years����u �� ag�@�'---d  �0� �%"yon6.��2�uaux$* �;kE�@  4:.�E�E��wY��2y� ---�4Q *$�6 �"�61/1�>� S#J *� fracF-%�5�}:��/ N0�7)�=� any� E��ofRA�A sɑ*�8j-box}zU3y}�]---�;�-f�&J&< 6i�So�� orac� � a7(� �H-98E�e,5,���h68!Al=� !�[Do�so afocus*�%on�!�� cern:��E!�!L?�o e�*3a])?[3�input�&&/sA�T AsHurn�46(ll�a�a"C�Uwi�%be��i�*!m��4 g�%<"P* *�(�)!Ym6or> plics� ^�h�%b;'s goalAy6$Boolean fu-$f:" �0,1i�\} ^"�arrowV%$=�uG8��talA/A `��D'�-,nected undir �ph $G=s( V,E ��I} th�*a( s $V (D\{ v_{1},\ldots,v_��źu $X=x( ' x'"� B��� A0!N $f$;!�n &\ $x_{i,?< vail+ eyat�ex $v%!W=�eI��"s $G$EaH�9�.s���,cr soni�)z%m�� ��eUWa�us a�O!jor�r#ya�u�6/2�?= !�isenATn`Iu`2e?� -�i���@. At����� �'�4a�-�Tm% \[ \sum\alpha_{i,z}E\! %N,z\�d\ranglg{0] HR)v\in V$\�a-X , represe,8�fq<"  $z$� a!Ot��(�f� arbitrar�/�/)f\ ina9l�� figu�A�n�(evolves via!Pa�9ng �c� $T���\R�R$T$�� :%MU0EefaTm�) �e� O�"D VC\ca)� T2 T :v v."�C1�An.� $3tU$ m] i�a�0)PE7�&iB7�6o.'U^ oplu�'i;Qj��Ea}�0exclusive-OR' e�,bi� z�An�G e�$=,2�Qhn�eL�� $1-\vare�, \ ife���_{~�4\,:\,z_{OUT}=f.� ) �\�491.^� 91):? p92� \]� ll> Ebwi ���U�Fh(>u_2�<� {L�F�Cr�Biau QX�5.�i^ eas|decide��a_cha�@@a"� ��ll�O*@Gaͷ$G$:\eeYif m�J.����Eedg�Hf>��I�� � &x�wcX<k� �4� G subt�1Risa��I��-ree c->�D=l.�4- $U����� �U�s�p2s4��81h1v��se |/e$, �"�s apply�pAFt��� ��1 Jo�$"� Z-%�ity} (P(zero):�  if, ��5pait&$non-neighbKIi\&1}6 .F$G�4U$ ``sends no �I''\� 7�>v_=�aA��corA]o��!ie�,!$0E.��~9,�C:��4pos�[), say���)�C08�ough:�$ �E���I��N%,Pt Bb��|�#�%���mbIwi��J a���a s�%ee;a3!thirdQ�Gpe9U�! ���istQ u�H):M0,Hamiltonian)m��_obN � E�q a� lly-�� low�-.LepP, fixe!Y�5��M^ More�BmO, let $U� \��ai  i�N,z A`��A@�! ��| b�? \�� ,Xb >�\ row�$Ua�?�0ion} A@is}n��=0� he16$i\neq �� nd(�� �)'��M�anE:�G1�;.�j�mRAAW*2 ���� űts $PFn P_{q�j� wenumeS} \�*[(i)]�-%��!N� 9?(E1<1�-E� rbe��o d($ nct �j}$� and ���te�$j_ ll69�<P_>\��e�%�6]s�3�xex� wo adja�'��.C?.A��m�!�$U=e^{iH!��e�H�!tian $H$� &�<^  absol�F�9��$\pi$,9� $H��% R�u�!,�� �Q�!rER�I����"1 isQ�št$� lsou��-A��tthm- �`I�"7 �2&� ��Uwr�3n $.� %�Z} n}��%]>`H;�Tj%S:o�M��A�}�en��Le @'s���e,� �� U6EQ� E2�B2�!con-���i���a r�Evr!Pey�<oxi�SiI quivalent%If��^en� cP�#'6(in� /r*��0 �fcA#K#w us emphaG'��se �Is��1,\,�C:��4Solovay-Kitaev�+G2�H�ncY)�BA�$nB: n�Un2�I_.&d� a*�e�nom�a-nECA�re\ pA��9�Q� � "A(�� w�1��cI-�deed,Reavqu�S.�AUu8ny?� aUle�So!- B)�sxi N � e�%�G,a�:+W orq� 1M)F�Ql�ENdu� Y , *.�E�A-(m�iet(A � >*�2�E � trit5�U�A6 �%�i2JU�)nyi9"�%2�(�his c\W�P>F�!?� !�� R��C� f  to5G��.,AGen�TBO�G"�T } GS+a � ~� Z�2�f%m�.�  $QC( f\p ) �min� :�%�L0s aq- We"4)�rs&�Vo(� 0 at least $2/�QL��(Ya�A� /�d)�&4% two-�d,)� ed-error}a�- , de}3d $Q_6 ( 5$ else�M7�sisE`Si�W�L&e��*��l1 �>e�t $9~,G-� $�!�6 ���7e'2�-.�%z!l��9���0st�m�;�I6$Q^{ZdAC��5�L!H!6 �)�s:#)Q��.e �G+vel�,Cl�$y5Y .s� j�`5�: 9V�% do  �$�gll� �s�>"<q��. �b'X_{G�� dEXH�"\ $f$ �pnde 6 te} ��ZllE���"��be�M3� } ��i�}�:f,G$,~� J� Z: 2n-3;� 9 f.i� 26Y!+1m$ ey�&� j[geq>2�! �v� b ] EC�/2$L f�2n.|Z� 2d�(proof} \quaW )�.� �)] Sta.ng# (o���I tre,e���t�Wr�.Q1[n*�6-9iU(t��]nowa�r�We�root)=2�W| simu#( �Ye�$=�CXv^ f � out � m�B!1}"�E~ing��A�!�Q�at v1i� s�=�.��O^V!�T�"s"�i}$ w 2F!c���2%e�a�= uln`�-��)f/A We,)eX!'_!W( obus�>M;2em� $gge�2��,Qfollow!N�;geu�2F�����-f�:U�V�Re�1e�6*��J�\�5aH]y (�sn)2< \psi�*�6 )] R�v��fi�"n�8� z�t��M�i-JGat �2#$� =*$*�>0.zE�A1�m�X*� E� ,-sor�#�+�n1c�#6 4&�#:�).V_2Q]fE�V��ty-�#2�e:B�] J�\� h:.,N�P"J[BL.|&.B� 2\&- �5>����aNh�K_ -h}t6�aG��A�As�#�<lm]of�=�� :pa;�nl�%"toE�si6�VD�/AJute*�Eruv]H0Qwards)kqGn.fat1,���t�b�4lq��!NQ#R� -�:�:��M�s�%VaK-�""� bddpeFD; cedur��3}U�.U%��.�$O4u&�Qin|Oe,�#�R�Da "�!� 1},U� P $\A :����s�"� Ir� r1tity)"�)(nO. I. 2��!bG�2A&�ofN�Y"� ��$f=:Z*ORH �% 1}% -,�%5��I�if� a  �w=��w $i W�!� ��uQSV�UnF�% 2 FerZ9?a�L�� \ (T&�E�'��CEU omit flo�_nd ceil��sig ;ry c �,no{(eqm�"�Ps.)��2�3�dg*U[y\F��4\�-{�v$A�D�� 3p� U � s� , S2A�m�  Ha��<ifN�%�i�'S�!�T�Sw�5 mply�P��cQٔ\<� �; %�"�,` .oc+hA�\��.�'!` ?*:a* {6�?n%:.-,E��,�J�[�I� m^W!c7��P�M��.q�)�5:u�t�I"$#dZ & C �"L Sa��s� 2!8= =\��kab7��RH S9 ��I��^�El2�2 �!�ls` OJn>z1�5C:�isA�&�-��gi�.���F$6nden di�0J]R`��́ ~_"W�.�/�~� � � %End9We�E�hy>Pn BfPn�Sum weJ� B ll-`'E$X_{0h �g/}_iHqDmagnitude} $\Gamma�&�**�+� e pr&� of �=� obot. leg\ �h��iab�+�� z�=\sum_{[#.0L�\,} z aW \R_+�,( %1\e") J Cc+.�.��T����>3*k�H'��;&w=T A c�Sj$ � �Pt"2$0B � q=0}^{w-1 �j=1}^{M}N8T-q>r�qBK1=w2�H�t��(1 a!�)��$. 2_.�QW1Y^^��8 {w}% {M}= )9}{R�}@%�Ak9��*�$f:�� %�Y1 �]i. \�}6^�0*�a�esPXo&O aq�\]E}�P8pQB$] 9'$�t�>,%+1$ 7E@C�IBu�9�VqB�3 m��3a&�3�P�R&' \]�l"� 's�t$5+�(�on��q�m�%ѐ align*} D|( q,ru� & �6Ve#:�:*�/�/�<^) -�HrZq������\ �6G�6  V�~�-v7�4!*)�'N�B�D�]�'1�e+�� q 1� plai� $9� -1,q5�\leq 4�ae� �qnit�Vym Euclideag@��ce"h->�j� a���:Ni;� "C()!MFQ�a�a�olp,ocj�&�B�<e�� 6%\ o�X$TI�a*�:%1Bno "Z/Lout :Q� achB1��b7val�R�N�*����/!3Ɏ� l$ � <(�����f , switchi��t!�!o  can`/�I����s�c\J�y =o$� Q�Z���A�i���"�sm� _��VftI��rU^��I>�����4���� f�j� �=B7% ݿNY�1�I�b�$\8{5�0,w5 w �q� w}:..�e�q2N0��� leq2w nM i1^L s T}{c �7 {2} ;��.� }!"�;a�&inequiu !,e3Q<� 7T2, Cauchy-S�M2a�Now Oa�=",a��3c�g2! �G.�:�15�"���� T:1)XNWr{��-"XgODDruat�pz!�`�u�r`�����im���if $cua s�2 eno��~ � �"3���qr���!��؁�deɂsN onen[:Ś��NTo�Q!�s,\)�W&nI#�ne>��tV !z�.�v,�q)���� N- J'AX�J�R&B BA�� HW �}2�4%Qe5�5�&�:�� � ( t"n% ^{st!r�ko\% �5�.$1ur�/ \ Sp{$H��su(mv1�%�d�T�}`9rbV\lH V^{-~�) $�?\ ]"�H!?diagona0-� Tayl/C��e�l�/�0q j" 0�FAyj}}{j!}� ^{j} �*p ] �'� S>763)hɯv_{b}�;b�!M*suC ;a:c #0!�XF)S$\ellx"AB >4�2A*N�laa�Yr%�$j<6]�% J� SA�Mve*� l�u�2:�H!=�� Z* % vMJ�& Z*B$=0� yee,G!�H$.�7 &�pB� �+6fR�)!.� 5 ��:7%I� *Z�$;� M�6?:g %�i �E�A B� U ��:W� ��J�!A3 � Ms�Mg�� $ =Fq � >� g}� E����m�W2��~K\pia:��G�G2H*a�^{%�}!2 .�-^<lin:j7 �.3 2-�b�]����$\�E%O�-�% ��%��J �%( 7j}/j!I() J�6h ٕBh/j!Qm���fourth6��(�>;2lR?.��a�G=)I�\�L����$*->��o7T)$=�/!�!�c�""� U>�����On�Gnow� D a Chernoff-Hoeffd� �to.�oZ�&� �'.Sspp�vinTMce߉, FZAU% a&s.p ��GI� c�")R!gEO�� �� 2^{-:~KU,�2� $c%..�[^*��B� n�  }+��\]&1 ��>��'ڄt$ bœ �"�uSez[� Grid"g4RIDb4! 4\mathcal{L}_{d��k5/�aB�� gridxfph�8�id��G s3edTh�R� ����s@\_6 $d$ coord]s\ $i.7i�"�K &P3%jd}\\}L a��5oKL !Sub2d$"��?�K! ade or aCOSAu$1$I�"�@� (eMJC�" �^t0S 2d$\"BA�j�4i9�y >�$\ l�`�_ee-con&a�R�C�J �AT"�[mEs:�&~4 J�%>&%])�2nq� {.g�ei$d= 3�n,'.j% ol�"*1~]9j k\�$1� . Be-����th�D�s��:develop( �(u3h.ca!��g%��#akAPv! m�"=�io�K P9:�OR2�R� n^{3/*�n$:�ys)y=)o:=2V�i{J"Ĉ%` bs�q�oF�.pya�6�Sy.�M�$5E{n�sR�����2lZ�1�Cny MA� $CT?��$C�&�G%�a Tawex"�%2S!�� %�TV�byņ!��5&f:$C$�s:��`��{2 F&.��>� ���E9�%"&!�1.��D5Oy B kZce� 1e�HÇa�`ll�( 2�I'�X3! 5�v$%i�} �Q^ou�E&ɠ%qny�E)ise�n)�s��!,p�|&j�32= �a>q689DQ��A9 &�_� �% x(�3}}�B�9 >4!�B"��einu�6cursid9E�IHmannez=yu�b�%?�?�O����Lm �bl^*!w,y&��dqNTnay%pr ��vx"4p%�re�/m�.Koftko? *� <�#�/�"U%���i�b��� atc�5$H.���ͼ�.z� or�9o)�n}2^{ P1Gp?Y�a� @=�!In�' 0��;!2&� f�C��Ԃ� g uch �yn �Ie:5�i�8�R)�{A�Q  Q�'AASEC� Wu�k�/scrib�fE�m& > RDE� , a 5��-ofF5 AV �:�Ւ�j1P. $\�Q,ZWZZ r�XE toge!��>a��Tb!%tN�U!�a}�d. (S "�]�@e EM]eIl��i��@ $iqCAq "3�@2wm c�a new[;�>s $A$ �u"�_{1C0imB= 4�DZft�yc) �(9Jb2r-"L�VuZX4,�� �.�iC �V9O�mp./v1 ege`"_5E|Ur proc.6цavu�&S/F<91)] S"BO ��!_{0���=A#>�&G82)]a� $i=�%m$�2Fbi+h d =ASAzWlS�Z�� +!/� %O-iz�L $W$ flipA�e IHc-*hM2�y:^UA:!2�F-��_a_{ crip- �� MoAZav ?� $S�����a�J���)C�]-���&1.)�>0�J $\sinn%=@ \PsiBgh&9m-� +\cosR? B@ fail:@*(Y:~F?J�Fa F�o.Gs�X!���]1�AD6-N��% >���a:%~F�e]�� *O ɛ.��}h�6�Z�uAlemma} [ݻ]���lem}$|)��Zy=%�� [" 2i"��'i\] "E� RN�IfcfdEh�j6 %m>k�-�NLE!�2=pA�F��9�z�ja�A:�Yѩ AQ�-y.� �=7>R..1fg�. \W $m=O(B%)$�y� ��5� 2m5�2w!�aKl1g8ou��s(o�N���  v*&.��" big-OD|�T>G��jz prov+ � !�%����&"U6}}S�0Nx ��8BY TwiZ� 9��#8�)�  $!Rgll�  $Ar $��er[ mv$\pi}{4\arc!�� Q }}- $1}{2},�we�� �B�EPb�lB&s�o cE6&} �� I��0AM( ��+ )�.ɉ-���We�WR9U��c"�   �"� ?O-m�)lls!k�N1j!� By L�6��A�isq�=i(�#)!��V+ƣsuc> Vy�fVkN%�V �^=Vd%."�%�У.� is1�a(!*%�v.N�I4 ] & �ߖI6 B �ge&��>�:>2�.� � }{6}Q�2 nmFs.�22h2s(4�(}^!Mͼ1d"q�(2C mono�Z�ga<� Ex� $' �Nval��[ 0,�t�t]t�6 a 4\2f.�!� x!m x-x!+/6��$0$�22%xa2% ލ NotAqi\�&�o]����j*$y garbage !�b$Am2"Uȩ.�,happensS62�sa=�^|ly�%��s with)D6���� ��*|Dfv& At L�P3s D3vOur&MiV� "�; 9A�(srchfull}If*��Dn$�$:��Z�2K-���A! ��6‡qr�C� �:�nxKque.�ex�^etT"�s �&\A�UNKNOWNOh�)ll "��w�2b\ \�:G OR}% &�0k5+}�!�� lemai$b�U��? no.�t��"?k$@them, g a�24<seg�rue�a&� 5�:jJ��1�.Q4I+ :���F.uB* Choo�a� | beta��/3l)�Q%� $\mu$ 1#�� %"�( $ Q mu>1�S�a�  =4/5�6\mu=5/11@@llP�v��"_C"\ �k!�"zx��I�+��p:�s $R$�#_{R� l g3��\lxE p _{ ^{1/�#%o\r$ �7?n.O}^{! %y! %$N"n�5�Ӑ%xZ�nR}]�2�� %�b~�ed2B\���(�� AdJF^Ɍ�~$n�Ru;u $R$;|� wordH��*)�6�*q"��A.oz��7�z�id-K "%@)�� L�qwxpre�e�� \w�. ConH��* F�� �A cIf �0� �� �+:H#!�� *�l��nP"�H>�#f!XiI0$)^XZ�CO�� ���2��jai�%x/J-subcub�q �@.N 6\U�a��T.j*>VE>�A:��Iic>!?xc�-? �t ��i%rYYJA�vY�$$C�8 ify ��.�a( ��\eeQ\mu�"�j�ow�hiWC/.u'vE�%O! g a^{e�A3soM1%�\:� ��D ��!hY� �v.Z/2a�i N do�{X .1�% ) &sF�&ئr$"�!ց�,pvela�es=>�!� fy"ō� �%.�B��Ehgby�# *�]��7A :� �wb��"b� . \ �Ap����A�trjC �a�~�Q�[ear���.kQ)�id�m�x腡)>_9�AA�)Q$!�|%U A���mp�M"�^�E�0]8 �8"�&Uk^Hs%�dy%�'G��Z'�<]�1!a� $S->n=%���.JidA�� �)�Os&>Uof �B0Ry�$��]q6�an rec�hA�� � �3:$p,bL��L!\]e"��., �v� ( Cm]zB2<a�FneJ��f ���UCAb*�i �aY]��\ $d$ &O(s�T�!�6"Ua�.Q%%����%� ��BgSfBewar*~li�F�2�2���"__�(\�m����� �>�- 2�A� �c.��way�F� e,6�m�"aik�d�8 �j 2��,�?iY&�Q. Below� � $ pseudocodc1���I1& ab�"�re�d�7 $��E4�)J asA�roVkI6�convene�� c*}A}y ,AWS� *�]l��ofav$� E� c4�� ctiv!��s} [y� t$�algw} &��a�a?[,���a*Z!e�'�|!6!�!����  �B�#Defaul3Fi.8I�:2�m; n; e,bf{If }$R=0$�5n:}"%*�\[�UY �(��>NwI(��e��obu!1�[�R !�R~�=8:n�1�q$mE�A20�%Y;*�2++1l�X(� 9 \��&< 6�C\$ec3F��,� $e�">ue�% #���=2)}� SKB��Oru�A%26�)nT��let $C.�/C_{� !>0}}�!�e6it{�� s}O2$C���E= ���"i^�h ��+ *��E��%k\ �Ub0O]uĺ-f2��.��HiL?.%m ( C&!) >v�� C*���3n�!2�a�&� � i�" ���]--�k��lap��}���_�6I=Q���"�! !�K6w=��he :����� ���B�IF���A� I�荐 �I�%b6n.�1 ��+"�J��2I�Y1#2Y>�x\���-two�"-�"A����Mz� i�a(�oth�h�5"� !�To�)ly� map ��*\ 6�A{�;\��= o)%>( *uE^{.=}��6>6�S�,R�>e]J& \�-�-��Jda'=qZ=�. �=om8.� 2R��!u�vr�%� \ n� �y��j[ *�az���"]e]ar&ҹ�θB��.*�p&��U[!8���$\�4rA�!vs �1Av=�2�4A�E�.�� }�&�6j<~�"�5d\I�}�� V�O�Kзdco� &) *cAj G� � at�e�� ,&� $�UB��c�$j2�6!�S2 �0}�%{NL  �A���f,2>� -�  =�Y;e�� $j�\!�d�y\2F$ �a;�^��&7.w 1O1}F X 6��*,A�� @�.� :a@m\2�A��f!)e Z ^|u���%���W Q"p >�i�"�!&I�Z� �� \ph(C'��1��#IJ}*.Y�- ��]*�� �R��g�  �WiA�ith6�2�m vw xZ A keyR�� ��]��W5�to� >=IrtwiQdoa�)��W]Do"��rY! e��al��y ҭ� .%����is�2�en�;��oZ�2��ف6d2 2�� stea]*"�32^.�&25\�:�j�:&5G�hXW� 1-}�3Ik%d3 .-��$�s�K�mu��O�%X I"��!T_{��� ( R���5�)AB�9.�V &��d�F�QzMw�"�o��e�08.D���en� �N�� F!U(E � %1��#�$ &P+6)$!�&�)T_5< 9Z+q,\\.!.|X d� /d}+R� R"�  �Ta�e D!+HJ� �'�be&� ts"}!���\-�\!�sD�=.�D A��4�� I4*>4"��Co��g��F���( .�VT 9U�Y) 1�H&l9� Ym���7U�^r+�%Q� � AE^o1 �Y� 5v�RIn � m�?�A�F�]�(���r R72��+-#.�2{(��!Z-P[�+�;sB8�.�( 53-��O���C �� \f� l} {S}+" %2 S�N�N'\L � -@ v6�  1/d--"1n AEs } sn~M�6S6�8�Z���i6R��N5^e��-��� ; i�3�q"7*.�)F/ pc&���%c� %'Y"�+2s%Ie�)�� �B��� �ji Xdou��x%!i҄ soSE�&�ach� ���v*�j�%�nth���@!+_i = \O&qe)�n �_*�6)^�! � �qo.X�%!=)67$��l�z-%�&; $ 1/d$,�pn�A]�<1�s Nex"1T!Ig*�>s�nspn.�>Sc�& A\�0V+�Y Keds2� ja4rpn++iP dardpv��M&� 2� "=Xb)b\&.� `>\^U�$Of�?rs� m.Afoelff!J��undeIy�* \��!n� 2}9'� � �@V+�(& $5��p*�b$.� 1e�AT-2a1[� �/j� P�� P&� &z *� F��:� �' �@&� ~� �2��cl�{Z�*� 1� ��F� y9&-1��s Z_. $-2P �5b2�2�&}F� ^b�� * 1�31�3a�( 26] ��2}R�*� V<BRV;�� 8 N�B� �",!a(�-f} �wfh"� B�B`�N_�] �z[M�ew"wefrac 1 چ{��-L�yrd�cFE ��B�^{6^ ) >.!� /^�9�Fs�w%^qtQ2�kd(@ \l� s_{r�R}%B6 j {\di&kstyle��F7:/i-�V�!�j�q��1�:0����^���K�2`.A��GQJ�-r� % 1-](1�eF$�3�.*�.� Ab�:�=.49/!�J5 Bc *�Tfb A�XU�(U&��x/6��x�5�n%��\1j �"�5�5��5;�>� �ׂF leq1�(ePxth� s-�$�!A^� 0+<�t��\mu;j7( R�z /2-��)2��is �~"C0c"�*�.�����(th�!N�""]t�U�Y, : � ) vJ6}du^}B44^:��) "- R� . A��ߊ�R./o��le ;��R�>��a�'^ ny $R��-~��(/I�e:O9n� IBst�."�%�A-% <�`+setTprime}���3SN �W?)2�3 �3I�emb�u�.�J[OOrs&"�]�6>^{ � })�  \�m9�:�OA��2��b� ^2�*)�f^.D2_% 6QKF� s �AlsD�i<�b3 *� �"o6,2�]&���n M�:H>?*�9�|�S��!<0�f��`*Y{2tesAdo&��q<��V =2�D2=I�'�N$<�' 6Q�Ba,�'�h 2�F^;2�3}��J;6�9�1CQ>���2}�Ov~ A��8|bN��s��6e�� post+aN to�/s�qɷr�"�+AGd�+�U I���t�.?&�@i� D3};$%��}�+A�par�S��ŹA� ger�>v3�!�ow)( (�2�*� �=oddB "?H��m=tϵ)�l�>�|?�\� ��� A�7�X�2d � "�+ �g#�s/ ��=�g �? $m"~' _{0}&^ /2�.=-�\G-�;.�HI7�'BA �&�#�9��c��pa�k of L�H���#A�B 2}%�A���"����"�#���d2 B�`!u� R!!^{R"�Q j!�� Ml]��#:�#h usj�#1^D&in�?� �rKI�enZ�# F %�aX�"F�^ U��*d*/H=h6�#��#2*C V�".�-���!#6!#"�$w ��2;!&� +2m���2]�Z�.T� +8-F�"o$�@+1})R�.M�� �U2R{��:�e%mRZ-i��?:ikeds` ٺy:��1/Y�� j�^�Uˡ��R�����2Ue�O�2��=^�� �A!|: QSp����� P��fa���PU�JG^�ۅGJ�i.�L�L�R�U�y�.�x8��q���[Y�2tR�.B0)f1� .NjJ2�>K�wR�28.o:.! �.� Z6� .c:��,">V9���;���map^[R}:k�z.�x�"�a�:� ] drop>  � $2/R�od[�He�x^(� �Yis .� P ��W�R .�h"U ��^n�U� 1�a��it"�q"�{Is���hVQXa�����2���f % }:60$u  -�-O�"�:+Aexi��I>�!��2R}��V&� E����EEM/96�il'������#Z�N }Bn�M2em1H��� 0-��� %O���5aK�D.? � "�y f�GB�=$R�sh�B$n�t_��A !HN�]V �AR��r�b� 2�CA!w! �$��I[�E��i'%% ���_4sHV 7Ųo� W�u/� d�Y�� &T� * QM��MR% ItemWn"� } WaY�H!�� !s%��"�O$iL�S�i}=1$Ʀ/dOf5s"̔k$�HB( be k��in  �;�n�a.�iE"5FZZh�*� R�(\!$ {n/k1��y�C hown!�Boyer\�� �[bht�DI~��*���Τ�wo hop�rٿ�D��P �)%'BA1eyjll�! fara=E��!�"�2In:x ��M� GX%�UJ,�Dk/b�<��JA�q�xan !-����(Zg.R��m�n}6�Q!?h�m�Q f�Q�4)8&.:or�P!eAdof���Z�mmiR�!d��s�S2,�r��\no�"&��.`%L�:�] M� }}{k�-!{9�.[9� "R���x�@�J��ރy��8�> $]_9�("),/3��$)nzQ��("ge��(�F �0just replace �$k$ by $\left\lceil k^{1/d}\right\r�^{d}$ and $n$ by the largest number of  form Q( 3m[ N[ h) dDwhich is less thansL. \ This only change0e lower bound�a �>order term.) We use a hybrid argument almost identical to that�0Theorem \ref{gdg}�LDivide $\mathcal{L}_% �into $n/k$ subcubes, each having !overtices%NsIlength $-�Let $S$ be a regularly-spaced set�$M=n/%`( 3!�k\%�) $\!these �s �any two� inn`have distance at least $2�D\ from one another! Then choo%d oD $C_{j}\in S$\ uniAlyWrandom%mark all6�?% %�$enables us!�con!<r !_6kl itself as a \textit{single}%~ex (ou-B$ltotal),!!�= % . to every % R. MoreE�0ally, given aRL, let $\widetilde{C}!-$\!�aF-�Q-\ �st�of �$\ a�0$E -1$\qs surra4it!�(Thus,Nyar�of6�3Q.)e�en uqu! magnitude7R�afta� he $t^{th� <0is% \[ \Gamma!^{M� t\I�0 }=\sum_{v_{iAOB6\,}" _{z ��!9, \alpha_{i,zJY },( X_{0��)�� B<^{2}, \] where $)$\!.!0all-zero inpu%be�Te�!� �i�!�la�w=Tq� c-a � $AJ some%� tant $c>0mAZa� �� 2�,|0re must exist=�B�$^{\ast}}% E=ch�vt)�%y$q=0}^{w-1}5�49�T-q:� !_4q\frac {w}{M}= {E�kw}{n}.!\!4\thin��$Y5>%V�$1e���$\!Q $0$ else%�;�n)e X_{q%�H��>W-� dura+-�o���$, but �6- .&+1$ 9$. \ Nex�H)QD\A�( q,r5�:� GA�%z6� I� >�TJ!rf_�  - 867 V6r6 . a�K {.}%!���E����(>�fora $c<��we�^e $- q-1,q � \leq4�_$.\ For�� he $Q�$\5�Ů:� \ through!�5�-1�G , no ampl��rigina��ut�FJ]�,can travel a�S��I��Ceby r��C��T�xf�ZswitchA� �!�-1�A��u$ affect��i�5b��mmediate᪥�ay2E�$ It follow� �0 qrt{-� 0,w1UE�qI�q=1�P}\..2�;2N/�$ }% Lw n.�����2 ��}��2- T}{c n}��He $T=\OmegaQA%/=�8 or��d$, siIassum!�A� algorithm!� corr!�we need u:.W6�U� �{4end{proof} Nou M@f $k\approx n$, t�P�G ofAwy�4mmi} becomes $6�n.- Ÿ"� j�~Vdiame�*5 % 7 A�Also, �d=2�$1/%�=0{ L � is simply>�1�9z indepen� �kqThe Lof��6�\eH�4(chieved (up��a5� factor%R b s on $d$)�� $d\geq3$,�� ne� PA$��We first ]rua�n] -�case w!�I His known. \begin{t� } \label!�ub}\quad$Penumerate} \item[(i)]�G���QU�op0Lorname*{OR}\nolimits��&y },B�5�=OU{1�}{}5/ ��A#��6�2v���0n}\log^{3/2}n� �ec.Ras5� To proveAn2a ub},a�)�dVP), tA̡� n/\g0 >fA�siz�� m�,times \cdots .$ (5  $ T$ will be fixed later)A���in Ū� �� w exN� Y�lemmaU�rm}If}a2 k�A�$probabilitta� actlyn <ed uachosen at ast $k-.�� \_ x2}�/ �qQ�>� $x� a�u-F�/is� $1 � e�G�2+,V�!\of.v�M, $y$,2r  �Rx�>$$y$ belong��!\ same9�or�qM\:they 3 differ6-�s �r�B� �al�.5�elj1}{ ~M� 1- k-)� A+ d� 9S 7 i�S�{!events � quotedbl� %6 � IW2$O\ af tu�� jointi oncl!%�n�.�eZ� >� r�M� In patD,a�qo$"$)z/3� �>�jK1��!�"c How��%Rl� tary�� l9� A�� a0[ %6wo9~$v�  $w� neighboT�2�v}kAt�wP  W� pl�by�,%v� 2� m a " an boxAm�.I�2 J. \A ��Al��between� ���LL ( d+&� .z[ Itq֥ aYB��6F� takeY� d._\��� A� ii� new u�a�9Q��� is result�b$an overall6"ofű~�V�Q� dE� * �� * 5 54*4 % �� � =2$\g obtain���}�uW�� J$�c \subsec�{Un�  N"+MarG Items� UNKNOWN}}�a|show ,to deal with!�u P� � F� % J� 9.� &t�lemaD deci8��are��no.��xrAit{��}�� m  � Qse true& "= -mmiub1}�� �� >�� �� f� ~��� 5�� eW WS� stra,Hforward `doubling' eac� Boy�u4. \cite{bbht}:"o .J�1�j=0�o�_og_�� �/&}$K?iz� RB�J�ub}iaծ&Q�=2^{j}k@� If> A�fy,!n outputP��halt.;� L[(2)] QVay �ex�nJN� v�m�P . � wise q=b� kn\gez�!�"�.Xa�.� $If :leq n/�t�Á/evs a $j!C9� 2� st� !h/382� �� �GSo 6� B� $j^r iter� !�,tep (1) find�2@E �|�� "� O�Y%b hand�.Q = q2nq��>q9 ���!�-l���d�� a1)A~at���Ej�6�r y<}>`� !n3 �%�n�a�[� �Nu=� s1}{aU<� l"� ] b % ZC�A�sum� (brackets be� a��rea� ,geometric se�& D ,A�)qi.| \� "$6V�7 ]>� 6D6h$te�iYr-ߩ  n$\�I| /� does I2)� N�$kad n��� $�l��n2�;� Tak![$k=1$  s&Q s#un� �5n�F�$ �ru&� !t(1)):q and $A�^)�*3�m establish��s 2�full}Y:��� Sear�� n Ir�" Graph� IRREG� In S TPREVGG claimed" ur-and-con� �Lha6 $e advantagy I��`it{robust}: it works not $highly symM�g���as hyper�#�4 any '�#compar�" expans2pr0ti� u}w�#A t\ tp �0. Say a fami�fnected�S $\{ G_{n}=�* V ,E�- \}A a�d$1-dime�al}�:a e  � $\kappa>0ݐ �$ll $n,\ell� v�#}$��1! B ( v2 ��� $�� \min + y` �$,m ���^Ya�Is%�-� *�#� $k$�V�$%X�S Intuitivej  )K.C (!$ŏ2!�%eger)!\itsY�Hp�%� r&W%Ai goodt�ᘡ�U~ Z�.�@.\footnote{In gen�,A�m' sense@ �ti'non-in��well.} �#e��@2�).*��zn/-�%�) �;d�$ Not% ough��at1` m? a�� an)<�eq!�=$usual ѱ�V $not requir�E�2mwj�,G1�.4;% :spolylog}yzE"� �{.}t2^{5F�� n�� ] . 6R�rov��� (i),�!�e�o�e:A want!�d�pose !�recurse�a�o� El s (calledU((clusters}),� wilA�rva eG roleaJs�) didM�y��Z�)ceduralM!v 6�%$ $n_{1}>1$�rst�os�ax�+n/&)��+$Y�.�) �toardesigna�ra�$-�6 pegs�*��) $1�T5�asF!��aX�n !qto�closestE-peg,pi&)Voronoi�hgra�(T�2 brokq6*ly�(� v�( C\�p "� pega� � $C/$�%, s�# up����'�  mt#t,!|$\��ZG �4-��� � N�0 arbitrarily-�$1�3, ���e �� ! F�'�%t)�pegAPObsM�"�#� i=�# � �NB{. � Eu!� C�)%} }{�6�< 2 6 i Hn -"�M�� ��n� ]C!�.n+�+ \�  jV����"g%�� sA�-upYX%���i�&(Mh�4In�'"u,�!�2}=%#�\betaW(Nsome ��) $\'  2/d,1 ��!�Ct-$.\ �-R.�.ea�2e����n�m �J�$Y�a;\a��7peg��at���s in .X!V��a$y'�- �-h]ith� � � >n�� q �uWa f �RA ), H `&[ r�1�J_2�_��F_2��( %1� >�!�\!)its1�!@Continue:f� mannereaaeReR-1}% } ���V$2^$)�}�R- 5 !���A�RI�A� Ś$R%� Stopa�� maximum� n_]�3�techn,2conveni(��0}=��a�r v�ex\s �wy$0���moQW{ v\��}a A�end��1a treA >s���be se�ed .��'�/!�J�Jm�,detail, basiKate� }��� v,z,� ra}1 $,\�&re "�+ex, $z �&ns�3it�$C&� (�&V)� curre� �A�(Unfortu�� 6"�a_�- anyway�27%K��e�!�#� ��2/pr�&� Ysɬta�returna�a�!�*�N%."� descri� (subroutine U}Q�A�($�e�2�2ZF��ts 2F, t\�,pi�a�4 $ superposi�!_ frac�)�J�}}�oB! �   �� � i}\�� 0,.iP�I n �s>� 3.� ,��  |%r ,\l-bB� }�mn6��ii�,e :$. y#�@, defin ŗ�adiusza2v�j �5� ,�$I5%�(^�\ 2� ����a�"f�}ZV� -�R� A��1!o>���c it�D �k !&ell6��( IU2}{M}��\ln*�( dY�!l�*&W.%glem}W3$.� $1-o1K*P)ithe\ic:M [ ��U z� �(m�Z�p�a�I" *� "� !z� Gi.B2fm �� )G!fb�c^AA�� e ball of1�%�� bA=$vESV>�"��$�has&�greO0n LE7&3R@� c iU7�m-"�-�H��5�7�26,%X*� �~q>X2El}{KR�) ^�-P�s�H)e�&e+"�%\*))vAun�5%gqw�}76'd\�K6.!j!��at :�^�,:[�1/� =zr�:rm[mLn%(analyz�Q2z� succ4B.�of*D� &�m�k'��2Z� -�! Atm�d}�$"&�7a�%l�E T_{\kBArk&* a�nd )AA�f%�m��+� *CF�D�  +p� v:in �4�a�&����%�align*} �� &@q?%Th}T_� � ,\\VF� &���!�+R~ &^p��-bi7�/!TN}0-^A�e�Combi�WR� =��YX5�� � f�.5   \ 1N[�+B2}} �"f6E0&1} i��}� �"�,M�#\J�}% J #-1}}}~j B1VB@0O�N� �\l�#y�2�yR�d-� /2�"� /}5�6�t�1X t >fu���� 5�2Q.��,�&=U�vBG9�Y�� 9I,:e�>efl�7 line holdpc�� >2/d��S�a� c)�/2}<1�)�/m�V�2J��<edsB�:a<1/^;A�53�g ing a� x)iz�R� �!a.���qu:6� �� ��� y �|C�&�.��9con0� 2J�\ FP�~ )�����%dss���oJ�f��<ٌ �1 ,9 �͗ 2�� =^�*�| 2݌9�%3Y�B^iB�� i�&�8  "�v {3}P�%�.�1V@^<�7� >� b��2��6�%��=Y}{1R.�yFV��GNf�+6 ^d �O.�A6�RN5}N@�m��A7rdV%�By) �x�R"5M�.^/^A� tTst r $R=\Thet&�Blog a5>qFin;H repe�%*7 ���K �*'atU@"�))�+s�a�A�=L'"e:�B*�\ u3ͥ.}n|�\� sL�Again�.hi t eq�&;�?�Fny�rn we �$y p/!}">O$Rs�� D<�C-�n add64 W leve�at��(#Y�L ��t� � $2�\��} ��E@!� < "�D uses"# 1pblBh%(�, 2�,�%�;�,=,� ]'��� of a@FA�L ")iz"�" �&=fD�-gh�3&; corollary"r�cor�@R�'ɟ�w�!�'�Kj�'\nBsC�,"�6 &u'&�7f#-�^��K n}{k6�C%*: j� �:�A�eB los�1q�A$k="], Go� �&V4;� rivi�gDa�u�� MX��!�4>2>V7��giv�P&�/*B�;�&|O��!��.�3+�J"�#�In  �5,�J�'�2�*�# $w�$� ,w_"�6:����I�'! ' ~�>m �eY, /insteadaft�0n �n!�G]� a�ake�J6����.d4 d4st~)"�4"K$C2��soUJam CJ�x&Q ��&� F �(\ should be`-�F �QI�1�hI.�-nY8 $j�. B. �:p"T 2�7 g??o&�(~��2NQ Oi.]�v" nZfa\7qu:r �"f 2�F$��A��1.��+. =is�y��seARay"������e�rIor#:),��\*� yj� Ty1 a:�� *>C& .�I )� �i�.rke#�L"� B}�c� .o E��/mai�B!Pupper-�*�B}$'sA-�!�n�Ue�8$j$|O�U .�8"� \ go�5�Oif� u-�&�j) �:� BeI�� \ln� �=x�'�&�!T� iM61�E�� Z\"�a�:,�0���\�)FiR� So�� ^�&�&�.|)&�� �&.� �� r3'�.%� y6? lem"jN��;� �y�i6�*7 RV.A,)FF1U f�y, ~&CI=UL�,�Z�� B� L�PE�I�}|�:j \]aY :� Z;��$&A�As|3,���ra� !락Jo nij �.m�#"� ���1by JHJ2 �(on�I�f"A`��# f�%F*�4 pet� � �$AQ��Qm4o boos&5|YcB�6j1�_�% gq[ q h .; % r+VWJ8 :�A�68�C"/=F��YY�b0N=rv=f4$Z��M1=Y�"� �� ^ � F� *� ghESO;$Rs�b����wa'n# w i5SY�d1# a� .5eq�\aW�E�@modify�B�Aj�*�= eper�n�:,�IɺAZ� m���- \mu}b<�0hu3 e2���B2�% �!-1R2� {^!@I�&C%���I %52"��=���>\ .� �%6l'a' ile\�-ɐ�2��IB���������"�Q���6���R/2��}"n n~ +2^�:.h"?.?^@:_�$[A{sJ�deAe�2&<&� �Pa�J�;em�!_* "= a0 2�� Dh �05{1Vo6,GL�@Q���.�ŝb�t�62ݜ�R Hand�F>&��ms ad=Dn add�-al�~�W��<� absorbe��2�:��n?ley02�8  �*rJB7Scatte<� �@�!(SCATTERED}}#QS� o�@HYSdiscusstcL way�bpack a ?n amount�entropV:a spa�-reg^of 1 "�?# H�NwO:id�<: h%Khe\s \�b�'ributed�G�1 p!�It_=bez�,,�O�R��9Feɽary!�[L � �!Z So w�% �1�"=:8)u;i&H)�`, $h$\ ��of7$n*�:�>}�m�awe�X�/ $hVQar`;A"n%6m[G�Ps*� determin� �-,�h$~is} x?.��� "I-*�L{Q $$@\?JI@�w �) az d previous uCs �D{*h�&�Vf���"�?!22� wish�;L .�V,y2xC��!25h�?bbch u?er"�gFor�?y�SIwe eMaU�C8<�#.�*�P*4bh$!� potebClly-�A��): N�Z h,2U�+��U&:N A<��Dn"�-"p &�XNNm,��<� isH Ad ��b�[TDt-"os��lb}�0�B:sU{,u*�J :�@M��"W0g ��:?*�:�^"6^B� h�M�*� � �2:�[P�^]%�G5�>�f� �}/ADCr�* $h.�i�Fs5�mT.FAU�8 N�i Spac�2A"P@�(�:"f�e �.�\2l �!�i�S�� pairMtk`:�Uk/h-%�l#!M����@v.��j�I��v29C S�nUGR�i f�i� �7!WexF�iR� �>.�����y�� [ �\l ��*f�A�^fa\less��id cal`a�62�ea� o�B*�Yyth2>�s�*y/F�Fal��:E��o>/���x%�be far66start)e6?AXPro�����7n�V�dY=to a  acic�Vor� �3Rw"&� �n�n��2�&x��Izr:�- f\3.�ʍq� � � ��.\ \ UsenGz2C9�� 6,��AafeVj4!�o�y .'�:hV*�E\ jv&a:G�. a  �#*#��n�>�.�� I �A� ev�{)j"�p6t!a�`Ea^ ��(�')�6>a� �"E)z� ���ɡi�J��@��Q"fEi hat{oRep�&�4i�n}% {h�j} �~:��*}�h*}\ \� ya� �*th:��� h�!n ��j�Z\Q�6�!�rX%)�:7J2I�Kv|A*���\ sX�pA�woi ase !�+ oc�Ky (� ��\ �ea� ced� �CJsol6Ni5 ��"��l}B���p �A�!�' wa�bsequEim2OD H\o �\!~de Wolf �0hoyerdewolf}\>�}c�� k�Z.j R`$c�.l G1'h[8+a{�scjo� fun0`�U�+)i�&�a��2< � Me�V�!l �i�n �&)4� RmatchT"e celebNk jA\& Razborov-_r  :cc}�nb�"�_U+Ved-errorUL6�xL)2[;Bef �;.�f}:@�protoco�RaC� $ �vA@a�both st#H theitpuBc $3$-D FWC*+{3"?]� (FigQ"a��bob})# acsy �2x_{jkl}��iS nd $y y� Y�i=�;/3}j+�`3}% k+l�)8j,k,l6'@ 0�0�6�$.% %TCIMACRO{\FRAME{ftbpFU}{3.6073in}{1.0652 $0pt}{\Qcb{2;8 %`synchronize'�d���g-Lre�9 !Es.�!Qlb9}% %{)7�6 pecial{ lfage "S�T� Word"; type "GRAPHIC"; %display "USEDEF$0valid_file "Twidth � ; h�f t 1. �G$epth 0pt; "�e- 85.1128i8�e-A4806iA crop�  "0s�K"1embottom/ %temp��p 'Q?.eps';-7�W"XNPR";}%DBa�E�YqfE�} [ptb]3er} \i�k@ics[ �=1, �=15 ]% 5���Hcap!�[.f��q��u&$6�]6R 2Q �jrQ%�<11I7� 1 %End9&Tx' out,A�qinP6 a ��)t] ��%1F31�} ("�xe�,z�4 B},c�*�@vi�A \rZL \o�s0 -c�� ! F!NB:N, $thw8m1�w2�� � 6�q�playe�M�r��6  B�õF Id�\iJ\�}� ���/8t�<�i~&%J)��\�.her�H,��6: VB( R9�oub$ T�gc�jwhN� fIw�C�������y�s> B�!aan"�g&>"SRJh�{l�k)�:F7W,�~�O!]y� in1s%&ph�=if%�� if J�;C"i8jyZs�R N:�Bob�4�[ٱ^3o-A�e� rase+ SecoccbA�e �movement^J�tellsi�H(+ six"�  di:lions sh� gorto Ws�*wayI1R ݲ ��d)q%�'~/ta"by ,�� L. � (��qhgt2S6=S6)Sv!U sQg�!F�BV��}*c, no f�C:�9�'"J"r��"P u,Z�a"5���b�� �-S�r*� 2S5* � i��2��}I�=-a��d*�2� %��T alsoՁ v6� A �"; Open�)-OPENG�aAs~M!i: bLOCALG ba sal�] oOprO rai@Eis �a!�jNbwr=A� hips�1Z-A� l, C A H �o ma�d�e:rA��7 I�:>!��9imI!�a�d�y�6=� � �iesZ A{s�_tru� at $"�f2T]2�9 Q^{Z�'( 2(M( :�+ Q^{Hn0 >�m�af,G$? A�ond�!�-|�(z�G�A)�� umodel�SFor ex�$e����9� � �� $\ gri�!s�$f��( X ��C/P%⭳�ry row!�"�>a ex $U�"�WE�Cl�{Z�` �3/4C!>:w�Y ject� e�t�� is optima%Ho�rwe�u�A�LA~%Rube�$O�2�%125�F&�;E a��pl"F�:!�Vx@0 on a 2-D squ�b!�E�s �|io�*>�"�eAmbain� Kempe)Rivoshakr�howN1q>�`O�C)� &�&2�n_{"{C*�\ML>MA�Ca�r�2!f>.}5�&E�Lremoved? \chapter{Q�Com�E~Pos��O&I POST3�qix}) dux Gil�cn�^sal pap^�ne| stic=� class1=dpN�e^fsszsf{PPr  as. *� * was �[d u|cP"r�!+(In 1990, Fe�Y�Kurtz � r my{�, d% �� try a new�)a�41L quesAA:2Z!r a ��likj>��8� a&t(�}ri;s,i:yr%ax � F��t�A� 5MreO$YXa�,�.�&1�� ---Lv! Fortnow, &it{MyM0 alm�Web Log}mf <$:blog} (��n!Edidn't�#�5 ough��hM� w/9�,c �a�mis` �me0 icsI�} I�it{2�}!R�p Tof��ar�L8u a�pu ��*� :)��ntoS not�An�,�h ~S wv9'P#$sf{NP}$-co��tee0l�*in Unom3W�`,� w��9gu�Da�"��y��A pu�.)QnZ���But �-�) �do5Kmore}A���MM��Z�m 4"� uter!�ei�!q s�e&�f�v�in� �F V �Q|l | BPP}�Esf{path�/)�A$q�by,4, Hemaspaandra)%Thierau"Qht@l Ds!1som�� 5�MA�����z�r stud�@Ux6l"Fc�Ke�^M�M��g�):� ��BQP}, I 퍶!}m��J)<�)��ost:s�5� ilar���$\ excep�-at%�an meas&OYW\���!1�id�!�qofM~�� 1�����y�:EueM&΅�b�9VF!- main�iulti�|*Q@5\CiI�U�2E:P}!�My" motiv��!RIjl�>jFANTASY�a3 .#P!��y�H��%���xfHnsy2��% 8=C3esMK�+I�> by  D%?3B�@o why5 �`)@e way��iZ�)" I��b�m+i�6��g�khe MI� 2/rul"�Y9� \psiM3�RH�]V F&p&" E�$p\neq XF�*�h�inear�nonunl gat��PE��{ simu>�bio�z 1:�A3~�\��A�I���MY &y�Ieص�an)ph }}: arq& �/s"j) you' � ��-o]o!�l�er!��Zwi��vtmhifA^n'�T As a�5�; �%�any-wor@M� pre�kofQz.� you �'k your� Ak� univ� s�I�mEer'�t�w�n�� \ M���2@F?��2ZA� techn@,2evX� of!3�ȥ you I9�� I#<*xa �>a"j i�>�ly daw�& on ms%T;��=��Pt3�oEX%y� ngepurA�/��cuo�1F *�)#Yyie!��lmost-;,5���^�R��2� ��.lo,I%�*� %!R� ??u �/T'algs�Osres�O�)D s!2����9�s pz3,by Beigel, Ruvol�Spielman� brs} i�ir�dly-*�; �a�An�( "�p "�F�myv character�G�4��K\!4J�A� gA�o��� % � �fr:pp}:E�*P�!>�&� -tiAoruth-�u@\0!p�Indeed��� a]�Na�ia ra�Si�� M�as far�CI[3�2Ɔ>x�3 }\� s�3��Kv �Mx{@C��m\$*#��5��Ou ��.?&3}#{6"1 bqpdef}B�$ (yse� ed B�|ed-Eru� PolM�-Time)!-�me�A@b s $L*;�  e�"�J�&�u] RPcircu# 43���a����s $x$,"�.!q�[ōA��m��9K �q�!a a�^ %�B^ P�6' �"m !� �i)]�?$x\in L~2nAK$8e�LB�M *yJ� �s  �O5&�B�I�2�/�2/32��not��{H F� ���J�.� a�:$1��.�. 3[�?�kAF �k�2��non$7n2"��(�.Pa�2 $Admittedly�!Jlread�6r�ja/Ateq�kE�tit�s�QVOad�S Watr7�$w };3C4�D4Ahaerv�� Nave"�n};>NQP� %Q =dle&DeM �EO uangρ adh}O�� dg(o ^co�ф=}} P}$ Kfghp}A��e�-�B%D{G�1i�s"�t�xe��I��.)kONP�cbseteq>cY; teq � ��ACli; !A"�%\!<"� �3e.rX-�!X�&N Ar%G :�%�,�~ч �s� �.�AA�V�\a�4enW8J iPId��plici� .��2q��}�C��ADV &How r�|K5�5�J$)as Ber�Ai�VaziraniM1bv:G� ̗�� s do9in�>� o��՚� X�u'*0K�<�%nP;8�6� �nsJ�AYWhe� c<�w���� .B:J�X=� y CNOTI���u~}�  ancillY��� lkiz� �r ^��8e���:wr��a%�>7,]T,�-o%�ANDa�a�Aw2�y swap� �thP��lI:p��a��U~ .U�= �5� *�� ���� �ig2�gap��*�/3,2/3�9e�)^(F2-pe�3F&}% ,1-2^V'}=� a� �$p��A��S!`%\bE�+��2b 9�trong3�&\& bR&"7"� � ureN� >2 �c,!���o�le�%�/ �}s�� �PB��\  >t ,��E�5�"�F&&\Vert ,>�6�p�}}^��K}$rgV% :X�W� !��3= � >P:7]�w $\ m�8nesat2 8�" &l$nonad�'[�Y����a�$ oracl�6� A)oAk\U* of} �9D>��)YT�M^)� ��� ,�]L�/,L*inB�AQ�����-a� � @\cap D$,�%m�ied��7s (� �,!�b "ff1/6$)m�6x8 h�tnd22s6 �,e�/>qAac�6�%8 ��$_BIe!c"$e��B�IDg��� ]At��% RBU� $M�=ubm:�&|$q!:�,q_{�E&Yh ��N�M�1Y�S��ie�|5hf� �,�3 , $\�:1}{10N�.a�*)��ۅ�:��j$ U2?���nQ �B} a � b��[Mid F�($\varepsilo�0E�a,qec.��)?� �:sfFY�)'2d +1/1�aQ�,j����{+1�cŲ:�%One�=w� r�B�5A���\s g�RS�&��}1�!N���sub� Q�|atwfHrah�xe$"�urei��F(�� �Ga�A@�!M��U�!�N��i�,��a��oneUD�D2�of)� "!(�����'���[:�ny}�`�F/�VEo�a� *�{i$[x)�'tood^���9�}4e.�&�"2�� bqpp�:�"g My?�"p�C}�(K�e E�N^ "kt&jE6"�)H&f:+ R�6 arrow % 2 7�#!�*?-�(ble Boolean"�4�S��sLV0 \ x:�& x |�& E2 u�r� !*�zC\:{�{-$s<2^{n�r{$s\geq % Y(?wcaF�"�guarantel[pP#�%�s>0$.)$�&�*���l��:mi'te{�+�K-n^hsum _{��52{^W� %-0P -S "*�=09H*?@ Abra�Lnd Lloy� al},H#(ly Hadamard��n pH; �(�S�+A*�\"]w���_!.c� overqa�~"Z�:,�vt � 1/4$a�"8 N��l-5 ^{�0 n}$.}�>a� dF1:�B #:� �)$=�^5�O"F.e1�\S r#g[�m��*i *0�N n}-si>Af:�+s>*5+E"BVUe+s]g�E] ��,�s�� vSa �ak�,:ki X��5���r, q+$ /�I�:�B +f#�[-7HB> $=~r* 1%/1a�!q(�b�T)N� +>7� n}-2N�:� 6��B2�!�1����� x-ppl&Ua 2�a�.�J �� �i�iD�ӅJG6� $.ACis�a�� �)`A=Ck phi_{%�/I%-k1�1�Ep ]�BE��>s5�m!ueOn b*T�1�=�'}-�B���-��,"_!$sZ3|Y�BU<j\�I�%�wZ im!�J3��#�iA�[ -n,{]/"�6 Vʱ%-��Si��"]k 5� 2^{i�X1�*\A�A+E#2B+��4}!��N� )� :� L ) /I$ 2}$:B�Y�le +|r� P k� � � 2}QN 6}}>0.9850B�$4 �� /s$  "A( n j>��r�#9ƫR� !��;!�9�� �vai�Z�`=�y�0+1}% :��h on oQit�5de\.J:�A%!!z ٫�  (�b <^ppfig})�I�y&RC�� ��InZ-R�k o*�C.�nX =M�/3. :'M\1n%�n�E�g 2z+1>� |6WF`�v��wO��� h*� #2� ���� �`0ٯ�[AG�eJ2�od �nQ[u&W2f%RZ?B�2! leq1�y<�r[?2.3694Q?2.3869 &[?�Ms-�% %-2r�Vth��ؕ�$|EWv��m�$9��� � A�e %+�u 0get��.:�i42� %B�%FE�6�-2��Ml�" dasha)s). %\J` )!a��%"� (do� �))-�I��M:n�@}�b�>%{\� �}@U,�-aAt-)�TRUE; Q0pj�@F�@e? Q&�@Q&Geb�@10.3511�@�%�@7.755 �@!� "0.2696�@0.6428��@!(772"�@"�@.2632+&�@��!H';>�@EU��@2�@8trim=1.7in 3in 2.770122�p�@1?�Odthe �@�� con[Si�+B$"�t4*&L ion].� Y�P�� Q�M�~� to2�EŶ� =e�(�W�« f� ��[�� V�����"�A%���*�B V�A ,"�E+,=�s!�2wh�"�<$�� n"���}Y (as�kb�^�ith|\ ߆�nr �?� ger *� � \eu� "��9n���:) 6u%&a0��!8� Cj2!b�H| "� os[ "�#ly  ,� 6E��"y2�illuK%� *�{F1) M 6i1}"�B1N�8h$=^/\� �sof*Ŏ beena��K�H�: a log���ons��ڶ�m"�4�""[1,g than B�5elf^�7SteTWeinberg&�7DreIX S;)�y} �& 2:d)}�'-! IsF�oisl� � oryspace�#ByAd:�$R3/I�e�I�2Lcei phy�%V��e{2CIn!ca|-Uv� ��few��+�s��AnF� ���e�a� q ��%6a natur��ndI�^/��h�_"���R �how per�(ede�t2�Stand�M�> &%�,"ywe�7< know!RQ"elc(M�a,2) �3�$m�;! coup3xa�]Ar. valu=1ey do!O LikeW,V ativLiylyeQJ�A� lter��ve":,e Brans-Dick�oryn7o R2 I#kO,HasF&�0um)�it{J0}�P�2 an )K:/ngy�^� ���F)�!wd��&y�or�*���!TD%��!ez�_[� pporͭt?i�: W-"g5G on'sT���Og }\%�� 2� der�6s2M��)2 *n� �e.!�5 �@deutsch:dec,zurek�*`\�Aj�tudes IL}A�lex�%s,� H�A�&�oNA'�0 { cfs,hardysn�q���eurR�!��Pce�#6�$nont 9A~/���U���0al,gisin,polc �ki�� pj�-ds��%o!O�Ɂ sor)explaa o$F"�A��#,Li�<H?8,jZng��!�al�0 �A4b,'0^��o�� �o�B�R:�D�� �)p K4��9u vari�V6�b� build aF�L1: �erN>� sn�=A]�w"7 \#��=*��A cavx~ '�`���2!�& �6c!b��8ne fault-toleraQ��n�"P!���A(E�ed typ�9o�8BF�J�y��S< <";V�*�'�<V."  6?PSPACE* ?1l ? �%�Ak.)� ��,t�:��>� �Q��9]5��_I +�e m/9\����+orthcom�-survey�B��aar:np}.�� One  2�8�R�U we�l look�0y ����]��i��i�!eri,-! \�!a�� 6u%�e<I�fer��� 2��U�.��e�0-\6)< �]�Not�at!LB;e|it{not?dv< #is>"_:+=me�8(say)Y isomo�s�>asBe9a�!%U�&,�7� I do�t|Shor'sOm!�a"=i1 �aZfalsehoo�\>�.9$]U�/H{T8M0�&I 3teilV,F�@�A"a<�ye?��� QSU�Nz9S�"p/��3E a%  one.�6� `��+ I �to">0>)���aeilar %�2�e-D2�.b9�F �=� ս�5a�:m5N�^-yg�(�l{sf{nu}}���cG+��14��Egby �H(fE7,�'F;WT7�t*eIg�l� �%a.w�["� �_{x!?of� *��2l )#-D,�5b�#_{y*e"7�y�"� } gno�kizGO*�%�o&�. nuglobal}�NS&� ^+-� "n4y�bqRX&\� e)�0v�4'>=eP2�Z�4Ѽdh�B60 �&LI(itt(M�z *�&by&� ��p"I\� su�&D.�& �$!!B _i� u��^��"�F Jq�FI$1\�n�"�z3r%a�&��} �y� ��g�Q\q7(y} [c]{cc}%"-")�Aa, & 0\\ 0 & 1� : ��a�_ --ie� *). $qZ.�& $nonneg�} "N c2,886_{p� si��ly^2A$, ex�.!�� 'C����&F/�0�%�M� B r �8s.$u�x:�p}/F" \"�7)��"p}$ ra&g.4>b}�k.u��sfE�% �0�A�E�A���R�+ �QK�%B�*no � �61T��"�� � s-�[.+R"a�8����~\��{4+��PJW9�AB�)  �.��ta��$gEfE�28L% 5*wd'n6*b4,6,80-�}S�E��qv�\2�AW-�d B�2!&&� &m�9�O!'p},��vA�i*f7[�d1}�'Eh p-qx >�4�-��20 �) K$c�7ť�).�:�EtSOq��'qmat �R�( sa�x}]�4 �>�y wHn"�:y&� bE33S�o�:�~* w�I�s/�3 x�is�: $p�9��$cu)�l>8pi}1t5O 5Hv@J�i<�j,JiwI}A4.G !G�4iA So��unc�ma=S�)0$p��mnK2�)At vt �:�!�esh:X;�s�u �Uxis &J|m ][�2�� �K�!BHA]�HRO YFj $�9,b��� 6�u<�Us6a�final920���� �> '�g�H.5[8�Eqy(�3&3 guyh�wi�}M ls0v)t eH �(u� F� ZQ%>9(.C6C%��?exB�2�6�F,"�!�FlA�ny copG8��1.�z�*!Z5w!>n dN6i�]$pA/�)�2 B�NG | �g9�tensorAq"!�,> $)<H_/ICF b� �oQ32�A�t$M/C� VB Bp�A2� b}!��S"+ysetZ 4;� Es�gen� p��;A��=(-I _J��#�) ;� J>j=�*Lis W�!�o�OP6# 6� � .T$p&% Z$ Z"H�2�a-J�D�x F-�.*�UI�n $p=2%�2��0 EDp BDD,C�M�ga%� �!$or Toffoli -�m��BSbVm�aIEf 6b�X]��@$, $a_{x,1}��N � L %�i� �io��pY�] in*�� �A(��,�/le{m `�/�>Y�#��� t��[7% ��Q�M]�j] ���m%mAׁx"݄, \� "�0�81� ,N\J } CO,*,�bZRB� �{ RX, �: B o  =�*kdprod \l�_� B�1>Ui{\ijstyle\7B6 6bh �%�1�y��i�xJGj�a��v9d) �3�. x��bO}39YO9�� *7v�% c���|'� surpri��o m��`o�f�NE<i�=��lהYVtow�"��Z ng m��a�ss*Sp"t6XPROLOGUE�P"��K�s a �er5�� ��to ��si�Nw(�#�]# �a��A�orW��o�*� *?e�qah"�Q�P �H�.a R�A��{���? eans�bQ>le�[f j*�&on�(�'6F�*��<ReGZ)/f:(� ]�d@2"'�E�B_R r"�Q��Pma7$  caJb*�K o�Q T�KS9 >!J�� "�PP&�P.�BPFM4�o `e�_LW*��FST�Xb`T�a̙oqE-%�&�ch��NP}a�t � .�larM%\ "�G).F?it{M{}=1�'M��G0�>YBQ.�]^GVCG\!�8>;W�/3��[&8Dc2��F>lhCpvKDy,-3%�tu�E l1Yo8 yOba�Q�$-�A��U �:E NDH eqs�;b!c� �(icult��%�ing�!se !#%��� ��garba�&f�Y!^F_\ �A��Ae�F\�w"('�7 �()U51Nx95)p}3L/%ZllArN}s� neqH n ob8� idea= ���k��:mɅ� �Oa Tayle9*oaU�^!6>$U*M\�  .V�� :��I�Dno �� to�2f��enoughA� vergH!�-`uVP�]Hiaoy� QCHV��U9�A m  \0�G!6���7!an IV ron �"6�TF� xN(dA �)�dHa*Z"}#�iit�silene'out�Vm����;�[it{P'W=� ies:�H�R��%J�!���#b�D>�  ime $thH$, �#� t%4"�!t� % ?�n Siie � B 0}$?;�a�u���ton �)l��2-�5{ess, unFc�\:�a&�*1}} (or\+�+�t6xz$1�H)N�$t_���A�se $�---pursuo$ Schr\"{o}�Jerͺsv }hohm  bohm�/�0ell}, Nelson n }, Diek��U�d }�td �s---t��!Q�恆�A,vi���1Yful >��� stiVa�)'B^1 it � �+l� S�v fic Tmp�{�(swers� g�p� hidden-v�(bh�o�m.E�+ m appe f ^;I�A�\-�%�|�:�e�aa M.!1�#!�6E�' ��m@~""'��Sentire(�.(.!�-p(selves), ye�H�cus)�.X�futi OG=I�cY�p� 's�urW mov�Yyus sod�ym�nygpo s ��S�o�&o� e�/ qer n�3�`�� a��G}r�lpl��� XtKJ&p����5�&�l P�|���Wi�x�'��k>Pn-��� B�OޡA�� ��)�b�nA2 studQRI�n+���sVT_ cu�0: !�I�<t�je6n!mQ=E!g�Q����~^���re��imkm8 ite-"l�$al Hilbert#2i�(��{)ogo`-�=�i���&p�^��g1�lV� du,F���,`* i[�=c x�y�I�netrflo�|Ho�0a5�im0K�.���Kxio�.ca�roa����I�K!IA>גfive 1 )�F�)j�P!���jVs]�r���a�Aa h�satisf�jA >[aC�6 "-lis Ks(Y�0O !�Qi��taneousl2In�e�^��mAH �c#�TA� �De>l(YQ8e2� :� ��2(/n�z�f�+ elowu*escri� �2X�lt�/"�6{C4lxW3 of Sng6 iZz(abel{SAMPHI�o�6ofttJE(^F~2�d�[7,d�n�>�*�I�Oa�qcE�1QP �.�,pi�rOeh�5jitN5��dd�?al �z�Uynamic�yt�Ł� ve�evolv!3�#iI add! m!G�Oa�(o�c�=ledge��d�:8�u):" � jMV~2 ���?F.Inms wordTi�Z��in�n)ҵ�[��hW %�n�3we�*d lnin &0� ���nt�d�)�for"CI�er��ues zX"�+ LAN� s y�!A�Graph I&�-̔ask�e �7g+s+u�u$H$� ".c;�Fle� a�(� a ^��X�X bb{�sn/ �AJ�x3w.|VIJ����QQl"� e$�]�*S�W�stshoh� aIIZes>kx�  eI)�"%�%���aJQ!bvi�W�Ny���a�sond��� B�AstR( spitA�decq^�f/1,9%� ���aX�� li� )�sY'($. \ Thus, �if we let $\mathsf{DQP}$\ (Dynamical Quantum Polynomial-Time) be the class of problems solvable in the new model, then this already provides circumstantial evidence that $�B �Pis strictly containedp6�(. However,�U @$onger than�X. \ For I actually show!t 6Y\vs Xntire- Statist!=H Zero Knowledge, orISZK}$tpurthermore, Chapter \ref{COL}�ed�X relative to an oracle,�T\�not�:%Cx Combining� result g�P \subseteq1�E$ with9 �8 separation of B�, one ob!�!5a]u�\n:a\� �h@as well. BesidesEp�2�$\U�,!�lso%J �Pby sampling histories ��could search an unordered database of\ $N!htA��for a single \textquotedblleft mark!�tem2right\ u9 only $O\2$( N^{1/3}\#) $\}que�!�BA�Pmparison, Grover's qui� �D algorithm \cite{g(}!a4quires $\Theta ~ 2u, whilM�E�\s r NBM�G�On �>oA� handJ�!$�3!�(upper boundA�Xbest possible---so even� 5ۑ�A�cana)!� $N$-!� 5� in $1 \log �^{c�steps%�tsome fixed power $c$. \ This iAde>� NP}\�mZ 6YZ�which�,turn suggest>Zi�is Ej it{still}� �$ful enough�C solv!���0NP}$-completeu?t poly�� time. A�+$is point Ia\a8 address a�}cer�Zaany ��0ers will haveI,ce we extendU� mechanicsa�posita�!��.a unphyE�2e= \ ability�a�eY , isn't i�+ �(ly unsurprie��#c�"en-1pr���� wer!-xeviously intractable? \ I belie��he ansA$is no,E@three!Lsons. First, almostA�ry ! g�o%KkEQe5,!�u% model �I5� , se��to make�%&Ao much}1I�AյLNP}% Y\ and� n ha�9 beca AT�, efficiently!�To give e0ex%�sݻN.}��%|beW�Fn]� A��AXa nonlinear Schr\"{o}di��equř,�=��nAVAbrams�Lloyd � al}; T clos�z,imelike curv�asF Brun�Xbrun}%! Baco } (!9conjectu�O$by Deutsch @d  :tt}); or �@a measurement rul��e form��(\vert \psi\I�^{p��šny $p�f 2$,\�in6sPOST}!�ItA��8easi@eM�we �'jA9�\ if,%�n aU�state �h ��ra�N $,� l�`est�[lase� descripv�Msu�Ձ� list� A�ituH��pr"�P procedure.\footnote{! asB=-�0al}\ observed �a�6 ar�!?ing����^�=0-�Dl!4��a��R�instancE(inter!7to us ha�zaNu!5, but\^D oT =\sqrt{1-\varepsilon}� 6� + /V- 12��A��tiA�8$�it�a� .} \��jst� ����  i!k�,rst independ��$ motivated + I knowA��6�K� * ] �v, but� �Zl� ly} so]<One��define �, l�0�, ��&` sam�`operty�6allow� o. �-collapž�9s2-�$� � e�s,\�these�are vņ�l��l%8to:u� IndeA� a ke� gred��i�g s{t@c� b� ��%� cer0  kind3nob�%Zbe9�imu�}�H&� E@ More/ I=Mkbfac�at*� * t�yabout *�  i�A�m�]��vA.a��!5N$ 6 ��lyň W2��-�- �,r� �Z�2��c�wtinue�� sequY2&ME�begins � uU��� G It w� be�n!K$to find a e�!#� 2P �4�or 5%X. Th\ cond% 2GA�.� a�at�m(hidden vari�,u di!�b� A it� G val%+t � %(. � }  is g9\LtandarJ� ,%5�erefor2 a�pl� o.A. uter�So��1 "��'s�  nf] �� extr� mpu� onal��E�n�R��tbe� au��Rit{cor� (ons} betwee)y1J's=(differ�, 1� thir5�) criter%��ucces I am� sayA>mer�lA� � �\ve Graph Isomorphism und2z!� ome}-�-�A5oryW "Y, :!�th  s�f���in�ce axiom%C!�xi an*_t�Yve ;�Hra�lO7>W.F�~Y sb�R� .�A; Thus�mus�0r� �"�eGpecif�ly desigA�$to thwart < n&�� ut w�-���1��H��? �*<at,�s�Icommun� of � %p who studyV�� � s Bohmian&K1�is grea�� in&�QG calc�A ing}�6h�K]Rra� ;I�-A �al sys"Z pdh,gm}�&M�FpJ E", wcm!�� ac} particl��r�bvt d� is task mna�funda' �.ED�_,)�if*� �e� avai��I9e s�tJ�!/պGs� ce, %�a�%K2�unrea{ ic2̀�)�� �� � often l� o new� ��to� V�s;� � (wise I expe��a������� leadA�fM� ��\� 6��!8�AP sens�xiv al0y happened---��� isa5lB�of6�  grew op f work�8C��� su�2�q@ $ion. \sec {Out6nH\label{OUTLINE}} S ,s�HV}�D�8SCHROD} develop��,,atic approacp iC�Ds;,n 6`MODEL}\:dEARCH}!�a�th�.�!�lex�2�A� ry�".� ��Pe:� sB>�5in my)� �1$ MBOHM}v ra�&�>[ �`�deP��� � � modaA terprei�6-: v(OBJECTIONS}�* K�S�b����A�my5�:!iple�_aŵ � cit > Y��bas� s unaccep�p . I5� �AXIOMS}�" oduc� v` y E5�L:����iafT� � ��t��e i� Epe�(; robustnes� s!� O urb�cs;%. v<-���tY spac-�ed ��a�r>=q�>ial c4* duct�FtA�and in�!T�dF�!�f m[� !:o pure !IdeA�, a)&y� �/a�I�)c7H��QQN e�IMPOSe�aX@or! �hbot�=� Af5H ; no� �f9a� o�ver�of=�VL.�,.,�6M9l; nJ�V�^HJ� SPECIFIC}�4shift from neg"�)�v�2�FLOW}@esent� :1��hyit{fl�!�}S �cal{FT}PHsa� ed o� �\9%�d aloz)L:>�%he main� ��JQ�A�#-��da�b �is�&r� 2 iSi��69 trivi�i��!.� �_�<�.�>*�ݗ9� �,d � tane\# w�t!oall ob|\q ,it{a priori}>�� 2[� �y)(I�Yi�it{>T /:bS�bs%?i@0�e a pair of��egral"���dZ a 1931 pa�of>� N schroajer�>�*k�!5un !�p�%�uni!,o/ so+5�O� J blem` � sett�� unti%D� MNagasawan }\�A"1980'E�Idiscr�U�:&�q�"Aeer��I a�� elf-&#proof!z�u ,a matrix sca. tech� du%&Sinkhor�s �a���a� �s:�wane`con�a!V taryq�map�<e ���!hani� ��@ �,whose $i^{th/$column sum� %(�]!0�@^>�, � hjh row .e��fc2�R�o d8�pf�replace �j.Ht 5Gby�abE�e��(en normaliz G) !]sum4��J*VF��C�C��fr�`�I�C ��� no ��er�d �@�% , soAG� them��gain}B�arows  iso ��  a� ��te  �ssM�g��U) t fI�E��%�k��a�.k�I56�LSTP\jE Awp��m&O �& �vio�s� b� 2 ��J�$�t�eB�;�v��a��!�� open0���%��J3 MO�� / atten�Aj!�c�!x �*� !�:�-ssf{��M<�A�lems k�by2\&�"-� "�$�P a�%2� hy�&.2 h  \ Gi�$*�rWf� circu�a�pu�is Q re$ %eI��rr"� F� �� ��W "�,�or�V!} some�&B��-_aT� (]cho��"~ M�2 *  ad� � lly,2 -*su����constrax$�H.d�Z&u � �o*��)Q2� I��a�$�ona�a�re �it{�l s} a-dBA� (.C e��>� RESULT�esjishm����c�s �-q: �M&�)?sf;�&:�)�r�.aW% � �ZAXehhoiE� gatNta�T��2U JUGGLE}% *� @2E(juggleA B ineR,a cruwing*|���B�u�Em�8�c` ( *� a\I�< + b6 ) /\U!2}$��nU -#X �U� go���, u19� tobc2{ �UǕ+2�:�vnd-2R�$,�EY� (in8��'2�&�,)�.26|A�~|@�d��hig2%M� �icultyq��s needp ��%?� ny}aZJ. Next,6 SZK}�xm�B �a*� of Vali~ �Vaziranip vv��o���("9sf p�- ���4,� B �'�ulaF/t B�� Axim� Short�$Vector\%�in�$.�-y:�" appl�Ł*F� "�-$�+&B-in j-�,6k-b-��'- > $�,���a�.In clud�6�DISC}\)��a dir`��fu0���.�He-V�-a1T�ies�HV�upp�{wee+(&N\�s N$\>� $U��k�v% \[ �rF�'$=\alpha_{1* & 1�� +\cdots+,N.,U- , , \] w'!2�6R ,\lR,�:Hɓ���orthog!� ��Let�UHN�bet�� +n�.��" w �x ocha82 �$S��+A�ve6a�� ab�,ies�\�"��arrow{p}D( [ \b�#{�(y} [c]{c�r�t��1�1}-�� ^{2}\\ \v!r F1NB1% \endl O]�in�dg �&N .�F���� �R�q��)��� 0���vf$!"_yeE� The z!(ME2a)�2�$: {q igno%|APi[ E>1{pP � � :�S_{��� PT}n{c>d)MF} & �' ]c0 �`E�J� & 4N�=_J�0�� Fm�� i�H� @ -�  &r5��< �/ 6*@%��Q !3.%�hy�,H!ty�!�$em#�� re� m@ tely�!l '�r� A_no &�onnɏ"� �4Daffairs at earlierm la�6�b� �(�!��A�# �d$U��t�� how,�%j�$o�,5� JV ~VC"�!$ $S$\ �b*fun!5�'}!i�nd�of.�N�m�is i��4�)aky�� �*�L�9U$ �($\pi/4$\ ro���95 +mA#le/.(.�B�-=:U K6� and2� - %:p2 :q*� �q!B�2�6� �щ :SASm a��S�6�6R ,U �) -CR.��00 & 0\\ 1 & 1N� *�as6�R> �:6��:R���\\ �V�� O���7�>2,Z&$S$�}�%�N4�=eo+re f���'S�Zmy�$N�F8=#EnE�. Vts� �edi����&�# perf��c1�<�ogle72�A�SoH �8�51among�mM&�#p :�%R#��!"} &O/ ws+ down� w�ul''%���*�r%�investi� �hPZ��iB��6�lU�gx>}�:a famil;���&��{���(} _{N\geq1�< 5$S��$\1 andimenY"alV#�� $\rho�U+*- N/ \ o�.y sJ� ��}rho>|I)�o�( supp69 the i?�� N$$7�)�e)�� occa ���s 5s N&*�PT!or*�"\!�c����Am".(( \ Also, if�rho.�Fh�\laa.T �� s a &�$ I may I�����4�)ᦖ .�.��2� �1( M\� )Ayij!Sde6!7) r%:!H>�!� 6G�%�$M����lS:laA!�Q�oh&��2�0.�B� af� $� sXd,�di��itR* BSBe"\ b�0�TEGttinimumA���$�.�*- mar_"lq$���(� $j\in%3 \{ 1} $,\v�' {0pt� [ \sum_{iu�:jNm�.�i� ( Ua U^{-� Ejj}� {.i] >say�sZlz�2� >BI.UA� 2� _�"Wz/B;ual B�I . O��it��b�ven�5v-f| � �#S$�elfp!�I� $P.W.dajo�}�{8i, �e�i� ( P.�j9�R� !�.1i&�B��YP�M� � �NHA�q$e 6�J?nJ�� �0�$E2��&�Fd��\v] ^ixAy)� $P�nn"Mz( >D:�Fu/1�N_A".�:�drawback im V�0he #R�A��,)-�y}>et ar=By8�, adop��'A؁��h�K6��im_.�:IIv0^{+}} ��4�famou� � is'0&� ' bohm_M$$in�7��.`09N�i�!m!� �wG Hilb[@�C!\�l�/"q mox4ATF�mo�Hit�=�ja�-o6= b&@!Ainuous}�omB for �%ev5 �*xI"rB�@isf=�E �  LiM�q@" RB"b��'��� � osS�!YinN�.z Jzt= $t_{0}y&v 9� �>A*n:�~:�� &�u1�m� � "L  re� �+�EonJ�E�opy $0$�� * * alw .e> An=9��R1!�t:S �nL\� 99J��0a $1/2$*���;A�� GHQz�%X�:.&2BPute�e!;a�'p& servG/eY&<'�$ult breaks� beca� �e 2p$ wave".2�n\ �LI_0 1}$i(degenerate,% Y aMt� conc!��?on 6�H��6"�*2=, �#y} .�a.�GtJD7!�AI6�'%E2�9�gin�atJ �!.b�G!a!ll&�9�'K*�� �my view��st�2�s����ol� at l�-i bl�holy(5B,���f�* atur�)  length�+De ($10^{-33}$ cm);M+s-are_E- in"�gra�4�) rs};f,$��d"`�i� !� though�% ��e� �&*u!1J;%�i�� of [um fie%7;\) � ausi�ana�K2�a� hyper!�)?J�;�+E�p�Oe��' rais�Ai"D�$�}umf�si�Of cour�9A %� *� �=@ofF�,�bm Nelson2�-�n��, � Hiley'�K.�.in."824�)�bh%E��/ not ! why�prefe�!Dto �z"�AU� �4M�um-inB%��per� �P,|isZ2m#Aqto ��abs�<"7 ---x*REa� bitrg.��.� 2�!�� at doeGt[Iut^?"f3 %M�# *[1&�)�4i="b;A�(idem-A5A*�9 6�s;�Dickso�/d <}, BacciagaluppiE! * -�d}�Ind DiekQ[d }\G �!�" 8E���l assumZI�')h�$y9bBem�"�$ 5-'4SInV�, 2u�8� W!5�G !�y��ll:g, �0y "%&U��!_4���N &m&H �"�S+%�.d�sessed~p�G2$m]�?�|�cur�� �!DiMul� �Qe�C�#*� s�8CG J�'�o6 ck a#)eAGQ�!;�iJ 'R+I*�; Lfixaa&&# &#��nj�B�'I� n el�L%� a�6�Aiss��{Y@ ix=La�e � VlsaxPFin��:�w � !"efs?.-&�,6X�Gr!�th6 g}eJGell-Man� Hartle�9g�9�6Xa0 igns!|&�#�2varP*{-i8�M3E�1�8�\�"2�uK cR�)&�Eos�-�T!�neglig A�Ln�Vpeaking)� sit1OsTr-)X�OP� �precisS�one =L�$�Z&� �voided:�O.2�*�> } H�,]I*8xre �0�� 6: & ?!'�M�, I�Ni��b�a�E ! yT*k WWa!�-_r"(E!�5�� , ac�!�.�8he Kochen-Speck�orem,\�� asA�}� s, 2 ��EuHG*�H@�9e e69�]�!tA} i�i/a���D�6&�! �?#�4a�IA\���postui +�6o:�'Af�2; 1inguish� Driw sVJ.nD���e&�Q� ny-���Ak&�6�!h 6�Q� �:!%As��9��v,VS�=%wa��1=&� )s!t! xAA�^TovADim*: ��� . A�7 u#%�CA�A�a&� Y"A�� U[>z7�&1g6�=.� .�>MM5Z)  6�Olye,di�\� %�eval�N-&:21InMwords�U�+%92�F' O��YV,W�e �X:�� )4FP,WV�d neq � V8.�:$,W721Nih�(�Zmi. ;@ made by Gillespi�?})A����Hru�U&Z�Iqpt�]�!TC��y:�dToH c,��!�am3ll.�U$%�>no��xKT:�\ �a $U=WV-�$=�J[�)�1)�1�$��ppl84$Vde�y� #F&b �gh����(�$ is, decre3h6� o� 0$);�1�Xnw �\A�a��T'sal���be un�9��_15�#FBF!�:E &�v,v�N�Q�Q]��=l."2�*%�2uNO&:&$.�7>�@F�!c�associ!a���=e,��K �W�\ deci03!Q�is�e =<h9 8sc�b;�$aexas;%�c ��w� � �KiP�}�$fO&orAJ�*a��W$B g��� b �>�?!� $d%�i2F /dt=iH_{t)�^'�a�3]�%��Brib8R$:^-{p}|�%�=%� $dF=$/d\tau=A_{}F!% �s��x�5�]� a"��ame�!Q /dt$��;A0d�cs��%iT �9&���&A&Iō;.� pec7ra�2Ii�6K"�&6�&&2,H�!}� ,� �Y�`��=T�S$� ��( temporal >of��,"�IO�U�? tunau(�?%Fa�Pen ent�$d�(� i` :#.�=,r�- ncil�,��@�: �qX�R- c!W �:I �\o�Aty"@a� cha�O�-�a�n*N�---%QJ2 dit 0send superlumA# L al�%_u8"��Y un� l � ethe�X� iAJS�) Hşb�4MD} I �Y� f�?a E�"4 %���F ���(�] bf{I*�J.k!q'�T�S*�#� 1%$ block-dia`4?n A��m?6dU2(IA�!�  st 4or��r(Z�,reof.��Ly� "� D�U�4� t $B"�7�%{ R"%*�Z �"� _�=0$�1 $i\in B,j�b 6 $i,j!� �;��all). s $B� -$� x:�#jy ryIn� t�arC�c�N?at �n �I]�!���Ntensor�d�5sN*\#H}_{A}\o7 s79 2Bg%DZ y'E�ac� �e�)"}9A��\&�  n��*�D -4��i�%�2 �)��%BV! %� � %j�Jj_NJ�"i� '$)e.���xj 6d#. �" as w hq�R"�Oe�Aa7or�;S?a���in��i�! J errors %�I or5�(�CAJ6Y(e�ity� S"�9 �h0 $\widetilde{�}=U�by�P�BQ��1�u� �G velyw .b*�B s $p1n�"� a p&�e$q2�m�0-,|.=)%�\V"&�#��,UMl) -06�M�T_{\inftyhq[$ 1}{pv( �9)  $Ml @�+ M=\max�� +e  *�+�� �"��hei{.e��}- 9� y\leq1/�{� �/�4.UU}-X �OEY�an �4rt >dvantagQ8r �um67f:a�!:6.<"� p0s0(*cm2a$U�7�+U_-D\ le�,[ce � 0olovay-KitaevA�� (� �k:ec,nc})#�6iEDl���VFMc "�� �d$*N'U+%>( \log^{c}1/&)�!�\;heaL ��C. ��I.rho_{ABe��bi1$#C �d�5 !;A�$U�R�^ ��`Z$AMTB$6  \!BnOY*GHmea,��� in$ m:y� w�1is � )�:�%��U�< �$-!��z)O*Z��%% #Am��*�-=.`G`B`=�5n]9� 5 �- 5�PMF�.J(4.'�TeaAit�.A�6� �Us �?.�� �vJf.�)a���F�( A2I�)$*� De;!�%I"�VE�.�V�T�I% <.�*=e/=1}^{N}pp/,!���i:� "li $@ �!*&�1�!a% y6�E�AN� bL!0` !��%.�z.b��4=�m}���5)K},? (ii)_�a�0D"�)� E=f=/�Mun� �!�$o"�*ng� �@COMPARE[ T�cx�O*)u�Zpe� bR a��Tthe-]ve �%W�B]�@qJ�*W �4i:PHV�"�je�j1=B?-es � �Q�2� �n)�q iy  \ "!�C�!:e5~a�Dy"�'it"�M .N:A�n�2a"�Oy.� ���/N$wo qubits,^�E�,9ɔ�s^U!��e2,�AnTh(. Recogniz il>NP"pro�!jU alterVh A��$u�X� ing.&*) [($�C�Fn�6 ion)� he w�&CPdef���or�pIoel�,o�E � ol'al��.�B_{m}�=e %� (s "0)A7� �1�)�� �d!�8�-'�bs, ci��j{ .%�j2 $B_{kthse�0��F�1=U J 4�6jjk/{��� hat{j}�n�;(�26a4A4%  }}�E� ��aL �J�0C�c2#ng�itI-�2 ory}$9?H}D�V.aQ.~^ &"lio�Zq�S," &�>j$";^(ori�(� � !�A]�s x ZGr�S`$0$'o*kt�?y �a�� nonzAx��#FU_"�;Qe�inKW �7%h�:� �vAN�YB�:!���>�B/e4E�� 16.1bo"ich�e� fouO(Ō3 y.Mb�FtB}�Ftabular�Fl} &:� (� ) .A (�T6� (�\) &��� (:� )\\ ."$ & No & YeBD\\ *� * ?\\ 2X 6%*No\\ �6� - q.Yev^� N2No�?5U i)x \ca�'[F!�b�Q;%�yq3]{�;!a�;}�le��|�q�K& =�!�.�.�� M� toge�i�A��CAIp/!x!6a�s3 w�?naW��2? �tQ?7 �t�[� � I,D �R`-��a} K: 29w!uat #ose �-��2��dnyV�t&T � fail��7�e�>aWQ &�)�h%%�l*  n�n�$mE�_x� t�%!�~!6�&Zem}Q�nogo}NG5:�Q`�p�12xjnE#/.M�c��H[} A+�$*Q0l&� a;��!���r N� � �& 00\2� *�3 116}{\QR�"��\�!aaF8$ `F!�%�}Z -�"woOa\ $-�F8$\>? 2B y%1< align*} U�6� 6��I=yn' �1�0Ucos%M{\pi}{8 RS -\sinb-:d+j- 1B�j�>�)) ,\\)$�=):UN^ �1}�M!~!'R2�GF8F�6=&�6m_Qv�$:@E�value�QɄ"�F?tz U^A�Ci/ I��;ZE= U[t�Bvi7.[:k Yqdka�4224>�aea�3d�If�� � " A��y��:$que `path'5'x0!to  �&� �+��2�� +1n� � So%Pr%� [ EI�]�Iqv .4> 9}�2}a2GPf*H9apE/ar�y�:�i%#B<Rg*�4}-~0>! jREW3:U!� 2�A%�^d�G핅Gm( markU!$�"onship"�)5UO`ref8�)Bell's�S���AF�%W��h�.g, t!��� c1s~Iimmed�%�/% � 2�!�2 ����w<?�5�f reX*&"�7�I �!5�se�A�;JV$%]FN� J��$ an�.�5Y� exploitEua %S�"�tig%�]n ''s qy�)at-�a�w!`9e�,)#EQ'.{ e nex~��`'s *AAkbA"; "L � 2}\quad%enumerat���[(i)]� >.� .��l� X6Y�C��4E��^�NQ,�uA .7^[_&�,�d��J� $�i.c:|X { !*�#{�� sK�d.��V%�} � ����� ajH�8a��X�  R (��}� �b�Pp / & � �W�  �T�  � arraz���P1=�vagy� (-O �R8J�in w%>�,-p1F9�$ ?�'a mp�4S2�, B} R��- ^:�,9� �) &�Rb�1#RvcQ!fr�g 2�� &��R�R:So���F,��($II�:T )0M)6xeq*�>I*m�� 5&N /2�&�MmN�F�5oIN�&e�.�>$ M �6�>-,�.� )j�2R1�`� R�Ib� �� �!� � 6b�[�m"G6GVz��$Abrho#l00}��Z'11'�Z'�NR��5P4� 1}{4��Zk3 B.� is��;�5=�E0' �0B�A+ Ɋ�T4 a�.i*�%�0M�o�0be halfn Nn�w:vN�e,[&qca8g�Ni�R��epi.=+N7�T 7��67}% {2� So��.x1�6.K 6�U6f)>Yk �x( &_'N�YI��e�::�p�:�JR11}+0aS-m1)Bb�N�6F MN�.� 5�j�R�F5\p�G�%_ �-aS�r$�� �!�)B^ + ���)6�4M�)�R�l��{ 2�2� (yEW�v�f _{01��& Vm �/�/�[.�F��()`2Ff�S1&gS\\��N� u) F� �R/�x���2� tr�29 >(  Not k4A/t�cocU "o�t }"*$)��es�K al--<�$"|1#@ &  � P� &�">7.L2�vE�rI�]la��2�2�!%8n�� 8F�2�a��I��in�J>�l.���� !�./*>0�L :�Tdelta>0!�; <$,.�+�BE,a7q F$���_A&� _!*T."9 -"� di I�,��׍23;lS"6�U�|��VT 0_ 4_ɨ.��ž.\\f/F.q�N�rh����2)S�ȩ+�: + &��>�B! 2-SGh :/-3�� Fi:�->�>�����Qb�Z&�: !5],��!�%aA^)a~ Y�:0�xMF�0V�= �B��K2Dd���er&�tj�X*��y�2P$ ra a��s&.J&SepO �# �notFGy givp up2�,���;an}�y��� ��,3is������:� [ {MD�ɑ�Y� SPEC؀>� p��p$non(}Y<mpl�f�:� ies:!x .�$i:.mFLOW}�!�:�#5N�7�!S��� 7�U�# �y �_�e� ah2�88b�zi?( a we�-ed �medqOph�n��.��� o��!�g܌�8oiq� n�K+G2v*P6� �\��R��%i� &0i N �>E~�r(�� �2ci:#N� J�i:/1N�Rb��ba"�n.�l bT�(4A08 bKiBu��i6*��IoFIoD �w)���o +j�n�c( bIF /�H��!4netPN$G( h�din Figur. ef{a��fig}.% %TCIMACRO{\FRAME{ftbpFU}{3.4803in}{1.778 �_{\Qcb{Af(u�%6�A sour�;�< ink)�|"̓�,}w�  %,� mF�$�ZQlb�} $.eps}% %{\N?{ �uage "SL�t��`Word"; type "GRAPHIC"; %k{�-aAt-�|o TRUE; �@,play "USEDEFAvalid_f��"FAwidth 1A ; h�� 1-IG$epth 0pt; �l- 8,10.3511in; %�l- B7.755 crop�� "0.1367�top 9215��E803(bottom 4703+�n-'A !G';-�� "XNPEU";}�,%BY*Expan�5�fEj} [ptb]�Per} \�U���ics[ trim=1.414995in 3.647223in 2.031921in 0.608775in, ) =1O�� dth=1q ]% . &z)V�qCE.�&bJF]Y� U�UtцV� B\a�:���%�!�a�� 5P�`1r %End9�"2 m�aHex $s� � ktnd�: �poutput <ic�ŎL"y.3=s2�16��8�; N6"� Each edg"�$B X( 2�t6�&�$\u"W�� �"�s2l4�s$, -0}P�a_ ;6o�ef :&K\em�� V�>:�ijC q-�v�:{,t\2}Ra�zu6o� %�A"#V"ZP�wEVp*K[e �/A��s�pC&wi�X�3g a5h%k~s.6R� &r�ly,�D��� �9�%�S*�?=of it)�+� I�WcknM��w� b�Yl�!f%�M-2� ��A�d�]��v�%�\&1?v ( ��:9^{1.�b}$)!#s"�iE|Id rMEeF�=�t^,�>s4apping ��c� 7E%� h�_#W�3"q ��{�M@� a �1�1n)�MT��4 B60}@A��anEBE�"3TnyO:b�.��� s�=*��IPsI�^(`[ �� s.g=clrs}��L>V2($�@:^C�r��ut�D�(Asi�4s�� � $t$;�5\�)}\9 a cuTF�zge/=MeNs c��a;nd � � &-�jMa6��>�%}\ m>ff}��i 3E+um]$le>�E\�c�'��%�]��R!�cut�Us�~a"h$���/x*27"x"%��"�A+}O�~�i�E6�edB��4G�"Q��gin�B$e abovLLu�X!�.n � $C�� �^ �at[�st $1e��+A"�+ 6y#i&�k V�F suchU8$\�rw�� \not�ͷA�$B�m�E�p7bI���2mj� a C�E�$C�)o�e�$aR]6� *�>x�G2�G!A A�,) j�7 �_��6�[e��los�Cgeb-�A�!� ��[���vS�{�-/i:ham) .F(j�+ 6VH B.��F 5 �,~ �2:�n�.T�(�gw�'�Bt4ek  ine�ity� \ �i �i��5��" ( 1- EJ�~F�D� j�9"�:�K1�oh}���} 1�j�d ��mJ=݁�V% . �maxeq� ΅|w9LLxed�� "����r%8-� $eW� (K, k) D� �;�ps6��tIL1�[) �JP�iN;0 �is�P��2laЌt eigeni�$\lambda�(%��emi4mitQ� �U]6�:�e�%� M;A�6�u_Y�r�Aa�F. Ja�&yv $j.;!&27 W=X:N1j)e6F��m�6�N.9�Hk�PEaH�4&�2�@L�P�EsPLn�RM.{ -I�1G �:��\E��r��HN2"D3nspd46dN.:!� Bh�vl $L�1S�J� Di��fiY@��-�JMA�o�2��le ��(.AJD��6� x�B���"�11r�:�$'�.�.�-�'b.M^V��%Qd!  L3�C$L�RZu"� �%Kr�9� 6�.�i|F�){) ?b2J%�N ^�!�K J%F��Z�J�0e �Lasczv&��E:�SoA���'y5��a!�A�[=������%�2�-}q�,4$P#=1+!   1+B6h� �E�,~% )l6��N%B2w /�D |63-i N ��I��� tack2� gamm���%��+.� -"J|- =1\\ �`�6>V%&܈E�2/NXF�A42K ���1�7 b��JvB��} ��wI� 4eA 9�U GP ()g-�� �Q 6:%cʓ�gmm� } O>�~ 2�5���Xr=ZC� -_GR$|" ClPry jXi(vex�Stop�qRE1�� !��8 sser�� nemp�r��a1)�$f^{\ast!;f7�6���f�a|llo�5@� f_�) Xٺxum� #� md $flB�JA}R � >2�a"=a Ba %�*\$.TEh 11}=h�N%! C�^+Vlo��!bAA\ ��;��co: ^Q,a�� i�IX9+to �a1+�8lDg��2�=th��M�i-�) N+j-.u"dx� "�]%J = >3}6�e��!�AsYcu m92,EHV}x�$.}�qeas�HW��sN % by �eF۝�, �)�6�$2atak@a�z�zc R8dJ 6TNche�|6 \c�6dn%��./+G!1Sho�L��BL�;AM�Na�Y�?Our �:��(Ford-Fulkerpa:�ff5%�{��UIp����!u��%L"2��p&�5U�N��ej�d)E}6f=� !er�}>��G��an"�Ky�90=��7"��d" � s $eD aePN,/[%!i��;� y $c�:�nd ����?.U2w$A/It Lb�3*���e a f׈t�n�z1@)�ts��un�<����n P-��!=� ival�oIlV1 �0@S"8[2�wew5y.G[G}�8QPA�a l� ��%D�j /EY:�-!?%����o֕)��G�m��a ���:���0*I\9e|D�[nb5�j�e31}$� � V$ BlIpso�>upEfE`�*[+f�tm�he)ɍ �0G!����s}#wa�<�Alai�b�^ all ���l0Q�m\< �h �C� &,f}A�-�-�� A1 le.�.U "�.�Em�<m>3�:)���=�is4Tәad!x24!�o:]&�St7�be6Ksub�vA�.�� .w6�u S���y� hang��� �==:�]��9 � �/9t7>�\&F]!mf�\! �0.�0U6�\�O��n=imagi� $N�2N$�����@p()d-bqG�ax �>#�1�E�#:,U}I�^1 8 9%�! d"^�)!L4 .�OU�f:�|_ `e x5 �n�.:�sN B�� q� s!06�;i6�$T�/ r.� r 6;:� .U�[ ��jj�z F�Tjj �� ��%�4Eb}{L2�_� eטl�L(��c��nno��mS�o�6P�2�}.) �&y&Y�����T��^��e�)QY"� �&� ��H�V͌�͊�/�Um�y ��^X \�Y >I��"Q%�$�Hae( `3) � ��!����� G^�(�7"<r����� � &�(�#%}�BE%�Uach $i���#, w (3#%��r�*�v��, IV�of��� �\ }=� ���6+)a |olline{e�� �,�b�Ml<c�A�"%8�~f.f��Ec�"K"� � IT�Nq�gk�x!a�"�A i}$'.�LI�ast }=��-�b ��3NY��kway[�5AM��& � �# tart� eI&� repe�lyJ�e�ctN��IyO�rW sF &����&, >�*9 .�0 m�!� a녇*�8a�i5��.�A"d u��\In�/$������"�) >k�Wv"1�� �t� Ab�l!�b� �j�n���"Ej!&:}:p�{�y6j b.F����E�NA�2]Gfu��L����2T� Like�[,�Qw� �,>����  3J{�P�2�A~t B�.��!8.�*�>}==Y��A �NQ$\8�E/��ޅ� ���ž-dF���de "��,:e� �m">J�- n upF��<��~2!�Put%�'���xi�B���Mt���V%M%)Y:%�L���v��!��=��AG�����wayVyw�Q: n�_. �.�.1%�wR�m�j:��BZ*e�.) �8�"�?�\�P�sB�?�aari=�V Sa��&�*ZP@!B(*a$���6�%�rQb����f��by�deE!�=:\� (�OF���6�B:JCJ�n!�phi_{�X��J�a $2$-�X�Y�i ~ �C4}^*_^!b��p6��syVA�%MYE�XY&��5�!!�� " =o6_!BC&4C�"�hI^l.<":i .wi�oN�j#�[I���n�We omitB�Ҷ breA� �;:'o/0B@ via ��Ao��.&vng---T�e�Ձf�me upưa"e��,aV6mr{rS8�2ri��-q2��>.bL/>����3~%��tl�ivelop^ Fortet �/ }, Beu� g b },bf�e�u�N My.R�t��(!xy���)1�e� �&]�,��fb��cceT`l�e�E=+�3E�-�!6� ���o!�er��)h+w!�I2nk�coXxt�� : as(v|� �w{aj��2stU�#.ak$�(5r�����`j��>of.ki. M� � tea����u�i"��-�,)�,na$�,..&���.�y�!y �=Ō�e�v ��j�sWk�=a*yoc!��Q �I e� z΄1C�b2b���2����K�hF��΍bGss*E�!�ere�Z a g�/zed�8�:&,iIn�( r,c� �-m�,a�A�ˈ/er� _!�Ve!�.reF�l�YE�Zb�3� 1"� ��9�E��� La��n2L �\ s (�Xne!�a g$1$).���qbiA���x�r�se�� ( 2��1!A�% ces}�G��,fl,lswABA��KM�� E�y�&�;�$A&R�"�$K�K��5%� 9�g�5I� �6bӅ ,UvcR�$U&��F\"�bqm7�" 2�\�] ij}:2� 8&- B�� Wa=0is��a d#D"̽ɬ�Uierk%a�A7Ns���U3 $� �RL. 1f( +BH6A!/�HN")l#.gi!�<{coleq+Io1�Y�o1jF�N�HNj6�f�"�1roweq�"U} I�g�D��� 0 �v M�]1�j%�d߀��rqm V7a�=quilibri�7"���w;1`s�1)d) h(�1 �)�X�!lbAdmitted�'f3�^<7�X� �mpl�la�\��'JzcU �w ���\K6i���6��V .SH2��\"JbYam��2�!benigRC�"Ln�O ^j!�� &I�G���wx/a�#֑&�  %>,.�� &�.)�`-�b�% !���{!3� ntu!� aF�� ch�u]G ��u^o. ��t7� ^7D $th5ĠNYMJq 2t+1�2tuu� ;A'/_�!g�kN�2t-2\k}%&���^0j}uF � 61+M)l2S T;O��BY�z�Z&k�V�Z2ij>�I�r�iwe � \2a6�$m���E-�y�� �qZU�_ 1!.<i}$; �)I�>�=zZ��K�:o�fٞB����%�!�B�" cru'�fac�=�!Hf��D �\Q������req�a����f � S��-�N��^,!/d,� ٍ!F� progm� me͒2"��\`6J# KullK-Le9�r�tqqS# *�@g)}�Ct*7\��*|-b� ^��s3z<*�@A!l��AF1v A�A�F �0,U &�U an B�0Tn(���N>�0 � e�. X�e 1)] �j}=0$� ��fa:m FNE � T2T"� +�N�R�.�-y O3 O&- ONjOf�yO $j��� = �Pny).array,Y�Q����)Z٨��=% *$Nd�� �& its_��kM:L {\di&Mstyle��22 6�J5�R��1�^{!sj�xwEQwe "q�A�veq�$0^�lC��"P) $� 6� geq  .9sl X")]z�B�+�=odW5 ep $I$�  $CY9.�=\{ R�.(-=G�%$:��  Ux-}2( ;� Ar%����F�)�R� 9�A�9f) $2t��� � ��had"zl}% j��S.�%�y:��jCxiI#of���m�mj�5���� V;ce7 ��jP$$'s\ occur~�2- .�N�.�iJ:RbZ�KculushJ2 !�&� 9�ofj� �xis ]�� �� >�:�.�� S�QS� ��3J2�.�`f�� �6r!W d�} B} \~ '��not4Y36��Mw - ed aH>,f��=Jre ��2T&6fa2�B3 h�H&!$U�=�6�# �@x�5 +?i �;& dq>.�*�� .%�$1*� tAD7 4} &��2[8&Zg6�0)t'��,) $Kr��}\$�kc��A�#�Oaai�r"� q*� Rasq��&`�D�"@$'s�$I�O2 Zeu" �B!�S[Q ntry�� .,&ݺa� ����"���NN�2ݍaW A����we �&fh�(&� �"ҼB*�rea��V� 2%*:��BL�/�� �,cT"qA$"�the>�!)#*&�"z�i�v)�6�"(Qtis�:.;�0!K:"�Ys"�s� *�9y���pˆ:|&��2P: bB6XBP%�~vpsFl�Ny&(�$"q&,�&w" � I�9c Vl�4B'UI� H}�&I�e��&vKB�!�4Then we claim Dthat% \[ S\left( �\vert \psi\right\rangle ,U_{A}\otimes I  ) = ? :>.NB) Kd. \] The reason is simply �| multiplying all amplitudes in $:w Fx$ and $ ���N-�@by a constant factor $\alpha_{x}$, as we do for each basis state .�x\�-E $ ofB� _{B}2'� $, has no effect on the scaling procedure %"$produces $-�B�B� -��@) $. \ Similarly�I1�U�Ab_/-Ec1 ) E$It followsE<% \begin{align*}j^A:U:��-3F��Z� &Y� �A}Y] a@But(ehJ 5=6U �B�)�.�F�< \vspace{0pt}\\ 2�B�>=1. �6E J�imB-^� :�1 pQ�. \end5�  proof} Oi$Pother hand, numerical�Qulations�g dily showEU� $\mathcal{ST}% $\ violates decomposi<� invariance, even when $N=2$ (I omit �=crete ex��e�'8brevity). \secO{��Comput��al Model\label{MODEL}} I now explain� (histories m1�V� H, build�1up to3  ,lexity class �sf{DQP}� Fromkon,4 ��*rho$\),wK nsider wi��$lways be p�� 4��Pell=\log_{2}N$ qubits�j$That is, $[=:Q)�Q� lɆaX Ũ$\!�re�� *(��(=\sum_{x\in ({ 0,1 M} ^{� }}% �� *R6�A�] ŷ$algorithms�$this chapt1!work un!1L\textit{any} hidden-ER ble theor��satisf!��Dindifference axiom!EJ�if��@take into account)�E�IAh$(let alonel(0ory\ (namely �FT}$) M9� both:�nd� . L!N quantumm�e��vn !i��t!.$0M�I� ^{�8E�n$nd suppose%!p a sequE�U}=E�(�8 1},\ldots��T� ��\A�-� oper�}s, each which is � em)� 8polynomial-size�ircuitA�T�a5���y} of 1� Q� through!�-3�\ .�H� v_{0�v_2��*� s,� $v_{t}$UaN~X's value immediately af!�- 3!p ied (thusM0-g� 6��G��)�)! Given anyZ�]T!�8we can obtain a� babil��distribu�A $\Omega-���U}, :�vA��>by just�a 6�\a�ea�lya�c��E'-",�_ �!\Hstochastic matrices��N�r9A�1Y�,~~ CI��%��G22Gi P� T-1}\ca- U_x&�r�%H =c� NotA�aY=� 5�f�,is a Markov .�;��iq�.�(independenta!� %(i}$'s condiA3edM t-1a�^+1Admitte%��`could �i�preci��ay�j�^��a�bi��?EUT2�i��7quotedbl!� sliced2% \ ���on! [s\:� But l �� in S� X \ref{OBJECTIONS}, such ۥx� granulara�of �Y�$is unavoid��\f-� than}�PT}$. �?Z=��=���Oi+(�]�$\�ԁj raclM�>s a^put�~o� v�teger $��͙��of>; Z ՜eq1a;i�a�6���a� l*; Here2��� specif��Ũ�A/( g_{t,Ymt\E=) �*�&�� osen f somef�=yGI ��� -`F��6return%�out%� sN <( n \ �a���y2: 2��f�defe�p� ously� Now ErA$EL$ determini�k � T� machinMk is g�) acc� to�*�!bX$$A$ receivA�� !<$x$, mak si� t queu NsV4� "ua?)�bas�_!vresponse�We say a,����ngs $L$!�a(� \� � � e!b��a for sufficien� large $n$��i�s $n� n}$, �Z� ��Y�T}$ "�n*� n. � s,�corre! deci�whe� � L� ; pr&�8at least $2/3$,!q*y $n�r me%�i�,remarks abou� e veI���!�Th�Bi_0real signific�^)� quir� %p�bK.��MA�, !� i, a�Ely g jk}�� E�I mada0W oiceO  becauselIesh�Dupper bounds; it m��interest1 o ��6l�?co� However, aspec +:�%a are ,� �%a�or�$��rs$ ters;� wan�nm�A�%L> ���z=� E�652�AAlso,xr)� ro succ~�%Q)^Bbsi by!&o� am�en� &,  $q�jN�j �a�2f !!O>�AZ adWry )�eas=mak �inmq�"�numberYin�ce� \sub�0Basic Resultsz4RESULTS}} HavA,%��] jJi�A�fP I establish its most�0ica�pertiIi Firs% a�"� E sf{BQP} �teq2A*. �5����d �h(as powerful�!$ dard&�&�A6F v# � f� h6� vX��edA&�S� N� $,na�se4s��E%�!��E�a�R� $� $�VD��>���en measY�)5~!' A key fur��observ�!|��ing��~ em} M�(anyuniv}Any�E�&U\ yield�]mN 2�Y("�BJe�mea6at� � y �x (� or;)�be!}"�,��p��ncill�������Y G}$\!m2^{\primebNe)w��� e�>x Zv Va&8 � $-�-iVe'���E݂� ov8 ��G| We h $T,S =O�'\� ator�*{�K� n\�   I���iI� lengthA�WS^assume }!�los��generae�z{ \geq n$,����w�eq�$insert $n-�$ dummy� J��@�  (b�p.N �` is \�Ja6�sTWe�2�&Z]5UE, y an�F�J�.7Us|�H2H9�~E.��t&c�6� "=NE5�GA 0n particular,iwll $tA-, \V�U�-\EM  _{\inftEj q2^{%� ^{2}� \�>!�4Solovay-Kitaev�,orem \cite{k:ec,nc}�c�� eis\ u.$n�e{ �Qf0 y$���iq�$; morea�Ake#%A:�$\�b� trucA�in�u� � !1�� N� -�N�!� �� =)�cN�zh�3�6c�2l luNr$. \ No@i��I�.o1q4-�v$,B� vE� 22�I�6 -:+ F^ 1YU��\lE񁿭g fm:[_;�� -%:�R�+6t $) �� T2� T�V4 =+e��( �-1T T},�alH � M�%#9.|0���0 �1� x X5{=0���y ~R.$$\ denotes��(ximum entryŒ�I betw? two ve�"��Lbb{C}^{-L}�M; i�aa�orNZ $PAYqo U O�joint� �v V ce�r�ze�T .T-�velNnS the F+ r e"7.�$q$\ "Bc.v6wB9�A�1/"� 1G)�� � [FJt-1� 9Q*N��2� E�UO��, t� .�%�-5rb]ak3aH}�� ��%R� s!h��� 65��Z�6x�$:� D2�V�6K��R�=Re�for> ��!Y %�\v!$tI R��Now� � F+�d\6�.� O&*Vf�%b.6&�UY rD"�&X "�v�L Q=$�! R  �n�!��wN p)��9 Pr_{.��#A\ft[nt� Lxm�u  ] -ve% u^RU p%7nq�F] z �A̕�A�( ��m� �A a�2%- . \].Z'� union7  ��.:Ev$�B bYv�-.8.~R  �e�� �C%�+�.� � 9�\frac{T}��!7.n}-n� zd�.�2<v�< 5 nguished� 6Y2UR� ith bias$� $T/2^�T!ex�ial�& mallaoSo�u� postF*s� "�$)�s� high .�&$H\infV�,�Fa Za�}:T��le�'A��� Unfortun" best.GU&�I��been �toT(i� ,B�EXP� ed�any%lem] >i*olvdin:b=� +!�p�; trivial:\:Tr b� e fl )� *5 % Oq �!H(Ford-Fulker�-U?��can cleI,ŷ77ks&&m� y� �*F in ;e�$\ (hs�! $n$�&n��ere�alt�%T8#of �possible͸� �4�� >]$\%�ui�ecision�J!vJug-/$Subroutine�JUGGLE}}2(!�� onH sent�! cruc &;I �\i��th main 5vs:%^�si�*ng�t�� +0zero knowledg� � SZK}rNRear&�*^{1/3!��� i>IEARCH}A?�  el"v.'�!���a\.�  +b2�() /\sqrt{2A Ѥ 6Q�MA3��">X� rf!)n� �sE  goalARa j)�9�� A.a-�$a�bqQ � arise<+c�OstrategW)ll!�to�2# u)5"�(�ble, s,q+fQ star��!M^y!1 �z( non-neglige=.�it tran%"_-tor[I^v��A"In �he entiry�of� hd�i�reveal�)=j,�,desired. To�)1�+behavior��efb-oi��c feat�,�(um mechanicesat��Pi�Fm+ in�Gs��9"un �+pha�67a"� ��A�6�*p$�O hide} .X=�s��;R c�.A�>lN��fgetF�% �-�Uped�.sF�o�U� :�e91 %�ine�t�#� ta��toy&A�� o�nj �j .iatx p�J8�3?2%�!ngotten2m�"iQal K, m�)�nequal�%��A��� $1/2bI�/� ���awx���6a�%:��4 ��\K!)����=L-�y,>1��� s��$f Hadamard�o�$ell-1$\ �s��%uniform�+t randoI��i-)�'-� �}E"ina O , $iE{Nex�(2}$2�a6�H:9 \ Fin� ��3r�e�z$ G�Let $a=ay6' a_" ��b=bb-\n�$a\neq b.�a_{i}6i�ե�.�aKastAX!oWAssum�6E�occur�O)�� 4]>Ncf� 1}� /2} 2a� sum _{z\i�ft^�1 ~:~z�!"i?*0^{a� z-�/ hI�z6�+{fz �yb P( 6yby z-$>y :y �)�as�$�$n� �'i�8a�a�aYa"�8E3�/At2}%���nok-�):o2�:�$,��9�0�,A�t z\�#v 1'E.!�i�{mod}2-�86Y�2}UiA,�Nqn�5�v��s���g  >b40a�%�r�TBm, I�izw�%i H-�,of 0�So��*�if;2�0>�� henI32�>k\��E.� i��)hFCl�6l6@AK�nBl��o#� ,k �yx7%�.)s^4�1,wre!?n!%ter85.).�>�$ ���$e��^$,lxB$e�!SoY6�&�G��m�730U�J� spread,�5��mo=}�:��� agre< ta�$\��A�$i^{th3it)�s�g 3� Fe�So �=�5Aq�*�vt9eA~*2%r0W ���i� �*�"?V�0Zas�7.R@�*p P)�)e�.�$1/E�( �)���---�1it;re���*�m��8�y, i2TR�0}�"0walyXs �7v� !�.">��R2���!�Fur, �!��m)O+�%6%K$ doet _,�!��� �$l ��.i�+<we�&4to do is pack mA2� callAFj$G � UZ�;| oset(4A%�E��(exceptI .��g$i�s� U_{5}�!�+%m U_{63�D� (Ea"7A� 8 and�9 o�)S�+)3z669 ll �)A`�$ � �E�� Ft-*b-��Vof5p��u�m=attemp W��e^- ��= ,� fail�.bat4�( 1-qt WU�  ^{o}� � *�I�i�lla�ve usefuo26�*�?S&s"�Q$ >�@��q�(B4"�*0"�sf,$,<S<;u3 al Z�K� , wa�L�-aze A�A2lemat*ey= cer�: kind(2�!{ � -.W}protocol2/�^---e�(� �� mnisv/�:a�a4w*r,��ɽA-ve is�va�d ?answerA�q� , ye�� �� anyth elsC2uE�A6A$�J��? pur�=!>�,ryptographic)r��:�0 irrelevanE=Sahai�Vadhan b( sv}\y�V< alter�.m�8AGer cha�? eriz�:�a��.v$� !i�00�\b�G;d2A�ed2{D"4, )�invol�54!Y 4tw�"�)�<s �cl5$or far. M�!�A�,�P_�nd  �:be funfC!���$ap $n$-bitd�5���#B)6!!��7&�" $qZH8.re6 -eMk4-�"�se\Lambda�%��A�a�a>2<s#+%��(� > � 1  � )� .X%,!�ff!g@c�nN\a� �� %�e1���- !- ��' $i!l��t ;1/3� r gr�>r 26 i�^t5i�hA��7�F�%7 i�0^� H 1}V>QDy*�*PD ^{:Z#�"^�" !o)�[�%0 ( 9�=y)""|"L ��Dn.LQ KL T��-3J"LY�0}J�v illu�i�us!why G�( IsomorphisV�A[E �1�S s $GA4Q�GA5f 5=��o�A�2DiCall permBG�U) a�Te�T|��vCW?� wamjF�/�Ni1c 7z&wbe�cal�Ng!2^f�*RUF J�!z�7n-����p�&:�&#�� �'N� !�M�$=1E-S��=��� 5K1A�re � '6xXf�� �4�P�n�@86�9f E� ]�C/_ ress �;�7��.� �BA� For ��� at A*�1Short�"V�+R�EF�:�9 is referr��Goldre�E!wasserlgg} (� 73Aharonov,Ta-Shma�0 at})a��of)��:aw)0��2 9 �};c& lemma2%��" :\foot -{&lC�6is D��B!�=�4��(ej^3�Hy(;%@ mpor�O��technaS �P-�"G 2/3I�)�j2}>h.}"�5�} [>� ] amp}���=-Y�a" Y�V�" cw#newV[2 �e"�&a�:6C�j�I�(!,A!��A e� N�.��)y5O�(�> leΔgeqw>a/���geq1- �t&M In .�LA�tDA�8`~ >�� F�6�eit�Nʉ� ^{c}!�oR� n;�E9 u� $c>0Hc� ��he ne�A�<faV>� 2� U�now �=toM%� ult�VO: szk}2SZb2)(y�� } We� ;Po s� Z�\�J3'�E�Oy oiE��� icity��# !spe&c'"�$~1y�P��a�re�one-to-� "� lI��asc�5*)Ef+6U�H V<=y�����:�prepa�. 2�a��6+1i���R b*R  0&�O ,*� 2�|� � B�q �j bFj  . In�#�&! F�-< 3����m��>*ɤ�� ��Dgis7A,�G�W$� =n+�.�6 i*g:�C�" hNU%n�:&�%�~AV�E�N-�<l,s:---$POH�Phad\ ��it{J>ed}!� rd r ���EB>]>ll��m�4���)k.CF:-N��8.��/I�1�*)# M�69�L a"\�(\?$�$k,x�  O .L.C S#� � 8A�>|% RB��2s�& $b,x��ep�� r�� > al�y&��bH�! 6 !�se!� ��s:�5AQ�"kS��f�hted� � ���AE�A =$F�QA�,-A8�a�uH UyG� e lEƥ桬A�?� uAz.SAd^��0��% �&w,&#l� ==�  �>j% ^l=0���7��&�Eb like�8ZcZa J`%�~���1�W�Fw7 "Gge@%T W �sF��A M b��!�Ourm�+���(��1#��E��4Tn���� qu�J Vali4G(nd Vazirani$ vv}.\ \e��D}_{n, �A�vaf�K&K mapp�pe�6���-�6 �k����'fA�� sets�(�OVf�C� bb{F}_{2}!�ni9�k}$Q�i3:W�E=0 10 �ed%� hat,�Y �F9A&( J��n�*"2^{k-v%a� 5�;A�w )�(�v$s&�.� ^�,�;h(�� 1��[.�$ A\cap h^{E:�( "�.�=͔\6ge5 1}{85�corolla�)!�exa��$R��f ����'�B� k}:3� .� �R�`?�� {""�(!�}/83:h^��s draw*��!P* �1Adn �%�,x�� h�*� �).�V� �}{C%Y 2e}!� "z 4)��"TI'6uggestF "� &���!� manya ���� Draw $k$\�M�$q+2R{ 2^3,"� !��Ien%g $h��,h�N�%�H5Fu�Dw ����.]*A�v �v �v �Jf)� h_Ry I54 ,A�Ut!Ym%�ee�� "� Z%R\��>� \  4gnor��6PN�m�JmR>7"� ESb�=. SuJ[ �>�Z��A�� g�R$x \in�ʁ�*�Ş��$iZ#$�IA_{i}=P��!i�A(-Y))�)1)!�$H4=h.:!Z;]L<M\�-N�a� q)�i! Ae�� A����� s,}� �:�m��H Q�A  =1\w�6]i  /12/�&��5(&y4 �) ^{2D]�C��v�7M}j0}j0>jI�2�v�1�*2�+ �(UQ>�YxIrsf/�4 �m/�4I�p F��  r.5% �6�F!ƑcS\)��� �D @1 ":@>�" >L<Y �f�!0!�un� el'Q� a:.�$\��15��.�a�B�: tras�� ԁ �1  :� ��#9#>�Q]�)�h5 !Oed. \ A�*, repla�5�Ma(j�\ b�:׎7� -�V�{A�byq!RN{ �A $&(@,Q@D%ea *{8ef.i� ). Of�\rzAA*A!�0S�!�$k� �(sen) EU6l e :�p-�;�a� M�,�ld!�as o=as*E. ( 16�"�6 To d�V�(MS!�a�c��*�S�)t�� &�  an $"dOq $xor,� � 6%al $k.�$ ��raSWez>* i^>*!describ� "F< 7=, e1*%�now>unc�S)e4:� �Q>[�i�Q���0w2s6� $)%�0 r�gut]WbKI.J%i�A�a�cyX: EJA\"�# �2��Q� x21[%��;�N � 2��6� >�byA�!., . a�\�e�&�&r'll(�;I�Th�*"�%�eIb�'G O,roc�l� guarantee�!�E�inEH"&�,I��C?.�"��cA�a�, 8 �? �o['�� Re!�� C�g?COL�y*NJn1��XreQj�2o�&)fs�)^Dk$ ��V��2�E;OhMP ��A!�Ws�KAxiz��FFz% = 9.ve�!ko�s�!�:�A�.��..�hch|BQPg�/��*{��@{SeBI@ Que�;]+}&�`Boolean"� $fF8n�arrow�a\2N a�datab^�@�'�&�ktoa�dt=t�  $*�f`*� *��V� g^�:a��F� �X�temN$x���k.\"!@*i7?reF "�/Q@wfr���s / ��T�!@R-NF� 2�TbDe]� .} \�>�[1lit cas few"cB�=f$�C> hWer�1��s 9�''� \ g� yA�)NIni�� &�)l�f&D$\Thethg"�[$t?@auxili��f�steps ( A6O$\Pdaf7s �w�/Bog9D � 'i Bennett e�l.\ �bbb�,�e-0G-V�j��"2M:��D.�!t����, Ig�fi�+e2byJS\, %�� :�3��I� }E"6>�I �64B�AQFor-!�mp�s �s!A Ea�k$12�Vg� �&�n ��a9�+G:����YP\��"�`e is � jto% ya �"��Q$�2JP�;yfto1�]en��total* 1_4a A�!/n" * $Q=q� +  +qIl��&>T�yit{=�}i %qO the &o_e*�66/ writ5vwni4"w6g$�qt&% �,�7b�t"�"�#ɳ thm}�!*�t$IO �� .l5��Z6N$ �Z_a � .�I�j�5ra�b^~�� �:"]An%��х� $n|Dd���7each 5�!�ms�\nSJ*#0A��**z".���n}"&>K!Za(FBN�gz# &^F}�uBU}�74i�in.o#ru��� N:lite�o�Ff�a�ct�1��n#\\X y��M x\� '+\b�'�#*/F3�� D��D�%�a%Q�W\�yxw\ !.��AX0n/3+1}+1}},\\Ct 3!FIoZ(o<9n checkI-��q,f�n ized}] D2�e ies :�D�g"$n�0D���.�`p< �6} �BRB,�)U.B ^{x�xjA �\�:v.�B�w !Zn�9�n�C2�)�6m=C$q ){:=B�E �"Ab�  Fe�c)Z laA��ia�JB.6an6&�E$� ;a�e�Y�Xs�i+�$.I>NA-d�]A�=ZRv��*�>��>x>�$^Ktzh .5&�-%�e-a<!��'So�b�sol�.�;�N�B=�6�f�xBu $ (�% belo/k�a$Y^ Z$),��u23�����6J7!���ame�.jEa�e 2H� un�bZ%6e� is wb �`e��'g/��,� we manag-"� l0=] �g�Y�\V$x self���F$"�e&�6a �m�f~0 all\"� *!8at end%d%�-u� h&FOour*� �a~�%C0h:�( to vJR�be��"�N�%r1ri| 's"� �^.�<in�6��too2w�,�1r�,�**oa way�rb�H6��'wo�� $sS�nHa�fW6 ^���*� 'ap*ts�]2o)�o)t � �#��= ]{>�)!p��y^"y]�2G^ �m�G:�< $s,6+ �)�B�64� E�6�E�Disregar�:!4��.���Ni��(veniep~jf isN$��_>~ 6 M!)]( 2#K�,%:{�� >��XK�� � D^$v�.�:>)�b�F� \a&� %ti�*�Ax!�J�-�8*U�a�St 6��"�X9A�:�ɶa ��9�F�H(�b{?�out�(�V� � wpBaw<�\ �� $s�Lm�� "� zc5�<se<- ^ � o9N!'z:!3t6�bE}�B����oed� �/ 2�qOO %:.D a2}z�.�2�.{J�* .b�z}{\ 2}� $ �x\on2$ l�O} =�!tKL�6lc��& 2�B�f wK ith\.>�\1/*W%��V.@��cn�:|0�a�6 %.2�}7N�fH�Z�'ZYo$YC ="9�E�FB2P�_��1; =.o�3}J�6ArW@s&�'w�Q�s' w)zJOaf�~�A6mo�A6�� vF E+ ��2i&�"j'�3}.-�r�% L>+""�some} ��4 s8 & :�\%t��V)�9�BK " � 4 A/� V \��P �q� ing2�� % \ !�Fply�7x�o��6�]��E��PeU2���9��?ble�`r' I�� d.?b�>aF�c s ,n}*v`"�n*Ub)�3t�+� �Yng�:W ��A curvz *�Y6OUPE!tradeoff�1�*$i*�A�͟� had\ $Q$ZC&�],�D�Yiord,/de=M]6$f�t��(provided $Q|#��N�\ͻ��>qX%s� �KV9��b�>�Q'/"�P mea1!AN^'/8\E�����et6�� �'a*!~!z:�#{x��Q$<a�xnimiz \max��Q,2�\��$Q=L a 4%� hand�Yd!��a ��a��9" R� �A�BBn�%� f�y_�M&�zc le} A!y!&�One:.$@ �Koo�G�isa;?2 ]tob#erpre~z�3��!�2���"��ies2#%�\�H~�$Q+T`!aE��EA� .} \����xwonz@�G��)�.,epus�5F�w $1�&vu�` tane�~y%%�Z<�x�u�C�Au�"T!&�rulc�IaKi f�lDxq{r�\>� �mSRV[e�A���� $N$-���v=�Xqu�/r; ��1nx�H.�!" *�"�!&�JNP}�"3�a"��e`3gsf1$-a(�eAK �ot�'�@G�dRa�^ ��N�"!1�Aa"�a{>C-�&hw�P�0U[-�e�e��!�YI[ $*l 0&�<� n� H6h�^�n�|a<at &� xx=1$|G.K;_{t� *J s&��B8 ��t�W bul~Qm�+�+�`���2m��, hybrid argu}2!��of n% ���=atx&��ag�loc���Le�laK� x$aj$x^{\ast�$#ensZQ!��Ʌ�*��6Y*�I:Z-4zV9� |5� 1� z7y�QG��}{N?2$ t9~2jr��ލs< ceV+a~and\ $\�^�}�f$a�A2�t�T�A&*�"a�.�K - 7! *݀�X*��n�u1�$x),a &5W$I�Amonit�2�V%�A��( M& &] B�5�&�Y*� �r�UA�2�E�d%��e�*{!)�( #Y�j:�a�"�Sof�I�!t=�rT}�5xE5l8TQ��!�.AG�&�:m1)m��un�M$T=.�# 6��#orE[T}2*&�e�+,�DcHK u�a�F�#6w ��n��.�!!��!�Ho ׌&�)B]��f, �?nowIa�C�@�*�;2��R( diagonaliz�� methoR�du� Baker, GiA�_So�z N& bgs}0 $#Han ino;!a*mklBrdG"ap(TH�A�mat!�"\ ���Vs!r"-#qmYM��a�2�� WNP�V�� "Jno;c U�m DetailnomԌGV"�*Conclu�k�c d Open Pr�S�* DISC�*5 idea �U�1w+Y�+"0h  trajec�r es gN�$by dynamnJ law7B$�a� 6�:m Schr\"{o}� er's 1931*����roach-�schro - }, Bohmia΁�vics &(bohm}, moda�VU E|#8d,dickson,dieks2l else�e> Ye��Z-�s�posals� ��tpredi�S� � le;S�5��KDw(1^�"�thEot m1gm�����/A�e�icalv)#�� message UוD6I�,aO;@-)] actu�T ge�* qu&�TTo focu��t��on�c�T issu�I�tri�BZnd�implest�q�/set�:���E0ӕi�-dimenA�al HilbspaИ�+a )v ortho�x):!�Z�B^ i2)pr!�ed �seem �A � ona!0a�Z(b�lć:EC��]*r0-A@t*Ɣ,.=�. $)eP turb)�t &��O�fte�M�m��%�-s�Ha�j�%I6nC@��� al]��al ���6�!_(But perhaps�]surpri%� y, I .+�|� A� o� �(an}�)SxaZI�nonr�son �nc> 1!,*�1n.� qE�b�u*�w,<[fpPECIFIC}7�mE n unS@edaOn$qb�3J ��a�ri�ano��Qasse�W etl``r�T io�j&ŽA &�Oo��͐g �s%� the :tG��s]!�Currentl%���6!ĉ;Av}x[D�?MSTc�rho,U& � r���2it{2�} R�A�&�R�?eon"3h�j1�if��row� colum��t�$U^"3G� }e4 �!tM�r ��  r,c�-�!�cesDll magni/Diny erro�I Gi �Intui�Ch ough�:8a��wa�w�by�Gerd�" A se�B�%�&A)=U2C_� IcomuV�e��?�nbl�$it{mix(K{s (!�F*p� �A��rd!C5�gv��ْ�. �qofMVn�yc�~�VUza� ipliV ve} .adw�ve-��9)�x���8,����AU�x��nE� e��Lis �W����!eof�s�eB�a�I�$ongly�� !Re���,���h�$&� "�Q��5,�s��tG �Z� �e dinq1g �er�u trouA�atF�&���fit) !Rframe�o�L P�6:A�discus��>�9O.�w)4A{� 2�8B .� E�e� de�hůfreedom�a# �!� Even)bseN� "����ginuou� alogI.�Nɫ\M�  ha %�mea�U by t�3a4AF�? (say�NJCw3!QY.�   e`��� �R5&- �err� 01[�.�406( J�RcXn�Z���Eor ��" �/�OƍeoM�5�be��.�� "� A�g9eII�t�l�s�26_&ԏ0{�zC�a*�(��- *W��ci�nz!ory*��zCa)im�1aio-�V��~�� P���{�s6F N� y�B.C�a�bٖn�U}.�c� 1/�n�� ���oy� ��\���{"� (ors %p��i�.�?9" 1�e"be ni)�pin dowŊePϒ!R6'�N�ZF����� a. AO!@.� !"\�u{Summ��of Pao�m� MAR}�3SUM} �ny �.'#u�$o�< suit[>�Fgoo-9go���`� :"8�iFIw.za&��$� $d$�&!(����e %�A_�9MQ!A"__;b-K0s����c�W9D$U�����U�It_p����hKo�iQ���F:�a�I "$ No^�Y��e%A�M��t ,jj� !Gspo��"�*�yX�kJ��a�%]�22D�"I� 68���.�9;f,Q�mo� of yAedeath,  re lifa�Qfl GK*s:bM!youm� � st�a�^��"� 0lSmF5�.�8A�ir\bibli4lystyle{�}6!sis�^end{doc0} iu\@\[pra,aps,amssymb]{revtex<new} and{\nc}{,} \nc{\vare} psilon} oi}{{0i} 'psib}{\���{} +psid}{$^{\dagger}9b7b�<(.�8ey� �ermP rm e, munumu\nu\dis}{pla)L �u@1� 2.R@rm I\!RWC \!\!��Dvecna}{\mbox{\boldJ $\�a$Sp$�aal{$g}{\; = \; v���* �Hcx� H}} )qLLn)L}^{(n)zLcuno21)7a�20:VbfJ�V$1FR F�WR W@lR l@xR x@uR u@vR v@wR w@jR j sigR"m9�aR% )�bR bgR s�rR r@kR k@LR L@impJp@aV�-:FqJf$qEpiN \piAdddovA� stackrel{�� }{v}Q�doxa� ot{x  i�LxRLxLpi M\p��do! Mpqa�vuv<(o�a( �aR�a��6%....}#G�{91 #!/ #oS� ot{S�6oJ (J�L ��� dd ;L(V�2� �=�5B65o}{uBhat!�|�a>p:=�I��e m�doq �qF +q(dMFEG)zWt!�w"}GW9�o qWt]Omn}{�"^��)t2��gAUgamma ' al}{i� �g!J�55�r� rm d�ta�]rd\ _d�� �cmf}{_E{r&para}{^{ llel orto er�vV v^{(�i)5 aia 2)TM!S�\!M]ai�0� 0H.��^E� CoMF�rm {\CK6CMF"�gEN%/^ V! :.�A; lao.�v.v-S.u�G.G,vb6���-�a:!� �S^�Si.�O"^ O}� {!OK ddoRa A�"- ��F ���|R5AHc.�HO| }{{ �` \ \Rg�' (Imp.( LongqN,rA�I�)�nnm 4NNM$^{(1)}$}\,1"_ 5|un}{1�1 $lq�l� Tr�]%t�]($#) ik}{{ik�e"� � re.� theQ�}{\fn� ol{� F D \title{ }� �{\em Pu��}1�.J.Mod.Phys.{\bf A20}, 2027 (2005)}� ({0.7cm}Non-�v�qc Fz�&��pinZ2 clesue{Work � �Zr (by I.N.F.N.M.I.U.R!author{\�PGiovanni Salesi} \addhq{U�it\`a�kPale di Bergamo, FacolTdi Ingegneria, Italy; %,Land}\\ Istituto Nazi�'KFi� Nuc�e--SeMilano M�e-mail: ]s� @unibg.ite,�1%�( \vs{0.5 cm( abJuctAqo�"nt� studt. !M&N��2�5� endo�!�. !� vanitd%Z?'4rbewegung} ter�/ ppea�f/� mo� y�E�u$$ mit.zeder"w��(M$ ork-$Qg��1Ts�`�Aq�%�2DotunnelHec'Bd"Xpos%a{ \5I PACS�(: 03.65.Sq; 830.+p; 11.10.Ef 30.Cp %03 +p S�m1ityE Semi�!/���:H=ons %c LaZ�g�'&Hamiltontach.� Loi"z+P� ar\'y�9ncemY@ ��N{Sf6�!�A New zM.(�c59@a'c"~"T'*�7tg/Ib� U�F$ so-c*dVv,[1--7], i.e.��%:fr �y jE�- k�=&�R by S5)) +oe)��Thi�� B�(�6 velo�o%:{um(aeI2� �a�/'raal*1a�p���i� $$ �� W,\,"C �1\,. Aa(in Dirac�ore1 Z��9# �t�#�ti��Uuo=�  c�no6��=-i\hbar �Fur�m�($M$, @&!$Aτ �ut�;, �.�s$J��JL{L mc^2$}Fq:l��a�1nk� �A� not.�+r���A�O½�" of Q�yDin-V��ly !�uB}1d&Wf���(}{m} \qquad  � $1! /rd 2��|�m}-�>�5 �'s LawE�(��abs_D�exG�Tl forces) Galileo's Pr�pl(In�� a do!- hold any!�,\!/�! m�@M�"g��al�<i��6^6%%dep+2-�elebrۓGordon d�[o�Zi� }�IQ�L�c�':!�jg =�b\gt  -_�}!] b(\po1 ) - .b)  +&}g4m}\pa_\nu\,\lt"b\SDnF\rt�[$ � dz �Z r  m{p�I6 $R{  ( ((��nu - mu)/4�Y�c!á� tensor"��]e�Z�|-$r.h.s.\,\,&ssoci.+W!��a�r �$e CM;��l�a,22fg�i��)+�Q�G�I��P!:iro8� . AI$ousM`-, 2eY g�-erv�*IP+ �Sten" -1 boj+ �l ��� -${3� $} fE�H(ig.e�0ca8 Rl� a-SchwingM&N6b� �()2h(mNR&� Q- PaulirXndO0�'%)�&� In �W,Bing L�2umo -1�!e ayi�JGQ9F�q�a� =mKI�}{a�lqqaL�i,reZA�za� q�ŵ�Q :�I4� M,, \l��eq:Curr����0 e��;a �2�AsE���na�\,A9usual 4�� (2$ �$2)#x.�B1above18 ea�ha sz ��& pZ"4 AAiless (') l�  ($% �\to 0$)�(�� �!h.b �;A��Ba:�o� �4@� ch vf  (p�A��boda#�but�*�mNR �} 99�c$��� \Q�^or�-�@� ��#e�cr;fondb A�D`���sbf�/d-3psi)/d=55.}$ N�etheہ�Z� Q ��of5�($2r)&&%)7 # !T curl?@ �A6� =b:���[.E�not� Je2'de&y�in�^0�ant). A�3 dL$g��a � �5d�� "l�Oe>��WÉ�X.a � �*�$c!�ctA�b_��eR��aPas#1!2whole: ��o��umpŧleaIs!�)�!�in.'5!�cnon ��"mean kin�! g�-u| ry�Esլ d byI�BF} wavefuԈ9_q��,�|,,Takabayasi}�\ae 'pa� :ur�5 NNM}!Swas!���d a v"�}e�ic�)�jfA�X>�arϠ~,n=��. �`!��o.l5V,l2� ce�2| &| (NNM)i��t*am�les�� eiA� scripf�out#I.hA�7T�%or�$ cial�jmalis=a�� A emploj) Cliff�#alg� �+r���� (=A�!llHsymme-.�+.U&E�!K0Barut-Zanghi Q"I}), 6�!q�izo?e)���o$�6� re-obyAs�""{��8=�: nV�!.d syst !!3 no:<. �Au�8 markP$:\\ a) NNM��fix<�"�6!�)>As�6�� (w#��1�x$$Db .� B�$�P�I�);\\ b ��below)�n�0M�,�/a� E*E2omic g n�7eNu� 2��*�,ͼ;AI�c)|:/��� � � 4/ain=-��lD�e"F� or:GNo�0(zA7)0� � )? "I@q9,�/� ,9�"} s [AZ�<��-*�squ;M�Etra��Xe��1i ��; cf. %�g# s i)%� iii))�]. �:{��F i % 4-v"����ers.�ax mUy co): te [!� adop� M�-�H(+;\;-,-,-)$] \bb v]� \dox2lt �d�;\; rdH! � . �&� VDEF} \e�h ��& $ 3%'����am��)Cd��the Ce�",-of-Mass Fra�M(CMF)H5re�/ O%v�� 3-� } �P;A��� Ԉu�f` T+T=e�: *�speed"�, d %@/%?=0$d Y(stt�C�R�X � (RF) "��)CMF�2 Y**vZ2 a�`E�Kon-shel�,n vT)*�2" � any �K*� �*��,!Ove_�a)B� (average) ;  e�cAvpo�� p� les�ii�"%�)�:K�`9E%� !ـ�2x Q��i� ZEu:پ9ime duns2t L ic i�lMc����.M K�� s&� iemacR� " � in AZ'"���1�v �E� rdt/� tau$�Ej: } ?iod. Ini!alq�sa�at)E-:�OionV-S)%�Isim f/&� 1/ e��?W�=R� upK��Zv�#� coa_!D�� -i�� 2 �*�}AumuV�5��0KLforward&�q!^!p&J*$\L�. =\um mv^2�O !i5 A�!%-&� � "� uQ�S6-ther� \Lcn"� mum k_17,^2I' c��- Uի�Mi=0}^nŬ k_i2)^20\,�^� $U$A�a�Bar&�"{�H� $k_i�_@ !�~Car co"�8:� a"r��x.N,P0=m�[\vid \rd^i}v_  .$ \� Euler--��A�!��B !�\pa1\pa x}�(B<}} - !otN /. } + �*6h.JN /Q)��&cELG>U�> ant-2x�mQgy��� �ichSe"�ZL%5Ai $F=ma0:��� "ian:�B�PeaM�-\,5 U})�;} � m\,� -E�,!} + k_2dd - )KI& 6�(-1)^{M7}k_i\,,� �9QGN��$ cano��"=  $4�Q@A$ �- ^Fdo #} +jK&�$ \!�jurES�$es�   =!6� =6 + =6 a�3n6\,%8�@D-)B,=>ZeroMom]�#� ��a:�Q��P�hn$� �A )m�: �e�k_K E /- 2+�0��a�AS-U31�/63Q�k_i VN.� LcnZBWe"ero��N\"�?r��(�:eAa i�der"#Z=:A� Եivo�Jd�_�S\&�Ficalw1&� jN� N �!�M6) �wa.weLA�5C'M;��Q \�N&C vu���$n>1$)ITA� #� mu a{ -nmu\rt�� \bb  =6�%fabf�a�.-&"��� ��&per��mby��ing, be�H�47-� /$�CBS &� mI�!2B<\p��$A��vH�( $qA��!mum\ ; i � �2��f v !S��9Bu �.>_]x� s��� �`way2�e� ��p$q!�&�!�Poissw�racke��q a�+:��{f,g\}"h �/(5 �8�gɣ�5�2�D* 1�F1��FY��Vo-sU o �Np\piV�%6q!�$$%'� ]����^ *G�2 �-��an i",�!idHc(� 8;\;x,p;\;q,\pi)%�%�$A��� �Aj- \Lc* * � q^� -i^2}{2�� + U���� Ham1�ɄAaT�&c=�int\Lc�e>A���m &� ����\S�qt\,�!2>����H f���%2EK(a�E2APIz:�)amN.I9:.Hc=.` [�AVB�����cou�)Q&���b�a:� v6�.�� O!S pairAm� b$(%H,\; �)�eA\{�2(array}{l} {%�M'a\=!N%�T Q��1\�Z31�ug0%�AP9�o\�3. i+. \hfil3Т�m��~�1��� �\b�J� ee (�U�%�t�Oɴ�O/��%��qa� �2O ��$;�<�!� QK"Hs)._,2\* TO�2�0Xbust !=�(am�$m$ �,!�ler1k $-Z'(^2/4mc^4$, �$at�iong���!�A-Ny#TcU�gmSa b}{c}�؅*A �� � ,m\,vB98� }a^2S �����VHc�� pq- Y q^2-i�2L��.WaHam:`3 "� :�(� _G , �7 [�2T�,�e Exte�D� @to macroscopic bow(aa�h,}�V, aMtV& beha?�B&�= A`:, b"G2E�eU5rS�I$k_1=:. n $m\to\��$.E�B6'"� "�&E("� )�^r"�%�%5%�)��2{m*��1�4m^2c^4}�7!+=m�MNN89�ڙm�*E��osc�(eM&�3``Comptoy��y'' $\o��_ c}=Ae2/�$ ($E�(/H �jR*��!c3fixawthe ``�'na�i� aj�T[wh�."� fix ``S'')=Q39O+ �\cos(6�{ _ � \sinN �� �[-[�Q� A�,{L�nJ�%�8&H1e�֫= =��= 0�� a�����S t�7�d���Ů�=c - m7bdo��>�3���*ew -��"o �o q� YI�harEdculo��$syxBl)��@%+6�^2  = 4mE�2H 8 �F99V0Q�InЬ��x"Z^�"#��)tl&�;�#Pr�6 T��3���T8,NNM,Staunton1}��F$SO(3,2) LiBT�)."b7��m"��$ Heisenber&$Rwid�B$t{G}}=i\,[�6 Go]$� &�cou%Pa��By�>l�4G}=\{\Hc,\;G\}bi\�t����! ,7$C'�FJ�0o�\4mu\!-\!m��)_-!_6^f�����!%kk�A�FT=0A�%,by��� �, ��d(m N'-�%$, ``weaklyn� ''.}�h?�A5� ian,:�"h# ; *<Ju ��|o�xVq0�]!D� "(�:*.* um PC0�S.q:*W3 s�yv 3YA�:~}�Y�.�NNM.  :kf a7�`7,CMF. In fact�, for $\imp\to 0$ we have $\doS^{ik}\ �(since the spin 3-vector conserves in NR Mechanics) butI0}{\to\!/} \ \u($kT0}$ is not required to`�), so that from Eq.\,(\ref{eq:ZBWEq})� $v^i\to-�|\cmf^{i0}/m\neq 0$. Therefore itvPphysically meaningfulstudy�LNR NNM. To this end >$sufficient3reI �in<limit !@ icle \bb A�� \ug m\vbf+\frac{\hbar^2}{4mc^4}\doabf\,. \label{eq:3Z} \ee I)ypreseA�4of an externalA�0ce $\Fbf$ and  poten�$$U(\xbf)$,AScan writ � �rd�P}{\dt} = -\vecna U = W\,,�a�n, by%�-differh ting:�9"}),)(fbox{${\disY-abf + �: ,\d%#}$} \5#GNL) \noindA�waA�Pappears a non-Newtoni�8erm which becoma�0mportant onlyCn $ re�4very large. \ rLet usI��Pinteres% 6}!�nsion!��the Work-Kinetic Energy Theorem holdingas clase� �me�� \�0isplaystyle T!�int!^\cdot!�xbf = -a1}{2}\,E�(^2\,.$ \ Wee6�0A�fG ^ lt m!�^�%�\rt6��< vbf\dt\,.E�TakAhin accou���?iA��$E]ab � vbf=MZrdI� \lt vbfa�2}\rte=��isM �B-\, 2EDaD - m�%y�rt$ weau euB�nE�$, besides �� usua. A�, a Q�I� depends oe�( first two ._ofA� velocity%�\}� Te� �6:�>B�5_= F}$}1�Iź easy�. show�t�totalU� al ei- $T+Ue�a�Yd quant�>MU�>JY]�we se�at, even��0space regionsiN $Ehj��\� p}\,Y = i6�po� = 0�l>=S =nJ?S?nAO�nu�`n�,;bw� ,ND $? mu=i5sx�=\vr$, Y2 Y9�of6�� lineara# anga� Ea �dops��-�\�0 :& pdot��%E�\m)9HS JT v^\nu -nmu\2�SVFurthermdwV" 4-acceler� � ator �ao%7F)OM 4\,!�{�nu}E�nu1�9ringly��NNM�contr�6 ng both s+ !o"� 0SpinTensor}) $p_\nuE� exploi�aRon-sh��� 8traint $p^2=m^2@U�-R M!�űeI}{4"� N� ��t, "0ly�Y2�%�),%�)� last5'� ly��\nnmun��z� �� r $n�y!� . BQ� abovk 2�, l�Jrecoverb�� �� ��Cory ju\he!�^�, J��. ( ppl��"�t-e Zr $Qo$I}doaZ~M�I ��� lambda� �,\;Z� = -4�r28mu + A�,ZW"RdEk ider�!Fp�Y�states�satisfyE�-�� ,Klein--Gordoك,� V�psi=mA� po^2A� $. \ When\lyaf)� 2ej�,Hilbert subsw �R�:�-4m^2�!0m|%1k��� � utIc�foru��p�*^b��ukjI�: ����i� � "t QZ�^M�" `begin{thebibliography}{99$ bibitem{# oe��er} E. \"{o} �: Sitzunger. Preuss. Akad. Wiss. Phys.-Math. Kl. � @24}, 418 (1930); 5}, 11) %1 �e�} P.A.M.� :� � principle%�QYum "� �>} (Claredon; Oxford, 1958), $4^{\rm th}$ edition, p.\,262; \ J.=Ldox: Nature 325, 306�87) %2�(Salesi} G. : Mod. %�=t-A11�815H$96); Int. p1%$A12}, 5103+7)�aeRE. " : j�j90k37?41oA19!q389(E) Foun�28} 76 |8|n|� | Rev�57}, 9%�`J. Vaz�%GB�Leu W62I� WJ. Vaz< 6bQ�6A9A�m�3) %3}�C�D} \ A.O. Barut: Z.�3forschM�A33a9�78)!bG.Yg(: Nuovo Cim 2B5e�92a�8�.):ygD2T363A�81q�D6�398� �>`4=28��85�M!�� son: Acta tPol �\1�375 H. H�,nl: Ergeb. E�en)w��T?2�52>,K. Huang: Am� 剂��47./(J. Weyssenhed A� aabeZ�!…]4 �E.P�� gner: Ann��q4q14q39�M.H.L�� yce:e�. Royalai. (iH) @�[�#4)�T.F. Jo��Av%cukundaQr9�13��184%�63�� Flemi!%)3B13�9I�65�Pauri:�Moup�.e� MethodH T ics}, Lec�� s No� in��8ics, vol.\,135,�&615�TJ.Ehlers, K.Hepp, R.Ki�,hahn, H.A.We m\"u�U% J.8$artz (SpriL0-Verlag; Berl_1A� %4}xef}}rNN. Zangh6�I�%�5!\200%�84%\y�DA.J. B�nF�in 2454eYyo�333y�.Z I.H. Duru2W.�e�35i�R�B�: ��."��3mi4L���R8A�!�6v21i�e89) %5=f Corben} M% habh� H.C.^b%#roi.J A17��27��4!1\:@hys.812 3261); ���%M� ��i� Dn� ".d} (Holden-Day; San Francis�196�>�D3�268�!�J�45}, 65�7� E`6�55%r�mI� �2g3 1E�95) %6=x$PapapetrouA� �}Nn A20� 24�5!ff<i&clcldd; Rcal!��#5{noi!��'-�pa}{\�a!�� }{\mR(D\boldmath $\nabla$wxbfJ%x$�im�(>Ep@vR@v@BR B@rR r@ lan}k ngle �rr  \reY�`{\thefootnote}{\fnsymbol{a��q� cent� elrg�T�#l� � s:} V)An El�ary� rodu� ,$^{(\dagger)�) \��"{6�&�+! sup})ede INFN��4MURST (Italy);[vanish�robabili*E� $4roAthe �+ (i.e.f,e� IM�+4\/}). We may a�(, ask ourselv�0f � possi[,to ��.�`ad du�!}in�!eX4$an average�speed},�S � �inggc�($we might t)4o calA�t) measthoseiJities..,seems surpriZ V� sw!�o such ,esAf[5 (appa�2 ly) �Mforwa�(has gained �FN0eptt yetAa� blem was >/po��d N.in 1931�YC�[1]� ear��ttempt!j solv�2 was due4MacColl[2] a y�$* r. A�&�s!��&ubj�4�(almost ignoR6�.��fif!3, aAK3i}0#a ��-I.�ob�6t.�%T�'in sc�rA�.y (�%a sA�e6]in)��.q�I�selfadj!?Ip but R$itian}E-�,!�H refs.[3]). However!vb3�01 %� up, !(lyA� � ��$ twentyfiv!�aT�)* creaEc60ofe�-E� elect(c devices (��d���A2cesses)�(Žasca&5*d y4c"z/ Hm�!Pn7 fis� �Rfu (below thres+4�(�10, aAI 1987!Pa�l[4-6]�o�re��s$!1ʁs�!e��!%li4 �,. Unfortunat�j��hy.idA�%�alway(*en ra�Z diff��a$ pe�m� �a�$�s,m�s5�s��or��U heck���predi�< s. O)%re�}aw$s various �� z3 sub-�� ``transm-�%!" (A@microwa�k!�opeW ��s)3& b� �ed�&:|&�ema=.f f!bbehaviou�*("{(, .� ) ``&f'' M�mago6�[7]�W(�,�-6L]�le (or �Ƀsh'Y7 back!�\!S[ d2��*iH wc$dea� �9rel�t!)vs. TE�m)s$$ mee5-���9�a�I,��$, disexcity �metast� sp%,N|2'u|�,0so on. Anywa0% �1yze&�%on79me 8al>^U�boug��a��4F�P$^{\#1}$ $V_{0}$, loc ,%��`rval $[0,d]$ (see Fig.1):5��re�2t�/en�!�cur�N$ employed : tup; >� �qyKpi` .C -LBe- ��q| will&a fune�B��,too.} Despit!4e�(ɍd k�J �[��=, a u�` �*p�approachE�EwE�zdoe�=�!ev , t�now. � ElK �  /��e� nto four e�es.\\ e�7 Aw�)n�br<=�  built�0``following''n [np+.� ��t � �=ha�&6 . \ �: choiɦQ�ular fe� -` W, e.g.,+ :a� eak,A�e��  3o incox��outgo� 4 btaiw��iI�/le�m"�� ao1a�lt=(tively, hav2))�he ``��� '' (E��/�- $4er-of-mass), o)sharp) -fro8<@f a ``step-like''. [?%�%'!� it�ng�+~ uEV},!�ch[ ��,�)ex!a*�WE� ya9�8��%+ ary-f| roxi�hon''. ItA� A�ag�>�����,so far avail�%��0al data. Amon� e l,!�mon"�7i#ye`"q,+le0 U�:�U AP �,Zco�,��U^0%:�"�7, a�Aa Fou$9� pone� .%�I,f�Aenc� close or�&� ,TheseO 2:would re�_y}@ ier, "�By trave�A ߱ less��tor���?h> � ed w�%��3ecp B low-�y�NN b*3.dispem+Vs (of�$�@c whilMoachA�� �6;ereAE{"�� e��<}K ?�)�. !Y f�0��t�2pl:� z : le�5A�nclZ �j fWT:��BPb$4main E�� �seXC.\hfill A:ond�E���ist@ass�iF�Tkof�dea��Q rBdom:�-i� system6' be e�* n ``&�clock��+ yieldہ��n�`�gi�_�@�� I%�7``-9ko��B�* or, e ta2�:KI A``� ��infUh&���r �?2on*,Y� ing.B� L� pl�ri�g_:�>9by"m �+� a exEg�u>3a squ�F1endowedi�a !� -var�0� (eUfr GAno� ��be!,. 1�U n EG``flipE:�=���$a uniform "� fE_��D�.5�T``%���achn:��7s6�m�y'�ue'��i�d�:aI-;�J���I�siu2� pR dur� � ��.\2�NA�the��d�'��byt "����l �sd<"�� nd,�� � 5 %8s, ��E]AGanu�,1~6, inv� nvas��%` �4afjɥ28outputs�cannotq?�a�U��&<.�(du� q,� 5-��HerA perturb�K, a� )&.co�0cC�'!ukaK��re�Z�2:�81 thir��attribu�)����"Y�}�a set��``semiD �� rao�'..�)&�>~ !Ibe ��/��KG upaLP�� t�݅V FeyneF"��*�"�"�CO W0, dis)*ion}. OC9�, $ i�se�\+ /� a�:��2��U nveni�U�F!�&� ���� lex n2� uf !����:�� �x�8"�se���T realD ---z� itud�M� C ar�D�magqK��=)� resuJ!�! ct*=E�som5��3! :�s. Just�is�m<��ali�"@1-� 2�%-%b� [ e��ngJC�E�S6z��,�� 1��%�rts5��YE~&e }. SMFFQ%&ed Ups: $$ \tau^\Drm(x_1,x_2;k)=j_L#^{-1} )I0_{x_1}^{x_2}|R7$ (x,k)|^2 #4 x, \eqno(1.1)W� �iG!m�"k.D dens���=,� �35A�n flux� �� $j_{�}$� mcy.aZ� %E8! �t�O5 �9\J& ,A�}a� ingu'.�2yb����nels. IK E�g�a�/Na`� Q.�bLs � if�eN ai��ce�o�=��iFL��iV two�) .�!�U;=|T(kA _v& + |R. Rrm.U#2E# ���i�-rrect,� cbe��&�Ode�Cine�qu��O:RrmAo �;�)��ykme} m [Q*,DsW6"� esxT�pi1li)S�#j iFF A/A.�EB���d & .ٹR; ndar2JumyU�+��B�]uBu``&���<nticip�e+��yCN��A���F@IwrE�!o�� sui�ln � s�2�BD> y doE� 6��66 }4 Sect.12)�Rdo+%�eq.(1.2)>  theyݜdis`&h aU"P C*6"�s�IP��lly (ф��o�'.�RZ�ll impJ@�V)*, �iSKa�- -type �v h^� onfirm� *���h��S��nD � X' one;�m��#s �ref.[8]�Ey!ion{A+p sE�no� s} %%�2"!m's|���@a*E =���n� ach 2!�\ $E=�+r ^{2}k/2m$, \A�d��ps��� \Ws{_�*= e�Ux}+��\e^{-i(kx-\beta)} & $x\le�T \cr :�B I{'+ =\ch i909 ?d~?Q+=��� (kx+\alph�$ x\geq D}� (2���O $��9E$e�!Qn. ampl� s, �� U \[ Z=\ K1-\!f}<@]� !�%5 = (k�S$ � =  \ be��x� dela34I�G��!�aBzwee� V(x)5�V_0 & �� ${\rm 5W&2' else%^,},\cr } \] wP�5�,\;!#,\;!"Ga!�� AH \;%��_ly1E��,��@� j�A(kA'-\kc" x}+B �E 4},\ 2��-n�R�l!j L�I#(2m(V_0-E)}/e�,&�a0b@E-V_0.@�!�$$I�u� A4 tyle{(k^2-$^2)\sinh ( �d)\G [4k^2 ^2+2+)^24^25 ]^{192}}& �2y zHF�y� ynx=1�3� $$ A|Z2k ����Z�jd %a��4�uP�0arctan\left(\2 -2�!��h.ot2�N)2��]9� ].� \ &$N�5ߕ<��6�%� �}� 6� �.�j�]�N]z� ,.\cͯ (2.6����8S�![ �%* ts�  s A�\P��taxm��k\,f(k-k� )\;�(\,��{_EE(k)t}�Q}}} =@E\ g(E-EA B(E)>EB.q�7�We �[�+�rho =�)|�Q\�2]i�-"�� p �*&��}�O tau_�5eq}}^� $, nx.�� ��i�%s�,�&�G� �� -ab"*]*}: K+O�Trm�=md�: k$j �4M>�[K� Y� m � -� �$� �/� Ph#�,3"� u� a very na�Sa�iv arMF a-�$k_ `S!��,f &�Pi��^"�"0Yo-,s own� � ve n."�$unw'"m�)� �*k,�s%1�R<Mk-C!%�symme�Q}�*a goodLci), neg���%�i �)![5,8]k��{,r�,SiR ifI-Z7R�a��^cXis>�!end� ^3*6m�A��D|!�&W r41�#i&*@ -J� l(z��S��Q�surE !ofA&br�d�%i mucM}*ter� destruc� VH� e�t � ed �s"�%describI��%s,*�!��T small �6e�� ies:� ps�G \sim- xhR��i[G�O2a + \��(k��]��\�K ] If�w`�%b%�U� $x_{9(t)"�Y!�B m3look 5� valul:=A%)��-t%�ah- maximum) &�0�'2}$i��bJn'2}$J�^sam2soH%�incE��h�'ll� :6���(��E/ k)\,�;\omega$,  /��k)E�1P,����n"�4�e 6�$A� ��Ii. MoreZ !�n&lQ( $v_{\grm}=2� �$I�$_ A �Frec& $ � =m�mediuw!e�� �E�3 es.}Yn�E"5; k}}E�( k.]- *2�}��I� ) =0�\Ri& Z�.Q= Q1"q  �E}�t|i3"�32D�r ^{\p�}(� -�e{ 1�_{}.���-d��a elta x$ c�_dA*���Nvi�Jby !� E$ (VK�S)!�o' ]Z*�  �2 _{4}1J x}{Qn }}=( )e:-d!J�~9K=-� $B�5.�-� >Y)[.X�ZWF2"E}}(  (3eNy;! i u�c!M-L��!�0*� at $k=%�$� 'l!6�+t�R�-�B�-N%�M!j%be  ed�ct)u or� sonsmu"� 93Ila�Hw��fine asU�b!�}� tPb�1�^{,]0(x_{1},x_{2};L� �$&�&�/wo4s,�?1}@$,�er]% � !L&��2i�-�,� s�<S1}\ll 0d 2}\gg d�henE�ta��Q�1.� �2}-%�k.�{ � (3��ogousV��A$"�h� s,.�RrmfuR�(-2 �� ^�h�I�(3�S�kX� m�9�%D6�$� �8�5on-� 81�>�6�poA�%� %*-� A��)�Xthem:��leti|xA�2r"% $I $d$6G . Ye3 i��ri% $$w�Yb�' a�6+��t�bM��"d� !�T*� { u��sprea���K Vi/L% of $\sigmAz-aN( 1bD�k�\:e� ~ N/0�% wW ]K,�$��. Thu �2( ��S-�eI� �h+"� �l)� S 0�+�C�� cer�.#�8�m� 9 )���G��1 2).  =ޡ�*?..� {0 .  �%�"A�* � ;A�&U�2L8 e (asympt�Va����-�Y��sC`� �2? 1�I! e�AE���^�� 24ű}[d��^�]��(3.&�RRrvR�|ROi��$llɂ�d)%As}� �to kee{% m�`!pur�9R` �*�Yf�%�.Waa :$*m��2�� (0,d�:%6%{ h mT �"� �{� d+� �-)+!� epsilon ^B]A9)}}{{4Q98Z7Y e :}; 5�!e�$.{=2mM5 $�=$d$�h,3F!t|a�� es 2| !�A nl��$ _{:k$i��3$2m �-g =2/o ) $. S1ax&�4� Sl[\��EthickcI�� bY^�e��(,��)>? arbitrarXu^.� v"�@ ${d/a�F�}$��fi�lrso-�CediLHa�@--Fletc�?�}[9] �8�<y( �@�H"�iati<�6 ---� "�+aS?���!@�p@;�&�*.�7$j �(Sn�A3 ick�- opaque})1�%�%e�T J!g�S�9+ Einstein 6 am@isvif�.by many�# [10]A�A� �)$reshaping}}3}&�� � a dee�D ys�&*� �s.�re� a�'lVh +.N�3}$On�s a)���t� cke�6en�,"g i18��lower� *�ar�-n g� al, F$��-A>;%�`aa4F!>U�4ata"%-a�ifica� �/ )I%{he $k$-���an I�� 23�HBy��r* KvG�g�by�s"�u"B<`/vaE7f.�4�e�g �i� ��. !� purp!� o$� d if�i�6P s��)�8�7���qj��!C&�:�� %@3no���7io�@%i�/�%�>�(, st�ei no!��Df2ise9A�m�!�7, h.�C�r�4�RM�b6O worsF &�Q2/h*^d2�qe�A5]eE� n $k.� +YM (2��}i ��dad, aquickly)I��/ o�q,isa�I,� �3A�(Oied� !�QN�EMŪIG%N�%* 0 itua��_0� >i�Acc�{�� �,� h��lsa.!ya3?se�(f.0�6<Q:XLII4,Ag-AU� ( qyA^an $v� $ (+o9�BU:av elf!� A�3,!echo�� suit�Mal .��a��f2"nћ��%��kuL�}n*�5 the v� z+� �z)}.� 4 how��wll�Cva���qzB5<� Q(f�5  achyTAKI0�i� acts�9fiD?�?�of��mh~n��e+ limiE\�ha�"eI)n-o �i��q�Bo 1!�:�%���)5*��*$k<.�, ���mon}M75l2� ,7��2N� 1_s,�ws2� �9�tk$�0. /lJ �?n ``oblw/ flexus" �-[� conc�e� |1xity.�"&�lim_{k��va1}��*�\5*+6�%� 8(d-�l" �"A\Vu^*�~{2Pe (3+>y�3(1^^ � 3}{2�\?# (3.9@#�H�<�!�$k>w��>eO * k�Q laVt� , � ULGe�� W�  $[/U]� $. E���t65 A�� -? aldy�V���.�1���C B5{if6�'a �$f~%  pa"��K*�m�Pa�bj?j0��L-�  *� 02 �I�i�9&  moves Cr$�� b*!w��N�� �cE�r+d)��V�g�6i&7!z�by9$ Br �N`<6 ]=L �es�J?rabZ�=�Y fY�gd� a�GQfNw�Hm�A\m�ing $|�*)S|�o mak %]R�a�-�rN �toH�ad!� sh�Png,�(�<� ),�BS$hen necess�2M�n�?: fva*x��$G:�,�n E�:)�Oa/>i��.jwj(W���Y&u[tf(k)]=2��+"Q� ��E�)>0�w1:w&i���Zt��8OA��i!�-sh;�l�e!km�6�$. Butj $��=-RF��}{*l��7ndu�#y+.!>0[wnF( ��1)�& �2V--�j�!n>0"�6$$�v �., �� a$k<%�$� ��2)� � �siN?� $k> 3,� tbF�vmhatK=/!�ys?e�to n ire�2 >� 9�0%�*�/,>A�� %F6 �E/)acB.f� � %mfys���m�|�8��!�-u#� *� հ�%e�83.13)"� ;  BE�: t��_!i��"�I$mHis7s ��A�c*8 +4}$!�A��*�=v+��n�[esimal. J�'4}$E[\y4d=(��y H$^{1/2}d\gg���:  ; )=T(v= 6� = 4y}{>}}�/ dd�"�Uin)�a �)A6�m6A.}�L� u*T��$hat: \ 1)  a3F�.����\ 2�i.��Di-e�Pe-��.�O�4%�plo$-f!V )i�0)h6� %���e*R��q0� ?�P�1QEb���k_:�E~"� 1 ($ :$ !VA9.9$rK�A occurs 'WjA�B"�D�&�&Є�]2�E?tho�RNeLsh�L� g��inR $k-$�_is �/!�E��d#�Ilue�-o po�� Kx9;���� �s� i���# $ ,iA+phi$ or� %>$ �l,ny& Csenf� �y �<"lE!r )�\�HenG>aY!=; �T-��aers�[A�or��x-t2FL� Y}�0�0�Ys�E-up�/� Q)Q�.�0 4 S*�?,k�lA�3-AE:v?�� �m2/,�O��� ����N }1 iTXc*9Qe.�zh�UioFn, #for�@o # Z���k~nanixύx$). AP s� ��� o do� w-5(=Q���A�)�" A�T�*�AxDE z}!2)"��j$(t=��locaFx$�Gl+0�zy \int�^*D fty}M5,0O5drm x�z�|<U�����1igE�'#��3li�� C7A0.YU�.�1`&�M�"� �$$t=��]�<�2EgAce"�S}Te�^�&-&ݒ)� (\bar{x}(0)=6*�)!t_{-\i%&5/x>0dx} }b/J.>� 4�-I!�� $<)=f(k,0)N�1� 2\piL�dxY1 (!��ikx}=|� |?\xi8%A��F48,� .��%� [11]� xA/==/1"!6LA< k yK 6��w \xi}!6drm@/} >� O�--si \xi � }��ran"�.4." W�,hل)�p@nrm}(t)=��r-}{8lan kS-t,\�/(t��);�4�*2_T�^,t-�n\^/�  "2~I� �&'��%��,��+d�X9�B} 6)\,,+\[�6>�)�%�A:ftyyV)�\,.�{o�J� -]-�\quadW��!a �M}��TE�}^)k1k'fz!X zv� Q�Rv{ � &,-oM;!)%��0�U kA�BF z ;>  9�EN&|. ��] �:� 1^�; k&6On"� $y*� -�(�kvd ���)Ab(J63_ C9�pQ�KNS.$t�X b, q�#Zd�6aDoi�Ja=%h, �� �hes�5o64I0 Yd$R�5}$JB2� u�.�*%� �+�xjP�g�# �lf`PK- ; W���.}bK �!�-V ) � "�"��6D1�q=to,(d)-t_%��� frac"+ }\, �3[ dK10}+R"O�o��%��8U�a6 Eq\ ]\,�H�*�A^{�S*(0�{ D���04�+[� {.�:G T�x��x}}+" ��%{ �~�"�8� Leav{ (nd Aers[12]Zd a��V��!���-0�+6�e� \r==C>= =�]l� y�cq1�#n � f�rA== � b�! to�i$�Nl�bv�5ing�An��ou{�!5X[ chie?� by MO 9wL�Luer[13]2 "ze%X� �i�Aef�@by �hins, Lo�@nd�� ker[4] wh�` cas&;0!B ' obe� � 0-�,~Z:*�"�R{L� go�`ven�teici���'a�^i&�5{��OA�A �c$ re%�no z"2��[F2���JUJ)�"� ��q+9��!.�[6]"7@go�@k�)�!*xOs)0Imea�@ s#eYs":&.7Z�CLMH U5&I�[O,ineu��$, bL[14-16�, 1982)�dLia2ar -osc��!, [�I��4%�%;N=Q��^SE�!�Bacd.�R�>).�"7n&!��1%�ho)$V_��upo+an R\" ;V\cos�< t�s[.Qjs�A(low"^A�im+���+e�slowly;"&  �, oYA1L�ll fee)I�of&#�-&' moduQ= cycle}{�l/b��Ario�9>45��(��j����&zi�}1���1�)�3nM*x?c&\g.!Bh�o*� $()uY�0E�` .k�) Cgha)!s.&al % .��8�absorb�i�)��iaQ�o� ��*4�"g�e adia [c& ., typi�Wͣ]l�iS�ؗA "J., �Ua�`d�Y�o W>�[1�:Teqv�l�g . A�g�_�9�=Vf�/e�F0bands $E{\pm}<|1#)��ar&:@���QA�EI)�M energy_%�2A aHQ-*�a&F�!_ MonFbF�6�&E42too�.�@8� M E�e6%ieE���-E���gA�pnteX-��<)fE�be": I"Cm�Gm5)�>|r {T #! T } |^2 8(81�� �Q^{�|B2�"\ )kY left[ e^{E)� m�!( �}}}-1 �]^2}W5j���-wo0+��a(Q �r%jV .�= 6�md / (.�)z�&2/u�y�,��*1 �>s -g 2u9v :w �x.rI��'(5(A�$�,ip�Hof}zES� ��Y�?l� d9$N� /, quitgZ&+ P)��7�ssD!0,E�MdT_+-#)-T_- }.+.}=\tanh *B�)"Z5ZV(�EJ!6&C )���omAk ������d2�sA $T_+�T_-�0��2;��9gg6. W���'A�TH�e�7�a%�eI��hb���1E�T�\ $� �:'�R$[f2fKAJBR�u}{R]�6�6� <�`{ �_;)<�5��1�Rrm>� ka�V_0�ne�.;� I�4)�SM� .� ��>�9�,eqsY�a�%^�T��a/c chT<�dtwo !�$|1�$G$|2 ,K&xf��$E����m�:�b$ht� re�Y��{2�c $V_12� . IfE�A whol{pg � di� `�� ω�pF7�q� �#� �vl�w�(V_1 t/I)^2� swI�"�(%s �E(levels $E_1-[E_2E � �uЗs.:���6#&F` R��]�$"$!kpLe r!?of2� G � !I g -Z:(2�g�{6D1966 Baz'\,[17,18]2� �oXk Dpr�'9�c��� *5c�'a0c7QMhon��E2i�h}� m� R collYN2�s& [`e)�:v, Ryb�$nko[19]>lis�A�?!utR B�y!a�-d*t2 "2*TbeaC:�-$͹a�}$�+>b3olai�a� 1 at{x�B���p $mI*��I�ya�, B}.>y�G�1#5;  r�r,6@  o���dp+����19E]r 4on axh%a���)a�$ya\R_!]m��� a w9rhomogene&WSA �RBbf�$vr� �� $\!" z}$-�,�:Ipt �e1� zXp�(lap&=@"i. F�P Y2�y�+)&eyO.G,A�M E�6�- maF<)� PK�Me@ �=g6� \mu B!f@!$� $gj!�gyr"�T > $=$#�ݠ��e!G�+!�w; stop�b�1 !',9� :�T��q*�Gw4)ve[20]� S_{xD�ş_2�c )�@!�;� ,*1Ny2N�*OsinjO��\s��o!bA�9DE�9 ,b�\si�%� �r� 5J�E%2_{y%8^{%"*Gnonzero��!��0mX$eT�8%�bA op�$�� R,f5� As�"&�R�2�=�4>�o 0"�M�S_{2��!1 �J%F:�� *RR�|]�ngmv}� did���!�mr& %��7 Q�"���� align�2-6��, a�}hav"� ;m�lH%�\ Z� z}$ {��$/� /� W�_outa.d ��B v 2� ���� 1&i�0 � D,5 y� J�E$L $z$-�fV3 (:/Zee�l)x)�8"�)c*�M��pin'�  down �� i�DT%M_i!џ= I��bSi�r&�#AM!�(( \matrix{1�`1�)+iky"� N��(|D_{+}�+ - tP/2QRYD_+[D_-N] �[D! =T+, $�}$� d��x�, :� !\ $-�*.�/ :%q��2�$�zIf�q�\��� �1vClan!K|��iL�#9n%>��RLa��zv` �|T5�- -�}{ 5�T_{9 6.1auy�>=-��_()�_+- - 0 |T_+�|} 4|^2+|T_-|^2}} � 6.1b>ixi hcos�h"� 6.1ci&�exW � A."N�T�h!�*�E �w$Q$@$�lBups+ (6?0b�-� =dz ��%& STrm1G !�!H�_|R_)]R}9[2^�.`9ׅ |M<R_+R_-rT_-r|��!�5�{>��#no(6.2^�.�9���>��6.2I�0aR�� c*�0�B� \mp: ~X_� /�},Np !�-19�x��[ �1�b���+V:1�J�b���%� ]�6.5I�OZ� velo"�c*#$:�!, m�%G.��7%�Q��E� ��1 � ^2-kNj.�i+��� .7J�J) h*9R }{ 2xj.�4..[}}rs6.6I�Y'_2��k2;.�"�R6���v"�C}jh ��� �R�I��2�D2�2+ m�2I)��&q d.�8 he goD >��d&DC"e)�� /� �T_ � �P6?29e29E15 )I"w8���n>=�:� ~�uo $����G�&re� fron�$�>�pin�4�kG�aZ&. toge�6� litK'*:��himw&�O,%F6G �v}�$dre�: JQ%'�Q�[�C� *�P�Y^{ t��nn�+�$ y]{${ �J�'� 9"�>b� gnizM!�s�&|qXLde�=i�cth.vatL:�!t  8& Dd}ze'� z�!|eAZo s8U7� �:�8c�)��"Q�geNu>*�&a �)m�|}))(( not}?Aa���^=� ^*� �a�!Q�TB,b�y-�.`"�heTx�2�$� ld r;!�at�: &a"f�A� `=W Z.x��Iin fay*�8"� e O:�� >��E�\B>��2�3�}^2 + ��7}^2}$.\�!:�#�ow� �{�� � U-7>I�,%��M.� E<� }; 3V��&�a ��Fms� �=!ssoci38wa��N�&D� Falk!�$ Hauge[22]��U 1988 �1#U$on&E}�� ��U�T�5(x_2-x_16�[)y5mR"� k�~ [�� (�. -2kx_1)- 2E ̳�. + 2)] \   (6.8��&�V��6��AE{yU���\,��+�.$$ A��m}%!R}}V"n�G69 B!g�x"�x�=ai� 5�s.5�1 (Eơfs�9��)_��m��8,~�W thani^�N m��J�ǸI#/ fj(�,�)�%�l.HIO!(6.7)�-E�ed������N�; a���!"�< idea!�JK a��"� c �.��vg %j�v�! �vv*� }���r_g !� =d/v"lp ]�@9xBII0vu�Ў9D�. 2^� » A�em[�Rx�x2B� �)asz�G5x�*Kut� E d�v�]y}e�!�}�=�YXb� � A.Ά��E-��2ilsKr� dd�"ma�,2�;Y3�IbtN� eqh.���v^���n� |)� |�;e !9aG!�22d}{v}"]"� �} >iG�� �NS}� sFև..��2Sre� �+�ߞea# ful�I it d��gea lB]���nyhowVT�b �Ny :�>�'�Iof y �2���ᎅL9G$.�""�aa!@ 1992 Hagmann[23]2&$� E9�i0�"EUE$.to �/� s\cei���@��  6 E"a�( i�!D� #t$. E� �%a�mc�jo 14ack5�%��8his�W(���$�.&�oun�Lty pr�ple�'c� cG���U� = �tI�� G�Bf:�ac.x%9/� Sokolӥe�$Baskin[24]���:a b#��DI;e��M0�Tep�0�v3 2'���h�9ap�� ir*A%�9%�Q<"OFem:E 4Wp�s $\rbf��O&;1$,��܅�"1�'1*egĨsmI:�#,�F�}ay%��Akrbf(t)[(���o�Nial $V(�has�#��U�sN�߇ $\O�q' n i�n�l {�i��b.C *�/? ��{˫^ c �y$_{t_1}^{t_/A$t\,\Theta_ (� (t))�N (7=/�E/pV7omS! (!()bng� � �` nd 0Iiw�\In%>e��-�E�n� ��̉0^d*C %, (x-x�Ȥn7�.I�en"vFN!�]���d{ U$��I;DLo+:=�%��L e�zѯ1�(�� t_1;x_2,t��4J� [x({��})]�y�  }.�$)%�an �ey/�QEt�x�b)"L7$an1�3?� ��PI"�c�1�b_be ��. R�v5ݩe =i���A1��-��A�Q^l͂�!�A�3\Q+�\Bf\O Z$A=T e�a˂ }$,\� B= R �z!fsj,p_)tR  � wrot� tb�� ��>.0� ��} }|�& -N.%i�(7t�n�j>:� >) $$ |c=� | =-.�7>7�"a ly^�_2�.� c*���B�F>z:�b�7| vx 8�����ka�y�a9yk�Z�e���S!2�*` i���OFb . A �B #5B6��A_�TA ƾ a}nggi[25�; 1993RNB6�x��; �gIa7ly  J �zG:it.�ms;X ��\,���8Caldirola chron��cf. R.C� FariSnd E.�� , ``.r�!|6:��T�i(` N'e1�&� ez;e� ��u*�,", LANL Arhi� e-� t \#� 0-ph/9706059.}2�a� i� ln��N�.hF�1 #�es.&[�he�=C pQuP��gK�./pacȜ~4U. 2 of view�;2D $Connor[26] ���F/ *��%�=���;�d4 6 ���i~�$ 1�`]�doubtful���clu TEa�~v� ro z V�AE���ed.�~m(go"n Y�'s hyp�qsiV0fu0|{ .�O:@orm��-g�����psi�= �Њ(g�=V�M �Ke^{\ln\�l ���(7�p*�4�e�;&� ��IX&�p!R!0k�X2�mwo�Pino�4,s:�70.",$k �Az� �`�d = drm(��T)!v%6t��&e�])��a8 neeEo dam�� signݠ*�/*K<7[L!�*� o[A��`�*�fsi�2B<$6JQde�ZA�w��0���o#ff���_"E.A�o iGt�be �P@0stc�y�s�blin�j\ levez�-, fw I.�7-&)B��y� )sp+6�� vA�'X3 8 S�\ P ��q�]�, BMF27Հ,�+rq ",������byws2j=# 0 %/( }K=sb%!?} ���%$�*�. 6^?� ��I�1��;o !�45 >5f�`�AAv� uVTa���ofu� s fuA_.���S�{o}Be&�E , si�&a�3�FA�aIT"��D"!~*��{?��EQ.�n�me��short ["�W��B urs.SmS�gen��a���J A� \in \,$I$��$Cm fac����a��u��-��\_� \,\, ��!�#����ph��r/�#\,,��82F$Q((\xbf,t),\, =\in�$R�p��T^c'pa��W)����i� sepa' �*8� u+�Ua� rt,P=7w�0��well-knN/�� s[28&��e so-�sMaS� � il��fla�(E����o;!,�B� �F�)�a \,e. 6T�+)�2$m}({\vecna�f phi xd #%�y[�} %�[�O@�%( KAMt%)D- x \m� B)] +U=)`8mSICA:Q�Ɣ J�r�%P �.� 2m} ��a/b Q�sS"��c�dVf�� �-�rho +1`�(m /m)=`8�=EQ� (!U,4�A���" � ���2inuity}=3a=� I�5EX�ġZ�j�E��sAi���E F�j<``hydrodynamic''�#m:�<>��$ O�2c Xg$ b5?a�vca@Kso���$u�q�<ѣ�s.�� �]aB&|u� ty d`D��$'�ch�r��g &g�%�<igo OX�$��e0� o,��e�[Lpcl�Yl'' v� &�0Exvbf�h;�imp?�?M~. "v#8�U*�rb�l���E ��: ����:z�G.SEY��m��E�2�(^"Ts>8\D��� � 9�NK* ���!r�NI mith[29� 60�� to �m�?!��.AH�6�=E�s� out ]*L�&��J<&2�A�u1iaiMhi&&Ma����[L�]�"�YG%is}� "��j&'�lL��*|�) YEE1$,�2�=��Fk}{"'D&l +h6�\�, �9T?B�j�+vUso��!, ˰ I7a�&�R���!�&}"Ra,B~�a iF:u�G"��C�a$-Snd vaW� !$k=�A� &"Q��)3�%a��+si#u�vlu� jQ�r,t�tx).` a��$����j ily !h�+e"d1�,9^�=|͚�9-RgT + &�{2�#�B1-��jU%�&�vZE,&�h���>�c+VZ [24]��"ZuaattJ ����^{ e+�Z��.�&"����f'S�� �B,�ge ��s�)E�=|R|^r�.����+6;\ \.��@*�.@*�o cr�;�O�* �" }ly!� Falc>Y)�year _�r�laUb� !�st�x��K �#�nW erv� law]f�2��um:��0C �~�d �6y=."I ���%�z9a��(E��`(Ja� , atioriAiD &U6B�.G��e}* ev@.|`� dqus^{E��1&� = 6l]���>2+6�0Rr�("�:c.�*��a�}�86�*{1})\l@e]9" ׉;(Zs��/�#���|A+!�id���d\ a h"#�!��v�)�!s-M~!�!L<) E,dget0\7}$N�j7}$*ͫ�H.(9e w�;.� $�6��\�*V��ő =NGb�=2z F<��b5>��^�,V�6E�j��o�ca6fq vedRY%�!�$error made�-g]:L9.5,$s|�"�rG ` �$$\sigma$.}e �Z�bD�9��,lan=�� +��,I�.2J \; � (�� }�� . .ae+O( /aoqn��? u|x,|� - \�*f:qvi� �Wll"�W�($~elto;sit�^g� t�.�*�!�ssion/�k$ion, would�latI ,\int_{{\rm B�T0}}|\psi(x,k)|Adx = jI3 |T(K ��_{E� + |RB {2R� IH�#e� 10.1)vɘd�Ga� ori requi�� t le��� $ha)a = ^$, *� ly��orm potentialq�. Be�lI�, )�1) had b�Qlobtained by B\"{u}ttiker[21]�6X1983 following a method�lLraised some critical@ !�(s[5,30,31]:Q,, even if ex��Mnpwavepacket. Moreover, except � rM�o2)���io!'�� sugge�ny1I(distinguish�%amo�+h�f,s correspondto�8 various proces�e� "�0lay. F is , try"ot crim�� r� 8imes, Olkhovskye/Recami w� iniA;l� uci�,propose --atE�e�R,nary level--�] 9s%�j�%�s:a%\!�line{A�ml}=$t(x_\frm)} $^{\IIIrm}-% &i &inrm} =y {i�-\infty@ < \drm t \, t\, J>` y,t)}}{{�EnFrB } - ͌zK���ir��;�>7! $$=�%0^) ) E! $v|g(E)T|^2� 5Ph}P{� },x_� m };E)}{ M{0>[E\,P }} = Cf!�-D(irm})\lan v� \ran_�+ E\,,�k2a�l�� 6N�CVL^\Irm]F.E!���FZ!�f)��@R<�:�:\]![�:R]:��^�:PE�(A0~:RrF:RrM: c10.2bE:�] $J(x,t)� $ re��ent�K� obabilit ns��a"  t�s/rough� 0point $x$ dur���$val $(t,t+ w�in orderPd min�  averag�O at�a�� $\Psi ��achesQ �we havo perO a we eddaO���$able $t$ b��anἁTwi � )A}�b�0�j �qt}}. u�3%�So� ft�howc �� � [5] i��.{%�) hold� !p` dv  ͝t�& s ar\ta�se� ted bota spac� �ime deed�en $x_��+ fr re� far enE" �  wall � possi!mto)�2Eeffects .6�H}E�.��#sign}  curr!dM�m$� changeB�"d R`  (aice�eak o�!|�A�&$ front-edgj 1#). � .J I!gral \ $ɉB�iW \,t I $, \m8:�,algebraic sua � v)�pnegative quantities (fluxes),}U�B,/$i.$,�$no longer k-M�e g: A=ach� B�� $be endowed�a phys� ��y� B�!B���)�- relevant U� � in� its dir�Re�, it � s ne� ;  rA!&[ ~%�into se��l s, �� m taken��aG *��w dA�9U�is)1j o ly5�a�� way we'll- Jy!��yw�F��w_+�!� _{+}�>+� � 28} } \,, \qquad\ w_-N`-�` i` 2},��� $�$�3 -}�P�%d1K#q  value� ur� A+ vely. TakA�s�cor<A�to� *� � � �� l2� az�f$E7� new � ions��>C �� � $ � + V< + ", F tF-x�  JA� i L ���72  6/* :�8� i^J >1%�� 1}��4&t $$B1� >t � - - :J %2 '��E��jR3!ufty%4�J:2�6 >n�ma��}\�4u Bgoa����t�,�! , stng��? �inu� eque@� � ac{\�al\rho }} +\," +� (xE =0�; }�ndardɧum-me*�p��stic ��rpret��$���$,�heasily�p}��hab$� $w_{\pm��$*W�to���t our icle (mov!U forwCor� back, .�)�Dloc } &Q ^� � M�)$. Actua ,4��O )) i�I ei6 $J=J_+$� -$,� �ap�Z> [� i@ ways��id]Ag��!H$�J:_{{}_>)h}2@ = -:1��e� UTx.=5�=$$bl<�l��Q�l & 5iq�!�i2�'qYY�ali7.�/et$e $A�* �.*. \ O��� MV� %��b�i�A$(�, wi&tj # e%�}-�=6.utf��!7^\prime.d65�l �l1�nl.�!6)�Let uA�so��I�strai�� rh)x����)=0��f9�.!: cb!s� n oef word�at &E�9o� R�*{ far�&$x$. By !�g�ngswQMe�x$AI�E��]�e�� ct $N��� ;E&\<}Q@ ,x ���1Fha�BL ;t)=�x".lM% ,t)d =�y2y�/� >0y�7Ue �>�=f-� }^x �A�T,t)I�=w,N�E�9F�..7I�The l�wo.: gg)u�6+(---as a fun�� th>vN ���$-ja6�, 6� or ٯ�ݡ�\$t$� ��A� $�$x$6�.q!noi��� q���Y�-�a�, \Z I�w�b }+,� 1val��\ \mbox{1,Q�,t[.} Fin�`on dif�$ti�|again0.6) (U>�!5),a" gete#x b>2 }�� t}} I�}�aK > 0� ,D  (10.8U�JI�)�[>R\I�a��.�m�"�:,f.1 6�B��j}{-� ��)� y�9���� ��� ,x.��Y9)Sq��sufficiAbfo> ifYh�j� ��2�  $1l�r� _$. A� i�����!�� �H}a��A�u e<� ���� Ye&� ��!�-�qve�� "� a�mc`(n axis�"10}C*� �)}\ =\ulM&t\,K "^}B� �*,�aZ.�10US2�!g��/��*�YZ10I[J�#!4We!Lo�o��x$%cgaR�xis. H���scuss6appro&��d�$ m ��!�nol s adop� !��"lK (especi�0&��$ESccompani) a figE%� ,AH promd b� .epaper$We�� ��u�2mP need�m8  ��nces} ��"�i� @43-&ia?usigma �!(Q�"@^�.]�<}�� *.�uUU��11Y�6�A���-��V�H)�I� �I�W��n�ce%�in#uc� a_malism��!�ows) � b"c%�g"C��9� (� ")�&-2mo!�s)xS``!�6-J$a*�rp"�!"�to  -dim onal*&� �.!b'yway,�b�*enM�/" �colliyw,E� :�t&t&���F(c)Ukin:%&$s.2&w�":& een,5:[8��!40? �k��$$6 }):��m}�!+}-GL ; ="bw( $�L<irm}<� $d< �q,<r_#�$0.11), .T.�_^� }))=.-�( � }))+VD))i*� 12�&t$-��)$)=�,$ ^}=d�e#�0e�2s{6��&$Tun}}}(0,d6|d)}>�0\cr  �^2%h!G�(^2(t_+(d)) �  0)). B \cr} 5�1��� n"�+�!#�$09� ����],i� �$\BI-V��'Pe-1_6$}�6�!-{+}�4%�oD+alogous�+V�ÁQ�%��:Mn�Ret!�x,x:��-.+t(+.`5��+i�q# %L!_�it�bI@>��}(XM�%<:� �>�; ]�6�At, , le�re-�1ine\ %(bas����i!����*ed��,I rev''.)of 0%s�d�!�3��-h�& rmerco.�&� "�mer3asympt racter)d� b"P2�0x deL'��a�o eplicitly;��ext, A�0-��results�agetb�� uh\to� $;�i/ D@�x)� ~c  -� ��hd,sè� any6�3 (.� t�t!��C�pW3"�0 ! $s. Similaral79��� E� *4&�[32,33�$6 }^i�DZ�#[>~' fty }t\;J�Dr ;J ��t*� 10ak0 \; \� ] \;rt� "�'�?.H,HS' \�.L�)�y!�E2�L>��isC 1g�.,"M ly � ingful*�+!�B$Q!a��sT."� ,�no! z� 1��*Sr@#��W� �!A\to!i��")= ** $ \ (i.e.O4]2�``E�pa#"):�/P݀!)returE: numer�m��/1�6.�>> �3�4\  analy! elsewX [8N-;  !y8 stud� �!(briefly. E s%3)y�-15) do!�� ow���6x�-ew���yB*�+&� !�s (nam�,� �,1.�)m� ion)�0� �Lra|sim0!�|a squA-�.��6 G3Ay-~59�calE8s�a du�o�$v"���& ���ga�an�A��a 6�}, `'D&�-��l.15�of�s.[5].�2�confirO�exist��Hartm�n'&� �9:#�1in!2# (du�&8ore)� conn�!on&~79�!�$escent-��!�)��P�yeI ntal data�Colog��0Berkeley, Flo�:0, Vienna, Ors; Renn�.etc. �remembe� at��0s�."��$ (s)�2nr8�.�, Cf(k*�!Hk})\ \exp [ikx-iEt/B4 ]��k�`a�fAbar<<exp��{-b !{2(5k �4]]$E=w�k5/2md $C�a�DE�!��5I$m%��o9 a_='e�:ron mass�.length.��l�(in angstrom�V9.<�oe�7�; In Fig.6a)�lor) show�l $6�� &� . �� "m BO18$d = 5 \;${\AA}�'a�.�6k = 0.02 $�%9( $ 0.01 \; � @} . \ N eB��3�>���G2a�!%5lear *W '�8%�.M3%=b�depic�=9a�!QV 10\ �a�"t:k =n�I�re�2W!observ��i�3!ImW$I^�HD� �<t]+}�26uiv:� >d)$ re p� �ly un�"g� � t#�M.-to 10U?:�6| zbrings�evQ,c� ,[eeTrX!�so-�ed�� ��. AE���-6�5�'A� $d > �.�$,�-va 4�9:=���$0.005M� 0.05�m �4A�� gy]� E$a�er,$1$%710\;$eV.�8no�6ntM�s.\,7, 8E{9> beha� � A�e�X� ��� .e*J ���+Bd27�� (�C&D |R$0\leq \  My x  d$),%��s�h6/;=- )Ewid�>d=5��0�;7ases )<�m�fIS�@:\hfill\8+ �C7iaa����46:G >+�HB:&u6�-� kin$M:.f(E} = 2.5,\ Q[7.�eV��Y�=�{�_ }}$ (s� 2%�3);�E}%BRN4.N�� S 4�:a�AfR%t o')�? }}$.^p8�uA�E�)w C 6� )j .�Bi:Jy,N'4e� a�4\.�.�s 1%.2-6��E��!fRa`�n`3`!MT>�M B$ {E}$V $I, y hal� m=9�=��A)� ]�"�i>9!�M� eH9�6�}-�nm$�>q=� to:9$"-E}^�� =t� BaeN��k�5�A{!^ � 4, 5'6� <��AD����cBe~R�V�;���? �7*8 �=Aq\._ e��0.Ro>:�.u 5$ e�F��isP -A=102�>tW�rF��;employed*m�<�%osesArk�h�)�%o�' dG#�3�&� u�5�  �' [-10a�3},\ + <]\;$s, symmetrici�rIOd$t=0$: Ayt�0three �� magnitud�$�Ctha2te�?al � � �,<ch���,a� *d $1/(� v}\,{@ })=(  \,\sqrt{2*� E}/m} )�}bm �6}�. ~Dis *�oE� e&_4�!Z�� !p� val [" ,\;\;+�]i��Cas2Uto� ;l>e "f-U $t$;�uQA08�"A" ppm"�$�&�x?ui�$�>2%�' }_{<q,�7.�(a � rk!��!1#ed )��'I�tve�D)�� !� centroid AvSI�8� $ at GEv>PF�B�� (ures 7)--9)!Aca+)erre;at: 1)%+�0� !�a.w� .�+��� �5 �4�J�%!�I�HEM��d(6); 2 �.N %�i"@HquickkA�)w beginE56b, n�eL�zreg�7cl�^�$x= 0$; 3)Z�24nFa &� A�� f�&�*B�)�s� $x�HtKwD"� N(4s*�5atQ$s 1)-J�/��ey cojCb�,us` /""x! s]F�9,�K�'c�$ie� .-;}"� �/A&e ng [��!�s X , la#ly speY4, "inco�/"s " � 5�ng]�j"C)6l"�in ;�ed]��Lose s:�Do *�#+afnd E5f58. See nE��e\(i. as$.3, p.351)-�61\s.1 \ Eventc0�!���k|of *Gav��'E3 4 >6X -* �� �9�$*+* : 4ijN�-Ji�2:�3H� 0) \�%�^�� �0,0)$�2emY�$}�%M_�$da�5)Um$V (\sim 0.6\,d�% J,>�x)$�E�% xima�N��ant; 6)OF�.z0 O��%�9&�� 5Fe d$ (1if�wasJ4�!z���Dq�e�2f�+)�G���!V verya�>e,H;yb�;�5,ti-$ H&v Usm�#%O*� it). ����34)c-A ult{ct�� like $1)�Lquasi-monochromatic G)q0>�Dumont� (Marchioro's�& [34]�%)t� �*fG Steinberg� [35]�� arbitr &�s�-,�!�s 5�6)�w�2Z phen%a�_ �0m.�4i� ��Z�E� lmos� ?damped d�n�G$xAot�TG�a neglig�>!n��i�>$ack-tail (k( .�(sl�Ln�A]0ll survive. W�ade�N (��0�A� non- �v��D is O(inclu=$2 asJO�, s[6"4cB�:Ja�-&� �� "6-� i�)�)BF.�?�.��@!�e`A�B$x� 0$ c��2� �} #�b2o .?!%0)}$: GM!explain,z!� �te�B9*-��F�2$�&6 .�!a��T&%�"K=�l9�)� �#.c�-ͼ�"nm j-['?%H an �accele�"�-!�� �AY��inua$>R�Becomes Silum� ��' (a��cq�� iNO�!eid9� 6+ } %SQ12*|!1 �we� d6E; (HE �CV�(Ammean t&M� � �� 9 �E (opaque)*^ K�.Z--veloc�� !;�id:Ro0� J � ��hfR��%\,3. Now! shc�g*cuF e va:dE�/�*the~2m.�!/me�6@s�M� �ri:Fhd 8&3#}A�.La�W%�},�' E�Ereai U��lex=s>�'j� �+�I Feyn� path A_Aņm"C �A�J�%�igWayoE �B angu/XMFo )�=l�q$Bk/(W y)$: \]C$one immedi� verifies�S11���� !�!�# %_>�R01}$Se�p� 47UQlowE !�31].}� 2LY}� "��X��>siQg&!tHE��E�A+�6 a)z#�.m6chab�=�� 1992qwe kn�m+nonv�=��ach�&� !��N�% d^Nop dr%NP4 m�OA�f!.&�! simu�Rs*� �� se�p�0s�F[0�OA|^"�!��s} By|�XiG``�.F''�Q_{z@B ^\Lr�as �(a�"2yQ-LM?u�imM"�\ {\BLrm}$ i�!�imapTrye $\Imrm�5\Omega4-䂲a -%q�1�6%cYtoo qS $q:� yiel �# md/(ei{) ɍF�-m��V[KRTa|�t,\a|� ���(r� al} RQ�i� �R!Bi?n�\eqm! \ �3�u�U�8]��$2}$�":�!�s R2��QI�47]� low.}9"�= um m>C� ��vanishe�&mc�2 eML�Dis�&&&ex&�%ly��#B�(micro��).YiE�.[37]�%} add�"o�U. � ree�X [38]e= seem� Z P �I"1���]&�5 cros1=. of a1(�$ ��8-&artAC�----^NEpM^au*�to��,e| �.eZX� i-ancO]is �Aw�-Q��@��fXencies��7I4+� aM"k@p����� &@FI�.��He� prog/b�� �%Iz1�:�", "�Ow!�f�� �&�!m�e�y҅�� �las�L�f,4&O()�ml�*A��l��&, ``6� "-��).�?y�E'A��$:�J�+=pQ�A��e�+; �'�� �b-i) mD�- 14. &� pt�$�H# "� D, 3 A���yg��*.� e�$�AB6$ J[$*�Fɴen yea? or soela ser�@of��su�)�Cmad� �)[39] B�)[40] "�) [41]�)[42],"�)�)�)"; tUmen�`eL0\�>�:�MO&� opt!r$ photons) � �2e�=%rioe�Y� mod9� �_U�\",r!2gA!3a�gu�4�m``b��$ cut-off" �M;``fruaA�Fref�& on''!��,��&JM V;ZY s ���]��[� aj8 .g.,14�aA!lso�#�: But 72��١- be sN^A$�e3 , {� l�gca!!me��-�inv.�a..(� [4a Josephson juXC�{RL\E�I-�Ob 10 f9&ndl7b�<of 1 f,� solid-st�_l c�AX]syste+��b%n����9o�h�@p�]�G%)i�:v'4 �.ac ns �S&�~2 m�u���m�� ��5 = 4e^ �� ��b� [43].k �lr � m", 6�S3all --F�� mEe2*.S4 {\bfl`�X}6of}� >i�!�!`Źm-}��!�u<�[/�ha-�%1��� e sl� fix ��en�n�.�щ�5 (l1�XX�-�/�%�' $EN"..e+ (one.�<)�aTVonAC! Z%ɒa uniX&d`�%�+%7 Schr\"{o}> er �}��ea5E �:s�J<a&�N�. `}&SE x}}+ '2"�h^�c(qh)3 =082aIf�+890i=R�BbY�D2.�;EX3 (e���7�U!(GA,��' %& HelmholtzA�9 "(I�ic�v� )&� AjAx.m. f_զ\`jZa �der� � umNg%ps>f).\�?�3)�0$$�%�0 0"�E2\pR$lambda_{m}*�j. }}n,JP$ + ,\;�, �ee-�+�H�:A�� um,O<8�o�c2 vacu *a�$n��L�x!UX�i\6�w:ea�8C �j.3� JMs sb� e ob�,.�aencV\5%~� }\to$:G.!G� ``u4"%<m�$ "�@s $a{\ʼn }b$ ($a$;=�c/E��O =c/2E�fE�4�&�(a�-�"$ S �8e�=e s�|"0 } [a�-�n/happen��:�&�}too.x A2dis�no'r Ei�EHe��$surprising�$�<[44] (al;�^x ``�Lec$ "[7]�^~*8a 2o�,�>DBk  substitg��Q+��bY)�_cE"�Lmc[p}}�x"6a;6ultiplp nC!�� r{.x*:�#Ec)^2A�2�W �(2 ;pi b^2}%�V�`^26E@-mc^2=�+em�?iz!�f��i���: 2VF�iMj.�k5��% ",} [~0""fa)Max�I)&N :a '"�� �K e� Z�� "� . \6r b*A6E]ba�@asB�,%3u!.rD�*��) [45]t,&�ly� b-.�*�*���,ong ``under-!� d'' (sub-�jHezs; fu�o3m�s V��eL.�=[46@,�C� us go2� eqs.�}1�#  3)T'ek>�ng*2*] 5)dI#a5v� E�8,&q�}�drmiA}{ �  %i}�  \ ;P^ Q^Vl} !�L`�3 R"�z�S}q.�T� �Ireplace1�m�e� �;�B; :U�^c}? \nu pXmQ!y�D�2 �8a mathe&r`dAz.a� "*� , �9m�F�� E�E�u�q�-*�w diT��.�  moT g&mf�+z� .�3}R�r.���6�V{)al�7� �b on $ML Ip =m%�$.}*�Zin �K� �sŃ�!�two��%GUn�A�3xomb�l�!6A�-PU�=p�f =e^{�ZiI� x}e^{i �t� 2k7� Fk5:rqm �4���er�\n$� ?F >J!�1 � �D)�  �"�]e t�1.Q $,IUA�&i  "�� �!>{$r"PK'A$�den6|-I|x�7&����� &��+�%g)2#�� !Uf�(o! ;,15q�5�)"9e�a�~i�!�c�Ran �sRDs��6ZforbiddN|T�� je�� i�2�A�i��upa!�Q�"�$5D3 $. Ol ^ espi?tfnK�mie.t�g"�en�Gces2�9��MwaZ�?6��� bJ "b in%�%s>fas>a��sai�5e* !C-�Aq%Y:�5;*r�L��aeh[O��2; buts ls"eF�$as� �0 ��DIc� E� ( ] it�u)a��!Rt761�%U�. N fthx,�w6�O�qowqe#-"Ni!�5 !Ji�s}1Eh.�B~ui!6]ak%֍�H.� Mdds &) as ``Ul*2 9Q Hn]n�5�%of�``2= [39-7xi$1o3te#wthN.um^", s RA�Z.� �!�zH�%d. �O tl� !3circumm��� %�6-r4 ent}U7� oe��E�p!�" K�� rFK 8k-Y:��E%�e�)� no� .�ly�K)tQ�o �riv�j6 o�lB{�� ��er !�v��Salesi�p"�+fou��EuezD� vers* ime �-%&i� ���-(-�T&s ("� �,s")�$�ȡ�BR$aGo/):6�f� ive "�$i�!JL*��� �s,AQR"+�n�"6�|:�2UU��co.�xmetall�<av��9 �I s[39!����� k4.�ٖ@!��!!z �.�St��2$FP. �Fworth�IM�pr{ �� m�%*�*� l9�*A�g �}ed �X�rad{�W�z``*8oscil4s")aFAharonov"4A{de�!!S})$�B�5�ʁ�*�VaH QM, �2BEtravel� €��*�3D'oM)A�$ �4"�A q, s�L� �)��a����.{�� cec t�pep@n cer�'��)�Uof�{2�'f2}*spef lhwAu�>�>�]* !�3yy*�?/)V� m����G^!���ara��.k�en).� �t}B��uJ�"�� 7G-�7w 8on:��#+s�R!{e=�g?PL,+, works[48,49Y-�rY*ly iم!�&J!.de�Ld�! m�B�a� ��v�Dar:F+bing}jw\grm=R,e:j k}}= N*c}{ n(�)+0nyh )}}�U!%�(C \"jOng �anomal�0�on}6�; ceŀ 3Q�y� excA�$c�a�Er��>�3 . V���zh@z2 n or /&Iv��Ũ �>�may l��:8@�0:�v&� no�ual (no�+5Va�)�q6a("(hX�$-�v62�! [w$6 �Be� l-C�2��j2�V"���Chap.7ZJackson'�C"+E�Qdynamic�o} ;3e�m-4rfeld's book].�=bjւay�m� - be fqV�;reshap!p��b?�en�����J.��;!ts�+ out~O�Eal��r�i,EQ(EYt�5Oat1�NT1�'� 1-� �&�s did ч e. )M60-ase*L,.�A�S93I�(��p3O2 7 �<eE��Qbe R}�bv�E!| s�="�b5�, ��U�+of�[�/�<�0i6r�`�eɎso&� �4݅i9�s��e�2 aqEnd��Nimtz%�5 ��``Is"8 una ?  �"&H��nkinkGa!��� �byׅse's a��bet), ���>ir ampl2I�s O�b!�*�B�Z -" an^5�_4Ht�6$9r��b � sensG�mn%��� �r�E�*'ill9@:CI �aGi�stru��;�.w w�P~�":����s \?%Uit��w���^Wm��sa^�(�qo>A��bmp� -)�"2� : To-�:&I2)� 1��-pl�)&!9d�/ do�Pnd da 3 by e��!�pul#, 1X=� s0�.9�8+�&E-_ t7 k%�td@b� cognP�a��n&lme�8sI|���5.])r�\7�&W j�t�s&H�e�2� v Fb� w&���in��)�A=n h3e��} for 'di�< ion; �de�AkGA?V��:50,51#I. >�f� A|u"���DgX):a � a��assoc�;�~m*n a��B'7R7!Qɍ.�a�q�*� g6� pub�x�l.�C al.[10]ZCc�g�L�� Supe"�?Y3��Q2t�u� s|8pI.�| wVvt}}, �@W".�/}A�*x� a�B #"&��5i�;88�>�52]�re�v!@ `& 1"[oryJHvon Neumann[53]. A:Bm � I710jen�m�$��"'2�a�s_]6 (&.>(&1�a�com� 9 �L p�|>)� ]e��"�Da �-�< Q$�!�-m%(� �:6��a�@�X~ty,Klea� (?un�urb��hK�s��"MtoZ"'62A:.�� �aIe%&l+��t��m"VeigenI��Bs�0���'1.}AUĂnot be"��@lya�u�#-� Hi .�Q 6��A�b���1&:.s=� "%�7��.� vN 5:o.� �� �_SwjxE=�k����73a%p*�$.[54-56,50(^T �7uU�e, "ug*2_ S�o R�(vS#.�l---Ax� drop Z��� Post� es sobt� 9Ge2�"�L�an ``ex�Ned� Zity''[55�:�y��Mrpon tachy���ez(Es3i_ �"Y�- w8i�4���-�)�mgi� ular�!U*���?-� �Sl�:tA�"�[)�Qadoxe�M1�IŠM��i rdE�� �2,� elfs,+$�b��*To-geogTa���  s�IH S� ny6�o)� (w�v 6)'le)i��eA DB�J�e9�� Z``#D�""�}�e2):v �!A5,57]��fa"�otf�%ACc�!6Y[5v?���ng��A�l��%!� ʔt� orr�,Ya"�[58$ WPl".(�UE" A?� �wP4t a bird's-eyeE�"�ect �� K�e 6�P&s u� �I��o59�\ n5DACKNOWLEDGEMENTS} a; Authx�!VefuvE�F.Bassani, A.Paoletti, R.A.Ricci e5$o C.VasiniY'st�Cng*� U�kixIte!�� anks~eSdue Jc�wifi llab�I� to A.\,AgA i, V �<, M.\,Baldo, J.D eke"�JNn-Amoa|DBl n, Gonera�4\,Bonifacio, Lsi ] ramb� 4rown, jCampbell Cavaller%0$\,Chiao, C occa, n� C.A.Darto~�DqM8 Antoni, S.\,Ese�Do, J.R.\,Fanchi, F ontan �$Garavaglia!�\,Gigli�ezolari �Horwi�XH.E.\,Hern\'{a}ndez, L.� Kret�$�Kurizki}\,Jakiel!`\,-y.Lu�!Mac8,one {0van der Merwe)$Mugnai1\,` K.Z \'ob )�PZYllo)tPernicE�\,RanfagA�� Raci!C$B.Reznik, !��&BY $z$={3%{E�,coe}s � ?9A�G+ cz=dia0,� �t�� ness�G"�C^ sBn�ra >3]x with.r=.^2� epsilon^2i� � ) itAx� over4 %c%�lo� $�ik_08,-(k Q*�i2c+� $ k_0=0.7~i.f_ 1k_0J[A�4!WPtW)Fu$m|)-Q���)� 6|W�� -nu�$k B5zCU�b�E�:�r.�1�a$ \ (�a: L=0.3\;.�; \��.4b"5F"$Ec:5 a=6> a=10J5F2:( $a=26(�|4� &c%t��� $�-� 2m�N/E� I.�/A(/*� aJj�CI��� Oc4a,�.�AT ��tB�peak.�^5A֡�q�um�\c� Baz'!� Ryb��nkoƣ2 "ޜ� Q�~_�� er aTMpre&�L 6�0".)�+ �HJGs>< e�Y spi> 6�^��Qp8b_r� l� !id�a]q!�=�a�*�n �per��G��y�Ns.6!yaS\,a): B"Mi�m�9BcI Bi[ń2{^(�q|n �)s�6M-jCj.b�=It \?i= x�Z5n �5n�}��1��c�Y"�m ��(� �l�>.02R�m (bro/�a �>�2 n 0.01 \2c�/�XH�g@!���aKicek��Y���b`�1IFr�.�� 1#s (�\ 2.5$)!�nd ~�sa�r`Q�Watu�''��A�i�>I�M ~#0-M1Ha.5r�I^b):v�in 6a��:{0o =�)?y!���e6�� doub]fic�e = 10:�$ �}a%4&�Q6i�t�Z}.t(tO V�T* X�.Bn uBn 0we�7o+)\M� \qp \�| 1&]m�@mCr�$e�I1����#G :��x7a�2�V�f��-s)�R6`$a�}�a�Q�*�"0 "D EO-�-�Ae�e~A��J9�$&�~ E} $+���$��\e� 1 �B�D$&6` E�l�*eV}: W2~W I� X"�[W5.!� �:W3NWF0NV7.b�4V -4 �%lm�NV>�YW8�WzH�sAM$��#FME>?2�D"bL $d� F�ES!m�4I 2FK}}$ ,>KJ{KId �j\M&�}T $ �b�K)��KJ�.�D9��ac��$�2��Nz $d� }E$�&5��naSz: �~m�6�TwJJ�aF2�2Ci�%f l� �l>O�lU]��N�>�lU>�l2:}NlMa�BD5���D9Dnl6�l�Dnl7l��YFN��8�m>mB��"b\�e��4bf REFERENCES J``\noi [1] E.U. Condon: Rev�bd. Phys.�M03}, 43 (1931)s;<2] L.A. MacColl: 2Bk40}, 6219293] V.S.&- , E.-| \& A.I. Gerasimchuk: Nuovo Cime\�]A22}, 26�74)�F: ``A4 operatoC�y J --�^x��Eon"� � U*�P� � F�4�#�QF Mz2}, �,,by W.C.Price�S.S.Ch�&4ck (J.Wiley; L%�, 1977).j 21; 6�n�� c�P�&�8�� Karpacz W#v3ool (R� D�]!UfU��QFT��)Applic� , vol. 2).�|Karwowski (Wroclaw Univ. Press; �6 �51�!r�$� rein!�6L: Sov. J. Part. NuclM�15}, 130A^@84); \ Nukleonik+. bf 3$99#90E#``!��.y� nuclB.rea�A�3�te�q�#es=m�9R 9 -�sm9� D.Seeli��H\& H.Kalka (World S"�; SingapL�199�h p.15uj 4] Sa���s� LowEL � ker:%&y�C2i3e"<89); \ E.H. Haug >4 A. St\o vnengZ�61}, 917!GHqa .P. JauhoakT"�Ve^EM hete'5tru�H: A&m��R9P Hot CrFr? Semi�Lor NanosJ�icQAY� s} (A.T.T!-mpany;!P02) pp.121-1505U5>�!�}pd���Z�-(bf 214}, 33IQ�w\ 6�:��� �Z2 "1%�deeique-I�� A�135�395�rbRef.[8]k�6] R. L~`\& Th���%^�6}, 2)�94��7KP.@`� B. L�*on[ M. Sands:��J/�on !; /,(Addison-Wes��ށE2,!�24-27�8)�*):E.*3J.yAtUn|H�:( X��>�]"#&0" [Lanl Archi�%e-�# t \#$-ph/010200g �$��in)� cs RI$�9] T.Eah�:a�A�6T�U342eV6ILe�FletchJ�18��55e�: A. T�cozzo�1�-D1� 3�. 88);a�2!^(E. Tosatti:%�. Script�L30E�88Y610]E����# A.A+3m%Equ�f bf IaJ1813 (1A�6F5aQv �A52a�2!m Cf�  K!r�g(\& P. Busch� LettC18afi�]�1 ��a alckQT�FjeldlyU&�B3aS420�87=2] C.a��'nsL G.C. AersJI89!�20�89I3]}�GUm�FIA47a�02��93I4]a�.6�nN=:4�739!�8*� 15�SScr-�3!�42%� 85) � 6�KI.BA_JAs.�TA�451�6�7] A.J�*z'&S��2�I�%{6.�8�?AW16e!2?9���Z*M�B�E63e�.E20]����kurai��Mecca�� ~ � 4a Moderna}, (Zhelli, 1 �t 75-7�t3�M.2FPB2AP 6178a{8]P22�.,&eJH�G28��.H23!�Ja�gR,!�lid S�[Commun-�8A<86C9]�,24] D. Sokol/��5LA,BaskinF�Ai�604�=�25]�FH\"#ggi*� �QEPath I��7� .� &� � p.352�/26j6�J.N.L�nnoJ�i�46-�N\ "*H��� g2�}�6Ah23�  :k B�B1346 ��.�7r�In)'S�0a* McM,scopy -- III&G R. Wiesed����HAG޺(ntherodt (S�0ger; New YorkW 93), p.10&5 28� Madelu� Z6��,3�J26 G. �B:aB .rRtMx A11}% 6)��5 5�Ea��B: D)y�'10 C7) 533B5BO2��57 ;8) 98:�d$28# 763-776(HK. Imafuku, I. Ohbal(Y. YamanakaNn6��14�97%",M. Abolhasan�$M. Golshan"5�$A62} (2000�I,ssue June 14�IA�Egusquiz� J.G. Muga�.K-z9KDecK�9NJ!e\`{o}n�0 Julve, P. Pi %aFAQ4de Urr\`{i}es:� &� 9903060:U� %iAE@479��9.9 9] F� Smit"��1� 34��60٦30�(rK2C SF IdE3 �*�31��0P.L.Barbero, �'�'a�' F.,Au . [E6�|28-�i R�V� &� �*8])j � �'. � qV��s ��*)� 248} 156,e�8�ޘ �5]�Se�{bL�}�Europh{��457}, 879%/2eFY."�3 , N. ErezJB��(.w ⡯$ no.052124LS ݃,32] W. Jaworx \& D��Wordlawd.QM%3Q283��9*� 336�By B8�311� .348S.hz���MaTor2� ��\8FK5a�.; !�G. KwiatZR.Y. J,2�a \71}, 70� 2�6��*�]�J�E(F�) �� 78D 4). \a,�3,�SY skout�5A!� nnus�\&�� Mign�"hA! AT 218� ` 37] G., H.SpiekM.BrodmyON�37� 2W8c >���i�2�� Le\`(pwMe�7� e�V.�,�L.Refald.ya&w�B#%&�0(fk emerku'aɍo.��%"gb.Gpub.; \ }M.Sc.�!|(� , R.&�.���Eervisor' �]4. Dept., Milan�ersity, ��"� 39A� ,>\&AN%�%�d&�%� I�6G 2) 1693; 10M8� ��D" � 960q,;F$E��632� F\��-�H. ML:A�dB�HRW. Hei��qG.�%*.uA19/ 5�^=� %j�in, WavT��8L�,�-M�' r} (J��+i��$kshop, Ita�/S!��uG?d. bya�2�/ lH.� �a:.�ity&rE^A�A��o&� E.Wolf,�37�.gH &�2�be�2G  Pazz D� n�>��, 145�]*�42] Ch��lan,�DSzipocs!� S�=l! F. Krausz.I��H 7�c23���c�UJ�: an =�ji�06g.H3 i� ; N�(e:�+0``��f�D�Zv7?" by R.� , Oct. 21��k*$st: editor�1``FM:"}1p.M�lu��by J\wn $ 26, April�&�cT"!!CBG]�45AF61�k�Y�a^.� >�!�ic@ B175M5�1E�A. YGU.X FER�YT: .H*� 5a�774E�[A�2� � � >�e���{}I<>mU; 5] H�s"� ,�+2�1��*�46T��� ��de*�"���B� �}V.SZ�G�6� � ,:�!�EFm�d&� )A. �8:�S.L M !�:P�y1a�.> 7-p.327-35]�8] C.G��|e DcMcCW22%�A�3�P7*u�M\hu�S. Wo,Y .f29��� e%B.S��\& B.M���]�A10F213-21Z�QZ ?| , F.�8SR��8�t Mo6A  27�� �,�;Ba�:�P:bMNE&_�3�G�` � P}�A� R. RGl�9Y�]J)c.2)�� 51]���{�EKa�*dL Px�� ed.b�� (ElsevX��ce; Am)�dam��Ax�37�346-40�$ R.W.Ziolk� 2  E^2001) �0� ��9� I.M.��eris:� ),A:Math.Gen. � %�L 7227-7254; 7255-7263P.W.M86niDB7,2002) R31-R5�*�S�W.H� h rBi 7) 81-10� .A0A.Haibel: Ann"@ Leipzig) �3 �163-171� @: IEEE�S0\yp �um Elec՟ . 9(1) (2: Gy,2]6J$D.Z. Alber�(L. Vaidman;-d� ]q60�n \.RA�Eq�E�R4� �Y�3.F�aTGa\q�S$s4 �um�Mc�!n%e{ 2N$A�.�54]E_ Duck�D ven�o\& E.�6 Sudar�F�D� 4� .~55�, e\.�``Clas��l"�BEatB ۿ>%s," Ri[�a "�&.�8%ia �6ey1-178* e)%�K�W�0Rodrigues Jr.$!A&u�e�G|a�C� wo dT'�.�$GraviQal RaS����%& ty,}�& J. WexL�M.x&\z(��ent>�85��151-203Y?6��``T �4@�g)`�6RE",]M�Q�Ric�#1��#8�&To] @ `Anti-telephone'%"$adox: Its �\ �F �m�',"mN=�e4� 5�� ��7�J��6.$*-$��kp.13612�� [53,54]I+p.2807��ZL 6M ^��A 582�S.�Y, M.M�V� *lBe&kP.C4fJE65�(no.045602(R L.J.Wang� Kuzm$� Dogariu: u -a0n 277 �d�'�\���J.-B (&�#�3Rapid�4e|M�Nu#lU �f� �4A2e 133-13dEU R�%Z49. �)e W.d Y�92��"�EX3�b1119-113 E_g@2,�X;$APPENDIX}}C0  1. -�r�ca�.}\hf&�� \hs3�*{5ex}X q'[of\-lumi�'($V�r>c$)Fs ���J �[a�storyzZjng�mhap� 50 bU|6Lucبus'' De Rerum E a}�D��XU{�p0201>' S�|�2^o�#J_V ets D�.5�N�X,��Ue.J.Thom�Rt�H0��" he g� A.S"�Ua�W�<�I �C&J� 1905 U?vPl c ?�8 %G $c$�l��Z�Y�� upp�jli�c�ny՜ Gfz �%, R.C.� in 1�)belie�Yo�UJ�b�As `��dox''��� e#\�8z'lVd&���"��8�WoKhav[ �R�q�2Q .� past��c�8co5: bloc �� E@ bʠa�Aur� -a�)�an isoX�d)��22s�^7�&JXG!�fEanaUK!dݬ �~.��eds. O��roJ?=&[Cack=W�� T��DM�h�xftoQ�six �.��ar�R� �s[A1]!� eorg�K  eQ�A�r on[A2 1�A�,�_��"T4V�OVX�msub� �.A�pop�K }��b fex�Mb"_�8e S� ���"��> H.C.Corbe�) Ns��Q>�}s2Ze!*b}5�es�?��f�;e"�\s look��.Q ��&�rby4(lv@$.�Pl.�yre�k��Ccheck +Fs 162� � �%A|�w���600 c� 6IlG�d; A285-290A, A 3]; \592-597!O 4]�� 29885];�3w�mP�T, bibliograph ��ve &�N�@Bk�.v^[�"�Vi w`IQ^to�T!�t�� reas��out� ��.#�[4e-of-the-art: •�@ˠmpa"�� ��y�D2�in%  ca!��zro�?!�A�e`N�Qa]%�co��BPad m+"�Y;�)A�f�ht�^c�O�C�-��I�؁�P� in fash�today`!0ome���1thy=sS rLA2Je#�e�E�S&� }.^� � �Fs�+��� �J�0 �SD (SR), abundantly *�g � ,��be buil�W�<�, n^al*�TG91)5W� laws�8>"�wsm�"�)c�8GGT��vNx.�uE�bw~W�SQ} ``inS+al"5� 2�C+ �E� homogeneo�d��i��� isotropic�^��se�Փ}�����)�oO` �zx,�in� a�pj �(s� �R!� tell���Ra -�Mat, $c��f>j `��S9�ghm�ss� �D peculiN�e!�+C  A� ng a>�!��g �i&�� �n�Uru��o7Eor away�TAob>fr.W�UۍE� ~p�5G]at�Zs quit]EU[io�Z �$c\/$:�d brad�V+ no�I� enjo��� pr�:tya�2nAn�� (known-������_&�WA3� EcL�8��d��O s&z�m[v �v��F,��!�XeOH�(�W�I$c->�(Icis�v6 re born l��aJdi�l�a� �u(��� � �c_�r���L�@!AKla$� �qj�r�#�_2�a[A4�� �eJ;$% V$� ��an!��LHA��c.:_�fq��qu�� illu��by B&(1972)��&w �8� dem eʓud�Y!)�a] p�r�IndJsub�[i2� : $<<$% S�Hsz].Y calmS\e+�A%�zno  N?pB Himalay�(qnZ � limbge moun�R��s! Ø� \n absurd^c`�X#y nI �� Asia�E` �ndIj:� y�fŧ�!R�A�in) 6crY�!06��2%� f7!-i -Ep �s$>>$� ���!6��d�M� E� the `qtwo.�(b��ir!�ven� 4��jG{o�l/\q��rsq [A3,�� �|���modata�soA e"�a� ;͹��te��2��+&� �_�d&� mai.�� SP--"m�PAls)d� n ``JP ''3 ��5�>17ł ݂i�M�!}v�^yݔevery$be�!�O�jE��# �f�d it�1�2�AL%UF�ct��Ao">^� >^��R�Z� much�otrictr(Fk^ c�kE&�`�� a�},���^asH so wׁ�hňݥe� t��ter\/}[A�/Th�! findsp -� to��5 ��k��y) P 2����j�xE wv�X��poy]ve�)y and}�@du7P�� Q ``�V X b��Z Z"�]�B''�+���hI �<to us a�-u�!V8�a��---re���}����s �Q>�` � ��\�y addiw''h�ges (|d e� �[harge~� vers�PQl%^ŵ2��To� rifN is xt"���S�� ZZma�cJ " s,�Mm~�a�!�a�c� ͉��ell�� ed d#R,!X���Xz��e�#�65qE�pyjeB�;A)ry��i�Q, =B7e> �"��b �n]Sa�u��C}bbys�ti-�1]�opE�e1��j.�M18 �4]�.[A3-A5]..8v�l:� �t�q��*x�� . A �T-.�m s!�Ao, � is baAH�d26 by U�_�b4{s"�dse� �,a�"� @�A �� �a� TyZ ---s�i���a0� $O$!�K�py A%�r��B,A[ G{�� C.G^{\���Z�M � T' �IX! �5�e�:_.&��by� ��܌}fobligHG�� do� e ``nteEp� (rule" or sw�itching procedure seen above, T' will appear to the new observer $O^{\prime}$ just as an antitachyon ${\overline{{\rm T}}}$ emitted by B and absorbed by A, andq4refore travell�\forward in time, even if�he contrary {\em space} direction. In such a way,>ry ` to[sy past �ev#\negative energy, do disa%. Start�rom this-)axp, it is possible to solve[A5]p� so-called causal paradoxes associated with Superluminal mo`s:0,which resultibebm!Jinstruc�,and amusing,"$sophisticaqhthey are; \ but that cannotX`re-examined here (some of9m hav!(been propos)�|R.C.Tolman, J.Bell, F.A.E.Pirani D.Edmonds��others).[A6,A3] \ Let us only men! �|the following. \ The reinterpret%�L principle ---accord�to)?�, in simple words, signals are carried ~(by objects %{}4bA0 dowe-� posi%|IF,--- does eli!�0te any inform �0transfer backI�U�)�is has a�ce: T!�$of abandon�he ingra%�convie)�judge!G� ut wE is cause A*effecE�(independent-�M�ereh fact%Hacase U,�efirst9 $O$�sidere�a�nt at A!�I�e%Qh"B!�ByAtre�bsecond.c�� ��co q/�QpB��!1CAhAll0o�s Lhow�2�MAe�h�,,n chronologia���b��$} its own )e. \hs��$*{5ex} Tak�n��Er or A� ties into�I?0always forcesa04to a criticism!�Lour prejudices. If wa1qui�{Phe phenomena to obey �a law}E(aYrded)�ality �� respA1y)2 52,Ino�SdemAl also ddescripa�,} ``details"A���ondbA�varian��$o: Namely,FfaHA�A�s i >cU_``%�''��``)� '' labels��82] \ To illustra���nat�Zof%gdifficul-� accep�6� e.g.6��A f%L�dM ir �hyo, l�ci�C8 analogous situI c�n ����y!�sent-da M4: $<<$For ancia~>$ (Csonka, 1970)F�0he last centue heoret��, physics led��in a e+al way  up0%qexistem�a�A�typeseZ� : magna@ monopoles, quark�tring�r� s, be�f s black-h0:e�bsectord �could aAgoa���!k them&� A�e.�nM�' �Wertain (��be�a atte�aseyeg en paidAC_ links a!�among[:�C, a6$ 8electric charge��ex��A�o behave��aFC;%a=%jori���p�source ax)` ic m�r)�,.a Demo��� f Abdera%< ryth�A� waainkab� it%hmee�� d� %%%$w� �� e un_ �(universe. T8 poi�view ---� {giX 0by M.Gell-Man/ e na� ``tot���l} P ''� Clelon!mree�$(T.H.WhiteaWe�humorA��  ``An-Aeforbidd� Ps compulsory''. Apply!.i�� -w,s, Sudarshan �%� clai� at��if 1)5��musN$ be found;Z  � �%b�L+be %�a�@ay clearly why...�&L\newline \ {\bf A3!}e!eri�߀al state-of-the-art}.\hfill\break.  Extx d Rel� mcan�jowA�et��unE tan� of m^ a�s��of�&� ary} r S ��E�f56w� �J%AkI cosmo�  asympto��ly fre�� e�4ready said, weZ dea�A�!zmA�T AYsi� thei�pica�A_(ently retur�Q,in fashion, � ia��la�) ac� at le��four �er���*9��1� mE uggeA>he "�%��Dfaster-than-light �!We wis�'putA�th��"� e� . (mai(bibliograph�a)��ex]i���eH eachWthose� �pͩ �.% J�)} \ E�Neu�hos} -- F� : A l��se !y�řa� in 1971,%Q= show� � s��8e ${m_{0}}^{2}$M!�mass $ muo��n�! mre�ly;�6+ too, is �;"f�vfirmed, ep �(when M�Lna\"{\i}ve language,��m7  adopt- s�� ses� ``imagia�� �`�m, M  .[A7. \ [In�6 �6��� persionm�onA� ai�t e0 becomes \ $E!X-{% \mbox{\boldmath $p$)�=-m_{�o $)���� no} need� � for 6� es.]_ �ABYoPGalactic Micro-quasarI|S�: A!�v q appaa�} S.Fexpan%� eA[cA5of \ [A8],UI��&� jg�m� ?\/}[A9]�Ash �U�� 屍�at/blT too far Xe  t��eNlpaper:@� �Wi�at !Ui�ast�m�& � s ��� 0 odox 65s, base ref.[A10]ACat��� �!<l�B(ists' major��(K if hampX by��walaj� �s). \ � X"F discus%�--�!Y��� plan �,%�``."�Acluded--���1]. Here"g-_}� +geomek B��� Minkowski���aI4single:�l�+a �wlook[A11a�: \ (iO it��A�� ``op�8 boom'' phase (&� acou��``*roduc)�a !<e *�E�!qtfsaJs�Gspeed),L nE>nsa �H su� lya�ear��", �eweaker~ !b�i) aftes see�)pli�to TWO�e�� } :?�� $\;V>2c$�cC�cEvanes�4 wav�n� tunn� photons''�� Third: Wi� �64ntum mechanics!~d�cis,� )�T}�� ), it hadFE3!�a�3 ---Ply evalu�I� ``I<�R9{calcu!��r�aEA/yg3 !packe� haviou� [��� ?b+r wid�s of opaque$0s (``Hartman f)[A12]:I> ��.� an�bi�ily l� 0(group) veloc!$V$ide�eno} �s:| Figs.6 � text� E"F � ,at may verifis!��  by, sa^yon5T �. Luck� �,5�Le S#E�er eq�I* � � a po2al� �e?ai� q�$Helmholtz ]� !t �"H!�A�pa�' e.g.�w�metallicEgu!Wa� !�$x$-axiSa�he��$U$ big� 3 n $E rB (���$frequency)�a���ns� siz!�w��cut-off a#e. A seg��!�5 ized JE���..M9%?��(�icA�3]: So ��* assuQ ]ina�likL 5 i� a�K t �c&$ ��lor�-numbe� d gej ���)4e, onen�8 d�d-�$x$�yIs�b an��e� % }y (.�!� norm�rMG� ]if��re�lam��ude, M !( narr� e %� � � 9i�3%� !��Thu�j.1eu�<bA)m�[A13]��� ng recour���sI�9�con�AK����y f� pe&e�$[A14]). An�ye8atFlt %76� ��s�( actu�g �� ied}�Fa*� famouK#0s (cf. Fig.A36�zM#9EsA�per�ed�$ce 1992 on�( by G.NimtzmCne[A15],!lR.Chiao'� 8d A.Steinberg's-J8at Berkeley[A16 7$A.Ranfagni� colleagu�t Flor[A17]� byI�sO$Vienna, Or��Rennes-a`17)�`J�"f�2�ies. S� .1�aq grea�al�u est[A18�lso%��L-�ial���A� nd w� repoR by S�(ific AmericrN�, New !*�n,sweek, etc. k ad- �N��pr�eA�9]J�^e..$c$M�;eOw����BaD�7��*[ly self��4��debat=. cur liter%&�rep 9�al">(i�s be c�� ctly!{*9 nu)sl elabo� $[A20,A21] "L Maxwell���), �ra�� ques� whe hey� owdo�  a�� �s�[�onEU6J �G[A21,�� "�e�u emC �T�΅emos� eA� ing}=�M� med�" ( �)��: n�5�bea�#P�  zf�e[A22]a��agrees)c� u�!DQu�  M"� | �non-re�t.Ot2 wo� cess.$� �s (Ct.= �� �)aoe�"�2", Q# byA�I�*�!�qdi�ce betwOtwo� [A23�E�u rep��5_�!1'a@of_u "� &+m� surp�> �2��%W ��g��by Aha�v et al.�: Inde�� auth�h���,��g!"QMa5� ��tR , in zero%��neglig�%!?or�AA� a>s Y)�� 2s. F&6 p.�,JM�ion�9<re-�� by Longhi.zueia� lass� )� s!� g��nga an +fib�#�im�J���!�sh b� A+ed, t�"advantagY!- circumM�EXqu� e��ng�1ce regi>!�K%as5���&&��|� ed manneX by s�#al ��� ,nd-gap" filte$(i�}"� crystals)  an� se, bo� �``� 6�"h ac6 it�,��A��"5i�f�N appl�'!Y-�� ofm 6 �-,�$�tUery. .LKWeI� skip�ur�Ya� ��.!!de�e, -�:� �brief reR� %.oneR ��M\)' � &h�I"�gto��(&\ at P�'etoe 2000�+J.Wang �)) rais_ lo�Uf. \ E� i& &Q!2 �=N*�� "�)} =�)�@[A3,A� nAv thel�����a%&mi�6.� is m�n�, ${\JO=��&2�)l� haveD!Y withIT�2_s}�A�ݗ���4]:e�!� ou�!�� reg�%�gun�ala1� ��e �a��!'' (p++cl�+:q�e)� �|#|}� )�� �-w �,n& f!�r��'*FM�� s��'�!``i�nti}-� $\��{1�} $.�� o�"��F�'*�, ��� �+�^K��8lab���M#F}$ mova� v mame} "�,�1�?(w�"h�� !�� � $% �$ pene�&w�$,fi�,fq�R(E�al��B�12 ,�,�<in� s6�)-�{-#s: ���ti-�R�$*� � ��t�� � %M-Y5�%�--5^��e� new >���,+ h AYv�nyield,q�w>/{}��a�\/}I�$�ɋ7� ,��bQ��larOKP e&Zp �f)18E� W!Vw / o �'sa  # )�A�!|vve�s &d� ���Y)ba&���� t�sis,A24,Mt�(I� ��&on-po�_ ,� %�F �(s��!|���a[ ';�aa��!6 h�_!0$\lambda =+1$tI&� ��b�OoQ� J?-1$"x  &'��6w b' r)�9,v/2�25%5O)4(B� !)6�v Ap�s [A26>eŽh10a#�  m�o�!� 2���usI�add} Ja� , vi"9 e �!ce ^s e�0ree-levels at system�Ax�b�1o:" diɼic)�!5r��dK-�rapidly� �%�� fun�/of&v,EA �,! pleta%s�+l;absorp���) 8!�� [A27%� 2� "a \�.��#e�a �um/  decre�o �x% valu+eiA "�0or�Ks, ���� pdisa �lI^0kne!ǁd s� & � y -�D�ro�3e_�� in Bose-E�hein|densat�� x#e� sibi�.o� duc��})�to fewT per4$ond�Similar��W6��---�A' a9�f�F ousa��ime high*�1�s&'3� �apen-B&x]eAeE�{ I � I�",minE{ nQ{�-� )&"� a rubidERo1�[A2�whS.Xs�!se*��3b� donG ��J� European3 ~,ory ``LENS''2F�F�(0K/:�>�*�le�E�53-$�wa�FnY �Zs)� kso� 5 &5(of anomalou~.�$n����b!� �non a� ge, s$di Mve��e�a#"*.two� a�a,���of�' m�!!�E"�W�(f. G.Kurizk�'s workf�$D&y 2� Loc Solu��s (SLS���j&@b*$``X-shapeds"H��(tha�tor (to�(-� the �s)��� � "�.��}�fi)�n)�b�schol�i�ginee���7� �Rons,  z(8$ W�5��f ):i"�0by2�![� �$ny�&M ---to fix�"A�M��!k!�!X:� A�� admi�s�8-� so m� sub-�8as)�(f_"`!�s�&,7� $c/n���re�l�, s=)a�VRp+)b!!H.BatY4!Mslowly��j�9%�5*s a� s�#: sca���1 $, spinoria�*%#N let-�0*-+� .(E1 v"�! [A29�Sub�t��{. su% A! written�1� � 30�'*)Zin�� 31]��!� j.b�!�3re� ����6�Lttz ``�8+"x 32]e�"Y� A & e�_sS:J ���hesI))�pc�0l�3,��-�,� ve��&A"�9  Cour� �Hilbert')� termi�7y�``u�T�ed�g�/iv($s�/� easy�r�-z�* p�� �ce,�.� ,�a radio�Wmi�'"�:ut!�� � &�9�+4. �7e�� EJq��But-/�'A�� �� of u:�&"�(A+��OI�;of�]� ary ,� 36yA O&NtS 1980Da�6 ��n4]I!�1lsZ � pl�.sublu{; *�/Lcei��� a sm�spW , �p8 asy \2��g&st)Z6[�'�=s��o/i�(s&;34�nd� \,A5E�A6)����''%��a dou� ca�.��6 more�AF� ��A=dDm�E� .e., rig� �\ homogene�um[A3��I�w1+�)i � ��"�bY�y�;���m!KE�5B nes,�<�a>,p�" kii ��,M7M`�� �$-� hyp���!=g7J7-usual� ���#<&\,C0�,icaY��� j$,c�ex�A�ame��to�,}_ Hof&�*a�� � eismic  (A?perha��viiyab7�)tooAc+#���)s "�*� � of B�)l ,)� � .v'.�for���)�,)QA]|+.,��Lu"�3#:E��!tc0��ed a%''!pm6� 2� �GI�A �qk2@EH!�6D&# ,7��� � *� �I� � �ith>+)��!�9s, X-)z�"G!�徥�m},�vel�':� m�*�s�5D-����n� #0?$� In A �?9hD�� .�y9��mselv��6]!2%, �#Mayo Cli�E�� p$re���w>( IEEE awardE�I�Vi�"� �},  �0,``intriguing�2m��XA �� %�I�:i*.�F&, �M&7�."� �% n,r�m9MIUby Saar3 [A381D7!CTartu�PviYDl�(t8�.ndI�!KD S Mugnai, R.:&R�5ri&"Cby�1ej[A3� F#eU�alr'i�7r!�g , Cl"y$.U5 :>�%�� nse:A6ordA�$o build up��Yex��� new �-�>" e4�N!�:i��QB  #iA�4�1!JY].;S?�)ng ��"a�#e��)[A41]�iO"p �aa[A42];�ou�2get�Ca �9of foc�U�%�A&,��[A43]�Ds�cE0 vacuum! emiE�V� $W$ (" A tq#&��itCt"� $% )�>�w�%���l�e6Q!6%n�K tang�:�D n encp!0* $C$���9 -Ax�!ax�Pm�o�8ne $xt9��4[A4!�4�4�Ao&i�+�CfHa�2 ppen�Elan]1o� ahe ai>2th�<#t� *r4 fs%p%�!�#=m3�Ke� �պi(A� �ts�%fac M� plac�/ �det<47go-uo!] =.rd i�.E3"5 ��)�� hiE�(as (cylindr+A�ymv) IkaiibXim�ItI0 be e�2e�a�o��!i:��6�5�c�cO!% A��#�ea �ing��exa+_s�(ax�6 ʼn�-� p4A%) $W$,��9�ng�rR#�Rw!�)Ke+&��.�qx V$ (��,,#aM���er�eA i+)�7�9�e��- W!'zJ�A� For ~$�G1�r �A��G W iwetH��A� "�-���>��s�Gto��  good%Fer� Us%�$� �f�!b Orri�a(%{� $c$)�):�:F'E$<edE �%)E�i�7�un�Asn�@�$y m  u��ULm+*-�A4n�;�e-�Fve�@hA�to doE��Ho_sciss�)+ ��!!�#ly �y� -"�3.�#9Al:ir�P+th<as#��'n�3 �+�� % * $L$�click$ a)a; % �erg$!L/c|�2�h*j"T a�idw!���b u.�Y�*J !�h)�"_�2\ �2 t�>ic:!�.U�6�.,A��Jol4 �4�B� ���end%�a�i!쁒�F�!� �4+"�.6 �s,M�B& �4a�jrB&!�a[du":� im5�!�ar| ehs}B�A& Z d< veE�XN�Fo2�  (or `'=-�m'')!wm! !� titum%� I�Zgethere�!�.C f >N5�4onT1-i�ofN��3Bu�,�%hF� ��?/2) ��-t Ps>*ifTK�+�� ��%� �OK �Y��ile eg.�*�$O�K!#��."���X� (!tak��"g,7��h�-��� !A��%R)� inqc*�Aj �j%2F�3in-A��< ltra] s�Ners[A48a_%D page�Cap��_FigureA dix}&G�1@DEkTl�'e@Fa�a"���X[A2-A4].6>GR2RDep3I ``swiVrule"E�f+S)iStuecke,g-Feynman-SutH8-Recami[A3-A5]:"� $Q$�M7�IeI%��PA�Se |r�A5c s" (9U�4"6), � 8�3F���4~Y5�AT/�H62o �{ �L�/!8Ew�T2) ),i�E�A�/ :B psoi�UA(,J*�,---duEU\?0�3we.T9a� $v(�� (e�,Lu, GreenleaY'�3�7"�7]RS8� Sche�Qq"�aFS>�Io *]uc  (PRL�,24 Nov.1997)H9D!�1'-%B�i�#F8:�is PUF �:I�8�: �,�.ON�\s��run*nd catch|a!Fe%Q]��0;2ul Rt:��M.�l&��� �"!5?23�5)�^$�jLw�*�@xAn��B� $REFERENCES1�"� 6� [A1]�Z� �O.M.Bilaniuk, V.K.Deshpande \& E.C.G."1 |: Am. J. Phys. 30 (1962) 718. [YZ�E.I�CR.M�>ni: Riv�;$ N. Cim. 4?,74) 209-290; E398�U !�� � Cf.� f (editor):Tx s, M"[W A�� ed T.8 s} (�X-Holla?TAm�Q dam,�P8�%;"iF�9�86�*ssu�A<.6, pp.1$\div$17 ��&�!+42���y�Annuario 73, Enciclopedia EST}, ed.� \E.Macorini (Mondadori; M!�o�3)�85-94a! 8\ Nuovo Saggiate 2 (1:�3920-29�5. �I CEEtti�la Fi� � F.Pol4� \& G.Tarozzi (Acc.Naz.Sc.Lett.Arti; Modena�9 �125-138�1&J8W.A.Rodrigues: �Vt"� s�SpezC)�� ", Fc I�ics 12%�A�$09-718; 133) E533�6.�6B 17/7) 23A�6A�a#�)o Ciw o 4E�(85) 587-593�!�(P.Caldirolaa<�YI�Wan�d�/|Philos�O�(Dce9� M.Da!��E =X-ray �", ƅ�95) 141��$10] M.J.Re�X (21�66��A.CavalijSP.Morri!�0\& L.Sartori:�Hce 17�S71) 525 g1�S,Os`i��a~y}TM!�on\`o!�Cor s &p app2V6�"1VKYser�%�'}H!���B9�i�9�OCxZ  Gen.�j. Grav. ���61 �<2] V.S.Olkhovsky۹�M RJ s 21)�2) 339��K YD��  T.E.H�Q:� aܱ 3�� 3427� See š2�,� , F.Racit��0A.K.Zaichenko^de �-I �x351-1365A"ZX�J.Jakiel!� Unif C;` y� >:�� nonr2�\x*8<" [e-pr#_qG$-ph/0102006 P!in� 9-iI�32� Th.Mdn�R.Landau�W1�v. A4%�!� 2611�� R.Y.�d,o, P.G.KwiatBA.M&"M:Eica�1 C1) 257B&!M , D. P.Faben%<$G.P.Pazzi:2�Ƀ5Ł91) 77� Y.JaphMG�4 �Ai�5E96��Q�&5a�E.Kozhek)A�ofman:�6 �4Q $98) 499: \^HVG. F!% M.Blaaubo!hpa�8�C�dIVII Se��(�H O;Ws#(Lubichi, BELARUS (May�9� 14.vF.Fontan% ,R.Garavagliaa[t� Mo, . A15 (�C) 2793}���a�IK5] ;O,\& A.Enders:a�di5ique-I ))2) 16 )�3) 1089A�4) 137E;-�E4)�3) 632arH.M.Brod�Xy, W.Hei�U!_ �:F�e5i�I�IQA22 ��25; A196* �5Ed Ze�t: Prog.)�. E=C. 2�H97) 8�o6]6 :<uT2� ��3) 708.(�"1�! t.�26� 1�U( no.2, p.38�U��6� 17��*�i�L m�Aq�2�9� 145 Ch.Spiewn$n, R.SzipoA�lQzZMF.Krausz2M-31�2308, A;� cou:L.D�_auxN<IY!�5��V.LauP.Tourno,VJ.az. Soc)`B16 9) 194)� F�P (Aug.1 3);\f(Oct.21e�3)!�NewEm\ (Apr55s�Pt Jun�R5� �PRe�\3]!�158E��16-11�1�5���5� R.Rh,A#,�>�)sA20I_5) 227�20]r�q=1�J2v J1A`4P.L.Barbero, H��ern\'�z F.,!��``�@" Xon � 6�modes�C��0ics/9811001],�R�3 E62 �$ 8628-8635N  \e�R� �'�:�. "��b�S764-77e"andm&"\# \�� :x���r�CinA�ics� 4by E.Wolf (Els�r�? ce; 2(97), vol.37$346-40�R� r� EJ-10�R.W.Ziol~^Q-z3ł1) 04660� �haarawVUI�esierm�)DA:Math.�  ��L 7227-7254; 7255-726%^ P.W.Milon�� B3�$2) R31-R56a� �:�0 J. S�.i �um��t 9(1)���63-17� 22�:aq�8A�H� k1�W= nd P� cl� L� b\M�)� �O.vaKr MerwS A��4uccio (Plenum;�o York�� J. d2�./2����5)|%�B47��3) 960m�3: ��&=G.Salesi"f .�"57, 879%F2W2"qY."�P,k Erez�B8 znik2SA61� no.05212AV S. �O�� LalH0a, M. Belmont%DET� :``Measur%9`2�)al� �� ��-bz(ertFic�Sgaps", =DE��a10A�A �Esposit2. E67%*3 6 1660�24B��j r�Z1 p.1361�b5��[^I�.Ubs U 4], p.280�B5]& e&� A.EAmndZ� �N7�> 6) 1a� \ �BA�re� D.E.McC�\6� 70) 3Q�6] S.ChFW+hW.23 t� V�M�Ptchel���= 8A23U97� 3-�uO'C� J. BAMz( Rapid Note$ L.J.iO!: Kuzm'�oDogariuss�r406��27-{7��AlzetA�A.Gozzi�w L.Mo� G.Orriols�R� B36B�7Y ��8X ArtoBPG.C.La Rocca, F.S. Ca�oJ$\& F. Bass9} A (i�xess�29bB5@�_iarA al�4M"} &B ZB191h R.d>\& D.HiP%t lMethodsXD�`�`��Z (J.Wiley6^65�B� 76a� J.N.B @ingham:!�.�5�|�11 >-J�th.�42� 85��  J.Dusl[Op� X 7) 6� A.Og ut et alU�M�14� a4� *��#0�R 2#� � 26In�@S�Nto6��8y} (McGraw-Hill=[ 1941)� 3�.� J�8ip 3) 5� 8� �mbA R.DoDe�>uPr Roy Lo�y A44\4! .�a�M."�\&BX1�EL. �8] �� ��>�-�22Y�%~ J.Va�28; Adv. Id4Cliff. Alg. S-�57) 45-�2#6� �2R Jr.�AT �Cel.�5-�K wo di~�:&�<��e��ty"� J.We:b\& T.M.K�Se (World� t.; S5 pore�85A p.151-20�J�33q 9�,2Y �:� >��>90,511, Sect.VI���-�(E? Suppl.) Bi�9P ��-�188C A�1��u�(Ignatovich:6��78)�! u:�1Ta�B;� e�)�L� 0 Broglie, Jan�4;d ``Q�u�rE�>��, ts: &,HdG-<,ld Schroedint%. � la(Y�  Bo�o"�.D IC/90/99 (ICTP; T!tE9w<$5�D:u�>�A)$��50�� P."�vI)�k�+. 2�p80) 2�#uA�6:J>%�>15D $35] J.-y.L� J.F."N#� Trans. Ul-n. Ferro� Dr. Freq. Control 3�E2 Q$�`R`437]=yA�ica A25�8�aC ���1C��L<'difSFo�I�Gto"pB�>.o) e�h�@"^"6 Hx INFN/FM--96/01 (I.N.F.N.; Fras�S, �1m�6>:_\&2�:��"A1�^7b o>P.S�$\& K.Re$8t!E*\X>$.$-invariant*�0lPew"2I�� 1� 4135-413� 39] ���Q�"S�x P84� 0) 4830.V40�uM.Z�h�)1�O&{a}ndez-�/eroa: 6, � al D�20�217-22�"} s"8.�:�M.yl-Rah�A2�4A.Chatzipetros�j�&�4Research (PIER20 A�1-4 A.T.Fr�]gE�agerholm0M��alomaa:� $Commun. 13�C�20U�;!�U J.Huttunm D.�ga/6`a�� v. E� 434_��^ �1804-181e��h�,:f6!�R� edkyR ��954-196�m >"@it Time's Arrows,�um *�s�*2�B8n*MQ��8 (C.N.R.; Rome,�&(1), pp.37-4i41� V�Fa��.� &�@����y�o:p/�@>Od'':Pit1 6660� 2p�!�q}z.�*�)� R���Wo0:� '@-+9g!8se":�"�$036620 [7 / s �!$ K.Z.N\'ob�6&���03!u.� ��)";ngI):�,�coa,<�/>�6��2�17 [10 ��^��#M.A.Porr�OR.Bor3b\a�Santar� .��6$in Gaussia�@am��� �20@� 83-18��42Fe:D98>h��U�S"�+.�YA��!!�U��(v�@or) d:bC��c�{Ko& w�GadX6�Lgw�qJ�02091� 62)��5-2 6ᵍT!�4H.S\~{o}najalg�Pulsed .qI", Laser�D"V 32-3W!"� 1Ee�)6� C.A.D^"!y=�.��lz�a�!�M>rK",��4 of S "<*� � ��1t.�59-�)w�,hFar /(xb) yb ���3F�.)!x1)!rFVEed"� (.v69N30909�VsubC�= pub.ZJ.�B� ~ Said�TeQal&�E�gA6��e $9"��i�SHAm. A20�3A�658-166� 467+].7>&G�V�r5p��Bnas" 4M., -f�8� u�  an,.��] ion:�ieue�6� ؕ��20� 75-8.6�#I5] 5�� amboni Ra ��A�1��,Y� �Ev1�?6S�0"p�", "z!#AA�. iB=e� .\\� 6�.��$A.D.Kipple�C2������gZTdam��ialA.w�)= 026615 [9�F��u =�O'0s? A bird-eyeC��0ex�[ al status*݁N;10110a; "�1E�(1) 1119-1136�%�"� ��'42]I+7�1C.�(i, S.Trillo�Di�p�� G.Valiuliy\Piskarskas, O.Jedrkiewic#J.Trull!�N"�Y�*� u�k*� 9y�70406 [4-�.�2�� �EP�!� ParafG.D��H I) 1090-1092),8"� -h.Z!:&n in M�3SZ# "tt mc �4c@aob.bg.ac.yu��,Re�V ...; >eو �bl!�!�tretchB�Ab3� ct.}�r�XUsetupY @r-��y3�/a�"*$, jovdNDgkE",$suicide" o�Ke Ru� roulB��C� *MK=� B��5�q ipal l�0David Lewis. Y�<�D9a`2 violF is w��---�0ng _BiveGba S�su�]~_p�c9ine?ty0\o�p9eJ� an�L�dpB� usag��J`��~s5 -def]�oe 1l�B ext.dKon_� �.O��S\�QE�/tt's ~JqoLJ "no-�}apse"9>ory�a c�{.(�;"re��Vja n co�^�? believ�'�ng=< cred%K w�D1T )T� �-myal=Ps�S��hy� RL)��F�on�=Wyl�Tnt�i�cen1M� Parf�d nd T�2 . a�vs�7{1 ��{I{`LC��2�-�mulA?rs��(T�]o-5FN�(h!2foXfPP) i r!}� 86) �A,aogh�cE our 1�� j�hA,�� all bd�j�i%�,a_uldi^|on�b�` esti 1�B��A 5Rss �5 . Pr�J8, Cr(A, XE) = x'@kQAE�܁ �, XaA�  `MM� �bj isUx;a>blG~�!b�z: 1, E$ny ``9 '' �9'(Cr(.)*NA`!/5af�m�0lhis gF��p6�if[)1�nA%�"ie���a2! , PP&��%swJ!�q��A� �l�Rut!�e?aY��)q� A$_{i-ve��Ki� on} C Djjedan} {\rm Cr}( A}F�p ,W.>uw%�p v!e!��9�!W �,A%A�d�N�OSd�dbz,�A�"�8*�;�c.ܒconveni�Wh��] ��.�|�H�stock�E͸IZoac� �Y�R0a heavy nucleP�"�R�J�m9m�sm�wuGblDg��as I�ir�ibmItocha��`etuXoa��Y�inZ0slipp��in unn��edaY$remote. (Rŭ��EJ!�PP,~�UQ�-�teK ��RQl�<v�-Qm �(b�h���x� &p�,�HA&��Fide�m A\ .) U)9a3�� embo�%�{�mm�!2^ intu Xs;d?Gy f� ,/�a�Kday lif3hwe�UA--�E� routŖsuc�l. xQPPtEbfat >��l>e��R Z �C``��''9Lw%�B� (��zrett 19�8PDeutsch 1985; Tegmark�38) �aq�be". H���Z1=ip#Let Hugh!�}5 t���prc��Y%LT!�nt ��P, D�,spin $z$-proG%��A� f:i�� B�eq1} \:K|\psi \3K = \n#0{1}{\sqrt 2 }- ( {\5 \upa�::+ U \�N"} l)B�(�a� 1�2e �)doH a�AD)���Oi�t� a�devicTh coup}NC; rev ��xsuch wa�&a�S� !�� (anybody els�jlse��b ger,)ymoe� � take�J�[� !d eigeO\temveftj $�Ua;fiӁ9�A>dc$)� Z�RVa harml�``�W?k One &UTprovisoI�azU dur�*�S!p)&��|re���QU`�[�)9 a/ shor�Ya�?�A ;����k eriz!�hu��peri'Ie�a��ai�Haj y t��tM]tpX%�hi0e f, h�Vpecq�oVC a�i ly rݥma��w[$individual1���:�u ``ba�dAP5c.!�prR �� [  os� &���^9lsYMAmnA �of $n$ ��ecu�M 24(pu�Fg���M�M+:�chieving��� comb*PM �sۑ �is9 byE ��st binomKdis�� ion;�[��ar,���3o x!�"E�">�I-z$p(n \!��$) = 0.5^n$�*r�no y~dgO � Qif�_�A   >Q�� theo�*Av� P point.\footnote{Meta���,I��`w+O� !�a lete *��'&Xg�e:XYDtwo cases; notablyk%�^�5 csa �,]ia -�-�a-� mil�ja����ach. , r �� ompo�U�un!v6��eahe��� &� m *9�yY irona�al de���I1ca s�Y� \{s ed �I��"_t�ys��@ ��>� ��.} Th�a� a�}angBr�t��de-�Z perhPlupon ad��a�x�%76{st<to7!z�t to )�y head]�HE�-�R�I``X� �'�� �''O�Oentire s�{ , af)0-&rst2, now �d�J(��)�(symbo�G lly)&�day"g ddva} \eU� J�\o%�� {\rm*� �^\ri�!�le & = &X6 {2}} (��v6?J  `)J�* F�= \\ �fra&� � v�� ���X}6�"� &� 6�L.I "dead>K).�1���}nOiat��� (&?or4xwise) m�\s� a�eJin A� �2� -{$M�(��QPapineau *3 ��c IClow).�2ce wehX:xd��Mer f�?Y���� &�.� of b��hee�he�@ in�,en���(3)��cg�d��f�H� �ur2K X�i��wOp��_Ɉa�� ѥ "upr� {it{0� e\/}�Xr.Y ��.�a�s�e� *Ɋ"(i=u ten!9� ����7��---?Y" 4odox" Copenhag 2��� d�Mc��D�---��q# ful��AX'��!��M !��*i"!"s X�,a!�2�t;U,!�ikd� z�nge&mk�� .� A�ittH ��, alt'o�.is loaeaful��al!"�!&�"� "out[-o� �3Ti� s |�o���"blo� deed�k[ �t n�repet~�5e"%{�ina��A qkd5^:u���s�U�andA����k� �[m�di/`�''�:�j,k�m� �k-�''.��)q�s (�RMoravec�8), Zeh 92),.ce6)%��=98�(it��m�V h peo�ha�}rri`Ldep�Emt�e� idea:58V Euan �bo� Sjbήwro�cbmit,& AQ� a SF$r $John Gribb�� eA�i�b G a year: "sDoomshD$", publishn Al�6uary 22R8����1UP�H.5vaJ. �).}���-q'|98) p JitA(�3�\Rti��!i,(h>tt� d a R�/A� phil1S%=circlesy (��0, 20gC2��04;&�+4). OfU�u� W4�u&y`N�3� 8le. It�y c{y�&orA�'s�mA�AV``coll� vA�:Y  ( geno ?�V.e.\ run*��l{0tOic*� �onewl -dK�Fler�.�tal�:s�sesСth�Es t�:-l�&�&��2� "up"��?�P %1hbo9{��}$�0x". Ze�("survk")"�is Cr($&� 8)$ = 1. Obvious(� AA�) A��< finds PP mislea�9e �z�\��r!`�,+=�erE���yAw� �6�7, swdta {�:=2��ded�! conf� �hvalidit�Q���ory��g`o)12-fa�t t�t���u<�th�yA�mCQέ� �|t=&�i yo e�v��krgued �!oҝso}�G ough��!�\�� A,x�%�� d*� )A� rep5oaQ��by Pe!�J.��wis5lW)e�s ~li�p��gm�(- ) ut�!��A\'s�  {6� �&a+� . W�����m�n0!�!"��o�u1o issuE"�-s �Y9 R m 7o�11k!���n�� eral"8W�� rreldɬ� pur�Vso�f�M� at ��`M�%�ad hocvn�C. Fx�+�]&W b� , on�a�� �r��z�y��A 4) wh��1DJ� conj� ��!Hori$lk"?0) ��, v0ov+ legicu|8a�alq qon� v"�!��!5t`2�E� Y��"� ��y!&sm&ٜis bodX��orD��'y��oR�so @1�  !��A&j�wo2� be m�\� rt� Ac9 ng�as�us#�ssue؀p UՍQ &M! iNF��Zܻ rue,p j�W�=� �)e&J "��m� d byb 8pEGp#����aFeq6 puzzlm%� .�erh�%Y"� ysis} S�<���>bڵ"� apNW��$ ��-6���?{�ly. Af��a4�a�jall&-%^ s �b� stoo� imar���  ",9lin�%i����a6 l E5[ �W�f hsf�^isf�vHmw4f�teHlO6 empir!� fac>$O2��xqbed\  i��1[.� ��unavoidy gea�f��=]s��ed�h�6Pi�iH%�[ti�&��� dl� r. S" lysn&� �,�63,E��aw&!�a x'�W���R&�h Q'+ow 2� we o�&�66N: ƃ�#[��kia��v��wa �%�B��AC�}��owaremains�lidN�tsi�ane� wP}�necess& Z��e�t% ``an}�pic bia�~ \ BoS*mJ � MI�l�A���+}�\�'it{��a˘ ie }J �!4��#2�Q ��/to inP�� /�i8R�� S�'5val#B� b�����atk��tri0�����^y�P' u�jerf٣scV#��m� rtun!�t@yac��n*le@^atEIfunda�al level.UqC��+ly y� ball!��;E�Z-uM s us�A*\"A�$exemplify 2)#��,e.g.\ Vranas7!A��$A�mf !=�er (if�x���>c1[�uf �l�B!)E.R�s E%=:,���)��l�)�PP-favo��UA50{\%}Mw. �!uџ�����.�z�pr9�s%�f�� � ��-���2� i�*njectu�A�� i"� �ur2f{P �& �: �)03 A:u�%d��|v��aIfa >OSekiAo ���s6%as�͠. H�pt * #,t  emm�{� un alAˁ*�&�k)^N�0��aZ0+% inap!�r.�!�ex� �N�. S&�"ea��eA[8� >ya�`` ''�at ha�t�?%{d1�-�ph�ss?�" answ d�is qu` oOT� A q:!peI,!*g !���T �ntc l��ڒstigat .m �P;���L],198�WSG�"�K���im"D�� �:%�!gu%:b���k;��4,��kal����y�te�=� !�*� �.�q���#/� !�6gun�� %j5�EMY#%#t�r���a %fihly plau��)�sHt� : (i)I!E�|��"�, (�EC"��e!GIx� a(iii) %/1 �/ �#v s. �&u�E alyzai�p25 V�� j� %_��r�O�0+߸aad� y.��?p� s ma�v�r� Y�s*3Fު���^{ A`�#i���c���,N -6t�d� our-�If)��r��wav"�-m%�-j�� (" i.),��n'���ke *#� "E~�*�"v7� �\:�6;re\"|w|��5�&k^ jZ���.�7j9u3 false?} 1zY�� Y�t�tz/ x%���I�� &q%�in*��@aq%�s �[ &,!�:jMy_*�&�(�+Df,�&}w,�A�rV-of��or �->!"v&w�5N<quo�} &�.jE�a��M�� �� "� x ! �#<��Bx �'# 2 �al�Os��k���rJiAl\/���~A! n� � a 1* e\E����ir�r*M�a �. A ���%��<)gJ��$al]5 r's ~E�e+J�w���8� hinkf as h�T��Z w� �$�*%[��)| og��$ŗn"�E� %�,�&.��w!��9!��z�Kminime[ ime-ɣi%�Xwei iS� s;mPo1 Q'1��xr�.!8 We ��%!^�.�*a�6��E!<� A4?g aro]Aa fif��AvZ��#u!RL 106-107.@A.���"do!;�"�l  Ae?gia�bl��un�e��!EQ�a+tBY�4S/�j}Us��!(&\�%�* a���10� {Ga� )?� nd��,���� �F/e�ɑ2AmruE�is.U@���m��=���!�k �.�'�ld <Ԋ!��-$y�� ��.�,$�� A*X.de��T}n�4ja�w.ŝ��4� ��8e?n �iF�b.�d�ome0% ��,(s)D06$_{1}i�c��y|�� is&$8�� e8�LI 5 " 0 ". ("!pa�$+��a n� "��� " uH'>�-B,i٣a�heU�' slice\/} �2�. \K)�h�c��%X%�t^|��Z����de�h>z��������ed ŜM3�&@s� �teness.)"�{6����lyP!��H&E��$� -�a� $_!���u�k b 6r�� amwzer�d\Py�^mcbeTih� �e� . Fi��� �!%�i $ �7"�Α�� N �8V� U�e)���,Ŋum3 0�Q���� (5()}:�)[. Nowe~9As6Eis)�!�M9.�;"ty6ED5eay�%�%0"6ie�6;.�� is�!%��-`.U#�.� fB�`,�ll= 6 . W�4.w=PP"�iD���w!��i� so cO er-iP6ve2����v)��!�2qQqvei e�w'��B$� atF�B&�_$@3 [{5m&�1 �e�3 }~*�! 6T,$# C=YI����s#�<>�B}�doe� �% ol�� �5 ]"� ��āiu�� �-&m[lsp0na�unu�i��r _, ��i|s[ Ya* � wz���� �NF!��V �@ � ���BA�&!@9�.��b���''� � �)d�1#�X�7b  �n�?�l?�,*dnay��tKax����)]� مpi5�A[ѡ�\J�!��%s B $ \Roa�7$ A>�niAM!ct�;k��>>�5��I���� B��YDe�a*is=b\-=,yB�E ularB��Z�)}*��2�� )�F�� ��*�B��[[ �!e��� LtoO *�&�*a��Discusx2��ce"X%CA��# 7 p� � ���5�� shipD&Q &pO ��(�"�stark�� ��m� h a�%i!�Sb.�PP�S�1�4n!�!v�"c�D"o�. �{@�"1) �b� "�T Jo4or&s  � bici� stip�R��=6�-Ѽ�( i�+�2\�A��!�s"C> (&�.�..�.�!1�"}5)`j*q.=G"@Jo�zRurAh�aD"�1h� 4 "�J�s��. He ����~ 7��to"0�&a�=-in-tAKhaof�pu�.[8�Tle-dig!�ntege ~�]�re*�� �-�w��i:vi��c��Ќ�Fous!�clԢ�Jo5�n hooksb�!��6 �. �6v��N, a kick�#ozon un$E:.ou�!Gzero;i# ALaG �:zm�9n {b!Aiyed�'�e0# qD~T h&3��:!eZJoeoa�"�%�e up,E$ !\"�����al)�O�  m!1�.l4*z�?f�Z#Y��k!�ofo`8�!�# ��l��J&t@�'Hpf-S2�a+Assum��\�,���) �y 1o-+�s�|�eEBy7�a�<she drawn`)��<f/Qh�� �� 1 ,a�ce_!QK[  ex#.˖�Jo�F"���h�=� ��e�e�=.- � H{s��7!#��M.��(2'� R %tru�6�q���!�< �<� tyata�a&6 r 3*T g� bey!�!. scopUI� studyNMT)I�A�A"�L �L�3� 2�"�L��� jVw-ǫ�E� 9�er-�1 �8>!fDng &] �-K���i"��*K �I1s| �ru%��H� in?$�W)!* ��������+Aby"i&� se�a%�2Ym�aP capy��)!p�|D�p���� �w��K,���'e�PPdMV�y :L&# %)bf{Ac"8&�s�=w� onym�Pes ����y.�D&ok��P8en��k_.smy�%.Em�qua��A��Q� manu��YN�XN P *{Re?ce,>ex(*v2001, �it{Sy$;eA1127}, 358cR@2@An�( Bias:"'S�POaAHEf�'O (Rout�'�� YorkX2 iDBH� FH�YI!\�� *�a-,q�J^i��IT2�Y4l _� \ III �H�R z�.f�ernO�8 bf{2)�45�[AݢG. C., ɩ,�!�ŭ, T�6, Iit{ �a��� D.�3�470A�f�616�P2�6P�2)gOxford �sers6>�Nu\ 2004\Au�"lake-ua� uy��Y82A3-22>�P. J.Y0Y�"si�> 60}, 22-2Ys7%�P%<8A Mind�ldrenZgFut�� Robot%{HY A=ll��� (HarvardT�2 "Z�Y�P�>%| 2003�F� 3}, 51-585>?�_153-169#&�&�R��P�%kfI-�ri�#H!x9]nTi&[j%b ArchBHes' P�A hF` >h�!�h�.j he MQ�:�, �rhIn��)iPs P�:��B ol�"',AU20.�B��shQ��`Y�g�II�051}, 99�Be=�F4a�157-16�T�Eb�9�ForcM?w�rgik��46}, 85Ke�<Q,�19r�߅tex��(Sixteenth By�Q+Me��I(h}iE;.�� ��Q$, Kansas Cm MissouriuZe��9�:!�)�alyi�[!q D��As%�Sp�+@er-Verlag, Berlin%�6ta��\�Z,[ [12p.+[\u��ckage{�?pag.def\to{�a�}DEPU�q8er} \L7K���Z\MECHANICS AND REALITY$^\B$}�D \big [S,rge{Virendra=Cgh2+ Tata 2�Fu&�.R�V0\\ Homi Bhabh}zhad, Colaba, Bombay 400 005 � B��:�J bar{)Z �!�N \med��? byhuu�``���?��� ont���=n Cu I,s^ ��a��"��a � macroO ic�. ����! �"O+at\ intr�W���1a�-�s*^i��z"�E>�! qis� n1[� :at� � �Z5+�"tb��leC1H!a�wa "�) one.��V�,� i �^�S. /$f�H>�7som� .QD1 H17&���N"-� a. w �$2�u�� b�5fhR �&,extra ingred2s8d&*�D"1&6�sX�� ed w� ��na�,of Niels Boh|# eise��� n-Ne_�,�) de-%x -Boh��2 %1`n look!�%0'e9`J12}�t17��e5497�Qas 0� -deWit+�nyI �,��Jgx>( �M7����I5rkE.�rig"g!K�al) f���&�# harpR �it'W�eflu\�Zvfill *� �_ InviAta��Workshop�``F�&E��o��s'', Nal6cAХ4[Ss, Bangal�:8(23-25 FebruaryN4Ŏ��{A4@atim} [e-mail: vh@R4y.tifr.res.in]��4�e��\h �.�0p~�#"��grge��0.� ��}���V��a w��r�G� satis�?�e�# edifice. �J7sA�w<i�!�Rharf�Ajep��m��%ɍ� gi[aoe~v)�2���C1o��ls)��"�9lya�7�i3�Aom1�+s. ArA���n�' ��u-��-e;v�ppEXecloudCBhoriz�WV��g�>'���$ņs�1d ��*&ά-, �J��*ra��Cah�tru�4MK 0\gy-ex�Sge%Atwe(A9%K<i ma�Th�$*��UB�q��%�$ 19��Planck.  <n�l��pU��ldDM2*�3�Mqu��r� tw��ej�e��)-�2PT���06�oi�l �;�'e�Gby ��K20Schr\"o��Q7192!H DiraLH25a�� )ZAYepi)}UV9Ka� , us>-@ CJz�,����e� d��ic%�%a)� To ��'�g�"�U� &�;)Jb�o�Uecapil�!w��"0 r � (ieu~�% B.� i� exhib����"y �"o&�( zweirdq<e!.,quantum real�ity. After a brief enunciation of the ``rules(game'' i.e.$ framework!hquantum physics, we discuss- nature*,reality in Q65. Th7��depends on whether, while interpreting the formalism of�mechan��it is to be supplemented by extra ingredients or not. �exampl9 $first kindSprovideI8(i) various typ�(Copenhagen �%gds and (ii) de-Broglie Bohm:)-.�:J, whenB�al 9is all!�$re is, are�$Many world9V�� �1��History approach. We close with a few concluding remarks!�!�Tcontrast between rigidAMt� and3flu2"ontology2Qv5�. \bigskip \noindent {\large\bf 1. Clasi!PI��RI�} \med @A�edific)�las68was creaMF(Issac Newto!�d his book ``Philosophiae Na A�x Principia Mathematica'' (1687)%�,is incorpori4earlier insighA�btainI�N.Eoprnicus, J. Kepler, G. Galileo�oaL gianBa^!�Lshoulders he stood. %/� 10�enrich v!ّFaradayeMaxwell-�4 electromagneta�din mid-nineteenth century,?byZspeciaE�4ory of relativA6(1905)/gener(A6(15)@Albert Einstein. =�B2 1.1.-�0ian Dynamics:.()�eEA� sistm�Trete mass-points, eachq/given ��,ch move alon��8ir trajectories!40a three dimen�' al space e� timeE;ey obey �'��7 laws�mo��ag influence� Es'"througe�or$ xert5�m!��7. As=>nr�fferent!�equ�lin��!�%)2 posi�s, d-���Hdeterministic. FurE�since A�dNns��0of second ordeS�, aIufic �ofKini�3���%QvelocA�of�u.�at�P!�, fixe!�e !re9�E�)� for Rime�1.�Y��!,th��hataDa � number�particleA���E�E�mov�j]� .�. -� alsoE�overe�� universalAmgravi�f : ``��two%$ i' attract]\q4fE�proporAa�o� produce{thaK * inuuma roxi onAn�� a b� result�>U�logic�;he�[0such as hydroZ�so��ela�g= �sA�M�>N doU� observ�L f se�wava�wa�   et��S�� xPa!2 `epi�a'. W.so!�e down,A fuq re�lce�at=<� epE#of Aabe�!On��:g Euclideanq)�� is take%�on�#*�(traight lin5 q~�ˡ�F  a �dA/n� � chU5��e but A���selves! I�e� �X��)IaXWaNus har $n absolute- ��.~, 2. -M� E2� c FieldA�ory2F n Danish��!� H.C. Oers�w ��%dtAdmon!`t!<� onship�x iA��"� . Hq � (in 1820 an 0 cur�  flow� in a wi��f�s aNc needle�<,ced parallel�iIAmper\ 5i�Ag� < nA�Hces during 1822-27 .o wo�carry���&� ,�; wed E͡�ri�is�_ ival to.�sh� in its e�� �A��3�hyp�5sZa^�5_e�ly du�'m!B� loop��sidA�. # c m�ials.E co� � , ie� can beE� like.� -�,ELlooked!vk � . D%� t6 stig��s, he�� !� �� c��uɂE\31�Cnk to unjtafthese �I~ ��int� )5��AUamCalB�fa�]�* clu�� old p��� streI�rA�illing@ e7a bar )�AGexhibi� )�l }'f� �9SA�arrangˑ�in[dA�v��To1��se  sugge�&E��� �1 whol�tis �edP %}$ invisible��s,!�� � dire)�ofQ�c �a� he assum!�at� d��A� Wv��!angt� th( M�1*0A similar pic�� "  CI{�.�� � 1d"Ao.�A �`��$), � ,jime, sur%�3|chd�d-!!In vie� ) 2 2��bet to cia[newU� t�� syj�. �t, begin�� J$paper ``OnQ@'s Lin�:f FA� '' (1856)!�vm�%ȅ�bl�f� o�� >� �%j!�precis�����u�nm��{>�!�Wiq�9 }�$ ``displac�a��''�ut�5n ly d�K A�naM��AE� uceda�? 5�medium�l��#��o be�reA�ply�ZvirtuE� presg` T%1� f�[e@ #:a�ana � lyN, Ri  reduce���ny ro�ng cyl� rs,"0 al gears nny� devicep fixmj�V�o (y now known� M� 's Eɢachiev� $!�1864.:n b�rceaNw_2 ���he�,�$by Coulomb� t"� b�� a����*I (��%��n e��A��� Olo��� ZE�A.y �!��j).� s�ω@um@� ��wh<  ���r��Ńis�s%. o lead to� ed 2#A���1a s�S$ said ``Ma�� can-c� a �noi�One}re% � even� ��aw�*;�:c5�JK, rA�E an `Z,a��Naa>g%A �1s�. A r��conseq>ofQ�'` 5 �}�kp^IKoF�� ��a  F, $c$ agre���iE+�lk i�3 u�s�� to regard '�UV�grad  G� ' � 'Qt<):��``�''�eara��� funda�al�t���au�psAw%F� ��n talk!�2|�eBoltzman��te!�xed lyr~e<� } $|!Ug)l{C}}_N}^D={2^{-{N}/{2}}}\sum#dbf z_i}}\prod^{N-1}_{j=1}(EuMLj})^{z_j z_{j+1}}|{;m $, %Br ere $z_j$� theMOof D$j$-th binary digi%�( integer $g|$ ($i\in[0,2^{N}-1]$). In order!,characterizeGef�npis kind non-%�it!�n immediAy benchmark�provide�O� fide4 betweenI�E,%�6�sI�$overlap $fA�4=\,^{}_{C_N}\l�:\phi 2�^D"A�( $ leads toN�� d} e!�N��.Wjz)�$.B�T%�Dare $2^N$ terms inibexp�y ion,i2.p$F_N=|f_N|^2$. %For example, De case� $N=2$, af�<aa�a��4forward calcul�� one find."lnarray} %$F_2=(1/8)(5+3\cos{M�{1}})�3HHowever, our assump�%A that� control o����AiducY*�� A�A�ioL$only limitɿ us, \rej�LckA�,knowledge ab� ��s�� j}$'%��K�er�D, ��$means each=Pthem must be averagedE�( an appropreprobabiE�distribu� . We�Xa � em�r�=}$Ein |v�k �tak�se:5=�bq $p(-�j%�standAnormal.9 %.�6: for)�width�!+ L deviI\0$\sigma = 1$%�ta fore haveN��T=\frac{1}{\sqrt{2 \pi}aq-�� j^2 / 2}~Rm1�%��? \bar{f}_N�e�u�< 2�j<I = �) �0\{\int_{\vert��)�} � 2U}d�\}�C�Bf1U>e�C%�}M�M�of vaA�aiof2#EjYC0{j})$ dependsq���ific phq $model used��.��ion. �>��natE�x e flUEXe�"e" ݵ�jwaysi�0�Es amo� elementW�;tti! rd �no)7 universal �}e�be  `. In Fig.~\ref{fig:fig2} %�(a)} we���)���IUF� I�a flatFt�E,m����Iˑ�s�,� proced!Scorp o!�tom&� � aI< %$[0,\lambda_j]�� aHR�( superimpos��! %(6) giv�� plot�% "  % hainсi tes.v (figure}[b] 5d \hskip4cm (b)} \center!{\psfig := A1.eps,e =3.7cm,he�4=2 Rpace*{0 JB3MC4.1.C8cm}} %f�HavfidGaussianeindiv2N5.N 7cm}6�?t� v=} %)c)�.,d)r�fidbidv^6� 2NEv4!�a+{�a)::against V� =� A�i;��j)=M� ^{-1= From topA�,bottom $N=3\� (arrow{10}$;m�b)}: De�na% ��multi�Q� 8 curA�fFgre� entY�, $W$, $GHZ$,:��w $N \N$>  (convenienceL caled��ha�A D$\Gamma{}=0.062$ (� �Hto $F^{C_{lin}}_{25+T5$). Similar behaviors� ��e�differ�.b p$.} %,:ga )5ps ime��!� )l6 5���q&%in�Med spread % (dashed)v/$(solid) %��j across�6_ XW=%�!}�ively).�s �� ed a middl������ "� BI =1$).} � �]���} %On� n see %w al!y%� $N=4$, ArgI�he� sAis-��w�  check�� $is qualita�U" holY C , i�zec(��"T e:Y21 ~\cite�dopo}ami alys'an�extenq�wo-dimenW al:@ w� analogou6�results:� %a�smallA�hN8 Ia~esi�.39rEm� ���4W . %2 decay5^�5y2!!*�feE in� a�c� OThu�fi!))� geneK"S ^�$S^{(5()}$ %on $|+�_u �'to be-�RBH�jb:;%:X JR\equivn\$s_{a,b \in��ca�| b-a �g�� _d} � \bigjC- �} 8�a}=2b� m}F� ru�@\includegraphics[n2.0in]{ � }% H�how!7W $rt EPS artJ�.6 1} SomeV E�l� s suitabl� " )�s1�� (We will oft�ntifyEt L�t�� A6[ nd.6\ � r as itA�possi�to es�isg biuniqul�4ond��"7����<e panel��p �t��$1-d$�[�� ��2�. PS� showN2Nrectangu�1!(2B)� le �c)}:�3GZ;.�ss!=tLs do not necessarily=ṕ$�  %lay�s � , bufpre�3=��ups. a�endY�W�bnow � !�4*� U�o�u: �quantum ��s has b9�T�ly*���w��т�m��VGenuine � $partite en!�$Ish��!4sub.iq��1cI�sDa�.2Q is enco�� !EaAawhole ��,rb0}. Any re(���, obtain��$racing allvr s%��rbitr3pair,�b� ae� doesEc viol��Qoy a�suffici�VHPeres-Horodecki criDone� \mixed � ��pHhG}"�qab}_{D�alAl�� �t"a� *�p N=3$�)�~!locally �^alօ� '�, two:� embed=�6�s%�V� 3}^DYiT"�]�!��ptoR 2}^D0}_{3}+ \psi}��A�2}1%.� %�\c D}26$.ŧ,�>dNrZK N}$)! ndb r� e aH� an*$ )7��5t� ��he lastILaD q�N�( �sA�5� &�1}$9�within.����aR� QrB�!\bra $Ok thirM�":�"/widetext�tB @\rho_{12}=\mbox{T� 3}()c�� 123}.�*M4Z,pmatrix} %1&mA -�A }{2}&1&- e^ 1}}(F1)2 \\ % 2!JQn6�1}O��N����2} ��1}}11��])D&19w�V&8 Y���� rh "�(2}\neq{k\pie� k=0,1,..$( $\forall\,�10W iX xeristic��y�Xc �\i�s J�i� s $3�in 2�.M�ul �(a)>��ja conc\ �4~S12~� ��G]1/vb6K62�6a� Wa�$�4�ia func� s&BQi}=�N0M*{i��i �AA#e�n-zero�  %i��w 23}$  .%3}=0,\, kz.- } Same�:� � � 4$. �0hill-shaped c� �2q�A�34��� dot-/ :8 r.; �-Xb % j�9g14}60% (� neg2 semi-planN�3���24L� '#bf A���Q�d)}�x�.�C_I6�0!�Fs treaYin)ws 4AL �  b)}$� �ly %a����l�Z$� �idual"2 2�#� ndant��!��#Q��A� %!, �� �%�,�� {!iE$� !�!a. 3:��I@!�d)�w2za �w %�%Eh�Ylyn�55�.� I*�!e �2� � !q�dGty 5c%y��M8($i,j\in[1,N]$)%R@$!kn�urr�<}, %${\mathfrakB<:={\rm{max}}\{0,I�\ M�=\max 2\alpha^~�q-iv(Tr}(\tilde{�}_ )\!T�$:8\ge22{23}F4}arpeigen*�{B� }=\s���(^{C y}�&j}_{y}).^{* Œ2��27~!�complex!�jugA  ,�$a�(u�(onal basis)� .�. A� Figs�5.�A�m�4w��d�z�-EGr�ve��f!�q�"# >�&4�6�->��x��. We #�  %@�$`&esu ighb�#:w� away� o�" 9-n9&� >C sett�! symmetric�al�*��6 (eqe.g.} $���� (N-1)Na>�$Ne�� �!�!J���due %�appearan# �. @ any�2ab�duE!0randomness, mU"pronoun��ŷirR�� s. %!�n0-� 5�on�& Inde��r�gon1B�jn ��%]l,;!�u:S*tha"%o�^�%W�"t�� at A �j� i\,(X {�!noBs:,a in ��sesi��Ds�+�v$. F� ht]6� �4��I{F� ![nz2�76� 5FF _b)�_.� ^_[E.�c6~in:ts�An %A#N"y(s. Each nod!n�E�,��& %denote�>�. D�_!AsrnzC %classi�+%O3.�ss"# %��� %�m� of f���v  _�R>>refer�)P. %2g achievW'�W~f8� d %�""(./#� e"�"Fp��&\le.}\ +,��3A�.M %Bh$tr�(�^�'� �Ղy(, �mtoAhsi�+ �c8 -.8 �7�)ed��6Ai&ETs2� ��g�%1�A��alF6!:��.�e"�-�í4J�2$&*!85�>�%� .4 , ar{.j=0��*bo .���a@ %� crea�/(u"$ x,*� �x!�!!9e),  frag�Y >�T � bridx%�(s} $(i,i+1)M��-2,N-2]$!��c, break!2nfhan� conn nv $1ue������GFfa}/+,+ %beaNto�s��YAEex�%��.پ�� $(1,2)%� $�,N))�Q�1)���d/%g�esPit�remal} a5 mutu��5,V". e�%��a@*^eveU�*'di5�' s.  V/ %r� ev>Oi�2 � is@quM2?ch�,ay52��#ngarger����t2�!�e$\simeq{1.7f*:� _ #0.0W% g(N!b�!C Z"� $N$,,3pneBK$ic]%�)ne��@��� B} of�"2'A0$|U2ng pot{!alsh!3off-diag�6�,��le�2 x � ^{d}�-F$��� �'%R#($mreRK(. %$t "�U,�'�(a � � "�6i!$]5�"�$�F�) 8+ |��| 4&02}(1+� �2)�� <7U�re-�f mO7��(F ua]%!o�0�K%�іsu8s/� $W7s �"�,R$ ($N\ge3�!���1� � �)GHZ}_N=:N })/2�X&W $�c)%)2-�)�s�e�� �2$)e a>($"�e"�3�"0*N"7N}85 h=0}i6B(N,h �Io( h }$,~ %\,p*sqo*N} A^2:C^2E^2BGt}.��( R�4,{c} N \\ h � :�t��B��}{2^%{�6�^2Rn^2~p n_ 9cEwAbinom�coe"z!$)]� �%_�(%�N:?,���al�$$N\*�,N}a6Tha &q A}�/���� �A�:B�/~{6�/b�t6� �*t =2�y�52#bR8B#-6z!N�R�. %��� � � bothe��*�!s. �I�e�$ntWis�of�,�!�\� it{useful�}*a5��%�QC��� 0!8of ��bR 1� & 6  M�<h:�6� &3f�"|�/�/�/�/�//\#?{ea^>[ (NF�= QC}- Too �;A�q513om*�'>obrieflK&vie�worU� A� one-�QC. I�= unit2&�=�  $U_g$�'t�+ perform� �pu�  $|�$_� in}}"A�$n$ log+ �U6-�%A�� se}4�#�:r&g 6A$�$`(g�"i�aD6}'�_z$� osW�,UD%{IX�!2 �sGng� �$ Hi�!� SGHd)T�3 !lf"�A. A� �  pa�)n1 M}NAg)� E[i.e.}� �?2B meHs|=rdi�*B��(he Bloch sp R(6l2�(:�except^6ar�>it�ch�%odi�he outAR� �%�O%����/� s�6ofH@!�rec�$d. vectors��-).%�AC_M(g))}=gB$\{ \vec{r}�B(in S^2\, | 5.\,\ 6C �o \}~, .��! }�fin!��=��"�-�I[.&�4I���a�R�% �E�x!' %ap�Boz3:�B$|\Psiq�0(~�]rebJ.Mqf5�*e 5%Q{{s}\&$^�5eft -�#1\} \,|9�)n)C1��%� A�} �)�$6*�t*!�s� %)_)LM}�AJ ,(modulo a %nw=i �or)e;'9 n by�Y %=P.�1-��{s\}}}-� M}})%� %"�1 ��BA�� ^�bh%�2j=)t&n1_{ki:tn1\�=+(-1)^P_k}uik\cdot R \��� k)} �'N�1� bf{3)} A�u�W%�"of,-)C}�RM�a� %@` proj�0 $6I�&_{Z_{,�H{ \{ Z \} %}}}} [ \� _i ]$� mutep 6I!�))�2Y M}@ctst3lya��* body����>�r wrd- �ofe��Lir9�>�7HBt �k a.�B%��!t��outA!%Z��},1�� %&=&61K{e�E� X) %V%�p \nogI\\ %&&\�brace{6[^�eE %.92�4E*94U��{ }_{|�DN�! "RQ!��5ve�(���1�:����a�!m$� ��.1A, x$-* ai newl11�s� b.1II��3be4I�$�!s�Arm� }}=U_{g�.: ��q �� B U�P� �"g �h"�Iia�� `:��( = U_g U_\S�B (\{s_i\})�[:8�&� ��1$B;�#a�� by  �a���Ao(iB6'B&� -?mak< is point�!$trivial. Ch�in"�� �&J i\-z� �d6:!�tS9 remo�f�9�dynamic%hsystem"(e would con�ZU�E�is$~,#�#ek PF#Pex(�=J!c^nP �5i-�no^;I��Gex� =�s s>�I, E�we�es�q��iB -GAIjalA�5�}�:g. %HIMPERFECTGENERATION %\�{I"�NG2&a CyS� } %As��st�I�!preiS�X%� key�)�"i��>� ,Hq%D %�rol&IN-�2!�s �;ab� )�-Xoccup %Pit= wi� CCFo�G@��7 nv rsel�@e�D9Q�s! , or���>2�-�Gmo�3onto $�3 %��=%a�`�b�MphBD u�-Eq.~(�S*yP)�� ! %!0:� _D&!)�� �� &�<���0aY-n�^:�2m � �OJ�2E 6� �%P}] hRg �NF� _D %Z�.�{��N\w�$"�H|� O�D,���<,��N"�N#-�rnS6!�AND %"� ��$>�I� r�'�!a summ %��fDi$� !��0a#�M-1� \sub�kPr}�{��CE2m,�!-$d$}2�(%%%FIDELITY f��ub��{FsOvxW It�&N*.���i�$�!rofe�M/t�by�OP�e�;*R� j8*�R %x/�R�EEu�}h.�M�anp�>Npis*\#*�2�? ^I_C](�"�L� i&T^N%r~ R��QI� %�Ky-@J.�A , if��yTAgc�O)��% lap >48%%%ENTANGLEMENT��.E Bi-p=2) �J�B�0BIDIMENSIONALv �M�ZQ.�,�gmKe�y�R^<H a�)�>c,�Łabi"�)bD�"�n�$21o�:*J�.�i-��<� $up $M$ %rj@� "VE�NL^��2 ^D_C &=& �n�{MN�>�Tg( ~<d^{(N):�T"�N^R�T %I��j)�H"� � �e2fN+RU�h dots�nMn(M-1)�sF�~,>���BWP %-M%}k=0�*�X13N(k+11�Nk� %�*_9���F�J���9��,A����6� � imi=:M�l�lA� �p�# +n� N�U� Col}=91!�}.�WQb{j}^CI�{j�e)0N}}F�W%soa��D�i� olum&H!5 � � in�� � � �/wo �-_-{2Ddirt er> ���%[�%)%m�]z�j��1�Y�jw�]Z�:�Substitu�$�� �2�e^Wj^{C,RW6�:�)AS�e:�! n %�^F� e�@F��I_C�#no�X'l a{at�*�|��sR;$��"�$ surv�5xe"YYt\!rwYC  ,F� %f_N�r��2Qz�Y��� %&%͉Җ.����b:�TK}#$2��n6Zuc[5Z$� simp�;$"BZ %To0�"�/E $_0f}_tOA3xE�i2*O^�  ^ s-PA Q+  �6�B��A'�WI}{{�/2}">C�5�鲭���T�Q\int^4Kmbda_�40} &yW^C6{WIAe� ~WN�K��F�I�� %�R6�A��� �b���].:�>�A�=-6�ZVJZV6�= F[V�/Q8}FZV .� of sM]�6^�# && �� m )�q 3"� i 17a�bf{[Ti#� inued...]�7-6$INFORMFLOW62Z W In�#�Flow "S� �� |=/�<{\sf IDENTITY} O�"}21"^�[:3�,,#}@H- C}_I��M�O$!�V�:�0 C}(\iden)$ %�-.s�a6P!�-we � $1\inw�2.�3.O$�#23�#� M}^N � �J  %��f 2�h�b�Le :"= �"C}1}$�D1*s�mseaAreb"s�d# is d�"&�follow��X&?B�sJ�� 3qubeigEPg_{x}1)f2gma_{z2)) >� 5�}=&B#,� x1cHN k{�2:�3)�h�?E>� ��2F�v�3b� ^>!. 6u3}JzAfv Av�%�&'�-Cx$, %�� $s^x_2�/:?#:jQ��4�"� �psiiddefA) �s5~� =P_{qM5(X) /.�Y.A��Do S �\inR$$,g  %$FaR�" 1^{!�}{2lJ>��60�e1%ua 6�;��(�-&���"} %F�6c=� ^ �-AN�(X)Y"�AppF R��C-:�Eq�mj2}L9� "����)$ 6;&9�!�6(hU")�V E�zAD�m�]}�y�w]d = %.=MaR,NIs55Eqs1-%}�K- 3})��:U 5�ʅ&��Y�� %= �RN���QQ��.� �M�%�x=��f�Rp�RJ� Now,c�� 1a� 3&�U��Bv"�a���Z�j���<p���� Theorem 1��satisf l&7I-=� $. C�4�K]%zIWaxACk}k�9 nd $s_1=��1��$ {x,1}>=z.mhW_%�i& , j&�"� D'�"{i�edQ�"bBy�a� �� != fullFs.!g�lb��4 $ U)E\ mz��1YNx 26*i�%6$$l��� "�#��ga!os freel� roug�-V2/SV� nC�X[ gio<by>[1\=��J�Al�-^ nee�T�W�o3, $U^{\dag}_{�$r�A~$1qE� 36�!HADAMARD Nl &b 3 Hadamard}eSns"� }  b � sf H8 rasG_&mp�W�0 2 �J�"�%� %� �%H* r8��2%- As�6T� H}H.J_�N�\4J2}}.�p1 |"9_2 + |&q 1 |-�Q)_2�j>�ama`fT�--.}&N� �h1�zN%�:~a*�q + b� \mapsto�+2M�(a4)6D(a - �q)J�i��!�&roK%o�9� typeaw&/�+(�%fir"PVol@v?:�.,J u= 6�%%^n�+q ��(C(\)� = jL_ :-�2�~; �+r fn} ��.�Ao6�.�6�N�By_ ��e? 1!�!�" $-��e " carr�#ou�"7 $U=H�͡� _1^x���H$ on���>�1$����J*}5�(g�o %���3��m� $. O3nll,3 �%�}��, %o����$&�np�1��second %%`F�%%�N�J�a�>*�E�%-/:4TK.�kJ�c {\it.)}-!�N��8H���A7 `A4M*woE/�HHS~G! A�!Yn*�Eni��e��o^G�E@�JP _�Y�^v�KC lu2Ap)T+In�&A�new6[ '6 y ��I"V �a ;�$5kappa' \Ar�'e&aa five-��-*�=(-��r(� HF$5DX ssoc�pd� � t s\}=\{0�Q�b&�Ht�BtX | one,/ply6�$34) D x.��5 SK2�"8hi_�1 �!f/���SE $\{ # �, 43%E�& s^{x�Q}=0\,(�G&|6�-M$i=3,4sA�-(�w+}$�- -�@OUef@hand,QK�8A!Q�6�8}E�7{)�&�)too9W�CLH��%a-1?GHon,:d��b�  2�W5P�stSJgy&>`�-�*��%P�i�&�-eD)X&~2�)�  emp�`d�Aj mova�d�Gr�:d.p, `]rmine�,(j��e (�}=�GnV))O!��-%f%� aog"s-R.� refefw�H�Y]9%�inherit!"&> �-z�or r��uro,zD�h�FzW EAsme�� isms�-�Lx�'1�  bE�z-9� �Llu\@��uoF�d*j�cr� f�/_weMs�La��Goe�]?cse-'��goy:j � ���a CNOT�� %Ac�9�to!|.]��9 -  �2A�is� c(q)Df� �^��0ARBITRARY ROTe.%��E .D�2Cz� &f5�!k�� �5� �a&�G�/$\c}�EfdiBN2Ba2u�.S �!0�L"�IroV o��A�yV�V! "��B �"�l&Z<"�:�e� ec� D%OX�o�L� -�^'orC�-�S_{1�+- n7�Jbet3 j}_{\�  %$R^{\del4WSF� ��0}�Fi +1})2~,�r0IA( != �,�, �\,\�a@and}\,j=2,3,4)~,$ (� �X=-\xi ==-\eta� $ J =-\z!��ne(Hit{onlyAmofr="�AR�)X?easya ��coqpa�d`}p�sR( �@�(;Qa%�c1�b!�^D+ \mu}^D)_{�,5}+b�c:1{#"aa%b�EB@%V� 0 }�^@$)��> I�subq�s +A�%.<��0�Y`1}Lq�NNJE abovL we �o�De!k"Z{&�z� *�>, �|�?�ީ0(o3z< ed) .�m"`$5$ �:pJ�5�?!�� spli�0&[a�H i\ximnukf (\xi+\nu+�({2})})+b6c t��1})}\\&iZnu J "A1}6L]i�+}_{5}+2�E8(.=3cBZ2Z(f�X6W}-\\&$BV2��a)]1e�m!0 [-4}�[5"�1x>�T��I�sha6b�~K�/A�{~ � D��ed} 6\A�x� �_s4E�0}+J Bb#19��Dr}Mc)na=�Ju/2}�~�| �a xi-ib\sin2)-i%WnI�$4(bJGQ:G� j�=j�s6 ڴQ� �:G��c e&� �ho*�I05 rotESbzte}F�Y>?Hr&rotBBB*FH6.0&�x4���%cFH"�/a ��&s�`us�A�Eu~s �Uxi=dnu!��.D �2&Scus"�7� apeKc :� 1!0�G�"�Jm�i'e ~�X~i$�Z.� �i $\xCi/4�nu=��(/d�)�4( pi/2,�(*�d)Le-%3 4$ (*�dV�� �(6p�edo�**Nb1A& �kM#B$( � &�#< 6B$S�@9&N<}�cnot}2�b� �sf t�Za!j59J $|c�-in"� =.�z*�i�a targe`l$|�r2� =c6�d.Ec e scheml*� �Ls $15$ �� e�^=9)�A�st� *A"N {x,y�l�bb�Xas��>�!SBBB�Ma)cpfw ah.b,�$a�R &�>a�trcU&5^{c,tH"z>=*�� � c,t}6�b� xGkc� �to-0 $7)�%D(� emC��7$q�� )�86)k j{x,��8 pe冉Bo"E?s_{Nk*���f.(=�e+h�XU�"��U7 �f�ou�u�z&�O%Y:~~6�C:�_C)"B�(.� _T +2�_T)&�2-a 9&��{CT}+a=0"� b1:*b?16**�&�+}�AdAT� e} A�  jB�c15A�i"��7h;c��%�oAstbt it�t$r�y*� zxJt��"FZ�1d�SinWu}& a� �D_{1,� I2�D_{5,6,7r&��  $S^{ _~aRP6 I�!�q{N+p �q6+ �� t�  Z:� 9""r�Z�2�2�  � S�� re � �&� 3$A �a�a=�M8"Z 9r(� )�UAJ${�0}� �] t)-t �6s~]\1!�}/g��� �R*T_�m- .�\� �1�KJ� F�Ɏe!���eP� 9 ����~� g1^� 5.0c@�kip1.2cm��Z $�*$ �m�&f*�i���6�rfc�A�T� ���F >� !���BoA$a��t $�_��2�Uq]�` $a=c ��1��!�-v To illuSp1of&��O��add�B(���MO-9B�G {x}~Zjsj.Y��O+V"��(I�_y��p�v 0}+iQ�)� foot�d{��!d:%!Npost-selF � ���.�6�b] \hs���T3{�m�q\ f�f)|4]�2> �3ׅZ0.8A�psf>O�5BeB3�fu ��q-�squ�e-}IAa��6` Q&� ($7��%9��1�rI;I�(�#)S: �+:F�. �b)}: S� � }���aAr� m��qc>A�g*��@GU !�� �/"d.�`*�/� Fe.%@to�c�o.slr, >Gr�A�P �oa��5�I �nabg_al �0BA�vyom�aҁi6��!�_re�a"P  o�$NQ N 0\�w �*7)"B "�i(15)}�o�i6accoun.!����X�E�a)�66+ 6^�2!�-j"\(w���b�eEa%� ��q�uV ��.�$)�p0.1,1]�K��ur�o!�decjx�"in�;�9S� e,Z �i��(�^nR�h�m�U$b2p1-a^2A�dc^2�uELwe)��X=0.5$^��obser�J %{ cho�qof $a��$c!So �[Q �*�ɅI0mod:r-Hgu��T�t 2tP �����d"�dŬ"�$8$� $160u& � 8s?� f'.@DC}_{16˖��b=L��a�iBu.y"viaJIF�$-݂)ǡZm��� ��tr�edJlS~m��� �� (A;Ga&M�val\\(!* $e��C;69# ). W� S-[�"�&�m faYd!L�� ��+M0(b�c�]�ki3)\H'*A, f]6%ak*�")��tudied.�/#"�� �h["�O�6$.��rt*er��(�M��Agm�']s4e wors�Z>9q��noIM�simportd�"�1.of2kA.a�>aM.2X More���$$a=*!"I��!�le}��ڊ!\Ɉa aA_�.9%�.}.�% em�n��yJM�F{=/"� f!.���J���z�!�#QIP�SP%6 Bzp6� Tutte�@{te2� *�- � � G,u5�?aa*n$u=�P�&�uTof^9S��.R�ef,����s.�J�v�Nm 騢�� �� !:.� If�I�!I8",<�t�: "ed (us�k�}�Pnsive}E'"�# esources)�!fOmetho� �"#h�4!�A_�Nde�P<�2��hDNe!�e6�etA goodD'�W�/M���hq�R"�1Suk( drop�USs͆r�"} � e �r#di�g�.��Slegitim���< doubR"�"�������B�r�on `e�st �k%searchE�m�u*SKn*n`.SSbypass-�*�$?Pj�62Ic�.8S"�&�qZ� ine6���x��&exi�-�g4+om�`6. IM��2 l6&��aRmad>3��%o2-���$M$3$ (enc�=U �#2�)�-�^x&demon*R*Y��\�#\ect���"��ab!so*�3o> �tV"2���_{3,4��.!mu6 �. A-yB!A~X�e 'h�-to(�"0"t"0�#1,� �{ 3{a �0�" ,2}-�"�#, ;� ;{c�0 �04! -� :�9d 910 � m9. M\%!��A�A:�L Xpm%G��+�S46 �1aF� te� $��"� a�X-��&� _{c=4,t=2#m�2��k|*1e� I�I{v�&!�%.�4(s�%,s_L!=[� �:a_]^{s_1/48Dx $\oplus{s}_%�$ �lYXOR. %cF75(0,0)=\&��=r� 4)},Br5 (0,1^;s-^{9�4xN?1z*2 �| �J~1~(6? %6� $. }y � ab}\?DaF�S}^���s� �� �yE�AL���i�o&F6: H��N��& M�� �ny.pa1�~a-im�:�z �� )G��c�sn#�:�:�p���61QCɪ%-r� B�invol�Jd-paramet�ym��Is!��5fact,;&Up!�"�1d�k0&��!E . al�~*�1�&io�:7 circumY ��"9 sugge�1: )6U5��)� "5f�8w a��� ,us optimal. � �ۙ�<")�|-n:�Dsetup,�Ab5��T"L)ps���photonE� olards�!�8n,P�. A T%��}"�+ +>�1-+ed*P#2'e�field�&#�i� .ate (ng Type-$I$QU ric-down-j r� (PDC)}cesse'kwiat}Eo�)�,%�.��!� pump ��A��#�! -Hpos�92I%&s, se�/>Q-a���PD�^�E"� � F�J }O�!p6y�)�h�0s2� "$1+�3+4$)ŀ�6 "dH%Ǡ);'sara}Jx���3�Kn51���n\s %s�"��E}'� %r�^�"�y� N�VZREMARKSZnSmRe��s}- Ws'�Ne�s�"\/� ��\� �A!�B_w�2�!�l�w&Q 2/p�-q-I�1��2~ E E�6^i�GeD5�M"by�? ��� !u�acE�.e1a"�V�"m �,�Jminady�A3ex��-Q*k dE^x��D %ezp�]4�[�u�j�sum���ʩ�6ba�'M. Our�}pos�x" )�B�"����gn!���ibR�IPmt�At����h)�ng gOiӧ2�-QC%_b thought�so faadI � �nt`%F.` "?wsK�� THAN�\E�ac�[~�sup�A�$EPSRC, DEL�K$IRCEP. MSTa|nk)�E.ur\"{o}$er In�S�V%�hospitaW�u�_�� visis J [�N�� thebiblioߛ_Ket al.}FZA V(68}, 022312X32X4vlatko} P. Wal7, K�DResch, T. Rudolph,-�enck,�W� urt�V. Vedr�:(M. Aspelmey�DA. Zei�{!N��} ( p\�)�52�(nielsenprl}X. N F�.K93�40503U4); D.�Brown .��k� -ph/:157}.=�� �:��C.� Daws�JO342Odur�s,gel} W. D\"u��1 92}, 1804�.�bloch�Greine�c611� 415}, 39%32); %IdibidemMP419E�% J�$rcia-Ripol�g(J. I. Cirac-�NewE� Lo76JE�%U� rb1}6 %f6a YRZO910_6N:��!�&ښbWEauX22Ad 1 (1996);A�Perz %�Z�77!�413 8��� ghz}A�M.!� enbe݁, Horn2ndi>LBell'�Z�H , Qu]��H��d i�s#���sU��e��G B$ docu= } �� \ц([a4, 14pt]{K tle} \usepackage{amssymb,epic,e} %2"color,�&&,epsf(ig,amsfonts NamsÓ,}? xsym2t[�P n1]{enc} %/�eng�,} \sloppy \f��'��p\author{ Igor Bjelakovi\'c$^{?+ \��Jean-Do -�Deu� l $ %0Tyll Kr\"uger,� A$Ruedi Seil }$ RL�Hr Siegmund-SchultzeA2B)8Arleta Szko\l a 4}:��(}9:3Fakul %II - MaZE atik �  wissensch\�RF�  f�EMA 7-2NzStra\ss ��J/2Y8sstr. 25, 33619hJ�3��IlmenauJ~biJ,98684LJ�4B�$Max Plancki�� 5�c�(S�cesJyInselp$sse 22, 04�OLeipzig� ��\title{A�Ve<$of Sanov's�em[ 8newcommand{\hr}�EHL�.boB>ccaX bb C>rT R>nn<N>idn}{ <f�> 2�zz<Z><eps varepsilo- ��6jv'{{M � % F�*e�?k�bb�p�ss �".I$om}{\omega:�xb%(f{x�_279(f{nBkk=kByy ]fm{hyp�(sis}{H 2$ ,}jP� }[�8]1 zW2Nlemma}[ U]{LJ%A�seplik�38�.6Nco�ryRCM % `�"d �+r!( -� �{defnID�CJ�e LQ 0 they e2�O�rkJ.F%�2ear�B6N*�S�Sz� \parUGnt=0exP2 =1ex��< �J�u�Nab��c�$WekF�P 4������\�y-e focus�EY� tes�&aH/J� 8:�R�5x8"a seqL)ypi1ub���J��#i.i.d.�cA asymptok� � n"m�H�Kh� =ref��ce H�e;onebH�IZ�W"�u infi�Iy3entropy�pe\"($x�%ssI.!r�. A��TWin" �2@>�%� CsV aroQ)��t�nd5$.9(20 mIsa~beb� >n�N 30G�p-�A�e)-aR+2)sa� %H���( EeN<Qy$cv�n�Va � F� w'y>x+;l"�~-} �-�� C���.!�! =���3�g+$I5I9>%/.�l��tex4cA+�� ve:}��#�e-����g�� �>$`�3���j��n�8�,�T2�2�Q�6I�x�A9�1!�bI-�Q�m"AA}),*���q�MŊmD�of�Va"�MyB?�� &�z��du}J�tBB�y)g}aKA�I��#%xYm0ȕ�x@�!�! emp���:4*�Sc@�a�, r� seem_ObzG� taskA�*�*����*[ %W�F]�RA5b)�) �� ifa!+��#o�9eo�tocha2sV poo~Q�b��));FE#,Am#t�yq1 a cruc�Lr� play�!�mph{Shany�0McMillan-Brei�} (SMB�4;!c_"�� �ep%�\U:� }, y"c r� ous backg�� for :�G# lossl�� data��i�� It s� % ByPorigîkU�P %5���P,�PG$w L.!1� %F},t�at�2!� $n$-k mY�g!Mr�Q(an ergodic �s�. b�� �st likQ� -D �� et (7 D a� very much��'of��le�sb3 ca �wit A�2R cW ~Ts g\r0. leng+% n�YB�!�v�� �x�RI$My� ("Q%�)".z�a� ru��w�4.!`, �� s2��bno��%�. 8� replac�$t!�!Hq#5 ub�e}%��nt��Hilbert  crib�hea%$n$% M�x�i �.�cDn,d�~��E��iS%D�!�x�Uly�5%�.� now 2�vo�e�Neuman5� 7}�� n$ gݵt�Xinu(cf. �4 {jozsat1 �y =� 'wir� 23M� m* � �We  iK\�Z_% :�>Yea� E�k!$]_�)n�v���*w!:�XD a;�b kA$G9� A��r (a =8surpriA�ly) am&�}% 2�:� 1��biLi)�� l95i8s}�chdUtop� ?2�(��2eM" -�+�6c�s# a� KaltchenkR�d Yang-�ky}). &e6�ny1�.� $P$6E b�R�E�|':% )M��� �$\8�])5!s�*y}���ly wellIn�M�("# ).� $Q�6�:�  $Q$-.֣��e�9 $P$-6�q_ ��M>0%@} $% h(P,Q).$ Fur�!a�B4�*�Yst acA�$(�) b on`e-ssaIoAp!�� &;&�: preY a�N�Stein's 0�L�_�E�-�cN��rx%W)�5�}�JA_no(< weake\ftoo�D<�!#e9 �\�Ga΅C]B��Sn�yV%!dou�e �� is ��Ehmix��(BA,�, cf.mGsh; s2} )�+��umy�uIY+.�� bwund�өkogawa}e�ʡ])U�6�7�-bZf?bs1:=�&�(u��.1 ��M1�i was �Zly inspi�7by �petz}��^�ompleӠA �w>p4$(d- st��241p�Dop� /�:f&�'��! ��$\O�$"�( %-9e Pn_.~������ BJnr���� R""N� F=8.� �@��f oI5�*alJve��y�ofmI� Rem}!2e��>� e�a ��*� 2�!�sa�Hat%p��qr)g�m��i�"i��o�ic&9 �Oet�7 �!�.�` *K!vB���goes to ��%҅�Ub$\inf_{P�� � }�{ O&� :O!N�+o,�"� �=��&�s�b�� ��in��;thF� . So�\'�4half'A���jA�k�� *�Q:��, nam�)i}�%�!l��ў% �]%ba�"�.d�vYQ�?.��A�&�a�<i��${no go ��}� - heur�_l7eaa : II1�etl I �4� es c�� ��inguixͩ�cer!/ty POY;leuBs��%forthc�#g�C��wirnext}e ��2A�Axs��� � ��j2{M� �![1�.rm {A5.� �z� zyA�e �nu&!�Ű.�$\# A=d$�3�U P}(A)G  d �X>of2�!fJ�$A$A=!6J $H> �mba�0.E $P��'z����ca:33 �ib as u�A:"v"�TK rel-� } �:=�m\{�%b�a}�{ll&V�a�,A}P(a)(\log   -  Q(a)),& �BPrm{if } P \ll Q \\ ��ty,& $�wise,��y' w �:.5���T IF$t"V�NL aoe c5 logarithm Ta��2 $eݠ A�ˠnoH $\ln$i�fu�� $H(� , Q)�Gcontinuq&��I.�ER�Z�� 6�Q�lfTs& rtI0O� ! ��is lowl���p �B2 can 2Q�z  �q\%�2n*eq:X1^B-AG� !':=S� � }Ii.N OuS �b :��:��'m�� � <*�F : %-�bN0CLASS_THEOREM�qbN�1��[1Dl.em]� %e-̓ �3Q%�E I���� 1Xteq #M���NX!, $\{M_n\}_{nY \nn}��  $M_nVA^n"B�Y. \limH�r\infty}P^n(M_n)=1,\qquad ^ .,Pp$ _set�R:`s%B~ ~��} `1}{�� Q^n � - Hq Q)..rn _&} >�:��H.��&mt�[ M_{n��fulfil� �k6�"�z��y*}%]x n\�a=@!� fty .� �{n� �)\geq -�Q>��*}=_�Y�,�Y��b:.9# �>Q� �ea�*%�r�e�)�we omiN_j&�7� )TM_n"�;"� Ek�'�r��Bg. "�!a�ll � ho�]�.0 ��� 0 � .�  fe�5�!z vali�yvM�m��O��uީX�� st"> %� &�!c�ogue. �a.Y��^*6%|' Io.r2},?[�ŵ�<�$�2�*[*-� (m ��},  also�3.2.2�t )&�E�J &� As3x^n}:+�a�Ո i=1}A�\gj$_{x_{i}}$ � � s $x$:=\ 1},\lސ,xq�aszks: B]Hst!w law��Be�_�2Asa�P_{~i��"�AvK$% �$x_{2},...\�~� ��#�.�ma.� -= $�g*DŽ� ��J {almX�ly. H !�� ֿurh�K$U� 6w�8&�B�C5u %�&# by:* ^� q-& �X~&�rm{tr� A}}D_lN 36�}>;} %/)}�q"5(7)~X.�X ObhW D � �9ve6�.�C j� $ co� F%�!�/  U,i�I,H���_ 5��"b#"��Q��0�d\�r��Bc�� �7j��sorm�ׁ�� }�E���Y�4�N6�%yXV��Afaithful�8QP%�i2 Zdn_��, "C i��:.[�K�F$7��**� �� �@�DyiFS( a,uoa�fiA }m�)�L6� wvA8E �1� ��m����2��.�NL4QUANTUM SANOV �fNL��L.L��� }[�=� � �q-s�}��E6�I��-b�(.4�R� $\{p� win "�o�1x�@$p�i�b�Иc�atBY�x���q&� �.�(p� \6�)�eL>a���enumes/Y F �pkt1}>�*/�2�Vr<  %�F�*_2�} v�*� 2}\�� ps$/ . 9e" F�� �}.��' F�� ���:�6(S(%�<9��ֺ,��2��2---�2!��Nfq��q�"��1v# �t� ��"�{*]�%�ch��IV�er">w�;�]����6�JN�$ICAL LEMMA��JN��N:N��%е7*�2�*�� � *^�$ k&A+�Qeps�M_{n���o sfz$$ 2row 0m��)(n+1)}{n+@}�D0 jN8{.8��|@��" ���4&�%���$�%J,a��(P)�%no1]"n� eq:a 1} k\ge 1- �^{=}  2^{-nb2�>�n=|:�}�b a&%. �+� �Q:���\�� 0�� !f�wtn�� ���� N&�� �.� n I_n"%6�%� !e,8� $I$.M,!��Acc .�Md n\leIT1+z$�plim %>*^=6�9?, %If�*�p,bability dis�ytribution $Q$ is strictly positive then %for each %sequence $(\eps_n)_{n\in\nn}$ satisfying $\eps_{n}\searrow 0$ and %$n\ ��^{2}\to\infty$ we have for $n$ large enough \begin{eqnarray}\label{eq:fin-In} 0\le H(\Omega, Q)- I_n\le \log(\# A)\eps_n -\eps_n\log \�n  \4Q_{min}, \end{u4 holds with $&D:= \min \{Q(a): \ <>0,\ a \in A\}$. K numerate}  lemma} %-�.�O>O�\textbf{Proof:} Due to the classical Stein's l� any sQ-Tof subsets $\{M_n\}_{n%\A9P, which has asymptotU8ly a non vanishAYmeasure)�respect�$product diA�I�s $P^{n}Q� ies:^NS�P-lower-bound} \liminf�to��fty} \frac{1}{n} Q^n (M_n) \geq -H(P, Q),)�U=�ere $QF, {\cal P}(A)e}!Mreferea_.�. Then"� � (\refJ� ) implies28first item of Eq ;%�P-result2}). We parti��set $iR $ in-�(_1$ consist!�8of probability2�s )�4are absolutely>05=ŭsome }][_2\}. :7i�.�all $n� \nn$j�p� ��)=0. BdMoreover2heach $2� $Eߒ~q~)-<$)= 1-q_{P}!3�1i((n IdB w��6) %O:=P(U_{M� {2}}2m�} +A_+f2O�iU�mp Aplus} %i2Ea!�A :�==� wP(a2��^�A_+A`a !  A S > 0\}�(� .$E�speed�Jconverg�in��eq%�)aPa�0h{exponentialAv Ini���:���we ma�wsider#re�1hcted alphabet $A_+$ defined�)?) only. �k>k<%assume w.l.o.g.�+$q�4supp}\ Q=A$ si�)o��؁P(throw %away�letters!P! ��B $� =0$ d&��� of %5:�Aour!�%Ca�/ofa., 2$ above.�'>'Not� 4at $H(\cdot ,QHco�OM  func�al � &w<_+)$. Choose a "� $� {n}.� eS$�\O n+1)}{n,� � 0�[%G�e followA�decreas family!6 q�2���{��Ra�2�$:\Vert R-P ��l��ps5��e�(at least on:�1u�2�2�$��Y5\�n line��1}} $. .��}��u���(eq:Mn} M_{1͕ x^�,A_+^n:P_{x^nť�n\F� �Z $ -a�not empirM 2S or type!�I�q� 8 $x^n$. Now, by $couAUpg methods (cf. \cite{Thomas_C! } seEm 12.1)e)Pinsker'�� equa  $H(PD ,P�� )\geIZ,1}{2\ln 2}\A5vert *-*>At7arr�rd p� -� 1}��!u� )<E�^{) _+}2^{-nbF����Bv �$ -�b� a&lnumber%4$MAd� 6�c" .o/ $.\newA�k uppe+ �:. r b N � �A� eA%B toge�z� AA(� semi-)E�  Dhe.� $H( �� �� comb�e�� eq IEAa� ��m .�Z�b� e9rst%&} � E)| qN H� _n�} E ѝ(>/, n'. e%}.F� We�3 $I�:=:w�^2�the��(6)_*�ia}�z�� $ I_�e�_  �pa�AC.�}*  Q) $,�H� � ,튶 Next, ob�! clo�} F� n}}\] eq \R#�K�(a�6.%�!�rm{a�N41%Q�1} �@�� L<R_��35X(n}}$ be suc� $at $H(R_n��=Q_{R? <� }H(R!� $. B���apb N' =!� $. Accord�~toyh1])%܉��!�a�reAAa:0PA�\in��1��$9r R_n -P_n-� �h $. U a�i�2@ $|H(P)-H(R)|\le ���)L P-RZ+\eta (  B$)$ valid�.s $P,Rl.�FC�=��}�� J ta(t):=-t� t$,ia:%�":a%�A_+\}ak0we obtain fin%% Qd*}>�Q)-a� &=&�6{1}  \ \ I�E�"�(by Y�))}\no͜\\YI��5�Q�!�Y Q� \q2W�&Y�)} 6_�| �P_n�e,Q)6&�Rs-�� + \sum_{5D} "(a)- P_)%�� .M sER_+2T_n-a�27NXN(>j& -]��F\�[v�n�iQ��oN.O6�4*} %To estimatA�.JZH: �>.� %R.�� % 00 � and used�  %�7�P_ rb3�*�4$Q$. Now, setq52�  M_n:=M \cup �2/w�e "���kQ)ɅS all �Pa��R�"�n!Z*��)+�$*� � ��e2�"� �֩�*�inferb�:�.O ��  sufficienK�5R� ^D\ge 1-F�b�!� R��.$�o \Box$ %�n�1�1��.�-Z�lPROOF OF THE QUANTUM SANOV'S OREMV��I:I- \� �� 0quantum Sanov�$orem} Befo{ej�eV+ �q-s@}A�,I �4relevant knowna�ults.� &8 maximal J��QH� \beta_{A(h, n}(\psi^{\otimes n}, \vph2)&���B!(q): q�wA}^{(n��# ! j� },\ >u(q)1` F) *}��prozon.Q b ��S}(�)�A rela�$entropy $S% AA [a&every�psY(0,1)u�1i:"�n} .���= -6�>$�2  The asser�A�P9>I./ was shAmby Ogaw� d Nagaoka��o}. A dif�t!�of ba��o�approWof Hiai�� PetzJ petz xgivenbs2�%F� ,%�vc� a){bs1}wvides%�l!� generalis"xv�4to ergodic staona�si-lo�algebra�li�&�3 st��dU be aionary�~2�\ e&:�m� The�T)��) :}\\��B�F�(LOWER BOUNDVfnFO�)#sl{1.!�o5&O�:}.rv�>xpr��|p?e�� |��{exmIv valu�th��AA�!�N $\{��^��: A�sr�ind��Z�pg �6} ��� �>��j6sia�fixed><.\\��=�Z >�6�.0�"��4� %�Z� j�ɖ- S(\Ps�B �2S$\JDa�orthogoh2tp� i� �@1�y�� condq-!nV,�a �0�0UPP�,J���1�#!zauv �.To9:ZHsupjGjF6D:@*� $eA�R*, i.' ly*� �^��X ��ach&=$\delta$�re exista�"�A�$&�> R�� .��5=1,"�for� �؅eM6F} �&:�m��y2y+)6~4*} is fulfille�R $.A7-cis� w��ppld"�%3$ , L�%� "M$,!�� es.Y(6: prii8abelian subalg� � � A�quB� ��On 9\\ Co�9ŗralwom[ q3 dens0operatt(D_{E�}F7*} =Pi=1}^d \lambda_i e_i,� ���>'g�eigen-�Is $e_cor��ng ̽].W#]A�de.����Y� l}}=�.v�.* =kTi_1,\dots, i_l=1 }^{d}�ftu�'_{j!({l}1{i_j} \\$ ) \big� ,l e %:I�Jich�dsAa!F5represen�JqD1�R�l_a� �l_d:\ �i l_i =lB�%�{d�i^{l_i�e_>TF� �2�=�J�NW ��(!� � i_l)��I� �}}9u�t�R�l_!"EvFrP: \# \{j: i_j=k\}=l_k"dE�} k([1,d]\}.$\\&�W e� u�l��.~&d��  $ � D}_{l,��}��f�e� �Y^{(l)}$W ��b{)�=6� 67J*Ajpsi6iBP FQ�a�$finite-dim��U �,� �,� :�N, F=ix %_Q�_A�cc�f!GiF���{ "�m _l}���of mutu�. min�]�-�2�.\\ 6a?Ũ�f�hiai-� � .�.&F), \upharpoon��FLJM n6E) + o*a%�irc Ea�� 2�l}>^ 9�psib�6E �%�/ofumZa^ �6� to)�eB5��'�-eq 8A� ��E_lE��"� al2I>�, anon�"trace]��e�p: %\marginpar{Hei\ss t das DU �^tl�0zu recht &.X, w� doch v%���% h�ngt?}"�$��&E_l :& �Co ngE&a�" .d29:!5m�\=l}FIe�F;, �A( (a)&�� sum :�.h��FjaF:~*:�(>���1?qp��6q O og (l+1):�-*s$e�, +2})N11�a!� %� iy ��) �&/nm�;-2�.A���)��q�,.pJN) - d� %B6 } 0q>�� _{l RKl} �:�:M�.� �28>7I�.6�� @)F�NexD.� a0 A�W r�*;0 ��B2of����)q$�p�� sens"!'�x1q�R7 �.l� � �qj,k d_l, az j}} �|g,kf~"O on6-:[�^�& $��j}=� �n� $. T1 meanaM�*F��pse�'.�$. It �~ monot��� X+B�2 b��{>� -2})>�q�e��3J�V�)��mQ�.�r5I]) &u&mQ�>))�s 5s"��6 �l( �qb�Al)>� } %W�t^5 equival�.�e.� 2; : %:�} %\lang�psi \r R$a){\oo3Z�a7Y`n, .} =:� \} &�k"�S}(�5 A) %>�2%A]a62�� sV�Psi_{R��, �9�nZA`��: �%V\ �4P!D}.>� %2'(in� lۍs��{lIhl 9fQ %�K o not�)mute ii��E ? 2��2i� e sameF@�5 $R�lA�t5E(5M7l( � weI"� brevi�$E�{lAc �%.p}{� �l&. line. %I�!�.s���%�� $F��-2h%"* l}S()!.�Am�65 :�6�AL"E%� Du� {l},F=�FM� an�p"�* �Z�)�0i�Ed;3!bs $1 �g+/J/Q�: �� &,&6#B?nl�@�,�6PB�y�=5FA��!6� %By H(��)we!�uctq�� %) jb��I^[g�- %N$eg4r�C�S*�p�:>������ _��@A,��iv�82�< Gelf`(isomorphismp�Riesz>vt�!�ed 1r�0.;��-�Bv�; 5be^9ntifiedi1a�;J= s $P kQ$M��pp/�#�9 sp�$B_��X�;1�v!<$d^l$n�6uI_I3F� �LP�"AL�=� is determ?0 byB�/*-;P,Q)=���,�|�jl�0:d -уJ� Similarl".P��2-�:��A&�1ؑH];^�)nd $Q �Z(F1]4 %ZA5Ne!�Fzy��_�BE�$Kolmogorov>� 7�#WB�^{\zz2Utru9fm<c1\\s fine>V *} S_l:=�� \{J� n�eK�9�z�5 �   \: *�q᳅�_0�0-+Fov4�.JI@f$l�/�<�3*^ unit�#&CT;�a)�&�3$transformsNR spannAJ��e NHR7_{0�0A�� leav�&WC2AL):V8{ variant. �1u�~i7 b!>p@frak{UAL}Y!e�)�)6�Ahav�these7Ap�& es. �-a�=!M%L%���otilde�: d�%a�-<9~iF�1�N� U^*_�#��nS�N�Y(.���Z���>�~k_0�__0J� �&�B7 b-�Rf`�:_0N<[ ��*s22�. Fura�=Ai���?r���*�>(>^���.%B�J1 -h�\O!hU2 � S�%l��j*�$*�>� � se�.f4M��1.� )..�'b� ].'&�"N�F���~GM.%E)!�_0dA$s; �4<)) &�>�1M�1N�" �Bv/ = ��3�"P�y5~>I�Pf 9,"�GB4,�4�0l\�=�0d } l;�6�:��!P$I_ �D`HQlA$��"'$&�=+Dn.�MED6HE;�J (Kd^l�\.+J Q_{ 5}(l) )y��5J�%ڥ�_0}JU"A; a6� vart�v/_n ��Nʦ."h�We sm�z�-> 0^ rH]� n $N#;*Y�O2::i�N� t<32r�2} "Dn.!�>\ !!�Ek�I-AcI�n%(] Q)- V�>� } A%�R�n�r] 3 s�-A0�&{l�J in $? *�� \ot�0S:z�� . �  arbitr� $mi�n.' $m=nl+r&$r%�{0"L" l-1\�5�1a��.�mB� mV!bN�8p_m:=s(�1 �,\idn_{[nl+1,�]fF+ ��d�ty!H��2�.& 6o}B���>��n({nl})=���&u�M��%f� F'&anR�)gLmR�)m{m�)+� az &� nl-)=F-yC.F��;�|�Q),.2}.6�2 -h})4 conclude^�bedR��)6�� ^{* \M=n}IN��):�0 B� 5ar�&=&N^nE�*K;� .d^ly>*ZEl}�wQl}���C:�`�]_n�[) N�-�V�U�6,;� �;�Nfo�; bed2>w }�(,"�MLs���pniI��a�&N&����@ �X*�= �\m&F8F�>��@��h .:CBr� psi-�} Oy�m}(2���2���."��� F(�F" 1nF���AK��������?$gl�p B!�lim_{m6b!2�:{m��F�B!�B�3z6�!a:�I?U9�n]8� 2$�*I&� 3 �N"I6iTcj!zarwl��*��Jy&T�sq7 by e:R�n��Zr�u-inv-)L} �@=J7)hF4�a:�dP "6*Z!'symme�/h�B�A��:SYM&M:�,n*; !� }\{A9�n}: A�86�J�is.�2e� $�M^{\dim6A��%le*�-u�>�ksym-ur},3rm{tr }>>�~  ^�2l�#LM�7�EBj. 2" �. ��>^��Hnal�v2�m}a"leq��V|/ogN 2<� 6� %2� LU -�d^-9max_{U %�nk }J�z\ͧ n} %iS�)�\ ))2�" ��\)�F� p 6Y6X( �+d��(�(Ol}:5� BY&�2.1,P R1$:|w �#t��* �Ox$l�>�A,*!l�/co=?+Ran k5�proM.�. �A YA�6;:6;ZA"�@T�+,xamples} 1. "4a��@sysY�� bb{CNB� �(under")Hilbert�ce� @ $v,w! �V& > non-*�8�� vector%% eq.?R .E \h*�"�(J k{B}(L%  C)�:u;(EF� p_{wD.,1p_w5&>  omBb(��J��^2$!4n3T�w��� l5�70 &�1P _{ &B�� :%Z�F(1- ])p_{v}57��w seems ra7 cleaN6at��R0onable attemp�8� &jQ 6GJ(%�s)!,ZCI�*should c�S)�$ �$ca�*N*(or m�C} !�]�* site� { the Rb3Z2>�?). SoEGV/,to�typ�/�jM�via� m�6to�%vsanalogy�IMeD'�@A $n$-blocktQ��7p�^� Mxag Psi=f> \F �'�RF$ w%�b�e 7.;9 t\uFH� &F�.�( �� G ]�6*>�)=(M�+U� )5'v,w' e^"Q�V!nA�On%BoA� hand)�Bo+�+FR��wre!9!�$% �Rk�" made&� 0HbyiŦ �$ɇ but"�;!w howA@at,A�a\rast )Yk situ$ M�re��onF�AX1 @E�\v"zY not}Vaccessi��Fon ,(^A�#(at most $-2� |J�| $) m] s�/ify� arguaXsai���thougHPZ@#i5��$-� ���Mw6i>�u%�VLV s re�Cs�>ed. But=�M�(A0(vU� n}��perp � #$#w^{ #6��v c"UQ�� $m \�Em)� yie�cɎ ���z)\-��%_*�0n}�*41$, h3-� >bA#�Ow%b�Hd�7�"w�^�%aA�B�=ane� wau_2�FslAFly�- involved 1 ��u; agai'#uAA$�6"�=�@�!R*S,nom8universal }choi�F�ng���+i�_� depe NpJ$Vs�_m��>. direc�U�q�"I��"�ioe 'smo!L�"'ywi�"�a�9Q 1W zreader� v�$&C Y�F5 T % � F\Ph%;A�� of peeM� _{t}�'�4 i7 s $vD:=\cos t; v+\s� Pw,t\in \lbrack -T,T],�b4c{\pi }{2}>T>0 �6�$��re!ʁ�����*�&A5to!< . As#^����aJ �s#F�$ungA~�L� �.�* per�onem_ly fastM�� be &NTan!�i&4 0Wr�:�$�K�K�I SYM$(n)�V r� �" a|b0$-fold tensora�&,�;U�U~Wi�e losT�� o[`� �-qp_{WSYM% }GM�_! Ip6ta�Bll$w6belongAO! $.BY D�t�Y(O�desired�%y)'7!�ID?2 X(s2] of)!�&� $x�2/& -�A>c�5��&,ef.�� $!��@zero sZ�|P'l�$t�'��ډcnormal�L Z!2%0h $w3,ka�$binom{n}{k[1/2}/n!Y:&i�1� PERM%�P i }(=�k}�O �|(n-k)})u�B �i� e group%�n$-Permu�AO $% k�!�j� !��C��$interchang!he or�b��he!Vsora�E�a.Y$�� $. RLB�N�Lat)S 1^n�k� �H $(.X^%V(�F )^{k�4os  n-k�[k=�#� Tqu�on!)whe��*�!&c$of ! ~sM�=(Am,k�H.�Y�F�� 2�.�^[m_{k} BN� tan �k�e��.F��� (�q� %�b�ked ��a�wE� (T (�$B be omit� !dit goAoeG�d GRi�@�� U,�4wH pl�.��[7s $((]X)_a0,1,...,n}$% ,�.�d.��isQex�d:}nmuneven�cI�-��A$ $�Hp��u��% �3 Ca;q�!�q"atE� N%In A� Q�$6O:� as b7V.%x $Va8!}Ac( Vandermond� trix!�>a�)_{m,��T!�$% L_4 }$-ih�8� vm� ��U�Z�a�J.� �` se�$L_{2 _�]by �@gautsch<E� 6.1�qf� ularIR�o �! R-s lik9pi e^{I^ }{4}% }e�d] 4}+ &5e}\6e)} 9 �Ac�( ledg�s.}�= workUuppor�+H=DFG��  ``E�7pie, GeoIei$ Kodierung�~C er Q9Xen-Ina�ks|e''Qfhe ESFh��j�3 ``Belq 'A�*TU Be�b��E14DFG-Forschergr�N, ``Stochasti Analy�und�0 AbweichungenaU�� ,of Bielefeldp7fb,BIBLIOGRAPHYb%z�Hthebibliography}{99xDib�q�^{wir1} I. Bjelakovi\'c, T. Kr\"{u}ger, Ra. Siegmund-Schultze, A. Szko\l a, The Shannon-McMilla� orem��)V�lattice )�sxD emph{Inve1,Math.} 155 ( 18203-222 (2004) EE�2�� � Chaih  �s-A�| : ,of Breiman.k SFB 288 p>L(int Nr. 581�3)�igar} B�B_ dataGaC7res8�>ciy+T sources, akzeptiert f%�r PublikeS bei ek. ij=Vc.��wirnextNu J.-D. Deua7lFR. Seile�]A/\2hN�mB}8�  Qrex�ion, f !�Gr!� \QJ$YFRR An EYzX!���%Hum Re,[��y, I� Commun.I� Phy�J(247, 697-71Q�=t�Y�� New�W&�WMo6C>� ��F�D*/LS�0s, arXiv.org:)c(-ph/0307170.�6�kT.MGv!�J.A��k, E*Q#IzI�%U0y, John Wiley%�$Sons, 1991=Qp}B�< D.W. Stroock, LzD�?s, AcadA�ess, 200.W�� W. G�, Norm��ion�?in��5B�a� N� a%�e�,k, 23, 337-3A(1975.��H F. �L , D.\�y�Yer�- mula%�Qt=�qA"yEQP&]w,1*��R�(143, 99-114�91.�$jozsa} R.J , B. �3ma�W, J��,Noiseless Co7 �3�?!�ur�KXof Modern Optics Vol.41!�.12!C43-2349�4).�ky}�SXKaltchenko, E. H. Yang,�ala��^ofu��S�I�+���-.%b Comput.} !�59-375�<�b ^ T. 1^,�1^,E�ngl EKV@z's4in� Hypo�7 is Tw �)�$IEEE Trans �0Th.}, vol. 46%40 7, 2428-2433�0.�?��N.��,�.pof�cduO(random vari�s,A�H. Sbornik 42, 11-44a�57��5sh'$2} P. C. S , �!d�g9-3Aner s, J�Teora� doc } y�\�H[twocolumn,a4paper,� scriptadd�B,nofootinbib,C@pacs,pra]{revtex4ku�Dckage{amsfonts,ams�9 thm,� icx/ newt�em�a}{�@c*{thm�-^ �{}{f6}.;{r�{}[ i]{R � \renewcommand{\qedsymbol}{\rule{0.5em} ��r1;$title{Entap4kU {)C(. o�M:l � m]-�C } \author�|p�D. Bart�uffili�J{S>lA��jicAQheq�� Sydne��;(South Wales�6, Aus�Wi!9 zAndrewA�Dohert�Ynx�~�f�F�$Queensland�� 4072R�RoR$��pekkens:�Perim�@ Institut �I?9 31 CaroCE@ St.~N., Waterloo�Ltario N2J 2Y5, Canad=0H. M. Wiseman:�C� }�9um�1 er Techno!�, ( *Dynam%�9�-J, Griff5`&x $, Brisbane!J 41112�,date{3 Febru� 2006A�I�ab!�ct};fa��7;c�ficEXAQbi-�~e e,XA�d< flc� Y�s* ;�a7�uct���*�"�|i&Gny8!�&�^.. Spec�lly�/velopD ^E��� yugh ˉ�el�f �  nd=1exotic a�omena�}5*�:activ)Y aristI�!W ����k. ~�aid$resolv=sI:a� ncep8V puzza�o�$udy!;1��>� 9 . InӀc-MmoC2�\%� yI 9�iv �- poss� conf!�-7G@� �A to��Qv. Also,A� F�!SJSn��mt��)t fwz*instanc�_#>eA�]NT� ���nce�Vqill� �)�ed+y� \�({03.65.Ta,  7.- 875.-b, 05.30.-d� makeŹ &*I��Ni 2�ofu��B�wte�p�ful�� cQ.�pro� ing~Nie00�uHowA��$k�  �nH �Y� urre�:)M�n�ck y* �}�$2�EgusefuLRnd a v�Le-=�>e9�d�Z�&M~yQ�2their6AprQ� �Hor01}��A=is | �6��Z���1og�n ��ed --�cribe�`�<��per6�/pr1X repl��^��of =5u�!5!�H��a`�5= �66,%��6>1%� bothe�A19'f�Y�a�W9Q6�>'=U. After ��uec}$of deb�&{ sues�(�#he�,�� a�le ph�SM@Tan91,Har94,GHZ95 L5,Enk05b,Hes04,Bab04K're role$ a ph+r"�i�j�- tele�E mRud01[2, �b,vEF02b,Nem02,Hey03,San03,Wis03c 4}, ���$se��чi � by d�D#Ebiud1��if�a be(� as2 0nd multi-copy.��)Q *�Za Z�et��pr�. cal "�*+&�unE�d" )��6�hav��-�����ont�.P&t6C6C!�%�!'a1a� answeR#i�mt.�I�ho�m�� (l) ue�!vc�)�Jd ]��;l of.�A'���z )9=��oni8�o�>f l��ra')forwar�F� dT" pretHl(!�?ly�4newu�� ixe6H��.*�C� �+M7S�1.�} STsec:MSE}��gs� A�aeaSK1I e� n��XjK,� our 0n)k�of ���Y���^�w�wll ]aA�ml2I�� �mpd�s�:� +of-�5�me1-5 �m$Div00,Dur0�S"<d 1�"��fink d mo��I !Nf����a6'a��%�decid���a $2{\�'}2$2�Z�<�2in!� �&�A¥?I �0#>N(5�bl* 97>O�&&92jpa�w�) | $\rho$a�be 2Z��1U/&� %�< �%��y,$Vq �H!쁌 Rsv��p12cal{E}$mp a�T*ap�4�W>a ffub�A6a=.e�"��� �2 y(_)6.6r(� th�W���f aí�62t�i�6 -3���s, 8ERL& #e�A I�!y N;� J�or6�! A�is �!,�6�]�� �. *��7��2"� 0� �%iE׭�J� :�)�(, C1-D $\!�et$ DA� �`�r�� nor}.�le=;shax:a � �as ?1-%�Tfig< +��eg�)`ics[width=3.25in]{Fig1.ep�cap�� {Illy Q�divisf�]�.� �& to fk��4WA�� 19} X$gap �  wasisJ��]�!8� L��ains -"-:�,f��a&#qU,sm�a�ME��PPT-p�Pr��%-�O:o � b�DN�(BLP)a #2� (B1-D)."> fig:!��V1� Remarkabsby�ro�xly�� ac�E� "< Bob�"�beyond-�! M� �ee�N�oF�� �� noAs���%����A:��a&Yalm �� }. C�-!=� �affeca�e�>a�\ofIV%45r%&� ;^�'$sA��NA��)Q.�mov!�erE��LPE� Coz %%���rA�%�:� �%���ityf�F 8�%po�C)���Rai� W� � =<1[,| 8)� kw�.b (PPT)EF.��5�I~%O�PPT 6 n�F�N�n�S!yz5:map�a[R�6������oV� 2�-gEgg%g :�-!�4,ble_y!�L F",N# �o�=# 9��sai�p ��}fY D� B�6�c��aGM!%a%not:�C {:��r�Utaj w�� X�}ݎ v�:��V�z �BLP�&��A{b6� W��; ��6;!�? �f�;"HOr� n-e�M%Hor98,.C (. See Fig.~�~�. �* catego���- �^v��A���P,way. Through�S.-h��=a� �e 2`/$^(Q�"� ed0V/s�"ly�CE�ea�f����c!�R�)-ZCi� Rew-�ny %.�M�7"� l~ ���![U�N-a MURu�T�for ever�9rh���<{��:&f �8t�$\sigma�<(P {BLP�>�E�"0K]\ 2a.��E 5A�Ba�a�:�v?`2��6GR�|$ only%�]C-�a9};_F�oW�� 2z� ��:J]��A{q -`" H� o `` Ie''%P>a.p�ID��P�6A1�%�!�6T.�@�X�j^ �"! An �F) e fea��P-)�2��at, alAAgh ��&A�e �2V�yE�:�cu/�}W-�Wat043 b Y?> (�Mn$-D) i .EW&) 2h��� $2) N)��:?�.�@J�j n�J�8ds,E jo�5)i%�.G!�6IF&�|isB+\�_nR�(In fac$t 9%b;�$|")��%U!�a� �a�Dr �� <$n$.){ � bGexhC7sNV Umea?9 ���).Yr�ޡ�VZ�.0=+WL2qT�]ain,���, m��ope�#�0{3regar� �&g� ��. PerhD<mFK"L"v(&�pE&ofo#�kormv!�k i�.rTall��.�= ?*�A�U!Cfo:*�S�&bi�(p � �>��#&�'q�I� p��$o� b;�� pr\��"�Iof!�%9"�+ ar5$� ��!b�C"� �*& B2��N_ a O0�,nA) . B�,�$i�Ca�$ well-stud�p�6| an2 j�� �&-�]J�*" �r{L+�7X �恆�vA��FG�� �(Ocoaznt �Jaf&j�'iƒ.{�R.k � out ac��me{�" s,"�  a 'yg�P�-6=M*v,f( �1>{.�j�, s�R2-![ �Ϧ1}{\sqrto�(|0&� + |1&�F$|n&�Nan�/I ~�%OC a mo�M �'s�F.�' H',she� 1�� Ez�:�� + |1�)��}air� s in~�|�P��$|.K= 9 {A_1�G9 {A_2�Ketc.),� au�����ha.�total2�M�����a�`'�y :�expN3nt֔*�#do��"rÔ�#on d!�.��c[ ")2*a m conn�� �I6l,���lfraLYca6� n�"�In �"al.�,)Ps!@a�'� %���alway�"ferred�R�%>8+. ""�0nE�� �ed ��)-4,I��UB�7S=B%�AB�third2y, Charl5BC%1 a5�6�+--a�Ѭ0 high in>ty laser'to�Ia1�Ep% 2`'s5O �-x%� red.�fu] RIat6D do �q�$�s>X*v ir ��tIQ"-k~w-'�Ams>I|5xhN �A@IOB!r� ��.)t�un .ͳnowB5, � ' f���*�Pe� ��jn. �E)}��"s'� �e66yK=H��rvK�a��7�J _A$ ��-o��6T� A&�iv�.Av1b �"9Q:Ds#E%LAy be $�"$,XcxV�~E� "�a�b�!La�$U ����-ѭzx �; Gi�H� �AcFY, �(mu�average70�An#� 8Ito.&e%) 1� � ��A���" qU %���u � ��EUt& �s..�z8 I�&^ ��5.��(�red#Q 0Mq� ��^ a�0ue�;w�&�% %%�]���er�ǭ�"� �f2� mis �mJ� �)e�6S.�Ul$��!�1�A8i�J"IZ�0s�Y-��* Iob.�1G,.�#8y� 2 " U}_B�M!,A}&&�a)+sBob lHVf�f !I� ;)���[a�=�*$a��term ``J�''�!zEFP�)�1�� qipinciple}2����4R�-�WWW52}�,P ��Basi�, Aharo��!PSusskind >Aha67�wER�)m�t� 2I{' ar o��Xee��!� "�2 mar�,�Y�K. avail�AW!�ir$}�s�#. DDQ��fav !� is�h.b�9�Kin Refs. �A� ,KMPc6RS05}�"waJ !� �� Vr�a��7i�)-�%~ U!�s! y[2�s[B�6<n.I� � s�1OuU�rPP.e�[<%��7v� 6�1�*�)! of�)"=�, q8 two-^ �7�E�-�v�7"��J�V-EPR��tfm�"� 2�&�B + A &� B)\,k<n�A� tC��!�s?�ּ*�5�d�Iply bec�of nonO,��.*�I&fa�c�9to�7i�:�*OO)s�1��!��al}�.E. �+E)b7�ml �viow a Bell*#{�n�F � �#4��oN"!U�^�,X&to �9 qubY or& e c�HA��*� � e��&uoto� ��6�� �j� fai`+o )�y�#!��1)_ .�&"9 !� �25 P26 !1���.�-�N�!� ( A��on �� .�a�Qi.�iA�A#*�"��g e0bQ�"�> does} fitM�A�Q�*R�C}X�^W1 �&$�3d7 ���se�=� a.�:6�co���nA��p�une�% namxbe���%�l.�"� !N$Z@IAaAqe�A�I cB�,�� �R�N �\%\�E:A judg2bnb9%hI���t-6.\WI%3{Of�Irs)ai�5)%� j�m� �i/q}aL |: �sm�q,!L$ s �van Enk͟�> In p (Dno)�J� �9 ya�;es +&-am:f �discus�in Sec�" :2ref}.}C��lFby� � fl* �e�ET t2�.*_��:pea�Y!^e�1@Be�;� lo�6inU5�e�: $E�m�� �  *�- }. A �2ghpX ect n>E�abd�����pw��U�H)%fw�,w� . C(��I9a�mj�E� Z�*~*|�&� |+Z�.c[3ly!�)S2M��^( �B can}����,�M��K� s$]� sp94AsJ��N`h  J�*V6m�E%�]y p#Y�v%�26o1 0sy1nni�*�$A` $9�"ma!�E�!�"�E!� a *�%��A��*6N�N��� S c3�R��n � ���d8/$�x �Ax.�:v�C8(Ɍ�Lof^�)*.�&B*�Vt -*ND.* it c�GaB�!� �&y"^!�,� r��e:I��AEcJ"��;%�&6#e�i�f��V9�^�"%*GB�2� �ppm��1le �w�� �š>���yp� C>� h,"1A2i��"D *M!6� ,w� cwp��eV9z %�1is ``un�d�\.�d*� of2 . %H`�P� % 2^��4 %``.p��[ �W%��%6e %�,l]�V �a��3վal.{+zD %R�'s)�:�6 NY, %�"=��16s#:�6� %RF� !v~\Cin�c�Fr cles %ul&�iz� also fK i� !��,!MbM i2 �#U��J��:ie��H}�%p� ``no�2�'';P5.n �*e ve %"�m2^}2En� %NL "\)�E��dQAb� �%�G9U recJM�$65 liter�)�Dt`A� &�9:V"r�J�j �J,O }.&b%�� ��&: .�.;�.e��-&B� A6��vt�8�^ $|{+Wj_A. B@ !-.! B�� �8HPi��MA�N F�nECx �.BJeFa �ref�}�b�\,,n�|�A. %,X����oi@m�o *��NJ\pm�)$. B� a�!YJ�� ��4d�5. staIAhAZ2B� .��uN c�_ٕ�4li �gap��5is� ���anb8 Verstraet� CiracM�I� �_Iv �A} a ``It�_of�3�_A+o d|J�6Xa�G!� Eq.~��Q7) v�I ard �j� c ~u~i  2@� L''�/!���s"u%k���)�(i311�a{R�I:�A5a5``lift�.Jj"�8� e*'J:�JBE��iA8&�e(�)ly�+"l7JSJ5�36�(as occul#��* 6�b�kteB�7 ^3�C�2�*71��{ �& -2N ��z(E��a�8Gr��#aip6=v�Afo��i�p'9&zXѐI1*l9R�"3:p8�r�%T*�I� �'9R 6q��ac�ya ��;�:�A�&N��2�A�ess a$%d>�! [ "�I=WY}l I�sf."�"i q�)E���6�� *:� *�(B)$ b�72�!�'�|] $|+�h| B>L�2s .����Y"�A8.>!�]H " af4-MMSEE��$Weor��V Pd c!Y_g� �6M^� ..-A"�TeV l�!RTN��' s} "�weN�&��L ��� �W�<C4j�u,*�QB�z scen!L��Uo�~sG$0es&n Bn (albeit8" >iO)!BR�m&�7�)a�;)�=?nt� �:ρf~�{A}]�{B}2�,"�{B�3( �$�kitself,X� not}6n : �\)��2� �* {B�xe"l �ɹ �is:�+ �B_ B_�ai*�;M@e3!:0%v���2�{A}�p%o�Ps� aRllo�FLe>�*u :O"n)�-�TliE�*l�>.�8,�post-�CD�#� n fin]ZJE�o�O'mRA��"E-�2{a��`} k�&1�KB_1 [Np*�B[ ��|2� 2�!z6[ ]9� \Z@*�F�(.�d&��AL|" _B) "z 9�`$�!g�utroNfyS)��X/k %O ��.�!2$��A4_��nB ity ^�!2�Yc�Wi~bQ cognizA�"�Y� sU7�7a� a�F2 �a6�� * Q�a.�/=JR1 N��ie� "Y�~3� *���%"��.r��0��$is-.g�!!mtak��~wDobives on �&&1E�i"�FN-��i�"� a��] Ref..��&&EDAD!�)�N� n�>&��, 2��2�& ws�a�ܑ A |6B"}z$6 5,sum_n ( , #|^2/2} J^n / \.4n!}) " 4�N2s�~�G�;E�d"�2��,`@%s� �Z%I� osc/ or"� homodyn t8&s,seach wingcN�h: $N�.E%��19�6:FNq�2@ "E/F�_, L$nclz��P < ].tomp�<e>�$ i>�z8�o��Tad�a� *r'"b7��Ja M$19 B$ (�u �56{A2�B$)�� ej @:�$� I�=o8� G 6[�0�A~�*d OU �utN �=�C1- �ofQl but �,C�}�%x6!X �1�e� *?4�����[�5-�JF. (Suc�P.�is�a�=�N� ez���a�alud VS�). L&�2;!es+e��F�[�ru eu��Aa!�-m�,t a beam spl�|D[�:n � 9�'%L� �]#Z outp"�rtI��Ei�Ypo�f�B T�LA��/J��E�l��'!��~p}b(Led ���� � �in� ���ճ"%��!�4nA��is �u����{)�EjF�, �ia�*�("q{y�T. !:�(�t�9)��Mab�6�a%O���Tq� Aql6�%O�b��s�d& �B,c . Ra6����e&0�x .<aA�3-<��y�t<)�*1 ��\>��p�h' � e�"�la&�,���t��$ {!�!! �%�n�����J�VbF[T��,.0erneѩ;pA$���A��1��..�%�*�ųa" �zzE��lM &* =@gi!A-n:aA�& %��b/0�"��-+]+eduVleFuMW A7��uC= wou�t �g�%i� 0�- �@+�a �n��rY y Rudolph�SaL~q(6) EDu�9nguag�(tel}� ynop?1as��-2� �uum� 9**ə�7 4��^C:���aR<  a�3 squee�1e�| gamm{ =� 1- ׌�nQ�\c�n}|n,�>$ re $0\leq #  1�Iy�]ey �!� .���'h�D~kIZ2|�.� :� $*@*P �f�g�e|!is �E�a� *� )�AE�y�4 ixed*|!�ARMCX� �.} a��m{C�pu�EAx|�C�M :�+pr�.6a�l�H�)"�>�� ^M.�s� �b6�"�� F� :��!m�ly�=u i:�GAf&�2$lGsZd. S�c"y,�!��? 6-5# � Yachie���!wV�a�EA� (��I�F�� 2� ����" U��p!] aY6'"vid�,�i:�JC�ge��P[v��a�H���.�U�"�02Z���:�����^$� W"IlG�9R'"��+�`ac GW!V� � %i�J� �*$��02��Cb��:�� O�h��i 2����b� � �� �k1��5�A��yQ*�2R ��J�is)�+��I���iBdu �8/$nd�c�. g%�rj`ai4.5AnsEmv&� ���M���z`:YBrAu�^� ���a.6 t (on M k ���\�����*�Nm*�A-2La:�:3]&M2}���.�B��#a2��&��ps�c2�= .d2 ��chu�Qs*Ua��2J�d�.�m{ 2�s*z s (c."�Shi88a� �* but)�"3� �{J�mc� down�e��<1�Y4� ? �in�E�A�a s,�/� q"WI�8aaa1�HFHBg�:�tZ*=�1{ w�WTSe�s�; �"X"�?��f��7EosOc � *,t' a"� !�H5�M *��*aj6��!V 0�Y FY Q��dti�db�Q�3 �e!W0�>2 pO�R�`oft\ �x)2�aM4)&L! � )T*� ��b}. stoo�5r2�Pcf7I^r2�,�"�3LiP�Fv�*QN!W �72d%2�d%� {Purj�NgenE��� }�w}OEy"�F -IQYʼn5nR!N%lAQa�ed-x��e-�e<=�;� �} ( .-��y)N� a�4e to consider �@only pure states, because, although one could characterise mixed-7� entanglement under such restrictions, the classifica of )Gs wgXbe at least as difficul unTed ^� . \subsez{R�ng opera{s thr�!� 6�i!k(scussed in~ i8arnum03}.) The:' �@we describe can bfined9!a!�as follows. Suppose Alice and Bob share a pair Aystems,a�d by a Hilbert space $\mathcal{H}^A \otimes \B$I�MkTon which were prepared��jX a third party, Charlie�0 further that%�local re%� ce frames!��,�� K, �transE3via a 5�0, are uncorreA�d: nis� eiy$ $g\in G$ 'A�r's.o's � �is Ah8letely unknown,axia#e ^'>_!� and �:[. It -� �a-he� represenA�%�Pdensity matrix $\rho$A�6��ve to�� is:W%�BYQG}_{A}[i]$ )7 W�YD, where \begin{equ�X} \label{eq:AveragedS�KhA f� \equiv \int_G \text{d}v(g)\, T^{A}(g) � \dag}, , \end��5D$T^A(g)$ a unitary9�A~$gNL, A�$�$%1E|l-invariant (Haar) measure. � �K E�Eme�impM�jSE�] by��M�posit!� maps] O}_A�a��mmute�9 Y$)�0$. A similar���Aholds����E� Aρ��.�$joint LOCC>2 �!B < <��th��= bA�ps�OA�B}J�= �� .u{B% Thes)p saida6be�ly $G$9��W��!�eQ��a�=6is ��9to�4a WR%(for $G$. A�& induce!���3��$structure �d�n2 s (we�si�Y�$):N� 2+8A = \bigoplus_n6,B�$i.e., eachN��LLsplit into ``charge �ors'' �E�r$n$ESMcarry�in�9al��U6e�s �_n$e�GA�E� ^E�be ѩde��os��!�< tensor product,N UU!D_n! ��M}^A_{nU�,Nn J.of a � ��=�Mn$� an iA`ucible 6���/a�VQ �.Q trivi�̀%E9<ForwAbelianN�, � aI�(photon-numb� .F  d*W T Sec.~\ref{sec:optics}��9.� M}^N�$re one-dim�(onal,�so�� addi� al-� -�}5�.m9!VpsA�no��quired;e�a� :� �yQV non--Q�0Z�1��2q noit ss.�.7J A��P map�"G���Kni00}��a� %�U�,��a ��orm!erm� t��zmɌon��Nq a[�]a!sumA�D��y':I (\Pi^a^C  )\Fn� $ #$!�!' proj�  oa�2j�\,=> �Atrace-erv�vmap�0 takes every 55onJ��Sconst:t� �identit6?9s� I�9�-�?� over5�s%�AzHCMuM�effec the �8J� E�n,%So remo he abil� to� e s� s� m ��hav��Q�between�� �2�P>� a��� � �ƵC:1� �sam��7 arise ] H}^B�tprovide2 $ analogous:of;G}_B$.�4�a$tails, seem�P� To��ra�!Yissuea�distill1i�%!c,anow demAYr�how!�8treat multiple �Rs ��N� . If 2)r� exchangesZ  \ made up�sa 6��s,]x�$=@E�_i&� H}^{A_i}$Q ~!�all d/.��'s� !,$uncertaint"f&� >� 2@ to*� � e�  Eq.~(ŗB� ) us� Ar,:�刁�4 �� �:�: IZy:�gre� nnowab our mai-" �.e+!& ofi)-E>2� A�in many�pectsEQha�q0ofNJ�M�+*Z]�a�+mA���e��RN A 7ly) &�  will deno/!Fq� X�bi-partF%�at_ �ly!`parablY& aN  $G9a!;, )9b�,�k�LP$_{G\�-SSR}� A R�!�inN3 iff (i)-�a�is J� �, (ii) d �>G. (Thus,�U au�&& !&Z�.)R' $|\psi\r�Ť1-��l�!:%�,1 1-DB, i��re exist�|U8�WE� n? !�� pa�:���a $2{\e�}2$.4 �&� e;�sE}[.�\l�� |]�M��&~  sQT. .�fro�_ei�theorema�BartlettAWiseman�1} �.��inRIE*�� RB~�F� 2w!~. BothR�N�E\!)Hempty; explicit exa2v � D F ���sQ�/C:���in 2$)�$2 O*(%�j9��t6�5@&� ��  ��} W�!� ra�by� Jj .^e ��qj�Q��� \emph{(Js)}� 2�.N�)}%b!�non%�.u� A� JC r�ԅ�per gap� ��se two ����r�d"� ;con��s��Ai�U �� =�i�M� t(fa1-bound 1��^� . AnB�C�Fa BmQ� Emis�q5�2� foraor�gie�.�b>bre �`%5%�)=t�anei�����nor6Q (.in I�J�} 9"N~})>l More� ,�� poss !�extend%Qe{i�c�wa���ny�qE"�ASb� 2�}U or 28. OneTply lif1 he6���)6>w b^` ��� E�;��i G z�2]%�threeQ9!� &*. ���*! resource,:�can *� a�$�OC��E%|�A�!� diC �pr=-p� J! N/�*,i&of P�E��llt�)�&� j�(�:T{�F� )M�IC}NV %�5 gives�d>��WD )��� BJ��5i� W directly&wfac�a!�:�!Fm�.�N�!f!v6G> ��� ���!� 1-D )�%�6"in%Bd >�2� 袬� . Z�N��Jj��J�F���2�e�a�JJa�aQ�EL>�!8!f�N is ``�Wed,''n�����R��i� ul.��N>) ;2K6N�)}� e�es .Nc}��RMk Aʉ�:f � weE*�d�!�"�!FigY fig:Fig1}�X^�!p&  .R�:J� ]�2��.�1�L#�ikmlFproces� �v�oI �-copy" P also1EYgR�"s, we �#Q i���!;�) Wdepth�L{ ext� js %5 &��>"� in R�.`# turn)�iQ� next�iona��ion{Act=p4ʥ�m2�&�  ann�} .�hp ��[#�$to fuad�a %ze=�L�9�Zh n!N�]� .�#� � ghtforwar�do soJK��%xv�%�ww.Y . InH cularvco�"e�ify��rJ� in *@e ��e 2A!�(thu%�*�!I.���� = &� ��t�&�vece�)��m�m� F� is L�9h ��� : >"� �H2�s�B&��y���j��w��:,�'H.�b�""6�$ \neq 0$. >{+��!�6�|AR"X6�����{aY��� >+qn!���zB� �R�~I�� ��b&�2OK u"0*N 22 z* �X$thmnonum}[&� ]izllMF �s�\$�R<&.�2OchK�+Q26�}.V2� Psi 2���2&Bq�zin s:s�s~>�:v$f !-Aed�>�2 �:6m�5�>}Let1�6 �- act1�- .n �- {A_1*�(Pi^{B_1}2 J*F�b:2�'20 on��2$b;_1Z�_1TD Let $\{ |\tilde{n���, 'M� =�bof*vS :�q& A�l n>(v(!�.��'!'� ')$;�se:.its occu�-,at $n=n'$ du�� �� ofV�" . S�-ly, l)5m9!@,56m=!�1a-�D6' $. B45m�-bm/Z)>r�B�2��Uerefo���$n� !Gor $mm'$��.M7�(��_2^j2}$A+�$ .ously�o6v�� I�R$|�q1;, con@4�sX*�V�i.s:N�.Ku�y ea2} + a�q8.2})�?2>:?6A2})\,���uQ+����|is�IV�".'%Ua)M�8.�6o�-+n')�a]2K���F�5B:$�)n�5byN�\y�:���9�6�3V�2�\}J�Dl'6�B_{m+m!32lOPQ+ng6� �2j�211i&�}nsp per�ped� b) stic97>!�c)�6eas� be showE� � 2� "� l S" "M�0 .D9D�lla�+ Wf &�'a��*"E W<p+�per !�|� 6�"n"�>��. Speci�:l�w�7m(J protocol�� ��of��P6.$V�.A;I A r�r�.  ��)�is�i49n*U. P � BK��JN�?�;0 choof+ ${ *|6�.�&�+B b�*m-� �~5.���^: "'2��A�2�*� D). \medskip \noinP.� it6�50A:} T�@1� works i.�,���V� �akb%@see!�${�/��,' �I:H �!}� W �bB'�CisA not}V�-�i� � �m}6� >��4 �RA'�Bɽ�6� (�u(*�aI "�)eXj�0ng +'$kN~ {A_kb� k}$ yield�som� �y�;t:�6�. Oeirs�8pyO"0�7{R�1},.�1v )�oA� conda�y*#N\:�\>�� �$by collaps]$A_2$)jB_1� �Jo*u���O?RS ��in '65.,*ma��,)$���Œ�2 +�M*& 6b  f"suG@i?7toE�Fns�=E^����. `isn,A����3�+>� ��B:}��6��y!��uOonF >�E� �k2�e�na�ss]�RG2bG2}{<t�T3e�ɷ��B�Q �2�&Q �P�2 Ao �zhe�Gf�!&SMQlK A�I�>� R� ,lambda_+|S_+� A. Bp (-|S_-.( bNw|S_\pmH =*- %�Vt2}\pmb 16M2}J�A"? !& $6�+4>��D $5e@n*�8_A��/ifY-j��V#L�(4ng-�B�R��щ�:��E2N�}��&�[.< ] A{&�2��(&� �1s�&� ��at mosa�ZD q�F]� is, Nz\ \cup$9&2� =$ R��#bp} 5y-�>QZE3� 2p &� �s,B2+succeedsA+e: of!�a� 0�5FO����choic_*6�A�u2�=��"6#�1$ a Schmidt� is�0Nie00} �=ofI�.E�.� .&�4� �Bn!l>|i0 Y � m-��J.�"reSDA$�C�1=�"�8& �I�56 �#chq,�et al} �Sch04bIn6w was ���7%<sB� v"canXc�3';t B),!..�0{\rm V{-}EPR}�� = |0 _A|1 B + A$B$. 0V9gu�]R�$-]�� L o��ed to�/ $d%�MW ��,;&�$ a �!-N� � �(%�U2 "�G-���E7��&-�asympto��ve!z�.�R` �� Ou@8���trongerAO w�is2�.�/e (�so6� )5�;7Dtwo-qub^3n�J�0 f"8 �6� }MLf=~obe�AEKF$�N�a���&�+ N�I2mPeE7�V*Bc=0dard techniqudo5( ��J"� maxim�:��s�%[9� p;. Fi�IL#�7)JwI c*)&"'Lz$e"G�� (19AV2� �n�#u< e�&�M��/ R�EA�{* reg�9y establish�PZ��"���+obs�9 N+5 RFKBKRF ..�!��7� RJle!B�). �HnA*2sP alig�H�_{Y{2-D}"�p &= \tfrac{1}{\sqrt{2}} (|0�.A�E�:�T�GB)D \\y ps:s�t{+��v|2u{-zw�x�2�6%.s1 -fe $E��L Fock�K�7Jo  ( * ). N�Mm!V�� �$A/�"002� J�~Q!&�0=�3A$->^" #!6>�.>�)9~� N� (aseMnw h (How% "�P� "g�4�� /"�:�a�K (unily)�A6*-s,͵-ZN�� �on� cussion} {+summar�`:B��" �B7 �S r=@�+ic schem� miV�Q��"�.ng ��� u �}��s�)a ?cqA���2�4 what!�-͊.>A�!�2p0. Deb�%�6A�2- g.���8"�Q&�G%I appe�OI$5& �*literaWJi6lve�Lrecogniz!/0novel categor�,of�E�R _�-.� F�rgge� �3$L �-�JO=�6is�/ic ś develo>[��y�S('sor -10���|promit=5Zfor"�P�O archor�+,!N inteU�E!+bi"�@�� s in���G�Satt7IGC�Zr�*�@�.�e�e�FInq:�,.< vari�AppQ!�t�TjY:Y& �A�%"�-h N]�tenApT rAXndaA8 ;  HWis03,Sam05,Bee05},!{9dj i\U-elec- �'-mode�7��$\B�(&� 6� *� 2�� ambigu!01�ETi�a�MX[A1I� �? �Vaccaro.�}e� int�AedY/5{a%�aP, �eda 2� of pE les}�e�if�:6G27�,N B-�N3 qfw)p :�.�no6t�>��z!1 �. aL reason,�!gosa�NP�qP make us�@ spin�!orbita�*g�1 mo!�um de�/A�"�//E2@G�-�A�3E�I�4�3A�,��U��A�1+ j+�tn��AFjak���>>L�I�5U6�*Iu5/t�W*�or �O5"� �I;P5�(ui ��2Q050}$j0c�X �7''���R!Q! J"QVey�j*Y unu�l*�  =)�X%D. M"4>qU+b�<aI Q V&U F1: no reAedvanta�2�K�>���.4in situ%��Ger�+~8es04} B. HessmoE�$Usachev, Hydari� $G. Bj\"ork:�9f180401f:GBabfSe� Babi _J. Appel ]A.e�vovsky�l E�bf `936V`Ruda�T.��E2B. C. Sa�Rs Q587F.077903�:5!\2:[VC� FuchBT8 T27902T2.� �b}z�a>.12020O2�{vEF02>�F�J�% C�1g%�5)�6�Nem!K. Nemo�'nd!�0L. BraunsteinF�207135 Ay2);ayY�68A� 4232I�3);��.�2dN,5� 333}, 378%2]{Hey03}]�� GU�AfOpt. B: 1 SemiL . 1�E4 �2e {Sanf:SS.��R,:� PřKnigh��N�9�3.* � c�M�L S�Mod:� 50}, 1797%gJI4NH-Q 9 .S84 �2{Ve���Ver e nd!wI. Cirac:|91i(10404F� �:�%Ձ0.0 ZU9u}2 sZe�D.5�UH�t�jU�&2U {S�"a} N. �",� Uإ7 0879-2[ ^b�^a^7Aaa1�?2^{Ben96}��$H. Bennett�¡�rassard,A�Popescu,A��m�rE�A. Smoli%� W.�!Woo�5 66}, 72�$6); C.~H.~|D.5 $DiVincenzoFeVcyW54�(82�j6). %Q�.B&..X Hor98�� �*~8!j523D8.wF.QEs� L��2�Div&B�RW. Sho:�%�M.� ha a*�&apliyal!�\p=+6L06231ɬ� 5-Poten� NPPTV�6�ur�W. D\"u �y�M��w�D��a� ru\sQ&9��ir� %�7��7��57IT7)9&Any 2x29"&��'f lled2-Rai�E�zRai  IEEE� n�(nf!� eory��47� 921`!f *A {EggRT. Egge� , K� H. lbrec��RW erna�!�M� Wolf:�# 25�P~U!AlM��e1*�LOCC+A88_nel2�Ci, J� �Y7B. Krau� 27M�*� �O54�B2�qif �-�used % I stochaO7 &�iav��-9}��*� M � %T6� \p2� 8f 056� 9.-&@23Wat��J tro�,TU93J 10502M��5�Exist1 �$"M��bu�Dt! N2�\.a!�6�WW52}�,C�ck,�pS ghtmEndA�PEm]. Rev.բ2  1� 1956q DAha67} Y. Aharonov%ZL�sskind,R5 151 $1428 (19672&K q� Kita� D. May�K�JE%eskille a��69!d5"� !b \bi�BRS05>_> A��0pekkens, IJQI&�i27 ess} 5)FN 5072169� yf��323��FFu��,A. Furusawa,L!i\o renS� .� C. 6 H�Kimble� E.6 Polzik, Sac7ex� 2e706A�19�55P {An�:� FzZ selm�6� %PY }, 427-44� 32  Shi88} Z.AbOu%�LA nd�2_Œ50a�88); Y.yShig C. O+le��9�� ;.�"HsL ,!3KnE~G. Ortiz)KL. Viola��-��!�0 D S �s , E.FPR. Somma�.Y�� 10��6�Zi�$R. Laflamm�Y�6J84� 2525E��� %uFWer89}M F. Wͤ2�4i 4277�� (1982?PF^Y:��Xko� G v!\te7) Bell^ma�g2��5��Samuels� E. V��khorukov)�0M. B\"{u}ttik�mNewe$�� ��17t2�{"A_W8BeenakK$8cond-mat/050848I6D�3ޱ2�  1570�6O�3V� C. E�& M. K�; rman, nd J�WIVekJu479�#20:u�4�� ��02680I�6����� �b��F�N��E� Pas'kauskfndaHYoueF}�� *� ��;�1}�:SchliEc:2� KE6` �D. Loss�>r2236rW�$b��.�>�6� ]<�it{Laser�? tros�8:�,ceeV]9 uXVIern�al Con�},�xannafordigit� .} (WorldɎt�?$, Singapor�4Jx 309046. }*>�  docu:} JV\h([aps,prl,twN@ umn,�criptad�jL,footinbib,floatfix,�"0pacs]{revtex4nu��ckage{+icx�xtitleci�Em��ofa_os��H vbox 0pt{\vs2\h.'h�?h-50pt\rm LA-UR-00-XXXX\hss}^2\v7 25pt} }a+e�t{2A0} \author{SalT HabibffiliE {MS B285,. Divi�.��al�+Dnia, Los Alamos NP4al Laboratory,a ,��< Mexico 87545} �(Kurt Jacobs����.�\.*Centr�Q er T12 olog�z("0Dynamics� hool!H� , Gr�}th &6,!N$han 4111, "*23osukeG zume:6Institu�|f Libr�x�A*��y\ of Tsukuba, 1-2 Kasuga,TIbaraki 305-8550, Japar-m@ab�ca@�d ��# tatu��iso%7"�!*,� ly*l* �QJ�*�� r\"o��er �.e!unclear:�Qn�al!(�1$ to detect\o��% ���'3 uum � subjec� to observE� --)ll�eF��+ Rbe'their1e/ no l�5 �!��+ ap�Q!limit(s)%(e evolu� ofvc�values�I�t�-N �!los>#d�ssbehaviMff6%cal tra��%!+�$_6e@3!y�-a speF��t;icɟic� tinuo�J �eJ {\em�:n far=9 �0�� %},��.�6�zLyapu�exponen*AA�8trulyE tic_ end.�\�^IMinvolve0sured,i$n�#�e �(�sim'�)!�1+V ��1"ch�l�<)C&�%�}Chirikov1 4}`; ea�onn�r �1' �܍@=|� !DoryU5-/s l ss�%�.�%iԄI�)�� Ymq�^'I>lU*Qp "},8,b12,b13,b1} � �| alit!Å�b ^ deri�^ encaps+�jX9m�,�%ich�m�mo� � !F�%�,�Q�12It��)�D*(lR��uA�u9%�q�1i2hL ��2��w�du.E�i&/$E��'wABDm=�((itself medR($�0environ!�apr4�#� ndGbalanc5�aAg.E. void�no?,� � b& VA���s0�*y�����e Ehren�>:@0��-SW2Land, siW/ane�M � �Jegliga�=4!��in"�mooth]�$y. W�)ito)Ew.(E{^�   AStic' they .�eno�NYUq?{ icd�E�?haZout�(s+�-?��C2he �=A��e �) . By�F!� L=u%8B��dZ� deep!V=M i�,�%[AE�A �*I �i�:h*<:)���:�+�8FameA1%F��JM-N�w;'%= . Si��� ��� abs��]��-�� �s2�8`Ktrength�:Jin�6s!�!�w�7 amin!�e �* qh-Ince*L rigo� �ifi�|f��a1n"v ���? 1l�%l��21� �1 (&�?) �?�Q ��div*twoyo��LAr�C neighboI( poi$ 6�"� %� De$� ve&Bi�U\M!M�JZA� )es�@�Z$ -U��!X�( eriz | X ��M�IC ���C�{IX ��!&pia�:.21D41�v) e� \!�)i���Y ^�e ^s�is sa"��M�.�+pN8Ebn�4 bel�|�6�� -�ed%w �ofI�um�:t ?.9o�j"V,&1:�J4 id4B i! � on>P pY0non� &� mas�")(SME)��E0)�� �q15}: �4eqnarray} dS�&=& - *90i}{\hbar} [H,(]dt - k[x, ]dt \�]ber\\J ,& & + 4k ( x* +1 x - 2�K~3 x"�])�,2(dy�9R+ dt) A Y�s-� � �a@� MS / $^ haaŏis��Y�,�>bhM Hamiltoni�+A�Mc�[0s 61�&�3��''uCun&�MB~��?ib"��or�$x Q��W meA/$k$a4:��a��.�ext0s .� abou qX"���w[6rW0�=�H��M}aE:oQ�2��fOE%X&׆������:� :� !.�1 ed)�:��+� $dy$!K ;���i:y}�outpu� T�device��D $dt@B�@, $y(t)$ fe�!Yusu�>)aW.�!rdPJYVA�i�by� =J�dt + dW/�D8k}} $ r�W$�@�Wiener��� ,��?�nghGauss2w1 E�-��%;� $dW%z*d &!�Ar�.��n*random. 2je.Xa�r;.@��#?Uo� .) nq�Ba��� &runG ��:be ! �Hy7�<*g ş � o���D�a��5%m� W:� s !�s$��figura�cue8s[width=8.5cm,h�t=5.2cm]6sal.eps}�� \cap��[e}}]{A1ʏfig0} P��o���>b�Jfor= !�DRT�sci[or)Y.��8s $k=0.01$ (red�%�0k=10$ (green)Ak�\L-in�y) 6� ( E�R&�;.�"es&�Q .} �-Q A�� ��"Tal�t 9�6�"i9��  d�2�"� ."|E!>%9pur�N�%d�]�an.�e�roF� iE2�U�%J.AAq�>at�gream: ��}�x: d@р,pR��(t)�F��[t)3j � usD&j F,Delta(t) = |��S&( x_{\mbox{\3sLKfid}}? � |$,G;:�'�.�zd��U&T5�2a �vit.�Sis{ortantkTmin�6�D� cn�e�� we wishBah8 b� )��! ���2� 0 r���� ~���F.W fix=8� calcDng-=�s U��� ��D� �Z\�Tyb\lim_{t\� $arrow\inft� I_s(0)' 0}� \ln $ (t)}{tiW^v DJa �_s(t)M P}m�� *P subIq $s${o�paBB!!�e¡K�?obvoE�vi2wf�EODE��:p�,sI�['�aa�HSEaɈ��A0I��de�� �" m@n (�y)*y� �Mh!�$�Q�AZs (2ux0})�� re���x�9/� JA� ?ct*#!�2. T�<mbat s�RguI���|B>a�)VA��Aan ense�'�� -� U�YgI�EK�mstead0t�Ci5&t DT*�Z��. �sD� ��f�U: In un�!��~>�]1)�->i�AQo�by�lo� ���Schwarz*&��h-$�$ishes;%�N/��)/� decays a��as $1/t��!bme�i�/ucod+I.�5,!Gci &�is Iϗy5!�H�lij>it-EuldIz%du�t�.�Be �em��p e��r,&�E�:h# �i� �q�bi�"�!p%?F� Cnot va!h* A0 cruc�QQ`p6� . %  %!: L�y~!�F���r&+. � eren %3 J� G -lik&�s�L M�. ch %s2?te�M@ .vdo! @if���� %�O%��word.) � s�co)A�=��w� &� � b26"}C�Aygl2ECit4double-well poE2�xsinus�l��ing�3e.g% �L �u�!� ծ` H=p^2/2m + B x^4 - A x^2�L\4 x\cos(\omega ��lbham}� P�^$p$r�m,IQ$, $m$�B�-�$A$, $�s�b ��;� 81 &e M� A ing!ceE�fix*! (���_be $m=1� =0.5$, $AP ��) v$)=6.07� &,a�8u a�A$"=�s var�Eei4�L� �"�s 2K݇s �K1LdRa_Pe� the <��! ��0!>&-W%!��o a tun]�aem�Kl�N�[���np�s�Gt"�� �� u{Y�s^We/u`$DlaF>p�Evice @a��&a���"8��� �=10^{-[a�dT��s�6� mٕabU� ���c��&� ly�!oa�In��waym~J%.Dq ,�ca|9tra>|��+�n dOs:�%�x �$A,�y�D(�Cn)A�ouRc"AF�p .� F����A��!��-� $k= 5\` s %�_ 3}, ! 1, 1)3+!w $k\l�`@�� *�!�pr� veIf!!r,e1!r fN��"�'fw�$ot satisfiBC[]n%�eV��-lfed J ^xI �M|9CI!G>S,!���i'��*�coeB#�e, $D_p=e�^2kt�ce*,�f�Y [ X� �@a" Y>)�k^aa�y goodO#xiI�. Strob�,i�plp revCi glob?j$al>in � ez$�go�V�nU�q�:�1})�e�#s��-��N� � pasIlt� Tvals �,v5�Go, A�=�`��Qve'b��$!�l ix�Ѿ*p ��Ys#�%9� �[!u$z%6�3e�V remarkabl��tA�mia��F �tdeU���-uF.���2 nont�=�eAear�@M+%}derŲ� �spz 3Uer��er i�s< a���m�� v�&mZto owsInd #I��swi�E g cokn>8�V s. A%�%,sO8aVWs d��retrie�h�"u-ma�C sea�Y�map�ge )�`holes'�I7 ic iEI�\ }i\)+2sp!k�Jxs�Qm 'o��we�. Cq!�tM|@'6A]�_Z.�rhorI�� �b tinu�n!spe�N���%N(�wa5!�`q�a:z midiya��H �`�o!Rq�!�m6}S�aknQ� �E,meA*E`i�GaM�rysl'Y`a?�,�"a5eaUhe�survive:!�""� !�|%�� �  �"gr���!`H e�\2�A�&�`��7.�2P#.�� 1} P&�)!:�e� ��4*N��k=56�$��01 (top�% 1�� (bottoxjC�juW-�-a ��!��aD�e a1�!�e�����&aYU� El2Z�( $0.05,~0.12345,�u0.55$N)�a6A&$�$we E A�gmer�'� io  y��bt�0�b"��5s�Uy&^")q"_i���4methoda� teso�w e-A1 aris)Qs!J! s ob��edE� solv�zaAexact X�5"�(2F+1K!is �n10� nten���hE��* tiX�&I!T-{o}��.{08I� SME (��n ) �� sandA.�����Y�{x �N!M��"s;� lleցper!]ut�={�inj ��aX| task. We��,�� s $t�J d� nonl>!qP�)�e�Umbd� feL� �E���>(J0{!�or �$, unt�Omi"Z ?"g ��D ver,\e�zl0a:��+B) as $F�$� �S�0is���2|2}!T t�d&�%!%�$kMN�h �T bjQ��$5�sI)�ord!�oZagnitud�%=12$ � p� -law fasha!�k!� �fJ0$>^A�$1!�b�W settC� y�%%lE_{Cl}A�a`!Rs&Y�2}�ge-fig3}%{ �3 }A�c?.+CAX� ���s< �*5���!���73�  2} F�F��t)F(t)�mR� :�� 01,~!� �N�3�322�A� � %�!A(�3 PA�=� pf(logarithmict,artom; b���V�aŊR/k��"�M�he>�8 (C4 tic)�M �\ -off�� ��/6r�Y�uB2u� e=�&�X paWE�����A�W ����fi+! �LI�}6Fp��&�� %its6u�2� �E�B�-z�`i, pl.3. TWa)9��6$p fi��>i 3i ��� 29\pm^08��r��N.(46 (1 ] 0.02RI�775sC!�us%R-0iK#ce <�ti�c� m3W ��C.!�-��tNb�7�F��� ��, $��)�X >1�wupZ�&�}}ѥi�[�1an�� �El�[7ng,a�� quit�inc� d ����, n#`tZ��" ��!r a�F�,��sopj�jv=8.�;2!$[t]�#\�v$$5�4�3Z|e��!졯��:a�F�Ug�|a.Y.�!��.�n(. Error-bar���Bof�� .~3,fn�nA<S(ime.}BIEK?[�!�q��+���t�c!be ��3aa &�'lyY>YIH. Mon#'O qE�&�} p{�IBI�X has �3� � B��5 �P!-$xɘ6�*� s do��o �hib !�2Of�t9o� Liouv�K[ �8� "�If � �&�]�$edqF�-- "'s15cd .bL2M �iv��oB?)Ythen �  wetA� ningk6.��',��l�=!���t��,� Ek!}&�q�;I�mia�5�I�F�;���� BLN!ZM� ways$b&��=�I� �xtkB�e6�:�0of !/�  L%'!�!��a�5�"* с �� K8�6 U=�F��R"n8YQA�7=�p�1nh�t�5�7ɓ.3�.�-is1[|%�\t�N>u�7���0m"�7A�1e�4� Ӕ���*�p� % a x|7 stepDZ� 5B5�D��&�Q!?� (!Mv <M%M)�)yi' &&  I� Lt� � %$ywe&&  -��&�4 y�^ ax �-&Ş2�9of Ref.=��be�S *,ABF-i��q�� �8A--I1� � �gB�  juH�U�": � \(Y�X!��E�1�)� . If*�"�.4I" �~x)|, �!a� ��sid������"ɧ�Cf�D#ndEe+im�q.�e"f"F�.�wa�may�CBA��t��"ce��"�; h� f |F��;e�� �Y� O!a� �j�,a!Q7R�gs/?��a (4&3$. ;."�M�H 7}. �7�7A��Lya2R'�6>�)�s, �� rQonshipq�"� � ;�� �Icx pen"�$� .]wJ[� ide�Hed::]AhQfa�mڸ� - ��d�+���ɶB� � b&Bn�F��f�y��!�in ��--�)ca{7QED%� nano"�=`(c0� exp}.*�`At,E�w�&�l��.�  2!�!eii�:�;�Q? i�a:�yQ'mean ��u..� i�"d�&>!_DHI�3�`dU}--]�%�Fw��2�bP� A=\Q1d�B"�� �7�G8k Tanmoy Bhatta�y$ya, Daniel�c�Sa�J�� Thei�"�h�c7fA�.�@��AD��r�� vail�b?LANL �G�+Co�cB InitgvC0��e Q"7e Par5S&56 Faci�O]=f�e DOE,�ARC�~!8s�uofk&K>�K:�d�D$ R.~Kosl�_A.~RiUl�b hem.�O{\bf 7�!340�P01); J.~ManzySB1zO219 19)�"3Qb3�8SeC.g.�U~P�W,O �ITOX\Hcep nd M s>.(Kluw�) Lond" 1993:l4lB.V.~�B,EL �sS9�b1)%F2 em{�B0 H.J.~Carmi`f � An O��S�:s A�acha��O�,T}d"vd �0; C.W.~Gardin� P.~Z0dr j P }&�dM2�e ; M.~Orsz�d� � �b<.�,9�8�aP.~SpilaO!wJ.F.~RaLgRLe�`-G9A#235�1994); TAUBy5I.C%� civa@(R.~Schaa��Vhy� L29rS077Apw]FA W.T.~StruM�2C3�_18�P�U; \ 181)��\�12�~6lS.~�M% K.~J2M�T rX- e,8�W48�e-�( �67� 0421�PA�Seex �^~G[��f.26XC)%05211�S6Rb1ifAA� Scot GMilburnRW�%��Q:14A�Y. Ota%$I. Ohba, E�Ht:�-3g308154. �uU21e� J.-P.~EckWSID.~Ruel�W%RMod2�57}, 61E856�26UWApL�+�R E.~B�~� e2�I�%�6!� 2927M�0);5�,!�Shi�M�W.H.~Zur~j=�O W_436@WAa��T1�O L.~DiosqiE�B 129AX1�_88); Va�Belavk � �'St kws�iBG40G35 G(9); Y.~SalaFW N.~G�n1.�81>26>9�W M.~W�c!  �L�]642a�C2|��>�d%�8;^ �6:�20%�A�UD�#UJu�� G.~Jungm>)EVq=3i�623ch1c.�foo�:� /8d�y�2�� \<� "O8bandw�9�6i:oodYJr1g }&?x]R,"D��J�� �Rd�<M � ��uu"�'" ��2.�� 6��%XK.qKτ/2<22-�~�_8J.B.~Swift, H.L nn�FveA.~Va.�i�IaE 16DA 8��a�.�~ �2�R.�Lyf��7�6�j"v Zf���)� ~Mabuchi,�� e9!" �uՄamq\E}}aE^Kf�X6H^D {nY:��R%' 29a/137c2� M!4LaHaye, O. BuuscCamarotaP KaE54b*Sika� 30��74�Z4&�A>d BNV�E %ZPVA5rint,�ed3,�$�O*8VZBtw�V�C��l�o,style{apsrev�md"W \VP{Ov�!a[aiEPR`ado�V�U$Ghenadie~N!�rtl} �+l[]{g.m l@rutgers.edu} %\homepage[]{Y&% web � s{ alt. U}6UR T~U"�o, 89 Geo��St.�U~ swif NJ 08901�(date{\today)abETr$�  8� deb$.be �&h�>s�"�")���<bleR�&�ty�2�9Q[ � q!��G�hBbe  qdORnotD"��=Pd"ǫA�;Q�S ex�(�%� o6�%��i�=.�Kb� fair��p�!assump��ec�)l�; �#rv>�!s]&>7dk�vĭP3a#tJOh )c E�dtG�F�xng!8-�2neg'lar�#beam-s��t�"=poY-depe���s��?or�!sU=2�S Ud, �STa�`.50.Xa}A_key�5A� �.�S2~�/�em6%�-��RL��!xC� hageK pret�. Accon O#;3,� um Q�-@�_,P�x7.hu�Y�~e嫥MuM�%�a3 3is�7! �IfvX �&�*o��bey%,���dX��no C {Ih�}3!�*KI��fm. Yet, El|%oPodolsk�?RC�\c�� epr} �A�Ra{FI�>�m�O[om5��+��DyU�Z)�%.4�KP�j!�. C[.��. A�c]���%! �wo��Bccome inA�.f|dura=�K ��1O��el �oc!s n�5`�s`�quentl�JM[pw� �4�9isQp�߉]�(�eq�ff!%A3!3M8!2� �QqK trad��'Act| �be?�e�4 escape�)�b�AA ���QkBY&��0how�>[ Wztru-�!S}A affec�#Znt�SM(� :a�q�S8ly!-�*P~53g $2v Cons1���� ty --- unn!=.=�!a �� ��<��".- loopM0A�U�����Though%6�H�e!�aryt)��8dox���a�l�' �J�� ament+zE�o A�"@dnC l5�5MF���#X s, g'�L��j� Wi�{�scope,�U2HD]o#\B i*�l5��e / s�r �\$0vAmtŠ��alQ�bln!f �"SKAIR�g�&0 .�ith� 1 name���7pa� 6!�)Q!�n�K%�"x�%f � ��av��� K:�$+!�pe� E�as��[�Pl|4i�q= F. "ͳ���1d*�q� �)2M�Q�il"� a�T)4"� �\n�!Cout��AUt�of �# ��bE3�U� o�L.ac� �ult, *i#&*�4*iC�;��&!�C$��&�^�[s�>.]n�B�<c�>�I�ivv"��� coinr+�3Tc2.�.=ob�D��1q�p.| exha!#! Y�a@N^ �hk�nd��Wq1�?is���'b����*Ք�dE�eiDw ��=�s�id�fys��i (-P4fi*�\2Y C@pre)"8*  �_2"er- ����!M  '4al� EB1a�fd��I�1{=p.H��K_^Y��� 3! phot�K%1s�67�a��� plane�% .� 1ŁP!�6�B"S�8:&!A��9.+ orig� 2_�Icb�͸��8.o�ue3 aɬa�Y��*l!�"('ty�*\��s TG��( Malus' lawp � 'q����r�I"xI��dQ�catch��g a7pop�[� Tn�~A� A%0<'��m��9:!xpl����� �!��/��!:.CU?q�Ps�ࡎes2��RA��A�]w? +mea*!� lyE9Ilm1:�'�!�A4�A8^�rr�8E 'V��&R@Q�2O��+a)R!�� %�swi!��{�� G� =O�?�� �"� �i�Kbe �)�\�], �s�>tB&j%"� D"�a2desir���hav.fJ�,{a*�'��of viZmO� ^ha ra4 y6�X!�JR�Dbl��L -��t+ r un-6d;� �A5��a��``��''&� . O�%1��na'��, n�_.p � ����' "�e��}X->31~s  ' k�&7��as �t�n�peculiE!�Q:e`U>�A)��md�- &�D���&&E��o_ ZX���qDQ2'gk �,��le ��ArrS�Z�!�%���E��MBc ,h.����# �.s �inAr4�v d(<���E�z �corQ�ry,}��-a��: s�ŷ�preJ�|1�-5�.�,H!�.�2L�+ 2Q-cenario�&3! �an*� $ .Z��$ W� =� c � [)�Ns �t� � �;!�!��(rioV��9r��פ (�;u�0 !TE%A�� l!�{ �@��| a%��yn, �3� �a:�=�3ruѕou�ao g�4�-��^o!�t-��� 76if\%��4 how.G.soo�:% N�l&B�!Cn���%Asam�; by v"KjU��:�a�D��(b'ny� �'4@{"��e��o��e5ZIn���&�.� ى�B}q.d ��'�2m{Bohm �bah},!�ea� be]81[�it?�<sk%|it.v !�rr�2�m v�e�� fv� � g�� A�.�<&<:X{! ,ɍ J�a(� ��a�8E� Aig� !���oA.�� �U�s�,�idI������8 �� r sa���� aH�*;%A�dw��g!7�. Co1a .j�M�s pair� B6 �l�?�� ofN>�I��p�1 r����B �<v�f,!��!s. �� )Q"\ nalyS"!t�~�te����p�f�@e-.lXϩ�ion. "}*]� .U �<�e2�iA�wo ��oX�DL�0�v(.g.} horizo3or�=. If 5� os&2rigz�c�c_Wu a�7!��� putseDhi,j �o�qyŜcbdW2R��2��Z~���p \p�����1����2ency eqPLNQf�;u*�%Lgle�Wn-5t)�a[��a�tak�o acc!4 �� &�wir� �t �O � )�1����!�� 6��n) � i�q�at"1w�5������"�c�w&Z�1�!%*(M�j�!5� b��Zna �_-fv�� mulau e�:F�Sr=�eDP_{+ +} +P_{- -} - +}}F%+ &+&B)��5*+�nd g�S�Z%g�,�Ct aHe|A�R ) |@!�ɫJ+ -2XfdX.Xo��itJs��U�hi)f���e� 1!y���r)es� AVv8 � �A�te*���>0� / b� �bA��W a�Fw2. �{(ncjd��A�e�$\theta�C����C= )&B>y�96eisz1byUqKs�f} �#�G}U�cos^{2} � _{1} >�a�:( si6 2} -B=1}B;(B=Rx}J� ��Nw+B=V�R�Fx}�"9V�&9vS�<-�%]�80�x _{2}$E�q.kB��N�F�f�o5�a��!� ��iEpB�W- " em# a��heV�#| tal� �=*� � 3� IA� $r �� e��C�e* e "8in%2� (3)��a�<, �le�Zt&� model s6.3�o t�2 ($r_{tot}a�a�` YX�DiQPp�(�F�� 1�28�Zo�1/ .}� s, regard&?I h�<�$M:!:�t`B!�ioB�ca�be l,��b}Qur{9&2 >8d$�����of un2�)V���\,MC��7- � \&b n\pi/2�D�$ne%�Ra�te���ݩn sign� #ig��J ihoo�2�F/  /����*� "� ��Me(Qa ۡ� 1�e '  '.�vMEp? *>�:)', �!��s^"|�B-D2�m!D49Dm)D n od�QalLger��"�e�)�%!�ettAZ9�6(�Cffi�+1JK��� sDLQ�j Yj�hbeR�*F;8�0�_yerb���ee�6F25)�ap�.E'� *&#ng-ruQA '�a��e|:�"b �#smk �a�iscar#�)2g2h "�Qulo��Ton��;&��b,��k�s adv�y�`R=��a��� fronqH�sewr�6e��} � hidde:r�s (LHV)�$Y, s�R6F2��h!��%(bom"b inno3!�*Rlog�lW�/��%�f"( Yet, as sh��own above, it was not any closer to Einstein's realism, which requires well-defined original values only for classical unobservables. Bohm'_ ��em)�eiiapproa�*lat could survive such a turn!�actsaE�$c��re�.. Giq��mwe �evalua-!possibi�ofr�inQ`AU(beam-splittEoIf�y �I0ideal homogen�media,e' field��L Stern-Gerlach magne�Ta1descrie�Ai�outpu��%%8be exhausted by!\$ principle5superpose� . In1Pcas�re Kno i�4As it happens,zH molecular properti�P, crystals doa� allow%�)�0n unqualified)m��!�au�� j �!�affec � m�!fa��, \a�sor%",��qu� y�, birefr�>ce. Fu�nrmore�reA}ear�Pbe a trade-off betwee5���puraA�Z�. Henc��EQ6 ?i��pu��( photons pa�but!��y go thr�%�wrong ��.Ms %^ty>�jhigher�$is entails  levelE���in each ^Notably =typEP ,s subj�f0to Malus' law! ��b6���. Grant�cthese arA\stly ��ubvgum_\ based on anecdotal evid!b�Bpoint, h�iAat1wer �7$e last lin�defense >BJ TesA��=l �x�7er��of uts��t�& import��ht!�(debate. In��clu��,��ha��A}�2�con��aYty ha�!ttenti��o bridge� gapU��A�$quantum me!�ic�u��obstacle!5ontolog�%: ��9lee��o68. YetA= e la�$��� be�!� r reAIed unt�Ihf�%:*�  experiI(is � $ed. RemarkA� �� ���͋%š9� =�Y=�;oR�eand�r. W�hb��r!�at2�Q  a�Je�all� ,S�P j��selem!�article!�a�� to ��lready�da�5lan�����. %\bibliography{epr08} \begin{theb�}{7} \expandafter\ifx\csname natexlab\end \. x\def\ #1{#1}\fi^G bibO font>J M#�Pf�Q$�R� ~R.$�Rurl^�url#1{\a�tt!O%8{URL Ipro�Kcommand{!\0info}[2]{#2} B!e��t []{S'} :tem[{2�{� et~� (1935)V$0, Podolsky, eRosen}}]A�A�i�{author}�5�{A.}~�1�|}}P�Z>B>>�}},<W and}A�v�N>P �2�0journal}{Phys��v.}� bf��4volume}{47(10):�0pages}{777} (�year}{!l}).f�� %iAharonov!� 57)}]{bah�rD>�P}}�/Y>K��2108(4Z2 1070N357�3Hiley!093%0om�0�0B� �)- emphY?8title}{The undia�(d universe}A�Y88publisher}{Rout�mE�QX93v%ell!8IKel�J>Cj� Spea���unsin� "�f�Cam( N�8v i��82:� ",� gi� - Roger����=nf^�B� V-v�P>X~ ���G>P �~� Lettr�9(2Z�91N�82r�V�}({"� {a}}a�kad��B� _��B�&�-��g{� ,-ph/0306045}j� �Aa*�2�b ��~t���� � 9010�endB�  doc&} �H\���c���, yolv��rd)�ambigui0��;+ W* , �3A^{+}1 ����q{ Psi}P��)+F BA�BA%O $`$%��ar��� d $W(z)��a):U�,E�:N22adex1 sey FnH_{1}=�A�V�S� dz-.� & �'�k)+W-2,WF'Bf i�30 2}=A�=�+ l2W'U2n1 �:�9� �'.>�Fa�w�.�'pe]�partner�fs!iF�V!\ ^{SUSY}=��V_{2} 92G+ ��)M�JJ�At p s� �%1/e� pirie�# ��N� a)+i�� byQ��t'' A �� ductJ aj�\Ph \Theta(z)B�I��"�, $9$ d�x� �"� &� ing� �* pieN�u�( in Eq. (4)A? le $ �e�N�ra�'�duD the ɗc/ermF�$%��!�of (9)>(3) y�+F�I9i�D M!#q] �%b}+2 >%ax Phi} ! qq- M"}Bt}N:s} |HA�� -EB0e� reV�Q! usualf��a�  $M� � � �S��%l6),��!Х�U now� VaJ���=W� \Delta F�; $+�1. $ beA�6�s*{ to�&2�o�)$( �� Iz�� $(> )$2� ,I�10)� rans� to%ju�-��J�� F6! F�'A 0}-E��+������A�A[A�BbBt1aB�J�+2� " W=>8-  E, U  Wj�eO� }��s, $E=%QVE$�^  aL)@BU $i�i E� easi{e4a9"s�1an}-i}  2V �a. ��&� 2�E than� �AM6�g-�!.�=��a� ,( scenario s�*0s�B�, �(4�&W�-�+miliar�1 (12)ɚstW*r�12"� � f�W-1a��."�5 �>13eRne�.e]ist*�t6� �6!+e���le�,. Beca!~i�0 �� ��by Ric� y�=�ᝡrhe�lArr ��x3 BV $ if,�Dcourse�? ��Am�ls.To c�3wT mindAja�7�j, {Alhaidari,� �.��re,|�F�I@isq]�3|e �arWA r�2��QrZ ivis�Dirac ��IE&�vaQ th�7ak!4A��2Llimita��"nsfac� ae>t.na�� fre �9J�a�� �E!F�Za �9M�(cedure. Bea� in %�P �0!��o1ɥct!��� W$R2\�$=2H�����"��/2�$�#1�}>diA�smto �6�5%,parameter(s)�%��WZly zh(sK6'3EqI�0a s get dec�5/a nQ!�-�e�#2M!G!cer���Y �05a|8Substitu� (14B to a�� ��  N B� -�E=-6@B�if eit�{n0$��� E�>� or :7.�$)��)�FZK._. IE�strBmy#min- 65�  akin �6:�0$A%� van�*�# � P�e� agre��`a�discus$b Ref.=:Moa}|.���5A8Bagchi e�9l 6 }�1�9e�a� �8 a wide sp�1��� $ty�# simpl�"Ztwo ex.<e� ���8�![#gW=٥�&��!6� w�sh�!g=under��%�h�:te"6>"�$AI!�ZK*�*tsa9:���� �I��-R"�!>cs�!!��"� %"�"E*X shap� vari�55gr-j!$ p ,��!bc.g&�s,} s a�-!�FDshift $\varepsilon� ~8BJ� V�(z,J)-� ^/:=*=2� >�� �F� @��!�* ��I J�c!Yls j8� A^!� placiss(8)into (16)� J�  2ɴ" '� W'\}*N ���.(BD� 6on�;n�heBB�!3�  h �'�8I 0}$J���.` �) N��=��� int^��(y)}dyB�6�(W=-(M'/2M^{��)= {1/ E '� o fin�� ful*�),%#�7�S�6k , $W�-� W$+ )e![�i1�� 35)�c- subs<t"x a�a�:s� bE�� ��c short��C�( obvi�=� (i)hM=�be no�3"� !�$e^50F . Fo��� �") � gs=in bot�'(:AP� n�{t� �Fz) r�l. (ii) ��' �(�%a�J�I�2��&l is (� grQ)� te)J��_{n=0E�expI[-J�� W(y)dy\i�=m^{1/2F�Thus, go! back��aC ioEqs�nd (188 A� unnor�zed2��&b[=r [��� -1/4�<(\bar{��] �a� F)B�� I=J>dy$msupa,e� reli��� F�Gonulhci�)stMAA5�BaT�:rm�$ A�7A�a� fash~ bym*H#i>p�� �B�in (5) EA�j�E�i) �,eA> , �7ly�&�6�a2r+E#���quI#&���wI)val�':' for 6yt*5�vq�A�asvn �\getJ12"I��1"B�I�)�E6B�aka d�>"� =WZ$"%%revealI� sugg�  A��Ep,&. LetRpr�%�n�� =� Mq��,&B�%��a+se-�Fv+N�((z,A)=A+f(zF��,�ciI�s&Q�B], $K=fx(z)��� ur&7 % 22& Bf ��iA+V)�].]:d(z)>� �%4> � VD�2.} A]YZ!08-\lambda)+R(A)$^d!�\6��,a�ory-ȍ9���g�� y{"P� $R$ &k.e�!,A��$ �$ ,Y �ɸ���"_0Z .)e l ��� carriou20 �U���$K( (2�n (8)]:*�)f���J�! , E", fR, f�2Q *�2ů )''=-G~)-22)�M� f NB�RemembO3� W=  fI�j $ �:.G $)�)G�A_rearrang�JX�'a�b�(z)� b_{2 B(�F�A5E� �&I=� �%-B� *~w��n"~,M]B�� (2� C- 1�f$�5�% ly $�$,S *1)�aE0~ �- ;& .j"�-iF�.a?25b45�% \{C+& gV ~� [ x 1}(t)dt~~ �]  \}\times 3"� %� P4V  $C�aXtp�nG. E�-�Y������D[ �` $M �[�$+f" )/(1 �]� eB�nA�y}�L>&= \nonua��..Ջ � (A+C=$� -�z+ �,-1)\arctan{xM\ ]m�z+}{@  � �)� _�:5��� isA5��:s.F 2B 2� ٣1�,�S��2 %; 2T " 9� � ou��a�� G���I]ͪ��*�W_|kis�slJ!�4Vr� ,Y k2VHQ6�JB���2��1퍺\}+MF�ͰQ��1W%�co^�&7��%_�6W4I:b0��a�RRhe *�s 0vedi8E�"MfK:S5�dd&s (28W/2 "�$is�G) atiA_ZK Zin� � |!1[K+����Qi$/� U��!P�6�L.]�C"�/i&�0by (215aIyE� �`&�(X-}$C;w�8veQ�:�Ne�7��6"y"z3!o *�2/!�� s�  a^Q!yw� � !CU� "�4 u��. P� !h� E]�23i�d�9obserA-���E[*1aH2X1]6�)�6-�B�S6� 1ue] YQ%� i�6&�2�s �%$ofnM.>Khop9�  �)�P�6�&��on�[M � *�76:iso;-y$�f}�E{:�?Ash sank!B�9ENA�helpfuIm�+r**��AG+th:gK99c+ibQI}: @B,FTutcu DA� \"{O}�NO 2002 BJit{Mod.@.W8*�C$A17} 2057;BY MBvm U}zg@ n F r �r453a��D4tem{Souza} Du�:A de \ , Hott M, Almeida C A Sm3m EuroaB�62} 843-UQ�!Oo�:, P, Quesne C�LRoychoudhury R ~2004�N9} 2765%� t X}6`$Thachuk, ~���C403047.;"|!}  A D��.�)(bf{A322} 72.O(Yu} Yu J, DPR%E�G5} 194.H*c; D J%:�;C B 196653� R2�J152} 68A U�*YzSG\.CB�3Zj�8} 2581B�A�Chinese8C.: }21} 1685�C 2330FC�"�C M�5F��.�A20} 35F�0, \c{C}elik N], Ol\u{g}ar EZ]B]1683; >u�� QY�Q983B�, K%�ksal K_ Bakir E; y50709.�  F , Kh��AC�B�H r*�H�U$[amsmath,l>S sym]&�H,\usepackage{}2�Sicx-I*EH MFer)Q�f CASIMIR FORCE ON A MICROMETER SPHERE IN�W�>IP:\\ PROPOSAL OF AN EXPERIMENT} \vspace{1cm} I. Brevik \footy6@{E-mail: iver.h.b9CXk@ntnu.no}, E. K. Dahl\B4(eskil.dahl@��6%�$G. O. MyhrF: myhr@fy!V7��gskip�`  D:8Ie�;E[� ss2+I Norweg�\&0I�*Sc�^�NlTechnology, N-7491 Trondheim Bay�%�ab�`ct}MGattJF�Casimir� Xct �X micro.'-sp susp7_a � dip,Mb� �ll,���T� setupi�B9\�'>H!]�exoW� r �� �r ��8_� o�mad"s1Vlae.#Iu �maOGala��K9'Dec��4m[M� �H�s�Hl70.+k, 12.20.-m, 42.50.Pq \\?{In8?p } E� s aii+� ��2h� �>1�6  (\ {c)� 48};!��3� iews-?${I04, ,1,bordag01})%? more�ere n w one mqperhaps/nk�rA�[l*\Is, �8EXne�Bss I5�Sparnaay �s 58, 89 �Y�a!�he1%�ce"�&�lWdp��s,U!�!��u���%Cpu�u8me �mA�g�`odOOi�HeR#ioA;Eu�7�Aa !M��s �hinitiat�!!s�0al C4La�Xaux�l97}. H�6�u1iT� >N��tulum �h �m�e)��$a gold co��3!r( lens (radi�Hba�12 cm�&a flatij�m 1�mouBa��2zo^%ckA*�e�aGa"RBÍY:�b�a�que, �AI�cvia�apaci�`-�(. Maximum � �b�*!�� uvY(12.3 $\mu$m_a �r �Ee,=�i.a�_i�d*dt4B �I��) fA e"nv��lU8hn!I Buttle�E% 04} he g{r[O) �a"YRta_a�8is�E!E2= s. E�Y�Y� ]<�sur Fc��,� 3�JAPRore�lZJ� � � P�tomVCced sc�(AFM)�^ ��ti�Hr�Mohid�Qe�.k#m $98,roy99,h�s00!1 as lo! � accu/ AO���:a eO U76 �'eT� aI�-Fu%�a /i�kgxion0% avoi$$�.�N �(��is�gaIe:_Afi�<cas�|0 �& �cy���/ �  a few � ;��s 6�: actu%�q/ curr[&dNd mainl}%c�6ofE temper�2ar�3k%. ssh��c@ gIj�3urA�!��iaPgar)- 2��tIA /ed!{h��!aY� s upA� 2001!�;HU(0ew! Bo QkrefS0d; earl�ki�"A + �Kje�#) `?����p�B fouri�!�M'U'�� o� 04}, Sect. 3.6a��c�Kaao�kthe im�%�(�c-I�9�B�-2. kb02}Ae� �to guar�WQuA�M[e�&b�8!an $3� � (5}$ rad. (I%,y�nb�� :� a��T!��F =��Zo�62,; cf. �A�E2V�!�)�hoye03,_04}.) .\Spur71 ��!� to * 87:v�1%�t!��Z-&�:><*��e� / "�E�� he���qm.O0lic�. SC8�� e 1.AAwE.� ?�3e,q1 roxi$&M � �IqZ2] %H���e, utili�l� �p?qA��hon�'~ � �w�yVd. xist��ve_dɘ&�;KFs r5 .s�2k -A;q'i�78M94,E1 02 a&4AnaiH-�Q%�y�a r%`i&-N1Ś�Xve� far��en ab)<. Lea�/� p�A�$�M� Ta�e1o keep�T� �FheA2aa�q�! �N�jM Cn!zt\s� PqIY�au"of � 5to2 ist�. ]I� }[htbp] �L���' re�box{0.6(width}{!}{\� �s{%�(e_in_pit.ep�a \ca �bm��Yoa?nupJeV1/of��ius� $(Du�-Ea!�V�F $b$.}L\label!:?�-�\ TZ���&� 9���+~#but,"� *� 3. �)R�: U6t�@�N =c=1$,5A7%��p ��h�. we �! HA�A�-LoZz Y� {Ge�%9 Set-Up} �?�" �A�f(:�$�r.  |2ADric8�8 � �p$shells sit�q8#$r=a$�H b$�H�ba<teA�� t!X&= of f�E #Xannhreg�b$aV�O�a$M(�C,�wo:~"M,�a�F�\la z( E_r^2(b-)\�-le*�Npi b^4}�( _0^\infty=�H d}y}{y} \sum_{l=1}6%@2l+1}{4\pi}l(l+1)~/@s_l(y)-A_G(ay/b)e}'>�h�h�m �,bAe�x!&a?(H`&�55qB % b�mR.0-%H_\b$(JՃm� %�Nb A�l%jc*J4a0. �Z���D ��ogH$erm� $'/e_l+e_l' ' "��Ref.~�&#]O'�,�|-m�� B*D. ��p&�nlr��u�IcoR� �.�{�{6{e}6{!)&� ���'��&� �� upward �'edc%2�w� M��7nH�m�"AHwnG G� G��)�6�� ?kit �:ds; n�7�hij8�A�P�nQ���a�Zm�&"(lyful�e ;2 Deby %an+�bz �*Z #,� ��in.�"�0 �A�b��pe�!�h��&8!2� or��en `Zx(�nstea�$�lor�R�e��$�sm!�q��� $d/aN5JyA\pi^2$c}{240 d^4Xwpi a^2)�I1��4}{3}�d}{"3Z�:9By �:�!h ]+%"}!�E#A�=�$� c/�\,d^4$5�h�����bH"(# 5��.�A���&� 9}v8� curvi�% ar g�y&B a slA)l� c� I��as. a�%"G) �:�!!�an*�N area�1!  a^2$JA�XH$a=50\; \mu$m, $d=1��M�$#�-]�a7$� 2.6 \%.�Di�P}l." char�r�&~ erty�!�Ho�1� k&t�6s X�2f$m�A�$ !9�m� �ic1�i�na=�o�e"�*estq zka�(�!&�Qs�9�':�qa D. Of cCWou��&�k2=i��#��.�2~+� a few�#Xal remarks: $\bullet$ �%ae�nnt�"�l���::-� � � !��6� �d-!���+as��f�,�o� dip! �Wrs&Iea�S� =�L � ` t"�.y" �s!A�� ��"YLer�e�� ��X"�n�$. A circum�FcYp<h�� d�-�SF infl�*�W��Z[(ae�� VY� O;}� Qd ! $) >rA�4.��.� Z U�or&!�g�%� g� � ��)9>fLE$a�U�a�P>4,�(��=(�� *�Qget�ltipl?��N]$\>I\At�Y�6�b aDO M*+a h�]�*� !.ha���)��<twVnew t"K.�)yJ�E �ScPwcchio&+opt�� paths + j3 04,s1>a50u ��2s�0al \s;�>�@�]='!�t~9C leng�]G%���C� "x I�y�$�q �$uNA���!L %�O mb$.4� !�5:�{Cgy��a �3O!6U;{6�rUd�5;�k��co&rs� 2� BbiF%3�d0o 9Y�"k /%1r:two�(��| ��d Y}:�c�v9�He�,gth $l_r^���d | ic-� ra�(gin y!�eng)��$<.11 $r$ �G%d�;>!ond�.�(� ��so-@enxmřm��H�cl6�A�oc:z. $r$-9ce"!F� $xa�C�)>��/(2�&%� or�� HFfront� m !!��p�& 1 ���5KL%]ewegX in gA�s wo un�lo# i of�*vj*�en nex�"=B�2 ����h����u �(r��!�dmp�7m��r,e� yet *W ,�\ b.�<�we�+Z�.4^ 2X set#�_I;�NM! two}�ed QjA���ethod�Te&a��n�� �B�" ~�tr���I is,}��� 6�%|Vm^��(�^�u!-��*6d {> $f^{\rm{�`}}(d/a)�Z!. m8Z�(�]b� &�(�� U�%hodA�isH\0} _ !Աey �& 6�wo>$�0 �a $�$d�rom�"2�} � ,�Ri�q�b�f%:�)90=1+0.05\, d/a"X10BYW.fA0AsF$j �re]"�!��,*ity&� �(PFA) �blocki73 AyI�i�DFa PFA:" icA( M��ot�{5|Ma �&�esi/1b�x J(�f)�ed��%�0 tE�m (E&�Gl͝�q��ca�Im4C*�b )�G �"si�A�%�p�)-,4}!,�&}� �7)�+j}Q=}_a]���� �� I�� ":6 �l�na,exD'y, �.>,a Matsubara � ه�>?=our opin%~t doesi�not},H�spe �i���96 1��p�/  SernSA� Bostr�K�{BGkis�-sC 04,bA om00 a,!1. �s�k=DapAnA�Y�a�A1rE�%�$eaker (by A��q2a;� &Z)N�Yn!a.p<�as�j=%/!�C ����- chenE:& �H &x�WEa�q A�=Fa� MH�=y �=��*L� t"�=,�im�3ZD�eso tA4�wneglig��Ek�OapaRtA� -�6(polystyrenej,6�@canti��%,an AFM,�2b�ot){a �5=9�,�!d8EQ_X_@�Dd�6�$-�v��a"i�!i�[��,a( spit"�%<excaXnt}��,�6c�� " 2it�� �\d��]�Iannuzz6b-�i Ej(by4��# tK:y\ rt 1s% !+]_ /*.%n�l62 nm^Gi��3d=62$ nm� *�$ =62+�� lta$�m#"�q3.5 pN (��al un�tyoi7�UA|a�\d Xi*r�DZa�? angstrom�@�n#t% shd%�%�U_  ai�preci�,�r�.ك�"� cl� . On�?y &��� real".%�9� �AE$d$%�hA#E"m� nm*��Z> !�d �� �F`!�.� &P ���!kY�2Ci��HOplasmaA~xa�0u�A�*�$2���� TE��^�Ef. Af�lix torym�X���J�ge9y,5owY%-�8 2�3lj!� oR8})�i� �+PA�i�5nfvv� $F$����� �.�1>shi& ���fS��s4=\�* F/ b$ (re()�] i՗ju�v�s"56&�4����$F$���_nK) �rR!!9+q6F�\G� F=�$� {L,m=0"�5}'N�4nu ��+��+"�013B �  $ �=1/T,\, "�3 x=J. ma/%X+ mb&"4nVl4i�x imG+ $m$zm����2��$ms� ake�phal7+D%. ��A$_<rT �  � M�� m". Fia� 7a�K {lic}:Meby�aa� "I T�(�E\��we� � Waly�� � 95-\�-x))w�Ox\_`ay0uz�o7(�BR&[+b�Dk02a}):A�gin*$%� F(m=0).�I�2~8I�.[ 1-\F.I� a}{b.^{2\nu}�.&|F�4 �"ula��9i�(H�(bitra�A !�M�� BA%�us�)A5!�of��5( or��2@s'���*���atB�ſ6 <WJrge ($aK\,\�)� X 1`j pper��te^"�s domin�A��`��4A�Ad UvH�Ad��:?�O0.7a�� E!3�>M&4a}E�e&���1I!j)?�� )3#e ��&�5)@I�)�&-! "6�-?n� ��G@��a�%���3 xi \�Nv�x�������w,asymptotic (�+)�5a�+"� \xi$� �1}f�= F/^.\lni| 1-e^{-2�h9(nu^2+m^2t^2<��/)��F�6��t�� ��%�&2,:=�!W� �E 6��-p0A��-.8 F��vQ\T.7$ !�<'%n5st &�Qsy�0/�E<�,e" led �sA.��914a�1in"� A�ir�"xi$w ��(-�.I 6��_Rp :q8�:in*>q\,dq\,B�qd�[)-=,\zeta (3)}{3�d^2&�616B��W-�s���! Ŷ. ��".Q � ��Ɨ�O . (R*� l2PFA�e�T�I��=���i�.��2*'�a�X�M[e�IN"���$4B!ߍ� k|�Rlo�&"�L�" . �au$!5!, v���}L �E�. �� $t�(r*[ /a�5�*�0$A�, �)b�C���$\log_�t"�1.3$,��a� 0$ (��6�\c�&�*I0ly9N8a k_B T/�/�ni; W�$T{42ifP.,�na��pow��������mA !T2W d&�+�im!g$T-L2��.�U!F!�*%XAM5�6�e�6<"�->4}�&'E�!�b�0t��)�| y 3./!�����&d=0.21< m� 0�in*�+% H&�'% EjDecca � Md03, �*v] .3cm} T=clude:{�2�[��&�[����Z�+aZ� &Va.��alrJ sta]iproم���q��5. � �U���) %A heck�<+��If.\�? area���,:1A&;4���h).��!�}8*��!7&r! ap.�%����N�ag�;x.9ck1new��"^tN�g�^�g&J\ mm, H. �.�e8. �^� n. Nk�OWe�Ech.} ϥ 51}, 7b"ce"� MH, K. A.�Q4 \J.e A:��h. Gen S( 37}, R209.BT1JT1 T� � E%�:e�! Manife� �*$of Zero-PomE�!T} (Singapore: World Sc�<@1)�"R BR, M.,"�T , U.�W Most?�$enko, V. M%��a R0d!K 35sZ1i] 58} 4]m!@1955�9)� 29R75NH89NH89h(A. SarlemijsVd�J. xedi�X,�W u�#E�M`:: Ess�� on D&�' 20th Cent�h? HonoOfY�1�G OcA�} ��,80th Birthda!��Amsterdam: North-Holland), p. 235=T*:] �Z, E%� 1956MN,Zh. Eksp. Te�HFizQ�,29}, 94 (Eng�*�la;56i:SovQ�- JETP1�a+3.J&l\ Sa�\�SIAA�\ , C.! 1973 �!?#f A ^ 7^90.�"X 7} L ,_K�97FNLe hE�7�X2<D98VQ.� �.Q8�-4549(E.W04JW� 2Y, W. TeF 4. arXiv:/.(-ph/0408027=&7X} YXu� Roy,A�19�� �[�X} E , Li%�-Y.a�2oJfFjD}�060}, 111101(R."M H�X,��W.,�, FI%2j 2000FjAjA� 05212["$! B�, Gdarugno $Onofrio, R t Ruosq2 q ]�2�AE041804 (�m2�fU$} H{\o}ye,�q.2g@evik, I., AarsethB �BX3.��MxEi 6a056116=�"� �Zk, 6�E�B{4.����*,��Heeding� (6th�a(kshop on Qu,� F�3TdUa�/I)6��Ex��l C�� }, k�m��NJ. RA@n P!ϥ54 [>/311094�Jb�7a..�,, DeRaad, L.Jr.�< Schwi6�%�197� Ann�(N.Y.)-� 115}, 388B�946�Skurdal��SollieE�199JH� 6H2!� 6853mEq1nqn:t20B�v.Yb�05a�jMb26�:Y�:ea#iR Int�� M�.i_�� 1�77J�2a�reFo� 6}, 02611.�5} �5%�L);*�5�`20��� ^�l." 9��70402=@s.�5} BX!;.}�rR604.�2Xa} V�i-hep-t�Z1.G) G%"H�angfeld� �Moyaer6UL. !�JHE ~�!^Clu�"6/ B@/a\ , Randrup Swialecki�J)yTsang+F��77�b�0a�42.2&#%sE# , Bo# �*�#� -wIn� Wo� �D�)�v8.\b$� s^$��B�^W '  6� 0527��9�Yv$a� �$�e�K*8� 475V�1}&9%1�>�B} 8�I 13916}1�01a#WJrk �k25910.�� �$�8, Klimchitskaya� L:_ �>` ` ��n�66� 02211.C*�" �"0, D., Gelfand�LisL$!� �CaY�o��4F � � v 11N 2043.ͻ�Bb� > )29��L*� 1023.�} ��N $ L\'{o}pez!�E$ Fischbach) t Kr�b$E%��kE��iHe� 9i�:q �a}nc�:rZ�� E�.� �>�b206�e� D �6= 116% [~>� d"�� ;�%\set?JXer{MaxMatrixCols}{30} %4�+mQ7�ɿ 6*C�ment}[ 8 ]{Ac�_l]�:8lgorithm.2:,xio2(6$ $LC�$>$o�#.):RA 6-�RF,M�ure6->Zr�ry2-:,r��i�9ZC6, �� -D� 6.e��+E >(ercis6) 6*le���L6$nV6���6*�PP�F(po%3o.�Pr6XW)WM�:&�(Soڝ>*umm6�S  xenvirona�@of}[1][Proof]{\noa�nt�`\bf{#1.} }{\ \rule{0.5em} Q*�u amssymb,a�udsfont,�`x. input{tci)8x!`\� N> [pra,twoc��n,�pacs,����(]{revtex4} �̾̾�2�vam���6�v6�v-,69* j1�|TCIDATA{OutputFilter=Latex.dll} !Vepk$=4.00.0.23�6LastRevy�$=Wednesday�uvet17,��$4 17:22:21Z0} 3���[�e}{":n^�}6#e#e�Q!%F< FQAit��{Bi��t�!� global��lVA��a n� *c^@ystem� colyrvu@J�ou`�}"��0R. G. Unanyan ffil��{FachbB�ch��w e&;w\"at K�� rsla�^$n, 67653, >G�pny:jIn;�5 l,cal Research�Armen�wN�� al AcademV-S1ces, As#�,ak-2 378410,:s$uthor{C. I�cu���� �Space�t, P.O. Box: MG-23, RO 76911 Bu�Ke�0Ro|U�M. Fle!�hauer����Q�a"yBir*�EndR�e&�'������(e!�a M��7 N$ sA�1/2!tA��J�ox�p6�-5LE�"]Td C.hLipkin-Meshkov-Glick (LMG) *3�a$ der �.�"�s"�,�%amec�`&p��-C!=he 2�q �9tl91U!�(ٱ�'��nan  -fer*Mcq�1!Van05&)F%�q�i#b ate zngO4a smo��cross� F]1�#inu�T$anisotropy�5�z $� $F'a :bl�' Ֆ�a$) ^@ m_r�@ �ԁ�d>�� (A0�)�AA?11���-!.mF�%z��"�In� �""huG* jJs=z��qy<:!behavi�Jb����s!�*1[ �;�E)$% 1N0�"2O$grows loga �Wly� ��-�i�u")b�v,EDt\neq 0$<$satura 7a!�3l,&�Zing o�gy� ��- u�?�a� $J=N/2 �-6 56)Usp�٢ _{\�rm{� }}=1/J$.� �� \� {�Ud, 07.Mn,73.43.Nq6���G Z�M6M�N.N�L2L�M�M�M�MZ�� ���2�� {;>_�����:�SĬ�yY9y d!&��Hy��A8u5tvM$-um�� ���@�c�'l| ��a~;w;/6aI5�Nco�yr�a ( % {Sc>�$er,EPR,Belx��'a ��t�1�) phen��5�3ed��#,V3B8 ~3�+�/l�V���K�-�� �of �m��s. "��ad�35&��r#2sf �4Nielsen-Chuang�@"Kt6Y2�ia<&�= s����eff�2�mpuZ|�{ndq(munu��'�mQaI8/ �ۑ �HQ��. WhilA*tb!RG Z,1�5byOL�C stoodـny"E B�)��0��open =G 6P�!�at5i2`�24�Bly �min)�� Ns �_e�b-f �1their roN��e�E�{� kill�ۨR{e^.@9_.<��gU4�� �2,ph� NU�,Sachdev}mgtt� uc�9��,'Two&2�U� stud R�er"|7�4cusycM�{Wooters�"} e.g.4|}*�+� chai�$% {OConnor,Ar�n Osbornee,O5%loh Vida!`I2�R ^�(�/s CA�3e��A!b$g9&�2of2�g>*sd����)Jt�7}%m3*%�� s�Cb� lQy)�q. &�2�9�� ^f��k-n i�/9>�-K.DTs qA��{tL eV aM� v Q�v �+n�e\**z;G8�:a<�� e�&) Aw�1]Ebm�:We|^E��Sb5�2�Fa��ZpA �.�"�r�"?�_+ �� -1965}�.��.�����ic�rE�ex� x��e~�ber~x ace +^ S#�H��k�Pu�s� q�g.� ��RlA'�mak�m&�L4=ess"A 7u2swe�&�8"�n bit{�D}Ob�@)���%%J�} 1�2�� w���Bj �)zF4E�*�CI��inE� ����H���E 9: /_M�*�  �s�!�s��1Oi����n� (��PWi��19�(�w % {C���},u!�un� b�"* explI�lyDU��nNiE-F�6��~�M��6�u��a�2u�A�aA> "��ZE���_zI�7me#T�h�.:�&�in $x�:y$ dir� s }w�����%��i�1�duO1m�΀~/� alZi�/I�&� 'X��B�4b}. Vez?A�d_lso^�_P� ��E{Stockto)�eT �-p�int},�+ ��q�2&}>�?LMG+3l!�G��4a"/ >�. Alt��lN� ase,�Յ:e��E� _no��>`3ihU��  inuup"��U�� �3"�:�td.AeD���%X- .+i()"�F 6�!Sec.II���6^��A��A�*� ��Neu X�\-�(Bennett1996v� wIuW ��� Aa����Tnt"�@2? �-�QB�!#eFBpy!rM��e subic�no.W83Y� "utZ non4q!��;1�� ����>.�sol} b�q� FurA�mpEit!<>���W � ��C �%raV!v�l.L:?��_Ha � -����ic%�ai7z"OPs� 9-BJ^{-1���Z״v� g � 2? � Ri\we�BA�A{ IV!�E��z�GE��J�b'A�in!�!)~Dic� �.�.�_6_��.�&%:�"�%�63}����j�Le�U��!�� � �| j��� aa�d � ?!�>0�wJ>Xmu }=\�zj�z{N}% \&t\sigma$^{j{x @6!$bioM r�� $'�8o�{��le&6a�M.<�ssu�ItDof se� E7�K.G  �<u�n<�� � {�Ja�} H=\� %-!Lz}~�x}T�+"y-2!v. �{ha�/i$�u p% '� � �C$�A#v>N=�umb�!t!!�UiSB JItype. $H�fmu!�� B��I@bf{J% }� �s 1Hi*s .s �� r &�oA�u> � $J.g= ���DHsel���7� f9G�K, �x�. AYks 6h�.� , (=@% 2�) �cten� �`I�w�T�m�I�.;�"� a=)�QXA;$:Vz�E >� x}+i]W-iEh-B�E>4% _{x)a�A�yCmu�E) - �. >w� are�(u% $H+2 U�d�&e,E�O>(=m� �L$m\�=D{-J,-(J-1),\dots , J\�~�QE&Idang?�, io�X�s|�de��Er*� E�obe X>�*v>?J=m2p\vn\Psi \9� =091<*}%"T�Hm�a�MCa2���*�[��U>�} |� �e�cal{N}(� ,m)�� [- M"A1(z}]|m_{y}=mCQpsiB�`% �5�[i� #� �&r �� {� �Qz tanh �)q-\g4��K$ ��@& D�:� y i�i�.!�dI m�AE-�Y]utu!# \{:$_$� K!��$ H �tY!�6�!���A�$:n$ "s"� �s@$% |m|D, which has no eff!$Pon $|\Psi\rangle$. I!�e follow�we will!Y8trict ourselvesA�0most interest3Tspecial case $m=0$. As}$been shown! )�,Wei2003} and24}`( collectiveM$$|m=0 � $X�Dlargest global ent�mA�8and should thus!d0considered asAI�EGPmaximum $N$-particle .R. A gE�lization!�arbitrary $m$ values is rather straighta&Lward but less instru� . An%�U al feature�%P %[i� presenc"�.� only% number of͡R each �_(of relevanca���]� \sub-�{E!p�}.4��distribu�Xof Schmidt coefficients��6� AѪly accep\q�ita�X meas�dR !v2��wo �- s $1$�$2$ iIn UH%�a pY�Yn � $!�p(von Neumann|r1=i�7MyA��(e5f2�)�Du�*} S(� )=-3 Xrm{tr}_{1}\left\{ \rho n r�\} 28% _{2>::2}:,�N�% we�� � ,2}=2�(2,1}\Bigl\{�5C\l� � |#$r\},\qquadFy�@!o$reduced de� y ma� es. $1)%�essentiaE9.% Finform%b loss di�divisa�-�I1E,ignora�on�the]S. IEHreAR�2u�� original fi$�.�� QEi�� nzero. On�oE}h�if>�$� oriz %�CB if���e�U�%!J�vQ e�JTheRa��s:�iq ical�? min� reli�kof E=�� $EA�m&$R Vedr* 2A�:_ � bi�Nseparab�H� 4s $\sigma \in E�cal{S}g$R� /$=\sum_{i}p a�,^{i}\otimes 2 E� 2(geq 0,\,\,,2K=1.>y�m . &=&\  set{ sJ�4}{\min }S\bigl%C ||0$bigr), \\  : k text����(��\log !3�-��)2�k)� �% A�$2=f5( |.$ CalcuA"�Zz of a many)�.2��gN al a 4 nontriviA�ask�^expon�Ybwth]�Dt Hilbert space. W�s8n<at2N:LbeMa��t  vari��l�� , ar�(an appropriv ,�limit\a��b s.  ��� ic\ i3} i��Rthis ��"# c-�ed�w� be d�]�&��vF$on. Let $Eh\vert�?IG�$ \�ote6�E<um ������wo�s Y ed��.$!��0of finite dim��o�s!�s,  '� orem 0DPeres-book} assert"a_ y*��-Mf r $H�g�c H_{2}in!Twritte����:B�} rS��\E(4s_{m=1}^{\chi}�_{mi�%� \Phi^{(1)PA�le �2o.2:. � j "� w}�$�\\min\{d! ,d!\},$ $�  A�5�"Z co.F2ig �{ A�v�� � 7J?n!/>�"\}?re set�orthon�l� s!���a.F� ,_ively,��$=�$�A! posi& -u2�  obey�ksum ruleNNsu~0^{2��"��B�I� easy� see ta0�^is:@q� .� viaJ�E m ����Aj� �_{m�.Q� �1B�' 1c$rank, i.e.��d!2�E�$ provid\8 simple upper b�n n&/ )e8lo�aH$% . I�chi\sim rm{min}a]$1 , d_2\}$ �if-scale�!ly���R,A� og_2i� a &� funcia�JB� smalle%0l��yչ�ic couplAƥ�ٶX �!�Q>��u,d$ increases�linear�R�mpleA4a logarithmic !>�h=� �i� size.�als.HN�$S%Rexa�ede�A$5�=�(x-\overaC {x})�� :� dxE�!�.�a� babi%E2�$G$aAis �-jb�A�9/A�$a Gaussian��+�2' chi =�!�q.:-1}) be"� as aA#tegrali�� �T!�ongQarrow �w%�(m)$, reV�a��8tinuous, smoothb!e�al%E�2Ide#��%���!�ͷ2,6�$��*M H kO8 be chos� $such a waya8��55�t goodi�x�^ ion J�m�Wigner}���� �-��1.� is given�&�� L )��Wi�iW�,:PE�~_=E��va6I-�.���]"]6\ausA�q�% q�)�)!���%a suitLbip��co��uY� ��-e})i��WIN)- !�*B bgudi�detail%Yinx ular<pre�o"6 "�( determinedm �""�ly iso!."S F � an  analytic�rese��Ȏ�-.� i��Qn 2�g!$� erb results%5���ented.E(start from !�6J�%Y make�-�6� 6�$�" angu!�mo�� J=N/�nto $J_�J_2-�0$% J_1+J_2=J$.�4 &&�.T�w��N}())e^��!{J}_{z} .vm_{y}qL��WwpsiCG}&&N_B _{m�} 2}} C _2} 1 J&\ JK \ J}\d {m, 0}^ -i �� 4,a2� Fd Y,"��notag:� H�$^� \ R*;6� (�Q)6�(m=m_1+m_2$.�4m^{^{\prime }}%}(\beta)"� ro�on"� defa�e \ 4iedenharn1981}ݕY(d_o m!i n%Y( t)N) =\�J m� 1qS AHi 9haIHy} Q !J m�)v��rotmatMD�jqr$- 0(J+m)!(J-m)!}�}  r( \sin ?� � E�) ^{m-5 �( h 21 ^{m+1 }} I0I��\�\, i -!P(.g,\ E})� �),Q>�j� \alpha, 5}(xMJacobi*8s. SiR#we�#��F�?�6���$J=eR+e,$` e I�6�hav� e bin?!2 .� EG( ^N.M9�IE%Z p� x} 2� \\ �21}+�%)C&V727274"7 }Rq m+m:e }&�CG!Hm>�  T �on combe����m)��.�&2�� %�w!�"$Ve�F�R0%�^2=��1}=-J����/ ��2 2 ��A��1,m_2�fi)���1-�JE�,:��<) -25o��%XQ3e&&�{1}2�=&��$\, \, (i)^ɿA`2}}i� 2e� \��{I�(J!�(I�)! 2}��% (2J���W1 -E� Q�A>� ~�\coth ��.:�t2}}�� }^{(Y1 _��#��h J)"�3 -fina&� 1}I�1�);&^if z*/s $%�I2*�.i6'(� �"� f $\to\infty$J�#$% $�7(% �+:�)(aches unity�AFV - ize +m"� �� %*� . &�#fd protect)�=0$# � �* Mak�,�� h�. of � A%*sumG!i$  )� � carr� out� -(�r]T[Z�� is�+ se�� In6�)!a%6j% El�a[ ]�� survivgr|,�"�:� �n��*BO6��`>\�" -m\  � ��!1����� %,m�=:T.��U-6*�� *&� /geq91!0�ssumed��!�@#of Eity�-�6<areY refo >6 .�-�� �gg�Ny�.�ort�. 6��5vr fv"I 2}\)x6xp�[ -��m�}� ��] }�* f pi }/�*�"*|m|� -ll 2?@&��m�.A�qows to2�"�iB�AlaAo:*� "ba�A!�&l 6� �} S@>W"�+)&(>k)" &� =0"{Sgama0�� p%0 fig.��"�-3-1} � plotV3"h �e �A�&p -j�k !)=NA=� for &�2S/ ; �1�� D%�i."�*$�&�1/2�(e nt. When G$.�$J�K-� s�/ates s3 5&�j:�2replacz%�Eeftea�J3 J2�&B+to&! � ��]l�rP)�"�.{2J$�{���,figure}[tbh]c"$r} \includ�hphics[width= 7 true cm]{bib�-g=0.epsM�CcapVbn+e]6�Q�"� II U" V�$Sr�"k4b�,!�>Q�2 QAo curvAdMn@4e�=A�.�,aPR�ɜ-���&��� � B� anZ� :� \ne �� &�  �*�]"�if�&���\neq 0� doub)um� eqs.�*� or &� remain�4in �a��/e� infl�3�%D%�$@necess�4to.6 e�EateK^2�1:We��N&�nu�lye a�� �(�upq200 ��s 100Hl $�K�,"� figsb�2.6refN�3}. As> �s�3� n�2}!pc�(astá�5� �1�=1���+Ze� �`ent�cHݫifR� �) _"�3,crit}}\equiv* 1}{JN�IM�, modynamic! �J� poiR z�7 �63}I ny1$\ge J^{-1}Ɍ1"">~��A�����Q^s � /J= N_1/N����.�8R�01�,J=100$ (full#) $J=2dashed �)V .�2�u~���3:� �}#f>X $ /e recogn�.a�9~(!�1�$i"�}�n����N���5.�5%B�htb��]BF7 3�<N�:/$*!.3J$(J_1/J)IU�solid~�x :n J� 12�� virtu<% in!inguish�r3��v�Our���"� ions sug^<V z p ���T����almV;s HmN�  f_ )&:$4�/J r� �0>���8% ��}-5��*} 9)4�� M� �'��!'�|$\�>2 *�:*t Re�=A!�d!3�On�=e=Z $F-"G z}}$*�,�> a lo'3 non-� ary ><% -?alway�(�� amou��6?3I� largh0l�N�Zi� msY=ni&�.)�P?peculiar>�=N� �hange!�q� behavio�(�C$ $IjA`_2 J_1 m� �eeds A�y��>���Q��B�4n�O9Cg8:*�.liz9�5*�^��j� J$. n64�� ���6�%e��8 no o�+Efi2p-e 1�U�� K4 erti| A� �Y &��6�Dp>�Dat � � ..?=%Z�)8kB�;͌��A�J samš�*s�u�)�(JOAe�%e�=AA�ia���u�qu},ona� �reh phys� sign�wFhe6""�%� ��&�8a 5��= >��l :l ��.�5�5 {Geo�C&..gFE�6��6��pre�..�@t�/h>!�8:�A%�wo���31�@11�qq�+ (cf.+^% V`"Axqn� N�X9x�;�  i6@# ;0e�-� �G�7�?�?#(z["isE um\)�(� -1: orN%<N}"<=�Km�e�5q) gH�I&I3�9*�)2o $w;&HltJi,9B�0Cobtai�*b )JNx#w�<(te�) a�:�,2 it2",!guGAo6a@��6�a�&�Re�;v&G+� N�2A��:� A>�;W.!��2�9It) �=,�i"O*29 �-/Da�Le�� e�ub-i� s. O�MA� &�,��rG��wysBQ�5dYIA> vice!�sa. A .,=�:�or �=it{�<}Y t"� rho� A;bn?iq��$ .  �<iC�=�f�8*a C?m�=�M%c-`$\s~?J�?Bv} E_{N}=��>N"�> it{\ }S(%�> ) �*.�-K��"��  :V )�'? v�  _H!�-)):�C}% 1B�?!Z�Han.` &�#%bJ� n�%i�;N�@��2�@ �@�@ ... @_�(iJ8�A$�@>0,I-$r&�BN�. u)�s�>vTQ�is"�8th!�2"�=�an�Ho��"96H�Gt&�&_2�5iO�Ns immed�?lyB�*m1�A )���� :o ""�:i6b"m4F .�:-�9�� ��.Jof * 1ute�1 )��U,&�#o9d its �Lst��%�AO�D� �A-:�" a qu�� icult �Ac0D;D$in��yi 9+A'�C how@9�w~;p!Q��A'4s aJ�A4:� -k62 H*leAT=�d2��G1��D� {�P, 4}.B#E"9\ ��-2��Lt6l x d.�4ang8J�%:F6ZV.�phi=#mu�(�$ �.%yN:t%�# 2�� �G/F�i� �,P�8ap�"zR h%G&a�N]�p|�5.>��tG2�monot�& and R�� �Rsense1a� id..J . It�A� Y�eB2Y�2�eI���somu0"�7%! Dick?  t.2�>hNG}= T2�}A�e Z�a�"9D� �4�� � � are permu*�MnW4t���e�>a; J % 2 �6 66 %����*�m�L:�6��}�:>�%Z�$E_{G\ r5i��Nm- q-$2�t�max��^�.% )�$N^)s��c2j>co�T%�� �jLMP�2MC� ._of0#sJ��A�Cak� �3? A{ #$% |m_{zJ/�PFC1*LS��$p5GSi228:!K4 N�3\"xi �}\,B�.6 >~I1��:�)�(�.� E9iz�it *Bx&alRa�Y�3 3s $�$ l�TtoBfFH���6F.X eigen�U���<\s�T0(}}{2^{J}J!})e^{ .J}�2,�/!U 2 )}*�2�_ao6��;($��&&p"�"z$:[��.2�.s{� Me=�V8PA6=�n2Ky}���2=0v�1eE��a�ZKi*?> $E_G� g+ u �$�5Oŷ�A��X��D���c J,m_&9W�j���.l � 9,:��Y�1E_N �R�ڕV8�M1M1B�a&'v���'6�' �Ho"�Hwst6P@E.68!�< ��1*� �jM��n:��.Gst #K*-R]N0 a�+e3E}Ix !s&� A�:s�\ _z=-��� e s�coJ+ >� of�4rse be0!�1|?6�emploMGyasymptod>anX���Y��Y�C#*;,g�-�an�&5^8 as2_%,#�n�.u%y�p>�^% *^%aO.} �JV 6W#E� P\1=��a,:��V < ��"V)>y��.)0Z�(6�$P `er�� ��H RQ&� lyi�.;J$�2g"%'ic� �R a-}n{�]�e ��#� qZ�aF��A>�A j!� V�  . BA6 y�%a�N�A������,�e�1*} R \EX�� &�0{_{��xg@� }}�! 5u 1�31-�#4b }}}e^{p J� (2J-1)!!&�  �% � rriv� �Mex5`�D9���"]%=(:�)^{1/= eB% Y V %�V,J)�?�7.-532%>B�3B����% Compa"�>"�-IVIAXI�&#>f%b�EA�<�$d� how E/ of M%"E & Nq�Q�A�Z��< �O< �2��N �us $� �bnD�Aq�J!�����F2k��B��=2=� C"�Q^6Q^�G6G;� aȡ�pa>w�0s�G!�&2�? block�%C sQ�8anti-ferromagne�PLipkin-Meshkov-Glick �`� describ�pA�q-arb �Pn ll!q�fpins,�cAi��� 6�eaJd4pJ�e a�A��X d�B(fo�)!2���+$��Lt&�h a &d �K :q)� �&{'�he.�� .�gj�J� :�Ed:�I 6�Ga�:N1 ��fF%�Y2�a�a�cvQ�$NI��˕���r(,�I\1��"� ic�"� �)� E sLR7gst��+� ���vg �f>g6�f�V(no level cr�Qng�mer%�occurs, ~, X�3hl#o�N&`�{-,yw&49L56� �inis0@9lb� gr�k*� %�%$��)A�&%2-�RU:�+ nonvz!&r �( ;r&::3�#�mropy � a^t%l�Z R"��k]i�ecum~��"C��-ѣ*>Ş2���S$ik�$�3ly. Fur ��'A�@o�1�&�.x"'- 1x1�Le 5~�[1�1>.kt�BeE�U alone)��6)��e.�F!xwo�}lppensA�a# $" KJc2�Z~ invers�,_ooY���F,:9B�-:Q$�usuE�at�,�&>�d��um* ��Pq�b ��)��X)6 �t) z8��Ar�Ha=Rt)��6���, J, �i *{Ac_W ledg���0is work aAsupqhyE DFG throuvpSPP ``Qg um I&�d''�$ well�!$,European neta(QUACS. C.I.!�2l a fe� hip �kCU2}$Marie-CuriE�i� ssN�\F992iHWooters1998} W. K. 2LetzO,bf 80}, 2245Ak982N,OConnor2001}KM. O' !n W.^`AIp6A�052302%12_Arnr _M�� ,!)BosIvV. �%B�-z8A�017901Jg8Osborne2002} T.!� �M.aMMl2a�$6}, 032110]22�Osterloh ^A. e�8Amico, G. Falci� Rzio, �-e)+41h608Je v3}KE�I. Lat,��Rm� A. Kitaev2�!�-29)�79-�32��1965} H.�,�X�e�, Nucl. �m h(bf{62}, 188AW652_W�d�RE. 2F B�*(bf{188}, 51�"86A*Ls F. ,�hanI=(U. Sukhamte) ics Re�wse251a6�96�.t!� G. %8M. Fleischhauer e�u)r190} 1336M�%t \��%�2�wA�,qMosserM=(J. Dukelsky2jQ�9A�541 d42yStocktoar3eK. EQ$M. Geremia%FC. Doher0M H(buchi,)��ZA�6e� 2211i��6�-pH(int�.�R. Or�\E.E�!] J.1  p9[ (-ph/04096116�$nnett1996}�H�� et al.6�U�5�� 2046A�96!6� J' } We�bP.!*old�EZS68},0423���vT1 S4��V�1,2� 5002.��2�ҹ)�Ŗe�5�74a�9ɚ6�.�hA. ɛ{�L��: �ep*|d Methods}}, (Kluwer, Dordrecht��9� �2a��a!�A{�Pearson, Bull. London Math. Soc.,5�3��80%�7:Y�] E. P�[�],) it{Group�9\ory} (Academic, New York�56S>hWL.C. �J.D�uck, � {A�YM�Y*. !�, �0ddison-Wesley}81 !Lt:� �&>&�J�� &� �PBP� docuB} �\ class[twoFW]{aP{ } \u�"ket}[1]{_+| {#1} >�= A� %.ams�q$ :r1AY!) file� :z1udV etlength{%Q)<}{5=d} %FOR 2ND PAGE ONWARDS!W@unninghead{Title �dots$} 9${Author(s)!�U rmal�};skip \�6paMAyle{empt/$ setc[?er{ }{1}R copy|�ping{Vol.}{No.}{Year}{Page Nos8BB.0}�%}{000--o 8 \vspace*{0.88IIalphfM= \f�� \cen� ine� �HOW TO BUILD A 300 BIT, 1 GIGA-OPERATION QUANTUM COMPUTER} {37{2`�!; ANDREW��STEANE2A015�B\it C��+�{*� , D�5ta��Ato� Laser�ics,}f�f lare�YLabor? Ly, Parks Road, Oxfor X1 3PU, E�. nd} \base!_A#=10pt.�22� publ? r{(receiva>ate)}vi: 2�211*D \abstracts{ Exper|p�m�wvl�� trol!trBd  D� r`zed.�im���$�s2�8�2�Si�ctYbcignu;r�um�1r !�O4. �,  out =maj�bmib$s or uncer%tin1 m@9R�� Q�on+ \ a view��3f)$a�k��� machin�+�13000)2mo!�/n020$\mu$m vacu�hannel�Ktma chip%{ 160Hehro�m�j ssoc�3d �`>!%� circuits;oL0 )�beam :J�uA+�Snip�te�R hyper`�i��%�yd� fluoresc�E��*out� comp�ld run03aC� algor�l r|5r�$10^9$��"�D3I�`lo qubit-��ihy� g�k�R�1 MHz>)a92!8 kHz, �eMP�Q{.mNatI�al���enn!u6mpl��dRou!5!fa��A9 Tuss'd }{}{.�a� keywords{�5N architectR4fault-tolerant�3pun�e6fpt}2��Ȑ%) USE THIS MEASUREMENT WHEN THERE IS2�Z %) A SECT�� HEADING %�� -0.5� %\no�=ntLBy5bleMmo S to5#(%_uwu���iss)K] clar&�!?�a�fu��v.."��q�3$arg~)�I{:4voke micro-fab�j�# 5�D��P�[��avail�,̌�dis�?-�es�7O <�#o�Hin{ *�3�JA:i �S aP demt5at2] lE�s}all�ingred3�Qdd%7repeti�xQEC%?eM���}��� ��ny &q+QC�� igns�bŪ2 d if!� w'tuKlax or mY �"s?Rquim�,w� Sa��!u exerci�.caAYun��c��Jsourc�!��M͖ed�n.qE��<� I�_pA s I�t�� .f=����Mj�?��i pY<x a�bK}i� �KX�6�0 fails�examp.W��to�|u���ES�,1�P*"�stochas�0,ƑS � � a@�-_2^7$� �,E[ .C\!J)l��9&�f�TE�- �A�sq/a�!�eno�)o� aR y%�*F Q.A�s.�8�ee�~2F\�;!�_]�,ular}{lll} EmX�tn.�N�� (p-r) &�B"�& 6444.)�cod��"[A& \�8dcolumn{2}{l}{$[[n,k,d]] \;^< [[127,29,15]]$}dancilla� ]sZi$N_A,\; w$ t13ex}z 1939,�(Y,data$+$anc. ��CM~4& $4n+k$ & 537-n. s5>$& $b = N/(;)<12 ;a' llel&y �T$N_{\rm P} = 2 b N_A/w9990>:m�E�l n$ & 152%�\h!� �́���nce\\ {"nA2a� e} $5�tau_g=y$\fe�2}{\nu �spl}} +�80 r ;� cool'pL1.2b� mu$s�syndrHpro�L��r�t Esp}:5�O 6{.���}11/(2w mg +�� Bm� sp}%���2-E�)e�Kq� \simeq � ilon_s +�w\bar{nuF&�{-4}$O1nO1%��{-3 0=�B~ma_`0 mory+ep� = 1/Q`6 `�H�|!g�h & $p �!a �10 8n. .eE�- 1/(bp)::9$� ta�F�:t��R" ��"a� �<�Y�/ NLz "�ߥ~7 ɭ bolde�m+U� ����(_� ѐ�rA~�m@Cd$^+$�H. _� Ca� �4a�� � �1e�<seV�a�co � wave� Z "��N&� repumping �+O{ A��o�"A]\G��E[ 2\pi�z 44$� 0(7on �cy<varM�A0.0�7mw0!��9& $e�c�'1�% ~P(0/ 1 -ŭ(1+ (�aa�ci�0.0005�~{�,.����^�Am��4 ?/� �7.2��9��!N�214 nmxF5����& $I_0 =p pi^2 b \hbw9 / 3vNmbda^3Q,11700 Wm$^{-�<\\ mass&$& $A = m/{�cu)111'~�)il�)�R = h/2�)rm u}n2n39 kH�E ru�!�omega_F(2�74$ T 6 ~sca2.ed ph�N�4�bVKP_0�m ���H2} AR{)r}/{o� $5.3�x 10^{� %�i�Rt� y� �i0�M|_s�R4.O5}��OpN/-a�Y)Ł��0..�~stretch�6i�Ytr}�4/J8e3$\\ ~c.o.m.nDcom}=2R/\%6�C& 4.6M �-2 Lamb�G�m.) ta =�zR/2W%m0.0 ~�w,r Raman Rabi:�OEE{RaE!�/ \a�$21p�,�l��y�AEbI_{P0U6 Q (3 �2}-4) ~R aQ/mII�9.2 mW$/�m$^2$nhp�y�! I = qP_0/( �U3 -�^2m186a�Mdi� V2r�4�8�@�.A�pi r^2 I,220 mWM~to�#)# 6 & $ 2 N_P%P4 440 3 Ting: ax�T(d.c.)Tv���� "t"_�W�10�? 'ic fie#t  & $EImaxEB200 V-yoctopol.NJ�f! mu_8v�q�cy�Isplit/.� A�� 840}{MieA}}�(( e�V���}{� ^3}\}')^{3/* l qNBRrad%Sb%Sb,ieu $q$-ecd�q_%�0.3!0 nDrur4)1ź5)�9ym!ud%�-vrf%u�.u4~r.m.s. voltag1V)�rms!:� _4 !1rf} / ��p& 106 V�~ �s�gar%��R nu_r5�1}{-Q q_r e!�A�t%�!�4z)�9�1/ �701�~%YA>��/)�` )��O�/ {!W 66I-� Elec�al6y#�/i� &g 50 N%*�a!�c�Z,n. }&�%& $30e�+ 20 N� 160,O_)�a?d"  & 49 (b��~capaci��A� & $C=20� ���C 2 pFp{pWeniFtan \d���,0 �%j�xdissipa] " ]F�%� C��.S24��-lThermal�� vib�*�� nE��h!'����� � P_"�  =%�V eta^� n#�� +1��$5ՍL��~�.��…0`1/ � A\ m ���hea�$�Y �zone& $d D /{dt;1 ms$iI�=du�� BA��� �at� d� nW$� -�Y\b� ��n mad�om&u%k:�C"�! ar�� PaulH*�'Jh�=in highPth>�(r�h trap|c)��g!Z0*"v6"� �$out7(6�^Nepa broad�as *� Kiel�Dkij302 }. Q�(�1� Rhe*� "���E�8re 1aF(ra!�)O�V2>�d a?���;��a�z s, m"*d {dH*� � *�?�O q �-stimc*d2|)eIC!hs $�$ �!"P��1�c u�dC@Q,�"�a�A@5����C�0!2!"a+�-&8Bq IC�n:mmus�$l�<�%� Dr oIC, alb4)i�1Gm!�+^of� toV mW��=  (tt��l�%3�pw "). Each_E �#�de�"�_d�NcE�-�0 GY+or����gy e\b�9ec�y� I,#r�o$"�%�#G�&eA&0!p+�^ŏos$S%kb3E��by � I�%igh-qKy=� simi��at� nucl�H"=Ireson[%Tt� = d)��F $du��0.1\M�2Y s1w��E�g# }�!'hmU!1!"J�� . M/sa "Jc]%u�(*E A��!�i�$ wEb:/de �:�c$2 � seJ��a��Can &aim� �&7Q(y�-�� g!!b�'��n� st� realn+#6�,a�d�J�?ngU~YQu�&�! �u-s�[%�� acousto-Y�A��+ҳ sand-fold �&�fuF'��a���dy�0 1500�P��-�d��=#, Iinvol!� 2a�Oh�� �%Fa�>�ei *!7��oq5��Ce�!�pa�M.X�0ise0,�5!aa߱N|�pixel�#��ad� i����O,`ca�f�`��`����` �6;� &�F�`�%݅���!ze dic!���%-q!�a�Y](&l(�aKd�.!pof����'2�tt�5�G4s�0e� 2o��m�>e��%fortably!@- �!,.�%מ�,i /cn "�1 s, I�&� benchmark�&&�1.�on F�1a�a0 �Q�Ad���V�l�y�m)�5wZ(a JIt�N r&�of sucA"�{AW2s, both=���-, typ�!lyqG�yZ�et�I� IR)zL�����Y[ DE�sK40 n^3$,�� -�.�� �le�2�%50e��� iz���a��p0rypto?9�5�&i3Z�4 *i^!Qle!/�I a*fI*"�ty�xpo+�*to2vFrZ ced toM u&`"`,z&�99Abrams,04Porras,05Aspuru}. Var�-typ� �/e�ypR);�8p .�A��Ks a� de�vI' *�!�"%OT3�! �I9�"E Б��0"�/4Kn�E � chi]o5"A E( � ; er_M �(a��( 7�[ #��\e"��ADise'4��AI�ful����́=��ela��#$��?2���!}/ 5se��$'!��bh - 5�p5:&& =� 29, 1� CSSO ba�*D*Ya BCH VM=6Calderb��96�0,1��*�8er s G �J&R6�d��rrors.gr� to �A�!|robustn���n� ��yp Sa"`", nam?'cHE�"� )e,��h�!i�,f by j� KvI shif2dja�ſ , or� f%��6� or m,w- K6� a two�{`�R� c� �Sb'<'�oncatene��a)�=�BkNpI�3oos,01. Af��!R�%B2akEb!Vc���fi�8 .�� %h�},ximately 10~�7l^���u���;, ���t� | ab�1 30 hڻ!ޡ�l�w�$O(�8)$ �&�7���� rincB��� is m�?� `slow' ( 6g��cwed$� ou��t yY���}(oB���): �B@ ^%QC��F/v���a� 27t�2sm9�!or,�x�-!2QC releo�lp<y�c� &x ��/ r*ca&�-neglig�7 &�~M �q � %�2*!�c -  step/y��Jpre)178�$ �"� �BCHE�. I� �Q67"���N�A �5aso" a��)a]� i7  long.&pA7� nble�sha7e")&h�/al�" 9.g a����1u �@ MY�� ion � !eas� speu<�#/!��(A3avoidFe )�2� e����ve�hV � }-I]�%�n8 ���,#F=!�3� ; I� B�;b)�.c �7{F�6V+�A"�:j ICWT&$nn� of � $20\,Q,:� �$1&&s reg0 10�~)an�&yIke2Pf��6l�cs�U!'e^�5"�1#aDl%]z.or!j? p�s�w5JF�rt� Blai��&�9MadseHome}4�2new*�5I��-rg� !U*�(� �i� BL' )l 0�" m a�N�2{ 5. �xs)A�is���e��3��>���b/U��!]o��A�IC.-� � roo &�a wi�}to�'-!P�w�!��M�� �r�1x �&� � d � i�(k�Balc  10 ns)!�?:�IUM�i:� cuYBp8i�7!W^tr3� A� !<silico_-ame��� �.F.� �n08� �8de&X8au ���P 6k�f��A10� &;%. Plac1�F  ��9�u(4�)� seveA�>��2yMw�vh*� ima?|m �terfe�+=llyble mou ^��y2�Mxocu�0M�A / H T���e�[ de�K!u x �end �al555_�^!n�ly *m IfI�iV&o$��ICA� $4\,�!$m�3���8!�M�d��e% �btuD�}��ci( ��y�a� fo���q� t>�$��=e%��paF�isQZ�7t�\to Qhu��d Watc>2��� and,� o=��Bt32A�%�J1I�����hk�ppr�. s6�i]+!�p ���g�;Vlan�n�4� 9�s hag- 5YPsurface�byY�żICǢho�5iN;f !�A#e�paE�rough��6(�4#4up�'c2��Mq A�a&���61:�C�Iea]�)d?e�d� Y�i�m��M�A�n��Za e�a�8 �?fy8SI�e� � X�����"Y to��a jt:�8 (e.g.]w mm awab�2� Aex��airAfssure flc+e��� ,)Ł(4er rigidity, hGF�51gYT�nd)Gx~�+A9͙rea�>���be� t2��Bi�7�!1��"�A)N�, �, �e�w6$� U/t�D:ot`!*o�J�a�emi� �uI2��. h c/2�-���11�#10} W�ile�X�=N Vi�wM�$"�)&�,1\;W鵵fO [!ack�fAid� yF�.�;�w@o_BEB%#!={�$��ep ��De �� B�qe)�6| rA �EaK�EIcQ$�=���ff��u:��)@ �#!�� Fct �$��M��g}o!=�k�=.�aira0a[ʹg� "�Y!�� oh�C%�vd ?"� �CKO:+ao�=~8ul%Pc�s �@�< metr�maC��Adk' 1 ��.� �#-8� "?ar($��� @J��x#%g�EKd&"�pa���mid };%�perhap&�O, engineYIg�l�2 e. H� , st  mi� ��bj�by MEMS "� �"� �!�$1�7aF band"(  =exM� s�Wonduc*dik)I3output� low-I�%emo%��\�E-w�.8al� E��ha��Y�? ��Ѿ q_m�F���f0 e�91+7 � !���^�%d �d=� e .���ha`e)4ik I!m[ Lw�! 4 too���)uv&` ]&�A,�vj��-itselfwpA���mtra��&�.�=�Z �QB .�fre�&,' 2905G&-�o�D!t�5dj"58:4� �KHIJs�U� f2�O<9/��96Shor,B"�98G��sman1,99 2,05F<z��layϓof"H:�u��@�Q � st�: rI�bag!�B}'c $EX{08XaMxket{01�� "XX �/, xN��s�w�i�(9!04�22�,02�)~u b�� ty Iy��E�Fa��x-red.�%�`�-s'ke�-�#t �6i@G�I��fe �BHUCzB( �l |$ub"�!fPV}� �,a��mpanizM��PA.5G ��"� �yA�Zm-�8��A;��me);�'fa��$Qs���i�o���io A.��V� ��#��to �#a�Fvc(y}�AM) "�HriW�\*�"|3"�10 @. Let $�<�����(�A��;�.�)��Pa�B� �m�6�o� ��1,���r1 B�C0a Hadamard (o.�)"�H!aJ ���G� m*!���* `!��fy�WiA��*��0v�.a�x"�4A��%�B�j&II, I��retur���b���nA�9 1�!�NEC$pq&�=A/n�$[&�qt!J!ulaem�2&!e&�CYK�Lvl %2 (���J�J�J)�n 1C*O9�3&խ�E9&�C1,��Cm�vr��ly�+�#anU�2�~�0� $p$S o!XRxs�; a��G,��5 ider.� F����i;v�R�) es 2.�s (,�Tfn(�BP]�c� �y?A)�71,w�A,=N��� l �Վ!�*, unl�".'��(�#.��Rda�� �a!�*�*�J&a�dy;e�&�>s�)!�\�\�e�� -s"\0". IP ��6YE�unL><�QI�S a thresh@ of 2�nA��2aE��e�� &��j�� a"�u �^[ s 0a�>s^�16F ls�F��;* !�mG5P#ADbe��apor3!�� �(���b�'*�?xe!>����s $�9�&rI�&�)��xci� "!�a�g�s ы$1/4$u$1/\2��g�uere.��.QE�!�*�?�4eq$10/D>10�S,An�Ox&icG\,�{e� Esj� @ �!E�!q.!f!�`"# e�"8  �D�U�!�l dLby2�-� Z1Wonep e7eQ�� > �nAO�s*1� dJ-��&�%,99SorQ�nA ��%#m*-flip%�� s2_ͧR,03"�Y}2�%�~����er �6SG� � �I���-~  in"�I!�"�1�<chl���3WinelanZ};�l�-r{2�Eh� �U�s-A�5nd /- aA�6p!�m��m���of|5e�� �mo��aS, ����"\'$P_{0}//9$�#� "7��M�N!�t� �?�'h"�!� ���}edDa E$-4ѱm@(J�n���-%� ing)@�on$%$ �i�&:-ӈp�J. Dec"�(-:�\c�&8y(� Rayl�S)1a�D05Ozer�7�T( ;!�R:H��L"� � �!Uz�B55 2�)!�Y!tE� S E�RIW d���1I�,�at�<-�� il $�Dk$Xime $t� u���8a+-]t��&�N"��\sfa=iAA \exp(i�C>F"�?#Ct"r�%�) orbit8a%Y� ccum[��C��n &�#e�M �*$N�CM�!���Dra#,r!U��%*^D [(N�^2/2$� M 3duu��"WB%��Wa�< ��hali�5"A�Eb���D�i� aE.� M"gat pod�`le�a'��9^��y,Ze� subi,sG( �Ł�Lual�^"�reclaim�:t�Xtl/st-1&$y"�HGi=%n-tj�&��nd�t favo��r $FcY�FB!�.�&ڤ%oF$9� < 154}$�� detu[��y�di�A-�3rуw%!�I�� r � a ��*���V�i!q+� �TG� ��(>)$���TP#&�i&�[%�o��s,*D� = (\TC2}-1)\H,L��� ���ki��)�m}"omip.byB�$ɾ� Ta `clock' ($M=0$--$0$)�$��, E�a��>��ar��� )r�]��: St 5�/ ��"l1_A �(!eX :�Hu /5�9M�^�rfI�!�9�Y� $F)t�k�  a�Bvie�~ dvan�Cous*�!8$|I| ��T ] A�CSc(�(ps IIA, IIB��Yb)� � � e�,}A o�1 <�s&1"Z^ *?Ka�� �y�"�L���  oc�.���G"( \&�:���4u��3��Vr�(�UuҡCA�:s!�en�0�ctual;0ngz==�>9IaBmper � �!e��vH� b@%a - /I$ ** $I$?�: �We"��AW��s*n +*�va/�a�.a���a, ��.1�'hJ�{I%j�@s��2�AFR�.x � 8E���q�(I3/I�R$D2)�I $.Z� 2�M�U<T�b1�A �`�,a{�!�. By��4-�92 ignI%E�c�� aH)nd�� �/�"?Eal�m?M 03GarciaR��l}-2iw�acI5�j)B��%�')�]!��eaړd�n �zc��"�c, I�/�%s�E  $1"M"�� v� � ��+(4r�2�N!�L�e�,"p^#ofEn  E=|Mn�Ttr}$. U��G �K \ll&DGs$�E+$ (� � t����Yd$�<dro� ��$then \beq ��p��I�"r/m) F/2��eq J$�ula% ma�a� e�ga�p"� > &3(>���� Ep!�c�&-;n� �`aN . To�is 3�t+e@�-��$`%`����'e'@9(��e�1ms)��'tsGm} / w�#0.2�&� AT��[q���U*:7nM&�OdJb�+}0.5 h!�E�k(s? e "�c3� �orRi͗�Fta=lOɢCdA� 6 a)�xt� �9z� m5%���mB,`�!��:LE;��poEr��Lis 4t�[h>�oCB� . AP Ba""��!N*at&� � �!�@ es 5["ps:) ,�e,` ,�haol, j�e `� '�A/�u0[ g ap��!A�5��'ge�)?�%�����s�Ł�  ), `t�_*� ���)Aof $2*�Qpl}I�υ�Y s� ��$��:b�@��@f��e�\m�! M w�\} �pot�$� ��eA^ �]m j G�6�A� Z �qu�=A�(�&@6dre;am is�(�JL b�c�:v�N�-��%d!(u/oCaI�!by (breakdow� � iscuc$���{05%�Q��!���a=��2;�>.�e԰f� :*�O"PQ��T�B$s 10^8$ V/� mo) l��9gly��n> )1�)Ix����k B�S�S/�@Ka��anQ.a 8a� @���.�5�E�byL� �(B�nO l�QTI1�"� �5J�2��`8s�;� ���@ a�e~iby*OPdt = e^2 S(\nu)/4 m hqO$M &'P��m * �B ntum9���� /� tR2dz)t 6�f� ɀ(} (V/m)QVHz�O))�1aA a &�&3*a�Au�$.��< !��9�F� .�4De/�riers}g�N f@5QR empi����$S�a(Wrho^45M�1�26 \pm ��(V:�&>[B:B�(:%�)�!o�I�j�iAis put�w"�F(0Turchette} ��&�y�4 $aA�Q�AQ�5�7m,  m�'� �dZA2 A all L#B}.j32naJ��5�4C%�? �Q@�1����6�e��l m�� #W*U��� *�R6�NA�� _8�ʁz�$r}:�Hebn!>��9�IAL �%(iL� ?r o �gI\N�N;��� z�����% 46� >�=lied),�Vc �R A�� 9Y�2be kep���M��of each1a�0a rectangular2@y rather than a l%; � reduI71 4 communication�. I tak �total� ment time�Pbe $10/\nu_r$ where $ i%' radialA�fin >fAmxency calculated for a Paul trap!' ing 5Lscalem,4, Mathieu $q$ A(meter $0.3$E�hmaximum r.f. electric field�t^8$ V/m, see table 2. I adopt f, = 10\;\mu$m�e[ta�A�0transport reg-�%� chip!�I Tto obtain a high speed!�le keepP!�hea\ rA�accep�(y small, so!�ti�o(arrive at aE� ��!Yn!�Hlaser-cooled rapidla��E uA[Tdur!u�control9logic-a# Q puls�!�it would���(infidelity,K:sh&be implE ed.8a zone slightlyA� placAromA5z /recombin!67, with-���Adetuned��ar�de� str� �� tingit�meaa�A-inm~"� E desi�Fw�!y� �nt���$I !�Heq 18\;{\rm mW}/\mu }^2$%aCd$^+!�,o ease align�1!{� � waists � ��b��o)cE�la/a%( di�� $4 � . For q � i�!�2K 0.2 ��I� 440$ WA I� (100  I()މut5�s in2 tane�{  cE��� zhe �  differA��s;I� doesesA�o1s w��$$\tau_p <  g$. \sec��{Faster,M,��100$ g!i�avail�$�v� $(i.e. untia�A�c]yZA�"  ��A,),a a co � sam or i- ~A!� �n,�p)�i�f� Sca- :7"�  ��%v:th1� 0I�aead!���t�aEer ` hreshold%�u� a},QEC encoding��2�selyE!�q%T size however; a very �rule %Pumb� $summarisesA"�!V�3S�}�X$N \propto \gamma^{2.5}��$  < �3$� � !�1h��;-e�eik poss) �aU+A�4Reica(t,04Knill2}a]2�measuA\ soAIiE0-�re�� i .8u � ��^��aJ en\ �5 >d� � coup�by���-��ise� AɅI� � �Qhe��simul��ly�� a�� maj��y vot%h0 nzd�min�!ul1d 98St�s}. A -up��ed� ��1� .�*� ��,E���-- �B�phase�=�%��rb�h techni� �Y exa�!CQ�0GarciaRipoll}%�ue���i"?q{�� �n� �[d�� mbat ton��t� ng. Ov:���!v IWbWes Swh� er&B "' $�* T�:�!a!�hA�2���s�ial)&\in P , o��� �mak |mg n~re rob� an� � relax�enginee��%A>x u��&� � �f"� ulti ly�necessa�� o abandon� al method�:q��Q��a�E?M�'nic>�!� M�,E�mGAknsfer� inN r di6�T�nd o ��ly situa� deQ� 4Tian}. H�) �IՅr' �+�@ attr� e fe>%��x)� pns T�ubjectA�a muchm6)J!���lex����pro!�esͪl�]to deco�i7a}!3si-freg.("�2�1́�� f�u� s do� 5rinfluo�man \eyE6��aet"���5!ir excit)�=gimfar abL�v m)nergy room *�ga\c switch-ff-T8tely. \nonum. $Acknowledgi?.' �Uup7��(European UnA�j 0 IST/FET/QIPC!�%� ``QGATES"%�b�e N%4al Security Agd (NSA)*AbYResearK d Developa� Af<�(ARDA) (P-43513-PH-QCO-02107-1). %\end{ac>�( \bibliogra�(tyle{unsrt}6{myrefs}!J \L docu�} F�\'�R[prl,twocolumn,superscriptaddress,showpacs,% amsmath,amssymb,floatfix]{revtex4} %\d n_� rintN^a4paperf�d\u� ckage{% icx}A7ew��and{\Op}[1]{\boldsymbol{\mathsf{\hat{#1}}}} \.4vN5- \vec? :A�oFkt p, f (T \def\half{ \frac{1}{2=8openone{\leavevv\hbox{\�81\kern-3.3pt\noab7 1}�begin=�$ %\title{C7��Gr� St�Molecu@�  Op�FeshbachA�onOa_�I I��$Tight TrapXlauthor{Christiane P. Koch} \�l{cD.koch@lac.u-psud.f affilie� {Lab.�Loire Aim\'e Cotton, CNRS, B\^{a}t. 505, Campus d'Orsay, 91405 Orsay Cedex, Fr!} 2gD�ta?� PC Chemistry���(Fritz Haber!O�Cen�"Hebrew����\ Jerusalem 91904, Israel�)-$Fran\c{c}o�,Masnou-Seeuw%R�� �4Ronnie Kosloff��(�((date{\todayya\ct} We��< � aeU racold gi%se%mu% i! ato/Bose-E inG densaV�diaba�Bcrnga"� ycremc$. We envis��a schem0��l\���4? lyz� ���!ar�amp�T�"Jt Ou! k $^{87}$RbEw�� &�we�c � �e � void5"fa�� re� ��5-E��7- e?� al�50\% 5$ expected.��9�D\pacs{32.80.Qk, 33 ,-b, 34.50.RkA� t�%�&� of]Y�!FE6!��#I$ar ^s (BEC)~� ,JochimSci03}h y to �y new c!c�(phenomena %G�ce�hr�degree%+S dom _a new,�A`�� �PRomPRL04,Chin04}. Si^no� "�� !+=%�r�!�"i%!*� 4BEC�  # a-DK!rom�ap�r&a focu�rec� _ . ��" e�x pplyEmn ext)+�#, � -4DonleyNat02} o$t� McKenzie!2 2}, wb lli� �� is�k deG b;n term�a� u� (FRQ/�}�r� A�,e` om�)2 coincid� �!�, a bo� -w ar l� . Mag� FR%e)v�i<%�Qsuc����!g%\0lkali dimer % Yes-3=Q ,Strecker!? 3,Xu Regal!r3,Duer 4,HerbigSC!ce03}, �Z }, % h'onuclear � Stanx4,Inouye }. Com"�"(Q9�! , �X }. I�trast,"rFR� olve� 'llyX ez tent��ere spJIXZqo5 0nce �u�6�. A���obstacl�I���)A8"�� #y�s ,$alm�always&Y �as9NFR�a.�a hyper!ma�ld��tom�� �occurZ5�e��ength���A�����>ri� s. F]more, .�o��flexi s�"two$ (s (髡��$ ��q�y) 4a���(� 6�)�WUC . W.1�2�employ�e�eq�"�3$d gases vi�"otoassoc< (PA�r0iorettiPRL98}%q��uisc l%jMoTheisiJ��+,(yet�Kb  NB�ex�(�"%����of Ref. rQ��� %"� R-��a*gU�s. "� 2�%A.��M�%��%��A�Y�. F��%�"��E�%z�%2���Q�Id �� in %�~ea�n (one-pA�n=�)�dx�lhe .�  %(twoF9s)9&� is Le�, w2/ ig.� to � weak�o�\.q�(zi/- tri�%6/p� botrb~#'.V'���foh!ing�"��$y��Z FR�e ag^)e of&� ʼn2 �� F4 ` (cf. Fig.~\ref{fig:pot})�h0<w$0fun� B&%onentG�mic�_ 2�s��l�v be`*�R�a�! h* step��N I��="nee+�*���'rremds� pr ��2� "v!d� eigez t� \b�8figure}[b] \i��0s[width=0.95\� ]4$1} \capd {(Col� n&) � �osa)� n �E�6� ,es: Step (1)W � �/"�AA(�>�(!�� #+��, L� !| (2)[ sudd?2%e-�� ] 8(2Rf$wn�$\nu_T/"sco&�3vT�6scopic d e %!u�Sch�rN 01,Kuhr`1}AEf-} �eep"��ic"�Gre� ]2� ��{4f!e� ormeH"t.g��(�� em_%ebylo%Y�R *Z zZEscon>"ra!�D?0ld| an isotr%a harm�I֡:�Jo�%E�g'�� (CW))�I� ��u,m)�/Al2z"�dynamicKaRs�*. R�#g��!by > Hamiltoni��equ>�= eq:H Op{H�1��pmatrix L_g && \hbar\Omega \\��.$ 5e - (\o60_0 -\Delta_L)iD"\G�$��� \,��$ c{g(e)�T} + V ((R}) +(-) V.O$!�%dIU channel2E with pT}�+ e kiAA�g) erato7 nd $>�$%��(��)�aB & . $R� = \V m -P*#^2%R Aw"e �8�2�0Eq $)t �dec�8�  /�ϽM �M(. $m$ denot�1�"dI�% F�eF�� (J0= 2\pi\�"s: $)|e&v�Y, NL!4B|! ��d-$D$Q�$�"�h8&�a�8 X$Eq.~(2 e[)� invoD# -z!ro] ng�2�*x�"�; (RWA� M7 Rabi�$i|� then�&a�  = E_0 �DU�\cdot(\epsilon} \ w/D}J&$,�+�:E_0w �%2�;%t��, $ Oyd!A �m�t� )�E polariz�� vecaW� f. =r�� �!]ed by�asympto�value d�9 om 9- dard:'3<2�� (DissMihaelaRV1Y#he*�"1w is(if�8B�E�i26"_9� J�s (ab+(4~cm$^{-1}$u120~GHz?:-st��E S"� &�� �7A  $F=1�2$F=V1,5$^2$S$_{1/2a��ꕄsJ���)�matcha"�sIn it{ab in}}N�Park200�oB)-)�dis�!� �.qasyU�= ( C_3/�L ^3 +) C_66+C_8 8$��co�ts%��$5S+5S-1 P$U�e / y d_in. Marte{2�*$G7resPRA� �<re�/V1b�<}� ͌�=�%�ad�h�7 a"i (�) t) *$#a�100~a$�-(9 ��*�,J.x &{?' grid, "Z  %a map��m�PSlavaJCP99,WillnerJCP� 6AO�&dur� 5{\2��s %+&U.�i�4ri�i!� :�f 5�.3 =c|/� wo s. FI<,pdiagonK k2 FM�8i"/ �$A"x)��� a�B�!��KX J���e� $-� $/2+7u�'AH��be�=Hermi�"8  lex ��ns.&t is �6Il_1 depek y"� R}$ � � nsis? a���a�B �$��?imagin_*p�1�o��+�/2$�+d &�*� ;9p�4� �cte~\footA {% Let'sR!��2C0s, $|\varphi^� -� }_v\��le$, �=�RjICc basi�ZuEU� D ( �=0$), %�52�=�SA��c,% J� g/e}_{v'}ɉ�~�A�� n by $\laq f' | 1/2 I� �&_e | f6 � = 1/2=sum�| w>@ ц�|^2 =YO e�:$��,F?�perty��eri�. �,��, we s�!�j -y�Schr\"�2er } a�D78t��sA�>�� BH$@}>� (, $\sqrt{2"� at}$i�� .=D/w6q"1aQ $>($�<}_{3/2})=26.24$~eq�3�)=27.703�/&�2�J&�s&V %�N.er9 � a\6cifp�?5R]�t t2.59. , 16.E�32~observlA�D"e�&� %bi��"E4done. Usu�23Oh�tu��Rvar�"`5�FR� J eqe^t���$5nderst� as �s:^xRWAq�a�eQ2��" >+"�-6'��q�@$!vv��ZX �&�"lim�NDe�� �1�  pushes!G$6��� ���Bevs <h� n�7uV!�1g It c&n��!7lu+$shifts di�J� U���4�' X(p J�e>a;o&�6ll&� is "!*I "aXIt� s, 6A (middle)�H%�. � )�I�Yone %�  �� " g & ~_{n=81}� |��7�t5ie�� ,$ (� cou�all E�&"$At $I=0$, &} { �=0}6�$ J�) lowh�W (FA, r!�). As%�9�i!�sX9Ad1% d� @agE��8�? shoruPB@s* it �(t�=Ag embl� 6q�j��E R�left)*� Alth�hY� $R_{max�?o�g(vO FP� o"T%j", , %|Dsh�D�*!^F r��'orr/:" n %$R"` 2�>.��!|d��2:�zs����u�s�(�Zl)\'a�M��0��. %T_i�9lso�� �+�IH�$A� y %"ICs"Fdiq�B�R �f�P y��A�&}#a@O(�^`"]��6�"�"��р(��W�q2s.�i�:�. u6%V�� G�I RQ�"�1ff ��XU6�� �/:� a roba�*to��m a:�h-e*!-�&� uR �E[=�6�eꡘPy ol}=��gK} |&�OB� (E�A{r2rr�;ibuko�wL\0, vP�?"� less�K��8ife���n , �Ev=�E.at}/(�pexc})$�UZRoe2�"$'!J6C5J e�4oa��, :���  pondY(Qin�nle :t$�= g.a'". B�(���"na�:� roj}�Z��.Z� j':� 32 Z'P}4&�3�M)F)(a'�<eV�F1j aT�(� ofa82; T�$(B�&2"�& > %a6 C�>��.%�!6�e�p+ =-.$*, at�#ey@nu6�� ($5$"�  \le I1�' )�+���c^%a��5!�KI�l� 6�* &"lI*.ed 0.01R'��>�J�t e0$\ge 2$~$\mu$�3Bde�0�  up�J6 �vk�8window%qiLc�% a8-9�&�Va�le�6�H��d , $T�Gadq] u%��r�C�0Ae��ity'.�2m�sby%�.vTperio�0O�cs�Ap� 2�vib��r[ %�QA9B�! { T�(D,tab:T^)�) }[bt�z#(tabular}{|ca� \h�*eJ>I$ & 1* & 50 �kH250 \\2O9��$(:m)_6.6M> & 270~n 124 42. 18.5~ns�zh $X^1�g^+Nh92 _137 48. 21rBh;$1IK$�/V*�VI"�B (c5: � �xy)y �a�a leb�..�+U��I;g now �RE�a�EL@8or*f : Ass�N�i�y|&�'�;F =�ad>%5e# : +-Tdi�;, �XtaR\)r  be �*al%$a� &� � >���� (6��2���0 � BC� F`ρ\� $1.4� �B�v$��j1*+�dO�P�^UN�6x)�/ll play�Pol�Go�y%�co/� s&�!!�- Opic [, �t,Uici,*D;���"���;es �i7"\��Q:V�,��Pe?�eq:TDSE�A\3 ial} ( t}|\Psi(t)�F f( (t) >\,,iu�al@bychev�hpagc'�A2�ce4>��((t)�#�C�7arib� $O�$orKOwI8X$�%L+P$),��"�!�./2 dyn}a W.'�6� $%/R;�bH�*Z���U[ .��!8. A!�Mhe �A�1�0��={a s)! %.�ofq ch��I� . %}"ދ4a���(23�(c)+(d): "� IzA� 2� (soli�`de`�E! J!�-" $T$ (das&a�s)!!0be ]�. E�w T No�Y]\"e>t):Y(d�sa � +(b): Var:-dG �'�9 $E�R �H� E� .:*.�)��� [2 y�VI=8&q �Qnu" l $I=5R&��JC �� Mj]omb, a�� �{� in��,|/� &X�� in 8� �54 6#, �$2Vj. %(c.�6R6 J(A u�.�(�Q&�Cr�1:% P<I(��surpri� E� glanceRr�XA��WmIs>^A7non" <2 �+cyc;-J Uurn!��K_J�2�&Z-%~�a Sim<2,�(!q out}R@e:��B!�e� ha��lea� $^� f a� @7�. %�16Apc�-2B>� U�, �m�}� b�nw��to6�"�?ile�Mut�]%� losti�`��b<!Di\�h� F�F�m|>�! d �0'��somew!�24\%, �� 4"stP 4�j30\%. C%:3� e�h%b!lWG(� or� t�"3�J ow!, �Se> �"WP�;E`�M+NNA� a E@.M!yAY�",+ wa�;� �le�K)��+alM���Derj4s\��?ei"6i�gt�j �&"�s�5 �I2" aly]#VT4ab�WE|.|hb�66 }b�Ah�-�.��EM �E4Wy�hJ���A""I[�!`is en�Ws,+x�i  �"3 �:^�ay"Ram|+�Hh�2�:� >�<(�� dv2�kF0�B�A� �i)�+]�1_by�Q�=����4�"�Dsutra�!�y 2�a�9($aI�)#T��$, *� stron�'�$9J2y� l6�=��r�=6�anZ�J �yre 4 ^�). Fin�, c!��ext�!P ��!�:�>� �1tly,-�Q93X��2a f�e �f=�  af��h�. �:Z 4�&}lj�l"� 6�T"� V$k & 0 �e 5 ns\6�P"�(. I .475?0.269 389 66 �76D͢ 0288 03 46D284D"l> NM%�2�ofV��F�� $P&�� 5>fA;}) "�_g"�,) .� , [*� )|U"El!��y ,6{Apb�[^bnZ3,0* �mideA�=.��in 1~n��:$��)&��e$ r�4by�tPW1\%. Sb�woff- �m  c�/�%��third j �7d�*b�t��� �* ferr�3ack��oWjsof !�1�H s. D&��!a���&i1Lb�Q�^X�Z�+.�. p���a��se�# �o�b�b��6 X$2o"|(�90&W+P$_�+$)&�%b chMn marked�3�previ<onOt�Uon p.2��"�%8ic $1/R^3$ beha=z'%���+"�+N��js�eov�Mex*�4��A� arge6�* ��#��$s.)($W�2&|l exac�4%�p�D��2O,�$��!��k*� j')s*�E�%-�9�E� *I % M��r6��3s�1�u"�"t %!�&(Al�" a*}7. )  To�azDGI� �J $A�eNs, loos� x2��3a�� u�"KR!�!H%� ����Jce�"� �%�NAS.�SR �W&�V)A:in:E�FBicTqra�=)�_��X5/l���� ree-body5 ect� neglS!Dou�Ldel: �$*#pplic_���+d� . or�� Mott-Ins|%�)h6BA %]2�97M2K*� �=�6u�*& %�  (�Q� a 7he ��{ %new:a�"e5�5� ��"�@.m^A� �sur-�, �L�"A�an;I���rno new���izbduc�' a�n1�.q2� $\gtrsim$��2p�SA�q>s�& �Ri��O�"&,&g seem-fea�deia! �-Y�L8��?"-3 s %"�8a�rt��uF<ElZ�94, EPJD�8 �>}d��B2V).p�da��2;�b!�rubidiumM�demon�3dGd�Yo.�es� oma�SLe�t�,�I�ELf/1��D�0�soa�atin�ca&},+F�W�>A��; welr Bt %/ .92�""�-1�Claudei;41,DulieuJOSA03��Ck��he6��!@}) �1of�e�j��A�� �S�U�$�, beyond homo�Csystemf�T�V�o� acB_l s� We >bli�@=ank�\ Naid:\ P. G� ier, J. H�T$ Denschlag��R%immx �fruit'U&�ss�&�`"U<�orAba`EC1Ffrj� CS�V >| ( '5xDHPRN-CT-2002-00290�C.P.K. 9�k�]1{ �&p DeutA��oschungslai�aft �) i"�\�\�� N ed �(Minerva GesA}cE f\"{u}� h GmbH Mnchen, Grwny�D�-�1�the.a }{33� x8:a�\ifx\csn!Q�n xlab� (\relax\def\(#1{#1}\fi \ZGbibO font>J_!M#�Pf�Q$�R cite~R.$�Rurl^�url#1{\pLtt!O%8{URL I�nid@h�abiblf }[2]{#2} B!efb []{S'�[:tem[{2��[4 et~al.}(2003)N", Bar� tei*P Altmeyer, Hendl, RieP[�X~�4�G�2}}] v\�c�{c_}{�5�{S.}~1� =��X !jDM>D͖BA>B1�?G>?%5�<B%j�<C>x!��;J>;�9�G5� and}~�R>YGI�5�jou�]}{S [} eebfE%�v�ee}{302�]4pages}{2101} (TyeN'A��% %J� QcN #, �[E� % JinA� �[�uinf^�B� @:�V C.~A.)u5��}},y!�.'VP D.~S>P�V��Mj�426:�-�537ҞZwierl�bj�%, Stan,!�S��tck, Raupach, Gupta, Hadzibabic%� K Wle!�I ��~W>@E���N�͢>H>�-�AS.~M.~F>D-=�D:�%r�<Z><9�A2�E�jiW>S9�V��f. Rev. Y! ��N�91�J�504n� �J�Ro��N�Ro�e� Mandel�Wi�., �A, H\"a� � Blih}]{ �=B)�=n���T�6�1��5��~�I>�-�!�!�%��5��3�F� 0730]JJ?4�?b�bQ!A�4:P  , Kraem> Mark��b, Waldbu.| , N\"ager�_&> BA��V�R����T>u ��>BE�;J| d�=P>�9S�A H.-C>{1�B���� '�4-mat/0411258} ƈ�e1�A�2:� ", �sse� Thomps and Wiema� ,� v v3EJ� @��~ N.~R>���BS.~B��B��C.~E.}�;1*,�]���$ �f^>417� ��$ 29R$ 2}] %�J:M�h1oN�$�|>���ffn��|Browaeys, de~Araujo, Fatemi, JonU? SimsB*EC Cho,oni�}]p�x�CB��R� %f�JG6�]jGH>Q5�@B<1S�?LArAu�Ur5��FF.~K.:C)Ɩ@K :@%��?JJ�U6�CD>�Ch��B�SiA�w��5UR 9EfT<^�88N� 1204D JVv�F�s }(1958)}]�fB�LZ> Ann.�r!�^�5:>��35J��r�S"lqށ�>�$��Partridg 1Hulet�e$�e ��V! KN� �:�VA G.~B!$. �BU^�� R.~G>T ��l%�f�f*^� 080406Ri~+Xun�0Xu, Mukaiyama��Abo-Shae�Z� , Millan6yX(neg~�:m ��'B� ��@JJ��DB�! �>DJ�)X@���*�*104Zs ~��n�! , Tir, Bohand�$� �uN�A��{B� ��> J.~L>,��|2�� �>V���F�4�v�$47a�J~�D\"ur2%>] ", Volzȗrte�wand RR��&&or�<B| a)䖥B^��;B��Z1S��B�-�W�WZ�0�VWCj�)gV� "&IA�a, Web�P�>bC >\��JL ����B Kr�>�PBy%$�wB�!Y�;�I�II-�j 30Z� 1510f f�Q� >� , "a~�*�a: 5� ��N�>���M�m �f��CC.����_ ��r�ZK143�aN�~�x1�NO ", Goldw� % Ol�:�ET�] 5�QB r��PB= ��>MJ��?B��d �d �d ��� 1832Z�E@JG FedisB(1996:D$, Kag(ShlyapnikovIuWalraveH0PRL96� P.~BB���Y>#��< G.~V>f �E��J�~MNL50RNBn�7RW 2913F�!�}ABf"^ �I *nneE7�PRA97} %Z"f�f� 6t�� %�rPN�!�A!.CN:Aj"5�!2C� 148J� 1997zGKokoouAAQơ�1:\&, ValAao~�}]"�e01!)z)VB�B&V"B��Z� .tVNB�,6p5�J. Gm��11{6F-�304J�#inU%}5� 1998:�$,X�at Cru�yN,B-�s&ć%�P�D�"8�"B#?�!K�j�F[�a�� B����O>�))�=F>=6"��2�% z,BF1�� r ! , Thalhamv  Winkx0Hellwig, Ruff:#imm�F�(] L�9 B�����G>�ĖAK>A ��>B�-,�>B�!a�;B#*Ez��B�F�A��b� 2v� b��zQ.�m9:m "�-gnato�ZilioI���] *~z9�QB- g���VJ�B ��ABt ���J�** �����'Mod�j7^@Ra 9��EkJr )|1n!�>d$��eueand Shor�!!��AB"?!�=V�B\T�V��NB.F;+ �A�%6U ΦZu10��>��usJ�"W{5�@ :�%�@Reymond, Protsenkm�k5� >�{��N>�C���F� ��>B�(�@2�9�VWB}9&!L%�2 b$fu41^�024F�!�a�j H}1eN� ,'3,�rada�% M\"u�Go�e�Me}6de�9�� �V+B+?���BAl�� B7 Sc �yB_1�?B� %PV{� 9�Vs-�jt2^278fs)�Jt�-1�At>�( #a .Ess�:�% .IsA,]5iC��&B� v��uB� ��-B��}�-�Gnam�8�&!B�.�uV�B-`V=)mj<41a$u$ 39�>��:��b; VatasescuR9�.�z 8�QV�B�P}, Ph.D.e?sis���(school}{Uni$>t\'{e}�$is XI, B��˜�I,>19zl zQ�aL>� , Suh, Lei% Jeung��&~= S.~J>?=|�/SN u.�j�YJ Le�%b2��*G.-BY4-V�J.�=. Spec! ^U'20�.) M�1Z,�)�J2/ 1h!�>0!.!�st� � ,4!, van K?!n�<Verhaa� C��+B'<��B��M!B� �zBh)#�=J` mpA��oE((6�9��2�0jBe��;5�ы��"s B�A�^�89�!EM�2�Cs>���Gu��e"FN�$, AmiotaO(, Gabbanini$zzo a��u��6?~ �VR"8~&5B ����B���<BZ�?B{5&�@B M)[1�5IQqj�B 1�!�!k���>�&� �,A��O:�]"���B p��jt�= B�&�%����.�U�Z 9865F� K j Wie�1r��>� #,Up. �� )��~�B� >!�]�V�f�J��N��~�2Z�54VNv� D�I� � :� , Drag5� � (urthe~Tolra�D*�i�P"��6�La.'���?��2M~�BJ1�!�וCB�fR8ZO225J\!Ab�jD��:A�3���K~b��2E��j�8Opt. Soc. Am. BjP^�108VP..)J� ,Luc-Koenig qE!I4{"�I {a}}:�6��2�A8 and *].�N��EB-����jtq*' V��n�YB =)!~Y��EurT\ODj3Z�23V=2�!�p�;�>(N)�.9N {optfesh}�&:`�apsrevCLLdڮ} �t>J� {epl_u&��r� bbm}2��amsCN��+theoreF+��B@X6g�J�$rstr}{{\!\Z�/� rt\m[�4.8mu \rm\`{}} 3mu$}C / u�(F.~Benatti\��{1} 2}, B.�.iesmayr 3Z�(H.~Narnhofe} #itute{ {1} Din�Po di FiѸ Teov�,&��\`a Tries�4PStrada Costiera 11, \%: 34014* Italy\\ {2}Is�o NaziB��yN�e, Seu 34100 6Z 3}In [ fu5�[$�i�<ikE7ltzٛ`gasse 5, A-1090 Vienna, AM�iaa=��(03.67.Mn}{E.�produ��,!��Re���F �ޜion�O�05׫+q}{L!�w�o�� �Xb�c�M�y� .� a"0��\.L-shar�Td��� [fZ��nitapi#�iZ�pz��d4Y�T(UE�8Sa���b��lU-inDZanC}Q�KZ a csf�N rix--2}�bS�pUmat}.�T�`T.�y\� such%0es�Sm���Tir sf{N�"��} ~FNW�Us����%r5�~�e�;Wuí2n an auxili{��Zy�� rix  ������ebra $�{cal{B}W�a combwly posi�� map ,bb{E}:7 A}\o�_B}\to$Qi݆ @lA}$�w!�!�&�k2$:�. G"ual5�al�W���WdiUGIAB&�["�hby�Zl�r 2�X in ()�) 6�nɏiculaݤIjdG��.=ZܑHby nearest-neighbou^�i�Z,�_ena]f�_"�_�Xs GS {Woo�`�Rf�`conneEre��5%`-%?X�gngaK qe�&@X&�"ńr��gwna�� ncurUq$${\cal C}={� 1}{\�r 2}}$ �Coff}1�6(��:���act=�be�jd. ��d "�á\a#ent d�qo/��\q'�$ rcandNapu8��uory@�witnes�ma�}�b�^!�A,B�2� ��i-q1�"cY,Y�A�)�s,��d�ޥ�,e��ɡ8 boso�c��Yhady�fari�A��ue�o��nmBa ��ehti]din�����Y��cri��.Gb B�e-�g+����4�*8�ts �Kgwj�]aA�c�ba%�A 1�g1�-�munic�� tasks,62i0�w��x�!(A����d�~��aoo;���dhdYetect,[!`{�e�I �8tIhd�y �w!D�rŠ "u�-|Ocon,Arne,Gunl,Zana,Gu,Osbo,Nar1��%R���hv^� of]J �s �[n %as�xMa�-P#�Rtes} (� MPS}Ȭ�� d�l %imi[�P�n{\iae[]�^rena\li�`bps %t"���� ZW-Vid}, �p%oujqbvbuA�du�&�� %>+%%quivalEn�nele��-b�%��� nMv2L-� Ver-Cir}.95PS �c�� a@�viq���x %y�s LSSVCW}��2�2&�9���of�%�� )�aQ5�R� ~��f��Z9�werfu?�ol�/ ��*t�:�\xinF�2�M���eē=� ��.O-}5�� ��~� b�Ä́�e�u)�w�ori���&�b i��  as"s F� ly C"� F� FCS}�ot��.c t�.�gH�Ke ail;!p< ���aB}"�sQ=i*mavi� o ��se��m �of *Jws�htaT�C�aw (se��so:�1��i!��`��2!�� sf ���  �cf viewa+�l~h� etQj�2 lawsE�id�nd I4RI" �)al2 . %�`l��Қ��I�%�R���%��, %bec�kU�!u~%�# FNW,y� Two�p&� !jk͉�Ed:�� d!�ݢc 1�&�of2H"n"�kA Mksubsets `�o"��� �an,LRV,OV Subr���|a~�d >� ��m� 2�-F^Jw�9t m me���`�Ver1,Ve%I�k"\�Pg'��hecx��ac�W�T2� of %� m�n�ual6��e�i��m�sit{ ly�?Ot����Մ�g�|a�lby� u�uU  %�  ���le��a�"r��tw?o �-��al�. % !2� Hy� ���N6{ of5=��:�"�&��!&�T5%�-s J� �-1 .�>A�w���j4 %"id�s r�n� olo̙B} y� ar&ys l&�ah� s whA�2�* �nl�the|���by�aicon� C��V a Js��j�u�on��kA� z� &���Y�� 2�Kmore g�l?o ��yV gwtuJS��"Y� ��Anl��:V��j���� ~ n"��� a  %�b��d �a�(�5��eb!�v�oA�nz�j�iZ�n ahi*M}. �s!  ��:kx�5a!�m Rxum����mN^. � skip*� bf{C2�* &.]�.{:}\quad�lw.{��a�.�it bb{Z:d� %\-sa�e !ls ��$$?Bt=)�&��h�� $(i@ A})_i={\bf M}_2$�$2��m����" Oj�ҡS suita Z�j! �� } tensor-J^s 4 A}_{[-n,n]}:=# _{j=-n}^n2�  )_j$. Any�P*�$�@f�is�.� B�� _{[1�$�{���a� ofnl������ ��u��� s $AS\in"�� i:&��*vfcs0} \�(G$)= {\rm Tr!1D \Bigl(\rh�.r) \ e!�6�'s n�satisf��ti ��sb�1} ��n+1�.�+1]� 1_,) S�oxC�.=.;Bigr)\ FŇ@a�y�"�c���f�82}D� ��=m�1_1 � !z2,�l) ��R�"���?��?.�E�yi/_E˅w��q��viple $ybB},AK,E��){������� $bS�b$: 6.,��rho.Ea�-&w x | h|z9 maps6= aE�> uniÅmap^�in` us-Stines�jg��mDdfVopa��(A-� B)=\�� jV_j.4V_j^\dagger\ ,�+V_j �bb{C}^2 DW C}^b.� &bN�� $A.XA�` d $B.B}�E,bf"3tat�} � �bi��i�t�pCq�:.�(1��I_ � B})=2$. c�M%4(^{(1)}(A):=�E9I2>)$;=z� (�R�ma�om f �$to �!$ Analogousb��"~ Z�ons 7�n)��5�\circe�(��id��g"� 1^{(n-1)�r)덡->�A��i P�E ���S� b�st)� Tr} �a�W\,���M r):=֥���B��l\�"� �l٪+r) F�%z.h.s.9�1�-��Iz�;z=�X�I��x ��� on6]�"$) w "��,�rm !+) �� .  1�w*A}q& Br)-9dV%�\,BӘ $\fo�\, >� y���bfɱ:c6( ��cr7ڀ= B}.. a�C�eA{~(�z�)� ��" Kraus �,� $Vz�2F�2Y�R.!� $V\v@#phi_i�p \psi� =v_i !$, $V�t > ��{i=1}^2 \�le c v_i^CE^bo1k! }}�!�l(Jkla�#�j  M*=�\X�, vFG :Jg  $ ]� {1,2ˀ� �_2����on�A $v 4 $*A *3 ��! eqnarray}� "; $1} v_1 v_11]+v_2 v_26>�/(��� �� ity}� �w{j%�2'��\!:= � L*Q "� ce})\;"� � "[wa���V%�*f ^� �Q]s %�6�qlZ2�, %(R��J b��?o�as %mix��� i. I>r0xO�a!CquA��fulfil�"V 5�8�4 ���� d.� b��se�#-"b]� terp��d�un�� p���ed6�of*Wy,�!�R�����G�x��~�?Ꮽ>$n=av�j�2]}=A"O  A_2$nyYuo}'exp��^�2]��� R����5��IQ�E� 2� m&uW�U�Mx�<} uhe pe-�%2�"� Ƃcom^e &�du��apml bb{F�n� I& �� B}$:�jk �;"�*�  B)) ��&: " H��T)\;*K � &Z.�~\:=�~F ^=�� \,V -�N�j� qbc1 x�NE}=��s,t��\� hi_s�u� t �  v�_s� v_t =�jpņx�W+� v_1&�g  2\cr.n��&݂$E$aZE� ofm�e�)E$u�~�e)O ~+\,�"\� u GAu� 2�/u�>$m� a!��$� iR� e$ ��q^, �*�&I��(is�# l12G E3[1��*�.f�r[ �F� P^�}t � %��Q��\�� Q12}&=&\ ijlmE� \U�� .�2� cQB$ R_{1ij1}& 2}\cr22i�.4},�ap1} &=&RX11 X1�a122j'2'2'2'12N2N2N2N'2'2'2'6�&1v� R_%d� �t(*� � u�;� (; v_l v_m)$)�Ӣ�^<� "���>&9f5}M/ } s},t}}E{S s}}X M"� 2\,"�(v  s}}ޭ� 7� )F�-5r�= �s_1�2 cdotn�$,� s t}:=v_{tE- n}$6LWe�llA�E0��2�of� v�$�#�' $1$ߌP�at si-d�[p,n]:�p>1g�R� in (��� :�resa��"� 8 $\omega\rstr(\Pmathcal{A})_1\otimes\�_{[p,n]}$. By the previous construction, restric( amounts to6 expecta,s \begin{equ8} \omega\Bigl(A�( 1_{[2,p-1]#� A_p� cdotn9lr) \label{qbc7} ={\rm Tr}_{�<� B}} ?l(\rho~+\ �Cbb{G}(N�)V$r)\ , \end�where $�=(1)_2� �,{p-1}$ and $o�$ is a completely positive map from /)�5� into J\B}$. Notice that while $) 12j a nea!�D-neighbours state,+�RAN` $ encodesI 4ntanglement of, spin at sit!<$ with any subse($s�A�p, $p>1$, after being embeddedF�=�4={\bf M}_2$ by-7%�@$. The advantage � abstract I�ureXsented above emerges in)Watotal)7 overHchain is determined�0riple $(�B}, bb{E},!�)$, sa_@at properties lik!�Aximal 2s shar g-� 9��a transle�( invariant �, A�<, more generallyi�2fDbetween different )�s!�latEtLpoints, can be studi � mean+E�- \only. \smallskip \noind^$\textbf{Di��bu�hk!K2�along� :}\quad AA� meas!�-�28of a E� $\nu_i1� tensor!�,duct algebraMPaN}��%� 2$, we!�ll us)�>y form%�$~\cite{Ben�4BE��entf} E��^|}(� )= \inf_{P=\sum_j\lambda_j\nu^j�} �� l\{ >#, SV -\rstr.�1"r)Dr\}f��� �nvex de��on �� p!�%�sA� $��$A!, von Neumann!� ropyAtheir ����䁭-���!}$, nam��M[� obtau�rac��UR0second factoribHdensity matrix repr�y8E�x�d fun�al]�. It tura\ute]J�IG,monoton} E_{��.&6p}(��)\leqf6U��B:$����� )\ .>y��proof)�is%^ follows�9a slight��izez2an argu�� iq�$Nar3}. Let6�03$ be another��1�<3��Qver:0>�N}P,and $\Gamma:5(N}_2\mapsto.3$ a uni�u( 5(16 2})=: 3}$)^Y.!@n�2}=�\circ(o  id.o A�5��)m�m���$4 j$a otP}�!�: F!|`the>l:E )7 L $�� $. A�2�����~ duc��those� �(are not all� 0sible ones, iY�� $�� ����)v boun ! �byJ� 3N _{13}^j}�� l\{ B �i ,%�E" J" Q�I#^5p�4.� ��0}>�F A )̡5of m$�NE�s9�^�N� 6�$�ed� &W A�$, !�� evalua��� eE� ator ��� $N"*:�02}$, coincideU��ioEs UT^j��mselves� us,�=Y<��\���1 343})= firs�,� %� @e hierarchy~(\ref1�})�� by taking:=6u1� .�2:!{p}$,6D3. & e aAE�%9 naturA L �gAF6�pa�to]��)�� one,�choosM2�J�6�2R���.�%B�d�3 � �>�>D B}$;!����� 6�B S =� �tR\�=�g�6,�� (ee also Eq.M<�)Q�aF� � necessary�dia%}Ufa�,av.h �$a�be� �dio9��!�}�V� must2f �2f>i�T&� -i� c� kes t�J� + pe0 A�$rigid shif� !;two a� s;%j�, oughnext exay s goA!7r2 diret 0, unfortunatere� so far no5�R !�< its sufficiency5 !�5� "_.�(}3a,should imply�Bsom!�qU=�Z} }E-:U Beca� .�i�� B.}tudd {\itA� currence}� Woo1}!� whic)�.-��D� i �#ic� increa�} � .l_$$ is given���C� )�(x\lbrace 0,,1- 2 3 4\r1�� d$  APsqu rooY�eigen�<in� �order��  �(\widetilde{��}$ s $>$=(\sigma_yqo ) 9^* b!Ev o^*&� � lex!Xjug%� ��Hstandard basis. In �co5� , in�8~>' readNG2� 1} U�C� � j�6�pt �LI R VFRr��BiWB� �s fini�{ correla� "�, let ��e $v_1= pIA(}c&s\cr 0&0�Mv�}(cr s&c:/�80c=\cos\varphiE4 $s=\sin��e1e�ɪs )� Ż1})( satisf- E� =1/2:� 1&2c�2cs&16��, u� M]qbc5}).��r�r djac�@qubits explicitly>�narray} M�sc1} && )�D[1,3]}=\frac{1}{2}: ({i,j=1}^2\O _{ij��4 \vert\phi_i\r�\l j o.>$ ,\ \hbox{e� } \\�a � n 11}=:98c^2&2c^2s^2\cr & s^2i 1�\, ,\, K2b�"sZKczK1K �021}^{\dagger}F�s�3!�$ 2cs^3& cs2�*e1�%as�2��v)�u�6� ɰ}$ *�q2��W 9c3}�8~� . N19 !� cs& - �!YA�� "2�- 'e!�3Os^0 \c)�:/B[Om'A�),$&��2eU $3$,�  ge�he -# e?-" i ��1.:<1&4U� & :�, leN�3$[ge�e� w two��s,1|J�2}m�E�y�31�!�!W!p 4c^4JC 2s^4(�83 �4el%�R" M& c^ &N�)��� 2csk2$�X!��2�m�1&� +=22��$. <�ermqLis clearly separablem * no2� "� � $1Il Iq i.e.4� B�2K. W�parti �<ng�5$, V$I{4\left� arrow1�*>tivity5 Fly lost�  $0����<\pi/4�usA�ha4ni m�h> B��,e same happe*}���one)� ��&~�$�<, if $s^2-4c^6<0�a� for ^�is9�-not1e �r1z9x�? . A� ict�.'loo-�[c&0 s:*� C.�R�:� �� ~) =�psin{2-�}�()!$ vanishw)�=%�, 5$, mi �12R�12}�t�*g ute;Ax!las � �Z iha� rs% x  $\alpha� �$l reporA in Fig!� 1(a)�xchb;�l� at,� agreI�A��<� 1g .O ~z\geq >(�&lyn��is�d ne� =�!Lq�dqA� �$A9&$\neq0,\pm1����f%)} \8 er{_�cludegraphics[width=150pt, keepas�rL\=true]{Fig1}\hspace{3cm}�F��capag{!��}$, !�n;:�!(, red; ciss�RG. �$0.5cm} (b):N5�R��:�� ab�ip$.}'f!H�1� An�V+  .�+ �-��Z� d1} I !�"&a � -s& c�� Q $sqrt{1-a^2> 0&1� 0&0F= �[ a�a 1*� s�a� :l � :� . Conw  n�a� > x&y�y&1-x:h � �U\{-5| x�,s^2}{(1-a)^2�  +\ 2� }!y ' (a-1) s c^-)7 ^\��.J Wv#?@choice $(v_2)^2=0)3a��in�� qbc1�%g?-( $ or ^� �;��refor�d�lc $a,sW d sd1a�4-*�"��s���� rmj�2)��>�1-2 \g` &i�0!o"&\beta  2&Bcr)�]� yG�  ��F�=2�b k 8��? of 2m$��na21)#2{F'A 1� v_1 9  v_2v_1F"# 2 A�^2)l ^�J�is� q w$ᝁ#2}-�cos(2  1)=�@%L$%#m!m(#MVc :�J =0.41$. O��0 hand�e .�! ~�$�A d2b}6��R  �2 �E s^2 \@ c} ^KF�I*�b), $a��'$ e%j�Hu�2a}--��)� plot< agains& 0\in[0,2\pi]$: *4 G hown��� �C ~�*2.ex#sed b:21!N�#, .Fm"�� the �[!��Q �[, but� do�  knowo!m�:rresR& ways��'� � .E(. We believS&i�$(be peculiar�ur ��E�qB}$: siQi� two dim}$oP$ bothO �A> FR�$��rank $2i�"��!&�$c#+ 9$0$Dsure. W�t�ZsG're �Ul2e�iť um2�1!�F�� each!A|!i�!s!�sum#�K  2�s, is lesvan� �to!��Coff}� usF�.T� $exceed $1/q�$If)�ipen�$ blem��$��upp/+"OA!achA4�*a�&od .). I�$Woo2} F#�consideg*�+yQ*al-�t�%pn��*�e})iD�� �n � �forId6�sp�  *o a� a�=�:� �0.434467� K&7>(+ ��E%ystemNP-e#ty,�.\�q� A}_0J {[1, 6 ]}$ defA(- bar i� bb GZ ��SL�$p%��� in2� BA�>��Now���a effv}�- sharwI�%0aF.��Qdue toTQPnA +e-%fI�lim*%]-&A�� n b�-�1}{q2�!I� (��� how !ґBca�da~bdachm8 VT +1�����Jv_�sM(�E �nz  1_ Z Z0V ��&� �"� d1} &&�11}{1+Jr aa^22c\ ,\; [ then��� s\� �Z~ )��6/&0&ac� 0&b%as# ac .p� � 1<\;"� 18! @ $\displaystyle C�~* �2a.�� A�ch at ,s!Ub.��$ 4Koa=��3iT���|/�*A���in*<#sd2 Tu�  optimiza�2�2%��u���K1�R�/"q!CoUs�&:I�e\tH0�.� *$1of Esf{FCS}��ini� quantumt2��s+)m&�0Precursw3"[��illus�ed M"po�) b�rN&H#��2\� 2��tr �ovestiA �higP,.� context��$AKLT modelT}� /arison uI"rappro��s 5 Fan}�7i<gress^�")Jbf{Ac� ledg� }:[18B.C. Hiesmayr a$|es EURIDICE HPRN-CT-2002-00311. �� thebiblio;y}{10�)bibitem��-prod} A. Kl\"umper, A. Schadschneider,!0 J. Zittartz, Phys. A-&P24}, L955 (1991),; Z. #B #87}, 281" 2); EuropELett.& I 293& 3). �,FNW} M. Fann�+0B. Nachtergaeand R.F�&rn�$Comm. Math��& 144}, 44 d^� 10}, 63& 89);�, UGen �% L181�W� W.K. Wo� rs,)�ita�temporh'Ue�$cs} "bf{305!8 99 (!�.Z�� V�ffman%�Kundu,% :t)�Rev5�,61}, 052306 ^0.^ Gold} N.  enfeld�Leis on pha3ra� �R} ren}3"0(group}, AddeGPWesley, New York 1992=7Oc�(K.M. O'Conn�1!�� 3}, �2�1.� ArneAGC.  ,sen, S. Bose)5 V.Vedral,.0Y�I�017901F^ Gunl} D.  ycke, V� Kend�9:j JkA A� 6A� 0423N� Zana} P.  rdi �X. WangE)�m�3AB 7947�2CGu} S.-J�0, H. Li, Y.-Q !pH n2 [70QB)l4.l(Osbo} T.J.  r�+R M.A. Niel%~ �2�6!�32110F�Nar1} Ha�rnhofa� C)� �2� 23 �2� Nar2>B�(it{Hi�)e� �,6}, ��$-ph/041215.�ZW-VidA\8 Zwolak, G. VidAL�(Mixed-s#dynamic� one-ݘ eum�Me s: a ��-"� supe / :r�*,orithm}, {\t)4d-mat/0406440}}o$Ver-Cir} FA��,ae�:!�I. Cirac^$ 060302(R)%�2SSVCW} C�T\"a(E. Solano, :mivMa9Wolf,�)Sequeny��l��(d multi-qbi4 s}, %�sf{9�501096.��ASF�DV. KorepA��8V. Roychowdhury2Is{\bf 9�v227203F(LRV} J.L. L�0�E. Ricoi�Y)QA �f.~Comp.b �c048F^Vea:LM. Popp `J.1[Z� 92a�2��2� Oste& (rloh, L. Am�G�lc��Rzio�+NeI} (Lo�)��41a�60 �2� Subr�� ahmanyam2�m�69�( 2231��2�Vea�FA(rtin-Delgad-�V" 9�%" 0872��2n* 8 I. Affleck, T.��nedy, E.�Zeb)�$H. Tasaki,!� mmun� th. ��AP 11��477 88);��)�5!799'7.a7A�N�*Rep l Ol50}/1, 1-H2�3;C� 0ett, D.P. DiV�nzo�r5 molq56� ��A�l bf{5�� 3824�96.��- S� ll)56R �R) e�(bf{78}, 502J997);>{ )dJ:8� 224� 8). �>H doc�8@} v�%% LyX 1.3 a-� tS$file. For�=�info, see http://www.lyx.org/. %% D� edit un�you2* lly *  w��doing. \�lclass[twocolumn]{revtex4} \u5ckage{ icx6 amssymb} �,0keatletter %r�� $ific LaTeXc"mands�Bold Zo 8crof�- 2�,�B} �um j5u�-3m�f6Db!%Dc5D (QEC�7^.�,bit-flip cod �five-. rh,�,. To describ�e 1!@n!�rap�3a�*1edAa5 lized&j, Hamiltonian�r Yr -environ%� inte�C� re takeno acc�F�2iX�7�repet6)Dt�"s�`level)pa�in1E!-�E�Y� `4A�also Kwoem$i.�EE �-9alA�igne�6\ %6ira�A"(ese results��. insM7A\:INDpro�8�( welluseful�-D�de�:� 6�)� �5��i!�r �<6!��3�� ofY�omputer6/�w \mak!�le \s!�on{Intr$E�% Re!(A� elop%�!�!<theor�u j�mge�F ted �fic�e�4 in utiliz!Emechan�e�� newu ^$al capabil:>mn�_chuang}~S �er�outper�#��%B�]er!]ep a i�t � to solaIiVt�pro�s. How�)i^ intrA4 c se��-�F�_r�-on��� |e� %@a�9s�!�4 surr*!L.R proh��Aϡ�)�� scal��"1- . To ba�0inevit+�}�@ ��#]ts~ s du��Te�Ebitrari�0ng��q�e�be&� 7)+C8mpone�N� Hzalka1996,aharonov:&� (,knill:prsl"8,�$k2 }. UJ+ a $t$-6yng!-eB���*tOed �CfA� y gaEɧ� r�+$$\epsilon$�� a log��-�,�O(1^{t+18D!z .e��9GtogN"�%A�!�ep� >��aM6�nf0ez��� leada�r �q a�q:�e�q�J�REiN%o�^�vl %P"R Q�au�m!WxI�t"� :�6� >) indi!�0� Q (I�in�Jer� M)-J0s a benchmark%N�e&B?of.�$s. A numb"1= oretA �� ���� ove�s`*zk�bNxo� �@a@,Ste99,03,Rei04}; h�sk 4s adopt ad-hoc��a�� �.:AaOg| �^ detai^ ���Hj[ 2} !;�� j5��% s. R�9� �;se2d� �%usu#�}cA;I!�pow)�:�x >> "� &@ astill un�6B I����ittle| ��l#e�ED�hy�"r � e��- sour. ��Oi"F&Nm�io�@"?.�(ofee�c:$OPy: 2  ��a �E�re�ts�Bm . � Ref.M�,cheng_pra200we)�R phenome�eoE t��?%�#� �� tel�4%DEY�r- d-NOT ��. S��U�+a�� ve.�� incor��O}(F�t^�bw�is-o��2 dissipa�T "^J  Ts�&>�J�I�is pa !as=8)yis5� 6���� a| 6T2JAz�!m�7��2E�:a�D(v� �Ric��A@bIDwe \ a-a��{ n s! al vari�#�mat%naE`X' L�!cj�. '� �- ec:I*M-and-� } we�A�^"t�T odel2qw�:�ʕQ�E��brief�7 viewMi Sw� �a5! ^ge�j�5d� is work B�� Tl -QECk�},%�&(our��VKi!�] 9IEstZ-of-D. Fin��,6�A y on�(fRs�U&� m&LJKJ<�Aɛof�&�.ah�RwWFCE"�� F-T}~F�.�� �w��bE"��+AF���U4�j�EQI� lude%�� v B�&`&� .�*Fnd�MA�o)f  } WG�G��� 0a microscopic�D�E�Xf�e��e) ��A�:MW�$ 1�S ��---_2gd[-ZcouplEm*�. DR_��%��N�(.\E<=�a8L� 6�s�Be�IB�i��"�aky��*!��I�)2e�8rSj im9>X6� e&� 2fa �l�$X$, $Z$�dCE� $ZZ$2:N�.>={2w,lY{i},� (t)Z+}Z0J (t)X}+V&,jLF $� �$n>?Pauli� �*Xng��A�$i$-thEɆ�,6�!W�$ &�f�7����pamQ]a�kurnxAEoffA Y��Xredw �a?.�s(s6,;:�� QWdV step"d@ pulses�f strengths 0 to 1 (uniq :") �!0{}``on-�l''A�v0^9 1�eda�:B: �Ury�2ne���a� so] E&t,l�4i]��NnX�%�9/Delta t� �2�Sh  12�$,xD@�.vaQ$.�>n���x:^!..� Hadam�M!�� wom�9EV E1Z1plus *m ba d��!�+a�it,ln ese "�s���BAx�1ed��N��.�in Eq.-Leq.�).�B� fig:-�-� s} � a1e�� �6"25uVZFB d inU miCNUZ�ǥ type�-Տ HF� an&d/�pu���&m h��-� ��oBP S�'1�C(s avai }er� viduGV�aR� thea0,  ��F<�I;t�/! 7.{���W expec05 Q. U �Oi%^p �6l&�0o �u \s. %�!IBn � er}\:&�C % �C0.90\�#, >�C]{A�s.eps�f V�$�C� b�""KU�usidenote ^�.qv� 9#E�.�. M ca�l�d>o�h a��ɹ�Zk%���riv�IA�k�pt�J.$�s.�A1� �}!�]� J �I�� ] P b�: \[t�� b�d�;����b� 6 ,� },\]� FV� ?&� D�t*�, diag=O-N56�resa��  Lorond�=*� si.g��� e ($Z �"_($X$)���>�� � "�!�P5ꁉ2�as|= dom GaussY#Markov�M� zeros�-E$-f�b�=�A@im� b the &u99of:�=R, be=j� {� RZ6;R.-5� $=0,,R!ubPFhj}(t'Ei gamma_{0}�i 6_f (t-t')Bp�gn^1�^F�vg0VY���& �Wkc-n�S�? ns averag {JA~R "��� $9Iq�-Z1}$� c"K&Q �u�ygy:�nd y�!G�E .�I.� )� m���  �0}�@��� ��- "@�i�i" ~Ipo on�axe5��gde�5��6�R�� h1V'Q�c2�n[b��"re� gT���F �T>. :� 6" I4E �4� c c s�,�E\w)Se=  "��rP &9�2"��\� m :�d�� IF� ��_@d�nct.^ (�&)K1er���remBl���trainc�>in� ���-' S �hh?!��' value�&[M) u*�of}.E��Ű�' a.%� z(`:JI�I� UK0N�a8%an/�A6SA�?�#!s�on�-�aIElEx� &  we do �)�guish��)aMP I�s. By)A��EYp<)%B.�-f�iR� �%4p��`��e@A� l. A S�^�C)�*�e�)�)5j"Pmada��%Qs&��M 7UNB�!wO a��um)m[1 %]�&-�� R�!�(,  5p&A% swapXs ">amployimshu�2�sS$a�&��$FHH04}. Ou�� �="!ڵ�c6D!��a� scenario.6m"� exA�up���,�?2�A[#"�fE1��Nu-@J&9o�# exac/&�Eo�". w$ �;d�b��4@&_.)-(Yeq.)^ afr�v$��mo%F�:�l龭\I� numer@ly� paehVB")upA�tw g1?()F�sizC5� memo�*n aA�so�� �*)� -K&�#n���)ly�)x�Z@M�`� full&R9) �-.�{6��Ci6"�6%2�}� A��p�fT&"%[�""�� #^E�&� 2 0 ŀLR�!&�H�":Id��� theyer�q5 )��a�mU/"I2�i�hP�v �A86�*#�)�$mainl�Tc@on CSS�s,  �ID{[}{[}7,1,3{]}{]} ��wCF)�$69}."�36� /ud*� .{% easEZ5�,�p !+�b�0rearMn 2&-+���Z���� 2�2��c�u f!7!5"� } � !3�1�� ,A� ��tC7/ WN��`!�y��+to���%# A��bM-"-A�w�,�vAk�i��Z`!� �>�QECi��v�m��'�4EC schem5Wejg:)�i�by*�8� ShorMl�+GL�"1 /eOt�n�versal"Ied-$X/Z$�k�#t{� syndromaY� �0dYcan bN �0�XXAN��sOw0: (1) ancillaupa�I�ver�/�%, (2)r z1%N�(3)�EGyg]�$��:L� v���(7 pr���I�!*�=c5: ~gFro ia .� to en�NI�magnituAP�.r���=p"J%de� $� ple9 fou�� $I.�J(|0000~+|1111 �n"k�J{͋a��aDY �4ghz_)C%�}U�AaȥLto1m9�jF�sM�[">K-�$a�_�# extr� �%i�oI9*� �1l�#2t�Q;�8a�*��a�_V "�� �l�� ac-ed6B+M(�� �6�it$ c[jsY mg_:�EC �fK$Y(EB=)�Rfulfil��2��5�EmpCz�PC >3Y�] �,1�6O38,steane0202036}a] &�2fe}?���].&�F�[$ata Vq6&requi�Pto)��]E��B. �z�7�`�..��_8� _8!^)�-� �pa�<X �灉eF�Kf�{~{u�e��Fq�6;5 �a ]a�)o'!�kJ*b >I�"!�"� "Y�5c�m V}� �en%�MW. I .Iise�- i�;�; ewisib 3discard ,�oAXi���+�  'WJ�h�&�+y^�<� Vaww)��n#����6I!VZ!e�E7zc.peM��Q4Ife��LI�abbz4�,�dat���#thV ��Bter�#946�%k,rJ;:�t�3pp�5��e{ir"�T+��e���"a�1Q�� &<1]�E��$o�;��N�cat..�5��er,V �t"O2I�)��AsR!�6�H�_Hs� !\&P./) "!..�w�Q�a w�0[ ��U*  �la�E�(ake a majorQ9vot>w{G� ';�;Š*�S]on . aTA�&dS;%btem [R"%<~P ~A~(!de~�~� ):]~$C6Hieua8i�5 \ &��>�W9��^��>��E "� !�} 7[et��6 ��r: &� D�� !�%��M;)A [�$.3 |0_{L} �, �|1J#&A.. T\]���A�܁- ,�qstoF +�*1}=ZZI3$g_{2}=IZZ$E��)2UQ<sM��;na�%')|��^"d��es��M� 9� ,@5�E�wBE!��%d ofe�j%�! domi>by�M�*�@wR �` iC�by�)��a��=p"� � ' A4��r� -�+B�G AŁt� y�9e�"w,re� �!+� �a�@. T�+� tab:�_e�} CIA�* ��Vw :ws�� "�}P�t%���a8�Bocts�sBE�AZ =j�!on� f��dQ>ng�I���(*g! =0$)*V�M� d� u ect �st�2 � nor�vitv�9 o�3 1�K� s�^� *(kaA$X"�oIx��9"�:� d "� )|"�B� d��=$2 $���-se!@� t>niV !a�un"�>"�e��A�a�!b?ctE�9$���ru �2�. & =�M:-J�MF�Z�/�>& �E"%�109�6��Y�A|.�T�- �P}{c} &::�P \QP  \)"^.{4}{c}{S�} K2"3"AH}B[c�P{1-4} $7-9} & M$�. 2}$ [U$_{RBN �& 0, III&B,"1 IIXN%1( #& XVJ1&%IXJo � �. B�md1� -�<Q�Y�v.-� .�#0ftqecc-2����� A��"� �A��6+ �N*� �R� F� \*� :a0 :�d�| �L"� ���&m�s�xJJ�ben W:mixed_{ ,LMP+VZ A��>Nr&�29J��e�|gGottesma�*r$G]J H�Q>("&4"� k � 2��Ѷm� &�W��f*5w"'�c5�jN � nine�W"� ���L�:� �*� �Ne?� &�Z� ^�!�U� "j w2H, �Q�� (� ���ly�� si* ghtforwarG �$In�M F��Bt�irQ$M�!&KF�4(�6C:m=-&.}�XI����(r �2�?C&x.ed�!{6f To �8Sted��U����"PK� lp�%>&��-ek�& v.(��$\{2|,2�\}$�s)�[ \rhob0ph�rI+: 3}}XJYJZ).� ��i� an5?D E�B"6~�Hus ���k�%a*("f*���1�Q_.�&�AYsetupU�a�D �Q} �X65�V�� q'�H�&�$ EF!� z��KliquiDte NMR�EwReq/&m8t�W�&A� per�q��onE� �6�E�1 I cell� �A�� r+e���M,M!�inI.� 2pP�xis es��ia�9%yy<g R�+ePQ .�(EAUF&�Y*�(&MD&�(ToYT!� �� /�y�"���� V/u�? rRb is � 9�<m&�;!��1� �"  ""$�Fq ; B# q %s�._� A�b��:�E���&;k��@crash!�� $P_{c}$�L%b�&�o ��i��s2#�F\!G3D6k�)�q�Jr7 �j�&� 1YW��ed&D fide�U�� \�W{)��+d�ss}A�W��uqz1U$��?a��1 z��)�a:���8��s!�i�Xk�o�T� � ly $n$ 0zC2�B��".�Aw$&�?%�=(nՓInMll,  s�� �/S�m��� eq>[iS2�1-e^{-2\��_{n}n}).m�eq:Pcn_�{ L�Canq�q���)LNvati�!�,M���1 fittAs�e2DR.a!��8��m �"/�)�^I�:)�U�t�p6p1���!=.~.��d1D}{dn}\r� |_{n=0}$.�L&sQ ls)E��Z���5j�_{tRxtxtxt=0}=9�/\tau$僡;$A�|�2��od2x%!�letBZ !�>��= JaW".Bg�O# [1A�21qFv&[B�7�B:�6FFe�F\5�T 80� �q�N�r�Af"-]*�W; �m2�qx����Kfl�)� �)�X*FBJb�@au7!��5�forp���)2�,��@9AMi�X o� � v��Fi.%.�e��R�)e��t~i�_ � regi� J�!��'or�&a��z' K�!�6i4�S06� �,"��F�is�f.� crit !�S�aN�A��I�ň pLs�65@����Nb.�66� �Y�!�� U ed V"�%�sA="�sl%-tM{�QJ�J��&}�"B�6y n�[nefit�-m!t%R :�� �% ja�'$�s10��}$ �>FanW�ut $1\�; /3}a��&���� "�ai�on}(�y=";�� l6�,~�fI,aAr �a�"�#&�D%��I�Summary--50} si?I2q��J�%=Սk�c� %Ev`�8:�Rs!�m+4 C!�ct�a#!%�u.4;'>�w�`v /�eh ".�"%t� Ydecay 6e�f!%6 *9YA{6X�E�6 F��&9a��n\{!q�/]�&{ _KX�()����\Ji%6�5J��pV�dbiE��4� A�.��Ma�T serv� sugges=Y.�&�� 2#"  2f30�ɬ-�C.�6simila�qR�)}XCRq��)�4�;-�s l�c�|3&W "�h�esu3�iXV�>b�e(3)A�� ?��(4)!�L U}$|�Z 7���5;=�antanez�V�/. CQ��H^> �9!�t t@s%��r�=M�� foo i ��-c*�8 �[��w�+���g�A~n_��9"@�3iӐ&�.>\nd c.uss�ufVN(m ~7k�F;.g��45\��I]{�@g1db_dPcdt_pmin_a�n"�ms[.4J>I5qc_db 8�U"TQ �T �xa��n� MR� >�>E  C~2ia!:; ze�un��M.9�2�+&C)� >)A~A�Rt  (_�-left�7d>� !��PaJ� mQNl��= ttomm 3:5) u� ��>(��g�urv2��"xM%K�-"E%P1 � t ,a�d V% a� 1> ���Y(d�%U>� V p��� ��d�T�(nA . �q�*��*a@JD ^� Y%8%�.�� � �Wj@F)!l��6AF'M:O &�::�h er�v&���T��6�� >� B; j2� 2� N�"� J1:�}F- \� 3*� 6-7� &""(� & � �6� >�,>We.� 1}$)3$2..� 2�ID IKj-�#ta,t8� *�!a�� V={&�]aAB2�>fBs�gB4-of�]*^B Y�/�sSn�`e�&�fAF�� ��� �CB&bBa� *�2�ierZ*�b>Bd�!�aim tȦ���0��o�_�Q&Achang��>�1J�ѽ� ./"E�_!�R�_c^�� ��\ )ee� ,+m�j�jIl�b>3� $+!CB�!%�8*�OPOVM (po��" or-��"V)!X"�,"�n2;J�7�2�VtR�/M- ^(1-\eta)"� �N0|+|f, 1|0/+>AB* A� A0|2LO"�R�$ ( ��s eT) yL�4E���` $ ($�$)��-�d�$���:] +AQ�K�s on o� lso wnN =�i�%�R=�.���& ZQ� RP� } Aat�P�A�I�5"�!T�tB1���Q^J�B�w"Mk � *xD�2�bS��".�y�le��Y"x� �#s rapped-��3m��TR�s��phonon%l)(CZ95,WBB+03�G���0o�p<R��!IJ�A!=)tePk2opic."r0B� seemM� adi21 idea!�S!w8d�&I��.{;Dv%@=F�, � q}�'7�8�.�c toBH|'�oB`D6�!Xp�6!FiKrs AlsoQ�J�I��I�^��-� ad�#L��;A8�&�J,dw.�s�s exis 5� Qiv*�;FJ �$ekert:pmpett�h�(ns�o�1qu*R���M� �R�$R "��&>�t�a )m������R%b mmonEʉ�&�(X %gc�0|U"}"&]��s� �5� >N" K5y�Z�Z�Z�ZJZZS*P]��Yb_9�Ve"�#N*O�l�&#69), 2[V.t.\Q�^.K;I�28���c*�h� ]�>�9Pc_�n*�9N� & #ns��7�  �INN.W*<�X"{�'. �a2Z> c����Jl�ly� e1�D6Dlocal� r ��no *� �ce" ��U 3��i����,!zllRve8^B^w � ex7|s�qeut~<��o�$,�2�Q!s&'!�FF. Alt9� }���KX������ �/Z<up"�Yݶ��y|2�A��.�r W,�Ѩ�vns "�0� a�1 f�d�"hole H��rt!=mDb6����]�:2 w�(r t��Iw iWOr��L ��3~�3� �be�� !�}%}Rp6�AJb'�!!�N��!22[ /�%O. Ca���d\�M (so�=)S:_�o2"��\)��'BCA�lAe"};e�V 6n�B}� N2n�A�.F�2� &�G�� H} �Y�� i%6M-O�+�y G1�1ijm47�b� � e��@�*�)�t.k' �#!��# evolu�2p.\�� /ra�or"� �*��6�p$��fi? � �B�,eI!%)_����sNo �: " � ' r*IB~("QMal~�%6�-I6-Ion��rMf4"hMdo�]h�~IJ�H!;�4A)�<6Z-&a)�#mI6G�Łct.k-�&�>PB�n>�H�-AnF�HJ�l=͆z�&�n��B�"�I��#� "����*�%�*:X6+M m�KM�mX<d"�B&�F�RѶeak�%L)� B)�M&Q0ej"�Q��>@/e+q$b�I� atwo. A2� e�. 2t��6� de ��fg%wo4�rT. S�#.8 [V�%��#Z &4by j$��UPVK97�" ��behind�� WB�|Z/-�3[��Qe�L"�H�\U��*�0%h�S�!�BI�e &:Oq�.��(e�/�`X wBtwo�T secu\=s9�1[�c-}�ٞE#�QB�!�c�X��2�R�l�"#�QK��3B�2�e("��:��ew!+A�&� �(Ua�B-�b bN .  �F� vcF #a ��m�z�L�tl��^Mo��;�%��DY2ja�oy'��"�FO��� +i�U�١ !��*�SI s�His�%�����-�0Z �a�R^�9�srst%�0� d-�r��E��b"M�"1�Rre��%��ᒡ�F0 ��Nd_Gism=P<�ޫ1VB�͂fY��^*]R� . FufPm��T*�.�o �I �]#B'�P mute�D)��(Z`ZZ")�0NB�6don�,a��[��UZ=35i\pi Z�B(Z_{2}/4}e^{(+ )/4}. -$2$"�;��E&�;:I�R�2�ope �&�ul�s&�;�[]U1a4(:"xFr lly DI�rb͉y^��7&ȕ <as�r�>�>.� (%�{)s%[5jE!re(6�R�2c-3��n)Z�BA�>�AJ1�#��J* &��FgN� Ka��f��6&�%՚�.��� 2t1Q��ɐ �J��|� th* R�:;*t�[`j� origiD ^ (6{4)���)D�t dѶX�'9* S��2=)_dRn���$12R%�S$22 %�� $4.6*�$i 2�r-)�i򊥏H� �� AuNs�:i�>�h.) � d.2fdu�G�)��ň�hN� N�l�U�Lun��llM vM  on%�U�);2JN��u&t ac �(d�!,: nee%t�d��t�>J� �='[;�9 n�9�+y"� cuQ6��� rom  A���  N3�9*6'�:'Xdu"K!�W�%ZR��!m%M/"ٌ pathN�H"� �uK� "� �$>a j,  �y�Ap`&ngB���q00x��.��L��� �A�686�1 �2��B��m\a_~�z����"� t.���Pc.6v� Z6�� >\"/Z). 2�&FT�S.�1 R��|�V [A��a�)O�R� das��d`��Zh2vNQ~uB[n-d&�.� N� �eu��?�l2�`Z��s `B"S/f We� draa�cN}:R;sbheV�.j� r��e{̑f3b�G���^O��>�9i2��dFz "n&��*�+�+WeU�=6�bas�Ft #���*�{� *e #�)W�$ y6�1�t�^�4�#�&�#�"�Pf$>"� �kq�gQI��b-�\-�2_)�l��� m��=&B{8�=�es��5Ύ�B͎ �EIs�G�0p&�`�d&C�B�1"��p.BЗ�Dm�:؎ei-E�A�>6" �NB�?iwB&�-v�I<RN �"�cN�>�9 Sc�8" �_��h2*z �$V&�'R7>�\:�.d����{�%*�R>.$.�0 4}$,�:a J��{1e"�r.��Nv�.�13}�\4* 54X�~�VN&�ʃ"��m~� s�4"=> �|F 4��Y%��Nz�NzT'aU��F�LdH�H.;=%G("�I��6p:] !� ��$���z&p!iU � >eq@auT�J�j��@x�!zҖ6�. A&��v�}rL��(R��e2)�r archi?Xu-�)�">*6� " M�&�`!� ��&m� .�w"%xG=���L���Ͱ>d"�"e2 s diz?!>pv!Ǐ`8 carrnP�A����2�1�MR�2~�*( ��?!�6C��'dsq�A��a:�x�eWD���4&t >|� "p1f�m���.  >�8.6��&7Z�qN %6 :3%�%Vc%%.%de2+ 1qK} � pe3!��"^��"�F �(� B)�$a�e*Kj"�FM�s,; og�JI.��p�oA6�}�j&wi alghm�A)Qk)�B� �j �66�� at��s��2� Reg۳�,Z^ &G )lF �+� , a�V5r� ��a�>$eF��[eA�lgA�E}�be "y�Ll&��8^hor�Q"V�im�' |&�,5 l;�+EB%�m!�AT tribU"� *>fCQ$�EJU����"�B�$ai/#i6�Si�@Ns��a��TkW ��"� !ho�� in r� tyV�gRT (!�`'a�@a� ��M1gr'`a���" 6� ���!�  (�/ ion-�/� NMR6V"O�we>��)��_ ifUd�� �������J� >� �6��"0�H fulnS��� 5a!�"� �J�LY*֐ )}G�J�!oA��UE� $�[E%�3 2Y!)�.�6骡O.�:�JPA���~��&��~n uch * MTa��fX��%�Oi">�BRx9��"~�,style{apsrevx�i8{../qcref,../re��ce qm i�`apn?�;d"z� @s:��pra, aps*��%Z#�ccn&�amsb�,am�\*C�psfrag2A� [dvi{epsfi6 %\setlƒ0{\voffset}{1c].`ݙm} %\ )Fbreak}7� +]or4U�lemma}{L2e%��}{D�P 2$�E�}{A�� 6$�}{A 2"con ure}{ 2$�(�:on}{Pro 2&co]aryI 1#@bodyfont{\rmfamilV�ne5 re�}{R 8b[ }��l} \def\QED{~\rule[-1pt]{5pt},\par\medskip �*c5�of_ref}Ͳ�� ��Pe�(#1\/:}}{ \h[x{o��neFM}{< : \ 7 7$ \Declareb�OporҖ ag}{�}Z"sgn}{Z tr}{tr^Ad}{Ad^ad}{a!MR}�{R�NNCCZZg frak{gppkkhhaasosol.lu{�{su}} IESU SU ;���*�G����$���&^ Av�|*osAm6@{Jun Zhang$^{1, 2K�K. Birg�� Whaley }$:*ϳ$^1$D�jt �6ӳPit�v*ڳT*��,, UniBw9of Cal$nia, Berke5�4CA 94720\\ $^2:yElect� E&(� �C�Tr S:�c�q%}(date{\today!�1�a��} �b>� &�analy �;_5�� l  of �-�m&�1�"; -�.�&u  d @A�K< �{# G* �L-D,��� 2�f#B�MD yQ-�$�{� ��b���bBlo�p,8Fe:hG"Z�pѯ b �z Pyo>ki6j �l tetrahedr�9en�l�s�/z�ivale�  ��=�(� Weylqmbe�W8" is I.�>*�"�CU�u)�W9r aN�� st-]��!1� �  guid(� � &� >5I�Kx��� Y��������D:��~�SUf� .��M�e M�� �ש�8��&~4 2"���,e��@W�N-|"��}T-&* <��&�%!�-��sx]f��5A�"": � c�edO�Ba��o:95, 4�:00��=W�6,� nda�a s ��uc��q:�A2�H���d�or� Z�Q��). 9X�&�Ӧor]u�1+�(�6ț�q���� oe�T�� ��glanguh�izbV]��d�*o�%*��F��.$�m�4In(and informa�Otion processing. The postulates of quantum mechanics assert that the state of a-� system is completely described, :�ime $t$, by a unit vector $|\psi(t)\rangle$ in a HilbyTspace~\cite{Sakurai}. �evolu�ofF G,s determinedx>j= U(t) 0)8 , where $$� �ary.sDperator (or propag) �dynamic%SHgiven�TSchr\"{o}dinger's equa�,$i\hbar\dot �=H(v) $ withN 0)=I�H�8the Hamiltonian!� the )� , and $v$Texternal control field� gener �] �A>8means to find aC\such A' z traj%�y U)�B� �G�use Pa%Xyagin's maximum princip!Iwa� !�set�l!� eren!"�!Hat havez be satisfAYby�optimal �p-4,Bai78, DAl01 P2, Khaneja:01}. Quit��ten how!P, e�0approach lead�Xa two-point fixed-bounda�pr�I� an!�alytic!/Ess�0ryson:75}. I!�Tis paper, we develop a�7l�toa�ig4Y� law aeg2� an arbitr�F-E�!� avaiE�.>s�5m A���$s. BecauseE� ( �ƁA��l��)q`��de4os�� combinՃ� le- ��!��Bt5]$arenco:95}%N only need!=��I5Q�of a\l!{ �sr pair��couplFwo6'-��amountE*!W�.eo)�B*s�+)$p �74)$a�pee�ly� key ideaa+aU����a!Con�}observ)E�!�m!� real1>�tD�� �Msubm�-o.�V-�readil��. �|2�iHnaturall��no���5�� quotient �~��a�� , instead1l!fK orig�L�8i��V:?I� of bo# } �Ra)L4)$. %BW 12/21 add!{entE� about NMRsX sv@Or!N*�Nthose q e!Blitera�e, but 8��ed �ia� unif��� framework�^also ��mpasse e 6�tmor�yx�� W�art9 +2��\�Su ��ebe view͝Ra�2.!�!�l���iBn!cm�B�4 ar ��VI �a�cw� rot��M3Bloch sp��o���|M a ��)� axis. In �A�U��J���� oN eas��-q�D�: $R_{\��n}$y\ u $ $aL�,priate choice�aZ� ` � � By maki~chang0coord^�ne%4$transform .� intoz$*� F� �A] $z$-)- Conseque�H, to iA�ma�2� 2�B� ���� �MV51�at6�M by a�J�u��uH$U_1=U_T R_z(\theta�� ,\in [0, 2\pi�kd��J �Yce ��Y v sqE .:�� ��.�i hA��!�. ���<heQ��ob)E?b��c� ��*?Ro iy. For case��$ ��n oscilKng�perpend#arpZ/ic ", w�r� Qlaw�j:�&� .�&� �ta��f]iarY' NMR ��ɽ���ve"��!� �p ��A� *B��tuh C��son�fre`cy�nthr� 1U BV�~N.%��T�\ thes) %��'e sho��w�at� :�aJ>t�to2��Aq�antize�isa part)�lyAort! i/ !!��� f lo� �].��u"� �)�s,Q���& $�s must���d!� same�%�E!,I%,&M varie� ed�'Ѡr�Ł  e% �~w.��Z to s! y alte betw��� ext��lu�&] �pa�ter. A�c gn � P.��techniqua"use-id�&"="� �� �A�nyy� 2��� aM^*. e2�de��6e��IB�s. PhyslE�M�O��YswoF<0V3m9m� Q A�t�1tYI� �I� .� !%!�� wo^�, b�)� +er *-ity����9&�"z $. In Ref.�*^"k8 {\it et al.} d��d�� �� y=�A�purVnon%�. H�2.�%=Z����o@ sef�ara� magnitud��� no-ul method� �*qro s o<� n numerA,Acedure�,Niskanen:03,ulte:04�aAi.pr�)�� avoa4%6� by u��zjC . Our�!�0ategy employsaa�p�gp�uy�#M~�&@ T$. First� �an ��Q�K.�a9�m���Xj� �Yby-�J$k?A $k_2h   eachm s��a] tens�duc�a�!]l� ��sV n��i"lo�ZE�5�1 2� �qua�or�� o ar�at! T$��Ua�u�al��� � will� CirA�^2�5�� �8� 6Himultaneously (see ve). Apc&� �*=��g"I_�� !)gǭ�!����sea�m!j�� fd�in � p��a3��ioV )�!2^�ar"�)���$ ?b�de� � !�� led, e.g.�"�� s, so5FO9 ��x M�9�is1 AYZkconcepE� LAP�� f<��$Makhlin:00����Zh:02{���,geometric re�� p.�" �Dtetrahedron, refer��o!�( a +B%�wbe tre��"�����.UhG n �exaX���J "e �.�h]�a�� i [ $as� I�B�y&��`exploi a��toSپstu� g�OA��Q���� a ty&�m�include����B%� ���rI�� �#� A�evb .� Q�5�in< &\"� *� Dsolid��O9 s. \sec�{G2 Z�:5�a�.j 0} \label{sec: >}"h d�^| 4>�s E��M�!���"J ��!�WqIs. j &�"-�or a�/lG ?eLbe writ�aA8llows: \begin{eQ"5$eq:t1} i\"h = (H_d + v H_c) U, \quad Ub", \endH�-$H_d$a0�}drift.�, c�" 2 A{-">-K. HS Y HCy � H�#tia�ˡDa� n $\C^{2\!A s 2}� Upon neglAIp ��lobal phA�,!6�1���!m a*� $\SUB`*!S =\{ U 6�h : UU^\dag = I, \det U=1\}.6c*}  task%ao) �-+-;at�gd�"I~\eqref-�i�>y � $)�$a�Nk#B` . Not2 we���,icitly subdi����S. iYa%���can�be��d, E �c$!� )may&- �K�E6 . T2 -q�e�f� y� Eq.::�!XfeVAMsta��"mBE�wah2}h a\sigma_z}n:�}46DA"kb�� arguT. With�lo���M��V assu�A=!` =a_1 �x+a_2 y+a_3 �m�  x$,  y$m� z$e�Pauli:"rices. W�p$a_1^2g4^2\neq 0$, let>�eN0k=\left( ��ma�x!W� \dfrac{a_1-a_2 i}{\sqrt{2a(a-a_3)}} && -a_1xM2+�)}}\\ ?WC}{2a}}&61 M��\5):5*}�6a= L=O^��I stra�%forwareverify6$kk�F�'�$$k��aZ�T%�lso:M$H_dk^{-1}=U�a� Then%�tA��kUi�9�Dnarray*} \aligned M�_1&= k�\+v�Y f U_1\\ &=y +vkH_c  )U_1�!UP {eiw� � recogn%�$M = H'_c��! pu�!(i�}���a�(\�52})� "N :A3"�$=Js.]v� �by�$oed�ga���^[2�� !��k��$k)��!M0�~ "J� 6�.�2�$\sg � .�'6{ If-��$als�appli ,M�v=�:B2}�zeYnuT 2�3a�Mt = a �� N\6V:x3}!�% $L$")&� $$2at)=e^{-iu? t�WW���=� J\��urnasof6s.  lei�����9 veA�%+  du�+un*�� $ alone. now�P*�$-*�, name�a�;E��U�� :4t�y�'yF� �-4!�U_T=U_1 %R1} t_1>% } �-egn(�i� E%!�4reflexive, sym|Qi�i)�5#�!x� U�he �+ erN�"n � .�#.1Vn �8, �6 su"�2"ni6jz/R~6�� w our� �(�+!%to �nt=." ��*.:ce fesj)�%~" #�Ct . QB(figure}[tb]c�"Tr} \psfrag{x}[][]{$x$y y.2 �.3phi]0 |0.0e11J4�0 \�dgraphics[width=0.25\hsize]�1.eps}�� \cap0.�&�M��!.c.�Cfig:b" X-\�he���$-�^Q� Re�A�^l+"�ɞ�b�f�1 -( =z_15r +z_29b��1z_i� �lexybers � re�-ž $|O ^2+|J ^2=1� Igno�)a�.6A�a�-L 2x � p�  .�=\cos\� Ik}2� +e^{iAi}\sin' &{2}�, o .f ��)nu� Q��5$Y$��a0$(x, y, z)=(v�!� phi,�Jn � �()$i�� -�!�ichA�*�/\emph2�}E\n� Fig.~� Y�� �N�]p� can w.xHopf fib���a map!0i: S^3\to S^2141 (a�)=)! z) �*IMarsdeny0,>] uaeq:hopf�� (z, x+yZM~ - M�D, 2{\bar z_1} z_2)"RW�!D*� Phi$��� >��&1� 2* by $G(U)=UUiyQ-�65morrespon�4r!� south poln yv&!�hen��.� �.U Jh �= 56, *} Fu 1r� , if��ETi- _1)=�U_2)$�,1J�}�R map)to�#s !�)�)$mN.C& versz i�'� �4roved�&��4F����&� r� �@z� �*�,�K�"��t�,!all�'.f t�� by � �AO:z�7R2?&T!L6�!.rre�R:� N�� �b�0�!"� :�H1� Uk �above%�"U4�-�� �UBE3 IwI)Y� Z.4 Eis� Tuq�A� !�8.�-Y�s.��trs�2ndE�1� � %S\���7J� rK� >����$2% ��. Apply L*JtM�in"�  6�e��M\65 \tilde� �E�B�ktC/9G�$�e]on�ep!�to ��� �* addi� �im*� $tD&G9!'=� �_zp��:aiH"�!ll �!�%���1�`$ �&�O*�(1�}�� illuIB$ �a? .M:��  a#5si�g��M"�3q%'u~<s subA�!�!��ero�"e+)�� $A/2 �4(\omega t+\del�* . S e�eF ults�below���-ni �e:) &�'iK�'&F � ��("�#!�9�look ���$%5f��A�mad� labo�<y~/, *b3'�-�*r��a�(custom[6� comm y.o NMR,~ usua�)ng!i��\5A�s�ify�% an Ia�*era� �Y"�:��6��A� .��l�)% 2�b�o�e �K,�a�i&� ;*�- >e�Fi�!�-L6�. As no���W,p�"�A��0'l�)gat*�: �# =k_{11}\oss 2}$Q U#%v"�"Fb ��2H.N1�/e> � %�,.���P3e�@ %Y�r>�+iheM=6� � !� %.�6�� neard�~\%4�.d % U,tl�3m�unter-~I�&�m�+W4��0��./$ZD#�0d/o�B��me��zl%2o5$A�9|9r !�iM#�sn ���P2-2J��:!)"7*!!A�i�!�7. � is :�,�F�.O/�'i&F �B+e�#&�8�Mrs,�!,Electron Spi�)�-ce (ESR��O ato�pla8� �4orm�t0)�S� direce��>hel12"n=:m2�.ա Nor�,T-N $x N� Bran�C.!@|5pi 2C~�5}�=\bigg(�{�$ _0}2&�+ A co�H �J,xK)J� A����E6�5}�{2�ce��\sim _W*f�=�"V�gI�to�95�� �2 2; � (LaB)&s04�iz t/h�}U$� nz &��.�8&-K-J B� !A�!zx !o  - |y�n7)"�& h4 "lBj&r i[ �+g) ]}�-#-J#\\ G%bHrG &\\ 7�":t�"�5WSia�f .�ce"�/)���2���� $e^{\pm �N�$"�2e�. fastT/a��t%BLN-$1ey�6e� averageS9tl�:�B�6�#��a�Օ (U�wave � xi )��� A�z!e`~'6�U�=YYArg(Y QCJ�M�x+i�(yoigg/A}�&�e�jT/��}!E&�y�)�lT&�!7.�2= �}P�!x�q �}h!z8 )U_2:4 3 Jw$.xp��>��C U_2(�({A}/4��$+m�_�)/�)t>_ *} C�AA&�4�AE�4&L.8�  ( m M`2�6 ion)A�F�as>�!}=�8} �I_f% � t_f� .� ]�"_��{}.PB��8ioGi��A$�*�#� ESRe�NMRB���wQ�'u0�Ik*���u2I;U� �a:+� el%� � Kion &��$�D 3��&�(~�a} �J(_f, t_z)=U(!�!y-�`Y�$} =�[��j�()�-�K_z }C } . >�!5langua{<� V& ?� � effem1he.q %)(�-��*<K"�M� l�oB�&8a}�am��bou�,e�=(A/2, 0,5�� )$ f/'B an4i�on H�*=,j4 +6 Ut� *.�t (A)H*"4(B) sit�� s. F�tA��>e, � .$��\�& 8 (]s$ z9c�� �H�v�4unctrl} z\ge �!C )^2-M���^2}F�^Z0Bm)@a�sha�A area��BS,En�H���D�Kny&Z? tu�a2m�8 s $A�']L"j"s�@f#�. C6?>achf6�I�� ear-5�N�=97 all}6y&� . To!owF�j#*�5E�4�����:im�HE�) �Q,=](AI ivKe"� �2� S��<��&�<�� � (tabular}{cc�n� zj z$} )r� n 1\footjw $"�2J��m =$z= n� R��^!32*!2A!&\q�.  "�!R"�f�.�B�\\ (A)6�(B)�1� ceJ}&�!�R2�.�Y� 2�,$ &�(8a}),�Ta�S��:�Qȁ�U�;�<�Y�6&"Ut �f#"�Um�ng�7 exac"?���2 "�&.X2� a"�L2 �A�3. �21? A2v:S ���qZ&@ 2�&9Y �hL -i_0^` � {2� -}��OFNOO T; hand��t:(Euler's ZXZ"NMa�� an ZY-�M1H*� b]co�CFz&10� �'Y (\phi-\pi/2)&� -(\pi-B"x} � \gammar\ &{0in>�10�#"U;�Av�wo��c�Hn���15"�< $�D, �:�mpaE$Eqs2T09}�.�10�#ato q� =2�*0(Z �R�18�-�:*54a��E5��ied*�[��l" 11a} {!)�0}+2m_1\pi&=& "�a� },p/.AbAQAFF&=&�Q  >8 c} -I5t3 t� -|}+ "c�<% $m_1�m_�< $m_3�#\Z �,m_1+m_2+m_3$�feveq:Any vvB/ � $2 ,�&3 ,  $t_f~Z BD!l--.p.1c}!�'6�3a�V�M#wiGE�t�D��f+� = >�|�2�1cI���aB�1:23�t_z4A@+)�IG+2m\p�1�_0}5�� $e�'m%�a�tegerL6�n�*:�1@ J m .E� C!� n�Eimb�6��o.�%�:; �-���*c��:it�9 �6�)D�;&�.2=F� "�=�[�: S�ar*{=��P>;byrnmv#>0E� Z�� �é�.^2���F5Kf V�}` !�.�O�Dq�t!V�3n�PlL�nb�)�addre�N�L� +�� ,%_ 2_'%28sl54l<fJ c�UG � off�S�:n����FyGS�t �1y|Bum�C �Diz�%c�C��QVQ .�D0�?�o  A�)�YrMl�7wO%"� A�he���Ka,V� $ ���1sGH"� NMR/�"Ja)�pul�PA�.f� ng+eris��� �tA�]�s �"r7 �6y�F :&2 �m.�13����}�2�+��63�#69c�$"��I�&m&asi N~6�2.� +4m� }{A}phR� &���� *} H��h r42.�Tdecre=h��a�� au�ٟmekHbyO@9iM=aHWZ{�3�P &S Non-6�$2oW o0�P"U F�e�:.Z ��6F>�%���R�#6��� 6GO: %x&% 2\4}i �[ �:\DD&"�"epsilonB�6) +Q� {A}"&J4kg]J%.�By * �&t�Q_2"{ y} �9J  %k/a�/��/��N�#u !>�%i&c9] �c6�!I�B. 5} *Q!g[)" 5:mS%0 -/ 90 ( \zet*"8(n2x)j]�:�=Q%$� _0�;9^2+)1^�$ J"�]N��2f� -�o=G@3ic��*bI�� til��+%#!�ari�I�or��&�Hemiu�e I dot&g" itto��. Le._-q_0 &�z} V. IN�D����r"� agai�Nk>(6z2K A 4e[E-�V�"-fz]E. ��_0)t\3P �n#yEK ]U_2BJ ?AB�Q^$��"v +F9,� >�6}��1>��4�A_0.�#JC �#RL�: $U_3824 8y}Y:� fj7} �h�^8.63�6R�� Eb ��� ]U_3B�Fin�G2Z?4�i{A�5��5L<U_3)i�8�6�9*�?"�E_4&�21$k `$��)e=g[ �xe�5bi��A"2h � \$eEa"y ��n26�L6�3#��_4@2�t, �$��# &e^{&�#_0-t�)�]} c7,u�F--| ]�:Z+�ZF-Z&�W �1B U_4I-R�@} ��L���� ly�`"Xx?eD�J�_0\gg��A)�$.B�9Vt�� p�?� &� R�20._4=�>{�A.z�e!J�"#"g"~�1�U_4"#aoQ\A�����] /(2w��x>� :4# �ser� f��@)�i��*>#&TtoB�5��V�_! N� q�Ea�z!!�"N��� [#Z<&o#b>m /2] �> }I�{&l A"�previousKmpl� kE�A�A� edom!.&��&�$��z$ {oN%#2�2i� i2��. � ���< *L d� b"�K a���B%�� z# �T-&� �����%� "<)�z&M"Vs�V6&� "2s��s %,similaO�+�%�>%��inB� 0+ &�kU�j .��* 24a"R.*�\24f9-�m�5A.2�cNE@�}&� :ZZ�� ��A��1} Ҭ $ >�!YI .�24�"�~_5} �t�bi7 p*�Q \pi{2�.A./v ;$ �{)% ^/ъ5$�1$$> a�T�F6C.v 2��i_�,*4:uZ��}JW�I�X� a nv%VH[$t�R2�VJ�91�:btNe��1 �m^ $[v_{�v_{1}]��A�@~e[E teg�W Bang-m`6�p�GsF�� 4 switches back.�zth"�.two�N2�^$�B  1}�@*fn�TuE�[12>/) J&)�2�!�� }F7�(�i)fO& doubl4t�D�R!*1'U�& p2 E$u�3Al5A5:��F�ca*���min�pHC �c%�ing�N%I��a�("0J��-re�#ly 6G adop�i� mewE��7Uuin�8��Tof �3%bup#9of��niN5*�$Viola:99, 02, Wu  Byrd�X� .RXper!l �eb�Z !�s�0D�Qly g8,set��i7W� #)%��<61B 2*�Ue �,e�*e�i�� �-8�*�t�Y�7*Z-�3EMWD<-AIG�%9-2�� �.(��2�2. �U"�*oR^3v� B��QRT+$v_0=0$.ytwiex>�=0�� $v=vx!w�g7Z li *�*�2��H_1&=&��H_2.+v_1H_cV%l�" h1h2�&^P}>zU� 2C6�V @ �m�8���87MH_20@4 &� b ABby FE&�12���"�k9)Q0� fg:2�T( H_1t_n�%0H_2t_{n-1}}\c�- $3.$2}=N�M��2=v&)hHi�9%da~ �&n�]�h9m�-� p 72vx\#- tr�9 �F��Be� 1970'�+Low71, 2}. R��8, D'Alessandro ��i����m:)W�� �l�E�'Hm�@he&tgz��@ �s6DAl02b�$T2�V ���&r�AEI JH. _2= um=b*�Ub_�y+b&�U:�*}� $kA."�O�#�6�J$ $!!ien�:�' } - �n 2 ?�cos=0:�} � %�Campb�yPBaker-Hausdorff (CBH)�� mula-[ Warner:83�$:y"�Ku":��*K�C�kk9U �U�~-2&=k H_2'b� � } (b��))�3 <0@=2 %Cs9S"�.�;b ()\alphY(M2x�VZ�%��&�b��^2� ^2}\Dand9�in�9�&�h\l�5�1,  2LN}&9�.'�O^{� 12}uMJ, ^2)C9���FH_226a H_1HQHgY:IF?BY��takI1�o�, � ( "�Z&���>��in*: "P nD:�*���a�Y%i�*} Wi� &=&k�Ö��� 6�m�e?}i5�1 �D2 FK23k2r'�`�In&g1C�-nH &[�)��"�X*J� 6)fo&&:X O'&s*�X)p*�I�2�eIH 2�g6� ��*'q.�c $I�q�pi}�+weEj2=b�7xz �.&�bX�&�p��FI/ofJ��E�� $� /� /*}�;4b<4"<3.'3.?U�!33�3 �3SbZ�3Rw�42u�4an4I�4b34*�33�3 &�b�A5A_1N hAVA_22VA_32�UA_425 �A_52665 2�4v��C�4 �A�4ua�4) (C��4E2�4]s�@6 }$ al2�9onH �"eL 0-�*. ;Y &@:zRE�4gD|#�w $_x=a���0B)$;�],$�ve R� �� ws �nd �=+4 � � �&4a%Iy b2<c:Q2� ,ached6�5#Hing��5.+2C(&vr�{q'b\I� �Or,T+ Ice�rJ$�� �W|��P*�<�BU ��tRW*�6 5VR0<r �:&>7fE\QNEI*� �<���xa�Min 6<;1I}(AI�(B3HA�^c�A�A�%�1DOR�!�1f: i(�tof�sY��vax|"�Oi`b�C�T`,�"S�0l ��5*�5U.�R"a *V.�IB�V}eack�/fo>�q�7t e�=Iw%AA�&�.< � �i$�=�n"(r-Cm!�=y�Bm�*�!�s. So��%&M!� �?/*D�1=�e�ClyN!m&�-�lb�im}[& "�C�HadamardL]"�x:h X Sup=�R��'3=N  � E |a\�e3 R�> �two6" :}I>@of�*t  2nY�"�d�"��H�2a � ��{B 6* zBx�YZ We ai� u=!�2}P -�.1  U_H� 1�f}}\&g F�I 1&1\\1&-1�f  \]$ ^$6W*}4XI��*�xM�ͯ2� mjeKT�ZI�s.��,d� 36�\-6�WH�B2 (. Computing�GI�.,�YH)=U_H"BV �>\\r::/*�9�'6� �[�%- �tH$= j ��"O: \ph\Ep>bb:T6�s�.Xa&E2:Mu]�wo"���yQ>�$u�]e"�C��A��4���[rm Fk 7u:�eg}��Ce>�:u2LMDz(���ov �B2� H=-i- Hy� t_2"�F!�$1=9.90/&C$t_2=t_k*1{2a}u{i%�q�3}}&x�D6|eg}��+cl�R���O}�,�a��6%2�&#� at mos�re*� s.ij ��c"� 2� h � U_H B� �� 4� ���er.qAwo]1d �H��"=�sųE! :�uN6� e>� �1��$6_a���axtw.�~=�m�a�2$� ��.Rf~�is6�QeRqm�� B q� $z��F��t��: .l �Z�6�=*U2��toE��$ >1��-r�"b *b ($� $)!�M�d9f;١scX�Z�Yk&���=� �b[�#�@"�gnot hs ���q7 .��a� $A_n: &o C)a�'=[�8)�_n,p-�_n]$,��"=�+2(n-1)�6/2- )�o ens@��1t�-t�C&�!X!,:��&�QNs���8�'%w"�&��� \ge �?/�+#in � y��; ����~�'�[U$\lceil !.s1\r$]3�#er�e 6 f�I� Ox 9i"��qa+�� r�T s $x�m!L�es�V�% to�ot � y. S�(�nq:�)�/]$Ue l����s�-,` � �e�.��44o"D �B�&� !!%�#'"�eJ� 1$a ]izE;Q�iBv#��!�hR�)&�I��1 &� ���"A�t�%�!�!2}�&�!� � *a~�*y &y�I�^0 =?A�f�h;3 n��6s F} I0>� $U�H�6�nAt9� Trot�T�#&9$Bennett:01,Dod@$$, Jane:03}D!� e^{i�+�p=H_1 2+O( ^Bg*�'��v�A�c/&�a�# ��CF�K!�Ń���Hmanne��Nu3upQmim>iHU�vM{g$sUZgVAJb �#99}n7ofAY$s��"x /DiV�Vnzo���$@OM7!�$in encoded"!f*Γ.��%'ex��.5A_DiV�~�.ri� ]6" M� R\E��a< >�i�^j(� %�B-&H �by�9=6�L]��Z� A"?��H�}� �z"Zoutq$dII�^�)�q�%W���� four���re ne&ary, &U�#�l‘;n�A "QA"�w�V>�",6iH �Hhow��� @���<n �[U�6�9h�OoI����.���9p6N�e�o)� $g$-�engin�f�q#Sp�eU.3�' &?)�fa�:��:�j'.�ɸA.B:i*NfQ�&( z�,6�~&�By�*�~W�����m"��~ two}�#q^2{&F�! .�ŵODZqef �e�2y�i�=�.{��{�!N�M�*s�k,�-#��nowAr&�? ���N[. ^ (l2�4 .�E��"�*� � l)!ٮ��*O"} H=g�!�& \over�yarrow{"Ac I+I\Lc g_�6dof6+S:."�HZg� he vC�1s�%xI�%,# �Tf:x{,%�($S=\sum J_{� \betap:9 ^|o�>"(t 9}'{(}^2�L �$ -� +$�_q  �� \{�p z\"�U$>�K; .��>�fst"�+co*�M4$g_1=[g_{1x}, y z}]�g_2 2 2y}, g_{2 �( regar�o.``g�s''n}g�syX4vӠe�-6-�agi� d+���#hlioG�,-, bits!romq|&� &|�� Zhan&��\)��e?2s�-BV�l{>8!�"".� �G���|�pyu� }uh1a�kS>" =J_xMPxUmx^2+J_y yy^2 +J_z zz^2"�$t��$� O��� ��)�!$ body�>[ 0$Se�always � a��>�����hyXm*����!�An N�rel��QB.5s(�WMM.�Wg�-a2H�NJ_yB$J�z7�I&��� U���3ontext.[*/U��!e-�1^* ,ͮ|x�fee�5��2.� Centrcm�#:mlis�&�I��H�];K,�ZU�s $0E$U_1\in �y�� �v ed {KlyMt}^NBڝ+* :� k_1�b k�PR��,aK2�7SU(2)�j&?M X�. C/3 "���ce2���m&YrOq�pl�wI�k2h It w�)�  i� 9�) ]�.�45-f u{\%di�e-to-9MY�Ių\�2j], $OA_1A_2{A}�Q�:o5}, ex0� n it�5 se ()��AU�M�� 6� �Al&Ċ 2Wey" )a%��!`Q3)&2���5gToF2�!>�!q}���Jg�m�)e!��Sjiom��}�M&�a��sa�V c-Na�r u�_�xegit*?.�g!�ŴN*Au !�Vu*� IDEzly9V�~��� Ry��&���p�� .T�^='��ex4s�!�"L ..$[c�,$c_2, c_3]$A����uX:*+���ecg�e" g334J c_1 � o3# g$4%$�� %3&�H2&8 2 3\�g8."�z�Blmlv :�;c��!!�M� F#�te2�E"vA��NG. As�!Y��]QL$+e�ro= $H$ " +aa�inu�@f�^n �sǮeV�EW�`. A�Qy �lO�:5��F2j�t)$> is q�1&�Xz) .!{!6� I3Psory�_ ?2�St3R#�� v&p y�$��z�,J��q�.�. F�v��� v2�.�mt*%�.Q%�to��@�"�U-A�e� F�!� �R �5� . Se�?� [92"7 \3�&�H`M' '�d2J��_�u"� ��6�� g"�a�R6in S}=�}� }AC��7q� dealE4�f!�!�p�t, R�� of)�mb.�a`:�rU�e�h�e -�M�.\6��]""�BO��c1�+c!, ,c_2$},c,"��h,h,O �OuB B.BL L)�#-5N= "e�T�al�2|)y6"� m7 F9�JnȚN�U�$*f��. Pi$sEaJ�� l�9edCB(��$\pi -��geq��� 2 3 G0 y$O(�0, 0]{ 3 A_1([\pi:c"� z )}r, $L(["�#Sm� CNOT�'�Dx.:42A � H SWAPH. "so�e#:C, �u� 2H��ai�>EY%�? 9�erqsitRB�l� "ם m�>2�?J Os�$)�flbs-�R ��&��& * ./.�&6�[o�r�|in�edih s�{to�tG� ��, ��ary���u 6G2�J� 6fAn "�*ve�^!3� � seek!�2_�*N 1�* g*FHam Vr4@��� �l��Qpa�{��5&>B$ay�1"�*a�!�n��XBg�?z;!���i  -]�@ed Vq�!�A%Sv�&!���`4�c One�C-:n�B��B�E!yhey� toge*��N>7-x6�I1� �3ba(�C� e��!��DlC-(�Stsi�2� v�[nt, i� |Ech� Schu 3}��zj& � ��.L� �A�J�. Mԡr� discove�[a new �� B��isIBmaS�&i>�=g�six2�F�-\!��8k!‰v�&�y F�Q���E�*9advan�( sNRV1#1iĤ*� `circu!�!�> i�*H��1A� BhA n�l%وW+IVeof M -3b, 4}a>"m��Y�� ~�M To6 �e��Cu��5�J*� �mp�t��H'=�?&drL.6 � R� �8� �� $S��.3..5g"  (is .`m�s`I�K� =[J�4J_y, J_z]\, t$6`24 e Ir��Q�� �� � juga� ��C� [�l�}"� P  ��@. w!4]��ai� d ^=�&�� o_��*e���b;na�EA{�y�icge�n%��.V�:nyc�����#words�1'&�u@.Nz��)��-&&�#A�2�-KaZ&-E��ށ� &�J�F� &�hE�!�)�A��mm%�!�� �^ drop<�h�5& �@M;5or���2 $� D x^1+x|R�$,*X!�i .�d}!-�superucE�� $%po�"��Yous��b�bual�e �c�2��� ��&]}:�0�'Ino�� �6)9u �bsm�`s!�p= (%��� �v��Ej $ {�2{b3 �J36 f1^byX��lex m��in.; -R� G�${Isotropic)� } !�%�s,� ��er�Da��J&$I !w$=J_y=J_z=Jcommo#IwoJFFh��ar7� "��^E:!vA#�pb �� -��S�ed�=d&�\T w*&�#8}T�"��-Jx^2,S]=�x quad�T#y^1#y^2, $ #\ �T%z%z%:e *��"a���6!�"Sk2�~�$10} & & [g�dotZ6$:�$1 v�$��D0#2�6?)+#1y6;)<1z64)e=*1��*1, ?A�A6�& �toAuf�'�l��*�5E:11��,Ht}�,�%Z9t5; 7z/!�cJS*C� CB�x :�2v4�- 2l ��O2H$Sz2��ha�,cF�?�9!� � :Ũ.e�f-Vey E�"8 � / 3FC���S �%�"�5./ 9�& just �� (cf. EM5 4!#�����We�ha�xi��� 9 �`���to��"��wom� ��e�M ur�mk�Qpvaݨ�Dpen-E��S�#24OM�wheT��� 1�,S'y�Z/o+t z�3hu�'*�& � embl�e �)1!Z. /..Ums �j�\�#{SWAP}}$� k�3a=����D6�2r ��&� =i * a� i6���" �"S � � %��.O�n�'�Wof)�]�!Xc!�!� dF+�[2�ɵ�&�d+�`n$ �!� �6s� ~�&e�"4i{C 422D.{�5}2�FE p(�G"H?26HBE>Zt:|Gl:[Z�b {-Z 50mmv�6 Ŵw/2O:^� u0�����&�  .� �YC�#q� AL 9E�Z� /a�%R*eR�v � F) � Am�/�u���nU� .���g`�x(���_� $[g6'�0]$-G��1~l. �$aD!��ot>�f>Bur&�\ons6�;5-��x;s�r� �2�&� � �s!z2$&�*6��com�6���@=\lambdaX* $B �U��e| Ĝ��is O�=�s�T�ing�I/o9�t~�:� . Aft �2�Usi%B "f�\A)A�:� M=*��,z�� ~� p1*mS �&= 2 J t�$c�$c_3=|�$5?�9 {2J}_�$ t)|l/q$i�*r _$ /=qC(-�(-1)^2||g_2|!� 4J^2�?2 $c_2�l7 ent?�9+ -" 6O.)#�(ML�s�&<) Fi.�5� a!\a9!���5�d is t"L� 2!%,�$6�իhW)�stitu0�a�S+��'1i�(���5êK��)���C&�yA4�L""��&~w0nM<*�1} � & pg2Jt&=&Ōi�L&�8jz ) |zIEU9}Q8ba posE���eyz�/�KEeh2>D+[aA� m� !,ch �V�� =a�$t�D�4J�/RF2�<�o$ ��9a5��c1;>H::5} V(=(16m^2-4)JJl/%6�Dp�w��� ?%�� �ɿs �Q�"��1 $J�File>j3[��Ja�B5� !�"�� e*�I"c��i� U�y. Itax�es��o�*e ��q�� @z=)�2��@a� &*�+,}_-!�:�Pu[*;,� "�  a:�JF� A� �:*�a�%E�$J=0.�&cho�9 $m=4� e>gp5"�p*�]�5�Zv2.5>*�^�ich%b�beY v/$��$,(aHTf �2$g$���Á��1=[4, 34����X =0.7709$,`m =1.6��nde��� $t�\piI&� ��� np\�V/ FƗ�AnYKq34uA}.�h AQge��&�a�(��eq:1}))�aV u�6r5",4�Jta�d)�ncoE��, many�yto5P:�T��Cm?)3se �&$*�Imamoglu�,"4aF��ng � eH�+SP�$Privman:982H on heliumm2Platz<> q!�<��cav�. +Zhengv=��&�M%�2��A��ach�p=�)�5��h�i�!a2M TX�<�Dr�Z diago%~!���YF���*� }��d yy71d9_{yy}=�7*h1=� 2� %2z%2+J 12("��<H� -typ>Neo�JosephX$jD L-�.�� M*1@E'ls��i)a�KJ mi%hdiA�-  '�J$�!�*+g"s~ , Twamley[ I����*X��O� �2s)��lO 6/1��6U".@�H{xxa�)H_{zz}$:>n.8� H3&Ey1�aA)=�E)2"v2U� � hB�W h"h%Y�2�.�J^� C*%}2�"vEg��� by�C5WOd%W�!�&�~B9yy}��M�'s��c�3M� ��!��b��E  i"4�-$UWsiI5ZD�� �% "w* eq:yy83} �2� {(f_1!N^2S x^2 +(f�^+  y^2+$ -J^4K�# /},\nowS\\�=&=0� g_�2bɜ3:L2 I)+J^4(8x%�w3)y^2.W& v-�% xMm / .�Z��-/�xb3\u��}\ I�$y2-C  $f_1�aE x}^2mN�+��! 2z�A2jA-jAƐ�J=1KI�<��)�&s�� Utur�Pat� ,�jB:q29�6o��&�.�.&tg T m�("`>� ���,2�J$j�(��C�W� v��e�s�F� �. ��*-�)9w ��mon erro��r�%protocol� W� �"I�)� ��hB F-$B� 6�'g_3=0:'r)T"1�f�#1/ � \B=[^ 4�/I>m $� �J �X)� et��F�F���is.F�,AE� %{!��5� ��l�%�ta'�:B�7� 2# 9# �{2q�a�1a� T�-�� ���= ' 2}}2�W-)��:Z �7X2^2X-�] \mpRW,).U:�gre%�i�LelyIqso�(� *�p� s �!X�:`N� "�X*� !�{iWB��N��"� reveal�.tN.�X���(�Ma�eQ�k� �\1.675  $f_2�* + �i7 M���<8�w*2�+2*y�� nA� :� 6}.*R(1a�"Jy�"s at d<)� a�ba�'pl&�2�.�. A A�i�1 �&�I"�e$a!����8c�c�)�1x 2x}=�OP$��z z}!f�)$J=)�^2�5��nex�<,J���B��`%)Eԕ��n��1��*1 �[ �C\"�ÅR��>!t�N2N& .��:�e��e�&z �}��"5 F*}�;nBS"� ���b2umET�bm1)Gi�=3.255��itha0 1=0.9516$)�eA .949E$Z{yE�4,+A�Uޑ[!�!�c�Z![m�&�> D �� chN�) LBS9 shorI�"nU=.F�eBd8"�.��V�V�Z���.�TZ���p��Z�:�e~�7n�M�u%�Vx � �uc�;" ��!*KYY CA�B"�Lm/ee:�� z=< Q E�.@� spec���s6�6>�.�+ Weak�*�:f,q�i�n�9V�j51>�2�}�� 2Ekw�&�* �DV} "� �~ >^ F5* {8002�*HF:*{4:$�� A:x�"�)8nH b� H �!��n,�Y��R Vk 4Rin BL98><:t L1 � � ory% y cltQ^�) 2�.�A�R� 6� 7>� � a �l�*�+����% $S�T"T&�� �=/�Ɓ) ��+�kinusoid�urv� "}�B�}2�yy9�*�e�Ec_1��J_x���q�Tyyzz z}} я}1>} 26))p(g�BU0 ac.B� '!�� �+p��� j� 0.ȁ6� 6� } Hered the local terms $g_1$ and l2$ are one order larger than:�I interaction strength $J_z=0.2$. From Eq.~\eqref{eq:yy96}, we find that tz��must satisfy \begin{eqnarray} \label ]�7} \frac{0.2g_{1z}g_{2z}}{||g_1||\cdot  2 ( 1||-2||)} =D(1{4m}. \endrtSetting, e.g., $m=3$, we deriv)2 solu% for B 7} a)nD=[2.5, 0, 10.0182]9�=[2h7.8177]$. After a time durac�$t=4.1778$, this Hamiltonian can achieve a gate%�Tted at $[0.5000, 0.000p ]\pi�Phich is very close to!� CNOT O<. The Weyl chambA" rajectory<\shown in Fig.~\ref{fig:7A hereO( solid line3A�reA�Jgener�by!�, and 6dot�.I|approximate sinusoidal curve. Aj,istic applic)Vof)M�example was recently made in Ref.~\cite{Britton:04}!$xinductively coupled flux qubitsE%_ $AvA� neq  2||MJM#�Pf�Q$�R�-~R.$�Rurl^�0url#1{\texttt!O%8{URL Ipre`command{!\a� }[2]{#2} B!eprint []{S'}Iditem[{2�T{Barenco et~al.}(1995)R#�>, Bennett, Cleve, DiVincenzo, Margolus, Shor, Sleator, SmolineP< Weinfurter}}]:95A�i�{author}�5�{A.}~!1�<}}�!Z=C.~H.}&@ ϒ@R>}%�; D.~P>{98�CN>~1l�>P>>S!^�6TB:)Ԓ= J.~A>�I ?5� and}�@vH>�.M2Xjournal}{Phys. Rev. A} e�bfEZE.j me}{52�4pages}{3457} (�year}{a%})ŇiRVNielsen�98Chuang}(2000)}]:00��M>� X}:��>I>N �): emph9title}{Q� CompuC�I&C}!�9)�publisher}{Cambridge University Press,  , UK �!Snfo-k!6rkSakurai��4!`�WJVP J.~JB� M �RModern"� mechanicsfS;n�Non� ar S� s: A4 si��tabil!�(and ControlfS��,ger-Verlag},��%�u^9r�Jurdjev~ (nd Sussmann! 72! Jur7�1RVV>W�_HNP�6���J��� Different� Equ � b�1��9>��13N�72�T!G97-Gd!f:O�M��RL(Geometric cI6; oryf=�0-�Lp�LRH7r� Baillieul�78�Bai78�BJ>;J �QzN�optim� th�e9*v�25}.�-�519R�8r,D'Alessandro�DahlehŮ1!DAl01�D>.X%�!2�e�V�B� �Za(IEEE Trans.*Auto.����� N�46:P-M866FM 2001�M%B2{"Z {a}}1P��zPeRBd�7ZJ�2002}:�j Khaneja"\ !A:\ #, Brock] and Glas# #:��B( <:�VqB� �qn2��� SJ�V��� 63:�M�032308ʸBryso� Ho� 5A� :7�� ~Eag*� >�K Y.~C>PH+ RJAYed�]}�P: �n, est�io� �y}.7*� Hemi�6� rpo�6�y 75r)Niskanen.3:$A+ Vartiaine � SalomaaA':03�� A.~O>W@:SV#N3 �C2*��~M.qP:�*��N}) Lett >^�90q��nm- 1979�R &� )� 2003r�LSchulte-Herbruggen .�4:�F0$, Sporl, HAja�]4�~{ T>|Fp9�%V�B`��;Bx �1y5֖�r: : book� Proc. 7th"�=unw, Measur�j��ing2organ�:}{AIP.�U+v� Makhlin �T ��Y>� <:�uJ� ! �ea^#11�Em"24JH )����/note}{e-� t -ph/� 045}j Zhang.:3:\6�/{Vala, �e; Whaley�%:�c B� ::]V*B;��:f{%P�( K.~B>�1 !(5�U$�9n6Z 042R^�3:�j�MarsdRatiut� ��JJu ?�v T.~S>O �)NRyI���o&�\ sym�j�:$, New YorkFn19zB� 1YJfa�|198"�RBN- \�[CJ ��^ m�v(Longman SciU(fic \& Tech� lN_89r�Va4sypM�?� yLieven��L�e�u�^�1 I.~L .� C~.���pp�in#Mod. �%�0J v�Plourde.�> #, �o����D, Wilhelm, Roberts� $Hime, Linz� 0Reichardt, Wu���larke��B&!"~4 B!,~T>� �M�a�ђ;��Vz F.~K>�-=�T�:~5t�B:�!��:B)ܒ<PJQU�BC.-B�Wuqu��� BQ�A�U=umeVifBj�7� � Q~� 140501(R).��� Viol&��G:Z !, LloydqXKnillaW��L>:��F�ڙE>� �2WN�Lfp8Zy488Jw!hvP!��?3 �� �hN�r� Z 01230V v&Wu Lidar� Wu��a�eT��DJ3 ��M8:Em�207902R�v� ByrdN4�6B29ְ �8r89V804�Nvv8e9%9i�� .R�^R�s�~b~�J03b8v�Lowentha�� Low7��F>aJZWTRocky Mountain J. Math�n�J�575F"197v��(1$�2�( �� Can.��24:,�>71Jv�rK2oa.zb*zb��z{V12p�* <. LANL�p�& � ,110120n,Warner!�8e� :8�� F.~WAj. >-�R�Found��di"�&,manifold�4{L}ie groups2E*Kj�.�yC8v��&.k >\ #, Cirace(Leifer, Leu_1 LindX PopescR  V�/� ?�x�^' J.~I>��-� V MJ� �?DJ %!�>B�)U�<B� -��� G>�-�!�5C� 2 J��v�odd.�2:�  , NiA'emner�and�0wA�&� JJ�<��MJ> ��@Bb&B �@2� 9�V�RJ�Th!!!��R".�͍ 0403fuv�Jan\'{e}.�>�$,�v�0D\"{u}r, Zoll��aT&��!� Jane��B� j9xŜVf�IV;W>� ВxB�+)�F�)F!fF*N>%{� ��b� WM@1V!v�*-�� �*.�r-�5-J,10N��*,�.)0>&h/X Bacon, Kempe, Burkar�Ma+DiV�f�,V�B2 ���B�Ԓ;B�-�.��U0Naturej/40Z"33J�'200v�,Kat2$>M <, Myers, Driscol�S GossE!Lev0AwschE"A*9�UB�9��RJ�#��>DJ>��AAJA-�@B�!I�h D.~D>� =�a�F��cnl29ZV 1201F2�n�Hammerer.�>` $���2�g] �� K>8]��B � %L2b .�V��� � *��b 6232V�vJ q.�>l!,6/! %�ua�%��B:��B;�1!�1!�1!~9 ._ P:ZvN%`.�.#e�#3�B����������r�Zm #0V�3. #!�j #$Echternach.�>&AvW�0am�� ultz, Del�=Baunste�9 Dowl�&]C��B� {�CJ9��ASJ��>B�-�=SJAB5RC2e�wjaJ%�,:5�ɷ@�eZ� !*� f� � ���143�J�!vzb*ch�ISiewertu� �P N>� ;ֲB��ZS ��^ '323�Y You.�>� You, Tsai� Nori�Yo�: J.~Q>_ YoRMnEVb�B'��� B< �2�U�=�~h^@�-�xLos�&fz6:9�6B9����NBn�5Z�B 199v?6t &/� : *6� 3, !!Q�=z@��t"B� <:�V�Z��(���$�%�n$5Zp 2070R�9.nz6jn KaneY���BJ~+<:yU��.3^@ 13Rz� Vrij6a3>T "��@Yabolonovitch, WaJiBalandin�(0ychowdhury, M�BK Di{V}CA� Y�}Bs6 ;:DV�B�2��CBu��:HJ4%1�>Bj21e�>B�=R=��BB23Moh ��: )6 A^F���n�62:�� �%V�:0r�� �!evy�� BZ 9Ou�� �(r�� 9�52306Ғ FrieqC�F�:y # , RugheimUSavagd,,agally, van~J,Weide, Joyntŧ Erikssona� M�� B�% <:�V�B� ��?DJ� �? M.~G>N -)�@N[2`�FB&%�Q���N�9ق�n�^, 121jFv Skinn6�>� #, Daven�L� and �]"��AJ�1 a��MJq�B2��V�k����~L bT'8�T' f �r & �v 5I]^:99��� R �E� �KJ }:1�I6�IB9^h(6p/Y�͊114048>� .\ !�j\ Imamogl&�@:$!]" *�.4 Sherw� a�Fma�/H�7 B� =y���V���VB���QMQM^� Mcj�B�-�ڏB�-�2�N�~�b�0204Z3n�Privman2F28:�$rgnerb�A�Kv�UeV( %�cB� <�S2IJiV �Y�L������^� %�r 23Z�14J1~�Platz�8 and DykmaKa;�c;PJ�8A��MJ�) �ZE��8N .���96J�2��r�Zheng%=Guo0 �O��S.-B�==�3G.-B E�Z0��8Z�'239VHv_�@"� !i:# #, Sch\"o~A�ShnirA�}]$��B�" `:�� ������2��͊^@$Ny+!nr�TwamleyE�� � B <:i�]�r7:Am� 1JS7�r�SalisU��,:�!, �$, EnssliE�P$,&.%A�"� A�<�2B�::�V�B���:B� ޒ=�c%�c%�ne ��:=�*� UxmT6^� 41�.��Ms6N?OAArpde~Sous& 2:s$, Hc1� arm�I>�TBW��X>�H� %5[ !9vm1SJW �V�� !�.-�S!J�!i��a% %p!���-v�<4jv�=�=rzZ)15533J"�Hyet:G^ �e docuX_d} �j%% TO DO %Find a re�Tced_�5fluoresc�_ lifeIe%Discuss"F5pce between omega_c = h/tau vs _DgishYt`rM` �c2c"�c2paper..���a�[prl,footinbib,twocolumn]{revtex4} \new9Jv]t�H[1]{} %BK�6,T 12ptE%ZFs6d#1}} \usepackage{hyperreffbraket}2+amsmathBthmBsym0Rgraphicx:� gurukNcle6E�ren=- onu�f\\:5Schro�dZ \" 2� =c2T ^$mbox{Tr}} :� vect%� )R2>!�e_%�:=4Im}{{\rm Im \;F]Auc ^en4L,ath{\left\laUe, #1 \right\r%�.#insertT68One}{"�a }[t] \cap�P{Typi�c8nergy scales $E�fa_co2fime&$\tau=h/E$ . dF\"ors�h( Resonant E _,Ufer�EWd�f(s. $\Delta$,hH coup?&u�� two !� moph�(, $\epsilonCB9c�g �oh,eir first ex�a�eatGe$\�Fhigh fr1d y cut-off H s�d edenf\$J( C)$��5spin-bo�Rmodel. -�$1/ 9_c�j{2�_\infty+p}s. !�_D�itf%�_D�Debye�axb3xj�ol8��5O_sIiFl� 2's�e[:2dielectYsta$gdhecMi�gH-Iw I�e_(photosynthe]lA� harvVSnghOplexe�! ``BChl''QDlbacteria chlorophyll moleculMh We observ�e�lRP-G{�rad}}%Rm�&lo\\"Dm oth1ky+, s�Qs�O't all 'ge�;XiTest occur before radia!* decay.��� als�kat bothyB5� $ sp�hwo�mimagnitunso�lm%Zex!�lq=(t behaviour�t%bsA�)�;nmt�L FRETmoscopy��'su�gr��rCka� cent!7*s.5>pgertabula|c} \�Pe \multi�Y{2}$}{?^0} & E (meV) &)�$ (psRef \\E 300K#k_B T$ 250.16 & *H$_2$O2��\ hbarq�: $2-80.5-2C�t{Gilmore\\ THFRR^S4S1-2.5 & RHorng95}�-RU= Ph/�'6�& $4 \A�$s 10^{-4} d$10^4$� f$vanHolde98iPr%�BT& gpF 0.02�16! J Loffler97I ��IIG�& 0.2-%C0�4Volker98}\\ (GE]$�$arrow��d!�} & 50A$82�3}�=@A�Y�!�ͧ& 46-1D0.04 -85� u97J� Chem�;ա& |f- LHII:�E�0.3 & 1-P�v�w 32�a7jH��6E�0.6I)�F�-� m� �lr tab:� � Y Z TwoB !. B�� of $P(t)=� 0{\sigma_z(t)}�U>qgives ��loc�GWO �mfun�o � $t$,�/U�=0�`%� \ll 6C, Uq5�i }J# s�s and ��2�$. ``loc''� sqm�li�s:``coh'' damped co� nt oscill%�* ``inLto in'�ki.e.,��To�b�� $T�{!~t�:r9%aheP �$\alph&R d� cq`&V co�B.V �Venviron� !�def)pin"7c ktect\eu~}. !�tau��fe)8Tr m% sMex\b�SY�(-t��)!�oq?p Po�,%A�nM2�n�[ is g s$ va�s onlyA iS2�*� $. �M�_r=I�( /�� )^{\� /(1- )}$} ��u���q������5�&%�& Key a���Ref�� ->1$TaX&A�1 =1$,z $t"�� Leggett87�<$0<1/2T=��coh�� � mini"}{4.2c�m#� \a�t �6� [ -2 t sv{)$_Wpi)} \sin^2"pi {2=:� ]$��\cos f�cJa1�^�i���Lesag��9$$T > T^\as%Jin%d{ ^{-1} =v��^�GW },sqrt{\pi}}{2Gamma() )}{2+1/2)}�-Ypi k T}{21�^{2 L�$ &�1���$> -� $T>0!� �� tt{".9Yu��e��B�6B*� TwoBv�D� wa�siGvd� �$�? Le etail? F�$�.�. ����u�Bc2.5acm� > 1, !�\\<)� T \geq Io _r$ )�U� & Fe5e i�=�{�ij2���^2��Q�����F�N�T  $1/2 <1-%9!M( & ProbablyA9�ݙ� 2&V)}=a?�Y0 �iu�)ρ>2�?��FYEW0< ���,��W & QQ��� �� ��&� xr��X'} \Pa {Cri�V[U�t\Eofn o�z�2� Bypolar�} �{Joel �R�5$H. McKenzi ffil on{Depart of�Zics, *cp of Queens�1`, Brisbane, Qld 4072, Aus04ia} \date{\tod�~-ab ct| showb�1 de-cer& rq� gy9,1 pt�ly �ve"sY~bgs�yby�zpB��^allows u% u �i� ve c-�>c��%�pU� mc��� parametRDJ��yneSb�|A �t�{2[ cciE�he2. E� tes�{�results!zuld!possi�Owith Fp\otf�()2$. Althoughofocus5l�as!�{�-pi[z&�2�!�"Vto)zum dot_ Jdc9� e*�medium. m�Yw\m��s D]jQhe �a by{��effec� re ``wash)i ut''ASG/A�oaH)m�{*{ . I�s b?T�|at2i��~)�A5t(crossover fƂqOtoF}a��r�P0Zurek03RevMod�}. .$places lim��a!#E2�rofh"~�t�]&h+ 00}.� $G lengA buil�= E2�n�}e pote�q of biomim,s c8Sarikaya03} raiiJ�exploi�}lf X~mofvlex`?�U�s&�lE*�:�p*J�)@Lovett03PRB}. How{~�I� � prof,S quUons"�ApofI]Hiքir own �: , about wA4rol��umU�pla 6��aut . On�7delE\d�0�QT.�m9>G�U ,Weiss99}E� TesStunne6wy�s��35a\�dissipD bath����(��eharmonic�[ors (seW e.��!`eqn. &�� ��,dard} below)A�is s hq�us ��s �!Se�(Josephson jRqu�I;�' ?to pa�-i.�eqRair02,Xu94�m�IA7isH+Pwe�w ��6�9E�beF�ap�.�b�!�2��me�ws���^�Es i����=�E eC then���st3����BQ���O=y. Ourua�%'b�Ef�e��)�Jones�4 ��s�0��Z� ; Medintz03�WTfigur  "� A� 0s[width=6cm]{1�.ep{cD:�ɻ� gaps&["����q�caaXt"�� Jy $ duŃ!�]dipole- ��]. I�(�mpl�%�W6 %�!�insd��p��� ށnic.O"F�pnd surr��f�a6� �&_ depe#Xtv]"d)t ��1�>� t$-� {\itwf��:�a�individu�qhr"d �!��I��b�#nMv[ �� 5%��,�ie7 M�w��]* mayr%ʱ�A69>��! �Mahan90}:u e�y} H"�1���  + \sum_X � a ^\dagg� 6 frac V( �\mu) \;\\;\op{R&���z} H� %E9���tre@�m�H%�l�D)�m@gapY�$�|heE[^&nd)�"7qy\mu_1*U& a� mo#2��Xfps.+%=.dC1E(1O+ 1i�p��i�Ure� fieldMOn�8r36,Bottcher73} eriC' �H.��Wd�z``cage''AMcrm���1 ��a� it�$�&P"q$� �ya eachE�Le.-.�n �dynamicsA2A letely� if�u�q>�#,B �leq:J(� ) defn} J��= 4�.A��}2�delta :-2K).Yy� ���pictuΏf1mFZ B��be69poi�qE���a�|�$,FML Hofi�"012M>�unHI(U$��U��K % *�*�tim&#MZ� *E `��{maՍj�#"��(exceptV$s,  T���*��o( co�:r]A�j,�# �m>�-+�SR nB�Y� = �2�}{A��� _0 b^3} \�(��2(M�)-_p)*u&.{&B��b�8�$��'�!3�c�! �y*�'qLi�x.-� ��J.�.�-@n�6���o�%a?� aJ'dI�Hsu97}�7 �l6�)�:�23�5�%�6p 5�_s9�6( )}{(&J(.-() ,=�lg���_E} ^2  ^2+1�` ��-��BA( m��m#��:<(* NF(-�1�.U(�tau_E"�9 ��}.&"S)�<&�R)MAwa�t room.� ��se*���=C=78.3�5V � =4.2���$D = 8.2ps$M�Afsar78}�l8/k&@(tetrahydrofuran)a3yBw 8.082wi=2.18�"!^D=3n�&��(��1�R��pI4--40 �"o� ��Qbi7� � i�PN a01,ݯ�4"�!_E$!rt)takes'!ueo90$�'.5ps$.BG ���yprF�aQ�}�)w��^ 6Q� �_��,&� &�� �Fr-65�� is a� JA ch!7du�a non-��$G !`an.� 1����FiX� 2� )AR.��� basi��� ~portin>BBb�e�&�+t� }. V8R�WeT w�%�total2�a^e sQ�f%<�-*�� �� ="-���:�align*Y fry1� m*��6� _1�&^16X �2"T ^2 +�S \mu_1)1 n _1 + � '2'2'2o; \&�1 &�  ( �x^�x{mymsC y^2)I op{B{+ `B}_2,� )�H _i : {i,w} + a&# (, ($i=1,2$)Q}b. 4�o�,q� $B���$�B�N�N�2"�M�sto�E���o a�.��Vs suffi}x�% ar a�&($!20$\AA)�l2�>E!� n byQ�����0\kappI21A^2}{�$R^3�8mu_i=\Ba4{e|!I\mu}|g}_!^-�,��Le�i�2�� `��!}e s (d��nct7 ang�6@!M1> du�t� �$�$), $&`2rea��/�jxS-� , $R5�r5r�&y��$)J0� t�So�'E��� D� N". � fu)conven��matrixL0 �mHa&h�&���%- wide�:"�#eq��&H ^} H&=��"�4"�# {20pHx er \tiny Y"$ M �4}u�f+�%&&6'( �an�{cccc=,e {+}��V}  & 0  \\ 0 1-.1-1I6'0 2EK-&� >>) 5l�.4:�))# � \�),�� 5� %� 9�e�q�}a�!\p<1=��a�6\pm�({%w=�'-1�8{��C (a + ��FvA\\beta D (b + ?%]6l��U�D1�2$�9*�'One app� T�$.�a��+�8a�&��a�Z�e�� �sN}�y�t z^1+�]z^2+2)� � wea�)mmute*�}�: $[H,�N}]�� H � Z�e ��5��mo��. ����assum%v&&� c&�;C2�2?4j��� � �"P�$H� so do! ne)V��a�fh.� 5(�4,ly $1-10ns$,^kf�!i�Qa-_ly)�Z�L n -� \ket{\Psi:+ @wvn� ��0��c6�9wo&�.v�bspac�{ Tem \oHgs  a�e}a�����et2i 2e� �<� t�bJ�!�7!�=���.��!�Az�$i�a!��(ce-fre� ��2H!� a�.�*�*- z�u��8tx#})M%yen�% $2�'2$ sub�Oof�9�� ebei te� ��0of new Pauli ( �A� )]�Ko .�"A ��7��<��ya N^ � �Űx��_z r�\op{V����������Fn �\2� ��qB�.��!�]"N�Q S= 1&�2� L*3in� ��./t.)s�W1�suma%=t�2��B}��� \,_3$[a_{1,�,a_{2,�H�m�TM� just6i�*� ra�R� a�$ ir caviti�ana ��l�Jang02�4=��� aga�! de  �"UV�"�AyD!�!����"!��!:�!"�UxRrLB^Q3uV+! ig6rac)�"D+ �"c3� .f�+ �B �$=$ now�9{<se� ~o. To���e��p5q�mu�pecif���sNf?w��"D$!�].N� �Y�j�l�>�mVob�edAIq���Ad<> �)I<&�Gfo+�� satz��Caldeir5~Mo A83BeAfluct)�" � via� `7&$�40ec{V(t)V(0)}$U�� *} &># =\�62e>{�PR}_1(t) 0)� 2! 2F1212 1h�a41 2. (M5eNtC:"e1e\� K�ProA�?)fJ#ZI� ��g�r�1}ed/))R%$R �M:t)!4= 0�$";�-nB~�}*�S Im \�t e^{ii� t#5i �5�\FA a(t)-]%�= J_1^ + J_2�U }�9aZR� is sb$i�&a7pri�:��qbZt#��l;#iF b�"�'lika� dels&a(� ed��@s�`PRackovsky73,Soules71,�u, but� perturb"+ ��� Fermi's g?n r[B�"we ȫ� a%� mi�,copH% eriv Y� A-*� *]',���plicit!Sm%�:sy2pE���rm�:s)A�I�.�*� ��W.� �Ohm�u*�If���F,�IG>%Q_�4agB�"ja�a�)�'�17Qє4m0V#���8"�,,&>:�):=!)�"�=$�r�:�innB6q5�$0.1-1$ ���� *� stroTFoH�.}(i� mpar_����%@p�"^E�*p0or*�,Ju@Z�,.) .�.e�22� push�@p awayi�a+}��)a�mak� �Y:�Eone�b�$+7$+YT:"+Dx �=Td)1r>�l,E�t*�?$y@�} z�B. S��%�. 6Diniti�5ll(�3n2� (!�(``donor''),� �3�to� 0)=+�?��KI]�Hac�%K�]g� L"!�f&5Udwill cau�0�u9"�: *l eU/}c0�� �_A��of�'s ї%��eff�cr" wonv��Habsor+ ��)�)B��|( =5"' ,� sZafly�/in `` U�Iic� r'' .3�M�Haw1inY ar� X�ics�)srLX72 ba�*� wo�s (i)lQond�NRt i���$I�  G Rule)��x�%e� 5� B0= a ��In� OMp �H (ii)�1t!lr�,no back9����fm8n��E os,5�Q��u BK&F&:K����Mly �� 1meV%"l� 7�m$ImeVc$2TA 8N�)/})�%s2%�pa'!�.��2i�<G�L*5 e@M.'s�" trivFB :�.*� 81<2�$ne�a6� �V�\.s Psim"m! >��E!�A@ ��@#�m ��y ren=��cb�1&%2�2�5�_) � 2�f'.U ($T>�X �EB_r/*n�*E->�#��a,p,ana�alway�ղ:B ��MO�%Y ���oj_M�2P. "V8w�4$Q�� �a_6!@ T<)!�D$ (~� ��=�sh=:�*2 ��B��������0n���-��*Fur!<,�:�m�� �,��M�$�b5pa�=t=P�u�(- �reo��J�:69MB ��2,m�8%�Ta�P, ��-M ��m����I!�F�;���'��� }8�va(��itA��Weiv .%8 at l�?emh�urn<>7(c&�2� very{�(or id�; cal)1C�j_!i� �:u9�V �h"�F7�7,)4 reak down�(F? }. A*�>ay!b&.SA!�>�KN�82��oe��6!�()S�gl5��s7�ir # $;not"*allfUa��(a bulk sampUhe6�sh"�?� �3�*%dl=ot� .� anisotropa�af*2@ nois (Yamazaki���;"���>re)L or paig2W(��$anthracene+rs�~!Hr!�5�tly bon�7A�5:"BF�,m���toP9���@Nl` i>� i��"� &X%�-aregim��z <_c�+ys "3�� � n"Bl!)u%.}�E�������%�+G /2$.��:,� 6�cF}�cer�N e DTA�Vu-jz; #C?AscCO�iodaL14ose��As~O�!S�!lso2* �Y��8c�ff*ti�:�T5�%4eq 4 $ ~ ��wQ��b!�2T)ue�&* !�F�y�"�3�l}D�@t,o"�A\�x �n =@C��R�, $E_r� >B�Q�WA*E�b�%a��&*k pr�� d gs b� ~:r�!+Z �M$J s>|"�:�A�o � nver���Ehem& % �A�2ha �T���"j��K0,' �{ 1�$�W$meV. �M� LL$,,�g >�2�%:�'$dQVP��eb�\W�>u11�D!^=�c;� c Carmeli88Y 2� stud�s�\&r T�%nd0'deloc� ZH2�X�H(7� 1G5�E I A��!"� �Ss1BF WrzG5&����*� r��,!:�,b<.1|. Fin��W*: 2)3��aq��- %�]�IHMz��.J=�ӥ"7s�Fan im% R9al �F-�5���J<prM�tzEq^lMh ]N��aG!A��-E�%- port�ya���s one-` fF �0.btowardi�:�*}+Two=� luJ"|BMnY�. (�>�C'o�&@�u5�_# �:H f>DMK><$6f��� w5=.$�*!�=ula�Fhol�$ most��s\*,q�7"kno",&MswR?ay�x>uA�,X���ke s � &� � q-~�M�Z6�n6Dgg�QtGi�&�M�Me�A�@kAa��{q��[He01)�N2$$E�6Aw"����l>�Jc��u&_b�tUd� c��)�'sP�al}�ityA�rac�Y*Z�work wa�3G�Y�"JPn�N0earch Council�b�PR�du�!SchoolBTravel Aa})�t��P.��Dn, I. Samuel, A. D] ,ty, T. SimonE� B. L�K$Nazir�G. MilbuHA*helpfu�?scu��Wq&ank`.FQgg&3!RQIPIR� Oxforihospit yBM��V��6 {phd2nd&�R % -�>�j{�C��4{ham} D. Ahar� , W.� Dam,��q�8, Z. Landau, S. � ODz gev,q� Adiau"c Q�*~��Eq���mtVrdN0 }, arXiv:i� �405098 �l4�E� tutti} C.S��,A G\'a�RM. LiM.!�Vitanyi�W5@O��mo"7 of2�aEIn��š愡 ce}, V�<. 25th ACM Symp.� �#6H,!��9�1993)�P��%�b��>�#k� 2� C�cof % 2�-�lview}, I��sJ �etخ{\bf{2�905 G"�2��ntem{v!�m}A�Berthiau��.=A(aplante1TM0 Kolmogorov�lexityN� 0501)�0)�~i) chaitin1}a� J. C j=� , Randomn; \& !In�te$}, World S�8�$�7r9� s2ZsO�e Length!�Pr��m')Ii � F�e Bin)TS6e�J.E%�13mu547�666�lorenz}!t D\"u��. Hart��,A�HԐHp�BriegelA�I;Ent�k��� Spin%Fnd Latt�/�Long-R�8 I>_�i��nm� 7075u� =Chans}�Eisert,:� �SchmidtN�a)At����nify!LHgp�m e�a�*�� D%Z6Oq 02Q��1) ayU�gacs}.>)6M� Algorith<&EnDY� �%��46 v2 g.�� gruenwald j r\"u���� zShanno�j!��z��vN cs.IT/041s� v1e�B�marc}Y8J.v�M�h-!xyR>QGDo S�Q5%�%307130v)~42holevo�]S�1B-eS�`�g� �}�nsmit�a.dmu��A��R�s a����BMm%( on.,ID�| 17e�732�kitaev� Y. K��um� bU s: aQQ� ��error{"�e}, Russ� Surv. ��� 1191�)976��k�N.]/�Th�4A�*�| the )4E DKdF ��=lairobl..1z$ �res�T�652�l�*�J.� L  , R. Orusm&[EDu�F��6y�  ph�F2 �A�[���E.�6%�06230i�6�li}&9:�AA$t<%EKto=\b����e�Its!f�����J�n�e�A. [�� L��8�1�MVuMZv !���}*[�.x � �!6sschumAr}? S:� co'%eQ.)o5E4�E�aDtadaki_omega} K. T_An ExtegA���'s��Hal�[A�a�X$\OM$!�.ؾO��!�f� FD� �Cl57S���Id��407023v1%-� �Nv^ ��:7fn�p�a�"�QPura� Aum�yJ�990703�%�9�wehrl�%W ,��G�al!XV.�of��9},!7?�M"�-�:�22e�78a�kz�Z�H. 2x .Z*� �AMTs�uq� z4z473{89{�(> 3�%:�v810p,a4paper,one;,tw ,opew*�v:?aps,p�+ int,�p| �< s,amuvGB�1ptB�~��1?�`�w�two�E]-$&�v [engcW]{b�l6�v �6Tntf�t6g����2~wfancyhea�V{T1]{f�nc24[dvips]Qx2�]vB�w6%xCatEn6�?tDs,epsfig,color,bbm!D�{n3a}� ��$spread{1.33p�eq 1mm$set�\th{�gT}{484&B%\addto!,hoffset}{-66Jmyskip}{5dB \!>sep=1cm�b�,1���^2/� J a�� s� "Ob C. Mora$^�*2 $^{1,2}$-*Lb+( Institut fn �en�ak �T�fen�6� $ \"Ocwr��0ische Akademi� r Wissenp�fte��nnsbruck:7ia�d^2.�{\"u}r� oret W� ik*�b{\"a}t RTe�ker�b@{\ss}e 25, A-6020*z}��2�b -�&�`�RisP{�� >�[7`� *� 6�a p S2�O *�_=[LOS"; ic :T'0# W"O Kh8"a@e�(a u��al ���to ��#.rr>ng�WelfenB�2� (mea&a!���� �q)>Dn (1n)*�!al?d!9�.�c �ua�:/a�a%�iVde�� argu�atH?�9 �sf��HintuizA idea!K=r�;&de``how M=yt�w�%�r�e�� �ppl�6is�-AN( an upper b �,�67 ic.���m ds.ij1K}2>c\8~6���wNo} .�.�$���~�<$n_C ofn�a *@7ob)BsH`Ga�!revea� deep conn s.�.��!0�rYY!� �i�x`."W(e. g.Am�b�H�+ Lj};.~j� +' r"y)!�an � -usu � iS-a�t! by E�!QX�K� bc[m� shore!�graL7W��aleLu�Qe"u� T w��er"�b �*9 . ��um�o�M�Thand,%�]{9A eptual TaM�s. G\`a"�f��,instead adopA *G r�Sp�nngnbe��"�c��rA���4propo�29S,lsf ��a�f�%:?�wo cruc{0a�%� �@5Z:�-^JAQ)3E[ shO)UZ!h&b@4scenario. ImagW�nAlice%Jc_ cer�@ci��A�lab[�a� � Zmc� �%hf+A_t�-assocv@d�Pa v/ natu{ way,� �(54)M�p�>�n �8N��P.� �A*)��9� m!Cz�2Ŕ�&�.d�� %<,wooq ! .&rd,ƁH��"(/}3�!al �p�D -ekz ed G" nota�kby Bohr-]��)hc+n�%�!ieh�9an �W�A�A�%&�!��}]��,u�Q�AS�3QE6�-�be A�$ �Q�In do!�& , sh�z�gop She nsediF�altoge e5,�3�$ (if avail�')B �E�A�&�%�!)�/m1$ � 6��ʅ�an�g!�i�d d��. �N�A�5{e��� -�&5 Z7� 5-����ite"7tA,-��Y�, �I�R�en�6 !�!�2 ����%W����b(2H �e-�%� }m � �9u�W�HN"^.K."rEe>%�looks ``�- 1S'',�* lack�" *�'e���at�`� �� �ks�}m�� . E>ifEb�G�I��+by�d��� s, he-��*�$ To 9il �2ived.M4r�2>�94,�c�if,� !�(hima�&m-;8� ���s2,o�e�W mgJII((aR;V 4mon language -�!"]n:p�em!�FutXcs(I�they � u6E�)K �4]nM�:Ide��'~* ��Q�``�boxe�cs��>TٛA-�He 6woG)�8refer�&o� ~es ]#m� 2w:�e�a�v! a�/ /�=�R�=�)�E:@y�Aw#�al��f�ueby reosUtLA@el��!A_�/�Fa6qiy tensor-�At�hK> nd d���&� We w6�cK�l �AN�D�(asympto�B(ly invarianCu�� coars�g�!�I.�am#-� (�d"/' !*���9S��_^})�y!iMi" J�)zus�bC5�! :� &� H�<i�|� oA�E�,l�~�tYw� A�i7�d��&E�s7e�,e�a9+���OYkE ��'I��a/lwN jy~ �en"& d� Ag=~o1Ai:] (Y�l�)x�`� :�. C� � at a"p� ��b�0a"XM� fI�i^A87 7 �� w��(�8FF = �� ���Qsit�j\is��� �5� of gS� (���a9���?suiz A,�eZ J(up� ��&cia�$); through!�uOC=y� �Ju- 6�1]rec?<a2 � ng3se*cs� is welg��<)�-�&� A�!� orig�,"� !=H`;z})2= �=� 2=!�M-!D!�R%v?Xs�3 F �D�e�Nll��WI�$\mcq_N�9� \�by $N$ �H%+ith4 \ni |0Ӓ = _N2{(1)} *_{(2)}�Vs({N}) �null �� or (~4 $*{(i)}\in�1^$!ف��ZA�!��?�al�9{L1, |1 � _1\}�J)Z7no�=M��NGcW �P��i�6WQ�nc$!���;� $\M5@ \sphi \mcc |snul�QC�1 -&�4�:!�sE�EEmaM/s $|\phi �$Iprm�&�3$-{ $0\leq\�5�Qq 1$). W�sa~(�Z �j $���% %\�= ~ZD'A�a<��3te�7ed��"^{�1Fs�� ��x�[y��:�A��O*l &� eF( (at least ���JrI5"�=�Fet� �+�� AwŶ��4*�v@es}[Standard basiPs] An example of a co �te gate basis is the so called standard � \cite{nielsen} $\mcb = \{H,S,T,\cnot\}$, where $H$SHadamardn, $S$j phas �\, $T$ a $\frac{\pi}{8}$-�and $^7 contro�4not: \best H�@�1}{\sqrt{2}}\left(\begin{array}{cc} 1 & 1\\ 1 & -1 \end #@\right)~;~~~~ S =bG0 & 0\\ 0 & i jDTfD4\esp^{-i\pi/8}Q  n]B� �!�4~\snul\sphi &= \\2$one# J#one#nul6�~. \e%�!�$represents%�Lpi/4$ rotation aboutEL$z$ axis, while $HTHI >3round 4x 4q�nd{es} Given a fixed (finite) numberA�ANTs only a countable setTstates can be prepareda7Lctly. If we considerBmDkai- itI�$ough possikto%hoduce any unitary transform)a\ u$ (A� thus, � $%�$) upO an arbitrF,precision. C �ing tha)jde%!of!H � xity a quantum l will! ,based on itsepar� by means6=circuit,54erefore necess� to ia�! a \emph{� a4meter} in such� . We �Dnevertheless start '�0e algorithmic�� �n�:�%%)� ex%� �ed with�,s built fromUn�B. IZiAE8se it obviouslyA notZ t5�;!9!| appearI�4when generaliz �is �%�to Y I�. \secP{Classical Kolmogorov=} \label!�4liminary} The.d�>VVpropoA(bya�6kr4,chaitin1} is A>t�giva answer�� ques�: ``I�G(c�X) sequence random?'' AV�^?6 8Hness very close to {intuit� idea�$``structurAp''řis!�i7concep�Q I�..�A�ibility}Va�E? practice,N .�R� $K_\cl$ J(b%� ) ste�($\bomega$ Q*ed asmp�length?short��programe(, running �4a universal Tuhmachine,-hw�as output.} It follows quite easilyiJ=�e�=@B�:�=\�_{i_1} 2}\cdots$a�8 grow at most l!0ilyi�o 9�:a�! 0n fact alwaysZ� the �61S�z ��A�I&wr!$�1}$ .� }''. Ta�actuall��56�a1&�� titutes (�= 8ant) an upper b�efor˝ ��itself:  q E�(Mp_n)\leq .H+{\mathcal{O}}(1)=nB ~. ��͚}Rq Natur�t�O ar���s�which�J .�is fa�Qo large1�E|lyA�wn,B" a{at� ��periodic1TEMQ)� loga�q�} �9AX9���. AKis said��be O } (or(�}�� , or�� ) if!�.*.��sA�eaY�itsM�:�s)Q��;s typ�,ly�ttedAѩ4 sourcAIs�as:AAY(in toss). �wa��$find a ``n)�''2| also%��- ity �|6�H. A difficulty arisA�re � in )�one elone�� $\{\F _i\}_i$ (au�=(in\{0,1\}$))>�( }=\sum_i-2� }$.}. Thr� � �sm!�is .� �]a� a (n� lized) sure�9!!3of5q1i0. Any $n$-bit1�I_Շ_n$�ntifie�� 1�N wh�firstUI�coincid; t!z_n$� volum �[0(a ball, $B_{0!Eis $V(2)\sim !> n}$.8 AI I`$us dividedaF$[>F]^{-1} Ln$ subQIs,I5id-��a�%7�U=2^{(i)}$��$i=1,2, (,2^n$. Once� havems" ll%�1�Zs� �(immediatelyEP ���mk��� � A� spec)͉Udex $i$ɀ a� by a"94 requir� ���som�n�(t) $n=-\log-� = >oIA�a�i� ``�[ing� rgument� V&>� n9:�#��Q�s&o a�� n by equW (\ref��):�VcV��� PrelC�VI� advantagA�i�reason�E�ata�+y adop�to��62 �7nhf��P��$ecase,a ��,A�� A<�8� a�UT  < :�  or*�gap� rA� model)ECY�s a ��W;ihW%�)k$ $\epsiloaP� � ��ateF� must8p� A�n r0|\psi\rangle$�� $\l� \l'�\r$^2\geq 1- ��ԁ�5i�se hs �L� �Qis ac� "� 崡� �)� !7� !�!($2^N$-dimen~al spac!Cmcq_N�tv�c$V2�V��{-N} �^{2^N}$m�=Rif $K^{�}(% )$� the *1 ��.� \in � (T��� !�)�=�)A�%� haveq� }� - �qV~\Left@arm K^�/ -2^N1 + N*� i�ndLinm�I"��li� ter�momitted;�eE;us" 7��硴�1d<�N� >�>_nd �  inota}� under�i|�\Ap!ef> ���\should hold true indepen��l5�way�@c��� @�[a& ��. It ha_ �t | i3 �/ Y� U#%{EP , buo�L stea$�n  �iori}��pertib� �!e u4U�e9w� Y�is �d �M�A�m�2E�be]�+)�*Z3���G�s"'coarse} A�|��uU�ass_ toe@ Y� mpl� F< $B=\{G_1, G_2, � G_k\}$%w� llA8I� � !Ip��>�Y��s.�$B�  fix� de (}�$an alphabe��O_x{�1, 2, � l� A�!� oced to��utI\]� ]�A���.Hi�e�e��Denumerate} \item W��!�� tai� 1�$A�il�-+T mcc^B��2�2L=��$�/zC!Jz P , ob|A0a& "o q� ^)k( f)!s� ��>8Bm}6symbolsk><j}Sfj}�W E$���=m)ioMm  c!YPexclud!�� .g."ew��'' in�����I�if��er� qui�Apat� be m�or �Aym��#�s)AI� ��e�!�A2i��� :ek b��nfunzi�assoc� s* M1It to a-� (letter)�group+-� (word),!u)c-p.�Au[4.]{�� n� ele� .9�}� !"p&� :�.Ap)硞} \ �uV>,)VZ�nA�)$av�%R$M_ ��m8.�is: �sa�K_\net^{ B,B,i8.  =�@ K_{\textrm{Cl}}�M�Q�)��gZ NC�es!�%�c[5.]{6�raE~8u� �T���sam� e�� $,�in pr��)!rrespo9ica8bey E�&eYᕥ]; �C�elf% d�ed 1� � u�2�it) ��i�h��a�{q .%S.=%�vBM���FLA9JB=epUgY4q/M net}Y6Y/ \min_{IF��tilde AIJ6>:tA;en�$D_B� ��q�-k��ɡ��$B��QH�e�.� �&Q,5�!�E�!hchoic/f%TE�)> are "h�2� study howJy�l�Y��k%��vs� {0.2cm} ���\}[``Asymptotic'' invaria��XmF�Aor � �] If6$\"� �1h re twoyEE�Oe0 an:�F �M�vM,Bz,Yv+Jk_ �,F-}~, AV MUr.Efu ')�Z !o� �� �vNI %� �c4!s�� ��\ :;$,� j:w}� L {i_2� �m�=2�Q a�B}"� = . }_{j_1V8Z.2V.� Z6nV6$��i0a��0aI� -^ $ usa���v��s2� 2%��~=�#�&��di�ary''p]7 2-�"�Gdescrip� made ���a�� �~� . Si�bo�!od�r^ �#,j�G�too[Z�H��c�[�gv!,z"'b!�E�big�6���v��is l +��$�%��\gg 1B � � We>Yi2rehn[ 'A�5�y�w%W��+( (see Sec. �}). Na�x#6�� -��n v does� �!� is h�"n�"��w�/nJ"&$*x��� �� �6�%��'� aBF B}$,Ewof � (.) B}$)�Dd& non-G �$`s]a�� +$����(� :a�A� Toffoli W'��) ains&W)��C-not)� e!�E�� ,ŬMeJY���B}U�a��"� a�a�><B�� ��i�i� �&� in mOa)longer3& '�a@#AY origiQ E���eir&� � chan�qZ a (small)!4e�B.J B}}$���{j� betw�쁈QYA�e�j i� >�6�'A�de-} �T ertyE�anI.� on� expliciD)n!j�%pc!=�!{ (a;a} magi!U�x��$E2�|%A?w�"=Py: $\displaystyle{K^BP �}� "Y&AV� `"�(� �)  M iz��>, wA we�]bH(A� I[A,�b2� "\( !�JX( &�:c!mex�5y4A�I greatE�rx.�f�Jxa. U� I� E�b �.� m:l#�2 I_- a��jDbecomes z���( 19%hN6��Ex���oit�* j� �)� >) inctI��!�Q�s#H�er�TU)�b(E� 5�s!{I� ite�*�elicm !wE"ar�g��&BY!�",$F$1�w�w"U#�z���!�s�F� R. HowሥeIJ85�^�kma,NJ' keep�A��W  W)�t��!%�+6zE�J& e"H&�Q$*+���)� h&m�` � stepm�is in��u--I�M��-. WO+��ideŷ2J-Ew!BEHilber�a. e�(ne!�yE 9i' L�� �r.�^rɌE%$k_.��'/R(>l !):�# Z�� � ith V� >�)�eR�+{ �,^��b7A$Tf�-f))�6g6� a���"B$���"x-=�,&�F� ,1�&#�&&5#^B2�-�}�B\c"2)��6 4 )), �m+*M�� .�A}Z] e5� th���Q?%�!0p\ �=. )�F�proof�!�. �=6�v,A �pre\/j , di�## �+e[ was� � "�/b8mFs;57:�&3 st}�is�j� e�0w  agai���� ex2� \b3]�F|aZ.z &� �"�"_P��isegraph�� veriU� ur:�A3"psatis"�&prJ��# in S� on T-}� *��� A�y to 0m �<.�+M@�Y>Ln>g Q�.�. is known :�6�}^ A (� inuous�(� � 1-qu�'�|s, plu�� n*�6 (�6)C2#� E� eH'a�� $U$ ove��c" � o�6N^2 4^N\�!)$ �"6,I"� !bnteres�to�z {��0} 58F�neA@>  $�3tCly����!�s>,%(V su�+ient;�&+ %�%us)A�G!+i쑥�Å.�$ i�H nul$W W%� o �0Solvay-Kitaev oremIk}��implies E$��L%<ng!%�� $.h$m$6+a� M's  2� MR�I�.m _#^cI9m}&9$-� $�+� B%v�?($c<$[1,2]�R*Iq*�S val�"s yet� eQ.IS% s"=)�#� ]knyUm--1I�on� !�1 !��7��� CI�m$A n ��dD7RQvia�� \ e�>2-ny(ita�d�pL-,asis; futher�es$M%<��B�{ eQ> �� M=\m:G-� .�N^2� ahb� #~\R�:a�%~M�&-�7a�lo"�%~,�1 �e��$a0 lastI res'a�iv.e %B.ea� �� L�bl*�"p vp ` s y%ar.�3 ��)� z1�j:����] e�s�d 2z]tw�8e"a �i/� is (�oral to)A'. Refer� )%?-[M3" � ���� sa!AH*��iE�l F0� !3 (or,�+ ivalentlyy �;" �)�&> B� $))� )�|aX%�-�($M$)�"� FF. F�1E69,)�%�}) weg#6ue *�3���P��ponw.al:,$N! wA��d!�S�F�d*nV*��4E�5T� � �� � B Uz�)R�.q�UpperB�5m� \nok(nt {\bf; I�s}}  W� �Q�osI�of, ng"�me�y a9 � Z}. ZC� n un/ut� 4,ity�2��<by |aL�z�i&�3f !tI�Yp�� )$��� �. Ab|5� .� � K;, *#; li} . pas��;&n.6� A<+)bov�6>�R .!minimu 5.�a��� �a�/�* !>��-is%�!5a�a(!F $\hat{�}F�A�nb� ded ( s5�()A^�F_$&� *�BZt'�8hafQ )$. !���I� *�&<49^m�&MY-1] y � s"$con/,.;N� �(��(>��Izi�>� &� �)hos� �&m`/'!�"��2��� �e  ing:>n*��a%'w)�=m� (A�[,cha*=er ?i��Dn�$)��E" phi$� 67��S:"��A���1mRA�s W3a^�9ifax�� �~�U�lex��� ��ndE#�����<,a�:\��f� $N$,n��( f�}>5'6NQ 2�$"��I��!�Fi? fv|�. L�8��[ 39� situ/ : AlicBs ol+EY)�( �<d�s Bob�d&,it (at leastq�b&"&6). ExC��e�a simiU�  �:> y hadP��DgrR�.���*�w�$�0at �t��/to��$�"5  on�% m�AAɾ �"� -&� � 2 m/�(t�-��~n� z!�I�"� �=Fu xف�"� _�e�6  e]�mec9s< �+#��am�EADi9 }I�%<�b-D�"$���.D��is��})(�o}�  co!"�9�b��,a��`�reflec�e*�m cL.�F��a x"1�h-R0!od � e:??��-�) � K���(�P �!���d eda<eaemtiv!ż�@):a��%�%V�.� � m<�e�A N{���&D``�m blem''"�1FE�e��&� :�p a�1Z tron�ZB�x)!\T�. Fix�Ua /���iZ fact*Wo��F3N s�D� >1qS�Drivial#;QrYrgu� a"A���n�Hl�$ta��0`����UL�0�A)핓1=Y�e��b�to Bob�Ith�Qv&FRq(cerC#E�)��n |��ojto��2^ � �?!�'iact(_� �(I����w<ot ��.��J��� [�2 � �A=``M''B�5� � she͐} to 5X@I/ ����!�&{&��ly9+A�t task \"�?�A�, HI�< k.�&] �6s�? One m�2J w$/rP&��'��a"���a�.���Cal9F8#e�s�,�*1� 2f�,:�Aed�);&Jbab nven� 8#iA��Yo E!1�at:6�w1�� �( �)�6� r�&�`�{.�/weX s�-at6�can� �D[$� any}E�q'ds �Mei*��1QP � ��B�0�  totalF)��kIn*J5.�theor�x` well� A�7 ofw ��M (bitRI%Q``�v'';�  k+ has�Pq t\#\&=A2�,�,],�,n} | �*,_n\} < c\}} �K\}}�02^c-1}{2^n}~.�G�2 card`'itycl9 lGow�-23D!!�uo;se:���%�Z�x���s,Iw�+R8ej�(A�A^ ��b"*W  � aA�"y� վ a $(N�)(B�(v��2*�7�]LV� J�@mQ� ���U. ApplyHKEq.�@2��%j& � �-h"r"K ^B$&�%]r�"�QX>� qi�i`-' $. Se a�P &��HM�� �, $c=c(N""|!a" 8. S2� wJ b�7n��z�I]Kis $oZ�:F �{!f meS� infCa� (:$9�2�Zm%�-� g.6}\ll 1,ujM� w��(�2�A�� "�A�2�-��P �F�C:O non151�i"��H,�,"�*E�py��9s"!&*JN��AO&� 2"K�emI(Eha} o a P di��bu!")�}$ters drawn�%��0�.6���/2 ^ �6 ship2�,Sh�n�'r���K%A@ V�.��� ���� �" �Hs��n-$�:9q$pH_m6�Lpro1$6>$gruenwald}��� 'D �} n) - H `D + eq c���eA2�!averag%dtaken�! $n$-:�s, $HyG`J&} .�a<2�m-� �p5v=�$c-��Oi��)�5H.C2g)�!a2&, Ku�6\5� (a"�)� ,of Bernoulli �s),�-��ak-Yim-U f $n�2i�1p-�Np�"a'g=-:�aq1:4Q&ffZMFB&M!}{n} \x�Ea"${n\to\inft,UCH%�>O ]>t@R I�5�R,� seeka�(q��Yon�<� ~ F��"�8%7 �_(+Fll5BYc24BxY/3��-i�_ a�[ rd!�(��a � .w� �- �"� a�`a�!C�?!�ith��N.� L w!g}��$QMe *�6$D$. Eac"�U7)}be &hV!� �� �N $A$; �[losg�6!Wwe ���D�� b�De���($\%`Vw�m )+ �Ub��Q) Z(or-sUnce})ok� 1ꍬ���F��=M2��L�-�D �2!XD�~)4E^�-���:o6h>M�a6�2m[gE�oug�!�eOn���� m4KUB�� cqA.�]RX& obje@ezin jI�:(IA�;4f $m l$ �"�QA�easy Qeliev l�}s�-+ SA,be high� !�L*fDF$mB1 (e�]t%�%o!k��x!B&��%�^�)�+�5�O� �H%'e�r�osi�()U� e��zerWd+themselv!�*�$�7e,"+ vtZ{m!Q�s�a"� ce"�3 negligiblny5%p7(\]�D a�u�I&�Ya��DV+ach *�DW em��#��PE\fB�]mBGL-��4Y ���]Os,f.Hle )��.��9 �<�X ~l�� \#�z!�trik �Wi�M� Dem�� �`��5�``([''5}?�A ��[!ar�"�i Ax���T9 i�@ bold�E@ }_m=� �Zc�Z�G$is an $m-$!D�|!mQ�is�uby "2 Fx) !(.�Q$i� i_1 � i_m) + � j=4?#D}]5J_j)�2O ) + %�&� a!D�. $i_k !I),i�c�6=&!.k}NE$l$!�2cob)�Q�!6v9 k4OD�=�ϑ6 "2��*[Zya�L i��Va���@M+�:e:� ��oi6Q��`orф:ŕ���A���� �0�):y E&�I�}�aa&�.  g�`itA��qiP��ne*�a��V� e����y,�ingM�� �Q&� 5|�%}_m )- H�  -��X_1~"N!Ako-�_p3Nat�\ , be��);R��� ,.� 1%lr�L) rem�=�1���2c too1fR� F&� m} 2� m&� OH}{m}! � \*< Qd� } B�;-��j*anyth!f�#"� 9����2;7 �[Q/a@*�[ource� "I�y mix�ht� be view�!x6g AAv&�$a,I�IA��:= �4 ``black box''i�� �K� a�\*� ) pu�^2�,�� schuWaer�Z "� �P�a� - �raN  a�� d(tur=D0{(p_j,|\phi_jm>)\}_{j��)N.�(�9- (�$)-\�ea")� a k�]of�G emi-"I ''D A$��� "��sen�c�EiL 9�)`!����n�9�+�F@-s)*� o� , it. not,E�!,%�t��'�DIotensorAduc �on�:" �m� =GthoA� e >� B)eB r .f&O�1: �vNs o�us) E�����60 $\{p_j.4�AsaN, � #I�� V� �<}j!�� �� "�2"�2&I4&Y)*�ji�Y, m&�hM��W�(b`FoIDB�T6<"� � mlivonI #3t "k� A�\%e86o�\y.%�"� eQ%� .�E�d �=��J���� �}��e �s (I�-I �s)�  u&�3e�e�A%��,"�;split}� n�O.�*|2� Ph_ "�& =��� -Z 2}� m�� �m�K^.�C f�= \\ &� J��� \#D Ro3�Knd1#\\EL!���� 5E?!2k1$.�/"�&� �!� �(��&. due� tR�&� ��C �"3 � a"6�At��� 2�P��8�eSb� "I_ pO M�i9 *�)>S -��2� ��j<*EF�m?f analogo l�!edu>��M� ) - &� r �D�� } eq c � A�}�"(,Q% iB� � �bly�%�&� X �� �p-� ten���"^ mA�� -� ``reveals1Vt�mi�ye&p@(Q�j�g�c% �$���J �����m�k!� S"� '*iselV*7H: B� !GE!��,��%Dh$S(\rho&*$von Neuman^.$1=E jp_j6�� |$,  qe��$#3 �$ �W # 'M�$a� a $(W �})6 _2461 2�Hre ?E"�p�) a�A�O�O6O��'�-+2�1@ 2�F��m �nsi|!VPF���.ih/Vf��(N-�)^" {N U ��;.��~i� "�<#�Gw �+.�C�X�Tpi#(��S5�"��aV�+ia�at?0� $�YA"� V$/"t'fre� ( M X9�Aa�|  &�" c�*�8�st9 c"{1^{(m)}=�MbracepvV�IA }_{m~�Xit{�-}})|me*��)+ 6�m!� mtBst�1��i!�o�m1bp !<t�((;!i+&*��# es�$"�$� &�4�ru� !��e� & �)!�A)h��!�*r ystem�S2�, s slU*door"/ Fa�(eib ll6�deniLt�Hwew �/``�,!�)�''L6���  ei��/+IK�1o �>W)Q�&"&d'�ffiH&d para�u.n  or!�� � �globa�5��& ^{\o �m}B@ (.&p2 (� >"B3 *�tq-��!�,!-I�%'�&/ J�(*(@}o���GF)'Ia8V�;B(2�V�&gGi� Z"V���i.� �G++@u�Ga�1 �wexa)�� �"�'$smTmind �� $c_ � F�u|6wYI&�~!ז���;��:�Q�M��%lbi:�( ���.aS'1 t by�D�2a� I�!.��c�aXcM�N�MFfO eE�.��-56gSi�NNaJ�uJ �]�" �Un� ily)� �U+�,"� � !Es!.��!|@L%3o&6���>&��: ^9j�.F&?a�aep�j�q +�o q\� �n�* 2^N ��F@"9}6 �6�EU��%��Dph2�U�M�j-Y&�1JFF�K=)}BfF!c cal �e�c)er"�2Z""F/4m1A$� (holevo}.\\  �C&R*R from*�*t@).�N6�< mY�|s �6�;$4 m 1�^{m+p�1$�N�y�@�6trictera��a��KB7�4@ irec��� ��*.��9�4G�/;QQy��=�M� -m J��� &�$Ent��ce�&� } B�$�)�n�bA�nH; sup�9i�$T ten aIBst e� ='1� �+2 ɴuJ ,~R rmbO}~ <n{N_j}*�R! it{diAx@=+)=I _j},5and}~�^J N_j=?l��e��6��u$A#�H2lyw%sdLd-0��JLa�#��(.R Ks")-/ $ . i�n�a���G��j� .� nXQ�/J}F�a;-.7!H� _j� :UJ�*�W& 4�uXD& "�zq�!�e�RZi�ed�"��8���A�:3!�e�4 2�.�A�>�X��56�-K2�m�}{J)9$�e) �.0'YOrovr;cMC�st^lJ*�I <! m��)�2$%� �2^{J-1�1oN4<>0 �%�1��st�Uk�(maxima�l� }�a05� *only}!�a truNN$-z7}x)� (6�i6be�Z��F�M5[ "�k�W�U��QL�z stf ;�-��)"+ �,@I�?ot&�-�3xhave F�a�ugO��� enough� |E�GHZ U7Mf>�4t� >+�O��t ���?�%� �is &-C stic�d"�n��|)�� � effe�e�:� ̓&X es}[ٵq!A(s� 3 %�]�&��>�z _��\iC�l�= mbigr�Nͩi�z,~͛ћ1$"� �2�t�U.��@R q�INJ� /N^�2 '5e~�Y{N.5���&�6p �+�bdž�L*"x"cK�F"-5 �R2G�Q�:�� ��Io&?�B��fvEp&�3�{�Bis a��0iem&� toK"�M�"�: . �ݍG ) .�9 bi�;Ois� m�m a��  se��3e abs��,gl� ,re-establish�&O (:1�@� %��.s =7:6da$al fe$ � 44 ingu dq��x u� 1�)�/&/e��of BNi�_GrV%�|multi��icl� ɵ s cy niqub�scribw& m�"�Qiep /J!��~j"t3ro�Bf I�# edge�W8*>� ��s2��v�K!�� marc}GGK� x$$G= (V,E)$!G�e �y� �&�#�# ;%6"�=.\=ps� 4v*�k\�o�> i.}]h�� ��a` $|+���n(|r+|� )/\ �$;6YZX V�%J9,wo9�$k��nl$+ ��,5lled-&эAhGk �.�  & � "v +.1 a�.��%�A�� ��: :� U_{kl}�m0athrm{e}^{{-i�ZW�4�m (�Pbf{1}}^{(k)}-\sigma_z 'S>*l6*l)})}}c�=�%resa0ngM , si_G?_���6DA�e:"�A�-!MIX$Gd;K����Pof5���� �$� �9 (N-1)/2}$*;^s $v~v� ,G_Q 22e a�exaA�� / nec 'g 1% 6�FIo)��*�"lyK�n�m�}i�Bt(v�)swsi_Vw}, \s 2 A-6�� [B.2�#��qort!h�c�ph\ r�p͕�'�s�2 ;iAS *& .%� �)��� o�Y)$ ��!�6 spec�[a �/� � is v�W{�h�7.aPEF>���W���ow>� \h)�e& m$2e:z$a6jAs*<$)'�zre"���V8e��% Y"� f6a�a G��%&LX�9)!ׁ�&Z -��NF!6O6Q� risW9� l L�RfA��}�}� �%�e� } um� of��h $q�$Mj� � }�.�B�>��o�� u�N+o �Fs ('H.�s,|K�2 i�� ��� [A)����/kA�b]݋�8�qG$� ���_�T� � �g� ��6�QV}��FG)3ldQb!sp9"��"x.%�2�% >BjAAA���(>@J&. �.{.b��`�ki�#-e.�"�"� /!�o��-u�(6��<I�+2�0X&i� a (jq��[2��>8&A�6 famIXo9C̓,��idF�Ain�+*9urK@%O����( typ��R*�Ci�*#. u�@� ��� g�C�#�8\0�5El� )X A }Fn}u2�]!*# yp�e{,�:!�1�,:OHK�� n�J��*�E��2gos��9Oth%u"S%�� $i�! .�C���+U��9  �e��O�2,�!�*,*UJe � . To guari<� � desi� �is �� ��*���Z &�5B  !� DNE/N^���ZA�2�` M&we �H�͵�wz\�A�H1� �*k^2})$ �� simur �Q-�>�)6*N& Apd!=e ],�2 ~IeV*J �X�� ��`&�; �,. UF8 .>&en?6)�-�D$\#D=2$)&�LAcP�%\�a rdin��D$Q��*1 an 2,2D �Aׁ�g�=)�&! *�A``U'�"r !�=T�1it \K�Q$��$N$.}!��GV�,N^2ENH~� JDifI%��we#ed.>s�v$�lorenz�2esi���g"@6�): `c�y�ap� ie a (��) v�9*W��0D1 ��D�+�)� illusts* �h�tc�:��B� M���f8 $6r� ,Pmust O Z ^�� m>�N�&�hi}*�����^�2(R�9W��!aI*y ��� ���!�X8) �d� !K��!KA��6� �i�/ ����>� ���.C.F�E6a���ldaR1�nIB$ N� �= 6�6�捷N^� _ ����;- G�N��[AXj�>i�?.�F� af2by�E&\+�, �eX  #A s�s�X.�/*���P$N$Bt#D\c!��W�5<@uRh �� it{W.G.}}�� �!&�6�`e�`^"��"H*Conclu�$d outh�}Ç�an o "\/A���$1j*:*:���}� ^ E� �X2|a:�4=< Sp�D61�.experi%A �` �f�m��invKka��jon~-J"�Dax�=� M,:Q4. A�!액|�Oforward[ppt��)q�vni!��3ca�{.�Ls�q &�M�!C�V��)��TarQ%��- 6&�r�A�9R�^nK&�onj�{Q� stud�f�a�� I  *sɆ)�pursua��'U)(�6yT �I�,e( �:�{ar�z���ex�M� ���)�AL  adiaba�A�utI�\^at�}!gcent b� ham} suggȜ���"�#o o�S7t�� )$.IIY� ��t%M�R-C�fa broaper���<�U� lm�Uto 9d e fu��� ionsq_tkzV�%4.��"F�6F�"`� *�!Hthank Fabio Benatti%�useful�4cu�i�,�a#1� workUb�m$r �oarV)!& Deutsch TForschungsgemmeinschafitA(Europ,f�Union (IST-2001-38877,-39227).}4%8*0�^ x A:��~A��a Vitanyi's6G%I�ov qee auth�;8%��I�&Г^��fonU�6!��3nU�A^�osoqen  -b=7fNmAK&�("� �Srm{Vit" )=�t4\{l(p)+\lceil  (|"4si�|^2) \r#\�q*D,a_�: O!Fs $p$�!���) O�!(fM�: uq" a�$ u(p,[&0�):s�ؒreq%&L m-Uͤa�uter),eU$!#2.�vUF 7 � Dl"G�hk&���B�`!te̒s.tGe�!��b]�rޕ�#E�lsi$�� w�OaT pe���a bad\�rA��m�%���Q TW8�'10� $2N%$���e$|ftPG6�"��si}'� ed%i�y�pro�J� E��r vecto�>a+basis: 8+&Vel&\��c�N H $|e"�(z�O�aV� m" %�+|�1/�%}�U1I�:�2�& (C�<$� FaK  $nI��&9!�`!�E���i�%�� !�Z%�r0wW �a }m]�6�#S� &�Oԉ�!�A�6�e"�h $N ֗/]��W2 b�sil�/�*zerma;H2�  &�_Q�!�:r��uB<�k&U�: = 1 -�R���!b��!u�eL-��� �Qw � �L $h �W-# ��$&<�:��,| 2^BogZ� +N � ��G 6f�nL a�&f2�&65�%�9tho�'�Q�. ��in*�.)��'��2!c�� B���2�@ �#ʈ�jk*&�F�o�HWK5%�i��*j�$I �.� :Oq���*�h-�o�0Z�5�^2@!�!щi%rV��*es &z )�`$�.ch�`Mrpolynomvd�$B� B: �H.%]!k*�T ѐa- We&���,A+if�]$ *!ntt�r�*Q3R��=(N,U�aC+'z4 �Lldx=x�A1} 2R�M N}$ (&%$ jR7 "ޢA.3���C N'$,�� $ j.1{|# , "7%\.:Co6��&�/ �)$1gQW� cag"��'a�6� $� �"  4-0 ��oneo|� NOTxc�ht 2D�B =�{ leavbinvaribquWU4e,A "�%�3etJc�A�To en�OQs2G|��$w.3�OF e7-&�w\rinciplo�a���$e�e =�46�k�� NOT A�&�.}�F�'(align*} I &y&'Z \|&1"}\\ Nf' NOT~k'Lj'EW LINE��� � &�V�XE3�� �cen�+,tabular}{l cF} &5�i� &��$�G &A��� �  0\\ ��i,&� .�G$uz$]�& >�($�@2+nG.*�nd� \J~8=4figure}[h] \j)� iE degr�%s*[�=0,Y{, scale=0.6]tZStr.eps}�G \x0[c#D� n�,am&�-�a�*a�t�G ;1��N�?�o�"N~L~~~I . I~L$ ��l�help viL�i��putsl1a\�$ breaks $Lv1"eB�Xagaj0*� \-"�6���!&#�".-%2ldx��Y,� N��!Go(W�;E�$.�F9K�e�i M$0> I �$1>N$) (�� �ҡ�adj��8tant}� f tell�� �?% sertWT ine-%s-��y�boldL�K�u�j iYm��u��;YAIa$&�G�i%^�)V�)2J ��"X!�netQ��- ��e�A�&�%*L�K *{֛ldx�Bq&�Swkc��il�'��r�\p�d<�dV� $q�=�A�^=&+m� ,input{Biblio�u��docp�} r�\��4[12pt,a4wide]{�lleu�Iepsf}�t�(\topmar�� -.6iH�soddq .4:�width{>9he�{8.758d \newcommand{\R}{{\rm I \h�H{-0.52ex} R}}%%% %I�N.>Nf>N`�=N16�ex>�� 9.00�� 2� be}{ k�7�}.�e#!�.!title)UsiA8caXsH��3�lat~( itonJ�v { {\X" Y1PBrihaye&� yves.b $@umh.ac.be�k \ {\�= Fa �\'e0 SN�c�U��i < Mons-Hainaut, }BB-7000! , Belgium ! }�N �Nathali� bergt�*�on.d  @ulg�g Tech"2s du S�fR� l'Im_Mon�fi�+I9, >�Li\`egB 1B-4000�} �#5m�D\��DAncilla Nininahazw�.� $@yahoo.fr}6�Z�:� u Burundi.=\P.O. Box 2700, Bujumbura - } �m,date{\today}M�M�E�pag� make \��I {emp�diOab�ct}&exwMh3 6�Hb)tonianA_cr�$f$U�os%A���ide:'ra aby J. D�nac e�R.�m&�Sh�a�e�)�?hok(a�UJd�N�m����?$ trum��! b.��#sDas"�k 0e �couplo ��mi��mi1a*l9Nw&��<dRfr o ad�? e Li?�ur"�59�\medskip new!Ё�%& {Int���( A few yearR6o�HBose-Hubbard (BH) m�=� a BkGar op�$�7 !�boson�0=�i2c�~l�1O/om�� tail�scott},�ea�ck:1�&� PǍ�O!B�m5��G � �.�T subs� !�Linvol����a�w�[rk��Mc�Z�e�PI��!)�� ed~:���%%�wo pie��!�NdiscretAE' iA�a�&��"so�L band"�n�regN6 6eigen��Mf� inuu��<.0�4yBHM��utu^�(or a3n� �4Ea.�.y0"�@�1 FockH ${\ 8V�Z%�j�,� de0 osedvA�B, flagq .�� 1�s f_�$n=0,1(�x�|a� leftAw�t C.Vr!w'E9�9 A ta�ed? ebra3[�R�,?K-de�J&�2izA�oBU �{ qe�A]TmE69per��Py� as�(�u"�j�6��. \par  qM��\!int���n�5to� ific�:�:� M��'e�5w�)vu% <� 2K !WQvaXs��jA��!� oal%i, $sl(f; R)$ � �;N*�Sn��fo��A$(diagonal)]�*U�Cartan�Jk�o�(!�urŕ��m��0ia<fix�h:T� ����$�G/<fu&$<; play8un1?eGa pick!7��/�rr�$Yf^� s (irreps�E��*cer�& . OQX enjo�W-ic�.!�����E>%�e&��"* �(turbiner1}.�&�1� �q[ 2isSVuh ; how�w�lȗ��&�M ser� �X!��S|��weakerFj�剘&R\:Oѓi�~ }�:�~!���!�"no��A\ quasi--+-5+(QES):b} !�� and/o�8)�.Q4 PHa�:ut a {\L�e}�dz����mpuaqU�5�2q�3 �p�'ebae�QES59 ��!�� ��x:� BH.�] a� _.=��\^.$5��ݚ ݛ�>a g��e�E�Y2$���\�A�+e2� occu��normal ��s �1w �aha& er�"S;�� S!� ,�c$\lambda��T�3i�o4%�re�%�] iE ���� ��!n ad-hoc�����bna^iA$ ��orthov��Y�u�I��(osp(1 / 2f ��. U/5� devoAWB !{�" isE;Q� ku��!{9 D\�(s0 .( M���e!a�kr�nin,&�n��� E�5s6�(@_E b�'E�.� D+Ah� ��M+( a'��� �(&�0Bs����by *��q�6.&T G{�;}et�zroa<7[ alE��:zis�j%,� 0 \be H_{BH} =2�J`f[a_j^{\dagger}a_{j+1} + B-1} +�4 gamma}{2}:'2Kja_j]� *�&� low�%mrai�*U9s $a_j ,2]$ obeBu�m�*rulv> [a_i6]= � ]=0$, /2 \delt�jj}��!�����-��"#s~&H a_{f+1}=a_1 \ , \ a= a_1e� �hcJYA��' $)�$at��!�,� �-ny�H�5_�S2 \f��, i.e.(�Sg�ja�� � q�  $�% n_1,n_2,� , n_fx[$(x d $n =++n_2++ +n_f�"LetuL�3� i�+���^s� eT8do so�\fix7d4�%��P9Za9� _j a�las $(j-k=' kng2vF~�%aNaZ,m��#$(f-1�D�s��gr �$+1�&S V,-:IFT��i���Zk�6ia,�[(j) , k) ] =j+k���*V��E:a�9P�O -1}$$ riBho%�3ZK2$ѵJM>C!p�VB-1$^�+�M�z�-2 ��F�+2}[)D vm gow  4�3�oe�2m{f}� -�.�{1f? &\�1�s�AI$(1-f�r�nachede//F� ,� �!@Qkx n:#8e,$0$C�2�!H��-6jkE��j�'(, ..., f - �we� � �! $2 (Mc=�p f-1} j )+ 8 = f^2 B9�-�qA�"� sl( � )J[turh���<��MF� $f=2�z��\ sign4Y�onsO.�2 E �!n� su:d&j �B` :��H, �+m�,J_0, J_{\pm}e�\pm 2\;��; [J_+ )-%J_0�ABbthree1QS MO ��rJ_0��y�_{2!�{2: E�1��= J81}$->$F{2�)>�� pid S6�+�CaTrU(� C =�J_-�X�M1�9! E[2%� convi7'�(PC |�� ��2 >OSn (n+2) 6%R�]n�G*�<�so-� ed $D^{B�nf )��a�A�]Z�W��,I$�#&+ �~ Q�5:nMQ"Z.�L�3B��T2��ayW(8N5ss��A+= 2 x-[$d}{dx} - n=�+� x^26$+ n7M�!�=2!%K�b�.�"$| n-n_21�e���=�� mon�( $x^{n_�Y� $;= 0, ����� :�(1���/Agin{eqna��l & =��EyY{B 4} (2N -(*#0^2`d ; ) ="^2!H^2� [ (x^2-1r[�  (nx ]21%vx -  ,A[E�-1)� nd��V�>��A�&� D .pDM6�"�  Schr\" j#er!cmA�>�f�}��!J x!�exp{(��\MM �y))�:�"Gaug�6� e"I�\chi =)�Re�eYB^ y#1}x \cosh���})} \psiE��0per~��L potei"7/e � V (y*$Vl^2>n-(n+1JJ�-BE-Q:  �.T -�e%�o�'ϵ"�Ůt�8�� 8$DVDB} (cf..170))��fe���p�;aS!�&&K�6%)YMt@�AnY�pla�a f>��i\�led��>U���eQ�c)��U�c�)6].��a#&� y $T2� : �CT$ ]^$T|2I , ,n_f>= |n_f�n*d ��+ >$ U:�a}sIE�>1)j�*K$T"*�&� *~ �ruc��5%b�,0�# . A r2�n9)�>HC5����EA1i�s ����o�E �Qd�S�R�2R$(�+�yyf���6 )�as�Q� ΅��"c _ $J��' ��e��.�9 }���6n=3�b�$c �^3-7 2$'@ �-Y"F"64V*p3�psN[IfA� $c�_�ied acco�Eg!�f.iM.�$T |3,05 |0,3 >�J,2s $c=�� 1}{6d WMu��v�6kT�*2 (6 - 7. ) \no��7r= &x^3 +�f(1�)�8��ҏ} x%&�.�2� N^3 d^3�3��2p29e88@(^E��g�� o�.T�.�j=0}^n i1}{j!Z �-j}�j "d^j�j��yk�*�I$nJ9 !�"� 3 .� 3�� 6> 쁷 by 8�zC��ery6nnihi������j"kf2.#iH3 or, eq&'R, 2`Z� ���_2��3 �L _{x_2� ..1 a_2 . -x_1ANpe(a 5 -x_1 x_2 2M2}+n NS�22�e �-2 8p:e2B`�hE_.�]3 �.E63� ./3�x_2:�2}+�B�1}-�2R�R32��-CJ�+2`6�-Z�\1(>6*�.�![1�6iR e B�x J1ńUN��-y�����(0,���+sluTas cl`tZ5&$y�剩2 �$E+, yak^:X  . A "hyper�ge�""$T_3$"M& GreN}�ELY� 1}{3� 2N!���>b:.%�{,F?2 nc� nd~T_3�+� 2} (BW -2k!�s XG-J`&w �F��8 eU �Q<�B�"* ��\C2{a���1) )|\!�UI� reUL� 6&? &=&" (6s^2��+6� }�.�1}. 2})+ U-1e!+. �x_1^):D:�&-(�E- E�_2_6G2�81�2 -� 8�b�%�����!][B E� !E {n-k�b�j,��\; j=.D-kk2�"A3�dsmg�[sV �� $f=3k Y�a�x no*��F9z m er�0�4)i�&V�e ]7r0^�.)HZ� �Ks2"�y�2� �� �(NL%e2��&�H�%w#�E�!*IF�<C��� a)"2\&2�����7b*�neih�no�lo��N vail�V� 1$ h� � -(A'` _2 ) (.5m.2}) +1��,�5?�E� .��Gl.��� .�GgH�Xn=2�9e�`6Gm&&A �da�� p\�71}+2px_�2^J+2}+J� x_1)R��.w2� &�G2Y%j!��2!��2^!2�  Q�!o�3&6=q�1� (23)*=� ��a=�Yi�of 9(�&�M_� �A��@�g xcepF4ts h+:es�9�/8y�a�*P �]� 3 .  �w�� yid by :  = �A+ �"�_(�seV+k(��Ӫn2  ]_(�l0#� 1}^f,sl(2D (N-2�a_j#r��V+pA��)� 5�$N$�Nv@ o>� j��I@?)$)��&��*R9E^ o�x%g�&&� 0 \o���+_1>2�lI�v+) ense uful2{, $H%���qu*�/ "�&� /(}@�V@�5A'�I�&.�%",A�� |i*��$EAB�*'.�}Ni�+wi �l1&�#a�5�Ya61 . NoHw)"�#pJ NAy�:g�leŔa�}���#�}�"! (26) .K^a��a���%� ir&�+p\u�Υ��I�\�� �%&� A�I\-� �W������whr8;�?al€y-as+�ÚZ_2$-� �5� B0*�26). H�:%1�s6jZ a �s*odd�3h?&�`y$ antiR�)�FQ]hVK�i�Qi�-ýyVD). So � �y� BI*�k�imjuC?s>1>e�`�;�@4anymori�� �J $(2�+� ��i�Ie��1�-&�$2f!�bdd96�cYb�� ^N o�-)/+)! �^"餩'FSS ��&�� t)G�]�x%2�& �2>A5S�g@s : 1e��<$,�a��!68 M96+3 gi�3a�u�2� Aq>2Oe&^|!4E�eI�"�� �B�o��u�'�F�`"�2] "�/50: !╣"YYM�'";3� 5&�+�}!���io��CCi"� ?�j � v�ń��b?!�2�+:�V �2�o���ur at�@��.�"� C�cf=1i�nda�/al i�E`1}{16�K�� 0��>�!},$Q�&.J� �M���$�"��y�,1�.or�Wmatri�Uj77%�5�S�r�e�$�T��i� ShKh]+aF q� \$0("� {cc} �CiY\\ 1 & 0�B + \�D)G7.�i�tft( \V:| h:w!6�\\ x &�"�D9vchia  Vr ll} "�2V� 3:�)-4:�& \-E�O:/ (2x(x�f~�&j+(x� �}\ �E .x-2�!%i�:f�2dF��lJE��.Zm� leve"<��i)e| pZEADA5Nu , | 1�bC1CR� , | �$��xN�/ �nergi%re�|�p2Ul�9at24�3s9�� �yF sol��"0�;�V�E^3+(-� +6) E^2+(�P�. +8 -6QYh#E -1 - 4 B!= 0�b i_" �9���V6��$/�*h $��s� -�-E� �H����� �(!,����A +!� six-"�1��1/4������J�a�>�xV[!�}�9�#�? BD}.2�֥`t>��Fc����q .)]� -vwe"zN: A�%f)���o+1r6(�$�5aim �p<0 the Hamilton�ian (10) restricted (due to the QES features)�qcases $n=0, 1, 2$. It reads \be H_{BH} = \left( \begin{array}{lll} 0 & 0 & 0 \\ 0 & 2(x^2-1) \frac{d}{dx} -2x & 0%62N)(-4x-\gamma  \ E(^2}{dx^2}-x }+1) \end � \right e At�level of 4states we have�gin{eqna�8 | 0 , 0 > \sim � ( %{c} 1 � \\ 0N� , | 1�L0G QZL �1��KxP^K$ \nonumber&| 2��]1R��2��Jx^2RLM!:�sqrt{2}f�QxVT. 9�KnowingAseQaAlla4actionQ;>;2v�2� RZF�6-)R� \ee and)(^{\dagger}_z%�\\ %&0 e1 Vl�hz�0�x�5�jIIa�j��a�e TA.u �--� 0}��pm 1 � !^2+64}!�nd�e.� \neq5� three secɻre mixed%�taz give� 1� o 2} (9�1<01 >) + (2-E)!D!2 >) ��forE#]%��1�� �( �+2)^2+8 �^2})� whilɆI{cc2s+ c_2��k1��3�, �;49�E� withf= 4=01� -4)q\�I��= y~EY(.2fac_30$(4E^2+(8-2�)E-32� )4.�(E^3+-70 + 2) E^2 +(2)J -10J E-8� #�A-associaR �%� solu�� s ofE^4 + :q3 + s 16 -1��^ � + (16� - 10 �230��2.�= 0a e \A�4ion{Diagonalis�� ��$} In order achievAA is d6=,�Xwill now use a suitable�_subspacP ,{\cal V}_n$,^ ,1,2$. It tur!4uty(be helpfull write dow�~hmatrix elements $H_{ij}$ in��.e way aeX ic �l � � $f$oscil� . Along)�T\cite{scott, eilbeck},& define  (discrete mo�um%�D\label{nu} k\equiv��L2\pi\nu}{f} \ \ {\rm�nuA�� f-��, 7f-3�� , \dots, �\ &E�The v�� con0 � no quanta�� note+ \vertp ,rangle = [00\0]:Ns.O a si1Uum�� t� ed by mea" !_ �Ufor- � \psi_1(k)� ��| f}\sum_{j=1}^f(e^{ik}T)^{j-1}[1 � ��\the $ Ff(f+1)!8$�=tw5�M� $��{2,b}�$"�&� & / � {2,10&=��2�6ec�2b &U5�71)� 0nd3�d0beA�&:C2�.p��� 0E2 wher��De index $b$ takes �) $b = 1,2,�u�+e�$Eh itaS understoo�a[reAPL $b-2$ "$0$" between�1Aw"$1$"���BfferentU�((apart from"� $b=1$). e��� $H_R��$H$�1TinvariaT-�� �� 0 \oplus ��1> 2$ l�Ta�xaD %%%%ICI NATH debu� R=? bH_{01}� &N  &!1! H_{1�\� >*22��V�%� $$ ( f )_\m�_*7 E ��delta_{"0},6 9 11}) ��s2 ..\cos{�s2 \pi \m��}.G\�e4{� odd}!�n, if�%is,�9�12ub,b= & �J� �1b} -&�> �M�(-1} (1+\exp 2 j i �ɠ})S! $j+1 b}, b=a& ...:%�E�H_!�!>�-4K ��i!� ; f=Ce� ! !�22}n�NI_f� 2}\; q^* O_ �e� f^2�9�Nz\9[9�7&-c\\ �e&- X-p�I_fN�%2�other��ofAE'f  $$q=:�6�b, \; p�9� i �2� + >%dE�M S \; ��E -g�$$)� $I_f$� nds�K��dentity�c of dimens�� a3��$~g$Qn: ) 2N$(i�V)$.\\a� * fur%�Hsplits into 1 block6]"w+5t�(!O$ 0 ��+E�$. \par�d� hsZstq be \ led by%Az 0 $k$ which, a&� *� } reŲ9 classific2 *��� fun���b0possible. Not�G��i( rastsE�bpure BH��2���$�/fZ%E�/) � occurence��� supp ary9]� )A � &�fac�at��-��� ' )'� a� zero%�one " . Th81$ naturally[ @�oneE �� 2$ i� :j .B@even}I+Now.EnF�E� �rF-f��f/iWfA��r�&-1}��nՀ�]+�L!ksecond � appear $when $\mu$�}!8 onlyl also"ٻ�>�csчZh"2&���-4ZE �[6 2 (�� �fc!s!6^ � 2f} �$. �*� %X)}��YG��O��M �a K�cO_{&7 2I-q IbeI�6|B�O_� ��.�3)2��/B.� է; V� N�E�� �j $$u ��A�"f  -1z �n+1.$$ �t��last � �not���Qm% (\; n}$ st2��H <� $m$ row�,$n$ columns�vl 0$B$e[$qual to $]7^* J� �(} e_{2j-1,j�! $e_{m,��a�!="� �Jfind ��es!Pry except ū� ter� �I$m^{thvuἁ@$n  � ma 1 is�. R/��6�=�$ ɹ�J224�7- R9&+4:."� � FIN &.(Examples} W  studie�e �r&1��)�few� Z<$f$. As said aboXe "�2uG� .�~!�{��plo��emra�EramI@!�2# set'horiz.(l axis. Dra,such graphic� �a��fi/3 ��'$,$��$ A!3(ame patternJCof Fig.12&q}.�.� b%a~represenonC 1!{ �, \in [0,0.5]I*fo�% =3,f=3$. �Q e�refer��(of�a �d*��u limit ��4lowest lines (5� $n=2A�k=�1$�# �~evN!\�4soliton band's2At#QES-ext� d�modelc� learly se�� se2I$stay belowP � Ia larg�<val!s new coupl��co�nt5L$. A similar analysi"� ci$f=5,7�d� eu I0henW on. ��"�illustra� e9+� algebraic�  u�A��� t��.c1��%H� superposeUw2K.�avail i�遄Y|7� womA�QF $. H �2Xree�A�as � < nu$;� ymme�% �(i.e.E"$�ba[-5) has,�course,�Qb�Z edI�!ld-black (resp. dashed-red) E� join2�cor-on��� �)i. J. .5$)M �ou2�~rq+�gle, squ!'!�Lbullet symbols accor�![" y�Wl�to%J'a�n=1�Ce�U t�#� A>~�r curvm�M�}�)fpic�' u� uggeV�persist&P#nd-�� > 0$�lN.Fturn out!�Noc�Xinside an envelope. ToRish� � some�#ai�calculU �![.p�m_ ��U$fA3,4$ G(figure: 8psfysize=22cm \dfile{eilfi1.eps} \vskip -3"cap{�Y}��energy �z  c.�A��e�$f=3,q�$E�a�a:w4n��nd�b� ��3��2��7��&A�3 �pq� =0.0i.5$.>�.�!qs�E(3}� EXEMPLE� DEBUTSAe�  : \vs� {3mm� � f=1�"%�A$�sf3� A*e 66)ES +8-6mV^i-.�����^2���@ iv�or  =3$B�MLtabular}{|l|lll|} \h�Q"�$ & $E_1 2 R\,0.C+-7.00 2 0� .1 & !4 2.016�.02�.27 !630.077 B3 !39-2.1330.168 !Z 7.06 2.22 B286 !5 B10-2.32T0.424! ��+1575-�!Wa~�T�! $$ &m#=�|0>X"# E |1>� !� 2E-4=�|2>�IN3$�,  :� � ��&� 4E���@ 2� 3. Concer��first I�reɇQ� is�E^4&�!4)E�4�! -4-1*!I�4M�-16-12�E�:� )E+9*o!-!�:#=0�b$� '����&$E_4$B� 5.37AwA�E�I�&0Y�5.389An 2.04Ie058 'ElM� 5.43 (15 0.212(Q�>-5.52M�31 0.3a0.503A�0I� 5.64E� 2.48 (53P77.5.8q64 x 357 &1.09�� \\V �W*�&�$6�&1*�$a!�q!�$! |z 1 (0)>+(-w$y.-8)E+4.~ 2{ 0)>:�&+k�$5a�(6-14q�^�$]�S2}S.T�+�:`u�idsy�a~j qjA�eXM�-eI-(3u< +�1) E+2�'+�-q�6q<: &'%ar�E=1��-E=-1 )! 3(2+E)Jor>v 2-��;�RBn 3.45�Q1�H& 1yg �. 6 !e� 3.47a!74 !eY3.5Œ! B9!46c !ej3.598��1!�D�.K)� |�"1 (%���$}{3}) �U-�*U. ;e^?+�?2}()�iQ})J{)R�$$�AK� A�-3(1\mp2L jT^�}�>C(E-a�)n� +2(Ea$+b�����4"� 7�"@e� obseT aa�fold de�&acy :e�)& complex�jug� ��*ubb2� 24} �� "wex/bnan)8%2o2I" � *tj *p � 3.+*2SJ*+(-32+1&2 -10B )E+B�)�3 3 �WW7RW2�� 5.78�� 2.02�0@'�s"W81�� 2.11�A0.1�I(/ 5.86��- 7� 318 (5 P�5.9g�360.525 (� G 6.03-2.50 P7� 2.78� �uq�.�]�m&&4(E-1)�Z^M.n E�z*L-(4�, +(8-&� �,N��1�����&&+6B*�,E-2&�H@H>?� 17m0Ii�ZK �*:-+� �!� J��Y�3.0�}v M�3& 1E�3.� 2 Ep 3.06"2 E�3.0�2�$$F�UV\pi� 2�0 եi)� � 4$�Fl�� 5,fj*� .�#�� � .hE^5&��4+(�/� � ? ��-8Q� 32+3yV-29.22y!�a]&,+25*� + � B ��:=0X>m�OO� =3$P5F� 5.19�e+-1.31�A� 9y95.2�66 /�p 078 /!JmQ5.2�8228028� 0.2�_ 0aF�e6G�h-1.270.590`�b\&w5e-2.631 `0.94720e�5.7�08�` 1.33 �1�<��ʇ2�-4)(E+3��?-� 2}�-4)33�dm��6(.D&+(-8E(E+2)-2(-64+�8);��,�(�+2m 2} �(- ABZ E+16�BSB112&�4�+2)(-8 3)-2y�))��3���ɕ2u4�ځԡ.E�#.�^2-*���2>�)��ͱҦb��Pe���0ee��� -0.0w .&aa.� ��'W '5u ak'�'�'13��eU 0.14; �20.�3�0.209�3�j�ige�U�2}� 2V �"e�y� �2 & A+q ip��m3.i)+�h iN�}-O�$-6}+3 ��iR"at� t�8 ��ies. N�finalI���M�A�4(� �E+*� :��� *���4IKM���A[E�E� � 0A�E^E�4� A2� 1� BE� 4.080'1.037 !E� 4.14 !! 1.06!s-4.21 0.1�1c�<6�<�01+ER�; \pi}{2})>&_%9�-E)u12�7�'(1[i)E�3.�]���' 8H+As�� again ��� a���2� FIN .9.�$lu remarks�1Nct"olv� � Y �BH typ�Ana�+bea8�AedOa f5?y��4$f$-body quasiBb, trans8 i"�3*{.ssfw $ons depend�!�$(or more) R�"(s)O!Hph96" mpha�"o;9rum��alized-'~:'n%-(� eg-o6(9 &Jk$,V#,Cofe�+Ce�g each.!" k$) �+s�"edI`�5K �,Hm� ax"A$.�[<2 c�4\no6Dnt {\bf Acknowledgj:} !Y. B.&te�:y ack ,$s J.C. Ei0:~�us�0;)E�organizn%bHSymposium "Topologi1;S!!:�ir Appl+$ions"-;�#4 Durham (G.B.)�!August 2���th= invi*. A. N.a�F/or!M by a�n5JC.U.D.$\newpage .;� thebiblio7'8y}{99} \bibitemG;} A!ScS;2(�YPH. Gilhoj, Physica %���ively� �%�"2B?,.>1&0>2{L> �>$ 2c ��m AA 4��JAA�'&�;�')5 \I6 I�Oi4�@}-,[71 N,a+A7j,tak�5�!�gi.N�;00} &= 06��:=;I8 ?�:\m (-2)\cos\� U8;FJ2;J2r� &q^*\� 2& VLVq 6  & FR�b &q&0}&�v, & &\cdot:N1bE�GG�I I & -�O�B& q&p\cu�F10.=Ac-R%� f]s 0NYQ�k=&=<=;Av\/M > _{j=+ (1 + �B$(b-1)})(1-<1b})\�a&��� $q \eqDB \tau$, $p ^{�� /2}+-1$,o:tauC�}$.m�seu�, e�i^.�E\muV>�@v (of Eq.(\ref�D)�3 $b$ � bA �$. �.pl���.� stru�+ �w(x reveals tit�1r;be de�ose� F4f&:~: � ��.� 2:52:�a $f-142(s )3).D w�\�;<[aps]{revtex4} %:�\rint,6'P \usepackage{amsmath}>�-�l,[ac�l(]{srcltx} p ,command{\be}��u��`6ne#e#���#}BEdEdisplay�� .H&Hj$be�!b �*T>H$IU�� 51jtitle{"� �  needs�Fi�5pre� 3tauthor{L. Sk\'ala$^{1,2}$\foot�F{C2�, 1�. E-mail: skala@karlov.mff.cuni.cz} E:usEϥy\ \make� ��� keywords:2� �,Nų6�<\\ PACS 03.65-w, .Ca Ta "#NIntrodu���7{i6F��Fn%b!�mosa�,oroughly tesXp�l!�or!o (see e.g.B|Zeilinger2,Bertlmann,Scully1}). �Z�*A�,�ndard�?roach to�*��B��6 ed �We someK�B-intui�^:t�3 es has raD�-��al than�cha�,e�exactes��po]��te��!VsubjecA��D tinuDMJi8I� is5Jea�Ys�iel� ��ng�:radoxund s8a�t��not easy���B�Laloe})n96�sg6orya��$our opinioIt�C!� (af%>lEB 80 y �xJ!�!Af�� ~ ci�# I�2�is*�=�M at uA usua�Eiq�s:#8 expl��Yri� al ,EX�Des�tY��.K"�<�pskF )� A�obey. ;n�n&e I�<���Winvesti�+o�Ampare��.!�.O!)�b�9V� �S�], way��ask w!IKZ6Jz ratu�5d b!�is sit� .&�Bways� 6Q2o%duKO ory  B9of ���o]ed, 5A"!Kfouu:�O6�A�� b�6")Vpa�. j �8he best!��!:oA�rtc}Yu 1Z� Imzp�%�S invR 1H"� �R �R �R �R �R  (/s k*% }-��IN}o�A0 i�z �z *z F �ugն� y��e �� � %U" �GX# ɶto UF� isW}�-a� �3 }. &A U*� re��iu�tq y&a . "�5 *M re imperf�� repea[ � b & e�s� e�s�D2�c�@�s)m����� s`Y"� ��u  .�� hen nA� WR�B , star� poi&� foll�d. ��assum�5&m"��=$A x "��)&1j"Q&  $x�H�<nN � .] JQbe[M�Ycaverx}6u=\�x\rho(� r}){Z d} V�]�B�g�A�c�ed�@ ov�[he whol�G� D$2[ \g�^1� normA�edN����+} �S\, �=�ee F�;�N\.�biQrMal��Bj#%]n Eq. { xIbget2�px0!S eft.)C ,|_{x=-\infty&V - ��d tial�} x}B�AAEj MGf�FN�Bis"< lsP Vp�lyfson �x$�#_i���:1-���--�k&L�� p � l]ten��qinnerA/2�,uvx} (u,v)=-uOo�-!�i' .�;Ecu^*u v 5�."UHer�!<�o�l+2�6a*&F$uv$ �l2�ux} u=x9{!�Ga.��v=�m[ ,} bd.� $s=s��ZaA)l�. U"� $Schwarz in�it2� %�u)(v,vm�|%�|ca�/Eqsub!�)-movx}) � �@� ce���E� 5�- �U�K1rh�5V�Jt8(!= rho}�ReftePb>i�)^2QV��1.WA�4��l�4 o-ca3UFis^WinA��� U  ,Frieden4 ,C�i}. By u%���px1��f�J e� �arON0�:x\pm��$�O��b&�'���, Cramer-Ra�Q� ��6|%B�2�7(x�6�!_!�����R�i�� agre+� "��-Ya�ask� )$;m*k�� �=s�weightu[)�"nUQ)s $���\,�tV$,^2)eT 5ZM:1. �Xpl m}ua}a� v�Qqu� . {\em Re ?m�2a�is�)A���]��)�k �J� s mu�ear� �K����V is kin��� .� Z r0_�@im�(|(+��)Ꮙ} N�F�<:� !ja���a� $�w/  x$. Si�M�, namely�,ZZm�M�$ $-i\hbar_.h, �*&iN�}.c B����5�.�&b 5}et�p��/A�e?l� %�-pre�*R =(�)^2�NO2 $(u,u)$ ER%g4RN�s:��NB�. Howev�'we�#� �WaU�e��� apsis ho=\psi^*N�!$�rR��)D!��hpsi1}�2|==.��e�� ��)� s^well-,9)�� "lL�q2��f� ��..>c�2��A- elucidsa�� a�o�b*�EZ��-ifyy oYiH�-�6�i�ubOi��, but)�X&-inG�UdQ���� ncod�in�S�G�!RL- . � M�proceed ilar .�Qco�.�,Ml�k1� � ߡIcx 2p j_k} j_k=�f0 v_k, \quad kSNE�� a���on8i�velocA! $v_ke"�d. Wri}�``,''!q!b.v�v_k�f�� s} x^kb ,tR !p: j1=B(bm=�5!+� $e}^{-is}\,}���i�/vS .�9S (-i)6=.8+ is}): + 8�3 � �A�ial%C�U^��U��.!�6z * �� ��)2x�Jpsi� ,t)= .�.E�w�C.<j2-ѩ� -i6:6Q )�=�Tth:}e yu{to� real. Ca�Q���D$jaJw� ]�7V�j3 � ��5�[�^* B F9 d-aZ-+c.c. ] &�2i [( [6�JS-J+^*-.|I���xw[a multip�2veTor�i�Nr�I�s&�Y93Ez� �4f�� .�+v psi9.necess�/to�nonzero)��jv9d�5sR�4�w m�* ^k$. =33> $B �Q�b$B/F~ j} ^k$v1+ refor {N��b� %�ge�&�2�!\ .�j�6�'%Np,<.H"�%9�nd��f (i\alpha)�B#$ $) �c�Y, !�F.i��N�6� �1BA&U�*Y �1�} ��X� ��c&�8 ��=:5�x�X��}a +^*J..�~�pd}V"uMi�y�2i*?byA�*%v�� ."apx��[(x�)^"R�-?BR^0^*h�M���A or:� 3} [x, -iJ�]=iVAh2�*�vi�$Fq( e,*4 (,>Uyna6X QX r42|UR���6`]� "�M�I�)�6r"yas.Oun1} 2�Re}�=-2�$���a�v=1x�\$F�4�. �s)aeget��4.�a�} 1=4 [E�]�leqTk�d 4\{B(+ Im �]^2\}=4"�A(d F���c�e�!l�* � })c i1 io6P uuvvF;i� 1}{4� �/B Z!N�27 k.�>|^2Fm� |y?:�i�|B �!;<}-6 �X0gɘ[.j !&����3%!q�� &n:��:�apo0�[(x-a)!]^*(:gg[ �.�} x}-i b1\bigg]3 V+{ \bd +[�L 2M^*�Zm�d�$aibI  �\s.]ױ� >mq'-�U�!|V^-�I��v�*En�+�a��r-)Lt8�xe minim&eA� ]^� \$�2T} a !�^*�psiy  V=\l��%�a�� � b} b.H��A��ps.)R\yz�=1i[>� !�2�� &&��N�� .+2`�Q#s s 9u*'Heisen{ 0 Z�$�� ��*d��!+�< -f_x� 1RO` x�UAy*N�*�b�m�R�EOT� j �2�'i*f yj�C!o�erk���t9a��(�s,*�"&s ',y��f_z$ c"H4 & h i6P,electromagne+31< "�1�o]B@}=(A_x,A_y,A_z)$ 9�e#ge $e�w% #cl�1x"X!�,r�e6m2*�nabla��a��-e�"A}�6�2b� to"s�  ( �R+s�0 M��Df�P%�%Wead81eg�ki)R�gy�B� $T=(*^2/2m)��| ف�|^2� d}V$�Xl�<#. �Arho|^2/\& 6�)�^2/(8m�� 2A Tim*�� q!d5(4hS!(*e m@aFsb&GQ�y,%J&��9�!to�ideh$. ����0���iN4aUd9&au,��=0)$ j�>0�$t>0$f)�}�c= .�AT0`rH0��M!d*)� unid�/i�egacz0fn � J�CI v6�ofk X(yet un�'ormed) r�I4,is.�a3actm.H+xr.�>�a!��� ��!��tSe�(.�.�'� ��QTt=X�Cme�m� "�*:>��,b��&���&�7j96 re�$'xo��llaps��wad�v��I p"�,R)t3e�4]A�m�h ase.ɛDe�g �E�!�e�!�=�.sb��:e�<2[/dIn� �4-A&g-:�.Zs, �"�'� .� int� ���i�Ql%�"�4 ! grale(ima�int_0^{�"}"T  V ` t$ g�q�5faM@Cis "�/���C�0e`at!��4re�4N7 . FoB)���ps���$ B� ()��is�&l�")bʂI�he�8$\�B$-YV�!,��� r�6can!��2se� e>reaso�K&8)doEm��" �I��)a1�,u�!]2��$t=0$!Ri5~S w/x� `l)8:�Q.5G5�JO ��'`mx+!!Lanalogy� &3 c}"%�RK m�B� EE�sh %S� ���"k���B*2}/\&F%&+:1f �~��ONn�!�mK)&�s�+&Ms���2w&t%e&� " &� t0 -&� ��.� aN� s�!^)��)&� "�9� 54�i�7w5!=�&�-)�F5$�,nges negligi3Aime, !~�,�."�!QAze���*:Fz�� q��O�aF"�&B�. .-�*��!e �/.�G c�b�%e�m5�oto.���p ��jtLt=-� \7 ?} t�!�M$*j| yj3 kj_t*QP2�N,2{~ 2�VZPQc&%%�mO��Vi Jj"� $j_0=��Re} ��%(1-�yL$x^0)]/m_0$.� � �u.� x^0=ct� D�5 �yss.�Rn,A2�,��c�!�".�apt�_{t=0&/�][>��N�^*v� -("n:�^?os"7%v d}t  On� �f5"5 $dd� Z�3�J��f��-d�M�-- . I.� 2R��/N� I�a�B�I<X<�3q��.'t�d>�t�\!|�-�5� N4ES|Ն=y>t.�C" \t�-�1y�M�Hbmin} dNN!J� �^*iZ�t)F�.Y! �:�'-Z)a�c fA�p r*�M�Q z0&D To *�wm&E>�swe decam. �(� �� lifeIT$OJ>0$I&p6�#&�"\cM{,}&�#8-i\omega t-t/(2)8�)B�/���N�!En"� �?t�0�=��� E�p*�=1��:� ) �E *1H�$EKm6J<v'=%^~�$d=)"�)cFS�F��4!�^2mG*RW���KY �8��%}A�;���sK0t&/ �&P&mt� magiGSE� �3f�/ency $)7-iQW R��� z�-N�.�7i9�? with�  9� Q"!^ "3.^ #P�9��*w � R��*zi �non-neg�.39"Qx�%o�:nP "�� �)A�*+8I�0j_tW7�8j_�4m#Q7tI �� 2�)t�d}V\get�� � i� ��g"Nrs�} ;�)�a���^*, !�! sig �Z e $sel * ):(s�#�  t�1Pe \� �[�� �>�fpt"   d=f_�J)c apt7�nF� ���Y +f_0!."� &��F 5]B��"& �GV�G:xW� !~!�A�$!. "H1&d�!5<�2�As�%pB�:{�J�I ���j�r��y$f_�\$A-$2� �:I�put�=eUM>f_k=eADb& $p{B!UQ>5".s���B.��+"�&%�%a&��/=[at�r R=ir �Hg�2rLD�6�L�W�$g��alcHu2�Q.�&J6����im�0�F����ed< �rul+$� ��*� ]3 b%-eU�p$2%.<2r>f���o�."�D})s�J"N"���&���cen�Os S;5 amԘ!varv=!.�UKEBU9�����8c4�oKJ��(%��>&�E3� � �ѽ��A@�Aϩ��1A�>���* &D � /�m�^�: FwLlNb>I losts iri��A%�Wb�T{Ka\am=� lL,than a dynam%q1��� ��>Z�La]r@ of py ��fd%�.�E��@� \� �=u"}ae�a.`$M}]�EwhG���e�c���>aikin.��'�uagt�XchEy6D� �u.7A�"RA_*�E�]�&v9U��o ��!�m wj �;�5f9J�3 . Ou*iV�6A�e�!->� 8Qi&oSa iE%I^iXO�ext}S &U?*Z7�� h}. ���A ��E��;M8�b �i�%1� $ or�7��d^NL�� � �DA|B�. Re�A�b��a�ur�%#A�m�*�"��7cמ��lk �qT*��F���� � � �E�F[A ;��i�] a=b=d�2b+Kvv` 6�\ �/1}{c^2}� |6� �}&� t %^2 -\E�k��3�;�4 bigg= �F"�}�6 8c'!#spY9 of l�?��t��:�|у�*� *m$ Z>J$%��*�. "� co�>�����]fj�F�Z�x^kN�, "� . &�6si�V&�!�)�! s�OllP ��? !Yd "�>6/x^kAY(M�o*uag�F�M�*U5�5m?a��%  gyUemug%Dd�*$%�IR$}.A0I}*72p a� ��*I^yH !F CeH�PWim2 ppZ[2?7!K27t:�9!}.cFp S8aD[AFiF(@>�36T�s^2}t 5u%�d}3eeY�A��--�l��b- �&%�b"�@�(s&�A(��}5)}��dis�s Q�Zv(z\,TŔ.� �n�b>c ��O%A�b�9�.�vao $n7@� �u�j�.�F8*o-~#�x^. cl[ f�LZ4D�%bey�"a�e � c�a&�e!�RS�EaK ���܍2�%.� -��wa4:�6Kv`2e�i?in�0RFg�A�p.=m_0^2 c�*�D^2$"��a}�%# ant,''BA+h mas� QX�*���F!+-2g{ ce�rd ;\ i�ad-`p�* !nu� on# �%x>�^0m �� he2��7Z� "�=�VwbmJ#6�.,S"�?R �@m_0!� t/(� )}\varphi.�$ "p 5'._(FN2��$�� (6#isQ nd w$��`"�,a @ $Davydov}. �o'u3A�: VC!�! � "��^�=inB+ v%Й�w f �d2�8 KvvD#�G�c�W�C`  �D�,^+}�6s vNo B#o! �B�I6e�2� !V cros7l� 4YKmit�conjuGZ�&ser�5$�k^�k}$�ri|.'1��E2� "T�m�|.{�>�M�}#FDZ� �`�6-�)%&|^0rU )^+�6[�um_T 6Bkrx!��Bz�8 ����}{���^�=c��%�d}t�DTh�$)�.v*�?^� : A3 �Ga��"O@�&�"zK`Ga�-E"~ pp})O86�;�jB F� ���b� I��"P �Dvvw$%4im0�r�t��] .���1�i��-�%��] ��{��+.� 9�_ + k^�MG "' �F"G�� .ntM�!�h��~ �~"at<�Q_�.F�2.�( m 1.nA;"�U6�ED6�f ( A�..�.eq}k -G�ր+ j!2q�i7W�m�m �!�kM #pe��[c!�bM^!N� � N�CAe�'�d�& 2] 9$�"��� �|&R ���EJ7*� ^�qc�g � . }  �]{C"?" 3&1"\b �%Nb�h:�Zb.aXDE�F5�2� e�-!O) .�rJk is/%$}H~ is_1 e� -s_2 2� s_�� $s_2& �9�-6%$EC$s$, �A��B�J��#io�x,.�?F z�can>f5!1Q�25HJ�d3 ��::U# #^2 NP&�@>��8 s.|^2G�1 V+��c^2�No@F)���.de�J2��W  $=c9�-29��> ^very smp��Qy!���@vic�2�n�]"V&�:tY&�0 Fit��s-maxu?A:G�I5 y$M@Aj �is k!�l�6�der"n\�ۑX s_8 �Z/� �|_{ ���� �?} =0,2�O)�6Dh��6M61�   �B�42��4}UL= �4.)-Y@6�by!PU"��2*!k��~s.5n(~aa X) �� ��I2O"^2� HJcl:T@ �1� s_1(V�,.1�(-��N8"� 2= [��nLt�E:h�<�&� �&�3q ��� �IKa�& 0�..Ea�)�0c�I2�)'�,in�Afi8"s) expa]iofJ�7|"wer se�min�%� s_1=s_1|_> =0m*Fur1<0)M�|�2u @�!�6u $ by�� bf r�{a���T�ass!�Be�U�m o�LF�guon $SqvR��  ion}�S-m_0c^2��3u�Y�cl.�%�2NA�=E��- Q{S}�at} x*)A�(M�S�m���H#J�EX $"y S* |\ll ��& �st��"� a�b���:�B��G�Z�8 .�}{2m_0}� �!Thu�&��B�q�h�3�6�.� �i*&!B.�[�"H"�e��%P6anxi�*e�v� "0(eA� �v� �8UD=�.HR!+�& $Q[23�  S2�&L y"�x $/ �Z��J%"j'�y y }.0[R�s&s �g.�(, "� �X�-TI=�>eG'An ory.&�if� e�n.sel� to F�&�ZX2� 1�bp( �zy �� $N$>�� �;�",4�E"H"�;2� N ��)_jH=4. �__1,\l��,E�r}_N,t&_1 {g V_N, \;j=6ee� vQ�a�6�u�u�|niP r}_j&f .�&16j$-th59e�n,�� !_m�te6��5at@1n b ��.�"�6 x�C*�; $onNZx��" B:� G^l"�*5��nv%bj$Uv�`L�bf A}z,@ 6*,-FcdI�� "K5� /�aA�2@�*�o m�iA-�2T i"h�� � 2�KvvA�f��.�:� �2��� #�jJ#N� _j0'qJm t�Z= G � m_j^^&�F�$z�qR!k��cle2F;U�%�$maMd*j��fW<�ach��e'��t���  .�6|"�.n�odNB#ş�2m_j})}=͖%�ќ!�2���tj�.�� AK2X:� �.� _j�  j rBa͖A�>��'1�# .s�*�= �cb��*��Y���h�?�SKtwoe $�&sSj$. H�}F�U4I�-Is�$ sy��nti>�ex �s.n.n-�{t4�~& isi�&�^�(�F�N-�b��%�&� ingV �.�0�-s, fGG>:� ��*R�ce� �DA�o 2\,B@M%Q&F7�*.�*,���0 Ia�3"@G�6s��AGF�� �}"�I�r,v �#�+&� !K@B*�a�Z�uN� ��-�� � �:X�$� a �a4}* �G5�:x "W&�U� . �!�Wm��.2� �� �qgnWyntE$s""2Uab�. %�r�V��[we}�x���s�%� �,�y2_|: to6�9 �6� /contr`d.�%>1U�)����(�vG".Fq���A�i��2�0&w}  "�5�0��E�a�ߥu*-�mpl!�de�No �� Q; \ac�YledՒ{TA~work was2�$ GA CR (grAff!\l�.I)E 5N95ۓ742� OFN@i1 �KK�@(� idge*�� P0k, , 1998).�UQ�Np T��jJ��om<�El�>e�]^'Pory (Wiley, New York`12< �6V�.��A 1!� 1992) 123."�#��. ,U�Muz (Perg[8 � .�76���>� �d&q� #� \��[[,pacs,prl,two��,jl�bmBg���B|�*z�{?R xsym�r6��fonts:epsfig6Wpsfrag}!�.J�ket}[1]{�A#1`>Q.'bra'<'|J'Q2 Q<#1|#2ZT nn}{"/�\\>Lul}{\�@��>f �$mbox{\bold!I $#1$>�fkR*\s�qstyleJ6vau}{>^vB]nc�:��B+be,bv��#A�*��2�e�"ord}{{��O> sumin%� ��a��� \\ {{\tex)-}\h� ${-1.1em}{\o�%6�}W�{.L{#1w� \}� �q@} :Q�si�o;��$$\f{O(3)}$ Aar sigm�dec0�{Ralf{\"utzhd�� (Sarah Mosta�V.��{Institu�"ur��etische�Z k, Techn UA�$\"at DresdxD-01062Ger� \\ Em�� {\tt�5uetz@t�phy.tu-d F.de; s�b !OI7a� ��&ose a� �B�!;/)�>of� abo�[y�H�g��Znt-�!t�ٛy�8 �� �by1�w)"% <��$!�Z�. % A� ' Jeva<Eon ed-m��QorP�O8tronglySe n& C 0�a�&%9 toy�!5�chromo-�(QCD)�4it. !� crucialj*?hQCD�Ei9�\�+0{ 03.67.-a, %ճ*�8 Lx. % :e 11.10.Kk F|� ��in "6�s��t�8,@ 68.65.-k. % Low-+aS$esoscopic,e> nano��s(�: %*�adnon4@nicE�j+es }5&8� ����PBP}&2a�!�hBh�= %�E�a?a�p� s,!�g� &> thwaG��+�of:�q` �*>`:syde)y�;domas"�}�i%% Bey�?A3:� Z*�s4\par@or semi� Y �/method^\�/�Nyt.tools &ı7tO;�%!C�)끭N�@ g!o ha��"3� �/i�i�Z�amoun�resourt.�{W_(����Fp -q�1qin!�*9p85sta&5p:S]"� �^�)�--z !1be p> �e�fN� polynom$effort�,o�}�B-us  �aseE��alP�7ufficint� (��,��ber"QuBits)%�!�5��haLse;al��~% . %�Q�i�~�t�(�`a�;���)�!|6�fw>�B���( +�0��icu�-B }(<e�est!/ d�e&>( ���b>gar�@��>�5�F;stead �u��8e[�cȟa�Zd1�re&�.M i폅�����w� �'a�8*� e�:��a n>�~demod��!be�-]ed"0��:�.L����B�ŗM� �������1+1&��[O(N)$ $\� $-�� �0�F,asy-��,in:t^g�=al,��(,lattice,reT3oY}%�d�M@n� Poincar\'9^v�:n�)A� a�� [% lag-��<�L} �<�}{2c}\,� ��_\nu\f{ �}/�\e�al^2JG�U["�S_tJ)^2-c^2x2T ] \,�,a %&3S�4!qv��(�%}E � D� N�d{,�4hbb R}^N$ refl.�Eea� N)$-y��So far,� �* crib�KN$(EC��!�s,�\�>� a�O %2� norm1��^2!Q � 1^2+ 2 �!N )�N}{g^2}=5"�W! nO o (JQcJ� $g>0�@%�va��! !\�a$)�A�`� �� sp\  (� �(}^2=N/g^2$) a�d�U�Z (jly� ef}�i�)e)��� ��`�Qu��,Roa� -triv�-n�� �U�$N��3$, i.e.=���B Abel��DA"�&tgr&�=� � =\rm)$aՉ2-&m�I/�-I�ai�lif���e�3c�= 1eɼ�Goldst�O���m�;(gap, see, \���z Ul:�1�1�PBP�5P�ies�6�6�6� (�nly du� K�� pin-% @�!nti-fer k�B��$-mat}), i�MR���/e��u�4�n"<�  5*�R��!h� ��,�6�Y�%e�6�� �R� eE2�s, cf.~i.e}�|dHNrun�H�(p^2)$� talsympto}l� . $g^2)\gg\L�� ^2)\�to1/\ln/$.�a5T IG�c!�QCD����a�-�ic�#x�$to\Omega\,�� broken�a�eds-�d��*M?"�v$gY ��1�.mo�z��� =*�H�[vacuu� %KT YS�( \hat�L�1�w�/��Am�o��h�^/and�W�0\�#(oma�:/f T!4��2 h�:Vyg% I�gso.�6�� stud� �low7Y��emh���+~u�e$N#�Q:�exh��;t  (mapp��u0" S}�3o0R}rB yF� 1%{09��}e|�b��߳:��-@ �+�B��"�����kaR EsG sub-e<�e�$1/N$���j� ermsz4I�<om���a֡f�Q~+&� E�Q*& ), X�u�\5�r2X&2�$-,#insrE� in hD0 � mG�radiu�mrho$ �d up at�$l+,t�#�G x$m�i!aWns bencaptu&>2arizab}(induEDa� �P� �LƤach-_ 6�� ��saT��ansur� 9an �n~#�O� uc�/<(5��$%� wi���7��Cpi�a���~w7�oA�,4g�7�%o�� e ��!��[d=Uvi� Z�;E)gma\invol�'length ��}NWtyp��I (M��c��!�l�Jx �!�-�� (l��' ing)�8Delta x$, the d�istance between the insulating and conducD spheres $\gamma$,4radii of :A= = $\rho$_$\alpha wi [�delta$ (cf.~Fig.~\ref{analogue}) are supposed to obey|follow��hierarchy % \bea \label{assumption} \lambda \gg \Dv x  � rho, � �( \,. \ea % `�gin{figure}[ht] \centerline{\mbox{\epsfxsize=8.5cm\Pfile{setup.eps}}} \ca�{Sketch1V prop�1, quantum sim!�or.\\�$The solid }s%g-z8 denote (super)1�or &!�h%B5�arU&contain!a`single electrons. % Shown4 just thre"ments�Da long chain (top)�t a close-up view (bottom) with�Xinvolved length scales.%�%�Q \end{-�!�!Ltotal Lagrangian forWsystem�� reads)�U5�Xlag-origin} {\mathfrak L}= \sum\limits_i\left[\frac{m}{2}\,\f{\dot r}_i^2- V(\f{r}_{i+1}, })\rigE9,,MYw�$m$ be!q!�mas%H �and $V(L+2X$- ir iA�acA�0 potential, wa�L only nearest neighb!�!�taken>,o account in)�m�yRs (i�yd).A�I�\is %(�4R� i�jed by� image� �AAr$e$aplifies� :�f}b{=\%�e^2i�P^2}{4\pi\varepsilon_0�^4}\, 0.q-1}}) >��+�U/\ln( �C)} =�%�!�,first addend!ja� minator o!Ke E.-h��(side is due!1capaci��-�N�F����Hse7 one b^ )e׭�2B;D�[R$�9ComparQ�resul�o.�in Eqs.~Ib}��C .��>�@.?8sigma}), we cane� of�� effective�yagae8speed>c0c-eff} c_{\rm9(}=c_0\sqrt{I)eI:Qmc_0^�"MOU}1/^2/Uu{4)�zRASјSi��!�IS term unde��(root repres��) classical�] �� us (of or<0$10^{-15}$ m)i�r-$=8$ is much small�aI�)[ of l�!�vacuum A0 \gg 2I��\realistic parameters (se�(low), i.e.%�ob�����:, slow-down. !�(Furthermore.may id�$f���couplA��$N=3$:sgIgY �&A3�=)�}{_! [4]{MF� hbarAImAO���Y]} A$�c:wN$isZ� us ov%�e squ�2�q4fine structure��n ta��value,J_a�be tun� vary!wA�ra� � /!C \gg1��!� well=U��E])bE$�StrictlyA�akingI� above equnn dA`min�hhe2� run U$=� (p^2)$ atA~*�( correspond�o�Jattice s�� ng $�$ ($renormaliz �scheme�kcomplete, y�$\L� I�QCD}$, %M� .�^2�\gg8\�0 ^2)\� to1��p�� Z^2 $)$ :,��� !�dynam�i4symmetry breaka� � s$1!r$ l-model (dimensional transmut%%�Tp$important . 4ity sets all oa�6P  s��aI�l gapE9H, e.g., \cite{exact�y m� satis�+�2i�/ ɔ. �50consistency, ��:�1� \ll1� Finall/��A(agG ��):�%���� }(x=i_)=�m\�}{3}}{]�}\,ɿ"���*�!� in��� ($ _g(\to\int dx$ �w A]$) of E2�p ) generatmx*� )`  �E�$$O(3)$ non ar  I8W &!�traint-�aUKu iaJ� ��$5 ^2=�x^2$. %�6�PBP,{\em Disturb�s}\quad�hBh�6% % Of�� rse,E<a.�� it��es�i�$o estimate!� impact�HA� ribua�(s which hav6en omit!�$so far. % ůadi�al kineu�-s ��q s $L$l �Tnegligible $LI^2 \ll ma�^2$l vid�hat�.�b} 4m�� }{qG}\�( */ }{c_0}b)^2 \ln.*?{� * ���holds���s(a sufficien�;:W (as�v,would expectɡF|ame!�son�pinflue� Bzero-po�<flG���ymag)�field (9(Hf��Le)A$9�. �E ast�# sequ� al�.0um algorithms*errmay accu{e  many op�� ions ��x&�ion� �~id -�ba{ 4ly a ground stA�problem � h% ,more similar�adiabaA�ouC ɲ"}��caaX deco !zv !'ecaas� �*a ��gw-�d�`A�Z� 7y gap .x2�롣� ex�v1N�QT��6-!�ist!j"�h E4bW>�$AT.L QCDc eref4 ��-aper�p!� s (Bimpurit(i� ��rial)LbJ9E��"� $ .  \� 7 -�(particular,q� to ' qC(behavior (& �!tA* next!��ph�variousR-�a  especi orbit��ɇy a��c (in� aris3o �2) ���*( pr͕1 0��F��6�Phase Di!em������B�Q inv�xng%�&�anUb 6b0, let us turna�%�%d)�A^)�#IQo�e}� $T$A�Ar� "L $\mu�v��low.<s $��$ �iQFm�muC ~$$, we�^ge�e usual f�j�2N  !'intro�on!;aJ� necessiᬅq defin 4��(le number (t is a!� trivui�� in �f)�ories= ����  ����achie+by mea��Noe� curren�B6�globalB in��2  � j}_\nu=� �}\times\�al)�!GassociaP `ch�a8somA�5 axi!�f{n}$� znr 1$��. H} Q�1� �D��{n}\cdot�\;� �f� ��TA��labor}y1!qe1P�$Q��e u(����ang� moPum!�uni��L%]� stila�ny e s $Q�r= quir/ o"%u �xlux��(�$cJQA_E^ermb �Fx E�ed%��� �jis &�less):")6�d-canon�@Hamilton�$\hat H)� gc}$ ds>�C} - -= 0+\mu_NN6QQ=�T8�ejis� ra��ack�ourF in ER�)observ~a�nJKFly &�f�BF& �e *�!� &UI�f{A�I� r �uB})/3a�BEi�f{r$J�e� } !xu|m�e��}{3m}\,B=z(`-� �$�� ^2/meQtF#E���itude �er�a�*� give� ���H�" � .-Wh� * �:��$� ee!�he � ���A�bar� i "��2 chan����� �ù� $ ac��U-vanishA%}� v (� >ű, R��AM�� calr $B) }={\ O}(m*�6� /e)$ j is��>� occurJenergy!h!�  ( s�M�X)�a�9 �E\mu}_sqB�E�jN �)�u� bigg��*) !+HOxA{Z4 �2eV; s $B .k�outz!�!� � tooc�Oq* hand,; also poss�?xplor��e full)� F � cros)dfQmonito��# !#� of�5 ticla  %��se/�Rdiscuss4�Vi�A�iA� �6 ��"�,milli-Tesla.�B �B �B Expere>#P"c�L �L �L �ba�q io�v�s�  *^ .�e�j}�8 EPf�!�a window op� y"Y��5T�z�����eduQ"�% -- "9 (f&�)u� �Dent-day technologyA�L"Py�l�$E�s#ultra-�8��% eZ&bod�of� sona�size,��reach2DS��10-Ku��gas coo]via�ox%"�If�!hoose� }��$rJ$�=100\;�! nm$,y(=4:E=5:(=2.5\;jrm m$,� "�=1: jj .N=\ord(1)�.0approx 10^4\,d/s$60p!},22�E�> j�$*le 601�,MU�!��M�vy's%�yf&Al� /#*($start frome"pi"1 f na�(Q� �facil&K p23R�:a� �EY !"Y-���&%�MDY)B'122M&2M$\2!]aa��� x.1i�""Q U 0^5\Y- but nowv~y Bl .�5G Kelvin%ܡD6)%,�K�7'�Y%�a 7v �! as"Y,5�i* micr)�s!��� two �%�s "�  w�&R`���optimum!��h .&rEUbab�!ome� �iddle. �thin *+�-�� �witche!'�>& by local :5��Q (F6ie!"OEs If"on j�)is �ff�� �ru"�x< B ,�har� cB�(ell} E_\ell� E��$2� �( +1)}�$^2.mAi� �.s-� $?=0i!0p21$,�%it �6,!7� Es��Yr�rn�t2S�nweCCo�!t��.E*@b�+2)9��$ iffe��-ie�f* of�* �f )1$x��. w lea�{��- enta"| �Z/.�%��w�#�eO_�.%f a�"(f@C .|���J) ��R#wa� ��aore�(4|\bra{\psi_0}dW(H(t)/dt\ket  1}|/�+E_{01,S $ inMm�tm(� .! $K0�%�typa��m��ime shqbe [Q�$a few picor� "U$�}]�'&� ���IV� �$in>�e�Nre�&lef��d�)of��"�tN�W�A �A �A Summary}�1�1�1 % AsZ h#demon& �-�b#."J uc�(�� �2USB�%6��T � *� �S�'i�)*  uter b"al� h�L.W"A�a�ntroll� cenh,��&�v4)d non-. _2y�metho�(>�)f�� sy-z",$e,�Z-mat},� +ons 2iF"or z�a�(2�!� dens', �,ev�,��m sum rulejg%alg!/S� rix �ex�( etc.) � � �3 nume �/O�*} gh�\)��Q � A #��&�� �nt�#mos�<�F,%�exa�'�� jAworks� �(&�) �<�$ I�no 3�ary��@perform a Wick roU$to Euclide im�* advantageB� stud&�vol�&�e�"9 ,7 � colli�*s (5�%�. 6�.!�5setY5e!f direa�c��.u��Ed,an *�0sD!g6�N�or _4< lS*|� %7c��d� ���-s�a�radio/H -w��� oscopy5 &�s&�levelE&�� )! higher-l emptZ isol��(K1% emi-a�uctor)I�a sharp� 2� (fluore��ce�sur+ ).�0 Ge��%a>�s%(a circuit (!-guide) BEo��1�AfUmew (vic�U�e�( loop!%6g!�o/>� A3] U lB�*� ) b� :� . I�)i2�reN� les �th�6anti- 2>� us9i�r$S$� 2�,%k� illu�5a w�7(p)e/�5))��' polarizedB� !�e�, �:Y��)Q�sub�( remarks�"�$3esE%p')�1robustne-8r�gU%� >��)er�&(./Ւ6sity) �8�0�B8�!3;+ gree� � dom. A!�i�[ �%ϥ�A�"!mof�/ ��1J �%��3%dedice�t� � W!gz�,cb��!-uf�b)\IHq�)�B�<*$�:���du�5$stood (yet�")w �""� If show�kavaila �ofe"ewl 2��#���Z��yM+V <ests/�� ;#ly� ds u�Fa*�of�a�2in phys=e8 m� y un�k*outR(�� �� �� Outlook�� �� �� f* �)ng� led�f]ua 1+1 .W3situ-, - �� to 2.-sA��-6 be veryAa�,�,A��25&i$b�&>s��� ��B� �%ac novela��*s,�Gs skyrmC ]�describ�D topBr"s $j^�1=\<^W\nuq$\%v$ (&%m*%U!�B9%;!.inclu� �a�'plicit ��-s2>5!�E!��$f�$1�be eas�%�2�&'we di �9 corp %e a2 (Chern-Si;��� $\theta$-� $ L}_ = \,>K�G1G�x�# B�(+� o7 �! 6�$G^*_-�}G1��n ._(h�"+4����%* a�:-forward��Fp:��%�op� A�a�"�-��n = te�?ng ��{th'(��QCD%�M6v) durs he cosmic�O*a4(A-�)6� of]�g �(m� b?�bp tool��= nos�(nd�esourc� % % S ???�A�,6,�R5ZR5$Acknowledg����R.~S.~gU7�!y a�e/ uitful�_i���I.~Affleck, M.~Krusius, P.~Stamp, B.~Unruh, G.~Volovik,E�8E.~Zhitnitsky aolY�Ert$ Aw$Humboldt f3eL 8COSLAB Programm�1 ESF, CIAR}NSERCeeK� wa�9���Emmy-Q%BV(German ReseGF F� (DFG)�:�(lt ${\rm No.~SCHU\;1557/1-1}$�������j�j~j\b]Gthebibli!�phy}{499�{ �{ �{ �6��B�< \bibitem{quasi}��,PHLTA,B59,796�">s>��,A.~A.~BelaviigMetast�S�s�2�al Isotr( .�!� JETP� �2E4%�L75) [Pisma Zh.\ Ekspa�e6L Fiz5�650ec 75)]:�(JTPLA,22,24%�6��.�a� hvarvA nd Y{Tyupk �Pseudo cle So )h2�E�C�f�8�:�9�8�V%�Fateev,�V.~Frolo5��E�q�F.�< Of I"�E�2n{@(Sigma Model!� Nucl�Md154��Ed9>d,NUPHA,B154,16d� � Novia@a�A.~Shif��!�,I.~Vainshteii�V��Zakharmt>m�s: ��Non�J@���%�-  %Chromo�C.�Rep�41�:1Il84) [So�X�Fa�.\ -.�c17}, 204!&(86); FECAA472-5I�86)].6f0PRPLC,116,1036I��#Luscher2�Non�# C�4s�IAbsŚOf�E�Pr���In�  %>TLi =^f35U8>�Q35I�� ��bK�Rhlmey �Scatte� Of� � Lump ��o�,� �>� %Cl�F*3��!�46!�j� 7,46!��!(.~ZamolodchA��J%�Factot S-Ma'�' �' As!� E�6o C�< %R�<vi^JM��*i E�Annals6�120A�5�A .,APNYA,120,25E�6��0P.~B.~Wiegman�U y!�N})el.5�Bos�!�w.�AYR'13� 12�s83>[�)131,12�uJ�6@���zE�VV�5Ū0�d85); %Gu$Hasenfratz��Maggi�0�KF.~Nied� Q�� ��� Gap2�O(4Z���D = 2b824a�522A�9B�-8245,522A�&�( G.~M�nelli,(P�=i�R.~Pe�zioE�(Monte Carlo2� �8�>aN� %�V�0A�4�781^ 00,4�9(K.~Symanzik�ConHLO.!hIm / ed A#*A�L�JE�(ies. 2. O(N=� %�4P*EA 9� JG226a|� F��1226,2� $Y.~Iwasaki�R:WK(Group Analy�OfB�6� � %A�:B��/��ArNR�58�4i�5>��58,14e�U.~Wolff�AsymptoDFre��ibo%�ALN<��b�33�5� B �334,58�y*# } % &T0on E.~Brezin,8 Zinn-Ju�e% J.~C�  Guillou�>�Of�9s=nAY(�++ E�S) �!�m'� Dc�261] ~.�$PHRVA,D14,$a�E���ҳ2���*�  To�H&�C>+ 2�� �3a@69ElJ�$RLTA,36,69%�W? Bardeen�W!�&d��E� ro-%``�Ap;i*# f�2��a��pr�9��J�5�9��S.~Hikam��5�%�T�.Loop Cal+4��,a4>�Rp�� hy?A)n11a�m�78>� $JPAGB,A11,$AQy<k"-K&@Tsvel���K�*�6en�m �H} (Cambridge Univer� P =, , 199��� M.~ChaikiI�Ti�ubensky, �Principl ���J.6Nf�*c�: phen? a}, �(Ser.\ Monog -�1�qU2>�IM� 113~ 9�a�,}�Farhi��"� , S.~Gut� ��Lapan� LundgraN=reda, %A5�A[ Ev' A�J��"Random� $of %an NP-�lRPr� 6eN472� MdChiLE.�![J.~A' kill� R*{"f*;-�� �Q:�m6b 0123e 20%y �[>�,�,�,��6���F�������������������������������� docu� � � � �  ����������������%w/2 filey$Jou�/of"J In�1� �  �  (QIC);&$ % LaTex2e�"inRUmacro ^ "qic.sty"� comm 8\usepackage{qick3%�1�"?s�)e bee_-+_"�csty� ile,�X�2 n|bto� put nV L�+b)!�^+) thRJ \�) class[two�V]{�cle} >�2$alltt, ams�f,,amssymb} \e8width=5.6truein $height=8.0  \renew-&{�' foot@}{\fnRol{} %use$^bolic  %-���HUSER DEFINED MACROS� \newb'em{6-}{ProW1<} \def\se#1{Sec.�j#1�c s#1#2sEw.g#2*dCDef& \def DDefzDpro#1�BFpro F�zGr�~\yW�r�F4eq#1{Eq.\eqref0eq q\E � ,�(ens#1{\{#1\�.)ket}[1]Ik$|#1\�(le$>*g+{1�;>0 0>1 %�.{zz 0B4zoB6o61B6o61B6bra.�\laA=#1|B�ket-2J72F7bra! 7- 1|#2^T proj � w!�}eu�pc1}+*FLm"-V"p C+>]m -> ebit 0yBZeb.� }B�eb5�01�N&1�00Lrdef\bellA�> Phi_%*m�ztwa�(\mbb Z_{2}^ �Bc ( C^2)^{\ox�I" rar{�]arrow Wxx�4.h hookBl�+BRdR��.LL1LonF1l1 520Lef2x+x>,d,�c.Al`?�/s � slar!dstackrel!E{1r1iSR"�".�ox}{\o�9^.big !�den}cD(x): cA}{!ncal{A>ncBBBC}{� 8athHC}B+DIDBEZIEFIFIFBIGGBHHBIIBJJBKKBLLBMMBNZNFOIOBIPZIPFIQIQBIRRBSZgSFgTITBIUUBVVBWWBXXBYYBZZ>per��a rm{P�al{�I ba{\betgaak�ZGa{\G�t1ret\da L eps�silta�ka{\kapp1la{\lAi}��La{�Ksige�{ ma�ta� �.`  �bba��� 6� . "+I=r�+;/�  �> {% } \set�j{� � }{"� d} %FOR 2ND PAGE ONWARDS� u� head{(*a al Power� W GHZ�tes} Z4{Ellie D'Hondt,DPrakash Panangaden� �gal�N��"(skip \thispIrZ {�= ��rer{}{1!�\copy�w�\ing{Vol.}{No.}{Year}{Pag�s~tB.0}42003}{000--000�0vspace*{0.88t% ULf \f��2?vbf� B %Pu�5 titid�bZ+�� �37�2��!rVv: %�$authors' nf/addjj�: 22�015��\it Der*8A�Mathecs, Vrij*eit Br�Sl} \baseQZ=10ptfg(Pleinlaan 2�.50K$s, Belgium�P}fQ N�=���S�Nl�i�er , McGill*��3480 ru=D4y, Suite 318, �$�C@, Quebec, H3A 2A7lnad�uy0229�hpublisher{(May 19th)}{(OctoY_5 .21Q %% \abst@7s{Zf�Hgraph}{I. thir.B�My�Dly �.F,�] keep�` TA� M�| Ilik:To�FY+K �RT %��f43A>[>t&>Yof"�2�K significa�L enh`b>�?m)a&[��s�0. MuchX the e n.! has foctAonA�l��-�Am�ua�A)�,U s. Howeve�f�<2.�h* knowMK}J re s;a�b3_7X � _D&< t�9"u&56WrN)�e GHZ . Our m�oTj`l:a*RIn%�s�e�X{.R thes@s��!QZ�o�X adig��h=s nS��+�i�ed oj . CozYte�Nw3LwY � KB\emph{ z p�g%*} /:JCF-VQl�^[B> of+@er�N!6" onym�f net�7s.�(SfT�< �%�5s!\!�a=E�:�s>� !6nsensus { n no=@post-pro*Ga��Zn7 red.$s�asultsY�8> a fami�! f W-E0�a�2;�2t�he)UMproofCI�r�[eB�Alie s�=args;F }{}{.�S( \keywords{pQ.�l�O=�,5�I9+,�'d �,Q0,�I��3p�� ommu�ate{to bet �@g?Ed!\ial2�pt}2�  �%) USE THIS MEASUREMENT WHEN THERE IS> %) A SECb6 HEADING %�V -0.5�%\noiEKtRm.�Apq� paperf�.Q *{In&Vf?�� :�$=�=��paskGs !K�Er"IJ a`$s�0Nielsen00}. ,EiW N�veloped7G�b�M-3�xK�=�� �-->�a@Z�--NFR��]ing-4Lynch96,Tel94}��� �cS<�5zaVTraRal��?�Qly �Fn�qra��A:-output*�W@2;��7?r�in�9H��YKI#"@�AreducY�%�lexit�G�GU. By�pqM, +Ap& �ab^`�jaH decim7 making}a��pc autono�� agen��I�Im��@ spiri9f��protocolF�PithV�.a who_iew!�naE�est)�-AVGb�n2G le. ���D�of ``u)ality''AQm�q�2f!�nU}le�M�da!�ŝnoY a �Q atź��� �gtwo (o-hre) qubi)LnNi Qbut��x Dhas] �X� �H�3yn one's a��%� l�/:(w.�doHaa�Dp regio6}On7��hde� �22�i�Jid�P�9bFrr�( out;� SkwOar�A��]�a��H��6L-- .�VI��܆�|1$=#( �s�M�7ea�Ye !`�fsk)%!�JokA�m�%P�\. A<*� m86:�\ QH�s buil��Q a�� �H��B�5)�carry!d>\B^]Tf  inm��i� } &�  W_cu )!Z��� (��=jpr�GelyTp)�}hePan�Gba�|5�Wm� +s go� s�AGS� howBv}AZ �S&�\&(YMa�50set�$. Lea. .f���A�Iv�in�R� ps%Xfa�a��-Au��In� �\u /Lx unique �{iAW!�" i!�� bro��9Q� o_me LeLann77 By!��!�n� "J� ly"�}%�>K�m�Ke:�+not��� can �} �f"#!�s��� ame D��Angluin8�If nb 8� a coi�eyw  a � :%�_St%a�b�f Da�i�]y>pa� qy ^� R. x2co�z��guarant�!� �DreAQ be m�6 than�� N 6So ��k�w�A��b� pe�� �ftr�DeB�dea E�ufE�H inBY� �Rr*� *Itai9%�B:e�tv� �I��e eventua��K�misA&=)�!" b�dVa�� a2 takVoug7�"\N&�g%!� ŷtwo.  lwoOax�SeN$�\�bU&>BS itZL��!��whoA0Xay,VI.a!eW�� 9 step!~ always� ceed�+How do<i>tYDtwo�H�C ? IEh��b ��i͹�SframeA�? "�u ��ly�M�)*d�N&� �# + �;�+% � at�N� ���Do�P)Q�� Յ�-m�F�!�so-�>ed�n a tos5 W�&2)��5A�A��{,%mW `�K( E�!� Yly9hEQd�IG �  one ^�ic ot$��* ���-�� L��n �mix�zL},�Wa�fa�d*d r;2�bblt'o^c�3ls��!��:�[I�&ЋineV�s!��Ual'e��oa sea!�en� in� 9 it sa%)�ct� %xes� \@�6ft.�F�curS=��se& ��!8id4^�soma�Sou�}�fvis� m�?x^+�%lt!�up��a�>��5� (l!1�5�wrtQB��[r�e�n� Aqa�&Q 9&�. More�,""���k� sIa��c �Ew�y igno�D&�p6�Eq&Ay����bt��"x_R���� � ����E 2�:%19 �wz y�Je$t�v�mA��a� w" k�� 1 �FjY�ɹ ncep��icA��� Qch�5�U �bof e $. She wri��a7 F�L `` [\ldots] it seem�tui+H��y.�T�a�%�$depend upo�`�l MK ce'�;�X��''� u��!� H veY@but%�D-+;e� u�dic6 dA�l(���)  .�Xm�Mn�& E-�detaizR�Gquite�� ent,� �;.�l]�n! a}�����A�In &�.e}AF|B]�"� !!� .{!: ed. .W ves}a|zes9AcI�s%\%v�l� �*�eM %�9iM%CSe"7/qlesec�\j.qdcurj >RA�R� �^�.�FluM�.C H }.�S&��)hc�  \"�A2��!� n-}&� ter-*�ng�  &�co"Q;sncu�l3Wh�2��%�uAis Igg�Cl�<��l-�EAfs� fic 6�Xs, i��}�e�onY�` d `R0���a�al ��E�of�b ivid��.d�M[��u�Cof.�q �,2��2��s�`broadcas�'p� $ �$!�q . JC _c�a �s �rma�F֗?(?w%�' ^orK� *��~ as �!KRas�)b6�]mN�  "�%{IAa�`fe�.1��O!U� !} up.�CV4Y!�5Q� T�d�n��-- in�d�a roug�:��we� �  U. �$Y ion -|��9�"� m�Em mess(�;w! f$c��o&=G��&�dnnel�P1��-���g6�Pe a�St�i���so�bi[dtox isI|�Aas LOCC,�� �Ŧ.kal�"�io��[���mZ,BΕm � dent!�A�aPa�y�X��inu��'�akyb*�CAs �AvA/A�u~���"h�invsntUH�Kt9�#n��^C� L�ere�v at5Azrt � in�O)k9\I�. &�� Acarv[��e߅�� ��I��s deed,r�� �D�i>��!� Y#"`AAin� !�a�d�m "!9�(�� �)*k ,�ID��itu%� �k� _~2�A�;i�!�1��` �f��5� :gq+�\!}�?n immedi7h� �2at>�4�s�*)�v��on2a�, %0�d=g&rixA��A o� I� �Q9.&�-#:��} AB�2�15-E}!8mFF�$p$�  $p \�{1,\c� ,n\}�ecu� e. &>nd%)�u�:�}d f�`��>��%Z /� �4den{\cH_{1}\oxj  n}�ao 6%oI0d'A(!�J, $I1}, Z, n}$.U e�w�ll ��v�r�;2� }.  "��.�&mc!ymC���a �izU�v� den��ed!% ver�=.�e%a5W-9$� $\!!{}$;�E��60�8= �701"x700!, Fi��!i"06� m .�!��! ����qua4!����vDuK �Í�receives����wA���to�� prev� I, p�o�lU"� I�� &de� 4�qionah��r�?�dE,��isG "�#�� e�. :!�ge��!,"�"�  i�-%Cy��Ud "�#t�k% W�vestig�L.2 ���%^.&r\! !����Gin�".*�2�� 6L k���I#U�$if!����Vxl!d&!�!� �!)� S7�#ct}YA�g� ��I�� �diQa&-��:�*2� �S�l�rr� @�� �.�. ��tcr��a��9uq ex!&.�ofXn6�MM�] .� fy�����H�].Z��+1�A��a-#:�}�%�,a&)82.co2a�Aڍ��"{ e.X�+ne �A/!ɥ)� ~n l3l � es�e :0er��%-�d�f != �P u� �� `�o�kQ6th�y�@�value,�)v be 01k �����.2 �#.�vioH ei!1|!�orQ�q7Q. N�L)9&*,��g� ly Las Ve+�#,�� i)�y ��Ave!% styEZ��B��!�re#�u�a�bi��!��<s.� e"(lli�ituR�����eaout�equipp��,5�)��ndo"�Xi��)0tor o-Uro�#J �f��j� q �����"6�&� ٞ. Any �A]of� rse j�{D� e�aos�)Tr��T2api** @  7)f& ^^Ye�D.M&�� l�qe��"�� .c ��]obF>�� �Wf Bia-~����. QgS�M �QhRe � a,�CUD���zB�� A;����of 1l���"�R���a .��o� V�#� ,I5�Y�J%!�Dc6-V � brancG(E㭤(�*e'q �03N,mb�&or( �"l��a��"- J �6 "c "& 6  $C���5A�<s&-� $A$e5 "=���ex a`.��6�$C'�p��^B�6^��XY � &+ i� s]6$*;Dp(A)=B�d �= �5 m�.>A> �orA ��%har 5� be-�i)�%a� qZ] i�aso���i��r6.v $A �%%YK,�|���e�Q@A �7.�i]%Xi� �sh�.c��&^��s}��/��s�tj����2A(�r X �]�al�3A�#l�&��me�s 3S%is �ba�^--��yfacF��^l��2Q5"ny� G͍b�t V�by�*app����pr��,t!��}�- d�|w])�_l��p<�"Ill]�o$frZtlyA ���%�:�3 ger ":�� & !��& lear�H ΅2?10}� a 3-9 w . N�.�:%x� � +q�%���m"Y qE!E cruxQ���[ 4, �[*"�r?��,ac�+A��b^O itud�F&�= ���?X-�-�s>��M�� �a#q.� mNeuT �+�diminis� stre"�ofIvM�,�O&RelM�LA"Q.e�**��Ft��:p,A����&�9eoI1��A��*� ��� ��r�N�=d84 essm��6��� )Ung:|�!4�8)IXa��i �sol#u2r1�5 qmore � �$ܯ h?. \s�8S�: ic m> 3 *-�D 8EWKd%� ��dxE/s̸� ��q�"Y�ly�?.� a.6. m6j<M���{��i�ɭs����3th!�Aɽ�!��a��7���a��9�m"E�Q3)��eA���Q k�y-Kocha^t�&�P( b!� R:bE�)feb�!�� JWX 3�� m owns����*� �� } Sq an $n$��t$��cH M n�M  �(a $2^{m}-$d p$al Hilbert����.`� r=�� s8�� " � $k"q{1z�[!��� $p�, D p_{k}����p< to �&,0 < k \leq n��f��A�AX�* ��a�rthog���O�qs&�A �.8b7 a[#O $�L,{P_{j}, j=1,�s,JH|6&%($� {j=1}^{J}.=Iq '}=oI_{jj' }$.}nc�\cH!� $0{ ZHEr�-� .I&@�ym�iD$?inU.� ���$J<1aI��2}A�u~8��!� n $k.A����as3�|�"z* �,� t��I�� �A�\de�(E�"K�t����.�< all}�z.�.g�)���)by�m+"�=p�toR��!VE &} � &� lemm� yCi1'�4I�ogniz&�.�z����F{�SQ�]}�i:F4E��� ��i0E�^� \in .� j � if_� F �A\phi_i} a �%E`}$!�e����ensa�����K�K A�q'�6[ N�� coe� �"� {l}}ɲ� ���!�;�!�Si!)/o�.Tla��5 -��) 6) {C �of�Ak��8 l�8of� ��Z% A>�a�Fof>K *� ,\boxed{\Rar}� +4"�F), i�k1�b� �h��Q��$�=͒�]q%~n2al_!w1 %�3��A�nJ�.�)� expa�x���UEh��Ej�!=!�jM9j!��$�re2� ./*����F(.el}ٻѦjU�2+ j}})56126a~�Q)Q�01W,BEosPwor��.F�%�l� l!�ap j_0" rnwM�LY�B����> �trE%a.�3 �kbaZ��1i}N�b�� 9��o�e&�$|E-0*� M_$. j6�is �NGzG J}YzQ2��_r� � \eq}?2�2=.� $R � b�W k>Y!�R)k )�$,Ÿ� ��Rr@e��!�9G��Y�a � 5tFn�xŅ��ac.g7 x7 ��veAte�|u�:�2: z�A�Z[��#�#�#�y$��:=a&��$ last:#���I� I#3�45. Likewi��:1w�1� N.)%.h � aF a;bot=ns�! ++++�{+2�>�.Q +++--R ++-+a}2!) �)��=\; ^{2}$�N:�Y� ly $(n-k)B2�%, 1cL-1F-I�%� Q���"��� �0$m $\1{}\0{�(n-1)� ��:� %bP��in6�'U."\�aJ,e i �,JToO� �> *eW�|"� - . B.�K we�,��/� &2 \!-6WCG� �7low6sOA�.�h-s .=�!�*�KBk \6o�_�:(N !�A�; �ea �� �, "w6�*�'@)^�*d S=N�1�:�L���)Q� � �A�E.!-�U�-�� c�� sw�� e�*�='�$l�EI�(t {��9inu�)o $M!V"w�1:�\)w�MP��|�iD�&�] b�Yub} *,&�)$2� path�&xKah1�=�5��#nZ3_��I6X� @� .�$(t�9� �R�,�pro�!&U.�&9���5��J�>o �`,ly-6�!&\IY} �= of{"�!N9 !>�KI���z;/�r�#���*cQR��.A�q4q�athbf{U���a;�ary&�#�2Ť�!�}7ncillaA�!~3*. $M$. If DZ7!8}*\A�i�a�N0�@ �/ ���%�$�]�n}� $;� �0af�X� ype)- we ��m�&# za��L[tg���F'^�/ for �}�:�i|h m'!�67m� .��$"w.aI� s $j���o�" t $. Kn��&�:o cAn�v�c>�� ��.� N��"�,* %'lgY�s�lieJzH,�,�HR&2U,e�2#"a�U�vP!���-��aA�B�-�.$irQ�(aQL.Kj&�6�^{ /p}$!%n�:�ab�a�� >��_muentire!��*�Tpro�u�Usq7+� �E��� %�O�PIt&&�erv�y.U���<�F�iGX�� Qi�Lat�pBA�t� �W H* ��&H%�a�A+"[H�)l%>J#X8 .��+��B.j%*l{�Pe&�%tqlH< \�o.{6I p �| 4on}"�;IniIe�N� �4, Z�:vQ1/���J*QMdH!Vul�4�l } A &1Q!6&��!5�T%���t. �cOa�'"d0:4 (QLE�5En�1 � �(v"BD7 #��(TL aVF���:��W�E�\e颁�� ܠ�VQ$\aV@{W�9.}l%��a}Ih��z�ec�<�%�"� i E� I� E� �MG@E�uv��KDtep� T?�9aW bG1n& 1&TW�=�.�2^��� /*� $W_{3�""�j�"*���8�#� H7�&�!Q�q� . E6�$i$�8r�4ou��. �}.�vp } 1. \(qfQj i\)thIMaV\(W\sb�)�Y b = 0 �z$ = wait 2.:=�W\) 3. K 61!��al*iLelse [:=/er �y8��B�0�� [= �W $\cO-�e�no �< p�=ng.&�W1ul)Nso�=!��M^$\ove��W}A2� o0�EMo%�)T��e�� *= �#-M��$*��g ')@.} ��/>QLE9>LvD�&-S2�<�CsS0in 2|H � B��.� a����^���Wa�ol �om \s| s}. 6R'w��a]��"� �%u6ig�3��)1A@A-.� � $P!X>bi"�(%��j�LQLE]� f2��$B�9�R`1!s$n-1$=��#2JW0� U$  #$P$ e2"�%� i�P[�.QH,8�Fh1. ?;� .9 } v� ����J� Iz $k \�Yn 0  n-1\}� ByVh e� $� g ("� ��&�)� �%eA~ \de{}�2$�`� q�or� & )e_�>,�6` �FE. a*��I�5s:�*� ��rPTe!���aq`�O N�4Y$m$ s, �2�m!_TsG$\{*y i}}�<tWPaM*A[@��-0�%t� iO.a�� "0�%��Di�D2^ \�ia"} :� bigo��s �"�q2!i� ll� genWB�H�we�Y�,extra ingredU�:!�b�,>_ �(s Ƚ�������2;3m *om��a�� HXe0 tL!��K I^.^(is sl4r>-�(�����(So�'�> $\cL�� span��b�' %2~$: ! c#lE� $\cFJS �er��eFU)�i�T�!i�>*(k>2Salas e�!&�%cL�< ?"=Hrke��n � .|�auapp�ԍ( tensA7Y���)EP�ST ��<d��Pa"$=\cL \oplu�3F���� F$l�+ a'%��On�_ qG&�(i������ �icR}A���jɟ��su�V ��s!1�>z"j I�I�!E^ ap8s�Ael}fM �9�g@ >]IJb�U?�>� >��a&�ev+��0!R���le"O w ' �y��*z4�r]!7!o%7�#2�Al*sz�8�.��Ji !- !]W)� dras!�.a�o�@�)�sBE&-b0ui�w�<� odd*/5�s%"v*�I@o  %2�% &� $�)0the Hadamard�lJ}by $H� =+�M $H - $.�A T� �o 2,n-�/�$��1}\sp�w2D0(n-2)}}�� F� cc� datev� vod 4� I� = e�b�  $ \(H(q)\);6VJ"% bs-EP$n��A����&�Z gets���atњ ��r� aK�Ii���&[8heEr ^+CblbY�H��y2��ZD����g�Py��~��%12 f�XZje|"/RA�6=&�4�1te(�O� "E�?q �)�D}���b�Zdapted w&-���.�IN � a r��K&y� h!?a "� "`.�g� �2os2:534ds�!��6bclock�Q>�; O�C�� V�l4Wit��_K�W3~E� A�7 N)�c��Abrr�Uin-�y1�A�%� !9"��qg/ ��4as*cO(n)$� ~�R�}Q q�P6 � fR5�> i���%Js��T=f"�g�/AS)X"�3PI�y�[4o��+py*�o{%=m,e"� .�4"[A�h laJ ��ar"�a� �K cave/,���R5Tid�a�=l�>Z�3A .�P7��8� .246�VA�b8m ����rea6%�La�awuID�eOK��ghtW�P-o)�"�bA�y]] a  B�a>�Bo�6  h& ��)��6ly� [aj!)B7ZL �5 sum��f�X���I�.��"����-�"�Rh (QDC)aDv 9 !����%1it�l��Mcu� #�^��p2 6�2/�b�au�O��Ie��qle�d&gy�"��.}! sk�2�2�!�0 ledg�^ �nA 5(1�J�GHZ�� k�_s n} + � .�&�%��s �B6�΁yZ�*� :��Y���b$Q�: � GHZ\s*�i6.� B�0. j��;J�PX;����5e QDC��/) ,S�a �fJ��6t^�[ ,�_ "1e��2%&�;u��g�XcL<�?A���� A�&���b cl+;�6i�resil� Zmaxim�$n/3$a_�#�Vs[`�p*2�m�.�S� �DC��en �9 jG��:�U% )'$B`)?$k < n$!�C� -V�CAL.�}�%�-�WM"!�&�$�P$.�uz;��"c�!cnn�*���be &�i,(�-]D;|+Y���eGk$ �sq yq(G.*mk=iA� �$C "RT�4��!a 95O�9�$�� �:�1le6���$�un�? "�?%'B���6 ��A3��!�����p'.z !5���!�����n�m}*�:��U;]8genGHZBAn c;$-+ d>�ALBM �&H�-� �[.)~,�D2�mv7�1-�Z �-u&{��g yp[�eL��1"s>�zl�]: � *� mB�{mj&R\a�VŁ!e@#al.P>:M}��"�d� <*��Ygener"�AuCIݵ�t���d"�tlk\, %[*Q:� �t k ?�l� &z� �e;Y"h !�a maj��%��e�d6�)2W!p"`��Ie..{E7��Air>!,�he ��} kU a).a��Uk e*�@!��K*� V D1*`-�!�0ytvnt ~:[�*�win��%� �an r�"di.!�o�nit6!�ҿ ��&�%6Dur�yuw high!�er�+ent ' Briegel01�>, u9B U�Am�EU��m�i�%��" averagEde���6�. 0%!�pro���langu�]� �K�p�k�OqFs9`mKvs.6��T culi�U�a�u}7��&�cJA�s:!�fa"�� �-�a impl�mA"�.![�yT h [a��d�{!t�cˢi. "�a =��S!�ol�� ��Itho�G�B�9 S!*�0�\si��wEgri�]- one-�l,c-LRau�� dorfA�k�qls?�/�P� �e�X�3w *�k"We������ ����'�{�L���ces~I �K%Jome ^pu�ind�K�&E|m��!A�1a�{ato� Mha"g0f�tak�2�XY ��_*�]�v�&1� �$presents t�Chis as a classical data structure one can simulate this efficiently ;�ly. It is quite a different story to ask that6t�istributed system exhibit the same behavior �J2�sharing an entangled quantum state. As we have seen,`re�no way � . �cWtlect a leader. We are not say}? withY W-xs@wr!@transformational �programs EcanX be s-{d9�ly;U}.yth�reactiv97s �Pabsolutely impossible.\ . TJ !y o^�.�0algorithms us)�)u x� emEHd A0ll (let alone.V) JU]� resources. Perhaps new fault-tolerant behaviorss be! lized. -�)� nvestigat �(se and relaA�qu8ons. \nonumsec!�@{Acknowledgments}indente$would likeA�`thank Elham Kashefi, VincaDanosu�especially Patrick Hayden for helpful!v cuss� Ta�4work was begun!Va3XOxford University Compu�Laboraa�EEN�E,institu� �8its hospitality!�4rakash Pananga��suppor!C8by EPSRC (U.K.)� NSECanada4 Ellie D'Hondt5�Vrije �Peit Brussel (Belgium)B�Re�qce2�< \begin{thebibliah$phy}{000} �l$em{NielsenM.A. �` I. Chuang (2000), {\it Q�bc%`e�/q�inu�(}, Cambridg�y PresEe�$Lynch96} N� (1996uD�1y~h}, Morgan Kaufman Publisher2_(Tel94} G. T!M 1994YIntroduE�A�.iAu��eLann77m �77p.`�j s, toward��%;�l approach}, Inf. Proc. Lett., 77, pp.155-160.=�4Angluin80} D. �85� Lo��a�global��4perties in netab s ofcessor! �ofE�D12th annual ACM Sy�Y$ium on The��ofy�,, pp 82--93,1B Itai90} A�Tai�M. RodeI �4Symmetry break��in�)�R�}, %=� ., 88(1)�60-87aMQ�(Tani05} S.  8, H. Kobayashi,�,K. Matsumotoe51�ExactuY�!�%/�A �Pion!Y blem!�2W 22nd�po2Let�A�3t%� �@er Science (STACS�HLNCS Vol. 3404. �Pal03�DP. Pal, S.K. Singh �S. Kumar�3�0Multi-partite�v� �w(us randomiz�: fair%=unbiasedB ]s}, �(-ph/0306195.�rs Z@ \affili�Y{Pd I� emIf/�K(ics, 31 Car�[e�,eet North, W�$4loo, Ontario, � ,, N2L 2Y5} \aA {03.65.Ta!V)h abst�.} Many^mingly�;!W� effe��Cn!Y��prediv sl outcomɾ�� medi��a�s mad�>%� p9�ed5�Y . De� eP eara' ,s|� do�demon�t�e")"(a nonY$0 hidden variaOe� y, s��xplan%��erm�f �-}urb��{8e. Nonetheless,����for everNh w�in all�5(Zt- I�ed proba�� !�0 or 1e&-�%a 98�s1 nonAD ogon ,�an assoc!�d8 of��9:J �pr(is obtained � ida=g�=3s involvFheJo --�� �io�.0��Ealter!�ve�".�.�saFN5.��aA$gle time. ��y; \make��� study!1�~M�)�!� both��2 � init)}by Aha<$v, Bergman�4Lebowitz (ABL)A�H1964 \cite{ABLRule}� has led!)discoE(of many cou8 -intui�resultA� hichA�r�C$as \emph{p��:� (PPS)�7} �HhaVaidReview}, some�` �re`ly beenAEfi�CW �+ntk �TLundeenReschSteinberg}sB� Y �$a long deb�" abou�E$pre  ABLA�bidy rule � Kastner7}� � rcur4in m e!z�!x conn� betw�PPS1)A 6c For��^, Bub& Brown �Bub} �stoodnp> !bAlbert,UHCD'Amato-M$Proto3Box}a%��cera�a���"� e ``3-boxq�''Ea\ imE4 nove��L6���a�, 7�c-�LBell-Kochen-Specker ��em1 ellKS, KSM�convinc�� disp�%�4claim. Althoug�% uagE�Ref.\ X=Hdoes suggest such a�ding,a}7 6AAD� ent}%�qsz rifia� heira7i��r� �t�I( A�n)!J4conclude anyth5I�h�� 6�iz2�a��A�A�"C =���-�2��4 ety,� tinu7� us%Ga9U�-;s implic�T]ontology->�& TS3}E�e7!�E cer�f���� are}a�of��ex � foun�he li+1��$Marchildona�Q we ag with 6��YV�mistaken:��\�tOose�>�` phenomena��is.,� xpec7 to��A,r�{p=jin�um %%�alŭE'6kit��-�ed by���au'��eo6�} m� be���!?ini6 list%�Lo�6 z-inE�nt frame� if� adm�4\ *� R�yowEb0 backward-in-�� caus% )�$Price}. A4 ple model%even ��5�K� > $revisited}� e la�!�c!�l�d%�a�o� fq5J correl�sM��y u�** asU � 6� ��� ��[by6M�als � rootm� detɴ-e@(cy loophole��A�- � tes�I:�@Fine,Pearle}. Fura *�on�) �#>n e� nonl& ��� shedolE�on!w0 venu� resea�!�s2Ue kind o>M(assu) 1r!�K ContPMT})�Ve ubiaF띭F� esta��jA�i+s an im�aEG�!�%Ois!=$ject. More �U�!��ponF�� iA�fR�� ab>n����rad��al���!Pa�!�� )�wa�n� will��� itu  U��ex&5 Y�!�,ű��is!�Qn.Din� own � . Mermi�; Magic}�0alreadyi� �F�E��`!�2� . Hi$ ��g�!� w+ � a�� mean J'slem''�$MeanKing1}� A����is�"li v!]& !fro�6� ��et� a~ �)�we� ll b�� . ]|)9.�d how)2an Q a typR�A��� unsolv� st�ng�2� u�_D� !\] �as�.RhowŐ���2���!8p���o!0! ificA.�e& ollowing:I�� PPS FB>b�* A��`&o� +�-Z, a�,� key���!{iA�at6��$tre� A�e���uc�or�'%.�:6��Yu�&�>%� o:� �is�ul� � � e ex�cE�a subtlŪcepfJ�!�2� �yet!be fuF!&� . Thu� !/e��Ak�܁��a�ڡZ redu� v numb�log�ly tin&� m�$* reveala>���!t�them. 3"b� � � uri��&�EABL<<!�hepph{2T }. S�!s|$�aat�)4a|bv�&� � b.�$ deno�T ei�p�c�!� �$j$�$�\vert jih $A �� �i�]em#�� l.H \phiL=9 h16h+�2b 36$�<}�B� X\psi 6A=. f� :�-VB�(% s�be � unn=&�$ ). A� �hm$� ,�a!�wo��6�erc!ed)�first . J sponds to�re" or valued�, (PVM)~\footA:{ A PVMg a seaSq^�u��su�A�i?%� ~!�$ } $\�4cal{E}_{1}=\{P,4^{\perp }\}, $I��#equ��} +==e:� �leE�\qquad Al.J:�2JJ .�:�255 �%�' secon�s�6�%LPVM:=2-=2%=2�\},n<8Av ��:6��9<k.<���<V5: Now1 ��at $P_1-�}$�� be de�o�toA��#f6�sf%hvecE�$|2-+|3 �Q -. Howp6 eva�hS is & ɗa�N$+�*,� l�U2;��[�:�a� �&� �~ 6+oc�� give5CeBion w�*i ful, must!j0.�nsequeE,) *] I>� $ ne�arily��8o*%�4$. Similarly,�26�j�M��)�%�9�1-�:� $=�%��reIa9�-�)��x. %�s�*�@ � v. 6. 2}$ z.2� -���� Uor A��Z. $1$�mfi�&Ax i"�t�# Vx�� x x Lh h2^n"n�ty!L�� minisQ�sor -�o9 [��Av ��ofZ� K e4+Ild,� � }�Clifto P(} a-0 �s/�"� � "�/�wa�� ly *� . CoIHe�Q�lio��iciFin our &� �*2v ,, but imagin���s�Yscriba "X� e�%ysat�}se� } (i� tras� w� ��!��2� ). I�N�>�,Adi  esumV�a�A�� �seA ���^�/taneousl��ir��( �)�F �pre 4 h6��� h.pem. � �e��c�>�# (A/� ext)� us each Ase 1�� ssig�a� , 1�0,O�0whi��*�vpassed7 not.!�pair, b�!M�q�% 1,�(�:?0triplet, exacA�a��^JF�'mg![`��by point)`�� b� ,�A� ;,a�C!2H abov� depi\aE�Figref{8n'lm�'A��s2xaD�b5��'�E>w�Cabello#�!it�0� o� ig]h$=%{r }, si}$g"�$1$ ��iori}is just�a1cs:%s��.a} bt epar�Sf�i�a�sub)I`A�$ �b��Ev>kaNF F�NFnonzero2�(bete �< � 8 .N�\neq 0$)16��w�v��eI�be"e �!A��5�YL�.e� + 1 to!7?" g a>%��,ceV�eyR� �� y*l- �ps5( $� yց1�b� $0$%��h����E� &c +&H  �2�6rt�#�6�BR2� )Ved � $0$. But.� �$,V���V �ma�.���a�)�=$)JR�&� �~�J� ��*� ���=6��$)G 1* =?:���{� J�\& theyA��"�w�7 A%$%a �Hl')�QledgeE�&���>�����2v� �p��"recogn�6�0figure}[h] \i� l+0s[width=80mm]�# b.ep)cap� {A�T�ѨinB�B  ��u&��r7�#i� Bd�a�a v��r�e�colour�qa�"'�q�t!� black"&� } \l�� �R*nd1/0��*� � �A*� 1�$is generic�*��!We6~sh !�ew�w�x,���~o�!QA\".�onZ��>�&w):a9 ! dimen� al Hij$ spac�)q$at no evol�7�&U.N . WeHtrictE�K"#P8;p}28aE$ thE*� �PVM]�*%!b.^ .��C!�� ��updtaccordE)o $\rho[(arrow P_{j} /"�,(P_j )$ upo� ing "j�� a��!� L�1 dersR�Lu},:c� IS�!ume~ C-?tandard&n!}� .�s�5 m�s*K A� ``p� es''b }eq*Z#to !1��?�1to-X��r�'N be gener) bey9�*"9#quoj:fu�#A5e� To d� �E�6)�),�p� a k � �tfEt2s. \��)l&#,�,Rfia2W hi-- $t_{Ipre}}��t$�� ost}}$!-�r��&A < t < V ;B x-ly�0ev' aM"� �!, �a3ŧ�Q*h>[M�s UN b�#�B� ion.K2;s���\# $\Pi 6� 6 �:��le�e�R��-�.�� A ���*� j}\}$. A" no�'i"�"\*If ps � 9�!�,$2�1�d�T[peWZ$I/d,$�re $I$!xB�� 6�at.Kx � �Bp$�� 2�=B�/$Tr$(B0).$ By Bayes'� &eha�d���i���H.�MU $k$#b�is�F(*} p(P_{k}|B� ,\Pi�EL,=�)=\fracm�Tr}�:0ZBY))}{\sum�t�2CU�%Lt}/jRE j})}:P*}u/�egal ca&^ most7al :F+A��$>�-a9w!�ereforB-feA� � 9� ies as ``Q2''�!��I!e�2He�e�%� }:k-1Y�u *�~s6C�$.�re!~a<�-A�o>"I!k|=,2�E|b5{ }P_k shi}|^2-�j 2$j 6%>�c-�I��"�&�a!S2� �� now � h��#a1o� ��VyEF|A���~ !W� 6 a� fe;+�=�b"bontic�<by��w��#teI�f",�)�� r� �AA�u( n~A�las�E���K �$�)sfɎ�� w�E& O >�': ���c28 }�) i�P� v �!��N�.TA�*� i;e HVT d<��D �!�� n�Ddetail%� .b2R;? ۱f�is%,r�.C!�I�V�s����.�i�%iqu`&fix�j 6A1)� abbA�at!�#as MNHVT� )�!n� 3 ,.:ar2�  u~6�pr�i��%�8�(ply rE� ��sZ- . S&�"MA�$s$�jo�/ k sser]$ hX�yAD}�"  $P��posse=� 8-Enne9(of $s,$ �D lA4�Gs6e $I-P.$ \ ]) ider��� $Q�at<mu�$P,�� h�.�BiQ{#t.$.�!% conjun� � Z$t.�s\wedge 2� �Q 6�;dis�QveO.� O+Q-SeD�-Q�")lo&�u$s R=%r( � � ,bf{Algebraic,�, s: }1usA�Q$�q\ [P,Q]=0$,b[P �1 % ac0} �I-P�!dP),!1!2e 0)=0.+2 +PQ9^P!^�%�PQ �p(Q2f3;E�kp(P!lQ!l PQ).�4�-s BA�ea�ea�JN� E�"��ed,"V"�C�c,�'�� i�a�eiq�:�eo0:#6!�y �)8�Lse�" vB ��n� �JA;�)t���aJ-����L| &C)�`":,2S2�?e�re W �.�!% �an ABL\:_� vioL���]�q �leB���(Z0!1�mx a � }> aTr*��,32� !63� ~&�'A^er Vz``fail�O"#J'' A � � Z6q4H, CohenAntiABL}. Byw �C�\^=%2� !r_!.k^ �.,KS,PeresKS,K�<ghanKS}.' Now,-+if}9y$A= ��* qBJ<!% pick�ut!��*Q !�aV8 F�K ea�}^_��.ai$ ?t �&�5�-ldz �+�Cre!Z,+:�)vi\M�$ U . �jz�� r�FrN . V��h � i>!dS'�7�h47Uo�f6#*6�3N�=�0�&ne�4o�=��"� ��A@gP�o"%a`� !7�.� 2anv .�7 s�y�a �ian�aof�-'/ �+�*`#may%�;JI.8Am�=�!42�is27V ��A)1&^�c&�'a%s��S !y�4j�A �S;�jmor�� !L<M<Lei\ Conf��BA)�ader%4� e maA�im)i�?U8to�׉&�� �iA#}4KAX ��ndj �0E)�A sf!��(� �0rn�":"�?J=5XD�Dm} MainThe}U#��� ��[�� &���!�p� �o2 �-�o;^�2��b �"[2('ALZ �!`_ ��1�a~��K�s defC�=�(?��*�i*g��>� B*�2!� ^���B �*�&�5� Our.<�v �xiz�~u gu!��2ed!�(2�V*\2�l[I�$MI� )tI IfJn,6k,E&]0�|j6�� \PG� !�j r�i;a *&a�&�.i�!�$R*G | =Q+R"�>n R=0$ 8.� Q=0$-��J"�E�}cR\� v �� (I-.N�),�$P &Q$ �K�6 �� EmlV�A�% NP �Q�iA<y-�e2��!.�:��!En~$I-P$� .�$Q.-RF=��R �I �I-)��C�$)2�%�)SF =�� F8J�!:U� �$��{ran}}(l2>y)5� .; (X)}c)��$)1X�($ ����$x-MN==)�us,6�%'A�!�1`dM�M��@M�If��v5�#�>�)�a>.>+�9%�SR� 1��6# of�&�.�. U�4 �1,/.Z�2 ���{i&&� y 1s s3G �t[lambda��alsojBA[RA{7cci��� $p(PV4"� �20=1%�>:� }| � )=p2�1i�nP2M,MQ,M;��޵���>!!M� b*OV9��P\BWP g 2 f3+ !Rdi�*#E�}  )}=1�)�  ��:� �a:�)�����$A^{\dag }A2h $A=0,$W ��x�4.�I_2?!Q���_thW\�+ro- С�ab� co%V� �5aTɹs�8��) /:2��E�e�9�E�$""�! . Go42�4iG2� �$q��4� yieldsaB�2( $eS:�($} have*Q|xa�R !�. VlaR0!|a�2�-p!�Y )BQ+l$ m6q�m�q�C� }��H ���F�"� �� �!��]0uZ�I-�D�4E��iA2u�$:�=�6I�i%}|�2LEJ=�9)5� [,4�W�em] \�Et"� Y )2� �y���� .�? �1 $ �A��nde[u��kQ� )=1.$&�/ogc251`�fitcD� ,5s� what��:2 � $\{P\�~ rise�! "o�� 5ny�^�JZ� Y��2V2 $ ����n5�=%1b�EU\�\ce,��=�6 J%��& ����*���,B{q6D�<�FDAjis ��6�%gRsEs. "+;h�ig-�%�-�4 Os � ��"+ u�out iK A&)E\fB��J addr2�)�,Pis^&N{�^ofN�GC�Bd&!d2�+!mg. To ans [l �),=)cha�Verize6�5 "x"!C? ory-*" h!�4�4�5af%doat �g��~Wmer)�2\h 26#a[vid�,@!g��!E2>,��ken"5JjNo�,mpt,*prfa~(h NhJ?e SsqDE c7� "�H(Kirk3box},  pa -kEB�ed}analogu6�2�!�AY ��a>�plshc,c �m})�1wy"=~(a�A[ i�S5�`:�R�1)m6�T]"#22_6�9bE; ��/� TF� �E� �7APAdat�!&%;�= ge�ofJ��A�!�..\L�/�u)(<d�'at. ~e�:LY}a�y8!_q�\ 2NR�to%aR�1Toy.%in�9�,* sY�>��w&XPtha���O�$-o=(}!))�.�e^ms un'o�1"!e.13es.]!�� V)� picu�F�Q� i�5� �% s�2�\()ag�cR ppea�5� }�6o�9�a!�|��-1z"N. All!��lpM���g�3 a =fIA� .6�,�Tsr"�"^� yi�F" �5���)f=�'A:�QOpy�q? e��F do �& not}�x,i V@aHo�'g -1[��u'~�Ps� su�r�0qu�&�a"�kD}�"�P�Na+t�kxrnesto Galv\~{a}o, Terry RudolpMe Alex Wilc��"�k�VsDFvZb"{j{A�pre�_!0� �4d"�a s�%%-*-t x-*- %% L~J 6�_SF�_,.~2Z]!�ex-fXv1.0 Ver�4� 0e IQSA QS20042[ka+cee�Bs;FocgdU)btL@aQ\�Rofy Ajap`EM*C`8 (01/11/04) % DOeKet Bra In�>P�"Trace(c1H�*�bart} %����>�c�16�c8��c[rX]{N�c"� �c��eN�caQ��c��c��c��c*�c�Q� } \title[�P}R�� ]{% D d�U6�&�c.��&�d�d \� 2}��6pd, ii�d �;d V;d W�;d�7{OctoKP 31, �Z!���(s{keywords:�&�,�t.2�,>�0 s, A�2\Pacs: 0��d��dm.�E$ Y"�%��� �e*�uAQm}< �+ suchJ9_'Da2' iquotedblpA"� ie i�"�!2;�V, bea!0;�U� embl2`(�x �YZ() � B# y:�<"u �� megg&�evap+Cnt� � $Vo�".0i %9in:� hZ�2,� 2��a��%=$�>5 Y"$=" "!g2�c\� {Int��ion >}�I�2� d� d p�dNdA�^�  (�cY�"VQ6an�Ev&�>si6skd&t:�6.�]��)����c�Se�ct&�ca� �d  erein� An: c"di Jd�k��%6'Rbt&�] nR_a[�Op�c�<%.� !a# t*�btK.�c 6�cd2�a�Hi�Va8i$-!(HVTs�\(% ^:�8��Ck�cg6$Q�#��c �a&{b�.�2�cA��cY % A��k�JFisx�(atJ�T�&�of Glea�r� of K�d �d [...][�"dbyBU��k�2 x#vak[�Wwo2�!F5 }, �t>�dse ��d��dA+:%kI-Vp A��idd*idK#&idp.TS&jd0� �9��i�|u�@�W�Y�"� edp{.Md %I�pa���EA�&�+ �!(A2&�) %it�%�@2G { . invo6�. Wa�$is }% %cru�{o�U!�,�\7,A��m&$ E~ac��s� %cafa!�"m$&.{" �I�;�#*�Phis %oft�ve�n�.�nalys�R��0(aGgiv� %�cof��surpris("`���ti�2k %M ,6�C(Bs 5�}pr ��/_e %6a� �"ms.n.�en���per %ua brief!�? ��$nKe�i M�3�h�7šs %����UL�0>�.!�l,�,��. F�& o6�-.E�4+�ou�N�"_� �at.02� \j�N "P="' U�� "�X)�%v�2��4p!�a[o}lI�+# . Af!zif A�aZ+sqm-o�2�Z�VUdJ� ���6� ��6� �)3��Ӂa!��si�:���*�5�ǡ6�Eiw1'*�62{� �1k2�qA ``m''.e��$E�� =;Q: is t�b� J.L6>�:�for.� ve1J ���HV�)��6s2���v�>G��T�our�� . � \SHRPPSQT!  !�;2l�>o�%�46|m�i2B' �- %eO�kst.  pa.�3 ``U�''��>3h�k6 �HVT}, %j�S�D��A,F�����in  %�ӱEc��.�AJB voi�#"�2��a.�� eL%E}�1�9M9 2Bo�7�=- Surp%� %� A~�inY76F�"��+ %opeAJE � Conc��^�uQ�� y6�I� \�.k{,M& s�Meف�nM s/�l+ AM eM�^Me c;��&}"u2�0� {M}$% � a�-domU����/- $X�0 M}}$��a� � �K�� �8�A�*L.E }}$�,��7 ]%]�by $j?A.�s BQ"M:|Mis0Z�JA\rC"nJ���"��7MH�&�h-@�0}O��)A��hn���oX"a�"6�:��D{!�Mډ�8��ON�����%�!O�!�P )��P.�N� �L2x#=$��%as�4C� +�dusc s) ((=*% K^3,M}K�Jg+MF�J $\IO@=I$�Y>� 9�-�6� \ =j b^  7w3)�m�"�7 $% uOj+E)n-�A�p_{}(Y�}Z )=iFT�|( �%��rhoCW)/f1 5���5:D� I�d odIoby�o��v��A ve (CP) mG�$\{*�J^ � M}_j&(H�4{* .}�t�L9�\;\#}�J(I)=P�7T�hBndU%9&�L.�{\#�2A�d�i�1m�2"7$ �Tr}% \( +M(A)B\�) B�A.(B)($% �Nqj�Ke��[FTL}II_{|>/}=0�:I(E-)}m9f���%~ 5�L�@{Up��y �5�% W./:�JUB�� >,a�>���sa^o� !� L\"{u>�Rp&�R2KN�e=�N��UI�_a�e�!&� e�Od�ral��7+�F�9t ~lQ.FQ�/�q"�/�-E�t_u��*�I31L51:&P%) )$. �F�H�Q.�<��Q�%M}F�QFd���"wQ.� ��+QQ&� !�>�-�Z.�/ Bs�Np&V =�% }�UQ S%&UQ w� �UQ%'Q$k$E ��F(��3!CBk| 6Q,B%�,QMVYQ9/�B�Q�F�/O%�).Q ! ��N+2 0F��HkJ� u%�h}� �GCoarse!HB�w�W2�Rbg)=A �_k.(^ }�1� &�� lCg.�.M.{[see][]>� Ftnos,'Ղ�Kdd� wisee L{���vaas� B pplye`5?..�s�M@p , � Zbk�-:�k�� 6�k� \ N0pat, unl�hZb!Y Born �=1�BF�Bu rough:�_N�he��Zr�V�1]�� \}$�Rnot�b�5��"3 $63k}�� B����I O"? i��K7?!��B�\�Ecri� fu�yo�^.,�G�-Box P@�0�6S�h>��&Tr� �","�!t�Y.z�^�Sup4m we�B��g!6-�F&,6ir� {Q i���*IAHLjj�N� tb�jr�57^ n6J�T� \�le � 1�Tqrt{3}r�(�Mf � 1T 4+w �2b>�r ) ) $, i.e.e�rm��=`U iO N� �|�8P# B���U t ON�-i.�>�of� -p�p-XN��4����/�s� �.me|$.J�r� �0�S&Yl!�N[ 1$ otl , or� .�2� Q�21�I A *m.<߁rVWLs��>1�% &�q7E; eF_�r��iqU��e�r��qx.L6�[1�L.>�� 5u5:-*z 6 �l6SjN =1�L �K7% .g$ds6u *N�fVqs $=:�N� �t9QN�,gr~�N� %.%1au �|i"Tv)N�:L6�6�L��B� :t^���� -�N!��(4tAa�i��6��pwa���t<�1 �'F�po2sk>iB�p9we�`Ca�Z a2�pa!6� An A6,6F�\�KC Ff<w��spiri$� v�f��bg!t 4���>1mDa�4C��lle�3he .�nBE.*upw7 aque%^.%diy(� o ~#o(esh=pla� doub.�6��z%r~&��O halv�I|ls&ylpƊz + �� �<8 t5m�mo�H�����wo���o�:�1��e�SinA fron�J� �A��� ��D� �44ball i�h . On�verifV\&�:0:iR �~\>AA;B��/�� �"n [M#!@ +ha6Z���+q�* � �.�J��2��!W#  le��e�%@-)O1��ex.&�<�n��bux�H��in@7�O�Dn�5$f�� W:sh��.H��+6ced�ST us��!�>�,�5%�i+,�V gets 54d!.}D �a}is%Rb)i�$3 a�X<%�. Two"� pr ��9q6��A�@M|eorm:Q,�qi~-!9�&Y when�%��i��*�]���8!;hecA�. �T g#�.�N%5)w�m-?� �hRU�r�t ZR .R�fQ�� ��ˁ�A&�n �g. �' : 1)�HQ ee i ��!�!�2N3$3�')��C�L���%I� q!!bp@I��+�&n?h�E��-.)|GoAXz�re "87e�n"�.�*E���R �!É�x�- jo$"rB>& %�Qyox� But,��!8s�wa�O� ��ZuA�>*� i :�{e�`.l'Q�F�$ �N�$wh Yb�2�#6�k!/f�? *>�?�<xXtB�; (s1�#!&I)!UMo����cAU|.��@uᯍ�%�is"� " chie)%�&�(:�'0sp (p�&X �$mm}B�&�n; 6 +E>zWAu� 02Moi�Y&_�but d� ;2���&Eo� fgz��"�E(�+ly2#�%�Z� "a�& W*5&�;�!HZ�.&� $6� ."�#jDAq!F2QB��erUN�!s ag}N�e�+*e+�c>ze"P� "-m�aofݒ'. � $\Omega $_KA�A�.r�AX&�/&�J \in I 'J�`sEs�WW� dire�"cK!��� (h�D��-h%�}"�"s�o=O�49�k�C���nA�*epr� �,�%�!�,��ly f�bmu :$5]^aBp�$bb{R}_{+}$*� $\inu)�}E(\�H)d �H"�3I��0��M>XiS �-(v_m^Rs"̀y! �} �& �qgrals w��� ed.�;�|p!+�H��ad&�)�a�zE��ra�� � A|���".7� if�KW���j��"ј ]t�(��F\93nd��sume���;ol� ��"�+Giv"� 5 ���6�$"6uR��B�Ge��k#mpo�%Da�or .g chi *lR:I.t \{0,1\/� *�# unitU� "�#NYQ� �J}(\o�N) Ta�.Y(]yor $1)$�J�!j$ 1#�Aew%K"�I�#�G �#lyF��mu6� =j)=:g chi^RfqrV� "�HVTProbF�iI�.�B�&M����e2{�!u  We�turob!YR�&h*+��q A�owE�=i^�o%j.5NN/ � .y>�cha�')aO.��o�!���J �uU�n�%��3�6m �� �%$DV� \"N��zD^J,Qܱ� ��B�u(1a �\:a)� �mh$ d$!Z�L�Q#��X&�"�+'5 >�!�2�&%:z-��"�&�I&X* M .�v2�s uSof�)� :%`~ � �>� $*1�w S&C�: a U�-decrea�3F%F�\Gamma�]1�9�=DZ#9�� B&��&7g��fTFOpl�� .aHro�!)� !�!�t(D� CP map���^� :��Ci(-�*Mory. In�/y$�8:(�9F9(6v�Gq =r.&�hHVT,(F,3 �4)+�LEq.\ (Q0*�()5+> � fX u7'���!Y.q"�#*�yJv*NZmu&� 2(�NfPt)EE% })E]�ANF� Y4�   }{ L� �L )d L 1� }2�b(2֌ =�(��*C/N�'� inn0 6*I���B��}�"� 2 Is�i� I ful prd��*�$*�%�ya�s>e26ݲG $\mu�5��#!3 N�&6~^d�z:� n� "� s A�{ef:Q,� &�+�T�,!uU,}�g%�?}*'a.ms)?o"��)@ y*&~-BH>� $�5�@;6$��X'i����Eqs�{ )%�$HVU�)� ^ ��*�j%�$HVTn"':? k|)�=y(��N '�)q�E 6YS1�.�&% !"a�HE�"� > F^f� )(N�J�+(�& .�J.�� ��.l'PPS!�for!�B�wp'E�2(� kJ�.v' k�i�b:��7ݲ&(>%*J6�it�4~wA�"cL�Q&6 ^� (ks) �7I%�0� cD�� &V3types29 ity]B�:& 6.h >B, �> vO ��, | 5��*.,e�./jY6c��N}:'<�.%ll��s�o�)[�(�&=�:� �l%i��"����d HVT.mV�5��2i�?l�A+)����Pi~ H-!s��N �"A( $P$,��,4�(M%6N ��s2 9�&��YY >� �^*SK-���5�5�sI) ���}s$ j&J� ��+M=1}�)F� N�uP��l҅MNCFJ E"��l�� �Y%G2�r�5?{5aTO U�� (B��&> � �$)�c.f6!��Wer2v�+?2�a�i�/�mp%�string6@cg�&:u i+*5�ca)��)u&Q�a�i��to н5�sXg.� Xb�\~FiX�Q_{2}$}�:�"�E�PVM, � �gK}+AB _21)q �d%"7 6:29�_(�iwe�nvi�!,� 5chi $A�$L �_ci�\�XD$Q=�+��3n�bA^ cd.-g!�A:b0�� 26�&7�"*�VU-1HVTn�}q=Q)' 1'/z��i�ie�$o &�A,�;>�g��$Q$ !_{P%Yk}= Q��}- Z9�v}.�_"�iM�j[��� null�;*l&I}!GeZ�en� b3 �b ,EE���ai��;8MnoMq �meyF@/ig�Wo!0��&L} &��cby1bPN�%d*J .�"� w�e.) iDAg��T� �Hy�Hy�Hy:��Vy�VyVyIf!�![`�$�.ulaE�"y" T�����.=\deltaY-�)��ye�e:" �d��-a�& ��4e�%$0$ or $cH.1��KZzP_��a$�Isey"�'m�/%*�� 'nā"Yao�ym5�L)���� 2�d-l� �_ L�@[ ��f!�A��3��3 Xto% prec�cw�o�a"�q1�atF�[seO�� somethazZ�o�2�&� i7�\n&�1ac8% ��a�v� �� $�v��[��Yy=]�!AB�sSgAG.= R� j�z1���)��-5��aK"q����PG�[ "P@%�[}!�N . Fמ all,I� u�pal(� ��abs��n� �xF ,VnC1!ZdZ ical?'M�E��)��on!%f� 9S9��@f_�-Ved}hx*�:�u�:s� �b&J�b>^[#2�.� >;5a�� do�L.��`l�%l$G�8o*rAw=+Q� &� .o.��_�g%F�,���DY�Wdox.�ial.| � $.� ac0}�ac4}% i  (2 ��6&wo��.�.�G A�e'�*m'.)rg�)� b&cqvoid Ru��%���� ��n��F� �vٛ��.��be�e@�l i�*�:���Fm� !"� r I�ed=�6�in�A��s� 'ofE �ing"��mW J.=es �,�"selve�5+M!�2Uxd�g�� e�Z ��vO �:; P�i6�o�#�m� �G�+JAF`sC, �%��A3i��:K6�A'%"�>!:�NpJ�IAn��&a�8�Q� �*= a�Fw��!��2wbc>5 ��]�!JA�� �OBai��fe�xe< AB 2DD� IM})$ �=�^-�t2Q~��(%im�*�m��m�<�a�J�. [/�l�a�_!l�Ta�%�:����|�=�-�A��r�.�j� *��"��*t&�)�)]��X;&d�J&"ch) jR@)�6S��1�J� )Ze��� �{^x*��WeI%� ��"�Ry-��!&� .�  $^z9ZA .�p&6 >�}�QAF+ �jfB=t�#Q��oA�z�72��Aŝ�)�T (\s�J2�a:LCP�G�V�E�N)��*��+>�! y5k4)6� �:&�M �%$� m�R,���hN�CP-L .�@�wJj?B�A%"p=(a,N&h ! !t#k�B' )>f9 I2��Y harpAX)� "t)��  "��!�-�2�*2& (&D ek.;�A=P�A�ta�i8 �i$ ��#9A:( $P�I�#asyX !�EWE��X>�! A� $1�z2�ɛ.2-�:M &;.1�s�~�!�|\"��s ^Y�_j^��:�.$mE�a9��}�2PJ3 6Q��Y[ o � an *,/~_�n2 TI �xqAxenq�jwA"a2P�J�Ru�/�Tc "/��%0�+� Me'(e&z#*�,*$�D2$ � +{ ���WjO a�>DCI'M}V#� ���> �V"TCCRCA�Q!��}ke�C*�&��c i�FBd <z s, :^ �P 6P E()C�gD�ۚ7 .$P#3EWeDAsi�b2�( 5y2edYa�!���"��� q!y�cs���*# ! ���u��P24 )eL� !�;2&p �F_�a�}i�-^�� =VM:�AF��(f��56�~�v%�, %6�e�n�}�Bj(IN�B:G=Û^iN��PP�} $% i��8�5��A0N�<�#�o2�%.:�"����QCP\u FK�D�2Sha�$k( 87\�� .��H>[ cdot�z�SzJ6mHj}( '>�Q.f%'��&�XFh k6)TN} i.��}Z'Qne�:{.-*�&�.H\} "eO�E%�.�-)�-W�;.'Z�!{�[P�| urn uw� �;�&�*xib �� A pS�]B3�.���.J�Tt4� �i:�(* )>�� .a�2". �j >@MV�i�Z4Et>� $. &5?��"id�ZT��� E*M1� > >]�B�:% yᄁ���� but?m ���L� ��n��Lof�"?w� ,�ny �Z��6[B .�K(of�"*m�.seC&�)�Q`.� 2>: "3�HctraryE+der�i:�A69# f %s�a�a�%� M'��R!^� a0:@�- )$d"�9s:+ian�.ing�w�� ܱBb (.�V�%��F��QM ra�ǁ�ni Br$a�Y* :A % M}�. ٜ�J8�f$*� s"v"bd)A"��R��NbN}}% �Po�$$ (by virt�0z12"� kJ�f8 ���9��PVm�e.�=.R s@��y 1J���&� >� �  )6mqFh3��� ^zN}% }>j&!Fj 6�Z\�@�#A�Ipn6�Bv� 2B v�.� �Sch6.� _{I-&� �!33�A1ʤ��%�* .�" .$&�!�� Ű�c�z%A�-y2� A r,��t"�ɛ=��!�HVT�&� '.b���V�V��"Outlook�?*ibW��� ��*���8���~*� �"[l* itsee���s�F J&�~k unre�{d*>�d f��ro� �V�p&j�   ��F»~#�F!�B_e�+"(t� uff��!��tru�?uNr#�5*!$�!��bkf!��'�/�Hwrd �%76fe�� �V��mA:u5�;.Ai re Z� oral�q4ogA�T�#��-&�� ���6�. %�  ]��UN ��HaN to %�.�;|��B8R!�a&@�%��u\e� � t��? 6e �)�} �}�ha�D���/6�h %ݬ��L7�ac�!�%�o Z)c arlier.�� c��n���@onito�!�< a�2Ta�e�#���J�a &�".����ur�v.���O0 u��)G. *2et��![&�e�Nnc�*at  J&��of��s+#�?ad�alm���,!��&f�P�t oserA�J1uq��In�-y�41*�s��ƒ.�of \S ):2�h�E(};� h��"9QG^nciple�.5 a��z>n��s ?�t�RJ�M�( # y wa�B���H^#t&��Qw2 �3ˆIB�Hof\>K��WR&��}#�k"tr_�jI pr1II!):2���/���$�[* �$cE���a=ɣ�ل �&aԳs"�" .%�ћ�DA=Ro~�&��Q�*��8uREr Yr�.��i����Y�@R���+�t^N�(.��ex�b)��:P1�u���J 1*�U�����a��pr���+�� �~� �lI.��style{p�t nat}f}�| end*X���>R�,12pt,thmsa]{$le6K�cmd&a=�(ar margens%�-ne&ׁthe"�W{sl.\�c& X,} \def \eq {>J? fim- �X}k ,tlength{\top�in}{-2cR�soddq!.7>"A;�� }{18Nh� }{24rj�J�s"=�"!�E�PGuerra \\ %EndAName D*7ta�+�� F\'{\i}�*)U��dHFe� l RuE do Ri4Janeiro0Cx�� stal 2385��<3890-000 Serop\'_a, RJ,��zil8сP: emerson@ufrrj.br\\ ����{ON THE COMPLEMENTARITY PRINCIPLE }�I"��- abs�AA�n`�esq�+�he1H��w:��iFtwo-sli���֭~ �H�bvC ar�-\��w�� PACSB� Ud; L�\7.Mn; 32.80.-t; 42.50.-p7KeԁV���Jk, cav��QED�!�Z�+�o&���Wᅊ̂n� �wJ }VmicromalV4UnJ2=*��^�'aa�op!� be)% y Scp�� Walt`��W s � of v�7k+�N�(Cles6j �v߆�m�u&Z��0{DSSW, Baggotk�Z�v��ߩ�J.�MaXEs r�ndeo_�ha �F. \ R1�p����) �(CompPUncP1})5go�s R ��xcI�^1 KB��G �iNb 2�!��sub�# d�(}eQ.� . AV\.� [re go!��8e�r��z E�EG $SLl8$ (�)\zeta Y@�8\6!2}�90�A�Q� $C  \��$SZ,Orszag}6�aw 4#1}! 5$.�� =Mc>�+w1��=dd B+-+�.hy ����$ \mid \pm =k}= >k})2-J�bbel{EOCSFL<)�$EvenOddCS}6�!�e ��ect \ �wS:1,A�, negl*: s du&\�*%��#wk�21{a t�d-level ZAZ��Zngmhe ����gne�6f��v � ��[r��e \ uppeWsJ^� de�)�l-��O� $|a1s,$ $|bm5|c�u3!�%e)AS.L\� )(o׍.JA�zN.��� �k far �K��nR�F!Do�vmiAZ!imt�ol�"� U(t)q !m!�-1b��\o5j$C2'D(�, _{Kn�}e� eqna,�X} U(\tau ) &=&-e^{i\varc�aL^џger }}9��a a|+�H1}{% 2}(�E+1)9BHbH 2}% �H@}}-1)|b\rangle \l �>c|\ + \nonumber \\ &&\frac{1}{2}(e^{i\varphi a_{k}^{\dagger }aYc>Yb|+% �H+1)FHlc|, \end{eqnarray}% where $a~ $ $( �h)$ is the annihilation (cre 4) operator for)Dfield in cavity $C] , $\ �t=2g^{2}\tau /$ $\Delta $, \ $gr r@coupling constantC +0=\omega _{a}- b 6 c d�detund) \ $Na}�i( _{b} $ and"c}$\ areJ,frequency ofupper2\�two degenerate lower levels respectively .h�-P%` o ,!L*atom-( interac%� time. For=�h\pi $% , we get \begin{equ%� } U(]<)=-\exp \left( i9>.$\right) |a:�4 a|+\Pi _{k,+}FAb-Je` \Pi @-}F�@+J c|, a�4bel{UlambdaPi}q �q9m+ � &=F�piVa�x.K-�K-1Kl� pi+-� �% A we haver�|\alpha 1�a�:�|+.f��K-6K\\5+:h�>z6/2L/0j�B--6j;2� hQ-5owhich�xeasily obtained from Eqs. (\ref)�)e�  EOCS}) us�~$% e^{ze@^{:Na=|0}J�d$ \cite{Louisell}. First�H ider�Jies��1}��XC_{2}$ behind each slit�prepare�P co�5nt st��$F�S\8J 2}$ .�. Befo�F�� $A_Cpasse��rough�U�sZ� ies M�%F�0|\Psi (t_{0})Y�^-SLe2}%��c\sqrt(|\zet��1}@+  !-)N: 1|bu7=>.�X>� .9R��2}% [.�1}+.�1}],2*2*�]6�.�B eq15FAfter%�~�1�R�Ɍ ��C!#>�45M[)� *1�(6�69-|c.,6G)\ :�EF v�v2bv%�Rm]2�6F�Just b:istrikebTe screen at $x$, if $Ua;1},iA^ G evoluV C�yr�1F���% 6�-�2^�%�z� ����5����� eq17F�andJ� x���i [\ps� ��%a}(xA1})^c'6c >+�c:~2�~>32~2Z32k8Fk J��V_�G9"r� 32�=36�9�ټRB:D:@1b�>o��%ȑ�, x 6 .�6�ZO2.OR|�� dropped � subindexV�T. The probability densk�detG ng a��om��U posi��$x$ on��isRT eft\vert V�\� "�)eft[ �`�{% } ],\{H =:e.�d d+f7.�7oF�2ReJ�^{\ast Y�:�.d[M� �6E_!�� .X21}+�z Qw�oF�/�6�Nl*� l - l*�  }N� Z����t=F:*+|jX|%�}�a�&α/�(2-e^{-4�Mz!t�Ej}f-a�� D�})]\}.B Ifa�assume $�xK,B'��'\gg 1$_:s� .G �~9>R=2J� }}% -��ּ4{Re}e� _.���)�Y manypeaks��14 �Yinj�Aon of a ~� $2�,& � mathematically represented by $D(\betaF7 =q�+\!�$�:g�� displacem�� ) )=e^{ oaZ }-^ 1@a)}$ 4,SZ, Orszag, &@0 Now, lets usQ�that a� a three-� l[6 has�d t�~ )� $|-m�.!!u B`1� send�wo �"� 2}$c onant witO C,� $|f�M�|e:��and��s2�,!�$� $. If��is�t>$AP the `d , un���\Jaynes-Cummings dynamics9�)�}�know %�;L>�|0�$$ does not� (ve, however�e VC-2R�$ v_ o :F |\cha�e.X2}" _{f"$,qF< =\sum\limits_{n�}C \cos (gt )|�$%� Z _.�=-ij\+1}\sin:^+1}% Vb�a�-|1:���}(1N�E)^ �/�!}$. mwe�+M�Q�4getJ� Nv �:2� 6�� �� }% p�1j:E (6�+VM )- \.C&&6 :F-ZF)B� �].nn&��>�2d]6=&� EQ29Ք"d�b�h� �>�SBA(we can writ�i�ofWsystee-A��.�,$ as followsJCr"BM B�Fr B61Ee+|2���Q)- ~VV�E�-J�6:-:?��6�J� !�+B�N�:02b :�&�E�):�1[�*L EQ30F� LU�1}$JP�+A�i��P2��nA�6�u���=U��D2}��EKZ�1�]S6� "6�Fa !�6S15S �% Con����;_f991}$ to!� &# K=zJ�gM�9& N& 2S^&� eq32F&andݵ���R��H6�1�� >s��b�3R�,'Q&v(,R,���.e:}(xBG.�34F�T=��conclud��O ��A�J�� $�$AB�h�7�r:v 5 ��N� j!:hZ�6 ? � %� ��Α @%�����< s� dr� � *� �1�!�>� � 6��&� ��!� J "�! 2� ,0a�!2� % A_{3B� �2:�3��� v� j�2B� �BD �k �N� !��� ��s�� l"� U� [ f_{j5 .�k~� � �D^ ]dL�q.� 2����k�+:�"�"J� F� k� k}F� k}� @Uw6�J� \N� k� Bb� k}B� kJ� k}� k}*� k� EMm~j=2,3 $k=1,2.$�� E�#"0^7X�e *50F�F� |f.�.3} .�" q a =:M&� �]b *� V2� b .'2Jr "� 2[�Rj; �"!�)��� VF�%:Ea�� H 6.*� 35��-�7%:���='s2a1!e�!( Z(?Io,*� q�p�,.��L2Lf��1�U %ZJ 2:<��6� �U5 V0*�)��6�V�e[JK��6���Y� A�J>�5F����J_6<e2�1�{��0��9�2N������2�1�fJ7#/ i�ZT m��U� ~�36�&� B6e�q�:6!C��5�&76�Z�0242}6�&�" �<� onlyesi�7 to57��� \� � �� �4*y hvN^2}=H�����:e�*�eq3&R" �% Mak�use\&��V�^MxBi!��%0"�R'">.��:&vpN(">�!B�,- \?.O��� 2*�e�� '���one�xiJv� ���" �nowU�6{�����J�+20 �J02�1:&�-�% in6�.,}. i��p>HN=2j "� D>,.4&K ���n.�#�9,B "qc��-�:.��Jb� Notic���^3�3>/�CU ic�(o"+ 1�A)s� ent�d�L>$�3Aand on�n�"�*�:vacuum 4($.�1}$ �*U42}$). Note als��s�I�� ingj� �+ 1�"�2?3�&�i:had��@ its signature ($�/��D NNRX- $F�6 Ik4arrow \lbrack "� "� >a*b21b��)$�2�N�jf^.�q�� R]$)��%�A;-�E[ ��$we would n*!Q�E�sB� :>�sincees3t +I�gat%�b�.*�2j2O ?%��*h , ���}eB�]�1�% .2}.$ It� 4"po� le.� ��2� $�4imultaneously \4 � tell|$"�"�*�� �harA�tra�% ory �*class�%�%�behav3like a $particl�"ad�$" bot4 s. Wh ~ !eALQX �!�=� � saysV�� 4{2���:D��k.p%H vk>�kA�(a5-!. )<or). Of�: rse until� deci�o���$ledge��localiz�!�, a>yth!�ces%]rminisN'�A� hole� ��E :.ccordR9 Schr\"{o}er �9X �TN'n$�6manifest)�MR4quantum mechanY[, takes �'. W"�1magnify �sm�i o come97� c s�Y�Dperfor� asur��'�/ apparatu=6`collap� wave fun,;happen .�.t-Xm � �A6_�oQ,NS(�� J��h��s/�7)A[�`�i��we go�*na.va�.�ca)A�a��{�'insteaai�fB\we B| 6� ��� G#�N}T �p:�(��y.�76J� 2s'��^`�J`20 � :�"G9���0A :��NF"f"�'$C�7r2�1�N'N�2'1}]='/"�eq4&�Mn%��J�I�ga"�2�s% 6�i):9 J � 06�2��=�A�A�!Z"� !�Yr)K|." *�� -ND2�A�BV&69�B��K�2��2D�D2�1}]=#@eq4&-��M(�t��F} j?��or 2P>iV\:� .Ye6X w�A x 1( shown abov.�6j�s&��p�5&231�*^��.�V$$�͢�e�ɹ.�g9)��#G6�. 9"*[o���/to �A� f:0AX $% :�!in or3/>� about  pa0uL?} F veledAhv\&* 2- *�m;vm.�2����?��=��=Z�=4& &-9% &n, ina$ng* s6p!�selmtwA ntrib9)s: (1)-�=�:U 6�ET� %�Md $�1isturbv r (2�a2�BaE2^�9r&('��a" super"�9qG�H,wo alternati= a"unles�( a* m&4 ? � 3 :=D.ica��$�i�B�� i��)eY�' stor22h�0� &�i��:��:�ns.AJ^p�  �%O+potentiaa H�-�i� , is experi bu6&ey ��t�B)=w"K/�5ecause�W�Pstill���� � %���MB�a� 5�"� I-�aF=��5B( described �8 �� ing,L<�ance,e^6V5s��Af!����8&+ their ex�Ed�ks7]� "�EY� IY$)�!(~AD*�Q IR�E0E,~! uf obH:�7 a B~2s m �h fere�f�-��� disiar eve/.6���=U�� i�=a�get��GF#E��EH�ea�Fya��P�*$) With�*�� a�t V�M�$ �A� acqui:G �e}t:�d�~A� �e��,been f�2ed.�.H]� �0�22�C A/�N* *kW3�kA,shines s�ls"�� a����=�- V5a V* *regions{)��8�$ be r�I�fy���1�+A�mU��ar�2�����\6�%ZbeAХ=a ��A�� �Q!�q,�+ we mc.str�agae�at�AUs�Egdo q ��2#�=� ; �� a2u�.�a"m!�1&�> GB� �.� wH/��>%��2V�b�*r�BeJK�B�FRK2� � an oddF�=.�@BZKLeB�w��!�N�0 E�ac%?"F*�!~IA,$^!;into �unt (�@ef*�P)N�2r� �� 2,-J�&.R r:"DB5(�'�9�&@ 0 VE$ �-�3%�3%j3%:".�$ �&�$v��%&�Uh- �R���$Exw�41Gis a � on a͆��front� a�}�# cerQ� R mL� 'Qil�J�V�J�\{:H2IGB�-:.2=v.2� *�DU�Z�7��&f"&X[�D�&>2�:�E^HYO>7*�)2''BD% �$qOi�mi:�=0I2i�Vr re no�"% $SN��:�:�:+2�ENtXD =u*�(:�\}]u�UX� 4Es��e>@ 6 "-f�9q�1��D$V�� Ju�#!"EH$:fa�ŷ>� �was� out. \ T� U + @par�K*] �L"K �ransferI � ynalhB"�>ceLr�"f%e%�71h .�w) H%F> i�Tr"4 ^ ion � ��gL!xwe fi8ZB5,U "t !�/ r!,]  $bi�)�b!� .b� �� � a:2!n� � E�e.  (p,"!# ! ��o1rA�a�, 8 $a)� �|H:6�s&�E�% ext�] mo.E!Pf as�� k)46� �#{ &pm� \���N~A<[Q>��-�I&�,+"�4 �F H V�6 �N}���2K:�&+�2&�Z�*'=A� a�Cu B� .C6� co]@ a four-f *��$��"F!1m� $% S" $� Asi(�7(aAH� 1�'a:$l aG22}$% ),&B $Z'� ZO ;et�7 1}$)Y4}$ % �)e�I$�X=v_1}-�Uo r��� v$Q!ja- velocity�e"� :�a~g2 g2g�� \ /�ibs6q�&t a$x$. 01 01$| �&��|+$(& (9+|=1�B����s>%�!,(�� 9�% 9���)��'[+��hMA!O? O!�f &� ��B(%?2�-.?% � �C.%|)(Z�S=�>� -Z4=�42�^+�BRA��5q!�Vo= �oP3 4:�9\M\% (.KO!B�3�E5~!2f%�2�+:X2�X6�X2�&"h<-&:h1bh9�|2�d2�-:Tf�T! FX2�^;%Q;-� $d� N� �q�� *q����.�8:* � N�fjf4y�zj� j�[1}��9��j2��jB�F:1Ğ:��6� =�5@E�e�b� +fH5H�a6:r%-NH[>�XY%6�!*sT]$~�2�y�i2�B�W6[�>�, toward"� 9 ��b� ed*| j�w*5I2"B9N�'n% ��(f�U|�6M%$b1 �1 ` -:6`�Lf`F�6�]��Ja _"�V\���Zye�Uy?>�&B�� we�.��R1� �269^�yu^  X!$�X�%vX���X����^�:�5�"�"� ����m)�.L��6X ��PE�YLP6�Ң2`.�ʒ2L.������>�F�D`!e B�M,q ,� �.� fin~ZA?�*2`��^F<N rEy!�> &�.�_�;"� }B�>7.�2�.�>5^� tEo[ >?Vt%�]��8^+B�JG �A=uD��57Jv�%}^�� �ǂt"�Oj��6BtB�2"[J" ��J-�- !�z �>O2}�OZ�"�a5U�� �F]\a��psiA1tJE/F�em�.x"�� )&�a�h' sharp � ce_Ir* n $�E�pBO�!is�h�jL=:$!�`-p�2P� J� neq  \62Eo2&�neq 06)5 zpJx&2�u�uBu1`E�-`>G\�iYy-?U�y��u\"H -8�I�. H�]�jgj)!�1�>0�E��M u?.z G8�pq4) w�%�$vanish. WT�*'ania setupE�d mmintrodu�87WaJ���9wa��e#Ua��m�9d observa�# &iorf�0qul[dif%c &�+%s�$ i�&e sit)�6� Pw�"��2�a:�; \"�;. &�;Q�:M�:sA *nda�,�,he!=� all ��&��)*=;it&�$��moTum%JugivenR'$p=h/\be�$)���hJ+, a�)mass $m�is larg�,hew $p=m��A# . Du1( smallness !Planck�� \ $h�KU=/ "�v�$p�?e �(length Ju�A�b��t�;ly |%c�)�0hyA� +IR�..�orN. M$rimpor�ly*(nvC )in Ref." b}��TLTd: "...�de-facsat�c�@(in principl�"ia�.]T enou�ro rub�%>�(..." ��ue%�!_|^s studi�,ydDSSW, d4CompPUncP1}. Ie+s�)eYcbUI�icY>micro!�&+b�s/W ��2� �i��,gh!)��, any\ direct>616!.+�j�previou!at�= a strong�.a�i~calw@!>N+-�s�A� �t ��s-%nec�"9�.�(>�fAZ/j��*�RG-8�� di��*3 �)�"�>�+?inges*+/J"�!�>2+{>_�Q&�A"�f|���X.*�!�"s"9,� )bK&�/r�&�)� deA B>  �M�2-��>}D�g)VU+ ����."�S@thebibliography}{�Jbibiteme�(} M. O. Scu�hA�H. Walth.f�Phys. Rev. A \textbf{39}, 5229 (1989); .D, B-G EV~rM/.QN�FK51}, 111K91)6K��4�01562 (1994); .�BDFound. ��28}, 399C8C5&,Baggott} J. $, New Sci.A133B6A22ASZJep)'Garra� �P. L. Kn_,I} :W55AB48I�72� 9}NG Scr9�T12a�1A� 86);Af0J. D. PhoenixJ�J.�,. Soc. Am. B)r bf{7e�I�02�"Yl W.a�Y1X Stat�E Pr�lt�4of Radi8$}, (Wiley,%�bf{\ }ad YorkA73)U->� q docu� } ��\� ([twocolumn,]>pacs,�:rintn�s,ams�m@symb,aps]{revtex4d(usepackage{�Kicx}% I� 'g�Kfiles .,d x$}% Align tz s� .5mal0"2;$bm}% bold �\ \newcommand{\ket}[1]{\h|#1K0'}6,bra,p2|F,[2[�M#1|#2VY(sandwich}[36/|#3V2 be}{>��:�e#�SuI:!kl�(�):%tr}{\AkՃname{tr>Ii2# e}} �:QB title{Ext�07 ��on De!��$TLasers}% Force line br�p L\\ \author{Bernd Moh}�$mail{b.m @@physik.uni-ulm.d!� @Marc Bi��t}V,Florian HaugGiovanna| ig-� EWolfgang�VSchle!� \affili�${Abteilung�&en �,�qLersit\"at Ulm, 89069 Ger�qa9 l@Mark G. Raizen} 2g Cent}7 Non!: ar Do�ADq4ta����'\\d'�TexasA Aust�XlTX 78712-1081 }% \date{\todI�M� , , .% < any B may6plicit7pecifie&�zabsE@}propose  chem@(�<�r ly eIw�6d 'a#dervoir( a�"8K � Anv,� achievb7mea��f r�� pul�%c���>to"�*s� | X;�I"1 trap� cond�xs9 � ular�7"6Lis1d�K-�QsW �&zero lKetic �E g7onf��,8 dipIL� Ka� e o� S�(non--� a�>^BZsteep �^&! .!��P= � ��a ,!�ed �gA�!O%8y9�n!�!� a�.)�^),Bose--Einste��on%zate ,� :�tve"`:)B+ ��%0 high efficie��e!�am"L �9m�"� e"1?s�Y� \�R${03.75.-b, (Nt,32.80.Bx�m�X�F \s�on{t sec:.�}I* } Re;��.rog �ulaX�*!]ic gaA��;ope!�> ing ��: �� �6�� body� , ai�-" fullu�A� trol!fstruc�=sinW��9(complexity~!,Bloch04}. Ap�*��s, likuI.<*�a0t��re verymip�?B8ly investigated � hansel01, �<,alber,Mandel03}�o)ts�O�lowa�)0�35ier1<tw������ [O worl�Zurekq I8;per�4tA�=D��O!�lat�K> at!�t���>�>is\Cng@$gle or fewa0�Gby64�/��one� 2��Je�n! X�AI�cPpu�+m�Bi�h5�A!)z!4aA�0o53�Rs��yxed {\it%AAD ri�Mala%loi!tunnell��Y�= to a mov1�do@&pGr�ˁ�cenarioMGdy02��%-> FIGURE ��>�0fi> }  a�er \id v Ls[width=8.6cm]{model)3 8%*� \cap�&{% *� �^� � -Yb� (BEC): �4.4>a"gr���a BEC,���'&� $V_b݄�one--A��C-�>T a�2E a$ (ZQS)A� e horizon�h� �5 dica Ce cor����ng � gy�DLs (in arbitrary unitT��`i�� e�?~v[upE��e�� roniJZs $|bV �$|��$�kkF�!L�0 >���5W1�ci�JJby ��r�!resoleI�ne! spli�C b�)��*V���Fy. :�M Fig:Pq/�zI�u work1discus69�ŝ���#�b !6� YV� u�depende7�A�� ag.� ,ew I� Qo�1 cedm��&utiliz��or��A�.clouds��$Ketterle03��b}>�>Z�X Zenginee� YA�A�l %��a- o�aD}t�7u Rabl�4Her� ?6�.�L*� loaѭ�0aA� I�q�� A�uitably)N!1wFS� sketch - � ���Oin Fig.~��I�E��b�$ mmar%|a"ox.��ini�I� a hy�%6uN� A`�W7Pn�] by $�{b&cp�ic\!--of--jB� 2 a��3�j^a ���. �� ^upA�R ���G^eB� ;���A�z� �!�u�H ZeXyp!Ba uMA �I�# s�I��.�byBe.�.�&w �A�U��%$ MF�)�wozp"� f��� ame spaA( z on,�*the�Pn� �r� .ly af6A �%[ occu��m�� b,Me�dez  � *% H"�!�*% of�� uu 9�3a87K&h ����Fa"Q@>�Մ2_�aCpq����an 99\%!U&� š acce�]�tY ? "��R eɬ �dorgan>� In ��,Sec:2}��"ATal � Fi7 duc�n�>relev�9�4 identJg 2g;EUing n}p��u?e�& � Y�!/YS5�.��:� = eZ�y,( � � drawFId� look*cus V�dNnd��ai� analysie�par2��MZ�N%3���u��e ��-q�)�Ty$)� D}Pp0 }�T"y<$N$:���$M@a, 5�� AdegreU "�ed����s�Bbs�c a , b�R� ic A�i�L++�` ${\bf x}=(x,y,z)$ a harm� 2? j( +)$��V� V.�(M�8(\nu_{jx}^2x^2+ y}^2yz}^2z^2�) \ee�g$ .x y zR*-,�nalo� � cartesian&�R $j=a,b$ r �E-;!ut�@e6a9A7�͏ �, �l�<e2� � ax},�ay z�( \mbox{min})4b)b) bz})$. At� $t�*A�!�eJV n\Q �A� tituhf�W im��aV��a~�� �&Q ��� ac�S2qfn A�N �� eep 2�=� . T�\)� gIBAI��"_ dri"�%Vm�� %X5ew���[���������ŋ&�)G  m/(���Sa Raman)�e�� )��" #fe�"provid�heB�%suf+� hort, /jin� &9 du� �����&egligiblUcnd6Ze�toF\$� e ic Es ��'l�Q)�[�+b�>A"Sec� ��IIb}. a�� ro� w� (A"ic ? �c.(�,��"? �QK!Z. �[>is "n*7Hamilton�$\cal{H��I �I!�as= $=. _a +  _b +2 {\rm sc}N$int}(t)\,.q9i_:�} \ee ��-a�k!�.�_b$6&c�W75<=!'90.�i,.u�� qt,!�*�|hf�ѥgin{mult�"i H:i}2j=\�Td��\,M2��^��6��[-\A4`\hbar^2}{2M} \nabla^2 + V�*6c x�:6#]�.x\\:0+ h1��g_{jj}j�:<g�:j�3.�ps2,�79W�D:)$ (>e�l��k��  an��ng ��ng) a $ tF� d!�e�] E8��{jaJA� $)6=4\pi-�a_!H/M4KZ �Oa�/ UH-A� wo--F �i� � a��kn� j�. j$ d� e$s$--� sc����-(�)��lj� o&� B� 8V��u1 �J {Hab}.��( =g_{6I �q9�E& >3:)�[ME s.� a�!�M3N�,�}�5R FR!� ab}$�!�-�1T�!X�I=���^ b�W�."U :�D .�ime--=51E�y^1�@:�t�s%��� =-E� z�(t)Xt $d}�� x��N�-� ���.\\ �q 12\\Oͧ_L�*A\ \� (�> b x}] >�+AH.c.} j_|� !��,-valued Rabi"w +��(t2�]G�a�2 im^ $&� J:&�ɓ{b}\to � A/. AllEMd 2({E�:� b�+��  4/�8�1�{d v�a.!T>h:�X�A��Yt 0$. B*.a>(  a�$n$!B (E�$n\lll N��~ 2i$�stLi[�O.�a$�$�|n\�'$�7��1JW.�Փ N-n$ �& ~*O� ��r5��F�pr�is�su!b*p&� $P_{0AFn}(T)sA �8%�.6U�T*K� en n+�$,!n�P�_~� B�9s"�s�� 2�=|w) n|U(T&�i|^2� ��8 ={\? T}\,��\�)("�� i}�t� _0^T d��]7���8E)�`$ i��pe�rgingn6�6n�� �2 ategiof�[�1�+L�i�$6�}'H}��ʒa&�p����.1� r]c�ub�Basic �Q��dU roxi�ds}  %a"�"&� A�A:�c��we�!y3�+om�'-:� ' veni��basis.B we[7 FockJ� �� ���*�9�V��&px$lewenD&9�gb� "A�������H_{\vec{n}_a}\phi_{aU=.a.*�-Z�L2`eUd6�"loscill�+0*q  $p^2/2M> ��n�$�d@fT YS!���)Jh�%ws �����C��� .U. rremark"$ .~F.Ces�$G)le eig!�atY1h��y� L8 .$A5:�S n�4�8(�s� ngi�ӒSQ� . NeR�he�h�(�w�Tit gZs laus� ansatz�k�&avj�%�kof �itN�a�shyA&p�s. Sly!>>��;+eʬ-&|A "�y�9a�a���N$e�re�XA:{�2:h -�b$���Ralar.�R�f�d�|b�r�2e�m� copi�+.�u$e &t ��n,�'*$\mu,s1�1!B6�,�a3=< affe*�' kFeYE�isM�*@at� kY$n�=N|:�|^2 �.c.o�cc|`Aor!�!�(low-�#).J �+.W$Z�_q^�a��2�{� H�M�7.l�zFSB��w� :W��q� b^"�_qb_q$�� , $2 "4� &m*_nd��on�v�Xa phonf� $2�[t n ad�%,F�n*lap*�E��Y�#� :�'a iF�E�!.H2jEq.~(�"�), �det!lal!j FW&�:� s� �/fl<�e2wQ�.��l%�J� Below�xt��L.M .��a��perturGo�haee�{toZ `Ae 1shift%��I��'�+*�@s����29\6��#%# (quasi-)1H5�2�� 2)a� n$�()� i��wo%�e�a� a�Rd �&h�sm�;"�o#"��� 0a?�ĥa# 2$Jf 0,1,2 �5:��B6���mg(is $E(n� �5{n}.A{n�Y$n=��svl $E(0F�y|%Յ]\be7W� tsum} sE (n)+E� sc-n\mu\,,��hE_a(n| A1 I%�n$~a�":/ .�>�%t2�"� "�onrdueko�>B��h�D$�$>#�"s!:RWof &-J�%�h4 �0|0�o�a!4 :��)%[�*� gral"��}�F� �6�~ >z>j�'�evalu,m�<ap"I � l�y�6�a�n$ '�| r$�* ��<�af9} Q� &= n*?(12\sum_{j=x�D\�aj}"�q +  E_nleqm a}\\ �er?{and} 2�&\) �nN.: \,�&� |^2 &� |^2~9 �oRB2� O. a^*� (�4)�$" =(0,0,08 � E_neeauX�Ba^�6�icle-- E�%�on�D�u~$�8 e{ch�y� o��� a�PDa� E_n= �j}-�1��}(t j E�9Pa u�Qh*� E}.)�we� em)=2�A�Q7 �}���s9ea+ 0�4eq:EoffdiagonaAMeeK6�6Q�&O e�: �� � `\} >� �L\^N(n+1)B�S��%��]� \,. p� �ve.�e2<$���� =sYm:%'A7zeSS�a vS7. A�W:o7iz:muZ��Jer�IM{J�Ac���in *y �})a��I�� )iM#�Q -~n_bz�:l� � n_b=@0&: a-7'r"l$9hK$$eg+�<�3.52�SP�� 2$��cha�perU*�6�F�f -2^{(2u< 1iQQ�$1)a�}}{E_2/�}� I�:F:2"�u�}� !��lmin�ye"~ 50"��A �C� -Z 1E�1�)an� E_2�V���L!* 2)-2� �;e2>,�\eqpqF�,D/3� =$�l��-h \ll !W�q seA)H.�E�N�Cohen��a{99x�zc"��� =E_1jthi�6b-^Im2z1$ y�Nu����E_1��1n3 .� 1)-\mu�� \*vV�"`&�"r#�%zcN��%�n#T �$check���st�=of our�d!6 +���!Y����� ��+�'n2�-� ula>�r�F� �'*�. in��R.q. We f�� focu"86�$ru�P�N�.2͊ Eqs.]�)(�--y a}1L�� vibr�al .� ~�I]1#aj�E(1)=�1)F_ A]BUe19 a(1) =u�3�$eP� a 2� ,.��e5?+a=2�# s 30�%rm kHzZCb$ %100\,%Hz������ � N�l 10^�Z $^{87}$Rb%|�P 2�13\cM<81�Zf*/cm$^3$,%�� c mui�:1.8 �� w� $��1) 0� �eYA�2��AN(��% a$e.�U�.�:�is%rm Tw�� 6-Nnm�i oreoB?QNkjce2 m� I��ed# qM�� [nuQusI��W��rap s�a�"7T��a�Y*6add�� ��I|D�:!�52��+ avoi���e8;�Ci�? ?V�EBk"�N�=7i��2is22s��$YI �� <e2iu2)= 3yj-�l�]� -eNSN1.�2)\sim 22�}��vG6�� f��  's*� �&m�!��=] G  F5��: y�is �\�}ikq��b2y�. �!�"� . : .3�d�m"�: >�-��:g".anCV.�)=�>�->O�]�� $E�~���e��; "��D��edZup��j�a�#�7st�2~� scal"� "HF�C{.�z�Qe�mA .�m]Bf ���)APu�q��\&� *�))  vi��T�M�K -t%P���1)P%^ M.i2�o� l�en�2 D�QY�2I�$2`2. - B�R��1n;^,�;�"��>2�0 {�A%�tely C�j=�!�A� v D .\ggq�sc�+E�C��/�bF,=�:K�H2� . NeglU'�u�-[%�-�a�%y`�!& e ��~ delcB��:j2ataw<E�%s :e�A+ c� ^d �x�so�.��!w�p}�;b>. 1\D � � RAIZ � 12[sum� \a.�;��5s<ci�F"<= .�d���%k �$, "���" mƂbe�t"�. I|�y`��;s�; in s�M��be�FAf��i"vH�.8d� nCHL����m��IHF+�9�. p'in�Z;GYQwhethere A;iIBW� ra n&�\ge�( p8��a��X fv� �#|�ow+#& Pw � j�$&� 6z������@�� j�-. Numer"!��'ha)+�A�t� �/ RIw�!u89k!�inL�ly �� `"inga00,�Ra02 �JH�=al�[E3�0zHuM5otci!���ex ]result�$�) &�$� ��a}' gh�H�$heaM�� . :�$]Ͽ stoo�<2 * !TSe3+?Q)�*�-  tJ@metho#Ff2e�?&� ���)� �f�Pf<.eB&"5� i1�g8���o �A_s*@r@-��"i � �߉J {n-1"�.�(��!"�@)m Eb�@,F�A �is#*�r�W �sSantȢ �%�%lhe.�%~.-!�.c=&�s "/ �y�[O�.� -=�� fj&�I=qJ�$ ch2m.� �@���curve.9_9�A��"erGV"� Y�qCŵ$\dot{NZ6ulfill��5<��'Rate:Ri�} |> =(t_0)| k 1�1[] �!j: |\ln�: (1-P_0  )|�*�-T�\! a��7"[-;%�P_0-hresh�T��*�2,; %�"�21}>Fp4po wg*Rsu�G�Ty.O�v deriv%SA�in�l}T�(2\q� �[A'�ZDA. jXN �&�Q>!��#�N��Q dL<�"�}N�Q�y��Uy!M}yV-� #rof!�ic��c�Acolor�P!K�' k' ��r�K ,�71�.� � >����:i����0�h6�Q,�&�:�6�i$, &��I_V'�J� ��$8>$0�<��,(����_^hLBECeZO1G*b!� palt�*[N2.>�O�Uam��{ �*� �V&�)��2-�D�7r.�. V�c .�!����"2 I�,Nev-os* ��)@q$"�@��q�j����4�5$�K�>���m�� �)endu� \c"�U5i* /�B�Top����(bottom)��1�Aa ɧ�j|t,(a)BB^�E�  L=4\(bN=v Z?���O�s��n"��,Hbl�� ,�Xl����o�Ipredi0 q Ae Landau--Z�{�� mula }shaAarI]� B�oni �Je͡6�`'"��O&{ ��},e_s99\%. EyE�U�b�n�^ew mi@u 6U%OaQd%�6qj>U¬��,upper quadra�8of:� �6���^� "dU!�E�o'UOI�q M�� �7" � ��Y)\P s.�M�{"I�Y��*bU��M"2��%Y�9p�\nM�E�IoM�� �y 'Y*q AJ. 0.99ɼ}+��"�#y%!V!+I�:$Ax�1��H�J� ��5�i"yQ \,E�,suV$en92,&SP%v.�#"NAa��A�ru�' }<r�aα,1}^{(LZ)}= 1�\ �+ad�/" ���F�$:2r�\d�+�9?^2 | >� r m+ "��2! � U1[ =>�Q"��gy&lY6+1 %���I�q!�Qu �����!�u�e1(u5 ��. �"����at fas�T�����atIKrm2�vfact,iJ�  � �`es1�a��1���E�.O�25B�Ng '(��*�� " >�st{Rng&�` �0$v�" - $ ei T�%ow'E9�`&!l =f Qxn�#(2�GB �R�),�4Tn&�TW 0)= X��"V;&� ��M(�?&cy�A�.�>!�� C9w� B� ��ta���Wl�1"����a drawbsdrk +�g%���]"&4.�%�2�'2PY��A 6*,"%'�(`I�F�()cisneA3raE�a`A:b~� �($,f�Zd�!��1a! &>�-m���lP& N!U߲4&X^n^��\�Z`�1r��!�oc �, tric��l�)"�'q�speedI�I���epi�v��!�E{I[�u���A@� 2NY�5O"� �.k �0m0eDg2ar>��28��� @epa��,� )�!��܍�:E���>�z�� �*� �'30 *e N� =z���� &�&<% 9|��#�zg�6�!:*���a !!�  &B�� 2�� &� 2�\ �f� P_{1: :$�#re $#to0i�!und02H)3 -8>�B�$�is �'�|�.�.�I|.AiŌ� 2u�kF �P n��}s��v�scrap_ ��b�Ske*q`"b;V�niQe �"[F�n[ � Pump)tOO"�K$2a.c.--St�C�6(- _1(t&s>�i���C"|H�H�,i�.LZ�b)�xaR� e��am$6��W2� i���GE�V� 7�C olid ( G)�2G h=`�e�#� 2o�!�%(� 2$s7Ve s�tly. }%A1� �EL:�f���Y.J �"������p%��"� .%a�so-@ed E2--chir^rapid�4�TY� *^3 , po;j�i�"- w&$j5 . by "�Wvar"{I6' "�LA��*�QZ ^�t��by�<<_^T�E�  {De���)!{�dug/�1u�e"Y�Play ���he\�j,. One c!)fa>Uf*l an, $ Jmh!�$�.�NA�!*�>B>v �c�~"�2`p��',9 es 'A2(A!�-�eQk� �Q�-!�*y� %� " OhaA�W!m f�t" t "=*�3 ��wWB��%�!� $t_�)t_2��v�+�4&--d!�Y��w� �uc�� t T%��#g��an]�q~mp�X type�j�5� � &�C.� %�l]z2�Y��P by ensu' t �qen6rNjK&Gu��@&� �#%��V}�~\foot5{I '1���Yi{�4�3ۢ ouldn�en�!�Ţ>�a�Z+%� brev�x*�Z &��b!!�a-�Em�� %.}. A�V`,r�n) -�e_W�0> ime"�:Hn�f)E:�ɂ& %�� T 8Cm� zd-@�2!!1�^a�!- =\takI�^h� )G1- .��TE1�=�6�. A�bE-X.g:tS%�& %�n "�nA�o�^�-r� !��;.�K�eas9�exB�61�"�*U�� b� "� �jh>�%&R*E 1#28F� �_bP��2�jV)*��[in V5.gy*4��.n4Q���.im�F��N��+��!U!�m E{c�"WeAfur�&q0, namely the �width of the pump pulse $T_{\Omega}$, on which &ttransfer efficiency depends. TGHarameter regime for`0applicability u�is technique is discussed in detail Ap` ix B. %->P FIGURE SCRAP result >%D \begin{figure} centerH \includegraphics[%+4=8.6cm]{scrap_ j0 \end?�P7.Ptau_erro�:Sp \caption{ (a) Contour plot 1b5� prob1iT$P_{0\to 1}$ as a funcJ)�$e coupling-�@maximum $\widehatI $ and %A )�tweezers�p frequExis $\nu_a=2\pi\times30\,\rm kHz SAV@a.c.--Stark shift �hassDelta=2T}PA��Detun�\s have Gaussian envelope �Hred cross indicates�U��2� =15 2�$�=1ms$, i$are uM�evaluat��curveA� (b). PJ�b�!> varia!� ~$\d!\tau$ be!�nginstant%�ime at ��resonanc!�ndiJ!�(achieved by'.��!eAr^�C(reaches itsUR!-�Qeat �$\approx-4\E#Dms$ corresponds to�dynamicsE�)v�$temporal sIe! adiabatic� passag�(s exchangedI asymmetry2U two peaks!.2� {xt. }%�Mlabel�^:6'eґu~�%usn�F��~\refV6m�#displayIܕ��B .�%0$i� _L$,�1� Rabi}�BA,\Xobtained from a numeric!� imulE�%�a�@�p withv7. TB�ies.�>99\%$e�Y�ii!whiteŞon,]ae�o�n��a>s�order 0some millisecA�. High9Y��id �re� vely��e rAsP�v, show�hat)qethodAtrobustafluct�Won�ESA�IA0. These data� been��ed un�3Ή�QyY}֍(J�a�Esam��j�d2� fulfillI�J�ELdepic�in Fig.:� }. I!�is case�idealԉ.��=�i�effec�9a%�--lag.�2ihwo event�!�nZ�-(b)�*report �B e��mMN�on2� �N)exhib�zaIm4plateau around.E=0պiU ���� �yŁH��taneou n�\A�wo atom� :�H (dashedARt�3lin�WR� (b))e�not pera�ly5�:2}A�w!�Ű _ceE�A�6a8energy spectrumf:� � Av2�iR �eQwsid)cQyA,e�;U�follow�lower M�j�:2A�.�}�.W�{ � "�!�� !J :2�. Here,tt�.�, largE� an $5 ,i���!UFs�xal."s �*�broad&� 銭O�2}$� eeds �Mf �bp"q2_ n+2M�Evrg �� �-2 kN.c�Sketc"�U� wheny�aba�t"?��:m. . J� ("� (t)$)e�.�(� _1 &a�2[ime�C"� �q�ilcoloreK��� �e�N $E(n,t)�T��6"EbA�2� km�im�kdrewstatey> 6�:9's�I���~��, $\ket 0 \to 1$ %Q 1e re driven�Ctly. "� .�2�E!xU3start�$blue solid ��R�:2}���Bj��E��u�� a�.�y��Z2�ZRZ�=w�Z�Z}:� �BSn 6S gE� by $\frac��H_0}{2}\left(\tanh ( t + 2t_{Jramp}}{2)- / 1- �-r:$ \right)� � $.\�Ua$��6 yĩ is�(po W um�l. ZJQiEg�?f��  \subse�{o� � ion}�4by popnin, ! We fin� Vcus6� # :-Qrp :%$ chosen��as� R � !f�_^�d 1$. P� �>� is&���~��*T �L` e��>� �D� Eod}@\, �1^{(1)}A�u)=�,$i limit�s\ o r choij{61 os���P ~c iwa%��qyA�{to� negligibl�-Sto off--1[ -U (see&*A),% �)dur���mRu�!� longe guarantee%U�al%�lu%���he"< �levels�6� raman}!)9�*k " is�t@�w�s6@ �u�!`ns�nd�. E ��cl!�to un*$re realize�th TA�.� N OZa �"L by6� sen � �s, 7@BO i>�� !� firs6���t N!eV2�m}�� reby6h $a $\pi$-roI�. A:QaB^1^2�e.q it�av% �}q� (E_2-E_1)OE�suitaa : area� J�, E�A� \ E_2 V, avoim�dur� �Y j!S�$a� �� !�QackAa$ bensat">9{0}+ {mfar--offe{�* }@ex? �� ��5w� ime scaleE�~�oa@V� j�Ra� &V>~� +~g�1*�E� c4 %2 "zby1.` pi$ Y� (a)~2� of6|. aB{eQM8݉ F h��I4� RX2�e $�$� rII�blAmw& Q�&*$me� �]I��e�(80\%. (b)~$�A�R� �strengt��\OG �co -�u $ =1.5"� ��A����"�ve:-(a)F� QUES�� �� \J� co? j D� y��Cs� �� stiga��!�feasi&+!a schem� at employ� d ��i�!.Fd�!minisextqa�� a Bose--E�ein!���� thei�n��ىquantum� A�a steep��p.c ��Qa hig��.wcan� �rz>� �U!M��4present experi�R tth microtraps~\cite{Reichel02}I}&� �`" 1a=S �ei �ew� qr thus� direct�,say, a magne!�dipol=�lik6 �Ke�Dle03,Mandel03b}, o!�!� op:domai]"2�E�� eir�#� *�AU�Y ificA^ail�Lsystemx$� s �a-�ed re� tod� y���t=0$ allM�-P0e�A g�� Q�9Y��the o%�ex!�d .�N-�q eiI �� non-- 2e. oms a�!�Ar ��a$� >c�%_s e%���& ider�!J~�a�&� sour�is�� process,�A�aw�!�1e�!��of�0 :�A0);�! titu�#a fur%�>��� FF�� . Its�)� e9n�q.l%A�trf��Ts poss� �*� �J conf!in�.j �+2���9Q�.-� tak!�accoun�#en set���sEthe�'te��Ke�a�� to2�A��u5U!Q8. Our analysis*E�restr�M�<of� nd Ɏ�a�6�-�s2�.  !re2E�s��y��!�q\one--�two--v)_�!� �:)�9I5�carefull� t, so�]<� lv%f desi w A;ey����ase, may%� advantag���ies, ru�'out�ugto�usmJbe�4but orthogonal,!dini 8�du����paperm> well�ended J�three��m�!k��o}5�!o% )we�~|��%�M�1�� 2�" *� Wa i��r�y�(, however, Ve�����( many--body�^1�e r����� � ie�?e "�eime--� (�e�manifes%�mselves�� �rap.�Q!qicE�E�e� i� )!by%~. To��*M���i�+�ng`dem]�%�� K���k� U�of���!�daa=ervoir�� f� ng"��oin"� ����nd openEye��ing pere�i!Ie�e study%%!Pcontrol�co�nt mar � s. �$acknowledg\ }�autho��at�&(epi� w� �Andrew J. Daley, Murray Holland, Pe�,Rabl, Jakob � 4, Bruce W. Sho�4Philipp Treutl� !DReinhold Walser. Mk+G. Raiz�Hnd Wolfgang P. Schl � nk%$Humboldt F��l�esuppor;%tMax Planck Research Award. S *E.!kLEU--network CONQUEST%� L� |s\-stiftung Baden--W\"urttemberg1�frameE�Q� Den\-auto\-bahn~A8,"� N� al S�.e�; > um OF s I�+A14, US Navy -- O��erNaval�G;P No. N00014-04-1-0336�. d. �Y!MIUb�.}*kL�s5[/~ �!Wa>-$} $'R�m��4p"J� ag T��describ�Vi"ely. Wg�summariz�KoY B�W" �a����5���6��+�ʱ�%�,de� ��ba�z ���¡G�#� of $n�%oms� assu�*"� is swept 6�-�^�D�-_i�?~:f$Q��rAT!!im�1$, suce��Q (0)= [�(Tf$&�*�e�� 0�  v"�� �%�"A 5�� &�, \1� eige�� !Z(\mathcal{H}} goodA4roxim%�x)?!he�.x,��� �!!�tra�o releM Yt��inv� onI%��%!� �=tL+����f�*�%Gu%Mi�u6 �pa�855{� {0},1}\T he)<% 5zre�&$d Hamilton�0�u� �+$t!�0\JAD�`\be \epsilon_{\pm}(1,t)=\� 12�(MW�!\pm2sqrt{ ^2+ �|�H||^2} �eq:�!y_2 } \e��%�01} eM�(t)/�.>%20 .mtak�s forme�3subeqD-}align} %�\\Phi_{+}(t)}&=\sin{\Thet}"0}+\cos> 1}\\.C-CJ,0}-NZ1�!�Q0eq:I-1:�76�w�E�mix�7angle $ ��de��aen�4 k�n 2 :(Q�)}.}\,,\;Am5\leE.!�tden�+ t_�xh�I�a��2�2��eoa�W na�+#, nU+��N��m����&��9 t_0)*��6,"�(-$�a�(liei�2 $t=�e�ak� Qw �3=m(u}+e{ _0)--mA=E� : Omeg>b1�u_s�ea�nowu ntif�3>�����]maD��)Xw3� e�����0T3�3��!.ju� i^� (i)& to ��le--pa�l c"vAhe����X�),�*\ $j. \ll\�6 � (ii)Y>ed �24ntrib� ey11"�+���$�]mWeq�;#V/�E�&�\ee isQ�ed�iH O�'m�$ ensur-0lso a complet\5e\�amp�2�qC a�,mzce�'a; (1)$A0le kee<�L%9e��N.,�is�T� �-e�7� �=W" 27far away��.�_2/ɿ�ne��s�2�]B� + �[&Z _f$ :unpertur� EZ��XAF��� <>�.�a��(�F�9�$arrow�a� �a� X"b2!/($ Y�Q�1qB� v�S .S: >� A:�-��dA�u�?� au--Z�w��56'� �7ptoticsi�,)�,Y�7,Iӱ�}�K ��2} &d^{(LZ)}=1-{\rm e}^{-\alpha�&ad}�V�- $:&�!�"� �"��,��as�6e� {�b0 ^2}{I� ^2 | \dot�I��|��.t�e�}V�propori"H�#�s�:$, m$in~Eq.~\eq�8J��$Sn�&&3Jk e�deriv�Q�>B� %XE�--��ing. H�1_ Fc%=-�$ɽ��s$�.&� B�, 1\R-!�A��0D and/or sm�Y,> $!�g }�/fix�3%thres�=� �5&*�i�\ge Pz ���M� uc,ful)��^�t� o�) �"I !�, requ�2�jly����� �� s. FE:AD(�:eq.�})�fi0 ��B� \ge ��\be |!X. \leq � eS�*eYm �� )eg |\ln2 ft (1-P_0  eg.*� Adot�  UA� Eqsn A y,"L}�rewri97is�P�"R�lB�^ �,Y ����ee}D%� $\�@1$ need�'2�ќ5� 1��� A9 "� !�Y{1}5 �m _f- � _i}{:� y | \gg6 �@-�|{^�� &~ O |\!��g we� � �/A1| ��)]|\sim 9x $. W�a1�x�S"�:Sec:IIb}��% F*\A 2A#"\Aaqa�N.B0=99$\%� 1�%�B�.; %�\gg 0. kms��&#v��2��*�[b��Ds�tF�g� i�gwd��%�  "):botjEas�a9B�'�$h�!�* wB� �by v6�"]4� � L(t)&=V%  \expEx[-I�t�� T^2_ 7M�]�Rtext{and1 I��&`�offset}+q )p � v�(t�/uI��M��l} �/]$�D:%���% � 6io$&'� \z %�lsMdth� � erm� �& )� "�'-$�9�L,a)�)�i m�20� �{� &%4$t�'�W<�&� ���� (t_1&�_2.�EPf|.a ,A�E�9 q<k���a":u:s � M,6 )se�_1=�/ t_2=���uJR ���w� ��/O 1$� vi�G��in 251})�5 % �an up�* �2�1Y {I �1+*�2�A�8"9 �$9Pa�$!ep<)�pr>�Eas�r va�E�2�smo��YRYn2- B.')!v�?� . �� reas Ci?>c�sh>>�2�EaIA["��t & �1omb-|=� A@.� of}՚mR4check�_ ��Oae2\F� Q Eq.\ "f .:)Fm�%Fr t7;<0"� 2� Y�a�* 2W!  ds�� �!Q"�FY(�� .���x MYa��u�o)�����ormw ���:ad} �\\pi}4 ��" ^2}{E ^2}m {�p '�% }{T_ ^d8ͷ Ѹ$K&�I ]\,=� r�:=��. 2�@5XI;8"��C2� .�_a+*�_bA�a�6���<�"A�is Ue�ed ove % i�%� ;A)d}Y�!a� %J%�-��� n��� �//*in.��6 jump��n �'to�6^E�.)&2"D�"nt ��.� E���2x�  2Q� _1/ 6r 1)|$�*$vitanov99}��!���@�[a�st �""P"1��P:]!Q�6 &7 s to� &�N \ge ��\m*�E�-eTM�[m6taI�� $I�]\,. ���fix�& ��6/s�O�Wa� A�q� �+)�ve delay3'$ple algebrDwA�%�2 sist�"�"�I�82��+)AD��% �*9Yv gg 1a�F�8!�2�P�K�mq� n�.Ois�� I�M�,,iK)z>���OP}��&spe�,�(�>:-. A�C��R ���ble�o��&���,ٍ �E�>W(� \ll�pta"b&%a��3!AH&la�H tau=t_2-tw I\ :�-���SEB"1Os�$ end{3"$} \bibliogQy{.8221204}%�N� AQe .'( via BibTeXQ docu�2} ��\,class[12pt]{p} \usepackage{epsfig} \addtoln2{\� 0height}{3.5cmN!e:}{2.2 !set@,opmargin}{-1 @odd(#0.3c#eveLB$2� footXsep}{6pt} \renewcommand�name{\a�!m2ab� ct6#?{\be}["{} 2#e#!�^!bqDquoteBA APS1�} 5Z base)E$skip}{16.5� \title{� P�cherr;terpre/A�c2me�Oics: An�e view!�l't{U. Mohrhoff\\ Sri Aurobindo IV�.al Centr�9 Educ�\\ .�,605002 India:Pnormalsize\tt ujm@aurW1 l.ne�,date{} \make��J!�1�!�oi�-t.��a�.}�v�ap�2@&k�.;p�/ed�3erecog�$�)�!e�Cd Itheor}2al6O' physpQis aZ"J algorithm���)�o"$&�)objec>', fuzziness (� liteV<mea�+$of Heisen�''VTrm ``Unsch\"arfe,'' us�.mians�Ld� ``uncert$ y'')Rassig ^�f ��� p�*le^- come��"ed�S��$s. Althoug  re�A� �0o�9strueU�; �<e}$� �U�*!u , it ar DP6@z'p�!-!D q#world�g owesR2hc2>b%�]�goings-o� 5�laboratoj.*� unl!�� +m�� �ed,�EDy!��.�$ mU�*can�2$ seen. Amw>`%Z�ra�Ell� �"al nat�.of D%5&[Rid� tAD&� ! R a 5incsp�!�ATLt^7m�ial)iu&sT(t top-down 9�Q�irT>t@a%%�rI,model!�f�VbotDKupa[e���� bae1:-i� nsA@�L�L��g& C.,orA�= mulf3d� `-(vidual buil)0blockvLŴ\��@{\it Keywords\/}:�.�ofU��;2�:�; _y�2� ;�F,!�ce;H[f� PACSA)ber � 03.65.Ta; 4-w; 01.70.+w % Q-osophEUs.,!@-w",,�Ta*V,�Nq�,;.U!�orynA4�?��\pa� eak*�\( ��6ax} O�A^0past five yea 4 new��� emer2WAf�.a��Aӡ�puby�H�focH9on�Pai t%��``f '' %�9�� WQM,��ABL BCCPStappIUCAA$Clicks, %X�G��K�g}. Howh6 I�0EZIVy�e�"�yi�IWf��=.�  p� �Ga�5}q!n:: pe  c�7q6 ^7 I�8 path2Ni�?vul 5"�Q�$�@X trual�"�-FI�  mogr�>5qZ� aLoA*�i.� IK� !>�  g�#ate p��A�lemi inv�gratuit��D; s. B�9�i)�"� �al.� y� a^l�``d! �j$ � |]e-`)�6`%4ty�.��a;ura �Zz �Rs a��n � itur��7�2 p-ou�)Ar�V7sy>�>Iwh� a�Z� �3e�4 � . PQ�sG � a�immens�ccm in���t A�(p�U ful ``sus� a� myth''q[e�<SM}---A�belie Y.%[wd h�U )!Kly%re. Ne�AGd ultraviolet catastrophe n���Va�wrEB� Ru� ford'� o�9� m�4i� ists�D)GiEth! w�t�=���3�� stea 8o7!�Bohr wEn!5D5o� ,��A�gy9angular ��,um. If todayV seemO� 3q�Ek=� myth� ough�^be *#@F�iw�M o[,a6\ ma�!twrz5�� �itYspur u�:to ferre�kem!�(fP ��.�._O�o\OrgeF� ,6��HmeE�e�:fu�\j:e�bryM s&O"' �Wxy "}��6er|�,q�"0out"�.��)��?A�,.�� n%FM?0bxde�!e�_req[7>``>�� n al�>$ndard axio��Q� unadul;��Oum9-P was famously critic�M,by John Bell�- }: ``To"�,JS7=y� ly#  pidd�?l>y �Ci�;� QAt�;A�great e�priseS );�m0?�dect%1 way�� ea� =9�[g�farw9SiaOp�� ��� _tiv��in 1905!諾��ha0^A,�FtoQ �taY``R�ss�e�K 39 LondonBauer � LonBau} w��f:�@\e of ``&Z role�`�Z�4c@G� �er.'' &��� d:./|���?!u�9T'1$few (e.g. �Wigner})��- �)�  ms* ��< i�c� ven5X �2w)ta"T! �H �-8$dEspag,Ulf��F��MvJera#j erce�4�+�^a>� ``� Zwh�1to most �)>,�>(sen,PeierlsF�F�5 �+?BinVEBM�Nra��� �61elf takUh�5� cEaRZM�� UrA�-�sloa<&� s� ��"j� 0Jf>�y5z>�� J - ��, ���� �at3��&{\e� nt�sul . S J< ignora�'� ies:y�� pic :-"M;�3)!H�Because���N� .� ,to�dike�B_| �)� fall,K��:� to x7�'M.\@�6���a�2�_J��i.SG(w�i�n%Cs �%zp� .){ impo�le). 'non�i5�=�A�aT �a �%�Hv�%!~a r .{Um fn texg�cA_!�2 e >T �@�"�\/mex/ �<:U(a����fu� Anies�'du� ��qtot�an prev���6 � &�_2&`' �prE�F �=��Z@�"_)�2r, principle''| J�2�" �*,)[&&Q\/} m� c(---"�W� , unlikM V"a -a al:�  be  sdimF h.[?!��=_}�aa��%6E�r n't��y ME�wo�fa�cA��:6�&� WA� ��,a� K ���|m. A� �iiJ� .�IJ�. Ordin� i5vnKaqI extentN�os9&f a (� but)�`nu�A�M!C�s PO nd n� c2\A- UR.��c��2. T"�Aamiliar�Lud��im�q%j 1. Each &.�#� Үa�%ti�%�!B�29U)pr)�s^-w�ll���]�6M�P  ,�2, clou^m vary!��w7"�ntinuA9��_�> ion:� t�vb6eL M� lOa �;on�TE box inser�WK� %�'g�.]^�7�AX50� de i�e�9p+/"���� . N�@ magi�P�"e& !^c�P��RnvOa�2�>���-t answP! a sidCyes/no":VN���);? B^(2t�Y9s��-AIout6 6if�Y #��.�of5e>> �cbe zero(R �MJ;-� :)�x+:y 1�it � f�x �.se23 .3e� 7� !1.EV� )*L�� u�affai�:If we w p.bam�>2���/Al� wi<$t mesA@ it� �H�be!3�er��$,��fa49m�WfV *�$���s. ClC"# !Yo�#iN�toB� ^�<l7 o �``pr+�W�U��i/6��V< yin�*-nQ�s l�xa^aN�� n ep� �uB I f(��>��L �' JJF�I�� �den�3��A���malisma��u.�#D"u�nd ir-Jib=Ky&x� ia ooe  em�W  "!riE�"�&�v�ne�ari0U"� . A��[��) �DmmW3� �%d�$pNE�YTac:l�ju maj�( y---� Z �UG(if an )V�t�Ik�Tu%� bembraIrgno�is.ta�e�u"j� �h& (5 �a� it�;� fe�&� or beyo�r k7'A7usiR talk  ��E� YW� �X0����0s (synchronicj >6.� Cs �sor`"on&N'D!�4N&�  /���aRz �.{fz!os�E�!b/"�'2&s� thir�p�!! i}r =b� !_�t�bq�F�)�,T 2�.�i{Q�!�HC��(� �s,�decla�-e|  l�.���'m�  . Go*��Ve�ton�f �� you ��Y/r�e�pi�gin ho�zar. (M��nk�}C.~A. d 1}��!k�!Yt.)i�qL\!YpS&�9hav!��� � #!GeD2/in�^at����> x`�#�&� &@ %�8x\)! .f�u�< :(reB��c�>�7 @IOed��.��z%*�:�.���se�-%��i�v*N1��i9"$�� l��Yig!>�$��R�.�6xJ�Ont"�-.�, } Co�1r�o*E � J; �=[Tas9=� 's �c",� abs�F�ei��4box�1g�/� ��� ``� P*W .� N|�l. M*W i�� . Ye�T�� *Yb� �QS�֭MA?h,�� LaAqIf�KA �%�A|(�ke��V&L~*��%g rn��#i�/  ~$R$- tantF�o.� �#F��``)>''�]t !�H%�w� y ^:e�!7.S!k�!)En�[6� .DYa�9� %&�2Uiy}d 0��"5�2J�>$M#!b�N�>�It�&�n�(aph�2aA�Es�%ely(@hea�x -3 illu:2ea�%l��a�2�Y�e�Np"#\ I Apa�1� ��$Z(1A�e!�2>(QL)UED-=)�%ub�%KV@e#�EE ).�7|0��.)f*�Ya�o� al��sTaC?� n am�Judg�YE� ��squs!;-Y4n�2�\d !ul�rIn�, :M-JIireL. `K v$dd.8�F�#2Ue$}��6z=&�e�pa V� 4$�d� Q�*Wa�E)�2�(NV, N%��\Z nd%�ingent:�%b��E c�� ~�''�b!�aloraz)v �� �)/�a/ ny�3� =�tA�� Bo7P.i>+;nt �%)>�("atD ce ( �n�).w; w�3GY .�,�u��̑R�ɵ�=�n���,a* �E��w xact- �A� turf|��0%Mp�5/i� Q���G}6K�iT�4�t�goe�TJ $5Ga^��lyZ� ' R� H$A ��!H��" � i�AA r!-�KEM�~6 XoI;6�.,)��.%��(< � �*12q� �&gu5t� �� �5�7tr��>E�1h iZ�5 mani�5. �o�_a �tJ��t� �ur�."-�P "* _uB� .Zw� ~~$\Psi$E�m(Af4 l<%a�r��s77L4e.�6z>�?�%�u��2� rdlyi�![ed` t&�. Virw+y p�4��paZHE r�� �6re�v"c!g.o ��(a.k.a.*z$fie�9t�:H< post�3�w� � P !�N! �"Q!,� pq]]�Q��s�AGc sU%i�a�5~�R� E;@� oi���4��aYŁ`1N safi"O � "�:� at s��OF�� doom[Y�f( "c�q����.� 65m��V;draC.*c� 4 7guish�Ť�l��\ic�Cndaŷ n �E3x )�!� = byi5!�*�s��!zqt �n%�C^u�posses�1�;NI:*�n�-d�AdE�v=a�&� i�7!�inj��l%P�v�ga.+$Rvol� *Ea� w�&& �E�c}"��j"[<tagd&out�)5OA� *� �/�� o< h {?"Z.��!`;@ �l ]�A�!Y��s,�J mo%|north hECT sou (say), ��8 en )$gBy6g eastNfwe  f $a�help asE %N ��%T� ha�iwe9Ymly!����A ��65\ f�NG H2��� *Q45�---M�sI� ?---&�ask�y q&61"l+2agoP�9sa| sa&6�kEw ��/p�> �3� ce''��ok�k��8it � be &�>ity�u V!�`�&?:�] TIf .e�h��!lt7 ���n4 t55�?ate�otE���^�*�*a �P� �%A= 2 ,alse��9 /�ise�"�8A{!{�0on6(i) {�:�k`n(�":rs+E�,a�>.(I�D :E��lavJ] �C.>8�)I28�,���s�@ep�--ぁ�z!hmer mH weakof  sK�� Ejir�5nkn�!of�Z ����z iA}(��b!ax�Q*a:�-d0;�ia}ay�b~�l>��N�e�p�N� ��mpt����tkB.i �='assemb�1:�A_ct]�.�2��x&� 7Ah9du�!.a>� :� �c:�By?�+-�tb�Buny ade�g!vJCAv�6��  97e9 "�top��,_'P, t �� on. CS.΀hatmyou%io�Es�C��A�� F��rn� �  (m�+!�es�c zzy)G�] �En�"� s��$ &*-�E�� O( v� 't �y�v�i�!�a�52m� le��eapparA� 2tDh a---%M%a`.o&�aE+( \/}-���&�8s�*��st�@��M�tol�o�#��AlghtforBab A�� 2q/&")NZ�$�rtq1of.��jrSecImp}.%� ( vari�*��oa�6er�!�A�6a aP�y (by��{),�a 8+ br,a truth%``�G''A�``#54V��M.��ch� �5lec+��|~$t$'')!��^�VN"y~1*f�``i�<or ``haH$�5��w!#�sR:, let� ask wh��+%��E��� ���,ion~$C$!I� disj C $A$� ~$B$,!�7*�s�4r]� ��8 Born rule�#eq�G $p*.�*�'!H&� in~vplu�b�5��@: $p(C)=p(A)+p(B)k�(��/�?elf-e�QV f2L'{��(�E�� qz;�� & ( e�'�o9.�� �Yi��C�QJ5< � -l�$� �"|�"aR%�(�*�$To.H�swerj���D.,�*�* A #ect (� hundj �7��ffC�t,tectors $D(A�nd B)$ moni�K�Bn�� n Ml.�  $!�$�q$%ǥ7w:e�an~0 (`� \$�t1�8i5 &��R �"c/Gd%�n't3Gt�,Dif�C)=1$~n>%J i�2pM wor !.UHow�L?�M��d 7 � .�Y86�A�iin�y*,��(tacit) �&�>���Ya.��r2�du,c7 �W� �2~(nD5(H�=T_ei$QyA3)�s. So!T X��r��,� aupshot!p �-*���9eU} 6!������=���A�A* �4m;�d�\erAMŮ,}ř }���P��2��*�4�)F5 IJ ��m�;,''!Z�8. s? A�%r�u.�>,�敀&V.� ---no sur� �� traj%�!�a7\`a laAz Bohmn% }�4�)|S�Ad")iA Schr\"o��ѧ@ �%:Z,Ghirardi, RipZe�Weber p GRW}!�P9,e  �5|��?s �|d�Yal*(m-�[)� link UvFi� modK�||�9�5 (Dieks�C�&�XavailG !r M�%o!n aphr��a�-ll-kn�O�:um�8Wheel5  �Q��JI��8���%"� \Q�Fa��c$$--- % Eb�>�hH� :5A T�<�4rA��<�.*�-�s� In��?�\U�� rA��`%�iATE�A�r�,ɐ in�(!�l; +d1Dife``u���� of'��A"�()pA�z ORted��/&�.� �4 � M��]B? forcu+bro�Dh�?toZ by Gre�Ter, Horn61Zei�er (GHZ)M�GHZ]oI c��T)���y q2dIin-$1/2$A� ���ZeE\ ?�K9A ���=!�@duct $\sigma_x^1 2 3� he $x$~_on� �spi�Apr\sN]y]y^3�x kyJ "V�'Ix^�!D< �G�$y2�8� �._5��!BM^ed)h]�$-1��bN�$+ /�remai7)L1=� !a�v�S �=�r in�A��0� m�� �(�` -1$) re.R.@(��e*P�3s> �'�^+9" j wzs! s!�$3=1,\quad 1Vyx0Ix-1D_M�p��-� ����#-be��0� �it�f��A^. #-�-Y Em.le� s~1 pl��2 >P=1t�)/�~ ��V�� fourthT� � a (Aat!�)�>� "�61���o-��Fat�%�thy�Ui!5at&`�GF)��sifa}� �eM)# -�A��� ("H��?�9Z� �"��"�2�$,��A2 ~�expans*Ly )l�}�����FX*P.~;3�F ing,>!�N� .�;!���ist)m if�LH�-u��NQ `�{>!��� e�.7)� :�`�� [8� )$��h�� if� �!=��w��3d>*�% 8�{��(\ ��[&" (��� ��d:Ycap ofQ����O;� �(eg �l)b � � ?O,�k\two�5y"#s:a�qBt�A��i9!9k)��,D)qs� �!?N�,"" �̑ion. M�! f'g6V$ny�/*I �atuM�l�"��y��k !�s.t1U{qd!�9�/d vI:����� I {R M%�M�� �*|4to%%<��And$a�����Q�~?"G�6o&k .�ly @W �d��,s -u��c�9acg� o]��m� q�/R0� n� && )"@^)���m��g���Bl�� ``upA*nd�Rown'' !N�`��(5super.�^ a�$s�"+ws y%��si= 6: 9a��m� ax\���-'�A;� d�s�/���A&�&�^N&��nz�+� k#��!mk!!���!WPl argua�i �?P2V'R�����.�too5�-��2��)E6n?;�[wAO�A2:�"kP�# arli5��A� *��G�$p#oE 1���}c�}: �eQ&ce $t-t'2�� kJ��rp���.����ȃ���6�A�) H %�h  v�'�..�N5CwN 1>F|�`4;Ā~�;Z{� ]G+ :U4abo�\�-q-e3MT8'�EE%�A�c���v�*�K�F�A!mp�sh�{devoi�B��ic4 YaB$plugg im�. OA�"Ex�.��Wl² ceivŲ)�W"�Vq�ŪAL\_lu�S�Ťncuhig PH�*�Zb9�&G ��.*�m Foura��nsa� o���@�m[!�S ompu ���:�M[6P � $um`-�Zr�"��is%���b.A8�| X" �.�!���:8!8:: 9� �� �/�l M� }�> IR ��-sv�ic2"Pw^(, Bergmann� LebowitzLABL},2d m*`��baS2Yz on ��eor��#?d� �;Movir�" .�?WExpla~i6de�$?*X9�7>/��B�� GHZ)� . By-\q�:� m�:�AwwoeyN NQ� t2V>O!5>�~�3���*2�"a�6esuH n�.�B�ji9Ϡsu9#z*�691unt.>�uwo H���GCP�P *�M�_*evD�!�%]�A� lEf��/�%�� x�F*H��n % O��AT���"T#���k>a� ���T�=�N�q"�O""H-�?�V a��b&.svOe!��Ys�+B�O*!%� �&e�^� ? C'�er"* : Wh<;sFN�[a��"�R?iwe .>-as "8� di�)at �!W]_����:XaM�''h �y ``lir!� t� Ez�"�U�}rnxhV�>L7� . Fac� M ��"U!q�\�$f�U {YU m�O%=�f�. Fi�v y����A)�?19Aki�&n�t� �-�&� i>Z-��]�!)�)�� , to�"� [aowE�irh �+ R�&�P&DH&�6!mi�#e�inZ k�L�+�B �K&p�-�w56ƈ"� ��FP'�60�a�2?{%�� Zght say, adox�) ly y�Li\ZA�-a"``E� �E=�+�>0�"�pla&� �_�f�`! 2s� �*a�:�8qua1c)�z$�[by1p"� ��� S.p. H�ds�)�)��G unU�i~>�pa56�b��Z&3�a$}{F���0ook!�%I'n��&a� 6 )1�Y⥊h�@m�:>8n���])��&``E)!=��J*0w,E�oX� mAl�M��* room U"�*.L���A�fSӚrj7-�(����A��u�>-"�, ,�,A���2ng=:�8�R5ME,X!D&7��J�Baim6$ f7 ''? �8"W1EisKU!omiseIpAK!�atEx� pecu=Rnonlo�-beh�c�(1� df[�0I9qu-7͸��jUai !J M.�*f  /�se %B��ou"�K �/h�@�iAe�,�*do�H�o on�!�"�,.cp�=v-V#s��`0Me �5!�no�t�?M�;k � ��;Kepler's� lane+m�M,bp!8I�NewtoElaw�gweAt O��"AQ !��d�t Qso�. Can�3^u�~�)�� "v Q)�i=��sm<prk�?%"ĽsyVLK!QE��Da�2�*pa/H4 absuA�Alaa��=n� �0�q!�A=dRJK��? s� � ��� A�b�Gi[,C"6:p��ste�J*8-�dstcǚtAsS �l�X�.ʬ":2A;co?~ A�of gau�6�'nc& 8&9H�!6�� � Gp t"Cbas�&fAR�s��<~�� )#'a�a�HT Gti�Ul��%�� 2F(:�S0yg��/ im�Ya��FAD�!�&� �a��JrW Yby2M\1ea ��M�XB�51�+��3� ��)J�r_a����R� L Kwai��]���8t7 �>g ����aQ|��of�9r�TN�Klyh eeH��N5� vN:!V-a�&"_%�!�a�fac=KWm�v"�J.6xl:"��$-Kjea���Z t�con+&XS troub�6von NeuL'sa0i��8� �&� avN}� %�i� �>L w?ddn��+no>3�Znz 6m6� '"~W�n m2$ ad���!�roo�I � ea�-�hn*hn�n�RZ,keM�E#rse���a� �al5�Id%|!��iw�l� �@yrAU�(�5F1�!��&���@E�&�uc E��dy�o�%A6�r�Z�xo���2�82�� �/ �� a�^m�F�B�. Unia5iBU='A ��FL Mwis�:e�l%�ub� 3o��Rm : ne�%' vN"�� &�9/shoAvL�a!�&0  o{*�2 U�n�R4����id�X2�!(m�d*"g�-�!�c�0L�eM-� .e� l��o&�ws��c�z�J�L�"�   2� N$ `�% )"1�mir�=���M:*R? %,5�d� la. (DigiaK �� ����N3s� � rea��r�A, �~han�!UA2�d''*�! *�o�E�1e�=.� � ���l�� Hilge}) EJGrrA�t*�-�2�Y�%>�'B��� ",r2����X!��? 8.�{," �/i}s���e��m�A2�#.b�>aK"� �i�lUI�,�@����oa�,��m psych"�G �_1� war�N�6�\�a���!%a� G*�TtQ�\ɗu�&&�at �2sG$�,��_ / l'[r�(�!�"��6Ya* zA,vh[! )#� BI*�y� . (�o�-&�Z ��p=}):� i6/�~eAR� � p5de&�$cg!�'6vaZvrei>ai������aV �s�:���M)�%(ii)~�� ��^"M�l!c�\M�unUW�3J �)mQz$.�e��S!�y��y!��a!�V��w�.#*5�o:-){VG!�pI%�i!$�с�a}+h��#onD rg� {��e �`w{�ep�� i)~G�NY+<�/A���@ gq�six"��� р�6%.)�}Jwix�<)?:j� �I]L8 ��$wL�' i���ha^uĔ� embroider� F�1݅Z7� un/q� �!6��=�ent� i�(�3q-� ��ly�SaQڰ)�)&a|�5�!.�med�e��pt)M%�9 a��"��)��um;n�� 9=�]�  �iz�`stuff!]��}ee�x ��!� } �b�f honesRbE adqZ �5(v�� �� *�i,�� "� ,���b '�r��!  p)>I}HI�U�\IvA��Csta:a/�(thf3B'Nq)a�/ee "`�:)�M��=M��,n�2s$i2�)$}6t�D!�� p�A�6|AW.41:�A.ioned�ile�*:"e����*t8o�abv4:��%�k cZe#� o-u7A�!b``#�)t??furK!;�, �9peB��s a?Ts~ ��[ \7�=*� em� ``�5J�ledx9)|qQun<e! wBly T �is�Ypen�/NY o����"0X�d)�*a��/�~&#5a�lpo�9�1�-N'!��� `a"�XToI(�kerMKL+ lexi� 6i�P= &Fea��&ngA�D.��.t'# a fl�Z���%P� Audi�ko ��dI��!Txo^ �n��)%�.&h ��2`7 ۉ_p&I-)�s� �SM?.��>k{ inasVc*� >� �!UF �As�>4 (��E).6 �=` "E` )PU �� ^(w;V��o�]R)%��;K)� p�_'dc4�V��a�{>`!�-"�& ,Cre��ic`]EaX�e*�ig�� x `ˌA�vpi�OZ��D��"�1�Scy�rabi�a`�:%s�$f8in%A�$i��,�N� !���; folk�c��c&�C '' � infl��ew ach&� o ,$��b. �_"o8�M�a�@Ym2$t�D m:r#KWa� La�un��M8ى�.. �( �G�M� I9�@ �s. Cau�TB�w5� �"Q ``!�����Ai�My>u``stayp �-�� 1qO BOa���4�� Dl�o�� 0��#uY]t�gof�r"hh �!Y%N0!51le]�t[ �T0n}�iͥ*��s� �+o� /���Eel�.`< s��%8�CfW�"IZ,��,FiFAd�vl� E ion.y I�%� k)�:~6GDj� raM *:+ Nm  )��h~?se�� !��*�)Ddw�#�@n����� m��� +.,0%-�efP � ��EF % ^!��\ - ppc!��A:AXhXn.�mo�[a�losš,�*k")riB�i  '� �� :}%�gF�zEb�z)�woEc� s� "B,82�l�~�A;%��w1? �� ns�%�i%v�wote��lE�su�R� *��!:��2�8 �1�h�cu��{H%*"�6*f:'')? I� 4�]-�>.�`��;a�'ra-=�i���8+ c!��d�#%�L\Vh��se�)�D � cruՃh ��!*� ^�� *��Q�A .eN��G�e�KR)hde�$�"�: ~$O$ !�"� �5 � A�i�� (g;��kt�kF�D)��6�u<56 �A�UarrX��}n�'i>�R�� ��J -�� �u!sharp���o D���i r�N]� �UH �V. %�-Ffa���e�:mҶcopicS o enE�{��� G>�A�u*H"q|,% e�%�!;'�KA�1%����yy�#��?i�^ʉ��E5�e��c vestig�!�!8Zurek2003, Blan#(d2000, Joos}I�E��^%�5fso)��5�6`.B�J�&Y% .e7RW�, 5�!t�#ld�� bJ s�A.�� gua�xcr ��=�-�Wh.� �sZer��YaL {0")Cq �.��(o�.D*/ 205��o��%P6���r"^��y� BN!�"O� �ev�-���"m "� e}f�6�M��/��ju�� KA�a9>�MBN�"�rs) �} #}��Q&*�x.���3y�!��ARnA��3a�a�fat��� ackg��E�-2��"%1�! �=A|�*K� ���B��r� � �-t!E>!�``smea�r�''�Ow�9+!"m_0`?�N���*6&V�v : ``E2[0��U%'%2&$�\'� 1!�comZt#=K%/!+&P���Q�29� o tE�F �ce%al3�c��X � mus��{o$cl0up� �je\ J---.0,��short---�{�L,� aN*{Azal�AT� s, Xa� � � legit�u�Ue�!u��� . �� �Uc������:n.�X�!�R .?R�E-A$maa�C 8sg} v� ery kaF� ide* /1%E�t#R���i� ���3Md){"�Moo�F� �*�i ��!myria�2J< њ�1S`��wa9�4����%�V Hb_h=�a�!ک/e���� so ab�/���$Ye Psoi�T")-)9e� Z D��t�&[ %�g !&�/��I� toQr�st*�fZan�X �jˠ���� eXPu�$Q'p�nt6m[ �"�" �&� u6:'��j"a\�4tˠ"�3=a)a� e�[K��.�]�Q�z�f�dD i���H ��^!"> !#!i�u"�bRb8�/�^�u��JB "�1��a�!\E'I+��IG v K�Z[uQ� !�"Ua�D(E�i��`` g �R�.`�*(BAwRV&U�U�Y�� �a6�-,a��E���0�{�"�R^r3C��lm�*nR Aw�6t�!b~= 5so-�-d ��z��k�  k��%]!kA"�L� Shs-f"()I)�(�.o"� q6p*: �8@J�6����G��F�cB�>�n�""�3U�*_��2)��E��,i�� A���F2,����Y�EC�|f8�d��)p��CA�#Oi��� l��t~B�[����m�'E�et�-N� �$��T, e"qaq�hGF�irQ�Ig�-ro�Am� a jud, ���5� �W ch�8 of the e�ntire theoretical structure of quantum mechanics corresponds to what exists? Independent reality can be attributed consistently neither to an intrins�hly divided ``manifold'' no . multitud�� matrix``E�nsE�''Q]opper} a ``po!�i!�ie%HHeisenberg, Shimonya%B transforma��!Pgenuine article (non�m$s>) by way�8measurement. (P.<�B t!i�$are boundaNarise!^one�d��E!|i�(y algorithm�|�,:phy�� �.) ThY� such-f. Nor!�itUV��}>�(. As we obsa�dA�DSec.~\ref{SecImp},u�-�Dal6�ssign!(s% made witic4tacit assumpti�e@=_ is�cessfuA�C:A�i�an out��. IN��ur funda�al=�E$ framework�{if��ry����ik$presupposeeta�(i� or�B nter� ual)�AMa2�(in=A� 0value-indicat���)��n� 1�s�no5�y��pffici��condi!rshp��ra�vE;EyE��I wse�%e�ra�a/�)� �e��re)Duncaused\/}. (Whil�. is implie�bLat perfect detector Qa fic�,A�doe��t!s����� invo��FFtoAgign yhw7��leQL%��CunNorm�.�s.) So ���9�encompas�e syst�&�po��onsa��| %JB�s)��$unpredicta���)� ? It���$e fuzzines�all��AB relative�=�e i�lete spa�u, differentia!� o��e���,��account" I*a least�y.un �ExA-at.� $time sharp�>Fex� %��REin +!is Ese";�~ofA�ep: M# z� both�si!�J !}cap!� . DIkM*.X� !�LwsIz-H��fI h�r%�aM, they��{?� ^C!q��@y don'< more a shortcomA0of��-�A� �B-& ɢ.ta�ca��.w#� any , ra n noAall. P��s�� rned�T laws��hEQ�inomolog� l!-b leI�d E�/ � 8!pQ.aUw b eposter� toɁ���t�3 �nu&�ZL� nI� s. Q� 1'i�c�> � it��it�MFUC&�m�a$a. We haveA� r utmost�wem� rated!�r E�-Ac$ I�U�%�2� � (�2(is trivial)� alsi>���Y����a:�n&yAs5 aJQgZ��it�(>>)!$s. Many as!�TZi Kh stoo@ te� ���rminist5)m, ��&� M everi- els�ebu�.1Mnj�%ben�V �alU(��a�t:�(s� b)�E��te abse�of  �  s���Btype~X��E�precl_aU .+analys � n!�G� E�seen, 1 in� toa> mula�� �G b!"��y%��tA��"I&U�5 nstead�nsequ1[!�FI�w��o p ular it# qX��otemporaB��F. \begin{thebibliography}{00} \setlength{\parskip}{0pt} \vspace*{-15pXbibitem{MohrhoffWQM} U ,i�Am. J��.a�L{\bf 68}, 728 (2000)�:MABL�M9}, 864M1NM BCCP6N,in Conscious%��� ts Tw�edi�,�by M Cornelissen (Sri Aurobindo Intern4al Cent�Edu� on, P� Pcherry, 2001), p.~333J�Stapp6��>F�>N32}, 217%2NIUCAAJOMoM Lett9� A17}, 110jUClicksJVf� 1295f�JustSo�Q313JQ0archildon} L M�V�4}, 59M4ND DQSE��M7 �RMElusiveJPI�J&^Inf9�%�01f�P�6W@ ppe�*n ProgrW in"�� Rese!:]�`V Krasnoholovets (Nova S�4ce, New York);��(-ph/0305095]�6� : Re� ider �ofI:.5`A Khrennikov (V\"axj\"o F��2i�46.�Bohm} DAIm �AC.��85q66�52�XGRW} G C Ghirardi, A Ri� IxT Web����J\D�4�B1982:} P f�A3i 2277�89.�vF�.$C van Fraa% J1�" �:8empiricist view!y8Q@2=T pp. 241, 247, 280, 31.�Die� D  JA4 �90�92�������eM�� � JJb 182}2GHZAMM Gre<!�M H� IA Zeilinin�G����em,:� 4��!2w M�e�O8M Kafatos (Kluw{ Dordrecht��89i7.� *s$, P G Bergɏ��,J L Lebowitzf�B1E�141%�62�EZin} A  LDialec{ Aj, L 32H482�N!�von Neu �M��cal24of5N��s.�-C�� B�52�Hilge� vo�>e�VJ6}, 39�792� Audi�W,A�, Cambridge D�ar5�� ($F�!�(95), p.~80.�� 2003} W H -�^�7��7Z 8.� Blanchard& } P H, D J W Giulini, E  , C KiefA�AVI-O Stam cu,.:!J , Experie2ual6 �!s (SprmYBerlin��2_ ���� , H D Zeh.�:�J Kupsch yj��a� A� a���C"�!9*� e�y.�� �2s�! S I<OddU��U�� 9�18.�!Zeh1%�5(E�Z>�B5��825ɻ2A# MsM%>P1O489�72�� K R ^!�Schism!q�l�$&' W~W Bart� �~III (Rowan \& Littlefield, Totowa" 2&' eU*5 qA�.�HarperRow6 52&w  A� �Z A%a�P Dav~�+� ��endB|  docua� } >� \�t[aps,prl,twocolumn]{revtex4} %����P \usepackage{amssymb}> math6�icx6epsfig}&'1�$} \title{ i*$ storag��s�&�6 based] spinM,s} \author{Z_&$ng$^{1,a}$E�$C. P. Sun 2,a,b}$4 ffil�{ }$De m ofQ�, Nankai��X, Tianjin 300071, ChinaFT2}$ I�'tP �=e<l`=$ese Academ�G� ces, Beij� 1000� .a!Abz abstract}�' idea��)?1Qis�#eralize�#describ� V� t K!o*P).�throughw 3 data bu&n�# u��al *Z"wfmpreh�$vely re� krec!|aa%& investigY kl��0�((%7F�$� h$� ;#� 1.�1$��)65by usR 8 .},�ma�&�isotr�)0antiferromagn!�I�ladder �#a 6&�� 18chain. Our stud�2emphasiz)�� sm�!fu&�#p�&s beh�& var�t� " # .5 Za� olid-<)�s.��Y�4 \pacs{PACS nuY(:03.67.-a, Lx P5.Ud, 75.10.Jm} \make�5 Z#{I.� rodu}�*cu�#>#velopq�-�6�}%�techn$y d�ds optimc,�"s &A as long-l+Ymemori�m"*�!$.tcarriedAa&'+ k"|  d*| "V�t9kerred +q-inf}!e��+a"LMnel or|qƁ*nee�, for �#�f missZofLe0y�T(,a�will *-3$"A~- .2xhe$ g ���-unique|-��d iw,J�.Erevh* schemes-6Hlukin,Flei,sun-prl}]!%� bout�u of photon ���%ll"��*, efforts dev#U#�--5!�Abit (a�ic two-lA�M.) z,Mpis ne��� i&'��8. For example, � �l� inter�yng pr�.$ 1,zo",exp} wa�@e��Xre�bly map%�e5 roni�E5 o�*cOc�%�_���he surr��(nuclei. BecJ' #e� B* @ 4ar��s,�>q�) themQYrobus!�(�)# as f�I�in szs}�%lyH !� homoge�/*#0with low exci'�.�*ny- �-� approxiwl�b�s��a ��(le mode bos8*o��e nAm�(QV��yi� �� requirg g%x-��all%�s ��n!�d�m�prI ��ppa.�,�� , polarizing T a�W!��&dirAon. W!7��$p!spont1,symmetry bre�0(SSB)!�e�recogn�3_+�0��Ru usG.ha�..p��z�1natur�!o'(�+( - of2O��hOF(SSBQ��' e�a�� between-{�VsaOgly"�"e)�!%ME�!�=a}l A=a&etwave,W+I���#ex�lB�%�9�se"&s, Wa�Li, So W � i/wlss}4&� aI�)�1y!)q > Q���)c"m�frey��2mb��2m�Pm A��� to "Z ��c4Ѩet ��!|V�ŕrE�rr?/5�ng-�. U�1i�prij#control��7c !XtV� arbitr� 5@a�Q�]L��q�l , ei{(pX5r mixe�,eOb� ���! �z�E~ar)�AVEthe�\ad^,!�&M(� . O�e /1hand,� �d%_a�)r81&���) a scalm* �iB-�&/net�.` �2be�XY�*� �*I�4Div,Bose}. How��>�fe�%\F _ t ��asnfinite:#M�c&' length � % {W� ,Dagotto}1W enviroa0�+uc�(e1(e�'i����yf��e�(n$)� lock, %@i�(tunatelyANaly� � y U5ǥQ}� � es���qmmensu.)���'�&nergy � trum�1ch�*�% �x��par�hPO e"� sA�&�)�0Matt1,songz1, �5BH�2 fact�&� �� � +-enginee���*novel�g ���Q�"g �����efs �. coup� strI � (two%x1+nec� ak+'� ely por�al�Fdi`8cE�V,�.5 can�6 �J��ͤ2B P!�� ��err. A�,er � !)Anear-2z � }�.��� giveI8 illut�w�Kli�>[)m�)"� of�1.y6� �!Q�1o�5">�*R� @ u:rm5ס�!}t,�(� �� parabolic:z ]81}.� u �  pa�!! a bro�tverj�0�  situ�!��)2vBio`. abov� Uet��a�M-2� �9B"� /I���s.�-� :,�����seA��i�h1a%��] f(A+g��0 �2���ag�0\s� {II. G7�S�J Dynamic� } � rd p�� r��!re�"�2&O6��e firss&�.J��Saa�i��a� ssocD3 �B�)'s �e�]orE�% {geo}.!) $M$�=�O � 69 subs*+�+nA�uA� 6 = �2 Ii��%(2t$ $\oM s |M�$EWAyfi� <|S! 3:t$� eachpex $n Jm ily��n Rs!S$ A�$�+defin)ew 5k!}�^.ja7� 9��,5$T!�$�-eq�� } |\Phi ()�=U  0~,�a%*0r%� 3!W:�Ne.9o�$ɨ6 �� �&?%�7�&]-of \ 5 f}(> �rf>f}Rr��5  x@, wri%)a.� U~9� =\sumkc\,>�ofetiJ�Uw):z�75T6qʍya�be!Z��}�Yh!�-U t=0$E $t=%YJX2�6�-�}�\��arrow F~6K�ڥ>n%>&�%$E/f b��x$% ��fN�B� f�.�:�NV9!>� Obv�� ancombi&u6thY� m)e� cyc[ 5� ,?aM�tot4 retur�4x5QTon��":P����a�!oneW �<k \text-*bl��:w ing"!vreviv� �:&N)o�9i��y�  3�:cO8allow~ $n-*MB$ unit� oruon!�W=W_{S}�31$, namJY��Q�W_{M}�(l6-2)V�3> A�� �L MVQ �Ʉs &��}&q!�� $�$aO know~ �C=d'1M8>�,�8�qeas�-E0�rom YJ% ��b15��:�� �.1�5M#us@9aA�N����ree> %�inp'H&( Hilbert` ce%6A}$�5iR1nout2E-i . As*y�9Fig. 1 M!$5�s6A�! B loca�!ywo �t L*$A)�$B$ r� ly � 6� he ��� -R~�Hasq&�(S_{T}=S^{A}�xD EW\ v "MF w $M=6>$�regara� N��:A( -�sp& 2 =&�  DT�8 �U_{B}'�qa52/~ H�U ; 6R �"Ti�){ UD� s!�|s !�lZ�sI~-�an$B. zC are 6l%$�l �"�ooI�2s&6QedN�a2�QDR. � � ,>��icE��.cES� 1�� \nolimits� �  %m1�A>�)7 a2$A$ at� 0m�2� whol"�C��\psi � G � ��aJn}B�"$��BG m;!j�N� i�2�F 2�ٝ-��"K � 6Jom "3 !z] $ 2 n�}FGT_P 6� &=&� S6m�.K:� "r FNex_1�B:S \a"g \\ &=&F� �F^2z1� �%����ɚ�-���� s ju����"j��3 e�eh2K !2�Q4�|�% � =(11|�)����I~��� s�L6�(A.�>� �Jw\#�lik�Jremark)�)& �%<g&s �8 =���typ61'� R � teleOC@  copy��!61is insG$hanged dur!�74�$gEE�  :c ..�' �);yq� � A.�. -�"9.`� AN��"�� a�Ak@Ps &; a."st �/_ �%w%��"�� i!de�"�of high*Q#&' � !=gy gap2{R�A�ivB tanteAor weo�tak�J�>eJ Ct �E�tf*!al ��u�deK"E-��Q5V�,1ae�!D}!�C8y (e.g, $1/f$ ) q S�ngA<�.�Tdevices. People believaL he.5"X A�pN= Rt\!"� �sss midd�Hayor�+V,nh3i�C��� l`��+hJli �Ie�N"�F �)��Jionship !��J��:|]!is"�establis��'� e�iW P� % /�'�)��:�(�#�Ed-amF�N�=&*�irreg+EQ�&!U, �ARn�9��[� sit�%be �!ze�V\,P1%I orem��]�%�]} �vm5>szA"at>66!o� �L=A sketchc�Dal1, letlOQ5Ua�'D0iSS2�he����f re�o��& (SRS)-�@ Hamiltonian $H$.5P5E�s�NHoperator%0 SRSӡ�9([H,P]=0$. NAqaad�Q$$\pi /E_{0�y-&$ \�1bf{r})� v�L ref�)+$8m? -2=[UeigeniJsw(\varepsilon�}$")��!�.$p( $1)L�UwayF�>S=N>�,I(=\pm (-1)^{4} \label{spmc"\ }% E��i� �� $E�F�H\phi�.K=>�R&,P%/t-�=�=hF&�#N��a`�V)��%fun�(�H� $P nU@�Q.Pq�c�)Eq. (DU%e) '�M-%�y)�!�">+ (SPMC)I�proofc  rigor�N�F\Yysae�� heur>&exerc&%in �c�RI1c��� !� �>�qz , $P>)% )Eb 2]%��QO�!5a�b,��.� ,t)\&'_{t=0}8. = /9�)$si��F�>3,,t)=e^{-iHt}>)= aIC'E�E�9t�Na�%��vtG �=$R��M ���$.�2���_:-��\frac{=}{�>�.+�2�)�B F�ris $\ �=�,��� O�2@.$�Zi�eBcͩ�v!{MIS}�qc$borQ��ѩ�the.R�S."[��yU��pm P$A�so];?� :(2n+1)��S8exp [-iH]e+ P.$Fami�arg�9�Y!�U(&�M�NS�Z A���a 1-D>lU FaY  odd-�4*c/i.e. �-a-1�re � d�+y .��\x2S�Po�? ��t.�f ��K0���discre�O- j/ter�)"� FX and odd���\.�A�-%�2�=]��2]�J6%�� nexth'u �2m�b�en63�e ��A�(satisfied. :�&�UU |A�A�� 3b��/l2to) �'o %:"g ��[� �0ly!�nI�&yQ to m��1�. \�3A�"� �:;(,�gideV8� e� CMIS)y*1R�er�F`&)A&u�5in Ref.m(�E�:ei�ionFVP\P2,s_{1,}s_{2,}�%s_{N- N��%N} '21,J5-�:�$M `Rre�9V. y=0,1$�o�J! *� M(n-th "/�ub� 2.�M� :'!Hmol :l } *�,>-�0 p�Ki�5Q�5�a�U��� u�"{;�7" . Acco](toe8,I��"� AwF�,!�R��Van�+� ��N�6� _-$�j1}{2}$.-+��a��� st" ,� meet� �IA�"M. Chr�,dl et a�6%  ..@ �+a $N$ � $XY$iseH an elabo�d8�0&>9҅WaSU.�N,��neighbor�"c�.� 1K6�.uYis eas�dfin/3�b�� N#/9%�.? case͝=n �4�3n�94�5V3- leafo�)P��$% ��}\neq kF�� �w*, a new"[A��tK hose&0��u�6obe���� exac�ww= "�-.�%S"��an9�A�$-2�>  the *�F�H=2 i=1}^��}J_{i}[S ^{x} +x}+ }^{yy}]B" w -x}, y[nd zre Pauli: rM%!�$i-� h a�, $�"� ��tc0!@B���6."�,open �cJ$"� �b^ odelE�qu��?+!r$-less ferm�-"/=s����^�H� \Q:�^{[k]}a)�\dag  +1}+h.cb�21,$%\��or|S�del-s�4� hop�"� � latv":�!�A��w��� ent y,\)4s (�.,b�j}8!k�ve%�� k\in \{0,2- \}$)�>a"�2a���Fasa�EE=)X=\sqrt{i�( N-i� ) }$ARb $i$ \h nC B i+2kC N-. X� $i$% . By�tra�forwar�l�R�/�!N�Le k-d"�`�$% B� (-N+2(n-k)-1�,$&�-N/2,$e�N7$ $2(n+2:N/2+1,�N���!|.�v ��s| Fz%b)8!e_qf i.-�r/E�^m7s02kZ�A� coefVe�&$c_{ni&#0`ici��^"� re�Ace"RA�a�� �P5 I�ao#*%��ha���� >1}��F��AX/�Csur� Lin $kZ�1�y $k$"� �'chei7t*�Va�a�A"b���l9�d���*�[G � a se�(!5u�ed q�s�i���>a�!4�E &nel-Va�& ( 20�:1 3. N.�5E�-}[#� � -body��[e daM�:�%incre��� *E$N$AeonB �� Am_ " !?:� � z z�D=2^{N�a�!'A+>��+,help so much�Bdl�A�s��-ob�X�:�Mtd*�&�.�$pa.3E��9!& i&ton�<>-� 1���1�)� Y��7 tJ��&pD!TA5�FIt �s l����]-*v6r�-�6{�/r�, na�����s�<�m� �� I� �\ 2"�6�a�Io�� ate=`�!;b%ii��:ha�oT a tr�fted Gazar. � "1nharm=Coscill�I��r.n�>b�d 1C 2#I�i�s2")�J%##eL��n]AX�.�B �M�)!�t&A]^� !Gpr��� +c;s��i >a"=9�@^:Io�RBAZ"fkI��is\a achi�`=tg1?�d f�iM�UT���E��2lco�;�!f�ediumI���$Bgap�@erturbl#metho0 Fr\H{o}hlich-��/,e���!_*� &�he� be m�B:*�:typ�?u�<��& 3.1 S��J}�,N��%�X�&�;dA$;,2e�mV5h��mD" eRs�f![-t(A��B)a $2\qs N$% ��lekK �Q p� �� y)QH`! �� �'A � dot`HQD } ��,. $% H=H<1+H_{q&h3�.[hV�/840 240 550 660,J�/l_fig>�/Two1*.^-M�e.3)1E�-)v�/nm�!�/a-M+I�on (a)�_�#G(tr�t) when �� ven (odd)\%le�bFMb�Esh#o}pit3 sult>�/�4�$A%�Om�=�Ff %�=J� �ij2  \perp }�S}q\cdot % j}+�PaWFelRT"  R"�2F�����opin-1/2.�-�A _v/ wo 9 �N�I���Aq102A:� L}+JL1/B (2�R�3��M��#���)$A�B��M� �)e term $E�i&*a�\�)F~}r�!iAiV�Z7�A:^��F@ os@wrubGi.nZQDB^ �Y�E�!�h��P) 1q� $L)1$RT�a�"�BA=� 9l��%o�penO�/-z�[<x=wo�u*�9�5�$.*A&`!I9) s= `�[�I= "2B2~2:Y`'�&�$\c}z} i; ��4RI� /�Pa�� zero (one�� V6Ij6Ibr.C+� � BJ�A�Q�2l�E �>and�Qer�\ Qs�~d �,-�) 7r9%zLQ 15.|��$0)�$1$�uL���W"(��is.� depic)��y�.)h��u�wo&�H I{.|famY&&0s,5$e�-� � s *�E7 j,m64 _{AB}$:.% 0,6\ ="�\k2}�( [ \upaB@2a)�� \dow�3ow6( 8-R) 2Q� ~ QRwO 8)nD" �1,1 &|�RTB�R&z� P1,-6n =j6�Z; !;Br�� b���+��-IB�B9�9 �_uKh=aWSXkQh�9en6m���a^ LunmR2Fer"H�J�c�&�� �pro��w'Q�� d nu�8DU�:�o dedu�=�!��2w�- e $|�'Q��$ (\alpha 6 �L$X- % E_*����";  (( �W�F� �~rm{M}� �>r�#o-O�z-�"��e_ �0�2� :� t�Qbe*x)�joint[&,�Ra6�8J�g} 6�8J$AB= Vm, &�8.�++9V$^{jm}(s^{z�Fr1�6� r� �N�� �%X$wv�i��$z$-com��S�=SAB  A B �$0 �erU�!� ect NuP� >�q}$��? M aAF 2}$ e�t-@AtM��za!belf!%2 a# &M�% l,)1��$zEd$%� =m+s! E� cha�er��non*�2mE�.=2+Q j $. � ZR� �h � C �Qf,  *e!� ,$Yd"� q��m�O �ݰN�g}�*�U� gy�\!�%$�&28 ��0EJ�3(a)." c="�4. �T � �<�� 0X}� �6 spli�&^ �  3(b�O (c)�A�"� \ll J�,)tem�,�9$kT& ] }{% 4_( �,� % ) }.�:t�I��� �Jy eՊ.� ��a>$.�D� �G��[�V.�$K-� )=�\�q;mg �) S_{KŃ +%() �S ( 1� )BJ M� K=S,L)��Yc&��� �D vari�.�"�:�m� �=r�Ya3V3XEG((!��Q&$for%9q�,off-diagonal93�&k V�vanish[#n�Ko9summar�W�*watry$H$�r6oR�%���seemi_ �� ��9�' < !��!")`^�a�\ g(L)uw/J�ere $�a6E7 L=N+TMO;ce&�6qw� �zn�0�7�|t>* $N=2A]s�#�,�c:P("t7% �T)�� ge&g=-(1/42���$(1/36�8�SB$Ams �$plaquette QhXC�Ndja� �-� �� is�\=b gree>� ��Y-|A�u v.��3&� � �%�>gA �a�B:bocio)�vs�N��.,?��$L/�D �W�$�W=t+n� &� s\�TcA �e�56dI�!�)�B �� �"h#�<ff�9��-"1��K is�ormI6!'�*,L=4,5,6,7,8, ~1�H%�$$J=10,20,4 A )��C'p ga&)?^.�n{!|=)r'�)"�#6/i$ cit5'�-��)�M.�lot�#inz 4����I K�1/(LJFt"#�<�[*� f�&�"li�0p*� �8!� guarante�e :�%P'B 2�of � &�BMCi&!��UD��/valid�_�"�^>y�.�e &�@mp!�!�.�!�H� "� os��"��C@:<O�%0"2�:0� c�^\.A�%(�Blo">Bnm�� l+jmg+jm'i�> �"� |\be�Z5 M�> u�#VI�\ \{$^2$ \�*a�)�Z-�^�[M"G�<ortho"��en�s�!@"�/� _�|c ��\lR�^�=T- n�$lWg�* :l���#�E�+�#azl�/p�� �A-B&�P#�F)�ibe �=byE_rMw�EA���Q�^X30(r 510 7j�#>[.s*q$���A�������p����6�.zF��n�����%��, �M�-?1NeG \rhoeB� TrAW(�JN Qwpsi�� )y�Q�I�0^">�  Q�|� &&+M�R;\�4m�R!E/ ast � M`y(V6J< ! ��� X._|b� �h$){$XJ�(� race-,mW2� #� By3f�.�XJ9�c_{1124 !�6%-2& &�]�D%3A( �10&��%0O���) 3 >psO��^�c_� D =��v� �"FB�"N>%&�� n�q�\\.�!gFB 5�1-2K(Fi.5V�^ �F�Ha cri�a�jjuf~ho,8A[�ౙ�Ё����j, �"&���si��"� "r.��d;C� �s �~6MVN"�F4+B�b9fF�#M "5>+T�6lB�%�m!e"2.C"6f E� �J0JJ1;=5F<2>"TQ� �,� :k6� �9K�:�N�6� EJ�N!kPW� Y�6  ��9� < >, i�d3,4����o"� U�. �$_e�b�� .P ] ::�= % �?of L%k &�* $10Q�  $$(�=10n�`aq(�1 l��d� �T7 1(a,b,c)�>61&�� , at BL( � .C"�<rs|Bf� le4�FA�XPb v[�c���a&�g d by��,$�'if $JG>4so�N|��E�se7+�e addO�'�t!/[h�K �I�fa+#Uinguish�P q::�6B:U�ee�# gb��M$H.$ Thoughq� igno4�&��+ s�6� )�q ���2!�F(|��� )�[.S a\h j,m|&� /y =.F $ fur�g confirIOur :�� �-�Ո *��).r�wo9BԞ.H&A�aaic2�$vAc�R� !-A.�� ~�28"%� ���$&B10JA* �Rre6�\>("66E�&�Al�_and Bob.5�d&�H du�&�-rge"J�yA�rTdwa"�3� �UX�9/!ink�3a�4l6�!�.)0"� p!��'u�Ka~�a6p�nbl� TTA%i ��Kas"�w&�G�essX�U � *4S&�6w ���zw Rw Q)Z�!�u)�e�2�"$ �8.u��8�Tand�;)�I�puhoA ��05�&$" +edVs7�/detail�$�zt3�l�7�. N"���A"�&1rF� �l.-�%�@ec�;�5+~-��.m�:�[sNe��Ge.�1AN&� eXaJa)in@d|Yrjr�.cK�Aj�2�c�ao��*�+�f�Y!�Ob%,�< 5�T.Z62Z6~2a�mF�7�e68 } L�S i�U!'*^SA�(2N+1)���6<�BV,z�&�� H=-�3i D2N*0+_{iZ" 4� �B%�"�?�}B(i)�Cz2"�%E!�uni�9�"� $-J<� 5�9�4:Zr %.F�~=2BT (i-N'SJX4)(�fz`&��In6 -�� Aw�nt"� E�ofixed z*%%�o�i%� N�4�!VjD %%�jD"�C�C}8e!D]F H=T J�H:eD 2N}(2#A ZD)+"�2Q�lQ+)�/"�DJ��� negl�u9na:� �D_Ay�1%g�-7i�V�9 setSs$\{\�,set{\qquad \. n&�th}7� n�oc *� ��B1,0...6(}|ZC\}"Rm'^f75 35�h 5 77R�0sN9v�0�5S{q��= .�]�>o[ %���>V�X8? long&�ho�?m�quasi-D=�F>7 !�6a yU5]��Joseph5 j�UiS6Co�F-pairlb`a�3*R Shn}EV4$E_{J}=J,E_{c}�( $. A�t4�+@��"��PR�U�� � - .z� ndeem 2--E� �\gg�"c�5 Shi}. Altb !%&2r .$ (36)&��qP��C j�iOy, �hPB%#? � A�Sre �P�sl?JHI(s�3anhb s-,Y�sъch Yz�  b&� ; ���� �(��* a�POv@��p , $x�Q�iAPIHi�ZsF%*s2(N2,Ts!le =CBDV6$ %;�zH�~.�6�FZ).61 p- ��)6 $2N$�:j�/ A�%A3$i$th'A�up B , $C�#6�dor�8 c&G $�$=4\ln 2/\D�v!NBG �m m�QQ.�$ D� �.!� B�gvolv!oB/ (t&)� &(X&�Y^��)�\$tL Q�eG!:V�F�h$�Z{ ��po�[�pN�1�A�o�gB� F(t)ݡ:l�B]�vert A�iHt]�JYE�B���;F�[Ia 5%2y�r6*�+s�7:. "^W� "^��2�i�S �p� �&sIPA}=�VB}=-x ���=q�mirrorz U�nj%ln� caU� �M,r we�$$% ` =8Eg�4:&)])i2, $!��5� ^��X��}�%�a�(1+cos %2t}�(})N�O`<�� iodic6&t�2�od $T=zYe ~�u�1����:'%k�}�|*��in"IG�/|3at!lNerb0�"%' )Q�q �|"�>�G $Lᆑ_EL=2%�e %[\�e. e�.2]�pu�G�$&WmE!u7H6�$!L=500, �=2,4,6%c�_\lambda���ס+  ���Z1����GtW!!eoh�� %Dribt EJ׃��pI6 e.��L,�$2(a),�:o(c)��_sq"Q�$a&*�S2� �RH�f� ��2!& �q�!l-j6� ) ��J�=C,�h� c->"M��upo4$% 0.748,0.958 j0.992$n pOdv� �Q��-�ًdeKL/6��ra NnyLs�i�ʆ?"�m86�H�+��I:%��Y)�j!}aB{�ao1_n9 :qtoMZ ��� Z,�wh(���� "wJ��m aUPcX1��H�s23�z tinug;:� �<nFk� m�XE�vfN��"���M�If!%z�*��q6��,�o6�*� �M&4�&~��L� OrZ-!�J�����be �>��&�9��/ix *ypi Z eL��"�W�Zi��� e�?i D&��+ma燍!A^6a$��:�Cis} E�5a [�r:"|O� "�\!�UN,=� �- .2ID s�:k؇.�L�ntuMa �Mm��9�ͳ�!kMn�M$|ft���aNI[�0��&,Ex6n*t� �BB2�Z�*V.t2`lɦ.F�v�!W�w<tud��V"�] ���FN膁F��.wY.ys��Br�t�� e��a�uc��=>K�rum)!Zdr>PVi*E7ki޻^ P-tsQ��e� ���@*�+FH(o�,$L$ٺ�pA��\�V��6��w"D$�$ via+f=��j�u-Z����$% * $,A�p���HY ��BO%N.?Oo��W. Fm�0O:o�B�|� �|y�.TR/Q2�2���A,�a.ST�N  on{V&0�sb&.�m�e6 } Rv^ B�HaF��"i��d�B@�R�V�PL@�3%�%v�@�M͔-�F@� ,+�!��/"�F f96)&�~ O�� "mp� n���� 2[!T�zl�� �t^�~80�00 60R�fq4:�Fa1�Q��ma � �Q� �k<t!%+i (�b�, Z�G��Su�h alyz ����ap�!Ye��& in � e��al�*�u��# =�di�<�>low�4�/ɞ-�' 2��� �� )2!eA�*mx4�1B� �]  m��yE%:����������IB�EC%Q!�et$� " "$�?lW�t�^aP� 1�2Մ��5�J !�7!sAPoG�#2��-^�y)�0 ���f��%�aru�,��9��wP-�ѭ ��`[N�M�=4cm,h�ft ]{wN��&g��� geom[�! �:�i-�R�)E7 ň WJz� cird�m1UtZ�E�a�9$y. To turn $.#\SA�pus_�m��r�f�"enter e�e�&g�ax�{�ySe�2u ��"plane>r�R:# _��age�E'�*�H87�4Ż!9 )9 ABi&'loc]5"� )�E)~"�r4!I �%�6��.� q��e���$ Rea2�TsC�S"�6� � $9%ea%���% -T]Q:TY"/ b� .$�Ye�Ynen&:It!�FX/qk*� 6D_{e}=g\mu�L�\sigma �F,$F.@.CFi H_{nSn SnS:$lp$N}S_{l�@�$MCbft$l�"�u�2 �$l+1&VW**F� w�.Ze)��Enfe:�.�$J> < ) .2.C .5���Ren}� �}�#5m+r _5 -%-�g�2rCJ�u?, e�Ag!�$�ZAyL� $g$ ܚM (�i),�TM L NLI��M�/[:a:T�i �8��I!�- c \Q^* rp�aRe+m�$l]��{B��-q2E�� �}#?N�2e@�� ef{*d@ rigigrsV Ynv��m�rm�������ecaY�-�~ FG �hy�in2�s"�,�i��ŭ��:��{of �@ xNic�4�L_ be cylind>W�ic, e.g.� $s$-��&Ldu� H�6? l�^ pto�L� ("g(r}/ )�G$'� u !�!�-,]��O \j /� ER�&z � Wr}tFourier�!�b� �� ic&� F� b_{kq�1RN}:� e^{i�Ikl}$S^{-}�F�k ��N�!{��G�6� �B��.�(�z*aFg�*}��T}�_N}O:k��^5 omeg��k}�3 6�"**� �6N%�4 a Jaynes-Cummf� (JC),�F[H_{N}=NrN.�#yO� )��+M� \�T +s���( ��bn+- �M�6�}!xAapre �E�>on�W�A�*|�F�kNf,+2Js-2Js\cos5:I_ }{N}F�!N �FB.!�T�Os>&�`f%tjo���bt��g����ye���S0 $N-1F4w��>eit.BI&��e� $5NN�5� 1le  spac� $M$=2g�J��B��b����4L"� Y,simul� l���B*�*� .�� 0 be&N"  inB�,-^\$N$9�9H��R aa�.��6�etd�6RI!�-)r� . S�6%w"�!%-~ �g"x�%�M)& s no���с��a6&��W� �%F�'$\r�?eq�0m��Bn,m�{} )nm *\�! :,ũm%�T) $ \�Gr2: + mvI &|&-:)��;!7�� up\ (�'))_��rAQt��&U F��@�(.%)?b)\��2% 0�'6� �&. %5D e1� 1�BS����1�F�.� \{0\6� �y ��.&�U�:� nX:,n_�y� s �.< �7 �O {Ck�}e'� �$ ( $k=1&50$ j��$6$ FockI� �O% .Q��we,/��}=@+T �(~/� )�N/2s}rA�A&�'f�~)��]� 8O�j�( a~���%J�A PT)Ya�_J�\M� w_{F"�W?){:e M�%�Fi �Z�C�.0,1}w}� M>nv� m 1�1�Jo� %1�2��GF+ �=-��!(�[��i��t ( m-��) !�)\]J�)F�ify�'ex�a�  /[ ��I_{++}MO� KBA�-. _{01.-2>�=0 _{->>11��]�*�;)�$i�BbI��an[ Ni�6�#e �>oBf�G�<So fa�-:iscussn J de�M%�:�u�l}���B�#� �s� G �*� ob3�1jj>!*h� o%X1. H6Q�� eous -��s2��sz�#��) �H$VGyI��u""�22D"' �F��"+kr.]i�QN� �a"�B) L*| �%�P*[*� Ythe,a5!�&� b*�P e{��od�AHy� iu#�K�=�;WF�V=1��2�(�_"%*�cTy�+h.c.FC qi��d7in���6Z�� �] �2� ��A[7�N}ő[i{ l/N]� }x&�*�*��>2�$q6=(p/�:�{bB)w (-(l�3/(2-8/))$�n �"}1rF � ,:�'9����is �U�3F�!I )I�1�-T -1=0�I2�4 % �}{.�}+JVBQ <#8�6�magni"tR���ft5�2�%e�=AlQ8%s~H�a��'2�Ma�A��arOkmj-1&18��)�*9w!ҥ�*^.� gets�(ͼ!��"Rq&� �b��2D>�/ � 1 h�  b��s�2er�2���om�i�; �A_,a�2*�*b%�on �Y%8� � 2�m�.�+�nd5w�ll adopt��r�N)��� >2�͖a��1"�cb%(d����@�If�S! so %� �)Q6�4�!��-��is�߁�07"� dard%6l"YU��V vacuux*� e�,|$Loux9l�.�!�l2�E2�.sZ�A� a�a�9t.^u�} \gamma�2pi �Y�$�U�=� s|u���a� � "Yk}^M�����8JP �@.�$\R� /� �k%  &eg )R2b�+��M>.�M�%�D.J&.e.s�F_B�&%>>�>�.�%�v�:�p �.�%>�A� $% (%n:7.�^�5 )/)�2�)�*am���.|K%]�+ٖ f &&55=|)�� �^|�%�% (1+o8IM�� t})\C s *Aa&\sec 8`�(�gt�( �+��t-a3)�) +\sin;V4)"� �%��=\arcAXN �a-" s},g:� % s/2��Q46�|�gB-[}�����curɴ� 1� $!��зgI~!Z�:) ��q`<exhy�|ex�).de�R"F7E�a�% usoidal o�}��A�i;c�z�/a9U"�"�79agdce2ա���'ba�$1-����/8$�refore,�������EG�;� ��@"(�!�F�� $gg<<!O�HR ring-shap^+�! ]2� ���%e2I�.�.�0G �-� ����Z:�{a"+�me�T*�Z�1�5�g��1���gZ ategy �Med �M5)��, GhA2 �Y!t o�.�� &5& &3c &N�XUC$F�5t�G�� 9\ES�tB�\� �m�I�t\ � tectA� }{2g�u�:h�B�i}�BRI�}{g"1% }{50��in�D�6!ke�C }�I�d:J� - 6 aI� reg8'�$T �B�pi �.>$.2%�?8A'd!s e� a=#!<�Q��3 is{eno^Oto "%^3 adiaS�c ea2=�2` � �7.e�j��ϥ�"�/|*�|a�e&��  T . A�5�+>��ʁ�N� � �2 or de-x�!���  ~mixof*; � �N)��bf{Ac�> ledg�o:} it{YQ\Y\ �*�`|\I5P.~,, Y�i �Y.D!�lB.Chen, \ X.F.Qian, T.Shi, Y�L�" R. X �i �c\��waA|z��Di�-*�2�2�1G ing. SZ's2�ai�"r�p*  Inno�P F ��. of N*�a8�7 CPS =-%, Q o�*CNSF (gr J,No. 902030185Kno)�x |�am (KIP�S!�ChAcVI�!N�x�u"� R-1T�Ja��8. 001GB309310).&x�B��a}���0[a]{email} Ela�����s: �= tc@n%/(.edu.cn\new�*< suncp@itp.ac.cn�+ Wb]{www} "�et www�X0: http://www.:0/\symbol{126}VL{ � D.A�$DiVincenzoa C. Bennet��t*mE�bf{40��47 a�0W>��r��rei��% } M.kL_� Rev.*��^��45g�3)a� �{��F schhX��2Zd�. `Lett,[84}�25094 �;.-A*6C� 0223��2.F�4 prl}!#V� , Y.e�� X. Fuy����% 9N�14790p�6�za-EXe} E. Pazy, I. D'Amico,vZan��s F. R6J.r B�6!�195�{�2��C'}��$M. Taylor,�M��rcu})Zb}=b90}�68V�M48r} A. Imamoglu,�(Knill, L. T��ҡ2.2�6E%C017402�2x��� M. Poggio�..M:�M 2076NM�1@�I2�"L2Ce<Su��an�� 409120,Ef]<iv��-� �l� �*�7���8*C8��,W�mit��to.�B.$wV�Yej��M��%^� cond-mat/ � M&$ ��6�"*�*9!��a� � U5a"l�suV�A%�42�DivF�,�9BacHr J. K�q$, G. Burka�A5K.! Whaley��408, 339k02k�� S.  �9*�6�D��E. �T.A�Ri=�Sci�u�27a� 618 ��62�€� ,��Noack:,(D. Scalapin� ��b ��73}, 886�� 94);FS itevP:m P2 P6H.�M. Chri� l, N!tta gJ.-ahlFi�92��879m�6(Matt2} M. C�hristandl, N Datta, T. C. Dorlas, A. Ekert, �Kay and A. J. Landahl quant-ph/0411020. \bibitem{songz1}UTShi, Ying Li, Z. Song,PphP. Sun, cond-mat/0408152, Q_��um state transfer via the ferromagnetic chain in a spatially modulated field, submitted to Phys. Rev. A (2004). \bibitem{songz2} �T.�B. Chen� C.P.� =06159, J�mission���in ladder as a robust data bus, PF��press.� geo}.QP. Zhang%iY.!}�@311052, Geometric5nInformat��Storage Based on Atomic Ensemble ; Ym  Zanardi:�6�070, 032330 (2!{]<�MIS} Claudio Albanese, Matthias C.�ilanjanaQ�Artur M��405029.0@QD array} D. Loss%)D.�$DiVincenzo:�\\textbf{57}, 120 (1998);A\E. Kane, Nature (London)5 393}, 133 6.�Lieb}C 2uLett.D62C201D 89);4 and�!&is,a�Math.-w�3}, 749>622�a�}y�Iw }A?231�35A 97);1 ^1r1.F�dShn} Yu. Makhlin, G. SchonIB4A. Shnirman, Ra�Mod�73, 357V1.EShi} T;i,!�2�%�a��|On�R�-/s, such��should!�sensit�ov effect�� {erm� �Hw1)s[(to vacuum iA�0duced through5�@losses, which ten> degrade � per8 nce. �,is paper we � ent,�ore%�l�Vexa0 ment��,2� meet!�$the above E:re/s�yY \�A {42.50.Arc .67.L� PACS��C� Astronomy6K>%� ssia�Ai� Leme. %\keywords{paraM  downcon�{on}%Use!�wkeys ��%^on if Av� %displaMPed \make�#�Hse� ,{\label{sec:%�<}First-level heaa:\proA�\\ Th� %� wasakA 8\lowercase{via} ackslashS �b�IM^!;<} High fidelity:��*(s are an esA84ial ingredient��& -enhAu(d technolog� ia����]�: c�](LOQC)�d�` Th�A�endeavoraFgener�2Rs�a�Prolled, well-defined �o-tempoh modes�Can ace� area�'4research. Curr! h ��-5 candi��s �%El�� in�(8wo categories: �� rmin��1|pr� ay g�I m�(ata� �, trigger tim!�ndz��'ying o�0spontaneous e!of��inguish�B � pair!\ con"� ��FiAf� rea�. While!�`� �V.62�5cannot%RoA�!� beyond �IresFl��d slots�Wa pulP8pump, it has be�lhow!$at wavegui�PDC���ZY%A^ 1�IN toge��)�� l�+x efficiencies\cite{uren04}. Con5Is�=O� � utilizeA^ vari!�phy� system�� AOa@ cascades u4grangier86}, e\��c` 5s +chou04} Acin !�Rs (PDC)ъase!�PDCkM%A�E%����-H reported by Mandel��$it{et al.} �hong86 �s2Ab9��m% to�$*_Hely true $n=1$ Fock)n1)��,rarity87,kwiat91,lvovsky01,alibart04,pittman%�In orT to a�A�e.�!v~ a*L tA�tak���Iaccount� r��aK&ePAt"� ��{� `��needed( ad)�f ���fulysider)� limi; �ex��ng�A���  s_ )binar1 hav�  valanch�hdi��.aAia�e Gei��aq whe��A n $click sign�� h ~��0of one or mor��sQ�.? der� � & a�5)�oura�va�lyU� :L��I�I`},�dnt�!���o�  V/�AA�ndard <ach u��tD t�c%��a light � exh5 �or�)�n`�E)�smeasu �@a $g^{(2)}(\tau)$��Tiint0 ,y autocorrelI+f� i=PHanbury-Brown Twiss g%y., semi-�X>t�yA��9�p�c �Tly} at�0) \geq :���all�;del� $�$� , �P � P 1$ �observ �of1I8anti-bunching, � sl{i.e.}6� leq 6�,�� ��,�Aexample� verify! 6�"_ �!("y VuiT� ��� glyted� cavity �lI� mcKe�� For��Mos!�e�ba�%�g� �#simult���wo1;wat"inE� ��i�m�saH���_pr.q� q two indepQ nt g��gb)MA� rvalM !�pbl� ates�!b!�5�L unless we employ sevem�� ��ident��/c� �C-!�onent.1` �)��j�a�-oed rao is usuk�)�vioa�ng7�  boun�Jsey� !#f�6�gey.valuea�}P$��stitut� H  eritQ� � ee��1�N>X�'3LV )eQsy4I��� }. "�a� ����t crip�f�$9�6 s, Gz �sl{et � �qd from� Cauchy�(warz inequa� ��milar ``At-�]''ݭ���izAq!�� ly�2N�acoincA�c���AI�)*E I�Ae*\!t ��7nD 8Fig.~\ref{Fi:BB� Sche�c� eI.� p� er: ! �`lpha=\frac{R_1 R_{123} }{ }3}}9ca� � n indi� s:R�l2for $\~ <1$A�$R_i$.�!Ids�Int)F at   $i�l>{ij}$, k}$Adou)A[triple =�?'re�B�a%\,s $i,j,k$. A2 a�@/6z]�6�Pgn�o stud�"� :?���_lyI�v !'�ha� pionee�by� userm|�ser74}�re+l3 en.��)d-�D!mSan"� �l��� � �dE�e}[ht] �g{:�8Sm.eps}{.6} \cae�{U�f. setup2M�v!�6�y�Cab�$} }JJI� � I< � work�O  R \of2��a � carri�ut� erm僙�"� sb typ�39, how9%� �f� direc!�= E� l� q|only un~ certaX ux�ry� ump�,s��e reaQ�t��i�Aat� Q e�y?2�Iez �! s a� >n� , regime, do �resolve  i}n absor� ev& nd�� a? a�onsgl%�us � t lea~n �nt{ � �� �edE n0w ll. W}� (x7%� 1�y3b1ad���.��E:mi:  weak 2#� �G :� ��� -. is propor!�al @�I l: F� obA= bJAa!2� a!@�$a � � is a��?,particularly��ort�� in s��es� �$ultrashort�2incom�%x ��gybcon�a6d!�sub-pico� � ! � M�&^M}dEg��the fas��%_)wora��A[q V�/ o go�# basic#" .�u�am�whI�E- ��Bc�4?edS6� �n- ���� � e a�jof͟="Q(ity. We wil�mon]t�� follow_� �4�⁑�. Fur!Z�� �.f*� b�$mT]2 ��n JMfce8is 5�  s�a�4� be negm ed. H�`�� appl�ion&� d logic g� � �� knill01� &ophole fv esBell � � "�@5}� t- �s��\rab�(as it leadsa�'� amin� ��$ latter diGh usa^ o���I�� es:&|  no lonI,necessarily E� �!�suc ful�B!?AN��M��:!4 !B� ion.B�� F "g! e !TE{2B �r eCes. Our]z�!��R bothE�p��'of�yU��!"I-j&]�1a�e, � I�-�.�eV>K�Cct�2��"n�is-��M9F� !A#a!��� in&�(al �zWsubdivt)subis, each �%to� a%2��j�Qa�19. Co,���t����� beam�os�|�P ies,�cg�� ov�hAC� or.�,4 $W_A$%�$W_B$.�2G���or�i! �a�w� trea� se��Ł�asa�Y$ite stocha�%c blesA� cribXa j�#2�.I ${\NTP}(W_A;W_B)$. Beam $B$��1� by a%, spli� w�p; ref���E��+� co�ts $r-%t$. Fi�#iresul%�)�) ed ��%� ��Bassum�)>2�ofJc�$i$th hor illu��)?��!�y $W$ is,!,by $p_i(W)$,�/etw! $0 �� We f١ �=�qb��mon�$�c* A�.�its argb'�. Uy thes�m"m m� easy^�i�a�T�2�satisfa Ůn arbitr� # }s E�%�$W'_B$J[p_2(rAM - ('_B)][p_3(t ')]  0: &* IndeMeF�&of�5facA�YsquA,bracket8E$i�a� v!V-�Q]differe���-�$;ir� duc:� n< ��a�.?+ nowO . oth �s�={E�e �J�e� i�$';W_B')p_1a� '_A)$�Y$is likewis�Qe �K �" a�A�g�H$\int_0^\infty dW_AB 2 ''�u$� �6!�� J *@R1R123-R12E13}B= .4--"4Vw"� a����� *��$ by a�)ges $\la� \ldots \ le =6��- .�!�) ;$�� ectavAU�l ~r=7na�.*} ! & = &p�1��\\ p^*i�_� � 43}j4i�Fh3}�hy� rq��IePs�/�!1}�in Eq.~(�6B)�{�q�%�to=Ru9 } B�>�Ew1�72Y�he�struct�'�"��by w {\em t� 2�H- `mea � � r s��t,zwe hava�cor^#��E� A��of�>�'. )� noteworth��Ai�Zq�&61���ay� ��a�O�s�Pg "�$ly�a���Xi�� " y. W e.�ap�tu��s�t� "� in Ref.~)}./���%<�KTPb � i�" �"��y femt��"sw�delock��f�' ency��d 87MHz��&- v( Ti:sapphirf ser.� � rF � � F�E "��-i� record��ed-��i* 4��A?tl �%-�s inv0V�.�%�5� 3 %8 a �� �thus 5e�c!I�alE A)e�d� post- �e��on���&0""w "�&�5ng.�&!�� a �&@-! sup��5 of ua�-+(gro�p�.)�1eof��z!�"u �(ra�� !>#��)��*1�,�  Z1"-a�eI � &�I s;"� i�m�"��qSM��6d6�4hardware. Draw!�W%%� e lack!?d,-Z7pro�� a�llA� dead(�"�o$\mu$�� subsequg�'s �!E�N� digital oscilloscope (LeCroy WavePro 7100)�!!�� ac�-gour�,�br/n�.`��ed �8a � NIM �ronics-��m� ��- �I�Aa "w$ra�ed:�� *� � !Vwm�poj edgT rax}ng ��a� )� �neSW �2 $t_{S1V 2 as�'�7 �-i�y�%��A(CLK}$. TimeQ����sc�8 �� s�  a�  �U �>)*�Fř0��7 2}$a($1.1$ns wid!6&@windowe� regarded �c�A�!Gign��c"~$75000$1*��;Md�Zi?mӽf&�( (u1}�}� �s n:�(by�rs)E���@)� channel�$14.4\% 13.7\%�&|g: Data}�� ��m���ata u� s<�e��,al band-pass�4 ter )�300$p%�th�5�7o� x�7� matcJ5FAPD j�)�b�(A)[(B)] �eBA��\'al$_1$-Q�[),$_2].x� %�,�-a�qYA�o�M�!l2�.2�:h(C)[(D2�&rb@d J<y%��*�1$.�]�DA, pa�maximummYA5$\sim17I[0\%$]v�E)1i>>�,�>!x12`i�"��in�#uq I.0�/��ym[E�d� fiAwI PDC flux �+!13 -#uA�&n l�%ee�.( � sg5���� E�I�s,%.!�m4ly vanis'�e)����=^~.�"{5*{(color� ine) (a)��U�)^ + �^&�!!,YY. (b�C2Cc)�u#NI�.y(d)..f 5k (e) œ�*"i��  (f>$*�� m<*�!�& on.}BF>��"j .�#>�FuD�2H�f.er [see{Jz]�86l�s��9�(bove. As�uL&l"E)je p��W )�W��` ] a�4J�>j&r" %= (2.3p 1.6)\! s 10^{-3}z&z%an ��+I�� n� [:>sum��t�)�ual�)"o1 $(!Y2}+ 3})/R_1$]:�$34.5$%E? m5��8�lo�/= m�unit q8D"�Z���oJ�� �VB��als�-�7 d duE imE|�/s��  remai� un ed6. Fs(e&I�I�� ('�cal� te.�=2 p_./1)}^2$��"$t�/6�+)-Eŭ� �9�ig� arm $ W=N� � 1baA �F]�=A23}E� * .''=(1.1aO0.8>�, amongs6;+s&�2�&>�s  . Ir !�;"Z �P�8 e mo~ um�*e fS dom,b-6nd idl"+-� 6o�m8 �A�ex#A4asJ�|\PsiRh=\sqrt{1-|\lambda|^2}\sum\l�#s_{n=0}��B$ ^n|n @_s i�I�a}j$nBP))�fi!@. )$ )mN2!|�FYj*r!in� e"�A teg4e��1F�%�reZ is s� eno�;"`:��%F becomes �!igible"orDr���t(a� �(o��%0v"-ump+or��5 �4):�'higher��' (e.g. $|29� i��|3 i$...) � "�*+8sen6� vL'!rP�"�6}8 via:B A"�m,!�ap��ex�&A� ent $)�*!�' 9or� �1it{� not}M�mm!olqAp&3empha�#i�9!]-"P!.�7of c� bs,f3mus49avo� . A�ue�earlierFo*1to1 �?iz��of =\n*.�$P�7be�� � qJY�,չ�O��"�to �". (I�"%�i��A@-2&a� ;)� ion u$8'rG*dM�6 ���tIz�"le�#� i"X >�BB�&Hb�9c� &�  b�65;a"Ame�� �m"�"i� b e'� �2[is u���ec�7�<�A�_7lor $1-\exp(-\eta \hat{W})$ (I�$ �!9� -� ��(� \a$X>&j%a� ��m�L &U> �K�IE)>�-�(A.q 1U��g%٭�er j"�XPDCa2 .!%1�llQ� � .� �_sV�d�2xed2�f5Zl(B�&~'�/K tV� �q� ���@,vR �%q. No$OA�a� ong ",QZ]���s$7%�%Llow� gw :� pu6`')�{�"�W(mum. ${<� Af��6� �AVw�0is �,rM� idea ��5caE, is $-0.25h%� &-alClFH�K�R�� very�� ��=�>tra�forward�r�}}�uGaD�� �,:Ec a suyF/%F!�!�!O!@!�y �9is�$lleng�A�aly��o'0��u�}7�/a0m$�.I1llR� ��. Yarm��&� ��:��be3 �-=lyeB� i�&J� � ^2"Z42+R_3�G ta_s("$rep} (1+f)�R��"� R_%��!�BuAy$f$ 2�ɍ�P:%Nof��� estWX8n�Y�gc�,C$ by: $0��/�PhO!� cu;�.��N#on@w. � cruc�%!Ba� 4$R<�$6L�<)��*�4A�our*G�.��m?'dEQ�2L'=�acAh&a}?:f J.3"](}(% P new i��Jif`K�"��� �-tC.� 81, 503�_986�,roelofs94} M!�R !��^a!� Bind9E Bierlein,�' Appl�^Q7a�499 u- enN�] %�@"�]{E�posPRL�\4Se5 e . ^� BibTeX�� ^8}\bigoplus $p:O]t"^)]prl,e[\,�\s*7]R]2G^}�F� \tik\ Schr\"{o}�er Cat*_ a Nanom" Res�[or�Fut1\L. Tian)\,3+\2�[{1}$ I"� � &`WA�ics, &�[�< Innsbruck, 6020.Austria�3$^{{*_ f\"ur`�@0 Festk\"orper��ikl\\"at Karlsruhe, D-76128 Ge�ay n3B�b`Opt/@��I*R0\ �n ASm��Qs � � . } \�U{ \ !�b�&& YW�9p$� �Atd'� �a-�it%_>�c�D!��entl5�� � us�S_n6!rQ!%� le Co� A9, box (SCPB),g1/be��"�. �f �-:c}It �::V2�.�-6�� ��be �& y�f ectr/ ic methodBwZ.�Y%/ �  �# fabr�@%q� 1bC-*b<�+th �XgKf?3�<oo�`rm{GHz}��@yA9s� r�Qv $10^5$ h 5�U achievZ�H*� s� u�SETrse9Js xpromi!�M Jd"�B!p�9um*`*M@! �e96^" ����}^ t� al�&VB ��>�of �Eorcafpreci�2�,A�� � .�0�*i �H ion,)_.K QIP_Uv}. One"� stepaOs�J1"^HA llA�%'� eer?�q��=Tz"�Na�! Ub�nn$X70h2�Usolid-�J.�1a<vicKX5� SET,�_am1:� � ) q��4�e {�9x�is2(SET)�p �>>teX 9*� SET1��flexu�$�2��!>!nYb �a4curacyAmu[!+1���I . }. Coo��!��$��ts #5�0�3eKpos��d feed>4Id\�a� z _c r2E�1*0  w3[do � wils�ceD�A�4 e�". ��5�Ip�b�A8%Kdam>8}h5�S��M&&A�&.%>i�A6� $Q$� U�aF�3n���1���&]spin-Q�W Z5�A-�_ v?1a�0@in_�s,  O�m�mp? rap u�co�bin�V,IonTrap_Rev}?c'"techniqu� manipuA�m� moA�alMA�@a#p!du by lL9U4ofFA�r8�1� �!lOgb�I6� In *�9Ub aIcapac�C���� ab��I�6-�.����]�aF --�l0�uc!�ge �j$ by adjus�">� �- voltag#Kge_G_mss}x< was 02#��J�� ed� b��DA� rfer�ny&o=l��H�g� <g� 5��;t�Op�c,v� :tBj jk ��2�͠�5�#��<%�m�b"�.��A���)wh � 2` \,ig9akv� ZH)� is?h���`r$Kz9~7 to ����reb �gt5s{5�/.� =2� �1T�I ghel A�inu�` vari�!^�0qc_braunsteina���Rp !�!�#Jt� $N,�@@� e(to.� A�a  F!c$\-N}$IdB� � &?Zenviron al �5K�\�,/a!�*Y nogEaM �=9�@m4!c�#zAKFu*�N ;���"�:EE�ic �[�'R�� ��hc�K tailQ:�� �n��c �^Ras�S&O |aenti6m�� le_,_, %�� ��}[tbh] \� �D[width=7.5cm,clip] 01} "�ULeft:2: ��e th��. Right�<raj~W���t(rt�A!YDorigin $x=0$ (thin �7�-� (se�$|\�harrowe-$ =;#M�8H !�&�1HIClf�iod!�<�D $\pi/\omega_{0}$&)M!� }} )d-}U�4Anh�_in *�" [�� 6�� goa"G vibrEOp _ �D"�8� \Hamiltonian $H_{m}=\hbar� +(a}^{\dag }\+a}$���/%$ %%d�.5��a� B+O� }$ ($)Cra� (lowe)&�+��U. %z9�is bi�-�U�$ $V_{x}(t)�)��'�� �la �$C:� x})=0}(1+ /d��I! 00&�&A�,y[ S, $4�%8Na N��s) (x}=\delta xt �a} �2S) \di�kc�Eq!6E[$.W�2E/2m)�p �� �71�y�I|%R�eB� ��c( �BJ�u� e���jQ�.� %�g)�1�!�$=v)�g�7W��!�g}V_{g}+!� @x} = (2n+1) e+2e -n$-(nY)tJ� 19n\ll ]z���CPya�%�v��& ��l�6�� �O��*� ; �� q}=4E_{c}�0 \sigma_{z}+�I E_{J!R}{2}  a1@(=e^2/2C_{\S?M�h��� ,!i "I�to��.�: !C �!�� m� HJ"x i)�aq4��HZ" m�B<\�� Ha�$�,� re Pauli "�/h� .� . To��yZh2,�w! ����"SEBX- * \left(t\�D) > �� '9��m�$lambda (t)M (�a 0}/2e) (M�j��)�1&� M�|� aZx��lś�0 q6\<.�"x )0��2!9& is ��=�0} \cos-&��ac}11� ac�% &� P�ٿ$L$N�XS���( = V_{dc}+�V0}�%�Z�� Aa d�Q dc}$�ban�+gz�-let� �=��e$ &A!dmw< �oB$�(de� (  poin��k mal_m &�# ^�j&j deco�0� E31�2�FzfQtas�X micrL>�m��_A=�Q0}/���� Ih�E$!�aw��� e f"�Sw��;bS.Xrong fr�gaf�c �����xm-� 1R.� afD*Z6&s *e}m�"�)s0 &�/H_{rot )=� �t" - ��e6{27A�� 56� }J�Iepsilon �� JŬͭ$\` }iu q� 98x�abel{HtE� �wA�"u+��' �k�& /2e )J& )EK!}&SR�,s+�=8�X (C��E�0 x0})uk)���,E-E���-IA��l��mo�M�>� ,�dynamX ,m#�iua8:a shif�JVyL.� $Dt Dɸ uwd.� �s>�*} D=�7�� --�Ml-  cYl 2� A�U#zAk�.�Q��Q4 *} T�cp:=er��FU�3m @2 10\,2P, $c}"5F"�e"2"aFQ�� ��+ 10-M��b�Ox0T1�VRA�"��m�!=�.� ]��l"�x�� Below�how�@ump� ph�ɒEF&b�Ps,r�6>�����Lt�Q���an�6 situYe<4i�5�$-"�0� �Nce>�3/>�M��� =\piw n�o���)( ), \quad Q7�}\,n\^lUN\ \ }$~ ger}�V��ep_�/�ndU�} ��7 �� �1�% $-iu0x� ata�e�% )�ɐ�w�ln�! �I�$���9�=0"5-� =�I�6ira valid�.7F�gg B�,]�$.&+ $U_{1 {-i�%5�}|_Ֆ_��}=� bDR evol@~"� A�EPs: nD epE#���  } �N} �jt�<s $EEa�$-�_$nq]e,unitar van=�8�t#� $U\��X%�\u =M�Q!9%-!^{n!GW9ŕreMon�]UD = ��$Z $e^{ % Z�} �0} Y�� w�r�J�ɒystyle -B�) =\{ zaBZ}{ll} (.�0)^{2n}, & n\i�h \\ [2mm]� !8^� }-�} W} :Todd�' ��[Ut>�m�!�o�=ph�x��jom�Od���6�Fs�"In �8Z 7a:�� D�=-y Ie 2nm�Ij& � ��A� Mf�nAⁿ A�a�DpUS8 ��s!8�!�ia� $|\psi ��Rle =(cy |\up�i[ +c�# *�)�] dx|xG$\varphi (x��r�.�a�a,&�Q.re xn 1-v2B� yf�hn$� �!9!v�,�PnB�3of� $n�E�X>m? } ѐpsi} %K%�| =QW5)int dx %x)�)F ( x+QS ) + %� 32?^Z |Z\ ( x-\ic�}M �-�Y��if) �Cr"�?^ 3J+bit. AsVc�ni]�a>E�A�1= � 1}{�2}Y UD(+]�  ) |0 eE� U 24$ �祢m����xt<0$. F"|7(}7Htr})ZOŤ��$ɩ%] $F��~ � |-2n\b/�>m�+2� /.�-� ��@! W_0!plY5 /? 057di�<lesoNuʌ�X!��d� |�`^s�5t)Fv@  �As g+ �� �2n c� �� m)T>�" A�.�9� !�a�.l.'A intuP#wae�/pr\Zca"X a*e9p�'Eno&�. Q>0 Q.�tur�<CnkGe9�st� �� \o>[�6,!"s. Each !Uxpo`eE 6xU �g(.u �s �:� . Wri�A =d��naypmuv�� �,�l 2}|+�y(�^aM > +�G2-���� 2}|-�I-ZI� O*!e!����> $"6�*2T)*4�A2[6;a�A�)�}�m0%x= �q=2\pm6� 18)�zJ�F�,�� _x�? $+$ �I-$� />sl* �`�B %:�i �e�����S/ly"+&d �,2�*� 1�9���Q�6� much � $I��Y!d$1��.A,���#2�lio�to "�P�9 (or)2�[ �e�e�VE�s�&wo.bH�d$.h96��$\D�g&�i� ;� �_{iK})ma �e%�N� (Q�_1M�V"Q{2}2T m6.-�.-�%05E2P+{t$x $i=1,2$ �I�:;�,�� =�� i?*� �7ch �� 2�%s R!U )�i� kraus_pra/� 9@�'��B�'c!:�-:�'W"�%#2���:*�$aq2Q�Vbt�J~&�Z:�4�&N-of�*� �|"Z 0u . DuB2��,%Gos�BSq' $�A� > 0$l;2���h &�L,b�D"�d��M _{d"@�!�`a��d�~� &�~-2~n~}� + |~&|~20%l��fin" iJC!�0i*�|�>*�� � .�e�(�� Ko� }|+LI�) |2�* _tauBVEL$c_\=�nIE(\pi\bar"�}A�/2Q����e(.�d}/F@ 2Ŗ>�*'.=.FI $B�}{� �}/ 2�D rD��� y.b.D}{JK6>*?$F+=\M11Vzy@+%Q (.w�ى�e�) .a�@]A��/�mE"��Á {? off 2�a"HbACU(9$"� ">'�'�u+}$ pr.% h"+*��/g?By :�6F E$�.��d!�$�� fin�U~���|c_YM|"&!$.B�w(|."� R"h%�%� lab � 2�.�M.__{s_[iE_J t�}F &�. �u�nV��PY B@a_�@�E;��pm"�$: $p�_ (1+|�;=}|A�)�!!% )+}=&C $#6�Asu -��>���AU{�Y�i2 � &&@�� "k��7�-$m 1Im+ 0��Uno�[ ����;qF�.�,�f5+ ` �np_E $}=1/2$. B�W@ FLi&)�db ���-��-u���� �0��7e�$E� �k��.>k� >ȃUn��aa1�0* O AH ~��V .���+R  )��.) $�l�RIE!���E"3y� ) � m�*!�`b{�2\�� 2}}(*t �+5n+A�� - =�^sii += |-6� E+ 2& - |R&YYs= ^XRIj e�FdM�$B{h� a+}=3/4��{1/4a�ithA" , z�� �>mi�^iA��^,�f(G.���i�i���B� .�of H�Ox*� prob" �\i|pXE��#;&ls~��%k qz18:/82}&/8���iiY8"�c8�"(�guA��� _�*� ,$n=4,\,8,\,1Z >8op�botto�'se q(MN#� {-}$Bh �*�z}=4.0� 0}$ (}D*�86.3.2. (do&�8"�&��<= .$)BG&Zn)z!L�' } Ided �(��Wi�jdiscu y ���vd"f�q%-r)p   �0$.�6��S 9z,"� _d, "� 0�� Y!T.[IiD�<actic�&fzH"L8���"�3$F�*;�a� "O2��.��'�n5� re upV����FY� I4Q�.��ch��l elow $F2F>z-�maKv*Dh G=�n*I3.��ow u��i�!>h %0u�!�&x�L%Ub�p"�,(� co�"^t����. �TI6��ime $tK ��si(t)ћ= �  $ |sBQ%_s (x,t�� $s"�!���2�� %B�&he:����ULT�#' q�edi�.1Mc"RnZv%�: $f(Q� M� })=\]|�"[��&idA"Y) -*-1/1P>|>I )D;_U15T0.99@, �)�%�ә'M� I>bu. af;>d��<2��.d!�var��e�icb'!�ݸ�ߍ�A�E7$0.5\,9C\,-\, 1:"�.8B;.��  "K.9.PvBe�$:% �F�5���@��/ 8t�.#�J!2#��{|9&�M92M�$��G�{8� M�P[ �1H0.dhWn���z2�F�6�s?N؟ Q� kfjN"y! .x maxuU{~)q �+ ppea 2Gd}=Ae�#�! q =0.8}% very*9d  aR� xyE�&� �i6 F�� 6���%,%��deu|&�0>��i4Ja��p �j�*h*�3�D .ra��^�,f � *C: � 7(O)�$.T M�4�F�5,1ge 10$4CJH� li"`to&.� >4)*�"� �5"�3 nsecAVI�D�Sa2 ;�l*�J�"JMu�r_�� .�2W:� 2�2�c7� � *�$w;��e� 9gGƙ*��!��55�-fl&�G,�u�'J젂�;I�e :zof*t�%�Ad���i�lUmHI$��� u�� B�� S^{0O m� n9�9 w |9�"# u�Npe�$:.qp�:6p P$�� scree�)~ &� �a�eFSI>�%Ci�" QN Q{4[_r%�$T=.�mK�1%$Q={4�<d�pp�4@z$$k_{B}T/Q=a]�6Ka� � �6�5 dec}�k�I(.�73} b� � ��(�� =5$ Or�ta�4Y�m *29�r H A�$e� "W m�. Meanj!�a "�msaS�3&�.F&s9.�b��] �R�(�..�5��q�2��+&� �a� F�J�B� & ��.{Lbe.s�z6l. 1fj � uDNysA�=,A<��}Zr� u� 6� $|-2 g� E���!�"�atj"~1/�0a��M\"xJZQ �- !���J�5��elaP�m�l *q"0.H�L( 2d+1�p&�q�� bc��EQ&  Bb-b -I4G nerg%rs�$% E=8�4!Je�J!�e�g�c�v"IH�l�*jE=4>_B`8baNe�"/�6E2�U!Meion� : $S =2Q/`"�*�A��c��=ko�'&�*"�NaiAic�&elAB!*"1� @Wn��e�;&|H.�F (a�)&H*��Mar�1�X| n:xv gm!�,&`��ki�"<+�Nc.�Vp=��n2m�!��%DwY4�f�u�&�_ ��[ 9(copy (MRFM)n��_ds����urf�4=�z �z&�0 ttac%uto� "�O%_ ;v�M!��,.�S�&? or� .�L�Do�_int*bU|ZL"8 �-���9In6�E���<of !Tj(�] impro�]to�u�n.�Ean�";(3�ioP#�- �cy�� adiab-Min�a[(CAI)�]%_nga� applYX� �)� dr�TVWpLkSEN�%g5�odim_J& � �F8. O�����vip��G��ӟ�0J�qmar�B�[�$.ynAj���b\?Yds 2F�P!$ �3/��M'i�,� i �s��� � �/�D. UAgs�*n�F|�aA-aHan>� e;�aa4LloA�!�!h$m�w]tip, $ &!$^�MZ:A �m 2n mɱ����M��ho�p6ќ 7 /�A m = 2 .�%Z$6[d �-��8!El� �Hm�-�"�0 T��s $Q> Q4 ��&���. ��Z� I�o22��߉)!�S:�eEV� �%��m�MVB�+���\�i]rF� w�F/>_:1J�_B�:� -#�"ed� 2sm�y�\�9 �sm��lR-��i� p�#iA��8of����%,ac�/p&�� `b�\�; cknowledg�"s:�r[k�kW'_ -Rae�hh��%h P. Z��r�. help��*M+!l�azo��A�fv���e�;unNqi=CFN�-DFG gexJ�f,"-: EU IST Pr]6 SQUBIT&nvtN�o i��"�d R�iKnobel�A.N�keland,B�k24}, 29�o�j�� aHayRn&uj,g"�i30��7dk42j�6d2�� M.L. Rouk�FN� Wno 160�j8); H�Cr}eadF�$290}, 1532Rk,0); X. Ming jj.�:m42VV496:32�G m�Don} V.B. Braginsky�F�nKhali�mP�1�M&�[ }, Cambri�� Univ. PA�.�k22�F&Z * mep2�m*m6m23819�6XQ2eN�R. Gell�oPhy6(l%R"�q�lI?6�+��f4 D. Armour, M.a�Blencow,�K.�n Schwan��88!�483 y6�6y,2} E.K. Iris >dfJbB �6_ 5531 �:�c_�c�Hopkinsi.m==B. bf{% d235328%�6dF�c I�7 d-����� A. Imamo$4+g}}$lu~�r07550��6��W�I�r ��~��oB bf{69!�253Unt��{t.�b D�oWin�� A_�pR8 Natl�� �].mn�E�col9a10s25Wn:�n�_��a Y�2���m&EA.&�ipM&�q 7q& �.�6�6 S. Lloyd%�S�Br�^2�Le.y�8� 1784�(92b >�\aoRug�t2�o,!G+�Y�43�A32�.4); J.�*�J�%�=y<7}, 24)x52�� &S�V� B�m bf{29��88(ra��HMD&Z8 B. Kh8 9.=}��"�04"#ra�h$>m &�oپB(pepjFpsvjour6p � xsym6~^�QbGnm \pal�` Ion �f�fCo�f: Mo9 IonsBp \inst{1,3�Nnd�uBlatt 2�` 1}._{{a����Ap*Fo@p ^  \�6YE.�x!�J�pZ :Z� NZ�F'p j'p �'p&pReceiv�5p /a>i�"�:Ep?p{A hy.", c5�s y tud2� 5b.{mպ�)n{h�h�� p�� y+�&�N�kag�ua �'-� �9VB*� �?or,��lbaV e2�g9�� is p"�fex��Y" � ��a�O�d�o} ��1V� -p}{6���&0r�&�<E} &} �n*��":�:)�)O��1}�R�D6 Z!sp=y g�<s,g� �/!�p6�few yea����.I��,w�`�Y&��%�tel,��� � .�2�8on_�_exp}; �QS�P�de,M!le )�sA�m�N�� L� 2002��f� � �s�A�Cp C��Tb� }. ��nM `n�|�{핡�to build��2�9�A���]���� al��thm�3N�n sim��9D������� pub�s �.�i+���a�1'Y?)p��a�4 )"�e�%�a �8 iƴ��,F�.�� � �)-�q" lif��;kBi� 1J.�]��=�f.y����,y =)!t�C�9iI����ombin!3Da�0e0���"tw�!iat3�% �V �Ix�s �Efh2XP-�a� with�>�.� )}:#w s,(|_��nc��_��, exp_%�_�_2000}��A�%�,"���n��/v b�n$ task�1 G�$�R.ev eV�2�X X/���zsL�bit*�)h�u2Y� port� �lu��)�B1�t!�6���U�hB�,����e swap1*s7!AA�s�-{ra pola" �d���6{�,E^���.�H"4s�G�ionfb.U <�1!�6<�PeNj"�scpb_m"?}_&)sr J%$� W�a.�fqo6�'W�)0I� heinzen_w��y�@ing_1990}. Exchanh+2�x�cz�ga)�AU2�yu ��� a��%�86�*�ȍM �W3A�*� �I :�� i��� 2�!!A�!�2�to: 1. i�-��6�q2� ; 2.������i��ho ��4�y�e�����  �u.�t��@L,�� ;A %�2�����AX* issu& �c��eyu�)�""cjy ~sl �-6=p� ,"Wo! �:� )I*]z�1ʆ� .� j2� �.�^� !�a�  sE�� a.&qw�)(�U�k�3Q�N��b<�rge��� *� � -�� cer5�6y! ��Mw�-���, &��)@�L �O�ua�organiPM��9;?0 svF on 2C m e`7t�� �2��X&X )JHea�Q�\�!V�&��Z�:6ibi�In �3�E�EB.�du��Q�E�p�a c ��r%��6�:�)($1/f$)Q�\.}�-?4�1�� 2p i�m(Ss�! ��#�k.V)_�j +Q�e��z!]acY!A& (��,%  ]V)���'� �52�"� �z� ��|W%���� h�:SE'4^N2}AO, +�]�Yepe��+�#Q�a6� A��v .% <)Nm!!r`0d��)gCF�ha� #� �?i�strength1�e!�.�v&j!�.\a���Q'�EaB> �#.^Z�\!���%zHQau�em)=�.1}�(I+��_nA*43(Mfig�"�#,�eft\{ s P\r�H,*b۴5 �� 6, &�D�*0 &�O!�C�J \{ q.k$>j.v)@(pt�t��ol  Kf!`AP1�0m`��iM ��.|\{� =0\}�*K9�C{)}}|\{ �"-E$%�s N\�s�I:0l&K�1@==2O) �=!3IZIo)� eir6��1cZ��#��ed��Bj�iE]i2��� �-��J  by"�T0 � 62@$%Ms-s_{j}"�)Oi)!�) u�rsO�� X�RD �Ulh,%�Q� v�+I�j"j."re� ���ȡ�!�sEVA6 T0^{\prime}=0 \QE@ Y@%II�Qwd/era�B$$($M[9$����"& ()/QM%jkE�q_ )�, $k\ne\, i,j)�!� ? �*1O� ) !�(!�i)�)�@ �5�� h(o h a Ui-� g!ss�j� c}_{F8a�bp% .�� $nK$ &� �, $V�.7�!V"� s��ns;�A�EL�6�H�to%�i},)Z�7]��IBz >�]w��f/ nd a!�9�.�AO-� �)�-�� q�.F#Cp]��er5E��c{5cm\{_@z3c>����5��3�.� � �dIOw���laM*o� �xt2�z:oM=}-�g�&icV- �"�z�wrfn as KP t}=H�0+WP�!intmL�T+s}�7"���� nce_B �s0�L@ �.=�.�"��x*�&$&��g�U6�/\nu }&n^:�z,X detu� $0B)"�Sz}^�Ք Rabi"� �h1\omeg*/RX1E+Ee^{i{_{l�w�4l}\g/}}+1W h.c.���5!^Fp (A�a8 *}AEza�b2a}^�{ger�_ ;�vq(�{&v{� �Mv@!@�w%�x&"�.��� A(q}C�Ef<}"U9�� ]� ��4�.�m��Mx} ,C�6W ��$U�Q�YP;�1"�[a��[��V�6] sF�:�2�0�i �X $( �AXa�.$q}) Qe dr/�3&�=0}ra��3$��s�m���!�*�a-����jp� $ p� =f͹o1�2$e�-,5�Wwoi-� �� Ns24e2�y-�in�gpl�} s $d�v$29162)Rl 2}dr�/�^Q��6rg !I��!"^:sctor �6Q/2�b?eW-$familiar d%=- U+s )u�!��j �_�^� 2}�AU(b�sV$��[hb�� �s� :� ���2} %5.�=�s:�:� q��Ui�>.%di�1�s al d�l-Om d_r K%�!9a�m &n8� %$| B�O$�. =9c;!A�)���.a#!r&� .; (cnBme�!�a�all#��d�1 1�� .�(}�;6�1�M 2lR��2� H�*k"�7.}2�#pA%�l�ed��.�X ��)�O��) FR*��NF i@��$�6higVA�vtu1�"`�s��.I�K3}�G�6{�E�4�^;�%( :U�0M� =|n i $% |Tb�:�VpQ%BQhe�Jbe�^*����%�..� ��=y�� J:f� I)z)c}&�y: 8 ��`d� v��kwgf %!��y�w/ :�K��a��66 ei'���J�Fmw�'M.� �%e�"%shn� �%K �%�strF'� j�'� ?��i��%ap��� C_{r-�AN�� $L �U0, and has eig�enfrequencies $\omega _{n}=n/\sqrt{C_{r}L_{r}}$, with $n$ an integer. In our scheme the cavity is much shorter than the microwave wavelength, so that the c B�Ican be described as two phase variables $\psi _{1,2}$ corresponding to the 3 s at� ends of cl. At on, 2 s part.Xtrap electrode couples %6ionKBotherl, QB31})T-% ,(!�}- 2 "<}{2L_{r}} \\ & +b�t+} dvarphi�-C_{g}V2<% -E_{J}\cos{(2e 4$/\hbar)} +=6_{![~�m�( fps!92� ��+!i�2d)) Te\hat{x}}{d_{i}}% \end-� \label{lU(_total_s_q} )U % whereAg$ first linyfsM�modQ�E�iuR voltaga~V�$ and  2}$ m\6.sE�2�C; ; 2Q�secondR�./9mwi�$$% C_{t}=C!�+%�m9 thir Ri�eeivm�(ings betwee��)i�iono.��%�$� disi�.L: .q�,figure}[tbp]�center} \includegraphics[width=7cm] 8_3-�3capa�H{ Schematic circuit1��&:��, super!quct!� �%�.�.Uh fig:z � After �raHout! PIN)Neffec2z!�\cite% {DrfacingA�:�M�Hint} 2� H_<}^{(2)}=m9�Q0}{C_{\Sigma }��a�E0gs_{z}^{q $:u } int_i_t_c-B^A�p\approx��r}$ when r}\ggA�m},A�tA�By inser%FA�)�) X �s [J swap.� two /s��`{Nielsen_Chuang_book} whi!>xchan���A&eR C��i$key step i�at��n-�and�over aE a� $!^_q^{1��!�+ 2� 2,t_1 $t_2$::�. Bottom� �space}�� m�eqOunder% kick|�ى�q�_z^q= s=1$. Dot�� �C�1 �1. }� fig:1�� !�!g9|asIshR� 4}��ains e� ��mdt�gi� � of $��\{ e�!y,-  2}, 2}�\A�nd T 1� i-�ɰof du �Xq !�eI uey.2},��pe| ly ese� � � ��!|9�s B�6B. When���t�4=5 t_A}Y�� (� �2E�we have!"o : U(T)�@i\phi ^{\prime }}�]T)��{%��`f� e^2 .1�1���}{2C_r mW \ (�+)}���q���sM )},"L UT�g�at6^$ }t \ll 1$o$a fidelityA+$1-O(..�2}t� )$ (Eq.~(� UT})a exact�W)�� icle). It�  bei.���?���spe� H�evis essen�ly limiMJ�l��pow��e &�)F i . Fo�Yte�alpha! { 1+$%�=%�=5&� nsec��. �9 8*U m��2�^j =10$� � @ is $T=14>f%j${^{9}}Be}^{+�$ T=26V7 ^{436Ca 6� a�on{Deco�nce"�� 3} In ѣcompuQ,U importan!�)� �}s rema� Yt#pos� -�[ 8. Many environm� l �sAT� troyE Y� aJ s�VA,hybrid)�, nois�� both g �  �caud9" \isd} ,�]study ](major sourc� <���fluct_���solid-st %L���� dissip� due� stray� s%�&� Ch Fo6� 3.1%�B}s,� �)= �a��o2�it }t$  o��A�due toim� I�R fabric��aR2ca�e2�(dipole jumpIdeWst ��ac>!p)dor�� �ho� s near�@du!� imag� r �. D)�i��w kir.�� l5�� occur ?a $1/f$� � �rum� E�8 nonequilibriumS0non-Markovian-�-t �)��has b��K.�m' !2re�ZdF�]K*�with .I-�0��M:�. As a� uli)m�!expos %8e2��� ��osubject�f)X. B� �6�qB ��"��d $.� .}$ T��ind�@1� �i� will!uce s�us2��!I   A.��  Q!�"� expr� d�Ra�{ , 8gg�M!�dzhe:@ �$Hamiltonia|� : $Hr�� �nM�/2e + ]�\s:-M�A�dynamic� $.9$$ term, beaiQ�]�!�� ll be neg edMQ follow<discussi �)�1>�$�a�e chas��o�8��8� { � ")tV� )-$� 6 $ 1L h N6M+ U7 7m� 66f�=\int dt?e^{��6�t� $, d�min���}�p ��f�A ency-z!:� �]�pto 1/ %�transa�� in FUnow��eC��T1+ ; !3-iI�W\phi _{v�� 5- *\e1�.s}"8 UT2>�"1 "{#� are added] a��� Eq.("o5 mvD�d-iV�}$_ �/7����.C;��a�stuH2db2g�$e�����Z]=$�(Jk �A)"QS� t_{0}^{t}Y� }$\Y���mf}M� M�>@"�af$ %��bu Bc J5& ��we extX!\N�n � / � �C� a R � � come�e�ectK_J� stead� directly� l%6.�� )�) we divid � o"� pie to improvm�si�!Ͱ6Le��=T/N$�&��una! Kdp�)th $NO 1-�an eve�ED'ThL� ~Ŝ$N$��Q � ng a �$i� =\pi/4N$�F��%"�i� w $U7(\��q}U�))^{N& af�!�%�valT$,� \pi�� ppli� !�-I� � flip�s8e|assuma~!h$K-�order or� *� ��wbe2h-!!F!�&�"f8 J%Xab�"$� textrm1  f15%�sub�;n2�!� �� F3switch�im< <� Vg1h" V5 flux�%� ++ E!&� RK(.&( U��\�F� }��2��ᡙ}% >@"�� f� �(Q�z��k��'"Gѹin�I!t�$$ J7�random�be��� :��� � W"� -:� 6� Z)��"T \, g J > \[:�:)�{ ;%a�),clc} 1, & t\��x [ 2nef, 0��,\\ -67 [ 2/,L( 2n+1 �)�H.�)\�( � \]�a��E b`�&��(^t�&all %fun� $>"� �m  in�� riangular>s:F@ =�*m1�4/�!m�sinc �t$�fx i�T- =m)$ �#/%t L$$ -- multiM,�980 (is procedurc5val�p��ifA��D al dens16 5]*�b��>�$�W lowest��!c� ���wcalcul-�E�gam�v�'\zal��"  barie ( t)�$ }. t} \quad 2and7%FJaY f��-�[ /u6(t) �,}.A�Wb��(I�{c>�%�Vg&� I z _{e!)a�( ��^ }{2e% � !4!&�2}}I�n,m�f�H(1}{mn}\cdot�!2��� (dI� }{E~�� `1N� !z�� � :_{n}- q ^J�� R 1e, a�BY.%6u'-phiJ� Consi_$ Rw.t|��vs0t��$�Q.+nE *�  ȭ�) %��:M $ _{ev} &=&:��2]% MM7p_-� !�e }{n��\ &\leq � 1}{3�_{\max�t)�e5?���y i"a�rel�� repl�!��2�� �Tmaxim& � vj EE%�$ (M��\ge�f *)*� "� �: $)X+%$\infty }1/%B \new�!� e�/6��� w at��BP� 6�V� ab�GHz: $�o�q��>�Ei�CEP 1/3N�� nd� q 2� �iN �d�Y!��t ips. Note:GHz.7�T J �(!� m�F�Xs, e.g. Johnson-Nyquist67rem a�8�� ex���%�iH6��s��an MHz ,Saclay_exp}.�-�p� ��� ! veryArt�e` s $m/!y4 spin-echo typ U�mod�n�is "\'�)ngine�-w)?:!�B dA.2�f,D2� RI�alablQ)hem;o avoid��5.[�.e[&!'H ^% e�c��u� local >�0wi�2o-�+�.� dou�j> o2 m)�:Y_s!�ecOZ �E�a ��'e�$!5"2� he ( $r$ * 1/r$�ly�by:��� ktA��$. Meanwhilx�sig�9-eB� 8E_c(C_gV_g/2e)$mF�e a n\borhooP- differas�7 $*P"�. �.!�E�eofa�e� offa{ . �I)_ �pr%�irO> +.D&W > 2} An ^�of!�o� ww��� los!) �:� iWiAa��2� �8e.te+ at� na(*�or% qua#!r�$u�YK�ne]$.X:x&�9� �%K,2\D�+/k_{B}T0, s� [*�! d 6��/4on� "�",en l�$q+s, ���4 drivon,Dscatte?to�>2��'excV%��.�� es. �#ourEJi(paperi��fc4�Xestim� �A+a����#=�s�+���re{ &path lgtIa�" bH a1. We��e����R# as aaOi�A��es I�bi#���.� ���-$R_{r}=R� (n_{ex}/EB)�.Dackson_em,tinkham_.�ivity}, %H$mO no�s�.x�2� or. � �%a 20'of mW� #� stay�1otonsA�!� ^{-6&�8I}z'����d*�$12T3'!BM�Ms>�� �<092=�_�!1b/�45}�&W .� IUdm�"Xtandard Caldeira-Legget�(malismI�@grabert_phys_rep}��treat��.�s� n oscilla~bA�� �+.��� � ar@+�0a�%*i7�.B[)�M��fI�* �8!���a� I� !g/~nPH_{R}=H_{cav}+\tilde{�;kjP8mbdAj}x_{j}�<�<f�p {2m }+  "@ j$% 8N3O ��; c_t_�}� H'"�  �uC �2'd%wd�\�(rR< ); $�$�<%K oord�$e ��]-b?�, $%BM1a-� >>, $m_j$Ep mas)&!= 5 f&y,Y� last� ��.-IW bosonic �ISE��;U+<q;)�@-]�:06&$Ţw�7A) � "�$ZX $J��,)=$A N NA$/IV)#d} 7 �1)&�c AoE*����� >z����4. � �"+let2_��A�t}+eN$:���E=d � �Q�q�AF�wk2 � 8 harm%�9�Y&reE�* edom�*& p<ed�-%s� �oK concer0 �NEV3" IO �s�2tak)� �7 �Dexample��R+���I� same" �;P*,L2�iF"R`=  ,!SM�.oE��e���0 [h%� �"E�J�,S_{eff}^{E}[D�@]�!A�^{beta }d��<�?�-\�@ =a.�A F�AP2���1M�=xF{*� }d^k�- )2� 6% <)Ro�_){"�?5e%9 -�� gaug�"z�M�.�Z�- $%{=1/k_BT�$T�e�*� I�&Zk�Q�:�-5)=W(C�D=t�B}2n r}�%m})�n=-4^{+ I)\n3nE`y=� EL }}{(A:�$� |?|29}(F|))},���kbar_tauJ���D]=2)G2��>�9 nd $�� n8�ta -�e� Matsubara��"�GaT�)$n$. ~ a�Fourij6�$;1�] $\wide��k}(57)v� D /4 {7%n) � retar�#:�U;.�:7Z�=-d+i� )=(IEW}�4�E)!�@&ZLt{@���o )!'5��J�%^B� iselacterizyan�TB"edance $>��.*�Ha�9 or $27/4�] parall� �e� !�!�� pJ:$�5$  =W Im}[6�:�0 ) ] \\ [2mm]6@I j� F>+^)\coth � ͫ���"Z � �:T � A�.2 E4,>�**��Ab)�*&\r}P($� 2e ~ 1Le�� �)pa < 0 )I*cc� g*�,��theorem:B>fw���M� )YE�}kF1])u }f|�[=4_)(_� J�eree�k}=)� /(2e���i�cnW=iՁXDa ���m7�"�mK2� � ���=5*�Dm� w.;3�o3nt2! t.�)x 4�2n4,ion_CAX_exp_review_wineland}, �(mo�J kely2b$�fl5{Ex�al Issue:6 4} Combi]?s\7��2�&o[ a32��"O sB�6�&al�F�-r exis��*;(al techniqu�Quh�arL such< wh�Cah�C�r�m27�R2+[ develop6�2v& onal �q�:k c%"�F%!� is -h�!inv�&s�2al�e_<n�i%A��S �,:5��& *\/"�D balA���aiu'#hI� "eac b�K) 6�c�iH�ET&q8FsSs'6M4i8zFa)��er �'"�>2�A_!�J �� 6n> A1�alternaa%��7ir2X�an turn �L f@(cF�L��a�5�le shor�)t]4 E�(i���G. Varh)�Z(s��7tud���$mesoscopicZ9n�1q�:Lp!��:>)le �Qn2,1z})-E�high T$J$  rialr��7&Q;a0� y a E��ic- mad��dc SQUIDA�b�Q�A[t�N..�C5}B�CVN>8� � �L� BO5HI�i��KR��2LOI4I}� � ���# ed $�_{a}$.2�B�-%= X�bser>�>�ɬ� R��� F2M5} � p��!� wo l�<"�+"Z��K�+$�8aAf�@9 A�Z/&�.s�,m��a5��N) w�Y�i7K glig�a��eI *N���2�<a Pi�. B� � a}=2)iS% \pi\Phi� 0}+H�I�oA�0�H� $B?AS)Mec loop,� :-0,�{-��!�a�h�#�yn>; ex}=r0/2z F�"o)>MR�<&.�`uof �$�. B�;�� ;VS2P���-�p@�I�hi� f0�3s`Wto5����in >$u$ psi_"B$QnG�d W�q�i�WO;a9i�H2; �NF�I�&IM�.!�e FIW & )q�!ra&A|!�"8 ��.�U2�V�)^2/2��~n�I��"`� �_L>� @�<�.�aB� +�.a} mnR2e^W_�V-z)� })�G� n������_)&��� $!GM�I.�1~asF� 6H>�cl}2Q sw} >?)(p_1^2+p_2^2&Tr�2p_1e )0;�Wi}p:%F)D1�X_2)E�X+-�p_aC_!�\ -&:/B�X �(p_MT+�# dC_t"J)�R h2  +:x fp_aFi�t} �a} j ��<a��.Hp�W(,\,i=1,2,a, �&oconjuo ��m� c2�[>���A�Ha}=C_m C_t/(C_m+C_t6 Here�v��a�6�vs $C_m� ��F2�a��zA��wo�*.rup�" $p_ay(�F���& �-�"� �J-��[�UZZ=�G i.e.�� �erm��E"��H�isappearQAN(% � t�R&�"ťs��:�e(i���2�.V7�.' .v is $F��U<-Ebm!�� �1� A.`>6)..8@a � B�=�1%7�-� �J?.�,a!i$-��v . Now� "m"m] �Ԃ�"�!��A � ���� �"{ �gKw4#n��Q �Q�B=(5�( ^2/E& 5m�%���2}��{a�L:�-a9adoNc2O G����a�)� diagi ized� o se�2r�mA�`k�v_{ki}{iT  $^\star p_i��($�0$k=A,B,C$. On�s1&s? C��A si_C zti3�Z� $p p_i �]�(value zero.B 7 =�C=0"�Ew:z�H2J�:�H>~0=:�\!_{% }��k�C��%  2L_k���l 3mm]>�>l .� 2p_k�/ �V.�_i}A 1��crEF�} !:�]k )�r�L_{A,BA�re"�� �\A  2��_4��B��22�#Y3sM;I�td_i)�{S$,  Pl�!�!Iȡ3��Hint})��)�"��ilso giv���8�.�� rec?w� rm�zF�2���6Ab.7^a��a� $�6IG>a�4E_J-���&d^slY{.;�le% crit$^ curr�. �S�ell[.G��of�is>BQ"xQ�j� a��$��| ��A�\in"�$@0 U$is mayq/!�<B5�`���AT=,�@��magnetic�F:�&f0 In pecN�M qe�pSE)�S0th2+?1�,e5�d+d&PU�2b!��. % � M-)(*=`�;cite{�,(cz_wilhelm}�*cB�C l>k2�O�*b�R.sGro1Hg I&E%�25�0o�}BS�%; a Paul�^�`J& n ac�DB100�;250HMEU350 VoltsK!��wz% � des;! a PenEu�6A6� gradiaBbp�-  B 2�sHT��&]'%��1tv:���Bs,=D��?Uh��N��� o =*0a�:�2+6 �co2���jong"� mV/D�� �D�- � c�<M by de3i�:KA�b�o32o6�BoA�>w YQs0g" Hgb�Sr(EC�4A*GdH'Lm�A(&: JB1!~ :8Z�PWAc;i z ^H�M!�>[E+�M͕� :( 6}e3&=��69 C_k(V_k�� jGFtV�,D ��_>a�A�y��taP&�DQ�v�hvi2�korsk�zo @c,"�E�C.� aF?'�Hv>� `�d"Ef��"�f�C_iV_ {ib�jib�e}�{z� &��6a9),e-fican��fl]!��QlMa.�9iXum}�"ed�"�e&9|,x�36v ina�TacU �mSol!�-Q+�eA�7?�1 -4}\"gV"�"O�6 �!2Q��g($d_iNFf%�are�/]� t12uxf^2�<%\A�� � ��y�.�"�JE MXz^qRXME=�"# M g �es�La-J���� $e^2� �.��2F� In adDfi�*=0!wBB��Oround�� 20��f���W;"�is ]aG more% z1^2��Q�`R�"�K��'l  6�����*Y Sc"� "�-�ޮS 8.0c&b7�:F��a$ �!x] !� a li�XŹ%� ��. n! ��."oa�hy[��5�!<*�#��>r+m:on� or/2�(dash"�>(e����j). "�% fig:1-b2+h 4.3} ;�2�,�hop�,� �"lA"�%� �\e�=mo�"!efc�#loi� advant�oof!\x�A� .w�"K=!��Mf ��:�7}� ��0�7m*�Opur�h%�N �gh%,r�[e�  numb�>�� -% >`ch �nFf~�y%&6sA . Inm �� �6{A�! �Qw clus�l:�R6��O%�;.��  "�7woJ�aB�I�B a{�small =�)��.��L�plyI�i]�S c�Ga2� �?�{ "� "� h3�]D Za�9q��A�!)<s�2-X, on��~dd]V�npolariz�)�� �9u�g push]!�e� versP�sM� �!��in B� . Ald;�.�I!8 un�!�:mOk�Ue#"IIu)V!�!-���a a9�1�5K� 0Eu���-?i\4/%�&�On�1�b�"�L,is ob�e�"� ��L ᥁�bitIP �j�0"1JlT�9H z.NN $U^\�dtP�>&�j_,1t�a}^�j +�dU D"5��?��K*F'&1g��e�%�exempa�"t� ed �Y� E�2{Kt�]�!�2� invol�jM�W%�afZ' �;"�  is �IX.�BEPrm\�anA!v i�#2:()�Coulomb �f: e �xR����?c�4�%�SB�� Ln xmi�e7=s L� fA�poYial �!,"GCY��g< lo]Un �]�gt�(r S0 ��Q(� . Ba9 %w��D�M��"n ͼ�j ���dY%6-#7x@�q w#�( As���@lu�$:e !�!!pԉ%wo: !'��I�oa�y*�)�F�E?2E i=*�� aajer2)��V B E�.� s,-�QlbA�ga �i�of � it� b���A�&� �=$F� �]6V 5} We^+a�.i}.�hE�,!��te$ ���.�/2S:.!q me�r ism,��!A� !� � iZ.�V"YUD.ifE%��h��.B�b j� �E�2jYa��M b�K�analy�6a cruc�[ elem m��:�5/��S�- +&s*�zt2d.- QR� �%�7�i�We~�a�q q)_l&� ��* R$ E WE� alig�inqns| n� ofwV!҅w.�a<I� /wn"$u �_�� :� Ml�>� ��� mjr)aSex� A�N1%<mer� of*L&�2 L��?�H�2OF��a �8%�� E�Zy�5 :R�1 s. S.jT2k�Z��GYm;�Kx�-�>_E�� cpb_8_8 _schwab},�_.R0 . O� � handa���- �95�9%RAH.!��Mch�3ing� -HM 3 �sSto work�; mill�4v��e:Jdil�g fridg�=;Oq�1 ���Z be p�l� A�W'�Ps uq[ �4�E�kfC �� �a��3�u&Oal�� �iI,�-db�K)5sH"+Li�5��y. S'/��� �4 X deman�$. We woul�keJpki @5I�� 2� < still�p�%�)Hnd some.V(orl ;ae�Ov�k�Ma�!-ct'i5BWPmK<"yY�Q�inN futur�4$Acknowledg�� s: WAjsup�n� �Aus�X S�ce9>nds4, European NetA��{7Kitute� "�In7=�%${thebiblio��y}{99zibitem2 4 L. T�k�B]Tit{et al.}, Phys. Rev.c_t. "Xbf{% 92}, (2004) 247902c*X8 } F.�2midt-Ka] RmNa!Gc42d 3) 408; D� ibfri�EC �C(12; M. Rieb h�},>429�734:$D. Barrett �i-,�?7.Wia92002}�LKielpinski, C. Monro}6 D. J� 2� %�bf{41� �2) 709;.I.�ac%" P. Z�jr< �<04})0) 579.�!�Today!�}nU*� day March`% 5�4) 38 r� HJk7� 1995A91.�:��!4 Y. Makhlin, GE}\"{o}�N 2�<ProposalW�sCo�t�s�[0~X`& avaicUa50ant-ph/0002072~K  Se) so:A0D�{mour,��$P. Blencow�#K.�5S� 2�Le.�88MI2) 148302Theinzen"�=>* .>199%XJ�!)%�D��,-�%�A5�4��A ) 296�&*� �>%�Lf�},i N�]8282�.�_?_ref}!dJ�Zg�O2CB�30�- 1984E�<8; S.~Chakravart�8A.~Sc��^E�U1986) A�.�RفM�1o)tI.���, \emph{ ]�%� .$ACam�ge Uni��`P�, �).�j>6�!+@J. Garcia-Ripoll,aq�g��J.�Cirac26�9�� 15796�n.�s Y. N ,:I0, T. Yamamoto�$J. S. Tsai)�(ica Scripta5�10E��$) 155; Y.M�lC?n, B.L�tshuler D.V�=antsev,�,t-mat/0312492�*bZ D. V� �۽ �596!� �8862�"�S!� Q Clas� l El�EodUo},(s[l Wiley \& Sons, Inc, 1975, 2;\d.2�fRTA�TpT|I��V to S*DW�T( (McGraw-HiA1New York�96V�gra:4S H. G EsSchram:� G.-L�golq� Rep&� 16�198��15;aJ� ,A-LloydE�T.P. Or.=o2�BL659�144512�����>WC��*� s> Jw Matl�st�an�echnol�10�W�{252�:�) MP Storc*)F.�AW*, Appl�$:�83��2389;�vCosmelliR�adi 40366F�( A. WallrafXF B� 3�@��62; S.a�<~�31067e��h>1 �% docu� } ��\class{Z8au ckage{ams�`setcounter{MaxMatrixCols}�M% :6fontsF symb:� hicx} %TCIDATA{OutputFilter=�ex2.dll"Ver�,=4.10.0.2363@CSTFile=40 LaTeX � .cst.'�V@ed=Saturday, Dece0  18�=$4 02:55:547@LastRevised=Thurs6;23;7:54:46;0Z2D-�Shell3SaJard � \Blank - 6 A�[2^L�hage=A�[Englis6Vnew�HAPI}r* .a"(�}[ 7]{&B 67lgorithm.16+xio2'2#�TICas�� clai.DC6D&�.'2P(6,2&BXjec6,:X(ary2,6+ri-No2�2+d�0)WD2-u*E�>'ercis6( 2PlemmaNL2#no� &N2)proble.�P >'�S )2/remark*R 2%soD'S6)umm6�S '*Lv�Hof}[1][Proof]{\noin�"�D\bf{#1.} }{\ \rule{0.5em} } ��Jth{1w��}{6.6in(�e2hsat}{9iA�(hoffset}{-1>8v2_7�<�[title� O$ing, Posts6*i�_nd�ba��x4Polynomial-TimA_�author{Scott Aaronson\footnote{PartPP 2don&4,4Ia �0u#��ta�fU&# �of California, Berkeley, CA (USA)]*��SF� ZFeb#ship.}\\6�Adv'0d� , Prnton, NJ ^\\a �@ias.ed Tdate{}7�ke%W 1q abstA!} I�L6��ms�)5ly�v� %Yum [utBA6�%�t:=� quotedblVC p5�Ec�7\e�out �measur��s. \ I �t�#s coincid_P4�&a� �lex�, �ed�Esf{PP?orvR.\ \ U�"5r��, I!�slLsimXY�u�o��{�5cntum m�cs et ���#6�- �te5� t1�!�# �C�ie�-� easy�7ol�(, a celebra�f!�BeigelDi0 alSpielm-at{?-:\rclosedE�g+,Q�awflG'�� g�nowzR � �is il��s)uM�%��*}yi3ne F)�r!=of�g�)1 futI� L�i@textit{Keywords:}Fu� "�a BIv,]�7A y��ys9{.,r1INTRO}� �2 }!|a3&b!OE0ar]�' ruv7a.�a�%am��f"�- �%qo 9o��s"�i� a Boolean} mulaTa23+��7�AA�nde wishu$find a set��"�/ar 0)�mak%�ef\ true�Pro7yd�I�5�'is!�blm�i �>ef�i�� ion:�E2yM!aG8�Fo�NtQ':��v!`� 5p�e�s�r2�Gi�7B��6A�In�ine�hw%�InI��!6�ostBQP.n �K ed Bb0ed-Err*�:M),\�'��W��E`�,!M! 2 �� Arp�� %,M?!�39!Oa. e�gW�3�,!� mainm�i2�1\�talA[A�ll-�n);�.P6� () �N|)��E6�\m9�ņa5>Si�� /8is��"h=C-!C T�,m�/n�6( ccepu�a?� t le#$1�IJa4il: ans�(is `yes.' \��&8 m� :�:�L� % $\���de��%��it{���g!��="�a�8q\eV ndee��}��#s �� to b:��I\ (�i��m�9!��/stf�0'.�$).&C See5```M0(Zoo'' (www.�zzoo)�W��b a�{2 E&ćU6!�G.}�UDCtiv GAFE�M�!Z)�$qc F, wo quite *�oS�!eaYorigi��+ p0 to k!{�u�8alٖ�A�  f�1sy2 v�e"�") �Areby ga�ins� i/ywhyF5A�!way�1. \S�p�ular, S� �fFANTASY}�m�*I,f�� �.�2na % � vert�D\ �;u$\A�j& ^{p&!��! $p\neq2$,#4�/e@"nB�M.non� ary "�.�"�Sco"si��ۋBY a�!^��^>�lee! ��\��A5I)+�;s#aA�ip(8=gan\#n we m%��dseM�%h g!,m&!�=��(c%� �E,&!�*J )��C\A�)��;=��t$. A/ued.�e=)��+dez;at �bNfl�E�,it{anthropic3 +�---�1�rg�ngs"�nw�*�*�%y �\4�� G� d(��ssi�o�A�n-it"� !�As�@ �hampC�unPp%' any-world��terpreiѡ�J�5�k�$ourselMDin"u&� �(� 4er fails! \ My-�� �t, � �%I.BR% que,2i^�M�� not ��NP}� Y�e), ly,\eN2PP���@�^ea�glDHc�en:N�\�!��a%� un%��mpl[�7  \=Irea�� tud���z is�q�a ,W �sl�-�%U8on)Yit�0}Y\s�%{B�alogy, A# fam�9A i}� er 7 iR2dyj2 �ŷ, yetA�i.(r�2 ima�u hy�)�hav%�v?�>�had ei# ers �Al��agJ��e�� oardN@\(n2A�:{ ness��A few �+*4�yt�\ ng i�!@i ��,�+ B*aks},?6edupo 00(!clog-sp=z 7r8gin">�g%F3-SATQ� \ un�Do*�!5l��uis�isg i"��!``:�>\un��} \WHo��ds9����E�� y[N s $A�? $B$,�Ve)"4��S g�rg0n\X \�r��nif.u�<do? \T 5�I f^ lqYswe\v�,aff�'��by~�Izbr�Nwho�+r bbr�-2Ct)�O �&����Lnad�v�.r�o�K� \ oracl�^ no��fu�;anB.�f2�qu�}�j%2, n�2 �if�"��<th� �z���!�B0-�b }\�/e�>�-!� Q-U����iz/>>�No�<�=h a�s trivi|�2�a�=%�2� >EZ* \ S�fa������ �=2�, immediately*� e1C\.>J|Cm992i�e5)=%� it�> 62�>nEit{��}> =i�e2E{�@se ou �!(! uld �'as%�!/�jv3���4]q^ne page� ,!Y5u/Q Ǟ�vs��7�@, heavy-duty a|p�2� lthoughE�1�<u?m� Ri:3d-��)�a.Jsimilar!th;ɊrN��� b&ex�ed}]m A���� is b�; chapO 15��my PhD!]s� lN �}!�S2{!�� Ys �Oe� nary�a��Iisc* before I [7!�c�4�<��X�6A2� .'e2{Re� d#2RELATEDB�SB:$,"%�I�. non2� E�"� .~d:} 1)� �l8!�#' Adl�3�#Marra] nd H��1Edh& 9!N� bL��ofahN'*��m� "#�~ 2nonW^D �* J Then�PM�re� �7�&� 's, Fenn����� fghp�W��a�Ia�sf1eq�2�!B�coC}_�Usf{=}}IP}$� Uptu:�� I do_  ��&a� ؍��elp�o+5� .��% ^�\a�2� � ��.'ob�d��( Also, Watrli�w YCY�QMA���6�& �Y@B�U3verif�s �onvq ٔa 'Q �1��Q|p�"�o �ie4;`!�!t4��C* appa�Uly weak�?0�C�, �$I6Ah !ov%^Naveh-:an��Not�,ll!��3@as�$conpDi:z �v'^2��20a�._ recur�j- hi < V �. :�Terha-2&v2 �td}�d*C��E��st}1 dept�� q�T�obably ��+ �I I��Tadv}\ u�I��j9�BQP/qA$6wbseteq�"ta�PP/$\.�nyA!A��� !6�\�<.�2}adv�V;lsoVI w���n>$HEfA� J.I�adJb;/2GťYN�3 iB�'S��a�9 ��upath}� �%W}H��(Hemaspaandr�nd� erauf-�hht�R Ds�= some��D�a~ei!V����!\ :�&� � a/F�!u� M�for":blog}A?:�A# 1990E, �tI�Kurtz �M�h�\6�2�by (1vf�q_ �� gly .��9)*EaN"f[ �t5 (3) �;i�tu� � 2��W�f��mptJ!�soo�<ereaf � 2"� succeena کi.�Xroa6��}&� seGSv��uof� x's "Ba_�ach---��itE�aEng �C"�%Admitted�LiM�li} g�Ep�v a�Q< �'sM�A)3!D� Li'���j"+ ���F� )�� Lintui� !�KK!�.� !�C�i=��:� POSTp }��wAJf�K�2k�basic� iliaA)�19�B �in &� *� �WUYu��~" `)m�rBer�N�(nd Vaziranim�bv�vI�!�%���X��& 9  lly!@b�X2s+label{�`bqpdef}�I���of =�uvP$L�Rŏ#\{ 0,1$} ^{\ast} �� /7uA�un�)m\"S*Here ` '.3::%z�_�.�7�s aZ�5mO#hn!�V�ٲn}}I*@��"q(���{ �n}�_{n\geq1l  : e�$nputs $x$,"O*enume�'�tem[(i)]�M �!�ap2$ZLA �  0�s [y\��\o�s)�)x � !`��Ch a N� nR5!�Y*�$"E`Q`A� ��$If $x\in L z�n�/& i�.� q� >b�� ۹ �6�B� � S at l�#2/32�����ڽef%B���$�j:�Ky$1�w4.U�4.� �L"OI�u�NP&k ����V  F��= ,w�n��TK obser#sddZ� �:����. 6��!sum_6I � .UH.zZhj�\A4�e>7\im�detail:u�p�=6yadhge��� 1bR>�*2H�.� } By�ulCSh�@ shi:�P�N�L�AH��?a�7ty�DEr�� aV��of Hadam���ToffoliDQ.wPuX�q&� ��seY:��� r, s>H !i4Solovay-Kitaev� �,S k:ec�cr�< /�a*�[�!itu�.F- c�|~V�Bd7 G � � .^�`�S��_{z� of �Vzs��2z\r0�5\%�be wr� � aI�f�#*�P �"��M�nY $�,1},\l�A,��of�� "�  real�W%�u��+�|�%����8� t�T.J>�� %6�aض!7�=e�(  ,1}+��+�y)o2}=qiij}%  i}j�]�`A�7_ ��:!1%c$SN�V��2�ver8& $z$*0HaPxPX&2K bK RK��\ But�=d3�U:V.r-pu't5��]M52�1jc�eg.6R!5&0�u�"���� �i�$the ledgerR\$fa�j�Y�j%5�Z�to�\=Q���1 of} W$ robus����t$RJasZ� 0 b�k�[ �� r*h� �<��Soc0a(���#s J[ easiC/ǽBn!�8� Ľ�VuJ�! Whenw3Adw�oA< [![���$jA�e}�J� we�pQgp CNOT ���In*a�U$sh ancillaOM �i��iz!mo.u :� C%#5���=2�%����,��e8N�)�%��N".��Y��*:hB�/<$Chernoff b20��� � repeat2�"���%�.����im#24 b�( e�0.< �, 9 ;$1-2^{-p�un\r��) �*� _&�0$p* A&5�!:��2� a4F��sܴ �3��ertiesA �o:J 0Z�"Z56{t.�nd�'�#!�* >��f !4R !,� na*V�"�F&�0\Vert ,}\oper9Qname**[(}^"�Q}$]2S2�% :X�W\�!���W4A8so.�82w&�0\ �q �U7�^A,*[! j��!i{6�!q �!��Y: C�%ly�D>��I,P�ci3&9  symmetric��z�e� o"�\ ��$x"+AQForE�A�'!6F!\ �8$L��,L_{2"�> $;!R��2N�a�v�G\cap K�Run� fied2Is (��2� �- $1/6$)�C o��j ��%x ݟ�D��!b�(s;��� !� ��-7 .^����!�N.�iW�*,.-n:�`��Q�of��� O T�4��s]�0A�"!any}���!J�e/be�q �rbitrarix�� er$toM�����?D"�9& j>"�haj bqpp�4:&"e�Mz?:'�� �-� E�.�!qBV��8%�� �/%A��f:X 606+�� % 2$-4*b21�ble&U9u#���let $sD� ] x:f (  ) =Z��� 6�E�jg56~N9"�-s<2^{n��or $s %�\ (T4tU,c1�h�Y(guarantee u;A p m�4!�s>0$.)�8a" ��Z/�(:mjpro��<� n/2!� m _{�%R�} �x-�-S ") ��+5H� �AbramdAd *M�a''A "gC�t�$n$�*eͅn regis�� a ]\"gA� 9!., over�5x. Z Z�w"/1˕:oB�:���� n���?a�~Ba B B"i-���6��r[*�:�2E=�*�7-��X����I F*��$( A�}-sI3A<>�+s>*�|"BV :+s0}�Next,�s�) v� /D�,/�� �<�5��H)r, q;$ /� �:�B +f#�k-aHB> $�Pr)~v*1sqrt{1a�!q13-� R�+Z:-2R�:�v��1� % \]�?Lz4�a&_a� .�J$�ߡ�!�m�iX:F[6� $.�!3A�A:aWd�=B�_{%�/I)-m1�1�Et ]�BE��)�mae+%�( ��/2M I�( i�=�'}-�.hh. �S ���� s�$���E� � l�%�w"i���D�4�i\i��[ -n,M ]3�c �xat,c�ڽ��-�=2^{i�%T$]k 5�":�*rA�Rv +)fY m�Z�# :� L) � 2}$:B�>l�+|r� P k�  � 2}q�$6}}>0.985.a��I �� /s$ PI&'��n-} re m���mG7� =� !�--!�9�2Ur��=�60+1}% F�f|��A�it�@�%u# :�A%V&J�d�  (see Fi�� ppfig})��Nwo��VQ�aW��� V-R��2�Hq�nX =i�2/3.R:+M\1n%�n�-Zz+1>� |6WF`�v�� O��� hand,�l��a+�-� ���� ^Bz.S\leq0ٯb�>�$\�iJ2�oy ir��E[�l2f%RVF�2! leq1�y<�$.%1VpMACRO{\FRAME{ftbpFU}{2.3694in 86�P({0pt}{\Qcb{ $sq�!N}% %-2re� � ��FxO](i��� � A�e %�Ku ' geY*�t6R:�i4�*%*a� %B�:�-2��I&�yxjDs). %\J`��)!a��?1 (d&,��s�/ %��6�B�I.}}{}�b.epX%{\� al{"�' "qbt JWord"; ~�<"GRAPHIC"; %main�/-aAt-)�TRUE; FM,play "USEDEFAvalid_fR"FAwidth Q; SE&Gef/0pt; "AG- 8,10.3511in; %+- B7.755 crop!� "0.2690�top 6428�� 7721(b � 2632+�� '��!H';-�� "XNPEU";8 %B})Expan(YzFz [ptb� �< trim=1.7in 3in 2.770122T^ �=2.)?, %)e ]% 2�"J�A{\&� Q~j�$Z�E�� =e[2FB!�e�Z~ f} D�.�v| V|���cv{��s+��%�'�5���'Q %EndY0�'.,,%)( r whJ�&$ � n"���PA (!�nfk)A>��O�D�Ur 7$�:s � \eH� "��SBtFt*' ��2ex6��r�!8'�b��bE0O 8&��#C ")ly.Oso  $"\R�;� R�SuH&W[��&4 /a�s��9F�K"gcMecha.��-FA`K�.2B�4"�/ J�$ory�D�"By�.�#�$R�#I�EkI�p�@Ovceij4 ���,o�MK$M~,�. ALm�yCM�fewDpbsa�ANx$ ���E�Dq ��� a no:6%�lF .�  n�YboJw� Jhow per�:e�&����0S^MoϷI���a,^�an=w��%G�4!R\!��` ng (�a�J)��Ka�e�8Gn���t0LtDd�$uld�h0 lu<h!co�L"�F��%�'is ��o�C-j��lt���1�hgnB�z-Dickror�0To�( I#�Q,�H}$&HFY�%�it{XA},2�K an )�:�=ngy�&����I!w����Sen���.senE�!T\| W) T�>a! _+��Z!�t�'opimE:�=�H, G� on'sT�oN>g }* \ �Q��� d�5s2M��#-�*� �LR.�XO �deu�j<:dec,zurek}; arg�b��Aj�#+c5ASu:o�Lxx$j s 2o (sayE�&koL,A.�r �9isl,cfs,9Ry��c. absuNiJ% � n�,a�!�non�i?@A�3�k"��0l,gisin,polch5oz3a��@-u)AM �>�C�  s��o�+la��o���'Y�I!�*< oNi58,j"�ggest!y~!��a.EY}�ld,MLt�i�@D/\PPnx$y rol����a�b ular yA")�� al*"��9uva{�%6B�,e�/ bui�FLA �erN ��N�� 9"uNl�  \#V�Ni.�Q8 *?Ay��'A!xi� �}WJaw3Y �\�b��Dne fault-tolerantl"�\\! Q2MFI��9ypI�9o$��F��[�y $1$-�< <�Xn��D�*g}$0!%��5?PSPACE* P�8l�D �%�d��&�)P9!Eg(r�&x5oOc=���0�^=`B�.�/ One ��2�Q�arw�!�w�a) look�?�=fo�)�Oi�(phPr3�!�"u�)&V6u%>E��_efer,x2� Sin)���e�&a?_6�S �,[K e^s�T?�gos� �)o��!Lilar 2^�a2͋%:q���is&�arHT'��me:6&-ɏ:�5N�e* �5�K _hc sf{nu}}` bDA��&0�a`$�f�7,}$ed-E��c�2� -the&��A�� jT" �!ix�$2q�%Nit{in���}l��z*��s,�> t�Jj�U>*I*)IiF2 \I���._{x!?��ac�2n���*hx\)�r]�s :s=by�1y* \�_ C��}s�:��HiYj�+ nuglobal}�N#�o"G,hof}~Bn��Ệ`R #\� &h-v�6"A=e)2xZ�6� adh�4HJ, ��:, on unitarit�Hy. \ For the other direction, by Theorem \ref{postbqppp}\ it suffices to show that $\mathsf{PostBQP}\subseteq\mathsf{BQP}_{\text{\textsf{nu}}}$. \ To postselect on a qubit being $\left\vert 1\right\rangle $, simply apply the $1$-qubit nonunitary operation% \[ \left( \begin{array} [c]{cc}% 2^{-q\left( n\right) } & 0\\ 0 & 1 \end{array} \right) \] for some sufficiently large polynomial $q$. \end{proof} Next, for any nonnegative real number $p$, define $\mathsf{BQP}_{p}% $\ similarly to $\mathsf{BQP}$, except that when we measure, the probability of obtaining a basis state $\lef-�x\�\rang!� equals.�( \alpha_{x} -Tvert ^{p}/\sum_{y}\lef R.yB. $ raE� than.b4>b2}$A�Thu�]�% _{2}=.*Assumea�condi��ed on =� v�� The resul%y to increa-�\��quotedbl��@ probability mass2"�:!eacaw3Ekzp\ from.��zB6(% $\ to% \[��K}\cdotl 2^{-K/2.> ��� =2^{12c 5�j�@-� 9�.�]�:} , \] whileBRN?B�notin .�H\ remains unchanged!� Simi�@,I�>Q�:� ga�t2�.�U�p-2 �f� 6�2�>��.��This deI�s� >y�']E;�kEi $2^FfA{�f-�'$,���& :�:�Z"�0final observa�K i!vatoR> stiO(oes throughIa�y!�For it .d (distinguish� case$\ .tel} D+|\varphi_{2^{i}% � � I�i�>0.985$J�S >SjQ(\leq1/\sqrtx \Lexponen�ly smy.�(of error, u" , polynomiall�2ny copieE�� �@2�6�:�%ZBut��can do ta-�any $pA8since� . \psi.2^�|\ rules behave well under tensor�ducts (i�Msen�a2R�.\betae e=)���"�.!:B $). A�inclusio�U�"� j! <\ follows easilyE#�U8techniques used/ BernsteinVDVazirani \cite{bv}�{ show "� V b� a Le!+�Kb��seJ accepaIs;AnK plA0 mput� \in S22�  _J,� d $;�nN>:=%� = see which�greater!�N� ! � 2�  e � "e Zd ,A�gener� ! �Pof Adleman, DeMarrais  Huang-�adh}, �handle� �o $p=2%�As�Propos@ q adhgen@1n write �amplitud!�%t!6 $ as � 2 mi�ntribu�X s, $6 ,1}+�s+N&t j %i!�i^r�� al real n>cE able� classical�s time.\ \��n letEfI�R� >�,>� test!�/% align*} Qhi.vF�!8\:  & =@A�>A5n�O\\ ,_{B+��( J_{iI� 1� ,N |} }�,i �) �mv`e�By�j^, ��B t p=p}% %TCIMACRO{\dprod \limits � B}$B6Expan��< {\displaystyle\7B6 %End3 �%�1�isq� }�z�"�����+��Wi1ѓ.��by sepaA�ng oui~ve�p n&c.5 $�5 �$$, exactlya�inb��� \s {Ope5blems�0OPENPOST}} W��oA�}^avlex eses剁.$haracterize�quantum Js, iwR�v�?answer!&�xmeans? \ A first step might be � rove� stronge�o�� pertii��P� ex�� e, lՠs\_{E(sf{\Vert}}^Pos����% of  !K solv�� by a}�($\ machine\ �� make�DiSvit{-@}!+ry���istq a lis�C��g 9`!��$ oracleA�TheL eAk�s)Vj  e$�b? \�dih ultyA�>a� seemob�A]u�� garbage q�s aftea��{ �f\ ��+sAlso,%`we��N� � ge�?pleQ�!�of�vBeigel's�  h27]/ NP}}�T��b��zrelat{to an )�? As%�fantasy� me�ic�� �eR  oa�1�! whŢ6� �=.�f� non�|�d&KA&4A natural idea<-p!�udA�j$\!�� would!�to usA� TaylMera�e��^! aU.rE��u�K \�>*pi�:&bra&<&|:&sM2BM\!{}_{\ �6{#2}}}>Cj2].V2\!Ewf���z6sBz%Jlk 1�L} \title{Asymmetric�$versal entEa��ph} \author{D. B. Horoshko} \:4l[E-mail: ]{dh $@yahoo.com>ffili� T{Laboratoire PhLAM, Un|`it\'e de Lille 1, 59655 V$� inehoux ha!.> ,of $\frac12$A�T A�A�Y1� $ . If?denot� *of al� !;dead !Ho|D" )� �v� and�傥�d �q�A]>i<|�) pfZm�A� one %1Zh�-�,Bl�%�4transforms (up�nor���[) like� �6} � {2}i %+}\longarrow!N(+1 ;f !T�Q#1� ndu� ��h E�of Eq. (p"1})A��d L�z��!�is 2�1) %M-D 6(!g>� act�`` ua�m�'' ��7 cat, beca7 theyA� ��e}�mselves� B� ��~ g works onasi�Q�%: B�``%�$''. Indeed]we�0 ae� �:aabox�ߥ�YAE (s( ca�%pA8%UeB;d�%� ffec)zA}) w�b��6��'+^�,�%2B�A6!C%Pe�n��<�&�M� �&we\e foun�"W&>� Ag$��:,i�#-��t, i.e.A�V.Aws�$input�� 5t#Zs. All"�$ Tw , iA��.� Q  sh!E� feat< �l2'sQ�:A"y requir��>Vto~"x in� e 2�ɖs�+�bite ``M�'', e.g.!� vacuum)�U� sub-harmo�nAprocesE� down-{0/QI}. NW thel�!��%te��! / .� AYp� � ^&t view!� ᒅ� possib�#o[ig�{E�-*q 1�!ƕ= ] V��l�zero �J� A>< c>!i\I. S6q ?�� importM�"it -clarify%yoon.& � %``U/�''%D.�!�iCf�lo' !t non- pr"�ofB�IS manip4)d =j��&� F'&!)5� %�_%�� 5�m%.ap��mni���cOE�Q U��"Ym[m0�3� � h��"fu� Ajn�(�moe�o" !��a�  � tu�A�typE�q$eavesdropp 95Xcrypt$%�)a me��' c7�Z� ad Q�->sb( !*(�".+) way)~b� �de�by Alber � }�#Bu\u zek�H3ry &(SymmEnt}. B approach�� im a��%��&mK s (h>+!� same�!��)C ei� anti&�)' � �"� � way!�e lat�ypEM`)�te-�� % recently |�+!en{� 6jE < � present p� wvelop�alternf14 �����1 %7M��)1EtoE�K (cf.�nd�� above).Y!a%�equ�, � |can��:�K��seL-\�"�*�+output,:�M�!�our�.� M�I*�"1.� F (AUEM �we; � �-�o obta!��� triv� > we n nel"o �%�d�+al% trai~ linkA� �!l&eW. OM�d deenMer!Y6>5a��Q�!o� of Refs.MQM�~ 6�)be�Ai���next S� on�a Iz�� truc�d� y%.�Sec. II!^p:n��.LI E� !Iex��it�(�# a>i }�a $d$-e��$mua prioriN��5 3/![�!�.� �V!devG-!�1�t� m�yremé�-�X&�,�Oicular ��s!OAK� ]�M�s= cuss9�li��!� , inQ� q�ic�417er6%,����:= +$UCM,UCMopt netwd �}%HY ?�C@, 2}�2[� ^:I�QID mA3�E(UNOT) - -, �Y~VA� turn!�Js���s2woI*M_s (�)�� u1*"circuit�!�Y�1��E2�,�� �9Q>�s�"ztB*.�onEM N���Q�c�re diMo.=D&wofQ�} )us �}��cisel� M�!m ( estE�vl.�r�ig�g�� $S$~!- spac���&H}_S$ d$ "u� � lh�$r��2� $ [+qAkQ��A$� 2�� �A$! $d_a2�!�k1it{�w};�' .� �)O� � �Blank�W% fine"x�1uCwal��ic �tak!�s ŧAk,wo �)D�(�� .# $S'$� $A'-!Q�*� =�of �-�d�)5.Oufu��A>�$often omit��m�n�llz�IAs�e��``I`" -�'' as9-�o /�A��ne�arz,�5Uobjects � e Bh"A� d�*d���5���the jo;5)�!%i �� �} ���4Q�Psi}_{SA[' ��a� �ws !��  -*UQ��!� � k A'$. T&T &�O -*)uUJ�we -#1�e 0nY(ai,5i,5 ket{��t!L!�I�-V22psi�a�epAm* x��i��ve S9abi��e,� �.#"�#!K=� �%a good-(�'of6���(Bennet96a},�edA�(von Neumann6ropB ��  a�:B�rE} E=-Tr"4\{\rho_S\log_2 q\6�e72%||d�ty�%b!�  ��Iɡ�-:�썼b�rho!t=Tr_A��"I a\;\�" �deq�}� �%� $E$1g� \3) va�%���+ $0\le E)7{de��:E=�AmaxFly"fd��a� $E=0�&A��&? ��s. No�e�b"�5APB~�}f � �a�'�s: &$ sh�� %��&�!=�Fw��qwH� &�E� � satisf� by :� ith�B=d{0���ard� �!R �s�I�� 5�U*GQ�ac;b�ma%&��_��=�{\�4d}o2(m_{k=0}^{d-!_k}_S DphA, Y�qwjps&S��%;$�š�se< ortho� vector"Afe�� F� 6�829� -[ <2��ofU rsI"&?�()� �)С�iM3� ard]Am�>g%(Q1,� 2 U�r�Ref:H(4A?�(�%� / })2� 1>Q�"<y ��-�, bute�deg���.Z9 � s�� �� .:-�)�� mo�.!I�d"� Jdo so!lB�(i 9 f!ity''.|�a� �2z Ʉ: �6�Zing�6`` mbl� T,�5C��be%�MA���AsŖfej)��"l so-� J%-�Jozsa94?�3)22�" ! �!g0 h^�F} F=E*�}��u�F�!�wz ������cof� 9 }��J�&a{� )���EK�5!u3m���  to B#tt@fS� � 0#u� -^� �a&� �"_�&0 9 �OA 7e�[0�r56�7� 2e�o�a"? b'c'da & ��&� )]%Y'.� �E}�5y� Ft .>+�6G_s"�A� 2uO n"�e w�!4$frac1d�e��)� n� Eq.~Ix )I�$E(1)� (�0n��<şJ t&2\(I� m�� > �&.��"��5%a c%B*!}� cs~a7��byS�s�s�C9 @�\:b{��"�notGo*(law� �&;3A�5%}per=" KAP �= Perf�&4 1A�n/<>5}�)5� [s2� ``1v�P _ (im t)���aUCM�*�V�&G(}, phase-co� �(3ers �C �&��&�! 4, :2��f�>�%ɁTbe"o X�!�I��'lem 6b3fin�"e o=- -K,.du�'� * 2�!�a-en��*(,+=T86 �1�&�^�=�u����M"�isy��analyzM�2U e3 �one. W4Cdr f2-E�( !f > x.J�t)� !ist�%"�6��{Pu' 5�e�_>!5�-���a��� ��|V�!' ure.b@uF"N/ ��� tz0�Kix�& �p�t �?*�Iat&:[�� )# c;J�� �0 .��6� �$� v��.� I��� �%9 a- !?.D��),m�b�?�i�d&I� � �w�F�;K9nrave2)\��~ r�� Gs!@ !� 6s��� e�;!0n/�tI�>��0G�?orP- �9� � a b� ��"�,E��| u�E:R)%�a���!�� minimNis�kkOv�lly�u<Pa2�� l�/itsf��s![coincid1MB��:REI+@eni�a�I�f��aup�bE,�Ull����z2��s6decki}."�*Z-22of\M��y% as $EC�� QG�D� ��km�m�E� O}�a�}$QafcOOrk1&�"� + �'6�t�P�� y��r^a�+y.,ube!�i�o�'larger �]Wse�"�$Z$>ad�E��aJml LambdaU Z}$ �b�a�,N �aE�" U> �s, �{��5PA%Q{Z}W� x� �\Q$. It��F�hn�(%�)x�J�!yA�� ���A�:�&-$W$AZF �AZ}$�EN%w Lemma@�~I۹O)С�j'aTA����.=6EwalwayA]~n m���8 @ a bigA$-��)� kR����>?"�<tJ�!� O�) ame 6:)EC:Oe/� �} �w�R&�"Q#6�B �O% G�%ny*Y3,>+M��Ften��4#Schmidt2om�ConBb�0&c�E�1}^d{\lei_kI�e �F��={7(,k=1,...,d\/an .��QA�WQS$, $K tzK �@of.�2TAE8�R"��8av� \ge �A7$5G��!Slex s (-n coe$B�8s),�4ayr^2aT&B��)~�Gk)�|�|^2}=1B�WLep�� 5�� B�AR1|\ge2....d|� Kɋ6Q�de! � )� 9��6�asFQM��6�c6�b�c_N�.�>� ��c>�c_^��A , �3E})C�#� %�F%m�exk&qaf8sum;HN@�B]�W�b,H(U1|^2,2a�!)BT�FZ H(x_1,x_2Dx_d)=-2�x_k~x_kJ�is Boltz's H-J.Y � taska�tol K �!�2�H (i)�iz�E�� $F� (ii)9 %F2% E$. a�start' lv��t�9&"� �2 iderd zas"�4?co0 ` sp6% V}$ X) bya{2����{M\����^ s EqsQ���),M�c}�� order�� *$'s�Se� ���a sub�� V}_0$w$|cE=H Now,!�=�;W&6: .�^2=-�!�.j:F�_0=-FMF}+}E�5X3Bd|^2)B�P Y�A��ZO� �a��a�l19 k by29_1$� one-�3er5KA�.g!Nw 9�=2� =...�R(1-(�  ()/(d-1)$. OA��-� $Ep�?� �4xu^ =h_d,�(�q� $ !0I8n0hpk<} 5.�-(1-F)-��{1-F}}Fa$�;A*1M�%�1e.�2 $d$ 9�sum 4up�}�\V�AQal5���iy�� stri'MSW�� $1/Y cY9�a~v10$h'%]= �[%/(Fd-F)]� ^ "AI�i-Jgion. %�� �6e�2�E���4YZE$@ge F$ holds (from��ũ�"g �i�9_1$�'~F�!�A�0��!WvalueI52�)$ {%mea1�l�1 ). SvU.r^� $�t*� t $E$A|6|F)=E_M�h}A��2�E"um%��)I.\we6�,� >`fixC.` $E�?�$0��.K6{>a�6�(٠$,!�a�2h$F_2>!Y�.`!��T�HEal I��gE_2�I �")�2)`_s' ven e-. I�y| 0)��,�} �y.��gi$ $max(E_2)AFe�aa��%e �IsisU 0CE�5mhigf�! . R\` le�9� proof. S�i,a �#�*d)V (:)U!�&��;Y�� L i1e$AN taneously�,�.X=@ si_1C �2� � �f� out( P�+=\a&FY@@ _*�1}_A+ #>x 2���F�&F-� ��<.j !1 absorb�� b�\�d8! US �:2A��V!%�J , ���a� nrefor��&�4'��-\"0in�% _&~! �9n �"P( B.�i�],���a$ exist��%�:�4 xibI2s�R�d2'�.y�ary���:T2�2E �& look �P&��!``seenV&/2C�# *8=  !1yB�)�-um�$nela�ich&�l�a4 �N]!�� cEa �)�Sщ:Dm��@by  �M��B A*r�,��1��b�depol} N(S=(1-\pi_s)Y��+ m�#}d}\,U�"^�$.�NcVScMtoe�-��(V$F= �+6/d%h@5ha!�"� by�� ��Dw'``ari>5 >�1!�"� �var�%�0�1AY�=s.S ed f�;''�T�po>o?�=�4ak�9���r%��� fo��(u&Sa&r-"�!�IsmA �!e"� UCMd,&� ,�6.y9�":i&�yMr ��-mis�Y�@pur�:�GQMe�Slm��":2�<Pauli"�/s} In�3�@�$v�=use9TtD;� !�ualism�.]By�:lI�p�V"�s 2.2�=LF�H}.� &t6--�f$X} $Y$!(i�� �� H}_,.Y�/$PWl�1�4� ���.���jR Yj=0%d-U e2�-baVV"�[@V�2�(�in+8��` &;2%� (GB)��2�X\o�^s6 F��gb�g{mn*/XY^*/j"*/<{e^{2\pi i(jn/d)�!8)1+m}_Y^�A� indi�6$m-�n$dM s�H$!nKte� A��(N��!� _isVn modulo�<� �C� ��gb��E"o�FtH* mutu�(o�/ gona�6us��_RQ2r A�R��_$d=ULhes� �/�usualI i�9Pbit.�n�a�SA�)�00}:�2�^(&0)�06�H1f)\Gv*\Phi^+},MJA� 1}\\&4 _{01�m-R�1bm-2m2:m1��16�0R�s>�3>m��16�bm-}.=GY�51�� also�%on ���:eR*oH}� a~2A,�W ] [Fa�2� � 2� (GP)0bU u} U_{m,n u�a3�7 i(k�7k+m/ N^� .'agAB�o&m�%w $U_A��\i m��}�u})}ab"DF� �U_{k,l}=+k,n+l}� i(nk� -�u���E � �1_ �M( roup�2i"@3�&"Wey =� ���E&)1(Heisenberg M�|�q�u�\ , GP=T�'orH .)�spi eI=�Q�!`,1M0)�0Y�braaʉ0$sigma_z,\\71,0 717 M F1}27x7n7�8:7-i py"��B�2Z GBb� !_Sn%x�CJ �"(�qEh���m,n�`6�&=&�x� e^{-�V i(mi�^(U_{-K��Vt l�")K��N]�Pf."P@ � 4of6i.�m�-:sumu} �1d�!�{�%�ho1�^{\daK#��� ETr�;\N o-g!-f:� mA� iden$(>1 �i�X�|nJ|EV[(j-k)n/IT<]}}=d\delta_{jk}u<- Yet"�H�4er^<�Bu!@Q�%4I� %C-N*kl}}=q �Z+ml)/d��$B�M�,]Ɓ�icnF A�� �.�)�-nO%%�"eD.hI�:�Ym7sE�� $Y� t"�uuk�1 id})�ygetB� )���`�-@�� > =d^21�k0} l� )F�7BFor,> � )ac�Z�a=Z�A&a�x�� �IMbM�aiA*E����6dń�F�!Z�{Kraul�!��� } U�&' �)�a�re"se6@� hNAJ�Mf})���� ��1 Preskill}b8�k�"�-C� �K� 5893} ^��B� B�-�k} B=e�\{*� {lcl} aED0},&\quad &m,n=0,0� b�n2\ne ] KI�B�a�)Gy�a��?"� s $a.  $bn@djin%�ir���qX.@X27Q%�/�~"=1e�za�-:�^2"� a| b)�}/d2 �:. �r2�Kfs �1�A\M�>� �!. *, namelyb~outQ}e�.  y�H[\vphantom{\tilde KQm ;�)�]h�?nj+�W.�(R Em#�.W2�f�?!#-�WraA forw�ztoriTa�tmd�7y�5! ) ina�})l :)R)"Pwe �fYa &���st�9A�r >r+1 -��!�;��(Z�").a pairm>�M2�EB�%e��\6�,n"�u�s  - ed GB=�W aA\equiv.Vcb�phiAu�Qnn� e^{ibvQ�s N�&� e%3-m\j27���� $ �0s�@%?� !�!�``�Jtu�!''!�D#B�-M�:�.�b.�"�-M"�&k��toA�qy ,� y(� �hjTin$3���!�3.�q� Fc)k�� XY} )�(a.�+b�m,-|"� ^{(S)Bk ^{(X)Q� )\no�1��)�f _`�M� )�!�3index�--��e�{n�#sSBbf�my� .sż�Kt�CAL��-���? last&W"w�bt�B9i6� �X=_%9v=M ah� <6 P=� $ME���&m} M=�m+ y d\�Het!� {SX}�H25�F�comv."? $ d��!��<  $}�.N�1� G&=&2�-b^�nP&=&bd=\8\;*�yB���,!I�Ogin&g,� o J| � |^2+�2dRe\{ \}�)b ^2=1B<"B�*�*a�"b y}),M���E�M6/&.�'Eclear#y}e squ� roo�!�V� � � �� e>�&.y�&O@$\ ied below:�E, encT9} h8i8)�c{ur"� B) @�_ bP; Aa��tgl�\�'isy�_�{,w@0��!%�3ue�77$�Q�!A�+�!�!i5:�a�to ��!&� .�#.>�q�� $M$,�-qb�-Ym���[]x"�.&H�UXS\��Ye`.�5&'�R*�Dp�_&Gc�Wc�Kc*/8���>��Dit�% ��a s�_!Z/?ui� 8!:�.W}$ sp#  <-  i�EI "* mE � " !�A�M*�$ IEmer�%*� .,k&d2� �bsPY1�$.S&� is facP:w�1�cAw�Cndb 32} ��������o^$�*#.V���0 k}_YB�)�!`5�=�� �"yR �E �)a!&8 W}�:Wi�.9cal0=�.k �ta�&� ��q})B> BPXY�d k}SM&M�l}S 9 2=�k lF��E��(U�.���r r�I.J9���&$M�6iW,��e%j�nn�F'j)s ��HOaiq�M$:2�\l6�hY�$"�Kit )2���{�V�^3-5r�9R$H}\setminu�YJO6YN=A���)map!�e i�:� $ o)|�:فJV] � iz�  by>|F&�J have��v�>�'.�M &V&�J�#e3q�� u�IcY40f ���"A=C�3rC�D7YB�2�� dG��syL�j��D� �!%�he�qU+)�$U_�bcћe�1"d�-:�U�nes�$How\z.�!�%essd |)�X?�_���t5g AUEM�P_"' ��I�&;B�K6� � !"[t�B/ �icB�� RK��\"-�= ��c�N-_='���[t��q �"�� $%n�']J!F��:�=>"%M�Ճif\I G�z K�~u,\nu�L$g�B� ��alt:e\mu>g\n.p\ p-?s.t &.�jtheb� kvk} N.t�\�?%\nu m n�}"W 6$B4 9x ey'%�9��L (Ds $(\mk)i�$(m n)$�asi�eas'' es).*< 2�) lead� q�.I ^��)�E��A171��[\n��] HvartheW �}j�yF1� :f�2,Z�22� A)��2 . )��a��a��@�rEqg 6�Q Bm��5M��>6� Aa^+J]aԅ �@�#�^�ѥ+>*  2)�*bI��A� ^��z�y�J� �Ir�sI�a� $ce. Differ�x�Bof�.�1s"� �d Y�>�@a� alsoa|�z�fny)=.�&�.�%�x2b �(-"��(of &� qaRl�A6��P��us,�8�e626 b�(�8y3�,�q���01f8yyg .%2��)�{R2z���,aBprQ 2a1� �^"�4� e!\ cal}�!b�M�]"N u"n'"�w`T�4un/ �C �/ B�G�m2���!�*�2M!���V� ma�G%I��!)twoNM ��o�&�! a��|��*� "/kb&,y �A: Q. W�e:2< %�5��Q}� �A� �SEfRest����a�� ��/a NsIT$ ``handy''aMn��s�Xit"���.@~|ng^in"�|*u 6��.*�8 K?cho�,�-12:we&c S�:|} "M�,����j�B7� �{ 1.� �.�K��e�`l%A�T1!��~#6T���B�\�s("Aypu"|Qq�threeF : $S$, *0.�( �*�4CD�``�XA��4 asis $B_i|@:ai, Nb� $i=S,X,Y�8u�T~P@�l>���{  g��h� �6GB:lB�^�?��/ `*r�J!� $B_XB_�WebT��b� A'�)� ��acA���i!�e�� hGSeC%�)�C& a�SB_X$aIM�!�&:V!�% ��G�!&�#�If�9Q""� s!�H 6�:r�*Z� z�e}_YB$�b le�Xa K C�a�9]-�:ltUi�ZSTinstead!�9Q?LwO 6L�>�2J say $B'_S}mV%,k}_S, rnV$!�� V�B��6s"�s8 6�s2�sE%0BB84,GisinRev�R�A�e" tehy�K� ���I!�s:Z(t message (S�MI�maj��R+"�X*[ticst��6�� ,Wfte�6imi"�6.5data "�/�" nounI*i���mim˙]��)@Nschosen�am��A>�n!Z�p {aa����IoFLer!�gLZW �� arid5M!� choo�\&n�^�5�.�1�K���%( �Y*w�Q)5�&4�?�i����F\o�4A mark�.L+.9���SX}��, �% vai�k�>2�* of-o*�*\_Xb;)/m� ��#z�a�=q�VD � CX�*�CX=V^*�ZEwe�$V$XJٹ� eV^*�:�;conjug)��*���Rnd~�KA%Zk > new BB��v {�Y=� �'umk){�%Tm"n}XAN-��$ݱSX�nΖu�=&�F�fH,m,n}{v^*_{km}v_{knHqm�� n}_Xu��Ym}J@8:GmG��-9�!$ �\ck}I_='2DaQ �=�l$Bzg(%�)A���18�`#re6�J�%�k>$&�mnFG,I- �i� IQ) %����Й^��q��iQ�� 6� i6�gX � 9�new S� &+&��ceFXY/\<\ rv�9eir�*25O�H6��V�.�wh� i��t3 &dyl�I�jO��-a|s�� .��� �t� *G"8 $"8)�h5: $Uu�,�� V�ge�M%p6K U^* J.� N�� �$U���I�B=�*F{%��asJ�sk67%�s �f8aPX$A7is;���_cm ]�e1��" �5._{0,0} WX}$ u�(:/$U-!*f�)u�q./.lk*�E�%_A镍&�^ O8Y�A��s�jNga.08u�:u �$�(-�)�/5�&�CS e>8%�ar2!L.�u�2� co��b9D�_%���|:J�rqp)[F�% B�%\�"X'���7��}S ^2Ō.�BdB�>�4VCX�m2N{t^*�5ps+y2�! ^&O]�Y-AN��BY�؁dY+9]K2.�0qP�2W�kF2���\4,(�E,��I3,&s EMJ�2w�Qn�M E �%�:m�a���A�2!�0Dy=�"k/D=-��;u:h"� �q�Q�� inaccurk(copy, or ``qd''P� �-#D cX�+�d) �� "�J"�'s.= h���@2�y�@T�� 8� �*6��;ݖ^*&�3^*�emerg�=V�Wl5�U8W)�x=�Q�%�is�K�[U�a`(�h`F�-��� or. �D���map�}\:�"� �Ano���A~ |�)`cvQrot�*"a'�I:o�� �d� roxim癡�z�rho:aCA;" $F_��� a�!�rho.��kS�_map"z Ȃ�e�x!<��winu:j ��ContConj&�F&o�m�)�|^2/d${s"g!e � b/�_�� �R���Vof:�ZE�"pr"���"� saq�|~ ;x#�q@bM�%kC��vgi""dUap�Q7fP \per/�c]�a�Vz&�G@)� !�j-"3)8'HQH�BO �)Mp (2(& e56!\(K{ethe/J9it{H&en CF�=\s�?y^�C 23}q\(d-2)(VV(�d2$V�  roj# $@kl}=-i%�k��l}+ l k"��ho�d �@� v� ��Y�D���� � It9e�to check�xb�z%!�2b=*}�&��H��mr:� (�=0$)}_&e�2]xmR?�/ �fi�naO?!��N�8 $b$�K�QedA���Ϋ�m� aH�E�AZ�Jt��e�a������N"thsyt� �"�H�i Cerf�%�kw?��&��Y�A�[� e bځu-��!C�rz�� {��-� (�nel�x. W��&'S�WYZ���vl�i���n��6W* N:� R �!���$Y%� �b.~(�q%�� ><�!�6A2�/x��1f��B�"�nnOZ��Wegg�@w-��L,����M:e ing,��vh>�:� �*� Qw� a.E 223�:F �w2i!d nn.  �=ngler. O�l�vor2�, y{ $)�s* ��"mbN-r��:"er�Tu�)a�re�TAd s ($"`tY'$) �%A4 ]"E!!/>� i Mk������EV �4d/(2d+2)����|a$���i� >&�I��u$uY'$Eڡ� m�s&:8 �$EA�e?� $F=(d+3) �; : �Xr|4����UCM��i�s�8!t���MX2nde��#2� (G)�"!��lyi�&�� 2  .�� H2U�8q�)�;h`� 5n&A*re0TP%dq ��OZ�!V��U!g-+e%->?qe?"�u<�aV�_1�"� a��P�<a�\� %c�����I�A1�@sf]�[��Ͱ��%$͏$X'�Z�z�&���"\ $&-H"�8i�Qey�;1$ N� E"�� ��= �3f��.D9_](�f�w�~6}�] � �M1�I0"MM  0"�L&�L&@ �B��s� 0�I0 .HYkenre ���b $SX�#!j: �2'w,5c"7�%�P��X }=-\/:AC 23}\"B�-� # XY+ 4Mw:�,5\}}{S�3L}XVBd JA =2^{-1/2}I�]9k �*L  �Z)3A6!B���@ wo�6�9���eq�"�oZ�cI}6�2i8E�Bn�5A|Y$:}�"���&( ᔩ $Y$) C���2�"9 >l5NO`w��l�a��a&C|6% =2/3��� R �!p���#;81 �'I U% �r��BL" W� t*)��8,rbitr�P$�XI"(!��� j*�a � "W~)1~ JL �d6X�wJ��&=�� �<92N ``�ed)�''��is�hal .%�$6�  (!� 0 s"G ��*:� )�� !`*�2/(d+1)$ �Qf � ``=���=�''�#hodY�$d,Esteem1dN is T��U�:�.>18!�(M~"!�aa�K�{N�"�(��}*{M�ual-�"a:� } So far�e-*�`Jg*�ru]P���M |��{p.�m&u��-F"l A�ew:t�-�advanta�yv� �1.�*~ !�",T�n!�nd�",Ag�<U}��to��#�iY�OS62( >�= . If� � N�`le�*�W!F.�e�ri� q��|XJ8l�eI1 2"iG2��Nh7OR$Xc M=diag\{a.\D-b+bd^2,:,�m:\��`�/\) 1FX%ecz&r$d r���&l!|:f�|&=&1hK>.�Db��ah�6 `!}cY�  _0�-�=Z�(phi0} \cos{4��{d^2-2}2*�{(j(1)F-d+1J�2���{M&A�^�,flim} F\ge1- v4�{d^3}5%!��,W&�Y2�A���.�^�V�e&?�;I3���mus� i�{19}{27�:r�e . I�c44�igC�o=�a��H1���'0��ngAa&�%�)i`U�O@:�;V!A@(yQ��"B� M�Qi\t60>W "�:�ON�2eQ�IY_&=&. !��k}1�U42Qd^-2I!{M^"8z�\��0p�����3�Ɇ�GOk��2��~Z*� ������*UΉ"��l�:���� ai*֞*���^*�+�&2+ingkteA4at"�t�7 m�"* %�K �M�@h $&� I�$� le%JAr�1:2�)Zt3intBpvBQ�"N��-��% +$F$h�- �W)e*� >�� ten f�.umG[J'( L- _0)\s"w 9!�+ }�LqjB6�Bs"�! 6`(BI"�Zcbe@=/��WA��>5O�W2�%�J�gTrd�.�E"d9&Y*�"qxU_WB VZB��@J�K�*[2PL_0}-b)Y�V�+bZ�J" Y�.u=2j�h h5�1Ma! r� >me�9�A um})e!��i7J�ܠ�.�a�� "�5GO"#Z6��N� C�=_1.,FSE by $kmbf{G}Q�="�S,9� 3wom:�����$B� j�K J�AB}K[&:����do}�:��!#7 P�n: �errele� "�O���3r� �l��2��)4..K �nd 2.�� 99���HS s. A�creėU����@*\jiݝ%� �  d1���!n�k� d {En�r!H�!P(}Yg�� 3� co�[lO������c!��2all t�6U��I!Y$�" "� 6�$�s&�rs8C�" "-V �.x, ��h���i���a�CA&F~/)"Jl9m��, to 2a3=�&cic��>vB� � } Af��.�6� � build�O!�H !w%dq2%iokin Fig.~�g}O$rizonõ line*;?I:s,� *�!�Xb CNOT�Ns���N�&d�l.W one ���` $\exp{("�z\xi/�A^ >y(�iy��� spec(�J $\xi sv�V@f�FBe"�j�' %X�$�� .P7�ref 4}#�4A�8 fo,J�, �f&:H&&��3��/4' +�;-R;-% 2;�f�f%f\pm�=s�m&� �h�2��nw���7, �:acqui�;NNase�e��'�,� ��n��"� �-$)$ �u)"EJ��a��!�� ;m\�_B�-m���e��eE�nex�a�CMHAJ"�<�� U�a[&Y �;�!0"BtO�'�!c��INI�C���)���LX{#��6%9�$� )3� )�Mthirdi (��*�J@mNO �&pBC"{*!?(h �M}�.b�SDfigure}[h] \includ��@phics[scale=1.0]{!R 6.ep�.cap�Tj�bel{g} :~-r�,� 6��)7*e=d( ����� igen?ID� I*I��L)S$Il��$u�o�/ g�LF�=- �/4�=wo�P� �.�RԹv& ��ar)$z�xbTs)�$y$ (!^laxi):f.5-� ��"v��_foz)�qb&h"}by7 aten=)2��Ia���a#���-�2� ����&�lŹπ>� !ee �,auem})�?� u BD#�.^&8�e���is��by put� T=0$� ��2V}Jx.�-a�An�%;��>@. Q!�6�?�o�4< "yu���S1�$G(I�;z� n!99�����De�$z"m &��&\M ���(�s:���>Iw .5�%>a~�e ���6W/n�z .�h�6remsBM�J� "� �^�[$%�  o!�"Jt-� ,�U�]PI�5J=m>=\arc� (1/3�%��(ui^m I�X A9.e� ;]Ig�'�#!� (�B�mtUCH�" ?o{Q�r.�b�JX)�!I�(. Our schembG�� Z`7n�:��e7�vol�Gi�,2���oJ a�&X{CompU'on01�U=r�+J� f: ,>~RZ 3 Jh.&&{��&.c%.+�Q�rF�y se�Ls�.��"�"� A��,�� � m be���8%z�>�� H!�y P Ha- E��&�u�3%�*�a �N��!��-�u�.V%o?~Y!pd!�r6�60��F% #rhoX6�""$=6�( � _"jp"\)%) Cbrm&�C C.�&&i]3��.;UFU �%a<�//!�E 1��%��ra{�re�1d��" �,�/Y�� (solid�� s�x*[)&�.ݑ��=�KN crosF�yj�Wooters:/! Conc}�"�Y�&�C2�2�D4aī5�� H��b��lr+s m��� .l[dcurrev�_� 1a��0$C�913��E�.R6�~ �$��2m�? 12(1a�1-C^2})\i�\q30.19$ e�� )�~\m �5[X ��56 s���B� 9:�:eL� 0M�.�R !FprE�of ��urb�/16NE��& es $��2Q�$56)=0.65$ %j.id.i s5�t�mQhe&���t���U�Ir^'*+emembeK25�K%��w$A�rsdu JT�0& a u~.-7��, �E�5K trade-off"��"~� . (&K ��&�`$ very�ox�� �pp&sac"6s�"`*y�>s*w4D�!-! 2`*�I�� .:����� � � C%&X"�!F2s�M�h&�nsixm�pr�H�E��&�V�i�IK "�3a �a�nco\� `�' � $W� �-t b�}�ɨct.�ear�0ne,�p� ? �+ ^�, �0 1�+!``�# onals<:R��&�mJ\bar0z{{l"�-&�barq-���-B�{�,<>�#Q�``> l1 F1 �0'~��7r1~:8:B}��NEkeye���A�iU&c�5Kj  M+B|0��e!CE*�k *Mtwo�64'\� overu���rh�-sect�0)sD2J�#tw+3a�\�6�+}[Exq��teg\L�~vid~2X�&A� six-H9S!o attach� ��� a��< Gi \chimto z�n��p�:�bg� N:�\�.F ! (A}�� 5~B&� �S (CBS lD^Y $v�ab[ual-�ev0.�8A%5Z��)&;�; o -d�ErW�M�L6�KA},�\CH \}�/B D���Re7 A-2.C >=2-1/F$A�� Qi�oVas�#&;��Mn?G� ��Eq"� U})%"$8~b> ��� �C�j�>kKt�2B0} ` ->'M��2{!9�9���80F�f�1��e�a�;>�M��3��8�1^!�<A��$�$�3o{� i2�rn0s6Em�� \"H *�%8Y�* 5�%|A��!pip��>� Ba C D}$&IxI"�s� R��2/� a3B�� ߹�oR;R y. A\�p.�� �}�*� �de �� way8�t� r,-�7*Y�re"���Rgn�]nt�#��./calF".w(!�:�e>�� � o�n��AdW�b�:;�E0&* &9"��� aB�#�)Kh.n�ٍ��W)iho��%@�W�hh�$�~��ӡzB,%6y:|�p�,u� �]>�2��� "�3���&�$/� b 7:�6��o�%�tor[�"��F 8� gene.I)>qE� x G3l^� �s^%';"y?�"�7�YM[e��!@�n%$��� _� }6I�i&��mod>@�� tudy�var��UI"� �&��(;�4�f��T �I,�=a y� 2 a )�oe%Vr"5 J.�-pg�years�#"6U.W� }"� r< �y:m8er�e5Oa� )^� . Al� smg��` &Q?@��|f!��HW�;(S�!�{�.d}*!���#d��Uua%A2i)n sLA�at ���1ys��>��a�ioA1�"��E01mep  a�e �freedo^� ailo�!V&��� . BeWC(�t������a2L)a N�M�G k%����%A�$in:�%�zm( [.�i*�Xgke�J*!�E�g-�for suУly�0&�!!M�a�="�� 5�Q>��q"�L�0݉�Me&|� MIn?�_%z(�z�]�$���d��opA of�,st2^�1=Q3. �p�fu&/�po��of ��i�p��n��95S!�led�5e%�� !KYYax=Fan��YDW,n� ("i3itselfaavni���e���&w�'v��mzmod�&�0(K�$sA(F.�� ��c��t &+.u!Vm"6�~����D=�K*pa ��.�m � )"� �sklife}�b�#a>�EW�A >���r*INTAS grh $2001-2097,:�pro�� "�#ImaND" (IST-2000-26019)1Eu��NP.p@Knight, Fortschr. \ u�U521T>�d2��.fiӅ�J 5003Rd%�(R.~F.~Werne6��8E@2��!� M.~Keyl�6AJ. Math �u� 40}, 328 �9:�ei��a� 4497�0);a�m !�od.��=�a�182���22�,!*��a6 R.~Bednik��77M�(; C.-S.~NiuC(.~Griffiths^�8}, 43�92, QID}J�2��Z>Y�6�05231�>2� UNOT� FzV6a262�G9)ޥ��$S.~Popescu26o8�432�66UNOTmV:p2 6� and ���$e (London)��1��8A�2002)].$Bennet96a}��HAz�20�P2�Jozsa94}A]Josza� J��3�1992u Perfmt W.~K�oters�H.~Zurek� �H�a�1982�Covar ^G�ZD'Ariano_��o~Prest63]ia�042308e�@1); V.~KarimipourIA��Rezakha:L 6}, 05211{2�1�b���382J:$Horodecki}eN,�anR�� .n�m 2014% 2� Fivel}��I.~ jH7H8� 5.�!�kill}�N M� it{QJl acomput| �l8cture notes for��ics 22A(�California Institute of Technology A��8) (available at http://theory.caltech.edu/\~{} pre�/ph229/.� BB846�; G�� d,� Procee� � Esteem1d��Derka,6caA�z� ��>�� 1571��YW��Conc}!��j P22!> 6stateeR� nF�\301� �Tlife} Here we consider�a of alive%8dead cat as difEkt�*in8 spaceA�a very a��t  docu��} ��\newcommand{\half}{\frac{1}{2}} \. $adag}{a^{\ }6Pds}{\displaystyle} \m8[preprint,aps,ta (en]{revtex}+3<} \draft \title{e�polat�Aist��realized!�Dew�ed Harmonic Oscillators} \author{ Pz0rayana Swamy dd*{Depart!$!\A�ic�U�outhern Illinois University, Edwardsv� IL 62026!t make��Dabstract} The idea�t aM  obey�i��N�"be IbAdy a d�o�< algebra has bee�  outstan�YD issue. This origi�Wconcept��roduced long ago by Greenberg is xmotiv���`tMinvFgE� esta��h � q-�� �� d toM�beA�.�of !�4icles (anyons)�e9/@continuously betw�Bose� FermiS, i.e.,aVcafal.a� show � the generMw%�mediaa��xI�splitx�e}on-lik�regimA each�d!oa unique=� -0!� e B-%�rmo�is6JemploAZ%�Dq-calculus based oC, Jackson der%�ve��!�F j s ar��M~ordy6�a1(modynamics.A� fun%n+ both��o arA�t!�na�nd exam ��yT \v��4{2.8in} Electr�m� : psa� @siue.edu3.22 \��mt December 2004 \pacs{PACS 03.65.-w,$ \quad $ 05.30.Pr,05.90.+m $\quad$ , $\quad$ 02.20.Uw} \section{IntramA~} !)Y�al mecJ c%+%� s exAjng�2+1ɆH-time dimensions waA�q�ed.(detail some/a�@\cite{RAPNS1}, wh�& many�!�2���perti5�se u�, such��9�5�,8ropy, p�ru� eG� a[8gy, virial expa��8specific heat w�dUe analys��f�:A�a��1d!$per�< $wo)O =Ju'a simp nsatz��a�,yon distribuZQ� . In) cular it uf��Wa n�alAii ari���bo.D fa�DI. V)8(coefficientE5!���ayon gas%J 9J%l�@ared with earlier6�Zsubject IG ,}�,re recently,.+AXg!�G ��ծstudiI�oA�:} n8Frappat,Frau}, I�F�U fiel!r� �lowF���.eIUre� also�Hgreat E�esAO a-0at�3�e;&9 � i1 9��on )5ChA}a�!R��ex%'HaldanA` d Gentile./. ���� ���r �:"Ys� playi�unusual S prq�, ee~ally re� to ro��oq�in��se fe� es lJ toi� ng result�� q :�ge/mo� XEť�.� givVise to2�p(�5h+not m5 ,in familiar  %�$ger multipb�H Planck!�? t�m se oE�ť name�@he liter%� i�,  es!�ng2�!D9 wh�acc�VglA��e� B� I��ons.�by%V)���� ng��m � etry�� �� body wave��� equ� 0}\label{1} �Dsi(x_1, \cdots x_j i \, x_n) = e^{i \pi \alpha| FBiFL A \, ,� �ͯ!v9H��a0 ter $ u$!�� 5# is aN  nu��A4Tlim� :H = 0,1$ correspond eca�l{J� . Si�Ppe5� 5�is)�� qTe���>���  ma� 6� e,braid group,FinAte !A� $N$ � nd��en�by�duc�G0Pauli matrice��Lerda}aisa!n! onU�R���pi�) 2U�,�mCi -SKs F.�provi�  a uLE�Q�uk��� !rea� why ! hA� ought��U  onev�5�1@s. It must, howev�b� �!�Z=�y`ofex� ge2�m�#�  n wH�� fromYF�Indee��or�tŗ�^ng|J� haA��)  ul���)pead�Cte clar� %w�aH iLIb iA�v����_ 2}, �� 1=2f ��> � � $veloped so�Uto al���}� � �]�� �.�@M��y! y%4¡��� , on�them be%�Aa�l��b;ricaBtoBH The �[t: u �ng.�MdirectlyE Mc.�&\ s,"+ ��/A ca��e;� ic���is��turA� auto�!S ' !�)9;A�a��3es� ndar� �T� ;e 6��g Iqe6A�`�"` ` !w�soly ofAeransce�;$�0M�n cYA�power se� �� ��m [� inued �� �&�0 aryIZ% #J:Awu�Rn.)�x2r uc_fu6S!Q�!odf!wy��,���*� p�!�fo��ing qu�on: Wa kind!�$s as possiy0ň%�%�JJF�A� e �|regard�T conv�o� wisdom�(t2�o���*]4A�e�no "Qto�5RofY�ZO"�a � 2 y &� M&w �v ���!� �lKscove�.+�NSciuto�] subsequen�Hh �!k�r in lD *� a2�L ����po!�d�%xa�%� �.q��l&ae?��Ez anti5�ylo& �%� �con�u!/���dm��a�cha�er�N&� stru�!҅a��Vt�� licit �Y�E �_�still mi� �� thu� # &�b��Ih�IZ5�u�a Ta*^g wo],psE�W� world8 1 ree ^� �$ bal�� . All Ais 5Wan indip)��e o�b�v achayAPN��EnI1�"e� %mis��marilNgoa �e�BJy)RM$*�[osiI I�harged9 �Dmagnetic flux tube�� at�� shall6!, term \emph{Ef s}, �jref� � !o "kfJ�`is a3 g�ic sens!�d%�asg���ny5 �� modelR�f4 !�2$ �IA72[L"�]�� i��� d� e�an1*�w! ^�`olved uk%T�J� � fund�2/Adt !��o m�is: C�� ���+B 6�*�? If so�at" I �be � ipr� .� a�Pa�� � ; yD0C>��?�%n� spirccurrent �[^ u��#I�Q[s � �%���we�6ey e��a_ t�b�osely�� &y of s!���m-N��%?!ludalat+�� ��A�satis�� ory: ��#t!c>ct�or�" someNin%stent;3s L"Vsui[!�MR�0 c. R�aj � �u�� �Vv & "X �.� a-m=�+wh�P ="C ����y� � yj !�on�%� !�-ca.of�� u�-̝�.e b�58 �� .���bbfr  by^2a *%0 - \kappa q^{ } Dq^{-N}, : 0 \leq q 1f�$ J = 1$ w�,%aa"���2 -3bJd#-�.@. ,'��he S%!��ak?" Fock�!�&�$�*es. WѰi� An abbX6e�s �"�&" for z y��-�E�y�ed. arbitrpA����M1)$Ktaken�7be eio 1a�-12DA�%x �-I�aM�=�'� ��'R�,�)gs to -�U�$Mf=!�s�&atelyeW2`!��rI17Ct���a9+-�Af J!�\ *a�:�e�� mus" s2,3�ere�o� .4h&��� � c�rg so qu�. �2�� t#�1of5�} Y�h$�+ed j 3} �a�;)��N$m��y�! $q\r� arrow�9�sA�!1%�l�����ad< �>�s^�4��[N,a]=-a��[N,��]= V��)&aP ( )dA���'�O�K�+i� ll-d;A&d��(.�AW4�� 2. N��theles�'t]in� �!to brief� �:�[$AEb&r!Let u� �$ȵ$($\tilde{N} -! at? �a�D: |n\rj;D6_n |n $, assum)F%��genvalu��pen� $n$};�wr�he�i.wI�-U�F��lj: �2-%�-�8in Eq.(\ref{3})��.� re' cY�t_{n+1}=n n} +�)$� "^of��%�m�ly�<��^�5, V ln-1m^{n-3 � + � +3} +1}\, �(h�+ Q cognq"a�"u".�^�6iz\� [n]=�-q^n!�^{-n}}{q 1}�F(!�%!�� A2U����f�7 �[Na� {q^N zN>�B"mannerA�sea4M�.Ada�: [N]$� ich�����>, �es !u#Q� � ��:��Tis z+��+isq+FIn�hbuik&m�%0$observ�A� %$a }�= \sqrt{1�!� |n-1q��F$i�8 =68e< <+<. �� thenn3aa�� ���!'A=U�0"�wfor�.-�, � obtai��^�8IF��EN( �4)^n} {[n]!} |0� V`erb�9 iI= [n-1]q�[2  1[B�A�� re/I�!��&of� *� s �:�no�I���5J8 hT � #$n.�$a�t�7*&gerF�To5�fu��rE�6� H 'toniaf�% 0} H!�4sum_i N_i (E_i� mu�%B@We�7� �ppeara� ��is.� do�deR'corpo� �*} (or��lB),*�occupa!J� d�A�" � w� see. F{#�� �,�8mean �Z^�11Iu� pm n_k��E� 1}{\s`Z} {\rm Tr} (e^{-\beta H} 5_ N_k}!WF��b�� [n_k��{Vzt[N_k]uB�1 cycli".�!R�2e�><*y $f(N)M����f(N+1)$,!Gi� polynom��!A�d)�KTk'ultb�3 �e^{)L(E_k-A�}= )}�*_k�)�c_k]�"Ff�Xy `  hn y"� �"�{�$!u +1]$ +iC�?e& "�9!)mAOY���:b�� n_ia�UT ln q) \left (%� $.q�}��1} ;f& j R I4� �$��q+.a� gnifz effeOf a�aa�6� �, "�'w1�re�$q� !cy� a�vFN6-�is�/ 6�"c�)Vm F�B�-{Ve�AO'� acP��+, Bargman-WigC (holomorphic|%a,%4��annihil %<�q� s,�,lb�15�Lo�Gftep��D}^{q}(xAx N0�b� $:Q $ de�/: JaB�4�"��Rb86} :[ f(x�,m"$f(qx) - f(�'$1}x)}{x(q- )�#B!�JDk &rin F�6�Extong�in�J� links1. G1��&"$=co"ͧ.A�JD � 0tF'�!o!=o"* Heis�7� ix PNS2% ��I *� ,VAP �> �6B$is �ruifye.�$9" $2 4replaced by JD~1, �. A&O",�variouEN*�#�i�4�!�1�� E_�v he$͚s*i6��I�9� adXs�8�*ppfo# ~J��Guca{0&�. S5�)w�2\ o set�5������G350"�now sumz�s��� RL��V�logarithL)�p�J������givenj�1���i�Z}=� � (1- z\ E_iO V@0$z�0; \mu}"ufugac�;Kiw@z^bm� N \;�; ���; z ��9(q)}(z)��\RQ'#�e,@ s af�0�!.� ToM� !k~�,#�/ven>6�mgAsu�v%+bw ral"#uE4b"� -�*�V V (2&2$)^{-3}\int!Jd^3 kn<V5�volume"� �#Reichl}�rmal �24length $\lambda1h /N� m k T}$�(,�M �$Q�0�a� �R`$energb�20h UA5f�?3}| �L^3}\,V T g_{5/2}(q,z�qR�^z2� g_{n C 1}{��A�D )�0{r=1}^{\infty ��7,(q z)^r} {r^n -x �9^{-1}>>c R�&���?"�-��:�� f8Rie!� Zi �lA� volva7b�<8 nd $ �"w w"-$g_n$O�b.� The *��"oan~�2� I S}{V"� � U-�\{%~ .5�A\,!�U2 -3QA�wz 4e� \2B�Re�_!'!v�e $:�!-� ����lA%�l�*:#,J+ + qI&)re smallph�#or&=� " >*s���Ebehavi6,<�8�>MK�) as a9� . argKC��s�< �_;is ���)� P}{TV�\%�5�VF mis �T� ���B� Fin:pY)�)� � *�*���&s:�.!�k.subtl�R"�@to� Er�Oan illuM, %�B�=�>� in /!�2�b.��b 4��)yyL {v}=u&z,qZk�$v= V/N$I %�pY3(L n*�\ly*2 �� QD�2b�5} g_I �= z + �[2]}{2^e�A4z^2 + �[3]}{3.38�9NQ� $ easy!�"�it"�o BqK $�){�=� $qOa�. Now!� neq �P&8#� !,"O 24})�B�^ abov8$�34-}r��  b_6} z = ()62�B >i�3-k25 � ) !�*H^2!�2}- =2�=\,::Nd ) :�B��:b�[ �Pv}{k��v}t���ZN? upon� _LiSwe .�*: >��98}-0 ��  �1�7/2}}A� 64+ Y�B(��EeI�E� U�" >�. H-:Y�M����)r �3s,:�>X2�A�ll� �� 2��" �>�e�>O� &�second�� �' ��[� %��/R��>��!#�Al�*�+or9H��B�b:�'_ !�f�%!deg;6^9IO?�$� +,5��� �3�Ye�K�F��er f]!!�!T"M9�,! �"G�!*�4Lf&.X:!��o��erm[�*s6~ymB?g@'.k ��\ed , Ѥ�B+:$*�F-�lQ� F K#r, >�$R�(�� \�� ��notic]�"Q--or�\ � 1� en�Ps�!to� eZ�i�!Mb$�n_iv�p8MO ; }\;�( 1 + "-q}seta_i�遮V�  $ /#3*�$%!!s����!ct�:"�?,^�3��* `(>��\; �  y_i\82'N 1,{\'t {1}^2�y q> i�A��:�E��CF}, beF �M��%�&�ol.�D1�AV �c�# mpac�m,`w?desira2�L. �_&%� w�6� � .2� rg~H(a&=s)�~ 3�n_i^{(1�Ap / y=6o� ) \;E ij1icdi�F�P iBaqN�#�a�*}�D3� �2��u��(:��_q|$1}�V� :�&}2�p�Gim.c�>ro�F�q>/I of2:�:�{r�isl/>e�] in!9l�fU�n)�< 3)}� HG$a�b�3�)<.]*1F72N� toge!)���r�(I&b��b�- ]�,Nr#f�., BE���L �9-]3NE�F�  e�!�2�-1k" 2}t,1��H�=�S�*�MI.9 U�wD3):S.^7�N�of �MD>�VQ�))��� F� <� . �[� "���!&*�\hat{N}%�6.,�"�.?&z(F by $ K:�)� 2�.$!�rf.�.  Z7�(� �"�R $ K�#b8&�. &A+ �Q� �j"qG  �= I ! �4r YWOso"��A�A# $1�&$ �!L�Kn%�e $&�*$yR�!ra.7e��kVof�8Cith.�9� jt�1�!5. d. A��,J�61�m���b�)��/-n*7& n�"BSWI8T-� 0 =0�/11!%!dO?nd--as vacuu�;"��Nn$�y�;G�4NN0Eb.�7- ^� ���O\, 1 0�$,A>�L\,0�ajPThub�4es� - (-1-{2��hu0!vB� *�$0e��7$!�2;�I�CT,�'n �@ddM�ih/a-ot1��+saD!ʩ�V-�".B� "J*a%&y:"�&�2t�ʅ/����R�,-�#�ultfnee� *b."A/��1}|"7/ =  ;!~�9�L�IK X2}|2 �3 =0MBACom�t$<**`3���`!6�,!" %�$�,n� $�P!�e�$in �p"+1^�� ѺR@%R excl� pri�N, j 8an^d2\ �Zdois�Bmak�n�1 `3"7@AIJD8=!oJ�I;m�QJ���2'26})�.not adm�>a2��a��"�N"� 38})w^��reaUno6?&���&ni*��!?Q�.�[N]rQI�= [1-N]%#����A0�"�@&W b� y��>%C �,�!+in�( ɉ&"�Fb .�fead, oOh�[�a$�y�?A> Z�4��V�.�"�"�ZN�ZN+��*� =�yN��M\{ F�Mor� *�0- )�>"[425eXA�A4 �KUt requiV u(�*nd.� we|em�_)@q}ra)J(1� �'� m�.Eb�4�%4n9�~1M�a B�p"&hal$ *� A/�b# �1(�j)Q#�lp*?/S0"Y QB�We� re-e(0� t{�V��e�"b�45E�,2}{\pi}\arcsa[o5I6I.�N�0\��/Br� ;x�%�%"!"HC6p n���R�\G6�S� $gf$��b�Jg1:��1{&M B� &U&IT �1r:AX,2�*R~&�-����� eful��us,�P�GM�Qmatica�^eF�A�a)- fm7M1agEg}!�I 7�g}}{6149 g^Y"}{1�(+ 5 2161�}{1680:"?"B�3 h-�8+-Rwi"� hH&�"(�C�=� � 6��3& AHA��&"qgH/"&�%�E� V �#. "�br� ach�; vail�N��A see below�J*u@6�.��} N0c� ceA��I 47})�Qbe d%�act�*j �an�B advantagDide�QCf^KftLU���1yA��a+�9!��M�ntIal�!�)L%c� rR(&g.� � D$n=s]�[ �F�Q_fer�&o &�44�45h $\sin^2 nR,/2$%��eɵs 0,1 `*D !B�Ld0hni��.�U�!)"� 4z1ao� Aab�8} cml���|Q�g2�BrO!�!V!+eR �P�@�E, A(r�>x'a��b -�samm�aI" aDWaE�M1*�iom(� 2�OA� ct� P#A Enow\)�1b"L>��J`I�k[is N��!-&{41Q�'O �ID (JD�m� 5 N1 a�6BWez(by�=� �l��0�z~4�ln"+0�um/& n (1��J�0F��r�R�n��!�` . 17})%��L"� A �s=Uxp�Gd�0�Sb����. .a^%5'�zm,\��al}  z��.)N�"p.Da�h^�1�}�8}). U�&cBTm}�um �� Z.teg"f"�F� ]�.er�M��@]I?A��0�c�0E��5# !C�5 po4LL;�9�bT� \Omeg'-#8� !;.J =>"5 &Y'J�)#--�Z4 \, f��0�j$ $f � Ib�f_n�!z� a@6�0\, {r�C �B 8^r}{r^�ANI !~g�1,ae�\R�0�4�nohE��&K& A.�.�-�#�]^�,a��u�q� a"�+Tu FX��6J"�(fajO�k VisJ;T+he zero "�gz�I��La"8/�(@� ��]� �ab�5aP� lim_{V2��2,�5� � I{�% (U�ip1 J BpW��!5ijX.�)��y��bf�4 �PJ(.#� 4F40a*n`�5��� �0yE:)ss � `)�;&�Zmd�_ty�8be�3 R$B�f 5�Genn!. l�5 5�* 15F�>#�learnA>�s>�q^y�"e�5 �UMw���e"��one 1"3N��]"�7 �<1~f+f��s���, � $. O`"p^���� >��z\Ai�Eu�=]3�)A.>)�.�2 ��2�l�+ �OC��2 \e�jn�A!, fL9:( !}@z88�quD$Um D� P&,�9 q"�O� cusse�kI�"eH�-i�g� �!��a�0B6�*EWe�B;!�Rehy :��Q<&fb�VJ5 �!^>actual}�L-&I!c%�!�!�� a.)�KF� Nkn�&P!�e�-"�q�!~AH�f> ��*�! �b��i�P v}{\9= � V*�2�� � {v���>[11}{8}v2&�2�� \<(R`�0 )�1'j�I$nte!�e�o* !9#02�/�ttt�;�_�#�|J3=q�*q�"�aI�M�`�Bitu%�a/tra�'��� mnk ?�bt� s�V�w*.t� edYv7$ndNcyv�s �sXi�'wo "�^.laPF)h Y�� (�F �q�^�l�%�p� g��n�5`Uљ�< T V}�*ѡ����N Zr y+�6C: ��s���b{��aS}{N k�c1: >�}2s�- z� ���!f�J�NA ��'$�/E2�!A�� -62&is^2��!�aeWu6nR$s IXdei0g8� ��w1�a�� ��+�2M[� ,2H��� �!b�\�{*�  �@G �@by,�3t@;!rnLK"�i� or,!K�|in class�'Boltz b1; a�n $E=\mu�!:��Q^�6&�qk �}{�(  \geqZlfj��W��($lf�Qs&�= ��i.(! high2�� d8�T�SaO �"��cl A�� ^`9 j�^ unmodgj stepA�m.ɡ��.HB����&on � @&A�{ter)IedN sole�� $0*� �I�NR^��a�igh em� �,�, �*��zd~� �&�I�&�%�.�$�.F� FoTeu:G��omePqsu�<%8�0ozpRTFu�h�>�,%>.�{.�l5 �-�K�+ ai��% + *�"g!.j�b+���N.7 g:�9fT z�� $g� �w~[�A� a�s�y2;b�2�92�4� g}{3}{;2vC{h^2})� (\ln � )��)\piW;8 10 -2})&�9�AV���D" m.� chem�&x$��Ah��Q-8!QdQ*�`PRonf�6�E_FV3 N>/(pi g V}^{2/,D-!:{2m�B��:�-.�p�*� b��\muwE{��-KE !��!��b��-;!=.K:% NR&��t� .�A�U��bey�:�k)�q�Zq�b����� +!�]  (�6-�M�1�' Q�);kT}{E_F}�Is o \J�X(%�J�J���]�::; B�B�+�}���r' Q ��#v�~dem$sed. "2Co� ^}0(IR>�JyE�h�J܁a�; tpZ�:Yw0n *�`e�ad�4�M2�/�� *N<e�x4oRo�i�BYn�h5|7-X%�!3�)��&�M 4"~'�a�A�C �-\"b&�MLi"�&s (�um�+ps)� &/loo�N"O *#/Nd�dv- �1�� � s� "� �]�U,�&r��5x�^\!B!�braid�l becau�$9 5e"j{ "j{�70r�~x,p� wF��..E_�.�N�]H !y9n Fin"s 3+1=Irkw���O1�F�F St>Mng C�> �6�to�: j}s,=z�nU!\�#!%"� sOca��b�#M�] �.z�[�� .!-T �tZ deline�* s. OA�J�"t6�>!�m�VV #�ntG>�6 �6=�V�&\1n�6mp�H �gc7 :�6b�hZ  5��Bdo� 1v �MV!}an�CPE�W 4� �C 9*�a"�S�b.� =�Y*�vi6-j��c�ARai$�r�e s �!a�n.�a n . While51�8lea�2s+e�C[ �*� JByV�+&�})đ��:�f: �\~"��2� ; ru�=of u��H�pw&{|D^�$��K%Ő����(�g�>�/�p�/B�/�/Q��{!6t� .��.�?$aݑ���.� C�2�D&� ~:K��q-��s, altPs both!@t�_I�� �l6H(�;eq��G&�i.6�-�5\>noF�o&�BK ��E�VD'�>�#fo�j-"w�eإ�i؍ V �V���v�*&) �'AE! �`!�2I)\s�X�y%f& ] ] "B� m�vanishAn Z]��aX 1$F  S3o�2E� �p�4&}xE�ide�U2,6"�;.6 mmod�?aY|i ��  P �"�2}=Btx�e�d�| " {�Wccoun�� ����t�viL a�!j|Jnt�mi�;!�12�A�E&�O&2" �'�p�h*[4�? �p�3��G~�? a�4��E o�3md�u�+at�b �LD�=�1�k�!j!"�x3�of 5�%ou sKwgoma| �si�\ l!��I?( "�PrprW�!s D�-o "!�L�x�f�uN�P"�o%<k�y �E�|yE��)�C,-�Ui&P5!+%��y��v�) ")b�nd&�a�r��BjmB"W�SB��mxE�aŖ"al�7at �Yt >b�+$ba-(>at)��A�&���N�believe At6;66DfiæMCwJoa{I�5 a cl��J� *cA�5[ R|�D%YmB\�a{Kx>�ep�/�;&�z< c\notp��9w5�E�%�D�.�ac(UleѨ I-��S� my�"?�u,o A. Lavagno!<Po-(cnico di To��Ita�Azfruitful���P! *� 2ew�d�n6;�nd.l�RR.J6>?�K"��# R. A�aya� P. Nar*X�, �yJb�A:�1.ȏ.} �27}��,4) 7247-7263*���N ier} �LeinnM nd��yrheimgNuovo C�Ho}^ B 57}�� 77);C�إ:'zܛMod �}"��64}��2) 193�� Arov ~F. Wilcz�� HNuc C.DB 251G85)117|� F� :Ge��Gzpha�kiny�},AM Shapap!�.yWov|Sc� �0�89)?,gapor��bf��~} L. ��u%>�.OAt2�369�96) 31.�y� MVu:Spr��D arXiv:hep-th/9407G3)�=�C� S. vedi�4 V. Srinivasan1�� ica 5�A 2�4X7), 576]�~ A�rd�@�A},�2)S��g�,Berlin;.� 3Ft2/�S"�M SuperJRu�ity},)� 6�90V�e`2�` �}_ЧGen. 537} �44) 2527-2536; -��< 6605=NU�AO har5�V� A 22EAA�DL873; A. Macfarlana��bf6*4581;.Y S�� �Int.J.a�A .n B 10n96) 683,eH ~�B�re��u!��1I ���gb� s�>�E �!m0) 1218=1`2�``5}` 2) 036101b" } O.W../=� Lett�64��0) 705; <&_ J=D: D 430) 407�e��� �%�S.��utoq� NuclIZ40�w 93), 613..�9�E�f H. �q-Hyp�O��fu�7���d sEf8f8Ellis Horwood PͱsheXC�e���Rf r^:�32�2003) 14.��&a� �A^�r�&urs���al�e��8) John��ey \& S�"�; K. HuaC��wJ M��},Xed3�X 87) r]( R.K.PathriU4` .` Pergamon �s�72) New��=c(CF} H.S.Wal9R?e:p^>g;6M)�48) D n No�]nd Co�#c.=$G.E.Andrewj~ alQ��fal³�V2a�(, Cambridge*H� �%s4 York; C. Olds1�C�ed�� R, Ran��Ho(1963),=� ��>� B�y Chaiϯn/�� -�60��A: � �|u� A 26�[3a�1.�Partha�� sa��`�� �_\�q%[;� prl,X@�4} \u�{ckage{\.icx6bmNg���{Four-WGMixC W�.Self-P� �Xch`ColW�>xAtozWRecoil}"g�$G.R.M RobbaM B.W.έ$^{�pc}$Ne .ff��O^|�e:AnderĕBYuʧ\\ &�� St!A�clyde, Glasgow, G4 0NG, Scotland} \�{\today5a"���� escr}�a methocnon-de(tN$ur-9f m)5i � ld s)�4-t atomY$b6��#�f>Lp�@��%c9n�Ubi��&~0taneo�7periodic"�1mod�f�ld�Ņ ��a =+ZLV!A ��6wd$'-f�Bency b��lg�. D&-� 3�Wy @2�,  -maM��!5 pump�� scat;d gsWa necess������ ��s��--�1x�Accur, qF��/�( ``self.�''4�+!�<%tō�eN}.b]� one-"��3� @iݪ�d sugg�#�of-of-� )��egM;ci=^!Oa�a]�cA CsE#sI thre�K fra-@7�!7M9 blu*ghtu$ybG����G�� M in�YD�r �in�tN�(up.*�%Id"_ăiZ�ONw�}oad�eV`X(�� {nA�al��r-Q� �!�^�i�-cs �t)g?)}+H riNG":����!�edi Mi�7 lian>; ��B[c*io-�com&��ELs�mI� of l!��DNviL" e��r��ai�s e.g.!�A�fA#lasM&N0.)shiftXC�ZC Dopp�gu"�u�rar�Mb�co�( &B*e�� rou�+he5��L��V/ X��vid�3� rs (��QL%{akAAt�K� ��|�Kf,�.e�΅�w��s�+CI���shortG91RB\٨��ic�5�sd�ch ��{ys2�X��e.�#�OI^By�]A�5u1 !.���c�� �rY,�iQ|B_�,cA�an��V�5.anW���=�QUBOsca�:`V^  LA� (CARL)5 }�i�ic K�ogשI�a3-QEi3. An es���7cf@���֑Me) q9l�ch/�'9�A��Mo��CA �>��2&��'\0y���- #1�Ud*7Qi���a� a2o �V��miSX%vBN�ix#AZXIa��3�up0�eWpqzaU��B2� 6�WA�6 ��J#�yeld- σe@%�Ss�sg2�� 1xdD($\omega_{p1�n2}R!3 �Y�5�) weak!�be)L6byQ \I N+�2�*3�:>` EJsE�ݥ @AMm���re� massh��Z1�d�~_ ly. O�+sum�Rm9^ ��.�*0 �E�c A��N4�}�1�yr. �Q4]��}q"ldemondx9eX_.�ABn :� +�i�Z�cen�%�i��� ig.~\ca���-s �Cn��$��Y�� Fnom4{figure}[h] \i\�Bphics[heH$=5cm,clip=vP] �.ep��cap]{S�,K diagram���+�2m B se��.� �e[ misalignm1�u.2"h z-axVR�2 aggev�� c��ty�� `}y?- Az"!�� m -![prU�amI,I|ܢ��Jnegt "#aY��o�uE� rele�I to`+&�?e��#al: est�Wr�'r�'�ƚ68�#P! 2@�(� ����!,Kruse,Courte-�,,Vuletic,Hem�]h1HL6s]�1�BNsu�lyE� !4����ct-,���,%�*!p6Z1Q.�N1�[spa�2:� ��u�q&#on�2@A� %4y �� itudR conEj�����)2�ate=q 5e>!���\� 2�Up�l�% l���Ac@}J��%6� unde�iO� . �LB�B�� � �$Rɡa�jF �u ���"0�+�$*V sS{@ p��"c T}/�c 'w+�/�u3p��>%B�Q�=c6in J@��Ccho�j"� �,�Aaga grA�ϓ alkalimsu��s�nd Na �!��E��Ku�}�93J�4s y eft|0��%�X�2�%�2| ����$$,?�X.N?yY.$?3 0Z 2~>c ��BB�%7dipol!� �aq�-'$ f>�N�JfndB��B).�forbidde�Ne�%-&�} �"�7iP��o� �] a*�W " &� ~ r!��rA46Au:bD�%ic�(�!2E} ��O:�l:ax� ($z$)a6pon*Ifor�:�e��a�g^�~q7D} F_z = {\bm d} .  6�L E}}z ��4 ion}�UA�M��I!�� be wr��n�)r�p:en̺ݭx�, (s $\rho_{jk/ s \[ �= ( �\mu}_{r ,  +.2�dH 23�gc 60 7eT c.c. ) \] �$� ~jk�Lkj�eHC ! ^*_� و3'.q�A!�i* uE�ly�1 5"� g>t�y �6 �1�atr2:�i�Slle�� DBqJŢ�]qeY3M�defd}2�\muJ�!�!A_ + !�  R��?1 . 8 �A�e%Z�!� t�`5�6�>�A�� eqnarr�EA�&=& s ��� i (k>Ny&N t)} \no�\\ D! D D2:D2bD!: D D3:D3bD20}D DŅ[ �+�j(z(.�+�� t\�v]R�31h Bh2 h3}):h>)zh� Bh1 hbovxb}E(z,t)%J)= ( AI �-S�.JA%++2}.+Z  +32+^�%�)3 �e^{A� z}EE� ~�' /]^Q�� defE�7q$A1�> F�/cl 222323= G/co �J2+ _{!� 3��7aՄ��[*4&*͒10) 2�e�3&� 0�� n eqm��.�u�zng��d�c�6�x��9�)��;fast-var~;�6we�.�Ke-�Pb�W_i \hbar�� ( �P��30}^*!�$2 i k z} -.�)>X-� A=�� 0} A݄f)�6�� �reson exci�'����&4k bf muchG of( "zF��yBx!�� far-detu�2� �c� �L�^� mean��R 8e%�igin�pop*,allX�Y;k� i.e.Q�0���E~ 11}= 22 33�`u(F� diab��elimi�er"�3�>a<2.%|�� s, $���U �܉�}{%� \Delta�eSs��J<��<2B<21}q:s_a�N?��?3B?32{Q���N��-\�K���'2!b ��-�ʁ%],3!�,3S�41  p�a!of enhan"�W\{$�8 \� .A5�%��}5 �e��P�. a fu�Py.k 2P�o&�iž��Dda�Max0'�ve�!�� �D{a^2!!f\�1}{c^� \�al^2 }  t!�}� = 4�T$epsilon_0 M M5P!� aT&� � $���Wj^N 7d}_j \dA� (\bm{r��/r}_j(t))�D6 6"�FY E�!v!T$j$�C0tom, $j=1...NASFi�f��aS ~X�a� vecto�r "_|穽5w. *� Q2.���u"2,"P���:0I��E�$ETv�=�i2 W 5Q ��A"�S12c6)n�b��q��<%��7j -��G��F:���"�l,���b$IoQB^2IBV�v-�Qe��Q!�P�4�*�a�lowly �env`�%�w!�4(SVEA), averag��[Irea $S)T% $x-y$�J�>v)7 XܒL�"�cb dadt �,d A(t)}{d te,e�i����n c�P}�BS\lI���0x  2Ii�"S"æuVWa damp!� $-��A$,+Jad�xtߚ�( mirror los ��!�).<�$ M�Mc(1-R)1hLi�6�wida�� Re� mrefDi�. DF�h�Z,E�N� 3K�;T��-Z&�z ��� �  ������ 30N! 20}=" 10}+ J�*2*���"" %�a'G�!-M�N�:FXE�d�th_h��E��G�"Ie�)muM�}{m�C"r � i JTcI��U� 2 k dt2}� �E�z� mcq0nx2 n,� � g �.� R(:e == 2� $. U�:!V� l!m� \bar{py�p� kf } \;,\; /� %P_r' tN(zW2(z / c,�\[ |a% -i \/h)6.}{n� Jp}N ��a�� ��%�\mu!��5��M.c2`_rA:-� ^{1/����� \p�}{ ^- *h$ �_r���  k�m��$m�8ic  , $� 6 N}{S}cL}�n_s LF� F\��i:ġai�����An_s�7 G�2d��ɒ�$�+���sc*?th�: =Jga$ g"o �$ (FE"�$FEL} (w�G�6)�-��0$��4(&@-�$�#}M bU� {dIt}m�i5xƉmfq\�7!B;�VefaDa�ns:Ta}BRI��h�<PB:- �)3} �3}:+"� ��,2ei] , T,1�A�~8�ϲs�c a Ga��an 2�G� A�( aI��--�T$%!\sigma}=6k_B T}{mţqd �S!]5 f(�,Lp})M'"ru��[ R}mXh ��!� �} �_{0�P 5int_{-�a"���)l�!�i�Tp��a^=� Q���@�:n����� �� Cֶ%�!��/``���''># \ll���af"!�7i �G.�oEE0��. A�kjG�CTb�Zintra dmod�,I , $|%Ea}|^2��.�$intvst}M f6dIot}z�k%t valuy" �5Fal � Z&spr@t BM$�q9"0s��I $|a(�t}=0)|=1���10^{-5�uniQ*ly"c?W� U��U�A`b = 0$B�be se��[�xim�Ow�F�1�%j(z!���&� :�")`-��2m���c�,��ly �� zero6yasH0ݭx� �( It��$�� &�&1��.�gr�u%A�.�2"R�!in1Ra,2�$�DnU��=86T �BQa�).�aBE� (2�)!��6� �Q�Y� U�} �� �� �6 z�Bny�Q-i�x� ���hunbunc��I��XydU!�YA�$u� b-�J!|to."%�$.�&",.g$.�.���NG6�&4Ixaapa�2o !i_/2vP1 g \pi /��3}e&p)�!-6� �-aF�opE9 ��L�$R4!;  4-�4 �4&/^�.�J-��m�*�&�eC2S�q 0.1z]��'FR��.y��YZ�%>![rx!3@Kc%!X�Ja cylind�� 4N"�10^6$�$�UB�� i6y4`2� !�u�t���� vis�&�4a�Wj+daL�����%�i6:"s E}�0|16�#aw|�# c���7�-!$6S_{1/2x 6P�[W7e$7�"%�@C�5H �(�M�F�L*�%�\ �2 &)~��6%t$ ����6%f6(% MEl$A� =3.3��$7 \mbox{s}�ixA� =1.2�(32}=4.0(6:P)mA_m=42SB+� %s� KuruczM>M�.P"o7% LU�200 �7\mm�4us $R*4B),j$A��D }�KFA2�18} xm!T�/�0i N����L} =1�c�pEkmitr $T_c =�&t2V �"3�r6hE���^�1���L /"��h15V�t�R���3�v�9 �%�T��852-9n6&P &1.4Q�5�)Ź_{C, 2.93 S,E�a�s:W,P�2��v �{ ZU455 T��.���� ��b��Y._�a� �i�/Z9��5JP�'s a `6^s2 id� ��g%c�g%*B=I�0 �F%s +25"VD �2 -:".l�]rM*�1m�&g= r)� Rabi"�"/�1 �� *�&aA�O"�36U/5$��!�/5�"�!|#32}|/5I �7٫�4I3� ��Ie =8.9�SQ�W c�R��+�~.��S+)�.3}=1.6YN..�. "P��Pvs 1'm.�y 7 t\�_1.8x{�:rad s$�zP�8.� !A�>0 $q� 1.4 ��e�KDB9�4��v).E�:B��e&�76�QA72- �9�F�*�$T52�KaB�Y�o� �:�Eum��I:� �F� :Kom*�  �1B�%;�2Zjڣur���Oery�O�;�8 �ld � e&�-Nv /�إ@1��J�_�  �[!4�;ed��^� ��S �g�a>0tya�12RJ} Ss�� ($39M�m.x���1!�� �)�%a?�v1�e*muI�sA�V�?3?B�5�.$FWM;ś��/�7�� s���RP B� �#�� �1� ^F�  /��!+ isfy�bm�� &Z,k}���,�(�3"� k&� 0$ (3�&i mis }(a)�&c*�4&@"M)$L: � / | p�� k}|]W%ml*U%9>J I! Y&�$�+b��7:�/�B6hЂA��62x/e�(aO/��A�a�2:SE(b)FD=>Oing"D�:F�9*75!I*&8%��eD%q �@�_9�i? ��(b)ɜB�� be l�E" 'Z�A<mmbda& e am`Xof>GYb�n����yz���Y� $\.6to|ft(�/ L� )^�)�$LE�a�I��CIisI���.�>K,e;b�B��@�"V��h>�[xd��:e������EporM��ke0 ic }ing�{�\&�ų�#yZ�d�Xo�BP �Ym�=>] �^ `01�a+6�:{�F�E r#�he18ismatch. The ef�fect of the collective instability due to recoil is,reforL``self-phase match''"< pump fields and\scattered high-frequency (l. Note that a wavevector misZ�, usually undesirable during a conventional four-D mix 4process, is ne ary for >�.viP5atomic-,, because itN!<8physical origin1S@force which moves-N)initiat forma�?)ic dens!�modul!@. %Conclusion In� ,�4has been shown1T1�ob cold)(levelnPs illuminated by thre-�laser)�%�sf�9space, w;�propag�� dir�p��UPI�!�d!Bmin���ejor axis1���xic �<. However, based!�0previous studa����` CARL�!{ \cite{,-MIT}�\i��:csub-r�"=�s w%.be=��sE�to)G, A[�pnsist!��y =�� �|(#c8�N8 $\rho \propto �^{2/3}$)eJ redu�E����I a�mUd�=��� (ii) �d)�!�ic coo�f� s a��3@Kruse,Courteille}1^ tend%�R:�� ]�C needF�Z~�Idamps oui\a�y���av tial�\of 228nm). \acknowledg�s | author�lik�(thank N. Pi� 8} G.R.M. Robb,6� A. FD ro6, P.W.���N469}, 041403(R)�4.�$Vuletic} H[8han, A.T. Black�V. &2a.�!g063003b2�He!Hlich} B. Nagorny, Th. Els\"as�ALA. -bk%`5Vk FEL}S�;.Ap, F. Casagrande, G. CerchioniAlUk Souza!k Pierinia}6�ivist� l Nuovo C�oI$13}, No. 9Ev0+fer � rein]Kurucza_L. v$B. Bell, A$Line Data,%CD-ROMn23�mbridge, Mass.: Smithsonian Astro"� Labor�a�5.�Cn��alFWM�W��Hyd {\em Nonlinear O� s}, 2nd e�(Acade�Pr New YorkI�3a�\.Y� 6e M. Gatell)�Martina�>B.�8M$^{\rm c}$Neil!?2bLS���12�88E�2�endB  docu��}+T\Lclass[twocolumn,aps,0pacs,preprint� (s,byrevtex,!�ptadd! ]{ 84} \usepackage{��icx6d m6bm}���$} \title{Q� cor !��6�solito�l��ons��ɣL{Ray-Kuang Lee$^{1,2� e Au�lA�Nfal Univ�ty, Canb�G(, ACT 0200,4\\ �Depart!� y oton����� itut�E�ro-E�al 2�, Chiao-Tung .�Hs!4u 3�XTaiwan} %\email{yclai@ h.nctu.edu.tw} %\date{\today!Q�ab�ct} We��6��noiD� eF�*� by a� l two-Q" soluA;!'A:n�@Schr\"odinger equ%�,K� /back-H �m . Oue sultA� clud� $standard c�Dof a $sech$-shaped�l pulse ,zed earlier.! reve��double-h+  ;`t mhsqueezedI�� � r���tu� e v 0 i�  2��s< p� ary. seO% prom� �)Vof-^�er-�-�� g3�� ngly �ed!] G �Q&in �nx�.Fcompu �.�Y� \��p{42.50.Lc, 05.45.Yv, 42.65.TgA�keywords��fluctI3s,�Nal��H�jguivs} \make��F(s�{IntrO A� } L9�]*� �concep�at �y�o att��!� ��Mits po$!rglE4AIjqFting. A� alterna<�ingle-p���s� e d"�i&�Ewei, odolskyI�(Rosen (EPR)dox2� teleI I� co%� vari"s�;Ane"QbyM�A{e�g)� )�U�~�`Ou92, Furusawa98}. Moreoy.bA�g�Vaxc�of��-~ J�!~�>�uMd �R�fib!�re�l� en r%-ed �0Silberhorn01, \2,Glockl03,Konig02}. To �� 6$ide,*F�%� @Ep))T��becomes� vital. OP�roposal:G��>R- ) "!}� unda�j}��"s Kerr�]'(of silica gp . Te� al (�M)�. in 6��h&oe��T��{\"{o}}�� �� (NLSE)�t�exhibitA>dP�) ing I�DCarter87, Drummond Lai89a, b90}Mwell as �it�RM>F�(rg, RK-fbg}i�bot� tra-% �7g 2 J$Schmidt00}Z ��  exact m1P ! ��s � struc-��� Beth� satz j�b}E�!4Na�per��{o!�ѶE?%B�n iz�approachl!L for Ataverag~� eas�+ $10^9$. B�$ Vc , many di��numera���� d�o�* � pastK  de A�&���-y � assoc�d��&k %�%FG �4 a�!� posi�-$P$ � es�>�-,N�}, Z� 5Lai95Mw�cumulE expa7$ technique 3Mj99}. E2I-�Y��Za Sagnac�R E� fero�4, 1.7 dB below�shot %8,, was first h&  1991a��� bluh��Shelby �}. Si�5 , largeram�>������ob�1�La gigahertz Erbium-dE7dk al�o�ſ!��acoustic� Brilloui���"\ a�6.1!% �!�R.�:�,Yu01}. As an�m "� �J��X , on6y :� ergy��an�2QɫM�' �ce �o�� ` d, emplo+a� idea, 7�  -v=��%�& �u��(spectral fi` �0Werner97A�"���P a( e��ic7#e�a&B� w0 :2��p� &!s � l $N-$13� s�!#beU|,� ��R!� �-0�"e%z rans� m Zakharov}u aW.6, 2y 4($N=2,3,\dots$�� � m.\ EJy�Ta2 $N^2$ ti�1� g$an��JA �-�$6,Yeang99,�~ 00};�� an e� , up7 8.4 dBM}( �predi�� �$ 5zt9 v e-ocAJq"�{ q�_B _� e�e�  "!2z <��veme]_pecial cF2��Mbma �e l-�input E�*� &&E�Q�Q�EVhe $N$C pv chaF er by N�2�"�&M=i roll���#entlyk�p�#,d �e�theor�x-G nYmex7 �multi�� �leT it ��tud_�M�m�. boun"C of !>��icula �.��.�9� � l�%�� �$6 most suit� !A�ga]aX ANJa�j�JUAhe =l AMp{$Y`e7_�@$��w�w inIc2�M�A.bn V�^�, e�� y"� same�X a� FB�2-�y�ɏ�explai��] V�.� �,!�s�*<�%�� file/�<zI*get!� � ed. �CJi� �#e&R)$ xŒ� systems,|rNA fFq ��Et$" w%#�curL 5 ology��T*w./&jer"�$figure} \i e9\s[width=1.6in]{cnt-13.ep>�*2 *ca�${��our ploM)Jv::��,(a) $\eta_1:2=1:39(bJ2$.�*insets� � �M>Q&-) $z = 0$�Mal�(s  y+y=XB� s mark%��[ Yt�( a� Fig. �!(."/E��ъ6iso-ca�.� .� (�� &"breax#s")�*n a� ��vanish�velocin� inf�B� theibx,lea6&!  :!"�"ly locm. but � -�-o.��e��ful�%�:��c�-"] 2�� m� au s-�#4,surface-mode}}� narr.i =4��_1 i�( � _2)}{|2-1|} 'Am�B e^{2 i $ ^2 zq��eoe��&� I &=& {�osh}(2J 2 t)�"�2}{1}B+ 1 t)�i �2^� ^2)z},\\ �i � *�^2} ; \rm � {[}2 3 $ z{]}\\\noM &+& ]-UNS \cosM.�Q += )�%^9_%� >) ,��e� �m�imagi7 a��*Aze��o :�, �+�7=i %�j��4�&��relA �g ] Z( \[ C_j^2 =-GY*$d_{k=1}^N )jI�k�Jr ,k\neq j'I�jI�k|!,] When �c = e��#���$z/a�ecific, &� . �7��pr� ,�U(0,t)�2}{AP� }(t)a%]f !?��r�M�)M1}(a).&fw�2� o���/%�2$"��fn $1/Y 8 � �B�t! ��)*; s ��b)��w6 � �� %�� In spia �#a"iceM�� ����� g�2]3dH \[ P=\intW0 d\,t^2, \] rs    ��.�V's, i P=8$< �I��2i�arbitr� )� (1�.� S� � ing} A#,d��(� )��2�� y� &�M5GIawe~ng�R�W��\it{Z2}3�cal o8& .�A�a��.H evalurSari��X)fs�repla� cVi�un1&Y n Eq. (� � )�� S�L&"� ��hat{U}�D!F�/satisf� �� l-co� �bo�&�.mmk �^�B. Next� subs�#H� $ v=U_{0}+u}$ intoF�to  a��=69"�$TI�v-SainA�a�� �3!�����ApRun2t�_output �0by:D#ngF%̀� 8@ VV3yO� iYE�t ;V�s obeM  Poisso$ribe�B� B�&@ei, d���,!.�6�asT5homodyn� t�! �8�Haus90,a|3}, %&� b",} R(L)\equiv�8mathrm{var}[\la�  f_{L��|M?(L,t)\r]}{�4�4, &H ; �%=  $6Wcdot ]$!��1���n�6$�$ *=.�Y�U��-dEan adju�=l6+shift��f=X e%Le^{i\theta }}{\sqrt{�w4_{-\infty }^{+ }��|<�}!]�:asaA_ *M2N m�min�1) ���:[ $R(z)$F ch�"by!?" "� $ �$. I �=0$��v>qu" ^onis ;8ct1nd�Z T =\pi /� A�out-o�>N .N�8N.Y�E("aV�3.0� SRL->��(!H>1vs.��m�AhQy :bE:�^%��Fe� �� ��� 4�Dashed��0 ��!N�cu�6q.� $N=1"� :�2G5=� 1Y * ���v( above, nowF�Q�9�>YG3~����ii* 2}. Comp�2��{>��J- (d9f),%:�g>)�A�b#2�� `ir2.�@th*��� #�x#�"*�%a� a92bdr/���z�2��Bt"� ��&d&�)�6�X�6�nv,I� G- 6p͌�6�Z_p"8 \pi"Ii1) "�� g eq_pM�.&�fE�I,�Z+sXw �21s �y�e�sq�� � fiS9a� =� :-EI��1��IYm� �� I@. �9y?�C2� � �9S�A�Qz�ind�$�x)>ij �^D t� )6�SNX�%'0 enough (beyo%O���x�"F<*�2}), irVa2� tailq�Z R�!a\� inuum�:��no[.}J*�'%�����6B� ButE!e�$z�N�w"!�nochro� Salo4 R��s&l&�' 1(� s. OL )�-�J on n�:�A2ՙ�A�;"�^^�>�ee�a6cI�E`ri�_>�#a�erB�.�:"�E"��)�@t![JBi�-��)8���be� 5n�(2 (�|�� ��V �k-13-1�~*2�*3-�H k-12�*3-5��*�C��G{traq�&<dom�<6 $N =��..�-(c�6"5.  5��d��t�9Nis, $3.1$9R$4.7$,U�%ive�!(d)-(f2�*� f�m ��2.- $3.5n�I:� y FouriE�m s~|6.3��U�2� In  @�)>� 3} w�'�)�/*��cg9a��RU -M �.'cJGA/;2m��two� > �3 �tM'2$d!.qco"(?�-�$t�A��lyH+ed co" J�C_{ij}6�l� :\Del��n}_{i} j}:� "�B4�  9}}~"�C-��!�} %�,1��(mea�G*MZgQ �5}Ew��C��$ � �(:$)*��5($i$-th slotIomega! M%�UO�\0>xi}�_{H[� )"!�U}^{\dag? +U^{\M-63(z,]��� X%1� turb%�q,V,  �A&oun�.urb�2"��A��,g�.�aken ove��@�!slot. F�,j �-�4� q�q���MPM7�'J�s�AJ��01,l7X )"et al}. �8 5) A cross-p�,5{VJ-�eޱa/%rr"�K!W~$i�=-�^o7Js�$��s mer =a:�"*o3}(b)��D>z why�&"�C�U . -g,s��uci�5�q,;I rem"�O[ y*� r1J2t �F� �ch��" � Y�-4��&sŅ6) a-c)�* must�,*�I� e��som& r ed -�;F�2+ �2\ ��'th( !�I(i-3-qF�(�l)"!!�$'R`�far f!�:�" !�dynam.< �6$ . N4 turnQ��� �Q��.�( >Q=1:�: �1�' Figs:� d-f)�-Mus�FSE��"L6�!eM��ea6��%ai.N1U� 5�EWat GJmi�.q��&3) �썓�M��v'3H Z*w�Q�at#&xs �S5)��!�% *�k-� �& Q� � . And agap9#. )^um�6_ F reA;�7> w�,"o�?m�6� F�d^�A7For2� �taMre sign+ 4$c�4R$J�aU ,A�, �H, J�a)%aN�. I�o'M look��!J9Fha!�r�j �N4�do�T�xaGclW>y�����+>�-�IYV�tha"s �J!��i�:&͐�3`6c2��e�/t6^@}SE<?on�Jl�l-��&�ɞ�.V1s�`�� !�#B� 2�iTE��Dp�6}5�2j]2 e� �} e� 2Fm�� o2#%4� . Co&�-�^�N2 �adP "-&rWs�A�..�3!�t a�u"�0*�N�R#it�.u ��� �)fT�/6�8�-6B=�AI41!↖�|:x�N3�A3t2" um8ar�to!6�9y#.�09s�%?6g��%i.U�+do �N)���2eV]4iontBb�Aadily�3ifi�B:*9byr��U�p c ���� �)�,h!�ces77 G [!. 'C��,k B. A. Malo�S nd EOuvskay use:wL��suggesu��tNSL"�G�? } Z.zKOu,>F F. PIra, H. JPFmblM�K+PeF �#-F]Lv.�J�Fextbf{68cL63�H�G|*J@�,s8L. S{\o }rensen� L. Braunsem22@ } Ch�:D@ , P.! 0Lam, O. Weib,!<K�>@nig, N. Korolkovai�G!# �b> bf{86}�C67 I1^�2F��y �y!�167902{6�G0A}�Gl �ckl)�orenzM Marquardt%�THeersink, M. Brownnutt)S=X Q. PMP.1  Loock�M6J =J)1it.�A9GE�012319�32I�A>��J$A. Zielonk-�AA zmaniA�fu!�01381NC>}A�J. EUD."�@�DaZiT ndPMM. 9=Y�B�) bf{5%� 841 (19872�&A}P.g�MSe���HJ. Opt. Soc. Am. B}  bf{4�K565JkLzA } Y.}A`H��.$, {\itrJ�;P.V�N844V9); oit{ibi�'!�}'5'.�}b�}^V 90} V��=�]�4�t292%+902�Q!�R. eZMachidaEJ�s=,A�Levano�T. MukaiR�L'Q9^77��77 �62��B R.-K����d �R\��P21801.�P���00}��CPKn{\" o}tOD� lsch�Zu�F.�h o�gEP}�N~:�85�8!R6�� �\S.-S. YuRZ�5Q817A�9�OB�99r�a� D.-G�A�Bd l �4� IEEEA{-V. �P.�2a�117%�86�2#5 V. I. G! $tsveig, Yu� �Q��M5 sevi���!5. Syrkin�No�C _T99crystals.�nt�� Engng Sci=H2a27:����:F��9�n�\8Z 6��c3�cynM1��4ͩ� �+>� &�S,9j/T[!5OB+Tam�hh symb*T %R!T% I�<E]�ffiles6-d8T % Align t@ Jddecm)point6< bm}% boldwih�n  o�O� 9 �TWhy�S�#G9er's E- �Var?}% F�^�jkj \\ &�T jesh��ParwaniUmISp  @nusESssP�T(n\_TOF Coll�Vion}% % �SS��.A�[@&O�SionK!�.�T&�S�olars Pr:[ mme,&T(ofZH gapo�T05-25 B�  ADM, KJ,R�WSi (.xT04 Septe0c 2004� i�F10 DecA�@always @T, GT, .% �9 �J%)ma�N�licit�6ed�T**�QI&0R-��� arg,WsMu��b+��k���a�}� t�96*1��� tz in�:.�hvio #Nl2.�_"K*s�b{d�0appearg*<&~HO3�j�y. �.)9 V0aB�+�Dorm|�Cer deriv�Qerm��r1&�fa �`sca.po�i �Planck ".i��aS��best 4obX evid�Z�,�9 &2a,in neutrino QS� cosm"�A�"a"�V.�S�PR*�E ]�1AoriesA$Review} MA܉!=p�k5""{�y�)�D�!),kibb~c�3"=A��@ %.[mod;�X �V5�<r*�K no d�ha�erh\al9�Df $tiny upper��!�siz%� ]�W1uAQe puzzl��� 8m� magn2hp"�T�c>: WAH�B?A�? �one�5�AeB"philos�\�e law�Q:Ohbl"|PsoT.bA�O���?oal%� unbi@4=!e7%zA� empi�O�c���p"�lof maxn22�5�. jay}1,�)tvenue��to��g��Z� P$reg1,raj2}�BVe���nlis��raj�M L�e�Nbriefly �je6D�hd-bed �9ya�Refs.� ��T fiylno)=�!o z3չ��8 $N$ t=icl $d+1$ dA�Ys, 0�� } i\hbar GL{\psi}'/ left[ - { ^2 \e� 2} g�% �C_i j + V \r�D] L \, G/schmul&J/u%Y}1$$i,j= 1,2,.,dN�&A�con�'2�cce RricA�& as $ � = \dc& � /m_{(i)}$�+R� ol $(i)$.A�- e���<$�.ge i/d�B�, $i=1�dE)Ki&2Ds#]&e9eby,Q1�I�ss $m_A#$i=d+V..2YSos)?san�!r%�.@<so on�i�mm)3&�J!1 unl�SfwO.�d.�?�utoBi�Ryic�Ei�WQ�q=3�/�4&�"�j �"O �$E6= \�6p} \ �6 S / E�}!�compo�h!Z�!:wo�lu$s,"R &�1E�S%AM>U�Y�S j SE�-{i }^2 3 } 6E��N j"HB0a0, q3hj3} \\ �p} +uDi e�( p�i�) Z.Zcont3} S 9 qII��A0"xN� Av!zu�u< Hamilton-Jacobi:�W C E�K� /<bar!�pen� sA�rv]\$peculiar a 3  �m.�?�Ninu� exp�S�$c@r� �[proba�]y. ! se<" "mT�$apE��Yin�s��}:�B9iQ�a� ]�� \PhiA� int !ϩ�Q��Cf� :�/��8dx^{Nd} dt \KY�I�8} I_FA���va�7pY)�%�(ect�#!P{ � s $p��$S�1e $W)�ityF�y \'< %.�\ Y�pA� eft("�I_i!-š�2ŀ)F&jN&\yo fish�nd. s es�i� �``Fis+ *�\"-�Der,fllH,"�Va broat]h"�= $p(x)$&9 �;g~Her2 in $x$�l$I_F$e�ctu�a�"nT.�>measure�5qs (g@1�,�4sh}) w ��3in�*�}!�0 e.�'&�J� follows.  n*�ri�"� �*�,IK� �kEq.6�) Els r��'WM��;� a�a�qT��r�oe adopPN�} to�7tr�1A ~�*�4�3�:�#cAi�]& �{����#*..Hun�Cn�z,�0�qlik�3!x"� aa� in � choic)�t ��eGU�(>{by���%��"va&�=���: $J �./8 E�! Ljge �SpHd�} work!��L0V7s�bin� �wo�rs: �-��%�%��&�S(1 inferr�6])"�!m=   sfyi!mad&�Ib��rel�t? was � �9}�I!  al ai�r|L� n�Ft"|�9tImot�d7� t ��.�u�: �2� *^ ��(9�Q�AFin>`{�= �"�S"4 (M�VS$I�+F:g�&Y "J�Gsixhts��M#E��:!+�q���% I$, �8�P homogenie�M�ir�� , Gallile�Eari��!abs�-�.of�7s"V:�� �.�9ZA�Z%E;�e�kvsabb]%,as ``AHD". �]8eA��'�("unsL|� rpreY�%�18rseN8)Dpi��3 !� �talrea�WlFd�)�YJpa&�: �� @;>W�s�VanythA�newhe%��gyFB� �-�e�U��>lsoG&a"/ue: ��-� *�X�1�6#.v6 �u�_^�E!_!�@X12� s�.��UpreciseI�{�i. � J4y*0tO)B'�"�()|)�kreb��g�2P�%Nu,�Gpic�b; �yW��o/ |,�쉄}R�I�AHDi)&�b�3ab�==:]m�5]I�t�+`[cFN81to �'�n�U"� �B QAza�*-5�)�%c�r it T��]Z*0 /o�Zc�6)0R/tfMfone* Z��!�&yy41.}��0details, pleak�=T. &+N�{} �o.m{ , am�=�me� "M�C%���)lax�a�xcaui� dra�=cham�lu�A�:���j"RK�N��4$AHD. Also,� �Drua�?�!���Qsymmetrye� �l2, !�+y�atin�_����*�I�9p*ed"�~V�Bad�rv[U�� �Ix�C=NX�*r=O$I= I_{F7(I- )$�w-P$� ��)7ic,G �L���,���M�mbl# � ory,%gHllud1i!:MBE�-� ioA���iv2���)�or}��* {�su"�65�%^a&�VU {Of�y�|mZ�isCk3vBn�6C� �e.B^"hNA�ic!"O:.�m#}�u� i�!t�5k�'M'!���n  �!)�@f i�>�Hme�� al gDO 5� n!qw .uY temp�&04/9a�E ��C ��Oggr+��6is��A�exist�*��Ej� cenarBSn� uld�aJ�M"�*-�qm��/�]F ���!�!�.�N_s. B1%�n�j7�$2by���M/��wic�*��+�^.F !b| E�N�K� ��daZ���TyY��N�!�coepa �bA�NB� Ÿio ��c�Xiltk!to� NU���}co�lly �<|�Dal9�� e,�prya��kI��/�uopya�hod�d!M��P��jay,Ku&�u��i�s> !k1.a1#tmJ�Z$ unavoidab� �\i�q�" 2n%e.� �E��1!'e�Z�l. �:<�\��o5 BN4M�%Y^um" typ~;involvef��.�s 0veK��o�o2IiN��%!�li�]T � ��eN� � ,doeb,aub)�r� �%;�z� t� s�!2��|EDap� &�e�ea�frame�!���� "� !iten�3� � [9 ival�of���h�8�6 U�I��. O�Kh��=�t s�� Ie\�,"ous!U� 7�&� �"t, ye�TA���a U�"�B %?� 7H ��[��qra�h) b**�c)isZg!0=�ɍ1�2eQ�%�yI�&� &�6 } Wi])2�9%��e�U�6/!establ�C��Y``�al".�&نof.�2rS"�6ei�9)Saq�BL�7��oA��E ��n�*�t. B� al I��� �R.E(.T2L�� ��2KB� �rv[@u�<�"ll$&h��e"U �Q�"me�:e��*g"��6��L~J�B�Y� �OLz���a�9�5�JD �at�so�tl�vɔU�:  Gg&"ea"��# N1U&� (if5)�$�7�S!be>y�� i#n�SM��#6 ^r#. Omo�hr9%V�!;� epe� �hooft}:X ��A�.5�U �be ``�"""�Qi �?vatbEy�j0� a:��"BP. ��x�n� , ifB2:C�@ exacMj�oo �� � o�y2��$!��d}�u��p,� nhe6� �BfJv>/���!�zzibu� � weak1�( �PؐlogZAajci5.U�uAq��- i�&>$6� ��amC:&�� s9�Y�&�$��"GQ�u�me.8NB� us�� IMjwre-��l�# >"�:R��p�&s:&�(oscƊ�;, dark.�AmQ*, m]be@H  manif��>a.m1[��y.^ �e-/7+]�� iMbXwA�|#��*E#��I$ ir m�#n7X � R&g*����!k@c�"�X���O�mD ap�Vn 5G�dO,J/ir2i.�;AR�=lM �j�gl9e��()Wc�vVN1bin��Q&�ls}��*e>��=� eca� . Pr le�������a�(j� �z ?���*A���gng�\��cusF��;li~ V2y�iH%te�wSmm 8��Jo� �� .�(�CY�nI��h!� keep�AB un:d٭�+ɩ!L"�3aan-�iv\�y"�VrolJ�8$\&[m�!2!~Lak 5��t2H ve*u �Araj4}. �S�h*qa.���pZi):�#�!u�2~to� 7o!!�a�%Mach O�~���.F1.Ri-&� Ac�"Œ} I am�pt@� rof.�3Elz3invitA m��p!(&�!� stim>%� shop. I0/��k�Dorganis�ir ho8ea0 J Marcel R�0 atto+ =(;��^bj.%=6"� {aps�� }% P�M e .,�u�BibTeX.^Vf$>44{00�1b�?I}�5@Bialynicki-Birula�PJ. Mycielski, Ann. \8,\�9 100}�976) 62 �iX@�} T.W.B_A�., �6 \ Math�8R64 Q8) 73;9Weinb�~� �\ (NY)619 789) 336 J%�V-E�� Jayn� �\�/.�106�57�0;�81716�^-} �:Q#a�6ZA5 D,98) 1775; Er�mr�=Pbf A6)e99+30| 5�7*�4,i�(-ph/0408185�T�32�3. �-2E!k>� 315}Z@5) 4196�&E�B1�?roc.\ C,�!��/.\ [?1f22%O25) 706�"�A  ,2�1��E�s�Gs ( �0 , Wiley 1959�  .mV} H.�@ oebn�G� GoldLKa�P.h5jA  �E��ys�49�49._�G. Auber� UC. Sa Ru^U3!t�� 82�b  G.'t Hn , "NRal ,"��S&uS&ҝ "� B�,"�<Re� Dh����Gauge�3ݎI��Q8, eds., Plenum,"��, 1980.��2z���p�6es�B�3>� &8d7* En3_�8 �W .tex  % Qm%2Mxy�;l#]ta� � g p�?on % un"�4(Hransp$��m�h�f�,c�6�.ˍ6�9,floatfiz��Z�� \newk@and{\id}{\openone!.V79029� ��se$ ��}"P9�cr�� �#�@)N7�of>� T0�!c�R~&l1 the Kb(d power aff�")M�b p.3�m&t^ we fI enI>a�BH �!lI!��an! �of�:2�,�Q.un? F�Y+8��:+)�. A4"�5)sY)s a m�!�Z�Vsi�� e~VY �mi&E���s�e�'&l���h:*a�u�E� !y]���Dds �r�@A�]6�9 for )P...o �v��Z ؑ$03.67.Mn,  5.Ud}.�=Z=� %�2 "[S6�]4sec: 6�2��SBSfS0��%����ointimC��xin�(��f w͚W���/T"�(�{t�J�r tasks 5w@%oI�z���+b�de availe� Bvera ��D!rҨE��s. By���@a ncan�+>�4d�lo�o�na�Ped� of.&�$i_ �R "f e�Nd�eq"s tI\A���{*un`�o!�&���� �� � 2�t��%�%/ f*� law�e�!in2�7ory��� 98a,E[ t03ab+Q@ofJ �vr%�I���)1�!��)���r� �!7c )(�`#iͻi��nM�E��*le\� mA�~ �����"y�I=s��t ?, �/M7of4",QSby % alon�4is q �&6a-qK4 %�Y�T94. Any �HofnF9&g�� aim�� ��&P "�3� = answato� ree qu�$o�?$namely (1)� -/���H >�, (2)e�uAi�:6nd (3 Sk .� �2/u��N�)L;%�nw;M1. O6�n�sx � �how�Ď:9$� �2�~)RIW�oryO ^"'�!N< XEXly�G�fpij b" E�� a.� M��-� ed +Yr7� Bennett96�%F\��sa/%at!�rea��8"� �� �.�. Ey� for &�!&\ s dra�ly Z%c o.�m�2� .X1"Y5 ��r�MW\ks}��!0�&���aa��Lo97a,Na(en99a,Vidal Jona�6 b}. A�_2���onv6- �.BIv��&�9�YH��-rankmDur00�Fo-��% "_3al��� �� � � !� � �<�>� ctlyv!!�-j6j/t`�JA;�(.����iu i���Oesm!Ver�W@ete02a,Miyake03a, 3a,B�8d " 4a} �@ .�y �M�Owari04� SP02�!7�_f�(� I�ly)ZY.N�r"�btU�i.oem�*U%%kim�xal(A_p�)o!<�\s96a}"'<)�,�I�@�)ZY(de�>m�beWs)' %l���� "-� Horodecki� �>#�Li1�� Gb�Hly e�a��b�e!�A�� �in&� ��{8!��7vZQGiC�"�r*U B, \� s.(�/map�'��co�.�%DM�Rz&01�Ia�� as�#"�!6s�rM,te5�!FNPT ^s)��.q� %����#N! EC�&k �Audenae ��� ���or�/by>F� FB 04b}�:* can �yed 7-%o%&b Y �x%a�$at !5z a끪 ����mlQ�)�igBm�]"< !�=( asymptotic5zI�27;q3i&Q�Bor 6� �a'=�R& "a�#�er�u�:��at CA�����in��Q�p"�focus I(eneP�=.  2� bPPT.!�:8� 9�8gl�~p*g) �V�*�w��*� �. We E'� qN in6_)� �E�q��In Se yDBasic��E�}� g��o?Ms7 !%&}.0"�;e�Secow�i~ T" ��e�6dJB�� I�Q�� N5�ym�:D� � BE� *t)�e =6�VTrace AY9o0"{B{R ���Hn4��}X��5���$�&W1llA�5 mple� .�4 .�ll2@ ��1lR�iFnC� W.< �s>�U&$e# s} w l �A�!�"Y|�l>[ �q{a�&�. *� 6V1�.\Y�T*" ."I��2}3 � e���)  �Qi"��R����Ǎ�� A.�R��L�"� ���3�J�Summary}b&� %�2 " :�2>%z�b@%�,��;~ ${\�H}(V)$ (')$� s��!�H :t�PI�o]��� e Hi�ftZQ$VK V'$). A s\�2 $\Psi$5(to *a�a �=� UO f���)$6�'9>T� l�00 isomorphism ��"� +aA4s%8 e�s �:j)Oarrow ')$ aJ! $\Omega(� )\in3 ) \o� �G1�G��for+�$A69�F$B2;����B��"97}�Z,\hbox{tr}\{ �(A)B\}=..� A� B\}. B�is�!64M�929%% Map�L�}Pi:*�8��B�vB_{V'}\1/{!N })\}�Q \id_{VBUN�!>!9!��+ifq�8��*& . A6(i'e� �.% A��fA�� $AU0$U�e_(A) and� F[��P $!WQP!/ A���$W$�(^{\Gamma_V}�D!� �$F$�? $uoS�aHF�&�EF92:1��$�&�L�6& laFP6�c$. A CP-map B�IQ: �f_A)Q(B)�Q��.'R/'_B��M�U�>2.&�)>v7 we h�=1[A\circE� )�,A\!\ge\!0$ (*B !Psi *B*&̔>�)� map LA�B$)B�By $'B$)"8�$a$� �2�~�Ko�Ir���0F0[�E(Z#y/{V_A}M �{!�SW ge 0G��~~or~~���YBJYBY\]��B� 6��=� �$)�  >r� S I�}5p<��+VA$(!M �/1Aite��W��0ijR9wA9o�� ym * ��2e+ �xtay7 ]��.,Eށ��&r"{]ly ev not}�, CPa ��:.:0  �0B� _C.EC�E2[BJ�'_C)$�Ía�*Z*Ϳ if�NBNRt��iJ�iU��d� eq:Е�,e2!W��>�����rhop E)I]� $\sigma$R � �9A�*�)�$p(T!݊\! Ea�>8�1i�" ,J ��Bg>� �/AP�3��ђ�,Bm #.��)-^ some�&%�� a�PFnuCPvU� and �]$G3@74� The &� dJH ^ ���t �$\of 4C:!m��P�# � %x)En�1 or��B�Bw�~L !, �(\id- � )\}=2%* EF��:2�" �" nQ�� aP.��Y��9��en Q-�`f`��*} -��[� -X=Rz\} &=&.Vp\id� \�.e[����>eQ�a�qs��*�:"��su)��&�N� +=!�Z��:�h�� ~ ib+�a$><9"2 �7�A6@P _i�- J- *- Ţ�7 "�+�L\�d id_V~k��2�ing�����,ew�do!s�(�!�"=f  dropݶ���/ psi$WX6�  (�K("�:X�`It !oM "�~fZ)��?! ��/o��ŏ1Flos�%�j��A�i�a I�chi.\isL�"�0M]!*�� mhi'*�!4M�/Idim}\{-��(')\}\!\in\!�����"ap%aB ����?y �S:Y,0he1,r��)�� by $:Q��a��[ One 4o�I��&6�"��3 ؟�WU}F�an��� �"�!���>�V�eg= _V$B�Mb}�cox.�EcA����� v� gsub�Ft9�de�6m$��VZ ��� R-t4�!��%��K�&g�&�X b6In �,� F� "� n.8�h$-���( a��{ev�.2��+�R{�C6*� "[�pA!%T�5>�:u(��F� wo d-"�$*&)w^7��er�"�!d)ͅ6P^+_d\!#f\!|\phir�<]�|�hereq]dis�z�!>@l�1p�Td}}\sum_{i=0}^{d-1}|ii m46Uqm\:$$is\�U atU not �)�#T+!�.� �%�/+�^��, ac1M*S !{d'})=0ihA�:��n�( $d'\!>\!d��f"�we6 ce�[%�\��e��.k��a2xi���u ! "Yty�%o6��$�� %amount�REwi"Z/����p)�2�9�6� \\!d\. !�\f� ���){ �� j�  i`� O��d7��\�l, \;\;6�� 1:� , \+�\\7�"nc-3?' 2c$}} &\ge& 0/ hs7 *{1.45cm} �U,,� jja��.�o=s}���I>�Ξ BV�56���F�� ��6p �1�R� R�*��I왜1 BAN\!-(rw%�_.�'65 unit*�61�� $U_1Q� U^*._{2} �{2Vr7� be�"f �^s�6or.#t�i'P.$� P)�$(4e J�s%e.�>�#��f�i�*m�e�w�a_16���e�+ a_2 !��d&K!Q 6KaY��a_3�:& ?W}{ ^2-1b4RbQ��l<,x)q_V:qb� + b6�Aq*�XFX ~_w*}l�FEqJ�(2|��*s}) y�� $a_3% !0Tb_1 1-a_|ta�b_22-a_4tf ql�L�>�elimiK� U$J Jd�}Y/a��B�5n�ulNY�� =qA(1 Av�EEe64..92E�4, && �� d'+1)a_1+ (d-2+ a_4�22- ).3B3 R2V1<-1:eJd(d'a1Z cR� -g2-�a_4+d��� ( O-( (F�E�=��kI�b%�s�Oom ����}�# � ��V"E- last�rowT dN� $(i�=�Y"|���Y��in�!M�.��hq��F��:� �� e�&+ s8y���'�Jam%�<8anP9fyF7&��olk�ya�hd(�1)/(d� +\!(-\!2d)$, $a�}��Ea_4�d( )Z<> �%�$d'>d� �.4 !��:J�%e# '���0/kO1��A4.� ,*�/:-"`��� �u��vc � d�(}{dd'+d'-2d6�'�V.6 ,�,�ZzZ .em���� � 2���onzero ��!��mpɛw?D�;"�28U �: ��F��[,n[,*fw+�9A�b9}  x1*�0��B���J�`&�>_*�:M3"816/$p(GHZ:cW"�a�A >%S/�ofq|6  |c��yf�� |000+ |111 v2}�2OtoffW B.dVd01r�|1�v3Rv�&"�;-�2�M0F,hisb�;!M�7i��6�0�Y.���9 e�w����B�Rpw_{GHZ}.rho_W)Z� 3�/\��mlop�!-�O��rFrR���$$i=A,B,C$,�KfK6 ��%.(� W--8� E�C��� J� :�$'i� �*_ "b�"g= F� ���>>6��5��^^&�(A�)��%����y|.���n�?W ;��9W27�b� "X <lem(}l�Ezb4O|M a &�w�Uie=5dfNu��= ���q�&g�A�� Z.%��J� ����5��J&(a)& X"�X � \,�", R�� Mb)& Z-. 9i �Wc)&:1.[q�VdBVn?.gZ{��� 9e)& P_1P*�. \i*sid51%FSf��P_25dP_2�2,B��8rZG |��q20|\K |�� , 1|e^{2\pi i=�R na�e^{ 2}>Q ZQ Q6� "rySy;�l��'`:E� j�9�"m� ?"�2�A�(g)�g�+P}(123)\*�5'P}(456)*��)R2T��! P}$� ���<*�index.�� �4H(a) -��IXa ider8;iWK*lIX6-���$_-d��%2.eb), (�d (e) eń&� matrix e)v����_{i_1j_1k_1l_1m_1n_1,i_2j_2k_2l_2m_2n_2}$�o�pb < i�ind�^5&$ ulta�$iM�i� $j j��$k k�21\�:8 F> D%�1 y!} y���j�u� A�1\8abcdef,ghijkl} # -yQ\(abc) def),ghi jkl)"� per�1 �1 E�n�E:��%Pa�"6]A��g~g��> -J000Y� Q�5 2�11]� +,� inv1�a60 6Ja�1 +"� inv2Fb271yzJb2�0+.�3��} Z� %��m Presenting all nonzero matrix elements of $\Omega_{abcdef,ghijkl}$ for $(abc,ghi)\!=\!(000,000)$, $(abc,ghi)01,001)$ and $J911fixes� otherB��by virtue of the symmetries Eqs.\ (\ref{perm}-\ref{inv3}) y2(HermiticityE$ �$. To obtain a trial solution we chose %�vVX \begin{eqnarray*} �_{0!U000} &%M&1)t} = -:911b_1,\\F]!� 0001N]|1]Z<1�= b_2N`1 AZ` 1F` } b_4`%:1%a. 1!b_6JE!#A�2cR010%090oJ�%1Jn2101 �BN�  Ca9�~ V�1)V�C =�2�%nAU!N--�6�< �b.E1)D)�B= ���%�>a�a3��A�1 = ->EE3V&2-Re"�.��A0�:�n�0!�AF C>`10� V!- `=L.�1]J�!!J�AjaBJ�A %�ARB�1 �a.RA� -b_6 \end.WV��( Likewise, �V non-ZE $\o�EdV$ can be constructed from��B�VW(�)�[a&} &=& 1!3-3b_42E� �/65a[!k=&:%�}Z6 k b_6+i+aV����where����b_1�t\frac{1+\sqrt{1-4x^2}}{6},\;\;E�b_2 = ) x}{3 \;�� = A$b_2^2}{b_16 m4d 9b_4$3x}��6x.�0}{8}(-2+(18-6 � 3})^{1/3}+>).����0A lengthy butz (ary calcula} l (preferably executed employ� 8 program capabl 4symbolic manip Ks)a�na�8firms that this>� satisfW " 8 i�aints L yieldB e success�bability��~�( $hbox{tr}\{��H \rho_{GHZ} \otimes W\�L6b_2. \label{optsol}6�}��B� We!@n%A ider dual%0lem� !b primEq.\ � �optcom}) \cite{Boyd04a}. Every feasible pointO2cprovid\ ract� G�B�Q�. %�a� yga� �ize a]�H $\Psi$ or equivale%R!associ%�%�",� #� }condia-���eq: -};� replac�%See incr�ng2W��F�bi� "@ _{V'"E ,\} \le \id_V" 7�G6G%�Ʃ���comple%^ $\p!�!g!6ma5�E�CP ; it ,{\em not} ne� arily aQ:�A7E�generA� aA�� findJ�aforM"6� (at are larg� a�\ ose PedTEJ]� .�It� important� note}�ɵny>posse aE]vanishA\F�y �%2�3Y�}}Bs)2ec�a �r` �`\ �R. T�{�is, letq�(a�)$�Ae� correspa�ng!"�aF-b�. Sb K]fMeis!kV7, �(A�0)^{\Gamma_V}$8��l a NPT-�. H�=if��A ��#c�'�')�\epsilono<�'�B/i )+ (1\!-\M )\id l\id/ {\dim\{{\cal H}(V')\}}$i�� $�'6� becoZ eW �eEu� val� $1\!\ge�\!>\!0oBoth $(� :band^}aiPPT�B� !�I�Yj!w6� T V�,{I0'$ acE( ishea�e same>zas 0\$ albeit with a smallerq| pr"� .�)$is way, on��n always�Q�.}]�;�a��) gi� ! sam*� p . � 2: i��0F`schem)�6��max� � dIXs ($d'E d$)  be �- v� fash�)�  III. E"�}not�w'aw V&-X��2y 1\ge a_1 0, � a_2J4>�V EH2 + a_4, \hspace*{-� cm}&& "^ d'+1)a_1+ (d-2+ @&\ge&�\^- ).3B3 R2V1<-1:eaF2(d'a1Z c�6=*}�Twhich%sJx,"I( $a_1$, has��be E3 izedIe1�w>w5��p(P^+_d .r{d'})�d-1}{!}"q�G}�A������wa ���@oI�level�e���,�O�O���97!Rх5_ +�%\$^2-1}(\id-,)Ͳ %�"�!b"� ������� � wor�} !h: 6 .!�I(� written��a y'��egativ�j init� �tz t�^, i.e.Q�(displaymathX%Y \!]�\!5�)2UN .)} %~-b2[e $N(\sigma�("a | ^9 |-1)/2$ �4Audenaert03a,N�}�� ,fascinai ex��s��mbl��F-6  F�*�, �!RNagree� ��5�a [-monot�su��me >!um�a�`squared Schmidt coefficiej")Vidal99�Althoug�D g{E8:in.d 6}�!.)�knot b�rogyet (6F!]�B*P� �ju�� e ]�� �e �.�}), � t�=�of:9>Wm9$ is likely�>Dlaio a 5�AB�fun�. F��BP Eiz"ZA&J���st�a&< e-�N� A .} �e2yyB� $i_�:�W� ����DV��� 4}{5�+en��k��>��b% $W:95$ ���B�B_)*W�sz)�!1�.%���.M� WA�!�w �R^R p{-Xse I�s� describ$ a� ces &�[ W��i.X!�-�XB-� � 2�F oz���lso/8bya^c2h 6b, a.�e��� may� � t1/3�erefore,:U� 0inter-convert�6��aincompar�"����s?�sxt� , A�� 6let�clarify%' ei��6�%�all6�x��e��� copy�2. �EBE��J�"�C)p1 of.�}2�z+��>���J�"mN�a.���copa[N$-�te.5�6R. By def� onB�2� . As a� *�2�s�Lh as $|\phi^+_{AB}\r{\!< \!|0_C&T\!|e0$ or �I |0_Ad| \!�BC�$�?�s�~�a�ynot%�-u �ec!�y $C$>�^,let us first�u&�>��,|��2!O $��t b�.4$�z6�0``genuinely''" d over�` $N$ �i���assump�meaU�\>\R�(.�\lE !|&�$i}\not\ge03$~~~and~~~}�Ch10ChVC,3��5-9+�������#2�" %�!�_a�(i$. For exa� , $i�A$, $BC$��G"J ��:2 $C7DABAADI four�f K� discussw��p���, su] �Rxace`}Z&&sp(�or"to checkj���i�?? V�1 e�.�T" .y)�xO")$>��t�� b I�&&I�BX%^$ /���.:2 \�%Snonumber&&g�"\ {V}}6_l0'a� �]'_{�' .KD}|M.�=ou�1�>x2=\!\in\!&�)a 2Q" �$,ma$  nd� ny ~� as*3belowyt&� N�). We6 om�dam~N�,4aus�*��� es[!(�� @[Ns,but only whe*3it� }or_$ view��:���2),��sui� �2*&���>�R��=x^iM�a�RjE�+q�sB�si|L%RH)B#Tr�))�y~y��&=��#}�A,6�2����4})El�*dA- n $x��FurA?�&, due (�V*�F�R3las����ە�i-ɉ�'_i��V�-0�n �!$�'pr�"y'�=\!x_0V0$Y) in�,Ishizaka04b}�Kd�),[C��BmN R�-;2� m \��=x_0>0"X/u���&F�& so %�0rbitrary pair�M&� "�" �` .�$��.�%��(�"an �� )at $p6<6�.U)M(. Jf  N� ��otR,re���P y> n�aeclass�&o % *\i�9��drastic�# sfiq��8on_!Bw L n, investiga*.� � a.�)���^{(N)*� nd-(N\k!1)9���{(N-17.Cob|(%�%�:+F�s#L!&M�hI#.�i�"f& ."�3%�6e&+�xF�h!.�:�i��� !�1�dr esx Z1�%a subseAACBMX�'!RB/(e.g.g3)}5"�Z�2'D5�|9v ). O�G5�:Dis*� e s.]�-E3e�bQ )�a o a Ne6by3 h/�;)F�!9f�GHZn� B#=�ZD.#E}#>aZ:��/�hJ�YQ%IV� �rh A'Fig.\�fig: .�*}��-F�-� (figure} \ce(line{\scale�20.45}[H]{\includegraphics{�.eps}}@a8{�:SVE@p�+R��!�'*� $r$ de�%� rank!�&X 1���E�V m�y�in N�)FaD� e b�+6 r^}k.V@]O �typC^4�>F.K �:�&60or��unlock�b�3 .� (BE?3��  (see  \protect{=Dur; }). "�F�� Q{�� >� Z�* , !powerA/6B,[3� .zR� �(D.y�&$�4 immed1 �..�1�f&ho�6� x -��-c#%�69�is6 Lfa� �+�:� A�&X(d (E7�,n�B*) ��Q> �� ad�(al# ourcE�� h! Cirac01a}IF�e,is*K �]� alon�7"� :��- mustaU�;d (=E� �>t �>�qc� � /+0tea� se�%�4,k���u~b  C-:_m�(Horodecki98$Co tly,ůca\:#)Q!$:y�$�,�E \!\left.�W"�?9��i%���A$l �of�V� s. M%a�&� �$|$aid_FZ��itV<per,I s�4al u licE�s$2L6C�! qre�ued� 9W9c,�=8,Smolin01a,Shor�&MuraoDurLKaszlikowski02a, Senb,U<,4a,Augusiak0�;�2��Ś �U��ene %{6� of m2� I0qA6�Iat� Iox�o\eg�� F� %��8j�8U&8 e�s��ver(n�B=�F��J�As !�io�&0pB�a�6�p e" �cl60E*,2 - 2*H*KEPRaс[g r�i >i can ��hie�(o'wh>�z�2�n89�����#�;>H�> R�;H"�3t��i���J]<di+(�D�"� <4��u�e,AB$ per�a global&E6�-e�C�� }. S��bf a�6"� Ks �6�A���� �-A� �&9*�w�cWei6b}� B:a�.���%�c*8�3|=���um��>",��4@�:�:1F�]�� �CEqz!.3)��N5t 5�&QG7){ �"� � ���>i 0(aRU"4 W2l �8I�"F�Ig0isw2�RDG6^ u:,�AerlN [ l"+ TL is end,V !�;:�by relax!�! &�!� �*?# "I "7 {V_C}��*��&� �is]�bl"5�kEA��lk�';��]uc6 map � $ 2*�<�Oanm��$�$"s��B���O} && s .�E�0�%� �� �E&, #H �=�}& .L && J AJ�A>�.h NEBJEBZE<(@^^ *4�` r`  $1j�#N�&@|Be z: $9�.#;:$� ��al��m� �$e adopt agcR:�Tr7e)�2�6>6U�u}MZ=x1%Q�3H% S"2C96�4>` � � � �OFO[ 4a�&�Af+'=Wu�/ \]��B� ensu�F["ists*)� R�?�� $0\!<\!f le�$_3@��� �=\!3$@ �2�f.�B$���now�&4B�2� l�-t �:_j�$!:g  3$, �K�ba"�J�#{>r \:�&n+�L.ce�2�%U\�rh�� 6Fa����"� �'� ^*Z %|GS BE"� ithKB�+�o� elf,�ex$�:"�< *�WA��zB�?�0�-� *6� -b�=�47 (=edO-�z�z� ��(33�P4�P4Z%:"F;� �#�.w $realizing � -�.�!a�:L�:LG- &=&�5%1QCJ� "B \\ &+ 61!g� ;Z� \� i�V�110�7*O�ME�>� ���|>|i)� 001�. 001|a ,� ,1106,110|$.���bG"QQ���atE1 ����nB �7I s. D�&Hc��of����a]C6�&{V�� ���9mix���:V �un� � "R�!:� � no�)�"e {�G }>1 e���isZ>X �0&U*�E��R�of :wB )�*:%j), � �>_ � %gnguish �;E� $�Ea�q�0$. Similarly>��osA�:Ki�4j4u� �II=3i�Ue")�2L (N')�'� �>8��I@J"')!n��23 b����>��X"9�*� &�(��9$)�a $N'&�&1Af&� �b��O(���N�EN�"�?"D93_at*"N�#� "�1^z(�� 2��� ��� mpos�2��s!�J ���in >�v a�aH�C*����J���*�Rll��F�AbeB &.:ed inde6Ue��U`1�#pGN$)�ar "�9of :T,9�:�-|�vai�� as a� ov ."i8�H!_��**>]6�a�M8 overdJD��!�-"�)�� %b�@differen;t�+Y8e(��ilY.pT!-AJ���cem��32�)� ��\"9 �"�((ry&)������SiYUņl�Z"�$/Tf&�A>A��J� So far&�con�'Tour*��G�$io������$TE�M=yDs�Jo �o�,Ea6RA�F�2� ����xi�L*{8 �>d'}$, PFo�l�Xpy��B�o* u:� &8 . �-�a- anti�c WernerQ&is K<�����s�F ^a_d"�^$2}{d^2-d}P&�A$\sum_{j>i}hsi^-_{ij<,p c: |25Ab", u%v��F��"r%�a_d !�projecAoY2� �)�LA�${\lHbb C}^�I2�},6 (|ijo � |j�4)/\F`2� �:�F$-�s_d:�� E� wed A��9&�$�:�q �"te�2 8R\A��wi�+g�_m�i��4ɮ��"�L �%ٚ�K (rSdc%��by_V%X "��UOz:)� R eCa=Fa$8d'+d'-2d} \Big[eH"�1�<+�N P!�$�$L!�}{�"�2k~d)!O�O-M %N%= + , (d-d')}{(�Od'}1U Big]5[1"�;+& ?2(�PF@7" &Z�"��/>/%�2\�&\!\R|d��sv��z��i�e��F c �XJ&�W�[ �q��'B'UV�BA%p�M��*BU )fe.(\{ C�m }{lci�\ NstyleY�y�&�7~%�!�>\.E G\[0.3cm]�ZUQ�6WJ. Yend �\�(. b d�.7i2w&>1-��>�&@!�^=. for %9�x . O��* ha1!�J�!w� >*�h .�(A�2\aQn�) �>\!2$pis[+bAo�L�: A�#> � >2 . }� )T 8"X � s{ "� C}^2��.���T!, eachV�&��+�% 2$�e local uni�g:�s V2e9�[ an "'l6 t�of  }R# $,6Ip2� �IG �N&&6BD 9 aOe-arrow\!X ��&a f�GU�.| . I�Z.o�3:A�E�EBA�>�=2^� 2�J�`�\ ��]�P+�~�b|E.�,a 62My]m& contradic� the 2K5&�(MA��DU�a��=�:XJ�)2�?�,.�A1Zb� �@/2�b i�b'6� �)c�ed{Qt ulda]�2d�BSJ�Y|J�2� q8�q)/�2�i�� )>��TiOat�!�2B2} �8A��2� 6q!!4%�>z%2) [bf�d�d H�#Ag direN72�M�{.�+l!wUigherR�Q%��qZ6Aby4:� S&��1.ha�M&�a��q�d�y".R�^d� �V&b�gn��GerhapsC" �.N ��4�a�#! mN�ib����FQ�M*�dis���case.PB� "4, Kent�4x8�;�,"03�:),]!>�/Er5�>� �,.BofM ��a rho$B V���<}�6�d^2�2$.z6&�l- 2x�3.:� �IN� ei�0��A/ E*i-�]o/ !t#in J6o^f� a, �.�So%��l�iA�e f"�:�Pe .UrmM ers �-��mio�:D1�-�' :3=ofFL'toR?s) A.l _� !\�1�nvY6��.� 6P( remains mK1m�ninvol�2�jgF�%�%�s������ummary:��>��N�I$is paper�!�.F�#*mC�WEx�A ' �Y*N�Gcl��a�M+su� �xJj�7W� 3xcGca�)mmunic �(a�)a3�#v���TAgf.G : Q�v&�^�mp�j*�P (a �02o� ;�4��;q8 � z?z8& � +nL 1>Be���Rq)NH�Rse�f�!�6det�n�)S"�r ly lVaeK� "$)�?S �O%=5�l~!to*`t�)b�XZ;�y�pvsRleO1pBbidden kA<:� 7I�S*+ZTIV�"|E e \ NX�3Y�a�9r 5��*e�A.ll .�"�5B�!�2�!t3%N:y � in� ly m�&H �4e��}�!P� merg@?to��=:e�o!a �J"�Jm��9�<:K%�76�occur� -�� �I9�. chan�4 �to:.�Jsh�emphas�)e� desp!�� � �K2�2}�U9+theor`6�!%�e���-�naEdesir>(� > ����x�A[q2�6x�k�b amou=y"a(=�69i�BiquQD�>!�$asymptotic��8"%.K _mea�0~ l >m ( .3�#l1r}?5:2�E{2�1��s an8A�?J�"F :J%k). MotivIsO_�owA��F%T���=�to� �%� effeofB2$2 �[ sult]Wy l�O)�1q""=FFF.N%|ABL%>J a��NV� ���E�_y�sm�\i�� up�@!Q>:%ց�. Fin�U* ��a��*� 2A:�s, namA�% ^:�!byBEWe J:��"� %:���� {R j~&�%��tX "��{x!r� "EzH�=�6lso:� >� '.�)�R�=�+& very&� � � , RT ofZ!���"�2b�ITpersis� !�= ,.%�e�2�JJ7}�ͼ.#�j�oe �p 5)$�� c; R/)&u?�r�bhow��!8ZY!�z*R) :�J�x&��+�F�;X�� }6 �C aN <syste c � stanV5of�yer� s�quantum2�!>G l) �qc�qc�qcbwx$acknowledgA� s} T!0�karch wa�6�l�+dur0#vis~#t 1ERATOa��$$ on {\it Q-,In&} SYkce8f workA � !r4 \QIP-IRC (www.qipirc.org)2�? EPS$,GR/S82176/0)%�BDEU (IST-2001-38877�7< Royal Society L+hulme Tr�H$Senior Res �Fe�*hipYB4wBE��� ��ׁ������" f�1al�M0�U]FF >� 6#^�����2�ixT,nA�Qit%*uQ��m"�tyn#BHz/"B�~2ք)�*rlem��w9�p&9��Lag�ee n� mini"�m�Xi� Zis����wi xt}&��$�L��-l*�:�_�1� �' }- \P*i=A,B,C�N�K 9lambda_i"�1i}r' [+.-mu6)p?\}).8V#&B�v+�#2v{e.�P(�A+ \) -�O� \nu2IOmega B�}8 WB.�%��p &�r� s>�FS{epB� �=, �6�&} %r$Y �8 $1�p, g A B C,!�ABC\ge 0u#F�� g�M�*|g�3, ��xJisw�q]aif>��( &&\!0�$:��'J�!%�+\!oM��+1 p2e�5\i�( nuI- 5mWWB5�LyN�-(z {e}+ p"C6\id + %�uvAi�+BB}CC&�R�*}' k f�9��&a�g�ZTe,\nu�=6u-�A��e p\}y*o�q��q� W�u��)es�=� Sec�Yj2T"WK}^' u'>B��z0�l >l �*=[��m4,Z�5�2��8�"h+Q!��>�C !��5�:j:u$�!m��Fb!%F% \!+ ��e`6}q<�xuh��e\!�h\!�坚���6� xl(, && \qquad�-֦{V_A}R��=>��J �0.�6�*�� F� TjEi�G 6�M"o �.�k� id��g "ݎ�A�a+&� � matc�|hJ� . >�Lch,$��2�, 8}{365��{peI@Q5p.0:0$�� {e})_{i,j / 0$ except���B�\[E�B}i�kϚ ~K��:&1,8&:8,W�C�.��1N�1F&�<,�F��L�(��{A)�i��. +40,}3}-.a�24.KB_+8,i+!U c 32,i+32!o\\K 42 e 62OC g16,i+16 O � 24,i+24 � O 6�66 Qb_2��a�4$i=9,\ldots,16�p��_ chooWa�mҟ�xu�&� � $O- &� �8A;&� �$~Z�> ���Y.nB�cycӕݟu�[*e�`ne�o �)�BK.�q $i,j��11M8kh �J�^�^ &&�C>�� =n!,56+i,56+j}=X�8"��&��-�R[ 7��J%_j}= Y�]+8,j+8}v^48+i,48� \delta f�D�D�'M\2*�� $XE� $Y�uj&��6& "� A X_{1�I��1Ʌ4,4��X_{6,�� 4 25/16UX_{2,3�� 5 B3,�P5 -5/48Y�Y_zYz -1/3.-2D�-%7,7g-�\�Y� �Y_� 35 -y�-26o�o Y_{5 8.596)8�>D6� D7 g7/8� !� Y_{7E #4/= (-42ɛ,59559})/1200"'5��*6*% A,*�, ide�� l �softw$"ca � V �,P?shosB1th�~� s&��1mOp^`��X �� S ���iceOO0Y$ $���a.ee?��a�sg:�,estab�X L6& ��� �36H��}��}��}Fro2+&v=non�Xc"�w�C�"�Z�� % >��� rmin2� RLfo*P: &M8{��"P� � &w'q>�A^�(r� Y"ǔPA&m�A&��>]� .YPs�cssWa�."��C*]� ">96"y��Aw.):d F�sBn�. J���X�m C"q�Y&�W� 6�(! %�&�2 u�GHZW} n�oF0TBmX)Rge 0,"_ �GFqXBoXG��>!�Z"yF�ZC>�XM �.5R6��Q�6�%��*�(�(g)I*n� in s�Dlme�*��  �hl� argu3�~B most� 2ǫ $)`$ ��%c�:q�{e�y���\ 3�QN Y�5�k}ˉa�reI-�[l�[ 6.iS�x.s ����da�=V"��. L$b_1=0.8/3=2b_2=4b_3� (t ^f )����2�2 .p�H�JI�"���U 6��ר0ʦ.\0|n��\=N\0�� C.j� v�m�����֥F���&��=.8���!3f\=\6� � D.we�bNbƦ2�8�0)�_ n�B0)A}�C)FC)�R^7��1C {-�.E1Z\%>�R�)C�\)�ZX \2�.D �.2�  ^`0�r�ayA�=ѩJu�%Zu�J�-v!]6�*B� �Ŧ�5^]Z���.8Ԫ |J�v�0�J\!�\N� �-f�%>]6�� E�w^e�bF� Now�+��ary�o�*� :{ ! senNam�0� fx a&�2� �andW  a^00$B� Be � �IYBj��+�%�w4�w� i�Dh �-]� eJ��,�+�in6�>6�>*e!RE L� ,"� 2Jp&,Y*�ZJ& Op"# M�.0!4cmV-!p\}F�!(*�-�*� "�&�"m �&{q &�C} \},�6�}f� .q9N"� B.l&� N�n� � B *sY�B� uE:� �6� �-.�e�5X.�.�9�][-�.I�0) C"�YB"1 �in�� �� ��.�-(pJ�M\� e�"�V&yY6 *�p ��nd.�.%)��s��}0�E�=5�l�� "$ .&��&� 6l ˬ$-tr\{= =-0.8$ ���M� ���� c$ �B:��um reby��v!P its l( r@0����<&? m�x �gs>�-� {p\,"V. .�e%2�0.4��_A_4�:6i�=�A\,�w.X�.��z=&24�4./Y-26# > N�57,57A2� 57,6> BYj.h60 /F 2,62^�64,64}=>Ib6� 61,6 _6�4.a6�nu�� 1.8F��4Q^A�u�B�C'^�Z�Sa��-a�$A,Y C$ s*at)h9qA-!�9B\,� $. D6B .g no6j �br#E"Q"�� 2$ "b mi�$g� ����Y�;�42�:{ o>��? c�9 vp���Ma�0�iBi��=J�="T-�g�to��(�� >>;�A�%"& %y�/!G�/^�,ZB� proc]\8g�3��9_ ��1��n� E�r[�I-. Math2� &+ A@�0��G>��3.�&�$+e�. O\+� W)� ���$wghznewref"����j*D y:t*�� n=\�*I2�&��*P�0.92cm}� "� � &\(O ^# (���j���6� *} S&�analogܮ@3�$��i2�"P �ha�>��f��*�3b_2/43=1/6$>�q;e0_��?R��0�= 11/90Q�E�&�4 u1, `�R�W>^] C-&I1.!2B��ahF��F =&�1g } =bJ3� =�.�,=y_��092�%�|E2J�E &�E0)�� /^|R=B\ $ C\0N\%, Z�C^A_\7!�b_3J',%�^F F_q)�6_^�1.y-7I\=11}/10A!7^�%�)Fe�!�&?�Ne>=f�:\7~\ �;.5D!���!b z�&�_ ~�~_ xa� _F��:�w J :� �\}�_1�+#�f�,u�Dm2�a�-L �le�"�0fu��� ,Z�,/ef.� �0t by>^1 .�0.~��+2?2�p*S29/:3/i m:�6I gya�kA� &&2��#(|7 ho_W"w.*� -b6&&� �i!�)\}:�&f&�/R��� F��� m��P�"�r�1� 6%/�0ֳle 6Μ�a�"L u�����n���� t�x�9q~q����}�=0 ). E�Z:�Qc. o( N�Z�,It turns out� -E�CaN�x he $2sq� \}=-�0� "J,ily closely.��B/�,4%�3"� �"� wF"�p \�Ky���q�>�G �03)2p\4�X( Y"� "9*6�)e9.3,5!#>W/2��{*F��.(5,3:T %�/2\; F%2 1A�@ly5�A��Q�Des9}��B��=��endXA�%��"C,6�A��AZjH%�cA�r�&AI Q-�.hroughN�.#U-A$.f�"1p�8,2,Y�!�9nA\,34,39F @39[ @3}{>A23})�.5N 2?\u.�A\,53,13�%�2@3,�A1ng3�s�* \b$.'7,1�. 33,3�,�q�17 e 233GS 1/9,�a2�al .s 8,18).!�3 0.3;�4g.#18, #.34O = 0.U[0.x2 19,1-�6B5,3E2$19 �235Hr4z� 20,2� =&6� 36,3�-2Y20q�=436H=0�r1,2My2� 37,3�.6r1 t237H^�6\2,�42�8,3h6Y2q>�8G^s.[23awe.39e�B^D23 #:8�-8FD.)24,5!�. 40,4c224 �240Gp1/9F�T�~l�I6YF��2n�������/2�6g/.@�"%r/r*��d�K�/cha/s. :� ver5)���&x &L� �fd 9�.h G �BM "Ta > g ^a (m�i"�N e /������ be ��Sas well! t���^�ooU! free.p$�^. k nu�6&�$omp�6 (.��"��*�)>�Hh�f 6$ ��< = $6$#Nnct@ 4+ igeni�N �tE @=>���91���!�-$2-�A&��01}{90}(13-1351�!.%�� )N NpN3��f�$}{30}(-2-4bM� >4>>4:=�� {\pm*�60}<47-30A�NW \pm"H$��1��a36h7i \�o1569-222V+3330.8�A+(6 �)^2}\;].p0 mupmu&�:qECle�zc�= ge 2Q�m{!�iF/)�� 35}$E���4 ]y�j� p[xveadw cani�[� �`in�9 ]x �dV��� Fv >1/9�rea2-nu>2$� h Qa<+M� $A�%��nU�eB �_:}vEqb]�"iY*�j!S�e�a�^:<� A�}�.!% U+ce�Ste��2:+6�4mac��s V�($p=1/3De al��4��4��4r�_�_ w`*�P:�4�B��7>�7�O JO >�5��A��:�Q Xd\QllE�pT :�S`a2�T9k��BbaTathbb{�t&CD�t$fni!�fFb2LBit E2e�zay�J�ugrho^�e$�: (�t)�a�@!�.7�s��U"-� =A>O+B��Z�s" P��>��W2Ó�i"on�oGoԮA)� J� i�en��B�BSp *�nU�)="�"@8� 1kQ�\} .*AA�*v�l^l�&A��T�U�����>�5;"� � boF��-#a�Z�d'�.'B)'=� I�HAI B� �9 �9A+B�?5� ��&�-A��ge\! ..�&��v28F��G>G�� $B\�$-�Jtr})1%8H��\ sp�<��B$  �dp �lYkernel-!i�H r��ɶB�h�J2��J�t$J0$��k$� $��j� �$B W��s1`w=(leav�n�l!()��&��:d$�p1|+z|efb}l� ef�~%w&�N��>�S $y�� $z� on-"� Q �d�~B~B9=(\cos u"�q +\sin u|2-&�3 )v:)v)�'1��D>D{s� d^<v�8' � &T:~"a�=\!B$.�$P"\�sor�Z_G%� $Q���@\!I� .h�|�����.�� n� �]- �$\pm Q.D��ԡ,��v$>$=�Щ4��:g$.R \!+\�M�Y+6!�{a�a  or,��$Q(�W)Q����' `���ت^�$P$`))V.Z;Bj͘ ݘ.96Ka/#Y�+�v.bс. .I �o*N6���y�l-A���>�\[ .�=rB� ��sF ef| +s^* ����2tF��]��B�a2u�*1����iBi!-f"e:� 1f|)!1B�1| Z".��PN�P��!)v esX��/wo-qub��qn�>cce $A��. . I�0>Px Fni�dnKy4�Ver# ete01d,I"�a}՞a�2�z$.�.�}�* �IJ.�5,}�a &� a��b���seU��� v\!\niU��uZ$��panl by $y��� $yd�yonD q8�ww(�y �y��nB�7 elf)-sSanO� u.lZW1a�( �( .�^�b�4 v4 IA�.�:F^�*-�-�Z)��j��~\�i tr}�!=� y.� .���,A�v i"k $ or $|��03��\�#Y� $\{Y�,�H }$ ("�2 ��Y��aCaN�fBH $<Z�z�B?� a���>����F��%\biblio��y{Ti onal�_. �{prsty} } the.$J$ ibitem{Plf�! M.~B. E�(V. Vedral, �@temp. Phys. {\bf �$0 431 (1998).X Eise^�} J. U.f$, Int. J.RgW f ]�� 479 (20032[DBennett96b} C.~H. , H.~JLrnstein, S. Popescu,~4B. Schumacher, �Rev. A �(53}, 2046 �62}4Lo97a} H.~K. L)(.e) R P6P022301 �12RNielsen�z!�A. 2� Lett-8Q43 �92NV�� G.  vG1�6HJonatha �D. %F6��B�1455 A^^b}�^356RDur24 W. D{\" u}r, 9�wJ.~I. O�,.�1�2A062314)�06g&�2a} Fa*�,A�DehaeJ�B.~D. Mo� yH +cheld��eO]0 65}52112 }22}4Miyake03a} A. R�7H12108 H6I�Lj��.�B� 68l3PZF�:diE. !*~G. Luqu%7~Y� ib��t:�qwk(-ph/0306122.q)04.NDJ�9�m�42o Owar8�a�  , KX;sumoto�Z M. M��N�70b50�!6a�SP02}A< , C�m1 M.��!8 �M�3A3 3911_2)��Peres96) 2�}�7E0 1413N�"�LM. , P2!�R2 � k �22��1A-19:f[͙�leR qŬ8%� 5239 q8).>Ra}�� E.~M. , IEEEp�n�v��TNvS4%/292M66�2{� K. ,:@!/�$^�9�02790%3B`&P b} S. bQ)905V�B��L ��*�( z7�� LOCC:~)edQ�&w��q� own). &�t2��ss�*:�i*���jr� t [t0 �:��3 99}}�c%& in��u�pe@�,blem whether� the class of PPT operations is strictly wider than t.3@LOCC supported byE�}bound entanglement, or not. \bibitem{Bennett99} C.~H. Bennett, D.~P. DiVincenzo, C.~A. Fuchs, T. Mor, E. Rains, P.~W. Shor, J+`Smolin, and W.~K. Wootter.�hys. Rev. A {\bf 59}, 1070 (1999).�@Horodecki99c} P. , M2lR2jLett. n,82}, 1056 Jq|Dur99a} W. D{\" u}r, J.~I. Cirac �(R. Tarrach,^g3}, 3562 d;jR�-6�,022302 (20002)_01a} J2pJI� 032306 K16Khor03a![~W.)��A.2�8A.~V. Thapliyal^�90}, !] 7901 o32oMurao�M.  %�V. VedrfY86!�352 U6�DurS2�= .�7H23040RKLKaszlikowski02a} D. .,, L.~C. Kwek!( CheM�C. h.~O61�6%052309 �22Seno!wQU. A�M. Zu �2x\ 062318N[%b2�WJ. Y�J. Phsu� 34}, 6837J2u�E7K2r6�6��tJ. Oppenheim, quant-ph/0309110.��4��6bV�9i20503a� 20042|AugusiakpR. �6b�405187.�WeiBT. WeiAp~B. Altepeter, P.~M. Goldbart�H W.~Ja nroJ� 70A�� 2M�^�b}��11142.��Note_for_unlockable_state} When $N\!=\!2$ ($AB$) !� $N'\�O4$ ($CDEF$), for example, both $(\Omega^{\Gamma_{AC}})^{\Gamma_V}\!\ge\!0$ and $B0BC^0ensure�8undistillabilit�6Tth respect to $A$, $B$)z4$C$. Likewise,�BDBEBF$ is �d.NKent98a}a� 2�.�1!�283� 19982�uiŐ~[b��'��1888,͑.�5�.6 _mea!^8} Let $E_C^{\rmd}$e $E_D.b)�.E cost- 5�le6"�-&�8. The transform " $$|\phi^+\r�(^{\otimes n2�`(\sigma)} \!\rightarrow\! 7}:! ja�a$� ta possi�by PP.�T in an asymptotic limim�Xhence a weakly additive!0, continuous -�< ($E$) monotonicA�er!�==$ satisfies!�=��mmE>N�d$ (see also \protect{\citeY�00a}})e.� rela�(entropy of 2w:�!7�s� an�F!� such1 s. Moreov�TY� !ЁI2$, 6�1�:E�)-2(|\psiMo)��666!$ ��0a bipartite p���. As a��ult� iPPT:Gh E6\\F7$,�>IS everyBWFSs��N�(s are equal.*��!��.l2014 �6� nb� :� Lewenstek G. VidB ��&�*� 2� 323102 6v�Imath} \setcounter{MaxMatrixCols}{10} %TCIDATA{OutputFilter=LATEX.DLL} %TC !A�Z2D-�Shell3XStandard LaTeX\Blank - 6 ArtA2^`Language=American English�$CSTFile=40 ` MJ .cst!�$newtheorema;}{T } .$acknowledg�}[ 7]{A:67lgorithm.16+xio2'2# caseIC6!lai.DC6#oncluAT.J>-�o:, >+jectur2�o:-rollary2�6+riter:�2+defini�WD2- *E >' erci2wE2PlemmaNL2#not/ &N2)proble.�P >'pos>�Pr2/remark}R 2% solu:BS6)umm6�S 'environ����Lof}[1][Proof]{\noindent\textbf{#1.} }{\ \rule{0.5em}{0.5em}} \input{tcilatex}) egin�5ce�t0} {\Huge What !@{?a�xbigskip {\LARGE Simon Saunders#med #�,it{Philosoph/ �Dics Group, Univers�$of Oxford}��� �!�� H(ists, matheS cians�pvPers have been engaged� this ques!�@ since well befor� ris� $modern phy�. But in=Hum mechanics, where�� w associ�x onl�  !�s��trikes�Theart!%other feal !lems: w!��nguishe"i c from B �al�$cesses? Or�m��l ter Xen��4unitary dynamiCS !EPs suspended in favour��%�s.ones? T!�isTQ.)lem4=}r�.l� 8most clear-cut q�%9it !�g)��|y: y ei%H8add hidden vari% s (a��pilot-wAA ?)ythey g�up 1. 0malism altogee P5 -reduc!-8oriesitwoategi� tiedAdifferen{ ncep?a!/%Xty:. �  %�|%}alY��!�u�"d�\Boltzmann, Gibbs and Ein� )m\rob u h, Brownian mo� ( !@M$s%-nKa stochaE prE|,H6�t� Smuloch�).%ierA? some4calledUL(epistemic}\i�m5 u�Ld�min%+.RiƁ a�consequ�@incomplete descri%�. I�F!la+,�,.� ta� is usuallought Au ���% ��s}\ �thu� so;!Y iculty!Dat has long bedeviP�������]a�k �E+ w couldEy be.�  �h -AOn, fail�/candida�uAUa E'� �OmonE� A�z(�I�ce}B�=��(e observed ���(al data. Of�rse�e&� i�#� are,.i-wm lievEhm!�be,sh%�# un�{�`!;= �� simple-m�d"^�se6 !Q&y.J- 'if ���.'q1@!�-run}"� fr� ie�u� M���to doE��obvious�wIM�Wng en��? I��e!rto!canA��U ��"v� to line exact�whils �in�e��n? act` (reached; so%�u����EV-2$? Presumab� fun� o9e num;of trialia!� mR�;�De0O ? OkproE<atE�rep� `\re�.of outts willI-ximat��match>.of ! : sumed i�*)� �i-�enA~�@if $p(n,\delta )$!p�5*) *7� m �3than $ < >0,$�$n$ �E�n $Ifet{n\�Ya \inftylim }.�=0$ (!/U�aw!� larg1�s�I�i A�toq#y=-��e/any-� N�AVI�as�is I���  e=T6� ���:a)�� isnd!Y � ous !��!�#H anw��,�1���U/=��>W � �$on between�Y@e�nd � iQ;�t2bearsA� a.�� imI|to � -�Tre)��  � &%�E7\�H "�� . C��A9�.!* .}�v.�y?��� -e�iFf��aek)�T� , at leasT 4U 2 sE<-X:e:ww lc��N6�����2Fsa�us!$those same bJ e�wri�Ea�p�? �a�8Eja?s�n�3o knew�`��� are;j �2=�!^ b��lA5��I P��ou� wor{� ��.N �be! ɼ�,��E&ong�ȱ�& Ec��As*~ ,�we�ly � Z;� atU���e�nex ial? We�Uwo5{s:"�enume_tem T !v�NBy (i�)? \ <y�=�]k� ck-�?�� "� Becauf� im�,� �kb| �eof l al��ion�2 principlaat^�M`track2 .N e sl7lyɩinvolved>Zit F, howg a�#o�"� onE�may%�E� (�� the CQ ��L � � dubb$h�i8�� le} �Lewis}�(acCi�9.� ru�w (a��losx � y. O� � a'an�u��I7� ,!)i�r�see how�~��it{�1}a�jus;�� it oo� �^Qʅ�2XiPdic�( �]�e&A�� fu��2en� �� �x��� �� iM"g.&� rest m� auth��+ciL.  !e�_i� a � ir�A"��qH6�b� fsM�!- based on st x!_c N� �Yit�a�%tenq��j ��� tailor{f^MQ�AQE*e7� �say%Qir ;s�M�.� w�n be �%�V+�,� t�aD name. May�Yo� � n!m}! un�art�U'a��d �a� �of pract� ��sonpperhapA�e =st ?� I!r deal� thY�<inM�)IG%�} l��|6e�i"�, like�qda^�~c�eI�e�M��� worl� at��2atE�a\Z^�p��wh�] ��2�A Iqact�q�!Y|:S fix�!���� . Q s (1 -(2)e�n���ўa��()]2�w�%t wasU alwA� so; -n h�~��o aband�%�k"j Jf!4�d, want!2��� E>mad4 n�q! � le-W P'no reycEhuman ժ4e=aim�A�4` �A{anq�  experiUAXa��� � di"��� �at.I(!Zgener��B�evg�n au(�� E)�itself�ves�#ittle��aN,u�A��m ese 2�>J� ?\MbI|�] �# �ZA��!@cqo %lA7&p�}%H�no�mse�F�%�y21�r� � n ne��f!�lan� . No �,b� o�"� �s. Ev��n ga>.4hD ecr"� �"1�iuAsymmet�@a: - $ix���� dih0t Y ; coin -"g �Jit�Sr�Udie�74� �zA��+  ea# �s,A��anyth� you�� . \ }/J�  seem 4v-rid1$�� orry�E� �� !��T&Lt?��is�f margina�i�palat%�by put���An"� �%a9n/&s� �!t(��atq�J6%�2~a8 typ�w2E� ). B�� �, adop� e pi�&I�Q�� trib�$& �!� anG2emA�(��)� hyp� &� y��yin�ch�i�sent *"� �s")�ve6�}#� naC per,PZ:��lual. 6�A�9N�� isz"1 a�.%��- %�� ion� cre}be"/ valuqvm�2%~ fic���%�bmaA�E�rld��!� is�a h� �  1%�a9�( ; itrLsotA�t^is9 � a�9�e&w��I�% �mi%^�yto�,b�s5�" 9sA�E~�AJsa�-�emU.� !c��s%�solidT );�be aS�!�" er(< es�hi &,}3ll�  quan2�$�a�!�Cup aga�#EzF.%.�6�$o� t"Z-5(A�o!�s-0��1� �se�tur+S���b� a%pA@so far���  pro��(.22)  m pric��Ou��ory mu 0$]&�g�ng�#� � odoxy;on��r�+er�c�t$:q. F 't�o� <���? �p� � deco�0 -�,unadu�.aA �'&�2seP {Ort �H)subG on's��m-� �� �1 $a$ $Hilbert sp$H^{a 4 inne��&8 $<.,.>.$ For $�6K 0��proj"#�?hat{P}$! [o2$\mu (R,5o,i�!>" (őitN. Born}): \�*b(*} R7{A���� }z }\R� ��� 2�=\frac{<@.>}phi >}.�qu� *}% Q@ RHSA|j6e$%a�n�dA�c5_/7 ove�<y��,�$\{�_{k}\!�f1�� 3ir-: eg�se�5��)mmU� � ity). Lo! LHS,�.� 5��cor�:o�%� �r�� � (%%�it{-� s} $��T]+i4 ���i-�\a�Ak�\n �n�( F e �;S�%�2p X�� �l i�������b<�Cto doi�a D#ɱal&��apparatu�� stea�;We? a fewd e^%�) orN9�� �J��em. GiC a d�ty0rix $\rho $ (X'v�elf-adj��ɛ!8r�eone� � )% vec�5inM�,$te� i.�u>���%�{n�rho:�Tr( ]W)>� *�Ih $Tr$!�A=�, yiela$ aU'ed sumE �i��s)�ed��E!� i �e��[}�o!3$ ��lgebraic,u� %�C�'��i�2 (myal %�ing). U� >e E� meet��.�|9%mE� A:4 orN4 PE��� ~g"� latt��2i4�o�"$a Boolean ' (S*!�ơU�pi /� ve�it%d(� ly) m�� h!\ k � �n0 al \aXdem"-� a!�&&"'!$" �*���!�O Fz!�tot�&-!�c+,u� celA9A�m�  #}& }[ ]?f$��!.�6�aBo$�d�-$% d>2$!,�<0��rv� ,� ��e*rѮair��!�!�tad�s!6 $H.$ !c. ex* ahqu�-�,>�\)�ACp2q Z,$ $f(.2RG.$�I1E -F'�� � deri�L!"�:!"�W Y�it�e �h2`Ũ�9IJ \ orJ0�J4 ;T+,! refl� !�} prem /�� em� V,2t�edq�"�2 !�y,o�"6�be����suq�!Y��`(6;i�') �/me�$ ano\  �p�s appe�! innocuous)�i��non-triv�0> or !7, laB]>_{i}$q> o�/ͩ� span��$\chi 1\i� , $i=1,2�CF^ \pm >aI1}V _{2}$Cv$6N 1}.� *^ G�n� ����ѡt>� +:K-K5sYet! 6a_{1})=2t��$, $\ $� b"UB� $f(%.:D+2w2FT+:#-d;� 6���,o)8�4��x�Afollowa�at�|% +B�k.$ SoA m/aA�famv.&�� �tr/t�"--M,�ug�&�do� � mutfC[�% E�,E$]\neq 0$)$�cxt�-��be sed�EH2��9a)co�a��ors? L JaB,N�h��2a�YB# (von Ne�n'�"-go�+�x!'h�5&Vs)�2�`!iF�mayC�7�un�4v�P�"#+��8expres�  ,phenomenolog� p� al�*�gJ1C� C�)X� &�+ &�N�G�$����)QA�(s&�'�re�d4O�>�)a#�|d.FG� ma0 pposD �5 us*"0 : ��" impla&�&�9a8 �E!&Z7in �u2�9�& as Kelvin� wed�� "o0l ws�y�9w *C�@!�(alQ4U�+m�#� b� f�tretch)"�6 !�iUi�lM#l�]�sp=!4y�?55�� ge-7ry.�.�p��>2o�H*�2 3y��A�  �u�U�aN.aJ�-�5�N�7nt�2BR9 �{)4<�l rtanl B�;�  }�o' symp 1 tic &�aAi�Gduc��>R+. He soi#L� sQaJ� !Z�F"SaveX7s%es�d'��Br,� it{�=on-free} @#� a�y@  mv zero �"ne. And).�c*{ h ^re exclu�;�V6J/g\D�n�:� !.lt��v % �,!fa�L��(�0�F)6 % _{� })=1�H$s�*�M,\nNJ���,$.�immed�=�4a�6�B�$% :�\~ �!��/ELo� ($% |,-C|>w1}{2}�K |�S��a�no .�����if>^�$L9ge)� $1$ !N0$���? ti�Kly roFdaOo�,� it.S ����arbitrar�c! . A�5!�a�Šxwr�3��y,Y9O � ,1 the levela�Az�ll,PE���6�� �3]O$)� �ьb�d� �&: al�7�� e6z�e��sig� %<&K� I�6. 2}$�=bm��!o Mdiscove� .�l�>�!U24simultaneouslyv@:q+Jr:-}$!�� w drawA�&E a�鍄a��A�`)Zontex(.� Bohr's CoCS0agen Interpre�\on} A'-+&��faithfu�, Di"*leA �= arity}% ,&5%!��>Z  "� a��bPfin62ea(� ��^5 �A���!� )"mea�8:9 ��7�6� be�S��dR<iss n��� Y+%�defb0ss� rea-d&X�N"P(�-upu&of�!pl9mk at~b�=O i2?ataP.�i��&.ly fit�SA"�9!��&#i!(���o*�?�'��8l:om%" genuP5 nove8&A H1�:<!�a�.�e&�4Un+'s publI�Dri s�?%`} yDemb�Ys��� Bohr��A�t -" wou� eAI;u*  M"to�it�#a�!�.  looph�;ISed�i*�� ��%f��"al �p � -�d�?�� 7� *��K ����1$)��j�f�{&t};!;ine~�d�5�AE EQ�5� hav[0� (ere. Such aorq=*h���� ual}>x 7.� s� ap� � ,Kochen-Speck�;%c� effV�>rengtheof�,��#�`:��*�!8:z ^!6%� as%� -��a@to>! %xum *�Cb� �#!u&E . Leavso� �a."U�� >��EKit80S��&�no� :Y��"�; ) if G!�;be usG �a�.S_&M8Z)p"!X#. p2�!� �! �A�@3�*��"� squa��modulu���m itudG��teB�(%�i�+��%�i+2ggestAl�?�6�!��(2)��Aso� ��nse�(1�E9T% �(=�i�S�y�&$2�$Q�=m�i�D��0�H��m�j�1-�Au(1�GneK,� e,,� �Qit{A�nA@s}�Yliea)� ft}"r��%b�=�� ���&�-)+&� �E��aqAQ:�"!>�&<%�2sN  �"�6�2i~ lev���3�RL!KW?.2�ker�F choic� &�l%equivalei&,�� basi!JIn/!�as he di�M�m$� �]� *�, ae�&a[!�r� m$�3M �"�&. �N"� �r�F[�3 ��h-g>a�5 r$HfeC% ���-��fr�Bor�Hshu�0, scr�:0or diaphragm bol- _ laborat��bench�)�!E� work��andemE�%4's fur�Ns%�A�Ja' M(���L�beyond*�J> epts (�����k"H y "�  @)� )xr�M�@in�&Rno}� ly��um �I� PE�n�E��5&�ZGR ��,Z0��did+N �U�o!@�t E-sada\ age;�p!� �n parc�>��� �A�re!�=pi �6e.AZna�c{�#tomic"�a� �an&�H�iori}��jude�� �.tFo5 � a��N �m "z3SfA�e�]f� ��Uat)]�!vo�eaf�/ uTFewL*rep�3to� 7�� analyA�ofQ(&.M�" � ly6�Eum fie, ��uGv��/ *ric}�.�ͭ%,��'`$ trapdoorsrLQE5s� gs�&u baroque; �A&)�b[0es|& ish  �$-and-fu= conn�"C@�gA��� ]!�AD.ibe�d�� %ctr} �, letew Y�,as unsuccess� �o�f� ye hope�-IS delgR%�biz psych� )oN � ny ins=(q �L �!���&� "�)crd*g$�#)U{P>`P} a+*�j^�*�� �4 n. T�6+ B�P(C/Xi�I"�P�6 � �"-����(%�Q��C*u�SalL�0� a =Q-"B"i @ /�#��u�Bl�->� �s, as'�5�I W�&ova"�Qnamely�; figu�$tc� &� re[D��EA� veloc� ). C�s�(in�7� �"o=e�& F3 guid�3 2at4���`lowiHra+  thr� 2$"� N��B ᅅ�!yN-V\, A  � �Xat>%+�B�&(� da�M�b�" ��xH$B�!yb i*S9 %�c & Eue�A>!�f� (u�6�}�[ ��er� tiA��}.6 . Di2���%�t�8>�aXM=ual, ex� in a�*`Hsm%R )(b#T]n-loca�>-F�y) � %R(macroscopic*= � hangፁ him�+; dvo&9 � &�2}. SoG�N"CGpK6? M�R}Q2Ra�"� �W.�V:�[.Z&�)on�coB�af�Xed4��V%"�)%��B!*�i"�� Liouv N�ophaF~+sg.� H�#�fan��~!�qY*N�.�*ilibrium�:�2 O1"I|umvG8O�2� qp,"p &�relO#�T �2r�"-�qa�� �I� (}IXZhid��=$Q�MDR mackeyp�pyJL%�.���sit�DA%e�1U� tha@9&� V~. A�6w�:y a'�4 (1):e|c�V� �ͧ6w<?Wa<-FG@(!+� nor� !<��%'6f ���1'� �_n5�(i�R�V��SF�I7ly do!`a=:z�!&6%��. Now��� �&*� p�d:Xi fir�I�p�isa��-mto �@!y,2)���lt�impenetrS � L��F�3�VB&����9-$�r!�!i��se&ys1� �"� P 26Ra��'n�A��<��s�B(l*%-% tude_;t�un��);=el/�M�6�� )l� piewu q�&thifi�6+\  o&��(  do� �L&:I�$CE�� ly*a&3 }o!�e� �S.s,�:Y%ny� �ce?L se#/�8���Bo�^b(i�@�,��j"�9i�r�FQ?DE�flo�P�Y (ms�p��TA1����`� � �&D �$.-�VV ini}E� �X.Pi9t �7� b9�fiat}�!���gitQQ (��l�O� aX�9>��ul#soM!�J�$rpcA�t {�S:-� E�u�atUEdo}:�c"� to?�m�Z�sp�9&�9SC >�_�InJ.!��pdu�9!k2�� �ivJ�O ,!|"� �(�SJ� emptO\veN�/) irr:��Ac� A�be� card yI Y"� &PL izqd0tr0sA�e�I ywI63�% 3ingWW%�4mid 1960's Nel�)�*|* Schr\"{o}�erY �� %# �/jMarkov bsB�a�^ ;�� 1970a�|*i>\5"� : by Dav4n�c�1&u�q��2� � onstruct.��els�&miA� beha�W�a�b=1;�L�&&P evol C)��= �dem��;���Ub*ardUVY� �9& -teH3 c%��cll-Zm"�O, ��%�iv�() Nt �/A� 1986��,Ghirardi, Ric�� Webe�"es�+ ���+g�oL,�[l��g origins6R�Ey'�N�Py��:{!"߁wrea:R� "Gdm(-v+d ���1h�� *gLw eleg�"RA\2A:�E4�c142} `�@s~�TdA]be}A�� m]�0rm&�7} d�s =\�)(&�:Q}()dt&�2\��bf{R}\cdot % dB}\) ?.�6o \aj��* (QB�(WR}�*�9o�7$ � ;�%UF*si ;$!?at�B�v a smooth �TA�!�q .$B? 4k5 ,3$ .vH($\g�y �xa�S fundOe�x_.):%No@d)line{dB83(t)=0,�� { }d�(t) j }=�Y _{kj} �dt:y*5z�nr -bar deno<.Q. �+:� u"8*�y�#a�!n6F. Each1X spea�d%.e w�)� �^!:" �<.s��7N4k custo�pK ti3`� "�f\L�6ao2DrC�nroj!��5o�?mgk!�an� �a�I�U�7P*J� asatB���yrq�:!��4=3's u0�xp.)�y+�)49z �]m�%2�H ne�$ c� �!",�F��D�g[��Re*� �� ail)��(R�,�g�5�5 �.�qMS"���!�>�i�";, Eq.(�'�R 3A�K&%&/1z�o� e�yC %�!X7/V�j �H*�(9 )=BA}}-<,N% >,,%"� =-\}Hi}{\h��$H}-0% �� J�6� �H�94Hg !*�� &mA� ���/mu�'trid1.� =�t���� Gali�C3-v F(�Y�?w��l\� on2� F�)s��](%�\�6:�f,% � E%�OKll}`��20� "F� �9 s atKrI� !duy!J��f����pe]6k [�'��B8��d.�� �N2,a��V�rem3"��z� u���� longe�%NsiV���z �2�#dr �0i�� � a�*嫩)!=�e"_`�w��ea�*/�v�2R5��� �g�X �({<9^�e�2VJ�\��=�!�o`as hvd  ?��n$�$el� eak�a F{b�S\ax� A8N1K@�/y e�Mr%7E��5-wr"�on��own*!�d�^ �"�J� �w|o�;O,C�cRf)^]�y�2JT�T��eE 2Q!-%�!T�Es͡�aY)  4VRrRo�y3�a��,�$.y �G&+*,6��I/�*^dA��=a�F& "[&DB]P} Re�Q�am� convb ow$��agPAda�� �&S=lesbp�-t���7%�Fp� e�Bf� ���3�G�(al 5)s��;d�B?~��#a�>p - me�-FjO\.�O!��oI. w!=-6��/D'9=a���in!zBs"A�1 ��s*&eB+ferred�. W� I�e/l!��+�ext�W$alz  (at +RY �& f_ �DŤ)�cX�3=#u*�*)E�s�!4M'-��ak��zinJ�R. F�~oC5�V�-�s|AT�� Z���/�e�-&��!�a�Gin��@F�X�p���=�J5W.!7 DDe �.Ja(u)W @HE+�o�� >Ma�L���-|�(PJ��3it{% u}./��';%� ��al*��)de]iof�sedo�{a-�e�= �Qf*�T�>�A0"J� �)"�C�orJyM�'&qL;5Mg�`!�eQ�= Ve� mass{��o��we�� coup�7�&.m�$l�e���h�v sis � h2A, 5}9|�L�:�ua��� (� �n��k'me:A4i&={A����to,�� regioE�nJ%�.�91�,� �G down!0"�M�-scalw VpPc&g��m�Elax�r9Y byA@Y a�v"\+ aAmo�a!� .><&+{(ime �n 1arse-g?I��A�e�F�|p*�%�  �&^1%?\i*L.|EB-<R mole�)!��*y"�co+5�Uos�@ed):Hplaf t��!~,major school|.�&�3 "V�  EB�*it�s��P"R Z%;�Gr���� , �@Zn�!6h$$ �+�$2c ~�a�qpur��6j_3ppP."�/!���, �gI�<&!V�"I/�lakaIa�N b�aP � sav�eR�g0[`o soon (  �VdwSKprek|g"?A��gD� tO$�� \&R�,m4:%�GK Z��ach. H\�,����n �_� A@u%�A���&�P}� (o dme �Yré�!�"�X� &B�6E�3E �G!�'if�7by�"E��7$�E lB~ ~A�d�� imV��qi�k{/!!so#���� !\\E�K)q9`fer�'mea��I.Bw�%18�I���a�,a�q�q�at � step�Y��%�.����2`qY���F�j;ruQ�� ��unc�psAB�� �{o 9!�a_� !L 1x�*R�9�=�!� ��n�o /� $ s.u]miՁfT�u�A�I\l�$$ z e�T&", �**)of>�,!7pae"ng� a� ,individual b�ޅ �^(�hat �A asise.i�c t �y i. Fi�h6o:AE�Jt���� � '��"�Iso�m��� a�>d%�der�HL:T8IK��l��nd&-SCs7� h�>��o� f&&". AAy� ps ���< is a=f�M�-m��� nc�� \��m ���VFj rtly ?ng!�b�5A�8 of.k c9for�h4Zw\��*s8��-�*R �o�� oZ &�&�mo2 /��-��!�bE�&N%�em*E��  -�}I70!no���[&so� . I� 5J� #@ ��5�=���];6QS�DBhb3A��8&�2��hy*.at!� �Amh �+Aed�4� it{\ }"�(&� ��� �N ap �a1(t�q"zu�` �!ginA�Cy0<�� ��*)~ A�i#g� Jm al =^T6��E ?U8�f��h!�"�9$|d �.�,MK�;�/omB2�A�.�Ek� v��>L��=A New Dw��A)�Ru�� 2k!�Y7! /-�>.�-�� JemergenR� z<�k|�ll�JtoW~�� k� �;E2�/b!�{i\�z"N{�&6�36� MvGzs hig��degi,m�"&nj4AT�d(�h 3$�4 $zero volum�(Nm0Fh�i'�-"��9�=all�6e �U � cy }W2le!!%o2��*e&jw \Pit{*� }q:�� n\�� ���_wm&A"6�� (�P;K:�A�lmq&�lE�k6f'f%�}<it>JZe��1yc�TFpZ���#OG6�. VNzB}S=M \ g}AUthird!; 6�yWW�ulCn! -* �D %�a]c2onship"�$["�� ���c �^T1� ���8Y9in�@� }%� Q;ɛA>eM{c �,�$��,]\"* (%mteness�cB� $C,$/h�:y $F(C)�c:�s $\Dë́$C$% �*% ���E�0E? ��<&�f1n��$C.rl g�` �n\n�oc�Wd1 &:JLB_{ � }$ (�Gi *�"ka cellE�v$�r�Z� t|e>Wm .$ W ���!�aa-������,u :H\ps �\1a�r \lb� 0,1]|d% �.2�/t)�&�i�a/�Zins�to!.H gVatl. jE�qEl q ..$S\�: (i)4,"o$P�b�� B�,2�$� �vR, ge (�S)ii) "Onya�vmap $U:H./H\mu Y�%&�%�`)=:$U�#,U�U^{-1})$�&%nceu(i.�j� \cap= ^{\p�N }%5�,N(v� � �MF��!�\�\&a.�we? n� 1d�B~inu� 5 . Our�imA^���s�  *�� suffi��UlZ�x��z�BzA�CUp*� fcun�gly�a ee��@regular polyhedraq �r� y }(m $C$A�$note $F_{\M� }��`�K�Cly�,J V�� W �".�<)�  un�8;�2e�:*)nevit#4 failx�e S���r!�,7*�%�Kizi��O� trout om� Cr �)[^.�a=�'F!. F�=�-�|i^W��M� �]�>Y�'�Q{\var�]�Yf1�% !�;4 ng }�F�/A di�i!��m>kfk}\mg2...,d�]f2� _{j}.��1 _{jk2$EZn&�3l��0�B���{�J ۡ �$ ,�.�,��:43%Xu�D|�gLpsi =\sum_{k=1}^{d}ck=R$ �ir3ak(��K�( �7:Q|R|.S:��� �*} ~�!kBvÝ�,2�S2E{, }j=1)�. .{��-��3p�Ы�0=\exp (i\thet!�k}) �!�9��!%bU_{ / }:..q W-2X.,]H� :��p&F,, � (�aA-:$� (bF�8e�?��i�a�i�`�A -S-4:,�� �� i�I= +4*F�7u6i�M By9��.� [ eH��y���e-��WP5�C:M3=%�.(y*1}+...+d}).$�W� e $d>1.$ ��e eWpi� byBk}= *(k)u�9B&aSJ� @� �M�a permu�y�Mj�u-b�F)s r>�ea�s�%"�). Si1b�G=$,e� &XV.yz��|>$ a*H epi (j)}�CyQ% Choo#ny:tk� ���$)Ň�:)��4 :1}+(I-I�j��2YjE>ES|j �� �i�8�Ha���.� �c�6�2}ŋ:?d�:nh5�a`��ȥ3ego�/��N�%5�2�9 }&�;!�2i?B�=I� N�.R�&P JF !@{����j=2%d*  \E� 5�A �&�Y$k$O+ z�% !�6{;E�.�a ,.<%q�" �x*[ $:R��!�.F^ ��t�!Sr))=�o�� $d�h M�E���"t7a�1eou(�e�;)�`x :M b�b�J $3$ N! B�%�-6�1}$� 62:  3}$,6"4/  �4P%�4}R=1m�� 46�kC���j��� | U!���=0A�k=2,3,47 �}.)�q>AQ3AQB..�)$t[A F alreadx)k+(u�-�� levEF\�,ariantW}:t�2.*:�6�3}�rA�2g>E)&!..� "0�g.�>J�P^H$E�� �Zi4:�.�NY�hA�.O� A� i+oa� .gs_%�0$bD��:�.0� EjsoE�d�V~N�t�z P �:eigen] - �B�} �i#�5H#�' thod� d�sOk�I2�3^tr�n Deuts"��  WalG��Q },y 3KJ next K2i �d�f 6 �(in"�@�Z%�.?�; 4a~ �- tYsh��~."��h!�� o goz^%.X%��� �.or�=" }��*'is $R^{nQ�H�jisomo�up$L� (',dx.)��k1�. $($���:"E (� & �ln�ser��'�:*��+.) \ {}"%�}����H=LR�2� % 7nd�) K�:�i�p�!�$m�|�x�{ r=&u&� u# P* ��sB$j:�SP$Z���p�% P�z��$\  vert&�E� j�F^ E� i-�N����.�\�w (if ��(i��O�)[# $n=1�\int_{-� }^{r}*�DmE}u*dx� ne�(v&c>A!-�C��$r�q�#Sq ��,�H&�.� s $r� J r_{m-1inuc�! �r� �_{j+1}z�=Ndxx%&�m!� $j=0tm-%.r_{0}=1.��}=-?$ �� s�+j��vchaƔerS51chh{M��9rA�n $R �[R(=[�}!�]�~"��to Fe�;menvUW2abM�E4} �4FX�PDU�M��mu �%B5 �*L a�6*$���)t�� iYz d: !y:8jF��&� . LA�)�&g d}\sqrt{3}+ G m�Z� nV@z� )=�f*m!�}{6�}R@.:9 &:0.L B.*F.��Ī,�M&:�"84,�2 & �>Q�y!�U>u�[m$���3"E��Y�V}$� *s )�2� .@:^{j��"�$:� k�E\E�b kL�Ew\��+=$"��1}2!- $ 3%�.k 2Y&�] *ˊ1A|mj}}FJI�.7r�qŠ iX. 5yY�rC� �pO� !J2�k^�>S,;wm:��h ��m����^3(��F r��+x*�m5NB+)�& WF?&M vѻ� }{m}i���I�a �1�/�&� + z$az :����-� z2x.� $�afixed%��a�y�}�xWxus�7&+ } $\a� $�'Ջ� -�5�P�6t6"HF=�..�)6T 2��=��orm7 5p� e'T $zϱ)&+�<Qm<��.���s����>F��.�O�E- ceedۤy��[!H� �5�(�%~� A?MJd!i^53 �p�`$2�_I&�FO�n K2rg(/)Z$. Hr4� -c,�@caveats%�:�(̃ß sume[�T� -��p�0cLat/� �/�!.�.�dSshacNJ-"��+�%[�-Gleas�� �Q�a!7� ce*$�pj(�*}U�h��F_Cif� � ��r �on�-���f,HAvb(Y�ly �I�)���R ��:�tly&.�.)�8"Kjd� /���e��&0!. /Z�"�'. -!5�"� �TX�*��5 M�x� t�&�-� G�*�|l�"�<�"�.g *Q�31H�to �����$ �*NlA��.�6!a��i2�llow Z5#I]F.�e"�c�O�s"Q�:N!�b5Y0 elow�Us�� a�l����1�<c!�_se� ?����}qY�6�ko7(!�CiliGI9u�mfe�A�.*U+ ��thE#�abV�%hUNf" -,�#no�6� at %'e1QwOAO 'A�P� ��ppr&�6uni� J 8�? � %��J�,, neaN% threshol� �,1.�$2l$;���)& $ \Ee.pa% )$RPO�],"<Y�:Pn��r�ej^*b!�@�� � $G��a�*N�"U�a�YdofO�ercub�,�2~ˈoon:+3lG� =]A�o �6u_�w'�D�� <� ;Y]�p��3ger�5�6,a�O\b">i�%�q -�"�C�BQ~qO�*oi��a+%�!�e}xd\=.��ŗZ0s�mrob*/�'Kb��0 QAE-+l"`�/�XAH"�`z "�  )$}�W�noIQ�9�7� �[����%gO�$�m=[�hE9!_%�-oNpIt�ef��iv����6�U$&�e�,K(wA�10^{22}}�W�#mWDck�2a.�(6�&�2�*Y.�@}w=)e"H���(\!��yet1wU�c�ofe�toE��7"<@m��M�.B�L4�-v��� mbig!� i� �i.[w��2_>"�]2AU2�yB25 0�� �A��5,� sub-� lM�9@ѿVx��NA5� N�rre�) d (bv6=�ab)i� x�EH�)�Cby virtu:�X�=�po�=6�y� erme�g2dEQh� n�a�1mi& l�{ �AmdeT�]�+ar�ey���s���<��k2 von �� t}�m�o�!/"�I b4 b!)���$2]V�j�.��)�$\in F�wK510�s�W�"��5�AD&�? *(`$a$,$b,cj�)ascrEE$� ւ�~--��al)I xa��Z�dt $� )����uX-AA7� �� B ��_I2> �p� �' Ya� u�7˩�8Mi�cy��'4o��&iz��iE���e�e��J� yAM"��H�� 4a=�B!��8�b�0�R#\i�.�-��a���ri -:� asx@# n�!C /I�� 9l�H_g�YZy v�"4D�[�):�m��(@s:�Kc7)ex20 <.sͯo?�<"9��mak�U$����* ��&Ajf@e�7: %�,���J_y?ey�mWh l��A�o!Ycb)s�T a2NNie(�x�kGo"���E��ha28�5!�( ali�o�e�-R!�����,won.x yB T�:Dm8D2�6 �!�mo�B�? add ielqBBj5o��IkaL6s�M#m vailS2��a���a�4A���'� B0A�"�A�?la?�i�J �����I��J"�Oe�xD�D;ELSneM*� fors�8�&l� E �O2" (���H(Q& �'ɽ%�vvJ�a�| tead�!�iU�[i��9Hle �r�T�UwB($(�O/@� Ɋ�Z^Ky"�V 5�ng��R��*/�� er-s�E��m,"� �r5�<an Wbper mix (ar�7bø��ut kal*+ 7P�E�N�5"UXm ��roppedA]�aZv�nZureck2"t$ ^vT��le'EB!<l��Iq6��!�� )q�.�G!��&�!o.�UW"R�s-XoM��6�:*r��*� ��K���� >y<6�IC&6�<�D2!,��F��  "�j�q}�)0i�GG6[Ra supeQ �>���L�[,�o�3!!�X����Te��Je.\foot{% '��y�l%� prin��,�Vmbi*O�UKEJrecogn�+�  �����s;%�in�pZ� �g'H �Rdva�o�"U� eh};�'#aG,GiE]N9m�f .} A���*� !%��DU!O Zo!��)� %6W@� .{U�;u} I��� &����iUq\e�#�n���E����, u^a=�?5a- %�InQ�'g�����\i�@��cu�(���&w�U�F�r�u�rZ��by�. B�LqC�i:ml�a"velop�!�a�p[Q}Re���iR)�A>eaEll=Y�*� "�cm k� &!�"%Yb�Ath��oal��f&_H�e e mo�5� ia�˄4e Heisenberg's"1J%p�D���[JDpoIi�3O r"'�)LXW�citJ7 !%A�s,s %�}E��_%J��@  �?)b�fa"�sjHl�tB��a^���<oions. J�0G�t,=K_a�zaej}��her���^o.9&bMp��=�%h� vagu�A}�E�OQ�A)bAe/-a/ina�:S0no/+rp �axJ. VX?�m'�s�iYlSL� �<'vaY in s�=O����*wOi�yBy� )��a y��ir��lJ�b� |ArWP�k�v�ic\a�cha�{f �R!��4݉������Ͻci ����8nd ch��tryK2zojj�4։om� �ar,��Vbi��mi@. 2���V,�]� %N6}M.��S�HB�LJ�{�=�96��e`�,���mxonfron���0 gram[ �KvaT higher-� >�sm����s2".2. m�.!SFss���a�MB�.��l�Y���^y�I�y)飥��� >�nAIeBO�U�S�: �!).:�v���7ii# ����W#p F(!�();&ϰe��_2F�v�vI*��rsF; ;���-�Ma��-e�J!out�?�w�sae�e&�-��;�y��"f٦ s"3S��t7�..&�aʅ�.A"w2�w .��diӁ4G/.�od�*�U��0 af all;5�NrW,)  e�� -+%~� !!wo��!$M�!�ݙ ٙ � !�A��ru�9digm /A�2� ter-f � j�du�Jpd �8!���&��K 2EWC� ��:۹�c TJet��z c������col�2�F��2I� {u� "��R��!*!)�c)M�Qiԁlug�Y&;-=�&3�T�Sra1EwmԽ�L�ina�Bb� t'�}yZcM�� t�L�ViA'�AA)�x�y ectr@�f "W[)}1�!�emplo���]�nirk�d+#o��� elucN� j-� red% it{)���s�<Pop��w&��$M�.yn ! E���j � In fact� !�~[j�af.���-G� ��q�l�c �2Q"keJT\�\�qa Qab!�ct &�i�X�!'E��0on�%m*?���ne�?�%�+s} N `\hee��ip�Xi�� 1:1$�e4e)��!#35Q�7 }*2� out� (as�{ c��� f�&L%�m9u�isplaF i ��&� 6E�l�� �)fP�a HtQ��o ��ia:t�� jx?�u'��o�of}��#�$7.\�-�!�n�a.��!�ZC*^ ine�Hwl�GA0�c��n�tmal2���isT,!�'�5��w�3�as I$i��-�&;7kil+��t���Ge I8`7.p [�<��k�ni�tha� 9�'V� �%! �U(1)�s�.ebS� G JQbqJ����l�++ A��Tur� � Z���!�t�=some,� � &k\E� al -Eu�$n����u� "dy�S� w �QIAA�n (f��vMm9I�QR�.�u@be�Z" �y e�sU#"�p� ��&b�j"�3_�Rf]"l�N�Msf]�s+�S�"� 6t!�� e ��B�[ 5 �-�&9"T ��&o(8�F2�anomal��q �j$.2)� r�(=2�"matL6�ea�3c�h*ZL1��a�oo�1oc��.�� �,��Z notha��am�I�is� )Ocan���y��a��i3btinue}a�vio�b9��(�  �^i#��G� U�i�hw�.;*�o"�Q�, *�'M j )��E�io'*׃s"h�f�a1�Y�iI)B �d-� n���eZ�ZR�5�a YB segGs�yof �7)�!�=Qw� tend��*�. �|�5y i#oK!6��y<�R�o9}�v. �!< )\8 } ޭk8toV 16iwIx(2 �h�4C�����>`�Yi ��*on-�A3��ur/�����Y,t least it i�Ls clear that on branching we \textit{ought }to be concerned with weights for =Tes. For it is obvious a !^-] personal}@, literally divid2din two, say - will lead to $ded expectations, and this ,0be so even gi�dcomplete} knowledge of the�0 process. The� sucors ma�Pffer widely, yet each �w!($as much ri!L4call themselve!e same ).(before. In �fac�9Cthere!c0no $% 1:1$ cr!9ion�identity%;"}, was!_(define subjA ve probab!ies (a�aftery�)�s})��erm%�A�2�f a r�al agent� a set!�4games $g\in G$)uE# some%-ys��HE_{k}$, $k=1,...,d$ 1$associated-��\�Lquotedblleft payoffs2�) -�Jcre���.4s, cash prizes~A�%�e �(values - be� � bsa[i�  revisa< nd sc fi%"e" a.W%�be��y�a� any %&) , Ty�X%�ar ��s (po�.!�$ negative)���#pos� �=.% is!%.naccor$to � ett?mL(a special k�vh ��� volv�stE�0macroscopic oe!$s, describI'eff! equ�s,t ��sta a"be�2% d�2.$ \ adop�E�nsc��,!~recogn� arbitra��ju it^ k�ly�a t) mpens�a�a chang� laba�6G by .%A,pa6}�cis cor�ond� a�1 � ines�E&�V��)6�saig M:���i��yש~�2-�I�PA{�f2+^:8<\circ }% f^{-1}$�i�ie/� $f�:�)$~ "Z5#y -�, &< !��� ���i� �D&�!�aF�  $U �Ź$m{aer� j� �d(�.R K! best? e�lA  a �r�2���� twi���s $U:�}� H^{bb� n�(an!nd�Mventirely}3�lof�s �t�Tthe}\5{%s��.� �{as ��d!�| Q���$U]�UM=l dA�U�1$��I2$:, )a�0is ��� S pe�sa���@!�e�� onsA ween.� U#ith�wRa0%eVme�y��e��lev�� ��;��i �)�� -� B� . W� ve e� ish�pwRinc�w s. U,our�M���G{ e ��s�� $, m�;%�b� aliz:a �Ble&�o . SiA�&�< L����7 )�al worldm�!�ec� �� i�=& S> ��i�yN�$��LetA�(g\thicksim *c$Um"��6&#$8 }� g$. W!Q quir�{��o&A B!�Fk >l'� ivalu�M"P: \begin{eqnarray*} �� bf{P@}�{ }EqJ} & :}&J�% K�g>\!- &6m* �V�T > \\ C bf{M&?�% l��l,F�2, \end.'��q]well-sui* AF���prq,itM| motiva7� E�gr�s;&�!R+� i� ly% {Saua�s}.*�dec� T8tic axioms natu�"m !no&� !f��q analy�����,;r�!,% larg���) its �����as� sh  see,! Z fail��h���f!+�al  "A � .��w�e a�ep e� b)Uis���H due cours Firs.�6]y-ZY�pro��r�is 0�#��)n�!��)�- &� assume 8�zP��,s linear (so.8(}x_{1}+x_{2})=e�e� (}% )+. ($݊a��v��A��N9 $).�,f_{s}:R*� R$A�%�� ' (x)=x+s,$��l�k-IN>$-I.-x.$ �$f%�%/ is:%�����"{bf{Sure-�!�}}:�(it{Let\ }g=��*�>�mat1,/^{�N9+%p}�� %>it{;\!n\�k):�9�b=�}% (s).K\ }���$% I am ind�%`be�/i�.H(s��iawW �I $g  nd��&enrQ!�$V 0i�A�� =M$f)coT���� Zero-sum\�!�Y)�}��,��� -I>; l% itP n }�I1�)=-%�}(g).>� \no�nt�m�!be&��GI%�my bank(#o��&:$*� ��!%�Q!�batWm� pa�oT1 $% g Ihim� mosZ<� b[least h� �faccep�w� asflay $g,$2 s*N  }N� %\�s.��}als� � d��a���"s +#A�explci�� ccount��A���, I �>Q$ �"�S$g$, F�%&�%:� k vyW!�oa;*��xi� sit�p �end2 %�as �hai�ed2`�/e��m2�swap \Y�Nb:p�� I � w���!b-sp0� q'R!�*I�pay�he�:jbo;� ꉙ!'%.�.$ W�*�it" a�.�=x��PP&V1}�% N2}c�.(�}O+ ��f�`)=% %TCIMACRO{\U{bd}}% %B Expa0 {\frac12End&�!P}(�2�2}))$���%�!C*48-�6�$A�invari1� <permu $\pi�#f hi C�T2�a�y!��S  jD BD5pP.2 Z}U#i5�X}�2P.$ By2 .�s� *H Zxnae !. |#�%C�==$P / f_{-%�Itb�8'2  pd�n!�q c(%� ��� � ���%%�Z�. �}-I6u�1 ��B �z������ag�!5]c�AO�n ),�.�V�}�X.�}AS.� V} B���*= ;�F<� P})+]Un����)�%; �.s( pivoA*� 2 , ��� good�-son&h-e�D�?���E,��� � � tail*�/� iv��.�)� e"�me�uo+"�$A��� step to#)� �a genO&; . Ob> �Ag, go�0j�Չ�>$a42�+ :+c��3�� �U�D1}"=� ��0$; o � furk�nteceA&��/m!d�} a 3��� $�9�hA�$1}}$ yield7%e h�]A<2R<2}sSo� Rd6�#*�pro�%orJ}� &1#*�: }If u iN�Y)d� u N2})E�{!*n }>8 @.� N(26(: }% F-� sA>B� re r�MrF(�� ogou�-�in yhe��}$�(*8u�&�P}qwC!��"b��4w�2�%3}V��+ bf{GilN���}:)|6��F.})�%�-�a6�V�VJB��NV2,:�*} Gi�5!'�Z!� �t)�W fullZ.) �E#Q-B�e�!�Dexceedingly weak -MV E� �Affac�&2-be� 0#ha��4a$f� �pr���belie1%��5pe#7g1�#>'�6isn0 t�nv�� h�al*�(� ��Rz�-a!�ca�* !�*U)"�r��&�+q5c+&�) �le �� �.�+�&� Jrag�92 ect "�7.�%it ho�ge not �*y�+f/�ala�de{'y/%&p%�� � ŕ��(a ohistor�-T l;EP�-ba�!�e� �U�,is `!'E�}��K5  B-�you)ith*@--l<well;�6'tE��/A��9 th.( /sM��e?6�6* neutra�5}�V��C� M�!E�d*�is2H0G0D"�)2$&�"��L ؁�] &)[us�-6m�KwB�,!K �i�e r���/%��- er. �Z JVaZG Jtz(unA lH+;5!�[mAy� �Ss� ak�8.mq� cons�k !�AlBon��4>�.d<itl"�0b  -"^t��axA � � !.-��Bu"�&.�%��'B8"�$��a�!� 8sketchAWe{5�� f�{�;0 fis ��v��x4cipate �9�"atb.� Parf psycholog� !�t~:!~!� m(*%b4*I}"��m���ţof">(�% { t} � look>J�e��ofp- �.iv.�H A�at!Wdoa�!�abF�=�A�n""�i� w3)�un�,ty� V\� ing v=e:�Yno"a one}E� �Ii�1M5:�; wO?hAD ],�$~7�+ll� 0���A!M�me�(N&9>n��G)8?abl�- rvey;e�@�f apa{rP9lrA7 E�a�9h� =.}q(�8��4X5q39a"@8�,hno}[1fA�|;/� {e� el7W%to ignor-n/c�Aly%;�;A7zer���Ls es@ sd &i�p+@y�F Q�criticis�5�L� adERA7/-5� iG���o.� *]>I1Jq F� as af,)a�5$� use gA*%|I� . I,V c*tiz �(m!^�)�m&|".�) &�9ly de�ed? D�it tell.� *re�,5k� A:�con�!*de. �ut 6 -lif.�'s? AlE�o���-m�l�$characte�;6��+s1;��& (althoug4+mmon �"�a.D variety�eracho*�!�3 Like���4A�.�Alic�$s!�A�.!`=�2���+aMon� B7.8���� G �� B #�~ olut�@}(elsy &&!�de�- �&*�? Ma�e�7�dbemyfe�# es \!=Q��s ��� 3�w�A!e��unt? LDZ"y ��deny}�� id *7*&�(+6t&��)L�*� �)W }}�$� suspic`"�ZA-ooL@ ong,�)��� unwarr�d or in|2� 3#p�� (o��a��)!�A�B��or�A���prompz'/ seek�/��\; �ApaXa�N� a����!a*�V�F2O V!!*hz *jg �'�B�A���� .t���,E7r�g��^h ; cap 7 , �iŔ-t��e&U�!��E�t?�#jof�$ a vast amA�.)E-i�@ it{\�}�O;,���re�Q�X.Ge�} happe�-in�Me �!w�*�"�  laboe3y^sum�e�e�))ies��re'a7�V goings-o:;>h�w;u3�� ����;`�"�9VD�2!�( dectd� (s � deem_; a=h=C�] AVp�Ho��� iw,��(� �1))w �'&��m�2ly;TA,�a���al, be�8�'brs{4nt&� *��g�<"0u�\� .q"e�ssu / becoE�L,�%kA=� B � ��it{caE}5A �:|2 Ne �Bitude�J!�a ���-8orHom�a�-g� ��l no&�6Z��ere�a�am5 l��d� �"exhib9+A4&)6�� enco�ntoa*B *�P4q�No}"E-"�;�a� ach�! is�a%KpA�p@a@!�5ws"e�#;a�}/��al li]2 y do%:n��~*�*0* (��a�d;c� l&� � H2we� s, ra!G�-6�!��< ��� ,sI�C&&Z� ��� (!54AMin*" pplq?o"|2�=� x �3"�FU�*� \ge�A�ZM3%� !�2| �=�����7-8� y��,c� ;���e>Bg� ! ")01Ma2�A� it \� �:K t be� e�A��6�CBut(z�%�� eX&S:1H ing,��!D.�%�5-�? ��͎>� r77of���xsfa+i )Fed�%Pan��3"/���NY�P"[>&��!�A� �4�P 4!���s�5�w<) do! �! spea)  �a"*Eh0Py� �9/ aY�2m: �f,.aBkJ�-m U �<� r 0;9%R Any9E!�7A��H3e pu�5" ,stic develop���90(sofarA� R� !� L�@v%�e�LM�). Exp-�s�3!� ���IbyIkz%� ��["!�likel�(7 "�ee iencnd�  i >ir �B�@ err�?+�w�'4gpr�!�lq' �!E���6��regarwEem!2}Jis�"�t, ��LCl��[�F�-�6���C4��0seem �l62� �undeal &�Q�9]� . I��[�d!��_ 7�R}�AK��urn!�)ran2M(�RA`% ey br d���w�D�AI� �aw9�5M�)Za� i:2�@7+&fB-��!*� a�� ���Q !AI� � akes�c� progiv!��2rY>rKof J�CAe�d?G�<3G^1�2a[&A!U% scalZs ext>Dly rapidE� �+%T9H&�A�>. coupl�.9!MOFX, =?��� � ��TAE�7flu]� s�a %A?� inuousx he�D�T���.�!Dpe�P� O"2�tt�J�] rol ��!��+�is!�noi�14amDbK��wor� se elimineg- \Xin �Ni�K&c>�8��A� YWC.[?lyw deal� �(Ax he l��!���ive�)O�� �OE��ke�;ena� Kh Q���is .::AeY86?ropag�le'eI�J�8�5om%he bus�>a�*@�"yaLper�it�ǩj���FlE�y�.t!� �� f5�>�AR%�N��O&1;ofZC:�IE!Z!q� ���r�7m[�!�i�&K2�#Wore�7p�sx*� 1U� �u��[�"�)'sam�7u�%U� & in�X7J.�2�Yldl�F6_Ug�"E��= !� zMCVta rol3 di�Zn�5"�`f#st?*\�w&�=�Fm�WD!�"� �1�(����9o�S-�>� �E�:tlyO qagra�N }� �D�F-eG-��&� our *� !�at�d:l?yA�@�]�() A��8.~���)�� �Z-w=( Z.�di�E4"s�Q�availa�!=y��N,�! corp�:�"�� �$Axfavour\ 2���f�1�� Pt�O four|:ceP(isq OFFI;��ldis} T thirt2-1� �l�Z?8Jn m^�al� >� her&Fb�[okA��:B�bN"� �W out b romi#*c>M5!&7<�%-��!9�;�S� �aH�W. S93�Tact ir � how' "�M)yli] �!��eas�>���}9�ofh3<[�-��e%e�� %�out �%e��6h�1� n� t�82��oF>RA-�Q$O1��?vio� ��M>i:Aq��-su�0=�i(sA�K!,s e�Kc&����. !a��2t��m����ce�bjRlse� :-8�u�I��� each1�, c"G���� �-��&% !:��A:%eEfbv�(@Yr�r9A�A)�%"4&�e݈%D�&.H���!B=*E�leaf !�i���A:c�Q,��JP"WE$� s2C�) on�& >}%6��I���-�&�(%%T����e< ll >Y P�� zD d.y &1��un� !\5�N�1�"�V��DFQɖ�- factoE UX.�ise � G �ata:A�#�O:t- a��Q �(l� �M(/aso�oa�nk �n���D"�E���"V���9Lo �OrA��I�A�Y]!f answ���"b�GbA�cd.��TAgno�E� �� )0i`�_#.]Nitn"�� \��mLTd!l�yup/� \Ak*�Y.^�ru��","��# ch aH e�R�EaaM�&)K*�&"2�+no �cgor~�.�.\s���2� Z)�M��N�_�T� �4$ rehearsed o ��ran im/%��< Form�Bsof�CQu޹l;6� n��&3 -�"8(�)6add�I2�5)�!&�S9�co� gqX_on� figu +T�eS� �,B�/%?:]HK��m"�3M�pi�Uin � � ory,0!wav6*�univer�t=les�)\�tree, �sA�a��e��sin� �.�?�[*$%B7-%"E�+it�\��u��Q-Th.cly;!n���ity%Q� �l�<.�gct�l Ita� �/�,[ �.�Fb1�%! se} F�` NE $s56)��Q P ��!p!b�j)��#�!���ueia�9� A���pKI�8-%.�Ft���pP� iK |3�Nle#LK �q/�Wr IAto�1 ��1�mld� lgU *���� o�U�Er�1 &?a�s�l4]dQ �O�N"w`�Michqs�)d� a+^ �Pn�b�^4 of���R s�Bk&� E���S;a�m�$% �be^�3r*�!QorYfK{ "7" KzBr�P<�Aa�*N � � lle:�-.** -�),"�  i�i^b1GfIa7 �!m&� I �:�-9 "4:� .� . MoreG �U-i,.�=}.jA�6� &.'hI�� (6�gqU� Edo P�0)�!��i�2�r� �-e norJ&? �-%�>4G YD% *�"�� >�+. ,�:.n/�V��g�8A %!=�V�`�%?S!IRT.�ad�te=�B�e quibblaLm negl]��#+ nBB+�Rof >�)����YM�z)|�$�K ��oA� #�H��t' cq&��=c� re,��0s$ /�AR B=_��L��=And�n} it�`�-2k���!nW)f roxi� �if �- merg�Gth.K.� � d���'t�>��!g}h { -"{ -\Y�� 2 2a�)}�SR<0w!3d�s&��� ,modulus squa�*m�y��<��&� )%vx i�C��i&i�c�p�G.l h� . S�AkAKLv.�?y -\I � COda seam7 ly�� [ed:��A�mI� $c clas�l I~s. "Nol W�'4A?� �� f z� to "b/�g�9i"g.�ure��Hf���thb-� ig� �I@ �~ce;� B��=� t^fth!�b� b "�*�h� it{any% }|� .�)�!$�.��!s RIg E �E#�E��Q%A&1 eKZ�a�PI�^$fantastic;p# nH�if&4'�.reAlg�+�`�!8 ��%. Yety%en�# E� J=�&�� I!&�8��M al)-�r ��q&.)8 r^/)!�ensem�e��4> �_F���f�!&�a�� ��� wtmQ_Im �.) I"w�*e &$] unte� z�e��4>U'R$ Igw-)�1��T0,�!5>�;��o5 !�� ed� 0�ka�u v�#�%: �� a�*i�V�a�ba�Tmr'�;I��.cic V!)F�<.�� G :-��+!3� ��tX,k�us �^�T�#�"�[�m�Pn�J�Ni�s%.�Wigskip ��bf{Acc4�wmmf}M. ankE�Ha7< Brown, Antony V-X tiniI�@William Demopoulo2urw-m%�� helpcsug�a . I oqUQF deb% Davidt>9s�� rk I�  drawn!�hx� ,to Michael D�Y��1om k!��)�� N`c8��DtF�AZr�U��!@��*� %vHM�QLbibliography}{99} \b�,m{Bell} , J.: "O��lem!�605�6in`� �%�it{RehC6Mod7[P�]spvXbf{38}, 447-52, (1966),�crA���E�3bR.�2�S.: w�z"Q�ou.�4:r cosmk;st�16x Nit{DGraQq 2}, C"4ham, R. Penros�lD. Sciama (eds), Clarendon P�%, Oxford�481) pp.611-637��3J� it{S*!�E�Unsin1  MVJ!�Cambrii{Uo M �(1987)e�/m.�tu�_, B1�it�w> of P"�Jy}, Johna� $8nd Sons., New Ya\(1974.lM�}�9, Df1�2�T�o�7 x%D�'a�"O it{P�l_FՄ,Royal SocietHLo%�}EՁ�4455} 3129-3137E� 99);*a on�Mt at http://xxxx.arXiv.org/abs/�(-ph/9906015=`Dow�! Kx  , F.�� A.N�i� CoP H{B{AK<a&moQ U�1Sq��it{Jour� of S�P� alu�=bf{\ 8a1575-646)5.�G�\MwHartle} , M �J. : ��2��A�YL�,%Cm�y�=�iy�0Complexity, E� p�<O ���I&#�}, W.H. Zurek, ed., Addison-Wesley, RxaA�890), pp. 425-59=�Gl�} , \ AR�WC� �Closeds�k�a6�c]�=�Mh1 c�5B|^( 6, 885-894%�62�(Ghirardi2}  8, G.C., P. Pear0iA� A. R�(iN�Markov��772rdC��) ;} tane���~l=# �o�%)Z icleJ� }�Ōal ɦݔA4A�78-89-�=�Lewis} �� QQbE�A Sis�t Guid�  O"�OCC^�R.�d Jeffa�Md-�� tudi�,In7#qL9B%;��$}, Vol. 2,���$California�� ��0);"�|�=�(s?%`Pa�A[}��:�� �Nk�M]6.F�B"�B��6as� AJPer d \ \�P2:Popper} , K�ɡ� s�/ e: A�+>;re�v"�z it{BU@sh&X�e�$Mid-Centur!mC.A�Mad(�llea Unwin, �N,��153-91ei57>zK.�1�%��?Pu�!RefuV!" RoutD $Kegan Paul2u33-96!�63.�� ,�(ed.)�a�� Iea��1�.�ofFZ Berke����6.v" b  , � "DB�*�% Rule�  O&]b A�:6=���-� A}�D460}, 1-18 (2004),��02�6�2>�%�2=Ti +v ���T}��SynP,�0114}, 373-404!z98.�Dat ��01�"y }.� V�Hc Var- , .>�E���Earlyq���.��2E3�� s: F"R2��A�p�2a(J. Bricmont�� D\"{u}rrf(C. Galavott����F���5�?,e, N. Zanghias.), S� ,ger-Verlag, A,1V,�a04067=f.!�  � )/OSX�2�z  G��)8Economic \ Beha�# r}, 2nd E�P� eton1{��  (1942/ }&'��2�Q�]�� � � ,�sg;"�w11104 abbcy atedt� 5$pub�ja��2�8�lR&�:Q#en6(� 's ,D�f�:�2�� �l��A�a� %0.ofjT4� 415--439��2�-�2:�" �!� Sa�k.hya��\j�m���434(1)}, 87-105 �; &�-"6 �2 7144}2 �3>�N}/"� e L�7ihood: �$oI)�5�!�of!w�=� �R�&� ����}y�rth�?�(Zeh} Zeh, H% �)n al BE�D.a��W}, 3rd�;B��lina�99.�� ck2}� W|25D&_1E?�T��on)q1�to�%%Jm i$C �s Toda`  bf{4��(No.10, 36-4� 91F�z�Negotia"� Trickynder B�f��KCn�~� �i��6},�84, 13-15, 81-90%x3)Seth6� doc�} ʁ \s{Qle} %����< \usepackage[dou�paό]{set e} hblDATA{OutputFilter=LATEX.DLL}!Ve�7,=5.00.0.2552�0C#6$ed=Wednesd�{Aug(g 18, p 23:23:446 Last�sed=Fri7 Dece�9 24 913:52:309.�G�ics��322�.2DMoShell3StandS<$LaTeX\Blan�Y6 A�Sle2^,Language=Ame+n Eng��$CSTFile=40 ` M�.cs�\newt�ema'orem}mem}2a6U}[ 7]>o:7lgorithm.16b�i.'2#�" Case:!��."6Do�8�.(>-�#6, >+N6,:-rollary2,6+�4��.+2+�,i�,DD{��2-�P*Ex�!:R exer�>2( 2Plemma&L2#no�o.�N2)pro!N� l>��:o�6+2V��*R��6%�M6�S�M2N�6�Sum'*�~�of}[1][P�]{\�k��0bf{#1.} }{\ \ {0.5a� ,} \input{tci�x��d�T} ��8center} {\LARGEt�la��uS�tific.� WL?Simon"P#medoFa�Z�&>O 10 MertLt.� OX1 4JJ�y\ �s��o!�a=bst�P}: Bohr' .�)� 2���/ a[ic�7n"�!%op�u�B$bas;�� tfu#$h��premisg&�*o�fluJ&� e-war'io�$$ 1927-19392J�/5 � F>ain �?(m4%�h1:&� F�� de�gliv3�k"�B�^e� �()P>��#ged li�� ��x6��q ppea�5� �;I#W�6�$�(upq�9B�x�cb�I�� tV} �{9;!�a��|�unu �1} �e,�+�uj fu� p]9%~n%A_0saA�(�T�\� K"�$$f;f�m�be jud!Ca fail��  iDL�\�:m6n�mLn�%sC��=q�e,m*6p�^ it{Despit3!���y�?�3effort,�a uE�8o�i!QlK_�(s�(ofM*2�=/.v}\ (E;4 ein)>s�2�G  N�I�� *$�r�YoiIIB� -!MQ&no�$?�phenomen�%�-until!��� ed (Dgd)./ }(Wheeler �(Hon{A QUESTION POSED�3��32��E-iIKl [s)tea5AD twentieth�u�$1�aW A�<2to6n6�fi�camE� age: n then|it ��d,07maj� {�fA� quA) unanimousnWse��2E pilot-q3 y andC! empi� 0)"K$ "�$non-relati�ic A;�zZN�� 1980#&rF`� Tm�`=mployB't�VSCiA�w5�� 4a)rmalism,f��z� on�*R���sK;c�#ao� rd-w�"ansF�� ."�-�� y�6il���?0Rur��i�,oj'w�D=F�_%�an8E�new@'ic�A�@Qula��Am&1 cess ��). WhMYt so �. ed? �{q�Z�&�J1)r���[W%"S��a<e9O�DdidA)�@���r�y�7,!rfA/o!�A fla!3�-�%�B�t�9e }?�(. Embarrass�� ,�>cA�l.�)fe��&$ywe!���AA�:E�$5AKjis}�*�I�R�,id��OH�r}�S b.�ZY�Wei.��5 � ��a��O[94�M�*mmq*9oL*Ia�V���I ofa�q<�c.U(bo&5�7s��a�NWIa� unneAkary:-�� �r��o���&75! 9�-�%�aRQ���-p .A�Iw)\-�" &�Y was}A�commitv-b)�6 o a  =s5�-�1a�!� oekneo-KIaan�]�#now ve�Ge�F,t (see e.g. -&Faye} Murdoch}.�f plen  e~g#-E5�% d�'ta�.�2 8S 91nw�pl*� aᯩ+AYvic .?�_ll�4� sd�-%"}�&�(\��.� , if< � �f�W�Cq��'9�Xsider��,�d uit�m�*d!,l"5�=mov� 77 itu�:al ��c;uX'Ji^ s�D�Fa)eme�Iersua�L:��� �L �� �yq� ���$���P��matrix&�0; 77as�� /�^ayou�J5�c)�0(ac&6[Krame�chi�$Heisenbergm @1$Dirac). Cu���m{  1(�}�er!��A%N<Jto�O�*(l%m j }; o�9��v\yA�m��im /(Beller}. O&�{2zg�+w�\ ��GO *��;�] confro@ he� llenge,+ d-onV,�igT�]iL9�6� �buU o ��!,Źa�<se�>.. A�Fl* "c�1riO$�KS2A0�xI�tk�� 8ty,\footnote{% ,.��lse�r�D�Ifea֋3�on�6l5heI:E��&�8mN%�&�? cred��,�a!!lis�MR �)��A�t� Wor�FEBf�r-!�"?& stea�Xa��en by&�M)&�mo� �06m�T�%act�G"� logZ'wor/+|/�>�>e!�s,R ��\ gu�t�2�AA%s �4loc&��Em**�Q �-e�my"�hbe ��!}.}e]��aA+sAY�Beem�Q�.IA�8?��b��a (I\�~l�-m:��in &�� ). Jp��� , al��no-a���(��\de Br()���3 o V3a- <}A-���x-v<�d f"�@�7B3A2;+/ac���� rmou�6 high&֔ -�Lld!h�>nשC` � . 2it ge�U�Ean� :�( bo�k!�imp&� o��t ]Xdeaa�+J ��n"�gf. ��Do� ri��zt*� . D&� ��nNJ2s�i��w. A�d�oC7U�d��7�wx ld dropnoverlapp��/d=� LRJ�*\ �s�%!gui(K���-� �h��HCnFb "�Q2}�\> -�� A�caen� H4t�& �j��*R a&�Z�=� �`}��7��}A\� L��(m�&S2 [% p.178], .k�G�S���les�66%y-uA ���6!�S�YAI!�f�to��lHeXCA�A+�^�8}t�"�O7}o say��%�ATo�G�]p�DYa� ity?.���argr z�is_h�A��I�zat6<�\7��D�� 1I'20I?'30s.% .HW'�= }�aU�wep&��Oea����, his Q�AJ!fon�V ra� � exege :&�6L.�>Ta�E8!eg ��>�*KpA�q:7de�(7  a�p)�r�as�aD�mNLLk�6�, ���^kA��E3&��>lau0 �E0&�Z�w&�@ v��eG �doj'a�@Pas� esoVncy���s�C:I_ifW�by �}63~�rMHal�!!��B���$unfamiliar�:Oh&FCli�O\Ta�ur�!��qeL[[��&�� M T�b�Ze �O��[%�x�B���l\Ad��"l�I�aK%?��t�� B?ooad�cop_݉�r�04 t. Aj=9 ^�!"5�� ��[s �V�Q .h8a2����=C scae �zq�i�ly!�3 �A�iw�a,2bl�.U�"�  priori}�sdog�)�� �u(]�)�O work'nut+bra�! A{GF��rr�a&�!(A��Nn(a��d�� ohr, �U&+ ; oldm1�tEourse��qvt��#s;�d5�puch ��6&Rs!+orS  new���4BA_ly}B�e q#*�T llow��so )�� �Cngenuin�!��-�J�ti"�!xn�����c�R@���?a m�\7�ioQ.st4Jluwis..vx no'!�2c !�ker2F t��eL 5�J� NCr"�)�lso�onՕ!�A�֡U��oft��r)tt���oain0��+� "�L!��� llel�!A& ton's�c(�]a�9" a frH�eI��pla_hzY�E�1 nd I�] A���+.}|�: � ��GS[ .`j &�&%Cp�r��!�f%-a�e�a�. A bA�^��ow�S ei2M ompa՞�!�%J�P� sm(A,a�u�AcJ� . F�,�~X uY �v�q%3�$<$�[!}a=��3��% uXA0"6�p�"� � aP�� �is timna~y��nG��83IM�l��or^R)�S-�x]� dd��eI� a� Cong�6;:D $Como, Ital#�27ߩ&�E" �Lure}), p"~2*�4NDu\ }!� ing � �2�c:�&mZ� tFA�Bre� *Divat4� 2S�;$ŘGermaM(�#ie � wiss chqn}/$�zxr<eA'Q�l!�(N% Atom�i�Ed \4beschreibung }2* 1931۲h!3%6Nic!�% nd H� KL�}!n 1934e ohr1d-.� ��UutE��yAall&~ ,9� Bh!�a� � /te)� c si�(!11��.� io  �~6� �Q��lg� e�O E�%�1�� M�2YI�>$ductory SutE%a%M% Y [pp.1-24]�$1�2eK:�29A!Danish)ɝn� ��n�"b# $ިn!��A!l�8.�E)�I��OD.6:� ����G��i� !G2����n!�Vird!OA'���>թ+ , Podo&5( Rosen�EPRռ>� 1935]�2}[aw� ,al�%debate�j}')f:9in'XQmar�a�k !�y.s े&�KN�E� < 6embod�!!��� �^�y���?pury� B�h�n�%<(t �M Umth� own  u���3����*io�j-  ��K�A0Schilpp volum�eit{Lib� nL��PY+� }dev�M1�:� 1949]3E!�A� ppra�1 bot.M�Cm�J��؁u��s)&p.M!s s�&� �{ S1!o%�" Qi��q��q5C�&���;9:!�a�l�#2P�I�+\9 1958=4���W!'sx(''j�!}:g.6m~! �c�execubT AageTzw felj���w��ed som��Ki� �q^Vo�ead�y.�Tq& 1962. My& ���E�aA"��!�:qmlH�&9be!��,.8 c `!o��%%go�%Bo�g!cX ��w>$"s"]5 \A�aly�i2N��()��Pe!���� i08-"��NI�{�� a�!J ,��Evit{% s" }7"l ��)��*�Y�F�UR&."or>�$ (or ��!�Yoot&O)���J����e�)I main�cK"����ful. N��%\)~C �`��Dit{6\a� b Y)E�bX embr�A�'�� "t.!�.*8� nd ��'s���!n!ʅ >~|� Fa �; �.za�;endTHE  O LECTUREP�� ��of�War� 4�Q G!�V renun��� a�.v� �%uv."  co�*-�2beJpI . B��8�r��ew @us,FS�at{ r\"{o}�ereV��!m �.�?3�j�b ryg�8� �47i"tmJ ?!&,!�!UpHB$� yma���%��? convb'*a� A�eri:)�M��>, K(EES���� be�hi1+a'��]gBq��� �e@Y�q 2e"�Q jump-�l$as unavoid�}�ave&p!oin`&ri*Q) (Sc2�')O&V$a! ��=rܒraA�A�&� clo�x alliUuLao2n $ 2� %B spok%cF�Fa m�c7 crip�2*Ŗ\�_��2GI�_&= ��a�plKu'-�B�Fp ) occa*�n�AA��!�2C� *�k2 �R�J�# ...w!�et...a&inevita&H|��i"Zo� *��p!﹭F��qnxj�wabarQ��fc�� ��J�%�s B[9" J&%+.bj:n�y &�j2�"tN��|# um:,r�&ʾs�a  ! �,�3 ���7�*2 �bned. N��  �n{ Z~�8z[Now�Bn��2I:� *� ! invo@�!�:a�w��agenc � O�te"3. " �/P"�3� EIm��k�/na1q�VneNg�a���e*{)nD0%R���of �.�qA%esYNBS�` �)lp$a���y*[ 1:ke�%*Z aJ�no-�BXF;\&� 9a�o"+Atd�in Nbly�6j5�&���ext�mi�4����f�[!��*� s���qt&�o�ame� ic�oh<�qedz�"�-I�fep>�a7�r �"x�!�"�pe� upoP1-"Za��/�*!>�TRAPb�n�J. UltCceA��$6=c/" �$ r�7�"04e per�i�V��g=,&�te�iU~>�T=�s ��`!&�Q#�m�yala�o_{��?�)��j/ar�7� "�$�U��?r = !5-�d��8�%B;I|\in� nt "2S"!��i��Fe!�I��s &j�preoccup�A� 2X�?.�2�@ ,7}/?�E[at ��ea=,�.�lym-�]� &�� . To� e�,�&�:�2 t6$� hk �6!Ka�J �:�Maw�E�u3!4*�,e��sp ed�o=�Y�r9ԁ�� �#i@p�x�����g����~)&�ex�aQls - 4�;it{�d�ed} -E �M�r�Y� ����~e "+ bt(%I�ed�&N� x�� '% is3�m��.� repea )"� 2_A|Eo�w��2E|\N�.�m&D-F> #�j$al:��a�(st�� �/mar�_:~�Y�p.+:Y�!5!��s*e�~vestii�l�$-x2�!���Z� ndv6d2T%H Ah "n��9� Z(�J��as��k2�!��a � @9�Q29 W�0�"3�:b.��S�:n��h�Fe��tn.�unambigu���YW���per�8/ A��9���!�m�F @ R4�, �$�'Iu�7r�  �d�+��i#"��l�=a�i�5�r~P"�k0�n �� day l�ag�ze�V,�w.���M�.J�09�5}r-( &hA� inue*��!�e�}�=\&M��fa��c%��aqC��������?�?!��.�a �g�/ ��%�{ ,� � v %7�lA��Ca�urb�1�#%A�0FF�"�E"t!�6�% �p ewor�e)=-F � t^th�#o-� �� )�-d# co-e�)a�w� Z�I�una�*o�*e�%y��s��U��6� ary}G'ex�v�.#AH!..,"�����z ��S]'�9���?�*�4nCha�-riginal�/1r����!I����%�F��":R8����aN . 4(�s�U5%��ass�-����g�*pe\*&tn��+noaKY\ ��g��6>e�+��.yJdoctr�Z�sdR ߁app�q�o*Rj & �P��#r2i Q�"��:�Aac� o] Δ�RL2� �q*� BeA磻On#e]�'" couplA�b� 6�6�L"t H��j��b� Z ��H.6�0U��顅�aK ab�$7!3f�>�� i���r: g:ald6. BAc^)�"}� ,\e�� � ~�,ofiit{���}!�`9b2M� �: ���� .} A2 ���(��{a�&�A��s�p� Y��9b�9n,*e�.�d a�'�; �B�z/�A�ᕁ� m�+��custo�ONvm"Q,"Y;�wB��#i qI� s rve !�g6"��)p�"A�aN0 ��o!�p"�5I-|�{5V 2&�c \ity �%H mbinځFur!h,� lh��t�M+�)R �h=�c� .�is3%k%�b�^�byag)�G*,�-��T~?� !��L&�$��J�.L&�r�in J:k ��.gb2 �06���*mptQg����сV� s ,oW,�/���3w��!on!rdpan6��Goll�f{,rM�&!�MRi���Q�i�,Gsa��m�7^" jz��!2=z r�.!z�/ R.S2y)� #l!�-S&89�:AQ^mJ�funda� %+8/s�N~8U������&��&*���enN�. MJZ*�3pJ�iOF� \. )A�aX��%]e�&�Cth�f���;��7.� ?!��" �� n�b�1�!]e��(.�~� ks:!����/�"�;uF�5E��H eloc ���! icle�e�0p-(�1� d!����KK��� =�-r1�� y. �2� &� � .9�arB}>�! av0youpE<�I ily 48mpab;w�l���harpne&��&� poB0�>)�^  h�~�1�{6< �. i�j+� s� by [3&.4Y.]*D `v1 �'�>���)_�#�D�o\�R�E��u�of.bQ(l��>C+Cv��is� th em ^ �whils =�nA�fv�� leMa9d"�P+B�B �B8;(���mI�( pro� A� adoxi6� �ve-u%lva=�Ahad ys�o� orb �RQsuperfi34�q�6~.��Y8p~et"'�Ir�.dhZ1z\"$\�A]��%Fa�j$$�� 5 k�(ho,NE�ir!t���M�RY��F$1, V� ly b�3��rs�$w�*�5 high��q��:Q �o an I am. z�&try�K1G� n8f� A�h ��I�~ out i��B�Qzech6��!&�:"�n��b\I�" �� M����mit{A I ��],�S46"�&�@a9  trenVE*�2(�b �v�M"��G��9w;be"�u�{�X harmo&��SDens�HlicRZ4i�^RTt 1*sts.\"�0.�t�s mine��wa����yB ��� t|!%h2� ! 52 �\8! M)it{new}� "�=E�,tA�&�2old(�}I!+�'o �A�9�����4a@�$5�J��)}%"a)��EA��i. Ou+ a� ?i��o�J� �K!]uvXtrAGsi�B�9� i��Ge�!��* "�AD bscu��z=,��-FI�2��|"2#%� � ��CW�� AI\ am���2Dnz  p"*��"iEr8!!�9J�!x&=#edH "n!F�GW�n��g�v  *�!42D)#?%�!r�.�X!�Aw�2 [�^A�0Q"C �"-V e� �F�!�A���LZJ^/O�IRZ)n��gF��- 2:) -���2n%��H -5�2WEZ�*2))a};?#way"VaAeq��}8ita�NJ�QevxOFm\!'j' stem�����)q�*�.o��%�a�Z�/�}�z!��+->��89%�o gݝ���Ba��%^e2�z��!t"QXIх�a� ��[fxs�X��N0��,��quick!o-maP it{.�!Aore�]�r�-"��(Db�B� U��u TA�5at�+s�=&����A)��dF:�~-"6 Ber�law�l�"4/�+�6�soJg�iNSI\�ٖd�<%sQ��F6  v�*� J�):��b��ga2Q"opularCSQL$���wy7��+��"1 fall�,��ob�o��Y1�zy��Ư t�?rI%5��]',!�Ahej"�l��, !�)�iyG!��7p��K@Kle? (�";k6�&&�&[}Jto�e��� ~2ss" U�)�model?.�Y �dj�">{M�4?�iHc��\!>0E!lŋ�.M��!�h7i�*�A!� �eyU!���%C�&�[#�(� � pP of n�it�w80e�>�TT�-�a  n��n�Nە� N\��L 9{a�dAc� 9W.*fi%sp&M-���s.2p\ aG not:�%���?.��s�*a��9$ 7�9Xg#�O Yy1�"� s�7"`%��dg��c3s;�0 X��� X,E"�_�  S)+ora� �f�)� :w!�k w&�G�&P e?�s�it��@�[!|�B)!,����B+�A���� ��!G-s�. �E(X eYA�sLNq"�m�Ty=��e�%�� (to \sF��-2��~�q�C)� � �a=u�} p? Cs?�Q���E��in?���V+by� *�\ inju6%o'�at-ais� st global.�s?���q�>�Aa&$on awkward�n��i=�� n d6�cۗݱ �2��Hhostag%�2�,a�� a�� ���$s=��^!Y.�5JA�!��nds6�trAšNd�ZicJ�Ah!{�8e�;N(�f!AQ`� 5)�2*ga��p.����Q5#%� arcaIVeta ..ч�oq(IWI)J�(s to physic�yal concepts is one thing; on Kantian bounds of sense is quite another. All of this flows from the simple-minded picture o-�e experiment as introducing a disturbance in LDobject measured. IGis wer�Le whole story, Bohr,�review€Heisenberg's operational analysis%Hthe uncertainty rel's�erm&6�on��<, would not have!fttinued as he did: \begin{quota} T!ssence �is<sid � is�4 inevitability +De quantum postulat'.estimc+possi>ie�-U�T. \textit{A closer invDgvDdefini!R-Lstill seem necessary!E(order to br!�out�generE�mpl�0 character � descriph$}. Indeed,)�co%hous7ng%FV gy and mo�um duz observ �c1� prevA�usI�apb�accur!Yvalues�A. space-tim!�$ordinates,!� wellto*�- �Dcomponents before �af�A�pro!8. A recial .�Hwhich always affectE% �oa&esM i%�i �!�be clear �veding q, E�tiall!L!�com%a3limitA�%"cy with �ch!�a�R�can�QuEFed}, wheI�Lwave-fields used forvdea�!oioU�V�-� particle are sufficiently small. \cite[p.63, empha�mine]{�R1} \end.� \noindA3" w on!�speak{�a�edbllefI�!�Q�i� !MB�>it)eb}Qright ,�z!� that 9&w agree` betwe-fbv%.(}eI thos%��6�1�4directly shown)�� \ (e.`); � setsM�EVegany�� itivist e)6��!t6�ism. B�Vdmost decisive reason to re�N!passimi��!�>�aM>is point!�a .�theor��mɞ�h��given,�  by� , bu ٍ, in a%e added�%proa�o wap�i.�՝RP:�has brouA-(to my attene=%{I ů$overlookedy� �%q!3 courIsev�� discussio�)�,. Above all,<2]i�Jr .� does!  aris%clu!�ly�� o�gr�({����)b�*iedU���dem�d�we ��e equal��ida���q�differa�&�s��A� up ine�$corpuscula��En Z han��n%���� $oQ  \��198]{Y(v|Ta�A��(s!/howEs.�illust��:� a���n��A�The Como lecture, first!��{me�-�\ dua���l��,�6enmAx r:\ N Y�Jus mhe caIr RweI�consequ��ii# quesA� �na�� {, so fara�wauhC o cl� �c ,A fac�"x $le dilemmaMa[��bgara�a� veryA8ree of e"� al evidA� . Inht, �again�ree deal!��Z A�radictA?�R2�y po 5� phen a�\5 only togeAx oA恈!-al� iz! -K9"mod!S.� �?56f0C*� ity,�-itsM[appear� , w%E us aa �%�rE�{ !extMp ��0x 9r,!�ex%�ed���M , un� a.s �tudU ��N foll2� de BrogliA8 ons;e �N�is"a�Crespon� a�� ��I�irV ultane� �r . He n��w d�@ � !4sem s. �&not����LassumpaA] pr. l� eM� �� �.B spokeP adhej ae�B_ -I�hy�Kuld we?� challe� A made"r� ! ,by Schr\"{o}!,�  co1?aV:��inter�\i�l� E�u �U [E3su~MQR�v���(\lbrack I]t �me im�vegթe"!�!Wnewi pts,!� �t� no lon!�0s. Si[w�*un�x��(in principl%i� aI& on� our�4ual scheme, it!�<�akente.7 l� ��Aad�tG e�ZYo�no mor%"Z)�our 6�i�A� Aric� th unfavour� circumst�zs" 465��6�� &CG bZ � cool!aa�replyz� Y+$I am scarc��in��) "� ��y!�st�f � h�<�9$of developa2�  new2� u. Not�-e �8I� see, �we to now!�c#such �M -arr  � �2{�old2 �1��Q}s�mwmEb�� sepa!�y&ne%�%&�3founde�! man'� w` f vis�Ls%(� �H(on shaky grh,� �� . It�ɡnsi� �E�H Euclidean geometry/suppo��^!0��zA�2` existE�of��he��i�s%� non-Bties not!,a �V��%$ on,��k ,t dogd. If a ,h�sta�i�U�bn!lof�  arguA� :� D beJfre� from: relia�!� dubi�empir�$ claims abla*2_EtpA� M�2)E� %�ca���Q�  Axgraph��2@iIn��  Survey2%e\!��/�tomic�� G ^D&  of N� e;ri� �1 1929zo Only�Nq`stself doa��3cognizA�law  grant2�mprehen� z1 diver��� a.��As�Y,knowledge be}s wider,�m �be�par� D� �,c��tere�"G E�-� ew best s� dAvG�M��[9ͫ��Zywe �rememb�a.�au a | !?,w ��a makes & ��Mmframe!�A�custom':�A!fo�per� io*� 1��vSLaa�oEHAosA�sE�u��� � ��|me �H re=c��E�e6��s �ir� verb+ � O 2He2 %%� mmit�ER�  he baO � ir rol�:!�in!Q,language figo�eated * sub} at ings� was,!�(!e I�ala�Fm� sweeᘁ� �� immediate��tAz�N iAB lik=��f��!eb e�"� o� ��m���erflu�\��T*�� phys�r]�!�~ � jump�/!K� �*un$sa5�� of eqit{Ayda�er^ } �a��]^hD%Jn}a3 unaQt{t��ho> @\footnote{% One mV wo�if,eO exhausa���avail. �I.�⁈9bi�uqF aa%� m� �y t��5�meic�>�H of���c"u , take�{a&Rly,�9ldv �e�loy� �mB domain� d gui�&L!�<v�� V�; ,!Llu��%�E�thef �(AKe�th�X1�si&� } de���J{ cribed)ߩ_$ piecemeal1�� ?� leasa�'s san�9�2words: �2��%��W�z!6Ym�V ��-� ystemK also�Ecxa'Ga� �p���ogyie�>�.}���\"�68,A"� original6V.\ (In��of�a�8 !l� lD����? runs quick���$rouble. Sh*�, Jordan�u$Dirac both edqk icul�of@� any��+ ^he oor �e@ � -adjo��ato� beyCcanonścommu���Qi�\� �, i:� �o�� ,spectrum. MaA�ataa��S�y<�!noi�] )�dur� u$� e fuGymYp!Y�)s��� symp�ic /,���iaxe� a Nuniptrans; ��M$ a Hilbert c.)}^ al\no-��a���>�sawIAa�weaknes�i��erpre)�+�!lyA Einste���i�� ritiw\see��{BOHR'S RESPONSE TO THE EPR ARGUMENT} �ea� 1930�!�� ,crucial year.ArE�a�j6�ea�ed� publiciz!snd_6c%in 3�$ �#�UanI��! ab!�%4,)IZ(no unambigu�ind �;�ob�FA .}qG�� V�����#� # MA�� �"zs; it &�&s%'sJ�no-�8F�\ "� ��<,! ove� lread9���V��7t,ten �.8aUdve 1(I�l�mKckH �)j.)�0w,� ofx�it{\ e�}_ �cas R�onsla!...� bolt!� blueXQ  , as~ f 0r8 �142]{� "}�1e�wt b�Mans 0* rely=! mili�(M�(I""�)of �<�@h�d �cip���i)m a�d�( him�"AY% � by � �� dardN$little�*$ a month -)���P A�Iqit{5) % �-9}�,&/� � tim,���c��S�er�m "2}2%� it{P$R�2} n~/"A� Sy%� �2�0'lA�r!Jbegan�j0-9n}z�$at*h!tm�a�L ��:mJ�IEP&� �Qm��5�ac�#� nvol��n!BP2t�co � �s��"Q � N%>lI�e^� saw8 t ��X EPR\U[Y)<Rac!,e� Yeu �A��vk�-!QB�Ein)Ft�f �t.A�az�� fA� lif� &�re� ,A��� "�0crndi�l a ��'"ZdV/=/Aj�tJ�  .�4����!����G�� ith�ty 2�E!!S�&n�"y� ura3]X 2:%� . De^> �m)��orm"H V� %out] �I��of��or�-two�C� �s.�o41 a se!= x!�ldi 6+ � ty. �'iis sovM�abs�#!7[ a��Z �~�)@@�224` atisfied;k%nit{s } m� Yl� fQ*"X1A��aL60"� AzsT h b.4y Q%l&�� e:IH*� al2P� -5y].��2 �3 E>k�&�ڑ7A� *�12Ee\�25=q2 5-�vH')ex^ h)�Q8it{% ��a�ed .� redu)�� +0 packetF. ~-i���so�al�o�'�.` (x7� i�Q�%Ge�um� L8Fx ). �<6e<#aB� �:� � 11 �.�.2l�ae��1���A�ord�!~ � ��ne"[aa!7� a no�8 agen���+�g.2�-xTo ��<lio�  h�� �6the��!�ca^sBl � H�qzit{e is} ]�� ���E�:;(�Tip E�a��7neged}'��is�%��AU 41��#�cr�9a�o b_� bullA�!t�):L ki�>��"��*�u� sort��� Y O5,.?a9�,�x ance.\ T�p� \u")!�a��a=�a�� dynam��tra m's� er�&sLO<N � d spins M�i��ipF A�in%�'s�ul�H� nA��%of � �� poal�� >d;+lu�q%�"�/m�!Y�, obvi),�en���Q"u6]Q�"].Aj�4 is��5��ai~�$O"_ q!��$I��I�dered�es!(Ua��*w>���26 =G<~ l!� �al�M�QA2��)�E�aa�tag�ere! ��,lk'�U��1�eу s�l ����typ� ��r�4��fu� Ba)}&�es�/ u%m titu�.���nt P�^>Rny����+a(JM ���%�̭��(* l�6tac�w�!%�%0},����io�!authors"� AXif%�i 1#�cM�-Q�A]*Cis.�.�� [p.700&�! &�!a�2r�!ATi5�7g2p� B!]phraseJ_...� i,!�5�;}3. ...J) .) ��#� ,9f�'�9*�&�2(0T0�9 �>lyu divorced}��.�7�i�� }is�j)�I��(l�Ae�e97�A�be�@ ���@���B2�r8\S����Vl�� 6$� r��no&�.Zmd.� put l�|�q� E�VB� �l}=, �<)$�ő��y �b}�a� �!.� ime)$4����a� oughm a� holdqar�'� ryremotRrt,�e�sCh{var�#*&2��!|P kI 9�T S� be!��1to" A0e��� U� � alz���s � ]ignQH2�� *+(2���9E�D� . A�cp%�0{=f%�EE�"��A e�n��.�!��5ngTV���c5 +E#-"� , "�/ell-nigh� oler�)i� &L6f dm�� Ei�m�4ver{ ep��/ if�+ tE�5��,PBmI#>�k�#t�F �*� �5%� it{n�}�E�5n�&y (!a�a�"�8�UA�t�� culu Toe�>F]�Ce�ofB�{ �?a�'al=2�Swrong&�3�ta�C 9own�U� e�i�%��d�8Y^P - un�!��*��+ x 2��%fu�)�tdE�8��f�4>s h�d �D�i� .��"is cH?�Wbul�C ��B1�B� ainA�k;!�h�ur[,it H?[por�7�H peca#)A!M"�" ty, � � en�Y 3UC�2v0a!%Id- N�4A_�E4 Whil 8�%�.�(�QE��j#�� �馁�a�"U�wi�I5 �4��e�5a?�.o �uce2"��sANd1$)or!qx�+,!9w!9 �?� rooAh�;dispens��j �9"a, ��e��"{ A�1!er.@st�5!�U��d��4ffi%ŗu�0g��*%" regulaK)p��w A�-,���,)�.�@>��s�!!�� ��b�@"� } nI.�> �)1�1�W s�Gat embod�C-]�h�n rul�ea�) u% l resul9�-!ja�2Wa&�:Mqb2#a tote�9�way.� � v� H�p����crystal- . H� 22"�LY�Y�)���Q�}6]n* C+\& ory�G!�un7�2G�H@ � /&� �L was �no�K"b�A�+li:61B:�$��"i�%]��� w{De' 7��� �>�2y? B������7�(h �n� �1a�genuin(��(�0;U� bG�M�%p� N�f% �!!zin1 �![aH.� .�2 � �vI�}9OA�M$a�/� !�nTIc�Bal��5?Un��5�. v(d , RA!���5y)2\"I�2�EJ� sugg�9Ftg s�"K1e occa�1' �y�ɍ)�Ip� akE�>�a.�M�J(% �NL"�5).} U��;�%i" �p�Ole)�1�A,A%Rs�p F\e� izes@#��2-WN�iPp��20Iea�us u5A*.oa-3n��aa%;i{M(u_Eigidly m�H�Ia� gm),a� wr-�stP roD9AIh!uB7 dB�a mu�%2��a<�G� @ �r�iveKc8B� apparatN' .l��tra�ng8 sl� a��of6M2 d�Q�1� ��2f�aF�~a �,ρb5&! 2A�%�licit��� c8J�\ (U�98;<2}). +'��k# �hif�I�(-�"~,von Neumann F�cuJ� d<b: ����&ieig�O�Q6J&a ��:�-!u ��  %3�'� anYrTsa��S�Q�m��can�x\?b�T\1ll znX)k4 w�hA���i,�o keepApc� c�46�f�H"i2AhU�)� !g �d (��"� UQX L, �;�(a�G�2om`-ub4%? -c<�o in( �)�.cL��a'-��NA��Im�VDOK� �K, )� �2]0See Di\'{o}si�{Diosi},Ai�Jech]6�%�!�ses.} A��wb+ insoNEA�K to drawkPU��03 cal-�s �D � !� veni!tid-up exer�: dIA�_"�C sr&�,�A5-Mo?..Howard�� a�hJ� co� d�Jm� 2��`PgP�&0 �%�� ing,e���a� b� 5� &����*%nasM� ing �ru!��%�I��D!sign� �s�r�}"� � �4{)&}. (M�s:�G�&J ��� ]@ l.)}�K3!�? q,. WO&)��n&4Aa��Bpra�E&� ,� � stip;X� mH�"��� a�8�+"ul`X� �!!id:n�7g � EH+0ily large masM�~��R�iv�l? YgF�4 irrelevv(kG)��n-zero?T ��E�#"��W��)2=2lFL!Zin�a�&�(�_�s�McksonI % {D 3�Pͨ{yRM&�m�.}M�KA�as �(� rA�3%R!.5Gdo, �.��2da&V�$uXGdY��  DKo)2.� � egA=ɯr ��"�: �s:�!C50ively equival����utv� & =701]%�)2}�hu�53O451rv� E�*N-u% ŵ8J�ecIDby�us'(s���2�ormEI� "�%� heav>�a�9lee�9� ��D- v&� �� Lc�&e1҅�9=3� 4}R�].h_���9l++Zf��r|��EPR)|�+� � inolog��. R&� |��34�� "%:���A.�0�%A ex� � I�"�5onB@n�EeX,�/Hϥ��cau m�"_3%dev�Va� ) %E���h�2�.�.�T6[@A%�� ot }��urbJH�E��Bi�as� do. As�Ye3!�oE6%���osal,y" at Warsaw�a 1938z�7I w�7 e�Sd\Ust�s,�6�<W!� li�I�V:1aN� �ajof� a by.�%%'2 62Ac� N �$al attribu�6O *D u0R f2Oej . Such s�)�A��^. � %uE !�s��=&3�,� ��� �ap�A�� f�C,��ce�s� 2��Q2a2�^A)*�&Jf ,�#N�=V�o=jJ6d �;s�� har�Ilat�?�i�Zmon&JPp]��*���@�!� ropr�I\ofa��Q�I advoc&�0p�0�=���DIsit{1oon�6f"�Ad]K A .d"� �$eY� mE����.�#� ��l��� a2`&�237-3*hD:�"v�7Wp�ttal"�6��9�Ba*�2��Q�it{�$lly} fal�|ipYO<�nN VYi� `de �(!�-� d������C� � . D� i2} ���u � �L��M ,L .�1*+�%�hd?�SUl/G""_&,�ge�)� doctr�� mp��\�D�9�Qai�c mu�alz9M�==6Es� a���A�Rof -�U1a�^<y�3��E%5�at*��/a� two-x]#�B ;yiffe� on-g�ng.E(kY)%a�,�'*�m�b�%+!%-� �F�`� AA�" eriv�S�R�l"�6 Y3,a.� � n �IIJ02Ab-�d�L%_s.�>.�Ild*�:!�a �? :noa;A:an � duc�Lm�# orks%p!b ���M  :o a puf6�#a_..|".]�= crocb "guI\teed.}�= w�/Zx #K in���;�!�P �Fm~Z� z�O��h@:$*i,.���z�R"� ��alk%�9.�fv"  )�\�����d2"���� �A<S 1Q?EO <s&�!�9)C�0;�w'ata��g"cA14��.}��FsC  F�fAMclB,  8h&��Ha��iuti2�All�M��of:);2SFWE��s�Mme�l�th��an�q�� rolla��I�� 2 Q�.d�S�I�f�Q|�y�z700� 2r*]"p no[iK` |1�1�ya shuKa�<le�A:Q�(�<Aa�S>L=, K:i�9��ism�27u6@.:on�>AX. Q� "Q+#�n ZT*!]"�;s"�2�fe�)i�D�#d.��Oor��y r�s$ lli�be!.so5Fdi�L�"-�e�A#t)p0? "�;&� �bi�&�NE�� sail3�[�Ifew da>jny�C�a}� "g V��)�1� answe&� n���%� umab�e�J�a!&'s"�,�m� � �9���)us#aOre�by9+.d2�?�>�'�a��ft&�3�c"�6�1ruxel��in�3,��a� l�D�/J>*?�un"�&Y@ur<� Z J�  . .fa�@e!D�"a�h.QA�fallac�1�, i2�Eg���0�?��' u d -&?Tmis*A�}� A�p- ]1}.)};A�AM[�'NC2�oton box2� � t� ! �DA� curs��Cde|5? 6th lMcolM. AO@�Y�HP�<��� We�����6of Q delta-�(�-D*�\�; FourQ/"�O �  ?8�&E s�>��A��OI�/�Yno c�a��4ai�P�l"D,S Ɓ� > o�a�Nx1s�Aun&-K�.�Ftrugg6Wfi)#n*� al�f it:��w�3��O�ko[ <5aso�".�j �W�1 puzz�(f� A��Zi%E ha�0 b LM,i! QE�s. How�d���h�_� yondF�$3toGPQ%� �;q8&ly? For�$ "T �ANsm���]�(ent�Adis� ed�Z�.% .FEqu�%쑚����e�]0� !!Gr!B.U@a�J aI\c" �W (��Z� ���uts-$J�e�I>!�ax!� !�e �-A ory�#In)n�!%JniM�NeE��#�V *&on-U :_�f���3Pa��i,Y�a�c�6s,� 7PD*J  3 J�F�j7*alt �jproZhsI+E�:'1%3%t co.�b�6�at� s ZI��yil� "O � �b(��!srROIt�1�5� Ax�new&<��67s >����@!5&� 1�%-eE�k } ai�t *� ing2 �$6�� s^f)ab�J�d? In��'� 6.(o2#(�E�!4rooN�A);�����Q�@ q�N�).�/�� �Z �7�clu�Ki(!o�k����& &a� a�&� � it{gV# al }�metho"�M2A�e �xon�@� dea� ��:�C�!f* !�'s add�� �Sca�av�yMee�\d al SA�tisqR�/qi� i!nnbT!1 19311^EnglishA�F����oro$�fu"K/&�1�] derl�"&*�)�0Je@\ �4 $[pp.102-19�1Gis�pP1}5g!�:U�+p8=, N� ��prom bi� blemN[;:rN6w^X�T� o��!9r��9 ɼonshipŜ1Mr scopxl�:qui k�B�*�!�(E^u#o*Jzw�uSar ���qSVk !�.�m��!M���24r I�%3,c 1 star=\AAddendu�i!�2K�O�-,\)^�XuA�v^��S?f>��'�K*^�adav6oc#.&�)an�{e�7ɭ�!Fk�)hip2��q�+,�>%�"�F 5wWH}% 27%�\qG.22-2.�x6_�!!m%�mX��*�)� "�%�� *� �}�Ay��  }9�9b$v�!u[4>����M��2�eg&�BR9 �6�I�+s (but# �%&���;�2��qJ.�� .A~"+A�2�g typi�,o��s !�erq{��1 *ix�a�����A`(�9�� z*%�^,� rY�E&��2��?2�U�.&1M{2Q &���ol�4C*�## 2o|ZM�"D6�]�.^�fdedvN&s?ae�G/6m�G�e� .��!����� �4�[9�en�-P?r"6 &�!� &�20�v}B� 6G-!Vr , dr�h%6�2� \ ty., �!�/A��X.z�Am comb6w�s� FAPo�3#F1�A�aA �Fm7s���&c+�"N,"5 2�@b*A grasA�a�,�d�Caffbb� F�� studu�62Yi��g�& �v�r& ar"�z.1�!v�� O�B> �U� daA�.�o�D8}nita zed)a��F��b�� 1929��n3 -:b�9uA�Pr�nl!�C5 mAHA H XSe�i�s m �V�2�6 q����t�+�29&�. 30%>�s�9�6p�!�rH"�h�}ce�%����r:��.��o u(al!r,� � declYF�w�!rAr9`Iqpr�a�e �$�*� <raiw by&� ��e�Q|8c� 2}7 "v3�B3}�W��P�j'sQ�'� d�W^+�a%��hc�E��&1�)��art2#a7 a�h"`u��-1/�=N$�_�0}�1elo�j!*��g��.�� RCZh� �L-_l��/ *%��� 2U�)IJ�1ach� �,]�9t�~woV� var)�%k:lq869(C2}U,�=@)�Rd �� 4>m8u�l9�!struc�l!v�5�0L^P � 2!�Rper�W -]:p"i� !f"���Z(param re+"+� U�TI���!�HE8a�fQ% �"n �d"�rI>I*AVgy-�)} }u 2fJ�(_2�PignpO��ULI�}�7"$ a�:VE�*?su&"s{=gv(�cqwc6� D;#av>!"�� K"�K&* . (H�%de-%�U��<%%c.�-�.K�JS  lin�%ik$.�yZ�e��-" EPR,\�N on��n�v� 8ů ��uC"� }�s,���.�!e:it�/-���-JeaAsi*�"!>o�|R�= -�pq�one`4P+Cd�vof �%ful��i�1��@�<,$�)��/K*i T�&!0� !^�+b�8f��)[m.�! 195~x9Fa�om&ng��ora<=PqX���baA!���.s{-�.��� ٗi�HL %� �D�eK by� in�y� e��!�.X�M"�2[Ag6 �a#!bteg8!F �D"� &� 4y 4Jo/5�6 � m_�$- half-hea4;��J-Ad�3!���15E�&Q5�da�9"�R%�d hyp��om� judg%�ail4,.b7�2��o!� !�",F�*.% 6�+��>.�2 �&w.�eT' 2H };z# ��vA� p�yee% summar>�Ut� 8 e F&,E�^^� m�� ɑi���it{�0i�9]�U�� 6i^!�� Z��:2�*�6��� n @AU�!$R JA��}I6�; ���!bVl: i?Bt#to��:v��neces�Eri��J�qch�xa2"*��a������_&- �!�&�Ge7nQc�zL�_�z�h�;6�F!a��Y!i�r�Qsn]� ��-�"D E�q*�Y.A��5�.*f�5�2J�&h): ��n�,7')��=�A*�� A �>�Far��eo2��I�46�Y0�-B��% some�D �)�m�-L� t��'I"mcf0�/�1s�yd��aX!�h�v��/oof2�5�e ��A>v+a0� �E�<��*�1�c�AL1g��.w5!Ax9 e imp+2��nlca�J`(H� s�qofF1}G�Nbe�mp&�JQ�e=�� i4*��Fm� pkBE]�` s*�H�~5zqIn�9�ȭ,*P��'RU(�,� no�?�s��Ay� -��pproach)!N�c new �3Q�$f9*�u� A�"uYoiTNd�onat&�*f*�)�V2���&*�~ )��42�$6�*!�cy� &�B9��c�K��a���2���.!?}N�M.nj"- an2�"6:�6DA�$x�s ( 3 ~�oA2�I�29\�i9. ;*}) *�O:�Y_J�dir.�a��%y�I �D-zG\lW� k T]u-s�`��1+&|��:6.�D a�. m"Y��*i`�LnTJZsa �`"����EV.^`MF�s fixzca� synchro��U7ock�*D,���>��J*� �ir ��in�b�seQ�t fulfi#>eFofo�6*�9,+ٴ5f�%��I� nk�� i��m��g�Nl�A�r opitfall�2B�`t�D�h!Q*dD�O�3 )m}e�!"� ޹�"êor X�r��J���x$aj�&"�.bas �[���D�&� !gŋalx1t(a��digm �!� ,�o�q�9�V;MV�m�:�QW�8Tb[�����y�f*��"at N>9 !�&� ����z r$ �_XJ"^ ies}" ��e-!-2c  Ր2�� ope�(up�>��6 it{i� y!� \�m�le }to� e�Ge%�i� �-����b"�xфt�a�!m+�e6 ��� EPY!A%�"EU�mc�Y��<scrute(�.0 � aHa%- ). �-z��9'xa.�E}� r��ucxnoabE�ory.�-COMPLE� ARITY AND��FORMALISM OF QUANTUM MECHANICS} I am!M:�VScheibi%hA�-�T-0 ewAC�� 's p�-.v^@1�%H�sH$E�em� *� mf�ѕK re{R�To�=zA!+&�s �o)6by�u6�H&I1 ��Tn j�K�!/��W]�}L no t=Z�1 labo��� �� Boh� Q���A�uU�x t�Le[aۮ?=ڋE�Arm�`�4 k)]��ss� �/��P�J"�5,.NM+rb�soEO� %�it{� }��F�o2%B,���"v%' ��5=es�Rin;b�L�l ;ѧv{�6/q��&^Ta. %���qM`khe�r*K���!pA.� C 6��H�gA�2S kn;��4>Ӓ�!U2C�b�%RB���K 2p "+EZ"0]!,| ��BreE�\!2 $1t�U"� �T&�2�1 �\Y�� g.��hso��"�bT�F��D- r��TE�i� "Y8a�G� &�"RE p뉡��x��� ,]} �%%��(�M.� on)��H�Pv����Y %�} �� (a T��02 mde Bro-�OcP l�FW!`I6 QWas John.Kc. L�p��  !e�:>ŭW��.R��n�[�U��; ��Itir� ]xio�z)�R���l� ��, �6 �  !XlbMl=�or�t��o� A��C)m�i��= etic ���Yn-�yTed �(}"3a�of' 't7�acy, \!!M�r.�e� ,%��sBcso3� ed)��< !i�-bu� �V&!e�&m�)fur(co�!  MFinuous -_�/��C ar�����re�* j9Qc>"+s�h�$LE algebraC8�3A`A��*a*=et� w��ar�#A�0?� u"�ci�]a ej �pl�X*^Zthu~�W56^�!k��^� �!t1���8 {�*�=-�4�8& "/V&�WS+,!~�^n#6�%�M�co"�c�f �8K�G=.Bos!…�o. Pers�P!9�omp|L�[m:!q#f��V �\a�aif!� ��I�+�!rek8ar2���r�%aib�BJ�"A-�)�Vof�A4u�6��w� oc��(�onHQFfo,�CN�9;e��t\ -��.�� � �y*�/xxx[���pr��r*���i�$�v �]d�V��a��t*�U�1*0 �aia �ual!�uh�tic*x2�ni��:A�B"J "��� &Ԯk�'a�dr���w�� �+��i�jAa�i �4�o$�A�0�/@�Fv!��A�l^ AC %�Ah Kf���;��de@���"ի�I�k�Z�¹���s| "g�vr� !���F�22�  da�er degr�~e�u���Զ��a &� "% ���io]D"�Y��6&]r�rTA�un�I�-�)Apilot-w�)��� �e��. Wo>���<$!.�2>� ism?� a� sterh�&2sta/Gg!���7!�d�Z�x�0��Dy�9$ve���3rN�WmeY �`d!A�o�va> � c;"to����XMW���8! m ���#�#�a'��r �.P$prp o' t� �2��?� Km�'%���0 � �)�$a�pr�[E� =�"��9#�� :q($ . �|�"meF� , Bialob (ki#  @8H�Un"U�!�ch0 "�Q,A<iewed, s�!� s��Z,.K '(!5!A��F� .�k��,%.AE))��}).�-��fe��3�5 2��B\�!ua���a�&d!�&�V��/�T$8&7.Dit� ��d�$XO.�=�'V} �8. �ZL 5r�UCa,�Q��se�jb1NF"o QG_B���Q*� \&� A�e`� opinl,X&��/ g� "�F��t 8��w�5cni���Lenume�Mr�rio�,�'|%{.�2m�be 0=T!2�84��H-i�y�oe9�(�ND&1|�A� a�!(p�Xe� DGY~�/ 1-:EaC`a� �CCdoq2N�%) solu.��u"� �>*�!o)%t��&�Y�%&8��A.�^unv�cl"l�%Ljv ! �@�o��yp����sllu�(�pca-���u�ZE" i"�a���!=6�!�5~�QG�=�/�:7!��W& $�d%o�2"�uu�M�To�1g��:2you),%�"�m� V"� �+`^Rxcz]I;Kt�0),�m% �EPi�I�A+�I!G*�6+=� -'9���I R\'sa@8� �q�3��rfQ�:�). Wav��cke:%llapsųalY� ��cha�F )�� �� �#Bm o2"4 Everet�0prs�)EltmA�o.f!%fA&Aa� X9p :ԉ7&3*7^MA:�] D -v�1����0��n�t��5� �XAQ /LzAGIf2Bŋ��)w�L�]E4J�l��xp3=F�#rpG � ��e"]IlƦ7'f�$ �*���1�<�.�" L meanY �l~9!]elf�'y re�it{is}M � al,0K?.�oA��*��" suԀd�xwA+a . �2v�D U a�6$�\ V��q"�5sd�%4z E� <� E�/r�8S A CONJECTURE}J�L as I!�|��� n� � �+�ly�Q�H:�M,%�Y�-��σ"ZL�1l:"��6-� s�w 2�@ �#�Ao%V: F cap��<u�7!��l� �s��A>qmԍ��rP]�P&T E� cosmf!y!4an�k� D�@h5"[�]))s�Tnv?�n��/ipF@. Clo����om%�RANli< ��%{ "Ӝ8%�!�/~� mod6pir�inU�*nb�del�1b�])= .1DH"e0s!�n Fuch�)� �N> {Zei*"er}x�&F�of enc�#&�DeAT.% �a�&�=�"or/ day�a��q��0 ori}!�M]��'n��   ategies, U���A�!�s�>�����?PuE3�� c }%�m�� lbe/FG uu�JM/!!*^+0y�nd�^�$�� ir d �2 �$�vW���m*MU&�th �lya�N�r�8�w{*\i��I�� ne �����82P d�y��6?��ý���]M�m ���� �U�� ad �R�)w-���a)%�!n7 �_:%.:a ("� &�<)A��)6Rgw�A�/U� �ɼ�Ż��F"� j[�  ��aSmaj�T�st:oozd�{whe� BX , GRW@q�o b :\ )v2�� iqjconA� �  "�!y�o��00xDV�@�cal.7[ 1�};ilev�!��o8"(#���Xa�e !+oD�&�r(4\J�0&&�B� ���AmH. H�w+��yh�Syed u|A A���C A��d/F�avenue -VTew&�[ �:c��āe#�  $6L�K� �i�J-��b�gn X|��a c�":"!i/�|`p-2 ; if��G^� ��1o�_t�&c�B�8��* j3 �./ �u�/ progNO � �:< 2� o 9!�QF ��=a+c&�~� W�6���e22"Nr�!�>�^�>D"�!�nd�M}Q� sty�e0�9E)&9�+o<�l�ar�VIv&;s�+}yA��U�0. ���,ۏFthcom�_.cae�c� �%� %o&chia"33e[F��b.�@��genre�DS)a� 2��.-�:!a���ree"�eۛro0�e}EC)Jyy�8}��a@� 1950!�D�<� mpf���*-K�aUC%�.^11�bu`)p�?oph.]�rt5rapdo�A 6s *@�-��d� �"$of baroque.�Ea�Aap�Cɵ!`&�2��L!� %'s.�Ls�;�ңA�Ih�]�pp�ɱ6� H F^F;so�x e� 1958�!��7|��< optim��C}�8EG��(��1El62T�f��~�S�?death:+V+�l}���h tele� �|�Xu� � �2� A�V8im�; �a �=1!@�p�at)},�4/�+d_��L!texsRT*��*)%O&�6U� owe�)s :� min�.��"a �~athirtyէ s agG�s��a�Ģ�#fe�d,mZ ]�#�\46O baloE.RF�aN�c���Ko і�<����%&*1^�G12} (�!�͙� a�:�%UQ��:�&�ri� un�Hm��qhi�E|�rd!�,/P "M seq�] �OA�� ���esq�I �N0� '30 r��� U2nW �,2�,e�"y&� �Rrݎ�?�n�SA3!��� A(�?�!%�A��empr� ����|�g��"�$���!�dD a.�K�or9Qh abandon�M:F��benefI,*x�[�\s,��M�9$l day*�b~ 5W<..6*�g � ept�d� g��h�hc"H0V�eBp.2!y�H� �E��'a�Pop�Ua/Kuh*B���-�"�%�L��UlLI���SaI�2}M�� b��-�BT .'Ű�A��q��כ�)v9er-% UB(.Walt�� ���o��?��eglig� !�A|n��d�1�t�0rk�=��-7NL t pu :9/u]B\��:!šl+" 0i�)fA0�&se�P2�� @�k�)���{+ Cz2 hageJE,\�"�,�h ?�V*aD0o�^�!Tin{Ft�J$eJ�*vS$;.+ N�!o��^d�.happy t%���n`>�)���M�, FeyH�eXnd Hans�whe�r help�� o po��G! (I aWYdeb# to Don ���.�ũ! �7 [*isQ���<�2�*'� A)��*4!`3Hl�����h��c/ �y�"� !+j:H worlz|st.�8��Vd)�|.hnRr� ���s�&m�*/C&��&o&B3����y ��bro�ndi,s'pe��sm�Ű8&�2kC$!����saU .�!F!; ��cogA�*!-belie��!�V& .(�#M e��*�*����v:��� "")r�Pind�Je6!�-re��cEe�D� �7^'�f*c�+�.!�%� � m q��Ѽ% ol��2�����d>bE���m(*\�)� �$���!B��+.epi/(a}, artifac�x kin"bT��bcu ��� qDe}l$%AG>�// �� ;s��YM%+e� �s�HA��$"�,cl �k�n~$}2��,�F�ce_n��Ag��st�!�, t� de"�e Coulomb.�;�1�E����,aI�bE{at�at.i � '�+ 1H�Brillou Ɏ5t�%[er��@[p.120, 137-40, 2���vlwD'fn-$AV!K�+�� "�s�\ ( �)?R&P):�� �11.�!-"� O B) J�&ht�5���thb5�s ity}eum&�E�v� ��Js�!�N�r!&��k& alH*i i�%>"�� ����ua� Q,oi�w���#� nc�E��B xl)7r�"E�!Yo a3"�B�U!'�war6*?9>< �I^k�_ER�&;*177]{&�2r8� n&rkŝE�Dn5St�3N�quTO�&a }%�38ft9�y��m�>� �( �D6F }� �έp�$�� 1952�T\<s�*� �/�!}c��*5��n���*�����#�4��@"�outaR1�m*Y <A�1�"�Ia}% . Ta,A,�Je A,6 ��a�.�pI1A*in�eOQ��*�]�I�7ra�o� ��{Brown1}�F�� ��.w�� !]a�s{��)"];s*](7�D��%i���P ai+!ZZG�..PnՓo6Z2�s"(bigskip $\q]0bf{ACKNOWLEDGo?S}$�c'M�Hank�*f a�Michael"a��.(�c�_�: .�(.�Cy�Na�b`l2�j+�M`a))Ru>_l� } tr6" o sht��qPo Guido Bacciagaluppi�',*ɏ9\ Antony V�� ini,w &��8� cor�^iU�CiW��yau���,,maie(� !). AbO�� m�1g!�edi� =�rr2�t��5m5��]8ec�:25!�of Jim C`��Af!�d�sJs��r��tD)a��Df�Nes�YG8t ����sEx@�${thebiblio�O%� De"�.�h0e} (Cambridge.E0��34B�7>����� Che��\&+*r�y !]t�� 9A��I��9/J.W@. Soc. }349 (1932B�9r�1�m"6C�x�F/�r�1A%(bf{136,} 65�5B�2r�Ca.�*�T.� !��W� ��!:iҵ���?�>B it��R�v.}� 48} , 696Z�10r�% "�ur�h۠ cul�>�i*~��!M43}� 8�aJRea� ��&�p��Ht K";�L} (Wiley, New York, ZB�5r�� ��&?-le'�n��>���T�=�in�}���=Hal Ini� Int�'K� Co-"�, P;e�!$6n3r�Di�@A "߇on Epi��"�P3gin �]-s~�% Alb3�_:.�t-"�}}, P._B�t, �,@(Open Court, La S� , IL�4F�4r�q�iCI+&}:�k!܁ iJX�=~�P]� t Mid-Cen� : A ��8}, R. Klibansky �$La Nuova I�ja Edi1#e, Flor��5F�6KQu�zL��� �D siteJ� # �2Essays� 8-1962�6��>e } (Ox Bow�8 Wood�U�63Bm6>� it{C)o�# W�L}, Vol.VI, J. Kalcka��d. (N  H_"nd, Am�8damn8F|8n%L.&�"�Z2>Zur Frag�4$r Messbark_)� elek&A"^En Feldg�FssNw ,���Mat.-fys. Medd. Dan. Vid. Selsk.} ��f��>���2��97'�F�0�s�a&�1#] &9E Y�~��S@ ed P"�L\'{e}on&b�I�CorA�J. Stp�lA�s. (Reid Dordrecht!�7F�1&4 J~�F+�g �Eg�G"b18R�*���4}. (bf{78}, 794��506�� H.  $, C. Dewdn� nd G�rt�e1qe� Bohm� ~Q!��+etH�!�!�� �Cu�Zwcfer�rV�p it{F�.=�& 025}, 329 (199:M�2�!i D�34�R:aW� ] I��X�C:*�-� �s��F*�1$E� m%B�}.zis){. A"on-�XLhttp://xxx.lanl.gov/E(-ph/0403094[ ? � }A� ��\MM :���L C��R !�&� HegemonyzZ i a'96P&2}a  �19E]R��%c" la^{7l'J�=��.��Aca��ci.+3� 641e12�V�it*�� 's U;Dn�/a�!*{��g5 *�of069y} (Kluw* �Y 1996�4Dickson1} M. D�Oickson, \textquotedblleft The EPR experiment: a\ prelude to Bohr's reply to EPR\.G$right , in _�it{History and Philosophy of Science - New Trends'x Perspectives}, M. Heidelberger#TF. Stadler, eds. (KluwpDordrecht, 2001). \bibitem{D �3}T N �A view from nowhere: quantum refere�frames�(uncertainty2X1 it{Stud. !. !. Mod @ys}., forthcoming6�@osi} L. Di\'{o}siN�DOn hybrid dynamics!gxthe Copenhagen dichotomic world�Q��available on-line at http://xxx.lanl.gov/%(-ph/9903088.�tEPR} A. Einstein, B. Podolsky,%7RosenN�Can1qX-mechanical description� physxreality be considered complete?R�4it{Phys. Rev.} @bf{47}, 777 (19352D Faye} J.  �it{Nielse 4: His Heritage�@Legacy. An Anti-R� st VAf\�QM]M �s}.u and \E.i� Bost�e 19942Murdoch% -�Eei�E'sv�E]cs} (Cam��geF� %�72z�lfeld2�J 2�=ina� thirtie�H-� Lif)+Wora(S. Rozental!5 . (N��H Holland, Amsterdam�6Z���B� r��  >  N �|uJ��:!Rovelli�� N�Rel�^al� ��o Vadis�Ӎ�c[ PC. Avshalom, S. Dolev�$N. Kolenda�Springd Berl��*�2k$Saunders2}UN� To w�m�( correspond�jC+F ,, Invariance�D Heuristics; Essay��HonouraR Heinz Pos� S. F� hq�Ka� � "^ 2�96���he `be` s' of re!�v�( pilot-waveayor��F� �  to�9��(Butterfield�$C. Pagonis1ڕ7]� ��6S996� cheibe} E� -�it{�log� analysi� ��U�(} (Pergamon�V Oxforda27:dolvay� @it{Electrons et P� ,ns - RapportDiscussiQFT  :8D}{\D �.�E 3E>1(e}{\epsilon:KgFTB5p}{\varV9Qu mQu>9qqB- 9 :� ar}{\long; arrow:"w}{\omeg>�sA-igB�laR ambd26B alphbegin}�8\title{Algorith�(approach to�E. } \�:|or{Y.I.Ozhigov\thanks{e-mail: o x@cs.msu.su} \\[7mm] Moscow Stat.� ,\\ ��e���8technology RAS a?� � �$abstract} R�$is based o\  assum�t any�evolu� mp��( system can� simu[on 6Jm��r with�8 polynomial tim� mem�cost. �s play50central role  but not�ɛthe��g�X"film" which visualizes:���"���is demon!ZAto a use� qmodel� stri(s following�'aQ\�ar.5)>level!�f��;��JDal laws. Born rule�T[ calc!��* probabi�as well2 deco!Lnce �rived� exis�eE�Ta nonzero minimal valu mplit�mod�- a grai.W limit� ��� � 3u !�esour� 9�unified>�B�E�isE"divided!�o unitX2�m&�iidoe > epen%�=2,observer. ItmpropoaZ*:-sa�:z nestAofuW& e�qother �permits�accounI�effectg allI6@ same!�A�uQic��ad Tha�ssiM#ofc-�,, because itAhbidiJcre-�f a scalO 5�)��is� owed��v� o!�1��lism. 9 �� \s�$on{Introdueb} The!�M�YJyha� ��(al methods �$ily penetr��a�area%W natu�vs,sA�is1vY�(new languagy�> I)׵�ra%�:�!gae"!ulaI�"� sq�co=KѮ�� bAYe seri: �ge�A�� �/aEݡl yet fully�za�� o?incredib��lexQR!�u�'of/�ic>'N!xXe. But we already meet�IsurprisaBfe2�t!��.|�d�nguishE�� �Y�5��these^��in1�,al establishI�e"�s�connec�6w�most a �T1:s -oL, or more precisely,u<�s -)difkX has been revealed very�licitly;!is jus�[subjec �a�� 4\footnote{Sevea0researchers h: comeaH!X idea �CJ in�Senz�� I ��aP,V.Akulin who��!Zt!vU talk9I� ; sw sugg�SlMeFna�ap���1aq��+�|an��b���e+ tist�;iaa#$ose� deal�1�t a0ir�.�(problem (se� ex�L4e, (\cite{Fe}, Ak}).}�9�.Z5wtoU&�y simple%�:� � mA2��vaA�amŇIxvic�[ necessar�]attZtY >waMvso eve!�e� re wnoASC s,!$ir : ed!ja ��A:fulfilA��![ �� s at hande�� s�A�> llCYM�result :5u+� J>equE�15>� We� ks.( s.�al��e m^ ���=.�!'��e�pithy�%%c6W2�could!�4ignored, e.g.,;2 a Jer9negg r�^Rua�as7Iw"� ng mach��a�by fix� or���q ly speakF�-s n�� p�l�� �!� �ET "� sS}kE� exac'th�A���B!~one e�ron mov���vacuumy�� oj *z� (t��\�� phot!��e-posin$pairs) lea� � summ! of �!ntHs!� r�!; a+{� substanti�B<!��E!fe�tGpriHAU� s ov e��l� like�b ��r i�a� s. J��su3iisI_6� �ren%liz ��(e*3 u"poi] )C��6�space-�(is sacrific&_ ��erv-|!� n#͗5F�� .p�won�a>"�<�=*� g�vIO!\msE#� �r�d�� p� o=4 : Shro�er����g"ohydro�"�a�ctrum af�) easy.��a�Z.� ye>o��W�m magn? m�% �wrong�&&% B�9 W6�  lc �bGMaxXequ%I�r.�a�ula energy� ��V Ͱ1�� >ma�)_noR�.}.sit �d� � dA���tradi!�al@t�����ts cMinAonflic� �new�� � me eun )!Ybnn!�melabo�Aa hypR tic"� �����app� toaord�Qo�ol�L����.� zaB\��"2 �2�P)/����yk. E�2� ɑ�+ly鹁4] !2�Y�P�lA,.� � easm repla��| >�p�dur"� !mr typg �)rE�!<6 ii�� mpt!�extrapo�CQ7t�Hr �rix � �checkah�J�m�� be tte� ri�alQ5tt�� 8we will return �r Nowtr?)&t!Gw� n obJ(�r9�*S  �( o !j1#A.9���� =�. e�keMpa�:E�"� -l %u��a�%"%�m'�M�d�tsAmeaOV�%;uses R<!(i`"� gan*� �9�nNB=��N�e requirvMO�$*  (�{�5)�  *am� * size nee b ay.% .&���~*r Ta�35�s�*� e�U}.� �� S�DI� show�� mo��J�rib"��%aYfinj y � �^�in� IWle ���nE�._$p$�suffi���large2a��u 8at $pT_{tot}>1$eB re $ $ -V�McCL"g !�a�� work�IUn9�}be��nA !�4a6 b��oP�}� Ua}%R; � only͔ � % beforewE�k z "���B�w�Cplann�8 o do�s!>�& Ofz r#'if!�a����D�"!�in:�]A�w�insoluA4du-m�u�-n-loc�.#Y�#MeSE�� g� ��WT anceN�!^ answ���Zqu�%�B�:)U�oQjO �}V nq��in�*r�`de�a� mpensat��lacE��_s�speed�I6 ņexeo.4{ s. P1��A��-�� grow a�'�9n linearZ=��of=ed�>s&�wi����hop%��_�>�um �bt!�y In Na�di�< >��i9BTu� roug+�ng��u9 �(ňclu��M *�al net�� ar��no � . �kA�id!�;>. �� N!ҁX8 ����e�0Uosi+"�Ie5 . Al� *�-�R �e<-als =i#%����bin�o*l$EN ed lengthj� � agni�2%=�An �"!�" (�2��binI� �I molecu�A. meanůA  betw� &c.) ��6N�in��:�prepa@ K^in� &�ion-��s",p� g�a�$%[54 phen�a2+c"�(A�M�" *. D �( t!�� rCţ� � -p/�%�*tap�uw �s (� � %lgebra)�&j2�J(�s)u\g1iby virt�!hX4��-�Mi_ss known� �.�� �`d�opI�topic& �%�t�2kp� e�%&� P\�u� ��^22.� ] a�pe��A;93� �n��u�& ; C � itself�-ru^z�fut"� .��&� �eequ .2 ]\ �e6�����d"�"G D�mo�CW�ca2"�(or�)h!ep ab�F/��sJ( E)� �1m��]"� !�( yies*�  below)�5re� �E2p� B�#s-���b�6�4�� �otI�I �I �!Dž�"&� �A �����=�S*�re <GAF R �re go��A�ii+es&� ��mp�K2a �5���<��of NO$��1�behavior:' chemERre� �i).j�u�_ͣar�8uca�^B� /��nic� �$duc%!n��.�bA*���. &"*�%A�F�q� Hca� b-b n terIf}]�, say!�W:�of��|b�mo�Qh�-ulomb po�4�%�9 e nucleus�%�m�� sa�a!�ag { d�!�=��jicultyQV�L�' ��E.K�B�� e d=;r.� �K� s�s �o��p 3num�6ofyAd��k�ex:L�&N5��< y � >Wxi� 2;�%�a� <�*-a�u�&l�!m�K Fock-SI A/ina_ �$� 2yfu f��_c�n -!con5! &; gy var!q�1�Q���Sl})). W��u�/d.�w� �o�!2q� �a� ts� a�7to>'-�� .H6 a�� A�!�0"&� I�� �D�(a��!% l]7s )�!�&6R two54;(r�v 0�S�� � m'se:>�)X��a��&��&1 aI.whY)i$� �e xi�Gm� �Mj)ilar). �8l%,�;iEK�AaaDh%�& ll��.�oc "����s�Dgs�)�"A�QF!q�!�io3 Q�icg figuE �`C� ��c"� �[  e�RH��chaH&/* E��� ��ai�&�e] del��ha� FA "�A��VA��im�3ant"� �=at Q:tunnea1 Jzum62 � ?A "5�3,%�-j&� way;�h�  n�"2<!mmonia� ����"�� Oťis��e,&xe4n ������a$lex5a!�A�bq.�Qr,e2 ��-�&+&l��*}*M 6's�edM,I)(� �J�F�Q��9nglIsb�qI�M�AD! .���Aˁ�%ͭ� a slit&w� �!st>8E�.�*l��X  4"��:';3�$e�� n*k&I ���bA2�-�! 1�� �n&�m7 "col� � exc�,s 5q�tt"- �) 2"sS"Z�)>�ͥXa 2��'e)%]�>�"m��:� NF})� ��W�"O 9=Y�Ga�7,��4IT�e way&Z-� �"*=�-"Mk bod&�0� Ona_���{-c �beyon�e(��jI�JJm-n E�v'an+te��6�N�a-ow�ged5kEq��6E Ս]alway�k%-ށ�-�2"�2a2��x Lamb shif�� � 6:�h $10^{-3}$& �e�;�� 0�a� I���B� M��|�.�.��!R �� emit4 a�absorpQ'+%:3� D%syqB.it� y���[2ů�a�Qm o�l6J�by laser�xul%2� B}�) {FTK}0 B n-)��z��,�5e���y�-S stud� �8ar�!n.H&��Fa�ra�,o_:":M chaoa��bio~!z�X&E�2���z iR� [,Q� m/m'��k6�8*:���m�p}!)�i�;dis#rsj�Ɖ�dsee4%�coordin�!��s (MK9sca�1.e ��ll<Q�^ es))�3� ���*!*2�+�x . InU9x�19i���4�# /#-s$%�BD���L*c� ofN����M-;�-?s .@)@) o�com�QF� KE�nmpC�$duca)X�7��9�5A�he.Kq�le:�m�(�*S3Ww�big�'disperWa��'�BlVAK.�F a. A��s&�!<im�a�?&RJwe�'�[ sA~YxA��nE5-:& 20!am(!�[s�[s�2�AV\.�eFH%@6�a�5EM�1�reA�5sov�]0A,m]E;2�+J�M F�I6�i� �3�mb.o�+c0� .m. �+q~q04F.��Lm�� h toolAX3*� � v:^� S&�n+B�",4 �I�64�.�leɳ2�%)!�CV3!=�"akn% :��t�� .%L1U"�C���g�pi�AI��"��� �8segZE�ev�;�also `���JsmFx'.�5.e'���IJhardl�+at�#"2S=15$��i�:" A/:2s "N&ceasel!�switch.�nd���� !�v&!��� s KdEB�If��x��D6�:ey !6�&&ab�#�*2.��ybL%I*�(�4fic`&4"�ai� !#: �&�#w�PA�de�#�)N;it�4o��� ,=fZ�orA�. *�${!8�"{Luc��Pn%a� Ō - at�C st s`M�M@J�'� �.�id%w"�/C� (QC):��!ur K-G� reteJpm��u�R/�R |%VA�;�0E|�r�&1lea��c"�+ver!��:6a�n��5 a QC5rI�9Hi�StI��N*�:�m�'d/�����a� >&�**Y<QC��Gst�+**.dz6`4.**�2ask�����ly .@%�e �l.~0 E=,Bq}w!jfaci Y;���Z���"QC�al~".K�up69 h}))�l9{- H quad�cR?Grl|v�9q r�?QCE�to ��)"#SN�1��eMI t^2&�)t-*!�4!�ime�:@� �.nt%(��&���5 x �*, U�s!6� �:!qas pu�>Q�FeynmanO�Benioff��ED�S �toe,�n�0�.�f �B�W4is gu��< C.� �!!8�s� Za})��Wi}).}ŋ buil2�?��)m�Q bankruptc,.q�ach�� 2d2J�6�]�A a�eU�(if� a.i*�!weZ*x/INnE�eE8 l: n�by bru��c!��ahY6bL8iD.�)2Q%! m\ � gG&q6 =*/E32Dle"n9� eta-:$cB�3�!R=;IF��!{we�m'y�(!a Church-Tu@��l�&2-lremot�)soc�)�B��lu�s�."������y��"o f\��at V�# �iɷO!�stretE�"��)A���"Ga��":*8s9er&� vwEeQaa��2�!h� ���2r� oV\a?�%l.�'��W&�'"�'��2�'}+�!discuss��2�&�=�>ork�� ��Meo�1+t�0e%O:�/ (�A�add�?1+m�'Pic ,@� J�ZA(� a7QCe5�H&ab ely* dir��<�Qp�Q���G*�$2� 5~)� 7.in: "c)ic ��:-ݩ - QC":� fund�G.K m�detai�>] stig� E�!�h !����/�"E�of!0as�)idf 5 do�@a�5d Josephatj"�!.�VK}))!firV eu�Vt no�hib��J�2� !��� -��d progEPl2��) g�G too slowl�a1DA�c�\bpro5NF3��] � .h<�abs�Z e*>I.x0�$mBc�M��-te-al�Rv�7a* 1�I�b�'now:*wo%4?o�sS%�!�pr9� �UTB8!B!}�/despi�+ �E� �t0*>Jq�*�a� firs�e�V<.C��.d'e�7� infl"+environR�v{n 0 "*an ir�r[4�!upq:C�.9�.��4�Amad��+W J� ��V�QC"� �O shor �3u�* sens�2t�rf1 dard�5Y lookH��. Lez)o4qubit $|\psi\r _{sys}$�]��~ $��)"32& QJ!�a�]�� city�A:}5��k a�ve$ AQrpaZL{e�arbit�[6T.},�h�env86ED�!�zvicin ��4 �';0�"�N�" HJ-=\a |02@+\b |12$N �}w\��n�!/!��finn�f�J.-Y*�.]n>� �(Cl#�AU>(A0��nc6[(U}etc�Ee:{F)�%S ���� $%�0\l+ Q� �1 �$ (^ mi�l�L ensos�M)M+�!F�+�)�Y� �Na�+thNCh�Gof� de���\�\-�&� !�ram @BE"�  X ��x?���� )/se.��UY$ap��F�$)nIuJ�;%�i�e 3s .&��,�$]Q � �@ �6���SɆw2�[*��9-!"F���,?�D� E�2Q!��!-�*�uW�3)��$L(.fcZ/>�9�,+�-� a� (��� r�v�m!!�U3U��)�Ż�2\ U!�%y"�HA>�AreJ!��&2@*a!9s��Fe}?[k �;>�F �.:g��s��,� �E�T�AaD�A_�j�p&50!�s��roeT:2 !t!et�l~- plai��nowaday�5>o !->�0r[wQz-# j l�e�NM�J*"X&� "� s�b�yn�L�6di�y0{� "�&�#�QN%�6A" " <"G� I!��a�a��@ %)Lt5�9�aV!R�lb�Xut�Hhe�aACMiKv:�?-)Eu ��2 e(A=i�- � V'�h�&�e �H!� A'*� Y stea)A � q�R�m,c 22.$���� � 4!1|e�s0b#g�)�/aU�>�Ai` 4�#�����Ts)satisaIoHhgre�+A�}x4o%�B good!7r2�/!5�g�ion�,Qf-a�spa? !'.5/!f13�<m��]� �=ing:�$2)I� �U��)fY¹]��X�6��d��2*�A��^&S"$s $\la$, (�oٔ.U8���`C&�$'h� 0 $1/|\la |^2$:�Di�3c���oo!C)v �3!��ive whug�i1 !��A����B����"�%ad�3�F� e�� rganiF(sA�� t fx �2�)imr�$I�es"�!1�I)zo1Bw��do�"�4r%I AWեQ.A��#k&�-%� 2,""�B ~ *�>�&N*$%F6WA��U�iBW��1rB-�*ql��G � ��s���Ox�3�SsfOHartree-.6^m�a���X� �d�U��2Q�oAO��T^;"�f�Z2--2�!�B���j=&�_.� Hs �LLy&�.�L*l >�Tno%�!dAJ�IV"(,ofq� es�\s$,!�rUPs *UB=S?!h&q*>HM2�?KLgm.�s�5bao�!� Sa1%tuj� .b?C t up�pverth�",�a�"4to.Ke0ythR� a�z0Œa�a�6�us�Yi��9upn�� wMB"�� y? EbeTi+� _cut�{!�2��oL��ZMy &�6i�r -�so--� �nvd)?i�YrQ�""- �;!� mp�4���r�0mtinuoc;� e$�Ke�a$�ke2XbeSB�w*�Wt7\!i�onePOA�6)?�B^<he Ap�^ ix 1*.�*1Y� �.�</auJvɩ�cj�m �u�� -"i 2;��ach�-�r "�_rO 9:�� 2�!8 jt�%\Gme usa2]ho1�=�Tome��s!ˁ�uitfu&BhoEĕ0Adn�?�w!*�OEM5�#;�U�#&A1�/e!�F'e�EBm(��-P�LI !]�B�#A���5z[J��+� 4 V noE o�h � unde�n� ��",&�\�66{�2�Oe�� 5��ɻ0hs1ma��!���}6v$s�$.�� r2�� ��`\@ ref� �>A�o7�� see!<�o"-.�0�J~A >�iM�1W*�N� ��R&taM� �F��j�� on{GP �IoteWh�5��O���)�5whJ %���!�|E�a�&�N? F�!A]xa7Q3 an auxiliL+oo�@� %;igs � E& g�&� rex�t��OZa�e"^C �i`&"'��lyg.1�forced@#�>�u�F�9*�;f �F A�� �a!�T^-"`%i��S/( m��,"`. M�ordbfBn!���tt"�_ !�k�b&tLd>)�N"G�>o�&cor�t�3+[ae�)��m"�is gap��=t��!�[@`U۩�7:�&�1��a�V��̀d� �=��q��1W6�2�>�+�j�(of�0m�fvdrawb�N�_ ZAC�:)5�635S�perturb�1K #D"\"s&� a�Q d�xge�̀N ��is &�,���o =�'E��1eff�RQ.y0se�/�!fat2_E~4�pY�l�a� ex= S>2anc�6�P�s� an  98}$ c.-:� reaA�F/�)we��"�&�[&�/�  �1�%�/� �2g)W���hs�,dW��2��J���� Q� B=� @.B.10p8 E�LE(&�Zqt��t"�0)_4le�-i&965Q!{���&Gt�2��R�a�%$Y)AuN�" &� m�!�!��_�F�*fiY |5n��"�Sed��i�E��� w �6�&��'pɹby.� u5� exp�_1�ce kAD.OZq -LA��� 2�1'�r#!.]L &bj�*�XS�T�82.�1p�fo�jdW)��&O �ERh.� 5-fa*(+ .�ia'� &�"a k�Wa��o�PI#e[�..��J6�*8+�s�#�!l� ���o��19f� - �Vsey �Ne !brgu5 q2�}c1 �y>|&Ha|,��` id. �? ��D&vS�.�U3E��Hf`A���J?m at�wd�2&ammf *!�&lwa�� �Q�m�@im������7 nume�Pɱs.k��pinA�BH�`6�jiN��,Asi�yBo�I�� .w /E��A���>zl� "pJ27.�f?j�1� E� Ge5*��;"cut-off�U&�9of���|Q ompa�#o h�2*y&�$1te� a-h S�d$i Molotkov:=�U"7�a�6�� sof6f�a cur&�#"T�2no*� :�<�pqA=���� 5q�ese2a &� a6[2�Wus� ;&9+�)%2�5n?�9m�H*8��iwish,!�A,me���_E/YL.�e��f"g!G%%�YicrGAK3����.a]s*�T�A��N�T�p��J �pugI�wi�M�*, "Z��32� . Nam�mlet $T$�1�!"�\�YVi%.*s�/&eL stepI�n�?""X'=B�AM mory�MAedW�'!��M����B� $�<\frac{1�wqrt{T}}�$eM��+b�� O1Ed.#s�um��"7��)ito: �*�M��Yn:c $!o..D8}©�U":L%?Qu.�t$T$UO"�|�"st�".�u capa)A-!��A��S� �m�� nyU݅�isMg!�a�l��m�@l"��� I�ta�.A!m�U!M���|�`>�^�\  $\e*�_`Vvv" vnY.�" v1�A V#�ś�M�4 ��!c%�$1/\e4 so rnE?� if ��on+�""���b� �a��ME�h��� �>����� �Q]�!�Z� OQZ WeJA�b�Via���e�w��B �etwo%t�s�/� la&k,B~9x&C-�� squ�m�wA|m�wը�͡]2�*�*j 4�F����yݝ6Xis))�� 9H5 )�"� .cof��o!�1�.)��out$:a�fi��E* �<r1+�zunF �8e1e*� e b>#ig[�C�"�& Se6!r�f�qh7l-Wy �IE�e�d���� �ej{�7�  is�%�,! A[sx5a9v��� *ad�.�L�"��� Ze"� �K onsc;GRA�229" �rPL� Ha}5�p&x�m �\?��.�� I7&Vfr*B*A"N� a�Ac2�.!� kI��c�t�"��"t_m� �sl" �5Z far-Ya�!R�Ac�#CFqJ^M$!�at�4�=F$��', bK*��1aY0�l�X[=�n�Iaccuracy��regar�.m� �kua5,�E"baifdat�=9��!@&� �!S)!rA��i&I }G�Va�ODn2�U>H!8debugg�"�!� %g� +pur�#�!��x�&eqR2ufu"6mLY Q P��t�#t�?_ v�*<&Kq�� x�2�@R1 �kB��L�M$���� erOB,�2a@��%<�}�i%e.���*� �y !H@*8uA}ep���9x� ie�q�i.$a q$������aG���se}Q`�d:�1���AO��" .&A����!"�Y���haac�t��",l�$y��A�4Aս�!_.y"�!T�#!� q_H�Bw@Fg!zh�drF�B�ni~;b2 wH  p!z�L"free"�w]�/t�y1 ��is� iK�N�7.�AJ�$st� AjpW�Aaiei/3%�A�,�Fuin�l�xq�n# j���o�8~e"ie�k!� �eQ&dv >J. B�B2�Jf"� qj�p%R�\��m�s�--a :�.23 �/Ej,$%�y �Xrea. Any����l���a�Rgi8��r��z(. '�gr� �LoP-�t?i��"B_A^&�#�j e sm (�xit +qbAM- ��)q'),"euIf� s� .� \n" R-�:�r ABA!n�nt�7�;�~�R ns (K�x�X�Ewo��.s��Ah2D �Mo�V ��b�1n�aRO���@� l����%��a. Re�,uX`ag ze�1�n�*!���Q!g�E5Idsig���de��!g"�j? e51Y�`e�) . Haout�nI*cAWn2�Q N� �6�I���9~e�_"6��� � 4b[���5 � 2r��4��ex�-,� ����by*�^s%�.Ws�xit'^K!:���"wS !�.L ?.�<8&�7d6M �ş ${\ H}$A�F�%�m�t�cho�J� A:�$t;_0$2 Y5��1F`�L$-}91\ 3,�4toms n>ea�~F(�2�A3:�(*A��' � k i�i oups� I�! �-R d��a2��-1��VDo&[T �'.eE&� 5�mn\,�!sgDŋo�-�q. +va� a'�e�[t5�͘9W2e�! & mx\ɉ���t�!�tE J}Fts�9y4)�2�!\�$a�g*CW9W�.3a�Z �/iA( E#xT>�er�M�X51 ! zu�.�$��a�"�S�� )�\E�A +~1M��4�(�%��"� F�9�>w(t)_0$�es�Ke��.�Au�(t_3=) $��6K.s $ \leq t$�L(< G!�8� *�$!� ��J�a�I�!�or! C� &g"�T��f 5�&�� *%�A$���� 6�I�9>)� �  �W�to�Շ �"�-2H>�2e&{B���.�0�g�!� �*,��;unavoid%(zny&�-W �D :N . H[& wL}!6� �U ��]YE�opt�1S2�vavEa-~�ݭ�'8� )��-f+"�4�0�?x%Bk%FO�M����en�0a�b �AEF ���x$ �AhYg� �9 _0�B %��a�@!n�:� �le"�E��immeduly��ti<insurO�E *� �H�Fa4!�t "w����&�e�Jfac"r z�[��:*k# a  a+v ough�<sA*aj10m�a9�)�T#�S#i� -�"� 3-4XPsx�, mai du">parU4l.���2c6��Mn,!%s�/A ���M�den�`�c���Qne cub en@t�`s P �{24��e^M�z+�/ :��Q��� i�9�+a�m_�m"�#15-GQ�.�� degre ^�do�J��nF� ealma�[��� .��d,�n%��4)21�. Eߊi o"*�/��Z�2p,1'�I�+he gyg�T�j55�y/e�E+O;�E!� �a netQȁ;.B� at%aS� "cal�k2�-",Y8�poJ�+a���83i�_/=�ro *�mE2�&�M2&P$A2O��T�,"� ��:�md reguy4crystall� % m(v6IU� 0LA��t0 �j"� Qc� �� Da�)Cs6�traEd��A��Uu�9e*l�I� XA?���i7h�-�."�X�9ӎf��G_EE��� �Qd DA�Q'�%"g ��er]e&9�� w+v litt��.GCL�D*I��4ss!�S����36fAt/J( !P5iacI�,�W� cM�KZ�%g&�.WS*embod�@%  !!�ٟ1�q� oke�S�}ier� �!S�E P%�a��&w!� !I�a-&�$Z � liev& �} I6�%W=�e�A�9��*� origYd�'s?�Xx semi empi6>)Dg��� 5"%�is e8�� :�d �!�!��u � 6�� �% �L�/�1�of���1��"�� x�qN . Afa�t�-1d!N!�}M�E+B$QH�'th��* ���thB�D%: "o[(`�m/�!�t���d�h_���+r49�"IO��B"�dT5� {$en�pe�{} loop ag��^ varyA���m\Ua ���)*=a&�:s��8hT���Eg2o,K AMe�suse$#� �\ob -^I�e�xA? G�)2u�I�1DF8i��!fU@en�Y�jl�jnsM�g# *�@ !&� 1Pas�:�[��pF��A%=�m�mQ��-s.� ���.ny��!H& "! "(n"��!�M� k�ɤ�EJ �}f!�aeT �X's re�H:b��Er6��-"�:\ r�ite �d�b.e���Hach�;�L�=m� !� I%:��}�Ge���se��q�!H axio�uc%:e&�-sIJBSrl*Ba�a bre:��- �7f�Ez3>��_xY2W! F�)io� A��J��be��) �!�{/�F�!U-e!0��K e ai�)mN!\5M�$�p� ��?R,%�(���@ ѳ&O2V�g��6�%�\ac(�>�Y���bD ���o �� ��M:�� 1�� p����b" �n�# �;U�A�aF�%del} �|z*� abov6t(e�!8�awL"��!!.J��<�1ea�:�X#.�s:a�1o� _r7no��!R�N���ʗ��i�`k�mc��$E��l%X fp�As)leA�>?Q7.� �C#j�s,�&L)WL,aV�p��� ��� &)�@~maj"��� /( ]��s:u5U]�b�a8Ste6�bOz�' S�.�;�P(B˝sm*8 ext��K%i���!��{J[�Q��&)�2n���at� �N�7!�io�f�@(s�ta�#�A�:<�&`�$e"�Xp<�iar��M%M�Zsfptrol. S"�f�� %��40j ��a���ſ � H+� �Tp�ah��?�g)e�X- !+A� �wVnsv�y3 `H\hM?_ H�*W:Ywm���!a� .g8 ,e:"K{�/A��T*BS�co�Be�e"ba�!)�-2�8��J"i&H ��(G.5 a�@?NviM�AW-�B��in)(�K� a�*L" B.n�G�+��II�:m�v&=�2P��AD�"g q�7x ����"qY ��"!�E0,"�:Ѩ�!} bX�Y_10_2gX �V_11, ��;a��8�=N�mib��  $\rho$%�o �f , �a#!� 5|2�$� $|2�$��$|kW�0�$|KZ2@"o=-acRt�?"�: L�j-&� �)B�1�, $j$, $j=1,2�|Jv�'�a�.*-"-!���lo�:�&!h6� 1QctIn��(�eyG+)�"�im�w;g .ݢ��$ Q� �͖eA�0I ]me4+b�b�#14.%�E�! ��)# 1���"n5TI��O.R���< !d.��!Z &(3w:54-�s.�nd5#K.E� �I��%3�d_${g��La��&�=�$7nZ��A#���e L g-�d8 u�@u�2*%�� �)*�|!�ok1ōA�i&��rQ�!���+� 2$� ��p 1��Qy�he)�� ^"$^�Y �1q�w 8"� ��!8�|n�25�U�g + �2�"@ ��2gO4�e Fouri�form�� {�i17�-E�b�8 �$ion: HadamHu ��J9�(0array}{lll} &:�82}}J\\R)-F=�x b \�)B�1�Q~QsqbahN���fo�llyv @�W!)�M Psi$A��k�A� !�m#�((itu�&.��E)�s me�qe:����I!�s�mi.Ffsٯ�S�YY)� J�R+�.�.�"rK ��&��U���:2}( |0�^ + |0qZ 1.1)i�$^G-.G- jGu.p7$1/2$ u� ��m�� !�3-����Z�=+"�6O.*M�1�_J)0&s*?y"G�=s�AanQck~� ��A��soA<id��weLr�&2��Fc(%1�$\pi !,phArǀ�|n"W5FA� .�"��� �*�,��5MM�%/�nB<� s{%�*�EtoV*�D � m�F� �X C:)gPC�� 9"3�e�'&�`�B�f'ng � '� X/] vn"TD#�:� {��� � Z)�#ot�=o�s;!MI�� �.6�L%�+�D&�r����E��2�hiFFpar�o �!g|;!? +>�)7pT��ew>�� "z/t�1).3�X!�!a1����Coz"�S( Vv�E���m� <:��enei�#���Ń �Mx�y�)�I*A2%��a�1� l e�-� GS3 &-h�YFS�B>)�2� p�q%!=?� t���E��$ nodi�!m-� g���8�� �i��eO� � @NZsc�;nu4T3%2շ)%����m}�� �E��z6�&��i�Y�e^`mUa2�h ?!Ror%�� .46�]S.Q.�� eʆc*+in�*�8�:dA%b�*�<KH�95��H��� 2h^0pseudo Euclidume�"5�K) 5aHhow�'Y69)�y�xl�� v��AGo~ m�>/���x/�B��y>B r, ��m8 o+R�b82��$a����m1,E�� lɨ+)�"�}�)�� %<9t-i1)�L!w. L&\dt�Z2a��\k FN:� ��bM[~CE�W�w m�o:"7@"�c&nE��(ar3e_� �ї�)��$a��il=)A�#+#u�>I�a֥Xl�6by� ulti�� �u:����:�m"1O c��ofEAfai�N�*%�W!k�taJ7m�qin.%�!���c�a�6�^�Ek% �Y`a .z5^3\"�>dN?9�:%)�f�#5(�&�y's2monK<c�'OIVX�s&� unQx�mr ,&B�frl  !�E� � macr=�;��a�sc\f�Y-&Зmi7(A �0 2�E24*����:.[8%�qk��.)Caj��z�j�Ci�w)�"� *�J��&%"VK .�D."�* � <��of:E+*� } )E'_D�TJ*��a�Jzp(A)=|\l/ A%o��c , \label{&�end*��$A$Aoa>q�;��r� (s $e_1,e_2,�m$6H*�=PqP"r$@&bT #� .��;��9;i�wyFvC ��"߼eigen�q�T Herm�An $H$���� 6�.)=�#�.lin��"� al (c"t�)%�r �#M�s5�"SEY}��n5�iM �jc�FO�!�J# Am� �Hu����F2 mhto�  Nf�"�eU�Qz�m*ichcQeM%%K)� (;� *�@(��66�H$�my�"���T9�� 4!t�fu&�By0end -�k)'c��l� ��!�m�cj>O%ail�f � �,�LTG0*�w.�:y�*1O}�I�R�7�!�7&/ de�,~�(*I Ei L�"�Cal&[uO�$�?�{�"f^Hi�Cq ban.��PQ=� o��bx ing)�Ml+Wm��!2d�bym� . Zu}��K��4 1>Be�X � swap��1]D�-��!D;��it�mSJe)�iX �+%O�� � ly �X.��Mo"�SF�T��b�F2�"�"�P �E�6Qiri� G�Xo�>N Ż-YGl}),G � CFS� Bu})&A��a'!?Awsh!P%�A aper mi�� Q�ZG�=terpre����`�)v"��eu�A[0�F�AHatP1by A. Sh�Fev�Sh�pb61&qk,yJNne�|v*})on��Ga9w% �:%<�ut�[28� ��!�q���\����[1L [�%l�(\ref{p}�H�� ����Bm�[=:�͸8��1e�4&��snda*�-1-B~!MlM�n tj?S&w���!�h �&.h��J�2hPer#!�s6�sK� :�.A "�)��N��9Y�!�|phb�)NK�P�]����s������j�J�Q*˳.�P y�6%K�6"B &�)���Egi/�DmrU�An:� ?i�!�" ��H�} .T =\sum\h $s_j\la_j|e"�B�e ]2��ppÑFin�t��I�e4!9�$^m ".�/���,"ڳ m�)uumrpum�S�cut��-a��anj�Qco"`��$�m�\� �$e�?�eshold6R"M����$�d$"�Ru��s. y}$N"�U.�/e67a��Q,�W2�="T\SUNSUaf& ���.��"{j=1}^N%0=�"� limf�Yt� %D1�bep� �9E�1!�eA�/!�=�1�� �.=9��T��a�;EL��yjz$\e >0@ -N� <OsA��).W���5s�VZnE� �ssMJ��%t%J ��d*y��khlL�A�;S�nulf* !29+,�<�|m Aj*wQA5.u-&�. Our-��L�Gv.91!* �a ��� ��� `"�!ٵ,%�GQ���-&� ?  $$Vi#N_{suc}} a�} I�$ EJy��6[-out�c(�I�B� Q�+K�m&�� �),{�Z.�8�A�Bd��0�>fIb%W R4� "�(l&E&� *j�3as-��]͓a$�A�F�)N;�n� D (&E�1+v A\ce~� U�u� @E��$�s^rN�a� $. A�bBR�i9>}�&67�. B�ЀB-'>gC 7 �2 @hi�@)0!*��� �~S n ey�Bo�ueo�� Śc�M�U&�%�+�/B A�%�� P6�!hau} JB+�.Հ\.���B1.�,�6�i�l�&�Jz�5��� ;V��,��t;G6�Lscr B�� ��8q\s�XQ �'� c}"o�su�Tf $l_j$6�(a� @of�\e;G��!tAhV�}9��%GAO�F.�>H=,�Q!�v��on%�X��S� B��e88u$s�ick �%�F� G�GAR R'U1 2� {ksH{l_j}\mu_{j,k}|\phi � �!e)}H6�j?A�cC�V/2} "va��Je�4 � be�hGcD�EV�$�$9�E�%��V �&�ak"�Ks�'��I(ZEẉE9K�F"�" 5g�.�)�5!�%�' 5v$���$ �_!�}$.�B�js�GQ2�AW>��%?"�� � nUus�ґH �#Q$�w��P^. &1:�-m�)��8a�+ 9dh4��|s c�ig��-9dqE�m8� W �at.tpI�newu�+q��  ��S6� cl�5-����eJY,"� 0\ =��7~a�% x�t&?a��;M'(F !F�� dE�#�se� �N�*� &�*�y�"���10R�&���&}Y * �+�� �N�f%>A%�[a�28I�.2� Uk�K��c��A*j"d*O�l�a��$b&dt�E6]��9�"u ��y��Ye�ve;�.j�b�6��* z� � x � Ip � �1n.M�(>� �1t umnar�nB��big� ��.�u &��e�=��n�bw�<��U}�Q?%�A�"z*�a�er5uo:Ba�N~��Kb��k��� R'�1e�*��$|c.=�E���%�u���(��onCBY�E�6�q��^!�l}U>�.����DYf*� ! �՜i2h"s%&@"�sDG K.aUj�f �#j�j.!`���-��*B %:�2 U�.%�!�#iL�law�v1�.H7 &*a�orra%���iH��G.���T1M��,iE"� �+�=.B��6gJ� S;��6�E_L.�4�*�: 1 dymaA�AA���dva"C�N�&k /2<A�������q�p��5�%o/��4)�&= �._PJ��� ^ɭL�()!��!`[`I؁�i%��.���-��t �e�aradox�,"�2��S!&�����!pI �1� \� n�� ntel� έC)!IN.�(!`�un֏eˁ��..��)!�З>��)o�"�)\ bc,9 �_Ym�V�C��  A�� ch"�Q��F6��G�fliv ��sF�v4�.�.*7 .�p*��wiI�� Ms2dM"~�.X)7 (i>�y)���"K ����� UP�WOE� +��,��� Ec �rES6$�Za�l �U�^Ew A�!�:!2�*f �!!���y �&e��:�S�& �o.dP"�'�J�);5�-!���$ �%�iF&A`b®a�b�DHierarc.�}(}��*�"w%s�6�$m5�.��K& ���w�cal{HnUJ-�]'..�<�[� f�#!?&����ns�;Ia"} � fRt"Y���g P@en5KP"L�a�e��A!:&~�S�\t�%&�5m�power�.��� �Ds)�Is;vba�"�B-��m�$�+�S|NsP q6<�iW� "\� !4.�|�-�$=�-�eal]Ie��6XJ$�/���-��`#..z��1 a��bA` �gen��%�� ?5�D#1�w$EL�ia�op�\a�.< � 1M�=� I����H�#u(hQ] �I2�i6[\we!��"7�� �X&��6jNG � !�oo�)�&f�ty�.c68:*�*� h� � k!ke%s6�P,, and we hav� in terms|sums and tensor products must be ��U basic� E&$N^2$ matrix�.�h�dim�on3\�s =%>�m step>w5��s74$Au�.)��, h� !>]  $t� B� them�a��a�n �t$a[akes �  ]A �f>� si�ed�NY)fFA� DE3.0we�ho�:1cha�e�"� �9~_s�� or!�=v �MXs about%{12}$=\. I2ls� gridID $10$� � 9�! oe)d���le uracy�A�5$N=1000I#�Za�wo@.��$10^{362� �m%�`2Ia_Eeve�� m� E� � ular%�s r)�.�asymme��� m. I� p!ץW��r� A*�� �jA�alM�s��Y���als (s&x LA})� ,Hartree-Fock @.N!�2g "�gof 2�:1A��Uof ��� ferma���a �-Slete�t nant2�$Sl})). IHan!atA6bZL)�>E�comes"�,ir exchange ݕA�(�Coulomb.! . Tof{>iJA�should9ZE�:y� su^d9�EA� T (\ref{sym}): \begin{�.} \sum\Ws_j\mu_j2_j͝, . \label{ge/end> K� :con�!�!<�rowe%�m[g�U:J��If� giv�� bounde�4problem instea�� rob�mAs= "��[no guideBil� choi�$%$,I&�if鹁q�Ai3 neglig� inAUparizon�"\�� a�o.�c6� ummand�OF��doe x.J2Iao;*s�6ٿ!S.�gof6n��almosI� 6$!e_ /n� als)�ato�n�8a� �AEA0��9�,ig error. � nowM % 2e\�� q1all%�Oe&2%�!��8 :p�l e%�J��< E�t6���\e$ is�lA�$J (1}{\sqrt{T}*:T$,x>� *d & g- fast �2��� *& ' ur dispos��_�-9!; call�� _�&. CB" firs� velR -�b� 1O �iq\, etci)a�c�20a#�nt� m�+e2�t� 2Bg $n+1$;!' �� ����I�:r&� �2s� wZ���-rul}�Ʉ�is"| y �C$ recommendeK�eA~a�cedure��H�M���J{noeFa�N� �dXR:�. Each5c $a +1f� us. itsl tYcoqM x_a,\ yz_a sp�y' $s_a� s8 "�oftZndz.c%xe centrEXmass $Cm �minim2E!�AL�!'��YUi�E$�� $a_1,a&F a_s$q9of5$+1!&m HTh�.���� )�� !Yp�A: �:� rela Gs� In w ��w�llA�%�qubitA>I�F@(Ar"��!Cv�{ : }\la | ��A _ } :�� :�oa bin].�numer� v�9Y��>�%u"  ; lea� n.w!strA4be���aman� ��"� bIF$.,(!��)�|! Z" cographicuerM �$1-IIexactly*�u�i!�2� �in� O1��14I:�( be g5 .&dA�>� FhmAQ !?Y)A��mc*��� ?tra�|physicis�!mZ�, .Blas��$ambiguous,� mɗwo * hing��9�T�I� in a� em�5�("�o tell a�PA�se.���Щwrr gr<w�$d�-qK s).}�we agreAIw *� !���k-1ebv-]�eAeBseL�����k.�it, Bis��l6a61ll� Az$"A T y�G��,(r�"�ir:�)�s*�mS�t$arbitrary,.i!��.�k=0,1R" ,n$ e�~�% %'�ydenotw%-�_%/� i��seg8� sequ/ +��n�� $k$,Eh by $I--thz F%&KN�!�eq���C=(r_k^1,"0# {s_k}*b#j$% I1�2OP j�1<9�!)%�,kEwN>H �Qs2�,� 2�"���a�=ycnex� !en� =2^{n-k-1�yI�up!0c�r�'�BdaQ���G *�� !'��lD#�u�\ #fi��u:%�Qs. � 6S�%�4 .&��p'3 z�$r_1}\left(�z_1}|r_1��\bigo� s.� {r_2J:2:2F:|%bJn.$_n&_nIright) F <hieB2n7 suffic�*"��sake.{ _j}$&1!u $j=1,un-1m!�$j= oq it;.U}$�A�!�ulaV�� �fix�aC��$�B"�%di��bm'.q�M*D �A<կ;A�M�E�)7$normed. Ac2J#A��KmMitc�Cf"�!u(8+ $f_�� code�ީ"$[�.�j}]$,"&A� _j)=6)�$K_j$ V%/ ��!��^��� $F>-a5(e $K_{j�$�:at,�)=[f_j]�  . ��p$j �- ��!���Y$AZ.v$1m�)2%k��fix� et ${\�ANfN�s.F�>�unique�+5��� %.b�� �f(&�Z��%&�,A)%�Ne)�&�%�%:ar�u$n$D !t)of�)��!P�-����i)n view<J@ remark- �E੼��)%�y2Ps&/ Bnar�sub" A+ Y(� zy�#�x,)a%,I<�k6 3,bed&} f"��/"Y& storag��Bv1Hmemory�h� o7 K5�"-�4meZ tea.�s -��Fb%w ? �F�F s!Yow)�! ���S+ al5�&- intrg/6im�Aad"� "}(�!�f>g4/factuq.���S#�ĕ��s� u� .� $rp}, +1}� 1�nly�*l�"W/�-��*e{ $p�5%� )0$�s} of non-�g 2.c �r���� non�`�*��[.!�W��e�0 N�_k}h$F�.:�k2�k"�"6 ��iz,bviously!en�)*��.r_{r �>*/-�s�}!�2� l G ��IA�auo.2�belon�" � ower W�%nveloyVw. W wcq �� p�details.@ A=H8tW!�og�YV"�$S$ �� �$k$�"(*a�.�usuc�~m:,��J( l�* AM_{i/]5}=Tr\ (AZM @:5|).>�In�ti����dE�m��2h.��on 6 %$!�potenX$V_k(r� �)ŊIZ�h$r$. G 0�1 xterT.MA��/�Bl'" A� )=V+� a�)A�QT�1�-1!� r [-A*.�!} C�� Dn$1HT%0Ohe2�b?-Ht��.wf �Y2}tc., upqr.R>�$0$. An absP3Bc*G � � a>�A ly nes/ 99�-@vIt tur+ua�6a�Dc @!�Gq�s H,k-"/ 0� i��!��.�%� ����i quW%�'de� ion.zA�~B-&1%�liz( or!�.6�<m7��:Ab�1� c}�9Bb� tierA���"�5�u�5&'. !�� mpor�7)"*^per� ed overZg^ i�"@'I���*�.� s li�a�`6X chosenZ_  i�� A>��v �u*ac� Z$L$ (orAs!�pI�grain) Tant�-� �'&T �2IV�/Z� �H$S� �<  dE�. nyɾ|!�.� ,g� +"polynom��� �$N�YI �/ �( +[ deg��$L� 2�:*"F���bI���6�h!%/a�val��X|$(body Hilberjalism5 �%!th be'-�� ial. Newe�+g~�se�s� :princip*�+� ca� QXum}�� n�:�5�/�-se:AtN-0(g!s,&�/�! alsosB9�NF\!7;� ed5y!� varya­-��'1.) L� �Q/�J�7Qy� supp�A�%}-TM�A. #�;P*ofJ�&�R# atora^�<l&).�ɀ�����i�ini�of._ 6� �&� ��/iaG=multipli* �1 4cl�A �to�� A@�S�c2K$&y3�&�2~�,�!�@ee��(_otu0+ v.�J 6�*): ŤJ%UteaMLfA�D2�%`>U��/!Dng&�]'umb att�Ma�< r} �r�p�3� �r�=��$�,S .�(I0� ��sit�85e.�]�"�>%�rU�.�e��m!�an��&7�<.�=2~%�� G)%�t} toi�t&��'!�1�d�.�#�)A-Q%q!�bP � �analogo��w�">p%QUWa�J9 2�(la_�(,f&�(,> �#in\{\ { �\ in\ y<\ }\psi_j,\ {no\ "s} �==+m w). 2��if��7^ �!1W�.�)��Teproc�<� �7�(!upre�%�,connecV %o&j E�f.:m�Qy� w��.(d before. A- � V:�gX sub�4 �j'b$ � t!wa&� N<\{c&cor�a��a8��a�)c�$W�)�" . Du�266uno@�aTwo�s�� �> 6)���s� E��L,9^!�M prec"�?�P(.;"dissapphaf'f�<tepe��A5;B�� ��x"�#�63nag��4.N�%��an�)Wi-?t9�: K)"�. @�Df1P�0"�in@ A�� �6� %`%R�.?.�!�impul�+�QX)j-A-��wi�!ac�0�"w��e�6ju�A�OA+nontriv� pe�"�.�&3"�stablish �2!r�.S2g"U(�"� e�:gDA�"=2�Dari�6�8 �*�52!@E�� m_(,orY)٣!C�E2�i$�3a�of��  V?9�~��F�"�j��� on- x�A� ,\nnn {\bf R�}.� c�/in��%;���)�"easur���3� "k-M�"S carr�>K s�;a@őb#*es�I�H�,!�h,!s���: � 6iv$D_1,D&�(D_"��.��?w%�+proj=��B��D���CarJ:JJ BornQoFy/ntri%-�"W �R&� %S6�� �4nd��2be�oc}A�4:re� ��;� "MB�5purO$$ aesthetic2�`!rv��2})"6� U �<#R"aG;#�0aeconom�?6�resource�$e"dis��g��-V���IOM8(I��+be faD(�7omW�a� lm o/s .Q%ce2��"KE� � ;is����Y[!��\ne� ny.J�/�bS Bwe doC ���*�)&� f�;� �Ha�a�"M �y�wB�*<>buMS�ze r�!edV� ly��I��> lo�^!endKY�imaj�!Et.8 N�"�;'m�H H?1!�Tyá�� oll *1 �<�%�M>"��g!big.�`95mZ4t  1ZIrX nsa�Q cD.�m& inflo'M�"�:�passag}"�*�1s*A ys}=+s�)��"2�in[**�througAJ<&�Ja�terval~ �$�J x�� %,P()Ij&:}} lim })a.%7cho�&)p.s"q#!oimpacEIQ�!�� M����Ŕ5�Y "u,]eCS�!com�-!U���r�r@Q=a� -unE�ARi�K �� � . H�!_e�KV))� A>�� Q0�;N�S&� ��� *%2c B�? I�sta��&o urnaue&[F� i7E*!��8m�).�y=���*�Y;ts. Name0 #%�Lx)�1=U:zcoBDM� �& Hm82A}}2:�{f_�h"e!)��� ulfi5: � =C\ y|^2s� � [$C�$t guarante��sA�.j6�7' dN�� ]<k� �� U�Y�>E� b96| iw!�� +�K�[� we ign��7smaw.�M�M�Te�;�|Z�9>�K/k��� :�J��Wv ��++"5N���06)m��2 �'4 I2$ 1. (% �)� �e2�}9 stra�* forward.)k me���J��1 ��>�acn�)�%%�MD�ir6r,is $[1/\e^2 �(If $x$q~�2��WB�ZJ�UIe�()�5$C.�P.v�(�O52�2�$\�,[�9 \la}{\e}\,�!����8�}O�i�Fu�w�&eps: a) ���J of 2:� �B#�;xedC b)vZB?!:i�R~d (�Nt�"�iH)��� 2��>�!�?�b��.�%-�>�&� � �r��I9a��v��1{>�m��A�� EybetkJ�ideolog� -�t�;N�.k.� �nsemb�@�iT+Q��hig Sve�`!��6�=�sU :!*�W�%�^W5g��(% | �.�langua�)&E�L ��e�L�Yat�Dng%�irIt� t&� �A�geh W�Sof6�=F,� :�D9�!/xm&Aas6�2)���by.L �GV'�%$mA%!&�"�)sE�:� ��G5 т��M��luF�#9c�"]'Z&we,Vcourse,l �{y�64E2|�JoF R��� hard0ee�anyH�O�C�$ �.22�6bt��. @��(,�xng�e�.a$-'$ satisf��&� CF�' ��6}{  M }E( )=0, \ \  \int(r)^*H \ dr>�B� ��-ari�R%�E�a2�XU�\F!��!���ry%6N�J`f�W\Efal} 41j�#3kB$3��V S2�k^�1���/&?2�� _j$. P�z@)�|emy })Q�&pO!:�&c8#�y. O&��C�"�M���m��6>MY$ $1�#i� ��a�,ep6�t:�"F�;n2/$M�#> �commo>^Z#$M=N^ ' $M�2aJE offE \T+,!w6-Rm Z.,i�>Z%���"�J{I� 1}{3 Ce�&� >F=0 �Jk+2L�Aa e .*:�!ypMo�&�JA��_"�!_�2e 2�s:F_ a� (�ZR\�6Y\r_k)= _{i_1}&)22) ;kk,�G�B����S!�(����;0m�#�C�11>:&/%�g>a>h�%UE�Et�b����$uus��!j�0�ZM�al �. AvC"�'>�6� �A{16P0D!�HqNB�(�T� ��3)� ne�tin�Xhe � ��Tmov�� Ke<d"Y )� �H��Tq��]� T" �m� �8 ulty;�(�Hi2�2�i��m,Mm92�� �$aeVVV,Hstructur/ A�"�3ic>f� �M�2Vextily largF�A�su�G&a@M7d�@�Vi�(fE�!~5 �YSly �X"!Y�$ >�� ����!��gm2E,%]? s �O,��/t.} Qw=1q܅�!e��� ablyA$pli Y1� !vid��& D� &�L-�e(Q���nergy� 6�:r� o)� �o�X"� *��t�&�;5�"� * X? R+:GE}!`%i�+�Bl�o:�W+!mw�u9�.eZ:�-%eA(or7si�.%;��ag=]���-g�s� "��� �^%Ro�ag�+:n�(�z�er. ":�E "�@�d2:e� �Z^1AA-h�B2e�8a��JI>lu��&� ���A��r�I4. {�Q@W:= )2�D)%%shwa��)�:kH&?P >(.�. �25�ɸ (��rf�����2ll�s1R�C�!!� $a.'{\pi}a (1)�7\pi (2)�7 �78k)})(-1)^{\sigm<> pi )�U&� h���*pruOn%� perm��pivA2I$�+o W-l�fC5;NA%�5)R�h$ Q�1>?bos"�f stog!��:H u%,!8en*�h J� ��_{ind}=_1"� �H&x@�_2#2F#)�B3k3k3^ noF�HiFch�e�&�.�6_8b ib8i_j}|�Q�9� >j<%�!�R�ex��$V0M* s. A�&*:�� �GT4)6� �%�J�\f�1:Ok}}�>D}(-�-� ,1� )�`9 ; %&a� 2, . k"BbS,�6"Si2�2D}�!�(�/A�al7(\A��c!S�u� em -q>i�Ii ic)&F$,t�<52[^*�E4`*A� $Sym%E-2yG1 �^ ���Jq/<��i�2��Q��M!Z"��W�)� `i�y��).���#ph/�� 2HHpA&9U ���"�U.�M�ɱA�Ri&� �,*�RK&�-s!�5�(!�&��^s 4MNs$-�y(yl ��e $j$ J!*, ��h 3l 1�+ s�. �cm*�B�L ! ;�]T"� *�4O�h���P:�n7_|mc�6�i�/&� &Hlśut&0& fs�e&J A�� Q���!�]r�� )I�A�h&��>�_%.: ePs./"�a"�mXBE�?.c�)ya:�B�G>+ �'�� ����9O"t%� e�q�A*�@ 7�'"GWe�� &�?d`�S,�#�H$ name� Ay�� �2 �!�F�_{can�3 = Sym (2~ j\in J�i�0�� �:w}>�-RUa!yonx>��d&�"d� � ied:�$itemize} \  AlW��"81Is $k$-u� mu+B$orthogonal� .k \Ea�0BX��G5�1o $& _{h!DH(j)}-uj,h1u" ���X$)s$ eit�4$:6&Bb v"��O �2]�ea.8AFE�u(r��A��!eM),�6�R$o]J�U6 �0s $h_1(j),h_2{h_k(j�nd �J���-"�*27\A�6" l\la^% _l|lM�$.I�A>EH .�&�d�De� .��eKq�"$��S�0$J$. By virtu%~%ReU��Y��NA ���;(!+� )6*:� =|� *� �N�h�8A�=2if�h \/q2#\neq 0� Mr�Jno� t:!��p�K�?q�} �w �Jj�')�EW}_�M AdnM�rQEokpbel{vB��*c <�*h'ŭ��!�!�$Jve �XeR�h *��3 ar r$ �!�Ps6|$��e9���G%�%� 7@�"���[mK"� "�!�Z%�S"(%3bM,n�Dpl��wX;_$1/>s&"3jof�3� VM$J�� . Re�B�o+tLNar:p�$ly �Ste*@A"�/�dw})a�Te�d��t�+/)id< �~(�:c� Oa cv}) de�6�Q*g)inQ�)%��;>>� "[:s � ,*� 6i!rIBcaZ���,!!pDUE%M�i&w>an"v6�)&R%��h �]VD�L�>�65w�Y.>7-cNJ) �Z�Ure�z rhAe�� $d�K�y� w�ArJaA+1$<�%d9aE@ �����6�$r^0_1,ND  k$ a�HA�r2 ?N"WW� �!y.��@a1�!l=T�%�6H���l�!����$s=""V�7&� � j,h_sC ��i�,� $ ' 2,+� B_{r_s}|!(s N +>J? $��Nb$�!JE $) -� �-;'ich!�lde� precv (a�] �Vt)���q s^0$)Sŗ.�: ��Vj� �2�2�\UaM��me $E�isY�i�-re�6� U �dnL $��ex24�NJ+b�e array}{ll���U*F={s=1}^k\�(.&).U� E1^0� " *92;{s-1}AxA6 ^0} E=Nk"MU& �J +ETN2 )A  �f{b=s+�BI�b�%)\\ &y�k�kz�"NugG)�� t zVt .�sA�6� ��er[;a�q'�$Imz}AmŦiIE���xn�it. S���e^$j��DJ� � e���m�u K�>aHY:cer� 3%:�� ^8 R '� : �1�M�bu$� ����3�.�� is � �.UD5&O"�;�$# ! �Xre� !��%d j ud�aj'}��j'� j$;�!20�(@ j'�8')q$vTin un �d%6L2�0�]-+2�"~�%�&�.m��$�0�BJC� o9_�)�al\NteE 5/�YO�APV =��6z5�A���"f3ymN:� A9 �i%D2:�@ �hel9.�<��9ulNOq"(gY<�:!owh q"f"�at=�we5�jH:N�>�"�3!�ep%�" alCy�aY� A����7tK/f:Q� *0�\Pi~sA foun.5ar�G5�&� l $ E_d^1,& {f_d}�4AN%�iAK�~-�~�-dI�O&� $!�r�- !-A��No.>u.�$E_{da�QM'&E�1���7�w�\� �9{D�T ;iXM%��jsA�d�*�1 }���pw? �2$�r '� i;?e�>~he huge.$�of2�-�ي�!p� Z����7:$eL3 �_)B� l:��[*u!� zR���a�5C���2^ T,�\� �!iaE�y�2�� $&*� &��+�+��da|��_ =|n_1,n*� n_L� �I�$n�dl�!yI>��$lp��0$i_l=j$ (popu'i�D�P.-) 8 E�? rtho��9Ő"=i A1"�fAE�6��$beJ .� �.a a5+"�qsecBz A.�I�A���A�F�H=2�k,l}v_c_k^+c_l&�+2}>, ,m,n 0 c_l49 mc_n, hamN�,<%or%bZe���annihi9�*�I�^n�L�2�7!�2JF�>w l} &c_j^+J�j�M� &=.�#_`$n)}(1-n_j)ND+"F,� c_jN.�rnV@-Vn1&�#� =n_1+n_2+�+n=\1}�K� � a�!�}C0� 'S$Xb$p&yY �v_E�$$R�M�&5[ k�ff",p^2}{2m}+V_1 "&!l DE�:Hl,.2 PV_2Am,Hq�l-$$ A�� k<�[�g�Ce+�6k�SE�freed��nd@Z nsJsta�+t�s (� ��conjug%��[:� �"� 8m$s,Z1,\�Y� �9Յ"�Y,^�~"�Ipex}. �Z�u�ms�� &�1 ��VQ�� � h�k>:�f �#�+�h����7 "1m/��� =v2�3&� �AVjZ6�a . ����Z�A� �� :��t^0� �U6� 2f%��"��AccuBWon� f$b��"s2�9�� A�tbE"-KF�AE�A&a���� ). A.� 6E�q=_d�66�J0^d�q�V2�*$ 1"u6� &&v 0� �"^$�� � <)� %:�� �' �6�:=��d�_ <fM\&�s $k,��"�4)&!�iZ��A� {d+1"^�23=n UWb��2�liX�@-!*}9M74A: +6�mo6�"�:AFa  ���x,A ��sSW�Ef�  �%O$a hydrogen&�T��"Ue}r!8a�����"[O�jr~��zu17atH2u�3!�"�_ 0m=� fiel"�zwa�e3A�/�p�{�#q���-�N&�Q�{�s Max�-�EInot �k4#Sna:l-1� ��{h��de�;w ��M>�Փ�hoMF P �XCoB ~&`" j�nv�s'�GPauli&pL!�V6nF�*"� � bp�c�6��� ! _an��A���Cs*�Mur�2"�l_���p]joi"�<woY��3�'� &P�third ��!&-�-�M��0^�!R6T pair39iR+I <<"%7qa�9y!>QfA�I��Uwo ��59utLy�4e)) ���mS@m�~ �A�r���0&ߖye�*�.PwY �� ԩ`!JR5.y x SmO>Ug 6of� ��m=A b���?B��6y� �Mwise. E9J3(P.��)�� ��be:.� �i��A �5& SR�:1�!elf�wR�g� U8Z�@i*�*��"eflBۖ@�at5���Q Q;��wI xHQ �&�be-�ce�)���l���"|���E!R�") >I A"�C�6YF!%r�C�6#0���Q ^ $2s�Lll��7a�l/�%�a�JI�S_1�BS_*%3 S_j&33�� } ��WDt � eqnE%!-2]�T>m} &S_j&��\X�j}4{2s| &#  |��0�  +2�r"!{j�,1ZA si_rA�|Q^ ==� (il4r)\Omega (c\ r&9�bw (|�|1Z))U&�?QB���$6�"h vacu�d!�,j7 hi_rpha�factor �R(�A:��.dsph2 laye�~2I}us $R$8cksp�U��L�/�6 �*� "� pola�3��eQ4m|��.!�y�3�unk? �qT�/b�t*>�N6. N�tڑihf^� ��# �(��^&h!�"ZQ.�converg� 1 $! �$g��to�a�y� deLb>2-6�*�O&Z���"`%h F�"�ayl���KE ���m��:&�5��Vous��m�;�8bU #s��&� 1�M PA�gedՌ�� T�_v�+1�&/))͜!%�2p �7 $ � -���wG�9"�>-��J fQ7�b �happe.�a� ��L1sTD wo5�"�| �I@�me%"�c," �ob �alway�I�n�B[9 ^iNF�G$ъ&x �q�UN* 1"v�&C�1��b �"� �aU�"� w�u�N&� !�bo�~�f� a|iT-��= 9vp  "k�� a�6. W�)g1�r@�9?lCW rigid%GRntu�irE!7lif"�B��2�4i�[.H �2^sA�- ��dX:�7r�l � :fI!newy�!�t�N 2>A ��Isel ]�0"R 6A3� iN�� q�M|9 }�io�U!U�j�t�f�.��A��@��na�t�oF |�)* :*MRH4�*; m�is �'�:! middlejsށ�] M2%��@inlf��&� ŏ�f �F[�^,A�B��&g�3���adsorh. O���embrac�Allݦtypg qᕞFr�fr� 1�Ayd�`$ ,6�  r�) ;E<�atru�A�,j��:��HF�9� H"zm�!��aC iRG2]��I��Q&�Y&� T�BU)�9� entea��#beI��>� A�ic"cAp%.d �alytic�x6 �pQ0�-y�"�"i�!y%� %nIdU��J�siA�yF crystag�e��.Ég nimF�LWu3zto�2���.o$E/<��A~U�"�ic�c\�&�ku$.)63>�B(iOY_K�* - AR��a null���too�"UE�i � �p8z"�gΉ�!�dlla�>�A��AR�EY�J\ a{�cla�~Q#um�= ���c v%(;+uI2��͊Wtheory�^A�xiom.͑ml� VD)">"-!Z%AR�/is!ro��A�AR�-i�Y"�f�= :)au� �'�u�Lagranj�T *"_mtra`eor�(is�JJ�Planck!��t (it&] �+io^ by Feynma�#(��FH�Cith]?e����od2,ܞ�A� dix 1I�i�arktR�^)3� auto��c age)�5�o.Iyϭ�* D �����A#��c���e| gram�� R�)�PA�wuB&_ ~�z|J|Ub�gt� 8�NTno tunnx�g� s�y? �block�&ARy# V2�M�R�&��; �M�>"3.A_I�!"u ing"�1vpr�!tAZm� �if�O ��576 �!�J� sH'y ��a�xs"`n}X"� sFn�a�e[~&�8&9w.�mAa�&� %���Pm$i��byp 3 *!`m D 4< 6E j=0}^N\f�^k�j^,,0%k��`�y� �,��S�Z.�Ycom�:�,j' �0 ,j'}�Z*z {j'}^4G���%.�- �5�).$j'�;.7 E!�e6*m7wqb�b��T .fO*%;Q�6�yQ:�6q��1��,"�f�D�y�`� si&��}��E�L�ia�+&�;��pcor�#ry�� ta^;=?5S �mA�1[b,.�� - i�#�o�R�Oa@��cQ *d!. E٧�"2tAy ��.s�9�� c� x={ro:� ���]2�t&�m`�>� Sv2 rks}ybe�kBV�!�&&��reB�3-I�'!@0�%�E� �>r�v��|5i! y>aD�[�an�abs�v&c �Ri-�Z� �%c�"�2� r�1� .�O� ow�!�)� ! B�fe�*Z+��$m�&.�� A ��RFj�IB�~�dsF�(1�;Jin����s�n�J& %ve�QX.V��I) � ar� ���$!���:ϧi�a�T"ئand;}F�-5%/, =a}����K'� �nnd�xV7��$�"����3���&�E��6 E��V �th~�%~5[�WaQl E��F�30M��$1���� �"�9��ya�aI��marEpp�~��� �Q�sQ�ev�-�A�w�?8U}F��-7��!K.It36��� �!nb"x ed>��E9,-!� A��A�- ,��� H9��o0�' lyi� a��? >�n�!EJe�af{b .�J AI.�h�rum&�WOq4�`%P)q� !J1�^�uH,%āXRq�QE: � �c�&��� \�y|;e� avel�|"��-6M�"�Mn�-p��or 7  u!� h !i��� �&��E�I<���swUC%!�NI�!.$likelihood9�Tb�  [�.}�)�D��Q""�{����'& a�� e�!&�~ t3A� 67L�W�ra. A%d��E�)A��&"=It�R�)-A:I]����be!�!<&|5��ep��choDF"�� ". H���iso���!Ƥ�XNm�n; dataq�zrU�qq� ��Y�?64-�r� C�:!�"� Q�:�!"�p emanI\h6kIE&w&r��4.�6�) �tr2G!Z�s݀b79�AX��� !*�h>�n"�PmX��E�6�͹�Fl��I>&� (eEJET�?tr+� V.*&� ��|�)�?!�Q1�Q�oBˢ"d�"� Q8F .!�t;ac |%?.�_�-O� heim��x��io$*t,�[�!,%a�P��!<9�D��M, may bB: &b �)i�y �O6R ��Yy��R�28�e�"�"0 $kx^���#&oqp*�P�"%=t 9�" �clo4"a(g%01�#�1$U'����\sM=C���outq3#��_E!DR�to��B3y#�funda� >RA)�-f�>&-9hb�e k �}�z!�-7���'@�nea�<q"c+A�lD�n|��&|*.L ��aP�rdew$.��!�t�|c\}k "�Dexperdbts@nowaday[m�Vorbid!W8List� �/c��l"�@ �eN��6�g j!�2;���� $���4y�� }J�8ig>��-���| %��� ��I�yA!rA� roe��>^8 Z�Bfa�O h�lQB�* nr"".m�� �� &� j��A�V�6��!_&r�FF� !9j a �S-X� ��R sly. T�?u�&~vi�5�&� �$1e�.ij_��i��o� �@-��� e!�:�c�\>�"w�� ~.f� elimin@� !\%��:�Iz7Ka"�G<eu|- g v{b�H`2M_�W,�.� �$� � �P��-�m >9�P ly�r ��ven3al2mej$%Xi�� ]4t2XP%��s/���4ACC� ion:/u�wl��o^9&#!bfrz�e!>&���EI%�q�� �g1q?�'"� �,)M�%���i�XA�5en!?�yir(Mp"�0�y�UNier'%�p�5�E6H4��=�cu缁O�!x� !~k%/We sawI��N4 �6_+!�![�J�2i� le*�R�B��^co= nc�6�ay� �&2%�elenem5�� Ő9��yl& �T&wd*�am.88r�*a��|ˑSqŸach��%$ �~�%eas)�pr"�����8�� F��]environM�A�����a�.^D� 8�6 mong5&A A3e�L�A�a�3 Y0.� &g���!� pre�!�Xq�.��� ���� ����Qv�*��=le��$-eh�� fayu.�-"a��"5 ���*D^.ǃ6�dema  �S&� ��"� . %%9B"�w6a��s��&�� ���-!a*��EW�Hf�%%_��!#!�1a�1�bsI�r.�H��"I�E *�W�m�n"E!Ѻ�t�m!��a�h �s58.2&/a�!9�m~vyJw:Ta��he"�" path<��i6f�� ��^o~iae"�� &(pseudo-Eucl9n-ricYeR�35� .t2�6u�p9 Il(�in(a[e6iQ��!. �ra�^�idot�$a�5�in=�nE_&�"FJ �Mo�w�5�1 s. J�! %]e]�Iv �� -m0c��*� ) :pQ(G �sms��*�&� y倅W�c+�-҅�)� �!���*.�F�6raxdA�.�j!����Av iner!. !��wo&�=.`��D�F�th�� !"��K ag2�� ����@4�au��2� u�.�VB����� �p�hani�U�C {thebibli�f0phy}{99} \bibY`�[VK]{VK}K.A.Valiev, A.A.Kokin, Qu��I, ers: drea���|ity, Moscow, Izhevsk, RXD, 2000.j4AB]{AB}A.Ahiez+ V.Be� etskymr��4, M.GTTI, 1953.Q(a]{Aa} S.Aa�1on, M���ara� �S��cisEq� � ing,f} l e-A�t �(-ph/0311039�,k]{Ak}V.Akul��y $., Non-hol�icA�trol, (?� puN�)�SPIE PR9Y�"{�%.:2�)��403227�xBS]{BS}N.N.Bogolubov, D.V.Shirk 1��1!O-�Nauka!V83PAs]{As!�3t, Bell'��eoremm�na8�f��&I��t5Lr#1~ � 2001kB]{B}Y�dan�xM.Chekhova, S.Kulik, G.Maslenni� C.OhATey, Prܙ�&dqutri�8"bi��laY.�11192�@Oz]{Oz} Y.I.Ozhig���.o�"j7up* D 2/r 0, Chaos, Soli�̡%F"a��10!�899, 1707-1714 (V�9803064)�(Be]{Be}J.S.!�t, Phy.Rep., 137, 49-54 (1986),7$Gr]{Gr}L.G@�rm"um�]cs"U� �_��a� le� a ha9.ckU%eq)-A&970603]��?^�005025Yn�!(Sh]{Sh}P.Sh�9P&֟ ��]pQ�o9%�ret��gakb�6�!W,SIAM J.Sci.S� st.CEA(., 26, 1484%��XSB]{SB} M.Shapiro, P.Br8�.���shemi� XD � n book "C(�aZ ��"�) Frade�O.Yak�|sky (e/���l-�200=�@FTK]{FTK}H.Fujisa!�(Y.TeranishicPKondorskiy, H.Nakamur�!�"� "� �, ��F6y- Az0302025Y�Sl]��!��,"9CxHruy�-)e�]: Mir!�6KFH]�- R.P.�-�R.Hibb5cGraw-H�B!�A�any, NY K}�THi]{Hi}T.Hida, Brownia�H�, SaR$ger-Verlag@80@,Me]{Me}M.Men2xme"��4*�,, M.,Fizmatl�� 2002bFLA]{LA!+Labanowe� J.AndzelmAiR ) De��<al Meۅ:CA� stryJ�) 91*4Pe]{Pe} R.Penr��,� iz,@s<huX/Lmind, Cambridge Univ�ess���pNF]{NF}V.Namiot, V.Finkelshte# � �$A � �͂�non�mA0, Journ.Exp.T�^$.Phys. (Ru@77, 3(9), 884-898!�79]�i���N J�q$m.Soc.,Far� �� P997, 93(7), 1263-1277]H,Za]{Za}C.ZalHEc; �OB:8�A��b�96a�6�4Wi]{Wi}S.Wiesn�2 n�%-d�e-ox&$z6y 4� x8xOz2��2}Y��6zp� �_ ��zA 5��66}, B~0310188=mu?%u 1061.zSF]{SFaa chlosshauApA�e,Ƅ�'Lrivp!�� "�fo31205]b4Mo]{Mo}U.Mohrh�Pro���env�RncjZ401180Y�4Bu]{Bu}P.Busch��|B��gB'P-����8�a��proof�M'" b�990907][4She]{She}A. Sh{-v,4 vd18�uV��jCt:� ˗{\LARGE�V�1V/ x\ 1 \\ A67a� �:�} fTsa����m� q�"%s�X+�"| AZC� must�*.w�1dQ8N"�%�",%E!�@�'�"oB;*�Uf -U�0h�;e2 n�.���B ��IN��#>e&B .��pB�C"4���l&r�O��"��a����*�.vDP�":� �madA#\0nO�&56x���"�i�1=�"���%�I%�!�2M&�I�D��Nd5 �e �I�(A!��-"�!� ".�V9�0 ,M:��}2u#� &aq+&�*� � t]fer��$.z A~is� �"�� �N�?sϸh.!r"NY�D�Bq�W D�� �9 Oz2}� pu'(��a tV>:��j's��]��2C"�>a=*���i�E� aim >�$h�)Iao!5orkA� modi��&��F�n �W�2�c�94V* ]tn3m% �uFB3. P���Vw H[�lj5��F!wV*x@:6AuvXr�"����2#�"�6 g!�le�f(ar"w�4�ll�,�"Aj�D.�����<.�6co���� L� ce ���� ermasofO}sur�jr��)q-�~���.ZĚ.2�< {A�.gKm�z����p��!8A���im�|E�>5Y��as;!w��sKx $��X 2-K.���   M�I��} K(2;1)�� {L�m(�^i��S[x]\�l<�x�:S5"9mLt_0}^{t^1}L(x'_t,x,t͐t �LKerB{L&�l�D�2�>$x(t)wat goi0$1=(t_1,x_1)$A�$22,x_2-L)!S*? $L=E_{kin�f {pot*t��@ *�$ki �A�p"�) �g;!�qEAV�3:�LOcaaF@hg�|Np4`4[�,�^,*�=V��m�u��K%�ma kernd�or GrJ*�! �1���$SF �C�n*L@5�y���:P6io?("�Fu1&�>^mj?"� tw=J%I�|:I�A)'�%��� 6�d�vc '3!�ime, -9�)a�8S ittl 1te&C}iC�F�>�] :l� �<*�,-! � 5 �-(lm�!ulaI?��(�U2v)% �5�,2QQ m�,� '*�.a�gyA�ma�2�(�� 6_sj1 . Nom[t\ backa�!-�$Il ���/<�P��3"���02a�B�.� �OA�n!! r�|qɖ�J��Gyr&�J��׈ictic��FB/ :� (a.q.).L�'�� s2� �B����V�ly�%yet&&,��!j�!�v��i\�&}%Kƺq���)s� }6�8!Cm��� *�� . }.:.8;�\�Eollz� �A�<t�a��b chao�69ac9AaF.q.�?��."n��)� reg��g hw�0uld tr�' &A/�:&�'���?sq�*�-�ionXQ�eactZ�/��� som�ar&ME�<� ��0��f! �!b�IR��nx�{\L��{Bo�)d*��Ea}�1Tw&c %FB��|�6�umaa ��d�moU�OXC.��s�-IniA�="� (�1s6�V!runs ea�:���rM) � $\a$"� m Ha�B�'*L ,]$,2�s$x(\a ),\ v B��%K/J�'0w�)��8=Hn=t.�s\la(\a_(�\�zT;-  +���A�5yw�A�!i�A��� (t)_��9��a solE.!� Shoe!�er q�y(in $C(M)t\d�C($M=!_$total numb!If�), or�,other words,�in casE�@steady Hamiltonia pI�ՋhfollowA#�,is satisfiedF�:�B��\approx\exp\left(-\frac{i}{h}Ht\right),�� evolB�!�΅depenA�2�a�R� aga�bu�6 sen)chronologE�exponA�alE�QJ���xeZpa.�]aA\6XIPa_represena^��he!�mA&rea�@s $$ \bar v_1,\  x_1, \la$ \D t_1; \ *2*2 *2 \ar @v'L M'6D'E #2,���$ zl�2Y��� pasta.mE\previous9��e�!�second%M In view%aȡ�(\ref��):m!�rol�+detreminA�a(H quantum state play(iKs $�G$. �,ɸ#�B%�Nth��;A��R�:a=sF%\la'_j=!�$j\cdot e^{}\D S_j}!F j=1,2,3��a -ampB)JkK= L_j%�jUHL_j=E_{kin}-E_{pot}bIeB`is� Lagranj�2 of $j$-th%� compu]��  ly!yM�middl��!�wayn . New ������ed9Ai�w���].�$re elastic� ��ë́ ent varia@ )possible�8ex�Ie6(could assum�at if.g A9_j� rfg�N$tructively6��F less�E�,more similar�� adhe��,l��j  t gderfcloseN5TE�trickn ad omiz���!�E�Lal resources. In fac� simplt !�A6� �-�au. afte���wre"< ^ randomly%unia�%��of^�=gu%��LI�W� n su�sq�!�- $�JE5�� $\a$,!� ]�� R� n�~*� � U�"g �fun��B&J#0requi!�5i2z�l:b of�si� "oprovid trajector� 9�=�a�Z�among fiAe��)E��- � Really,�� A�6d�kernel !��Ker})q�9aN.)a�� summ!�ofJ�ove �5�!*!�* u6�  � 29I!5ini Rwa� A�zI1E�*A�m"�B]�r Pj-[aq� ls 1. Our�cedur�]fineF� _2N� then an=aio%��6�� Q�})� it ')�9� E3Y� �mom�{$t"U�J�1N�N�i� �1%$t_1$.? or]W)!F�58discrete analog!�4Feynman path i�ralrE�i�"/ ��is:�he�� ����|n|$�~. �.f4��NgraH-|o��xi61�$g$��' e ma�Ll�is�Nch�A�=g$. T� situ�/�ݍg-� next� !�. � numerE eri!�s s� �in most� IA���� modelM[noͦ�e�slow dow �si!� }2 reas� f>� Xed��&� � �%Msyste� �Ps mov�j chao� ly sC�si� pot6 !1!���� !� h&�S�tg peak|A�s yet �a Brow� mo1i� �Ւi�5p&� �E�sized�)�mak-�BK��ab���5 ; ��signific�!�o��$urposes.}.�! meanb ck length!55� larg� | arizo"�R��iit�*1is <� such�)�j *� a Markoff�� cess, nam� as aMOof>�H (see. (\cite{Hi}))9� Bashelier� �$o investig� yi0(about 1900),�!��%�!B* =$nB�wasY by E�/8ein (1905); fur?%pr�es��1 by Wiener623-38)%i Levi$37-40).}. $u(x,t)�r��e$xD ��.���A�e9 of heatA�dux ity9t�(let $\phi(y.��%Sof%Co�so shif ��� from��x+y6.� it h�disper��$C��$ymmetry. FL)�f����$� E�hR)R<+t_1)=\int_Ru(x-�� t_1,y)dy$bnow��uffici�zBxp�$u$yro]degre��DFapp� bo�  p!/a[MREU�N�A\>�u_t=\!~4{1}{2}Cu_{xx},>��$CSa!� :a�w!6a%#00)=\d(x-x_0)$5� �(Gauss curveJ��8\sqrt{2\pi Ct}}B�`}{2Ct}� "�b��BPO).��hand,E�� %N���0� a free on> menAT1tA�M��t�  � Y Q�)&^.�a�por!PalA!$B�\a!�x^2 �$�� %�&� A_!x>� E�weQA�3�2FH}d�tails):F�$K(x_2,t_2,iZIT%� \ ih(t_2-}{m1�^{-1/2=� 4imT$-x_1)^2}{2< �5�Ker!�B� substitut��I 6 &O ehcalcula7!5#&? of)�pI�%r/�!��robabil!to#is=��2va2y�7Npr6F�. a Aq�1+ \a^2h^2t!T m^2}BM�1RVCom���� s� B:)N u�)%0 oncl�� � )5�^ia�o "i"h 1�0s spreads fas�in smX�(���hez� ( a��I. &1��k |�� �_l��nK s�lcoe��� e"�.J���$1-At$k r- ��(Bt^2$4 $ve $A�6$B� t wo>see�<t t�f��st��! Ra  Bu�H rawb! � �ct� I�� un cours%&Nbetwe!�!<perma� re21�ego:5��["L � eac� an�p��did � de�a lgACA�a�a��e�d�����V�.�I/ir 4 8*f Wes�  &40c�gn�ne)�x same� +*!%� a���2{ .} (N�!� ty pl!�N��). It� �kpr0t tooe�m�<7m��� RUe� ary%��descri GPelectromagnetic fieldi> phot�e��A Fch� *a . Imagin!`L�u� shapE�sp Yradius�!E=L: $\{ r:\ |r|0� &� ��:�no�2�happeŪa.y�B� -\e\�!W!L�� ;�%Z�^�� �#2�?�J' �c� ed nar8 - �Y�A~���2��A. Sinc!��� ty%�݉e�# ,��gb� � <hi(t)|��iC f�despitE5���9�!p6s!� � ��i%��u  dymanic��$us guarant= `��[�al�!�� )i�sR�-$y!� nee�:��-� ����ta�tru�_2{�g nonzero~impuls�qualiveX.��9���#4principle good�G`2�at le&or6�s, becauB���!�e =]m��1qitself%[i��sedarR �R�^a�!�/ seac�2�by����hmethods like Monte-Karlo. �5�s%�a �e�we�b$EC!�!�nt-�]ec6hi*� �Fth�#E *� . aNa�ir2�5fm�t ~e�G�. �)�"�ble�?$ F� a^Im � !� modul��s��\&}$A3Ka)g � they�v pha%��!��� pict����,. \nnn {\L��{S"�IY�}} %u$ �is basedq�( dynamics�ir:��E�ua�Q�2(%R��b!5�j$s sequen�ly.B&At�$wEk�im)�remarkPJ )��di�} �n wo)�:� �cq!� to user��!2#ad� strato^%. For�,��'/V (phys��).a�\'-� ��r�!�   .q}$�ua#)N \tau � underst�@&+�observ1 e "film"Ia�h� to himV�2~��is=e� fl �(r~  �e scale�i�V� ��VM��h` �;yjd&�� P a��e\6�eB!h� ismu �  �'tepe}�W ��lgorithm=�by 1t-Iņter�hva)w!�u�!CiteP �-"%ő��n toryc�on"p' star� anew6�q�i6� �m!IF>M(I a�(wor�!nd�sh��� ��Qse� ~�*�8�� � � !,s �b��p"�%�_thwd*s�%��%�� !� %x$ɝ��dir ��� valent;�W)A tI� so(WD �qco� ��"�(E���wves!w wio-=)n :L�� jumps�� hQ�(neighboring��do!^ �% kipws� �(oH)�i� �E{#a0, ct aE4�%�A�termedi&9&�T1���9�^�'D*��s �����,! highe�"�y"R#so� ingu�#!`t-�5&��/rg�=O �$� ��?m.�1��  #%oon� 5EE.��%9i�i;IOis una�pta]�8#5 (F�߁����'6\ *:9S a�!pas��byJ�ѐ k]tS#��}� 6'fy) -6�&�cox� z��b��� eN�IV-�YrWeQ���re�vit& effects�u%]B��x�1�$E(e:�� alw�1!�a#!Dm� !_�E����=��yV��I �$v�:-/d)�-et%�u6 � -g-\��BP$v�!�at�canq�. bitrt�s��5� :F:��N be lB1o/"v�/N�"!dmi��A%of wai�s"�� _{max}$ (��Eae��frE c=1&ng�� or)X,6 C"=�������.d0�(erm�% "M ���a�agEK�\h.] �� re�!�2�5rvoirIWaU2"k2&g ����!��!2� �qw�"n01A�� "f�ula � We supv ��ite )} \ I1$%3� ol�rA�S2lo�icubr �� A�f��)-&onn� mass�  $�%�6 founr��:ű{ �Du%�W�! �"��W 'ose8#JcKAlQI���39�� law �of F93��4� ize}E�ho!-<�%@Q�m�Q): $k_0X4? (2&eB6S�!�&n� te�r)%�"M e�� n| �)Gti�ly Four "a�2:Q��5} A�(k)4=A\int\��s_R,r)e^{-irk}dr"� Psi2B�n%x%�� �{� !�.�"1al�$, eez&,�WE rodu��w&lgmu$��`CS!%o"@7!�E�& aN mu�=@/� � k}5�!> S2��* Psi}I0ex� �a��6(P 6�S��u  |tH ^�_0=�6�7}� e^{i �( �-7�a.Y)m�our"u�! &Wu� A�=M��# ���Eہ�um� !�a�96�to��C- =$|�$|>\epsilonr-J�$"a~lnegligde� %e��wr��.<1 nm 0:k:\ .�<�5�UUiJ�1yea��' easy!�kI0�d9J/y|:J!�6�byMie�)�wek/ #-�>J9�);)�en� � 1�!��Q4�p�9�e� al�Ecw� C o fulfi�o�1%Z� |.*ilqU(q�A%j�1i"�2lf �A��%1iE�typIj�lexp:2=�� V�s:#!>am��:� A���um>�,of many body�*s"� �AT� g�(7�I7�ùdq���enɧ!pnatur�6�'S6= S_k"�'BZ� t�� (usu�/ $k=2$)�/l�,M=A5 J� a_1 �= \a_k�4!�-qa>� )� V*��0m9objQ ;:u/!Gwh;6)M. A.�Ap� ��5en d�' %@ly;.C  "a��!veo4i-B6�lex �s occura�%3� �I figu�on9, etci{�.�e"!<z����� m07 vali�%Ex1���Z. R%�% 7rul� t���9nV�+5�!� .�i��&-�6)�?e f�on al!a�*�/��&� Nf-/�E�C �����>Xki��*g� U�D��9�"� /">N�;��,����E?i?��ShrF�!sf� n. 6!X cont46�%1�Ja 2�m}!�es�!q*%�a(�m�DI3!��� i�A���inctnr7l�+ a_1$ 7�!AX.q.Q*7�elC"� ��;� *-�&U4mea� device (ɞA�").;08A�a*��ao5 theme���^:7 a-�ron -�Ca�;��8a_s, \ s&m-�*v ��A -jN�&sd$sumes �!�`�zv���wM@LAIFao!!}eF�A�as��5�+ �V.��we��es�� e hkf@� �vol�: $\Delta V�t�.�� entr!�xA��#si (x�#.'"� �ed]I�itary&�IU8$6&��5�!>$a���MN���M���q�uz6'i�4�-ti�.U�jm�����e!&.�,*s .wi�y4F�!�t� tY�B�!m io�toB�E�J fact�C�0*H?aBc$U  cl VE urn schema���aNU1e*�-PIb � workj%J�#���"��e�J��%�і1�B :SHilber�$alism "�8M0嶁�2� -�un��pe� �� uta orthog%mpro� Y�W�%�A�E� �� tY(l�>ex�8�U��� bF!ctM)!n% bodi�6����"C"a28of& 5<�#n ens�-!��5dL abov(6G&3 in!>_ &�� W�G.{s s!�act:""m�(6��o�K ,atomic nucleH8:A�Ec�= �4k& fa�&�C�""l19EV�M1]�h lr/M y/h*�(c�`��Ad��r?� near 1� �a�.��ih]����i� y�ja3M�!� $|00o �+� 1|11  1. 2|22 2�L\6�ho� o ge�� s.�,EPR pair�6demonA�ee vio�%B2in6lif0"�8w))[chang%T! apa us ���A�QgiG%E/l�G�a��[ 2bef�B/�a�I�> '  )%�:�!aJ�] basi�&f �e�;� nywa�@�!"�-�B�6nQ%� �:al1V�1Q���ng�� ����A�b�}�al ex-g, %� �e�31ng qu on:� to �= �� �6la~E�>9 �2�%c? Wa�� *�a'I� ouch�>��+s",.^ �u�a�! Um��"��5� B�".E=_�(�L"Z)ome9 stor92To�f�! reg��!�dissoci��A\] U���A�ge]a�%%�\ ))P"t2]�no8OgZ�2gl�� lo<p�;�0 ���mannihi��.'3e�� �&.Fr�of  .� � �sa+.C�Q :��i�3d 0igF���!E�AB�&A#2saym)y:���i�i�B�)a6�or�G��t�).}�N�A�v �. N-�$�carry�0.��thought�%'Ao B� GP-�k�����explanU�B nonE;"bO&�se5Fe"9 *w o3I,�5�9As} >AH"� �(s�)A�I��m�?� �a fil�jpr��l�07;M%�8I ��k-+!N �P0�7yJ '���&�$ al& � a�s%�!�o�2!Pf�K� "!h a fu-ueprogra�FasJ �+&� �=�-5�4%& �7�et� I���&�Q&�+��>�* � E0C look�idk6 he�&�)��,� ing:5�travell!��E-��abs'.� r���P+Ai��M����#1..tze�u6!��)��A"�" "2� "A!� I&�?funda !h��#��!"� q6-�lGP6 doxI QWai"y�r�@� �ơ��;arst*H2n peA@cur�Q:�N�0%0ts&���m"/7�2� B� � hem�S!á�I�itU�Ma��Ti-� asic��>@2� &o-bA�s&A k�@w�Cis�5A�ums�I ��2� Ihq�*�I)QAD�:weA�:�%e ��#�": @M2W i6Mn"��4l9)��0��� im�9./�2A�&�5 �ta>R�We&^:&�9&"�N>�:2Vsim<ly�6 $t>t_0 <rB � ��  %J���"��3(hetic: $x^s K($x^{-s},\ x�Y\a , \b\�'$r$-remJ). WM���g4pr@,��? e���i9A,�!��.1 ye�:�*a*r�E�6�5�d�|"� �:ded � !�g%.; *iir���S.� �r" b1sur**{ s�E� lrecyc��E8�qui�.!����w �?A  A�Uc�js�%-b >F�)>F&� HA�R�& � �# . AnY�d�9mY�!\�-t��py��<�pEa.qa�> "�8% �.�ic1 bJ.m1!�Ik5]& "� "�Mr �ש�i��4su��"B sof2�*� IA�e�/��A���!�&�KyrzLno! .a5 E}1n6;�(e5s�U�d]b!�2>��]ln2D Me})�$(�`� �iovI��ot9spi� zpg\5�� &s2�"� �=or< �Te*I�r!�SSe�b� tamJ�upS� �j, "��J.��<"�!25 T.� put��'i�b"r2?�a�� r��&�`� ">2� a]>I���t��(a��,�E���V�"�L���DQ�n&ntpZmJ�5��BD2~-behavi�;�� #�?,%Q}^e&�4 ��)of"&2a��DO(@�Dbe vis�@ RA$�A>Q)s9#!���e�s�!F7 s>-�A !�'! ���69����at+,�D� "�2�5� Q�oŻ�2p.�Al�!=X&e�U9.eD���6S�Ua%!��!��@!d�D�:��A�! �qN&�1:5 ;lJ�J� aresul�$�%2!�����2-�mA,� pF��V t�)r�Y!M!�A)2oi2�bue fuperlu�lZns&d6�?"� .p2z . U>?�}at9YB@�m�&B2@c��!W#2&����b�ԡ & 6�a^�(�/i H7�A]autho�Ait&�"al`E�mit>���4%A_���v�B�! y�Fat���=� * learNIe!)�+�A�dE�?X+K��$�!��{3 ? �a/jae��oU�~'%���#���"*fe��O6�I�&�C!I 2�U�m��% "�!�%e�&�"� taskm��@beyci2�!� paper.b S]up6�����%�.���A;Y �%�%�uU"�b"�5y6��ń>"@P,E -� "�"��.T]nQD J Free*@:a:(� e�� �BgD lgebraic �"g"� ��H�"�!��C�]� l.�#�A�&�,2�#H��we&�6 oXM��$�E�s�l.�����@umm�3ɤ���n&�Cn{"Ej���pre ���R�%a�ua�'NR���ng��&-nf6&"Ez��;W!�a?e�5�*]t��e@.$3�x lete{he>�� iU�2!�!)�)�-"�[colt v�Qcu��q~C>uWYG.�d)�e�M�a�nti�o.ma!&kA�ideolog�.�^� �,�1!E- digion��&#h�2�:%�� l nvennXA�po$i�]2�J7 N8�L:Le�um&�� f6��A+4dev"& 'DE5� Gid^ &Q>w$q�Yd�m�ʅ�� > (q WE�x���=!?�""h<r#A�} x^s_r,�2 �B�2�J $� \{\a,�� �q� !���_� ; is�:!5l (�7)z����$($\b$), $&q +,-ds�7 q�y �e�$r�=$3/� �($r=j\ r_1\ �$kxq� �}/ $j=*�qN-�/�:i$�?c#+_j@%$�8�9y ��va�J�&�, �9DC 2w:��#�i�k3auxili!bopA�<->. �"##_34�"�12����!�~ W&��by $[ A]j]__pB}M/e,a�@-n .�S �+c��� "�$�3 lowe�4dex�F�!f?"0oft.�qWe�H $ [x_j] = [x^+_j]- -_j]$�c� ��&"ta*�"%,�� �a�s $x_rA_rZ}E��C�uł)��4i,n gO-D"�y�p�kf�n0 [\a_j]^2+[\b }{ 2|:e�,A,\\ 0\leq k(N-1}[x_k]^2{:6�;!*-�$pzj�� �`*V��ͨ8alm1-i�(E3,)�;��{ A,\ 6e6��%al#l9M��MJ(2� e�)�%2�\"sr��"�  .��!�&� Oi�CZ � LH2�&[-� �wo0Xth2Xw��v�Ene=ve*�:�$"coupa�"b� U�n SfiA!�:lon;Q"j� fu Fansam�� spir9->- �V(!%}�7A7ZJ��q�G=2�j=0}^{A��*j)�r��O?� yMl��Y�we�R ${\rm Re}�a_j�nIm F@$\a_{j,�@\b���C.�$,nq"y  a�#p� ��Ne M�����B3&���u� �FL Onr Hfa����xB) $x,y\in A��&�$1ws�;Y >r���^�}{[y_kax5\}{y_{k)v}.HI��s�Z�?�Q7E m24d+%V�5 c_" ���O� 2�]i�w Psi=ka���\l��>D, $\ ��|I�^2!Hat_s�J. T ��56@a�". squaA�:7Q!.�>m �w�\ar ri�c}ŗU�� e"Q F�)Mll*Z!g� A��VR�� �!"'+"S5p/s�csA{ik�N"kyA��i#� ��}:~K ng� eo�6arg 1 ���9� A�ten.} Bzd  array}{ll#0^s&\ar\b^s,\ah" \ \a a b^{s�d =��%�-i@B�� 2>��e�Mk� �$� d�v9�ȡ1z={)+�o�%\i*r4�-�@aKan�  e F $v(\a )�6&$+ ,"�: $$=v^0_\a\d �f � A!�seg�Ep$�@e*�s�"7X2�� �� IBH�� �;��"E�b�b5 yK"�$v�$�WeN T�9_*;�B ?a#ll��!JbeQ.��#ig�Mn� memo�g2s"rGni<�a u��>m�"�ua��BmH�#�� ��mY ��I\!�E b Y?�� ake�Wy� minus (�**"t��5n�d.=)A�N $-s�N�z�$_9* Hq1sNMIFs"�S� �&81$I�� &�A��� E�q �:e�"� \d Se6�UG1\_-��B�e!TcB%�#&�L Q}�$Et&�"g9SE�mY�5&!3�\N��,In�,�T7���E����O<d)0#%Z�(G&oa��U�aUeN�r *�����`Ja(\bA.)*�Q7u�CaO=)��"%$uI��y ( �fpi�h)}I7��_j=2j(j /N, �y:���y�� rq�9��Q growta!@mpensv��P*F(� big 2'X s"Y�?g#2�)���:�no�si�!��~2�IM!�Q.js&{5"|���e"Z8��a/intA"�DAA��� C�W%�y o"E�����f5�coB0Eit� l&�C�OIU�IgO>to ` �6�)�:�-'i�Sd�&�w5?)&�Ki�N�C�/olN@2�T5oc�Co_ s5%�>�EFJi^ $\rhoP> =C\ �   6��a&ihs n�taW&�0"EzaX�I�# We,2E#���Do �+)��.� �EZ1=���JDco(l��/��&���.!� ivar� 1�A6s (\E &4.!�"1F�Faa�Od�m�1E�Amɪ�` N�ee " iof=F)fu�w�1rkiމ�s�Zl&��Ha�lic�X @��n"�%�generB=p�t"�$*=��W��!d."�0!a6�s.� � fo��R �YC7be �&� 6�w*-�HAy1r�_ tl.]tu���2�dKI�W�VXD�N{�Uad�m�@in��) �%��I �z�� $ 6�JN�, $� F2k.?,�$�s $J$A7*#!;? m�@l,2�R!�K���"�v�yJ+x5� �(ag/��.e_�a��=���2"kU�QT"!I�ix&~7 eva harmon�scillRa"D� ��� "x%����B dard��lJxRa��_ngi��.�  �"sb*='6k� oc Vo� +g*�'�Z� L2�a�$"� icle+�&"]�r�vFH}N�qL`mx'p2}-V((v` MX 4+\w^2X^2+g(x',"X(t&"��)�^rx Xf{%�&�+9i% �$5� , $Ve !͵��K!a=,e"G;0Y � 9 Au:16�&��= . Ho�#,�3��6Q1���> e�Z d��f�v�jj dr܍A�Fi�� � �Zi�iɈG:� s�- Rk"B�"�u�:e�.�1" "5 ���� /+U!�#� $X_0+X$��KOO�<v(߉�$� �I �s"�$h//EGz�"���!5%k&O� cipa�o� * nd%�? V�r}�%g7I�B&J�8|\D X_0|\gg |X|(  2h�es�a�endulu~&��!N��7� ). C.6�(�'Hl1�j!P�7} Y� $D t�U �ex�+> % MF�g.�y&�#-n2;%& d"�2AA)?� ��tZ'��Y�!��BK�!]� �IA $t'!2EID&�-#��Ay5:��� '^{osc}_ r� \Ny�d S !�_j =Xw[=TM(X(t')-X(t_0))}{2(t'- ����5Ywx_j-_1)}{41},'),t'\�)X + ]\ dt"#!� R-�>`{x8a;ez^e�a%�e�fu,>j�I���1�N�b%��pe�l���up";��\$t�0 eM&MЈ�k�z�A�AJ����Ra���>s� �A>�5n;&e]q&ykF>��"�'"._ "���q�P:(u:�-��ykA*�  s�.Pv�e�B�*X_R��N1,I`i�R,%hif%I6�/��I�ѽ�G&Q5KN"$T0LX_0 O I��A�%,I 9"�0y1!,r�25f�����Kof� ��& well&�^la4~L,qeE8�A #A�unc?,�IA1�bR� regH e adދa=n 4mF b.~9m . AnJ� bQ#5��A 5�1�&� *m ��0RLm� -��9�� A S�<acU�% 7theory:6| gj mo^�9LP(�8.kv,�m�:"<$�-� P?"� U*�v> s.�$.DRJ�L �J�`s��E<��%s� !"!dF� @|�(A�` V g6P?8_ �r��.y_A�V�i�j:E�Y-��� "� A�*� g5J_a_&�2�)��2G�F��� 0� [&Jv�K�+�.�$��${ s tw�V!)4put $1/2)\�F�co&-�vW�E�3 .1$z�I?-a�Gm�nic��aQ�w6&�,to#6\.�{Ba�o organRQe��(%%u>�:�w!atS>��pE�&ѥ%��e��,�M��hi�D �^Xn�Ns����, s�&��&� Q"�@iL���&�AZG� hEf �Kd��u��B`Sm �X/S��Ve.[%<` S� Fu"�ym.>�� �m���A�I��r$ar Coulomb�llUK�Dt! ^7��paraet"C4 [*��jF9me�Qcer,a� icul�$V�4wF/� s$�9!;i Sy)�~�*.:="q2�?m����Uro"d f7 Max� �%R%geI�Tq� "]�l6=ex�9E��;%ext��~0 �.L, �/�>ra��D3a�,]gE���rOAʕ3*�*� a�Ry> S&�� h�W*�dDeF��Yb�U��9 \.�"�K� +�H��}zp�e�:`� permU�ga�vft^� as Qv�1�ec�*t�1%�v�R �vea��C� V�+I� �a�:�0� �9�&�Sk�F�s�"-eI s�$ag��T%{u�2� �,.�B%}�wei��u�E�� [eA�H$� ��*x � �CUF�p�5!��J ��s. Ph&�� e^�� ��)�:�8� �g�i�I��6 ��&?6"*P8�a�a�J��h�JQ�2gi u�4gJ �s�:U�-ILz0�AYbq�s�#J�a�k2�Z1�t�@)c� 6� aHY�i`-�~5 ��c l*J U�< . F5�our�s&/ph��aasu�& �;�)�[�'1<)�"["&5Mb� visia$vic���?\.BtH �o{�_ h�d adr� :a���&�s anA�tsѐnd)�r e�=��U>"�f��)!!/u%i��2�� }str��s $E�Bv�*IA�3f�Z�)�e�Ɇ $e �-M$R,�u9G%2 aA�F��׎ $q(y�\as $j(R,t)=eq'(t)\d^3(R-)&"�t6�z db-�"a*a�4D(� ��%�5g��y ^VH��2!�er�@:N7jb@�a*�+8nabla\ E &=4\pi�",�+ B &=0'A�s E&=-�1}{c} \� al B} t}N =B:=*��CE2C+� j�)Q jK:�2<.� ��,�v 1G} &bMZa1 "�4N�M �|"�c0E=--ZphijCA:�$$B�f'as�%�@���^BUNB*Ae&=\�!�}ces>�a_k�'kRM d^3k}{([�)^3IphiC�sphi_k(t�sr8i�&Ǔ j�3A.krho�8"�pex�.Q46Y64�00(�.� AB, ��._L_k=(a_{1,k},a_{2,k})�B2Mv$_eoE@� �Js o&�a?ck�.-�$�?�� K �6&]8 olarI� � �B*1K�v�� �>!� $k= b�za=fi�8� hoiߍ)� KBF8�l$S=S_{I�les}+S_{�8 int"]9��2LIN\*Jtj.�mq'^2_j�*+.%l��He_je_l}{|q_j-q_l|}\�dt���&�!1IA� (a'^*Ia' -k^2c^2a + *A0*.*QO �ardtmt quS_%*2�.� %tQ�q�j}+ Z 2,j}i�qo)}�:n�Pq4b�S>f ~q� j},qaj}A;�*�dA^A�Ml$�jq"��dir�(6��z/ �vB �%i��oa�.=@7 _ulRB�}),�6��9����eI�άN!�* 9S5<q6�$S$. A� �ur�:� ���)&!7��B$,BX L��DTe*Ns:� A qge�4� %_-�e�*�.TCwه9-�fd�ca -H<( �1���4!7d�o� �7�IB�-G��)���4�K,[%AB8m�i2�f�MK�.�,�as��l�J}�.8� �/b"� 2�%r�:), �2�a&?�)U>�d�<w�G�(%�"�6�nEX6�P!�p.��^: 2�M)3G/�O�' eripher� :I���dE�y�&�sC=Nn �#i&@E��|i��}�,k'2!�!�/sW6Z.2�.vs20,�me<�i�L*w�{a�V uppl$e2�4bir3�w"' %�2��� scr`�j�&s�%!_o :Mmx-�k'U2"�O!6"T%�I`0ryL![!;�IQoš$A� /�$R6 +O��s3`�o�&���ula $$ w 6v ��{\tau�+[t,t+%] =a( )C_{R}}�=X�| }a^{i�{ R}},k � � K'b;��% )QW%�languag��eei�j5 ��"�[*� C � -u��.� $pz<�A8 2F<>I: �U�E!�-Ʌ\���e�peculiar�conecS �l.�.V�(�#u"��i�l�_Y��*�$X_{0,\a� �2q 5�9*2DsQ {1E,\ � P� � ;h :�*XInstea$ .ZC:�NR��"F �.,���-2�2(6)�q����Fo�!0(*�& :V�&D_.iMaa�TM p���M��e% m�W,o*�n�m|3A]e m�p.81�4Y�"pP�5erv6-ie�kxM���� 1T"Z.�d)$I�!@��� refl *�N!�"�*<!e6U���P:x�M�o[�A�-Vu�-�%SA���mgc0q��0�[A+�!n 71� c� nY+�N�n&��"�)(%�%6s"ͺke]L!#�(S~ �f4�6+yKNTv2��=!h N5a-mBNv�l�#h/AB:, As earlier�OU� E�pr7m4&BJ!.$�9&� �T%*�(*�N2b�C#]j=ŪA�� ŕ�'u�!JA�!� }QqY7)�E11eEo-#W��F��Q�&= B Z%+(S�v�2�t) /+��6 [|� \a}(t')- _0)}{"J+\z|^2 +:<u< Z<-)\�(|k |^2+ <|^2&j+~�!�*��\�=(�Cb})�v\aRx%b � .,�.22,2 .2)� �,x_{\b}g-!6�$5$�,\2[&��/�fѹ3\b&c�B�;e1�Vf e� mE� M�)eI�}\A�t����Q� �*d.4%z a����+u�TFL6H��}�y�I=�  D �eP& |&q2c"�let���j9%!�>%U$\gM �m�(% 6�'#�7��:!�b�bA�l�bn�3A�V�qm6�(I~e� _1))^2#�40e_\b e_\g}{|x /\g |})�.�p$$ �(:�>�tB[5@M] -I��l*�Qp�o T��&D "J�-x E�d�4e��"$FAD� � � 2(E,& .y$ARGE A�$dix 2.\\ A"J�*�.of Lo$zo�a��ce})W�z��a}� of �W�GsJ>$!olaweKN*X�%a�e�.0pseudo-Euclid�n�ic/space-M1�� ag�!inert�FP�O�[rev"6�"%�t0�;� ��a on se"�Ep�?QE�V� IM�e�& mO,y,z,ʓUJ ��b*�$�e� ��&�&��iq�?��a�"q���&?�a�� ��� �H� ($dx,dy,dz,d�PZ�`�"�d,ds^2=dx^2+dyz^2-dtOJ(��|�� of�zsn%�>]ofq`% � F�1n� Ai��Tby0nM'E�b1 b��6u*^m���6r� )�f"�!��7s i�: -s'^2$r1qfBq/�(%�fac"a_i� & .�g"|&\='�b�A  %al 6qplK�! �Jw2R�0!�im*6� w=bsM on{M� hKTu0ma6)es}.n!�*�,&�cٵ�  7^U& ��v�NalKm�8� <(o� �hA��'. Cell�$utomataE�y %Zm�(it����m�R&65no&�r > �Srec+u�%�%3n�&i)D�@"|\� Ή�N�A�apes �B# 0F cells,���!��%6�B^ s�37&$A#!�WtP�62.3�4{j_l}\ ;\ q_{k$$l}��ar�j'(L'.) N'?2'  ' S_{rMu l}A7__� �t};n-%k���!@��symbolF�s�� s af�wfJ@ $�ˡ e)��� ���a ��R�� (��: B�e�h,� [ c�launch"�: �\!2 M�I���!!I�d%ID2��H "��R-�%�!�AYAM�i5��.� ��'Mb &F �l�Nu���5U�.�:A?t�2V�exaֺ�g6/ ��� �d;�ɐt�*�- �# A"#influe9I�$LT��yw�,nN�)��Two Xn� :��hierarh�/�j"2,s �@%oa�i.�u�Ei�u� �`)�u*� Lt�� {/�Se>��&1�.� �db�.:�:� � �:;!�i%�=���ch%v� Us�Aloc.8ir*7�a)4�� i�i� >2m:�HA$!�v� n� s Zr�1&<Y/al "kaJ,al"�,a� ŎD��o� uaq!��5:�#�8a!m"�3e�!:�!}i2*� �xf�� he job� >l7h>b .=s'�V�j/�] tanes�x�^�| �um���at�/*�,Q1R�!Ci1"] 2f� �f� :4a%A": Mlg3�}a��Perhap��a�no�p�D2�!�nq3/�au�i�A����B\s&p Wh�d�c��+-j2" aM�e } E��2A��7&(b|1��R� ( umm��emoryI%uL �!�s��E��A�]�ruwy��!6gage r%�!�m�u��ͼ"�4of i�lie&i^::#U �.Ure!2!�t ��U �[h/0�� Q<JA� toms� �.@ s. GRd�3�1�m t/6��P� w-! A��L%1n� %��^_m�Fa�*�)e'"�8wo�m �#�8-�|p6wse���� �mce~��"i�"�ic>\a9� }V,s4M)��v�L ��£ 5ã%,� > `�oK�b&�2�.�@;}�e��Eub��(��a�A:e�n9^AjD A� argu%�a���e+!E ?F3�A�N��z�as Yy�$`� %���Ct�|�6� �[�}ad� t�2?R %K!�� 6� � > -�m"�E-_��C%!0P&reckon!�i��!*gY2�bym�of>�:��(6` ae$s�z",!o[e� $dm3MS�Q 1�(�U"��ߦ�!g%P.�3Ϋ�hthicki���ix���\AP��ots��Y+iAI �:F "�L2|�7A: um%�%�!re-�o��6yM{�%/uQ&jI&Y�th;$|��h� I*e1�4�&"ar��&�� �*Ȏ�z:�e2�� �mE�AO�8I�)Yi �A�K ix 1.j#e�uxOD��nWIU J%82a�"�%T�`a�:X�n"�m�KURN �F$dZOie o�m�B  �I@ �!�A�P !�%C�9I�� ��t1+%is"6���s`I��:- �H%�X� �a�K�Y1>=�GdS2(6l]�neP an;�+��if|�toR��is��out��%�" �*� I�w&)m�!.��{%l�Y���>! :�W%�.!JAM>I��e�./�.D�)a�у��8}p� Y�ar��@�� elf)Q�6%�-�|.���Y��"� F>�UR�!�-I$dSPB coef:h&"�9ue��f�i*'JZ��^�S-Q�e�%1��r���?/��>v�6�� [i�6x ZBqt-�@Hz�� subt��:&�o�9vV`�5�iHP>�V� ��7/C%�o$c_1!� -c_2��9tt{_"� is�)U4V�Uo(|�3 ed)> a�� �!��A�;�� � ��-�An[;"T@ɞ69eJ2��xt ވe��aI:T�qa. H�� �F<�� !�%�quPi;-�a-')�k �HY*"Y Eu��a�ue.0A�l]kI*w:�.6�� H��E���s��9�?!X%�.Q�d��JS �Ky2� rigo���� %XSmeA-qg�dZE��.��n��t[�V!�B5lx=@M���]adi� j�!5�t �f#doc} `} �I%\input{aipcheck} \!� [ ,� %� )qA merakDdy runs %% ,draft; <  while you��я* p�y ,��edJi,i%\Oom� )�]r�-@ �.�%� � As�AO"�� ]!�+} \lay7 tyle{8x11)� } \ud@ckage{amsmath,ams�6 ./floatfl�:5[bf]{ca��} \renew�and{\�e�� }{Fig.} %;{iopams:graphicx�b,>1�Ttitle{Kochen-Specker Aq�gQ���\a�}T{Mladen Pavi\v ci\'c\f�^E-mail�R+ (c@grad.hr; �sXb page: \tt{http://m3k. $/p 4L}}}{ address={Univer�i of Zcb,Cro�X}� �aɜ} :�1�AWQ4y���:(KS) q�( ($n$-level�Xs2v���a���r��/s�a&�pbL;"O�E�"�. u�s \ "�Hlin��MMP di�\w�ge�`t' &�ٚy KS �, �"�z?"� � ��c4$on �| ��t *�!Zto>�oWdo�� �eiAN � �-FB!6���sO ɧl��heK!��!�,ow {\tt 0-1}�r� �H�"��>=si�5lynomi�New"o �e&�5 help�:E!�=֩sY� \�e| U#R#I![}�i�umK��s,� "�2%�/is�  ax���d � bl}fe�]&�$KS�WM: (1)��ofR�4�� ��+s�$ed 1; (2)! y"I a3.$0.~0�4zimba-penrose}j)�3e���4qh�0�ll {\em� }.F�D�)�Y!�r�QKS3t msel���] b���E]Y�%k, i.e.~.�by*Vbi!� �ls�7[em�i�} (�qu}��n}-� digitY�6Ad%Oima-  �� � 1f A�KS�ore��at"398" ��!�!N=��<�� tH}^n$k nas j2GYF�R.E@�  w���ai� "r���lyilisE�-�� .ZF��3���>o}�s3re~�;hie)"� im�L5reI�s� a20 ��m an� aym�a�� spin)�2� eSL3nK,��.I� &C!� �� g o� .-${\� bb R%��R�XE6E . H* % &�<\tri+��2]3$,��dr�-%�24�tc.!<�} ��M L+Y�al!vigT9�]� m��ll ��tV�n u{  ? r�� =l� me�s�\��M.��zir���?(�Ce3v�.5 �Y�� L �,;D�Fv)$ces}. Grou�f =�qJ9�a&9F�* .dedgaV l&� m��! �s} �0bdm-ndm-mp-1,�e l02}+ .�r>=BJda��s: 1.~��ex.Wu"h�1� ; 2/��s+3H!+ ; 32-i"D!�s7�yP r9X� ai._4_� �` e��P � {!!#1"�D0 isomorphism-\h7T-7 =:� fn ,mckay98}a�r�x��mi+behindi]a.�A�^ A� de�� else�)4pmmm04a-arXiv}^F� %� ��2is( � pa�0-child.�tp�A ��Q ~1 !w���TarK!KAUA � loop�i$, �s�T���ww�VYL�E"�@Q�Q� [��WP�95��a� � m�YAt���ur � d�* y�}( ufaE�sird e>��t 21fo!� 1ow\Xe.��(pr"��W�).� "�~tingJ<}{0.53\textwidth z#ce�%�XEs['=66]{�,-qcmc04-1.ep�Lepsfig{file=glas-1-0BAL BLA AL %\�{PK� �Mhe�zH�end>� \nownt {\bf9'} sN $(D$ {k:1y ;} $\beta��ger}$)$ Gif} $:)�):e} ttheu$\]out+^D$F��} fforCrmIV.ueAh�Xs�+e�bf do[r ��e,Cm(D+e) '�% ($=, �)B9�Ud} 6)�Q $m(+<)���w�� JW}� en �$!����unique2� ���m�5 �u�sm*� $Djaisy&of}mrs� a��y*�sS5lleY �6��on clu����&R�L�vex];ǵ�i�4 ha��Eq�|r&�S�'%�� s Ū#u��$&� �-B�w s�[:� b�� to !)���r՝� `�of2~ . B����y.� 6 3-�I-per-a+%�6P� 6�59�w&19!��x13io !J�>$7447274324:?2:?20 ?,D� { ?6�>�o {T��D..,A,B,..a,b,..} BIj$5�!m-4e2/� PD�oq}�!'h"!�!/) ..> 0-1 &�. ���F�375�27B2���� Y���,� )�0*ӤAQ.����Kz�exhaust�B sear�n%f� )� �� trac�� #Y � � �elabo�!�c-��e"�B  / mpoa99} E&&�*h0�n-� Mven$)ls�YS 1���. A�8ex within an ed�ge while the other vertices within�edge are assigned 0. The algorithm scans.BXin some order, trying 0%$n 1, skipp2constraic0by an earlier z8ment. When no �D becomes possible,f�Pbacktracks until all._s�Lexhausted or a valid%< is found. AgainBn�y itself would be exponential, but��hts build up quickly so that) A0 behaviour of9��is reduced to a polynomial one. In Fig.~2 (a) !�} filterWoeJoseJon��ch)�ES sITcanArbe def�f(c3cnd>g solvfnon �equ� s describ! �ities m��by mean%�8interval analysA�oA�!$(ventually -de!�Gin2�Dly complex way. FE��3a systemt suchN�4. \begin{floa!KXfigure}{0.45\textwidth}'ceA� } \v��-20pt(eqnarray} &m�(f a}_B\cdot. 2.9e( 10^{16}$ � ---w� �jmo�o n 30 mill\ year~ 0 a 2 GHz CPU@� M�� !�5"@ to 1002205[ (� able�w<30$ mi�k CPU)� ree! w\t 2680Q1� mslY5$ sec�9Wa�$so develop!� check!�proy �� findAvI"sŮ� um�et� @ay $\{-1,0,1\}$, 7 m��e>r ($<$ 1~ a )@�%e� remMh-�� �erA� ve b�1�,. One is bas !/$specific i�� u�(Ritt charac� stica calcul 'AsA���e�.! ,!Ppa� ulare� libra�( ALIAS\foot �{\url {www.inria.fr/coprin/logiciels/3/ .html}}. !�wag elaborate �se5�presentu�detail� � ** (elsewhere.~w 8pmmm04a-arXiv} *� S+R�s} UsA� i�l.� �AE bove��wrote MKsVp{ $provided u� a�� of %�ala�ultaTata�w�pow� ��� (i) A�feature�s,a� hold�uall6qqH� .Iwe �ed4 e"{���"R $a$%�E � 0s $b$ satisfy@!din��� 4: $nb\ge2a$, %��� xeSs� . X2� n$��3 ���arrive !Yv sW� unkn (� 5E\� �n�� (.�  ndi��s�� bigg�Pk9Q c�j�tԍ����� �to u�� =!D192A---forMk!�9aU$ violated.V� AH i) S�a�Hlf-expl��� �yin�3. As��sewoA&them h��,miraculously��preN I��m�L$genious {\@umans} (kWbɪ%� pos)yn1�� take� \setcou {= 2}  :� {�T 15,  Kernaghan.�$kern}}). S"Q givej ~5+6[}!�endzB q MEi{ i) B))�i�s-XF�%63, !��"!�ofm�e=re 62 )�6z3,�=r�? )�937] whom;e�T 2 2 . S���ii�* ^F�;2]cae� :e�f 5�R�.��v) All6j)upa2�Yc#!Z12��aq��Z�2��do ��- .A 1t��least���)#sA��(e  in mw $cases also!�7�<~3�KS 69 RZK�MEU2�8M nei( �Alatte� � Te 22-13:� �4*R4,4PA,AN,FG,GHI1,2ILAq.ll �-d 30Q��20*:�F�,BKS5 amongA m. T�Q"�mea-Conway-K�'q�& � ��6 oughZ�It tur��at�A� drop�!��%�bel�o)��� o"��bec�` M�� * d fu5Xa� �� �� lTe 7M � ��8 5CK�!(.j!� ot MU So,joac_=a 31 �!a 5� �ZzSe��Ylarsson� iAp��cl�lIm�(non-KS)�i{\cal H�es� f��R! .<)�do- {� %|�� A��}9��L}�co:���u� yiel�desired�(ix) Peo$�h�- generalis eyo%A�theoremi�use:�o @(te Hilbert  �$,$al Boola}algebras� y quantuA� E3 c�MM%ser�s� K�A � uterB�)� treat , � impo!upo�2�=b !wU�># by direct1$l� A#N� butn.S�rAN6�5��'�% t�]0�^pA�FI��%%)theac8 ledg s} %��N7 ibli* ,phystyle{aip� 8} % if natbib�:avail�n8l}>7missing>n{/home/m)(/ql/m-p.bib&�the.�0}{10} \expand&\ifx\csB�exlab� 0\relax\def\na ,#1{#1}\fi \p�"�Denquote}[1]{``#1''flurl>g jurl#1Jttm nZ� urlprefix>OL {URL I8 \bibitem[ZimbaE3�>2)]- �# >!�IC{Q��Com��<, Discrete Space%�$ Entangl�,�")�<{SCI} 2002/{ISAS  P:$ings,��6th WorlLMo# conferenc�� �0ics, Cybernet !eInforma}, edi�C by !�0Callaos, Y.~H � J.~A.W �z-{P}eraza, SCI, Orlando, Florida, �A- vol. XVII*�i!��Astronomy*Xd Chemistry, pp. 65--70BN�207003.�MzA�8!�ckay98}Bn)_ J. A�-B�6A<306--324E�82�>�]�5)]: Z+Merleta�-P., �u!�6�_e�J.%C. A�38}E�5V�990707221ewi>�A�a� +ڢ ��92Nq�37--2379�0V�i�8.�&��j1996)]>� &<, A., Estebaranz!w~�S!g<{Garc{\'\i}a-Alc- }, G�rA��i Lett6v�12A0183--187E06V�9706002j"��4)]� �Y��R� �7� L829--L83��46��e1A� } )j\ b��( L175--L178�12bL� A>�,� !u-{\AA}5Z Eurox.)\]�t58�799--805E!2)a N006134A#�>9� docu ce)+,put o�% * StarK$f> (apssamp.tex ! % w!is } � APS�REVTeX 4$tribu4EVerq)4.0? *, August��1' Copyright���Ameri� A�i� Society.68 2�README�S re�c�se �i�onH TeX'� %�A$ you$AMS-La�2.0 inst�.d %�% well�w� preOsi�.�)! %r� %�� Cres run�BibTeX#�+k�a��.!$1) �ex.�2) bib3^/4V\Qm�[p�0int,showpacs,!�6c x6d �6bm��*� 0MaxMatrixCols= <%TCIDATA{OutputF�=L .dll}!��,=4.00.0.2321 Last!�2knguage=��English�i�� {tci�"xb2-Q%qh�{APS/123-QED} \title{Berry Phase Adiab  Bd$in Opt�dModJ'of- author{Eyuk�!{8l{eyal@ee.techn�J4ac.il} \affili�{De`'��a� Elec'+al�ineo1, T C , Haifa 3T \, Israel } \date{\today � �ab�5ct}e'consid�5n� it{� in-fiber}g{m� *q(�$ resonatorNe��. \ō��a5>toran�# is+�ed�ogeome-(%�) p)�c!1Q1a r 6=p aik��chang brup�b�) pi $�D�#d��6e23sivity �9du<finite �2�#=�!7E� �+ussed. \ h�'�1.lCpro�u��be sign�)an�enhanf6�ymumgnE�> �)n&9�s.�Y \��H{42.79.Hp, 42.60.Da $81.�i} \�e, % Forc) '�\\ %L�- auto][3A7an 4f@d �5��iways I�, E�,�v-ny A� maC&�. lici!s+ed� PACS�e͍�"h % C)%V�T Scheme. %\keywords{Su�'ed  }%Usq keysl� if' %display%�r�"6 Intr�2ion} �L5��devTAg��rt!�!7%�An�unx/B%� f+sA�I}sw5 Ss>ext�$lF)tur��$on, e.g. e�!�mag( Q,!�employ� ��e e��on $%A. thcal{T}$.3m$�bo�z� port��m�keyZ+ perte*an/ ~or�>�,  ls*depend a�$�6��,�0ed2!AEen�Q>b��highl-���#O1�A&W9$Ref. ��/ 04}I��Yari �AZ!��sE �#in"Ran up+b� �ir2d�!Uwa)E chie[�2*!Lby )��aN�i�Aqu�+ fac!�$Q�dThe m�ple<%�f� refl9s occur��c7�`a� ��7>�0��is|8it;c��ofe less5O path�� Such��uwa.��"e�wby Yariv-� 00}, )� 2}�"�/ed��eri�� /Choi 01�8MenonA !�It��5a�at)h��J!�)ǡD�=cri�coupl!0%Ysu &!DJ."6�9��a� �l� eq�d�p�;O�O��>hand,�i� {" >��fVi h�3!�pa�5/" � � - similar� Fone!��a}6�a I�u A+7��� &7% 2}\  {!�!�polarizIyin�� t ev� , E  we stud�>� birefA���Lbf{\kappa }\left( s\k) $*[ Q��D ($s1} oord=:��a) ,)! We 5r'�a"1 �e�ɱ�$ � slowlA���i�s�' onveni23to��r�t� of 2P(SOP)!�# basie�lo��eigen$ �Yis 'the�%�5mo !� both6��;itude� de��ULlow81o�B�= �0�Nex�!Q��-T 4� � �(�i�in�#regim�C� Eaxi� ��,not\3�1~_*� � i"� 84}z� 6� 5�V� q#*h M �  ����e4f �N�4l� 5T 5Tŭ1�� }�orm : -orb�B�1a� (s+"�B��ari 91}���RO &�d��.�in �Drs�difzt�.x \ HAVw� msE> $se effects( 1K�m�*�7v� sw"�>�"& � � A��ha� e� intrinsic�F 8<�;".%��^#62:�a�our�is� !%4 %w,�/1X!�!7 �st�rd6Cmai�; �:@tw�8ng�t��T�&iz h!{s� 6��~ #i9� � �I� our �@onC o-� -�Simon 77" Ulr #79�8Y I Idu�cir�96�!x�%,)= or�TA!VerdeE�!_�a; eriz!=#maa�r#7Ay%Q,6(]!#!#of�ag�$ WeLI��C� r num�l *�:7%���p���a��&AiWe��d5 � /�YWNA i� aJ��Os� {F+ R!+R }AB��-":�>�;27 \ref{6$%�It�sis~8m� N�(� !,Gp? ui9 5{!C e� X\FRAME{ftbpFU}{2.9654in 5901 $0pt}{\Qcb{a�N�$.}}{% \Qlb>�0}{fig1.gif}{\�al{la� "Sc�u� Dd";type "GRAPHIC";q�-a<t-!�o TRUE;dS "USEDEF";J_f� "F"; �;he'2 �L;depth 0pt;original-2 3.9167in ;4 3.4169in;crop "0" top "1 # bottom)�� 'F-'-�,4es "XNPEU";}} �^SOP4eac2 ina�M )�K@�FedAPa"�� or}� Q,e� s associaO "$*� � �9�*n "l6 - � �����ap[ ix AE�B=u�BJD �e :� SOPa�A~� ��8$E_{\uparrow }$}� � a��= TN!Xas�?t�5e4a��ta(L.p !5he �MoreoD��;� W loss��u�'m�PJaryH%�y�?} � �:a�E{c} E_{. 0}^{b_{1}} \\ V22=0N<B 2}}%@�% \e) =Z�4ccc} t & r & 0�-r^{\�6} & t # & =5V=Z�Z�N<an<a_��)v6B<Bf<$, \label{Eerq(�FuM .^\E> t)� ^{2}+� r> =1. u0|r|^2+|t|^2=1F{Int0:0A�Q�a� 6� �8d�"� to a�L�)A�2.�t ends^�(� ��f�=\hat{M�zz]foY�1F�b� �b}} M_{11ae 2I� M_{222^9)1�"C�Q�, �,��6S<� I-� � Z���� or�,B76� ZbI,S�,�.1bj,��=�Ee��M $ES}�g�>bRXA?,S}=\frac{1-t M}^{-1}}{��-2F&(if }M }�� ( ly,c):p\dag }$)�NC�D�:n,>ex��72�oas m$���!$�>�t/o' �i*=i& =0$)|&�D �\�>�*]B9�%F!oR F�c} )�t-�!�1 5�a�0Ņ� / 22}} /22/Z�.�r5SFvToi���2Z!�h�P~gr�N !� % {de/ds}�.close cu�1dRb� !�We*�  , toG2� �n� n *�;��bCusRRqly� g9� DU�aJ!� i,m�db r":�nV�� ~ed�Z-X.�? A�Case}�V!#Ι3�6�-/�:Q%I�Ais�`Mn�1� i\d�.� �)"8 E�exN4�� 6Z�^A$J�\ f$%��_q�sE�{ �upa B}6� 5�m-;g�5)�!xa ����V a#Af � � !�2�*� ,q�N0�9� 1-\xi _{l1P1�> ��V�"� -�����0\leq � 1�  !2T� ,)�ia�S}N�$E_{\sigma "* }}^���Qt-��%J 2JV0 a1.���C�:f� v\in)�\{ 5�,]� �\}E%*MAsnoC $t� � _{c�6� theta _{t $�=2�cU q=�d $\va�Q ta =y�� }-^$E�getR���2�� .� S�2�6K2J�"O>�6<@g)�).e iU-�) N� ?Z%�=Y<<1�!&���h$q[$ � !�,%u� �v)v \sima�22^|���c}-= }+\x �2& t(a)F C>j!�"s�Sn% %�= �c}\equ9"x}(j�a�;%" �Eәq/z �p$ vanish�(t9Ή�:�%proba .B# ��4�� V* �-6%M~F_1�eW &QB' �}{1�(J"�}&Tb��$Q=1/25a��,3#�$��8#&� �7one2�$ $Q$ �$.h B&;"d$*F$*)d} OasF� "Gl ,� u>� be:�#�L 6�A�!6 we� �@w" pri'8�Fto pay�ak$s "�#*��EA)��al�% �#�!lin)# #�oAs�SL�+)z.�$ 4T, U%rI�Z�$�p =2\pi��$$}{ I�L}{�#JHCAg\-!%�bchr+:�8�S�a��u�d9i)4N���Lorenzija�&>$ ) "r$�$J�fm�&^{\pr !�]&}{%3>J-'1u�);NV-}5z�u�-FqAverag��� ��21!^Eqh�B?b >� resie�AE�e>C`D � l �>�qay!-t�#\bar{T}f) &=&\tint\eY$s_{-\infty��  }d9 9���B� NJ"2\ &=&1-)�1��Qj�:���)�N<!���a/ g�1= ���5%�eCzR'�Fq� o�,M�i�Bk' /QL$.�&0B�1} Whe��� ��$&?�r�!��d�$��%n0��$%`PA��D��A�^�!-4�"2Y�%&W&% b�&c6een��&F���in ���́�� �B�&�o&f'���a�decy6P�FR=0�?.^ �G q�.�l�"toFC\W �3�VA a la�ec]2�*�%ͭSgamma6� �q"    bEX�( ing,e M"�Ev�Xlanar:�� *$(B� 2�sol`iy@!�� $\O'+�n&�*n%�;wi6;g �8��5�n[a�3+)��A�>GQ�%.�ros/HA)E�?8, �)�s.9' one,����o&65'm�B��Z how�9]�g��� i�m"$%��V� ֩2 ,%qE�� 6��&sE\�8 alt�1�� *ac re nee�` � a6Ces/.��9I�� !+-torE��\ i�:1��.V+ !� shapmin�Ni@�+�P}�<-�unm�ede!�-% zis made�*'half -%le'�� G 1-3 aEeUZe� a>Q% )�, a 'diameterK&�$ �_{3xa�A�!0�U�x( struc�]�cbr.a�&by�a= &�,m&�&��*by*����&y38qu�!�2=5 � )5u�%(a M\"{o}biu�'ke�� #�l2^��'!�After�=m`�V��-�'O'/%toAPm%/ % �9+} �� N�2F9� ͔.gb_F�is4� �d7 a :�&on2�?{5h-9 �!�!%�*6��O� "-r�'Yv2}$&�"�nWNJ=U]�9�"u � aA%�>-(in\$�(� ��7�N*�8-$:�(� mode0^6O�y  ^�totS3.�m�>&!%�"efF^��a��� e�eɱi�饍�� �K`G (�(O N� ��6dA#v%�-)l�2I\ SA�:� �&+R�� :rndb� :O(3.4056E(5.7363 6O(6� .'pFcct�GJ��2u>P .�@$��E�upPlots�NP�U!Y)�]3 i �<� u5b)!6�par�!y$�4alpha % =-0.2$xin"�[(f)B-=*_)]).] fig2�\)�\)1�\)1�f\)5.1975J\)8.7813�\)\)%'�\)Z � alyz:�(Cmx�lb�*�_*�$p_z vs. La�5�9Zen]"�>2j$p_{z}$ � �a�Pie�� �ZKgd� $\ _ _{n}� .Y/� h@ ,$�bQ-rstFoof ���/j )r6namd0L=$.�1}=1.022�On�vantal choo�ᤍ� zero� �f{@ &$ )j|4 m�Wum<�� n 2�4Qm weak�0K1�: R=�� �V� .V &9d�SE? �le'�".?��$\� $9���P=V} ._qš=.���A/X cho�X")6*�6�B� E���82G8< Bloch sp|3 �ip�l " ne�/ve $PI�� ��op�ee2 2>2ab� ���8I8xm�3!� $% 2Q��)/1c� .FH L[ ] a:o�1 BFX=>#_{0Q�"� +>%% �M�'&>>0NU� �ݏ:�!�� heNi ��>k }R�!bF2��3/6� �p 45?(K�L� f3�#1oJm�=: 0,0,�.I{\b }5rf��X - < BY] R9�m&�#��"%u�-2�%Y)!_�=5�B?-C��?0V Qs r\ao6�df�*N �0,-k�vA%:[� %��s5��N�-B ] },0 )f� A=50MB=0.6$/ R�!�/!.Q� �BE��6���c�m$2B)�5�e:[s �?��lyj3���R(;o�)��n����&A$H��F+a�.g00Fx�gV!=�q-2mndl 4}��$�B�-�0i�-�-ed|�Ms &B�A"�1)�a�� "�54՟}��fx 2x�9^ b), (dWQndE 5K�e�on2[�Tte �&�$a�Goff-d$ %e�U>lowW �Z:� 2�.��)2m�kain e*i��z9n e�}� �lin&��"�  gradu�7&� *� :� �� e�� ��" _e*A�"� BF<c <>>1$% A9A�)� � �)�+�>!��e-p:� a �<� ��) >F�A�an in�*K86!X�<de/pd2� a�&g%  sta�H}� u35to estC>�O>x �EW =�.�1 !=я�'q�} k =��%�( ��Ņ)�E�}JX +!) ��2p_z�*F#!�in52!nA�Gb��] dashed%?A,["� 6�"E+�]D)�) �aAemai' �&H !|6���^�n�i"�Dw4R� QA# wZw�&q%:G �m�. to *bD�^�E�jm�s�=is �_v:Io ��A st� .�"ʁ��!of-^s�D$���bia�� Ich^�M���3 &,oEM sharp Q���cKO$3$4"geɺ��+F,^}չH"�2� cus�0-�q�work �! is 2��c�IeF>$j�c)e�R��&.�"C%�SOP, 112�S_.b��!h�WN!PP�4. SJ>�~i!�entire&�3a8For �E*��dw�max1O(FWHM)A # 1� 5.1\-}s c 3}L B�267�2.34026�D"pL5.� *�':-� l� �C=�,"�ed � ly (>f��px�E�i��ѭ�7� a�\ S8�1N� 2� 2�P1AV\ ÊNFM �MBK<21~K"i���>36e% ~�> z�> T��> 3MZgQ`g J�>6.4792Fg 4.62N�> "��> �>%Bf .�>"A�`us� �(V(vFi��&Fs*�eFwith �)2���� �~it�K�)lw�p�G 6c w�E~ �#O6�^&� % ]6�#on��LW:4yomp� p �6�s�@oa�X ;�M�$Ճbf{#RSource&V* - }�!��F���uh*�2Z�I�R�ba�ȋ.�$�V�D�"E2��H�ha�).D&o� � p�Q�^dynam�PHU*�LR" *&�O1�.!bA>� QXO:G� ���&�H-X$l!�9.)�, �!I�16�A��'J%L� �~ �H�Tl�B&� =v) "B_!=E��X�E=- *�369 5Hif%BM�+�1&sEq= Q�"/CYDing} -15>*��apm Zn� 5�� N.� ~.� �\lA!ly?nFQ�/"�K&<*.�3$,6� % &�/� I�VJ�e fulfv|�!"Rj��2_�3*i�-fficult!�"�-�DiWjes� zGi���E�* (�NA"EMA&2\F���  =��- d,zk �ttjiS��e�10081l ��R*\GA a�2�>�� cee)be�L!l�H�a-� ���EIq�� �$0 SMCM���z�\!-6�/Ł &  -&{K� N�!�� �� p&g �1��2BF*X� .) X-G�,6� � "�2A�� %+* 1.7>�  \Y�asVC sinc"�M��T�*6�>OE�I���yb'�*�V!T2^a06W imN[b;m�%X!-ts�w�=�W 04%�asbe !�ai���Z �>YJ_9#!� �P%=4&�WG A fu&pub">��0P<�#�:􄡎�{Summary&�;M�." Sz�N�Z/T!�B|Y���6 �W mn��ar&�,i~W�qpa�Ye�In*�2!" �2Bv) j��p�:�"�"4�쥳>���ZeU�!O&�N sR�t���+o*�OAd�G�� 6EF&HO!N>mp�,2(#��6eIZ�s�uA�PX�4 2 \�C guisSq 2d me!Zism2[AcCp^ ����`I�e�Ki�%l+( ,ank Avishai a��d helpful /��e9H[s|]io?[ aqA_� Steve Lip�Y�>R&�Py a�da,�.��OP Evolug Ah a F�(2�M&r\)��,��e,spa�u{��m!�Let�a�-rJ��5n arc-��&"�V�Ll"A, �!a+/n ��=s}=}dr/d�VC��~�K.:M \nu}ar�a��x(? �A as $| �/}ds=�%� \�K" can C~Ls"�T6�1\cdot6Is}}=0�tak�Q�8��,�2zsF)0}=1J6t�\A�tA�$s�!& !s:�s}= 6Y�&bi=a G,"�B!-2�b}}&u �� ]0 m a #�bl�&�M *�Xframe=�Das Serret - Frenet  � Ross�V,�$Tomita 86}# &�Seret-.D, By 9�:���!�e���e)� $s�=o5:l1�Y�5&Es-Mt!� S�Z}F�U'r�b}Q(m�a% b�n�M6  N �.geI�62b.�*?e�(�TUUBo%m�vB� vY�.<s}T6�\nu% ��:�Z� n0�" W�aa1i�Mg)�Reb-�:e.��6>�b}�y��lleϖ6�%��f ��$\tau?"%�AJ`M3,2� Ub�bovA��iZY 3 � B "Wa"mJY�!d}{ds��~P�P2�smP2��H2b}r�N M&&J0Ic}F/'_P \\ q�& )&\ *-& 0ZF\!$Fi�9�fJ���&UdI9"�O:t2.9118j2.810h-6^-��2�"�% J��46�~���U:�U�&� ��V�U604��l*�U791�T,T,%B�B�Uqc]aF - { rh���}�+��i{ "F�<� port2b" [s�� Kravtsov}"i$F]i�gno*� Ev(&> gathpR2M�,\nabla \psi ɂ q� I") E[ 3�I-  ( \ln \mu�):hzm]j+ �[:y6�i�Xn ;) ]]�psi =0UB*�<�Cr�}b!�eikNC8�dWx!�Eb;i�V$�;!(permeagC� DEV*� 5at�Xe}%��i E}% $*/\sqr"��1k2 )GU%��A�~�[ %�r 0ŀ�erm�6� �$��2� reaj�E�(N���1�J$ ��~ �c5�.5s"w�q�} Ex s �xq(!��I"* I N.�--=e_� }2�+e_T.5b},F�on+�[��$�o��v�.c{+}'bJ$�{�\n�iN5�.NsLBx� e�) - �B#�}5��:\J |g,�DF�"�Z ket}GGN�|&e �\r�!\�=��N��R�^3-J�5�N�%Gm$b�=i_�K}_{g �� >�� MXA4 (e_ni,e_bJ�H"i�^al6���� �K/N��/=I �Ff� -i%ein� Vbf{]�y E2 y'�k՗4as Rytov's law>>��In��mB�O)'J6 &6�"y���x�/!*%�>�2 f' 1+,]wSBa ة�)��z An��f���at.p�92T 7&-&�s"=or  elas"0:or�o?c��p��In e] r|�+.�E�H�tiau@�f�KMfnF=ie�)$fVJ�9=k�I)G> � ��)�K,�[bi�d�4 4b�I��2a 2nt� �, $�'�J��calar�W�bf�f � ,0, 2 3�� Z t���e�iɜ"h�E7�com�`�e Pauli ��.71$\ec�z:Ny)H�b211�q1jq,M2~M��N3nN���T-1ZrFI��-.u/c� u�.( s,sA��) $1��� ��s�7/� �+a5l5&n�X����( .b7.�r|�dAXb"�C$s>;&� �} [:g� c=Z�B e 6�:FF`&eT �J�Z�=�I_{N �a�b�I\tprod!i Jn=1}^{N}&�-[ i-�s}a��� � s_{n5� i]*W^u(!�0b s=s-)��<$X=+n�/N; �::y$N$�Au-)z �/�-&`2�40)� -B �{0�ocal�h�#�Q.��� �T���us�e�v?"{%�8J�9� ( ix.{� 2m/i�px%�[ I\cosI�(j $+� � ��qB���}\sin^I u]be5!2�1o*!-Ns= F!�0M&C � 5B�Q $> �>%9a2� ` =��i�%v@ɩM �+�q��6�%��)$Q���es#e� a�'x&!+2�4�Hc2yecy �52��g����$Naa� bf{P�\5ile" �c%U�r> F�"- !'&�L\T�2ablis�� �w�FbwB% main���of .aoerry 8F!C4H!F"o�$��NV �6�^ +:v��2d_ksiRj 5QI:t$Y,s��&:ck��1�I�!ԩ�.W e2l>iO�N$ "� M7� �hny�'e!~��!a>3"@ Fs1#� �i;2�sN��UE~ n �:�KŚ!]$���@9�(K|n>=K_n|n>b (n=1,2,...,N�N��qcB�|m �>�\�] _{nmJ�Raa��e�t5 v^�i��:F \sum&&|�n)�.�"Y)[6int�D^{s}ds^{�S2� p�] G �B% ,�NFpSubstitu��u��&Ra�a}_{mB�=-� e^{i^�%a[ v� -K.~bP8QGB5|�% J�2�Y�adot_m(sb� @&-!ն1Drii>B*� 2�:' ,�MV3>E�ͅZ�~�.V\AbM-I��_%<KAU z�}{2� V) )�ZX�|} ��m\neq�P�/neg�~�#�Ya"[/a.�w����7`"�S�Uk�"olv�>�ma.s�=."??e�%�( i�?>EV)J�����`��?;�YN0+=e]��0B\�B�qF �eiy�"� ��fc"c"LUwo6� {$N=�F"�`R % V ��!:"4 &� � ��� *� % }� J�C(){2 q�NU�E 1&�#@2N�a::�"jz �Yphi�]��a�n2 W_ , 4 'Q[FWCr���"� E$R.v&2�.��_�M�� �� g�_.-& -h�d.i%.}�>�A`bR-�T��e �Q�� F}- �}{2*#"�=� BnB NAZ#,\;.�3C�x��-)�n��>N�)�cos �Z _NA^�"?up,�Fk �&=�=%��85�| 2 )�/l)A�w 23=J�g ]j60�^9i� V���+q�%�2� � Q F@B �5.�96R)B( �-j�^AF� � e��5�%\ �$ (�\$nN;g V;g)�-G �6�2�%1usR�b�s��__rds)8M�F� % ] �z)R>p:�%��`�� tF  �>/�R�+*^AIQ1�%z@"_B�.'�IF�:R�F�&$*��.a NEip-inMB�r }�B��y� ��=�&�s�cva��}}}{2m$}\func{ctg��ݎ�2�BK��B<-�, :��.�  .]<9��, Stock']3e����-�A�1�p�d5 Nsurfac� �y1��e{�Zf@/y 1�mK%^*�R2�|�deK:�F� � 'm 41�6� S& +ai� �m��\��N�>4 EiEP:� BN� :�#c��"�֭'B � �>�� 0F�6�><1a��  :!�U � o:) ^{3N�Fgj�B� v 2��B>瑤��n�anR�q=5��$%k1�.�eF�B J6�j- ~�1s% \Om��&m �uJ�yF� ,_'' rp_����=Db�AFA 7 -����D�% subt@�E��&�*5�;.Fl=ZU^3,�D�k"W+al na�4��"�� e9�?$9�� "�O% !a�r�<l�x Y�"ThuR�Mg�qj Q8M/{m%6�� I��s6�s�F�&�� �"#ksi(s)&�ZDN� F�q|Mpa�+a$N�[ �  ( J�"� -�^���v�� ,R����"0 ��A�F�"cZQT"wP6:s�6f*y&�j a�f�� oZ�t�[�Baڜ>ma��.Ha��k&&��*u)Nma_}f�m�Z92v)a_up,a_6_)Ffk-jJ�-Bg�t�m�q,�2��O��w^Q��:SH-.U-iV�c>VG>�% �.�Af�B:6�ZkM��.���F�lū�g!8AM-ֽ�&=&vY~� jc��� ifi �31&=&-2r���j�"�d)a�&liA�2_m�&CU��oDh�Legligib�;~�X"! equem�non0�8&�tw�_j~ ����To"$h1�0C.?M� 2�Pw&�@boff dV�s�ge&0� 8;L:ސ. Te"N.�[�Ml>�rI-:uQ�0)6!#�[exp: .+>5�)�z:#Bx �"�N�B2�m� &�0 �Uv"7AU\c��atv?r&N"1B�&0�2�C�E3� a>M��j�Ց�$�(�o w #t:Q2�W�hi�Beso.m1/ �kI��"�(A�L.���"_"(6by "]r'.]Uy��%06���1h.2�=-ac�97Vi)�[ i�( � +" Zw)] >�-7 �|6J�B 5�6��9Zv�2UQ M>S! )s2W!ao �|!Ar- ��]�� :)E �t7FF"-! w�aJ�2�`��&!sAa|R;� Omar� a� ==��te�E�"}F�%\ ��b "� V"���A^SF�4b�>z�^�% F�"�@�}u&�0V�*�:��?)�AC�+!Nm9e4=s�,t d)�2� i\ze��� C A�F�E�N Hm�� V =2 V$}�� ��0 �R \sub�IVRw�U^ �Y*�o.�F!�BT�&� X2-:\sǂ$% .RrRE> )O&��� �:�h!�� ( (9}�c�� +�_�_tgFn$ >!!G� on-n�f�"�Uant�o"�c��of 1/sG,�� �NN;l?�\�A r� �� �I0<X/��f#f��.q3�%�"j \gtrsim 1�i2� �") �a�3cA�"T �NAWi9� ��c--J��E)BDe� U@ O�N������' �A�.F�Vxr:�{pi�{0}J -2i^�)P6+�FG��id 6Ni2��%�J� iz.�=\pi JWE( zF5o�J�&I�� ���2�8;t�JP�L�a��n�`f+��>(�5�6Mh�% v�]\bK� 6-lB �)*�$`��ndtzr`� �Vu.��f��F�� % %��Ti�5d9X�EZ4!=>x2� Nn�).:��� A�U m2�UA<�,bp%��/6p��dep���F/$ (�. 3...&HhY�TWE5e@�� at.A2�o\S�X^��VF�at%�r+ )y �!9�NZs tru�O"F+Y{Q B�T�OF2��3.4Y_2.589:c_Ex�Vof9��IaIĨ � A1>��� e` n \ a%oT>��Q9$Nu�p��W�9!�:2i4oen"�Gn�O fig5��G��G1�&�G)�f�G5.6879F�^ 4.2704��G�G%'rKtC�]: EZ�a�I�>1��%��&�2!"eg�#E<3�|Y_6�Y good agre�S�4�ͺ Tr'4A�Me"H� �� sssim 1$*�\wkD��@& �9&�_ �./z�>������*��F2}�����a�(6��B���L? T_la�u_mFI Bw388�c700pK&fK�@�a�G�'s.��Y9���:�`��lyu�AC]m�6���)y�) f�4.478N�3.562�bN�b":�� �b^H�%v��tt]l�m��f��|<e9�h:� 9r�&�(����"�I�W��]=C�l�_J�� (K"� G=�= _ 0,1,� qBF� o")>^7"3 VzsB�*s���'�Ie~��1 ha. w2� ���\�� :��X��"�FB��8�� [}��[ 5%2\E��� % }+%h �-jA * ] ��E�:[&& �"�#_�Y}^VD:[ � �CB��2*�}{� h z2�-�@% V0(�� csinh 2z+"�dzp V�L�]k�@O Aa_#OA{"�#oscilcs rapid� ndE�"ki�.I0� (bion���c�  $z� k�D ��e�-fc�"z$"�aJ�0`� zU&1v2:7=)� 2z+1F�Z��=i�}�Rn+.eM�FPm�nM tegek: "D";#+ $1/ �z��!�-1}=-�/6S�` ^�z %!-10 � M]��� principle&x=� ��r���To ��% thro-�0oz_ maj-�y�B�a�lj| "g"@�9 adiu� varepsilq���4�h`  )�i*0M�5 ��7doh顗o#�bua:��>%LRٰRz�F�a� �%Y���/V�0A�.���A���20<* #�2RaXecF�i J�����i���1��D!%"���(r��4 �l =1$ �9l2�<<�OR (�R�>Ē}ٺ �[^p_z���Z�>=�{99c�iw�{6c�_�_.�_,��b�s�<"6� A.Y�,��.7_)gZf36, }321��0��>D2} AmnonG(IEEE Photo.5�>R1m� 483 ��.��� John M. , R��ald KL�2tOp�"&i 26},��6�12i�rd V.h, W. To��!H S. Re��~,.�  ��.)1o343o42o�C�]lV. , E�. Roy��(c. London Aj �" Y. Ly�� - ��,}�.�>�71}, 65$�36�*��$ Rejendra TL�AQ&157}, 2A'96j"f�Ai !]R. o�, Appl. � WV3�51�772� =��KYA. fXEQ18�41!Q792RR�_��N!�ss, >D�.qK!�455�:�*�_Akira �aymond!�Chiao1PRe5�U�%T93�862�"vX Yu.�eI. �ov;� it{G&�� �nN3@Inhomogenous Medi�zS�t(ger-Verlag,A� lin Heidey�g 199���>�0 \newpage %JB�bW�of unus{*��rds� cked�� end �f:� �{���P���H.�� via �� �d"� 9d6��{n�le6��� ,xsym,amsfont&�&�,�of, epsf24 [dvi�� grap��}���4fullruleb[ `�f�gu�3ord&L Y�ef s�# F:=D"�" ]F( \U�� mee�Xbox^�^�\hCe{1pt} (-12) \�F��}}%� �aG� bra}���!u�|:#2V#|�%} !�A9� \ti���� r�G��AI BellO�u� Atg { Giul!� attilottie@Paola Zizzi \\ Di7���@ MateZ�$ca Pura ed��rJa0Ut�4it\`a di PadovA^G��Hlzoni n.7, I--35131 ', ItalyHg�@� .unipd.itz�:!�V�}Pk��-)a.Z�invnvgP F0a h�u��mp��� �- qubi_� %mr !�, �e*(��dpp)�)%j�wal$xa۔iG�=�)�j`kaim�'�i��a�Pt)� (rݓsible)V�sur Pwhich #= &Չy� irro� 0the states. �We then obtain logical judgements for both cases of separable and Bell's states. \end{abstract} %\keywords{ } \section{Introduction} The main aim of our work is to look for the internal logic of quantum computation \cite{NC}, illustrating the point of view� a hypotet%''c`observer" who lives insid%;D black box. Such a!M 2, i �ed in \c�DZ}, can perform "kP" (reversible) measur-�in!� q �\system. The idea is thatrernal6>0give rise to1� asser!*s �B}, �whi�r�Hn treated following� refl)�, principle a!# basic n W SBF}. By>; <, 1al connZ!q � result!�import�0some pre-exis metalinguf~,��,non-contradi �!q4excluded middlA�mH do not hold. Here,!��) a )�of%sq!�s!is mak�}t pos�%Au deal-R wo differ!Q�M� occurr!Ebm 0 `nha_g!Qr:M� maxiaentangl��} (+=a�,a Bell pair)%ELnonz<EM!��U ). �%M.!_@Mirrors}\label{mi�% } To���:��%b%x exte%�e definE�1�� ��!sO�)wo-E>C��D a Hilbert space, <Y.Xof}�is��dn by a unitary $2\times 2$e�$lex matrixmZ}.�Asʼn�r=!�� by�nEE�ticularR���lled "m%�;!})" ��9�o�{�,ces: \begin{�Ki��5�!�P1} M=e^{i\phi }\left( 3darray}{cc}\alpha & 0\\0 & ^*\x( \right) owhere $ 3  ^*=|  |^2=1$%ơt: B� �eq�0(a\ket{0} + b 1})= �}( W't0>� So, �)as%�\''quasi-identities"; act�M they!�if�V longitudI�h� BBloch sp! ,��s ��4obability amplEs: $$ a)Tarrow a'5�1�a% $$ b.(bB( ^* b'and� rv].p truth"6Dp�8ies, since $|a'!�|a|^2$�$|b b . Fo0 is reasone�!� chosen5gQ�a�witnesO ey�c!Q�yequ�f�22 , as��shall seF6next s�(on. We now.�)�2�8$C^4$. If $M_15x_1�"a")5 $M_2Z2fZbet.{Ny$, ��tensor!�� $M=M_1\o�� M_2$5�Fmk)2�eZ(�_1+2)Z& cc} i~��.\\  ^*: ^*@ 8 @ ^*i�2~ ��n� gammR�del)l�}  �' MR�>  is alsoo�~Iv(x. In fact,E�,most general����E��Q| H alS s iJ�-�reg} �/\psi} =�!�I01�Uc&1d 1}>� �K� hafteqABCu= ��)���m)d�� � ^*.� ;^*�B��agZ� : $ fL �...i�so ��t�2�J rved:: ...z?. Not�fa�f $9$h!=m he� � s (L_{\pm}}=1/{\sqrt 2}(E!/ \pm  11}a�its��k A $9zJJB�MZ%^*b . SimilarI f�� ���hNo �1}�0�-��R@�i��P�X. T!� -ZbeŃ as a��g ay l�+i�ing��!� A� same!mJ(\ref�). T��Dfact will be showna�Sect.4� ��Dcalculus. \iffalseI1fin� #t/Ev �1 �&�� 6�s:"�CyB ''permu�4s"~�above `zent} M*_ V/ � EC�G�8 �K  )�e �/ ^cqquad M'��EE�.�� �' 4^� & WOuld sa!�at!~)�''� �� s"�(.... \fi \�{From� 7 J&3"j Box��giudizi}�recallz�� ought`i� e "k he��� � el. IJBr,�he�"r � {\bf P}�equipped� h I�-" ��ta���&�. s. Out�2 �instead�� �6�G}2bstandard"�m*  , re�n�\by projectors. As explai�"xB��G}�EaFc� � vN}. It!#w�kn�Eg-��JG��!�asm e.g.�a0},�C1}$AGa-��~q}=�6 $,bnEwapplyE���9 T $P_0$ or $P_1$, break��2�%�o �S�!1� S71� 1WA"''read"a valuM�� as �0��ng:+Q$!rtrue" or .1Z.!7�.�, let us�po�a�v� pplib�k$A\A?{ �,��1}}\} �).ed�enU] �s "$A'�, writt�S\vdash ACon�e�� deno�by $A^\�$%No�it�,Nq01bw )}�no clo%�theorem ?Wa9af_A5]��!� ��onI�}]�%&� does�0 happ\IQb�,})�8��a1q)$*� any"!he suT�A�y!bisomma�"f��= &| 8 P_0+>^* P_1W ٺs!&aJE�q}�L ZS $. HeEe�P}M�![�2}�!A��n&+�*� togeV 2  D  q"Y�W�� couiof �ie��G���wDque 7 % P}! N�p��I&�*�s to a�k"P�ń�;��,` �E�S"&MA�A�)3 �, put�f�def1}�V\& -8 \��v1[�v :dB^� ^saxVpBE''$��!�a�58�UM�R�concer��2d  �� w�� iderDwo- - �(E[BF : a r aL$A� aO��q_1���q_2apFix�`�Jof? , ! comp "I�0&01/1�o�2W �5�a�"S H��A�%b��l*f��; T� P_��1}$. LJ�she] ds,answer:j� }\}$e�-�_��� a�9 $B.�b9%�A�~h|5�: w��as� bits� d her &(�b� 2y�, B>��-�m������UF��h�.�% 6� 0e multiplica�K o�#�he A0�is$led "par",���H "$\oslash$". "Par"!NE�s�"vmeae�!]he: "[$$ �, how ,�usB linear� and A���76c���O���,� in �����pu)W�~b)e�z=�-  B\�~ua�nJ���"��s? If%�}��%b"�Gindepen4,i�combin�# b:  �,��+, B� �  B. $$ ��@� �C Fbaz troa`y_=f2Z RJ$ 6� AB�\V "�:irA^ un&B� . Oit+ryN�!>� ��1�2�!; rel�"�sWA=.�%d9��-�, B���O �$ )5�,�� � . "ZO G}K in"3 unaw����"�"�>�2 R ��v�; bis�1o�x n�1%Uof2�,�cY�%`17Hb�dueZ�f 6S~bA\"*��EM�B� ��)�Oe��. A� J!�ťB nal �!N��y ]��) ��%�NaݡdaA��]�x�*�Fl%@ } M &� ( s5+ GM 3c ? B�SoI�8#�&w$M��QqM� ,��~� 3 F�L 0}$:�J �>6/P�8B�� ��2� 1�u �2� ue�d�/aE#lyusd  , ��y&S Ei� d��!n2�Q�"��Ind s aV�EgNeh(:.d)aK(s: ^� sovrsepՐ(�y)\&�F u�R %B�N_u$-M�ex� &s$, �� $MY�� *�(m A7.�++ Mu1YY ")$�r���%&� �7�����)-��'�]VC A!�AR� 9� )걭.�f#� �!�j��=�) !�-�5� B�NN��U�.��(ouA�y^*er�"��ne �i�� achie5*:6� s�i�.^ )� $B\&� $ F0U %i)��:�ed�!�&�'�6!s� *% "J,�e�B@'�N�'�">o'� �$\asymp^ le �xi>�'$ $\bowtie M���-.�%��!� Y_F�ͱ:'&�) � (=fB:� Z�:�X �vZ�+�# vely�#A�!�N�,s I2 ](:or� ion)%�' _1$ (%�um 2'��p"K,� ry0 �r^eq.�= �_06 � y�6E)63>�v�~�16]~���SoA�X!�ki_of�aY�!W@�u��~"Dn�2� (*�)Zs�@�_1z�A�r�g�� nor "k+ nei� �S.�,!Q argu�at!6Q��M\x$, $x�(0,1)$ (�$x a degreE�l),� �b� tr!&ed,�haps leaT/a%�!� fuzzy�. "�TowarN �� /9� } OfHrs�(s*$ se)�i��2en)�) must�Qal��͗R�Ѭza9 .a����!|I�o %)&y1�cf� sep'~:�Lo�"ft!a�)\;.\& (A>� (M$ -F-B= .�d �h �1�!j�ent'v�>���>�(^��P#& �. RAbe�d disPmb�2�]����6#md wa�!ouns EP$�!BUJ sa.derive�f�ent'(} \infer[\&�gr]5 � 1 ]{R_ 2�}V-��6+ } { n [\&] [ Zw�W&� }� � �7I�"�C  01�}}�SB 2B%�:�# ^'E�b� epN�tJ�0z�:,�6�J#�-���R�J�>�)ن��-�H�B)�bH nB�O 9V &%rZFF=. *q.$`Y���"�uEO��=K� .I.. ~(0e key point, �+�76. � *5�*�����P�$�e&Q6*b�69" K�� *4 al  b �� G�-� �.� #" | 2J,�d'"adm�7 tI0be�� �6��8ulae x#�$ $B$ (visi y���)2**B�%��1�3P"�61y%qѳa� � �$C$b<cjZ<, C% b?, CRB, C>BuIIt+�nA�e w{ E�e�itributiv�2oab@� $ �G  a9 >�(�&2&!)..�(&"� (at st!)6� d�:ncte=� � W��"w�n�&�t%io�5!�5���a7b�>ovrF�6)N�)�j�B "6!��>���="b �6�9b�sep�� N�~�z� @:��N��#N.���!�$�+is last9�ce b�8rivr+�+A e��<�#!��n,acoG a#�ian6Y�Lrul�$.!i�~aKa � us@=Bext. B�7 U�(�Y�)yU�?dd#�W, ���to2L. /(ice moreove�,V1d%o �j,M�m>� eq})&�+�lo"b� e�bzA��s�iO@�4ih�� )Y�Z=S<eI+�2%�V���,>�8 h!E%��j� b�[" p7,�� DScepticism sugges�" sus�& .�'�O&# ,�)͋at Let' g�>ck%,-�B�-9"� :N�E!Mtwj?���7%�i�d"c<al=�_ r�A��z �im�"it.�eP, eac�?F�a dir�o"� 3�BF��fEqmD)x'!��� s, �1�7 op-d.s$bottom-up,�iiH[>qui�@ �&�A"9��2�:em!$+ $,a�U�VM,�x/��]$ yet, beca�Y�4justif,$o!�Y �& 'S$nder study�@-=� ia](Q�new%q (\&congr$�#� � s �}R�aͲ���3''$ R�� ''u",�%!v%�FG�hy8� . It9+��al �A�.��n~a p�4uD>A�AA2� �!)-"�)%%A��%!t5B�"m�")qCm��R)"� ]9)�i%I|"� �g>"��� a�.� $ -�oG<&Q5�?A}opini�76O desp�.their sq�y,p alaa y qu$in!Q�&!a5�c�5q�aim�+grasp\$ efficienc � *r)%�fa�9y%�#A��> ntumA�@lism"E�Qd �� �"r b�1/ half!/:�[( branches! b$ac��a�Eto 5!p2In,!S. 962^relizI�� �VDll� (2�� ��A�C �/at.�I�e2)z�] !�1i�A�on�aqshow3�� "�$": $�� n.M�?T#�  (cf.� BZ})F2 X �� v"�� '&o}}>� a4� sense�Fthinki�fD"�9s�G�*(%6�e$[ss9:15to3i���le�%� �-�Z X"�p4!�!�Bd�\ mbed�E�JA�-�)�,ve geo|Fy backg�-pZ}.v=t'K a 2�-�@�Eca �AE��r e�E5 ells" enco�aBV�ng�^-!0"�-�,�"11}$ (� fig. (1))�!r .8a�sE�e � �{!`�&� � doubA�surfacj:a� �p�.�,B�qp.� See-�2a�e!latAsit� �ImblE��a�ut1Dy2x�Bv(� =w>S�I6v6�6e3!e�1Ez:�(asF@7����er) ''%-ends"A�a >y<�ileo ipi��noBsC � rigiU i)�. doxeA��)B1 �C�# , ''E locacD�{ ?*roble�F� �&|M a ESG -tim�na9�N*�&S B*F(, `� d%cha�_.. M ifar�'] �3�1��7coe @e cutŞ 4frac{A�:B�IB C}C}\,cut�,G !� x��� . B�-e' QDJ���&� A]� %="�3�, �EiMta� �:��4#e�+*=h 5� worlD8u�*u!musu�NO/cau9\abNM7q�5� q/:@("$�  (3F why2��A&P � � , se[��m&�AW (@i f:��Noٌ!�3���u�!Pa [omFq� >Hf�9�SCom&y3 Loop Q�EGra(CLQG)ѱ2}.e�;-vieH V76�<or� FR}''-D� *� uJ��,e Planck sca�C%{�J!�a�<r� sial issu�ndCP authors, N Sork��8nd collaborator+QS}� inc�1d��belx&)�sor�'micro-�ity�t�IdiscusY Q ofM� seJ>H2A� �� l�J!+e.�- mb( smeared" 3 very��ong"�fluPJ�$�=Ac�(le9U:} W�Tsup�R&5w arch�) "LwU Tool�q�I� on�5ory�Def�!,Pur�UA�=Mathe)cs, Uni��, Padova. ��M�thebibliography}{99} \bibitem{B} G. Battilotti, ''B*�Sa"6 �>�Sa2KVA/`r�I�hProc. FQI04, 16-19 april 200Camerino, Ita$> In�#A�al Jou�/! J9)�|3}, N. 1: 105-109 (2005). arXiv: �,-ph/0407057.=Z:�,P. A. Zizzi,�D1��p.\Sa R�-�Q*�P�+���ing''�B� 8068.�vN �Xirkhoff, J. von Neumannn � �. Mechanicsh Annale�]5J+D37}: 823-843(1936)4S} L. Bombelli}(Lee, D. Meyb: nd R�@�F�S�P�  "�(set", Phys.!%. Leti�+D59}: 521-524 (1987.��SL M. L. Dalla Chiara,xGiuntinE�Par.+T1q%%Ph�EM% �ic-1�891-90 �96�} ��R�por ��)�xal ��2 Survey�B�305029=�8G} J. Y. Girard!kL&8�",�8eE s er S�U0bf 50}: 1-102FfNC} NE�NielsI%t Chua�H {\it5U `�e$��0}, Cambridge.�Presse�0.cPE�Priest�:��h�Handb'Z,of Philosoph�%,}Oond e�V� D. Gabbay�* F. G�O4hner Eds., Klu�HAcademic Publishers��2=� R} C. Rovi #9F },�� �, U.K.�.�4.��9�|Sa�8, 2�%_ C. FaggiaecB��%�: R"�Y, S�V y, V" E_�"�=Symbolic D�B065}: 979-1013F�WE�$A. Wheeler6 it G�(odynamics},=F!�, New Y�"(1962.�0WZ} W. K. Woo��,W. H. ZureckA A��an� be�Ced�Nat�!�Q29e�02-803x82xZ} 2�''QW%lQ˅ɥ>��5��!Gbfݶ287-291%� 5); B406154]�Z2B�A min�/� � 1=gr� ''\gr-qc� 9069r+HJ>- J�/8figure}{{\large�� F�1�med1   Two2�s.-l�WR�D bc�)r�aY�ics{2 ;epsS+�H(e} \newpageP J�2}�B� A2]yL�28 T ~i:��1���3Z�One)M:�3�����!U docu� } �p\Q[aps,u*�pacs,twocolumn,amsmath]{revtex4} \u�.ckage{-�0x} \def\>{\ra� (e \�&${03.67.Dd, Hk} \5I��*�20 INTRODUCTION��s1}?re�~ yea��rw ve b1inc� ter^#A!!y�.!stds, �i;in  crypt!�phy� rQA�nA�) r2},� �He� �.rS�$r4,r5,r6},"�G-�a 7,r8,r9},.��%10:_ thes~s�4op�d_ lway;6frV$,R!4obsta�UofE��1,�w�!&6Lf*1�5(is destruct2ur�==%z evolu!<. 3 erv"݃ s esial=�&: o�eE�i� h��s Vs�% be so�Sto � �2�^�a� �A� ects. Up5atem v7Zc!5?f sche�`of2A-� �@E�pro�Pd2m, e�T-c��ct� avok$ code� �iu����� >N = Mzl11,r12,r13,r14,r15,r16,r17} �$��al feed��+�y !{ ensa e�_"�!on:(=N orsip�&. E�� �U�$8,r19,r20}DN�H �a�djDALUtIT��,environment 'oi!`7e�@p1he�66EVf t . D� al�A�methods�+%�d- oUto!T!?.I-�X21,r22,r23,r24,r25,r26}��de�,s. Haeberlen�(Waugh pione:g�wqjI�t aA�ging efE�p7}��tailo�&�k՟% � �iUhaaVid�!��!jrefoc�LU� in nucl�0 magn�$ona� (NMRy �9}��tiv� bT�����K "�m"1P�or��-L}�qo!�m8v�by�*��iA= �i�T����-��%Bs�/l� �J��0��2� li1p�d nice toolE engi!�!v!��8)�a%&VWsubI�s��p"\ @[Ea ���=�to b"inducp�depha!�a .n�� ��YP8P$u�&2}A �� consP!l zv��&�  u�(�!reE�t laser!s\1�ies $$� _{20}=�PE_{2}-E_{0}}{\hbar},\� _{21B*1*$$2�?wh[ n�- f1}.M4 $|0\>$, $|1\>! $|2 b, eigen��un��urbed�g�Rhamilton�.${\��H }� $ =!�, e�AzŪ"O.iBFU $E_0�E$@�$EcS2iY!�assume"{0} �}_ � =-(ge� z,0|+g_{02}^{* �2|) 4E}A� \cos u� 0} t D1 D1D1 D1\�D2}�P.D 1} t�z6��"0]� . -�E}IU�.>A�M_ . HH w�e�"� elecWn *e� arl9 larized ab \X$x$-axis; $g_{ij}=g_{ji%? =e\&M�. U�3A�I�� j 8 at>"$:�0)�61  � ,2 ,-]X�=E E��def$`y.Se. With Os9�l.7��re�9as�G�6��5����1�.�+)6/2N/%V/4>^Ew /�X�P2}}{3}.5��)�0*}�V*�1إ�>��.&F�&n�.$$ U'ly#���nt �igy $(B� )/3$Sign� . m.c0�ˁ� 12}(��21��l 0 0reo numbetb\XYQ�Y�� &&=-�81}6 1}t Qy�+0:+0}t:* 0)} �0Z4�u�v(t)F-+ # #2J# 1)}.�H5Le�I��� *��Hn d8%"to� eruK$rvoir)�FqijRX \Rm)mI}_{Ek S!=�!B�S2%�,u 752 �bD0c .E$� !�>�cri^ i�3 e4})�:15V7"I ��  u�I}$E3Nh���q1�.�Y �55�.0�G.� )�.�� heat bat,L�.�)�iyunc� osonic0 s, namelyE)�oBWe��rm-oscill�=�7nBRq� shif4to zero�2+,r27},y�1�I7!PE}=\sum\]s_{k}��\��k}a ^{\dagger ��8B(�)��on2e�.6 Bv �!�S�, 6�1}q�z�0)}� k1����� * )+NR2>R1 R27� 2R R2�?�=E'J@�mk�/A��`k�W�S the Y�c��sF�9) virt-ex�%gWf i� � the E�� : U mW�%\&-�$ transw�/s.5OՓ�J" ini�Ya���iKAdi� d, �)�^rho_{+}(0)= S �� E!H^>[ $*� �o&�.librium�U ��p+or� A�xdB�]7  de!y*� !��;�F��=\prod.m�jecQB10BR0>^ *} Za�,&=&[1-\exp(-NC Lk}}{k_{B}T})]\\ x&=&F^{-1}BEvX� M� *;  $|%�!�Boltz�(U�iT"temper�#�e�v.&gSup� �B�.�� �:lS="�!$s3} Firstt gketch�m�q6u�&�oF ory��9,r30,r3�A*J �is a �yeTM�&�G�e antaneous��P :u.� Dtur'Xo� negligs� amou�A�in \tau�D(arbitrarily�� strength.W?( $G_{B.B.}$X��p%�is&�_�:�[ &Q��|W�7j I GI?� �sf�me (of=]9�a, L G}=\{ga8\}\ eteq ��1�$k��slp� s�.ex�* $K1U 2v~oll�,n x H� �7AD��(UX�+,�g!2!�9A��"� . A�e cyc�'%�is $T_{c�eS!9rG�e2�kU�U8�g��\a | .� val $(t-t�)=N�� N|��G}|\Dwt$ m�a��@ih.dch�+te��q. .�>o�Q$,(k=0,..., � G}|-1�YI!�/!=e)<-9, $U(�)>�=0}^{ N�-1}Eo^{+}U�( � t)-e^{-i)� eff}_!�I�e�~��y �\�� 0��N.7Oty$s �iv6�mgA�approa�= $_{��1} �!+aC*= j�� H) =\Pi_{ G}}( H}���� $^#"�loorY uponaO"�6o�#ip^��A�&�=pr)tie30}& =num��e�m \12�6ng.9i[�!r�" r $Z �G})$: GA6{XDUEnd $!�S}^{s6/})|[X,E!]=0,\fo�? k\}$;���tity:$\RV:o?2u\OIt )+:{I_&Qr�EF*1j _{SE]�=FFmHf�f!K pert�U�2�o�D "�}�� $[~A�, G!@$, 1 is�l�%� ompo_p�un ���ncJ6 u b>�� tFYe��.s(d� by]A�yo: �,invari��h��jGE��fil�#d�?/ �'s|�-nb[)�=!.�<\ findQeL/ m3! .5��11�*����2 �%��*�%�jі��UG��0%�!�Vn�/U_��design*}�s�"i� �6� %�={S^��y�t�"Q]G< W v�':��XY&Bte-Ls . ry Eq.S94F��ve8@n�^ri4a#�b 3 I,h�2�lA�ereB� I=R(  {ccc}1&0&Ã&1 0&13 #ɴ), hfF0&0&i\\-Ni&0ZG2rGB\\O-Pi��6�\ e1&G!@th:E atis���[�8��%F�� 1�(\.�%^"�F"!'��R'2})�N�6}��.�1�j�1)x.q:x1)�� '�"�1F��x very�Qe��t j��'ba�*�d%��J�&����)o�&:>�%bf�U�E�0V�bA�iA�eZ�=�i)� \pi}a�M,x 1)})�& 0)})Y�,A�5�I9 �-h�!f�adm�^kb!=_ GB�2�)#-r$�%$v'!KY�F}9%�se cS,+A�>mmedi(o͈� H/al re. E��#M�]�=&wo `Q%a/�in ��5})�0� prx.$![�, *� %�*a :<�. o#.�".�/:,, $eI� �ɵ�:�-V � l�Ma $\pi$-S& ��y �! � $�=d ���� hanvG >K5%2K�s�2� YHrly. W����f*�{!��+d &5E{(�#2J� k2���e� .�)/ :7.1an  "Hycf�-)F&+\{%���.�2 ݈� as 2�% �%2}�:$5::$2::$A2�iq4nc'��s >r �B� �)E �(� !'EdQ]e�vAX e h"�NK K]e2K 0}$;I�y �upfE�$-aF$ dow�'�{abel{f#"�$Fi�M-&,� �Hiu ";=M �0}+  I'�.$�\leq �#eq t_{P��"" #+ t $;a��>-$U�I�e�1i��)ied; �}$2�h$@�} Q�%�A�switchO ff;!�`� i+Tve0by� ��+s ��2�" �2�> n ��%� widՓf Usub �� }j 3 e�A�� %�:b�s-Hy�=��� -^Ey� i1�2)19}$&81��|R�%�=��$.����.Q��ly>�$ >�2)}+4Q !� %�!�%�31�!� 0}+35�. �D2�3����)�Eq)B.X['�qs�!mplet��%�. BY-a~/u��Al6�s,"�V7 .7�nl0 ��F��\��0F$JG $.E�,���non �Xi*�4�4�Z qR �s$!�2�anG� remo�ZQ q�!`^G Z 2�G2N���!�b: (actly fulfi\ inptym�is9 w llz6I$ve analysi�W�� �]eP -&(�s �z2YQmioZ�&p�.)t ��.ed�%�i �picture.�-�X^+&�S:`�nm�!��}.�  /B $� Q^t) F ��{H}�$!ld*��} \tilde�.�� � X�i!1}tF� 2# )\noh"��� 2�2�F*� 6�#), @2& --/%����ary���6A�!�a�2x.�$K-xU}(),t� ^{ �&"}.�1}[a_z!��2�1}\ }\xi'"�-h.c.]}.n\�s A`^�1)J�2 �!V�2�22��&% � } jq."�5=��� t)&=&)82V()IY! }(1-2�1} 8 t6r W ��BW2�1E��"BW2W.5\N&p' D9J� &�6��& �1}=%�+���p�H�=te�� paga+��*��1L&�5]�U�� Q�)=.4}%f"� <,< 3��hUV3; _{P2Iz| 6I2:I16;�;y�,&�,2F�:�Ep>�"�%�1�)�2�2�� )}�I�b�a0&��ZMUS*A%sr��0)z)>vyxrw�]ũ HB�)X.� e2&�q�and�Pwise,Y� ѵ%�2}��A7�.�!�Zv/.m:�~@i 9 :$^d4F�>CaS d2� �R..} &|-S$ Substitu� Eqs.(�e13}, 4})eo� 27}�_e ]B�9�)~~l A.������.hz��)�.!.�� ��a�?b��INI2� 1��%�z� �+6�J�� _ �6�* >V�����>�J�2�2R�2��iI!c��40e�1}� 2v&O-�vI��9 K� " �p��lh�e��_U g.2{fw-� EA� �N$*5 ��;*��N)�0},..ON:�N-1lN})...2C�� 2��.^� S ,�Z�'$t_n=t_0+3n� (n=1�N�+!$e��" � $n$-thF�� �Eq��8}�0m7 eful.7�arCk atj�� ^{!.��b�f(n,N,un/�� iZ1t&vYA�-V] mL6��] ��2�*�  2�.�R�W6�.�� t~��p���g:�2},:"� ^z�ZX��R�2�4R�RP!F�����iN �+"�}.� &g2�'� $.�-� 8.�n=� N�3i(n-1)�< I' t}.$�fwd g�_�]c y!s�e2-$rate accor�,tM1����.DyKdiago�56�<s�reJCdev1 ' wt:K%r "r��Ec*?he"�@+B ��"9>3��J)*"�130"� �1�7�S}(� {\rm Tr} h)\{\<0|2��) A^<0"3�&C � @e�3}  =�� :� 0)TrH�[ K $k3�\{2?kFd52�"Se�2�| t)+6IF[52I" I��  \�] � -i3NI� Q�\}vr=-\�w ( k1yMk2\e7G#QV8$�n( .S.F�6fd|-.I|HQ��coth( )��2TM-q� t q >� Hq.qvq�q0$$$>����41�.�y-L�6� t)(2V� t}>�fK.a���z�v0(1+2���2:��=zy�" h���:�yA"�&*&K2*:�e� _m�W�t��7e^{{J5�I� ^{'}6�.UQ t).�3F�DŞ�G��6^i&i&bQ&NY:v��A�8N>&=&^� tJI ,i��A�",� 6�q� t^�2u��2}��q��6>F�U��.'�/� �U*LE�r��5aM�coffq~p�:.�-"E#c}$-7 6,r3)7@j"�jP9�2B�%�5�Wnee�m=�0"reciabl�9";-&Htau@=�3�8$, so�!c�*m #c #�5OEshortest �%d (c�emory)�l��/9kͬ8 t\in[0,\arccos��3}{4})]1"Qn�atu( kY�� 2O  ��R�w  quiefvgimp3Dz5H)!c}N�$!��%llEO�&"&%*�.�T*}�W�� s monoton�8 ��%V $�$>5"*�  0(J� ��#�8!��Gs�?��6�-. ToA�q�we@er�`ly2(u3m�!� &N fact�h9�+�EJ�inuum� I�=a-"v(se�r�*�_ =v ( l . int"�<2+D6}di  I( )� Z8 t:� ) =}���E��* $bu67�a = ^{n. - /  _{c}a�$ 3$A�sur�o�:q�L$-%>* Ba�in�9$n$�TLks&M.�at� havi�����;ce,JOh9Z�*�?c:$n��K,�NJ) W�se��%�?i�A[$N$�xsl�`ny") m�"s*7* 3"l,�Q�sY�}#>�)��c+[F�_[w�&=j#N3:�)D&�Zm�!I�A��f"�)S"@Zal��R�ow-*Y>=I^ ]9 {T}=100$.�KMA=0.25$U��x Zim�Va�i�*=%�a �!a�@ , $N�_{max�9%JMsum�(b/<f=�a�ro�`� $ ==30$�&�Nc}t=10$.�f�/5�� " *"�%Summart\js6u%E5pao\�W)Zi�8+6w?"�,2|&��t:�� *hP2�O �."� %"T4ETGlsm�l>EA. )2862R��V$I. Cirac e�.-z�G27f 1207RC6}�0M���d�mC. Guo I�G t. 7��53!�7:�(7} S. Lloyd%& Sl�X8e Jean-JacquesEB[-180}, 408I!8:\8}!�Zanardi^$M. RasettiR2=� 3306Er>�9f�R�A" 2399%J:MXI*Ip�$Y. YamamotFN%�2}, 3489�:�X��N1Y�s �A*��273Il:;2� D' H�G, V�o$otopopescuhR. Perezq#J.)��7 6}, ���7}%23E�Los�bD.!�$DiVincenzo�k�,d�� /0304118 2�24}�. FeynmM�AiHibbs, SiM�s 8%"Path IntHm,ls (McGraw-H�/NY, 196>f5��O. ��ir)lA.�Legget�J3-4�e2� 19816�26^JA� KSQakravaDA. � orsey �o F�q�W. Zwer���#YtMod6�5e�AJ87)2�i�Sw��CB�5��587?726�2xY}�tt1A 2E�7C9Vt.ik:�I�-GA 6A_012307Ea26L30e� Dq %"" �Ph Z�V `83�\8�\:�31.\P]j.�Re�u^a�241R�3�[U*�cX J.S.�cZm� U17!�453E�82� 33} 2T E High� o%NMRk S : s: SX[H3Avera)d} (&tres*�r)y76;a�R�en�t G. Bodenhr�n�<v kau�Pr��3NdMad Retac�2�o� Two Dimen�% Oxford*�m'hs, �96 034} D.G. CoreO��ri�c.F!�v#Q, sica-qD�) }, 8�p8);M�_Fortschrm~ 48, 875E��u]�35YW�FL6�A eE�� �_���>�r�d"�p�B�p pra,�pt"�p�i]Vpto"�p*�p2�p bm} gr�j and{\beq}g.���r$e$�"}A:" beqaGS>%e % HV#Hket} [1] {\vert #1 &cqne�bra)lasq+4>�raU[2]�q* | #2ZZC� }[1]X�#1}l:Y mean (�"r.�mod}{~R!� }~} �8�9��qEconom� ; um/vi�jy dqU!�� or{Thomas��qffiliP,{TONA-TENA F� &�oYpBrussels, Pleinlaan 2, B-1050� BelgiuA< rLJarom\'{\i}r Fiur{\'Av s}ek:�Y&��;,�a! satz!gen3��:Ws��+>�N6�� �ly Se �l�<:+&���G<�ed=�ly oَin�5 $d=2 T ��a �>YnPP�� ev��ce up� $d=7$. AnkZ�o�n nlothen b�"Hp� $d>2�B lbei�ED��| fideE� v"G-$%uer {si�)�E�. Fi'�,�FJ�2�!b�]M /-!� �a2�YZ%�Fourie�o.�er�"O �lyf��ut���a�<�itsQ �F!�,\@Di�le��J�C��sO�s-a�u\m� itl.�sIn��<%"�8A��>d�n, mj� promNg� ø���*��Wi!�e frame�n��.jp�U,T@�E$.�s>#singi�� >telـ)m w"i�@lFa*x�F %"Zq,RMP,Cummins,@8,du,Gulde}. Alt�.I?cer��whe�[�qse PBatw>v�rs �m"ޅ pOcal�IerBqJones}"��di/��esL�ed3k*�=ryp"�ti�J��a5�*6v$�*�Gechnolog�o!na cerf�radA!;o key ������s2s2&@I-%U ɉsa�8��?err �as �� secuGT1Q+ա2{(QKD)!t�{s �BMA� BB84-n}!$guaranteS+/] no-Mf}!�*��Dieks,W�rXe�]^`" I�q cop%J (or�ing#K$e��.9conAase!�J�,ortho�,`@y�(ler�!h���Cto�J��aKx#-�p��uO�� i�(�N �Xm�]|"TBu\v{z}eQ�erQ@buzek}a&rB��%�-� p��2�"c�" -to-� ��_�"�I wa��e��M4  8�� �7�s��y���,t eavesdropp�attack"lBQKDU<�J�!�ext�C!�r]�4�y �d>��!� ���[A�%yA��� spac]�B.V�� }S2� cop�J!^mu�al�F biasaaww5a^٠ '0bourennane},  eR2� i&o� �%al��C�ed:�h/�(%��D-' � NG,b� ,��durtg��p,Fan02,fan,Rezakhani03,kwek,L_^reux04}.�J9��" �1:� er�!D"i ��is y�nA� ����da*ous:o�7�!􁚕��icU�� �*Æw0�<>j kuIyr�Gųiv� pl|�e sl�r� reUm#1Ek�)o }\6-2�%�6 ,bechQa-%�}�sa�I+ #t�W� shA����te� ��:Q�� E��buc��C�E���� >ucenario,�n��� d�legit�'�ib�=i,-�X!�ep,�!��LerX $1*�'/۩oyXE� qud ��typ.ly7H&9e�_&��&Y"o)P�0 �0�O�" W ---�inp��a��nk�K � N dzN�$  �Xi��ntly a.P��q+&b �len k u� ���� becoz<m&a�m ��ea3Eto2�"�*�Y� ,& �b$B:#m��b� !��"�  ��xneg��"s� may drasҊl�A�%ee�IY� � , 76H�|�$�s!o ``&�''a�a��8R�as|)�-�> {�M�Iz�2*F�cAGx�E�O:� E2e�A�blQ7g� ��B�sly mu��{ �a A !�wQ � es 'M�!�W� gata�u�q���&�|�&�.� ���A�FBZly  tוlik��to!u��2eno��{*h �n a�}V$i�Z�A��0+)t ��;e(M&rU�6� �SAmo �~�!~ $igh��2$5���7��6�.�ٚI B(? [er0n Niu%Gr� th�}V "cE \\.C1%�5 Ccos\a��\,B& +�qn6&� �1E"�|NG �� eqa �[ᕡ����� �w�IB�ar=.or�%bGq*p�A� ={1\�S \s�� �8(� ��5phi ��B}S�eqe�^� of!�'�Eve'si s �))� F_B9bra=�� {TrE�(\rho)�u= ={1+9m �2y�M!�F_E:[E}[BJ[E [s1�[ H/�=|\PhiEl��|$e�$)=I�6�!cE}$��se.Edo�<�ݰzimutha]gl�\phi$," �t-��(��xl�h:�  � AcasKE�=\pi/4�"ʜ��}s:� ic :O rL { s�L s �A�l�4y $F_B=F_E=(2+M~)/4$I0.85$�� %In orq�to��} k� , Ali,�ndA|�`l� ��sh! ,%Y.���di %��B_{0,0�PA,B51� _woWm}�Q sp� herm�4at %random %ei� a0k $X$� Y$. %*v� NG�po m�p3�͏:aQ %] �t� 6�^Z_ �*replac��i"& A#�%>1��kd!k�3-�V ) (r �)� [Bob Ev�d}� )� %b �e�� on %��!Q�\Psi}^��(,E}$: %\beqe=F6� %�7�0)} }� � E}+/1 / %0 :0)br0 SABE}+��11 +Mki} % ]x!� BE})�0NG}��aI��w� ema�iz!��?@�a�P *��a ���|'IVA�is Ɂor�`"�:  � extrA� (1�� B� 6 MxA���H"� a�al, ne&arw��� ient, cri�lo�<� �* * iAZ�duc*�M���/to j�� &a��wna"chaB��i�@ J FB%� {���2�.: � B� � goal�l!�)�%|o fur�~Q6,ş�Mnv�Bg�AS �dit�` ���soe�>d1�S s. g�1��IaimZelucie�ng�c���%^n .-o`!��o��G~.�pr� no-geCAs�&�@:�99 L �8at�� v��,A � �J֜t6��(K�rm��)��! -<� �"�!m (S�on II)-�A�6;"�)�>��>t ers u�)s��xs $d>22{I� isB��a r��r��h���6S�vmade �f plau)F�p*check:s!� ide- �, |wA��i2%u�<=�^�)g�"�|�mh!'� y a*�5Gpe��as| a� r�I�*E�=�V)iJoveI�^ �t��e�%E the mQX2�ZvJB� i���� Q� C�6!V)��ms�r<s6J�y5gg!�� Niu-G"�>�i�er � NG"�5s �=@��*�uni��am�!$~�� & 8+$F�!s} �.a�b #A��A�(an isomorph����comB=�YWmaps $\ �cal{SC` semi"ui�x�sS \geq�rmjtg��ng����� out 2�s�9w�p rm{in}�p�t�.!out}}$ )�Jamiol�5$72,Choi75}I)ni�a Jy I��.c�^{\�q �<2;( d ^+� =1}��{d}�M_{j�I d |j )BO �+*(ua0"�yd=1dim}( !�>�)� !��!�T pp�c���l % $�"` nothA5hap(�� *10�n((g$� m|;)"�@ ��Q}c� 9c�A�"�Y� �p S3} S= �IE�1�S}_2 (d 6� ^+|&/C1]�pre�or���6Rn{ lipurposWA�Gce@s�� map kn��!d"�9F2�rm{g E�4 [S]=\openone_A�. - trac>�r�"nd9@�CP�0IeIPACS� i)�`| &s�"^�$S$�Sm)asek019@����e �)�>�[6/^T 5�BP S]^�@T$�Got�eLk���!��:�$.�\$���CST�,b V^� o&� of�iONA� endokl :SL&uesyS.%9�Bq9Eo!�H}_E$a� !�cript6��!� � s (-7R�$c*�#� eyE�+�4user's (Bob's)� e �py� ).�. ea�?"ָ��r$|��`�E�#�� "< �eM��%Mҽ��- F�(]�G%CI�Y�I�U�ps�1z U�E S),6�F_{E}(L\psi)&=&\mathrm{Tr}(_{din}}^T\otimes \openone_{B}�psi_E S), \label{FBEpsi} \end{eqnarray} where $Z$ 1@s the input and $S\equiv | rangle\l 8|$ is a short h7�enotation for a density matrix of a pure state. We are usually interested in the average performance of��cloning machine, which can be quantified by0l mean fidelities, \begin{equ�0} F_B =\int_{�} F_B%�) d,, \qquad F_E>)E2)5�AB5�fw%�!nmeasu!�^($ determine)� kind!3+:� s we!: deal!8with. UniversalF0Hcorrespond to choos8{to be j invariant�o)�Lfactor space $SU(d)/0-1)$ induced )l Haar!q� @group 9$. The=� (\ref{!0)�, linear funcAPs1 opera�$S$R� {B}=Q�Tr}[SR]1� F_{E:" R_E],q+F�Ppositive semidefinite�s $R_j$�given byF\�2]AR>� 2�Bq�E d9, M�R �]�vXI\�< X.Q�RBE �ionB�In case�u>t,E�0integral overUgm�Deasily calculated A�8 help!�8Schur's lemma, �\we get,�[ inst� ]��*} � �{B} �X&=& \frac{2}{d(d+1)}(\P6�(,B}^{+})^{T6�} \\ ��B1B[5s2�-�$B}+d\, \PhqQ�� z].Q��$Here, $\Pi��Hnotes�l rojee�Donto symmetric subi�G1}B �4www} F \leq d ��U�1{IɃ�tљx�phase-coѼ<$1\rightarrow 2$Q8 .s� sidered i ^�nt pa!vE�%{�satur�� if���;�=\sqrt{�2 d}{2�P} (�{B}�" E} +6E�6B�� �rtildeB�� >3Ita� clear tha� support�O(any admissi��ѤњCP ma� $ must� AWAs]1A(ceQ.%]n $f]��� will`exploit��w�follows!� prov�u at i�not� � to implema����ft ��in��Deconomic way, i.e.Evo5 �, j�y applyaF (randomlyM�probabil$p_l$) aa�-��� tary>�$U_l$��origina�e�Da blank copy. If��(convex mixto �e eies9s1� Zce+iz� Syᵅ�n, uity, �sun � �ik%Z sens)� it yieldlal� k . Coɾ onA�ch`Ee:���S_U$ r�� nts .�, sin� %� btai��5�$U%�.9��{+}�� � quesIA�us whe��exist� %�F� |S_U QD=\sum_{k=1}^dc_{k}f!# ѧs!"e��=V�S_U|$��isfAActB � . Afte�seZ algebraEAO  $�4Tr}_{BE}[S_U]=R�}$ turu: be �ale�oF9�y� +1} .;|)<^2"  +2. -H,l} c_k c_l^\ast |l-�14k| �B� ��9/is6�%ar�r�|�jrank-A�"�  $|c^{�Q]��pro��io���ident�gq, i�is��wmpo��ny*� $d \geq 2E�6onclud� ur pro�P �&� B� �<*�i�| |��\se�{P:� ��� 0} Let us now�afgat�De�ީ_�e.~E����of >> >n��Ey�,well all bal�d�$er� � compu hal bas?��[ .Y= U�;dSe�je�8 e^{i\phi_j} |jM� . \]g � proce�imila!�as befor�!first&g a�Q$s $R_B^{pcR_E [� /4superscript pc�icates��s�� S re�A�Zd� .A� in Eq.n 6�)A2Q�� Vs�!$��  to e!Q fl�."C\prod_1jB 0}^{2\pi}-�d-}>��� ^� B6}  b �; + k��^2}V � (B \nonumber�&-UKF.E(|jQ;�E jj|)b� ��5,In ord_ o:L" �ki���&: llm�lezk s $SU~&F"#Eum7 !�e i�U� $RFy +Q��A�J6 *� ��>5} Z2� ^2} 5�2\�B>E:� &ٖ 2d}\left(�B V�� _E +B,E}Eo -�Q6)B� YS2�]T{ �[�[>E +�CEBCB �%.\�I�} Z�"��Iper'MQ�'QQ�e�mak�^ ansatz �B��]DDM�$�K2�0F�b{zzzJ{E�;&�alpha(�aB.J+�32}() +\beta|kk�2�,BEQi{rmaxpc����yy� �� �}{z}=M��<{4}(d+2+  ^2+4d-4})"�% �J����verify��F�6y� indeed an]2i� e* .���sa� (d. However,! is m� m��J icul &� (A\Y�� �est �8�� �Z� �-��R\emph{�} ^s_uF�. While� �been �to�(is analyticj aSarbitr$di|��4 checked numer /�}�` )��>L$d=2,3&7�a�on.$Dho�7any $Tp A{ =p$$d>;Rhdesig�(*� ~{ �/doe� t2 �n.�� a   w\v �rbe�� F[|�u] 2s 8 Bu6�"�Spc@VMJ�� �I�afeJzB+F] ). O? s��ng>�i�igR�)A�9�2� �(6)K )>(|)&=&2d^{-1�)k |c_k:sgamma�}""�Tk|:�&+2.^��j \neq k�j�&/ V,6W:# \[ �=�f^2�4�}}�t 2  �� e�2 $istinguish�e�s. If $ k0$�cE�J ��e�beMSi�sety $c_kdif $k)/l� $c_l�d/2}$e�some $l  \{\( ,d\}$. Fro�%�UweMC $)/%$=-͇}(4\pm 2 $2})/4.$ By*arA���exa8w& 6#pan �!����y,�v�$teger solux �$.� � part�Var%��H &�"� de(b'&|0Niu-Griffiths� &�"z�̡Vqubits^NG}Ů ,Accord�1/s..i�NG�},b!S3[>�|0��2�}|0B�iz1Q�2}}|1R:(|0+|1F)�eFo �/�f�vmI�0E�ſ��^�t[ impl�A� cq�<= C \delta_{jk}$� $C>0�E�co� nt. J�is lat�'raint Ք 5%yUL , heGw�. �!��#�&�m��8. Strictly spea�, our�of )M� q=�� 7� �we25� �*%�the2�IKB co�$&� e�� al Jg of" , h� wea�e � itM!/�%32 Subx9F>L��mL6S�!~@Cy�5can� lizede\�&�,�can askzi�b` /al=roxim�-! �e�� .e.m0� 5H%Hilbert;ce!Q two 8s0 *�'.,_ ��%�um�"Z�AJ� lism��F�i���eny��A �or >o��p���ies: AB}[Z�b(S!-Y�!�0t$"A��e�n�l}�s -v�AK�M. FS�(llE �iHit�"be &Z'��* #swapp^� won�A�� $�E�� e)/out�)B!z"#b�"�>$ uUD*�* s $|kl���f$fa�2 =(|k,+|l)/��$,*{A�d $|kk_=|"J$#saMd!�@A�51�sh� be�Q "", a\���. f�a�"{ �+ shifta�l�0��:+�,~w !Cin�)e @ @ !9�. Mathe�#� azp �Q� ed!{B�*[V6�(\bm{�})9 V�^{\daggeo,#\� V�J ]}�="�} " %.1�ceJ� ��$����'t*,� V�= � F&�2� ] �-�2k$1U5�. .���� "� ���)!�ei0 $|S_{Uy.  ��M(a��Rs9�w =W&=&" 6�|lm}:_� "�*� N m6� [2mm]�d.�Zd6^:Y2�s�:�2Kj. "�>� J� 5 �%y9�1�)�a���, third�>on,N viz'�h $s_kI�$ \theta_k}���>1؁�es*-�ap��&&,[2U(Y(d-1+|--)�l}E�u�2} �l}|^2) A�k )dq� (� �}2%$.j)�f�!af� 6��k~'>�O ��M���� I0lso�#��1�� 6�[ UB�a�'6A,!�F�,d,\}�{u�ō�6� "z! ds��F_U*�' !�[!�%���)^2�] &�FourierJr *� AlthoughBi�always�y@ y2(or2� A� cer�!E��idE�m.+I�q01� (like Bob%�Eve's1 ies)!# edu�d guess�often_X$. � iT ce,���� show*�verwhelm �jor�f � al 1�2F��P b�Eun"�)liter� �ey4inprep}%�� �in Refs.\CERFPRL, }. AW���A����a��,��� B 2b#ra�(4$&e �$>=(8� ��v� � ly G]$Aa� $;( $M� = "�# Alice's S anD)�llyJ�!e $in�1tr��&*+vious � , $B� E*\$AD'i�EF }s&�� �,M6� exter!ab+. MoreA06|� !sassumej(be biorthog!2 �B� basesw{!c$d^2$ � "R+*1g ��s:�qV(R`} \ket{B_{m,n}}_{1,2}={1\��d}{k=Sd--2^{kn}@k: +m}_{Ieeq��m,n�,0,1,...,d-1\I K�� �$-th roo�(� y,�$jjj (2)}.s��Ey �/1$ ($2$)74sebjcoB�!~ yh+bI]nt46d5\ndE{ �,!�nP  "of�%�22)B� �,M|� Beca�-! q�%�A%.Q�!�Qi�U.k2�626��M 8\Psi}_{A,B,E,M}� m,n9�aI.%�Y:A,B-ENB�u�`}�1 $ D%�a ()C�) �$,8d$ {7D pecif�"�19i a<t�$[i�1M6�. �F s�al exO es. 6�1&%(g�-�|a")eͦ is �"Z6�*�wc� �/u�k} a^U)k =x_1 m,0} n,0}+x_3 em. {\em&�}�>�+!er (the������" � al, �1_,insS�� Bo�5.5�l��6P!�) c�7@ $x_1^2=x_3^2=d/[}-]$�cop%e e"�0m"�7�5w�c��eSv5dari�ula���of=+)s _3(buzek98,wer��e�m $F=(3+d)�1+d�I=T m n �er�%"ly �&Z mut�& unbiased G� (��-�u9'orF6 0a�:px �*�&�I� m� squa^2U�G'e��6�T-y�0?=*s far�$w� n� know��mo�&4angerous attacv%� BB84� *Ekert' }� tocol�quiresA_Af�!�DofY)�.o �(ess�woUer|(ng m�iz��s!ir&�: (a)�%�: er� (b #V) er. Fa�ZF!�al<2yb�E pr� �;��l�%�QKa%��( %�a"tc$��(�(_�"R�!|�1gcribed (��"� 9�)AzRef.~i�kwek} (�a˵�E�inMPfancr1Q8j�2 g2g=�5%�cov�� {PC}��{1��J�{22+x_{3B#� xL" x7&1�;rea�'�;param�=sE�� itutA�he:x curry�n y�:  >ofu�pri��)A�A�^�i�G-�8j��恭��discrete[���%�015\9(bourennane}�  �)d2� g������� �r�( character� �f �naglerk%bVt-\ cov'AwF_� �t (3A�+ @)I�ZA>Ap1օ%!��)"�8��6� q� � %�37$��Ah%\sub��{&�iing} %< G@,�p[ W:�1 � legi�;tz,e�1�[K&e{MA�^ pB����7�yq5 , so��say�aq$"rE�a�s.��<�mak�8��("jCone/�4 :B aT&ib-f�A$l&��:$A��4n $p_{l�v[CF-� ary�;n&Ks $U^l"at act� *y only)Ja�fzlowcost-l} S_{AB6A _{M}� ^{opt*� "�j-� l=1...>�} �~+^{lE}'e�D� ��p=|d�|��,$hB$hi|$ � �D-2�D� r6�Dc�1f*�!=Nm) :4YE��}.� ={1 � \9 d J�:�A}1�@/{0PE�60A��� equeh �Zc�6CE�ve>E.� �Ping, �)CP �$M*N�6� @n�@M�:!�@�@A }^l��M}���6it � i_7� ��k�1�31�$oci�=��D. se( fulfI9%2�� �*�;ы^$> 6� |r_pM�$= _M\bra{p�&.�>B^^apR�2 :3F& �� �$|\xi� B�*%�6m0.x@��  &�> $R$ appear z{.@>� , $F2WAR S�� ]$. & b��%1� �x�t�A6�")E(%��"F�. Our�ul�!9ie"[ _ ve����O""ru5 rA�"�Cu>JE�@!-#�� ? :��M�$ $d=2&�+.:w6nn�+~[��foreS%�er*r ., If*Wu�1�is�PA!*�+%39A uctp&�'!⡀mkr�e~Ir�b Eqs.�:�)��6i}) a�?ne(ombin��oM6$,p"����ea4�e ��% $d >-6�;)�^l$ (�� $"F |.'|^2=1$)��F�V�i} ��= �m,n,j��j+m}^l �� �4^{n(k-j)} |k+m5�B}|j 16�A�$l&�F/!fE�s;�/:�i!�r�-necessd "�E��%��I� &� /n�. @��=�'��~�5l2�>eJ[R� �%�pa�pAp��. %M�&�'�?�sitc " �"st):d %G a>�Ia�F� m,�AQ*�3)LZ��r �:>}� eP�LFK�+~i��� �"W� ���� �!��)s�A$whole clas���a�� W9 ��p�-*� al� B� 7ersIts��92"%���"�,�"�a�J0 \@�!�s� %G-F:40A7NB icita �)�-)Z- �1�&>iq0Eqf|���@�F �"U�r ��j,mF�m+j}[��d  j,k}&^"\\ � 2}(d!5 - +1)]� m+� � V� . �d"��n!�� (orii�?l7 c=&yI)vt�@1�" })) �(� ���C��u�f� uni} �%� $k^\prime} EN"y )^+|��"a- k,k'��}} p8$k=k'P� ����nd �Eget aLAs�0HAJ��;�jk2@f_d(x_1,x_2,x_3)+�1kg:=1TOuad \fo�&k"�&diaKB��f_� $g /�Hd)< polyV#al $x_j$J�f_d&=&�(+dx_2^2+d^2�$+2x_1x_2+2x_36�g:(�72d) ;*31x_3+2N>.6?\�Q�I�J�con%Ka� �($S&5�1�5�i�9�W&&(�^F�)4jN {j+k-k'}�3y�|&&-$(� {23+ '-k}S)1&3{ &kv=06xm�offB�N�*��V��a���i��� m�AO+g_d/d=1� virt�=�O~), eid s�(E /d$, $U�$�A� =0.$l B�0�n O�?#'��nor b�KF����� i0? ��! #= ha.w&.6,R�� !S����& (a priori un4n*� *Y &�Iequal.�.�?en�T��G��B("K � .=�ˡ�l .$)|is worthA 1 I20 � ��Auco'6%�^*_{i8 R _{j)�d��  $;e!�%(�%y $i-j=a4"n�%if� !X1 7 $k'=k-m��q�2��then sum�+ $m=0, \c�L d-1�:��b&��s� �+>��*{jq�.+m�( j�W mC)0r4�1ie � B�� Y�and/or  & Q��f !� � z���$. >� �aFyUhV8_i�!eJ���3ŋn2"4C"%2V9G�7%/�%4e���"!C �Dol�7e�6&�$ofe�A� s: %-xl" ia+kO-l ��  = A���\not= k"�Koge�`� %$("y-kw+-1/d)=0&8=0...A�A8�� {2}^1u�2� -2k}էk-2��* �_{��) %��{1}� -� H'� -k})�� ��!-��Yʩz,�2�9�?1�;;0�`R*Ono"�6�  1�f�ny$2I W� �_�qc^R,�N1*�:how� �?�&7b7:extra inYE ab�|,�=s#N�d5�J�!��r�G��5G#1{w]��zj�Pbn obe�hL}�$�mqG()�!֕7� &=&A�n*�F /_��+�5 � i�" �W(3�!�i�� /A��x!is �q� ��in&� �!�o�N�(�#)� &3Mand1;A�&�a+,��66�;&� 8 � h"QKio�%�#B  (V��z!���J)�'*�u.  wai"ud� !' etaiL�reYUc�W:e. � !�0V��2-k ,A� t^gu=in!��Q2$*� )�C���aN��_kQ�{+ �mQ� {k-m�4ast�D = >"�Dfu/�:U�ѢI� B nienLD�i�I�� ,�Ũ $\tVT�E _j=\�H ��K$|>&|� " m=1$l 5  fP?E"V B�% re~"c��>� {k+1!6� k^2 : {k-1)-$. Wiw0 t lo�!t�3n�B�0��M�QE^>�j5 term��BD1$�& s:B>,{2n}=(-1)^n :�1^ɺ>u{2n! j9+1��Sub� ngA�s�<re�@�aA� � >n*� *�h< 2$ l�XtoF^�ѝcontradi� z �I�6�1ET�>F<27EU��caB1avo�4b<-$m=� modulo� �eime ^2�)treat�����N4 er (�jA"��8[ ll) !h�T mB�O�2%:^BoW:y�er��%us)�KSgQ$ II, excep�<x p &r��is@ ent:��!LM s \A��&��|�ii}� �HY ea�3 deri�Wa���D!d�o!��060&92"� �  (g_d-2^2)=1, " "� ,2`%(I�d |I *J)=1 ;\,ZF&& =3��� �=0;B�ql)&Xd<&" � yy�!�� {k}=\ B�T_0G%R@� � 1�@ 1^2+�5���kisd>B�e�,�)&�Au"�Tx 3x (�+� 3})2 $�5"f ѤE!1 Yu� .T>�%�%�.x'=1$� �& ��rA��.B� u{�5tsbD .�u��L"D !�& 2. NoX& �@wU%��)$a strong e�9�M\ sibi�2�&�)f<:���i�_y f�e��G�2L agree���st�C ��.� IIIB, Ws 3} 7 �% �72(FS� N��u����) �s�%C6�,�� 6s-�:k b  , bu�i�e�i� n('�ANjal!?up�a�)ngw4�(�9 to a; be�h-�$x$��e�+"1W�'l]�CI0Y �ae�� focused ob e-to-�.q%�� J6-s,yI.H!�A�n�TqVtw�M!�\���a ouE0:b&`S, establishedA�e�\of no-gd@orems f]�a�%#)+ m beA�firm (>� ), sO�+�"�]o�M�m�f Nte�k.]: (EZ};�M �ers). %"�:�E�i,@3*$ ���� % WZ��B>>� C�}�2A~7,�h%Corbids uU��i�  %�*� asB@V��>'1 , %oL#T-VB��Uw:sP $i7ivelEmC %plau� argu��1%I� 3e�if*�it�N�+FD oo %{Q work!-9*�P,�-b�s[R�-" %A��d$AxpdW3yet. �����approach&fig�P�grit/,sa%��my��it seem?%/ oA��E�=n52R[.�m/�l $1��2 ��(�%�ver�4ada� � -� non- m}.�En. N�" theless, �gE able6�!validR" �6� �aX ORpenU]� �5XV�!p���%I �)"�T"Ou&H'��,gg technolog�F$llenge. AnŢ(� �b1 cour4c.�da sub-1�~,er,�|� S� IV�- result�%l� weak�6T@q"]*� �$F�Au limi6aaS>g i�:�,��f �Eers tend�R �!�1/2, K�wf�$'s:%oseq.nA�replac~: noisP.�e1/2E,direc�oto�Z,�enlqtB! � turbaW�le6� Cise��/ra�trivial)\,J$ �EC�1� ;eme�pheap!Ca fut�U��%�U}H_�8Votudy %" XI�o6�*p N%�� Ire!:�E� s.�� drastica�A3n T� as:tCEh"a�%�  �A$�F�5<123,12N,buscemi-�p} ��f2,. \bigskip :!�2nt {\it� $ added:} A� aw!b� k���u �9,Yre�/e�dъlyjaX QUITitin Pavia �J�� d"ion�mhad duXa visit ��6b Janu]5 2004A�ch� ��)�^Vn��! �ac� ledg� s} SpecA�thankq lHelle Bechmann-Pasquinucci (�,�u��P��ohoA�p�T38�i�A�e@!�C ��xmeQa�![ o�Xsti(t�== . TDt$a PostdoctL% Fe!i r3" r0voor Wetensch� Llijke Onderzoek-Vlaa enWEsearch! �+�|!�4Belgian Office��Sc��@, T�h�d� Cul�ol Affai*�0 rame! � I�x-Yw!`At�'�Pole Pr���.�g3?n!� �?grTw V-18 F�F� � R� - Fl�s (FWO-V�*e�6er�+A �$``Photonic�Co�Cing''�N Solvay In�e�  Phys2%hemistr*I��%q"r cil (OZR)- VUB. NJC>JF Y�E@n�al1� 2!#\Communaut\'e Fran{\c c}a�?dA�lgi� .80ARC 00/05-251��PEU +p�t\s RESQ (IST-2001-37559) � CHIC.3578).�� ��t]4�)�LN00A0151 Czech Min%>EIio� ]'XA��:thebibliAEphy}{99}��F�bitem{RMP} N. Gisin, G. Ribordy, W. Tittel,%�H. Zb�q,, Rev. Mod. !�T. {\bf 74}, 145 (2002)��\b g,Cummins}H-K , C. J?\, A. Furze, N-F Soffe, Mc sca, J. Ps9AKJ-A7 }�LeCWs �(88}, 187901��tele}�IQrcikic,�de Riedm�Wn2H. 5N J (London) % 421}, 509x3!5du}J. Duɯ* l.}, ��. A F302}, 22 F%KFGumpS.  %&Riebe%�P-T LancI %a��� J. Esch� H. H\"affF.ymidt-Kal,XI. L. Chuang, R. Blatt,n�48J�%�� r@ �61n%b@cerf}F. Grosshans�0Van Assche, J��B� Br�(, N.J. CerfE6PA angi�f� 23N�W>}C.!:Benne!A�Goa�1nn��$jing�� IEEE��ns al�eAon��pur, S�x�Sig,ProX2�  Bangalo�yIndia (]\, New York, 1984) p. 175( i� Dieks}D.  Rp9Eo71 (1986oWooeY}W.K. �W.� urekV�$ 299}, 802XU��E} Buz>V.#Hille�$� }�A}i54e�44 (1996pd�b*X@ N.A!�e B"s@�jKarlss�Q!�N. ��pi�eҁL 1279Dž�;��bTG. Bj\"%��c j���hysy�5�<006R>NG}C-S.�JR.BA��]-ӥ�A60�@764!z992�bruss} DA�u�,M. Cinchettie\M. D'A�!o)�C�!(cchiavello,��2r2} 0123-&02sa�durtg�e�om�, T�rf50���_ Opt�^49} 1355�h6��(expe}J-F Du}4P. Zou,9� C-H LA� I�A. %/6 1010%ZE{9ZFGGNP}a�� ch�" R. 6{C.��8 A� re��6�6��163%C7!�w�}M�%45 2���!1062316�E�SJamiolI�72eI., Rep�+h.-�� 3�?5�76l,Choi75} M.-D$ oi, Lin�;A�u. Appl.L1��8 LA��� Fiur�1}��$\'{a}\v{s}�2&�6i �)�E� � FU3�U�� 5231��ET�T5F deep0s��w carPof.l 0!a� alis�-�"� �>�:xis",;anz B�5L�>�\e~H8Heisenberg-Weyl 0. �a��Uar� )rfo:� cycl�^kt t8>;k�'in )�9�-{V�at4�ric� &�als�{ made&L,� !+"�)I���)>o �,w* thro�Wa!�'!���Id� �Cs [}GA�iribellae�2'�v4A���4)�If�2com�p6s].�CW6]���8A�449 `6fG6� JBdFq>4A�18B; Acta oSlovaca,8��e���}gnJ�N%�6�,K 6�04232�46c <98} V. Bu\v{z}ekVM." .7.��500�[��y�Q} R.F( Q �2~�827��:C123 �� S; aunste4��"Y .�A5S� 3446h��f 12N}O~ Pv} 1։� 4230� %\%Z c-k}�CsiszQndAKo)L  TkYa��I��-��o�to2A�339�� l� isU!�i2X,f Rn�!mO�DJ'syblem}.�$401037, 1-�ajH!�yl:> Gr�nthori�0h enmec[ k }�28), eng"\l �$by H.P. Rof/ EDutton�Y@36J aB��^ �iint2T71A� 8T:>�doc� } yq\�?[aps,��pacs,�jt]{revtex4}% \usepackage{amsfonR:math}> symb6�x6�6id:epsfig6)Jsub� �set<ter{MaxM�LCols}{30} %TCIDATA{O�eFilter=3zx2.dll"Ver�,=5.00.0.2552CSTFile=-$ .cst.�+Ped=Tuesday, April 20,�17:11:563 LastRevis7hur 8 Dece 3;21:14:13;�Z2*ForMod.11b0DMKShellcA�m8les\SW\REVTeX 4E\newtheL%A�}{T  @a"��'}[ 7]{A:2Ualg�^hm.16+xio2'2# clai.#C6#o� r&'B-Mf6, >X%H6,:-rollary2,6+r�_io2�2+fTR;WDxh 2-uZ*E�Z>'ercis6( 2Pz�NL��6#�&No�6)�!YDPr�32spropo�T2P2/remarkUR 2%so-5'S6)umm6�S 'enviro��ffili� {Key Labo��Dum.�>� c��#=h China, Hefei 230026, Peopl�aRepub �*�i�?H{03.67.Hk, 42.50.Pq�b�0ct}�7I{eB# chem3&c�8*Y")��ln larg9!detun�ytoY')�mmc�!��2 ky p�s�+N�x c%�.� 2WQB@`Q@ur � quUsuc��$Q+ �$as potKc�-aVic��"S cu�W Ne�� l9� � QED&�$�&�9V\FE� Ena� play� ;&t�"�0etyof�nA4�{� � um2(��s� (QIP) 4c(�+�,�Z' B f cs aga�e lo/(hidden vari=(�y �\}%�lraokeyE&+�g`QIP i��x'%� Vg��r},!mmu�%� snielsen}�c&8'�ejE;r��(�Bore!�l � 1�lM:b!Q] F#*!6 or m� , su�!s spo!�ee�mS�d�< conv�&�^ouwme@-r},֖ ��trap �sackett�tC�Bemble9_dua�e'E| =raua (nbeutel}. A�(�qmesZ4Ca� Ԅ�t �$Q��%H ntal2�:�( long-liv&�cin�,-$Q_mv�5�hiJ miA� tool !�j{gg�e'!�p��I2j%l�) ]:3I7}9c!-.x��. q�"�df�P wo-l8-!�=+�/�$ob�Ied5N�,hay}! 9?a�dat�On�(a*ma�� bstaEx! f�.�+in �-�L!G6 E!I��2a,� decog�|�-��d\1f��. A.E^s,� � B���<)0zhejZ!�d>Op%�-asE�d&�Oa& &ev� �%!%�_o�by d�� fL8} 9���%h%� O e' 1X{9y{)<�� �!\�( rmodM�5ic popu�EEexc���< �Bv�-s#g%�l A.b�#�  (Pz&�@at�;Kh _{s}�gav3 negln)��%wordsS g6��Pkelimin�'du%!nu%!�Bs%�v!?ly-�ir�nd ��Pce9h�))j->)�Zklso�?r=3@usefu�i gredient,��Y� stru�;or,��!n idea%&5� by Plenio$KnightM&k ?(Recently, H.�Le�M� ��La��t�86Z�T in�4��y�s�tߝ~clQ�hong}%�th!?p},ŏ�)�� )qsh�tcoupl�e sona�M�wo &�6 pola?_1kE�9Sref� !,Yic\Vt!� ��D'�&reTto�4 h*u !p&u eohy(wqWtrMeX�M�1�'s�0al �h . HeH!w5~+ l �!�im�R!n� 7 e6� �rmO'l}��a"�un0N�pedI�l>�e�*d � a�+%A�m%Rwe �c7��+0toY3a�1�,]Ie .>_ !�Yboms stepA��6.�Q.A�1R/�\� n,m\ֈrU _{i}=C&( #) ��fs�D 9) ^{m�� 0 ^{n-m���D1}^{n , �e E ~ ?$6�-��,col��i�W�s $s_{k}�l k=0,�V>�!=% RMACRO{\d|J\no��t�}% %B�+ Expa�> {\disp� tyleOPN8 %End5%= �kB�j-l�5%��;4 6�;coeffi�* $R�=1Dy n!m!� ( n--� ) !�<mut2;����x GHZinM� l be� A��F�,_� ��s� ELMar�B��va i� �4A� infl"�^n�/M dur}%�s��& �� � �2\ in\ �v preci�2measu�/甉ca� o��I��� & ��� z>,� F0Pa%<� �Aor)�Z t���� $g)� rI=) $ be;:e ���F�H�� g�+ast�7 -s pass /��in�rre��` . So�Q we t���UE� �NN!̵��bimodals  ho�zi_�g. 1a�� p�p%*��em�[_< ���?�jrempe,ki � � �!sE Y� ��K  $L$ (� -cirf�� "ed)%Y�^(�%Ged� s�l�3��t�o�!� mirr!�� � e0`wo� gle- E o��DqL)LD�s$%��Jfailu��s0� &�mtri�{e �$R$�H .� ��l$ter-wave pa (QW)�-%��9�j)V5�@A�fiv�� �%f?5 depi�3Ybf �n�- $E�0I��$�R!� 1>2<2:!�� y .o:�xOom���^��1��G}2( $^{87}$Rb.�vel ��� .fB�2�F���@ >�,e�D��n/ F=2,m=-BX2� %B$:I1NI�s$$5^{2}S_{1-�;27>s>�Bv j��rD F$B�� �P �. Ag�8J.� :g\�A��*adz]>B�(=� :\�Ke�� {��z��h[L�a_{R}$���m$\pi$-����e�$laser pulsm�$varepsilon�zIu.2��re� 7%3JT�! occu�AE�.MB�^="B�\�� Rabi fz:enc8$\Omega�%~ ( t� �9 � #2 # .".\.\e�e}[ptb]7�?e,s[scale=1.0])$1.eps}\cap�{�pSz at�$et�� �u Jr� �'a�Fy:W. QWPs F�, PBS -٥� beamspl2u�!�*%�-�,'�vJ�.tq� �gy cXr�4��)���\ �%ǥ�B�\ �he hyperh� w!>�\-Ip$manifold, .�����k�X �z<:� ��2<:�KB<�� Z@�  \m_I�'K��� �O,�"\߫h.zf�NN�bbMJWe�Ds mplet/ Z]B!�%�2�:���*o� (N-n) q�wt��"FL>bE�$ .I� beyo�2a�� &�s�}()o +1E)v,z v;�eb J�V dynamicSXduUmev @v � # 6 #h�%cUR6UR}% +`_B�g�� �:Y B�"� ��+g �D2AH +H.c.5,��O�1th�M[w1 $1�e� 08[1�@.�#i�ehi[��G2 ::"QC58F�6� �)M�\mu=L,R>��fk 2�����, \mu}� g_  (��ed� �pI6b � � �(���^eY�= �/QAG R.�d���hof `��.o�� > G . E$,2, �$A6۱he�m��/jG}ŝ���C� ��-�2BlC�; wr� lV��xQ��2}Z��D�DRD-e���Del��L(�i9�}% ~�BHRBHRJHB�.q�2y�=_x!��A�$�e� �ta�Ya�e` _{e}- � Ai(�$1$WIt_���A��"+J��NG�a�\ggA\mu^{�h}B�E�]� K�mtot"� Q�3 .� �&{��s�d%꩑ %iq:&S`�ca;l� �~Ke� %X� Y0��0_A.Mc 0_{n����J�L6"_X�.sH�� ��] # .�Bq�6� �TBa�&M@� tempD � F6o $�Y$�%^!�s"Z{~2�.�F=� eNfbLvac2!f$)�:m>� e!�6=�VYY 1�% pEbPR6�EF X >�1r�:V\�SiM"�IDUp'Ag��!�&6��~AH$Q�d(n)��&M�Y3EA(�f>CT�R|�� $2&)� ��6 =�B�rT vIo!�>n� 1}<�n}� (.�9�)�J�+ � � %!�2 8N��.)� 9:�:N �2��.ZA�1B� ���^���Gn:7 E6�B4E��E�j �jU}" �i.C�byF�]*�|2� ��=cEna]&2Fp${T8+cE8:8.Y%� &%�.:.'L)� s>�"/a3NA.� Schr\"{o}p&e�p�$i\4)al_{tI� s�}�*�6�=H��%>42�.� ��bve%1�� idR{ /dtBT �� ZT��n}� c�� ,\�e\\ ��%n��� Z5R� ,�e 4th}�N@57\sܷ��� qN�.54-�T&$we utiE��Qow�$ambda_{\nu ",F� ar\nuI}� e^{-i� L}t� +�, eqs.c# 4Ig)�� &� >kd\�F 2���*� %i �0}% -i2]WF�!�]O�Nr5�-��[�H��� & Fed) ;�?R��]Fa)�Fv -i� #V�la5I|�N-.�.�5&1}�b>�F� .L�LZ� Assu9=R}=�=gT -2L}= � %r�% , R� $ .� "5�9��1ll g${M i.�*C 6�2`Bpis &�* �weeu�$���dz#biswas} r.l 3UpU � ( 5r� >~22sI�2� E� Q�J4.PV�>FO2�>1m/�29C�.�U��a��Aing|}{Y% �I^e�q��Nd+i UuS[ ]yF���i�6>�N-� �2v:�v�%�� I�.A}��( �- ��a� A>7N�� @a#�� common�W $��u�t- � o �a� ( 65��F��`N�E��� � t/2}e^��i\O�0}tA0% �4!Ucos%aUt,1 ,�Q?2I�-b ��302�1}}\sin�f n]Al��U Ni�i��EH9�a�J/ !�- �6+22�`;2 �-�>m,a��7&� > � :0}��1`n+) J, 'z+ų a1� :A3)@> vn)"]X,2}i�AhuYE}�!�+2 ` n�# NA�)-YF�a��r$n=�lnd b=�u�Za�\@refP*��.25�'& f",\�#]i_n&�Y[$n>�y�w+u�&�B(��"1-n)_1�/0Q>8Y>W��2:F 1�0IM�V2�/1/2�.6�9�M� e*�  7�$&I# aconQ�on51 M�%���6��b�:���iPN��6 "�10Ne �,Ŕ.!$"E�sA��$a�g��*s. � � ""�$o 1}$,�g�4sewm$t=t_{r�wq T$ (�@, $T$\��3i�-.%�2e�=ors)t8 Jp/*+O # �" $�YZ+ $�$�immedV��4terru�c��&��`g; jump �0�7 } $b.= ]�!>b��S "�$6�$. x�1"%�kՍ)y6" �*xuE��JC%�"i  � ^{D�1͊ {b�H}�d\Vert �E �D T�� 1*�� "0�7cK'c&onF�aft�"rac!��-!|m" mode�/rt,�e!b�KL'Y%x�9X,`%J� �)p���61i_{ent-gJV�ef-�W2!�Y.�nX$HM1va^�aW � a WM�32 of ng=t�=�9f_ $��0_%�($Ku�\ 2�2.�> 5 _ 5$. Notic����~let $վ� �hin:�.,�G u6��|_��_>�E+o��&a*�jt�a8q� refHx.�� wiwos0r,8v�$1� =$�f8be me>%rK"�8 �2�� 6�$)M*1�& yŀ; C5X�ct �%s�j\�acҝ16&rL}/h�e��G�at�4Qwo A%!wMcOL.z�bv�fly*�/�a�m� relap5LA�9��R.>DFf $�3�Y�+!#�1�w{reisG�Q new a�R�2� �3��� �ame�8 Co repe�3 ntil/ >z*��VW� � Q��:ho���B Nxp<@ auto,-' z itsel_bH3\l�M�!�@b1"|�)Rth Mf b��)��bD:)<-ed ��5R2�f��BZ�+=�n�Anaƒ�/ YD�'"K: Fu*K:��1�(F��>��$ɤ�Z�OA�Eachieved5�͊.�7�i�n,:'+�BMor��[�:p )�n&�hn-�k.qH"!�r�8�Y"�:=[*!;� �Cyu�7Nowq C�A-"TE!r9cgGs"� ABabsA C tan�Ce�{@'<5, F�,6� 1�&I,k@ can �e& *Q�� E�ed: � <) }{ � $.Kpiceab���1ft-j ��SFZ`Vfi�+8�  d#AAf!��6M B/.Ei;�Cf-�A� T\gg/�"3on#1�s�� c(N9 $T$I1�6�W h�A�p>�, A��HcI2� suc}�/>F] v-�t��d"V0��kal�9�0a&� �p_��\arx6>�R*�=y�%[/<'z>intrAf">�� I�.<& 1&iS�42��&ux�+\"% yv&o*\(-�In.G  m��"�fY@ŋfifU� hn&Z E� mini<���7s�8�4>X0 � "9��s:XF- $. E&�B<=n&9 @���� az�N68,9 � , So��Z�M��^�9�4�4}=�V�!�5.�=2%|� !�mr a2 "^)L!dif��sr�1Hg, �Z� r!hes�$50\%$.ʊ726�7=F��$�pu�5*�vW)a f_� $g�n� HI�o(UI=20g$.��225W� �מ.&Z@Lg g=]���16$ $2��P {MHzN���XP name%%:z �)�.h.4�iBireM#L�mpe's�7p� �?}�X�K0choose $T=0.5R�\U{3bc}s��\mu sJ�(dl�Nɱ�im�9� ic' g�� s�a:�LyMxR�4��T�D kuhrw�}.E*: $n=3~<7a  G,����% u�\sim0.36�62�KeJ high�O�Nn�G�Iquai-Ak( �A�s�>P6`)K%-Fp� morV an $99\%$ Vt0r�G.Yad� R!��,޶\(Rh CHy2� 2�96HR��o.�<6/!$&� ;A!u�>>��6lcL�Rc � ��Mur�.. �x�s s1qon� ��he.��{ss� n $3!?�RY� abov!�N1�A.IT�3V8,%Kc+*�P"� 2 n in ec�Qi"XK ��  F-P��D�l\�92�L $\ch~! ���arrow�)�6&�kz\exp[� ( x\ % +y$/w4]quQ2=Q�gрr3^0����6veZ��!S $k�Kk�F/�$ a�Cn �Tv,�w dth �!��8 vU e Gauss�7� A9�e$J2� x,y,9'>�M�loc$'s; $zVr9�;��@�axif � �� Ii)��> weBO�4&6�4�,h2'82�F%�8s0 all�iUaddc�REn�c�rQ�. An o� Z�$ is:�]L_{�9+"�x=y=0�|pU13M�}s尉�dK#dVY�Fch�zi�occV)6#H"�zy��note *�V]6ib�an qZ;urcŎ�2le"��spsI�i &�D?B?@��gEPo^�*�}V$has ultra-�"�|,aOc_�n- R�zR}I,�or��by2�I,M�[RQ��deN % 6{Z�Y!7.}n `g�N*k`�Vs}H z�\fessor Y�kZha|X.-M.�j�6b p "�[C%iS�[ � it{e;].}F�u�404}, 25'i:.� AC�u�f�8A 704�s2h {r69\ A. R2 �.�m� �2b�r �g0).�S. Zubai�iM. Kim� O. Scul{� &yj6�033820R3).A�Lougov�rE�Pla�tPi��er, e��t: x#-p]s08059�g�o {\ A. B�, k4aun, B. Tregenga�s.*X.�Ψ}q8s176s0);a�Pa�FG.�%8it{ibid.�b�t8a� {tl2);��F.�b6E7}..� A5�7�p]kp�i��\ E. H�\6VA�9�N�1�w�� S. Osnagh�ex��D6� bf(O , 03"�w16 \S.vzcI0G.-C.Zc2�6$%~2391~2�:T!��u\�Kn��!�v\o lmA8b�$91}, 09790�v3);)umyIH0xK� �5�  bf{9!�253601 a(HCNo F$W.T.M. Irv��ZF� 1104� D.a Brow�M�sP�Z)DS.�kHuelgaf��67�}36G [.]�6!Ro~-P���0z�} 19986Z6 J. Hn[H��Le�L{yV:�a.2AM*9~Y��YL6tnde\]E{lf, OmdCo�& A��s ��199:��$W. DurPmVidal)�J.�mCirac2��2Aw3u�W&+p "�VA. Ca�V^H��03210/}�W$M. Koashi,�p,p!N'y�y%�F��$ 050302(R)��:��P!yunzH�N+~? don&1 42��5��:�%}J.McK'FW͕ bf{303��9�:Q)%Asoka B�4%G� Agarw!�]~=�+}!�0�:[ jumpa&��YMY�6k*> �> 1 2(yu}B. Yu, Ze>Zho�|�@J`sB5&' 8R��S. KuhJn=6��E 21�hE:E�2}L� �� uzmiÏA�H ��Jg��� 0323�2 0B.-n�d W�MoeBrb�0ot49����M. Pe|K)0. �6��36Vn "�@J. McKeever, J. R�m. Buck, A. D. Boozer, and H. J. Kimble, Phys. Rev. Lett. \textbf{93}, 143601 (2004). \end{thebibliography} \4document}$N\\class[aps,pra]{revtex4} g0height=650pt width=44headsep=@ \oddsidemargin=2"top �<-1.2in \usepackage{graphicx} \def\baselinestretch{1.4} \begin��L \title{Multiparty Quantum Secret Sharing \thanks{Email: zhangzj@wipm.ac.cn}N�. UsualA�!kinE�is �vided)�%!a �EhACo�M, $m$�.V$to produce2EA ed resultA��#papj wM�focus�+ �΍5, ����~ needA:}])|-� . Recent1 Hconcept has been ge��iz Zݷ after%�pioneerA�QSS workA ����M�e-a�icle & fourGHZ�[3], 2�UE*battraceb$ great dea� atten�+am both� oret��uexperiG Xal aspects [4-16]. All2se r [3E�b�e. ��aUs,��i�� s wi x��eX�M�xs (i.e., bits)[5-6,8-11,13-14],�g�O .O=�2$[4,7,12,15�i� the Mji!�0 arbitrary un��n)q��A� bit;%$asother!� studies !O����s, � �!�ofN�and MV2�si5aneously�(i�� ? !�,:"|Ap>Fj (%d, entang��Q�re��d E%pan ex�� [13] )I�iY���t.Iemployed49? hande�B� [3,5�,16V�A>J8,>�b���, a�{icularW�fn� a�t� �3� e� Deng!� L�� [17]�&�  si!yC )6A�us!0I!0is�b> W-S's # t�,�? �� c� Aa%��ay.� ret ��V���CM)� ��E � "� � then~� aCM �� F I�a�V� q�Q=E�}�.� e show�%@U�� J1nn�s�Din our 7)w*� . Fin~%�j9��r Y c ՠ<�BQ^H @ Now let us turn!o:�6y F� veni�� = firs�KscribA[ٳ-э�. 2o  w�o i�f o �o a�>o � ��ro Zo %��o "o  two&g# �d �,�8inf)M��igby� iAGtu�s� c ur follow��^�  achiev} is goal��05 steps. (a)%qprG� bat� f $N$m$s randomlyE� � polarizl iUs $|H\re+=|0 $, $|V =|1 u ,=1/\sqrt{2}(9+,)-dn---. F�\{�$,�$\}��referP a�,tilinear bas7d H�H�H��diagonal��is   5 n h� ndbis9w�[a�M1!� b) A[ � )�� /,�1O = 5��# unit��"C � $I$, $UU $U_H perk �F<on it re $I9�\l%�0|9� 1|$!han��ntity �or, $UBC1|9� C0| ��=Y'Bt�Q� &JW1|)U}$ !� Haa�rd ga�v o)� nV feat�o�!A &ionC�t flip!Eei!aC;  measu' �� s, i  $U�=�%�U�9*aUU�=Y�!�=-#$�A�� �$H%���H realH/transAi�between��A�q'�!@nd56 �_H�&yLE�)uZ!_H*=>�_H*=>�e: his �ions,.���to�e� pur� e?ax a sem�{FsA��ro�! channel1. c.i� Bob'� terp .�� exampl^fq�mϽ�aF� V�  $Ie2A�ɒ coul� l� b���$He already� � A�Y abou P` i4 �MU,dily check wA �:c�� did,  �< Ctr��e� lete�J � help7 C� (c) Z sto��mofi�!�&�%�sel�Pa subM 60. Y8publicly announ�aB posiA�AV Zed��s%���: X�  e acT"�*#woA. ices� f a�" % sAz� tell ��initi)-� �!�n A-Y?� F0heA9�Wbo^iAatS� �s-\ ^\ ͳ \X���n� .P$j�-�'s st.g��!`)~y�ev�ei/i�&&'ix-re attacks�w1� � �!e sameJ�as5.� 3b �u���&� � 6(belongs to.�A+ O?s,-�a�determin� e error !A. I_ce .�Y�ces%]�� O!Z wise6#continu� nd �-sQ�.<(-��or�)���u���encode�A� %�at if w" 7a� '0'�eq)�i� F� $I$;FU 6U1 U��BL�] ��A��s��2m��Od� i >->,�:� .�, "UAV��'s:�Y�corYI��I�Z) )Cd͙�%7��h�fB�do�2��� N�$not get acE�tb�O� MFű$ 100\% cer�ty![eѪJQ a sm���a� WU� �>�t��yeaK��(s�velL�P�)sit&-�� have3��ed�� is c3�� � f�� 2zG�8eavesdropper Ev�nJS�useful["iP rup�] miss . So far���� thr�6�AJ�]� �k� 2��Y�>%T�ura�yp��Zz�� asAz!�D���b��0��t dep�-let�oi#R"J� M(� Q� . As!?ven� ���� +uncond  a�ur�nc�=a�eas% fiJ ��`��� �[A�A�ins�M��e ��� �L�� lso6F�" ^�to�!n$40y ($n\geq 4)$:r/� ��!$!2��er who w� Ja a ma�! Bob,�Di�%\do�nZach (a� e�ly6�)} v%�I� � ^������ ^)� Qy ness!��tepQ!� includv� a�(I��������TA�a�e�� "���o1��'II��%s bM�&"��}!��� �)6�a next �/ say,E�.�8*5��53I�I�p &: ��=s��RM:���s�Similarcedis repea�until e�finishes���!O e�'2!e�J 46 IA� �� a j���"� J��p&�>�- o��# �I�erf *���o BaW�by!��him� .   "���tv$Cy �%l]s')s� ����6G �YM�/ leq�'s, (��'s,��Z� 's).VF� A�ha:aA��5�&* a A�am"�.& as��' $(n-2)$th5�n �!i5'"z &�L �/n� 6 is� !��~�  6T� 2����]� ��� 6��sf��.!������)M�s.� �H5>to���AV�E��m�{s�}o�)�� (aXa�= $n-1$< rs (j�!�AQ1AQu)2a %�&i���� A �7I(�� �� �"� Y �-rsN� "� 5(� n� ��� 2� !���Jc�� F��� !�!p�� �� �� F� "�,d  � 2� ��6�!�ʡ6�-J� &7 .j�aeYa�"� ^/ �&ch is  >G DBG a���%�revioT$�` �/���b�i�q.o A.mi?�(�l mo�&1'� &]1.P! Befor2is,� briefly �e�!-b� epor(�an�%"[.� [19]&� � i�"��QaSkan"\" ?$\alpha "�$_u +\beta|_u$�}�qe&.9 pa�a�� pai!]%sB�b, $|\Phi^+@_{ht} =\frac{1}{\J}(� {h}  t} +� {h} t} RM� 0M� t} )$.%0!� ��bERsse�f2!9)��!�Jh&�q�1ch�(��2&a����accordu�-h�!1* [24Y@�Bn�afe�)u fu��i+.!"mzl��EA�ad .systeɀb�wri�)*�2(eqnarray} (��)N`&=&N> B�)~�} Aln�$ \nonumber�0 &=& ]2} >�ut} (F�hB� h) +>Js.Q.J yhq��"_h)6�+N�-u�.X=h -:'Z�VJ2� J�,%2Y3'�F�=6.6:.6K*?!,V�:V��-9[���{t.Va.��ZY=M{t}6X6u�� �-"_"6a�v-en.O )���6���lab�[\he2�  outcom��%*��$ (:�_$\!�� hi)�q��`R��#H M�# H|y ( V|$ ($u_1=B0 V0 6E H|!�u_2J1H|9� a b, $u_3J1V1:�b)� �1nstruc�2�ǭ��0,bit $h$. Sin�1tel*iX�EPR�osj �of�d"� �/in essA=m t�-(in Ref.[20-�T�5. :�� &��..s$32��'s & "g ��2I��) I��a &�*{,� \MN��=r�sN+ e��re�ed� �(V� "N3$'2al�!!�%Z  6��=1�� �2� above,�pa�e p�1NW^ to!jf� &f bfoHo,X& -S�-[ y� 2�=t.w JAZ!QvMJ*G3s��v6�� 1A�r�0t#A8by us"� (5��r�.*d/we justa��%d�6.�9�Min a Y , 2�5 mM*.5 . IV�-(F��*�6)G��I�H�3*�3�llib e�8n�-[1]v u�A�4though in [15]�8plai�!� �%%�)�6+6��p"�aUe�J�\~), .p�>� �&1_ ly d�(A�2��g� A$?F�A� �� 5A ��aDFJ1 �en!#���aB��<Pfx�9� 5-day t9[25]. A-mc5r!Afac�:3nC09ZV7m�N�� �63: 4 . Ea�-"�b`!P9�3A͎Q�6�ofFW6�1ZG-rb!�aJ&�9A)��%��Nn%~a- ��v'up a Ev ��-�:3!�a g�8A(. To summ�.S)�j3�dBJT�k�TB[4(.�o�/l.5� ) orBe<-9 a9du&<5w$'v~&�a 0el;6CM�6,Y@r�.�2E�=��G2Xi�-Nby�3�2�?ou2�I� 3��2R4Ek@� 1M�)�a�r��r!�-�.�>.B?bf Ac�7 ledg� s} VC�(nk�HProfessor Baiwen LiAencoura =%K%Fthank��704/�e�&�3ve opin� u �s�?�&%x he N^-al uralC FoundAE Chin�Tder Grant No. 10304022N@: Re�0�*lDi@4[1] B. Schnei_,Applied Cryp">t(Wiley, New York, 1996) p. 70.*�@4[2] J. Gruska,�1��;C�;A (Thomson er Pr ,London, 1997a5042b<3] M. Hillery, V zk �LArthiaue .=C {A<59}, 1829 (1999)2Z 4] R. Cle: ,D. Gottesman ] H. K. Lo,X  G\83}, 648N[5]�Karlss� M. Koashi�N. Imot2Z 2�62 NW6]2�, � A �061}, 042311 �G06�@7] S. Bandyopadhy`.: G2G12308 JF8] W. Twl,!+Zbi�B�Gisin.: � 6!6�0 �16�9]!�Karimip�64!�(ahraminasabRX5�42320�26W10]�F.uJA 66A 6030!|20BB1-9gh�=ezhad�V.�6ZI�67Z44Z3:�(2] L. Y. HsV�8A22306�>@(3] G. P. Gu�dC�I�-�$310}, 247RN4�Xiao,ILang,!<G.�a�W. Pan,.+J d6ay�F0 e4:�5]�M. Li,agS.I%RK.�PevI� �)P 324}, 420I�>[6e|[a� T. Symul,�� wen,�C. Sa�Us AfPi�am6X |e�9a177903V|7]>'G.9B �RSK)(!' %(19%�>�48]Z. X. Man, Z�K���Y)?�. \�)'2�8W5:9]�H�?nnett%�Brh&rdC�"u, �#Jozsa1L Pe�nd!L K. W�3H)���%070�~95 �~:�20r�dN�LM\.M� :ce557b:�21e�Inamori,!� Rall��(V. Verdral,A�Pho );3Aa 6913%=:�22eom�X.A�LiV�5}, 032a��X 2�$23] E. WakU/. Zeev�(Y. YamaF+%^ YI<��:Y4.�%�.�^�%%X��1i�>�i��$im,�a> ulik%Y. Shih-�]] 8�l137 �)`endN x}K} :0N�=Hpacs,superscriptaddM.DNJ�M8,psfrag,amsmath symb�fonts,bbm,latexsym,color,dcolumn,epsfH � !:8skip 18pt \text�N 6.5in �N 8.zN2�N 0.1'%&�N"�N 0.3in �1O itle{Decou�in|FU zero� fluctuD �� (Brownian mo�&��-or{Fern�;�LLombardo \footnote{l 0@df.uba.ar}} <$Paula I. VbEr7p:4ffili�{�Ma�(o de F\'\i 2D K�Juan Jos\'e Giambiagi}, FCEyN UBA, Fa�Ead?C�>0ias Exactas y\ u9Ciudad "'N4aria, Pabell\'�I�P028 Buenos Air8 Arge�#a!.NtN1�ab44ct} We A� a n-analy�EpproachR dF� by a)�tem�:l(environ!+�a9�te5ar�� � i0 an Omhic2>b�<�7oupD�,n osc!�tor��+�O� mas� eqIT. F�LjG usivvef�Js�@ evaluO;>.�timA u�I^��� ��p� -dow.�, (a toy model�U�Q phasekion�~end.�\�S{{ML5.Bz;03.70+k;05.40+j!�*�O \new�O and{\beq} gin{1a.$e$s^"@dalam}{\nabla^2-\%�(al_t^2} %�6 \s�Ion{Int�J!} �"emerg�Y��Sic�>ehavior,29_��/q blem9�1A�in!branc+of phy�R(cite{giul}.X0it�w� �n,E#���$�;�Finvolv�&wo*�Cre��d��0s:�Wcor�}�<l( Wigner fun%�UJ�sh�/h peak a, 2�$jectories;�{�O}}��0/@ X beN%@�"Q osit2,���EA..wo&a few �/�#s (degreQfreedom)Y�ngi~e r2b�3m��ath[+mpr�g�Z#of c c.3 �!��3  ?ro(%�Fin soluA4,) b%9�#-y!, vibrEaE/lax z%�M excieVcemi>6u�AS-&�4coustic or optv6%non��s. �YprN<�!xden� 7zly�Md�f�Q!b�Ws9!� B941�A� t�O5a���%�!�. 2� iJm�SingrediA�LJr� to 7�� ity.�.��hosE3�.p s a p��R;'�9�&t�Ta+Ts��i!te���A be�"�� HTe�bert spa���ed �.�fe�p�er �)�resil% i�xing�9̈́�v�%\\ ``ein.2ion'' (=�B ucedzer&)A�H9-�� ���>1�,�k. I�N�;V�a rapid� �caNAuX%/AD�[ a roo��4$non-observu\�i�|��B macroscopa3�if�l 4�S2) AC e�YaR�!�-"1�I�i�*sen�Bv�fto be�monitoE�yA.��� (�=�8�+,J%��XX�� 6TN). eGlesi�M}>�mm theyr�l� 5 eo �o*I�-r -,Ac!�!��mFe�3#�UrJ;)"=e�� alyze8 eff?\�6he %�6� � sourI�*~�[U{�M� �.Ply lead�" xgy6��2� �A��*� Iu$nagaevEPL}�%��5A2 gralA� w,N- N�� �Es�e�= occurs� atM.��f32N�>!� sequ* h�7t� upe� �.�6(I:)���9h�x!�!�j �Halmilto�-�iso� L does� �m�e\>!?�LHaI . Vacuum6�� seve��iblQ�v ,he Lamb shif�� wid � �H�JF0�-�( CasimirM��!� }4Ii�Y�v �� #% |DE!�rea�N-#"�]param�Ds.! erizm�խI2 tras�!he6we �V)WE�iq�[�#�#absorbeIo ��8� �A�]cle. N��n��!��}�.L,�@$�  a.�:� nois&{I0E�r�dweE�"-=��/:+ �.� overB<����R� (mean ya�)r�no.�e� 2��8"�ity�A� ques�  a"�Jinfluq�>�2�oE�i?�6c�9e� �G�#discusf E,e last years���2� d8*a&ont5H.�Mguthpi,���6*�1> at T=0} $nY&au���_(ch"\e� +�E $M$�bH frD ,y $\Omega$) caF��_ com�'� @ { �haro c*�s (G7ass $m_n �.~o~ _n$)AeX6I�.�6�sp�Gng!�a)M2 �as (we�,$\hbar = 1$):"�4S[x,q_n]x6$ S[x] + S[+ S_{\rmA�} '6�5(6@int_0^t ds \left[.:6 M ({�@ x}^2 - )l<^2 x^2) + \sum_n2#6 5 q}_n 7-% ^2 q$)\right] -BC_n x,��7eIre $x�4 $q_n$��!= cog8��3UM�B!a&�s��s�a�Ey�.� edYH])a),"�� � $C_n$.rel�ob�7)�m� Z� Ňb-�A��re��67 (�?edW* 9>(� gR�ju� �b.��1B}/� e�f${\A�q}J51[associ�E>B� \rhoI�(r} (x,x',t)Q� ``} \,\, .&v/ t&K8 \\ W.VpUf�;2\pi} E�,{-\infty}^{+ 8 dy~ e^{ipy} ~ .�(x�8y}{$x- U t)�ou�/ Z�satisf� a :!$. Hu-Paz-ZLm�� hpz}�  ��:<�g!�M[ �d� ��X (alt� I�,P����QHFokker-Planck type �#l�>� .( Y �yA���Adynamic� d)" � } �|{!�}5�(=-i\bigl[{H � }1�1!� M {\tilde����x^2 ,KJF8r] - i\gamma(t) l[x, \{ pF1\8D>1[ xF0]Lr] -fF0J` 0 . \l`!{)�}�E Im�"{ �&I  (�N� of� ��� /6)�k giveJFF�{\delta��}^2(t) a�-��2}{M}ea�E cos( /$ s) \eta(sy��<5pJiX 1}{M 66NsinjN \\ !� I.�2� \nu�)Scoef}�!�:mܚ�L,�JZ6$ cutoff, iQreMN��T$0 Q���^ie 5.?!�&hm:'�9F \propto1��>h� ݨ(in Eq.(\ref��) 9)G�r� �j�P]�.���g+(x�F$DArmeq 2�{ _0 kB} T M$�h 1�5r�zs�i`� &�2K�N6Ka�iD5T$G.�$f 1=T^{-1}$�negle�n� �a�e�!r�Zeto $D� &� �^n4m6�(�>��N� &�(*�. �)w�9� ]n�mH � � �>� U�t et $e���tai�/2 = 1$%sAA5�sM *�d ��IA�Refs.)�"�,v�jes;�F� 6! �Vis,F� BM , =4Q}}{� m�^26  �Q��� )} 6U}an " ros? s,l I>k �C8 "No�NweqN��2 䱷�3}{ 2X�^��1 - e^{- $ t} (�� - tN)>R � t{�6�2:�0E�ev|,haA � t > 1$A� I�c'$Fig. 1 (a)J� FA�.� �d%}� (  D��2b(�b)�$,m�J-�lJ�)�M�)m2 _I�)f��z�sin h s,-� B���&� �72v,6�^�2UNA�Wf,E����MA}{ �} �>� .�B����T!�Za�asympto�%�,��>�"�%{IS U~�4Z�v2� ( Q/nn��cN )� co���(�j�� =Q�"� }n\"� �\ I�:b\�O� 6\5&DJ8&�!��exact�*\���#ul&%:=�� � &=&\��>� �Mp�J�,QyIˉ�Y� Shi(  t)�h` @}�S� cosh " t��y�t�~2�.&�  &-& u.�΋:mB�2� � >��L��x�!�,�:Du�1�� , $Chi(x  nd $![ t D hyperbolic CosIntI ,Sinre� � ; $S R")�e&� �, 0. � en e �� , by]hq�Ah ^O�hS=Ky!RC @2� ��8�Vx*t $T=0� aXs��~P3er *.�A!��=�l"�� s longe�ca� mem-� $1/M�m.� /&2y .1A0 �$�/r��= �a2gg 1$�!!�$ g�"o $\pi/2� �n� an.� �$D_<�`m M��q���/qf�e�^2Nr�>c�� �% &�}&Ne))��E�$u� 2? �!a�Ck�2eA�E�ac�2!��:�$ K $Si$� �c��6�/or{ t�f�C2  o��&asIVe%!�ll%�Bq!� "sgr�>�,~ 2M(*  5� l ^2 tb��zC_�!�c�~I� )�s%#�&��B���Za��J�� �� �W�W�O�Wf>WI�%ads�S&� �����>���i q'}� �� ��(Z�t 6r� 0Uc!�W�[� b�V� M�}bZo�2���� C��logV�g&�fB:AX/,��>�2o���te���dR{ A =�(-��-�""fR�.:p�"�2���w:��*$f�� m -Y�Q�^2Zc) %�I�/I-$9Mf))�7it \)o � l *�(K  \Ga )$,�J` ($ $� Euler 7�(�W,figure}[t] \g��s[w�10cm](41PLA.eps} \cap.$ {Tim&8�-�S=�+�"}�,eOpXp�<fr�&�*�EziY*H6k (b). Plot[�low Q��s�(c)��� $f$ WnR�� shorts2�a#b�~N:9Ik% d6 �;# {m�(f)u�',�P�+� plot:" = 0.05�TMr�00��".�)�1� }�(���~�7"���..�.x2 easy�Uprobe *j7i�p�!9(&c s+)t�`noO )!��UBi>f� (orT/(-2ed$"�� ion)}V path�7��map'R3Ats,itim2at!� rt � �A: � k_BT$%�is vi9/t i*;t-u�&��*~"=��E2? )+})�`.K/���)-�u1�BeatFa ��Z��ae5-�(t&� %Xva�hm@ly togeu3��&*ld"�e#.� >6��:�iY*dt#e{�4%��OCrv�R42T$�f turb"� upA�se*C(�0k!� "4 �'D �1�&�"?nt. Wiˆ>�!��4weJ.*QE�*�*�&u N+&�+��?F�? "�?.�8a$�T���B���%΁[�riߐ�,)��\� aa� s�E)�o�#del�.ed�!r m!<tum) sW-m�!�i*+;w,Q(ackets symmzzry W��i��A space,�2� mm8.�#:H Psi(x,t=0M _1(x)�Psi_2�,��} #�� = N \expJ �!$(x\mp L_0)w2`^2S 1,(\pm i P_0x)3(�&q N^� ;! N}]\pi_=�1}7&�[1�>�L_0FB-  �^2 ]�>�) P�j �s�3U! R" �7�1� =�.�W�i�a�:�%G e�/!9 jbis $W(xF' = W!� + W!� "W* /� rF�W)�8- 5})� �_1}  N x_cE2Y.�%�_2^2(pAMp_c� $ (x H)5�"�_QE� >Il( int}�c2��� (p� x) �$82k_p p + 2 (k_x"k_p)x).>\All%�.�f �)�i�QdeA�# E:&Z"3ag�FQM�':�� �Q��q�� licȁorm� f�R�>�JH ;2Nasi M�_1^2=9= ^$!(=ak =p_c> 4k_p=L_0=x_c$. 9,k_xRfdB�=��6�5 � �\�.l,��;�?�#�Xit2%% Sp3A$l&:$(se�k�mpl�9��}�` %r.^�� W�  1 pone�Dgor�#xp(-Ay�a��as**qaM62"��!m�}� )|b �C}}{�:�H �E}�P  1�&�g}}B�I�(ly, $�=> A��alway��un�m.*�q�`^2/IX^�#e�^�� = ] � max}$ h��! 8>ssuP(in�MAstaKrH� ? frozla<�8� �y4��"����=1/(2�$. N�#!G!B�"���> )�^Eqs?%@= (R%td�"2 -�B4top A4� s�$"�M&� '2�A� aQA�6�h��$,�! � 0$ �� .� �u$getN� dot{.a\i 4i�im�eg K!a��>jP 5$�!�.�� $t_D���� $1 ��(t = t_DA N" '�)�� po�?G:�Da globa�16�6-�aJ$� $. N�>the�A, M�FvK �<�>to!�ee�era�Z]�.  �:�� n+al*�,��� )�t �Ü����7�F�.d X2-�F� 4*�t ~�Lambd�-  M� t""ͿFJ givA�a�U[B9)�N3&t_�(� � M �P�&�!td1>�J8�be��i�3l��L�.t $>g�81$}:uq)bl�|�ReB�r coin�~snRDqbdh ly  "�$�Fh�*- �X/(I�� �.F&hpy�nw� (asa�o�`"_$Z�d!j))�:"NeZ,B�O (P3!K $"�Mn} < t <9�i }ai� ���*6� �*��6 $�5 $Ci$�f >� �� �� �8 ��i6 e�^�' $�,aB[m.MET} &D!>ag^.- 19 "HB%�?ObngAaB[ b ,��X"q � 1}{8&�%}�ich-�be ��!�?!H rdampI@J�zEc logarit-�Oc�[*1$�Q� (un�/*( a},.rqz0&Z waڜ,�is ��wa��Rh� heBD ,6<� A>l:�>! F�O "�6"e9. �j��IK5,s��.�s�6%?a"!�psat} =��O>-)"�6� r�9� (ts maximum �y��i]2�"%�i�a2}) [!��(>PA�``*7J''� :�R (IW�]$)]4 ��J��i�Y�? iy}\s�i�6,{&�&�2?U���e(QХ)SM�Ye��PJ� s " 8*� qF�- We wE�b�# ext�BR�E��A�er!�s,�DnewM?@�%�"W�BFyAiN���!�+o> � e#BI��� REA=a~.�WJ~>�>���B�50)L�Y�m�: �TNV '��p[G dNa@�9� e��z=�uT�alih5�>j0Dld9Am\ �m�V��� ��*NS�R ory jray3�%N A)i�Z task�5�PGaussi<nd �M"K/1&i0�1�d���1�� �m� )"=Y�Pin�51zmechanicAM GuthE�Pi-<�A}!�k=nM �YQ &P&�.�Y�[�]b�{%�is un�MsŽ~L'�)� �  good:� fo2�bA�o&DMJY$�&ň�A can .% �OC%it=Ho>Tal-)]ea ���;r{1�U�- >�!� a�*���"[(F�B.5Y ]aKR\V�B>�BE ����B�e .F.���B]Qs:�B�f"� $�,�BAa��5�Mv !<%�l# �Yg�,���be� ʊ"�@b�|pla�J#� $i ���%�2A?�. I�7� R�#,gEGremdTA�PoA��C��&�7!Het%�� itud� d sp2& LeE&�m})� �ansatz�AmV�F8�>Lr (\Sigma ,\Delta ,t�NjO3$(2 a - C) � +A� 4 i b  5}�1newrho�!1�} w7.�:�A(Ely*� asB� W_rf ��1}� . � + C} - C}}�( ) @} � F�2 x b[�- C)}.�w>R�C(N=�Ud0% %-2$= 1/2(x+x'.)y - �)IU�� �R.� ,;9=8�(a}U;4k�\� �3 � C)++ 2 b:�;Ub G;(a�2 b)KC! -�"� ^i�i�}IFOb� �M��� "�;#0�C �4 C b���ZDA� - 4 �JMN M2 N b.t3co�Ueqs1�-P2F��!!�o�*e`"^+�A"�$t@6 %�.&6 f'a�5( = -)e2 �_0�2?7&�G} &;&-W �>;�*"�;2q!B�>e2 � �J"A��^2}A+O2I HB;&)�= ^�6I�.�d(]1 O t} bx*\).� 1m �On��O�neww}) "|���G&�/.�  l��]6�]�w $2a-C$�  $2�� =O(1)$mJrL� /Jof �YY�)�k�|d&� NInI'3q$ E�.D �� a��� im�"5�O�*N'a$%c� #9|x cKEr�Lh+|6�(�D&�ra�.2 e&�e�f�((j(*6'*2J'*e�o"E<-R��e"T0"@*e dԢ term��6GYt.�G�v6�!:% . Is%� �r [*� !Ro"� " K�%CHozg . P���(_�) 1$, � ���2�4m�00B�)3-��0j ��Q �is"�� �̥�I2to}^ybCuddqbench "� �$6� t*� ��Ae�s >| ray,� (,raynpb}. W�,9K M NX,.� squeeq �81*�#, $�Lp$��&�U9rr�Fed: b9Ma �)�Ut"V��``��� ">Vshape0E�5. How?,�n a� � M]n.Xa<� true5�Z�LJwes�c�� :�-��ak$r� a9!!�b�baM- -q�iz$')667�  0$1 �Ue��6�aF��t �Q�9s��7"*QB�i�U�_c�a i"y &�a��a�l�&�AifBjC����ccountM]nuno}.2�aaS�s2u�cp o* �non� r reg� "&nx{Vs�Jis��2�wxUBA, CONICET, Fundaci\'on Antor�G!{ ANPCyT,&ql\)6��t�xD~,Xzzitelli, D. MonteolivaK J.P�sr 4�con���kbC>thebi*��{99�jbibitem�i S6�#, W.P*A� Hd?� �n���:Qxtwo�waps*Cx%:(�2 rintb'style'eqsecnum.0}V /~V0\J�x! def\btt#1�0 t$\bV�lash$#1}5y ef\BibTeXq 4B{\sc ib}\TeX}V9Y\tiUxNo-clic}p E�� UmKey Do�*io2txtWon-Young Hwang,$^*$ Intaek Li�c$nd Jongwon�k�. xV�� Educ� , Chonnam�w iona6��Kv8joo 500-757, Ree�ca� Kore�w� 6�wd�c�d`n9'  t0P#i~Mrmful�legit�$$:�TBO}-"K} 1984�num �"þ ion:U } be95��rt9��s� u|�A5-�s͝� double�7�8um Trojan-pony �� cuss^ deal 6hN�4<.4b���*� C�*|ne  osed1byF!qmaz�u*, �G!M/ ad�@arqremoval�)?��nr�{6m��Y*�w�q&2Sw�Jsec:ikw}�P I*m��p�!%�1��s9�  p���v � (QKD)A��� )%Q}����epromi%�-@ *qtL9!�techon!Yy.6u.)�-t +'�\�����uKse�8!(Yi��!nelV Q��or�OallR"fec4 Yao95}. H.no=5hv.���e3. Lat� >�2��e�".��i�h�&e �E���5c��% �%�)�pMay00,Bih00,Sho00,Ham03,Hwa05�RAnm cAs rk%Z�#of ��-�A-s�t!�(PNS)�� } Hut95,Lut�0ra00}. MethodEad2Fc���:)sc6Ina01�% &Got04.�!GM{PNS��Vs�p ser�5w�9r-mb\7i��y zJ� T�0au�'long-���E QKD ���Hxue�h�hiS�IJe.�՜)Sy��hoF!�,3,Wan04,Lo04%7% SARG04>�Sca%�Lwo�"Jn5to �l�tF?�%Ff�ђ�! {= %��suppleme�����+�be5 "z$ q m�7��aC� step�U�"�?~n.�s�U]. Iu�rA�u#C,si�[ɀB��=*P � <����ly6n look8ec$u��s?2ex#..�>�2�aw2t-"v P%�G��of-,ion-loopholeQ�~Sel88IU Bell¹"�vKB�b&R�ɞpap"�so m�5�= �22u,f6 a� *"_V : In^& IIa&j  wh"Kq-��9A!���E F- x*d2�BR6CV �6B�( .�4.' Gsde.��&� Pr�F�.� NDE}��  &%d>;Ni��Ƈit��-eFF��E�o#noM�)p�� �t%�)q� carrie�C�� of kˏY�a pul����{6��nto A��. Here-�Hw�+��"� јer"��e��!:�s,�0�^�Q�s �ij8'ivDd0a#-�"}Q��� �:lLl�iA.o2Z.�RY�� did�y%w� ��]+��|'faiB .�� }m�Sion!a?(, �� ��.H can :�!I4.�2D:z EasL~ b� d��E��8Bob���7i���6.�S%q�Ɂ31F @H�4!  �!e�hd^B ��� y "c+�r�:ly" a�:�"EvDsQMd l ...�s$\eta_B$R� io��d$cy),..." (A��oton2�� .) W!�tzmea�wA}�t:P*�� �d �� a%�-(m]�ZH-�a6�)R� Bi��;y�Y a�7�o6; t� ll�9 �M1L%6�v /Eve's A� %The %%�9�� be��&�<or�st-��10�hAm %An T� �if��r�  !jhn3X�� %21ou�1:4�3: � logic$in+ K  %ERFu.�#$ӻo�+U .� %uE� /�Fpar"�la+� | -A! -B!e %� �)�j�e��%J~IZc-A, %i�w�� K|~e�b-B,Q 6+�� u��me&%sA �G�A %e�oA� a�?-dGifb[U�% �*��setupS��'s:�"�!9'�i"9 %��,*���z� t�syw�m)�-�%/ %equiva vA�2H�out( �U��.Iq� E� g-B� lZE�$� �-A. "�N�2poJ� B�a�k�1�2�!��25!��$few p� � Rc�DN�is �in"� XIII�*,8�Z� i  ngl�F� %�N �OMCur� ndhU� Mak06  Qi07�3e(�5c� ,,lap���A!,�{r�[�,` �/b" �S�6V. % Our S�g��Arxivp#� tv�� �.AA�$|.�S��R�"v aaBn�-�ehos�)3%�,%a,�,%�Sgpe��G �d�.;}eg�i1��D)U} � ���DyI�& (Eq. (58)RJ)e�^key��t�l��.&: a&E'$f$'Mi�XF�vnotՅ- b�us� No�BK��;!% in��ailv@~�,.Q� FrO�ien��in8 6"�8G=��6��v�.8 ��t��� ����in ful�X o��aW�Iᅸ!mi2w��&\ %z��5hA�Y|b�ԑ�Eve��"C2�O �i� uworst a"! a hyp�[3��,-Vm�a*� help� f)j!g�}>�iQ�& %�W�*� n�off�h��l��(+� exaet(��!��{3*�&�~����:� ^�sedYC�F�2.��mightP��J��>[���s׃B��fA�2Wn'a --rw�!fch=(| ext� :eJl�(4s!to%gI�Aci� powerful1�r�~fw�MH! 2,�-��m%]���: Like a*�t �`� �'�i �r},a2�j0* opaque�3teL�-9Und:�Gis02�v��"/ !�:Te�E+68�%VXsmq�aaA�su��)��L�G�pic�upg9 $Z�9$X$!Z �@��sN�7�mU�e` ��!N$z$��, $\{|0\��, "P� \}~1�$x22 z{0}81>:� %In %�i��C� 2�u���5#�0|, %�l1| ����: @ � F L:<| �, $5)% $�$��ortho��s+; $ `0/�N$ �� = (1"r�)&��+ 8)�1 <�^<-.< � !fEZ$.~A�$0�I 1$),��Qp����p�Vop� !�=(=$), namely " ^{\oN}a�2�D��sh�zwarhem�S ��:�waQwZ�X$ ]Z6�e��$Z�_�ba]��5|2�5�2�!:2� �1foN���s�@g�����e&�: He �s%�E� $|km� 2v, ($k= 0, 1, ��� 1}$JNV:�r�Q` $N-11��Dex�R �Eܬa �V�h�reliaM. �=� AiA� ��3"� )-t ��#�a` 8�? �� ->� [a�1+mF��&� h>!2t L� �fiswi5�.w . No2  ��We�+��% �� �eI t!���B"� .xT_au� o1m 5K{!�%I>� &��match;��+Wa�� a� adop��m� e^f� �(\�)*c����<e�ak2-��� ]e 6�1� "V2'is )�1�a]a�>or�he2�a�*rN�u&X"6�!� _Q�9�B�q#.��%B,!�in&+e:� * -C2 .��J0? �ůmp�D o nullify2�E�s� ma ) &� .f'e6# ^�dat� a2=!fak#J��ack*AIg�c�MJE6�t!�!P�Ew:� ]�6��FA?� Ae �/��|;6s�5 i.�5aB! Ri �sQ) � g %.=_#/�J��s.�A�re�p: "�8 �o&��K�K to�s�� aJuio��"�}!�P)-�a F�as &=7� -dark�) . An!y w�o �!�&J�or>��!g!�^|n `�)�'�3� �+IsA2Q�f� 1 (QBER)q�d .i�L$R@� � l �l�-b�8ɢA���A �|a>d  N no �� � 6ifry� e�J�&T`&( m�%"O(I� "8HQN��$+B�s}**�J %�fa�u&�+r�#AtH6� %!^t�#�A%Zo6 e `fair-s�EngMA%B� Ѣ"� �*go�Rfach %*� !�e,i p~GitfG�K}$%clear. So����p�F�J.��! %\ӛ6,{A pr�S� p<een �;ham*erՌ�3.�" ��w � N��\h�b:q�msmB~���KeM.��ne��o�<e �i/Wa�g�&( AB*,A�@H �Lo�`9jrnjJ�|tQ!N�)�E"�siEnN��al�ces.� �9o� ��. �5��r�$N $1$:R��ralt�*�.c��.� , POMa a�b>c ���he-B�`�qss��d�PaJ } �$1fc��� E a*�!�.O*let u���M�U 1�val��a�ho#noWnvinc� ����?QJG,a `black-box�g�  r�+*zRuCV* inct����mi"՜ inpu6.F�C�|�$ p.���r���o} ��u�� @�� utpu�Al�6,}�aʻJ�FalK P!K�, tice����B E�� beJ�s�,u�6�X�tQ���ft&iffe�y�^I~!"amEbe�ayI,�QJ�,  V� eW!^#n:�>2ith2k$�Cw:n2�Nl�]0�KdoActo���po>ZJBs*ɐJ�hd �aA��� MnowA�.�F� A�J_. �a|L$2)� ( [K!mh'��lof.�2 �mov$��5V��^�7v�d !���.� �W .� �� z.Jy! �r a�y!�`"�J rs� fre$"�3E at �@eaŝ� }]y�sdein2� ."��k,&L � �F� E:no@� on�m���(�ad"k4 �al%��.$�"W 2���*.OC�a)0���s; �%�lM�-�A�.%�.�B� know a bo�@und on the fraction of adversarially removed event, $\Delta$, andP is small enough, the Z(security ofj�protocol can be recovered with a reduced key genera�4rate dependingB�$ �` \cite{Got04}: The larger}�/is,� &6z z0is. Therefore 3problem�estimat�� �(s to how to&eqB�<. However, alth!H< Eve does not knHhe ident=T�quantum carriers that Alice has s%�it!�0Eve's freedom )sh!�place 5'sS S,by any otherB. I%� �� Trojan-dark-pony attack, for example, itQ�a? v@ $|\bar{0}\rangleEir �d�ei� $|0 "8^{\otimes N}$ oC1RiI�4$Z$ measuremen%"chosen2�twe must analyze Bob's detector� A�differG0states of $N$5/bit!+ znumber#-5 0,is unlimitedIlysis$impossible�us,�assume %HA#B^}^bound)B a certain 3 $M$ so)�J{m�donyis upe�amountA�5 � �re�a |a�,light intensA�at-X(site, whichucheck �Bob. W�,��i, wA�wA�veap do i��ze !�9�-w)w!�-�leseGn!!hen,Aq repeated ]5)��e�8 positive-operaA$correspo��0to a no-click�7�_A E[ U[$in each ba!�$b$�!L $b= z, x$9 Jvthus ob!�AKwe%Qcalcul�Q!Cld efficiency, $\eta_b(|\psimA)$m��%Ha� $ and�<. Let us consid�^sia� st case w �Nn= 1$ �0=�$.�$ pes!.��isZ, F�U,has no chancEtur��i�switch;%'iiB�@ is zero. Next, l:�anr� �0$�(��He�i)0$A��alQ�$between $0) $1$. 5!�quA�onA� how �N�><�, clea�9at9 N9i�i�$1- �a1!�U�e� the )�, but��wbecaus%p��no way 8concerned. %: W��h�Y %��>� ones a�,. What %matt�is final�Qistic�7to!��e~ ��t"  % �Lb some�H s ar�� A�"� {\it ef%[vely}, %!(fE�on :�E�N��"%�R$|ez6Dix6 |=0$A�a, explained!� follows: �Hrec� �R�k c st� g"b ��BA; suppres�C(en�&s)�J���'I��9)e )0$T �atFB1 @*� �Sa-a ,iO�keQam iD friendly}A����Bob: E&!is D&� fixed� �1, ��w ofE���F��2 ��! naf&z = J� 0n}$ ($n < M$)�Ainputm�]:p asA)zG/- $sPtwo�e)d both�Q�)�(R� )_z=�A^x"P�� �s)��8o� iI�$x$�a�re.��2k�t w�:S $z$ � AQFL�՚�q� E�.TAEva e��Aa�is oppg \a&]�)�r'� �� TF N;��sam ��* ��BIF@Fvn})�I��IN'�R�X  $�Q^z�Z^x�c:]�-)�aO�%Y$ &�ly or � zly��a=�s m� $("�+:�)&�n}� �Yan' usingD \a�.�s��as� y�K Ec. A �alAM&���amis part�2& whilIC%*JBA))iis JU�I�simil� rguvs apply&1 �25 ge 5s� ��>  s � �67 .�TachR, Dq la!�2( \begin{equ,} \label{A} 6� \leq E�� , \end`� hown)���Vo � iV�0�%h y! maxim!�ne�ng+6� $'s,b�B��4 \mbox{Max} \{N�\}.>�Our� ipe��,Eq. (\ref{B}Š@still quite loose �ak �$. On� as� � � aa) gives - GA�A S !utilized�actualm�E� word, situE $ b p=%�~�so��iv%=0eavesdropping�q Eq. 2/ much"� thaA�e)�eNP all Z tr�as *Ft m� for j �- I�in�6�too�< a "toV1e�it seem3be �/design"s s%��!:.� ��}�I �$�#��,�s�B�E5 In E Mif los�W.q�n mp�� vf� A(ab/h��� if �� G all} �j|% 2�EI>��A��"�io��,bsolute valu%o���� $ �E8%N`.OA}). �4!�6B� be easi�� rans��xA��:� *���rh� 1Q��i& �$� $ abil�of�n-double"� !�t�Q"� ,.���2��!!�!� useful:� easya*mak��M�S,most naturalmOE��s. %� \s $on{Discuss U Conclu}�*sec:NDE}�d�result� Ref.�Mak06}E�lap)�ours.7see!a!�y��a%!�� at� escape6 's t�by kee��=1:�"�w � A 2�����"� is mKg�%�& they(ed �:@�, a�7 tg mis� .r �LFr% no� . .�  %s b��s����� way%�or oy��ity. GivamaNof !�=F��^l>j e~as R-�>7f�.���ed~AI !DB7s:�A�malis�A26�-��d-m*2$(POM) also� i� a��)�,�is�n��EM}. |�?Q cha� erizA�aF� &`��efy3F���V=Lmakey��� , againsA�U% ^hi�A�6da� a%� ula invol�!�F��a&�!����os a�a�6�. \ac\ ledg�fis� k w� uppor��bS @ Korea Research FO grant f"_�.n G� nax (MOEHRD) (KRF-2005-003-C00047)�m2jSqgEngineer!�y (R01Jl6-000-10354-0). We would liE.\nk Eric Corndorf, Hoi-KwLo, RanjbLNair, Xiang-Bin Wang�(Horace Yuen!� &rA&ng��ions.�� Zre@ `ces} \bibitem[*]{email} E add�X: wyhwang@chonnam.ac.kr8 {Wie83} S!esnX"�Sigact News {\bf15}(1), 78 (1983).@DBen84} C.H. Bennet!hd G. Brassard, Proc. IEEE :I� Conf.j Compu�, S���Sig�:<Xes, Bangal(i,�0 York, 1984),B>p.175.�xJoo05} Jaewoo Joo, Young-Jai PaJJinhy LeeFRJingak JU,Inbo Kim, J.M�B�Phys. S!"!n$ 46},763 (A�.k4Sho94} P. Shor1V435th Ann. Symp%FFaj.r:11_q+.), �PA6B�2A�&Theor=)D$ing}, (ACM]iB= 1995)%67=$4May00} D. MayeJ. AssA _ch-*48}, 351>_A!1.�BihXU8V. Roychowdhuryn;>;0Thirty-secondA�ACM9^!N)J><of �!Y%XM�}� 2000F�p. 715;�(-ph/9912053=pSho! P. Wi<��e�85Ap41%z�7%�<{Lo99} H.-K. Loa$H.F. Chau,qpG283Q6� 2050a 99.�Ham03}!�Hamada�Gofm m3a 8303>��42Pwa��W. Y. H�R�{iaSocB�� 4i409X2�HutanB. Hutt�E N. Imoto, GisAw�M{B� }2�1}, 18� eH=�Lut!� N. L\"utk��&FE61}Bl052304�!�5�BraV2�Bc ��B�$B. C. Sande��Le��EE 1330F�Ina01�<Inamori,F�!D�9B�� a010701.v� 0D. Gottesman,��E�ZjJF y4QQ* I*����� B�aH4��25%4)}�0212066=�A�3}6�VW9A.05790R(2� Wan04} X.!�� ZU� 2305F]�}2LoTH.1PX��E(C(~f4>0BfScag(V. Scarani,��Aca_Nui$G. RibordyF&Z�2},-Cy2;8Sel88} F. SelleA� ed.,�WQ MeC'�#.$us Local ResmFL�E 4ein-Podolsky-RZ+q adox}> (Plenum.1988))l& � rein]OI�P Curt�,d!62EBp=-AE� 69!) 4232J)�}!�Makarov)�nisim a"J. Skaar�m7A�02231 6);B�y�511032�}B. Qi,��H.!�FuR Y��I�>\1�j�)�07B�A�72�512080�AciA�A.R�]�>�b�123ͧ2�Gis02}!�͑}$�dTitte�nd!Zb�nBwť Mod. ���)�14��2S&Hwa96��-�w I.-G hI�(Y.-D. Han, :��CM�21a��199= nNie��M.!RNielsen%� I. L�u�  1�.�B�!)] CambridgeF6Univ.�.2 (, U.K.,� .)�Ch�A� efle5(ontemporary%k�Y%m4��B�40i�0),R9#Ben92�!��F l68F� 31a�199!�Y��1:��hn)� S.-W"z .YF��6e�64302eJ� nGis( �� R6*42G �" >BaraS.A+Bar"� E. A�o6� b� 044307�6Pat03� K. PatiEPSE�Brauns��1~ �Z31k208h���$Hug93} L.P� ghst�R. Jozs�W.K. Wo�rsFjF?1�  14%?6p!?4�Barrett,a^ Hard�! A. KS3 %�� 405101. �٭} doc�!} % * E�5f fZ"(apssamp.tex  �g\8@class[onecolumn]{�"xcle} \usepackage[english]{babel2`{amssymb,amsfonts,mathrsf�C8dvips]{graphicx�-�."�ڈ} \newcommand{\vo}{\vec{v}_{(1)}} 6 j. jB Hilb}{\�scr{H>@I  bb{I> n}{\hat{n>pab}[1]{a^{\phantom{\dag}}_{#1B-d-$N#LOP$$\underlineJH LOPF &;%X \title{ \textbf{ ExploaWPost-S"�Cw2t��E�1t Lin�/Opt���  �5�date{!� make{5Řcenter} \author{R. Coen Cagli\footnote�: $%�4tt{ruben.coenc)H@na.infn.it}$}$^{,a&P��(iello$^{a,bN.CesaricF�$ncellin \\ \�%$it{a. Di�%�@o di Fisica dell'��$ersit\`{a}HNapoli Federico II,X!�*o� M.S�-�an ��f�0"y8 ancill� ��'�"�* $0.25$tTly#e��e!� ��1B � �p��&�*�A(&a behind�"!+f5%�o�d�C!�su)3o� p#Y`ie observ2-ZFin f�;'cout�.%<I(y�~>~"�"Introduz4to�: al O�8�}��>� ͊eT\al \emph{passive} (LOP) 6bdMwas�" & !Bm7P>;O"�(�!mS! �;6%| lea{ungP%h�'�|U�ms �"�_|th�ry LOPeB� ai�� thre�*the[2�objec�i $N \�<$ uniteRatrix $# {U}$� 56��field �:%(-�<2���el0 $U$ '@ng�c�,�%��e _/s a � infin�* � �F�re�4�>ngi�Fock sp�>��e6�.i"d4ex ��sQ��*�3�)���sa}c-, �6cheL>h�6bee2posed~ #0klm1,pjf1,ral2 3 4,giorgi}aH�7,orm a wider U�6�r*NAt ,:W# �mplete Cg5a�A�t�`i ��0el,lapaire,cl�8n}.&p@!Aj%.mE=s)/oncep ,ly!�p/3a pre���'0U6ed:%�i!�27ed��ost n ion}���0�du�&n 1�wA-9*!e"9/1���;$\rho�7K.i82, E@a�s�?� ~< �S���$\sigma ���.Z�dwqCyat5i��p�,!��x& exac%*�A��r#%$1$a�orAU!"�Uj: Q�A} = � n_{A%�k)}0?f9��II� d[>@%�$du�their�par�7e���.A�-an ent&F!�e�:i��BETKas�rho*F-c\/+� �1��y� A�be�1*�& ex��% $U(Bf ) U^9�6�D*%A a mi;�X%�6Da=Q �S �^{'}=Orm{tr}!{(ry)!�Ł well�)��?6�R�a%ce �er CP�=$\tau�5��1!+al�,ft у"X �" %� }: %'eqnarrayC/ 10} !X�Attau%h) $sum_{\mu}M ) -y \no� \\ B3 ' 5UI���noB t Af5B�!i�2 re7��O mS}$A�}0$,�o� %�$$\{|\alphapE��\8{|\nuAi&M"i�asF��ak�B !�E���� e =gu){�011�7eft\{�()� {ccc)� & = &1A�,\beta%v_{  J�le�  |!�i� V>� . \nu|)� �\right&�8% 9�U� !)se_'��rici� e�,� e�9I���!Ӂ�m�de.�!�q�,�b09:�2)AA�<_{\gamma\delta} � Y� ._(1muC|��)$ QU6x )=\)!*ia {} & a96�vnu:r-đ�| ��M�x � ))�VWA��Je� elP �m�$ ~>�,by25:� 3} ( 5 ^{(\nu)})1|a�%`} h)G �:��]� �A�7��Dnu$�A�J�0H�'de�m +�f��, *�"^   $I, � $ ru�rough>^�F�H5verifyXLY ���U$ gu�"tee�I�:10X.We�&�IcZ8i�A���oi� �D�Prx��V\7d Mt0} (PVq0A�6az�� $\{ |-�Mi \} $, nam� by�r*�sn;4�"P�P ���gNm� mu}s ">|6Nr*x� r$p2�3�L$ b=1~Qall��9�%YF Now8 Ual (unn�D�)���  ir 5�.ar{�) s*y-&N� � $�m�O �~�(*� aX�imk�� 6} p)�%�.�S}2AV6 �Q�S��PS}}�_� � Ε� ��� Of c�7� e 9�>��� $sh�? �"ksize{G}}}�� frac �2}{-}� ��:�"G Non-��/-S� Gate�;F;%����wb�9� "��9�m�wež� es��i�#bRj"X� �w\  I� -  (NS)� 2-�&n�8} .bO���|0�L +���D�|2 # \longr� arrow R*NV� taV- BV6B.� �2�[ io�Sl2��unot r�\> B5X�(he2Pa�am.l)P1t"�:%.b7��pi by KLM uH� ry y�&|A���Q� = |11�� �T 10|$,vI�^i*� -1 p�cp2$P_᳥%.�jy=:s%y-��H"� � �j�22� 10� 10� nAF }^{n� {�=� S6 |U|nM���� Avx[; $ 2H� !U$n$ml}k�eE(./�Nz a�q�a�C9 hat � 9$ sho�6be=iag/ )J , siA�!�vanis�L �:p�;c$n=%F�W straa�forward "T>n�nd66� 2` �)_{!�0)�& ��_{0%�  {U}_!�6��R,1�1}^{1FQ1%? R11} 22}��LO m121~y2}^{2Fy2yy ^1}(.  �2:�")-^2� MA;��� A0eh D�H�,�. m�Xsk�wvuc(atn�4J�-�= ^�= -B)Ir�  meancatjH26}2sEO & 1-\sqrt!�2�5u!�� ]12} 21}}{1-81�%ɇN��. ��"Vi&�WEy+=�< �F 16})n�5� 10�|BV)�|I��/.�nrk�D%Hum�n"\_A�=R1}=2^{-);1}{4}�J)�� s $p�N = %n Two���Z circuitsY��!-i ! �# in�s ral1b�� ^� vBBo9�6�#An�"P$� 6 I�a��Awe�i�a�1���?%j|$)�"^""a�XA���G$W�=$be increas�adI9�Tarbit�-٭_� pa�xi�e vacuum�. "� { D"!]approach.@�;lo���$�f%�injK�'%s Q>4nipro,knill03,� elpro}.} �uUIYP� at!��a��%�i"N=� m_{ie��( bf{i�.� | ere�O�*>3"egI��5 in�?  $i$-th%� f@Z � j�� :� �jn�j}|a�&�ItA���(I�� b!My�90l �roN�=K$����mut , � �N swapp�Akwo��AA�3 �^�E"�b&@ �C holdsE�WbS !5l�From a !�"�#viewpoin�t��, s��i#exM$%(wo rows,�P �-��y!fW� rst�2oE�[(�%�"� &{#n stud�A� Ւ�'!��*\)�t&oy9� � in o�Fbe��K P B ��R -�toQwp$(k+1)�$ $ � �� satisf�)��� in �L 26})�T� )M k2$� �bd�$i$��Z"j$� usI EIj�3�:(+gin�:c} 1- "�& \ldots "� ,i� �j\v >�>8^j,1^w } ,}{�7B^V�\d�|a� �"� N"�*����lB]$��� it `A}b|xim�PyULI�Y�b" '.WG�!a�uJ/�hoai��`�+E\aU$j��AgWmuS%ortho� , , ?y'" eX toge'UA֥�:c��I��n��0l9�1,l��1�>j \quad BlAW=V9lA� 8> N�W�%�f�%�al!9�(who�Qa)a� b�n�&e"`  K�&V �Gt�.Vv�es �i�,H\�P k"� �0�f e�FJ�. Nja$## ��2�T �32a"�FI}"� row})^ 1�ibz& |U_e� \leq 2(q�-1):" LSj�#*�& R�R ��1+i� �F }{2� )^{->hpI��&6�Js��6UiRU�!J��>�.�)"�-� �G"�d �fur�T' l�g��0 regs$ $5Nɨ�$A� t�P ,s (see fig.1Y&|T��E��n�agzaq y length,X�(��,$(k-1)$-C ne�� ir�41� 7\cdot\vjU_� �"�VE�� � �!�alY�H�)E�~/� e �dm� �Pju�3� A�&&��j��n Q�coBc \vo$��w,?�#caD�PnU-A'q3�(ce, mak� 6fMW(Schwartz in�a��scalar �1� be � tenv�#3�e{6�( e^{i\phi}|A�E` \cos� _{1j���FuA up%5ub�6��$-�=]_{j1}}A�E�k\T �:�Xeq>Y34[ n ph6 amodulu6�M��46j^��ph � \pm \piiOQ.Q�|Tb �|E� (��i^�iq���3 Ł6�2X& ,.Tsb/getr7�M6����%�|�)zz|} m�(2}�}�H)(:�f)�;f �/m"ex requ�� e��n exist ! g�P�a�r.h.sAM-37Af"oawPIkTo �iq�-e�;N�g�`2�n�(8} x \doteq�%;� y.%���E}\B } A = N�x�*� |\\ B >T& \\ C�C-�� %�V�&�Y��nP7�  l)h"�%h�s �� ac_2� �� !�A�%f68�4�)� depiiWin � 1*,(figure}[!h][gin�:�+!a i�Vde�>0s[width=0.55\D ]2/cap�� {Dom6q&� 8$%D� y!�$.�;�,=%\�!=Fw�>%A�Ui�쵓 � 39} z = � B}{A�+BC6��} {�SM: A)u�AM)-�2�N .b�UI�U�.\j}$�io�5trivi@n}2 "����%�)�on-e�y�`e -��C|E��I�a�  curve�E9rţ[ �$�a<A���� variE�M2j�41�j:��ɯ�����%�T�),}�1Gn �=%�= �1�� (i� i�2),-Q = 8$kan2*�a�%-�LS fAngM�more g�&idt�cat�&z1�&N i}$:�;u�� :f �P�t�=&�2�2A�enJsv*a� dim.�!^$k8�b&�n�!vf� bex.n47� r;8�^"�8\t�Ro�[z3�"o,pchi*�"�!�i=�Ns%�\ad{i}|0� .~$$wa�<���J�|J"�5 $V=6pV%3e]_�c&x<$5O&�S}�# |:��}�,!T'2\%�>�6i*$I,atJ� �BU�$ =UV$n� 4} U2khfB�) = U(Vj0�))=�*'}�-54A&i"N{ ��A�rob��previMB��<valid v u�K'"��@E�k\) �{f��PoV�F} Fur�g�iz �"�9�B �"{�d&�:b�&P 6(n�5} �(5H.|5�k/&>\)A0%Ci�je�s+j W)_�adjm� .�M ^Z t"yaV���%�!F h�= , du�@K&�>��&6cl iwy �} itud"��hbe�5min��y^c �Q/s 4C��!�$=w3�I�$�D9�8QWiXb ppen(/�� T =|�� $A�"�W�+|ݓ|_S)$s$:3 "WnY6} P_{s� 2 >��n&q8e� )tiYof��"�FinV=w� !�}'!�=�?t�m�(.g*jFis� �I {tot�.q }pA�6�A���qp�sI/ld� �t2 S =fN+��$P6� (b1 +|01u�A� �� 01|)y�8��w!rq�0!C�fu% �B&� "�\V8{48��&��&&/�&VF'32�� 4.F'3�F'�5"z�1059 V<"�0&'12i�/ (21 3 r_InшIs�$k=s+mA>2� , be!�tP81&.�#��$i{ s�; �al $m$#�+ �|�"u5 % ��a� *�fs� "+#to&�&��!ed�5�rFY�aW�5�ns2,nC�n� �&m2hM�5"#!� ar�;�"!"� 2�.T!2 y*z7\\ Z� {} LC,s+1vo !�Rk:OB�j2C���r!.r!I����b�J�����kA�A֙��Cn����ii�a�F1j1 &n�F�x�j.3� &� 2.2�A���aatх&* /e��s� I�5:andMR�$)6Fp�a�" hQin� 2&�r�oe� ?��P� 3� !��&.Y)�&&y6 2��� }*�+co�w')ljrgu��! �4d��.RA6� 2ZX,2_��P2v` N� )aP!   &� _{+J� "#0"2�  +# V� n@l=�0� s lrlbU6�!�% �> >^�) ^C>�S>: +=�>B/!b!>1)�_{-V�l,mF�m-�� mf��_{-z`,nJbn]I oni 2l��m 4 "� � indi�&$+,-$�� ��i S ��(�adpor�&t�E� ��R�=|0" S}$ neYMaS%YE+���6Cbs�*ntP$V$&�|& s P��)to g b��:n ."ɋ�keav�.mdp��H5&%9�H!��? &�.) � �dJ�2�D sDҁ� map �dVb�,ndF�, �q��*52�"to an�&oBsM �3�>mAJ&p��ZV� +:�� &e��.b.% �)������B�����V�M$��B���O9�q� :Ua� be b�BtMaqitm$�� �&� $2.2$P�#s, $V(n�m3)�^{'Ɵ$��Uf�U&�xs��?F�?J �el4pap�l�>�p usue��, Zt �pyQed� . Up�nh%l �0C� n_w5��{ ion:��}no2 ��Q���Mc�-pen.�|�.resouZ. OurSategy 3stotr I2 6d�=&�)�q.N5�w��M)�!!� �h�2�ol�{�;,� J��.�} fact+o7%�at& /s\"�!�.B is �YZ}�|[8JI"1'S6l:�O9w� s. F*� hav�pFed��.A�&"�"� �'d.�Frank-rje���E$r>�E�!5�Az(V fu-{��\�A�ae.gl"�GrygP}|�fBfBD thebiblio�"y}�2 " mT9}d�Kn7o(R. Laflamme)�$G. Milburn�^�U (London)�.bf{40@i46�c�,b$pjf1} T.B.d Pitt�l$B.C. Jacob�4J.D. F�A�c�c�g� bf{A9e231f2g: TV�Ralph�iG&|V�0 W.J. Munro, �  G�Rq�d 0123-d20Bq2BqLangfou� Bell nA�fl 6232�n2.oraloeP%DLun�� �VV6�j 3232&�e5�ral�dLV DoddFrC.R� �%�r04232&�ecY G.L.fGY8, F. de PasqualMh0S. Paganelli,R�70�8k�p2 j�9}G�Sch�X K. Ne�p.�P�Kn�@Vo 68} !=1�o,f�lTY} G!� �L , P. Kok�q.�tqJ.E. Sip%!v>�o4Un2o�Ygl�Cl�Y�fKnoAfaD�Welschj� 4382{h2c!;: �.�EVrqi�2�a;:H�[�p30701.�w)��;:���qu& r�dJ�k��51�{A>���H>�H g&�f]�B�gtw� umn,�\0pacs]{revtex4Ueu�,�gugs} Ybe�([ \|e{Influ�Fof pump-�].T�s�clA_ cal-l���� in a�(ic band-gap�#].8lanar waveguide��e0Jan Pe\v{r}in�tr�$affili^{J�: Lab�=oFf ef�t$alack\'{y}Cewey In>.�'Av�f of Academ� |s6�Czech Republic, 17. listopadu 50A, 772 07 Olomouc, 3 3} % \alt� []{FacultrN��alz, � %�F~�}\�{{p�|Ha_j@sloup.upol.cz} 1u� ita Si� 6-�Da"ga TriccM$g( BertolottiK=�> gEnerg�djg��Y�u�rials, ��gőd�j)�smai2e@��sJ�c�SnNQ � v�fsl�EIus &6k����mn��vm*̣~ harmelf3-�aD�5�b,sF � g!62!D\�Sca7F,1997,DumeigeA }. P�E.L�!taiL��r�so�fulfilP!���U&�Q9<�cs�jr���nd!�Jj�is "�!!���ay� 6�$�e"��ofulkgt)�,�.,i�9\m�@jE�� �E#[>cɕstr<2j�p2U��'!�a�Fz u�.�A�Pmayc�@(it91!q�]Zш�*.�.N(�� �, 3E�^��z�A)Έ"� sugg�S��(Sakoda2002}2�8P�> devoz�'�e!��2�)U��& >J&$ �Y�&@o!7Q��'�mu�.��  uջ%5�:rrL;a�o�Htop���:w-��rol_E�B= fund�o�3-E� 2004a};��(iXR;��rR�"�..QKHiod�]�W!g��ng� "q���r��c�!�*i�%� �"G� �,iW��Ӟ �9L1�7achieved�s��au�;.�zsusH7 ty. C:��� bas.qS)�sj� }����V�p)�P� Jr!�@�a9Y� q��pa>, IF��I%Rset%�s~�( down-conve�%�s.el�#oҟon� exte�:��al��A+��M�6� to accoun��so��A1� ^\�H �jqEn�.aRQJs&�-��M~��&q$y�&�pr �#new1sIO��j.�B .g I�E�ciN ng�EaY�� R�3"x � .���superpo+�o�s7��n� . &+ K4vu'Le�(s gEje+ *$l��F8i�[$in Sec. 2.�X 3,&�-O �cB+���ds. 4���I�-2 }Wa��)�3Q�P*�0t�Cr t)'v� "� L�"<��5 �6Asa *cݔa!&�[Fx)�p���UR#}6��5>^:�0s > a� M2�5uPprwqmoaB�jpeH$ �yG}(z)1`t�." (s Heisenber&�;!� moi:�Qq} % 1 %-dcX}}{dz�5- ixz bar}\� ft[ (G}, X�`I@] ;w�$26@?$/ $A6n"�N*Y�, . bar _P !5Planck)Ba�N� ($ [\;,\;] $PY,�{�Oor�$�͔uJ��n��'bu� -propa� ngIw\�;%2\,gh�X.#sA��#J� �G} $ C a8a/�B�.&7�wO� c-aa�{�F�0}. 2sp�AY�ᵙ�moW l�j�d �^}���5 ���C Vj�E�a�� $c".0Au2 11U1+ id,�%P ($ i V RV>+UR� Tp T�z �lyV�:6_L���K_s��$ K_i �5 p +fP_Ͷ*�U qbi���R�)y, �6!�s1a�O� AO aorigi�E6Z� r>4!eqya<Ml_aG&� bo6�A�M�y�� U�Q=QFaFnd%GBAWt% -IcxN co"��W.�EQfH �.�ist�7�5 �`v~6 8�m"�mafterU@od�,�>�� 8ZFO, e.g.tk� Yeh��,Pezzett�1}d zFN}���"s���p d� ��� in Fig.XkT��B a fige re�g box{0.7\h }{!}{>�Bo,1.eps}} \vs�, {2mmc�F6��"� � .�U>$; $ A_{pF�k s A7i [ pB( (��$]���m<H�oIY.] [N�] e�4cgn=F`��)~� K�"% �A$�8iA�re �2Q�%�u�2ze, TaQ(]��2� =jBi MG� (�)�:b .!�F:fi�H= MG ��w����e �F�Es�:��iNV�)Q�Unew� �ux2 r���� nb}f!�v�>1 a�vJ� � 3"� /�� �Ya�h�b} ,J2�N2N2� N2,6� �a�F7:�q� R�2:�� rd�.\�RA"R R�2��1})���v� ^� !�46)F&=& i&� � *�  � i� s}B" )^b=� � 2� &Q0m�1{ 2@ E�� .ZFy�6H\j:�;G �>�2��i��!��� �2 �f�>@�-6�B��� >6 -!�^*� %�-: )�!8�Gb�-%�B)�.iA� ~i ��!OZ�)_R��-�f�-���A�v�!GA��.��- +!�_{p)�2�)�>lr�%�!�"�i�%�t!��:\}G>q�2|!��>6)�_{p}^*-J��!v��J!��.�A#�S W6ST%0a�ie� &��.S;.�?&q=��(s: 1. Retur jP M l�G">�� �a} KEqsyU4})P P"�*s�3 2. T�-��>Ein�"�on �Qp#(oU��;A}_�'[i6�(z] $). 3. W �*Ɇ �=�th2&t yas�/= A u+ : 2��NTX� �0 ac�i[#@#� i%�$6Q�= a ���� �%!��2RU��r�I *�&� "ʂia]]�Ra1Atn .S� � VY�� :�9o �%��5l $���n"�* i*�&)�)w&"YmIs*���5 ��A���{i�A���{s}z)� � :�NaE�"�{F ?�� A�6�, �+�A�A��2% �:�i Q�����^��9 -i�!:� ="Fr���)"�M{B ҡ�1#B�^$BF���{=&���! 6'���B��l�p�B�2J-Ɉ�CALM�M�FM2�J* �5*�!*9t�D6�+ �� �C1�!#� �!���\6S$�"� �6 �X_��a |�*({a_F})_z| +6� | -<l�h�,0.5cm} a=s,iB� ��_�:m!�FmA� - 2 =lF� Vb}FVb @.�s .i,2�b=F,B� 6X Any"9��u� " 5}) obeyQ"|�e֐lawE� (in �1uo�terpre�b , ``��of vir�SD��:�''!�erved)R�U7U܉�U( |m|^2A�F 2!�|^2av�O:� K. -/A�? �h OB M5|0�+U� �����*� !�����A!�9� :,�<��R, % 8 e�a.^{(0)I�a�)4-i\�sM�a z�G%)) [B i^(�()H 8tilde{B_a} \sin2 E]� >LAa�BV�v�216�\?�:� ( �r�}{2K_a}J�~D�� _a}{(EV�) �7>�2��=.4r�:r�-V�F�)}�R��� p\��zN6J2��Ka�9aG-)y�u6O^2:ta@ K_a|^2}; ��1c� �u8 ad>]�8{[�{$ Bn� $!�I�{s} $B���5n{i :p'� .>p" �s+� ccor)%� bmr�^* ,E� "a� �"-�(vole¡aҙcof& q� ��i>S0numer� l���"ir�(���$x�!��~pD8� A�'�� c� ��z��BVP!NxRe׾s}&o*P�J"�1%� task� .�%�= ! �%�3!Uղ9NRA�10� � A��N��{\� K} +� ��H$F7K�# �]�� ;"� :*�� ��] 6f i[ ��� N�iB����.���[:� ^�s + � � * ��x���^F� Nt� -�| �? �j �G�-o>$�)ny�_&� 2U!�.I 1ImJp��2^.n + �!(2)>�.�� B1.O�_{p� .8 \-#��](N�A��!"/> 51j��^j�>_� S#i��!�U!!D��>8A#�16 6U�"���6#AS�1:� iɯp K}_F�$$xin"L��7J 10})Ű�m�JL % 11 Ta�� iK_a  �� &_ ��.�FM 2K_F M F z�5�66B6B 6"�B z A6^������ �.ߢ�)>[ !&ő�^�:Ng ��.}!��\6�gU-݉��!��'p *� �/E���F,V%out� r �$ %B%i���KR-�q�FF�T XA�crQB:# BB} �NI |{ �i�qNB�% ����1wc)�-�YN��3�b�= R�!H�z(0) \:EA2qF$ F$��~@��(0V@��~@ $}F�){�,N� ,)$�L�2@B� $B@� b@$B@�z@ $��~�, � ��INAsv� B}(L~�$Z�r1�8 �J��@<@�-2� �:� �aG��I�2A6�BA�f�z@� $ �)�Aq� b�$}#*�F� M�w�5� ����$� I:$.&��1�2*>3�2r�� "* ofx " 10})�.�b-�^*^3�-:,VW�/�^� �W; s��*� 1R^& �*��*b Q)wu��E#�\d�y:(]K$ݞ&Ş4, 15 fUn��.kA f5�=&K.�F}i 1� �U}Gx_��n�!�F2 �YK+_E$&J;��.�$9"a��2!�����z14}��  �V�K�a)��>�#Bn�qvF�evx}7=+�6d{ "z ��3 bes �i^' b+ 2--.}+ eA�^f:F* .Fco�4 �f5 !�)>.5 �j5, boso\vm3���5iXWV%%! �"�V1w? @inB�: �!�m�n�' � j�Ɂ:M<d�? Luis��}��-9�o�pe����P?G+�ny �XQ6WiaFd�;c hamiltLD2-�ofJ�7i�BF� ��v� ough%�se�?J9*� �� A 4}) �kal�a&l``52�'' �A��#��@ledV�% 16 [�|q5i(L),6k(L)]�V0�6�{}�B"�J b _{ik� �T��k} ��J �i�6:� #� -1��i}k� �4�6s kN��K-3�i,k.�5:��io bar{kH s&�5&�6}>�3T�A���S�=�u��i��l0preci��a�a"D�.�,�%"�#"78X?f>� P�>�><��= 1991} (co�# I�o�I�-tv4"/? n�<co�Eed)�y 0�aED�-�"�1��ot�0*�0�j� C D_{jk.�!�D} �0 �i?0}R*% 17 B_j�I���7U�j6��G. �,Q� R_j)^2 b= �.@2�y\Ok.LQ�� j \neq k,:x2-i-�2Zb�k �Vq&�;7B6$6e_j� �&j�7Ejk$�bolB $ \;\;�6�;�@n�s�H6ean��$5e��iƁ�c66�mazTG]�up��EwU_7a��X�21 5in;Kia0�{j in,�  A��  C  :��rD �M-�n���;,2 ���s (�deHa�eeNCVx % 18 w�6�A]Mh^2(r�ln_{ch,jN+V�F�1� (i\vaq ta_jh (2r_j)�eK�� &Y9r�CA3s�'�יq!�S5� $ j ��E5fy* >IwIE�$ ��>�'��beplcha�p "6� $��A6h"� �J%�annI_! to6��2++�e �=�F�Hy`�2d1\� �RIAe27A�r�a��w z.� 7"o8{�elDiC q��*� R�>^9A�� �=k�d 6} \Bigl[�( i�Ua$2j-1,2k-1}_mC�J��<c*���R?�^2.�� F�*�U.1}^Q�2�:<!p��2-�� H%=2R.=):|.�% iYK>yl-1.�kAV� C_{lF���lF^ \A��^ ^: �aBR�v��B!2a av)�VgH]�1�Lj�1 R��.���V��n�S)&!��m�BhmF�grhR�-19Bg~s - �]zn�RyZ�RGa��4! -�; � ��19J� uB�z2J c��c�d�qwTSDF�H}�level��) �=Z ,*�2iU��1q $ [.=�A�Cat.��L"= :wn�cqXlK-&30"��H->$ jj<�& �pt�<`= -i(�- *Wj) $] .zHb�� lowe�vaV :2*�T6O�d� n�Fspeak/���-� 6P.�Jg�+�<ByeF<�L�x vail\Q <- iXIe&/�some %�� :2U-&[VzL�T( homodyne-mǩ}I(�� ��"#�aR�|U.�"^M2oryDpr? paXP��ri��$_. mbdaA� Luks�?}�f�toA�binT m&�U%cs!A(a beam-splij]�rHstd�w>`Z!� @. Sـ %�0a�X"�2 �-m��&_(6xU tB�2�>-� ��p.VU��vP�O�' �y, L�ml `pfRg-?  @ ,>���vneap!�")qU�e��-#�� �^I�!Av�!�pj)i9aB�U�* �"4.kq��3��Fl co!�A�e�-��^k  s@e�q}d���� �� q}_k&� ��p6-�2 -p- . U1�-��BB�s�%*lIs�1��w�{�M%&\lN¦'���und��b{ij� �h !T.� *��h20-21}�<1+ 2[B_j-|C_j|],\li�%2�,[1+ B_j+B_k �/�� Re}(.N -B�/.�5P�/� +C_k+2� |1 ]FnV���n;ᐕ�S�=����ica��q�]!K�U.�A�. �|V"�S��i<)�((two-mode) �case if values of principal squeeze variance $ \lambda_{jk} $ are less than two. Similarly as in \cite{PerinaJr2004}, assuming $ K_s L $, $ K_i L $, $ K_p L $, $ K_F A L $ ($ A $ being a typical field amplitude), and $ K_B AL $ being small, analytical expressions for pr � >��Us can be found solving equations in Eqs. (\ref{10}) iteratively. The obtained expressi9 for 5sJx Lsingle-mode and comp� !�s%�Xthe same as those given� (23)A(25) of N� whereL, system with%�Hp = 0 $ is analyzed�0us, no inform% aboutDinflueA>Tof linear pump scatter!Gon�,d-light gene!=on1yob)=. InZfollow@discu%P$ a strong !� dent!A@ward-propagating �field !P,also nonzeror9 signal 5idler E)~consider!Sqe;d �$cannot be �ed!�.�%�$. However, ,l,5� AHtwo separated parts 1J!/ic!o cessa�nd &E��e differA� E�ac�i^Dly through evanesc.�s. This � ]co.lhas b!�5in �08Herec1999,Mista ,}. We firstAJe �6�l2� !�A� K_p \neq�f ). IEnre!�ph��match!�of all�onsA� e greater%���+�P$B!��j� �� $L�AZy�� is means e �XADnon5�.�1�-�along 1 structure��(modified byKz���a�,in such a waAa�amount��N�z��!F,decreases. Oe�, other hand,1�coupl.�Mr�$transfers ��gy�o�!Gpa�e�so�i� observedi�in��)i�ݽ1�F sup�^%J��i�!� ode,�+is show�(Fig. \��0fig2}. \begin�ure} % fig 2 \resizebox{0.7\h X}{!}{\includegraphics{p��pa2.eps}} \vspace{2mm} \cap��{P�{  $ !��6�a funcL$foB�ep �Kitu%�A_{p_F}� n��5��� tantUh�� E��H�s; "pF = K_B = 5 \times 10^{-2} $, #s#iK$, $ \delta F p =0 B $j o $�s�= i 0.1 ;�B} s i 0 $; "7co nt stat��a� ssumed. � ى unit used!x%!<i phys�2quanti�L:!0[K_F]=[K_B] =)+<6} {\rm mm}^{-1}  V ,3s3i p]= 61 , [LN 9m-)8 = B � B]=C�, [A_a[!��V � $.A�label{e= \end a:� ��l��uÁ�AI-�Z�� low>�p�2. N��F�sM����OBd ��,U way. A+ �depend� f� s $ 6 �@n lengP L������J,, because ``q over����X�fe on''D� or� al to $n; Jpcha< eriz�ea5��^�K!p $�T�>e.�)s��ongly �Q� mis��y�p9���" backj� s. A drao c���f�2�in���CL �.�> 2|K_p|� s�$ in�$��fA�3}. Ao 0e approximate"u!iEqs.  8}) � ��mean-%h s suggest�is reg of�  ers� a 4of�l� $�MF�n oscill � ior?A]�s (as�Fb pos �a�O C )!�M�2�26 ccurs��%y � ����� Aexceeda�1� , bu� Q� 2�D;a���2&1'E � ec"�2�to�~��sf+3�+3�+R+F4!o6+.� V�F���s; $ L=2�$5 �oF�o1�`9�AGo .��gAq�qo26]3B]��R�]��-��eda�M6{nl} = F = B&� Ų��-+.�|.U(describ�P�=%.�)e��ens���9)� �BE�` enable!� Efaeu. If,�p we"��r =5 $ mm${ �s!�O .�writt�� ai2v 4},j��q�a�~ ($ &� !� �0.8&q����N�Ha photonic band-gap��� . Hav a j& w' suit%�9���i6���Jr��e�reachEe 0.04 �}pri�}�AM�asY�YK"�o�/M��9n�. S6� ŋ�E�!���lie t�r�v curv�,=��a"xs�� � 4�|lso"�%ŵut re neededAh� G +&� f�4:�8�� 4~�Topolog +A�f�!QQ�� Q�*�!1it"� & b� ���ԅ`��� L!�V���:� �$ }9�a�B2!�z4:� (possibility!��jmy�-�Zu� -5<�%xs&!di~�",PoDong2004} "poi� view!�$efficiencyDnergy conversion. *� �J����bei�com�Qd ��z6"�*� ɽR�� �e=!��mum)�G ��c-"�!u>� c�A� N� >(to�4$ 3\pi/2 $ [$ ]�G�.[2s ]�� respect$ "J�%�w� q/6�,!,�2�� ����6iU!alysi��f���!sicult� thes�d� s M�Bry�U���introduc� ome)� chang�\�C��w9�L�.�gA��)j�R>��  =�� s". )^%�� ���~y chosenI�%=���e � r�� �6^ originin1=6�adown-i�h E>i�����y   i $�ort �Q�2��Y�< "(�y&� !mgy �6os3 u?!�� � �O  s �-.<amm�R�) !�?�"�stimul��K2� �V- t|indis��� �o9ANn� +q,``an alreadyM�!� @"�)]� V��ta ��$�� r�'-tX!s''. B�in!-*�m% .��� m*B(�op <*I s s| ��� i i| $)F" &! q�� ��!yy����arison�i�7E�:� probab"�Y�>��Ax V�-�vacuum"�nd{ť�@ir 5K&n � y setK=� . InM7� �m9 U .�R�2�(5�p &t�# s�-�i )�i��� aQ�FQ! low ��"t �d v�!�"u F� t� me. �a�a�bem�ed��a wide r�La����!nnoR����*�, e.g.=o��effec�d'%�7��� which acgains>�M+F�Ѿ. A"�cu a&� �:WX -�in .j!�V=s$ clea visi�=O "� 5}, �!UQGU�Jlmofe���is plot�Qas�hes U�Aq�i j� 5:� ��5~� ҅!��!���!B�"l �ZZ5!,� ic$� R�h �Ww )�=��F�5:�  A�XC direct��y �l e substit7to9 95})%% 10}�ir"js� od o��e 5��!tps!0-\arg(K_p) + s i)"�Bcon+ s�ou� v@"\$� u>zOV� �.�  had min&o s��� �� :�� a�A�e���ts�est���7TZ  $���5 on)~�q&�N9 >� B > ��"� � A� end��a/�1 of����w�u_$'q%�A��, �@"&j���rn&�a Xr?% =Ŗthen  ���� A & g $combine on:#�zN� �}mgz .���%�U� ��s *>�^ ��(6�nr&a R�H��*� &E!~� %#I"5}.�!. 5 \s�� on{P�-number ,istics} WheB(%U��detec�ȅ� clas� o>al � &' TY j(r��y .! n8)lly-or/ mo 'Iw g7& ns�$ \hat{W�= = A}^\dagA�A} $):�"e�*�" % 2�"lab* W^k \� le_{\�'N� N^{_ k} ; , \hs�"H10mm} k=2,3,\ldots, �o* �� de� d* electric -U opera!�of�9l��%t. Typ� ua)�al�$ trib�laA m�+em�d Yk9�� Armi�(eFano fac�$ F_n�J Be~,E  term%�>  � a�+sf�3 �= \frac{5�,(\Delta n)^2Q } n} 6�9VAWAYF}{A+QhL  . �>"2�Y&(Symbol $ n Y!��m�B�� � = n -^E�� $, n +W = W +W B$��tm�U�M�W}_{ija��( ���i,jai1 n.E&[re�on�[i� Tm� W}_i!} j�� �� �$)��ndA �$�X�M�� � $�j �C��eT s obhhau!�_I�\ge 1!"N( �h!c�NN smalO-���if �u idF'��� �4(sub-Poissonia� ght)�**�l��!�at fl�G� ��IY�:��e(�eM2� limi�ab, "8)%�XJ�!�,a laser radi�.H s51 Moutgo5-)6�]�$ framework[9Ql�#super"�!3 �.enoise,�� ��a.�narray�z % 24e�e�W_jFP&=& B_j + |\xi_j|^2 ,�Fno)� \\C��W_jR� N^2 + |C N+ 2B_j`(+ \left(C_jt ^{*2} + {�'c.c.} \rE]� V��N֍Y_����|D_M3�� |\bar{D}6b & & \mv*� � F �*k^*��M�k^* V�. ��Qe1� Co�5'!�$�gC�a �a�$ .~ $ a9i .3� 9}). �����n %24}) "&�)*� $ j $th:o Wi=6{di*as well�{�B� M�* i"an expan� i�`Laguerre polynomials (see� C��\/1, ova1981})P�l"�%a�6�s�s�(s mostly at|2 1 level.i1� ason�!�a�in3 �H&J!�ump��t(RC '� E'� 49�m*�&�+Ak A_�+  A_�+$�+� zero. O2 .��2v M?��B�2t� I� just th�*�J�cor�n� �uA� � -f��6< �Q$� b"�ztat"�,a�iC4 ir�s�$a{�  A�j�s<*a�K_i p N�7 a�!ɜk)1�(.A+b�,a.re�5�S2�seconIz )_ m���8t was dbV�8is N#�)� !�s!�� � %�aos� blis�)30�31>3e�a 9a!Y�!n@',0 $; i.e. no�clun^V7 7� de�� WB�3�#V$y��no �R% .V�8 ). SJ� !m�8*-!��% a su!��.ing*�1as6�6} X s, i k a� 2S&/  �7i:stf/$6ƙ6~�J8 : 2�%Y>x !a~|!�7) 1put�� �2�y��z%b. ����es Il�.�#xi��mp�2Rm{4 x1of�Vm$ {.�(�mean EU � �8O"�� �m2I� �26�*�$��Z�2m�r^�2a�� # �)+ C l 6�2%��1�n+�e����+v�2���HC-�+��j lk� � L3 �y= p v0 :26}fi2:J(!�j�for:�� ���0lFp1 ����e �"�*�"�+ɕ Be YQf�� IG�A&�I���$ ( 28�nmJ).�š^� �EleadsA�� 2� of&�7�����"�"<8H,s ��nBi��O a�>n)5!�2��� " 2�*5� E��9:an�m.�&!>0���%��JD�2d� {%z> %�R=}�/C,F���Yr��F_n \Y 0.3��se:�7 �.��!� �.��8 �%5M�1 t:;JlJ�]�does �`9�$2�F�%)i�#sef)7�)7�)^) ��F'1N*!�� �#�>�)A� )ą�2pa�.�%>�*6.2K77:/NBP&� �"�*"Ea1��wi� 2 �6� resK(�O=E��N�Y6n ��yi1 6!: "�#* E�Z�#�>C%*.&, !:( eBK��%�!x��$RZzz$ More3,�zS VS F;�?4 ��,%v�$to fulfill� �) $�]�:)���:) �L \p�  U�A>�)N��T��#*� d�"s��!Z>^5�2  ��N`��_BDz���FxofR�7ach_CIn y����F 1�bi�7ly 100� D��� both�%B Z>)> �2"j8j)>8��8��^�!\.Im ����/�0%S:�8:� �Z�'ɣec��5&[ � ��Y&^ ���I>ic F"4�VR Rst� <'$Out��eE^�i. E$4*RLca�)n�4za$a�;H�lue���.4A� _" 4aQ somee�a-n���e�K&D�  6%p �� )?be�) C&� !��-l� �^ �Fo�GIf>"�a�~1 : 7�.s��/ i0�Ci�H�A�E��46}� �&�#b*���0.8x � /ic%�Y���&w* $}+vid�5*9Z� �lFly� �& docu��e��9�5ccord�ItoRA%!9r�<i� �%,-sp)+/] ��*�2iJ�� J 93� &03�6�A�*> �k"Q-%> �z6!>�?�6�/!�"w)9-� �"�Ic!�is�tg$$ �  � X"%%?* �2� � f� 9:�55��69~�R�6J� ^�i.&sA�d f� U)� f� ki�t �$e�!f an 1�)�*�)nDY=:��)�3v39>3ANad= m% $ \varphi��A;@N '�F {528=� �) ) $]2beE�i�B step� �k%\st�7lوNw a a Jow�+z�n�o.�P��ُ'Q('$�A!4 �EJ�f!O%v�t$ 6' Lo�y(NL�yusu�%ed��2sdOtF�$ W�*J%�9 � ��4W�2w��K!�25�J= in 0* full�(plexity� � OZ= �H+T1�O�?��| a6K67� %P"� �Si�6� ��6��Q $ deOy>� �F (�n%E"e6 F $)�����10�^$J10:J��.10~JJ6�5�5!0!��6-72Z���� � 10:�k$\k$A !�p���4W2V7E>5�8-. M�S2I �Az!le$Uz�W��i�� !w!�A�eTa�z�;%�4$�%qui� n'8l,2{4SF;6-$&� �6:i4�.h4a� p4!G)�7mor� veni;K�{�%B& . Vj >!C)a��l��)?�/�j>2 /<sH��/]�A�'U-s M�hI:B � �[��%�!�J���FUZ%��%!r/ =�/PE�= �/��Fen��"�!fg6�3�Q&�"a *�R�GL,�"�V%e"�6�b$.8 i"1��+SA�QA�h ose�/wo "SA�-n:� co-p&�UI�sDM.xR"�-I�e'��(�� -to-�& WV} !@&' �!e}�!`improd:�T:Oa�aICieb\is I6Wbe� la6,claim��"�! �%!:�R�y < "� e�~�=eras�ficc.�%)��1mriT. An a^Lgef@a t i&/9< Hm�sa�rn-��-mx;�re exis�.�0�%�"� 6�is max.T �Tral V�� 15x$(�# spon�aP*R&-�i$Q�3�!o0o?t 5g$.�(wFa blu�;� .��F�kf�So=��:�)Um E���� S-NTE�s�psVq� bes��n 9!'r;"of�e| �i9Mȉ�I �"� yI!Z&X%�]K!� La"8Y ,&"���*`*pi� ����:>�Qa�Bxi�N!|H s�)�C�:�-E8 ose �$i� per\:ly^;<�n�c:�f�&>�.�J��E �Rr!`lN� ]$vw��op�?m.� N ��FDq%�#&4�ons *H���� &H%����� .� �#�. S<&E�eD&A��(B�) $ R_S [$  =":0W&1&�+/B�,^2 $]%���Aߑ� q= 1.7UK(.��rM�s,6�!aAH�s�R�Am2g11}G z"�I!� m.B#. RI "NN��V�&f<6�11}��B achie%>%�!�1is 1.36f�11:` ��I11~` R�}(:A�of]I� 2��'�.�WA�a��v�.�Bd�$!h75;F�Y(6� A1Q7 �A��$�3_{{:/h}, 'A�%$ . 87��e؅p�Z S�C:!tE� :@11:/ Capa&Z?)�Z�_es��p��|aDb��:=Q$=: 2�!�]m�ou� ha�S�?�("& *� ���U ��?i�"~ �h� %� !<� �G�� &eV���je� dem=�8)x�12�*.��+�3 %�a2h�1e@< h�� �& %�v�b5�j@�8��[1��[R�5v��Mc�u$ T�]��A��4^yn�[-i6ue��5�chaotic �o��b!Ё"�=� ^e�out} /in ) � ( (�1 :�h&XA�lI  (�4) � *m8|.�=V��8z����(�zN� X��6�2>�.�<Co�-�<A planar2� ��.� "� ��� �<j$*UbC?"�a�a�>�N xqh�>"I#  -� :w � -Mvs"�2uc����9 �2�D Tas �36� �betS2k>� oM� �*�1; 2"#V�NE�&�Buccessy�E� :�JZ'��(� ad���G�'�pf�\�.y-xI@!�:�nom�.C*tbnV�h�0.p*� �H"�f�5"� 95ե8� �b�� @_som�9�4Oa1V;r��+EenYW�2 �&4 "'+ŐVi &I!=j��at�� &Z � .��0��pr�3ty makO)1[i0=�YCs6misas sour�ONi+ien�4�@*�@��&ifOis;49i�ݩjx�9��i2�:!�!��c! Qght{M"A?S.��$acknowledg s{%�:�3\*�> COST!8ject OC P11.003�zech Min�7FSEdu�((M\v{S}MT) � \�ESFWdP11%�by�U(nt LN00A0152k Rk. Slco^ �Sco!�?agree� 58Palack\'{y} Uni�Sty�(La Sapienzaa�Ra O5E ed.}!X%\biblioGVy{pbg}�the.}{�~0bibitem{Berto�I$i2001} M.  , C.owden,� C. STUHa, {\it Nanoscale L�a+NU�O+js=bpAIP Vol. 560 (AIP, Melville, ~)� �Jo3k0poulos} J.D. ., RMea�e(nd J.N. Win���C �, M.J. Bloemer, A.S. Manka, J.P. DowVg6d( R. Viswana�!9 �W�Z us, Phys�v�#L{\bf 56}, 3166 (1997.�Dumeige!\} Y. , PfXdakovic, S. Sauvage, I ,gnes, J.A. LsZ��.�LM. Centini, G. D'Agu!�� 5Appl. �Lett. �78�021 (�.�0Sakoda2002} K�%7AN,. Soc. Am. B K1B#20AV5.KTriccK4a} D. !tY��tm�A�u , M.�C} As� JV� 21}, 67 �4.�P�;8@J. Pe\v{r}ina Jr.6��and��-\RIH\textbf{70}, 043816%b 4); }f(-ph/0405051}p�0ap:�w6�, ifroga$��m�)�4�\Ed. E. Wolf, (Elsevier S�X,e, Amsterdam�$0), p. 362�Yeh1988}A�Yeh�uk al W�min LayeS XMedia} (Wiley, New Yorka�886�zzettA1EP 6z:Ju�U�6�A2-. .�a132)�2Numer� 0Recipes} W.H.��Sa�@Teukolsky, W.T. V9 �T�0B.P. Flannery)8 W X$(CambridgeJ�!A96.A$Luis1996} �&u����]:, Q�hum Semi�=m({���39��2ZI� 1991:� �U S"W ��&a :~al Phen8<a} (Kluw�� Dordrecht�2~ LuksIv� k\v{s}, V�ov\'{a}� J. y� �,Opt. Commun.m67}, 14�6�HeSo� G Actam�Slovaka M49}, 731%@9.�& L. Mi�t�We�~U7FU.�\ž�u$nd A.G. Kiac[ݡ��} %�93� 3390^ �@Rf i� �Q2A>74� 81);N7A >�ZI6)�E�j>6 ��*} "D CrBLani1999}�B�P. BanfiE@DVrgio,Et(L. Tartara,�))B%= �7�S 11985�pG\�eX4{article} % Us� on double��or re�^cop_�3 &��  \u�(ckage{epsfiW am1h}2)amssymb"� �}� egMorontm�u(} \title{Loa��u�6ol eZ�� �4e�$Pan et al.<eria !�$author{WalJHPhilipp$^{1,2}$, Guiume Ad�"Dr$^3$,\\Salvador B�F8za-Lopez$^{2,4}r Karl Hess\\ 1 D�st~����P, UIUC\\ 725 South Wro  St��hampaign, IL 61820, USA\\2 Beckman InS� Advanced �AE�TechnHbypD405 North Mathews qUrbanan 61801 n3 School�0UkMd Sxs Engine�g\\ Vej).Dplats 7, V\"axj\"o�B, 351 95,, Sweden\\4 63A�ic901110 W_#Gr�"f�ATead{wp)� @uiuc.eduI[Vaxjo]{B�# �!�,-{]{V~6Karl A#)dd [!W]{6�>(.B' �^'.` ��, ��.�=@>� I�.~�aM�.`5� Z%n.�%y} \make��L abst�}  Q�0! (�W EPR�8adox, Bell's %irPi�GHZ\ etc.)t8PACS 03.65.Ud %� �f.� \VIn�dA !( papeYK=��G pan}1�.�alMs u��� �Vin adO$*'pecial o�9n >:)e (POLT)!$ actualA �6referE)��e�=-"�5!�0!��V �v_+f,BirV��~detail]�.p�>Mr�H;W�_c�a5a��(i�H*eMd? pai7rreAtd) af� ei a� ar� ? $\L�_$.  may,�!p re�� � hidden�lY�A{!�(OOY-�-��Kay%e �qm� � b�orm��}vefWkx��-�=M9s<~4n�2� p�9m�erVtO)i�e �Uu�fmWarg�8w�&�ykind. G_��a2�"�orm-*A��'setŭ���\$xyy$.��_��8(]�$ $X_1, Y_23$,Z coul�d( x�.:��1� � , sa~ $yx6� or a $yyxf�$Y� X_2, Y_3$3 �X�hk�`,i9�s��$Rb$. ��&ec)g:�]� has +G15-�=eQ0refore, extenis 5��ll!gi� e�2)�+�-� N��(A�@ s�Zfy ��^ e�[4 Y_1\cdot{}Y_2 X_3�?1,\qquad%X%Y% -1,{ &}X%J% -1�(bel{sau&�Su�<}� F�{Y_i} � = +.Hfn1� ����%raEq�Sz)%CFm��1�obq~"as"(Me�l�}predi�e $+1�G��� Eq.\bsau5})A%T%ult�y���' cont�W). ween �3%��w. "z�"z! else�A�m<3�Q�� khr,hpnp}�is�s��&�  �>$riously qu�bon� K�Y�7 uD�bE�H0 critiqu]�aV���� . }� n!�mm]��:[%��6�QHF� opiniqT� ye/1u�@n�rmD �%b9 2st!\S.&~ a�s� f`��~�N�����.m-K-*oo�@�]U�I�_oEain��all��id� ����'� | .�VE�-8'It r�5s sJ al"& al 2�A@s.\\ Obr(Z ?! '��ˇerm �4;��,��# tart �A�e�Ur,��av0o%!oinvol -Ndef�2�0qV"9 �e. fout +%vsHm "�S hess�}I9.aBA� "w ���j�Q�� V�N��} simp�aso?A/�Md? a9"n� �=� ��l�A��6E& sens�?�v�E�,�=�.�4vof Gal��sX n��� tA� ify�e"� al�,&� ��3"} �l�upsG/,.\footnote{W�� mark�$�vconne�� t { e�?��a5*� 6.&w�N� .b;r-�-�1"s%�.}\\ E�s��"x.+ �)�Wm3 ��pr?-���gu(Phing'' (���?ͥ ruY�<� l)\Ei�,favor� ^ard"�mu�9A���5��Wx&�{����inc6?!V?bpOrried �b`!�&i k*(drawn. Needs>to���CIn "� �����H�}ingfu!U l��1 s� uA�Q�:�E have~�/ere �Th�F�"qba!��Ci2�&�� !������_�� Odiscus�Ņ=WZ"�� p叅��E�g�Ybeycwdq@���煳ed&� . &6 �Z� I�b� ՜xn �CZR$ �aw�*� � �iet sygj��3�e�7�W�\�6Y. I�so6@E3acL��1xi>sur�O%.h�o�ofkA�5G��s*qTta|I�� ŕ�A�؍��s%�, (%�employ� ��n����!61��2�As) inad� .!s&"�_de�~��ojv�3-E!;�~a��Ž��S �wa j�~akCatE.sA�uB� Of"X9Tal�,��*5be *�oA�r��7h��AUm�T,3i0:�9�mcw�m�NrulA�u9:DgKA$BU}��9��O�9de��v*�. ��&ug 5G M��'>�F.. (B r_k(t) =S([sin({2^k} #Zt)].{ EB }t>0*HfFuq,h�,$k$-th Radem�Hr�. N%"E� $r_k�@s�Diod $2^{-(k - 1)}$EE�t(��A!�ka�net4&�!��@}[ht]�EeU(c`U{Fu�+ S��9�� `�Q�1��"� �t �Mtabv}{|l||c }\h� &8(,t_0b2 b2C�X=r_vQ�''^`.'J`3`�2R C=`r�)0X:6.a1� p�E,:m�#U,�+} �( $t_1 - t_0"��b��imE(%�2is run* ,C2C1^C"r8A�Ya(�� wit���et-upc6an �>;6�.�3�2F� �68a� �� $t_4F3$d� ?o �Eso�eth�8d�= � in Ta��V%t-�. Each%_h!^@����C*  s entir? �:val !a�"�.9we� �Bu�*O��E�>�� F� �(of�� ��F?imic �  �r� !�2�ac8Y!�"lan�lum� f[Fur�cX%�  Y%hls�or $-1��lf�e!ݩ���nt�$+>V is,* cour*t�Nf5 � ?!�w"�TY�!w ^TZ" ,!$K� Aat�.} sucZ�Y�" Psc"��a"}J��q $YF ���le>�# �!$��. �9���� \-]. (� M� madeIPVfac0 � gŊ� .�.sN"s1Nyx$� s/ndV1a�h�od!�%�s+  $�)ion"�:��Iis&�bhSb�QvelocS.) ��a-q �ne cof�Kj^�]� eAV�"AV& ``;<n'')�I_T$or��tS�$�y[.���^ b= e6� the "� $ m3 �plj6IAv,'rq " ��Wc"Z� themQR6H ��N|s� )�y$R�ar� he;SES� !U=U<ent�o��E��rO)��ch(^B-�ch!EU,�<ou)� toge�fAWJb4��r�^�C��&�XM0 . Of�YPVRVfY�=�pla�'b-�_E&O &q �%arbitrar���a&/��,cripts if fa�8.Jz"I+1�n�Zi'Qs�U.z*m� EqMI"b � & ps9am6?�Q �Y@a�DaK<(ual Basic ts�avail�A|ina nd e�1�s���%tKA� *.�C.�~J�o�)< (A�Y#eI��sVe� romw@EFne\rt unti�.A!�&� EE�C W�8�,to uWE�oIE�C.Tremai� 6^~|LEAԍvo1�nQtby"K[?ize} \ {}G>!�CRPort S��}A[|>(b�fa~i��to /FZ�%5;z% 600,. R�/ 7 !� rM)S Numb�,C)>��P3E8b�!���-,��I+� -�¡SK0E wQ IP;/K$be��e�;by�p�m�,s ��^A� +,Z�1IAleM5(s )�� 6t6�sthird��:7-%�W6Sxx2R sv�gA�s his/:(E� (A,!� y$) 2�( ���?a. 6.M\�a��! M� J�4�iY�I:�!t� =S iO(nt$y&sI&c�^yG�" ,aF� af, E�-)��fin�'TG� rely�� E�E�F�Q�e��unaI���R!#. V��im�_a"z, dur= A�= �s �6�� 2�� Z �unixion�}-�  � Z":ey��� A<���t��ɵy� card�)H!*� �3exhG�AZ�H">H��R�6-��8 �%>�R!�E$ 1 ��Bob����6,y��� *�"�&-~  ��&\�.X� JU*& N&�m�,��� RXR�B���5ųz=)��(�*�z_#e"�$)�� Ra�g� aD.�m� u  Mil up�3��q\�&#��ic�+f< : gu�>.a�> @msi.vxu.�u�C"�)�F& a g�1� �,,A>" %i)"�u1�T��+O)!,;��!fa,7m=alC"�9WE3�+a�A lI@,�}IoutaAoX�\�&�7jPan�:uwmee� 8, Daniell, WeinI.er�Zei er��A[ %invalida�$G7�_ �:�#.��O�'a.�B��� . Fu�*������� co ]� �%f�[%���; z�$.�Ack�M�$} S.B.-L. *�Ls7fu� E�8CONACyT (Mexicoݱe�!s�Mteo )䆢@ *�@,*�@AyV�@�)Thospit*y�H � st�S�M�O��nNaUdResearch (N00014-98-1-0604�!P\R=����>^D{99bDb��emi%J.-W.�,JB.�M.U� H�2�A.Y�FF{}N�;F0�E515-519 5K00de7A�Fr];ZL5) �E�2T$:Ece(and MethodsfGewer Ac3 ic P!�rs2lkhrBH0Y. Khrennikov �<@�A � 2=L7L,, pp 307-314A�1A83�K�A� !K$B]�be�aA Nal �y�"R@s (USA) � 14J$1799-1805 !B�K9B.�b��#Hnf�:und hP*K0�-FA -3[ �9p-Ode0-.�K 1001�N�z0! F�0-ANA��to.~��or�&its�FbQs}�O 1, mK Serin2@��B"�9.�BN*�K68%�1-9.�A* N.VN*'eQI�a�>/ its xN��( VII}�I7-162A�6-N>� d�r} �C%"uG8style[prl,aps,p;0int]{revtex} )�G[% twoc�&4e*NG�Q icx,kG@\font\Bbb =msbm10 eufm =,def\Real{{\h�1R}}} C  C}}�Tef\spec{R_{\alpha\betaid 6 5I5kvec{%Qk-ll`duzomniejsze{<\kern-.7mm< { wiek>> intu{\�4opU�t}\Z�s $�N#1 �#1{be{"� 2ee{�>ben3na��3n4>a 2/bb�HnewXandei}I{} 2#e#�Z!beeDen*NateFF%F.#j�((em{lemma}{L2�$olary}{Cor 2"�Vo�}{Pro 2& j}{e�em6 6w}{D� A� E� ra{\��-�la{\lang�J"bGU square{\v� hei�V4p0 dth 3p�pth2ptHce,a L!9def\dDpPhHFA�a|TrdtA�{E�@ -.0mm\rm d}}#1\,a�w tr{{7id IH�>:(<�')' ic{I_{coh�ot{\o1 q�rhoab{�rrho_{AB*sigma .3261{0rhoa6`b/PD{priv�>+r�MVi���%\draft�M�G{S�ify�m�a���["�-��B )us!�IBL{Micha\l{} Horodecki ffilғ{&�Hof��et[7���<A�r?�s, *XLof Gda\'nsk, 80--952Pol� ��ra"�HWexw� �a+ vex�  .�,j` w 1, 1val1(onoP��'V;5�Hs� � ��#"{pd<ej: 1)Y ri�.Wunita�, 2�}v%�< 2ng �anc)��y� te 3)3mix\ s of s�e� aMog, flag$p&*�eU�9 am���"!}multiEit�� stem,_ip1trigu�_!!��-e �.# t�AS� "6GyP h�CC)�b�xAR��xity. �\&q��M���n��on��ly.��s. �#�4�7sU!�2x)�s� 2�f%TT6A�nWCiv)� ��5� %aO%\be %~\geq � %! %�%m&b9mix�t���-"W ingu� %�ly�. ukSc�c�a�d_��m�. �e�a;qO�"�0a�Di%su] [@?6 &y� 6�# <��9�s 1�5 2). �<proofs"Z%c�4���bi!�i��&0 s, h1d�y imme�ely�e���%2q8. TgiZ�, let u$%t�[re�cisO��g)ؑby2+�~ !DO_"O5�@��^�ء�j%q"�QeɃ $�2$)[M'.yE^of o3��w�* :a�a�f )E�f( {()›$eq:monweak e IfN/LI7� a���E�!��'$i$, we� rewr!�2�V����"� B}^i���F$p_xB%�o�2idY&�$2C$ b)EL  /��! A1OneI���A-�u�>*� �l�ch!1.( adopƖ�p�x���*�1{def!|} A��*AMAmQ�z�fa�� �!Y�,���Vc5`%lq E:c-a-!"��U,n� TX}i�2$[cF"Q d(von Neumann��s (��ѡ7)�#lete),J��I� ���^�-��^ieGIpaRi�a0M����`�,�_1sum0�*%FiI�QD �^Re+= .} F�(A���; �6�a�tqasy���%�<�%�9Di8�4��Z2�se��PB@oq]�IE�J ~6&&�3s ~ z:j A���5 \ #eP1}� R b �l:9fM���t�Z M�y���' f(U_Aa.U��q" U_A�� )=Ad)]�^R4!�>5atK! =^ob's sizF:�M�XN�!�$m�$��� �)N� HU1� 1�_�s24 iH ! ": =$ 8 :'_Xc @ 2��-f3$M�B �,.2 #8*!��U^JujS�C$fe��1K( �>o�,%"� =( �) � enougha& chec�@�� in �9"�#.� � e�a��(W elegl&�as���!]�}02�0y0 \noG:nt{0[LUI]}%*&?)yu3qQce (LUI)at�9m9� �FLAGSB� pU[�VXb�.� EF� 2� P ��nd9��#YN�\ vm&� :��� a"��� th-|��Q�Eis L�on�*&�P��Wq�E2��EA6� �� 6MI�ɵweh o/ I�&c4� �z�b� , ("M��ua8ٿyս�#w+����9zLUI!x-&!/verify�!��"� s 2t9�*n�pـed��T"|%�!>��P�!\�Ace.} Lh argu!>�%-�1 t. ��!YkLUI���%�9 j"1��0��� 1}� % o*��T��Qs� �/�.1e�� Q mpli��j2)J� . To e8�,v$a���P"k !%"� X�k q_k |\��k� |�Now����&8M;A�*GX>�� $q_k$, e�b{fvA��Ir�^i= V gei� �-Z>�%|To9it�!,)�2� ��� �f&� ^i)=2�� ����� eq:fl�)�*p3�.j-.����a�](�s�J ���. ��w�IBe�\]� A\y? Obv�V-Al%A�"T) fl})�06�3)sS�en�*��of!V�ceE�q�. .GBN�} ($"\Rj(arrow" $)We�a�4!3)�&�s 1-3!/�  ��6� .LV a�b2�"�"6C.B &� EN)N�  (wK � �v &nFU�} sNJ� y5e�9.it*�=6btdV �.��\6UQ ^�lzb"7��c���enesse�a��7� �at@-� � 9���i�MB'�CE�,J"}$�no� a&+m}� |� K�*|+w�V ges:-� +apK suit��9( Lc�K` ���$���f\tau_{� (� $�Oxiȳy�ed K4%Nub-6 $B'$)�t$ r�e �/,bYecoupR66�O-� tage%�< �&EKoL15 �LA�LUIEσ F6 F.E"I D ���4~��d����donM? 3)(���=cal.4�0���9�$  2�O nsem:1�,\.Q$.�E&�I2@I�B�� way:Ń�� attF��L!�"IJ$|0\>$D @pY��*� $U_{e#.-2�c�by^�!L]cEdis|1��t�6A� to��i �ae Kr �%���B'�6 �AB$A� llapC�v $F��8�Ar�<� �I�wf �gde�} ing} basis � m���.��35�� H�%.�M!i!� #���[�}�==��C=}� � AJ to�. �e8b�nE_ *!.��w��w}!� &oH4"���a�+)m�?&,i� idn'�ŞIIndeep9Dqe+8��%I��1  8dnm�Z�����Fy b�@AO� N�����!~. 1)��t7��.��� K>3 *5b:gBc�� uA` 2 j�t�Z II�is*�E��dDN Lef&M �- �Qw�d��Q�iu� .�a .4 )Y ����&CQ-e� ��!*W  c�8�SV 2 s a��b) &� >B.=!BD �&�&��� ��*�#"$ $"aځ�9@��� fa7DJ.FX6fgeq$"AKi&�.��}~dA�fE�t�H�(incom��).�f�!��={/� �6@2� >� f illus��- � a>aex��� �zE  1.} A��2"�a�2}is :ne��vity} �DZyczkowskiHSP-vol, Werner}� n�e�E_N� )=\|U ^{T_A}\|B}\��\ $T_X9Z�ф���f*! X$ �Peres96�4 $\|(�6 ) \|Si�BQ�A�Wbeu'Qq" |""2_2 . AiP�oWm�� 7A�`&� �) �i i[Ohirrev,$-errata}. ��,��E Ʉ!��� �)Rj�Yaz��'N!ofJ. 6�D�� $E_N%r��&� 5�!�n)ׁy�Car�!�A� <�3� ��?������ ��Ay�j*Ff�7>=>�)�6�/ � . Nam� � $U_AW$W_B$� have/�U_A�W.�i*� $� = �\tilde6CB=%D) hNmo&%���� �y*� w pas�9`-uaofY]��>!)pors $A!of� �\ ���%4%2\|�� A_i�;� \|̱/ take\ =p_i�}x �%A] B'Z $. B&��.�*y e�h!�di ��,+�at!�$�$n &&\biggl�z�_ �5r\|��\ "� &&&i5%l��rh^�Or!7.L && .N|R)%]�C� �1BS1e��� racei� $\|�B� |A\|%� \|B\!{�fѠ2.}V7re�:v�r�{�n*Gs ɑ>�*F�R� )=\inf_{\i \in S} S| � �Se���|r�F\ " $6C =\tr� \log -6~$h�uo�$ak>�#�&} ݂!fh�_�$�:�+��" S/n�;2��� some3&��h"T', d�o.}��]�3>��ub>�6�i�uvex �d&����keria. .�5!ly)#*��(et !�J.� U��k�`a)Iso��!�iӨ gain� Ֆ }"$O  nWF"&FBU. r"MBDF[ �"��0nd�<) p2��=b 8��.>�a6s��i V:~ B'�ba���Fby� )-A��""_bP�|x".�-inf� Llh�%*agsTjA�" ��[^ Fs $�3p_ii�^i��*Kre� s# > !�B�&5i� rt�;aof-= %�'�)0am,$A�!X2�| %@)s�C*g %W%�Q�n��EAAum_Z$ �N�, %Anot�*�~�58 &&S&���:h"�ū|�b�/)2�.��i g�� )�$nf�*VK?�eft-h���j^�af2��3v-�0�1. eh�B2� summ�wKP� m S�F�.�0,�.�, s� ��� � "� s,m�� .!� a�. �.F� �Ԯspeak��+�����-g�wn,#(s,ixI�!at!Wa�b��P"G.Z :=.>.o(I�E�6�a_eGm!X2��� m��>.V!��"� s�� �w� �&;..�_^�1iEw�rn��F�-oM0T�,���B/xs��^A�.��-�).}is�x�)9��v�4sb$E ^��lso p���B%-� -��&-@Ak�1E}F�ev�dk!V�&�� ~nB6A[ a�(ort�$"q �=�Ab#lab� adigm. H{/wU��mP%�i(res|aactO9�5Ds ,ShorST(5�1we)� Ut���6E����. . (��3#!�!�s�FA�Sl�Eu�@ t"3&�.) Fi�I�op�8m�5�r �d ��]�6> �x.}��s.� ��`n!|t"�jt Xel��"�R,Y,��|r6TS�~K� dual} QlF7 (tho'w;V4 not know whe�&�4 5D pE�c�ne�� (duA�F timeA-*�$is system)A}enii ��keep Ck Bx just-$ rack��� �es.� situ�is Akun�on!N� m|!6!l�)Q��%k k sH�a��oineYea(8 no longer know1H�%�-y. And�Iwe� do�orAZ�involvl !�B��all�!_ � }6�� e�� !M)q!J�4Y{q botE�s�sesa��U bec�co�tely BO3ye� ffi{5< arbitrary label�ith no�alb�N(� ��e}a�(Bob})��U " �`I� �$s ambiguou�\� so-A�ed rit{ex�g��gz Xcy} appears. %arise ver+ �A�new"R a. %�proble�� f!BneL corr<a�un�.� for � �� u �] r�r� ����a new�tu, B":!Jb @.\\ % Not entangl ��weP ll �a�(\ref{Sec. E/}�o%]bf{^s} \E${Post.:��M� -��/ !W!^s!�_ l]�E�V! ��6 �[�")cE�or )�bI�vectors� are,i�resto permu�W� osey�:�I"@j%'A�i�i}Rs�+  in�q � ��zi��Q�bosons};"3~o antiJs ��sfermiu.ua�X i6eplA�b &]&V, S wo . Fira9tends��to8 ��]S5! �9!�� !�t: �( ccorm! L s��-�A�Fxٔ�sev,A course, IE7Q^:�Ds< �found� �!q unde� 6+c1�N� @!n�`}� nor>�. I�cr_ to not�iatz!� zE���d&� �ndard� ɘe%F��A�60 �!��is ra evoked�hsubqSpin-*� Conn!�on} eM��i��nUga1�� ai�, we nei�investig���`���u�A0��z� ("� one))%Q - q�.}"[� ��ly��n��rul� &��in  a =em�"f prov�a�#2� 0 }), ����A�proof�| � *[cle�:na�eee� 1 sy�� anks!�i�s easy��qL�,UU0�xNPAs ,�t� is Con worksI�� �M.���quite *�to �LE��"Fa %�,�I�t* ! al n�!,6Hw� 5 s I � �ms�!r��� stoo����{�*�%��2���� �?ɜuniqu�'��4encode, transm!��!�sta�*" o��!Yl� @ ��eale".5, �"a r&?!�`� z&ckAc�"y'e�2+ ocie7s !2цconceiv��ʡ2 day����}a��"�$� "�� than�x ��@ �(}��g�2�� hN�5( =]< �try!-toc�at���P� ask�sel�!if� ���o%a��H" �se Q0world�erm�mI6relev7%����kingg� kA��E �E�.�ɺ;A�y#f2.%w!�a�jW#ionx)�sh�cb!Ced:u��Ts \foot�{A� red�as6 1�)};h!3aTe[� ��r�ably.},��!^ appa���� ry�is j�MX}icolN ��2�eca�s. Now,-��%đ�� plalyc'i&�=�A)-� ? CaX� �!@per� T&1F.Ctasks? ���u&�.? F� he l�%coupl� yCU�' I�ehe �ofF��i��9��.z� thE��%�� YS N� �� rec��"mp�$A?���!A�of�� �Kj�(uao&� ,$4divincenzo-losI)tonio}"���dikara� Bglaser},� Zlloyd}! sougat^and any�- 0kitaev1�#&2�ɖ atic�A%on �!!,-uic])v�#�/+(a�"/ak"e�6  � b!�m "pub�,ed eion!��� �  d�)o length] "�).}. W�_ �,-�D� }�A�e:3)YT!����q\aU�>W szas�ns�of2�-�,,,�Id"*mZ2^.�A�A�./M; Paunkovic�ndf~*�% opti�$�i6� in a% erimin!Wtd- �$Bose}. All!Rs!��$�keuf� buncuof Ft&*imLZ � beam spli/(a�~\�& .X*4a simi�qa,th� ) ' J?U�-ByamamotoUs���ir��1�d�/&!h#� ��"Z  (�)e'��( �)Ş>A!eS-� N[qJ� �- J�9 out�  P6�sN>��[E� . FuNr ,, sub-ensemb�s�� �7�&B%J�a path in gJ6 &� amouL*>R���b'J� depe�2o�6E���0K�d4 n,�**6p s� C ��a3�u�nl�'z)Oy�aY&� .c�%2,Fca�IW,'prm�itself l�&ly9[ B 2Y�. Z#U�Y2ll��I�0��do Rstage�n+,Y[1��0�!dQ�*���"x ���of�Hm�)Z��I�$e� HHelst_)_a�le-sho�.a�#R.N$non-orthog�)���wo qub!�(en� � h}�I�.&1�e@$!� ��$) �be achy/�1��Urp&E/of��.8 . .��k2ReTngH D&� ��6"�2%A�e�urk,7�mix�1t!�. �"m� fe��s emerg�A abov�\&R .2��"� so�1!�%#replac� trE�.]6(condA0�,t�s)�Ya:eal}�6�d^� F��  *�!a�] 2�� ob"e+�Z�� �#tes�V���0 t"�5.�t#s?%S6!>d.s%��Eĭ(Anp� \!�&\4Z� *uIac"�*4�R I[ *{Ac"&�5\�'���2b1qalk del�%�zA� I!��al Mee�o&L2��3ce: F�E��.N�,Xe� Came�$, Italy�., April 2004.m**l2I8a+8�� F�$\c{c}\~{a}�%(bthe.�7}{99} %�7ABF1 W� uli,mn@Zeitschrift f\"ur�k}�0bf{31}, 765 (�1)�X8_�ure2]� it{N�,A��um "�3},Z�, ^(, Stockholm�46) -- &� in �it{z-Lec�s: �cs�,<2--1962} (Elsevi38Amsterdam, 1964N�*B?. Rev.9158!116�06O:�} D. Los� D. P. DiV�1�e A} �(bf{57}, 120g986ga< A. T. Costa Jr.%|S. �J^0Lett.} {\bf 8_277901 (�:6bJ�Bouwme�!r, J.-E`\n, K. Mattle, M. Eibl, H8in��eE$d A. Zeili.$�x�390}, 57E�976��!8H\"{u}bl �<gowd� J. G�fJ. Ch�&%]n$113}, 2056�:��S. Abraa S. L*^UE2T79\58E>�VM!�%�D. Hom��Ar 0504-�26%k�A Yu. K�Annals>30%%36N�  Y.�;, N�Q \'c,2�$V. Vedral,I�it.]�(65}, 062305s:�&� Bo�M�%6vxM慣bf{%=187903N|!�5�,!DEkert,z6 � ��)� 2309}:l"H R. C. Liu, B. Odom�Y;v(S. Tarucha,�qLe�39��263�2;RKAa1Z.�uJL. Mande!�#F�1?5E�044V8m��">� 4K>} ��%%7. �@m by �?0 Word (R) Ver�$ 2.5 %% St� ng shell:��>R�>t[amssymb,12pt,thmsa,sw20lart]{Dcle} %��0 %TCIDATA{TCI�= �$/art4.lat,�, } 2Cre!5L=Thu Mar 03 09:06:31 5}+$LastRevise2/18:57:20 /( \input{tci'x"�%1V!��<"�dis� 7 \�?4Zai-Zhe Zhong ('(EndAName De� 0 Ab<Lia�Bg Nor=U 0i.4Dalian 116029,O.D, China. E-mail: zq(zaizheh@hot.com} 2v=bG &�=I��+5B, f.%�/ = w��� `� 2�'�� & a group�< � ):u d�d " A�a ququar6d a bi!4it�:bitPv%�se A%F !4�"�2�� cuss�"�fo& m. At�[ �+ o.� * ''�imp�ly-cl)�C ''W  hold� PACC�%:?Mn(?5.U"2?Hk.K89� FH!�"�6j s!i BBCJPW[1]��$ZZHE[$2$] �n-��yc exBA�Cmoder&m--, �(i . F*�KQ%u�=�� telet8� swL9Aball la6��Ear�" ce.�r�*k yErea�5pers (:x5�*((in [3,4$]$,�)pm�&QoDd-level(d$% \geqslG/ $3)\Q�,\\ [5-10]~,qJaCSY;�1 wA��1A��UPB�&� from� ��&ary�i �m� �.nelO_' ��iLFch��T��#, at eAM#Iia>1�.mlw�TS.a�wee� use %-�%��'%�/"�G5M^ �]�awIn!&eL9:<a�"v!hHof�O�4�/�$: look up��$�.figh:of"�--e>�s �?s"�>eque�zarray}{l } \;\;\�line{� /} & & "�{(/ %  -Clara$( \\ \mid \�H( ?m\r�) >ca�arrow;.-n,, > =_\alpha3DT E � �\�;� tyset � � down 4� ;B>�>� .�betN�& �0-�}E&{calsI�} j%w6�9; ; & >�& .;N�U return}% v@=��8� Y]wa� $)�9)? �,$ p-veqde�ma� n*z?,��m�D�8,�4� mZ4 an un�n�V�$,�4 (��q^channel) e (n+mkB� �H)�max�UdNrQ0 M�9U�.$� sendNRto ����Fa8H$"e}0%9f. 7,G�$&lF��)�e�c�Ain�-�� �e$A;l.�,�)(ultaneously�y�: ll b�(s��or�� t+$.�Ur>_~ .$ W��3��s oN=A�>Nto)HE %B�-F/-Hby.a&�(d9't�4�� �� $U_{��,� }$, zA�� �#"�3�N*�JDn = }�$).�ar��ca our Z�s��!�� n�����>&:�$����Gњu�F��p.��empR�Fsŕ48F >�U��c�t�e�F�����2�.6�F�J�^5Toe'23� 2]�����\ %e�k*~�a<})��t�PkH.��of���Y �k6�yQ�w7/D� �o5f$�`s G�'ZRY%�d�I�[�" �<�o [Uc6�Qi ,$F��1 bols ��"me�9aP'� (1).��H ¥&� 6@ ,���"7�� (dGbelow) �YN ���i!y�-��[s6�]$v(Ʉ: aQP�x,��b[��haM>.2 (�  2�1��U ��$to6�1�"�E�= ).$ Ob.6 sly,��K"O;in (2)),� ly,@<�.a& ijLw gYJa �A{�]�v�H$(G)\�!vJ �( )$. Sum up��tio=(ɢ s (1s�_ ,: ({\rm i})\ }InA�,y3�a"� :I-m�%i%-�=)�#Uis��&!��:Yi.�.�,$�1��YcM M"� "$% (G)? /8RinD-e�.�= 0.� �]y �� %�(2) oQ%�.a 2,1rt�4!�: a`invari+Ag1)�3 (s ��(�Xv9���= LI (2)�&� brok?n )� �*!6y � �]#cT is��!�at sATr�8`X> ��p�=s,*�*ly. H�&�{:�`.�'���F�W�)��&�� of h�D4, $Zn+H_2SO_4\:YZn !\upar�$,%-��s.�.�,*w �`��� ��,$2y�3B�ё mid  W � 0 &x9�a�!' zinc�?0sulphuric aci�Afa;n�?96etc.)i� =R$ME aV�'. L�w�0lyA ai KahTT%�%EJ�+�)~. Kev�1n?8&TG :p�-"k k\��>��$�3EF�%o�� � � ed `2�'. �n�.�s,H'oa26p� ad'%�ye' 2Y'%"ͥ� �B&�w�R?m�a6�#.��emv�-�t��� ed `0J�aDorem'sQ:3�SA4A�$Hilbert sp5&P(N�s�|$H_i^{i N� },$;7re $i$�fLser�y�=L2a.�.�E)|J%{!�pB�A"G.uE��E�{% �yI,II}}� 16���H_{ )&4%otimes &V'$ ,Adri�(:�3$H_{1,2,3,4v�1�2J�2f $�3j!H_4 ]\ homov,]D1pQ-,}1,2J� �G H����-AB�B� re HrE5�}% �Y$� ta=�pX)e�� �� a�,�B�Y�{$r� V� $(or:��u*�four-dh�a�Gy /T9"R�s, �in�j�Zv� rc@ :�s�Mn 3e] �+lemrL w"wR��on'�.�\h��"2M�M9��8.]h,M�^�5�e�-�ZL$=w� ,Yzv$Z A|�d� -�,"|jym�16.�6v�&�Cɡ12!Kt{XT8P�gs �<"�:z (Rk6�*,��ρ[SH!k�.F .�[=�� [11"���g*!�/alj��fTw�M i>,i=0,sW ��Gr u  i>�rs>).zb�<9T$rs$ $=00,01,10,11$. 9 we t4� A�p@]`\{hW�� X  Y  Z�/ \} $a��ioZeq�ay} &�  &o =\frac 12�� �A^+0B6 C6 D �) \no��\\vX_!W�p-�p �pY�p `:��p�Z�e u�)en��9�IP6 Eq.(3)Ae@DPc�)q Aj+$=Y�)fA��i�o>0I}}M�B.MAi+1% \�O{mod}�v;} L1V0CF\2�Z2Z% �DFL3�L3L}�9�ta �0�{N o& 3V�"H ��% �yq>�X>(R&Y>&ZNZ>(:N ~�Jof��.�V��P�x��% Q�rs.3)$n� {rs}��(_1s_20_30_4U� M�1-r � ) _1s  B1_4bznR �1.�D1 rVr1_r>��F�"� 123umYA.# N#Y2#RFZ2#:F)RU6%~� $� �V�%&�P�9 2�, i.e.bib�A�M:����IKNE���B��UDQX V��R���N]s_ � .]��� 2]12� iD�� :]b)>]B)5�:[B)6[t(� �^� . ?�.AE(� �>� �z �>7�3)"  � ��"r &� )t& "� fB� ��AJ�&a $�:2�$,��!�� (�a &O8!5+pu�i��kp6*�h�j�1*R� &� r e =I >e )V� 9:�v v�v? ~v Vf� F�&� &� z� Kk�W>The.=�fa�c��P� 圭Vw ;.��KH OZ �� } $) (h�R V��Ki/���ee/A:e\��.iKH�P}� ��p'n�'  W-a~e�O9\phi 5/ ���=mw)0&� }}>+�"P &Vgamma 3.+\delt 32L,$1b�(rem�G�s�=%U8b1wo"Ns � I} (�K1, 2 (-� s�gk=bhe+d�!a��Gg�cE�N X*%)=I,:RZ51!J%C0_10_2mI57*� 0_11_2iz!? o- 1 @e�!�6 1 >1�$,!eAu G-r%A< �\Psi _{tg A, f,�R. )$ ��(���#{c83i��.�a�,r-9G$+\cdots )"�D"( ]�-�� � 5+. A.�VEqs.(4I= (7),{L)7BYjY�u$�f �L4 CW_k:d�� ��,&Xn(z ;YR+%�}�N+!{ZR. � }>.$ Sub*�D $ reorganiz�^�3O**i.�(:�>j(sum_{i=0}^3v#W~��A� _{W_i�*� ɹ~�.KXRK E\ PB�.� u'�z_{YRO �H���% KZRK�end>�>�5$&�4%|\{^�W_0f� }>U!t0!tdag�U})W�1*�Y^91N9&,��68 >q&GB8�3p }\ \,�N!]X��XN�. ^�XN�X��XJ�X��X.� }\ 2�Y��YN�Y��YN�Y��YN�Y��Y=�B�Z��ZN�Z��ZN�Z��ZN�Z��Z6�J�\}>�&\ �JM.� x+*� N�FDm� �&RQ6�/bullet }�� =W_0,W_1,�� ,Z_3 T�$re un'0 matrixTF7�0} &=&`[$���5} 0 & -1e�10!��- � X�S] ,\;�1}=�� J2] apg�R�6� �2�Yko��R�13v}!�B�r�R�6U_���"U"-.��R�)��#)1\r��R�6E#X�#Z2���R�1z#}.o.& .)9R�6U� �G v�~)!.�R�)�>�$I$~�R�\\I቎,e�� .  !& V�1 �%a\o & �-�#�Tm�6�~.� R�)p� J2]��R�6-�A����� †& r}M1p`-".&�')2& `i�3�a�z Bob �:*�S� I}(�,�+Y*�/ $1,2.�:�3�:D`a&Kh.�9ofB> }and' \ ~'%w]: �zg�R of 16.2�3� �~�� ~�&~^ & �: ?\�left( "C" n �Q��,a@A$"{16�&z�"�4�' s�A0r߆s$)$. S�wt"�;�"�$1e'2$ql6�.�;!l�I[6MV�� &.��% B&V�>L.w.L U\} VU<*6U1er( \mu 5! TEXTNIol{>} (.:is%:� O W_iI �%UC �$:=taCV�)$.�^�<Y(en ��u��6>�<Wb�S �  ^3>=�<mu _i2# ^3<&�/&7y7KT.xV7iQ ~.�e�% �"&fEAmu `)ly-,=0�_Vj�s v�o, S+l2>� JY_1-�Y �,$&2jaa|~1d.�Iz�$d&�noticy�u` `iJted' (�)!one+5.�s `outpu /E��*wo[1if-�" �!�V�82�q�Y��yi� wait% �(.�)=6L�~s"2V*�r� �*�1�1P��� $**&8=!�&a4.�.. �)*�AA�!� ilargHs$m3�Hea�&43I�s,A��9�ca.o���(ly^,"�&� 2� vU RU]-��u�Y� &>&UF� .ZUj=�FyJ\ ]2�R�:� .k�R ~�F�Z� j= �R�Ja2#$9�y[ PZ�n*v�%U��F, �V�n{ �J>2� 'N( J�2FN�jQRPr}���B�J�=E &�E]K"�6}�fd�X�X��&2���}�vR=�r!r�s�s�s�tVtfkvVk��U52�r���f��]�z�B�]r*S8v~��F��5`V�25"HR�6Jn*�In2���� ��=�� l"*�EW ")@CN =�@A< $ e27v. ,�6�(� n"�=� 2C8,jN*38�8idecIU11]&�> X&�Ut�+5sbe��2A. p�tr� �l(PF�(sm' , 3, 4�?J*)\II}\V"�&�% \ }�'!Q*)e"d 6EPB�-/�$�!�s�%�IzrxF'� 2h .h34+*2��r�UHI'�x� Phi :e'.[ �,2�;.%�.�%uO �P�f"ALz*> :J& S9�. (�8!$W9"�(&j'! �2&�  J�(V�( } <1�6&&�@"� �0�4 ٤�%�4���P)�4!*�)�5"u(�X 65:=6f%zEWZ�89`%0�-.!L%.-\6 N� .�8� \b&5*k ZW��6�5�)*�$:�5 .�#6@ �.# D3) �. �f(��} �.} QK��:�Q,%D5�"�92`"2�#>��ى`1_1)�!�$�iA&8"g#013_4c�9$7$�GA#/.�>.k/q�"}B�'^i3 re.�>6n�2�Gndu-�X&�#��6:h, ��f�.�(]N74!-Z*���2�E� .�(JE.5NEE�J WpJJ~�'I�f��.�b�J2�(J�r�( �2.RE&) b�).pRJv�*Ej�%.\z�.�J�.�NJ%c .?)JE.QNEE<JG"� JJ~�().pRE& b�J2pJJr�)U<.t)JE. b�).�JJ.NJE .pJE.�NE��:� �}f( � �Df�*� 1 , � k |� �@��%67 ll&�Z��fMonsG �816� s (s̘�r.[6 $ )PfL�E�w*�N�:� �F .{~e)$"�R&� )�}� "P,�F��1SRh��=!2�amPcg%�&i >0f�n �� yM&Iu.w w m 5F p J)�I' 3I. R)�JO�c�S%)*\ }�[y�J�^ ]./+i�+ll�_�Y (� R� X 175 �� �&� 8.�nc ,�&^*p������;\F} \�}$ �) & +�Z ;�Uhr`{z?_ !�a�RsN�D��1l�@)� B *49c=�"�2B"�� �&�vp*�2��3��L$�5�*�Z�#Ɗ�l�D+P%� .$Q$@�!�}!�.#XZ!� n! 2g!)�$E��!� �f"6�{Ԟof&��>ed��B� &Fv] �ee��:�"(=�]>N( BqI�UJ2� bg����v�;�;�;� �E�E�E�E�IQ=FY2EN��M��:[&J_ . >�.�\�g�8#m'B�]�}iN� BM^ P��% n -�k�k�k�k�k�kmk2�FCnn 5�u"�D2Db�%6^\S�b\/rU.| ���TB-I�m5j36�q@ 8Z9� !�� �5J� t �~ �� �� � 1� zc.� "gZ�e5���*� 6��R &<'�] "�ssince.�b 5 �2��,rlp��'D�Q 7�[�_&\[12], �w�c���2�/lӝR(JA2�Ahgq:d\ � m�s& ot��]U�&� t QR�@"b &? >>� 5_{21��}~P� 2=.n1�5lEm^&�IrD6F(< �1>$]a��bh�"�,�_�0�Q>�0q �&^D9&�Bx�B�G1�ma��es. Of�Lrs[- ��6�&� ��1R�N��Dr�.�= �F*�=3r�\Xo*�Y�LaL@�HM:L�Hs �u�_� ro]��f �x%�]6�Z� Q�iN1���! u:Y �R}2,Y�:`2� 0:�1=c11�s�QMvʒ�Zin I\P�f2i.5e��$� rega4�a4� :Cy'' cop�i�bn, N�`�\� `&�a����Jq�y�''"�a'' qέPe.R�#� VT.�nV�a3}>��6�.!J }�ZSR�]�n��/gN�2PJ��K1Qallow��?�beasily!�4xat{1cBR/a�p���7Jv����M`5ﱻ'@��eљu�A.�iPJ7abd�BdŰ�R��YU�cZ�y�XΛ"�Ppai�c*)9ofZ3�3be i�X5 acts^�.��ctness �m!55F�|,��re+ �-s��H:W�MqE9 . ��DfN ion.}{\it�Estab;��1�m�R� e meg���� ���KWcr��Chig�7*pa� �w�$ yet �15c2�8"�1�1p:be�Bed else8�Co�:�{AKӊ�4�4Y �� J'�16m` /�|��'_` a gq3 6.[��*X!��U�K�{�gIu-�&g,�2�1��dE�*!8 �Tg]>C)�ގ� q7 M��`b�."]{>��6�"Չ} �\H. Bennett, G. Brassard,,Cr\'{e}peau,��Jozsa�Per�c�W.]�WooT�s,�.�, e070}(1993)1895�i\�4} M. Zukowski^*,�M.��Hor)8oA.��J� i �i1 i 4287FiA. Neils�nd I. L#�ua��� Comp��u .Gw York:��bridge*ł P!��]�>wG. Timpsn�e-prin��(-ph/0412063:�Ff�r��et�nd!�)�cheldz�hy- .90}% ۉ 3)09�:XJ. D.��uEH^Y %\A-i64 X1)01230>X W. S�J.�Lee#�S���^Y. Park27a% 64}�1)064304F�H�e,M^��S�OhRT66 �2)052318:TA. GrudkA�cta � SlovQ`5 �4)9>�<�R.!(Chhajlany, PPolOA}\i!104% �3)409:�G. Rigol�J007219.\ "2e�Te%�U��.���A�T�WVghs hh��"P?�,�� �2�z]Y"?�Yj�j$\%'�%&�.�e\ :6iJWE[Zurek,ɠrueM�299�82)802.� >B���B�12p.:�,\usepackage{l�}>��2[dvips]{��icf�Gps�k86-node}���itl��*� Games: To��s�� ArR�+m�� llig.�}"��@Katarzyna MiakiszP=�eA%M"��s, &��HBia\l ystok,\\ Akadj�4ka 2, Pl 152672& Poland\\I� : km w@!/L.uwb.edu.pl\\[1ex] E��d!�Piotr�\\ޢ Lipowa 41 �424V�m3: ep@�T� � Jّ\l adɶ>��.�67Silesia,!k8Uniwersytecka 4�,40007 Katowi�)4.16sladk@us--��� d"��\def\mȩ@{\mbox{$\frown\hso${-.9em}{\l��-.4ex\h'_\nea� $}}$}Ayef\P�sIC3em}\big62Z35[{SS2VhFV16RW7�2WHTW%\� #�skip8mm.��-$a"��6.7. noin� On^r3�� Eed�N�p> reas{�bout � fut �dG�op,G= ga�D����� impact ���]2/ t%)� ʗR@ )>� ety.�[ idea.p�Zfi�z��1��!9\vI+5mm} � PACSJ2ssNx0}\/: 02.50.Leɉ7.Lx, 05+q 30.–d\\ H�T�Vj�C��fF�W81-02, 9$A40, 81S99IKeyMv�phr� ;.isEq�� 7 tegi2E� y0 C  �s�N.F6) \se�' {IntbrX��Dn� 9of glob�9�infra %AAca���'�  m��0paradigm shifthuman hiƨy:H"|is�A4a "o�f�C� m[��Ѯ��.~' sc�!x�tyEm� ^.��pc ��u|��a1�va�m�)�5in�dr ����lS�=fʗaZXU� . I"u�!dez�����Z�opened�K��w2], crypto��!i�� Very ofte&a� approach !,vidS* dvanȝst��*~setT�. OH� v(� ��C�b!&�6�";� illue !��E�ai� ?�� ``&~�x�nents''m(,urXec !�Mey}- inv}.:�p�s ?�stVle +milw)q�"E�� 9 * IT1}$�l��a^��%�n�AZRme�G!�E7!*s" �Ican hard�B peakL ut r��al ag!�lay<� N��thelest� B�, sor2ZQzt� ked wR*� we w2�con��a��a_A��x��oY�!Doryqab�g �� p=nt&�!22�sugges�J$� oner!�F�!N ��pul5 M�Ax1�m�A�p us&ȐYX�bea[�qm�li2��y �, �F,�ic]t��!�if�8Bcious� ores"�H��a azu�x&���� as m�grN a��x�. H����ve�G�l� ) tr�ies�~or AW� cess!E^E�J?�@�y. Does�����.�ag�F-��Oto�^� (cf.%�� hrop4�"-�au�Y�inm�$qantpri})?2����� saCR�al �ess�.�pA4� toolL{c��/�!)��wai��!-U������*P as}�K��l.0%���l=�v�way�r� &�{�/asympt K(al ``shadow�Iof��s�rr� U���&W.Ȁ"9 �ǵ�,j�� �. *��}g�[1 --a6 �%E:] Re���E H�i3/!�1~r!�sal�?�#�mb!prem�!��.'pr� � )lrn�&�r)`u� �A�of*� &��(��5�n�1�S�l>aT5,�J orbiX�m&x�%R�oo� !N (enң-�\,�[2!MFJuce \� {punktdwa8��t%3�%*1�ut[�"�ӡb� pe�� ed (@ed).��sP���o`"���1.one. O> wise�x��@��:=B�n��!3prQN�,\>.}�|EkUW9�� �x%�$um subtlet�` * o�?(KO~.�1,61!����lve�cdu EMEIs�nl��t*�s etc.� 2���Z� �3Onf�E@� %#8� �*{�.P� infl�� each�.ȡP\�� v�u� E ��komp}h�ډ8 e�i�@��� CNOT%/athcal{C�z$��جts  �n8{\e�^ � -NOT}\/ ����b,�3� 2"_�*La�g� s. M Akwo-E51� )������ �senj���/0 � 4 o6��@a�� DBE" Lom�A�@� ��L��IbJ���-�tI�ce$N$�d�Oa ��va� "N�#V1U}_{z,�`}�5T��xRSU(2)$�_#�ne2 |(x_E��s'.qaC� shorE~q>d� - ��$ *�jat��\,|0'-�|m =  ,\ p@m?Q=��nd.�I$m2d=20,)�1�vTZ*�X diag��r?�w �Fig .}�� sulokitek�t��<�Z�)lu�A���bl�% �X}'M(f#5��>@$�oX}$"� �8 }[h]1�{�er} \ph� m{a}"�(ex} \psset{�$width=.7pt�c$put(-3.3,1%�?{A}{$9�$� 1pt}�c%*(-2.15.1}{BJ0.9\ JC}{W$|?Qz\pFp tom[�color=w��,fill�solid ,lightgray]{%A:(3.6,.5)�1.4)(.61  .5) �6�D}{}} ��E061F 09L05LG~cu���-� �-�-.6 v%  .�%��(H}{$\oplus$� �!#I �6JE5m�B41!IKK.n "!W"L]>YA�nc�[A�sep=0n-}A�C} ^ D}{Fy4V< G}{Hf< H}{If< J}{Kf< K}{Lf<BrxEZ� u�cap�}{��� a�:n��6��a s'*� =�Vgn ``i�q�.06em}�� e��e�!ts �T^�N��iz|e"U��7� �9 ̍� Any���3 demu��&8K�*" . ��� c d " *� � exis�f����As� ques!Y � ignor*� de�����2�To&$�lwZ aly� re!xmple ! � !I1���2"� av r�� solu���/ lC� i���s� o&�;W��Newcomb8�ox}$���i�5Q�uit��X B)grasweta>�ny5,M��vulne���an��error) $I/� " a b 0^�nu ��� $\{I,NOT\'  i��  swit�/ g-ofE �� ^� .��A>b"ψ�to� some �&a�Bk m�a -�etP�ext� zug�to z��(o e�isturb 1�� ivAIY� , cf� NC}R:+.2+>R�mc��ɾ4.9��( �ٿ(-1.5 ���� ��BB0.2\ ��4.8 � �O ɾ-4FG 1/0.�< 3.*< ?1j":C�kZ�D2l��`V&EJad#F�bDQ {� GD�� � Ar2�?6�"C 3.25 , I��4!�jJ�- .8�(" �6M+$psframeboxV � 3�E� ��9M�:�4.4"O=*eJN b| A}{Cf D}{Ef<Er�B<�Z� H}{Jf\v� L}{Mf< M}{Of�I<��B� Neut�ׁ�����m�a�� -���( \Y� �,), �n .�\.�6"�$��@��).}~�� ���N(u��'*8�s�Rfamב�xfre�킭�PSNaF,"�u�e��Wi�mV���1960,n�d��. MGn Gardu �&�2Lway. An alien Omega�Ѻ=n^��f & civil (Q 2) " �j!�� cho�d�� �box��  1%O��2,� 1L�E"1seS� �- ,�Hܝra�����<,ains \$1000. �decla���pu�!�bbox��Xopa� F000 (� y $|�sf{1}�_2�gu�$�f v%�saw��-V1�id�%�"�-�box (Nr$1$). A mal9iՂnks: �$I�fs �dI am gob�  en I 26�-!Z %T�� I �:9+}v, �fen��bΞ)I�f�%0!M14Q0 �� I0!:� �i�!���ndE2� vbox�- Akma� on dy�r�,is}q� t 6Whyw"�Iq�2 --=2��8a >es}Rj0Uj%>a"� i!��!Q�,E'eU)f'sZ�be�0?�4f3� A ���  F6�;%V value ���!Ab)= *k3� %��K1Ns $��!�J_up����-s�-A Z6 �Ms>p�!Cout�>��"�&Yo{���c|��C%!PS� Ɖ�w�k��WprepaOby I�bI�!? P$����u�$&ta �Z� a break�" <"y ( i��ftej%&� r��E�Qkit����l��nZ7� adopA1�6p���# Qm��� ��hea�(@�>��� �5)�6blepa�t��D�*fP-��1mDZ&u&& "�tN#e�l�� �� � 4-"� $ �� �� � �.2u (5P.4&~  ~ � � -5.4f � �2� "� -2.9"� &�J� � [&0 ^� 4.1&E}{�� �fF.� "�#G*� -6� � �� IWV1*�J�5L"� K^� LV2%� 2.05�Mz,H2� .fNJ&4.1.]� n.]5..:P=`%�� �� � F}{Gf� B3% ^IWb�� b< M}{Nf<v O}{Pf<JZ` B3S�ᩡ�&F p�: �dev\ �2 "A:��G4� �� "nisJd�F �trojaE�0/t���d��enE�V� ��& ~��o�De,%�&Hadamard�s $H$&\_ cc-;��2� �T�� "� .~}�R. I� nsA�in-��B-�53byNA0air of Hadama�Rrd gates $H:=\frac{\text{i}}{\sqrt{2}} \begin{pmatrix}1&\phantom{-}1\\ 1&-1\end{pma"<\negthinspace\in2� SU(2)$. Due to their jamming effect on the human's tactics, we can call them a quantum Trojan horse (qutrojan)\footnote{Problems connected with the definition of tr;� are discussed in \cite{TAC}.}. We can hardy use Iterm t �^ resp�to��>circuit-breaker $I/NOT$ because of its paradoxical correlation Sh!1\. Note that $H\cdot NOT H= :�-1�&0\\ \9�0&\e=�t$, hence any attempt at measur!�Xsquared absolute values�coordinEd!X1�l strategy qubit will not det!-lI ivenesM>female tI. \sec!� {QuaE�Metropolis algorithm} An obvious generaliza8 �C!4a consists!�add�`more control bits. Let us -Tder a cellular automatE�at �blE� implement�pop0N�Mkm�$}. Such an`Ab �truE�by foreK a network�4identical sub- �a (A8���!j sameQd@) joined by classI communicI�channelsarA��N! q�|admitynonloA�(alliances), �ystem�ed by1a6�0arbitrary oneM\M, would!/.1}{Cu2.9 v D}{}%%�2�E�s_{k-1}B�-4.�HVH�1.8H$F}{$\oplus2�iGz���6�2)�Hr�PI�!��1�J�+Z�.5,WG 1I�1 xK1�-.9-LLV�~M�� qN.�PO�.�0�P�=��.9+AR�.6 �S��%b2:T.M3 U}{\meterA�>4..uX�%M� 4.,-=�Y psset{a\M�7pt} \nc[A�sep=0a-}aXB} ^ B}{Df< E}{Ff< F}{Gf< G}{If< J}{Lf< L}{Mf< M}{Of< P}{Sf< S}{Tf< T}{UEQZL F}{Kf>L}EOZ<CzA�F ,!���dashed,=3pt 2%�>}�aER��= W}{J�= U}{X�=Y} 0 ђ\ca��{T�c"� $k$-th���&� ��ng�6 R ( 8chain).} \label.F ��B Th�b� on (C )� ��xa way� the �v� does� � ge � "� $|s_k�7 (ɛ2�\r�earrow2� $ w happens � 2@probability $p$)  if |iZ �neighbo� �s�2���{. hav� � Z. !:A�ed E� rep�S � in�%%8 flows between B�. A!�pl� an"s � is � � 5pinflusresultUCQ*onx sts in�lacM@ switchX�-� one-p $U$ } $|\l� 1|U"�|^22�=2 p$%0� N �in" �$of a time-`u� P pseudo-random number�tor) is necess� for ct per%��%P>��.� !8an be reis�a� �-keM (dimensional� � .} . Go!�farther�tb dir�,� choo �A�F(basis (in a7 lej r -# way)%A�M�yE�u� var�conju�dY� �(are equival�o�!�alF &� To -p ��,8!1Hply unitarily trans!�s from��$is we wish� TS in� � utelal @,2n/� �wiesner %�be x,%1exaa�,5�!�ev�M�cliqu1+m��=m!�%0 market gamesM$PS1, komp}*�)�so�a@verAIQ�R�I�&ly&� ed oA!c.��.& ��� -2.42%FB� -1.2*�G long&� t�0*�H�2�"� 2.45*�`�4.9 �J�|0�KVF�1!45L}�c�1��3  �NzV�8�=E �O9Y�:�F��&Q!|� Ff"Rf!��dCR#]� D}{Ef6vdB<�F6\ H}{Jf\Kfb�L}YZZNfb< P}{QfxQr I<���"MJ\���na� ��"d��"��� f"�o � iz�^is�n $ll follow   �PenrosHho explo�PMauritius Renninger'sOa�[ {\it nega�.�a�1r9}, see *� "��h?j ��s 8gradual unblockd ��:" ($n�1ep:$�$[n]{NOT}$)�at each o , ifj��� b; r"�(���)first�MXobserved�wh> 2!�� up. Sy e%� stoppe`[``%|bomb''&� "�)�$ $s7 actually� pricel=n "d a� sI+um "%s, cf&F )� udolph}.}2�!1at som ep��18auxili 5�- d afte�"� � !#&to�* r<�Dew�$and{\bang}�:N3pt"Fpspictt0](0,0)(��.8��Lpolygon[shadow=true, $size=1.1pt ;�=-120]% (.00,.40)(.28,.44)(.16,.6440,.52)(.44,.7 6 6)(.64,.8$7-4) (.88 % %1.12,.64�82 2 e96,.36o\84,.28J,.1e2�48,.0n�2 24,.1632, $08,32)j.61,.4��V,"c\tiny !x!!lD 5`��Fn �'� B���"�N �k 3.4*� �  M  ?� ��2�0j �1B�z 2�? %db nk ' 'BY &� �3�C1.8�] KUFJ H G 36}H 3� 3:��& A1V� -3� �B1v� Uy.}\hsn-.4em}:<� {% 2- o� 2D1� �!"�F �!#G 53.4Hz�Jh XI=�� %O&� A2:O �E(&B2.�A'CB"� =,+ � D2�!:FV q!G56H 5A5I�S& XV���%Y.V u.�'�Zk .0,1�^qT= �m2�*=��� C}!^b� D2}{Y�Z� A�J.bottedz �bmv�a�B1Nl[a�C1f]C1}a J�~?Z�1}aV^PaqHf�auIj�a4F2N^Z�2}A�b�2}A�bzX!�^= Y}{Zf;Zg�s6`0 p`���none]i�.~<.3,2.7) \lput{:D���# L\bf repeat $\mathbf{6�)-2<1}$sm�[:�"� ��q:TToal"to(2,��n���JZ��{d#2�"�he/ &G;of™ 6� :� % o^:yZni��'� oper@: ` equ� *} 2 $:=I\cos\tf�+�fty$ :� oXopp�%`�'� zero&s!�vcbe �'by appe'*+� pap+he�~a2 plet�new�Pechnolo�!� ybe sh�� thos!��aS�}1� �s. For "�<"%]m;r�!a$� � H �r!Rn�� h a �aG�%a�I7at�,e�(Deutsch Mul!�rsu�.d 2Q�+� t6 s turj.��m�! isonl- #.�-�X1 5��2p+t}A�fix�!�I�*d��,is machineryEqb�/ldemoli���!�j9{n���s� e�s�� dama}. fuseE� )2iv"\1�.isY�F�ane} (�haded-in)�%�>�-b�,� theyM$redundant)�5�$�o(�2)��atAM9�zN�.T}jg I$Q���!�1-�W!�e)� �jRn%qa3i 0rF. Ax-b�- f�-2A� �,����������3.3*�\ � Wg1N" u�9. @2f� }E'Y� u��z*.59�"3 2.16�24.�4�41}�^p��f�� C/F�Z\����CR� �2}AK����:�6)%�1N���:�I�&��F��-7�f���SafJ��Stester6��@K� + *l.�{.� tell8�W ui�*��7s 26�dV s�c:.&�always �c�ii��to$$&= At� "s >N(� .� ). Of c/6"� omb )2 (�}\� B� �&� b29"�89)19�,-^F 2� ��i�s�e5Gbut un-?�� lert:�2�(T nstea�'`` $ing'' it. k9 altern�-J� 3&�aneze�w� � omb %�sB�:MF$nb6 ages���5.5��.Z#��nHb' z^{�n-1}{n}}/"�# -2.5����12�Y�pj6NOT^3Y2 ����3.1=���42�~sq6Y^U�� &@�)&Q�?r�x �.4>.��X2�42[.��5&>�&�"�b.Z�1.������Y1f $A�FjaSCj@����������E��.7, V���:�E�����B�I͕-%@jh >hB ��6 �0incre�z��$��.$�ph#$\varphi, a-cu�>p4]5csCdDG 1}$.TAd�C0e $V(\beta):=� ? +( I  alpha + H�B�A H � ) K $. I�@ easy? show� n_2) C �k � _1)= +S_�D1 �wDAs!z.PB# *g�$.�:o��6�\,,$$ � $)$2C>�[0,2\pi�E�}forR<680,\pi$O � be#,?Elasb s -Q1i)3�4 t2� !0$ � *q3" �r�� �Z ERneq2, �we (�2 �1.� .nNG �?�!��es� /(s��6 spon(�3a"<z ��4exY � h!���� $\expY� H4����#��#:�#H �%362V4 32� 5 "� &5 ��������������������������������z�upply-de-�&� osrede:� C�J�8sF�GB9^^� Z, � now V�= I\,� �ҥ�\ + H\,� $. Again"�Mavoid�.L:E  high2� � $(\,|wvZ"~!� 2�N�:.\,>$,)^n\, >\,� �!2:6t :� *B? reveal��/h��8subtle�``��''�� R���<:�?�Lju� dU<lwE<$. Neverthe@0�0t being�H 2��9si""�/M1O &�<in �JN<Imanag�reN rpret i{>'--theore4N�Ps. n�toften� halleng�!� cL(ss. To illu �%Z]=le6ROWI�'s 1-$eit--proofh0kn�P$ Y�T(l;he�Ulsecrecyo(�M f@!�e�!dro%). As "�>%!'t�BaQa fini�=er�C5M-!osB� 0 �4oresyt1%�Ner Tren� od�a pair� A �C\psi_{T*�.1em"I B $%':��K�e polariN�� ()�gy)KZp!zknown| �� is kept)�q#� ~�; �-o-`1UO4DO16z4��4 ?z4U-2.7,&'3`OI2 y�21pt}}*�2O�JL]6\2f>&�DI1 w^�6w�uF E}{\c s��2�F ?6�bOhs�3.15��e1 M�&�> �ZIO)+G2OI�r=2J ?��K$2�E6"E6AUU^.5:]-Q] A�ExA] 4�%1& 3�O-11-h.�Y B}�0%��a5)N"3Ax"X?!$xN!$n�NCfn!�>�2bxHr�NIr�>JbNb""v�>,?J #]�?E�b�F�b<J}%�RL!:� ����p�Hwo Rs&~"�2a win�- must� ��� wit� ��"�X� 0� by . I(*r�no&�Z� ��d�L���`��6)/'s� 0x��ih= dV a`J� grow�[n�KH & = �-=�Vs8? ligi&X even�m@m�0NE$. Although �� Bo�T[� �)\�Y2� R �: possw if�u�� r�=. 3 {}�*j = "l+zm:` , $zW over�|{%4cal{C}lmeq S_2$�K-�j 04ve nonhomogenew.*T\�*X?�Z6J iz� :� Y"N >kZ  n)mQ%A5m &�Y6ZL}Ha�*rd2 s. (S1reaycan eas4Lr�-�b@t termI#By+A\16�N�?.*� )�Z}-as:� A#?�,�if1 dopt� �+r�] $F� �$���=^< r<:UF-\f�41-z}{1+z�>w "�$Fourier&9)BQ@2� x$!�origi}MW"�ide7R�encod�at�2!�!n4"C-sul�1om-f��inu NT�n oK wise�*A�a�\ PD���issuer m�tak�v�A"�J� A@ recor4h.�_z�6� 2.� �+Yl�S��� "�.`n[he�^ա\3�A�y� s�5A�+�'whe�oy�y;�Aagsa~at-!Ty-4(i� ��en� forg'04 p ful)ލ mK s6�9�� J� �J{  t�� �J(�9*�J (�J:� &� �� �2� \B� &N � F� h.� � h"��  j� �� �� � &� (3n� * � �� 6� IZ !2&� �KF�-� A�]b� �� r� VOY�� ni �RK �d� "cR���S 6B (Վ�.YoU;/��,��i�ddu5e�D"' ly�6o o M ��s�Fbet�secJy�1u MHttack (Me� �X ). E.\����.m=K��P6� in7�M � �Xm�Yhimself9 2� � �n�>{"�,>S\�# 5,�an '8og� �-Ѧ�s*976C -C �lex?of1V&�fs� i$-tE@$s may somecXj %Y� f] ` *�,"�5��bli< oTU�h�  toE �8x!=bt"�7�S}�g Kern�� shell � \ ers:eSX of mind} 5k<rTT [h#�Zput gro@ em{&i d�n%z �Z�/� 1�n�:!( "O;laA�Ld &O7in iF� na)��W�K� i�9 j�7%�uKsci�Z"� �guXJ !#g$ing>$t)%B#k%R $V��)�6��Zis� ceivrs�"�K =� N spec��"4�&dj4 �%h @V�Ued� the �Yof ab+ ctL pert�R� %�Q��,~software)�r>D� phy���lE�E�. �w�kN wFgcertai�r7 re a lo ;"8 al1bA�� atenoryM� (or �s !�-G� star�Ua�-wa��U1 . Adheren�\0fic�� lligAO (AI)�(�hwel�V��iJ rn<��Y^)fe- | approach8 AI (QAI):���i�a5SGxM�gi(Mind (QGMM)��l�^!confron)�+1�dichotom�N�M�a�i", $principal  Xp�_psycho�|�=< BV�sc\>]un��> reud�rSXaE as f@Qs"C'itemizO! ��&�A.e Ego,��u�>mWl precisely ) leve%O!9ܩ��s aE�%n existI �a�?Id)< is Wiso]<�iue!��coupl� M�IdR?RP�� nt (a�yened) car\E��%k�]ou ��+�Dq�teh) )JS�" )IIqiMm not ��I_c!��+s task�monitI|"bl)ing) ��k�O. Meme� AI vir�memy},���n�)� %ϥ�!�!f)�.�A E\���pl �q para�!c %_ys!!Z""peCE��(��B -- no-clo�S�orem). V�litC"��&�A��Ch�Mpo'!by �Q"!e��0`!~o>��(ryptography 7 epor.�=o"�^�Cful��� comi��o� �s�9H!x w(A�� worry �� saconven�3/F�q�" lo99d63�!.�!r5~itAw�<de�S� namAEH�vua616&�"of�!rp%���F��v ��� ?"= ��2n� toIrom��&� tdBy!= ���� �mrnal u)aratu js$s''� a (pr�aV � � �a��rU�� nerv) �7#i�,A� ``orga�#''� D� environ�e� s�Ea�rF6�P0�  t6U$� � admi� �_@u�b��0+pay�EQ<k�`Con4�t 1� r� forwb�bert �ka }a!�]c��no@B��Z--E�'�gE�o�� (% EE) EiUa|t�oe�R��:nf �aC i/Id��inf�c%mem H`�����Z�A Id (���cm�t)���of QAI�� neu=_�(!�re�u� way�En ͵U�olueN NV�A�dox-wPSNa� �Abex�� uniqu &.l ]&� i�v��.I�Klem�decE�b"� p 0if any) faithhJ�[cr�"�u !� fascdra�;a �Gary #� cu!1� v� rian��"�;�Fu( sugge�t�!�D�.hI-`)�Dld k'���Xh%QAofa ��R�?�u���de"���f GRf���  domain �<uA��M indepJx@E� fu� DFo"�E drea-�hypnoYc�_2��c�& G zsn �� empo@�u(w-&�)isA�)��G di1�#!/e�v�&8's @ja3 intu�@FnG�a&�l�f�y�� belieggh�2 like. W��tA) is, a�*s� �J*� th�(ts "J��(��%��>i=L deal�G�') situ� �["�G, vai}�%yZens� alyze hyp �(H (ima�� *3QAI�j7DJourdainian: Molie�\� ak�pr�I� out I %kt;O"�Iun%eto ;e�-!y� spoke0* Xp$� * *Conclu�,} Sin+ pub"7(of G\"{o}de{� 1H�)l�t opinfe݉U�Vdz ���6con2�p� vai�w6%�A:AC*�.�,�� ��NC)�sceptic�+kr� e$r"�m@phenomena in brai%/�Ee�pe�^PJe��be doo�'toe�ry &� coA ntݍpm�zr1!�)&�{. AK. fielA@� arch�&b�&�8ed.\\ {\bf AcAtx�s}�*p�v�& 8up3 &�Q<P�zhb�x�O SV$, Res ~��I&kM T"� } un��(v�]d)�Rnt NogP PBZ-MIN-008/P03/2003*�vthebibli� (}{99} \bib� P[1]{Mey} Meyer, D.~A.�E *� , 3` P�Review L^ s\/}�< 82} (1999) 1052{ k`2]{Eis} Eisert, J., Wilkec ,M., Lewenste60 M., �� �1�&�>� �'j� \/ }%�83� 3077��3]{nova} Piotrowski, E.~W., S\l adk � �nvs�A" �!� ory,al%/MatheDO {);s FW0iers}\/, NovaI ce P�!Hshers, Inc. (2004); �$-ph/030802.�4]{inv��A��vi� t~bu�� ��I�JCo� �^of!"e. �1� 4!�A�!�89=h45]{mil} Milnor)� �s"�nature%>$Thrall, R.A H Coombs, C. H., Dav��0R. L., (eds.)M D��1P!{sse�, JohnAney \& SoAte  YorkA�54) p. 4.�46]{IT1} Iqbal aToor A� Ev� %Ga� non-a~Ub4sM A�.~Rev.!�A �6 �0) 05231.�D11]{Lom} Yimsiriw�na)�Lom� Jr, S! , Geہed GHZaHo���Q��ing.402148.92]{BBC}QfAY e�( ., Ekry �!�"� `%Qfhy=15!19A\34523]{7 Nielsen%��<(Chuang, I.~��eiE um C&�� .8\/}, Cambridge m&ity Pg.��0).4]: :� ��J�s���)�N�L adox-#r� { K 1�� 3) 36�05]{Gar} Gardn� %8Aha! Gotcha. Par�o puzzlH)de9eMFreG9��$Co, San Fr=(sco��8226]�$ Timbleby,�] Au sonI�CairneZ A �~B7 umE*�A�IAer� �i�q�)�er �RaY�4!": 96.�7].T� &s<, N., Rosenbluth �.M.~# Tell!ZA.~H.�Eaq� �  calcule� fast � gU�� J.~Chem.~e*%��2 �5 2#8]*��~+� �,DJ i�B: A��2 Shor&�M��3ee�0 SPIE� 5436I�4) 360.�9]&�� V��, G.~Y�i2Eng���yular auUa ��Yica��D). 1��1984)6 20]{,� Cole9 ~H., Ho�7$berg, L.~C�V%� Praw!�S.A�9���v%��{�{E� �u type-{II}:`Q%r� 404143=21]"�7u)��� �: c�j-SIGACT�Q� �15/I2�83) 78; http://kh.bu.edu/qcl/pdf/wiesners198316024137.pdf.�2]{PS1>�~�Ma+w� � 2��31��2002) 20.z23]&�m�m� MS�jE|�Qb� >� �4.� 24]{&�m M.&�m, Zum Wa�Tn--Korpuskel--Dualismu � Zei�Yry�I� 136}ra�25.� 25]{fl Rol, TI GrovA.���H�Au*� datab�, (or �Gwe[6�1E�<rZ �[l!70bomb); arXiv:Y�20606.;26]�\ F�\��Gki, V.,!�moa�M scaz= EaWjreEum6�O@�@of�� �� p?K?�Q�-9912011;�!a�ej?�a�/q?Wor�b�s�J]�&.�3]"�A�a5~!�O"�-mT@A���lL����m� 98}!?��6� 34]{���xMlEson-free.�E&` %61003.=35]�Nagel�m,�m�yJ� g G{\"1%of%j New �& Q 195.36]*�EAflarge,!� �4�u�pR Rr�� (ed|CJ� ��N97A��*t:� �! docul} ia\�H[prl,aps,twocolumn,N pacs� vtex4}%B4eprint" �#H\usepackage{epsfig}20!icx} 2amsKi6,amsfont9iVamssymb�nY F{\ket}�|#1�9} 2!bra!\��#1|:"� #ket{#1}4:( halfexbox{$�3s|� �3}{2V6~id2.jb{IQdef\o_7{\leavevO \hT\IGL1\kern -3.8pt\normal�j1}!�~? >N=��_Q$(} \title{Me0%AH�6gef+�Cw*�* mUbsn~a�� le p�&(terfer;Py} \author{Marie~\sur<"@{Ericsson}, DarylAchillesulio~T.,Barreiro}, �dra�w}$^*$, Np'las~A?P��}NDd Paul~GKwiat!�aff�u�{D��t1��,.6 of I�o�&Ht Urbana-Champaign,  , IL 6180DU#wo di=*nt�s:1(A�p ���biref/e*s;� W6a�9maxZl!�taQJAHwiH�tra: E+ T$m,�Eorl!remF DprA�E�. �YM\��({03.65.Vf,  7.Lx, 42Lm� make� W@6a��u�h�E g6�a?� progRion, be@+!\e� alI-"� �.@*�QHamilto�E�re�,s�#or�)moa� i:81 �lyF�actor~�HPanchar56,Ber84}. LG!�Mv:u ha�en]��&$gnXE8���%J=hS+n$ ��~ 91},A-I .�r+two e��NMR JS�/88}. Re2`q+it�y� �(�=�vbe`/!iedmx:%s  }, s�yeaF�" speI/�#q��_e;I%�%�War&�} pathE=I��"�Hi�  s(C{"{epW$to inv�*�Bresil�0a� ���*�#�&�?��V<a w a|'nI�0.i>U� needP2 Some%�&50B�o�X �s,1%�0by Sj\"oqvist�-�sj },�!IrM.I YCDu HeYweB� ��al stude�:��q-�%�s�i��. Dɚ; exquisitnt���je�! =�a�i+r2"`. mapGbehavio0p e0�q��m~0mixIy� ��2�xn vh,good ag9��,#a"�predi52���ps!E�$�.e�'ti.r� cour�#ga� li�!of-��ka scal�"�:ar)XIB�-�klm� .���da>�� ����!�~"a@=4I�$ei�)�c�l�A��%� spin-echo�+s( 'e�magneticf"�HE�00}, !�n`n!8qMl�nsN� ve��]ud�ens�AY>�isr�bll T6�3paBjBpi�x��L1�I� � $A \Psi(t)}$e$w |\dot# }(t)� =0$YRM��4�+�r�1o�@�I��=Bq�Yv��.�+d�,�sҀin�Ms�[! $t$*7 �C�C!Ie� "ʐ�oZ4 ��y�*> glob�B+K� le'&R��*!�is 3 `Қqu��:z��A�-�@!4��l curvaa�am��9�8A����%� / ]Qerturb} sQ�, e.g.��,���N��� (~cce� Aj)IE . Uhlmanq�u } �6�W  &eT+��eM RL a &h"o#,�TSq PBesB�is�Րq� wE�purifI� �)t��y�,Q �5� &�5��u�sE�a�(/]\A�s N$ den��rix�$N^2$,�(�*9n -_x=��� a>GAfo^7 $N$ ��]��R2�a +be 1�8 a -22��XP  an�1�w� lla A!�NogeA�)�5&A2e� EPSBO��9{o}.;5��Z I!no *�ub� ![�-��,}(�!b��"� e aa�&Se�ILa * s�3_A�C=a ��y"1z! �S arm;� out�t� u e� Ax+r0, ~ !�no>y���>�>3h $\rho=\sum_{k=1}^N p_k |k ��2k|�BR� by �Lk(t�Ik2F, \; \fo� ~k, L�mix1"0tr}$ % i.e., � el9�A���S�9F7G�)i!)>k)Z?U a&y��0l0�2in�eBFE���ibuge inek� �:. O9onseqi�Q86 �8a"�2ͰU:S, $\gamma_k$,[a�ssoci��U<� visi�:y $v_k$) to5 E�m\>� f�A�tA�obe3�n averagѵ individ��}f> J )�$p_k$:%�s��@�c }% v e^{i �g} = E�kE�v_k. k}.QRg�>e��S% � bx!�a6 �xe�u,��Q���m�2 writ�W�-�4� Bloch� �eec r$EJA�i� Dces $\vec\sigma=\{ _x�[gma_y, z\)�a1e�(�+C r\cdot 2MdIt�s��w��}��w ab�$h (1\pm r.} zXth!L�6�r$�3�� m&�gty"z�,w2� a�E� ($r=0$)�5 1$2=�� S( $r$, Eq.~(�WQ!)s��=q\D{(\Omega/2)} - i r�\.��mJ�ɧ$ J�I!+.d �JlH trajI ��&-6 )��J)usp�6�d>> �/NA�Y[��)�same �i ��A�he�V'+4} �J>$-) /2$)K�Fl49�yage})��v��:V,���~v�=:�}2tnarray�t &=&\sqrt{�^^2.� +r^2apn6}�r }���} \\ ��X&=&-\arctan \left( r\ta2= \J�). Kե@�Qe�%  ��gEHmT� n���er� plot��%�`�� !�us ��[��>!"| shifVNA�9&��. �5ay@-�)��e&� g$~�q�o �)�:Aho ���.(Y��KHur*,����J���� ��[Ъdeb� � memb��a�O\7)^�gtaQC) �dow�5(SPDC)M},hong} (we al��ook data�>3s7 a di�NlaserO@S%D�,��� ��at 670 nE�%<"�� wave��737$re ��:�!� pump!TE&I��mat� BBO�V an Ar$^+$ �} (mbda=351$ nABy��Ton1oo�( a�$-nm ``trig�'1w(w1;A�val#�)aːa 5> FWHMU��fiBt� �)I�2� �H@Uju{C'��%큶g([3��Ba 8Qt FockIy~)�MS,E ,I � =�sp�R$ $\delta\l%R\sim 5$~%TAs|Dwa� F"תfig:inYa�670-nm-Jqup9i�q)� �fiA�to gua-�*6~ 2Kfor�h � �. �? U2�cEh#is us+&� 72.> �%t��X.� �<$670$.$PetE��"Mx>1�E}�Ce��Bthick6Tr�aW+!^)Z�i�'DA*�_�r rrivAim��+v�m �*lund,foҭ:��Co"<�horiz�E�-?e/ | H� $)�. a��tN#ly:+V+ �!�s6���delay �dBL <s�E �Z�+by�: �:! '��� ��(�C�s^2/\D>1490 \mu m$), up:{c-j k, 2--C�8�Flec=�.� �$|=5A;.#�tip=.�9du� Ş Q�era^9� ctݥth�dbK�J��ds;/�s*�SEgr@<rjX5�nc�I� Z.�U fidu�H �^[m#���e�1�6.�s 9�U]:W&.��M�e֝, f�G!dy a -�"pG (HWP)P fV L�e)8rs (fpi���%�tz $�I$3 cm�R�ck�8�_By rot�!s HWP�6)�;pu�Y����superp� !�$F {\theta}�H} + 2 .V�N�%if���m�5pZ=�,!� E6�[!off-diag�7{�  de� I�! &�>", =�i{2 �|A�Je the! %%dnet*� J�!(}0�j��.s;D�, �e�O�6s )���mL��!��q�M rter.@ QWP)Lo Q��  ($|L��Lv (|H  +i |V )/, 2ך� @R "F@-^@�a!q� ght. Our�@+�m}83"��-.F�ש6� �.�_p}|HQ +}�VQ#$-P� 9�� I��.6�Y&��!r6� (at� LJe �D>?upartner8� ��A2) -ins�+��H)- >�-� ga#2�� 5Mrho_{ � }~=~�,^2�!E1^��$ H|~+~!j2'1k' V|$,)�$:�V���}:~t�qf �E�u�Zle& p �ij-Eb!�2�*� � F R � a� EW%�#fo� a QWPa ��0in:O ��>�$��^��$ �a:�Y2�#er��yS��c7iCde?+s[1�8.6cm]"M) Fig1�Aive.eps8�F`�-0.63cm�d°M&�)./C& �6���|7. F M�d" �Ts: 1)A&�&!�2�of)��aZ�67%�� , 2)����* n 2h 1A_ 2�'����cq 6<��*` @ ~(see Z�box�FO �Il�C�`,>�i$ �Ee�I�. Hal*� s$O_1M� 2$1�B�d��t�k_y=e�meNo�Owo cro�I"; ":low� \,K X JE��ensp(A4�%"O6� ��-$e 's&#:� shap�� nimi-�unw��:� chan��ari��1>n�- mirr� nd bWIp�Per refܯ ions&!f<>��)� Atn�!ab�5EM�ib���M�s�� ij"+ (F��)I\)up}�arm�I�v&T volv�nit�AM M]& �%� a�<atf�, &/�l-�l"% *1Jd :�A0��on"N *qS !_� � �!$|R� $e�vel$ a�}- geode�6g� O28�,$|LI�� *�a>�T"v en�a�*� �=4(m�e�e 2)��dwpH�� a.� *)�]!"�� RU�7Y �:3�~l"L_$RW]�ͱRof*A7rei���E�ube]ed--&NY fulZ�EF�, "2��8in� B�is&� titu�]/2=� _1$��o"i�|��} ��CexA mot^ed��s7G��]��1$ (to�� in $0.01^gn. th�:!_l*. &��y�� 5cm} HY.�3 2=�1 Fig2y,� 0.223}%0.3�� Ii9i"֌a.M�$Qxd����E�12�D m��MDe.�� A�uW xPj!Y ����6" i� f�VEfhe 67 ���� . (a)-(b)� -w�6��L/�diMl!���7 �0text). (c)-(d n_6 _�6gb&��&� *�b�S . (e)-(f z�= �- ���mb�&��6~��Z�bar��ri� � ANfi< rawE]A�5$�%�1` P���7"3o/esN���hunc�dE al g�\#(�$[$s3�U���df�:y�th�_�4�`asT;G 9 d�lm�>�8To�h "e )%O =2H6H}�#C V}$ �%zH �����R!jAlO�_e.ina�n�c"� o�~.)l�i9����\%�a=6:A����&�*:9������l� �#c##?�$6>�zZ�c)>� d) �68 ��^!��:��i 6JO t�'-�(*iJ\eB�ffkw2�w �I\kXd7�Oa� �cle�:f�]�' ;%�*�surviA�\9)e�p7$.# q�o1�iqwoB_a�s,a�Js�6+�}��a�flipped i�� $x$ axis:A�� setu�<�'e+s�s{Yd ��r r� -� 6m �0,l=5d�e .f^C9 o��n1#��́�� 3's� % �C� ԥWS gram'sql� y "Io&�0}��Ih` GC���N �&"bh��!:ndard &�.�H���A���m s [�r&&Avo 6q*� >~����D#ifyE @!A:y( w�3�� hi^2$-�m. F�J< (�i5��� 4&� E!s$0.98 (1.36I�(1.14 (0.94�f ���e56�D�%A >:{4c�%a.�+fit�lsn�elue�$r$ r�ف 1�@&)�):Z?)��06�BA in.s!<�BlF]>:� �~"�-p��/��i2>i�, =���+��� thod!�6V.&]Ao�gof MA�1�dm �~ ri9& two (sJ>�>R�$.� . B<typ)�.��B@<:)�in�*yN#A aV s. G�0#�B adv�7�linear"9-evyO&�H���@� "inu%�te��)#9�fD $y@u��'���% at!� haved BM\AX� A����%N5������srk+�IG�=Jh�I �Ice inhJ�e-9$al"�a&W1forte fur�*�1�4�&�t".�-~&�;E8A�ga.�%2 wilczek841FfJlz]�6�Sz!du�^��! 9aH0i� J �pacho� W� ank J. Bb�epe'JE.aJeffreyZ VanD�@ der,�9 T.-C��i%ѡf�&),cus�'�te��!n@�2K(ce. M.E. ac"es O+n�+ ei��F�ۥs4 BLANCEFLORBonA� agni-Ludo�L, n$\acute{e}$e Bild�{W�. cogn!A�&ia�re gAaNcal"Jcx (G�04 \#EIA-012156836"�.70�F>�P3e+0�$�L�d*]{db}�WV add;J:$\,$�Dept.!�pMEM�_!UEnHA �[-HuA�~Inst.~of~Tech.,~Terre~Haute,~Indiana,~47803.�� �& J}S+]J0atnam, \emph{�U( Ind. Acad.!). A} � bf{4A�247�R5.;T{\J$ M. V. Ber�d.URoy�c2O392}, 45O8.�X"�  P. G. � %(R. Y. Chiao�|_�e.�St��$bf{66}, 58991TR1 :TJ J.~BrendYSW.~Dultz�X W.~M�D enss�_ �t=5� 2551�L95); D.~V.~Strekalov�Y�[~ShihJ�.N� 3129NS��J D.  , K.]YMu�Yr �A. Pin�B�Le6)xF121%*8A�k�|!"P Jones{ \izI },%,!�Vedral�I�F �G. Ca�noli,JAgN�D]V 03}, 869 .[80); P. Zanardi%3M. Ra�63�!4�W26A�94%09GLf Duan] I. Cirac �d ]rTScK�2E� 1695�1S S.-L. Zhu�Z.!�Wa�a~e9�,187902O3.�3B}��.�B1m ~al.<%B]%�85}, 28aT202�a�JA�Du�U �00403F�� E.~Kni�g~LaflammTG.~Milbu"a �F9�6\1); T�d~Pitt�VB.W[�d� J.~D.~�a�a Wj8!55z2d� d1 Ze}�6L03231 �3); JX_~O'BrieL2�B�2a�264�2 e?00}ao �2QJ. Mod.�'=�47�01W.�c&.�d,ET40), pp. 109-11*^.� M. �#RKf8E�09040�2�ht; C.~K.~HondeaMa�G~���5�r2[KEF�B.-G. lemin��!L UK  R�]:5^T6y, Cosm��cud !���|VaQ pVow�^aqW. uV�@atC!� Harp�2JrcEds�aapf ]Z.)�E�2�i8A�~J.~Bergy8Wtmouth�blege B.A^s�k�<� -�l 0100U�; N.~�V:�E[�f.�.�$�j5N�f6�8!52Z>5simil� �Ma����2ZI$"�0f"q0$�&v� $\6 1 m �<�9�cj(&�\{b"h3!�H!py3:'~�8�R07�;2F � 992�6` Fa.Lw R773���5� wps}NW!7fix"�2@N�c&l&hL� lyC$"�&a&Ree�$%��&� wav8’2ybe ,d�O!�pa�Dverlap�be rui�w�1h ?`8&D6N� Be[u:agU&?'�PZT3�y2&ӫ���$�� our ��1sinusw�w�#�nQ)Jkok arguUZhR%/Y�*�s ��'5�:�A t� 6�N'"n�W%-�YJ >cdrift&re2�I?�2��a�.� "�-*�:HW"l-%\;z�]N� ngA used6�:o�i�<�A�J�\�� �%��8\+�t=-B!+�Q%Nu%e#�04$��b"C ���"�8M�?^x9,&�-4 �U��u38�+r=0.57$�als)y�-, ){s�Bre�I�t�<� IK�%�Edisplaѕ���ab��&�<=)&� F.1c�%�A. Zeen fo?11?6�� P��# � M.~R$ �o2u� 010305(R)�z] >��*&:_hZ>ma*ea�<s:��,��[,A_a�s,a�`,onD[ ,prl*�a\* a 6*�dc�a6Jabm} ��\t�_E.� n-Space&8l�E"P}# P�& ��( \\ a Noisy�h�� AtmoI of 13km}%�F��M�}sI�\\"(` Cheng-Zhi0c=bf�_Mod!aA?�#a�Hefei"� Labo�Qy� *&�sy2Mi+ cale:�_ *L  T�+ ofn�qn/l(hui 230026, &�`Tao Ya�������,Xiao-Hui Bao�f^%a������Jun-Z�5������ �(Xian-Min Jia������� Fa-Y=Fe�5�5�5a5Bin������m�J���������Juan Y�-�-�-a-Qiang ��������Nan Li�������$Bao-Li Tia�������a�-Wei P�������Uaffiliation{Physikalisches Institut der Universitaet Heidelberg, Philosophenweg 12, He� 69120, Germany} \date{\today}% It is always , , .(% but any B�� may be explicitly specified \begin{abstract} We report free-space distribution of entangled photon pairs over a noisy ground atmosphere of 13km. It is shown that the desired entanglement can still survive after the two en6�ds have passed through the Z��<. This is confirmed by observing a space-like separated violaA !�Bell inequality of $2.45 \pm 0.09$. On this basis, we%�oit�5a ed e-5]8source to demon!�te7dBB84 quantum cryptography A�m�e]!�j ance�>j p%�$achieved i�E:erimenE�for|,first time w!beyond !leffectiv�icknessoaerM , he�present%l� significant step towards satellite-based global �ommunice�. \end{Y�@ \pacs{03.67.Dd, Hk L5.Ud} \maketitle I �`future large scale realizh� � 2� )~xs \cite{bb84,ekert91,bennett93}EE�to sol%/4e problems cauA�by%9pii)�RCAAv. In rec�years, .�progra�ha�en�, -�ex�,al��A�of�%^5*vu5�2p= _exp2katom_naa�, 7t_sci,matter_light}, yet one st�a� long-� go beforA9e aboa�echniquea�n bA�(nally integ!ġ6to�7e unitA�I�tU useful�J �O stic�2J�S����(s. Another!�mA� �outbTze�-6` 6`is2��>f& Hri& �ITs �e>��Nm Z}Ec�i�, G=M� are �i�$ .�.JtheA� flec�. from!� v�a-4�>f-�V back!�$earth. Sin�rhe ��!Go�3)�8of 5-10km (i.e.[whole�5equivalaoto 3 gr:  atmosp��)�mbou��� �);V�Dis negligible, wit help�5 s!/ n ���a YQA:�asEh��-� can i_sur*� penetra��79ͭ��}A�e�? ,line, import��e.pF� made very��e�r�>��&nu� (laser pulse�wV� �T_23km, 8600m}. However,U"ne hand,1�142� � %�>� ��pz}� huge.��N" leav�  dro�  loopA�# AL>!�,er#l�� principl5 �SaR�I�l�Kor ��>� over>), � q hq�r�tred��� aH�m�:0io2�, � eA!Jf�E-e�D-assisted synchronL method��dex � 0elescope syst we drive%Z�� ology furb���+Ac+6*� "s�)Ta .;ݖ913km. Wea�>e � �!f�1� ^1a�-�s 6��.�.daV ay�a�� tf�. addi� � alsoa<��uUedB�*�yo! *��.�6� Mj<}ց,��!�.�e�u���#.� ��)�u�in ou(� e�oR� NT�c�� a2W ���Lfigure}[ptb] \includ� Hphics[width=\column ]2(1.eps} \cap!�{Schema� diagram!;"l F%�e �.f�X@eA�!� fooMa� a�vi�tow*&to� Dashu M� ain. Alic: W w $west campukUSTC,�MBob!� /��Feixi, a�n�0Hefei city. Pis�� Senvt��?sM�� i�@ environa�%rD , strong� flu6d��a�air pol�� P�   l� s, evtf raine G air E��@�� ��abaT30,000 �secon%$np^#u� � rfs5�Z( kwiat95} �$Argon Ion  ^ d!�pump BBO�s8�a wave!4th� 351nk��5p�3Y>300mwm(narrow band��q�L2.8nm!Rfro�a�"�� orsl a��col_!� ut 1�6 �R��Q �(an average o�&.�m55��C.�Mo� to optim%�he6� *P a its stabi�%�q� g^ wo set%2� m ourselveK � �� 4l ��� CrefFE$ype. EA�$ weighs �800kg1 focus -�)2m. Len{ � Oaco�toh1 peak6z��aI�6[>� s (702nm)�.� )�of !E�Y >��of� ve $70\%$iwilN �<� top of:$ brings usi�di ulti!�!�wc�Zaken s�$al measure�0 com� em �:�), s��!l��ie YA�,robust againhU�� winA���Fg b��bmeFtwom, -modnberU�� conn�t���ing] M�6�D�4�f urba�6�&y�sAU!Vpos !�)��d " vagandomly,��reduceA+��I� !��1 y. T&is��a��e?�.vt� �%�di��eriR 12cm�Q&�ag/. MoreA,!��h �r�imilary�} �dcZ�5� q s. A� �e�ed,(� s-�uplM 62.5um mA�.%�2�Hv u&�. W�s�orN wnag�Akeo:P m�to work�bly%C@ � of h�(:k�� rJ ��of:� �nse�%?� sid�Cb D!ܡ�E djusEB�J%�: . "�E�A�� ��� j\to9 q�aliAs5� �ns�� l ar�Q+qra ��0 '�e� .tw|c�CsQ9ceeVa+yYresulTa.��gPce shake ($\Delta T$)eYco�dce���vents�%�woU�c�B�Y� C-Q � ��ow sh�b4 han��"w�w *� VU!�geIadd �rut �nt ts)�accid!�l.�* �increa�\%� hus )Y�a B��H$6/��B n�ofM�� >�*cn %�9cej/ (See2D2}). � I�,, Q-switched.�A�t"6532nm�{ s"�!i�A�� s@ !�5t�o�s, � � A% same� cal paws!�5uL� �lP!Q�4i!qQ:+al of:� E�-�e &!��cor�on�*1�B�S)�subsequAgU�a�ia cl�cal:& link. Con��r� ingred�$ T�e� , we� �iT!i20K>�.��2:�Block�4�!&)��%Gx !�setup�9�5 . As&�? leftA�ur~a�~ U�"o.�%�Qå�ig��bE4ic mirror (DM) � i �Q�^m Al� y a DM��n it fow �6Upolar�analys�nd)�� "�-! E ��"V (BS).K���5% se� ioni�a�-a� pl�$(HWP) toge�we�6�:wPx�# !�n app�%usA�6:= A �tB  (IFDus�%t ridasV�.} &?2>?Fi\ �' min� R�,���� ���M4�!��ha_bE�!�� cl�&= "Eadd� 4�� �lA�402� � wea%�{^ is�]-��J%#8 vis. ($>15$km)!#9I�mQ.��:ZaBob, �18 �*$ Iu�tRc32N��6normal �~ � ��99o �529��3:�Ve*�$� � Ee&|#��Q� "�ty�q�(F2�$>��}k m];B`as a funG %�'s :�gle� ur�&���A�fou:���6�s�&~pa�6�� z,5&�~s �Y,�� 4ion} |\psi^-\r%�L=\frac{1}{\sqrt2}(|H  _A|V B- A"B)�^wI#�  A!+� EM,B.�H%� V re� horizs l vert.�)�= 9�:!��98IaIU �rA7 MN�,�,s� i*1(� ��A�r�Y�Q}}��M� b# 68 (�.�3 HyDM�.�I�s>�*9, 71\%������>� �:�._ i*Cl�lr-Horne-Shimony-Holt (CHSH) &�-W !��#���6.ie�& chsh.!��E.co tW defined a�� J0 E(\phi_A,B)m24N_{++}+N_{--}-  -+}}6$+->2We2$N_{ij}:l$V!Y��c.whe $i$��,! � fiw�le� $�A$ E�the $j$�,RE�se��.CB$EB!�=�,�  $S$=m aNeS=|>h-:')+'1�B')|>`I��#a!l*view, nwP" w�,�s9! and 5.!to.�S� B#b�}y#2. Bu9!h!T�" me3. ics,%�x��-�alue $2��$�=�F�� $2B5*-14')=(0^\circ,45 22. 67 )$" t �e� �z"�M�d^es2j>%"� b�&3(tabular*}{1.L }{@{\�0}H/re�A� 'goARShow ar�3  s�+-:)4��r� o d�,� >e(Bb2}Rax  .( "(�'� 4� gl" )s�to� for�%e]�UEY�2Pjkemphasz'wP|at7V�&�"6&�'to�v�a bona f !ց���%�ityU6r �5�*in*�/!�low�-�1= h��.T� cl�1 ;(�- ly uOa� s* � w�� !_ �.� e*"|. h "�,wa�6 mple� in 20�s. No-\,e,K16 ���� ^ d siOaneouslI�, "sR�.s"/�t=Ib"�a��cyl-f� �cA&"8� bc2peE�ed ed!~lS�4YA"4d�A.�me4$SAg�7\pm�7"�2 A`:9�$5� ndar5� si�T�� \�#�5<details�A�b;7$mly ascert33� !�! ��!t>?�ant9�" !�ZG.� ��ari>k(of�(i.�"��!�(W a�,'H ewT0n 2�` ��� ��lyQ� her/hi~� w�  or� A�B2�6��pendic᠁; pert�3t ��96g$ =en the�# ve ck.� s�b��thec&rivkkeyeS anti-h�dE�n �) 0asily got, if= ofzP ^#a�ll1<%r4ut�we obA5 ed 29,433y�ce�s.6�f�&�� c"�&�pl)tɪ�EFa�5�+ card�Vom� r)��E igh-�c�rm&L�.)�Z���al+((2�<�$got 15,3082ps. Di��}�6�hadQ�� "weg7,956 biS#sif��key �_ QBER��5.83\%.Pn>did e�EN� 6de��key� to 4,869 ne�an C�!;1.46\%|E�cy :"�8�kced�deeIng�h�, h � 2435� sec@keyai��b�!��cion� 10bit/�)2��iE�nt-p7ns᫕�  �-\|;Ax_-}eta�m�i! �Z��0 few hundreds���Q'lthoug"%m 9 p"�1��s:alͮs mq m@be� a �"s=for=�* impl�6. F�=,:j.�.1�~���#i$5Rň!-J�5 >�5"^/a�^ .�EO A_v�I�zR  Ob o#A�d,6�6��&h , to guarante��96;�curA`��qf?2^ ��>% ��eT5JK5Sc,%�&:�U�� ��/ (I�per���3.d�F�"�2-��d*.2�.e?m 7}Ar�� �2 s develop� E yA�e�"ish�ighj �"2|'�neu ":o "�*wo�g�ѽW%U � necess�%.:3or �?�a�Avesti%%�( g2�@2�Q1(�3�in*S9�# \$� sup,� �?N7al u�'Scc e Fa� &�-Ch�>e Academ�� 0���@RFundaa�0al Research P�=a(7�$�3"B�Alexa00 von Humboldt�% !�Marie Cu Exce - ce gaz 0 European Com�@�Je auth�6`�\ank]great � a� Anhui TelX1S){&:thebibli�%}{9 }vEbibitem �  C. H. B�A�G. BraA:�94Proc. IEEE Int� f.�> Comp�; s, S�5[Sig!�7es�1175 (AH, New York, 1984). �eBB} A. E �, Phys. Rev. Lett. \textbf{67}, 661 (19912G&�B:�Gl.jU 70}, 1895V32VG�A N. G�>,!*0Ribordy, W. T;e�!SZbinden, � Mod. ��74o45 (20022nnA} H.-J!�iegel��8h1 5932�82US@4} M. Zukowski,!nZ"8 A.,A. )%� A. K��7{ 4287{6>6,B6s��$6}, 722-72)�6R�p_exp} J.-W. Pan, D. Bouwmeesty4H. WeinJ�'nd��bm8A 3891�6U.�:��Na�A5�42E417%�6)*�Ae Kuzm��1%RK731JKm�C _sciq Va�/ r WaYJ�?�30!�196NR�_B!_(N. Matsukev�-S �,J\!�663\6��hE spelmayer��? journa+S-#ed Topich  Q�EG#{:cs, Vol�7<9}, Issue 6, 154N8fre�>%7Kurtsief�>�1V450�6�Ld<^�V62N�kwm2 P.�zK5b�75}, 433i�52;� J.e�e�, S. %� R�lt��J�E�880a&692i&��E�!�ct,DailibwACG. Ro�f�4!s�Al86tl"}TWeihs�0�B039[:�[�}���BrK0l,�j����1b�v35a1>v:aO\H.k1/�)Au�26�h03�6�� .>C.]�E$Oberparlei�5�G�U�A,ts023802e1)�+:� N* docu� } % % * Enn&f0@(apssamp.tex 0 �6% TAR %\@�)[12pt]{a� le}s prb,aps,p!(int]{revtex2+ tylej*:sK,\$draft,show�K, � c4d twoc�; %\u� ckage{txsym,ro�"P,epsf,colordvi,uklein� (2,feynmf} .?amssymb,G:A�/(icx,wrapfig.g�~�R� \newL and{\ ent}[1]{}6,n}{\nonumber: be}{�"�":#e#AS^!beaE07ayFE$ FV"ke �\�* |#1\�0�#:�bra�,\l� 3|:-no�% tBnc� erB�!�Vr��$:wr�Ij:l4 �:avf�Vfv!�8varepsilon} \re.2(})A(B)}{))B[ 5[B]5]:� x}{x��%\e��%�8 } \title{&O energy� fer: vibr��0 ntro nonar�/packet �a= ometry} \� ,{Dmitri S. K�@$^{1,2}$, Jeffrey� Cina$^1$�h Oleg V. Prezhdo$^2$, \em %( Oregon Cen���Opt U�S= (, EugexH$OR 97403, sSX D�&ta�$Chemistry,:LWashingt�,Seatt�I8WA 98195-1700}6�S��m�ab�Q ct} 5n--_~ exci�� �c?�rom�G8exh��Tc dynam. ofFNc&  si�N popu�$� nucl1��). �"z<cas�}s _7  ite-:O�-G�tude �iK term%HZinitial-t���0w. We cusk�Qenario��2�� F by -���Bcha; erizy9�4)eal 6�N�e,xa=� K � in a-stme%r '+op�: <T-�29� kineA��su�>n YUg"8Sh2.30.Jr, 05.10.Gg, 31.50.Gh 70.Hq, 34 ,+e, 82.20.Rp Kh, 89FCc�8��{PACS ��s:QbG} 2�S\s{I�Qdu+}asx:ud)�!mot�U0f&��nTi�J18of few-l�2EKuIt�%ny-� fiel�8.g.Q~ !�%�s.i�major goM�;chexNhe poss�)�v�Jrol�"� =�MCsaw:A�E�amofE=���. ";P2�Y�G�+ FN�o  Ea� )0b�i"ultrafa�p�J�;�ac�.ma*" e inu~�umb04}. )Bs-� were�B�poa�ap&giM*�!�p�VAMv�6_I,%MLN7 )��a��6 P"al01 ha~.�9 �(amer00,zenk@pdE] imaBź o���-*�V&�ies Skoba96O�-2yn6]T6�Y mole0I�mI s de�Xed a l�Ft%Ton6t yT �Tfoer65,juze00,yang02}.�N: hEbdipole-  .A�$J$!�mo�q���:q+�4��!�lneighborɫ �rein8�!".W [MU64�ausu�>troyed*]C Pe -�b��.��mreorga5 0$\Lambda$. V��us P)�2!g$J/) embo���!0regim 1� �4potm98}. Prep�4Mn@��F��a��m��affect�" g>I>mbing00Qn\?8t*U�L�O�,rF2wc!� �al fea\ �F�.cshort-"7�tr�e . Am�U14 suitNime-remYd.3ic ��UEe<+ X !F9�rfluores@  (%<�,�r��Yd-�Tmatr95,jime96,misa99})1E0ei5�.u[or kc�6.�E!c�golle�maa��� alterna�G�8o%ump-prob"/%�%��B(ient absorp� _ zewa!�� both�;eBsme26Ib�# homo< JB� O know���; beaM�i2His1) echoBreeM givesR�V� M�! racje.,Q�E��"� Mo�A�@Ex�(Homodyne (�!74th !)&�c){]" �%�n!l"�(of A{)�a �=on: FUpc2��$ Os!��� K�nj)!O�CS� %�!���5� . F.�phase-8�(�# R� M)sche91, 2} 35!w%~QAps �ook!�)q�� !�k�]�y۱}�1�VZ2� �.])Oqu�B�r.�h!� Uj� } � l dimer � . �fpa�GiY���H���1: SM II i�  R��y$aggreg� !)describ 1cal�!ơ�#�eť[==:���ec i% ��I.�V �s eigen, _ �lp%v� summak 69I.&5 Model} \)�{ BTwo� A�deQURm�B-W�n�:�%array (E&,9g)!�5>>�$(monomers,Qes) de, wo?� )gs WEin �J8O$�{g}$ �[ ed e}$���%mpr�gez$S_0$�3 $S_1'-�. A��r�Ib�O� $\�?e�h�<g$ �;''$(T%ᆁ�a�)�+c/<�'��!�wob ''donor''U''accept A�)o��if�G �]at donax � C %8ej* 7ly. S-��:or .)��1��}h� tray�&2H �)ve��%U�*GNO$equ'riu�nfS��Xa�vioned J�� .+e�1�E� as illus�[i^Fig.~�,wo_bath_�}. OnlyA� h!�z,nP f��u�� Accor�)o�b��'h },E#m� ��egu �#!a�+a녏�[B� aQ,Franck-Condo�K�I� $q_a$%�$q_b$ �&f���C9��8of benzeX`retchH. "�/��/i!Zn�S� .��& ler:!*or,%�s,&_��ndcC�Te �[ dom vBhe03H%e�I I (J6s �es)*tA��(nq(angE]b;!�MeC@ them�to !O�9Aj co%�aW. �#:+ca9.W2�of5�H, c"Y*!mM�� ��0}=��_a} b}%�i�ed +1 +q+e_a}$ (e�),'^\pg .YeY(�0 or) pO�F�.!�2k� �ren�PA��Henon�inA kili  �doubly�i� �2 ��� �a�E���MI�?��A  ol $d��nd�X� �is= ion. $Hamiltonia�l*s��2xAds� Ha�m�= H �0}  H_03{0}1+&1&1&1N&1� H_{ /F\� H_2-26& D, �C Ham_�} \ee H�$D = J\{ �iJ1}� �1u>, $H_j$ ���=}s:)c_j-X= �fO?$p_a^2}{2m}+ bB4v_j(q_a, q_b).Fla�V�nu�8 ee �we assuC,at*�w surfa� $v_j WJ< harmh��h�1a1�j0y $\omega_{via�> mass $m=T7��Ge� cina05}T'ea v_0: &=&1V)+m �%/} \�^2 1+!+^2\), "�\\ v_1Nq&* 5�>a[q_a-d]evaY�rj'.�:Q>�qAD ,+ [q_b����eI6a!b�2bc2�2cM�PESeua{ ex� �NeV�re��b =R� d^2a�u�6PxE��r%C%0 s ''6PE D'' $E_{\rm FC}$. F�56"�_q) } display� s&��fLnd� E��&�p� ���: )�81}$� ������e�Lce�ma V_I(t)%� - \a�8\mu \vec E_I (t6 <vec E 8Q E4e_I A0-t_I) \cos[\Oe�M  + \Phi_I]%�M��! eea �C$S$, $A_t T3$ Q��ECP2�:�Rv�.K�,� :$,���E,h[ $V_I� �E�~kT�$o":!�Y l�0?!-dC�^ mo� !� 5�5q.A�!|\mu_a"(�1ɰ0Ϳ2 1'} \)1� !�GbVG' 9>HG + H.c.ur ��_ee f"���dA�� onP� nge  one.ɣit ɦ�n�Frn6f"a �lis� ! b&� �-�)4.�b��not:ll�&so V6EY�  �1l�� u3%� ively addBGfu� or y 'Itr Res�[? �Ya��"= � roxi}Ak�#owcI�l�o aA �e \delta(i�$,!d��� �(& !GI�% --M�.�$;�: , prop�V � atorA�a IA�4e^{-i\int (H+V�9d(! &�eq&AΉ�1 + % ;�O2� O+A�!0s_{-\infty}^{ 2'Q H(t_I-t)}� ��}d�/K �o�%��N $I$  ��--�%�� O$A��B$, ...!� %~,O )L�GX. Subscript ''x'' or ''��of 1� den�q�#.�< ma���a aJ:G�at z9�nmlZaZbe��8 �&M:at!Ewi�Q �G $J� .:�~!sM: } AfB$A�Gauss �t�Y�K�=>xa  it9<�Yv@!�yr:% s�&�a�.�ypis��#n�%�UQs�VofNveni4�a*j  (1�B rewr�1�b*b-=C"� oscilla�21� � �*2I&+ j�[hbar | (1/? N M_j6jkDf^Ja�sum_{M_��} N6M_m1": ,F_{FC} (1' L E4; 1 M_1 N_1):�6-,�( S N_1'� e�{V � a�3M_j�N"st�ǡ�"Val5�u#"�j�j�j}J ,nonadiabadic2�2�� �<o�''2tic''[� t64 faGv,� ��overlapE`Am��4&�)at�lngaD.[9 9 . Ui �gon2�wj]�~(�-�)lN-sXt@f $k=1..k_{\max}$)G7ie={\l _k �!� >NF3 Dr�6�8{ve%$�50v^{\tilde l}$�`�vOaA�hi�>� ix $T_k^l�!�o5i $\$ �e? 9nSeld1�y= -th .� w� = (E .� )_k$�1�lQm�s. Soł�;@ $of Schr\"o-�2qud iOwabA�a/toadC�P ^� dia} _k*�=:�$l >_l ?eig} (0j�T^lB`2 \exp\{ -i� A"_l t \%��numer5_�����_l�� &�.O  "b)K !OŒmE_%qE����:� .G! !.*�  T^{-  R5 (0).�{�)�A 2�i~B �+�:ro�? :2� expa�����~6�  =.%�{j�x��JH�.,FMketL,�Q�_�}h�t� Z�?b�u�+fne ''su� nde� $k$.�k �.��%}�uv�iN� M_j~.͞j �EPo $j=0��I("� ,1J'�-��0(>Tr;A�B�aa�a�, � 9��E)��.=>�WbB.��N92v.9�56$.-cJv=&S"17�20.f3FTo"0[a �4�*� precdnat5%�o�<�a��|%! so c�A��fcoA����'� � "� hA: eXB�MN}2�>�N W _{j,r �W\alpha^* /2J����M�wb! �^MF���W {M!}��%bet!��%�^N�9N!rQ�XE����q��Wa $)�a��.�a�F. >���f����U�y�D�!��~�B�fE$| �|�|�|��&/ 8W � b� I�'Dsetha[� &�a�teN �pl��=\sqrt{iE }{2}}d$. ":"re^`'� �J%a���dX�1��,�z&}to����f�&S%�):��9;9�1��! td�� -�=0!Y%X��c"���.��7i��. ��(�� l$��"�':=��a�b�N'Q��C_{DA6� ~ � c%6N-� ��) �h -,"�-, �#2V.i.� ��r!�a� 2"��!6&=&:� �"j�!" q_b}2�20F�jM_j�#B_�N>)`n2H^{a,j}�t�)�D H^{b5�(#,V| �1q�}nARjF" +!psE/} .i#.�E!�1-DNb��U�)=i2Lr� K$$j����XEB�d-�$!=I%H��.$>8� *� "� �l��� &�-D);��Edary|Y�� fer}mQ�(ary_act_of_"�s4Q"�3a<�m�+�$7==snj ce a"�gHw���<).@!��>Z1� $A(tKs� 0}$-��JZ �fgz��Bd�j�Q�1��' 2��ea� �87�9.(vec e \perp�! �b$k!A) �� ws� ���27 tohe: �68?as!RwnA�&,6�}�_ 6iCku,sh�U+a+d �S�= a�> :X_1A��)|^2$����is R#&� �5� B${\g2A}\tau$�� hV6��/y\c+$ ''ridge''5.by��q_be���q_a�#(\"�/'�# N�{ � ^2d}�mc�}�# nu_1���|� 'u�^5>.�1 ���. t:ppr�QB h(a�}R�&� r=�&���$�Q�m!�q�.Dnf5 growT!sm�YiQV` , #ly�porAia��t�-t�=��#�*0Y �!.� O��h.�5,#dsi_1'%h�()$ main�^ ���upRE�&A ѭq, but,���Vs#� 2�7 � e.Ds gover� �#J�*�*{�. ���p�B 2)����/a$� �-��at�A�q� a�U�=#6iD1}{\piN�$\arccos \(2d"B- Iy}a�q��y/bR�(D F�\)NSm��{anta6E,p:�zua)���~ \� q_l(t&�6� �F�l# d��bJ 1'^*E�(q_b,t) q_lJA]� )F$5(N� {F>��Bn���T BA�.-�!�)�peUas ell��NA�2�q�5�F �M. Du"=EeaiovR5ߍavQ'sta8_��"P*�M�ҁN"�'es��*uʍ���, 2 &�".�"�Dre�s flad%i�'��axX` ItqbbB"F#d}f�4aE� q_a(tYl�x .�"~/�"n�(U+ ^*x n{ mY.] .:G� 1',�",�"}'a,Ns a!�aG` � N �N} FN N+1}"�Ao_�uz��� ub� Step�&"r }� �&U��f$�z� .�U� cycl'wɨ� M� $���Y0Gm2��{)�D4 ����.�A� ularly, o�4_.� vW�ak&� � � iBWK��pl�  Wd]jq,A�_O< z.1x, }kEI'+�?r� G>W�'�&^��b�Q4:Cs�se mutuX+etu��9up�o modu� IyZsQ"��J*�1garr97�+5x:�rt e� or � "c �) �y alm$"le �G��J ���\ V��(-�M �\ZWX thh)| ioe but A all.H .@>�x(a!�d9c=@� �.�� sim.�1/2(�"[�1}{4}��M1q00}] )^2 J^2 t^.A͇_��/ :a��)�$t \ll f1}{2J} \�>DMQs^Mon_Qjs}}]�}a: ��� ]b�F$# (t)$�slightl.<�L?�%� 19-� $.�=f=F'%Aj�!ZH uish�W�'F!Joff�Dn-&�2"&<s�  _0 r&�0AFy� nu^ s (=.�) C dis�+g���Y�In��ful. qCed�#��9�8�Nve agre� ��y:e�/}�K(s behavior !��=�Usin^2 2{�3R} t$, V# Rabi= +2 +�(5�B� A�$ + 4J^2}$ m��tQ~29" $A�x4{6�F"fs6I��6NP)@� "�,��)imeiZ6^ivals} �(EE.}}ex�s �O!�> 1[A.��>-�2Rbon) )qx$� �/BAI1�Y�i��A��lrabi37,bloc46,alen73,muka95}&�i��".���� $ �T�!&})�:0�/. *$�҄ow&� 6�~�*�_df%�!6��t��2�de quick�?���}C)�1 ���&.�� 1X4 �( �-$&{�b$quasi-damp�originr%v��d�2u�?�ence: Mٙ �, �9 Ial�Nof �"/  (m�by &' $k�$*�&^2$) �hsj�j&L,�Y`5 c $l >>J. �E��m?�=$J*H �Y FC}(l,k)$ n�&�f��si�a��o^ "r%� :!.�,�n "Sq }),��%{tIY[.��G1'�um_{l>26} |�l|%Anst!�pG���(su�,$TVibu�3�Ss&I?)j�}�IE�a*|f|U�>y � {J�6\�X[F�2J6�6=��lk:� \Y]2 Ʌ(Ոlk}�+:}-Tk(0o"*h_E�s�@u���oY�D=�z�<�alk>�>H �J((\( H_{kk} - ll�7:�.+ 4! M�^2E�>�&�0�qO�<Z"typ�!���f�`a revea�p a�jFGWb��/ ly~Ai�_S>̈́ magn=U�S͂jayn63{OInspit �&Qhysb6R�$=��"�6e( o� }�ڥ�� [4*�* 6 �g;$be�Ka���,Jaynes-CummiF�Å�p�Sulaaf ���M e^{-^%^}Jam&A�� s_N.2iS@{2N�|!A�4 �;� ( gMvTe^ .JCM%� 47g� J^2� ^2 /24� �!9n�.�og�>5���=m� empiy/ cu�S�w�t �l�2e^ ��val. "����šr.�MGce occu%"t]>� �+� 6�FM�&AD;�X� B"�.�{kgQ;�ic ����b�2�%�&�)G�+�W�!��;ocez��!#e)c�v: ne�a�-=JCMFe nak Q)BN Jahn-T�jr �n-$ BRaman�Pzf�JV�&� a~�+"��R�QO��Ha}�Nac a�Palmu�1!�?�� u�i�@ma�a �)�m(t):�J� e�i(� H_1+E'}Z7at D) t :Mm0)}Ղ to-c�Vt�^�:�a�O���.�/+mC �T�LEQ $H_1�# ��?D�2�Shrin^ۘ�'trajecto*^AQ�2{'Aw't�n�-^�� " �}� i\sha�X@|am ^� tar6� . St"Xng I䭇Dz=0$�'Q)F�F"� 7 sS(�B(A�ou�=&W^ seBi�!�he�7��!�-''2���.*�M-"{1'�2�= t=\pi$�,-)�E t=3� ��me��3� s�wpoi\m S�ime� Ŗz*�%� / !�"��peMO�J69(8�`< exac�&�. ~M*1d)� spbDwi��� ���A mak� n impPe"W U�U/9-2�*!A�.�FO� �N�1'A}2HM� q=$e�U�M�Uany�MVdUT�� q_{||F��=-�� �F�%.(pa?E�s�i�>�6�!�n���""�EB�-,.�&i�"j�At� ��ma*DQD�#*�Lym.T �A�,�,mv2�a�C i�oKpe�=esa�9/��A��*2~�L� �;or�  !� #�.��Y, namley�f%A�*"o�k�I+{I4� �6� "�Sr2 z*� al�h���: *���&2!�vA�KEerQ�Bca�coo� -� H*ua$-�~��Eaqy�}0)�sOin Y�Y�y3IA 6,H I A!o&� ("d"1!1"t�>{sc"�6�TZ" v`K* V�AV.#�} In #XA6W, �TA[�]e��of &\H�pE~n�i(�l�] Ac��&tmf&oL�- two-�&�9al&�(��" �' ,�:&U� ��F�$ x$-:� �{te5� !-\ �� �(��%/ !�2�"�a�of2zI,d*� at $�X=0�# =0)$i�a� R�D�.6� b"'D��-�W �6�`V�9in��-�,!r�2� �� dwZ0ITQ���ƶi\�T����: Let'�V�W!� .�- a $yB�xA�):r�8:zperiodQ.a*5/4$��se?�n x�\5u���qu Y J�r]'�<y <�(irD%{5�+ -��B�irE��!�b("&5�.ng $4E_{�LMh!�w a�|A�N$2d$ a6�!bbs �'� Gq_a=d,$ab=2d$5� &-�lPd) � ppl�4��a1Qq�6��)2 )oA�pr@f!C��a7<�lZ�U�!aI�N-:-9,f� nouikSf ��nonzerWmenr' gi!P�� 6i1 �6a/ /2!D��"6���;2')1�5i��*���%r ��. �5 |:#<�1%zeb!j���*����bn�Q�F To!*�e ��co��#�<n�tG�UM��5� �~*.� �($m)" 5a�{`Yb�=XAWb�� ee*�in��. vib_Yt _200Q#F��&�!5"��th +"�E�� � cros�4O2= �I"� � l6cape~:2� �`nL �Y*=" ��n�m_M,� �5is9+ �J1m�j`lfLrda�  L��u-Z�`� ��32yge32c�C+28+�yz ) \ as �h 1N go���+ \j2�5�is ���l inti�% %&�����no6����Y ll (�7.�K�85.`">-�"5o2�m&� � ��0'R}�|NO &yy &�$FC(1,0,0; �V)�ES� rA��&�m6! #las�^�ach&0 /V*�pU���$��� .0��11��&eX�*  E5��`\rm a� Z���=�lea�:�A��� &� -� %:^aps"� n��o3K& 6.�%� ���t�D##|:� � enha��u��~^L�XE� � �I2���O'%Gpa�$QQ!?&��A{c�D��3i�eter�B�:e��i��E� (��=d�q_��" "� < d$)��I� �#a?zp� ���5!&م�e��.+l.� Ri8��R��e(%Cwe�S$45\"J#sR�=-_ N��s �H|$A�||) E�8 1,��K5�3��&�per��)� �&��2 E�$qr�\x�"��3 �FJ�q?ʹ6�N�m� �i� ��[, +D�e 3�& !4�a�!�7��xha٧vO)o�7 ! ll sibl&� >� iGW�5m�}!�:%�d:r A�LBOnŒ��&mpe�� �a�� )�e�j9�or %I���tǪ loitE�(  "w�1�e�m�>.(- DҊ����d�ce}\ ETa8Jqb"�s'l �1o�� 5e�`} !b=�0-�"1n5-}{m� ^2 d�t���-�gy����%a�} moie�r$6��N�B9�KQ�9 .- - 2�Q E$=$�^�Gbn� o  s#�$� � S� rol�p� "� sS��ga$>I:o H�. B�anu,aH�`�IB-a%��o�c�;fp�[�%ɶMjb*�*��H!�Ty..}�fo�T��&�8� �a���d.� ቴ��-�%As �@auF"k#�n�ǩ%r#Y�\noL(I�%�NW�\s)U21 - a $"�l{-R"��,7�a~in*�iz.y.�)a�.q+ )/ .v�:�dJ+D9��-�9�{) � er�.fRe�=� �6ոa�Ys/�tUFj.�&/16� ]V�2.(w� Fock�/" ��Y�I!�" 8'rХf/)3�,w�Y�zA6�of2Yt|8D<!ـV�� �sev-�)<HD;m�C�.Q�0�so-s(ed !A-G$P$R4*- �I+ /MM�$alFBum �s $M,ND?�MsA��Hq[� �e�4�@^{�}(1,M,N&�7.6�7.�\p�al^z�K) K j0:YzK2Y��}~3�Bq�g0f]& ,5�B� 0&�4%?e' k$ +]h0�T�!_0| )$ "bMz�8"b)$yn�%�r�.�%�.  5A�{!on2;��5WIWt3two, sH��s .ET-�~q�`O-kbnjzQde�`�^s� d,&�>s M�Ns>�O�(�>�>5�^M"�,N:.�hZ�(6 *\n�(�"E�K �z7�*5�^4�?�8+ �������b��m+\�8�Fm�,��]��@�I�Qq)j�����-������Q_������]�Q�I�. "*i�Va :� O'�ll6� kus' hump�*j�� �st2(�C��#.W,�6O �L<�_�$�G6 "q&, � h *w R� F�  $G) no admixtB�of 2�" ^�$ _��*=}.R�`&��)&]D!i!aeu�: by f�>eΣ srtuc�J .8S&Xume����� N= -2V�#5p"�1po:a$<�um p #2B4��1O�"B'xh:�>Wsƶ�o&#t&~� �u i* � Marcu ory��ch%7a�orm��g�hҚ���G ,�9!&S2ot���q/`��<mark86,-99,Xt ,kuhn_may�z8atz-ratner-bookAD�IsW0te��divid�<reM0[�6��1��{t�!� 5��%��%t�the!:Fu��%[c�d�|n:C62,;%K"�l1 � }. U��R��} lege such5��t�:-f� �� �%�fuchsĂ" �8���A�]�\"-!*- Jc� M�� �AC�:"���UWaȻ�Up�um!�up�"�u,���;q�a�M�va.xS��bee&T�@ed 6far�^%!�ea�62*�R��z4VfO+��'�m�,%�=s9S"�Sw� s, (like �mea�& !}UO$B)o%d+ mple� w"�H$p)=m\dot� R,P�B %&�k*�1��a4 4ll2.�k L����A�� aXpla'�i�&�>�pla��o��`�S��.�� a ��ii:K%io`}���2�c�m |�{ e}>���7\nu P^|\nu>�P 4�B20�$�+��q@a�^�A�&�0 �3� \nu6�3 $\nu�PY���/0ILa.�U/?d!�)9�i�invwi`5��s�v`�n j��''Q%� S''<e.�2�.U&��M�",*_aVwhyZA �Co�4loy�N>��E>�irev yvmmk$I��ntrasd|W�Z*�3/sa�4d"> em��< V{-+umt �in!3e*�k!-�����s��%�!+��n!aE�A ��A�qQs,��b��,�p*$t*�-&G�J"�e G�Md:  twlnd.� �<2�A&,�<B�")J9�x9W� turn�!�2* �&�2��-|ch 0 $W1eH%xuph��q ''�&��Q��?4Ued e*a4� o�,�es 2 $�4 �neg��F8 .�Z�>�< �"�m@)� down:�� manc0Q�A� �"N�:,!�eq�) �&!�Jda�N)�i�>�:EE&q qre)�oS!"w "� [6�z1É�bes6�%?\nt�v6� L�*b)s'"���Fx.E;6i.�KN;��"W �#&@ is &2� factu^��*g$�3* %|1{up�J��^�-�sc \�U\pm ["VB��l{41�:<1'}#c" \p2�JgYc6% \(2W- .W \Z�@�GJQ�m>�}�0 �I$'.M�so ͧ�� AUͬ .��H�/>YOH,)�� _+�y)�-$=�U͑�*!n� ���Qnd �vof.�� st_�a� aG-�IK� �wrR��yq{��� z}mE]�6�1�@�� �5a�:E�"�Y�m2X�@Z�)l5HE�,n��c re. *A� �Z�,*��'�"���<��B-)i&13�1/!��� �U��� 02=~@)�m�/[a� ���*~z���%3���p&�I:�]m��>5�.%�]#�A��7N ��0e�i�P]�>R0!�d�L]� �0��1� z�"x � �%so&Xc.QE�-+ A�M6/&6["�2� = 0�)her��"� -I��� 28"y "1E ,m�w| ���' launc-^=���k+�=�c�-�/Eon �� klq0p  }s B��<itu, f��p(!!,$�*"�ay�E�a� �KP n {G�R���r�3\-؊isceՎ trivc7Ba2C*�F ˮof ��*y (�F/�May)�(A�1�%� �b�teƚ��"�to� �S�meansw9AlQ'.���,m\'.lإ�-ee �%Enovel.5 Ka���ov  �?-5�zG2��yX% 7%q ��Udb��.�!�A�ܝA�qui�g four&e:d7 ls.a"�Gs�]tgA�O!��p�\&-$_5�g2-���%U: ��:J(yB_xC_xD_x$6B��q3c*$t�F p}=t_B-t_�} wai%�w C-t_�}�� delay d D-t_C$B�!l���Di�,jona0�Hv4>�ur� �"�g_� me},''��&''�_.!G$I�$9�pon��C2�z20���.AB��|!)�e����%n"49 z6i��3�^��:�_*g �&�/� �13 !i� vre3Ofew�Aary�8er-M�m����uat� �)  B� �l/&c�(���#� lz�a E�)k �;A�u/J�s�Aby��#"%�P=ho YA&���c1���!���1�pr�����3P �Iquadrri��ar�T1�c6\=%�� ��'y%Z � r � � P�* (A}�&�[>`2 \Re�!\�M.J&1'}& & A_y([JDe� B_x}q-iSp d�^\n�~��fJb aJBb+ kd�i \�^ T�B^��^B_.^C! \n\\5�f5C_:FDFnBO1*�dJ&.)�\&E�M�ǂ���Hoԅs��a! me \underA�{a%O&Q�7*�@�V1lQbra�IE��$�-�3[.a�>: . Li��5��iJ �6Vmsn� � &�=�C8R -#�[ЩMr�<pA( dc �Ii\�$��e��n5��r94inYџ}\e�J�B %�<A_y \)%B$&:�n H|H0D_x C_x J B_x QI>^{ KÒ�Kv_frac14 k\{��\( &�20,0W� -��({��,�[ '+i(.'BN.'0,�M u  �\a�Y'iso�Mi *z*f�q�� �ij�� o��GL�"u�qF��an ��ramMweis89�W�2� 8n}@Yl��WQe�j-ed ''�K''� � ^��<9�z�~ X!3%*�k�"�b -by[�e��s $B_xa7C  � �}� ariy@� R:U �2L>Ome. ���!fi��g\5byC a��rm� e�6��o����2 ag��ac_=.of �=$�6�%*it^�g>� [Q6d-��"�//ke��''� �>,��" ?3^ M~��8 part of the Fe�ynmann diagram and promoted from the ground state to �$\ket{1'}$ by a single $A_y$ pulse. �@As long as electronic transitions in this model dimer are coupledvnuclear's,��probability amplitude wavepackets change their pos�Lmay not coincide forV left"0right part of-,l. This argument gives reason��expect essential interference population of.M�Lsome specific values~`ime delays only. \subsec!E�>{Equal site energies versus downhill} Figures \ref{degenerate_w51_�oA }, \+ Bf) show%"result �y A�lwAI� ve si�Ws hownuk,figure meansa!�1)�a�(s evolve un^,$H_j$, (2) F�, sake�conviniq$C_x$, �s%fAQuu betwa' them��q�r��''5& '' s����qo Jh: \be \to D_x^+C|.Q 4\label{redefinE6@} \ee Mean while,.��� arrival�ͳs�#-bs�, unperturbed� (verI�solidLow�� Fe6�~��0}) symbolized�{ square br����9ae^D$[t]=\exp{(-iHt)}$�"teri�ure�4rest contribut�to J�reads%x P_1^� intyn =uy�t\(i\Omega_{lock}(t_p-t_d)\)} \Eg�e{6Xbra{0}A_y[t_p+t_w+t_d] %� [=] )�}_{/\alpha��}VVn$|[t_w]B_x\�0}V \xiSI4��!ɻ_��EAd HerA-e exact Ye�#�!Ia f�:C&=&: e^{1Rpt_p -i -ad t_d>D %#1'J�eF��0} - �_e%aZ u�.�1R>UR�� %� B_x>|e2�� . No� $hat becaus��bra-$1$ Eqs.iz2�-e�Bdrepre� � {\it�J}�Kfun� �   %! $1'$. W�f prepa��9-��6k.C corresp��nga�pr� �68.��!� J���followV�4!� %$$\psi} \sim)�j} E� beta}AnM5;Ei)wj��tandsl%&) -'0,1,1',2�X.n� u$3ndHcoher� F s Eq-�}�$modes $q_a N q_b$� � ivly. >"b ��a �M� &=& 8\sqrt{\frac{m\o��}{2}}2$i \{6\bar q__ +i Sp_aB: s\\� \}, \n \\!�t^��Z�b B�b.�v��g9�EM a de��in� b� � A�QI. DependA�� a�6�EyA�@� � $I (t)$,A�et  circl��D6&` 4relevant harmopot4D surface: $(0,0)$E�| 0}$,\delta:1 0, 2:�,)@J( 2}$.5�$Since $t_pa�t_w d$� $chosen oneTf�7�(phase-spaceL trajector�of1<Re� �y��6)�sJ� VFigm�/_j y}. In c�ast�&)~�2beA�in ei� �of >sK �H{�� dynam, enta.ment �X�  $|1>! |1'��2� . W a !�w$ to half!V vibrZal� iod $\tau�vib� \pi/w$ to�|v�)multipA�c&�� ���p �duŻ!X$A"!�0discussed in �ɘel%$ary_act_of!�n�)�i7ly'is2�u�excit� in m4A*r� in pa���I in%taneous�continuoaA~j @Rporw@]��K doe�,maintain its��UJ!�um,� stara�omIL��:�"�$parabola (�+ 4wi* J2��-)��it �Dsuch a�ner2�(1-Q�)]�t9R� ne�"6 withj�-x��=��i%�N"�>�x��� \bd -� : ( r �aj }-1)y�7 -iw -1v:) �-ii �� ~ b �e^�([9�]� +.) �-~��1�V)}"� 5�f As far��$E6�(trictly fixIbe>m/2$E�PU&m �ca)8�a�as syste�* algebraic�a�E� ec��k.�s�p�  d$.�ysoTAq�zT �a�*:when �N�� overlap�best:���6�\( m +�Q�/2 \) 6�QQt_dZEnA;+rE5�VB _sdz ItA��ger"B��i>� shifbar off!�onaa�5&) dir�!�small�� %fl�r1��^�eq 0$�expacntoA�a bit: than zeroX !�A%���� !�Ba1/4� he�qivE(les!�sKщB �� go� "�JN^DDs. E� calced.m p&e WM�� "B &: � _� }. S�� nd eoi5do� Jy the :&x  (L FC)Ny shel��H�inc9e%� ite-%wyJ��E3I \� furt(closer)�"0 �AW� (�v ). 69F� e�wF s�* +-�j* also play���-�� &�W$�ya2�TatJ7IO��)FRa� ?l� �O>� �.v*a��"�`ar d � ve no Ks I�ka�p =��$L chN  �N/=��SfoA��a iU�9 suit� :u�Ch^ � net e' � -�Zfa�C$�-i|��>�$ *� :�C�$4i�Ub!9��#=te(a�co� a�2G$+x$).0!:r)� homo�%g����dwadab�s� e��will st*Q� O�t� � situ�$�og� t( Ab"��oto&�echo � ario�tr� l�p aS�e rol%�A���"'/he ��vA growthQ�� dipT� Om$� (!hdyn�tɹ ). �[��Ihs refm�/ misof {\bfI�} . frequency M&�A�iX!w�#$A> % \com� {�a { -i I � �{\� iaٸ �< &.\�Ns|N�&� N4N>��9}} {\T<� � 3| . ] KbV�NtJ�F*e 2�1+ \� {R�J-+~^2d^2��J2. && P ~+ h~Q�(-*# )}1�1��,v�fI8N�fM|f!NU�N^ ����=�{ q_\xAk�\x��8�",\n}�������F�p������DO�_p��� }��sVs�ے� ��s[�r)]���x�x�x�x�x�x�xyA�x&��fx�#a } %[4  % In&�+>�&&]  � ]�Fr� &�s� � � �(y� �', � "� K�� ce?c un%6,� fer. AQ ternv(i�*preJ$�$   veloc8 . v")*<. TABLE 1. Po& of� : �+! um�o*%Sc "� akenx�of ;�7)T�*hbegin{tabular}{|c|cccc|} \hV�$=F & $� {t p}}{6O}$��>PdNP] �&R; �${\Gamma'}_�}{�}$�wN��d}.� ��-�hn�+, Qn�(& $ 0.923 !�& $1.077.8-0.53+i0.01$ &$- {�t semi&�) }1.000>}00.} &\\ j�2*],�} 0.75.]�2& $-7.52� $0.15 2�Œ F��395$-2�"i� \enduǁV\sC{Conclus�}� inv�g��1V_�_ in�0m��r@s��0l r�&���ion�)mG- of ultraf�&�.��Jed2��yfer=(.�Qrevealed 0i�)gu�L-�tk! attr� a�<ro/ physo chemisY/�HquiXoptics��ukes&��tF"Y���*x"�/"&�("�sgets ris�*����q1erJ1=eC2-�.g��"�F0��.ucollaps�nd!o ival�/ milaD-t�"�8Jaynes-CummingsI �!�$ coordinat��!�*o�sE8��Mim�5s�A/!FRU��I$o� Ddep� �wpenetFinf�region�is E�!��N�5�!:K  amU ".|"�i�!"�2�&� (per�%�i�)�eCor infle�="nt-< come�-om �-.�)).�T"ce�~��� llelE.6��ide-z; four-�2�)=�ș O4ria*�s���l������sM�1�#ZW provR/)��"al ponse)� N�34�U:�*�~-�Q� A6ac68���  ��4qꝉ%Ys.�1A� �c�$dibsatis�yci�^ u�6�"N�11���"��C2�(possible fu�2 deN p)�N6i26search!�ul&%24 ~ BGdis6'n�� . F work� �#��2�relax&T i2� t-���- �7��induced ��Or spa9 �f� di�#ces5� monomers,� wellapplic8�these fi�)"- reaaqle� aggr=5a� "2$*{Acknowle�$}(�-%jw@ up$Ɍ�NSF, CAREER Award CHE-0094012. OVP f5 Camil'dnd Henry Dreyfus New Facul�8 nd an Alf� P. Sloa�1K-. DSK�nksm,armichael, L�' e Horvath�)0Jens Noeckel 2( useful��AM)gfruitds'�.J \biblia�4tyle{unsrt} %2L{NONLINo} %\input{Th".50-Seattle.bbl}F| he.]}{10} qXitem{humb04} T. S. HumbKlJ. A. Cina, Phys. Rev. Lett.�<93} 060402 (2004�$�U,amer00} H.~v!hLmerongen, L.~ValkunaAZ nd R #Grondel|�/P\(synthetic EF(Hons}, (World Scient9H, Singapore, 2000).�pzenk01} E.~I.~Zenkevich, A.~WA*drt, S.~M.~Bachilo, U.~Remp!�,D.~S.~Kilin,&t A9pShulga, C.~von~Borczyskowski,�nMa�5ls� . Eng. C,)V18} 99%R 1); B�2�Af�6� ���.:�@ Mol. Cryst. Liq �361} 83 �.#i)�koba96})�J-u�!�e ,. Kobayashi z�1996)\Hfoer65} Th. F\"orstl9in: oModern Q+ ChA },{\O.~Sinanoglu,~Ed., (Acad>, , NY, 1965)Y) juzeA� G. JuzeliA���J. Knoe� {\em J.~p.~e}1� 12} 2325%+2�0yang02} M.~Yaf=,nd G.~R. Fle�  {JR275} 33 Q2.� rein82} PA� inek1G.~Hoh�#(ed.)�itq?� �m��c!�all ﹱ!��Spz!r~T� s~Mod:�094} 111 (1982�potm98}a�O�tma%V8D.~A. Wiersma,{^U08} 4894Y98. bing!�A.!WKing,UB~:2?�� F.~FA�im, {^� 3} 5018 F�matr95}f atro�J��TEIQ 899} 2568, (1995.� jimea6 R. J. 8ez, S~N. Dikshi��$E. Bradfor�aGraham]3.^|1! 6825, 6. misa�K. Misaw)�.�, b�10!*1�9)�i molly�!�N�6 } 4180�2� kili!g2[�S. ��T��H&�b���1�46%�3.�cina05}A�"! G.aͭ�,%� VA R�� 1119 U4.U garr97} BO G�%wayE�N.a6Vitanov��em ^~� y55} 4418%7.]rabi37}a$I.~Rabi. {�Cq`51} 652@32@bloc46}�JBlo; �FB70} 4A�1946sukaAEg uka��  Pr�Cpl�*N"nBO� al S,roscop��(Oxford�6}4alen73} L. All�nd!� H. Eberly!:itXRe�*) Two-� Hl Atoms} (Wiley-VCHk752�jayn63��T.{GF.~W. �0, {Proc.~IEEE.e89!d62Vnak��M.~Nakan�gK��guchiEW.� 116,��6. 2);)T ibid� ,bf 117} 9671E�2%A�Raman��.���~:}e31��J(land32!�a�Landau!< 8~Z.~Sowjetunion1 2A/�!32� zeneKN���6!�C� er�^ UaK40} 50��1:Mmark86}�HMarcus� � E�%roanal�� �438} 251� 97);F� R�: T!�\)�\ �\Aq@bf 24}, 966 (1956JH�\� �\ �65}, 5 1993);"=  B�.�%, N.~S@ , Bi�m.\ Z.\ Acta e 811}, 265�82��E&M.�� reib��D�B!�U. Kl} ath\"of#J. Lumin!gbf 83\&8!2� 1:�4kuhn_may} V. M�� O. K\"uhn!Cit *rg�E4Gy T�H�5D�7� M"� Sx0� .�>Hschatz-ratner-book}��C�atz�MR$ �r me+�in&��XEnglewood Cliffs, NJ, P�ice Ha %�*? fuchs C.~F �~Sc-� �]Q�1�� 1023I�6{anc� TA� ncal~.�TI�I 121}W5լ*� �;20p .8�a�ajona03}PJo&Annw� ���54} 4q 31.\�weis89}�S$Weissbluth�it]n-�� Inte� �}, %%L8� �:F�newpage�k�r�"NO-e�Oa-*��:/!(e.g. 5<WM s - �ar�$ reorganiz�n "_-compens .tg- �o�= �6�� XE6-}}6� �!M�}16cp8a"m.._.<s]{Po=k"v?� d�illusJng!h% �< PES}:� a�K�e�mu�KJ""lasA�:O &�B}%��.��.� �ASpec�"�BM]}2-`FBdje2)ero{��%q age5!m}}��6�=]{E"�=��#�A"*[?energy � fer; Cont�H�#��/a�Od�&�s: $|�D_1|^2$ -�*�� mbdashea�} 64"�B7�I�) are|played6�ti�Oli $t=0�?t=6y$/4�A:2$; ins�2h)J!,c"g�* kine�,�gr.��ita7�; ridge�E=q��conne@''0''E�''2'';j�"� $J=�$/100$Mt6�pAR(july5_SHORT�Q ��stepwis�AnA$]{ShortB& "�'��cVRa� strength .�$��M�co*K&AZ= {1}-asP�/=0$ (E)�&�$F*-&2$ (E��47 5 3ott�3.39 62o$uot- y; �% Q� �3epKB2Tpe[B, � <S@aly��!�s0J@; saDs!�E�-]�c<0"log-scal�uK"!�$P%w$.Fj2�mdNngEpUo�-�S��qq�{�� f-re?:�Y�;2@ ]A r()� /16$U>v1 2815��54 5s)�m��Bc6� %�� 4/ N> jcmC�=!&35cm�JCM6�Y1_re�#]{lon6$ .#�%�=cB�,�_{Tvib/10}$�+VG$,*�;�a :: JCM}� � s %ofX"m�HsE* $g=J&"(\UJ1/)��GyH= �3 /2}d!���d�@�� RN2~N LY.,"�IJs>%>��%�� 8=�shrink_9"A 67u��!8F�< y_sc9ing]{?  � 2;:>�:���1.�JULY1_�+��T%I&�P" 2L"e?<& E�6{.�F�Q���2f"Y�Yp�?.�* (d��B*YH�� -G$0���!?%�ectoryz�.�� %�y$IMPORTANT3�zBm I�7]��/ rolA�4FV4c"�'_of_vib_� _2001]{D�G�=>�A5��?B fwhe��� al[ i��V 9 :6�y�� o�Y ->�]�@ anel�Ab� s��>OadYrS" R�IT(_ of E%B�. ~2&Q5^\p�'} = 0$B82b B� each9,y� 6� =.uiB�"��Io�He�2D'�y��2,Franck-Condo�qK,' �a}$�FI"(F  J  q_{\�)B6ɭ7,b7||F4Օ8Fo12 �I�-7i�fLe:��� OR�apurpo�B_Aaa-Fn*aVbottom EL>�&� � �1�� iB4+R�betZ&��L!hrm!�-�)u !K>�.�( D�T*�Aa�MS�.R+M�in%2adjac�&0-&q. ��"�+Z�v�a��� 10cmRg PAR4�.��+_Fock�I�R>3 �>�Xto&<)�a�[6+5]AGB�3�> -/yoM A�ledNURB-T55��2�>Y(no/F]}� - !8 � %"�f!R1`}  eqi�zPBOX��1ws.� � �7�R� $t=2"N>�Q$Ba� a*�  averag^ve&�C $T=100x iB^$�8�=�6l1}{T}\int \limits_0^{\infty} )(t)dt$�1X>�z&� mini�}{17cm2<2*�%�Npar0a6>D.rR636�p"�>�pla�8 on]{>h�]jC��Cae 1"� eige&EtVket{l}Fp�ld�c�.a�$BBmhorizontK0�8��"�,�J>Vl}p�|�e2&�mean_��_ �um}B�vC^��||�i�y� �ar�B�N$. nD/1J   $J$-F�h.s s�et��Od.L�p"bUz&� 11Z;�1cut20DA�2C.�2_*_reultB� �W�D�A��m�4.�s:"�[ofJ2�:/*,L�W3�6� �Kq_9� :Nhav!�$.� of6N� i�� �lyE� itonD�Fq=5($\phig�� ), o>~ L2J 6#,ɸsB� !b�<0BP;��F3�I�+9�ha>� 5�:M�~ ~sɷ�~&kV�sulF��6fi;f2.^/s~8ei �/ej�(�9c6� �fdiabaQ"�Myg>8"�;>���� >� mFE>�RX�>SE�� �� )�� $\nu_-B�.� �3d_.H :+B*gaussianA�file "~do6� �Y2���B� k �> �U� '7!ᕇ� 7 %�N� C$af~D%s-#xN ]�>@f�N�i5d> �" <�eme]{Y�:/ "tb) ofC*38F� ensa�37�18R�(o2�l�*� mu%��a $��}$)�%w�!2X 6 ''�6q''" setup'' ga�� W9� rt8B� re�t��.F"QC, ?�^�?8 capi lx�Xubscript ''x'' or ''y''��6�[�2polariz%�B� �:�8F6�!*>= $"�BB wrd_w� �0s p, w, d abbf�!F�Kk� �$ '', ''wai�  �"''��WjcB)�"O!'� %6ed:m�[su�%�`�O or''BV�\�2Wmp=.�e?ibu�t&LX ''Q� '' c�$fo}Qaly�� text.B��{R>q��{� � anisCINA1�k"r Faj]{D�$e-�<>�% �p,�p�f� `fe[ �@b*ga_��*�>_�0>4=<0|A^\dagger_gy}| \a s |D x}C B |0>B��q%�ݿket-vec2pbR>�xVa�FBbbrabR�F�d$sr^%eF�!�]uaX � �<lB�I�p:' (two-l<-s�*B�  wigglyBbac2Btail ED)��emi{ >'up) pf9F�+'Zoe�����s^9Q��5!� a0SIGo2C)�$smB�  R�C-A_y�n}+JB_x}�$m�T F9�F�>,�EFoJs2W��Exs�WfdBL1�ɤBq dark�[a�5.u:�rB�bi]a,* &n�n�ve-PB;z2&* &D��ab�]zs1�%�B�0l has mbm�Y um a*_-�7oO repe[d>{8#�E*\c atE1BL]r�ŷQK �� yel�ht�ss9F�o&NE& \Ih$.bV, �>��IB8dF�teiZsoe9*ll�@ peak>[at% =0.5:d,dJ:�^@��>Pj�:Q�.�P&�&�wb \m]{�?>��NA��MF��S>NAo}B� -�_2�>�enegrB�N>�by>O$`)�$�zbd s A, Ba CBD�� Vk ��-��-��d�#��;-� itud�la�aF�!� �`tR= L a:Lq� $t_d=1.2 ! >+���'io��RP��d$-axiFH22B�� �D%� f,K X.*�ZZ_ +7.5�YB�T�M�+h_[%at�L s at>AP�4rM0. �RCn�"��~v>�206�����q2F�rem_+ y~E�6�a>��\F� !�b %�-spac.�g Ok�$iB��"=&GB�Lef� nels&(�` �*b">�"9�}Z�:&}'�o�e1 +�g�� ]V�gw)} \)$>t2�"Bh)5hQp=Bgf�u^B�3�B^��U3& :�!7�cBoR� �2p�b&�#>�5m *-j>&IA!a�w=7i-eaZ_#g}��1'g.#t_wF��}2�i(6� -m )�r�BM��� p-�A�=��9Vm9>7mobe�(f>nZI%en(seqi >DiiK�,�?V�B"? y+u�y>���7>�{>~R��a'.�JULY2d��L L296��Z�'��Ng]{C:�gccB�R5ZA'Fi3]��:>)b�*�.B8f5. �%�?2B �%F&�*�,��0�>�#s 6�ɤ)�9|y><ispalcedJ�u (Fran*;' �F)�]"B5UdocumeV}( neccessary�K �V\�Va90column,prl,amLdh,040pacs]{revtex4}se�t(age{graphic�mnew�Zand{\be} gin{�NH}.#e#�^!berEsub's}�eqn�ByFY8 Z "2D} 2� berbmY*>&e &.[$%2K�Gixs}[1]1 }#1; :�av 2l�u #1\�hle_\rhoB,Z-:(mH}{{�h�BH>smO.OBR.RBE.EBF.FBU.UBI.IBL.L>> }{\m� :ket-m eft|!k�-q:,bra,-�2+\.�tr�rm Trsɩqe(} \title{En&�w DeciXLo!�Ortho�Observ~jaa�author{Sixia Yu, Nai-le Liu} \affiliaL{Hefei Nex al Labora�.���B9�MeYQat Mic�D5 \& D{t�; ofB�L 8s, Uni��]�Nce�8 Technologv0Ch�O�H, Anhui 230026, P.R�F ina �3 � �P$^2$Institut f\"ur Ex��� ysik� \"at %WiebB oltzoKgasse 5�D90�K n, A�;abKct2Zpro�+a famil�e.� witn��� &eing=xv�zp��wreo�<lew& "&�lA eKoI oY .Bm*�RXeR� �$3� 3$ b�>�do[P.5Rodecki, !�.~LSQ~%H 232}, 333�C 97)]q�icitl��my#nd .-$d �nN�!� intrp@ d, w@Y�!��?wk� perm<%. 9. 2."&-�dΆ�Z���H��m �Dic�-re${bme�a�ym� �Yr�on�rix�'>�6�\�Q({03.67.Mn,  5.Ud TA��fY�\make�@ �HI--a�.---}�W-��K(�?"our@<�?� �umE�u I�m�[JUAwK�� %�B�H1�xnd-[�!e@O<t�!at )l&%.by!aԄ->pe>2pD�!� fun �.^ ]sym, (}�L7a -�CA�method ` wu},!nam!few. M�� �aN�� nN�M$ reduE�G�� rise�')N<AB<((non-CP). A���;��eifx�ifeE� keep^] q��J� all V m��)?)�CeC# ?2r!�:(PPT) be64o ePFA dbe}<�%� fvioj~thV>mX5YCVd�(��d a)|}.�.�џ very easy!�f�-�y�@a`B+!iRr%vDs��+ }%i�ZAlB�YinA�lit� �IT$}\�Jv!kmuAT \Phi�}glw 98e !H�3qA� ere \E �iT {i,i�*v$�H�}e �iu.. a�!O�yof qub*ha typ� |A�2��C0$\{I,\sigma_x y z\}/\�A2$)�l�]E, we T�� �-U`�>kd\lambda%}=\me� m0 m,�(4^\pm_{mn}\}$ $>�d)$�Jer 6+4&=&�6!L [n+ nh m}{ �}e(m�set��)�M�-K�the��&x��ed �$\be�-$ew} E_O=I� I-����=qLMX ���EV��an!<9L�!n��m�O$� ib��!� ny pt��t�9 rho=�V1 z2$!~ᝅg�d �rho�)&=&1�}\avv�. �}_12�,}_2\cr &\ge@���!VF^2�HZ(Y(\ �Ztr�1^2 ^2_2}\ge0!fnd"}�Fu1-!� Cauchy&�y�e=zI�a��Ones�Aze� I5TZ�soA�jZ��8EW=m9$E_O$v�}s;�.�&�&y�En we obBaFEW. F�l�proofq *�above�is obv�i��ead3�7��]~Uu�( $OO^T\le 1`�noughE� (xm�:��L �enc/n�#A�k�ofa F ` "~p��. �́5pp+j��&�*� �aSq�H&�� Ref._23}.� ��� m,n$ � �Us$$3(m-1)+n$E\�Ky9 &�� a|_a@1{1+8ݕ=~(� 5 }a&0e60 ,0R$:&Z$2&J$� lV� ��JH": 1+a}2&0 � {1-a^2}}�h69aR�a " e6Wn|�-w\g2� t�t;��PPT5 mH�����($02=�R} 2)  B_2Q�%�.03}-01)a3a{1+2a> (6 (2+a)}(223< 2)-.�3(EI)}}{2+a! {13}^+, �Bq-6�93-y���A_4:�e 13}+.��} �2��)B k)\ [-`A_5� K 13}=B_5 7A_6�726,A  A_72=7=86=2[8x9.; 9.~*e"rA srucho�^~KD&� O�0S�u�Sto�� qc�@�I��,N�qL_L�7�[X� ^�� � m�� B_\nu^Ta�bcoe^�* =w _a�6DEfa��w Eq.(��a�)�de5.�Im $O omu}=1$e wA"7��M� h:��Y�G M �VE�m$ {1+n��M M_{1�-0nu 1}= 3�{n!(M�7� e non>���7 �  $@= �e- \nu1} ��>="h9$��aa &  n^2*2}^{9} cfʝ�5)��{e�(� )^2}&OX ly��h  $M^TM/ . So�"� ���ew��E_aRc <�!R_�M; B5 "�It�^�,*F�4nT��xB^mx} � 2��A�a�)=U � I%<� e�rx�!re�*&� b� 6�$. Of coursI8b _�b� �#EWEm&Q6"�|aEW� a$�O-J �To �EWq2� ��an assocK=a i� map�5^ qJamio\l �q, isomorphism��j!}>� \mOg)�m_B("�= ^T� *�  .� �Q}_ &�>R\�G - ^om Thus�e�!>�"F:Ha.S�e52t El%�neH�m \mI(A�_A �$^{o_A#,�qJ A�*� $O�erRbrh 9�(m6�\a"%!)��e��^T"j?oN"-- � � ~� �a~a]�6#6�!22OA[6Dt  e� A����GA�"Bg6�aZ� �r�� yJy$&�QQIKre�g�!� M=UWaJR�}. ItD" D"�%it�exactl��}� cha�noD�2P"�%T&�j�^cru� �&�"of�2��ia6ll �x�6#is�!�os�], i.e.� �)�eS��&�=� map��&e0uDdVw�somew.$invfd, Wd,@@�" G;iC or�}i�cedB�f max}&�~TR�e� � > � s�Y#� Here�|~se�0V9i�=5s {LfA��&�?o� !�A., %n� yA#\ 6� )�Օ"w%( PPT. �con�.$0'� ��H\�"t��_{\Hj)}�=�Qn&� In��ke�$�#t  >\�"�{6X'1(.���0�}R�>,6�> mu^T��^$dݤe�f2� \mu)��a�is&�i�=Zve�e�an $d+1$.�  un�8d-���m5��%�p eL fix}0!� 7&�! i�&� J^ n�M�efr� YL2�among�2�UWm$�_!�"�6�-oF# all o{�(rem%?5,�.lqL&t+s 7U>%� .U?� >e2TiI�� ket n| i���$>-d>%�($�$)� X.�Ť6� j�E^oñm3�G&#&�"�#dem���H��p�j��s -C�&���� FO���%� hAV}B�(�tm�E��iR��'v� s.{$ uC �+"� �"> b>q"as �E� ��j �j a_1}d!��/+�{k=1,i� d}.i}d"�_k:?{k+i-&d!�A:�4 numbers $a_i$}@ isfyC ia_i7v%e e��=3���X����͵d3,�)g�A"�[��*check&i.)W�Ga_1�"i\ne 1)q� .� ; i8${i+1}a_{d- E#"� �8�. Le%Օ2,$d-1$ cyclic.�y{ia6�}�r�%�rul7D��4^l(m)=m+l \modL.$(l*# d-1m�A&w I��/"cU:|!aF@ �{AH^{w_t�� t1dMH,iɆ0}(a_{i-l}-a_i%k ZFIEB!�l�NW a��e%f� � � �N2� ����A_v�R �ire $1�!�(!9aA'�� $i=X, e�Now+"5�a�(al�y� Et=J$Et2 @TA�����R��r�Rd  b+ e2�h��$a_��a&&4!6� the RWI�&�)R*�'�!@ � .�1J � piX�-�SWAZ �"�})�>Y��#�Epen� ��e $.�2�da��ramu�. 1�s�c�|"n�A; \w+e�7{mony}"cDZq���� � de�_a*�curve�2�.Am!��*�PPT�� O� � tri�6�lC��NN�B-il�"O0!;h->CoutJD-��3�A�l2O� gray-coloN �� V*.e�nd9V 5r,vskip -0.8cm�!j�)x�O��ilemma��A@��)/i �.#.  lyJ)� � s� ���-l;�i�-i� �$VC�1su��� �-���t� N�!iNq%�2�"�!:DL 5j1J�%.CBeir.� s beE��\ew��orY����"15 6@!.� �O$ imL6qc�� =6�"��!>�F"�ű lurA�sumYɛ� &Vk#*� Ye�=�� F�snAb ver �0po��&� m�w� �TTj�' $T� s,�!iw��& A�.bw0��  $T�"�A ��S� A�is q�}B !�sb3*�]��A_sooE!no:y Bed�$\tilde@$2|� �!� {k,l}= k}8 n,l}Z �DX&M!98�muZ�l�,��)fi���� "�.6]�*�I�< -2 ���e��ity*�ur}�%�,]u�' m holds tru�,:�_#m��l lB"�oU�O$*|&*�""7,� b� A+5yu fail} i��if�@��!a�]�)V�Z#�}5�~y %9� b)pZ�'AIla g ! �a�J�6��( �fd��FG. 1PYake�a)��&�7,!�gb�*eni3� la"�+br�\mB���=1-I ^T)� \for� O5%  e%�� �36I1Q)��:���V&*0$J�$_ p�iv>T�fhie�/"�-�0QQe3e�" /_:2,� X#X�xa"޹��Eׅ%*9+� `��I�{e�&2U��f Qa%?!�� h[ � n �%� uild��-$VF \ X� Itr (X��mu"�q��� �%r> 5$�72�-n2�-�j� &���r ��{m�/av{(Ih#^o_m):�m^3\>= n}^+a��-1 2}R�~0 ^{+o> u}-�Q� -Z+-u}},R�-�� -u}+��+u}, r � � ���sent ourcT�:� �� m:} "A�2�.�� n� 3q��$X�vp &�0z/�/a 69�!]�<Q��toa�*� NU��-O&MC- P�*�������*%:4r�tƒm|*"�) an �6�4 $C�Xyn��v" an un3"5?_{ABCm{m,m,mJ]tWwe5��rj .�?R��) ��]�!�R.fmap[  X�{AB}(\m�+= \mU��_т+C})H 92F ��^{o^T� nd $[)=u2  u�X6�,f�f��7i�$!HE�0�!E�*�,  0$�@� �/o � $s�� '%�;s_ms_nX E�<enV^MaN0F� n-}��� ny'peM" �is %��oLr� msY+}�&��uo�� � \Cehn fac"76p�uj&F�� -D)lpm� B{Nl! look�.�8reA2Q M�8BGEQ/�V� � ��=� $X%i��1f�,}l�/AL �e� m$2�1�Z &c�aF�!�4}�%P B�6� . �8w $d=�&A 2$.�2���q�H�*� s= ic~>T�i=%�a� �.i���/"/&�>2� @ �$Summary�Th�$I�]'.�)q_%u}�effv:\w2~G.���%�89�p�<|�(^IʞA*�G�"L!��s�  ll6YDe � �by.�A�n�"->��se" �l  ��u- � �V&��2&�F��RM=�G."�'*62(if s)�i�� gn���.� 1�AL�dg�EY.S. a�;n�2C�_��H"�JNf al SA� ce FHH��zCJJ(GroRDNo. 90303023). N.LJnÛ=!S� EducT Min��of ]A�*k!��� J �7� g�fu!�� ks P.T�ungA� �2i7%�����2r!�*��:�{99��w�F R.F� G2��I40}, 427.�8@�\BmFJ�Per�J��t.Ԋ77}, 141J2΋�2 1} M�rGJ 2UJ� R6 �� aA 7�223deJ2a�K4Le�4 d L.�� u, Quantu/�,f. Comput. \-ebf{N93  �3�i� sym}'�. D���5PS�P�lo �F.�,Spedalieri, Z88�87904 l2:l�m�K)�-�(69}, 022308g4*'� wu}S.-J. ! X.-M)- �Y.-ܔha��2x)�27׏244%*0.�be}�� ?�-�%�80} 523c�6/��&2eE-6? �VA5�59}, 420Ɛ6y�;F}J�jBEF 3 it{S`eya�UnsinQL MC�} (Camb��*�NPress, , \�and��87.@[F}B.M. T�Flq�`M�27�I319%�2�yu1}S.�OZ.-B Ch�NJ.-W. Pa=� Z.�%.g q9�08040|�2 g\r!3AK�g�21790��2g/1 H��H�Gn1�9�6aX034307%2H�G O. G��e2C�)�bf{92a��4.���3}Nn Eq#:O.�@<-A.:f-, Rep.V�h"�e ��275 (1972)maxaLew�vei�P. KrausNN J. I �rac6f6g 0443��2 ��O2}k�AK%صQRj�z12%�2Bd>?61A6N�!� )dQ�8%�05}�Y> 4&\S�}f�V]r�Vx�I/N�S  most rob:�� p4;TSuth�S.J. v|'nk$^{1,2���$Hirota$^3$02�R1$���Ss, LuG "LS8ies\\ 600-700 M�:'(Ave, Murray�El̓$ 07974\\ $*8S(�&�EQ�� lifornia fS�|$y\\ Pasadeo�CA 91125a3$Resea}�Cen�;&gC.GPs,��Tamag֝�GL, Tokyo, Japan } \@&�S �:a.�S study how&j�grp�+�Zl� d�&E&"� ^ !�5�' 1�H �I�quQo�����,#'hai]$��i�est�{&Yp�js �R�fix@"����?e4 (aAk���Y�ag|t ^= ?,�2A-wh�k�� squee�s� Yans�\.&%�"�qui�JR0%�79�.�R"��.�R} For�-�Na� �J�R&�Q} a�C2;-�!5m�sm�du�$F.l�wouldSn58to/)gtype1�m�e�]��,/�R�W/,5�!� ��, b�M�_�tu1�L �i<� thin�'%��jU��fe!� MY�1bAre �. ��ٗ�loss � s�W.B tenkiW� qA��(]�� @!�, a ca�f~P�h"1$NPu��s Ӯ�atqSTopt�al!�$N}+Z�-�U1�S�0�t,� �,-ma�X opic�.�>K%u Xt�7 ise.E�2p�$�>*( of Schr\"o�( er c0cE/4(.��m���o�� } |\�Xa�Z\pm|-2,��1%�$67$ {1e ��, 1�At�Fe*Bh@|�AI enomenon �*S,d�JC��G8��ex�Mmicro\bM -QED�haroche}Es�' mcb�51�]!�an �p ? myat�R Also}�v� �nv �G9D6>6 -:�:B�Q f�{%�-~a�=l ~"{%dn�U!s�Prtic*�apers:LB~�hI} u��UG*Wal �e�? �_[a9D telea[Ev fi�'tyA�o�na�wly6e|$G��-�lixu}.- t�5�� �"|Bw��A�90Da�. &�$�)`"�8�trF��<su�e��  w� E"_�] ���� � �@aZRB�e%� 2 �n#+�"#j1unec.Z�n�5��!�a=S"on II.�7 see,. A^�Mi)Hn��is���c��w e6NOH��nwIA�l:���e��I?c�a":c�o ���Yi�pu s (��GZ|\ t�Q)I�af ZC�>8"ڀ%�.g�t �2s�ft' j 1(e��hMGsubje�b�� "� M! X�$2uis �!�b"1q�I�n�Gof��FQ�by�&B!�nv� � �".!�A���Jk�+��=�E�uL=woyC8����A�61Օ1�;��ityu#%�s��trict �#nA�!�)��%�">.�2sXUdu�y��ly�`A6$�r�/:N�O�a���e` � �.��7} a[.$ Ai(%yE�!>��von NeuTe!Wrop�%�R de2L9!���#A$ or5Q"?��uwr!|.� !�@-�e� asB�  /ABV PsiT _{A,BX#{n,m=0}^�i _{nm}|n.A|m B�&9 �,pb�_A��e�� >  ���� !� Z� ��ma����~ :�.a" -����rmT�<� s: j�u �+%�)�A e�l"="�le��#�� bsn 5 UBj�de#= 'is�� io:t�b�! �I��is�� �4|  A<!th.="�Eo2!F)��ځIs�aEB� \�:("]L)\�#n�1^n U��� n|>�@��e)8�QPb�-@,qp�)��(-\hbar s(/kT)$ if $n�!-����� $�=NTb: t��r�e. �6���� �c !�I�a�UN�<u��BNm�tm} \e21-|\g��|�2-[2Z�B��%$ 6�$2 $[�L$.�Q�� d !vY`�i� )5iF� E=(�*ԑ{n}j�$+1)\log_2(  +2)-  -1B�eL`%:Q B�BO U�K{�N}{U�9 B6�&(!`��{nRL �h�t/2*Ao.% ,� $E=3)(3)/2-1\Vd x 1.3774$� �le��its6s [�^�� (i~876�By.�^K��)�� �e ���.�"�)wo��uaA��see hrpN �KmZex(C� }b0͍|p+ $,  BX �N�,�IE)2� Vn�%AT��aR��+ily�O]n� !�� e.j"r "��forվ!k��JU&3b"@.���F �be} w}tM$�sK�y�EjF $|1000}b -� + |0���b  |001 ;  5�C ;H$M�M)$%�� 6��c�(�m_�i� 96.:%���� 6!�%s6!�=8��YeXtwSa�2].i�a.im�eahso��`3Aj $M$ ZOs)�%���Mߍ�$2/M$,�tob�.�a25I+1+�yO}(1/!Y� �. "�2n]���I s}�����/"�!a- �BMof��� two}I��!2h�r�� H�n��e�6s��6���j�&��!�t �+i��.t>��nd �6u na��RT�7&�.Ul%O-�&��:��a5��]. d�pS� ,FS g�:��߆B�)Nl! 6l�L_EI |P\��>. 1-JEB�/E:& `enviro�m{)�-� sum�r�un&+�� h�us]'c�;u�!�a,@ $�$_ +UmaE>&� (!!^EY�vi�%J��=�-\N �6d=1<��� o a nO�ych�g l. SKG6� |e !�c�F3Hsl s���l (�T }) n)�7;U��d. 2�WeY�Ila^�*}%� w��r�2�,��!5/��-�%#C �V�%��A��pU e;*. A *~  - AB})�Z�pHI mixtU�-�=1� F�l}). C�neU�*� 0of a general �mixed state is no trivial problem, as��well known. We follow two paths here in order to find the entanglement that remains after photon absorption. In the first subsection we consider states for which we can analytically calculate t>�of formaYfor�= �4arises from ph>� This �8of all includes %Zs in wh� each)�!=mo*x$A$ and $B$ contain at most one x. )at caseD0Hilbert spaceYaV!�Ttwo-dimensional, also)x U a5x,�!b$an apply �Wootters!$,mula \cite{w 4}. Secondly, ?co-�A�� squeezQqI[t�$a Gaussian)2�rM' afteN� so %� }��results! � giedke}. -Le s� suRd arbitrary �s�calcuET (numerIl)s$negativity svidal1,2}. Ha*too!o alyt=S�ions become tedious or impossible depending on !^5��t matrix whose eigenvalues havea�ba) �d. AW both=s%�1�I�$ with a fi�4 amount of6�A� wishg�% @%�preser� heir6= best undN�. \9�{E.V.�}�� irstY� �of% generalE�( \begin{equ�}\label{�D1} \sqrt{p}|\phi\r��_A|\varB + )1- +^\perpB1^{}B, \end~ w�H!�parameA�$0\leq p01/2$ fully dmines2e: ���% B�L E=-p\log_2(p)-(1-p)  B�%��Jnarray} 6)<&=&\cos\alpha |0 �+\sin |1 0 \nonumber\\ BaIbetBH^Gph>� &=&-� �^N)�6�� Q�P +PO)�1-!��borthon�� l ba�uii�A���s��nned by%�zero-es one-ɞ %�s<�ts.]. a thena� $p�w \eta plot!2Ma��� ZmG�(\refm.)�Y they�k(lost a frac�� $1- k Ci��,s by varying? eis $I%$Er$%M$ ind�ently���� as��un u l average Ie)0fbar{n}$�a{original��coA�d pure)6�,y�C P=p(A^2 �E^2�)+eZ(A� si A3).>R���specific�$s are%ted!�Fig.~1.� figure} \�pgraphics[scale=0.4]{tdeE} \ca� fa �` 1`(in�_I� combined)��EYbipartit-as�jB !�"�. })%�In!ti�r, ho�E� =0.5I�fiA�=1/3$, ;!�.A .TA.!]Lis $E\approx 0.9183$ e optimumM, ound�bJ|�pop�m0�-�W1�>B�Z 8 s� Mۅ�f} �.� leftm�dM�nc: .�<3236$. Now clear� t� �9 t ob� edE�l small��b}, �is 2/3:�j2^ c��T min%jb^Wat:�\q>�min.�1N�0b�but its6e� :` only2e@1622$. (One notic��similarO ���-�)%� the i 6i .) The2 wo facts1� refutK intui��� a lowerF0( should leaE� less.�. Oɷ,other hand, � trula�c �wU A. largA, Z �B, 4/3,d� . I is,��FUb�ax5�� 5�� p}9މ]U!� �2Hsurvivѽ 50\% �*^ :2 0438�2Q�2TF7��"~ 2���-,A�in%�F�family!Z%'s��k=�$ o�explain%prece� �n0s, let us giv� MJve idea�wh�x^� 1100� 1/2}B�u>�isI� robust (w�us1�2^2�as 2measure)a I�v�00"+ ���MV��B�although�%ks�� 1-�� -�. For!0creteness, ag4ssume��l��E��6M. Supp we we� be aYto �eIF( � �E,environments%�o��a�!��� (e� a perfect �� ctor):� , if�don't G any 6��"�an5�� ���� as[ X V��,anoa��8betweeI h.�!� �%ӭ�E�)�h abil�� $(1+$ $^2)/2=5/8$:%no �� e.� �}� n {��0collapsed ont3e (unr ized) � Vop}) � � Tt�eiY-�?ie�ss �* ��). A�typ6 9ESN AY2.1 B 32VapEse�Ld Pnt tD. The reduced dens� �㡭 � has ranka�, a��rt�~n "al:(sp"G* differ�:�� YL �E as $|��[ $|-6. A�� a|��relevant:��� �, �:� $|\pm\�a�}:��!�distingu� hree%�]7A�e��7A| ymmetric �!�inter�Lge ~ 5��$&�F� ech"6 p}|+-H_A 2X\exp(i�)|-- JLZ B=wd^� ech2���r�p��.>� A�third%a&E�e�� ech3�649.�Z4�F��heMV�$q�Adef� by9E�E� 4 &=&(6"\pm:)/I�N_{\pm}}. &=&2\pm2�-2 R|^2x6N��� an *N bas��V|. J6 as bef�\y�$-g�6i0����VP� �ted in�2����M ph�$A���e"�i�if��i�groupe�curve�N$y correspow� �A� e{),2� 3�):QA He[�V 2�2^���~�"6nda� s�l� ,� pective�a1�2}d WithinC%; p �� �propertBat fe t b� J�M]� v0�not9�9i5) A, �I�Io|al v)S� �sW�sag� �s .l! ut aboveQ&� Z�I)b[I}M|flimita\r� arrow 0$�� ECC5����N >9A"� J ."���"�YS1a5 ��7)�aB >�W* inf% wo�lu�c!�Y:5 s.~1e�2 t makeX$seem unlik� @>�" "�%@W . F0,Qe�6���A�*� )�?,S&)MN����� nc�� � NevertheWc�fB� nydE�V�A�� �discuss���q�Yon�n� �,*O�iulaCS2 of= �pK!2�,� n�m��EBr�{J� are>( $��0.5138��*�3979$!u&/impro�o.���sidered�B0. Unfortunat��A`�abeE }" u��Y.~ !z complN M, �e I�M�y���@ or l�in��r6� A}��"~ tq�d!�y�O g ye�-u�Z� �!�.6Q8 ����E��exa�B�reason �%t a�H[!C�# 6� eas�c�d; �Aeb�! �!2� N" "} S� s��ga#"Z"*V�1wo �- *F . �:$always wriE(is)�X SSchmidto 3"�F�  |\Ps"� <{AB}=\sum_k c_k �_k� &� Zl !�$c_k$!� l po�(ve coeffici.A� $om^2=1$,�:� heD |x$2� M�$on systems.� *�#of�"� M� �jermi �1R2�as&� �� sm} N=\�,{1}{2}\big([�)^]^2-1F�FoE�i^#ԩ�ii�� �sum���%l�v�#A� B6 $Akhe2al trans �N$��Q� N&�$kexp� �;� in � �E%.V�.� ,to-�!�)M 1�J� \l< h n_A,n_B|\rho^{T_A}|m_A,m_BM�=++|8%F�nd�-S��B N(})M|.�|-EB_i||.||$!Go�q tracrm���es�fix�N!R����!�a.c �n")6�I �� . Si�we��no�yed��*ImeD� .�,�wil()����oN�m�$� B��i�d@)a��*s: 0��!Eloo��I���M$V�$c_1\ldoF_M$-�M\geq 4G�e� $E�r��:8N8�. Itreat�3��ixe� n1 �$c_2$� "6&��9b$N$1�5��%��9%Fsimple�&u#�{R?A�w���.� .�+��.LA�� M� a�$� oA�use a �) method�d�2�2�3$g>#4=� . Nq�q Newton's n,! beZ+%P estim �$c_3$, such� !u>}�"ach:%E$,M(Aڥ�NC>�6tr��6~� :X)�� stra�forward �s!w1� keep�#RO� a$�a�T6� i��1&4�vKs��H�v���"8 �sm}). An*�' $M$-*� �A�be� y be�%ih$M-%fglZ �#alogyA{�2 EuleA "�3-D�ce.�'�,�� �_��s A*� .u �$"�),"�(,M�|M-�"$*�s�set�)( l!l�(�st"of%��W�j2� ov�l �, choi�"*( g0$2\pi!�d&�'A`s0 v),E8 ut��al | cy� son/� 1"(of randomlyIsIa3MT�a�*.�%&1!-e +I�se¥���A cer�``�ance''!�standaN Fock)F�:�l�s�t max %�qU:�By�05 �bv4& get fu�A�d way� Z� . I�s~3��4a��m���Uue�rm���a��%�-� �*� �FQ &��#��).F ri%@Mytoa��!�n 1/10g$\)4+N�|unG�&ezN�!t��q��6�� �������(,T �#��2�-^Z� s0, exponential*4A���Qof-y s $n$ (sert�, H��A� trun�AH2�2at yQ�2� $N_m$,� <  t��>�*�+ good�1rox�;ib=vided ]!�su�ly�. se�=6$�i��anEt���qR�7�s ���1FE�&of cours!��*6,� �i��I�."�/+n�+navln51`%@&�AB6eqa�2- 1000��ly�� �y2M� 2�]�9h(�Z�,] au�!�!�hey{Ob�hs�la5�a�R{circl�H� �Z�Bs,>2��pi}&c-SasS'vF�-, excep�6r�[ nor�#��WHw�4e%= �> �8 %�M|%1wV� itself ise� �!amo�/!M*3��� 7> confirmedA{� lyafdeV�eve #��%e3�(/�8ably w whilH��l2T ie� a� ��"* "A M�r�. And ^.8�))at$j|e-���\���.�, �ded!�� !Ն~to�-�o( . A� auQno@:t m �7"x%!��) o r! in Ref.~*R1})�F���,�9or��, !�or�� E�``I��''!.�. Howb)S�N �w� word>I��quw"M.">�.)~P.�i refY9to how m� of u�� s ��>y H.�9O�D���2)I' o�+ remo�+ll6��U�%|.� a�tr� !�irm"behavio�2YU ���2a�\atu< 1, i.e.)�{�+�\�"��-s $B�T tdeN��n�B �J- �k � C 1F:�2�/se a9=k � rastA"�>I!b� (See��1] dot�/vor�E)Jsgfar��y<�E,concerned. N�/�'ee �)�do �%�Z�.� �19�> qdo��:t��2~. ct� �\(re necessar existAple!yone"-of:��@�"@'t�({ j�9*�<. L5/inv�ga�a littlH� �] �:H of�a 2�!�AC- at eCt�-�ej�,-�} four1E���d B� �{��aliV,", >�a/�� by so�!7&mY�.8, �9 )�� pend�  6�M6��]/in}ce�0,���iq#�Ppu�3�?rV�)aEo�rd2��*�R& P=1-=(c_k^4&4 WP!�Pb .� its S-e a!@�+%�es��+�hl!�_a^s n actu�Y��?�!e.6bN��!X.�N6!a� di�8pr> examples�U#Nm4E0�(� �b�%$%Sʹi�-jY��.�A�U�� q�m�a�#m�L1e�B� �.~6� �j s (aF2� &g)A�6 r �6$ t?&$�*wO�+=.2$E=0.�>�(=H$N079�;Nn showaqm6r�(��! lin�B poin�4�.)e� is exacsp!�Fcha�< eriz 3 iC �"Z���A4�� 2�u�uBu7�R,Q|� %� data��N�& � $P$�R-�)�a mon�Eic"v , ra��u�� bistT#.� 7� fact�8U,aHhap< rpri��I�A�{\em m r� �,m++6 �. F/FFigs~ 6e�7�?6GF �I�B�� \not�8�� oq!-of:#R6�#c60 �sen :zE,#.e���: a trifle%5ua��;B� AA exten@3 u&���*W �to_k five, ��ť� ��+a���o'[ s.~8%�9��Nm56S� as!ۡae�� �^ V�:� �<i�5�2�7�T )1aaJAD6ectM��E�tᅡ$ extra deg��� reedom �?�%�-�Nr, -,9�4�$��DM��Q�M` is. B�&.�6e�i�*, hardl"e (&�0.1\%B�G� (�(rel�GeA�e[ (bT�i�ca�QB0Z�a|5.�j�) "�7 �& Hs ( ��� ]2�m@.T iS:!�a�V� �,a�comitta�C gaa!�^2�<� i)��,��) �IF.�n>�I|Ir{� � ,Uingk sm�vk88S�.�� 6�*T�69* :*7&�!Z�� !SBY�n tur�A��2\% �M�tal@Za��."xB E�.L�)�abe� ]EE+�797a s wa� �B*�Jtu 6eA e�Z�a"�)�� n.>����;�( Ű F�. ��e4I(�onmexper Mt�achiev!) J!v)�Pa��$ CEfin 1\%�/-� *i�{D��}� �paper% *>aad�Q.�_�ye*lu�er��� -�(r�E>s�aim%�i�a[s/giMB�A�tz �KsF��K/7��*�Anoise�*EA��ansm2��D���f sM� ��P� ;F�Ei�8�=wXm0(s)!P:W-ne �QD� we m�ix|�>�L Z s $M"& M_n$!��  p" E���y�6� WV0$uL>q(�:B� ) to "!�N�sk .9C�%p:6A�p}���=� )V�0{6�uAr �^�s�$�E�Q�u��s O$A�b �2'g)K�%U $M_2�$&W,y��AR60$� ]�%sz�>NE � �� �%.:�1%+}X\!d2  m- qst=-#Q�AU)�XZk��e��ie\$C!)��'!�zZ�=7l � ill l���!�� �1 ~"0=6n�erk;�y., �J�ԡ�)c��a�!&>�S��i:>�)p;.�.� "� ough�is very 4� )!V:a��Ob"�0Ne�#�$M_0$�!\FNl7sA�a�^��)P:\ :VS� real�<.#L.R�if] {\rm� }6�F�A�a=��Q;R[6N� �:���quantify=�Q!�J6�A�� !\uN (�Fn��q�(n A��&� " thebiblio,My}{99�M`ibitem{haroche}J.M.~Raimo�HM.~Brun� S.~H ',, Phys. Rev.�lt. {\bf 79}, 1964 (1997). \b,myatt}C.J.~M  j3l.}, N: G8403}, 269 (20002Ghirota}SHvan Enk�1 O.~H.� A Q,64}, 022313T12T(lixu}S-B~LiLJ-B~XuILe� J30�321G32G0pz}P.~Zanardi>!#=$65}, 04210 ? 2); .�R474 2230 � 3); Y.~ShVb .43 b6�"�VW.K.~W2v �%�80!�245%�8�9�xVG.~Gi�V:�Y.R91A07901 !�6��11TVcV%�$R.~Tarrach2�-�5!�141�9�UoM2>M F.~WrNN)�32314%�2Q�?>= 0document} ��,�6(�\vspace*{0.5 in} \begin{quotation} ``Attention has recently been called to the obvious but very disconcerting fact that even though we restrict the disentangling measurements to {\em one} system, the representative obtained for the {\em other} system is by no means independent of the particular choice of observations which we select for that purpose and which by the way are {\em entirely} arbitrary.'' \end{quotation} Erwin Schr{\"o}dinger \cite{Camb1} \renewcommand{\thepage}{\roman{page}} � �P�P!�0 |.�T>�n� �H�X�J"!I��!I��!I��  �`�$�� 4��D �T`�d��t�� � �$�`� (��� ,��� 0� � 4�`� 8��<���@!�Da�H$��L4��PD!�TTa�Xd��\t��`�!�d�a�h���l���p�!�t�a�x��|����"� �b�!�$��"�4��#�D"�$�Tb�%�d��&�t��'��"�(��b�)����*����+��"�,��b�-���.����/�#�0�c�1�$��2�4��3�D#�4�Tc�5�d��6�t��7��#�8�c�9褣�:���;��#�<��c�=���>����?$�@d�A%��B 5��CE$�DUd�Ee��Fu��G �$�H$�d�I(���J,���K0�$�L4�d�M8��N<���O@%�PDe�QH%��RL5��SPE%�TTUe�UXe��V\u��W`�%�Xd�e�Yh���Zl���[p�%�\t�e�]x��^|���_�&�`�f�a�%��b�5��c�E&�d�Uf�e�e��f�u��g��&�h��f�i����j����k��&�l��f�m���n����o�'�p�g�q�%��r�5��s�E'�t�Ug�u�e��v�u��w��'�x�g�y襧�z���{��'�|��g�}m���~����(��h��&��� 6���F(�Vh�f��v�� �(�$�h�(���,���0�(�4�h�8��<���@)�Di�H&��L6��PF)�TVi�Xf��\v��`�)�d�i�h���l���p�)�t�i�x��|��矀*蠄j衈&�袌6�裐F*餔Vj饘f�馜v�駠�*ꨤ�jꩨ��ꪬ��꫰�*무�j뭸�뮼����+��k��&���6���F+���Vk���f����v�����+��k�覫������+���k��������,��l��'��� 7���G,��Wl��g���w��� �,��$�l��(����,����0�,��4�l��8���<����@-��Dm��H'���L7���PG-��TWm��Xg���\w���`�-��d�m��h����l����p�-��t�m��x���|���߀.���n��'���7���G.��Wn��g���w��砇.�����JL� Ⱦpmath0412439.extracted_bib240n16trobust_detect_lin_conf.bbl6X36;d general_parametrizatio^A66A6^76, preprintB�5n�5:�2g526g6:�64n:5n6n:�!� ank2rootsF�n�6n6n6n6n6n6n�6:�2n68j46n7n7n7n�7n�7n�7n7n7n7n8n8n8n 8n"8n"8n"8n"8n"8n"8n"9n"9n"9n"9n"9n"9n"9n"9n"9:"wp�X�bonceleBb50j50j50j50:�Dsp4�.50j�50j�50:�2W1j�51:�$ descen% � in_aB�1:�6tj�516f�51n�1r�j�52n2:2�2n�2n�2:"A}dr3foldB�52n�2n�2n�3n�3n�3n�3:��llgpart1B*3n 3:�E�rBEn� 5>� 2�4n�>� 6:n�>� 6::�6n�n� 5n� 5n� 5n� 5n� 55n�n~ 5n~ 5>a �j th-p� 0>�B :�B :}B :�B :�B :B :�> >�B :�B :�B z>�B@:�B z >�B@z >�>@>�B z >�B@z 2z >�B`z@>��isserto�!>T>�B z>�B@z�>�B@z�>�>@>�B z>�B@z >B@z>3B@z>9>@><B zT>_B@z >B@z >B@z >)>@>�B z@>��$Uint+dP_pVN�> Brz�>�>@>�B z�>�B@z�>B@z�> B@z >>@>B z >B@zf>  �ap� BMz->B@z->>@>B z->%B@z->+B@z�>1B@z�>7� nlinB� � PJLa�6(:�6:O6:�6:6:�6:6:�2>� 6: 6:I6n">� 6:n">� 6:n">� 6:n">� 2:>� 6n">� 6:nD>� 6:nD>� 6:nD>� 2:N�uT>� 6:n�3n�>� 6Wn�>� 2:>� 6n>� 6::�sgorskiB\>` 6Hn�>Z 6:n�>T 2:>Q 6n�N�U>h 6Wn>b 6:n">\ 6:n">V 2:N�>p 6:n'>� 6:n">� 6:n">� 6:n">� 2:>� 6nDN� nucl-exR�2 :]B :�B :�B :�B :nB :�B :t> >�B :�B z >�B@z >�B@z@>�B@z >�>@>�B z >�B@z >�B@z >�B@z`>�570long��>O>NB z/N�.�>.B`:�B z/>B@zO>>@>B zo>)L roc_HP200OBSz�>4B@z">:>@>=B z�>CB@z3>I\ wakas�BN^��$B�(finalversio"�E�4^� ^ ^� ^� ^� b$ ^� ^� :0 classical2F1^� z>� 5�@z1b5 @b5 z1b5@:1>�b5@z@b5@z>5� omeg6R M>� >�b3@z^b3@z^b3@z b3@z~>S> bS `bS zM>SB�zMb`�:m�#beN�b* Jb* z*b*@z*>v>*>yB zJ>B@zJ>�>@>�B z@>�B@z@>�B@:�Q" emis^X>�BPz0>�>@>�B z0N9.N92 :B�zPN92`z N9.@N92 z N92@zP>\)> NL2`z@NL2@z@NL.@NL2 z@NL2@z@NL2@z�NL2@:�>�9v@10:�&:@1N$�1b���1z� 1z� 1>�B�v@1b��v@1z� 1z� 1z� 1z� 1>� >N�physicsR�DOE_arXiv_submi�*W27J�2 J�2 J�2 Jw2 J�. Nw2 16�*>�Nw2@:� XJMerrifPhysPlas26OcR<NZ 2\J2 zN: .@N: 2 zN: 2@:>\N: 2@z<N: 2@z@>: B�z\NM .�NM 2 :S�" article_1"?22:.hErdmannEbelingMikhailov�   vari" .L>� 8Fritzsche_JA�B_18-11-&�2A:�>?N� 2@z�N� 2@z�>� B�z�N .�N 2 z N 2@z[N 2@z N� 2@z N� .@N� 2 z N� 2@z >� �eca> >fB : �unific2�).�N� 2 z�>K adv-dif9>�N� 2pz,N .@N 2 z,8z�N 2`z-8:> >_ )PamczakAmarand�4>@N� .�N� 2 z�N� 2@:�:�R� @R� 2 v�R� 2@v�R� 2@: �polemiN�1z RN .oz 1>� �J shifN� 1z� 1z� 1z� 1z� 1z� 1z� 1z� 1z� 1z� 1zh 1>h  nau>po&8>�zZ 1N�.�N�2 :�B�vN1N'.`z; 1>a ��>�z 1z 1z�1z�1>�Q9texR-z�1z�1zv1zV1zV1zV1>>�N.�>L>@N.@zY1zY1>YB�z�>it(HI+-PTodd48R�z}1z}1z}1z}1>}� 9Penskyjordan_3_2_fixedaa�Bq-bioRa�techRe��:-:@::�::w::� ::�::?� �-repor%�61>!:r�>6<>�::��p�/jtb2_3!��-RE :<r!>�:<:!6>�:r>L:<r�>h:<r�>��Ha!a6M>n:r^>J6<>Ha~quant^Z:F!:F!:jF!:�F!:�F!:�F!:�$$hasebound-&CF::�B!>�F!:~ F!~B>���hesis2aiFQ~> FB:SF!~>JBB> F!~>� FB~8>�iinfodis�wBR>VF!~�>�FB~/> FB~�>�#q��L_Josh_howard_v4_arxi�Fi~&>BB>F!~P>� FB~P>� FB~P>�AGmodal_v�FR~9>�BB��>7 FB:_�ULDEstimRU>�FQ~'>�!FB:�F!~8>�X bang9R�>� Bt>� F!~�>� FB~�>� FB~�>� BB>� F!:0F!~i>� FB~�>�!FB~!>� BB>� F!~�>� 8entropicUnc�@ intyR�>�!@KS_DWELL_udisF�~9>bFB~9>�!BB>�!F!~9>�FB~b>�FB~�> FB~�>-FBz�B/>BB0F!z�B2FBz�B4FBz�B�!FBz�B�!BB>�  B;Bc~> B]FB~�~> 1>> Fc~J~8 1>8 �sho�LBo~# B��2?R�~� 1~� 1~� B�B�>� F!~2~� BFc~�~� B/Fc~2>QBB>� F!~)>� � ionqc_n�#FR~>� �'4noise_thresholVq>� _FRET_PdRJBRB�>3F!~�~� 1>� @ContABL040705agr� Otweezer��$B�>v F!~ >| FB~*>� �"p�FL~�~p 1~p 1~p 1~p 1~p 1~p 1~p 1~p 1~p 1~p 1~p 2>>->�2>?-F!zp 2~�2~. 2>�F�zR2>���monotonRG2~� 2>�B�~� 2~� 2~� 2~� 2~�2>� ��,� 60(wp.bbl 570long.bbl�d� p$I�dH��!I�$(!I� I�d@X2 I�� �$ >!ɐ(FF� S~IH�\ .��I  �`�$�� 4��D �T`�d��t�� � �$�`� (��� ,��� 0� � 4�`� 8��<���@!�Da�H$��L4��PD!�TTa�Xd��\t��`�!�d�a�h���l���p�!�t�a�x��|����"� �b�!�$��"�4��#�D"�$�Tb�%�d��&�t��'��"�(��b�)����*����+��"�,��b�-���.����/�#�0�c�1�$��2�4��3�D#�4�Tc�5�d��6�t��7��#�8�c�9褣�:���;��#�<��c�=���>����?$�@d�A%��B 5��CE$�DUd�Ee��Fu��G �$�H$�d�I(���-+�ԒK/��L3�T�M7ᔓN;�ԓO?�PCU�QG!��RK1ՔSOA�TSQU�UWa��V[qՕW_��Xc�U�YgقVZj��V[n�W\r�EW]v݅W^z��W_~�X`� FXa��Xb�-�Xc�=Yd�MFYe�]�Yf�m�Yg�}Zh��FZi���Zj���Zk��[l��F[m�݆[n���[o��\p� G\q��\r�-�\s�=]t�MG]u�]�]v�m�]w�}^x�G^y杇^z��^{�_|��G_}M�݇_~���_��`�H`��`� .�`�>a�NHa�^�a�nh �z�!�!�8"�%�x"�)��"�-��"�1�8#�5�x#�9�#�=��#�A 9$�EiˑH&��L6��PF)�TVi�Xf��\v��`�)�d�i�h���l���p�)�t�i�x��|��矀*蠄j衈&�袌6�裐F*餔Vj饘f�馜v�駠�*ꨤ�jꩨ��ꪬ��꫰�*무�j뭸�뮼����+��k��&���6���F+���Vk���f����v�����+��k�覫������+���k��������,��l��'��� 7���G,��Wl��g���w��� �,2ĸ����L� ����\begin{thebibliography}{99} \bibitem{DVV1991} R.~Dijkgraaf, H.~Verlinde, E.~Verlinde, Topological strings in $d<1$, Nucl.~Phys.~B {\bf 352} (1991) 59--86. ��ubLNM} B.~Dubrovin, Geometry of 2D topospfield theories, Lecture notes�,mathematics �1620} ��5) 120--348. http://arXiv.org/abs/hep-th/9407018 �(Cargese1996�:�XPainlev\'e transcendent�property, one century later}, 287--412, ed.~R.~Conte, CRM serie�9al phys!h(Springer, New York, 1999).]"F2004}E�.~Ferapontov, Hypersurfaces with flat� roaffine !��2�� .�PVCFH^�P5@s, vanishing cyclMdFloer1L y}, In ``�GB : Fronti1�Per,ives'', Amer�\ Soc.Ij0.�DonEj>=!�o&��canon%cclass!V.v4-u���1���4%@ 2003.�4FO3} Fukaya, Kiothers,Mh�Sinter�8)8 $-- anomaly�ob�xion2�2(Kho} Khovan�,MQP(A categorif^ŧheN� Duke��J��101A120Br:CMRu,Crossingless��cA+=omq%$(n,n)$ ? �se� }, C��n. � mpQ1�6 �2�KhoSei:�E!eidel, P1Qui�v,-��/� d�  a��J.B��1� 2�@Lic} Lickorish, RAnA rodu^� knotM },5,�97.o4Man} Manolescu Mf4Nilpotent slic�)Hilbert �Nmm�Zn`�^11015i�2t,McDS} McDufft!ASalam��պIn6���O �(2�@d.), Oxford Univ.�� A�2j8OzSz:DBC} Ozsva�tPi�Szabo, Z1� Heegaard-�.�Ցdou� ɘ2|F{$GT/0309170)2Pre} F`� � �$ on contac�t }, A A{�NYpQ�2oRARan�A�]> 0of nodal curv�=n10037 �28Ras} Rasmussen,��`��9hAA�E� genu�nz!b40213N�@Seg:CFT} Segal, G1�D2�con�?�&�ApŨ�5&,U�����0(U.Tillmann, I�CUPJ  Sei:a��:r� 2-spheres�� be} ally� @ted}, Jour. Diff.�ܱ5ŋ>��LESJ A long exAa sequ� �}�ɏ� �xFDJw�Պ��irp "egoceed 6 ICM, Beijp82002, Higher Ed�)�2�VMJ�VN� �mEu*ae�g8��(, Barcelona�00, Birkh\"aus�B��DE�>ve� four2�$Dehn twist)f� ��30901 2�}K3JH*� mJY a�quart��%�z�10414)�B�^J�Unpub�ed���A�7.�Sei �́O>� A link&� from�]�g*n:8��405089 �2  �22�N�In��� &� SeiT� :� Thom�"BBra>���derivU a� A[fa�C sheav%^^� 8X 2gSmi:GMHa�:� �<Z"��A 9�=(6) 473--527*��d~Pa�selski� Quad�c��%T.x Pos}AJI>��Bog` v'�Q'}, Harv��0Ph.~D.~thesisn8:�[ www.~ ,.uiuc.edu/K-4/026�8r} S.~Priddy, )� �Y��rl. AMS 15e�70), 3'0]?ST� She�n~T�yMCOn`�*�a newa"�, of Artin-ScMer re):� 9�241��789--798^%8f�xx%h)v�"[Astolfi�Ortega]{F}{�}{ " &�r>R.~  �3). Im�!!Gce: A% tool�� �bi� / adap!: trolanoXear,. {\em IEEE -�$on Autom�"4 rol}<48}(4),~590--605!E.Byr�A� Isidori]{F1 _) AI)A.~ D9Limit�s, zero �I*(nal model�� problem6outputM:!7F 9 =r.=10),~171�57�� N %`et al.}5 .}{1997}1  2 , F.D�iscolE15!iW.~Kang ��7). SeMleF�6$!-Ua �D 33}(3),~369--38B� Fradkov]{ 1� )� A�L.9�%4Cybernetical P$ : PrincipExa�s}!�Nauka (I"�p .�K��]{ %s4} } �~A�1�-Sync �XaM�5P}. Enegroatomizdat (ia@�B� LaSalle]{ �76} �!�76%�e�ty w%�� p5$. In:%O D�" al S# , An"a�%} Posium}. Vol.~1. pp.~2' 222>�Ott`Y�>�90}A�$0} Ott, E.a�� bog�1A.~�%e�90)meoll� chaoQ�A.� !� Lettq� 64}(�12a� 196--1199>�Panteley:�RE�2}��2} , ʹ�a�P�%y��(2). Overcomǁ�detec1� �acl5@certainty equivalN>�M�N�2},~1125�� .Tyukin]{ � 3}{t_fin_4 sA&Ti� "j~Ya)�Dorithm�N� :�R�� ob� s!�e��eRemote:W!�6),~951� 4>� � P�LJ �w a}2�_arch}6�e~V�\okhoro�&4C.~van Leeuwen��U a}> .-� Subm�"d%#�c�b (� 6�)� OC 9254)}�) b}}{ECCA�36�u^�ees�N�b�F�e�orm reb'�;�>�� M;�� P2� {I}{E&-��fCon�%pce, Cambridge, UK, September � �0 4}{ALCOSP!,4}2$),�$4Av al� J9convex ��' ized�ow-tria�#��@%$, {A}ugust�-- {S}9bo�� 8-th-xF}{A}{C}&on �%ׅ�Learn��in!�%���Sigl %�� ()H�A��J6x6 \newblock Yokohama, Japan��I� ca�pt�� _tac.�^� V.A. Tere[+.�cA�%ivA�co ��n�>�%0�U�{E} {T}�'.Y !�t[ {C} Wd &] 54--567Bziper�'��� >��l.�7}{ �7} ��H.~G r�# E. Zebiak%�M!Can��\ m��A�p�tempo�*c�A'a�s2 0{E}l {N}i�odic�3� -2�� ��2�79}� 1034--103BVorot�  �8}. , Vf a 98� P� al S�% �}.��!�N� w f<MMMM} %�P[Ft]{Ft} %L. Fejes-Tou Lage e� �( Ebene, auf@Kugel %und im RauJem"� -(1ag}��*537a� &�,H[FG]{FG} J.~H. FolkA`a�LR.~L. Graham, A pack�:+"& comp��subset��='OemAIad� Bull� 12}!�6�745--75w =+$\"uredi]{F} %Z. ,, %%Zoltan %�densest�o/l cirg%into a�x llel�*ip. %eWDiscr� )#��6�(91), no. 2,�06!Q� {GL1&�[GL1] .P%aB�8 Lubachevsky, D� P)j%E./l�ks �+ani�+arT�le&$m 22 to 34 `eyond\ em E�*r. J.�bin��0198\#A1. Also see:�fwww.arx�2�M�(6252} ]KGL2�2}��Repeak)P�of) ^t SG��v�(1))� 6), \#R16��394} %9�L.�L]J�How!� simu!� billiar�* simi�+s� MpJQl�� 9p/5�$55--283. %]gLG]fLG]B�E .z, Iem�Eecongru�$m#Ajrecta~&��aS&-,q(�0, in: %�e;etev#+o}aIetry. a�dGoodman-Pollack Festschrif]@ Aronov etc. eds..�%��0. isbn 3-540-J#1-1�� 5148!߱�{NO.� NO1] K_0 Nurmela�P.�4�'@"{O}sterg{\aa}rd,q� upA50 �'1RI�s.�%.1�! .} 68I�07), 111-120. =�NO2=�NO2�2}��Optimj�n�3l C�( nyq!�%�Co�@atorics,�"ph 6o34�:A"� },T II, YKavit R. �',%U Schwenk (!�), �5Issues�$�&K' azoo 60 %pp.671-680.23�bF8 [NO3!3�More o) .&���_pb$m�2��~39-45��R�R:�b)^n%8R. aus d��, A�!tow behavior�W �M�y��QM�i�CaZ�4�380�Oler]{} N.  4� -F�,MHblE�6��$153-155. "' [PAS]{PASa.emša4-any-shape.com. Ruda]{} M.  $, %Mihaly��@��!i%�. (Hunga�n��4summary)��4Magyar Tud. Ak�. Fiz. 8Oszt., K\"ozl.}!sbf 19�373--82Specht]{ :�ob-a>�$SMC]{SMC} H8.�)M.~Cs rko�1nd T. Cs:$s, Global�i� A!���� -���G � S��� �"EssaysE�S)y��Ja}, Audet�ns�P.�ava�Z G.S.� Kluw� Dordr!,�5, 233-eJ�\inf.u-szeged.hu/$\sim$ps�*0/Pub/cp2.pdf}.bT[Th]{Th} %A. Thue, \"UqHdie dichteste Zussa�0tellung von k�Ren %Kre�!NeiO � %,Chr( \ania Vid. Selsk. Skr.} %j 1 1S-9. R| ("b_=F�B� Sneppen]{:? 3}53} Bak��%�K.~ 9C 'P�8u� �libriu� c�#c3 �s9impleavev�8*3iew ers}z .��%G" >2 ��(�`0~)~v n�D� �T anlo�9).A-fi��ng law , earthquakesz� ��88�78501B�egl"Plenz]{:�!�(�!� , J.~M)�D.~>�). Neur� aval/4e�neoco�( ui*�J 7sci�� (35)r167s17��2�renA�:�J�0}{ �0} 0, N., W~Biale�,R.~de~Ruyter�$Steveninck �E*�re1�maximiz���n�:mis?-�)))� 26�6�#702>�4Canudas~de WitI; siotras]{F ed9}%ah9} 63, CSP.~7is9).� tirmK�"vehicl�trs1� �v 38th �{ Deci! �B�Cao:�>%�3�o!�3�o��0A.M. Annaswam� A.~Kojic)�A�Par'�v�ncA �-&ly���.M-�6�"�:� ��9�@B�Cor}6�J%�5} !�5} (i�M Perez4~D�az-Guilers A.~Arena-�5 elf-organ���a��synchron��a�AticM)�t.0grate-and-firA2a�ll� 16�N���74��18-�&6 Daya�NAbbott]{>E1}{ A1} %�m L.F. @I 1)-�Theore0e�sc*=:� &|nd 'u. al M ��of;a"$}. MITz >�Ditchbur � L.]{>!�52}_1 (#)W���)~B.�; (, ). Vepvs��simage-Nature-� 170}(4314�--F0�6�0}�!�0} &E���\ym$ philosoph0,J]"*�39-th {a�}�f.m{D}�a1 {">4i�4FzGauthierE� C.]{:!�96}a�6} &�a~ABienfangC�199yA'�nt los. N`coupl-.ha A�mH: Tow�%�$riterfo�high-qx-:�-�r� 77}(9�751--175BA$Guckenheim-0Holmes]{> e�2}2!A2} .4u%CP.~ Ti�Aȥ N"s$Osc%�A,ѽ�#� HBifur.!n Vector Fm4a�Sp�*e�.t Ilchman]{ %�7}_� A�en�Un�8al&�qs$�5�a���d! ��7 } (7!�9A)13>F�$]{ �89} y} �8��n9M�sM:�!"9}. secon!� ed..58-B�t>�>E3}A 3} ItoA� ~NikolaevS-Lum;7M.~��uke�%~Nakatan�!C2f�).�$ceptual sw�ri- eye-movem�H |(bus-paradoxi- A�4ɥ#!6B6�'.9Kaneko]{ !�$ 94} . I4�Releva��Cg# clu�Vto bi" ? netwf+U5m� D �75�E37a�2>� �eTsu�>%�0} _and_*2���IF ud�"��EV�lexq�: C�2Dm%^y>�1J@ ��( *M< %Wi6�A��it4 ancy)�s): 13� 926--936F?rs�E �"'KN%�6!I 4�2,"�'D~Lamnabhi-Lagarrig�G 1sti2�A� u�o�B*��A� �� ��(%0�k %I� 3~K9B� L|nd Qi�'.%�2E 5#Link=n, �C.~5�� (.� ��.+l�$�8��� smoo�K eedbframea) �+ �* j�*47}(5),~757--77Bn.�]�%?��+#LinA�2_ ��b� i 5cas� �&� � t*�+ 7}(8�j2�K1�6� Loh:�>E�9}{" � Loh, Ai-PF� F.P� antz ��E�E��thP prp4ceAg52al!�� .8��e�E�+ approachI 2�""M!mm44 67 6Q2�Marin��omei]{>%3} %93_i�} .� EQ�G�$��GP"%o,-9��!Z,!t {II}: ��}P%1).j+38}(1 zK/.M� nez-Conde:6VZ h" O%)��zaG4%" Q^"N Mackni�Dy Hubel�`�`aro�,�/fix�al "Afvis)pe4io1  Re?�z."M&5�;�240>;Milnor]{ A85} _85}  %�8�OW7��A�att�or-�C�C�. ] 99 7 9Bb-Mirosh!9����V�a�F�-a�)�)#� if"�(A�7�-�e�kY��Ae�i%mv�:F}. �BVoreauIS�Ag]{B��a{,AP3} �=E�8nta�.: B�� at�� bordein� tG( d.alM& ��6�02>>�Narend��]{V!��  89}  �~�KA�O%}&� �$le5v� � P�Nce--Hall>�P2%�U.J%o2�2� %, R� �2%xN.~E.�?ab&Gi�2b"% {P}{I����,f {U}n�,�( an'l�:PK� P}a�3{A}T)�iB �7�QA�Q�6 47},~25� 7B�Pacejka Bakk�F!�� 91}�"9, H.BU� B%�����magic� " ty�&�A�2 + 1-st T+$Colloquium$ lft, Octo}"}��8"V)Suppl" !EV6 �, vol. �:6P�V]{�2} 9�.��-B��9!�Remark.?suffici)ia)�!��=e�;�5��( 3%6@)wPn*1!� B217J 4B�Sastry]{ �9} � 9} ��)��e@Y�� s6Q,e�i']�e�SZ�Sol>dB�ole�olea�~V�MC�nrubi�<BentoP~Kauff�'P� #1��J >4�in&�ary ec��5 TRE�&{ 4 615v1�76Q�/�{0�{0�{0�{0D �y/&y/ah �y/�y/�y/�y/�y/�y/.y/a.w/s�u/�u/Fu/ �Y�g/Jg/,�g/g/2D 6 t�1�g/�g/Web���"7 N8 � 2}  A. F#�]5 " SZ�;�M� � just� to<2� bl�JɊ�/o�}�5�8z=8� R�.t f,"95 %*�+{A2}\l�" ng{M�ADndersson} {Residue^?�  ideal�.@Ff$"�} {.\�X&qD �12)S�A�512j,{A3��of2�0R �LyJg�4} {Arkiv f\"or�J1k �4,-200,@MC�`2*,A4b�.QBY1(C.\ BUHXD4\& A.\ Yger} {C�`�YcTnuE } {jCnal9Q� 75}[ 98),,55�X&�-{BGVY6�~6�R.\ Gay�$Vidras \& + �RBezoutAnt�G {Pro Lin%dcs�*#\.L Yerlag�3)A�y({BY]�rI!%6rM��;�Inon�W pletV S�YKPase-^ R�% Angew.\ �.\)g527$]0),sB203--235 ��B9mB)�ndtmL,Cauchy--LeraUm)�vbundleE�nni=�D$\ Ec. Normup. �2H)�0319-337��GS�J.-a�Bismut!�H!� illeC�Soul\'! �immer" � Araakelov"L} qIthendie6�- , , 2�331BYog�V , 86N�N Bos� MA�S0U�C�A�Bot�queHf3!+9�I268 pp!+5�HL��j�MTicU��ema^�ZJ�117-%af 8�H87$02'*Lj�S ���E��<-Weil �y�0� met�)�ita D"Z ���119��,  --15�22ULevy ��$Levine} %%1��DnM��OU�i�6co��x�/�?i�` D�NQf�)71�196z,5!>5��5�Meo]f�@Meo}{R\'�d s dans le��b, n\'ecessair� �&"�[� \`et�b�vb��c( Paris SAe Ii�~33� �� 33-3)E.�]k�$Courants r� et�dmule de��WW� 3); cappMGin 8 $mat. }{}{}�*E6P9��Passa�X%�calculu�)me�P)�cuW %��2���� 39�18� 37-��9PT*� ���� Tsikh ^� �� Bochner-M8lli�Y��ub� .M�44" �Oa�6� SABK9!�l�Dr bramovic� J.-F< urnol� %%!K4r%*.VAr��Gy""P@ stud�S�Md�!d!�� -]3} %%6�(�ty�ss��2�ځaenF�d��m bar1�Nh bier65 Dikranj[#�il^)H.Ser:x  $t$-d�.�;�f!��_�) Abel� r e�t� Q14*�K bar2ތAnswera+@Raczkowski's ques �cK?rg9LY�ˁg�_Top. A�i, 1�d�K�X 89-1G/,bibitem{beigLP�X glb\"ock:I�Y��z*.t �S�8~B!a iiro1} A>\'%$-M. Deshou< �cV. T.��os:�8`�xi�.I �� !�su1�,in $\R / \Z$)�SA�aE� �4., 38��� 97-1�&.� �|2�Str,�in�:uy=wOdiophan�6�,I0P um��+y, 99G��405-41�(.�3=_�$�-�t�29%oI:�L�>)� I.:�prk� ]�!�Bx4�x xy� ~w dik1^Qy�;*"hply tom  el�u(t& �,a2� f., 26%k1-�2, 505-50H1p dik26��. �i 5onolo: A%�N�1 n1�L almo�?�*dic>{FJ.�Ui�?:�lC^AHeaC�3>�I. 9 Prod�aJ$L. N. Stoy2HsGroups.� IQ�*u�4� BMi *1NieL ��\ De=�e�ew �J? Base' �J�� dik4>�K. KunenB�Su�M� Aױ��s�H��B�eli)m$ Elia\v{s}/ve�(forO^v1trigon� tha�e4 !`c. Am�kSoAWM`No.10E_��3241-324�K1�0hew} E. Hewit(3K. yW: A�e� harmTf%���R�L 1,"M@Xlag�B - H^tX -&9rG1962� kuip}S Kui-r%�(H. Niederre�-:��q 2�zqof�3�* WiXL-,.�  �QC2g win}A�,Winkler: Erge$%� RoCs9rt�S��A�KroneckeA. S�`$s, Monatsh-��,5 �b)3 4! VC8�m bake�\sc@�9I.}*yWa"�`domai~Z�!^��re&�.���� London��Av 49\/�8$56�76.g�inf2;^�Inf�J limitO$ƣ%�!:.�  ,.%. 8�� 550�)q�kotuslu3>�~N�8�A�, L\"uK?.lIte�3� .: "n iiiIQe��d�knFpB� �11 �66�6{ &[ .���j� v: C�c�\-��B@ResultsM;22�,2), 651--65626ock�ock, H2j \"{U�\ das {)x�$verhalten}9�er {Funk!�G {Juli2<gG7&�E� DissP7, Aach5)� 0tr\"{a}ge zur�9 k 23�8).�conwa}aC AI.;s�tǁ�on�&,[  1}.Z� ��[#Q�d/eykeewD ,�9LM�K�[L2�m8�.�dq: Mjqz&@n�iwarzia<0�a?$.���" "&)#. 4-789 wH2� elfv� �E , G2�U�{K me}> {Riemanns!� Fl\"%�} �Ihn7{U�hrmisi�I2h �<�� fenn. Q�342�eN �r ko���9yubich�.-xal�y���ome�m�Xene:fj%fIns�@our�54�eo8wY1012d gold�]2G �'~&��J3Am�n|�a �1�{!�F� us"� %D193� 278--26 po en�P>+�Mal"� 2�VPnhoeck@ Rupr�GGŇtting�E1972Jrel�Ree!2��D�)�map�fno`zBM�dZ. 191 R4- 59�98.Zrippo0llard-�R,�+J��St "d ~6�"k �+a�  *l��Q3 ȉE1���32 3252� schuu �S v% Ma\s�Fatoume� 2jA�r2. BtDJ�32�barto� Skoru�e, B2�Non-ef\ !E�-�PA~{ yBIndag)2emZ S. 14 (1)%�2�x, 1164urbanski:zduni�U � �Z� .i����� y� non-]I��!�B�����N� �n#(}��BK~ea N.~B�ra�~Keny�.$E.~Mossel}�*Y$�r�i ``Gls{r�t�Ge�r�| ,'' "Hh){.q�BRSSZM��.lenJ.~Ruiz��H.�Xonm�t(S.~Shlosman�0V.~Zagrebnov}�Rigidit%xA2�A3 ��� a Cay tree,'' �jMpi�6( cal 4jal\/}��|a3W36� BRZ}%�10[Y�B � 1--82) EKPSI�W.~EvanQB�d�P�cL���kx�Broadca�?� �dA�]�U�7�,AX�ed�@ba�3y���P ,)�10--432� FoSchSiM*R.~Font!�R���j V.~SCiavicio�y(``Stretched2�";A�stoch�F{I}y� s at� �]erH.�O��!����:��2�-U�95--56�Georgii�} H.-O%a�o� ��efn?qn�ߩ9de Gr�M�i#YJs�a9}, Wy3 \& Co., *҇2�Ke�(�t�>~ �S5C�'Rute}(muQ��9U4�AWRoyA� SocietE?B�"47�"85)I�379--392� JS99-XJ.~Jon�']2 J.; teif� AmenM� � >hA*�N�Å�e��PrJ�r$6 a�5�+552�Ioffe �D.~ !gBt�q�extref�dd)der;BtҤLe�t��3)�.\��E,"Y�2N�Eֻ�� ��UEP-�in Bs4�s1��[�L ��[yo�o ``Pha�C�i���n�2E.l,�aph�J.ao.��mm4��%"09�(127�2wLedoux �M.~ �q concenr�"�4 phenomenon,''��>� �!ovidenc 9I,}��9 L�g T.~LiggetT\``-�� ng pL�isI<,''��$I,2�82�Li2��:g�=�$r i�c�>ct�;�Pa�exclu�-pro!)e�)��}�!�9)=�A ��F+ . 'Bn  Tz�]��{C���.>���^��0s (Saint-Flou"�-,2I_^�171�yAaJ191, >x6bMaSiW�c2�Q ~Sinclair�`��Weitz��1"u on T: Bouzy@dm4!�MixAGTim�A �BAm3 250}e$4 301--33a�U� ‘]��Fast m �!��p�Yn.q�;� � �1r-��s�j �. ExtHd a�!�*ed^itA>o�15dh ACM-SIAM "gnn�^h32*^�5)"4�F46~MPR宂RI�>D flowt��r� -�1R,3� 817--846��6�,}� �Z:  ?Z�+ it G�v h}s�3��U p�B�$IMACS S1G �$th� ST`ut� �63�>>P�M�V0Q�1170._ �Ts �o �.� i9ab&� climb��.Up&Y �ad5o(RW�+�4 R NoF^IW1�S280&I$�J& 99. �SSalofB"L.~ -Cost�y`2X� Ma��'i� Io �ek��F�6)}, ER?I 166<��>�e413, V@7�f�ScSmR2�3.(� Wulff dro37�V� metastaM rela�G���r �d�ve�^<19��19�x�F 462.�T98��b�N.`Nanaka�LpLof i�5�T in f|JmagFB@ X�ram�rHA �:�)I�2�J26`Spitz"T%F.~!kMUrandom �EKeef�$ax"@ �}����( �3/N36RCDN-TF.~Cam_B,E.~De Santis]C.M~New?�CQIrE�YEtw6w��-*�*�I*ɥZ�. �"�Fj,���56�+dY4CN>bsc�ȅ��2�� ``A�L�."y�u��%�a+hexagoKl[�I�D2LA�}8O_$(Mambucaba�k:. 5 5�51 l*P�2E167 Xh9H1�C.�K�V= C.M..�� {Ko��*[ %��;hefJ�+a�:�#g-�1-2��P2.�HM���V�WE��72� " ���omo� l~aw!o�m gree thre5�J�0!�ba]�37!�No. 3�p5��736--74�2R�Bv�=�Ati} MW[tiyah�kit K-���Benjamin6 6��4BL97} H�2umg\"art�(F. Lled\'o:g%�5��:�ze�/\sC&s�-s X Nontriv�oCe�=��it�Kb�� bf h7) 785-86j$BL? r�An�}X!�!�Dop�er-Ro�s D'.�=���-GrO.�E���5� Ca.<�B��>�in� z"1��63?��-��ntu TO�orc !bz/�0t�i�sRY�%itu�w*�1U3jK� 1-10.LBL�OrS1+Xg(p�1� Hi�-t C*- For"�A8[Y:er/t.aT!'�N ol. U�aH�2 4) 759-81�]�la\�Llcard: D\'*Ɨ{-� \'ebA�de Ho"� Bull;mz F�V A�1z? 6) 141-21:.�m$Coh59} %P.�mh�/Fa�Zi�3inIT1�sm &I: J7P 2?59)* -205+n�Cun77} kuntz: S~e �A!s Gj*aH>y I( triei2 ind�B�57� 77) 173-1/�Dix�Dixmi�.E�C*-��A�North-HnndD/is�Yigny, Am�Edam�/ o1.�7��vPZ��S.y�,<7PinzaV7R. Zucc|: ��-�!A�aQ� bimoduK�BoAtDT UMI}� ie VIII�  B� 98) 263-2�2DR86} %6�J.&1�l�dM�|�#&1�T�cI&��1MM.%*�Y!al�?s� E�6I@86) 67-�12�EDR87}:Cn�a���Li��R%z.�PE���T�E=TA|!Z [U 2�1��io}��m���9� 8�"57-218.��Av6�of%���, ���duc � R�&� ��v1�w1�75�6�U�n=WhJre�#a2 ��TՑaug�(oup describ���su2�st}{��"B"���,.�� M13I90) 5�J��.Dup} %M�� Dup�>���,i"y���6�"Fm�Memoi\B�%� ican�M#l� �2�p�N21��z�%:� up74�J�C!ify!>���D I++N�, 1/�74) 244-�S2EH}�$G. Effros,c Hahn: Lo21���5o*k�RY�:r , 75�xef:B�!867)2�"Exe�CRRel��6 Look��zeEed-�8uc� a.�ɣ�w*a ,-A8��3 temso" 1733-175� 2y4HK} %K.H HofmaN7 K. K+dl: Shea�Fjg��X"�,:5�E��A�Banach %�,C(X)-�Os,H�z ;xv�N� %7�z!J�&8>%9! :�Hir# %I. Hirsh�0:F�S�C{KTrace.�qo% arXiv %+ OA/011229�Z �*� Kar}�rKaroubiF� � �)�b9)��2�KPW8(%T. Kajiwar�F.& 4Y. Watatani: I�M&� %�F ;_@he %\.� g.P �F 1$J�.>�15� (8) %295-322�{>�%��������?y�%�-%Kri�@�?��*�V4wM:  R�3}��J��Indexq��Zf��8%;vX+ce��Conjug�T��<� 9�. g� %Izv�Cja 15(1)��80) 87-1X%�Mita�P��M�g�:�I$K$m� Spe���!�&c�5 �*- 24}(2)�/ � �9wNil�M�=lsPX1���$C_0(X)$�Indiana~.M|��4��463-4S.� NT�%Vm store5$ Troitsky:I�xe�_ -��t f7a�A�a -Douady %,,�[n�1MS. 35�A�<185� .�PasAW.[Hchk? W� !sW,RWe-.:F�r+ -�831E'113-9�Pima"M�kmsn A< �!�Q��li�Cbo�Muntz->�%K��= by $\bZ$MPin"�ee N#m�}, �D��ic) �Fpl �8Nm��$a� 89-2a.�RA���a��I. Rae?p:s5hee�6�-�qR@( RIMS KyotoE�ers`L �3 ��� 15-4�$.�PT00} %HA!rk� (Trout: Repr�e�$Eu��dJ9��*W%AY2�A177e��178-27+2�WY�-Zqa Yone~KMSx 1)EVp�SV�{��{,ri,�� FullEO�� y E�^� 213.n331-379�|"L PR84�Pq9i�.�E�.*A�sA�l� unitX]a�f�*� p �alU M�=s��Q�)��08I 15-2�^�Rob�E.[ W..� Manuscrip0%a�:� Sta93} �Stacey�?!�^u�Q��*-.� zustral�{�<eu A �5�93) 204mc.�SW7A�R.+a Wilde : F�Son� �Bo�Ye�- Nucl�MR�B %�7� 61-5a4.�Vas�Vy lli:�i`FAri�+fP�Ec#�%(TensorE�&> �]}xqw-319: �2Ә1522�Vas02~�,B�D��2N�:�PhDA��UdqImp�8ee*�c2�Wż� d1bI.� 16(� 5); F�2:�)�a:�a*�i2��[ fɌ��*�I�J2� ,]�dx.doi.��410.1016/j.jfa.Y$.09.0gK2�Zi� P.A. Zito�Div�+L�f-s!y.WalA�< Wald� Morita� G�$of FedosovO$r9� �� ed H�tO-%�,�*Lq� � bf 6��?� 12%6�Wor>%S.L.e�,onowicz: Tan�"-�nq]�p.Matrix P��E"s. Twis�(%$SU(N)%$-% �itRI 1�7) 35-)G��N�5jH 9} uAZ}8 D�^J,ndk� Zafrullah�d"�( �-�bA�'f� Hou�YAx� {!} 2c�d, 433-45#&+� {Ba}�IBas1 5ubiquYof *ӡ!)}, f Z. k82�6�8-2�.fS}��Bazzon%iL. Sal�,kWare[ DI�� "m��0bf� h�. 836-868. !t5sB2.l-^DEX8aForum � %1� 20� 397-41�&�DHL%�E0bbs� G.1�, TLuc� F�git�R7�ed\%T.L Pr\"ufer $v$-multip� d5 � 5�!�/�E2835-28!�2��N�� ]�r��:�l� ]�4 !�AMS�0��uH37-642� yH elb1%�$El Baghdad1�On.�;9B JD=E)C� I�T��8, 3723-3742. 6Cfhp} a��4ana( Hucku$!�IA pi IE� Pr \";{u}!� 9�"\ITextbook!G�ON �edE��s^03; bO.�,�7!c]�Fo}�M�ss6k���a[F�i K���*(�-W1973.2_gabi�Gab� !�it!�Na�'sto�Y: � � ��!yII���n�*��%app "0l. 206��2qP 29Z(�Z-1!�.GHI] �eEaɭW �Co٪ -like cG�Y %� pull�u��MichigI4�a�W���� 9-12:?GHE�z�l� 6{�=Noe��A�f� ve RzOE&-2�2 � }%, 520,�pFZY�.R�0:�1} Ab Gilm~"E_M��ve�ba \}�mR!� � �7ap2�V)laz%�W� #3l�j Flat `s, IA��u� ]`)��(1�!,�?-347},GrWGriff�%P r&D;JX��A��� L"���\(1�, 710-7�.�HK}� H�7-Ko�J)��#C037 � to .$:b�P���H�^11f^:�H}!�J�Rinz5�O4g�g��A�0which each �?�( g is��i�Mat��k��1��6(, 164-O 2,HH}�R�dlI�%E.6�-�"�o star-~��v��.6,11 ��37-44:�o�SG*E�On��mm%z�-Hv���+< 55-62�� �PHZ:�E!M.J� B�l|!� )� %� $t$-Z�V3)�8!� 291-3�N2�J�U Jaff�Les1RLt\`{e}mes d'Id\'{e}a}� unoda�rie�197��� K} B�� Kang��9nJ�-l% �� a�0 $R[X]_{N_v}$)�2D12�� 1� �2�KP} R> Kwg�Y�PuQ(!X���{!�ChineseA�_ v «�.17-24:N� N�Jel Abidi3�n"��s�!a��rx�$ anneauxa� nt\`�+s�k id\'"X \'�B Th\`�de Do�'at, L�B199:� Ma1E� Matl!��Reflex��-�6l���-3:EMaFOToZ-free܆�f "|y� Chicago !t-LfUR�M2 [MimouniM`TW- �EF2\�6� �e� �gE� � �, 79-93m�"� OA� O**d �%@G]{Ny *�P Y�& AX2�20i�k 480-50��y[O2R�S���"2-&D)��)a Y��XalP�".�f,MW(!� Rend�B$.%�l dov51,AW , 261-290�s91P}�ZPopӼ%/bF -�W�aS"X�aT6%��"� 2� yW777-7868�Qť Quer�$!�it Sur l�?ilrif{CanD s��v� XXV9� n. 6_7e�222-12>�FM}tXg Fanggu� RtMcCaslan�On $w$-�)s�~ V�] U� �M1� 1285-13�=Fa/W����Z{R] ��gg 9tH55-165��Z� *�EPu�*g�|inverti�Bm usR��/�` 42ɖ8� A'E"^ Kl���` R��bɒA�,�=Ba}�� BaadM/�S����G � an n~`c�}k knotAOsaka��1�x$\bf{42}$�5)ag,8-�^skip 6�O �$M.~Boileau� ~Orevkov: �Quasi-pF�l�\'e d'uzWurb��Mque^ Fg b�E��-c9cx!�C*U ~Aca�>ci�3"(g.~)g J�33�1)�P0~9, 825-830. -\�1sH1sK.~Hac�W�-� 6��rTokyoE�41CBF2b1D Y.~Ohyama17Web"�7%�*�����9UvOu�v�gby 5� J.~K�M) Ram"\)s~5 9}$ F�l ,no.~5, 693-7| 21#OTYM��~Tani�EYamad�&-���unA��II�"QA�)o �ath�25.�2-�1,M 31.� .�:�F�$T.~Tsukamo�itOn I's5n�fv��dj�of I $nr ��8�1}D!�2M*-26R�2�Ru1 �LLdolphQfC�O�+& �qa�m�e)hE~�٨�{ AV s, bN� "�ula�\@es (Plans-sur-Bexi 8!�2��45� �EnseignvU�31}$,�YYU({'1UUr�Ru2b� .�n�clo� �}, �!W �2�V��V!�91 ,ZVSt �A.~Sto%ow1�u�"��t �J`al-�of}m }!�����AC1,�/=R��j� KSMJ�'"� �[AFP00]{AFP:BV} Luigi Ambrosio, Nicola Fusco,%gDie� a+Ra,mX�E�b�BeAh��A�:� �C�*�j>l$o,!3��s� &�?+ Cl߂ouFess6*B ��2��O8. \MR{MR1857292ˍa:4900k�[AT%--T!�} L.~�M�1SC8e��7"NY�`&����("}, appuntic�izi�Scu!m'u,ale Superior his����@tk75]{atkin75} C.�A�!4,{H}opf-{R}in���Am� fals�"i�=dA���EBF6x %�S6G� �=A�3� -�-r(0400283 (53#4118)}]�BCSܛo�pSh�XD �ońSgern�Z.���JX���^ -{F}insle�`g�9"����99 �$o��[Bre86]�zisB:~Br 1V� isi fun!�ala�,Liguori Edit%�Nap �(1986, (ital `��<1e��Tyse fongalVMayw�83a�;�$ut89]{butt�89:sem��� �Su},.�@� Hg/n+l%e�/��"pofy�}, Sft��L techl�_ 207,ABgp�13*)3 [CFK03]{F�2ras:AsGPrpi�O.~IR.~Ke��Y�>�l��e�mu�C���/M #wgng! empiC1l s�=ic�NINRIA !ort 48�.�TDac82]{dacorogna:weak}�Mnard D1� Weak�0�#��3 lo�n%�5� ai���fuQ*�Lece�R�0�922�H�/*F�7UT4EE70]{EellsElw�8y�%~�K��$Open embed%�"N�B}j1��.��nn.AN . E"�Z[-�v65--485�T$263120 (41�T 77252T$Eke78]{ekeW 78:hopf_r��} Ivar E �n'��B�  D.�� W��G197d�2, t�3� 5kFom90]{f -p��au} A.T:!-2�P} #�;t"ra�develop�tE3modernE$�Zs,s !BrF�b��Gro99]{�� :met} M.~ �M�;c&�57?���A�A�.�:�A�2 KliaRPWK:RieGeo} Wilhelm KlP[3�.c {G}��W. �Q�2a 1:�! ]{S�#stava:�� } E4wKlE'n��uj (�Q <t ji. Sop anu Joshir.�ie$planar�us u� ��des��athE&��?�K2{Lan!��a :FDG��rge�a1FundaAa ;d.��#� F�0Men]{ACM:AsymA�4~C.~G. Mennucc" �syU/�la�},"Y% verb+m�8cvgmt.sns.it/pa�8/and04/+.b MM]{�or-Mumfo�\Pek�Wb0chom�David #12  �)�%Wi.!�e�vv� �front.r .ucdavis.��?� 31232@;[Mum]{ �:G�X}� � Slid�fe�g' l��� �0www.dam.brown{pe�H/m)/P)3i .pdf.5Sha49]{A�0non:TheMatThe2 E.E�n [M��+"/��2�&� he���Val:�] -�uD,.� $of Illinoi /�192�o([Sim83]{sim���J 15��eu�ic {M}emceҴ��� oc. �C� �L�"�*�$� A�+��N�al�緁vraA�H.k7��dissipajS Boltz�, Qס3 �Fl methodE�2�xM25co*B� M9 -� h-e��dDeg��L�zRusso E!$B�L=�, ��-U ��2-Fu a�G.^��]},M�I��-ers 17 (N255/ �.H� T} %=�%me`` ��.Q���ea��V.''�u chefra �r��0 &42 (1-2) � 179 - 1��Z�un j�0}.�Radٝ�NR.~Adand�Roich�O�g!dFla��jor Inw<,G'CAD"Po��'W Europ�*���&�43��4I5�b���M ��AntIPY.B�DesJ*�6�/�M�'vte�UNU�ZMk��to�euza�?:� CO�?0i���O } % 0PFt~��aN. A��sIQM. Haim�G. TeKU0emLLakc DiapR=f"Ex�WP� R�!.KbA�EW�� %142�4pC3�X/!9� � _lam�J�E4�%_�M #gn�{��De�:os:*a5�o�AE9$S_n$L2 Co"�: S�"\ti%,$}, Lascoux-�S-�, S\'0!LothaN�,bin., [B52e]mH�{bc� �R.]� giolIa�Rs�+-� IE9")�Mqice�P<ssX Weyli)Ak"9{F�!� 8� 2 .Ah6�`y CLO}�.s�ZCox�c~Litt�JA�D.~O'0C�d}�,F etie�&��}2 der"�p<) 26�"��*Yor��997.UgaA� _ges�g�dA-RG� I.~G \em���+on*,^Geʡ�d�=��bf MG(79), 288--3�L�#1�g�k-�yI�� ce ${P}$- M ��*B skew!��jr"��Aq�=� !�C�  �G��e��-~34A�DDe;�ry.z y�MSa�k# 28b17@a��ordbe�I.~�Q�2quoti\r byMe�u�I.;�!2�%5�'�,w 03-5CJ�h��hilb}������--,E�� 9U%B�B�),�, UCDM� 2: C�^x�>�!�Hon�:fr Schmid \&P�usztig,�+rn�>J< ess ��s �D3)¬�@�umphreys5��sc �AH!Bem�'���E �Cox` ��a���i"zN��X bf 2�d6*K�z2.�ovvm�R'���iR�%B����MS-6�R,;J5, �>,!�1.��Y�6q�FU��o� em \'Etud#e��Qz\^o�/�N� �Q^�ralis\�)���"QAM�.U{macdad�Ilj �SyQ�&�a�w� & !�n�2V�5,�ond ed��a�YUMDr�mi6=��wreath ��K *�'���w�-�]�"�Q-2�9 .0 stanley�R� F8���)F�Z]�t�O=iVUto6�ZB� SU,(new series) �7�� 47�Y12W>���A�sc �ei  �en al*�� u����f6���3�bB ��Б!^6��392--4] =�Stemb��,J!\em���� eigenvalu�f%r&A%zN)i� �ZPacI)�'!��40�?625�bOfr �'Y��HXu��V.F.R.�HA�F. Xu�uer+��  fa{.i� subfacA�.�(�1��s ׁ���)[  717-7J-�Skau} C)@ :Q�sub"�Do9�vono��F T�J2 =5@%* UG�23�)yt�"lasQ(Str\u{a}til:_,aT'�Min"9F� s.} Abacu"�(Tunbridge W^, K��!�1 �T��aki72}   M.�@��ax�G��N! Ne21�V9e72) 30��2e�NoR fS10}�,inp-Andr02}  uskiR�4sch,~N.: AboutQF"Sal {H�!9>*z�\Btxin�n {.}\� QuNYke%t�eti#�QA�ztq ( (Bariloche�p0't, \btx�m�r k 294 �2 txof��:�% ��{Hpal �o�1--57z�M"a2)=Ba%@ SchnNJD`and^-a�0r,~H.-J.: Lif�( of q)( ���a�po�d>|7�' p^3$.�Dlmb&�� 209}��8--69�R98V��F���� حQ�nd �ta�r� .�&� J�15�b --45%�0.�Q�!gZ���PVm2�N�� {D}i�� �\i-{A})�sAyM�6�~43�Z� MSRIb9IA�C� B# % 2�4b-BourLie4-6}  bakii�ur�3alg{\`e}�[{L}ie,��,4, 5�3ǁ.({\'E}l{\'e}�g �?queo7QN#$�S62xb-Clif' 61}  ford,~A.HJ�($ton,~G.B.: �r�u���fy a �"��!�%l:�7^���Csu��K.>} P*fmhode IF1�1.�a-Heck0rD el �+8I.: Finite dime�nsional rank 2 {N}ichols algebras of diag&�m type. I: Examples. \newblock Preprint math.QA/0402350 \bibitem{a-Heck04b} Heckenberger,~I.: Finite dimensir��@I: Classification~�4008 F�c}J�pThe {W}eyl--{B}randt groupoid!(aF@ of 1A)?v211477J�dN�LWeyl equivalence for�4~�6212�Khar99} lchenko,~V.: A quantum analog!t!10P}oincar{\'e}%98irkhoff--{W}ittAVheorem.�AI�$ and Logic.x\textbf{38}(4), 259--276 (1999)2� Rosso98}  ,~M.: Q �%�sd�shuff:�,Invent. MathN�0133}, 399--41 �8�xend{thebibliography} � \beginB{!Y %\m-�[Bo01]{Bo3} N. Borne, %{\it Modules galoisiens sur �courbes: %une introduciton,} %S\'em. et Congr\`es, SMF \underline{5}(2001)147-159. %Available on the web at %\newline %\verb+http://www.dm.unibo.it/~b�/+9�([GAP]{GAP} aXGAP~GaK,5�GAP -- s,Aorithms,%�� DIhara-Selberg zeta"< Ata tree l�,=6Intern��E� 3} 9� (2) 717--797�FZ]{FZ� Foat D. Zeier9�]combin\ i\ roof��'s evalukm 2�5c6�R� 2�a5 sF* �5�49) 2257--2274�LW]{LWuW�HZ. Wa�i� ͯ Walk�2�, Colo�I�P�UD��2� Z!�F� =�U� 1998>�12039}.��FRT]{FRT�� Fade� ,N. Reshetikh,L. Takhtadji�%��iz5�Li"��%.!Le�rade  Jour�1� $0), 193-22�N� �f� �L {ahlfors� V. A  �. SO : �.D surfaces.} Prince���,$, New Jers� 1960�A({zeghib} T. botvAa w Q�$on Lorentz4 ath� 0al aspects: a�8vey.} "50 yea��CauchyG lem", edi��by P.�|usciej� drich,���8.% � paraitre*� {� Sim}Bartnik�!Q imon � S�$like hyper1Y withA�� b��oundary a�e)� meanMature.}�nm.E..� H., Vol. 87 (1982/83A831-152.�miguel�V�eAis S�nchez � On smooth1?2��4Geroch's split��!o�.} F� 243��4no. 3, 461--472* calabi} EP �����ste\!ځ� slnonBar&a�� Symp. Pur3, %;15,7aq223-236�h-dr-goi  e( T. Drumm.,� Gold0M.� rill ��"4te flat affin�'M�ia�nifoldaq %Spec��$volume ded�edA�A� memo�LHanna Miriam Sandler� 60--G. �. D E a 975�187-198.)g-yau�Y�eng%�S.�Yau � Ma� li�-A� 6.i �$-Minkowski 2�O .!�a�. (2)M�104�476), 407-419. &{isabA� I. FA�ndU�Con�u of m��� e{iso� Julariti�I�ea�A.f-l-s}s\'{a}w, F$L\'{o}pez %/R  uam:�{���lAembeddedZ� V�1Z3-d" 7al^h $\l^3$���(. ArXiV e-p arch�r D�1330 2s )-!0ly��*!m�M! 5 [ �odic Z1 15�1Zo-��e�. %vf41219>gold-marR2�G.��Margulisi& Flat� 3-mq�E$coA act Fuchs� K��Conte��i262, >�� ovid�r35-145. .�grigor�G 'yaѤAnalyd�g"P back�nd `recur�( non-exploA}!Ɓ�Brown�moa=��R��R� 3�99�� 5-24a�"� circ!�0domains} Z.-X�ir O. SchQ)}$ Fixed poinKoebe u�jrm� �Xleing%}An:� 137��9��2, 369-42"{hube)gH ��Vubharmon*�Idif�tial -yQ� larg��e"� |v., 32Ž57%0-72� jorgemeek� J��� II�#u�t*oA��� minim��>ofe$total GausE��� p,�� 2!:� V22�9�kly-mik�c�lyachiTV.�Q iklyukov.-P��et���ur�tub; band3 zero:I !\:�.}!�a{!�a Scie!�rum Fen�;� , 28�K 239-27.%% kobayashi� K ��;1VŔcon+ � A�єJ� -Japanm+8;#V 4, 609-61.�{lɳ:�� կa>�B�ofq�%!D~i Michigan�of��w 4�v  4aG92�ma�E}RU&T N locallyc �g)Ua f�f_ aCal�d.}Soviet � 1�I aP 129-1�%(RI�) A"�&qi�numl=,, II. Zap. N� n. S�#"� . Otdel%�� Dst. Steklov. (LOMI�q %�190-205.{{e�-rose�'ŏ.�,RMyပdof�l>����>u 68!#�4, 538-5Z}�mes)�Mes� Q0 ,e�c� ant2@"�L Institut des Hautes� tum�fiq3 8.� ,marsden-tipl���!tE�iT -#Q�6� a& foli 6�6� a l D����  Rep. 6��8aa� 3, 1�32�4oneill} B. O'N �Semmi-ri�!�\1ԁ�"w!6$${osserman}a�O :� ASA> }. Dover ��)s,�,York, secondhiA 198.�{wolf@! Wolf q %O� > (McGraw-Hillj�67!��Eum-yabUme�%� K. Yamada nMR 2o!�FT�#Hokkaido�7�l�A�N�T#f�.P0{\sc AdRu}]{aKdem��!Y.~Ru� Vit Twi�"orbB $K$-��}\a�A��. � 237}a�3--556���bi�+ �Ba}]{bar� sky}� , 5*�O�cohom�as � cyclic�!}'( tt{arXiv:~ AG/020625U(N�Co�c�um, P-$A.~Connes:�Chern cA cter,( discrete �  A f\^{e}t� t , 16h :W>/(BFF�&bffls�yene~ 4o, C.~FronsdalQ8A.~LichnerowiczE� D.~Sg heimer: **DeforG)�-� I�u%�� %�~1�110}, v11# y151aI78JblGe!bl-ge:.f } Block)#I� E.~Getzle�@it > �5H�:�$XXth `�_al�feo on D*$ !�& Methode��e2�E���� CitA�ol.~1-2a!World�J@c (Singapore), 47�8� N�E��f'} Bord !��vit (Bi)� es, �",es et r\'edu��� gr-p�+i�l� sy�/ct��, feui�$ag Fob iona%�6XQ�/3334}e�4J�r!� yi:poisso�$ Brylinski!�L�A2� . xe]P <&� )�J.6�!�Y� 28},� 1, 93--11�N�rI�rg}>�B���The�v��� pseudo-.� !mb@1� ar�cx',ve residue},�o)v bf{1I.85--403 O FWrNi!nnZ� V.~Nistor�˩?�_of \'��alea��0!t��!e34s65�9NuWe�w:picarde�ursztynQ )dA.~Wei�M�P/ �e�Q �},\\ �6�Sq04048I�3F/CaGiW!1 giaquinto� Caldararu� A.~G� S.~Witx& poonUAic~-�Xs ari  from�OE �3 �'ionJO Appl�'m3 �A8�_4No.1-3, 51--70qz*��fCh��cr}��n�)j��� A new.�%r}, �6h�[0�9)h1Jho83}]{c�F�v�T!d]���ie��que�� !�b� h& 6_/�360a*85N+945+2�)�:���|0�:M(Sa�� ego)Ų2  C��craini!� �c�it z�Q$� "S$J01A� 319--362.!99J,rMo}00]{cm} � MM�(I.~MoerdijkY<A��M�����),J2 4Angew� ��bf{52�o2�n� 0^�1�2001} ��F� ��WtheirI�.�  Adv.~�&z 57}��~I'77��J~Do0a~dg:6�� } Dolgush�V.9�oG'�/arW'!Lmal%%]ems�+%/6307212�JwDo0A�dg:�V- s^�A F�QTO(�:�� Z� 4022�J�0DoEt}]{dolget:�+ P.~E�of5&$Hochschild.3of: ed��plY c����th! @ --t C��^� 1056-SJ�E��(eisenbud} E , D2^mR2veѮ. �� a V + Towa*0�ʙ_< Graduate Text�A���15 >�,(B3)=!{ 2Fe��fe:�,} Fedosov, B� A si!V��R*1r� of.|1�� %\/ .ع�4�21� �JbFe96}]� bookZ�.R 2� !�IndexI�)�Ak�.e-@/)%��.��� Fe00 �g-iKZ� On $G$-tr�5x1edeaj%F Co" Mosh\'e e!�49 (Dijon), Let�8& E��:} "v 2�89�J� Fe02��*ity6�х�+ � *��Halbo]0G� s (ed.),2�.�A�((Strasbourg�(1), de Gruy�Q�+ IRMA`&.e011, 67-8� R� SchTfstA��1ure�T]�aW.~Schul/,N.~Tarkh-> )孠��R��/�~.~FX'er, Gren� 9�� 5=601--163)�RTs%�its%�ig�$B.FB.~Tsyga*1 ddK+&%},!�Manin1�!wA�9�Eۑ�, LNM� 1289*�2, 9a&09l87F�� gn} w, E�Cartan_ topy!ZmulasA� and �-- �� zinF�E �um.�6"BVU*�7!IsraelMwa�>%oc&a 65--7��J�G� gro".}-%, A�P3�tensori/�� s� e� s nucls air0 M�AMS9�� 5J� Ka(kawasaki} K #&� xI�of ellipfope;5 N $V$&I�Nagoya-9J9084}, �-15�8JF K�@keller:derived} K, Bu�V!� 56� ��<6G KT/031022*)N9F�K%Ko:�� } Kontsevq&M&� .�.�!CS"�, �F��,bf{66} 157-2�>V�L�loday} L���Y �}� ��w2B�M!��5} M�5R�Av g2^ PhD�si�'\"uns���$aX�B�99062052�,< M�m� } � , ���s�"� : a\5?_��~ŪaV al.,C6�5EUpQ3 (MadiN>WIսA:�5+2�!� bf{3� 205�+2^�MoM�<�-mrcun6�8 J.~M5�I�s&&��L�*oij *�- Stud�-in ancede�>| 91%ICb'2 A�FRoP�pN�D.~Pron*i5�, sheav 5�i�KAjP'1c1�d  9J�)Z!5} %<.17! ,)-26�!9J! �9�99��: *�C0!>an�o%AdEX� &V337--370%grB��( Birkh\"a�< Bost�MA� 9FTPf}? pflaum} P~J����D�ic studvstratifiu,�6 768}"� �^&� a:#6� �3]{P2:���n!�.�BX"]�x� A�u%9} 343#B�R�y*� "� e/U�Rigidm+&E ->b�E �� (q-alg/96070� 1996F�S� satake} S: �C ]m�n�&f�����!t.��&i. U.S63� bf{4a6�4-36e�5N�h}]{shFoShoikheti !:i��.��9� � �co� � aD �179*eM�ZJ�Sp� paniT!S *� �T&!&Bi�� 9662�(�StW��s"� %# B��A. Wre��%G*) � +�(.�!�a"�&; � J.-P:� ~HomX "&6��e���& (BaltimD@MD�V8)N�):�)1�239!3251�d9F�0Ta}04a]{ta:th- } Tang, XE$)2�of>�T  �.}, UC�ke�9a�&� EJU�b�lemmaN�.� >�P��/�( �)�o"�%#u�3 �40537@N�e}]{tel�} T , N= MicroF&issdRl'� i�B *5 }�A#�m��S1 r. I��6�� 26� 2� 264 �9J��wei�.W , Ch=�AnB� A�loglm�AD*d �� 38:9*�3� FX�"xu} Xu�!V-�q3��Am.��&� 11!) 10�2&�RX#mfX# 99} .�&Guerra}  , F.E�3)�,ken� lica sym� �3m�C�%aC spA�H�9.�/�o:�3} K72aL�%(@-122�0SherK} ��$D., Kirkpa�*k,�14(1972) Solvabl�>a�a��" Rev. L  �35A�79�H2�{SGa�lagrand,�24 S�G�`#a�lleng�\!�� ilI :�2� T-gPViHL�|ediSi����Cezt2re��3]!oy11T *�{T-^�Fs2�%�g� ~}*�&T-MZ�� A=GCof �i's�*Xal 9"rl6meter. l�� 9, 625-622�3T-PI&TB�4)� meas��. "#2 a9N�&Vrq&� BCDT]{ EBr�"���rade�DiamoAm6 $R. Taylor,)i19: �3H "Iq.;(Hver $\mq$: wild 3-a>2exercish �dA:c 1��), E+ 4, 8� 9�)"g Q<A. Brum~%��averag�Ak!�:�.� �MŮ��9��2x3, 44��/xCS]{CS1)B)4e� N. Snaith-'� i�)���L-Hs x os* ��p�int*�;FI]{FIq�BdlW5r%�$H. Iwaniec t�&]>$ $X\sp 2+Y4$ cap  its pgDti: . (2)!�8)" %� 3, 9! 1040�|AGRy4S.�shtey�+I.��Ryzhik��!of�*$egrals, Se[>1ct�*���HrR>New/&� �Jb)GZ]{GZ�+ Gros�=agiU�Nna�x2%?Sa�B%�$L$-s�}.B8A�;+Q2,{= --32.Ha]{Ha} 19(Halberstadt �Sig$G�uxZ&SRQ�2- en 2��R�i! j� 326:�IH047--10u:5, H-B1]{H-B�>R�2 ath-$4 �AEqCa�V.1i�},&�A J., 1�1f#91-62. @ H-B2�2f�PE�����; y $xA� 3+2y$W#Act��@ ��>��-8.?He!1�@Helfgot1���behavior�root I0rfam:GE3:Z},.�LarxivS /abs�O$NT/0408141}CHe! 2N�!�p�dyIl�r�(ijcub�0orm�}2}IK]{IK|�KeE3wald(�Z"INT1I x��ica:Bnal3 ietyB@loquiumqL��, Kb;5vF7R�<4. xii+615 pp. U�IS1]{IS)�.�PL?na��DiO>lete�at�� cent?R�'A^ ��6pU���*F50Zakopane-Ko\'�> isko��97)�71--952, & ,� l�?. y�IS2�In�A�7vanish���>of*�Mc>� nd L�u-Siegel�5AH$J.Q w30iX1 ,A�t �55--17.^C Kn]{Knapp�8 �YEmC�O}!�.�@er��ADP , NJ%M$2. xvi+427%�5�0Ko]{Kolyvagin�6�J�/he>dell-Wei_@ShafalR ch-T�!��T%>� "s4 Izv.� buk SSSR��%1. 5�8�=� �Q154C+8�- 327;�nsl�ii>. USSR-]3�8u9C�73--499}� KM1]{KM1}.�e�P.?hel-|!B�($J\sb 0(q)$5�7��a*R5�u'aD2�G 10AA�����I52jKM2�2��A lower� f a~Ղ�},��� . 9�20I�!6 4, 3�34.KM3�3��Exzit uppB�(1P)Z� kZGpamD7d[0.� KMVd�P2�,.�a� J. V Kam-�Non6 high>�b�. e�� c�8��stripAJ�B( 5�-��,.� M]{MN"r4.C  �OneZW two-level�"��(re.aln�: e�53��ly�#e�[Hi�  Bose�h. 14,,QB952--9K�rPP]{PP��Per�(1� Pomyka\l �Z it A� eWt41v:\ �M�80X�BA�149F"�R]{R}� Rohrl��Vx(�!*��nr�c8�MM5�D�3-��*15.�Si1]{Si1� SilverP ����~"ofJ:�,2� �65�Si2k2Rk�d�.Q�B�~�+~o]{S}�6S F araj�H%{Non2� quadA�cn{$$s=\frac12��R� 52��M4� 4�M�TW]{TW}� �E��i�2� Ringb $pr"eh$of certain6�N��d>*1{ �$���5�6280T]{Titchmarsh! C. ](l A�@ zetaՉ}, Se.�8. EIH�w�GaM0I\HD�H&� .�Clare�LdOxford\6�.} 86. x+4126�W�M:jO`�F�8 �Fa!t's las~ ore��f452�Y1]{Yq9Youu%� Low-���r��� ��>,�Qted�5 Sept D r 7,X5, PII S0894-0347(05)005 ("b]a�p�)��Y2]{Y2N� er-O^U Ter2UP1-L�Den. of Fa&� Fd j� Res.�N.�;(A�587-63�WNZ�fZACGHM}&oD[Ba]{Ba} Bayer D.:XZ�� Divi�2 alyRth�cdA� HyNt�T}, :HB82) Harv[,U�"�!*9([BeI]{BeI} &�I� Iarrobino�&�ZA7 un� w?a�FG�K�I Arti�:3�'od�F fiva5PQ"� N0} \# 8�JH232�!3362�o}cj1} Boijh% �{G}� {A}.�i3p� �&�[A_��DF�P�3 &� �?1�P6�2]{Bj2� �' nent��h;\� riz`!N v��� given {H}-�e }, Z�R8�R�E�U 6�3�3F�Betti�� ataa>ˡ�9� th�AY 2���.�K [BoL�L�, Lak�.yNoU�j yOedu6� s}, #c�GM�4%�1Ay!�v108�80� �hBrH]{BH} Bruns W. , Herzog /"i4Cohen-Macaulay�%�ur*� "fM"OsA� 39, 2�6JN, U.K��993; �1Tpaper�G O�?2L [BuEaAEaA�H baume��0=cWhaMTkf%"Zexact},kC6�5}!G7� �g6.�yaER;y ,.zu2[s"��  cD �9olu� some2A�� :]� E�Aɨ"c E99 �7,<# 2`ChoJ]{CJ} Cho Y.~H., Jung11I D���y tangent)C$\Gor(T)� ���B inarH Queen's.P(XII (Kingst�$ON�$ ( P!���O�F;�bf 11p+3A`�.Wa X@02CoV]{CV}�b ca A�Ealla Gիь����p� Waof� =�},e .iT23� �� 4, 7 7�y�4Di]{D} DieselAy�SA ir�i�!!ً' eI � �height 3�H�u��a�PVX72E696), 36�2�F [Ei]{Ei} .��"4�.��$_t4 ic"SJ}5F4.�M 150,F �2% New C?!�6c!@GMR]{GMR} Geramit!�V: !�roscia Pa� Roberts]A�>!Xaa�du@*$k$�%!S}0 Fv(2)� bf 2"S:S��YGGotz} �?�EfBe�ea�$f\"{u}r di_3 chhe�nd das � �s�Vuierten�����E��315 �78), A��2<.]TGH]{GH} Griffiths Ph.,� ris]���Fe3J�, John � > Sons&�!�:BHar[ri2} qima T�m'e� �ianN�!�}����s;rS�r)��-�13�a� 45--56.He�d�e�X , Tr!� N.~VJjOn�Gplane s�1� e�ed� le variet �|.� �)�Kyoto� %�]A1Y?�1AB-6�M[I]{I} R/ nce�?��vector� ���>m� -�nJ&�>27.�530-582^� �O, Kanev �EɜP�� Sut.� � �J D� ��n^K LociA(45+xxvii p.AeCZx�5ANot�+ !R�� 1721��A id�[. IKlTl.O�j Klei�US�7�iq�� ���� m�" A��ax C� . 28=12�4A.98JV�bnev, �0 F0,� 9), b#Eu�# [Klp]{Kli !ppe�E~O2�Wne�!���QPGOR(H)%0q*UA< *� p�[�jBLJ. M0�E 3 606-:�"[KuMi]{2} KusA�;� M"� "�b��/�a&"n�  four ]�S}�.ans"� 2�AAY), 28�*07.h4Lee]{Lee} Lee,Ww5i"AY6�e�}in�"athbb P^Fhonors B,t�), 54p. "{ni� F� Mac1]{} "> F.�!6�-ric1 ! LH#Bf}, "" ���9 ~(1916); 4"edsforew�bV[��,B2Y ��awNd!\:P Mac2�2j�� 6Nen�#��� 7$ �'u s@g� ����W c. {�b27)>1!K2� M�"Mar} �U�� �ELresul���gseff ]'{P}^{n}� Open� I&ic*�0VIII,�i onf. 4Ravello, (C. C�o,A) Ghio�r!�(F. Orecchia]s.)B�-\# 997��: =N 1�K� p�990--31.|' [MiN�N} Mikm�� , NaU5IR � ��Q}�Tg and t>ic9[� topesE� m�M.�AY )�1 {4�.--62�4No]{No} n:pJd0n@�GZV�P`. Ecole Norm Sup. $4^e$ s�9$rie, t. 30%R97) 36��6� 0PS]{PS} Piene�,Wles�Fer*�O�>�z_"�fof� s�6K "�merS�Sath��8�7� $b&v �d �inley R5�182��d� s}.�*.K � J  57--82� Va]{Va} V�0e�^r�p��&� ���IP� ��"�+Bi_S�Br�k+. 1�;2T� 81--89�?N�3z>)55{BCu~BankwitN H.G.f>� Gt$$\ddot{U}$�T0ViergeflechteApbh�h�.�T�`Gmburg �.10�32 26L2h {Ber2U~B_{���kij=Rg�& y�p�l�xpNb}, unp p�\nu�`p.�m0{BingM} R.H.~ a� J.M�5�{Cu�W� knot��holp �d.�A��!��5d 7�%21aV3.�4{Ble} S.~Bleil�'I6�d�( many in�FxE1�91)|28��U(L6|L{A}%BI~L�J�)1L9^'{D}eh�cger4%�4 . ��10�89��127�: 4ro} E.J.~Brody{ThK�n��w.G:����3��7/6�#pQ16z(Rice} Y.~ChKU.~NaL(ra, L.E.~Iy� MA$Cox%P!@9,r Crys� "#� a {F}lp RUwbinase -( olliday j� H`�N: �9 emblT�8c�) oligom�!8y helix swappin�u Mole�\ Cell�6},�80N82�JerConwa5w {O}n2�omI�k �Qir rels: &1 }, {C}/v2 al {P}r&m{A}WP�^{A}� .$erg�- ress�?c335.�{Cri} NA<Cr�<a�:L?N�i. J.~PBGECumner �$N.R.~Cozza� 1�>{m�ksr{8phage lambda in�+8o�U!9�Bi63 y (4Y� 289}��  7�77. {CGLS� .~Cuh@ 4 McA.~GordrJ.~Luecm$nd P.B.~Sh�q=Dehn sue��J��!�.%.2&13�k 23��2 {D� I.K.~DarcU0 �e�distadrDNA ve0E8: app&J.to XeA;�j�N ��l\C '98,� �m To&�)�-�{�hu/26�$� ��Ern<| ~Ern�<PhD�  @ FloridaHt[ er�v2�K{�\b�m ��7le &~}{I}��fB��5}��96S:{EAC �%JD]�1� A calculu^� al tanglO3 �* to ��{N}{A}yal)��ѩ�*g Phil��eQbf{10kOj4�512�ES2�1%& -&\4� �=.�Oin�^�h el"�ŀ��q 9���2� {GorA2b�aGu�sat!to*�� %< 627 � no�M6702�me} I.~G}Oge�� ~Buc�iM.~Jayar' ��>�o$site alignP] do!� I}nt!!y6�X: Antiparallel synapsisg� ɷrq��� v� (5��9A2�(749--76.� {GJ.�E�MB�2�of.� s: organi�KA "� -��=!A1�'�9�ewy�33}e�% 4�428{HS} M.~Hirasaw\$~Shimokawaq�]6�n onglv- vert�.�� which� {l}&q "B]\IZ(1*� 1� -l3�334K#&� Lic} W.B�� Lickorish��0 �!Gm�~fp \tex�26� 98� 321ory8�%{MB} A[ x"vuA.Dv tes, {{D��t� T Z�$�!3.�<,{Mos} L.~Mos&G {E}lea �l�alojj torus�!a:A��3A�1� 7�742�(Orl} P.~Orl4i�Seifert .�<"�B�ls{2�D"�gM}%�22�8Qua} T.C.V.~Qua[n �c@�em��+ ially sum�1�a�{L}Q���jX5�9i1��� 6.H{R�_ D.~ sY {K}no.H ,I1sh or~*E�Ber>CA�1)]�Sch} H��Q�6�, �ir zen"X?��^Z.�6* 5�2�(Y�Sim2 �o{A"�icJ� e���{$S�3�Eӹ79iN71.o{SECS!Q&�  �S� Spe��� Z� A5���  6� y���Quart+-v.� qH . (3�2i1?)2$36 Vaz�@VazqueqN�G �. � Gin >�%A]�sO� acc�'d&�'�}26l74{Wal} F.~Waldh�E5�6M��*o!eF] r 3-{S}ph ( a}$r�!�+oR}� )6w�2�� {WDC�~W�a,J.~Dun�f� B�m� Disc�:�� *dicte�9�Ax sub� ti�o a J>U�-specR>��ci�k�22�"�171,32�W�A��N2` �Bio�|ic� ��:6 �� 2�[repM }�:�3! 9�B=tR7! f)� �9{bs}{Bau�jT/ Sze�gg�N�* Higho0�) d�� abel�".}M�Zr2jQ1�, �5.�fa}{F�J Ay_,-Jacobi!��> } Nachr. fT�UssXnZse�-�? Kl. II 19��o5�a732�(robenius}{F �U!� �Uan� Faben der tarh��!�J�Oine6{Y�A 1885) 2v6260.�\&1}{Gru�Xsky�@, Sal;�ni : ��Vokˀodd�*�y�j�57��20� �!59B�2��Two g�HE)�'�ri�va%�}, �( m��9310106.�igusa}{I4 -I.:)t" s)ae�T�sh1�U�s�s0 Wissenschaft�B�� 194.2��N�#-H"C&726�>�e+Onn���=:,.} J.m>E210m��A�2, 40xV4:%injB�mDr�! ta- Q��,I� (II)��� J*dt�86L 64�1�46 !D � 6) 24 23:�� B�P>��K&�atXtim|PS�\'^ �atAGҋ.} c, ��L �� ��-)I 1v174.�$mumford}{M �mo-N& �� ��Zf% III}"�@� �� 6��@54�#a�41967), 75--135~?�215--242�ri�Gn}{�:<, B.: Gesammelte6 W� , wiylic��a�D �% tr\"& (colqH�orks)."�!� eABerlin>;2�rZmhai� ,L&e;M�� oire�  le��Cs�; deux%d�@�U\`a�3$tre p\'eri�� qui sontBi�seA� t\'�@ es ultra-�p#f�� l{mi\`ere� e.} �%s sav� s \'etrz*r�.�)a%85<62--468�� SM}{^�M`nonidEq�2 NullwerB&f�^a�`th2�� odd "�i`dv.� I�EL4� � a1, 88�@2SSM1��d.mhof6e)�2��D*�vp.p.a.v. ��% �"y})t*(;V[ , 231-241.� thomae}{T, "XHBeitrag zur Bestimm'von $\v8(0,0,\ldots,0)$zchKaen�&! �^r FunkN �0jx�8�2�I222W(weil}{Weil,2#,8et!.�en�B et c� �&�B. 4/,mann \& Cie,4G��8!N\�f% 9]�BE})BELLMAN��,most orthogo�s�,' it{\.��}Ԏj5�194�517-51� BOs$P. BOAS, A�4 mo�"�!r���Cj k6�74i�1-36I}BOM�;BOMBIERInnX�o Sv sieve.o�B�82l1� (401-4=<&qDE}F"DEUTSCH,� it{A��*��i�LEP�Zct9P8ces, }CMS Book��e��c�E�5ge��&e"��.(, W.CDRA4} S�1DRAGOMIR!��ervEBessel'~�.i�Wner1d������ u}ssu`�#9 RGMIA6 �qColl., }5�}R Supp,[+�x,10. [ONLINE:)^tt{�rgmia.vu�0/v6(E).html}]:3B�BYeri �i�Z]2J�td��� So210}�� 91-6� DRA1B��: Boas-Bell�)�y��7 uoU�!F�692� 217-i�q� DRA2B�%� it{A*�VI.5�Schwarz�_B.V)Ih Typ$tIA`:}, E1 Mon�phs, VicOX�!e�(4J% ZmQ/6MPF�=to�)/DG/2�G� )�U��(E. Guadagni�i�C>'�+(2+1)-gr�}, Nucl��� B 61if� 30-35%�]��1 aa�e�S�e,"b@�$i$j�pl ��:Aj>� 58�[ 0), $ -2a)6--45>�:�yTeichm\"�" ow� ��CwTP B 44N_8) 60-682zPJ CX�tronioM {&��" }-*!q0 ��26qon� Bonah�# �>desic la�2� a � }, L�*ain dy��,��%8�h0ony Brook, NY��11�^, St&�9�9J+Z�-vMce,�L12EO�ke@��J-P. Otpx �.� mesu plissX}��e_s��qc}de "2 $�0"�} 2�o11q6�Ph�#uola No�� e Su1z}� Pisa= 5:�VV�rN|Ş��Com�,�? �Sz�}�B��D�t110196�2Vt2+1��LM@tˉ�� Alin� stru�E\($\Mm\Ll_g$}AB!Ca$.wCa�=Carlipm ��5�al black+}, y��\�� 12e�-�2ǂ 2872�Ca >Pm��$2+1$ �!S&S&� �9�%al�%cm.� U"�2���MJi7.  Ep-M� J3EpSBE�A.�1dI�Convex\ �@&i)�, a���f SullivxbndWd pleC)�J;2���6 Ser.GC*� F[�!��' 113-25��%Go} Wl b�Mi�l�]Yw�FF.?(ian holonom�JTfO{g ��m. Y[�� 297-326; ��623-657   Marg݈� � iū�#o�@f"Dy (�eE�``R�a in D�?%�" (5�� 0)'' ��20*8�@-/ {H-Ee3Hawʇ��Es19�cal*�? ofI -�>� Q�=�I�2�Ku�� S. Kulkar$U. Pinka��I� A caA��� �6M�ius.�AvWa*n.5�if: n. 1, 87�2�!� } G.i %�1�ۇJ<� m��IM:A� d2:�.:� 1��7) 6�.�Mat} H-�s#ol�!�phw-E9xmulti-�k�l+5�q��!�las� ����8{ p ��7, 34en356�M;{McM}s Mc M�uk)/x eartqu�Bnd6 �� �;r��!$ c. 1e��283-326x!� M��I)�K.�of%) �Af�:X�F� HIHES/M/90/28, Avril�.�!" 1�J ���'�$A� fibered 3&� �MF/,nct!��, 7~1BrU��U� .�;<iété%;é�rTzde Fr�,�2hPeʄ0 S�J.L. Har )YC�Y�cgTr{LTrack�J?"�hi��{2; &$'t Hooft, e ... Mq#I1|;32O Thu�d P. Thurst& W �"� of� 2  Elec� c V!8on 1.0��p -!.�X msri�Xgt3m/.� Thu2Z�Earthm��9w�men�Jal.��C�r)�Az�!� �ic AsK��n*Q F pZ6[ed.~�s 111>�:!tUKL��1982*W�WA�|_ "W AK��nan[Gly �Fb���:vm%ys. Be���89) 46 �_Rd� jE9}*9anand1} \H A a;Lh%h�_#:�~0 ingu �dk>fFitB$E}a�6��@2 69-2.�Q 2j D. P , d: D:| �<g� ��${\rm SL$�i&*=�M��aE!:867-8���F�d3V�C(@!�A�=2�B�-p�6a}�8�s6�S!�!R�<>��c3)Q�28� 2883&#O �4V��C�R�R~U, ��uj-/�lCibG!tuni,��&finHI&��%�Not�� flicker1}�?F Fn�&.�MzR�} 4�996139-1.^Rr26r��N��Eu��؅ct��*,�� } 1�sd�A�9"Hm*�gelbart�  a hA.Wߢ app:Ein}xa)|�$RC oup� � So(I��G-+.��O�3,�Za�101-1ؑ�ow  Gow:R% � ( ity-Z .9�Z@.�of W "(HE*m� GL}(n,q^2:�Z.} 1�1d945-54.��hlr�9Ha(� P. L�36�A�,M. Rapoport:"LA, Zyklen auf7< -Blu�hal-F+��%�CZd3��a 1.�a{hakim1tVH >m $p$-�d:7-�"8[ J!��qE�-2*�_ h3h� F. M��ghi�Tam�"(percuspidalB@��?%�h i�C���.a6�-] oɥoQU 1�\���} --$Y]% 5�:=� Gelf!� pair�0�J.b_Q` P\l}lm269djacquet1�`J % Y. Ye: Un�mar� ����A �#��Wque�.���. @.� .7l�s3: "�)J�+676F�2^�2]B�� �c �ch����9�3ugZx2�4?�Lr �e�93J[3B�Sawl>�Un!2(� m�dQ�F? 10�aX� ,a{12.�k�} A��: Asai�0�)-�'.=g�f�`�h�12���^7m7820.wlabj A��p%�R ng��, �[R��6)�6�:�� }, 3� 7�726-7�P��dp eV% :ZE Y' ex���Q���ty� 11} ��3�3>�3��3*�r$&a� a� 6[B- � � �� ��.�109e��UC2� saitoE�S PTu� &"f�+a)!=���zٔB 80�v9g]f85 shel�g%S :�;L$R,Y�`.����s,o�.Z)G�x!�'Q�9 *�os�O�K��33�t t�EY��0.[t��cYT �>Pof( -Archimed�-@A�n�m>6�|i�x3� 3�nN2 Vf� 10.� Ayad:9rHohamed .��oi�W{$S$}-�(!�.�&l_).8a�Ma�Ba5R$76(3-4):30� 2��_*c Bel�7P�ltjukov�cid� !G�(u9�1h��n(ali5jad́�,�P ivis� ��"�St�{ \-ru�@m&���al ~r, VII. =9Zap.\ �\v cn.\�D\ & �\�\!.\��\�u�\ � 60:1&,8� u7CK"<~C��aG8nd H.~�eislerF�4�!<�.N( -Hol��7�<Co.��~d�;197A�J5�%"!�Foundk9E"2I6(Cheon:98} J�B-�S.~Hahn.�E5d valuad%�on6yno#��E5ll#,c�H.Lb�97(3):�){2$X{Chud�6~V!} udno�1�G:.p Sequ�4��jJ0�-byY�i�x� I{new �]m�'!�f�2"�estF�;,s?(�7(a��C4�m.C'(CL} Ren{\'e�r Dol LascaJa5�yP�eI2oZM;,  6�ACor} Gun�OC��lisse2Stoڽ(diophantienj+Phypoth\`ese abc g\'enn.y~ \'ee2EC.\ R.\� \� \�i� 328(� I),2e�7h}��eds��"U_@O!�rE�al�n"of �Cer �Ù�; e<.�I7i.�UR�Ho02 ZR��,Karim Zahidi.]TD7�{D}1��T�rG k"{M}azur2r 2�Iem|'stL�B,:�*�׭�2�� VKic"+ (Ghen{'963O9meQofM2���4}� J:�5 A��>�F�(Davis:73} M�I .:�K>� i�1sw.1E�� �Monthl 80:2�2a!��Y�De��,:04} Jeroen %�,Jan Van~Geel.oA���Z.^ l {' global 9x2� �Monatsh��147:2 �308%62�EverestW�� Manf8�Einsied�JGraham (� =0s 5.�]@��c6�s��.5%dLMS� CBH�4:{:3 (el�001.E �}a&2��* M�i �Nelson phen2� �266�2/�� ."SocA�132�955--963%x2B;Stoll K~ �Flynn,�k Lepr�!vost, Ed��~F� haef�$William~A.�iˌ%�a�\^ �,Joseph~L. We��el2t Empi[l e$Eej {B}i�1�7{S}witon-{D}y�$&\ � (modular {J}�:�3genus 2��B�i[!�!:$70(236):16� 16�r�Goss} a�d  B`Ba�%*Cv��KeG ��}e�ume~35�mVErgebo �:�\6ihrerC� zgeb^ 3)2�SS.u0k0�3.� Hsia�B -C.~ . �8����a� :��S  DrinI�)�e�U& int�2���� Lip2�V4onard Lipshitz.;Und �H���s)�a^  in2� k9s. {I6�vL,64(1):122--14 �q2�v� 6* �E�b�.�f�235:2N28}�92�1v��mjm*< ~� 41:1�:1f8.� Lip3v�2*�ED*��v�_:ޟj u Mee (Bruw3s/Monb8�K&N � Bullu och.\ Belg� } 33:�>5,8�i9�$M1} Yuri V Biyav�.eAm�tOXaN�W.2�Dok��?\�kk4S.R� 91:2oq8��5�2V�h2� Z�2$:]��u%b�z�1 n&*�,�2y$Pheidas} T�w� .�� ffor[-prove th�v.u���{$�9Q}�(3 u��.Z�� �� B� UH252�� Poonen:*} Bjorn .�Z��MF ���&ubrvT )b\�bb Q$2�E�J�$}2>��D90�2 R�k0son:49} Julia�[i.�DefinaP ���A�8] ��.<�%�b2L���4:9�;142J9,Rogers} HartKX, J2��m����s*)"��Effbvem2 �2[Mc&}�196.^ {Ser�Jean-Pi aqr2��m%\'A�ce�p| >-\'e�=B! Ense�}V�&0&!2@2�U26�w:Shankj nic .a����-E termp�(asymptotic &i� of {$B(x)Ji ���Ea8: 8�x966J �2 �%� Samu�(.\ Wagstaff>�48E�e �"d B.A'8?aG�`LqI�q#.E�6� 64:1ʽ173�m92��D{Shlap} Alexandra entok2X�Zy�Te�!B��ne�%�O�  E"\�2G=�30��$f�*,:an�.",uAEC} Jh H.&DuBA"y�!�:a "~ 106 ��E!� "(in%h�;}.hBp &�;>�� Wief��%e}Iriter A�{$abc$}-& .��B.�y,(2):226--237�~L%"� Stev�} %:�z)o.l%&�!hsig1 ~�..: {\tt6�0.NT / 0402415�&0>�reng})QS .�"2�"Rcom��&�!�.GMa%�h�UUtrecht�'�q2N 7Vand} .r%?^]Q"�v�)k.�.�In:Y��!s&�, ngsik� Ober��ach>�nk 3/2003 �.i-W1Dhop ``y� 10thq��A>��.� 9_ '', +4%2��:48} MWSB�MemDc1u�.fd.E� *�70:31--7�|Q NZ?j�K((uACZ� Acz\' 0+ A sh!U9sI]����s,�'R�H�.�2*<��i-B1 jlonso%kC:n\' itez��t�A�)in nor�_ �.���!Y� X�&,pr�x,���� 3%�%q 1-15*�!A-B>zf��3 os OžI�K�s betwee{�in*�Bi�?B�4�9f#21-�]5PB-D�4T6[�?L2uncan�6�t�b1$\N�AnZG-S&e^�� korska, S� �M����C�vŭ PoZ���e�. t��)�;.�1436F|{GU�@'ud$�D.P�aw�./l�vi��5V creaYQ��2�k> cifi�. 5/#7�427-4�X5'HYE H. Hy=�As>"M�}}F�����cas$USA 2].41�J2�224]� H-I-�}�G. Isa�T��#ssi%�.�m al Eq�ap Seve�Var�H,2��,��#���L-Jp) H. L� nd K�(JuW+ G2�M!]A7%40-�Ulam�-R �6? Pexi!��w_GMD6..( L+&(0) 627�63.�J-S-K�}W. �D�)Sh+[,nd B.D. Kim,1���R�Ğ��1'00!�.m%JI�-M�gE�P�� hoo, �-!#6~&�#1!\�G�%.Kor�!MKM ���m~3, 645-6�YU�PA]L�&g5�.)\" atz�_n� :����y� .A&es �5�0ag?�1./�{PAR1�3-G�ɶzhm�aA�Ban&Fes%)2=75E=2M 11-72�) PAR2�9�Ƃ�&�).�PIN'a�P���Sur uns�nelle d l'es�e�2� (F��h)�q R. ().�URSS,�60 2%�3�6411-41.� RAS}�_.^“��vr��)�N  q1:h�8-MaU�RATJRE�O.O. -��QsQr�1�U35-49\a�Y�E�,Gy. Szab\' o�%Y�Np IV,J�aw1�1|)1, 73-2�'SUN�� S�"res��6v��&H�qxaA"nQ�z[ 87El87-190.Vk2� f�%�C �C D%�A� %�hombrAO����C2B:�(�7!��� CHO}��W=#ole�^R& ��2�9�� N ��8�*6-293CZExI Czerw]^]Rq3 QA"`j�%� z7^j{.A 59-ud CZE2�0�R\A�Ina_� �vJF>Ƿ, Rk Ed�aNJS .�.CZEKǨ��of �0--��-"XT�hHad�Bct20� �DRLU , Drljevi\' ce�&Vals`i�dra�on $A$-�^ s. #���(Be>J(d)(N.S.) 54�6),^71]FOC�)Fochi,.�!r^r;R{Nx��28-.���� �� � U *� ^�l3Jr*V �ad. Sci"�i|�O2�Y �Y VY �WAboj=�fMountainY�J-L�-� e�Y%8LeeE�FmiR� a pd �*j0iq�y)i7a�q , B6 F 93�118]��� �� Z� MOSeQPMoslehi�d{Qs.# !>}�W !% �Dq�2�DFɻ124�]�V�2 ��fu� *0%�>}@�udi�N�K,be\c s-Bolya�[!�r� 3, �@6� V � �Y Y ]SKO�\ Skof�� &��a.��:�o�+/n �Mat. Fi@�Jo s�83)�CA�2e SZA}:� Sesqui�E��ly=�JA "� 4# �3190-2�(5�VAJ�Vajzo�G\"�]as���U$al $H$ mit#Eig8\@: $(x,y)=0 \Right��pw H(x+y)+H(x-y)=2H(x)+2H(y)$,����%� III�;2)"�Y3-�R4�j\<22}* baker-oz/� B V . Oz$Co� x cobordi�m� "T?j��D!��`Zflag �D�}r�Ior7, ��}258�S�51-1�9� Bonic-Fra2n�r �J.#& , Sm^�q{(E}CGfVMe @15�L9d[ 877-8�-U chas���suD� �Fa�-"�?&�^:3, GT/9911159,G}T cohe �L�he�WJ.���RUh��e�re">_�%Αnj�( GT/0107187� .�cq/ ~B. ~qA CouBinA�c�al{ysi��p�"?V  4)� Dolda1  ,*@YT� ��fi"L� ([s�'�G �G� A7B�_69�m*w.95Af�1�Tv%Pys fib -#�Q!U mA7A�196U4��25.� Dyer�(  A�!� e)i� Benj�L6m�U\ Eells-Elw%�AbK`�Elw��y"2>[t&�, B��P+,!�::c5�p� re-O�15}!�7a 41-4.Y�-McAlpi4s�J. ,�"���� se-SN'%gh�JJyY\6��1055-102� jani�hK. J\"���-62j�rA�1.� Kuip!�N.� ,!�}X5V_VE!�� =o"�<��,z%73�6�9-��5��� } S.�<,�r�#J"�RV�5.�michorlk+ �*or� nQ��H� \bl!�p�T,# va Px�!Lim��%&&�?8milnor-stasheffE� W. MA��� ,� �er�<ch�  �BoLu72!MoravalAJ�+edholm��W Gysiy���U� ��~A��5.�;� ��O C�C.FAc_�� As"o�(to Loop Grp�?g�Ag�,UB6�|of��gow�9��5��1l5� �c�S�sC��in�����0 $LG/T$, Turk_lJop>l6���wE�25dX 415-4��cenap-is r�F1��Ux,��yal��L�� Quo.n's1ic"�� yi� �]>l!}e�s , subm�E�/Q�palais>.� , LuN(nik-Schnire[��yB?&��9 *9115-1pssegal-p�leyŕ-([%\&S"�NE;A:�4.45��8׮_-[ 6L  , El�$��p��%"%Ire-�f9}�ory ueSteenrod� !�,"�5AA�i���^ 29-2PQuinn^l��/(,N"Raɨ );N�a6e�213a*) bIg)�to7�:o!Ca�s� �yj��=m�Ks��62�)b[�1,!mel�:!bpri\'e\-�&�c�  ��b��J-O Helv)UEn5Y17-2YtrombaED J. T, d,E�e]�ny�ma�E�����S E�Y�T578-52�Zei�2�~ Ç^�*V����i[�incipl}% Their��wF�!��R� � f�� \q�ada��J.mC A� !z HL z G�sed� , ���;Chicago e����m�L �L �L 5BGG|v�"b�,�!. �C\&�!I_nhqr c� !<ݔM]� $G/P$, ��M�Su�!�u8l N 1-2.�� �� �� �� �� �� �� �� �� �� �� 6� L. \bibitem{Dyer} E.  �, Cohomology Theories, Benjamin (1969).>4Eells-Elw} J. � \& K. D. Elworthy, On the differential top h�Rof Hilbert manifolds, Global Analysis: Proc. Symp. Pure Math. {\bf15} (1970), 41-44��-McAlpin6�J. h, An approximate Morse-Sard�$orem, J. MsMecy7}%08), 1055-1064}@janich} K. J\"{a}, T �@, Springer-VerlagM81.a Kuip!�N. H. ,!� !�,topy type of�4 unitary group-Z spacez%73 �5� 9-30��!u9Ţtend{thebibliography}�\beginB{10} &�BoRoBoA� \ Borceux!�\ Rosick\'{y}, G.\ Van den Bossche, Quantal �X C*-algebras, J.\ Londomz\%C \ 40�089) 398--404.�0CannasWeinste� A.\ ( da Silva, $, LecturI��Geometric Models for Noncommutative A�Berke��%�\J.\ 10,)�\!�\, 19992�onnesAf\ , :m �0y, Academic e4N4. \� CrMo} MO rainic, I�$oerdijk, A�}� ��� \'{e}tale- oiv !�(Reine AngewG� H\ 521 (2000) 25--466�8Higgins} P.J. , CategF  �� jRe� ts�g�-"E�M�aTA. No.\ 7!71, pp!v--1956� Idrissi} %� , Sur la��\or\`{e}me de Riesz dans eMlgbA stellair�SThs53 @me cycle, Paris 6�2� John�7e T.\ , �Ee S� Hs, Cambridge Stud.\ňMP , vol.\ 3!U'�.\Y82.jElephantNxketchA� f an�A* --- A� s1�J endium, �2, �� Logic Gui��44b�, 2002�JTiJoyal,E�8Tierney, An ExtɾA�ZGaloi�of Groth�eck, Mem!/��-0�<�309, ica�]I ala� iety!�82XKrPeReRop\ Kruml��W!qellD r, P��esende6 On q2�spectra�2�A�a�a0�tru��1iy(3) 543--560.� KrRe2�.�6that c� ify6~Cahier�X!�.\ et��.\ � ���5�(4) 287--296.�(Lawson} M.V�, In�e Semi� sEgTheox fa>ti!�ym��0es, World Sci2f�� 1998.r$Mackenzie2d!�  , GeneralcLieA6up���mA��� F|�).\� Se� >�.* E�5R�B���J��!�e6�N):��!24v� 1987:�La��S)PeC���=a� WorkB �"iNian&� �aX9>�bѠ� %� j2� Sheave%�)'�z��0First Introdu,  toAɕ��i�22��/Mrcun} 2� �$Mr\v{c}un,Bk Folir �.i.���B*32�u86Bqulv�\&, Ren� Circ%-A�HPalermo (2) Suppl.\4  99--16& Mu89>ZQ��, Invi ABur��ummer�E}ce� Loc� i�DG����$ura\c{c}ao!b82 Mu02j�in:�Yv$s, third s! , Kluwer*? Geri�2@312--312�MuPe91:� J:� A g�iz%���aHahn-Fn em, PA�th.\ 89� 91) 1--5:#Pe9>%N{�Uis2zcalculu7 relEnaA�point� ���xa 159�T1) 231�T6;uPeB7FZ}�n}7��2��9--32:}�]C.�6`A n6' %�yA PVse til� Ina�a�� e$Phys.\ 44%5) 655-668PaRo00h\ Paseka!:i}�aIB�oecke, DA{oor!.\ Wil  (Edsa]Cur�\ � arch�rO al Yum� :1� s, *� ��anguag!pFu���ies �� 111��0, � 2A�262�PaterkA.LS , ����Fy,�) �or�Birkh�us� >� Renault)� _ tA�roach��.� �WFs m�793R�80. g:dual> oid:�Twohl.8 ��3"� A�a���:F=!C��Os with�RF� Ergodic!Mo��9>� 1132��5�y434--442oRe:SF� \ A�R ebt�|�(ly distribu�i_ se_ ,!@appear as a Short� in&� ` Forum; arXiv:math/0506452 Re04:�DSup-lattice 2-form)8���!, e�� 276e� 4) 1� 162s Rosenthal ,y�%sI��@1�, Pit�!1e���� s"� 34� g2&X �Tec� 1992�Catia��z,�or�de� e aE�L\~{o}es \`{a} l\'{o}+ moddMSE:^{.\ 7 isbonD %�N�uf�$McD-Sa-2} X\def\entry#1#2#3#4\par{=�[#1]{#1} {\textsc{#2 }}{\sl{#3}} 0|\vskip2pt} %{ref}{author}{title}a�inoFk*6 % �� {Gr-Ku} {Greuel G.-M., Kulikov Vik.S.:} {\it On sympla�c coveG��a� proj,ve plane.} AA� A�L. SG/0409027, submit� to Izv.��"��Ku3}{.�\,�LAlexander polynomial�� �(ic curves.}l 42:1 94), 67--2s.�1f� ic rea*�  $C$-�,R|5|� 7-20.�.}6|= factor� �ul� !�$full twist doubze number����ng6�,)68:1} n!12�(8. %123-158&�.�.O�a O.V.]? �nda&�%�the c+Hurwitz9�ZN$ will be p[ d�vYV�9%o200wRkz�z`Yu6�a methoŽ const.� Bt59:q%�765-78.g 98L}{�e =�aaG$ddison-Wes�C any, 196.�H {M-K-S} { Magnus We�0arras A., Sol� D1� CombinaAN1���ory�e�� A6jTe�vof �tor�%R� }��( @ ce p-� 0New York - Lo�- Syd~ 19� RyAfy XX} j9�|{Bat82} V.V. Batyrev, Boundednes�A�degre�multi.�!.c Fano�s, ��it{Mosc.�Q�� Bull.} ! bf{3� 82), 28-3.�94>� Dual��hedra�mirror���ye�TCalabi-Yau hypersurfac� �� � �it{J.-.��.��(493-53.p{Bli14}! Blichfeld� new `ciplea�!Pg�� n��sa�th,aq{9L�.�-MC9L11��227-2:�@B93} A.A. Borisov%<L$, Singular~�A USSR, Sb�7 �93!�77-283..rCon02%'Conra� gh� �A0�reflex�VolytopAa Uc$anuscripta)=0A^��15-222� Cur� D.R.~ tis8n Kellogg's dio��probl#U,�1�Monthly}29E02| 380-36�8Deb03} O. Debar>FPin K.jun. B\"or\"oczkv J. Koll\'Z Xnd T. Szamuely, Higher6z"m!/`eH BolyaiAQ�%I� al�!,12, Budapest 1, :��%rli7 3c  93� �s {Fuj �Fujino.�oG� from%ia9ore%# view�,]Tohoku�. J]5A�200A�551-5%.�laW. Fult�  >�:��nj a )*s9)31�Fp "�# , NJ��92�DGKP89} R.L. Graham%�$D.E. KnuthOL"Dtashnik, Concreten �: A f��Ÿ�$computer sɎc!.], Readil%MA�6Guy81�K. Guy�#solvedq���)�{ e: book  �ZBintuiV2,Vol. Rw�I , NY�1 �4HM04} C. Haase%? I.V. Meln� , ��k����a d��!�7,�.CO� 64W201 },en83} D. Hen�, L�vertexWs�in&orwi�]�Pacific�A�]�10A�198A�183-196 ib92} T bi, �O�Z� conv.�ٌ*+ ca��1%��237-242�Hwaa�Je HwaAe0b�four-�)�Pic)MW1� J. r%an%>  556}�! 225> IK95�� IzhboldinEL�(rliandcha]Unit f�'�$�MSe$lR%b 2}͜bf{16�1� 193-202XKas06} A.M. Kasprzyk, T�%three-�termi��3%�it��fo#2000&01-122KS00} �reuzer%(H. Skarke: i l�_�� of}6a� i�nu݃]=�Y -��YG3 � , 1209-12* uQKSa�^�, PALP��package��a�+z3 >�mu .v ���� Yts ut.2�$un�15s� 87�+.�KSa�f�*� �>data, Webpage, http://hep.itp.\linebreak tuwien.ac.at/$\sim$k)�/CY.@LZ91} J.C. Lagari�*A�Zieglm }#F- cont�",ng a fixed m�of��堥�a sub H,y;Can�>�4g 1!�022-106� Lat96} R�terve�Lindsyste&)�"H.<b$48� 9a$451-4582>ut*I!�?.T44-"' RE�E Fg)BB*1[B]{ble� r} B �ax8*� Gaug�&7e�aT n ri i+} 6�� �&&8[CNS]{cns} CorwU L., Ne'em�!Y.a S. SJ.berN!75,6 ded�"��*L ;physic}pRe\ t Modern�# } 47�~.�&573-603��0[GK]{gk} GozeD&^0Y. Khakimdjana� 1996y� Nilpotentq as,}>. J4K]{kac} Kac, V%�77,�Su/6s�� Advn��P.} 26�I 8-96��UspekhiN$pauk}{40e$5}{214}\ ;>�,UMANA,40,214k!A0M.~Jimbo}{LetL%F\�|�T63NS LMPHD,10, �R V.G.~Drin�} {Dok!�Ak�$ �2!�19�1060}n�=�\ M }{32�5�)6T(SVMDA,32,25�9S�+�$M.~Rosso} T H %L�] }{117d8}{581:�0CMPHA,117,581!KbM)�4J.B.~McGuire} E�6[5_64}{622N[(JMAPA,5,622b�C.N.~Y�8{�$!A�%�P6�31U6 PRLTA,19,T�KRS �}�,F��H>�~ �1>�a�39a .}I3 5,39I�"? ZZ �A!:Za�;d-AlB } {A% }{12E�79}{25>y,APNYA,120,25:{Ba {(R.J.~Baxter�Z~Stat.~ ]28!^a�> JSTPB,28,: Ke W$T.~KennedyV PA2%&9�F809:c$JPAGB,A25,6�Jim�myA�m�6�10i)6}{53>zM�02,5376aTL �(H.N.V.~TempN V (E.H.~Lieb} � cA�oy�� $Lond.}{A32|71!�>2PRSLA,$,25:6CG }AA�KirillMNJ�Se%Q a98A8�;\\eB M.~Nomura%�6�3E<439>-i�30,6-KF;�,F'c�a�#M15��EU6>$LN�e 51,6:"�Fad1} {L.D.~Faddeev:} {\em Howz ic Be�(ansatz work]� gr��4}. In: ASym3tU�$i�7�&s Hou52[ } (N6�/�$D9 [hep-th/9605187]6�HEP-TH 6QJoIV.~Jo'5Q�B�iC!�459NFM�25,45eFZ.Q.~Ma �M--i� 3f%�� um envelo�= � } (R�03)ZF �jF T7� [Alon87]{ } N.~ @. \newblock Split!neckla ,{0$AdvansE�} 63: 24�153� .� x8 x8VxoM;c8 c2� 2�of�suk-t�?+em2�_!�1Extrem%; nd M�7.� s, M�Dez�. FranklG R5'}edi B &O5y/�ess,}*g5�08,K6�-12*[[Anis9!} S.S.~ ov.�5�$o$RP^n$.#(Trudy MIRAN#itx-V.A�iek��!�T(cs Institut� }\ 2216.$8), 3--39.*/ [Arn96]{0} V.I.~Arnold.��&6fen on �.>�#\it Ya.~G.~Sinai's MoscowU)narBDynam�S .} Provid�, RI: �u�Soc� �1.!�}vis84]{} D.~ . y Non-partiaÅ�� set2���In�%� roces�-�\ } 1�/84\25--126hBar93]{$2~B\' ar$�Dic�Q�2'&�=HtrendE[Disma1��alq y, J�,os Pach, ed..Q�"l�9th�*2t�: S3g"�C ,} B`165[BM01!MaF J�stou\v se�n��i�#aneous 5�� meas�;$by $k$-fan:�em9) :#etrz< 25:317--3�*�.� BM02�2�� Equi6�two2� a $4�.=Ey5�.�.} "C . (p�)2�Quad]{��~Btt6ait�/(d}. In "Col$�,4er Plays", Fab��% 19�8ylBj\" or9!�jo34A.~Bj{\"o}rner.LTopol�5al �'2�In R.~J �~GrG tschiA�0L.~Lov{\'a}szA���E� :�"('cs}j�%%�CoFl64]{} P.E.~�. r, E FloydBO*_�p"�.maX*}�:.B'.�[Copp71} W��elJu,sconjugacy}.V/ure: :�-� 220&d/�6 197A�9D(;] } T.~toaDeck.K%y�%�&�^ G�5}.�deQyAYStu�#:�8,%�#Ap2{ FaHu�A�IR� e,0S.Y.~Husseini.|��a� M��&�4iguN Z=2�1�B FeZi�FeiZie� M.~FeichtA� �~Z�.�On orbit�{g sphere:�it�a itsc��)�2) 11�\ 85--10�:,[Gil58]{Gilb�N.~ er2Gray co�=k path( $n$-cube.�%bBel���.\ �/s�(58) 815--82�8r\" u60]{Gru} BL$nbaum.eP�%$mass--&�1on<c�boAd byV)i.2m�bB�", 1;B6;H257��6a9AuMa86]{} L.~Guv u, A��ri:�8it A la Recherc�KeM�ie~du0��BiY4 aX4u !4�9 allE�tu:Ep, Ch.~7.2.1.1, prefascicle 2Aa��``�>Art��Sr9E8mming''} (vol.~< 4released Septe�/�, .�Dwww-cs-faculty.sta� d �kp'/�2a.ps.gz�U2Klee99]{� ~ .� Shap�$a�fu�E. � uJ;' high-d*3H& 'N.)� -��,cs.ubc.ca/co'<s/CCCG/� 8\_proc/klee.pdf6�osch81]{ } U.~ ork2�E�,Vector Field�Otj* Bundle M^L -�BT,�LA�Nach2�Le*�e#\ 847.�"�Mѽ 19�'9�$Lov78]{Lov�: Lov\' asz.*Kneser's���3]= chro�]c� ���N.c �J. � . R9,y A}, 25, 31�:4�6�Mak�XMakAzA$V��kee2�F� i#inu� ��*l7��o,L ���i��, (in Russian�K"� � Zap.�0�L-Pe�0@burg} (POMI), 279��mK1hB12hB [MVZ]{MVZ� ~�O-Levits;0S.~Vre\' cica80~\v Zivaljevi.���F*� cŔ6� !es by �/Ƀm&B8�)@310377} v1 23 Octa�l+Y;(Mat92]{Mat1�9~MV$ Effi2+t�J�^^ 8��)3�332� �3�2n�Range s�! ing �"e�$hierarhchi cu�F�^���/1�82� MS74]{M-S� M�Pa1J.D� as�P.�EoV�P2"-!.� #I-(1�P=�RampRamosw ~ .�FYA@6N:�.?�vZ0, 15:1�16I6Scho54]{ �J.~ e/BfAn^A&�2clo��� cu�7 in even&�, al Euclid]$� 2kAct)1\ 9�5�*;A�y SeSh!_ ��~Sedyk\B.~��iro.�On Yo hul�82���$\Q(bb{R}^{2n}$.Toot56]{} G.C.~ il:� em�IEE 103}�It B"pBA35^ KG43���VZa�� ��E�R. r�0he ham sandwih>�#em revis�C.EEIsrael�D��}, 78:21�@�62E[V}94]�4:��MB�.��ca�$o�U,colored Tver��oC� Jerusalem���6� '93, Barcelo~ ~Kalai (e�@C� Contempor�U!�K,} �,S.*��GM9�0YY85]{Yao-Yao�JCno�!F .XA gO �Qa!�o $d$2B 8 ic qu�-.,in���e�0�r� 817th ACM Annual� posium on�Rof!3pu� �90163--16�UrYDEM89��O~Y�D.~Dobk�% H.~E�N brun�M.~PA.�"� �e��,r�J��� SIAMA}5 .�Œ89), 37A���Zie04]{�2r*�%�PeBal�muC)�},�pober :1[A�iv�Y Ziv2iR VU� gu-*to#iv�,nt �!�26.��4:� st. e�Wgrade} C 59(73)�3896), pp. 114--12~.�8!v3��R� II��64(78 �8�0j3��9�)m)�vTA~�v_eCit CRC2)�7$Cy4E*&} ("9ed2 ), J�4 Good�((J. O'Rourke�o(ca Raton� 6��V��ZVVX,/)��.V��>)'�T�7��%es �.F ive fuTFvB1 4.r.7 FP 6TN)�2),30K 1 NtA�f�99� �BY< {��3OUA�3i F�Peh� Pr/�2�$�ic`6l "�;at�m Specw=ParabolhS�4���.I: c$oldwfeeml} �j v}, �Wa!�$ront evolu��%� eq�Fe] lemma},A�mu9&%I�22�7P557-5826�a�csf�.MQ?���nQof Ord�y *�l� e=!:"��G>Heidel��) 19�;(t6�X: &a{78.) .�avgF�,�[chenko ", G--Zad�?M�E&�9:of �b\]�8�+� {\"a�G��pZ j�82�b<` 1{wF�}M >� #?cauw]�wU,�K�L�Wths�,s?@ vietEsU v62@.�Q�tpwp}b�.ek�2W.L�rarbLaL)oJ� A7� I�3�55G$8--1786� �8��V��@�to�F��!� and.A�bf z2A��$65--1856�Davidov �  A�NormalH ew6�/�-eks&�zresGV�deriv�Z��a n!�bourhoo8E�? Q4I�},V\._d.l.)�19}:2�8�]1--896�goryunov\<�G �C�>�2W of �t�B�Ho�eJ��H b2�8� ) 27 28116�k.�,Kergosien Y.�2��f�0}B�$705--710. 2�K3K wegp�� D.J976Ode pliss�G }, �N\'eer1�2�:18PR=9:3hgtrzLa th\'e�[ g\'en��ale�����29>R:�LLRmkGv$.Q(vitt G.,&�% H5 H��[a� et mFh (�'��w�!���a�[ur *�&!L�+)},:�(Warsaw�8F7 �SCeA�� ��0�88)�P52hD MHdi� La c qT-n�Xq��9},4QcR�5q�z8��72^Levelt1f  Sengers�B�e*fluid�P mix: \sm3 XL��� 2ola��_r Waal�$Kam$gh On�), KNAWA�m:% � %&. m-1�� K�hifrin T5%�����ve)���A� %J.~� .~� �*1�D8�*a 2766)adriana-* Ortiz-RodA9guez A�Q}ba�l��� g�om�#+ .�{+�br��U elle�" �HeLSci'R!�bf 127%�1D 14�W7.*! {Dim�P�6 D.�"� � !�S*yH!H T�?D*�P&:N�^!W�2F34}:4�`76--2876\Plov� O.��GE��� mutu�8os��a��a "t .�ur�c 36}:W8IV= 249. Zbl.P=1402; {SalmonM  G5� A Treatis��% ytic� Aof&�%T 5T�$Chelsea�7�I27�%yS�Jx  BwTh�#n� Cubic5�D lare cb�_ (194>� UribetdQ n-Vargas.� 5�\'� ymp<&I�et�: act en� om\'�+e��*��A�E�courbes =e:KA`PhD��Q�+v {\'e�7ris�a�, (In �5ish6B�pdl�F�On PolarlDi�_Lag�4and Legendre 9��:e�phm(�of'�#�eK'Q�$oc.(3) 87 �O(3) 701--7246.surf-"z�i� EL$, Implicit.�l Eq2 � Paired �ian Fib% �OF�Z�.] f�68BP�Brodzki�$R. Plymen,�'Entire2cic�PVof�oatten Bl�- ) [{\tt�0.KT/0409164}]&F{�'Se �Vi�Un-.�e�0BJ_}, �� IHESw 62}0g �N:[ k2}� Az �6�co��`S0 !�ch�m%�0$\theta$-summ�&thodu�= $K$-�� RS8".4no. 6, 519--54���{Cur Cuntz-)Cyc!� N���B"�Ch�="R},�Z�fe pri�h!>��~1831, jD s~73�., {Cu3!^� � t �5Sin�;.� } y}. j:^^��E1.VY�g.^� , IIb/"5A$4. xiv+137�HISBN: 3-540-40469-42��2� Exci8� Peri�*--��a*� �%s}4 +CY�!�N:�ԁ�{CuQue�%|7D.�l llenM8.�bU.*+ �_V}�Rven"I�27}�~6 V 926{MSa�a�[D:1venso�^ On a� ized� 4-Hochschild-Koh%t-R>2A�� }, A:83�P, doi:10.1016/j.aim.\$11.006, 34I� ({t?}) F�4329}]*w{MetR.~ -Wx<sNNAPh� Th�CM\"{u}TE r �\, :y9906205Jy2G2z.��ӹ�.�0nEu"x7��)���)��3, 269* 6.�Perrot}�o~ �]D�r�E�f�ofHgl tri�'},KUm f7 �23�2002),�1, V^&.U�Pie�.� � Nucl�Gl�blJ+nv��i}, /-la�G8P�< seco�Herl[i�0William�J4Ruckle. Ergebn��ňE|`k und ihrer Grenzgebiete,�Bd �US�eB�-&��7��us�[ gg} .E �.M��ki b_>�KIE)m 2, 2� 322%7qE"�q�P�� Cochai,B�}b�LI^pp.~139G�9T�=F�o�kve1�G]( svst^�and K�j �.�m- !��]NY fa 8} 5��-Lucionni} Inta Bertuci2�A^x puzz�l:,} &~!{this \c�uMKT }��1��93��32 {db} P.Delft!�Bo-NN�3CR ve P��theHhld}6�bra&v1I!B 75.}=�j:Vaughan .:6D �Gno�\%`a� t�I@knots via von Neua�� 2 7��6e��c.-'{P# �.�<{rolfsen} Dale R 2�aK�� Link�R=�� vorsh In.7�p, C1S762s�;l�G n} Mk/nd 2�S�0/$\br^4$gQ c�* S7s are �D dardB+�i!�-+)'7��X741.A�N�j�ri]AG}�� N� druskiewi��s4D Gra\~ na, \emph{F�Uracks �.ed HopfY�T��� y bf17�^e��17pR3.�BL�ijarczuk�!�5.?�;R@�A�@���Ɲ�88549-1091.hrFenn05lR. ,�XR.%q�R�ba�l���Zcod{4;�����1y:��u�$A4r 3-406a�}��KCa�N�B�v�d8��Trunkit*)L %� !Categr.�s1 bf� C��21-356B�2}�V��Jam��2� %*��")t[�$\\protect\vrule %width0pt{*�3mi"8warwick.ac.uk/\� ng~bjs/Hg .�Fox �R.� Fox1IA quick �  through�ڡ��!inN5�'D 3-Ma.M %A3ReL ess..jjRotma]�J�" 1[8:�{�E��-�(ourth E�1JZu* Tex�_�=�I�eMWB�52�Rydm�!�H. �Th� ngr�\ st� aVr� i�i�] %��3Y�4971-49�N��"\FkWRemts}*�%{BJ}{va�&n g(E�J\'araiaSA.�j���Ka�!to\ dens?~d one6�(organI forest-fa�l,&�J��R��}.�vdB&BZ�Bro�{k8(d ). S�de)��mperco�z!{em�< dom *5��"�J^!*)lf�%% Rev.iL �8 69} 1629-1632.2�grass}{G berg/P)�� C��be�^�dt9 �ߋ���e�r=��a%Jou\��XI�� 4} 17.�a.152#Gr�i�nt�9R)9). WP9�}BHL2JJen , H.J L8) K%�OU���*�O�Aur8%t �2mHMMT}{Malamud, B.D.,3e9G)�Turcot^D.L�. FE� F�:-=Exa �"A F� B1�wem�'-]2819403.46�SA�Sc�2,F�V��a A �i�seq�-�}��3lar�?c�xE )0alA�iew} EI 65}, 0261s�-8.�&V�`�f�50.� Gus1�g Gusa#cOn�E5l)!Z E w i2'�Uc��$: Viro, O.�7.A<i&[I of "_�Var~q}. �B�Pib"��!17�j2. OW". Gus2�N�l �o��_. �k�" ic t�yqu%�I=."K5)�U�Ht` i 1 iz}� � E�H7�h5;(an��&in,it St. P"�C�f��M�Jv569-604*A Habiro2}KY |, Aru musubime no kyokusyo sousaz0oni jme 3D Japa'E) H #x], okyo2 16�= �1.� }s%�M3� 6M�a�i� .1-b�af!G1-8�5�Hab.qB<=_' S�� GousE-V� liev V�,"�.2!M-Y�r$A. Miyazaw.@A. Yasu;&�oB AC component:� up�$C_n$-� 2{*L 3}�H, �=T�wA�s$ulo pure %{subj�^� �'GT/98050�9ky}qd�L�! iof 2-�F~ 4-&�`S �?c. Ed( 9�5Y6� 4-38.tTan!�Taniyam!`��similar8 of1� h@ Gakujutsu Kenkyu�*@G/Edu�, WJa2�� ��t� ZA�Pn33-362�-Y0.�%�6Re.{-9!�E�afa� �0��,�4�G a 581�a�nl9=�T-Yv�)�As� spys�b""N�M� 21!(��p:�nT-Y��1�l:*B!d&�!�I�N�1+� cXAlC"��Philos� �W1��$325-34G2Y�$Yamamoto}Ma� ,�%�13[Ld2�a�lete %����};tixi%C"2�3Zk199��291-292�j}2\Delta-un!%t�|=��%2adaptabi� �cer�mIfsoc*�s X(u� eG8 "w[.^q+�:��2$ 997.V� �^ג50}9wGus�����������}hh , M p-paW;�oni��unpH|d,�>.O��.����V|a��1\B iro32vr NV��2=�MilWq K�jnkS��Ann��}5�#~I1n6)M-NkMurakaml+Y. Nakan��,�au�A" gGa� !A-/(遭��28�89�' 75-8.�F��}���{�2�c%�^�A���� ��-Y0�K�K112rE0EJf�E�y�u�, %��J�*��f��͖ 501-5�\"� ��f=$"V>�iQ$LZ?Q<^>.�z�IPA�2��5)9^�E`BhV1��3�r00.�Yam�`������9+Yasx*F ~� .��2>�)!V�a���(�ْ�V��f�4�lQ {Baker�~ ��rix�Z�I*� to�m[[�>x-a8=� {Beals}] m�ysϣAn2hU6  U:|�,_m�o1 �or�%vL�v���,Tnd en�.�>�19:BDBo2Bf�ms `� Ri) Õc<-}, Hindu6*, Book Agency@.c  {B�@A.~.�Essay� < Hist'of!� �J�-� W q��1n (+�d�� <14o=(%�.�+ {Cr�:~�((s%�6t�N�3ofIO:F�IOne�+Sev��?(lexAbF<, D�=%752lCs~CţlQk��4W}�*tC��]entm�3.�*� P N�,h} C.~Chevallr%�q)��/r^SF��26��5~Cu+�mHMa}�J� /B2ED%#Dieudon�@ J:=9�� iK Repre6��.�.f0 198. {D-K �ui�maa8/ ~Kolit2cF�1202U {E�~Eisenb�%x�u�Lveq�aB\w Toward�-e�R��&2NE-H2v%5J+\r�Fhh&+7���m;$BzB�Fa W.~F�R_6�Ko4�A �Cours`BmB�8G} F.~Gouv{\^e}�it $p$-A�aN-��x1"g��Z*6!JQ6�?HaEH.'��-�F~� r�6�Ht�nHarts+Q�F_F�A�:o@He� ~Helga+)EWRB;z bou�3Jzk142bHw �ow�$Very Basice"�Z}y�6�M�2���Ee!A4600--623; corryF� bf 91}.�!24:�u)�umphrey��.,P�-r�;6��J,76BjpxN.~Jacob9�.b.2u� {Kn�Knapp�2X Bey�6aB�*�Birkh\"�`��6�S�E&�E, $SL(2lbf R})$B�dAg��*�Re~Reid; it U�+$S -M2�*�N?86URe�fc�,=;Z�z*��BRudin}�� ���i�8��&�*˥}, 2y% McGraw-Hie1�3..Sl1} }keliœ hM>ar:F;19�6�; {Sl2NPR�al.-P6w Dekk�J�3rSC"ǏH7��es� SX 6l~;�_.�4N�Bz.g��))NŧB[9�F 1300VO:�Sr�-P�Zrw��P:� N6 Sr2��>H. *� .�Z�6�Sr3N[.H!&� 60�05!0B��<:\t-We} E�=iG.~Weia�%<:{ D$ed &�\�9�Cb{ 7iYKT{ Tai� ��zNj6� e�I�R�76�awe�A�lm�B��{f7!:6Mhweyl� WeyM� C �})�:ir��a9)�6�z2� AFZ�bz�71i({Alibegovic!� \'c, A�bin���?�0 �v��a�UfL��9LMS�7}2��25�>�zJ�2J�M $n-Razborov"�6�l��B�� "\��7�� 666.&~{Bestvi�JM4Z , D�Fea�U�O.,� Duke��*����7{_1.uFA� |  M�3igh,�.acC ~)jaireӴree*ׁ:. ��2��@�c8�o�5} BFSela} Mb�N�#oț la's�(: L=y �^�.Lw owdi�h 4 ,�2b`y3.BH!B R. Bridso��A.�nefl�i,&���t%�%On�ros�� 8:J��'l�$, �SJ�G (Swarup��!!��C2��CGAFmp���V(#irardelD miq;��eK% freeMkY�>�` �14�2m�,oV�i�R}�3ChjHrj�K. Ru��Som�i�3�  =z(Rapid Decay+per�/1GAF�gn � �3�t3�u�Dah� t ��"f*��E�b��/P,��~)8"��(3)-'8-& 66--6�_>�2:�o��of25�9�J��S�933--963}8-36r Acci�Nar�[)v J� a-�1w%cM�r�,� Is=s�c�]!{ToN��6� Hype:qJxVW}�1�+D%ˡXA��kiee�i�'"v!^cerka)]!s*�@growthJel Td�s9�&�51�9}, a�34�]C9�Se� Dru\c{t}u`�=pirٴee-� eZ�=*U,c�?o�-�s �4��9�10��� --RDr�=��--with re�dZ� IMRN �1m� 1181-1194.�S-��r�U �ng��31.2Pic��Aspl�{%�v��eo8� �N21mWG131CK� 5I Farb�� ,r59��͉��@�}, 810--8\�^I�Po��MnA�O�/�;of^� xpan�"�Sx64/�M �5�81>� 3--7.: ���!� mov,N�in5E&PE,���: t"�ersten�v�Z� $lag, MSRI ���)"8!�75-26�#5!CWIF}.c�%�(:$) CAT$(0)$M56� i f%>, Ulg.�K:R �&2��U$-13Xi2�2ʌI( $C�]��E��jC| arguE�*`  &�qat)�t"~<0arxiv.org/abs�qGR�O 8080=j�{MR-Ro!��G%F)�x v@�j 1ZJ��23NO232�G-Man��=Y%J.�? � hn f�In�;v�5�>�*l1��H�Da�� ,�MG �J�_��w�isA1ed~�%hD!��SCqs*��5�HKo�B. Kl�r, Hadam\� Rr�t1� -15�)~KLe�Kap0�B\1eb�LB��oquasi-is� y ]=u fuN�$3$.I*�� i�ap� 582--6�o�M2}�.Kharlam��+asn�Irreduc`ϓ�% s ��" . I, tP����0� R472--51R7--57.��KM��*� y���*l��G��6�3y����d451--552]��qt� �� dD� /d�[s�heWa ro���1 Rm1�:9+6v 62M71� 2g�ת �A;���� $\R$�F� �e\5Cn29�� ArboI%c-� } (Rp���������1\�, 3N�34.� � Bour2�A�Akzes�9 �ar�,�_m�re��rba >6�it{Ast\'M�qu"�3�-97�7BSb ���a*�_\'el\'� y.�li�$ [d'apr\`eL>la]^�55��e��-3�? 92�.36�e0M~='g r��;�7� Rips��E. %�Z 72?"89Arigid6/inJ$Iy? RY i5A3�N-37.�s�� i�4P6g �%l�e�ed)� <�c"��JSJ< o~o���()!� w�,� 1�#� �Ac��inIZal ac��i'-nE�zV1�Eb52����2v1}sD*V��;�cnI:f' .�3� I .Y-���:� a|1�f2�ICM��%�!�*���of��ndFOR=q� *a.OIn��Malg�"T��#i�P)j II (Beiji8��%Bb{�Ed�/e�,1-�2�2-6����--VI,  ously �MedaA�6 }%0eH}�A�Hyp�q�~ VI9 ;R�aB{*� =z}� Szczepans�8Re�;~�B�DMj�3�6`618q^)�h)n@tpH�Q��E!�r? "� J. R� �E/�56SZ418gV�(Hf[10]} %&��AM}{ Shm�R�:Marsd�(J.~E., % {F)��I�echanic�%�V&�$enjamin/Cu�~a�&���9U�BS}{ B5S �Sm� ��, {Rayl( quot�� ite��� nonsܽc�5r�2},�!.!��., �k169�i^0.*�1BBR�loc3B6�Brocke�<R�� ��u�E, �O3ly *���� flow� -�;\2|� 57-7`} 92.}.�BFF�Flasch�nHB�% 2H;X� ��e�isoedb�of �!i5/ %a�a ��ac)&� }A2�, 61,A�655I]YCK}{ Cas��L �Ko� , YITTw�&d Tome�n �!b�ITod"��!C%�M�R1H309�19s6@CD�he�y,!�W$ks,!�!0SA&t�gfI�P,, 34 329-350��>�Q}{>Y�a68�5u\:GE�0���9876�DNT`eift, Phn|IE}): O�2=%r��!Oy$eigenvalue� ��LwNu� nal. 2�-� oq}+ DRTW6��G� n!�� Watkin�Xa.A monot��A�"� da-t�Dq5��) �U6P_, 463-46i��>�SDemmel� �BW���ed�e)��)$� IAM,Z7adelphN9:�q�}{2�%���.�, I%a ?��v. B %�24-19j� 19746�FH1:\E�Haine f orus��,$G/P$ h:G��g , 25t7�H�-2lFH2vlg>�e\'!drapeaux�er de���. (208, 545-55��%�}BFried~|� �&E�3��aH~��A#i� .�#�So|G98�T�:E 8�XwGi�&}{�p�vP y�+�)F,�.G�VCri=Vo� m5,c���n!tt τJ�(SP/0207041}6�Golub� C��.kLow C. F �m���+oW! %�HHopi�Baltimo$MDa�96s�`}{ �BGE�sgv�`�5a.�E�r2�,�|JA:a. @�E]33%�7�u�LS�� Leitב. �ZSaldanh��ՙm {New in�gel��YV�9���r�608558:�L>�>�% {�w��[�_e�of2r�p���ju u %���g g��. 3�223-246�36�u�beke}{  �D ~vanS)�p2�u�:%�qiye�X},�Y8;\}YMos����JICFiZly mans"�toE" k u�)A1 infl!I %!an exh@Oyb�ial �:ML s�DorHa��?s,4� �$) % 467-49����� ^U�P!�Pal;J)� TakeOa�{&���A�se�H/chaIr_t�`clK� bifur �}~y*9!��m]ta� a� N��>&$-E��Pr��2�T, kew�sCliffsGO`02)Sya/{]�S%IG $QR$- or��)c� ����!� omf.?%��&ica 4D��5-2���P.��� ,� {Hamil\a>oup"5.*� M&�',� a 1D�9-3� 82 �a}{2i!cT� ş&Fof�iW al T�"M�"> 1, 981-��6�*l Wil��o�� �H1�� icV� OV�A�6� Z`'�fL6]�{aldou?�J.~ A.�~Ex2gea�a&ed?ic2.I��\'Eco%t'~dHz GzLSaint-Flour, XIII---� �d� 1117!��HRH*:*j�#196�.%_.(\MR{883646}&=--83udR TaiѼRKr�bic�and-dean!st�d�{al�/. � �av*�a��ApKMC�6��NR!� � {AF}-7 FxFM�Le�$ rad. OtdeI'.���be�<. (LOMI)}, 172 ("�sialnayaY&@Gruppy Li i Mekh. 10):55--w���e�j�%S�Yo����D.} 59(5): 1063-107�BQ � -170�289�610156eĕY)Scra%TJQ_�ntQB allo���!��!WEwens-iR s!s�0for��.� PDMI�7�; t, S)8 �%Litu�S68Q(19:fX �dis�WSA�A]%,A&�W:�Y �s";g8 nd ف.<!��2Om{;6|6��eoz � 86�C: youn�F��A�.E�Y+"b��m� F2auxB ,DIMACS Ser. �~��;�Kmp.MU�j4:133�.�>�B� �Mi 3635% �ooYeCY~ Okoun��GNt >!�{Y}% }G'({J}ack edge&� itiJZ�1� Res.�2� (4):�T-19� ��160962!��i8@� F.C.~ Kin<:.=?E�� � Gene�D�_*Z.h�� �@w591w�. l;��� G.~L � Lero/�E rgolC(R��$nzani. Sti�2g nz? 6� u�l per�@a�w�(f�dden sj�. EJj�� �Xn�'22Ua~1-3,�m-K �1887486�o1�20g�G.&� .$q$-PafW� anglze.- Nove&$� *bM n�4.�{jp.epe�wJ &� pp�o�&4 leq�� F_� "�.�j2:1>u15~8A1337249.� jp.pkZ�Poisson-M�Z�In'�~C ��&ito�G&ZYe�"} �A Fesprif�q(Terry Speed"v~30� � 6t--&� �S�xage34� CA\i<�"L  +yhC:lifba.oX%330:6bm!�^:!�!�*� 6W Brow�G mo(��s�v su�g�F� Bernoullid:79�3a�&� 6656Vjp.def2�A tao]! de Finett/���em.Ƌ.p2�I{[ $10: 268-27"\ ��csp2z&� 6e &���.5�ee�< ���€se, July�˄��m)[��_621 Depb aE, U��s �Our"֠stat-obI�.۠tech-rXtk2�  �9:n=jp.bmZ: , brr�,�"u��E0meh&.#Q{by "= at �ip�� nt u rm timJ�E*9*u^ro)0y}, 4:1-33 (PDDaL&�8B 690316�reg�eA�Agev�Y�icg7]y�a�w�vhAduc�<g�P6u -S:�," A4,�mf���43�"C tsyl�E� T .�X) �/4hodI�ob2U� *�.� ".�F�@�v st��a��hypotQ| tng� �4) (Perm\cprime�0 '��78,�_ m. G�VUniv.  1anewŰ 66 �J�Sci� 75w9�"60�k1�*A 2535�>^1 *G. 1`�=6.a�v5]7 1A2T� �$&R�� edj�s9B�=�=15P$�> Gor-! k��.>Gorki!8  9042�� Ve} A� M.~Vershi��5e .�m& of 6��i�N�Cl�;sE�U%�*K.�;�$} 30: 90�)Ee 4?N�dQj 'ABCDEF�<[Da]{Da} Dalang E�E E�nO6v m� ngqy measb� J g�2 %�-to�2�lyA$0ous s.p.d.e.'� 2�G��\2�,9) 1--@S&�=[DaFr�Fr�e�ޖgos �)S � ��e��a�tw� dXh� � A�\�g,E� 1, �2�(199���?2�2�Mu�Mu>�Muell��iH`o�_�ar=3 that�oor<�9�im�>.BQ_7)Q1.6�PrZa1� � Prato���Zabczyk�I,S"�*^�i!P�2J"�Q��er ��sX���E�2��[!�!�3#man��E��x�ǀ�!a�dterra�stI�1� `UachA�c!7�F��m6J�\�W bf 1)�(��-.--148. .AFrSh]{}.�%;Shinbrot�' �Vo �uD�aY��{�M�67)�: 92Gu]{Fu}��ta�( �g$����qwhich��~�� heat��2U}, Osaka�� q��l] 309--�B}*LIto]{Ito} It\^o K., � Foun �%�}�2��~��p�(F'84.<Kae } K�|e\m�-andFA �!� 6!�]in: �E��&$�Y�B� �Y7 �Lifc�i�eV#�BLGs� �+ "� � inWb+��6q�/Eb215}, E8511, � cel �J����. .�!92]%@��@�Z PDE's �cf�S-�)d"�%�e6-PI��D��Kn�p;V}bP.~Cl�t h~�H��QJB$ NeerveI�B% Pag{}C�G6�Wa:�oqup�fRoyal NM�rlandsFcenn��ARS-�� ,�o�m ��Kste5��Q}@!o3)oB]�� Regu"�c 9U��95��� )? Rendq Ac-CJi. s.�)E<11}�-3�2 1�/15�| D[Mi]{Mi} Mizohata '.��k aᬙ� 2�6o� �k�k�>=:Mj]{Mj�jnheer J���S�e�� pe"�spAsse���"�Centre�f %5?BF%u��9�1�%2M4Pe]{Pe} Peszat%#�Exa.nvFuniquene&��� ��95��q�9� Rep.\Qe[~� 1�F1�`=UPe�>�E�.S �f *�Ur�a�J\ Wiu!�cesA� Q��p"��7�tn6 � .:�2!tZ��5wB�%�No~�a6c�a�29�O �{�y�3.\! gz��0) 4n�4432� ,Pr]{Pr} Pr\"��^xU��[ar"�1l=Q.&���a}"��RBa\-sUH1�'&5 [ScWy]{S�>cWy} Schneider W.R.\ and Wyss W., \textit{Fractional diffusion *�a wave equations}, J.~Math.~Phys. {\bf 30} (1989), pp. 134-144. \bibitem[Sk]{Sk} Skorohod A.V.,�HAsymptotic formulas < stable distribu� law�8Selected Transl � in �Hematical Statistics�, Probability �1} �,57-161, Am.\Ct.\ Soc., Providence, 1961. \�HYo]{Yo} Yosida K., �Fun1Yanalysi��(6-th ed.), Springer-Verlag, New Yorkj�80. \end{thebibliography}V\beginB {99}�l{ChMe} Chow P., Menaldi J.-L]LExponential estimate%Lexit p=6 for some Y,process 20Hilbert space�Stocha)�{A029E0890) 377-393. \v0{-2mm}5^h{DKZ} Da Prato G., Kwapie\'I� Zabczyk J�Regular!�of solE6$s of lineaAU�Y�A9��3�87) 1-2f�,Fu} Fujita Y�Integro!:er1om^8 which interpol!�$ the heat�A�2�$}, Osaka JY�)k7�<90) 309--321. ^o4Ko1} KotelenezE1\�%\A submartingaale type in�eN(with applici� to s=jv-��R8�,82) 139-151.ZKo2j�(topped Doob.�E�� con�!y gral�(��.\ Analpp )v �$4) 245-265b�Ko3f�maximalf� Z�on:�E6ea-time r.#F p!�a�e>�R�21 �$7) 345-358b�,Pe} Peszat S}.�tai.�!�8infinite-dimensɯ 9� =��Bul!�Po Acad��ci.\ %�7m 2) 323-33f�(Pr} Pr\"uss�huEQ<aryU?Y�!u .\}, Birkh\"auser, Ba\-sel��jS������^1(Tu} Tubaro .OAn�F�wBurkhol��6for.��?$defined by��=�q� }, �Qe~�W!l a��}0, Marcel Dekk!l01984, 187-192fZa}RUThe f&( calculu x� V�B�(ona Seminara�N�P(St.~Feliu de GuixolsE,1), 222-234,:�Progr.\�babQ� 32} voVZ�fZ10��P[Ab1]{Ab1} Abhyankar,e�{\it On%�valA  ce��ed�n a lo� domai��Amer. J.~ X 78 (1956), 321 -- 348." [Ab2|2V|DAlgebraic GeometryAw Sci�xst)�Engineera� = .� 1990.*� :} B92%0), 629631=TBrM]{BrM} Bierstone, E)�Millman,� E�Canonic��esingF -�in>� zero��$blowing up!#"�strata!.q� invariantI�I� 12e�97��07�30.�lBEV]{BEV} Bravo, A., Encinas)�8Villamayor, O.,�,A simplified�aof�F� and :�to( in Reva�!�S4 Iberamericana2 Ch]{Chn a�ensen, CQ]Strong��inE�/w�)6fof thre^ &�� �02s}, Joura3e India���45AX8�,Ar!�ndent.�A<.�e�:M@Fourier Institute.D5]{C5Z�To��1�of24-� proj��ve1W�re0t, AG/0407258��C6]{C6>zI�Re�]S��ti���a�=�ociety,!p4.�P]{CPBhAPilta�Oq�Q6 r�l� �Y8Comm.�ZAlg. ��� 5935� 5952�S]{CSR�Srinivas��H-F.M�matria��F�1}= D1]{D1�nilov, ��!B��ga At oric=�a @ USSR Izv. 21 (83��6ů2�"LEH]{EH}6�H- "��H9oxհ!�!T:h ��},%sent�$. Helv. 77�EM8�'84.�(E]{E} Ewald�=�Blow up%Xsmooth�����e��bh.!x��Lem. Univ. Hamburg 57�$87).a 4H]{H} Hironaka*� 6�6�of an]g �4y over a field%R Ann���ath, 79�64), 10%�326]K]{K}*� E��s��B�tEBu J.I��  14%�5x6e17.�KKMS]{} Kempf,nud�l(F., Mumford� 4Saint-Donat, B1�tor� Pmbeddings I}, LNM 339�� Ve�! 73)=$Mat]{Mat} AK� MLog>�y�2z,ContemporaryI�>. \y8M]{M} Moishezon�Gm� On n2compact-�ies� $n$-��indep� mero��c f�E�� AM6d63!6� 51-17.VMo]{Mo� , R1C]F6I���I>� 5 (19975�78.+ ,O]{O} Oda, Tvorus =��:� ,TIFR, Bombay378=�(S]{S} Sally*� Re e`� a=R� );.Ń� %R . 17� 72) 29�300. 0Sh]{Sh} Shann!�D.eem�vW ��s39�B� 7�o84�Q320�W1]{W1}� yz� bDeAMosit6�i�� �k � !Z dowAD T�J�34�_ 373-411.�W2]{W2F��`Y-w� JN � }, dionesM�15�m%23%2= Z]{Z ris���A�!actnes%�,Riemann mani& !3��b ct��y�f}q�B%, 4A�04��68�69.� Z1]{Z1N�Introdu<�w��l�min^model%�!%2>2�� P.1��he-O Soc.Jap� 1958]kZS]{ZS2�%�Samuel �%� u�ve�� Volume I��Van No!Rnd�inceta196e�!ve<e�5�Con ur� PraU:�., toX�ear. \\ $\mathsf{http://arxiv.org/abs/m�,LO/0208224}$.�Z]{BZ!�4Banakh, L.Zdom %�Cohce!kSemifilt%� in%�a�.�? J. Chab~R.PolI� A remarkg< Fremlin--Miller!aaA cernY9(1�y%@Michael +noed � *I.�(GN]{GN} J.G�(ts, Zs.Nagy � S�6_$C(X)$, J6UB14}(2) 8J 151--163eVUF$Hu]{Hu} W.u� {X \"{U}ber Folgen stetig�$e8Fund. � �bf{M2� 193-204;.�JMSS]{wJus].W.!�M.'"eepers8J. Szeptycki, EThe��� ��open ci s II\/aui�y�^H�73}� 241--266.�8JR]{JR} C.A.Rog�J.E.Jay�� $K$-X!6"S� in: � (.Cet.al., �n),emic Pre�� 1980"--179.�Ke]{Ke�Kechri� lassi�escript���� }, (W,19952�La]{Laf� .LaflammeMEquivalx"a~famil� of&� aD,natural numbe�br 1|3�#492), 307--319.l"��LL�!�C.C.Learm. F�  game�$\omega$%�a�du�deal},I�,�17O!�), 159!t3. �Me]{Me� .M�,1inigeu7ldeckungss\"{a}tze der Punktm7,nlehre, Sitz(b�0hte}. Abt. 2a1� , A�omie, �$ic<# teorShie und Mechanic (Wiener AkaAPe)�3�41924) 421--444.V�,GN/0301011}$.`Ta]{Ta� Talagra" �A�(res: Mesura�%0\'{e}, rapidi  ��ri 4 de Baire fort2Studih��74� A�283--2� ��DTo]{To} S.TodorcevAP�Top!yin A\B16 Ts1]{Ts3}"zM3R�splitt �y,}*�P��� %Log�u��%200z 1�$130�p)� 72252pTs2]{slR�" �J����EslalomsA��[)��",} ��\�(bf{18�" �27!�8 � %%%.above �( i cluded��$ish".�s3!} -newB�=new di�T&�"co�8al � !�f�Va]{Va}�� Vaugh E70Small uncount#)"� �},� J. vill3M. Reedv )L�� �C (ElsevC# .)X&197--216�@ ZV (j� 10}9c{bh} M$(n~R. Bridso8Andr{\'e} Haefl H. \newblock {\em Me�I non-�ve curv�-a��#me 319�]= Grund�+n�AES�8schen Wissensch�n [Axam_P�iplw  ;iv ces]}.�-f, B� n%Y.{4{jb} Jeffrey~F!ock.Ia�({W}eil-{P}e� !5vis�sp� �,{jbpants�Um)b�:)C%g32�hyperg  � vex core�6��6j\.}, 16(3):495--535 (elecWic:00$" {tc} Tien%�Chu� �i�moduliI4.=A Chinese�w 4}, 4(2):29--51!�76.[ wjh} W.~J� rvey.R�)? stru5ofKPp��cR  group22I em Hom�)EZ&�E18Sympos., Durham�7)}� page�!@5--269. Cambridge� <2�8ah} Allen HatchA Pierre hak,ELeilaW ne6�2({T}eichm\"u� /! mav%�J�� ine Angew��}, 521:K 4,�bib��{ht:��(William Thu!.�A��sa�7!gN��(a closed ora$�� 1�.W� A�9A�2 2�!� .Qit} Y.~I� shX",M.~TaniguchiB\A�t6�>n�8sv�Tokyo!�92.c��,d%Ar!ed ��a1�'authors.��Tnvi} Nikolai~V. Ivanov.eAut�s+complex�k��e��ofZ�.M%qy-rna"e% Res.�� 14):6�666�7.�Hmk} Mustafa Korkmaz.b.��N� on p� u�&�� �n a.]�Q0� A�95��85--11��61,fl} Feng Luo.MB�!� �!N)\.22}, 39y� 8Fhdm} Djarg..LR~Ŋ�..zDukaJ�121a/457--479�.P <{hm} Howard Masu2"E�%��J4m��to!bound�o��qG��eE��43�623--635A[60mw6�eV� Wolf.bZ�iso�y� .1%D�v. Dedj'8a}, 93:177--190%A.� {aj�*��Tr.POn a pa"S(aff��conneoon%@%$!nalmoste��i!�A}� 11l�! Jd0,respect to c'b�.�% Manus�� �506(4):475--497!�82�4sw1} Scott WolO.WNoni@te. b��H:��)-3.X�Pac )��}61a�5� 57�!& sw2 �~A.N�Geo' c length G9�{N}ielseo.B�J. Dif&0Eb }, 2��2!K29�H82Hsw��me�+ZJF-mioeŊI5 Su� � d.��,h(.\ VIII (Bo-) , MA6 �},D�. �,1,Y 3��3�/I�+N rv�MMAeu3�aN�\ p'\def\cprime{$'$} \p�6\command{\bysame}{\leavev�l\hbox to3em{\hrulefill}\thinEaJG4MR}{\relax\ifhFu�p\2D\fi MR } % \MRhref+ call&�/amsart/�/proc �/"7 \MR.F� M}[2]{%�[�www.ams�m� cinet-get� ,?mr=#1}{#2} J�IW \bV#76sA�'$t:1942} A.a9 H, \emph{Non-associa���9I}. {F}�' concep`.��sotop�; Ann.A�e� -l4$42), 6�� 707.!9P{MR0007747 (4,186a)..HArnold:1988} V.~I. {M=}d�a���K-ethode �yt�,�o� ry 6%�5at, (second ed.,z0 �2%k�"0,e. 250a;S(b.98�� "� Russ+pby Joseph Sz\"ucs [J\'ozsefz\H ucs]1{94714�&9h:580492{Barraud:�'J@an-Fran{\c{c}}ois�"1�DCourbes pseudo-hol� esa'equi�%i\`eres �, 4>4�4jIEqceUH 128}A)�D), no.~2, 179--206�1772440j%1i:531546�,nAV39H lix �"�{S}ysteT6e� m3r {G}l� ung� q�o �q�539 ��t2$226 (1,36e:�0rs:1954} L.~B&i�7al-E�e<TG 2*� �6b�a�ell�c�4O(n"�<,2O� �Q/.suN,�al[!�isdes%� 33!6_� �ers �` , N.�6!,, pp.~69--949K70009A$16,11146O0Boedi:1996} R_(rd B{\"o}di1�S�(�2*�+ plan�Ph.D.!sis�Uni �8{\"a}t T{\"u}biAt 96�b��7�!��VpResult�#QS31j$ e 3-4,h% ;\M�dH1447427 (98e:51021).e0BodiImmervollm�>% Stefan ,�I�0cit*."z�PY @*incg> � '��."� �8�5}�1-3�63--7r.ecAz issu� ed� Helmut R.�&z�$� occa�A�hi��070th birthdayQG1800011�Bj!218B2/Kr&1AN4FN%0Linus (1,*Y �ŘO#ou�hom�9�/ betwe1I�loo'4V25�94)!+� 1-�"3.pD1262081 (95b:201006�reitspr��7 iegfried 2�P�.k;{E}ben2\die {M}annigfaltigkeiten ind},�. Z&g1f;7�11l 17y�@281216 (43 \#69356� CGGG!�1} R.~LGya�. S.~S�!ern�) ~B. Gardn�H*G�0chmidt�P% 0iffiths�c rior6?s�#=f� o71Ic92�r072��/Gt /Hsu�5} Ros@ " , Ph�p + � Lucas Hsu�T)aqpAl j�a�� �#�,, \& physics^.nf.�#2 ges<."� , IV�7t���*xMA�5,��1--8 ��(358612 (97b�06�Cartan:7�9'Elie � Sur �q+\'e43s \`aahnex] ��2x�.>z5�>2-4205--241, Alsof\cite� WorkA �P{III}� $1, 825--86.*: 82} {\'E}F� Le p��� z it-(et la th\'e�6)x &6l t�9- � c. mC%�x4�2�.361--372�)k:153} R~Lo^ ruM\'10S�9 �<. vec$m �}y$3$47--159v~�.2~ 2 13�1402� �)�^�{\OE}uv� � \`et Gi�D illac$S+� 1952�z55.�$Duistermaa� 72} J�Q�On first� er&� "b os��m�ex�@ b�!�CoZ� �472|3�43A�i�@0367476 (51 \#3716 Duval��$9} Julien �Un$ �&A�. r��pre�6 �a�A�/0311299)<6� Freu�5hp57} Hans`'tK$0kta2oj:��9 llin� G.�Dbf{O 5Ah�#3��� 8478� 8,921c).�$Gluck/Warn�083} H!�n  � k~W. '�Gr�D$circle fibl(!�!7 ,9-O},6/u50e8�)���2a&32� 700�8 84g:530566��u arriu 77} Bi� Joe '�A {P}let�!����,*>H�41w�^7!x��4�6� �049860A�8�&#16696N�8f�*:�DOn {C}ayley's expl� F ��H's porism}, Enseign�2�24%�78�� @$4�Hmg 4972� 80g:51017:� omov5} M.~G1}Pp"oicj�:vJ]ic"�/� .0A� YJ8��8��-�?'47q (809718 (87jEH3J�/Shubin�2} Mik�* �EBil~A. +�R}ik0-{R}ochUQWC g�&al� operato�@C.� Ee. ���e r. I �AAm�31)�*(� 5, 3c 36�11537y 93�136 ���6� ~�V� I. M�Gel� f��,nar�<.vie�7f ~16,FU- � "�KRI 3, 21W� MR123783# 4j:5816z�4B��� anQ solv* "���&ad1//� �)�Tac� subs6+M�)��w11�/ %��96�xI%�x126942R95d! :=TK:1) David�HQ�Ff`y�3SlN..~�� e tenth G�T/� by Leo U0, �$�4t, LaSalle, Il�$71AG �0275262F 1016�Hofmana�� (Charles~E. , III�S�*��ascal'su��$ ov(+JYg 9��"� 4�53�o(0307037 (46� 156} Hopf�1�t inz �E#� �4B}eitrag zur r�n {A}��mŨ" 6�1�194�21x3.� 4785 (3,6:#IvashkQE/Shevch :198 S.~ a V.~'h1%\�S.U#�mod"�#�oa$eighborhoo�5 cusp-}e\m&9 hull�i �136%��C�3, 57�*021�16952� 2001d:320:���J�,-��/&� & Arch�(Basel&�,6)�.�nv��77915�k:F  �T)} .�%90Stephan StolzQdA od:sm�$�e�m37sOare lik� c9"� (.GT/0505621M2� Ka��G/Kulikov�3} Vik� �V.~M. 2�On Ros�8(kad. Nauk S�JMk"�E6�G20^4M%�118EL�H99219�84i:14016� 0Lalonde/McDufa� 96} 7 {&q $�Dusa -�{$J$}I��Ma$ F� g alIHd.) {$4$}-5��nt�8͡y�cT �� (*�1I�E* NewtonhB�8,& :U�16G6� 3--4yo432456�d:5704:G(ebrun/MasonA$2} Claude � L.�'$1<Zol�H�9)>�II&9 J!�*�l�U ��N�Q3�93�(�/97936�ahdE 46_Loewe��ainer L�wY� End�N �1�iW�%itee�&^��5�Q9*� 1�18�}13582 8c�/16}HMcKay:unpub} Benjam�U1W['s ����2}, >l�>d.$E!�FM Dual�  pZ� �e�  " (N.S.)=�}�2� �1 1 993 4u &�!�F� A#U8rig|0��1bbwD^2$},��SGE 3155� A2i�f/White�A� arioE� %Br(1{�V2�*b/Fh point "$'�&&<0248855 (40 \#21:�-�� , Di�- Betta� Theo�h�f� n Hy hl, �2 .4a)Marku}r��x �Wal&M9ACo.2�.E�WPVF�*octon� �]�:3843001006� 17!�%�~*1�m)a?&vAdvMI�=�1�7M�fas�A,  �67)�02201�.3� 3206kSchwartz����~E�1�heP Wgri�н1,�A�Br�;2RSikora � � e�Ne�"� (Actes des j�L\'eN� �ati�KS la moE5(de Jean LerjCS�<b�c %�aiKe�/ngr\`eQF�)5�"008S�1� 2072�g}* T.X �A.>G proo1Na$ �l,H�#4H}opf}, Nederl��� Wet2��S A.oV57} =�Mag� "�B16MG5C33--3�00604 15,6786�T e:1896�$ �D�errN%�"�O�nctuel!� l'�"�MM/Sm$%�uT$@ordre $y^{\prime }=  : (x, y��y^ )��2 � erst\"at:0pzig, ��A�/��� , JablonowskiAR�K!�LeI;.ARt'�f#B [10]�iJ0TB} {\sc Begazo, T.}, {�1$C^1$-esp7dad�a��e�,am9 co�#<�o um do grupoa$ HeishA}, Do�D" sserC�B IMPA�)&hC{BSB���Saldanha""�Nilpo<��gq2!;&*� i�� �$ Braze�!pa wA��36(� 5-38�5.�CL �CamachoQ�Lins Net�Q�T��A��M da�0lhea{\c c}\~o�W(jeto Euclid�,! , Ri%QJaneiro��792� ���c�Elfol(#a .�Yr82D l Denjoy, A��c(& d��Z3&a��.^sXu�s ��m�  duK0]J�9 et A�\��1�`s���G32.FF � Farb�C%���ks� 1�GU9hom&�EKone&+,: YysubIv$}, Ergodic�(ry Dynam. S; 0 23, 1467-148&3.�KN �Kui�@L �Ni��rZ!rKM�U� rm 2Yb�5equr?�B#;���%,<4ey-Y2sc�6ei �a!�74.� Mane � Ma\~�@R���&�:*1&ble d!ic�ѹ:68sIN\��s2btm^erg\'!xa}�F82~�u.f C�S�� 6O a)0E$$\RR^n$!�� onA�J�Ms}.�> kele2�R8' MYOe10�3AMS�6�el-po:K&i�Q+;Eliash�L�8L.~Polterovich,� -� �K&eV ��awu*��"bQa�s�-1*�c {IM��0Iglesias-Pont��o��,a� IRoid*� �, $\cE^1(M)$-Ɉ"s���Yo�K 35}}%�� 40i41{b� 1060M;y�IW^��PadeE-�w 2��$2��Ug��U� 4045�L�@{KaKS} D.~Kazhdan� ~Kos�]%/ �A,2& h � �PFUof Cal�No%4�Iem�'�~�O-��2' 481--508&i {Ki}�8~Kiril�]m[���8j Russ� E� �:͙iAY D<<9o1} B5 ,6E ��un�R" ��zrX�� 7A�8G+.� �m.~Mi�Vcoadj� orbiX9��in�Vq\�[Breadth!�S&��m� �e#,(Festschrift�Honor9 Alan��)}.�#E�frsdenET. S. Rq Edig'A�og�O!�4�=2�i�5}O9N$ REx 312252E Le} C.~� , Thicken� �conZal�avit�A��� Q�13d ��2pLI~LiKtroXV�s 2>0�9 et leurs�� \`eb�de E� ssocr0~C�f!"!5�T.im6(1e 4(488y {SeW}�2 \v{S}everF� .5���' 3-!& backa�YS �P!�����v } Su8No�44�!7 1�+54.Z!�1�2^sn:�/�.\'6���s�\ea#Min�icRhm� R�5� 1X, 46\ 2_o�-M.~SFau�"�igU1�que)�gB �>=*�H%�nca�P Se: y-�Q%M 31n6� Su}? Suss�uO�of.!S%1 �`���g�O� .�"� *� e� 18� 1F]171--16�tPX.�Gg, DeAT�B�� .�(��) A�pm Z1 QA 53�� {TW} {e��C&� 2�Morita.`!2,con��> �j2, p��:��305413�Db l'}8fIf)N 5m2B(thi2�(Va2} I.~Vai!�� Y�2YpZ-F "1� J���Q��T�~19�� 3339--33.�c {Va3} 2���mM)he AN �M#$}z 118}6,.m 9*�f�16ͽi> �C.� BMonats#(-�9it8 29|12� Wa�~"� E�lB1&< Let"kI-}eO"u 3�/3�ob�101� Y�We ]��e7Mup re&�[�&I--�&W Q&� /M--1�*89�3� 402Xu�|Xu,>� k��^!IA�NQ� j 116} �)10�d25N��jJQ.+1.{bl$9�N.C. Leu(p� - enume�'vug�] $K3$P�EQ+ar�8�9�OMS)�%120%�371 .*�${EGH} Y. E"�� GivdMl�F-8�I:�L&� ���or5 GAFA� 0, 560--6EX9 FP} �0Faa[� R�0ndharip�, )�Ho{�+l ��0-Wie#uI�q\�.\�39A�173-1�.��l.n� �":dc� taut�" "P�!�EMS6M.vg1a� Gath�0%\Ab�375"-� a�%of �QN�D.�K-�1P=� 71-2�F�{g�sB}�6Z*� � he mirroIoula}, )n�l �3�7 393-412��3N.�#recurq) on%� b� of higher�u!� �2~4N~rZ;S9v H�1Sth&s.�$Kaiserslau� -6�iv �ue%�"3�:$ Frobenius�, at:� IMRN� � 1265-12�Y�GP� �e.Bd |���virtu�)lasI�mZ-�q13Ai0 ), 4>5=-VJ Vakiu`emYup|v�Aqvanish�I}n� �,T�b80r,IP} E.~IoneR-T.~Park��x�Jln.?H)! Au!5--962sLR} A� LrAY.~Ru� yS&surge~ n�$Calabi-YauC ld!Om�#&!�Khe27Rmorphic � �9�6�dQm& 22Jz� >�|"&ycA) in niTvo�+o%sm*-8gHof�� �N�V�$�j�$0}=�BF81}�#BedM%�(J.~E.~Forna 58,it� plex&�!� I�convex�V�3}*� J�$48}, Nr. 1ĉ 1),1�6288.�z {B86�b~BeB`~a�$ti� �B!uBe.�` �-x "�!A.�H�9I�8��'-4�}Y�B87P.~Bo|�E.�WKerzmaZ4���nn .U'�M�6�"+CnV{a��t �+!:3�80�^46� BS93.�%�Ec6 ~Str��,�De Rham *�of*� � i�� �3�$n+*teu+ Sobolev9l6 !�$\A�line{\&(al}$-Neumana�($m} , J.(i*l� �I6�9� 2�G23�~ �,\"�?T@$it{Global -s8��: a�veAl$L_2$-�%�y,} Sl{a" V��bl�5�jn{{rE�Y.-�6&j,��&�:�37�8a.4_e�O &1 6;G78�WE#tl�<-B�>ry behav4Kuol�U�y �rlymEm�d9� s,} V� �4T4�c8.�C�B�N�.�6yjr�a&�2� 15} �h!6)J6252iC��B�Necess!.w0i�uA� sub�2AJ� hypo.�$ "��� ��6e}, Re�� Develop?�mjh6�3U*�g�� Stud�-eU100B� Hes!� 81, �16�` C84}F2if Bf $\barq�F��i1A���_ � }Ee4\ Siu�P*ymp.\l. ��4i.�� 39j[2�aw.-C�'e�MShaw,q1PLSIV�2 al E"/in�J�} 1hin�5d��Dic�^�6al #~/�-np al �2�}M�ris�Bm�R�pe�g�� ir=��Ah!���,j� M. &�a %�!��n�� "�Sy�y2�F�%C�k S.~FWO �48]�nw,magne�# Schr\"o\-�, er o�F,���(PAharonov--Bohm effect"d6�75�� ss*FDP} K.~D0icWBP.~Pflug��Nx� >eIVdVi}, �D �D� als �}.�D|� ��FKO-d llA>yM ~Koh�)-�I+w3!^�c Cauchy-� Alex2xl�-�6�75,h�b� 196 I�Fre I�&� Levi�g,�dx f"�3o�7Am3�/Hc \19-#no:2, 36-702�s{FS98}i%4Z� ! a"2z��:��W�X. ��%��M5�JK6�h641.�S01J)6�aa��N*w ��x~McNe�J-\ Ohio Statmh)rR "0 %bl., 9, & <&�n41--1606�2J��-W4"��g �e>c�E)1��� V3�le! *>���ysi S�%I �27�9, �:,267--282, co�}X2&fY� 28B20005Ak16�HK+ Hakii N.~Sibony���Htr�8 $A(ٙD})$ po=T~ es fai!enI8I�� J.�o�!nalmZ3E�h�27--1�:=� Ha04]SD3ngt�8E��1���: � Z����Y� �s$my&sRX��}>�*No! Dame�:f �2�HL� ~HefI�eb9mY�o� 9z� *� �,}�Sc�idVulouseI2 (I� ��41�dQ�H65Z| ~H\"{o}rm=��$L^{2}$*Oa�ex�Snce�9)=�  V��cta ��1C196sD8aR52 *i5JPI$M.~Jarnick�F�I� Di�"ces %A(p� ���,A�a�,}F�@(2$K�Kim9� InheX#!ofpp6�! �Q ��8�]8 California Los�nles:i196�lMcN~D�t9�A suffic�nO?���v�Z�AA\�Aal����alE�aHM95h00�T90b2OT�Ohsaw�)KC'keg�n�we�� $L^2$ R*,}�PM%� 9~)b#��t6�R~M�7ng*�H*����gral Rep. -�.a?�e"6}3eadu TexA� �10�Sp�)�� 1986]�S1}N�H2�\'ur l'op�AateurR� ,$}mD�� 27&� no. �H9�#"8 SNz Une5,i�es2�&S"\"�5A?1987, 29u 12�SZh  �oM�si� �9y:jM�n}�j}�.� "� ��efa�E3���(6�7J'=/S��2���(M.~K.~Sucheyj E�m&qc>E1={� GSp(4)}$}.;�l3� ���"L!DmA��Ek4ELory (Shalika volume)3U�kH. Hi?�D�0makrishn0"? $F. Shahidi�9�lD65--81. Johns Hopk�CD��(ltimore, MDF$ gspin�YAsgar� F�Sl.G "zC ransS A5l G#/.4�<.�ckpss&%� Cogd�Hh3Xm, I.~Piatetski-Shapiro)RV�� or��tm�A�&��-2��%f�$H�%$s \'Etudes'?�799):1}Y233FGcog-ps-�3ity.�%�N�.)U�3�!� func�.'��f:�:, 5�p16>�792� grs}y5 Ginz��,5Ralli���=Soudr2o1�B�9 m1,SO}(2n+1)$}:� lif'r )GL)�Hendoscopm% base�:ngeB����1��No=v�Av7t76~x2jac!�siy} H� cquet6g:hJea�.�$Rankin-{S}9�� a�� F_�J �qx0%�3s4�1982� �sham�1II.�E#V�&^E}uler�� duct1 y S��B�. �b2�EsJ�3(4):7~;81\u�:ٚZ���~� >�gc��3�|\|586�kim�Y��2 esidE)��ru5y odd ortho�^~z�0(17):873--906�t2� kim2%OKi2�����L}angWs'B�jM2� ^��3:�}GR4(7):27�T2796 B6~2.kim-exR�V�� � squ`Rof�U\sb 4$}e �._8icr'�8��026�E�P/F�1UK:18183F�3. 7Q ppendix 1]D6��"2" H. KPa�Sarnak>0s1�GP.~,\n��Rƣ&I�tii�\ ramanuja �s����.�~E�2A�2r \czh1�B�b� 2�V� Cusps��"*Jy1��2.�)B�i� . �z12(1):1��1|xg .�lq6-�2}�k.^ED-2_kduc�>��V �2icJxI�A-.�A�L *"� +�onMic.Lieu��iume~31�%��"�<� ogr.Z%��3ve"y^So �P�C��R�a�A�@lapid-tadic-muic}�-L,�Aui{\'c}� Xd J_i ic"=�sof�6sisj��� InBG�(26a�35 B2Iluo-rud�u� W.~Luo, Z�- �R�M#�%5ed {R}u�c"y�T ��(/ . Q.� N� u�B� �Akrithme�(Fort Jth, TX��96gy�me~66!]E"2؂�QU'385�6I'QUZ%6�#I�CM.�A���f {C}�07� �>'�Q��! I-E _]yDZ Canad��6e�4 298��|06zps-corv> } ~� Multip�gy�t�wem2Ej�:*�?e� $L$-% + {� o?o�=)�, Orego`�f" �.!�7m Part���e�΄%�QXXXhc�"20�12J� Fv�".I j2Ops�~G{$L$}�~q*Sp��4J�P:Z� d0ial Issue):25�7� ��M OlgaN-@ssky-Todd: in memjm.- ps-s? }R�%�D�=:c �<{$\varepsilon $}� %�2�,}{\rm p}(4)\Q�s� a )NjNa+I��� U.S.A!81(A�PnM,):3924--3927!�;$R�-five��ȀkspVa�.�����BD � =J }.-��m E�s�l. (9��6m�~l436A��Nٯ u -mrl1R*�.m�� coef���d �.-��j�L�;�i (2-3Ј5--30R�A��� -X-n�} Rce@�2I:nevi2�F��s 8>eNDT2�� 81AMJ} V� On"�E�-��BV5�!3�2�]35e�6� �:90Mls^�A�:. �lon�[la��rel me��es;�9o>X�(se�-!� $p$-� ZQ�"$(2Ay132�� 33�2� �-borel^�Mrj9 quas��b�s�Fq% }, 8(4):85O8abQ.�soueFk9Y���� S0 �} ��L�� N6�.D�,0+ ar.�O �TN/ CB� �yBHin.� B9!�� �-ar)U (؎{A}!�medT]case)F�68S \'Ecol Drmn p. f�� (3):| 3�"p.�r�c}| 4Takloo-Bighash.lSpi6G ${L}*,ht2rr�j kjsse .�.UN�vo7GV ./Geln -{K}'I*L4ſH}zt(h-{C}handra�16��)2�:�&8� \9�6M-Za2,A.~Zelevinsk2�I�HedB�of�ve>�!@On^z� A���~>� �Qe~ Cwc��Q A3:�m21��L R �f�2ABR.�2U-IA8\ M�$d�.F.\ B�+qY.\ Ro �anHDa.���D(� 6YKoxe=b��BO(I)�dvlp����}�, a&�URT�U9364. %o7,�~03,\\ %{\tt ��@>Y*�"U-�x %R��-�� %��I� in �(U..�%���!em Des�.N mV vW1te�h� }, %�\�]\)�O�"�E�E�enumbe:Jnd major�Kicd&oT$?octahed�5E qF�~�7 %1� 2�W&�YAPRB�A�. ostn8lJ� �^hadz��Weyb�Discrsm.~2D��3ڒ6� B} %!NBj\�&n�'���2.sGcY%��!��^.4BV2��\�bas`. D.\ ŷ, \i� Primآe idea-�N al i.�~� x excep��Mou� ��AlnF~8sf83^N$&3822�W3=\B ��Wachs��G*� quot�<�"2�!f�~30%��%�K76�W2Z��ir Perm�[C�S� �n7<%�pos�t %J.-�.�)��e~5�J�R116A5E�ourba � �El� fa�,!csrSM'E��N-�!%U8->��}]H} %B!�rin{�J,Howlett, %??2G Deo} %Deo�Fu�DJ�$\ DippM�G .\ J���|>�$of HeckETa�N� ��London%H/52�56��0--�P�GR}��!�Garsi &A�Remme�CShuffloCpY�)W Kron�"rh%ph)�6�1�9}Q%21w-62^ Geck�)\  , %L Meinolf(F-LYON-GD) Ż i� a�!9ZT-Lusztig��R�\-(\�%�~j20�]608--6:��Q%!Graha�!ˡ\L��!��Cellu�IVI�� �~12�9!�a�6�Hi}ɒL.\ H��]�J9� �\\ iM ~�Pit�  Bo�$f ��Y�HA�P=soefsmiA��^��!x;�$BN$-pai� %& type�LPhD�sis�-.\J British C"#bia���u�%�E�umphrey�R�>�J.�!6�����b�*New-Yo�7!5u�G.���A� ��A"�s"��bnt�re#�&D Murna[� -Nakayama. "gEaa6� $S_nCA� Alg.�c bin.aY�a2�255.xHum�"\>.%- Refl(EIK%"�j }, &z;6�7U�29.%Uni�;=!�90.� Ja} aJ� �L4R�A$!S"�%P>6ZB�1:IJK:�%�KerI�֘}, En[Eope��"i it�} h�son-Wes�d1�Y�Ja��Jo#� , ??.�Ka��.\�, %�go���ung j .�KL3 �?�!��G �6�e�Q(m��ż�},:�H~5��79�265�S�uXKRbW\ KrilofCs�� � J�g�] {|[�z+|~6 ��2),�la uLo�-\�-zoncy �Sta�� d Young t�>aux�^A�&{ ��$D�-. |~22 9�2} �d=�Md}� !l Macd!�&� U�! %a,all Polynomi , %s2�}, ^\��, %'^:� e�2;OV� Ok*vH!�MP ershik--r*approach��6�!3oɼ&�I8}, Se��v\ (5 .) 2���)5R66�.P}\� PushkarevM%m�46�E�/"wreath p+[ 6�!rF� Zap.\ Nu9nJem.-P'c'.\ Otdeؖ/ `$8teklov (POMI) 2�R0),j reds+Di[i Komb.\ i��NV(m.\ Metody.w2�4�94--295;>cfo�6A �U\�((New York) �#jT~23��3!�'1a�8�b>� SkewB�$*M�S>`�?%� ~325��n16k9P!=� e} %pReutenau& �;2��. )Q2 �� A7�36�1�.�R��6;u du� a2res6p�����X>� <)134e�A438�8.�Sa$_�Sag"�+�,G�:��r*7�) ��i43leEhms \& >�j}, Wadsw�� Brooks/Co��M!�r'lCA�5�'9�Sc� -R Sch\"utze�`9�L>��1Robinson!�NC��s�e�que, %V� 5�� pp. �113&Z�"� \2�v\%w S|3BeT!bord o�1�$Che!e ]�I'��6��376Qa�=' ta76%,tan�MRBin��R, MDb2Sin�E�6Ao*� "SW)H&�\����~�VAoe>33��7.��nJ�E*�W5�ri'p�~1, %�B6�SSt2�2z%��y2.� Z� 62%6�CdGE��"' St_sig�\J�So��a�s_,-bac��majp)JA� 2\�, 880+2} Ste� SteH�V� 7h 9�T}CTit %] Buil�>Sp_:�Tp�AhF� BN-P�A�V ~386Jrf�K2Z6�V�"` �L�XEa�3m a���'s.:!N!��QT�mKm�"2nach C�2�M�26$AX%PWN-Po�C�fic:5Warsaw�: 0, 4�6ZR�7 n�CDE*�H[BGK]{BGK}�Byun, |�Gaussi�7H.%Kim, KWJ,ͱ-q �fa"˳2�8m��%��ch�!�"��V!k b� b� by� &�"sm� � itw�.�9 .} 1B�� � s qm��fimov,z�x�z� �� Wong-Rosa&�oY unbZ<�S^1(�3{��f) �Sb'} 1L�9|�9!�9?m�GKK]{GK�D=y�1v%2Klozh2 ;�Aw;"��J�*g mani�U �n6Vad�� 472 !C72 768*2[A0G��oQ��:�N�z.�co"x�!�!��ly�@� -�irJ��2�N��, ��1�x, 882!'[IKra1]{} Isa� A. VRgDomaiu9 ith � �actJ�&�M-gAd6�G .} 1�u �2]�2 �7bz�� F%=\b�>� J. R�k2q� 5!8�Z�-1�aY� IKru�uR6 uzhiNNI�E�H dj-�$%���!Rl.-?CanK*J-�} ��A�1ؼ6�Ka]�0 Kaup, W., Re�}����Js�|!�und�aEWe RAk�K uf kI� en R��m����{Iq}#;19�e 7@�-=40KK1]{KK1} ��FN�N1a��F:*} 3=<27 &282�V [KK2���inx� ;re��on=��1��F0v6-�1��g( } 28��� 4�4���KM]{KMN^Ma4��WQ�J.%��$S �/} c2�503--52��Dl]{Kl} Klembeck, P�� \"ahJ6�aCeB�v*ͳf$�-s *n,%A Ńa�H�DKobay��,T�E -�8>pQS-|^It ��.$2�9}o]{Ko�� ��� S Hype�"Ef�.�@M"�=a, ��.� {|197.�[��K��KBr.[.�z���hardtU�~�%�\�� -IzvaP2�c 9), |F6�0P]{P} Pinchuk! I.,2�. $\CC0|1�>A.B�[@�f� ���Aq���-T. III�R?!I*AKoAWZ��� .}M� 17>d [R]{oB2 = E�Sur u6AhW"�Ais�z�laA�le�rmi��UA1&����' e d'.�eQ� &"�@.z2 � 91--2 ,*��imizu!�,* 2sI9esedF6M�J#�yI& } 15M 3�4�u5W]{W}� �q,b�uni in5~ :���a�qn25�R; �f; 6�YAAK4} p�AdamjV?D.~Z. Ar] A�8M.~G. Kre\u{\i}2�(In��( nkell�ckt�&���me�"!.-)ja���H# Ar�. ���!�.}, 6$.xc1�/̕*� {ACC} Gr�seۀ Zoia Ceau��s}}escu�) T.~Cqlin.� Schu=daKFe7�i���.6�Li��R� �9:1L�H�mUW{CP3~Ca�|�d R.~PepB�)8 pha��knoer2�*�O�#Z7 iodi<�7F�Z u�M GA ��Pp]!zGE�(X$-Ray Crys!$ ��s7(�a ��S.)&539--34n05. {CS2�scha Cot2 ,nd Cora Sado:�* Two 6oXish�(ub�Eh� {BMOO2N}edi-A��* �'U�_E��t��B��<pG &�UOTS`9��.0��96�N DGK2�#8 Delsarte, Yves��Gen�*!a�am2T�Pla��least <� tG"�= "=�Epr���F� EEE � Circu��� �1):59--��2� �3��Half-�\�oe�8z"Ay*�4eu.�In� �4):46iN7%�U,\DG�Phi��Ji!!X�7R}udi�]&�*�s"��E��Q�B�DAcoust. Speech Sig�#es%�(8(6):701--7�����P�_ DGK5��=��P*�matrix- M d quadratn>�C��Fb SIAM� �%ic O�*e�{!�'2192--2Z�82�(Di} Bradley��D�Onso2\Two2��ov&�@&>n�� MGP�`:1V&1W�NR.� DG79hCarK�-%$Israel GohGg.n"���)\Od��� !g" pu�汉Ft��a* 2w+>�79ϣ��b�B�ce �b�ZI36�H2i�6G5ޝـ[; F}redholm�.�e��e�h� 42:5� ��2/6�DDFL} Sarah~H. Fergu !c�~T. Lace2�1ARk6�by�m�*߼&�9��R�189eU�160�"2.�FS^�^�>�E�x m|oscp�� ��YA� disk(0 �7J�!"�<ޞon:�6^�) %� 81:2o26�M002�FF} Cip; Foi�&K~E.Z�zh2�H%L�;$�}lif�2�!)-4��$ }.�2��"�+asf*^�2�F90���� , �>44e|1:�:&!��2L%��GK1} Y.~�WY6�Cou�lexa�lY -sq�{�O�g zati�{\rm 2d� hqvɧ��FNE~#� �:11:33��3�Y9�~&� GW} Je�$S. Geronim<1Hug�Woerd\. P������ F}ejwU�iesz f.?�!�@utore�}A �%wo*5B�7"v'�9.#.3" GHX$~ͭ��BHe��.=��r� {T"� ��R46/ng)el&�.a�o�V����.hE�$Rev. Rouma��.�<q 9��6LU�KW1.��`��Kaashoe�BK��J�� ſm�I p1�aco �2�5ߕB�J.>e 2:1R@v�Y2~GK�0I5�����:Q nA�aD�bve"|!hr�FJ�8:m!�2:3��3�*19:J 6R , Seym \1�d ���nus~A.5�B�C4;H�1) *#I V}�4{II�p�)63A�A� >��+�+*"U�HE�nry�:� �"�>�o"�v�#2�Ae*y� New 'Aq�8wL6w%�G�(Lowdenslage2fR�'ic� � ����K>in sev�?n�c)9�9%:0�W�69 LNK=!��z� {I}�Bl.� 106:��2}$��=\L-APK� nG�Lev-A�Sydney��ua!Thomasswl�(w^Ed��a(�ximum-��op* PfB��.AE?I*BM35�=4�50# 6�LM�"�L�KN�Z Mali2m!+z&�BtB� � ��J"�  � i6� B�F�"G, 6Hing�n9:4H412 p.UV(Page} Lavon��.:. �� ({S}z.-{N}agY�ia\c s"> eem.K �n*�m��JA� 20:1�014K70/>ز}, 7:532�9�y2"Wo��.~^�UM�%�1.�6�Stich� 5�:Cafum voor7�kunde�� �aa!Am�d�͉N�Xj��'�5{AB(*~Aizenn���$D.J.~Barsk��Sharpn�l�# �-�m�K perc��� G�l�%$ CommqL�G} 5[�\:7�z�a526.�ANF�C.M.~NewL6 TreG�ph&%�J,�c�59'"`ojb���Y:.2�3 ]�[ � �9@ BBW}sMBal cr� ~Bollob\'�M=�� !s-inuum24.# stepeׁ�iR�>`, )RRandom �uEЉA&O,-a2��(3�46IGVoGki��>�O. _ior"� e�5QaaAs�r � O2�,R$is $1/2$, &� "E&.��E���}ed H}. ���t avail�N& \web�QB�A,math/0410336�AU� ourKesten�A short�ofq ais- F �emR��Me!�./#!��@59}. \bibitem{BR�note} B.~Bollob\'as and O.M.~Riordan, A )� on the Harris-Kesten Theorem. Preprint available from \webcite{http://arXiv.org/math/0509131}. \bibitem{BKKKL} J.~Bourgain, J.~Kahn, G.~Kalai, Y.~Katznelson �(N.~Linial, ��X influence of variables in product spaces, {\em Israel J. Math.} {\bf 77} (1992), 55--642�@H} S.R.~Broadbent%DJ!DXHammersley, PercolatioDcesses. I. Crystal)}maz�hProc. Cambridge Philos. Soc�53}�@57), 629--641. 5N4FK} E.~Friedgu � G.~K%ET Every monotone graph!perty hA< sharp threshold1/ � Amer-1.�124�896), 2993--3002.; Grimmett}� ]9/0}, Second edi!@ . SAm�ger-Verlag, Berlin, 1999. xiv+444 pp. ISBN 3-540-64902-6.=H2}��I.EY$connective stan���42!�5.H4��D: Lower bounds fore�critical!�babilitA�{A�Ann5�tatistQK28%�EK790--796�5N�dBornes sup\'erieures de la~\'e �$que dans uuu/filtre<, Le calcul des6G8s et ses applic2|s. Paris, 15-20 juillet 1958, C��(ques Intern48aux du Centre N p�DRecherche Scientif� , LXXXVIIeq 9), E` 17--37. %�L�.��Y} T.E.~ , �~l9�r���a certa��y@!A�ou[Q�.RQ6E(60), 13--20.�K��6���~8on boolean funca�� �29-thA�0ual Symposium4FA�%�s��Computer)�$ce, 68-80,ociety��sA9882���1/2} H.~ �7N>tb��.Xo�squarA8 ttice equ��$1/2$1s Commqv Physqs7�%8!m41--59F�816�(Analyticity!ڡ�ia nd pE+,law estimate%-5hA#.�t῕J. �2�25E81), 7A�7562�8leitman} D.~J.~, Famil�,of non-disjo& subsets. ��J.!#$binatorial�f ory}�1�6�J 153--152�LSSa8M��Pggett, R.H.~SchonmannE�A! Stac�Domn�b%H meas��1�Ann!�ofA��J �-9�z 71--6-�8 S.A.~Molchanov-*,F.~Sidorenko:�I4( some2�17AJ�-142%�88�Z766--1812^$Russo} L.~ ,��} ]�Q6TZ. Wahrscheinlichkeits�Lie und Verw. Gebiete�)'7�39--42y016�n�roxeS zero-- law�֋6I�82!� 132 reli).�Appl.m��2M�5� 6--562�VWa�0Q.~Vahidi-Aslb(J.C.~Wierma��,irst-passage2�-� Voronoi t l ��2566F5M�eed� , -�The�gB�5�j�7���357-453.�Fri�R�igal�Hy�n��geodesicI ary w�� V ( determined� their� @damental group}, eogy��9�4� 2004! 9-81�, {FriMaPe3} %��F �!�$B.~MartellJ�iD Dehn�l�g of cusped.�3]�w��B�fw6# 200Au425-42� {FM>�%�� J.~W�0rgaE ``Smooth)�9���co�  surfD'' Ergebnisse der��ematik] ,ihrer Grenzgb  (3) 27v�.� {GU6,C.~McA.~Gord}�L���)� �!�a9�"�N:& memoSLng SISTAG, Contemp� , 314� -82. � ican�DI,#v� , RI, 26� {GL9�6�-�Luecke���E�N�2����A� th.~U��8�371-46�GS5b R.~E!`mpf�8A.~Stipzic}, ``2�!O$ Kirby �usA0Graduate Studh i.1s!, �fKYPr6N�*[K.���>�2��  r No 1374r�82� L&�0F.~Laudenbach!8$V.~Poenaru"hA"� �.Whandlebo!+� Bull-�M%�Fr� ��bf{100�h(72), 337-34.1{survey5��^ � �؝�BM405250},�appear!с,p���� nian�l%fLondo)��:n Ser.~329 ��6).�magicN�![26 �.c��``K''�B�2042282;,Mat:alta:dimy�S.~�atveev!K�� Spec�skeleto~ piecewise1 !2�L,} %� USSR-Sb.5�2� 7��?296�Mat5:�4 ``Algorithmic�ˁ�classif� !�=�e;e�� pu�on!����a�Vol.~9j(2002�Roh9DV.~Rohli�n)@ New resul�!�kofɈ.-5H}, �@~Akad.~Nauk.~SSSR5N8�195�221-222'Sc&� P ott!� m!�H�.��� 36� e�J�C� a�\1 401-487.�T= * �algebra�knotted� valN� s � Turaev's�dow worlA�� T� ��6 !(��), �O62= bibbiaUx>�  `�ra� Eqh ogy !5\,.7Ao mimeJed�s�;inca?&2iTu2@G!%��$Quantum in�nte�!&I�2�'',0  GruyZ�E�18, Wal(d3\& Co.2OEWeJ' \p���command{\bysame}{\leavevmode\hbox to3em{\hrulefill}\thins�e} BG4MR}{\relax\ifhFunskip\�P\fi MR } % \MRhref is�l"' P amsart/book/proc defo a�of8.NxM}[2]{%A�{�www.ams"�$scinet-get�,?mr=#1}{#2} J�IW ^]EGAIV-4}&@[Art71]{artin-alg�,s} Michael AqMAiIic ', Yale&Y"�� HaveS�n.E�H1, A James K. WhittE e��6� given atg iO69 ��cal �aphs, .K�3 �rep} MM�$Th\'eor\`e�de � \'es �\'e p(�e) �`\'ebr�Les�'"yAde�tZal,  Quebec�073, En collabf Xon avec Alexandru Lascu�Jean-�\c coi�Bouto�\'e�irc %)at� S.V0, No. 44 (\'E��0.]%D4-D74BC Vers�fore���D��A9 tack!%Invent( a ��27P165�.�H[Bor94a]{borceux1} �cis B 1� Handa�a� cate��A � . 1}!d cyclopedi�  %#���its� s, v��5 "9 5�q 6�94, Ba� �y���� �b�2B_��2F�.�A�ndb�1*oF�B��)X  stru�B�c�3��3��2���of sh�k6�TR70]{benabou-roubaud} a� B{\'e}EAJacR &Q� Mona~et� cent$C. R. AcadaSci{ a�r. A-B"� 27� wA96--A9.l[DG� 1! no.~ bib�� II-2�3-F�� {II�5!d!�ohomolog�a�0 faisceaux co�r!<}},j� .���� 17, 2��V-1�4-1B��� {IV}.2�E� �5��i morphis�G>�!�'E!+sF��4),�20, 25B�V-�4�-��� ����!�24, 23.R-�3-�F�������� �8!�5.E4 �F� ����E�:���7M�32, 362��J�){ Di��Gru2hre�r mat� �!n W� nschaften� nd 12Tp[Gra66]{gray-fibered} John~W.�y10Fibred�8cof  i+ Pr�+�  CM cal l (La J � li%!19e��,n York"66,7(~21--82Gro95�� 9�\Y�TechniN)!�)�Ct�&% 'exi�-�&��qie2 �_.+ 2 . {D}a���$ fid\`el� plats.�+c � 4Bourbaki, Exp.� 190� ,E�� Q�*R 95-099--32.a4[Har77]{hartsh�*} Robin�. 11-�*r X�T� :�@ �t� 1�-o,@1�76�hir62]{hironaka62} Heisuke H �n exax� aa1 -{K\"ahle�!}� �-a�' ��6R0*� },�#oi . (2)���7�61�+202� HS�0schowitz-simph And"�eGCarlos S (�{DUBour�$n-champs}}!iarXiv:e�$.AG/9807042�HJT84]{joyal-tierney �El J�My�T #�%kte�! � {G}alois or - }�}, Mem. ��8�C1@5�84��09,�7+72�Knu�5 knut%>�  K �F�By&�.�2� �6�,� 22�[KO"knus-oj\$ren�h$Max-Albert�cManuel O.��i��.n et �_`eb.('{A}zumaya}i� 38nf19�v�.�KR0tLkontsevich-rosenberg2� im K$E.&� R2�Non�ve* )fla��,, Max Planck� itute�MѼc�.eprint!02H �b]V��>>���� "�#F�lLMB00]{laumon-moretbailly} Geirard L%@LaA@t M+-B,1ACe�E '& �X 0. 3. Folge. A\��Modern4%veyB� 3nj2002�lMat89]{matsumura89} Hideyuki!� �o" ve ri � }, s�2.�3 .5�)dW�c�85 ��aKTransla<x5��Japanese9#M. Reid.5 MFK9W t} :6, Fogarty,%�. s~C. wa�ic "� �-, thir�3.,����A.�3v��� ML98!�`clane98} Saunders Mac~Lan"� e&=3 work!�"x ci?#=� F !R; ��a�.�4.96TMoe02]{moerdijk02} Iek� QtInt�6iE*o!k l���� %� gerb� �_ � .AT/02122� 26�" [Ray�raynaud�"�R �F"�'4��"� e4 �3l�� �g\`en���Z�no. 119F� �,0.�SGA1]{s_:6 Rev\^et� �eta,et� fo&Y&(({SGA} 1)},� 6� ., 2xB���6A��in� � � r:� �4B�Maz(--61, Direca� by A/ G*�4, With two papA�bye�)�. � q SGA4% 4)�*F� 6^ and <-LouisV/di�*�"� z-po�&�e ��dA(�, 1, �4 :* =F 72--s6J G2�A*1H-%HE&463--1964 (SGA � Diri � M. LA$&� AJ. L.�!~�la:de N. &� P."�,et B. Saint-� tbUe�c� 0l. 270, 305, 6�.,[Str]{street&�Ross Sq���\ndT *i3aspecV��Q��� *� CT/0303172@Tho87]{thomason87� ertkT �&� {K}-�,��g��7eQ26 1�+E�# ic KF(P&c N.J��+�0,o%�.�� 113*� �i 016.PJ�87!pp.~57256�N  fA/Ba� marginpar28 H} \def\urlstyle#1{{ - #1}}&+ {bhatty} � S B 1MY�4%J'y�polynom�$ of pretze�/ }, U�Eg5honor> sisi�,K.Sou�7labama&4)\7(dvisor S\,G�0 liam.9boyV�D\,W B��%1�ncern�� rangw {M}�'� m�5}S nad� 24)81) 4Y6 469 \xox{�!644535.bBC9^J� rown� �(R\,V Church�!�Co�*�>an^)a*�:F R �0�Th�7�lest *�1~#},��*�7 Ram"�&s 8�99)�& -297��1Z16914332�K�A : anerkar�-_I Kof�.�{O�41� -�i� {J}o�ngM� ���}� hs2403442&E}\G8AesS(�T War�' �Heigh�Y�� t>opy ���dynamica["� ex%# �(Lt��-w(1ag.�1700272�gS/�C\,M h/ �%�%dx.doi�%`10.1017/S0305004198002990�M@(ph{Toroidal&hn@0�1e�5�*� lensA�\�!2�> 125 � 433--440)���1656802�6r�E��I2� jour�;.cms.� .ca/ams -redk .php?J *=CMB&VoAl=44% &�7Pag0}5 he~ hmer=����Mm8Ս"�ɏ�$200��40--451� 8636] 2�{jA�� V\,Fa�E�F���.jstor%�sici?$=0003-486X�*�709)2:126:2%3C335:HAROB% G%3E2.0.CO%3B2--E}�H�0Q� ��&�Q braid� s! % =%E� M �F126A87) 3�E3889908150.�kalfa9E Kgianni�K�(V� 2140/agt.-4.4.1111]�N& , R)e typoF"�*h vE0I �< i}},� :z4�� ~--1123�21138�Ykod�K Kodame���}, �Cgra�c� 4JFM}{0007.1990.�+{L�V D\,A���E��bf>V Auto��Zsolenoid�W $p$--adic�f�'rgo�Jy D�h. System� 88) 41�1���h961732gmZ 9bK W 5_On som�*�>fo.�severK�7�JU ���%E?37!l 62) �=4]90138592L mura602�urasug�=On2�a�~Osaka zJ�x0_27�F0��0137102� z2Vz�hre�~aBb�2-9939�#d210)13:5%3C771:NOTSAL%3E% V�Non-ampA:ei�'c ��a* ��i�Am�(=}O 1%}7�C776Y�<116.�M* K .yM�Ja�Przytyck9��vskein�a�a� ,lanar star p�� ��th�� ZQ 06&� 273--2.�� 542c1D�R�A StoD=ow�)2�d>J \6/S0196-8858(03)00021-6}G!{A}leA.er�2� -et/3c�L!�O.l �A)�31�r3A�R 6*� j 622�seifertY�H S �?,\"{U}ber dasD0eschlecht von� note ��<�10aL35) 5AG59�1512952 SWh�$D\,S Silve�gMIW W�0g? n{.�5.5.14725uHyp�Ac�>ing��& 45�27218616� SW04*�V�25nɼ's �,P ,���nd �<&< Z� 509062� SWb1L��vf10E�(040-9383(01A� 14-35l�*�Pe�/ h�)y& wth}}, i5 4I�(2) 979--991��192399:<!�� �6�Gy���!�j�69ey$4) 767--786FO2�stoi05Y�2Z �N� -=Y�"� A" rborz")j}, �B*5 |�0R|�ypQof�N>�� x&�W;contactp8y^�008122M�� 1�2�>�O numdam� " ?id=AFST_%(_6_8_4_677_:�)2p,�-E� weak  of ae�A��� Fac.~+Toulouse�� $(6)$ " 6B69*B1815161.?�03b.A>`H07/s00229-002-0332-�.�,co"DA a�2��Q�E 110�@2�AU# --23* $53E�R�4f12wAlt�L97 / �6`�9c6�4%� n is^T;:4oric GorensteiyiBHrity"mK2�4�9�:28}Q7), 44u 79;{y font> G/94030042V= Agan�= -Vafa01} Z��@2,``$G_2$ mainiF(, mirror syTr� �;� ginee��" �4hep-th/01101716�GM 0Aspinwall P.,�Bene��Mo�Von D.-ZU�--div� �map976 Res.2>}��93�?1�(37N>309006�EPBPvdV84} Barth W., Pe!2�V K Ven���W�X� lex � s}�&B4} E.M.G*>�(�84.@Batyrev9�  V!!D�Q� hedra �-5�� \cy ���� E�� e�K1MJ..]<=F3} A��47V 535;=�hA�31�2��9!H�Bir�al,abi-Yau $n$-E� have�Q B�J number��trecUi9 �=*K*,� wick�B6} F� .� �$. �� 264}�� . Pr�C!9),�11R7� 0N-)�T�# de�)� Fano9� �con57/-�"�?"!I�� ?+-er�P, gnoc"8} (A.~Collino,  nt� M.Ma1dsio eds.) Dip. di Mat. del�: T r\��A*109--122= U*712036�BC-FKvS�\9(, Ciocan--F�,nine I., Kim�7�NS�V,en D. ``ConiIEt�%�X%;1.>m� te i�VsHX�AGrass��ianY{uc�N4TQ4 B154i&�P6+666�y&E26 ����MiB� i�B[p�=al:)g ]AI>Ac�e݋98|5�'I�39; r:�8031086�i�-v-� a�O6� ``Gen�iz�IՀ " :i0al"/7n��5� .��� )�2�;(�:�16iL95ᇩ3VI701:� eauv�X 78}  �4S�I�\'{e}> �x[?Astrisa0Qu5���X��78)*u%�]%f erglyS�qKatz S.%6Klemm�`Q6S��� moduli �8�L��ic?�Pe+ :LB4�X!M>V204.+H9506096H BKKM� N�,�AQMayr PAJ�-Higgs�4 between $N=2$�/�P odelz�48� 42��228N�605�2�ogUvE   F�Hamilto�l \ka���EE~E}E SSSRy� 243/:0GU� �2�,${Borisov} L.A{Toward9"�%aO�a}O& ��2W Ca�� 56}  E�h�-D %etric.�ProceeBR�# the .F\l�� gres��%��Ksterdam@$���*qQ ?North--HA4nd2ad5�6206--207.�CDLS88�ndelaseoD_'�X4, L\"{u}tken C!tA�0Schimmirgk R.Ź�"t6���B�eY��"�B29��8����2.& {CGH>-C.�GraP.�H�bsch T!�Qdi�Rceu7Di�!ct�vacuaE e� Rev. Let.� ��6 95oX92:����Ro�g among� 2�.* 1�B33 ?�U4�6 a CGGK7 Ch�U T.M.*�  �'M�Ja7 Y!/B Hole� dens� %��webE�cy=�m��%>A�.SuW�46� A�82--9.� �4112:Cs�� \ C.H. ``Double Solids''��dv�a=.�47��'10&X302ox-�c� Cox A.D1"�x `�2p�#aic G7y:4 � �"\0aE.�E) ��J(o!P R%`992%DFG�XDiaconescu D.E., Floreac  i�, ��K&^  J open�Hina/to&6 %T�6cu�!�2�, 6�64.; �02052:: Dimcaa7 �5 5 Ar6!:defh*li4M sys�q�Du�.�J.Y�60}, 285D&J2�E{En�F 46}  ��Y Le�berpV��2che} Zan ,lli, Bologna�. 46) .eForbesA !�� "BM�"$B$--�� "7 ��s"*� m;0408166�eman86}  oC ``Simulta{%resolu !kthree�  di_F^''m�)S�9U24�F8a�6�62�F�6�F r�U triv� canong,bu�;a�in ��lex1 � Li�W, Sund Q , UT�/89}eRc.  b. Purem��%5;.e� S-�`10�-3.m5${Gopakumar��=!lA�&��e .!��*��j)���6of BrC4,5P� 1} S�ee� H.E.� �ZaD >Gravi7E�Z(IoP Bristol�3), 210|2� � 0209046�5-Hu(88let} fHPossi�lphase2�� �7m.;Q���ZT�98), 11R0166.1����CJht^ &'!{Lu��n819��43� 4.�: � e-Plo^r90 �"  M.R_��-i �2FE0.�B33 �A�32� GMS.%,}fL"�R��Stromi<5�d�hb�un5�!=stc F� !u�B45)�"c 120N�5041452c (Griffiths69!M  Pv `�?period%�k#r� al$grals,I,II�E�i�=�;9H YG460--5>�oss97a�3 ``De1>pA�YQ"� �" �X30-�w18~ 6q�7:aG}97b2�Primi3kZ�J. u]�4i�288--31R:951�62�$Hirzebruch�2"``S�#�?%�9�B� �ڽ8��5pz5�<~II, 75��3S�+c872 HKKPTVVZ Hori K[� &d(, PandharipO  R�c^3 Ͳ, Vakil�� Zaslow~E. : :� 1} Clay IB� �`�.� J .Joice�} Joycef � �"f)k�1EHolonom�%Oxford �kce�H&�N --n York�]6 KMPV 5L*��d�� ``Enh�d��"�in �)II�U�4q�I �q@B47c A  10��RU6�82�Kawamata� � ,Crepant blowa�upY� d�#�`"� &��- *�s�B�l��Z�1 Q�o �15i8{7Zman66} `�B umer1 )R��K:nes��~I�� 819H2{36%[8Kleppe-Laksov80�ppe H�\  "�&�/�h !*d�;�� jfaffian�6Q��W��_0/)!16a (Kodaira64} �q �P`ome2C " D5�m[Am.�!e��8� �8)��1�o8.�K|r-Mori92�ll\'{a}rL!)� Clas6kZ�2-.�Y flip"�!:Q'���2), 5�/72�B {Kon�A-� Motivv>t�A 1m8at Orsay} (Dece� 7\ 952�Lynker-"rigk} z!�[�v?*��b l ies"�"NR�4M���562--582.�.9511056&Milnor68�; !��S� QDA<2��.n 1A�E69�(��6�T" 9�e�g"HTAd6A9 82} IAT*;hos�q:4 �cnotN�ly ef=ive"�� �YO11I��d1AQ176.���   D� ��hrougH4 loo@gla�� 7+6�y �L, �b�`EB24�!1 263-277.s "_ 7050>�^, -Seiberg� �E� �<$``Extremal6 nd fiv6�0��ic �f��A�MbNA�J Q,��5 �#-242�Q�609076�Namikawaz  ��OL� e�A�A m%terX?l 2�ѷT]�g�"o\ 2�m42!ye �Jified�P��3-J "vF|4e � �2126 r(-Steenbrink���%�a�``Glob!moothof%" �1b�#�1�, 4041.xI{Ooguri-2 �Ix  ``j2*K2��=��� 5�EAB5 �i� , 4!%43.� "y912126�!RanoRan�o� E5�ma��u�"�aprojec�j"�}cNllico4!�Cilax to C�Dds. LNM"� 1389.�@.l#6Ran�rj��g# tor�  or nega� "� tq�J.Alg.�.!i�A��b-6�b{Reid, �dC��MM� 5B7*H\ g �U{e}&�B&dd'A��xSijthoffq_Nordd  �N��U � Mini��y) r�5� "=%�O &T��@`.v9�}�\.����w182��8� �Young$son's guid�k&� 6�''� \ń�)�a�$wdoin 1985� 1� �)y�w ure �㱯46�MS���354--412.�; �4. !yQ�� $K=0�'y n�2tho be "�XlU� ��ι�28; ���36���( ��1 -norA del Pezzo&� Ͷ m� RI.�0�$ 695--72iP{S�/s�fer7 �Rigid-of quot7z6�~�� 7�p6.�Schoe (� m� i&�n�5�n �pUp%�arJPZx5�"�22cI{Sieb^MW#an!� q�& �4``E#romagne��y,t)pR�confin\7�r8!u�Fy&*8ic Yang--Mills �~�2! %��]5.��\4070872��t 85}  J.H.M�Vanis��e�6nU�QA ^#Y�13�330-3�/a�2� &� ``Massag b"'��c� �텖,.97--102�%� Jt'Hoofta  G!#A�3dia�:%*y�#s*tg =%����Z+7��a�8�E~ Tian�� ��n\a� u�D:P-s�e#qact-&�A�uaWeil--�+I,��ic ��o"al.hG �oxT(S.-T. Yau, ed.) WorldS/z~c, � apore���2$�P.� ty ��tZ�� ordin�q2Q٭HEssay�  M�}"#�6�*H)!Kf 2� 580:.�Todorov� I��n%i9h�!�!Ņ�8�2,$\su (n\geq v;(\cy)9�� Comm.!�!&p�1�9"325--36hVoisin[ ���Sym �Miroir}� oramJ�,t Synth\`{e}`� $��lO�ri'62 W�Tr-vanGe�"� . �A� &$ &j� $c_1=0$1�Z.�0��211�<2�# Wall� C.T.Ca�:0p�|�� y V:�v 6-&�r�� ��0%�355-372� �� )�4ne Aufl\"osungE!8pezieller dreid&F er V�Mt\"ate"_Bo��r.�8�b:�Wilso� P.M#``��[�l�PicjST!"WV �%�$�J:  u� �e�&�"!���,&�6x"C �;a+e�5>52�Zz3}:zi/Erratum}��2�'ڋ@ 93),_�32��< �0Chern--Simons�͗a�6���܁� Floe�7mor�y6<} Birkh\"{a}user%�_637--678N�207096�Yau�)�0� "NRicci�a��5ͫ%AQP����$Monge--Amp��r�0:��qo�A 4 �J*R;y�3i�*3Au41lN�4� ��4?ZeI L.\MZ,Irit{SeK ed� ��Excep�al Set�@D.~�Nos� dJKInc�"�n�M62�ck�} \ Ch� !D@ A.\ Kiselev, WKBM>tr���[siUone2 Schr\"o?*er�%r�( �lywy�p7<ti �!� un.\�n\1�8�z21F , 24%%62.Wdk�� \ DaAk !�R�(llip, Half-�%��b� no b���> tes,a�&,t��it.�/*]9gi} B.\%� Goli�ni�I.\%[ Ibragimov}ml&i�mA�$G.~Szeg\H{�|(it{Izv=r\ �, �,Y3%,.�fX 408--46� k}�5�I2~ed&� �9inu�J)�um� 2� ope)�&c: (VJ/�SP�6�.p5kls:�Y!,astwW!:��#!d�Pr\"ufe� EFGP� form( �v�6�Y�F� ��Q� {\bf 19��2l"2kreiniJGAq re\u\i n,�( ideae1P�8.\ \v Ceby\v se��IMarkov i�M��ofI)a8val܉of> L! A�.zfurth��evelopIh,i@A��E1h.\� \ IY.��1i �1e4��g �nudelJ���>N%'�u2Th�&� Mo� P# 9"� ��%8��P.�TNCE -A5TC F-D9}z.on�k"� SF�L�,�z197274r} C.\ Remling)�ab�(el3nBDof :0^� deca�*�M�� �.1123X{r2:�B���\6d2iZ�r�.��~\26zqV��2001S 12K` {rem>�U"���� �al QE)®J%�4 ngew�y5�2J,� 16ogers)_aRy,Hausdorff Me|�B9e.q&9, 16B[{s�j�0a]�q-�e�ho  a�%6Pof2$K� �)Int�A�s�vo�fE`��} 19[E 1986.�sb 12�QOrthogo�Po�U%š�,Unit Circle,�a1: Cl�X�-���b�F�2002�����2: �# ��� zego(�   oYBV?},3�rth5��� �͒�2"WvN} a�ENeu�9��E� .\ W�oPr, \"Uber merkw\"urdi�n iskro3 Eigenwert�^�ZB�9EQ30�02� 465--46� Zygmund: 9 TrigD%�4 i�>VtI, II}��ir�_� , C"g<U�K�>�<-b2A�N� �f� Law.\let\ol4qm�@ \�X�M#1]#2{#*x} &J 4[Big03]{sB03} %( S Bigelow�{{eqa�{L}aw�<--{K}r��:�P}, 'a:x�o�,"2�"� (A�ps, GA%1)kz��X2p��. AZ. �ea�.�L2.�A �4 ��068 \MR{202462.lL$[Bud]{rB?? �R Budne.��.$ imag��0�f� � :� GTu- 2246=lDJ86]{{ Dipp�H%{G J'y}, �Rep>�Q{H}.RŁ�9aS7�[D)KF7?(3) 52D86tC--52 !-081244.�I [Kra�d dK00 �D K)��Abr"�R( {$B\sb 4$}?{ a,�-� 142%�0%Z� 86�180415.M�2]�2^�B��"wIxth.�b 15jI2) X5z887aS" R[ed ]{rL%�R\,J Lm 1~:s associCdwith {$�Q(thfrak{sl}}!,m$-M J. K�#�� 6�Y�U6)�60). 4140�� Zin01]{mZV0�M\Zin��Q�U�'s:�!.�$=�},m�%N32:I1)�--211 � 8573� R�� f�9�g*3�(style{alpha }G&�H 23} �:W� l�L��A lemma�5��O��u 3�� Acad� ci.\ USA N bf{9�2�93�7���b{Aronl= V.\ �rnԙ"�P4e u�ep�"�e�ere�ik!P`�"E1},a]i#ndi�Rq-A�i. ]oviǒ , 21�ul�F�&[bifurc�, �%91��q�6F�196�8egh} Y.\ Eliash�,�BG�}tallH��fer2� nO�Ato,p�6%~ GAFAT (0 (Tel Avivi( 9). �. Funct.��. ,,) <\X�t ;.5�/66� ees2���st��-@\�jof�� �3��OrTIP�= � �A�Ex�L�nCX Imѝ�:'2} ees4���ow"N0in $P\times\R>�2yICI"h�r y�$ductory Le }�y-E�T"% * 2vY;F , 8%07,��\! \" �Tr�m�2~F�[ .�4FO} K.\ Fukaya%� Y.-G.\ Oh�Z�� loop��%��. cota�t b�8FMorse%ttop�Asa)��� iS#K�_�( no.\�f�|:�#Geiges%n} H.\ �Jpto�2���H*"�3XG!5��d\ 2�GoryunxAV.  ,�it{Local��a�mappin�@oe%+D intoj��&~�.DS�r. I)2 323� 1!+ 3�;1--28*j {Ng1} Ng9]a���ـ� B#:�22Ng2�``5 pr�oB�Ng3FcFramed��~�2�OVI1i)!YVafvn1% =&Rc �� NuclAS_ &�2j)_k3q)�438.rWe_>ein�$A.~9�Sy���>�@s�x}, Ad&��ef�bf�>1�&�Ny�f� ATGT-F&� 0[AT]{ATF} Apo�:ov,HT{\o}nn�^-�<��� 4ؘ�A K-rk�6�uU9DaL3K�3scalarK �R ru����qf@9PQb� DG/04112 &7 ACG�CGT:�Hlderbank, D., Gaudu�,%�* v�5��."F2-^��Ka�v �,/&��@>1E&A1� `MR0433520, Zbl 0333.53040V�0BdB]{BdB} BurRD�40De Bartolomei1��8P1QxS1KAeve�����e�/-�.}Ć �B�?# q"�-07,�936089 �645��..x8LeB]{LeB} LeBrum19N3�Po� EK���T �>7� �0S(�orA8�qQ �E��6�i662� 1359x�%�874�51���S�S2�A�S�6ca,�2�.�"�>�:q�*26�.r 1~4�B9�:36�274118-}801�.�DCEL]{CEL} Cutkosky�, Ea!LIB(Lazarsfeld,A�`1��Po�4v�� �9deB0H�}1rCA�ubf{321���s MR1866486 �$1029.140225Y�$CT]{CT} Ch�}X ��&,�&�3y��. �m Vmha'o'�c foli� �p discA�Rk 4094".�DP]{DP} k��vT -P �PaA�M�Q�N�8�ucha�(e.Pa� U&�"7W!t� @q#}. %p!�� (2)� v 59}, 124�)2yMRd0�|A� 1064.3201W'2� o1]{Do1} wp&�A=��979zRemark �B�o,���"|'AD.�~y�F��OXMed;1sts' 8� , 38h. 03, "�(f/_�<MR16229͂6�2�2>�AC1�S:w��*�1�� , IA��02�>u�!y 4y[52�e916953Q�52%y76�Do3�3N�2���:A:DP}.J��62�_289�(9�c98850m� pre021719A,6a4�4N�>`!\%dR`; !QuF�rly���@e�3cs�5�03�"35�21612��6�5�5v�2�.w�n��N���}�� "| v�02;,Ful]{Ful} Fu=O, W� 77).&Axjt@ -Rie& -Rocu�rmula;"a4$GR �C �9C &�<�;R.} >?��o�&���VA�283!�046032M� 0367���%�([F]{F} Futa��A�8��An ob�<���&M� of %�bZ-��"{ {��76 4 '443A�&Fut![tV�IzOq�� .D�Bv} !=�c. {A. A3M�a� Օ-40e�0726535i� 0539�A��0HL]{HL} Huybrbs� a!�g�#%c�wM/��2�,� shav��Z=K6�60. E31, Vieweg!�14508sB� 0872%�.![Ha]{Ha}2%�R�A���Fg4.��sN�z R,� 631575;1�16Ho]{Ho}1., Y-J�9BIC�XZ H�9t�d �(h xgA���n U%cgou6�*�5E�s51�~180606� �:178262�N[Kl]{Kl}TA �_L�6*� T�R.�@��c�"�@.}: q�8e��344!�02060s�%� 146.�o2�La]{La} J 3��* in*A��. II. &�U6� � �4er�% ls.}F�� . Gre/�.�, E%9�2095472I-!r21348Ԟ�/DMab]{Mab} Mabuchi,)�m�\��nergy-%e etic%sapproachr��HHitchin-Kobayashi c2�K�UB 66(1��  2:024��211627�; �560�.�o]{Mo}�ri'�IEE80�Pr"�:.!�I�.PV��b2604!r05619� 0423e�5a��Mu]{Mu} "Z�D�.32���,.� Ense-!�&�"e )5B2a�S,110�45027��76�:p GIT]{GIT2�"gark6J��Ki��F�2� ��ic!8a(t�.} T23! ErgMӝ>�B� ~MR13049� 079�.�4[Na]{Na} Nadel���F�Mul�7qa���e�-E��_p8Ʉ! �0bo13_549���0��(73�6:� P]{P�2ul� :�9f 9- ChowE(M_Y���; ue8�333"& 03�6 1050�G�.bPT]{PT� 2�.>l�Eic&�A� K-U�*�&: 40556#Ro]{Ro}�},A�!��c�))�Fs���A� PhD��s*Im_Lal �JgeA�y�$RT]{RT} Ro�mTh�}"'TzZ< stud���--� cri�on�".�}�6�2X A�25{ � Ti1]{Ti1}=�*p��On �Y'�nj�� �z&��� U�f��yrnv�:� !,UR0�10��~MR10557"~�]716� 95.�2�2:�EH� $K$-Ʌ� h�h�� AZ9E. � n�nalM�A�239--265�1312688I�084Z�3�3:�*�b2E�"5N�8&h �Vb1�: /-3`1471884�92a��/.�$Wa]{Wa} WaA,X�0Y�!- map,� &!H�^���C Zd1!e100�C0 � 2103ԋA� 4707P YWe]{We}�8nkove,�7a�Ei\�%J-flowe high�n &�K��aZ*��ed.�:� IT� 6bV 30946WY1]{Y1} f:Sq:`8ab2�RicB^4%[>�5T!}�"%:�� a88 �2�re.[4U�3a�S4A�04803ќ!�036z �[.>Y2]{Y2>�9� �3Y.�8"� � 2a: �bdif&��a U\j$Los Angele4UA"�-���A"3(��*D5� AMS q�c� !12165".�$Zh]{Zh} Zhe5S.!�/:� H�|��� 3 semi-a5l6�!�i�>h�o, �k105a�MR142071�{092;y05�N�Nf�� }Y  B  \F >~s���?Z A�ac ^%�bS\')-&A>.*u�,[De]{De} Dem*X%�TI�$L\sp 2$�di:<@` )�ve"(.��9djO$�� �2ce�Xta�/�.�&FQ�( (Cetraro),��9.�/["3 63K��W �N ab��:g Bzu�n�5@�\D�V�2"�R�A�i�V�o�hA H NE"�!D"B.�Fu�>89��K�g-�.^ .Z4Gi]{Gi} GiesekI.*b -q�Im�WA%M�g��Kype.}:�*�4] 2L'2822�r]{Gr} G*��� 60/69�"}�Ϟ�X�A�e�7��r��2�� o�"H�.�"�. IV.��"�P�H� .}a�"+�&c��22�5� Ha&�&�-J&� � � ��.@8Hi]{Hi} Hildebr�cF. 1972!2U(&S f nd E�*�, �?�T2w�t�t.�0Ka]{Ka} Karu,�.*�.�I��4&�a�.�u��J%�y� 102� KM]{KM} 3�" Mehr���2)qRAmP�>cJ!rM�-Samuel ono-pe�8a Cohen-Macaula�} i�$ ��J�.*��# }, 4l452�^ �@>8S�7oQB��F]��'{% E L�@{�Y Y2�o]{KoTar�19 {"�it;�Nl�2��.F���`2ց268.wj�yI*�^�.�Xss%h]:2O9�/ se*3}�e��2� i]{Li} Li5&3՟�p��Trf�� !��p's.ei"Z�JN9�37AC=J42�^[Ma-}�l4E.A?73)-���c!�2. ���zAJBC8lN( l] � F��|26��73 2�Mat�t�susaka�1���P]"���a ��m�=;.}ֵ.�6B9h 10�102�:[�"US$!1�-3U�e��"e>�Z�2�2; MorriB1�T1T�Gs �DU "DU!R@U,"9U*� �  �U!�&�"A%&�9���2"�.�������R� b�U�n�.�No]{No} �kco��� 6�2mRiau%"Q�f� .}A�f[35a[�212�� P�a�>�-+��%A������&, �&e�*�U'S����#]i �&6m{a} )f� epri+y�4�2�@Sz]{Sz} Sz\'ekelyC�" %��Ex�W%#!�K��oBo]046"]L h����j�q� o �A� u%92�.T6|�9b���")~ *�ZY{�372F$V]{V} Vieh)�95U Quasi*�!�� p�x"�.}�.�U�8��30�� Y]{Y}�G��N�S8�1N�c �%1>�%�@� x ^��)��:��.*�u Bu�Gbt ZpAZ)�roAZNR�fR :�" {AAH4=<~Aramova, L.~Av� ~Herzog�:emq*hk^mT=ial�%k"�y <��*�er�#� �jC� 352}�'�= 594.�<00c:1�'*{AH>�J� T.~Hibi,H�em Gotz�$Ao�R:" ��mb�,���%�U�191 �7 � 174-b9�98 �5.�BB(EH~Bestvina, N.~Brady��39%dc�� Z��8of">< ^ 2 9�b a N?7b!]98i:2003.v=,{BNS} R.~Bie� W.~�?2~Streb� X� A2� � �"of�*�?gݘ%KV-90R4�V�g<7��� 89b:20108.ICD�Cha �, M.~şs, �F��4e $K(\pi, 1)$s%���Pro-D*E2y6P��6U�k124, :�<,Y�B~13�gK Uni&W�&1`,K 95. �97a:570 ^P8ranv 5�Oa��O)}1, 43�% 4383-�$2004g:52032-�Fa�[ Falk �A���V9~4 C��&�6�7 2 5--157 }99{17.�Fre�Fr{\"o}`�C: ��{A}rti�QQ"S a>��Ku&���/Ge1] � i6�a|%.&߸{E}�FR�ie bf{8��NNA2 8, 5hC �x�Sd:1406Z�@KR} K.H.~Kim, F.W,�ush"� �����b��� _���*v�1�38 ���\ 186� 0MR{82e:05114b.� LY} CLibgob�SFC�I�!�Orlik-S�5"C,�v$�<�;CoZ� 2�~20�N��.0� �D!]j��2��MMV ~Me��H nert,� VanWyk�-Hy#������JFI.�7!�1 �2,�j -280 �6h\ 92w�MM!�r� ilno+C.~Moore� �X2�# of {H}opfU��  H8 �T�|\6-?30 \#4252� PS-chen�6Papadima�~Suciu ��8. !���o� �Res��Notices�9� }- 1,t*7&aa^� 4m* 42'PS-re��a21 �ŷ*� s,RD �CA�K pr "�y]g"�C� 8} ad�d10�125��5g��22�PS-bb&� �  ���antc�-�},CAFM52�� �j9�Jw�8e�al $K[�1]$.F5"& �;}<�����L114S �)-� , 15,�6��e���k!6� QI Qum�nMWR�g %��`Un ofIX�L��w2&t2�H025803.�$ {Re} P.~R��ln�ҁ0H iA���a flag���G��F ��20� ��6�6�*\�3i� 6�RV� ~Rothaq �[ Tuyl-m�_ �[ n edgXl�Q&)�tt{*�NACA1816' � H.~Sa�A���}�RG\�u,�yzygie�'h��mW!: Ber�6Gelfand:2�.�E Z�,6 E�F�502438:�Y�S ~Sheu8JB�)E���{,B�mF�bf��2D�'49� 9c:16�}*}Stanley� �6raby .f�m��cq���,:oj�67G ~41,{_ay_k��, M�)�E� 98h:��.[{Sue�BKM�I�h itesil� �,`�Z!I}, �E 4� 7:�339a^0646078}Q(N�nN_.�B} BҰrko�>V., {�GLe�dt'UJ_-� a��g�W�ab8�n [��dx&!�!d��val�C 9rs}// D� �O�K�h5�D6�469�G \bX�{!� F�Exp/ t@irN�� �s�� b�i@1_t� idue �} (RusJ)// Tr1St.��burgskog��<he Obsh'�a,� �P.�6,!�&�� =�%��f��6'e�q4z� I:�� fibreW� a a wild 6�1 good&6,!iAM ��� }// t&`��Izv. �_�_�6. *�U{0}B�Vostokov�A� ��j M{:�. �nst�veklova 2mk�), Teor.4�sel, � i2ebr�E�43�c; ]bs?a*\ S \�U�3I�LT4�mP.  2�%({clb} BreuiGg,��$ese~d��؂s,U es%�sx)o%es!�l��!�:I:��. �� 152. ��2 �/@54M'Y�co}@�nrad B�>M�/ cY� ^22low r*��:� i5a.�Q 9. va(9.!G32Aq�gro6�* A%�Gvr��M*"]*�J$�7 I (ExprxIX)AB!� ��Rm�."N�"�:�7--Heide!5g&�~ 2. %!�13�V:� 1} &�� �{ ����*�s}Ά.r {mY%zur%�Tate "�{C"1s$height pai�via bi��O, : Ar��e�@��/I, d?gilh_� 5, Bg� Ba�n>��@�%{q237, .oA� Oort FA�Dieudon��Q��@e t�yc� �,A� Inda"�v.  �:Eu)�%�Ն ot} u94�Z�(prime orderiis(Sci. \'Ecollrm.��A�}�e|4e|2�=]�r��ay��I&� ma2S�3ty�0$(p,\dots,p)$�M� UE�Rl~4in02�24|�|sz�rilv?�rgel Zarh~Yu. G!�ReGR�-� N� �UhF14Cic�r (Ban�ABaH_ NATO%K Se�� ��N!c, 548C{ǽAC4AC51ew5�sz2} ~�k�"le6� �*6v�z�& smg�degree!��%&Y!�L L  v.132���� � ta} Y{� ���E��x � �G(Drie�{I0� !%1�o183"�0.��6k^ z} Zink Ta�{CǗeReo��ko"�r� e�SbE�:%�ematics,�$191} � 6� 883--9086�01��coai8te intersection!�4J. Reine Angew>�54-$1), 55--79>2^�Y�6>Izv. I�Q(66)�42), no. 6, 124!�26:E02c� 2��� isolatedB>Sb>193�445--47:G03�Q�E6B/V�11a� 2003a�4e�436:#3�� iter%e�M�coverA$!�E��O67I�3E��5A5��tend{thebibliography}- \beginBp{CTO} \addcontentsline{toc}{M�0}{References}�0P[Ch]{Ch} I.A. Cheltso����w u di&t algebraic-60ies }, VINITI� 12! 7.�Isk2]{I2j�M�zE�A�Y� Q�U� from� viewpoint; Mori0ory}, Uspekhim4� 51:4� D96), 3-72; English)�(l., Russianq� urveys 518585-652�(�3]{I3j�O8 Noether-�" inequali!L} . # con��E�42v$-M]{Isk-Mayai9�aj4Yu. I. Manin, �� ThreRO sEjcou��exa�� s to!R@ L\"uroth problem��h. USSR��15�,71, 141--166.�-P �Pf�G. khorov�% i�i� Encyclop��� ,v. 47,:I-R]{I-RVr��5Pre} � bookAYi� "V�".K Ma]{!�K� suki]Introdu6 bA�'s!_E� Perdu��.��.�Br-Z�^Bruno!�i�Log��!�gra!�IM a�9.�P1]{P�>V.���-%�2 }, 2� ,E 2� � � ]"Pu]{Pu�V�6؝�*& :zi RAN.e3.�R]{R}5�) sl.Vgeometry!�� accor� !��$ preprint,.�$of Warwick%a1�Sh]{ShE�V. ShokuA��p log model!F-�� )Fi 1��,2667--2699 R1 ij1 1} "� $ Bondarko!&VqDExplicit classific��ůl grouJver""  discr+ valu 2field, 8 imperfect resiA�} (��t)// Trudy St. Peterburgskogo��� he HObsh'estva, vol. 11%�<5, P. 1--35. 9�{02} ��(Finite flat�mutative � schemver co�!te f�I:a�B(c fibre fun� , a f owild cr@ ion!X good re�.$of Abelian�%# to appear3M�eAk���%� 2�4} .���!plV� i s II::4 , tangent�s,�qsemista�z�$, G\"ottiF�� Y�}.�E�$Vostokov S ��local E�s%pProc.� ���h.� 3i2 (24� P. 35--57��L{clb} Breuil C., {GaA8es $p$-divisibl!eYesE& s et� ulesA8ltr\'e� Ann.A!M� 2002.m 52. �2,�489--54�940co} Conrad Ba�m}2� basem�low ram�0}// Compositie��a��9. ��19.�239--320a�5�82}%[Fontaine]  J.M�V$ $ les corps%�ux!�$Asterisque�<77. n. 47--48. S!�).4France, Paris.�gro} G� endieck A%�hS\'eminare de g\'eom\'etrie$ Lique 7 I (Expose IX)A�.>� ���s��288. S�V�ger-Verlag, Berlin--Heidelberg--New Yor�f72. %Al13--523!X��81} Hazewinkel %N Fk ��c ap�饫s}Ά^woAX Oort F!�(Dieudonn\'eQ� ofA˥rii2uATIndagqbv. 37%�5EH103--1 �YI(re} Raynaud �S��as en `es!�Dtype $(p,\dots,p)$p BullI! I!u4I�a_ P. 2� 280!mU�(sz1} Silver!�E3Zarhin� G! R.�aN�(The arithmem.�&�  0es (Banff, ABt� NATO  Ser. CEl. PhysK548, �/0.�495--51E=�ta} Tata�, {2�)M%� �Conf. L�3F�� (Drie! en� 66).�58--183 Q�Q�&20$z} Zink Th�CFer�ie ko��r�8�maler Gruppen}. Teubner-Texte zur% euk 6!$BSB B. G. , iwTsgesellschaft, Leipzig�8�uRm �LW\providecommand{\bysame}{\leavevmode\hbox to3em{\hrulefill}\thinspace} \bV�10*m <{BGS} C.~Bouviere�,G.~Gonzalez-%^!, jSyst\`em��a��$ur minimal. d��eurs e+el�~$${G}$-d\'eois�/aP� � mqu�  T\^o� %{.� (2)� bf{4�� no.~;25--1Ũ\b?8Da} V.~I. Danil�emph{�� w*�}, B z3�197Gz2, ' 134,:�:-C� � #}� bfNY97--15E9�:3f} M 1�*� .��-.�F��  *� �� !s 1982,~5, 971--982� 2����-n�2�198�-M269��"�(Fu} W.~Fult%�>F�Ann��e�cs!| tudi+ �131Einceton.� 1P , NJa�9���3on Neu� i7y� it Sa �}�^bf 95�89� 07-118.�{Co%�Co2�^Kin sev�&!�-)̡(5�@. I, in Spectral�aT�Kits A*^, ta�3,  69-8.� {CG1J�P$A. Gheonde!�Repre�(�5�uH� t--p by meaA�f Kreс��.e�ariant0-Y�])Z=Q 216}� �409-43a�z {CG2��Ona7DSchwartz's bounded�2 condP �!�it M\it��2004,& ��DX$}#Dunkl%CY. XuJem �@P�@ of S-�V!��q2�$.\2001. wFl� $ Flajolet,!N binad al asA*%��& inued fra�v DGa�}A�3e�8j*,16.��$A. Lascoux!�em�ic Fu�A�Co.� Oper��� =}, CBMSMa]9 mZ�1, Pr�nSRhode Is I�.UNi  Ni�� $R$-"%!yf�&j�#distribu��non-cros� p�it���.,5313��#271-2d(Y%Sz�  Szeg\"oLe^A4olloquium Publ)�bf 23R f 1939A�R� (VbVMSY} � [An1]{An1  Ander�� {�T �����i�(bol�(�B-Ez6!�(< 47P9�5H [An2�2��h.�-:�n-� � A} �"Ip Helv�bf 58},�$3) 264--29.�[&)B�skunuza %U� ,rm 1-cochain� Genu�,La�E_}�`�8y]�[Co�)o2}Rl PlanH!)t1 �!�� �12�� ) 821--83.. [Co3�)3VzG� ic�qu"� $Least Areav��"; X GT/040806.;$mI�10}, �7) 37--7A�\bHS]{HS}?Has)�P�ott �� Exist���y=S�0!�32�. AMS �3�E� 8) 8�12�La]��� Lang |Re�nalysiA^8Addison-Wesley,#aj3).c_A)/2(( 31�/��,Di3 ~confluV ~�9:X VBh1�"�U �}%Qharmonic7finemen]f?$, 4.542�$ [Di4 �pr!�ta8�PA��� f! �Aof��oKvar�, G�D �)�3 (9�2�'2P=�5 �yp�Au� cn/(/ally)Z�.�%o��s, q�qdRes�>� �200���g 7, 3412�DS�$-sto:multi1Bb�a( J.V. Stokm� M.1$ $q$-Racah}gs, DukemSJ)P CaV 8), 89--16@I]{ism=Ls�E��Ismail,=S!K���-W�\��6� SIAM����ip�,86), 14��16~[IW�W .�M.�-)A. �, 2d����݁����w���,${}_4\Phi_3$6��pprox.�B �3�482), 4W*.�0KS]{koe-swa:a -<% $R. Koekoekx R�_Stouw,1)b 1Fpb�ndu �A�o�*DelftevTechnf&Rep�2A�98-17m 2��o �w%� �mA)keQ.@!p .O� U  in: &� �%�on Dom� of*�, k *�� .p (D.E9. Richar� ed.)�� ntem"I=%�13�3A��V: �\2�1aS2�7��M1k#c2b I.G�:� 2f �(.� F� �5h2tha�2�i� 4�=2000/� Art. B45a#h6��2 �"g(�M�$><.. 2�&� "� SY {��%^d4��,�j82nce, RI%^2~M3 �af���A Hecke�C�A. V�,rVCC�, ��.Mi]{mim:tx {>imaW(A �h"q-}6�i�.v6�� l \=*� N� 10�>z�F6 81.�,NK]{nis-kom:": {Nishino�xY��mori,�(��  to��(: Rodriguesi$ �) inner"�id�J� Ja � J+E4�, � 5020� 42� O]{oko:bci� Okounkov,�K%Krp�Hio�BmuB�bin2%�for.�6����'up��J3�]1� 20.,.[O �-ols:��s2�%�,G. Olshanski.�s�+ Jack6�%�&al"�E�15�*9� � 26} St]{4 k&� 2 V�� �n.�y�8�'m� tet1�  N�eM�2��:, e- --106�Sz]{sze2�A�"Q"Z� �1 th E�$,�) J.I9��V�� ^#K**"{I�,%yP\,Di�:sco},(C Itzykson}&it"�-��rs�M AUfrom: `` �-i�a��(Texel"$1994)''ao"?1�*6�*&41� �1 88�7(MR{1363054}�� {GP}IUL 2@B �bf A P./2( 1he"y6}0blow-��of�K2$ER*�, � y7K�+gP~ . 48�8+ --90�62260�C9 {GK �G-M�3uel�U Karras�F*����#4 ( cribJ�N $�)��th}(��+p11�0986816ZLSb� C Lo2:�E ShustiB/�.>3!If�no]7M'n,%u n upqjAmveK!�ŅJ"350�ň8, 2�2741o443875., IKS1 �I Ite0;� V KharlamMeB�Log�=$ic equival� �Welschi�?E2�.�.in!�antaBX: �2ys 59�4)�3--1116]�I1�uh hre?9 iete 32, "9:iBeC6))z44018!z��KM �M &�1EWbf YuoLU1A*vU��:��i{�R7&�R�>:�1 -5621d291242�Dusa2 �D McDuff�Imm��dQ��y!��Q $4$--=��<. �.}9 4I�!3�< 392 E�162567}]��N�bf D Sa�i5<I:/LS�$%}, 2nd e=OxfordeP\al o�, �"�, 4 �698616.�M�h2>J� $J$--.PCiP�FV�A:i Z^+ 52F G7 RI�,�204562akY�Mi0-~ G Mikhalk�� Ş Coun"�vialat� # i�go�VC.� AcadY(i.HF�r033�W$3) 629--63Ռ9881222gif�E*8 tropI$���T$\R^2/T�:^ 18%& 1F37*hN{N��A Nobil�o%U peci��7� -*I}f�28e84) 739�)� 073216gSh1��f �A��ac�^� A>��17 � 170@4]W-sJ-Y.�����r�)"��' 6'E�lowerM'�U<^� . R.�H 3�34YH 76312�W�V��5�n�%�� 4��b� Z�2�O "�L , \arxiv{F, AG/030314�N�&n"6.38alougessoyeur} �>,{\c{c}}ois A �Ala�3).&�;A��?$l weak solm0 �@Ddau-{L}ifshitz eques:&U* dnon&.*.en.Non�XarI�,S8(11):10�>084�2*�,{cs} Yun~Mei�XM� el Struwe.i&�,�r� re�]y result��� heat flow� &`mapF�� Z�201(1):3 �4196�6guohongeO�< Gup0Min-Chun Hong.�� npa�0the ferromagn�?�> �/��Calc.�3��� D.� E1�!��311--3F1961D�8inAt{\'e}d'H lein.�EH�!^,��X� lawI�mov^6fraAvolume" !J"� ct�c!����K"�>,��er.GYH , ser5 "O�%.�x "�%�01996 French o�/ nal,L*h aARew� by J� EVI.� lady} O.~�4(dyzhenskaya.{�A! 6 ary valueU�.���[ �al phys�%ZMume~4� of Je:* Sci� 6;"& J,2c!}*2@R� )Hck Lohwater [Arthur�].mel�! } Ch' of M .y�ofq�la�e�� ��� $�CR}^{3}$.l%���.� . PDE}.�s��} f�-eA�E�I}''%�{R}Y#�,�/B��>4(}, 60(4):55>Gx*%�& ssb# -L. Sulem�=~ �;WK ardo2q ��7 ous limitA��Bs$%m)l3)A���2C%H�.e��%�n007(3):431--45� :N  Qj69� "� 0BM} F.~Barahl\�A.~ Dahjoub. �ut9 tope�(�Ual�MXmin"$036}: 157--173�� ��3{BGVH Buzzigol�0 Gi. uoiEAac�]�f�`F ]uph-�E� el"an y g�C marg��s,� �*S);st%� Data�t� on �$5$Hurostat, Luxembourg( �1!�16AICh{A,D.~Chowdhury�?~T.~Dunc� R.~Krishn 0S.~F.~RoehrigAEB MukherjeeHsclostdDe�@"!te Cate!@!��b�S : Aung�#ua��L(Through Two��Matrix&:Wsl Manag%j�%�'9)tw No. ^71d .:{DL>~M.~Dez�DMiJure�)�@et�@f Cut� M\S��� I&aDbiP;cs ��bB� *#&7.�DS�'~Diaconi U4B.~Sturmfels. G ici | s]!\��6i��a#L*�:W+�NAn�LU~Aa26EO�"363--36� EFRS�~E.~Fi�$, N.~EriksJ+a�A�do�S��livant.�;hed�>�s�a<non25MLE hier�0AT log-� �Z. T.vXJo�1l 2=ym�7d�@�MS9 issue on�D al!��ic=W\tt m�A 0504}b206zF�7( S. Ho\c{s}MD��B1� �!���ge� p}a�� gap. 2�I�Cc =icat002�,OH} H.~Ohsug��T.~Hib���L� �U s al%*whVr&se lexic�Z�U$>ide�NlVs@je=QTPr�(>�}m 29} �53 25466�>Sey���Seymo�c�oi6,m�jcommo�9( s.<0�!pean ...s}�B=}:2�#290�#.�{St} Rayanley. ")�"tc�85P1Y2/?1 �$/?$333 -- 3422Be�(IL/m��Gr\"obn�K�XE]-��!%�}�4eAn!?&� Societym�,�!. 7{Z>Ziegl9My3X�1m�2du���T� 6� !�r� yV<8b<{A}"S [AM]`L�2leksee�MQ: �*� ;k.�#��Lie-Poi��1 "=x M�6!18 1�Y173&�1$[DCK]{DCK}�De!�cini�V. Kac �62C����3at�(V�:O�+���s,�8tark ienUo�,*�j��%"���ory� , �9 �0^?�,6.�r1]{Dr1C` Dr�Q: T "�GP\�`i��t�>bP-�_ee4 , 1986, !&!�V. Glea�oMS,?r�< 7) 798--8�[� [Dr2��eN� AL co�]� ve Hopf574[$ LeningradM�) (S!)\#�\3?a�.�3��e.�E�Quasi->pFn-�o14- 1457.kGS]{DGm>Dope  ?ure��$ Shnider: )�Miz�of �!5  _i� orbLF0in $\g^*$}, a�H:q�G/96070�m9�KM]{DKM(!�P.Ku�f � A. Mudrovm On aA�) ooa�ref�8, %� Let"H!�$-=63}ɋ3) \## 7`"�MA�M1��i�)3Dynam� Yang-BaxM�4q�(vector bund�U-,SQLI06028.�(DM2^�� em Ec�:Gv5�n coad�D-�= GL(n,\C)!�^-�y) 17(_2�A�M3^�:)%R9�� , Twb7J E� �.�!� Isr.af�~,!vbf 13�D�) 26EE]{EE�<En�^Q�9r of��.i! &#d5�r-m� ces� nona"]� � I�=�11224=%EEM�M2� < �I�irshallR��/͜ -LieV�k % �R genesDE��>�40328.�FRT]{FRT�<FSev, N.�$hetikh|3k,L. Takhtajan�F(2�!Z���ndы!Bn��ҡU35>Su�G]{G}�K. Gupta�/Cop1[ Q�r2 insid�(duced� }.Eg{85)B=ϡ[�Z�P% P. Sapon��.@non��Ym��.�6/+�&pk �411579.�ZB]{GZB0 GouldGS Z[RIMA. Brake�Gen/L�' Gel'f!�"E �-ac�btic!nti2� �Pum-�}b e��Zј3�.1991) 22�23� 5�Jan1]{�3C. Jantz��ra eymen5 Induzj_den Darstellungen halbeinfa�A^-Anen}� .#�!2P4 77) 53--6*�?�2��q.�.� 6 . Gran tud.� %��bf 6}. A6�"o .J Ji]{Ji%�JimboM�A 1&�5<3=0aV$U({\g})�%A�N�ia6� �(A���t9�!�}k Jo�Y � �5UE�th�Qprx4 %}.F� *�2w!u2� .l A:�han \��bu��&)�a)�1�7) 480Uy. JT]{JTp�D�Ddoroi� \1�KPRV deMZ�yemi aS�)��.�Alg�=p�2Q�n��2) �!95� K]{K�2K�nt:��1A�al�EL@tensor>d|@��A4d%;z,e2�E6�$I 75) $W@[Ke]{KeE�K\'{e}bI! ${\O}$ \`<\%Ci�aaWJ[ S�� i@)�32�OaV--4�$KhT]{KhT} �+K�o shkir $ Tolstoy �gal�M��x%� �(zed (super)=�B �1?x��59C!17.�Skl]{��� E E.��Sklya� + M�ic &� .a�J� ,}��dIe A�bf 25� 1$ 59a�2�S5� L]{L�tLusztig:M7�SO to)u�i : aj ,*+L�f M]{Mek>� -y"l S� ov-Tian-Ss/y"�bracket�qm��!2Z}h[�0236*XA[N]{N�@ Naimark: Teoriya�*,dstavlenii g�e.&( [:��ey�~ v ], Moscow�7.�R�oR. �4on An *�hL!��[M\*`to.j J����8(�wI�84�?81��,51]�S]{S} T��m% Conjugacy Xnz6-11�}\#@g?U STzT|Mhme>�-"� � G<,�yD�t4inciple�!CќDM~���*N6�17�5�2=2�H�VO]{VO}a�Vi}+e�p], ]d b�We]{We�\ Weyl:�8&� U�sir#b g6� 2�d,yJ�(yA�6.� Y]{YXOYe�1M91z r�:`A� mono�dc � I�=8Cambridge PhilojT� 10I� c26�c^QR�|f<�Y5H{AB�g Alex"9.~B�p.�ToL!deS r���p,!a�..6�ftt&h$4033792�AESZ} Ge�A lmkv hj�?8Enckevort, DucoSt-ini(Wadim Zudil6�!T*V!� {C}ah]{Y}au. �.�20�_&D B�503xxx6�>�  b�2�"*s,u_�"Az {V!2�InsYui�\ itora�em ,_9y {V}}, � in�Cf�"�B�/MS/�5_�gr NyR238� ]Ll9~Almq!�.[$Str{\"a}ngs< m{\aa}nsken {I}.*No}{}�c 1:22--33,�2��\Y.~Andr{�#BG {G}-7 %X�&�"13E!FAU)j�9'2YVieweg�6b%AGViJrno�S.~Guse- A.~V� enkoB�Sin%"rof.'bl??ps, Vz$ {II}2�MoU,!��dMrkh%y�d�6.vBa�Batyrev.�Du�#ol�%<m�a��/>W9T" �t�:R%u+"�!�}, 3:4`1535��"�#q�*�`10�@2� CKvS.�0, I.~Ciocan-F�rni9hB.~Kim�ED.~�m�Y. Co�Eld/1]IN�com�W% &�_%�{G}rassI]JE.s% Nuclc<}, B 514:640--66@�990j71002266%�f�:sed)��,ic") �al �,o�:s1 �r�6%Y#rB� :r0�#68Q&3E&Wj 3070106  COV1  gshadsky,a�Ce�Vi, Iogu�<��Ca�f2 'H*�2anoma�Di�6M�f�q� ori6�R�405:2�3J]�(F�4hep-th/9302103B�2��4{K}odaira-{S}p�'�*or avitML exac drom��L ��F� �C$n{F}_{n-1}F�'Inv }, 95:325�z=&92�o_~Borce2N {K}3"]'win"�'A�m��pai^f 6e & 5.HIn��GreenS.--Xb*o�JIIM � me~1��(J\.{$}, pages 78739. Ae',poc;;6lCdOGP!Candel�@X.~de~la Ossa, P. Ʃ�L?irk6VA%�6� ma���E�ly�)v�gA�con�7lAory.I����� 359:�=U.�DM%� Dora�J�kg6��� �� &� (FL} Hao Fan� Zhiqin Lu.��+ {H}o� &�%A�{�J} AG?onJ�nji.U2�#F��D�0��7v12�4FOOO} Kenji Fu�,l, Yong-Geun Oh, Hiroshi OhtaI'Kaoru On6y L}agrangf �$ѓ {F}lo��C�׉�ob?!io2EAvailAD�&�6�Mk{h"�o.��� acti��s;8P}icard-{F}uchs.{K}�hl�GoD�i�)n"�p..�%�>� 89:1�18�(�B���2�*6qKo# �sB$.sHos�I�! :�.2In ��eeaY%;y 6�fsS vZ{\"u�4h )*�| 1�H1| �C%O~/ �r182�KoT V  Talk.� Rutgz ~�GNov �a%6�Z��Y !�D.~Zagie2f3Period2�� Engquist;W.~Schm^v:� &� Unl�ed-2001:beyonYp� �'808&0 |4�F.6Le��Lef�DtF?L'�@bd Situ�x la G�oP 4Lbrique2� Gaut .-Villa� 19m#�mLi�Libgo�I!F0J.~Teitelbaum.�Li�fB� e��h. &��(]r�.le�I�(!�&�R"�9u/E�2�8Lo} E.~Looijeng2- X�GE�on^ �e\uy,77*�7Londo" ISi�*f�2�&�Y� ����={M1} D� ris6@ f !g�O����g.hIn��.fI�#Essay�(��" �  I�64�*�I�6 ; Ro98%�R{\o}d�[.�ŮP}f a> ,4���I!l\����.$ {$G(2,7)$2�E�0EGI`22� 2):1�D49� ��{B 801092_yUVIRoRNze~ega2x>� amiB�9v.-"%�J.~Lewi�t��)em>R or5�%O"}�_ elds C�Zlc`�'2F232N�� 9 STi^Paul Se�}� Thom6 Brai�b oup ��o)n deriv�]"!+co�Fnt sh��2#�n9�>�0001046SYZ��y�G�"��E�d slow.�-J��isC -dualit2�E~&rAyB 479:24�\��EUu�s 6060:�TjI�Y4~N. TjaattF�"MxC�C�I�l!P�6,rminantal Ne�X�5=MPh*�bnl,�of�$/�G$B�m4� 802036} Tj�8r�=c:a|b:� y*!y ��5�*3y.�� j�906116 Toe� Tono6�Can�Z�-*�l{$\P^5$}E]:� t�Eo i ,6J��c.�O{E�C�Erf���:v�6��n�I�eepa� �R;Yf�9A�Rre�5!5HR. \'Alvarez-Nodars�i ��q-)!��ran-tdzc\'{A}:��M P�Aomios ]0lizados y q-p:�&pieda��e�$rales y ap�r,ciones.} {Tz_toral.}� dad CarlomvI d[ drid����Spa�!).�an��hiperge��ricB�!��f\'{\i}a|el `"io Garc  Galdea}���deՋagoza. #$26}densas1t"d4, Spa���!�1>�smibE��F. Smirn;�{ �Gq-}WHah�H!����)-b�HT $x(s) = [s]_q[s+1]_q$U�X|s ]�� 2A�IqJR A:- ��7�8(|�g35\32� as96�'$M. Asherov�u..�yV.5/�(i, �#�+coeffici�� $u_q(3) �RA^,\F(s)2)$m:SMJ.�P(}.#5-#�859-18���sa-w-1} R�ke�  �]{A �noR|Bg �2�or $6j$ �s.-}SF|^a��(�+79!{008-10�56�2j�S"�g &���-_ �M��R�g�bf�gej�6, 6mx>�A arsuslov}AAFtakQyh1M. Rah]`� S. K. S0, ��&�%V�Eem� str.\D#_ �1;65!d81-T19bdri87�7G.�7'd,"��'e�V�n�7}. �7!6, �7820, 9<ic��: RG�1982>?fad86�2Dŀdd:L58"�2m9�=).8246�p8s,83=g"{r1}GWG %�9��4em Basic> q].}z.�&9�jim�M.09�R *�,7�7ed Todai%.it� ��^U ��)10c-8�*537-56CB ki88�+$N. Kirillo2!N.��Res"4I LOMI1pri�oE-9-88,&�3�`�(�kse� Koek&|a�M&}a{� A���~a�(nkuee�Rias� the Facul*�a�M&4%�I�m�XNo.�a}.z�a, !�"=oe��)�h , { ���j>����m ����): �U&aHN�� Acta M�>4�l�>295-32_�{ku�.�9cbZapiski��cnykh �ovE-����81.p mal92 Ae� Mala+_, F Ʉ��UJ VJ�gits connyEx ��:]bol�!l"N8 [ 1�la�6m .�+�k Janu�=zj !$5e�A!�1"N�I. FXit�6m�bJ 53 } 7�3�/5�W2�!nsu-r} F. \ Nik}kovm��\��%5 V. B'Uva$�8Cl�HO&se@Q�o�2"RA�n.} V�a.�/85,� �\ (in2� nsu����FA�#� Com*�D��ica�+-� Berl n�O1. �X�,aw>.a nu83E<F. 9� y-�9�9�Vx�azyr�W�!� on� :� ��P*.0��VPriklA�t. Im.��,Aeldysha>���osc\'u�83_(7, (en ruso6�9�U�E�dB.�Yw Sn>� u&U trz*�7�<��ir_s"�}��gG�Nk#. �F. �5����p�242x ro03�/RosenO�X�J�:a*�T2�("G ,��,&�(�ell8�)�V��,�<�C�>1232Tk{sk82C1� "�4� � ic!�C�{�,7��5.>1��263:�l {smi� >V.c06�Yu.6$ {Meth�� ��3�#�C5� q�9�����"���, mo&NDum. Clebsch-Gorda�*!�ir���� �7z�u�^  ���zG593-6�/&wsmi2}���:, �G- -� -*�%���.M , 3j+@6j���K5*��C+aAV� )5 1069-106. smi3�p! ree ���=��9��IN_Q;m1. 9�� j��42� �81604 .� smi4N�� q yE6 � e��%���. �4�a(.OB/1� At�N-.} � 56 N�u690-7�]�vk� Ja. Vilen?:(A. U. Klimy~ AF:�G� �;�UL�����9Vol�s,�s}Zu�Y$Academic P��IsErdrech yWN^An]&I{}� Belshoff,�6Enog"a�J.R. aia Rozm*�*�(�5 lis ���R�Kc$bf 128}(5)�<(0), 1307-13��"<<P. Brod�/�R.Y�Farp8it \lqg%&-<9)1 i.�^�7��*b9 s\rq�Iambr.ssQo�K�P vaani-AazX(T fE�it As"��>eE .�� �)�6&Wer�"��"�T&�9{�3G. Evan %�$Zero divis�iL the,E-like �(}6�\ �'oi1�7� 05-5:�C6�|AD.��ber�� it Ecxo�bm r'͌*�� �Ol/�m�$= Co�iA)� �25}(4)��7A.215-125�0b7� {} W�Q�qD.��tٔ Lask%�e pert(.�I1'X5K)7���81�01-11i/H%� sumu5�$JZ��4�S6�X*!�z..-�pE�idg2�� � �(�L �l�/KE?B Univ}<20D7ן9�N ��a�1}%7,9 MI�B;:+off�aq.D��)Ha�!6Qx�(1;�!8�'f.�~--�(''}, St.~Pe+:c��e%`x��-8�%, :8)_E�~114--1@L�8We}%7 A.~Weinst�<5�+va�_ clus���(Lapla� p�-a "�-�#2�{,) bf{4e077), 883--892>�4}%8,10 ^�*C7 � �>!-݁ of spec5! [�!�Funkt�4alTi�lo�`�H+ۢ �532B��aXc�]RY \ppa�EbfO��$kar5}%9,11b�L&�4} WXscale:� � um n�d!�r�ڶ�1}(�!� �78--79N����87>� 22}%10,12b����Jo��%�� �Qin����s � Y�Ses!� ��, U>ʺ]�O1(a.~12�!� 6}%11,13 6��V.RMNoFper} on#Il}v�sY!���1^� Russi�|t��N:�7}%12,14J�En^Novh�a:eitv��e*ta"��nѾ�%d@1��TC5"_<M <�>r@ etry\/} (&���} A:� V� er.��? ~187��.!I 8���202.2$per}%13,15��M��rel��*I *� ��^�Ynp+eir��@}FK�.���6�Dkurc}%14,16 J.~Kur� ,p; Leb{\oe}u�S(M.~Saraceno���"V� roxi�r ?h�I.�:'Ga��0v.�KE%�-�M@� 680A812$0��3}%15,17J�7 J E�>!I�N��&�| Y��x s*"��n($\su(2)^*$, o(4 Z##X !]~ ��`3�� 4986k|06.2(Fadd}%16,18�DH�dd�TN.~Yu.~.� }L.~A.~*"%Sit{x+m��*�HlARA� {\rm\&}1k�2����$�26�kar8}%1�J�f�Qu�B Ms�&oe��.�},F91B�, �l*���(phkE7 ߣ6!�J�3�&] Kir}%23a��8i;"}.El~7!|:gMT�8N�76# Kos}%24 E��&� .%$uni6�� RMM=�7i7�@87--206��Sou}%25E�.~S�au�mp^`��gs�Wq�� Duno��&� 0. 9P(Gust}%21,26=gav�U�O�Y�%uc�X� mal�4l%ja *� an{8(ilibrium po�#�~tro��J=7I�69$67��2�$kar9}%22,2:�=%�um ?.,� M "�;�n9D tunn"#g effecIB�Z�5 20qbZ52�T9R�14A�,2f7Con"">2���hof:W�� }, Z*#k "Y. Otdenst. (_%)M�bf{17q �x�54J�]� �w1�bf{59"2&05�y 062;:%5ad,29:� H� ew gb��&o�!&F/U�*ʚ��� adia9T�v�,n%�Fun� 92�Fa�� �0� 1F��Yv� Q.��0a�,3f� E��!&�3� >S2W� J�b����)� 3, 36J4�"Z!<on�a�_4 dg-ga/95080036�11}%26,3> R8��O[c��<2&L <kA%&um�Ue7�� 208J� �., � 32*� F� JT 2070:)ar1� 7,32fIn_?s=� y�9 ctic&7(: membrane :d�%phasea2du��~�+�)9NE�/K156��308��:3}%28,336��V�moF:"�$paths, hol�V[DULH ory2��N�MY1�Uj5��62J Mas-Op;MN�O�!Q��F/3J�Mir.��2�1�1 9,34:ZE fB" M$�.B:� re�n�f�@��Eu�Y�� cyl��~a toru ōZametk��bf{" �m��$6, 854--87Fv; Fh�-��JE779�2KarVo�D&��YugVorobj�& Adap`$j$4," ��,&D e|g"q��iso�z2������2��36  0}%30,35�|9X:� ofTJ%�6SD"�  via >" Hydr�b atomŶ m^wGN}, �Ye�X. Fiz�"*V� A���{387B�A�o MFcO.n5}%5B�N6_�F, nano-yg�AE]umU��/A�by&��iI (see% t~I!m1 `rp��; "W ����`��>��.+ �kfsh�v� 606I 7}%8�*#)H2�:�q lass� M"�J��_n� 12 G�rNR.~Ƌiw� ``Peierlsa���ion''E�$Chern--Sim�=1�&t, N�$� B 33Ce �$1�18.JGJ S.~Girvi��T�h��ism"F H�o : ��e��0yqux��!�d��688 p.~5�^ "��4o-/)�H%�?a��!�"+��Pcoo��z� h�Q01100�jin^ 1:Y%~6#M#*[ aJ&$%��R(���+TT1�J�"| A�*�6L 2K3?n)V�Z�v� 5��|g�+  S H,�C* L-Zenot J-L% Hwan&M� �{D,8m�$e��Engng+)bf 57} 1�w4{$Vielledent�1Vie! Dl1� �m1�m2} 13-�21mSousa�4 L C�� C F�, toni A C$Santos A D2 J/ ��es�YZ���& 26�73�prekels}R"  J, Gold�! Hs,Troeltzsch F ph } DFG-d< ``Anwendungsbez��e OD�erung�f Steu", ort S4 520 U Park�/ J�Rebelo N�Kobay3 S�:�Mab ToolB%R1 23} �G79h$Kim90} KimRZ90 �QRZs Manu�_�� B68`Zhao94}�h0o G, Wright E��orandhi R�h5} 12nT�S�.er04}��l��e4 Y�it�htoΡk"( oc.}V�o n��?1�[BS1]{BҋZ.D�z�D�Iil|y No! ve(s outside ��supEo�l�I�^�alv1tri��&large.�e�S amplܬ�>e�\x��.\2�w� 34*�' [BS2�2}~�Qs" A�� 6�fF� � cova�(cF� �71(� 1536--155.�CF]{CFajM.~ �SA�xDga-Talamanea, Idem��=A l/ed 2��!Ua �v %M"\�:.\�\1I\ ��LQ�),� 82&�) [Co]��asA�m���*������blq\ HauE`X{ .\ 6�2e&Q[Cu��u�k~CuQ)K*Se�|amena0(�U��3%s�fJ.\j�k�5 34���!� %uCu2]{Cujk\ Pe�C[! z9~ !�86)=?Da]��, K.H.\ David  *��� betwe=l�smo�^n\_l&~/, 9���5��� 2��223�0Fe]{Fe} W.\ F�!r���E2Cga\1Cg �n8 2�"�^II,E*���khn�?ey \& S~ (1�+�@HT]{HT} U.~HaagernHnd�(Thorbj`ins/bA new�3)ra�+r�pX: $\Ext(C^*_\red(F_2))$ HkaIaepr�5SDUA�,rMkbu!{ann1YYL]�hE.C.~L!�,Q�EM g6�-��I�&\�!Em209��0.je]�N FVJhn!�Coc7�DA � e�>,�10!g= �&�3�>.\E��2���4I4U�PV]{PV�.~Pimsn"�,~VoicE�cu!iZ�m��Z��b"g-by � -,�"�Mfޓ8�31�"6=�g76!PulJ-\!eut��2E;f pen� 10u !:2�rendl"pl�c�z6 ��J:' ��. (AvZXatm tt *�STimada.sdu.dk/$^\sim$sc�/m�F.pdf})��T]{T}y\JmMix���5%�9�'s~P� >�,q|� �V��$17n���F<�UV1]{V1Qg2Circul0Es;"E�M t ors, ``U �,�Q�a�&�s,��"]�MG'',%���6* \�!\ 92,���"US0, 45c�]qV2]{V2B�L�g��`:O�E�Ps,��ro�Qqz0�i�62P 4D9c3]{V3B{�+K}oHF�6 �31�Ny.�����G�.�4]{V4} �JYD,m�~e��non.Y` �!�4Recent advandc�,��&f( Orleans~�.!�~�que~231� 27.: VDN]{VDNB/K.~DykemeA.~)�Free R�8 �=ПMR "K �<1�7b�C�3% N�/�fs 1.� BaY:(=~s���S.~Yokur2CN��O"�WU'0Ned�g subs3N{A(XN{Q"9.�(}, 13:�t�c� U�{Chan:cp`�E��andb*�MQOHausdorf�NI3i�2�Q,Marcel Dekke�kT`�Yor�.6dDKU:higs� ronaPN. Dr�Jn�&�P ~Kee��gD#�.�� �j.��r{HV}��Ӈofo!� 4nt�,�:�2�N�1DMZ7:7�8ō6$CGJ%�s}$ Gill��!� M.~Jc�:UT�Ec2�oQ�uy&.�Van NosHd, 19Fp9�(KTY:babylon�Wa �$K.~Tomoyasz�YAj�Bob2B`Howy mile��T $\beta\omega$? --- {A�=" ng}6# b\�# ic-d��2�.�%1^Y� 45:20�23�2002]O KT:a� } K.~Kawa�4%g�.f�� �SSt [ -\v{C}echA:�abQ9c : .a�*�����u.i88�^ �2�KWo:|@quG. Woo6>Y� ��umQ�BU�a-|I�B�FunFNth�47:v5S5.Z<f�'P�� {Ba}-� sc{T. H.B�}�An}1( it{iȏ�h �Yme�a$}$% C_{n}$3\ crysta���� .\ KCwar)�,T. Miwa, eds�4  al C*��s"�1{a^[�1�T&� �: 1��}XFH�Q u񹁉�� ris,�R6�{X? }% ,��d2��]%s&2�=C.�GW�GS{�:, =R Wall<�5i6� �e*S{�&S)� }�m�pU&iT�7.�Ok6�@Hatayama, A. Kuni/�M. Okan�T.�J agi,�\.�al }$R$� =r a��Q : $E$^{(1)}�F% A_{2�g ^{(2� ��.��wY�CM>P IOU2a6 SF3Z�P�Y�Ok�GE� sc{HA�% \�����% Ba.) ,D %% ��$+1- &��k y4247}, 577-615 9�HKOTY� Y. Ya ] Re�v{ f��UA � , }i[q J�K�.\ Mis�:�C� Develop�;"dffine"{ H�  5, C�or�D��s)�bf{24;A>9}� 291c�92EKT� @sc{S-J`��>�sh��aC���u'C� b�a Verma�460>6.�KN]�.���Nak!uma,ْ-gV� �:�!|�e�it6��LLi",B�"yfQz�165%y5��46;�K. Koike.4I( sc{I. Ter� 0it{\ Young di�4m�/c$ho�&�>��/Z  XH}$�},�����d},$�VJ�07}, 4663��:f4KT�� Res [R�e!,}$GL,SO,Sp,$%f\N 9����)135�6�Lz%�sc{|� scoux, M-\�ch\"{u}-���}m^4it{Le mono% }$4�!�ddot{\�1h}&�de��x}�n:z&�!!m+���i��Qcs�,de Luca Ed.,� Hderni della Ricerca_��  C.N.R��o��/1)%it{2 LSc1=��Sur une�$f'R?de H.O�lk�CR�D�_i*�%28��95-98!�76zlec�(C. Lecouvey}�A�?"����% -֏��rA;>[B��.5>3 of wv�I�ex&'�saN,Cs \ or }$D$�b ), A+ ߑ0756Q�lec.�V�$Schensted-e�co����>r , Pl� ci��d Jeu!�TaquiY�:}� Z��`�+D�Q31JDLec�%lsc{C.\=�i��2� ���g��%��ka-FoE42#��Ns2 ��ٟ\N}��.�$.�EurΑ6�.�y��8D-E. Littlewood]� �u�  ch�5�;A[�B�of /��Oxf:�>� , se͔� f-(19582bLwN%lsc_ q���eE�,&�>�&� s�a6a�T�I��uG}���e���nem1 �e&$s szyi�h(II-IIIa �<i�� �k0E$02}, 208-2�6�{ma.I-2_�& wA>Dw�$.}Y}" Q ��-�0Mathematical �HMonograph, Oxford University Press, New York, (1995). \bibitem{NY} \textsc{A.\ Nakayashiki, Y. Yamada, }\textit{Kostka-Foulkes polynomials and energy function in sovable lattice models, }Selecta Mathematica New Series, Vol 3 N$% %TCIMACRO{\UNICODE[m]{0xb0}}% %BeginExpansion {{}^\circ}% %EndExpansion $4, 547-599, (1997). \bib)R} 5HK. Nelsen, A. Ram,} it{6 p9l and Macdonald spherical fun%�s}, preprint (2004), ArXiv: RT/0401298.=�OSS�M. Okado�dSchilling, M. Shimozono, }1��A crystal to rigged configuration bijec ,for nonexecpTal affine algebras, }P.�2�8xiv QA/0203163.�ok3�(% Virtual C �sEb�CFermionic Formulas of Type }$D_{n+1}^{(2)},A_{2n}^{(2)}$% \textit{\ !�}$C_{81)},$ Represent)Theory,)�8bf{7}, 101-163 !�32HSC.�A.j�$X=M$%l@symmetric powers,a�>1]412376.]SW=\6s4S. O.\ Warnarr]pInhomogeneous lattice paths, ralized f�%�$}$A_{n-1}$)!,it{% superno� X, }Comm.\ Math.\ Phys.\ .�,C.U.P.D94) A0s.$15.1,15.2$2�44} F.Y.Wu,Rev.Ap���64},109)�2275} J.Wes)@ B.Zumino,%���8B (Proc.Suppl.)P 18B}, 302�.�{16�'Hlavaty,Y5 :625},4��19:�7�DMadore, An Introdu� F Non�I)Lve Differential Geo��y.<92�eLDL.Cerchiai,G.FioreE� x H�A tool�U q��HEuclidean spaces, m��A4002007��19:� D.Arnaudo�42�, qhINah%t28},5495%s.,{20�aa37R��21} H.Au-Yang,B.M.McCoy,J.Perk,S.Tang%B$M.L.Yan, E=�~� A 123},21E�86�22�:4J.Baxter,J.H.H[Tz E�U A1!138!:i023} Yu.I.ManiV> Non-' QLY? CRM � 0. de MontrealNfH4} M.Dubois-ViolettIM T.Popov, �E�%%6�5�gNa ra"F AtSe�D Atiyah, G. Segal:�� index�-4elliptic opera�5(: II. Ann.i��* 87,}�068) 531-545. pHBrHo} T. Br\"ocker,,Hook: Stable��Hivariant bordism. % Z g129 h,72) 269-277.gCa}�DCarlsson: A survey�q`s s \ topy�q0ory. Topology �31�),�92) 1-27.�CGK%F Cole��T Greenlees, I. Kriz: Ex� al g� laws. �+ Lona� �Soc. (3) �81�02000) 355-386.�GK2��The&� jof2p complex9y �1x23%x02002) 455-475.�)w@omeza\~na: Calcul�sS`.� 5�In: J. PASy (ed.)68Hom)�� Co!�%�t� $CBMS RegioCon��ce Serie��e�s)X90!XG $ 333-352. ]�CF}� ConnA� E. Floyd:.AA�pperiodic maps. Ergebnisse derx(k und ihrerA(,nzgebiete, B�33&� -VerlagAw64)=itD1eG0tom Dieck: Bi,!�,$G$-manifold�integ#tM�ems. 6�%�197A`45-35� bp tD1a>s�9 $istic numbE of:�I.�%q�3)x(71) 213-224.TtD2�pI. JourAof pu��applied � I4 �4) 31-396�3>�P)�yTrans�9��<\s. De Gruyter Studies ino2�8 p87).�GM3 A���i|: LocQ lA�i�{en ems xP$\MU$-module spectra.B14 �$97) 509-54!� U`Kochman} :Q�, �a��Adams vl"� s. FieA�(institute mqs, AMSaT96)2� K} C{4sniowski: Gene��AH�$\Z/p$-�� ring�4 rendipityQ�314qX$6) 121-130}�KY:uYahia:G tary��� circle a� �8 Edinburgh%�.�;0Qj 83) 97-10.���}a� �� �.�)�� �Contemp� m� 1999a�7-2232cLMS� $ Lewis Jr.�/ May !�/$teinberger6� s�UE�y. LNM }12�S"��=85.=L1��L\"offl>hun)tco1��fy� �ee/UInterne5,al Symposium)ROits A���(s (Budva, 1�(, 158-160. .�Pe�Pze:�dt�6a��. Bull.E�%�8����$5) 721-722.(S1} D. Sinh�omp� on�1�.1As. Am)n �r��212��,2001) 577-602�S2.���8semifree $S^1$-U�b�P 24ee,2005) 439-45�_ VE!f <10} % \provide1�and{\bysame}{\leavevmode\hbox to3em{\hrulefill}\thinE&LBJ4MR}{\relax\ifhIunskip\4\fi MR ;P% \MRhref is called b��\ amsart/book/proc defini��of8. N|O0}[2]{% %% \L{http://www.ams.org/�$scinet-getg$?mr=#1}{#2�} B�K\" &� Bac� ki} K.~l, \emph{Cohen-{M}acaulay {C}o ctiv�a4{G}�$ic {L}a�Europ.< Combin� ics �bf�D(1982), 293--305. 6�ez} J�eza��98, John Baez' web site, \htmladdnorma�k1?!3L.ucr.edu/home/baez/}�-c^$6�1} G.E) edon1( Sheaf {T}� }&* ��, N.Y.�76Q$Brown:TenP�� ies} R.~ gTene��8 ��8{X}\times {Y}$}urt!v � �,�(2)5~b(1963)�!196�AQmb� ~�PEllis Horwood Limited�886G3} W�un� J.~HerzogVFiR}ingADCambr. �����199:g0CartanandEileŭ} H.~ E�S.~|� log {A}l�}<inceton |ez�, Z Jers� 19566�4} DA*�l-�) {C}arrier!�Q:.p1� Soc.yq7VII�957a919--24: 5Q�CoouR.L nn�i� �{C}ellka� P9 �-V6:�(6} A.~Dold1.�5lic!YX*g , �6_7�Dugundj��]�0Allyn \& Bacouc., Bosta�196:�PEhlers&Porter} P.J. E:T.~ �Joinse�\({A}ugmented) {S}implic�{S}ets}E�C� b. Alg y� 245}�0a�$7--44, %\ A�-%}dt: \h��breakEb�front.��davis�$CT/99040392 �36� 8} .^%5 S.~MacLan�?� {E}xte�) {H}oma��Y�of�P(49'43E�42)6��B�@N.~Steenrod,\ \no%2I�Found T ^��ue��%�&_1952. { f����ve�� details/f�4ofalg033540mbp2��>} .\S G.~ForsQ�A��.�im!{R}esult\E�tanley-isner!{��� S (T�PItalyA�(2) (A.~Simi�P.V. Truna� Ah G.~Valla, eds.), World SciTfic Publ. Co. Pte. Ltd�g(4, pp.~69-->��J�A Y�����$ {B}ased oA�ist�a�$(-1)$-sa�$ex}, Tech.� 0ort~3, Depart�  A�� ,EO�YM�StockholZweden�P946�4Fritsch&Golasi� - %;M.~ <$\acute{\rm n}$swi�-!�, ���and�catego2j��}X#chiv :9ј82��� 468--480.��\ ps-p�"at:\ \n� A܁�%)k.uni-m#4hen.de/$\sim$f)/�.p2  � zB~B=6c1� R.2S0R.A. Piccinin�s8Cellular {S}tru$!� {T��!Q�%�CI�0:{A�,G.~Gr�be Hq�8$\ddot{U}$ber d SB�a�v�( {Q}uasima>�},E�. Nachr.5�117�`8!�161--17:1� : J�R} �uZieN�! Beit�ge�2.��T. 6�9--37:8s T.~Hib5�Un�1nd glu!$of a familir� :� a�ial! rder��� Nagoya-7J�10-3� 9!2>H 1� :2Level�ar �8s with straightm! � },u�Oqt5�864� 6:, 1� :~6� on ! 4nvex {P}olytop �slaw �i��>^� . Hilt�nd�� Wyli��"j *$ .j esi6:@Ho} M. Hochster;��Y -.�ɀ,�*o,%`6� C&�  Sec�!$Oklahoma RA*�&OfLrch�76 (Dek"� 77:�1 -T. Huq�!"=Academ���`5:� JandTH Joyal�M.~Tier*� An i:V�� >H��ug.\ 5�9,��df��(of chap. 01��a�f� hopf��.purduec /�- � /JT-Q$-01.pdf} ���=6�$KanAdjFunct M. K���Ad�t f/*oraF�. !!�t�qS8i�58)��294--32:�1p J.L. Kel�! p�l!�&� Van. Noa�n"5:�Xkoch:frobalgand2dimtqft� KockQF Frobenius&� �? 2{D}u�ԩ�`%{F}x!�{�aa�mbridge.� , 2003. F: mat�a�vC A\h� \P j�cf� ,uk/catalogue P.asp?isbn=97805215403�7Q'�J642PJ.~Laws��B� dis )�war" no� weak L& dorffness!t9�� Not � !G�  �Bt  6Mr07--215�rcel �r IncD-w York:��J�*� }s,en.wikipedia%�4/Saunders_Mac_� } -  e�q{W}ork�)��t� cian�Sp��1B�y!s2  d�op1 " � �#smco~iF E�!� case���!r!�s�or��C O&�  (�6P(J.~Ad�mekR� . , 1-9a�ugust�,�G ragu� ��,zechoslovakiQ8:Q2� C.R.F. M)�q���.� �Van�U Reinhj+:� $J.W. MilnoX Cons� % ofd� al b�l� {II}�0Q"ofM�(2)! �16�5� 430--43:^2� :�!�g; �#i�� bU AWl����C357--B M, M! yaza& �3, $E.H. Spani��-�F.�?(McGraw-Hill]>j3�R�D�6��m"�).�2nd. e�u/��/n9:z3�WBn�u}$ckradgW.~Vogel�B�Q&%TA}* }, VEB/2�>|�xR� Vogt`Chnient"c�0f��sn !�9�]!��rd���XX7)545--5>i 3�Ja�Wal�)�Can6alo$eomorphism��pos�$-Js�C��~97--10:�3��G|Whitehea" A��4%A�� %p�o�7F� ! S�)�8*�55--6:�3�:2x}�mS!cGTM\ 61}*y> 7:Z1 4kiAndSamuel} O�4riskiAI P. ; {\it .-Y�; Vol�'I.R-Vq 9QlNg,.b�49}&� 1} F�ook+n� e cut !��� ?!�,Z"&�6K-hly, 78� A{10� 1010*R%2�&~Dontch?2�$0ra-continuousd%(4strongly S-clo�i,"�# .\ J�� \% �(>*, 3�.�3:��pH�  On sgv% � $$-\lambda$. tes% Ans|8�&.\ �y, 15(2)�7�5�6.*,w.$~Kat\v{e}th.On%}-valued= i81 -� �., Fund1, 3!�5!�85-�9�5�,~ 2nCj3�& to, ``n U 6�''>�40� _ 2!�22�&6} S.N!sheshwa>3R.~Pras�&,On $R_{Os}$- � � ugal�4Aw5!U� 21.r.7}9�G��9$\L-�5��(associated At�oZ/,I)� Issu�/J memorH�� Prof!�Hzuada Ikeda's Retir} �.�139--14.8!�H��o4B� ed`5 pert�,inU -lan#, Cana!�u, 1(1949�&76--189Z�8�f230}.�2 } C.m-Au�߉�M�E�)��@a $\sigma$-point- %e basH:AMS%0"�'',29:}411--416a�712�:,2} B. BalcarPelant��]im��[[ �!�ultrafilR: on NW/v�A� cs \#89*� M, A�E�863136�I�Cq� metq��kV�J� } JapanM� 5}: � 70E�36.46~)�a���.u��oll� wise HauqJ?Saitam*�%�2}:K �6�15�P. Hart �CtA�%�$\�0bb{R}$-embedd�1%'�0 $\omega_1$-!��Indag19�44}:27�8?826.�4�)�M�ryV{So��}�� �..�l�+1!�151--15I�:�(7} R. W. Kn�M/$\Delta$2 ,}e��a4 s �339� --60.Q1��. q T��atile * z m ``Y�al :�&Pr�Bm LanguagW7mantic�65 bya�Mai}GMe��2Mi�e? r0chmidt,u� A��"�puSci%\#2�-:�, 134--1�86�9���org��|&� E9E[t B6cm}}MSetim~�� 87--11�p96Q20} P.a�Nyiko v��y.�, l`5ly}��%� c"4\8u�D� Co�1!��34J\'anos BolyaiI( 55:}409--4B 6�21:��-��pa- 4of Alexandroff%)Urysh/8on certain non-$ imed�#}.(to!`ear2�22R�M�2 zabi�2yE�� $rees} (in �%ar%�6\3R\Q�$-�?b�Qked-�zd4Rd�����j&� B i!�t� laye���� Scot�d&�l� ��``� sq � ic%et:Iand L�. u�u�A{�$\#274&��#��7:6} L. �H(+da+eebach� %;erexa�6 i}TU�� arlyI�A�et� i6� B� "� !�r�  (N6� "� (), 235--293!�:�2� S. Wat� ��.:��m� 1;6�6� ��} "R>K4}:10�&0-N6T1W.B�S+�a��atbZm �^ F_,290}:831--84��C8Nj�� &� ,ah} A.V.~AhoR$E.~HopcrofV J.D.~Ullm��0Data str�)3 algorithm��AdK"-Wesley*�>U"2Fa�In&B<ProcesspH6F, Rea�8 , MA�83.S6${84f:68001.�4fk} R.C.~Flaggg]Kopperʍ�ityM: r'ciO domai���ic '} oret put\i&� 177}I,7), no.~1, 1�138 � 98h:68152.�KMP03�.��!tthew�H.~Pajoo<, �O, To ap��A`qB*na�p.� kv4-P.A.~K{\"u}nz�V.~Vaj�)�We ed q٠c�P�� gV#�.� (Flush%� NY, GGn./ Yorkc)?i 728b4BcJ�.41Ud:54052�M94oGo1G �P�Jal1�tW� ��V(2>� Aca��J �18p9� MR{9 �4.;ops@$~O'Keeffe,:'a�M.P.~Sch�'ken"�0On �\:��8 between balanc� spe 0f6�I}�Q.jrs�C�S.~Rom$ra\B�s%Norm-wE�]  Rieszm{��d�Q�lexu�}&TMFCSIT� 2, EOroA{�&T6�I�$~74, Elsev�(, p.~17n  \url�"www1.�S+\.com/gej-ng/31/29/23/143 31/74009.*��!�.��BM�3 7  of bin�") }� N��3�2����0. -G3g�568}. .�Tat.yorku.ca/i/a/a/j/44".�ms8B�:Xmonoi�EH��i��HT� ��6m=�m��V�a"{S}myth-'��: a mon &_6%Kdenot��C:E49f a�},U<i �W�>,p*�sL$(New Orlea�qL�95)�b�D��1����" �!5, �52An23Mn98g\03}��26��$84/tcs1030Z42{3B�a�.�s revi�> d (e�8ded ab)ct)]<��:he 8th P4*1�PS�B��y Atla'"�%p348f�$p/p/a/c/05F�F� On u( ݂5 �� g�� GorhnME)�>� Sc�d( 806~��&48�)3i�98ca�f�m�\6(B� : lifting3<directy},"� � ���619� Summ%4�425��g�49:�.Yb�Y22>�schFZA�1�I�ABp.� �: "� re�Jn��� 30K+2003)���qd2 013 572�ms4B ��&�S<` 2�c�[2!ArN�9e:| =�sm1 B.~S� ����u�K rmities: J�  with U�P��l�2"!scsR06B�A�L � 2f+rl�Z/,� ~236�9m92 sm2F�otall�H�/]����edͦ as" u�;AP�� @a=:Eory iA % er s?(�B�� V, 9�%91��0>29id 1 145 776��N �#f� 99%new"PF�enquote}[1]{``#1''} %\expandafter\ifx\csname %natexlab\endcBFdef\n  #1{#1}\fiY�[{N�(ohn(1929)}]. �P.~>2P.~�ohn4 \foreignQ�t{french}{M{\'e}moire sur les eI�� iques�*s}} (BOdutN(Koninklijke� e van We�?�5peA2�22�[{Arens!$0��R.~ a�)�{� �onv�J� Mq,}4 y� s Magazin��$volume~23,:5�/0E:234�6 �E�[B>�a �(J.2�B � 7>concep�=c)ax��$iae.d}e��96�1�14.`�hangel{� 8prime}ski{\u\i}�EAW &skij63� ~V. R<=�Some typ�*,factor mapp�/%�Es���K 6-��I�.} -�Soviet=s�. klad�-�4% �F!�172�$ 729,W ansl�%�#{R per}.�D{R}ussian original:vF7M� &!F70} -=,��{S}��Q%! cardwi�N{C}r? '%as!�< biM6a3c emphz* -+11%,7Q�5�+601, t6)J.~Ced2) �*1>p71V*On� �%ditar�=satis�M1L'��nk.�+�aP%_�L)<c�f0 D>[12�Ic�*Ec25|257>9, {Z.~Skalsky�e]e2B;2V;AefrE*c�N �N�>Bi% the e�ifW��i��^Q]3 5Id]%-1n* 1189>-{� ilv�g2g8B�8j� star� hod, new.�)%%�wyWacE_�21IK2,;$8u�50--5H5:�(Y.~ChoudharVK Ʊ� Ponomarev�8>Z68�JV.~I.Pw�� On dyadic}ʚ0����6I0EG2�$ 1224BGF��zus}q��.&84>&84a:���o-aQ7l��G � �IV�,"}�LAnn-�*L &� 38 ��W37) �-562HBourbak> 66� 66} N.~�AK>;},4III� �.�2*�s (( n- 62�'[{O5F !D"!O�MB� I Filtr= t&O-r� b:� ?Rendus�_l'\'emiw-sW$ s, P03w<�k2A2 �)r7A&7792tDudley��e� 64}S M. �On)e ](�2����LA�64 �4�507V�Y �^S C"�1�  `{O}^�'���48ɾ"A 623--626�Ew king�w�zR.~!~Z�2ed � }(Held�n"FS 1�.2AFra�A�65ai65�! ~P. }M�S9aXwhid,C es sufficY��a*W At���1�115b����= .> �n�.�lcS&�Nieuw �%,ef voor Wisk���1� 66)i:12t2b��c�7:��>6@"9C��.Ce7!C�P�):P�'��69V�On two �AO�{M}W/${M}r\'owkau*��� ��6�A o 596���Rajagopd�43 !/ S2�3M�6.��ex&�% & ��5��2�" 30 /1>Qpchet(190M�e06 -~F"�b=Sur!�l!�#du ca�b fon�+nelYuBL ital�D{��ic�'0 del Circoloa��,o di Palermo.�2,A�0uJ--76�HajDA_$Juh{\'a}sz!�Ő 74p +I.~.=On6 0 {$\alpha$-L}�Gl{\"o}*}-sh%bl�6�hq�  y��� �28�7Ѹ147+-24Hodel�� �8�j �C� f�IC: {I!�in�H�4of V�4}ud^X�K.~.�4~E.�4�� 1�� bK' 6@' [{Hu�Z �u4S.-2�K.| B� ( (Holden-Da} 2k/[{9�!3�Juhasz�B�!56F56in To\-pw)---ZYears La�V F�g�@}&$sch Centrui62�6[2>�% �4Vr�.���v�6�10���K�0 55�.~L^�K� } (V*wGAK524([{{Kisy{\'nz%�nski60j%}.B�z 6@rg�du� $L$}վ�.oqu�`&� %�E 7��6�2��2112�Levine���� 7� �O�:��H P ��b1�!T )K�b401--4022�Malyh I  72} � 6�"��n� m0$ X$1 �7� �n o7"��� 31, 0#�\"E496--4�O:&zoV$McCluske� McMa:(�}]9�-~6/M 2!1��q  Course6�} ( � ^R#�/}aH6k Weis��8�}78J>~ r����{M}�%n' V;B�;"@��& .�0e�78 �~243--246�Willard��EE �S.~ �AFJt�-&�7I N�# j�H2�21F L� %$I.~Namioka�Linear *t �K.�  &�a!�6L%29 \#3852|2�J��L)[ -Pin4GIg�9]rrP"e.:`4zeros due to �icceri}, . nvex C&o(�'d&N357�%99j:470G&�( 3} O.~Nas)v1A�� � a�5@�`&uA,!60g�a�V*;D minima do coincidIO./�"bf{50�-1 �5-6!v4/411 �1 892 91245�E~R)!�*�M�a�# orem�U cern�)setw@ conn�) sS?A] .�:hods Non�7V{�� 2,�B48. C. 97i:47135�&bib�kGE\6w*EFvia dis�� Fgtex!Iv*�1-�=29na36k�04.�6�Ky-m5C( further imWme�)L)�x5TofAo�%h paoA� S}hul$'$m�WA�9B�P>���TM�7 K83��02e:490�B R$� f�' BCMZ71�\[Abu]{Abu} J.Y. Abuhlai��� Hopf pair"�$in� i)/|�~�^�_%-�"==�}�kAQ!$�F .�.�Abu03��6V�R[/ al mq2e�Mco�,} �1 �1^�1\"{a}ts~P,eme f\"{u}r !=- �en �b Ring(1+,Ph.D. Disser0*,,} Heinrich- e �{ers�um, DP!�e[-G�y � 1).\a��U ^W8www.ulb.uni-due90d diss�h nat/A�/aM.�ST�:[AW02]{} !=br�tnC. WeibeUCCo�(or %� -�+l%p^CS?G1354(602173-21C2006T I�]Q� T�nzezi\'{i,p;Caenepe�G�XlH%u��<Zh"�`&G^�Maschk�'q�� Doi-!�U�: entw> � ��: aAf�w pproA>} Granja~ $.) et al.,E%s7,�cicZy:�\.hH_HP]aZ1U 1Q221P-31J�Brz99]{VG���asN�co � Galois �1�\!�JF�215��<-31�J96 +BW�N�%�Di�Ze"�C��� , }�1EjLe7^otw&P309, }Ca`y��0C A�2E[Gar76]{} AdGarfinkAr)9m�X.�< ionlMA9trace1X��U2�5�15!�19-14lM76� G-Ta���, G\'{o}mez-T(� N ��}>����I }In2q' Sc*�< 30(4e�03-22��6�Guz89]{ } F. Guz2i=i�{�\s, &+v�E�UMA �61�aco&� �}�k�x���I, 5224&6\D�5 �5��|Re$~ ve C� Co �4��Thesi��yracusQb��y USA9: Wis96]{} N�M)� �s : Bi } St?"G�Ac%^t 3AG st e�\Pitman�T6Gph] Su��4�W!w�[��*8 �-. � p#elygg$:L��5yT.PWis88�88V�Grundla�|_k�-�~ �O�{ie : EinzKdbuch�qum/OPschun\\ly`ard F�CM�]nQk%�2�C [Z-Ha�$} B. Zimm�n-Huisge�aZ%2;. ?5�of�*.�M�U=��224A�33-245�e�R Gf �1� 1�#$ ENGELKING&uI�tof2#��R!�in }, *�" )L,|65*KU(2} E. KLEIN>A."THOMPSONBt65A�J�GWi&B S�(f3  RICCERI U� hA�d��� solua a �+ n"� Ċ�C.a��%.��%, S\'eA�~bf 32� 7), 65--7.aW4�4 SAINT RAYMOND �P�s fixe&s multi23A$\`a valeur�-vex%+��29�<8�7�RK�jK.L Gel}aXoel'fa�gR�~MinlXJ!�4Z.~Ya.~Shapiro �>Ό!}!�Rot� :Lo�z�ȅ��U ���K (Mac�an6562�{BG} C.�Be�edDp~Griffi����~Rev.~D �M2���qNG}N@E��Harvar�5��60 (unpublished.{BOJ�S%WOrszag-CAdv�Ad�:� Me��7Scirs]wEnginee ?(SNHg���<=Ca�9�31-.L3{POS}�G%�irreduc�K�pe"Ӓ5�1�8�if8 eJmj, $\ell_0=0$,n $(0,1)$%�- label exa��/�:},. Thus, we m�ssumevWout los�g1_�at �1$ Sa�]it�� ,e Ref.~\citeE�.& {�}�Trth} laimP�Qicult��0i+*heavy nu�~�"�UF  believu at��{uiis�lila� t!!�a8eigen� ̋ harm�^�anos � . I�sfv�r:h , af�8bGa%4is divid�Cf%�: �sf�88g�BK KVa�0ple way; name1]3~runa�ngE!��� H�te. ���$LBz�removed,b :� dorV |e, bu%}y stillu3k har's3: one �-veA A@e�-lly.0At} G�~Andr�G�5,%��5ym�Spe_[ "�"} ("� ��Xpfm�.~KS}^Koeko�,F.~Swarttouw v[-� -Sch�of Hypo!}� ic Orthog�� Poly"5���X$q$-An`/ue} (�@aw.twi.tudelft.nl�t�oek/a!/�� NMf�aa.�4lm;67} S.W.~LeA�n�,Mittra: "Sca�mAo of e}AmagneWZwavesA�a mov%cyli&�Y5R&", � itj�S�H*4� 9�67�!$\ 2999-300.-{gt;68A" N.~Tsando�� : "E:���>,by a M� Wedge",7it{Radio� .�3}, �0=\ 887-892�dc;00��De~Cup� �u��G.8Httini: B�=\�n OO a�G i�� W EMMTn�� �Magn.~W!�~.}-x bf{1, 8,?0-`1037-106. #�W����� beam��=u6?3S%} targets]Atti d�g Fondazi�*0Gorgio Ronchi]&LV�b4-5, � �799-82�$�26�$P.~Burghig�i"�~=�M�JrzialeJ�A� sy !� &Z ��uc Bwedge* �"�#)�m-�ur�I�!�6},-�2 � 345-32�2�3.�: "B-��: 9r�p��a�ja� _ ��techn�",qQva�comVә bw;6�bBor� E.~Wol{3texa~�i�Q�`nCd�.#{no;5��~N*5-$it{� +`d H=Wi�� f{�},�d�_Perga�_ 1958� NQ�fQ� "={aw��< Awane: ``$k$-sy��c%Yt�s''.Rsl�� U 3�H�M 4046-4052�aw�hG�b :s+ g\`e�\tߔ.2t1 t4)ib152y aw3}��,�Goze: {�Pfaff@ systems, :�  }. K�6/�v� rs , "�l (�I2�(BGPR-eblhf}Qb Batl��om�}J.Ml8B. RomOW -Roy!���l�" JD(the Lagrang���H�ytonY alism  a��G� �.QF�2v(86) 2953-296lCL-�"J�q(Cari\~nena,�L\'opez�m�� e�)�H"cd� higher-xC Ru ��)�J.2a6�7rQ(2) 2447-246eb�cgtS. Clark�S. Goel�Q�qy�D almost t^@nt U��eE/Ten�(N. S.)M��t�3 `a��CMC Cort\'e_v \i nez,@8Cantrijn: ``Sk��r-RuskaQ]7b!N -dep�nt mech{o!) �e� �� A �3��A�� 50-2�/�bar�/ E�herR(\i}a-En qu�C.!� {o}p!�Har\'{i}n-Solano, M.�(gO${\�' K}$-�A� : .� as s�xo� long LegeW >'s5 Acta�ASth1�T 1-42De} H.A. Eliopoulosa"`}gesq�!i'6FE�\'�is  �irE�)�CR\[ . I�v-�25`,62) 1563-156.V6{FP-90�> Ferr~a,��Pag� a6ymm�[]c%xant��AV r� �m��ͣ��� #Qb NoeJ �em�J.I� A: � �O�3��(0) 5061-508.�.{GaP-0�&A.jc\��e�� Rigi�o gaugty �s�B���)�"�+e=�, 15}(29)�/0)ڂ1-4722�Sarda2�<0 Giachetta, LA��� rott� )nashvily�p New y�B�M�in ?���xWorld�)�K��S0., Singapore y72|�;d����CoA�ant�\&=J�-_Y}6"?32}(32) �9) 66�G 6642.� GP-ggf} X�d\`acia�!�A"�f�ͻ ic framew\Wfor�]J�)�T A�om'bQ�S2) 22�2@ GP-g" �{a}F�&nN�c�$ingn�"�����.��e 7}(3\n(89) 175--182�GP-92bvG.q��_Y� u�� ����)J9�N�5i�(2) 6357-636.h(�a�-RJ�A�> : s�85�&�s a�#�nL�'~�)R34�& 3047-30�& grif�( Grifo �0�, que-�/e� %�xŽI� W{Inst. ^kierQ}I~? 87-32^-2A �I�+��91-332H gun�xGF��a�� ���(.VE2� �����<�� �9uŚ�dE\ I��n( case� J. a�e�il 1?�;87) 23-52�Ka-82}�kKamimu�Y`R^ ��c� .��C6�c"Gu�1�0 Nuovo Cim. B �69�d82) 33-52(Kana} I. V.Ђ4atchikov: ``Cg"� � �GI 2^+MhJmo�'um ph,������&? i 41? ��8) 49--92^kleinE�K A EZs9�o[P0 m ca�{a N 1i  -12z@{LMM-+%S<1 Le\'Js arre�D�Z 'Diego���w �=�V�g!�>N�Jori� ��Cl��X̨l�ge} pQ+Cen�Pub� bf 59},m�of?., Po$O.� , Warsawa~ 89-202:mt1. {o}n�M\' z�  Salgad� $p$-^� ��'=. =!B�=�` II� XXX��xhc2�mt2�.�{e}ndF�1Gle � � �RY�i�bD!� H$p^1$-ve\-lo\-ci\-t.�% �KHungar�;58}(1-2)B#91) 45:�modBp(; Eugenio MfGbosE�� Oubia, Paul drigu�Ds sto.�Jg�co�] "L�uHR� 39}w 8) 8 t86�modB�F�o>�f��=&=��FE:��r 2}(5q ��092�06Sor�MorimotE�Li�W�D"�P�)�� .�toUB $p^rA7locVi�Na��Q� JQ/4�.1, 13-32 fam} F��teanu� M. R��T�y��:�M'L �;U�j �)Fy: ��map%pr��]�\� } {��55_7��1752�McN@W McLean;� K|) rrisi�nt2� ooame}� fibe,gU�.:� 4�)0iX4 10, 6808--6822�No1��� p2� y y 9 ��*au<>e�� given �{AMS �Y Research����onF}e�i1990},G U.C.?�*8 No2:�G�ӡ�W&`͕f�5P� roc.-\.�&��} �� 50Part 2 (>t),�x�XU^$,1993), 435-46sNo36�r�*�+!u4$T^*M$ derivedS $n2=.� $LM$�A~��* 1+�# 51-72� No˰Y.�\outen-Nijenhuis Brackets�rg)"6g 39$�$2694-276mNo=)x4y:�!, of observe�u7L&���m�.0 �i� 42 ��31 a 4827]�42PV-A FA gliese, A�pVin�(d= "�9~f"g*�����J-�3` � 35-55,]��b��Pn�D�2t;tra~=b  =!j �"� hy��urfacI �J2> ��O1�O 309-ύ�Sd-95�:�G}�.�F�<is�F� �\y�qt SE}F��>�52�s�2� ,�'� ^�dynamic0". �"`�ne�Q \opj TQ$�(.w)9 24}(1!:1��258�356� Tu-�=WAk Tulczyjew� Les sous-�,e� lM�enn la di�_h���" �eis � t 283AY7ȥ5-1�V�'GjI!5% haundy}T.u Mm�2qE��RQe��"Oxford 8 35)&<faiJ'B. Fair%�A�"a�>�)�mJ�fnli"ϭa�}B<� ) 256-261*/*govd�+ea�ovaer"'A@rozov,E� EմsitC��S �sapit Nucl��-�B37z�14�c}l0eis}L.P. Eise�%t�iitN�2o��c}&�9 Um>$!o4Q4-5�~1�leznov}D=x2 A.N,q�"1����� 8nge- Amp\`{e}re"�_�dip�G'#,)�ou��x!� ics}��bf 16 (95) 385-390W�hep-th/9�34]� fai1E?]Ga�]A� an E"iE-���Ri�en" -�St���p"�.-�S+9S1�hY�dbfintAt�" le�]H� D11s iqBI��J2D+ l� ��} trors. T'ami:�R� saki it "@of Zet)-� Suppl9}� !�Y�<!��32fab�}b%�}e, ~<*�cfhmB A 2M3"39 7}�W��(E.T.Whittak�jGA�W r�G!:r&[E~�3�#*U'�63) pA� 6LndB�� fC!1xbYNRZl�E�nls�T gg)10F. Zertuche, "�G�1)�$2+1$&�.alU(De Si�& Gravi�� ��� B33�)� ) 516--532c���N�%��, Q�iC�8tth27�42[� 216..��NP12 j�Picken, fhol�Y�i.,2+1)$ -2g �J�47��� ��76�P2��i�x;s, B)b5� n2�U26car�(!lip, � ��6�s̈́Q�"��� .q��t.U�yU��h)�CN�!anwY�Z7pa�tveImϥ^2+1>Rev-D5�80aQ�E05643--5653. "�"t VF,�ofNV){��B3[!�#29 �0�}sP߈��.j bW�..�$Z5i�Iwn Lie�0�x.� flowE�o (:�0s,ZeI9a� �l8? 6%�OA�]� att}�Attal%�W�"icr�|'0an GerbH�CE�Bnd Curva�� ��,-ph/0203056,�a&vnna# Fondńo2.�nonabSt�� Bro�# ^��Stokes)�e�{8,pF``�rN� �D)� �R�.W. Eva��6* 4 468,�#1�y� pick5-�9, Y �7(s zur Zahle�P, Sitze��tos (Pin)IC1a�18�311--319e_ e.g. H.S� Cox�2, AA6�� �y, �H����:�. 209A 62�<{MPh acka�2�.�d8 H� i- Parallel E-`��1�I q1]�17���87--3390 Rk TQFT�gEiIlg�+D"{� 4i'3-2722�hil HilbertTt'ohn-Voss�16��Imagin�, (el!J$menyi, P.)�F lseaG)�/CMny,F"�4�. % b*�� �SU0should follow{�Bt���sDX �DsDelow, ou*2 "%"�-b0�n�!]�A|�evge� } %A? bano�S�tz, %�GG%'s Fami�PB �i2 %QuinmXThreefolds, %Manuscript�V�|%�1� 18��AKj�vThe\%ma�:x, %E�.�| q3�1:rDD} %S�Ashok,E�$Dell'Aquild0 D.-E)C��escu, %F�/al�6 in LD(u-Ginz_� Orbi1 3040113"V;f� 6-top�e(M. AganagicZ�mm] Mari�0C. Vafa, {\em%>t*�: vert!� � 3051� �� AtBo} M.\��E)R.\ BA�X��}. �c"�>|C ��bf B���4�-2+ Beh}]XBeh� mGromov-Wi ��;�b*����12;,V6�T612M BehFe��� ~�B.~Fan�/i�-Si+nsڻ�co�l��\��\{*����9oBO%_ Bloc)k0A.~Okounkov, �Aa"�a�a�I$= �3: *9}, �� 0�04�i+ "Hc�Y 0. � jbrp ~Brya� R�}ndhari�o� �"6�b �d�?~ň.AG/041,3.� CKeng ~CerP[ R.~Kenyon. low-\�erk p�Bh!Wulff !�x!t��. I�-l �\ c "F��2$3),147-12�b{CK�~Cox �3Ss��L)Mirror3#R� Am�7��"Y �e,8,2| DonThomF Donalds� R� om�C�Ga�)-�in �.&�!�in ,As�ic�,o*e: sc�R,D8!{�'of Ro%�P�s2@S. Huggett et. al��/�gV��6ES~EN�gsrud,!iStr\o mmY����ul��eh3a_; �y}�JJ.~!ty�E\'�bf{4� 5��HorV} � Hori%\C.~�j-�m��-!��e 0022�}PIK:!~Iqba6d A.-K�A(shani-Poor,Y({\rm SU(N)}� C Ak�\HStV:Amplitud���603" .�NOV; �1~Nekras�.�� cH' FoamZ��M1 3120!.KKV��K�4nKl�>W� ic enP@� Q�*�S� Nucl� ��.~By� 497}�i��OaM-1TD *y�Oőͅ�O:�mF shap%co�6x�g�5e�S��*�on�o"�KOSbj��hef�JGri�Amoeb��\s'\i�1.~�1,"�31�'R19��121 �2�PKon1} M.\ KontsevichU �&r�2�o&�!�py������ Airy�},m��I{��4{ 2� � 9�on�%2��QE���1 ������R���},� �&A � (Texel Is��!6�� 33?f�=��, 1�uB���ܡ"��Boù�i7�LQW} Wއ$~Li, Zh.~Q,{WJ=ng��s�?st��� hier�#�%xV'gP 3022�T]�LLLZ}/5� C.-C u,��L J.~Zhou\,�Aţ"� �A!�.jVF ��408426m LiTi��2G.~�V͞Ip cyc��6�i"� ��&D  et�� J-%�1{�V�M->�2Z1;.�ProC#�tCo�!o-� on �aTK�A���%30643s�Y#LZ2��R� 5wo-��CFs=�310.�MN�tLosev��Marshah ����mSmallp&antJ LittH�i�Fre���},�p21 �� mnop�~Maulik6t2^EFp � 2.�/"� - asA�o� IOf��-�12059}A40609 5�Mir�,~Mirzak�"�Weil-P�F� ���A�bOZY�S��s!Ӊ��' vaile�-��tt{YT�G޲ha�H.H�$��m�/}���NYP8 ~Nakajimae�Yoshi�Z-��.%�`W,n blowup, I}.0061986b} N.0 US�Trg��otIalϱmYQEb|%g]72061616hO2i%d.� Vx��!�Random�i:6�62 �.(u* .c�!�r V<���}m�� 0901�5�OP12V �>� �2�U�Hurwitz@AO�e(�irix�EelC�.� 1011�.�:\� �H�� xP��}}[ 2043�!.�3� !v.]N!�$\Pl$6y7232nOP4�xVi ro��73N or ttDu�!��V080� =��<�o�E�@�E%�����unknotAn �*��8}$�675-6992OOP6�� &�6�pTOrpla9411210�9GWDT} .k�Bq�2�/B�cor��G,f���gF� �OR  q��x-h��I�"`'1" Calabi-Ya�Xq���&00+'|T�R.~ � ^A�!m � c Ca�mU�y 3-�%Eb�2 n K3/? �JDG* 5C�k�!43}U� W} Es�y8 Tw�p&h&C!�jA����on��u��G�y�]'.\�.��l,M33�Z? �?LR"SH.\bb0B.\�*a�_";F� agn`VTadd�N�!ofv-m�A��p�|��P(�)f)I 1938c41i76)QLPg!l� {\it Some�~v�!csu� �T��of` �T�[er. �� �8"--13 �i.Q�LNaTh} H. Narnhofer, �ehirA it��r�W{�to }, Fizika z17}, 26b26TY85)�Yu petz' ��z iQuasi-)h�a�!U1�v�-}, �=�-� |6U!:S�L�en!�\+$#t�Q6%�A MinkowL� TypeceIn�lA)!�S�b S.�!��3EU7A!� .��"/�8�ޡ6�96�!M blad��n-;� letely PolQMa� ��M �_B�4X2 -1�!� �2wehrl} v�W �it�daWI.g ݔ�*�[�V^ReN��J 353-��e]6r-M*�.ai alsoɮ�INat CPT �4�F; yQ/ |FZre�� in S)#~\ref{J31�owe ar�"atefuvr Iu>�4is� ta�$Her beauti7�^ew bgclAbSruskaiJ� .4 �thorough��r p!btó2jec2�L6E�Co�gAxce*�sA�!��St� �St�NA�6�*�8pini�cs,*S+&��f62#liebcoha*& B� �D�O0 ��rof�����fB�6%�5�eL6�+ S04}�Se�g %��Th�{�4�s!xva Dil[�FCW Gaa�:| ]��6 O.YT�fore��b��Mae����w of D��ty�ricZ4��Q16̡72�b {ana� "1  Loy��gV�}, $2^� nd}$�`��h��(A 6�LArakib \  ,Fj �.�v]18�u60��,:?\Bhatia%� �ZMaC�.Q97�&V�$@n� } ��24JMU} M. Jimbo��Miw � K.Ue�N ~/dromyA�:�d���(A��'ar,���M"�E�� s � al coY�!ts I, - ic&�d2D�8�306�9|JM�e�T�!�on����~��n4$nU1TKAW1} H. Kawamuko, Oenno�V_VV!8�=���.�C.AB�@2�f�77 52-1uF.�2^��G�al2.&�F!ci|�%�th�|<(1,g+2;g)$ type�5�T�IM �is �d�IeIhA�� ��7A�alNNʾ� � �E � H�*=T�as��MaEa�+7*1�O89��5-5.�5�%��vK�a�BI ���r �Wa�Ga.�� =f$ ic *�/f sev����A3Quarte˨J�/- bf{328� 61-8.�cKOI} �� Koik! M���p�0pCp �r2� &�Da s: B��a#&�8h���h(!�h�7Z*�q86�6LIU} ��iu�^.i��N)AA4��Vt!$A_g$>9!� ~, � Ph.D!�si��(� Tokyo����U�MSD�.T�sud��UN��&�Y,z2QVI��,�^ d?min2or�a�le� cenK� ��unk�_. Ekva*�4�_2%�!17.�<MSD�O.�Cl4I>u��2��E� z�g�?!�, 2�qTohokuIA�� bf{5 ��W= -SI/03020�!5yOKM!y2� Isom�X:/!8V�a�m� ' , J>�Cci�E �. IA, ��EZe�5]'&.�2i�O�O�;�eZ� ���>%*�5uFZ8�047-1�.s3>s���9-b">o�Z-��2p��y: OneDKury��@3RkA�bCRM���in� "܆l&� * f1��SUZ} A�Suzuki��f�� Weyl��&P+M�-��Fq����� �120�YoTSUAc T. Tm�Un�*2�E\�RLle i���Me���TSUA!q"\tB|6�= 2��sSchur* �C7I8Ro~lpQB��� , 2341-23lY. AF� Toda:�� z�fVZ6�, submBdZ���f� }�,} Asakawa T.%�Kis� to�����:���,� A�b  D*A �8*m), h�?�)138 %\no�cnt.�0Bayen F., Fla>� r�dal C.~>$chnerowicz�A��StrtA$imer D. (1�{��� . \rmH111 �61-110B111-150.*B}�%off G�u(1913),VIAt7n U74 T122-16"(} Boyer C.P)d,Pleba�ski X]���x�� �\26 ]�L229-266SD} Brezin E., ItzykI0., Zinn-Justi�[n J. and Zuber J.B. (1979), \it Phys. Lett. \rm\bf B82 \rm 442. \bibitem{} Chau L-L. (1983) BHChiral Fields, SDYM \ as Integrable Systems, �(the Role of @Kac-Moody Algebra�, in:�DNonlinear phenomen !ed. K�TWolf, Lecture notes in� ics �189�t (Springer, New York) 110-127.2�$De Wilde M)E0Lecomte P.B.A%I5L%CMath. )Us7 �487- :[,onaldson S.K K51�$roc. Lond. Q SP3 P 1-26:Ounajski�Ma[$L.J. (2000 [ CommU�1213%, 641-67:�Husain V�94MHlass. Quantum Grav.F�11 �927-93:W\Fairlie D.B., Fletcher P)eZachos C-9�J.�i31s (!=,1088-1094\\ .diW,ET!.-�\M� 224 @ no. 1,2, 101-107a589):Yr�nf18f(2, 203-206 aW9)6�(Fedosov B.V6~0J. Diff. Geom!m.E"40 ,!� -238zM6-�(Deformation)�iz a�,Index Theory�\(Akademie Verlag, Berlin>� laherty EE�197o Hermitian`4K\H{a}hlerian � etrya�$Relativity �q�N>�u�-v��\'{n}a+SiA�Moyal d=8of heavenly equ% s. ��ility�r� ons to otA� non-��<�. PhD��8sis Tech. Univ.n0Lodz, 2004 (��olish)2�Jacoba�NE 8qBasic�: II)�dFreeman, San Francisco, CA6V��E 121 !� 659-66:6^!�QuTwistornsletter ��31D4-1:�N�0Woodhouse N.M�(��2m$, self-duaa{,>t�iraS��XClarendon Press, Oxford:�DMuscheliszwili N.IE�62),( Singular i�ly�%*(Moskwa6JNair Va#�Schiff��.7I"I{!+B 246):4236p(Neumann B.H�49 �Tra��R*6 N202>u:7Q� �Re��D18�02901-2908. * Parkes  915 H2�8�656�B Q- �UU2B��3 �8 No. 2,3,4, 287�nT� Int.!�Modu� [A� Y(7, 1415-144:� Penrose R%��� Gen.��.�bf P�� 1, 31-5:K LA$Ward R.��1��m[$s for flat,Dcurved space-time !�"$ Gene� �56� it��0 2 ,A. Held, Vol!R ( ,x $on: PlenumiD)!p 3-32: Pleb�PJ.F)!� �J:� bf 1E0(12) 2395-240>!FT!)Hacya- aMb�~Rb� c 24[ 40>�VdPrzanowMh��2�bf A 212!~, 2F� melj� (190qcHMonatsheft f\H{u}r ��und _\bf 19 V11-24>3ogorzel�W�96Q �).�!5,their applicE�� Pergam�" PWN�&:P(rasad M.K.,�haA;ZC  Wang� 9��%+ .8 2> 6pWF� 199Z Acta _ PA�!*!� B 30 , 863-87:l2g,I��!FE�y S.3 1 a�-]� of�E a��E 0bracket Lie a.�w tomie�$Exact Solut s�Sca�qJ� i�� eds.!~Mac'in> Xls, J.L. Cervantes-CotaL C. LW Hmmerzhal (Kluwer Ac� c Pubb ers, USA: �6g%�57k1 b-8bU of $S� 0(\Sigma^{2})$6W!�&8Developments ine;e� cal�Experi alE$ic ��A,.@0ias, F. Uribe ?M az >%E.�5-:(Ruiz J.�03mThe�  y�Po!Serie �P(Braunschweig: Vieweg� 6Y,Strachan I.A�a��eq�u�� B 28��63-666�NM�CZ�ei1"� 17-1B�NX� J�:�2( 255-27:] Takasaki "#>� ��p1877-188zQ� ͧu:�14�T111-120E( 332-6M6����3le sy�a�� o� ,`in:����(matMމphyA� 1�T� Baile��R: Baston .� �� Wells R.O��>� geoy�f���ory�0rm Cambridge�ersd 6Y�"C��#A I�k �$�  13!�3��x\end{thebibliography}m\beginB{Tototo}�<[1] {4}A. Figotil�BhKlein : {\sl \textit{ Localla�e �` Waves I $: Acoustic  .}} ] u6�, {\bf{180}},!496) p 439-482.�02] {De-Ze:92}�Dembo%�,O. Zeitouni.6�$Large devi��..�}.} JoneIC Bart� 2�BoA1, 199.�3 �4St:89} J-M. De/ fD.a�oock. 2D:�$}.} volum!�!TP�A_�ed  ����՚� 1989=&84]{6} W. Kirsch:�Randomt r\"{o}d�T operators} } A Course:HI')�345}} !��� !�89!�264-370�(5] {Kl:01b}�\Klopp: 8Weak disorder l.q!�Lifshitz tails: continuous Hamiltonians%WAnn. I.Hl((3):711-737LQ � [6]{kp8�6E�� rnal|s T|��< long range sing��0ite potentialE�Jou"�e� E� 43}}d2) N$^\circ$ 6 p 2948-2958=;<7] {ko}N. KozlovE}�$Averaging 1�tru�axSoviet . Dokjl. ���19�1��4 $ 4 p 950-954�88]{W0} H. NajarIb�!(AsymptotiquawP la densit\'e d'\'eta�gr\'e'�,Verch!3IXg�ly cova4t�fty �Xciple -- A new paradigm�7��A_Y8` .� m2��237},���-$�L)jB�,  Lled\'{o}�D�![1�group� $Hilbert $\ rm{C}^*-$L ��: ps !�]�centerER � rnaE[)� 15},A�8,�? , 759--81E_�MT%�D.]^G!<0ck, I. Todor� \em%�current oi�" le3!a ger=�.� im In: Con�}!^o"e� ed Topics�Bin�ruy e�.,%* Nucl�B (� Suppl.))5Bi�^20--56. . R)�A�Y� G. Ruzzi.e��S6�sec� ���2�sang)� Work+ prog��6�S1 ��B!�l,�W S\'anchezY|HOn smooth Cauchy hy&urfac� Dnd Geroch's splitt} tem �b�243y*461--4' 2.S2��S�nes���fun��)聩�ic�of%sgloba!Q�bol%aceHsf�to� e��0gr--qc/040111�%�� Die}�'Dieck�.%�-^5Yin��% Oi��퉁9�PA�578.P DHR1e�S pliN"�>�`$E. Ro�QsY�� observ�$)Op��l i�s IF* �i2͇71��99--230A��+ DHR2�� �/��z�3�� �4��5�$!m�.D!FS.D9F J.E.1<)��V��qey��6�.} N Inve�)�%�98}#189!857-218. 2�R} :��5� �Why�re is a�.� �a�!Zgauge�l describm�>/ ��U�F�@�131�!wl51-J$.2 EHA(G.F.R. ElliC'.W. Hawk��. ��l� sca�a�& �"�J� 1973� ]�FR� : �-H�hren,� chroer���SV��{braid-js�iO�_ex�ge��1�s. II:�et��asz i�c��in�c � MA_.�� � Issue�<2113--15!� U�GL!�, Guido�@Longo�!��spin--�e �"J# �A!��11--3�>�RV^�6��&+ iC� dQ�,�%~�in" .� on� �"v�89vQ�� ܡ�B �25--198F U5wHa �RA�ag� �>��^(� icmy 2nd�)"gTexM)Mon/W 7, �6��}K2},� Kastl2�AnQ�ic�roach�$? .9e�>�� 848!�6�! 5 Kun ��unhardt]zOn infra� )�6zE|yiyY massl>��1B&�&, G2�en5�4math-ph/010900 %.5KLM �4Y. KawahigashiE�e7} M\"ug2NMulti--�$rval subfa �modular�Z(of represen�=a'�� }�J}N� )�219� 20E� 631--669I9�L�x�Y�+g:m=�A1w of d�MK-��a�'a�  10��BMac)[SM  LaneuCateg�   work��!�OiaMOu"�N�,-Heideg g-�)�7S %kU�May �JpMay� i�Simt �mobjectey�ic"�-ChicagoJ�(1967_%6e m}�*mv!�$Dirac6�sR a #(. =N%�77A1|# 219 ]�HW @!�Holland�nM. Wald.. ���,Wick polynom%(�9 �ed� du!'of� GE�%>.�#< �f�2� 289�t.:�JS �,W. Junker, Ehhrohe%Q Adia.cum�,tnxm�5ds:ADef� on,a��a�: al���!��4Henri Poincare!Sbf �J1�118- 2002) %9�Key� M. Keyl6~ s�a� s, ca� le) X##rei,�cto� 1�)�'  l�q>�� a���22a�.��W` C. L\"udz!2� %�IM,quasiequival�!IaV� �b�13�29=63e�90A$9JOnea� B. O'Neil&� Semi--Rie� �-*e�JX X83*�Rob� 6�J �cohom��:�ISura��F�i�5�n]/(x. 107--11!�u�Rob� Z�M2�Q�#i:mU��%�' 1�ofB��%F (Palermo�).����2,eWorld$u�#ing, Ri@Edge, NJ�9�.�3!�>��More )ur:3�b�IFem�3commu�veU!nC.I.M�1O, Mena�.a, Italy�0��Edi:�t*��#�ց3).5RuzEgG~B EsJ��pr��!��AW ��%��Wao�#!t>�.-�/@+.�a1{No.10, �, 1�" -12865RuzE�B�P�u�=H3# in�24J��ln?56}��200R62 34 UDS�!�(D5J 5Thorpe1k-��1on El�sary�y�x#etr�J1�"v�A�6� �VasA]0E. Vasselli. I�C&6J'ofb(ari� from ext�ons!�of or>=c"� .}�F!�.v�3-�9j Z%12� !�.�V�rR.� �e� �!��4ympa��"0ly adjoint ma*A�y��!� A HadamardQ�>U E 24� @J�WJ� E�� No.5A��1635--676FVee�0&���3on re�/di�*ds.}, p�$int, avail�2ps-fil�\at http://www/lqp.uni-goHen.de/pa�/��YYe2}  R. �" �AFJ�NGon-A B�: s&; a�V�frame� .�F�[� 6$ � 2iWala.R&� �Gt.i5ŎUni�%of"� 9 1984_ *� %� %.8)5`e� , SP P���1 A�A��%-Gordon� inZC/S� !H%I�L&�9�1A��(297-310 � V��f�99}�Oa�#,Aboud. Ph.D��|inE�arx , :QN�+&Q {bagoS-ouendi�0C. Goulaouic.�ea�tic-hypo�� ptic�*!;soms"geno" "$!s, b4 of A.M.S,+78���0$p. 483-486�y!:72)�u#ch}�HChanillo. \newblock�%v!�$ory, Tr\`e?'strata,�%o�%"7� � >��um� squa1#uP� August �, �4arxiv.org/pdf/".AP� 7106). � hela2��Helffe"&!Laptev.� Non �7igenval�#nd ��.�. N�PInstitut Mittag-Leffl z ��Z�211308.�T�A�Jou�%ofɱ�"AAPA���4>1A� Christ.YSAi�8�2� :�sv+ �.K�6A�$ 16, p.~13],0i�2�=�2Z���):;,B�of nil�& s,A~ a�B�. blem.� Duke� J. 72�595-639 �3B43.�.�^�!�"U two26 MSRIU�e�1996-009a�96:�(dusc}N . Du6A�d J�9Schwartz�2em Li?"=#}�&2,4sci�z I,6� frsh�*FriedA:a0M. Shinbrot. a0-hEu/�!hs,�1I �a]125p.#,2F 8) *�gokr}yGohberg zG. Krein � Intr� ion \`a l� \'eT6�' non 6cessair�  auto-� s}� DunodYB0hahi1�(HM)���#H�$�J � s"2��6�A�iH���.A*P.D.E,-*6}� 8/9A� 1503-151199�uX�2}V< ��$A. ���Nonu�>n����Z$ &� ity}E g A"n"�@126, n2*eY 405-4M� 8). ��he1} B�6��6"Condi!�s2� s d'�&�� it\'�*ur!� 2�)l�<`a<ch( r un�e�N gradu\'e�.xdi�=+&?4i^~44�83, p.~460-481 �2:�he26� RemarZ*s � r\'esul�* deVM�!ivier%leA�! 5�%A�S\'eminA�= l'Un !.de�, exposAs9� 78-�/:cerowa.��[e�Xue P�W6�y clas�/%���F)�Fs��P0N "+?i�~iz`6�E 320�>�o}8) H\"ormand�= Hy��pond�6�"�F��m�� p. 147-17i�67!�%Ry�ke}M.�C Keldysh. 'a�co5te"8"he �&<"of0 %`�f%Sc=��1`-D/, Russ��. S� y�v2C4�t15-A�}�o6.�(ko�# Konl��*= , M[*5 �X8�ӕ�kr� M��%� H. L�fr9 � �I}i 'y !͉&�,damped osciof��/a�-�D�F}�~�4 � p. 3*099,�*1/a�..)3ma!� rkus2�2�to� ral o�&x5�$ pencils}.�!/A\TI>�2-m"K�@ican !�5PSocie�ؽ�M�� '�m2�At J���Ul�m. ple �* acte� ݒ�DE D  1-90I502A M�6:�.�Unem d'2 � �)V �h�b .�IndianaE��th. J.��2�823-86�*B me3}B�v�����,.�s "E-� ,  "��&C {ne��Ned7,2�Exist� �sonan0'�matrixL r\"� 5�. "I1cI sis�z35�: 301-324,��\ �${phro} PhaM) Lai,�!�H. ���Hprobl\`eme aux vale�1��� l )aire, J�EA�.e3EG 169 �0UJ2�ro1} D�$,� priA��w�"a�pO.2 Pseu /'eelTY�� � 3}�C755-8 �:� � ro2��&�{�8Aut�$ l'approxi<; on s��A72#Pf)� !i�s� @0$ 68, Birkh\"ausN�����ro32�*&&� s j� i�small� ametY �4g��&s=S Fn��7ED23??0)�l!5.se}sSeeley.B $plex powere anN< &� �s%�$. Symposia�6!.l bf 110}M l$p. 288-307���&�Sim �0.��(Trace ideal�n�ap~i6�LoE�)�al��2�( Series 35.*;& & hss!�79�P�jSj\"o��L A �>ula�!R�0!����A�I��cRF$ .� (E.D.P, \'Ec 1 PolytechnA�,>3.� �� �Tr17�2�b�� � pa�o-a�ee�al �� I�double>�> s! �0${\bar \pa}$-F��6��2 DE 3A�~476-642�786�Tr:�2dS"i"� �Z�.��?�&� : La Pie<4!� (Flor�A)�201-219,�� �os.}Q, 65,B�Fe�vidV , RIeZ9A�V�sf�3�(W}^ WignM e�M&)v. \/?77}(195K=�9#-CGreen'6S$FeenA��A�ized M�4AX��&ize�= Z�90�s270-27r%�HT��Kl',djiivanov, I.�0�N'dromy�K2�%  he B�)G�1�� % { \em %%ZAtom.N�0\/� f 64 }�1) 2059&O2�-DQHE} B.I.Halperin� �R�}�52!\84), 1583; \\ R.B.Laughlr;6%Y}.267�� 5^anyons}  BLeinafB J.Myrheim �Nuovo C,&to B}��EG ?1� F.Wilczek 7% :�49�2), 957�bi�Squ�LChi-Keung Chow, O.W.E�.Y!$ A)%283-r , 20; \\ :8 J.D.Delga%+`�E.F8F12�M {HA|J�I?y�):�O Bose&�* :eJz �AQ� 34 !65�-54�>y�Pal2} T.� �!���m�a$U_{q}(\< l ��� A-g2e�%f7373-738�uk Ques3 �0Daskaloyannis>/( Kanakoglou�f( Tsohanatji9JN�41e=�V 652.��ChUk��� rpret�%�E� -() 's A% %� Para&,!K.��m=I�1 260iE�$437-4vQ�gPalcmp6� _� A%�DEl ��P�y��a� ?Alt�5tl$ChevalEDe�1p� of y��m�A�,2n+1|2m))$. \e{_ >�9M�19I��4429-4�:UKTEKamefuc-Y.�Fh$-% �% ge�6�U+�!8 9F��>e��3�62), 177�BQQRyTE.CCSudarsha.f �R2�-!�!�f�� Ring��4eL6�206-211*GP G�7v,���A NK%"�"a�D&�=��U��.'%V2�D80) 797.]�RS}a��"=")L�J�N#.�Drin}�G.  fe�,Y� ��um�sGKq��i ee�s!�!>�Hne�al=e99of��K�DEkl190 A.M.GlezZ(ed.)t".(�RE�9 J&�F� 1987)� �@798-822�( JimbC!  a%�d� c�Ka���$U(g)$eT��H-Baxter"� E%���:�1 /'3-J0�FRo FaddeA�N< shetikhn L� htajmv6$%�q��a��m ��6"��I�178�W engN t&: MLenin�-J�_1!�V��19q 5 KhTo� �-horoshk�V.! Tolstoy!f2�xal $R$-Y���&& (� )� C%n��a , 599-66�V Pal42�,VStoilova o=�(On a possib�=+, morphism!��v1|2N) Do A�"��ly1� $Wj NŲ��� ��E�2-28�ڡ�187-194 �% � 393142.�(Kac��Kac. )�Ad"�;# � � &@ isa�P. IsaevCm ��&�9}Erf/690ax10.� ��CP�Chari���%~ uideFep�^ oups�/.Ca.�L F.�!%Y�GM} �KW�o � L.Me@�A=��p�Ru5A��i�Mi�X.Abs�*� %(-t�B�Na/,9�e%�F B1�138� 6��1155-11j+u�OK}�Ohnuki,�"�^1;�A����.��:�+��2*� 4 {unita} H.-D�=ebn T.D�Fl�OI�Li����I+ \bf 35B82) 9367 %-9380 �L]*��55�317-325.Vw�fw99*?\v,({-1.5 cm} 5�FoA�% brov�GS.P�vikovenA�Feko, M'I"d/:]I�*�s&?a , NY��!�2�Meha�MoV ,  J�!e��u� al &W� gy l�Us,"�;(@4{�$2{Deift}� A� thog^KP*i7� �M� ces: a R�4-TF ach,Pantv)6@s (AMS, Rhode Is�70P 9�HaakeX ,UT Sign��a Chaos, �<"�bF }�X6�BoW;}�N 1T Les Ho�$s Summerzool, S�a$on LII ``x%Q�" ics"F. by M.-�UiannoniF, (Amsterdam� rth-9A 1�%%MxO�?X�^o.��K'+ 41E216�Szego�mG.  �<^�, 4th5 zY ((Colloquium�(9MA�3, PaQC 1975:�saddlepx1��Wong,2�.T%��<�!�U�x,2�28�]P�y}A.  %�(H. Widom, La@J0+%distribu8s "Zi$Airy kerneak�J -�159��1-174 �f94)6� Forr�a�J.�reA,��" um eV XP�(x ensemble�Pit2�B[FS] �40�)709-7�)F+2mPS8P&�NX*�Ebina, "; /3 lgS e&i*s*�Be a&�vry-"�' � � >�J�aKP �8 %10�+7:KKSn2P�:aXH��(N.C. Snaith�u)@��"yg'L-&�%$at $s=1/2$asit1� O>y�98R1�&>��Yhov} � , M�K�Mf:�*i$s!�umes08two-rowed lexic�A6A rray1�E�4.). �d!�torics}6(1) R2�Q>�DGA� Diaconi��$A. Gamburd՝%Ccea�MagB?0 !N Matc:9.F-L��1�T>�BH}!EBrezi�(S. Hikami, � &�$.G of Ini9�~�2%�111� >�FW%$e�a��N�Jtte, Ap"9 q, $\tau-$ Qg��� |gain�"�R�%�>;-��A357-398�1:"MN*/L.h� J.-M�rmand.�af��"�threey�� �m�9lJm9 A:A h.� �A=4627-4�/c >�FS1/ V. Fy�M�j?trab,ODexact�|! �L al c�s�'"�K�*Bk��ces ��r�6}, 320�c13�3:}AK{&Ak�=�,Kanzieper ``�$�M�+ve�y"kDQCD�AOpe:* : a Novel^0k"M��v. �-i85��174-1177�B�SNhH�So �A�Hces cl< to &�lor�6�::�R view�m��)rF-�J. �oQ$ .%%d3!d3�E� 6� fluc:�� �$͹ �Ene4 vBcap��Glass|X� ��Ab;0e�&u1�l D��-nt�d [��d9��� ( 92}: art. o2�1 �,4); Erratum: C ibid 793.6$149901 (E)%�>0AS} Aa2Andreei1B� %s,� m &!XSp�Vl � "� Cr Fj ��h75}� 304-2307� 9>� SF22%pY�q�*xQ+aݡrrmąt}UV�:>�  Z ach u�)gf� �[43-382)�>�BDS~;`k,"S �.�P!3M�� f�a3�SJ�Mda9F 4�36�67�B�E# Bor88�5� , #\"k .f.#inqZE�\ , e-pF8arXiv:m�H407065 .� BI�YBle�oe�. I�!``SdXa��&a�2to�,e}H �&�-��:��% �u�;�l i�Ix0IelQ�IE!b["N 5�(185-266� >v sycl�v$R. Zirnbau��Sym�?" Z.@x �HN9BA>B 40586VerA�J�>baarschoI� T. W�= g ``2mm ory�nCwv�in�x= u�Z NUcl4rt�Fi�P$!a-4Z AFB 6� "p Q��x.�!� uC: ]� �O �idgV4 ��664��457-476�]>:T2�KBessel�M61�289-3 >�van�L'�2.Fbe^u�C`�r� 1@origi, 9Num6�2� ys/030607I�Z:(]r� & BBHSrBf J.~M�rrbaroux.R4Yism},&. B."�P22_# 3791--381*'b {CIL��,�)�P� LGD1)�� II. Var�e�J> �F&CL >�) ean-E S�6� U .�815�28]! CLB}t-,. nc\`�:CZ BrizAitA��A-depend�ZHartree)�"7 coupled�a �Bnuc%EE� R.T d eyK it GGY e.�2o !�A���X��Ae V��)�M�� 1��;(�, 1122,HUX�D1A�~A�\E�QmTh{\'e}�<u��0}, Solvay r�w� 3--2�\P G@: Gauthier-Villar!�XXV%J3i(3�F() edAc{!"�4(WE FzumJy�}wi+bya~�4iHHD�_]58*�b{D2^�Discushca!�in�Ne2mn" *&�po1% cA�mb il�.S1�309150--163}Dy �>Dys O�Ł�S!�&5��xRI RRtd1)A4�!36--1752G EsVe�  Escobed>jL_ gaQAR;�8E5"S3�($H^s(\R^3)$E�8$s > 1$}, SIAM!�I�1abf 28%�Rah$2, 338--36*Rj {EM� teba�R� g\'e�&qo��>-�tom� molec2� 6�� 203 �!A�3, 499�b���`BEv�Non.� limi]ELN�4�i2�P\'e �}R(W�$5, 941--96* ' {EGS-�%C, Vx orgi � NQ�onxK��-\Maxwell�Aa .}G ��Zalc. VarT �1.AHM4)j6)Fa!j256--281.�FST�Flato��, C.~H%fi=O8^~�.�J q�11��7 �1, �L46}�FS= M.~��*�8.|=,�^�#R4JaV �,edMVacuumFari 3 effeXUn6n�� {$\mu$}-m�6��A�3>p12 �6�a�$2, 609--612�MR�n~GZD�"(B.~M{\"u}ll!�J.~Rafe�w �QV�a�S� g�3s}.6�Zq�� ics,>C#�98 b2 {G*;L�$o})���J�Ax� M�…�.�mV�os �1�1x �x�R�F"Co#inz"D � -�Po=�D�Oty�Ued0���) 5bX�5�G 37CS�]1%{HL���M� w^!!�JR2=aL�'p �ed� } R� �*� {�q�!� it] ap�c}y��� H-K��S9consis�ou��K!�N�dC-phot� EDk }, {a�� \&"j�3}�j�S6DM2�-�N?�FPe�mv�Is/�ge RenNl�;eo[ n� Z�� o>e��24m2�%2��22bHei�: Heise(i�Bemerkun�]zuri~��n gi�Es P� � Zeits. f.%�ik �9��� 20�dZ�U�KJ Klau)G�]arf� �'�QSesEѯ*:`^ *� Hel")]�A�{%5 ��)779-8.�r{La�fLandau��#&� �!6�|,� 19$ R�&� )h"ec p� f L{2� D��r�#r,Bk1�9ZLaP FƅHI�|$nchuk�U" ."�PrXDokl. �,. Nauk. SSSR)^1?!489--�6 r�p��6� MNO}� Machihara5Nakani`�OT. Ozaw"� t�h��I���nRg � 2� * }= M�!Iberoam� 19��,��1, 179--�,*�Rui�~N]Ruijsen���On�� -/T)���l #.V@g'�+}{B�Ci.e)1V e)do17--526���:\�� {QED�!|Leb}�A��!v!,MA�&}. IvC,of)TLfTA 6�XSTADC28.er6B*K1B{Th�Th�6rMo��� C�%Per?Wl��6�y{Ue�"A. Ue�<5z2b 0 �A2ory!����II.�!? bf 4I�37.5�W. W��,V.~Weisskopf�em{\"U}��$die {E}lek",k des {V}aku�Nauf {G}r�,y{Q}: en���D� {eF -Fys:"8dd., Danske Vid�lskW �C6- 3*��9. ����N�| %fa10.a8Anton84} A.~B. L�q`Twth0u��investigq&9;rti"] &�.[<{$C\sp{\ast} $}-�2s�8�>by ����~��-$Sb. (N.S.)"� 124(166)%~84~~)�5md. \MR{MR743054 (85i:46088)2�rnold-K�. n} V0 �� 5+u��!in hyd2�vo�[125J] .�\�hy�$Bayly86} B�zx$-d�?�a�$2�ell�:cal flowqs �Ov.� 5>5�8M�~1�{160�6->88d:760�B:� OrszagHero$88} Bruce~��(, Steven~A.00z�T�hThorwald�:, D �VaI? mecXsm�shear-���Q� ual ree#fluid=��G 34(%"�F'��GM.~!al��iew�Galo AlOCA�(88�6pp.~3�s391*c2H{Browder} Felix~E. 1�x "��{y� 1� \8V`.B. {I}i ha�n9�14|60/196�30I�35 \#804.�CL} Car��=gon�8(d Yuri LatuV7)�Eq�TG�scq�}�.K itA�>ip9��} 495--1�x�� 95i:761072�C��D Craik%j W.~O. Cri�%l"�9�of|like di�{baaMi�;eU aUN'"3M(B� {N}a�S-{S}to��e�zi�-)�c�Lyd��Ser?5"��*�t830, Do�� %87h�t2�DGY96} !ickin T0 amch�$M.~YoshinoqvFirst=S [I.�.e :wtorus: ���CX{D}iophEae "5�%�q  >�V�~ro>=fwe�H ``� a�"� s'' (�d$ian) (Ferr �H)��4n 99YNp.~ r64�".%G MR1471014M 98k:582212�0Engel-Nagel} �-Jochen �Rainer %1UOne-paRM�L E e�;]+Fh� 200�� ia�75. FHϔ�k(R. Fabijona� Darryl, Holm�e2 -{C}q* Y�and��6 i�DɅa�nq�-rem��)u�mod. turbuOi�Y� �csu�! ��$4, 853--86>A,MR{2 060 0392��ZLif�} Susx�ied�)�] Alex7V Lipton-��chitz1L�0�< �ie�?in�2��Handbook��&�%al "� svR II��.�3 *�3�,�+�#-3�|�1 984 156�S!^�Ro�[Shvydko* e u%��t�)u=!6��|y��-��i&{.+%�5����f 3~su�z�S81--S9! MR2126�u*! FV91b^�Misha~�$�"�* criteriaePthe����f�invisci/r�5!��u&f i8�~6�}: �� 204--220M�92b�51:�$2a} \bysam�lN�esteady��Ua perM �O+�� textH$}��WD no.~Q 46�93j�32�LebGod} � en~Modefe�1Cla| Camb;� S.~Leblan"� ZonalDa�s �}rifugal,"� @*�z2OaM�uart vo�es�"�afroAINy44U� EdPa<�n!132� Hx8Z83} Lars H{\"o}r�0�� ��Hy�;of��P=�{ry I{ G<l�wBMaT�s�0Wik2�C�Cci�>s]�� 274J$Qr wu85,�T2�&o.%.87d:3500A�&� JPS87} Ru�(l� JohLKenneth6 Palm!;A0�e�lS�&� Ergodic �~p����.2�N� Q�18�BB�!��e 88a:58112.� KersqA } Ri d��E��6/J@ i�& �� +]�)�b@ ]B ��83: ��,�r72rLV} Y.~"� %�M.~6:Liʡ& i)�T i2$� � Rn1�23*q��361I]1 962A�!�Y^(LatSt91} Yu� 6�\%St{\"e}p� i�Weigh�shift AO�6� QS�C�Eh"~ | $}, Uspekhia�.��46M_���2(278)� --143, 24�h2kx 62k�chn�h6&%�Ro�/nlltUy" �U<, �z�expon�`di�-+R�+ocycle��ufJ7 �N�:�P�#~H$�!36TMR1730780�54).a�^�!�'e} ��?�Nu)�An illu�V% %#Dlink between rib%�VWa���er*O &t+��2�$7� �99k�0660if2.4 f6- ���� cert��mo�A� aqa@yR��Ein.A�h&_ 1I1& 4�4�43�5 �62�if-� B�Exact� crip�A9> * ��al ��2�%�magneto2"_ :�0 1�3Ɂ47, 162Z'6�6e!�2�p!�, J��Elieze/meipFI_� ��܏d���'B�A����H��X264 651;z9x046�H1B��k ]AiF3!mex )�  swirl}." R-4� g~�r�D��08. �5�2:� n2} Zhiwu(8��.� �b[ pl'.�(�$�(�c3A���)�SɈ�( 56 (� nic) �� g!�6YMane7�4icardo Ma{\~n}r+�Q�w-{A}n���om JE� &� �a͢}/mZ؟v 2n 13E��%R58�#28�2��(Nuss} Rogeribau"mh �u�%e}�1�q�},�j-XJ2UiH7,%473--47-�41 \#9022�(Patera80} S�,oe>A.~T. !1PSub` %*O to &��I�nelU���6_ 4A�{9796�L@Pedlosky} Joseph � Geop;�BwTh}, �-�}�98EX�V$Perko} Lawjg2u"�%0JX seco'���ibZ . ���>�*�1���97g:34002m Pierrehum R)�.�U�6 short-��|�� E@*3� dd��' N b�*0 2c�-2159.SSJ:a!�~�A��:L ��t�2a"ze for J  i�rqC"b ���)7� ��3�320�mU58 \#1866 �`65}-z ��Qgr6�^&} EUl bund� T����B����11i�t16}�04��LMR0173174 (30 \#33872� Shub�Me� �cZ(E�al8�6�B��� 1�`l��wn�g b�h=6aAvby Stig�#A�ss���` dv 72 ShvC� APN I"4M}a\~{n}e sequSS �iQ ��:Nt2�hvt-survey>w%2B�1lOn re9E� elop�n_�" 5l4�cA� ev+ed�u�r��� ntempC �:M537 � 271-�2�L�aR�6� �E�t�{IT�m��a�{E6�%{L}yap�M -{O}+�d��ex� ��("������D.��2�i �bBn �lF^�A��A� .�"`� ��UN� banAdvanc�;l�|1�i9m��aA�ɸs (Bi@gham, ALe(��z9�6 327,-��.��.AIRIEOf13�V � 2QShv"R�� #&ď��5�=B 3{DC>��:8�DDE�~M��1� --�"��SLJ^D.~SippA� ~Lau`3zL.~Jacqu&*VW�Jng �.�a}��typ.#iTP3� }b*h�C1� 716--372�D�� 22�Sw� s} Gowy qlI.8sto {H}am��� �Es &� A⩯ Chap�(\& Hall/CRCeb�.!IS�� h.��%N� 102,NX$, Boca RatMFI�b���a� 2�V�Nq(tMns-1�Qioc�Q&- ��a .UJqCJ/s� . (9&+#7� H3~�W5��557�j97k:35�4]�FV9�B.�!AfeRnory" #�!&##9� �b� &n � �118�5%31N%Lj�a�%� % S�xmacros t�avT~fo��b*͙:��og�Pal use \JL :jnys  \andvol :�"( (Year) Pag A WindiviZ�A _PR : i�� 6\PR� � ?NP?N]e %2\PL 6:JMP :]��z\C  /:,_|PTBPl.�(o;6F\JPSJb �4JpI�%[��m $2\NC�Nou[ezIJMP:�\.>M&� \ANN :7C�� % Usage)�0\PR{D45,1990,� 9 ==> �~!�\�+DV[345% \JL{^~%\0,A30,1981,56}G HAh:8X56 GID{B123�5,1���=,}M�)"�*"�,rf:KOS} T.~K�`�-Y.~OhX�fM.~Suzu*X� it{�h � al�=} ^���%! %2yIKMyI�,`D.~Kimur�!T.~Mub~ JiS ^&153K2M��N0)\37)hep�307289>�K2%T.~SakagbEi�%�D6/�06��C, eth�B08>eS}�XS.�ul�-�,M�n�l�{�P�,E�atha�R�� } (W?�-!�r�{6�81)>� C} E� ~Cop�#j.*�8 expa�!�"�,u�<., :1`*y/Hrf:O} F.~W.~.J.~Olv�:d ��� ~��} (A~K~_&s,~Lt^K$CFU} C.~ChO�C~G %P�F.~UrV�EN2>� )�5��No5�59�Q57�2�F}*`�� G�� 280 Jl9) 6?U% ��Eb�zEߔH6%[2� B} N.~Ble6� "��� �1�No.6, 53 NF�KS2e��D:�ro>�iW0�"%4 89 3B5OH}�,A.~Osi�Z�B.~Hi^9Ev�iQ J. C:t223eF4� NP�fa-.ك1}� Y X�Tq{."�D4 in $\eta-\xi$�U���� D�� 0,42:1988xp5*�02^ Ferm�M�4' Z Z�:[$2,45:697-7� ��5vu �G �G%E)o r.�:�42,46:1869-1872�4� Study8new�Z#� China ��. (ineser�,2:28-3.fH5} Aldrovandi,R. \&  eira,J.G., i:� �� �,&"��f��u(�( Co.Pte.Ltd�6}W� (nholz,C.V.,�>"M�3%�2IG (Revi�:e�)A�*o%vX�(� mpan[��b5�47}Niemi,A.J.\&�A(enoff,G.W.,@@Eb94,152:10AXN� j�2�&bog��"-G, %�sO 2-��Fvcw� Izv.�6 USSR,�G���Q1947).�(�Xns. ���(4).5a� 5SeE�so�b3�m�R_sta��}, �E�B(h�8��gin�E( Ginibre, 2�&�M^+ne�2TH a.�YA" m!�bo���}0" z+g )$26J�zag�? A.~Zagreb�`$J.-B.~Bru, �Q9��(!� weakly im�%4oga� ~Rep �3M29��5'BL�DA.E�V,.�y8/,j7�6�S34�722sLi�4H.~LiebQb��,a�&GC-� spin5Iz>5HI? vm�32�Q7�L�simon� 6�xmU"zU!:J� �7A�24�8:BSP�~Buffe$zLh.~de Smedt, J.V.~Pu�z2�o,I sate"�E^��B�TY]J.~)�A �16�*430 �3)lg~A9,escu,cV2uA�V6cMXO.�8'sYY>J1� ~ 25}, 3476 92);�JS���9 �&�82� 30}, 4895A= 9�fannes1D )< Pul{\`e��. �u�%-5Oion}, HV�<5Wa19l�}sut��0~S\"ut\H o, %��`-E}!R�.i��s?Q brea��},u��8� 2+k)r��~�-(4B.-S.~Skagerst���CohŤ�ej2�ainѦ�.}�1 �t�3! 52�fe�c W.�YZhaW8D.H. Fe R�QlmoAY�N�:a�i� E�.�}, � *��X2}ܹE���\��liebcohaf�]M�:*�a too%0 ob##E_rigorf� boun]- w�6�IGz�~� ��9�M.R.~�Yy� ��, �{67-^:\Q.e$pethick} C� P , H.~Sm^ �2r6w in dilute���&� }�h* ��9J HL} K.~He�>NEquilibrDa�qal&�5�zmatBm"�>ngS+D��� radi�� ��A��9E�O�51%�:�LT2� L.E.~Thomtwq� a$�&nd�eF�%4ng-�D�C�&��~��cE�18� 511a �� Ya��4=ald�E.Y)� �var4>e�P�H.�F*�JV.�60��b 2�5oW �:�thir} W!Iir�# �A li"9� best poss�.aDta�5@$Coulomb Ha"%a�-Y5h.�%Y79=!VG�.HMNJoh3CPMI?n�e�Mi�co:0&�7ٶ( helium}, %P .2! �.wq(griffiths} 1z GzSpontane�G�&izI�iy'E�ferro ! �E�%15��24 662}DLS� H YNAJpb����Phase..#ini�u6V )�isotr%5A~fu�86���2>1A�33�w~.= roep)�ffPW~RoB�wE5a��AJde ��mK+($\nu\geq 3$C��F�1�� �R" �f" 27'0Aref1979} H.~ . \"�M`)a�b`5'j^.${\eHw�}4�(3):391%0P7@��h Rott�(nn1992} HasQ4, Nm+ las '9 4s�Lnn.�Gr{a0bli's K5 �� ree-�ex�.=�AR�;�4:��92.�Ba��lor2000}��rge~Ke��JiAq}\toL�$sH5~��erU��a�o,  .��! } David~M�� .�Ideal%�exJ+A� two "�$��� ��a>�ڤ�.awF"z��� 9(9)./27q"�Newton:3Paul~K.�%to2�%�U {$N$}-�ex5�!�aly= &0}�ume 145WpGFp*�12�Bt#"�&!2u=N�l�TJA.b�l.y��W!P"k`a� !�A�Rm�%]L JETP}, 41(5):937--9@/�.Pܣrd1976a� }�%Celesp"1ani�+n�& 18�(!�Carus��e��$�(Thb��o���eVQѬ��inC P_s.B�-����ureEQL.  �z$H^p$ ���b'#!A ��$., 38, sVK�>-LmJ!�70zdelRio�  del Rio�wJi\�rskaya,�wLast,�^�{\it O�i� s��c&3�sT' . IVaR usdorff d"� ,ak �DI9u]�� no���1ys>0e36i29A1W?2�i��i J. FG�h˵ �SŒX�^�, q� t�7 bin�~��E�"��or� �#gy6�i� �8�J��;N� 11841� GMP}-,Ya��ldsheid!�A2:LP�pM6A�m��[$E���e&�� h;A p�@ver"u�Wall'�c ntin2T e! L^2(\bbT)�`J�mroxA�A�I=10��. 16�r24��Mi� Mins�� �otu-30-FP.a multi�������FZN9� 17� ���3,�v-72"$ M&�6'��R�uc��aa���on� )�h�C:@N�%I 7!H 7/r( �܈-44"� SVan�R*W�� .�BraN%- .�� "����F�&�"1`&Vancou$&BC( 93�[0��49, CRM� .: ^�, v :�4\%v:�L5q� OPUCj�.�OrR�|A#h|�$t Circle, ?� 1:�DϞ, �AMS �Xoqu\Se� h1 icanw95!Sp�F��res��6�"��2:9���z�S`~B"�eA~'sIem#Zc1x�{},CaB]1�S/�B� FineFe�ZrՍA t�V�Dwo pie�� �5ri��SW.v�n olff�/Sj� �ZRV �$v %"�� .|u�� � i|� 3� 8��1, 75--/iIQTep��V[ plya�M%���p� 6� ! �v ��.} &� >�Z S"�Z32E\Ch 4:3;Z� eGJ�A[x4T[ 2, 40�A1�* V8 f\Z%"�arai1�(Ar= �^�b^l5fa�W-M�e ��a�23�el�qom3,�wG� :} ��Aq'), 42N�caha} I�ht�6nd.�_ ;` !�� (�2�QED �J.0 �20��5), 68XF0. 2nch[*ҏn," -�eti�Mfr:er:�_��t�,@��� ed 1Otid�S07R�$ mp-arc 01�q�F�cvv�V;��J�S��V ,� incre�of"�-^3enh�7d in n:]9b!c.�rE�-�cTS6�fr2� 2f/,ncd182�9:a�%�y9tfs, �.F�chritt�`rE�ikM�jn��� ���8A uFhasi} �� �a%&R�^C9l �z RJ @yL4�S�G!Qa�Re�F�a!R iEE��.L*A8 8�F�+�"hvv � �,� EV�FU �":'1Q3�11�62�hisp2O.٩rwSmkH!P pohn!� Gr�)� de� racy!��~i-Fierz)�m �', �vH�6� 0bq110!�=�isp3} Fz�%�> Z6 2�w03100 to be p",(bJ2��ic�K.A�I(Ka/��;t2p Fock )* �Gnd-�er7ric�,. RIMS1��^e&_ ɫ5%9)li��� O���Ycs,%�s�Y!��#�r�TLt�T2,/�00ۧr��4.lilo2 �� _M��L�h AA"on�����C~N��So"0�ф�Mw�AB��"$2� 10F1069 =Gne3 �Nel�2 \A��J>�_�J)�a %L�!ZX�$,�J. ���T }�e 1�, 1190�97.!09�rs4} !MRee�\9�m� aM�]�O���"; ��VIV}e�A:o��5. .sp5�"�EfRive)�� hPlaron: A"3+�Nq4l� r�Qx5 #1 ��1�:A�WO$ 278--318) 9 sp��"4 h(�d�r��$ �ix|&Bj�9 R "' (CA7�śNr(f 6�_ak97:P8} A #).H5Beh"�,$\epsilon$-E�0pe�a� *�hive ". .w�� � �7��-&25E^5i'90)=k:�$i/nagaoka:�� } AmI�S.-I.,iX, H.:"E]�I*|��2���: %�e�!Pr��t.�"0a r�k a� en8�a�f�C�M��t ors: Ojimn��Te#/��*�par{�<broya�� vap�ce,��*�?4T|731--7VJA42�%ble��!�1` Bx~P.a<G�&�jof ��Mod�. J6` 9���6�y2Q'96.�b �� �:9&�;��� i�X O:0�.$�?,aI)L� 2�e��KJh-��Y�t�� Q��| 43/%5h7V� /dan%��5} .� , D'(c��r��>��  ^.�>� �7}(��gmf5N��/|�o�0n���g��:�=gM�E3ar9�*B{II}:�!�x�l� �y.��:t �1c�115--138��6BQo/jacob!��U6�J��:&"�>eFty�DV5�� l�3�2~L>����+3 3^487R�junglas�%9>zJ 2�2pE*"-�de8 &� ��dc2aY270!d89R�porIXnR;P , M.:� �ki^2�*�x�qy?*%���* 2�%RxU6wichma�\L68W �E��C����r|cw EM�- =�[:��0532X4 582~��/hy%nds�T4} .�,_"�sy�itya�ca�F�SZ�`6r��P�9j2��� CdEd���|� &^)[: $106028 v3]*(effros/ruan�0} ros!� , Rua�Z��O� zs� 0.}v�u /fewތ/verch� 5} EZ ~P�� #^x��+, R.:5In0Ili��Y� "�'.E�H61{e}�qAA�#2��:>�HM!��I�>�a�,wo-Di\-men\-�$\-Ɵ�2#�2�>�412028.�fidaleŎ 4} F , F��2��j� �#� l��M�. ]cJ."� �5@�72�21�UJ Y�" 6��:S2s�6 Incl�%s�W$W^*$-�$��Y ProcJey��],�����2.� haag�}� aDiAd.Vq�� 2�Be�H"��&�$��1�e"�m6}�/swieca:�0:. �, S, J|O: W;dDo" ���1�L�be&L .r}, 30� K��.'jarchow�h 1} J .C �6l��vexN.$Stuttgart:@G.~Teub�yZE=mohrd�ځ 2} MiZ+1� &� �S�R Di�2ce2� �V�ie2)J2JUH4�56`�5,Q�"�4pietsch:1972} F�s�A�J! �b*��ock Berlin, Heidelberg, New York: Springer-Verlag, 1972 \bibitem{pisier:2003} Pisier, G.: \emph{Introduction to Operator Space Theory}. \newblock Cambridge: Cambridge University Press, 2003 \bibitem{schauder:1927a} Schaud��@J.: {Zur Theorie stetiger Abbildungen in Funktionalr\"aumen}. \ne ��Math. Z. \textbf{26}, 47--65 (1927)=4schumann:1996}�, R.: O1�Ideals and the Statistical Independence�8Quantum Field �y.9Lett. � Phys�037}, 249--271�96).�%�:1970} S , I.1�Bases�Banch %�s I2�D�0 \end{thebibliography}�#\begin{> {ZZ}�8Alcubierre} M. �C, `The warp drive: hyper-fast travel within general relativity', 6Class.5�4Grav. {\bf 11}%Q,4) L73-L77. �DBSM90} D. Buchholz%�H. Schulz-Mirbach, `Haag duality!o,conformal qu)�f!�A* ory', Rev6��2 �00), 105--125.� �2���68I63)���.M �PfenningJ�Ma_ R�`AqXV�y �spin-one ŁX curved.u��A". �e�44�$4480--4513JrRoman03J�T.A. , `NullQcondiA��u�6x .� �6�3) 044A��FTi} 2E�E. Teo,��s�c)-!�sz�%.59ɵ9!� 40162�VdAIJ#�=��]�%<)� }A CommunNW 25},%@2) 33�[596�lan!D \'E.A� naga!��ܵN��two-dima�y $ Minkowski)B!AJ@Mi-�5��<1997) 4922--4926B��02}�� .�)5�!�Jn�20!-1040072�,ord78} L.H.  �Vcoh�yeffect& seA� law��0thermodynamic�q���.A$,Soc. Lond. Ai 36a�01978) 227--23:-HR!� .�A�rlfT � 2�DSpatially averagedq� 2�,do not exist� four2.�F�J�.i240122iRworm=iF�Q�.@�cx ins/ rsable mhole geo� ies'B�F 53i�(6) 5496--55:Rqis}=mF�Restric��b� �N�5 �47) 2082--2089. � "�0FullingDavies� A. �P.C.W. , `RadiSL from a moving mirro�w6^E�9:!� anomal� E� R.N�4�>41976) 393--4146ST} P�rl��G.MH tkov�,I.T. TodorovD 6� &� .,B�,Riv. Nuovo C��to,iu1� ,89) No.~6, 1!h6� QS840 Fried�Z. Qiu�S. Shenka�`�  , invariance,� tarB a�cri� exponent��2tN;]�LU �5 �04) 1575--1578.oGlaesX G. R� `Racd car� e d'ueonE� i \'�tiayBd Inst�Curi!Grenoble �1iy63A� 3--26� GKOEGoddard,��Kent,%<0D. Olive, `Un!U$y represen��on"? Virasoro7sujlgebra!fJ[� (1986!Y192XW����Goodmanl N.R. WallB!6$`Projectiv�tary po@ ve-Q J�0$\Diff(S^1)$'R�� unct� al� bf 6)o8{ 299--32� �?Hamilt� R.S. alhe in� e fY� t�em�� Nash�H Moser', Bull. Amer���,ij| 1982) 62�Kox_observAY�� KgA@yU��nsea�s as 8Ve8. �6082B �abs| �b.�A !str�-� tens�P< CFT${}_2$ model�"�� 3030532�KRYE`J. Kups� W. R\"uhl!u B.C. Yun!��w!��w�2��g.�g ��N�eυy,)�8 75) 11a42*,RehrenLongo}a , K.-H� , `LoL���bXa�� QFTJL �1� $4) 909--9627 Lu76!;$M. L\"uschEF"�pro��ans�4Z vacuum �6CI��ѡ�� &� J|N� �50���23--52wLusMackHL\"{u}�%�GA�ckm�Mq mome� Mzx�n2 �1+1.�X unpublished manuscriptI72 ��I:U9C� t� %��!M�mor2L!�Q$Nonperturbx2� ��y:� NATO Adv�|d SummerŔitute9rg\`es87)} ed.�'t Hooft�t$Jaffe, G. �, P.Kot*$8Stora (Plenum Pa�&�!1882zMilnor}a� � emarkUinfinite.�$ Lie group�5in)Rel!ity, G%>Topolo�HI}, Les Houches SesA� XL�3,�(B.S. DeWitt@� �(North-Holla�Am��dam>4)2� (MorrisThorn�S. T K , `Wo� a��{e>!�their u�k�5$terstellar��(vel: A tool$teaching gA�al2+ Am.!e.��88� 5� 2l Neeb�4��Rc `Cen�ext q^� 1�J�\v+ � ͘36�o42�4OlumGraham} K. um%ON.h!�`�c:��n�4a domain wall'6�*B��55�R ) 17�72 �_em��J.*�"� i�y!��el( omagnetic�'R��024009�. 2�Pstat:% L.H� K `ScaAQ��D2�in2.A�' *E E\6���348i 5:G P�~�u unphynaof ``?<''R�j�!�� 1743--175 "EPS8�5A.�� ley a�G. Segal��em Loop�s}R!((Oxford Uni9 � � �B:�Puke{0L. Puk\'anszk�! Pl�eree� mulaU=u cal cover�eoH of ${\rm SL}(R,2)$N�Ann�1�$6X6--142RSi!� Ree B. SimA${\it Methof� rnb"�)�(s, Vol. 1: R &nalysi!S (Academic17N�!9722PRSi��� 2: F� �4, self-adjointrnr�56�I_review}:�(ome thought����g�IA�+�a�~60 Tenth MarcelA�ss� MeetA" on Gjal�FjGraviE� gr-qc90:Schot�m2ottenl"�X5�i6 b�2���a6m43, (SpA�e"� �e�2�e�81}}�n,s!��� d+aliM!x��.f68� 81) 30�6�StrWigh F. StreaQ A*tmbJv PCT, %���i� s,all thaQJA$(PrincetonJ�ej8)*#TL�� V�lo LaredoR egraEruf�1w>� n{R�16�1�Z�!8--502� VaradarajV!j��G@y�m��"y�� II::*Coq@t Systems} (Van N"%2�06�g ANECA"u��"�nuJf�"� ���� einX U�A�J8 th� bf 4!=20206�7.�Volli� D.N.��*i.�in�>FsN#e��\v. ~%� �22� � en�E. �@onabelian bosoniz'�a . R� � 92} �4) 45+ 72| YuWuaH~  Wu^� free Ra-Schw�# %��� >2� 6z20� 06406�Zub�J.-B.  , `CFT, BADE2'!�@tt hep-th/0006151�V$\ b$widest-l!{}�u8\pgap[0.5cm] %�:j [BeGo]{}book{M.�$&��(B. Gostiaux* {�lu�4: Manifolds, C Surfaces.AEng�W nsl., :].,�g.1988}���gapJ��2��I��{%&  measurabi& of f �2jBvX}{123!�95}{1S124b� ���)[Ga]{GaQ�(D. Gatzoura2�Lacun��Ź� simi!�stochaM42 set2KTrans~�3A{ 2000�5u 98# �:<!� � r]{G1�� volume{A.� . Tuba�?!S��,g��� }{221]5(Birkh\"{a}u$FBos�{^_x��HaLa]{ ?�!��#ab�nd�. Lapidu.�RandomQSWings:�ir zeta > $s, complex��)�J�' �!'b�0{No. 1,}{358}�$6}{285--31� e% eL>  C. Q���NGen* ized}xconte �u�m| drums,�Q&!knRie !A-1A=MemoirsJ�!% 608,a�7A�9 --97�Ki]{Ki tA��� igam!�A on �N.�C2�(� X?  2001�� L]{L 9�A� S. P!�l6� PackX!d"�\f\ 2H-�.�Indiana� �� J. ~�}+-�x {699--709^��[b/[L2]{LB�6� 3iRenewaA eorem�6 symbolic �", �,�(կ�(�geodesic flows, noneuclidean tessel��!+�-+2` Acta��� }{16�.89}{1�!�)vMLa1]{La��!!�^zMoeO,� ersemqal@bl!� $elliptic o?/�}a par}# resol�)o�)$Weyl--Berr� ur.�����1991}{465;b!����L��L�� �,��&�\+1&�,nd5�j#y: From!�Z�d!+�� vibr�!Q��AF#R�,y in: 2 Equ S���"e �ics�(Cb nnewitz)��th UAB"~+.z+$. (BirmingVbh0Cn892, pp. 151--18T !~��3A�392��)�Vf`,2^ hypothesia�avu $� � mediaY!�V�:�Ordin�!�PmV�h$(B. D. Sle��:R� Jarv�eds.�vCIV�$c. Twelfth>�_,Dundee, Scot�UK, J�" 1992=�Pi~ Research�/�AW Z, �2899�man� entific�Techn�/,"d- 1993M 2m0L!n� MaA M>N2vH�Hi2 SqZ9�.�!R>�q�MY��Lo�1oc.�*} � : �9 LaPe��Pe��:��E�oearse5�7�   tube��E�9 act� =iHin prepa����Pe�q5(F�^�� �a?�:� of6Qti�'���o)vo1vR*�(C. Pomeranc2�heQg-g  0�@on6�VP!Uv�5L Rrw3)}{661 93}{41--6�Po)�o1��$Counterexa� ��modifed^�o�|B��yɜ"�  Philos))2tD �7 {167�8^, I�"+ a-vF%�-s� F�M. va� nkenhuyse.L D "UA�Numbe�8y:�J�:q9 zeroe�ET� .��0} \\ (S�- ru� enl.8�"�3)'D2006.)%\footnote{Aie ref�c�&4this paper areHA�first e�a��(�cmong8 \cite{)�}.��E�-vF��z�CFK>qN�(Diophantine!9 roxi�4o.J. ExperaE�Mg} n12m»-vF*  W�E�a#.� �A*F� s�� R�.��"Jubilee!c$Beno\^{i}t��<rotՔ %(2�� I��Symp. PA8%]"< 72},�  1Sn�Provid�(, R.I.��3�;373��Man]{MaQ5�B.�M17l�=H�LBH of N��)B��W�!rY 3��!PB� $�D MarVu�rVu�UO| rtiy, M. Vuorin� F0 {Whitney c�(, $p$-capacEqAa&i�g>Exp/,oz .}{8� 7--4 xv#Mat�1�Υ�P� ttilv ���of Se3M�E"�[7s (-ɩ�R�,fi>)=���A"��1` V���%�Pe]{PY:^� Cano� 2�k  by IFS,! ri� Nov.�#5Uy 14 pages.�� Sch]U BwLa wartz=%Th\'{e}o8@des Di� be.�F HerM Pari.5196)9:�MI3 Sch2�2Q�E72� 7A9M�(#es���,$ques pour Sci�~s�bF�Y �196� ~�t]{St��1�3h!s, ?S#*6S �(3ie�(�.s:I,P Z���3�� ), 7�< 817; IF^G3-b), 33s 61HI~�4U29GG 4(=�NTr1]{Tr11�A�C. Trico2�Two \de0\d%�"D!�����'6 �.}{(1982}{57--7{ >0��$Tr�m!�E��/cg[�� D�.RB_>V�9�z�We]{W���!eH.c ���?��.��1J��h.� }{61G 39d1--47a %(Re��ed[4m��L: Gesammelte Abhandl�D } (Collec;works)O s. I��IA�:3,liJ��#6�#�z,Zy]{Zy-!,%�A. Zygmu�E!0TrigonJ8c �A 9Yz��er&�(N%195�R`D$f` TdCMP9<�E� AER02]{ea�� } Ar%dis A�9org4:E#�$Laura RuetH0.�E��� �* awayo�-�$i� mj5&�|# �!"'�>�;.s�% Stud�#Histor�'i�oph�ModM)�}�c33(2):I4�(-*�#[And85]{Z Trson85} Michael~T. And2�($L^2$} harm�m�a� �aE4{D}odziuk--{S}�"2J,+� u( (NewMJ)=!gavica� "�Society�1 �063--165, Octo> 1985.�(Bae96]{baez�G!�~�aez.�Spi�Atat7'� gauge�or2�G�AE1" �*117:2�272a�96.lAvail�5�5\texttt{O)9411007RU�(BSZ92]{BSZ}2� , Ir�:~Ez�, 4Zhengfang Zhou.x�I6s) A�7�Constru~7�&6�H2DH"(-���M�� fO(Y.�=t5http://m�&0ucr.edu/home/!� /bsz.html2-Car99]{�9on�Gil3 Carron.r<{$L\sp 2$}-cohom2ieS# in\'!PHit\'es de {S}obolev2AA��w%��5d Annalen}, 314(4):613--639E�5�Car01�yb�Formesqw� � s g(\'e � non-�acte \"K�Rendi9 i di��4ca e delle sue�zioniA`N VII.e}21(1-4):819PE1.v�2�2}f�9��Y2>� {R}��'m�%.�I�,_H�%yE��-eoperato�D�M (Canberra �)� ~40��%/T entre!.h.% . Auq?l.s.��.},�  nBJ&p2�Che73]{�7 noff7 P.~R. Che.�Es�;ia� *�.�power g#!to hOK� e.X� Jour�,of .;�BAo }, 12:4�,414A�732�dor98]{corichi} Alejandro C .pI:���{F}ock�8iz��M}axwell�L.J�Revisex�;aa�8F\'{\i}sica}, 4e�40kC1��8.G��s ���0/98�D86ndW87]{crnkovic87} Cedomir C \'�Edward�*.sC" ,deK8� of c"f�;lisz9\4!�2�In S.~WH$w"z! W.~IsraeliA�)em Thz* Hundred Y(2 E%�/0}, chapter~16M�$ 676--684.*l >� A87.Dim��4dimock92} J.~D .�w�#e r"5)��a�.9Uewe���P;͖A(2):2Q:233�92�Dir57]{�F\57} Paul Adrien~Maurice �FB{��ip�sof �um "L2=�~27�66�JY CM� �. OH4 Jv�DthQ�57.�e(ed 196./ [Dod79]{d� 79nsef D .CZ on ro$2$(nNic2� 5�2�%��mee2�K� 77(3):3�800, DeceK192�7 [Duf duff$M.~J. Duffq2�i"e Worl� Eleven*�: S;Ag3y, membran� M-t/69 �8q;of1� PZ<ing!�600Ehl66]{MR0207 G@ J{\"u}rgen Ehler2MG��'>G30� �.To�#2J�VPeriv� "�(Essa�oHonor�,V. Hlavat\'y�Xp� 1�G 133.,S*�%7 BlooC"t Ind.!66.DEva�b(evans98} L.� EB�v`!2�re��*&� @Gaf54]{gaffney54}ALPY+.�A: � {S}tokes'��em��-te2$j"d �at| t 60:140�75�54.6`Ger70]{geroch70} Robert G.�D�:of &�T. e*%�alQ�}, II�f43e 49, Febru�"�T2�S�Dgreen�AM.~�/, J.~wS warz�E.~�1B�e��ng�� ory}<ume~1..f�!96�Hel?hEJA A.~H .R���B-axgy"l .&%;C"�R� Q&T^7�,13:L129--L13a 6<Ciin~toKU.PHT86]{h�%aux86} �% H vDClaudio Teitelboim.�ot�8�(.$�.�/��# ,6(7):59--617%T2�$KR74]{kalbwM.~Kalb�� am�K*� 92direc�K�>�, a~G./��(04}, D 9(8��73--22 1974.5:Wgir�(2YKSA�yMR16056�/�: K_ans-T@Sebastiano SonegoI�DMarek~A. Abramowic2~O�v� 5!L� \R}eissner-{N}ordstr\"om 2)F�Gen�K*�@MWF �0a�275--288!�6�(Lot97]{lott�,J.~Lott.'&� &4��ClDf�A6t {$3$}-R� %��Qi2 V} 7(1):8"(v�9.�PMaz88]{mazzeo88} R.~M .�a� {H}odge c��a�A��A me�.B��2�' �a� 28:3�E382o MP90��2�e R.~�,hilip2�H�Rq &� j4Duk��s�},�75�55�2�4MR80]{R&S} B.~I�M.~�=B*�=M�R.8>*1986W95!#��Leonard %(Emil Wol2!%�qTC{</0�q6�e2E0Nel59]{nelson� E.~N 2�%�,vece .�AXof%��70:572�&�9.2:�*.�6bR%�01110�^"� >w�b]{0j�� *�L.�v�$0035}, Janu B�S��S� �����.gEB��J�\Rud91]{rudin91} Walter RB�N .%R<in �$a�[%)5&2 4. McGraw--Hill77i^ nEHal.F92�Sta84�776077-hna chel.��og �U�ant� �5"�'sV��J.W+M,E�${S}esquice�5n��{S}ym$um (Amh(I�M`��8�� 37. v�I.po�01694235} G.~F�@$rres~del C�!ll��DJ.~Mercado-P{\'e}r6z�2�@�u� �pa�5%9#' e��ry��2*E�J.�v 0(6):2889U890!6rTV,b $ Charles~G �EW Madhavan *.A.�]�eX����>���.7�&� A�-��}, 16:26,2`1���R�>98112222xVar00]{v&B00�^��>�R/V~{$U(1)&ol(y NSB�� i� �ew� 610.,R��p001050B�16�1n� Photw6�)g*{�lux>�.�%�N�4�2yn�1040568VH51]{hove51} Le=oAmn~Hov2�S|6 \`em�s����lr.��@�bqu2�%3� ,^ys5lg$. Cl. �?<(5)}, 37:610--62e��JY�:& i�.�Wal��wald84�~8dalF� G��"#t6�Uni t/ h?ago�1982+Wal94]z9�z@ m�5orI�2�P}!,nd Black HolR T2V\2�L:d6Cz�96�il�wi �KQth�W.qTine "��quarkV6�7D10:244�4� �&rZucl zuck�(,Gregg~J�C .�A �$�!; glob�H�F.1�i&&a�e)>p\� (Sa �CA!�6���s�I�dvB>�2(2Kh�(#6�1�endBwh  f$�%5?@{Sc} O.~Schramm, ��E118ui2��ALSW�� Lawl1UM%WW.~WernA�;ma \87} 237� (m� TPR/9911084); \em ibid.1&.57553 5$0003156); SVUf38} 10�22<5294)..�RS�W~Rohd���,�A.,*a�e�106036�H=0 REV}� � -Me ='{\sl �@planar%� -� -Loewner "@`&�L"�Kq��8)9`=X354); G.5�|a��\ ly I�\t�ss�,{ cOe}�< *�6, *� %�c�Sll�"\~lE' /book.ps;�Ka&�F ~Nienhuis�6 t� -�1� 1149� 4 � Y120%�J.~Cardy�sl SLE � oretY�ist!5i2�2�8BPZ} A.A.~Belav�(A.M.~Polyakj^A.B.~Za(#0dchikov, Nucl�S241��Z�]F}�&^ , N�410029;Bau 4nd , %e$PR/04081572�JCmult;V1J�">b}, L37i3 (�!tumV)123XN2003);R�S8521�*42�DNR]myK>*JF#EeJ 16(4��9?�}n2093436�D7�Dub\'eda�WkProbabZ�30312�W=� D25}2�FFac�Toulouse�I�%�302115:�>�=�50��~Watts}!; eZ "d29%�6�6 (]d,-mat/96031676}SS.�%}S.~Sheft >�;6Yqas99@ talk�sqd at `�G �Ec�C�� hd!�c�ZD', Edinburgh, July%�2EBB_m}Da�r�L2N�723!!493, I5� 0210015);-OL!aq�543O 35�e2V�5�h3�M3 Y3����E*V��� >�4I�e�3050616�JCbccE4��Jb0324}, 581, 19�c]C dNN}�v_3A73 A6x8DF} Vl.~Dotsenk�$V.~Fateev,2�4 B240��P$84R�B25�69 s52� Kond� dI�*h)�i7�432 9�N � b�Mddd} %1& barnas,Barnich, F.B�ot E�M.9�?$cal BRST c&7�q&%+ie[$it�p.} �33 �9 �N0 U%2� fulp�,Fulp, T.Lada�J.Stasa�, NoeDh DNal� oLI!/�BV� m5%�it �(. Circe8. Pal�h (2): pl.}�d 7!�15FY�f %3�lmp!-Gi�@tta, L.MangiarottqX G.Sardanashvily, Itera�:; �)�_ )5}�5e�43�)/4�cΊ Lagr�n �c�#�*p*(ng on derivC]eseo1 J) �J�T0} (accepted);�WE-p6 arXiv}:"QPTra %5�ij �:?CYl"F=� �@�Cield-h; )o� �Mod-d-vA-l3a1&f3�%6��)�f Hern�Ydez Ruip�ez �@J.Mu\~noz Masqu\'_)9� calculu�/graq" �JR_d*�s�qB6A283 (keA7�t$01}u�(, Jet coord�e1 la�% y� {F�i�5��� a��� %8y tak2w TakeqLAd+&�IC pr!H1�9f9,9].V- 1��5a197�s%9�.r} I.A�0, r�b�toAkal biMG- CFL.�hons�hrEa�h+)s}.��10�R�%%M.A+ 4705�G0(�WRW MKP2:�is�A�F  > k�Mmof� ic�ei- 65(6�1033-10*�^N^ MKP3��4/� 2-q$ J:r 6791-6806E0��Z�4����,in $E_{e,C}$�!�Y��41A�� 20��V� GPS0�F�F�E:�Q�N453-5 "kQ�N KMP-|:u �;�21� M associa�polynom:/s�as. 9 45i!A?2�ms.AE&�[26439-646:96�RJRDKIBHAK} Ye.M.Hakob�ML�z&��N� �*�O" : In��!A+IH �rbasis�W)}.},�L 1(10�M782-17�9; [in r an Yad�!ya FizikC(<893-189�78]�tRtWMPOG:�G.WilliaGgڀ��hSKre6�0:t}. .S͋l!708-725� �0��F�apHYP:����a5 "�Qal �9oidVB� 5416-54M'�!�� >2�Z�Z!�wb� I~�^�2291-23�a�1���qK{RANADi$F. Ra\~nanc"M.Sant0.64 Kys�s-� 2��=w  $S2$�}1�ic�*e $H2$�.}�,E�5026 ����F� KMPW>| .�J*G�m� O8"r %Q�-breaqHp&� in N.�>X}"n ) A35}(22)�u5r 73q �k Rk KRES�J.� %�} �Mul"S �CS.� in�-"� �\ 8^ ��R�MKB�6�J�V�a��.�"of noncBj Z�g 970-982��f�HY*lleros�&H�nz�u�%�Tz-Gil1�a�_lJG �$N$. ^f�[>I 6�*93-�,��N�Ghs�kCezary  �Isochr�S}�  new f+A27e�%�6/ *4085-409A*�VKW>U�*:�~��a�DarbouxI� �&� to$811-5848E���V�RAVEL�FE;�� &��artes, .�%!third?$ ��/Hmog%�F��%00��`��N� BIJ1HO!u�..InomatV  G.Jun� �P29T}S5D 2�!a2.6�$c��t-�A2�+62�)n4�F BIJ2���� 2�2��111 ��N�WITTE� E.T.Whitt�pN.Wat�)�A Cours!�p�XAQC����ZR؛ ?L�A2��R�8HIGGS} P.W.Higg"���a���#ex2~1'T/�(�}N}DLEEMON} H.I.Leemon-l� �48~��"V�"ZEDAN1} XGranovs�� Zhed��I.M.Lutz�/ � Quad�l c AlegbrafY$a `Hidden'1���Far�nn&�9�`A 2c�"887�$J$VINETAdLet�UeaA�L.Vine!2� ��: �5��� Q( (Exactly SolE��Via� �1E�� 2� 144-1`?� �3?�&� @DASKALO1} D.Bonat� 4C.Daskaloyanni � K.Kokkotau}e�7ed*��V �"� al! ntum$!�!Cn"�% �'�%5� 3700%4�2�� B22�B�Poisso6�'tw2� u>�;Z� e;qu(r�F) s of"!1^Fe'#-I;�Q��\-1�K20�3V3 WINT� P.Tempes�1A.Turb*��J e �va� �k.� yW�F- ��42 1� J  �2�%Rodriguh0J�'2�� ea�.�$n*� �N�ŢAG��F� KAMR�� D.Gomez-U�%$e, N.Kamra�RE#&*�� ����di'Pa*�i�t subs�" }. A�2:�I.siY:103� R FLUGGE� Fl\"uggea,&5 1� 1�&�!, V.1"�c$ - Verlag,߈ - H"� -*�c(TK������LAN�(O.L.de LangR.E.Raab�;it&)�6IN�}, Cl"�n?B�X�1� N NATA�?A.Natanz" �/L%\.� ^{&A^SchJr& D beE�edkMea�| pAic Gaw@��ap�?!�\�[)15�r*r 9�BE� Erd\'elyiQ agnu.Oberhe�-�(F.G.Tr33i (eds.)ͦ�$�ic��p�(�.X*,�f (��J �J},]�195�sVsAT3,N.M.Atakishiu9.n �7E.VWJ�E K.B.eP�F�R:x*S*: l&�mۘ�Pg �``  9381%R]1�"�f gr��lzd99-94jP��6� YOSw AN3RD.�z�L�)me�L[DSy�2�EHil�X�� }. ("lzXt�(C>[Cs; no. 2"9(�vU 8�HNHINC)L.Ince �"�{2 Tfa}, (N��: D��)A��R,RR, WATS� A.H��7%-[]. R.SwQ��D�W2�1R1POG��|:�J�6E*{bxI� subg�0ba�C d -.U y�%�#.�� 43}(6�m87-341�uju0T-4} L.G.Mard� �9,6��4V.M.Ter-Antony"A'�D6y,:&"6,D&� k�j'e8�� ,\-men\-sio\- 2IF��54�6�9�;� F DULOCKq1DulbMD �/61��*=V�21;��J�4PONOM} I.V.Kom,L.I.Po�r , S.Y.Slovy�- S8oidcKnd5�&9 <. (Moscow, Nauka�^��F�BOT A.Bogu�9�Ot�G. �Kbl��Q��S,res at large�r ��:*��.g��Ph@�H s�$� a Heun�UEF�3�559-5��0!0!&� PREP!V.2eA.G.Ushe�dze-�PR(int ITEP-16�EM.� ��0V�0TURBO6� �*/ ly-S"{A$sl(2)$A}. �:2@�)1467-47�68�5R5 USHV*J[ ��ly�le� ��.T"�X}. ;0�ar>�-E7 04-5<2RF� �Y; SHIF}"A.Shifm�� fin�finF� (,Y�izeFq"E XA)}.�&�&�B-�A1�2޳295�5BG�� �USHA�.�'4)���� N.g, BzaolaT9� * �BISWAS�*@(h, S.N.Bisw\K.DuttamhA�6s&]8e^���� X;�onued �w�@N�8D� 1901-190��� V� �CIN--���"��si`^洁RqxB�q�M�"u�46�181-1����b�E,;C.M.B�)�G.V.Dunn��6��@7�OrthogoL &��vb�F951113�0R0$POG-HAKOB1B+Gzu S.IcitskyM�Is0;.]�'h;1�}"\Pove&�7�it +e�� -�ic��g7\�B 8;+ 43-5��n� AVTY� S.DavI� �$Z�%�5�ie-AI2N�ad6 $P2-87-453,Y 87, (in Rq.)�NK2!(Kustaanheim�DE.Stief�$P"��o<)�Kep ?m A��q�yor RegA  m@,J.Rein.AngewP�2�>20� [���F� GOLD�I.I.Gold�!�D rivc�4:>"y &.� (Pergk,"�����R�LANDAU3a�D.Landu EX!ifshi ����eӾ: Non-re�`zuic��_R�8��V� HALL��L.Hall;Saa�c�V( von Kevicz��Spiked&lx&� s. �2�-,�U 94 B(�KRKCALOGER !F.�F� &!�a� BodyQIAHOn* ;2��1�  2191`6�m.Vm.ISAKOV� B.IsAX.�i" S�l|f� 2�: ;jm by mB$1/x^2$��me`JalyB�! M&.� 1�A�2563-25�,199��(R�(TERANT� H�4�F�q]Y��$1D any"�EM C �:0002069}��N�LORENTZE�� Loreng%�G� aadeVAi64O� 5��>�A��kLrb<�9�W}W &� COJO`#A.�D#nd P.D. s)� Wave&~��2�au�� CoorgQ. �DeFS�#jr._Q.���!rndo|� bf 7�815-82M75�D RD HILBERT�L�) ant %�D.��!��l�*�s. Voume߇(see Ch?z x�dsed�Qe�:�53���� YMARDO2�����c>8A�� �YA8�[324-33�� j� A�_F.M.Arsc�q��IyR�dS.�Ed�Z�,��265-2�`196�b+.b+%"�5TUR} %&�%�'i�#v�� J.D,P����8), 2��#V�# KALM695e<5�2:�!*xof�6 SIAM�Ma�SAnaB��2&5M6L��$R�$�6Q1N�V��@&<sˈ genb�_qmcobY�},n&{T{Ke=!���Se��l:�?� .@: A Leg�KHP.L.~Chebyshev (18229;_ H)���stavaSZM�7ssi�4A. Yanushauska6� s., 'T.�d.'TS��nNn!�6�@%:g�*�1�^�D&'Ni�| x&�MgA�_566'i��~.~V�Qv�Q\@� size��mot} N)iri�R�L� tlD�Cubic tw*��>"xcALz �� JHEP�90�-�2 ) 56&�^403187).�b1N�E&c� [&`�)�l� �- ��}�� ��9 .�605F �7 cart��Efs NBT�.<&MIT�rECa#ͩ�Uhev�T�Uv=7"ZUA?ic�_C��bi��P�E� York�"��lb2}2��A�,��ve:|h�)�)$� N=4)r-Yang-xMsӅ1�^ RИoM9�I11601.o 2045eW5b4V��Lx�n�ݘJ6W �!�(h[� 4092�cc ette�e B �its�ec2�. ��asslesU��tsIi"+Z #�7�grscw;�.�}� Sch�}��B��0M�I{�}s��\&��YtUnu�I! �� baylj� W. B -A�K&vmw��T:&*l�g�Cliffx�(�3ic)Q�J� A`� i� �� ��EngineR�E_Bi%�auser, B�&2Cx{porto[ Porteo])6�AiX d Cl��Y GroupA7V>�D=> crau]b Craw!->5�/:`'�@I� m�z%�,�0nc���|c"���%��J.%;� mm*V576. �abla} R$}l$},J� Ozie1}�$J. Rzewusk�HitB�U� �]�&�`kphV�2��) 2�_u� ke97%@K�r->��,qjs, mexe�n�l a���pi��M�} �m�o iff.A5)�R 97) ��pe1%%�y �T �1��T. J� 'N345*.p {pe2.^%sW. Rind�lE� ��Qank�.2: �1in0&72�U�2�6!9cru�"$Crumeyroll1 *� !�Sy��PU�qi }, KF[ "F[aA0.vah<� T. Vahle�`�o�beweg�� undPJe Z-5��DV�n1���02) 58!��maks}e=k��,Modulo (1,1)2 VofF��GWl�F(](-)M\"obius �-=5H !Ph.D. t� ���O%�ersite��I�_�lf!*: .l atia�]( F. Atiyah!� BoB�r Shapiro��5�m�e��=���7}u� 64) p�9-h� D. H�?n"~f�q�g'!�{au% �/�� rA�om .i2 z�91):��l�Y� Lauf�y����� Map�0�Q{U�~:��E�Gaw��D!�Tv\ag$s T^4$}, %�$ sis,9�\"at K�Az, A�6�� harv�c( Reese Harv"� ���CalibQ9oE+�te����@<9�h�a} V. F�4ir �� .)uO��i�9nd�a7��4sP,�jC.z,��ic�vL�YͪY9In�"!or6|2"F� 37�e�� wal1�l2��WQ�-����-Qt�%���o��!�I�JMVWQ\48^z 2908*k21203V`.���A� snI�Wj�A�bu��m��n�- ��45>�3:|�b�Ben> R. T�t-�AnJr.�e.�� yUa�N�P� � Adam?0ga�$M .e ced1��Ceder�� �I:��d��lg�W��G%�*ain�".��)�e�-� Nc�q�$at NORDITAA,Kopenhag�g��"( 9310]oY tete�qP.& KobakQ��yi�il�C orb:"]ma� in �3 A.j� ordy�JC�Woo�� �H��9$� gr�)I }, A�&Eu��= �lEu@Vi�8�%Launschweig/Wiesbaden�.~w{alex}��PAlekseeviski$\breve{{��{i}}}$1(TacQ�C!� � � Funk�,al. i Prilozߛ��6�4;� l�d cl�uphB&L�A�q�=106.L wolfL K4.� lex ���^ousS t�"�c%k�\wa�EPfc>��i Mech�1�1Z�S.�guna} AE�sG GunaydtR�[ loshO1Rahmfeld��Yyxx]�[=q��x��%�$SU(2,2|4)}A�)��)w0��# ) 19Y�9051122�crC. DrO�#� . Elduque�Mt5~$F_�6":v,6�q �Li� Jorda�i� iy t�en�xht�\"�` May 3 - 8, Guaruj\'a, SPE�zil�g4�N�o�f 1��� cst}� Cazenave%� Shats �.di Ta�n(dar-Zadeh, �?Q)5 *��e)�6 315p 98� w��Bizo\'�26 ���lA�a B�bf{V189�n2MLbt.J�Z. TaborFQ� v. DN6�G 1217��62Pd{�NAA�QJ_�5ce&2`}&Lx� N�Y-f�DMPPT} ^� 99} �}Pcommand{\bbtm}[1]{% "([#1]{#1}} 50 0{Ar�CО"�iaq: YW}g;0 �� as (Japan originaY+) t BK04�7~Ba�Av�<G��c, �ped� �6 latt-�vertex �7:�s.�V�{.�{ kshop on {�ite��>ɐItoqqa�A{ (Var�&Bulgar��u) Ed.L ,H.--D. Doebn!V.K�s�Br�F4ҩ3-26; }8.Q�h033�j btm{Bell}�FByl�,Me~ 9��5kE� Schu�L�"Y. 19�(651qL�1NV�Bogoliub!v�^ Logun I. Oks��2 �5EGe)����m!v2-e}, Fet ��  (0&2#87U#op�R.E� r�ld a: Kac-Mo�"U%the M� !��N{s �xUS�y8 88�068-307�n%�o���~B� >� ��Qinme*-C�imiCFor�?�edQ�I{Kyoto�6�35--77;og�~, k$bf{160}, B4{\"Y�E M , MP<98; q-alg/970600sq �64a�J�s, � �|,$C^{\infty}$&� in[� like&=9�uov�.� 3)ct160�p~FK!�W}>�r, D.�{`~�� D�;minF lula�]/��f�)�\(N=2\) /&OMBe4d6 s or�Bresuli n!�[actb���KL�x� B17� E=16-32�p� ou68gk~BoM�ki}H�esaAlg\`eb�4 A ie},!� pitre~IV:�Vu Cox! 7! ��T� Tits76engendr}�par�  flexz.6I:�.Wra�� s, H'�n,�`is�UAB�Y BQDv��� , To�� s a .�' KMS-coy�,2�}eBbf{B~4_(4) 291-318;"�.807099��u03�G ByOnE hot bang� A��w���� 2�qu�F�0o;�4un2q~�239l� 27��85 MT88�~� GA�ck[�T.~h��(��%Q�:cir�h� ge�uu.�6EB (��Su�x)I�5B 88) 20-56->CD!>A.~s� �}ois-Viol31����Smmu� ve 3����30827�}CM:fH.~�8vici,�'�+ Hecke15�ir Hopf� y0�8� �! � 4}:1  67-109�`Z|(89; Rankin-Ƒn b�qi!� k�-E* rans�"��y�}�304311LQF�, Delign��By�2- }S]� ,%s���XK~1, AMS��"7�r -�DM�~Di:'ncesco, �Mieu�`Senw+l�&f��( f\�r�ȁ|�199�Di 36mLA!�, �&"5 am��?= �-�eN01936) 429--44�KDK0�Sg wk�( K.~K��"�/funct���Ira�c �v���|Ŧ&s���~6/E�H) 4�` 32; a205021l FBZ0�#~Fr��l%]Ben-ZvPV�� � ic CurvG!�, v FK80} I.B\V! �0c>G�A�af)���M� rdua�nAY els6'v@� ones.�6��0�-61�FLM��I�՗eps�@ ~Meu�(� �Op!�or� ���� �caX+B �GFNTP}\&���I�y.� k,~WaldschmidtQ�q~�A��895; see�"�ti2,"`(2:��~�, >�com�l:�facATJa�$a <belianf~et�w(pp. 64-211;o3:���,Y�dfT2212-237;�D4�Cn~Zag��>�ar b_C38-29UeS"P FuB�ɣ ٣6N}��5 6�R�ta6�ib 12}:�\� 1-20q�Ga T.~Gannon��?�� Moonshine(��twenty-fym�, B�L�*M��(("�)��40234ѣGA�D.~Gep� ���J #z#-�~d+ #%�:z �Gs6��l29^m�757-77?GO P.~"��D.~�, � � nd*}�b�l��o5���sE��8M&�~�1& 3��3�YH�+ ��~ R�}��=: Mit{�Ls4 ��s,�}, 2n��+&�q�--Verlaga���HHW67�~ �,N.~Hugenholt�[~Wk, equilibr�� stat�GQ�i;0al&�=,�>:� )�Pn215-23�is��%C it{H4&0TE� �ury1"<�:���+nf lchool7Q-V@ ``Enrico Fermi'' ��VLV�VW�by C.~W��,��S., NY�C 7. SJ�BD~Klein,�[ b~�ni��G�13I�4, pp.~1--38; P��(~Dirac, Rec?�of� exci�y era� ~109[�5AC�=~Hurw"4R� u3.�Io/� n ue*allgem��.k��en�ie<�ptwFu"}a�� Belri6�|� K;��h�wInf�K.�S�Amo� "�&Nr eA��Ka|gdQ6�,U�� B%�e�AMS, ULSI�1z3P::�gTjnaP8m�KP��u�/.~PJg� 112��s�|> -��.>il.��#$E_8$&P )!osawon An�� O~,�#�y�� hica۠I��H)n7+"E� 28�&s KRǐ��K.~Raina�VNst�� ght >4of��m#Se" �m� a�.��bf{2}v �&1�Tc��:{ A� qs��br�("S 2� 61�$W_{1+�,N�MVA�37) 57qU� L} Y�$wahigashi,a�Longo, C[&fI!D:;I� net#'\(c<1\)� $2$.�vanIOngete��categ��j�244v� 4) 63-97;�M�43��2�W41�A.~Krame�G.HC nnO "6Z �.�a ferL��2II*��60�M41) 25�6�7d�27��K26} F�}������8die Entwicklung�rA{kA�19��hrh�� rt}, Teil��X��r޷19227� La=Sv�ng�"W &\4, �_ �aduat�xta �cs)1�\|N�8Q�L�6t>� |ar1}v� �!s`$ n Wiΰschaften ���*� �'�M L� La�wn, ����Field Theory}, Eds. G.~'t~Hooft at al, Plenum Press, N.Y. 1988,!k$~353-383 \)kS} �d K.~Symanzik, Currents, stI tensor%�,generalized )�ity in9� inn , N�U07} !�2) 247!�1�a04} BA8zur, Perturbati!D defA A�� (�``near--misses'') in geometry, physics, and number th!o0, Bull. Amer.M8SocY�H41} (2004) 307--336�dcKM} H.~McKean, V.~ Moll, �\it{Elliptic Curves: Func� -�, G�$Arithmeticas4ambridge Univ.)� a[~� AS)reX eyA�(Automorphic"JPrince�� 1971��95�W} R.F� reatA�)Wightman&�PCT, Spe� d Statist"M � That%�n[ a�e� �� J.�:1�T86!�.�Infinit!nTal Lie2w�� QFT�(el�hA.O.~Barut, H.-D.~Doebner (��)י�GroupIW� � !�:�* Result )2 BackA�nd}, �  N@ in�zic�� 261}�738�843,F� &� k ToF*ESit�Descra�o��!� ningaoticle��"] ] JmMP:� M.C� ntch�V,V.B.~PetkovaNRI�c/  Q��:� Scuola N� l�perior�isaA�8��LU} A. Uhlmann, Remar��nefu� $tube, Acta%r. Pol.��24x @63) 293; The clos� � 2�5 it ibid.}��~295-291� Weil�~ m�E�h��Accor��EisenstemE$Kronecker}9��.c84>eN� i�. An Approach Through History. From Ham�Jpi�Legendr��z �#Y�_ M.~Yoshid�� Hypr��j"�  My Lov`pVieweg, Braunshweig/Wiesbaden� 7 (see,apaA�� 0, Chapter II.9Rͺ-� --59�ZS} O. Z�M ki, �� amue*����v"�} vA82, Van Nostrand�Ñ�L1960; Graduate Texts�y�s�� !��4Zh96} Y.~Zhu, p*4 ,of character�vS operat�\ , JJ�� 9}:1�6) 23�@02 \end{thebibli�,y}�\beginBD{99} \bibitem{Af}  leck� , ``q�s�� chai6 es4Haldane gap'',� �%,.: Condensed!-!����3047-� �89).} KLT1:�,Kennedy, T.,��,b E.H., Tasa!��2ҴV � R� isotrw R�E�n2� -j,15}, 477-528%j6�0} Albanese, C%� Unitary d��-ass s $ and expon� lal decay below threshold for� sA2system!` f�$34}, 1-27,E�27%j 90)..\AH} Arovas, D.P., Auerba� A.,Q�, F.D.ME(Extended He�z 'a�:Dizm: analogies to d fa�io~�(Hall effectf7,60}, 531-534%�8.7BZ} Bovio 0, Zahradn\'ik�eaxA simpi ductive a��toeproblem�convergA�lusaw expa�of poly mo) �J.� � I< 85}, 517-M:22�\R}Bratteli, O., Robinson!�W.:�  O��2O�J "; (al Mechanic� 2nd ed., "� Verla�Be,��1, 1987] DK} Datta[ ,65``E9A�one!�si�sle� inI�1/2]�R$108},� 399 2&dNR} �� Nijs)�RommelapK%�Pre�ening emiAh�a8crystal surfacee|6�phaseōM� em��!ٝ�B-�4� 4709E�2z(FNW1} Fanne �,Nachtergaele�, WernA�- �t2��Yon�)J � as� ��@$ spectral :> A:�6h. Gen �2�! L185-L190�91.� FNW2��F` ��e�!ofN�!X�� 2614�443-4 �A%�ZG} Ginib� JEExistq�%ѩtEsA� %-� lattice.� �-+)��f� 205 %(1962�H1}��ᴵ&L ``Continuum dynamic��� 1-d �;:2 : id�fic�%%�8$$O(3)$ non�sigma�y!G �L�fA �93��64-46ɲ3.�H2R�Na2, of large-ef�(s: semiclas� ly)�� solua�5 one-"�Hal easy-axis N\'eeli� v �%�5a� 1153-1156A�6�K} Kato��H.�!XoryA -U/ �=�":"E-�; 1976�+ KLT}6!LiNV  ``A two2�B�>Iun$ disordere6� !!Nx5A383-415%22KT1:�*  ``Hid�q@$Z_2\times Z_2$ s`y break�inq�yRW I�%�B)�4�30��e�u�K� 2� R�F��acD �in $S=1$I�uB�j�7a@31-48R�$} Kirkwood��RE homM L. E��"/���ݜ���gro�Ͻ/I< �� &� f�8�J569-58��:(n} Knabe, S ��!��elemen� exci� ons ��,certain VBS-:���R�$2}, 627-63��6�,P} Koteck\'y�/ei�D�CFx for ab^ct F� f�0a491-498 ,6)}� MM} Malys� Minlos�{�,Gibbs Random{s. � & `.} Dordrecht: Kluwer Acad� , Publishers,�1.� M1� tsui��a�A��k betwee&AS�k Potts v� | 81-79%�9022>yU�ynes��Y �G�t .�aw�ks6� b� 126ar53-467��6�N}JE ``t.�A  somey ca! h cret��%�šC�S17��565-606A%92%RS} Reed� Sim� B�^Method%+!�rn `� , .} v.2͑Fourie%!A{is9$lf-adjoint!y.} �!: U<�"E775]�Sei} Sei E�Glf� �#*�  constr 5�2�Ad� � al m&` z�1Em �?82.�im}BI%ԁz.u�� g� #`ey )e[3m(U} Ueltschi_ a[m�.� �*� "�A&Moscow% JN ! 509-520� 4.V,Y1} YarotskyvZ``.��.?�  weakste3ng5�>S�a� �iA� �b 2134-2152J�2N�F�.�a�� p.G#!�non-i�gapped�-�*o to $arUN:11��119-144�5) Z�Z+�� KT} T. Ao�T. Kawai%�Y. Takei !$it New turO pa�%�bex�{WKB�ysi���!-� � ary diffe%�eq\/}, ! \cite{BM}�~I� 69--84.A ~��"&ic�of J 6�-fF��Jap�$: S\=ugakuEa� ���9--315 �Eng��: S .Expos� A� � 199x"� 2406�R��  Koik":�O� � x%�of&�  ad�aKilyy� � Ad"��18\�%165--1892�$} A. AvilaM;C6=an ��iz� scheme)gb�24<4&&�18.|0BB} R. BalianE�C. BlochAS>u Schr\"oAerU�a� terme�&T path-nn.�_ (NY))85E,74) 514--5452�PV� , G.2isioA. Vor^ W Qu� oscill�)�"!Feynman� �lZ \/} (*�"(, Marseille� 8), e� S.�ev  Q� f].6[��10���"a79) 3062�BLZ} VE!Bazhanovs L. Luky%�A.Bj molodchik>%�S�de!�inants���Z���Q-"��"� .��Rv02*"(1) 567--5762�� C.M. Bend� d T.T. WuM� AnharmoniF�ɠ m[B(9) 1231--12:F��p� A stud�.�!Cor�% ���eIp>�D� 03) 1620--1636H} M%�err� C�Howls- High f!�� Weyl&w%څ um b�(ards:�&��d!Zrbil+!�E rein.VCV}!�C��m�:�Un�+uve�h��rpr� on de laA�mul)ntryde Sel7� C.R.. Sci. (�$) �30�$ S\'erie I!W088) 143--148,%'� 5 �%�t maYGg�&si �b(�ݥTh\'eo%�)IA7� 0)A�9z!DP2>�6��|UnY(o ��qV� ��͙�%eR 7) 180--26� DI} R6 DingleA40it Asymptotic=�:xir derivv v����A���!R9� York�732�DT�Do�ΡGR8teoq�R s,�rmo Be!Ansatz ��&��� "� %��E=,A3� )�(L419--L425,Ke� rO/C/ multipli6#��T-Q�= f@ 2�/��B56T0 �5�/602Y2, (Erratum: N*�/ C60C/5816{.|i! Du�'�>�D.�"ze�g�4 $SU(n)$6�eAa�.o 3 �0) 845 8446lG��J��rmae2$nd V.W. Gu� m���s� uw *ve "a,6E p�  bi"�$&� RB,1975) 39--79.KE��caluLLe!&nP4s ��s�� �H� �� ~� @-Sud (Orsay) 81-0�1) [unpu�d],I�E� Cinql�s� fb� (chap.��pre:&t 84T62,>�, �a�84j�We�+ed&'"� $parametric*� A!��*� c �*2m H} E: Ha l�0q�' of a��igenvalu�I�c� J16/ 60�= 78) a�92� �L. H\"*nd"z ��uYvI�*)j{�1t71) 792� _RjA�� 6of�;"al6. �� 1[j�83)� 2n.�H[C.� R��21�Towar�'F#�V�, Sr��- �6X RI1 Kyoto 199� mN� , �g �Ob�JLe�Jo3V .S. Lang Bas:re� sn M�riA>#. 56j�96C!�R| �Se�*��t�+��F��in.�Q. pp. 85--1N�.KaBS%�{.�Heun's�!hZ��)A��!55--72� )�Leray �P�&\`'1e"chym�`:S�)�Fr.y bf �(57) 389--422�M}�$Mas5ng�M� hod�m� ��� et[�(� Borel �:|it�� plexu�, m�1�calculuI_�v�� l �y\/>���Houche�29� . :I>���_j�80)E/170--172� OSI8 Onis>A. Shudo=S. Ikeda�K kaha( S[ la#�utu?  pd7a< via co%B -domo chaoEDB?E 6v 20�8056211A�fP}&^ �wD2ip%�Huygens!�,trajectoires�es ou ketg vingt a�, pr\`#y58*�1� ,.� �y$�^4g . 14e�502� SKK} M. S�#*�M shiwar[/MA�"�%#pJ�"$ Q�)�Hyper�>:�Katata ,4M�H�m�, :|i�%28B� *}3I�265--529I�bSI�E�%K]� �Come�Y�Q BndE�i U�%0.�L�&�7�(5) 682--685 � o� *��)A�a� : pru�tre�=fQ� s�� cipl�+ex*Y-o>cer�68 96) 41A64152�S}tSibuy�G�<�� a sec/�� i  2,� �Alynom coeffic�7�( North-HollQ1Am�,dam� 75))Of�J Sj\""�1e�Sin��h� i8s��e� , As%risquW9�q716EPf�U �uzuy��2al� �CinQ.� --- �).D$x^6 + \alpha x^2$�aŎ� -yX.�102� 047~�N�� solv�@"ls �Ted to $U_q(A_n^{(1)})$J2�2r35 3522/$V�16L6p� spoB2`<C �1:�case:&�aA� homoz  26uQ��. French:>�F�29��70�12:<-��N�AvL1�;!��K[ re���Fr.&�a�Teh��RH�;1f 211�C8.B VC�].�bal*�@D a��RE'� zeta � f"11� 87) 4�<465.\footnote {I �VC}, eq.(6.25) should have read $\zeta'(-1)={ H2) \over 2\pi^2}+{1 L12}(1-\gamma-\log \,&)$ (o%no= sequ�-�/where).}*�#V2=6)�� -�Vi=,�aNbs (in�&'?)%�*�130�I311.�Mispri�"� V4}:eqs.(13D$D^\pm(\e^{-\mi\va�=,} \lambda)$ M�A�.-f/ (twiceMjust und�1$ath, $[0, F=infty)$qY k+Ji ,6 5=p�!i re:/M0%g���Z1D�4no;��\-v*�!N =|<5993--6007 (Corrxd��VE}2�V6Z�2I� ;,��1D2�F���{��� ��= 5}�A$also requi/�, �!see end��/ic"� out � p�(c�E�&;�two'J h&(n!ga�F( when $N=2$��6, but.@ beyond); 2) rega%>he��ze} in T� H1, $ Z_1^+\,'(0) \a8@x 0.0861126 $, $e�(}(9174909('- O'$1.2585417 :�8.���[7[(�!"A��.ni;1Dq�i>@ (or Sturm--Liouve)U�8A,&&Z� !* B� F�Gro� enrB�ɖB.L.J.�>aksmaI�&T World�(fic, � ap�Na#2A2��3:9.-{g�?E�-��t�s�!a&5;2�*�o^, �.�t�4U �'9H92�ZT (Zinn-Justin��> ant� e�um&5-: NumerE�e�Paza�ture%�JX*�2t 4) 54�?5.�%inLE�to) �AultfA ��2s*�68��N�>6 v^+"�3salp51� E�lp�&E]HB1h, �&mC bf{8B123�<5�Vgrei94} @�"�" ei dt, Hit{; El 9j(.BGF%.4.o�2>�2�E#�3�;52)Bgo85}tGodfre&N. Isgu6ID �bf{32�=8L:5.Nse97}� Sema LB. �HiQ-Brac,2IAV6D-45�97.W br98 Brau%�C}0mzIs%��5�-03401 N8.NglNL.$Glozman,!�Plessas& VargajR.�$Wagenbrunn2]>r 9403�46rbr�(F�qu r �C9 0552�@yL.�he�HI.�HerbstV�2Q�5_428% 77);31�877) (aZ7dum.nca )�$jDinaxCCea8+Nardul$>��I+ ianoZ929}, 266%78�&uMhhG.�dekopfR *\6�YI3k9703s 84);�B�B202 �2�ma8��Mq&Ja>M�(�B5V23!p407�9.Lra�/J.A� Rayn�TS.PVa>ngh�K s' ! tubb��>t32!10%��'=X 01a}A��a�W�+chI�FE�(Sch\"oberl,nI�=f� 5059�2ha01b�`K fQ�4�i52��e!��haaSR.��BnN.�1� 1931� 2). 2.3��vj�� 2657j32jba��V#/rgm�HSc. Nat. T5.�. U.S.A&�U3T96F6� sc61chwo&�SQ:12��62�ca65a��C.CerovkaK�962IHb:HNuovo C�'� t/M36�okA1>DhTK. Chad��6AY��19%"6: NV. Glas�SH.5 s�AAqs�wW�ir�G�:7H.B=%A�*p. EMuL)��Studi752s7 s7 - Essay�3 honorR qAtine BM rN676, p~Z9}7ma�)�v�� 29�I7:�03I��F�*loI: 1�'A155#5h�� br03IRVrA990u;6>cEM>%�>��ZYN 1202i�2�daub83}�Q$Daubechiesv,9�n51Eb82M�d�6#�1�#363�� nick�qL.!XNickis�FL�%�J�Bb: �Rg brau "�Z�3�2!��!�abra70�$Abramowitz�IL StegunyHandbookA� mathx:"I D��%c\s,"  � U@tri65%f$G. Tricomip�S e�6},��ers�ceb �<New-Yore65iF�)m8J66� Magnus,!=Oberhet�5� R.& Son�L-�:n�# orem���!6q�N."A�in% �Bd�.6��R: �f: 21}� 1} OgT P.J,N'��Q�9pEI2� E-|&8M9�vZ6]Q2}A4phani H,2H9�:!ir"86 U1*�Q , Ca.B\>q;75�3} Blu�5G.WE�Kumb9&R.�s�*N6�.~T4} Ibragimov N.H, CRC . !?G�R 2i� .s" V =v%Boca Rat�=192K85}Rodr\'iguez M9A{W�r�1. P�pAYA:Als.Gen 37u 4YA�re/3ces quoh�%n=�6}�SbEngel F,!���5WW"ZL| gruppen Vol.39 (Leipzig TeubnerV-E��N 7} Wong W�5�Fu�R .C.W#Nnuo c?S99B/J .163� 8}Zheng K�,mV a ScdA� : �AeleNDbound `�Ea2�� 1163--118$ a 9�AM}h7��� ol�Lov:V��7z g�.E ���&Q01,! � � Chenh) RHLength�� Limi\ 1N�\�8$t Small DiI}� D��%X P.D. xxx.lanl.gov/, ]305051:�2B�$L^r$2�=�&F~��a L�b� EvolK}, �V�407037�4DGL} D. D\"urrR< Gold&WJ. Leb- 1a*3moQ��a *�%-�O in aQ} "��d1Ss:P, dau �".} CommZ:S! 209-2�8� YDK�d$ von Dreif*(A. Klein: J�3m$2u&�" � �"uh�aNf�4u 13��4\9��EY1} �Ird\H �9 H.-T. Yau� B�uKaseJFC coup�)lE�o< � 6�A�eomm. PeYApp"�1i����a Fermi�!J�F�w},?E���3�# �"9�K� UKP�" Ke�RP�EicolaouT�G%Hem�stochaFI accele }. fQ&7�19-71/. .��]��)a;��LEc�R.(wt�6iw uE�3/ he 9l�S}d?�H Res.Y1}, 39�0�1> Kl2} A6�Spreae�0of wave packe�G!&Z� � ��pV�7� 7�17�962�La�kJ. �114Obser�:*�O�Eh a�X6h-�Q �w!'RB�* �25�G�V:D RSP�L A�Im� Me�1� !�:�L I.�c�l�X��5_"�Nr�b1982Y�Sp}� Spoh D&�;��^N porty�a\ e�ns moq0Q"�-impuriti* 6� �bf �'385-412 �M}.�SpU���$�n�1A�Z�u�fl� &}.f6�Z 277-2�V7űRDHfD190*E8ZLF}V.E. Zakha�k V.SA| 'vovg*G.Falk, "Kolmo�]v�>X!�Turbu�]"&Ga"<( 1992*�B� D�!�@�P.Saff 2�Dal�D<, A(1966), 289, �' 320;A� J # nn FA.C. peO*��3X� 431$D��62GS="A.�weewGR.Z� gdeev0``ReviewePla�"P�o''K@ 6 (Ed. M A Leont� ) (NM)�_j!�G Bure�]nYa��Ne�c� :�Geoah.�{6}��8AZakfilZHE9H1�LN.N. Filonenko, Weak�L-�!�capZI ry � s, Z��rikE ekh. TFiz. 4 (�12-�Q67) [?au ec0!)$. 4, 506-5 67)]; E�Y�>�aa& �/a�ݸ|A & �a fluid�[d, Doclady Akad. Nauk SSSR�5 , 12"29�66) [So�<0:(. 11, 881-8�U�6�sse$e}H�C``Fre���_ing� driB �ea� gravity ��RP J. F�!R%�]- 48)� " DNPZ} � Dyach)�]I�PushkareZp.%:%�ica.c!��9� �Wi wyld��W. Wyld,B�A �C61�5. lvovzakhB�����, +fUD�a�`2cg& A!,�Jj\zv. Vuzov, Radiofizika 1; 0�70-148� 75�� llnz�;vAY�I %Gm��2=�]�pZ�aco&c=�''.5E)� 56 }a�u-32�(davidson} R��D  ``�iVe\���f '', ��6���2��q�PRL3 NKQ1:� `U� a|�D%�s'' PRL �76� 320-3� 6Et�35}, 98&�5�zakpit} 6�%�L.I. Pit�brg1anbLal vari�)�Rossb �:p��dH ��_ A, :!�8L.�d N� E�ͦ1�%86-�w2�B9-biv� L. B R�.\ ''B�dow�:����y4tXa6��!�A���bf 28 28-32� 1);2v:�f�R ica �M�, 520-5�5�12� yokoDz YokoyamaBg50��, 169-17�1Z(]� �L�L�L�L�L�L�L�LbL�!E�F&IN���& 4}:��Eh+B9��``" F�_ ``�D�<�<�<����f�z�N&��� .O XV�{(1� 1470*0����^� "?c�����]z� ���]n]=��y��z�zz��y&yTakA >P Tz?  %�? ��J v Zb> 3u.n�l fluctu.��� 2>  inB�  %pp�Q�}RE ���"> V�ż:8�����"#� �^�� �� �� �� 9�� F� {��� R+�j�*10} %�^*�AL�m .~J.~Ablo�1� ~F.~Lad�x"� i$h- ce&��6it{6@2}m�6}�L598�C2�UAL�m�� �e]�O-Ls�l�4��� ��a76� 04I10�1YAPT� 6/�;ri`~D.~Tru�zoDi�m�puv"5]6( System�con�#"q&Society�OX'd�'i��. 302=�f�0C,�-4.�%AKN�~I.~ArnoO,V.~V.~Kozlov�(I.~Neishtan�>&�& al a�fc";H��#sYj m�m,9"{v�x ���Ihjii--xi�.P1--291, Encyclopaedia�!i?!�)A?��>z1992pCMV1� Cant�8L.~Mor�;HL.~Vel\'azquez, Fivago�/ma_YyV�Cof �No !&Cs=$ K� circley*|)k �m036~\�/ --56.�CM�Ji0��Minim�N.c���("$M%��*�G�4�P�,}+Deift|^~ m5�le2�M�9B ��|; ��G/p�=�*@] �'$s (Berkele�]A4694)� 03--138,qEL%~IOG>�0 a|-2roC , RIW2�GGHu;~Ge~Dmo, F sztesy��~Hold�)�o-&L��&� of a 0r�.�Ot�EgA� mNgt& lem,X1�J.��^��� SoliG+)�Thl5���ic"~5s.{"ume II:&4rm(}1+1{\rm)}-"�.al�. �M�~,}�� .:#"�lv�5��in_p"M2�� MEKLI�.��l�;N.~M.~Er�(iIKri�!C��L�kmo�dF7|�Jus=���D-�=�, 1Z�'�re.nm�$�(A.~C.~Scott�Cak/J Eilb΃B,�"}<�"dї"&�-�0�U�2'5�7U 1), [r-512HR} D.~E.~Rourke, El"j3(B�acklundR'"6$}>_�KvalueY�1h. A �3��$GmB�G276�G�N1mZ~ �Ort��Po�T� <� C��,Sit~1: C��<"Ж8 AMS Colloquium���^iS52F��I2kexpec Janu��20027_�2��>��2:&Y �!}��W >�s@�� zego_~ \H{o}yEV�.}vL =}OI&T<4 XXIr���h\Is�V-.h�TK.~HaninsPu Symp*icw���Z vo�9�6Ŏ��f�PV+e�the cub�xchN�9� DukeEW!.}� 9U�= , 38�.022�2�6�An ad�RalSz�S� r� ��r5�VE , 5�p56*j vanM� van~Mo���\�'� �- of Jacobi"� .��I.�j-�'5 ), 45--81!NhJ�rW�"�D�x7 @e�Il��c�nnda�V���*ἅ^Ctr DZ] s: Smooth)A4&*5n S�.9}"� AM}�s�\41&�=[ , NY�88.Mazya1}V�* V�!�J�Fssm�D {��in� �4P� bM ular,�k|LV� |/�j Survey�&���v 52� 7*��26�.��)��$l9�Associa��W�-�2��r5�A�E1�"\ G0� � B��\r�.HTB} � H\"{a}nng$� Talk҅AJM.akovecgz 50 y�,after Kramer�)%�;od2m96�# p.25 *9�2u$Freidlin}M�� )V4kov!TcS` And Vz5},�na�� Bos� =iHelmh:�2L.F�7 tCr p , Bd �1862� Rayl^g��W�)Baron�I K�l�!�Sou���P2, ӈEd., D�B&@A�4.R>Berez} Id%G� ri�-Y of escape"�0a s�:hole'' �J. �=1� bf11i^22�P9574-957E2�Holcman�9 , �.chu�}``!��6enarrowv�Q�l mle+,AMPA recepto�td2 postsynap�Dm�an2��*� �Xp .�HSj�S&�4c�>�reavTin d�bys"d$ZtP} R. G*``:����cipb�"� a� "� hicD d3� "�k recuؠ j7%$ope�!f< a ��vQpeur=G�@of^A� al A�tism�20b �#dH77-19��0�u� Jack',�!D.�A]em&$  El�1 odym* �a:�6�NY,�b.4Sneddone6N.  [Mixedb[ in Pra*� Wik��6�-$Fabrikant1�# p:P !7_�in 2/a �Kb�i2DW2^iv�t*:� ���p"�E�Cine5},��5� Lure��� Lur'�Three2��&l�F5� El�7itA �GruGp_mr�GY!x.=BVi�#dov} 5:. �% D. Smith,c&D.�� Cz-�'��a&6!54 �� s I� ��F\&��l/CRC;.�.D�0A. DembP#��eitou]�=L�� Devi� Tech��� .�}M,n �tle�B��:�4MS77}B���)�2��� exitMleu9 }(ly�o�& ed dynham���"M� SIAM' �kh.}:i%(1�(365-38C�6YL� ins1} W.!� ��$On some due�&}%�t~ aY�uk7s�wc�8spheroid�Yap��Ac�LPhi�5  5f2��367-384a�6.S �2J��o�, �T� circ�  disk si�ed insid��0 earthed coax����= cyli�C���6. C��623-6\�16�N�E�?�Nk)2�Dt<��!� 4 5, Part I�Ri�we.)�non-s� �wAH(�E�YWE��?DagdugZ�S� Shvarto ,�LH.qss�2Equilibre[a�Bchamb3t conn; by a&21T��. 01��3 12473--2�MS�} }te��ia8.'*n ^&TJ}�.ԡg ti��s ,� �:��Garab-n�E�m�!�A{.�2� �  192��M}*A"�M,�1AT�M% .�J.� ]g�- :�NYa�24ErdelyiŜ�B'�W^�M�.N� T�3ofř�v�J��V�,1, McGraw-Hi�9 �ui5dRoy�� E. Ab�w��sk�R%�*emV!k.�u� Uni:�L62�G ��~ �6}N-�2kNE��3 FSpe6�!.�kN Chel6,9sh��CompanEo!�2�JW� ,aker} E. T. e�N. Wats�L!� A G�e�o�b"�LCD��F)�7.�7!�eG�  - Ion�� hann�h of E1�b�3embH !�� e� SinauMass.�2J<Kd9 Є. �#Steady-a�e aL� Tra BPJ^Into an "�Re0oir�IRc?�� Kqet�.f*�al Bio�&ic"� �� 57-6R:2�UIm�~Iʑ�e�x� Ion perme�K��s�li:!>0ompf porin: aAO oret4łbased� mole���s, brow�4"� ,c�Aum�=o�)@u5,''I1a ol. Bio�3�3 4), �~X��,2.Im�V�ɺcouiq.�4 bio�!e�Knel�F���u�36% f��eG�^ia coli]p�� i3}I�� (1 m kcl aqu�jsal�r�I,''m- !�5 ��=�s~1� -1� P2UcyFa2~0�~HoylesȈ~W33l�M.~WalkaS.~Kuyuc6A S.~HCungAAU�JMa� in5�e d .2�� ��-cs5�M�*�8op.~w --19 =�.�Shela; Фger-Abou� ~SaranitiIyR.~S. E%�LSڎr�i�DthuJI�si1���ee&rJal�ic&"�Na�jch_� p.~443%�2Q4Trudy1} T.~A. �?QStraat!�J.~Ta!o>� U.~R��ol � N.~�� luru!�� d!Kal}{:� ion &�B�}.�: �%�{ge� tribELA�!X�� regDo�O5*J.�c��u!&C� iEA335--340%D2EK�HR�9� Mw2K\l osekIZ�F� as aF :.� 2rrbe��f�ψ cent� "� a�Bi �ojw 176710.%92�PNAS}.� Z.�cE�srkoti Calch�v!|den^c spin� ;�ekM�;� mr��-t�9pp.81-91).g�9 ka}R�4 , J@�PCP�!, RNHlI�e impac�22��w�on "E���@ion--its role in 9-h�HAl�8Trends Neurosci�8�R(1�pp.444-5;�_N zi�% ep0mj�9es skip1.4mm&; BW",~J.~Bisognan@E�U~Wich^it ���~subfac�rMFZ�s�f.\�F �3�f�A�p7 [e-p=��r�d�~  f�3"�%�Oper.\� yI�4Jh $ 195--208 B  9810003].6�Q 6�FcJK.~FredA�g�W$K.-H.~RehrB.~hoe{Oit Super ��zzrs)� brai�p�CbFSI1} (� issueo ) 11�&57:�IUSI1,11:�GLl#Gui�{R-�:�k&#�� � s?Y'�Q�\v $SV>8�15C e�5:�CMPHA,18�6sG�ND.>�'-W��esbrock �å��Son$lEg �:�!�W!~�& !�Q--244V�92,2176�H}![Haag:ZX Q߬%i� �* �<:QB�* -- He"�]--d: Yoo^6I(I9| ~Izu�^H�+ sakiqwO�P�,oguG�#se� cowlo�Qf�.�RT7Zw��3:vILPL+ �Qw, Popa�A Galoi�Lrre&�w�cPct=^�("Ͱs! f yUNe�]n '�i|a eriz��Kac&�,t.\`�h155�D8) 25--,\6+(FUAA,155,256 J--J��Index�5�A�o"uQbB7�# ��,>H INVMB,72,:FKWE�K\"ah�(H� ~Wq>�!it���.e0ArAi*��of�0. 2H�Xo� )D�A�1D4ɩ�74Ҳ:MO 42,7:k�)0Y.~Kawahigash�m1RCN'"i� T���w: z $c<1�z2��/y�2=S?201015>=EPRINT�DPH &6KLMm}V�k ~M\"ug�@Multi�v�" %���� of X-es&�-i���� !�_(- �Q�.�2-�6��6f2���219,63:nLEm��5��s�_� i6mhte*� nO2v%20�7--30:< �37,:���l.��?N�of:�b� 95) N�3$2%�y 7,56B�29%An&D �Lo>%�� bo�%��QFTabb�1�!(004) 909--9~�2��A� 4050B�X.�F.~Xu �Top� � �|+chotom)7��U|v�5, �3mW3=F�� 30936� &' P}�0Pennig: dipl'W(thesis G\"o!� work�p��'b�P CTPS�(=� "# te�I�25v�va�n � 40>�M�11,39:AS4͝���f atorv/asK &\ 3ask& &I&ci4Zs,���1|Hel2RTW� J� A�aza�<ent)kof � �t�Y�:� s�)�`--159:�(LMPHD,25,15.@^ZF1 -B.~Zuber5�FT, BADEI�lڂat�Y�[��h2eo�2) 23��66�YEH�006151>HEP-THJ��N�j�7i�U�GF1�zz>�`V�",*_.���#F�#�y#�#��#V�#kF2�#I. �>`>�!�AN�# Dodr�� 1989.9a�#JrM�bi$��#�#� 1�#9L�#I�q��#>�#�6�#|Vi.�#S.z#�#.�#��#ޗ#�"*} H�*L�*�*nK)j�(&b/ b,) mem�:$�(ope�)!J.X .I) y2WCho$Q} ARYorgdorff8� �Re�-k A.�)�\e� move�e#"Na�} ��4� 6889�649-53~�92 Mark2R0f�I�$�(�a�p�P�Va�S (3�=s.�:1:8Av�.?iSM/521.�3��>� �8 III: �r#.�&�*��*��*��*��*Y!B:-�� �s�k-�k-�k-��.%�.%�.%��/%�/%J/%�/�#N f e�& Orsz����Ad/fd� "x Y��� �Ens+J6P$�]�82͑A%J^%�]%J]%9M��3��3��36�3:���3��3��3N�3 }.�Dx6.2 ��"�4B�x6+,Nx6 rx6&�4}Fx6}^x6�t69�G�'�"PB�udnik|BYA� Bryc�2, O���= �`.=eq SK, 1:D g�i��}, GordoB�1h e�ce6�is YsV�E� z ��&n#��&N�&9E�< �< �< �< �< .� ��n�9�.r2A�z ^ w];�f.b ��1}Ha[ , Jr.m?*�,uJ�9c � 2g�12,����r�&�,2< R`e- �PJDVlw!"-K/.4G {Aubin}� QS�0Non�!ar�-�2� ian HC�3�- �18,]-������b�*B, -Evai��5yr"���5Z�5Jj;/|���<<3&��$Landkof} %�h� �F�n�->E }, %Q�"<>�� �/9,3h, D.��3��3��3B�:,:���3��3��3�Oksendal�\O M��YeAw�0.�>5th!/.��&� AOz9@�20 qAT:�;� ��Ko�h,*)z0� %&z0*6 ��N��v� �Lito} It\^o D, Mori K� TGiere E��7 dq2l�}��� 1119Wcook} C�P A*D1 BL3:I� 1} 42Eui} Ui H�. da G� 4 L�8%��)e 266�bal�Lkin} B A BR5 R3G�� M 164}nN mosh�<�M  M�(Szczepaniak�89 ^�(\\ A��\ +} h2�p816hreno}!�eno `Z�lla�] L821 �ber�z}�$\'\i tez JhBrt4nez y Romero R4PN\'u\~nez-Y\'epez H N �$alas-Brito�m�0 � ��E �!X$1643 \\ Be��փ 5} 2085(E.�+4cq90} Quesne C�.�19ۂ�3} 2263=udelange0�trge O LSm"�S4} 66.%�Jers!�\�s J�Deȱh N]F�} �V�"1255\\ Mf�ME�N��=�\!03.� cq91=\�I'D�\�Mody�/�6} 152�m� nA�.�-y-Y�%:�r2 r!k.�M�33} 183.k|szmyt} Sm<i R]Gruch=�M�6 �Z-R�34} 499.c�S9g�.o� Loyol��93 ��9(�DAp19.Wb�H�� M! J*�+>E VI} S@�8�&Iq0 Plenum) pp 5L-514a�>�,Smirnov Yu Fo6 ��)H��O"P�|� �q} ("M�: Har��"@m.�to}a} T4 F M, Nogami Y%@$Coutinho F��97 �z� �- 2585}� rozmej} R IfArvieu R�9�[� 532��alba} V rlba V)���hys.\�L��49} 586!�Ju G-X�Ren ZA�-�v_18} 572� p�eco} P  M��P im Rm0Almeida C A Sn ���m�36"2��dom�a�Dom�t��-Adame F�Gonz\'al˅����Eur�7.\ia 13}َ=�dixit} D@ V V, Santhanam T��Th~xr W D!Ă#�4dyi66ha�Del�8 Mes�q z 29} 422$ho} Ho C-L[Roy P!zM"V�3�116.q gros�k D J OM7� P a�88I�NucN#%�} B%fE1 } 402lagg�؉� I�M�C5�J��.bw��n}eJten� 11 BToday��a2.�(kempf94a} K I4-!qN�5} 448�Hin`sen| F��^F7} 212.f �72��{ 22020 N5N� ng=3G)�ann R� 95)�-1~ �� 52} 1108 ]��8g}W�ng L N,�ic OkaP�� � uchi TAvm(6f"C \ 12502.$z�} ��Ac�,7621$akhoury} A ��Yao Y-P�nu5# 2��cq0�z2� T�juk��B&)S!� �V�6} 1037.�^b*��B^e �, SUSYQM appr��oU�� �5�� .non�Y���2u;� tain�minZ6�and/or9Wum ��X}ļ ,3)�:� per� per�Kha�US( Sukhatme U�>>|p\ ) 267\\ CozH� ��2ymmetr�$"|0MX[} (Sin��: >̜.+ junk�JQq�.gic"�ip!��><2al�a�@T�m.sg�Tnsh�} G L��8MYPis'ma�y\ Eks�'Teo�Fiz-C( 38} 299\\ jJ JETP.�3��Eng���Al..�da�>ska} D b�� 2�):�1} L19.�carinenaYri\~   J��Ramos �00� ��6�-����27.�s��Y�!��4\"P��4 SQF(\ R.\ IrishY .}�46} 9, Y JGM�~G7� �h infe�yI ��Hull T�5 X �. �� 2b(spiridonov}��  Va�F��}M69} 398�G2;�;� 7} 1242��}^1P�M�23�. 6} L901��Barclay D T, Dutt R, Gangopadhyaya A,u�Jgna�j e�2�3 ���!f9�aZ78.��q4b}.4��..R� r�^��+9�.]> edmo�� E  As 5SA3� M]um.��, (�ac!�:*,�Un6�E. rose� s� aFrE&�Z&d&>�}*=U.\koek� ��(Swarttouw R+4b A_F-s�P�5h��"M^ &�_2�`A.= $q$-J�56E Reт$} No 94-05� ft.  of T�L10y (6�1�;$CA/9602214.�er�G&�G�z�F W, O2>�� Tȕ FŚ5m/Higher ��c�@tal"C s} vol II.g*m#.� snyd� H SȐM?2�!71} 38]�&� O�� �38.majid��jid� Ruegg H�'� �G0 >34��Luk�ki��@!�ZakrzewW JS� X*�2�90�ameli{A -C��1I< New.:*�})2�8!2ӨB��xzA?&�Agmn~ S.Z3Ral�1per� of��{o}�� % �*D1" sc"�7�In�AuS��.�.a@CNc��4) `^bf{�A151-2�(n �B-S} Bir3PM.���� mjak, M.Z.��( %StDAN�"�1-4H�_ rt S���RB:�-*&� A-L}&��M.;]�C�&1�yOemi-cla� �4FO&�T��5_9\.})�I�a� 5,66}, ��42[v� *{l,BF} Buslaev w�; Fad� L.D�"�J.:�� a ��� Y�"X� BH"�A)N3.} [E��H��], Do_�AN��� bf 1)�51-454�0*�NCA�$Conlon J.G�A newA�ofA�y9\Cwikel-Lieb-Rosenbljum bx.�Qcky M}HK��?�5�d17-��2�~C} ] M�WeX� ype zgmatx�5/>aiLnu+O��>.�H 5I!���. AMS � 2��93-10@C77=/ FadZ��9�;��"� �edit{KortC�-de V:"�e:�4 pletτ0&�K�Rsy2e.} _Na�al.$21S%R 8-27��71�h6 foer�� } F\A� ��y?%�T� inzfli���) Z;tN�28D�6rbeit,.a,Stuttgart/TUe�s)fG�Yy �44�Glaz}��z�l�.�Direct"� of� l'�ve�Nt�C"�W"9eK2�6!�Israe]graFT-'A�c �Ks Ltd. /65.�L-K} Gohberg I.C.; Kr�M2A Intrӿ�<��� <��eR elfa�7q��M�MC *K]�fIfbf{��AMS�9)��HLT} HM�tl� D.C; �L2�A sharpiA ��n�F� !i�onUjme�@al�`>g.� gC� �s\���719-7Ǥ�a� HLT�7>�k�v A.;FS dl T]>New��s��6�c��?�.} �>i?  -$e 140 3 ,se70�{0)�+Lap�y[Dixl_|nd"�?E&[ SQ% %on2��,in Euclidean�0�J. ��� 15�� %��45A9.�L-W} �N#S%�62in � &���A��Mat-%�*b W|, 89-1J��=�LWRz�Re�9 Resu�� on :�I��}!Cc.�I vist&�Dynam� 9k(}, Nuovo Ci�o A �52} 1061%[7) 9�4Hietarinta87} �, �0Direct Method&# ��<2nd Invariant}, %8. Rep C{K 147}, 87 �8��#�KaMiPogo96} Kalnins E.G., Miller W��,ogosyan G.S.�Sup�=tegrabila-!�DAssociated Polynom�WSol��Ds - Euclidean-S��9aySpherea�2 D!Ksions.�#!!avI.�37} 6439؁�=^� 00} ��(Completenes�mul�) parable sF�0in $E_{2,C}$ !�J � A�s. GenAt0bf 33} 4105 O06 KaKr!n01>� Kr�J.M!� )5�!D$9�E�>�V�two-d1talե-Hcurvat � } �-)��a�705�1)N�2_PAN:�hv� R���two`� s}, �  Atom. �tEX65a�47�2!�u14Ranada97} Ra\~ ��F�� 6le N=2 �?,��d c C"of Mo�>,!� Pot� E}Drach}.�!g m��38EK65ea�.RaSan�q6�eSantan� M�2�A��on the!@2si�$S^2$S%Xhypebolic plane $H^2$},A,�q�40} 502�9:eSan02>dhJ�DOn harmonic oscill� »rB�(, Part II},a�F�3} 2479E*3�.���b>�}�6��_m���� he com�� x 2-)�} Pre[ tAm!�TWaikato ISSN 1174-1570ĉ�2� KrWi%��H G���AGa_2 e�2[�* in aJTace�non# E�}^K�S970�Re�:�Mi�3.qN�=�x6�F�}&in� �!>1 I�4} 5811%lA0\1��Mi05a�� �econd-� 2�6�con ally flat �. I. T>�l� struc��$ 5 J��B� 46} 05350i 56�K�b����J�0St\"{a}ckel t� !z�1i�=��} %!�@em Some brief not� quivFcE�>�p��ina6�con&!he�  I $. Workshop� 2rleقtDubna Russia June 27-July 20052�PVinet} L\'etourneau P�� Lz;: P& Algebrar0Quasi-Exactly v[ *�R Ann.�� (NY)Eg 243� 9!�uB�BoDasKo93} Bonatsos D., Daskaloyannis C., Kokkotas K.p� - �$ic Descripᙁ� !BZ1[!�.�  a Rev Aa"$ 48} R3407�a�F�4ʼ DeA� ed O��9p�2-"M al�>� ��C �50} 370�4.�Dasd Fe��] Pois�aQ for Bu �x��>!�g pY[ar ive6] qZK} Czecht!�. If�12��B�1}^�!`� F�of��quWR�of��B� �42} 11!�20� ]��2b�=�Z��� :��-�"�� Nuclei ��  1008�4��u� Higgs79}  ,��W��"� s2a� � geo-y � I� *� 1-3A1976� DGGZ91} Gal'bert O. $Granovskii�I�: Zhed A. S � B�w0anisotropic s�&� 13 ��c15�7�c2{ z 92}  .�."%HqF" �� "mE" d�iV4of su(2)}, Mod� .�u5��%�9�GLZ-19��I.=.,(M. Lutzenkoe�%.5=��Mutual �"�*d ��09d���bNYi 21�� �Ul�R!�>�, � �q�I � Qu��j� ��Ftoi  Curved %� 2�Teor.� . Fiz^9�25u (in r��n.��2} B� ,���z�Kep`Pu}, f�39&2v�3F��A.Si�UZII%��� -�I�HiddenU3A�w Hart���5&:* -GenMU4} 388y�} � Po�cva *� .3�G�l2e set=is�l d��v( that admit���Oble�Afhq��3} 3592 �0:�,Tsyg00_TMP}  ��V��$ Degenerat�?*� , A �a cubic��g� of m5A8�6� �1!x 121���u��00_JPAV��~b<� �2 2 }�7� 20{%�2(R�rlovini�%an�$Rosquist K�E A unified��!7%L.at fixedM$ arbitrary!n!�gy�A�Q � 41}  �2[Gran�_ vel mx2Oix 2� %� thir�1��L��"0  m"�>o �3} 5902�:�GraGr �,Y.�]�v���� �?.�f��1�20!Y��4��)U,�em27 i�� in Cartes coordin!�=`�9c.YJ� 4� 6�WiOu6� Williams�C.] Jr��*� J�I�ree2�"P�e��!e�M0S"I 19:r KrKaA��k!�G. e^M* �!W2� �6� �2� �X� 12z�6 9 R�Sv�YuHHo} P. C. HohenbergBRev-Y15�38� 7*� LBogA} N. N. BogoliubX�+ USSR �� 2C4.CGine�Ginibre,��mun6�%=�P68.�0SP} E. Buffet�$. de Smedt%�,J. V. Pul\'e�� �16�!3T 83Y AVZ1�$Angelescu,4 Verbe+AV� Zagrebn2�.f �25}, 347%~ ծAV6h[A.k�y[�2�3� 'KZ26M��30}, 489"�j ZB} :�� J.-B. Bru �gpMI35a�29 0=l Su}  \"ut\H o<v5�7� 0236��.<$Gr} Rh iffiths%�.�EB5\21�6.�#SzKe,Sz\'epfalusy� I. K�#r,N �o(N. Y.) U#R 7.SLSYE�H.", R�&ir''A<(J. Yngvason�ete �$94}, 08040)3 5) %��Justific"� H$c$-number %substit��� boso=:�dlanl.arXiv:math-ph/0412023ZW��W$GMW}T. Guh!9. M\"uo -Groeling%He=�$enm "9 Q5299�! 998) 189.��0SIM}B. D. SimM"!W8B. L. Altshuler2J)[70$93) 40635��%%yB��I3) 5422.wPAP�$PapenbrockCN�� pr"{ ).Gefe}K.� Efet�= Adv.!��"!32�8�� ``��y2Dis!!DChaos'', Cambridge.�"P�,  1997.�vwz}J4M�� aarschot,R��0M. R. Zirnbau.v1�12)�85) 362qalt}A%�land,Q Iida, 6�U%�A 26}1� 3545�N�$Z'n�*�#l[ALP{\.{Z}}]{Zycz}{R.~Alicki�I~Lozins P.~Pako %vK.~9 yczkowski� 4) ``^&� en��d deco!87 ('' {\it J.\E .\ A} �? (5157--5172.2�@A]{AA}{V.I.~Arnol� A.~AvezA�67) ``�4�mes ergodiq|*de�%m�can� @que'', Gauthier-V�$rs (Paris)2�HBSS]{BSS}{A.~B\"ackA R.~Schu?A�$P.~Stifter�98!#R0of"N �cw"in* bj rdE�%'a-�e v. E-'57}a�<5--5447; Erratum� it 1\e�\38} 5196TLBGP]{BGP}{D.~BambusiA�~Graff)�TAul�9�Long tim�mi"/  approxi&`9 4flows: a proof!� EhrenfestLQAsymptotA nal. �,21} 149--1606�ar]{Bar!�\�+ nettY�OicEz|�6� chao&&� =� submit$to)��(\ P( Appl.�% th.}.�BdMOdA�sOz}{M�silioA� Mato?A>.\ Ozor Almeida%u5!uebiz�(Anosov maps5;nn�-16aO46--6565onDB]{,} {F.~Bonech)�4S.~De Bi\`evre�0�Exponent%mix��($\ln \hbar$%�scale&� izedZ!� �& toruE� E�!U: �,11} 659--686:�ul�ulA~Boulk�(ii|E�$L�!estA��.2/E -V1G�� Func>�1� 73--2046�%MDeB�zouina � %N~!N{e}!P�t6%Oquiparti�a./f:&U�!E M�NBY�V@(178} 83--10E "e+[�� \ Bo���S.\ DB�8) %``�d.�, des ursa�pr�|tyd$� %semi-�0qu�*�0plectomorphis��duAe-�fi�U�C��8.\ %Acad. Sci. ��, S\'e\+IM2326021�2:�R]{BR�A1-��D.~Ro�� 2!�Uni� �~,6N!�propagq� E\�- bser!�Duke M�/\ JQ�1A�22A`5��"� 4[BV]{BV}{N.\ L!� alaz�;VorosAX89�7,}A5 baker'1,an* �''irF4$190} 1--312�(Ch]{Chernov�I.~ x�``E�lc%Hst�,z/!e�0 piecew�,�,ar.auY E�!W2-�& �a�Staa�.�69� 1!�36�lCdV]{CdV}{Y.\ Colin~de~VerdiA5e�� �,it\'e et fon-Y�(du Laplacie�2����M�10�49�0%�`[DBDE]{}{FmA��0Degli~Esposti�' ``Egorov�& oremI �!2�of:P N!UY sawtoothqBA-�`'�SAnn��> 'Inw , H. Poincar\���  �69IH6�DEG]{DEG�6��! }a�3A�a*�. al a3E�um�4��.16T,H/orsIKa*mat] Z]0}, volume 618�LeS$Not��A�i62Sp,�"3, pp. �9BI%IJ � \1� Isol*&�.liL-%e��(�rtor!9}]1�r�,67} 471--5072 $DE${}^{+}$�O'KW} �2�� O'Keef"-B.\En%�5!�A>V stud�< Casati-Prosen t .gle!��Non�F ity}B 18�*�1096 0DS]{DS}M.~Dim &%](J.~Sj\"ostr� �Sy5&A ��S��9�L!�}r��.� [EFK9CEFK}{!Eckhardt%: Fishman�\ K�17O gam !�qin, K _�")\� ach� :m ՚wave "l1TA��gev.\ &? �[$5893--59032Fa]{FaA�~Farriɒ1!牭���em� a ma�Zld��6rac# b�2ary�U��*~ D.�6Equ��sM6* 1* 6�FP]{FPM�Feing}a`A��e�96�D.�U atrix ele��c3 "�2@"�8)9aL9� �FDBN]{$} {F.\ Fau%� Nonnenmac�6�� � �"/carred���|� �um cata7�minimal �0og� 5d�n!2H 9�2 9--4:A,Fo]{Fo} {G.\e�Fol�iFH�,analysieC phas7ac+���d ���s� 4 12�""�9F� 19892�,GL]{GL}{P.~G��ar04\'E.~Leichtnam!��&��6�)Ru$��@ Dirichlet/u;Q R� 71} 5� :JHB]{HB}{� H.\ Hanna5��V!U erry�80A��o�' ��-��)/ $---FresnelyZon by a-�ic gr�9.�ica DmI 1} 267--2:�XHas]{Has}{H.H.~HasegawaE�$W.C.~Saphi��2�Uni+4t � irre�6b inFKN�qL�+ 7401--7426�HMR]{HMR�P~Helff� A.~Mh nez�*� 1987) 9�"� �V�&� 1)n,,109} 313--326�4Kap]{Kap}{L.~KE �<E.J�N"8!3Lin a�n��Az ory >�  scar��*� \ y*-�264} 171�:�M]{KMA�P.~�jz( F.~Mezzadr�E�Pseudo-s&�&of *�;� � ���6��N�$3} 747--776 KR1]{KR1e� Kurl�b$Z.~Rudnick�1�Hecke-'%B : �9�2H�;eH1�R�103} �2{KR2�2��O& ���f���22} 2a&22>�3�3��y >>X � e���:r�I��[M�161} 489F_ Lak]{Lak�(Lakshminara�7a .�o�map%�$its unusua$/c|)4 ���6��272��6�$LV]{LebVor%2$Leb{\oe}ufjA.~��(� ��a �5pl�ve �2 esen#���e+Aa1�� ��23a�65--1776� ,Lin]{Lin} {E,inden� usse&�"m9 measu��harithme1Wu)Y�'' To���i�it-S)�.� LS]{LS}{W�u )(P.\ Sarnak &7�%AFi�% xs''�4)9��Eco�6 orm. .QX�769--7�!�mez�%mssR7 %modu�? � * � B  M�(56} 874--896T MO'K]{MOK�{� rkloIV� ; �E��'s law%�1�9��a�;dividedr  sr '';%� ndix h4Zelditch ``Con�}um\q�N� 8} 277--3:��d M�:��V�umMs�4A�:�7?�� Geom3 unc *01� 554--15782�Ma]{Ma�] "%�AnI$ rodu�9 ����&microlo � }"�-�C�22vO'CTH]{�G W.~O'Connz S.~Tomsov>>�Accurac6�d)^ ��p�_�3� s1��MN;33:y"� ,Per]{perelom�QF~) ��8�Gj'alx�t��e th�Eap�on�*".EHeide��6uRob]{Rob�*�(4) ``RemarkQimUpe��t6eF �FS, ].�:�Xin�'%c�Am�>i��m"�' , 13�$58, Trends�Xs, Birkh\"auser (Boston>�s�sen R zweige���6 }�e aV($\t2$.} M.SaT�E(Tel Aviv UnB2�RubSal]{  Rubi� N� lwen!�``A Cans!�3D*A�H'!p\m^nW6y) 1 186! RudS� RS}{�4��P��G�E K behaviour� �D�O���*��U������8�195--216z RuSo!@SoB� K.~S� araj�ina���A�-�.:Sa]{SLSaraceno�_l�!{"�8u��e� & 8j�^ 1�" 37--:e SaVo]{SV1��!�"�� ^Tow��-.���A"�um �'sA���.�79� 6--26����em[SV2�2�V)) �\&�\underS {wr�Dtitle}�L� �� 2} 96M Sar1!� �%�3), ``/AfHypx�E�Bul( Amer��thSoc��)(no.4, 441-4:� Sar2]{sarX �nakɻ�vesus� A"fl�:%�� 0 �sqF<}. Talk given at%�mee�I:�bandomarix�Ror\  A&0 A� ef�%P''Q0Isaac Newton He*�#, �9`004.\\ Audio file availab t {\tt *�FnR4.cam.ac.uk/web�nars/2� Schn]{Scn��\ I!Bchnirel 1(1�&[�p.sK�M" Q6 Uspekhi!.\ Nauk1�29�8�W86  SchuANch�j"s1))�S2<p�d�>&D.} Ph.D.H�KU��&<t Ulm. A=D .D4vts.uni-ulm.de>1uaach26�``Upper�JAWE3rb�" .'' "�?�;,2� �:�'503045}2�Wil]{Wila�~Wilkin�9�Ŗ!�&� sum rule�"E�"�of *ly( � :�2 ��_ ���41�>~ Zel1]{Zel�~"W �J>LŨU[��compactݨ m�UzR�(55} 919--946JZel2]{Z2B����j� I. .�q�..�.-( 160}�� 1, a::ZZ]{ZZ6���M.~Zwor_&1G"� >�s%� *�#iG �\ ���T75} 6*6m�N^'Vn^'}��.�="� 4{BBT} O. Babel�P0D. Bernard, M���+Y+I�'*� C"N�8&p?}���Xyb)��.�/b6R�M|lq2{itUu�N�2Neu���R}, �L�hep-t�+07005}6ren} Ss�$$ Inq a tensor� 7A�'&?6�0e*�%#�Ren_" em. A:.�0. Pol. TorinoICh=A� 2) 3� 341..�CR12��0ChanuT*$G. Rastell�.� he�Bne�betwee�k addi) .3E �--Jacobi "� e]T:�FCS2�T9 �c ��"aJa�� ���Ci�!EJJ�0�4�2) 51�$526{, BCR2�3�3�3=3I�:rst &�4!3=y "�R�3Gh�/�.1$ 52532dor}et-aGmSwP'existy+d'unew &B d'ordre nKllojApv�&f7�q�m� $DG/0208171a��ou)� ouarroudj�YlyASi�t��map},>~ �|) 51}:4E=0) 26�74. MCa) Cariglia- � M�a, Yano�:�ac�iL��<�Y }, �+. P�1a@4�*A�4) 10{ 1078.� BCar1} B.�ter �>�A6~i���s�N� Einstein'��AA��6E)<��68) 280�%0. 2�W B�Black hiJlibrium=}!("s/L�stPocclus (�d'\'eT%de%�(Seor , <Houches�7�T=# .$214. Gordo��8Breach, New Yor73). ]� Car3F�K`-�,�I�um [2�*�Ie�>curYW_.A e- De�16�077) 33$3412�DCGLP} Z. W. Chong,�(W. Gibbons,0 L\"u�(N�ppeM+S/b�7A(�T��4Kerr-Taub-NUT-#6i!UQrn1in HigM D(OA6u�>n5066�CFH)Qordani,�2Feh^�B$Horv\'athy �$\�.(rm{O}(4,2)$�al�LKaluza-Klein monopol=i�2B%j201%k88) 4\ 486.oDM} H�1 Dull##V�9�T veev �A new��=ecyMS� �(}L,h!�s. �mT1}- 4) 7��7222TDO1} C� val,� OvsiB �C*�Ja_2u6;$}, Selecta�h.�5S�5 7}:3��1)}6{02O2v���AwDsymbol calculus: n�Lmmuta�Z�Dic&^$}a��UF�7}:�5 1) 6�#2<3DLO.�P!�comte�R�f: ����N}, �. Fouri�]Es 49}:�A9))9H2.�% {LPEWL.�$Eisenhart,Km�l�,Ah��"� �R}of-#w35}:2��34��4d5.�GHY} G�S�FSw6�A0noll, Y. Yasud P.�$ some five6�<�a��< ) z�46�*4732GRB�(P.J. Rubackm [ hi�B �#!ulti-CQ4e.�om:�%111�Y��"30:�vHB�R.�z Rietdijk,� ,W. van Holte"S USY�E�ky}, N"�W�404��V742.�HW<H�d�.W Y-%b�A� & F]9�U(\widetilde{�e@frak{gl}}(2)^{+*}�RAti�bC, ^A72Ms�'263--282sKL�^$K. Kunduri%1LuciettQeMi"YW!6Ţ(A)dS b&[inE�6b>o 6�502C2�!P.B.A. L�%@V.>p2�"]DAo.�R����<�:192yLD� @E. Loubon Djounga�.��%鍝/o�^t%@f 64��3) 20!�12p Mos1ErMos"q Various.�,!�]c� uA�!in�G�`  (C.�FE� mmer� ool� ss e; 1978)haogr�W�-&�', . i�8eB:*23�6; Mos2B� etO M!d��E��$~},��`eeding��!�0(G posiI7 Berkeley�9,"���80)�Z --18� &s Per�=M. "%a�emu&\��y�&� a�Lie"`I}�^I,6*(1990)GrebceGerein.yPle%0F. Pleba�9��!*�R_ -Maxwell��D�է �v42(1975��5�2=DB��M. Demi.�RoJ charged � F4ormly accelera� m�!in�Le!�Re�_v.,V�I^$76) 98--122mHPh< P.&�q�0Bermerkung \"��^ierbar�Re��XWRnmuk"H �*�. �27) 7^+752�a?,M. SakaguchiB�0 on F>��i� HoI^T�Q82�Q"�S� J.-M� riauA/TtrNrfs�\`e�5� f;}, DunodEL0, \copyright 1969);�Jof�Z�Q. Ae�� ic View(Apicc�/�aed�"C�*Cu./� V:(R aV G.M.~TuynV/ **b Edi2),2��97�5TotA�AthQ�V��u&)Ga>Q2WQA��J.i8 �"iK130 1�1--6GVal�V�Ut!�it�]�l�#usI�1C# the �L 24��) 59*592�V�DC?asudev�K{ Steve�D9EPagR�� �s�!�-�"�/a[A�!�6��lass.�. I-P)��? 39-36cWei��Age&� Th �-�1��(%i}�Ai1-56!�E82 �#1# NZ�vZUvN8kA� 4Nayfeh, \emph{>�Perturba� Te�e� (John Wi��\& So!�?q812� F00}�+ M. Fer�da}ndez�z�1�A%�u.�c (CRCB$, Boca Rat�gL.�AA_+�� Amor� A. A�3a,�.�A / bf{316�j18�M36QL� 6QH. Mon�$ Lama�S�0FW27}, 158EL46WA03b}WE���it{}=+h�D 30306�AM6�M�>�( X ),g% Ni 10062 SEUP%�m�!� ��3 D S bf{2�S291:*M7A*J.L'iBI�e�� "Rof�3cl(nd���$cond ed. (�;�&�A�7�lyK�J.bec� �Y1aF10�a1� 2aFC��%�teca,( F��E��C�oqL�� �:u}p 8sum#�eRC& (Sp<8Be�", &'.L�Gn,!N8is, Tokyo, Hong�Gg, Barc a!:96:BK:97} �$P. Blencowu]PHr]U�eEB}� bf{�*942�96$ JPW:�A�F. JoneA��=ki�D.�d�1JhDh6Az12501�..PR:`;J.�KneurvB. Pi�T!�R.�VRamosy&u$�\d-mat�729� �z KPR2�b!9 %9�} �(bf{89} 2104�N2). 2$ab� MP:9�>G.Te�DuMenezm^MzG%��� B�370} 6J962bPR:&.MjT]I+D\%  105m�992blde} a�,Okopi\'{n}sk���D��3�J83�87); A.s k!�M��shRL.\)|\ B)c��1C35E�88). R��v�U)VVZV (it Vladimi�iV.$Y }l�+h IFTr-Penov Ye.I.} $p$--Adic y(7�"(al��ics Jngapore:2_ld Sci�Cfice�6� l1 �:�}ud !� p�3�9e� ial "�k 5field���a�@ //��� �.30�N$2 N 6. p.1 24*ur Vl2},*N� ��82�� F�&^��6^ type�Russ.�x.RB Izv.!|�(3. v.41. N1�55--73�Khr1c K�Fnik�k Yu.}� dam�1l.bver�'fH bH!I2. v.4\ 3�248-266.AlKa} � �lbeve[FI�@Karwowosky W.} A S om w(onI�.�7''Stocha�AD ss--a�icn� II '' (�{, U�ttaneo,��M��i, Eds.$c:carno�J1), pp.6�7F�2.�5.�o�Ii: ET A.N#uE�--VKA��F ph�Vs. DoI%,cht: Kluwer �bc Publ.� "0 �1Z�BfE :anOParadoxA�D|�>E|BiologModels. z�isher|#97ݲ��H�C.�}I0dA�%�mwFreud�Cy!�u mc� mil)V\"ax�Ek)e�v, , Sweden:*�4 v76e3M�2� � ,%i.���� its .�6 . (I&�bf cow:�B6izmatlit�." !B4N�Io�!AgzJ!α��@72�CM~" cogn*  ���th.�$�e#1� � 4� 0=<BKQ�(Avetisov V.�vBikulov� H��.D A&�7!�y�5^toQ�epo�q$eous break�%rep5=�7e�J(���e�9��3�m8785--87� R;"_990436� PaSu�\Ni Ov( Sourlas N2� � %�r>��// Eu� an��.�B�*0)�4.�535�S^�.� 60959�Carlucci"� ,`k, Dominicis C&� ��"&-6 // p -us Ac Ser.IIB�;m.Astr%��) 325.w]527Z��70920=��W D6�, � De T��  T.} R-�F�6� Xb,4 block--diagon�:A�)-1$�@mWU�I��nce�# �7%�105--1� z}7031329� ABKO�,^wAFv, Osipm�.Q��aQi aGic?Ip � @inK Hie&l 8Energy Landscap* �6�20�  3� 7�89~�010650*� SpinG�q�Mez�G�u 6�VirasoroH 8--:c | Beyo�_S:6:;8.�KI���R�~l R!j Toulouse��A.}.h�2%n��ist � �� a386�58E:765�-7.L SerreM $ J.P.} Tre�(&�7:&� �> �N��f�0*�~Wald}R0 ,�y&t� (U� � of C� go�  8.H^ Jack�[D.  �CA�El�o�s(�* �*g_Belin}w2linfan�!m�VII]99(19408Weinb1}S &b��or� PI:�dnd� s(C�\.�P�*N��D" z26zG� W�X Cosm� y: KipC�ne��Ge)�j o &!B@�"2= �;}Ricardo�Gamboa v\'{\i�0!P(. A37, 9573a.�VolR\}D� t y�Z D57, 3484�.� YW}H� � P. W*ga4v. D69, 064008>u,Ashtekar}A.  6t36,�c7 2�cerochA� , Unpub d>�; Lie-deriv�*O �9�HHZ}M.�K k5J4l}, gr-qc/0409�N�:u��5�8l/97)!��7�=16 � 99c:330122� a_1982} R�Bax�v�,{S}olved {M}k�RS}7� ale"7� *��H'mb�BO!�0} �i͎! G.~Olsh�0-K.(\s&"�es, poin�a�esses�0A�:(9kerne,fOg I��1!O 2, 313= \MR{o k!Q312Qo�$1} Alexei ��~gap�ba�,�7Ad��4{P}ainlev\'e 22&�F2�17I�}r�U42I$1 979 056B�2>��(Dmitriy BoyP;J��!ifA )�cleA'�ortho�]� ensem&7F��htex�S46�2, 28S�!�1 962 462�Foa�2�qR�SeQ ca�l� z.lh�({$1/r\sp 2$A"~ any-3�A���a� .* '3q�2� 67�;99)�MR�2�s94eEZ0).[ FFGW%�aJ�N.~E.$,kel, T.~Garo�#AXXP*t���P.`t�fc�Qevalu% �X�J; denu"��01��impenetr�8'rv�23���x�$1-2!2�@69F�3F�^�DNIyG7 �%�x averag�2�l**bf{166|��I1942( �2b��q.{A}6�AW$\tau$-f�joryaMu� {\'eAsF s to2�(ces: {PVI},@( {JUE}, {Cy c��\le�o]!�Nagoy�$J�7ml4), 29^J�4aB�Bi-}� {P}oՑ���{U}nit�ircleP%�� QL^�RW}e�4%� {I}�ble���=000J�3F�V{E}�b, {O}��>� N�%[$n$-rf rreQM �&( {$U(N)$} -#�{\PIIIa)�{\PV}> �Int�"R|ot9��Aa@!���4r!�82�F$Fr_1976} GENza% Q��Lcoeffi�t�!��: G5u*�;�=�&\���9,. Roy. Irish�vct.*)07aP�2�--6� 54 \#7912�JM�0� Jimb-T.~Miwa�S��onIEonomic��*=>X}{V}{I�� �Japan�r�g%�*"i �/� 9, 4�410ů$MR{85h:820*�&�Kh 93} J�` neko�̓6w:��$O<"4�\~ {J}:F6�y%a� ��"�2a�18?�x4�v 1086a��F�94h��6y Kx 4�P.*ge*�`� {R}a�R {M}aP{T}�4�Y a}� glI {Q}�� {S}pf C}h� ���R�>q%-dx070472T9KS�%G�J.>�$N.~C. SnaiS8� uS�&M2�<$\zeta(1/2+it)$}|hb� 21!Y\5)Y1,SG89Q� c:11107.�,Kl_1933} F.~�75B$V}orlesung �@"u}ber die {H}ype"�Csche {F}�LE�� vonA$ulius%W�&� Inc.,��33iha�A anZ;!��&$<{\"a}t {G}{\"o}t<e1 {W}A� rsem�  1893{/}6#/Ma%�� 5 agnu(2`7({MAPA3072A}�ecial tԈ��6�t)� �-9-!t:6/j&> V���� cŇM^ D ��&.uB(ac.be/\~{}m�/2o McCW�a3�G~McCoyA߁�TS � T}wo-{D}Hal���\ },�BvarA�U&�H Ha!�/�aOk� 07a} K.~Okamot�c��"^\'* .�.!Eixt�X*� "�8 ${P}\sb {{\rm �I }}$}�|Matra/. (4)*� 1Pf�?7)O � 81��88m:58062� SE11&>~�=�[R� �/YWB Twne roovBF�v2Gi fv�2���}.;6o2� 1 882 4-�9�Y�2�J�Y�;I* @. bin sev  .lD.\�sJ<B a<I���� 317--1C !�MR{94${ R= x>b��BDJ�P�v ift. \new $� dhol\ ter�dnt� ��}-{��,}-{Ueno} tau"2  � e�(�1�!���b#��unE�.M��$}, 55:1160y/30V(2.�Co�CmBCosgrove.^Chazy�$es {IX-XI}� th&��x.�3uNs.G�a�.!�n -��^04:Ph28�c"ECSZ2�A�EScoufi2h&� ��4)9c  V��o� Y& CEes degre2!n� 88:2?(��92� DE�I.~Du�� A.~EdeHZ.=Mal� beta&_.,�u _!��(:5830--5847%d2Dy�� F.J. Dyso2}S* ə!&�gy lev�of\ plex.A*II}�� 3:16� 75!#6:�957N��qC@%mb�\id%���fifth *}2.�,In S.-T. Yau�shRem�(n N�'8Yang}, page 131�Kv�EUa��ͽC�# MA�F4�DM�9b�$M.L. Mehta.�Vq�~u��V�u4:7�i712�62�F��WKF8�.�Log-ga� a`  qA�ces}. \\��m\(melb.edu.aup tpjfTpjf.html.�Fo9J*x.�A rum edgeA��6� "�.8e!�.i Ba 02:709--7��? :�9�^��Jr-"� hipsa�hWF ��a< �}:�X�S� 3:(g00E�2 FW01B�E�V���n�1�"�L�"�{Cn�PK�& 55:67ŔJ� FW@ ��Z��^�:�b��.bI�hss/em�� A�: Ga61' Gaud�N&j �\a loi i^L l'eA��N]��\�oc�a��atoir2 �j*6�5:4�s4�k1962;GuR J.~Gun:Q Proofa"a�C']!� of {| [aIqj�I*Zof  { .M�1<�n�$:752--753,�2b IIKS9�R��AޑIzerg DV.E�Eep��,N.A. Slavnov.|2�>&�@�nde3�  2�b� %��1D:�^zo�2� KH99�A. KapG�rE.~�?t.�A��${Lax} pair�.Ny'.@�ah9�a�32:81[9815�: Ma22�Malmq�.S�es \'y�A o]�B@&s/��o�< dos" l'inr_n�e g\'en8aFk �"s c �$NE�F�Arkiv�. �7on. Fy� 18:1�tAA6�cMe6N&�.%6�E�C�-��U in n� �p42X%|��{18:�_41�6�LMe9�V�A "* !qB# AGa {Fr%} d' &.�� J. d*�`I (Fr68{� 2:17��72�6W�}Z�[� &��X AcadHM�ss*35 2kM�e!�6t OK87.�.S $o�_Z�} {F�}2&�� {$P_{V}$2v��qMj3:�7eC�7 u�Ok:`ҰVea�dz�J� Funk�NDaj Ekvacioj}, 30:3�33�6� Po65�^E�ad.�%BQ-{m:Act#2Ff�1962�LTW� A. T]vA�H.~Widom.�>jR. ��]yIh� F. Helmin�Oeih%H()nd"f&4) wW!?&��424A�%"Lec� ��in?�� ��2>H"dNe7dE�22TW9C"C�LB��2S ���{Airy}�'."�V!159:1Cf7;!96��bA6����B�(l��61:289�`��2�"vM0�~.�+.���^�+s:>NE�Mbpermu�6H������3�� 406.*oFH'�v�WW�5E.�hitta�+G.N. Wa�k.%EiA coursi �A26CUP�zB'69Wi55} E.�9~.wCh�v���+ v�r� b�ed� � in�'dimen�#2� ���Sxth�$62:548--56e(52� Wi57b�G�C�;� ��,{n neutro�F.�Oak Ri�N�al Labok�y��8ort ORNL 2309:5e52\\WiwNR�Gap *y+� dou�� valr {H}�tm"�"�I:�s�Js= �iit��=cas2�d ,-phy/0307063��'N�: r/���@adn} {\sc Agmon,~�N� Lipschitza�-}���"\�19�+1) 349-�"]Q Girault} ,~�� Ravigh~P.eEe5F<4e �v a �xaGP4AVZ},"�΀#@9.�KalexM ,~H.-U5H� ��� �sm-?1&KBingham� i��non-sm����Pwo2�h9<Z.�O \"urQ(ysi�� d iha�nwend�&bf �k(p" 4, 509-56�hkm-88�ozlov!e~���G��{l��Z�  Ĺ bundles,�f�by��:Hu��aAVa�F?'Q�tc2�� 88) _ 14-12��q kmr1��,��s@. E�J>�.�-� ��Q �Yi�.&urvey�  r�s �52�%}4K� , Pr�74nce, Rhode Isl9 �4.�kmrVSsc n�V�.��_�B2�*�� 2�A��~to5�2��8?�Bx�8F206�kms��Schwab��ROn6�B��/D���!%&hyd&�E��verte�Q��k einem�w1�E�4�,��65��"�Hlad} %Ladyzhenskaya�.e��2`����5F ...}�MMo�M��0. jW� U�&� viscFiincom�ai� ��}, �bA�Breaa.�re.� mp78#2` , Pl9Xevski\uxE~B�1�$L_p$ �U ��� " jdm���!��Tr�� Mosk��<)Obshch.)�a�(�i$ 49-93; En� h�l. in:Nns.GcowFm�2DIiD2�,mp79} Maz$'$!�V.~�M^VitA�A�a toti�W�fu"TW y����reg��c��s}��b �� ��61i�{`-145,R%Se >%vS �-�U$) 4, 363-3> -83m�4A�7Z�v &�,"� !.2 �JŨ2Dp"ݛ��h�  Zγ-3Uu05-359, 523-55��&mp���,� pyal| L.~IuY!%}m.y.�s' -st�mƱ!!a�E+a free���},i$. Uravn. i�Imen.-em Si|,Protsessy Op� lqrav-j��IUVr>:i�lMV1 ?8�x71L� *,mr&�:CRoF\"U�/""�k�/LK�s ma0r�$wertaufgab�/'kUmgebSkvon K�K���. Nachr�31�71�7-5�]r-x� ^� &� P�;�= for Green��2toQ�y� "��&ty!�- Va�2hed�^co� Z"�g���m �8� �1() 5, 291-312M%����W�6ed>4������3 �m�},r�3� ,3) 7, 435-466�r-��& !�:�of5� � 2��B�9�oAu�' ESI 1419M/ 3), Erwin9 * ��rP**�%�A�"9�s,Snna2r-�4�r�WUN�1 �RR� to appear.�Nazarov/�} �� eJ���"R �inQI�6j?4,} De Gruyter ��s"�=oM 17fQ -"�4 �& Nic)B�-&�# 41(7A71--4283%`0a t$ AH97t$%a�U$M.~Hirokaw2�"a�heb�~![gr�� j 5! spin-b��)uN�.@L!51(2):4�h50](`}�$HS} J.~AvrfnI.~Herbsm�B.~��2kS}24���ase!y%�d4p!S}Ԃ� o�!ce�3�mas��homoge"^>J2��*Bp � 14:4e45DI972�AHS78b��~��G}4t4i�aщF�2DG*8:8�"8Ag>� BFS9�V�J � J.~F� hli�2I!�ga2�X:�!q�� \2-I�qFmdv�AW 37:2�"29S(92m�a}®Renorm�]I'a�x��s���E3�*EpR�3I.B�ց39�2B�9��"Xq 3 of ��molecu�' coupNtJ� �a� rad� �B�Co:�K�7:249؞0�"2�BCVa-M7L�zoux�)Che��S.~Vug�?2�BindinD{b � ic {$N$}-Mfn�o0�2d {QED2� )�nnE$nri�car\'K4� 1101B�Y�G.�� M .$�Y-���infra� r:kaAc��rue����1-q��.g�� mp-arc 0�0%�6� Coh84�#(~Cohen-Tann:�2�I:��Q�-aN�I�% ~Gry� ��� �59�4 Tend�(s actuelA�e2���%� /� trendekc )cF8 Else�: � 19842�oh 7CB��(~Dupont-Roc� G�Bd�Ees�zd'�[}�e phot�4�[tom�8*? EQ�du CNRS��T� CFKS�?L. Cyc� R� �iese�~Kirs�rR��Sn *Y6a�1�me�N %�globa&��21 TextBXin� aj�&�&cC stud� �'�w�i=DG��J$?rezi\'�R�C&Z�.Z"c^<te^��ۥ���>9 �E ssiv���A(uli-{F}ierz6� FfMa? ��:3�j45J�DRp:� G.~D�Q�]#��*V���{H*g �sA$��g� �F�� LAGA�%�D� uf Nord�.a=Y�F7�GFr{�D��.�W ���!~a � �x�5:lM-a%�r l,,Z ca!\ F����8�|N�� SVI(�$�,19:��i 6DF7�G��j���For�o&� 22:1�J�6c�FGSray�12�,� G�em�F!M� "�6�4^AV�Hyl�!���inF�.{F3:Wu|�W.�FGScom��^�C}o�ms"��.��R� 52:4?�4�-286Y�GL��j"ƭ I.~{\L}ab2T f���q��a ��an�i�m��Hv�c~9^�;R� 2��ica.�al So#�y>&�I�z2�G��US.Jn2> mE,Eu�6* .;%�z.3.p_� 10039J�L}�5�,E3��M7�s2'G2�E6��@��N��In.g 45:55M�� !Y.�3Fp shim26�} � �2Tb� �H�%�F(0(12):62�@622�#:�3H�������C46gw6v.206�H[����� SzZHM B q�2J%a��.eX�� Soc.e1 53:4`�45BM"�{�D�B"�of]n2n|"Y ng�a �ag �Sb� In �"0L�| �8Z } �l]E@t G�% ف%^��li�jB�*��� �p4l�&� *F�NO-�O02075&��I>�E7 K.~R�:2�3M>� i��N%��O��>��� 4�/�� IT98�Itwatsuk �H.~Ta�:.\��s22!��}� :6 a b�.me">> 93:5Z5a�1:�LLx���a�J�Exi<��,e *&�j� n��~�jq�� 7:6w�71;@2���z��7t�9polarZ��0]�~{b��n4��+U�Mo` S. M{\o}Գ.���X�on�-a׺�  {N}elK�e� :3bottop'�J�u2�5%TN�25X�Y �pizAA.~Pizz2tOne�� (im�9) �S �.!s4 �.��� J� �O�8E2��4eiB�&��E�!Afra�7 ?{ one*�|2 i���1H�10* 5GRaiG.~Ra{i}:AEбe�Ii�� >�![Ai�-^� Vg� F��@ 9:16~?6&>�RS�aRee�K� imoF2 ���odG?N &&�9} ���$, self-adjy#6/ 2�: [Har�4t Bө Jovan/zNy�x]*�:sS6AShi[@ hige>}"�I��,߶� � a� {$\��12$:>�B�J6�90~ 2�28{�UcSob/i�- �.X�{L}�� {T}h��6�$Rq.Ge�>E82(3):60�3 �2�$Spa�H.~SpohF9�z%[Α�Z�ZI:�2&�Mun%>A�y N�4�3f�HuLMW*�!([A]{A} Aizp�n�: {Loc&{at weak���6: some��Ai+� >�IT1163-118L��&` [AEN_�}2�, Elg�1 �0Nabok{@"chenktJv,Stolz, G.: M��&� c2�in�'om:� &N�%2�G]{AG}�:9/, �rf|M.:} {6m)�an�ynB}.a��"Uv G&p�41}, 6783-6806,�!8)2�M]{AM:�,��lAovKD: F�l�� d.Z�extreme�Ei�: ��|ry ron}. !�SM�4^{{i257C 45-278�20�[ASFH]{F�.�7ieЖh, v Hunde��rk, D.:�3� ��� al-mI�Ae�A A>`.S�. ��-��U22D�219-25�� 2�n]{An� ^��: Abs�ZHAsx]�ertain�8 lat�gEp&"t)H09�$492-15ō5:�oa�e�oAF�Wdo�: Effec�g �!�CHal8Enduct5��c >w4��:�.Solid S,1K1?3  1079-10i�8.��[Ave�Sa�sJa�ei��!��, B.:[;g#I_cy,�ZX port � �0��@j*X;I�2t ~)l5!l�#��ш [BCH]{BCH3$")J�{Combe���yHislopA D.: 2s�9bF &%E�rTQZ ��� HelvQ�Acta}I 7R16-43w�E�\�![Be]{B_�B�%ssa�J.: O]G�E eE.%?non&lz>v�7� logy. 6�ia��edM)s (Badzhandauv 86), 61-� Teubner-�D., 16,, LeipzijH88�$BeE��ES}:�, q?El�!�%(Schulz-Bald!� H.: l�noTm�>yZJ. {:�I03�5373-545 �94).U. [BMR]{BMRF�g]`A�Rivass; V.: S���N�C �E a simplif�68 �}� �sma��A� rkov7>yPu�9}, 261-�278 (2003) \bibitem[BoGK]{BGK} Bouclet, J.M., Germin�eF., Klein, A.: Sub-exponential decay of operator kernels for functions of generalized Schr\"odinger o =Xs. Proc. Amer. Math. Sh \textbf{132} , 2703-2712 �4):�S�S��,�|enker,J.: Linear response theory�magnetic1r\� oLj in disordered media. Submitted =�u1]{Bo1}!�rga!k J.: Newults on� spectrum!P lattice 6� 5��s and applications. Contemporary !bematics5b 307}%a-3I926\u2�2B�Random�Sc=.� withI9ing potIL�: some higher dimensional phenomena. Springer LNM�18� 70-9 �E�.�uA�K6�H, Kenig, C.: On locA�%+!è the continuous Anderson-Bernoulli model inB�!kPreprint.wPCKM]{CKM} Carmona, R�qd8, Martinelli, FA x 2� for �!�ot!: singular 5Z�Commun. !�t. Phys. {\bf 108}, 41-66 (19872&0ChD]{CD} Chalax J.T., Coddington, P.D.: Percol%<4, quantum tun�ng�!QHinteger Hall effect!�J�8C: Solid State �q�421}, 2665-2679�8.�Che]{Ch�en, T!@L.�lengthi8Boltzmann limit!S �1r )�at sm�q�m�mI� 3.5셍E~u�$CoH1]{CH1}!�bes, �iHislop1D{2�!�a Y�, rie$HamiltoniaE�d-u0}.!KF�y. Anal1�,24}, 149-180!8923 CoH2�2~�{ Landau.�se� �Yx:6SA�Ad!7t�7s!�s}.!A� E� .�7��603-62%�966�oHK�Kz�, KloppiT$ H\"olderq� ��E�ratedF�5�-� .nt A%energieav IMRNU�(4}, 179-209U&.%KR�R��X, Raikov, G..: Global6��Ƃ� �N��5%�. P�� al Differ�� Eque�)To�p ear .�N�N���Nakamura, S.:{ The $\mathrm{L}^p$-t�of%�� al shift"t,,Wegner estim�NM� �az1��}���KI����K21�K113-130%�1>�T!T��oj , Tipq  {B� edge2L A�BLE�acous�'el4o"� wave��i� �`}. Ann. Inst. H. Poincar��T!u.U�70� 381-428�P9.�DSS]{DS� $Damanik, Dc ims��StolzA�:6���one ��al,Q�um,��-6�A� Duke-�J�11a~ 59-10)�22�D�} 6��l�!���: {Multi-scale analysis implies strong dynamical .�}.V om.N���11-��20:5DiP�8PS} Disertori, � Pins�H!Wpencer��D�` �a%U)� bAmatric��f�(32}, 83-124E�%3y�XDr]{vD} von Dreifus, H!(\emQ A���sa� �(ness in fer]��i�69 .| Ph.D.Wsis,  ,York Univers��F� DrK]{VDK}>��� ( {A new pro� f2n in�FUp tight bin �!�bK�}285-29��8a-9KEGS]{EGA�Elgarta�, Grafa#!�Sc�  J.H.: �wl� bulki��-^ $conductanci�a mobi5gap. � %�.� E�S}�;�)2 B.: Adiab; D charge transport �!� KuboA} mula�`-type2B. %>(. Pure Appl�a~{� 5a�0-615J� dErSY]{ESY} {Erd{\"{o}}s, La almhofer,!IYauA�8-T.}: In prepar��2rQRP2B{){B}"O e� as%$weak coupl m of a3 {S}2. @ }. {AUF}��,53}, 667-735%� 0) ]\@FK1]{FK1} Figoti�:�2y p oE�gape�!��li�"� 2�J.� � %�075}, 997-1021a�6� FK2�}�� of classi�j�� I: A��v�80� 39-482�6.�FK3�3� I: EN~z���411-44))� \�FrM�\FM�]Fhlich, J!� :?D, Scoppola, E., S�*4 {Constructiveb�%�v� A�unm�. 10�� 21-4`52xFrS]{F��B�.� {Abs��!�diffuv n��sl���  or low� y&z z .�8� 51-184A 86� G]{Ge}��&,: {DyN� II� an *� to%]almost�ieuuL� .�9aI(273-286 (19y Y GD]{GDB} 6�(De Bi\`evreZ b�(for discret�d�Fm�S2�o�]�FN19A�323-3M�2�G��G��6�*}, {Bootstrap � � �� and 2�in�� �d>�"[(22}, 415-44F� =Z��GK26�6JO- "y � "� �R g+sed^T�B0131, 911-920�:���G��jREx�Linite volume criteri�.� !T&� 2`!�� &n%)B� 1p(13} 1201-12i���GK4]{GK42�6m{�,metal-insula�"� iI�V �339�-57�Q�.�5�5n�A ac!EzZ��the®Z� � 309-351�� ==6�6j�> � .�I���regio�V� �'1�Z.j] GoMP]{GMPA#0ol'dsheid, Yaolchan�$S., Pastur� :  poV.�stocha�<*;f�2$r �� -1&7�| 9aH]{Ha} h perin,  Q�ia�h *� , cur4-carr��s,e>!zexist��, of extended &aa two&��&k"|�FRev Buu2�=1� 19�8� U9HiK]{M2�ew"= JR� �Es��1�#�$nonsign de�w� s. JR#�� 12-4i���$uLMW]{HLMW!�up� , T., Leschke� , M\"ull&$P., Warzel� 0 The absolut"�*] �/^ Z  �0certain unbou%���*.�2�29-254e�Ŝ5�@JL]{JL} Jaksic, V�ast, Y.:K ct#� b of&� J� Invent� i(41} 561--57)�0� =�KM1]{� Kirs� WA;:�  : {OU ergodicz pertie��.��(BN��4J. Reine Angew.� 33s141-15} 2). KM2���z� �S*~6���s �a P�Z|%Y8a�32��y�9�K� K� :�B��,P 6� Qm�!eur����%�2�*�!c��� �j��Us �6�41-268!m�lA�"� : EF����oaon�Be�a1 Adv.� 133g63-� 6h Kl!�%��A�Sprea�of; packet�qsB�6�j �755--773L 6lKl3]{� .�.� "land6� of1�aB�0s. In \emph{-�!�o�.m:2 hods, hɇpereiv�\ Panorama \& Synth\`{e}sI oci\'{e}t �  U que de Fr�. 2��Kl� KA��poin+!�{A�framew�� 2� ! :: I� homo�D� %Ide} eigenAhA�Ms �:Z . G�  �R972�.�A]A^��6��JF�I.q�� 2e .��6�% �LS]{KL~ �.wLacroixQSpeis: {F�6� m� a�jip��J��V:� �E '135-155e*�e�i]{vKli�hKlitzing, K, Dorda, G, Pepp��N.:� meA�A3 ` 4- accuracy det���ABa�f�P�,c% ant based�!�� h r�h� Rev. Lett�4��49H0).R .�o�l}� �F�&z m�^n&�2��n16A553-56�9�=aoA�l26�W�i 6���8Lifshitz tails:.�*�s.d .H.P���711-73T� �(u]{Ku} Kunz� :} %�um)~b%��n��a-%&d .�^11�121-14E| !5,L]{L} Laughl� R. V� iv> in� &� �h{!E*� !5632-563�!86� 4NT]{NT} Niu, Q!houlessV.$�:�reali u ary!�dxR�3A�(2188- 2197 a�%=�PF]{PF}� � ,2e:  7 aa^͐�A� -Per�_���$Heidelberg� �#0-Verlag, 1992.�S]{Sp} h Te 2 * ~quasi"�&� }�!vq�e851Y00C1e96z"St]{St} � � : CA0 t byu>.�%n�"A� -M(& Birka\"us���-U�SZ]{SZ:� , Zirnbau3M.R� ontan��4symmetry breakv%}< hyperbolic sigmm A� hree.� &�".zT]{T} >�)xs�S��T>��9i�� I�Cջ�3475-34�"e5TKNN]{}�y 4Kohmoto, K., N�ingale:� den Nijs: {e>��*�!FsQ:&�&}Q-R����4M05-40 p�$W1]{Wa} Wa�� W.-M�Micro.�,s&a%!V&L.)E�!q�� "�("' �a �ua>��14� � �6�W2�2>�I�un�"�Poisson<��=*�qdi%al>� at\њ�!6�6�365-3%(�c.�We]{W}4")$B�")d&Z�in }�ystem�VZQ��4= -1�\1 tend{thebibliography}N\beginB {99}U=,{GopiMeyer}  0krishnan P. e�$ ., !0rse cubic lawU"distribu� ��Ek p  varie�s, Eur� J. B��� 139--14�9.�{Bach} eli�)ŵC+of��c�i� x"8Sci. Ecole Norm/+pmBj300); V) from P.H=&ot�# (editor),%�"�x�s, sea� 6� (MIT��,ss Cambridge�n6��y8{Meerschaert}  M MD,@ffler H P, {\it L^(D=o#Sum�Indep�nt�"8Vectors: Heavy W ���#yeHP�8ice} John Wiley� ons, Inc.�>�Fama} E.�-EfficivCapital��: A��iew!5tEmpirsWork, A$of FinanceI2; 383--41797� �Mandel} brot BI]uU-�E,��"� "Bus%�36} 392 vw6�wRepRiA�4Repetowicz P,  mond!�M�l�sh�$i eE! as a�tim"$&(walk (CTRW)�[non-i=� M�ge�"wai��Gs,�ica A!�I�i+ rrec�(P�"8, Available onl� (1 September!�4�\{Masol�m}   J,��AQf)� : DiiEZinO#blems, $! rint�8d-mat/0308017; .Z M\ro M,h.i9-T!(�W!()� T(.�-A�. EIW� 021112 '%2�}�Cg!|sI�Slowlyar�:�1�.Le�� CopledPREJ�Be�&, D A, GovernaO�"I�f�anomal���eI##M�]� 060102(R)E 3u�Ku� Weier+ ssFl� sC, R, Hierarch��sp��-1=+�#innc� al w��� s. (I)]-�r f s}�I 2684--106,��99:� Levya'sVaryVe� Extreme e�s��f���}vy%G-�va)�0velocity, Che�(v �1E�28�48�012[Rab�(}  M&fW.��Eretur�t frequency.� ata: an e�Xstudy, �0a A 314, 749a9J�Dash1} 4 Jan W, Path Ii0ra�v Op!�s - I��a�N-�O�at http://www.physik.fu-berlin.de/~klqrt/b3/pa-/ bUurtesy��H.Rer2D@usielaRutkowski} 9�=7A*�3U Math�3:g�ٷ�a6edT��: T2  M M鷡}C}, b3pp+lin*� u"U�Ito} KE'8sas I, Shreve S (Brownian Mo!��S&I4Calculus}, 2n� .��)V7; WWW:1�.�world.wolfram.com/ItosLemma.html �E!�(einRaible}   , Term St%-%0s Driven by G�! a��� cess��9�al-^e,i]y�8 Series, pages:t/ -430=� SatoA� `}  K-I, WiA�-Hopf faU iz�.�;�E-In�ly Divisa) 2� } C& .�-PrA �&2�mko�mko S�Kilbas A� $Marichev O��)H� �7)���DeE���  ., rdo�gBreachI=ceQ:ers S.A.�3 �$Dzherbashya~. 4 NL syan A B,J -%.#the expa�8��f�5��'DE hlet s)� Izv. Aka��@auk Armyan. SSR S ;$Fiz.-Mat.  �U�"no 5, 85V8 RRWvR��0adams} {\sc A (,~R.~A.}, %�Sobolev8 ce�� AcadO)�,��, San�Disco, London 1975.rDauge-88 u,~MrqEllip�2"� valu&� �jcordomai��- smoothm0��asymptot�of&� }$"c��Not�.h�� 1341f 1988����-89^��)A�ry�k Navier-StIm:e�t�.�#m �s�5 1: �.���,} SIAM��\�a820}�� 89) 74-97.� FabeQE.~B.~5; ~E.~B;8G.~C.~Verchota}A�ita�Y��lem� a2� on LipscF1�},:'� 57 �08) 3, 769-793.�(Grisvard-85-�,~PFWpr�AH�$E9�Pit�� Bost�I�(, MelbourneAA�]�Gir�~ ,~�# Ravi�1 ~P.-eVE�F) elem��W%+65�F�,� -&= -NewF -Tokyo�62�Kellogg � e�,B, Osborn,~J!�1�A( ular�re�>�=�p%P!Oa00vex polygon},12y'%�21%�476) 4, 397-431.�kon-67� ondrat'ev!S��%F�aW:!ie�F 5B��1�co l".a"D=inta=(Trudy Moskoq". Obshch�16�<67) 209-292; Eng�*l.,TratMoscowm��@%.E27-312� kmr15zlo�2> z'ya% G., Ross�6~J5��E&:$in6 d)"�i�%,}6� Survey0Mon��35K>�,,�Avid�(, Rhode Isl��196w kmr2��qlu� associaH-��0s,?�2�Q32u�=� alr�%��2��KB�$'$=�$Schwab,~C.�sOn6��&p>1!�hydro�+s �B�!vertex!e�e,}a�Zs' 456e94) 65:KGunzburg�M.~ �jincompZ � vQuiow� >�����9.SLadyzhMW enska!QO.I2�qu><_5! of a ��I.�D fluid} (in Russia{ � a!e� 1970.�mp7��M6�DPlamenevski\u{\i},��:WeighA�sp� E� no2�$ normi�jC N  ���@.2�=2 �3�123E` 84) 89-102�!Fa-ߺG �icb"(on manifold)e6h},A blq#2] i! 85-142:�8ڱ$L_p$*_2.� of ����7:�T������ 2�3 78) 49-93N�:)�.GN�37}�480 D>�8b���?!��Green" E Schau�Aa�@s�$v/,j<a dihedV-8angle}, SibirskMZh�819E�!1$5, 1065-10s8� >c�inI"� H"�Bla�% � Miu8a-Agmon maximum�nciple! R�V �bP� he?,��INachrL 8 $8) 25-82; FJ :B[Is� Vol.�*� 4) 1-5� "� mp83�`&0first�6G !1&�)*k ofs?&9Xc�:6x piecewise�hia� C� Zeits%0�)Anw-; 2} (�,983, 335-359B3rt 2:z86) 8523-552�mp�X�upeli�== !@B�*� steady-s3 m-�j�T�� a f�$surfacax�317�"�Y r&{:�"H &H \"Uidie ASk �PL\"os� �|sc�I�w�1ufgabeC70Umgebung�@Kanten},_ �%� 38�@� 27-52 mr-0 ��P� :��$'sA�rix# Z� G 3!�L"�i�+� �con!�Z.�&�1M�8A�2002)�291-3162r-0 ��" rto:� "�n��% },�-�.��qO$ 7, 435-466�r-03a} B�{\ss}�  ���:�of:�qM��� 2g^�" B14�( �60&9&Instit5z/2" "�Vienna>�ZmN_>�of>�!a mixedZ� tU=��t�H.�Nazarov/| �) ,~S( ,�� "P Ubin M>��j�D,} De Gruyter Expo�:8E9zk1 %B� -"~R4.�r9qP5y* �4woɼ@ wY �,-Slobodezkijm a� 6 ,�%nsCen��cs��27}JJ wA 2) 399-42�%��S�@} %�,~L�PZ� irre�}�Kluwer"� %�s>0recht,?�!J56V[�+z[ %-�2%*j benn�Renn I� Tu�" R�?AnAro F� to Spinor �2,<1�inq�,}, Adam Hilgb,Bristol`2�0lou} Lounestos#�8Clifford AlgebrE%�, �}, 6FKO�.199��max9 xwell J C� Tre`% zCi� %M�S sm},�>s.1,2!�v�N) 1954. ]�$abo} Ablam4&R, Ozie@&Z ezewuski ��a �!Wroa��w!<r�J* �Q %���e82 &�j�Jh'|B,33 it A�!i!�icGc!��Bs.x Coulomb% Biot-Sav lawe1(anisotropica4, *�$hy)"�bf 24�'�27�296�u�ja1�:n� cz B, �6 "�<Gra�5)� \RR^3$},+'p. 28$Baylis W E*�) T5o(M�ic)Yln�:� iEngine�#}, �/ h\"a�/�cQ��mis} Mis�C{*\ K%i Whee *J�eGravit�$}, Freeman:+� dpauli�6uli W,�7��he��*)trum +�4d��K�Jqu�Sm��%�k��36}A 6-36H 26), z+ed��va�=r WaerN/B L� SoursJofF �Bs� ��4ABS}Atiyah M F�� tt R%PShapiro!NIQ %5�Mod3(}, Topology"�-� suUJ1), 3-qB 1964A�&�W{gre}qi!�WA�it Re�Tv�.F�: Wave& ;+)gerA#�A:2/bayFWM� na"parav,*)��j&},aEL�f�App"�C8)�c�� V��� U�bayoo��i� �Multi�sub��$\cl_n$:A�ok)�.{ �Ab\l �v%Fe���5�ji�theirB�8 .� �.I�R�2000. .t$por1} PortT3I� 6�2�alCoe(Group� (�� Stud�>in Adv�.d�_s),:a!V5�5� itz}ItzykR1C%5Zu�J,iit�2um Field� �L�!�� U,pe3} Penrose�� Rind��(./%r��� .2�'� %|1�*�(S!�0"� �L 5�pe4} ����Y origO"of � A)���d0blipo�Nap!�R[.� pe5Jp��cen�CprImeeRw ChaoG' olit��;FA'al^ 1�N581-61>N9)2"BH8�Bohm D@H:2B �G0&�Je��he9\Jy1baU�gy�7Bras. @\'�s�0(1985a9� Kl74z<tz�U-�i�(conformal g�TZ�1� 42-223F197��5�Koa|Tr!an>>�C^q�� re'tedZsif076��5 sAO�bK !�J �� �= ��u�rL � V<231-24RQ $Cw91} Craw� JM>s: not��Bsi��~ic�-+�)incar\'e�):��J.J(,  576-58m 916�$Ho95} Howe"U2su�-�:�%u�+!��Zc(High Energy" L *196� LD92�=senby�Doran�P Gull S-.2-)s,q$I�2���aF��1�7ceeding 'S�6,Max Born Sym um: �2,65�Ars, Wroc�7-=.�Bk91a�u rkovits N �A ���descrx'&�(Ն�p \c�4 ten.�& � }, Nq M�B35��193-20381a�u��b� �z�1� , $N = 8$ �Yain�8!�aH!F+-"!rz�Ain� B��Q6&_�� Wi86�KW�cn E-/ �-like���%�e�cm+:o�:r2�224�`�8=rmoZ8p1�� Motl&d C�9-��/�9 ng f� !ɧ' JHEP}�04�I -@(hep-th/0403187).�b1=�s �9� ad��Eg�I��- �?e ��bf�_ 4) .�605:�b. ME� �A@ter�Cve1 p%� �I�ŝN=4 �$-Yang-MillF"�M S w4Lett.-;9j116011?.�204��U�b4:h ]S0�5 ar�d2A �s}.a9246@ grscwi}I� M��Q�J HE5>�S�+ta vI%vo=]I�.II^� &i ���A/0Chiou D -W, G6H O�X H]Y��Kim B�>a�Mitra02)M� �n ive 0&�@al)� 9�1�6 ini-�tor6 �k&|CkD71} � 5) 1250169p50207i�A*� twis6} Bars�Moi6Picon�3 Ѝ$�a'A�d D��a� f�7R�<? :�2ŭM� ��,2006) 064033]�512348).�  *��8�b�YSi� Q�>!�� , ive%S���f.� �.��5n�03=�120��uYpe�Z 6��� Fm��3�E6��.V2.� %��� 1: Two��4G2Cw!yPb�8S � Be00��.3M-2 r.�6�� Dira&�(}U nsxs.)-m"q� �y�mxBirF]"w�KA� �,e�< RodrE guez A%bYamaleev�B2�gqic �7�k*� , overU��@�_ inedGtE�oN[.).Ap�32�D00�>> �2�hval�?�� � icorE8� ��Wbi�*&�>� =6ABS} �E5�m"C��ry}�z��*<  u�4coq}Coquereaux!� K� o 8 ;E@.�Neal)K#2O�4.#},$?.��n15B�89-39y >:L� ��j�.zke97}]�� -�&$ , mex�� �O�pin4=9^a���Z}-�7}Sm 9-4%;P-\ .�Gu�0 G\"urlebeck � Sp� ssig"�QuaT i/ebU%�9ũ�Sicist�@A�J.�B�@diana� ]� Ku99} Ku�Is0%4��Ro� on SH}, Vi�9�:e�?��{30��Q�Y9��!�\��I:?Mci:!�neuro�b� 79-8�I9:xmak/akY�(1,1)Hoiod�ofyv�!)G�Ded (anti-)M\"obius&m �A�6g th�P, Techn�&e59g$eit Delft, � e8  5�o�F.�� A tu�h?3n�9g�� (� ��omplex�(y@!jTR��n8s (Warsaw/Ryniaj.94)=> BB{"��,137-150��3�.:Zsaw�/6..�cru� umeyrolle��Orthog[� fP al}E D�VaC�Pmpany6q��ri�! ieszqiA�NuNi�iQa�&�%by�EF.yin�0��P.&$�'� %D.3����J.�-G z��% �qyqzi{� � @>R C]~_SfPRotesize��+v�+ rol1^? �Rw�5߭�)�1IIQ%"�y  SU(2,2)�+"�A ?%��e� remarks} 6i7:� cart�*C ��=O� -�W$US.Y1961��(��(�B��(��(&1 dz�u�P Ay�!C�)t",U!�. �G. Roy�LA11�#610-61�2v inf}�Geld L%�vf�)Die Wel,}*�;des Elek�vM(�9llgem2)�_� s�i�S B preu�J�FWi�-�ikPR� 3 (193��huang} H G2�&rks�p"#^ "f>=J,&.J �i� Ch��f�": fig}�r ueiredo Va"pelas��O�Sira E%��$igues Jr WլCo�t,q�ic��n�"}, {I�gJX o�W�L 371 !�>>p"r���%�f5L.�x ��T��&��&��&��&��&��&,�&E��&}�hen.�{� &(� }, G> L,.86�5� hes2�� N� .a3Na,Observables,"�]��R n� �_YIac��J( {16556-57�7� 2�66�%H� DŠ���� A&� �Al� 7 (S�97-14�"97�%l15646B�f0�Fy�h�*�0 inY\P&�,�"� h�)w1�� Y,"v$,} 50-81,�5.� � 6gP���m.c xB����9��. in  02�2)�J��/��/'�i�].f].u!��1��1yv} Y�~J�E�{�e-Madelu=&"��e�] dium �18-��194{�8tak} Takabayasi&A2 6Gr,u�matterY2�2 ProgNk" �� �W1-8['57�=� las}"aD*�(L&�(I�Ez� '1 chap�99����f� ��]3e!�.�p�pqqU:�]3^]3em .�, e�Y3�Y3�Y3�Y3fY3 AU\VRa/v<>a5���N:x.�2���I: Wey>,�1b,6{3,0}$�9 0,3 �%�#B�.�lr3��3��3��3��3��3��3��3��3��3��3��3��3��3��3��3��3��3��3��3��3��3��3��3��3��3��3��3��3��3��3��3��3��3��3��3��3��3��3��3��3��3��3��3��3��3:�3.y�*A�{�"W p:q�r�rr���1��1��1��1��1��1��1��1��1��1F�1u?L�LL��L��C25,�"���CF:E�.5�=z��2��2��2Ό2U��f�d�#7b�5���!��#�oE{2i5���2��2��2��2��2��2��2��2��2��2��2��2��2��2��2��2��2Z�2�<�=in "�(ed.)�Q���N�N�NFN j�M!6<�A.T�(����M&�M�5���4��4��4��4��4��4��4��4��4��4��4��4��4��4�E�4, �4/f�4R3�f3} \set�*thb 4emsep}{-.50em}��81} C. Crncovi\'�<E�< tten�@� THo Hund��Years'i*#$�/d�K*/$S. W. Hawk�-)/ W. Israel*�Q UnivL9Kse�*"� �86\G2} R.C- s-Fu*[vil��C� .�<A��.@, 3571 �C2.�G3}�7E �D`sed,�!+tt)*0Vol 46, No 43v,: 1902-1512.9@46K�=t�`�-j"M3M.6 L49c�0�}/.��5� �%GA.�,!�2�Q���  gڦsa�"ic"�8,# .�QinB�EAbSV�4"�1ReG<, Nova�%i[v!l2�6%!�v$akov, Nucl) B ��8)W406; H."$w)�7 B 15Y+335=�7b5�(�+ Can�?al}?malistd�$@Nambu-Goto p-bran[r�;- ss-B�Qt t!WJS!hN1s�� to,�r&$Le�$,RB& 8} BI�7:�1iwB�&�D�Ft�[9?!�cosmicG� Maivor�-�D ERec!qDevelop;%�a'�' 99�hxro �$nd Mexican&Iool]s9rR�` (Tlaxcaa��Y )} ($|kaluza.�ek.uni-k�:*|2MS) ed.A� Garc�<4C. Lammerzahl, Maci 4D. Nu\~{n}ez (�::�<4o U@);e�.\\Q\�@04�&48�1lTu�9} ^r.�9B,���h���/D10m�po��!1'GnOM�� 51, 67,@9x*H$1} K. Maed DN. Turok D��,aS002, 37�8�0D L�4sseau�P.��E�r� M^5 v. D� 1721xj�6K�-׆Canham��/BiJh26, 6KS070); W. Helfrt�,Z. Naturfors r28c, 69�97!=V��2f�10}.�,AizenmanENSS3d.\ A>\ ElgPt( S.\ Naboko�H.\A�ϲ%G@tolz. \newblock MX�t {A}Ψa�{L}.3�in {R}y�>��{O}g0s.X"Pd"�</�23,�G�\9��S} .��B� imon.]"N~!ha�$Harnack in $��6�doN���8.]��A�,th.} 35(2):�s-27a982�+U?<a�DJ �d�C�n &��.]%��ͥm�<, 52(3):197--209u�5�Co�� H-94� %FP.~z���sA�&��,��HamilA�ians} d .��F�J6��^24:����Fw �HK-Ol�� EcկIcF.~Klop2�H\�� "$�1�s >�}�%�o9yuc��(4):1799�2  �HKNon�� �S.~Naka<�.���{W}V�qTtedJݒ1�J�.b�e In�M &ZI �ޑ!�12(1):3b� �"� r� ias.ac.inՇ sci/.�Z-NAZ1��.�.��$vM�6!L�{M�@U=v g���vIm/ {2� }YTBY� un1I+ }, 70(21Ž�30e�2�s8CyconFKS} H.L. , R� Froe��W."R�7 B. Bl ^�:*�e'CB�7X��J.� Text %*A~&yl&� -ey Eڇ.CZng�B6�l(DeiftS-76} A*�B.~B���de"��of��ite s25~"ki� �}y &p��9te���hobbP1.�.�eS�#,���aM},��(3):218--238�76.&N -80" .^%~cU6�of�C�pc��ge����.9�N| 4(5):417-�o�8 �{ �-��M.X��It" aR"� �M ���i' �ge�N*o 1f"@: (Pragu+ 8.+ 108!�Opw�e7y � � a|9 20��19z k"'l el!9CO:KM� ), W.~�a�0I.~McGillivra2-23�2---m[�ms�Ijerm: t occu�ns�.E�9�GeislerK� R.~ ,, V.~Kostryk��R.~��Q.S Conc�lyATy�� K}re\u\i vv" 6q.I%�B� , 7(&111%o� ���K�, b} F� �A%ei2lb�� {A(Gson} m^i� A�n�s.�(��Tma.utexas.edu/mp\_arc/0�6� GeszH�MMe1� ϜB Mak�t�}��t�ov.w�T%�lW!�cZ�����qk*��pr�0:HoM�y: pn�rplayM�� (Leipz{�1��q� 29u�CMSADf�joc.x� 22�\>�y�v"a�I�2�� -04�^�,�|F�.V )K� �A"%Z� .Th�` y�  ��b)�&8 e"�.}�n 95n 12--47% Bn R�! ep� no. 01-13���aubB�S%D.~%N]An op��l"� bo��� &VzD ce>��o*��F� > 221�%�&�%�2 �f-87} �t.�S����&$�! A�%�3��Q {Laplaci Kong� �zO ��.a%�) A�S��101:5S512��6� �9bZ��lstax�qF�� .��&z u�� very��2 B��&���2 :, 12:�39�6Q �96Z�k "i  ��l.�� alloy-typ!�"΢F�( . Z�!22!t7-1tgxuP ����U2eC��0F�M�z longyg�G�mRhB�N ��(3):495--507AR�SN�a=���2 ! �22Ao"�:�� b�4�om� *nE�C }, 6� 241-q���&ڙ$�wwV�.�)� V-02.�Iܐ seli{\'c}.�U�% spaq��;o1M l��E� ���'�P1Q1�!2.��FR, �-bin/ "42�"� � V*� .\�s�BQ��* S�M&2��92�H���ksi8�WTH Aac��; 2�� �^�&� of�� s��!���Z�.���Jt 76t 00--11Ʌ2� �S-01b}2��ZO R�~6c��F���87��{-2M96,otaniS-�i} SA�N� 2inQ���-d�ha"õ� {I}{I}� {C}��TGS6�f*R�f1019�6N Lein Q��L.;HPibEpf^�%sg-fq&�.WE9 J.\���1e } 9!� 16�7 �3�*��$RozenblumM�\��gaard��!, G.vE�� aE%tot� ����ly����a�Ka Z� �"�"� ?aYful%�k.��)�P=pal2O��� � 8(3-4): 6�736� ��9���Z�" �6a�K�p���A�e[Иla^� ��Z�P�208!�17!�9B2��cer-90e�V. .]Hanke.��M.\�'hu"M�selfadj�^_�1 "maigal"b6b"� 12K�ML>8�P�nA7))},/<529--544. Dekker�O ��a�6U_$Pushnitski%�A.~.+6�%�q~:�o�̇aic=$.T�6OO�80(11):5578--559� :��BT"���.j^� �^Q�� "�u� limi^�v{az5iza�uy2��R�A.N�E (M.~Ruzhansk6�v��� {II=�P}Tfve2=F���! 7(7-8):13e�40� 2.���W-02b} GJ# %RlQ��-�q� sus B�U�:��jdecrea�QXicn* Jt$14(10):105w072��!��Safronov��O.~����Eڢ�JFK8h��-16 2��-78} Rb&�-iI�S�*�i� u�a�%#tK*i~ �rn�&"� .�k\\��J } 30� P,--2�78.b �9c�F�Ud�9i�E� ���~86�z? 6�i6��2���/�'ss x�,&�& �N72 �82�Fq6s��$B7 BullJ)�$(N.S.)} 7%F44��)�'&!$Erratum:``^s"c!�t1� 4 p6�H�939" .�Effic�Iwj�.<�%��. HenriP� car\��#"8:���!,2Uto�# "P�#�#.gS&8by obsta��& capaq.6�J��4�'E&196l$.�a�._? id@d&u �3 ed {D}u�ZV a�u�vIBl5ol:u%70�~I15, 58nIAJ" 5}%^�A�� verg:.AFor}�D5 f�� .� B)�!W���q��vJ� �!De19:s-28�2��00bf�:hr Bc&BA}���� ls ��$�u o2u�.S%�Ar�- �(Basel�75(4):38311�2 �1f�aF�: A��@onѠ 0��)�.�'2YnVr��i.ɤ*td.�6�u��YiV�c"\'c.Df\$R%�tdf�& ^� F�N� 59���y�u6́J^�%(�F�� J�D� ��#In .� illegas-B�_]R.~�� Rio,��or^hem6*� s (Ux6dadF���AutonomaI`�2oE�1A�* 34A5�a<,emp>� 98^4FhRj4.$arXiv.org/*07062�i� -81}� .EBsa � {DOS\(a���nys8.5�&��� 4:�+5i82 (.-�R6.L����.|��m Ł2;��%�b}�5})\�4 �zjociety:k*6���b&�[Russi�Poriginal: Izdatel\cpr�� stvo��k{�ter�.skogo 8-�8et�2�.l4]3N��C$f�299}�U([AK81]{AkKr!�{M5} Akcogl�3$U.~Krengel.ZE,��^e$�~ad� � � .8%�J4in6&�5x23:�6Ś2([AS82]{AiSi� M.~�2e�NN�2{H}V�2��{\"o}��e2�B��(d6`35:�$7o�2��[BHL00]{\0~.[0.�M"&*.���Y0 .V%�Nd2:BW0� K]{BoeKir�B%@�A"�2hU}npub�9edA�bJ2[BK%�KS "S.LB�%^d "�E�y� �!�6�^eP}h!20�=� �03��,2�2���Zutegrier��Zu��sdicht��n�DWIoTe�x��$zuf{\"a}ll, i"C�n "��en2�PhD�s� uhr-эtJt Boch��20���{I}n Ge�32�R�BraRob�OA��(lzD.W�hbie�Bi P2^B�%��5al* ( 2: yi���_'es,6 F rA2�*,��l 6TBS87]�4Sol� ��S.}� �4Z.}� omjaFBJu�-� 1��HiF�t�ce2�Rvn*in��2([BSE�dMSA�$A.~{BoutetVonv��aw^Z �1 c"� m#�� B�*� �#0:87--9�$.�[BSa�dMSe�R�,2���N�2*t� �t�"�typ=��"N��ode6�  04-16.� [CFKE# CyFrE!H. L.}&�-~G.*�-2:*N���k\��Y"2R�7.� Cha99]{Ch��Z�2Sur lx ns�'e� t{ g e d' t�5�9Rcla�)ont� /n,��s � d ~#w}9�pour u��"e/�rfa dDB^H:�8Ad 72:9�2"�:�French: �mCh��4��5��G!�4��:�B�" � \9�2f4[CHN0��N�{�.}~m1 , {P. D.} 4e�Zm $Lj��6�,�=>�3�U� �O%EQ�c���GN�B��B= � &05218:113"N'6�HKN02��}z,"*�j� &0"��$#f�Z8"� 9�%12�3&�3&{$CL90]{CaLa� R.~C/�?J.~La�BeJ�-��6�­��2[CSibSa:d%J J.~Sahban2%�1��!t*1&� As �}�*ni���V� 5�.5� �=sDav89]{} {E. B.ѾviF�H;kee� �J �2�CUPTpmbr��2�'[DS78xSi 2y\NR* ri��)"�9�1��aM.���; �|!�=|BQV�$63:277--30W(2 [EKSS88]{ �4~E��c6h1M�0)���N���.z�{��B��l)����& 1:12!�126�I8.��ao�aoH��"v�9"�s"h�i+�l but�# dl�i6^A2V|128:6q6626F�HK�HiK�9AP:nz%ZH.~Kalf.0SubY�� It��A'� _*�A _$)�Aj J. �?��&��  04:1<513�46aHK�a HuKi�aD2$�Wu 2�6� (�a6 l*�("�, �o^J1}�(�~28q)�^61!� 238.X1 .�[J&JaL�WV.~I��Y��s2�Corrug'm � a.c.�hum. �V1465-n=�8>�1] �10#v�S2���B�V�459017%%2JM� JaMo 6% S.~M��.m2'��I1.+%$Z�08:'r16x"[JMP98!'MoPa98=)F�� L.~P��.|�#=ag� &���w=�.:Q�W�.@i�m��� (Minnea� , MN�4.�9"� IMA� �"F$14� ��&� 2�D2^Kir�X*�,.��0fX:���.8In��HoldeA.~JenshN;N&�B[ "�&} ��ofIZ%�|!I�5 264-�2�9 ����6�KK]{KiKl=e^�4�E-�E behavio;� B icJ "��*t u&Q�*�KM82a�rMar82.�0�M/(I�.�M�.�ta*!H9�\->+�m� ��._e�"�qA6 5:2��215�6l�b�Jor��eEyy!w�-w�L. �*� 2��F���3iA1�uV�39�3��Lh�evi�A��{L}�"u*�,F� �fMT!�-�&�B�V6 89:2�<NB82& KM839����גtkE'){ {�=�"�EI�\"{��Du*��� 0:12�!126N�re85]/7��V7{\�iem Ergodic theorems}. \newblock de Gruyter, Berlin, 1985. \bibitem[KS86]{KirSim86} W.~Kirsch and B.~Simon.V`{L}ifshits tails for peri�Tplus random potentials2@�\em J. Stat. Phys.}, 42:799--808,�6.6�7]{ �7}��$Comparison5��the gap of {S}chr{\"o}dinger operatorR�(Funct. Anal�(75:396--410�76��00]{KoSch00} V.~Kostrykin and R.~Schrader.(The density�states1�4spectral shift.))o �\"o�� Rev. Math9�@12:807--847, 2000:�1�1��Regular ��urfacJ�. Q#:t,187:227--246�16�S98a]{Kb]%8, P.~Stollmann,%QG z.vAnderA2,localizationE6)a schr�>], with long +$ge interacAF�CommunB(95:495--507AR98B�b �a��LZ�perturb�sAvu�2� jRi�Oper.%^$Stoch. Equa+ 6:241--26e�:�W03a�W.� D.~Warzel.�L6zlcaused by anisotropic decay:En emergence�la quantum-classical regime.e8math-ph/0310033Ej3.�Mez��D} G.~A. Mezincescu.K�, chitz sinm ie��5k�y.? �A2TV@(9:1181--119J�XPF92]{PaFi92} L.~Pastur%j$A.~FigotinBgS�t!>m��almost-F�2~Spr�W,�|92.HLRS78]{ReSi4} M.~ReedaRw�MethodE�modern%� emat%�Pphysics IV: {A}nalysi..�2�DAcademic, New Yorka|72|Sim79]{} b���ionale�greT inQu���9.(�2�82Z�B� semigroupF�Bull. Ama��`Soc. (N. S.)}, 7:447--526! 82.$Erratum: {�G{7}:{J }, {1982}>�5 �5Z�mz*m�H!߭�A �"38:65--7 �2 Sto�} ...�8{{W}egner estim��B/$continuum �S�s �* some� distribuA;s 2E�Ar�K%�!�5:3�311��2��1]�1j�aICaught�:disorder!�}oundxinq�media2�Birkh\"�a�oston��tend{thebibliography}� \beginB {99}&� ,{huang} K.~H H, C.N.~Yang, {\it Q��Mechane�@Many-Body Problem�0Hard-Sphere I��},w  {\bf 105!^467--775 (1957)]�8{lee} T.D.\ Lee �\ �F�in� �� � is��"b� 1119��20� =68fetter} A.L.\ F, J�Walecka6?n ori �0Particle SystJ 4, McGraw--Hill�!~71)2~ Lenz� h4Die WellenfunkA� A^�Geschwindig\-keits\-verteilung des entarteten Gases}, Z� )�5�O778--789�292�(LY1998} E.H!�ieb! \ YngvasA�EIGrE�� e Energ%�_Low D� Bose�6�pLett. \textbf{80}, 2504--2507�982�4dyson} F.J.\ D -( �->�a2�Ga:M�! 20] s:�yck} Mo ick rTwo-dim�ů)���a1 Core�ont � i+A w3}, 10a, 1073y>|hfm} D.~F.~Hines, N.~E.~Frankel,0J.~Mitchell, %�~ disc~� �~)n�68A�2--14|6h LY20��z�l )zBa Dilute%(D=(] 6�U10!509�> (�). .�0baker} G.A.~B -�S" $y Structur� A�P*�  Series w �J@e� Ferm� )�}, � od2Q4�47�31%U��_ hamm�_H.-W.\ H, RE� Furnstahl �8Effective field��j�d)Z� s�j Nucl�Me678aS7� 94%K02QRSf� T} R. Sein EK!�HThermodynamic Press-S5� �e] in prepa� .�ru��} ��R �a�B�@. Rigorous ResultA� World Scific!d96�robin�$D.!dR  lj��iR�},"�  LeIYNo\ine`$ics, Vol.~�N!�=�,anal} E.~H. �LM.~Loss �h },BU mNGSA�M.\ Graf��,P.\ Solovej,iJ(it{A correlE q A applic s to"` MP��Coulomb� �U�&��T }, 9Ak99��42k LYau6N H.-T�Qau-!�Stabil�& Ia  of R�vE/� �,N  �11A�1�21�d886tliy�!>Li, S>�O� i&equ%8 ��>,eigenvalue p; n�8�3��318A�83� R� �!f� 10.� acgh 0E.~Arbarello,AgCornalba�Griffith�J.~HarriF� Geomet�D{A}lgebraic {C}urv��{V}ol. 12� &�. 8.* {ba97} H�� B��2! Z Abel's!\�5hallie� of! ta fVi�j.I8Cambridge Univ.��,$, 1897, redted 199>�8b�M hype!j$iptic sigm�.� �0 Jour���$0:301--384�.8 {ba0f,Multiple&5 .{� 90| �,{balgib03} S�b ldwiI�J.~Gibbo6�H2 redu�-�4 Benney momentu?2�%J.��(36(31):8393N13 .B�4��(igher genus:���AU�q�v�7(20):53� 5354�4.�bbeim94��4~D. Belokolos,8dI. Bobenko, V.~Z. EnolskiiR. Itsi�0V.~B. Matveev.�%?Ae�o {G}i�a� A}pproach��@{N}onlinear {I}ntb ble {E}��6\y�B"�96� e02aB�e�6�.�R.$0{A}belian {F}q�A�z allyB�S}�, part.e%enalA���"�Hc @106(6):3395 --348F{�b�����I��8(3):2!37I�22�esaOE>�6�I� alerno.rWannier��!vel� one-8"�.:)�.K . A:%�L. Gen.}, 37:9685-970 �4.<arXiv:30d-mat/04014402�0o95} O.~Bolza.=��first a� econd loguh� deriva� �"2� $\��$--R��R� 17:1��O8:}el97a&(M. Buchstab*N�D.~V. Le.�6�{K}leinai��. .?Inn2�0PS.~P. Novikov, editor� em� itons,�V��^@d {T}opology: {O}] ,{C}rossroad}a� ges !4. Advaa� in Mq�(, AMS Trans� s,�  2� 0 179, Moscow �  er � A�MarylandT llege Pa�9� �!�b��N�,6]( {J}acobian��2��I.!�KrichevA;6�Review=]� i2,�ic� (volume 10:2=�(125, London!�1!/ Gordo6Breach. .b el99FB V.��a�^�R� al b ogui�a�PU�.�e�Funks�.|  i�$33(2):1-15�9.9]m in:Dc >Appl.;1�, no.A�83-�,]:l02J�n�$Polynomial: a��a��6(4):18���2��6�2 �A67-282^ cl55�A Cod�t-�Nwv�.u%�Tp!exH{O}rdinary {D}iffer�alb�VW!�55.� du81 A. Dubrov6�Th2B %�no$ f Russ~S ya36��8=�b$"{eg-rm� J. Edelstein� 8G{\'o}mez-Reino�bHMari$\tilde{\rm n}$2oBlowup mula3!@�,dson-{W}itte�g=AfVgr� $hierarchieFO Adv.%�.� � d"C503--54� 0.�0hep-th/0006112� eepP (J.~C. EilbeLN�$E.~Previat2� On a� erY ed- r9 - gh780at�#faPrinc�sa*�&�y2eWiley&CA52d! {gmna�� uckenheim� %os !.SE NewhouseB�D�al�� 8C}.{I}.{M}.{E}.�#s� ssanone� 4Italy, June 19}1 ~8� ProgG8a�u D}, chapter VariousA�A}�')#*� {H}�=2(ges 233--282� :p8asel, Stuttgart!O6' im75 �%=��>��'s*�$� 0a finite numb) f lacunaeNmultisi� �[�4� Teor�. FizA�23:51--6 '72 j#R.~Joh2�Q*.�rotg ����$&{"�FK��6�'}, 84:4G43�&"#�kotani�#S�) .� Lyapunov ces det�ne ab��elyC"��EFr�% *� ry�!�2�F $"]&,&,E�`Taniguchi Symp. SA Katata�25g)%}��r��A��az6�*WLehrbuchz��ta en2Teubna�LeipzigAɡa&�,&�by 5_66 loop�����E $g$:� stig� ��"#*i� ela�#B�J�om�*�m=$ 94:1" 2.�matona6.�%bY.{\^O}nA�.g�H i!Y quan6���${$\bf{P}$}N4{K}d{V} flows:��S}tud�2� c� s aAQ ext "i {E}uler's��|� of 4 )R�Y &Z}, 15� 55X 28F? on!�Y.~VD�azxE�+e�sE'&}"-!)�tw2� EmGlasgowAu h. J�4353--36#06�onXҤ6s�, (�b$n Appendix��Shigeki�I�: Conne"���fo/!�Cantor  of Brio�# -Kie�- type )�K%8Proc. Edinburghlh.�)��0�'toWear.�p2,� L�+B,.�.,lJ��,of�#b(edb %�%��bod��xi�+oF� R� 75:1�"19�: $seiwit94a}�? e%E.~F .�El]1ic-magnedua�, mon�e� dens�.�confine8in $n=2$ supers��#(-Mill2F%n Nucl��I B426�e7�����940706�b��M �s,�%!chig2 �y breakin �� 6�qcF�F�31�484--55hN��&tweyl16�Wey2}U� die {G"ch*M(,von {Z}ahlen�L.��iJ���Anna 77:31�5%}16.� zmnpaV� Zakhar� S�+Man� 2�I-u/. PitaeBMESoŨaoryɟrwca."!��2D Nau�+A- N�+6��+@IZV} A.Yu.Khrenni�LS.V.Kozyrev, Pseudod.�a�@5 on ultra�spa� �� �le!Phttp://arxiv.org/abs/"�1412062] Vl1}�%4Vladimirov V.S!��:źr��,p�e�� over!w �&,of $p$--adic7 s //�a�y�$.~ 80. v.2 N 6. p.1�-12�bBVVZ �>�, z% ovich I.V Zele" Ye.I.} �A�u�A��al�<ics. G(apore: t& ttt&Aeq�Andr3 �:�} Non--}.imedean6}it� �%. I�:Q�$Fizmatlit,K63. (iny ian)y��1} )�Yk A.j�: A-Paradox��B�%$Bi�i!"M�T. Dordrecht: Kluwer Ac2T e�lKa} �Alb� io S!�@ Karwowosky W.} A� walk on)�.M,�K''S'5R �ess--��2a,�$$ II '' (S.{0, U. Cattaneo� Merli�Eds.),S.�5 rno �01), pp.61--74F+�Y+5= Kochubei15 A.N.} �--D.E�!��s ar BcF/*s��3J rcel Dekk(P+J�2}A,>�(Fundamental +aߕ � eqi�� s, r�'�%o� quad*c� s // Izv@ a MBiE��ae��8.62.� P. 1<�!Ya� u �h�t} Wav�*)�v� ]X��J!//qo � Izv.!@2 �6. N 2.� 367.z�012019�8Benedetto} J.J.,L.A�let�`ory�,23�mI1r�4,� ��"m ic �, �-3)�_4E� 423--456N� 1} R6�ExampleE1}!� � � s,F��.CAŢ0312038 rnh�W�U-� �9}IL��Fٍe+��2 �//!&h���!�4%�138Ae3-)( 322--332. v]303045Y�trudy}Ex�, �Z� ���: � �.�!, TW MIAN, A�45-�$ p.154--16�0403440>�$V.Al. Osips V.A.��v,ɱ Degef te U*���u=J�k6##y .�ABKq�Av n|, Biku� A.H-�%>}� �"�u5�y�to� elE� spon��us "t ofG "� //��*:n$��9A  3i�$8785--8791Z��9904360Y PaSu�PK?i G�$ Sourlas N2�&)�rep6��// EuropP� J. B��0� 14��53 =4^�.� 6095}� ABKOm~^�J�, MV%�.s M7!�RP�s�e�< H�sES4 Landscape�5V(&ať� 35%�-189~�010650.�ej21�ziL �,�Qe��8�*� � eG��or�al h148macromolecules.b�. 55--6.�V9ng} Vo .�St 44Class."S7Gravity|987�/ bf 4�5$. L83--L87Y�,Freund} L.Brb�9 G.O. , M.Ol06 E.5,�' �& � 1.����02,/08) P.365-�4f� 5�: �ER  um �-��d|.y%�nconsc�8mind. V\"axj\"o*?&, , Sweden: Uni���2.Serremv $ J.P.} Tre!�&O/�+:"�+ Verlag, >�KF�N.KolmoN3v�0V.Fomx"EluEmt�# "b%* R',� a,\6� #� V�0.v:"S ww*3 T. Whitt"0� G. N. WatENk$u�of�ar&^ ,, fourth ed.*�%��%ew3 1996* gr}A�Ddshteyn, Ryzhik, T+#%$Ql"h( A0Pro�. s, sixth s� � l2 D�aam.�7A�ews� ~Ask�R.~Royo4ecial� �.L2� :_Xtliouville} T.~Curtright, G.~GhmB4ur, Weak-couplC'� �S6�LSE y<L�9 B 13A984) 5$#me� 4~Lucietti, unpz ed nD5.V2�v29R AAB:��4} A.K.~Agarwal�3nd)dD.M.~B!�oud, x:it{Ba^( lattice}, �UIa�#. �X5bf{51}��7), 5�<2� A� 4} G2|nM��1s�8 R8"(s-Ramanujanuid'�}, Pac|�� ��bf{114 �4)"t(�'-282�!49} W.N�1��Ik!�RogaeB�!�L�) �!(2)�50� 49),�+12%( BMS:6!!�~Berko�, B!�McCA�A.~SchilA��$N.�e-�pairs��Ba A�228� 96)  62 (�5121822�6BM�4j�5�C# ed f�:�f� onic� res8s ch�%k$$M(p,p')$ �X imal͉�iU)��Y~37�, �%66��36�9-we�wM�Schurf����mi.�AV ��1orc F��19ij98), 3O�1((alg/960702B�W!��� S.O$G naar9�QZ%� Bose<}��coset-�\ $(A_1^{(1)})_N \times .{N'}/6+N'}$!�N*�;BU� 499} [PM]�u9�u62�!499�! 262� Deka:2005� ~��D!{si?Z�;Dobrev�� 6} V�Q 9!2]=Verma!� %.6�ira58ible highest we�� m�(�_=i�žY/�,}, In� usthal�L�eeq,s,�"�"�"�Finɷ�&�4, pp. 289--307.� �!7ZC2�af�5&(Virasor& �-�-}l>��Circ.�. Pw3moU�Aa#42W �a � ,ٓF�unita� F��%� �z��@��Y�1A_(᷁�R,12CDa�8{A0D{\" o}rrzapf�� embet.E &�? �y �6�fl529�^�r639X 5}g12165)2�EG�6�^~EholzeM.R`*berdiely9U)YtZ r�al �EY�� i�6v%-G 97) �8�6011632FQ�@5} O.~Foda, Y.H.~o�*u0&���!��6�!TInt � � . ��195q291--231�407191J�6z�u6�wB(� from� -5� tA/io�Fz�2I6�6S'16�FK408086~FW�|1�T�BWelsh9gicombin� of F�?ster-Bax�� �l:4(Kyoto� 9}  103,� g(h.,�391�*�Häuser��t�E�HMA�02�GKO�6} PGoddard�:Ken�.Olive�I�yB ` 5�: E�R"���* 03%�8!�t31,�H--119.�K!�(3} H.~Klemm�E�=diagramU�R�A�� u8K&2(a�Print M030606 �4� p\8!�P2�irt!x8B.\Tit��&� ъ� 2!Sa�I�%/-u(.�  $N=1$,V�ݎr�-��;$1871--1906.�_ �OYy&�qB��$C<1$��6�  E:conJl �a, rog.����: 7E �57''76�7Paule!u5E�9pOn.c)B�BJ� A�T�.� ���282_=RY�(7} F.~Ravan� S.-K�KUMM ar�'ari99�N$7A o�b�HB��(�202--202�)S� �� wi�F�H.$�a�eno�!�,N=3,N=4�#5�Ur�2T*廡.F�8 O1�`1�&%��L.J.~Sl�**KA newv%of!��� b:E[�+inf�-�a�Z 2i5B460--46�-�12�A. >)F"X>�'a�2��W�cteToO%%in Memoi�AAmericanE�"!So�y (�(O/0212154 vSR#�e\def\Rom#1{\uppercase\expandafter{\romannum�5 #1}}4@u#1{{\accent"15 ,cprime{$'$} , ^O1.{'Fhn20C*R�rma2�&Bochne�)��L cel�k plex�)nd.y�8R}icci *a�j.'�$Discrete�'put�*\/�bf s ��5%72Gom!e19xTC&3(dr{\`e}che,a,Y��(I.~Yekutiel2+T�'o�!*Hec�u�;�.� planar P A*oJ|'i�Revm��6L 2� 67�M672e Magnasco � M.~O�� .G>nMbub� raft="�[%o PhilG. B�5*�8A922��IUZ�C� l� 6;pa&J'V�-�397--422�MwUhevP<0<A�ly.�Qa�4 *�Ig��:=�vi .J%;Uspekh@+.�5@5�]^ # 6.�Negami �S.~ .] Diag�/ flipc ���W�Vs�&�Z�D ve2�)In: ��k����� 10th�%kshopK.�GFqU �/. NsUrfV�\ R �!�B�."rV%FR�vV(S79} B. SimD�"Tr�eideal�At�A*C}, f8Av7� &G Thir�%�0 �22<f� sche[> E�ik�%5W�6�wehrl3�  W ] Thre�! ems about�muCo�Cg&d"�[ Matr�=}, Rep�i�& 1�[1�816�U76�CV\#f� KST2*�,[AS1]{AS1} R_ Asherova�$Yu.F.~SmirCB"?Projej#:I,Clebsch-�J(an coeffici�foru- $SU(3)�\nupb\ {6 6399�h29� [AS2�2�(ysame, %% ��i�itV��&�e� s} (�%(, \usmn\ {2 �2h282�T%ET>F,:C%VV\"Tolst�!��2�&�,�a siX�J �%�mf\ {�!7-71e&�/)6�%GA\bH��NW��.\ II�Y�?&1cheme�� S�v lowea�Yb.\�% #�T%  $T  SU}(nIRt)1�7.&519j3AaT3nb�Ag cr�Von �sE� $u_qa�E�RacahB(�( r $s*2%�Sov.\,��\line�-[0]Ato�N�!\ {59} 1�bk 17�01807 \,[\yafi %�4�18�< 872]65%5�1.|K  ytL+ulae�,$U_q(su(3))$:8 .JN]=,:6��! �(80x5!� (.QA/0103187.�BT]{BTb`erezi�DV��ij�$Grassmann i�2$UOSP(1|)�\A� \ {7��8��4�[42.6DT]{DTg;-D.~Doe�CE-6��# Adjo4(``extremal mF ors": inde~os�!6 �P)z,l(2,{\bf C})Ey�P���1[ (H�\ 6��'" e 7 92�6Ri�#Ec[NJP+3D4 ~229�D*�.[KT]{KT1�2$M.~Khorosh�o6�EB % �Cers5! R$-maxE�-$contragredᢁe (")�lNG�ieh^edHic��44~���S�\, .'%>�X g!�$ $U(4)\supc'U(2)\oR'  $�A�m.��G5�},�2~"*+347--35.�LS]{LS�IN�Rz;<NM.V.~S:8v9mA onewZ��+% �f��act Á�\fuaa\ �_7�47-348��p 8=r8.� L]{LYL$-O.~L\"owd�/q&ADr \]um�7�/s&�eZ31*or5)�reE 36},�Z64) 9�L97*3[M]{M!!Hol2 ba$n��J�sy��cBLie�z��� �����5�61.T N]{N:j~Nakashi�1�(���b*c p4�a!�2�529.�PT]{PTrD�Cle#PV�F -*�H��������4 $U_{q}(gl(n/1���14 +�w5�#55.#P�@$} Z.~Pluha�@A novel DDachFa]� !��@ y calculu!��!les�0erVYpAi$PraguN 81 %%, 698=*�PS�`:����`SL Y�f��.�"uJr�2)$�t8 technique�@czjA�B 3y �!53"6016�3]�>l ��6t2< �#1��W 9�p8r<0\jopa\8pM 86 [2.=Sh]{Sh} !hapiro� x� �x:A�Aa2a.E��!Dj�o� 6�"16� 169.C ST]{n2���V{N��usu�1e\?qnmi���us� �> ving Yangv'&�e.1Se�F"O!QEDh"ycal�"?\Niederl�O Fich+*.` 2jBTeaneck] 09�<-35*H> [STK�p TK1}6:,:7���]Sh�^o�JM�M of�V �V� ogQ5ZI Չy . I.: 6A�* tens>� sjnp� A#� m� " 2E�  9 980.JSTKtTK>q2o�5�y�#---Q��a'b7<og8-A��.].7 , $3j$-X, $6j$-symbol3n�%ir^FD�8--1086�_9f( 1746--1771:H3a�K>��HYu:|9G�8 �y�. >a�)[su��Q�^.\ $99!��1�� " 159r604=�� 863--2874:�4�>k����.� �*N FQf{ {5��9_ 690--700;=2!2� 246!�ƥ�(D.T.~Svirid�$:"A�V�� &��he26�*� LZexcep��al�  $G_2�� u)7��3M 36.�TV]{TV� ~Ta�1v� A.~V�<�Q�8D�LA�P Knizhnik-Zamolodchik =�<al&S� acamVaw8Oc.Jh154*^ T]{TN.~Bd��!%J i* W aMa^.�(h4tit�qof )(�ic"�;:e &�< <( 1969 % 52p.� ?=2�2��Z��ived�YLie���� non-d"�B�P_(ized KS8!��qCA�U2� M)f 1988 �258�vb^tBrZ�^�J�U�2�!0I(��wth�@rums\ {4�198B2�<22 T5]{B��� iOac-MouR6����ir.���sl� 37�90���d122X6]{T6:Z�C&=3}�3��Eoot�$AR�:VJW(�?rn�]chool".XX*+,gr�&v6Dubna, ]� JINR$McYs,�dna#@1Iw13�.� T7]{T7�J�� �%�um� 2� >s@�0: Cur�Oa&K��and Fu%jDir�onsC\ BustozcE�"Ismail'S\ Susl� K6EN �ZEN"lN�-#4A�48B* 4045.� TIS]{TIS>9IIstCa �:�]XThe Gelfand-Tse\u\i tli:p�6� $\�,frak{gl}(n/m�Ⱦ� SvI ΰ3�42ID]{TD6!� �$~Draay��uD"i�1� 6�2� Eg=u}�f�q(9%\fA@�B�359-1370* LZh1]{Zh1} D.P.~Zhelo;q�S-2AV2�<�k �E�I.# daknS�� 198 �I78.GZh2�>H>�&Z�� J� ���2�1!t130. Zh3�>� f�N���g���MiEg ssonوr� \maui\ 3�!�P 100 � izak��88), 7�W773.�Zh4�4:�f� An i�'|E�oJuj[]v�.Re.�A�B�Y 3:,�!, +iJbdya%Bemporc`.�bf{7} F"kBm,"�G �15�21Z #jf #�f(�% %�_%*�M {Aubin}e�sc{T.  -- SN"[k�0lM$�Tiem9ran �?y;"�$, !}~ {DEFc�kalatzfz$R.Ellis}--dA. Friedman}-- The Asympto�behaviyvFrReal E&�y of SrOrder d�w O��� a Sm^`\Um�]�� �v st D"QrH, II \emph{Indianaa -%4J. 23, No. 11% 074} p991-1011*p {DF~6.B-�Pri�f1f�u��a Sjlyturbedich�R-� 2�(.�7� �$8} p143-15.$4�1Z�V�6� >� d�4of Mk�2~�B���!�19�527-53:� obro�S�Aokotov]�V2Rx'tsov}% Y�V!=9 ,}--, splitt�IM�low�+ levQSchn�|affJ�UQ"o$ $hu_{t}=\ G {1}{2} h^<\Delta u -v(x)u$"�;�x�& ., jN561-9�)6 @ {DoV5;M!;nsker}u�S.7hadhan}�Za var�Val0U2�"pU�*�} A��m�maximum4le,�c5t.�K.9 USA, 72I�$5, p780-78.�I {Fl�W. Flem�O--�7$rolled Mar5� ss5�6, Pisa2�FWOM��eidli��}(Wentzell}--f�. �s!�B�Y, ��-`N�.�8 {Fr~6Y6�j^ �^�A-�^^ R^v�!��[0� 73} p1005�\52jGT�(D. Gilbarg !�1kN�Q����ti�Q&�Ybleu@�vx�a��-|!��^ % ed�p2�Hel�Y� B. h �A J. s�PnSnd}--MuB~e�s��a��*ޏlimit�oro�� .D.E, 9(A1984 pn 42> �2V� S6�lE�X""m���>���9*E-�Oa�*&.s&'.�b 1336,Q862K�W$D. Holcman�. Kupka!���23�1z %� PDEw88manifolds. C. R2�U( S\'{e}r. I �38 2001), �B,5, 465--470:�35Ff�emF�� ���f�̡�conp=�F�A recu�se�?�)"� �, �2-!}t6�MS�9W�:r�xska, Z�8hus� ��9iv�&"�:�dff2U�k�f�~C%��y } --&;]K~]e��edM�cycle�k� J�A�. x$ 311-320 }��2�KvS. Kam��Expon�Oal8+��of"�e�ellD � �=����� �a� y�2)e�}p197�6�Y��Y�RjA Hami�t-Jz |�l:�^O� !� ory,�1�S86} p9�Q6P Kife��Y. -}9�E��|iE pres��G;^&eqUk%8E=.866|805�~}--|��ali2 valuNC&1 N=I��hbolicMZp�)%Y cirAf�.�L E"�_3�< �� 08--139J�8N� N�!G�� ��[rk��AM:�!,9R,&# &G P=�$%�, AX s&�as"�of� ilibriumt�VIsrael ��70�a%�5�*6ra5"�wE#r�Z�ur S�e (Graduate^l�Cat�3c�V. 122�)ky�R1gn,� harm�R� E� ��k. C"�uStu|�� .�45Hc.p�&LL�c \b�e {R5��5D6!�U�S, CRCi���1995}2�R�~M�;e�Z�5��"%�UK:��� %Z>�W198.� {R&{ L. 0F, D.�u liam��a�%QEa� pro�des@XM�>nga�z9XBkS�(i �:, -���^ ys�"#Q�qF]vxZMe���}�"47��ohn1� Inc� Nesd%�Ci5�Si�=�^ )uow ly�%�] Iw�2�MmT:.�ekF�`�j �8. Henri Poincar� ɪ XXXVIII,��'�6R e(on�T��.�tunne�V. �of�� 12� �_  89-116�Si2T y8a3: "S ^P!�V� flea� elepha�)�~��� al. �73 123-136ZSm5�S.e}:�fN� �of A.M.S!��e p747-8302�StdDx$roock}--An��[; m of Large /|"�:O�RmCvn��{LiD294}J. , ``CaM kin}II"otz!�s storag6 synaW memory",6DH Trends Neurosci.} �1D9 pp.406-12A7 94).*� {Baylor}F�:eke�D.A. �b6�Qlec� origi�inuEw$dark noise)(rod photorem#� Xit{Biophys J} 71:2553-7.�{kahi}�  �d H. T�, �A oCo�]in ��" },>hc�r��-�Z%�M��{k �rA8 L. K � R. G�{�zQueued/ @^��1 Soi}, �D-$ rs:ce.�. �8 �9�8�7 1�^YO PNAS�<c�Erkoti�� Af Calc? � O$dendritic �1� mot}Q^-�.!�AW87}�81-91,��EW5CHK}&�%:J�A Korenbrot�Longi?B"]!��"rod�cone ou�Rseg*N$ cytoplasm���Sequd<�J&#&F�.} ��&�G$pp.2566-82�@:�S1>�2\Ki�r�Pg$arrhey� ��ns", (pra�9)S2r]MeAc[/b�)�g"Zt!H SIAM����6� �6{H2I%�2�E^e through� �opening:ep:2tra�<k�i��.� bran!�2�J��j"G&�Y.�NNS1}B[dler, T eh,6��Ost��c��6X ! 07 pendpIve ' VaAH��um�n 2|rb�b�ASis Poiian".d %k"� .f bf{62},LZ4g^4JJ�.�y29U� chewZ..�u�b�2sur1 "� o vN0'', submitted2v@TB}P. H\"anggi, P�flkn!aM|�� eca�ReaE��XA �4: fifty years �OU merA���MMod�H2Q�I251-341� .�MS�SB.J! tkowp% 2�!� exit%��(ra&�ly�ed� $f&�N��#bf{33��367-3�% 1977:� B82}:�2�Eܑ4!PA����E��re3Kr%L'M���",-_2� :y4[2)c835-849�5:�`�#}ySM.\l osek�a.~2�``A d�#2�(.�V�m(5g�! �595-6s-6�B,Yau}L.W. Hay��(A.R. Kay, KYau!a�le�ic GMP-A�va�uJ nel r[i�{cised�Och�f��:xme�� N�Q�O32�506065) May 1-7E�66-70)x625 matthews}�~ �*]�� l_-sF|�a�ic �con� �U��!�B� : � cX�Da � J*F �(�'<(�' 21-6N�Koko}AP�s ,J��2� fl�]E���c�d��c[&�U6T 6�s"�jem*���6�2 Pt 7pp.360-5� �� sigworth}O S !��`5� �d� �6�at�1 nod� Ranvier��%r*ol.�2:fE amit!GA���Z.�a� N��R. Eisen��h-�nե.�pFX�F4ng between two!Z}r-�Z�book}.u��A A�f&\*� b\ f[ "| ohnH V" 0*! (Saaty}T.L.  * .�j� ! � With2� }, D"$NY� �NsQ��MasYV&�~M�A�it�hX8+p�o4�l!le�� optim�� �B�S, [mHRussi�W. �� \/}]e� �$V'h ~3, e*4.U{LiMa95Y�$~L.~Litvin�02� s  Uoqd� ψ�id%��� 0:E@,�;� l:�p? {<4IHES/M/95/33),��0;( Hautes Etu�NSc�?if�98s, Bures-sur-Yv��A(9534so: \cite{Gun9z�p�t0--443� &"N.GMYB102.W# :0 J.~Gunawarde7*(Ed#x%Id �c}N�*.�C�� Newto�s�e�/)�1GMCf:�B�Shf >��6~PU{�kB.~ShpizM��t"a�Csis:  �^ic��}, }ZJ` N�k ��V�Ib� 6ܱ729)�*�O.FA"�9122�MaTi2�Y�G���l-Il'ya"�=(~M.~Tikhomi5~�x�Jx"�1�*��..}Eu anslIu!�O � ��XsV. �222},~�PI, �.� Ro70}�m0T.~Rockafella��:���eA.&P�, AN��f�10}�CKVe \ Ch%& A.\ Kisel�?WKB^$���&*8*�&L� on6�26�$:f#slowlyw���p�=ino; it{5;�.\�.&h 1�MQ�42��47..�2��nd&�a.;:�� \F!�� �varb�� un.\E|.\,�21�CmM24 *62�chAT\ׅ�W�HU�ʌ(it6F���o\.\  F�2Ms���N"� 1953� dhks�\ Daman2q�!ctm>�RE[�l/ B.\ �,�%�al"��sE>d4]SchblY&a��3 signY9Zp� 23-m�r5!m52mdk2�%m.�Half-�Ivno� �es,|p�_1�Act�|}�dBb.�!�=Qrefew ����A (��{(U09074)yBDeK c \ De:�w.�7LeXN~�H� :Lv�squar"mm2%9���%S bf{2�e`� 3Y932 East�S.P.\  ham, ?it� Z&,�AnLin#9.� S .} L&'q�]Oa.daYSev�p ~4, |�&g9 � �5}� Falc�Y�alE r6�U-�F�pal Set�j|.�1å"E GGMLl\ �n�VNVei��N�, BV �z�*��(V���59n 7f0#-2� jac} C.\ �" , Zu�"iL�y�-RechnL��U�-.�-Gleichu 2���e Angew��_ 1r<83� w?��a�yNe].� um r\o�W � �Jc��B.��`�5�P1Y��\!���58}�� 2ˋ �lsT*&Y.\ Last)��Modif�Pr\"ufe�' EFGP>nNe�!��jsZsԱ� ��T��199�m2"2��up�L\�'ZI�N�pLEe;)z�r!z9���ާ���Z*�3�0rH 1377�#8.JLNS)`L��y\ Naboko)aO�7af��OnH�az7"���E�$�of>�EdI72aBU�1PI$5P�W�H� ), �I1�uU-LW.�m�W�, , Re� rdWu� -Thi�V in[.l�v�G$\'ees ``\'"�  aux D\'S1 +`o�s''} (�it{La�Hp] Eņ� 0}), Exp] . XX, 14F,���n�/N �6��MTT�YMuscalu� \ Ta-��sThiele,,bounterex;�a�a �Ear end/& qu�o�m*� � 5�M�ReLTL�rs]yi;-�282�c5� MTT2��Ca�I�i orem��a�bsNg�>U#lAre�ce� "Hi,IEit{"4it�$ bf{1�0�� 2��6� NPVY�baza FA� eherDf����Vol<���Yudit&,a>*�  snbZ�  mu)}Not.� RS4Z \ Re"��"� Q�*�$rneq"4� , IV.\"��!_�&��>�$V York�8]�Rem�Remt,�� � deca>� �Co�n9;�!6t�19 C19��kq�U�RemtamsI��Emt��4 *� �uI�:� ^� �T0z�3Wl�e 2�24Qn.�dim:�& �t.�����{��l;61--171.,yb�� Rybk�a�V� adne�ve"� ��oV� ��V��@؈lJ9tR? glob�- �  �I[Iz bf{4�G�4u@42. Schm} U�� incke�.2�'s facto"�QmT(�#Sturm-&+��2��-�Roy�o;&N�A�8��Q6), )��$b7){sz�\I%��Zlato\v 1��!�!d$Szeg\H{o} Bi7��o�i *��6r9!�yV�l 2l�� ��423]WZF: E.\ ���L.7Fadde� Kort � de V !,� :� mple�&_�"�. �9s27\*� A1l\�N2�)5jZygi Zygmund9T\cnoQic"� U, IYja *} 195� N�� f��;��.�,D�%ese�4]� kos}�/o�'n�~warzb��``Lie bi�"->�B dZ2�E� s''.oV_ , B.pZm-co'NK.�!TamizhI(edu)``�gr�+� &��I�j�Qeey6�ndZP�1India."�( �7ū6)104-6]4klim}C. Klimci�P�vera.``�J%A_���a� Qw$ double.''��� ?S1�"5)455, !w95Sr2. C. u.``}#!n T- f!TN)] X�.�pl. 46]6) 116.^909.�B.Dy�( elav�$nd :8``.��l�6.R� �E�SA8Q6��y� . 1�83)�b1 -\��OFAR}J�!,Figueroa-O'F�$ ll.``N=2 "�F�� solv�Fq:� c=9m�f�''.���� 17a}A29-15=7%i.8 zW;,S. Zhang.``Cv!Tlow d*E�"or%$y\!&�� A 2)� 8)71-81 ,ph.�]31151.�0J.R}M.A. Jafa�dev�HA. Rezaei-Aghdam,``.�US�Bianchix�1K�E� B458Aa9)477-4�AQ�90315.�,H.S}L.Hlavat b�nob!�):1��,62�KM�w!-pl�.�20220�%Q4Gom}Xg�mez5�Z�'e6���6z�#hqT41�,0) 4939-4956�1Pat�,P9wa�k T. SharpU&W�rn��A4H. Zassenhaus.��]!�!rVow U$�2J�$I 1576) 986-6��parA�E.��O .``E��W ʈ&_x�! 1��;��m>�:Q �JETP. 75A2)1-3.�$Getzler.``2<ae�2�"��cor��QU30704.� R5T ly i1� s� eJ� 0405�4)010 , ���164� 6� �� r� V� II:N�%a� � wA�diA n puzzle� �10 �45 , �812.#S okolov�Kme ���Lco�#��y�  �%Ima� �b�>� Shep}Ry�nd!�� � $``Homogene�/�FiK�Cos�Rgi�t2�U�y >�5;  H�WcCallum" ``An&M��Inh~ r~in��%EaeD�ɝ: R��� ` E. W/lbg M. S. Tur�*Ad�� n-Wi7  N.Y.e/0;!D. W�au:E� ��q�+C��E$�Field�,>gamon1'i#�7My1Magri.`*� iiTe �:� le y;� a''>��g1156-112�maj� Maji\ E.@ Begg��6�A[) for quasir�Q�99060b�R� |�03AC*,sc{L. Accard� C?CecchiniO�nd��;xS�| W(��NeuDH�B%�a���(of Takesaki�(� �l.M �45}� �*z6��OBN�O@34rndorff-NielseK�emI��b�expon >f\=�in �is�S�g#~4'�e? �! CA'r'\&D'Lt�s Ch �UF"8.�" BN-G.��,>���Gil($d P$ Jupp�O&��s���n8ce%rR�54ESo� er. B�'. O���{2 77~�6A�BEH��� lank� ExneoM<,(vli\v{c}ek}��%!O�&� Jc��#A8�&�)� ic?����BR�Ar�lI�:&:b ��O:?2��Q.L mEw� . C*\ W*-"ZN,&�[�,�ompf(o��R�2nd�u Texti-&�A��"_C<[5 ]AF)9HanPed9F!�nseiG.K. P_i(Je'n�鑆5�a8 L\�w�e em,E�2�25�'yh}�:�. HJPW�1ayd�=R�5 zsa,!� PetzwA � }, 2�A� es waL Ǧsfy� ong s.�v�$1�e�Npy���,�$ �!q�� 246}A�4��^:�koashi�M��$N. Imoto},M_t�do not� turb6,Y know6�" ��1A,m� �� 022312FL}E.�� M.B.�*ka��Proof��a�n>Q���)I�O�� �514��o93/A9C Y�MP23Mosony)4DA�tz�lt�@Vsu�4k*5�(coarse-grai5s, �J�685��2�:{N-Ch2�A.!b�B%/ I  Cf{!|&��A8pu�gGP �t�1jV*�.�N-6>�9�2�p~�&�y, e Y$ 8130v4.�O6� Ohya% {�X �2}tIts Usea��,ge7I, Heid���9����J!2� Pdir9�z<3� � m9If�(e^ intoR��? udia�,Q%Hungarm�18E��2�-� ]�petz19DE!sc�SY��{�+��aXre�*ve��0ta���G J6 ,A\V��| 6. \132%-�bNAQY -i���"oEum��N)v21~ pp.~X2� 8N~5(c�4s o�nJs,�rˎr z%a�bf 39�!�907Bc-�h �9�T�2�.�%c8�I-*��w%��f aiC5)V3� 9�8|N-7�F�aN&��im���Y>2��a:�~ observ� s, JV ..Q 120!.�82--9.EC{MBR1��8�&IQ3Q,IIy: A (�ew�Z"�A�j:��/43��2), 43�V436��M*� BfSchuma�g���&� �� Data���:�Error51c9, r):�-ph/9Q 22.� Schw9J.T2KwarŪ�W*" },FsÁw�1�0�+�0 ?-�L�!�F*��Str��H� ait�"� � efA8� "� �+x���=��a&|R deci9 F},u�>n��N3u��I0novJAit �F A.,Z�.}:6J�Zz;.L.::&!�2�J{Pika�H1:/ .�Z� & �)N�& ).]f:::>#r4>-:M >%!*6Tro$y-+T B:A�.85.V"."�B�H.*�м���as � Hols��ider M&�oo�_)��:��\�VI.� MM97 i.�: %46`ZN-:G:?: 2$ // \mmrus�.5%d / Q� y2D!g 97. c2�JBOn�uPvv$ckeyev I.,XZck ��Lymphocy�cle��1Z��Xvia�s&Ytraphy��(^ Bio0�� O F�"�, N~7. 376-382� my3z��%�Z�)& .-).. V5." >(�)�=�.7 8��9)�2� aa20�%�$Stepanov R=�$, Shukurov��� ff Dy>-=��=GalQ> c ma�f �n-b $��A�omaGi!��. 3R�361-362GGqb��]�)0!h��b�? M: ��B�aM�"��B�w�X)� R.} Four>�s'[|; � -"�. �� ow-HR�CG1962�(�XY f:� j  ).E�.Q�. >9!6�Levin �  G.G.}P:~??5� al T�3, SPIE^6�(frick_etal_��F P�M,Baliunas S.,A�ya�IDa�e(, Soon W.} B6�Fellar ch��s�':�b�E����� eI�al F.�c7. 483�; 6-432�.�8-+�j2�� Tch��h2Phy����ignal gap��r� "� �e��*a��y8.�}1��� Ny z�%y Cal3�~ Cal�o, .u"a �b��>�one&�*Z��. ;�$69) 2191-2:� CalNjt4:+ $N$6� with�dzand/oriersely� ��2�5:� 1�L 71) 419-42HN��@ J.F. van�jI,L. Vinet (ed~} 1D-��-Suther�WS-l )>> } �(6M. "n�M�N�5��9�M � Miyazakp$I. TsutsuiT"P!V�� tics�4e5b7" 7, �3M 2=_�]) 78-87;!�n_@"03E�A"FTC@���!F\"ul\"o�4T�e��Conne�.g�A7s�j4f�y ��u�(�$�A 3��3) 275u)6�9S29HDS} N��[�2, �7OU!��II-���al��M _'�M�R66�= icht} R.D;O chtmyer, �=�#�[Adv3DdRD�?I, B�1:��Me�  ( , S�.9@�non�`)�u̮�� Nuovo Cgo 3�� 64) 690-76�indPLA#� Basu-Me���P� GhosS%$K.S. Gupta��equtKen�B%the@J\ q��,_U.T%.A11�=3�~92; [!2(2� �� s} A� res,"p���cepX�=, K\l�(*bn{GPKGalind��Z�asc;zF�  TB��"1 ]�Poly1ZMoly�#nakos��2�b�-:eK?c-8&?!�clq6B32%� 89) 597-662s2VG*�i"�EQOne DA,}�L 415-471 i.M�Ae�%���6�mKs Hou`ISesU LXIX,WComtet?���5W%�9;_# 99026 f{A6���N6 ,B�a'�KYR�6� Krall!<O , �1Nv\� an*�:���5OB��=:��a!�s 45 L�] 28-16� Koch'��JZ , Self-a.�"p�%�`hJ�@� N� Sibe����."3�9�01-409,E�re�|�rei.xb{GorbaPnI�(r>-uk8M.L=LV!L bj ��%)ey`2_"�72�� �Veigy!*D.',� ��sol����6��its& 6%� 7V��\�!�ishq+5kI"T'9603052�GR�Z�2rS�oIA][� TPofņgr�B"E0�ZP�Vs, Fifth%2A?,B�5��2? AS}�%bramow�)I++Stegunq{ Handj �2 �,�I�6��� Q S��vin, J�W��� b(\� 2 (Se%�11.6OF�H. Fal�E�!A.G�LsanW �b$Wipf, PoleZ�L&�.]%$\zeta$-�E�&�_�ue�a A 35ű2) 54�i 444;%�0112019|WN �$r�1 \tSY�ardip�<~Aa��6�b(Eine neue Pn�8nraumlokalisier�>iØ0Vollst\"andig/�hbeweis f\"ur Ha\-mil\-ton\-�4en mitBn�etK2$Kiplom� 0zRWTH A nM"X ar12�Go��r�PIn4  S&#:� o/ k�ϑ �� �rnd u� P*2F �M��h.~%�~�3%"7�627u�9Ad�d2�)o�tre[ o0@)CdiemS.}g@!H �)E+Ph�4t%G>F7. Logos�3gt�� bogoS::�BogQ�j�6��e]*ɽѪ�-h!a�a�coU�o�W comp�2 ble �um�-)]�kl-^2̓09��09�c 79);�;�on �U�D78Akad.~Nauk~SSSR)�24!�10�<104�7 �5�bs� ~Bor�s,ש Sohr�7����s�top{��rot}v=g�t 6div}u=f$Iczer�E��&Y%Hokkaido)~J-19}, �7�.�R�cz} A.�KCalder\'*�A.~"U6On&1 *0  Ame�� k����/m5uR%n dc1}�LD.~Dolla��}h� Cones I:y9#, �q52:�;\=12� �03�62�elr�7~En�V�sy�/ $long-range:M)g| i�"�Z"LN�xu�Z}px~Demu��t��~eds.%�B ,(: Advances �Land Applications~{\bf 57}, Basel 1992, pp.~61--70. %(Proceedings Lambrecht*�@1) \bibitem{ew1} V.~Enss, R.~Weder, Inverse potential scattering:xhA geometrical approach, in:4\emph{Mathemat$�Quantum Theory II: Schr\"odinger Operators}�$J.~Feldman�xFroese, L.~M.~Rosen eds., CRM P�!10Lecture Notes�%5D8}, 151--162, AMS,98vidence (1995)..2RThe2�A � tok .2  from!D Cross-a�, � new5�, Lett.\��\� )X4!X197--200ae992# lssve Leinfel� C.~G.~Sim � � �u�ea%\�Iular m1Xvector pwsBK7�Ka�9�81.�$ltn} M.~Lo@ .~Thall� 9I![p� (s by long-r!�!d�f-���).\i� �59--18%876�r^� hort l.inv�:��Q�cas��J.~� .~q)-�� 22�R36%,8.�nww�Neudert,�<@von Wahl, Asymptoa!��u��!&div-curl"�in exter��,domains, Adv2�m�6�134��376e.2�Tnfo} F.~Nicoleau, A ste[l b\��.Pfo�dZI{f� or��perturb_e%� al Zb2�1527--55��72bab>�nN�4 e� PAharanov--Bohm effect�2�Q�a�$5223--5237%O� �pt�M.~Pesh�{A  nomu �-�:wEw)�2E!��i340}."l , Berl� 198.� rs1EuReed, B�,o)t �Method��Modern��>N IXFun��U"� B� San Dieg� 0ݤrs2�� � �ourier"~ s $lf-Adjoint�� :� .�75.xrs3R�G�,�6��J�*� 7.�dr� de Rham~ HVari\'et\'es diff\'bles.�*l0es, courants,a� mes harmo�!Het 4n~\&~Cie, Pari�62�yA�Ph�@ux, D.~Yafaev, Ona:} Y-�y��}UoNUu" _ 74a 7492eO2.�r� S.~N~uijsenaar bEh!B�,Nb4��3� 3.~siso}>kH.~Sohr�(��.!� Helmholtz�2X�#Neuman�ob�ino -spa� �ed4IF��G.~P.��Q�.���s��n��6�eZ��World/ xf� ublN Co.~Ser.~�vo.~*d i�z11 H1--35�9!�&� stb} E%�Ste��ijSin�integralrA�Q� ilit� pr�ti� f��A�Prince�� ersity�j 2�swcsr�> Strocchi,��S.~WightProofM� charge!�sup�le� rule!�lo} qx�!�ory��J2� 1a 2198��74.�8ttrr} T.~Takigu�R6l_ Re%>iz�b�� �&cy,!"�8Eng.~Mech., 153�%�2�ts�Ta��Shadow.by>� !tw�"��nn.\ Ins tsm6�9��� of aMgymm� ��A��.�A a�al�� a*�!�biology �phy?,%enginew}� �� P�i�i�U 133}E(1) N$p.~313--32.� th} 2�i���)nZ },&�A��( Heidelberg/2.� wef}� J�! an Ea�ri)Sn� ~�8al139�4�6��6w�RB�=�AZ0N-Body System)�%�T^D"\u�s-heimpreso No.~40, IIMAS-UNAM! 62 nl. �:�A�Nonlinea�*�1�B~55>~.�w�9!�:� a EfQ&O` !�}�\���m���Iw� 10!�105� �h"� z W.*n On necess� nd suffic��xcondi�%�!%solva�ua���2�$\,u=\gamma=@ $\div u=\epsilon�:�oY��ary.�V�s0�"� nume�m� a�NM-'4�52--15��5' yhs}.� 2mbsmoothZ  a&� expamx"=�"�uPtmQ �20� 6--570� 2 ycd2�]�matrix%�"G&�� ���� 0ay at infinitEOt�.~��� 4�21�49�� %03-28 \end{thebibliography}�\beginB{0000} 5pP[AS]{abl-seg:solitons� (J. Ablowitz%w8(]), �,adelphia, Pa9 981..�4W]{ask-wil:som`R. Askey_J. Wilkf$Inc., San   , CAA�$&� Hu]{humA"�%��,E. Humphreys� I:�%Lie A� �Reen�q ory}J��q 1972.�I]{ism��� $E.H. Ismai2�sA | � -� � $q$- 6X) A�a�.�1�7%�86 475--1486�W�: .cM.�%�J� �, 2yd t &�%�� ��H ,${}_4\Phi_3$6�� �(x.-eit3" at 42� K]{koo:a� �son} T!Z*� ske1L.v� .�%}ype $BC$&��:>.� Do%;P�&v� *m��� �K0} (D. St. P. %*ards,O+Bv) 1#"A:j F�17. 18�(6� KBI!6$r-bog-ize:J�!E. Korep��N��(Bogoliubov,E�$A.G. Izerg#%�$-.G� %�CorQ9?}�)�E2�0Ku]{kul:facto� } P.P. KuJ, F.!�=class�.O � $S$ �d-�A� laws,I�.~.�)�� 7� 1332�(M1]{mac:sphD� G.&� ��S 9< of p-Adic Type}Z% � Ramanujah*st.av71.M2 ���*C %���Y�a�H .�!�larendon�, Oxford��2� M3 uo"WvO2���� � .�, S\'hLothar.� bin-�� X2000/01), Art. B45a, 40<- (Eronic2� M4 �q�%A.��e�}�!!& .P.]�� 2�M{(t-lie:many-^(�CAttis (ed� �\  M'�( : AnB� Exactly� veG : One D�0},B�, apore%�2jN]{new*NA�NewellQ�?i6�aRr=00 CBMS-NSF RegH1Con}ce� A�)�&% iq�% �MM;82�(N-Z]{nmpz:tjy}Novikov,�+V!�naL�n0Pitaevski\u\i��V�HZakhar�8!��@2 ��f6 }, CzorMJ5 !: sult� < Bureau [Plenum] .!� ,& POk]{oko:bcn} A. Okoun�(${\rm BC}$-�� rpol� R�!� bin1�Q�2.�.�.&D.�-�S 1998�� 20�J�$P]{ols-perٴM. � lsha�k�A.Perelom!�ѥ�8l&� re�.to� "or . � 94P 3�|46YO]{� l�}2� EL LSn Dunkl*�-�Reas �lex RefSion-. SJwoir-<�y+al�oof Japm5w,�� =Wx]{oxf6 S.���i.�of � %Wized Z�"��� h. DE�t+ UCLe��#�P]{pea9� D.B. Pear� �uum *���y t�J$Lo��e8."8RS]{ree-sim:met�%��%[ B. Si�%��s!\Mf�%. III.���= B� < -�6RSc]{rui� new��� *�#�� n�� new��J���it�"ona2v- (NY)��171X  370--402DR1�: e-d�s�SB�, F32(� s�"�*��S#"��} (�@"hmidtW ��.�.s#, Teane=NJA 90,8 16u*062.2 �aca�-angl.:A map)�*��Y a�s�F'J�QM" ��- % their ���ubl��9 �A�i3 31} �n�2D!352�R3 � b* -cAQ6� �*�t*cl��!�Gumenoff�L!�s.), 2���� 1999%� 2:352�R4 �9 ed� 2 �2e�$&�$ vs. 5=��mm-bm.�0228;2), 46(6T $S]{sah:non*� "N.L6�nd%�s=#%0-�15i�99), 2�282 �8�6 $ 484--530��{JR�8ciw�Rebbit"� Hf�2q5���]�in� ��g' �7epA�Y � M#AI��,��A" 15�:5�� %***2'0005018>�6��Chern--� s � �]�supporgauge � �^�M9%�6��U ), 087703A83�Y8 211276 %�N C., �N B�ash C3Hopf in�Ato�n!.$ Liouville"b(�arget 0//!E�U)u`b�&9B�C2�!5,-�-2�3�� creYvia�x�� "v'knots �j 6230 (6)�1K�D105027!? 6.��:inMM� //q�(9909189 (8% ):�-9D6�;E��18-9B��8ES} L.~Erd\H o�=P2lovej!�eH!3kernel�`��y }^c$:8s�)$\�@bb{S}^3<* R�dv.? 1z� 11 ��id@-phae 1036ae%�GG}&/A.~Gey�9E.i3 Grishanov�6ap}8�| ���E7solenoiO i*XRussian). Pis'ma Zh. Ek . T3/ Fiz�@7�b� 425 --h 27. (Eng �%l.A%t JETPeer���9.G 35��5�-9 VMD}w%~Vidal�GMosse0B.~Dou\c{c}ot5 :�cag� w6��"ure�-Ev Ex� �81�R$ 5888--5892� VBD~ J�P.~Butau�7�.�k% Disow9�a��C� *�&�5�2� �/)K6Z20�15530�8�'ه;--mat/El11An"a,Oho -Y.~O� it Eff�Bof��\ u�-N��aB bi� te Q� l�ce2��.4567-452{DN�1 A.~DubrovESm5~k!%cGr�D2;& > �} (iny  Bet} 7� 8�H 1006�A16u �(iEke)�5�1 D�I91�49� Nov}:� �T:�S2#0 &" !�=y#d}, Itogi Nauki i Tekhniki:�r`ny�/emy., vol!$23, VINITI�C scow�363--23V J�+vie�/I � �1&�+1#6ARB� v��iiP.~Redh�0r�B.~Band�%�;2onQ in a:� e|�impur�6 &�.: u ��a�3re&�.� Jt l 2�+O� 883--3882ARr��>�Q�ic��%�a��ong:��I{�\qh47 1997 20�102*AAG6�Mi:.~Azbel,A�(A~.GredeskuE6xNq��ng`�(1} ies}�J� �$17280--17227{GM>4V.�' Marg�Z�6tat/.�u-inF*nt� o�J>\ & ">U.:JA�}Zametk�b"i�$768--773 [^Di1�5Aka: �B5} 0.]�? GZAA0HH1�, !�Zus�'mV Y1�'50"pr{!�e:L9�87N U�I>p�%;)��I�e"� ��.�ORep�bf(I"�&2�?25���BS1aSh.~BiU=,�9$A.~Suslina�c>��2�.�i� ab@ely�tinuou�.F� i\%iz)��6-6y8]'�!�M �B.G St�@ �MM J) M%�21�7.� {BS�!��A ���;m�,%�.0%�disco1&�D-0R�De:� �  ZB10}�"~>�U)362N� rB:M9� 579--6�C.Vg >CR.�Eht=@^kjV�(ru� BE %R2���)]5ANed9)aU�Bmzof curv332�fl 6A��7�4��75�oU�:O�: =1 -1016�KL}�(P.~Kuchment�wLevH$r8! v \icit� )K�,u�F;}J }4�%"}435V �53�D69?Q� 0p_arc 00-380"%.OMo�PdMorame!*�}Abs�!�"�G �um%�՚(�>y@Laplace--BeltramiM e�ro�LEU)�g&���3*� 75�47602� Sob!��Gobole&l j���6���X.=��S�� �13��85--112-,Fil} N.~D.~F�9)pS�?d�FU�!_diverg%�form �L�P� comp%�ed"" ��M�10�I�$ 3078--308<�K AB} �}� �C�FGit Sign�Aa�$ofJ�5��9� �(� "$� 211� 5y4!J46�OP}� Olariu�IJ?pescuU��3l� PRF� fluxc�Mo� ���5)�8E3�L���mHamx~�K13H?other �04ic phenomena.}B�1 "� et.1987 (A1^$��&�!���e>2�AK! 5�$T.~Kaufher*� he-&!%.. lux �=o1P)�� d��9420R3 0704^.n'{KDP} KZ=~Klitzi�U4rdMQIpp*� New �"a h�Oaccur�"j4* � + �e-"K*4":���# *r�#tA�f�4I�V 494--492� QHE}i�!W�#`��A R.~E7Ca A!S.] Girv�Kd"Z1�"43!�&I�6=3({Thi} H.-P�< iene&� � mech"anq� homo�ous� %Jel�a��-E'tub!7�A��'bf 280 A��6JThiJZ�S�"y�BQQuanten �k einOVlek+s im �n$Wf�mit�em�U3,n= a uni�� �cy E;�$p*M?E�� zero�N *5]��+"� .A�$bf3}, no.~-Mu,�B�ZM ~PF� )��(2K4�532 AGHH lbev�! ~GesztesyM8H{\o}egh-Krohn,HIHolde�uSjAle��e�sE)um& !e|BX*�6.9' {Rui�lB?J2��\��o%�7᫵5�"e ��b&�4y) 2+AJ� DJ.~Audretsch, U.~J7,@4D.~Skarzhinsky W it A prag�^�"r�^F�I�* �;adj�9 .J�A ��" s� :���s �h D�%3�Q23627AT� RJamDITet&:w�ia�Ʉ�%cE�4� � �#e3z���9702048 A}� DSt}�D\c{a}�s�WLP.~\v{S}\v{t}ov\'{\i c}ekti!F:�Mj$\�7.�,aW'}�7�,5C�S3� �7--6?Sto1}F� \i\v �Ej$it Krein's�A mulaB�<}:�As%��M��X��,21�2122� Sto2��*�*oB(�!iE�v�c� F�8 7� 19�> 30�6qN� � Namb65 5�� u(K �2�!�30�2�A{IT��IYf�%4Z�a9��B�C*7An"?I3� 199--240!<� �/02-2942=ESVEwExn�B�u(,(Vyt\v{r}as:�" G D5 b��0�:�GR� � binu)�_a~Nd ��V\��EvC�( d212�C{Min} � Min&�j:�q�� a�� t.YlA� 2I/04-80!Y %%%?Y�dSG�<.~de~Sousa~Gerbe�4�� it F�& qn>�A�/cos�]:Fng���a �$�? 1989�<34�342�Ha` C.~R� g*"> c"�[of"5&��W& � �"���199� 5�b5E-%&VNHa�_2�%-}�-��o #�.��e�1�9n BDS}QG.~Benetano,�0De~Francia, EM Sa gelo�� u&%s%�� back�Fnd!>� )�!� alN.V�%/14AO!1!�4�= -4762�Ogu O.~Oguris��q��,N��%� 1/25����M]�6[co2�"1 N� .}: 2-495a��GG� � +c vril�(D%�Git�A� Smir=�"�inu�& !)�.} Eur�~J.$A�32}c �yF2}GGo֟Green&J!p!VIL����ѝV�M+., 1873R8�� N 5,�:�"310007} GGSŜZG�r�)L.~Voa*>.�F�5�Fo�f� A��s. (Novai��0i�*s�6��44)�131-168��$308093�LaL;Lan6gi�Lifshitz�EHQ.� :f/-2F_>44PergamoJ�:7 U�VB}!eA)8p�W M.~B�gI}�k roleAN�ED��*-�a�u�6�(RmB� *� D10�� 2�OMN��#a97�4�1$\1312�BV� ��A@!�C�U*z,2 m�� a96�.�i&IR)�=76�766�CFdC}; M/-valcanti�S.�gA/�}$de~Carvalh�E�n60by.v ex2 B)�m6� [.92e 9246.L CV�C�A?B�Bn !AW��0-$\frac{1}{2}f�-��2�&P 6Q0�-706.*4{CNFT�WA.�!Coutinho�Nog��mrn�0aVez� F��Toyaman3QKi6gA*�e�.Xd��:��$ c>Zi[��Z!�� Hag3iR>D �!�non+"��(�= 6� :�\ 6Q� m���5935--592:L{Pa� D.~K�frkI�itɭ 's-f�Y6�wo-��+.0�.#G8�andG�pF i:�j�JF63m6a546D72� PO} �,AkG.'^ ZT>Y\��--�R R�u5�1 7715"22�#PYow Parke)Yoo&��?U$le $1/r^2$i�\Pauli-N<y܉�8Orog*h*�I��9�,F 2a�22GB{PY:iS.-K.�5jEquival�� of renorm8Rw��.K �Nq�@ Q�"J a�@s��971213:�HO.�,M.~Hirokawa,N5 Anomal� %M&�s;39G�, � tail'L�1�=J1�� 1� 112�T\F%Re!��jcon"�in !E! P g�F6�B� 3-196,2TamS~T6h.^f u�Ks���e2�0� smal"� �two*�2�,�gscala� �PJ�3722M CFKS0L.~CycGm�!FPtW.~KirB�6m}`VK ��U2um�"��global�j�Z7b� V��!.B{.8��O�CI�UO<�$6< 1je{^�W3 !hJt4� t , A;75 .�Ara1}� ra 'it�9b We$� --Weyl���(l�p"o :-&�q_ ��34�^9�^93.�>�2F�6�K-pe�8)1�:�+9� �C"�!v>�i: CanfFa�Q mmut��| hB.,X*lBAR redu��@l`-+B�#J�)* 2476�&� Ara396itV�.�+ Wei�t rass zeta��,��Y*�7al HiM^]3��ne"PM",-j hp $U_q(\_1(frak{sl}_2)�9JaMatUE 7}EE)42�s4212� Ara4�qI6AcN�9 ��aI��ECy,Vw)a�N �  �B arB���a,!�Pr:�5F�G�5 �.7 simp�(nec#�j!��J�z � �"�)�*� 25*r25�hY�Hel} Bsff� 8 t d'��a&81Ppour un \'etat born\'R&Yde 2�.} �j ��� 1�:88�-�;326HN.�( HoffPf$-Ostenhof,�$(Nadirashvil�&P��32������&2 *� !SM�/)W��A�G7Vt6�HH�9N�J�T.NG" .~Ow%�Nod|et a�nd of b��� K>4 �n Z��!�un�'&� 20mJ 62�)6��16�� F���,� 7+���fcon���O6� co6Y�L�c �-�.3 62--�}� �ij� G*3!�a s��=.� :�}��4!��4 333�5342EV&�7V ugaltaށ"� u %Ty �>��e� measur�ivald,&�m#�!M;m0Y;-p�U!39Ws2�U {LLM�%u.'Latyshek.~Lab�5�PaAnc�o4S.~Klaumunzer.��*��v��[ deni�v0$($CDW$)$ mov� @rough columnar de�5�l>�8NbSe}_3� ��L� �$�^�96[LLFM} n� Th.~�]niM ��߅Slis%�� 2�M�,�-.�s ��tf�r�H6*%1�D 140� 14022c LatB��">�a �-�6�37B�contain!�Y�lu&�Uspekhi�9��auk%�16� ��924--92&~6.<0!� ics- J aRbi�- 830--8322�(BK *J !�,FS(loo&� Weak6�4di�b&X32��&B�Y�6a��B).F*0; MOR}��Melgaard�,-M.~Ouhabaz,�m Rozenblum1.N�2��%ed��6�.|Jr5272rBalm �6lK$eHardy�H in��G� 6q93&� �9 ��AZ iJ .}���_9M�0� 1b 172JLW� Lapt��T3iid&�( ��� ?5� Dirichletm�In Op��;y:u *��Q��%08} ``� "�IRe�P��B� /Q. .7''�teds� ~Dit7jh,��� M��V(Birkh\"aser"*Bas�6aC299-302 RSIIIM�M��>a�%Җ�M II'>�ZNe�19 s��Shoz��G.~Shiv Semiedi�.�!= $\R^4$!� a=0i�5Y�on2�  corne�Qint�4>Ma ;106�41996) 17�c99R�(%�Fm//B3166>Pa|!�lV�nk: k�Loci6of�\d|zc�m� � �S:�SZm %�Ma.�7�v �N��>8�iB(J�7E�� �g2=3�H3w�9�PevZ RUX�completօo�n�N coh�4t u >O5�No�<i�ab. fizika �~ 7!2�R224!'N�J�1J.(,R.A.} 1984 {�-r velo s���uQ.� :ul�$shear flowi �,it{J.\ Fluid~1bf{14=63-2jB[Arad.�98� DKLPS98} W�radav, Dhruva� W  Kurien�#, L'vov1S.�Sacc�I�S�& ivas8ZK.R.}S �% {Ext�/a�(anisotropic r""t!ur-��it{�.\�\� � bf{83J5330-53� �4% �!�Pro �!�99! LP99 J. e��2>!.�9 {Cor�2�A��.��ce��%�s�5�Qp�1% E � bf{5^@6753-672�%2�BMV� Biferal`�)MazitD;��5F} !�9 {Di�ngl����|� � 6]!�#&"79i#2� ���8�>5040-502f[Arneodo2�6)]{a a�9CSe%�1$,A.,BaudetuRЁ�VF nz�F�as�‘PNCtJ varra R,iliG oiKCam'� , Chilla)kc�Hul!�B�pY., H�qle��r weij� ��Mar�8d FM�Nauruzy�"^Nae��A�ogz0V, Peinke& DRoe�2Tab!gU,Rq de WS* aW�ime, Hi{Sv�ce-g�R!a��fig�S�eB,at Reynolds �U$between 30E@5000, u "d��9"simila�GQ4it{Eur��s.BJ% 411-41. [B!�2J3)]{b93M�sc{'-�5�ȡ6 Tripiccio�WA.f$Massaioli,G \& SucciA1�j3 Ext\ d>�aWq9t%L Eב2�:��84�8R29-R2�3[.�2�K�/b�-�.r8} 200]{A�N�%�2VK port�Submit�to� � ics�ort�J alsoA@(arXiv.org: 8 .CD/C=01.� [CaF*ca�&9�Cao�a�� \&%SV 6 {S�nz�lowJ�Fin .�2t�5MN�� X2#bf{77uR799�B2.� C��Mš� 0]{cast90.���6~�\&>�E� 0 {V��&a�u"�' �ofi>u�-m�2� �sc-�a D.�!�77��.��E�0a�d0� �E�0A��ex�;gD� tudy�-�yF�!��   atmo�i�=%�etrth�>, Yal.�j}.�$Kolmogorov�$41a)]{K41a9�"��N%v41�*��I]S�"U9�in?ressi(v�Gu)�fN � very�6��p.K(Doklad. Aka�A�. SSR �bf{30}.[QpKoed�5rocINRoyNc.ec�3B4�69-1.5B)b))b 7scJ) 1941b�;Dissip� f Vg�}he)Cly*� 9B�s�2V� 2} 16-18.��-�VE%)|FLon- 1991 (bf) 15-1.�;[� m�\U�� .� '�?� ɇV�� �T����E�Ache.� atR�s!�uic&�0 layeAK��e$��\.�6� pp. 407�#2.� ���r9Zj� �Ր]O�� cont&� қ��f��GCqC�:%5.S��1%2� 2206-22�F"7Q\&B1aS02;%/A! �.6�� � {DynamS�� ��� AU &� �$a�ariso� �n-|� �� G�x%7�Y2m 90m�>.HeT,bf{64}, 05636�)n- \�>2,��]c6+Mj �U;Hjaun]Hsa/2� a8�� zit{New T&o% T"Le��,Houches Summל hool!�0� ee�s, Eds:3ieur, Yaglom�6aw& David` ~�12�a[L�!+�����2 LP96 �sc{) AT!(1 {�:nC-�al#lem2W�� hbf{� 35-�<&�� ���>(]{MauTabZocskEsc �.� �Z]�G�S94� a��2�"t + counterro1ng�k%�� �{era� helium ga.G"� � �bf{26� 1�N� enev�m:��F] {`�reQP� 0�:4M�� 7 {Af%eOf��*as��Xel�fu�devel�y Y��i� �Uv.~6� �1424-17Z�}d�BEz 7)]{S&A97- sc{.)�k8{ A)�7 pheJX�!�n.-����2�)�it{Annu4 Vt29j4A�2�X>�z ��S&D.}b� 7� 1998 {I dre\�n?-?�?�1es����,&%i Suppl X��eH_3_102�22�q��a� )]{s` F^�, Vainshr�S.Iehiladval%�, (�Gil�]Fy � � 6 {�@metA�oinc�X�k>���Y ���A#a�ofe�� w8a� �!U�F�6�{� 8-�m��WarhaftA�Che���War0ݙ +, ZA��� Shen� 1 {��com� s��U1cz ��of ?.�t��>� y٥�Zofi s2z13}�32-156|TaylorA�35)]{GITY �#I%�35�}�9�e��. I-IV H!}P \M \M \N \ A"k A�5T 421-47.�-�U�200� TayKurEyi��esclor�xM.C23 Eyink�Ld3 {�~Ing&\ E*�&2 ࡑu]��K& 4/5-th_x�!E�M|*�68}�k310-18.V1�9f139} \Q�ddafter\ifx\csname natexlab� \x\def\ #1{#1}\fibGbibO font>J�M#�Pf�Q$�R cite~R.$�Rurl^�url#1{Eott!O%8{URL Ip9_�mand{!\in�[2]{#2} B!eprint []{S'.I{2�{Bray}� 4)}]99Kbii{author}z5�{A.~J�o=�<}�a�{jourr{vcE��bfR&v+e}{43:?pb}{3�RUyear}{E 2�Q>�<{Dubois-Violettea�et~al.�78)6B/, D�!d, Guy{6ManneZf< 1ie<`4k}}]{dubdusol} nf^; E.}~�Q�Fz:V�G>G ��<B��;P>w9@�an vKBR9V��inߒGS title}{n?"{� . 14}}nr�J b�B editF�L>�Lie}A:Ypub�B}{^�},lQ�78}�B� 1M�1472_:�ZiC�2�KramerA�85a�zk�sW>�S}}�2����V}B+ �%�i ,�55:E-$4(2/1V85rBo�.chE�y�8>�'As9e�1r }]{b�mB]^:�V]r��!2�js��"*A(P)n�9:�-�18�h��5�8r�IGE�PeschA�9E�annrev��b�%#25��B� �5��U�I�R�!5 Q�27:K-<5�Y/1;9v�Ka���89:�K�eChizuWRJ{ KohnoA�kc�DS>DKai:�V�N>9 ���底M>O �q6��zAn�0:�-�65_^�X1�89r�Amm�o9>� Amm,+nn�[�AZoss�`!�asr��H> Amm:�V�R>9St�@2�%�%VR�d. ��u0!�i>(@hq%=�.?-�17_.1�9v�Huh5�E:$ Huh, Hida*�AX and E�r�hX'��J.-[!�5KHuh9a�VOY>� ��<)�6x�A��� ��2��*�!�1�61�-�27050)�!�rq�)�"! 98! Rok��=v;6S!8�Bb�AV�2=i�N% `6?-;�<T)9�r9NasunE!b9 "�o Sawada��  989-�BG =:�VB�Sa���X2���B^�V�" S�JpG6�!5oQ�58:�1�^ v�敲�l6� !��&)N1�Kokub��$99+v� ^c�QK>�Sat��fe��B12�2n��r6V�35�U5Vur2�r95:�1�Yoshim9�p ]  ~if]��B� �񌺚B��2�N�nB5ZB15�J�v? Denni�!� 9>% "E*nn�E Ahlers� !998��Bk ;:hV �^E.i C �@2�eK�eVRBJ���Z� 63�N��u6v�Ribotta� 86:7 #, Joet"U Lei!� 986��B <9^�VLA> ��6B>͂�:�5kդZ�15 N01�86r�Sc�8�M:] 2{ 00�~~U� ?֤��V�6Z� 0511>?�\r?Rudroff]�B0 # , Fr���Reh/ " � <��V>� ���I>N҂�rb�1�4Abe�Q�z5 Sasa�0E�asa990�g91(��r�A��E~�8,e.Mg 82c\F�v@ OiBQU�2�j6j "&����] 00�8B� X�}B� "%�6�� ��Jou5� j� 7!�.d -�291�L:�!mv" 7A� roth��v�2�ty�o+er%onZ E\s�&}{U#'8it{\"a}t Bayreu� B�1997}LZ\"� ,{http://www.����$.net/ag/di5~ �.p$:Kom�<0��  6�$ , Zh0M�}] 003�IF* ���B� �� ��B�2��Yf �n06Z� 0317Z�3r���LR�sa, Mizu��)��!�?��B�9��T>y�?2��ae V� B� �V�bJ(�� 1Z�5�4>H!ir�Buk9�@,:4 � B{\"o}rzsnyi� 'E}b�6a�A {\'oo}th-�?n =001�M{\'A}>=9zjhB�B��GB�{ �ژB�F"!Y5�u�=Nur,�in#!i;�fb^�2N�!�rCladis� 1�[ _d�� P.~EB� S �eK���Chij�t�1Liq=Crystalsfn B.�add)}{�-r v�� ���a� zhao00:_s�v_b�b_�3l_p+g_a 7% _�Yc��bPh.D.5'sis2"Bt\"a�rB��" Hert�I.�4:$,#mkhR� e�7din��$�%$:�"=M1�VT A.~P>[Kr�@��Oc� :�G �~u��6^�i"�� �WI�1!7.KG>� Boha�p)w&��G9a� bost�kBqX�KB�6q59�|Zy559��&+ a{"�( {a}}!> 0J�5�b�G>�@��2:AM4468�S�I5�}:�j Delevu�=:�!, TothKuX] � �\ uL[:�V^B�%���*6�M)��sA Liq. r�3wB�17�QN�n�6�!7>��!Ya�hsu>' Hira���Kai97��B* �2qV�B) �9�5�y9VRB,�2��I��"yAtb�ZO2|�:�1!;n�u�eF}�b�N$softmodesX�����CZM81N��.M�jM1�P*26l$�Be!���a�%$}]{rohekrp}@���}VhB��|fiE�2�P�`V��H&=�~7Z�472J�!�v�F�> #WD&S)�"�]{rzk��$B� ^�[jUB�� 6EV���6�I>� 5!U�N�~�8Z�414V�vD&�*O 8#z��V0B�I��� � 19z*L'�imbegaoka -6l967��J.~BD ]� B��jI16[ .a) N�1���B�c��tw��d�?����� �j�*�0���man���B� M)�R�"�Bve "^I.G�[&r=f�6f0.�a���[r~\ ^s��%51 bk�BnT�Le>PL.�jhP�LlAMlZc�ZbZ�cv^"Lindne)X��inddp�-4BYJ) E �.��.�BO��jO�qE8Q5\ A5�BZ��5�c f�.>N�rZ[ 509^�%1N/� 6f�90� \add�Dent�� e{toc}{se.j}{\re�7} %"i�PIbSha} Ibragimov N H%�S�N�Bt@ 0 EVa�}&/D�C=htrivial�,--B\"{a}cklu���� \FA�z[5 �a28.�FokasK A Sz A"Q a��4ach to exactly�lP� e�� \JMP �[21}/x8--1325 1�! SoSh� (Sokolov V VJ4 �U ssif:V"=$b/�V� >X�B��;S�e} \/C � 4} 2ґ280.,MS1} Mikhai�AR�5 XY����F.^@\ @oo9� �B>�< $\vt{u}\sb t=A( ) {xx}+F ,x)$.\ I!rT1r�f107--1226�!�~�6���� �:�6} f�42AE�}6�7 S�SSanKP�-�A�SAM)� 77} [�992YMikShYr2/,}�? YamER Ia97 "V;!�cl>�lD[ &��2Qf�te lisp@f.�QW���2�Ran}Y�?��ys� 42}(4)]636�SYab�%?:�8!BExt;goe��mod�� vertMNPA����B��K)�*��\CQ�:/�1!��;�9FujiWaT  m��A�nabe Y!� 9 &�R)of not �sal+d ad�PN@no�e.VAW \PLp� 1Xm2O�FFShSok}fb,2��LnAF=.qu)h E Wh��-G)`���D/K;e`; Z � V E *��Se���o�Qo�J��>�_B��)!� --18a�5�AE_Adl�� E.=%�.Z� q�6sAa���H!���1�16ep 1661.� ���g�F� Eckhaus WA+7 *�oJS , re�C�,A�el PDE �i �=l\h�[{1pt}:. I \I�3�}�62���� �A, Why are c�#�m�> �both w+�%D�aaY.le?�#�#�� .�S�t�  Ju�ng J PA4 �c6of� �d��N�5 �cO��aa+ \JDE� 2�D-�72�Wo0} 2�!MWolf T!��d*, tes�g�]si-�couplOVMdwQ8:L5--L1A�y=Bakirov�� I M| Popk. YuA���-]QM��P$of Brussel�a��2�n�27T�76viA�,Svinolupov S��9 5e�a ogue�he� gers"�a�.05} ��36.i�lsova� M VA�Oi\le5PBui-K ns.�272} 5x�2�Zhark m Gerdt V P%\  A)]9|�u��r�1�KdV�=�JSl 10MH3��2f w!j �3 n�!p=�B� �euni�|��tI�� �5}�96 ��E� Kulemin I  A Ga �CTo�r*1��+1$.�zͼ� 2��f"�b=B� ?� \ 1 (Kyivd97) ͖212vM^a� �i!�Ee�y�6C ��72b Karasu} ,(Kalkanli) A1,Painle��e}J25�0orteweg--de V��!�* �13616--36� �LS��J ich SMߍ<��KdV}Eof �bta--Sٲma�8JNv��6Q�$Addendum:\a�1����8� #�12)2� -�A�N�J� ��J�"�m͡���dj 5�&, &��61LJ6186� ��� E3`Ol�d J�.��a�FA cally-1�� J��  ~ wZ�d "� $ by Andree� K5Shanko!�Vl(��itu����C al���X$(asnoyarsk, i  �0ab 244�z2USvia^B4��J|�n"a{�=]�"�2� gy6�SviE�6�! .S�#�V|����g�X&�#s� �O�Y+:&n X9a�96� Sak/arui�$Tsuchida TQ)�Eu�VerOno� Lm{o}�T er �:\ �_ul~_�ysi6Y7 �.P33} 7��7222�E�� A��:Q*�N��fs�gJ���&� 9 �de���(.7�5 ,�1363SWoa6:e  * e�Z&���N�24};��1116� Wang�� F� 19sg^� .[`2arb�| NJ 410--432G"$�0I��eJ.��ZA&313--31�ZU� Beuk";  F,f� !  *� doesZ�~q\IK!��Dy 62x zaI r�M&*) lw �^J`2�0 396;�2: Kamp��� P�])=8? lmosf�"� V{����a�-SeTB 8} 705--76a}�xp�4� ({\sc Crack}K �P��.I 5�&5,�ap,�9�� Tee�� s (de-t ad���.SI/03�� UZ TWshort} }�!0S��&h���ۆal JQup�!�=�� ��kSymb.\��u�%C3} 367$����HeremanEG\�_kta\c{T "{U}� $�_� z�ܽh��Iu7 �2�� ���� ]�T�.7I�Q�\I"� 11} | �� �� � 82�Nˁ��{02a}Oh>�,Ohta Y 1991 �)�A�ofUs�%.��v JPSJI�(60} 798--80����Dodd}  �FordyI� 2 �*�5�a-�.�KdV2H2���68--172�HDS2} Drinfel'd V G)� okol��V%� New�!qXs hav��Lan $(L,\,A)$ pair ��Trudy Se�0@S.\ L.\ Soboleva}%�PP} 5--9 (in Russian) =,Wu,` Wu Y T, Geng X G, Hu X B�Zhu S��99!=0A generalizedMb--Q]��v>YMiura��E�a�.b,255} 259--26.�$Ma} Ma W XAJ3 A6 �Burgers-� s possess%Z her���( structure ��826} L1169--L117. KK} e�DiN0 �~���mlproblem for cubic eigenvaluee|�2\ class $\psi_{xxx} + 6Q x R $ = \lambda$ \SG62} 18!416�% Gibb�� qP%� �Factoriz%�a 0operators I.\^��_1!�08--251ay� KampEqvan der� p P H 200q�proE�6�A�I���Y405�_Fuchs}  steiner Baj\ ,Lie algebra 9�of deI�te2I�� bi-2^�� &@ 468} 1082--1104.�Gurse�G\"{u} "� rasu��98 J � Q��{ m 9a 210O112�FL�okas A S�Liu Qi�$ G}�condi� al s6xexact��� !$ non-1�l&na�ّ 99} ��582. Razb}  oinik S I!��DVeAr&� e 4modified water6�sف119} 28!82��� 6���Mdj�4s on Euclidean.B���Int.\ Ja od.\ .N � } 853--862� Tu} :�AF�Q Z��22�094} 340--342 .�B{ ! { eon J J�P.| 198A5(A recursive��A6A8local higher-ora� sine-Gord.� E�Dtheir B\"{a}cklund:��&� ,5} 1725--1732VH!:ͣ199 .�yta's ��nea.� a� �ds� ed� ��465--L472�Adl7 j e[& sZ pose] bciple���$Jordan NLS5� 2�190} A25Q ��TW1�$Tsuchida T�"1�J��Q7uGr��^*[ 7} 117!y187�BLAKNS} Ablowitz M J, �,�ell A C�Segur H 3* -N  of p? ��@ignificance \PRL� 31} 1E27.�(YO} Yajima� Oikawa��7� �U���ly!��&� N�!�"%,4} 1576--157�9�Konope!� (lchenko B GaDA�]"�eG� .XJ@ �jFortschr�e8!2A026 Lindena��q !�TNijhoff F W, Capel H W%�Qu� l G R W�6 9aI �lU� �(multicompon� 9U 2�2�� � �93a�+437} 44� .�Kersten� �8Krasil'shchik JGv� qKdV-m�d5 em AdvL tu�� Math.}-k7�{=$Lie Groups: o�c SJ )Diffe ial EX---One Hundred Years af��Sophus_---!� 8ed by Morimoto� Sato H%�Yamag� K 151�412�KSY!?vh(Kalkanli) A, Sakovich S Yu OO ari� from�prel�k(hip between��� 9--Shabatb B > & .� 2} 24L 2503= �p} �y2k,B����19�LO�me pJ�� � �ޡ� ��par!� d.�U�J� �jk 10a`42�Das} Dx !�$Popowicz Z��4 Bos!� reduc>  susy �)� Harry Dym� &��{ 8031�4.�Leble}  S�Ustin�l$ DarbouxY1s, deep�i� s!�. 50�502U2! 1987yysrn $u\sb t=� +3( }u\sp 2+3 +xu)b x4�&8 8= �8--555 \end{thebibliography}\ \beginB {99}=�1} W. E%�HB. Engquist, NoticeEX� AMS�"@50}, 1062 (2003).N$2} L. M. G�schWJ. King,�WPro� Fol�s,} (Am. Ass."B Adv m��Hof Science, Washing; 19902|83} P. Imkeller zT-S. von Storch (Ed.s) ��8Stochastic ClimHModels} (Birkh\"aus�,oston, BaselA�12z4} H.ż,�g.� or..)7433}, 423 (19656@8b} R. Zwanzig,!1 Stat2@9}, 215?76uH5} D. Wirosoetisno�4T.G. Shepherd,�ica D �141!�41%�6K6IJuA K. GelferA@. Baba, A. Rieger�L0 H. Kantz, J.F�112�77k6�oPK. Hasselmann, Tellus �8!77%776)]ld8} A. Majda, I. Timofeyev�E. Va�� Eij, PNAM�96�687!P992�aa}YEind, Ann. d)�ik-?7}, 549@06�aA,P. Langevin,� tes Rendu�}bf 14�530B82�9 �Wentzel� M. FreidlPE�4Random Perturb�a-Dynam�:S�} (�-Verlag�  York��2|810} M. CassandrIK-L.\ L�GO]:,�Asympt��Y��Period2� l} (North-Holland, Amsterdam,6�11�I{jd �P.APram�P �Rep-�314�!34� :�PiretalA� ~Mc Laugh�G.C.~.�v\ O.~Pironneau, SIAM Jouragof ApplMs-a 45}, 780,}86b PK02ehAahvliot� 2�$``Homogeni3� portg a sp��tempo mf flow� ,small-scale r%yfl�7ns'', ifoc.��IV rn#al��ce�d�� and V \, pp. 1-8, May 24 - 27,��2, Wilmq0, NC, USA. %"C $Leo} %A. ga�hin��Funda�al#alIssueZ Turb� ce},DGyr, W. zelba@ (A. Tsinober�i�0), %pag. 257v�1>SM��RAur�eu.�6�u066306���yVA�*M. :�M. Avea!e�X.q0�;148Ah 97) .T sg88�$H.�omo��(J.P. GollubO��M3�628��86�4p85} B. Y. Poma  Ca� Acad�mPI��30�u13� >MV�m�AP�9, Euro�A ttqف�53��6-126 K9 ffatt���� Mech C)72�86x fu�� enci�C�,, S. Musacch�Ra� sman��A. �{ed epareT%�� N` �` [1]c A. DaveyxK�Hewarts�hPe�R!�c. Lond� er. A�textbf{3%�101A>7 �b?$([2]{2} D.J.�n gG Roskes, �d..� [4AG3� 1962 [3]W F l!$,a�0\emph{What is�%i!}k V.E."t ed, :� a�2]�[4]E A.S. �!�P.M. S�9!� Drom��a bo�ary-2i�¡$%p-S5i 1"t" F 9��99--1� 6_ [5]i M.YE���, � mn��F.*d!�qAn13 432--43F 6�[6]� 0J. Hietarinta=}Sc�%},A< Pike!5 P!5 �jeH� � --I^,�$emic Press��1.�7]� 9�� mun�4� �QA23V 1--39 e:2).N8]� .NA��Its!>Y. Su�&�\s5� ��!�half- (p6#int2j9]< A!�\utet de Monvel, V. KotlyA&�� � . /&�m� by BMo Datar!this �i��2�10]I 6��"�, 9�!� �(i�nX�O1}2LIni�-q 2se� .�inmʉ�DIII Potsdam-V Kieve�"e0 Workshop},2�D�upC.Anel%q�,E� /':>F 612]�$V7�  a� Anal��� 73�j66�3]{136BA u�ed� �( F) �(ing ���cer` Y� PDEs�c.a�SqpB�5141��97*�[14]{14.�q2U,e-da� �� ��RieQ--Hilb��"s��&�Sci=;��10�� 2%AN\vѢd{ara} Aranda-Bricaire, E.,a���U.� Moog�4 H. [1996] ``L�i&�"0discrete-time� "� itE@ J. Control Optim"��� ..�m� maouA�, Sietto��.X!�$Kevrekidisk G. [�a�$Time-stepp�$.coarse c �$of microscU*�tribu�proce�$�l A�Robust N9� ��5 89-1116�26�F�V@Theodoropoulos, C ���L-free gaptooth-basedl !Xcde� for di�)lex /8� �,''! �<. \& Chem. Eng.}!�bf��)s}�(cal} Califa�C.,��ac� �No�d-Cyrot,��AC9��%m!�feedbackm�M^-� ;1r L� -x36} 6.scar�rreY[1981] �``pic�j�R8Centre Manifold%�ry"}, :$ &�.he}!/ne$T.m4mi)� [%D%�<"}, Holt, Rineha�W�� (.q(oif} Coifma�af)� ., Le� B!�aggio� M., NadlB., Warn Fi� ZuckS.eB] ``G"^�uj,,s as a tool �� harmb2P&�% defi� o�"data",� t I, �V Ma�@��Natl.  (} submitted=4gant} Gantmach�F��[19605~�aVr, Matr@!u0Chelsea Publi�E�anyR�geAQ Gear%�W�'B�A�n}�Z !U2A�C���P� �/BifurI��1�via M�� Simul(:�� -Galerkin�g��i�e�7a�%Z 2�941-963.FJ�ap!NT��,�� I.�d�Zag���݅�Project��on a SPqT : Si�ly�edm�M0Legacy Codes"5�0 to SIADS, M 004;� b�#�$as�,ics/0405074 V rXiv.org}�]8gil1} Gillespie��i�7��"n+-^�M nume�&l�")��the s&�t��&�*_-ch� al reac1�u\!�f� 03-434.�il2Z�7AdExaG(��oe�c�0� >���K EF �8�2�&232h$gri} GrizzYJ.+�n%IFR�!^.in:E� Le,No��1��A�In eA �s}&�lRB2, G1y.Fuk} G�� nheiJ� Holme5 ��3�K��Oscil�,F��}��dp)Field���[$isi} IsidoA��<�,`�1�#����@jac1} Jakubczyck,n!�EJƾ�r�994.�kaz} Kaz�� N�R1A� A fu"�e�# appro�toY � :R"Jsta� thro`4 pole-plac��a 43},6�� } Kex ,pB%�i�N�0� �+A�b��A��+ �eF�."m in�H. Rabin (6),=.�]xŋry, (a�~[Nej )} 359-38.akel �y��T.,A]xIterat�*M�6�� -i,��M sere2$n Frontierd� ed�hea�cE�PA}�N�Vq Qiao�, �hŋ$Newton-Kry�1Sol�7��   -� Ca2F��C43fCkevr1}:�G.�*"Hy� J .K, C0., Runborg, O�}:=Ki 3a 6 � -graine�9� � u�4: enabl�.� �]0to per�M� (-level task9 o2� s��4715-762; origi�!n�oc)Yob�ed> ��2090432�2�vr2>_ !2G9` aAHum��� B+:�)er-assis� "� �Q6x, . �Q&AIChE J�r" 1346-135.? lee}� H �ArapostaC2 �Marcuq�a`�tOn��mM�^0�rP � �-�D178.� lin}W*�� Byrn��C�� 5!CRemark�/z� autonomou&�3Y&�obO9er �Niv&25},3.%lu!Tuenbe\4� !�196eOcA�� 7# of a �-�U IEEE T�:. M". Electr1� 8},72�u�+:�}9.� by�� Space�$}��T�~]� makeev} MA&� roudabI�F���.Y Af��tb�)u�F ors:%e(Monte Carlo�2aU��  M]<116}, 10083-1009.�nam} Nam� 198�b�Y0mxEFa�Dc�.tr�req�.�Automm�X11.Vsiet1}6L, A*g9��nVs3c*� /.` �cũ��: a kibw�it\>o49!o922-1926]:�2:���rah!�MZ;�-3ba�� Brow�;�#�1 N�@ Liquid Crystals:.i, � v"�;��� �*�&�io�Qh&$� ic�f18�$0149-10157:3>�_�<,-.� diagrams�V<!�ape-"l \�� !�F.� �* Chao� 207-220:�4>�6Q&�&M L 4%�&� "� 6��-Pole P y (One Step:An"J/�A�  D��&"��}(1�or�^�lex��i"� �Society��!�)d6W Coa!�nci�)0Olympia, Gree�) 22-26 Jul.� ti}>o K.,O n,�H>; I�(�t0}7a �sd2E"b��.A=r&`�{Q2 F�$097}, 9840-984.�p3-en� 97] ``!m � effi)7i��"a��=com�� �stry �E�0in situ} adap tab�a� # Combw* M�* ing} �vC1-2�boe W�"L�Yu,�Yo�D.D �^5�0GMRES Acceler�2�� ` � 1985 AIAA��#}, 67-N`��`8AR75} R.A. Ada��32>  s}, ^� �75*�{CH98}C!ChoFoi"D.�� Ol� E� Titi� S. Wynne,�*e� CamS)-C&m.b%8" $.} ��."�+33}� 99), D -4, 49--6�&i CH99���A�_ne;"Q1� �� *&�t�%|channel�� pipe6: � �'M�16�8,��:3536�00���.�.�v clos5maH�s 1�t� ���.} �F%- ��%�8)� 24, 53�/3�.�00 .MqDYgL� Margoli��-. hang� em Direct&7w0"of%�,Navier--Stok�5lpha �.}-�vt 66--� 2�OT��skidov0 B %-u#m4 On a Leray-$\�$-r�u,}��Royal��. A, (to��ear�b ${CFR79}� Clark�H. Ferzi�4!�W�Reynolds-DE7 ��subgrid�@le �s�\4an accurately �< �i,}�EE�.�%�F (197a�1--162�FkDP.�nst�#�C$�|��HGlobal Lyapunov exp�8(s, Kaplan--�"�r�i�a�d7J%bhe attrA� $2$D:)y�},��m. 48X� #�$38E� 85),�27:�8"Con�M�M��s,} @ Uni��FChicagoi 1988.tEFNI�Ed6� B. ND.�:AR. Tem� !a E-Q�8A6"Dissi�* ve E"�:.�Reseak2in%%:}� bf�4vs�=�(��94.�FHTM}=���BOth�5�al visc0�糧��,Lt�> rG7�A.6�V�ce+�}\� . p":5I( 14} $/2I(3��u� FHTP�� �M5--�Ii�A�fL. q� ce. � Ţ& ma" %s� c�}+D �52/153} �1), 5�C5�� OIAS.�AV 0(do!0:�9\ tb>us about�?}<7J�;5uS(Ri5de, CAEge�E; 80, �mpm�M�20)Am�)b$Soc., P�Dd� , RIMa��MRT.�OXn�R.�)&(:r6�]3a�T�Y%�Cambridg2 �' B�'{GA2BGO, aldi�em An+ro�8t)���alaX�FU� ,} Vol. IO IIJs1:�KR�@R��Kraichn E*Ine�9rB4E� two-.�Y�,}�:,qe0��67ae417--1422K LADY} O1 0Ladyzhenskaya흥o�' Va�GP�Gc."�ic!B � .�w�Ny�:pSemig�>Y Rs 5�."IE�.�){Le1974�1�*�/�0Energy cascadg( large-eddyB\ M�t �k�0! g? Ge.�#1�#74)� 7-2J0TT7�.��(B!�A��&%Nu."� ,} $.�2 1979.� TT84& �n m A�(,} 3rd revi%�?i%#:13lE:�8B�In�"e-D�al�U�s in "/ 6����I�App:s4 ���}6�B�+A(6JVrGeKu�'S0VrX(� Geurx ��9uertenR LN4 of� &3ixMlayerb �hmixed� ��,}�� m� ] Dynl I^96), 309A^�X�7����* .�Z� 3�I(!C�5E��WWVJ20� GGWinck :�A. Wray�(V. VasilyevJeanm�7i�(xplicit-fil TR�9g tensor-�< usivZ  �Fpl�e/SaV4@ Smagorinsky termV��20# 1385��0:N�� b�=16*M#X6S k�Two2� >�+~ a�vex� ygon�:�+K ��45�2371-393� 1)*2} 2�+E�A`< abat, A s�u �@�#A+*�&F of &t al��eet�U V�T�(, I�II,r5ct.��1��226-235 } 4)31�,66-17�+79.�3�B:M/>6P/*�. �R e Zak�U-S%,.�0semi-axis, In� e�l�b�/ 1813-183I=�=uD��YR0and D!�epelsky�G&;)l g_" r!�&j *�0B�0, �!� bf 6h81a221&<@�5!k���.Q���.*C2�.oy*b4. �.)_ 4"�.-1443��7.6:�.R.�1-�1�r$ h�1, avail4H4on http://www.ad.sc.edu/$\sim$imip/04.html}�76�*]O9�&'}vIr��<:�2-�2�3�P.w;BM9�!�Fo�K "�Kde:uWB�KIQ Inst:J�Seu 2UM9!J�f��21(�a ��� rval�#R&,+N7ra�Sy#I�&�7 517--52J�f?R�6��2"�56�2a�M�I2� B�Annales4 Four5�Z0ial issue ded�$�o LouisJBVp�<>)>v4ChaoY[ prcGt`�|*VTdg4�|B���:�i!� . ("�*), �*:e]AP/03071 U/ 12} &$ rine*J4$S�i�%\-ab�I� seg��&\Ho�De&�O;� �So-g".�.AV �~\.�] 307026 v2�1`@X9klyan#B� Sɑ�b.�R, �A2:�v$86-)C8214 O. TarasoK!n1)Z�55��\&c, Zap� uchn��m. LOMI �169�C51-16R;289�5} I.TLDbibA,�QacN�Q8 9 -�Z�s,R 9Ё��t��2� �C�" orld2+t�OW3ngapo�3130-1�52�� h AA0ZUur�7WG\"qU�3H.��-aryt3���Oi&��8 3505-3513% 617a!D.�7�tT/l 9ʑ��}!+�7�X�]m3ofIEs467-49�=68.y18Au*Z7`*� Ex�-u�0>:self-foc_Aone2G "moda���A�0media, Soviet-O JETPM�# 62-69!N72=1ş�)� A.IR�� *�#��v� �B�Vs.*')�. Anal@68-76 :8N� f� 92`J� *�=�N$ iduc"\ isc o�-ng�its own �eE��� ��"+E-39I8642 02} F.45�=%i(S. De Lillo �BC[Q�� !o� !��!ge0;�"]X s at%��)� ![Me 2e 9Q#��9Z ��03,N. HunOIBoGh�C}aA|5/tid�nd gra�E�"9Is1n 343a�� 636 4} MA�0Longuet-HiggirM�[ tran�Cin*�Xs, Phil.�'A l24m535-58m5:m5�m!{�; Z2 f�."surfau"J�.� 293-�B�46�@6} Lord Rayleigh,2_ circm���airT)dA�(Kundt's tub)���s�Oalwamt�n?94 -417!41-7!1 883). Als�7��2�H�-%� 2}, 239-2�%]<7}�!RibA ~6ea�DE�o51)3�O�>349-356A&9�l^8}�Schlich��c0echnung ebner�,ioa�her $nzsch/$str\"omung��qZm�� 327-3C326� 9} G��5�eff����� fri� of�L+AJmo�1p{Klu���*5�!��%h c8-1�D1856�VJbJ UnsteadyU�� s. IF L!�ar&� L�L (ed.v#Ros3a� �F@347-408. Oxford: �eCPress!�:�@!2�Dou� qH �a�qB ory ����F`2#'673-6 6L>N� f�&� � ��"L��\&=��5�:� :�%�"�.��26��pG���H Dirichlet NeuC>79� Ce�>&L*�nV�ADD A�@ŒL"Ce�=Fh&DZj 4} L� Fadde&L@Takhtaj� nd>J?A&p�edescripm4�oQ3�aSN]$, DAN USSR�21D+334OD�j); .� �AA �?it Ha"�f �2i��1� �B*�6-�N�S.o5} M.J. �[�"�Ra:�A��H�[, |%�AfP*II��\ $1262--1264 6 6�] ] �] 2^ y2X% S.�bvi�1I� zero%1��ion limi���gra� f�Q [ @-�_5�2nd Abs�"� �;�ep�2*8!;A� if< X. Zh�@ steepesEsc�*UV. )BF(BBulK"\�( 2�:11'B21 2); P��b�!U�N�A�M6E1k, A�RM� E{1� 29k68�:96zN� R� �� Na�labora�l$ coordinat�Teoret��Fizika�9�;387--40�689eu+Venak 9�$New result��!.lN diU�!>b�1&�c,,M+ofFFforj3 IMRN)~6�O�29�H9>yk46]��_@ xGo��h&:J%7h�y�to apB'�B |my$�9in&�6�*�RMQ��EW� 14U 5� )b�'�.�:��VA.B�<� �'"3h�@!�!�Q�!a.RL �1� Ck1�T>�4J1jm����^ &s� J��9},�p0`k]5�.O��Sz!n�:EA��sG5?q v.�b- �435--4�V:�1 XE�\quantu�8s,&IBs�23�c 2389~R6 1�T MacInty9*�1�.���yB����&a@:�10HF00�96S�!a�GhoshE�Zamolod�a�U�$S$M&rix%}��2 �:�#=�16f�>!�� �2Modq�1EES841-388� 84), Erratum-ibi�TU D. 4353 �6,�E\ rrig�$PeDorF7�$RietdijkpMDSasaki, Affine Todseld-iA�2�)u 7h3�I83--9�G6� 20} ��A�1f a��}I5>�[SuU�� 5 1�.164)46 l8Bowco�?�ACl;c2 =�U,c�j��B�Ii� NuclQB)� 4�4�m5.�R� &f� 6�eck :�%$} J.-P. E E�D. Ruel�B ]�%R5�l61�R6K auer�T]a� D. A �$it et al.}N��aIO \a�23���ZUPO} �TH. Jens�L.i-Kadanoff+I�caccia2h�3�� 140�� 87);�Z{<un8SnMdfG.�a�1uRJEI0Cvitanovi{\'cb�6_272 �63biham!E9} O. B%�W. WeWV2��6e�1 V6�grebogiX8} C. G 3�T�i_ . Yorka^9�.?3� );�(%�$A#17N� =�la��U Y.-C�i?6Nag �.���7!{6�� 7). .chirata:"MM3�%SaussolI,S�$7i/x tE�2�V3� 96n\ zaslavskyk1} AIM5T � M. K�^ppe!c [%.�6!232� 41); V. Afraim�f!GA Z_LE �5�541' !=zbw6sta:200 ^S `ptN��W(A$[) c287A}, ��H);a�zI . Plasmas Ca�44g]1). %$U��I.a� Cald&%�R�312�5"� ;�hadyn��W�N�F�38�224502H%26�hartma�G6��P�Œ�2:v- �1a�610!�D%� Grob�BDok�k�X Nauk SSSR <�88=2VkacI� Kac,j�5� 10�194� &[halseA�80 %T.a�H��%�. revu�Q�b198�_.sfarmer�s�cJ.�^FzuR�7D;3 n .�[sae�1�%� b(TroubetzkoyF�R�be�6NZ9#ٍ�\ length} I� ex@ thaKllow,�� bovp�hS]a�long orb"i� a�)a<020�8wevaL� nc is not-cru" i�]ta"1ZUfv*"Turd~M.~Tu(|�s ilos"9AOA�2 T 2�3&5�XC�hV.~Castew+ E.~D�Q J.~BoiO3a�0!&P.~De K�R�:6p6�295��'n0Ouy} Q.~Ouyan�V H.~L.~SwieZ,�"o��a��T1a`GKon} S*Pe.gP.~Suzu= M.~�_� S.~K�Z, g1c !6�O US�'1096a�2�gqDan03/`Tanak�(Y.~Kuramoto2 ��- 0262��NQ4QNA7� 0152�1N.�Nik�<~N.~NikolaevskiiS!�+Re�.�3Engine�Sc G}, ].4S%�Kobh C.~G.~SpeA�e�Q:�L.O�139&e�Sa@C), p. 21.@Tri-VelC ~I.~TribeA)%�M|VelarA{�o�-]5Ad497IdC5�YTsuVY K.~Tsuboi2q��7� 163> 2YKai} AQ $K.~Hayashi��YAx dakaa8 �wD�I]190073���PXi} H.-W.~Xi, X.-J.~L Y$J.~D.~Gunt0= .��104�h5Xi-Ext.`R.~Toru6\a0M6�2&-{6O Rs r.�K84} 2E�! � .zN, W͂)>T�1ce*Yg,p� ?0�(Do�|� >YTor} �G!So \ J D 1F�H=�A��3E3�hD�Mat~C�etthew���Coxb1R14A�B2Fuj!�~FujisE?$T.~Honkawa- .~Ya��>^�s10� 9� >Kli��eKli7-n%%B.~�flomR_I]IX�23��1_ 1� .ToheToh=JņJpC15!Q9 0ER3-f �U�fal01@eFal�r�B( Gaw\c{e}dz�!�2Mc,� *?):71 913d^� jkra68AM Kr"M6)$6#ѧ!" 945 a�6Z%mit�� Mitr�7 R.PaP&2+!u�*9� 024501 �2� kol4�, Kolmogorov,� �c� 8 P+ 9�42�8Fri96} U. FriscYAu��le�T�fP#ven�Z:8 a���9Zlvo63V. L'v�ERddivil!�I^8��[  7030ہ�ahay98} F yo�0C. Jayaprakas�*&�T�  R4867 TU!�b�& m83G% 17!y>�kan99�( Ka�e$T. Ishiharm�K�etaW �Iq.�  2154 �Z�bel87 BeliniD"%S9oSo�%_'I)6a� 30a L=PwirA+74irt L f�j MH1M� 4928 �2Kjen92�"<G�-ladh+A2Ie^-`� 721-2� goy}�Gledz� �~F~� ��721�6 73);5oOhk0i�M.&wygrB{DI�83-65);�q&�)ohsm'Wa���R!�nz"�)� SG �)�N"Df1A^Y,3 }{V.ajZ0'C3�em��) one-d*[8��)e &�)�A�-�� d3�>1): 6�)�c 72)}�Akh}{N��AkhB*�pA|-kieTuD,*��:*v, Pulsx&�packet� (Chap�nHab[ � .�@VVz}{L. V\'azquez�S�yeit�/hM. P\'erez-Garc\'{\i}a, Eds.em�KleinA/6x*bN:��!��9�[�j*-!Ca�.�Sulem}{�$ S� M:"O$ �{\""�xM: S> ,%X c�mpsr ";q&&  .�(Fibich}{G. ��'p�:�p �6she�H<� unp�q2��.�y�Dcriu( U�A��m. !o.�Q�6� 183-24a�.� Wein�r}{M�R �No�03}ScR�m sharp� rpol_E estnu!��">�%�8��567-57���.�B�RE� E�Nkezents�$J.Rasmus��s0. Christianse�Y�\Gaidide@%�gui�1 light!jl�'ed*f6aǁ Opt. *MdT1037-m� 0)2�M� }{I. Tow�)aDB.� -rSt,#(2+1)6����a4+�Vedium��b-a;n�9 Kerry! ity} �  �"��537-57�.� � 2}{A%�-,�Vxs�$j�4agE�all-opI�switc�w�Wa'�!�e-�3�aA�*�*�R�KJ.�� �Q] �22-528%�26�$pisaUeda}{ &ainHnd�-��D- ly s�Z�rA. 2� >�Bose-EmfD ensatM���l YP9a�040#� .��Boris}{F�&dull%�G. Capu��6( enkX2�%� -� �Co�ding�!�2�� ��; teIal�7J-� ��*�5�2W A 1��013�t36�Gaspar�n�Dqs�Z� P. Torr$�aNil*c15�^,�d&,}�^�:�e�XA� breTF�+ %� ica &om1�!�,4) 193�2102�IMACS���NuBstu�Q?Y�Townes�}�8CY@0T.�*�7 )�tt{arx�a/� ,.PS/0312020}2�m5�04b��H� �A�Jrd SalgueiroM�1� ed vǑx�A������� e-pr�EnV��b596�MM ov}{��Ona�!%rKZjv4t��aryt "�4��Y omag�VA>!� E9.k � bf{3 48� q.todos}{T��n�o$M. Lakshma&cFE&5M�6_L�b"@ E�>�8s:� pe-�Og�#i*$s, logic g�'�`!l�#h�HuŒ�� � 67, 046U F� PRLdual}{);3� MEM���R�es�fCJ Wi�C� E�_Cor��MJ��-mSM s&si�Nbi%�mix{s!�b6���� 8�1w1r1.�NaY}{B�EsreClve 5Etby -�"er�Fs�!�,it up� }, e �3s)4�l86kHumberto¹ Mu��S�~> vector]�.V2�339tg.= rig1K Rodn� ki%e�2�d'8o��-�*zs �ty!� $N$-utA�NLS},i�27*X<9114}:�2%= Pere�~zz�v|"}/�&.s ��B�b�-ph�<9021}} ׅb�)az icaDp^<)�+ simila%��1a�/ ec�V&�+ m�Cs�zLm+�V!211-2182�� or aWiew see�wA��) in �� bf{4�6� :� Kiv� }{Yu.� ,C (P. Agrawal,%�^�DM-s:}cm� to Pho��cs"�[}, B$d$San Diego,]33NH�~pp�, %a�SbeH B*�&r&a�ies�b&��%�z4kso�� A, Sg ���� J�K�K�D&E, ���2�K Anco�}   S� J P )v0�4e�cur~�in�(�&iaa co�hl m�ns,�)Ou�%�0�Z =4Bakis} B��? Park Q-H,%)(Shin H-J, L�\ngn�c* ��c s�`*�*, els,�em��1}� 372}  , 45VB.�2counterG } BeukA�F��nd J6*a�5:Օ@\mۋy doe �Zy Q'�ay��!.R�E*h}�N146 �8), 251ؖ 0; v>��S.� C �;)� z�IJ.�a�"�. t�JkI 561--5QZ&T- o�� 6�� J�6�)%� �396�02�TBijv  R,�Kre�!mor�a/e way�jf\��IA��.K$Monthly15IP7 R246͖.R8DauriaReggeScuiɝD'A R,  TM�$ciuto S, A"(=* Jbi*F M��a&��lYjset-���.:�(�00) 363--366; �, G%P-� ��\��ba�� :x-�K �in0EseE,=]:=law�A�ucl���u�17�Z�1�16ANE�nherrFoUe}  He  M,e he � �5Exnon�j sigm�T-3Z�b�$(1979) 38192 R�Pohlmey�� � K��x Ǝ��xI1�Se �.�� �%EV�!Y��72F�L} �As�Yy a$atYec2�N��Z*�)m�-Ik, 131�322�Rw�#32�f3�F�� #a�̭�S}� Ap"�� v77�=87)�9.�alg2} &�C Ia�*u�i�Y>9 ov R�� M��-c"� �l��s���nonq�ivgqG, �&| !�ics�i� ex�&�F >�*�s\.�Helgas!%  S, 2bGGy,1��(ups �1jc�_, .��� vi�V�m.~9 * 2} Ibrag=+ N H�=itor), %qes,AS"�  %!�Con�7LТ (volume 1�� "T�=�The/4B D lop!DsM�Q�� al MO Q3Q,CRC Handbook��Li-#&89ofZ�Y,>T>$, Boca Rat�#�52�5~6"�  A B, " �q�gnRivIILie-B�GIam�F�Hm;Z��2 --30.�Ku[vSI}  PJ� E��4O(N)-invariant�́�>Z ---��aI,=*! uJ �a".��nU�ApA -352.� Mari-Befa2� �� J� "4 �Yre6�R mJy �_ �}1s'�" 32W=�# ikha! A V,.E&.��V��5f A�y�YP:5� lis�(- �Rusl9 Surv�4�? ,�^52�4} z�So"��, �6����m*\>Z�?�E��:"��rpf+e.�>992�O�q �} �e��.KJ3�5� q�1g�N� 19 U�,,F 2�"]}  a�*�7*@1��!�SNion=-rt quadratic� t�qt~�� 7�Vj-222� Rehr�� K�  K-H, R.� >| ,${\rm O}(n)$�~$\� $Je� 6�;m�2�[( 262��632S�0� "נR } �K�$L� qU�R1a�h�eL`�ru���!zy���' 7(2)�*410�4"� N� polynom�F� �6�� , 13�A52X-,!#-\ /EsjD.�����n2�f�Moscow� �^ ��-�aN��7136� Sue}  R WbU v[�_",�1} �5EC.�8^�J6� ��|�C �T#98�:22Q82�algN� vinolupov�� , De�L A�:� ��S�B6Sa"�Fjta.� �4^a32�36�-4 WolfFA� v>]�ve8NPg J?A�h�^n�A�$ AG113�B 1148.�alg3} 6L)��3 .]� �tri�q�k��-\=O .#�D /1�J�?7�60��62�1�!D 02}  TS�[���oo!ca���-xunknown1l4RIMS KokyurokuM�No.�Qgm�M��P��$ ese)��F8=�=;�X�'^� �J . I &6�, � RT41�2/��} � G*!IHasim��%NyW! ~V�tpl-P�$i�Ey, � s: Abenda Gaet 6Wa~�rBm?6�olEEv] E�CRACK���pF�*�~`, 5; 301032, "pp?RMbAcee<$s.RZac \"Q } � �G  Re9%v�$3>��a� >X� of f�?��w�M a>��le�Dmea)�jګ�, ��i� JEPTi�4�7�10�X1022% Zhiber�"} �� <L( Go:]�e�a��t>g�2�*++��, 6ӝ609ud-�!#��P $u_x=p(u,v)$, $v_y=q .R��et� z��z3� ɬ3� h8R�v+�vAg�wO.~ �8~BettelK��"~Wiegm9�A.~Zab��S it V�ifܡi�6a�'p�an  nic dro�A�KDQu�CQ* regim�$�X[ d-mat/0�>33e|2� AlekD� v} I�1 itIa%V� tin�m3 A��$y of univa ���LNau�46 b 76. �_� �9Krnold} V94  �!�"o I�E$� hme� )w,F�f��3C6.|abelonjg~ , D!�rpf$9alw�sIn2�h.��J}�%iMon��� .�f?ics..Unih`�"�%�2^�nko} K%8 -9j+)�eSxtel�'�"5� 5�-%\ $S$�roc�, eklox�sJh19�E�1N-. �Ql.�i�~.� S�v6� R.I.E2�Bavui}%� �~�o � On �L��^�f�(�~or|/a)em�U0Nekhoroshev}, V� E&ron�*v(,�S 1, 13R.>ol�&v}a�V�: ,T.~Fom!� �ݫJ/. &J topology,)�i� ARI.\&e�/CRC, FLE"2�g Bieb�C} L�� �\"U��die Ko wz:A en derjen�� Px� zreiouwe�� �LT(e Abbildung�P EiP�tskrei/ver��l�, S.-B�3e�?Wi @(1916), S.940--956 rangu�L.~de~  �AA�ofA�������ur�# Acta-�� \�jnnA�-2,�Cl�24,Fiorani} E.~ I�iy�t+��:,ardanashvily �a�Liouvk�-��-]��Ge�]G�+[i"",���36�n3: o. 7, L(�L102�e>�U2H�(Poincar�-�rounovN�bzni5:!%C2�CF 2 �a05!A72�Goluzin��; -$mic!� ) ��s aWx e�bl!Αq�h.�i , vol 26,��_6�0Hohlov} Yu.~E(9P@$;Howis��C.~�Yingfo>�$J.~R.~Ocke�U,��A.~Lace1�A� ` %�sm��!YBH}inUeufw! }, Q��.F[ �!#bf� HJ 1= 122HowG9D� �ź=*lex V�` �F!e��Dng ".KTn}, &~|:�0E�1991�3, 20�22� Kost�/I.~K.~ ,_~Kr��; M.~M[>v-*�0 P.~B*K !w"K �A�$\tau$-Q3%�z|ly��� m�x)�Zgs�"� z+�� ��)�., 40*�8嵅���6�1, jP.@Kufarev<P@ �O? -�"(meter familA;of���h�ecM- [M��,Sbornik] N.S13(55�43), �Q112CLoewnfK.~L\"�,�'it Unter��5Z \"u�8s�Ze k�#e � en� ��he� "�,SEA= 2�1m�6�Marsh�+}�]jc I�vo ure� !�*MXm�y�A atwo&y`�*B� ;i 227}`;a�B�@1�@2���} qA.~ �Eͭ�\'e����:A'�Me���kt�+a~ (i Prilozhen�8��r),� 2,�}-69; 4�oZ#T>�k)W.G �q�1�122�,Pom1} Ch.~Po���0 �*vSub�Tym��"r�dke6e.tAngewQ�E@21h$196��1��:z Pom2Z�o :� ,� chapa~on &��n&-ialW1���L }, V8%nhoeck� 8Ruprecht, G\"ot�K�L1:�~$Pontryagin#Z~S!1:1~G` tyan�C R.~V��(mkrelidze, ��>��*y �+"A & �3 mal "��}�[r`w��i�-s John W�^�Son�Rc.\]A ` "��19628 Prov v�D�t��#aTs��*Df!kins %"� $�����8�0�2, 16E! 677;>�F7:-SD?$��(2, 499--516.�Ri=d1!EM��g�Qb;a.�Jb  i� o2. in� narrowA�� FNy<t bf 5?� ,��4t��6�SSHC.~Scha�_Z�pOx�C c f&�qW�-U`��ca� s (With a�GmBAy 6!�� DerivA���a�6H� Arthur��)~ ?3n%�Q�7%�C�Iqu]7PЖc�~4ol. 35Z�@E� A�3 52�Vas�v%, '�8{A�Mutual%�g�i�92E�U�2�Mat�.�T etki��.�}�e$1, 56-65; ���I�!��B:� 543-56C�}>c �fZ� �e� orma�+p3 &� *�#}NtO �213��� � 3, 5�532�[>} e_�  ��� ?* Sel �&!%I2.F'BehH�,N�-�jfK40*\0 {AuXe Au�@A&{Spinn�tops}!(""��er&��\=&p {BS}�hBob���/Mu�ng"��i� L&�,"&��Lie���n.� �'a� ?e��  u:l�Eu20 99)�Z2h) {G1%Ga= Diag)�ise� d'une�e d' h� �/enospin}}�Xdeiqu-3�6)�7--109.U {G2F�La fo��qondmo Bethe�sgo�Oarigi!��<9� {HKR!�N.Wv n�<B� znetsoJaO.~Ragn��Bf���!~$sl(2)$-4 �6�&4�)cr)%�.; 2477--2492�MPR{iMXO�� Petre2DF�Al��ic&�]��)�A }, h(s&y8abs}8o 410016, s��A_�y��̡ W�ics=mK�V2`�~j�SeF ���w;�’�[�g�e , ��"�A�5 , 84�_8512 KNS� B. KQ*, F.W��QE6�[a� ^��4A6 Ruijsena׻L }�1omV�1 �855--8727KS5 �~��~�'��On�V$many-body �s,}.BM� 8)�Sf 26&KV{�6�,P.~Vanhaeckeyx�(�G��Aivk.@-di\-men\-si\-o\-�)�jle�: a�'ic�>r��� y��*8M�i�4�0�'c0.VRST��Gq!yDTM�b Seme� Tian?�z �Gx-�ei@�*p(e XF�e-D,5 *+�}8�1�}�,V�y�&�:\Skl�A�>Z��� trends}_Qgd��.��\69 pl.\);�[{5) 35--6%���2�.�>2v )�%��:~$rn 6791:U1r2rKr�l J M,6m~.��$ �}-@^}@4} 4705 %--4720 ("W: {\tt�8;102006})�gra�#Gravel S�2��s %S(�a�g2�thirdO� l�/in�*8c� �"V ..�]w}33} 5902�5912 j�206046�a�V����.?>�"�8of�b5t}/8�>��970� 983.j�1080152�baljs Ball4�ros�c Herranz F��.6!�$Sanz-Gil T!�3.}��b^6} L93�L99j�211012}).k:rw�Z8Wojciechowski SX 3i;�� Lett2��27. gon98} Go�t C� 8 %O)��M��!���ero--Mos1�uther��� �1} 446id47.O�gon� �� �^�(�97} 408 X095}�rodA�,Rodriguez M �,��6a� N�*.I ��|3}�'9!�1322.nJ1} 8Ao&]Epb}>qM �;�  O %Max'GH.4le" agnet: &��6 %�.�[$ (3): 1645/{1 DEC�.��ben93}4���Ee9�ߴOrtho9 C�BZ�},)1it{2�5_2eGits�*�(Opava 92)}H1 : Sile�#.��?0ava) p~163; &C�at)�tt{% h%M�emis.de/|�'*?�7:� 7 %\��#insic %tac�~z� a% � -� �HS-Jacobi"j&,M_Fw �b�E 6578]�c=�Cra5��Sar�rW!�1 %��.���6v2�  o2?"�9�b� 2} 4312F�W$\l aszak M�3� A5bi-1� ��'*�`��"tIhrs�&�0ls)���}&�*sH.bl��.�y21�[���� %:�cha�x[ dege�9s\P^^&�.�^.39} 32>.1}2��%F��:�uEto.eofU|s:�DA{n7^�- %`���A� KdV "(��2�2;Y�N�i1a�> "+2 1})V�(�j� ]�AF]fA<\ow� P�F��qit�M�|>{�Tl L269-L275�iDf.facF } A"�B.� !/&�BHl"�B�u-!7"�8&ABF�Br��.�bog90}�� yavl��iiD��&� Ru�ح��6ey}AiV 1-86�902*sch���I�Holm DkH �� _})X7�H66z�6 k3^&� chh94�� R., ^ ny�Ta-o%�)�.X s�[-3.�lngp��=�A 9,a PJ�Pil�%@1�"y" ��463-147-@7�u��o  F��  Nuovo C�toU4��3-447%�75:Sdhh�Deg"p�.��-�� Hone�FN�H, {B�oQe �!��:reh� (Est\'evez P�!, naez GY�qmMrG*B2DG213�G4!�� o"�e� NlPr�J�e�our�C�:.� -�I� 4-17+p0 2jff�@.�G�6)�n�?kH \%�7-6)�81Y�gpW Gi��KR)�.[ m=&� J.�g7487-749!�1*4.�hqA y��Qiao Z�|-6|N_!%�5{%�>:\it1�A��P-c!�37-42,P6�hw= 2Q�Pa^��Ba!��129-14��200�B�kğKrusk�>��e�F :�] �&�}g���� EdJ z�Ap�Ab~ , 310-35)�m�\bibi%�kp_ KudrPcova�Aj.�id�\6��_�� 9505-9518�9�]i ma80�� rtinez-Alh� L ]Aka%b-���2342-23�p8%�VWeiss}�Wss%A!�M3Oa$1405-1413,mP�PN bƐ���J�ars.�~J, Ra� � S�{ H)Q�i.�i�A�$1978, 333-�.V blmpSpBoiZ�f�~P|'#QM)�*� pB�i(�N9�e27)6�8blVn�e �87, 3e382-:�}ډ9 ~D �A~�vJ�993, �� -1662D)CFA89}�6�K~A,�Z~L*< !�ECJlZ1/e�989, 11IE202�%Deg� A#.)15���g Assy���gY,D�J[6} =?s:Fg�,�on��999��--3!��Rvezc ��~G,"�~RAqm�u��M� a--Reus E-��Thy*� �g�~264+-�915--19�F}`�5}6�LLV� S#%A�]*ob1��sa5, 92h��>�� 6^ �In>Q7{0�*10Wu06�.>/~ �. X�-#A���6��6�~=��1-�V���-����.y1}4�rd� l:"E�;�TF�9aEn4���72& honeaA� ~ N~�=e3AE.��1�A2�sI�347�D2�NG;JNB| :Ur *D�K147BWS:�d[WE� ���Z{D:,JK.rks91} :��MEStA5� D%����991, 242�k�l9+� ch##Ba��it8`'��~Id .0,&=O, Plenum�5Ne#&% Lond"�2�lrWFLevi D*&Si,R� 8�\AK4-42�Bm!BA�veev V~BWS3 M��Dal�1*��� S}&^@)%� r� ���p� e&M�!�2�WTC"�, Tabo�nC_�^+��E=1��6� 83, �]2@6 -=HN$H  ��xN �v �QiT0}r%S��T�Mb."}T"uO,_5t:^�T*�T "�TR2zT.O Steg(Else��, " w,��1),�p 4a��ga-�\ic�6V%�Krugl�%RšVl���Щ�)$1��4C98�gT�ZI[D%o�$ov,=�� ���4608%��yOzJ�dr�+nX�2� �"I H7��245td7);EP�b�_�s!u$oto-Crespo�f �)�6�F�a` 15Z�5�6Y AMI-ob"�Msv$ Tik�� nko,T!dE�� B. L-Dpbv 2�p5);:�L�e%�\rtore�\$R. Vilasec�q)�`�C�jocaru,i_=�� 444� 98);%B. BigeFvP. Zerom)@RE Boyd2}aQ)<d[083E�4268ed0�(,Quiroga-Teix�_�H:�_�S�;�c� � YS"e,AN�I�Sammut,!�A��YL. |CrA���D�hal49��q2�y9�y 1); �WG �6��~ ); 6�aziluA�6�^�>�Z6@:%Fa�der��y}5%s�075����9* ��>�A�Vm E i�c56608 ! 3i Vizd "zd:^��v^�D066614M�eh^^ .-:^a�E�B:Ѳ S��la)<il S3,�6�,(doulides1} !GN. :|R��Joseph2��Fbf<� , 79e�� :P2^i,=�u��i�һ"�_(W ){4� 81]��|ole�Q�anPd�}#R��11�6�YarLY.B�artash�x]��~ . VysloukV(V102EaouY�3QAZeleninaav2IV�7 �e766Mg2 f}s�S2ar39d A.R�z�Y�x�E9f2o 1375��6�Cohen}��  , T^+�zA�W��e�6�,!ev��D.N�jU�2��Qi9��1"Ja6�Efrem��E8 �< S��� F�� F�apM. Se���=�q�c:z6LA3q\T.� m 4 cN2��ci2�%6a~6�Ƅ�cJ�H14N�NeXB0m� F Ostrov«Y"; IW�i olikM$V�� 7^�_2�Yar3}T6�e@}�!l}ġ< Exp &�j" 831m�.S�} ��XP"�2!�VK� 0266� i2` YangMF YZ"�s����6(_ 20��B�# ;} 6K]J�s�.F0 u��)9ny6Y)�-��,!�� ?lex�)%�A:!��3&D2I6�� 1A�% 6�U�W56�o١�l����O�� nela.���ud#��D. ��e���.8Su�9u�i ! ��,A�=����C.��ouk�6/��.0-7�U�N��a��f�; mB.�u.��bf{�z72��],2�PesHche} T. Peschel, U �eand F. Lederer, Phys. Rev. E \textbf{57}, 1127 (1998). \bibitem{Kobyakov} A. Kobyakov, S. Darmanyan, rtsch,>sL J. Opt. Soc. Am. B y16y73 y9).y@Malomed2} B. A. �, P. G. Kevrekidis, D. J. Frantzeskak,H. E. Nistaz ! HA. N. Yannacopoulos6�@65}, 056606 (20022�4Xu} Z. Y. Xu,lV. Kartashov, L.-C. Crasovan� Mihalache)$L. Torn>�� 70},y4).Xgeorge-PRL} R. Iwanow, Schiek,! I. Stegem|E-�. Y. Min �W!�hler, ]$Lett.�93!�13902J�(Yaroslav1} Z>�!�V%� Vysloukh,I!6m29m17 !}4);FU>FZ5V UU� U399J�LSilvia} S. Carrasco!��J.A{TorreItArtigas,Ah(Lopez-Lago,�Couderc)\HA. Barthelemy, IEEEM�0P. Di TrapaniE�Pօ��=^E�}O2� 1004�e�| \end{thebibliography}�\beginB {9} &l0brown} D.L. B @, M.G. Forest, B.!�iller \& N.A. Petersson, {\it{Computation��Ustability of fluxons in a singularly perturbed sine-Gordon model of the Josephson junc_}!�IAM!� Appl�th.%�{54}}%�04), 1048-1066.�davidson��D � Dueholm Kryg�FAderse�DExperimental inves��� �rappe6�Solitons�B�ACX{55}} (1985), 2059-20622�erks}��D ,�� Doell,S.A van Gils!�T. Viss�%�8Travelling wave)� ��equ�}}��ica D �180!l,2003), 40-70.�hauck}�H M'KinksE!roI.� long9� j-�!/ M%�Me!�)�Sci �2%� 2001!�189-1217.�katriel%6K � ExistenceA�tJdiscrete!%eM� ring� Q� � AnalM�36-!� 1434-1443.�maksimovA��� �(I. Nekorkin!�MRabinovi� %�SIL�in)MHI-V characteristics�nWInt� Bifurc%�sChaos)^5�199�491-5052�claughli�;W. McL I,A.C. Scott, �Pee� janalysi�� dynamic%^}#A e18 �78!�652-1682qust!RV. Ust!2,aDo� $R.P. Huebe�; N6�B�Fyi�V�� Oboznov, )tD �!V.�s)�EŁ�ann��Z�.��� )k69 �92�$815-1818. ��u �>�%[M�Jo�12Fz.�23�o9!P315-3292p watanabe}� W , H.S.J�jder Zant� trogatz!�T!jOrlando-�.? circ%$� y%RJ��$ the N�.�>�97-K 6), 429-46�zeidler}= Z 4, `Nonlinear F�|ale�E�and its�ii,s I', Sp�Her-Verlag (New-York!�99a�!�N�/f�x10} \expandafter\ifx\csname urlP L\relax \def\url#1{�$tt{#1}}\fi^I$ urlprefix>OL {URL I&1|Alvarez:Survey:ICCST99} G.~\'{A} ,, F.~MontoyaR~Romera ~Pastor,�o�Ctic cryptosystems, in: L.~D. Sanson (Ed.), 33rd Annual 1999 Intern�ValA,nahan Confer�� n Secur�,Technology, , G0, pp. 332--33ay\bi�carev:�-C�a :? CASM��} L.~K , �s-based � 3@ A brief overview � CaAc Syst�$Mag. 1~(3)�  6--21.�X�fu, Z.~JiM~Zhang4~Cai, Performa� *y } U�-�� } attack Ad clasE�6�u�2z�1��,8, an erraum!8 been published2G 309!�ap!�3) 165.l�Ergodic!!��~!�.�U �%wM�U�311~(2-͠�72--172�r�4�G.~Ch^K.-W. A,5�Y-Ƒ�-type���1� : Problem��(ountermeasu\:j32]�4a368--372pHu��-nB�y:CSF05}�Q$, Z.-H. Gu�%X � ue� keys,�s "� F� als 23��(5) 851--855.� Xiao:Deni�dAuthent�F�D.~&%DLiao, ��,n efficient :��� ��� for d d a2g �"�����5) 1327��32]0Katz:PPK:Euro%*A�J.~, E� non-malle��ofe�plainG( knowledge �  app"� I E.~BihamC Adv� . � -� �^, Vol�� 2656�� LNCS&� , %6 211--222��N<:Chebyshev:ISCAS�.( (Z.~Tasev, P�c-key.�bB on H map � A� ceed���� $ Symposium;[ !P_ a(�'��~3,A}003 2a2��uBreak>54��� a�.~�F �H �H-A���V� 326~(3-M�e�)�N"� Bergamo �5\(:arXiv} P.~ !�~D'Ar�A.~Santo .�"Z of��c key>� �.�d polynomials, submitted to�it{!� � 5�!� . I}, pre�t J� �,:cs.CR/0411060 Dai:Speedk 0arison:URL} W& iA�e��om �op��v .� � nY es) X H~weidai/benchmarks.g ��N3�v35�[Baroud\ 2)]{ 02} #sc 0, C.N., Plapp�B, She,��S.�0Swinney H.L.}a�2 Hd{Anomalous self-similarity��a turbul�jrapidly�ng� id.} H�it{ɞR& � } bf{+11450.� [Bat| or�69� 69F� �K.} 1969-2��he )gy sp'um�,homogeneous, :two-d sio��ce.2��Fluids�1�(II 233--239!�}[Blumen�78�782Y!���78)V {Uni� pot�� al vortic!�fl�Part I: �Theor� wave �a�i��=n� s1�J. Atmosi=�3� 774--78� CharAb (194� 4B� � G.�4�On�sca�f a�-ic mo�B� Geof�"�~�183� .� {� 71)]�71>� )� 71 -dsstrop* j,^B2Z108Y0952� onst��nu�F�, P6�Ene2�$of quasige��j�18>��!]94a!^�94aBb�, MajdaJ��Tabak!I#94I�{S{ front a9a�a x� B�a.B= �>�$6}, 9--11.]�� �b:�b}U eBsc:���F� A�!�Ah�k�� ��2-DF�thermalM�activeeJar>�N�ݥ��a1 1495� 33. ݌(Fj{\o}rtoft�53)]{Fjo53.9sc{-, Re�53-�m�c�� Щ�al�tribu� kine0 �� D!�two��,c diverg��R�Tellu����225��.�[Frisch�95�95>� 0'��95 �%� it{T�4ce:�� Legac�� A.~N 'lmogorov1�({Cambridge &� Presj .*� [Hasegawa��ZF\a^  MimaP ��j,Pseudo-threeZadmag!�zed!vun͟lasma�_2<$��92� .yp��9)]�7B+�afclenn��\& Koda�Y.�� y behavior�#5�Q�a�drift�Us )��ORossby ��,21X1��B$Held \etal�E�F, I.M� (ierrehumbereqT., G�r�T%�Swa�!�LQt1U�{Surface�U-.#� F�J.�7 Mech�x28�N2XKraichna�>67)]{67:A�?H%�67-u{Inert ran�C�� ~>�1�"141�426��!�471 �i�sc�71 ��-��nsfer in��-EQn1� o it{J �>�4��5��532_Le  (196� 68>�Q E){8�Diffu$ � roxi�{��Z6B��uF��671--672X Ohkitani�9A:97��)scA�a� YamaVM�97i�!�viscid%ti -limit� �  sm :vW �6' �a9 876--88.0[Pedlosk� 8�8F�, J�8��|Geophy(lm�%s5�{2nd Ed�", New �O872m:e��!_S�W%� 4)]{2'94B�2 a$��M�� Q!��1"�  {S� ��local%�non �5#L:���4=,1 16.� Rhines�Œ ِ asc � B%��rf: M^1�Ann. D��>�e+401--442LShe. d�EJJJ, Td UL{.�%hf_��aqla`.� zKje![:�^<18&.467--6�[Sm���Q/]{& )=sc ABS., BocMtt�(, HenniYC.C-rg#�I., Tam��Y/lM�A�Vallis{� �"� t d�$��he .Nh'$rse cascad&^ ���V�46�=13--48.�Tr�R�)]{T0Fr!�VF .� tranŇ�b� �  in1)$\alpha$2-M� ��io'�19��13�l2 �\& Bowm.�Br�2�C:�Robustne!�:��f��3 ��m�E�%�036302�!|��3TB03a� \sc=�5�3a-^ F dA"MK�� m͡>�7�24�552N��b��b��budget�y--� --� I�6�F�&� 5�2�J��%�4R��&%�� TS022�B�3�Y�(q6r�s o���F�mta�en phyIdissip'in� cw� 2>�4199�#26ungA�'%03Ue(!u�dK.KE� 5�Wi�Y� iffe�$\tw_2D�QG2�1j it{D�*Contin.�.^Ser. By��^1, 1�,N��v�� {"��G�, �u&$G �y)� )�B�j�� $s 12 (II)��69�!t�LW. ,Xfor~J I��D�0*6 35� 78) "2'� orue) V.  , Inv�$)0.�s)Qary >�*�]/1;K � 72�494) 1475--1478&� ��J>��, �� F�, 2� 1�848)�� Wx6gGR�,)0r� 28�71)2I`"�! P.aY, �uU�N �KJE89�2)" Jz!�:zC�1i�6��Oe+Manley4ects � force�*��7M �in.��4m96!294) 4�4{R�a}>�A��EA�"� ��in��1X��&4)z & �59h:U^�&H!T�@�I2C, N*5 E��215OEyink� G.L. �hanis�"found��� 2�pictur�02D2�le ,delivered athD American Institut>�0e!�5S6"(ces Fifth I[#n�al 2q+�I�/al�Nr A�er�[2a�Cal�a8nia State Polyt�+ic &�, PomonaeA�555���A. � �b�}�A{n�:v21 Ax���J�9�/�fM&vY�qY5&V!Ey�m��2c'.�>���79)2K9Lel7#  m :�S, KA�"�2.� ��e�� 282!K96$ --202�"5 67} R.H. ��~�=�: 91R.�9 f�k^xj� n�B4���&~5�Kuksin�S.B. ,a�$ Eulerian �P2D�� 4�hydro2|af.'115mQ 469--4[z� 68} C.E. ,eɚ�j~1 !~8)*�w�296a/}8�.@AB� "� Ri:�*�"w> %J�*�  9.,96) 515--522]#.OK. ,�=@I#e� �1R�,2� m:7)*5>���:%,# Z�, .� S^�e.=�R�2��E6$ ޔ~(,&���D), 4AW�`1"���&zPaK %��p6� �02O � I��C&K5~"]K.S. �2PC&QI6"N C.Y.I��G& E%z3Ame*4Ft6&�  �CP7�, "��� ofd inN���ia19�?42*��B��J.C!Lw�:[ 2�i>��62{7dD�.&�2|b��V.-2| *� � r�B��v t E 68��3)f2�4f�f� ��)$� M&4 �36�5f�L*�2t a in �%2:=��.*�*0).�a.,�*U� VBi82@! �L &B�;B�M�6�h� '=�SC:�:�`H.-R. Cho, Extensivity of��9�Aag� 1>%N��f�}*�""��r�(�(�(J( Boffett*5elG \& V<, ssol� 0�( ' 00} �bsc{�, Ek!6I/X*0 >{f�f�: Devi� sUm Gauss �!urZh!�p&�,61}, R29--R32oh!�9�9"��rue�>2"9�{�� l exponen��&�vb�O >�V�n���7�39.392!<� �"V�j�*>� �^� wz��>�:"*��Z[[3*�!��0%]]s'�3� Ecke� E.,�� , Wa�XE�b2ZI�1�� ,ma�"�>��T͒v�r�2 -.*I), F-ah&E�!��>�� DHzE�4-�{Ef�~� ��(��Z�� *�'6MJ"�9�:� 6)]{96>����6 �,{Exact resula�n2�&�%6d=-consequr=�v"k-rv��R��y�%�9 42|*)�~I) \o{}e)A���I)�I)�I)"y���%��%��%��%��%��%eq ]&�i%��sc /(�"20&( Th��2�� ^� ~�~�Z��115a�"�y��E9��&��&��&Lindbor'Alvelius%z_ &_ )sc�.��<�.R %�6-?&7fz�*� ٯ�� �ձ>��299942O1MerileeţWare�78-75>k��E�9>��7J-R� ex�Z�) non-> ..�E� �����!65)66.0Paret, Jullie�! Tabe�>A�9�,#>D�)Nsc � >& �N\&E! �9�, {V�wa7!�� �5� :p n%341(94212���Yakhoŭ/ 9�/ e&t%L.M%� 5>? {Bo�$ondens�L�s;6& stru��5r % a�+domce, ven 2By�pR�< 5+E55�y�:�q 942L��S 8 {Finite-size ei "�!,BW &�B�JZ�2�1�12�E�#q�"&�"&�"&�!&�!&�!&�!&!�B*R#uc�D"%'�\�&� �:�*>O>� Jf l�4:� 1�&�$Eo�,%�,%�,%�,%N�: f�,30.} \addcon�9s�K {toc}{sec5 }{Ren ces}" {arn} 3#I. Arno�*EM 2�oPods�CD��an�N ( �K, 1gkn}:fViVozl?WA.�Neishtad(O6�A�!Q ��Celes�1�6DJ�97.�shw�!Ashwin#B�TFuVJ.�ZSWy, &�ha�Xx  3, 6jU2)*V+({bbb_jetp} V�YkWU �Y��skip �R,S. Bisnovaty�Eg~4 JourO<of 2nS�A�;e�Bl�ic�P9 �37T2��mnras��GuWJ�Mon. Not%+A�4'ocR 334}�L8 �9.� x4} Z���L!~9Jurazov�5s�izikaQ 2�27�8.�x5�] p. Sci. ^1�212�88==got} A ^�Q \apj E201}, 29%$756he0[H\'en,V$Annales d'%:� que I�83 642G�^M.H-xF-~2!}22% 73) %"�ip80} IpUJ. 1980 � 238, 11010 ls} LightgA. P.@apiro� NXa�,$ ModP50, 437 {pr!P.wKlinko)� B. N�"l�]E�q �Y$2}, 005783�I0=pr%.V,�_SeI.&Dkhorena� Nh�)0661313i716i3�2J.��5�56�`206�hysd} ,`Lehtihet�6��KMAg93)"86�Ly" D. Ly -Bell,~�13:!�� .LjD�%�Ykk��s! Hiet�h+U �3}, 1I�93�x7Ha9� K$V. Youngki% JeLa18 "2�pet16��$Ya. NatenzeR:E�CZ6Qgde�^�rK. SeryBbvV$. ZaslavskW%�b�  A �14�M25�*9.zvogEPalmer �N. Vog�1~y20A54e�8..pet} T�aP�[b��@ 7, 3�)86.�r VRasio�R2�, TeukolYS.�9�336, L63y�s1}��Jr�' itzeiSH.��a2:�16�{�`1971a]s��L.�IA�48E�71b.I3V�S��S���7A�5�2.K��J�T.�Th�J.IA31a,6H�xJH�evaliK;I9565J.�sA�JJ�#�ua�I200�h9I52pau�J1}, 77E�752q8VqR.�n2 ieuMAe�24L618��80)&{x LRe��q�R J� �1��8.$ zasl�d}��A. Usikt B��Y&� ��ics�eom pendulum�H&� ��*( (Harwood A�5micQD�Nrs J��zp} Zeld�Z��B�=odurets��1966,��0n. Zh. %[Sov. ] 29, 742Z�^Tf> o%y�Tref:handbook} Menezes ��l.: H  ofXed8L�U, CRCp@1997.>\CHES}T E.~Tkacik Vhardware�n�>�WL�+Not�A1er, �+�L 2523 (n83),�L4�S453B�wolfram1�OW : R�Ym ��tS by c B4lar automata, OM ~in~�] ied~a7,s �7 �12WF69E6^�26�)L-m�'F� b-:%02a�CRYPTO'n_ pp. *Z-4�:new6�A�; KindA-, -A Media�*c.%N2B� hort�!us1lL D.~HUvPar�NlV!�for VLSIU MrPB�N s�.�H�L�ae� Vol.  !1466-�13Z��2j�C>�kPp5CrIpI���ors�built-ingKte�bM>�@�-aided DQXM�8I�842--85I�9B�nandi%�N 5�|y��ap&kPA Br�$91M�2N��q443, %�34!�357!�94B� chaudhuriIRC�Ad�>ve9�Aq� �11�Societ"HEN�6NX Sipp 8M.~Tomassini: G�at�2pR�l=�.dpr!0mmt<Y~J�Ud.~� -�71%�W190%#B[ 7} .�5�high-qua�d2�C��.�� Fut{1X}b �O�\eh16I�291--305�B�8%f5XEz M.~P�Dnoud:�LFF�fo9h6�!�lex�1-O12 �7zT1��0Bpdie���Q0Marsagglia: D  Ta�\\ Q[�"H.fsu.edu/$\sim$geo/ F.�O�8BiNIST}�X Rukh���Y"�alp Suite���� �1-�N�b-��]�T�`ic��c=s, �, �Dcsrc.nist.gov/rng/% 1B��ar�Hp[rdell:2�ZF�u.^as2]uttern}+�d�1&�3m762--76�99F���ed} B. ^neier:):� (se~ ed�_$John WileyR SonsAT I����414%�B� :CAC�]Sen-�:��qM5SI��� (CAC)l��$2513 (ICIC. 303--31JQom�gs�(R~.Blackbur� "�Ct9PAp%QM>�)) J�in �n@C���<4�<62-6�1Nz reply����P.�!: R"� ������8--63�JK M1�� ihaljevicaY improvedbY eamy-MI�8 �Ya`B�,fU "� %� 1334�/�~1E�F M2F�%�H.~Imai familyIfv^keyst6� s bX2��pF�gb GF(q)n time-va04t^WICBJ edaa�V E82-A �3�)�B�:C��ll5^ H J.~C.~Muzio: Synth�a�on68M �hy�M J�rB -A*� a� �8 grat��ircuit�E:�5�_3�J� �22�ɚ: 2-by-n �J�{4rem confi � :ZJ!�EB� B� 28�O9 �F� Guan� -U�\%�Se�\ $\volJP1>approach�&N ��of�'trollVOa�u� � �2� g* �9�.a�E.� �%+��L No. 1)�c��ZB��_��Z�%M�4Qu�!�D CXmriu%� �Xasymmetric neighborship�J� .� B.� �. Aid.6� 2�[37k"88rF�(knuth} D.~K : Seminu�;l A*/c$Addson-Wes=>ReaB\d<ss.��8F�fip� �d Require�� 6C Module> \\  6A a�,/b140-2 2.pdf�F�ki�<^im�%~Umen^A.~< :95id�Che�af� $ 800-22 �M G, ISM�2ortA�ResearchE:Edu �+5.1�3J]29�F�ki���One~� B� MS B �TK=al�f I����1�],No.499 (ISE�f 3-87B2�;7*�  g iacr.org/�( /018!�Bn�]}T\M] %+O�(ffelbach�q&ni<�'�a �,edZ b 9#ci�,�B054-�18e9��IoenFWssvX\�%*� Acz}�X cz\'(| {\it�sAG�A1pqɝtheir .U },*fr�T|N 3:=&�$beals}R. B Sat��Qoch}R.~Ca��D.�lm]A)gr!0shallow water"B�[ !B:uVq},�<&�) �!\og61-1662�ichA\�A� �-�M.~Hy�)3�  S �W�E-5}&�� �&|#1#]7-3.�L({calogero}F� ,�&�#many-bod�jaXs } �to ex�1 ta}s,}�A& #MonS @"$�$ �1)2� CaFr1996}�fC �-/ -P.~�coise�"A-pletelyE�-�H� tons6�!�JQM�. 3�(6) 2863-287>+*�=02�3 } A.G� H. PmtKe)$1�ZW� urle E��. P�!�� 5C$99) 949-982�K��(F�L�|et-�4Global weak sO . aZ�}�Jm � < 211 L$0) 45-6).��9/2*-?1�9sc� �T��� ��m�-Holmu�%-R{c�Pr LA2� Eng. . 457�(1) 953-9702o�4:�%��tr�8-IS.Kz�"Hy��b�3E� 0) 6�61^��\6�K@B�Orb�ps.��� -b>� 6��PhZV D 1=#75-~N�6N�Col3h��!�geo� >� �a��i+Eme0�(i��j�. A{LC R51-R79Z�7v�i�Geo2cZCq��N�2��c��)�N19��{ 16� f�� er}O�ing�9[i�]�vs.A�]�g����on&M?:�5 �1WR 7-262 4ff}B.~Fuchsste��%�A.S.~Fok�O ��m�Mbt�3s,�0ir B\"acklund�E�da�A�h�Miŗ� =1 G 81) �6&�#f�>�, %�iS�u�ks?f$ d@olboxERX\L{Uj : %G�lizJ���.�0 }, %9�9�(1 29-24!X�,pick}C.~Gils�snd� Pick�, %I�(A /( 95) w -288.Z {hs}U%�M.F�))�Wave S5�&��Bal"[pa F � 1+16�PDEE�%�*CD�*2059} ^�� Dyb.z �C�i�<86� hoho:��< �NoU����ta f�Oor�}1� �} 3� dyn�O�:1)j1� � 1459D"� &� homa:� J.E.Nd t)oMmum Map)mM�s-valuedJ�� (��a Fil> �heets)E�AsEP�&a�6� 3120�T2� ne1}FN�; Dci[6H E$yKdV5]}�U).�pL307-L�]�hone26i��?$m\!�oErm�+-P�n1�,}i]."�+26�(�347-36�y|36|�ReciproU�.%_2+1-d* n�FIof V[s\J#ed� 8&� ers �2?.�]2.l2 wang�.�%nJu"P�B �Prolong���p ebraIU.�opera ;!w5=A� B^�)M�2A�5 R.� pain.�T%F4Painlev\a'{e} �$ r�k�� ��q�e�}& What is�� ?},�8 A.V.~MikhailovTrince��U"'}�(to ��ar; %(�)�pl; "rr43) UKC/IMS/03/�j.5joh9g�S.2 0� �.+*���releW�Oc X s a�J2�9}"dI 63-� .Ir�0s1}J.G.~Kings!!ZC��g'>8I(1982) 261-26o$kraenkel}R� K R A.~Z�ruk� T:c\1�lg)�q� .&U�}��.e#� 260�@218-226 mik}6�V}Nov,l&� m"� �!s��5m 4775-4790.�$misiolek} N5M  jA 6� ��#a "v �l �Bott-Viݑro 3�J.d���24.098) 203-2082�olver}P O �����Lie G�s to �3e�Va A�2n#i�&6Q"m12.}osE,PA~senau�� Tri-.�D�&B�]"�d0)�H1�BY�(sk}K.~SawadT.~Kot� %Prog.!`or���7�355-136P$tzit}G.~Tzx4ica1ref1}�2 FathV9C8116� 8)176�  .�bell1}�;8a�$Biosci., 41)1816323�5ƒos_� Quar�� N42F4)*u�]�Lahiri�D MajumdO�a��4inha Roy �. r!zE, 65� 2)0261��\7y{Kem�P��&��� 47�7)556=Z1 r1}B. < �Anal. 2�91)101F>2.>J.�@ . Eqns. 9%�22 Hag�Y Hagber�#E. Mer$2~� 94)8��� ref3�S��"�b), v�0%, berl@x1^== ref4EV/arpentA�u�,s, 23(1977)3?p.�5K���a̍g��JȒI(2)2476� [U*$D. Goswami�| dasgup�: �9 A�b�5)1p�$Rajagopal}:Qale�� 9= 4)496�7%�3�anfT A�C.�Zemli8k��12I�8G.� ref8��(Cytrynbaum,D�Y�:D7�D new1�p �JD!�8a�95)545�newi��G!� ogwefHY !To 17E�3)2952�3�1H<>�o� hil.��?`Lq359!*1)131:�4>X[A 1998)5:+91Kar�uH) vin� X. Z/��)7A�94)113=�I0}��Courte@�6�!�L. v �_�^ ., 5%) 6)11BR�Af�50.5AF} Aben�r�RFedor!UYu.Mq m,Kowalevski--`'e�q�y�/hyper�pGBly se�1 ble .�� Acta.�\/u { C60} (2)0�0�Z78�/$AlberFed}  wv2�Al�icj�al�L �certain "�)"P � .* 1 s on�K�sub�+etiq$fD%l�xJacobia�� >�} � 17�0k� no. �/0�u0�9�|Aud�Q=besp\'ebr�A s etz \`em�8t\'les: )od\'es -des quad <-� Expo�-th!� �lM no.34��3��6.�MM77}aAirault, *S A�J�+B R��a��Q19�P Ay.�Ba� B�! ��unJ� \/ �30} ,�77� 4--14.\Birk}  hoff�H��t&|e. 4th e�videnc�UI?6. Enol} $okolos E.DV nol'�EV.Z^dueG1 ta-fmhE� 5*f�K gap "��1�>Z �?��!��Z17=�BEBIMF� Bobe\CA.�r2�, I��.R.�f(Matveev V.B�Ditm�o-G"IA�"�"ale "E�D!agin6-�s."Xa"�#�u.!(Braun} von  m\"uhl�E(Notiz \"ubeO,od\"atr}e Lin_Oauf��4 dreiaxigen Fl30hen zweiten GK&4s welche durch1���"@& en d�]sth n lassenM� n.}� ,bf 26} (1886av51 =�Cayley} � � 钥M8A5!�339-32�Ca� "�$F.���olv��BE0Bys-���Nuovo C�toMz13��F , 41%v1*�N{ClGor�\ Clebv�P.Gordan� i� r �P!MG1k!: Teub Leipzig3D2{C�._Fri}�kY S.-J�X ried R. EllͶ billiardet0 Poncelet�s�)-��С+��. �29�19�5I4 1550.��>�Sh"z-J�I ��em�v��c"���"� ~����9)��.�m7[�804>�0f� J*���� full�'s�a�$n$ dA�{Q<:JI� 34E893��2Z<2256 % �(Drag_Rad0}  ovi\'c�Q, RadnM� ���^i2����%ɈsoidaY-�:��Mi` 3-��v-36=A�����On U#|�al�jecto��oJU Q�5nKi��!b< ${\mathbb R}^n$E-g���{8e �6��2� 21�9ߚ58�> 5869]=�_3�� �-!� ����"in $k$q 2� d$. �R{ . A:�GGe[�3f �12�W127.�8Dub_Nov} Dubrovi 0�; "�S.�A5� p� �!S�";"2m(Sturm-Liouv�J&b .�ir!�ne��%�� B&� y. (Rr`)M PDokl. Akad. Nauk SSSRq4 219e67�531---532  ERP}.� , Richter�KPr��DouEP�Da�4$\theta$-Divis=� �-� ��, &3)�'��.kFed1}6� C�D'int� U��to .�&m �> �5mG,�9� �Q2012PF��2K ��:)���C aY""� . % �5..�� yS�aS��$1��9�/0.� $Gavr_Per}   L.}�elomov!��* expl��FG 7 ��� -06�-.4 Hno.�>5 !26B -635.�Gramm} m�p �zF Rama��A�$apageorgiu�� Do.� mapp5 h"!UJ`?)Se� &�.5Q�L�%H825--1922JH2�iffithsE�HaX!Aխ�ѫspace�X :4)etici1052ivT �w.�GH@Z~On�'sF�A���� poris1�(L�Enseign96��-�2�@78), � 40.�G Gun~~ �3pRi�n tps.me "�A�f� 7.&Herm} ite�Oeuvr�Pe� rles�Ll. III,le thie� ill � PU�,�j2� �A'م�%�Abelian %y|#MC�� 96},V��M} �� Vari�*�V*T).�-�. In:$C.�nE!5&<s, Bressu��>tal�-1o�.Q ,Mum} Mumford�3 Tata2%z a��!�ŧ� ٛ PrivzvAu/!;.� EP1}%#di�k.n�)1Br12�2��E9, 2547%7. "� Smirnov�O.Dp. ����F�*^&-�M�Z"Y4��Y au7./ v.vF&�����>�R� 12�2 TV}a� ibicE�� VerdieEpL!�n��ΊcM�su�f 4�*ai�l>sg�6��z �ᘡM51�]2Tr:�H.A t>�h&� "t s*& *Uspekhi!�' �!5S*s 6(34m8��36; } ns� �� Oh.�vey�BS�V� 151�2} Vese/& /�>� � {(e ZB ��1��&L'M�FunktN@Fiaz lozh �X2��A�8�2,�13, EndThR���V� NR!F9.�Ve�S2�M %Ia3�a�y� ��e��&q.�crystall:�urv�A s�?ar7a"${<�.�TersburU\9.�VaU\$anhaecke PR�� s�%i� ��� ��v��ZK�22|Ou1, 93-�]W�=} str�K. \"U�di�&*�n6�m�chs�"� �i �*�� Werke �125�&66VE. b�]�Y�H�� h��\\& Pat�=V�'�:1>F�:p�Ea N� e up`$a Reynolds�`!c3��> {\em�M1�]!j\i�Xt�v78}R->� �Lee�9e,�20pAl�"tudU�unsteadN�ke�0�P�i<uni�#  at�!E�2��C�� �C�H. �s"� E639--6�"�0Tomboulides}  !pG.!sOrzag�A.�N"�Bin*[�!`p���tug��6�%���416},f9-/�Dus�(Ghi �as$\& Du\u{s}��J�B$�~,�xim�D6'me�-��*�Vw!�5Ml �Y2NUII42�[τ696U�(Ploumhans}  h", Wincke?�s�4T Salmq!�[., �%a^ A%� Warr�/�"�2E4Vorte�� �m�&s sdirectARQ�im*D'F%}bluff j0!�s:��)rto%/i�1$aaYem Re}=a�, 500ɘ10>�Q��-I1e��( -4632KBru�x r}Br\"{u}c2p��Sp7 -tempo��r3M�- Pof oexB1ma�=in Y"icE.vJqqu2VG1� 543--5�/]�Sch*&i� ,D ��rovansalwW�9 �Ϟusved %lgz�ej%P�)R1��1,[8�R38:�Jenny} ���uchX=�6Bu3aNoS)� ascenh or fall!{a freeM5%y99�>B�f7!���:� �!sL9--L�=r$Nakamura}  }� _qSf��t� 5--8)u�Hartuni ,� e�SeaRTWp" 1957��i,>b.0!#sNj gas bub� mdg�=�?Zou60liquidN���)8���r72�(Magarvey1}  �H�BishopL!K61EhaI[WakE �- �:.�R�A�H-Q&=��2��b �Pũ�Frm� F�w�! MkCJb#q$�d�%�Q�14yl14��J�3R� MacL��Z��/F3n��ic)D�T��4!�164� 6D(�NatarajA� %�\& AcrivA�9i�`-:���� ��s��R"nd k.@J�wUu27�|25!�@7 -344!|uJG;}L+ � W. G��ieshet+\&�Wijnga�Sn�Q�@N�[ pat#J!�agaac2�io ri�3��p�B�2�MW��G hase� U(�8M18(=�Betchov} %� 1965�  a�V!X5Ͳ an i�zsI;f`7�By-m� 4LV4�� Lund� �K!SPe��s�JE��bseAv!!H�� E ���"� �ASME-2sFEDSM97���-�J��12�6tDlՔ�K4\<��O"�&� )��eŔ! rɬ�Mş�bݚ.�q���Zr50R 2�2M� Rw'� f2 _udodd} �>od�>A�<rdyal"Y7�o��q &�e� s. \emph{&Roy*eDon � A&^r385�8^38���.�H{bf{ �o74E&74�)�hdbt} CdBenselaeOW.~�0��f B.A9=����y Dym (52sk6B�$R�>A%CC id�L�LI�>&�2xd�6A�6� �ibr} N.�YIbragr�5,�� nJ6s�8�`^ � �jc}. 0�Reidel�ba�4Co., Dordrecht�8!�u?cfg$�S.~Ig�Vv�>�f͍��*: ��DHS�Q�s3����1�eT6 7$}; arxiv: *.�B3016�)kdv-msak�E!�Kalkanl� .~Yu�2k�cE�\'Irdu\c &" "K Ker`�P-Krasilshchik coupledA�-m2�: "�b69PoLax pairq~J�) & yz44�*�'17�G 1708F206046 ]-�!}�� �{�Q�. 4lete  ��B��M�Adv�u-l���C'�Q 3�_z1.?�J(�, Tokyo�n2F�01004.- khab�Y V.~Khabir=e� D��hird-�?�5Yc��I$-nt.� �Di@ 12�_�19.�irn} E�� Kirn��\. On Wahlquist-Estabrook�n�aY%� heat�Q:)T� ]7��7), 7�X7�8y�konop"]4< e;)k*��V��#sky. +CȺQ#le*5Nfin $2+12o& 1ZE� �(�1���84), 1D=5b���C} I.~S.��} ��1���1� 209.=ab�Dŀ�8�2{Md�F�Darbouxd ���(8=br"��,*SC�iFB�1J�DhadwickJ�� |��S2�S. &i ��S�02���:x�0MiuraBsofNT���JY��+�(3f&3�Y�!� _subT *A Oa�� .�t�� perm��"� F��m~�1kVا�kdH��~van E!�AaQ,-Archimedean!o"�Zp.�:1�iG�eY�� �,2�"@ ��90�g��%�F.~B.~��.N G.\ Tan�,%9\�S"tt. \�� 0543*�Е�8Dia97} F.\ Diacrv P.\ Holme�Oembe�vEn�� Origif�#oinSr $ �#�AUniv.\�s�;7.�7 Gut9�4(\ C.\ Gutzw�( @��6�� Clas�'�p�� �a: x,2�90.p Ezr9U% .\ S.\ Ez�K!B�(1^jD.\�tgen, J� BW�L4E1� *�5RW90a�^\",)�.RJ� W�sW2�TRR��Q2�dJ.Mvo�iRe!�Mod�M#��e�2cYu��Z.-Q.\ B��Y. GuI!^Y�p!i�KEw11�1\!8. SanoW�;,MC .\ A B3xs809R2Z�RTW93'9~=�~1� D.~Wi1� X) ^48}�D182%Y3.�Duan00_\�An,w�5`YE�:� Z�� 0627�A2&G] Gru95}ecVDruji\,�a�A� Simo"}.!f �B -�U15sp95.a YK98} T.\�mo\�orQ )s�p 10�w;|)=��%�7�%&)1@*�= Her8�-!́M� ck, �a�hemy\ N5��x2�Bue!0FB\"urF6:�J-AJI�R�A�31UI21Fea86}%gD Feag�-V�Brigg�i�9 �7} .98�M6.� Wa53�<\ �� Wann�sXW Q9![8i<52(Par65} L.~A}�r��$A Treatise��!yv� s} (�:%h 1965) p 5[��RosAB.9��\p1�29a�27%�6��6�!�� I!j>IT�^8)!U� BA19!HL��chez��k�8 \'{E}cole Norm�(���E?26� A63}>�|8us;# 36:6ęs�F;E.-:Fa AZ9 420.*b<GPa �pikrishn�i"Bler>AL7&N. Amar>!MeyC (:3);�wE 60�rQ53�D�GM>{zM.^ByA�:n Eu"jH��P%_99�@9.�LKpY. Lid VD.�0�izeau�!� C.-K�(�:f�� �Ay {!h=gA'Bt=g�B�$X. Gabaix,�>!p! A �UeA0) 365�SA:<BjB�q�2lB l.�GKK�H5;$Kim, I.-M. !��]l;,, \jkps ~ 40��K1A!�BC�/G��nanno< Calda�B,A�Lillo8 6!E -� .a�46�JhNA�Y.�"jiIDJ�0m4LE4S�ark�A�Koo��/e�  W�[B.!�HoEO��)Rs 44129.�DLL KŗLeSJU� ?4) 668�sGD�A./G\'{o}rgS. Drodz);gep� �aAN312� 2) 42� WH01��H.m �HA=Mw�iE �Za�2)� 1) 55GKC �E+J.���A,SE; YoonM.~1'�YISKA�J�� SkjeltorpIuU�48.�IKYAgKE� w� wF�als 10���2�AR!bz4lvarez-Ramirez�FCi%K�!4C. Ibarra-ValdA��pI� E�9al [2� �2) 65.iXX� Z. Xin-Ti�;H ao-:)B Yan-z�.T&�\6mEK!�Z. Eis�C )ertesz2O34 �4)��.�BE�� rshadskii6;� DV5~j5�AI!KM. Auslo�K. Iva5�,\ QZ�7�i4�� 2) 5\MI� >�\B��h1�86�ITP �Turie�!�'e!�Vi���Mn322e�3) 629}�K��K�ag62�a 0) 22?BEat>U�� A 3�1) L1[i�MA�KC tia,�� Ashkenazyi�:"� 6U��%[XG[Z��%_R.�6ca�M5 I+3a�.�BM!���Bu�\'\i}a�MMitT l �P.! Rikvʌ ��z�� ��1.rBM��fMicroe�^�=c�:\ s�F ME��W��B? -mat/0210c1K� Meak�g,&Sl} growth fa��m�ilibriCL&Q  UB�X� .tNR}��[h�S%WT&-�W. S�� "Ng)~B.!�Fl y, &�.oSS'For'�b a;pf sci dcY/iT�F �8�w 42��KHA:A� wiec�m��.by���Dx�lbp]/n ��&) 1587wq5�B'�.P�6�zz�|A�{T�]�Y�9e�<�461,+PLR�Y�perforbL 'oupcod�(s checlx4a s@vtic, �fɔ �4 se�,�"0which it showz� indN.�U ?ityenFS�sfF��^��natexlabU.��g�#1{#1f�^G(bibnamefont>J� �#�Pf�Q$�Rc_Hz�.$�Ru�����Ip���\p�;: and{!\,info}[2]{#2}F!eprint []{N�#2}*^[{2�{Cazab� t~al.}�e0)R#, Heslot`Tro�and��,les}}]{CHTC94ޡz nfo{��or}�5�{�} 1��}�z@ F.}~#= ��< S.~M>| �?Xan��v�P>�C�?N% jG�}�,ure&�^�me}{346:< Bs}{82�"0year}{�})�+�teB� Broc#�-Wy��a�,e~Gennes%�3)}]{BrG@��f�By6^}�,�2A��fWBC�65F[ �%rjSZQ A9} JP3vPert�p}08:0$a)8M{\"u}nch, Fant- ae4eva5 BMFCqz% A.~L>�i:'^v:6��?X>? �}},���5�>$j�81:�mC516V�8r�R�Nre.2a.9�|v�G>28er:���68:E �7�$��"2r� VanH�&]�5:� #� hatzE�cCorm�Swift� ��A�495�SS.~���6;�6�V� M.~FA *tl6atz�?WE#:�ےBJs#:B%�HJ�5W!z�M�:75:�M:43�J<5r< Thie#o&<>  ",A[ti�  PompeA&TMP��U>J V:�^!>�e�ڞW>N ��%���2E-�28ҳ Oron.�7:� , w�"B$ Bankoff!�ODB97��A> U��S/:4�ږ S.~G>P�2Vu4�M"-�jM69:�-�931R@7r2�?}�T}]�T�pO>pLZ��Td0.&�2j�177:L �15�A�z�Z886r�S��r3�<04�19�'NV�B^: NZ�ZFh�j�50:C �V04v�h�� ��D 6�hRe�!��S}:"� �M �vJ2lloidKeC�j?17Z�3%B'�{n� =6� 93a���Langmuirj�Z�134V{ v+ J�\s.�> " , Seemann��Sb EOHe ghau^ JSSH�-K>' f:�VuR>< ��=B� ���:�2!+uV�Պ�14:�m�496V�8r�� .�>k #.=  , "i )�"� ]4�� S.~Jl.} \bibnamefont{VanHook}}, 0info{author}{+f, M.~F>@Schatz�? J.~BB? wift�> W.~D>>McCormic��and �j�H.~L.} �:$Swinney}},9Tjournal}{J. Fluid Mech <textbf%,l,volume}{345}.D,pages}{45} (!Y-8year}{1997}). $tem[{\cite��eemann et~al.}(2001{\natexlab{a}})\N3�, Herminghaus, and Jacobs}}]{SHJ01} xf� R.}~�>���S>=�A[��K>S�2�5�8Phys. Rev. LettAG^�86�%-� 5534F�!�}:�j�(Ruckenstein!�T Jain}(1974)}]{RuJa73}~�E>�V}I�2LM��V� R.~K!.�ZOxJ. Chem. Soc. Faraday Trans. IIr^`70N132F]!rWilliams%LDavis!M82!MWiDa82�MMJ�W�M S.~H>M �jNLolloid Interface SciE^F9!F.�M�220NH82rHde~Genne)?5!?deGe85�? P.~G�.:NZ�e�Mod. e�} b�57:D �827R�5r�YiantsioI0Higgin �9�YiHi89��SJ�Z}E�.��BS-�u��.C:�Ŋs A<^,12B-B148J� 1989rCOro��Rosenauap9epOrRo9�pA>�R�iP>K�ZwJIp4ique II Francej}2:I1:31N|9vcSharma%/3:0� har9��B=8ma:�U$Langmuirj�9:< �86V�3�� �(192�b}}�b�n����358R;6��j� Mitl��93��� V.~S�.8;i>` 5�Ⴞ415Z�49^�n�)��{KhannI�8�ShKh98��w ��B�r�:� �Z �z� �A.�m% 3463R 8r8Thiele2� :� " , Velarde� Neuffer� TVN0�� U> Y:V Mœ6� �@2�,j�B� �2]U㮢Z'01610J�� r�ch{\"a}!pE�S� erv ��ScSt0��B� .Z�-B��ZHEur��. J. Ej 8:CU�Jm 200v�Il.�2Z�MAPomeauE�Q�E�NPV�mB �:�V���V=Y>i �x 2'.IVN�{eiu,� Surf. Aj�20Z135F���e��!r03����ߦ�1Z� 409R�3rBertozzi.�>�$$, Gr{\"u}nA�,and WitelskiA�BGW��A��IU4`��G>��ڋ T.~P>����6�,Nonlinearityj�14:��n156V�1z�stehorn.�3:rB%�Pototsky�nA�l�mBPT��M>j\:�V�B� �ک�QBj�33:�-�45VvQ)feKnobloch�<�ThKn04�<E�u8�6 B��Z��ica Dj41b�1J1 200v�Q6�4:F6/4, U�E� ]�PBT�pn���:� �9b2�%ƅRV:����Z138R64�Golovi�� 1994:� #!N,Nepomnyashch��Pismen�E GNP9�  A.~A>� b9sjaN@2�F�� L.~M0b*�Nk!�ns8 ^��Y8��N�!}rG0Israelachvili�� �� J.~N>{;R�V emph&/title}{�moleculav u Force\&9`publisher}{Academic Press.Ladd{London biI"{v� Hu�9 �  R.~J> ;�A�V4Foundation of "� cie�9 vol.�E�m2�=Clare�12�1Oxford.:���26� 3��c��������$.-Cond. Mar�13IU�m�492V� 2�!�j�L��!:�:LB VT>p�:7V;S��%]���>DJw1�AB� .S�BB&6�� N� 5�2G"��Żn# ^� 237VY v� :�>k.� ��.bI�52]4�t��ڬ��V��muA2ED�tVTj.tU-Macro��esj-3G".C��3972�ɳ��Merkt.'5:�!,&! :F *D ME �(D>�d���� �� � � "� *� 5�5})!b��Dnote}{(submitted)}j�4Brochard-Wyart*"v:�6,, Mart��and Re }]{BMR��F>�6\��B� ��C>� �2[u{�368R�"9v�Zhang.t>�!!�ta�� Cras/ ]{ZMC��YJ@Y��OJ$M�ړ R.~V�.� �V��@��26Z�13J�20z� �e � 0�CrMa00�� j�e�2W.�VYn�.>U�:�( b942Z[2Z0r>%0.�>�!,Q�s War\}]{MCW�t�VN��2�%�j�M.~R.~EF�� B^�!�^�46R�8V� v�Danov5� 1998rH/AeTPaunov, Alleborn, Rasz�'e)� Durst!�4��KJ�+;v��VJk ��?N>/ؒ>H>>9 @�CBQ-N!{�A6<d Eng.~((5Z228NA��%�^Ln6�/�)�&oyA��V�1$�W�WSJ�S �Y%�V��������I�2J#>�A\j I`2�:� ", U�q�j�4�������?�?�?�?I?3J=E?n10Bandyopadhyay� 1� ��B�8O��R� Stabilityn dynamics�bilayer>�"51})*U3m. ,-thesis, Dep�/�*h, Ind. Inst. Tech. KanpurnaI 2y2.}a�6�42}�� - PBMT�����j�B��� B&1 �F�I�(n�%V1D �# 025201(R)��!�jUWunnicke�WJ :�$�M #`ller-Buschbaum, Wolkenhau6 `Lorenz-Haas, Cubitt, Lein�4StammA([�O>� 8�m�1V~F�J��JB"��AB�=-�AB)a�<V>F)���B -�A&5�" ��1Z�851Vv�Morariu.�>� #�r4MSS��MJ& b���������~R79^� 5610JM�# Fald&�'199>�!$, Composto�vWi�9]{FCW9��ByW��N��A�" K.~I>N �A��IZ�.485J\!irG LambooyuI 1996:" #, Phela�"Haugg%� Kra�+��LPHK96�lB� a9ej� K.~C>S ��?Bl��%B�)5 V���7>J111J!!�r�Pa2�$7:� Pan,ij, H�-�m�!�PWHC97��Q>�Pa���*VHJ�9H��ec2�.TVM�E��Z�175J�&1~\>Renge2�0:� "AEN �ammi�Hinrichs�& RMSH�3B� q��BN��Jb���B�.!JF��Z838J20�� .�B ", Bugu32}a�MBB��(F�_��B� ��vBw>�V�EuropS@~�2ZT342J� ��(.�)ii# SimCski�(�NeSi9��~�)ii֢4IT?��2.�R(Pmm-J. Appl &h.�dC5G0yL�49V�v�._�.��7%^��~^y�]�]Q�5�D.b%�^x5e@B\14Vcv�DTeletz*?198>�$�visa| and Scriv�O TDS8�X:GJ�F\�e H.~T> �A%U�$M���VL6:��F $A� ej�2Z�?Bq"!wr� Deryag�DLanda�?4DeLa4�y:BJX��?LJ3 �ZA Acta%AicochimnB^�'63R�4v�'Verwe�@Overbeck�=4=VeOv4��E=-~W�.?! [�9JA��CM�U����R�Theory�the��$of Lyoph c�-9ER�.Elsevier6�"�-Am�"dam���194v�OhshiaA7.�I}]7�<1B�W6�"� �"Polym��25b J� 197�h2�NH*��5�?��2NO6>�j� Mant#?l�7 VettB!�1 MSV8��EN�AZ�{B]<�IWRtLD9$e Algebra}.�*�0HTeubner Verlagsgem.schaft.HufLeipzig.qd72r�") J #�Ԃ)�'<�)�)�))�<�<37J�!|r��d5�199>n !, Reit�0Sitthai�Schul�O]{DRSS�� M.~O>�dM��V# B/ ��<B�0 ���.?�� J>y5 A�Q� ���� �x=� 566J�/!�r� Sferrazza.�>�%, XiaoJones�(cknall, Web�s)�Penfold�<9�,F1���B���:Rm2�Q%�"���AD 6>B-�AB%-K�tQt5�!�Ft % ~�7Z�369R� z� "�L�e�L�a" EM9�" SJ�Z�e�EMfo,a�^14oF9�m�34V�v- Doedel.�v�S 0AKe]i�Kerneveza�DKK��BD Y��H�%u{ �?�t+��V�J.gB!t.��=m�vInt�Bif�"aov#<��-�4�0F�1199298D jx ):^�� 6# 0���� ��������%�745A:&p� 6�!���>O-� Champney�HFairfrieve, Kusnetz%-Sandste�K Wange�e�X��B!�y�j�BL �@B I5�?BB| 1K?�[X>Q)�a~Vx Continu�>and�aurc LSoftware for Ordinar'Di*L ential Eq >b@Concordia Univers*G�"$ �>Montreal.y�2ZX&��1 :� " , Brv�"�C�WBMrNBBB�� ��&VL>� �9�j�B� �?�8FQ1 !(5�Տ�� �����͍2Nt!!�r Mahadev*�::�%x$Adda-Bedia)�PtM��MAP�~3B�^9k�V�BY�@��Bs��F�J�9 jX45Z�4Zg&>tend{thebibliography}L\beginB{FP(tem{rey} O�)ynolds,�5it{On~t"�lubri��,and its appl,to Mr.Beauc��H Tower's experiment,DPhilos.�[R�[1DX {\bf 177}, 157 (1886) %V�(oron1} A. �W, S.H.�[�,S.G. Bankoff�Long-scaS�C�C@thin liquid film�� &.Z � 69}, 931 y 7��Q64} L.E�;� C.V.�>r�Lg�On celluEconvec�d : by s�E tens�Dgradi-=6M �1�32�64� GoKe� , D.A. Goussi)'R�C y��Ewav2K,thermocapill�w insA. ies �-= !< flow},R�223}, 25%?1.�cH A ��H, F L.M.�H, 0 it� era)E0between short-� Marangoni=n A�lYdeform�ual �y}, ��ZE�6}, 34�.q4burel} J.P. B bachA�Y�EY�9�N�N 1fyD evaporating/condAng.{A�J2g � 195}, 463�88=x4deiss} R.J. D le�:uZ1`HStable localized pa�nE}BEs!0�S�` �68A948�92�a�2y�%#P.�[9#On a n5(:� effectA�� le� �0Z�7A�36e>2��`00c��9�d*D1three-d��a�alIaePU�.Fy�>�Fq12� 633 �p0=<be!�M..L A. 1%LU.1� 3D Large ��2%�1� 6wB )�3!D4��@�t|X} ��E. �N�T�� o o!�slightl!,c�Qd heatA�late}�)y$O �O , 21),.��b E. *�b�R.c�HSpontaneous rupturea�A[>���EV�b �70!�32A�7.��K�J J.N. "�K�J�K�(f�K, 6�K,�S��.n)�ap5�h Open ques���-promis�s new fielde�dewet��}, 6E �E�409E�.dE$} K.D�n�V��6 N.*$7H. &�:%�F. �:z.��4of �5 two-�ed.�i~e pres�K of-Utant-Ia6e e_ W2 pproxi�6}��d�4&;)5a�:,%�2��!�bS!St�:��!I. * analysi�|I�V�23F�pa�=} 2�.�����I. Non-�va.���3J� poto�R��, 6�D�&1G�}�&�(Alternative� hwayE�u�� a2�u�[�4��m����5,e�.�yian} _ "8�B���G8Rayleigh-Taylor.R � � visc�^> AG2�Ai@1�548l 89�[ vanh�J. Tl!KFa}"l��B. �k, WaJ"�k�H.L nney.G- �length�e-� -� B\'enard�1:*� b = Z{�k, 4 .T burgF Aurgess JueD2�.�r�Sup�����Dripp��0from a Ceilin��)� �)�8� 120�U.� smit!�K� S Y� � ve. induced*� 1a ~� 24!70� 6.sim} I%�&�*%FR �CN�� 8systems with in.i}, Gord��re� "O$��.�nep�A.J� >��U�AI6� 1Won���� �� � �a^�'cF�*)�5%N90�.Y tillB.S. T� �p& c aM&� �g$perposed f�ns�a�� c�ce�� �ch �2"5i<.� maju�R� jumd�TM�O'Nei�4$Vertical BT ry EE s} }&L Electrohydrostatic�<a&la&Nk J.(�ths%m=@1�34� 7.� moha� 0A. Mohamed, E��Elsheha�'M  -Say#�.��  � " Two S9V�����g&u "l � 6)z5�� melc�J%{ R 6N�Ch� Relax�a� ��Perpendi�V-F� %e-��� � �; 77v6.Bsavet�  S taserane,.T. Pa* orgiou, P�� Petropoul�k2��T7 EH�keEAic ; o��eBT 2 by f der Waals���W� ���641�.yliXZ� , T.�RT� *TAb�#\"aW!wz�Q.Struc F/ ate)1�% Lz/  Bi��a�)� ic %�}�L.�P)�3�397 �.� �h J�S�,'U �H"*U��, U�inM�T��R:G1�խ&�atN /i��!qH �Qi�1�ntS%�.Gwil;M��W�*hpv,bAgF QU��n�9�22��82d� Lg�,EE!b Lifschitz>+�m� c�� m��k2Ze6( BerlinBtpef O.$ros.P.C. Fif*�T��� allyt,sistent modei0 phase-ex typI��kinet��of & tOri�mex_)�4� 4� 2%en� A.� e*J!�w �� Plana s� i�&� M -"� �� �6� 6�� 6540EJ.��ki  V�C5�D��solid� :� ogy�0spinodal decO9%�"5, 49� 2 �o!1O�o���oYU�^!�&p"4 6�ityp grav�6ax6}o)�!91�.�X'9�J!8Bp. 297��1B S!6s far> $EquilibriuZ Ed. Co@dreche, Cambridge*\.�Cahn65� W. 9PA� Separ� by S-� D.��Iso��iy� -�>�4!9�6��NPOfP1�5�avm23M. Adl!@P.��Mo�0ke, \new�cDk{ The {K}owalewsk� {H}[ 4on-{H}eiles moe3Tas {M}anakov geodesic w0 on {$SO(4)$}��ae^d*�famil�*0{L}ax pairs,}�\em�?mun� .EC. tsyH113}, 659-700, 1988*�! {bbe�8E�TBelokolo� 8I. Bobenko, V.Z�/o�g� R. ItsBw veev.&�A�-o-geomet��a}ach to*� gr�  e�}, Spris;�942�ob83} A2��EuE!a$e(3)$%^$so!k�,omorphism of� cases.:^PFunct.\, Anal. \,Pril.a$20}, 64-65�862� rs89>�A� Reyma/  M: PSemenov-{T}ian-{S}han{g��KYztop 99 � s Xr: a LM(, genere{�ex�it�GT�Y�!�CoEO \,Math.\,��..Q2a}321-354�9.�clebsV A. C .�@\"Uber die Bewegu�U0ines K\"orperX r Fl\"gkeit}2GemAnnale��Q���0238-262, 1870.� eul68} L.I/��lculiQlis, v.1�.Sc�ׁ�,oli, 1768, ({ ian �~l%]0 GITL, Moskow! 56.)&�|{dubr} B!� Dubr�d, !� ta fAaio-�"+ Y�}, %�yeph. Surv.�3�� 11-9�981. ves2} Ha�Dul�\PRicht��Aa�V1�A� varia�! �Regh( t. Df2�!�!"92� Golubev}  V. V.: �Le� e�� gr)uof���� M�x H a Rigid Body about�(ixed Point}�0scow: State P/dc Hous �5eqLn{L0aV �53 (Engkd2�23� ) Pr� m w% fic U� 1960) .�HHA�~Haine ~HoroM'Au�Tk6(>�a�+ .�29!�73-18�)7AE %"� hm�%Dg Holm�EA� rsde� #oto� ��ulum, %�e In:Z& Sympiic��&�mathe� cal E>ic��%e{. Donato��al, Birk, usA�B�Fna�9-203!�9a �arl} E�>K amova. �RO dvigenii tverdogo tela vokrug nepodvignoj tochki v tsentral'nom n'utonovskom pole2�e�Izv�Lya Sib. otd. AN SSSR�ka� 7-17� 59.}}�0kobb} G. Kobb.�Sur le4bleme de la roPon d\'un corps autour pa fixe..a�Bulletin Msociete��de(z� @bf{XXIII}, 210-21�895�9� gyro-k} It"Komar�{ { A 6�q�>}2T�A�.L�� A.�1�!14-�9E�Ukomkuz1>�V�Kuznets� Quasiclasa6l quanti�X � iqf@�Y���F.�Q�=+X 335-34E�N�~� |� 's~�aLie a� as $ ,  , o(3,1)$.9�J@ 2A%@841-84��2Qkst03} 6�V!�SM �V Tsig>, 9$Poisson maA��%nt��blA��� �1a.�&I.�6��(8035-8048, �.kot92}��'", f�fqn +6��ss�. I.II.:X J 0ine und Angew�;th2 0��051-81, 89-111��2:�ter:�m�cas it\'j$r $M^{me}$.?de� d�Ze pesant� �>1C>E�:� 209 - 26A�89:sw S��H !�,�$probl\'{e}J��c�� � ����� 177-234 86� 4mink} H. Minkoa[2�b� I!EL6!j� E�,Sitzungsber.? nig.tuss. � . Wi �=p 30}, 1095A0�888�m�� neum59} C�umann.�D�.0ate quodam me� ico,( od primam m�\lium ultraellipticorum s�%em revoc" B�Rein.iR�6-I:52] P81N Perelom�_(Some remark# �� �&C"� �o( r( b( i�  ideal�.*�f�� 83-8��� 5�=,��7 ��a �� . An��*�:>S Teor�e��qG]��<7-205a�02IRS!M~G��*�~A."�T�SB� {gre�en[q a sp}� aramete"�  2:���ts:�s}>��� �B�� 55-6�,�@9rshott� f ottkHm�a alytische� blem�R2 ��s starre:�$Raume von �A D�en>�}�t  drerq�/&�#�A�n %�re�en�>en zuFo  22�� >x S-GC� (K. Sklyaninٞ�P {G}oryachev-{C}haply�D1�aAmethoda4in�1e sc�8 ��emB�0J.\-Soviet.\-%���&�4!3417- )�5..�kl�RE.�, {*Zof&�---�%t�p: "(PP� *%o"�}l 2�11�)3QW9B�8:Q�Takebe,.�.��_!;e�3 Gaudin>j�V4 20A�17-38a�92$ts0�B6u  O�,Steklov-Lyap�$1e��� mG.���prirXiv:#. .SI/04060� Z 2�we� Wei��a�lJ^�ia�1 curves,!'�m( Arithmetic9GLy}�)�EO&| �53-359, a\"{u} 1982�� y} H-Yeh�1{ Novije��(iruemije sl'0(i zadachi o+j+HkaB�4Vestnik MGU, s�� mat.�a.�!� 88-9��>� zhivApA. Zhivk��Okristo2{ �"so�!�� !&,"���!�Z?azNS�fS9�S$BerryQC} M� ,!�c.�*s*=1.3%41� 87).��He�;} E6% , � >�#�( 1515�84); i�1it Les� ches LII,�Q� umS ics,} edi�+by M.pMGiannon� Vor"!J(J. Zinn-Jus'l( (North-Hol�r"`#e�12�aake}F.  �it�Signa_)��; (& FU LL}A!(L�enberg�cLieberma�4{n ReguHwdag�2oNew Yorkq2.�Cat1}J.H�nna�=��i���26$3980); w0Ke*0,�(�(ity 1 4} 3�+p<.xBalVor}N'Balaz��dF.V)�Ann� (N.Y.) Pi-�89.QSaracenoA�  �G6F� 3�90.G$Almeida} A�OOzoriop -�Ra,2�21� � 91);A�7GA.�:e79} 206!44.� Schr_;r��4M}Num��y��Sxn��u��} U�-UG,]�86.w0Allpaper}J.-P#-oa�V$J. Shallit��it Sequ�,)�their�$|���J��0 SETA Conf. y�C. Di�4T.�4 seth�7Niederr�E!_RU9A�e$ Auto�c�:-#,2��G6s} (nJ�<3.5B, rAG _$J.-M. Ghez{%��C28} 23B0�Z.L JanslV M00 �#Rep$%2x3e98); A�Mi� F. 326}5&/2Luck}!�GoN� JaJ��� 3769��90}��Zak� S.Pikovsk�^A5KurthsFK3�52�H92� Halsey} T�! }+H. Jens�LKa�.�7I~ocaccia �B5Shrai�E-ńA�^U211�$1i��Pe"} &+"mxFo�{���ist�M�AJPergamo�{��70). c SchackCav+ui�ac:,C!I�a�5K"g,e�.put. ΁� 305�!. *:�� NMR} Y. S� ��,Lloyd%�V. Emer��+ D. Gar�,.;� k$89}C9902t�jt AruleLakshmX>@ayan, N.R. Cerrut��)omsovic2�6.6 016��3)G R�I j��[!Hguido1} Ciraolo G, �V`ndre C, Lima R, Vittot M,�' tini (Figarella C%.(Ghendrih PhW ��tro�g cha��por?6a H- toniaP � (rest to magA$7 lasm� �� A: L ��.} %�$37} 3589 (,' } �.CD 204.%2% 2} = Briolle Fy 1$Floriani E�-�.!*s�!a possiWtool to~%!R anomal�%2Pfuw.2)�hu E-��056�5^!3�.7.w*ichel}U )�Perturb���bE Co � in C]�or", �$� an In���$ula ���63�,J�30305.�'%�32�Ch5�>��P}5i ��of-�in2�s$ �Celes�,R-8Dyn. Astr.} (in>r0b� 1100.I+ vitt��y��U�� �!�5 L"R:1(rolp non-reson8.�2�N:�% e]18} 4��^�405056)��HBmack93} MacKay R S 3 �Renorm� IGin Area-�rv�Map�N Sing�;e: World� t�]� escaDs(Escande D FB 5 StUy��� in &J: u�C al a -�qRp.1�[ 165 &3R�}9�%�JauslA/ %�2��-group(�5%�we�i� �� G�<2�B�365} 1� chirq Chir�( B V 1979 A��#*�many-d.al osc�>;v52}T�twt=,Y�, Doveil�tI��, or A%BQ�A�4%^n��`�Mbuildbarri�#6�< } ccsd-00002248.�$zav} Zasla� G �0Filonenko N N� 8]K>'trapp5;�^cV'JP>%�. �A6�quasi7=�8i'�%�ics JETPM�%�85=� gree!�$Greene J M1� for det@�!,a su�nMoe�J.�bEXt0} 118=�e�2>�2 �0's residue cr�"��_JcA�6� lask[DLaskar J, Froeschl2i]Cstti A�[2�� measOJoGM#�P"��jQ$�Rc*ң^R.$�Rurl^Iurl#1{\*+tt!O%8{URL Ip�'�.mand{!\�G}[2]{#�F>!b []{S'*�#>��� � Reny�b56�Z56� f��B�SUև^A>�J�}��K"Js'�vsHu�y. Sci�N%�bJ>�}H!�p<�R{a56}RC���ung�(n);��K+d in: S�0ł�* of A nyi9If�32�&��)0)n:t)(1�}] 7�.�V JrcR*[ Prob�$�AT&P�(r}{2�M1�yea��7v#dM* lbrot�d(MANDELBROTa��BJ;STIIR�FTG als:� kce�Dn f���maY!�"eNSan�&{8 �$57r�LBia\l{}rd Pesz�-e�8�`FRACinEP�!B�[ֲBs�6�u�Nucl.\�.\v�0Z[W80RZW88rE$HofstadterE\��)8CM�8D��}�0�T۫QZ��a�v.r�1Z�Z22Voy76r�ColA�"�P�1:�N #,, Pietronero��afa�r��)A�VPJ�m c:V�B�N�@5xa�z�R��*�a�dܽ�U� on.\�jA��NA20R�gLVk�z�G\'or4*�2:�$!�$Dro\.zd\.z�� Spet�qazgDAX��V A.~Z>�a9tjIBv��@��BM ��!��5�a\� n��31Z�q496.�a���QrYHartwig�?�[ #$�V�W.F s >9.6�� l4ol!�b�1A�M�A�28R�z0[Skrzat.�>�p "�!mi�CIz Usar[ ��pF�{:VNB2|C��^B3S �2VUxMedFRkgw}fa 3:�-�4�&= U{v )!m Wa؛a}(�,� 03� bte`2�.RV�BM�Z9Folia Q� (Warsz)jA6^�g1J�! r�J��^3:^ , WrM!��>2Brase �mAbell�U4��W C.~Ya�.�;:*VgRJ�a ��?B�ؒ@<^6 5B2<.��V�MJ�-T!z!(>utCleft Pa^ $--Craniofa#CJv�4�Rq�0�BLynnerd�&seny��N>�<օ CJ� $'�ZSAm�_�F2,thropvj_6M-N3N���"mt � blad�� ��R� �"ent�2f� }of�n�%m/al energx\or6j��@"J$�"�0-dyn/9804034;�Q-aiz��V%Mart\'in�!)� E�V6is(1999) 4993}n9R20b� azgPSEUDO� �[![�u�&j�3Z� 793J� ���enF�Y �H(ib8B.&�%c J. W�?N� SIAM!` iew C~=42�R 68);D�>nde�, PSV,ng Finance D��^ity!nc�7@, Risk&�> D("'7z3a:  f]$}�F ^ac� (Plenum[�D�86ESDB#K~<�$S ; Buldyre�o'v�;M.� ons,sRE.?"nlNa'L�Ald (erN!49v!685)2&� arn1u!HArneodo, G. GrasseaeEM. :shneid:a*�!6�'28�D8!�0J. F. Muzy, E[crR%.j2M!�4�J87 �/%�p{}!3Ohashi,��Lu\> Amar,:.!&Nav�!$(Y. Yamamoto6%X$065204(R) a�>|le}� PlerxI( Gopikrishn�"L.�.�MLye�%H.2�B� 6A�651!%�$�chen} Z,�$P . Ivl7!H)��f�H04110�G~#hkhu%_HYJ Ce2}a�J�(Ns�!� 64Az 1114%V1Bg} ��m(a%Mat#.Y hkenaz�!:�:{ �a���[6�gopi}!�6;V.UW�FAF5�%ō�=� �� daub�9 Daubechi�/ Ten �=ur�ng]lets (��a-iladelph!1![2Utaqquw(�% ,�Tever&�'W�6�$�?�� bf (7���(]�bF*�j�\ aud�'�T�re�qiZ Jou. B)�x.59&�&bxu}!tXF�K.eU� A. Carbon�(H..�epX/� -mat1%804\?5 hwa}�'C. Hwi= Y. Wz�5��. C �6�054490�N> osa}!USakika N,O. Narikiyo,)=A `SP+of Ja*7A�120�I: jh � Jha,!K. Kaw�L�Kulkarn�J.C.PzhA0c�of Pl&bf�� 699 J�'r�a�4 l��� el� M�O Shle�YAJP%,Nat�(caO . US�)9�~3576 a��]f�*� {M12�1 PoloV!r'9(s�tex�_L�5vis�7 du Mond�Lch!fLVII: De�?�&.Lop, \&-gr��Ldesert (manuscript /�9n�A,1556, E. Gro�?aA3ar�D144 p.:J 4a-b / 1914�x8de WC Mw$},. �1taxby AF+Moule�Paul P?" ot, �1on:*Routledg�,/)}` j (�3:q%(8, Century 2ish�. +d,Chapter 11: !�a � s#j}� 261-332368LCCC76} Lindsay�+F.a�Y+riswearT.L. AMR�6), S�,-p�!d!�0bwV�,5�Geolog�SYBy5{A[" {B�mY8 t463--473. doi: 10.1130/0016-76�0\76)87<463:SDABS>2.0.CO;2.�0NPB97} Nori, �P. Sholt�M. Bre�$, Boo*�:�+1>' �.�2�U 64--6�HSBN~qP.��q%/F.A�itM7JY!�$ avalanche*�Z[)em�cA3m`A1C3�829o92. CWG9A�ooke, a� A.,�r^ !��edie �.�D���K� ogy}�_,.LN�QegeM� . a :�(22.2.2 (a),�ay[�4�M�$313-314. b:6.2Y\rock p^4a� pp. 46-48.� QADD�Qug&�:L.,DA�,ott�@vFuadp�A( erru\�75a�a��in�a�p�km�Q�!���E]�#Q$ 8299--830%"$R�Raj� �eJ�fJ 0, Dense, rapi�Xow� inel�) �s u= v�1\�Lett.�tS144302. alek03/4Rev090.#�$GDR04} Mid��(.D.R. (coll?hve !o cle))F4)�:+fe�nu�6*O]�Eu"�;Jo .<>341--365.�B66} BagDA�A� (196���& hear��A� dila�>of dry%��&"�S" mmsm=�sRoyal*#j. A=Pi3 219-231.�LC�OL�"�F.tH-N Char�*dis!+Re�p=g�����develop' f mu`l�2�5qVal emil]: �ee�)EFY 12th^'e�_onal Aq�E 9 SymposTRSapporn $apan, Octo_61�@���A�502=<BJ[�Bo� H.C.�.AV^li�� (1885), M� : It�'(de distribu�!� prop>[e]S�. AAAS=��3408-412JL36} Lew` !5%�3AHRoIC��55 Kalahari ��South Af>)n�<m.�-k3--6� PT22} Poy�g�HI3J:Th3n�422), Text-bookA�UK:�:��,Ei�Griffin.�DRV83} van Rooyen TpE.%{(`=)�a��Kic=x}AOr2/i�>souht-e��n k-=96i�Arid En&�Nit{�615--22.�H�� HersA-�^�.a>� g�n�sri��des�,x.$es, [Ph.D.�sis], ` U�.it� ( 7, 243 p.,��8:!SntS s,��T 191-206, 8.3.3: puiss�sonore&R-202%A�ݙBA�20Յ�on&Wl�2wave-C-Ň lockA ��238001l R3. $�B54Nx5!�z�M�AblowneEe� �} (2nd �9io� &C� man.V. 9MSin a�526RDT �Roy�aHF��vid�6V�� TuponogoveS ��o1�g� A� `i5bed�l�Ve�E�ee�u; ce(G� 4�32e�245)w!v\016/0009-2509(90)80216-2.uP'Patits4�>�aa�� � ����p �ge�ar:�a��of�Jidr"p]yC � B8�C6QJYWI Qu JianJu� ang YuanPE�Z� Weim'$Dai FengNi�TDA�GuangRo�Sun B̖P g ShenXia� 8D "�px�! %�*� ���bo� q! zE�2�inese1�� .@ �[210��1062!GLK Goldsackr ,M. !�C. Ki�yIw N@u/d D fiF'-�'��6/1�3e 29, � e�(038/386029a2�MPePye��H. Tso��!O� VAe i�I as��}, Unwl+ayma,�p 8.5.4�*��al weRetredde\1of silic�O �h7N 5: S) a co� g �c��&[61-26!�"f H86} Ha<P.Ka;�;&� s=�� I�;}�7c376--3�Uf S01} supp�Qn�I udio_ e 1.�1,m Ghord Lahm!qTFoum Agoutir, Tarfaya,�� occo.S02j^2 ^el Ca\CRel�^o � a Ma�2 Dun�DCopiap:c3jc3c erro}!madorbJL4jL4ag push�Y.D5j75#ndsR96j96 ��labor�5y e"v ru2 S07jO7.te, mix�Ns�alV\s6�8jY8�ereo re+{ng� an&,�2��� asyn�Anous;[.i ,�j9j�9. Same�previousJ���jin6�]f* 0. C�l.�c�yk1rk1JAb:AnN12JAaAN��fa2BG�@}  z` blum�J. A . S-�9B&x9c�pt�"dZ s5�s�F�_ P[#[k .<Cout1985� ��!��O72�86�D� D�K5@ilT DiH� ==12*�: A19ҔQ�  Lega�H"manzadehl4J. Lajzerowicz o.B�135a 92�ba� d_N��} �[ `�n"��R264�.jXY�N�aPTV� Ginsvmnv D�8 \�L53+e2byNiez2}zG.��9 Xlit�\Co�wedcPU%C:-""�8 (�bton) "% xD,\A�>h(. Editors A@Bisho�7d T�Zw . �E:�F�7�  95-198; 6���J.��M�40�1Aj7.G>M{_Ag_Pomeau6jeg"� #.�}1� 2{�G�L Tut"�FujisaktJe_Bi5�927e\2F,Skryabin} D.�{ �a YuE"�qichae�^W@Firth�! -L. Oppo,`iP*:eK#Fa^derer, �eC�056618B6Park} � E=� A�g�"a�A6e_%�E/!r� i)5�2�T gx�#; /�#r�Z.c YSqe3�21� �FH.-�#a�J y%r ~3J y �; !LGomil!��Dlet.GwM�n Migu-^]� 19418p2&;)5Utz W~Lmm�K�TJb B\"- Ri5Q#H'/�E�e�*Kim� Y�dKAL�1�A� 0462"*"E�1-�n�C8pB��8JA�t. B: �MSC la'WO%�S2a�mA. Yo�Ci��.N��6yɍ E�#�ss&k NasuBL ��Fr�SGRicQ�/[IG� ^{7�H471��94!�S�e�F YoѕISMY��F�51f#598G5�9nv�$C4 v, Q. Ouy�z 6ptm8(v)\38K6�p7)�`9rhi19#St4XQ :~ad-�%��g12�|5S.�g�%%�}{2�86��96); VA�S\' z-Morcil�I.�$ez-Arjona,��SilvaA��Valcarc��k{oldan,FvA�95�%G�"m��oggz]nd2LF��H 066�H.[ );2}.R�3a�2��=~; " %�(J. Vi\~nalsbx� 6_s5a�S�9Ki�hL�Korzinov� I�zbic] L.�#sim�2i�D5e50�1!��7�F�I Aron�'=R]79�L��- &�bKaminow�$P. , IEEE! �L��Xon. QE�E-�1�(81)SNe$� ^S �J!:Mo�By�KNo;I�yO6[,(Addison-Wes�)Californ"X% �"� Raj}k#RajeY� nd#SWei�Q2uC 1a4295e575e�T�_M�j�* ɵ .�� 322I#89).4d$Kivshar} Y!� RB. Lum -Dav�1��$29�\8� �]$Sarkere �iE. Tr�f��!*4 1E) �5E+��76.�V�on[)C��n , N�: �z 1I^3� E9TSub� } Ra$-��>O�2t%1h ; K.R� ubbaswamy�S6� NɝE��837P 81); P\ wrylak, RQB82�M829�C15] 84.(Ourpa�QbBarash�E�,$R. WoodforvV. Zem�Za�1�v.)� �q 0541�y3E�.�Tr��%� �� Hael�Em & heppard, B=!#97eɵuM�m}fPW�_l�J�tlK �14A�45I��A�Da{o�{�4��Pu4 �Larraza2mE�)6�15< �%�A%itz} M��EH�]guao*� sL�"�[��fc.Y/AI&�)/81�z�; Ito}eIto.�' �A���e119�8.om�2�&g#)��.Ye�/�x477�Q7�5 Hiet}ta}!�I �)[9 2 I8I\%]4+��H� 2Tet j�I�2Y:� � Izquierdo� Al�� A�T#,nz\'ale Le\'�{@:4ateos Guilarte�%m�M 085018Q..latticRB8�~od  Galvin�HttQ�F��+_7 . ) �}6a17z9f G.+� S.-Y� �� 0�,[ N3B"�� O�b7�/62�I�.z �N3chizhi,1�YuM�#60 h7Aa32�5^=�Menyu�T�{ r-%QE-�T1�8.PBDW J. Blow� J`$r��D�5F} e[2S"\.bTS� V�am\�J�'Sip64m&201��8* Ch*N�/_\doulid�J�1rU4G .O9}�#  % dE�m�6�6% e� �j�  %{��B� % X.{�D��e6� 8E} 57� U56.� fib�@  � Kutz6(% W�KaMR.-D. L?�{ u� %>��8)��v�� �I Mecoz�2�2qc�C�GoM,Ns96 0 n %n~ o68/nX;6�573, 552�g6.7BBKN2M�VBog| !�V\ Korob�^%R 1a��&\=-&WO y} Na Alexee� �j2�pDa4Pel� sky, %N� l8�e��H1; �xSh�)nuVhKBa %aA*� 1���^�A���KIK!�M$iseX ��A&�3dAU o�q�@ 1�.1�\.� Vahit�NAVak UAv vv�di;1: �16} 7�1U � �Ba� F E!�. M"�!(��4},�W6 16.i6-.E�F105�B�Gorshk!K!H6`�st�2)f)�I��428��Tr� 6� �*� �Jaa s^jA`�| %.aV�J#alFP%�Bg=��8�25�tE�2�Herbst���/W�7[BA� ,D �NP.1we3� 4i����*t AUTO�a����R��G�"e  .}, 4, 97, ftp.cs.�o0� .ca/pub/d�^l/ l R��v�&a newma9��JDk �DB ��#1�`�+ . % (on networksYbarabasi�ji��b\'{a}s�&R1 bert,j�d�%Z��4��3�Bp�TskFBG*DU)"E, �M:I:2�T!kbI}, ��^1). %'F&-R&�]Vh�ZU,�s �a&URs'=_ mosekildeA^�w ,\5Ma*� DD86st�)C uF o�RLiv}@R} (>QW, SnW�_!�%b�)�(ubject� parl� UՃ �z�}�7� 123�{aYmaybhate�K M �Ru:Amritk1��s-64�20$]X�guchi Sak 2�G� 0272���taoe Tao%�� � D% �&gR^9� 3620D:�b_p!a2JMcor��2 arro�2�=Y8�21d�= %msf^ ours�aQestre&E. Ot�� B.R� nt̀ �662C��_�N, � f�?��BS��!� ~I.~�}-�~S�~r (eds.)4YA J6grpsg]i:�)}, ���y SerI� in ,^�w^%�m2��1A� E"3+y \ N.[f9.YHir1977�~Hi�v, �"� �* al differ7d&�oh�. �$-time Toda"��J."�NSoc.\9an�q bf{4�@�)a�74--2078>�8V�{ 6�d�Pal �m�����W�B�4285--42���HIK+N26 M.~I1yF.~Kako5JTwoF�25(�� Prog.\�*tpi3\7m\509K��), 42--5B,�( RB� Conservedg) ntitAf(of ``random%�)9�q''22%�:�66}!07)283--2846�a�2.Qd�+Dir��M�ninG�to�_"�eMct� .) bf{1| .y �4,} ��KMNOY�� ~Kajiwarapn~Masud(.~Noumi�E ~Oht��Y.~�@dy:D�Zant�Z`s "E� dis71pA  Funkv*.\ Ekvaa9�4A�a49�3�4U�K��:�v J.~Satsum� $q$-}��`o�}RW>���Y�J�60I%�398�)9 v�O�3>Y=jb�.IR��|\�x\ A5F1l���|9--256]MKO� �Maruno�U%Sq�>U�A note� ��X SZ�;toY�7I-ZA�8SIDE III---symm���iV"��=�UI (Sab�*aE, CRM �3! ctl\ Notexl+.\e_�{!�Vnvid����00, 30,31.CMJD�$ T.~Miwi2 Jimb�)4E.~Date, \emp��h{Solitons: Differential equations, symmetries and infinite dimensional algebras}, Cambridge Tracts in Mathematics \textbf{135}, Camb .�University Press, New York, 1999. \bibitem{MT2004a} A.~Mukaihira and S.~Tsujimoto, \emph{Determinant structure of $R_I$ type discrete integrable system}, J.\ Phys. A: Math. Gen. \ �37} (�0), 4557--4565B�b}�� z�@spectral transfor!^�on chain associated with biorthogonal ra!�al func %�submit2 to JV�9�hOHTI1993} Y.~Ohta, R.~Hiro S=�%�T.~Imai,� Caso�d1uGram t%�ete1� representI� of solu��theC,KP hierarchy2�8\ Soc.\ Japan \-�62} (�0), 1872--1886.�KMS .�dK.~Kajiwara, J.~MatsukidaiM� J.~SmaF�.�� for�drelativistic Toda latticey��E�\ Phys.\�34�$5190--5204�TSch2001} W.~K.~Schief�Isoth!{'Q�Darboux>�,%�Q�-time6� �A�XAskey-Wilson polynomial%�Method!��\ Anal=�M�,5), 369--398�V�,8} L.~Vinet~�An 1�le�'3bi-�:�Lett.\)rBj4!|41998), 233--24��tend{thebibliography}� \beginB{99} �Xhreview} S. Aubry, \newblockE�icaU�$103D}, 201e�,7); S. Flach�,C. R. Willis>H. Rep.K 295}� J 8); aW2m19m�D9); P.G. Kevrekid`@K.{\O }. Rasmusse)``A.R. Bishop, Int. J. Mod.�. B�1� 2833�C41); see also A6Sie�"�$S. Takeno, HRev. %�Q61}, 970�8�5CDHomma, Prog. Theor�� 70}, 308D3).=� target1} ! opidak!1�d,G. P. Tsiron!V!{�e�87!}655!ʁ�Jh82} H. E. Nistaz lP.b.� B. A�#lomed, D%9 Frantzesk6�AE1��E �466}, 015601(R)%�22�fourier2E�Lepri� Liv�� A. P\ i9�p��37�U6R Aifantis}�C. , Q9HNonlinear Mechanics �3!�797!�96); E.6Bin:!�8 of Disloc��s, eds.:8%-J%ňHirth, pp. 127-146, ASM, Metals Par� 85.%gaid} Y.!� Gaididei,A$(F. Mingalee�� P. L. Chr��ansen}�N�2}, R5i.02�pgk2}QA�ey�2�2�kNoE 4662)�6konz NvV.Konotop,6��+.�.#,E 70, 047602E/42�4bena} I. Bena,FSaxenaځf. Sancho�6_e~ �36617e 2); FU,!M2�M. IbaneU%pJRA� 0376m�6� tsir�IRbz)'6�Europ���57, 6a20��,29%j���� 0419-z6�ACMG01}YF�JArchill�LJ���>�Yu6 ��{aq�A:�| � en.})�34}, 636I�1); J.��� nz w�LE l) 16609E nCueva)\>:au $Romero2�r�hD o163� 06mA�S.ɨH��R�E�7�679� 862 roto���<R$M. Peyrard���HD9I140 (��U�ͿM(5A( 1922n97a�&�dmi:vs V. D  {\it � �Report��0�&3 �� Fg O*c 1d&d "+2d %15- g -2900�:(Ch. Eilbeck�0M. Johansson,� ${\em Local� 'Energy T�er)&�S4� L. Vazqu��R.S� cKay �4M.P. Zorzano (�0), (World Sci�fic, S+ pore, 200� p.44.�4} U.a+@Schwarz, L.Q. EngaZ�A.YA9�:� �~223A�99235} N.A�VoulgarM �Kalosak�*� s G�"� U3v� %�6A� 0203&i 1); re��ci�herein.�5a+ $Tr{\'{\i}}�J� Mazo)cT�Orlando2�})8�74�0);�BinderC AbraimovdV. Usti8a�e iY!�lotaryukzj5��6� 6i�a very6� onPDlatest developmenti� , e.g., D%�Campbell�%QY��vshar�/.�y)�5ay4�P647} SebB� B.AA�p g]2�1n .H 6��8��Yomosi"�A �2�212� 3);3�474A�:9T�.TFE�j`10O�=P ]� jys.� Jpn `254� 862s1.�PN�D �9��?�.-}J��n4Wojciechowski}a�W. 2,$V. Tretiaka$M. KowalikQT%� o� 614 6� 12A I ! $ &K �H ��->< .+13� Ak6�!kV| 14N S  e�I%�S�B"%�>�~"u (in s2� compFwNVzK~ 2ME�E�066614��s FX2GY.*e��Pq�99� 6� 2�5e& A. Wells,AFT. Dove (uck�}KAnachenko� k : Condens�z tter �1��46�]6� 16}gVallade,�Berge�� DoliJe� ysique I U!�14:T�%_9�D.�Semagin,�Shigena!K. Ab �Nagamine%KT5AslanyanI�-�B �68�521">;��] k>� m`�Russ.�r��7�?S30Ea�>RA�Vasili�,N. Yoshikawa&+ RV Rese� Dݰ' !�ic S�Pandalai  T w E Netw  KerajIndia" Vol. 4,� t I,�267-2���18H Kimizuka,U Kabu�,�#ogure�-�I�e,( 5548%$6�19EbB. Smir � rgorodsky2�X7!�241w F ��20x Rnsk�J�2Chelik��6WM24S 1622�X9!�T1P Alder� KR Eva!�J�a�22550&6 22B�G �5C 4036�:^ 23} O.a�Braun%�S*�� PThe Frenkel-Kontorova� el�cep [� ^i�P}, (Springer-Verlag,� la�� . �j�10.�Per84}� Pere� � �� | 1610 �:$pro03b} T.�s�,T.~H. Seligm� �HM. \v{Z}nidari\v{c}jN ��15�� E�6(Nie00} M.~AUel�I.~� uang� �F���E��#"�Mah69} C� hauxSH��,Weidenm\"ull!I%�(Shell-Model�roach�"0Nuclear Rea%�s} (N� -Hol�(, Amsterdam%66�SchE���5�� 3� 3289N� Kuh00b} U�Nhl,� Per;M. Ba6!iJ+Euq�թ�17ſ 25ͽ6�stoe0C%BPf6Z�19 �60Ber77aV�dr� : 1i�08�1976� Leba� eb{\oe}uf�iebA �E �6T396�q�Uda�nz�a�anz�,ivate commun� [N���f�!oPZyk} \emph{A.B. Boris�S�Zykov}.R� d�'a� of" #>A(a� prolifera�%a�n"�"z(.X or. �$-4� 11� No. �8) 53�$41.�C2d�I� nik2�O_!#�$ of �two-di*�(s)c cw((l O(3)-fielits q1 danalogue. Yadernaya Fizika��:� � (96) 120-348.�fe�EA.Feraph 6� atiI%Poi�� bracketsA�,hydrodynamic�(&�&����'�" 1-12�viniti15n�(Hamiltonian%�em+) B� �� thei�&�on hyper"�'�'4 pseudoeuclideY(,%�. Sborn�VINITI� ��,0) 59-96; (E��*l.��Q�.j%�,B5�(1991) 1970-�'���Maks+Fb�HVA�vl:�(% Quasiclas;l limit�(Coupled KdV.�Riez $ invariant�  multi-2ttruE����Q�5�'�(211--219.zO#1�W. 4, W. Strampp},�strain�*�*!� BZ��omm�th �Yx15�,�*), 51-82?Or!=� � .�HVolterra operator a .H zero�*atV� &�+. (a of KP� ceedingA�A�4 III Potsdam-K{ WorkR' at Clark`) M�* .X, NY, USA, August, 1-11? 92� Novi��2��P. !:KH}�e�s�%on��+1iit{M�&�$ iews}, Se�  C:I. it{%��e�-cal�R)s} (bf�PPart 4. Harwood Acade�yPT ,rs GmbH, Yve��e�3) 136%*Fer��Non6&l.r 1�%�Bt:`0g�⁋.�, AmerQ�Socn�2(2)�170�,5) 33-52�Pi�M�M�2Ellipt����inZ�n�V��m.��%�. Sci�k"�,� � o. 3%��74-377.R�%*$Mfu��Whitham2�usg AD z�T $5) 220-223.$�xTsaU).` Sa+e6mThree R-�E%vF;9_F�0.(- A6��y1!S�3) 32-�,�1�Q^�OnB�Eone2 2�� ��B�,���� DE Q31E�,85) 488--491Q^�k u<of6Rj�M gen;ized hod�- ��, �USSR Izv6^�&1) 397-46�EKamch1`A. atnoj�On �t< f!�v4A�AKNS "�1ɽ �ers`5MuA3-� 269-27 �$Mok�O.I. :� Lax pairs��b � � #2v�. (m}) �% Mat. Nauk�5 �. 189--190Q6�&� ) !of const�4� � �{: �Q>,&t "t 2 .�Funktsi�5m�0 i Prilozhen.]�0�),�3�0 --47, 96; � inWctQi�y$FJ196--�2�.6A5�!�!�� ular bund� of �6� .� >��2�(34�1155--15B� MA (h. Surveys Q�� 6>603--602Z-e`qrM�mrRra,},��aR`4Lonship between a 2x2n�"q6problem.CA:�.:� � �$ L13-L18. R��jpM�� wilkinsonmW,B�2�36�1996Ab�A��^,Robbir}N London A b442}, 6Y)6�tulio�) O. d�4rvalh"�".$ Agui� 3��2v269�#96#jarzyn�"C3 b{ 293 6G 0cohen99} D. C ^E8�495�):�fishman�M�3 slae<&%W�, Z[ Uv7eE6���RTt# ttos2QJ 9}, �1�16� ott}!�Brown�Ott�� C. GrebogbK� 1173�q4Y�caldeiraZO.�6��3Leggen!� ("�)IZ 121}A, 58%�:q3ramshaw6$D*1I<� 198} 1�,6�izrail�,V Flambaum�F!�I !YE�0E {bf 56} 514H&96�costa} Ft)PotiguaIU.M�)C S� �342} 1�"6� adib!K�1dibe� Statm&1�"5�"B� bara�e�B �T#B (Davies, Ann6V77}�30,�86� ott2�B�:�4A�51eE:Wrussos}��B5 nish�#T� $Vadivasova�G�"0OkrokvertskhoG3G-.Strelk,Ul1s2;199�2L+.� forest}�F %2R� �3Q�p&4�f105!&:ekubo}9Kubo,�Todi N�shitsumeait%��3� gs II}� "� HVlberg�86� fick �i�,G. Sauer� lE AARx� D� �� esse�F/!S�U}�percivalA� Ca-iiI�5P E�!F.-� � 80I6Mbia94I�ianuccf6Mannen2B�+W+�P. Grig�%6��y26�$1996oj5�jj1} 30<3B� reif�) Reif-�Funda�+al%�Sd!stA�Th!�lY,} (McGraw-Hi�+& .1>�!�)H�!6r&7} (John�;ey \& SANYv 3); V4 Arno�&v�.�Ergodic_# k Ci "�7} (Benj'�\8);a-Tol�"NA�Princip� ..N:(r��# X7�:F�ldg, LP0Moyp/A3C�0a";e-$tI ,d-mat/040263v NR3 �RFordy&� ( Antonowicz�)P.�ldy, Q Liu2a% EaOy-depW nt third-� � "� o  earHBR ? 1) 669-682���� csA!�>�� T���'Ě� �1V�:�A.J�%��*�schemeN B Kaup-BoR nesq��gD� % 152/153 �04-102�f�2D.�D�Ҕ.Ir"q����95p��E�=dY�J. GibboTC*rB�qv*q�1)� 21-3"�� Sokolo�1c)habat, }*$LA$-�a�Ric� � substitu_*�% a�al>RM,� 80) 79--82� MaltYi YaA�l�6�N6l� �.Ri�weakly�-,B�]t5N1� �1) 53�&A2�2\ � D.��{a�OF� Intern`,of�!�q�3T !c10�2)� -612�)�9gVR+ khaiFR��Y:�% Exte�G��modulv#inB �" �;žf�Waql��se:ba1n �% 88�-12Olv&�P� .@ �%} Lie groupF d."�.Z�ediI�Gradu7! Textf!�gs,YE0�.� .&+K" York�@513a�� ��k2�A gra=@E�?c�"�,2 ���&$�. 9, Y9eT �Z�173-16��Q\^�Re�5s 66u.` �.�"%�A~4Korteweg-de Vr]J1�� �q-2m AJ5-6%�8)r9-30:�ks��2� % Tr^A��E���o�.al type..XE�2L�.-�N�SS1�Sa�Svinolup��6 b� B% \"{a}cRoG�}�evoNI5�s�$ �Akad.�S!5�71 �83) 802�*^ F�!z7 small}XAF200Z6~AbenGYu.~Fedo- �ĥ��5s$i]I�t �Si$app�, J.~5 ~��3,$3) 42C4206�� *K � ~'d,�$it{Les m\'�H ath\'�7 ques�la!can ^!que} (+ a, Moscou�74) (Mir26�BV1990Q~Ba?� C.-M�Hallet,6�}!�~ �R�;~�S~f(23�$0) 411-416.�B!� Thes�ES�m/$ Squared e�4f�:� ��=��l PhD� sis,*� �LLeeds, �6�BEFKb;6~�<, V.~Z.~Enol'ski�/A.~P.~� ��m��potV=iADcouF�"�ys11MM2�B!15) 16E�2�BWUC$~B{\l}aszaP>M/auch-6N9 A2�(H\'enon-Hei��f��e|PdLle�i!=��Mhqe����93a�6~ BSV1982�~Bount!�H.~Segu-FApvaldi2N2� ���Ju1QL5P~ ) 12+P1266QureauMF +~ , 2 5�O fixed cri=poi$=$ Annali di5e�$ca pura ed�Da�*LXVx�0 1--16 CTW}y.ng Y.~F.� ~Tab�#nd�N Weis�@ nalyAsu�A�!":� Ha\-&�&ik%5�and� }Oregimes��� 2�F5-U531--532�Chazya�eE~+ )\'9MS \'eSelA�(du troisi\`ordre)d' sup1@ieur dont l'int\'a� le gA�! a ses-�)��I!�!9�y �I��117--36cIC�K(se1996Contew~ �m]�ap&r.:i*�in�Oft@:T &�FP, one FCury�$er}, 7� 80, ed.~R�CRM Se� 2T&� &p,a�r �5s8Solv-int/9710022� CFP�&�. AHiX;ing�~urbative�&AIalyvi�aN69�!" O6�$ CMVAU s�.� M.~Musett5 Higher�D�� �K�&[R ,eL��1$bol $P2$, �S~�1s�10�z --WW&} �c��6�M:�81$, http://www. `s.usyd.edu.au:8000/res/No�/Cos/� -6.html 1:ag{prehta 0--6> SydneyEZ6D@1919KdV�����y� paradr $� '��P $\D^2 y/ \D x^2 = \l�.\vaA� (x) + h\r( y,$ \CRAS\I:168��19�)��42�DS�0�,~G.~Drinfel',1V.~�U� ExZA�*$ $\e�si�An,s, d+�9�I9 1) 4h 462.��4��v�,� Y��,o"��, Itogi:(i i TekhnikQeriya#(: nnye�,9y�� ki 2A�1>= 8� 80 [ES/:.)283�K/�36]. Erma�,!�P.~  , \'9����< e deux. . Conms dY�Q3�sou~P0inale. Univ.~o(~�-(18mSer.~3*~9�025.��� by��O.~Har�829 e^2� Q0}-&" e:� LsyIB�&�/ 204�/2�FG198�+*� E�J.~A� me remark &� :� ~:� 7< 0�* 5--3!�FK"���P.Kulish, ��V6 r\"ot/er]�� }kQ��munQgt��8�r7--442>,GambieXe}�< ��es6�ifFts"�& u�E0mier degr\'e ~~ /\`a�� ��4 5Q*GDR)lB.~Gram:c�$ B.~Dorizz"�Ramani&Gf6.M� �%�iVth-�ee�E &�Z �33�-89--2292�HH�M�mC.~: &�z ��l��mo�g: sA�numer� exper97t� �@n�E)' 64) 73--72H���� Hieta�ta, C�, Yu&e7%QZ m1 8� 186�s7BsDirect�hod�he �EM�"4q�`Z �14f387) 8 52� JMIBM.~Jimb*(T.~Miwa�)�a%�~a d!X�+�y��10.~RIMS, Kyoto��y�94 001.���l'~J�^up"Wi"se *nHingO��%f  valul��!1H $ \psi_{xxx} + 6 Q  xR ~ambda f �_�0-26�KitaevP;Rf , Cau[" 1+1U?l"�VD*N293��96�Lax�J~D.~Laxu��"��25&|�m!��wav 7~P;5B �F� 8) 4�492�MV2003e�fZOn CKP{BKP�sto%�ge&:0VJ .��=orJ1u�) 156�572"Pinney�%~ M=>�B� $ y''� py+ c/y^3 = 0,$� c.~b4� �+m�� 50) 6b 66 7RD��IK��>�: * conje8 :V.Lh_ �4m�530:�<RGC� Ravo�HL.~Gav�/(oaboz, S��%�pa�0��6rZ��M�238E 392�RRG6�A.-)y>G]Q{ � ca.�non 'leQ���s!G2��)�94) 91--6�SELeSaler�LNND�:Leyki�anom?BvebJ/ъleV]"�  �'-�� 5897--5892S��-PVd%T&oe AR� is�as"{O-re)D��.N:E� e0eI��'K 2� [d 3397.FSK1974l'~Sawa� T.~Kotera�mF%�fins  N-��on"��:K.d.V.~�3�  -lik&e, \PTP� �7��3�1366�klyaninQ�kK.~q6�! vari� s --�trendtjm�11 %35�12(taeckel1893�*�Ea �,eTi1m�DyQ> que,6~�8a�4a�487. Sur�Nqui se ; duisa' \`a �qu"6fv1284--126iN�6�� 1\NFof>;��t�>as"�hQ7Qe_D(`Vrije&feit Bg-el (May ň.�VMC)!�&�� .D�ai���a2):_�ec�ii 4g ��06'# 15. �FSI/011(XF�4��O�m�ee� KdV-!f�^)n linkV�6�12},"=Big�c s - fromI�� togntum,�7 tinu4to"^)}��Dvan Moerbeke (Kluw^EDo�chtE). �%A405032| Wojl S.~:�2=o�E.�.T:� �.�"�10� 4) 2$26> �T>�m;�'of��pa�leda�enl1�", ��Scrip�3�)�: 47N�+�z�! Bax1�J,xt!�Exactly �ed�P� R�,�!ade�>rnLo�56�D Fa2}=dFaddeev]wblee(1+1)-D*: 0 F�E�y\G"�!h� !(Houches Sum�MSchooln.2, Els�?r�D6^,KI E�4rep�A�- Izer!UNs3Bo�/ub�# � It  Sc"t �Q� Corre�*�7,&�K��LA!8 Cambeo!;92�AA� AbdV��C`*K. Rothe�n21 �s in TwoNX 6X~�]2�Dri3G. 2d,5G�')�.R'�(ng� of �Z>cHf�Rke�/�6)�f�9V. GleaJ A5P�F4dence, 798-820!7�V&bNe8Er Mezi�]cu�g I. NepomeSm�2 V�:�%�T�Fy�I . Curtrig��L. }/&.�rq1> lt1> G\'{o}m�0M�3 iz-Altaba+XSi�CB�in >��icb�Y�!^6M Jim1� �Do !� (�&10F+5�8:?\Ch1} 6�I,i�VL0b|7�:9�Sk1a)K. ") �-�^�G2'2375882jNe1�@&zLfGg=�% 2�9L�g�:a�Y$J�VjM&�l](A 6}% , 523�+96_ Baz2��V��zha�?) � &�(B 1593]�.�Baze�2G�unV�1sS47�:B7HYS-Y/f�-H. Yue(..:� A 18�66e6y5 Bat3aMBVM.T�tchelo� ucl>� B 43�,430 :96�%AKQ A�TWY Koo,�KJH�Z46�:�;ZA�Y.-K. Zh�Z�C50�):CFK F�A Koberl��V�1(T6�_:96Ne9M Doik�B�VS5e547%*6MMe�Morico�6VC6�398<6�MS} N{Mmd)7ShortvO23A 313 � 6Ne7��rT 13% �p7-K6�N�t`8N|[BCD �owcock�=! ig�P~ Dorey!PH.Ctdijk � �� B 44eō:��PVM�JSTAT< 017P�^7;#�CD�n.<.R�4�?053e�BEB� P���6R�VGROqJ�@Veg>n@Gonz\'{a}lez-Ruizb�� bf{sd612�D63 JWWXA�-X. JuH��Wa�OK. Wu,~8Xio~)d�$K$|8 rice"�"�781D open XYZ spi�x@AY��C/ Y�BH6��r 2109N ac2:�~NA�786dh6u AADF��;aud�jJ. Av�)4N. Cramp\'{e},.�L.Ctppr7 \'{E�ugoucy�E��E6��EFgGR1�a�m�,L5M)6�Ab�p Abad�  Ri���Let2� 35F 9�7:�M�rM�Mn,ns, X.-W. Gu%6R25\ 721�G6�$ Bat4A%b\ DiageH2 � ! er mZtspecty{&�|�X$\mathcal{G}_{2}^{(1)}$R}$% �rx�D hep-th/95�k96Bi7F�6 So�'��refle�O"mI��6�U}_{q}[:�]$ �7ex�7el�%&�6080632�HPW} Z.-nA(u, F.-C. Pu����~G1 L19:� BGZZ!��TnEYa�d�� H.-Q�� .. y.51A�58gx:j ZGLGa.EX� GeşLinksA�D�\u'^e�Z7r:ZGbdMZZ3��L1RrHY!2B�H! W.-L�:��Y.1Imh!Qo�!]n&\ ��259R a�D>� Cyu��: 7U 2026��6� Bat5r�.{9�45U 552VS�6_ V�ridk1 Kuni�YC� � B�9I#86;Bati�k�akag�ugux  J6K�A�9R�fGan({/ anden�DV054��`J6�MacKW&& 2� n>�  17I16/DG>WAAoo$j)fb� 21��6lBG� &n 2� ]� Z6\ �d82dK20:� BK>Zutoizumib�|G� Œ6�GZV5 Ghoshal��$Zamolodchi�mr� �G38�'6 Li2�&�� 61!�44N�LiS8�G4a�56�i6�Li4��5G4aHB�LMFFR� l�V�6Oc66N�Ch2��4�O35e�86] VGV}~K78, H��de� �VA8V� 190},a�06XFC#D:!V> FatSov> N 32%9��:�I��Iz V� K<n�7E��N:�Ne3�� 7 65L 6W ReSh� !Z Reshetikh���P4Semenov-Tian-SWv�k�R:��13�C6�KJ� Kim,J5x"W �_ M,A|bat>F � 4121922C Ne4�7VY tt��6k"A(, ��:�AFE�Ca") -Alva:qF�NGB 6�O55iQ6wDki��VB7�439`06�HS6NK�fhi�\&�Q�<> % �k41:� Dk���~a�475� 6LSW�) Caoa�) LA�Y� R  6u|4�B�Ne�tB�~��U43G6�AAC��B�"mN�=.�̃Exp&/ P0 P080��42 YSZ}2� R;Msa�02� JHEP"� 04,046�X6SLi5% Kurak�W��6:s595RQ6nQ~�8�}BXLA�GE�L�uyiA�R&H6�5�{0�MBODk5�$Q�g0�XZ�a&� models at)U$it{q} root~un�^L it��060311��R��z�K %MGncare,acycle&�lindnerQLz@B., Garcia-Ojalvo �9i�LA.ESSchsky-G�lL�o;s \!#4nonequilibrium�~-�*090: 210201-1-.�jaffe%J � , Ro��S.D��TW�rsd� , Fa�#l%i�UzT��2) �.."tiq�&n8oid escape rate�5"Ӏ 89: 01110>�kramers�H� K A~ 40) Y@^�3!Ra f&%ofc c�9!g�/u�2i(Q�6PE�re�n��|&7: 284-3�=��anggi�P!V �7Talkn!!1(M. Borkevic��E0o-!�Pory: fifty years afteZo �mM&� 62: 251-3Bl� gold�r } G d }x2&�4y ��:�,Addison-Wesl�ea�,�.murray�M ��DQ�$$al Biology��a!�t"�qm13r�x��JA�\8.�kat} Kw C.,�L!lThoul@& F�i��h�yrT.�aI��js n��f�D�D (sb�,nus�( avail�� upon F reCt)='��bB��5!� �"\3Xi=)'.�AaYTe"U�{$ive: q-bio U$3020 ) % %AK >Pbabbage.sissa.it/PS_c�}/ :pdf>�B pdf H %Uj zhu} %ZhuGM., Y� L., HoxLPAoa!�4) � Calc� ng�*m behavio�gep�He�E�,a�phageD$\r5$ life �L a�W�*-C Genomics � 88-1[1R� Wv/*=kdv�J�"J=E�G��B, %``����gE��d��long 95 advanc!i�`�7anb %can�A�WJ newc.C %s~XoE6O''�XPhi�gg.��3(!2*8:+GP�_(u�3��L.�j�6�I, ``N�O%jry6� a co�Wiona� shock�''�CZ��ksp. T� Fiz�ڀ5C`73) [{�Xkp�!�JETP,�!2�!112A=wWh%B.�Lham �-�-disBnPE::rFaRoy:L�+ x 2.23652� x2J .x�Li�g!�&W W<7}b ey--A� rsci�)�1YG�2. Poteminh:n ot\"�d@ic-{V���Q� x���(elf-similar�0m�W)<'s&�05�U!���.%@)0,Y�j81�R:d22fw1o(2�Kr88} I�KrichI� )�3Uver��gaR� .�h ``\ g$O''�` it {�,.�i�8 }�@2,}�}-213, �.~�iev1�z�ar�- � >cq%�>�i9 of h*�mi�E,M�!k�i-9 31,}�i491�:U^ DN} 2n�S��V, 2 n!MCVde��edAi�4latn 2�KMXN **2ѷ"Q ��3veyU4,}w4124%d92dkaup} D�baup, A h.�Ewater-a�5���5 for \#�Wt� rogr_jp�U�~5��g4?�:�OMY} Va� Matv�M&Yavd)Almost"� al!FiV!�no�1 ear 2� 4!� �%��aInst.�Po��!} �o. 78E 25--�76EKS} V.��udash�S�Sha/t4v, Inheritanc�XSr7v es ue� yx��2�4�n 5"G s.� �X Rh.�87E 8--3/�B),GKE��V.ѧ� L. KryaX�G$ El, ='Ka�� breakEV��.��cit�g�} �4854} 102-107; Ev3!�a6fin.X6] �p�hm�7A�957--96�>�, T} F!��, 2��!n�r��onQo�! �E8a�U~.Iv w!re���46�10�PD'6�EGP} 9R.� Grim f8*�W�%�� � low-e���? undu��boresm�xIJ�10�1!I18N�KKU�:�m2�j ��F Umaru� Asym�Lcaץ�ti�!ia�.o^q��L�� M�BN 38E�E&6T kamc� 0} B�n�,&LPNh%;2F ir M?[� s---.� ory CoursE&n�1 JF2�� ``=�! 9&�L��.����ao:�o��,''iB�G*�W1K10��1mC E�"(pestia2�39'16�EKcd�L�XA�j G> "�ih C� 66}� Il876�AKNPV)i��># ��2� ���Wt� zon�!�k!��#�kD s&SZ SZ,�295a�45-34+8E"� F� Uv_ 564-5� 122� MGaU Myint�BIad_e��&_ !ͅ�s<6dissi3`ve ��1� k��>��M:�2� 215- I�R['�U���> 7)��=� 9�A\1�2�; B� E,.~�BLu-��ag%�M� L87���54)qcnoidalm�mV.:�, A[22\448-462��, ~ 89),6>zAq:3 l �"3 Zea�.i&�=63 or �4�35�?2EGP05�{:?� 5), E�" ��g���2�� �V�� �>B�,} V��? �1)�F 6F ��6G .�rA0��"0 !i!�6��>.N�W:s=FML�+Apsch�]�$FoAn� D�($McLaughlin�80), M�zph�D6� �"lJ�-l"e$RF�_ �u A8&8I�,�a3�� 39-76�=��E�N��=& �pertur{?� �( � SIAM>�I� a� 287>�bfr�X}�!F !?2z� Lehrbuch wU�8,} Bd. 1, VieweڏK�schweig.r grim[2N �$N.F. Smythp86)�%$onant flow��a�atified�id over��� �J. Fl 1�s 429 -��* 5���L�6+�sj��ET��N�)���&h-�2�.��,�73)�Qs&�2�f1 �Zh. Ev/;��iet�:T 2)46l �2 �a�9 FH -B9 )y"9 B9 -88v��7 -49�&>; GP�&z �E�&S�sk! 3�ndq �j damp�\ :�B� ,% 1470-1478����821-825�>� jacobi�/G5 J �U�{DVorlesungen \"uber�"k,} R#�lin; �X�a C.U-�L�Hsche Werke,} Bd.~8,�� lsea6�62K johnzR>!�q ��0)�no"�< incorp��ng -n��&� �6�� 4� 49-6� jYZ���Y ^`�_�` S s.a΢��o����.�:�%��C°=v���2�uzmak�E �5� 6&�&=!B�P�� PrikN tem. MekhU_2�515-522) LLV�0D.;j" �m��E���id�_�d,�.} (propag"� osc"�&# qve ��al val.�SE#Jmi?&s � it Import=DJ%��aSo� �y}�DAa�Foc_[  $ Zakh2"� ->�� HeidxN�  205-2�!&�!~!�l ���ɊB"� �c- M2�..�sag�H� Z�+�6�� Coll�%v�U�x%�&7�Grar� plas�i�%P�� P! ory,} �'$Leontovich!�.,��,.~5, Atomizd!;M�iw,2�P _W:^ 7)��AN<gre*t Z^ 6� }!Nbf 409A�d 9-97=� �8�02� 8)�"�e�*�>�f�� � � �`0, � 12�N�!�8E�Z��^� B �v$�q?N.� �2<"� �90�V&��.���җ �j� �� ���e��Z :� �65f ^� �6���LA "� .R t:� t74)��� . V+^n..ѝKPZ|EKardar, )� aris9A<Z�'�2*)�56) 882� BS^"?�Ab/� b\'aWH�V Stan'F{,al� cept�+���Kwth ("+, UB4�VJ5B]�JE�L�VB.W!�g�>�~ez�0R.N�w nsbup~�weh�7+�\62�Wali S�Stromat��e�>ed�Nt�% y 20�� M� F ) (EWN "(��:ICRڥ��E�Mseb:, M9�b�mats: 1�D(�"ec }$of benthicj�1[�t�s(A�]n�:ietFq ]D, W�ngtJ(19:{ BM���Iurne, L��Mo�P��osix7) �.4G�=��! , {WoCfu�\fe��� ss�l&�*N?-�His� } (Hutchi+ RadlG� ����cer M.��ehAT=Har�hԙ `�4pc�0 ) 75OK/Kno�~L��  Cng�nnet (�}e)"F��R6�WBDa��E��F BuiGJ.S Dunl�� ��+�w�*:�aARR�  Ar#"++�0,A� Reit�+- 292( ({702�Lk"RaUwe,1��*,'DJ 36RO HGHT!"J�Kfd o�Gr5+A�GHi��I�orpe, a��U�of M�, Bulletin 11K%99) 1252W SP?6k�chopf,P0Pa)l,�3�A�72�B!xD.1s�bֱ1f411 2) 72tGs>R3nG S.T.e,ZCarner�#\$Christy, �Van�,ne�v�H!<Wel�'�3���6 1192� BBHJ�6?R}�B!iHen�$v Jack-Q��-A 3!20{1 319..EBSM%^�1�C d-Sarfati� MH~-P]Ski�Preca�Ran|�Fh aH8��02�Y BBHW���GD 8t� �28I�0A2�\]d�^j Sa"�AI�3�8 3) 7:!BHS�cT. Slaty/to be p�d26RAbɪrotzi4�-Kot��,Q�3UK>p&v2GKJDe���U%Earth%Pl���*�%s �� j12aLGLMW<"A�o>2!�`,t kH�>�NseQ�7�q;Y�2Y;�t46�KRS`AU,m�Mp Raab�1� Sem$<t�%"�emy�B�o�#` ���>M& itut�ransa.- s, vV7Q:�*JL%�B;BmGine L���{~��s)"�/p6at� of Colon��$Organisms,2$Ae8b Spec+(Volume No.  �499 ( ����/�+tPy 'NX�4f�(34} \expand�1L\ifx\csname natexlabU (\relax\def\ #1{#1}\fi^G bibO font>J M#�Pf�Q$�R cite~R.$�Rurl^�url#1{5:tt!O%8{URL Iprovide# and{!\0info}[2]{#2} B!eprint []{S'*y [{2�{Gutzwi8�}�� 0)}]90}�(nfo{author}5�{M.}~�1m8 LY�\۠#Ftitle}voo cla�andG@ meq0���3(>�|r}{o3�}, &ad!�}{qN �bi ��4}{� }.}$>Reichl%2! �JVL> :nThe�'nsi�>toq1-!onserva 25. �:95anifes�s}}�8a�1J:9W582r8$St{\"{o}}k��AP9!?S�8`�mRQH>>6P)�RT�[C���tE3"�5fJ"�B mB1.u59rHeqg84! ׭hRE> :-�jӢ}�M �8.} ��bfy�vś }{53:Dp-s }{15:�y|�84r�B�eJ�� 1)6l , Kapl� $ �]{BKH�H�wW>W:�VHB� �}-̕�an�rT}}%%�9K>O �6rJ�Bj770:@17733Z7z�ogomolny��88a��35��=:�2�' Dj�31:> ��!N�8r Berr ߥ���B�9:��roc��M� .�'b�42Z�2Yo5wI�198vt��k Ke��!�����^���J>��^��>37:KQ"�iB>z�Aga�FY�%=�:9�:O>�8�6S>K�^;&'[�.bt7Zs80�F5v:سEv�� 3{"g {a}}�RTH93a�B�b�I��HZ�140tFI3}:*X>� �nWb9Wb�W�W�Wn4Z�2�n~R!jRWorce�B"� \[6� %- Cornu� , Dzieciu�Munk, Ho~ Merc0Sp�Hl,+o~ Metz�S Bird� w}]{AET�� by� *`�:V�+x>BԒBŸ:�5 �BW>�:B!B�=B�!v�:A>?)��<�m>�-�@ J.~A>@Rsij?"U M:j+&�T>�Qn>X� *�"��\coust.�Am.�bA105E ��u318V�z� rownqH 3:�!u[ �, VirovI*olfC and Zasla�aq5p�$Bp{9M�VlB���9�j��jzB�.��B�-I1�UD�*G>�=�2�r�j1Z�253�p505 �~ on]ar�e&�EU�ޒc��F>L�����;������������Z122J� ��Abdullae�yy�1� AZ9��B�W֊ ��DyF�Df�6^+N)91r�!03%01Q��n5�9V��ŷ"�Jof ray:�/,guide media.�P .:G�*��.^ Gc�aB8Mh s�F "�r���<� vY2���o�0����I08: �8VzvFSuihB6tqSZ�B>�V�s�sE�j}9�-04831 >z` �jE�248��8������+�C-�5b�^�26RA 8v�Sm��� ��2:A !,��Tap\8 SBT92��B�W:AV Ba ��p�_ B ˥`B N� f�9^I93A�_\ �tr���5��F�r�r :� aN� �IBC7˒��v����aK�Ej�b?362Ȅ:�!��JN��� Q�V������%�~712N861�J��V4�V�[��������%�� ��.�3b�v�х�&D ��7W ZA97�R n=����� q�"V ~���.5182Z 7r���j:%% <��VJj�> >} {]�$,6P*�7and U /�K �$�5ite � �F5%BEKPr~� �M Papa�f�"�=%�^;*�7�\&S%���77}),�� 22��84}j�Brekh�*ik�*Lys�z!��BL��B�!.X%!�2E�VBB� �\ R�$F� �al�5 Ocea��QE1��xpT,��&)� ~q�1�z�PalP�& 88:$ ", Y ,E�Bezdek! PBTB�* D>y `-<�Vyb" a�v;n�;2�OB�&12��Ge-�R�4~319.�m656R] ~�!2:1a<6�!,� %� Go\^ni!�BTG�h����9�B �2T5���j_jD ��J�9JL!dr�Grempel.v>� #f� ange1�"� ]{GPF�'(Bo Y�pRB��� �4BS�2Y5�&� j�A2lJ�16V�z�(Jense&i-56/ ", Kupeٶ}PtNr%��gmid4 JKPS�#B� c��B�(��>B� ���BSc- !$VC&��al�(AIP, Woodbu�@���:J�.�v� ��}]{MMPE�� b��U�J a�.4 n�A�D� ��23 ڂ�Tatar�^G 8���V> 7J)����I���pekhij�26:G �3��& ���)=note}{[6 !�v. 139?�.��pp.587-6�{ 83)]n� &� & 97:%oEdeC�(and Niyazov�CZEN�� ^5c� ���Be�2�5��59N��~�BN�4f�4>*�;Bla�7 Bl��5N<zab��i,*FfR�| �Q^�Ebysu�: ��(2ӌH>$b�>orAfM��V��2�$ 10345-103m�� tem{�=a�yG=n�C2�]�W��Oari �for m�O�al�F\�2,�;�ka���6��Sr.)�Tec��տ (196�;019-106G �q�u��O:1�s�2tP9mEticity.E�!d���Gch. (  Stos.) �\d�7=R817-838;@k. � 1972), 3-N���ZzcY^cte�;��-�'z.� %�Ual��boli[I=,, Sibirsk. �� Z ���,1970) 279-302�AK�? CanU�B��Keyfit˻ use�?4A3>ɰ&;4M]ar�� �3 ICIAM 95:X�=vt 2: ;QqP AnalѦ,�:L`Re*<�CbfR�(zirchgass�>O��� holt���xennmQn3 ors)�XV� >lH ZAMMA�96� 3-132�=Daferm��C|� , HZ�)�B in co�um�A��:�?2z>Dinu}h , S~�rR�se cern�JA�M-< invariance, Bur��nat-Peradzy\'nski and Martin approaches, Rev. Roumaine Math. Pures Appl. {\bf 35}, N3 (1990) 203-234. \bibitem{Dub} B.A. Dubrovin and S.P. Novikov, Hydrodynamics of weakly deformed soliton lattices: differential geometry and Hamiltonian theory, Russian � Surveys {�\44} , N6 (1989) 35-124. 2� r} B.�, Geo s\of 2D topological field {i!J8Lect. Notes in � |T1620}, Springer-Verlag�096) 120-348. �DFer} E.V. Ferapont!@< D. A. Korotkin %cV��Shramchenko, Boyer-Finley equation Asystems�h=�d type, Class. Quantum GravML19} (2002) L205-L210.; Fer2B��M� Pavl�Ht reduc��(the heavenl�� J� 20} �,3) 2429-2441:�3V�E� Tsarev, Sj( that arise!јgas chromatography. Riemann invariants !h$exact solu�, A. Model-S3E�2E1) 82-9>�4V�PK.R. Khusnutdinova, O�(tegrability!�p(2+1)-dimensional quasilinearQ , Comm.�h. Phys �248)�|4) 187-206; arXiv:nlin.SI/0305042D Fer5��8The characterizI��6��.� 6�multi2�disper!�$less PDEs:e"test for5%�, �q.�45�6 �, 2365-2377; B�12015:?7V�D.GA/$rshall, Di��-g�.ic�c to�1��!�2�chain �� . II1kLett. A �f13%t3a��f167--172-GibTsa96B�S. P.��R>  Benne�s,-�� � 211}~�Z�.� {9z{0Conformal map%KJ���5�F,1999) 263-272D4Godunov} S.K.  , A�� rest!�c��A5��-�� ��\, Dokl. Akad. Nauk SSSR1���,1961) 521-52A:\bi�$Grundland}�Y%�TR. Zelazny, Simple wav�� � �( hyperbolic��. I,E%J"a���problem�s` a+�ions.A�MaB�},c N9!�083) 2305-232H��4periodic opera! !���applic%(s, R+ )144����45-222K\ �=1A]�(modified KPADym��� B}� A4" 11191-1126� Shabat}2e�jA.B. $,b� �2i(a universal�y, Teore at. Fiz� 14$�U� 216-229. .M !gV."Z  I& JZ %�I�i9�C 4134-4156.� j%�k&if�JQQ� EgorovV�Theor.%+� �13i� 1�4) 55-< �� �2:�8S.I. Svinolupo{R!� ripo"Ve�nt criu on�24�� ��kt� �� i Prilozh&K 0e�v ,8-29; transl�6inb.9�h2��1} Z.  �,jV8 nonplanar $k$-�, Bul��c" Polon.�� Sr TechQ�89} (1971) 717-76&�2N�No\�e!� F �625-63!*YSev c� ~S\' H, G\'eom\'etrie des��\`emes&� 0��T .'id��F. , V.P��pee�<N.N. YanQ�� of d*�%v trai�>i a�9d� , ``� en)���c:(quadrics. D��, lin�F`mechanics, 173--199, Amer��Soc. TM ��. 2�60 >,,AS(vidence, RI�92�0clebsch} A C ,.;"I�(ie BewegungI�E;U�A�r Fl\"ACgkeit}2Gem�� h. Annale.;3A838-262,^0.�perel�I � elom!� SomeM>sA?� �;� QE"9mo} a.:i ideal�>�fLQ�1�83-85,�2�koe�a�ttNBF^festen 46e Fl5c. I.IIB� J. R!�$ und AngewM?}�H109}, 51-81, 89-111!}92.}@reysem} A G Reyma!)Td M A Semenov-tian-ShaV}w I�BK\Moscow-Izevsk}, 352 p., �>2�bmszV Boris� S A Mama�Modern ��E!�Qf�>�296V� gibts} J 2TS P ��,.� *}��" U���em ��},���AJ --2492�hh} L Ha�iE Horoza A�� pair� a$Kowalewski�>��ica D.]2A��180�82� misc!�S M�/ko,"vqcgeodesicHon�symCic-s, ��] /%bf 31}(2�� 257-� 1982��foE��% A T Fom� >L on fV e2NLie}up� ya>Q, ser. m���42 � 396-A�72  Ram� F*�=:)A� V�Jmu�. 2= 085) 3070-3079.  ��  McSweA\nd:��su) �N��!1� fD"��� 4�957-296��Y� adle� M A z< P van Moerbeke.� .�0Henon-Heiles s a3n� J� so(4) - ah "� 5A��r �|smvA].�� %l�/11�659--70�f2,vesel1�hP V ��O�G1W�condi�xs��E2= ��� �V%�@270}(6), 1298--13 ��9ybob�]�I B ��6|�m $e(3)$%y$�0$. Isomorphis��le cases>� BB� 420}(1), 64--66Ų22i� �# urce>]8133(1988) 493-46��89(1)B�Cap� a�" inK �1it� in nAJ,eXun6s120��451-46��90B�New1)ederiv��Qble�dBE31}102|Leon90% J. ,, A.Latifi, ".!�anz�coupled�w�*�2R�385-146\ �90(2)}�N1p ev�Ish&(S!��ced& ��� 1441444-452� Dokt� 91} �',� Vlasa�(Opt. Acta 3%�91) 336�9�2B�͖e� 9�$Schr\"{o}d�(FM�In�"�s 8�2)a -14��u�Claude�C. .�Q%q!reson�sca Az(and plasma >a��:I""d mC'F�u1) !' -3332y4Zeng2000} Y.B., W.XaL!yL.L�J6w" V2��S�I��5453-5482bLin� Ma2001} R�6�Mae3e�� #�E� Z� by�( erse.i� �� A 29r 1) 2�'92�Yeshuo�)} S.Ye,�J4mF� �`l �A�Qe}�35�2�3-26)!()&FY.J.Sha�wo bin/Darboux�?"e-�+JF�� 42(5)�!0113-216k �2.p�Az!�-<l-%Z��n%�NWZ��, oI�3�(2) 641-6r,u� �3V���4W.M.Xue, NegatQ,Pos��a)�*�A�q:�E�f�.6�+1-2/��87B�A directM�6�a Mc) � �&�*�%A�ra�,A��g�x,y�, � B�1�� 87) 639-66��9ŅJ�x�A� �i a$ describeda��Kad� 8ev-Petviashvili:|aZ'U.� M-1 �01-212BXiaoTi�U4} T..G*�Z�5}KP:�b�.%7e� 4) 7143-7:�%,Zhangdajun20A�DS.F.Deng, D.Y.Chenf D.J.,� E'%{on2�E� KP EM/!S:9 S�:�is�Jap. 72j!2184-216v(Oevel93} W. ��Strampp!�nc�"�'�*Bi-.eSt&UR�57��3) .��Estevez} P.G.Est\'{e}vez, P.R.Gordoa,b�via Pat0 ve a�;6F 1� 7) 939-956F$hen79} H.H-�Y.C.LeA�.S.Liu"� a�Uw %  �/by"�S&mM ,�.ScU0� 79) 490-46��gYik I?gA��=��e�2+1&�al�U!(�|�1, J.E+ A 25%�Y%19-432�(Gengxianguo X.G.�(T.Wu, C.W.C�Q�/-�(�졙� &E%v5�^ ,9) 3733-3742.8Konopel~2!# B.G.2!��"�(�ᘕM�% 2�r��q|, Stud.���8�92) 2�,6 Ablowitz� M.J.A�A� rks�Sd(" E  JS*C!�6�Dickey� L.A. � E �$�gE�ton)U% World Sci~ fic,  aporJlMatveeb V.B. ,, M.A.Salle,u�5� �5 �(,��&6Date83�  dJimbo @Kashiwara, T.MiwaAy��_m�-C�-���Q�4 �83; Mi \ (eds.))(�$1( 2)86� Ohta�� A�Satsu10D.Takah��Tokihiro\ Ele�#ary IP#�4� Sato�Prog. �XSu ,9%N26J5JurijA)J�"q� �SPyK��zK2�)2}. 7�a 1) L37-L4! " I�95}2�OxCZ�,����34�H$95) 379-38�f�H�#�F[�.��"� !��s�T2s� :p5!�{,�fyp9 P,nth�6giee�ir2��l�mF 71%p5) 661-6� end FD!f���bib:KSA K. Kajebe�A0Q� $q5 �3ce �}�(o��20 Toda lattice��, A�Ş"�an}6�(� 3986--398�*5|�4MMV94} A. Miroo ��PL. Vinet, On a c-num("qm�$\tau$-fG,, %%� �� ��$10 �5)� 0-89�q+.2o+,4�19�0'6�WZZ�Z.Y. Wu? H. 2 �Q.%2hZ "89de�إS!q.MM MNex*'8s: %�>`Տ9�A:4%�)270((, 5307--531j'6�F�I$el96} E.  , Dp�$2�y :<r� �U%�'In�,h�s;iceM0�(\55--76. :� KLR97} B�8es� V. Lyubas�:%k 0simal B\"ackln#�.��^�9��9�& 5--1�6�KM81} A�"@ E�T�BD 6� $ MB� I:I1�D9~�2iF7A�r}&Ja��(a�r. A,-��3I�5ip8� 42--347. >�DJ⡃2 "3 �� �I�O�5 �AArA�z�!�"g���5�^ �80��812�%2�JM %M �:�%c QX21���\%Publ. RIMS, Kyoto Univ.-{�@19, 943AZ01�2�UT84}8 Uen �K. � saki��. u, 3 Okamw4(ed.), {\it G�":)�� Ai2..�$s\/}, Adv� �sCMU vol.�" KinokuniyC okyo� �"p. 1--95F�TE��T�eb��Q;j lI,���8 $W$--�y�,mD1!�Z�2�;3��S,6F�TT� 1{l.�ST>(2) �14 --- .�6t.Q�2i%r���a��B -214BGMPZ97} F��gri� Pedron �J�/ZubellA9& �>�^��zP=k` �~conne{`a�discrete>N��f18-� 7), < -325F�K�"shmidtB,5Q� KP or mKP� ncommu�+ve� h;E� Lagrangia�7*�hVq \/.}� Dal �E%�Mon{.si78a.m�-�"at7 ocie�2PrvF�RIt F�9� , {�AI=uj�-h��27�J Taax .�A noteW&�.�A(y�/nother) >�@e�f�5�s�a�T( 172.:sNO"N. Nekr�{`A. Okounkov, Seiberg-Wit/o*�random pI>t�9 &D4hep-th/0306238F�NRVy2iNB hetikh�,d� Vaf�  $Calabi-Yau���crystal��>� 9208e�N�0+v�Fur#:Bureau Ba�� C. Carol�%O� n� � �~73 PUFH, t.2, S{\'e}rie IV�(99�1).zcar"?P Carls� . LaVH� Rev" BS:647F 89.R book-7!t��ers��Sli Fri��: �1Principl� :s},*4HeidelA6 � �bt} F.� BowdW'D��bor��ity%� Lubr d�A?d4+Clare�3�2, Oxford 1950p rabi�D( RabinowiczNfW� of�er% }, Wile�),ew York 1965.Z)�RHc�#A.�Ru�=!X|* Me"^95�;34�83.�hes%HeslotB^B��rrB2iUw2E�49}, 497p94.p bau}�x.�i�it f F�W cess�B< Tribology}, edi�*0by G. Dalmaz,a�!ubrecht0 DowQ�M.A?�F(Z �30�=Leeds-Ly| ymp.� q(, 2-5 Septe�, -, F@9 ), Elsevi$ Amsterdam)3 .3=�bauIIB�$P. BerthouDVXB)X6%�92#2ZsscB\S� State"��02�.7�7.�g32� Glendinnivi�#Ts e,ChaJanar.�N?o�&�n ""�}*�n ers":. 19946\2B�=KU���%t��M�51A�00)5. lim}�GF. 7K Kan �N58�166��.Jr�5K�nj�-��J.q�e�M�a��4$�i����Tbfiq34Q#. ��nb@T64F.m�U5 , Na3(E&36�@(10 February%u, 5}K՞my�#SzkutnikQ&$u{\l}akows� I�J�Lrn�. C h1�3629ŀ�,N/[v/*`gyorgi�4G o%~F�,,�>(Noszticzius�,D. McCormic �H�SSwi�H,�Ch:!��12m�2)�barkley�<B ,�BC89} 554$8A"9Ypetrov�A ,�HScott, !gShs2�4J+� 97, z#16koper95�T.M�Jp����% D80�/5) :� z}�nrneodo,AIArgoul� Elezgaray� Richett�!YD6�"93) 134�2(A��'re��w @ein)}.; J.S. Turn�J.-�oux!�D. 5�, H.L.5��.  A8E<81) 9;!bib{KK.1U5F�Faradayə . 87f�%23; Z� 2H6�:��h�NI93 !�89) 27�+.�alba89 ,N. AlbahadilIE Ring=J! ScheM�c 9|  812r)�2B�$. Gaspard,�N �L 96I$2) 7797; M67<J�Sluyte�/6� 9E�H82- ]�krisherIKr�4r�Lubke Eisworth!� WolfEv�ud%�G. ErtlDhyEs.t1�Kyb chay�5Ra;A�Y.AYOA�  "��Bifur. ���5} 59�/abraunbB �� isbo�t�� SR4} 1483)x�VtamosiEer�Gndo�AT�Hennequ� Zambk E. ArimE>��+ E�Am. B6A�A�45.� raj�S��jes1IG� ntha%�naise� 140 0) 193;�:D E 6��0) 36k49Rhauser�T!B�, LZA Olse)fI��,:� 9��6�)5 $_r���, n� A2� {41mb�Mana82} J)@ M.C. ValsakumariuA�. D1EL8�T1�N�Rbasic�el wa{mu�5inN�D. Saho)�Z D1 ��08�lorenz63� N. LA'Atmos� i. 2�W63�-�,?):t�A R%FA. *�@nd^"Institu�f\"=Banga�M8. coffman86G G. C �6pN� 9 5�#(86) 999; KrN>�R.Simoyi�m >�$�)1192_KR���R� sse��J�‘�:/A��088) 6963; Y. Xu,AM.%�m�!4�07137;]��Hu�LP*rz\A�#��JPaޥR � A70;e��V�|I��4 �jF483; C.J� o�BSIDoumbou�B8��I��.guct2JxP ckenheime�bHolme2f%6�E"1@$����N� VectorI s&\Y2�$eyg�X84�(�fNWapral,a�Nicoli�)� "e"� 4!􁫕]� nTlen� � $C. SparrowE�ZM��N �76�X!9WaJ3;LI`4� 87) :Mm� lin� O?���P.E�illip� Im�A18R!�30a3� fang� H�F��JJ B�A� 5) 562se���R�29~-49E���2%.�bagley��R! B%�Ma[K�H!}D.�|I�� �A11i��4� \�2!� "� 2 6J�A 92� p�6sky� �U ��� � �1��.sbounti�� B� T��B >G10 �4�W2�nusse\+ E. N !A.�:�6 A12! ��36�0$parlitz} U� � LautUr"��10 L&51;-8� A3� A�46ikan I.��� Kocak6�An"713& 2%�9�da��2P� 3+ Grebogi6Tr�e s%�� A1= �249U ZVH�A� E4�=��66�EAvR E"YxN.Issaz g .RA4k&0) 42:[ schi19�"chintupE�mdt� P� u92} 340�6geisel81�/ G DNierwet�Q�!�Q ]� 72� mss}�M\p�M�Ste�� �. � omb.X)y 1P7 ^2V postkT.�2�Q.W9pel ��DA17��1) 62.{ga� i�  G �?ln.$80 ory,�hodɬ App.�8�^06�gav>Pv�K\ ; �Lil�:e .�K Sb. 1�7!.67; 19�2�16_aguda�B��AwLar�e )�� �=M!79�εnewel8& �xN, VA�van�*A �elides�@J nnet)hU�54 �6�@� htomita80[  T ,a� Tsud� roK+I�{ 6��� 138.��%mapPKanekoH F"�+ 6%��^ 669;�2.� .6%uqY:_:corbet��� �M�A1�988) 2�?�s���L:9E�D7� 3) 3�*y _ &{ zM&y 992 johnR" z#. John�L<: Hao Bai-Lin (E!D{5� c�,~�-� R_�f_j>"`5�>�H8��ɇA�: 493�38�=C9"�sIy.u=451NI� >F90��.A31 1=A�<;>  JcK.=� B��A�X"��.8!�?Z"�;  Y B � W X ApR L�BQ��8x e;W:d; F, e^M ga:%1auA ;28�C8R.; Ye SLj!�1�(35 L283-L29.*|l}�2��: Y JO1O.<}:2v:� V2.VK6�2U�T�W �38 :FW3bWXue W M�3� LA 36�9KU�  M"87�.� 112 N9RJM9BM^�6 �8MZ:-8 Deng S F,�#n D Y%?' D)���B�7 72 "�7`p4a_  Ma��kPqaKB.i��4 ("U.�"  L:o&d%A(*�#�# (Sinq4:�4� E-fic.jm4k  V B, Sx4�F��1"%f&;*~1 (qQ: �4).b>)e( E,E) M,*D)MP{4 T�3 I*�4 =}E��4�) M, .Z�4v'��n419�   Y!"x4A'hashi D�{4 �8�"�f-&V4210h&N4 urij�Ven Wa��2e:)�B/4(4Q�: 93}   W�7 BWD3V�57n:II�N Q�5ͬ.34L4A�K4  Y�}2:3 377F75}.75V�71 �3�FF�3 z�9�mel� �� . K.�)92�`"mC 8,�.� �aX��.x a��HUDWV S1,�[&eBe2*H2���aJ1G [2n�3,2(2), t"� Nak�  zawa M�PYomadaW \Kubota H X1/ *266, 266� _D%  de C\\F5 Y ��22,�._mel89a}R�89Z�52DN6�0Hb�H6�(>�90Z�90F1B321 Kaup�i  & )�I�=i59�62@!S� 1M)��GA)]0,%^ Q� A�85.ZA`aqR`Sh�pnovichTS W5Q � 207, 15�Yj?�6H I^AT �]213, 7U�a�0V�!~@!*�E3IT1FI1?a=88'.;2%z12�%N6�1UO4�!�� � unq;a Wenxi)� unl�+�FBx41(�3�F.�\%� \19!�� -th�:8nica, 15(3), 33�R���e� %�BMF��!a��$7-Fs" .} F.�oYsE �~ 1996%)`6�d!�776`I!01}nf^ ijuna>01`=� , 42��11Bd&P )�LihV ei�h]3] � 36, 5032h�4} �C �C I1�20 '"�A, 37, BC2LiGuZou�= Li Y�a Gu X-�Zou%S 1�ME �SM�`)�Ain\R�70 ��8�89b`..dp�wH Da�55�2�>�;S�D,Camassa-Holm"C-L. Its High-Frequency�,i�+ASinh-ZI&aF,)Me��Tc�,1j67 �1�8�%55-36I%U�do�A onat,*Ol�li2��; \ alSGng ��to't=�hy"s�� into\ au�,m1[or Jon6�it{%d porty9!is�!} )��5}\��3-5�V03-3222�ub�w�6�|, Sp�|6 *�zGa\<$Cs�� it{Soviet*X iewatS�7C:�% ��"�64�R�0wa�t]d9}��t 4Y'rwood��emic ;�)8s GmbH, Yverdon%U36:Dhf0Z��E.~2V|2�Decwysi��Syigher or�e5�Monge-Age t@|�it{X �M�ٜ62�{2�(-16�fceeQ�DKFairlie� Govaert'\�.r�_2�% <qob.u��i CoE�nt��Pyo Nucl4-�Uh B} }�bf{37@:�14qu;-Yb�},wearis� of >�5[�"� |:�\ 2du1�-3339-3{>*z ts>6)��%ibbon�A��a}.`2�avx's.�!#.@ �a�>|x,v Nv�E"aFux r>y�:#.�&yx��-26degzQfA�� Gure�, K!Zyb�g�No\8ssipative gravi l turbulpf%��)) JETP}���'� �mQF��0Large-scale\ "+ AY�VM]e.\� ytic� R�Usp�X38�Z�#�%68p2Uh��� J. Hunt�'R�*xto69 �'�5�Sor �^�.�a\�<925� � � 1498-156X jean2�. J.�Ast�Hm.5osm�6,��o2 �q"K%P�6e" �k  8262Takm"VA�1amchatn& *�6� new C-*� li.re .� subm�;ib���P���}.kbq n � :��-�waterUrx�>AwmW _}i! rogr�#�ti%�bf{54Im2a 7#&Id02�! kshgv�S@{J� : an iI �!O�[B 6LP�9 �` 7�!5--6skUoN��H�$ udel2RS0 R�VEmb=cular!^ͼ5�6� y:�|�i�% 754-37�/"% yavu�Y(tku.�1 priv�8 @( } at �,quotedblleft�CG"C4u ysisF$right\�@fer��2L.j�V-LaOAa0J��v' M�eZ� 43 }!�3�/n441-1452��31F,�9Sariogl2 An\ ��family 4=. "�E�their\n��%�A E/bf{A}�1� �' 70-26�O&�P. Ol�}P�?senau2hTri2qdua9� bet�e� � ary�i� ha�]5 a�up� �. aE (3)��!�"�2$1900-1906.M�M. Jur�FI�3 ders�Q%&�nA�"�sD}e�]a*����ofX, Duke I.*��8�\h 1--362mplQ�^�3C�UA&� ��LiouviIw< B�b bf{12�1\?* 27-9x��mpc"R^�*��1���pA�c�R cu�}u;E�igNo�))Caq}{8. 9�pplT��"-}Yl6�9 mpwh~RW��'s*7u��0a!JKo:�d "�G."���1\c�9�{�*615-66c";F��'�5Shadwick2� B\"{a}cL :L�!�i�J"5BS@(�VNA Enginee-Pf1.*� TInc. [Harcourt Brace J�*T, &-],"� -� � 82. 334:1sagdeev1�R.Z� ,} in:u�g3 eonto } ede�A�Plasma%�r1|4} ��8��H5 nsulAys\D.� York.� zeld�Ya Zeldz,+DA�va02�"�T!� "N$�A@. Usc�2���� Nauka2��(1� 7r#F�T r=v%1y�8Szabelski1985}  K## modud W. Drgania ukladu z niesy�Jyczna�*rakteFHyka sztywnosci przyP a.0ym i zewnetrz$wymuszeniu�51/ika� _(i Stosowana$5;23:223--�,%2� Thomg319�f JMT6ao� Phenomena��ggE�!� Escape� a Po~m We�}DCee�EEl the Royal0I!�I��t�;421:1}O2U!%3�5k199�y1�-�� Vibr� lSelf-ExcD�5ePa)Wic 3Ay�=-�Xlasti_n�6�Seri, Jour�Pofyor oalD��&�A� ;29:�HR.%4.� emplinskaAP\'$-Stupnicka�$Rud"A J. l6� s p5��H*�AM llator: aS�xim �^t.G stu��us)'3��4:�Wrea�s+�� ;66:368--M %5^�e%Z�.!@.� pred�Gve ��a � �-%aeIq.�j�s: A sV��k� �( ;7:129--6%6�Reg!�5}   Ga�lv!<i�Bened�@ni�@Nu�K%� YM!Q �siE� bifu8� �� an aNc eIl rp~�/��i�cs!�� 249-vA%7�(Litak1998}  � WarmIUi�'2< Reg� 2�a�v2Ma�beiO�N �r���yO�oB�,ity. In: pro�0 IUTAM/IFToMM@\posium jG�YNTHESIS OF NONLINEAR DYNAMICAL SYSTEMSp�,24-28 August!#8, Riga�.via�A$Eds. E Lav2rliIVM Zakrzhwy 5q�Blс ity;P:!^ �$ 50--1. %89�Ru3k2�i� inekB:�2� Rayle�� ieu]�%hnZd��U-ity!���. Folia�] atis�$tiarum LubA]nA�� ;9:1T&%9�and3G}  RH�2pAv2v1� �b �9�X. 6EVBreach;3 York!A 4. %6u2I uRH�]}��NsA &eY� . Ithaca:�? $rnet-First=�K;�P3. http://www.tam.cor�H.edu/randdocs/. %10��1984}2$,] GW. �2.l�� �K ;ChiP& ter:Lg*]G*�</T} .a��s P�� O�+�2. �� WK�aם���ve�<�<� er;0�3�*'Wiggin�C0} q">``ŋ. o M)al�ois�j|�m.{z3%1��Chaco)g1}MCconaQPalmero/Balibrea�� Ta�$ aA�8a driven Joseph�. junc!1,�i�QioI��>�(;11:1897--96�Casl$4a} Cao HJ�/ i XBen GR,u� �r induc ��L weak�`ln�A �teklyb�ced FroT*pendulu�CnD"B�,4;14:1115--2q>"� �b} ���qmodel robot ar-�mͯa��nipQors ��hnd�,B 04;271:70�4. ��� 2004��E�4Friswell MI. �#��g/K6*M� effec�ap&�L6G�Bd�R� ugebauer]6 s.) i�-VCH;WeiJ@:�,�!331--4!wR Yj�-2�$Lvolart} Poskanzer~A~D0(Voloshin~S~�08 \PRC}/;p167�ov2over  } se�! examI�HAdams~J \etal (STAR]� abor��) �*04 f�RH} nucl-ex/0409033 (�e p�|she�%.�)%�F�IY4kolb} Kolb~P~Fa�32B �068} 031902(R)=u{wor$Sorensen~P E>�30900�|7!2}{^~CjU1�L ��(�E3new�} �K2.K 9} 132301HGS~S�PHENIX:��%0 �91} 17K9%��x��M4� 92} 05230�'huo} Hu�V!k,5�(, Heinz~U~WܑuA�"~VE2��x \PLM\B-�503} 581[0Q�AIP � .~Proc.}\)�6 69*} huo/.� J' 2E90$figpiklv2}:T�>T40500=qeos]��-3 �Qu��Gluon�3�R$s. Hwa~R C:sC~X-N (>�4*[h)},F��V508=co�,els} Molnar~�3>�:W 09AY1� �~ �Yang~C~B �B�u064902A@Fries~R~J, M\"{u}�~B}6aka [ Bass��B A� ��68�4:]Greco~VA�~C�ILevai�"F��g 4904��Hq0} 20a2@���>T��figv2~ing��~�!:4 -8F���y#ja�T $stillo~J (�JK \JPGi��b S120*�r�w ces}-pE�K)��pJ�70} 0249�9@ Dong~X, Esumi~S�l�, Xu~NX Xu~ZVB�d32*� v1v4pap�$�F6a:9@Lolli} Ollitrault~J-Y�3~�artQM>"�{2*��H�Pr��2s A 34Id.6RGWJ�L.~Gold�HeO�K.M.~Wat M� C�6vl23^ (NexO 64),1t.~9.6�Jouni�Y~Ni� F�29�Fo$ 417;!���2f9=f Reid�_~ �rnY�(N.Y.) 54R8) 41)�N�� r� S Y$ RHIC>Q~�2i%/T.~Ludla�[S.~Ozag %``.  ,'' m�1�\%�� �J 499}�9~3N[{Karsch 1cy�W~ j Latt�_QCD at�& te�, aturd d�ty���N. tes ͑ �583�0[2>�czmarek�4gv} O� , F� Zantowa� P.~IZeczky�P ic q� anti- $free energ�(� ru ^��at 5 %��l �clat76036; f�.��F. ��Heavy��eno�5n� Polyd� loop�-d��%�54!l4��:kNecco!g1xg�M~�R.~Som�OAd�N(f) = 0S��"�� �2 short to �$~�i� dist��s�M� �B �62�_3n\�E6�5} B.~ack�:��$} [PHOBOS6G]�Ch�+d�ticle3%)!�@.$ mid-rapidF�ent��$Au + Au %c��sAs**(1/2! 56-A/GeV%0130 � �Re~ -� �8^ 3100@&0);*�kAdcox%�ry} K.~F�F4 �Measur-#�A�2�<"5U�!�riby%)� s(N %N)���- 6�}z�7},sI�16�Adler�nb} C���{\i� !�F� �IB�if��)le �5pa� flow!�V����0��18� %��&�m�2pb.—1zd��P eR fero�y!�s(.�z���:� %/��X53k�jSZ�N)�Sca��pr�_tibfY�� ��pr*�6+ % �V�v� 91},�%�:>JA�3amnR~��P�iA�typĞ1�+!�azimuth�iso?8�K�2m�u&�g %u6 V 6 �!z ��L% 4e�%J(msb phi etcJ*p hlmsb�O~Long b��D�M.�Of ��{nge=#�� s At0er�� P(T)�H! %Au�=� ( S(Nn�I/vB Rhic!2� �i30��193=&Y }t�k�E]X��ofk�n��haJosA��6�:�u�f�I�:�s�}��ewisY~j�U�d2���)��^�21O;; ^�kp� sk(tVys, UCLAmA3,�P� . % ``Kao�Lambda.�at��me. p(T):� �/!�� %)�iz�A�� bulk��(>m�� creat�R %�Y�msbv2wSchweUHb�;l �� �AI^k6u; %? 5&4030322�C�AC4jy�JjCB 8 i-s�ge bary�Xi �.Omegab0 %f^��q�R�:�x��bi��.ANinV�:���eB�9. R�%�4 ptN� YR,pt.�qi} %S.��M� � i0:I larg[=� m*tum!� 1#B� 6P �C%z"0�%�3)A�[:V304022]..i%�!�3kv���=:�A׵��6P!��b�2 %`1!Pd 1H� ultrareN�vR* ^v''�@!$�oY!Z%R!4rj��b.~j� Delta, K*�rho�"ce2 n/���of�ze-out %K!ޱ :���10a ""Abreu�0nw�>�DELPHIS"| � *��������r�kFJet� Eur&z��Ct1] 20�w0� �lp�% 75jm>>�(British-Scaeaav�d�:�P&g"p�p Pi+-, KRho+-" Le�Angles IHr� P %\i InM+C4m 's�?ng. rage�]%� 94n��7375���J�1s J!>9JI� PE|YM�iFl�,�فq*��� u�G% Fourl� expax� of %��"� .�% Z9 M7z 665!96��A.~M.~"u#�q .����a-z!~�\b ic)5iZ��B �5%p�#�8!�>98l �9sAcker�emtr�H.~>��N�6n  *MB�6�6}, 4�� j�$%%%pid v2&n9pid� �YB5�- K0(S�$� +0 *% at %28� RH >W,z6$�2�! J���� 9AI%.~�#AS�P.~�o~Z(olb, U.~W.~�" V.~R�#^L Radi�d:� at�a: Fur�o!�20�'�>MZ��8$ , 58%"E[&e��3bf} %P��,What did we �w �w will%�h.�E�?� %AIP�$\��c.\��$,�$��m�s dedxt� ~Bai�@D.M iff%5 B.~G�kͫ�E�los��perturbaBf��d��art�i�x�;�~Gyulass�u0.~Vitev, X.~N�n�OB%�t� Jet UHh� d r!��1��e��y �*E�$207̈́M�6 Rec�f��9h$.��$Eff} D.~ %wJ�6at^8 aI&6coalesc��~ Y%E$ U%Hwa�bnE+C.~Hw��C�v%%��2� � s, ma#�-���ll� ,1�! %� �2�ͬv�%N��$�kq�J.~,AGMu�%g~No�%v-|�%�H��du�-����y  &": Frag�"- !� mbin %e�aM�/on phasF���S&N��$�mm � M.~KP.~p&�a�on.ALN Rc��&v�xt��gtiI/p!Zanomalyb��}U 9O �&N�%�%(vb��inZ�5�EPf23 )�F� Z���B�4ng} %R.j�6��ChowerM��C&c�-!�Y݁>.�'4010$ zB r*? decay? V.I�%>C KoE�EC/�"�' 7�3l6��N�� �'E14��9^�'A04ve} X.~,�E�',aTS"^N.~Xu�Z �R��@ � "�/A"�6er.�MV90f�R� �r� يDIS�!/5idenbach�{&�, \|:T{\PRL}{23}{935}{1969}.�%also W�]�EPanofs�6:-:�;< teea�7�aK��D On&P b!�$ics}, Vien�qAustripY9�h CERN|6fic I�å~Sr0 ce, Genev;�witzerUl�" 8), �j.9CCRz�I Bϰ .�2(LB}{46}{471!7� seߎso %. 16th��>f. HEP4�shw~D�#c�b�A.~Rob�M$ (NAL, Bat� , IL��%Vol.~3�~31���S%�~B>FB�sF�4}{537 �. 3BS}�{j�E2�� �Bj�#D.~Bjorkw.V(D}{179}{154�EX*P# BBK}ap M.~BV�NN%0J}Kogut, :_4}{3388�1}.�IM!$(Blankenbecl!.S.~ProdE�*.~Gunioˇ]�2!� �2�� CGKS_$F.~CahalanNM~A.~GehJ�gu�(LeGV$d SusskindF�1e19!+9752� occoJ%G.~ 2� R}{1>6 > 58};2,L�Kop�r +D.�4Perkins, LRL R (E UCRL-1002��9y.(A� 167 as c?{6Ref.~\%�.�G�n}sAntreasy!+Je >~.���3!�12%�76� COR}aPL�nge�t6�.P!�A�505P8PSm�,K!g larkn�F4}{26E� FYCRS~a�$NPB}{106}{A976.?ABCS}�Kourkoum��8�����}qFFFE�� eynm!�RerBR��!.~.Fox.i �2!�%:7.� CCHK�n~Della N��jA L!=L�$MJT79} For"�on�%ora�iew_�8*S#is�iodI�some mor�tails,�6Me T�;nbaum,*��%s-1979, ie�Km��Nu��59F3B}-rgoEDO Stai@F(A�?��&�z��&�E��80)�7 263-�vUUOwens78�nF.~, E)�x(M.~Gl\"uck,.\P��!�50)k���C�JEKim+r]�> 3313%�a/=�CutlerSi�EW Ub.E R!�9A�a:;B1 6}{6a�19:eo�P:dm��L�mpͿ�= Kripfganz�J.~Ranft2�e�0�4az6fj>=~{\AA}ke**��g.&Oe35P983�U5�4MJTIJMPA} e.g.  �Sew^�^ ;��7%98a�_]�82} {E�. 21st�'v �(Ed2E� e Petiۋ� rneuڀ� . C=!}\ �w2):eBJ.�=Rep n� C3-571;/ seeQJ.2h p. C3-134{/ Wolf<:2��51E�:���RMP}{59ᙥ�82�Darri<L�~,@ARNS}{30��o80.�DiL��Ņ~ .< >z0)�6�COR82���K��0{209}{2�� 1982.�confu}�Ze�Mt��deXJcy !D��4glibly ignored.U4JacobLandshoff��e&<.�PLC}{48�q�.TMoriond��E�se�% . XIV Ren���� +�orch 11-26c�gL$rcD�rL 5�Q,s,m�� ets"A�T f Thanh Va�s�Ys�>@nti\`eres, Dreux,�n' q)^y~BoggildE� 321,N�351�MFS<�U�x!A.v�aZ�FSc�219e^7I016*8 U�76:�:�Y�EGE�42E�K�*%�EPS��A%vc. EPS�4 @Y 6� on� -6� &u $27\ June-4l��79 � %%{� umeԾ5x473-522V�bR4p. 512q5� j � �.BSH�<^U�$A.~Kulesza�| !E�Wxgelsam~9Lũ66}{0140_ �,.�Levin �$�M�i Z� .~Ry� 8TW�5Y 42)�5)\ 7CUM�C0�@���9��6妁�=� Ap99��Apana3�v D�_ 0740��99�N=1� r�.+Lutz_�=M.  g Klimtic W. W[{,��N�5{54��� {19C9-BR_�>G.E�ow1{�.JH !� {2720 JD5w0Agakichiev_95z6 ��FQ75J27�J*D" ova_f>D.�9ovabJ� {042�eAm3LPost_04���A�|Leh� U^sel.�);741} {8�:}=:$Krusche_95�� N�L3?3�A{4-;.�Roebig_��HM. R{\"o}big-LandaufQ�T{4%B996� �_A�Bn� EPJA!�} {309!�A�9�HejnyGV.  �.b F83E.* leber_00}G H]� G�Ag�I�A�s_�9JI�sCJ�X^{37 G2� H3 e1HF�1!2E��>�1bAT�b�� {277 �4J%V_02% n�!_49�O9Pfe���M. M�iˁ{25�7F�MesA�ndorp�J�g.bXC{22U? X2�NovotAR1� Kc.� IEEEA�8�h�1CGabler_��A.RJ~J�NIMA�34!�1+@K2{irata_fM. JI ANNPAօ�20ip79�U3R � S.6�admand��PPM�^{3a�!�RZ22Le<.��V5�a{28MZ.m$Siodlaczeke7U. JPm1��36�EYc�0e�J.�<4�ffј�fL6e���0[Rambo\F�GmboJ���66�6�&:"0Drechsel_99a}�3,zM42aQ:� Frommhold�tTh. O.y)�2��{�XO2.Bianchi_a�N��KB�2I1��Q}.N5L��%�N32!�33 �.Bue?iR K. B{\"u}J�)�57!�5e ��" BragQXiAV JO)636�i�92qY!Wrg��74�63e�6JMa$��hN�R�D5�� :aHae�_{B F. H{\"a}NKe�4��{22-�7]��E�M�JDE�=!�E�.a�7�43({1e�192�l���*|�J�)#e� 0552��N.Langg!+n��1}� -0n&�@.RLt ��0ݠ.�T�8A476A:�J:NrK-���34� �yB�X�j� 1��)Pdafter\ifx\csname url) \�,x F$def\url#1{VY(tt{#1}}\fi jIprefix>OL {URL Ipr�gIand{\e�Pt}[2][]{~ {#2}�8bibitem{I28-Fra!�%kl�ey@ (INDRA "t+)6�>�?89\�]05.�ZI37-Bel�� N.~BXizc �@r^(]7"�= 36F�ChoY P.~Chomaz �I�~Daux���e\N�QNThermo"l- of �N�Sdp�gm_t��Hi!Y&���K��o32, ԥ 602�\est>�>Nu>in�i��W16qGr��E.[css��� �� � �A�~�%[4:�oC F�i�3MT،6�zMorIWMA��A� rettqAU�Ag�T��.Wt��(rkshop on �c6�"�f, Catt\, Ita� �p6M�Gul�8Hlmi}�. ��vv tt. 8 b9)�2./JacB.�] I�, E2!�E2C6) 247.BGua��ua�� .�C4n#�=) :�`Mor�V]B�7�.�66"�I41-Cha JV0ve� Nucl}�.���) : �I40-TabI$G.~T\u{a}bcar_ �Eu"�J�91�* o0�x��T34Gui�;�)ui|�th�s+( doctorat, *_it�� Caen��2)Y�H`ccsd.cnrs.fr,tel-0003753}.�RivM�M+ Ri9  ({Jh})�� {�Qξ�11--20� 0kR 20506��Cha��M�ia�6�K@MX6rD!G72�TamEPSa�B.~Tamai�!���vALADIN6os!��.YMDA!�,M.~D'Agostinq�ͩM�A 6j�N�6"�MDAa��EVEa�36�T38Pic�MichQ!�Y6�,T25NLN��� E��#t 2270�Nll� Au@&:1974j+J.~  6�"%��/r/03�&1�76|�^inbxwn~Ebgu�c�d6C:dp$}���$>�[�<:'(*J*Biebel�)2K�O.~ �)Na�[A$B.~R.~Webb�$2DV,66}, �*E22_�Abed 3iy}�MAben�S9S7w�36^Dokshi�(�^ 1fd}�6L�* , V.M& Khoz�I S.~I.~Tro�J."FO�Rq81s ��12� Bodw%� 94jh�~T�� Braa?!0�N�pag(�Q? �����5j5) [ErhJm-ibid.\(RG589P 7)] };,�(ph/9407339].xcolor-�\letf�2� R. R�U ckl,&��� Ck� *m�`&� SoctQP� t,A.K�ibRhEi�SD@!L��50, 626J Yeva�$6�V�vai:%X]�B�eA�e5) 30E�"� Mz2r�Z�Orz2��54��E�6�Bedji�E�gd} M� :�63-�031 �.�vog)�$Vogt, talk�/ INPC� , GoteborY-weden.=s:ns#`5ue�gC�#l�f, D�vSVFEG.��uG-261FǗ52!O� jz�'z�2O7a�57� 76V cost73ax�~ :FE]qH2\�C 2418��16_RAffold�I0n�$�d�J28Ͱ06�dam!� 95isE RNGap5m�2�.J :lѠ 83xm%�V�]*lSe12��2)�8�yMue�3E4wy}�H.~ E'J.~w.~Q@�U �U&�242� 8�S^cLe��eyx9HD. 6ƛEskol�edf�0J.~ ��,lhine�D:.~SalgadD ZM>A�+� .@ [�1a�K�( RpR� t>>A)v69� 72�.jO?i0�,���re6c?Z�47A+CN6�a!�#<,��l).��� zeeva�6!�D.~5Lou�)��~NardSDH!e��J�=4}:�E e�*�7 �!vaz��U408��1�YcLeitchWeaes"���2�� .%(deCassagnac!�4kb�� ~G.~@��OEB�_]E)u�\AI3�P6��Oh2wJ R PU� u�Iv��J, �9-(phobos-univ^Kb,͞"/ 30106�q�4mr2@6& ��Gpb6n{ Gazdzicki%�rk%��vM� G04ɝf�fS40�A^2�An1Ji%�3zva~,�'$Braun-Munz�fx0 RedlU�� J�&a�5w�r�57�&3&�6oThews!�0rjE6L.~!'$SchroedteriRaf�pj)��"�� 0549/��6�dl�� 3rc}� S�z>dPZZ49}, 014901 (20�04). \bibitem{Dokshitzer:2001zm} Y.~L.~D� and D.~E.~Kharzeev, Phys.\ Lett.\ B {\bf 519}, 199 (M2iAdcoxd2cg} K.~0 {\it et al.}VRev\ [88Z 2303]26],verbeck} R.  H, These Proceedings.�Adl � 4ta} S.~S�dler, arXiv:nucl-ex/04090286<ams�4fc} J9ams�}JE 7006.E$Zhang} H.  ��-@3nr�@C):(69}, 024904%:6Hohne�2pb} C.~�!�Nucl.\1�A X715}, 47 V36�ltT4wcTAlt:RBb 6031.Cleyman%e2hy%e$, B.~Kampf!�,P.~SteinbergE�$S.~Wheaton1�4hep-ph/0212335.g Goncharov�1qe} M.~:�M�I�D)64A�12006%^6��^2mp:�Pramana I0}, 787F6NCalderon�  R/�% \endbib � \begin{thebibliography}{9}� ArseI4fa} I.~ \ [BRAHMS Collaboration]1Ty10020.R Back� 4je}!�B.~ [PHOBO�P2P�)Qmh]�P ENIX��03PSTAR-wp}�  � White Paper can be found at http://www.star.bnl.gov/9/public/ -QGP-I-I .pdf90Gubser:1996de�n ,!t(R.~KlebanovE�$A.~W.~Peet:Mw5Aw3915 (T).�hurya)�$rh} E.~V.~ Np��I| 391}, 381E}�!� ToporPop!�2gf} V.~ Popn �~��054902]A�],Elias:1978fteE.~nY�s �4�28%78.As�4mr2�6qB� 9021=MF2wbjF22�%Y05շ2�$Benecke:sh� 0, T.~T.~Chou,��N.~Yan��E.~Yen=��)) 1�# 2159A69N 3xkj�: 301017= �g%Xvy}2|F0502�DMcLerran:INPC} L. , t�p.�U'oharaa�M. O'Har�3.7Scienc��bf 29As 2179Eq)J,Fermi:1950jde,#g.\�or��)X5}, 570!U50)= Landau:gs� ~D.~  , Iz!�4Akad.\ Nauk SeWFiz.\ V17W1V: lenkij:cd�( Z.~B �� k�A�Q74AU305�6�.� mp%���n U�0Braun-Munzing� 3zI�:,gRedlich�J+ achel, .�!N 304013. %ii�!3h��312022Mcs� LStankiewicz, Honours�w�sis, University of Cape Town (Advisor: Jean C-F)%aA~�Minh:sgE7V.~�P..TP�� �)�3�133��[5 Koch! 2uq ^1A[108J�AbH3p*v2� :�2�U 2418}�9A�bkvEb6_�^ 1723N� star-mte� Witt2�i�36B 2hbteE,D.~GutierrezN 3012.� B� �f� 9}9�@mar71a}A. MarinovE \ J. Batty, A. I. Kilving%,G. W. A. NewV0RobinsFTJ. D. Hemingway, "Evids for� 8 possible exist�of a superheavy element with atomic number 112." Nature��E,1) 464 - 467:�b��J.k Weil, !$. Friedman� � �� ! S!\��, "Spontaneous fission previously o� pved in a mercury source." � 234�212 -� 2�842�$S. Eshhar,.� ���, "Cons%�,t interpreta�!�Dthe secondary-reacexperi%�,in W targets�E prospects1�du 9ofJ�4s in ordinary E-!!os!����i� 5$ 84) 2209! 212; 5��$1120 (E) �� mar9:�S. Gel,e Folg0D.) 8 W. Oelert, "O%�= ree coincM�events)�F�, search via%[($^{88}$Sr + 184}$W��` 8$^{th}$ Int. Conf. on AiMasse)xFunda!�al (stant \MCO-8, Jerusalem, IsraelAH`91) L-46. (Unfortunately � ; confere�was�c� d due to+tenE�in P�� an Gulf).>�6�"Stud��long-lia F>s ^Ym!EU�E{direct^B �.)H Symp%HStruc�Qand RM�sA�U!D��� @ei, Eds. K. Ikeda1h Y. Suzuki, Niigata, Japan1^ 317 - 324:2>�U�U{"The e.DprqJ �e�Z;Z =a6& �n' Inst.moEo �8 No. 132, Sixth)G A�)" Far from�bil�%WNinB3r�ZM�d Bernkastel-Kues, Germany-�R��ugartm�� W\"{o}hr �2) 43!�442:�3΅͢ 5c)�ed6l�nk !lt.  ol-S�9ar !OH� Ion%�ics � ." R��chi> Acta�2003) 43�440Yn8sov04}S. Sovenae�.� $ - PSI - G �Mainz - TUM - LBNL - UCB - IMP - co*� !WU:_a�"ous�5�Ta(ahresb� (ht der Kerne�e, Paul��r ) itut��w��l�(2004, p. 3;�Scia�$fic Report"3, Darm�7t-18.DLsar03}C. Sarpe-Tudor� V�Jr�!� 8J. Anton, W. -D��� "Theoreti!�predie%�<adsorpe2� of.� ,a gold surfa���8��eic033 EichA%-�r-�a� PSI-!�>�� -GSI-TU�ich-FLNR.&E -IMP 2�" "P�iv�!� det�n�F�)%� cal n��?At% ei 6�#3)���� 151 [#B���ibiN'$Bodmer} $ A R 1971 `PR}f�! 1601-1606*�'Ren? 8 9846= 30} 272 9Kse�>$For a summw� trangelet�e�tA�(strial mate s8in cosmos, see `�99�itA�)BG: Parf �25} R273� E864� See a recpa�#f �mJP Aa_� T A \ az1�%g�3}}".|Boltz} B199)jit ��}-3�7�B6�R raumA�� P�Stat Jd5.:Hys.} GI}21 L1.bG@ IP  C �1987 K \PRL-l058} 1825 \\ 6��St cker H�I�?}044} 352�ZDC��8 C , Denisov A,��H*.�urqmd13Zeicher M 61�1��� 185.�C21E�(tkovskaya E6G��\PY9� 7 \nonum� �al5uKupplied5E.�$_A�M�� �]�hgm�6rB�22a%�-��Ka�C%wshwj4B�2:�roehri��R�  X.�B�02��� na49� , Afanasiev S6N INIAbf A 4E�10=[e��^20!�]6M2_ marekqm04NeeNQ�R�I�6�72�e895piS2Klay J:U E895:u�6z8 �.z e802 YAhle ��.� E802:Y!p8./57} R46.E% V�%B� STAR>W�)%, Preprint}� 031�.=rbrahms���n I ;5gb�4 )Jd4+de866kap}^66e� E9176�sE�ɞ�6476} .S ]m�] ]90} 5.4!�kaA0��8Z2.V!� V(B�Z��]AYb�5954.Wa�@lambda} Anticic T)�5�J�A2[R \9=2(2�95\$PinkenburgB�JA_:�8} 495c6_6_A�$oB� E8966 \�8a�6232�!n\�p2a�-8��9:Z!qxi�  Y B 538} 27.Nmeurer� M Bjf�6132.Z��Chung :2!c>!��� �91� : !cVastillo��*� ?+ 518.Y omeg�:uirF Z+3BY470.Y!�ph2��4~)6�! 2' e917WA5B2B�%_e}��C�: 86.�! phi1���[5} 04�.(R)}} ^200} �hn60}�9B=�f*�+ALB� D.�s-� (EDDA)�� �7516N)97.�2ALT�MQtmej�=zS8�-819�25EDDm �uer��9�44aF S�"�)GAR�M.g\c{c}on XHP  A�44�66>,82�3VPR�m B. vx zewo� �2@JC5%;897a92X8RATKF. Rath/vG65p!6FBYS�dJ. By�c6!C!�4chanoine-LeLucF�+B  (Paris) �4�v?)'J12+51}, 274 �2�STO��V�!J.�ks,k&A"Klomp)�M�+ntmee�rJ. deSwaS+ �E�)U�79�+ 93).19NAG96�/ Nak)H. Yoo ^Mt- suda*2 ogr.6or�d9E692;ARNaC@An�C.H. Oh�"I�ra� $R. L. Work�� F% h�(n4.�J7"6pRNap2~IA SruBD6E7of206�MAC01}fMachleid8)� laus> S%.G5Ra1�A y|LAC80�2Lacombef�.6782S MAC8� !� ��3 Holinde)�C. ElIF�p��14�@�'82PA�4}��C.�# F. T�0gge�J.j�v295569;U�WIRp R.�LWirin�#>4A,R�)iavil�%�v �Ce�3�5).{%�a6�J�6g5240�52�7BED02�6�Bedaqu�U. van/�AnnM���a9E!52:3��2.AEYS� K. O. EysY/6�!W!  , Euu��_2_105��2h� 8�� �]J.>gCgn60��2���4+5ZWf�2�$2�N5e2AZTRP!�35�2�EVE��P|3E8 heimu�-��5)� A626�B7cŶ21LEH�A�J rachH;/ SPIN�, ed. Y��Makdisi24U. Lucci��W73 MacK4AJ� 67��1�)�\ BYS7b�%� P. W�2 nitz��(.�3a��72�ACKA� K. A�staff �"�)>�>was1W� , 4��!".BOU80�!�,�) LeadaA��H2�E)�5�95!�66OHL73}G�Ohlse��!. Keat�5Z� [10\4)2S BAU�#� �WD4i.�8 \"at1��2]MCN�MIcNaugh'-b 4u8d>6uWWWe�(ata access:rCLkaa.desy.de/Home.htm�&*�C0iskp.uni-bonn*,gruppen/edda*�"BEL��D. Bell:�8B�-94},3�,1:�MCN81e�W. ��e�8��82ABHAK*hatia:�3 ��ŏ113I+6JYS" .G MI"�! �2>72� ! }�LEH᫱cnF!# 101r)6�LES{�g squeV� �30��7 G2�BAL��a=�6@�� 11},�>�.�ALLr ]�� lgow"� A�ye���%06�N2�L1�Ha�A�L�� �J2�AUE�I�A&) 2�=�37��-�76� UE�vKEBD3��86C PR83 C Apri�92� B2d 2 C2RDIT84}aDitzljeD2�� R213I�2>�3A�< 14�16�PERA�FO'ro860I�29��5m2�FON�J� F�9in& FZ3 2� >�98ab>R�!�3%l6�ea � 0},4�s2�GLA92}�/ GlasLF�CO�v92�JAC59� �.��GWi"W �yE=A�40�:52� ALL9Т�/05i�>�KOB Y�9 byas*("N�/ �{ 5M7*42� � 9 M�0Lacj 31r269��9FH)�D.�H8%%NHIM�HI�f�dE�b�,m HV�EHmcL�jmbIDab�qa�7}����� �.HCON!�H��Conzet. rog1�E�5A�iS�xenF��f�9�%&HStatModels} A.~BialM., 3)2p A� 95c, %"f!# �%essier,JA� @7c , V�EchNm,102A� �� � ~Mischk&�,z\56.KKaos} R�Mrth?.�Qa�7)m}>� 400.�Oes,rQ~ �#ClP%6�&�>2�Bruno��Quno��<576?NTC4)����G 30 S72)Starpp� G �2�,)�seO/�%, R.~�+�06qr�(M.~Estienne�F.�$PBMA�c .7 ~�#M��#,%�9-� *�B�#,6�#!GammaS}�IBar�" kovaV�v7�40802�N�� z�"� Raf:UngeSig�,yo�>2 �*� ��331��Phobos�*P�, } B.�P6 PJ�P)� 1002.A���~ :P�:I�.�e�A�} �9 H�8on��6�$Nd31!� fB5a$:�% NA57dVli6�M�[:�.g#B�NetPr!4 ~�G:��V2i�>v93} 10v=9 sKR�I�n5J! 2�%qA661} 4.� NA44�I.G^�#:�aO��J.)gG, a23�.65,=] E866bL.~A 6�N]�tBT? 2650:98)�� �%~�C60��V�"�${~2���1q .S4} �$.9�Q� � �  Xu} Z.~Xu �^Z92.��:�:@Markert:HotQuarks�% , �@,view, "What �Uwe G0n 52resona R&18?" Z2[R�/ LQCD�7EKarsc�2R;�199.BSat�+.~ )R: E�� 3.:�� j� 8 �E �E nE Flow}4p�cs)�s on one�.t>�).�A.� Z.h N�.@}9�@Y- � $$2g?Lin $p+p$ at \sqrts =�) GeV".� `=2�Dimitruz >n�����{��$446} 32. ' Blastwave�~Schned4En'$~Sollfrank�&�Qc6�E�C�246.�>J!  H"Q�NG$QZ� ��� �.�M0bk} UY�M.~t, %``E.AGa new`Df�6$ter: An asATd4 ofAQ�)ultMq %CERN�Ld q;A(gramme,'' a&^*Pp002042. %%CITATION = NUCL-TH ;%%�44\cite{Gyulassy�4zy*�!BI1 .�L.~"$W�New�:m�9QCD � d�E�Bt3J�405�PR� � �� asev�Z9iu�B<_e+>� [�6�]�h?lcL�pt�� hadrwE55�N�\"�\�.\"632�9d:�,IMA,A430,210��Ga�.�8vd�2%� M.~I^�.�OnA: earlyAxge of� eus�,i�Bs�&/\ Polon&�03~S1]:SHEP-PH �%�M� !�9st]�BJ.^8%" ?��th�J,l freeze-out�%amX<�-1-A�@to�� !� �+ \�(bf 60}�x9)�908�!E�L9903063>��M .�Web�T2pk�6H.~�~L�"M0�@~Cp S\� t\"o,%Heic�P(M �SIS� SPS �.ies�bythMe<�A % �J?b"7�8 01� F"0209079^" %"Q�B)$3aa=$:^rtke 6� � -SPSC-�-038,�C-EOI-0�bN��j�'9��2 T�26{AF 1Se(\G19)"�� rapp�#R&�X =C��6� 0179$"2�?2�?eE.V. 6*` P!;�8T298�I�so�dC. SoM\V�R e L �59 3026e$� &�U park�!Park,GJ"OA���Quantumz Tory (McGraw-Hill Inc.)�>�R ed��,�?.�Z&\6J!�6.�2� ���`�c2�brownp B %T*'ho2K=N%�27�R1992M!�45��)H0< 72!D25&�e"�shb}2��G � Q-�R�^32J�abieHYT)Caffner-B ^�8�32R]>�&�3��J. WambaA1Adv. �� �� �,#2�focus�M. LinkR�)wє35}, 43Ř6ho1K,b O�92cg9QPbKb�52/ B �Hu(�4�}!)�G�83�SOH!?2Vlongacre!B S. L ,y�[�U68}� pbm1� B�9(priv�Ocommun F.�kol Fa�lb�MJ+ akas6�q(p NL�W�oniow�+bhQ� 0349���.�bar�SarzRM)�-�2�\ 2�,>xpratt{a P �Xu�#)���2�6�6B�graneo G :�.� �140}, 38S72�QK�)UKN;2�5EI8I�2�p_��M popesc>��DI�!�127 �2�MMs}M.@atR�%F P 187,6�a�}#Z�"�,LC�)8 e ���(:l3ahe6jY3}IlinA-W�mE!C.Mab�202T\6�henixPRC!�;G�0N�%2Ix �a��7.KsLav2���fi�2Qnonak�N ~��1, 031j:B�?Rpt�~�Iɥg!F %FJ�tpc�aAnderso>rii2�'@TXxC, 6A->Y���7}, 112�n2�pd�n HagiwF�fFj#010�>�(kshor~H)C�_07, 1��2�6�$z� S%>!� ��2�?Rr�3C��I� �6�3E;Sy� haiba�H"9o>���S57� 2�>4���b ",4��Lphiffto be $lsh�V)�)>B��7`(4.d�82�h mfp N:�i�69sigma�h Gaud��t.t C-<49�!<9zrhoV.achiniZD !446 �2F�Ph�z thes�* YaleNecA��5og�>�6H,SUBATECH, FrRI2�u�.��>[2&b![� mean���@�� >c5Q4N2� dri}'Drijar>�>H9079�,2Gakee Akes^o �-�20�1n*a��Xy: �CEI��2�pbm��>�GN�iM �51m 4f 1);,St�N�-a�$A. PoskanzKLSdJl�72& mE�167I�2� dWX|7n�F&�I6�9� 3�Z N�� v�ukob�$P.Kobushki"�.{)�~}�sexG B42!���.�8 azh1�K3zhgirey"C){I2 R� S B�s22 e�7); { �n�n~�W49D*w *�ayy�" S.V.r"E�-bxB43��-T6S45} V.P�pdyg9, {Few-Body S�\s2� p1a � ; LV�.  7��� �45_55} ZP%^)].�3�� �5.G morl�E&gLNS-E28un"� 4). % C.~Djalal&�NInternalm&8ort INP DRE 00/"� OrsF5�.�zh9^� JINR�id�lm�Y2[88]-9a�1d/%�U� egleFP�G kalo�E�umasi-Gu-5��mZ��=+C5A37�\�^2q~TFNMt,O BijkOA�*viataH F.~I�ilo�F���15:9.�? lad1^3AM Fiz.��1179��v[E#�d.2B-�2992*snadia�:} RN5(Lia,�.S6. 18,m2)r� +Y 22� lad2 � nu�a0�J.�L�RAA&4<0m�B�N5A204n �n5-191)]Y� ljud� $V.Malinina�~ B�N*�3}U�ayy50bY.�.B5��42\.SddbU\itp� 40��J� 1G� 2bpol�?aUN~'(Anishchenko5{~"�9 R� 5-t�gCQ: 608 �e 89);AG.~Able&?]D {Pis'ma Zh.Eksp.T�@�\2P47�58�m {,8P{>64[43]-C=1/9 ; T.~Aon]e�a F7as49�B2mf4^�PT�Nb1��� 7)[6.��Ex�ch.� Kx`]; Z��R M�VE��7Rn;M#A4� !���y�zhyud3>��n�Sd�Z�. Mkarm1�V CarbonellJV.Ab��Aov6t�A58!)6>1:)@pi�M N@A%�.MB10M1M 6l �:}<0"�A��e.F@06@V�TG��TSUL} Yua Zdes2���. 2nd�.��(UndergroundE�6!�icl4aksan V7iP, USSR, August 17--19�{,7 -- Moscow,JO�za)8, p. 29��116Cd-K�)A.~DanGk� y� e� e�E( 4�89) 417Jz [JETP-�/76];\\J36F.J@]� 1) s243VRFV�rc3-r2�on WeaYJ� E:fmagne�d� e�a�,ei (WEIN-92):tlN� ,+2!�WorldZB Publ�p�W93%�575���5-u B 34� 5) 72VG4A.Sh.~Georgadz&�9 IA�_. �G5Ff9�p!�B ()�}) 4�C6) 23Z�V�.V A 64��.317V��HB�6s& *.� m:Fb;%����K� 0) 045501V� P�EBizzet��.�B�1* ( 389ZW��A 7 �O 129.�W-$l��U 3) 014310.HDanfCV�P2.� F3!..F Ge76�-�7Hlapdor-Kleingrothau&�;� W6 1)�Zm4NC7Aalset*D.�M 108;J$/D 6E2)007.�Arn�A� Arnid�rW$ 4) 46�TeF�rnaboldY@ ��S B 555�167; 5�:  26�\Xe136}� Luw8B�>T4�wa{40N\E�dabeb�4 2�.,CAMEO8$e>~^A4�I# 216N�E�]~Ja�'Ly2s PWO-first6G.�7�vsk&�i��  J� A8$1-> 2]&h Kob�FM$baN�= fKK?_4262 Ann0�Ogn�"�h6�J450v 0) 72IKob�A��4M�!L6�K2�K��4M�@m42CBora7�+ oris6�2� � `press.RBac!qS!� ccar&; Dum�F 3��%q02A* 8J�zV�CaWO} 6 ���VGZFVh\+�,9014, submit�ltoNc�|Y�GSO} Z[ ��nA 6j4) 3�,Deo�NbwM�M ( Technique � &16� BurO S.Ph�-�Ia� � SM 3@M64.DanMZ�"� A 35qFC432<GEANT�"~Agosti7 �� (46�/).N<R�5�n�250R�HDgeant4.web.cern.ch /.�Po�0O& Ponk�n.]�� Cp�]135�gB��x�(5 282].zSta(IAZdaud&�Europ�w�_1� 0) 66Bro�GR.�-odzin*'�HR?2IF85) 2:� le98a�(~Alessandre�VrO!� 45�?NL�j*g10.�,ackToVbU-FC*�}V">A C`izq %:;FT 08]%y� flow�=�"�ii3�)iYingHQ��Guo Y�VHot�,rks  �=��%�LPTK H�� )I%-�; 681c�TriggeͅBbr F2YZ�X03 w Q�R���Uod� A�Z9 766-77.�� ultiz?5z�J VEhf�4 ��J�pd!�=z,PythiaMan}SjE+� T, Lnnblad L� Mrenna S!�*l &�]�'10826495 jetSFm }Ganx^H �In�s�nCh�4d 91 *j3Mow6um Sp�!ra at $@8${s_{NN}}$ "H8�5 p -dAu�C<4 �5}�" Z1#�ZaardSQM}Ln R�&/%FtMBaYS205-S�`"L$GVWZ} Guyl�6�k$Vitev I, W��X N%mZhB Wvq�6�_J7 3020.CKirill}T=�e-k�� �12xN��j�188};2AbreuV47ji}�6 M2R.} �?50%��y�p)�7J / psJ6D�t -YanVx-se�q�b[u�P�5o�5t�!d:/c per5on,''}0q5}"r54109:7674PHLTA,B410,327435�molnar_3f4} r�"it�%e9��11Kniehl�80fe=2:  B�fKR5r GE)Po�9 B!( Fraga/%: fun-Sw�as, �6�#prBe, next-to-lea; %or�Q1$N=8P�s9$5 514 6g70010289]6;�6 %;�6 Kret>�0yf.:  Sr�c� flavour-i�b�4tagged e+ e- %]Ehi@x��\�G}\%��62�+=KB�03177^�.��Q!�ĉYC6 S2ee&PHF��e( Mid-rapid�8neutral%�!�g�ioRI*a9�\$%s**(1/2) �V�7Ny1 ��_4Q�.E 3�c8JEX 6�}�..#(.%STA>�EA+�Om�OAcol��7y dependͅBx  p(T)O; %bh(^?in Au +H!A ultrau{iseM�xqO]]NH�$1H"� ��15:I�8)J 50152J&��ux.K6 >�e (B9h6F!O�; volu�:M��omod�w��a�q�8 U���%�tra � in dNLs(NN)j��ar:p�3�J:�<CL%*Vf02*J�pa�2xm=)6s,Schafer��� �p�k"�p W!*Ne2V �Uu>cor��ţto Ak-Ek��a�y� %�4i�znally �zed p p]}N_��7��5QY� 211007]!� pN�46H�� 7.q deFlorianzj=KFde . D,~I�?analysi�?un9a�L�- baryG�6I��3:�)�vCWi5811 :B971138Z� %(",h"++�A,k&�'� �Z& 6 � ^L�14i2M: NJof�=too?�!>gQ9410219V ���A�ae3q2 2��y� ��b�!��ai0.:atA?/e���yen���+ Au %!n&. ~| !N�0S*"'�� 22f�4022�?Tai!34b. .Tazq^�Measur�@of open ���C�c�} %206J�A!}\56D 809u"�4�> ս .. Vogt�1nh�G2  R (H�,ProbeJ�$CA:�=�=botto.�W�\�Mo����! 12} 215�q111271�P 7.CacciarE3u.BQ"�vSs0ngano M L, Nag-P� Ridolfi G��>_� bb �� dc\ t 1.96-Te JHE�ibf 040�b32 pԘ 1213>��E ^�2p.~@�A�} ��Is�'re�}ign�nt ex ]a�-��6&��4? Teva }xA��%�V��X12d: 2A�5:�� .�Ad� ��-6 J�� Z� Oy�yield��j :j 70066}�.� Kell�Gqw�6 S f�a��m6���� rt�ing�[�!n%p p, d -��d��q�^ 1189Q �305>$=*.*q�A�4md=-B��Bb�b�083176�Q� .���t.�6���e0Vj�C��6� B��B�] %b� ~�fQ 90�^R %%"� laue� Laue>�xi�s�� R��\beV�� .�wglTW. i|{o}ckU�H)dta\l � . H\"{u}b[.H��ma0j�(J. Gola*C6fh22)1�C1�.�wit^ZWita{\l}Bh]:�B����pC�aR1�$4u,9|kij95� Ki�,�Vivias9p$S. Rosati,�6Bl�gR1�*6k66k[ W. TornowrM.��Km\ �A60�*4|:RI8}!�!I)�:6�5=�9� �=�u)N 8?) 118Nw3�nemSQ��$K. ChmieleBu� Oryu �P.U���A��5K/ 25� 6zste�c{� tephR~K.�ek�' Krug�I�ubc� Ob�Jnns, H."yuhlE��%DE� mM�Th]'rneliu+-hoe3 .?��,2��}^=9str89"+�e�k(Geissd\"orfaj*min�FPp�Cubf\( Ebneth, Ek nckh��.51�Fuchs \b�t%�Sg<c ,Mr ��A 53+�,:�(geb93} K. GQWm��C. Jeitn�E�gh� T. N%�ank, !T Janu,]�Sandh�]H. Haberw^l�"I��^43&7:Y����%Rىtze��R!m welljq�R.T0EaunJ� �2A�nHusse!� J.M.]e�oG]!rteRB�c%D�_p!Falin�J+I. \v{S}^nD.E�e nzales Tr�0, B. Vlahovic�3 Woalt`mځM�)<}�B38a`2:f:9Azho�#Z @/�A.S. Cr-?��eni_!qC.d�YB. Qi��pacri,w8R�H. �, � f�Nn �I6!e545c ` �2�rau=uG�Jup�E�0Lema\^{\i}tre�� Nies��K�Nyxn R��N@I�� E:C53<14�16�ishm*Sex�%Space�;r Anoma4�( pd Breakup"�*13V��� Ishi' T. Yagi�S. Och�Nozoe��TsuruF�s kamu��. gY]��aga M>���Ad<3G6�< ͉�/vwiT'A. SiepeEi�V. Huhn,!oW�l zold�9 �P+�v�.it�Yn6Bse7�i"w,.lub� �G\�Disser�, :�ochum�092,�1� D.Uepe� E. Epelba1A��ga�6��� U.-��iep��6�F��O0&�j2ݙ�tor& *� P\` !�(�� BBo575z  lcoo79�A�on���cR , P.�jmmeeR�B.a� Barr�eD�nEdMaf�B���Jc�aI6/ �+M�3 O24�7:2��^ a%�-�"� B n�Q 66=nog97��N)��Z� :j>� y.@409�G�2iQ �pae�Da�F��(*� J. Ku�'s}�4< Skibi{\'n}ski, >>)Z_F�L!!6 ��J:�wit�cM�D� CR 5�>y2�M�}2���hvglo�lw ~YW��RMe�y ical^�lem, Sp=vTer-Verlag, Berlin/Heid�� 1982x)hue93} �*) 6�A�:#B� ��? �1:817���9g{77CH��c��b�q  �X P���B2� 16�I1M��mac�6Uv� maruccO=�E� U3�b�8 R14 �:\A51"�M5>5�BAq.A C ��16mgA�qfri99EFri��i��!�U2�w>�Jo�:5E�9B�a�S� CooX?H.K. H}>\:�)�e�13=�5�Wk�� S�pit��8.v 2�o28�4 0); FhB 3�x �16�1} ���2��%��1�Q�J*.U��V4��6�EMq $D.R. Entem%�6�=�E�C 6A�Q�N6XEp:*6�M��cU.-B�nucl-E'405048,�&V�.�A.�BvK} P�S�z *z ]�!�Qr9��� E2!z%=A 19} mBw)�U�i_pB�kbj4-�6jcer�ERN��` Libr^�zU Writeup �Q1@PAW� 5!!%30=&gol83}D-|^Tret� � Burg� �nich� >��h�J5H.� Helt�?��6� Pr�4��OswaldNR�{hn�!m؁�ZJ�B�a~ 1394?E�= prz�KVzybor V E�,tYEn��Menzel� = ���s%j�eh,sBx)�C�],- ��gY� cah7[T. Cahi� reenwood%lWillmes� z hado��B*�{4B76wsag�*R H(�u�i�himizu%�Mae� H.� �a�Wima]Morinobu��*l 7K576� � Z֒�j�*�pne_�H!$ l\'e&$B=��~e�795_7�74 � Stin����gg��m�Dt >PUppsala.� V*�?Moskal�O> kal,b#�3=�Rah�2P RahmJJE�C��10h �5`Sto�9�MP7~9.�Bug�_' V. BuggE/2"]��EO12nQ@.SRenb6\8C.M��nt"u�R.G!� Timm.�cJ�jdF�� pGG340��_:r)]MBr \emph{a}"F{6� 5253�m0; T.E.O. Eric�!:I ibid.1�^�.�BloA}�c�� shop�@ ?Cri���*!{�rmi� ohPion-$ eon Coup@� 0�tant}�JJ omgr�Q%� B��2pRdeS20�-� �M :�2C9�"�2_�U�Pet {PP�don2��(�D9 Au�43 X�Xol ]} RAS Poll%� AnnuAvv�6Pޟ#�Ve�3u=B.�Eri �n�%\i�6H7�JkJ> nij} \und6e{8`nn-online.sci.kun.nl/NN/}V�jj2165xp�J M#�Pf�Q$�R cite~R.$�Rurl^�url#1{EWtt!O%8{URL Iprovi�hmmand{!\0info}[2]{#2} B!7�[2][]{S'*� [{2� {Giba�8and Hungerford}I�}] _,5an$ (nfo{author}�5�{B.~F.}K1� B}:and@L�ZP E.~V>P�} Cjou�P}iJ�Pt<��'E/me}{257:A pages}{34� 0year}{a�}.� >HDanysz!956!9 195a� f6 M.}~#53 <:��Nu@�ento �+�+b�4:H �60R�56r�Niculmaet~al.�98�A,8"�.f�G>�B}Q5 m,j�v.��<^�81}.E- 18�J�8r Abbot"=6  %tq�2D> ?>/- �col&�$(}{E91-016})N&�bŵEb! A639R#J�" {Moh2 et.\ a��}}� 3A2 �&2tr�* R.~Ma��^VazvE^!C6Z 0552N& 2003r&ZeidmaCI'� }]�1sj,f.B>( XZ)V.n9a'�Α�m)3�l��rCo"qh�b siao�48�$ �6yc� S.~R!�. C>�_��:� ��A450:B-A419c}JH8vvEJ-:@En�/h@5f<R><En^a2��r�8� j7�T6@ � 0546�;�:Uzzle�02a2�  f�A>�;:�type}{. .8school}{Hampton*��@J�2rReinhQJ6�z��J>�A�5. a�^$.-�47(ra�%�� B��|�)1�6� "$, Fabrocinɾ FaM�i�(Sick}}] *�f4h�.fO>6 i:V� BM��?S>{ �1W"���I>O)V�.�j�57��A:�4�>�!�r� Gillespie��64a�19�~hVrB�?-r�Etitle}{F�9J$tee�@e��"0r}{Holden-Day.�add�6}{San�\ isco6bI��n {MV�L��i�T\QAchsel$\ Ben�}!1N 9N��T>;m\ t 6vt.���.:Af!4��&� �!235N�zR o��E5 barz8~0;v��.K�9�)�R.$ note}{R�;s}*�>� {B�/� a)�1A�`�V��B�2S6r5���43:@-�158V�v� Fuji.K��� ���3q�� Y>�>>� �2��.�j�72Z� 10�A(�,U� N�E� f�9a�Otem{War�qY]*Fbr9 , 64N_��Pri� B9Prity^~�>!$ 011305(R)0�ZCot�P�-CottlT K,sKempe�"�-J� 06130%�X�XUts� Y. Utsu:[�NN70O443i3�:.�{Va/T(V. Tripathi:�:�[�M {Guic1Pu�0maud-��:F*�N�3�d 18':D0Sak��uakura>�)��B P41�T�K2�Ari�@�RrimVAq.M2�.672KPav!}IaЛ6'>+ �'u[Jar59} N 1rmiIM.Gi+r�6\\ �),��5�2S�|�SM1�i9�196BPMid64}9iddle5 an���ull��� Sp$�OL!/� Mor6���re��-��E��i6�>Nig�  Ra4Night��le:wIz U1� 93 %(197�5�Pil�BA�%Pi�> 9}, )z:�* LaF1LxaGf:�!7e��oXL�W:LYou'K.C���:K H.��)|1�^�StaA�M\עjXv-36� 0343�X%�55 Try0_$$Tryggestad���x643�d2� LaF2v<J��� f)@YkBer�Z�or�=6�B�A2:(59(�NRut4AA�Rut� ~P34�82�Tq6 Ger]Z�"2�> �i��6�3�o1���Til�S'T�zy��63�2I|>THer77��H�~�28��Wih7�U3Kha00�h KhaVC2��� , 45��06�( Goo71�2oos�)�Ins.Q .Q. 116, 4G1�x.%'Pavphd� ���.�d2I0F�Fda� *W0F=Coo��M��Co�5:5)�.��0 05130296�Hofal,5ffy6�JV2 a�04�rak9�Hin�L�# inds:N)H T��3M+.1966�Ajz�"F. Ajz�&-SeloveN�430A�12�$�"�Ajz�-�J�s*l�&UhGlMH�<oeckn�nR!�LawK� �2r53} 3V5�zUMcG73A)Bt�Gr�� BfWisth�$ W.�7}, 97m 6�Vol��A. Voly��V. Zel,�s��t6�v.n C�ZD�1r�% -Gil:�� �%�9B 0625Ri)endsf} ���ods�s.&��4a�49 b�i� �OHenv,L�+�Ov�„ ��9T;Tv $�-#%iA5�{2�f@|Tav�OE�:vukcu͡\Q%k) North Car�kF�� �� �7c+Vj5� ��>543��2�Gut03�}��5���=$. L{\"o}nnNc� i�i"E"J29w W � 2AG1AA��> Bjer����]EM. Hj!; -JenEWF�%gebret"?MhSArsseA�=�Ioa�S�-4{\O}deg{\aa}rd7q>\�|021306��ͥ9�Vo�= :�V6_ � �Pr R�44���a �!P�a9P Ph.D]|* of OsloEoFaHGut�.:�{ tac,�<L{\o}vhidP.p4- Rams:�T<1 Thor�%�2nZ�I aznyT.\�*�STq��F��6�)2�2^L����B=.'�d� �a2�F��+3E3�5:.5Gut��:LT�>5"!�r~ MetJi�25�51+487:Bri�uD.M��in�E2Oxi%]y155.2�Axe~ P. Ax02��12� �xs YRKad* S),Kadmenski{\u�?}, V.b� arkui͉XV.I. Fu�], h`~�nڥ2�, 83), [Sov��-� �/ 1�d8�s�Ge�;4�ervai-1Tho'�7@!�W%�O��� _6 \ ���R13 �� 9Fi�bR�C rest��YV�pShirley,V �I,qtem ��a�Isotop18th��} (Wi8ݒYo�6*)!�.oRIPL}�6dbook�.Ca*=�of%8� "�� d,, IAEA, Vien�uR��No�8AEA-TECDOC-1024A:982xD)fMBobacze1F%� gier�:Ws1zar��J3atu[8�,Z. Szyma\'{";N���430:�� b��S�X��!��R��D��24��2d�aB�RHGan��:�. �26?�De3RU1�8� .�"/27FlE�QB� 2�2&R��G� �!�>�3bB%� agher^D C51.1.6 �I��R�%! 6430&MA}�Sch04exF�V�"�g(FlBSDr,�C�ern���?E=�q?:R. �Nel�2��&�2401036gLip�aE. Lipp��BSt!; �S\ S30B\rm, 8sA� Zil9P Zilg�zP Bren�8 W�$lbo�DR.A�H.�bA Kn�H*4�� stru�H�G.��,�;Se�n,BS��,�H\���A5jR� �j; 19} 84p���Ma�8�@(argraf {\sl�NV-%6�2 24O� _f�23��.��.��.��.��.��.��.��.��. Ioffc&��e$gevacuum:i���B��:J( \Z�E� �}=^e!��2��Wf�b�B� �q~n!^' ���sigma:p��f0Mf_%MN�+6h6�"�PiNC sletr�/16:B-1ZY(v�'{L�2.spin:�\����E>� >b^� hys.��}f� D�6@ �07401V�+� !�teFKa�91-D}]{pv]:k&:8��$ D.~B�.�#>e6�U7 � Bj31i$�$�A�-!6B�v�%SpaydVwiv$ QfiV�&D��:� >5YZ�%�j�B58Z�#�J�v�' {Ito���Ito��TN�.Pr�A����N� 1020p03} (\bibinfo{year}{2004}). �tem[{\citenamefont{{Aniol et al.}}(10)}]{Happex04} :Rauthor}{KfAK.~A.} :U }, !GDjournal}{Phys. Rev?textbf\&,volume}{C 69:A0pages}{065501��Musolf�199�(pvsummary:m":9�� M.~J�bi�:azp@^23Z�J��v� Friedrich� 2003!�4emformfactor:f(:03� J.}~6FgZEur. IJ. A} b17:DM607R3r \Marciano and Sirlin}(198E8ewcorrections:m +:8� WJ k}:$ and}.V^A>\ �ZP)KaS DjM2ZT75FL!rL${Eidelmann2U%Kpdg:e:�NS>�J^r� LettnPB 592:CMKJR2�?Zhu2�0aLaxial}Ozhu:00�I S.-L�2L.ar���6Z�033008F� 2000z�uteneuer9��!MAMI:e �JHF�?_^� meissner:�� T.~R�2�>h� C 60:AQ�4V9 �r�Silva9N�goekeA��B� :`Z�2�j A 2Z�48��@Lyubovitskij et &3��. faesslee�� VF6l jZ� C 66:AQ55204R�2vWeige*< 1995>w$:95�F :`r��� Bj35Z�20F��v�Ha� a-��Bh$� H.-WA�6Aer j�CjR�xend{thebibliography} �\beginB{9}&q8{Bjorken} J.D. $ 1983 {\it� �0{\bf D27} 140"�tem{Brahms} I.G. Bearden \etal (BRAHMS Collaboration) 2004 :_I$} e$93} 102301gA� �90 1��X3E� -Jn{isacrefl~Dombskyk~]E�%�"B I�1}, 978n0%�5melcon� ~M ian6YM' S� 1�53�2005) 9��( J.M.~D'Au] �JH�B126}, 7Ak9�4�H {gorelov} % A.~G 6�Hyper��"; �� 127}, 373�^{swans� T.B.~S :^�4 Opt. Soc. Am.Qb1a%264��B�$carlsonhe6AkA�LD, Frances Pleasont�} C Joh�, ]=%(1�z((1963) 2220*� l}! Tl����\@ W69}, 2%6�q5!gao} R�Ga>u^n55} 175�m8a4N fras��Ga�F ,!� . Jo�M� Spec-�21K)�2)�({arminusexp�0I.~Ben-Itzhak�Ir .���8��870!L8��4geant} GEANT vQ 0on 3.12, CERN1<94). It includesL low-energy physic� EGS4.v  {kh}h dKofoed-Hansen, Dan. Mat. F� Medd18} no. 9/1r !W5��T 1 %� K5 {wilkiA�� W.�r�E@A2��50��90� Qg��26� Comp� �1s!1� 22� H 6 2"P 8 %S.J. Freedman (K. Fujikawa PaVetter2cM���3) 02271>� v�}!�D J��}, AstroA. J �465} 48ee96 N�)jX��fatemiq R. F - (CLAS co.�i�e�j{� ,�H02 �}cyun^J. Yu|�[C{!, � V Wdodge2��pDZV$proceedingeI,workshop GDH@, i��g. U- {xji Ji, C�nKao)�$J. Osborne1ᘡ�472, ��$�burkertA�V.�B @�(D 63, 09790 ��C deurA. Deur2A �93, 2120Ya�Eioffe1$ AnselminoA� L. I�AE!�ad� SovE. { 49} 13��� =5a2�L �VBe� �B { 29�2 92); V�.@Zh. Li<)1{ 4�� 1993R8.x,J. Exp. Theo"�#{ 7��6� 1��90s!r� S �O.�eryaev>�5( 2� 95�J�;- { 54 3!�.KavakianA� ��D{�&, 1AI\2(hermes_ssa}A`Airapet� �2� � { 84�047e�2�efremq A.A�E 2 36a�J� _gdh:�J� , Talk at�� buch0a�� ,A�Henley2�$C 62, 0152��12�N2%2~N!�!�02131)12�� _lee_�FoAj4 overview see:!J:TTV DLee, nucl-ex/04070� u�$alexandrou�� C. AN�$D69:114506%�6�:�VKZ � 9122}L kjoo!/ K� o, �N�), *� Uua�1��f 2). .�z} C rtz d2� M86,�y3�2klibuli92��t:�J� { D4�� 92�cano98�C�'(P. Gonzales� � { B431}:2 J8�9�(capstick95}jC ��B. Keis�.� D{�� 3598} 5.skrewaldK%.6,{ C62}:02520I�2�leeA F. X�.e5gU208070,"2;)y�N*a�,Z oble%�2priskagD.� R@ MENU BBe�l4]rwarnsX M� rns,�=Schr\"o�� W. Pfeil,%A$H. RollnikzE~C{ ��6� � 9�aiell%� M. A 8, M.M. Giannini X0E. Santopinto.� { 24}:753k98[ pace�E�ce,�Salme RXS. Simula, Few Body Sys^8uppl. { 10}:407Z9Zaznaury�L I\,5�Ju%�z C, arXiv:�xt5 7021.� arndt96� A. A@, I.I. Strakovsky �R Worko 2�C { 53�i3k � ��koniukb K %�N. Isgur>2�186e80�cJcaprobFTWAberts, . D 49�m�2�lichtend69<,Carroll, D.B�R E �kl\���,174:1681-168�V� kirchbach� K ._$ A15, 1435eb\ HmokeevadV4 Uq�>% , ed�� KuznetsovY2ripan\ M. R Q\Z�]^� 9!��%b3.��is�MZlli�J6� ��}!dpp97}�t Diakonov,! Petr M. PolyA�, Zeit.f�+A �_}5` oka}���oretical��s��M. Oka* 06212Mnakano�T` ,Rse.� �clas_dE�Stepany�b� 91, ���W2jKp� Koubarm�fM: 3V� hick%��o6� K. H'.8�4)9^ka/er! M. K �HaipkaWI[IV_- 7, 3j�>)�]g10) }�e>;I�), Jlab 1*  E-03-113=�g1j ,Battaglieri,kDe VitaEVJQc JLBe4-0212e2�cP_�a Weyga�)�OJ�4-017Meg3Smith�Gothe,z R�10Yna49}2 t� NA49�dEM4��2fT!� J�% _2 903�N-�f-11*.Lsevil}Salur S (STAR f�"T!} �!� 10039Y�(pi0}Adams J�!~T*�4C 6744902XenhH}Koch P, Rafelski J�m Grei"W � JH"�12A 51ZPDG1}L1 S �aEfF�0 DAe�} D89} 0922N$8cosy11}Kowina P J(COSY-11�� 0102*%Olga}Bar kova O��J2 0802=�4THERMUS}Wheato!��leymanAG=�N� �#71.DMa�}  C>th:X},qcoal}Bir\'{� S�0Zim\'{a}nyi J!�MZ*9}3� 5259�ALCOR2U(, L\'{e}vaiA��>c9ei�&��}Q�347} *J%Levai}S%*PI1private c$ unic�&.�HIJING}VaW S E, "&M,4&X N�%8 Ri���443} 4�Ppast}Albrecht H (ARGUB&'>T�1�#,419; Bogolyu�M YM�198)&Yad. Fiz'&�119n:9 �>:450} 683; Eisen!( R A (PS185>5P H) Atom� m�5K(680; ��y�; Seweria#(^�C).��x1e�b!b4682; Baldini A R198-�To�(Cross-Sen&for Re*|&High-E�.`icles} vol 12 ed Madelung�+Be�: SpriG!8Landolt-B\"{o}r)y* 8pNe}Yuldashev B�� (FNAL-343J�1>��rA279�|0Z0}Acciarri M-(LNV2�6�3�223; �L�.�LyP7�)9VY(Ef�9.�*i'12�hGH =v B 72E; 1�"; :I�EFD 23, 8�1� \�1zx2} R�.HE�D*�s8�Q1� 2R U3� 2809 UT�T2FT.� V5� 74011�2F�7b� ach!k�Thesisp$Carnegie Men*�)�.Z� t# Meckin�#ig }.u"th.x6� A 50k5/2 weis��W �z& � Ohio>�0'5S PDG}u�( Data Group� Groo�)� Euro�J[#�C3 �b4zhao2} Q. Zhao� LiE� C. Bennho&�'2�436g2�2�T3�TE� �E 23.�%5 U4U>GC 6!��� 2�?>�=l-KhaliluJ��(64}, 052210W ]6� 5} Y. Oh,.Tit��T�!e,6( ��)�6Vbd/2�/" (th/9901066}.�!�}�'�+sec�BPgha6 �4��4��Li1"�Fp5964 :%.:& We L LEgngNN�[ R217�"�ZOgoers�WG )�`"!et�y4!� 3�*99$UJ ben2\Q�:O*� )$ A 63�"09cY�N;jI2Jhaider86L"QW(E0L�*Liu���!iuB17ej86) 257;.BC3I*6) 1845.��green97eAgfS. Wyce�MgE�C{'97)!�67;Ym703009*&; {jid� � Jido-�� R62) 04S0206043.Schrien88URd+CNY)6�88!9.�sokol91IGOS�V$Tryasuchev�?4Kratkie Soobsh�  [Eng`< �9 sl.:�i,-- Lebedev�&Xitute Reports] Issue \#%� 91) Y"U� �9:�I�?0zika BiX9) 81-5exa� 5006=�M�0 .�M\Pisma v EChaYa \#5 [102]��0) 71.�hay| �%HN�{80601.S gilitzer0%s�. ,[,posal )TOF6�, Oct.� .�baskovz: )�B6�'3�.:pfeiff� ��<)�E�IF9/a/5�9o03120_9� SCANZS�Afanase�(JINR Rapid.e$ , 5[91]-9%�I�!sN?�f?,26} \expanday1\ifx\cs�F natexlabU (\relax\def\ #1{#1}\fibGb&�E>J�CM#�P"VGjQ$�Rci&�G^R.$�Rurl^Iurl#1{�1tt!O%8{URL IprovideGand"A }[2]{#2} B!w5 []{S'}Y�[: IThibauA�(� 5�9t  :197��9C>�:X}a.{e i*|AjFI C8^ H1�;Wi�I�:64�1my J��&) >�-�&6��-i��X>�R>�F�a&���.OnH25Z�C1�0��Warbur� ��$�Ew :199�'�V�GE.~K.:�G]�V4! B11�F 9v�EYamagamY�ay �>�8fM> X�V$LB 0343�b>�r $Motobayash9 =! mA�T> ^��Br34�>B9}B �r Iwasak9��!i A�fB�> V��� b5^�@2Z=J 1r$Pritychenk� ��>pA 9�f B> ^� Z 46R!32J�E�r Chist\') Qce�B�AV�Z 514}.g�&23V2QvUtsunF u�Y> T� � Cj b�@543�1>� auri�G: �E> V��+6^�H37J& A�rPRodr\'iguez-Guzm\'an m)5E rodr %guzman!� �V?BHNn�&6&t ^K �7N&�+>'r&Kes�>N a �5k! �&IO>% T�$7�n$E D�75��+J$E�vuglerMK k��H }6US M6�"7 [7�C�b�1^�Q� J�v, E�'h.��Kth�J>� T���=in�.�]�r�V& 3� JvOR4w "]�� o!�BJZ��2�Av 81KB�44A:uL�Fedosey��ef!� B,Z�2!n12?MF��O}�E!�6�R book�RkFn�alc.Kienle�w��[>/X.N%0P.F.Bortignon��SY"�SŅ� � 1}�!JN\OwA���clx� B?.�note}�Hputer �+gram CLXn�KuJ�uingA��sB�I.��rAN.�gSheetsn� rY%�6LJ�199vW Bhat�7!ibha��%�nfoZ\ B�I�� �V878�>4;R� &E�and��. Tabv 782u�B��' Ke\��%ken�B�P�.�!3:� � 0643?I>����U1vB}]{!���!!�5!�.�-20N �nFAld*u�a�FK>Rn�684LElectromagnetic exci% :oryB Coulomb  he\`^JNorth-H�?nd6� & �),N� Xf�� L% dissipative binary���& SchrE9W.~U.\ rv7Ś\ .\�!F1<9 439c* Boug4, R.\  ,N�!BT8|aA) 427 LaroS Y.\  chelle>UE�\�\"\,5� U8.1@ Rive�6M.~F.\ B�VR8� 1�6 219.T LecoTJ Tl�<;$ 3#B��6) 460.W SkulWW!�ku 0Z���\p05� � R259.l9Dorv99�D\  aux>RR�65�W��CK % Ar + AlYJDayras8L8~ >]V^46-) 22 FHRbS-�)�M�6I89)oD.B3HagelVK.~ B� U OBI�2�GR2�2� {Pete�:JA�\'e�;6�RW51J1& 12.�R544\ �R9-�5) 2�#E�F}�*.\  >� �)H�256}|%7)+"3}� Angelique� ~C.~Ang\' >ZV�614]61\ PRL-?�JGhettv�-� {\bf�8e#�E9272�"Vol�7$V.~Avdeich�1>�R�7�2~�".�#Lanza7>Ga� n\`{o}>VR]�PH%8.H/G.~ n{\`FTR�6 /�41) 566. % par�.-vel gTU� Lednicky}%nZ�-jB%k37Mk6) �5u!�1 Q���  a�!�;F,RLd59 4) 034601.HGourio-:\ >��+aj�'\e�3���.) 2�'=9!�NIM�F��A .\ M�,\]31��92) 51.J'Ma�M�Wi, DoTialv�-&�,<{\`a} di Catania117 (unp�cd.�;Brief�7�_� .b27!b= Hodg_MP.~E.\ 8 Betak�(\�'��<) 1.R Sing|1� Zarbakhsh>�-���M�E��R�RAI26.�? KopygNG.~I.\ � F��I3} 4)6H.�(Pochodzalla�\ r�-P3%i:4 ) 162�Deyou�ZPm ~DeY�T�O��128a<2! z4��0) R1885&,refere�Ntherein.�VerdeE� ��K!��*5466�*Koonin],E0 B�%�Ey�1 6�*$Tilley1} Db\ >�R&7�h~) .� Huda � >Ln�E 3080�,E�.k �2��I� A 74AT" ) 15e �SKotte�R >��a"W �A%;�� 8.^Helgese�->Wi�Zpar3.� Boal �H.~ e�J. Shillcoc.�v&� � 542�,�S GanioTnU\ !���O at GANIL�4-� , A*pil� }, ���]Bex � \ Galin (� , Ca�O� -95)x?. ��� Borm�Zv��:�@J$XXXV Inte&�Wi Meetqon>�, u, Italy}�Ad ��Iori (�4.\ degli Studi�! MilaLLF) 536a�N]+jy=v % SN7.@< FRS}�?G�e"�b -��ru�?�]�ods�50�p�28*:plaRG@4VosDg�S A 36.5aW*�;(degr} K.-H.�mid�4�W2/7) 287y�target�Y Chesny - GSI&�W�. 97-1�7).L*�7GLOBAL;1Schy�D alWq fV1"24 44*�= karo�].J.P7ol - iOa=X�JC 1�7!@203.�*�aMUSIC�DPf\"utzn��8�N9a 12d*S>Au_Fanny�IRejmund9^1 �sB28�4 54=�Pb*C T. EnqvisJ�.DL11) 48=;Pb�C�D752��5Y+U_Taieb@  n�72N3)\-43�U_Enr� ,E. Casajeros%�D�7&1 ad de �H iago �Sostela��*� LS�Lindhard�0A.a� Sore�Th UY6A 58[ 244])�1F"�w B 19"G�9J U2UWeick)K�SI'2).�ATIMA}!= code  can�`download4^Tt http://www.gsi.de/~w�/atima.1=� morrissey- H JNC 3tU� 460.R�%NPA_loa}�5Audoui�3 -+Jsubmit�toF19P EPAX� S\"u�ge(5B.;bnk=Xy+7Q7!H61 *K6Au_Pep,6lliure)��v�13JWlazlo}�6 F�Re��� ers 8i70��76KMoni3M�rnaJVTA 7/R� ��R/Rj/2�+ smal�p9k kars�F��s61 Lect!&Notes� �}0 58z92�<� Q shurQE. Shuryz aB301222j rafMu82}J�b�D� B. M\"ullbT{!X2�74B<10l61982MOsta�GJe>E�1i�0��F�E Bi9�88D��2^FHSX�H. �DHeckeANorg*U N. X"�7+E.)G8�J57#82� cheng!JY���<�&2�! �C � bf{6 �9�:2�<Oll�PsW. tr.MDM4�-2P_6�PS!h3}RLaU�%sj �&UAei } 654_2�v2C�B� illo+A� N�J. �G)T430} S1207-S121�5Y�Raf�>rJ%� essiAs �)�715A<�5e�ݧ cain�AH� r�B>EJr�AL  :�JRed8N,r?est_(M. Estienner�nuT 1103.�glauber%�AaG� B�N�H*XI3116?J GVWZ�  E�O�J'WX-.akB-W<< QDP30207.� Blasw�pchnwnn6OSollfr�1�TU.;$nz2�5�C4e6246u;92�HuoS Huovine�,.�2 olb,.X 8Ruuskane�S{:�shBgL&5P@5a >"wSo�8A�%� �2NI�2k!�bf{5z 0523�V2��|aR Rr^�6��cJ�!2:GrecoVV.  )[�M cPavvai2�X 0349�X2XMol9\D�Plna!jn%m.P92�Iu��N�{j*D12*�7 {MajzA�>]r�la5it2P"b# {A68�Z1�:2�N:XM�N73�P3�Z��VKic!�!z8ici\'nska-Habio��P�ɤ�B308}, 2��#.[Pomd K�Pmor=*aoJ. Dudek- XA�} C�+ {67eA 4431� 2ZDub07{EDubra�iUb)in<.�]�)� Zakopane>04 Symposium}, b:/l2 Acta �Pol2}E1�@u�Pap04b�PapkaA�*�Dsb� ls ort IReS (UO 7\rmS2�S3R_ 1C4roc. 10$^{th}$`�k=onD *�ReaoH( Mechanisms� . by�4GadioCRic�T. ed Educ. Perm. Supp.�eA122*�d3);�A 30702sE�4a^�jksF343% 2I E. Ideguc�6B�AdB�eh222�qa2k Beck�5yC:E * 9(f A738\rm,  4);3 3Ined���o :E139�8a"N�Y]ul',F. P\"uhlhof�g6���( {A280}, 26�a72dT Bha0^Q0'tachary>_e�!>6��\14611%:2k RouS�Uousseau:�ZTHF+12FTMahboub� �U�CU6U2YHuikS��wkuizeng�4!V668�n�`9�Zin12}8A��ZingarfV�� 48},� WnV� Usum0Tj �n�t�! �e�+bf�g, 145�85Y � sum2� FRe)eron%�e��`1�_1�@�isum3}!MVandenbo=�k.EEA�.�,t�Xi� 4�@44E�N 2�4}!I�alantekiF N�kig]eA� Mub �70�$7 Y�H2Y5�DasgupWUD�Hinde,]Rowleye�5EStefa�[ :�lJ�!�4�19:|hagi0� Hagi��2�)o��5ar27�a��row�q ��[R�Gtch�R�V�t Stelkq ^��+%�B2yG2E9� `jiang0� L. J �rF$,} P�U S89�e4!1�a�':X1.X'Esb�_d%��|R.V\ Jans>P� K.EAWhmI� v.�~�i�146+ a�:}2.}��9�01.�6X beckB�J. Ba�[H�geL�] omaa(JSperduto�(S. GazesDiRienz JIMolitoi�Ze�%wM%2�158�stef3aKMI]M˒�7�I864�-�2��:9fU�A�83e�:� acke��Ac�y��Ul��)�A60Ai9�0J� rehmahU'!�U`J. Geh*QAl Glago_D ndera- � Kutschera%�Paul,�SoramejA?m Wuos!� ".B31� �. � halb��L. Ha�2t�Re.hD J Hens�'�ZonP,Hp�emkowZ Aben�), D.GAhrantitAR� Z.�b�I@-M�� 2558e�1���dave�Nv-vide�I�La%/-���6I:Oe�B40/4� 121 bQCT!�u�K. Bind!y��5�:�T!L�;t�l Y. N�Ae,PSugath�\A�amayya%WmWal�!IaB� ��R 3�q*.� dav3�O5,!DANL�Div=ins� TAN[&-e��$3��1�b9z hendaG�`v�>���p 90-1����`pB 8.� penn9pO� �bg(p>rD.S2Uyni��� CA��.�=C�gLpdB ZabranVrA�!� lankE��0N?2� ��%�Z� 1R�E  �A�ods A21ace} � GavrTqJ�A�2�b�S9��A>�! 2� )�-95/1��!�& p. 742�uhl�P\"{u}"F I� �E�J< �- �Charbonn�tNa^De� ro F�u�� L'Ecuy�]4�o�+ Bull�r |So�q16 �76�2I�VidebaRP�0)NstAO�N!NK. Ul+ * q �5n3� 7xP� brau��� BrauGW�J.6N8ushaar, R.P. Mi.H��Mitl�e�iA H- Blok��Vri��)�� �3�8 18� U�NDSMo� Singh, At��ta-�03 Tabl�bfb�06J hagi�0� > MW. :@ �� [%��� bass Ba%Jp�� 74� &�q��j�FS4%�535�V95)�scsyF� arlassa�gS�ugh�g���`8rL��Corr9r  Montagn8DA�Nap 6= E�Z��Li!EB�x"t�R6�� B,��H�reR#L/{u}1�A� �$P. Spolaor�EidY�� w(2�S4BEX9�jan%�2� A� Holz� h��W� n�$*a }, R�]�N6� free�S�s�h_ rnstz i| eesan�J!�Human� W. K��n! Rosn�J� SchiffB.6fd�7��F�bo"=AH)�6! i�5�15�lB�, �i3B A  2292��9� linrEշ6L:�T V&Vd�(�x Dass� "{�4 rolo6� �q�)� B� gira�$Gek raude�KI(aglidQ K.Amo�  |Rob��V�9�646�Y6At1}b'"Gt�6['&�@ Fusion03: From azunnelA�NucX($Microscope�ess�Ma]v�/N�s12-�i!,sushim�ap �2�r�(l. No. 154,<4A��  2 � A�"Q .� p.6 Qj'84>9�rocx20,.i/209/�p rink 6O, A� a�gp.�v2�roc�\Va�Sastry:�=�Book of6�� "LB� ��AKroF���!843%� 3. jdX1~BO7phi-t�ty��4lt>�c;�Ko�!B�;j!�m J.~fy|pi�{142} 1a 86};*iphikk�'S �*.!���"�y�,� {A707}}�c 6"bphnxtrk�Adcox2� (PHENIX:�`6� � �u 4Vt3.�,phirecdipali|  P�B8*�phiprc} N��p~S.~Ad�6(n&q 0012� PDG�S.~Eide��6;)6��B5;911e�97 BackEBq�~2H (E917B6� 3040�`�G2#pg0mK�� �6� {91}} {17�} �<3}.2nhiRcpv Vel p��.� {G�!(}, S835-S84k%4)/ +X 4050.ˋ��l�B��NoLmJh!; RT�#ujVwm%U��j�1DhʜB -)eG �E3�[�4.V V���YAziAn< �EJA�%&K`~�!~6�j$. \newblocAFem �5�G 93:25!ʅ�2��`�d03}�u>u1:E?2u2S\BB�3} 8B���0:0&Js Flow�qVq35Y2�dAu%�XFX0a� 2tJacA=P.~Jacob> X.~N.�hB+2c}A ,�Q�(ar)t *(405125)�~ugust��.�Nim�"!t K.~H.�.p�� ���&{(499:624--63J�NimEmV! M.~Bedd���On{725--739F�HNimAbsEnCal02} T.~M|\rmpD�=83:73I 2.~Et%}4�}M}},ݐ: �7�>�TPC!�M�;���.�!�59--678~2� dAuPhenix�S�� NT��>1iq"� ��Vog!d,W.~Vogelsang��'��R�.�CTEQ6M%� Pumpg46#!~�J.�j �j� 207:01i2#(AuPDF} L.~F�' furt` �@StrikmanB1E��[ J^(A5:293--306"�x�L�anZ Guz�}(M. McDermotrNxr�hgk �� ��v 020�0�y�,p�e �WB� 3030�=9�KKP�4BW9 Kniehl~KX| � P\"n7rB�)�8}, B582:514--53�|000!�N�& �n.1:�&_NS�=.x& E56�&�%A2�6� ""��&�.�&>k _.�] 731cx$&�&*z �&3% PV�&Vk%K�jC�b�&d04} �&� �J�&4��&>��N6�&is*�. =Lz M.  ����3�/3). k9�=" } F�* �2)�.�V�2�4p2Simps  K>  e[=�A35X�2�.�9E�~�57�18E!2�H5- M.G.~H�#�C����� �M?I�� }Y� 203B�%�38� �#P� F:$&PNnJ&&-�=�KicS- M.~Kb-*V�V�B3>* R>*S�^*`�^-"P%2REh�P^kN�e+2�95AJJG} J�,Gaardh{\o}jey�6�$� a�$=��$�7+aNee82��,Neerg{\aa}rd^�V>110A&C!^Gall}�f ardoq�r {Alt��1&TDo��D! ssiuZe�Brekiesz: �.6�25T #ni�?�5zon&Y'Q�V254%21ژ�� �2eHerskiqB& �>�� t*y�5*24�82k�,�� pSchun�mN/-�,z/Z)(�j�.����0[1]{Agakichie�V3gg} O3&�  (CERES�G4 \PRL4 ��&�0[2] {Slivova:b is}  J� 3 PhD}is,W�U"�U�- ague*�7[3 �s�i'wu} %�^�+ \NP � A638} 467� 3]{Lenkei�R9xu} J�J.U6��3 U$4]{urqmd}  SAI>�$}Avb! 0C225Y$5]{Eskola:S# yh}  KJ, Kaj$e K�67; forsqy�XB323} 37; Miskowiec D,d2NR:\~{}m(/overlap.K6]{Po�2z9�8}  AM, 3! �\PR �C�167.?7]{Dinh!�9mn}   PM|@� N�Oll�6 J-YAX0 \PM� B477} 51;V�.�8]{AdamA��/ wi} `|J�=�7NJ124.UH9] {RHIC-combined} &�&KH6{e]1! ��L402; �K:4s62.6�17]5 10]{�4} �4 PF,"�4A{ Heinz UW, se�&g H�� �B50ɚ32;2<R &�!��a�lI|:��3�]�33.�,1]{Teaney}  D �6204023�0301099.A2]{Rak!�$4gk} Rak J:�=Y�xy} �Ge8309-S13.�[1���Lsa�0bs}  ALS:j$CCOR) 1980]�[�16�Mը$[14]{Bielc6La�3ku} �Esumi SPp limonov K.~e6Wurm JP!إ� �C��021901 .w5a�tqalT� ��Y�%�M,9{�1.R6Ramf�4wzR�>�a))��7007 aaN�,v"�ph�tV) nJ�* ph�t�7�l� W)�and��wu(C� %M{B�� } 25�C2� pL i�9I�� &� AH;V�sol�R�0S �V,�, D\GtE� ics,� achusettsi�r0of Technology��� ��?tdsmqm} Debsankar Mukhopadhyay *}the{2t���-A �;496�h���.�3��!�e\�]u"x;lRD �&� Ev U�O��.N0� f0"jR18 Bart�>�4 ourn��M:�1A4} 1���%5%2HP.�Azio�DF�$ A525} 479xw12F 3} YA�Ki:�6zve�6 6K�!� �*� 4D Bl�)fel&� >V I 6} 5�1�I$5} E. PiasS|� ae"\w�)�H12�.1); \\ �% Bow�#�J , ibGt {��5��#{(6} B. JakobIK>* D A509l �0);\\ ��Y>[?y>� @�6�y1�>��B2O2�2�|�76�, Aug.10�"InvOJt���en/Data3 6th�"rdita n�JKop�g orway M Y�8} D.HuGZ%, >5 bf�V601@.�9} �ynG!j)%37"m�6�W�WdB&=�<Cv!6v!!M�~�G�CŖMISi��"72%� K��8ه2��<?= Kras:QCzech�� ��!�5�06�h��13} A.Z�'IsmailK >R�3�5T"28�82J14} PB(Ja"MF.a�C't�i'=5�L� erryN� B�X153�?6�6} 08olynski2�<A5e�m�6� 7} N��And��"1�C4e��2+18} VƑng"�w�iin���$.�M*�%k�� Kracow,�<�!&6*C19~eNb<SB=mN�& !�jPantnag-India, 2��!S�20�JK ddin05 21st ICRC�eR paper$5del5} , Autrald 8, 8%<6�~0We�P&akr]IQ2}) 8 �49YJ22�YE4"XL@m]C52} 33� ;5u2eDW$ nagioutou�!A.}EK49�@�� \\ AA�Goo�$N<7C� 851!� 82�%�w2 A428} 313�p6�24aAE}u� �ic��bf 3}?4 (1962�kHP�Z�.��5�6��zB�XII DAE6�V�Guwaha�YM�<rP=�7v`)"C��JG>�28 ?�pa,6I%Z30�A482�=G&�UN��7��04�95@ Y.-G�::5B3v )�6�9� %��b8?>} ���132IG2�30�8 Stau�,A� 5 A7��u31aC��t&�j: R4�9q�a LJH��6�5�b=!��J�1� ��( � 23E� 0DN�0^� 2} XHmpii22�B2�?3m�8�Wb ux�otvinOB"K %\�a175QZ&i� i���� 2} �) J�M�..0 B CK�1nK}bbfpK pK � lineD*<2P�hp]d�]p.}��>� 1.�{qmf R+Nr H GRy�X (CU ors) 20�Quark�,ter�} (�#"�zics P�Z ing)*�P{nim} Afanasiev S V �N��6' ��Iwkr�"Ď4�� >� ysyssizep��}   i�Rn�n"�� �603*�,{45913} Sik�F�`>�!,!�A-�� 45c 2��.200B���� E�4� 59^��_B��B ^� Z$2aA�Susa T�)})�-5� 491c5� Barn> DPh��&�\ $Budapest} K�Hύhne CLM3 �nMMa ~g}B IF-R8archiv.ub.uni-m -;R�e /\-z=/0627/} .�Anticic59R�y�%2*��Rc 02�J }#na35} !Btke J:�3>A�A�M_& C�_48��912R!�a}c2A_(NVZ-kFZ@a 3672ZA55%s^YYFY64�5�Y!�Mߓ U)H�71s.=j0helena} Bialk�sa H�lRetyk WA�~, R��� } G -_�| �2�]�-� !49>GAe \R\� 474c.B(tou} Tounsk��mO K�Vm�N�A 2095.S stop��0ppelsh\"{a}us�{. �N��^��|� 247.SFA.0} Becattini F��M #e6r�}.�be�+ 2E�J2%�e�9}a{490*Y{&�o}ED �RLeeuwe�� XR�~� 161:=6`�Ir�]�0fodoralt} F  ZE Katz S DQ�v JHEP�'$3} 014 (6Nw,lat/ _�0CVmcley} "E�) )'ep %6UixX�907.x biel-hAll��C RX)�M�.�D2�74507.�% Vb�6��;006.Ten Q�? 2q` T�Ek� ���� 5284.]ref� e=-MunziȔe�!Gj.ZLe�B- 3�a :��=bNV�i�3H 4*m�4Nb ��:)C O 5} 143�=IEH Kښ��c�} T]�ref�"�?M��9�}��]0a�2� ref7�>= ppe Ie^S8L el J!�2�-� B �4)�*wb8Nbf� T1�51��4.Gna5AAAmbros�FG NA�(NA52>p*� ew���1} 22.:b)uno G E`��5>G5���J} S71*|" {mus� "�T�M L] �p" 65.chwaNb,}��-5�,;)*)U th/ 63> to I�arse�o Glu�xlasma �Hed��>HwrE"3�,B#�*� ]�ke} Kafk*�  ~.��16} 126.�sV!\d�)n E%� ��191e.WC�50��7.&hg} Fi$H�\��E��1182�le Le�X.y�Y` GM� 427&� �tBroni� i W A Flor� i WZpq�i�k 27� �6(numrefs % �nr9$t$tem{texono P. Cserna"A$J.I. Kapus�M� , 13N62�@86); S.�GiyIYA�y�dvpN@*1�|�Stf ic" 5, 2�Zf; �ctoYO%&W�V �,5�2fN6 �startL'Hote6*��A4��457l2�scii@mag} H.H. GutbrodLM[Ua%�H F� 52, 1R6�Ppdg| Cav4D����C4=7^d6S prospects�H� rkasS� ReseX Emul�>{"0. 1, Academic�mD4ew York, LondotA66�pr%{} S�Iiyr2F�=�4�T.�a�� Bomb�@�UInK IRES�1asbourg%TLEPSI ``Proƒ� a SilicT�0trip DetectorSTAR''�L97); VECC, Calcutta;� �Dhubaneshwar; Rajes�JD., -Jaipur; Punjab (-Chandigarh3k Jammu B�Pho_ ,Multiplicity����2�eledaq� Powe�F F. F'QI�V"VkihA stud�El|tary ,-icleslV�x�ic MehtA� Pergam�FrEY59). ">sigmanue&�A�LTY�-�*�" , Banaras�Q)*k�ty, V)Masi�Wdia%�2�m��_.�f.� C17, 1707:= B. J�XӃr"�! o��$Fourteenth�� B�WA�Cosa6Ray�#unich, �w.yi`Klaus Pinkau (Max-Planck-�, MunQ`i�7VA34�72���Kdngotr&j(IL Nuovo Ci3$o 87Aλ�0:CAzCl&�8"B*4"A5, 7�<�t=6 ���e�_.��+R��!M'6ied�V�C2��43�836���bd|7la&t"�| G:�0 �28�^75 �#}.Y�dy@ҁ�AOJszk46,Vfsensit� Ba�Qi�g�ga�l. B6,X36�munup� E�KA^/���J2Q 22, 3�1Ku�rdk� 9&, J��N , El-81-6��1._(proto} I. O�lu��(LUIP-CR-76-w!6pcsibkg� BogdLN&|# Helv�i<ta ��48�66�$ } DGKLMTW>O&�Dubna�hmun� 1-83�E19�J� lens�; Ahma��.�Al�� Muslim���� .�2gso} Z!W ou-M\Ya�Rn.!�Ig80, 1�52�naicdmf#K>> *h A5|�82� nbeam� R�� seph�.��[6* lepsd]�Znj�c2�411, �� 2�kimT+. Dabr� B(  C59, 321]Y\ amsr�\!B%ob4 Kul���$Scr. 13, 3�%:� iaea�K.�)Q (0<:~!By�=�_� 3500�)&�J�a1�H 8��9� K2);�� �B561, 8 D3);w�+- �@�խ6wg �ISp�U�ort�N( random num��genera� p� ed�"�Pine�$. ACM 31:7~8� Ne6���. 4th2{ &LJS�j�py,�Lke^ZLBL-776�;�F15; M� !ov&��� �$M: � AF] � 0�o�/�U Zipp�*q�ArXiV�pr�� *L$8��4) S.�sPhda�h�rC* ,tilquin95}I. } ,�y�� arlo\ �lla�M�Xda� .FJ. LehOV#lle?Z ipn�/A. Nina1_FDn�,%C Bizad?��,9 Mosra���Y,A� R�gimba�F�<, �D�%":��4S�2�y� da92}K. Y E�Kasagi�YHa�$M. Sakuraih`Kodp FurutaAtK. Ie��a_�r�6KubG� Ishih�X��walo_],�-��>�961-9�12* +c�`00a�mhu��2?Na�3_��IpQ�s�B. Xia��Zm�!�i,A.YR�a�2q} �.E�A%� B 47�^in2��hm�00!�H %�Wa��J.��SZ��%��.�B.- �x�.��nasera�>2�)�6�H 3460Jx�)� 1}J.%�:&$in "Isosp�e��u� -�� �(i�sy3�V medi�E��6�� 89&� * ٶ*� Y. Lou�wG� �>[B݅re�.H�yn� s emey�]!��$Guinet, C�3st� L!gne!hK. Zaid��Alarj j Gior!�DzFuV%`raCV��%^Mazur Ngo� LeG Auc�ME� brage E. Tom�JQ 39, �8U189]� Epax�-S\"��"�e�z.+6 K�uُY�k� 04}*� �,p����es. =na 0�>���9�T K��� �@ eF� ��  ��%2C.Hami�', _ �65N{618Ŧ2lsobot��L.AhS A��IharqJ. T\"o�́& �,�bh�.r�-��13270H2�m� 97}����9���-F,=-� � deiwayeh�!U�Yyya'J��k2�<2b4l 88A?l }���th�H0b! e�� MouchaM.Nmboodi% ��}�R.!chmita�*/*�B��k�^ ᥙA48f4H �p"�g�,90}w" �Co%�Y��]B� R.!��L hlomX� S]�stava�uTurmel* R�� D!���N>�lli &y#R�qna B���+P�e Ni`�S= nuschA�2�A�.2JI�L2125 660" rivet86}M cꔁH orde6 �"auv� D. G�s�� Cabo!�� nap�d&� )�m� �V12p�#.��D_�F�Y?2���:�$, �� 1�MKɲ"o 2�EJ6AH 0316�2)& G{�>ton62AMA��e*i���BA�e�$ %Addison-W�&�4���, Ream�C.!�6��&v\moniz71�J��iz|}Sivq� hitn��Acenec!I�K�e�nW. Trow�����%26} 4�g1.�lou95� e�yO~� 9���=�BA#,ui�D. Uto R. Tezkraa��=i�T+Y/�oHur�e O'Kell%G!�i6>�m�:q�Н|Mq{!;u![A� urch>pG�Ugnay� A i�M� B���c %ayoe6fA�%fA58�{3t��q��c�z88 � ,�zJM48�)375' 8) -4Z�lchemistry.wustl.edu/faculty/ k.html*bondorf9I��C �yiA IljiF�I��Mishus���Sn�,n� Rept:2�3&(�!6Y RE1.Z@OWf�0.}0Lar`cT.L.~Truh+i3�/30508O�u%*�jE�_J.~Toj; ?>KmJ]u�e�R�W.R.~Lozi��EtL�fTcNIMn j�kR�'} IP33 1MP>�run�O.~Jinna>� ��L(/CAD Accele�m Note�j$��.�Jet} A.�I~Bravar et al. ~these proceedings (2004).; The talks on the jet, T.~Wise B ,~A.~Nass RZelenski fgt %% \bibitem{WFD} D.N.~Svirida Ax ~detail description is found i�V�2_DKopeliovich} B.Z. �< and T.L. Trueman, {\it Phys. Rev. } {\bf D64}, 034004 (2001)6hHSQROOT} G.G.~Ohlsen^$P.W.~Keato]NIM�d4ics Research} i8109}, 41 (1973) etend{thebibliography}�=\beginB{99} % lreferences} % In Intro.tex 9�0Ito03} T.~Ito))�},�.~!~Lett.~�(92}, 102003Q?PSpaP(D.T.~Spayde-[:VQ B 58}, 79JO@KuS01} K.S.~Kumar-\pA.~Souder, Prog.~Part.~Nucl.~!b �45}, S33 �0).�BeH\ D.H.~Beck[4B.R.~Holstein,!3.~J.~Mod2XE10!�A9QBeMFV@R.D.~McKeown, Ann-W ��Sci �51},18)6] Mus94} M.��usolf, T.W. Donnelly, J.~Dubach, S.J.~Pollock$~Kowalski,� EFBeise)�I�ports)�23A�E�942;PDG!�e4$Review of � icle!�Pperties}, K.~Hagiwaraf`EZD66al 1000)Z22uLieA�0A.~LiesenfeldRR2\46A]20aX992QBer02} V!�Prnard, L.~Elouadrhiri!'@ U.-G.~Meissner, !T�' �G 2`RN�Bud!&A_0udd, A.~Bodek%!�Arring�"LarXiv:hep-ex/0308005.�@KaM88} D.B.~Kapla�f,A.~Manohar, MM�B3E�527�886�McK89} R]� <.?21E4%?8>?cAu@IFM�)�EA 3248�?@% charge symmetry}<Dmi95%� Dmitrasin��%�6� ���jC5��6I�52�Mil98} !�ill�4%%.?7a�492�96*LewAxR�wis�N�bedJ�5!207300 M �(EW rad cor ��� Mar90} %W�fMarcianobJ.L.~RoEt.�=�6�� 2963�6��*0}.*V:�)S B 24!J4-I6U]�d��Ramsey-�� u9}D 6s033008�R6v0DDH80} B.~DesA� ques��(F.~Donoghuem6� �g m (NY)I)124�g49!48i% Hton EM form factors]�(HaM84} See,#@ example, ``QuarkIPLeptons'' by F. Halzeq��@artin, John Wiley� Sons�jc., 1984.�DAkh68}A.I.~Akhieze�M.Pai kalo, Sov͝-Diklady �3}, 57E�66�Dom69}N!Ambey,��A�6�41}, 236!,6E�"� Akh74} ��A"�≡e��27��76[Arn81��*��V:nucl��401030.�Gui�0P.A.M.~GuichoiZ!�r03a} Jefferson Laboratory experiment E01--001,2jeBDR.~Segal, contacts.lPe!��`109e�(Perdrisat, S.R,JPAC04} JLab�mposals ( +$s): PR--04�08 (X.~Jiang),9 (�Dck), E . 19 (�uleiman.1� 6�)y S�<Wel� G0--94P), private communica�.�Ga2  Ha�o��t'l�RurFAE12XmP!|yJ,.,} p.~567 (avy3 � %neutr͜fsyUBLAST�' larcA�6�! collIF��3) (\url{http://blast.lns.mit.edu}).�X�� W.~X���00n02� Xee~MeLC6� R01u6NKub�{Gbon:�i�y�B 5��26�%[��Bruv E.E� Brui�6N Q�/V �7�Ns Anks H.~Ankli:lKB 4I , 96�Bro� ��9aB17,��BrooksR�Sch�a9 chiavillaA� I.~Si-�-��041� 29CAbb�] D.~Abbott>� Euro�~Je*VA !�4!B20:,Ma= R� d�����22�64Wa��A4 Warr��Ta�0�9i�6�Ost M.~Ostr%<�U8�27Z " Y��gBermuth>M)�2<5%�194� % S-q�  model.� Jaf� Rc Jaff� "� B 22��275� � �Hoh76%KH\"ohU � �%�CA750C762 For97}a#Forkel2�@C 551~972?Mer96} P�rgell,>�E�0D.~Drechsel, B�A59b3��1996�Hamb H.-W�mm::Fd)2�3��32� 6eMHD!( ! 6r� 2� b��%'D5��7<>'uH��`2� X:kZ�8�2533 :�!$9a!�9%ZFqJ�6Z 0452I!: \b�\ \4A� \%%A sec� loop. Han00a} L!�P4ius, D.O.~Risk�#(L.~Ya.~Gloz8JT 6�35NuKoe92}�Koepf, E� Henl��!�2�-�=�aUB 1�w:�ur�(%}INS4M.~Burkardt, Z��E=C61!1>�GeiA�P.~GeigzN.~IsguyBEE���1M�2o Chiral PT�GemA�T� Heab t, U2p�(S.~Steining� z.43�J18)�6=Ito�%FH�J� �306��:~ueTB MueV��7!�382 �6UAni�LK5iolV�e��8��109 ��%��emR%6aC ubis)\:o)\fI! q�5�1mJcam: 6�I�Fy y&GJ� 56�2 ��� % Lattice*zDonABqDong, KLiu eA� WilliamsF�D| 0745�(6<Lew��Y Wilcox _Ra�Woloshy6{%=D ��013.�5=Lei8 Leinwebe�>A� ThomaR�%0��f % other=��b6�eO��FC ^���^�yuy V�HLyubovitskij, P.~Wa!�Th�tsche)&A.~Faess'-�2a� 0552 q6�Kimak H.-C.~Kim�~Watab�K.~GoekeJ A 61\60iao��Silva�q \%Q> Ds01401J 1) ���vK� �$ph/0210189.h We� H.~W�ll�Abada,�AlkofeIH�inh��-O�B�z ��6 Sil!�����<2), erratum-ibid D )�399� a�U@Par91} NA�Parv� y2�2�15F 96�O2jOF�  5�4�19�A2�Axial FFE anapoleO 7 Weak6% deuterium�Had�EKdjimicha!� G.I.~Poul����� �.�26͇6MDia� L.~Diac�cuE0&� i�$U.~van KolR�  6A2044007"6eLi�C9�Z G.~Prezea�fN�F�� 3�I��U�3�.�J:�M�!=b`2ũB`HwaY W.-Y�Hw��B G��i��2C .Y.)��1 47aa:gBo�1HLos Alamos npdgamma*�U BowA  spokesp� . %F % Ma�mo�um6in��GonA onaovj?ќ� 1120�B�La� H%Lai6OB~D/ 128�w�k9�Ze�wG!yZ�. ,18RKFIT�(``A Combina� �Hreliminary Electrowa�Measure!E� (Constraints�"$Standard M7,'', CERN-EP/!#-98, ���!<21.�Che71} T�Cheng�ER.~Dasj�2��59 76|Ols#M�OlsI�2$4 5NvS)��e.g., �Sainio-�Pro"$of $7th� !W,al Symposium!+Meson-�_eonņ@ � = StructureN )P}, (Universita\"a t K�ru- UCLA 97), eds.S�~6` (pp. 144-149��&�"�reiaO�_Pav M.M~Pa� �Ra�Arn PiN Newsl 1�m$9) 118-122]�Gas��JssH; utwy�Z2cJ�25�r25�:�WriA�S.~Wrigh�/"! `2" !]2� A6� 137cJ�Fil`B�FilipponL y, Adv.� ��1A�6�Air04}T AirepetiaZ���A� QZ��� 42)Ahr87� A.~AhrensNa ��D 3�78%�86�Gar93�T!� rvey� C.~Lou�N and � Whit"�]C 4� 76� Pat!S��:=� �8 %��F� �%si��%&� (Pre79a} C.Y�scott2#.�.n- �B�5�7\uPSou90} ��%2|O%BT 65} w 6U Hei89}geil:HB� B 32�I�142< beam)=�Far� (~Farkhondeh:wJ,Fifteenth In. Confk'� Appl7s��Accele�s in R�' As0Industry, AIPI.z$. CP475, 2Mq6}Lev94}L $Levchuk� InstthMvA3A 4!Eu5Pit96}J.&� 12trO�Recent Developments in Microwave Beam-PositL@Monitors at SLAC,$ Preprint -PUB-18�:�4Ave99}T. Avere:�f�43�� 246 !8E% endAj�,U�q2��Bei96}E�&ise�c 3�)�6�Has03}B)a�Ph!ow,�d��.~Illino� 0, unpublished.�LiH82l$P.~LiJ):� *� ��14�b3�"868 HaD�.�e�.h Zeit6VZ3�19:[Che01a�-W� el�S�H� � B 50z2�Y 2�L, fL>Z8D 4236PGEANT}, � �e,gram Library.z Bae7�W.~Ba�K�CD } P.~Truol,| dvae,�,a�ear�0ics'', vol.~9a�7:� er98!.CA�rgstrom:�)5�%5C �'32�!19:�R b} J2S2�FeD57p BF a97}�":�%S� Bean:*R1b38ţ:�MoT69�W0 EwY�,Tse �MJ�%$�%&�:�q848D 72� Kuc8�-V.~Kucht zN!�Shumeiko�v)w%, B 2141� 86�Ols59�� M�L!~Maxim� K�P11t88;5��Ս;.1�**;.NA Maryland,�A12A8, available at � www.phyA� .umd� /enp/��es/��02�f�e� �$&1G�wkD datag�'0��(:d�!czbf 29��211�\52Car�.$2�, VE�row��BGibF� Kv �C� , �� 65Wir�5RvWi�,aG*Stl �6�Jf�. 3,:CHax� ax-�.i�2[=��94�t 50Pol+-P/>�D +30w6sBal!�"� )�aa3}, � T � E�B� ]We� S5�$�:."yFC �064*/�� Note that�8 numerical valu"�aw-4 has been updaQ(using �fi� dilu�+��$are to be ����an  .KAfaA�� fanasev,d"$Akushevich TN�MC k�_&08260.PVDH$F�'��%Bau� BaunaprF0�-3tPAVI04 workshop on parity viol� elQn scat���Ppp��i�4�&R.�Pas04} �,Pasquinf0F�6240530�)$%%% HAPPEX]BAnHv:a$��}��2E}�T�A�uoKuma,K�r��36�3�44V�!;2O*�6, z<+ `(Arm�!�RT2� Ku_ JLAB*� E99--115�*�4D.~Lhu�T �(.Ar!1')e.�)0P47��mM[&�%2SMusD93}.996w ��E%�B 3�2P-:�,Maa00} Mainz.�``PVA4� (D.~von~Harr�4�ma2�Wie03� �de Wiel�M rlet� ��A46�(�CzechX&�ΥtbA��,A��9]al�$result wasa�vided�/ this!���/~Ma�R.�!"4}F06�^�a�.,F� 1019 G0���C0N:1A:5�1��*.(%MLP %*9ad�fu���w2b %:]Ben99} S Benn�C3Wio9.�)��248� 6 AntA*P�AnthonBG.�9�312035.�* 1}B�02-0202c0ini5 "���M= *"�2��204007.�Dav02!~David� :J. .=]�02� �6� Erl!J.~Er~A�tryl�J!w3 2�"2~e+D�/160� 6� Hau01}M�u�#� .N�O$38@ �.?!��5 tche�'61<�64A�5zRa�M&5��%.560\:� o� J *16�A�erU�nt��\�,�6Zh���B:@LOI-03-106, X.Zhe�\�� FeCDR!�XPre-Conceptual Design R�9�� The * and E�0al Equi�+012 GeV Upgrad CEBAF � (*+ Hjlab.org/div\_dept/> @\_division/pCDR\_ c 12-1/)=�KuKQ�J��S. Su�!C�J M#�Pf�Q$�R cite~R.$�Rurl^�0url#1{\texttt!O%8{URL IprSR2 and{!\0info}[2]{#2} B!C []{S'}yZ [{mig()}] dal}�*Dnfo{note}{A. B. MiP, Zh. Eksp. Teor. Fiz���22�$71); Sov.   JETP�3�1`)72).\[{2� {Tok� WW}�@9�K �}A ; journal}{�z\�\��.} Ebf�i$volume}{42:Gpages}{�} (^year}{���teB>Delorm�,it et~al.}!F80{u� {a}}%T,lb_89_327_19&;WfJ> o>V�<~,f%��j89BV �J80}:�*E >k �����}.- b}})6� 9, Figur�$0 Giraud}}]{![91_328�[,��A>��}-|u��N>P�2�6���91b�8��!�j�F680Q�92_265���5�5~92ZE2u��/80r/Alb�oe6.:�*A Eric� and Mol*%iU�2_153�n�a�*/i:�V�M>� ���BH����6���b�153Z�n�1�F�2ζ(npa_379_429!�S�^f�����%�j.\#j} A379:��429R�2r�Comfor�.�1�� rc_23_185�31�� J.~R�.> c�� \ Cj23V�R1rT5 ucciB�94)$l_73_3516_d4� T.~N>e}� ��5�j�)���� N� 7!�+M1�N94rWakas"�H"� 9 c_59_317� �$A j�T>. _�-n-5ZA�R9rBer2F+3:� )��Frankfu6and\*ikman��sci�L_259_77���'zF G.~F>` o:V�L>��?U�� YMVQBSt�!�ն�n�^�77R�93v�C2j�!5a��~593_29� #�V� G.~EB�a��. \ Aj59a�a��m�29�(y 95riz:h!� $69_054609_��:� a�2�n6Z� �F��n� �::� $$, Ichimura!�aa�aka� F(_ex_0411055�9Z5�V�By�� B} ����� �j Orih*7O�>82Iel_49_131o�� B� `�d�S4Aj9�my�Ff19z� HosonJ; uz30_74l8�wK>w ^�nw30�'��-74Ra8�ad.A#$nim_a482_7���#�a&a���+0rum.\ Methods� ]s����^� �2.� 1)V�v� Fuji.�RuM� )*22_48��� B<b�<�-%-2�Be48R�z� Kawabat>�,"}]-.59_171�߆� BYb�.�. B.171F��r�K{U}�allfit��J� "* F�,�� compb: cod�sc h .��..�(jk�/ALLFIT/ 8.htmlr�A5>�}]{said�� R.~A>�Q��b� ��gwdac� .gwu�)r�Ham>�199k rc_41_273� 0��SB=am���� 41: ��F��r�8Ajzenberg-Selov�\� 375_1�PF> BZ6�"� ��%j� A375:C �J��ARay�e� dwba�.urV) B8 D6�b� f0, NEA 1209/05�-99n� Auer�Y ! ����A� 65_024322����B`>��ᗑ�VBJ� �65�%���vz�6Z� �F��r�Boh�# Mottelson�6�bohr_m~ Ba\�AB��)E emph&stitle}e5j*se;}.pN3r}�%jamin,�: York.P �6v��e�VL�&�A�31_48� �� MJ3 ]�B W.~G�7.@�)=Q�Ƃ3Zh48V� v+�:OA��S!Fa�64316���N .N �i��.�IX�r�!higash>;r 5 3_04H�i B� f>f�*7* �36Z^ �RvU GiaG!Thieu��83% lb_126_42�.$Q�V� N.~V>&]>��PJN �vu%fG!126Z42V�v�Mahaux�;Sartor%B8!B�481_38%B8��C>� ]�AR>M �Z?�" 48Z�38V?8r�Machleid> 1Y?6L!+�HM�cand EGcr� pr_1�O 7�pB#c:&V�B �L"r ��B���u|F2pau^�1.f r� 7r�Dickho&&="�6�15����5�.Xd>��D.Db�15R��Nc)  fd)"�`tem{texono} Home Page at +hepmail`siZc$.tw/$\sim$ =/7 Nstart} �A ChdH / Le�0H.T. Wa29:� �* B} (x@s+ppl.) 6�;�Z1�:!� nA on N4[ino�+ics \& A�3 }, ]F�a4von Feilitzsch��$N. Schmitzj�:�11 B]ro%Q s} H1��7, �art2!;1�UY5�pr�= L~AC�J.~Li, 4S!Fgh�J2G=��C61EM9gA�gsoDCC2Sx2��w1 M.~�,~547� e2Tnaicdm� BernabeYPI��E�B 4�J2�A0),BS����r�K�n�D�hZ �QM�]i B 53�-"BmGlepsd1YY �(/0307002, 2�7r���2�kim��JAbm�vG 45EK71FWamsradio��~ElmorJF�APhQ:ps,XG7@34!54�E K5ciaea� S. Jfc�rTB bk28]KA�\\�B9�361e,4.�\Spring8} T. Nakano, LEPSђ)�IJEEA 6tA71&�LR �  i- ref.B5,} W. Gl\"ock/ H. W�Nl ae; H\"ub�;H� mada&:F�-J. Gola�l�5M�2761� 6) 1680kistryn} St.K -�: ��& �CUA�3) 054002$j,kievsky} A.K �OVivia]>S.Rosati2A%ICR[$1) 024002;J�bZL.Marc�'N\�1\4)4W01r\- I�5ME!G8) 3085*2!{g!{ elek�7)� {\eqw�R.MBN5) 1638.N%�.pdc.} ZS� ZI���8!0-�2�8muon} R.Skibi\'*FuJXn�9) 236'lskib2b} .IR,- J, KE� H,U� u( W, Nogga A�T.����Q~1.3{3�{�{2. *Cv] fun} �0C:�9>�B=�C.��m} W.X�2y�Y�f!0)�E2�B pisab?qs�ummw E�C.�4trento} V.Efro0M.Leid0=n, G.Or�F�<$E.Tomusiak��B��:�26B�� e$.benchmark1<J,�Fn70Q2) 362�@hannover} L.P. Yu DE�.K��!2) ��N A.DeltuvxNI.[�w.J� .ele�>Oc&,-th/0406065,�2�EAV� Re7W6 G 2 GIi`gR6B".�6�urbana}�7S. Pudli�t V.�Pandhari6:e,���>�1J�4Steven C. Piep����6�^<F�%��a 1722h�J�y.V�� , H.�xW.��, Acta hPol� B�bh6A]sagara�k AkiyoUf��f�n06�pickara� A!fL3>* 37. %�!�KarwownwJ. D.�%�R.rl� Hugi�@u "�H)�Cupps%Fatyg�<A Lach cy�c^c,1} E.Epelbau�:.�50LJ�G.�A.M Y2} T-Ayark, D-P_:n�Rho, 2?��[g!�6) 515.Aw V� eR�z10}�H?:�4g:�dn�~E�VtU.� \newb�xP�~ �lhy �-R4�M` ), a%{H003276�{LCITATION = ASTRO-PH ;%.NQL�bmer�nx�N~MItt��\rakash2�w� E8%>5 �2f`6�223� ^�6� Dean�2zxF A�ea2?�A,jorth-Jensen.���*Z��l6)^3),Y_210033:6NUCL-TH 6�O'Hara��GM. �D~L. HfAh~E. GehmR. Grana�큸�B. 2c])/ �29I 21j|�y@ Gupt�S�bp�&J ~�;bW_7�3."-{Rhq�3~AA�ga D.~� 2s�\��q 2304#c6eBourdegT.~  B�Ze��DmA6e!| �M6�=�S�49�Ke1�n��EeA� 01kc(R)56�8Friedman:1981qw�~kV�6] Nucl2KA3� 5�TJ}�NUPHA,&,50:a�n% wme� ��~Moral�J.�A�6��D� $ Ravenhall.�>025&�}�3!�1^� 6�Wei &:1990rz%�dF�]�B2�28}kE2�PHLTA,& ,2886uѨu 8na}.c�[~G����FrzFAE�m &�}��F�644�C99='98090H 2��� 6��S!�0fx%$R.Xn1\U4 Bedaque�C. �PD)����F Savage.cэ"� 008064^� >���2mn�DF�}2d=@EW��-J>32}, 339�2=M0203055^� 6� Kais�/1jx�e~ ��Fri(6)+WE�s2' ��l�297�'f�}10505� 6�͙ 6�MudA�9cpy M. M{\"u}�E8on �RekY�b] ��T��|m044320%Q�1�99�M8ZQ 6�Le%�4si��L�|B� rasoy)K\U�ff> y8B�7��h��4.O40207>�q9 6� cA�3vy�-We�� D.~Bg�}.���q92%��%4��lat�801>� HEP-LAT XJ1:� Wingat)8��M.~ .�AQ2i 4090�R2Qi 6Lus� ��6pf�~LEO.mCozx. Math2�10��1�h8z[2CM��105,15:g ��3dav�AP uoI0n�� 9{�a>�5 6Duane!7de��j D. K:Ndy,A��endleton ��Q owet2H I1],B19!22�k� :N͝195,2>Lia�7raY-A. L�%C�Ko.�J�:Q-�� 9701�L2�q= 6) �px�u{M��)�[u6�IntQ >� E�'1�h986�701>��6�q�4rq.�,!����ZtqU��040804b?  R�!2�ZZ 6�UKUK>�I enquvI$[1]{``#1''f�K��J�J"� [va lA�3)]{VanKlA�3ee} "Tw~L�.D.� sis,�_e�gy�!$Texas, Ausނ USA�3)@ uMI-94-016)i��?�6)]{v�6rm:�, Fri�� 'Snd� p, \1-� ��%B37� 16�U#1:�wR�8:�7fuB� B6��酎Z*texn@� 4386--438�Z92{N[E��(Mei{\ss}ner�9)]26 9zn} 1#a�6!�-G:�>�B�Q 287--2�j6S[Walzl �a� 1)]{��0cx} �,>�~��6�)��=2�A69�a663--6���*�[E XU�1%A�9zr} � Q51! F�=�C6 d6w4>u �I�aRq!3yv>:{Pay? Gih!%Co��S-N�4(MM40a~$y���4:YK]�4caz� Rentmeest+M.�IoTi�w mans��?�}�a .V` 4{� :�.�Q6.�. �>xf> N!_Palom�DE.��04070��Ab}}2Arg>AF�:�2�3.�[BG!rd�md]�B��A�5dp} &S�O , N-�N)�F2yE193--348u�RG[Fette�'dA� !�1ca{-��2����709a�B %�&(z!6��!77ii} a���8� 6yF0c 403--4\'�)Y<>�!6�8k��奄 Gloe� W��21�A63� 07--13KY�cN7 � b�T2'+okubo} ~O ,�)guUR�t����6�� 1954*�! {LS8ZDaBvidenci�C.�[ ShakU��q�[3��9�"464); K. Suzuki)�.Y.l+R�v�209�"8�%Bj5:i82Bv R. OkamotVx��4;1�1*�+UMOA} ����b � ����9A104%B6�#Ptr6�m( Navr\'atil�9P. Va�lW�O��oend� 6��)���i85�8E�72amőU{c12lett{ | | n�n�� 5728�_�.l�hC��! 0543�D=�*c"F$e. af+='Q����npn�.mB.~Mih�f�� ~C.~6�~B�^%a�& y News�1i No. 1, iflzavr!��F:M�oMcBb��5�R57�&�(&�p��shJ. Elli�mE. Os��E]*��4 7W�.) {arg#�n#n*�~G�?�EbRv�)@�Ci�"�f; >7B.�5�Sn ��B�&)�>oJ�6}��*7)Bv!ASQJ� 6�Z70c�z98FCI J�BAnnu.)D��&h 51, �>"bon-% " 4,�/ Sammarruc�BY.P�gE& cC>" -�A� R148I�6F� !pF[nh9'� 6�m8� EЩU��%'E.�(�M2^Q��z��%u2�marsden�b!�� �.r�"A.~` ~B�~NKy��#0� �j5�GFMC3NI}.��d�+�q��R6pV�?"  �Z�.Ihayes)CAe Hށ��z)~y2� 5R901Ո2R1�1MP1@ bH�y �T.~� .~Ku���6iAe��j�-��threecl]dYW "J6^8�15�24m#n*� W it{>`8harmonic oscillA��h.�rn � ics; f�oatoms7"R� s} (GordoMHre�eNew Yo "1]?� MFDM)5�E� � Many-FermWsDynam�34Code}, Iowa St��?revN � 9�%:DEcacibid.uv 4) (*or.�,brucefest} I� etcu|�y"6ACe�ҕm% 29.Fh E [�h��&9072]=-e2exp}��>FC6��bf{A49 Ef�u� enge�}{�. �2�!��22%}��G�s4= .� {varsh}D%V al��h� N.~Moskal�k!V.o�Kherso�*iY�Quantum�b��,of Angular M�~ } (W3v�!3vS�pore, 1�, |6leN� ov� &� {hqs}�5I��M.�#�� � B232EX89)<92;�?Arem{,i�2�Ed)��*�{hqet�& Geor&.R >40p90) 442>Be�iC �"� dA�� ��V '� �3-J)YCUKQCD1}  "6"O�, �n Booth'� b �7)+a�462� C;wlf`5 D5 75) 5067:a<�� B}63Ѩ 29.S �,2} U. Agliet/GO��ellC C�7Sachrajd�) `�B32�:�V) 85; LAllouc. F�44 8 5) 46t( Sh00h HAJE�H�tsufure)[�D54�E�6)C28;� Co Bn :6>�  �5[-9�HQET2)Ne�)*�5p.? 24�(!�25�g6@$} A.F. Fal�M.FM":4U�eK 82; J12�3s9-�4;A�G{$oziŗ NAE�)5 �7) 272;.n , Ser. DirectJ�i H1 G8�/9;�>Ca�2i %�F�2� �6) 376.@�.Z�P.MF`53�!8)'._QCD=�m Jenki�A.VAgG� f�� M�=84�B1%�4556euR.B!�ins��M\N.�_�iZ\=� $6a�8;2��Sco4T.eYB�X)�3 �89) 799� D� or5 �.� :��2782�LFQM}a�HogaawM�# dzik�+Z2�p3�94A�427; H.Nho�R�5�%�B46-�9) 46;0ypSumRul6S�ri�)`D �B32M��197l de�9aeJ. Tar\'� B=J5 �4A�2(Exp1} BELLE>(K. Ab&�; U� B52@F� 247� Exp2} CLE�<�}Jo0 Alex��с� �  n007052.fKS 3} DELPHI>�J�dallah,�u1�J)A C3@Ys ) 21!� Al91e� Albaja2�,R7�540�}=9�pdg� S. Eide�j��6O-�5� �4)2fvHBF���B� B58A: �6�"f HB-L�,ceZ'KF�"ch.[�8) 69486�61 ��� , 36A62� �2�ZGottlieb�.SA�mhanka��FM�A]�A11�E� ) 64& .NCz/�TcA.�/6��-[i�396ءM3) �%.R��b� K=A49O4)�=2�1HB-��BHoldom�� Su5�Y4� J. Mureik*�6b�A�3��.�SR2�d6� O.�Yakov >] B2N�X2� 1. %;� D}G)u�<M.1ang�$C. Liu, %JR38ML�V9�6�3 S��rN��Carvalh eFN<�ra%'Nieګ�8Ferrei�;H�>DoschF:7D��0A$ .�LC�-J�)=l��72� �!�BSE� A. Ivan�q�� Lyub&���:. K\"orn=�aG. Kro~2ns3a�B =niga�6N%Kr\"am�[42� M� J!H���?�%�͓ Rusetsk6�aQ0 a�!) 074 ( �SHB-NR�*hakraver�� T. D+,B. Dutta-Roy�*gٲ A1� 7) 195;VQ�.Q�ͬ o0>�.!Yf� A1+ �9s76� ChPTA TanakaNm3) 496B|�F.A�dar" S. SimulR�B�K�� 2�H:�]�.!�8�� 3ByA66�b0) 936�HB-SR1LPt e' Liu%YHa�S[GJ�8�0V03� Q�SN�&�Y:Qa8g.5�u�1�o3;E=GI/5V=Z �O1%�.�Th�DunietzV��28) 090�.� HB�>2� H. Shih��"�HN!7JX61%(��002>Fa@2��ppelՇ)).2TA02u=��-IWBzSW{B$B34� 1� 6; H�9z.93;h@M��/ Rob�d�Z. Ryzak6k�_ B331�9�Lu9 {��uk}B-2%��4472UGe?Æ� Y�� ]45�!�P`-C.L1�>T9�  �5% ;Y� �XACG��Cac�(Fk4�#72�Al� C ertmEJ!2Amaro�ZHern\'� znJ.�yvesaCBlA7� 32@#{si96���hestre-Brac, Few-Body System�f�� �A.Ib�B�E�6^��� phV$80�Htgiu;ei���a 89N?2-<^�.� 94� N>41�978�9WBD�Q9H,. Bhaduri, LaC]�Y�M gami[ovo Cim�A9p�6C.�S�.� FV99�?Zvlanco,<F:(A. ValcarceF �B%�9) ..`S���Suganum�  SasakH. "r�&�7�IB4�=EY0�t9ZG���Gutbro� I.��twa"E =�136B}�84) 412�FabreXM�0bre de la Rip֖F� 205�O� 9�� Ru752 � \'ujw ��sS��GlashowFUD�p7�D_F�9��9� StrauA�e����i�G ) 20�enF��� vs\�P sep -2pt �DPM�\D."���~Pr*� %``DiB�B{tio�P rel;virI}Com��.��'' 2F��\$pt.}\ {37e� 99.6�1�2 >21212:1 Grab�5D��sXL.~Tif��Ge�Tmov-Drell-Hearn sum ru��PsF�"�[*>*eon�BS6059;6��10�B5b2s (lso contrib����ec�Po�abmayt>D�.pwPD��tR �) Cabibbo�Ltia�\PLB { ��1Uz 412mDiV01� �@icu� R. Ve^ @ { 5Z!�1>.�PHV04} $@scaluts��~��o�Vi<:E�AT A de �S�v�!��{ 6�  ��%�257313]ZW4�2�KuM4~���U.�$Mei\ss D�Low e��analysi%�]4 È magnetic G"�'' \NPA�jg�# 69�8:�^6^� ę�Zan!��".~Zano�S�8inepalli��&L����W�Lam �J$ZcU�El��R�, with FLIC fi s�e�X Kt$\ Proc.\ S��12�%�3 =u8~ 29Nv8 :Bab98�# Babusci�G Giorda��ton�8PRCA�A)2�*98)�A&Q"Pas{o%2�E% O.~Scholt�A %``O��BQ��N .Ga ex:J1%"the % )$(1232) reg�~��below!`%MH5�:5) 65AH%FX?591,65:�:PaT�,2�%�> iz��a�a�� teracting�3 -3/2 fiel��a �isobar� \PRD!Y!��096M:�9802288N�PH,>!�2�%R��"!1!�F�t8-y���_#higher-��$baryon traT�� �A .Y4$�.�O(-th/9905065>�� �y�PP:/�n9 �akP%``Effec��5bMinN>�Z*���M�6��o�2^� 2120�t:!�:5^:3G�W%``��e�I-�E/ �A�V=:~��#K:�l> %u9vGH�!c(.~Hildebran����iessh��TɿEt�B&" E`Signa����cH dY% in l�"F�1� %=��Eur�"�\ J�A {;�[ RUA�F�_�tFOq{A��S70^� %S�+pre 3)+��VK  �:�! >ar�\.Oal��ope#"g#N.~�@%� �B.� \NPB\ 37f* 2) 346; ��et�2� %l7} A 35�6) 352� Lvov�v(A.~I.~L'vovEA * looksauM p�rb� ory:� eoB@ %polarizabilitie��$LB { 304} �� >$ `=304,2�5�Geg��D�ege?��-aparidzB X.~Q�U�Is heavy�Happroach necessary?�!%?t�A�} G {�{� 2303�'� KA 260]:3� A^T.~Fuch{�~f���chere� Renormalݬ� vis{ ��f�IW(power %coun���ͽ2�67�2{ ��E11�BN� v� 2��� % S__macrosE�"��~ A���"��:_og� al use \JL :j��s_L2L\andvol : Vol (Year)�_F [inъ dualG  \AJ :&7^�\NC a:�>NN>nn�^E�0 �A�&� $[A,B] ECMPNB\P,�o "QL��.EIJMP :a�.h\PRA -EE[A-E]"1JHEIN��' \PRL�I� �� :D.�B \PRP Dp>>"6.\PT!:� >�6�PSJ K)�Soc. Jpn� KS/Ea��*1�  % UsageE�a� {45,�,345}= ==> h+�\"�+D&x �E345�\JL{N�,418,# ,123NG B4�R��2)�\3BI�{B123�5,��AB6,�5<020�� ��bm�m���"�l%E�ear�u-�0Vol. II} (Ben&�l V.7�:�Dre1��nr�-�Wit�m< NPA{W 19�C65}*f-fr�M�nэ4%,J.~Krumlinde� ~Le+�0Z.~Syma\'{n}s�Gc 361, ,147.c -C~Skw�/47!�87,40..w1�E�urr>�a`{7E_5,4062:2r:!632! 8,22sp5Cw3�~M.~C�H2b$!BPRC{60;9,064301.ysmptp�_Ihimiz9K��tsuyanag�-PTP{7H83,144.Em;� MO.!��33!X 79,46�ma2,LRf rsha32%#77,n=�br]\~Bengt!�%� I.~Ragnar��A{436!�5,12�dFG.~� ac��F�KondevRP%K Walk&2�� {419!?8,2 fnsw�F$Frauendorf930~Neerg{\aa}rdx9�� heik�d>`!�1�%0%�22�ba�_:�S.~{\AA}�s, �17A86,27�VI]�vNg���b%*, {BBH86}Ga���C ��ul�\H&-b{c�] ��A4R\1�NIIu {RR88}�� Rolf�Y Rodne?3�E,dblleft Caul�8 Cosmosk)riū�ۓ̯*^  {BC92}�6�L.F.Cant���K��A540,} 3�:�6T BK92r+D*KalasN&^9/55b5G�6��8 {Iek93}K. Ieki� it{\���a& �=73+�5=�BB93}G>.! �g!%�6 z 3556,}�� 93);:7e�.[��GC49,} 28�=94)�+ Esb#U2ARR�QU A581�K7��6�Ra74}Gn Rawi��D=?GC�2��46FSYK86}�1 akur�} M. YU0r�6J amim|�J� �n�13�>+NT98}�b Nune�I�b�Up�ON��R28�d�ђ U9�U%6Q�2;� {AC79}L  ArnoB#Cl�X �� �B8�=�?7>Ql%�J!Al-Khali�$J.A.TostevYJa^B�� EhQC58R � �<= EB99}HYvEhb� R9}, 324iV:�BCG03�b.FC�Campb���TcasmeZ� putQ�� Q�1R*8>�Vri87� De V��%Wm'JaS�C At.FlAT cl. RlTҥ&�> 36},� !68:6BBML77���#�6Jj4rysowiczW McMan�"�WALov_7>�2E3ؾW>�RaEZ R&L%�C 20,�%�>?Sag04!Sagawa, ~M� {EB022���6��5�A70!-3�<M 6.Ro7���v%:�/1�C7L�4�72;= EB96Λ$,*!��-.UBe��>W�A3|^2�l>�K {Dav01}�)s�R5��=658�16,Kik97}T�g kuchV�"MB3f<2�f>�G9cL!�"� M. G�,R�6E�2�:5Sch03}F�2h\"umanOf2�6�7:2�"EB�02Fs>��:E��C�$ 0246�>:vEBSI�Q�JP K. SXbZA� to2�c.V� I6f�32f�OP�.�m��m��m��m��m��m��m��m�6�vKunihM E�it{�M}.`x9>Ǝ-, Mut[0Tak�-TamagaG�� Tm�k eH93:_various_phases_#_ear_m��_&�_{ts�]wF<| l}Ln nfo{V\wB>��:5 �?Bx1>��wB�5~m*5^}{b}I bf{5$volume}{11���K1Un�wz��5/A.U�w�*yn�.�UVU2?��~�&r;yWamc��� ,$, Ainswort��C $Pines}}]{w O!�quasip��BZ� f�T6R:G��B2�zY�VD>�| �V�*�j A55Zԃ^#��wX��),�  4av{\'{e�4and Kh�!� chen!�paVI��4�.%{o9wjG J.~WB=��>R�)�5��Ca�~�V.'�m�:1"N�.�8�T!��-���5�5.��$Elgar{\o}ys:�6:JT6�?,Evik, :�f kLAeq,oey96:_tripl� {\O}>Ex9�%%V�LB@n��<B��2�C5�E>�- aV5õ�.i�N A607�%M42�2XU6��B�!r-:Barnea�,�b $98:_s_lamb�ԌB� `�*N>O �ZP*e CjQ5^O0Vj8r" �+� � %G<�&s9:s)M_h�2_admix*� _coreʡ ��l��jt10^� 04aF�9zvnii7.��"6�T -a�M> zO nba��t $$03:_possib1� artr_bogo��J. �:�V�B��?��B�Ch�!5q���>68�.� 0158�.>�!�r�Glenden��}!�e�g$00:_compac�� k&A�.s.e)emJ4��'actKMrs}.��p&0��y er-Verlag O� (address}{Ne�.��6:})��ed-�}{2��2�[{6�Bodme��9��b 91:_1%_mean_�)_�)% i��A_}EUg n6�U3���D6B��70V�z�mucɦ�g92-��B O.��Z"�j�A34��%8. 387}>U)�~r�5Кa~�ok�J��sug94��Y>B^�%B��6�5>�^}�5�DF?4v?ero�+WaleckI*7�s97!<ce�� K�!�.H^�<JJ� �ZBFQj�E6:Gme5|K�E�U�7rGHorowiy+�?iekare���{h $01:.�31 radiu�� C.~J�.k��n}~2O.�Zo�L#(jm8^m64J`4rnCarrier�&z�-, 1#�с.2�]{c V�low_mass-�_equa�2B|�:HV�v��2�f ��PR��B�2�UE�2@vj�b�4rC�iI��Lalazis_6�.�*\:� /�K{\"{o}}\F%� Ring� lV�� new_lagra��G.Fu�t��B}�A"C!�%�%�V�P>� �!5p5�}�r� ZL5K9W)�!�r�Ma�� 8� ���89:_m�т}Be WZ�Adv�Dj�19:E�18R�8vb "!N�89:�.!��I�]{a!/N4_i�6_�.g_gaps���D��jnB� � 2���� I�~`B2��.}1�7R4 z�SchulzJ` 6b ,, Cugnon�Lejeu�i Bald�<ombardo��s _96a dium��H.-B� y:�V2B� ��<A>n ߒ=B�%�;UB�5U!w��:��>� �96r�ŷrm{Jam;SM���}A��:�1:Q$RA, Peth�Krm��appa} ~��EPawela�Haf(�l �d�V_urca_��2�Z�u�eF��N� �j@B~Ma6�]BN)19/%k_ :Y�"~^6Z� 27N19z��P)�.K7 :K-�kminke�RGnediWe]yNQ"� Z�f54B�pj�>BXB*��>O>  ֲ��BR 5vpnb354:�ѕ.+R !�rW"�a�29(;.� 04:_8@�!emi6� ��J�kahtsuka}} \bibnamefont{and} 0info{author}{%f& R.}~(Tamagaki}},.>�journal}{Prog. Theor. Phys.} \textbf{Il(volume}{112:H,pages}{37} (/8year}{2004}). $tem[{\cite�@suruta}(1998)}]{t �98:_therm_proper_and_detec_of_% neutr_stars} ]fSB d:�9! Repn29Z1F�rMurray)t@it{et~al}.}(2002)61 +, Slane!�XSeward, and Ransom}}]{mR$02:_discov!6,x_ray_pulsat�5~S!. |:7V� P.~O>?��> F.~DB>�?UCa~S.~M.q;:1/,?UAstropE J :^ 568}.Cm226F !�r %$� *, HelfanI 1�]{sA!A0new_const_on_y8��� D.~J>� ���S)�R���71N�L45��Horowitza�4 Piekarewiczm� }]{h $!�)� urca��CNV K�-J>.�^0eRev. Cj*66:Am055803�YFlowersF 1976:( ,$, Ruderman�,and Su�Xl�6 }]{f S76:mLpair_emiss_from_fini�.E>F :V,M>=�Q����.�VPP>P.�!aA�0Z�)abJ�205:�-�54R�76r�,Voskresensky!�, Senatorov87a,v&887:_descr_keldy�1 D.~N>�.v}1P2d9"Vb A.~VF��.5d,Sov. J. Nuclg !�^X4!k�-i41Ri87ri TakaR -f" x %et"497:_nucleon_su{ �4_core�tT>�~֣�� v� 97V�3N�199vi$Elgar{\o}y1�.� D1996{\natexlab{b}}:�?T, Engvik, Hjorth-Jense��Osnes��eqHoey96:_model_s_bonn�� {\O}>�:VLB@��<B�2�C��B�-'V�.�f� A604��7q�6J� !�}:�j 9r�0c�0:0e��)�)�)�)�)*� Lett�P^�7ZN 1428F�>-!�j-Kubis��$ Kutschera��k��a��B_֣B��Z})T~O B399:Bm}19R9��tend{thebibliography}�\beginB {99}&�P{balantekin98} A.B. B%�,N. Takigawa, Mod. �0{\bf 70}, 77 ��8.�0{caldeira8183^ O. C \0A.J. Leggett,�c %. ^L46}, 211 91981); AnnU (N.Y.) (8149}, 374 (19832�HFZ99} V.V. Flambaum�(V.G. Zelevi� , �)� �83[108�92\ yuki!<H. Yuki,� Kasagi, A`0Lipson, T. Oh�i hBaba, T. Noda, B.F. Lyakhov�lN. Asami, Pis'ma Zh. Eksp. T�Fiz �68!�85�8) [JETP �)!823 !]}{L{altshuler01} B.L. A,64H, M.Yu. Kuchiev andFCJ1�G {27!� 345 �12<FKN�2e. B S$61}, R7869T02T(zakhariev64� N. Z%�SSokol!iEM6�14�29!,642\BM2A� Bohr!�$ Mottelson� �ear structure, vol. 2 (Benjamin, New York, 19742\,rodning82} N!�R (, L.D. KnutEFWES ynchE& Ma�Tsang2*.Aa90�822ts% uk97� A. S %*V6i�  C)�55a02!*97VZ9ZXAQ2qUC(Neudatchin,�\j j6�c01460I�e� R�)f�*Pov: hep-ph/0410324 v3O KlayI� �s.a�PThesis, University of� Tifornia, Davis DissertE�, 2001,�3 27; m끠ear.ucd3.edu/i�Djklay/CV/JLK$\_$cve�� Afanasiev��V. -rRBJ�M%2)054902dBack2`��5%�0) 316�nticic1}5 �� :?�N) nf-10.) �C51A\384� 95),] $th/9501013.m nlb�n}2B34� E�Jn4.nDas�%I ug} .�%PJ.-c. P5R�%�C513i?962�12028:� NUCL-TH 9 6�2�ff6�?!��JM.~B. � r�%820%�2�609066^� 6�Kuo%0(qt} T.~T.~S�o� ~Ray�Shamanna �R�2S2�^�E5 Q�2.50D 2�9K6�Ray�7S^�2�BF2[9�'i��g�E�608j� 6�M�8ua��� Mr�H183I�8.'711003^� 6� Borg!(8in�, I1 Mishust�J J.~P�ndorfv.47��1)�9.�809079^� 6�Qian:3!$kj} W.~L. �R.-K.:]K2s021000^� 6s�te� {\em �#.}.�Sci[ )�30�7O2006kO'Hara XK� e? L. HemmerK~E. Gehm$R. GranadeiSJThomasb�29��217 6�[�3Œ.l�a6z6�ME2&>�>Ac 011401(R)%�6Bourdel �T.~ buc}�9�o 0204xBKinastd4E� %b�M%]!!�~Tu:��.�2��5�6� Rega�4} C.�%�G� A uD�fJ�R�>r 0404�D20:rWeinbei�0rzE�.H)]WB2��28�U2�PHLTA,&,28:La�e1umbu*�iKB36�[�D0 2sNUPHA,$,:� Kapl�6xuP B. %\ avagmM�H Wise.F�47aP6]:H50G :���66a �!8tgޤF�42��39��28�4fx 10346� Epel�na} E.~�~G� lee' KrugQ� U.-G� issA�]�BVA64��4^*8j�908:�Beanea�0fxEhR. , P.~F daque�C. Haxt~D.*Phillips�dMd% M)�aV0.^00806^� 6YB ��2mn} 2�e�,U.~van Kolck.}� -J art.��m3� 33��&@ 0203055Z� 6�� !�9cpi {\"u}� �7/oon!R.~Se���^�I���� 0443� 202Z99�^� 6�Le%V4sieTLee�Borasoy)�� cha.[B��014007%�4.O402072^O V�qd�%*Z�! 6q1�bqRq3mbqM t I.~CeIpL"RU-��� 0640�P3.30805b� :�us  6pf|LER.�Commun�h2�10�115�2vCM�105,15:� au3davAg rrenoI3n !lat/03!�> HEP-LAT )Nq vrH\expandafter\ifx\cs# urlQ \relaxH"FC {URL Ipprovidecommand{\eprint}[2][]{u {#2}.# VogtUR.~ &�pt."v#31= 9f 6FSatz00�� ,�/�r�0i�\�!7 1511eG� "�rapgra� R.~Rappe�L.~a dchamp�:RG�S3�BV karP$D.~KharzeeLK< �����A73A�248�6 djo (M.~Djordjev $M.~Gyulass��S� cks C, -�{A��72}.�ASW\,N.~Armesto, ~ SalgadM�U� Wiede�9� v. D�69�!� �!6�bralE� ,Bratkovskaya� assi�,H.~St{\"o}ckEN.~Xu� �y04090472� Bats!�S.~ ouliŨ y� 6AJ�Nag�)�� 1�B5m 26%d6� GKR�VA>ec)I M. K-DMb1<>Z9E� 68phenix-e^S. �{ V'f�1186c star aF.~Laue` STAR:q5�6�$r6�SZ�,E.~V. Shurya4I.~Zahed1C5l�q219&%6� BLRSZG� BrownA�-H=e%�Rh-|E.~ {^4�l71 �.%ShakinAKX.~Li,A�C� �Q.~Su6 �a  06520VgD0e , F.~Kars� (P.~Petreczkm�(I.~Wetzorke6�,Proc. Suppl.a,� 11�4�B Umed|T.~ ,��Nomur� H.~M0,furm�W.c��2A32��f 4b} :[u' 2�iE6*F 2123ZEThews01}��L.iwsE Schroedt�S J.~Rafels� o=�q�5Mx�>Ko!�B.~ZhU"Ia�B.-A. A# Z.-W M SLlZ�65�@ri�6�pbm��DP.~Braun-Munzinger%?J�7\_69B49E�D\ .�Goren!6M.~I. ste���� styuz,g:�W��i� -J{]{B50A|2�&�2})�32�i�>b��206179Na2:`%UcN&c/�eA7�41s%6o SvetPB.~ itsay]*��3�24�:5com79}FL.� bridge6�q�B1Z4W76�MT!$��3 staf�M�)6� .�!631116826MSa2P,�PA�a��,. Srivastava1�e�y'� 889a$�8).Y Chen��Le[q+ �� �2�5:�olL D.~Molnarn>100412�AH-@Asakaw)=T�tsuY(V"2FA'6�KLR����a]4n �!�in R. d w@X.-N. Wang (eds.)V`Quark-Gluon Plasma III, WB$ Singapore�!? p. 1D1G� ��3 2 GK92}�Oa�ttfried���. Kleva�)P� e�Y�28�221D65Blascha�D.~ ��G.~Burau�)~Barnes,�Kalin ���w�:n�81%07�q'1�4�#6� r!�ZY� >wVYudicheI)H .�<�4�P�4��182%�6�ebert94kE � Feld? R edri��al,H.~Reinhardt2 rB43�6]52iram89> Ramo�94\emph{{Field} �f�Rory:} {A} {Modern} {Primer}} (Addison-Wesley, Redwood City, Calif.), 2nd ed. (1986�georgi H.~G `, Boulder TASI 91 589--63�12�pythia�� jostr�:(L.~Lonnblad� MreR�,�Wp� ,U-Z � 3\ 6rg� -p��te}*�  � unic�#.� Rapp��aI�:&D86~kolbrapA�� KolbEzV�p 0449h 6~levA|P.~Leva!�.~.�Ap��^���33� 1>.�a�%��S.~S."�%~al^� � ������3 0902��NIf40*�*$IA87} F. I l� 4A. Arima, {\ita�p4eracting BosonG"el} (Ca� *�%Press, , 1�8<. \vspace*{-1mm�Jolie02�( r Cejnar,� F�/K#A� Heinze, 3 nnc!�V. Wer*X E^���89}�2) 1825wb� Warn�D�y UNa- K420L 6!bI SS72%j'te�'R.im���OJ( A �0$(1972) 257jC�r  P.00)��).}2�= 90} c 3) 15z!�u<P9�}�6U%gU12501j�I�!�6�N.!�Zamfirb�2 �4)� Rg�9E-Iac00:iV�8�>�  3580n� ac01�T�C�  0~gLG!eA�eviata �:(. GinocchioFI69M�3f"�BRM86}A�Bengts0$S. Frauend� eXF.$May, At.�,I�D�, Tabl�ec3!>�'AQj<EM4E� &g��e�Y{(E�4)3rW GK80�Q64�&M.>/Kir�gE�)F44}ay80) 1744j�DSIjA�*,L. Dieperink��Scholte-�.n.�/y �6yn�IC8�/�Isa&�J. Q.= 2%-F24}�4 1) 6"b� KM88�0Kuyucak�" Morr�J�4 a58 _7|*5;�� ibid6� �3�9�  77.�-DobesA�J.  \v{s}u=1B:()�5) 96;.Y f42!90) 202.p,HS95}K.\"I�Y n,��R4)E )A95) 637*�+LL�A. Lku RE /Lifshitz�ZJ*istical�ics} (Bu[(w�<���� Oxfo�F�B,q0 nUKKbook}C Kitt�A�H. Kroemam�� rmale� (W�@Frez5Company��� Chap�(10.b;SRJ� !�Shu� XG�  Ji) Y. X�u2 -�6�/3)� 3�� Heyd�%� �8R. Fis-2+De Baer�eY6 H�+maም}9ɾ�g5:}BFij"nA�2e�F��~) �16jKI78:M Chem� ]�(a61) 581; .X%�R��~8).I�7!b 1982) 304J�9qNaz��!�Kvasild$G. Nazmitd�Nm69��31304;!.8Puente, LI. Ser30%NR �BR\4) 12531.2 Longr6G.a�N�5!�1X6 3163F��H �"*W �!a�Stuchber�� . Anders�!I%sA 5q;  53.�Sam8263SF:�3RB3�l)� 36.�e DKA�y�&P.6� aroqui�G- YeM�!mb z �9wCD6x160�����;ON!�� C]� B 12Mu �U6�x f�a�& �F6od�?6j-��3�)k FJ966de��nn� E. Jacobs1w� Sheets)�7�n>��2~3lac�Jean  ho"�F .FA�� 59. Tuli� JE3.�2D� ��41.� ingh�B.�hbCA� �387�NM�fMiI\ Kretal03a�0rassnigg�SchweivW}~Kl @ %``Vector mesons�a �tiv�X point-form approach,''�1.\E�\"�9�.n! %[arXiv:=(th/0303063]^ " d bib�GoIs85� GodfrefGbIsgur�M �In A Rel� zed �.L With ChromodynamicsB�DIj3�(y1A�:�,PHRVA,D32,18:�+CaIs86�Cap]<N.� Bary!m���e28�� Z�4,$6\FeA87~P.~FeyngJ� Kisl&�$F.~Ravndal%qCua"t�1@rix Elements From=�!.�bq�=70.271^�,#�%U@FaHe68} %D.~Faima4 A.~A�endry� Harm�9 Oscill�IM For -��%�8Q�I17�172622�#I 173,$��Ca!c83�+ Carl� J�0~Kogut0V�'1d�>'#e�A.>.� Based On! ntum���?�$�J�D27,23>�lRi95�Y.~Gloz1lD'Q~Riska�,The Spectrum&8�8�eA� *ge hyperchiral R� pt.\-�2�%26�96�gEph�3 5422>f�$P�26�Gl!�`L.�, Z!�pp�JPlessasj Varg�,.~Wagenbrunn% Ligh)��bm� in a�c�Pit� -qM �HA��\��\ AI�62A�90C �?2�U,A623,90CR�6:��%�W.�� �m �C�Ayr�]w�]%�DF^\�A38��$���'1�60135B&1� R�8B��! z� Unif\�Mip�=A�l!�-%#-�-)� sE�a!�28�I5�09403�:98F�706507^� 6� KePo�B.~�eisaYW�2~Polyzou%�� ��(Hamiltonianud!�e�a�pK?7T�#Adv.\O U�I�2�22�AB�,ANUPB,20,2256�Th!��4honhaus�9%`��1U�N+$9r}+M�r'=�<4Karl-Franzens-\-t\"at�2z,�@48, unpublished� "s�8"��6$L.~Theussl$~2%�K.Ip%�B� exci=�!��@ decaysAur�a�=�4 %semi2� �/::PiN�Dsl�I�3�D9s5:"$00076,14,9:W 99JV � �H}A�e]%m\�+:�5GBE %�5>�,Few Body Sys�/5A�392=,FBSSE,10,3916�PI9�5 ��� %Y<&v �%�^6%$oldstone-b  -exc�#e����!b1,2:Th�1�#n��.Des�2que�K��a�JNE Delt� so}Z�%inK&of%.5thFern$al Symposi�n Radi+ e Corr D (RADCOR� 0) }:Ho�Z�Hab��4C� J��1: Ac)�١b- 010099>� : E&� Bo!k�1%* offi>,P.~Demetriou� �cAFR�NS � fa� 5`}f>�6" 2�G252� 99���81148b� :����%:� M� diciF|y~%'���EQ:y8Covariant axial. QA!�eon��Qz= �� %"� 16�516K783�19`E1�"8b :I%^:5W.)%�ʒ/9+el� oweak5�EJ+bD�A�DMG0108271>+ :* CoRi� %F.~Coe"0 >� Sca�!���>� kit& %aT�� 72 43�#�5�30600B� � �"�KrK�{.v G5�Y8,��* fron �. method 6��X\:R9�R� �:V� Z,90,>� Mus%T.~Mel*>��:�2� stud�F�icB3b� FvAo3�"39�Qo211356^o 6� �4d@ ���>�%�Strong �!�f %��A�alism�r� 4060q2�q- 6�� 03bJ� vKA�:cL� �L system��3coupled-� nel %.9��40'�.2��1$�PDGApS.~Eidel�_�  [PDG]EfReviewA_N� �:��.�4�02�== 592,�w� TaNo! A.~T9*�wJ�Norbu�PretieE�R2T traj%sieE �\[6j 0160q���[Q�00407BUQ� 6� AnSe� V�1~Andr5M[ Sergeenko%KvJ�/2� �Gum meA�02�991229>YB � 6�WX!`BM ��  ��%�&@ �+ �����magnetic�c") U`�� :�  %� �.�-�:Y| �j/ 4B��N 4:�B� 5l7G�+undell%G*A B.~Phelps%6��`S�) ge A %�%�ыz6d� �2�eG371OSN�10245Ze9 %�& Ri A%R~ck�"MU�D�[rtB1;Metsc�-�+�3��G�umA�a cUq6�b� 9�h-^�822b� 0�DK%�� �2�,& ,v�.�J� :�C�� a�ne uDo9 �in%��viU��) %E�&�%\href{�N www.OM .stanford�N8spires/find/hep&l?irn=5441498}{SPIRES entry} ��Prepared�H Mini-Workshop on Se�ed �mProblemE��֡�Atomicg�� Bl�6DSlovenia, 7-14 Jul1} ]��2a} %&� L.~Canto� sG�2n�i%``Thre�dy �!Y one dimen8": A test)F�as3-� ��2 %t4irreducible pi�diagraS%5��43� 2�:��CT@F�"M 6� VaSu�y�%bYb7z?Z!,Precise solu^few b!p1��stocha�v�/al�  on %c�la!�Gauss�baZ�aA28NZ5����950802B��q 6�P͉a} "-A.~"%& % Faddeev aS $confined tE%�s1^�44004%�0F�000200B� � �ZxX�nt]0} %1��HK�0 Hohe�F � KohJ ( 136}, B86bN�Z%2MKSt<HL'�LFW# 140}, A11�O196n1%3LOGK�) Oliv�],� K. U'Io4.�W q�!���i;6� 4�;6%4f FTTZ�A�y�%SM $Tolokonnik�Hv4.~TrywD_;wischa,|��.I676},E3?%5wB�  Bulgac2���<051305�I4%6CGi�OT.!e ert2eB ��21�7%e7ESTV�1 �!oubbo~L V. I�N elya�3�X. Vi\~nK3)i�K!14�U�L� 8hRSEfR0NP�# uck,10�*ar Many-� (Spr�-Verlag&�\ Inc.8%]9medm�Dobaczew�:kazlX( ~R.~�/JB- r, CChinn,�J�JY g\'eN�0 � !. %10�BMsJBlo�A�ssiah6;�%3�95K6%�1}� LiebH�) &v*Q�SWemM��H 2�6�`%1}�dG%�G.�$G�� s, S}hcond[v7WM� � Alloys^H^6�R\N$f2"#Bet56� �'Be�.M&-,7�!aryU#46,y}, John Wil_#S�[Ne&�^56;%M.c%t�V.S-W,I kopfZ+ TetZ+hA�icB,�i2,8 731.���LGam28} G. Gamow, ZeiCChys-�42� 192?Js3Flso Le�Schif �5�MA�� 4}, McGraw-Hill.w+55�1422�Som39�z$Sommerfeld)$ Atmobau u�mpektrZ0ien}, Bd. 2. =s�%4: Vieweg 1939 .�Bar80j<%y3PcM�.Z*!� L. McLerr�0)��E�D2(59�ae�*�'Gus1<S. G\"usB Je K\"u��`P| Zerw� a� b155B}, 1V�cFadcA)adi��V. KhozX]ovietw\�����4;�?1NX�{X,U�T. Sj\""�7B,C] 613 �c���Bro�'!J!�odK=A%Ho=?F( v TeubL1��)) �B35��35��9��Cha95a}!�Cl^erjA�ndE.�_2�%$�V 21��*. .�Won96d}D% �=e,�ceeding� � ness '96 � �D Budapest,�2DH6, ORNL-CTP-96-09 (~960731iN"c� &V`II��20���=�7~�Z27C7�� 52)�7 89g Yoon�)�eo� &a2d� "�K9CG:0F34I%e Tka#/Ko"#`S�B� 4a�4.qS� Sch79&��w帍`;Mic�3Source�6=;��B;.�7�= Vol.�=O0s 4�56@Bay5$G. Bay\g Pa2�A,2�A61�"86) 286c-296c %� Cra8�*%H 4Cra�" P. Van Al�Ue,4NI+6h�5kI�&:^�62]' Be�0-�c��-t o�D %!� D�h51�19B>�Pes� M�. Pesk��DB7�C�-{\sl An�2vck %��� A�<�W�< P�"� �2952�Cra$.X2�A44, V$ �#�Tod *� . Tod�r2>)3�35e�7�#C Dir6U6A�7Dirac�:nad� Math�:A�1z 50);��. Roy.i Sect" 2%��;58)�4Le�gs�-H��$ (Yeshiva $ty�?&�t �A�27]�E&6SJ. �I-!1cA 9I�2);24E���616��I�nA��s�( 53 , } 157 ���Van86��6� �R>KW D34,} 193��NV!C7}2CT6gNX6,} 3�P�6>�7.��V 7, \!9�@J1Pny Foun2�_ 24, \ }2)�94G��6bheuk-Yin�f� ) .g� )UE�e;2��E"5@2 115 7�n>�!��]�Ňi�)�H3$ E�a�$H. JalloulD"�Sazdji&c �@ B366�0� 1`- C��p) �  Intl�od.�m-E Y��589� 6�!. U4���i�;Z�n 124@�-]�Tai2Ao�m=0O809-S81�A::AdNJM@k $�A$,�SB�L, dA@ 70062�Ad)F�4 �f6QPHEB]g, S�@.  "2 � uc^D S�tr �9�.%�\)}�Z5�J&�=BJonesJ M.K.\ �\8� 139)\N .ZUdias99�8 M.\ !�Al2aba�Uo�\ Moyapu %E�%ma!< T.W4o�lyj�8��54��99)�~K,J.R.\ Vignot�19���034�g�>�LavA8 P.\  �\ Ryckeb]T0'\e�Overmeiln�=�-�N& 4071�l.=Laget/8J.-�640�U=�Wiringa� R.B.\ V G.�& Stokc !Iavilla:R-��D� 2�PudlinernB.�o^Pa.1_'"91! 6���1�.�7Af439W2o .�(Kievsky93} AY /!� vian��%{Rosati]"�'��A5�24 93)a9\O�:36J>9�q� .�V }!�!� �8W%!<�� I801I=� Nogg6T� n�-��3"[�UMarcucc"sLew, D.O!�2�!ׂ5� 30�q���oM�sA� R]��d:x�Q7��.`�!w>�K� NolT-��\.� �.8.� 2078 :}p�E6" ܡ\�i Jk`�:R�I�iu[��q1��O 0240�SB�  oineaC��-LeluceF har,bij+i>7vanOerse W.T.H.\$;��2�3"^�r.�Ya90}>!6.'�83i�Bang�=70� �� -�>ot:��:�1M� 7>`Darves72 � -BlancB[ovo C&to2���1��7�}5$Jeschonneka8�0%�rM85�24��>�Ho�p(76} G.\ H\"B�c*)�8B11�!l7�.� BrasJ;Eŀ�oz�uSh!��@Ge�Hubqf� 5100"�c>- �!* , ZZK.�Pickles�L8u\ %jJ�� Orde_:�� 2M��0=�Sch�ud>VN;�.�� Fabrocini:-�w14R�>^6sX.�6s.]�t385E��.8 ��.]B5*19^� urdano>uhR�60 �{'={MorgeaTruTN%Z�ez956�1��2���$6���A|�ŊyLu( D�GLu�6\ TsushBLAEtT�f�z� lli� A� Saito��=M�068�AP.AemGui�\G2if 9%d3�J U .gP�,��� ^N�6e� 1�X`�m% % 90f7}"4 1�@R�9BP (Holi�PWi�;>2e�E� SCh. 8, p�R25-200;, Bart}Llm�sic� inv�%d har�<o&�<potenti�TYc��%166, 32�; Z. Ahm�#Tu F,through asym=2c* abolP- riery )m A:<GenNQ97�C15-3116*A2q Fl\"ug;VP�Ncal�"u I F� Berl�W1971) vl{1�(b. No. 37, 2B37"�GE5>�G1az(Perg|RO%� Lln,1_���Cors"Feshb A�3/R+.�!�!�(.TBook C�G Ltd.&�;53)A"1650-162�C5�wN2�LA clasz,exactly solv L 1:V%-d0E�4chr\"o�er equS$, ]>1|2�Q1�q;� ahu<) K. A]xl�$C.S. S�$ry, Abov;A5*�6: AnalyC*ex� �for egz�Dwidth� %6>i,35, 4349-43512.�6�  Khar)�U.j0Sukhatme, Sca�IA�$amplitudes�;�Y�shapeinm%nt u` by �,a)C!�b�,21 L501-L508w�]7} Z.i�F��Icba%F"�D�P57, 1-5,6xY8YN�A . �6l��8 A, 47 4761-475:� o9�d Znoji:�[A"�T26�M99) 1�n>1S@"{O}. Ye\c{s}ilta ~ \c{S}imeko SevAC. Tezc�ra_�=a&sVT*�J4�v1} D. T�rclayYDuOAT ngopadhya�aAMR�6 Pag�dnta�SDKaTK<_YFK>�530�H�4 2� �2� L\'{e}�TM9UJu KJ872�F13#��K��bL��)4QO�2}U �18.�H14�'�96?�V2l >1) x�5�0"e�I�E �6tEg.BL3�� L27.�G162s=�3��w,T2<7�!BerkdC=�-TEc O& * 4101g subm�Md�(! ��!NϏA%�98�# E\u{g}rif� D. D�h�$F. B\"{u}ykk{\i}l \c{c��xSI�,�5 I 9) 9. J19�sbs6�R1i�t�2�SYasukJ[Aw5zV_�v5_ to1�!b"v� z�f�1" 5�e�95� A� ,em�7 A*�*��E�L S�+�_�/�+�$-Woods-Sax]�+,�be�Y-al�_}3A,F.22~L imse�H. EgM8Y�2�  43$s2}23}A`J�J(C. \"Onem, 5��Y�Fz4e\F. Nik ~ov�)Uva"Spec`; Func�,%R�)�&Q" (BirkB�Fl 6E25���)%�C�wen�&a�"Xa�� 7�^3)�o.726}�)Hamamatx LukyanoiX.d"Zk?�ɂ&�E�M% 1+X.FuM�4zego, "Orthogo� �CHnomials", (American2 ie�.] 3y8� Fakhr'rdeghi,�H�N% {A \bf 2�FeL 615. 2�9%Boztos�S%WA�.n 9���02461.Q30e� M. Perey,A!G JbMD�2"U J. Sil:�a+17��1xI (� *� �2M�minG a(. Jeuk�)�C� haux��33�86) 468.Vm)UV=�r5�F3!04} A1E�SRKa~T JHEP�G0NQ2SW4;: 4!f S0.�DKhgnF.�DygC% &)G !� HS8qNY)AnEttyi(�R�6  , Pe�#Koe�)RLarry~D*x(8.$!����U�W2�9-DatrP:S�}�R�c2%lH?1miyoshi f �%� e3 eV�d Koch�M�P5�`^^\"�~ �.Zg +%:Rept. d1�VA(167.�greic87 �C.Yfp���t&�f2fv��tk5LW7) "]Fk8k "gwD. Risc�bH. .j~$c�wN�3 u8)!�2�Bravi@u!DL�$ :� 19v.:'4Z&802490M� 22&)fA 6�A�2) 383.��mQ�A0�"�mv�E+�Z`eO4902�Cleymans)aJ.~%EK�bdlc�.� ^.�]82�RAHMS_PR�WA I.~G av�����o �S0�.e5l `E"�l �N� �LI�O� 6<Hof�c7��J.~ ,I�\"oN'W.~Schei��Q� {aEortD w*�6BeV � on c"b�*heavy iN- how%�why>-�0ounta#�0Nov. 29 - Dec^f?4�gBNL-AUI �1� �76)2f�U�<�`]8^�:=�3i[76) 82L�Z �LB�M]f�Z^{ Fluid&��k �i2�9 19592%t%��i���\1�.J.~�'ar" .W��<xf�.F^�[�]kW9v ��oB�~u��684o7k�Fo1!d.mBtZZ5W�862�2[ v]J1�a~82���F�M���Ae9�.)�-��i�13 ��+76�sIi�>AL� ^Vzohr�� ^]�B 4ͬ�=452�� J��6_�2"�$4.0���"9��%a*� k ���Cu!W9*X�YO Schmidt93P!C J� T&jC 4)PC 2782.VMurong h�A� i*H��I)%��1� C 332� <0 �>N D.�.4]��2<Nb ��O449�a=EnelAMi�%E6g *�&Yx2� Brac�nsS!0J%p J�N�1� 1�92Toneev!= V�R 6W�'2# 30906��h } P�4  {U� N�c!Ɂ#6? Teaney} | ,N�� x>&96Y��� 1} ��r� 1222m M� �.@i1�.iQ>~aQk�N?�T)r2� Paec�K�YeM� ilw$A.~Dumitru!�~B�&� !ND6h�1j.� NA49_v2pr n?�|lN}Ja��$6�u0� vsR�7�Oi76L]1�])�J���� ��6� Larionov� 1� =�R�M�!� 64612cXuu Z. XI�Cy�*k 6272��m�De�  �>�.R1242�:h�e%�U9e�&T�V22�Aguiar��C.��  ��? KodaApyT.~Osad�AN�*s6U!2�t��J�ݶ���9$5.PH/�-�S�nlyQ.�J�7M 3�2CGG)��g*%~Gallm?[ �*�%�{.i}��A ��e��nV =3�q��0%��J\2X 5�a�6�Tom-T�Hum�> ��n�F6�Tom�(R.~Bellwied��Cai�f�JT{��-CvE�a�!�6.��oyŁ ,cOtuka kA.~Ohe��60L9TJAM)�Y.~� .KG�� Niit aS.~Chi���hJO:&22 Zabr)#�KE.~,��~Fuch��Dess��w rog.^ 5�Ii6�?4_v1Heta �An Ta:�WNe4u��GI�.�86Oiq2k>w�� *6Y�: �4506�q SQM1F. 2 this�G�>.P E��9s: 6�Kai)pK:�e)Z߃ `JZ%��<5.�P�5m�.�v-��JZ��4'26 A5 X��6JU.V�uk ���02�E Wv��Z072: jE���W2� Kopel� B.~Z�Hpeliovi� J.~Nemch��(E.~Predazzi)�A�yashigak��No4�=26oPYTHIAII�B�B1�iRe� (u"�D zE�z�ePH��ID9;L�glJ�R� .2�LA6 �� (y�V�]4�;!�6��.�/ _UrQMD ^&WJ`Na6���26D(StarAngCorr ]j�^�-�3) 08>�Kovcheg� �VAB �K(JT"�!�E"i�%�A 7�I 4�9u�(j� ��c{�IZ�-@Schafer7 W�\"��*� B�>�6)tc�=1Blaizot�-Aq �GAp� �So..y�Finitey&kvMIT, Ca�} , MAA�86.r Thouvj�D+#�1�$ �1���g60); �x*��J7�?61.w$Marshalek}FR� �J�r*>.�EU�6)5�21!�$% require ^w%Mto 1��S!!!=tPjatov'I�+zna)rN�K , Y_DFiz&��%7٭752?s>U-rpa}�� O. N`B&X}nP.�*�]71nC U60H^2)� wobb.!�R�$ nsen2��\V8�@42503eS2)�@endB�����Mat�CT!�tsu�etz�6�B17�;4`8�C��As�>M.ή*�� H^��=-6XR\ 01o��(YP�>P2&"B�"� 1!G} i&(, S431-S440 K; P. P: JA�d�9012�Wo� )Y�t9-&�8022j bar��!H�M "E.2 ��&w�4�]13109!�5K wong~6N� n1��OC5 \ \�:�I52�c,C1,(W.�CA�e�!C"�v�D"IN�B�D. t26tNZ-21�D70, } �>26/+]# X3} B Li�.F, �;!&UC67,}001�. 3) T{!`�" two *n�a�2 r2_ 2ous a�ms��the applr�c&oraint "�Xto+ r�W]u two-.�W |rb.iqZ textFQ4�QF�1]E+16dHB\5a �:�F%&HY8]�YD34 P2HU�ad1A�qdQ]�TE�SC} 63,�907%��2VsazI�&�FAnnal%�O�ZNr�, 87D+2II�I6�I,F2��620�388)V8*q f$ 3 %\H�{A�<tW�3x.��:J.',� eK [EuFa:,��T "A��a R�5 Of� ,\n &�-F2 (N) uDIron And %Deuteriuddc !]�(B1�r275��MN,b123,275sYUArneod��2wf�1~ ,9[0 effect6\st)  fuZ.'Z�*} #24�X30�C�q6�(RPLC,240,30�[-�GeesamanL� 5yd}�BD.F.~�\;E�#;~�;�!�n�kar EMC ��e�e �DSci1lz�33�55L<.(�,ARNUA,45,3376hP�!�9wx�4~ �W.~�U|vy�(deep-inelas�7lep�]sc&W7nd coh�� _� omensF�33!���0); {\tt�q? 230}.6�" c��-�NoC;�cb=�: P.R.zdo;1�JyE4)�� Q@� 12��� :�RP��66,#.�Smith�hu�6\H~%�G.�X%��Retur�`���,_new hopeU;�I<u ��I��) 31yA� #804ۊ2L"*]32�ta�ns�4y.}BF.MM 0�2Wq�p�s�>!�Qrbdistrib+_e�a medz���a�6_0405096Z_ .��e/t��tem6J�(,9� Rupa( M����%`iRon%q! �f��!�or\hthout�`��a�� �oA6b 38]A9�1�990205B�1� .�Arndt!�1ye]�6D��d� >�Chx���+to�22'|4of Twist-2 OpeZ;v�9�D4,RR-�� o45�V�?o4�p�4!��eg�25� ��X.D.~JiE�Is!� Sulli�� proc+Wcompat�b�a QCD �u ?:�m��B5�>10D1�� 105197^� .��tR�t}j�$Large-N(c)�eB����s! �logarithkd ; %6<�s!�eon�7� -�=2f�10Rn.�5&f�C� ucY&A�conQ��� V�:���-�)�8A�15Aإ�!� [Erratum-��v8� 2499�0)]B71��2�;01RpvN#fLe�[g1�con��� spin*� -�pro�''6 �-ѱ�0!I2B11J��R�gZµ��6�>�Ma��ele�Ѝ�o��A quencheTh�perturb� n %t��YJ�70A45I�a3�1��2��� R�yiN�v�B�z�p#| allyr�� o�&�;D65�9�E��a��!�5R �� .�BeC�2vq�6S ��>�!���� wo-flavor�-n�>�M:�Û3�oF����2�A�� �"< Bel�A� 2jp} A.V.�!�Xվ��&> ofEY�g�5�|6w��)�L�6-�B53��89F�˛20327B��PH9272�YH�3ah=�>�H~ �!Mos�EM}}x@haeghqK %``P}Dp&}[i�q,eply virtual�:� J� �D���%V"R A��3@U֛B�� %�:�3j.ѣv�Sof8  em��� DVCS�N�3a�4�4�g�o� 33>z�o .�Kivel!�4b.l6N.~h-V.~ =akq=k tratmaQ�J�"�p�A�igeed�E��]~-cone %��) tt9�P40705fP �ytutl��9sv� en5�0 E:( &H��ino dZon.Sin>O�767!�5+! �9905059^� �M�K"��8��:D.��la��Jt,���M�� %``A� �" H�!�in�o*� Jx4GUR98B�5�b� Z�w. ��� Two-��n4vz- F�B5\�0\R�207b 9�tF�sz�g���A*�ve calcu&Iq1 �prZWtN he %qi�it-�; �zC59}, 61�F�8C�b� .� vanK���7u.0 B6�J�]�eiso vio) �*�71122B��" .�9�6n.� :.��M��Vy �Knon2�&� �itN�49�S47X7B�610j\ .�� �=0f.� 6z� (RearrangingGDZ�j�A6�5�m! >�001106B�N<� ܵ; Ando�4��S.I3#C.H.~Hyu�6f�aH2od �5jdib� + �:�1FT �H\2�Detmold�q.�>W�m,E�>M El&/�m:= i �d �#�y��latticeF �R A743vca>�D |�0Ba\LAT�3002D ��kw�>�e^Flavour �let phy|��)�backgrol%�&�: �1A?>��6[ Sargt�2wc�t 24� v���%�a �b. ((V))5{J6� BR� "� Cj0��2BvUq 6�Kirchner�3wt� ~E\D.~"�C��Dez�  of� i�u��P��yC38T3�Z�7 !�� 200B�!�� 6�FreunEB3ix� �!� trikh��VCSa�!<4ei: Observabil#4 OeveM)itZ�3},�e�"� �906B��� w �)bB$"� �>�@n+p $\to$ d+gamma�fBig-B~�eosynt]�F��6.��YJ� 9070f .���rk}�6G.�%�P�wA:�n+p->�cIu ��*�V�!� �&7�!M� �A6v#�V� 1101b�9 .���]Ok.\>P� L*F�a�p%�B��T�w��WM��$Short-Rang*ä.� N�##44�pJ�8�BL�X Z�9v.� �!����&�'�ETri.�N��v3XSV�060j� �R &� fu �+<%\vskip -5 mm \i}�ep � %[1]&�SLR.Sat�� G.R. ��W.G.Lovg=f�J5��1�%[2R8Knyaz} Dao TienrLV O.M.'x� El.YD $\&$)G��27b"4Q\�Y[3.d S} D.T.Kh \��.)`A P6�a N42NOO�9/0$W.von Oertt�Z� _L 56}, 95I�74[5_Gla�sJ.Gla�! +Le�linI_Mu^Euj) : In|Rci��<*59�*31 [6iSi�QG.S��ko, Ukr.0)Zhurn.%[� 1t2F) (� �usW��%[7VCzyz} W.C.MaxM�� of�.*d�|5�6�#%[8Q Form�an�U%��..�y�U*. %[9.Besh} H.�Y�A �},i}�Y; �bi+�19�n8Z6iX %[10aK1�yK. PT?$V.Zemlyanaj�Jk*K�ISiI r2l'� %�.�Wa�Ha-o}r-a A.Wi N�55 3 19�s%[**]*��(Simbel} %~MF t H. a*%� ���RRe쭞1.6LZ26~�>�J.ModI�E �1�169"�(%[1.<Ro/|8Roussel-Chomaz,�'J�4734 U%[1.;Lig�K,Liguori NetofN5R 73B�M�.GPP!�D.P�%soe� R.J.RĜ�?�9�K71�23:1 V2.<FaS�,El-Azab Fari z�4a5259-8��2.(CGu�K.Charag�. S.K.��J�414�v��22&2!��&�%��� �112039�V� �v� &z 2pt&u Hagiw�G�� I. (���w ֢Group���& D66��NT00�:"yLutz1}M.�%  ��E�6lomeits��%�� �6S/�L2p\?26L M. Soyeur<thk%712 �(Azemoon}T. �M� zB��1a?��Keden}�0�K , PrivatB��.8(ulday}I. Sc , Do��ald siB�� Bonn%N4.o`Ahn!�Ahn6�A7��3) 712����}�2��,4Kar��-�C1v741�U�Ԉ}L.Ya. , cm�Ss4Qp. 26�39�M6.]B� iro}v\ Z}12Q&7�c.i�Jaffe}R�� , Top�c;�(  R"�� , Ox� (Eng����uly 5-9� 76,� DaliA�R.H. 7^F. Tu\�*" �-59�].�XSiegel}PB� �B��� )wC �j8�T5K5x$Callan}C.G�� �+ Hornbost�ZI.|�ban�Z � B��X6.DBlom}UGHomQDannb .�6�49��89U.��(Veit1}E.A.  5�6�13��84) 42�42b?�+ D 3�85�a�E5!,Garcia-RecioV�.��i;� ieve"�21'5" l:\H��gway}�t 6tB �+�� 7��A Veltman}M! �O_?6BU86*MZI�1}T�3 :N-1%��307��sSakittr N@13� 5) B72\Cib�ski}J. F� G e�5R3.*�Verter}R��CI �2IT�N42UAr�$ eros} R. H.�B�d���S.�$Humphrey}W�fo4R.�rs)�m�12E�6�k3�=5WNa0b }J.C�: � �QL45 �) �]V�j!wV�[9 yLM.�K.L� gank�ξart\'�(z-Pinedo, %WMo"k]75, 8�# ZCNOV.'�E�[ur�P�vr\' ati�� E. O��ZWA$. Vary, �v�8, �431��q MONPq N. M�Ll7 , Okolowicz, �_ owac�8M. Ploszajczak,6�P3,��� ). n Eng.�lJ.�lM�X�#wDo2I� Na&I�$and R. Su�2#C 60,�6^w%�.5Bor%�I&i Borz��1% 7, 025802��!�9� NVFR%#��(ik\v si\' c�j.�=.�;S%R�>>�6k4p 2�� *�=NVLR.�] o{\v�2A�:u G�JLalaz�#pFPng, :9, 047�2| .���%�`Bl06)�J�Paa%�N�2�>� �=Z� .(?>�!�3*?. .� VPNRj.CwRn�2k�B91, 2625R�4* @B_2�� l2j�?,a3�*\ }; Vre.o2MA� ndels/ X5. �B *�S 3346,A�.~7=( Zhong-yu MQIguyen�7 Giai6 �E� Li-g� Cao,2 A 6j�,�,..�MIZ-Y�< , B-"%�N.|!<8Eu6� :y n&+=6Ike.63��Ikey<D�uji J*>J1�)7��� 63:`Rin.809!?�*gB�� 3Ma:i�, S�geFk�68v�Ber.84[@� <��9 Giro�D�g��>�428, 25c�8ET.[GET����oriel6�V�K7B55g.��J�C BM.7�eohB��*�ANucle4ar Structure �(Benjamin, New York, 1975), Voll II. +�L \bibitem{KR.65} E.J. Konopinski and M.E. Rose, in $\alpha$-, $\beta$-, and S�F$\gamma$-ray spectroscopy, ed. by K. Siegbahn (North-Holland Pub. Co., L Amsterdam�465) p. 1327. �d32, 60 �8). iIsa�4 V. I. Isakov,A`4I. Erokhina, HAch,!�,Sanchez-Vega��@B. Fogelberg, EurE70. J. A 14, 29�.�Fra�S. Fre oo et al.2�4Lett. 81, 3100%�82�HosmerA| t, contribution to the Internaal%6ear !��ics Conference, INPC2004, G\" otebo�Sweden. )9�NUBASE}  databaa�Lfor availability via �Det see Atomic MassVData Ce��, {\it http://csnwww.in2p3.fr/amdc}.ALane�G!�0rtinez-PinedoE�,K. Langanke,��a�v.1c3, 4502%caU .�NUDAT�DAT�N>P2�C ��0nndc.bnl.gov/ /nudat/+9USheE�$J. ShergurNCia34313Uf w� \end{thebibliography}A'\beginB {10}��DCapstick:2000} S.~%T|W.~Roberts, \newblock Prog. Part6E0{\bf 45}, S24� �0), nucl-th/0008028. %%CITATION = NUCL-TH 0 ;%%�Penner�2a} G.~ �U.~Mosel2��ͅ��(C66}, 05521 �2)�207066^� b�b��2-�>�9r�9^�1֏!�!a 2001.�111023r�VPhD�6�D��hsis (in English), Giessen, �A,�Rle�O q_Ltheorie.physik.uni-g 9 .de .,Feu'(:1998a} T.~ �;58}�/�h9�9708051.V� 6� }�bڏ9�6� 9.�803057^� 6�shklyaeX4} V.~S , uc� Rd��s�egA21�45E�4�0403064B�$PHA,B236,1:CBartha�3} J.~0 {\em et~al.}.ON�1!�117�3). Zhao%�} Q.~$, Z.-p. Li �(C.~Bennhold.hBWE 2393�K8�9806100B�C�� 6���0�.mB�3�� 2520�2�01003fc6~O%nH0} Y.~Oh, A.~I. Tit7 � T.~S.~H�Ee���l6�06f�0 6�Babacan! 1} HA � ~ �Gokalp)� O.~Yilmaz.�R'!F35I�21��^O 6�%-�2} =?�>Ū15204E�2�205052ZU 6�FrimanA�5} B.~ � M.~Soyeur.$. i�600a�7�6.�601f� 6�V�22h.�>�D4!286 9Z 2<$PHRVA,D46,$fr42r%Z�:mD49!57�w.�93aMb� 6�HMoorhouse:1966} R.~� Z  %�1!772�v66):(PRLTA,16,77: pdgM�� icle� Group ~HagiwarabkBM�00m�2).�\url{ pdg.lb }.�UNSTAR��S.~. .O0talk given atB 4� renoble,d 4e, 24-27 MarchO4 .u Lutz! ,1} M.~F.~M. �� Wolf�Hu2.�F$70!�43��2�112j� 6��2sq��E�^~J��74�3}�021105F�ɔ R�rb��>v 452Y& 25:�N�6�Lahiff�;9�aD. %"$I.~R. Afna2�F���024608a@6D 9D ^8 6� Yaes:1971e�J. ..>�D�r086~71B���3,#6k Grosl93} F.~�Y.~SuryanwC47}, 7-199 JCC47,7036w[!v6Ew�rw5�242��9F�� C53,$6yPearc�% 90ujžC. �0B.~K. Jenning2�F52 6��199BvN� &,65:wGoudsmit!3cp} P�1A. H!�HLeisi, E.~Matsinos,�(L. Birbrair�V0A.~B. Gridnev.>J�7� 67b 4>.�75,67:�Ose�7it} E.~%8A.~Ramoz263z99A�6� 7^� 6�Sato_Le%�6� �^�>7C54}, 26� :�600^1966�Krehl!�9km} O.~,� Ha� t, S wald)�J.~Speth.�B�62� z .�991U Z� 6�Sch���jx} C.~ 2,~Haidenbauer �%V(J.~W. Dursor�5�14Y oN57,$:�! �C0zf� ,{ -M>AC�)]*� F�68��328 �2�M�680,32:�Kaise`6js} N.~ - Waas)W.~Weis2k J�1!�26@7), hep-ph/960745>qHEP-PHAp6- Caroat� 9j)1e���S� tzel��7�4�:v205^�996�Davidsot rk��M. EbR.~Workm~n���10%�1>��63, &6�4Manley:1984} D� ,� A. Arndt,�Goradi� V.�vTeplit2>�D3Al9m eV�D30,90: �a�26�%�hleski.�B�)40z1j� 5,$6Vranae��TP. ��A. Dyt!��~gpt.\ 3�)18� :I001b�96�%�!#5aEE9�I_Str�sk)�L. QT�M%�Pavze5E�12� �l950504bs Z�8:�RET�F�&r�Scr-fT8�y6�2e80708^w 6�S�man�\7�%Deutsch-��)[W.~Noren���I�*lB40�51�5\7�b j�4�6�L. ֦34{26 �2408j� 6�MachleidA�87E'olinde)KC.~Elste2H)HRyX1C�87Bg RPLC,149,:1� aA1&� ��$W. Van~Ord.AzK.~�B�R�;C�o209rK C45,$6/prepar����2��320R.�2Wc Brisco��A.A6A� 0352[.�03� >�"� 6) �19� 2�F�!�6Yn�M 43��6*�9509005;6o63�}6�%-%2��67 ^� �2�Batinic!(5� ,!'Slaus�SvarcijB�� Nefken2� qqv�bC5�3x196501011.j,Erratum-ibidA 7}:1@B Q M6�Che= 2 -Y. �KamalS S.~N-,ng, D.~Drech�EL.~Tia�"]F� 72^ 44k 3]02�^� :�utkosk�0��E. �� ��>vD4�35�.B� � D42,23:f Hohl� 79yr!7~ ,g� R.~Koch)%0E.~Pietarinen.�Karami�91 b�BXB1l5,7" J� &,5>-Danburg}1�S8 b�BE%D5� 7^E2,#6�Binnif7"/ �|'278�7Z'D8,#6| Keyn{6��w1��7Z% D14,B� ling�8�! �� 5 2�Z� 8103B� � 6 Pilkuh� 73E� bF���F�B65,46:� Gold� \8}n�17�.148e�6B�i�166,156:t�3-s. Ov�>��|�s 6| 0603b� 6|Sharp�3� HT#arp��Wi WagnV� �<13!222�6ZVWeiU �pr�3�� B131e6Z� 133,%6�Bellucc��V S� , Gass#lM.��Saini2F�4�]8l!�q401206:�q 6�Toubl"�D.~ nD�66��50921>" � 6��gJ.~C.�� Faya�)G� amot�^B.~Saghar�� 26 � B� &�61:�RaritX 41} �%�j . Schwingv��� 4Z\ 60,6:�Z�)yig 1{ ~G�lfn�C6�04��2|1a�^ 6� Warn� 89�USchrodA�W.~PfeiH�& llni2Z�)s� � 62�BGZEPYA� 62M1ND' �^E'&�'$Jeu76}J. P�uk�&�  Lejeun��+ua�+ Rep �25}2 76) 83.XMah85*�,,a$F. Bortign:�. BrogliI? C. hA�sso&a*j120k85) 1jRiz04}�(Rizzo+Colon'+� iTor�T+Greco, �7 2vA732}E4) 202cFar01�,F� "�(F�� A696 D1) 396DLiD� B. A�#C. D�D. Gupt1 Gale, ���054>�-�&(4) in press2k6jI4)Jamb�-9�.� 40} q9)�-L_-�j- vf)37H96)�/HCel86}L.u,Celez5M�k0w+,Relativistic%�-,!�ics: Tk' y of�uK0�%,Scattering},ld SciT,(Singapore, I/�SchAE��illa��-\"{u}thF�# A11U15OUly97}� Ulry :M�6y56)17) 1788MMzy/ Z. YY,�LAduyE!C 6M�2) �.JRon03� Ro� RA, -"Am Chinf!bf G 33 �3) 48.JMac89}R��,- The meson!o)�A�!� forc)�s2}, Adv.�q�Vol.1� 8AI89��̍�P�)es at � InstituteA'�-Energy,E�.�,�!^Lan62}a�M.�-e-k �*�8��62!�1;�1��23�@!672r8jo76}O. Sj\"{o} 6@A 2�2(1��51.�8Bom91}I. Bombac�%U�mbard�dY44Ig81) 1892; W. Zuo� B8�G 6�� 99) � 5HG���Z,.�E�(J. F. Mathi�FQ�0Ir 2) 4k, %%R�� b�{�!""4wong}  Y?A��^Introduc�0�0High-I Heavy �00Collisions}, �Oi-$tific Co.,�V1994; %P.~Cs�0�it2n o.�Zp$ John Wile�ons659.�Jpsi} T.�uI H.SatzM�]�178B},41F Q4R.wam�\Quark-Gluon Plasma},Worlz�0�m salva�( S.Terranov��$A.Bonasera�E�&eUE�C7�02490�(p 5� bon20* E FN�52202(R)�Kg IJ M#�Pf�Q$�Rci�<mr�.$�Rurl^�0url#1{\texttt!O%8{URL I8providecommand{!\0info}[2]{#2} B!e� t []{S'} "� [{2�{Isz: and Karl} 8,79)}]} 8(nfo{author}�5�{N.}~�1�5ur}} 2 and}Abi�ZLG>L� N� journal}{��\��\ D} %�bf�*$volume}{18:C4pages}{4187} (�(year}{1978}OjQ9VQ265�FQ9})*�>� Bean�$van Kolck}�2!� Bea0!�v9S.~R.:sWֈU>��!�>��9 }), M{{d-�;�%39}j� Jaff �Wilcze �3�Jaf� z�R>�R��F>L���@j�91:GM�23�"NU3r7WeigelE*4!0We�~0HB� GZ�F\�@.\ J.\ Aj�2Z��N�4r�"�.Vic0@-Vacas��85� Ose8��vE>�W�M�$:e6�ZE� 1Fj? A446:CM$58�ꑩ85rAB"rd:;( 5)6� #, j!a�E4Mei{\ss}ner}}]&�#�V V>j ]:�V=BF �}},���]�H U.-G!j*�{2�]D�(�R�� B457:�-�14RQ9v�J� ^-Mir� %�7A�Jen�)�V>�+:� V��A�2:P�Z<2�Cj�55:C1<�*B& 1997r�8G{\'o}mez-Tejed�Dnd e�A�6!EGom�'zEJv(:�B^�I2�ELV�Z���;6C-J41R�96rI(Alvarez-Rus�F~m?!B8:3.(�!k80Hern{\'a}ndez�8Alv�#!/jL>8.b:��_%�2��� B�:��Ѿ: A633:�-�519R�8r� Hirenzaki.�6:�%�{F.�~de~CeArdoba})�!�!�Hir�7S>�p:�V�P>?n� % a}R9�VfB� �!F���Z�27Vv�Y2� S@2e� Mano2�V�)3) U� V�,:P��<n� 4Z["R 2r Eidelmanu 20 PDG�Dz:B�PF��Df9 \ B�nN�592Qʥ���� �r�2�.2> .�A�ai�� ~e e�er�zBZ2e:'V�BC�1Uɖ� N� B��5e�Ģ�6Z� 06�>F�.f�Yamagish9Zahede��Ya��B� T��I>� �Z;Ann� \ (N.Y.)j 24Z? 29V�v8OP"�7E8�; Oll�; N� R�8^�.yUr�p A620:z�.43!!Uˉ03 ;r^}A65�~#>R07(E)F� UA�N��f�.�RTbcs} IBarde�4$L.N.\ Coop� and J.R.\)rieff 2�h10�.117�,5\5g ailin} D�� Z A.\ Love,Rp.\R�(32Q8Q$alford} M �$\ Rajagopa�(F.\�, W%y�B53f4�C" . %q' r flavor dOineHchiral symmetry bre�%g� high denswQQCD!�!�!g �2V)G�J.!Bower=K6�2gD ��; 0740� &N�. %CRYSTALLINE COLOR SUPERCONDUCTIVITY 9? loff�CI!� arki)�Y%� Ovch�0�SZh.\ Eks!�$Teor.\ Fiz1��B 113[!69P!uldER�Ferrellv#%13�@A55�,p-�$shovkovy} �S E9!�Hu31$�� X56�0W!X3); %GAPLESS TWO FLAVORJ)OR.N&A729}, 8Q3!rPZn, AT ZERO AND LFINITE TEMPERATURE. � gCFLA\ Q� C.\ Kouva�a�n �%U92}, 22A�4�aplE�-FE�-Locked � S.B!�\"uG9 I%�1x�D.H$ischke� "�~A7J 125}�PHASE DIAGRAM OF DENSE NEUTRAL THREE--�4QUARK MATTER. �Fukushi� �h@04083;He�6g (-)2 -,-Y� kaoniD�GBedaquI�T� \"af�.9��A69�X89/q!�u%�"qt$ mL under (ess. �Kryje�, D%�Kapla6<:�4290; %SZp�s��CFL2n:aE[����"O735�=A;of:&���(Non Zero�*ang&)ss=Mmue\* 3\ M\"u~�Sedraki�R�!N08502�Me�(BREAKING RO�T4AL SYMMETRY IN~�S�one���T Iwas�ax!oIwac(4 \PLB{350}{163�495}; %Superconc'v!i*2y R.!hPisarsk1y.P@ \PRD{61}{051501}� 0a GAPS�KCRITICa5�J FR���M.fsJ.�ICh46i�Ge�Cow�?�7� 4018�3�SINGL�i�� m�Z.�Bub� ,�Ho�Zek ~� OertGVPRL{9!i8aA }L. %Anisotropic admixY]!pcolor-s.�ng2�.��<hkec9���v7�%��L�&F� weak coup7.y scha�$} AZSc�H R�2�F940"�F. %��hadronv# tinuMv QCD with ="I�.~leggett��� L ,�Mod:��� 331�+5|A�# oret�!descripY*of new�4of liquid He 3.� voll�#t VesGW\"olfKN B"m-ehflQ��sbHelium f Taylor \&N�% LondW$1r] .u QCDgapeq}6����pq�A�14?� 9e >e � FROM PERTURBATIVE ONE GLUON EXCHANGE��HIGH %�ITY:�D.��H�+Ve��s�CN�L.C� (Wijewardhan�Le��L60�L Ee=�#j=}"\ El5bM:�("5-Dy�.approach�+es 2s�� eA�.�s�PD.E�!�� 59}{A�19-Y.NQby long-�b ymD8tic�&era�,in %h�,�a.l��re� W.E.\�3wn���G$�� H.-sR ��A1��0}; %O��Perturb�1 e Na��of^%. \!~{62�a3�Y %No^ mi Li?Behavi-aq'$BRST Ident��k��{�, %�,�� iA.�B�6 � asTra� ion Tempe�?re!��e�Pngi����at %�Baryon G'ity2� wa�.Q� ag :e E%65)&05�2A%How�)�self-e�0 affect1*I+Bgap2� chmi�� , �ɞR�6}I0�WheIZ;inJ�8ors is not %lik��BCS�� orie2I i�'} LH  f��G6�Y198i��de)$A�broken"�$. Configur_Ds. Hidd2!}H-<2�T�=L�!{2423��3!�El�du� Meissner {ct!=spin-on-�2~or.) �3��D{6����4�MixA�!.screen of photon*+gC0u aIw:�.rcjt�?�Cornwa"iJackiwIs��Tomboul��e Ek428�-7�EE�ive a�bcomposi4e�6review} :�L`\,.\N� EP19� �%HE����PLASMA��(EQUILIBRIUM]/abu�*� A �* og.\I�~&1H 11�/93 q� Z�A^�~rue��X.�%�: %nE 4501� =p!�ɇF6 masIradiu�a��ta.�manuel�I\ M , �2�a0 0A�\ Noha7�Takag��almeie�Wa Makia� RL{8. 3700�  Gap fun� point nod ,Borocarbide .� or YN2B2C�`weber�F\ W �1em Pul� as Astro"�2Labor.Jies� �} "� �04160b�3:6XE�W.!-W-GTanE(5AB! W�EFr1\$R. DonangeA�S.Souza�� B�FbQ FF� Zhabi�E�)�!r}.� 0546!��45oMa_�Y�M6rY[a W. Q.A�n,1GV j} (uhinese) %�2�9��2);KG�C�FN��.��. Tech.}I$1��9� �13}L2�f 9}, 031602>�6TVeselskyMw,�A.!�liotisX  Jandel,<Np�044�s2�'��� TAMU1}FY�t%gttyg2�Chuba�P L.�ycS<A. Keks�E!b-rE$��n�=�:2�)�6�)d$A9gE� JS���Dz!�2LA6�LiuTX}T.aQeNMZ�5Go�m,D�u:~�Hhomin, ywA�A������� F. Xm��/M�JE�J  JU Zielat a-Pf�%H�[l%YL��aulieu�S�Mn�  LarocS<e��efo�aR. T. deAhza, R8Uez. V.!�Vio� R%ChLMy�Le�SobotkwC�:E�14��42�G�i}�p � Brun �D'AgostiTE. De Filippo, A. Paga!ba�d ? AlderighiU< AnzaloGL. Aud0@e,�Bar�$R��r��M tolucci��erceanu�Bl�>s�LfC�$BoruexBougault 6 rzychczykE�Car�=K^ Cavjr � Chbi�J. CibY�sDe Pasqu~KDM F. Giue i'eAe rzeszczuk*HGuazzo! D�� inetB(Iacono-Mann �Itali%US. Kowalf_!|La Guid� �~a5XCN�p Neind!fSa4�Lo Nigro�U Mai�[p Maj!R�� nfredi, T!�duszyn�Mpa�Pet�;!� E. PiasecCS rr%� G. PBiI(op,aoPor� M.Fnyv!Ec{a��us�M.  t$G. Sechi, �&imi�UI. Sperdu%!�.� ckmeya�A�-ifi�M marG(Vigilante, �N WieleczkoE3W�9 �a�uFq Xiao,A�Zet��Hip�'���Хp} A��73�1�fFia��D.  �*%���ZA�i�GhYJ.�Chen,> Q. F�Gu)�W!�E�L .yK. jB. Wei��Z�xEZh$J��ZTArxiv:��11097� . � 2�   306 �52tOno}A. OA�P�n!~ wicz��2�2Y � . ' � {6���5��~���� Ma} "�� = %aR)=X.!C-SJ�p%|!�B|.hW )�CQ ong2� 6��� 6461Kd6�Botvina!3S �f Vlozh�N�2� jm_ � mtp9y ! R�� 6� W.!� W.P.�  M.9�� R�� 7V !�} 2�mY Q%�9�A�qR�)�9���uw5�, XZhou,F� 0116I� I�e�F�5Q 6� Frob�}PY \" ��Ipknt�E ^ YRep 9. , 135"�]9� CDSM�MI�H�m�� tnev� 6w�� Comp�  mn1(,2� 19972�(Randrup}J. q��# N� 32f&49�*q\� Feld� }H.  N�) 5�15eR6� HHof.dO -P)�R F28� 137G ��macr-mic�~ M\"oi�My[,W� Sw��� e�J�j.eAt��ta) D Tables �3a2�-:�Ignatyuka�V.  Y et\ �8. �Fiz. E�hast.y Yadra hZs06�O$}v��9� V8�KI�6�IFD 9# �Ark Fys1�33,.66�ch}R.SH�Y,  D.1�� Geo8.8%Oonship Macr��ic�:A -(Sp�NIHec5HQew York)688.� rev1}am2� �)�lem�1� )�| 2�935p6�RiskeE� ,�D Fokker-Plank equaD, 2nd[� (NJ8�_Y��h}��4 trJOi�T�'�_||y� random noIl Vols. IE�II (Gk n&BeaG&�1>� pret� }Yu.�Klimonto �%: Nonlin!�(Brownian mo �-� Uspekhi�3�Z7�7Q2�obd��Bi0�one�!Nix�<��M� b�~� ierk�>�� 4�Q�1oy 3�d7f^9fit��G��Z! 2���"�Y �FI53cB�Width}M.j�i!3.6e7�w�"� Lynn!1E��6&"W�R�Uance Re!$s} (Claren(Oxforde5625Ma_ ����Q#u� if j� ��D�� ��� ����25?1�� �b*�R�m D. H A 4 R� &4%%~ 6� ��s�[6�io}�Gat(�1au^ 3� outhas�Tarrag� GaNB. Cauvz� ira^H�� fenel��QjYh7c6)�*9= GSI1�EnqRY,PArmbr�0J.� lliuxA�ern�Z�ud�( S. CzajkowVR�gra�� eray9Mustaphp ravikoff iReja K. -�g&dt� St\'ep�� aieb� Tassan-Gt�$F. Viv\'es3Vo e�W. Wlaz":��5" 70!"4�2< 2$2e� �P�o^#=axCasarej�t! .'T.9vR�3 P. Nap~A1�Qx1?M. -V�cciardi -H. �Q��9R%;C.-I.>).��72{ ei� "GSIYZBeUDFew�$J� :�~Sb d�׭�J� 6�o458� 6�Saw��`awant� Saxe�R� Choudhury%aK�hunG. ThomA�m *BB7Nay���. Bisw+�)��QD���V�Z.Ma_CP��GI Acta�w Sinѕ49 }, 65m�senFN�Q f�85�AS90} �6 Adel�%�B!Sb ���( C4A5�1�zD)cWJC92}cWilliama�0hueng-Ryong J�R.Cotr�O%J�x 1�)isSLA} J..?c F"?c�e?c�>�Zv�""c�# >8T. Mizui�C�ww7:9A��Be�Wuari<C��n$J�>�E�C�W01�Wa0);.H) �}�U6�T��ter�Z��� ��X���� lU. XF� bgAu0��Md�0fC2`W.T, i�FNba�T.-S.H��e�Sia>��. B51 1�xByd03l�8Byd\v{z}ovsk\'y L5�1�9~039BHYPZB!��a�+a2�(86CDW/aR.a�w=� }w �.�F� bf C�;gi�U9eLAS} J.Wa�McNabb X�9A��Zf�04A�&�;)%ex)%��zSAPHIR!(K�CG�Uer p6~�N �J.\XFeyAZ 25I�46 8025.�U LEPS} R.GAaZegers:| 9a�R9�09Fe���Mot�X otob�ait�in kroc3a>b �.p�-p&W_�cangeni;on��e.��ei�!. Send;ap� 16-18 Ju�6l<, (Eds�Mae�9H.Tamu" B� S.N.x' ,O.Hashimoto)��^.,X4, p.22.baR 6I�lw-�ageVTrhaeg�.�E��M!�PA6X64� �5�ChPT} ��& inge��-4�*2`�m�/3sH�6 18853aic3A�6i� G r�`D3�I19[m730Dsto�+ Kru.�B.V(%c�J.]*�"bG��&4)!�H�\"@*r6o,2 p7.p lut}A �Eu�aC.L?wr� \NP{00}� 2) 3E�Uleu�Leh $L�,e'!eup�*� �-M�Z93\\ �os[� ^CI�i)74!QE@ 81�kno%B. Iv���noD*D.b+V2@-F�67!� 2000) 313\ cas2�qksi�'j uch`%JH$ 3� M!� �d, 417�1 0)\\=CaXme,JT727P� ) 59�� � fu1}� FuchsL)=S ��q%�3)� 02D tol}� TolonC[k A) 054907�ros} Gy� lf� ��%& F855!��� 549\\HHD. Ion� ics � 281\\ H.�+ar�d Nau�,1� 1K)K04190� �cc1� �%�E�-atk� aya.�S. TeiX7�(ibirtsevF� A614;d97) 415shsd�� B2eW]p:7!� �A6��U5eR8V�=!�q30!d) 6�gim�D �9n�er, E.L>�A��_v5o� `44614 i�2WDnis, Uni&e�� ,\\ 2�liZ�/html/d.r9s..\\$chaffner-B�(� V. K>|M6�,.�1k�A:0) 153� A.B.�( ionoɁ9 iArp�*� d�$6�#%F�B.@  53VB� 712Y@che=@C��K�iG� Li6 -�G G2V%E�oD�ag-C"7!�GQ T.�-�A6�J7) 372:IM!Yi�W.�h%0] �C5oG8) 43E ��>����B\ GXeF8�q084\\ G?Q J= 8C �870� -J!W4�9Osl{ibidU� 84# 9�M. KoN8495�P89)^0c�},gai} T.Gaita(����*N'ol-+J:�|�99) 97\\�F-&\"assle�����Ec-WA1���)42�n joer5  �h�X2;s!�1) 233�iqmd} � HartnackѮ�J�.���1 �8) 151.!�8o A�~Zhux�1L.~Ne���il$3�osenha�H.~Sorg�(~�X Q�~G�". �~EF~ �!��%�0*5ur�37 ~Ble( :�e6J\u��W��p 5�S.��=� �>�7 � C)# �A˽�fuc} y hekhECYZ6MS%Krivor�n�)� �emyY �S%C.Q1�h�pc �6ע 759%:�@ 12606\\ Y�Zhengf767 03}k}.�. Zabrod'Y��[Y�"����Y�s974\\YD��sov>cZ�܁��fT� indz�S)'��B43!�v�"Y fopi}FOPI�Cl�9 ion: Reisdorf,- Y� ^!U)23�B^er�r Eric6GndY�� P�#�au�*� �vP:c�"T� d� "N,-�Dt wig}: P�5g�o)�%q� (195wz4._ danlifjD&�*�,-ratG�M2N��24*�vs�P -��LNG(eU0"�G}�R5F tsu}|�>���A�%���69���`Sewerin-�b���� 8��G1� B$Qc)y*�P�1�B wI1055->d�110189�sib�*� �In7�t95)��kplK ~Mut� T.~Tu=mN=!�\ L\M2�2[ 65;\�es���6�&�57m[4) 752�oud}Ru{<& �4 Jar�0v amys�!Kulessbq�� �J-OA1��� 303�"��-0.�nek6�5�4!�40N� , ac�ped 3EpyuI EPJ A9�brof�"�!.� %l)kI�B38�H *� ko1T~�� Q�)�eB12 1983!�*�ykvk�|E/ Kolomei D.N� 2�<nd%j\"amp�R Int*Mod1iE r!fB� 31.�yhartprl�&H. Oes{�J\"orgJ�6��!�3) 10230}c cley�Cleyman��N60a�mb469�foeeKF��E�1 Uhli��-���=o�Q3) 156�!pz�E!��p}38� 5) 8ΌՎlE�F�2a�EWF�J.119.��ko%B` JU�I�>�5)��266��sturm%�S mH (KaoS67)1�>\��3a�Nf|9'Fub S. Fubi�4G rl;A�C)Lssetti, Nuovo Cim. 4>65) 1171.#+ Gol5� ��M�ire��2�1�195 4729(�6�j�2��F�.�3A�I6�"62�Adl��SAdl �F� G[�:�5�+H4'A9:Sch�yW�: hmidR!G. H\"o��,*)*6^ 6s 64) 34; N��<d4ALik�>�4) 76.YArna5#!�%R�"7��th:�3002;.n0 ,�And:@�C�0��430.�Che57ΌF� ewM�6�025�345.?Han9gO. Hans�,� Dr6-�C3t�7� �eA 6@- 8) 56�Bjo65} Jk Bjor�M�SDr4[``*.�(ic=Jntum �?4s'', (McGraw-H�? . .66�-Bal61nS�8�==12x%69014.�BexfVkna�)N!A�� Ulf��l,�� _C �+��4V�Y�BKM96�I�.�Z W�� B 37��^337:�W���6}A  %9._E� �mP06U �8�LD 32502�!^2�26)a91;�\-( B 38�%e�42.�Dr��4Y�2�SA,�G,�Lb�49) 145; 8� kph.�4mainz.de/MAID/.�Kam!�6kG2��N�0S%uu�6522�!2Hem97�R. Hemm�Bo��a��amU; Z��D ��,7) 5598; V. >+a Fea;I�8.cTU� y#>'5�) 1214 A 64�\�<2@WBec�Ta<� 1Hy utwy>aC )� 43; ubE� Mef�79 1) 6�T��ch� GegelG� paridze,~H.FerE 2IA��V5QNNkz�M,1} "Few-Body� blem/2z�'95" �#��#K2 XVtha�opean�R eren��Pen�,la (Castillo�Sp. JR�5-9�l95, E"8GR8=ardio�=�Syste$*�8:62�K2z�f�6p��S�GroZ#n�3N�@2 ds,�ly 22-26�7, �h*�/ cela".E� DiepIP [+��Malfli2$ ;� Ho;�ElsvRrh28 3z� '98Z�IV�A 6-�2�C�c%Y.K� ��-�)�SS.�~b��.�5z�^��EuJ�Evo�&Portug�&4 September 11-�:�]��ta1 �Arriag�HCravo�onseca#M�\~nA M�(Pe\~n\CG. RuppEf orthJ�% ��6�b,Bled, Sloven�r 98-�� 002,fp #3�Nox zo"�ChL51Rm G#c Chew��N Lewi�z�A\ 8d 51) 772LaF52NM�axK\ Feshb�76L�52) 56� BlL77L;fBlomqA a� ]�("�$�"�d A 28.76Ş�Lag78^AaL OBF9R 78) 36�9 Lag8=>2F� p.\ �Q198.aScA9 )| 6X� )4A.%P�Pilhelm*6$Z.�3�6) 421E(bibitem{Lev� k�Ivchuk,%�Schum�GraFpiss � 0011042��%W�%\ D&�%\6�!�SB�%� 5��A 1�A[>�9�Faes0]dI.�RObukhd yA%� .0W-�Gs�2202[ Log��1' A.Yu!( ogin��TSidorV.dkStibu8 j��S� \ 63v##9FE+�FNF� �"12v !�4bq �� 73�I��2�HE13K:��|�5�E ���Kp2M;Y5JG^X.��("�Z��4.5)5�Vk!�4}%J�V.\ Osip!�A�u4 40706�a�.~nY" )AdF/<2/�vk� \ 93�-P2�1; �`in/ >V 3rdU�6� Sy�\um#/� �Isimov-�8-Hearn Sum RuleFF wTExten�� (GDH�y4),�P(folk, Virgi� � 1-5&�2A;��40901�0�(Ped. UA�?  , private]]mun�*W-C%�R�*l�iiploma�<s�Univera} Pav��FIy����.�HaP8485]jA�2v��qP?>sC �=84�22�2* ibid�O�1422�Ern73�5�D�Z6��:Emh4$3�]a�32�C �73) 46;6��7�7822La+809�uLacombe AF�:t2z+ 0) 86� Gar9ZA�Garcila���&&�65$\pi NN$&� >:�.4�[%2�BjD�= \ �)�Ve]"2Qu Mechanics)> Yi�62�!\*�b\�-[�MB�5�}5yO Be+7��eM Benz:�69B 6P73x"2)ChD75Y�jChiefar� \ Dra>�"X<kJ�biacca� �&�\�_1N> 122� As+.%`Asa:�0> � C �A{�N| �~�"� polariz }�¥"T�d.���2, sub�ded�e!� ical�?iew C.qzplus.Y.N74,DappC���cal�BNstrauch~�uch [CLA:@ ], arXiv:��7008;H�v8�'2�pD&�hEcear�"Q/ �s+\HCEBAF at JLab (NAPP��$3), Dubrov� Croat�� 26-31 May&; manu k �*�(=� enta� �5no2  [76X]:V!d���%�201�6��3);\\�arm�2� [DIANABb!s to*w _:171� 3) [Ya$l=F\6$� 3)]�% Pp!�304��>tepany:3V�iMm� ��25z�Jy7018.�*$�&�7 [�3^ q�!5/_�2�Z�70��*UF` ��C*03� 4) [�k-��5� )499yr41�5�� 6.� E. AsratyE�@�WlgZkH*M�W�n` 1�R*V*68I�4) N)#700WE((A. AirapetiBHERMEFM�:�8952"! !�\ leev:fSVDB� 1!"24>�bdel-Bar6 $ [COSY-TOFnH30�V��fk �3 Iach�`\�� A.Ar]a� Ree �Fng Bos&@Model}, Cambridge.� J& �8�xNamp�  uv$M. Mukherj�={%�)�}i�B209}�48). ;27HY. U, DF�H�! 14��>� Beli�gT. ae. V.G.Zelev�Vy YX� �39} 5A�196�>VOn& T.ka%a�F5|^XA3�:PIP1JY J�2?77B->:JK?< A.�!E.R.Marso k Q�'!� �63} 3dAa7�BaV� M.B. ^V A.MolinT F.PalumbIvM.R.Quag�%��K ��28.\�{Cini�x%HG.Stefan2W@;n4-mat/0204311 v#h�~A�mb1�v4X�5 2whQA. *u\ �^�{qI [�ories}X��) �, 13.2 NegeZ�  lI� %h-�"� any-P[cleB }�,dison-Wesley*sd �Panye� &|�Vars} %D�, h�ih1A�Moskalu$ K. Kherso*Wi:��1�0angular %momep J�, Co. Pte.Ltd�V�+f��"� volo�}�-V �#&'�A0bf{71��3�2�9hwa}R�Hwi�C?2YPi~e3C��Ţ�,��;|064�P3C�7ń ;9u3219&�*2$greco}V. G 7 �0�P. L\'ev@>\ �0bf{ _00'Z_2}\3�aC]�V349�2BfeR.J�9 ies,M\"�cC. Nona�5�%�@/^#c ��5���!V�1�8�04=}=Rmoln}bQolnar{Y+P|)�.�B 09V�lin03}Z�6L�fd �2/��^�-c^�R�TS � �B�vbf 59A�2M�1PuEK-r�SQP�C�AS P.�7A� 0249 �2Pppi}K$Icox��. (, % [PHENIX>��x e �� 8!2�qE��d�adlv2}�!A��m^p!�185�22�>adams9;A BkSTAB� ^�9} 5Vzalcor}T& ir\'��}�a(J. Zim\'any�--4BgS3ey-Ο1)�Gu2L15c�� 2  icro�WCsizm}�v.� NM 61, gb903(RgbI"�/�6!�199 2rvitev-62)RV 2! 4052m+�ss.$Aampt}BM��U�B��H7!<ZE6n6��A067Q��T �)�"b�%)u6aaK;�"2);n�0gV��?N2o�W 0119&M1);� -�e(A49!_ 375c�$}�x2�: ���Z�1%7!:�C.�9@A�q�; L��3\2J_J1�F03�;A��GI����0"� P �B�E � (*� 802!A��U%5��]%�C11110:8 -MPC:<(M. Gyulassy2e%u΁�� 495&F{i�G6�.t?82�-��04|�- mx30��123I�2�m�s}� �e͡B� �Yy�30, S12�'>1g[7}Z. X� C��im062�,�� phenix-etn�f1%�uYl�n ce}FV*rscqq�UaeR�, %!he� Quak�z�z3}, %2� X� "6;I),�.� xP�; �l� 3 ��colGe} %�iW$D 0SZwIyG�4�ܫSer. Dirvo5�Energy-�EW��1 (19(9 pdfs�SGluck�= Re?a��k ogt,� LH[��R4�%�8T owen� F. O ,�M&2 �a�4�87.B(vg-quench}I�TtT 28i��hi�� �l2.l�pqcdmsT}679���`%�I�929.p�gm�1%@ _4"a !F�ѧ��K55��4N*w  9��37 ���:y+� 5ӷ�G6WGe��4���XGCA�^ �l253��u�lS 1 �iC"� .��A6ŗ 631 ���]6�:��)�)�1!3��2o>�ffA��ewS 'jnie���G�Ea�r�H Q��4!zU�.Ost�+,-par} X.~N.~%< �;yR2)�>/juEtU��6 &^ P� �B"U68 �Z}S�;V rU)K%�8��1N!1�+}?hydro}U�,inz2� 7067;�nlb>6 >E-shuryak_iS z�<0T73E+2��+ specn-Z] n� 07"� 32� 4phobos-raa62}B�B�>�4U�%ŠOBOFTş�S#'uGp��idpf� [N, .�Q*�f� ��N|v/� BW91�V?B�E]Elini��&�E&], Vol.�'in�un�qs A�ics=v ure >v���v(A2�,, Redwood Ci\CA n �CW76}P.R�3 ristensenB�w= e65B����.T LM80��LozR�=Madurga2� MA33�� 3>B��9JCPR96}L3Ch[�,"�ZE� Ross�v�<ilv�pDi�!ZmLos�j�"P.e�evi*Fw592�e�42�SAC01}CD kM.A�fAlvar�mb�M Rao�+�L!�Gl�N ��t�! An�[YLubw !�S#7m4Cs t�@ Carl��S� il!A!�a֮j,%(ngh, �ShH#sta!K�fhat4�ant�+F)679}, 2"Q32)HDG02�Haw'�( Da��IhAGonch�.�" H>� C.R4rt�kA? J.O.K5�CJ80Fourth �#-Japan6�$ek-*@I, Toky�^-} (*"��Z:� 02), pp. 87-98�U��110066�$GHDN04}��g.��V1Y�2�P��is9},46�8% 6m EB96�fEsbyĵx�qY P��3109 �266O L95}�| LeiA&2�.�� M�36� Lemm!�Ja. Lest�m2� H�4�3�2XFk!�N<:w/} B��31�Vu.�NMD01}2h2U2�.�.�.�2���/M�B�v646�\$6\HRD03.�[2�] )�5"�q�x�/DHNH04��yl.�2o��3g.�AE�Su:3�&�{:�NBD046s`� Bu�B2�.� :"2�:� �� B{�n 1A�e; %B )07�0)�N� ARN88}M.V�gdr�NB�Augaraja&� ��202�296>.�TLD95a�TY��arZ :A��eg2"B��2� �A*�0�Bh.� HR04Y�%}N)}=X�� A�V�JER�-`Q J�\H.��, K�� Rehm�B;�zR.V�] s, J!~ Cagg�r�oll�U]e�YAlHs I^eQ{� I. N�T�K�]ing�OAdU�weryniak2! =�7 0527"�.}wJEB04}b���>� %=Vj�u�!2�JRJ:{MBQ6�I. Ahmad2�=dC�Da���P9s>gZ&� E�P��Raul, ���n5}6ylin�e!�Z�ou6m=�93�15�� � RHT0ufRum���]N._kig,�F^^4�e:�W73}C.Y�Q;=��/�766al7:�HRK99ym�~R���A�4Kruppa,n] Comm8 1���!96LW8a�owA�HvDM35�1718:�SL79}G�� Satc�@�W� L4�1�L55�l�197:�BS97}M�Brөt 2_&�Q2 �76�KS00}̐ Khoo :PJ� 6�>w 76�bCoU[Sertozzia �ms�6gE�Konw W. Tu-vne��C�Il�d��L�Rrd5C ivoz"#'Lightb2;Jr.� 8�{=��8l 10-c:� FS85El-Azab^�d%�jAX43! 52�+�o.( KBLSyإuK��>�M}m,ILinds�iA�:oJ�4IQ20 oYN���� nlee���ib�1�2 L�$��� Rysk2+��5%10&�G 1; A.H.Mu�I�J.W.Qiu�*q�9B2 N���587; J.Jalilian-M�}A.Kov�IL.McL���H.Wigert�sR+' bf DF�>414vUA.Leonid�SfUGN��^0�WNW34007["�) 099903]=%%�J.G.Milh4�L�61�0 �,2; E.Iancu,:�=RN�#N1) 583/ ��)�51!�� 133; E.FKm iro,�s.}8489; I.BalitskyF�B4&!�(6) 99 ; Y.VA.chegov)8�D6�-�!o�$",mca2dR.Venu��-h6P4M&6233; �Ka �� ��9d0- HARD PROBES� -dO8eira - 5-10 NovD�02�0 sandJ�DonnachiH.G.DouR�I�I�9a�6A P.V.��h�mA&�jPN-5�P3, 29�I93,eks} K.J.Esk0@V.J.Kol��i�b RuuskanenJeB53�T&B 351;bME��Salgado :F%�C9�q-�<61 ; M.Hirai,S.K�Y� M.MiC�V7NI�E#3.eDde Flo�� A.R.Sasso�~6.tR74�f94frank1Ak�?kfu�á�M.Stria��A5 �P9!�3;�. LOL,V.Guzey,M.McDermott>b JHEP-�zUI*22:�22�\>P``Lea�b twist�c1shado��: unchYi�s,�6par5( to ex�A�' 2�er Meff� �(ph 0303022.�2�n=r��Arm ,A.Cape��Y Kaidk(<,J.Lopez-AlbacetiV]e =�R%�C2a�i531.� qiuv^P)��!�I.g" Isummed��$ power corf"RS�26''"�309094.��bob`*0E.Close,R.L.J>�,R.G..Y3Ge�os"<��\ �D.r`�wY�noi} P.ADoriO@A�E� � OB21�w 5��?�+>�Har .n� N I"}�I535.fack�u Absstaff& - u/� aborg4 -m�2�47�zA�>6�Eb8>j!E]�-P%�M.Soldat�..�10LD6462BmP��*S.R.LuttKS.Wadw �GWe BJ�1sOE?2��NFN8���2�00; s"IҐ MIT y�(rt n. CPT-9}�-unHRshed:.�%P.M �-P6�]H 2760.r$.�nmo-Arneod5� a!�NMCV�3���E}.Jakuc/V.Akul� hev,�)Kul�� G.M.Vagre� Ix2�VO!A5) 482~ved.M.Sargsb� imul)(h@4V����2 C�]�r024001}uacc+/Acc�G��Mu.for _H.J.PirX�F�A7wS��13.Xnmc��Zd.� {\bf B48�[1} (1996) 3; hep-ph/9503291. \bibitem{nmc11} M.Arneodo et al - NMC - Nucl. Phys. {\bf B48\ 23. N�molti} X.F. Guo, J.W.Qiu and W.Zhu Phys. Lett. Q4523} (2001) 88.� 2) 097502.B@veditu} A. Bruell ��.- HERMES collaboration - Proceedings of the X Interna#�al Workshop on Deep Inelastic Scattering, Cracow, April 2002�@helmut} N.Armesto%%$C.Salgado �L2)0 �L1) 124. For a review�Lthe geometrical crit transi�, see H.Satz !$ARD PROBES�\4 - Ericeira - 5-10 Nov.!Xtend{thebibliography}o>\beginB {99}] Lgao} H.\,y.~Gao, %``Ab�$PHRVA,C64, &6�v���� of >�in B� -�T to Q**2 = %5.6-GeV**2�n� 8}, 09230i� 2). Zk11101A� �)8arrington} J.~A%�ImplicE|5�Ddiscrepancy betweeejton.H m]�T2�5�9�222 �4>��& 90116�8qattan} I.~A.~Q6� ``Precis�p$Rosenbluth.�!���pr�Q�:� 1001f6�Dmillerfrank} G.\,A�Y�΁7R.\ F"%wE independe��tof QF(2)/F(1), Poincare invari�������8, &6�se8�D(J.~Brodsky,!,R.~HE�4, D.\,S.~Hwang��(A.~Karmanov�The c5� structure�Llight-front wave fun�sNauPbehavior of %hadronic2�VD\,�;760^;1�3112186AZv(AUJPA,42,12:� hugo�,H.~Reinhardt�H)�� Of Qa�8 Flavor Dynamic.?.�B\,24a�316�9B�4PHLTA,B244,316B>dq�>Calcu!�on�Di)� Masses In1JF�,D\,36}, 2804�87>Ei� D36,$6�,mandarvertex�h�s8hagwat, A.~H\"oAa�rassnig F,P.\,C.~Tandy%�AspecM/A�equ�{E� a dressedI�-gluon �A1F�C\,70M��RB����R4 :�cjbA0���urden,6��G��:  =�EZ��47%�j�476�bentz���4sami, N.~Ishii��B �K.~Yazak�Sta� properti)�+� � TFaddeev approach based�L %Nambu-Jona-Lasinio��b� 51}, 3388�95V� C51,$6�oettel� M.~O , G.~Hell�<%�~Alko� �B Octe� $decuplet b�m���b?(confining dixI���V�5�4245��98>�Q�980505:xhecht �\,B�cht��A�D.�u,�](M.~Schmidt,2p�0A.\,W.~Thomase�Q�mas��p�_ loopE�Re� 552�N20F��� 8:�birse��%� zaei� N. Wa!�!u� C.~B2X � �� in ac ~ -�� lo NJLU�%0408233:��� 6lcjbsep}%n� L.~Q�>�.��J)vso� 4Ground-state s�rum&���Rf�5> 264I\B�1�960502:+maris�� P.~M E EffectiveE�M��,Few Body Sys��3�4" J�p20402:� cbm}E6�CH Sym�y&� Bag8el: A New Starta�� t /E� ar %A���AdN>Z1�1984) 1:� ANUPB,13,:n wrc ��D.~Young� Binweber�}kE� V.~WA,``!Eem�{ corr!zo9 �{L 6��he4 E� lat/e4>�A� LAT 6�XradiiCh} E.\,J.~Hackett��esF��a�)�\-�@% Incorp`ng�s1�z xtraR��oc�z�m % "mo�( !�.\>z 48� 14300);:w�00400| aE.N�.� � ޚ���heavy��!�oryJ� %a�2�charge %��{��}.iV49d 89 �:��80j ._yA�} M .�N��Y� %`q~5��A� intrinsic��A(�-��8 �86}, 501�*1B3��12w &��� rev}���:}�HDyson-Schwinger equI|�7 tool� � phy�'��29�B��nV 04:� lane} K Lane�Asympto{ Freedom��4Goldstone Real*� :VW D\,1 26 1974>;� 10,$6 politzer}� D.~P ��0 &z �� �Limit�6p�B\,117� !G 1976>�0NUPHA,B117,39:�cdragw�&�E��$G.~William��b2their� lIic. Prog�7ar��J�33}, 47� 9BnM�940322> owmLJ� Zha�K?O�~ Jad, U.\� � �d>��>  ``)��Lagator��L� ��Laplacian gauges with overlap fermion��i�qt45;qrefer� therein> !Ŋ 72xfischAsC.~S.~F ZR"� E� Non-� urb�e�s, �Ń oupl ��d�al��� of��r86A�09���B�܁�S9>�%5.3(M.A.~PichowC.:�P.6&nalysis�� enc(lattice-QCD6+=a�2�e�� 01520�KB���400: �� ~c `Detmold :�2h с�A�6sM�)��!� /I�A�J�D14014%�4>c9�907:c-�2!����a�2�eW2�n .2�ataV���!��b�40716>�ishasvy �A.~Iva' Yu.\,L9linovsk� J/SurveyA\�-v  ob�blefk6�i03401�B�QD98120>�I gap �D6F ``OgcomplexC (pseudoscalas���(-th/0411065:U � 6�cdr>��> )em-�Eneu� (decay widthAJWA\,60� 475 B,M�9N�b� . 6��!C2'~�4�S� 0B� 5700506�.� a�����0L.~von~SmekalN  `�infrared.��� Green's&�: C��,�� %&� break�!�J�� s as6Eb� �A�*�p���8353F) f� 00735A@.  markI>�])�\ .9�$�1 ! N �B\,37@163V� 371,�72� r97}�� �%:�w� v C\,5� 3369 �$fv 7080�.wsim�S.\ Cap�k{W9,�#gZr �I�2sB]�8029.�mrt98�ɮD����\ &�P�Z?AFi��tan� �f:�42�$2�"1n707Beentire1� $J.~Munczek5�:k17a�21�.86B�M175,21>� l2Q��"�Ib�B` V�28�3�9F! �285,3�.�stingl��~S �gPro��!� :ECo�sNForU%� �#d Yang-s %Field�{ ��E_.|38i[86Zq$)a651a�87Bq$P�! D34,M6Qk* �~K Q�rl�On�2'!Of!fi� zO%A\,� 560� 2># IMPAE,A7,#6�ahliguA � ~" C"� 2���EC$ H.~WeigelU�6�6!�� bjk 1228�.?hes%~Hess,S4Karsch, E.~LaeLn�I�tzorke��``Va�e� ��F�Q3� 1115i�Z�98 A.�S dqff���Ff& M�of.��appea� F.� ems,*�09008b�6� piet� � %:�"�9$Bethe-Salp/ studW ve�'�1XFD:uv:&� �Dp1�99B���99H�{>RJ2&�0);Z���&C.-R~J+"1 �K(l3)!'i��."f+U�3F���"05a�.+)�e Y,%R:�F�!5045�&FD}�'3>�zn ���L.~Von � �&� ��R.� three�b*y �separy two $ %sxi�ف�Compu� �CommunQ51���N�9 010928� *�&bruceCBM�!�Pearce�I�Afn����_Ren�r4lized Pi N N C�Con"ť.P W�"(Phase Shift�Cloa2Ba�ZAC\,ş99�vN�l(34,99�.<i}*�M! exc�\#�buA�s�X�n�*�!� % %�ach/2{Q�:�43A��:/! 431,>�I�pB2�= ._%�j M�E� Curr�%� "�&iK�%w-��1A�b�%e220f� 99090��.� loch� � R.~B�~"g!�&B�Regar�.�1:')��B����2199n605:� bc80�)6\ Bt,��T.-� ChiuZ�2��2542 �B� PE� D22,$6�b�(r6� A.~B>n��'�i33!1J�  10,$6�HawesPQ�99} F.\!%�>�%�>;.BAk�&2C%���*6 � 9e-71�&Z�980602:�Salam64� �(R.~Delbourg�/���� �dfs� St� V���^ s. I�6�Iw13+ B. 1964>�I 135,%6zbrK(�& er92� �c(�aE&f(�� Universala!*R ��>/.interaG(@of spin one %syst^ ':�eND\,4601�1 6n � D46,$6� |/[n��-�"K:ZS�fL�!452�B$ &�!1�������*�#&%�F�Z+p&�$V�� ��!~r�55�B]�006B�%� gpppIRR�tanch�k ;%~� %�2 descrip�AA1pisc<4 up�( sigm�)rho %"26(IP \,6AQ11601�2>� �21015ES%�R>�b %``Ladde�(67c*o(��Hanomalous gamma 3piE^ %�!�*w �19+� 036006�\800:�drechseliergell (~G.~MeissneIS D.~D ,%�Disper�/theore.5a*Pa��:� %���e*A���6 �A\,59!�3�b�50637:vWal�03�;~FriedriMbT�.� A co^nt ��pre�'oEa��Q51��aGerms a %<  cloudE� �.E��bT�=20F'Q�303B�&ga�'aR~G ,Klein,X)Moritz,�(H*�&D�ge1�J eckwenn%El�cё�7Deuter� yx��k �. ic N�on5-F�6 %AK$ ur M�"um Tran5,s 5-Fm**-2 <53 < 14 A�J!��2� 7B4� 32,2>�0kubis� ~K %�U2�� Low !g��&+AQ:� .-Z��7R6�5B�1� 0070u�fuchs}A�F %�Gegeli��S%�er�.&.�k�inT$��o� or!f��3Y2BR�3�4��ashleya�\W AF%� >�%2N#�\A��n��1la�ez�� R�h3�:� walk. C�[ ker ��+l.}�*J6�FJ�4�AI 156/c**2 <=m = %3Cat SLACAj�=*� ( !�567e#FE!( 9,$6( satoEhSad;6�9!��/al&�aDelta�i�J@in N(e,e' pi) rea� V�LO"6� &ap::�r�onjai7\,P.~R e�P.~Jai��a.�!�"h5�*���V��!o05300�9RI� 204}� thes��*� `�+v\a��d�[�PhD��sis, � itAT\"ub�%n*�0S7fp206:� mN3C.~:;P;��on.T:�;, pi0; ,�, %F(pi)(q**2;J��  365�+n.406B�litsky� \R*B , X.-d.�F.~YuaI@A�?v�e^ 's Paul� P F2(QR�L�>\� 91_9V� �w 2123� Rs>YBfs>48} \exp�$\fter\ifx\csname natexlabU \*5x\def\ #1{#1}\fibGbibO font>J M#�Pf�Q$�R cite~R.$�Rurl^�0url#1{\texttt!O%8{URL I$providecomk4{!\0info}[2]{#2} B!eprint []{S'*�@[{2�{Masera}� 5)}] :�ck}d*(nfo{author}�5�{M.}~�1p ?}} (<2hB,}{HELIOS}), " journal}{.�D%YbfvK4volume}{A590}}B(pages}{93c}zyear}{�}).��> Agak�ev et~��5%xb�G>C%�50 o�:- CERE!,a]�D!�5.10�m}f1 75}}2E-1 1272.�28AB�!27au�2�2/NA45})2�:7��j2 B422V440xE5�538E�i�{� �B9712008}jLenke�BU|9!J !G9x�GB>y @}}Rtn�Ev-2C�B�e� �EjM A661N�236�5L9p>L9�?5nL Port�.9K7!K !J7rc�� R.~J��� B��DLa�%�J� ��9N? 1229ZA7RA703001nAWil�E=Ae� %Asr�A W.~K>A B�A^Aj|C57R<865Z<Z��2n< Rapp� Wambach}0A�!=9ej�=R>�=>�and�A�EVV�J>K�6 �6�/�fQ2^QFN 2000.�h�K909A�j Gale%QKapust�1!Q!Q1pn�QC>=�Q-Q�ZQ� �LB3E�.��6Vj1r�Urban6�6� !(, Buballa, Aa~a�LM�}] '!e8eg�eB e:V�B; ��=Z.�q"h �/V/��A64��J�43e9u���F�th/�30n/Haglin&� !�4�@K>' ?:��,��584:BM�719F+� , 2��32rF Gaon�uM a�, Ernst!�Stock.4andB- inerA�Gao!58m�\S>5Gao:�V�Z��U�:ВuH>�-� �0W>OGr-D2] ~�12059n� Renk5��$6� , Schneid-� Weise!� :8md��T>�=�]��.6 �B2d~�Bb �2'u�&j�C66�<m�01490J !9J��4r�!;e\ Mishf 2004�!�3huޑ%:2L.aV:A>� ��O� .|1O549N)!.O)y331203�T 4{"� {a}}.S4c�b Z�J��:m��� 1F2v�Sakurai��6 :1960j�JJ� C^�Annals�| 1Z�1N�60ry KrogU�67:�!, L'San��Zumino��!7it� N.~Ma�.lA:VT�:BLee�Bx�2��1^ 1376R�7r�0St�ckelbergA�3� Stue:1939ii�wE>A6XZ� Helv  Actaj�^�22R 38r�RueggAi, Ruiz-Altaba�A�3��ps��B;>�F B� .�ZE�( J.�D-LjGA1Z�32NR ��:��� 0424rovan Hees%U��$HendrikDis�TO) emph&�$title}{PHD�c. publis.> {GSI @�� �jn�a4c:1941�B�<�Pe�� ��132D�Z20Z64vBecchi"I B6I ", Rouet� & ra�� :8�O B� ?-�1�V�B��1 ��B"St�n��5Z344.�Iz!2r�).�5ښ5�� ����ښ�1 Math�4Z�127R�v" TyutZ7' a 5q�' I.~V��.� BF����RZ. 3VH 5076n� Baym�z62� 2sx�{Bo=�*%>�zqj=A"@@�v 1391N� 1962r�Cornw�0&T74:�$, Jackiw��0and Tomboulis��%Aw4vz�JJ% D��B: �1��B= ��a%q6� j�D1 J� 2428R�v�LeBellace4�� : �R�Thu:l w<�$ory!b0Cambridge Monqa s on;athNal� ics�E* D*7%PF(+7r�v�,m�B�.98:.&�Hauck� o=�-von I�7i�� LB��:=�� �A�!v��Bz��Q6*Ann�26 J�R�6���A327n� Maas5�<:� , Gr�.,1��a6~(�2if�CB0 =��B� ��<j�%���B�"�V�V� 1017r��%m Voskresen2)�$6} a55n�c:&>� D.~N��.& 2�f���24Z53J�Aj>� ph/951041r. �2:H}],� 1i� �qEq-�a�!�6c> ��6Z 02501�iY�i2Ba��� �x010720r; Gedd�198� :,!xV� H.~B>} B^w�2Z_27R� 8vaLetessi6�$>+%, Tounsi!P(Heinz, Soll�d�0Rafelski�17a�3h� B�B:3VrB� ��< U.~W>��>B�5?2�yV�BQ9X!|U{"v �<5Z<340R=9�(";�21221r:"��b��1n��za�.��!9"V`B_ ��]C6Z� 0EJ �oJ010524r&aG. 1: ", �Ge�V)eium}] #!�0kv� FB��G:2VmB���� B��V�� BP6B�57V� B��U,323n� �e3F�!�2s�+ Zu+ Jk��C681�@-06490R�~2Bm>1 =30r��%.�b6�3g�=#�N� �P14� VH 4.�F31034r�PoVl&�S:� #,GkA��[e�y}])AY3k�FFa �:V�^���EXV:B� �y�F��N�7ZE6F!�.�&�!D�(AO}]e1%�f��^�Y�6G�(�@q�(�J 0113r;U.�>%ya �% !A2t�& z���r�2��'^�V�V� 0218r� Braate2�+0:~ #, Pisars�h %i 9�v !� 0w��B' @y�r<~D>� �A2jY�V� T.-C>S �2�6<���^+ 2� *y�199v� -.>�!*�-*$"*�-9im� Bm!_9fj�B;&�-%�2�� J>� �V�� A67^�5J�>���\404r�ie�((���ie��4k��B� =�0BO ��M74Z228VMV/`9r��'�y }]{V&�1p���Q�Q��^' 1050Z5*2'!e5>' 1119r��xc� *�2b�v�x�x�x^�,25_0B��. !Nx202Bv= schk�4Shovkovy�C�R �rz�� D.~H>� C�L�y�d���ZR��^r540N2%r*n ��02050v McLerra#DToimel268�"5ay�dLJ�D�eBW ��a3Z&54R3*8�#enFπ �f]B1(=�HBT��dHanbury Brown R, Twiss RQ.?GNa~x } 178:104v 56) Hh�R { U.�� B."a,Z�R(�8�h Sci�bf >G29�9)-��sta�D{STAR 2�< (C. Adlm a�a�Ze �:'�N 87}:Qq01*1.~,event-mixing!H0G.I. KopylovT� K50BJi2M]�j9Bbt-�IW.~Bau3 C.K.~Gelb�[(and S. Prat�v-�^5�K�iFO Z��~��ZJ$A. Wiedemai\1��Rep �3�J14�_9De�p�D-flow-and-lifetime!�,T. Cs\"org\"f�$J. Zimanyiov oC�26I�9Qpr��2iD.H. �w,1LO)�A65U88c%�NBOgyulassybX%� M. G )Rh03G47)h2hszch8&> G. B�z�]SoTkA$M. TohyamaJ3_189e�8�G 2JNuc�C �49�173�82�shuryak2�C.M. Hu�|E.V. S '2�eZ c�a|i%ZwR��af�50�,G�,G�,G�,G�,G�,G�,G�,G�,G Talm�^UnnZ�4tal60:4�^nb.GI>Q�LBL��IiE�&b[G4}}&�number}{�C>&A46�W.z'5MҀk;�]��01:693�DDJ 6PZ�.�AjJ)�6C �394R vo0Teeter"(urathe#7�D tee77:275��WJ� Z�:D>� �6�"(�=�6C-=6JM 1977r4,Otsuka"% 1993:� ", Fukun�I� ��Sagaw�1ots93:7��Q�^<:�$ ]:�V<N><�?"S ��BF���5�q� �!r�70N�1�C1$-�138^ E3r�Esbens6�>�"$,; �a� 5�esb95:5t nbUB/[9j>B��:�� Y2���B���5bN�C^INN�L "�h��m0>�274L/�� "j�5 Nune&�)':s!,|mp}m�JohnsoDnun96:�Y� f�FJ�/`��IJn�A2�9~V�\i=.�"���5�6Ab�9�qc7R96r`Dot\' Horiuchi�J�&dot00:1"7��V�B7 X�UB��^�Yq�/�,nA�J�!:9^� v�(Kanada-En`y+���kan02:66��Y>.];4����b��Cn�A�!{:F 0243b�nGAra&!JF , O�, Suzu&� Varg�ara�H�S B�F^:tV�B���; ��3B�-2��t2�!�bsR� R1132KJ1z�escouvbty%desa%99�&P>&2QZ6uf� �6C�u46JuIvjPudlid_&�69>�A$!�Pandhari�We, CarWO, Piep�and Wi�E�pud97:5�ZB |�͕?x:�V� V.~RBA.��FB| �=S.~B�)?ݎ3 jF�5_�y�H� ���LME172J�.19wQjF,Navr\'atil UJ�:[(6�>6,�#y/&$ Barrett�!nav00:8�1Bt]9}�V?��>?Va�7�C2����WVOBJ��aH@N�Lb[f^}L��8 2)-�-� 5728M09 !�.a}r9Qf����6�Y�VU������2�r�Z�>05431J[ >�!�j��ץ�Lee�Z2suz80:6�mB� R�c S.~Y>z�^'Fa j-Z /209JGS3r ��38 !12:6�^v�b1Z F��s^ 68�D 246K> 198z�>aur.�3X:� #, �)�Ozwd�ۥ��cauK �B�' e:�/V/ W.~E>� �2��V�jd!�QCNr.��.A��� 1V���and Now�@A�i]!� 99:3�}f�%(2:.�V<B`&�ZC�J� Pol. Bd^B3R@R�70^>9r<M�" �q6, #!�Mar�K(nez-Pinedo,1���v��Retamos�d Zu�g5�5�� f��U�V�B�C�\'i�:�VG��V=B�P!�xB� 1M��A.~B> -�2M��59:�m�20ZbW���5Z���1�/�j�� ������Z�051j#R)ʪ�� �.�4a)^ 4�IR�Z���2! eid}�U31^�+:Rj� b� }]�_�z �f 5432V�B�5j(.r>� #, Nks� Nchiavill�wir����:�� a:'V�V.�sB�b Stok��[A�8N�5�2{œZ�(3b�� Zր�?f?�:.����1^�v�Dolescha�I�Tdol04:�"z� B�N�*Z� -Zu>v�K����;:�&!h8Borb\'ely, Papp�� � !( 3:67��9v6(V�B�$��?Z>?�ڙ B�75!2U0��y9N�064^�1v��Bw �E����Z� �� �C^31b�v3Stetcuu/:+ ,\!�9i+" ]{ste04:�0�0B� m���)VlB���24Y�VR*w}~1!�S-&.^907r2CP%5�JE "g��a*Pie�:��jB��%>2P.VR� �E^�443b�In� Y>���)�3 2:8��r��D��%�NC�PVCRP15U6!�>GA��_ �� �_�_6_r�^ 3b�"v)Coo 6HanE�- coo01��SJ(S�HJo�Z^ Few-&M�AB��1-I@+R 13^%v� T�-y.�>�D ", Kelley�6 Godw���-, Purce�� Sheu�KW/�Sti� 74�-N� :OVe�> ��?L>? �?��.b�Bm-Y��C=:Z!��8 ��>O1�AU��o��#A 6CQ�5J�8�Ej9Ajzen�c-Selov�dajz88:49��B�BU6����6C�FE198v�cLazauska�0Carbone.laz��B�[�BV�6�5A2�&f 7>�@'440Z�jv* Li�FortunE39e+liu90:4�G.-BVRLiu�7 H.~T>l��8b,`6J^1~�DAo2*>&'PAoi, Yoneda, Miyatake�,�)<, Yamamoto, Ideg�,, K�10Nakamura�tani, SZj&l#(}]{aoi97:61�9B�1Ao�)�� B� �:�V�B�+1�>%8�;B�*1l�>B�1��>B�>-��=Q�>B�FNE<�<B�Mp="� *� 6d 6�A^^bA�.C�81cNzp( Hira�;n� $,t� modaA�Izu$� Yanoa�gi, He�N�lv��ack2u�a�hir�Z3�B��9`%JVIBTSh’=B���;!(�:B�Yag�tB�9��z΅B~Lev�� KJ�M�u u&� V�B�Z"6Fj3ZM2�dAJ;  ajz90:506ã~V�> �> 50Z�R> �L����cEne1�levels �l��ei {A}=_)A��4 �B�manus�). Avail�|WWW: http://www.tunl.duke.edu/Z �(/fas/11{\_}h .pdfnUG Hann��197>�!!��rri"�Oln� }]{han71:�;B�X"u &��� .and~Naga�2�VW-�.IH�?2Y +jJJ [���j?u\�b Z�219�>�!�r�՟198>�$,-��Warburto)Y�n�mil83:2�wDJ@8i��%"V��aV?EJ��namj��OE{�u8I���2ZM4'�F�8v�GeithnTG~i�9:�$,�ܐz!�Keim, Li�=B�Ne%r�=L.:R?5��?B1-ڒ=VJHdU�BU>�QE�> V.~I>�izi�u�M���N���3R�.R�C379R�k+r� Winf�qB�>r$,7ie�+Catford�6ta, Or� n~de Jle, B؋ ^, Chap�� p4Clarke2�win�#��JJ57���B�xi����NV�WJ�-�}Pit�� NJ�Or��B�V=���B� =�AB�A��vS� ~G>�CAR�DNf{I�?��6� � b�aȝ �4J,'�F& Pali���hJ$!, AY� , Au�MA�B�z���9, Cortin L@ramanik, Elze, EmR�, Gn�e*�6}]{pal��B��9ej� B� ϒ<B@)�<B 15�>BJu-l�@B�G-��=UJSH1גA��>YA�=B�IB�<Mv=��2� v�� E�N 3431V�v� I\.;>�[ "S0ܘ�;lamuth�$zMBlank4G Bush[>ggi�David\olasma>�20aum�$<�B�Nav.�%IV(T�>VB-9�rA:u B!6�;Bp%j�;JJeCHA]�V�JJ=7!��{CM�AB�IC�<B&Yw@���� ��B3R�6(�thi�&9�]+B:6r9_j VB ��<B� ؒ<Bx% �HU!�B�N"AA:�"6 6l f%!�6H l 2V_ v�%Moas*%#1F D%A3Mc{D}ona����� Harkewicz) Sherri9# {ot�Ste�DJW�"DNQor�2�eR�:V�KJ� ےCB�%�;B�|Bv 5z�}�^ BJ�L1�}GJ�U�BBWMS�=N�I�?u�j�6��b 2R�h22V�u7r��Qd2�>�& "� q  � Imai, :�ha� Kobayashwas9�, Kubo, Mengo� o2� fuk"�t$B� �9fjB��6Bz�!B9!3��B�1g�>B�5��?B� -ϒ=F|ub�� B1 M7�wB1Ik<��� _%&� 546fImj�'Tanihae���&>e $a}5�� makaw� $EVPNgi=$Takahi� s*�9�(}]{tan88:20�&$I>L �9i��˒?O>}�#��>B�% uш!Vz� B�%g�yB;S-��>BD5ϒ?B��d!3�u�� BIC2A"� iO� zNCA{J�JRi7� 5^�z*Fricke"v`�:e ",`� �cligT�a�r �-D++$e��(and {De~Jag $}]{fri95:6��B� ���C>Be ��?B�He�<LNx i:!2V1 BSc9Y��EJ�|< ���56.�2�U�At. D���  T�!sv� RBFV�077KFc�XR�f�f�a�R eZf To73} I.S�bw�A� J.C.� dy, \np �eA20��3pb7��GHa�]7FVN�c25�����bPKo�O V.T. Kosl �E�g�.0��H�f hmei�c(R.E. Azuma �.� i����$. 7th Int.��f. +3tomic ļes?fundav�a��ants, Darmstadt-Seeheim}, ed. O. Klepper (T.H. ), H�p. 572�Hav/9;,2� f%d2�I��|)�50˭4��e9dHa�HyP./$ submitted�� WKW*�{TohY8HW!� =G��. P�h R�2�197"��\PDG04} S. Eidelman \etale�eFB�!�4.y �2z�prc G66} 0355��۸� We58�Wei�\p)�bf 1123��582�Be82} Hfhre��T . B\"{u}hU��~�on ��al �F.��I���Beta-d-�} (�endonމ Oxq�M2� Ja57} J.D]j�*S.B. Treh%�4H.W. Wyld Jr.,�0ж5�� 19572YMS2} W.��ar3�FZA. Sirl� \prl)g5G2�i 86);.%y�)�Tes&q�Stݭrd -*x�MC�e�iA�by P./�g��tr (World-Scientific, Singaporea�V�9� OB95�E.�9%B�i�)C �!�245�i5�Wv:-p�86Vh��r8��4409�7��85���Sha�!sheri, � u�� 2618��.�He2} P�lrczeg9 D �X�34R�%�.)�Pi۝�A��l!�41��1sR�{��ILin1p1�sAlan D��|� G. ;����jStE��?R.)kThorne,U���$J. C23 73,��2; 2)���1v�5q�J. Pu���b4�0 JHEP 07 012,C:��J201195=�Matsuh�86��T.~ E���a&8%``J / Psi SuppՍ��By�� - Gl�Pl�"&#ť\�@\ B)�8�, 4��8Gk2�P��178,4>��wg^�X ~W��M.~"�k� �Shado�r�$Jet Quench��In A + ��i�s t�$S**(1/2) =!� -GevB��� \n�U�1480 � �6�RLTA,68,#!�=}�EV if} :�X.~F.~Gu��(Multiple pa�).Žin,,:e��T,oss�e%"��A)�6.�78z�1>��Q010223 �"� Guo�0���E0�%��&s�,��;0modified frag �� ���deepl��eh�e A.]''Qn@Ut � �59$�qn2��r�44%�� bwzxnw} B�+!�� X.-NI�6�r�Beyond&/���a�tude ��x*b�arXiv:a���19>1��%~95��LQS} vnLu*� Qj7G.� UN�2t�3*�p2.m�279,3�֖c!� DF 5�\19��1�:�m�50,$��b�r449J �y:��� D49,$b=7ow}߽Osb�����st-fȽx/M %matrix ��A�i(off-forwardQAdistr�A�R�7�p2� 2) [64204046]b:�'��� .~Airapet��{���r [��2�s����)�i�ine�-iu�posit| �&a 5( environ!#�Bc� ��4�q�%>Hal�}��V��cciforab�9Cexy�604�2@Z1)Byx Baieߋ6sk} oD, Y.~�v oksh��, Aax~Mu��.~PeignIu D.~S��f�b� �>@(p(T)-broade�of high(���E)`�6O�4%�26f 7)F�PH�� 8322>��� gk} .���Vit��nd>,H�� azi�#al as*��$noncentral��at RHICAc�]>� 253� B� NUCL�A9 ϵ��Veyh.�, Z.~Hu{(I.~Sarcevic%�g"�g��he opE� e di*b�$a tagged p�n-%�--� �j ���v�7At231�BW A�)�521>��pe.����� Medi�� nduc�� �u��� + jet e�wr���m�504*� B�� 7012d�9�ww��E��:�L 67 {�detail�alancev{8!{ 1423�fm�14-�1�8ww.�%sS����"��e�e2����a!~p p, p A� A A ]A��SPSnaB)�ip�6K-}�� 6491��B< qG 9812B ��mmB�y�6�,.nisotrop:back-to-�rr��o��!~>���-y�.�:�=�01 9�bkkBinnew!: !~Kniehl%vG.�m�/�ext� lead�or��6� f"{ for �ka7� Z&� 1�a4���%6�9407347Z� �ŕ������ �~G"�(, W.~J.~Sti�rling and R.~S.~Thorne, %``Parton distributions: A new global analysis,'' Eur.\ Phys.\ J.\ C {\bf 4}, 463 (1998). %[arXiv:hep-ph/9803445]. %%CITATION = HEP-PH 9 p;%% \bibitem{lw02} S.~Y.~Li�$X.~N.~Wang�,Gluon shadow�phadron production at RHIC,'' �Lett.\ B �@527}, 85 (2002). �4nucl-th/011007B�NUCL-TH  �� dauphenixİS.~Adler {\it et al.} [PHENIX Collaboration]�HAbsence of suppress�(in particle:�dlarge transverse momentum5�s(NN)**(1/2) = 200-GeV d + Au colli`s='Rev.\1-),(91}, 072303%/3)6.4ex/0306021]. %.�%.EX %.5�$daustar} J!'ams>' STARN% Evid%& from�measure�@s for final-state2L0of high p(T)M:s!-Au>JFr4v4v46wa  EI�>  a�4Jet tomography�dense,A�4ear matter,'' q J�(89}, 162301�2). 6�HEPa�020210I�5�I�-r} K!�cox2�, %j�S]�!�e�s withF�.�( % central Z�sM� (N Na13ev�88A�2= ;F�109003b� !�S�{AB�ed pi0~� %.~R5Ei�>�1�+3>+i�4022]61}�! Y2a�A0CA0>" , % b�C)� ity depen� A9a�}�2�inU#E8��a�:�&a2206&R�20601��$J.~L.~Klaya�b�H�,inclusive ch��d��( spectra %�V� S)�1/2��!�Nucl. �)� A715}, 73��:!�210026^� %�:�c}b�b$Disappeara� $ %back-to-��.�correl�G�� %�\e>0�82302�$,3) (I thank ŪAU��Ńprovid� the dataA�5-10\%�� 10-2 �A�bi � addi� to? published>-^�3f�!�3��4 \end{thebibli�J(}G\beginB {99}9�@Vlowk1} S.K. Bogn:�,Mg} < \textbf{B576} �P 265,%/$details on�RG see��� 1042.:}22},, T.T.S. Kuo%a$A. Schwenk�Rep. � 386}-� 1[Nogga}> (, H. KamadaV,W. Gl\"ockleXv�9^85 ]0) 944_%73NF.b.C� N�v\C} (R)AO& ,9(405016nFujii!'  6�-�5�C70 � 4) 024003NXchiral3NF1} U. van Kolc=`vJ449} (1999) 293.�H42} E. Epelbaum��6Q=2) 06400.�,const} M.C.M��ntmees D R.G.E. Timmermans%h4J.J. de Swart,% :67)3) 04:ph mat!_u,2�Ra FurnstahltA.QX � rE� David} D7 Dean2(M. Hjorth-J� n, priv� communic��=�� oEamH A. Zuker,M:a y pert�8ei} L. Coraggio��8y�034320mMe�4076EDFTB�$J. Polonyi2� 3011NF*indint.I, %� Brow)8(B. Friman, .�u� A703)�2) 745, �t also�11070=[O182��"5}��A�51301(R)S RGnm6����b�1 �3) 191N�30208.-tensor.xm{26�92}���#825e�NK�Ki�a bosted} P��B Z� �68, 384)�:��1B�R9, 113�>�arnold} ��A�olz�1, 806�8\=,schuetz} W.P�r�38, 250M776�arre89�$ ArringtonrL82, 205� 99):��:A*XD Thesis Cal.Tech, 19982g arrd�t$C 64, 0146w 16�nicu} �0 I. Niculescuv�5!�8� 06s(dy} S.D. E@�W�Stit!� I[B 256!8!9:�`cps} C. Ciofi delgi Atti, Pac�G�flmeZ� Cm�55RYlRX�SZx1, R126E�>��yx �{Z@ C 44, 232R� oseta�$ Fernandez{ Cordoba�Marcop Mueth�E. Os>nd�Faessl2� A 611, 51�866�smAoR. SmYKG.A. MilK��)��B21"�:� arr5Q.� R. Ent, C�tKeppel,aMamme)y.�(, [{\tt ar4 - j307012}]61ku1�� A�4A. Akulinichev�Shlomo Kulagi](M. Vagradov2d%  55, 22��:1pol� J. RozyneBG. Wilk,2�0211320:�russ} !�olochk�2>% �M 77:?��03>�$D. Gaskell.�HJlab E03-103 experi72pgr��$A. GurvitzE3A[�Rinat, TR-PR-93-77/ WIS-93/97/Oct-PH; Progres�E��Av��Ar(ics, Vol. 3a54i�:bgrj�K"xN024310�:�grs} HB rs��L��Rodrigue �Phil Nm*2A 5, 13:7:rt3!�S.)!�M� TarAj6� A 59�t��:�rt2�L620, 41Lt97); Erratum: $ibid$ A623, 77�#650, 0446�2 rt1z�6M5M22� %�:�vkr Vivia� A. KievskU .g6Z7,` 0"�:�v.�� F.1-�t2Y7!1Y 4), A�.D 7uBe�k�sss� M�WS i S. SimulC:U P2 �66,��0a��_arne>:D1�31 10R� prim� �t�a�~a158, 485?>gomezņG .v�D * 4348� 46�0burov} V.V. B OM. ��G� mirn Y�4!=� >� tpdf.!%�6�darN.wmaQ  Amadrau2�c%�B 4J 3,��:�ash%!Ashma2k 6E202, 6��1 e�-�)W al$�[�B 333eE199:Ebodek� B BZ�5a�43%E83); A.Cqvenuti<$m1z189A�b8��S�s&i , ��.$ �n259 a:� arn3.�n�6!481i AC>E8egiyan} K.Sh. E.I)�qn8a 31&� .�gura4&����65�>w0christy} E. C b�Ʉ52�200:rt4!�j_ �1�55!8�2�bba Budda]M��J2� 2�� � 8005:� bcdms��BarY#1+�163, 28�0><nmc} PFa4$, Zeitschr, fI�ik C �38��1:.rjB/(B. Jennings�M59,E��7%&gr4} %��B �15�a�E��jOs2*O1� J.-��)L {\bf� 2�.��2�hB["^N�"1�"�� "3aO AdB� ^�BH .�4aSSPB�ZP��#&6�5} Th$,ecise defini?��``*M$ '' cᏐe.g., be found in Refs \cite{1,2,3,4}e�referu#s herein.� 6} QS,8 Liu, X. L� T. Meng (6]27Bak? T�%{KHesenfeld^59}, 381呡yP.�KAIM38}, 36?�Q5�8��%PHow Nature Works} (Sp=�New York�6);< J. J�ATSelf-Organized Critica<} (Cambridge Uni�%ity P &,  , UKbeb�9�kRu:for%4 ilos. Mag�XXI}, 6�1� @10AJ.�liams,ivMod�z E17}, 21�}452� 11} -�,R? l)�Y. Zh%ߩ�B�2W044!͉��2�Boros�EW2bKA<belowfn D)�6�&940)1l3} See,m',H. Abramowic&A.�dwell, �:" 7a127�9HI (Cooper-Sark�R](E. Devenish �A� Roe� Int.!�bM�13A�3�(d) =y� A:�14�FuNDqvT1GR� 861&96��16� 5} BR M�lbrotx�>){15o"63� 67). >0 e&��8Fractal Geometr�&i{}, W.H�ee� N.Y.� Edg![E Clasi on f Ms;estoiew,)4��N�y�V !00}�mfopi1} W�isdorf�G.I�r, Annuv.� art�imS4aS66I �� N. H�nJP: sselI�WieF�Z�"581�: hydro1 St\"ock�� A9 Qp �13�27e�8:� tempa�~Fuchh.~E� T.~Gaitana�H.H.~Wol�2� �� A 62Ad9�7Ac u�gait0�gS)�'l.}6mR5�#9�e� �, �J �A 1��42Q� ; � �TU�NBL% 71-620��A(P3} F.~Rami, Y.~Leifel>�^ B!]112���9W'YA.V oshi:w- 7�%379�3:; daniA�P� niele��VS7����20 �5�larionovKA.B.~L :�Q_v-��k% 6461)��Xga� �Persam4Ga:�#�C 6�kLLdancroz>� Acta �P� �d}, 45 %;6NDBTM�T -Boelting�qA.~Z�� A 648 10�6< f#Dal�!C.Q�A� .� L74A-227 �R � .�btm�� ~Bot�k��$.~Malfliet&t u�9�1 �%�U 5Wm >88}R� UProg.�D�2�A2�� 9�f�^�1IUad/�]U! �$%����Y@pdg} K. Hagiwara Y�X �e��D 6���� E�aN84A D.N I*� B 14K 168 ��8!�.��;5!� R�c ��� P�U9aK23"�T5�Diqmd} Ch.~Hartnack R�N! 1} 1� | Oeyser�K. O. E Q5�["�31R*]�!V�(�Xf}9.�THyIT Tow�(�C!�rdy�A-$G:q.a�PArrbf 29�7E"6b Sha�'her \e�, \prlI � 2618R>TH73}r�\np IA20���+1i9bHT7x���N�25A�2��1976� KoA�4V.T. Koslowsky�Hagberg!6l� Schme��$R.E. Azuma+.� in)� Proc. 7th� Conf.� 0atomic masses?funda�al �'lants, Darmstadt-Seeheim}, edE^Klcr (T.H. ) 84)�5722;90� �.� f%dH.�.l�A50A942;�ue PDG0� Eidelma-ee��}�B5e���6� Ad83� G:el!�� jH'�lD. Hoy�H!�$Swanson, R Von Linti �W)xt!e �CC �&528I�  this&a  replacei  result orteT E>�C�J�%f:�2�=!�'69ł8��9mAj�tF. Ajzen! -SeloveN4�- �`5� Aj91� �G52G�.�l69��&ld�,, K.W. KempeH��Plendl��30B��6�69)2^70�%a�lburg QD Wilki)�)�Let�32S9$6� Al72:T��[M��27+7��9:l��DB�F� Calapric*�CeEx 16 �6� Al77:�E1V�.�� 21 �V Z��D$^{46}$V half-lifee6Wi76}6�78:�N.12 8& 197�5=082F� Alkemadea� Alderli�,�" Wi�4C. Van der Leu"� Inst) Meth-�19� 3�:�nAC*"ntilla,� BistMKA[ rmin�Z�@%�234 E�>EsV<@slanides, F. Jund �Lal� �I�[A15�e>\uᇡudi� H. WapstrXC*ibaultN�72��32N� Az74�Azuel�JA� CrawKEqKitch� �.p_12L197:�za� `�Qe5: Ba62R(y.ard!�CAG Barn!tW Fowc P��See�4�%v1��5I'62.iBa6�J.[ti�5 � >3!�17 �66; Ba67A�H@`$N. Drysdal�&W.RA_illip_9 eSoc db 56� Ba77a:cC�Scofi<R Pett M*8�'HoathREv cham%4G.T!F Squi�jF�27� 37 !�`e same �M.�4$>RWr�%��J2�P9?�.�))�665��22���r!,b2,PJ�Nod)w"� �Struc�,, Tokyo, JapO1977.:�c2f�E. WhiteL Naylo }N� WyatR�279�9^ �*�� Fj).��153�g .P�U�%S%� erguJ FS= 193�:MBaa+Sj BaE�MA�&�0�N?4�4 ���� @�GAELeona�*.4Y":� Ba9J�PAAmundse��Re�5��25A8);>eupdate�dH10}$C $Q_{EC}$-valu2i%2; its or�14}$O><was la��8<drawn� � To032�Ba�>6ME�u=��6��054�763 Ba�G)� S. Bishop> A: � !oisveU0�ricɨJ. Cern��D'Auri� Domb� JaHar�V. IacobaRv6slia�.� d�e� Macdonaldap-B� k, DA�Moltz@ Po�e,var��2 =�e45d6� Ba� PyG, I�śa�Geax!���A By�B.op 7a025�6Y Ba05��!al�_ to be&>92�e68N Bec�*H�,>�1�2� 66� Be %qI�'R!�Ch�-rs, BWat@&>� �\� �&� )2B9 Be85� �ergme� _ PAeb  Pampuj M. UhrmacU-6� A�+ , 69}� �eis U�)Z.2�]T 625: l02 Bla�9Ra�Q1��%� l04a.@U�E�Do� `z�,G�nch�M�"IC!��i@>r��Z. Jan94R�)rcheGI. Mukh�.�l%XidtpJ. Zylic>#�69�155:� l04bZ Blaum�6 A� DI�Bol�C�, enau� lahaye^ Her�4h�Ke�.bau�(H.-J. Klugea� Lunney "�+z� warz�58ikh�CCzb $C. Yazidji��I��!�A},rto64� H0ondeli�pJBut�/BU5b610'6:Br9^�irindhabaN2~ �R*p24A�n6;J� ea� r�f!�= ceedG# !� �=ory2fu61yWY ���R.2L%F1�177��6:]u79�� �UAnd25��5ydu R�� urch�� gliard�0R}TribbhF] 3�: C�� Cq�Be��2�FI�l�E�ndoov�C. Doss�/,J. Giovinazz� . HuikarS. Lall v Lopez J�/ez� Madec�? L. Pedroz�=PenttilWJ�]�+N�v�Ch� N�yChaud�Fizik_bf �^9E :� Cl73��$laW"6 D�Rob�J�Ryda�.[ Eu�� �|�7�(tj�h"%� i� ��J�I_�di3� 5*76DaaC.aI=4#2��J��r4G{E.B�=>2�|1��1�J:, Da80�nin ``A.�efN� 6"�s�!>le���,ene� (�.Y$80�419.kDaW�kDaehni�X RosaN�3 14^ :�De�e|f|9�r�61466� D- Ra DelVecchi�;2�J�r$1806� Dr[M!E+ri���A lijn"G.c Eng8ti�o� $ Eggebhuis-}� �GB�A2� ŏ:�E�Lj Earw� JJenki)�E!�T%�M,�"I�19�2L 66�En� Mk6~F�5�9�:� En� j=63�h =6aFrG6Q<��2�X��E�J.PQ@ff� I0���<21�&:<Fr65b�?.�Ge�r�=.�M8�,M�E73�&66VFr69a>\=�| Mui�C.�h�6xF� �5T 69F=B :M+6�J!XMontague2��Y��� 4��65)32j V)6�=�.s6}, 95e�66�#"]Fe�2n2�.�2�b}xIH53�4�w:�Fu�FB+Fujikawa� �- szta����d�KDel�nque-SteRC�w!ll1SAF�&E�Greene�-Y�e,d7Lis2A� ,Macchiavelli!W� cLeo� Aheiy � Rowe�-Q. S<)F���%hWP.�!mB4� �&5�Ga��A Gu�j�E( cob! &i�16� 6�G&M<%ele!H!|(ndrzejewski� Cam�� cy?� Huys9 Krugl�2W.F�� � (Piechaczek,]Severij hSzerypoe4V�#aeyne5PI Dupp�� Waut�N� 1�/4�20:�Gi=HAGil�. Flot�2� Loehk i 6iesg�=� �.� 1�%1>nGor D.R. Goos\>:�=���c18��6� bpK�-r�3 !r limit �=in> is sidered�J��O much�Ker r�6ed by �Aܡ�e^ �.CN�13če6lHp&5Harrii#Aa�Hy =I�5$9�?:\Ha&�Gag| K�Mai�$ichael*}y26���:: Ha72Ł� �a�l���.RB42}, 3�B:Ha7!� -H.��! Gei,R� GrahamNf225� 74j��Ͷ�w} }��L. z��q290�B �(.|R.� rews�^S�<�2}A��+�24]-=�3%6 =6��cY.�9 a�� ��� rawl�EiLshI H. Na�;�m�9(/5EUJ}]C}|�^���I!�I!em�� "UN�:`N�byE�%�2,�q 5", eq !��.r��sJRt 76) p 66.r Hay J=lH=�=m�~n�"� 75�m�mrmtE[''&>?%.2�[ HykawyA� Sa"sT�inozuk6�}vp,9�(4); uncerta�$es\&��G�1-T< decays observed�U��/$^{50}$M[d not�A[:�,but have bee�!ived �Sy origxX �Q\add�Sere67� �ar�N��Bow�*�Ej���5�8326k02.�Q2��]=j�625"�6�Ha.�V���M!�tz-Vega�pG. NeillA Azh�>�EMay� X. 6L. Tr��� Nz�* �LJ�)He�D��ri YJGer!�v*�X85:� He81�%H"�F!�~� 24��23F#:�&He8Cz�V 29�:�#HeAFY20�,V� I;B�H�Ij(fmţ*1/Ausw �$3�6:%oo#.� .� 6#� .m1v 3RE>!u!YPX nge'7%� "�r� �)6 �>ayaB�yzE�mA4+V�BMm2Lu?�A�Jam�JF�0Sharpey-SchafA�ZAl-Nas �"ehbeh�F?%LUPBNol�>�6�S%�G)V4��6SKX R�Kavanagh����%142%:r K�:uY �A12_ 17_ :]Ke� 1D_bd�'6��'"�� ���.���A V�NEchN���6�)�R��&, �E�072V�Ki�$�,ika) `&x*�Aa��EE0 Jurnmm2c9bM�A49%j86�Ki~-S2zZ�o�6�*PA�E�Walki�6ZSt)r�0T�*��52A S:�-Ko�/>� . J��#�/1 �H. ClifY*!�C. Eva�� c�UaxSchrew�K' a�maN�4,�"86z! Ko87VF6�1.�.�.�*>!�2�W� i�h���8�~47�41687� e� �%4-$^{26}$Al$^m$:J -dif��&kF��� "�� give8&>�.&�.[b& 3 2�i�e�)&119�&� .�6Ko9+>�.|.�*;#2���KXE�u���*�A4028%��;"`�bF{^���zI6D �>zr�I�Kroup�"�>�:�)�� �J �in-�Re��31�&6�N6�Li/S�%n�֫"30q0J5^M�PrMagnus�`��d���rcV(IV� R17�/>ac�-W.�c8� Mer��IA*��Hee�.)A qi�: u#66d MiiS �S%�b�mA9c26>Ro71�E. Mos  Detra�AC�MZa�asNN17[40�6�Mu�Kukherj�>D�%R  F. C�R�3�  J. D/9<�org2Gu�%2"A� leV*2�%U�7a?D&�%�9)�8 1508< 6� NaauY�gai.'KunihirorBToriya��S.�ada?�# Y�>T�! mura�ak��b+Q�� R��6�Ni�F5Nicho) N&$Ia;Maa�MhN\E� TwF�1���#:1 N�U B BG�milu72�I� ~/to"�9�:r1��q76�Oi�,M.Oinone�o8�1,B�Paa�* Pado�Di�RM -n&4�D:�P;*AQ&�E�Zganj�C*^ P. B*-M. " -.�^ HodgM& -P Klag�W!GKul�-*!-M��poglavs)%��%-�*J. von� { eb8� E. Svens�ݲ%�JkWo�F=6z`5�c!�3�.�io�"u(is.�l are*��)��co*kdiAYyN�a& less-pJJ*XmN/E].aPr��F� P�@f G.U���Da��:tJY{7#:�Pr�"6N%R6}J_��90); eV��135� :'#Ra� &K � � " A. Outlaw�=�2�mS5118�A:� R�-4 LI5i�F�Wa�,aOberh�/!Y��C�m�$ Rens*�"�H�:��dA. �ZE�eyeI�&4 JzE43a�3 ":&Ro�7M�ou�HLZMG%DM�CRQ4A��:�7R�� *�(a!a�g Thwaita�J�8� 6��$B�2mu#_ �2uk r��6��J&�%"�$R��3� :R�2�)�*� NS2�1u:�Ro�%;lfsaA�od�-�R�$nN^�inkVj-�&V/@ Ry73�^J�15#9 DrapA�6=.%�2�q<� i�4�#�5mV&� Ry` A Ry�2At. DatITable�IvSE6S�)AAg  orfi��J�); *��EI Warbu�'F�2�2::�Sa9�2�� indo-Urib� � V�A>� IFadfor�^�![� � 15.6'S�32��Vy,F�."")��S;� Gul(.�A@Hechtm-E*�4K(L8 F� vand, Bundgr- N�>Sciel�-*�d% ihat S�f�Ca Trim�.�?v~N %�Z�No.�5|e� n44��6a Scq4�Scott�$P. Rassool�oN��omp&�3V. Webbq�B� NU}rK1Se.�SR%h ap)� rmbruI�iI�� A199|F"6,Se�KA�Set�Sa3*�,!fA: nA}�� %]B& Wildentha� 5 ]�D!2�j:�Sg(D. Seweryni�6j�5 Sh55X2 �Er�B�!�H��<&HornyT�%�\, 9�A5:i66�/D idhu���GjBO�102-A:�*S1&J[n�Indiane Pure Appl25de:j Sq�:V.v!�MA��=&� ҹ�Y9)A24��6; :e)Sq7%22=6�j>����e^ �)U]9n�<Ti�a`&TilU#H.Ra~5��p#hev{ asteZ5�-�!:/T[: N_Tol��� �Ԃ� 35�0>N"�Vo�H�Mnac�^ . GlLEPuen P�ier-KomJH�,e6eH!�Scheer��H%8u�Qeo mrad��)yeA2731r6�W5 :� B� H�J>*�� ]�;A4��P:T Wa�lE.A�am�2� .%��LyVq%4 159 '$j5�WI:X e`Y!Xa�ti�r`eu�yQ�109%�6%Wh!�t&�-&JF4ZO28O.86��B9 BambwhE� Behr M�Ch@ B.�Es8n� �oitzpat�2 K..Le�9+H9nz- Mu?}7�'Int L %�M:YKU:} Fi96�B. FirV(0�VT� �[Isotop� Eighth Ed�[}, (Wi�� .68g��S%y��l�N �X�42�=7);(EgRtc� i8l���199��UoJR!�WAU-�G c� \pB{9� ETH�$*� �� :Jm�E��"6�&OB��pO1 .sK5�24�m)~:- B86���3v8n�O4465K��.�SVSA�aga�2N�0Giaq;�uzu(1.��21vGA.UB�FayBawG�5�W1M#1B�i!�>�i�B� AI)40(6 B2);�@5�W3866o MS86a�J��n286�-�5���F:�S�5&�P6_i�Testsa��)StandCElo}oweaka�el}E,i�0oA anga9Y (World-�@ntific, Singapore!F:\JTW57�)DaFck?S�# Trei��H\Wyld Jr.e�)t10�;5:!B�&�#�eW� \"{u}h(A�} �$n Radial W�*FunI�8%�lBeta-P+} (�=n�$s, Ox 1>' We58�X�h2A�W 1�J1CX1956�H�RB.R� lste};�29}, 6��64HeA4�'erczeg)7� �34�:&He=.9Z�V, ��-4R4 BBMS� �$B. B\'{e}�^VKd�EWoha���]�\"^TP?252_:YER� J. E%�Ma,�QuaI�M�4nics}, (Prince%vU"�b�19:�+De"UGe V�~W� Ja� �A 9?�!��u% �3��4T6� Ro36AiE�78�0�k� >436� MJ�� M�JDW!( John��H1e .IZ�Xd�X�z,Pochodzalla}A&�-.2� *[ �( 104A 95)oV$Dasgupta1}A�Das G� ZMHk�E%LMha TscAdvs�W!e��` i�r vol.26, 9g 1) *��E orf1 �?inA Donac?o�Mbushust��andA SchulRP^4�\3�86�Pan p�E���G�%�51 },13j1>4Sobotk!3�6. ��B�-�1JQkQ U. �'o>B89�93u27"�G .�March}� HAh\EW. You��[ampant�I�>�g@Many-Body problem�J��>f(1967)p. 243.�De%��Bu<.R�hAva�f��maddar*+p -�5},R16a972�Welke}0 M.  n PrakaV�a�)2��+CG<>yF%��(21 1xF.�Gale1��c,A?R~S�-Le)��anjNO151902sZ�=%R &L%Ff��f 16�942XMahaux� k��Bortign�>Q! oglil���9�"�_2�&�:{Huang܋  �2Statis�h Mac5. cs}(�/ �� Sons6�87)Chap�M14.��}a�`"�B��6�0) ?*�hV�e�?�� review} %�ARoberts:^dr.& ~D.~ �A.~G.~WZi %``DysonK/��er equ7/ = irD6l���ٌic phy�f''�f_ \a\��0}\ ɺ 4V9�6��� $9403224]; 2��HE�� ��F��caaN�S.~M.~�,�Lr�: Dens�4t�Zk�&y"@inuum strong QCD�� 45S1�;0>��z00506B�N�� 6�Alkofer�wg�~ �L.~�#mekal�PThe infrared behavior) QCD �A's�G5 : %9Uine�^, dynam  symme�hbreaki�'!(Is as ̊ve] bound sǐs97A��pt]% �%:&000735BӒM& !(y/�!s!&3vk�U~�C.(%$b[� tool� �BInt.\]�R\i� }\ Ei&!K�&Pb01049R��TH��N�1997tm��p� K me�B�~-Salpe��amplitu�Zu�1�v���33�F�,>�970802b� ^�h�u)�m >�(P.~C.~Tandy%�P�mas)��a�s�a>��}"C�4�12���J�70Z'�TH�6��y!�4hh:��( magnet�P� form-factQX neut� �width�� ]g�6@14�]PԹj823BZ�mD946�emf.peBaS0s>S>��upB++hRK0 el��� �J.z�05520@7bK15>H2K1�#�I �1999bh:EN� quark phoC Wex�Oq%�� radiu~�� 0452o 7B�910^ �A� 6�8Politzer:1976tvmaHI�ffective� rk M|Gs In !�Ch%� L���LAT02%�y���1aw�, D.~�meinwe9VJ�(NonperturbaeLim4�5 %$tree-level�_ w �/�K5z �07= 6�% 10201R�% 6�Bowman!2bFOMm, UD Hz"�JLI-B��\� ggev �aGa}$La�g5$E Y�6~m�67 0145 )�?�1U20300B˛U 6�!3f*!��.:�~*\ %#F�mR!E]= %[CSSM 1'2g�]�S;wng2� A!ovp):8�C(355�[&NE9~ 18>~ 55 65�9!�m�� A.~Raym;�v �F� Face�conp ,&s j�Jy ��Eur � }\ � 2 ^v 20807B-"1 6�Bhagwat�3vw�)� � P�3�l2i �>XA���a quenc(���-� d?yed-eE] 560� (0 0152kV^304j� 6�): b)2ge6Z%,A.~Kizilersue�$-gluonT from1��JHEP}��02z$0]A�:'20531RPH@�Z3qu�I..P22�>"�%�>9s�dAa�)�.R30�4&h.�!303176N�! !��M�A�4hnB�A.~Holl�� Krassnigg�� As��i$oeE��Hf a6�2 �R�7� 0352�.�nuc�� 3012>u�4fkj:%�>�J� mode�(2�ataչ�!�407163.6� ��!� 6�LlanesFi�"r�.� %�ym�S.~ ,��J.~ E-E A�R"ME�& hg&� :� q�B�294V��%%}�6��jz�%F�Ev�%�:� Semi2� AzemwjnB�3�2C =�33:BF)��3rUzv� Non-2�& s, ru�) coup"��&�1%�ofc U 1��:DX �4L~�$:(X A�9B�1 !ɝHend� 96bb`J~ %�:�L.~�q*� Goldstone� ew3Di �C*. Beyo-$ainbow-Lad�=ApproximA an.�: 38�E��D�@96X b@ R���a��W.~Detmo�fF A.~W����:��E�a n:� )R8R?`z"#2*W �5�08b� 6��!3ghE|1~F�R�W.~H.~Kl�\�Ve �6 a 2Ypoint-@a!�Q. V�E�p�3�3N�3�BA �) n�wy6��2��DSEs,�{5�ed� ��5�308039:#�6��!�4fr�6�Z� PseudoscaV!%��al exci<rq�I�)qZ� 6030j�6�Ivanov�8��Mq #5��alino"��F�Survey�*heavy- �odQ�*%~.2M$}\�1�0 0340�e9HB5 8120fL 6�T 1999n*T %�>n: stud�v}8�'2E��a�xr� � 55219+V�90505BZ Q� 6� HoelI�BJ ��A..2��,S.~V.~Wrighte@O�Y1>mplex�� of pB�%�:E411065^E 6�pdg.X yeXa�S.~ E4�k.+��i�$G�E J8�R��1Bg�:�>ky2�$PHLTA,B592>�Edward�b�i�u >� CLEON�SQsBI]s'� moni1�$< B $\to$ eta/c K%�chi/c0 KN���"E�]R;6�،00x�>J�­ 6� VolmE]�J�>Je�I: Lab F(pi)NNew&�@�o!g �onR��17�1=�%%10009>e�% 6 Am +li�6wj�*�>NA7N�A M&Ǯ Of� 8 Space - Like P!E:F�F�5:�m27��16�)�*2�m277,16�&� �[8h�s�E�2p�_���Kcomponen���۬I�gamma ��E (q**2)�m��I�5^336^V�80406B�%� 6��<erHeide��3kh�pA �8r oc�3E�ey0n)!�+ �9�i�d�[ :%��%PI�0u��low͋Z� 9},� 51/!4]�� � 1202B� a�� 6B�!  :�8'~G.��,, G.~T.~Flem� R.~Lew�_D+R2_ rds %[LHPN &�mpu/ ��Q?.�!ɥ���28:�� 6�u��6u��f�%�R� Kaon�k��R/uB�:�1X94X? 6_Ņ178,43:YMolzon�8py"1� 2r�K(S) Re*�On�K ns F1!�v/C To =-G �!J�K0Z�a�>}%'A78) [��-��$ '5�/H78\ ERRAT,41,1835.1;>�PR!!#2136���Cmzz�>TS�|5.jE�lF � B��}\��45�s�}��p�$201017>��� 6� VanOaM� 5eg��W.~Van e~Devin�( F.~G�GEEla�'�J n sc$�B��acdee on u�fgB"?at� ��>��, 4�"K?6�%�75,#6��"�7qf%�2�"Ha�I'�globa*Wz;of�c�rog���^l'�DX^�#5J�1�976�Dzhelyad 0tjs&I.~F� >�T)I����Omega�Y(Pi0 Mu+ Mu-j09 R 102BP: 1) [%� JETP��<�( 1F���02,29:� y�n�}JE�M\%eM��Z�ȩ�}H904>�1��04-�enF���C*&)��4(4(��*��5(.5(-�R0(�k3:/( *��-(Zy A�P-�%F �(R(^(�U O4V� � (� (5}c"� �*(>��'^ !J� ����N�F�B����/yu� �/&�%m% of d��"Fewܛy Sys_*�����0�>�020402fR N{2004bp>�:� �ert�5:�:�40900b� 6�* �7�;)^;).V"& >5)1R� �)>�� PHV3)%�:R9)�b�i(Vi(R�Bc(ޑl9B(>)�y !�&$ �{/�*N*R�A��"�)>�(/1B.� șsJNB�3sE/L.~� F51�o�{�)exoticɺoscop�2�( ѯ�e232&���Mg8�341Zg  �N[�f0��CorsE!itr $h|p �. �fYjpupָ�Sst�~, topics that- y don't l�Dto get lost}\\ Car�ho��:6itr�=ofA0 Old Library,Eques AbbRl( $X^{th}$ C�" Avey� (�*ifral),o�nce8� ;INTROD 9LVa��$inPRC3} D.ECF�}x_  C�B72) 676.=�Kri� $NPA336} H. �P?ne� O.Boh<+@GEv 5 �)0)��." � *�B8LyonNPA627} E.Co~�| P.Box$�& Haen�IJ.MuS"xc, � v6�:97) 710.�j35�j jc98)�%Nj��F.DouD�%����65 0)�_.U BombaciPR2LI� Z��") L)rdo, MaRep�hL 94)1sY8 LPRC556]�I(�C7ܻ<8Rhonote} We rem�-�ki���llN�3m��I� a-�w,4presently usedNx9 schemee�pre�W ing stiff-a� } si4term,(ore!al�ibaryovll5 c^-g&$\rho$���"��� ref.�Wg[!D08}. Actually � uper.�b�4ur�sobum ed when a&V!to ���d. $\delta$Af d�s �hKubisPLB399,LiuboPRC65,Grec 72}X2� S. ,�g"JE TakiVEIbQ8a�e796I�U�(Kut!�G@EgŢ �JAi6TA�} B.Liu�.� B��XCb�na Di ]q �gI� �02�N!$ 7} V\MNSKJat� �a& C�3�Y)�(2�aoJMPE7� -A.LU M.Ko� Baa�� J.Mod�E "8) 142� Isospin01�< �a� in HO;�i�Eermedi��EnergieȟE�qBao-An L�5W. Udo �=\"�= NovaETWPJ�rs��1,RAYork).�$DitoroEPJAZ�M5� VJ�5z$ S.Maccar�I M.CabibboamE6 J. A�2)�i��GR98}��u�s��Rei�jSQ��G%�',  zLanza��W6�6�D(99) 1c-446c.�HamamotEY0�a�@A; C�yC 0313'��fM�y�^2�M\"1� D.Se�6���5)��2.�e)PRL��N~=1�Zi�ZH1) 4492^m~`8}!�q� Ph.C`�Ayik,.� W8 a8Dirac-Brueckner�)achk A�>ic%�A�M"} EJ��0��.��v s.�"�4��G.Fabb#�.�^%�9�Y�66$EOS-NONRELrF *��%2A:� isob�  , W.Zuo, "EOS�b�",W�O c s pp. 1-34� refs.V �2$MyersADNDT�CD.�Cvn_} -v6;2� x� NPA4��M.-Q$EM��{�Niemb+h A.Bouyssy��N.�Q6�4��88) 472�Bao�61} � .�6"+A��22P�F�2 �hS.Bedu'� �85) 1112P :J62J T.L.Ainsw���c C3��87) 342^Wi�� 38��B. � Fik��a<r�� C3� 8� 012hAkmal��8 �Q R.PaO�rip�d�3G.RavenhJ~^�P]� 8��&�Lom��%in��~]�� �zr %�Urzs %�t t *� U-280]-� U%�IW��2g� L+  E�5�� ) �222>Fa<� 7� �,Sar?�K.E�F>X 8H51) 1811 9��-:-Y�A�7�l������I����%9V�Y��ڥ%z�Lu ,70} Y.-W.Luia�H.XLblo{jT.Toki� ~.�Sk� �I� &�v�/ 014302�"�25A��� Wojc* OIq B325!� 12Nl PLB426} *� A.;�:�.[4�@�{.p3���"4J.6 l 6#��^282��e� A�eon Op�N�: }, �Y\ti�Y 1994."�cie�3K R���a�62� u Rizz� 7��J.A�Nu���& ;1�2Z&��GalO�C. !FF.Ber�� "�P� =��199342t��59a� , Diploma!Tsis!�97);\\ �A��^��.�C�-9) 810.HN�Eento A1 -� 865�.9TSapienz�7!�5����&����-+PR1a�Gb= R� i�� 8�� 6�~�.3 RPA_z�.��o 6!�~|. -=�]�[�9=���%���� ��C��%M �Vf��E$JETP5} L.D�%$dau, Sovie�<� " �/5�z �;$MigdalBook� �� � TheoY�5�e�� mi system�! ap��#a���i}, W�b \&�S��bV.� Baym�78�U�Zh�Pethick1�q�T�Liquid�[8Solid Helium} e"�_��B����Y�kKe�c�YVol 2, Gc�-�%[78), p.2@ �AP1���Y G.i�%� E 1&�13VYe;NPA6� N��!�&� % �� C�?�6� I5SPJ Y4Q$E.M.Lifshi�h%m.�U��U(, (Pergamon"�_ 1989%( 263Xu�5� S.Xub<m� 0) 765Y!�lloHIP97;5,Uc.�School-�@nar#"* Io"��DEd. Yu.Ts.Oganessi� ��.�7 %�#�Sor�>A� frag�=�6ingh�in*��Agy�: ��H�}{��=���n� %�2�%��; % b� l"�"�P&}".-U�78) 52WaPRC49H 0, V.Yu.DenisB_Ae 49B 9� 86�a�NPA��D�aymjA.k;�Jq�.� �1S71) 22Ey2�#�B��#:)33Q�]�1� �}�P&�� .�19�)BK� �eVL&�=�� �7 ) 6325 �8} N�C*�3� %Coulomb y$c�7n�1wthAi�Sbilit�*in b� B�PL3��*� .� V.L�N,a, A.Smerzi.� 30�3) 272�-�!Q  xD%!.k6V%5 � 12t 18�:� .26�>7 86�� 6YZBB2�M.Typ"�2Zk��!49�F{Pr�xg jaJnd�jm5Xug2�$ %Neutron-J7�{.�Gregoira94� Ch� ��� &�P8x12'Bon$�a�%3$$, F.Gulminʚ"l7!is&Q�4�'!��u�� PPNP�*�`RbAL& � sBr�!�� ��65$FAST-FLOWS�`6u � �M%� 1*N�N?�ᱲO�� BoalRMP62�H.��K.Gelbke�w K.JeqG�ev&$ >t��56�Q$ARNPS42�6[S�tt�z [I�art.SM�4 ��2L,ArdouinIJPE6� ,$our� &#36 Wied` PR319�A.�(Hei8n��p. 31�q��Y��nPRL90� -W.x)C.f%�f*S 90%���6�u]P� 8�` �v�C%>&>O�ria}http://www.nscl.msu.edu/ria/index.php� +(phy.anl.gov* := 29}L9) >% �6�7� �80K5G�L� W.G.� ^�"A� 2114.�<+3A� K�v�9SC�1) 782Y7Y^� C�N19�1R46�Kunde�#0}�}^II@� M2>�el�oosR5f!Ja� vW *#$3082�Led��y?73�A�L.Lyub�� B.Erazmu� D.Nouai� �B3�j96) 32�VolIae7�)�-uS�itk nd N.Xu�]5� g���M476��G� 4.XN# LB4G��6cPrattO 3� "�|��:�iH3132�$GourioEPJ7�� :�E���(�0;��}�Gj�374!� :L��B A6m��2� 2� ;�7bJE��),&r��6�Kooni!yA� S.E. 2a BI�7� 2` 1j53� 9}�� 84) 1219;k4�1�'y D3� 86) 6�(XPRC� -ť M.B.�i�.�23���� .M.j ** A�*� 2�21�%7� ame}z?]� �7}~z&� .+�� *�%146� ScaloneaX61}L.  { D %GI4 B461�a2�}�J"C.B�:�2�*�11�9������!z.97nx���� 7*��6Y|E'6*%92%Vs%ba 9  054606.%dL78.d���Z.Z.Req�O)�p7) 16-���8b� *�.6�766<L+LB4�w&�e=6� � �.YZ:>!Tap 4��P.T2��..F+2. 51901R.@St��erPR137Vt\"ocke�4�i7��Ri 1����2776�� �6� ��Q��� C͞2�-(U�DnnPTLSa9pn G.W.Westf"$$ics Today Q3�$.� � SCI2JP.��acM�� LynC,[ucen"2�I 1592�r2�&]F�-v2��LV A�6P.Lev��-R�* 34904;iD.Mol��dS*RP� I)91� 09}�=" M.Gyulass%kqoD @B�x9) 45>P.Kolb�6Sollf���U:w ��096 )uPLBz�6uPG.Odyni�.�15�.1�&�&&>i���� L�12Ly�8� 9) 502&UdOlliPRDAa J.Y.tra��D DMSA�6 ��3:�,268 �37��r> 2�.� CQ��iCAJa�%8 U.Mo�7649���.� �c22} T.A��+H.H*!e�'es�+ 6� 1 k_6�%)�7'.-��i, ��Qzɬ*v6� 7B�)4=1�� ^N1��LI�&�>q&0B0�/� E C��9� 66@$�08�N��� A70"�136C8� PLB5!�"2V�.�=� %�"�s �V�215h ePh.D.T&��.L�4$U�c%xachlei��haK CC�<702;\\ {\it same�} Phys.Rev. C49 (1994) 566. \bibitem{LiPRC69} Q.Li, Z.E.Zhao,.AT69 (2004) 017601. % G0GalePRC41} C. �, G.F.Bertsch and S.Das Gupta, %.]41�0) 1545.�E m9) 810 M@Nuovo Cimento A11�!�862) Ayika�12} S.,� ��6�212���2692�9NPA513VG=�%G� 8!55�RandrupI4� .6J��0�/�9�M� PRC4ee �6���49�4) 1908.�)�v3Z ==�.�J�e^ ` if7 �4) 3512( ��6xO �k]�M]ZuC4����395!�B !l80aN �Aj Mk� A. y% � % A58���R��6F Ma.E A 63 C8) 136cN��66= =sZ)xA567 %1�63Aj��t� [8)��U�LB1 %� A|ys�p14e�84)6nYen��o���w S.J.��I3� !�6JohnstonJ71} H.VH7���182&,Ramakrishnan��7} E..6PE�.86� M rPRL82a�Tok�.R 8�s��1��5hKundea�7� J.F�mxi ��89A Gortemey�C55L , W.Bauere Gf-�� C5� � 273��YfXu�5!{Xu^�85 ��0) 712wTsangA6a�B.bF6F1) 5026T%�$64} W.P.TaR�64@ 051901(R). LiuP0T.X.LiJ� 2, 4603*� ShettyC8P V. F� C68�3) 054602� 6GR�H� :�K70~J70�16BGeraci� 32a �.�732K17!�U�Martia^6D De�Ap C6 Bm �ECasinia1A� FEmi�3) 25�G8StefaniniZFA351 A.P&� 5 K 5) 16Ja��5��7iF5) 292aF�MontoyaG3fP.  eZ5�f072LLukasik��� �=hy�1902�Lefort��!�T. D.�69�36xGingrab5} L. F�� 20�061604.�DavI65�~C4612CBocagt676} F. F2�7�fq 92-Col �7!�B.�7E�a�6�".�Pagano!W8Es F2�8r 313U. 6e�� RF73��042FDempse�i 54} J.F. J�5� 6) 176� Pogg�6�G., :��1A���Milazz  509} P.M. 6�i�%%^J6& 6!iNI._*l466Plagnol��1�� 6����9)A�46:Carochel=aFY.RN��5c>�obotk> a� L.G. NLy�2102��CaKHR� >�f��z��31603:��� PRL9sz�9)��627�UFRam�84a� FIA8i�16�8SouliotisPLB588�\A.2 ,Velselsky, D�� &� �*� 58�� .Zh�CQ$Feng-Shou F� C PIi4:LiuA�,26} Jian-Ye .�2�2��. A 5A-�B M.B. V�)C1�6� On A. On:�i5 .�JkͰ!�6�. 6�nB56�72�Botvi�S. 6I �&c3442=5� � *N�K,2:&� 6 54�32� 2m��0�-. ,.� 5J� 272R^K86�2�2589�J�2V8BrosaPR197} U. A� GrossmanY Muller �� 197$�16; Viol�31N�3%48�552� Hind��472� J.D.�47g I2�Twilcz} We like to call�X$r-r1$-correlation plot5� W�$Balianbook� �@From Microphysicsa.Ma}, SpA�@er Verlag, Berlin�!e�%.�=<QHD�V.\.((WaleckaAP83` D. , Ann�(N.Y.) 8EN74) 4� &� SerotANP1&D.%�JQA� %��Advanci�-��ics} Vol�D, % Eds. J.M.NegelI \E.Vogt, Plenum, New Yorkq866��IJMPEr���Int�od � E�7) 51�"� SharmaAP2�D M.M. � (A.Nagarajan%P.Ring2OY) 2�_�R810,\\ G.A.Lalaz��� W EP(Y.K.Gambhir6 %<. A60�6Q!26-�PPNP37} L,�B�3"�193.� Type� �3S.�H.H.Wolta�!�-<A6�/> 33�Y0Mu� rPRC52�M\"��PBQA.{C5�G95) 207agN�{ �� .�KoJPG22M.K�G.�#J�!A� . G2 ��66zDeli) fiorI�F.MateZ"H�C4�h45E�UsHorowitz AvCx %9K.Wehrb�QZ A531 b 1) 66 9? �P��Q,V.Yu.Denisov2�&�286Y Vret<lcD., >� R.Behnsch  Poeschl �$Q�2O� 7) 86y$M��TZ.Y.Ma , N.Van Giai, H�24M.L'Huillier, %)v*�38!5uMa�'R] A.Wandelt� �%< � 2�&J173'B�$9� Liub� 5�Liuu"� �"�o' N&o 61*�452�hSw7 X D� Q] % C*{1526�Nikolau��% B.A.�Ho!�(D.G.Madland[ *�%1752^Furns+27��J. ah��$J.J.Rusnak�&%� A62��7�%46 BCNPP2NS�� Comm art \ +0) A2N�.w%h!v4�vG!%�5�:�&!�2� �A��RB*�2�7f"20�442}Buerve�<5} T.J.B\"urveniB�J.Asuh��' G.Reinhar2�2� 43086�Hofman�o _ M. Kei)�H.Lensk.I C64 % � 03436�Gaitanos�32�R� *j2�yK5j706:A,2\70>2) �pCmarX04E2Bj6]A2]m O� e �� ector cha `v( point coupn L %models...} arXiv:n�(th/�006.�ch{EPJA1�E�H.Mue�), Euri/J.>! 1�6����Z���L�eƩ��2'4322�Bogut��50� IC.E.P�"6�50 9) :��eNPA399J.RZA39� 83�j522Bouyss36 , Mathiot.�hSaI cos,aF&� 3� 8 380a5վ�e)�$����= ��i�rX-p')�35:_ 0DegrootRelKin�"R�+G�� A. van Le� Ch.G Weert, E�R�M�Kinetic�#8ory}, North-Hol�&4 Amsterdam 1986�akimNCe� !�.�#%.7!2�&z � �6� J.Koni� ��]��&G54�y�Kub�E@c-bis%j M.Ku�-& 1*� :n Fanto�87!k   SarsI�K.Ea�mid.H ] % 8-1) 1811U4Dit�}21�"M\ Drag{MH!v�, �iDIsospin Dependence"Cria4Quark-DeconfinF Densities\�hV�h-�h 21006�� e5on effeI� mass.B Rhos0 solid lin�Fig.4 ar!F t fu! symmetricE� respec��<$\alpha=0$ dashe M. T�is.�fa7hat, �(ixed baryon�,Ttotal �ar w%Y�%�!S$gma$ field6�(first�0"(Eq.(6)) is �5\$N/Z$5Ft.' Hube7�Web�M.�igc0u C57"+7) 348� ��SY% NPA2+ G.,H.Ch*a,&�0.� 264Q7�%:N f'y'�6y'.J.Si��s�i�B12�j�2;Jaqam8%29�R. �eZ.Mekji;L.Zam6� C2��' 2067�y��VV.�F�E��7 N ��^ 4492a5[Isov} Of' @rse we can have o�  aY�($NM$ instab��y regio!) at higher6� ies,E�D a different struc�� o�2uSle � s \cite.��re some�p�?onseq(even predicń$quite exci�*"- -�} (a��1se�3��) �oscil�0s. Unfortunat��a��ears x ��� e��al��si%0ie2MJamineC�M. �Mahaux,� ochuQ�� 22 �j62022� E�� 2UQ C4$ 352rKozac�$x0R. R�C3i0I146� Ua ;��"ZK.�50 M�666�lugPRC67;J."��*�/!01R8/M bidem�-y�8:\�3*{��B B Bib_relin�.pLandauSP� L.D. 1 ,E.M.LifshitzS*!)��(�ergamon Press,Oxford 1989, pag. 288[55�HAbrikosovRPP22}A.A.}I\halatnikgR2E6 _5�5D.�ymBook�7G.BaymS �e�� � 1 Liquid %ZS�,Helium} edit�/y K.H.B3-xZJ.B.Ke< son,$ , 2, %(Wiley,�-�78), p.A�� �AP1m.��2� *0 � % 1�8� :S���32�2 ��� eA.B.L�n!m!ܩ� % B42@_2�GArVFd % .�63.�98��9Ŏe��" ��}��_���'�,NNN�KAL9�$ �Q�0 Fuchqgh.��*] �.304:�ch�5a�.SV�~"{"7322��!�56g�VI6Fa�E��9-�9�v.Chossy6SE�!�W3)�06�phi� � re;"at,;;� $\phi� has self-� terms,�ead_$f_\s� one78to use $\frac{dV}{d� S}$23e)�~ j~ 8!�A|P2�2h4% %�05�*Y��5� MatsuiNP3 ,.�3t198H+6�#�bRSb�2�?&k�._!86}R_R�9 ���I� A6�. *�NiksicA�61 �T NM�"�064302R9T�0Pa-`y6T&�!24310TCaill$=96}J.C. � GabiC%��,J.Labarsoque`2L9 �=�(9m���b2�JcJl�3�3�� LMU02}S. %&�� �4private commun�'� Coll Modex!V�!M�in6�Mean Fg Theo�} P�%� LMU-�ik Sek� , Myh �/2��b 6b �,L�H.SR�,7o.0o49�f6$HIP97} %S.�!c.z"4School-Seminar�"Heavy Iq �$"�"DEd. Yu.Ts.Oganessi) World Sci�(97.� Di��/"#" !��a�1 426c� 2X��(�.V�VA �7� � �B.�7� 20� 129c��9S���-�%��� � �F FRBREL-DYNbN=�� 01} B.-A.�FW.UA�roe�(�%� � 0�j'in E�-�*�=) at %I5 medi�pAB}vaA�m� � .�� ��(FriedamNPA3^1B. Rw3`1�506�Haa^9�-B.C,, R. MalflieBm�-�166�Mu0UV#� �G�G5. Ainsw���� �p B1a 7) 4:6>Bombaci� 4} I. �Lrdo*< .� 1896K���V 8"�}�ee NC.��A"yHG.a%G.EBU� 5.Y�*YZu> 0�9Z�H��&�029OA �*~/�B, J�B6��>�BLattim�LE �(U�%�; �b? 19�%>�20SumiyashiAPJ4�[K.b Tok"�~4�_�J70�u/M�PRLa.#JE� T.L.]�.�]O� mG�560,Engiv,8Lx8L.  a(J�Hy**)266�/EL29UL!2E 2�8�55�o%Sce�r.��APPB30� a�*� Actad.P�D. Bd?9) 27�5G7� 2j<�Niemic=86�:58� Y�Κp+�k�%b��E�61}�#E�49�?WBao�+7�XC.�)Z D>,F�+�'1%�2N�2NA�u�/h=�E�*&?500].Jr�L�r,&�DA�y� %>kb�  D�'�.) 6&�9r�  %� A֍���� M.ZiI(ska Pfab\'e��  .�*�8DK.'%q5=q6*'4:yUma<�z V.S.Uma M�varJk7EB8) 92��u�B�C�(B��ig "�O�VD.a�"+/�A.X�]@B��"!��#�I�BM$�>"� dML!�d�a6�'�&*�&*9�H�6r�E>E*!:iFu)�Jo�3E�F %��=y&#30~KU��6�48f-B\"ol��2A.Faess7 2�64&���B)��FR)Q)Z�N)a1 &M) 6�al.�(7�4 N.E.�%Z�% �2&`Dirac-Brueckner Approach |I&i��&X}ͮ�(I$407�@��!\��I"JB`+, Z(]+%%F0)^+R�_+:]d�&) 0J]+EF� 2O.����6&�1�6 i�LB5�"�KVK T.t+x&c �Kv훭5�=3) 215�KdPh"�S � 9^66%�xJ. j$AJ"y 2-376���*2e�E,]�!6�-}��6+8. 1) 4x!�Ur|9&R>�,�HK��9 e R�0 4�)]�<W 1084.��k3aVS%.g3� *�U.gE�� CY�Y.�B���I!�S.�Ai#Ain,6H!� 5:�Stoeck� 16WH.St\"o� G�V�#-I�R3�8} 77.�R9� Dasg�WPT12�WG.W*VPToday �V3U20I� SCI2�O:�R.Lac�W.G.Lyn� Sc3A� 29@2+X92z�RHIC-v2*�QSP.Levr3�S [�904;\�OD.Molnar�=Volosh!�P6�9�D;92301 ;BGYA�M.Gyulas@�BI�B4"9) 45 <P.Kolb!� SollfrankA�Heinz�] i�H549�B9�OlliPRD!� J.Y. trau4�CD-� 2) 2:�}PR�B6�WYHs�+PiEVaV6z�yF�:�PIO^��Uu&Ba�D8� �N�/� A7Y8�>�.�'es}h(ou->meworkO=�,p0qerf02�(;(!$should b�$whaj) cludKXn�'c?spond+B�)%ls. H,�,i?n&�)was�)$ realized �+ar��$vi�=Bc stud %t%s7}w�(<%- �s wi:�moB>um&(2E( <�+force��)�e*" & ces -us�G) y e�>�%Y)z�%R0 supra-normal�(��0@ pC? unce>��I�*�&sul("in 0l�[ �s�&*�)earv7"z,em�:c-nd�ticle�-duc�.� FOPI�(Reisdorf ($$ c 0bor�o"R� n&�p$]y dataA�:3R%,iso-stopping:+ �v$Bormio04} ��.w G.Ferini"�..B�1UiA� -�h%!M!6}, K/v&K/402041o XLII5ern%> al W  Me�.On �8ear��ics, � (Italy�;�I�� 962�*g����59M4f9.hG�4} %F.vG (A;.�ġ� Zf�GH� 66} B. d zX .�4349ɫ�GRv taken fk@ B. j, Y�Kim Leifels,6�!�.� GSI-Re�0� 5�B PYG "@ .� ,N.El-ShabshioY5&.7� � 240L8y��;%��x\end{thebibliography}�\beginB {99}9 ):Kmc} M.~w}}� DI.~Vitev, X.~N.~Wa�1 nd B.~W.~-I8, %``Jet quench��"ra���m�losf7C/e"�^~2,''>�p302077; %%CITATION = NUCL-TH %% ��DiscoEk of jB�beyondJo405017.Zo o9Jdinezza��$A.~Airapet�-�1F %[HERMES6�(], %``Dou�,ha�^ leptopYF�����/[0ar ��um��C\�W\�I8\ {\bf 96}, 16' E�6)[ [� Ŗa !#�#C��iB^6!e2s=9in1� %at>�9},230�<2]&5206011f!Y(amxnw�Majum#$:��diI:fun�7its evolK8a�2�DI�7a�01400�;4=�A�p�? 2245>�A�PH % 245� %``EpA�a{parton~�sB��2Ap3�5���X11174; U.~P.~Sukhatme,%0K.~E.~Lassila�E \E� \ D.)2g118KG80!�.�� je "7 0col89} J.~C.~�$�5DwSP<� G.~S� an� FaWA^6Hard Pro�� es In QCD!%i�;Perturb�9=n (Chromodynamp2&�1�g H. �( ("�'entific �2), Adv.\�;.\:(ect.\ High 4%y� )(55 188!$�I)9313],6 5=!=C2reX!A)��6 Luo:Unp*� . M.~L�#Jc Qi�3.g: Anomal��i�<nce����0ly �2sc�)andFpho.p !� 1�#mM5aM19�[4)F7 HRVA,D50,&;}�guowang}a�F.~Gu2.�� Multiple�F4ed.A �modified6$ %�%3 B�e A.]''67�,I8A35w0a�:005044^; A��X.-e-��M=�in� i: PB��"�A ��-, 7�V1J��l30^� � J.~Osborn�BǪ�Twist-f M�( %matrix e7R�Aoff-forw�+- dis"�f�71A�2�!.��C204046^� �*�1����B^ helic��,amplitude %a�xi� b�7� �;J� ��301195>}�� й�EW1} E*�:��tomJ���aj-�*�2k64<6xV�210b�2�*�qEW2�j�F rdetail�7al�!va0�'& cibid.}�E bf 8- 14" 1�!J10604B2  � �9�jetsetV~Tso�3 zG�+ staf]8$G.~IngelmaT0 T.~Sjos dE�-F�VE Astr D�I!5�p��99��Q83�7.%$PRPLC,97,3� F} YTHIA 5.7E5(JETSET 7.4:�M�AMmanual�&�ph/95083�E2tM� %C9Dbin95�Binnew*>$B.~A.~Knie�LG.~Kram�N %``P�kaBX2ee+ e-e p*H  at next�leah %\B�5Hh�)o 49iS699503464Z�  ��maj04fr@ z (to be publiB}.1b�ufq� F� AhV� %``MeasurMJ�wcI\at �!L- GIN3��S12�-]m"Te:Y4010]6�e9I 4%��7 ��&in $p+p� is known! �@Med ngroun�Y�Cmx��biaɑcoss� in � � .eCdevelopsq$on-trivial���(nd azimuthG ngle"�cn+�A$ ) $A+A.� . Ref.~\c�@wu@ { two- �� ion J �85��,�GIbas�(e, �Yle.vM. subt��@ 7c1Fboth zV� Such"�t method5.�he�EEmex~H[c� inte��syste�dcp1 }Lxna03}*� �C .��At"D.�isotropy�!S��"�\� �-� ��1&�a(# ~M.~YP.~e$!� coL_cŻ!�/proton/pA�a6y!�񿍃r�1�.N� 1093>�5��9i�.�� \��Hwaa�4sw� $. f� DJ!�e�� 7#%�J�:�M�C549-C "KU�P+81L]��%� A�%�Y� �C�0ed&"of"e�U�ojI�eed +E�:�6W4�&�� V�102�Vm40!A�R�W*v��2. % S�Imacro�IavailaC�L��.: % jPg�alE  \JL :journals�2 \andvol :�E$(Year) PagF [$individualG��cAJ : &i6 J. \NC &"Lw� \ANNz`!�e�0 \NPA,B& $[A,B] �CMPC�>�9th'\PLEPLE cE=2E6` : Int�Mod.D \PRA -E � � vD-E]g1JHEIcc>�' \PRL2I� �J �JF� \PRP %U �GH>:>of .\PT!:�g� eor.�KSJ K fSoc. Jpn�!TPSI!�5z:KSuppl�UsageE�@\PRD{45,1990,345} @ ==> h~�� \textbf{D&�+0), 345�\JL{N�Q,418,�( ,123NG B 418}� 2),�WBI�{B123�5,1020AB}}~5<020��A*Text �dsZ�c��q in80} P. �C�� P. S��!|aDh! Many-Body!�$blem} (SpIer-�dlW2�tbla�60 J.-P. Blaizo�cGypk8�Qu��ArFinxNS� so�MIT�'ss�cm%Review�%= kle9� KleAndvwa^rshalek,.�h"�CAx1Ax70��,dan00} G. Do�f�c `�N.R. \e#>e� X36g7A�6wc kur0 �$uriyama, K� tsuyanagi�4 Saka�$K. Takada,d@M. Yamamura (eds)D %�Se�Ced Top�B*Bo�Ma�(E6 %T�hD�St�(tree-Fock M�} b� �1�l�1%�Eq*of�"8Y 8Dmo� f�*� rowds Q� Row�R�B sser�L, Canad�Љ�%��r(1�RAt41.{*goeVK. Goekd@- ?�2HB301W*UvilGy F. V$Qrs,eu>D 9D7),B~marDT!� rumo�'i�iPL �7��I116�@ bar78} M!ran�hA� M. V-o�*6}T14~��M:]!#T1#QP.-�"�_RT2 �T32�?55mar:}6�� skawʂU�� A.uN���6(�¡�9B1qgiaqM�)GiannonHP�jg�4�/ �dT 2�dob81}�$ Dobaczews�d J. Skalsk5J6R369%8�i!p.r/goe81�"Q�Bn!uRo3 4�a4ka5 muk�A.�iukherj�]�V Pal/1��100� 457;�:��3z�z2��yrow�= De�a�V�91 hC3�%Cfio[P$ C. Fiolha�0 nd R%bDreiz#9N�39��83a�02�!s3.sF�p\"{u}mm%r>� N�5-#e50445kurg�8��Y��,RiE�l{!XZ1675; -,4E� 7oyamE-2_| �S. Iidry.b09.?mat85p+�IsAU.�^�74)�g 2�C�X6��K�DrB� )6 F6�2shiA_ Y�Shimizy �Ef��f8��112E�!X7��|A�2[J� �Q�_2�wal�.N.ti�q�= ��Ap�226�V b} E� A.g[.kJ�2C4_96kan94eDKanek!��56���9A�306�enak98_1T1 N�sq|i".�FV�9�i>� V2�VB 1 V3�| ��lib�. J. Libert�0 GiroM3/ Dela�yN��F_9), 054W.��yula E.Kh. Yul] baevYDuٽ%�M ��F%|d���Cs2 nak� T2y,2v>c2�KF � 01�O$$ Shap� exist�N,5a� y~woo92)L�<od/ Heyde�9 Naz"V`M. Huys]&P.�d Dupp��)"Gi�215)�v3ct naz93a} W6` C2e30 F��6~jFbBFJr 5Q�F489�M�taj93} N ji0 H. Flocpi. Bonche9.���$P.-H. Heen!R{�� {6�boe�c(E. Chabanat ?QenF{�3Galc.�2 Meyd;�AvMbyWei�N��G�T18 T5+reiaF>�< DeUO2�a�*� �A��ruh� M�Ltra�UE0�IG2�14316.1andaj0A.N. Andreyev���4�h�> 430;�5:l 6N %� 822'fiskS.a Fisc�^kI��?I��R�|Ua�4064;N���#,�S12� bou�$E. Bouchez�x9; T82�M}�ro%:R!�DRodr\'iguez-Guzm\'!�J�EgidoI�L RobledoL*�1�� %b��19;a�c$24304�G 9�� 9.�egi@3r�E�j�.r=�6yB"chaJWCh�e�L.12d _���bAQ322$ nik0�H ik\v si\'V &�UPa�Ga<&vir2�.i5436xdugAHT. DuguY�|hr,l��n6�I�6� M`$q�(ben!�V^^i2�.W2�Zpet��A1yrovici��W�mi� ndK "�E J�'amilt�] V. F�yy'- inV).2Pe� k482�pet!ծ�N�61�ބ 33; :�(EPaI246.(fos!�R. Fo11!��G� iamo��$P. Van Isa�A-�2y.�a�6or�6Q&@>Rf;n Vargas@"IF2d.�343.XUGd d0C.D. Dracouli6� R�.U54:Mkan!�K."X � aseg*�:izusakiR�# �� 51306(R);?t)� 41006�has04a� s�.z�NXaz���!?2�mbfmB�p:X*�8062;:2�sue�Y. Sun!�E5� �pi4!4� 1��%A*�k��SCC�# ��Y,�4����1g , 6664xF5)� G%%΂1227; �0.S93h 5F596��XM{#�< ~R.~uIK � %cee�%%Q�%(Niels Bohr B4enn�#Conf.6Y ear S7gYn ed.�Broglih�~Hage%0B.~Herskind (2mp85)� p.~16�etak89�x!^�4A�HՄuku� �QLMI49a~�1 26�I9a]R*��]32�]b]Q`J�5�Y�6�yaib90} H�Vba��v��E>? �), �*��yam�K�!BbF U , 80�/H 96] ter[J. Tera� ��"P!OF&WbG.z 12352�f2}fb�i2P529mH���4), 5:^mat^Ms iGP4Trend�%!�a�4J -},R��enY. Abe�K Horiuch:4 p.2192�shi` NN�|m�RZ.�1&+ , 28%a %A�KV2a =M>�A:�R�E�1e/ 952kkob�(M. KobayasiE|*� %&V�b�1�swA�hb O(4)�,el�tJ2&82�%~�1�J�6�JFJ 141;�.��Q�8 t(Workshop, T te, 5�pOct�^ 81. ���W Dasso, R5 ��%�A.�D�J�2)E�6�mizAY.~MizobA�f�� �c, 1450.� suz88;~Suzu��W7� 1z7 , 482Vfuk��T.~Fuku$F)}Q 1�!i>g!E�.�2!L 2+QQ�2J bar6�B.P uma��%�. 6�h6P�13; �I�196�� �Z241"7 66s��88 ��ieE �492�bes�  D�Be�&R�&Sorens)�rք(Pr��9l 196o vol. 2)k~1(L�y�alm� D. Alme;s��N � ~� / �"� Tb}rTN 606��� �J 3� �\J\yam��Dge�64%l�fR �X572=benDT. Bengt<5!�I� gnar,RW43\ 5��o� Y!����in A*arf3�� ��dav%K.TƕebT&S. Krieg5!YzQ3b���� 1wO�T!TV[*� v[*u�AV�&RB�Wi�%�[� Stoks�9�%iav�"� 2���=5*E3;X=+jCDBONN}�$Machleidt,9 mmarruc9AongBk�+7 m3}, R14�o9�%pNIJMInR2�A�Klomp".PT�Terhegg��2� �0 J. de Swa�B�49B9�z~2�Friar19a���/a:�aH�31!:{@9qDINogga19ɐA.  , D. H\"u�wH�m� A�MGl\eTժ ��k40�1�lM2lwit TH (ta{\l}a, W..P.zJK"l)�5&�=* zy8�1�q9=@{se�Sekig] Qv1J63B3� }CLwit01#x W�nLAF024�Bj&5�4Z�`G papevij-s s: o��% .�fer���Erm8R�./6}, 58�20���abf!�W.Py faltere>a%2.R!�"6\.22O^.�R�)~5A@303��99.I Rupp��%up�Gm� Tje. L4!�213�c!�5zSam�]�$E�r)�Dew�**. Ik2�/ 8\ EjV stadmMSta�K��G�QM.F�UBw5!� 23�ma�);a� G�F�#o�*==�7;G 2�z6|bakF[Bc'kam*�z hom<Ue9D;130_x52>foldy�L�Foldy20 @ ,�d61); * Krajcik�Z@D A�3177%i72ke�> �\k�|�h9 5�PrIm�.RKv by Paul��(oessow, AIP�'E�`. 334, (AIP, Woodbury, NY, k-p.1�x*/kei &.��W? Polyzou, E|� �w@22I��,U[kam�zK��6>�2��Ch. El)�6i�i6An04�;J�rel�K}:bT-S�ELe� F�e e!b c f3��70�86)2�ki���6�2�]�8A254Ee9%wit� H.���C@Cliu( W.�� Y0i�!�{3}�3�98�Mfglo!6�2sD.�B1�J.G��),"�! {274p#I���,p-�1}2p HelvQ=Ah� 3�%6$ 9�/!���/Mx�cal9mA, :v/u/2� Wein��h�   ?emfqk/t�1k/��s},o0I, Cambridge ��ers�=P�zƔ2 rose�hEW-,# ``E�Daryg anguI��L��Dover�?F?s, Inc&�m , 1:�kam002} 9(I90A? 1�;4�x}.�hatn K. H]�*9� 6*G A 42a��82shi95%o� H}�i�A119E�6; haMR�BG�4�7�%27]d� �2} �B0�{15A��6� cadj R8CadtC1*�.!,9K�\brATM!*A����k� N)r31�C2479�� S:�Y6� = )m2��179�786�uIX��S. Pudx�&U [>� 172K��.�' epel�,E.\ Epelbaum5#�ebE"!# 0640*YN�kN�VO�� SUP!�,Super-Kamiok���"X�9 =dU.�)�&�565�5�SNO �SN�l.Y$Q.R. Ahmad�=L [9�� 01139\KAMc!}�X LAND>�K�".5 F^!�D��1$m^APP� 0M. Appollonio� � �B~�� `15*C REPORT} �/uhone O. Civitap�&� p. � 96~��Fae� A."�!E�$F. \v Simk�!,i �G 282o1�KCIV`2�M�6�A 7"RI 867�PAS02a� Pasco �S.Tq"co��W��dejohan"G,1: 549 !��6��SUH�.� � Atom� p� 1286�SUH�z>\Wa1w�|VOG.�!oge�x�'Zirnb�9�v. �B �c 3148�CIV.2o��6� T. T�O� VB 194 " 7) 16ZUHU .�2d%�]0>�543YWb6ջ�TOI��� oivaQ�.i)�R�q 5) 4Z�LSTO�c.;ic� H�Klapdor-.grotha"k� Z C 63E=\�$4=VRODA�V.�Rodin2T� }% 1�,.C.̣�h2fAH� m�� g @of NEUTRINO'2004,� \'eg�F /ca�@aris, June 13-19,`Y4,_G.lHvGAR�A. Garci�x.wC I 3��2tFIR� R�Fi����ntr_�S.Y�Chu�Magli��� Zipk!S\emph{T">of Is�Pe� 8th EdiT7 (W"�� Y?�6zBHAa�h$hattacharyZ�5*�4.mBOH?A�)h�B�CMottel�K �*�!  � I (Benjam���62�CIV��FO.e"�  65� ��21=�SUH� .:a�ai�Zj�4�X� #uWCAU!�-aurieI�Nowac6A. Pov_JaOtamos�\e� ��� �t19�1RS jS*&FXRT1Bdy,�A. Sn�� %,,2�% �� � �� 59);�'K. Adair2�:24^3M�<oE��A..�2?k123 63�6 5`XR~*E.A Eric�:�ych�� � �*19}, �7�<R3FP�bi�� �2�A �2�14QxuVH d KoiB:T� r"�q!kaishR�'�[�U5z�!�"d��R.�HayanR�,5��j22XR65P��if {\it= },��Si%=�Se�i�$ia, pp.185!w6�XR7} V.aQMarku�k%7TEeJ�6Te�69a 318H�;�S. 4EE�$ Z6�mU68a�5�]1);:�)�Pe�{|I� calcu NF�.|DEAR1&9 CargnelliI��} (#�"< ), KiM!�F&luvsA�Miniw"�# (IME�ie~i9 Febru\ eq�x�.r25$Hadaf03uI,� -17$$oE�4003, ECT$^*$ ('to �h, WqS@L22� IV5}�.N. Iva �H�1(,Fab��4uhC@� 3m7P�o��O Troitskay$J. Zmeskal�_�[lNQ�Wpla�Zof �biAv $np$��t��S ic U�},�,�-102.�IV3��TFsZ�7�>�[ �Eu"�)* -a��!�)]-�31008.Z BS57}%*� �͡�E�eSalpeF�A e�4QUANTUM MECHAN�JOF ONE--�S0TWO--ELECTRON�S}, "?-Verl&���B��BIV2�:!�Y-� A. Hirtl,�1��...&V��41�F���4����Y�V�� p�7" nucl)�406053�!TE&  T%� O. E*t W.�/�*�pS%�*M0EI}, ClarendoP� OQ�!��=5!JG?u�C%�H4 utwy�?d � 2� 321,�4��WG:5#�|5�H���2&[wN�^6�PiN� slett I1�k_9" UlfCMei\ss �q N6!�_��6f R=35}, � q_);�FE3r'(4O�W �36D] �6�Av.�5-N*EFF1\5�\1��;.�.:-�27���1N0; a�)��,L=�N?�_���AnnNL.�15�1|8!+)VAM<]�UM�&U.->�U�%h��(A. Rusetsky>'%3!K341�'ݲ22k0u TE77� F� � H�����J � (NY)I�10< 4c77![ JM33�. MeixA� ��. Z.6w3�QL. stlei�R�Pratt,-I�)N a4��1962#LLC*L.�"2���"���GB7 n--rW>�w0,y}, Volume 3�\Co��of e��!'�:ܕ ��X-5,MA72}a HANDBOOK��|MATHEMATICAL FUNCTIONS WITH Form�v , G�n� ath�Wal �s},5d6� bram���#I< Steg�4N� al Bureau�St� rds,l2b%� hs � $\,\bGTt\,$ 55�rC�TH�k Wolfram9� , A �em�PDoing�.mby Comp� }, Addis!�Wesley P�[5Co..,!�I+d ݖ�Rg�.�2DT�I�<Des� ��$d)K.u�3"]% Thir+'2�E�9��77e*52 TT6.Lu>46� @I�71�!�6KEKfIwa�2�"�  KEKB� A�"�e�"30��"�M. Ito�X���23f��URB�: R. C!Jrrett�A.�Boff2� P6@ 0252�.  PSI1�8 D. Gotta2� OScrip�LT �10$9�r�0�3&XZ eJ.rj9}aty {Rapp�U 0ej}�.R.~�JX^mbach,�VChirS"�wrestore�/dilepto-[2�&�UM�spX�g��\���p�"�1&�Vhep� 9909229>�VHEP�i �T�V Oset�1eg�2EeA�}<~R�� Phi decay$, ei�6�A 6�* 6�@BY>f6>�) Y �U�dani}�/CabrerM� 7$�) 5�@�=�208f�2.�,Yokkaichi:wn�6S.~G"4 [KEK-PS-E3256])�&�b s Of%�ME�Da}dl�A�\�At Kek-PV�6~!�435. %.�d0NUPHA,A638,432��na�2�+A�\6� H.~��� A.ITesC�!�re�|*�\!�$ei through&pF�km�Y�50��P�3�s[arɮe�0�]B,u� %�x߂ZU~Muhliche�F�+��\�J�\hr% Pos�1U.~Mo/��0P6�a�!e�s[ �A� �Z \ C2���B�21007f� 6��W luis.[, L.~Ro�/5�.��v.~�qM�g63�1a �X|iN�A��� A 73G$+Jwh54b> �xMagas��4eb]�MRO� ~K.~"�E��!�The9��F�u�x)��^0[ uced22� %9� E�40� B�z  ��Ahn�id�imai}�l�thn:_ %`�QeF-��]�C, Al.  Cu)�i�E(gammaft.5vx - %2.4 A��� 4a]6N��a �u\DSalcedo:md} L.~L.~ ,5}Qm��-Er%�C.~|-Recinn  Si� �2Of�(�c #iApA�Re�V34Qr8N�F��3484,55)��Car� o:vq�b�.W? ��Rea���`s With �i��$100-Mev To�� !�.> 53/6"46"N�536,4�s*d(BZatraA\ 0ex}�ݽ DIST:*&ɷ��3 omega��6� p p r1wA^p(labA\ 3.67AR/c�B��g"24��2�A~��0V�A E �� Titov�b.�t� ~I.~$�L~KampfBE�Reznik�!Pr̂:�Tin near-threshold pi N%(N N9��"� ujA � 5��2�gd0�p7b  �� Barz�zz�= barz��~"�B��rol��e-bB\co���A��.�p�[%  %?% �>�66> 5�WJ�506f�c> 6�cNMj~)10}}raG�kooning�]I�% S)v K {�-��  A�- ~356�;223y"�.smmXA2ond��Jet~al.} e Report5H< ~257W13W6�-f� G.~Fa} J} n� RV�81R5Z 1982.^- gulmiflow�&Z�% P.~C�2�MemV^7�1 p.~5f2e�= ubal��! ��HS.~D.�� �1`O1^64�04��,Y1.�ale��A�wr�$�$C.~O. Dors?emR[)p.~77197>X9�$�Od���X?� .~28 X9.Xnoneq�g\$Chernomore�� M.~ID%$S.~Ort\'iz��.~z�64�9p.~< 6J(�Y� sa�_A.~On;OH.~"DE�R�0)���3m. \newbl<^y"Mias.�q{JZ~��%IH!�o�.s�  B1�17iZ14eY6.V%�b%Fʢ X99)�2�campi��`mC�K$one �Rc52)'46�6Y ecraeU�a>�)|: 30i�328X2B2! 8� 8%�632X8.bnumrec�T~M2B.~Fln��5 S.~Teukol� W.~T{^̀ ,1)mer3 � pesg��"�z� ��.Zv�26u\ phasP�d%6cPTklenzuel�6]R�72E�a�29e\2�bR critGR `A�8.�!�6q)� ��6aam�13r22�atG�[N )qR\2T5%�034618F^��to1� G8c �E~G��iI Ph( #K~Ts�LG' Wozniak ��ics%�6�8��249E~2� �2B�L.VzKzJ�:� �`583%5!a�4NP L���Pieper} %  et.� wf��,F831NF8Fonseca} a C.  2��#Q8^40V���}Carbo0$���# ,V�5T�5 0L)JS$1} F.Cies�MkEW.bC�Zgnoux � � �B44�1hu�Q2�5Pis! M. V�t�bS�0saA�A. KievtAcA "T`% 81 } 0,��T��} �Lazausk�;D�si�S70\'e Joseph Fo�+ G��k� [Phlip[T�SPP�ipsi L-#�$��� Se��v�."�45$ �3�6�Pt_exp} �"JarmieQG. Sil�\D�.Smith�"S. Loos)�)1 �{{1$�5%$��LC_JSPQ_�/2( �.�:�w.V�,ovP|nj } Se�u$it e.g.} A Meye*-.p.)d102�>91a��#�&��]`6�]($"<�],�]d�@�DSIEtD��iVOKE oltei�F6�u��� �4�17280AYA:Y�\:�$+34�1�f.�cs| -M.�� , D.0&en�iR�Zl�',?M&�nE� 62},-6% 0"" "�G :� � nh�Ee8)�76��W ��F L�S.RNa%<=GM�&125�:�9ELM�/$L\'opez-Mo�hU2asta\~n��J) Y5!�23��$��4Mex. F{\'{\i}}+%49}, Su�o j �66�FIBRx�8��x��(�)S8��05�\�8�AB&u-13&6�RFC!�F@aia�se�dU.KIBM2�%KA. ArR` }�4�� ng b� 5!���6�JBDW��hn��� ��%�&�fF$%�8�' 2749!Y96YBF1�� i,P�=kbP> 42�.�BF5>O:;�K�ua6�6 News�;�HONo.*a 6Zelev��y� �A.�8�35W @p,�Om5.�Zhao} Y!� �>�UN. Yo7aaQBY40!\NWBFP.ZW%W�Dittel2d�HD)HC%�6S JBDTn�N�:Y��2almRl:6�3�h �6:BF2f�!�.I��L M�O>M3�MAd061M6 duke}�!G�Dusi# R.���-��EL�i�� H!�SofiaI�� r 42�G86�BF4��I�@1P�6�ralla�k%�O�Gori*enkR&N -s7A~0rE�j.KN�  Vszs�Gsc|ft-�V M�mid>�*l}�I�2i�D3� V  ��0dagostino-00}[D'A � :^Y&�n7�,2S�6\�8 ott-e J.�>Ell���HJ�ͤ�442701 (2002). t \bibitem{rayleigh-17} L. R �, Philos. Mag. {\bf 34}, 94 (1917). H$moretto-02 G G. M 4, {\it et al}.Wxys. Rev. C 66, 041601(R) (2002).WHfisher-69} M. E. F4, Rep. Prog. PR �0}, 615�69Z�3>��.}:�W 68}, 1602� 3). .Ddkrishnamachari-96} B. K2f}�%B e5!^ 8899�96:�ader-� C. M!�der.S �! v, C S�064601�=�binV 74} K. Bp and H. M{\" u}ller-Krumbhaar e-� �9}, 2328�746� ferdinand)� A)�l6�)�%%{ 185}, 832_>�Plandau-76.1} D. P. LN�13�997K7:aKA‚K!�25Eh>J,ferrenberg-9�A%�F �~b4b 5081�91:s8lee-52.1} T.NLeeY$C. N. Yang2%M87}, 40e�52), � S2�S10�526�M`8!U`, ZQ�MA4!�11E�8�]�$heringa-98eUJ. R. H �(H. W. J. BlA� o}te�A �2eY156�986� elliott-0aF. E  , L.2�aL�air>�%_(71}, 024607eo56l0coniglio-80} AC Z W. Klein,�i �I�77En80: (stauffer-99!� D. S , Int%Mod��y�1�)80%t9:)5�)66�8LBNL NSD Annual��ort��$| � \begin{thebibliography}{99}=�dne1} Harris P G \etal 1999 s)�Lett.})q82} 904 2J42} Altarev I SK6.K$Atom. NuclL59} 1152.M0q1} Smith K FJ0.J �M� 234} 191.Gw22} Ros�ry M A%�8Chupp T E 2001.VF� 6} 22�Lw2} Vold T G, Raab F Heckel B,d8 Fortson N 1984rd52d29.�q �EMv13!(192x8sush} Sushkov O!,Flambaum V V��!�2�!I9-��CP Violation Without Strangeness} (Springer).jP44} Asaga T, Fujita Tl$Hiramoto M2o Th%KP��1�$06} 1223 !%5�ta�8r�H 1965.�m�� 14} :� t2} 2A,B2r.B2AA 90 ;A68 iJ5ӍL1} 512It3�& tley!�,, Lindroth E%XMartensson-Pendrill A-Mf��Bf23} 3417=qHt4} Sternheimer R M�B�1V83�;. t5} IgnatI�V KAE�ksA�)�FY�5��019.�6} John��HW R, Guo D S, Idree��Aw,Sapirstein J�82�I��Q32 093.x t7} ^@` \"Oster P�HM�E\ Scripta-36} 444.[8q11} Kizukuri Y Oshimo��92I O �DIl46} 3025=,s1} Barr S M KZee A�.B�2v65} 21.J(2} Pilaftsi�CM� �M�M�435} 88;B'2�$58} 096010.j(3} Georgi H%N,Dimopoulos S!Q��� }}w19A_52OA� akai%?=X ��11�;3.�$5} Cohen A�+Kaplan D�-NelAfA E�N�- 388} 588[ta1��( to be publ�d..R�����FJ616��1.dq12} YoA�$i A, Asahi��)�  403010]. Z! !!UGams%ep.AZ- !JAYamsj K(892)* R5P9E8+Au%p+p%]U> sqrt(sNNM: %GeV at !�!B�11], �8E\ C�5)me�^: >!�� phiy2s1,uxV, 5��yr���0], %``Phi m!$!�Q2% iXA=p + p6b su]H20u`-\� \Ѱ61�185)BH06003].RRe !)+UF�� 4hv}yMA2ƌ``]/ of $\phi$)*e(,mid-rapidity!0$\A6{s_{NN}}�s$ A9 R� qiB 10012];\\^I!!-,MukhopadhyayePjc.$R D.~.f��'2 f~A�\i'\ Gb 31}, S187m2R12044n!! % ɪphidata](Jingguo Ma �  �o8bu Xu, private �$ unic# E ��Bleicher!l�!�3i2�B M.~ee$H.~Stocker! %``D��nd��A�had#��E�QQRcmS11i~�� q~� T312278FbHEP-PH !ayfFachini5 !4j2�> P.~  �ټ�nf�735E32����q26F��� !6�M,} Z.~b.~Xu � Bulk�perti!r!�lowv�92I�^�403r�!�m�TorrRes]�"ier%�1tg!�� +2G.~E�(J.~Rafelski� Nqnd QGP]�! JB�2�9Mz2&Y Qx112195F�Qx ! ��Af1h2;B.��Letj eis�J�s%9 yjH: A diagnostic toola�! = &T !Rs ^ 0549�1!,Erratum-ibid*� � 0699�2)]6� th/010404V� TH !F� �}�JJBookA^��5Z!�2g2�FJ.:�.� H��)�Lquark - gluon plasma!W�*� 027�� Kampfpf}�>B.~ ,!� Cleymans,� S+�#�$S.~WheatonE.� satu�: Depend�E�Hystem-size, central��+ �y!He��Ionz 2x2� �1304269^ %��&�!�3a.JW�+Z# �B.~Hill<%``Thermal analy0of}��@Z�-ion %�,�*�B& 034� 3Y2"&306� R  % �yblattica"FAY(rsch, E.~La!nn%6A.~Pei��EJTh�Oessure�#2, 2+1* 3 flavourq>- �"�47!44�09 A)lat/000N* LAT % m@ Fodo* 4nz}>6Z.~� S.~D�tz�Criti poin�t finite� mu, -3A ults for � >[  %mass�8HE� ��M%50>0�4�b2�6� �9� suddenPRLR"2000by}� G: in6� A�ear& F�-� 8i469V:�$006200].y�To� �xi=�B*n%ҽ�%�Search%��ف�tm�&�a��� �� New *� � ���z6�� 1210B1!�� %�M�6�1w.� J2��W..��Ex�� of� X p(T)-� in a��model� expan���m���6�� 723== A��010605!�2�� � %  Y� RM82A�> 82puJ =�%B���.�*�InP#� -2� v4��106~)8��:hI/56}G,3�*86)>�PR 48,L%MPalA�3r.�. S.~PŸd�� Prat��Entropy.�a&-�-��5��3�*�Y�5�u7B�5� ���8Hagedorn:1980kb}�HR.�B(R.~%�=�E� Hot �ic Mat�"And���w=�6�9A�13)�z*2�� 97,13)�UvBar&�.�4x2�B .F�$Multiplici"  bulki�o��^nt "" 1/2 = 130�N�<! .�$Conf.\ Ser"���246Ŕ�F�40916a� 2,�� A Q�� A�4pp]BJ.*� .� M�ne�&� %ANH %``C&� d*� ����@parameters deduce�om�� %m6ziZ >�-p!bmX�,�,7 �!Z ���0409071>=U07.�K% %Pzr=P:  .+�b, chem��^  �T��enWat�.��K405068]>I�L AJ R�"(Gf�"54} \��ddafter\ifx\csname natexlabU \�x\def\ #1{#1}\fibGbibO font>J M#�Pf�Q$�R�:~R.$�Rurl^�0url#1{\texttt!O%8{URL I~V$B!/&[2][]{S}$}&, [{2�{{Sj1X{\O}deg{\aa}rd} et~al.}�,1)}]{expWob1ms(nfo{author}�$1oZN}}�& ]A-O journal}{2Jŷ} %`bfl.(volume}{86}6G4pages}{5866} (^year}{� }).j D�2Jensen22{u$ {a}}92�2T� :wj703V 3R2}:��%b)jen+85xV%��9V14250��nI. Ham�.}e*2Aham�2<},z Cj�652Cm044305uJ2v.��B{G. B�gemann �3�3�.Q>and�z5>�j5�evzn572C15143�) N53r5$Frauendorf%2M�1(1997!&chiralZ'��{S.}~!�+U�6QJ>Q�64�{�p61!>����-@131Fr!r;{K�6rosta2w�| Chir�}.F>/�t�t97J��sT. Koike2�3):�&!uSt)+<, Chiara, Fossan{Lae}�!:��_:.�YUK>U��> C.~J��*' { Ȓ? D.~B>?�an?u?�[VY�D.~R.��:5F~� C< N�Zg4�g9�.� 4f1 {K�)5�I&:�]{koi.;!�e�.�5}2=V,6w1Lf�#:�A�����9Z( 172502F�r���"- fraTAC��V���Mo�$�j�7Z�46V�v Matsuzaki.v2:v% , {YK $ ShimizuMw"yanagi��msmjW y�M>rH�y�j���R�.�.��B���V�%�"1j�� .��P 041303(R)R�v� �!$.�>)%��^S9/��������Z_ 034325R�vK Marshalek7 77 ma�iE����9KZ��� 27^ J�41Jc197v� �(1979 mL.H V|��z�331:)m42�"�tG�rJansse���0N. Mikhailov}�jm�#D>� [>� �L.�.FUF�R�IM.�(\ nx3182E-7390��9{J.�CEgido&�A:i2)A�{HCang�j {P. Ring}�hegi80Zn9 .~:VQu1N���Nh )���!�!�^i 33���eI=�J�80r�$ZelevinskyA�80a�ze�� V.~G�.� L%��"� >�f�344:E �10R�z�:�F���A�� shi8��>l�K Jts�RAa�o?M'j=702I1:44AXF�8v�:�%<%8r!595A6sm^�5:J���o�v58��a}:�5sDF:95r]Bengt�A}(!"bZ��R> F6Vhow"�> }{http://~.0matfys.lth.se"v.,}$ragnar/TSDa.}j�Kurasawa!߉�=^��H>�I6�5�Iܢ�6Z205J� �Pr��a��熊 ����Z� 1594R�2r�{C KA.NE�"( 1�K:�- /, AN$linde, LeaH]$Szyma\'nsk� Z��a_:.�YZB���?G>� DZ)�n��Z>O2 2BU��6Z� 147R�v�Ska�6E�m sk��BqG���4b�0R�vh &�U�(:�&' Neer",  A; eikh*Z M. Walker_ fnswZ�Yr�2.�U�2�:rV5J.���yP�P�*d U�+ �xA�  �06432R�!�v�S. 9��� fra0�� :>R�i�� 67B�11^�z� D. Almehe>�:�(AM:���0{F. D{\"o}nauE� alm0^�Y\2!VtS�'.�-TP�M9!VEFE.�=S:wv$� b 6uQw�19>� ��4S. -I. Ohtsubo >� �t< o &~`:U� 5_>�R;��71` B=V9 �.r�"% 3  magb/ �InZ�5 Ai.� .kPYJA�eL"� 6\ submit�%�.�7�@;%.,BA09nT Boh�/ Mottelson�7= b^< �A>sP�7KBJ�) emph{5title}ELz*Struct1Vol. II}!~yZ%#�Y}� jamin, f. York.�"hvI TanabWSukJra- %C=tan�_B� F�OBM>�)JK>��$\ Bj�3a�.���57R� 7v 6�Exma^� Y.ғ(��f�1&J�142Vvv*Y�#ur*�ya�wBjH^��R��10JK ��Py�Q�Valamove� pya�d N.~IA.� U� DJP�ZA$Nukleonikaj22:?m12R z��i�Not2vi kis75��A!D>.�|"&|"3Z�55J�19z��O � and :� � sak8�N��.I�n2O>n�B:G*t�'��50�G��M(205, 2426��u8v��Su�P� Dz Rowe�epsuz77�6 K�/.{j-A�nV0)B-46R ��{E �V�EN mar�IB@R��R"z�>j�5R153R|19~B�a34���/v3B@��nI 2R64Z�8v�:K �$>��!���!�!j!�XB7�^F*�[r� {\AA}�>%!X aab8^L&Z B)JZ6iI�v; 15�JY V?vV ":"c17c6�%vLaj*/M��8 Nil��^gn*�, DudekG9T�}SJ�-��@I>�R5��@��V�B�E'�zB>�6Y�DB� Q���"�n YK�DDA4^( 2FB�20V<6v�(C. S. Purry.?�w�Z.@> �7 &7 b�$9`&� z�2���98���c��.�U2@��� � r�#63��A�� V�$98v�DCQ>*5�G�!2A�����*n�6� J�\VQ9v� "c������b�(T>dV>� �n:3 �743ZQ7cF)z {R54Fireston*�0E96( - / , {V�`Shirle�b}]{tbC>6(yh>j�56rB�.�eN Ta�^Pof Isotopes, 8th ed.}.�* c4 Wiley \& So�H Inc.. ��v�LP bner��7>�&a1VeE@= H@nig!elo�@>eٰK�F�%bjvFBj �B�$V>t��>#Da�f!�sjEAZD 49V�v�Aud Wap�E�^�@a�UB9 N�YBJ�v3��nZ59Z�40Rw ~�T�$Dumitrescu�2d8���#dumRE5�V�BS�D�=2�.�:i�K38R�� V�z�#GRp Dracoulis:�:�-�\/,@G�6 ndevT: ]{dr^r9)^�:eV�F�$K ~1_Tn%>�* 5�I� �P41Rp7V�zf Dele�Hque���4:�'��&j, Pashke�l8u��UnzhakT!�f�Df� M.~A>�uj���B� ��@ V.~V>�ޒC S.~Y>CChu�9�B=W!��a:H�� ADN� �=J"Av� F|Xuv�&,./6E�#V�$ WyssAEos^�yi]1pBq,P6}�2>�$->S� 9�.O9�BS+ �L�>�`vcPk6E{ 5R�z"/ � "��6} b^nj�U��PB��6��?1�-�%�1?7R?8�N�i�f,G2�tGL}CoG�P�!HemutwyleEWnn.� �$ (N.Y.) 15y84) 142;  Wein�,*ica A 9gK79) 327;NY2V2�a199V65*�-{C�G�\l�[lo�Tf�Nu \ B 60�X1) 122WGLS�,2�Et(M.E. Sainio �! tt. B 253�W1) 252;2+ PiN�!sl-16_K2) 138 (J11�8).�q�q � �| BDW}C]< e.g.: A.M. Bernp,wDrechse�Td T��Cd (eds.)�|?al d:\.y�Xvm}� ct. Notes-=5�Y1�; alsoF�J.L. Go%V4U.-G. Mei{\ss}� n�\ 0}, BA\��1.�D{KBW}N6 KaisA�� rock�C�W.A�se,2� A 62fx97) 758;.DS. Gebqnd\"orfmbJ3h{98) 395.+M^9�M}F,�Mse Pr" k; ~ Epel_u�_ Gl\"ockl�#BXB�7jL0) 295a�!" eaneXFA9$daque, M.JA�vag[$ van Kolck>V700%�2) 377.�4TW} A.W. Thoma?Y99O^)V&%�M%�eon!��-VCH,A�linj!� 9?LTY} D.Baxinweb!�>xR.D. You:!|ű 92X4)�002.� PHW}�,!�uMBT!6Hemmert:V��� D 69U034502U,CPP} CP-PACS�P"$k,�,Ali Kha9 al.�WY,U2)>N 505;m)W3 9901.� JLQ}A�Ao�>NR8�>456 QSF}�WSF-UK]AQ�G thierholz�k (R�h2�Io}3G Ioff:� B 18�;1) 312SW2�:M�� QIpth�Uic �aof�}, in:%�.3|SchZe!��n"Enrico�~!V��IOS�rss, Am@udam-b, p. 473| refs.� rein.�SW!�|eroIgJWalec�Adv�{�.�A1986) 2� RF} F9,�g �a6;��;93N�64�9�u75; R�Fu�fahl~2�j� ��K2�!i"�n]�2526� Hoe}AkH\"oht�?Pion-��eon Sc�S�:,�olt-B����n�RJi�)I/9b2, SBtg�4Be�c� 2�0KB} T.T.S. Ku�~G��Brownq��K1E�65) 54;2&�Unijr�8yA��ar�BelI�,Forces}, 3rd , North-H�r nd, ]U197�9aEF�Delorme�� Ericso�[Figurea�pC.�venet, � )�� �W� 273�K��A�{ Nk <G�a�1197.2rzLFA�LF�Lutz,�Frima RC. Appel6SB 474e?��6cKFW2QS.P tsch��!!gq+ A 69�02� �9@B!?-P[�aizot>�64?� 62jSHaj3eeg"' M. Howard>H2� 1F'�d2$FPa��ed1V�v Pandharip36>Q361m !z:� FKW2�&.�436� FKW3�VFr%o,&5 :zIi B 54վ73.� FKW4�Q*,T 6038>(i�g int)2U PPWC`C. Piepa�NTRHWi�FUJ. Cary.Q��C 6I�1) 01406sNAE$B. Natowit�2B)8&A�127016fKFں2 � 3) 42@BKS!��ogn!:�A�chwenk��� s 38� 3�b }2CFG�D{ he�"2EDsGriegy�%H)�1� 96x-�A0199 882qDL} E.+ruk��and EasL�?>W~K0) 679�.J2��� 7>�RV��Ap�lazissi|�JA~ D. Vreten6�eds.,��ExtCcd D�zy Fun*wal8b���& a7ic�L*s iOc��2�FKVW1�� Finӄ}�,.���Eur�< 1� 3) 573Bb2�b�cA 7��) 4492aVW� 5G:�. !#.=  66�LKRJ� J. K\"oni)�& h*�E�C �97��02�GFFA�0 Gross-BoeltiU C. Fuch��� aess�6�64"99) 106�K.�:���1a$, subm. to- ��>N�=j�2�baldef!�~Drija�� 6P�B 1C>$1979) 269; g �$nV�/2V Ba���{yk- P.~Dan�g wicz# �^�^�w �8a8�#9�89.��jFBJ �N �%7FC*�HY 449� "� phdmsu��TonjeQghD� �MichiganJNte� vers� T�STARbal�$ zz7 ,�y:a b�9�;O6) 1723���,my1}P.~Bozek*~&.b%FbBal�{f����a�rg*b&�f ,'' 6�i03E��%6S. Chem&Gale,!� Petg ni %�sdSkoby, V. Topor Pop, Q.~H�|�_.�p!��Q $of Charge �{�e�"�I 6U2�}b906�td}!C9UI�:Vb��20:%c; %Wz� �b�249 6d��nN� ActamP�6eB 3O) 4235�starbwA�~I�� �}, R�6b"Zdistribu.~Elp p%�Vnn�{ %"YA~2��\Zc9�1)�11:hbt1}^*�:�%& ji 3c�7:;�p�u�w? HBT radii�AIPUaD�66}�8.ghbZ��~Akkeli �4Y.~M.~SinyukovE�P�r-spac+�5���Bve\!a�puzzl�iAk}*�g�J�3.�hbt3}FXr tierM ~Lisa�Observ"" im�bjfsa� geome��ddlzxf%^`"�inR�rR� 2024.�h4u*�g:F�unuJ�404083��XnoN~Ӊno%CIn-�e � YXof�zuGe:re>st>tl�f+e�a+�75!HNA�fA1H@ZYau�`�`���cHi2pB%-�l�V� bf��5*�h.�:eukBc6Ve _C��`�6��f`2nfB`H r�X:j6�onqB�� ��96��!13fl�ږa�.�21.�8��`Castilloc4j cX��vbf G3�44) S1206�"�oR2wp�!���� n��, 185--195,&� 212052�Cot:1974mv}2o ,�gFryj"h gD1�3) 1t9#���1�":�:�M.~� &>�^�76�Voloshinq 2wa}JjA.12 �A71� 39j�wp2%��Ŝ:���77--184>�6�a�3nm} 2 Y.B�f/ �4A76� AnnaoPhD.k~% Th% un�*d.%��} T� %K.~4�.^-rCR � 0�}�*N�!f�99}^�� % Y� {TXsy�A4},  e\ , We�4��R.� Hale��M.}//*Ia�92.--�1 A541}--P..#  $1VI05 o�Viviani M., Kievsky A., Rosati S., ��e E�� KnuL� L.~D�e�9�--� �86�373. �9B��XBO A689 Q08]4P0FI02 P4Filikhin I.~N.EAY�&lev�Lg Yad.w� (lAtomic�ei)z0�63x79(��^ {Carbo_� � Jk%�fX.! A684Z218--2262�Hv�I% [HFew Body Syst.Suppl e.�12c439--4442ca8KA41: kko!? Tangj ,C.}% //Prog.��.y107j83. %�1PF5� Pfit�} B., Hof� H� EgE��&M y�'AfB@C6)?04;{2�D8PhRvC..43..371K-DKanada HA�an � x� Y.�/I��eb.�C4A PV --37B�(2PThPh.107.!z o>_)]&v of %deau�ics�Zl --83.�8 {kn:vv4he_3chE �Vasili�V� , Kovalen%�~P-a< ppov�jFA�q)!88}48%�217A� 3(346--35�y 4kn:VVS+19904Hef� Rybki�Yu��9.�5��871--77(112--123.b A 7HO0q�QvM)��]]r.��d�A61!�P.66�!t!c97ebrNeov� ,V., Arickx F � Leuven�V!z!�. ��%�9.�60%�~343--346�A6e �k.g, 2i� �+D�&? 5th" p Sem��!4����--"̀: B�$Pub�!199�|6teI�ITP+RUCA1�2�~���ZH$Broeckhove�&�qʡ�=�C��~0346�6��� ����B��3-�����0:�61 VNCh!DE���J Chernov OU�A�.A3.(�b�w.�6zN8�4409--1415(1486 99�6�Fil_Okhr ���a�Fi�7�koP�Sov. J..���.�3�D ~4802fknt8Q�6q}/\e.yF\�Pp\6Hkn:lZhuk931q B.V.i� M.V." ov}/�� � � !g.� 1993]�5� ~u462��28�B58.1403C-XCob0� ., F�vov� ��!�ob S!.})~C5�C[!�26� (kn:Minn_pot x='p��% LeM}� z��" 9r7.7A� ~1--68.V5uf%�.��Spe } ``El�ic%'MagneGiant&����8ei", Ed.~Speth��B![n*�GR�T�Z�'�x��>jrm Osa"'(June 12-15 j��|ShSk Shlomo SE�(Sanzhur A I!; �R}�y�04431I :�!; C65, FoK�so� (lomietz V M~(Agrawal B K~3)g~��64 �*H�)� C68, >~GoUE Gorelik M@�Urin M HoY(<A(47jo4, >oClnClz�,H L, Lui Y-W��-blood D^{3��130W�^�3,0# ~*�/AuAu�TYR �}j�'103��R2�+:c�81NJ.;RNTsRa�'S�Sstor C �Tikkan | %�em At%!ta~�T �=e� 78} �E2j ADNDA,78,�}NSagI�a��%�I�em$~��pA a13} 87>�(EPHJA,A13,8�.dKVG00} �.��Van��i NAF0F�vL�2�}�472>�P�:66,472��2*CoB%qColo GEW0Bortignon P F�1, .d{2��> 42B�1� 96,4��.�Mat!�} �Woן1��.U\37B�[3�}.[KSG� 1[,��dul�= N��assq�6s!�6(��6}.02430�%2Q�=6, aP]WVPR9[ ' D, Paar�vh P�L"F' G A-2�-" �6N496�$2�5/2,496F�%/~�Niksic T�26q�Y �5:(�{:1,5,0$:�HSZ���/y I!�m�!�Z֟ X Z! 6.{�!!532�7 72 �53,765>�aS�b.�}�f|42|23*R}4,>~%7a.~n7N����&]& 2361>��w55�V�72Š)�6H31� R6,R9�9 � m0A 648} �3>%q$ 48,2B�P�m!� PapakonstP�nou Pa4�D� �&Un"�& of Athensa�&� PWfQ, W,�c Mavromm{��$Ponom�+ V Yu~.�{\*M 6���15B��04,15ţ: LN19E�Catara FF2za E G, raja�ɮ VittۨAa:�)�I6H��21� 14,8>� �b}��B�2!�924IR�24,44>�KST!.(} Kamerdzhih&� �;(Tertychny G%$n\:�328:�1&24,328:-Ciofib*}  4 degli Atti C 6d�~�.J r+ �I16B:$PPNPD,3,16Z� ]�ReXX}� nh1+P-�� 9bH{``Skyrme-Hartree-F�M`�"}.)| {inP�putC%alEar �6I -"8.}},34 5gankej�Maruh"�} ,Koonin S E (�e,:ewj^)�p.!�y�B�Berb3J�)' Random �&�3 roxia�on  `* Exci �s=-! ibid2Wp.7.: {BeTC3}�FIzsai S F 6�Y%���.i�18}}C.�127:PRPLC,C��B� V�< 81} *d ��;8: �"��3}�>�M�371B� vGA�$3} Nguyen~��62� in��emU3=�3+s2l(>�) p.356.2�WH1988�ckebuy5J�� roqu��M, HeydI�oz6�Ryckbo0D�8.2476H2�% {Ryc � %J.~U �. %YM Ph.Dg9J�Gent,�:�-v476,23�0} ShBAZ}"�%�yRy�%�24�c�5%N~243,50> Tsa1978} .�8:��  172�186B� 17,:^DGL� Dauga��M.�0y��)�21262�P� %S1>C Sch9��SchneiR f�;4/ Z��3� 241;>l ZEPYA,A3�41:� Fae9� �1t�.nn�.f5, {GSI 9&ڷ}�;~2� � ABBW�QLB�/8llon O, BlachotM�Wa�L A^�] 7tR_2,M 729,>*BDZ� Bhatԝaryya P).%�1 PRL��� 06�}> �7, :1 BQB82} Bc�la�Qu��n�Bracka�Guet CeHak�won H-BaV2��3n* �R� 386,�=mGTPBGoriely-Tondeur�� PearvJ"^ ��.7} 31Bw0 7,31>EKST20���.2��r5t.\6�483:�Ef 7,48M� LACE%Lacroixu Ayik�C�Az� ��%2<=' 5 %��>�Y�HDNSW90} Dro\.zd\.z!�N�azSU=�EW� ac� %P�"~��~e� 197}J�P�w1n�:�SW91} .p 2j1, �oh=>- " in [1]a�AR?'s$f99�?'�?'��L..88aO.LV}W.~{Vanroose}, J.~�, �NF.~ !}.�s {Mod�>L\makebox{J}-Matrix M&��*W?2?L!�i�/Review�er�888:�,--+, Januarya .�)�#VA_PR}�#.�!A�F.~�!. �* Algebraic�1 Q quantum s"@:A� ormu/�>���! numer�strateĠR�.��2&i((5}:265--28699B� � 92� �$,�ili$,�%�&�!�ѣ� �".�CouplinO�T�V�j�"Dcontinuum: an applzk/89� $^{4}$He}.a%�J.%� . G:/ }, 1G18}:��u$42%B��!1! S.��V."�"2and J5M�.�:�P 9�� th[ s-clu�� ���U�I�Q�T}���0al background�K#:G#,A�Bu1E��$s$r2R}��8MH!F-DYR�'5:$^{6}He$aT6Be$!e6n�/qQUK9C7VCeD96�ET&an FF� ��X\alpha+N+N$} channel in.�6a/A�2G 6$LiJ���0 ITP-96-3E}, �M~19e06.�U� K'���T2�mj� six-Q<;iB��FJ},�$60}:413--4 �B(Simon68E}Yu_- �$:(�$Z|7}:72�s� "�%CFabr93}M�br7~la RipZ..HGreen"�:!� �Ga�6tudi many-dA%�� al sp7B3 Few-�, Sy"���/ 14}:1--24%�6�+kn:�$ �V�:�7 J[>qBp.�231}:151Z](B}F.~Zernik�7H�+ BrinkmanB��(,Kon. Acad. W�@sch.33}:3q!:6�4n}I.{& Guti-�A�8����I~+*�&B�!'�%]b 50}:I\�=6v,AM_12C}T.Ya.O�(elashvili, An$F. Smirnov�b�M�xirokov.~�L�B ous �8$rum effectx"(monopole ex"�aWthe.-{12}$C}/4eusUsidered  Mmz9a&�7.��R UY48}:96�P8BI'HA� r1}Ec %}He~Yxi.cNew�L^2�� ppro�toRh �@�HyB�Q�6F 9?01?08AH76s)kn: �}.��L.~�:��$J$}-m� U�:E}�Ca�s�Larbitrary angular mo�%umjto:C}oulomb*nB�J�k.,�]�16�0--420�.���M�E}Y.~Ia- chae�pYeM !.�Sol�;of � ��problem e oscilla^ �� esenvB�vo(35}:808--81�n86� (perelom72}A�0 P J�Commun:/"26}:2��76bkn: eovBe.� � Gene�� zed � rent�A�'a�ir� s2� &L!�8B�AM_AJP�c� ,� .� P.*� ,�0�� ޮGA�l .���a&� &� !�� t� ILݿ.E% Amer.A�>�62}:362�1E�9B�(Fedorov94}D�� � S.�*�Sr�iisager.��(body halos:;EA�F�B��y UC49}:�321��F�Calogero!� .�% Vari�>*���Pot�al^� Acad��O New-�w�. Londk196B&Babf�� V. B� ��B���M�nH.40Nauka, MoscowA�7B[ Dani91}B!�~ J-Bc al �� 8 ieqrowea �1�-ex/ ge rea�HF�.� 1:283F43��e4> �97}*.,�SogY�S.N.Ersh��H.Hei`X-�l,en, J.S.Vaag�J I.J.N-, %�&I.2Q��o� ofE� ��!��l M u��BR5�,R5I>�Csoto94�� .�}R&�EN� ,6�Li6B)�Xsoft di�%�a��J*'�a� �2>e^.�6�30!�304�:J�,SM-tanaka}N..�+Y.~t,%�K�Mrga.;Өor&�=b�XalyV6� )in� cP� .iB�"x C56}:5�:565E�B�Volk65!�B?=g *� EquilibZ de� � calc� o�� �� ���� 1p shell^�#()�*� 74}:33--5x 6B�!�Aoyama1}�I F-)r���oALj93}:9� F�4f2�fЁENX5Ajze88� n�Selov2�V.A49v !�Fb ��89��S.>�I.�7�7.�mvh � 4c 6�6VA�:]sl, iue%Rqh Lova2� Micr�#p<ul�0" des���y�-}�0 with a stoch�Ac v�G3�.�.��9Q4}, A571:447--4��>�typel+9EvT 4BlugeиLa� � W� Fowl6p.�studyԁ� low-e?y*� ^3$He( ,2p)$^4�%I��3$H &,2n%fuJ !Ws s�onF"�˙?A33�4iB5Desc94�K ouvemon2�.�� �2�He(^3H�^4"�2�H"� !�á$a O CB�.� �CA�26��26�SN���+!�99�+%|Kb�)�.pL�K�H 2�.:s�!�2�.�$p$5�qV�$n&9.�:�.� A646}:387�<9Z� 5dm}�����.f Precise s*� few V � si�Z� �cor3H�ts�I� SizJ�ŀ)� JETP�1��&"6fb�Z86}R.~ECow<n�Jarmi2�%�Radia!ff.84}:4: )6eJ60w51}H.M.Agnew�ET.Lel�ZXH.V.Argo, R.W.Crews, A.� mmen6��& W.E.ScottIu, R.F.Taschek.[Measu�5nt�A2��K�Y��$T + T \rightarrow He^4 + 2n$} + 11.4/MeV2� %)��A*8 !8] 86d51>+kra�87�4K ,�W�ac�� P. Trautv&�p C.~Rolf2�Astrophy�ub($S(E)$} fac9of2%JZt��ar"� .g�&.�,A467}:273--2 ��>�(LUNA99}The~ \ Coll"�`.iF� m2��0^{3}He\left( ,2p)�) �*6dA�to�VlowAr�� so�$gamow peakB�},� -ex�20R-�sR�(8}M.~Junkerc �~2��D'Alessa�, S.~Zav�,BN , CHpesella�� Bellotti,Broggi}S8P.~Corvisiero, �or3Fub �^ G.~Gervin:�e:968n{ 5{1�d FU>i.B*}ES00--271�B  dwar�$ath71!k R. D�H.~Wink:d ]LJ to��E?- �]s below EKJ�� ba߸.�e=.�*Z�3�C54�76,A1�� 7zf}. F� t�� :�J�mk=��r�C57:2n�Bonetti�9yt�t F�N�!`:�+� iꩱ� +2p$} :�B� r�*�:�#t$82:5205--5� e� Vw$� rw$*VKD{bethe}{\small H.A� the,�U^. g%62}, 8s��F).*���01KJI]att�a�MOakash,U�p�L333/�2*d 0); �W|,? �55�i42N^ 1); �cedN $�� , 53 $46�ibook��VIsosp�(��� ��-���2i� s ate rme�e� ie�Eds�Y�]jW. Udof>At�$ie�_\�BI�Leb6A.64�^ASA 'CI�VE 0628�dN*);��d0 $G 0558 n26� furn�R�*g*� MA70O8�b:��{{-BJ.R. S aj]F�R�0<��a:�ir�'98U%�L��M�v ! auA,tal 9, Iai�Mo�4E �7a�!_�D6�daԲ� P. D.�]R+ace�d W�aLyn q�29�5�k:rdit]�9r�TMkblonna, Grec5$M. Di Torog �4120602�zuo�W. Zu ?U6mbardo,�p=�1re>�2P nsac7�i�FDOE/NSE�3�Advis�*aqLe�p{8A? 1927��I*);�D��Ae70'36I�3);.JmHA 017*]�2Cigz04}�G.aYonma)l,�-�10�C�2�� "�1lidasy/QqjCpeDas� GuptS;�u^.= �9}, 011�q4);�:3�563�:z ��V�h ����.�%�)] 3461�F36kbetty=�M�Ts�PeF8-��19��065�:�chen04b�L�o�_��=6��= 0703J>� wAd4*��6$97:?B�Z.Z��FS �7A�1648�976'li04a�jn%�!nRS%3�=-��2+6t��1� h:��4�~�F�]05460RK !+�*M2-�.} }�si� sJjS E;J.Oe�smu��>(��4B 88V�79>� ko95b-�]CI�2V)�5A�20�n5JR6>R6� G.Q.E�BY_�8M�6 ZN�W�v� ����u} ``� e�� aper�L.D.L"''Bp6ved�~Ter-HaarbAr� n, Oxfordx2���,mi} E.Fermi �6� 5#i50) 570F��ha= Y.չ�Kodama��.Paiva2%5IAg1455; FT-/)K2ei7) �*�{�DC.Agui�Nr T.Os�T�)��69�r2) 639c.Uha&f K�F.PottagJ Bras�s. F�85) 22z{c�wT.Cs\"o~F.Grassa(%XT1 � B5�R 107-115}=elI2H.-T. ElU� O9d e��lerdJ.��  H3 G�vVh93._ag49O�`)F\& s .QM �q=i.h)g Y*me�� D.Menezes�/Navarr�NielsenuU.O�*-,r6 Ce 3�g>�3}�?:lA32�v�\.��ha��)V9A�dul2�D�%8�w237=� pa98EhP 4,\& C.Rold\~a&* �l�z�w2906BcGv=L ;]�S2) 637cxgrt9>e��O.Socol�� Jrq O C6��0)~J961�gr�]�nKIǩ�� 1770.�gr99a}vON�33.�Fb�F9=7ha69�FQ} Z�Y C&�{50.�nabF1awC.NemA�Q�\&%�>�4��2) R2552�gr95}1i,�:�)dB3�95) 9;�7I|6W}.?.{ma�>V.K�"g� Cs.�$lik6,P.Csernai, �W.Gsv )+���8, Zs.I.L\'az\'aek H.Stkzer� �45"s336/ .09:X 6�r��596.�ar��N.Arbex�� �M�� �qCc6=�8yogiro} Yu.M.SiGg SPk.gg�㉖T �8� �c52328hi�e�_B7x \e-"V�cq� 0119YOT E� Mori��Muroy� No"% �BG61902;G K.E`22 ��fd=#he,<0 U.Heinz,K.S.c�$M.Rhoades-.��)!��87)��2.�l�# KaU2H�q6� 37 (1��1462:gu��� Hu[E.Shurya*�r��h8) 18i!"�leh�:�F�, U.~ ��E.~�>rd(>,q� C 480)52��CFart} F�opvG�u"�c!, DH�14��?..G 0Bra} L.Bravin�Uz��)dB35� 5)g*.�C68 99)04!�.T Sor}��SorK#6R73 � �\2�Bas���o` :�C69!9)�2$�be�LS�rnard =�DA60�36) 566ri!�0D.H. Rischke,� "�t11th Ch>�4Engelbrecht Su�}�oo�5�o�7�!(ics, Cape T�y Febr�: 4-139 98&C9809044�biC�an�xC�\nde�m68,.�L�� .~�Q�^�I).A88.o��b}.�2�.lv�у~�J*�׵�1:N�a�I$K.Tamosiun�2nd2� �> �A� 4� y�csM6=.SE.Moln" A. Nyir.~, hep-ph/0406�a082 \bibitem{ma03} V.K.Margas,A.Anderlik, Cs.Anderlik, L.P.Csernai Eur.Phys.J. C30 (2003) 255 \Xtea01} D.Teanay et al. 88 Rev. Lett. 86 @ 1) .�ddu00} S.Bass and A.Dumitru.BC61= 0) 064909.Cbu�(K.A. Bugaev.: |90?,3) 252301. �hcl95} C.Slotta, J.Sollfrank��OU.Heinz, Proceedings of Strangeness in Quark Matter '95, AIP Pess, Woobury, NY. 5;8re94} K.Redlich-;96aac ,RJZQsC73�76)153FHcH I�hO.Socolowski Jr., Heavy IonM�4 O257=h B!�>�,� \&F_ >_iA41Ja8� mB�, �%�e�80%�8) 117.� C99=HJPJ�|G 2 �9) 33.qGb�:�, VG.�va� Van Heckem�F�1!{8)5764=|b>���Kg.Part.e�� 4��8) 225.B,ravina98b} L�� K .�951.��os99}F�� Ph.D. thesis, april 99, IFT-UNESP.Y�WA97art�(\u{S}\'ando�A( ) J1G0 4) S12.N NA49I,M. van Leeuw� ( )6v715�161.vh�NU. ��R�22� star5(J. Castillo1P(STAR^�8.^ na49omega= AltB�l$ex/04090049C na57 1 F.Antinor"Q�9882�fgsqmYȍW}�> F 6� n� 02004, a parec�m�]�C 92a��J.1��� 2)31. cl93�,Cleyman�DK C5ɘ3��7.�stA�St�f >,6e�9)419.%to8�=>�17Uf0.�r�:$R.A.Ritchi�,i���C77 7) 535.�y�MG.D.YU�azys. :56�7a�1.ye�;!�(M.Gorenstei�b ~59D9) 272@ le!m~; �� 7��!y53.�le98}z~ �94F00���_ �`A� �^�B� q.}.*sandraC Padula,��e.� ]�G��00��S DZ�.�C62E,� 4490.� ko86� (KolehmainenR$M.GyulassyQ)wB18%�8� � �2d� nhbt} U.A� � P� E�Rept. 31KA 14.�hbt04� >AFa5 ^T1�`v t.93� 4)18L"� � ��:�V4raf83} M.Danos��$J.Rafelski1Je*g 671BbanBdB.Banerjee, N.K.GlendeningUT.MatsuS1�27 (1� 4Q �@mu85}B.M\"{u}llerF0J.M.Eisenberg:� 43�85) 79.�,vi91} A.Vish��.pD4!1a��5trusse� 0Yu.Peressunko�4Yu.E.Pokrovsky�RI- A624�2X7)738; hep-ph/0002068v2. 0flor} W.Broniz ��W.Flork M� v. C= 2002�,5; AIP Conf.�� . 66"�17��2\, A.BaraI�.enH8.�cs� code�P. ���� 4010��| \end{thebibliography}�\beginB {50}] Johnson W.  , G.a^Bertsch,%6D.uDea��I�Em8 {\bf 80}, 2749N .�iY1eZM. Zhao!/ Ari� !�0N. Yoshinaga,��p. ]40^N4\YIEA�O2K]Y.w �)��]A13}, 10� 2); 6CA[�.M"� H35}, 857I.� x} .@:Z2vM�!^C66},H323I�uP,Mulhall1}D. `Volya)0V. Zelevinsky2a%�85, 4016]0]\ Kota  K. B�`t�lK. Ka��E6! 0261��22O! -1� - 34302 ��2); ibidM0=-2 ���PRC-209�%�5�J�4!�41301R1� %5%Iachello�  :TD%{\it The Interact�� Boson ModVX(Cambridge University P�!`, %England, 1987), p. ~382 Zuker%� Velazquez�P. 2~%�m�8� 7250&%5�(Papenbrock}�f_H.!< Weidenmue�XFgI�$93}, 13250�a)N�$f�99.��FAIR} http://www.gsi.de/zukunftsprojekt/index.html �I�Fal.� {\emph� gr. �͌�5})353}E�4��� N Shad]+Mosel, E Ke:})M�24608Y6�,Ericsson-Wei�?T. o�w!� se, ^ion�@ Nuclei}, ClarendwES OxforIQAH�Kienle}!�Geissel͆B�IB �EC12b J�H�da!~ , S.~H.~L� \PRC)4��3��%}j KAOS��Fos.�"�30701�y� Lutz� F.M.  E�E.E��JEq6OU.z�5� 293� 8); S�Q  !-i62131 2�Postneu!�  !��%�� S-�41�O1�����CERES�PA�A��M�Qu*�� (QM x)}, Nantes, France, 18-24 July ,,� �1��27 3��Petersc 5! @632\1H.#! 5N<89}, 7d��2<Wambach! F� 422ce�6�$Cassingdil� ����M�B36&  952�RappWam}� �� PAdv6?)2!^�*6sGPiIramana ;6 6l 3)," 2011,5�Ko!*Va�c�qS roc.�d. Workshop XXVIII on Gross�pertie?�e��Var ExcitPs}, Hirschegg, Austri�$an. 16-22,A�h0, GSI Report ISSN 0720-8712ERen�m 1�- F �301490*�5E. AdamY� :�)m`  .9A�09��6���U�d QVj�gJg3 - 18$ 97# 201�q�Me6F�VI�42}��9*g 56rVIx vx��jx vx �xJe��G�U{�XGluAlasmaa <. 3, ed. R.C. Hw X.N�xng, World Scientific, Singaporee3.Hermes} � irapetian��N2� -�C2�479; V cciforp6�Y254��}y(KaempfB 4S. Zschocke, O�k Pavlenko, ), h� 21226y8Bratprot} E.L. k�aya �eg2bB52��2x!�u�_ HA �  1*> 5B9"TAEffepi�u �"�.B�^027601G99)=$;ph�M..H,J�:J*W 1�k 04461� 9�]�!6-��.�Rk2�pa30��1�.kFuchs} �Shekh.N � 68i�20�"�]4.�ianchiP J�60}�617�!2�!L>�>5M&��55��14605 6>} incE) ,�Gallmei7 >eN�7} 05460I��eErratum-2l8}, 0199� 6n ~� T. �J%7!%l9e�6X offsd6� *m 72} B6JuchemAFing.I� S. !.' 665}-\ 377=� TAPS%�0Roebig-Landau�LBI7374 42�72�Kru'}�L D, private communicUzKEK%�Yorit��r476} 2�=0);� Yamazaki A.2�520( 64A�Hom� B."+ 6B3� 19:�Lehre@J��hr,�5� .�em�AM� 0 6MMlectro�%���NK3%�6KCHG$F. Bonutti2�77�1�6!� sigm�%G Mes!�Up]RL �� 2N� Oset2��L. Roca�� �DM.J. Vicente Vacas��LBs 5 7C]&4Ruso} P. M\"uh*�& ? �59| 21i�4.@ �!a ~G.~ :��k�~��~J��A�]9i�16�lingl ~ G~Wa�W.~�2�5E�9< 67F;na=~ , Acta�*PolonnB�O31� 19982�MuehlOm)- i���.����w��2^u?C3e�i6�Accardi I�� , H.-�irc'�!� g�A7e�13NR�alt} u�����59j 61-618]$4Kopeliovich} B" N�074 � �46\-$Ciofi} C.  degli At��B]m�N[A1��13��6[NezW$P. di Nezz&L~�)1PhD� ,.�of Gi��'D� is,Z4,�Ltheorie.physik.uni-g 4�html/durt s��N(r( �v%� "�(style{ieetr*� {kn:H2}E.~J�%&�+H.~A.� �ni. \newblock \makebox{$J$}-matrix method: Appl# 0 to $s$-wave ! 4n-hydrogen sca�.ing. ]�m�[ d, \textbf{A9}% :1209--1214�:74��d {Reinhardt72}D.~W.~Oxtoby��P.~� T.~N�kscigno.�Compu)�A9elastic�< phase shifts vi\ alytic co�&uE"=$fredholm d�Pminants constructed u� 8 an $L^2$ basis.�:�9,28}:401--403%.�P {1995JPhB...28L.139K!4A. {Konovalov}%I( {McCarthy}2�Converg�WJ1�calcul�9�elium�.on�s6K\ 'ournal!"��@ics B Atomic MoleXr� L8:L139--L145, March �2d1976PhRvA..14.2159B}J.~T. �3��W.~P.]-6� One-' two-� ZoejecW.p from $H^{-}$: A multichannelR6c!�A~ v. A�4:�@--2173, December �:�H93PAN....56..886K}Ve�{Knyr)�(L.~Y. {Stot�6~�Dthree-body problem�5�i�68�!�of1����,56:886--889,�!�.D {14JETP...92..7896��I0~V. {Nasyrov}# Y {Popov6�.mof�� J M��Me��, for Describ�8the (e, 3e) Rea)�inHI�A�6g�]�E"b al%7T�9etical%�icA�(92:789--794A�yP .n$4 {vasil_rybk89!� S. Ved$A�0I.~Yu. Rybkin.�Astroũu�ffactor1`$t(t,2n)^{4}$He, $^{3}$H( $% H,$2n$)$ ! r-s.>�Sov�"!��, ��50}:41� 8.L5 {mirror_Y90B�,6�)�4G.~F. Filippov.�.ea�nsi�!� j� $d(d,��e!K p))�� statIN5� euF�Rը51}:7%902�kn:%�92!  %�,� �4, F.~Arickx, J� eckhove%! P.~V�- uven.� Coup�Acol�iv�M�͞ um: an ap2���M}.aiM G:Z G18}:1227�42��96�kn:E�97e! 2���Neo6a) LBT��clu9 m�"! six-%� on system.Uԩ�a�ic ��^,60}:343--349�7>� ITP+RUCA1�� 2�.l Algebraic Ɂ�&0 )Ρ�s� �s.=�I!�� T}��$backgroundZ :{ C63}:03u,F�kn5Eڲ��)��-�R2R}e�9F >y�95:$^{6}He$�[6Be$!e" ]P)C�'9C7vC3�G]G�S$}- 2#.�3H(^3H, �14�? ^3He#p) $���# � W1Oexit  .�B%�;!%% :0646� 02n !� L�La0404V}W.~{Vanroose}�3� �4B F.~{�T6�(Modified J-F6S"� 65�3�zR�-� w!Uw*��, Januar��Bz 1zz ��New=�/ $} approachn quantum�+:�8y��A9��L 120�:a Tkn:SmirnovE}Y.~I. Nech(=��Y� !.� SoluA*aX�b�� ͡oscilla�reRen� B�v�$35}:808--8�B}�ni}.�� L.~Fishma2syJJ�Extensa !�arbitr!�$angular mo�um a$to coulomb=..EbJ.� h.Ek.*p 16p 0--420��76 (kn:Newton}R)A3to2�_Y�M!�, Wave�'"&6� ,McGraw-Hill,Y-York�66� ,kn:MorseFesh$P.~%H.~B�� � .� ios2k.� Ne�2Y0 �@abra}M.~Abramowiti'A.~SteguFHandbook!Mathema� Fun3 6�$Dover Publ�s, IncS5�:�,kn:Fil_Okhr}6� %&I��ko.!Use�an }/ba )olv� "� qe�� 32}:48Ak�1986�8kn:Calogero}F.~ B�Variabs6A��Pot~!al]�}.AAcade� *1Q%$Lo5*E�B� Babikov�MV. .ZeP�1�M��Q�JM��n� .�0Nauka, Moscow�76.V�0v��&L {ar:ajzsel-NPA490-1!�AjzE -Selg *� ��0!-,. 82�Ytilleym]T�KP ,Godwin, D.~M!� Purce�SC.~Sheu� �'W<r6�3wA74+15�23�B�.@r-PRL29-1331}A.~DA chUFsmini�X~Conzett, R.~de~Swiniar5Ho0?��J.~Ernst>J.9-�s!-72.#$ {AR:darri9(-PR-137-315�$DIgo�Pug�2( H.~Holmgre6�2113]3�; 1965.�xTostashko-JPG-20-1973}Noena� Bari +,~Cavallaro, !8'Arri��� azio)�G.~Gi@&&� �97r5:�Lkn:wildtang77}K.~Wil{Auth%jY.~Tang Nit{A un� ���P� uu(�B8schweig: Viewege�24�x81�6f$Lecture Noi2y�9iA|, (Berlin: Sp�AU�$6war:^78hC.  n LeMej&AS,D.~R. Thomps�B��p."@ 4!�16�#7F�wheelE�52-1083�W 2�Q,5�#)E�:ar:�� @53}D.~�J.rY\  11�-1952�e�,saito77}S.~S �g�eo�0�) SupplyQY$�19J�4arai-PRC60-064aLKA�a� AKrupp"vB�  C&� �% 72F!%o�-284-264.rSm%S8 26�'J&8Rowe-RPP48-1419A�,�, . PrA�I}S4!,A8:O8ar:suzuki-PTP75��7a�SR�X7Ź3%#1�<2�a{ echt��!v295-34A�%cDau��2��5:!h)F^ FilVasNes� "�Vdsil�!�A.~&�%�>�42�-}H8:�(AR:kruglansAP RC-4AQ289 ~Bay8 M� &2�C5��� 13�':� ar:PRL88-�98,��.D!�*�i�6 Le*�8e"��(FpMJM4shor�L-j�A-7769�>.rnWA���:�"hA:� . G q_ c�F�AM-AJP.P2�,>16~�S u.Amer.��Ŵ3�3�L2�A�A-!VRe� uof{ A~\55}, 2>,F�PRA-9� 4HY(JMM)A�f�2LAUL��12�(197FG4volkov-NP74-33] V,�M4�7���!F� ar� ��86-n& M�7&+ " ��5A28���)Jtonabe��53-67�FTa��TohsaAA�R} mag� � �t5�(6��7F%J!� G18-�5�� YHy .�Pe��u6�5p1e�2,LJ 4vasnesarbr-PAN +>�V.���>��.AO5e�*�![ 34g J�vas� 3-_>�2x���� C3 bf{!6 \�F� :�B ���+F��7 -alhj�.� ��ve��A(.=Iit{:�)its<"�}� AlhaidaKI8d., (N.Y.: Nova*3ce �[Cs�4&�'6�ar:^ gawaar38-118�(Has�S.~Naga,See�me��& 1/ 6F�.h�;786�i�A78��7:� kn:f�*�9h�!e+�ar �� ics."!5"7}, (USAA"Wiley-�?sci�)p&O�6�+ {TwoCq"�*j/2�D�:ven��QB� N.\�6 Int.� Se�$r�~�a�4ics "Highlight�rn5�$$ure", St.A)�Ma$"8�|Cov�@�5 , (S�5:9l.�5E�.]"8), 4�DN'�"rz �'"�4 jilaT02@lS�J=6 EnA��R�thews, C�= WiDH)L$E.A. Corn�Z6ce 26A 95NU>2ymit�HB. PUshO. Mewe R. AndrshUvan Drut�(D.S. DurfeeWM. KurK!x+eb'l�W�:9 �:@%) 396�!2�(huletbec} C>7 Bradl�C� Sack- J�-n>l��R.G. H@X wBx168�2xbriA/ DeMarc�B� Jin,5U340 �I0FH(thomas-flow!^!O$^\pM $Har�?L. Hemm�M!� Gehm> R. Granadt! J�05�9v+2) 217BCji�FA�gal!� Gr*I�)�.) 92Ű4) ` 0J%2+kinast1 K ��1� E � A. TurlapR!!� J. E�l!'R� 1504�2zwierle�M�GZaqSt�G|9 . Schunck�(M. F. Raupa�0A< KrU^N�..��TB� A� ChA3M�rte�M�9ltmey!�S. Riedl�Jochim �R:&alag%5R!�imA$��30 112B� pico�0Ae� MigdAe�[E��, 5E�7�S07; G�ym�X ">.�m �/H�T�M� s, Les HoY6s ses�4 XXX}, R. Bali!�M. �1A G!pka-;?"$(North-Hol;(�n~Co., Am[#dam, 1��0745�PD�0Campb�in/ ��<i}, v. 3a Rhq�� kiJ��')9) p. 10�T6�k)��Hpla�DAe!Nel��m�� B1�!86) 5)�E,;ow <�(. Beth; �'�� . 42� 4)�Z$; 506, 780�:8);-3,R. Pandharip�Ye5� ethia)!�Ve�r\E2��t�� , 45�9z 2�chiral�!Gasse�- twylA� �R�? s, 8`82) 7B�,rhic-inpc} S�p e.g."P talk��N. XuA�1u*Ze�8 J.-P. Blaizot�2ul*eD,vie-hE�ios+vA2theB�N2�glMR}!�KrawczykVG. Lyne���Gil� B��J�K,, Mon. Not. !�%�n. SM33�h�2)-F�+rdL5 Be�R. EpsTR!�B. Link)�icaAZ�92) 1; M�Alp&�J� I�5,87�d52.:�(leggett-rmp�J� �v.�f. �S# ) 30F�b87��CPU�U+W � 76E� 6) 6>�st s;Sar"n2�?I2360�:�y0 h} I. Blo�6T.W�\"a��)�xHssl�\PEq  403 8$0 4B�a[ � !�"j CE;Townse�J�3 Mies�廖y �*2�P�T63B~ha�i2�"% ��8 �T�r��9N �2%) �Y61qfs} Thi�%�  isC edappare�GI�  Fluid�zSol �ah( Low Temp. Q4(in6);� d@0/04084-2�AbE;R�!o-Shae��C.�H��R~VogelfYn6. 5n�1)}<>�Haljan� g9C�I Cod�at P m � ~ 9iӁ5}�Aed 23;.BI2\ P.xˆ^��:00J � tke(Z�V� weik(3i8E�� �2�96�N ud� Z6�.V.P. Mog�;ff���n[9�< �32:c5�N� -�=� V. S,-S( n� E� �EQ�52z_>resize�EA a8) 0436�Y6TFG} U Fis� E'm�R�"�d 14N�Ho"7-� {2�Y�06Nd4a�>G�9t>�A�C� N:��L49T>� Coop�DYVd �\M.F. Gu�aiGZ q(th-H͠80�a8Z65;2PA�NS%6B4�Q 0) 6?R���VZ�NG9X� �'2� ViefC*A� �>H��an �S�ReitE6�A o20� 0536F$Rea(=�= Reij� , F.! [Lankvelt�C Schoj�kN!ad u:7��� 1;)N%]� 02361B� Jolicoeur�DRegnaul�ThV ,2�601Btku� Kasam�Od  Tsubog!EM. Ued" mA 66 !@pW!@B:KBa�Mhavoulaki�uNew� eY 3) 51.1; rf JackQG:L:[AG\�"%6!WE DB6��M Lundq�)��D5�q� M. �R� !(m�>�70&�36F��}�H >? ��0@B�dalib^ �'ret�S. Sto" Y. Seurieʁ D 1R��N�big�5�6� ED Holziw F. Lalo\"�$D. Vauther�)�MU+ m9);=o!S� =Z317FEsalern���� % � B: A� Mol. Op  t454Bg_r  Gr\"ut� DEjCep�yIh92���7�7�g49>�hol�R5UEq�r!J2Q -F8Y 9) 2J=arn�RP�? RG�L�K �2��� ��>�kash}AKashurnS*�� kof'ev) B. S�unai- h��B�bbz�Ymz>za�(J. Zinn-JuseEu8b4i�0)�>�) trap%�A9B,T�h{\^s}i�.24�1)�RB�n]XM9ƝAN�B26o!)'B� �log�qM)�!)r� 2v136F�corni!�S! ish!���la$^�E Rober:� -el''2 .U��!�79Bcar��C �-Y � g, V�P6E!K.E� midV�&� 0� B�hh}�Heisel{_��: ZT)�4) BR��+gy�E�)e�S�"|K�� O���6�}i ��3) 011J\ens�TcIurd]�f ubiz69C. Khayk�edw�B! Gl�' kuryakf$I. Zahed, z�k 4100/2i res-sc!��{�AYV�MA�Chiofal�+R. Wals��>Q�X�P6; J.N�il9< .;!(ZJx:2� ,n� R. eagllɨEF�1�69)6>g tonyBDY� (Paris) C!a�F s�4Nozi\`erL3�chmitt-R tL$-C59H8"F olorsup� � \"af�F0cze>�u82W99) 3956FVsu2e�Abu�"T. "[K. Itaku*2�D"�  074014;2,�&�A7�3) 859;2c in t�.Vi>�randy� EaYtreckAyGP�Hri�^A>x .yig) }f804F�r�5&��-icknorT L�2h�D.!��o 4� 3s>��zmo�.k.�S.:M �J6}�2�B�j�b��BbGnC. MF&!� D�lag &2/>~�B�M�W.6II *I��&GS. Gup� ZA�dzibab�UAV : ����uN�di��} RAxD XT&J.451B�cv���J�0 �& as, .U928B 8c} Q��!-j�K�vin23110�@2b�m�*a#Eud�o�"�203�V2�Hebel�^Ca� %wC.P�O� .r1�K1959) �>�georgk �ruuw "� .KQ�J�AB�sanjay)� undu�S� ddy,#� 0505��R�"�"f�"ll}&�50{MONI} P. Mo!5J8 4Nix, W.D. Myer�W�$Swiatecki, Data�� T�7s {�<�W1� ". vP G)5A A 60�X141�9-$Y. Aboussi�I�tearu A.K. Dutt &F� ndeur � ��TB�6h2��"�#NEUTRONd�;t��0 Trzci\'nska Ue�n}2"� �8p3 0825CPz1)%�refZOs���!.=�HUBERetxH. Hub���e M� Weigw )7�sC 51}[v17�-�� JACOEgJ�����mayR�436} ]�wP LKLB��-H�(eb�7}%�8) 3488.I NEEG� Neega�c"� 3�m0+$SATULAWYSS�VSatul)��Wy�z>211044. �(DANIELEWICZDanJx wicz.l1116�^EOS-rhoAei>2:R�c�W�Lynf"�%2%315��H2) e-Print Archive:�080162�BVAfTFrag�"D. "6%��"bad'n2 52} 250�1>�PA�>hF2ex(m��6!f13;| m"MY}�x:9709 9 2) 46l m�I�mYd 5 �>=�(KUTSCHERAW1� Ku�kerI W. W\'ojc&�P[ B 22�g�j8]M.Bq�2234�P16�8{KAISER|Kai� U�H 2N �aVIDAURREa�848  Vidaur�7$J. Navarro8 BAmb\'�: ^ *V13�/36�6 2{MARCOSk�nS�(rc�eR. Niembi� Qu�v��227�<2v�*�BERNARD r5ef�rdu��Nt356}, X#:� FSS2�jS�[nto�;A8 rsa,�� � ^�9ס� 1811�0N.�, {VPR!�\~�:A�ells)" 'gI�Z�X$C 65} 0358ay�.� VB022WeK�ombac"� RE�CXW 0458 �263{ISAYEV}�A. Isayd J. Y ;�C 69, 02I 4); *�030==�JP-IJMPE>� Brazb2�OM�33} 2f=�96� !,J<9,Mo�& @E �57B� SAWYauR�Saw�'�-21I�4'' 5).  oIwamoto%r�":q9tD�e3 �8�ESPANHOI�gy8E.S� rnandez�!��,2� ��0(a)�B�_REDDY~ R  rada�M�� ttim3J� PonsF� b 28�� MIGDAL} w(v(WjSaper�z$Troits 7D�Voskrese�o� �!Re�p 192}��6�\AKMALQ2 DHARI�kma� V� P2�.�)E�$22�92�/@{ISDGR-YOUNGBLOOD�} D$Youngblood4?L. Tl Y.-Wi6��: 82, 67-�H;,.8.cP�]bC h2$ 031301(R)��6�YOSHIDAEWr�+a#1a Taki a Y� C 58} 279�06*<{P!�.NT�AinswortF^ ^]!. )�61} 25g1 88) .VGAITAN�lT. GaitAvADi To�� G. FT'T"lonna, H!�Wol� �U�2UGRECO)�Vz eccoaC J�mF��p,��2�6x ��D>�.t�0IWARA�$3, Olin!�PE,� il, j� );(D 13}-7, 12�)�.*$BAL-CMK-WB ^-A. Li@�o� Baua�r1�Q ofJQ� 14� 8� ��8SCALING-FRAG} D%Shetty�Jit"� %�eW}60 +6 *10�" ONO-� -e�OnT"�*� W��Fried�% .` MPTs>�� va516yR���RIA-GS F=xampl22��nni&<I�WA 734} 6ig4) �A. NolCNuB� 3�86��-�.�^05n)299{IPHIC} .�4 see: "Isospin�bUi!� avy-��Colli�- s atA!4ermediate Ener�Z ", E�-Bao-An L�@W. Udo; roք, NOVA"� �H�2�H (� �I)o6�BOTVINAi�A�!BotA�, OAlLozhkp Wraut.)��p%�V ,`g0�,6 JYLIU g J.-Ya-uJ� th/0Xq9RU�0COLLECTFLOW4r�`Q�wlewiz(:� 685} 3@6�8EMITTEDPARTICLE�P���.G %�a� R. D�Xge4C�$Gelbke, %M^�3Go=.m�^D��G.{6 ouza���a$ %G. Ver�2A~%g�*H!�x-FP 6A� 0519m 6�*1Q~ �E� w�Dg!�� C.�e�-�62D41}�{i$:;MMA.��U%� 1202b_�BAOANLI}Y�N�7a�5"�;N�9}6ha� L Che:�]��I�9+0162701 E�6~STEIN�A�S�-!2.�Z%L"� P�Ea�.�b66� R`]�HABANATX#Chabanat6��l2�&�6 �7) 710.TKRIVINE Krivi2/ T�kO�ig5�U& A 3h�I1986 PBRINKVAUTHERIN-NEGELE} B�Br-=�C�<�B62 [I%J -Negel.P.|B1472 %�>�y9 SULAKSON���%so���urveni� Maruhn�+-J3�^a�&�-An ��308}, 3͆6Y BENDQX�Y�G� Heen��P6p* J/mDB�02uFAR%��5ar-�A��*�HBV15}�MW�:>zm3� B�ONSIPP� Onsi�v$Przysiezni�e@�.�%HC �gA� 4) 4��9�FLB��6)�LH�C B 44�D9�1 QB22562 ��62�"�� Kubi�� �RT399bM� 6� LIU�@ Liu�!A[ V5 r/*p  "& J1�452�r!�e>�-mass2���[�,5,MULLER-SEROT�F M\"u"HbB�� Sero"�"2�2} 207E X,BACKMANBROWN!O-��ackI G.Eh4ow�#� iskai� ǃ%�124} ]*5�FERLIQ, Pin�P zi�,�\The�otL1 Liq1}a�6njamin&�QL , 1#Sw GIAI�CN rcia-Reci3"�Nu n Gi�JL� Salced�M�X ��?) � 214�2) 2932SAYCOCHO!N AyikE/"a PhK omaz2���BMm�>� �� 6 also.�@\cite{CHOMAZ-SIM}2uSPINISOdelta} �Nishid? M. I�9*} 21 1} 2�*�2d CK�Barl#�#�-s��" Kaha�)5V}�79}+�!6�&9�,BALDOBOMBURG��Baldo/2"�GH Burg!��n. phy. )�32��6�WIRINGA}gWiA5a,Sm�i�>�.� C 29�iB1>GENGVIKN Engv!�E. Osne�Hj,-Je�4, _(tga����8�79 �66�$REID-PARIS�V. Reid,�)�50, 4�6�Jcombeiw^ .%�C5k8� Bk8HEISELB-HJENSEN��H"�&%?�(2�5@�!�, 2�&06�� 4����F� NEOR�W"�H. OrlaY6QhTany�"�kS�^s, AddiZ Wes�?$Redwood Ci�19���BA�$S-GUPTA-GA� "nB�sa D"1!��%@&=�5=[� �K.-�)��HYo,t!Ma,� S� u> 5H2-� �IS!f Mosk�,jY��X}� DEAN��JQ@:� MU����Y 4j�9DONATI� tib�R 72} Y4�35.� GR} %A efao.�.} �E�6N, 3�K� �<Y�:d.�.V�2�D9>� AGHIN*� !��_�e:6W m7� B 33�289 �. .~ JHX8&� �e)YHanoi �o/<y . ?C&0 late ninetie�Mh2-17th �, pre-pr�0IPNO/TH 94- 42�PO�JchodzU �J��7��7o6c� �a% *�Y �:< 731} 18�*4)���x�10024. ��͗LFerrei�'O+ Nicot�{A]��I}$IEZ20j]� BETH��><.� 62, �19MYenF�Lf�"99}.�CCG_98}�ICiesi��J.~Carboe-��~G�kux%:.NA�{{631}�3c%��q��CC q q%�Ft9K $�5� �=>bG_� c��- �q��� aIiB�{447}2j�s��GF�a��6f!: c�Fonsec�FContrib�_toe�XVI�0�S2�> :Few-Body�ic{uPs�G*�Viv!� A�ViviaTT%os�z A�D�HJv)8E�)= 81!95"+�rAF%� Al&1^H��402�|HNKG00 Nog� Hv m�!0 W. Gl\"ockle�Z��944� ��5�Viv01}6=9!]:�:G�&&L.�� Knut�%FCZ�*37����AF_ >BE*a�>*a��b� Few A �)�3%� c�cTWH}D�?TD\y5Қp�*�3. vF�J�x@2oK��5�. .B[=1� }440*}�AV18+G !� Pudlb\J'��2!� C.Pi�5eR* >�F�_172ɦ~ �KG!Z�:�V7��2�}1�B;6�.L�}��"97]199�KF�u �ey1�MeIi�(Y. Fukushim"RR�?) �#9k FV_90� Ka QP.n R��17�?6�S*#� V�P�8X���%,�5��3�SV��AOK r�S {\sl�ha4E vari�qkpf to"f mech�`al few2�o/ S ger-Ver�-19�L�VKR_04jx!���,��4'96I%' M.��.�6JA��32#�RK 2:C88q "35FzLP8�882Wea��RR�qW�Cav�Ji� and �F�GJxV01�2@N�xavr\'ati B�� BarraMF� " ��9.Y5�NVB�2W�PELmV6c 2�}�_[572� �F� �54s�2�>�BLO�N�ne�cL��ml�G�a6�i� � , 05ZC�p_alphav�{o}�!� B�"1_� e�\�T��z4{39`Y��O�%kubD�ZTZ}��V1�R5�PHH��B. PfitL��?��of!�n�J���}�.rsGSAGS_�PM assb�u�UWx'�Js2� � 2~ �, 181; E.O. A3@6M�DS J.\)�{1Il.7APibdvINRn$�� No. E4-66 1��Fred_ԉ>� {�kTh\`es���BFoJ_0 (Grenoble)\/�]�LC_FB17_[�,zausk! �� A�>JZ737} S�jV � LC_Trento�iVR1"�N�^}�B#6JV.ADJ�k+@RY)iavwkB�FW�. 3�J6z NIJ_� VGf�R�Klomp} PP Ter���J%�de Swar6'Ci>49�09+O�5LAF_89. f� F�13_/6HS_812 aber f��2%m S{24A�35'82fFS_76��C.R e� P� Shan�FT1T17Y7E1�EST_73��fC�Shaki�*RTh;@Ny8�4�072w SMcGF_79 Sofi�%xT McGuR'* $Fiedeldey,2�k{31d2��72�KRVǨ.�*=*2N*Fc�WA57� 5GE9.F���bre d, Rip- 2�.@1le2816}o2. KMRV�.�L!���;*�n�F� �2" a6� VKRipE~U2�!I9X�i�Kpar, .� RL_Thesis�3L���sis, UJFs�7� �3), http://tel.ccsd.cnrs.fr/documents/a1 s0/041/78/9�XLaz_PRC` joi$�ix %���E6��PBS_80!)NPhillips$��e� �9eagrav-e�2g22} 38�� u�KH��Y. KoikM>�F�4'*!�.365R 8� aWG� H. Wita��2@%�Tg)�Kiu*,6J�9\5� pKRT:�A�5(�p6^ Ni"60a�4!�1�O.fWG>��6�>bF�5ӕ4ɀ�m�].�F��-03@ <ACS� <,�0� chadowB�N`t 310&�(6�HLACG_59} Los AlamosG�'a�Cryog_"s GrouA�.1��! 5�T�MSS���Z chle�AF� mmarruƉaSo��!�.F-�`R1483���qDe�['olesc�,�00rbely, Z.Papp Pless�:.rFv6A@ 0640��rZT��bT�Pu�IBM/ A��% F&�F..�|3� 10l 75); E3� @.iFj]mOe -Y�*` pf6, 1�1 WF�*��4A�7M!��.M!qu�=t}::�(Isa�=�Jolieh3 Heyd��A. ��kb5m65�G:V!0metz} A. Metz.bGo w� Hert{p�$J\"Or, i�G\"unSI/War� Y. E�5m5ZM�154V"6+��nt� bN��,�3 it Directe~rR}, (J�r Y u$9�wirth} H4W �" Gr!S� ristA6�(A. Gollwitz! RJ0-�A. )g0T\"�Dr,�� ToneNt�#Valni!.52N146�+42� baha!�B�l���+�4a;,1ijk@b� l�(176r$83);\\ H.Z�mn�Ewe9�n U�J�N24աZ�2�IK}B�hAuyucaA�ZC#136*&� 9�IFSeC��q,�H.-�b`5��18i<6mBI}!�bQ^�=3�1>�PvIF��?�vVA�N �_9 6� BBF}4Bar�6�1�\ pr&f .�au196DWLi�� �} R. KnLc�CQ+ Beau0�&T�o�:F3i5�CederkaBt ?Co�Q'os�boeuf,��Genillou6Ji� q�lM.' HuuA�I=va4uecek6� T. W�)l61M�643H8�YUJPA%z\��>A*�jѮES025�>6Ualgora� .�Zs�.mbradi�:Soh \Podoly\'�)�F\'eny8$J���443y��R�� ch82�%W�1en�``Ixxi�yon�ory," (�kican A�e�Socie5# Prov�e�4982), p. 28-56*B ja:F. Jam�� Inst�nu6Res-�211} 14�"�"audi2j? Borce�G. Au!o"s1q�s�yex�Mo]ng �)e farv�@stability", {\tt � csnb�in2p3� AMDC/J8ons/bernex.pdf}�po�B� v�J Ri46� c�O��F��t�V, ``Par�$�*!ei!|LL�id?LQ#%g1.�� be03r�MJ_nd��6�,� P:�,�EM&h:��! .�, %�<"mfO@��fun�Zal1|9�be���'~2{��~�-n��!3=]FH} R.�eyn�*i�d56�>Y3�> 2BelML�Kinfuehr�Xin die -&en5�,ie (Deuticke�a ipzi�v3��Uzch98}�c*0�YBoD Hy\eMc!uaeffer6�1mA6 231� M 8),E@A �S-(43}, 441(E) -.-�bo�3Pa" �o#B}u>I&443} ��DauAOuXA. laps�"��IhibYVZ�72h3�0/; bxLdata file is availab�t2�a�Dnndc.bnl.gov/amdc/a�t/s/\\ AmeZ.mas03.�doO@�&obaczew�zj �1�j�)5go�Iori� F]�ѝ8T�3R�.Kbb-} �4-�FB�:2E�9 �note} JV^ameters�8bjtwo f�l re signif��tly diA| ent;*C-nor��)�r.m.s.�gfbweb-�co�er �gram �Qlcheby.py} may be downloaded ��\\2�gen3�.wa,�0gton.edu/\~{}Sch8�t2.tarA�N&/ f 10.�HFowler�+' 7r�UW .�Th�liz�!�$long-lived��� isomer� �u��( stellar �KiÄFD�&-Jx),238:266--286�/80.Popeko1y} L� , G etrAVE� KochubLq!�TG8(Zvezdkina. &t�HOn spontaneously fi�g�$u$^{236m}$ � ex�/d w7 captBYg y)(rmal neutroJ�Yad.Fiz�$17:234--24�7�Eu�Mostovoi��} VD �GU3gev.�Measure;!�a� � c�se�� 5}$u�by��At.Energ�57:241���82�,Blatt&�skopf�� �V!�#.�� eorepa�Aj�<P�=�Doverki&A� YT^l5a$deShalit&F�p�u�~�*�p.l~� v-Z1a�"׊���iey �S�B "��2? WongI" } S.�^B�Introdu��V�^#N�.#�"9#$Rose1958} �mN{er C۔_= Coeffici�2k Ho0U.z58.�0Hamilton1975}?M�jito2�1� EleA�m�;m� raI�i&ÛSp' scop6��j�75.�c�Hll�w�A F. O'Conn&�XO.?# roll.4�!/c9/c=/.,�A�R�},� 8:10H�105��667Ald�� 56} ��~Bo��T.~Huu�~Mott�k�A6�'.�Study�)� AS struց by e:l��[m( accelera��; .\�� � �� 8:43�EFY� Band�&} I�:�M.�WTrzhask;"ay2�~o*low-e�����O+^�tom.Dat.��@ Taba� 55:43��2��${BrussaardI2L�B�j�%�<(B,Co�&��2[�Eeɇ� OxfoENq.�V�7�I��BlPhotoa7v)� of I��� S� �leɍ Recent *K�6�Ak��ai Kia�5Budape��.�M���MA�rit2��]qY�n=�%� 2�� uran]�235 s&g�ME�Lw�?Q�$49:1574--8�6� Claverie:�"zv} G.~ et~a2 Seb1foruaV�ic.�in u-23_��[ ��aT}, C70:?,!b�UN3 Wf3 6�,RINGSCHUCK}R P%_Schuck Pe0�{��91��5�.r5$m}&#C&��:))�b�@�=N }  \etalo3 % Pb�\:� -G.\&7a\d�it%*�}� 75} � %�W�Ɋal�ory b)����2FUKUDA}�+da--4))lE� �.�2 �9:5 833�N0VALIEV}Valiev �F��ndo G W[7)!�%�IXeA Y<227} 265 %Our pK9!�PUG02} Puglia S J, Bhattacharyya A =�!A-6� A723 %�EFTe,dilute�mi��z0HAMMER00} Ham��H-W%�Fun�ahl R J~!0��Jz678} �O=8tA} %AJ Z�8 H!788-�eumI��~+�.�8We�8) 2�,URNSTAHL04b}>H�6� 20051T.�B}�;p`�! �int} ��-"p,4���JY74E98�.��5}6�I)�nw#!�>8BULGAC}Bulgac A% Yu Y! 2)�) �I�M�88%�04TA�YK$SCHWENK}Bo!F S K^�ZZ� �[�cyWhitePaJs} See "by "���gMcLer��L, %``J form�QCD m� disc k-g�� %plasma?R�heR������HEP-P �66>�M�A� kk} "�AB�Had��c�)deconfin�-R�=�4015},��=�A>��� dn}  X N�DMA jet qu;�zbeyond~�501V�o�A>�S�j er_wa6} St\6er H, a�K�ve �|5y]3 I2a]�]w%px} and  J�Gelis Fl� !ea�kxb glas��9h;n�]�30��]�30%�a� d���ew 1��� � --Cdvongly= a��( QGP} (RBRC�L� A�, V�9,� okhaven N< al LJ�X Upt NY, USA),�_appt as a specɔvolume�� �&� ,.3�PHENIXQ%Adcox K 7�} ( %�C&��)Z <0�]6PHOBOS�dE B �/&(�&���*�@ٽm�  � s�ae�ialA�9O�+ can� &� at�*�phenix"�,WWW/info/com�.�  �aP1xi}  U�DKolb PiIEarly�EizEBQ�,'' \J#Wal��,2}{\NP}{A}{7 269};6�q 11107e ya�!F ^n3n21}{30}^21ap��9���3dzq �%� Hydrodyna��det�p3�ulR�{-�coMg!)2 y�Quark-2ܹ�[edi��by��uwUX"� nE�)�634^ 30508> SH� � 5, &��J6((``Anisotrop >ŭ���A�)�h�i[�&�'']P* C .�s��.b$0}{\PR}{C}��{��9�G"�Mu�,a-�  AA_ CausB�fof�u sipaR�Re� v�}z D)�s�<��ear %���R!�.�4�,9}{034903}; 6�G30905e!�%A(Rischke D H�E��QvhsJd �%jc in 2{~��6�js 7114bM46M angr1tm:� 4IA��c� $739} 163 [�� 7067]^�46{HKHRV01-�(Huovinen P,]� � , Ru�4  V%gVolgDn SA%%�``Rad��A�ea/���: furt�predi�sA�@.1AL}{B}{5��582�P�+03�e2i�Chujo Tn/.) � ``ReU�d Ideed � �[ g E�b� '' 2�.U15}{151c2� STAR2�B�Mna O, � F^L��6�`� Mid-rapid�pi,K pnt'a�}icle r�v �J��4586�2�Wosie�� *B�=^�1TAu+Au��!Y,\scm=200 GeV��5106�BRAHM6�Ouerdan� 6� ,B�R1Udep���of,# rged&�I Yiel�% �at �.�>47:b!� 03om�� Suire�!.i %B�O4el ba�<�Ein ����1303�z�:gKRU#��NRapp RJ�t7}{04��.J Sor]LOkp%  P R�3"GD&H�%���� �03;�;�J *Q� >C&�& typ 6.�azimuth??�=�q� m)�ca`� %Q��2� + B�4s(NN)**(1/2) =� -GeV�6��L}{}{92� 2302 [arXiv:� �600V�EX 03�� Ad�S S6!6X .�>�P �1}{��}2�+Y!�1nb!� jR$j�`N":=E�NH:I %13=J2�1�P �87� BK107003RJ!K !K&; E coal�Greco V�F C M�5 L\'evai P�Don 1esc�e�1,antiproton/pa�anomalya�� F�[ �90}{20E 6�301093R�� ���^�&v I<� �v.}%�bf :&� 4;N� 5024j��&��(^sAV3vEV R�*� Nonaka C)oB��`�� in*Q�� : RefPini�!� frag� ��e�� R�>�3}N108V�1�8m���:V&�.�F2�� A�m� %�% a�*GrA�p,� ҩ\{N���2R�602n�6�Molna�,3ffa5  D�6Z ``[2J ' = P�ae�.^ �j�*�� .Xi:201n��]�,HK02HBTosci}o G �?$� ``Em� on anglىt �0interferometr� J�> %.�M: 42}{216�uySL ures>��IConcep H"u`P��}_,;! s giat ��o�Lat��B'anZoolK �-o%yP (Mexico:BITMiguel Regla, 1-14 Jun�3)$ &&f73�Y�9 asHBT�>&c .M.�3}{01230A*��# ��2�6��$ S M�2 m��A�al./(ed fireballF�%�R�6� 4907A� M�1205058>pK E�"T�� T�� D2 �p w8}�1�, )* �.� ZG�;� Zhang B,>K�)MB>�-'_ �4as�E�e?A�.�[Uj�; 4U JcP455}{45a���!�1uxB�&����pZ � :��%�Pa�a cova͔t?��6�V el MPJ�!�#697}{4�1(�\i� ibid"#�-893). U. ���R7f 6son!Kovtu$Son D T�pSta.^ts A O!#A vn� bW�%&j�6M�q�4}*�40523ab2�A��! 6�$NA49v2PRC}AhAlt�.s ""> %U\A6��/ %''D�9qnd:�ofɲ���� �Pb+Pb�� at 4s 158 A� �@ikEzav!d $ D, Lauret��*j)chj_N"�A�SPSQ*V .�1*E11003�[R# 6�Hirano�eu�  TX Is eR��$ved only nc id"��MB $ %at sNN =� GeV?M[q��%=�5�+�d�+�*}800f�1:���4E=6�����4!�B[t�u]��� �� {V� }*ڟ art.���/3��12�XB�4suf� 6�� 62v2!�� �1.G��41�T2q HK04^%E?uh�4S#NJ�1/*J R&! f� 0}��&4F~Nakan 3,-a&h!� bf 3C01A^~#3);�VBarth)�:Cp$ ?bf4ML<�x��);�� StepanyanRB� �z%��25tS�V.~Kuba��E>:�H� H�l{�R4rV.Vg�*;RFFtom�. G� 17"��2~*�2�"�M%5�T2�q� C leev6> {\sf� E^01024}%GNVzt�#z� 3073�x%q*�7 KarlhSe�grA�M.~�'$H.J.~Lipki=f\ �\�9 3"�YgTitov\wt\A.I.~�, Hosai� S.~DKndФOh93� sfrI�����"�yu&ji!,} B.G�!�KҨi�C.-R.~JBM312075�2uNdhgarndt} �y~A �CI.~���,y lR.L.~���8%��_311030!B�pdg ā�i��{G�D:!E8:m>ZEE�i�<�liu!��k5e�C�-lo:� 0803�d=nam =S�2Nam!� 1�!AH-Ch Kim-�� 3083$ Kki K Hyun-ChulV7242-=*(Mart:1995wu��:M~Bennhol�4,C.E.~Hyde-Wr{�5%�\ ���G0 U6�Mliu&ko)�WA�uga�2e2%�9�|0���!2��a0edv6�qr�2C�;�RX�012��>�6Vjv!nK�:�5:�t?38C*&'4haglin94} K.~H N�53N�P^L5�wjcm(W`Jam�q�A(ш ~Cot��.] 1?{h1��2Xguidal�P M.~G �?MU�geti�M�derhaeg|a�aB%#��A67C6�>6ZLLeeA{9kd�]X�Ae�i-i=��L�LY�~6k9 $Pc1.�&jOr8eq:�OA�B9M%M> �Tmtu���#: ��M��]R4"�:] Da��A� 1rk}@O~�R��\>ks#�Ra[E2EɁmybU�qT�Kja'�FD��#bf�Q26�A� R% Cf% 5.& lep��  .\saphir�W�2 ��claP��A �A *A �di �U�� j2 Ii07357}%y2L$theor_anal��@rndt, I.~I.~Strak�jA��h=�nucl-t��1030} g0; W.~R.~Gibbs--I�-��HE��T��,A.~Sibirtsev�4 Haidenbau!�S.~Krewa�58Ulf-G. MeissnerAv)�Lett.q�59�Z23I�4.�pdg� LParticle Data Group:kEidelman6� Vh2aO�2f cahn%^N.~CahIG,G.~H.~Trilli�6 �Rev. Di0 1150JTkim��8} Hyun-Chul Kim-e\)��585�9F�singer�S %�G.A Mill!rF�3A�141aB86.Q(haglin94} Ka� � �-�5�A 1688B92-wjc%,A��lliamsa��A�SEVCotanch._ a46!�617a25 deo}��B.~DeoQA.��Bis��F�E? �74A�8G.~Kn\"ochlein,6��L�Z�A)�35A&32 �5.= regge_rho�DonnachiC P.~V�;ndshoff�2� 478}A�146%�0);�}M(K.~Tsushima�.M�-�67O 0552M�3BRBQ!�.~Thomasa� VG �0Q14�ay.�sbass��D.~Bass,J<A�7);2xjanssen?J  ~RyckebusA(�uebruyne�9,Van Cauteren!;.n� 152Mpeti> Bydz�(hprivate communication. \end�oXbibliography}w\beginB{0��Gl' ��3jwa^H.~ B�Eur�� J.\Q{1E��2|Goers�z9sw%DBY SEu�]464 33�99.�McNabb�nf} J.W.� 6] [2$��e � E�2� jlab1998}��Pl Proceedings of the �Pshop on Jefferson LabnicsA�0 Instrument%�T with 6-12 GeV Beams},6B , Newport,s, VA, June ��(S. Dyt&H. Fenk�L�� skinE7Semihard��(sses In QCD2� pt.\m10m a�8� 6�$RPLC,100,1�u�BK_equEwu Balitsky��5ubq�BI� /� Oper expanA�E�high-ezscatter '' 6�Bi�46z � 1996>�9509348Z� �m� Kovchegov�9yj.�FY%��(Small-x F2 C cture funI� of a eus inclu�h multiple pomeron exchangee�Nv6!� 0340)�B�901281^� ��MunieP 4xu.�:5��v.\qp#775034>�0401215Z� ��BK_FKPP��� ˥�vcQ�:~� GeometricA�� as trave wavJ��6q�ż23.�>�09177^� �M��s2�:~�T2� front? ���nsi��toݱa�R�9�4)M�B� 1035f�R�v�~�����v�E�$ R.A.~FishO { 0Ann. Eugenics bf �,1937) 355; A?$lmogorov,Ia�tAe�$N.~Piscoun9UMoscow !. Bull! th. `A1}�Qa1. y[DIS_fixaEe[0Golec-Biernat�g8jsqbV K.~2�M.~Wust���S& � ct�d0 deep inelasti��T, at low Q**2P its %impl�(s on diffra��^�5F01401�F�807513Z� A�97,BK_b_num_sol!-< tsma�4ra966E!0sKozE�v�U0o�� E.~Naftal��Towards�� ew global�� $ysis: Soluq�X(non-linear $x at %arbitrary impact parameter!L6� 742}�� 55>�^� !I��24��ym67.�h  RmA� Stast� On s-"`�-"9D��6�3��B�30627f� = Ikeda�4zp.6T.~e$L.~McLerrag I:�.� inEj�!�6[ 410345ZZ �V� lv� u\AFRS} T. Alm, B. L. Fri� G. R\"opkI (H. Schulz,  �A551 �� 93) �^BL] �62}, 8�199� J:P��Reddy,M.�J%�L�%� 5MirallesA �Atrop-~Jq51h78$9�<Strob� C.~Sohaab%$K.~Weig Qstron. Z3�49I Y G.~Fᠡ|ghelloEeA�#VasconcsmDng� nAs!�B6E�8)��=�LATT1�.�%%D#(Ravenhall, f� J,-� 223,} 314�-78!& D.~Q�mbB%!5� ethi�"A4Bm%@*2A3 459,l 81);!�2�C%_>[p�Bk %�A43An646 k5);.e�D�O M�.� B61b 49�7);� Catalano,!�Gi1 racusa� U.~�KJYI=A68~90c4 :� WALE%�$D.~Walecka K" 2P8A�49e��ReQFre��)e�2MB7�69!�7z#]UMULL}M S l�nA� M=) � A4�60eh8!*H.~M\"uz%n�.~Serot H ���-pCR 2072���BERT}!sBertschU��Siemens,IuW� � B12�;�:W KUPE$Z \"upp��G� gmane'E� HilfuGnn͐ e8E+5iC�eSATP}� Satpathy�MishrI6!�Nayak_�)I3C3� 162!�8�`JAQA1}H� Jaqa�{� Z~kji�"a�L.~Zama�.+%� f27,} 278!�8%R��Su��D%andv T�$uQ��M C3�1539(1A..�BALD1}�A� Gc".Q2MI.�� �� S.~Ferrei!HB �A5e% 589c!<>X!<2�$((�=i�6<9,} 206�8:HAAR}ater Haai�$alfli;W~!�m���5A�1r%1�!;6.��14A'20 �76pHUB�HubA�FA�be �� ���� �C5�348E�r%2�OMB1}o$1��%]#A�.�6��242,} 16(:GGRAN} a�Grang\'eE�Lejeu M� tzol[!r�thiot:tvq�C40t0L&>_ LEJ1Ag.�f W.~Z:� )�B47!;}�ZU� C���BhN���Q�706}, 4�+:3aw2.w�* !3�Burgim� 56 i]3K,27I:p MAC}I�`#d�� Adv. �Id L19!�8��:� PUDLe?S.~Pud�r,B,(R.PandharipY!�Carlso�� R.� Wi��GY�-� �7!4396 ɀ;B��p�C�e�E!Kv~ xCi�720y:FWIRI} >JV� J�'oksI�0R.~Schiavillab�5���>d OMB2.��2�:��44)��891); q>\�M#  0246��"}0 JEUK ��eukena�.7!zCa� haux.n � i�\ 25C� 7�$e SONG�-Q" �'M!.B��n�If�� 15VF LEJ26lP.��e5a>�Cugno�$%�J 45% qY:�� 3^ Le�b���iZ B215A!i�86� BROW� E.~Brown)Weised Baym!c��SpethM���):N�q3 q:R LANE%dw A=Z;�67686:FPETH}Af. H�B� ]% 1133e�:M� E���>].A�P�)en{.�K�2}6� 27v:l HUBE} � :�S^` iJB3%m48�7 % �gMC5128�>� BORDEH.~Bordb% �� odar�>�Y!�7�>� ZELD� Zeld�Handbook�AD7G 6� W�reF�#.�ATU� `l�.y�%)�2�39�,A���� ?+Jj+M J.~Gary Mizutor�,0$Nazarewicz �Ng40!�1 �1.�EDRe�Sedraki-0Bab(��6p1:l L��2LH.-�HB�;bne 92I�:�c1}.c%� S Eq�!AxSt_*of Asymr^A�M�,�%�Isospin%N�(4in Heavy-Ion C"5$� Intermedi^�$$ies,} Eds.� �+%��W5r\"od$ (Nova Sci�$$, HuntingtO New Yo�5�) p.352 � G�.� � ɠ%z� �a{6�A47A�3 8:� HASS W��ssP��=���̓17!�31���b�+ s3}%�+yj}]�b�:1983�� B �P>"�%� � � �ai83) 9.|schmidt��Q  Hipp�/J. Dol"pW. Kronms"Ze�Ŕ) ~8X)�2�"2.� gobe~F�b�B. FarizA M �i1;1 �'2�L 2) 183403.�lopez-O� pez,.= �A 685�1) 246.D guptM1} �+. GA�.M*%N. � B� l26i92;matsuiA6�6a�suipF. Sat�-��} PB 178I 6) 416; �� �� ��Aulzq K^ :=� Cl2N586�bonch&684a� B�� �&�D. Vauth�%:jd A 42AW1�E;6�%3!91985) 252�m/^ 5| :A�A2DXC 5�1�2�pY�8 " I�mb%i�%�!{6�R. "&1np-� a� 97) A�!�&r rQiK. u �2h �nQ9)t; MM:l AE�.lgD"oh�>� �%CE)Q$82stockA�2� S�) BoR. BrocK7J.��H-se\Sandova�� �troebele2/0} 4� 198� 236.�fuchs-� C. F,�Ess�T� itanhH.Wol� �\2�A 6e�� 987;6?M.�[ onna}  Di Tor1 2[ a�+"B7403005��B}��p2 .�=n!a5}\B. Bar�jJ�� stei�� S. KahanaZ�40E,a`744.fj�hq6.!�*�>L. /M'���bf C q�3e�2;MA�+a� Yang%�T.�#q-vK3�� +.�l �5# !�y�CE�*,a&� � Q. L�*pI�A (a]!164�wD. .� .�S2uR��eK�90; N��2NN�H- 600. w�! 8}!nB�1�V. Fiki�A�brociniR+3�h8) 1010]6 Akmal�VE6WRq��97) 2262b�Ta�2`.} X�)� C 44%��1892�zuoT9� qn`N]6i�Ib.balonsog3�= A��mmarruc�6�301032���7%��(Lect. Notesm�z641I.4) 119M�&v �#x.�fd A� v �V�Jr36|1�] .chaaex7}Ak:� "�-g\ ��Q�207.Tb�!�5.uBY.$��� ����# 599c.�h��8d"� W* ������ _C �="6)._]�4K "[.%�*v$JE2R'199A�"&�$a 2002a eA� jWg J.-F!�)/ �EA 0��2z 8.�gh 9 � x � ��"� Jw pR=uC Ѩ9��4Z�A(:E��Jn�!O 5) 32�m�aK9}�ZM, >� �1���86�)�L6�9$P.==M!��-/ *R��� :rjU66�#� � -�hCy9&"� 5ce76): u�9a�2(&0The Many-bodyory�\*a� ear J�i�? # Metho�*nd.;F:u<Ed (World�tific, �>apore,�(9), Chapt.1'6����O&�.R~�2��-UI+ B 21��p2- song��Q j�G�|oiW*f �A�q58��%"�(�%.em�js�!M� B.D.� E|�. �"JY1kE�; � ourn�' ��E i�~512�bD�7�E� V��V *V VRe1A�2U u1��/2�QJ_M�&]�G.FB�j� 2� �27!�5�rayA.7� Ray,!RSh�!n� .dZ&I] B392e�_�N�>Mf13.�i92}:�%��*�-"E��l�F6ef5 �F ��)�2255C6)i�F/ ;��H��I] D.�$Mi$��Rh!0-�D( kAsC4>1�� EgQ.S*-H.��� G.E.��kv��DE�� 5214a�6%J�62�37�#�Q��G.�C2�R. RappVZ6Z$455#8�akaplaeM6yq MK�A.�Nep�.o 1%�5+v]politze� 1� !� _�� seV]2+15�7�^52��)� K.xL��~!�nV�Brs< R�2�53My6�g&('mA 2� IUa)�D �D27%�2u)B$�J�affner�3 lich�Q=q]456�!�)>zC ,�H8��59th)�k4}J T � "<A�:�+R�57�)93A�4�$bfaZp!851  , Erratum.~ elli�5} J.�A�"�M&�R�34�1�6�yasuhir0�Y Z�S�mLN��:881P�Ee� A 67%-218  J Muto%Fc�`pN. Iwamo�2B�D �E:002Y <9� pons , Y-J "0-.-s�.!y͜p�JM�5F 38�LFU2Y?xA�lm|A� . BiI�iWambaE�I� 2�5�F�8� 6jc�#�"�#�3 lberg nVB%� 0176a.�no}A qT�rse��Sy �.^T65804FS kubi%/3�Ɂ�i�nu�*e��Jl72AT189U6�bkr����2�i$��QV)�E�B 1�J27a�t5�daniel�e�De�Lacey)rW��0 � ce c29!+�2)1592&�-2?�dS+192� �)�E.�Df%8ink, Y. Dewulf,�A HNecK+Mm roquie� Aod��B�O643"g.*�91}��b� !�2( P. H�!.z�) J�!5�*TvO.\{�fCN,A2?1�g�.� A .� Q%�` K�%6��66lejunea(0}�t2\5U%�)�=J&)5 kais�>2�_�Fria4]:$R�697},: EP.�&%5�U. Ainsw�! i:� )/��S 2518b6[ .�tp}J�*�~F&�)8.�3a[�Ff2b��&f �j^A  5 � �i�2a.H.�S��F512pM��K73��6y 9H%R� "�)V����.')9ia%)FM)3!�:(b/� V/aE.=+J8+iL� ,� � � U�:qK!q&�,%@Q� -F.M"�B�4�;04E%6�ma�+6~�P .�+�wei���*�!6�!2:�,��~ ��y��,i�;M ��A 1�#46�6#"�3X 4j�MU9ŭ�.�>�9���)F����A :" w�3�4�.?&�2 (N.Y.))/�0�F4,1�h79-p D. W [j�756�5f�-T515; 2�W.����w_jx=Nit4 >%�S ~%},2R�Q8Q6Kdonoghu�85bu}3IF.�Q%xC.c2 Napp"��OBGSA 0�]:d(61 A��#,�Laga\"{�Kcl[B�D 5a ��6) 5492V baym? %�2���Q 13%176 6V>M*%� �c2;�Y�DL.�m��$@ 02432uN6 grec�1�G C7Z>�� abbr�[>� BVC��V�96� zhou� 4} XW Zhoue *�#*�^K-��*�( W���,018Q;k2�bѯ8prc}!~�.�%U2M$,J�iY3�U�쥙C�055�m)RQ�$fQ29�@0vspace{-0.5cm.^KoldE�Goldhab� �+c.�� WorkRCorrel�Js�<M�IXp&`L`(CAMP - LESIP IV), p. 409�Q . by< Pl\"u=� aha)/R�We,>�ebA�5HBT� Hanbury-�%xR Twi�+Phi�Eg.'4,1954) 663, N Ee 1/U56) 26, �1 1447*�?purcellP" Z999 GGLP6r�'.�12�960)wM? bartuA�Nrtnik�LK. Rz\c a$\dot{z}$ewgJ.UD18/78) 4308VdeA� D �9�XCERN/EP/PHYS 78-1 (Janu�, 1QLNPA525}�$ra�Pad#-�@yulassy6a(4�� 33T5�kpg�W�ishine�$I. Kopylov%M.LPodgoretski\u\i, Sov��) �fAH71) 638$�� $ �.72) 3�+�cocconi%�C 1e��49B^!5.�I�Boo1]ic�NDM��,Bose-Ein�$.r in "[� Nuc十�ic{U,ohn Wiley \& s�.�GKW%�9�9$�$uf!�i�L.Wixa|  C2E�79�".Yw�%N. Fowl�86���70B!�77S(1; ��D1�A�3118;�4W, Stelte46a!$. PHys. A3g 1�32�grDY3ss��� <�Bm��31]��,�B�,:��>�73c< heinzchscj:M<�Ccot�!� U. H) TD!E]  8!E�Q 4403Y�za\W�Zajc,�Qic:�P��, Bbp1P�%rr�*�W.A�fu boa^a�Boa^V K. G�C�B�Je�>s,)�M"�C 6:0�H3=*(wong}C-Y. W�iInt�CM�e-�/y HJ�/},VB���%�"!t GT�[ikN -�>$ A. Wiedera6�Y Wuq1!��� 18.Gcsorgo�,$Cs\"org\H �� w0I�15* �)-8.  rhicq Alde�E STARx lab.�A@�. 4� 0823awK. Adcox��, PHENIXnC�`�923�,5K�*raPhDF�!�sl��D\c c\~ao entre Bos�T(Id\^enticosOzidos em�is\~oesE�\^o2\�KAltas Eia!�PhThesiFesented�L�ZitutoYG,F\'\i sica, �MersidadeS�(Paulo (Octo�=16�N��Bj�)yBjorki4^�\*Gisrafs}�f\AA ke)5�L44� 73!%.�pratt�P 6e�D3�'6DJgyupadOMiklos��!Mb  �217�z8&2��B.�We�U�2281� �89; M. &Q, -TH. 479� 87),�s c. E�f8h Balaton Conf.PP^ (8by�Fodh4KDKI, BudapestA#6�NA�,T�  Human�$"QbC�=A�79�Bam�� �3�k)B2l1132.rgb}���� Ş M. Tohyam6�C3qu 18U�qm>�%�U"# �_. Quark�2ter '88fp 555c�FKGa$ Kolehmain[6c� �1�IAq2$4�Bj"�� 9I�2 � 3) 1l(7pg:nio�����F�E UB3\<378�Q�a}��� C4E�UR2.�lorstad),ulk �B.L\"{o},]Q45A�90) 52>npa544N�2q� A54e$92) 537.�pgg�KS�1vin6 B329Z �35.lPLB348FWF�)�M34w 3A&IPe8�HP bott�. (E802��a�Ec!� RA!@0) 847, ibidem 6j"u"7;�!#9i 1T+6�E%�1!O12OadrolZ� Cristianei Rold��D5<98) 290.T e859šAkiba=599B7I 9a18057, V. Ciancio�L]# A59 ,� 59c; O�$Vossna!46.-E4!5c;:Z F 0to MIT (May/1-}rhkp��\P!Kod��� >�24A ;$7) M.� sono1} D�PGR4QL�Q Crum0 it!�Acoust�)(c. Am.}, Su�9. 1�&8xSji 90),.W,.TC.C ,r�JR.A.Ro�' >g ��$1-U$�,Sonoluminesc�;}.f��F<TodG(I Sep}C 6} casimir}VC V<y�]a?)0hrical Cavity�+a�s ric: T�V a M"�`>�?}�%A. Miln< hep�l95100�C. Eberl�im�E��A�"27''6); <>g%��,d,JA!�Oe�olo*� Reviw C2�s) 4492mhpb2P"Tt Z�Vyi,:(� 91) 621c;�L"�JNNix�9_)eC5E ! 2694; T. �"2WW\"\>~��~25� na35 �Al%�O, � �O��C�� 5) 7.�zpXu H. Z2a�r�=V2492� shu}$F� %E` D 42^7��}�MW;  7+3]tafI�C."�=[SC+ 2132SRSAS* S�= rkar0���D Sal stavZB.�0h�9Ji kG�g9�k0cA. Aya�CA. Smerz:�9B40�f0n 2VYS�)Yutyuk2^.�@A5�$58=O2�green� } O��G2d���-70)/�aJ>WD4�A41�2KAGI�,!�AnchishNe!!�avrilnN. Iorg�Gg��� �7} 22��)Mod1s� %�1e� 162�zp2A�Y��nE�. gAocS. Avg n"60K�7�-,A:j h�nV/�M�@\ 2� sma} S\'e�M!(Antunes��$sl Estudo �8feitos da estat�tica no $ extensiva�Tsa�+�interfer6cp�h0}, IFT-D.003/!F}tt ?  K����2�47.\n=(} . B\"{u}ykkili\c[  Dermirh�F A. GC6�A19� 09; Q.A.W�<A.L~@'ehaut|#I=A!7� 2Ja�eH22; U.Tirnakli, F. Z��I�VMo 24a�U8��=0 wilkahV.Utyuzhb WilkZ.W\l &I czyk%I ]G2Cr L�2��sn��_ 53} �8�821.� KLLQe$Kaniadakise�Lavagn`Lissit #ati, ngv981202s APW_�\ico6QG.� A680� 0) 9.�\\vvr} Victor Viscarra-Rui�I� imatE�A�n"c esp o-de-faseA�co"�a a� �fias u�o> }8>� phsp%H �)���)�7 4) 26, star�LauA�r� .��G21�y&$77c; C�<Χ 0�]�phenix�Adc"�iD.�j�upkolbGI� nz�+� lb:� 702,�E�!Y� spqm�San2�>B� 3) 66�s| 2� Jr.a�F* ��&� F�9""aI>3spWEo�E. Agui1M Osad� .���2g7�29nexusc3 resch&� % #HladikR+0Ostrapchenko,Piero� �DrM "� ~��L91�/].� �A63"604��(5�bbcapw}$V�re5a� �!%aM"}!B%}W3 347`�andwei:^^QiqB37-  12(asacso�Asakaw%�!�&` ,&%D 6) 22�acg.G%�.DAS�&o"� ��R9F012�m}��Makhl:D6� y F��4!�>354; Ye z%�!!�!63�^F �F ���982�c�P.Kr9nd2o"� �� S.S,�!qg) �B51�8D 2Vjpflow� ~1h H{o}Vga:6 .� in preparp$Z�b�!�$�b Suh}�%uho�OUvitare�:%d&�83L/!6�;22�GVer}JGVerga� =*'9�A)2�<PriRo}H25 imak�nnI� Rosen, C Prog� 2I5�25.4/ HaSt�@C�0x2KGg Ste� N7�4RarC�t � 15V_402U;Tom~ AReEe%�5&.D� u�FB!�.aeH �>� H2C!k6�H Kla1�;�� Klapdor-K�grothauJ b$ixty Years?DDouble Beta Decay}F� *�>ž���RadxZa�RadutI )�V�48}!�2#2. Rad2��5 J=%�DaUDelio:�%g*4}�85#ey#B 3ey1 #>�3!��>� q��6�^A 6=�1762�om%�Hom��=�`�� Hir�tK.7H�gR��T. Od�Y� �CQk�'96bLSar}P.r"g� Escuder7A.a6C(KzoV�5!O8|"; �#/b�ga|A..e}h �A65_> 9)132��� 69a �8636�$) � !0056>�EE.h} Pace��cu% y��imkovic�Y).H �? U 04436k Eng}?En�eM�Qn�RDobaczy( W. N�Tie�TzR. Surna2-)7;%�9)7n 302;n^�:�XkjR�#B20a�054322.�!}=%:Nb~>733} b 4) 3\2h04:�6G2]B��6�F�69E3*r64F�>�BN�Q Iudic6T)���%��82� Rad4>a.P�I�) UrsuN�5Qa�5.� Rad5>=lR�j]Ad� ��vm�B�p_ 9) 8�A2�&�kNB�,��P Jour XD �1) 65 2�6>��:ZgF�V�ŻXR4312� Nils}S.G.  ,Mat.Fys.Medd4Dan. Vid.Selsk�I29} no.D5�2�7}XmR%^�J�I�S.Stoi�KF�53&-1 Wose}M.![ , ElUftar.�FAngular "~z(W�*,*W195gZing}P.�P.S�V��eQany-BFG(Problem, Sp�M(er,1980,p. 6�Vog}S.R?ot [ Vo��4Ż-1SciM-S�o16>EBarA�= arabKlCzech� .y 2e� h+�Mol}P�"�gJ>ndrup.[ �� A 51-�0)6� ��}�����H.� qQ� WB20��� 6 Gro� *rot��:P-6&g A4:Ny"39.KEjiM Ejiri" ;2��y1) 17.BKir�  Ki�Qn,A�Heuss�*aYmr�� Oehm!Pernij�Qich�RPF=�Zn� 8al Symposium on�A~&� i�DNeutrino, T.Kotani��}Tdn4ugi(eds.),p.81GyI:B�+�f;]#Va��sVasil'��� KlimwA� . Os�va�" Poma:q�*�ol'ni� JETP.u5�1q 66S Hen}E.W.H>bceO�Manue�D.D.SabuQ]eNE�C1 W75) 13�#Y�$Li}W.J.LinU JL8 AA�4@Su2�$.�.U9��052�Au��Aunol.}.�m2A6*!.6@ i3r2B�157 B}�&5�2Hir�� 5�,2�>f 4Ching Cheng-ruA�$o Tso-hsiuɛ� Reυ�^.EO4$9jKlaGrV. QW�1�}�142 B��36� Zha}3U*��("�A�.q�-+]P �O�122 O Baly���lN(E�B 356}Y.\Bur}T.W�grow)�a�D� Shee1*6�/> .A(Pek}L.K.Peka�A͂@66�al}�raj�ghj�mS2�Jea} J;a BachCnf��N�g.�Fre<De Fra�%�E. Jaco׎bR8�X�) 4O'YDJe���HF1;v2!Kan} M,Gbe# Kito�b�� L222LBalTa�n93� �V2�Serg}�S�u��vj�7�с�5�'9#SonzSonzog�MJ�E���2�P2� Mad}�adlDB.S.FJ�s�0D1e�E�*@aldwi7=#at $ S.M. Austk%Fop�98J�*�R5�!�Ak  Akim�lH.�30_ujiwa�EI. DaiK3T�8oma�RBz�& A. Tamii,dZ Toyob�Yos&ڎ��B3E�Z6��3}��,� !�9 %�e�412�AF}B.� %RU" hittc]rF~C. Lebo)F-��3�nd�&�1��6a��C�5%�F83Mv�b116�XZam���pM� Auer~HFL  \t/:@Cha�;C:�齾 [7s623�83 �T�2�iU2�A :m .�!�4}X� �1M&� tau�&!���FF�@Rui�P�0�FHsui Ho,Qun.� or2�2=Y3��21Audi}Ga[d� A�#WapJN�5e���)�; <�]Bersill�J. Bl��e�AXjW 62��{_.8La�. Lalaz�s� Ra�O ύiS'Ata�t�i!�/Tablesp 9 6� Ike}K.�}qkT��2JM�6�9 34; 1S�B jita� J.I.�9�!Ix}��� 1963�]1;JO -�K. ~�6�6�88.-Zam1}D�%t��eH�8yEf ��<�$!�<42!Cau� Caur�IA. PoG� . ZuW� M� B 25�� 6�Aba, AbadG Moraz�LN�" -LagosadneF�heT nnh3. A 8�,� 6�arcx ia �*| }N>4��2916� h�2� aW;y� \�� Hind\ No1*�� Orti�d$. KaloskamA�CA�vid�`C*>&\J�~�242\Leder�Miyahar>�i�6rum���WdB a 3."!� 29V M�dern;R�4irl��eT/#a�_Ћa. 0411002 v!v.�l$Tret}V.I.  yaF G. Zd�9!�.)�*�8�4) 832`Rad8}.���"�%o2�)�*z��S"6 Rad92'I��XD{6%E! A 47��c47&.MilmS�/a�F. Avi�re,III��Ldz�i%�I�dlAAKJ��Ree�.Z����306 bAvi�$�3 z III����L2�b{3�!]�M� O��>�L�LfL. �h} * QG Hahn�\7oe1E?=4-�20{� Hel}�0�%lm&2$N�I1w 2:]jKli�IA� �5�i3�ZA�I�B�<J/2�Tu՟� .  evW T�EconomoI�Y Aww *}B=OK�21��jn00} %&b6 labe� Text��*�ic item0n�c:F9 \" subb+" (O�}l"� ~1}BX2I@� re i�>h@, it should come `�F�3�% �G.�]!�F(02PR363} G.�~])�.V[5wp. 36'� 5; M�2Bir�Yټ 2� ��537; S_3 Klev�, I�M&�-6a% 2) 6�&�^ Cola�o01PRL86!GA ��GJp$TH� utwyOj %�v�[8T+�H0�Fy2,Cohen92PRC45��Kh�J� rnstahl�+Da� Grie� 2jC 4�-2ow�GOR�&ell-M��R. Oake zB$n�'6�1 (196(819\XHFG�em^E� rz0er% 8{\em Quantum Me)��E2nd� R7�%� % $-Tannoudji� Diu)F� o�L�^q(&{Yo�r1 E , Vol. II.#,Peng02PLB548A�X. >C"���* LoewtHA�+�ѝ�3B 5m:��:�cV003IJMPA18} Gk.P P.Z. NmUvmb{�)0 �aK"�0A �}�?15��9�S� %*&�0RAdSu%4����2s;!VEuD� � 9, 3`m,7 74PRD9} %�e>7A�LWffe {f-8 }.�D��74:g71; %% %RU10} %�W��1X 2599>XDe�fd75PRD1�%T|$v�D�&�206� �dWangp00PRC} %see, e.g.\ %P{Xއ%6t)m0B"52��<$GolovizninHZPo�;�W@oaDrZ3 �h���67A�Peshier2;Z= 37} z e} K\"{a}mpf��O�g PavlK �G�6ff>39@��23�Es GoreJ�PRD52} M~ Z S.N.%n\�D�1;) 5202�Ioffe04ON. rnodubNBp !Ag�9On�9c�] l ph�/tr`�Y� hs=~Hmnw,}, %ITEP-LAT�/4-10,"� 4050�*e79e<�MJ�93PRD47!�L�et�B�] D X�a�06�(BaierAjL}QJLXMed�:2H��84�0) 2106�Kapusta8a�h �28em Finite-Tempe�_re Field�y�g((Cambridge �Fty�I,�%�C�-Y,��78PRD} B�: A~L�A&А.�D "7�16x4Toimela85IJTP}�8 �U2�2?H90aAy� Bocudo94P!y %P.J�BiAi=�)r�<� 6%ryel�� nLowA��J����ow")��/7�7>�nga�R ^hJ!�r2'�eAU�:2."C 68T��A5��]ce�= UkawAH� )eA%�8xN7�@�elyaeh0Ya�Kog�� 8)O B 13XB�273; K!BoPE �K,�Pir>�T�@Wal��PoZerwa� �EDD 4%�8�-6HY�Drukarev'�E.G. l �EULz� %:�51�10) 67�p.+.2ɝ1) )�� krUMzRy� VaaSadovn�!a, %%% &�10604qfr�F�!M%%��- c e�l'1�,:%4c�35Eu!4�90$Chanfray93�F %�?&ric&�.�Vam%"��A 5\ ��)9y��Delorme�0^" _� BQ�b < 2�%%.�� A��wam� !d�-E��3�5 R67�9 Lutz!� utz,�#��t�c �B�4S 9=&2 Hh|�0�Q Ch. Appel2� � B 4pP���� 82�JkO%�B� &x pN1A��$Banerjee77�MU VJ�� Camm2� Wv. ծ�332B*Gw8ni8r�e� �ovo C6to/i���6%-�8� T.E.�EM�"W%ցm�W�112` )4 91} 93�%L"�M�> inio]1>_2m?�}52.=CS49.B$\pi$NC)sle1C� E6�(Gibbs98} W, Li A�YW!�K*T��Eө "( 8) 782�zyz�@ANPAsk Z�?Z, YD Y &y S�L�Daio�*) �traub: ���97) 59; DRn�� e BJ7�W�Y>�-�� 62fB�1Z�Z*�pS�3Lu!�2;*� 258�ym�{n98g 67} %W� UQ-3�7�6� Ballot �1} %J�e 6�M[-obipD,>s ���E�N�n��5sth6ݭ{� � luc4brahm�D.[lK�{�S�n ,ٷ 4060�oHD5� Arsene o : al}, BRAHMS �P abor�)� ~��{r,� H.072305,A03; M�Debm$T"QQ ���30e��,phobos} Bn Back �et �PHOBOS :� )��l 46�� 297,�<2�=6�� �~Ad�W&�!2 T1 c! q! *]349� a5.�@= w�d�%w�T>�E�c�� 9�1!k�< 003;V) 89 �c02301�2;.�)a1}6` ��E� ���-p:�^�M�3I2-�l 3): �!�9� et ai3I d6{Y+W�A]N�Z!f3;]6I��I.~Y�%�h� k�b� nuclE�307%g �hVURT6�,^ U�0;2Q �I�%u the �b��H�..�lucifer!2P�Q:R G*��, RHIC Summer Study'96},175-192, BNL�BJuly 8-d|w6� BraqH.��Y� CaN `35z 19`># 59},1~��.o �2} 2�A Vv~ v�m 3190E�1>U3} �.T'te&�.�SerM�.!��+,_��E�b�20806Q �Wrqmd} Hӑ�.r-�.v�1ip.Abf �.�L77�C 6; R�gtiell�?A.~JahnA* � Sorg�iIb .f>5t�6�q2�S96�3�!��]6�E7ޙ32 @6?bas�^�h�s�-itaua- clhAOK@2.$�"�frithjof�C�(sP& k~�fIngle�M1��jo�&nd9p-sDl31)p�MB.2c6b_'B.~5$-Almqvist,� �h B�2Sk2Ti6F44capella} A.~C \ J.~��nA��2~` ~ W9PIL�K4) � � }.~)P�501�běk����U�405�Rhe ����5�we/B} ��W , Z ~�T4�K 85)X9);�� 2(J.~ Aicheli������ } 6) 1027-�S H.~DC, M.~�B�fOst*�B�f��'c. �0�@ ``Wvd �U%O/ �� _ Di��en��P�s�=�"�s'', LHouches�[March Ak- April�F98#-L��v�Zle��, give˧� Pan-"�OAd_Jed�( }s\ e "�S���>�j�(M4aW�s" Camp0JDe Jordao, Brazil, |c 7-18,+&G 2061eU koi�m  C.~M��B-A,~� Z.~L%�QzD9904075; Zi-wei~LiE� C.~m;eA Aait ��054904 a�=E�mY})�.C�69�i375-3re�).�,ranft} J.~R �K�i�]��� �E41��;=EQm"m�� 11m� 9). .C�`~�`e�*%A�� *U�I}�C5R��eS��� 2206aO:�jeskol��KeVE,i�Kajantie)H�indfo�/.� �� 32��3'��,wang} X.~-N �R�a�G6E� D�I�r3p��!;.B , {QG000814} � 405029; x�T��405:C���M.��X.)��U-p-�~����m307�%, �g���6G UB.~Mue[9��-K 3� 60( V K.~ ?~ i 1-�E 4965 )  86 �G�zK. ���2Z of D �3'�.�~A6-4Q� 257�e4�� �.4~D%! �7,�J5PF6!y&6� 9!%1D *kQ]��;B e/5�qJ a߁X B�� n�g�O5�allmei�0��G  ���Xh��!��.it �$, 0449�]).( cassh< ��C i�2pCOrg)�g A735�r7-299 ^0!��ei�V9$, E.~BratO�a�,%h�qMo��W)[i� 44� D��I��s�j�} D�2C�aa_.~' d&,G�aJ� J18���^E�}�Au qRh��Q�"6C � 2�I427 C6A�!M �Bz�89A��4m�% {cgcL."ŭR�Venugop}�� 1v.u�4Y 2223!l}.&q��  094�*�9p a+ harzyK u�� �q���� 5��L:�gca�.[21; ._ "I 210330!���$4���A�2�>g.B&� 4032[O).3Y�goulian��#i٘A��X106Ni�Y S@ua5} 1G.~EkspongD[�UA?W"�]�%h 145c!�� G� ~Aln1 P"C WN�x+Zml� )�2�44�| }�uaA�C�� baja:�� �1> �i> 33#N261-2�g1�=�uf�S0lab} Y.~EiseaV�"� 6�.%�7) ))��A.���)=; F.~Abe 7, {yN)�D�� 2330M:�p(�U�:'L!�Y>@n mnem�� 2230q2rw�}� W.C �� V- %�31�W1�l�=� bori� B.~Z.~Kop7.vi� %UYe�/0301206� A (in p��`5�m��H���DI�~��e]e\9J{Gzahed�Eۻ�f�[I�hedy� 3072�a�y�� 3080�� latt�]Datta,F rsch�=P�eczky��I� tzo�]: lat/0�12;w,1730�.�molna!"DL� g�f" &� 1020�I. 4018�MB, Talk �Ns"|jw"�on "Cre�%' Fq�of Baryk.!HeP�gis�W", ECT,<1n�:,Italy, May 3- 4 (unpubl�d2�O%|� ��iI�!h!�mCl>D�I ɱEKE��S& ��j2� _ܹC}H.Z�a Z�T1)�Manly,��:Q2U T z 20th WbY 9�*�C Dyn�7s%l lawney B�j Jama G L15-a�> a�U� gottP��G"P=@%�y^� 957B7����q�Pol�� � 7�7;�ppB�5��� H-�F�HYuev2��241803��� ~ au} >p�2,o��&>b�m��0$fwhmprelim#�:7 nuc-&�%�N�v�5f�F�< M\"ui2�" Fo��R#42��1�vs �U=c812448; r*Radyus�]P� ��B85, 33s#� "���i�78, 6�+6�^dprDUDieX/ _R�3�j4� 1/�ԥ��1� .=�gui�8\uicho�M.b*�� %7F�$41, 1���5[ba �\"G� this*�;(Sab�V 2*aYca�fE.�@�Ar�al.��.787,�D/1):H2E5CanXIB.b&�)u23%242�1;�Y�uze��+ Stri�1�v.W'8, u��*3)ž�Hch� �>Dl]Ik�� BJ@32, 3�%Z 5Mfri!OJ\+F - =�CE�23M6�0@i�\c@4iofi degli Att sl N}�BO�18, 96M)92�d{�: cope.� C 70-�Yj �� ;% V. V�9=ND 69,� )NH� overBZ >��I~Q�"�-alm\`�% `idB 1E�4a�ð�gemF� Kie��E\:P�a+ivi7J6>56,�37� �av1ԚB2��G�"m��2�Qchi�6\/ 51, Jo']t�EA���S�Va�^% -3<,"�(!n5r�UVC@�� �1O449, �p�� gari��Gar3Aa ǣv|p��ý:�73�n%�6!D�grjE2�&�100�ER��,a�Robasch<\B�,yer�;M�3tte���PJ. Ho\v{r}ej\v{s}i, F�J�J�J�Dfact} J.�k��fL.kfu���&�M!���06,�2!�a=Ϛ�…�=�=2E71�33��lqe721, 7�� Bޅ:{2#st}�*����ʊ�ʼnA?����jig��} .�94 ���82ri����θ:�����ֵ ��Bj2�[��2m�B��ݲ;��� ���V��j�)17} \expG`\fter\ifx\csname natexlab� \-�x\def\ #1{#1}\fibGbibO font>J M#�Pf�Q$�R cite~R.$�Rurl^�url#1{O�tt!O%8{URL Iprovide�� and{!\0info}[2]{#2} B!e7Wt []{S'}&Y[{2�{Piepe[6�}�� 1)}] �� 1mp}i nfo{�osbi9�{S.~C.}�?1 B}:an�*jP R.~B>P� �@j�� al}{�H�[��E�W}��bf5C({volume}{51:Opages}{5aJ��year}{V3 }), -g&Hc#05�(2teBi��� &� !T98!m v�8qn�n J.}~k5k @�l:N�Zl%gM"�=ja70:D-a74JbR)}. B��� et~'F7):� $16ɧ -', I� UW]{;!�7ck��$�:�D:�V7V�>A.Ի�Ff!A)E�V�n�?Uha�~Qi��� }�@u��7AU8��N�,�}@MK1� >��2})©u�9705009n�Bruck� Aa5{�# {a}}a� :1955a�(K>b@:�Nf�97:?1�L!%���V>}:�*l>j�>bJb��� U��-g�z�jNav�! �ki76k$Af(KamuntavicigandǮrett}}]*�Z9pw�0P>2k:�V� G.~P>W2�F��B��>�B���}�N�8b�6቙-�0H��7B�!�N�9907054n�1K%�OrPd�3a��3ef��2`!�"fH WA/:: �6�Naf+C68:@1a 3430�J��.�N_5090�_�RZ`i�9j �`E>X�!��11036nBlo�~Horowitz�I5� b�:8�^C>�X�� B&�ZZG �j[ZYu>P195v� Luu"� �:oLuu, Bog�I Hasm�  q��lLuw�xc�`TJ� Luu:VeSB���<WJx �?2:E�j8j'��u޺7^� 01431�RY�74R7404028n2Zheng5��:�!,�U, V�� .  UgA,�l5td�DJ�A9�jz�%b5����C�a`.- ے}�HBHCR�:���:��G52:@�~248BU�%bIE!�ri*�a��+2� �2k�Zn<6�� ��T>��~-n`9:E-< 1825ԝ>>�1R�2522n�F�@and^E{�%\ &:���1�YA> E��Ϳ �- emph&�title}{�O�HyX$lj(�Systems:�p�% r}{D� P�s.� add�'}{<4 York6�I�J ji �-%wion+70A� !o0�oB>o >�pM>N �6�� -~,A�6AQ�4J� 1970r �n6 #,KJ .�}]$�0w�9�6# g:�V9V.~�+:C��A�M�~R>���%�vj: ^"H�R�F"940801r1 Nogg9Ɂ�:�!(fma�t Gl*<H�a:lK�1cz�5B�>9�ŘV�H>sK��<W><������u���65:�m� 0540�11202rP��J ",�� �a� "!�4q�fSJ� B:�V� 2��5jSB� �2J ��b� muJx!zRC8409012}. \end{hthebibliography}�\begin{>�>{99} \bibitem {Bet} Bethe H A 1990 Rev. Mod. Phys. {\bf 62} 801;Glenb} (denning N KC�7 Compact stars (New York, Springer) �,Web} Weber F?9 Puls9�as Astrophysical Laboratories for Nuclear and Particle P0(s (Bristol `hiladelphia, Institute of0( Publishing2�al} Walt�MNDLattimer J M 2002�. J-6t576} L145\\ Drake J J et al.j72} 996 =o\Cot} Cottam J, Paerels F�Mendez M RNature %�D420} 51\\ Miller CZ$31mHVil} Villarreal A Rh4Strohmayer T EJ4 a!�(-ph/0409584G�Shap} Morrison I A, Baumgarte T W, #iro S LbLPandharipande V R 206e11353\\ 2�!�$Schutz B FB�11470�KA�>�DKettn1&0)�n. A�8. {\bf 353} L9.�Schr}�ert!iK, GreiN,�`, Hanauske M, St\"ocker H�1,W�2 �{� LettmP$89} 171101p �3}!n3.D-7} 12300B_4P6�>hA52�4 .�DE.70} g.Zud} Zdu�J LgTensel P, Gourgoulhon EdBejgeri�4 �6�i 416} 1013=� Cook�:ok G BFr(Teukolsky S�4.�J. M�422} 227.zSteA�,tergioulas N�Friedman١�5:S �44} 302�Sch96]>�/!cMishusti�ENR6.�M�a� 1416���99F�RScB�X8.XEzi�81} 4564.�$Far} Farhi-�Jaffe R �84.JMp30} 23792�2V�$Moszkowski1�2��-�A�241Y^{Fri}9� E, G��(, Mare\v{s}�Ciepl\'y)�9.�-U60} 0243.^Vie� etri�Stella�99N�4527} L43 \endB� f�27&��he} H.A.�,�%MF�,� (�). p@{ASBotvina} A.S. E I.N.Yl, -�)lB E�(584}, 233 (��.\GooA�} A.L. 0, J.I. Kapust i0A.Z. Mekjian, f��-v30�5�82c8Pethick} C.J. @, D.G. Ravenhall,JJ 471}, 19c!87.�$Ogul} R.   t�=VE, �$7(3)}, 419G98.GLarionov%B. ,BYSova Nucl2�57}, 636]2�Ago� o} M. D' \emph{S }6�A �65!O32 �9.�Bau��W.�erEA[I#.�%�(C52}, R1760�5.L HaugM J.A. >��� O6O024616EN2�Schmelz S�� fUQ?55%�17�2�Mahi}!B jJI��6!>19)�82�-(%�yL,iZIljino��4!712�82\Bondorf}!]Pa� i � bw�� K. Sneppe}wp^2E}1a�196�Im��!;f})�!<);B3iu75�96./ �1:=>�B#A5��73)�2' SrivastavWB.�>Z �.w6A8 0546A:� .�Karnaukhe�V���[a�R011601E�3.\ bugaev} KWB  {\it* }.�)Zm;44320P0&� ��!X��%�.�2O�s66a�05�2�-�87®47!U663A6w U2��J�3}, 06�1.PReu�  P.T. ,%^)]1A�. B)S51!���2P$Neubert03}�+ JWEur��J.�W559%�2�-W.�Y>�= ���9��792NV(Landau} L.D�� [0E.M. Lifshitz� atistbfics, M$ 1 (3rd ed�irgamon, &�(1980) p.340*aTrautmanW. 6��A68ARsSchna��J�� 4, H. FeldmeierR�409�BAm6�Sugaw��Y. % (H. HoriuchiP2!`06460�n2=C�z}' . j E �6> 046114E2hLozhkin6, O.V. ,:T!�A�v��6!S04461�2�LeFevreaLe  j�.i� 1627Mi6w,hetty} D.V. jV�q���02% RV j 99} %&� XNav00a} P. Navr{\'a}til� P. Vary,%�B.�B�tt, \prl)��] 5728�L0), nucl-th/0004058.>p2Bob,W. E. Ormand2a8�525 �!��4Cau94} E. CaurE�A�ZukA� oves �G.� @t{\'\i}nez-Pinedopc �� 22�4�93070012�~96~^c( F. Nowackiz �JA�tamosa� �. �!h�a�20n9.�809066hHon!hMa�8nma, T. Otsuka,!�� rownrMizusaki.ri61301(R)%�2w02050332Hor!�wroiJl0V. Zelevinsky.n%wR2274��2y4060042jHAnd01} F. AndreozziEF!>An!�JPG)�2��845ŁB]AGue!+V.!�$Gueorguiev�9Y� C.A�Johns�� P . Dra�.�):r271100472�Hon95})71�5�k9�Al�)128)1��Whi92} Se�White:6EL8d9:Q:3F:b)J4e�03!L199�vLPap03} T. Papenbrock�D� Dean�M�6!�051303Qb3.b3010062+PesaqI�b8schel, X. Wang,k Kaulke)4PK. Hallberg (Eds.), {% �Density-Matrix Renormalization Group} (}8-Verlag, Berlin����8Duk04} J. DukelA 8S. Pittel, \RPP)A�51$, cond-mat 42122�Z22Z,W (S. Dimitrov�A!�Wtoitsov2p��543�� ��202046FDim~S.:f�a�)vM.6~�2070252�LegA/,{\"O}. Legezf� {\'o}lyom�M6E951 3), 9A3053360Xia96E�XiE%a@ M53�Z04M�6.L96030202� Bro88} B.�f�@%�B. $WildenthalMfAnn��v. � art� i.}I 3�e&]QKuo68�T%|KuokG�${ , \NMSA11n246rLPov80}�W�H�&�de p�7� 23�8h.SapA�2���$Juodagalvi�pZ���� �.�0308026 Shu83eShurpin��5IyD.ptL .40!h3� 198:���66�V�a�.�AG 7��195��6}T9601016�r9b�sNPTA65!�973�>�Lis!�!�F� setskiy:����H. Graw�'��E4| 2�402086�Fed79� Fede� [�/!5 [2A_8�197:OCau�w&� F^X eiRA70!60c�wa�V$ �fB�a *$ ef7e�M Nefkens6o. �1Ev91e�7:�Bos91e�Bosshard�P4�196�9��LDrechsel:2000um} D.~�~V!rhaegh� M.~M.~Gia�: XE.~Santopinto, %``Inela�4 photon scatte�%�Hthe magnetic moment`Delta(1232) %resonance,'')*\ + \ K4F 23�!�[arXiv:�?t003035]. %%CITATION = NUCL-TH ;%%=Kotulla!2cg` ~ :n(%``The reac@gamma p $\to$ pi0 ' pF�dipole� %:+ N55I�8� 27203� .ex/02> 0REX ;.�Q!1qu2�M>!M1�>�>�+ from67 !> %p5\])C ��652� E� � hep-1 105060>�HEP-PH 6Ch���(4pw} W.~T.~ N S.~N.~YanI�.D!0Unitary modelP"!� �Q- i0 �%f+q- %�V^(7�015204��� .1409078: B} R ck� �̸, spokespersons Crystal Ball @ MAMI experiment.}b Lein��D.~B.~webvT.~Drap �]R�oWoloshyK\M�14Q3069<2); I.~C.~Cloet,!�.cWA.~!�Ws%��w baryon5nm�sI�l�#ce QCD=d6�5-157%c3]�l�  08N� LAT !~"ILee�~X!)�8.~Kelly, L.~Zhol W.~Wilcox�BZ�inEPPexternal field method֩)� ��GSS=! J.~Gass!�M.~�#ini� A.~Svarc�� eA= With Chir�% oops�.\e ��309 779� .�4NUPHA,B307,7796�PP8 ,V.~Pascaluts8 D.~R.~�%lipI Effective!2oryJ�!O�&:�of�� ��eo���6��05��E16�ͦ212024F�b}��M�z-indep�% nt e�s�I� exci�on� �T spin %polarizabilitie%�� ibid� c �/�M�O�305043>��� �U�RaS41�� Rari�$J.~S.~Schw�'EJOn A Th%�Of 7 �'sIZ$Half IntegAaS &U)��Qa 6~ 4�M.�(PHRVA,60,61��Pas98:��Quant" of a!_teract�(!`-3/2 i�����)�isobarB���5) 096(S+ -pa� ph/980228RnPH �5nPaT� F"R.~Timm� i!F�<t)qofU3$to higher-ݱUtra=ionE>7����!z042d1� �QA99��b� 2�DPW00�~De��F��aldron%� Massa��!�4electrodynamicF�-�fm3{.� !�� 3011>�}� 1I[9�Bu�':6ej� N.~ �a avageE?��.~��E �F��o����decuplet^p49}, 34`1994); 1��An308317N�An !�0M.~K.~Banerje �J.~Milani5U D �$ revisited��chi(PT)�B��58�1>� 5083F !}� �=}�) ga>� B�<Holstei� R A de$�T-{pGerasimov-Drell-Hearn sum rulf� 60a+23�4*� -�040731Bh � �y�DG=�giwar6�  (�Q Data�)N���*� =Q BeckA�9geU ~6W 6,L�)\��7��60w;6� ,PRLTA,78,606݅e�ݕc 35 a�V�4 f�3�P�gak�4R. Gibbs, Li A�#�%uf�4, \prc 57, 784A�8) 6J..�K(l 74, 3740M5)L matsinos}�M �6, 301�7.5jose}�(Piekarewicz-�)�$ B 358, 27Bq gash0, A. G ,6yG. OadTGE&���W�) S. Woolcoe 4\np A 686, 447�1)6sshM,�l>l63 l.�z��n( Z, Helv� ,Acta 48, 191�2�o�}�C.)�)heNJ4, 16!�76�ru�y}�R , Pion-�'$eon Newslet, No. 16, 125H\�1 {nordita}�Tromborg�ens/m� I. OverboEA$d 15, 725�2A Rb�S2H %I51, 5e#78.�sar" E. S � ovo Ce o, 6:1�(69); Ibid 60 33%O5 dispE�Hamilt�BM!1 � .�,np B60, 442�3);.10JAN27A�814); J. oFortschrQH23, 21MC2]>���1�<��,(N.Y.) 100, M6vM�.LReportE@ J. R6coe, Q�adloIE�5�:�34�9�2_f�s}!�F AU .i\ss n`E$63, 045201� ; ��A693, 69�"Z8 �f8 } % UseH 1-9 references %\fM8810-99.8��ba�AT~Ab"anU�K�7r.�4Meth. A479, 11�;Nkekb}�Kurokawa�M9M"�Krfarm}� Itoh, ``E� w�,Real Time Ev� Reco�u[ Farm%6B� >:,'', Contribu_( 209, CHEP'�"�HSM!�~Kataya�#``New coE9hierarch�(redhat2k >)so�s2*sun' software/ %aNE2v[f�44} \exW8`after\ifx\csname natexlabU (\relax\def\ #1{#1}\fibGbibO font>J M#�Pf�Q$�R cite~R.$�Rurl^�0url#1{\texttt!O%8{URL I8providecommand{!\,info}[2]{#2}�6!eprint []{S'}Y�[{2�L/nN/��~al.}�v3)^&, P)cl��PaiN,6Ch� @Ba��=O>= ��=J>=J �:A^}��Cho}},6 and}ad? fBC>�1�2>jou�}{Appl� �cA�bf%�k0volume}{83}}(�,number}{10}) �-(pages}{1915M00year}{2003}).f� Akahane ef� #, Asano�SoL'and NodaQ{ �v3Y>3 _��TB=��; B.-S>����S>��:�5�??} b�425:<-� 944}���.�4�hBorsellisu�>_���_�_~E>��bM>������5��q Bj�70V� 081306(R)R4r�Levn�L�,Y%a�-YB�ga�Mab�1q�Lev�UB>v56��^��/j��H>5L!o�%U.4Nanotechnologyj01Z+ S556�+Yoshi2>( "qB erer�HendrickaKh[,RupEShchekiH0 D+9QQ [[ v5B� 9�XA>�ScȒ=Bi��AG>~1.�>BE%b�;By)��<B�Ell�9BD1��sD>>M>A�U3}C�F(L�;n)jD432:��p200�DReithmai&"� >H&, Sek� Loff�Ho5Kuhn, +z�ea9HKeldysh, Kulakovski� * neckuR: ���B�<6bV�BbSek�9B�-�=B�-;�=B� !o�:!-1��BL>�-ג=VB=Y A"� � y!V�BTR[HEKA��_R_197�_�n�!aUn4Drt�Martr Lemaitr�3Bloch�8�(E>| 76&VdB"S��?B� Ւ=Ff- ڌB/-K!mF-quant+"04110�LN� v� Cowa}Young-� ��A�!i u;}:a3�� J.~F>O �Z* Ej�68:A͐04660V� v�8Solja\v{c}i\'{c�*�2> :.,&�8 Fink 8 JoannopoulosqD;cic�� B� ;�:aR� S.~G>�s9�@B���~DF�.$V2Au^66N5N055601NJ2r.�$rd6_ �` J.-M> <-�KG� title}{!�,id State Cavk9?)um �&�'3D Self-Assembled .Dots}}.U�r}{'�96�address}�many}� V.=, pp.!�� ps 269--314}j^Brass�3}|0:|$A+0Lutkenhaus, M�and S�3uq01��B� ;-��ViN>���@B`Mor�hBT5!5�" }`�g5Nd6Nd 1330Zb0rbKnill.1:! , Laflamm� bS burn�m'��B� 76-V�RB� �ںB��V�+&� ay^�DJ"681R�46NJ1v�ok.�>;Kok, Le5�Dowling5�ok��B& 56 V�BA2��"���P>��V�}fAn�6:��@06381V�v� Yani2�>A!, Fi#anaHFj�olj���MN� �:�V�BxFa������F ��}}4N 2739Z[v� Pe�'n^ ",� toriA�VuckovV%Zh�?So�#36 lant� Yamamotoq� H��B] 86V�B�+;r*�[V=B] �{B %�;B�-N�=B�%�ڂB� 9�!���f`89:���299602.> "� v�McKeevv�$, Boca� Booz{%� Buck�zmi&and Ki� Q�C�� B�;:�VB,��:F �?Bp)�<JJ�!R�=B�K)�ڽ H.~J>?1�!�F�Sc&�8b�30R 566R�19�G N�viMcNab.�>R!� ��SVlasovY�Nab} �VgSJ&[��B� Mo�%]�F Y.~A>��V� Opt.�'rv�!11N� 22R8927AJ� v8Notomi.�>l "�[iny�|Mitsug8 Ryu1� *� :-$ 9��BmS��<B; ��-Y>�%��2N�8N�155^�v�Bogaertsn�$�Tanae3. uyss DurR Camp�-ut, Bij�,,Baets, WiauxI �& eckxQ.!��W>-���B�˒?B ��?B� %3�; J.~V>]9j�CB~5��?BP%��;BcE�gB�MFA��%"� �\�fJ� Ct*�>Z!, Rieg� � U"�$j�2&aR G.~W>k �9�29wVQ����J�61�x* 2�{"j- {a}}:q 3,.%6�& >�& 45��P��$�:'B���&��&E�z29N67N669^* 4}:�j�Lonoa2N>�&a�NedeljrH, D VuJW$�7 Pearsa� �Lonca�kB��y�jGB::��EB��:B�>&�FF. "�%��2� v�T.F�9�!�AՑ�,77N�13N�193^�0v�night��1�[680 " 0ung�Jacqu�=and Birk"E ,��B� 867VQBZCh��<F>@ �ڎB�- !$F���R�15R�12R"!�r��s5��/:� #2� %�:�- *������2�9�VMBY(��F�J. %�Soc. Am�-�*^J20R�1N� 2274M¶Sp� vl1$�KiUd�X:�-Vahal"w13��ScM)k5}>��TJ���COJCB���9�VKR!�* 7{1$�3�3��*���9R�R043902��Li2>L* Chow*�#z N�#Li��1S.~B Li�fBa�����#��J�>�6N���2R�#2Z�03�J�vc Dinun� , QuocSc)�Garci�"��B^ 66BVdB� �ڏB�́�a�6��� 8V�R�295��L4T!� Tsa�(4�(��B� 7��2M�%V�BQ ��P)P4RR�274^�8v�Kan�.>y$&#�4 Iked�bana�b Sugi��8kaw�^ Ishi�G��B�:6XV�BL���B��tBB)�<1O�>B,As%��!�!9�2B��IEICEins.A(nv�E87-CN�R�114^�v� Sore R$d Bennett}�C7�,��RJ� :�/�N::�baEE�Dw))bv^2R�RP 12R5198v Almeid�Cbr3 ##z rrioPanepucc Lipso"`' 1�oVJ| =:CVCJ�:iiY-2�V@RJ���2H�[VTB12�ut��'3RF 701R108� -�� �3�� �+ r�%I2[���]�� RB2R#@238^zv�Carmo2� >� ", Y�%� �  "��B 86�V�B`5�ځT6��V%�Ex� R� V�47�tBoy:�/~�!RJS9 �V�/ Nonlinearpicf�/AcademicWx/*� "�/0San Diego, CA.""�%y .nedi I}{2nd}Wqf�B Clapr>!(, Raghunathg ;i�2�Jalal"?7�^:@! 7)\v�B���AB2�C2�E�ju Bg12��/�!V'27b�v� Rongnk  �U0u, Nicolaescu�P�Ocia�K�Oand Hak] 9� B� 667V�BLi� 8B גyB�1 �>B�C!=ڛB�%!�uFUt�:R 2Z{1j�` �f�b��.���E����jFBZ�����#E#N'^Y2�!�j��A151 ~�HJ� :i*V�Op�xbistaby:|p trol�2 l�w�P }}� &�*{7�� f�(Orlando, FL ���� 1985v�Hn�$� *�F&�F��"�� 4�fn�.�V�B4�-�1V@��nam?P�JB�52��_6_Ro36`t�_Le2�F>�5�5Ca_ h|vWeEO'BriuX and Dapku")O�+ P.-T>T�5� N�.Ca�zS.-By.ܒCZJ=We�<B -E��P���U�1�2C�~R�V33b�&v2Cutol&��:� ", Iodic�Spirit�QZen&W M��B 866VCB� ��<B�* ��B�) *%5�J�=L�� wave Techaz^�0K٣GQ>H4505F4!�r�Cocorull�j Rend �A2�#��GB)^��I>P�6"5_IEEC�Zttz�8NBR V�+�2n Agrawaa^Dutta%W31W �U~B�:<:vt ��N�f:: �)WVb S0onductor Lase�?.r*C Van NosQid�I hold."9�YY�NY.!K 9vQ2AC.J >; #, Iban$Skorobogat;v Weis�".3fCa K6���. �] �-�va MJ�.��EBT 1%�>� 6.\E�5A�1jB))�Vh*.#r�FZ�P066611.�I�\|i�Ny[ #r]^ tem{ei�A. Ein�i, c���j76Gp13�Alan؇L."х�_My΅Hit{�jcl2l:�"m �ms} (Na>� Mosc�#1k`*� l2} �lo�pawity} �bpr�_ R.J.z ly (ed.3X�!itM�dbook�jl��� s�l ed d�E on ot"�R (Ch��al Rubb֔K leve� g 71).*[{va!�$V.E. Mkrtcnu , R.v.Bal+�J�b�_%�)lbf{41y} 956 ��iR(u"b�`10.� AbdE�#A1`dulle� W�/$ \newblock��ite dif�` h�c8ogeneous multi-Rre Ms�_hom#iza�( problems.\{\em J Z!~Qru�qal%A!F,1(1):18--39,��3.F@All92} G.~Allaire.dH2��two �converg�`.4� SIAM.�MathemaAnalysis��0(6):1482--151i92.�Bar� M.~B\"arBjR\"aum��e�}@ukturbildung bei �NHr Oberfl\"achenreak!Y� E�sche W a8n und Turbulenz:ndA�O-Oxid%� aufw(latin-Einkr�ll-2e}.�PhDa�s�~LFreie Universit\"at �!�92�$BarBanKevr!1�~K�ng=I.G. $ ekidbXG.~Haas, H-H. Rotermund�;G.~Ertl.�A:o*o cat!�(t surfaces:�sAainertE�r ve ]��sa�p�{nA�!�on.jE]�a���)�tr8I<100:19106--19117%62enLioPap'}A nnsouss�CJ.L�n/r�G�upjolaouB�AsymptoR|aM��(periodic stJcu� , M]~5"�JJtudiesA*MU�#e its icE9s2 North-Hol�� Amsterdam�78.�CioDon^sD.~Cior2 � P.~DonatoF�0tro �u^s2�2�OxfordY�y���99.� EEng�����(B.~Engquist.���~�F�Comm.%H���j ):87--132F� GearA��LC.W. �:.�ProjecOq�usA� stiff��tial equ)�:���� g�yTir eigenvalue spectrum.rA,B�?tific����84(4):1091--1106��XXCan be obtained as {NEC{k�} -029� ~m#*Keneci.nj�d home�/cwg/p5.pdf#.�L{CXf�[A�o7 -def��manifolds: a legacy code approach to low-dimensio��co5'B^JI2%K.!E0�f93In �s.�A-LiE@3}�e�~Li�@jHA� gap-toothMKApa� simu�'on2�E��s5,ers A%u16:190��5��� ics/��,010 at arxiv%g2�rah�Asa/�D. �o:�Mk~q'ura) a9obaTDK.~Kr�/r�^4X�`{�Wboundar�1onF,:͂��o�q of cA2!OnN]C,, 264:80--82��4.Hadji�JN�4cA�kyn6Hybrid aA�� -continuuNi5؅lzymovm& act-� &� F��� (54:245--265�2�HouWu�8T.Y. H�}X.H. W2�Ae d fin� elejQ����a� ��inep( material �por� edia�� 34:1�P18�j9972��9}��C&� A&a��9���, rapidly osc]3t)� effiA^tF�.�of�|� D}, 68(227):913--94�p:MHuma��1� u'{EQ:�.bHCoarse molecular dy]z�4a peptide frag!� : fr�nergy�ki?�)�long-t-.�Ke!@00��o.gJ( propag>aK�# le"W.C%`P�a D�36:7� 06�v��'bifur  s� M~lȁ icrcpic/h�� Ѻor2Plenary |u[(CAST Divisi3MAIChE2ual MeeaA,, Los Angele3+20�Y Slides ca6��9.�arnold.(kHceton.edu/~yannis/#>"��HyebRun�02}>4h�7 ����y�DP�"a�V O.~Run�v�(C.~Vdor�%.�E; -e����}a: enab =�=} � per�nOo-! task2qEA:A �g,1(4):715--76JF �$NicoScov90J$B.~ laenko J.8t cove2L BackQ� sadd gain� �er � stedE�!� {K}uraw1-{S}iv�q��f1>hApplied.�0}, 50:760--79�v992MPvLLust!04L����Sl   ��q-g ed numer�.�.b latt�boltz�{�eo�F�.>� Subm��d.�� a�ˎ� B�"� ��Decid���na��K``cɖ0 $'' through.��X :;$baby-bathw` �me.HE�%�M-iD%(�andq/i��1(3):3: 40�:2QLiYipq�J)D�IS.~Yip.}Im ng �� � nd**� {MD}�! fluids: �mal& co#aXnd buffer zone feedback.�%$Mat. Res. �< Symp�ocA�$38:473--47?2= MakM#2�G_keev,�MaroudaV��0��#%0R�us!0stocha8 9� ors:4 {M}onte {C}ar�xampleF�Js46:10083--10091�2.� �P9v�A.Z;�nagiot�Ƃ � R�ofb�*: a � -gasI�\Bx :ka�u�$7(18):8229� 40N tBab��ab0��zt�~Babus�6A�C.)�ab.�G ��$ed p-{FEM}��6[.1E�N�a�A� ,k}, 86(2):31�\7�2�����2} .�B}���iveR��� -stTjr basZ�F��.K, 15:4�v51J�Sa�oo��G�� maey!s:�!xD.~Roos2 DampaXfa�� �z&!]6:In��At� �mP��umo��kos, �. ors,)��b.\���eS"�}"36A�%�Lec�Not T al't c&Engineב}, | 9e�2. f_E�2�SamRoI 3�S-F11�TheB2�6�� Vo9! %!�!�9: Aɮ3� rdiscipli6 �b�s�& Iu ess.r, 31�� V�i�Mata-u��A}�B���D�lz%9�201� z��R� chap �S �S�Z�Q2197--238.�Q=�a%h2Set Oth�T3} �etaye�2 Ha� Othm�!j x h ����grto bacD$ chemotaxiF�R�Ui�DIE3.�UE*� ShvartsSc|�Imb�Z� � i�ch\"uE R.~Imbihl�QD"|n� � 2*�&L��@�!%��F&.��X� l�riew.�;3:285A8W�>[$SietArmMak�iI.a�tt���rma�iA!�M z�M*-&��9�8Y c� �\x {M�C�} �B�{MJ.' 49(7):192d92J>?as K5 .CG/ �17fciet V)M.,z {B}�E"Wa�n liquid c��s:.��&�2B}c)Q via*d }BHJ@ ��149D 1��>�JPk%8�211455bQQi 0Y:(, Y�$�c-T"D/%R{ z .�� *�akon-� u�NvInmsr�HNatl. x/X��9W 2� �SanSu�inB�K�,nkaranarayan���e�!�jg- .�*�bub^flow {L}` -{B}*b�AFm�.��59:23�e3&8��J�eu$PS/0111040J�N�$�fy"�� ]&�$Ref1}΃Tak��%3 J. K�ro, N��@��� #A 4�304�" %6S2k� cM��`h\�px6X43-� 45).B>3}�� Veks�^-$= U.S.S.R. �5f@4H�Griff�Hc�kͣ andt� MacL�~�A#A.�hetti, A�ee� PAC83, 35M �Blaski��< J. M.BrenE�:>EPAC9�_373F�52z�5wMX�kuDD��hia�z��M. Wake,���v.��. 8%\4803�2J^6:uD. ArC6�K. KobIM. Yoshi!%�%��H &87ډ��> 7 oorika 3 al��ro.e!'�$, MOPLT066F-8I Kose!#Th# (� Gradu&U #y�$Adv��d S�� �!Gprepare%%pM�s F}9}͈��aporasoB(RPIA20��KEK2-3Y�1d�3)�'QCo�g: XX� . Lina�nf.�^ner� CA 6�R�U�=�ST-AB 7.�A ���>�10}2\"V�RL14���JVE)K.�FeV�PA!�3, TPPB0�$ %V<'hv���Taylor7e�B. mA�I�_( bf{32�1��197!IVainsh�v80}'�I.  @@.��Zel'd�eh�l$A.A.Ruzma Hzjsl��"�%t� o�˺�}N�)80) [in Russian].} Hʚlm�(K. _�Wi�((enz, Zs. Gee&�(34}, 3�6b��G:!�(�L.�H�/tthaeusI�. 17thA�@ernat. Cosmic RayBA�%!pW 9Y�812n* Kich ov83�� L�tɋ\s'ma Zh. Eksp. Teor. Fiz�% 3���K 83) [JETP���#51 �83)2PFelv} Yu.I. ,*Ka� L.L.�4 \& M.Stehlic,"���J5�w260}, 49�+��9qMjG R.R. �w$A.Tataroni!d�cF�ԝ 380 �92NI����G)�:G4ur94} A.V.Chec��!V.Yan�y. TuqePlasma�% +256�6dX�99��37, 43�:�V�Rukhadz��E^Ginzburg)�.��#,)�sl{Wavq @���}F�,75e� N��< in98�PI.Vaih.Z�8E6879�982� AleksandrA�A.֍��F�% SU)Er&H�> �-like M�!0} (Mosk.Gos. �Vņ<. 1999f� Jagg�s D.L. d*R.Mic_�on H.Pap-Af! ics q���ԋ��6�UFNۓ@Z. Katsenelenbaum�\N�rshunV�A`� Sizo9'D. ShatrU�a�[%/I bf{1�1��T") [�. 0�40}, 114�976b Novikov64 � ,v�4��191E64) [A� }��}��129��66mKlyats_�V.��e �xu�l, Izv. Vyssh. Uchebn. Zaved.wD diof.}1��14б7j ��Y�7BK� r�58!Pɪ7�:��\ 3�j87E06yMѳ�� W.H.Az.4 �i A9Q�� 2135a�:�Ra��97a�Ought� ,K.--H.R\"{a}�52o%�fEU�56�875�972�V�e�F.c��K.-���Mean-��� ohyd}���Wo0 ory} (Aka�Fe,*). 80; Mir, * 26O Toptygin}AKN. �&��planev� �ic �V�3;J6d� Dordrecht�&�Y`я>�D.P.Soro� Vݸ, �*� ilva�T.Torr,P.H.SakNU0N.Reggiani, JO7Sf of J�1�h��8I�9N R/�fl18�I��I��I��I��I��I��I��I��I�calor&�S199>�P #�ew�� Bowd�CBloemer�K +��(4-2023:JAP}�f��B=A G&�;j=JJ�>VoyaR�i C.~M>> ��<M.�r�).F_5%, �")@��&ђ<tex�v,~5}{7zCA ��23}*?Hy��!�<�=teBF� ToccJ~A�X�6 e!,1�!�-�Y �511] 2A$5-2324:APL�~D>�z9�%0V�)p%5�9n-�r@:OP �}�~�and �j�I� �:1a=�U>];O>^A6VA324RA5rAj]z.OB>�E!h\u�}a�� qa�7tyn�w'A67-1192�6Jeh6�H��S��>>a��@HB<��al5�!�-�j�ȩ>P. 2�j�B N�^�!mR�7r�Ga�EAssanto%� 9)}] !�$9-267:JOSB�B�K`�NDG>��ZFJ�ffG1a<.��6J�� 1999rFMujumda�2L6(amachandranlY1!P%I�1-929:O�QS>F�TFgS.�ZY�T�jQ2ZQ929F��2rQGawQO 3-C6� ", Hua, 6!� and �� ")n 4106��C./�E�.� L:!V�BJHu�� P.~GJ�\�z2���j�BC)!*�:ֆZ��!h����r�llo�b���Parames��~"Fej� �t)�31��^�j5*V�BdV�V=KJ�.���MJ -2���Z8���B� J� LHM(�8LHM-foucs-issue!� 3:OE�d��,}{See Focus ( ��Ex= ��1�6_(*�D>o�Nefed�Trety=��b2� �2-3�G:PR.�V�I��i�u� K֩S.~B�}�Z��%!r�HZ�0�R��HZ} L&z %�6�Liw�(Chm�J-he�Li!m3-8390!m�J>L�_ FOOho�' �/>���& B#- V�=�~�9b7�!]R�3r� Feis2=TvAx/�Shadriv�a��v�,�#!�4-1451��M.F�yH: b�V>��Bu�� ~�Yue�A ;K��� � 8;L�� !3v&�Q 206DY�y*�!>Yeh� 88��$Yeh:1988:O:?al���VVB�TI�V�O ^ _�"L���8�f6YO'�ey !Son8-���d���O ���)�r�4^6�hLiu� 7-158:MOT��Q.JGi>\�n-w�snol�j� AMr�Q58F�19z� Lid'is"w 1�>� %, Buscc �ρ�/SoukouliXT!?8-346:PD�JB9qGMP1�V�B� ��;QJ' �L�:+E֕M=[2�UG�ig?j513: M634J� Ar(BWgere-Bh!�4-185:JC�(NmJ:��):G0r�4:F �18V�Vv]�lu(�l*_}bB�`/!�Schneidy3BPcq] &� 2955:IT�`� J�>f�91U�� P���:.���5�IEE"�nAnt�,s�pagv�5��e(.!A�~!�jT�=�ranA�6-1138��BC$ �5� v6tt!�^�212?Q�138N��r� Chen.�3:� ,o�,�hg, Di5}Lu����](A�3�P4:CHI�$ L.~X�.WpYx%"V�B�dKim�9 Y.~L>v�M�jv W.~Q>=!�zWNE�u*ad��R�fa Chin�&�4 �{2 Qe51JH� IcN2Oj�0*�{a��v85;.G�v,*�297 Finsc@geomett3�tivit*g ��7��2 P(D �# &q� Co.�f�#$berzi69} V�Qr � V.~GoH�.� ``Recipro�V � cip,Dnd�3orentz �Zs�DC9?�&}3�J�,h-�}�<bf 10�=�T1524,@#9.�{bogosl$+06%LYu��.I6``L �sym%O vio�Lon poutof5mst�l7,''>��s�]�rs {A���3��5�6#6^��BG.>�CHl� Go1t5�"�V`��a possi�Aof phase)ziTCr �9MJ.S of�AD"FJ��24�'�82��F b�9N�~�m�8�s�es�Blo|Xq%�j�Gena!�v.�2vitUr�(156!�603Aq:�#budden�M~B 6A�7r� !n{M}in_�an sky:A nisop�!�pecial �tN]E3. H�S Phil.�> y�KEd2�325�-3��:�(duval�r C.~D 4&~Burdet,A`K {\"u}nzle��M.~Perri:� Barg�F*WU%� {N}ewton-Dta�$orN�a1!�v.'K�) 841-I %:�(�:�2��h"*V,P.~Horv\'ath*�})CelestTme�icsHم�l� �grA��al XbN����FAGJ�'�)>Inewp<�8A�@��[fI_LVd%�theO�RdescrP ?�iJ�H:�±�7��542--56�0:^lee75�F~R�t<+Ta Kalotas6���tra�i9a:firsta�t|SN�Am.�9%��4�2434--43�,�8�#x9�6��Respon�Jo {``�KenSn �}v� {po �'"}JsR��S 1000�5�619767 leutwyler>Y H.~L%� F.~S(46uR���%&�= on a nullz(nRknO 1i(112}, 94--1I76�(levyleblond!q L\'evy-L 6�OnQre���K271--27I6I macdonald`xA0 �: 6�8World's fastestn� 6���9�,I48��12Imahajan!R�� 6�.�{"�E�*� :h Y���998--��F�(mashhoon90b��~M 6�E:hypothU:of��� in_RJ>e�� tW�@14;-147�^%@9%`y��j�Lim ��3q�?s measuruU����17]8��:�0inguzzi04c} E� 6( Diff|žag�FAFccele�D\ explicit,�VJ>Nr7�8�88� 6;rinh177�� .�� Esse �&�6� F��"�/�,772�rjX59}��R BrABd.� �,9 )�: fF.�156_ $sardelis82�� A. S .�``Unif�PJ�G}alilej���� �:}�NTE���?�}!�96ayax864 wein�Dk64a�W6�D��2�-6�"Ps"% a Y��y assumpf �k3�<2�Q2�=B5NS*fS}.�4ILLEDM} K.~Gre��>&JAr2�É440�� 381^c2kPAlt�a�~AltareG� [���0 of AbZcmei [A� !�96) 1152^70*�8{Heil_He3Mag} Y�ri}��2,�Leduc:$ Lobashev,����,Y. Sobolev, �N�� �440} �0) �j2jP$FRAPLsOPM};�GroӖJ.-�2xck� R. Wynand, A.�iIa��l=��46105 v2 19 Aug�? 4, s�RSI!H A.MoreauGS�s!'Ls%)O ~��C��2= *,a1 Hame�HE. No qH IIIp��&+ ) 9FF15. O _He4y_�! ���>hf�h �R� Sci5�Š7�(E() 2253--2262(Kazantsev84� � A~S� mirnJhA] Tumaiy5uI7! Yagofac9 h S�` osc. �5 �(84) 189-191.� Alex_LIADŏ(B. Alexandr�[ov et al., Phys. Rev. A {\bf 66} (2002) 042903. \bibitem{BreitRabi} G. Breit and I.~I. Rabi S\ TRL38} (1931) 2082--2082V�DAVLL} V.~V. Yashchuk, D. Budker,d,J.~R. Davis, ^0Sci. Instrum.l 71 �,0) 341--346.�$georgJOSA}�j(nnamalai} K! DD I. Puri, Advanced6�� Engineering (CRC Press, Boca Rat� Fl, 2001)2�(Leff} H.S.  A�F�J�x, Eds., Maxwell's Demon (Adam Hilger, Bristol, 1�2ZBaeyer\C. von @, Warmth Disperse)�Time PasX(Random House, New York!�99:e rune} M.  e�$Haroche, V� evreA�MaKDimond, N. Zagury, eĩ�Lett. 65Aw!�97A� U� Y^oJ2cL��dovichr r6�4 n2) 519�OoArbab} ��Khan, M!�ZubairyL �A 254�9) 3012�Imoto}� 4, H.A. Haus, Y��ma"R�K32P85) 22872Q Roch} J.-A/o� K. VignerAn Ph. Grelu!{-Poizata. Grangi�B7a���636� �z Fortschr. [46�98) 416�Agarwal!� O. Scully>`G!n )!4 WalthA�(Science 299i3) 86��9� Sr`Quantum�݅� Cambridgei�. Lond!P%2�  Q E� ~U.~Gro��BF� 52}, 997�84:� edin} L.~ B�$ 139}, A79�K656?HGorling2} A.~G\"{o}�M.~Levթ�WB � 47}, 1310eN936V0Kluner} T.~Kl� naN.~Govi��Y% ~Wang� ECareCJq�)! 11!�2422\ �>�2\{59)��h3592H$Shepard} R!� ,in QvLAb Initio Methods in6�O @, Part II}, editeA9Xby K.~P.~Lawley John Wi \& Sons&,  19�}/$Zeiri} Y.~ %�DG.~G.~Balint-Kurti!8Mol. &i %< 99E�83) 16�ilv!�� ~ �(~R.~WorsnopU ~ dm��[.~A�olb�^%� q{84)e86) 43782uHellman%� , B� zazneja� B.; Lundqvistl~�� j120}} �l4) 45� =: GAMESS} M0 ~Schmidt,!�K%=d�\ A.~Boatz,5��}�PutM��1 �� 13472� Slat-]C.~ 2�A� 3� 192��36�ZieglBT.~ %�Ra�!�E��Baere;Theor�im. Acta d43E77) 876�HDACAPOCODE} B.~Hamma�<``computer code 'T-1.30'', Denmark Techn����, Lyngby�((1ap2PerdewI�.  {\it5}1,r���x�19 6676� CI:Sq�a�P. Zie��!> H. En ig (Akade��$Verlag, Be� �1991), VaZ1VsBtK8rk��,M. ErnzerhofեM� E�19� 38652+Grice�� �2De�Herschba� e�e�S{27i�74) 1:� Kosl���� ,�͑�� $-Dependent��(Molecular D��� by � Broeckhov �L��8thouwers Plenum !c6� Feite�D.~ ,ZA.~Fle�!�uteia"�24-82? 6` RoseŠS.~ ; ��Ros"� A.~H�q wail bhe6}91)b 89) 741)�NM�+\Z �30} \expandafter\ifx\csname natexlab\endc(\relax\def\ #1{#1}\fibGbibO font� ] J M#�Pf�Q$�R cite~R.$�Rurl^�url#1{E�tt!O%8{URL I8providecommand{!\0info}[2]{#2} B!eprint []{S'}& [{2�{Frisch}�25)}]{f a (nfo{author}{5�{U.}~�1iH}��\emph1B0title}{Turbul.A�=(publisher}{N�  q� K}, A(year}{1995}teB�&� et~al.} 3)6&�Biskamp�(0Grappin}}]{Mu   zf3W.-C.}�56o-:bi)VvD>v �}-Xand�zOR>O�)�� journal}{� E}��bf9�$volume}{67:B,pages}{06630�[)�Ar� Goldreich��SridharY�GS3�~PB�T}:��<S>P�Z<Ap. Jj44381�ED-3763!�>2��$Kolmogorov%'1a�K41�' A.~N>�LZ�Proc.{S�. Ar�4:K �_ :5 r$Sreenivasaj Antonia�7�ref_sym��K : ] �2f%�V�R�!�2:�m�@ugAnn�$Fluid MechB�Np292I-L 435}N97rN�R�3!>BisBook�>j�RPNonlinear Magnetohydr"�%qYz)V'{�ȉm199vmMeneveau�lU]%eIMen�C> W�o��2�UKJ.]DA�bC2Z�42ΔIroshnik�64AI�8PiVuh: NZ��Sh !l5�uE>U�n0�#j572:F-633*����Ev Dubr% 9.~( B>�:n�*n�3:E �95V�v��,�)*� X 0a� + PoP��f?�)�l �.e_\ PlasmanaZD488JG 2000rEHaugen.� 4:� ", BraG burga�and D�r� Axel�gN>] [:V�A><�Aname�%�e8VSW>S��ut6�I�n� 70�}M�01630|$Zi��$r�Benzi5�B:�!, Cili2$o�HTripiccione, BaudetH!ssaioliTSucci!�A_`�V2B� :i:�V;B� ��?Bz�AB )�<F>)M1I?�zB -�!�5��y4ZzRZE v� EmilyUv�6�!, S�"Weidon� ZhengpingA](�S.~B� :6V]b�2QV<B� �� 2�.�VOZ>,= 2�2�}Reviewr]65:�]�U>�]2�]5:�e�:]i;�E Chav�!a!�-�I� V'B�;}O�:V;B��Jf e{��GJ�=r� Dj- 8ZGZG ��and[J- RL��~�m$2I%[j�f� fB�\ �2Fm447J� �0 Politano%HPouqueth �pol_pouq�EH>'X֢B �6�2t�n� 5Z� 6Z� 5rmGraue&199>l ", KruS!$ Marlian�gB$_krug:mhds�t Bi c:VjJ>���Bw�2�2�B&;tn�19Z3Z�zr oldyre�0"�2> $$, Nordlund� and Padoa�$�B�:6V�B��ګB�����5�]rE^�6�0R��Ant��� ~� G.~Y�* :Z����,tt<^�@2�a 0550�r)p.} >( " , Jimenez~1�,E�YA]{ -�#��V�Bf �:^V=��>��NU®�Z 1911Z�vlCanuto5� 1988:j " , Hu�ni!�Qud'on�Zanm cN:b�4B� i��MJO��AB��@�C T���8)!1Vb'al. (�"#� ��*S� ger-k$#.W��!�rKurihar76I k 8:trapezleapfrog��YB� I9V� U�(Monthly Wea -� j� 9Z�3J 196v Orszag@ 72��o:alias@~�SJ� T)�� �Studie�)A6ied M�ma�/!�b�51(3)�T%F��25Z(7v}Vincent���guzzi! �v _��:simu�� B\ h�[ M>R�Zc��Z� 1R<v�(Bershadskii� �FB17 LZ��4��1Z�461J1�r*Carbone�0� B0#��So2o-Valvortines,�,EzVeltr^ RFX `�3V>96/V�L>=2��CB�M ܒ>B� q��@�B9 1R!�F�I::*r|62:��nR4��"�U;�">;�"4 E$*c]K�&�V+B�|ڪB ��r��n 7Z�198V�5r�Horbury%Balog((U#NPG�|TJ� T� F& �Z:N"_"�$eV:in Geo�4cvl!L9�M�1VC9U#N�+ � f�+7j�)Ga.k2i>� #, Klank�M Telly< ":04.,N2F�)O> =:`V=BO��&VMB���/s.e+RT$,Microsystem .=Xof Lab-on-a-Chip Devicejf$U3 -VCH�/}]add\=}�nheim6�u �XS�r8 Manz6; :00.�V�GK"~W�.\ C? 2�SA VTBj�6�"� T52 Anal32em�^�1�&��mZ364Fs \r�Bogaer�1"'>� #$, Rousseau~ {Van Heck�7$and Impensa2 0�{B� =:*VdB���>B#�A2H~�I>1!2AC%�5�� .� "�4j� 111�I-�7Jk ��L�0�'Lifshitz� 8Ŝ :87�< L.~D�.9 ?֢ E.~MBP�)HR���)an��}, vol.d/%-"\-}#< >N seric- �E�L w, Course��5et� k�6!h*_Bu�<$worth-Hein�SnROxford ����8})�9�� ion}{2nd}� M6��= �G stei1(99q:�V5EJ�BA7i�G:���1jpWorld--A Wolfram Web Resource�0R.Resear)6=E.1� 99})24Dnote}{http://mathw�.w �H.com/Triangle.html}j Phar/DSmedleyE$�( �ID�5��% ?�� G.~T>P�6+�Aa��)n96:@�8126lHF��N� 'f� 50*� {bou9797-�Iouchia'C. , ``Par�@violaa�b (atoms, '' RxBFB �R8@ 60}, 1351-1396 �97.�3{bud98}�I8K j$NonconservpA p�E�$Beyond theBndard@,�ceedings�#,Fifth InternS�80��K^I.�>Khripl!H JETP V�A83A802Rbou82>Y: Gu\'ena,xHHuA�iLCtt*kGJ =117��358-36=H 82);�;-P(I^) ��A709-173�E86B�8>��J��=:�} bkB 2037�88); �yLCz PikettyA�itrO1851 ��` {woo��[?a�od �"�?�Gcbf 27e75�63 �:�en99} Q' Bennet�E. WiJ IM.�m82�2484-24�FF�>CB91}JA=Z1�C=S91�1a�*�@bouam.�D� auv�I JacquEAE h M. LintzqKSangui��L$Is�AM2F{@V. Papoy" D. Sarkis}�I� �9�2143001e�)D}�jah00E J �.�Ph��6�EUAa���1JB �471 }, 561-565 a�6�chaAP.C��}6�K>EPliLA"C.�NGoodwinA�*�@ P_Bmun��,138}, 249-25�KA� .EO�L5>�A�N2�.MFr5��100-10(F8(F�z gue9Jo� =,J~,119}, 403-41��9F7��*f�.('.�>�J. �S9'SI,14}, 2+I8 �:* ou96F�>^ u���3)g 5-11��496). Note that� this work�``� o-''%�@``para''-configur�$s refer to4@tive or�Q#4 exci �(probe trans�Fn dipol�res�Sively u llelb$\�E_l\we�L8 \epsilon_{ex}$[ (pr}$, hH>��N� � quasix} cor� o@ %go� RKpolar�Nions}. :�8AT~�T:TQN$Semiclass.e�a� bf 1�733-7m�8B�9EZV� Can.A��o:D;D, 7-7tdQ^ % �#3F(C �%�y4 Eur�9 J. D �2��331-342O6- sar89� G. �[��Melkon�* .W. Exp.EF�� 3�F485-48��9), (9VNGd fro?DDibory i Teknika Ek�R�$taY'. 21S2-203�9)2ia�9F����OV-�B-06!011l 11�:���1��%3BeV�13�B21-22)�1B�z� .~ z7  E ���E�19 85-9ɶ2)9Fo0104}, 157-164%�CLY� notp� \The $E_l$ field is pulse�X prev![t��discharg�!vapor..>gue02a�q,V .�SA�n&+ �@M>! YX-Q w 739-74"� �bod 0B. Bodermann,�$Kn\" ockelk E. T� ?Ba� � usag(�pr�W,m IodineSpec� eu(itut f\" ur��enoptik,&�I,\" at HannovJ' .92B} Forɮof�~4we are gratefu�, EmmanDs Laser (CEA-Sacla�S r Pi�"2�car88�O ThioulEV A. Carenc=.R!�glielmi,[ZJ�BA��El�Z�m�0  535-54Q 8Q Yuhri�Ɔ� P� 6%��UrisohoN�71} 6-1� W��!]6P}A�r)Q sevei&,>�*]1��169-177 66 san >�Ph Thesis ("�N \'e Pierr�&1ie Cu�'$`a di PisaLd_  htel.ccsd.cnrs.fr/documents/cpives0/0/00/67/85/), Sect. 2-3�Vu�li�&� .76�.� toATear9 $&�` ., a9`�U:`100442Dms r} M�ic�V 20 CTss Stre;P�J(nce, RI 029! USA. www. J�Ocs�Wsar!�D.2 O�U"D6�m6A��`���c� inB .�lizr ,Lizon A Lugr�ŗ PAM ќPrivate� _2X 56B1�%�>�^i2� 25)J� 0314 \U1� 5} Nb� rMe,&o�7 89-9M 6��b��in� ?�5.���M�� mDFic di} ampl�,e $M^{'}_1$�P$cludes two����� :�]�,8r one $M_1$ ari�^0 many-�� a�rel!iZ` effect7��o�,G ^{hf� indu�_���dia~(hyperfine i�a�!,� �Mnly�D$\Delta F = \pm 1$*|s (! �I�@<{�( use a sign! ione ��opYo our's Eou88})m_ 2$=v (seer - does notq)y e, se,!�  H��2} with a�CE 4 axis chosen a�B3 ex} *f k$ it bb-Q!� -U m_1W22W , as)5 ![UX�which-�s b [ [0 :W�$E_2$EWU�!.E(fere. MoreoR we n�Uct $\v # E_2 ^2/ M_1 @^2 \ll 10^{-3}$. 3als�abs��� anAjtew(nce term, $qP pto \beta� q\a�!*� abili�aI eJ)0$\pi/2 $ phasy  mbetweeJ �rk� 9u�s2MP} �M/a,A� &��do�� sa��V, >�.hlin� J��-.4J.� O �5��I`1 T2� a� C} Beforea>(h�!!�!M s� sapphireH s w $controlled!M rejecU in c!$of birefrK!�or �s�ism de��dnty YanneaWt 1200$^dRrc}$C!�.� atm$we have ch�%�at re�tr6�surfaA�,akes place. 4� $\#$ 4� subs�Hnt�w �$ tube (ei��54or alumina cer*f) wasi 2�45.�.G4G~&G�E.~D.��[cW ;\� 1250�; C!eC0"�V,�.F$ 030502(R)b6MA5PP} I!�is seI2we��A6mof unitsa m�employt p�.cle ists��0$\hbar = c = �]accor] to-�a length��givenat{in�`�m mass%� mo� k*� pre78} Y.�M cott�&�)m*K 77B}, 34778 n�$bf 84B} 52�76@ant01nI. �/adis { .r JHE�0�^�44%�6& delg00} �elgado2=00� 0Me .�all04�B. Allanach :���at TeV C�(ders, Les H�!es�gl3, hep-ph/0402295 v5 (May 6H� ?,*�Ic0!l  "D7�  sX\'e!�ai�#$de l'espacMHque!�V"9""a�!Y dans les�!es.\0LPT~ENS (JuneF�che� 5[Cheun~` G. Lm�a� ev.� 65%�760u�.2si! C�] ehm,3[Ho�u~Silk�~C�h� J.~�Paur"q]�92�013�4)� *� e�\%stP. Fa[A�J. v]y �YZfayZPLQ 3226`��60 ��erein. ::4b!"$AJ^10260,6l �)B ; %�m$RcLav1 Y1A]l'annihi� on en pI�t($e^{+}, e^{-}$), %via un bos�e jauge A�g�de� ud� 0sombres} au H7re'no $galaxie.''~�noe�S C��r�`P`+ ster�!�C.�bB =6�L318A�YW��2���]Ywn orse>�# R� 0052115��26VforN�ts�h��am�L� let"h� )�a 2857�e$���1>c�2/6�X1�5-�$��3eJ�n�jtf} %�rG.ll1} R.{h Creg� E"6"�%s_�2L%53 ��qu� HCPBG1.5m�0n}�M. Smithu*� Z�o/#2657�>!W �42} Benabid F.,�V�)729v399� �%QOuzounov�hG.  �nV3�� 1702ED2�BEC} �H�o��AD����98�#e���,r[; on1}�� wmeeaS>�e�'r,���Kof"InfJ: _Cyrpt)py,y3&��3=Cc}, �=,"�=%H"n�2}vLuko�eKModV }Ik-4aP�,).rW3} �$ausoleil>jJ~d� M)5�k155I)6� EIT1�lAB�l��Y�e Khan� Jetp� ^4A�6 �>.�EIT2}��E&tl�!�& �_ J6�n3�%*�0slow light1}C,uR�6p09}, 490e �WJO2}A�M. KasV�Z�&5o�%^tored �2}D�Phillip�B'^c?"783J��f96}H. "�f!� A. Ip glu -#�)hIw2E93�(�i�- pn switch`?S��H�LcndAY�p n�8n361��n �%$YAb.��Yvbe�A�\ Haw�s.�ExpQC1AC27�W�)m gilbert}W� Swz�S.��G  XF�-<U12R(206 c2h2}� aL eppl%6pe�l�i��  4-%2�0ritari04}T. R �6V%�9 % 4080��2�m�ees-co/ nce1r QR[�-J�8=28r2'Ja2jaZ 8�Z�*&� 9�sr}!mJavZ�}YA�eaU 0138�l�Q.U pano�pC!�ano-l6�l K17& 276%b2`j�Ou}Schlos� AqA�'�� X 1h26�62 nakagawa��$deLabachelX4 �Ja� [ z' 84v 92a�ga�dEl��chtouk|l# V. A" gJA��hSt �21!\3sq1YN� (bg�#9�2loop�n$Ts. AdzhemT$N.�B`�.MK�wi� )d N. Vasil'. Int.!�M�)q�'.21� ��im�eed} L>�$J. Honkone�uV�?1�'108� 6�Pismak�:(J�Yu!XPis'mak^�e6��8� � Teod�dich $\acute[i{E}}$a %,]k�:�k�912� 6 R,Lj,�@�(8Pieper_FB17} S� 2K� -Q9�~e� 252501;{ib.�I %�refs. �ein9 $MMM_PRC65_�KF!UMarque�a6REC�440t-�!�8�Baumel}N � , p�]ju�� GN_PRL84_" uard�� NuV^748� 11*� AV18� _95} R.Bua, V.G.�tok�Sy6villa,��p�� �5�* bx8gziz_9ihziVela�56� V9�>{f) 8047VNIJ �3!R� �� lo0jCa�TerheggixJ.SwaP�.�)�QE1�9 2950q MT_NPA_69p �MalfliL!J. Tj* Nucl -A12 81969)�5S PhD_�X Rzausk�D.*�"'� Greng^�3)VPHfP40eL.� � >9}�I�~Pmear �ica D13� 205A�� .Cu-�1F A.~Cumm�9,�O'Sulli� D�=~Hf!rn6 *�)��6~B3��340C|.2�!�7A�>�yN>~Izrai��� m%ux �25���}:�7b�t� F{J��r49�9H7KA�mB.@us� x���44� B�!r6nrJ�>�.� x2�;57�.u;�>�B�!�:�?m�z 2�9�:�� 9n�:{�?(C.~Harabativ��271^��~Gr-��6ml S.~Saho�b,�� y43�1�� ]�Br-812�S~B�k, Flor�J4�~Ff� E�>(o�PG�w!�S.S W�`)�*v I~!�38u&�-2�Ko�u.@V7}B�I�1=n ��>Y3�:22)S� �Nu%T!�$el\'azquez%�AeP.~Zuk/�� 2�*= � 0725%22�BaJ� Hirs!EA!PanJyZxC �6�# 0343$� F7�f- �n)3(N.Y.) Z30�5�=>+Ja%� Ph.~]:o8XA=! ~Sto8eZ�.2��938�{061~lhassid� FkWob|ZhM�R R133Q0�.$� ibid� � 0152 �1:UaM& d:�z`A 0261�!�=JBe-U!��.zmerzi.�I�%�]�� 0304 ���Dk�6.HD.~Ango �jpp͋i�pVnAgbm�=~Ghos_u6w.�vMD7�&016206>�bauche-�m+ a~B%�V!-Arnault.s6� ���1 ('6A��a!@�Zr1W,= En}#�,uku�3A�inuma �Ko a�T.~Takah� d  Euro�� �8x ��-12�S��Rl>G 35�A2<]6 froet|� !CF~Fisc��� Brag)cP.~J\"onB�9D !du�alR S�'j3an MCHF ?roa�t(�9.A,�u� �.�grant}I�U��t�+>�M& �6�'8�}?2.&TJ�&�:il-!(!~&a� 88), p. /=Rparpia.1F�P�E-` -`E.���Q� Comm&Q�?�62L.~Vis-�O �!�A�;, H.~M��(A�u? NieuwpoorbD�"@?�hy.* KE�Dya_5.�AlT.~u��6):�E%�Plu�@�$5��42� 96JL Desclaux,a��ay�&y F.~O'Brie.W>� �6@ 19�]jud7{BZh~Judd%+e-jHicG5��{Op2SM=� Hand~K�L���( G.~W�(Drake ( AIP6�962dp. 56ip. 88.���,� Hond�,n� Kiyokawa.za��&#�4!70i;�P>� Mo-�gK) Ma�^J2� �Z 9!�9752jL.~Ben�T.~Rupm}He�lenm��l��k2�v�J�Ke-I��t�`�J�4Ord, Kendall's2j*o�ory��"2 s, f@J��d&of.;V} 1:��0%�O�~(OxCO&{"�xN*��8>B]�Ja-972� BO z ]*�7� 183(B�� 2vv ar��=�Vl8l��1 )>� ImI.I^M�Pipek,.#lE� J? 0262[ >� Ks6.D6 lωahu~kaT q�J�Ab-�T=0M.~Abramowtiz�E�egun (��),2� �XAoMat�0al fun�-s2�NBS��6:/s S�s�T55.*( U7 Govtm-int<1 Offi�72�.C.�^6� �"� !U2�&�h!�fJH 1�B03710z�J68Horoi:~Zelevi� cB�EBrown2]I�I!7!�519.M&>�kE�J�ar^eˡ� 1�.�Pw� :M�:Yxr.�>� �93c,3f0� !�.qGJ[� \'om��:���etamo�:ǎ5�=]"a!Ya!� .�A�-ơ�ai��V6�=�.h2�543� �.2��RE8Mol2�2�.S���� 0573�f>tea:e5BZaQF�DJg Ch-71g"OC,�B� en%�T.��A2�^�e�� 5 ;2�5EA�.��U<�-al�!t �opy ( ��.5"6=V�"2�ra5.A6����V.~MP.1A�<e.�11��igr--;B=J�:�.u]:-�956�a6�Ze-96A7 .�Bt��}-raz�M!�8!�Nxp� 27�a1&.�papen:`TM�iH.""� B�a!`:nucl-th}"30�<=_lindgren.� I.~L ga�oMdbMany-B,Ba .O 2nd ed (|+"6i�� &a6+Al:�e &P2�u�>!zA��bst.x)C -mat!6495.VLWL��HStaruszkiewiczPole}aR AMU968e��A`�PolonicaH% XXXIP�D 1007, see eq. (15Ap ��Bohr} N 1913 ZPhilos�0g� 26} , 1; 2-&5V., 476N?n�ld}� ld A 1963�it�� �X7:g�Ha��An<.en CM%�V"r� HC� 2�&4 X5% 5U02y99 Dirac}  �?1l�Vb�'�ML9�per. A�)�148�5_no�;act}Cur1B0DG, Jordan TF�4Sudarshan ECG )w g&� �35} 350,-"8mo G, Mukunda NJO 1984B\+1 30} 2110.�Dri�  RD!N9�=�D(109:�Gr\n}�A �%4em Asymptotic"�;Relaxa5 Osc" g?&ITAs �2Ok�rc���+� Bf �f .�Eliezer}  CJ 194qr!�C�%U�A1�176؝�w De Luca Q98BM� E8k680>IrmalDelua�:OBPE L 58, �R72(Y��J rete.�ebI���e4I$Fey-Whee} ler JAE� Feyn�RP!C5 YA�B�o% 157 ; vFA��U1}=.�Bel"�Re. �,K.L.Cooke, Dx>tial- ce EquIm% Acדc�'U1A263Xo396� Rohrlich}�� M� Clas��@��H�urticle �Addѥ-Wesle7�o:�to be�Dshed}Un7. .  �[f[�9�AB86} |". Ama�� )2rw�N9%�4 5a�� ��JBU J. Jellin�T� B"���cO  2783�`��dKJ�!E� Krissin�L2w�+QfQ�)e�E�.X��� BBDJ�(2�.�H�ڧ2vAdvl��  70�< 75t�7�8ZKBB02} Y. Zhoul: Karpl]\K/ B�o2�JFm 116�, 232�P�� WDM+IN!_ Wa"�8et~al.}�RX� 1�.�EAT�XF. ErcTsi,�VAndreoCtE3�satti������ 911)���ESZ�0M.~Y. Efremov�c�)v�r.XI�3560 vVXSJ!�  Shvarts��%oM� Jarrold^� _253R_ BBS+�<Gw��aux��9a% 21550�32vLWH�Z.-Y. Lu�-Z!�-�K.-& 2�B-k ]329NJKE�K. Joshi�GA�n�1,S ��zeH={d6�K55329!�B�Gupt81]�P�Op�!FH2�� 626m?�UTMB83}7JTom\'a�v.ukherje �K B�[�90� 10340͵6?BB!�*8l�Z����23540�:6�KB6�R. `Kun�.2��4A 189���+U<CB�WH.-X2et?^S0"4�796��.� SKK+F 9p:����7 9 S6�SHDe7�S8�& b40�*B9BinpF} �S_y>Al$_N$ u}: �Ma pote� sgV$$E_{\rm B}�F.4955$�@$1.8331$, $2.0649 1828 2957 35Ay,$2.4725$ eV/+�$N = 2.345$ ,$6 G= 10$,21].�RJa_C��PH %.ViQ89�V�+R 3�-f 27bT� 7�U. � \def�T�T�K*�m���bibfn��>�O"�PcijP��."�PuJN�G�L� ".�>�Lj��L�nL�{dolby�%!�iA{lP}�5d{C��:lkD��Marzli�s7rm � wV3{�:}OR�%�B� weak@]���#�?V�*n Dj95��-9888--8 ;F)942TB)i�? =�>�� ", Thor�1"�u}}]{mA7��uC)>X=2Wb�Bd� �= {��zĮI�8�,>\u����}}V��maVBwSan�cisco.IQ�7v��Ne�Jo�Wvn 6 UV@A�1:}Q.� �``RBd n.�, {F}���>�,ceeTa�s0geodesic devi� ekV�n. �um�c� textN�1u�m465--4N3unrBrehm˝6��b�� ���*� MRWA!�ic rep�[)",of {G}alilea${L}orentz qY"�LZD�� 3RD489--4�"FD:� >D Sear =G8)}]{Fxs68ijj�FJVΏBu} �!�RzI6Y�dm&� �� Z��� � 82�{foot�W(}{An extend�j�is�Yinf azBgru�IAB0timelike curv whil0 "D 01+1 Minkowski 9B\�y��.*9x>�Manoff� 1!�m�4B)� J!�#� ��F�s�"�T�� s�Xaf!!nYI�inZ4�y����y111�1Z) 6 B?inx�%A}#?�hkV�B/ NRE@taneit7ggen2h ized28in ~g �B��*-B$2443--2456.�}��:2>BB�Llosa�'�bel�'zBL>�Bel�vJ>H �.�U�Spa� lyQ�mo�"in�o>o122�-o1949--19Z,5roRomai[ 6E�rƬzkJJ$ MR'Y� measur�C! .�~:V_.�"bZ3-��-0376--38J��&�.4{"2 {a}}�,-<4b�#�=Rigida�criteriaUone-d�[al XRZ! Nuovo {C}6Z�f;R� 1060� 6V=4}:*>�}�Ex4�rd4�brS�N>� HRs-c�c ro� � r!L�lu2�=orZ�&� j� 7R654--5JȤ 1947roAsy�Eend Jennc$�76Apa 76�q D.~G�.� ^�!R":� �R�S�y�!t%�ngk Z���Qb�92oq�< 3F~ 1976rrDav��;%cd�aC: MRM: �~9�96�LA� 钂 Lass!�! lass�B_�FR AAJe��clock�]VAm.�e�j����4� M627��!�F$6vDeslog �H-pot�8��!ogeo"5}^ ~A�.� \ڧh�.O�R�Uni��1�e}f-�&�����5R�25��N�w#r�M�-E��m65�*L3:� KR0QTl.3�eZ��3R�934--93RQz=�� eN.�b6��$¿e5����Ao4�pn2EEnA�"'b�B��R@ 279--�_N-2�!(j�TiRFok!`v�t �!a��nV�D>�NRxG� &�is%EU�- flatQofstant pr e-U�ioZ�1L({J}. {P}hysa^�5R�8�y86R���� JJoX�A��j6��Rs%:� KRJCo(`=L��ssocia��w�nuR� �2��Y͋124�J�196v�Borq Biem!>5�born5��B�O�{B+��R�(Zum Uhrenpa��on.�2�Z�Nederl.�k�W}etensceVP}r�1${S}er. B} b�6� B11� 20.1; 56�>� Crampin*�59>A� #4, McCrea, McNa��� �c )59��}��" d2~V�B� ��:F>u�)R��Y�V�B M;"�A c� ���Rdb��4{R}oy.A-E4L}&6A>{A}j@2��FA56--17J1ɵ.S{m�or62Rf\o HC� � R� n+62�x . 8.��)AJo Wald�08dwald8� B�Fa�R�ѷ7 ty^�{U}&=�NC}hicago�+b�7� "�"C ".q�8v: Hill�4, �c4�+ E�+:iI.�U�O6�&"!+ U E��anw �v]  m�}^��6+j� 672��m358--36R04v?�(��%8���8�kiє�zAn�)5J j}omoxt,���RG 1�14Rz�Fulto.&62:I2�( 0, &�6A.W�~E�fP��T>� �2%V�B��Ԕa���B��N�&� inva��c>%�V� �5R� 442--45�[ޅx�\62��)b*2�b ���u�������ץc�q�~I�# &� ngSV$�2�U �H6�67JC*1:$!�INe3f�-1*�{Holm98a*5D�dlme1E�? rsde THRatiuU)BEu,� Poincar\'*8;�F��dS�PrI� �=�3�CodHuum�ies,''�>79in �H=130 1-81i:96�2 �b��B�M9��Ided �N"[����'' �Ae�<[(�2�=4173-41�gQ3%�y�a Chen�3S.Y�5nX75�C^qi_E.Fjl4E!�Tit�5S�ne1�Ca[wa-!"g#s �x > m�t�dt chan8;M+ pipe flow!�z�1Y>338-53�:��9a���D�E. F���k$ �ceUG!�C�@12�49-��6�5 �b���� `W on} 2�|^�2�A� !�iW-�!�.t F3��tEr22343-235*�]6r9c2�=�L.Ge�g I�9R>8B: ``Di�nu��l s"�7e8h N�r-%c�lph�ydelr�, 66-8N�Fa@"R5!4y `��2�-�a�f!1U�E-]�2.�G05-51�V:��Nadiga�B. T. �R�hko} ``Enhanc��!){casl@�gy!�!two.� LaUUgian-aۉged6�y�2ls�s}M$�61528-15SBc5�;>]A�s�I��mean ��al �a�QfluctYA�i�\)� 26�2�7C253-28m-PU� ��� �8 ``� -*YdJ�I���B�Z� Chao5Y2� 1� +o6�FE�2� 7+s� homo�%A isotropic=���>�524-5�i:�ininn,r P� A�C!ntgomeD�A�7"&n���#!�� !�%�)��>� eoh*��t"�.�.߉(}K� /0jT56�Ponty}�z �nDԞ�J�J.-F. Pi,p,r<?��D .(o`.�1��o � at �v �gFandtl!9b�Xq�P5�[ z�04�L�"M5��{�-�5�e� n al�tiv�terpre�"�3!ǡw `=�':�-� ��"336��6N� Matthaeus9�W.H� �2���S�� decay hyp����at C��a�5i,Reynolds nu6k�XN� �G. Sci��35| ��A6_? Ting:GAa �D.�I!B�[ptZ�Jpro&�� �2 6+:�27>326! :�GKinney)R. � a�cWQxam)l T. Tajima!hC�ut s ^ %�0t���:� incom�. sibl��2�I� J�IB�Y 3623eR]I"G���C�n XfY܁� J. L\'eor� `` ��ce��Cor�*oQBMHD�Ab���Ra�U}�. �lQ-12�D 51-5y:6D�'I2�M�pne�+I1UQ��_e�$ Growth�M�%{6���?�v3 4266-4rvBQIb�HS.  ^�A=�N��e*;�c�� helic( in dXNn/dissip�f:8RA�*� :�{l��1y�:SILilly6j�KE!2�"� �>�Q�Z� S�� . IIM� 240-24E�66~$Mazure75} =��A6�A�A�5a�O�� e poaYm��a��9(�S BHD)alN�J-I"t �68�69--778��76oM��$.���>nStrongE�E2�2�[n"i�0� Y��a0c"7��32� �Y76Hoɾ�!I^� :� Long!s��6�!��3�H<�maximum � scala��� J.PlQi�-s3� 479-4Aw6� Ben�J���%<K�wR\ani�h� s h��al�Mic y85Bm��a>-1� 5052ob�TM���I6�:.  ``H� � non-> t-�a�).��yD-04!�"N,%�812� Gal7�+EB. � L!*R�x ``Li�:nd��2ar� >�!ABC"� ��Ge� � ߿�K183-2�gB�E4Podvigina94} Y�%�:S� !N �sta�A�1:1:1�%�YT%\.n7 471-`L�42R Arch�s� 7{� BA�Do'�!?{\AA}݆r��!�I" in��&� -GE�N\4� 59-7J >)issaud�:e& ,.�2�}�esieu���i�E�����lf3� develope[��|  1366-13�Y73)�Tua(O7^LC.ILi!X.� ``Infl��eN�o�!2�N"- . "  Y$�o2!�187-207A)76�GJA$Q�S Ga~ Eyin�a�jW1`���A,B  2�M:�06� A�361-374 F�G_�VD.O. _6� ``UnX=v � ough!>e��29M�aq"� 4� 69-��f�Y��dE�'q�E�o >G!8��a�-�D!F&�� Y%lal {z ZNe��X4)��5}v824-8�BT(Kazantsev67��P. stLvF a:�Gg����-�9YSovcOR� �� 10318@�$6�N7o)�L�!�rsei~E� J.V.� Gl��%�D. Sor"� e, F�Y�l�=me��R& �(Analysis, EolUM3l J�8al B 14, 579-60pl6�vittig}�5�M V5�2�Ae�an��PocketEPredic�FintOlex AdapwSe�s, (h�s .org/abs/"�\ab~ 762)]�)7o5Ao��!?t��sAx(autoregress�vo�"W�ϕ!J�B(ce, 4, 75-1�a1>1M B_et��Bac�E.! Delou�V�Muzy, M-�f�al apom wa�5�Rev6� 64:�c0�d6�DBak} Bak,~P., How T�� ks: ��Z��$Self-organ�9 Crit���(Co+nicus,~NX!F�_�6 BakPu,L� M�_czuskS�om!�%EaJ encyp crl�&3{& USA, 92�89-66�:�B� slev�� , !�G��ac::�A4i8��fGR�dE,ity, Journal� of Econometrics, 31, 307-327 (1986). \bibitem{NYT} Brody, J. Push up the weights, and roll back the years, The New York Times F 7 (June 4, 20022sBurch} D, T.R., D.R. Emeryn��M.E. Fuerst, What Can `Nine-Eleven' Tell Us About Closed-end Fund Discounts and Investor Sentiment, Financial Review, 38 (4), (2003). 5&8Simkins} Carter�A.�B.J. |, Do Markets React Rationally? !*Effect!�!c�>September 11th Tragedy on Airline Stock Returns, working paper �$2) http://$s.ssrn.com \.taf?abstract\_id=306133]Cutler} �,E oterba�$L. Summers-�Moves �8Prices? Journal�Portfoli!nagem%r,Spring, 4-12E�9)�@devany} De Vany, -b�Lee, C. Quality signals in inform%c$ cascades A�and%`dynamics�!pdistribu!�mo Lpicture box office rAe ues.PJ.eTx. Dyn. \& Control, 25, 593-614 !�12�mukaNL�llago��8S. Mukamel, Non!�(ar Response� Classicals��Fal Systems to Short Pulses, Bull. Korean Chem. Soc., 24(8), 1107-1110 �E� U�Amazon_E>2�schatrYFI�,D. Sornette,!wprepar%wHDodds} , P.S=lJ. Watts, Universal behaviorODa generalized modeED4contagion, Phy) i� L��|$92, 218701%~ 4). �PSBH} Dunbar, R.I.M., a�soca�8brain hypothesi!J`Evol. Anthrop. 6, 178-190A�982�,Eck} Eckmanna2,P., E. Moses%�!8ergi, EA0py!�8dialogues creat,oherent struE�E�$e-mail traA��, Proc. Nat. Acad. Sci. USA, 101(40), 14333-143371=(Einstein1}  ag, \"U��Ldie von der molekula�petischen!= orie!hW\"arme geforderte BewegungE�in ruhenden Fl\"ussigkeiten suspendi7n Teil`, Ann.%� . 17, 549!y056y �2:� ��igE�s�Ga�Theor%{Brownian���� (Ѻ: Dov�� 19566nngle} AG<, AutoregressiveA�di�HDal heteroskedastic��$with estim!� of�variance�4united kingdom��l�,�v��8a, 50, 987-1008!822�,gilsor} Gil,���jA�q�< Landau-Ginzburg�-$self-organe� crit�}ityi}.az.aw8. 76, 3991-3994�960Htipping} Gladwell, qx D point: how little�eh things can make a big diffaDce, Back Bay BooksE�6$Hamilton}  a�,��-expect%^s e&(  analysi�* change $regimes: a�ov!�I_a�A^term u�$interest r!�, �*� �ى+C�Q(12, 385-423!\86s�2>�4A new approach�#� �i:� nons) ary   seri��84business cycleB�$7, 357-384�92�,ETAS} Helmst���bE�U� D., Sub-Qhsuper-x�Fepide��!� earthquE&$ftershocks!� GeophyE��E�07, NO. B10, 2237, doi:10.1029/2001JB001580NPSpredict2��2ZP &abia4�!G!  M��IAact� 8Triggered Seism�), J:���(8, 2482, �3� 2485�����HSG2�!�!s5��DJ.-R. Grasso, Main)D are A9TA�Co�� Fore *$: How do f  EV��$al propertAV,emerge from 9� lawaN�, (B10), 2046B�2�199��6�ipo} Jen� 9T� $Ljungqvist) Go!�Public:�{�'�6Evide��n�Compan�,Raise Equity:FiF $e, Oxford ���P�!, 2nd e�!%�6# @J2web} Johansen A�� e�of�Rnau�   @296(3-4), 539-546J`crashcomc) Com�$on ``Are f� 4es� A�(able?'' Eur�� ,60(5), 809-8\ 2).� notedja>| Prob!�human r.�� � , 338(1-2A 86-2-�42qJLS2000>e O. Ledoit%�.� C!��� ��ɔs, i�n�#al.� E!e�T Applied M 3 (� 219-25i�02�outl16�K2�S� mH5�a�>i� !�opeanQ�B 1, 141 ��:� JS1999~�C1-*, RISK � ), 91-��6�$JSdownload~� D ) relax%n*� n�@$WWW followA.(newspaper pe� 4of URL�,ica A 276/1-�G38-34^�2~ La��)��� Draw�s a8Out)�.�Risk, 4E 69-1m1/:�JSend���a�B, Endogenous @ us Ex-��tI�a� �s, ina�s``fempor��Iss� in:� F e'' (Novaf � �0shE�2004) (yparXiv.org/abs/cond-mat/021050>"LF�F�u�, �\A ����$ 8screte scale in^ B� 1 (�5-3�>�ohnbookEn�C(N.F., P. Je� ��# P. M�Hui.K q�omplexA (���:�$queen} McQ , G)�K. Vox k, Wh%}GARCH? A!� ,-based expla���2� voI ��?of=JStudi�x17a�5-9t %�.;music} M's brer fu: _$, industry, B!�A}Spe!�,w �$Friday Nov2th��6�M_etal~z�-!�J. Delou� E. ry, q l!�fluctu�(����Y� :�?�c� to stocha�=I� �Eu��q 0 �.B8 , 537-548�02OOmori} ,hO��& �&� + Co�� Imp.n ., 7�1 (18968�} Paga�ZG.W; hwer lte��ve �sBF!k .LV� 0s, 45, 267-2916��}:�A. Ulla he � �2� � L riskw � &t�I_C�, 25 �6N NLPott� , S#&�impd&� func�!�{ si*� \.$4(� 1425-14� 60Roehnerspec} , B� Pa�I�aJua�on: Ae�o ObservE�al �I�,s (CambridgeA/�@"� ; 1st� ��6ORSfrenzy:��.� ``Therm�ers''�c� ve FG, u2� }2, 16, 729-739J1RSA:�F6J.V�dersen, "G F1�"�S4�SSc��(s: An Empireԡ� Nume �/y,�3.��Mod C 15 (6 34�6�RomAo�$, {\it Adv d macroi8ics} (McGraw-HiG�, 1>u ruel�R [Con!�E 8nonequilibrium M!� an ext�r�rial, -�(s Today, 57� 48-5� .%Schump}  �� ��C\sA�*Y , Histo)l!zS��� al A*�� Capitalis� ��} f236�SS &�n2�Ren`liz%EAֹ�.�,:w , N13!�81-190:sSrcat}�D.&�V\of catastrophic events: X!� rup��$s, turbuleA �� !e� birth,� cg h �ph99 SUPP1�22-252i�22sor^J 9c�Why2S s�  (u�E�a�wlex.�,) (PrincetonB��  , NJ��6&PRgmaA���� (^ �ports 37�p-9��6b.T>�F�&dT.�ber�Y. Ageon2� Ver6� ��1$Net��� T�Us 4 Sale Ra!g ��E� s. 9a��22.V*DSH� .:EEA..�� e� 2��-Ӊ� Memo� � A 318�w�5 Feb{ 3.7SJ�6e�"V Signific�gaI,log-periodicT cursor�!B#(, Quanti����+e 1� 2-47�6�feedsoc.�A.�� I. Dornic�p6j� onto6�J.!).I Fr� 5, 325-33�952�VolMRW.��eY. MaRrgn"F�k {cau�m ? � 1m), 67- �6szN�0W.-X. Zhou, E"ef�� ���Y (y Bubble by� ign �� Inflow: li� �F� VUSP��it�.,.v(32, 412-440J�ds26HQ.�:of N �Cainu�S��6��8� a&0 !5 orec� ng � ~�304601.? t) } S��4onovich,~R.L. .�N6>� daI: Lin�!\"B  F&� -Dissip�KT��( er,~Be� ;%�N"�996[Travis}*!viq!� 5M.�!l��(R.G. Laurit  Ltrails reduce daily era�7 range,aure, 4�z6Z6�white} W E.N.,��68 and � � a anias. IJ )5�� a�2 F��h y, 13 (� lg< #e� , hltenham, UK; Brookfield, US%_62$ zs1}i�M�!K2 Non-Paraa � +Log-P�TPr.T�1*� , InNB 4 (*� 2�e0:Z�>�2���ݕR�#7 ��  D0Hierarch� OI�of Group SizM 2Q�Roy�!5 Londo��40329#� \end{thebibliography}b\beginB {99}&�hirata1}9H : Par( cel. 22 �7) 57.>929 Pe.$c�#0F. Ruggiero: �#2lett. 66Z91) 1693\Z� 2[K.�KEK R� 95-� Rf� vf..c B.\EYe, Ionic��ne� Exci1�brane�&)�nauer As�"tAW0Massachusetts%Q6qhhikl} M{ amalainen� \ Hari 0J.\ Ilmoniemis �\ Knuutila, O.V.\ Lounasmaa, MagnetoencephaloIs --��y��#i��c�eto��l!��W�g H� Brai�v.\4\ �$\ {\bf 65}�p3--49� 9932�c�"} �C $e, SQUIDs,�.\ AmerM 271}x46-�19:gese} D.!� Geseatz,�) ic F�* G�$�!Outsid& Inhomoge�  Volum�{nductor���l Cur�# Sourc!�]�\m�6}, 3�34%76$Pdakar} G.\ Dassios, F!�ariotou��/ mulai Biom%�*� !2!��th� LXI}� 7--40�6�grge} zGrynszp]FN�>)\ocard��m, Bi�.\ !�E13}�1--92e�76�ihk} R>�M.Sey Qy`ForwardE�.$rse��bl�i� Sphe���&9=sm:6�#�y, ed.\!�(H. Weinberg�\\ oi�..\ Kai�Pergam�New�a�86� sarvasiS  # sic Mathe) \E��r5�� ceptNN �c>\ M�BioA%�32}d--26872�helm} H!}elmholaMUeR&EinigeE�tz8&Vertheil(&Elektr]&r S�  Korp ct&L2& rn m)nwend:(auf Diethie@--LneDsuche (Some Laws a),!D** 1-%5%Dm��>�s,�Apk  to Animt D ExY�9s)�&��C�)��89}, 2A�233%�353--3�85:�bc} A.A��oannid�I,J.P.R.\ BoltABC.Je�$�inuous sa�"K Sol+�!B� :� v.\B.I(6}, 523--54E96�,see} see ImaF%PConflict: MEG vs EEG,a)(R.P.\ Creas���f 25�374!�96a�r�m�p��@in Ellipsoidal Ge�a��/aQ9�E�44};$0--24�6�sch�Sche��.aAaDipole�lent A��b Audit�'Evoked �цL a/ctricDs,� .\ 6A�AHE�P olog���� ando3Mo�L��G.L.\�4ani, 40--69, K� asel��:�dem��C��eMunck�(io4Tim�-ry�) �Ezasi) �v.%s, �-�A'li�,NeuysqK,77}, 156--16Nxhai= >FB0inimum--Norm �0in a Boundary�k!� Torso�&26Eng�omp��C 4�;>�fgka��Fokas, �,0\ Gel'fand, Y��uryleve�ers!_Method� V�-A�rob�1��L9--L7BM$ecipes} W.���$S� Teukolsky"T.\ V�'��a�FlanneaQ"7 R S!IFortran.�5 Ar 1e�tifN ompu�(2.8 "�G."�E�2œNH !f� 00}*� gem�xne} P�.G��al.�� �� ,) 5398-5404.% F��_N. Le' PA�Wentz].U ��N? 62$2) 171-188.�m3A Pein5�v Nagyp�I�6p21,`KustiR.�{. A 10I'$2) 3899-39:t�(E!�djaja 4Li�CDw"/ Garl��.M� 4499-4502MpioneerAHA�w E�Syl�.� TechG0s801971) 617-633.nuz$ Nuzillard�Q BourExM2J��gnson. 13I 8) 358-362[� -� n, X.Z. W�Jm!�f. �q $1) 992-1002(ladroue0} C� , A!� Tate��owea5R�,Liffiths, Lect. Notes +pus . 24�(20!�441-446.!react�r, Triadaphill|A�DMorri�.BVE. in: dc. 4th�q#8 Sympos�oUdep13t%onentE�0� Blind�t"�5 (ICAE(�ra, Ja�,, pp. 879-882�-?6>Ff3=Yl1� � 5- 697-702�re%�Y3�.Q!�%�P.C�$FunEdG. Sh$F.H0,!�t.�!Ely�  82-92(chin} X. Bi`:ai,3Wu��5 Ch�0#. h O1023-1022ischolz��� olzeGatzekAr St��O.9h �Selbig�"�8 cs 2)+(4) 2447-2452�piS A. Pichl� M%ow!�c6$�2. 229��5! 1-232�buy� Szabo�Edelenyi�&imo�7i� Postma�Huo!3,M.C. Buydens�l��4�"5) 36-6*huang  H ��J�Lisboa��El-DereQ#�!.G gA�) 147-16!&� viss�� E. V !�-W�!~O  71z Z55.b= shaoA:E�ao%��S��Q^ 9 ��&%5143-514�e�gUH��o�M�KA�A�M�S.F:aM�J�$&u 32'993-996�on} N�� nnet �� UltrF: rosc�810�!� 27-365it�M. C7J� Thom� El� RI*�; Wiley,"�f2�icaw C. Jutt!J; rault, �al�1ess��� �-6 H� CoA>:3�ae87-31AE5� � Hyv�8Q E. O�c�� . �8,97) 1483-149:V biKB�* chraC,K. Abed-Mera� J�* Cardoso):u�;� EEE T.��X�4K 7) 434-44��icac} L�  Lathauw�+BMooy% Vandewal��i om. j2000) 1��49.� ica1�2J.hu{1*Ir�J�!:l2lCic�'c . Am�Adapt:��1�� \1*inga�arnb Algorithm5��V�2.� jade�-F=�:69) 157-16��max�J.A., Sejnow< :P7E�5) 112-052� nmf1� D� e, H[=Se�/N�4��788-76qnmf� $Buchsbaum,��Bloch,�Cion~>. 4�2) 559-56� nmf2ep Sajd*Du�%C.ov in M�,UnsA�A. Al� b�p���8 (Eds.), Wavele�&=�Em�N� X (SPIE�c. Ser.,�.5207)400�321-332mcMd!�]qP�orgie\EICa��d.��c�EA. E86A�m3) '56^plumbley' D. P e�Wm�1��%.8*2L) 66-76.� nnfa� a} ZADY?q}*� �"� 319�24S����pmf%�Paa�< , U. Tapp!�Environm<- �}C1�2�a�F P.K �BABegAfS� Bisw�9Atmos\ knt �+A� 93-26� pv��{nor��H!�tr� .+ 5/97a�236-1242�ksfa} E Maliq�Bi� �1�+1982) e�:p!�Da�BM D V>,E�.sc. 5 0I1�B22�sm��W�N.B$ lagh!�J�Sha�> . WisR� L"/ ?20!M 85-92��2�1G� F�oliV}5 517 R�G29-232TesteLKraskov��$ St\"ogbau�a[ rass er,.A E 6� 4) 066132�mil!kH:PA.l� Astakh{rk"� k22� mi^Y>uR Andrzejak� 2��.hu<�+ m� 78-28�u�radjA�G��arned-M] E�W@ h5, *c0Ma� e L0ing e�" 4%�3Af�29� namb2�A. Smild*�*� 1-52�E� oB$K. Esben`%!}-b f�2o�"32z der1y C. O'HI�� Gre& q�s E$76) 312-312�weQ1"4D��Stephen�5.N6d 2) 27e742�sgE�Savitz�$M.J.E. Gol/.Jt 6�562� 32�aQJ..W P�!�9Ta�H�)wicaL,)$dq� 4u 3) 9�2gd$ NIST["��8 Data Center. S�S D, diry0, ``Infrared _ ra''�Ji9y WebN,, StXBrd Ref�A k�6 ber L�� VL�C> nd WaMamME��� NaA(al Institut�)n� ��Gaithers�B0, MD, 20899 (2�eb�.$.nist.gov}7!92}"ftp.cn"pedu/pub/pk.( dset�S&�D!��#rt~1in33-6�wE�22�!�f\I~0 3-12�Dfootnote} In \cite�},� auth�,Czed�mix)s !�ead�#14D, although two of �s�ra give� �r !W set (!\#1� \#2)�<q?[=Py also measured threeLgr�i6v[2HQof mois�e$CO_2$,�8ng�< �total nuE�ofTto 18 �percJ�e" BTEM)*/Dn all 18�) tra.2@e�s�0!N��=3kn�v��Hno  r�Js�8!`61� comp �J*e�@@it does not seem [on�? to tsHKm~an!i. %�upK �bl} s�$ sep�I�sA� our E8!(we first de�s)92"�Kto-�lea3�;�s U1 of w� ,-�%�INometerd).�B tha�s20(were projec�%out! orthogon�3FiIiva�spa�A���+lly�YMILCA onA[a'cleaneU�ENF8ul!�b!�eddthis waOr~:!Dc`!�0same as thoseYmost e&�EwEJ� just negl �Hbacq:�didE!do anyxGA�minimize/�<ct!� view!��%�S&�?weXMcus�ly re:�e�8l�8�me�2�k�Jt�K kMilja*1 S' Sobottka�Schacke�mR.�2zJ in: G.A�gni\`�G, (Ed{Diagno[  Op�y�%t"in�&mCine IIvrvu144űg 230-:$ wtu BOo< D.�) O�JLi>Tv 5) 257�82�opa ,C. S\'anchez$ Toft� vaA�n Boga%6�P �N . 686) #2> )�12�;2$a��m.5�0-62? camp� CaGE O�osurg. .Ѿy 1-22�ga� GaigneauxBDecaeste!��# yc Mijat�0�Kis,<.M. Ruys}5%� �7ghtigh,*�%�aRReg 2�*� 294-36�))22)��!Qyst 130� 070-1072�su0�*�Pfz-juelich.de/nic/cs/e ware�N!�f!996 koh|\ KohamJr& Cook!�E�'usb��(Horizon6$ Oncologic��x(Go�8�.\'#�$y%e<)q%348r%48i6n% joni� \ Jo' et al erba�/Spab%WoGAg�-ory�p�,s, Psy�.\R �(oti)# ��,3m.��15�#94Uy< �?E[Ra�sody Act�N4es Right Hemise Regionarc�$e��'6W62�v��Vor�-p��, Paul� N�#Las� Cereb� T -raphy,�a� Scan5�7H'4�B�Vlao�%\�3z� AOle�)"e�B� Du�M Migr_ Attacks��R��Em�4o6��.)v107�.�-86�=le@"I�eeU,HIPDM--SPECTAl Pati�;��M�L����� c�:�1(Seizur=Ic��stu: E4A�3��19:�@ tybya&�'TyCT.ar(Byme, NeoplY +�Q��� h'ical )king: t;ipl:Ind Ap"+s}�,�'J ( Mazziott&\�:$man, p 166g,(iladelphia:q\ D�5eo22� mazz�c(VMov�n�)� ƿie\Gi�244��ino. (\ MinoshimaU/A.�A�Oa�$lzheimer's�4+�;T --D_,� tereotacta�urface�� �U*PFluorine--18--FDG PET��\p3�-EV36�-2 Y1>D:junck�\ J �PETQ(* �f GlW,M�Ligand�9% *6��4al Benzodiazepl B�ng Si�!T\�R� 2�752A0:Pma+F E�9��R�7d� Gluc] Metabom%�symptoZ/ Sub!N s at�I# Hun�(ton'sA�!�, acEnR�1�35�:A/ andr�A�gLn, Li�=A;d��i��0�!m$Mental IllmG�;AQ��I_)�� path�yA3�P27�Q15896�/ reim�7,Rei�M�yN�+�Hom�7 Cor�Kt�+fMWic�9 ory AnxieVTT@ /24�-10U):� tjuv!�,G.\ TjuvajevyA G�3ly?Ue�4--Inva�4�!-Trans�3s��Cis--!j(ed Herpes Sv'8ex Virus ThymidA�Kin�.�>ia A� 1/3�C�.,yu! \ Yu�H>~a��d-t�� 5Pion���� R�6erB$in Liva,�0s�#�*N V49�%�.�gXa�X0e�In Mon�.d of E&�L!z Ex.�Positro=E�\ & (PET)�0n�1�ic MiyM -} l.M�UA:�%.� doub�$\ Doubrovi�ma�� h crip!�alg�;�. p�1D"���r�in Vivo,�\�l AJC\M�LCE<9� 9300 �6�0'| Lardinoi&� St �ofI�Small--� L 3CHr1I�6gr�6�-- .���� uted2� j�� &�+.�oD.\ O�A�<Fe�"S.Z. sil-�5Solit=8Pulmonary Nodul�~. 53�6. hutt�+�0Hutq�!iac Si�Y--PhotoR�: Is A�"ui���]= En�? (inv�Y.� +S\� �:2`2I�\ 6dw6. F.J.T.\ W�s,� eF�, o�e�Ceror's#Q Cl�\? 2m L F�40��3�PB�be�%F%�Bengel�&�`�(�6|Reinn�J 1hPerDA�4G Hearti}�Nb:,]f�9��3� 73*.ena!�!�N[�{VIAR�3 7(M�ri���}B"Z6l foknov p �1\�Ni�DY>Ana�]of $\G%�# \par� $--EqIU�of Radon)!0�\ �5.< Paris � \ � ��J31�J4, W6&ovi��HNo �At*J2Formula3�Q�,ed $X$--ray ���e, ArkA�at�IR4i�22� shlo�mShepp�!�Log !�Fourie ac�Z_�� aA5d Si~,K!��!�5>�]�X2�2 6� A/p<��= <5�<�B�I&7�1+1a��$2� kuny�Kunyan<3A.*R6�"�$ v5d ow -�#l0Z�e4-�R�3�2�G0:_�P�$P� u�R0!�Jau�Heau�#\.�A� �,  Trebo_On�V >Umzd}v��*d o� Ex7e �U�NonuniAy5�A�� ��s&�4�\�42�-.4gu� @9\K1l �:� A No�YP�Qrtye��of ��? �PN� �M�2��a�Z.�h@;�)\ H %n�h� Sin�F>MLE%.ISu' an ��rmediatz8laa\� 4 %D��a�Dp�HK�Cn, �$bc#6� :~l 3} Z  , ��HBayes�a:��97 1C2���78�:�nuytsE �y�Y�*\ Fess A Pe�ed kelih' �.� M�%m��K,�B� Q---Smo�d Max`8Ld�! ^� Reso�;6�h/\��{2�7104�'6�fo�?A.�>V8A grab%VA�R�GeuE.յ,E9�(�Bda���ar���1r1t�(ͱ.B9 189�v:�A abfo� �Ab�A2���Iaedu� A�.�o AT� ariz�0rRS�6� for�?O \��,A=� ical�Lde%�seudosl] hods��86rr59 a@�9yQ"�9az�9as��9 2�9}� >�^%;6�math} 7 Wolfr�H%���A� a�N (4thM ion)}, z�9�6V�E�z�%i[ ocee�A'E�1�kNOhop�RF�b�Civity "# R_JY��ribP``R�4Isotope (Heavy/F) A�G$erators,''qs�� . %PU D-D8$ (RIA) Faci�P� '' %# fordq�.6C�#,<$!�l�Unia2�P}pkP1�hiemj��-a�XXa|&�4 LinaxBf $},�G SLAC-R-56@R<000, p.\ 331--33�%``SC Dr�V�ac�ga% 5N��Eh LA-13782-C, LANL, Los Alam%E�Mexico,�0 =�IN�HWu4p�$\A�{�9thGY  S�d] 5} �45--351!��gQgZ}/R rimm�``2�ngA�kit�GatBh} d3.�U�Zi���KA}p(Facco�Me_g�/De"AJ`a 161 MHz, $\beta = 0.16$6mngAr <.�)naK�G Stee�& EARIA,''wsB�``��o�A�0LNL Bulk Niob�7Low B�QuN~s��E�KB./& V. Zvi� tsev�I�203--20H %``>�-,qium- �?High-)�$ :c %Z%m!A ALPI�a��!$� I`-7PiscatawH)a�J�Gy443.�KC.6�/3I�1�BJS cle 2o���849--8i�``Un BeamYP%aJ 1 %:j �tKD.�f�J�� t�6�>�1095--10(6E�r�)8 of beam-sq0�# low-veloc_A�i��ng %qi-wave c+ieA�.�E}, N. O�X umov]K. �e,�\ �` . ST �. !zs}�+ 1101�2"%`!��%``3D �K�s�A�Multiple=:�cT&qkin%:� %�yfor�2''2�F} QGorelт�XXI� 2002�/67--369N�!bv�5�D58�_.�zDM. Dirac, \textit{*�ofA�ntum ��s,}�<ed.�ha�6.FW50} N;L. Fol��1�5$. Wouthuys�t/ Rev., }%  bf{7�29,0 56BHS93dES \"{o}� Z >$it{SitzungX0. uss�-p X . Kl.} 4bf{z�S (1936sB84} !4OIbrut� Zanghi=?��/}.\52}% _ �:2 BB81>`X.�ckR/^D23 _454%18e5�A^�/ . Ar J1(Fou�4�9 1863NLH9!|D�9stenes�VM��av6VRV93} a�A. RodriJJ�5J. Vaz ��%Y� % B3�62 �96�R:} YuE�Ryl 2Is �E� tcl*,site? (Avail  atP%6�f�1$ics/0410046�MA67} � L. A�#.u6fre(#4 S}. �`#� New-Yorkaq67L( 75-6�BSeF�(ut. Zs.)� }%�$bf{63,} 80)33Mmuy6�V295%�:S5M�Slrf+VT$it{Atombaui�p�MJ M#�Pf�Q$�R:1~R.$�Rurl^�url#1{e~tt!O%8{URL Ip�/mand{!\�< }[2]{#2} B!eprint []{S'*.*[{2� {Aparicio�2 Chabrier}�'4)}]{a 94�X nfo{�2}�5�{J.}~�1|[}} 2 and}A,�*fOG>O�},.>j�g}{\prey�^0volume}{50}},�up�P}{4948�(0year}{�M2x4>8�%8Ok�D!88!8c-J98�8j��5P�8A>8��88Z81Z88r8�%81E}\0!8pot%J00�8j��8j��p62N8 8554N8lr8 Saumd=6 1992!6s9�vUD> W����aj�46N2208R2��2et~al.Mb6� �,5Q!�W�Or;Xie}}]-^��b^Yz��V|Bz �1P�CX>&% �=�t� ! u&/�1j�1R�3� B��Grabosk�-)� 1969:�$,� wood!�$and Rogers!�`G6�_f�H>_:`^�~J: *$ {Ha�@2�~9FR�:�N�\prn�8!� P%�+ 210}B�!or�F#��)q� 1977:�$, 1L�and#5 Horn!�s J77�BMb9d�V�n�%�5f��BPvan ��A �uV \apj*� !�35q�81�93AF�77r�s�%oLifchitz�8��Pau�L> V�YEBM�)1 emph9$title}{Cou*^$ore��M_ 8`5\tis�����s,�< 1, 3$^{\rm rd}$�}.��x�A}{"^ �.pI 8v� Week5*��71{"� {a}}:,/qtOdlѫ�ee)wR71a�'B� ]-e�I�Q��$���y$jcpj�54�.# 5237Z$1}:w�!teB� %'.�.�b�b�������R� 5422��!wj� Kang=�85:W qT e, Rp]  �zkang85��B�U�NCB�e��T>9R9e0��FVK. �}8R� 41Z� 85r�Ve4l!��cs��7� v7�� B� S֝J5i>49)pr� R�939Z�v� Mansoori]�71:�$X"rnahan!�Sta�,g� Le��~JrA�m U7Z�f Bu m�N>C ��>K>>��� BX=!25 9�ΐ152^� 1rGrundk;E�sersonyg �Bk Z�B��Z754�  bf&� � 2��.�p�269.� q z( Aziz�NSlama%691Faziz9��R>lQ�0M>K �Z-zd9!'Y�-%804Z�9vdCep�a� Part�)Ae86!/c 86�B\�7Bi��:8V:20V�86r�$Le~Toullec��8>�&A�Loubey ^and P�Haux��let M8�� B�e:V�P>���GB,��JFprbj� 4R�236Z�8v� Nell�7| 84:0 ", Holm�� �3in�WG14no, Ro�D!�Young!�nY��VqW>q q��B ��<B)Trג=B�- �=B�!?�_BW-�b\lj\53���>12^ 8v HummeMi�C� 8h8�B� V�6BM�^0apjj0�.�-17*F��Br5�eG&#7"���B� W�1B��^2v� 4Rf51^�z�Wi++*W2:�!, Kelle�V� Paquj��wD�' B�\:V�B��Q>�� BP�b�nv�يM�113^vv� �wsk.� 8>�%�Halen&M and Madej!��H8��B>E`��B� �ڠBO ���&7 ze1R�75^� v�Sei��y49> ", Arndt �Neft!�sA9� B Y��S>��ڏB�Kr �Z�zE!R�53A�N�95}n�W+Nn"3�wa{U*VUB� Jf�j�VV 74Z�3v Kirke) 33��k 33�) B7N��RrVk 1933r����"�"��!�LJ (N?)j�51:��607N 9v�Eb邙&88:Z #, F\"�Me; R w�R��HesZe N�� B� f:�VB ��?B| ��uB�),.��P�a Aj�1�%.?1�5R8vm "�$1��/:�$6"!�G�?%�"�$2��B�`��n?�V�E �2d5�z6R� 3641RE !mrjSal���!�s 6��BN^�ar� 13RE6+"N�6vV5��FHQE9�H�E5�a\. Plasm.�,�^bf J^ 4156RBvu u]�Nzz%aY &!w%�l B �:�V8�Y>Y H.~M�.�#�2d5�A�n�!99��.�71Z;t N�4 � f>.15} %�*�j0CMS:TDR} CMS � abor%/, TDR�!�,B(7INC#772Sinor�� P.~N ^~Braggi`MH.~Lev�d���z<A� B8, no. ��G*3) 56:>{�pley-ramo�E~ƒ�rJ .6 Z:38)�{,5 \\ S.~Ramo���nIRE 27�7$9) 584. %QW.,&�� to C�=�eIf�ed by a Y�=Point͋29jG�� s �kG 38),�`635-6. % �v~p1� MoI> %J�>IRE e2�V 39),� -585.*0rora} N~.D.~A , J~.R.~Hp�Lr, D~.J~Roulston\\ %~�hS�mo�HAainQ� as aAG H7� once��>*����{ns.��nED-�<292Ax6�~caughey�=.~C aR.~F.~4u !'.�J-455 (Dec.~1967)2�2.�ErY}4_two_peak} V.~ Mp~�^@itskaya, Z.~Li, %MGorigi��Tle > ee�ic ��T8"\f!7heavilyJ.�sv�q.\�p�E��7� �9552�$mswartz_sivPtio�y M.~S, %��#�_��,��116�2:��!a��88-91��11F�3) S.� vchiR�a_iee� V.~C BOS12%�[H!�I&q �^P6 �Darison1E~ �MekiU� <1Tc ��ce �S�|*R 8-21�V^|  S.} JOnV 143.JV �temXmBp{a~Kr, !*indrod~Mandic�p~Mikuz e�8M.~Zavrtanik, %# rmiz�� �Bhvtr��t��_ i>�b�w] F\ ��� Q�476M� @� 1 January� 2� 645-65ڝe�I�bm� RA�N� �@f� 4��<�<�<�<�<�<�<�<�< Ben-Jacob"� 2000:�%ė0} i�� hBeCoLe�C7B�\��I.:�<C�?�%B�����"�Adv�j�4�Jj395Fi!kr)Harsh�' MatsuyamaZ�= HaMa�!�VRJ� Z�9!B>+�Z<} J8��'b*9�9�p }{8631FL 1994rLBudre`� Berg%G5� BuBe�� E.~O!�.� U�G H.~CBQ�ZEi|j}37R� ^�I�-J3u��199>� %�$Czir{\'o}k�|cs��(and Gutnickh�0CziViGu9�!�5^5.�V;B��:�V@B*V%ڱD>�5R2���pvz23@. mg18Vfv�!Bre�^.3>] #�3vitov}AuL]{BrLeBu�\A M.~PBC ��� L.~S>@�tov@2W��V��&-P:ܝ�5�~� J.9^'/7R�16e��1&/z�AY�5��M6�&!���shiTj and Q�](MaVi0���RB`*�ڲf�-�%W5�aU� Ej�6Zs03191V vYA�ͿReynoldr*�0 LeRe�?)b�E�U�a��EFT �j�-:L�Zn>��.��240iF�v<Kf\E�)H���# KeLeZ=TV�"�.� W��:� ��=nw4Z�48�JJ93r5 Nagano%-�,Na��B�& F��~8 0J482�!�e��Ru�l�199>�1 ", NicolzS��s=_��˓and Loom'8$]{RaNiSaLe�s�VTW.-B-B r:,V?BK��;ؒ@bI���J~F>\1Q!u5GN��4Z�124R\U4vT2B�{eaNlV2F� $���aulaz,�_$cassi{\'e}! Deneubܑ oThFoDe�eF u��B!��?V>�5f�D2 9�V� J.-L .e."I^e�N Er? 57w A�R 4568RN8rMa%&ux�=�:= $A�1�t�3!�MaDeD�<A.-B0d9s�na%�5��C /jUB�>D��!�=5�'o��hava�^� 5ZI10�R>�!~r�Flierr� "�F\"��um��)�Ol�;(}]{FlGrLeOl��Bh f9k%V�F� ��@S.~B��q2�.V��-!'F�J.;" or. Ţ`^�19� Em�39ΡParrish�j�<�-Keshet�9� PaEd�� J.~KA�.� a�� B�@B�ZPj4 2�:.�-H9RC+z� �.�BB+)j�scido|a�]� ]{PaViGr0�B+rl\!�j0 S.~V>�V �9U��.�2���E��`.�Z��)20j1J�29J� �r�H�ng% Moln{\'a}y1� HeMo��Bs X��P>&�Z=�]^0 4282R�v�2����,He��f-2�URev7���j�7^� 0�ZJ�� p J� OkubV�� OkLea� ~]Bl S�n��R�KDiffu�wandE�׀al�$;�:� rn PʽRs^�K��.X add�w}{NewK�Z.!( ,})ݴe_�}{2nd}��n�Mikhai�`�Calenbuh'U)5 MiCa��F�^}�v.�� !c�-V�B� �I�R�$From Cells-%Socie$�Y�*_Mr�� o�5{v �պJ�. ",.� cu �%� Shoc;}]{ViCz�Sh�L�WV�Bn&�-�1V@F��?�f2fO>5Q!tɵ'�~�7�2.��12ZvAlb��1Al��1EJv I�� ��J�212V� 6r&YFE�i� �7���r�%Һf �+2"h�jC28<J;1JT �>�6&�V��:� "�� ppel�: ��h�QLeRaCo�\fY.�V��O2�%�jb.�2��n�b171N�!mr�Niw*!Ni�!H�� �5GZ���7Az9[��3R� v� ��…� Ni96��S��r�eWB�ZJv� Schienbei,Gru����Gr��B: Y֠ B� �Z���h� b ^�ZS8JBmr��� �!B�"Gr���B�B��n:�@.{m[418V\��j "� 1�"}]{He�"� z� R Verkehrs�fk�� 2��  y� �~+weitzer�!S6h&�>�� Tilch $ EbTi��FB� `:M^�:# ���B>O ��� ^� 5044R�v\ �.� >� #;�1��an=�Eb!oTi��B� `�����g�9nV��� BioS��j ^�)N rMErd�55�@ : #,uE oki^%����Uky-Ge�g}]{Er%�i!���U>� x������2�u�>bhBF"!HF���5�oj1^30J�!ؾ >%-�2 and.�shchenko1�An�! ��^�%V2���VJ}An�V���6Z�06110j%j�"%� Meink\"oh$V7MiM�AJ�_�A��QBY�}~x!�6_J�"aSt"-�D�nyQ��8=8o΁ Eb�VYB� P\"oschel%+�. U9%��+ 33˼45}_3! J-Ton�QTu&M ToTu�K B�INֈ Y>�T>�!N|�543�5 Csah�-eT&c%;eTCsaCziZ %sfxZ>�]�Br�f��]4Z�30V� � j��%93Er��]�V1� U'Np�r.�m$1^�_�%5"�p {�r www.� [.�� manuݏ\_a�$.php?10536���(e��XU���i�r�b�)2j�$�?���Er�C�?6i�e{K}ollekY {B}ewo�^�Logos6k��200v�e"� � :� &A�,Baraba{\'s}i ��.BaV�) �QV�A.�&ŗ�B.�&� �1 B_���um�}.� ~.�c.J�%20V�v9 "! �,Za���-�# MiZa���^E��9VSBy ��Bn�6^�,57V]3v?Rayleigh�(4�Ra4��T~WJ3N �R��@T'���S�|�3 vol. v���"I R� DL].k�:z �� �45zdI+J� @l�#I:#&A���]$��"� �V�j�E�2.�VO�G�� �4.|�02111J�1!vD���Er �<� :�*+ �:����J �@�on>�I�T"�Alex���on UnifU� Them�@�A&a1 �� B� Bar-Yamf) �" eus ���uGuf"��!� �c��.�ix�B L-�1��161� N�@ _ f�@����@��@��@��@��@��@��@��@��@��*�U>g(Kim, McDona�_Stupak�9]{kimPRLE��,�_V/KiuE�iKi�l- K.~T>Q��`>�%ij�GY"��.:��Af� ?^�/,�m�3Rv%An�[ Jack/� }]{j � �z J.~D>>QR�ClM3(E^Io\�2�U*s&W�.;�#� , NY t>�� =0��ion}{3r�'IaJ� Feyn��347>H? #U6igh$� dCS��� f E_w�QRJ= b-Q�V  R.~B>�L �Au&�� Fd ��V�Z����f�r�AddSI-WesleV�Reaˆ , MA v1��%Yn�Brabe �1`usz&:%4brabecRMP2000}D \bibinfo{author}{4fnamefont{T.}~ Brabec}} 2and} jMF>M Krausz}},.<�journal}{Rev. Mod. Phys.} \textbf�g$volume}{72:D0pages}{545} (�/4year}{2000}). �$tem[{\cite�telenov and Nazarkin}(1994)}]{b JOSAA} HfC E.~M�bib>c�G A.~V>Q�ZLDJ. Opt. Soc. Am. AjO11:G-O168FO%%Oxend{thebibliography} \beginB {99}9�8{Penrose_1959} ,~R. (�>): ``The Apparent Shape of a Relativistically Moving Sphere'', E�QM,.d0Nuovo~CimentoYB12M�168--181.cHickey�9} ,~FQ�7�: wo-DX sionBa .� Cube.V� 47} !S�/711--712e Burk�� 91}  �+aT$and Strode��@91E�`Classroom Exercises with �I�s Effect��5E�0) �912--912D0Howard_1995} <,~A., Kitchen,~L)�D�2��9�.5D Ray-Tracing: Simu��ngEIA#�{Techn�lReportY495/21}, DepartA/< of Computer Sci�� , Univers͌ Melb^ 0e, 13 August ��. \newline [\url{http://www.cs.mu.oz.au/publica��ls/tr_db/mu_95_21.ps.gz}] R fKf xx harvard� P{Anholt et~al.}{1984}  !PR, Andriamonje S~A, M�o@zoni E, Stoller C`litoris J~D, Meyerhof W~E� �(Osterheld A��,��6�Reed K A�95�.�AQ�2}� ~2693 0��d1�sw�3.�P,.� ~L, Scofi� J, W} lin B6�Ma)� �1B�.�H67}(17),~2272--2275Fjthe�� 47}{bet47A ��H~Ac47>c-7-339�34��6y]m2004}{B  ��HSt\"ohlker T, BanasAwLie�� D, Protic 0Beckert K, Be�P��Bojowald!84Bosch F, F\"orA�3Franzke�c$GumberidzeA*Hag��SH HoszowskaI Inde�o!�$Klepper O,atpge H~J, K\"onig S, Kozhuharov��a Xa<nilvTMohosc I, Orsic-Muthig�Nolden�Popp U,�j$ionovici A�Sierp�i!Spill�, tachura Z� eck M, Ta��ov�0Trassinelli MMWarczak{Wehrhan : Zieg�`E��4IDSpectrochimica Act�Part B} ^53F^irket.�9�rbcd�r B~B, Bri�J~Pa�arles!xDi� h D��Finlay�K,6� ]1��us :�Si=WAۍ�J� 47i�R2454--] 2�luma< 82}{ :8 lum K`8ͥDen�Matrix���AppEcDions} Plenum Press�� V�luA�l &J%Vmjs%V9hr!HJoh�VW>� Sapia' in J�2 ���48) 2615--262Fa!� �f   F.bAIP?feqa�ceedings�b295},~3B�randau�200AUkms  CB�{\"u}�7A, Shi W�thia�sa- Bart�?����m� eR knechtDKna�H\"un NPeidZ teihK! FA���Mokae P~H,�Sq�.6q� Ze��q.�.91}x~07320Fj reit!� 29}{bre29!Aeit G!�29i���-�34!�JPi�]�0}{bcid9R m�evallieE�6my�6�Ziocki\90z�  22��761�6B� Brown6b Ravenhall!51}{bar5a�+G~EZ/ D~E!05�� R� London, S� }�O�64�] 042507 (7B� �g��!s94 �% �?� ,2 1^� B���E�>�50}(1AJ47--25B� �2`-�AF 77}{caj77�R-�� 197Br =%16 �6� B� �]8!�js} K~T�F��\Q�66� 960--296R=2�A�ɨҏ~�� 1817R2B�$DereviankoR�!�(97}{daj97} .AR01�9n� 56}(��128�29B�h=� 8}{dsij986�# vukov I~Mj�$Plante D~RAS98}xB���445�46B� Desclaux! 75}{des75� ��c7; �� muni�49�31--�.�Diraca2�ir2� P~AN192éZoy2\͖4A117},~610--62Fjunford.g1}{dllba R~W, Liu�� Last 4Berrah-Mansour�� Vondrasek� Chur� A� څiCurtis L!#JM�� 44i�764--76Bj Eich.2\Ichihara2}%2b 2JV4 A;� ��6� 6| 05271B� [6� 19A� !;�>EShirai T%1�&2- E�212�-\Qe%qAN0 %:4 >3 W�M�R*�F��"v� San�go>� � �87}1  B{8�IDNucl. Instr. Meth.d � 24/2!�1B Jft Pot{ 0:c9�%�ics�r 19��1F� Fritzsc+�$:97c  SȱF � 1025BmWE�1!- Z:01:h&OJ. El�.�A�l��[t14-� ,~11F�zU�N :032�, Surzhy��: � {}�ei͹4in} G.~F Hanne L~Malegat6�$H~Schmidt-} 8{}cking, eds, `.?and>b(in Photonic ! s>b$' Vol. 697�  Z� ���FI � aspy1�!�} dɏTrappQ Highly Ch�0d Ions: Fundaal/ :0 Nova P�shers> Gran� 70}{gra� I~ɻmAdvA4�im1��74B�G&C��{gsbb #�B�\'{s} D�F� ~F,�  &�:n&+&MMa�o&eOr"x!K,*l2`Tasa8v :�Zou YE�.- �6~* in p�}>�HenningQ$ A} ��I" Inte;#< Accelerator Fac� for Bea�A5 iAntipras} GSI& �+:Tgsi.de/GSI-Future/cdr/>�Heully5�,1986}{hlll86�J�&�Indroth�Lundq�!:[L M{\aa}rtensson-Pell �86)JM� B: AtL$��U�� 799--28.5J�b�mn�l�6�j��86b �F�D 33}(6),~4426--442B";qf�  ehhT���B�*k4!<18F�e�6} 1996Ɗ-�F�`495B� &*��5}{ind� ���F_ 5�)�32--11F� Mf6 f�{ica%OF�. 7�!�3323--33F2Rk7 k7}F� Hyp "}108}(1-� 39--4FG�=� 2}{ibbc926j, Ɨp>� FrFp =. 68}�$ ~130�310>C�2�Moh (1}{iam�C6�F/A((b�63�5���1$!�[ �R�~{ ��.��'cta�  80��0n�9� 89}{ipm896 ,�eF:ar7�B�.'0S 3505--351j�� {isv 2� abaev V~M6�(Volotka A~VV{ &Q69�Q062506--R rhess���ET� S�Philips�(Kroeger R~A.|N\"nzL, Kurfe� Graham>� Gehrels N!n�FEEE �on ea"�!s  4< 14F&v�(88}{jbs88} W~R, &%6o>8n�37}-$~2�B�rY���jcp���" 6�:��F��05i� 2728�FTq�5a}{jps�>�x2dSaprist&,5a�<� $B~Bederson> H~Walters� Adv{$�'� �"ecular� �+� �ic� ~35 Addi# Wesley*� p.~25a�FI�.� }{jsJ �22�9�F%� ��_09�)0B�Kelly��(63}{kel63}  H� 6.^� 3��$684--�69B� Lamb6�R�r�u(50}{lar50} +WB�/ R~C�5! >� 79Ix549--5F� z(74}{lin74} �#197� R� �-z-S8�4�47B$^}�u�in2#/2wI�M:E  9Q� 1159! j+.G c:S lpslaOI, Per� 'Sf�$ab{ y+.`B�M116%19B�Q��t {lsa 2�f�.�%:}A�p-� 38M16!�FE�[s�*�$1P� SchneiderA)94} 2� a} >�$6B#ZD DA�.� ��- �EOctoberOB�p;�$:�%B�b2�'%$6�= DZ#.�!Pv2T'a\2},~408BA�u.� 89a}{mcib� �$"H!.� , de~Bi�L-" zi C6�!*� +&��>< �!y89�e�!�3d 372B� �2� $1978}{mam7.� B)� +i��^$^ 18A�F& aq;� mscb! R�n~VicI V,��".��9!.� Varga��=7* J��68B� ��9}{msid6=�069�l#�F��i*�#v�*j RT :8p �500BV Mau2�"6�gi�M!\"a�(A�!e�0 W2u2��~ 9xA��n5�39�"39J�z ��}{moh7� w#� ��Ann�(N.Y.) b8�5F�C.-*���ma�"0} -pZ1x���}�62}%}0� 1>� aY^�mps�U lunien G:�offL"*���?29� 22/ FC�6�t�#4(��6} &� 2P~H^6 w�F� � Mol� `24-�3e29B8.�'%���u�'�w. �4�bl�"Dissert,>�.�4kfurt, to be p�d>�Pa�=�4}{pmi'!F�(rques�2].e � Europl�� �K26x4`64Fz Q2eA%�5}{pa� (fB 51-�A�j 111� 3B�<*1 �}  !DQT�%�* �j*_*rch�*G, Hami)r�)6*,LudziejewskiO Ma X6*���ɳ IEEE�- ransT7s J�4�710�4.� Saathav�3}{skeh� !XG, Karpuk S, EisenbarthX*Huber! rohn 0Mu�oz~Horta�(Reinhardt  Schwalm!J Wolf>GwinnSJ 3 �aW� B��&19�904F�$Santo. ��spi�� e&U�6{B�3Eur�� J. DU�3� 43--F�&2E�8}{sap �:Z) fR�M*<�7e$�7Bse.�4}{spA�4!�n�chucki K6�*���B����9�"022113�9>hS�"Q}� M��2! *&2�v�"R1~EF"��i� 7 (5B"&"G 5'1  M�Levine M�ad�8R.~Hen� C~L�,&� .��ar�/�-9�*. �"#-8B��o�*�72}1� 'HF tzDevaillef!Kalata- Sohv7�Jones: Wega�H�(7Fs.w 29B�a�/�I#sO1� J�lkacem� -enf�0L, Clay�(N, FeynbergcGould�Kon;uNV,!�y6Misawa�pMow�:2� Prior M!�N�d>n K'�>4�:143B�Sch�fO �M 1999%�ae!�(H�u, "S$>�Kr\"am�;>+nrinz H�'Rymuza` Sarkadi!&��[Swiat>X"�/�99y�0ica Scripta T�LW46BLS���0}{shaQ"  V%gT Soviet%n cs J�7al _��6'(6F�Spind�$9e7!e 1 IBe~:,2 c.7�R`42},~83Bu S-��#}  ME��.&�� e26���߭s�# 6�#�� 53�3Fp0=�>�oe �2�R3&�"S,:36��A�6� ,:z225 S& #S�2> U�. a�]�M5 T110},~38BV3!�93!�RG&�!AF��0aVLewoczko�/1*, ie&�3&o36�6��R�B �20�%2F�J�1NS� (�0y0 GallusF�Menzel� &3 p5� &=,*�'�j2�>� ��" .�4r��VF�ݔF2JL9�q$19�.*�(T>LivAton A.�j�s�sZR D1��12B� ��5]��<>�:��z0U~"�, G_C el H�Sc�2e�zN< sham��R s*b�9 > 1�%�� a孋��1~09F 9�= 86 8> B~ eich�u��"",�� :PR ��,�=r *�7 ,z�%  N � 204B�J E= :��B&2��4t&�anescu Ou��-=;H">926EKr"��9!]�YJ�2�iZ92:� 8' 983--986B� u��8�uc8�C(198�bU�22 348--36FA�Q��-a}{/PRL: +AA��*>�6S=�X*2k5 �R]�+^ 1530F���AF�:t+:�z�2��[28��21F�z.�2b.>Frir>z�2�&:kE�lRJ%J��3�37��3.�:03b}�?:2,)�1) �. �B2039FMNI3.I�,'>�2i\_�*�a�3)Q2� �A6��02271FZ N�46?�'�4)H2�Q�(p.~submitteBG{}46C�(N |:�*x %34)3R/ �A+intB�wi���35}{swi3 D03�p(32&3�8r15g 6F�5�.�}{,d % /��T>Z S.�>"� 2"!�"�?K� 6u*m -D �: B�Toleiki&,�{tm�-!S�?Berderd?E� �@ �#Czanta "U~W�6^ .jFf �@�G�>A!� #[:�2:to!�"� >� j�-��*�507--5>� Uehl�-1E�uehA�  E�U�՘Mx��F/8Van&U�!} C�Kraus�AF, Datz!�(Grafstr\"om� Knud?BH!?"� >$Schuch R~He�f�62B_Yerokhi&�1�yabV[Artemyev��N�Z L691--6F��q�� �9}����A�EScrQ80B� 95--4��E {yas��JW=N , Sysak M*9Z7Qbtsov O:i�0�F*� 85}W>46b/47F�%�1_v>Ia}}{yi�3a>h.*:�� A �r L �5c��2I20)<3Bd f�b�b��b�8JA >� ��F07� RtS�fjK15} \expB(fter\ifx\cs�T natexlabV (\relax\def\ #1{#1}\fibG*�T>J K!�N"�VbO"�P.�UVP."�PurlVGurl#1{�Stt!4r5 urlprefix>M%2{URL I8providecommand{!V�V }[2]{#2} B!ep&  []{S'�VJWVahala}(a��V ~�VK�Q:X ;},="�WNature} %)N�W4242:�V83�O�&�W3�VN�ernoo"�4�W8)2�{ # , Il�(ko, Mabuchi�reed,� Kimble}}]2� D.~WB �2�aR�Y V.~S>>��?H\V}y{ Պ;EJ�S% =�>/Zand)�A�Z��S)-81M,&CZU!Opt�(�X ers}:UN)23}.AM(2�R��yZy).b($BraginskiiјA+0:+&, 1�IGo�RtAA") ��b�B>�?.CbA�(5x�� M.~L>�2�N�`Uspekhi Fizicheskikh Naukj�160N�15hTF�0n�R&�H��1:� ", R�*: ��:J�Vi�5� ي=Bw% �9L>�Manin1��Amirf-]V>K6}NAALed�.)fR792��)86V.^1niA#r�'�:j #4, Fattal, Vuck�N , So�SIhYamamotoAd 4�0C>09.+V)D>; ��:J>:ъ<GJ�->21�V�Y>�9FN-�n1R594F�^!�nEM�746> PURCELL��P>�EM1e7�'�3�iewj�6R�681F� 1946n� Akah*vA�3:� #(, Asano, So�AaLaodaA� "� B�9.�VB�b��9BR�ng��S>�)֘252���94V�3})��not&c,37KY NATURE}f�Gayra":.�9:� ", �Z$, Lemaitre� puis2>Pelouard!� 9��B>8 8.:V��A>w؊yB�D% �:�=�=J� �2�D9Nw�<R�190`_F� 9rN52;BM"1;pp�,�$lla�\ and []{ ,�] D.~K># ;.#V`TJ�K��ASJ� �anUg5�1 %Υ�V�oW 81��7�fF 42�ew�i2V ro Srinivasa"��24:O& , Barclay�!rs�W Pai�D�D. �r}6�h<�� P.~E>) ��>M>|B ��JO>N5R�rXiv} N�h4n�Q�"��6$, Y�B-%�)�Q]-���j��e�OJ�:cu^��N�:� ��9R�$art. no.} >�!�n�9�.�>� &f�$���%��8��r�O��7q�EȭV166V�rX WeinY@}(169_ � dV1Bp;�M emph"LD{title}{Open ResonSJ9J (Waveguides}.sn5r}{5iol��J�Zadd{B�.er,�aorado�bi ��69r� Datsyuk}� 2p ~VJMm<.��A>3 B-?N�5ic)Las#(hemistr^�n5�Bl18J� %)n� Remp��.:�!$, Thompson�����Lalezar�)�9G>� 7.4V�RJl��??%4u�"?%���R>�9 NeK5�O6�fd1a��Am�36�k>�99)�N�b@o}kga(Ttem{BaketalOmo} Bak, P�h. Chr�Dnsen, L.�hon; T. ScanlA %UnifFsca� .Ne�6 quakes, ���*�0. 88, 178501 *2`4�vQ�0 4 A., % Local da ibut�_�(rate fluctu�9�Da u6� %law>� - �� 035lQ�*$ E. 6803(3�6t 2), ), �!�,Mega} M. S.  !E Alleg� 8Grigolini, V. L�a%XPT4 ella, A. emsarda�HS. Vinciguerra, %Po�f� time: of l�Q2� {\i12.�,, 90}, 18850F�0network} Abe,�a�T. Suzuki, %Scale-free ,}.� w:�:, *4!H81-586|{01KpaczuskiA�iesi,!W� M. P , J�3m�5�shocks �!�- E,�#, 06610j�2v��Ulex1 ���QR at 0k4arxiv.org/abs/� /0408018 �a�13.� !��S!'8precursor motife9�, pre� R�cond-mat�619.�Relm}�# orle�. , D.%�Ge�b$E<Wieme� D. Jack�FE�%T likelihood model test�U�F(4PisGol} V.F. Pa4er\!,T.V. Golubeva5K�$ of stableaA%seismic�lysI�!�u!> al S%ology^4Geodynamics, 4aE27-137,�06.Ogata} , Y��SVmt r:� occur�c %�residsanalysi 14point processeQ�J. �ue,. Assoc., 8�r9-2�9qmKK�Kagan�Y�nL. scoffm4J.�A�a:Hs., 86}, 2853 (19812�8HS02} Helmstett!�A YD()rna�ub-cri�J%Zsuperregim�Jepiyk)��n]�F�F�10 B10) 22!�,doi:10.1029/�.JB001580J�Forexp��*�m@ explained by cas;l�$ triggered]}bg 108 �!n 457 �3�2409 01e2� Athreya} , K.B)�Pa�g)L. }Cl�h�gAv!i rn b�uh�[Uk } (S�8g!� mE�72 Sank.v aray�r�<6, G., şMf:h� its � m��qo (Wiley,2892etasdif��DiffusioFvepmFr%�Yf %a�$)� , Omori's�I Xgeneralized continuous-�Jgom walk%Ylq���%sRe� E�"60a\061104%�2.THOS036�~vrG. Ouill� 6jAre.&� ) Californii��s d)ng?�NQ8E� 83, F�503�2�Sa�vm u. ,� �!�1%�2� Anomalousz ��of OffsE�0G%�  N|8��YZ�-�-�-9-=~V� 111142� SS99.�RSRenorm��i of.�.�i�M���1����-�t��X24rus�[orshkoE�� Kossobo�_!�A��8loviev, Recognie�6�$prone areaI�%5NonRvar i ({!�lithospe,f=�predi"}}�8I. Keilis-Borok/ A..��_..�H�.(lberg) 239-X�' sta[}.4 , %D*��increU_s tic 9 cause�����a�-�p 1p 71-181%�2; Zolo1} tar�mV.7 !�Strun�$B.M��]- �.\� aѷ2of{ defect�*�@%�id� /x$}, 481-482�7E51S�2F�One-d*{zS� .ms}, Ame�ca�cS��P�*�~ R.I.w82� Sorbook1.PD" � 23v� c!yxChaos,�:c=a,, Self-organ.�v Diso�2:�a cept�Too2nd ed]��li� Synerge�(,]�, �6HS03nB�%�2j%ImzV!�direct'in �2� A�a��  l>&> '�1.J 30 (11)>l 3GL01767Jyou!-}�" �2�Ma�L0ude-Dependent� �8: EmpirV Stud� �Zy, B���V�407208.Felzer�2} u $ R., T. W.Xu,�nE.\rcrombie�Ek�EemP J9 Rice %T3 ��of%�K24 $M_W$ 7.1 Hec�EM_G�W by2� =2=3 Lan�G9�>, F ((B9), 2190,>�E 091�22� elm�@� 04} *"� Y.�Z��D. 3, 2� �����t�Kf� H=M�]�>�}, "�8���,xxx.lanl.gov>� 70182�C`{leE3}a� sole!�$, M. Murru)�A��Lombard� Refi�c.�clufwAe��z>�!�8}4, 2468B�2812� 2�Zhuang�} , J)��!ND. Vere-�H %A�z�=g�fe�/s us(stocha rec� u�Z�( 109}, B053�:�879)�.v$GK74} Gard !,K�P.�� ��� a'��$Southern %&1 ,]�.T  remov�/Poi�Xian� Bull.J�#c. ɸ6C363-136�Y�#Rea} Rea7Ner3�S!8d-�Y mok�(U���.�yj 9-82^g 5479-5495/8�8�$DF91} Davi��a�I�(C. Frohlich�$ingle-linkQ&�2� 2�: DecayR�!r� vari� f�96}(BW6335635�[kVS�qfaa�f�0so;14} A.\ So�YK, "\"{U}�Opdie Fortpflanzung des Lichtes�q$disperdierŬ Medien,"�T\ (\ (Lepzig) �N4E$77-202 (19: br�L.\ Br�u� ����6240V�60} L.~�� �� pag%ŅC$Group Velo|} (�m6�602SLou;97} K.~E.~Oughstu P��~ShN<> E�k magnC  Puls6� in Causal�W.�& -VerlagE:rlin, 19:�ac�A.~Ciark=| , "AsymptO}"�: r9of a siga�� ��te rise� in aM=�sive, lossy medium," Arch.~Mech.\M6�&,5, 877-892, �6�ks;96�~K� � I.~Saz }:�\�!/i�O�� 1�E�$Fluids}. K ��196*!8}BFr%y d� R�n space2 for )�5�+UDin=5 . eI�F 1, 33-46)6(<>�QfV"�R.@<^R.$�RNd< �f< "H<>�%8�fn�(Kadomtsev}(�'}];y!�C#VN$B.096�+S}eDBjhS{Sov.G Plasma� n�#:H�#8J�'�}e<{ >�H2 e�98� �M2f78%6� =:��A� . S� �Q2 #, �= Ross�- �a|V A.~F54 :$V@J� :c�1�[&a�!�f��=6� �V�G�  Bƒ7(F�8�1)=J?Wh� �Ca�7::(!enticello�$Rosenbluth>Waddell!�07� vRJ�<��D�:]M��C M.~N>C�C2��PVE�4�2F�:5,!Iin :v+�z+BedaS���Con�on.�*��rolledM�FaTesearch �gad(Gt yC 76}.8*�+� rnal�l E�y Agency�9��+Vienna.�+�=77�6 vol.e'eMי1Np.Q�z 569}*G >cParai�"Pereverz�_80�r �P�^sAB�< =}I2�Gl,�:����ƺ���.�-3�JE?)JPfeiffer�85%< 8GFv�W>Z<^�N�}I�j� 9*m� �67R\+8v�Nishikaw�) Wakatani} E- ).f�K>�C�6BJ4�I1eN�/*� Z�"$�UF�OJn� Wang� Bh�>charje�E3 �mz4X><=�7B�9��)sn�:AM�17RU=9v�Por�W& 9 1996:�$7}U!�a����{'�i�V�B��<:�V>B>@B ��* ��ex9�*� ��.�B�#^x138�Q-�21Z�/{2)PJ&DahlburiKarpen�1I���N ?�J.~B ? �Z>�j100:F1G34V z Ishiy]A:!, Azum: K��6C!02��B% 9:�V�B��QN��{2A��aVMB��a�?Y�&&i%j�8�AF(2�&2.yI!qr�eNit{et ��A�86{"N {a}}#EdR�s86��A� &- ? 5P>|�)5�3J10F�p6�j� Buratt2�>�> #!�$GiovannozzI� TudiscF '�aU VLB9D ;:+V=B�H�A5�A�Y�VSO-�5���Y���45q~.�LJ����bI�Taylor��$7Y� ;)=5��� Z 3N1O>��j�>��.c)!Campbel�5�V'D8 9&@�(�(108J�@>)�j)Kim)�Ki/�z SJG.� u.E  �j�Ayo��12��F"@�n�N��Bda;~��>� ;���63�F0N�=1%N�f� "X%�5(Weibel} E.S�, ,|�&����$� ���, 83-82#Neu� }�  H. WrightF\T12�41963), 1489-15#���j} T�5 VO. BuneB� W��196�!A1300-2�$Sudan} RZLu[�r�qa� .�8d�4�. `�Q 1966�56-162�"Wurtele}�"C�� J.A�: vies�'Zh�J%� 1,B.:X ers wY82), 73lp5)GK} I.B(r�?wM. ��,,M.D. KruskalFme1=G195�546-550�\{Taniuti!� %5!� ashi >5.� 2II6�'454-4.k� Shukla} B�ia�$`P.K. �IK-�F .f 3�e1), L1786� OonoZ"Y.-�N�7d�nAY. &Z&E 5?, 376 �2',zenov} S.I. ~ite2+ary2�)6$s} (World  tifi�Oingapo�J�Fky,.lG5�m� ])�ΫG, �a1}Manak ��- ,�'ˋEkw$>-4tal'noi i Teor #XSoi dSki g��197a�$505-516, [�#English3�O�9- vietms JETP I0��y�(8-253].V�%m v�STW76  I+C. Stwal6 \prl {7/628az76); %5.TIE֙A}+Tie�(a,A�J.�(haa�:H. T. eoofv $\pra\vol{4h 4114h9�1�REGt ?�=egal, Ticknora�(Boh�Q�,. J`$gi.(e (London)~ r2&47�6qSTR qK.�`W뎅�B3=rtridg�A(R. G. Hulet �!>c9[0080406 f.?CUB fJ. Cubiz's \,*,:E24<4 E.�GRE E��i�)C.=(a�v �426}, 531.�JOC f!VJ��e�ce C302�310�.DZWI DM�-Zwierl�" �{!7}�%825Z�A4A�2�.J�] \�0!O3%O42O�\Z�6G12�wJGCHI GC�aUmT5.�j305a\1a\��..KIN BJ. Kin͗)(E�:�!*2 �.EBOU E$T. BourdelFD#0D)�6TIN�, M.~Tinkham��(Intro. to Se<on=% ivitz8 (McGraw-Hill,�� York�u752wTIM�iE. Ti* mans�/Furuy�A W. Milonn�pA.a�K*!��o5 AI�28!a2-`12HOLr� HollandZ?J� (M. F. Kokke��EQ�bChiofalYZ R. Walser� %Q y8��Ei�6{OHA �ch4E�A�iffw*!� K�( 1304-�228JAV)�� avan=�AnPpr]�Ae G6�CHWG0Chwede\'nczuk%�G\'or�rT. 7�ϙgP�CJulR� e-prH?A�@ 9192.�DAN� O nn�@�@Macki� K.-[6uomine%�)diǡ[21a�E�32�MA��0 Ri>!Z�q\ 0536�r!2XTIK)�ikhon A��A.��di,R�74��ѼPAZ JE�8zy,@Y.�NBE{9�a�E<9�6�(CRUTCH_FOOT�DThis means we will`�(a�fu)�account*�8atoms being ferZ�s/+&(VAR01} 9�V��Yurovsky ��3At n.Z(006361��12ISH)�,A. Ishkhanyaq]!�UI, 04361��.�A�2!��:��2�2��8�j22`BOH00`J�� "V 6a& 0534MM6E+���m&!�ani)�(unp duNrB��/~&�/: ��/. ���/n{�/�c14,� �m X) i�10& "�/&h/��Ɨ02�>�/:�,6."�-!�G�/ "�/.�o& 0��c�.wav�/��.os�/K.vj0 ��j0.)�bf{16}, Nz�5eU/7=�,7}6U/:.j-*r0 >r0 �+>r0v/i:r0 .r0..^/A�97M��0A��0��/�/�/*/cf;XbC.~Che�7C~Fried�A� F.~U�V: An ext�x_D�%method�Bd0ǀ\ Camb�  Phil�4�G�:y�%y599-611=yfm;73>~B.~Fel�m�,N.~MarcuvitzI� Radg5!Sca�G�Uofe�s}�e�' Ha& 0�/4ubh�&0 y]� ^&0� :&0 W.&0 �9 ��ac;�2�3:�CroxRF e re)Cen�Ionv J(/i6�/. To ac��nics !cTS0 ommu��L0( Quarterly,� 2:�48}.� s;64�3Mco!�%�I�(<~Stegun, Editors)J Hand(!�Mathe8G�GF�0�DNat.~BuSd(St�krds�4642 10.4%PNF�f�.�HB�>, m9&]9*�;z-D2 �DLet. 91%Dy 6 Davy�rjJR!�P� Dvy, %Fault growth O;!a�u�� al f%lengthn4"�E, �A�>�. 1�P0796� davy299y,�+9ome} {:�)a�4osed f�� al n�3!�[HA� ��< 5348, 5{ 6? KK}Y=YJ!2;Spa�1>�A9�s:G? two-po6 r�mE�P3.� A�N.�:, 62, 306L�%303-322�kagan942�, �eCeC NYD��oc.XC�� , 17992BFS9���R�R; Cor�;��R��RA�v2N�RJU1J papeG&�IEJ�un80CH3��Fo�IM�IM>�$,% "?�CM��@So:�i��>o��J*�J&�3j#'����LJ%&+K�MJ%ZNJ.{E �C04612NJP��QV�Q�Q"0 GoldB]}]69��&B(PZ�$ph�� j�!5^m672Rbe69� �b>� StilhOe�Ad Web�/%]82�� F.~H�]�A}2�%&T :�! �ZHgj>0�. &9 �R�"v�(Jo`��Ag�+�" ��"B|s ;��+H�6�"B&�f7M%^-602f$%$22�,R88vua�^*R69>eu "��$~Benedetti�a�Q��. *�9SX$5 ::V�& P.~G>�D�E^��i2�!^4]�&�%& 7^�393N�55!!mE��+��9&1ya.�9:~-.(!�0Broderix, Kre�Zippeliu�9.1�V�KJ�i.C9��^E^&5���>R>>�1jS!�-�j�A>L=!?55�:f]j�4Z�,44�%ZUv$Angelan2�,>�v$�HDi~Leonardo, RuoccogalaXSciortin�,92�V�B�d<ּ��A�+5� ے<B�S!�:B�3=Q!�5GU:�j/8R"-535�#>0��5qS�-2>-�Z6"6WCavagna,�,I6Gi7Mna��>�5Bn7<���t�tB� 㒂B=J'U��z9�VFB�w9Y!��=U=q�FA r@cer�i�/:< #�Ma�I -Mays%Paris$1 Verrocchi�f 3��VTJ�s >��B<.��BBh ��-B�1.!C5�.af4.42Z�82N�5!�:� Phy(T � icaD*\ n�t Vari\)��J�spe�� issu( A (AcRrdam) D�a�RD}, I.2-�'7)n>.� >n A�1�Deb� �5B �>#ن= -���< b< 41V� 5J;Ra:�2�FQ�!:3:5}] ��zf U�J�0A.�W dens�!�j�1RS7�R�3}:�*c!>f Boar"7Sukhor��%ER!Boo�nfo{e�>QA�֩�U3A~3bRP>R�}D[aXVN>S9�n D ^�l!^X>IN " q�..� "BDordr#�.� �T6Qe�$Torruealls9v �tB> <�oB�@��l�s)tYo.�#r}"�?�P.@5^� 6 �]Kivshb�Agrawal%[ � :\V!YJs @~`VQG.F�� �RAO�mal=Z*� =X�")�&^*�5Y�/Z*.5Y3r5Ass��.? > # , Peccian&�E�o #�^ ;-,��VlB��?���� C> ҅~���%��R�vg$n�A1Uq�t�gp�Z �v��.�>�x%�r-�-e�LucUmeton� 404n����V?�yV;B� �YjxB� De%� �2>.�V�B�1S2�UA�� 3Z� 7�6��u�4r�Hutsebau"�� 5:� %�!$�Nc%�elt`. Beeckq7a�oeytV<05*W V,BOEH���Bk��@B<Hߒ@Bh�1�;B,-U!�5�U:\josabjS ^& 1�3�[U:5r:� .l>X :� � �Ly �d6i3�1B�`��F1�ڮ�u9�prnG�6�E._� 025602(R)R�� 5,f�_?��b������v� rb�2!�y�-� 2231�6J�2�!zj� 5�.{>�%qm ��Rm5�������V]?4|�.� ��E2�:�6R/!�=��B=�#05sΜ��b�.QV��S2 Y�VQ�lV �5>�2��9$j>%P^�azZ�bŴ q] N�@�BD �ڪb=2P.�n�9�.X�� 1839 -J�2�!p2@)�ai:"�'51017��u J�LSkupin.�>� "� rg�7Pe��l3der�0 Meje�AYu>�spd1alm^ Wolf��dr{z�9=��.4�0VB :��BtB̒;U>� ��=B�L)2�=B�)f�<BT Yu�8K1Β?BaJI�<�>�A9�=BRQm?�Y*f.�n^ 7UJ� 0466Z�vH�n�%{n= ayou��iu5�,e�)s,�{lzΘecklum��sloffe�aux2�d���mj�B!�9�j>�25;�{�U�BWSchol]�j+�ZU�SM ��EQ?�?B8AsBzq�.T��6Z�P036607R� v� Sege"f��F2:�!, Cro�7n� Yariv�Fi��&LT�z�BL9�bB���@B[�B��.�V�B�5 V��"#4��b^�92R Zf�)xJ�6J.m>� W5ar�A� �C`�odoulide�"-�]50�\+Z>Lm��R���>B�* ؒ<D=_� �H: H"A54j���� PNASj�9� rM 5223A�JM v,Hennino2�>*$A Debaw�ul� Wp� ghem� )�"B1 <9d�R�@2���B�����5�M5�(Cryst. Liq. j�3o�F�U631R�v�YakJKk2|>� %�Z�{nyP� and "�]'� A.~I�.,g9�j�YJ)/�B2�9�V�J~X�O�5�B@nlin.PS/0411024v2V\vQLitvak�n5g:R " , Mironov!� Frai"Yu7Mski /6H!e�V�AJ�- =:�V?VJ� ��@ G.~M>  �@��."m#:2��5�RVbF^t.�2YR�GN�!�r�Ultan*hA&:� #!�chaelisA$�I;=�R�H /��EJ� >9�j?B�^M��?B� ��\ GJX9!3u5�4\ol} p. \bibin�fo{pages}{251} (\bibinfo{year}{2003}). \�tem[{\citenamefont{Fleischer et~al.}(3)Z%�, Segev, Efremidis, and Christodoulides}}]{[03} ��author}{�f�J.~W.} @}}qjB M.}~#?��; N.~K>}�BZand �j�D.~N.} �:B&, H8journal}{Nature<textbf%,$,volume}{422}.<M147�$Khaykovich.2:&!��Schreck, Ferrari, Bourdel, Cubizolles, Carr stinE($ SalomonA"T02�#L>�>9�%&VcF>@ Ē=G>= ��=T>=-,�=J>=9`�@ L.~D>�!��=YB}%�Q|U�aM�j�C>NU ASa�=u Science} b296:�q 290R 2rStA�6 > $�HPartridge, TruscottE� HuletA�.�� K.~E>�?:�V� G.~B>A��B A.~G>B�A2�9�V�RJS-!BF���f�417�E21�5��Conti.�>�!(, Peccianti%�$ Assanto!�#��B9:�VHB��?��B��V� \prlj�91�.�07390ΚSnyder]@Mitchell}(1997)}] 97�6AJY Z}I�24�� D.~J>"�Z:��7^�538F�!r�,Perez-Garcia.�0:�.(!�KonotopE� ?-RipollA�.00�t V.~M>$< �:(V� V.~V>E �@2��LVRJ%�-�::�N� ,Phys. Rev. E@^� 6R� 430V�0r� Bang.�>� 0, Krolikowski!�Wyller)�Rasmussek .��O>�89pe�V^W>:��AB� ��l)�E5�=!,F{\prnn6Z�046619F�20zo=#.�4:�'�!�D, Nikolov, Neshev,5��IEdmundsq Y.04����%��N N.~I>� �MD>�)&�<f�� _�� I.~R>P�)Z emph&�Dtitle}{Theory of s� l �!U&�8publisher}{Acad!� Press.fadd({London, UK z�1�1986})ݞ$edition}{2�edj�.|%�(Vekslerchik�}] &��� V>a.e%���BU.�6U�~�Z, 061804R�3r�Crasovan.�B2 $a�Kartash��Mihalach.orn�Kivsha��6C]k�� L.-C>��::V�YNo ��BB��?B�)#�<B�-W��‡�� �E�?V" v��M*� 1999:: ", Glotze� oole, Kob Plimpt /99��B� :��S.~B� ��@ P.~H>�Ւ>F�ob�'SP 6�9Na���Ģ#0�7�y 31076Z�99r�Likos��1��01����u:<:b�! (ics Reportsj&348:E �26V�1r�Weeks��Weitz�2��� EJ<�Q D.~A>� �fnU89:9-. 0957Z�v�QiV and Habib%10!1q��B R�.S>D �f+r� R| 7430N;20z~Dmitriev.�>�$,�� %\ Shigenari6&�~SJ�?:b�S>�� � n��} B��S��:a Bn 1d �?M�13�JStilling1Weberf 3A�8��FJ`AV� �,�V�TR�ZC \praj>2�Fu-; 2408N�198vICavagna��* �,A>� ;^�Europhy�/Lettern/53:H �4Z�v.Parisi�83{\natexlab{b}}A% 03a� B: ;:�uTarXiv:cond-mat/0301282N�{}:�j� Kaneko�r Tsud)���  Book��K>� <��I>M �I�RKCo8x Systems: Chao��BeyondeqRTSpre�8-Verlag, Berlin.]( �� Sciortino��JL %= ��T$ glia��#�C J� �-/VR�� *� PB����U�z 8a�7m� 3214N�!kr� Scopig=�20B#$�\Di~Leonardo, Ruocco, Bar]Tsutsu� ssard (Yannopoulos)� q�@ F <��R>z��AB� �< A.~QJ� %)�AB� -]�=B�B)� ��SJ� 2�A��9T J�025503R=v Griger2�1:� #wMa��-Mayor,l isiI� Verrocchi~ 3��T.F >��B�.��BB��<%���B�.!C��8^085502R�vu BoydsY Spectral��J.~B�E-mVT hebyFourier w MethodsfYDov�New YorkRQ1})2`��Grein*d# 1988B#bStrittma+ I� Honerkamp�� M88��B� ;-J�o.�B��BM����z J. Stat. s� ^�5Z�!95F�!��tend{thebibliography}�\beginB{} �)�tem{1} Ya. I. Frenkel', Zh. Eksp. Teor. Fiz. 6, 347 (1936.� 8{2} N. M. Zubar�Pis'maGTekh. A(25 (22), 79F 99) [Tech-X . 25, 920 "]*H {3BiR�116, 199D8 [JETP 89, 1078NZl4} W. Kinnersley, J. Fluid M�77, 22�762�45} D. G. Crowd :PNonlinear Sci. 9, 615 x.�86} L. P. Gor'koi�D%L�Chernikova, Dokl. Akad. Nauk SSSR 228, 82� [Sov1K 2$21, 328 (1�2K7} V. B.�ki�Yu�M� �]9}, 13�22�(Wijngaarden� A. Y6>� b�$63}, 01250� 0:j$Jentschura?} UA�4, G.W.F. Drake-2 Can.!�e n8!�10i6-Sh��� 6�%& LM&W7aW 3553!�952) UdemA� L.~Flower>�NPL r| CBTLMMvv)�6tT.W. H\"ansch, priv. communicaI 2N urrows} SA� 6� i!�em Las"] ��py-)1�R. Blatt:=��World��entific��992��Uaccuracy} QED uncertainty without nuclear radius effect $\sim$\,$6\times10^4$\,Hz, nucF1.[=7\t2= 3:K,�,2Cdue to �? �@ $�8:[. Fmw2\,S - 3trans�!,a� situ%�l is somewhat less favorable |a l�f$r relative�tribu!� ofR,R$_{\infty}$.��t�i E�$ linewidth.3FSFSMAm�� Proc�D�P6th Sy�on$ q� ndard�(Metrology, �ill�. J)['2),Major1968} F��, H DehmeltB�Q�70}, 91az682V4NIST1} R.~Drula��6w Appl��&�2�*365X86�X(2} D.~LarsoaKit:T�u2)� 57}, 70X6D @Raizenetal92} M.~ N�_� A 45.493]96c Waki[I.~vY��� 68},!�7J] Bowe6P.~ �Y��207%�:BHj#$kaerthesis�L.~ {\ae}[h� !(, Aarhus Un�$�A6�Harmo%d02} T.~ r�iewMmխ07}, 013415(8)g32{ Schi�+20jS@, C. L\"ammerzahl^�k!w053406 6hBarrettg M.D.~ ^� icalA�.� 2� 0423N 6lSchnitzl� H� NliTOptics)= {4� 7000%26� Froehlich�� Fr\"o:asubm.���2 � A}.�Tu�%}A7Tu 2q� *�3�M138e p ItaerR�JVy�>J"  1994%6� Winel� D.J.~:ain�͹�0, pp. 361-368. Blinov} B`4~ :O5Hv�^040304(RI�6�KarshwG.~  b�N�  f� .� Davi- R.C.~!�� �of�neu� Plasma� @(Imperial College� ss��12�Dubin� D.H.E.~�a0 T.M.~O'Neil,aT. Mod�II�71}, 87J�SX ery1980vL.~� D.~D�%. yeWi�6�. pA g2g20 i:�Walr 1987�]~Diedr.:� %E.~Peik�M.~ChuW.~Quin7�0G�N� �5> 2931!:P��$1992} M.G.��� , %J�G igan�8C.~Bergquist, WItanoX2/Z�J-�]-�,3�33�:1Drewese�8�~ -el-9�roders!3B�and J.S�c ngstZ� Z<8%�8�6� Lukiv ���F.~YeliM6Mr !>hau@(FV�8� 423V6C Berk��19!%y.� D.~M��J�-�f+��208:+>�~%�C.~6�=m\����3:RS:^V1~Korobg submitted��.i.��g� :U9^�>j{ �, AaThommA�iMU�b~.�}���>N�.�0�B� D� R) ~� Ba}��8`R.~ 9�~�/ tage�J{ � 6E�� )�ZZ�.��+� 8�rR%2�% ~H.~�', Hgobf �H29�:tHuang} X*1~ Bͼ �A 1656��:�. 19�)H�;~ H, \newblock Adv. At�� Z�5�66�Tu< �FL."K )' ߩRa�319�:� Babay 1996} T� b�0� , Jp�@ _ X�L 1134�6; &� \�a�� �T U� * bf 4�gZ� WenzK  ,wat�ZyRot� B.~ , U.~&� I~�&,��N <f r "� shank; R.r (, ``Convers~s~T Albert Einstein,'' Am1 .v!47--5�66 fresnel}A7o�IrekM \`{a�I Arago� r l'influL du mouvement terresE`ans quelques ph\'{e}nom\`,es d'optique� nnale Chimie!�deEJ$ EM��57--6A�816Cfizeau}H�eau�Sur� hypoth{ ses �s �l'�q $ lumineux,�(sur une exp"rA0 qui parait dmontrer� le=2(corps chang�< vitesse avec la!$l{� re se pro�# %Jleur intorieur!7�%te.$ndus de l'�4&!F� =s%P�'i�PXXXIII} (15), 349--35��85�`�= == 1= . Et�= �9= �= =={�= ~t)'LV%% 3$^{a}$ s%[rie!485--40��856Cmm1886ab A. Michelr\ E.�Mor�``IuJof mo*( med�on� velocity(lightAi�!�� a�377--38_886sfoot1}Fe-$ also esta47d t�8dragging�mov @air was not detec7e�m,hoek}M. HoekaDetermin��Al^�(est entrain%ae awonA�i�se�n:$ milieu enyo%rch. N Frl280--18E�:xairy}GXlAiry, ``On a supposed alter �i)�Damount of astronom� ab�G1�)�a�duced by%cpassage=!r&$ through a9sV_thickns$of refract!�I"��,Roy. Soc. (L�8)I�2�� 5--3n 876.E�7��O �R�M2�Earth A��L!� iferous E�^�AŮ.�� 333--34�88ibid.AErr 2r 2r\AE�u(Philos. Magm(2v4��463, (w.� swen�=L� �They�-i�-2 �)eru$ts before !$after 1905!JuJ"�H�Kre�AMFy)�1}, 56--O76� a�}D. F���``ME�moi�G�yuaO2+, lu �� la p^L�ECla��3$'Institut,��10��(cembre 1810�6� 9Aca��iXs!�6ل$VI}, 38--4E�53); ``V�$~2�!�10)p� \OE uvresl�4tes} (7), p. 5 Gide�', 1856:pe }K�!P !�Water-f(d telescope: the pre-h9�FZ 's eA�F���%�. Exact! .�5E�99--56� 6�(bradley}``B  a�b,'' or ``star�D�~''�a�4phenomenon cau�͍�compo��\�4(finite) speedX� Mobserverͯ , wh��+ �:s��:8� (>�"r�Im�Isee same 0in dif� t direc�Xs). In� ticul�;du��orbitalUw�,�tar!�nually�Z4ce small ellip& ��skye`-zAAcc�� new disc�'ed � sfixed�sA��. Ta.��� 2� 1 63� �726�e�2B�{@�4} (8la�-��.s2� born�Bor�V 's &o?��ity} (�(Yg66IX 2�IJ"A � it���2} Sinc!@ rays are perpend)�QY$wave front-� i�frame9�I�y;0 should be un�$tood as a al�ed�c�{w#A`p"� their o" t�� wheA�ss� from$ uni�l�#tolo�? ial � . A modelIQis kind� built!�4Stokes (Ref. \�&oR{ �@Xbut Lorentz found it mea��ly in/ist� K .Kl =�(� `?'GW�a��=hof�Cy� (3�]9--h'846�!|�A.�i��F in w�VE�,only measure Foucaula� 1850J�f#ltA�confib geEHvalue $c/n$ ($n$ is1 ve index)A����8tYD.� b��nu� "[ thode gg � ,rale pour me�rN �)�� �al'Q eJ"� x ��paa�s.  .�zM [ea*rojet d':�F k��du calorw�w onnai�� fn}, 551��85� R@�v@�� ref1!�-E. Augu�T talk� sen��aX 4e X$^{th}$ VCIE;�(4, Vienna, Feb.,!4,��be MFdA� Nuclu str.� �/2�2}�-Giomatl�R>. A376�66)29. 2Ka?PC& a fu�VW ar c3dp+0DESY LC-DET-E-082F 4}P./as,��.V� j*10} %�@ {kir:1} Kirilyuk-P.:%" ncep�A�lex �8Dynamic RedundaJ4Paradigm: CausS!andomY, B te WNM�s,� �.UltimKUn:'e/�J$Knowledge.�-ova DumR- Kyivx#7)l&a non-te�!��5 �!� �-b9t �,/9806'+$at http://�: .org&F)+2F+-� multi�#0d self-organi^A�, probabilist/- trucEv form �pr esf lid 1�^ a� ��d�#(4) 21--26; ��-/0405063>�3F�U"5 symmet-� )�eits maqs� s!5&< levels!�w)dI s.<(eedings of �� Mathe�c;NASBUk�e� 5HF2 9 8�828R� 4006>�4F�`&& �2�(s extended falityQ�ly 4tu � an��li� / emerg�%Iope� . In: Los�+A., M�;4i, D., Nonnenm]I r, T.F., !�4Weibel, E.R. (w* ): F �� Bir(eYMedicin/ �0III. Birkh\"�rG:$sel Bostonpp5FpE��  cious� res�of ex--qal in�q. Ei�.� 9140>�6F�&q chD*d�le sca�5�0in crystals bH generaliz��%al po� *#my6.B� ��. K/bf 69 ��--231>�7F�Q�Nch?>f�j }�p%QofQ�al)%:s. �Fond. L.�Broglim`2T-1996) 45s80; q|4-ph/9511034--3B]8f�field" ?o?9�-�m of�dڭ�E�ita��al �N9io�N� 7R�7 (ac��ed�\g�P). JC1164 �ded} D�(ichs, P.H.:���api;]by B Isi�$Ehrenreich�+v`itz, q�Turnbu,Du� S��pe -: Adv�ne�researcapT!, a� 27. %&�O.& 1972) 136A�7.9F�75 ye��� fuIk:��.��Hs!' 1original: realism%��� Sch�(�PV9qu� �U�0101129�N)�� ib4pdata} m4lmB%A ���I-B 5N3186�44.T R$supernovae WPerlmu�M�Q��Today� 3pr' 20032Mfi=E {5E�exaa4, M. You�2it�%5�0: Inclu!, FD �alo guid�`}{5S4*`Bn922�CLO} {_ agniS&L. Lar� (O. Lombardi �Cl�S��. Grav1F 69K(3�^0211166zLe!NJ.,�6%�Thermal1R: Entrop�/4e Energies}, W���1 Singapore�6qB` y5 :�h$M. Sanchez �Ir ducta�� � al M� },!re�R=)Oxford,�a2a AC} kAquilan�DM.2p�M&?).�$11}% , 755%�4.V008046� Whee�, C83Mis�Q.S. ThQ.�J.A. , �%%�i� }, W�5 Freeman A(eompany�Z�76� Dick!�R= ^� �et� Sig� Q of E��.,,:doZ  Brea�XN��65. �j�;ABC`=tem {BER�!V. � Principle� CosmV %&A�- dmbr1aH % �%� �* PDG} tir$Data Group�$%�/�s 1� 4)*�WEB�K. Webb���e.R"86 �*09130 H1)��FRI�,Fritzsch hep��$0411391; XA�lm�WMm * 8pe� k24} 6�!.�DON�<�%�&(jerrum-Bohr�&~F�+noghuI| $6'l{# �\�+\ w8d0 0840�*�C);:8%�J2^:K%l\ �9� 2016�/4); NR�!%th!%0097.5P {LEM�+? is�a f��ach[ Rio,*�6- eA+N�i��l{>�>{}.�Hray} Lord Rayleigh,x ����i VcM 1�\!76mel} J@MelGi, �AF� -coupl�urfac�MITI�} , MAe�6"%sav)4oSav�-�24'1�10(71). 9ugro} S.aFssman)�"\"ue2, Z.~E�~B - C� n�M� )�5161F 84)..b0tay} G. Tayl}: -FL%X, SerG�u+38,(6J9zu1} � @K 2�@6@ [F@, 2(92�+4]2�cvM�D. Cr_m~*�? F�+95Q=mzu2F�N0a~m�152-15aM7r/2�=.�zu3BCZh. \'BMA�1�;19"�@ [�@ 89l".�@.�cro} �v@�:\`283\!3.�weg} R�dgUXM"�@��� 1�21�/2>�;shi} A�O.B; ryae�@AVBGrigor'B(T. V. Levch��xM;Q~Ryba�, !/*3B|73} (5),0=�6%$4�+527�Q3�@Nmsfm6V)$yannis} Y.*�a��1bourgea�J(J.P. Robert�1 Mrpak, NN�aG3�� 29.�v��>&pI6~%?peltiA�@``Ion back-flow p(Micromegas �{ V'', The.(�H, DAPNIA 04-78, LAL 1 ��biagi}k B $, Magboltz�(gram, avail$� � � www.0(ult.cern.ch2�5ch�nphorougR. Hu2E:L#:�m $�q8Cm.�*8�.84)C0.ja�}"� i'@ce:!lbrech>I7f�5tI�155-1� M. Danilo>r5bF202-212Dmadhu} %B. Carneg�.~:``GEM%� R\&D in ?ada", %i� ��I!KY'C orkshop+(L�D %#5i�, LCWS>!� 2, JejuVOrea), Ed1 S. Kang%�S� Oh, %K%n�� ociety`#464��� . Dixit%�Dub�+J/UKK� �VN A 518� 4) 721.�hau�ld  H 2D�3D Clu� C�!5with GEMx S�! Pads:eZ Digi�TPC?",!w�H�j�i9i~h y�ro�ao}� Bellazzi�``Reaj a� �Da VLSI pixel ASIC $ � R#�rg%/lla#E ode"=!6_.�harry}��� lE`,' read5@%)�-�$��$- equipped!��me - (pix2 CMOS s�'r� $ a2���(CERN-PH-EP/� -0092 7, NIKHEFa4-3� Nw8!fw3Kt�sit Angel�P.�R 2)]{.w2.,, V&�~)@,Bursty bulk �$R� i�H c2+8l plasma sheet, Geop?is.G em�7 4027�,39� Q\[��.�.�9>�9}2,�$, T. Mukai�64 Kokubun, Evid[�D4O5ncyakE2*'s2�a�2G;*��cri�i��" ;. r36� ,1, 4161-4168� 9& �Baumjoh� TreuS }(��]{b }.,W��@A.~61(em Basic Sp| ��:~$p.89-100, V�:"%36�Chang�AG�#gA@{, Low-dz*� al Behavia,nd Sy6�ka�of8$ch[rc  V N]C9ZL�+8se Effects be O( � �Labora�?- IEEE�&-ZK�}, 691V�Chapma7 WatkinW_]!01}'EuC)��LW. 5, Aval)��Self O�ed6�awa%Av8 magnetospheric�s� ��, 9� 293--307�01>t Consolini.b6�g5&� c$F. Marcucc� Jndi�Mif�al &��p urork&��"i# iB�Gx, 7a< 4082�+8�6f�!RDe��helisE�82�8}:��P..7 , Non-GaurLR)tr7Ef��AE-� fl�wm.fAF 2kM�6g,� 408�90E�8>�FO*�y0)]�(f} %�P., N.~W JE�!# �8 Ri�12� a solar w�'���pyH law b�  life�di=�*AE!�ices,N� � l'1�1�F��z%�5���U.-PTurbul����3(gacy of A.N�,lmogorov} (Cb�.���. p. 8B�Hna�E~�� ,a)]{hnat03a}, B�.��@,[Row�&Af3�M.A�-�, ScaqF��loV&erme- seth geo�ic1o!�.�$$\epsilon$� seen�WIND s�craft, J�1��9@2174, DOI 10.1029� 3GL018209!�3a>�B"b5"b)"-!~C4@�E� �?5$] �, s)� A�Fokker-P�Uk�roAto2�Q�]���pa�+terk1&_!* =*.�FE�Dl564�%� bBorburBalogI�7! } $�W �A. ., S&#���(��nt MHD tmt cas�l�o"�f  8su�, R85-199a *��Hor!��]{h�tq[�JE�Smith,% Weigel, Cebtr�I. Dox&B. Goo&1� ary,�)�-��driven2e-ion�e N �#�(��uQ ��s,� $ 4178-4184�B� Klim�"m�� k} & J.�" Vs-lia'eN!�keyD��s �%T n=-ar�1�6��6�I�10� 1308�, 3113��B< Kov\'{a}c&e �]{Hc�"�_ L~Carbone, Z.~V\"{o}rs,Blet-ba�fi�6�of6�eve�4�2��S seri�;L lanetam:"��� , 49\ 219-1231vB� Koze@ +a3�}!VA ~VzAa, Cellu� autoQ) " /��I|icY�i*%up��MtA[<-�(icae 21 (9)�931-1938�?>>Lew�1)]{l � V., �.ppUt r"P(�0substorm onsea2�  �08), 1627-1630aBQLu&0 ��ui}E� T. Y�*A I-(�"� �2 Se�?-6J�,; 911--914,!30>3$Mandelbrot�� m�~B.o� � -Aff�4��9&:Qmb�&i�;(, $1/f$ NoiS=$nd $R/S$},&�U-6�b��26b Pag"Fnd���!��=li "c �#2/;����: A�,�etw !minimub"max  u22 Ulys�/atajr No.A8,.' 2JA009331 �>�P�?�.e�Akasofu� 7� a '��!S.-I. 2, A stud� . E�s��UK��8�,�6 5�@�+78B��s��8� numrecep}�W.~H.ERP=Ga y, Sh(~Teukolsky,( T.~Vg�#��Num� al recip�$ C}, B� i��*� ZD490:WSitno2�ja�s�45 I.e�tNharma,) PapadMB�!Q(A. Valdivia@J. �0.��, PhaB=�R-like b%C .V�A�F��s,^\10�129�'129� ��>�S�!ttee\%��C� P^,a\�2alt��s;� os,�(�lf��nDisorder&5.� Tool�x$N-F�tep�W2Tb��s} $&, E� Anto�%, O9os:9_6E @Vz ">�-�72f� of PC-/ ./^| 30 (3��127!�BTakalo}�9�t9�0 A� Ti�QnU  H skinwKCor�9o�me��ba��of��� bico 6d n��m��]R��S,�%15�153�~�A�)] � I.�$K.~Mursulaa~ �, Rol%.�� rA�].�a � -map&��:-� tail: Doe� ue +<] low-5@� ?%d6a�0, 27665-27672! F�Tsuruta6��}$�X T�Sugiura�Iyemo��.�B Gold#W.h Gonzal�&SL�5E� � �A��Va7Wsp- !7AE to!&$ IMF $B_s$-e�Rsp�cD break at $5$ hourBx.1�0279--282� B� UkhorskiyU�[ )]{u}$�uY. �� ��6�6�Combin� gl�E�1--n e fe���a�7 crip9+!Aa?� -6/Elinn� . 13-192�(>�Uritsk� Pudovki�u �(V.~M., MBM1� freq1Hy 1/f�~.��A�E� possibF.�1,fq�2�SN 1c!2 580-158K 998^ �� -" -, �M����Ɇ.2�A*ZsJ �<al"�� � b�5us]2e-63�4�!380H81�8B� ;KampeI� k �G��St"eV���#� Chem�y}T2rth-Hol�, "f;e�B� *�.��� vass��*c9 J. , J&J � D.&@  &�Q E� We(4�*em/. s��T152Bx�.��z.�3}.*��S.~� A$y~�SNNK�pal �(Mewaldt, Mo�; of e�, Ansfer%:i��~N`!�{\��'No. 2 63RWV�r�a�)]{voros�e2& , Z.�\.* \'{A}. JunL a}sz!  KXrm6@%�A,�'e��laws 2� FV= 2621-2624E�B?2�.�aF��j6&���(ankovi\v{c}� ~.��A�@ula&M4 acte� iI��; �;..�ic61 "y�1, 9 (�?< 149-162, Sp. Is#8I!�B�I�|B� A�w�� $A� S.; (�8*�8ty6� invaria�-, $1-$minute �1-zone .�4.�,�*92�E� 3, 2193, B�470�F� �.�.�b} !�~S�>~�>�~�" , So%���a�AprU7ta�9t�r�A)�ic ��~�BE�derivōsV\ <8 (A7): art. no.� ;zN�casdpubx%( M.\,Newcom�3 W*�\,�$\,�\,NS-4&890) 690; F.�GX3) 630; H.H.\,William� �Np(\,{:r.~!��7\,{A36`:� 14�1�{otr_det./\,"�& � (-9Outer� cker�,up), �#6�M ctor�e @&�0EIt I: +'f,?\J� A. %!FCap�#,n� 446}&0) 317.x$ daqpaper}LDam �, nP5�,0X&56!G �m�i���;} &�(-A�4-b.desy.de/subaLp/Oor/tr%W/o!e/ej8nics/ docu.html*�%lh]� K.\,}Yhan�`L�%�-t��%. ASD-8#Sp R�'�!%1�5th .)(E�� , LHC (SnowmaT]|Colorado, USA 20 - 24 Septembe�L99), g% 99-09 (/LHCC/99-33�� \,562z* tdc_C} R.\,G��!a<$e, `A High��ol32.>zi�a�#Z, `Zeitm� lek�Oik f\"urhFa���0tektor' (in G�5n)�ma>al!� sis,&q3\"at R�< ck �!<un"cB,\\jxg� al/tQc /dis  \_raoul\_�.ps.gz.��% perf�&�&II: Per?@nce�+RS�jBBaa.Tso;14} So!�,feld, "\"{U}A�R.A.~H3QN�be|J% ^C(orm asymptoi!exp�on��l gral-at X�#au analysi($precursors!�rch�`t.~9 .~Anal.\ Ee3� 7-236�Uou;97} $E.~Oughstu �G.L!S�9(it�["o Puls�bopa-I�-u�DDi�4i (vol.~s*�pBuAV 6�[ks;+&M.~Kel�0%OI.~Sazf, �it{��fO�P 1�&�o3 (Kluw�j.Hdz;� S�bDvorak� W.~Ziolk��$ L.B.~Felsa "Hy~8 a!��)-n"pap<" for ���Ons�l wav YI�inL�Ta," J.~b(~Soc.~Am. A� bf{1!�12� 2�XB# c%�A.~Ciar � , "AY{�IQ^,5�of�%igl)`.�e rise-N in a d�B$sive, loss�J�WU�E�-�bf{\ 877-89�4:�as;64�.(~Abramowitz!s IaX Stegs+�it��dbook�_7� al F"%�N%Y3*ureau�S+D#l >plied@ s Se+ -�;:F6bh;75U9Bq��Rxy�[.-5jI;!�m�e�} (Ho�KRineharI�W�1on, 1970&Ch.\ 2u1 ac;8�,:��^ �^ �^�aNNt{)�a sadd�KZe p�� a brX* p"�+c�}I�L�B$%�!� 273-28v986eac;�>�Improvedopr�J%� Q- first ��Ay�O$X" Engtan��� 43-5�0:xTrie0S.~Rikte, "Ex��nce{o#L�C5%c�� ity RMemsa�R� stra�>�O temp�*ly2-J$�0a", SIAM J.~A�m~A�}65�k1373-13*x. 6+hs��~He+,~St�AyV.+ge`Fm�4it{Time Domain�-SplitP2�HInm�� blemeKK?&� y P���6�:jae'JneJacks�%%�it{�@j3� :@(John WH*E�$Sons, Inc.f75)*l ��JF"�deLS!� ons'��A[ɗ��6��" ���\��\%imonyō~E.�)11� )" �]�$o�F�QHaxB:�� , w&��TJ�c�a�Ano�9�M5+376.VN-onE��, Hil��Gallagh^��.� ���t� 103}�~2GaF!o:4� ,���B�.�!ZMarlet\)G�0D0Q�q�Iy2�10aE266�F!3�� A�~�.TruckUaRa2i�u�Scuz-bQ%� Robb>A.!Cheesd4���N(Zakrzewski,q!�{Montg�ÂrA+ pj �LR bBuran�=�D��MuM��mmA�Danie!�A.~D., K�KLK��,*�a�M L Fark�/$O., TomasiJ�Qr�. 4-C�!�C)miN� Menn�4��Pom�_��, Adamo Cliffo�A�Ochte�#g!�R2N GiWAyala� ��C��Q.� rokuh)� lickM(~K., RabuckP �RaghavaMi�),8e�y��Ciosl, Ortiz ). Baboul�5!� StefD(e��LiuA�(, Liashenko, , Piskorz�GKomaromii�Gomper�0%B��axeFox�A�Ke 2�% {Al-Laham��M)&Pe� C��$NanayakkarU*�J�%�ICha�combe)��s� �M~� � %���t , WofM $An��%"a�&/&C� {Head-Gor�A�Replog E-a�PopM�./ ) 03,R i; B0��3-12-16)�Kaux8J 0Pittsburgh PA.��:82V�"g ��oy}��.�� 6�CMoe�� 34} M\o{}A� �l�t!l# 3���- b4# 18.� Lide:94}  EA2��or�W9S{CRC} �<��# �- sW�m : 4P�)�Mth[ion.�CriV%; �}�616� D:8 �P62� }�|  ��Q  Soc. Civ.a�."M� 51) 770; }6RyKBlau ��YAFSimaikaeg-T|=(Storage: An!]m al S.+A+�IbɌ�O��q� [$E. ,.2Ake�E7,� � YorkO6- J. FzY!� O�9lenumA-A 4 !170]�Lo} A.W�, E��4metrica, 59(5)�n 991) 1279.�C�I� }  , S��BuldyrN2Sa�vS|�Iimm'%��Z%wAa��/q��hA�P E 49�88�o9942�,�rauEm -CO !yUgO0) 396.�4Barabasi1} A-L�; �D Vics?rI �A4n873~�912�I��Ch."�LA�ar�*A�<l� S. H5G�Msenbl!�Z.;Qtruzik%./,�/9 ` 9) 4[F6m񪡺LQZ��{7e"95L-42�Lo2]"�#/0P�,C.2�F���Re|[.{ T.DiaRo� %{As�Ma��� ��E�68ťN��^� �e6� RPoi� } P.yon��G. D'Ago�ei, ``� Infer��� �6y�� M�� �e limi d&�%GJ itiv)(�a case �/n gravAWal��C )S }'',�$-EP�$ 126,�f�<9 (hep-ex/9909046�BR}�B.� �Bayesian4Kson!�jat5�� : A&0I�Y���>YZ P� c2�RPP��i!y"i5_�6���:k{�X��a�c�"_� Repscg�tR6�'3��6�0Zeus_ci} ZEUS�&lcHi7 -:Sf^�eqqtt95A*-W!Leep inel�HXe$^+$p\,$\rightarrow$\,Xv1� �at )�cX��J_K bf Ci$�5 0) 26�Higgs:h% A�issi�NE��Gws o�"H gs bo=<�'�/d qM��!p�:�mSk�BJ�%rC1X*9�*2Beppo.�Q*�=nco&�7b�<GRB's %xPRSAX�J]q�(s EXPLORER+NAUTILUS�-tRIZ�DQ5%`0�Y��N��)b�:ZabX!��Fg!~A� h!. \new�{\�[Ha"p! m2Q*.�b}}.6D�gi��aL~6=)aifI� bizo�>~C. A%6 P.~B.m{MQ:Wfha� black holMC.st<.2����$D}, 48:607�6) w_een11�Y~M��� Cartm�%S.jHaw��2�y]fo�vws���&�cF�C�� thm�}, 31:16iL6 begeha%�B �ɍees2�%�G�y'��� at,�b :�"�+U�he6��! c Am~>n Libra�.6; bekeng9J� B2�G3*�Ds*d�2!I&m"U �=[:P�&2L�:� 9:32U1972Pbi�l}�\ D. B %SPA�!���N[�aum �0�furv�[8I6AC�PJ8�bidcbjorkenE�� �S%NDrellB�{Reёik��%a�-6�(McGraw-Hill   1:�boy�'dq��Y~Hlye�FR%,Li !2�M,Ba!WalV'j���?Kerr T F�J> 8:265�2[acta21eCalvanɺ���$avigli�J� Irreduc�9.,unincreasabl� gu�2m�x!��?eal �'*aaRC$�� ActaM�Pol�9:1i�2zc�X6�ou�]~�X 2g��r �!Z�$ �itii��=�e �lic�����o apseF��� pp-��h 4:33� :�%�2} 4&uriI9r�so!jBh]6-Newman.�F�Vp"�C&�0felice} F.~de*i�C!~S.�dke2x�pusty c�  <olK�.2C�92debney� �FD@P.eA� A.~S�d.r{S�0Ŝ_ E�(ei�M -Maxwell $hJLB�10:184�>62deserW`~D e<O.~Levi6� Mapp� �Y o Unruh��fpro<ieJ�� th/98091��9] �Gd� iler1�L�Qtw2%Klein�5�ro�(ngvg:u22:232Ef8:� witt23} BETDeWit63��f&b!ory>c�+2XE�� p. C 9:29�-72@i(no6��d'!(no2E�� �Q''s }ity6NBU(I ��=yr doran12} ib!�F�Geu algeb8i�l.�k!$.�  $2+P&@�R��2+� kerr>��~N.?jnbyi�S3e Gu:�),U^����-i�)��lI.�;Y42�%�Cl"'j.�v��s��96 !_4������S� �k�ino6Ge>A�2��)n5�B�A2�Im�� Elec"Ĥ�V:27�6a droze� Droz2IIsrael5��orsink2n�I X]insidS�2,aaTics�(}, January:�y0.me�Y��q2BR�mea7o'�� >P8i eton� �a�A�42�f�r2��F  ~Smo��S.-�Ma6G�Vex:-�&GU��a.A&?�s�0c�2-Dirac�_7Fh(gr-qc/98100�->� �1���A�-odAv>!�u��XLa Reissner-Nordstr�?m.#%cg�" tpp1fwV�?s, spQmZ$complex nu�=� c�e���tum*� B���+]9:101EG60-�d��f�Observs, � ?`f�a��Ki4J�Fu 6:55Y�6� �pp�R�Curva }� ��s6EL�%C F-IntXz or�a 25:5�+e�. wilczek20P F.~EQ� lzhe� F.~W #2�.� .Yl�ary�KJ�� 20201�<:K itzy�4qft�I E) J.-B8�e6� e�n Fn As:� b&6� jan�A.~I.& i�lE.~T.a"man2 S.�6jsourcNB06:9$i1:K k�Hd�} W.~K2�Type D v��J}Bu�1Y62� kram� D.~K &�9p~,�MacCal�a�E�6rlt2�%�Ex2� R �%�&�2�� 6�laby1� .� 6���&$ 2�t, gaug��o�$��G;!f�Rx�0". A��56:48�8.*Jlee4} Ka'�.Na5-eJ�oin>!2�A�T+ abi9�~Z� 9�[�Cfm�" T��V�2�%�* L�, 68:1yfB�lee��.sin&xm�(Rr�� 4�5�2.ymalkuseeV��M2d��*�!)�" ���Ӵn�}, 83:89l5� �m� lini16} M�:rt%� h*u&] ent4 �qu r-Ru�T treat f; -J  ev z�hn�%D15:241� 2� mensky� B. M2A2���Aˆ��D2(ct�r� l71207 +196�1mtw�FW.*�y�y�J.cWz2���� )2&�can�%nc��A�6� nak6:.~Nakaha:e dy�Hpo��R� Adam�2>%BfMolu6hne��pi1} .�\^�n�_c:� radi% y a�iho��� $ coefficHAJ�B3:566�62�2�2��NoA� ndi-Metz�Sachs �p2�%yB�7:8;196� n^��Bz�N-Zonoz%M,T.~Padmanabh:�5&� X/I,q~� 9XF�M� 8120M7>No�hei�J��O� H.~Sf�2�On�"inued:�co�aF���}, ���A6�"o�2� E.�22|� ed-� F9J;u��45:R258E<6�paani�P%S�Assa6!�SchwiW�m�~sm%����Sp&�.of accH~ay"&� F;� 6+�7;2� �_kh%8K.�<ikȂZ� %Y@� tunn�%gf� 9070:d992� perCP 2��b� �&� �!Jarz3s's� �F�B}14�  6Bredfern� R 2��D!�Maple&J2: V Releo'46�S1.P��a&3rdR2��6�ryder��LBRF�� � ;2�� 2kst��* "��F�.0 � im�|rps :.� o��g�Qk6�*mac'-;0196X �96����c�kD.�kMacDoNtv��mem�DeVa&o6�YmU�"*W!�HavH>�ub3� G.i�2��G 'y� � o2�x4fxOrigi"U �/ފ5:3d!6� �62�ER.lWa:wWh �a�Vs whe@��ToOe�N��s a%Q2wuy�t T�Wu 4�Yan6X�2� xstZ+��M1 h�R~&Nuc<�=107uNe�N�) �E^�.{��&Qmaiman/F|M, ~>it{Stimu��Op� Emiso%(in Fluoresc� SolilSp�`��%!H@�Ey�Yhys. �*ybf{12.:1151--11˞19661W?Vifca} C.�sRR1 �D&�b ���HVCH�z,sgesellschaf��ei� E6~Are��� T. zG�2rri <]?S�ed�4�� 1SCG�}, (SPIE�>�IespLwA. MS7�9322P/� ��mb�>Z27giato�@P�-n F"�%bN`��R�4Nuovo C�dto9�3 --L�>3JOSA-FI8 M]o�MhX?:��Lw� Nard�> (Eds.)lg�GU5qB{�issue 1)Ee�Io:�+iŰ Ac``1g�Ra�5852B�8?7K�+ndy/_OraevsEi�JpFThZce��5J�N"a\Q� of�!rs�82� Boyd86} R@5 !��3ay-:�L�2:T1�% 1 pYa�%evit{\ }B�i.����562�AreHarE�y| . -1�2�(be A�ы�A�&R��5߭2�NarAbr!�6[dJ2�i�E����!Dm 2�a�>]2,.���66�A�N6rP�(#n`H M.5�1 Mal 2� Pul��%��$�Progres), XXV, p. �o$0, Elsevie���B.V[Bm,��F!�KhM""c� �Pri&~��U�:l~o�L6��q�Single--cTeamulti*��/ �-rIqrC$*W�e#!_��A fbf{32F576ʠ�8dJ2Haken SH�k �AnajE3highe�Q:�f� � �!R:� Pbf{53� �>�6�R z63}�i 9��]W��.non"�#���%. AtmR�S$�� bf{2�#30--14}[66��KlischeF��� �On� ��y�orenz=�[ 5 �6xu]U�Pjp4C�K�]U��LF�JHo�<�it{.�{ �--���a �5�� L� F!�@2804--28&�2-�2�B���Ue� {u}b1��% Homoc�c(HG�qa���J� W bf{6J5.}15��:� WVACRVPHT:�2� :R�� rbalw% n�L_mdn,�>J.� Valcrc�(� ujt:!Du TxP�it{�l�<�[$1 &�` al M*A7\a Far-Infrared NH}$_{3}$V\):��B�#�Vw���M1� � l},�i�&� %l223--24� 6�RVVCMGe�Ro�+2� R. C9r n, V� CH\'{\i}n�m!ER.�Gm���&��!�wDally-Pumped Molecu�1��nZ,uon5�})�h!��"E�a��� bf{9}, R1���,6�New83��H��NR8�Uhe:�A!�ultrasL{i� p�[s% be:�:G�W61�f97��86�Si��}���E ��)] �-.��* UK�:g Svelto}� *��;"C _�@ T! �4:�XTSMe�L. i9H. Sta �!�Ga�hC��al�put�`sp �g2bt��d--st���J.2�1Y3BP22J{22c�:MOtsuka�VK. �M��%bU�3v~in Qc-r2�u�k15�96�Y� 00u@ yGl�oR�EquI^De2�oaa }:zC D�>431--4a��E.�Z6.jTQ�e6�R milt=D. Piero�E!�.Q texa% IntF?Co۪ aQ� Nd--doa�(Yttrium Alu�xum��net)`ꗉ���& 6a!063803 =22�RN=�H. 8HezK��mmeda=W& � off resonXbSs UT �L2p26 275-s�-:�GH���r�%8F� Q6@adl:>2^i6�f��ng �-�ve�Zum}, Z�%�? �� 420--4��1>�!/(b)�E�2Self-���i� },XAp":�|/R4662--46��>}IkedaS]K.   OuyAf@�atsumot��Mi M5--Bloch �c& � 1Su�?���29��24zC:�)�7�1f=it{Onset!�0rB��\ͅEJ�NA$58}A, 440-�O-442 (1976). \bibitem{Ning90} C.--Z. Ning and H. Haken, \textit{Detuned lasers %�the complex Lorenz equations: Subcritical and super(Hopf bifurc 1<}, Phys. Rev. A xDbf{41}, 3826--3837�902�8Fowler82} A.C. 4, J.D. Gibbon,�8M.J. McGuinness� The ^�}, �ica D�(}, 139--163�822�DMilovsky70} N. D. iuOn!@� stability of a single-frequency travelling--wave l!� �. Lett.�833A}, 492--493 !�6+ Halford73!� E. �Modifi-� of�theoret!�T model for a self--pul� rA=l �J. Appl.%=�844}, 5644--5646!<732<HAw 76} Q�%�H. Ohno�T�%5(ultra-short ~ �e!�(Opt. Commun�016}, 205--208�6h � ��ransientn�A9>�59!�261--2I=:�i78~Onset!�%F�p: first or second order phaseAWnsia�?},V(,26}, 117--11)(82�;33B!�19--22��92�Mayr81}~ ,A5 Risk�Ɓ�He�Vollm.�Periodic$8 chaotic breathA�of IP in a A�Q�R_3!7480--48�812�Zorell�J. = 2QinI�Ds with detuning}% Z�38��2!�30A�:|O 53�4�5s :� �86R�U%�le��lan :��f�6�4in Ref. \cite{�(86}, pp.262g 4.�  �H." 1ű$%�o��!�"�}, {Jz0--33.xͪ86��D.�ݫJ� Tredicc.���eapproxi�yo!E�`, physics: A }que�H a proposed improveAq22.�!� 1109Ÿ61 �t!SL.2�J.R. �L..�N.B. ��A D.K.�1�Mode- ��et� /uM> behavioumV���ԝ3��$1842--1854J�5�b���M.��0Squicciarini,i�8it{Exact linear,  analysie�plane�8Maxwell--Bloch "p�y�V��3101--31�b6�4Elgin87} J.N. �J.�e(olina--Garz��Tr�i� solux�6�&)br5}, 398�98� :��88�R. Doe�` � :D Holm9�Finite d�usiona�i�� � good�� limit% ̩�E�bf{12�3��31��:& �LCoA�ntin,{ Foias�J. �_it{% �--d�$ attractorEAG:�}, NonI}ity Obf{% 2��� 6i�6Fu�H. Fu�cAA�� vpvYa their 2L!Mab��5U� �40�868a�91e�>�< ���W�Bua� *�"� !5RU4!44151--41�:�$Carr94a} T^� T. Erneux�> � -Bݘr!50�24--73%942� �94b��$Understand�*� toPvea� �-��� u% a deLrate Ginzburg-Landauud^��4422� B�,sini97} D. C @, G. D'AlessandroiLA. Polit*�4Soft turbulenc>kb5� 7!�76z96' Tartwijk�G.H�& a(G.P. Agrawa*� % :6dT� modulTal6�aVfiber){/ amplifie�b} 1� 26188 -c6�$Jahanpanah�J. �R. Loudo}b"I E --���gaif�� 225�26�?:�P� 92�B. �0S. Dutta Guptݮcw=1y+ s� --s��!G� �$ in�Y� parametr>)_:� >�� 7260| �_92:�st�94}:C �&? �!kPirova.0% Rabi resonaM�&�conver�� by fourYmixa�in �I4its2nD)�K& )��6t *[ 49%403�$0�6�F95�Fontana,= Begota�E.Pessia66� "W :5 lock ���0erbium--dopeda5reI�a�R� 1e#8� 96�Pa:�G.Cf��,!��j�Exper��tal o6h!�� 0-Nummedal--Gr�-�� ʡeg40q 409�:gW�Q.!wWilliams` 0Garcia--Ojalv�_R. Roy��Fast 2;olariz����n1�=�*� : incluE�$of stochas{effect!�R���$2376--2386_:�Roldan�E�ld\'{a}�� Very�]�*� in a e--lFiE�i>in o� pump�6� � > 4| 23��4N\ R98}6�EXG.��de Valc� rcel9� M[{ �r]}�. in EiM.�%!� Euro�.: ޥ��:6A Desurvire�� u De�F��A����L (Wiley, New York, 1>5P99]M.�_&�|edondo,6fH%g fg&�6-I�fibre9%E� :36� 25�252 96� I�03b�%�n�J.J�yF�tschke�< RoleA$Field Loss� v&y��.�&�7�] 748 (2006��an03a��Ja@Urchuegu% \'{\i}a)��. Guerr���2� ���$Nd:YAG{:� :�!�816--824J�dea�aa��EQJ�:�)� 0�-it.al exp�on i� outside�= uniform f%��}, B 9� �25--830J�-�1��F. Silv-�FF�� emis��i�2�-N�K!j�1%6 1611�6��Milani83:�%zMa<�� Disappearu  of)x}�r$a Gaussian>�:�)��!O 57--�86.Stuut84}�  � SargTIII�E� of �,-beam averag on!conjug�Akbeat-&G ,spectroscopy3:q];�95--10�:�6l5�l��E�6�:� :���1�]:�,SmithDykstrauP. %"� 9r$-like [s iE1~%� ��radial.epend!� R� %� 07� 6� �ia&6,�*^s!�E. a��Q�i6\a�V��Ut�~filA�:;.1W15_152 �6�00��X���S�4� �����"6 ec �l.�*t ��i>@&�63 041801(R)��6�$Voigt01�  OA nz��F�����%B�. �y finEo confirmed�;"w ly},A�1Intern�Oeminar�3No2Trend%NX�! S�.%d)!--Prec��Measure�B�a�S.�LBagaev, V. N. Zadkov)SArakel�Seds., Pr[ SPIE ��I429a+EL15 {6�%d04:pL%m2iM7qA5eBj 2� Investi�^ofv�>��>}!+q E(��7�7��86t* ɞ~� Q!>C 2x* a?C� -BI"��� >^163}, w�96� �� ��>: @Generalized Rate &P!�&���b�2_'3_'7e�6��AeJ.H,�;Vi!�ca � AY6l5jCoexist�H5�$--longituda��k .K EEGyr l},!�pre��.��an01b:� s^|Q% 9B�E :�*~A B�s: bey�'�R� E >x " 053805%�6�%q!���E�Y"o6�F�% �� ��"�'�!]�%�%�"�of��QxB�237���199��6�0Brunner1} W. EzFi$%r �H>u�Regula�&(eorAz�EG�Journ>�"��2}, 2R$2N6� �2��Time evv�!ito>el� ic � strengh!��&�z���,14%:�Zhang96�L. �Y. Yue�4W. Schinn, W.R%Cl��%� J.W.LitYIStabl"w$Apound-R� - ��� )�0Lightw. Techn&` 1�104--�96 Guy�M.�� Guy,� ayloM5$R. Kashyap� S��*3 j2 �y� i.U,hase-shifted$gg grat�narrowM&filte�E%�on.:Z3z 192�925�6lC1�D. I. e J. �S.V erniq� � H+ Kong�v�e% u��A� tw��d� t!��!},f�6 17�178� :�0NLPR} K. Tamu�He%HauIa��P. Ipp,�� star!g additive���Ock" �!�er=�F� \ bf{2r22�022��x\end{thebibliography}�\beginB{00} % "�1,label} % Tex .Jic item0notes:F9 \" subb2 (�}l6~162I:0re is a�(, it should�"eA tF�3�% % .�� \newcommand{\enquote}[1]{``#1''} \e�Pdafter\ifx\csname urlO L\relax \def\url#1{%�(tt{#1}}\fi ZI$ urlprefix>OL {URL I]$ide�,print}[2][]{~ {#2}�-�@{Barrat61} J.~P.~ �tC.~�U$n-Tannoudj�-D{Etude du pompage b�$ dans le � malisme� la ma�0{\'e},��Fadiumi&A�a~329�%6 � 612�Hr67} W.~ �(B.~S.~Mathu0��aj*or Fo �{  al P&,2$.%�$' � 2�)672�(Jessen96} P� � I.~H.~DeuF,AsET{ yT lattices,} Adv. Atom.*����4�3�9�:�4Guidoni99} L.~ �P.~Verke�5>� : c,atoms k. ed by l��)�E *l�R23--R4 �6A @Rolston98} S.~L.~ v�Lics World, October, x032I96� Lounis92a%��B.~ "~Salom7N� J.-Y urtoi��0 G.~Grynber��QU"�/A Spatial�0 of C!FCesA�!�� a!� 21{Poten=,2uL2t568}(26)�6�3 3864-��&j7It92%S.M��,Gerz, P.~D.~]  Phf ps, 6�@ R.~J.~C.~Spreeuw9 !9,I.~Westbrook.�6Aqu`%� mo� ! {Rb}I^ an "�8 re+5�2:�1� 93} 2�].%� C2��M ��1�QJ�e'c)�e.� two-Ed/e.*&�p1�a�A�G !�&3 7�2249��4 �32sRauW nbeutelabA.~6�4$~Schadwink�V.~Gom� D.~MeEd��S�$q�)�)� �"V �.��l! variR t7 ���@B�4�45�4��:��=�2N%o.q]�%�umr tetro�#ųca.xa��c:5�j197�*98#6v$dalibard89�JD �Nd5d;  co�)g below O {D}oppler%}mitD"2�g�(ents: simplo<9H E\>� &!6}(11)�823 G��86� HemmerichaVA.~�T.~�{\"a}ns�4��0dY!Ta)) omic crys- boun�[b�)gh�X=J 4�)41 :(Treutlein01��(, K.~Y.~Chu< ��]#$br��; A� source� E��ountainA��*j3}�14&j6�,Petsas94} K.�B , A.~Bq �6�d2q� -C)<l� �N{ �l&BR��'(5173-�518s*:$4Shimizu91} F.~ %E !DH.~Takum��04-{B}�{L}a9 {T}rapq8 {N}eutral {A}Y,}�6��3�<34�96@,DiDomenico04��Di~, N.~�%ag�$ G.~Mileti��Thomann,A�V�i�6ch�aE�V%�Y�]q�ll�/ of a�Iinuous�m�w�Z}eemand*�)-{R}aidee�6�A��texz ��063403X6uWeiss� D�Han�� Wolf Oliv��,C.~McCormick�~T.~DeP1!D.2M=3D R� S�C�����att D� y6�%��85}, 7�6� Esslinger!�8T.~St{\"o}ferle��Moritz�Schori�K&hleE8H2�i�0\from a {S}trongly {I}nte�-  1{D}U@fluid�+a!�M}ott.s*orJ�"� 9� 1306�N�� f�1�"� johnson03 R. J % $S. Safrono�UA�..& {\bf 67}!(062106 Eh32n�es!�JE+�!!��(aC(V. Flambaum&!p. _39�K 63J7^�# 1351�6� wood[� . Woode$C. Bennett�:Cho67~P�7sters' J�  R} ts,CEA�aT�C.~E. Wia�, Scie*�27A� 1759�:�(grossman00b=!R , R� ~Fliller d ,L.~A. Orozco%�RM%a��90G.~D. Sprouse!�.� �!�502)�6} sims� � J�S+.�6o% W.~Z�o:kC! Q  2448)82caubinAb S. A &� z>|!z:�.�I�F  042501 20:<$dzuba95} V�D,B�lO!� Sush�.l �5 345j1>�*sq��MaA.�W.!�u�q0A. DereviankoyP�D �I�447%3 6� � ��J�E~e�Rm3�1I86�ho�0 B. H ��Yeh, T.kekosh}:c Knize�)�&A, 2%P71N62I)3aT�*� Sci. 1rum�� 7� 434m6 zhao� ]�!=Eg%m7��~ ~ �� �� 3737)�82$oconnor84}�V. O'CE0D��{\em Tim�r�ted S. Photon C� +J(Academic, L�)n�):E$,gomez04b} E.q�FJ8uM6/ ange�to bemitte �n6���AP: Z.~W. Liu�rJaIp�De�50At. Data Nucl  T�si� 6%�27��6Y��� 6�.�6�a�6�% !� �# 5� 195)�6�m�8 escuAcM��riŠVrincean �HeYSadeghpo�.�iC5S R4259 r6R$theodosiou� ��H2 , Bull�% ]MBe�3 �210 X6�biemont�,E. Bi{\'{e}}�  Quinet)� V. van Rey ghemaS pB �e 5301A�19:�(wijngaarden!�W��TW%�J. Xia`�+ectc'. �at< ansf�6��55m�)�N� ~f� 24f5natexlabU.:�#14j3�� font>Jv �bi#�Pf�Q$�R9>~R.$�R�ppIR>;%8"�jpWnfoqj ‘[{2�{AryA�5)}]{a h {author}{5�{W.}~1g F},>nfo{j� al}{I �&K }"� D.$volume}{582E� s}{1�<-year}{�})*�">�Sk��ng�7�s~�J>�L���$Monthly Noa/3 . As� c���iA�57R� 72} F�7v�(Ryu et~al.}� 3)6�Rynim, H��4 Jones}}]{ryu� D> Ryu:V9BYKim�9S; }%zUu�16and%jm)Z�S:O-� >5�%��2J9t2)5�89:�M�338F�21r��;onA�92a�c3!n��N�:� KZ��xEj�45:A �24p(F�92r�GonnellaA� RuggieriE��g ��G>�Y}:�M>O��>Ej>66:A->031506Rv@Schmidtn� #$, de~Keppe�and)lera�s G�gB> ]:�V�P>=�?2�y�VQe�V*q�5�N�]��)^�90�\Ţ-�1183029>���EdwardsY�e ~� B.~F>�M�� �f{^� 1045�.J�v�Legi�Passot�3��leg��B"O��T>r ��4r��� �bM 0319Z�v�KeA�e�Segel��71!1ks2�EJ R�5oi|u� �Z7J.�&or� ol;^R3aR y�-:235F� 1971r<BJ> n-RousseaDPocheauEs%B��GS>,:_}a�!�5�K�V�A>V�ZLB�j�^�761Z�vPJullien.L0:: #!�iglione_Tab��PTAer�t M.-CA0.� c:!V^BR�A��BS���%�" ��Z< 363V�0rLeVXY�.90�.�> que1�xI�5N � emph&� title}{N� metho"�!n&7U lawse*�5lpublisher}{Birkhauser-Verlag.�,address}{Bas�0.("� v Tysor�!,�Qr�= �]1A�tR>�Y-<�V�.'>|S�5m5��`.VP���U�J�th��41:���45J�20z�Dehghan��4A�d ~�B� JI�B�;5 �).�#4put. (avail. o$K)%Y^�14�[y� �307F��r�Othme��tevense�7!o�H>n T��B��ZM SIAM�9Uj��.�-; 1044F< 1997r<�DE1��g�D�0AK:� K ���*2nd eG/onf�P�[ice Hal~5U���$New Jersey �Q���CZec Pain�20�p ~NB U�NK>��6��{v,]K!�^�2Z,280FK!rKEdels�-Keshe*� e�:L>�BUZ����Bz$ 6Z%693R�v[ �9�r89�rrB^��Br H �R?vb0Fokker-Planck&N�mRS<0g�3u u+ BerlGL.Oi' 1989r�Gardiner��g~C�F< Oj�Handbook�$*�H) �?�95rLifshitzb$Pitaevskii!8% iFL erho� E�: `�CL� :R�jt{ � k� ics}.".x @utterworth HeinC#�NFwOxford.� Uuvb Akir� Levi�%^l~yB�P�SS�:S �jNDiffuF+E'ecolog%^problemj� ڹ��Flierl"� 1999:� ", Grun&� �]{fC�~B@ Y-0�V� B ��� B� �*� �PJZt>f�� 19�RY�� 0'��Q�9zerimI� Newm� �ng�pBA N��TJ� �I�1�56in.?} ݞ �&�N� 4f�12.�6 Post% {\ith5�_A� Clu�'�1�Cns�a�K|=q 5 ILhumus J H ( Cambridgb�D�WPA,v/:>%H�&P� ��2�(}�!67} 62]��pkFras93} ne L J �odl�*K�M3 J"h! ?E Gius'8ti-Suzor A , MdIHF H, DiMauro L F, �;rron El Yang Bj5 �p:�#Mo�6�!} �28} 309*D {Buck90} s�S8 P H , Zavriyev � Mu�H G� >um�-r D W|#90 ���.}3�64} 1886VMiret'#  -Art�"s S�Atabek O�4)�a} A �$49} 1502. =m Ludw�*  4ig J, Rottke H\ Sandner W]7f]56} 2168.: Nguy', en-D!� , He��"� a�2.~�* 512mDunn66} ��ne� 1966)CZy�259Ay%Uz� z%B/4fJ��Ko�� orskiX � Nak�H H!�B!L)M66}�M41�y Sero!�v V�!�A0,6MBiiUNgj��t 05346� Niik0�% ura] u$0re F, HasbaniG $Bandrauk A $Ivanov M Y��V?7 neuva�}Corku@B�2 inNature � II17} 912�������3b�21} 82 UToy    XM Zhao ZA�)䁱 C� B{:m (91} 233203..� _A�h.\4I�Int# Mod- } B-K18} 165�T�Hube79} & P� HerziE GvA9, ]�iVY D�t�?&=q (Van No5Xnd Rein�r,n York) %%R9�f8ref�2%.Kmcbib&HK:�;�SI} See e.g. NIST site at http://�|.nist.gov/cuu/Units/index.html\,.(C2:�:ord�2 L. Lr p5P.Spla�nC9Hng�C J.A^lC�5 rcetA )jD.A1{Dilke�� O.A.W. � athe�pc om |�W� aOj pas�^�7,British Muse��1992@4ock~ �yali�.kkad�Out� e��De�/!��weiCs �< � �+m�gsystem}y�,tuM�t�806.P5)�C.F=tri�An�=t|� {}&�8 =�ColleaZ1926..b Rich,,�/Wk-� Numb"oiri�aclaUx w�J}, 5� Duck)P�%i�D19�5Agnoli�D v$Il senso d�/misura� ck  realta�tra�Q osof7s!&za |Ps/Q $umana}, Ro�CArOo Edito��2Ald_(K.  ��mA All T�s:S#,-Year Odysse�Z@dden Error That T�7oC[A1L2)e� Freet20j5AukIfxW} �� www.2.com/h�By.htm6�Hahn} Rـh1��an?F�Ea)Qt��Wite: ��� �Oe 06@A�<1666-1803, BerkeYe]�vCal[bnia��+.$Rothschild�;�� Econ�Fs~L�,�tdam S�_,�4E�!oEnN, }, "��j�O.�luglio17�\jrbogast�9b���,� S��'�Xɲet���>0\`eme g\'en\'pZ$ des poids&��s : r� etOje�E ��cr\'e!  \`e�PC�kn���]�$ au nom duwR �d'�Yruc-pa�C��vitoyen 1. � faitvs �YlesW9Hs �M !�Eq.O !�.�Zupko1A�E.  m�FrenchR@ beforJ�4X: A di��4of!] vinc#O��lo~Ku��Blooming�Ind+ ]�՚78.���X.��-gap.dcs.st-and.ac.uk/\,$\tilde{ }$\,m�/ATopics/H_a�l.h> amine} C�]LaA U� Nouv�.projectO Il invTCbA+xre%��+ir. )�Sun touteSSsMj!-in� �oir%�h m sxe caA�� royal| &� E�17�@M81747, pp 489-512.M'n��> , �Cogitn?� a:�S��aDe Waar5 B[ieu, 1642k Huyg�)!h M�Ho� ium osc  torum, s�Sd�ztu �cul ad h 5 a adaptat� m% a�es geo�.& Regi�*Illustr?ami Typ|Kx1672?Proot� h ��M�c S��vq-s.aol�njackp9/met/.�Talleyrx,C.jX fPrfz�Hat ��Zn !5�?J,EM. l'Ev�. d'Autu�#M+� *� 2� Jeff } T. � lan �_esj[is���($ Coina  W0 �m�"Z 7 �BKr s, i;Ve�I��HG�� Repr��a VVouly 13Z oQq\ The a�plete�2j PadoVK 1943a;. 974-9�( ]onic  on atm \-ou�$ ld.\-compAveEHhomepages/ Gene\_Ny�@/t\_jeff��2 AmChSoc.h.nesacs.org/nucleus/0101nucA[ric�$emL\2kGeodesyA�Rug-�I;Qdu��Kg *.��P��concep��Zrn-��N" nS�$ey \& Sons� 92� Moutj G� �v*iT��ite�soli�$lunae appa�+uQ Ly|  Exq�0fia Matthei L�nv1672�#uxJ -Lavois�~aA5m�.onRs�" Comp���eus�dBXs� cA�mt1882� CE ni!��3sin D��ur�dfig� Terr�� ^i�R�)a 2�&3 So\XJ �ong�be� true q� 8lone genius who!� ved �Rgre�Pt �# �&a�his2T60Walker* %Iany Inc992�Z�J�R&�in � .�o�#n peanR�>�c�ag�\-�� hiladelphS � Am@San osoph�'SocietyE�!o"� Leblo+?A� Q�� � x��6d� 'un� , ��2 mai �QD�Ev:AR�1vxR�n�QclSN} .0 lles g flexLopu es��IsA  a�/��BLMa$�W 2� r� %�e��p Gp "n Pn MeY ��(Envoy\'e auA�% �J�[p% ue 2%�$3, l'an IIm�Re+}^i2� %�2�Bul�OEarth2.mathp�sՁ/k182J"4�!W ��P�*a��tep's shapepQNewton �GClairaut�DriseP~� al s� a� 0eenth-centuryI�xm fally"no�]"y� .}'Cj�>GGuedj1+!.  q�Le m\`et�u ma��' 0; (Ital(ktr�Il�o�1o�qo�ganesiF42�stamp&� @sio.midco.net/map /arcF��!�:�!���m arc. !m,Peru 1735 -- ,5}, FIG XXIIer� g<Wa� � DawUS$pril 19-26 2Z  �fig� pub/fig\_�(/Hs4/HS4\_s� .pdf2'TOE17} D�AL��%|�JɛA(E�}, Bo�%, Black %�ɓ�)�89 R��w� �6 "� caltech�0$.li brary.  .edu!�hive/014/18/�B�Mer%�o2�bnm.fr/g \_B&aise/e�/���/1�F%E�N� a MCidiŰ7 A�En6�1h� %he �C��go,!�� �t/ �12�DeVTr:J.Bb �y��� f"� $rogr\`es ���Os�e�at/depuis�e9��}  i!6e$ !�Y812�B�aa�f% !8�2� ��AvGN�� ale;"FeF E� �5 nM��& 1792�0� pr�r�%\'�'. Suivi! Resp <�^isq ��.� 2.�R�?��y -��Ra�� ]~Ocq�)� �>Ath8 �es92�$EncartaMsnue .ms�Ζcl�z4ia\_761561345/�\_�.f3�&� FIFA���fa�H$en/develope{pitchse��,/0,1245,4,00�Tgeo_tu�al} X.~L�c(H.-J.~G\"ot.SIeT )��$Ellipsoid,r rA�, �"ge(I\-�3-�G ��(e��00 %-1668. (��lct��rl-�n8pdf/ Li\_G\_TutB�-¡�} Entry ��oA Micr�t +i1��$s �^�/ion�^6�Pianeti5�cha" .a�K.in��a�$nomy/ninep�ts. J�Burn]� T�M ���a�u� �\S��eri�iGri�/a�ca� 167� N�0�f�6 ZMcWeeny ~ ,�hb� TM/@ofL ar Q�bum Me!6E"Tq�m� �%:�c l -rev^|R�VMo"( n!sk33Af66�XEMC-1�f4N. Kantorovich.�v�aC: Solid!ht�Tys�QPV5041 (19:PnBQzdi�o6nS. Seij�zZ"ia %.{%2�oJ�Ra!2*�6W 6�x:jT\-:z�g�zK�&:)V Curr �$v�4�s%V992U Wils]S.~ .�EE�m1#CVi�|*y!(Cladj O�7#::VKlein� ~J.  l]� In: Group� � ,� appl� \�.~s1-- ��V _ �19iIh4 /lyast1}@dL �K&�2(Soviet))@ 2}, I3:B�N2VNZh.ʘ ukt. KhimM�16f�7|a752�matsen1zaA.�se�7�_B6AnM��,%�m\18�|76D a26aXV9�%oD�g Foy2y_FneRn3%�C O�YW. Kram�4 oF9 �.�jq7�>q y-ADR&�B�: Zapol:f �)K%E9!�842{6_i f2�6��f\p6f0Danyliv-LK-20�%O.~ gL.~Z ǥ`B �] 0751;eN2v Vjquartz�q1�: dens%�ter ~E�723N�bl�h d-ADJN.�Y&Ř�� ^�5]�63�pqk �6=%P9_.x��2d�5WN��j�13���so1�R)qa, `` C.M.q@obeJ.�Iomp15>173M��1��6? issc];q�.c ,} FEOGenRO.�,f9�0 6�f `b2�Ba }, �W;#r&�� �! spac��(a ux m:�disQ)�� , ac�s J#<.pmars2.zEA+rs,A�%hk�-r, /.o c!mb!qil.h.9u2�k553--� �82�moore�{���( kReI�Jq.,b9P�5��6q \}f[N�h��kV9�625:m6Vr�1�ny�JTq[1k473--499�69 pdemb"� ;qs,}�� lst�)�H�: E�, uHuSN"�#]N6�f66�`Es+�.msl&~6�~%�. �}��F-�G�O�ors; n"BU�Z hamilton�pd�  t�.c: rve Oity.n?��;. ��84:�/�0.�Dchristie+.prod_appUC � Griffiths/tMitchellC�kanz-S�.�Pr�%>*���nooSarx#� �Ifinite̓� m$.W�IMA"E�An , 1:2a[2662�-di�L~DickeF.�tonYJ ayH=�S?)s}.�]�y2D&$deligne+.I� D �J]!�Q�um �� �S��0A,zsvy� cian6�T �#u��"�#�! itut HAdv� �ud$2%78faddeev+takhtaj�4L�oF %%\ T#B�.E��E��S�Jy2Wq�XFV4karasev+maslov�q~V��VrM B�NU�Poissonckets.�� %��72�zf1:�4man� Y.~M .�Algebra]�p��y!di�*�al"U s.AE:TItogi nauki i tekhnikia1:5��2!E6�.��den+pa�)k+Zp�H�vM��,a�P !%Xpe��.������%F, y.� ��t��M��tPDE6��Com*�=A82���$�9:3��3952�novޅ�oasN .�.��A��E�valueX{ alogY moa�fMFPRu���a��Surveys� (5):��82� palais�P .�%F�z%TE-Global Yաysi6NW!� BenjL0, INCN 96�Is�$rod} N�vee B�Top�8! F� BundK�./vg852�=;g+fixE�Str�@��G.~Fix.X%An���@%� El�@�o2�Se�AIAutT icAepu� .dn�W-g8!�6i/w4pn�+~W .�-�}�cura� ai�.-��A�.$4223(2):422--43e�8�N��f�9}^ � P[1]{lgc} F.Wu, $\it{N��dard}$PicE of T"-�4(The\\Second\\aRevised2;�18s/0308012(lanl.W ) $ V�<4f��&y etdr}EyCM:L A� ECAL����2Azep<}� /LHCC 97-mZ2� alice jALICE6plʼn�Y c)or�o��r S�ome�(PHOS!*; �9-N: btev � BTeVR�&xQ�0 Ox�9 CP V"9aDR�@DecayE� Char��3t�(tic@� &atiSermilab�i^�--�}, -P819(;y�2���Pr SCINT97, 6nf. o�� orga�0S"orsnd�ir!Z�, S؋ hai,�%� !�,�W� W. YP1e!� al}.]RHieee47:1741} X. Qu,9Zh3d R.-yIxu, IEEE�:.m� Sci. NS-4�0)�(2� nim490:303 A. Anne�] �orzhi�XP� coqh�� r.%�6 . A4903 2) 6�paul}CLTen y�yA�$lead tungs�2 *$X2�FrV4)/�s2+E�14:149n�q �JXA�ec`A41I�8) 142t Y 33:6!8ȩof�z- mtY@�u Nessi-Ted�Lr7m� 9) 668tn95:1NNR�ipaux%qO. To�)a��s TN/95-126! MFY�5��; �1�A*U , p\,274,Z(ft�(Ne�G land�&5I�P�renboqCm�E�t Eick.���98:069}"Au�yI"1�� NOTE�"8/069�UB�tnim530:2HVE�Bat'vR��>Q9�5[��6V2�55D HuhtinASN�T"8)2�p686:4x�r�nqvisZ� ��p A6R�: 462�3x�-9m\N2���8/038R:et�*tt�PprJ�H.� irra � M. GZ��)� �J-2�{!� 9) 72b a�Te JG� Tuchsanweisung f\"ur de�< Dosisleis�?8 er 6150AD� F on}o0st� k AGa�L��bu��Ge�?�$1.�fluka�¡'arn2��$ TIS-RP/16��86)eP%��"L1987) . \\ A. Fass\`.ea+roc IV:�Calori�  �� Ene�A1ics, La�_do��edse Menz�h�A�rib��  ;+ p. 49"G� \\ � ���M.��MCd$� C�/Xte Carlou"in� ��ZA j� p\,1�J.�Kragowi�P3in�#M.Y(bank, ��� ficEW�!Jc�!cSpep= ists' Meee on Shield�BA"� AccelerU; s, T�t�.IA�i�  Faciͭe!wr�#tMTexas,   28-29� 494. NEA/OECD d�� p. 2M��&\ �r8:415} Q�~�BZA!�R" !M.(��43E�am46�KstzsC Ranf�@K�|ebel,I�HCh1��&a?0r=� $, HP-70-92!�:��02:0192B�L. Nico9e3CMS ��+/01�22S�#MSl}cca\� A. Fޜ12^B3�rg6"]TN�N5/1 �95)=vhelmut}�� Vincպ� renyuan}�Y� �Pf��� PWO Cr� �2 Bn� A�� $ NSS/MIC03VP�HPortland"�� 20!�206�nim206:1hMs�bay�2 �^�Y5206!�83)xQ2> -dpf� :� ^ �v��-z c6�8extreme environYs:�"�<<� DPF xe� , RiversiaGN3ugust �31� 4&�4 ETHZ-IPP-PRAX 4-02H .�as91:1942�,Bb&� 1G 2) �<>M 50:1:9E�F� ccioF[9�45Y � 55.[marc5ə��F�Hakul�b.� �U�}o�, �',Vol 248, No )1) 38Bq62qe�0la-Heikkil\"aF��.7``��-�Prp�2J��Induce< � ctiv3A�si7 Som*p"Mat=.Mxsa� LHC#�1ad6��(�6��5�A�2T detu��. 1q`eօ�� /0�  2Tin� :1#�J? INA� 1/011~.�a� bor}��S. Ilji�O�_q� O�nuklid4uk�$ bei mittl��izKW[(dolt-B\"ornohA*Neue �,CP 13a,"�N $ N�"jj`�&�Q,Jonas1} Piet�{9� thN , %{\tt { www.�k. ttF0T-greifswald.de/$\sim$jY/TE*>N} %(in� ), Gr;�2��6�(Bruhn, B.-P�Hc��PX� �I/R�/E��5]�37M 6 O}ŖYE�.\ � v. E�)61}, 307��6�(Golub} Yu.B�lub��i, V.Ai0O��kutcha܍ Behnk J�K � :�� 03642�A�A�&�Let1�er��� Dinkla�B(H. El-Nagga� . Wil G.�� hommj427��1)b"�.Bultele ���%b8�r�/)bdx)�]32�26146`Gwinn� eazeAK.X�lyn��G. %N<525j �!:�-!mov4Sh.�c, J� �2~3N�PRE�c:4!�.�m̩|)�G�59!�1#% ��$Fiala} V.I��lob�(A. N� �30��[yyPo }A"P;M;�C.�lchforVN' *�υr7�#77j6i-a�M$�rtsBHA�eim��>TNm81a�07S172�Kol6�8 R.R. ArslanbekA�.&m-mD ��� 2��� 9pT�aun��2���% ��6�1 .*G:pd�$ Qi~EŤ1��89).�3� YGeu@S�n��'"AWon"8�EP�6�)12), 13C488:�4AVO. PazEa��YuAiGrigoe)B26()1��4|2:Z5}�jit��h%�S!�Prasad!� K. Bhatta�+jee �RTharejafzE�28I�3:{� RE�si Kum�V.P8WNampo_�an��P�Vallabhaj�D412 1mM9�us�� M�%�m�66}, 66$.A�22�u� Yu.%�aiz�����B�>�E���174G��). %E: � a403025�PREuwc}tW  Sa"os� Caro�,J+55a����] �� P.\�� � em G�bisAg���} (�"&�)1996RW8��Su�I˥Dg r#ҁ�S. PlNRv7�v51���U!�&� b) ry} G.J��HagelaAbFw+de Hoo 7 G.M. 7o�F, %N:14 �20::KGM} KA�I"2�m�;�483�6� Radev� H.*�6k  %%�+3|,��DirksmeyAwR�whm7aT chme)i�H l�ndч�� �1�r � �'6�)t�_C�dF��6ne�FE?0 NiedernostheY.� �4!i742%'96� �2  !F�:}�V�2�a25�֡3}�Xo�>"q c� Stefar#0c, S. Vrhovac)J. ZivkA=E�a.�F�e�},no�T C4, 341-3AvB�Mue� OhYu.  Logvi63 )��o9� 98��/1� Hunds�  dor�JA� VerwAp N"�)S�T %of .7-Depe�8tn'ec+-�*u�-Reyo*y(�@%�> �o"�"al��+c!�bf|k&=�u5..�Wes� W/�i��#ipl�P6mF|�r�ڡ2!m�"�'*�.�1~� New�L. Gu���\Liehr 4. Amiranashvil �/2E2���� 0362�9��(my��.F�: *t"U&O],Eindhoven,\\�M2��� . ISBN 90S�(-2035-7 \\ �alexa�k8.tue.nl/extra2/=1��B Z^#�,i�KRgPGGyv$ookref {K�$ l C} {19|@ {>pQ�)%*�@s' �?ey&)]} .�aLiboff2k  R�ChuprD-16� N LR��@ A: �(6"'t{42936�J2jbEu$Zhabin D NO�q30:e Pedr!�� Fern\'��z (C\'ordoba Pxt�{\'~ĵ�%JFu�] ento]F %sT�CuU.�Z a In�Ver #a�ݲ�,� vicio�Pc^"su� ad P?1 \'ec�*,Va���Span0.�.�:_Schulkijv Sztancsik��a� F�Kici J�4qq>V7�7105a��bib �If�+53������������������������•�Gersh�E�P:M arev��77Ʉgers77} F nfo{V�SJ6�\��AnamМ{�^jS L.~I��(:�}*c"r~���.~� \�8bf{m�b�722B�N}{N� 1977r��И�6!:86)A�! , AnWz�Caffrey6}]{jon�q�bjE.)=6`:�V> A.~N>>��A��bi �@��f�)�_1b�5RR�5��FP�86r�BreunlU ��7:�%)�rg�AKammel:}]{breu8� W1�:�d99E�V�B��C��?Bp� �<��F�Rb� 329}N�vb Ackerbaue_~�:�9:�&!� WernQ5g=��8�!A�jtB5b99j@Bc� ��<�2��e)~�Arh65R31K5-1�9�i>�5�,m\!���) Le �mh9���6j�B�>)j<JJ��k5��.q���)!#5���Ann(?v.~-�art.~Sci�x^3^E�V�z���a�K� pono��V����5$NZ�ContempM�}f?3Z`�2�+J�v��Fr �ch�?�froI�~�B[JZ�Adv��b=�0J=��r�Ve���6 vesm��z�?N!�. KZ�Pis'maZS~Eksp.~Tۚ ~FizH^�Z��11J��1967})*|�-}{[JETP^e7l�� 67)].�6>�{Yu?~�v}!-85- petr85ZU�>?^!�# ~Bj�ƾ6C� $F�85rMensh�F 86�mens86bZ�&��N�]� � R 1q�����-G14R�zf �_ 8{"�� {a}}5H8c�HV aF~Elem��� ts At.~Ya��y^a1�F34�NO8}:�>mq$Sov.\ J.\ Ŕ\�.�<�gG 5788v~�QE��!_s�"ڊ"j��u���J�i�R�n��^�946R< v� Faif�*� >� #, U�AWan� rizh� faif�_ M.~P��.  _:�� �B2�%�e�VTT�XE�.�S �]�"L 0Muon Catal.~FX?^54� ��8�an�no"�91�4!�9�w�r�%-2?��f�N��� I��r�2^��2N^�'�#�teB��9�� leon�.f�B]FZ] ق�4�J.\M44;F�94r�:6E#{V.~Yu-"�9��yR�5�:S��D:�r4� 376J6RN9v�An���>2"9hm,%mi�;�)�� ver0�pY.>��W: V�V��:�BoӔ.V< A.~M><D`�z5� �N�Hyp.~9act�(^��.DM�2�@>�!or�Kaw�� �!�3:�$, NaghG� Matsuzaki;}]{kawa*R�&� N>�b94j(K>>��>B��?����eR��^�V^� 0434A�F� 02003}). \bib�Citem[{\citenamefont{Fujiwara}(1999)}]{fuji99} \bibinfo{author}{\bibf9M.~C.} MD}, Ph.D. thesis, )iO�school}{University of British Columbia} ([2year}{� }). �j�4 et~al.}(2000)V�$, Adamczak�Bailey8-00} k��.�VA A.}~�5B�}}�> J.~M>� �?Z-,9�djournal}{Phys.~Rev.~Lett.}�textbf{�%v!�e}{85!�,pages}{1642}B�!�r�Porcelli1{!�1:�$z�porc01�� T.~A>4b96�������9�6N� 3763R�1r�Marshalln�$z� mars��GJ�b������,Hyp.~Interaczd138N�20α Lamb��3��lamb3�� W.~E>'I6�JC} b;5�;�\�Z�=90F�193v�\Singwi and Sj{\"o}lander�(60)}]{sing6�� K.~S�bib�. ]}:�and���"6��B120:@1C09J196v�${Van Hove}!654!6vanh54�IL>�L��9Z%249N%54r�Fukushim�3�fuku93��K>�K��~Aj4a�J413R93r�Silve� 8M�lv8�� I.~FF� LZ�"Mod.~2j�52:DM�3V� 80})*�note}am0 references L rein}j SouersA�86!�soue86��PJ� K) emph& �title}{Hydrogen Properties for Fusion Energy}�1(�2 publisher> ��>5�R AafR� 197V 7r� Menshikov�88{\natexlab{b}}A�mens88�� L.~IB\Z�,Muon Catal.~�j Z27R�88}:�jOstrovsk Ustim-� ostr� V.~N>Z}%�.�a�j9 V%V��UE�.�u�HZh.~Eksp.~Teor.~Fizv�792I�v 1228F�1�w ���y[Sov.\ ��\ JETPU�$52}, 620 (>)]n�Padia&' 1988:2 ", Cohen,�� Walker�0 padi�� N.~T>� Z:�V/JJ� �1J5�!�..VP R.~B>��2m5�%in8 37:�-�32R 88r, Fano�'61�fano6�=UB F��j 12>� � 1866N�6v� Petitjean�x��9>x%, Balin!� Breunlich9}]{pet� C>`:V1 D.~V!#.P��> W.~HB>�BU�j���1� ��1�27N�9v�9/�-z�� �zul:���!~���.��91F��@ Jon2> 83:�!, A�soE�Caffr2�jone8�� SJ�`Y�V�N>��A A.~J>� �@�����51���1�75R�8vUJe� r� �E5>� #,�:A.Cargn.� }]{jeit95�v M>G b94�V��jBB����z� R�288J` 1995r�{Yu�G~Pe� }L r Yu. %���petr9^��:S� DV.2�Z+R� j�0Z5R391J^F� ���73}, 29� 91v� :&&� a44:4:-,>�,!�$ Schmidta=%�^�9h6�:h.33B��� �� HJ���YՃ�օ�~Bj�33a!!���2V 9v Akhiezer!c, Pomeranchuk!�47�uakhi4��F Z�"f5hI>�.�ZC�0Z: 76R: 47~0 6 11}, 167a147v1Wic%tm wick�mGJ�IZ!Id�ja9^{ Z/zkLoveseyAP8Ilove8^�Y S.~W�. L �R~Theor;�Neutron Scattering from Condensed M�R�Clarendo�|y�"zOxford �q�"zv{ Josephson!� jose�� B.~D>N6�:a!��fjZ34R�zMMompe\'6| 6:%��0Garcia-{H}ern:dez@rmejo� ( Bennington�momp9��FJ� y:7.Y�B N��JN�B �@��v]}uNz"S�:.)]�NB=��U�� 5A��u^�vtBethe�rlacze��3�nbeth3�nH>S�kG>L��IjC� -�_ -145R�3v��.y >B #, Strizv Armouri1 Harsm. faif�.��V�TJq �:YV?E?~G!d. �BU�#M.�-�:5]�u :<^"101/10�B'179;�f�#z)Toyod2�%>! ", IshidaArShimomur7 }]{toyo03�lB� ^9nE�V�B ��<�?5�j�&���n�9. 9� 24340J�200vHub6>]!z�#hube9��"T���5_9-j�B��>�\'\'�WZU5R� zU�nJ$, �T, Ponomarev:96a�Wb�s��N���UKj`(Atomic Data�Nuclear Tablesrs6R25J{1~�@� coh�� n��-� ��Sr� .A��271R��� �,� ����:�j^1EN�R�z�Wo\'zniay��c: %wq4 �k}]{wozn��J>� ^y�7b7�} �2�!�^�66���06250V�,��xend{thebibliography} ';\beginB{34 Dexpandafter\ifx\cs� d V $\relax\def"� $#1{#1}\fi ^G*� >J!M#�P"� jQ$�R.70^R.$�Rurl^Iurl#1{%�tt!O%8{URL I4providecommand" }[2]{#2} B!eprint []{S'}f�0Krommes�2^~T0J :�� :b�lasma.�!�trol.g'r43NA25V�v[HorX�J- ��W>� :^�� f) �j�7Z!73Vhv�Griem�7�H7��Hl6� < �R�LSpectral Line Broade� by )�sf�Acade� *) New Yor�(Lo�6)�7v�Ok:*95A� ~�E>�5 {R� � �oscopj*S�q$ger-Verlag.�"�@Berlin Heidelberg }q��z<Capes� Vos 0D/7�7ʨ9֨D>X�6�"� 1 e:n� 1Z\.17N197v� Bara!�%<Moz)8R$bar�V$BlX�>B>>��:ji12�IJ72Riz�$ Kubo]�N>' @, Takenaga, Sugie~$Higashijim0zuki, Sakasai�osogane/ G��B_66fVB:��>T>��;S>;=�AS%K�<Bw -�h X:�.1VENB�5�!��y�� �R�11R�9v>(Stotl&� A�>� # , Skinner�,Budny, Ramse uzicI�6)~Turko� >��DJA/<6CV�CN� ��@Rv":��>AJ�*)�?DJ�,%TڎB:6�!�J�=;"�fWZB 4084FP'�H&'A}B�A_ChuE] Hintz�Hey�TJJu86bPC>ChuڑBa �}ȕJ.�%�B: AtD l. Opt�I 3�.��35Z�vJ Koubit2�<2:� #'2r�8tEscargue.� <, Godbert-Mouret�,amm, Micheli! uirlan!�Mattioli!� c0� V�B� ;��Y>�M Ғ>BP5�?B�%8�;L>�6l�DR>DS!��;CJe1גAB|M �kBYKA�UBup����BQmk26V�v�Ql"O 200>u'$ , Genesio�M�FbFeltsuiEO�E 5_ ]{nfg�H�P>\ ��B� �=�aB� %X�B��UbEo�� B�UAAFNuc���^�E�JiS�B6Efn�5Q�.�>�-$,M� BVMI�-n(]{europhys0��-��b�.)V���A�j,%��7-Q2��FE-e. +} N5})2>�6acceptedt<X<catior =Q .1>�$]1L.6,�,Z<CNSNS�!z!�75�>�֗VV��d�dCommunM,s in non lin�sci`?@ D numerical simulEPnP6��46R$�r�Zaslavsk"�I��>�I%a4Edelman, Weitze�2,reras, McKee�2avenehFonck H��IN�F@�=B ��=B��>B�Ca)"�>B3(%V�;B@B-�ڢ BP-�A F� � n�Z/36Z�6vPEJakubow~=^"A�>� &���| Mcke�"ι 8 ���F�6�ڣGJ  ��^���b; 8^�!65�&N8v< Rosmej.�>  "�Tpe�N") Lisitsa*� Meig+ ��] A�FJ3= |��B � �;B� �=V>� -�=�3 B7%~ڶBY-�V�� qCon�F Abst�K�^� 27A��#�11.1769>7+�3Rautian�Sobel'�E196� ��SJ�,<:���I�Ae�"v �ZZSovietR!]UspekhijSZ7N�*!r~Bransde)LJoachai�286J�LBJR=:�MCJ��)LVohysic]S atom�molecu�(6pp&�HLongmaO4ientificE_ TechE l rRdzQ<Frisch�_ �>�4�zA Pope��bE book�*SJ�=��t Flow`�4N� �0!.> ႧSChe.�18>o , �Kraichna�48��-F�he�" B :6��nRJ��Vak� ~�6Z 26Z�?9r�Dai�Kawy^Das�[BEDaAQa۵��4B��r+P�n� Z�149R�@z� SinaIYakhot!,8�%��YJ$<��B= �r6") j^`196J+19z`Tsalli*% �`B�D ;^� ChaonR+L5�TF6�1A�&<* ��M��&Princip@NofM�:&e ͔ Mon�,s �;e," v���r�v $Uns\"{o}ld!#5�Unsoeld��BWMI�R��C`ik des Sternatmosph\"{a}r�2���:)'7/'F� 1955rLIganov�� Sunyaev�� �/NJ�+ =�)RJP�)O� "UAN nomyōSfW2^E Zv�D}>��]K)�'+MJ;>7 _V� �. �n�3^�ULVSLz�LiuE<�� }]{YingLi��BLiu>���M.-B7?�Z6Chin. J-7�?Z�27J�20z�Jh"�9!;etJha�qB�Jha>7r4�z��#1B&.��69J�4�� PaulE/Bas* gel�l\.�iBX.6�cB�$�I4R�XStochastic processes, F}B!U�$to financefr:�N�z{Jespers2� B%%!�Metzl�U(and FogedbyjJ��Bw b-5��VB� �#�� HJ$E����)!�� Ej$5Z$273VqI9rgChechkijGonchare�(3c ��AJ}(]�I�2*k5{�rD� n� ZD7J�T�-BeDGuO�b�v3B� 8Ql�6 &p !^�1876012k"WvR3Resiboi�DeLeener�{0� B:� B�IR Class< Kine�&�Gfluidj�2W~f-bsuceNz�0Wil3$WlodarczykeU��#B�8�EZ>�)G�6v�t8D&J�27N9Z��a � l=�uZ�NBZZ�q��E F D �j8icar�232^� 6V� � R+;�f+;0m�ptem{r-ZHU1} R.Y. Zhu {\em et �i!� ,Nucl. Instr.�(h. {\bf A41w=41998) 297-311.2dETH1} �Nof��PCTcomte, F.~Nessi-Tedaldp zu3 u$9) 630-6366u ZHU2 �>� ` zb37�;�-) 3196^ ETH2�F.~�, K.~Dei� ,��>�1.)_149-1556�0Bornheim} A.  0 (CMS ECAL) i�^ %U@``CALOR2004 - XI ��n%*f.�(Calorimetry�"Particle4 '']Proc.F Lbe publ. by World Sc�, �eapore.�7I(Batarin} V~ ���51:�( 488-505};\O V.�_�c!0 ) 286-2926�8ETH3} M.~Huhtin,\.�D.~Luck�/f�%H-�$8th ICATPP.�on6-�, Spac5�y�Detector�Med��L � Appli�&0s, Como, Ital�#  OctoFF6-10, !X }, arXiv:�(ics/0312056N�3}�q IHEP�p�=g 4-7,! 0tvino, Russia�46qlAUFFRAY} E.Auffray, private 3>u l', CERNZ,va K.�KobaBGO!�  y�6M�9R%�^20�*(83) 107-1176�XCsIzd��$_ 1993) 501A�.�>N�f�� Wave�,Random�a��bf �.4�-7.�neviereE� Nevi\`ereE�Pop�Light0pag �in!�iodic d:6���$Design, Ma�t Dekka��=�optlettv�to� :ld�Optl ��ersQmc� C. L\Vpre �F1< in prepar�. R�Cb Iab2S8VI nsiW�I�I�I�I�I�I "�HR��IvI DOP(DDOP nfo{�2 J� de BoaT� Mil�/M 0C. van Gemert�� J. S. Nel!da63��2�9347); %gM. Buenoe�P. ArtalJ=��6 <9<0A.H. Hielsche��i63 � | Expr |1}, 441{4 B. % Laude-Boo' teix�fDei t� 8B. Dr\'{e}villoj L. Sch ��pp�< �4y 282y ;� IteB�{ Klig6�@0>�<", Lew�(�%�Call  B��&DJFj ?:�V  J.~Wd.x��na�|a��uC.FDo�x V� Polarized��in!�jafvp�H~�G�&�H, Inc.N�90r%Gi ! beu}"RGil��rJJ5*Gil��B�?�)MA�a�"�O��a ActajX3Z '18R�CzKR,Roy-BrehonneO Jeune}* 7�� LeRo��@FF� 2[��2�%V�BmLe �ZC8Prog. Quant. ElA{�^�2Z L10J�19:$0{aiello2}A. A  . Woerdd5submitq8" *�, �q�(-ph/0407234j�p{E[lf}�mWolf03�,.I5l9.UUy � .v1b�!�%�y{��.�;,{gisin}M Leg��,�j Wegm\"{u}��4 N. G+J� 1�(91}, 167902 Q" >��M-B�!0E��% ��L>� <���I�R)O�lk�w%(E�um�oec9��� r}R�-�1wy�)�@ ::;edi| }{1st} edj���ѡ~O)���.�"PSFF:�d�d6q(O!r�+RR Perg�n.(842f5Fsixth:H�f0.J� ��=�u�J�ES�Ama� u#u��a�f9��#�2&(I��Kim*�&8B�wisEey� �s��]:8�OB2^Ki�%Db� ��� B� � L%�=� A8�c.-�f�42�-�DJ�1986|*( D� 5 �~W� �  E.� , �>it*� l� in oE�e�s.� , � �1� � 02�0mckintosh} F.acK �X�yI�R and D.A. �;2�B (RC�|��4 9342w89.w>��]��,��  04_1��B�+ <֊J.F�{���B ��.AjD7Z^'02380V%#��.u 4029��`{POF} For a review on POF�, {e.g� �& Zubi�]Arrue�  Fib.�nQJ&U10�� uun�} W73measu�� a pinholeA� sizej? ilar /fA�klr:�we derived many negative eigenvalues $\�Sda_{i}$1, resulting {�complex-1 d} eBWp�~$E_{M}$0 not g mathemat�8ly well defined.4Eq.~(\ref{eq:1�#N(fG�#!5tm} T� ruya�Q D.-A. Luh4 Brachmanna�E. Clend/V�L.Giwn,S. Harvey, R(KirZC a�cotJR.post, %#hI�> })�8U418q2� _�(clair} C. K� ,�M�el��!� PricAz!��eedings<!�� P� AcceleI�o:�2-16 May6 , VancouvO B.C.Q0na)ep.V.� {pea�X S�� !]W��Y-(M.�< vola-(H�nCryst2 ne S� ondu ,} (:�),*�V�Wy8$ide} Y. Id M. Yam�)�J�c�iy�-�A1!� 1858�W9�Y,baylac} M. B QN5th�~0ional Sp�I9Ps Symposium,} 9-14, S�Em��, Upt��X , p.�3��N!z�! �! EV"!QJi�a�($N ofňmediumN" MU{ 0} %% OK guy�� U!�kkels!�8E.~ Uggerh{\o}j>�b&B�n16I!�435-439�]� .�Arm00.h�+.~Agan0, � Z.~Ak�*�5.~Apy��et.~alN=&�76��71� 577-583�A�)��of�� beam�0�͡�0E\geq 0.2 GeV�+ 4.5 %el# ons a�amorph��-�3convert++)!2�� Yi��Y�T� �1�)1�* j���of�N�%� nano$Y�s1��A01.$:K. �~vetE!>�hE!1~Melik$���7������77-282j�6V.i:C�!��9rQBN�RzitfWR 432�, 11-1i��~{ �*.AG.<�dz6�3�;z4��5!496-49� 3. %� cryt�LPK�Dla�� in ga;*�V �.�m!%�B2��Q��BO VH5~Biryuk=�H:�5.�9��034801�7� 9B04=}V��UiaD�i,��STams�Q 0235 �4N��7�N��Korhmaz�N]�yE>;badjan'5 �4�5%% �49}(4)�9-��5=$:�!��A.R �4am�� �~�2"�104-10I�5A�&�� a =�}|w�7 %eXi�2seF3s takn �" account*� po*�  * Our -2004&!]��: a:Gb-: .� �)-� �4 �4 4 35-154�4 m{}|KSG!2_X"]cC ��z1867-916����@�YarDubG)�I4 ��Ga�ryshe�7,�:a. Dub�7aya�^ Grubic�� e�eʉ� "�7�`�� 61-64� 80Z� ��Y�L�}u4.�V:0~Berestetskii�o?Lifshi�1n8P.~Pita�ii.�� Quan�*�dynamicǡ&tk), M���  9�Kudo1981YYH.~�xw~w$189} 609-6� R.a�Planar��@ofU 2a .��ET onPicrauxU�iA.~ #, �#T!:,� �]U/. 2� 8� ��X4ChesnokovKotov�,MpE�M�uy� �ATC 5A� V. I��tov�%\C� *�� its2Fat�vh-E��@e�#!��#2�96�JY�Henke.�B�:~Q�Gullik 5%uC.~ Davm�YrȎ̈́W55a�181-342,@�"�Hubbel6��E !ySeltzer9V ``T<�An@X-ray Mass AttenufCoeffic� s''-- �>e�_�3{%a�<8V<im1iXYK-J.~X-:�ersA#synchro�� E"'9[Lg�ce _Z'-E�3 565-632�{�%}~!�st2�0R.~Bonifacio,fECasagr.&V %Cerchi�#G 8 Salvo Souza L,�#Dini P, Piovella N��%pR�� l Nuovo C{ � . �*��Baier.BV.} � Kat!�(StrakhovA��� Highʨ��mag�L� �!�Ora� ed Single�=���j�G!�� �lDRullhusenArtruDhezYH� , X.~%��P.~,Yb �N!w*s Sources u-� R"%ic�n�1�����w2.�L.�G� �XE�5 "u=8%��&fNk>of Field�_N_7R>i�sd ��i�A��ܡ0 � let}, Law�3Ī Labo�(y�kl�HCA9�Ch. 4-E�8V* � NIM1=]�U|�b. + 246�( 67-7!y Angu�&diV&bu�uI  po�M,an arbitrary9-le�  %^ ameter K&� �U�*:�)�Q�^}���71-�1 �Br>ness, co,F�2Apr�@ng .� %AhR��Y��)auptRuB=�Hm \"ul,� ~R\"&]�%�Hypers. ��� 23/1"M# 13-3%��"��p��ofZ�N�N�2�(K.~Hagivara2�1�z�(����} D)�6A| 0100f* =^�2�&8=_2S' fP:� !.Co,$K ù62� .rY�iӽ�MwtarF##~�amy�) :31snews ��3No. 2� 47-59D�$�WebPage``�1^� X-Ra�rserA# ject XFEL2d 9 �xfel.desy.de/content/e169/index\_eng.�JF�Petra.K�( lews��et.al\5 P``PETRA III: A Third �wr� S* &&ɳ( at DESY.''� ��,hasylab��lity/up�(e/summary/S  \_02 J�Tesla9[``TESLA�/&2�D ��.S �tB�new\_&64/TDR\_CD/start�)N�-� j�'}bX���D��D��D��D��D�D�D "rD!�BF��Dv�D2��{F�jbac�$ Talm�>+@�`fi�vXBO9T�\7 C.~L�?bib"�9�[7eN����S�%} Non-Newto��.vit�f�,"�2.:G;�a2?[:TEinst�� (190�> �$. <�&(=A.:�G �->"�:Ann��jO8"�6LZ�\�+�-n�^؊.m1�43r�P%tc�(�9Cpri��i�.�K �R�S�*al �.ys\ Time�%f @�;E4� w5N�8�8AOtF-G Gren�\8�gre��B�nHj�Ab� ct I"�7.�*�@\e� ���Calle -d WelÐ5�ca�@<HJ�n S��; >) �)3!�2�X .\, J='@83:@a}{3�X.q5v � and Gr�^a 5�`a2��4>4R.F�� ��4SkJ%7N@� 1952r:Hoyle"IA20B��!,K6B1Heckel�Ad��erZ~ndlach�R�$* SwanB� }]{a+:5�V~CN_�:1V>DJ=IKa��?BJy �?EJ^9"�CJJ�pG-Y�AB�S)��A"��{BHJ�K5�A5���}�\ Dj�7^9@4A�.Yi��AZ {hep�H5262}� ��J% Hami�A6�Aham� W.F�J �V�8�1`!k �\ce; E.(,/ot�5 Tes�8i8,Least SquarebFR�<d�G Co.,�Kjr64� N� �lf� 199+.f*i�@"C�"�:I.��&�y�~B.68�P ^�$. Nauka, M�MwN�red�uK Tsytov�� N., Oj�9��4 M. (�0)30BP*}!al brems��@hlung. Plenum, NY&�� OBrS Z s:J�Pratt� 90 ~R.H1���eZAt.~Mol.�� |]12&V$ochMot.m,�W.!JJ. l 1959{�� .E�. 1� 920*�T�198*R,�4R4In: Lutz~H.O.ށiggs~J1;and K�Vpoppen~H1��Funda!al&��e�.Co�ion*�^P5�� 145-1��1 �Feng198*x$ �F!� !=!~J*1326� Cras�0�(Ed.),�IQ�-Sh�C�Z�A1B 533-580.ZWNakel1:�5�, W� o.!��43, 317F�tyA��Sha�X~D., AvdGZa,�., To@ X.-Mv,FFlorescua�9��=8>�Met_3, B 99, 156-1A�%il�9�At�}h9� !�Tse��!.ISe�� Kiss�*L2�MacCalla��CR�g;N2�779p AtI�� � !,175-2099& (Erratum:AQ,1. ibid. 26,7^-48�FU� �*n2� Quar�F[ A.:aaD!y2�832�. �J�8, 381��f$ % First P� pa�m5�b"� Buim�ovT�ten(�197}� %A]!�.-, Z�2�7.t6!J1�4,,5V�musia19�  A ~Ya��alt�v�S!~aizie A:�6=�J�Y*$ 24, 332-3�Q5C9*0PindzolaKelly:� ��&� Pj��.� A �$204-21.�Y�17���Giler#V.B:�.H6*X*-3, 45�) �Y.�yx%�Cf�ICa�47N�(WendinNuroh� , G�  Kj=�I!39, 4<3 9Zon:�Z�F%2ja6r�6Re c.�>^c.`Jc'*�$ ++*Y'$Golovinskir �m� �@aeR���4�.Sv<10a�yj� %% e+A"====>mZimkinaK�_evT=� ! Shul�#Brajko6" #,�'��,�b 5.�F�`�� Tverd la 2R0&��i� x �198.p #,�� ,� 4u]jE�=�-6�7, 86�E >�AChern�*� 5} %�Fip&�% �� �A"�J�;V.,� 6:��K"FB0B 18, L791-L7*&( +�DVerkhovtsevaGnatch�30Pogrebnyak198*�.. ~T, 6�?eS6w��JI 8~B 16, L613-L61�o-�=,� �΂f A5R9�T5�u�fY; Izv.�;! SSSR:x.I�M1261-12jHMB � ��s� .U/ 7 �����2 - ch} 31 0-�m �� ]Q ��.2�90����(5mA�HV2>�&�m]�B 2899-290��2� wZ1ҿI �"|:{��.{ 251-32ŗ~dep`Pce!BACal shap� in��charged-:---atom c"@ upo�@rx [K % veloc���$.�C5�>�%M�N<yo��*� 9A�� -!R~��9S!��govG�w, %- e-A.�at2��iesy��2�(6�424-22*���� stap��&z Kr�-Mikhail� &� 2�;� � D� M,4.&� Mi ^E�� . I.�U�2�� 93 Di60Pheskoe tormoznoe izly��i�Sly�EHskoi %zaryazhennoiA� stitsi na��e�^�IonE��0---> NR domai�& p+A �@9�9D);.4 y�:o� 4%oz .>, F� 80ZWIA52, 41.k���iMorit��4��9� �.9�!�4�N� {&�5 8; %?%,inuum x raysT'duc�N$light-ion?:  % xJS��}� 2v�5>�1, �aR�6�2�heavy� bombard6&�9N`GonzalezMiragliaGaribotti��9\'\')���2,KE.,�U ;sR=zL9�*� A 3"E834-284)�'b� ©K\ �$] #�� - u.N����b� � $10, 431-43�'B20�pA;ٽi�̆�]C��56�mv 62, 876-8���f��d�pIo*N*:9�90bYU>�'2�9�90�^I<Bu2889-28w.�sPB��s&^�of a mbY�� ion!��,Rel�- >�M@��*�>� -nm)ltrvl ��76�2T ;149w;�� >�ם��9�886�Mq 67dW)I��BrS!�*| !�̹� nJ� ��90* ) )��'j�Sov���e.416-42 Freq�Ly-aF1>o.r"BFHo� %of6n >��u28 % Exactly solv�5�! blem5(*X:0iusMaquetJetz�61�s��2�" (6e. �0e�~�l~A��1888-18� �^�6r4Z��.Zw4��288-429&�  H_{\mu�� Ei�jn&Z*�]*�  3663-36� Inel� c2�$n muonic h�[��  H_mu>�$GribakinKh�MI + � �j�=m~F�FA � 5[X!�Z@ Q&�� H�.�.143-14&Z Ps>�e�6j',��6.� Zeit. furE� ik D�5 347-349X;F��F-pBXronium=�–� ��ino+n��q % n+A>"K Zhal);ro2)fO:%,� C���5��R6�t2���s��n��i.-�e"Z_21st Winx3S}��LA` /E~� itut��!���ic%Ipp.1@�yin?| n). � v�%&]�jaF{=%��F^@:��,66� 7-8� �A2Y/4Varfolomeev197���A.�+}%Y}vFizika �103�B3*l9 ^t.�zt��9.t� 1268-127�R  I�>�6RA2�M�fo #e��!�9� Sushv9OKe (e�"Mo�+ Depm�!inB�0rQ9�=42Lٶ2}EE��*y^[��1w�Dalgarn6, Fy�d"�-Lubell%( catorto�B�E#A��TCPEACS,98a�-+*� �Y �- 5�Y�)�c �)5*�S $�%� . �� A��XuWPum!�`U��yN~�[��F_8tom9@So&V 2� T1,�M:1;:LE��b=��1� " �� ,� ��*� .�R� 2, 290-29� C"�8� "� of t!t�^"'!ic9L]1:��>�:�'"�0:&�50KV���47&D �A�Early & on%!ex� �&5�>�f b�.�8� ~R�#1� 269-33A� F]V+e8]�6- .�%o%� zdat�scow 2lג� pe�_��� Verweyen1���+A��,th\"ohr\&� 0 R, Gerhard E :!Q?Mˈ 17��S9�`.�8�2�%:��)$(Hamburg),�� �?21��#:�^ M:�9!�rJф=aB_ Port�x 4�>g '6� !9y�=HZ�v, NZMZI 59S.qE�:A&ie�ReJ�Z.@IP�*�' 74-1�!QG��-> _PRL���nA�u.(%9pU�CJ .7u 9�732�Y��C�KA��(a)��Ly����95*�"a �� +_"4$!�us9�*� (4947-4962 %b, m�'�6�.�LF� calc�_iR(� ����9*� !�Ų *B�!.��� -�A 5� 230-223~=orE*al treat� ��Fhz*��vicin �SWt�� reso>���Y�� �.�N�բ���1�  S�ed Topi�En E�@r�~hh�&� Camp� D��9�+2&� `P"V+. � ~B[!R r��"�*�%!�A��V�2 # � �) UT631-6)�S a�ht��vbe��y9on La�V�Ge+F�JroF�*�lch+ A��>�a�E q�.�75ة�JohX3�+�*�1-B� s�m� nnta�g�:� >�G���389u��!� 4�64��f��,(b) approxim���G�� �#9k%.199.y$A %35�!#22)�%L341-L34�) '�jping'a����q�Z��; %$EY.�]e]rt*� N� �6�}*s)��m52��Lp\L16� 2�T.�6� �91*V��`DGaint�ic�Ѝ�:.��eBRO�b6*B*�-.J.~y� �.~ a�8@Phenomena 79, 323s"N�f�*�*���.�9�%1�%<؁� �a�� F�a,4d threshold�.�� Obolensky���8N�e�.,1I��>�"a � �i�5�535**��P behaviouryiR<EtA�@*%�!|�)����.�: *,In XX1 �J�< (Sendai, Japan)� 240. �� c) wide r�ȵF:�Lyalin8Solovyov1997} LKorol, A.~V., Lyalin G., 3 'yovV.,7E�a. J. Phys. B 30, L115-L121. % Total bremsstrahlung spectra of 1-25 keV electrons on Ne and Ar %%%%, \bibitem{� � Obolensky� �8��<, O.~I~�8. JETP�48 87, 251-259�`Investigation of the role polariz 4al mechanism %"emissi�Xby atoms in a wide rangHPphoton frequencies.} !Z!=9�31�:�$9. Opt. Sp!�,osc. 86, 486!Eln>�on!Җ�� +R��LyovAvdoninaPratt2002��]� I, N.~B]�Z, R.~Hk.u.�,5, 1197-1210�8 ---> (d) slow%�Lic + excited targets�% 'colliE 9�199�6�2�A�� Zhq�D 24, 5�  p+H_excoeaKuchievV{"� +, M.~YuNI 52�R@(25, 3379-33� �%F�u��b�-��9�Techn1544!�35-114��Featuresa�a�b6�,accompanying=�H with % a hydrogenEenUstate9�. %QWe)9#e+H:�1994cZ.�4�]�827, 4765-4777. iBe�Ridge�� 2000Z�>gZ�}��VR�33��79-L1��1.f5.9)AmusiaE�!/� I�a.,6��4�� Lett. A 1�230-2345�z Connerade]�6�  , J.~P.,J�yR�6�.�,9, 3529-3547J�4GerchikovIpato.�.�& , L. /e�Nv�f�*5939-59�C 9$v=$*�J�F6$79$ Zq�8D 42, p. 279-28�&*jJ��&%&1, 2331AI�yJ�gU�2=DOurRelativisticJPBYkE�%�� Z� $%� jev, I.~A619b]�3�=589-1619`% �9�>�ETP^�� �� F�u����.�� ( 94, 704-71� >�mymIje�����l6l@2. Surface Review2 ��ers 9��91-119��-mM calcul� ��po2� :�� ��/ r�9�%1+B 9�:$%.�5ׁXz ~�y~B �Q110�5�  book}$OurBook200��:w:^j�GY� P6HB2.Y�]�ical University Press, St. Petersburg (in Russian).5U�RPC_Clus1�=M^�� 9N 2005.�Radia�� 8Chem. this issu*��elBrS_:�%�e��_9J����, % Astapenkoe<Co afterA\.�.�L*� 3 Kukushkin6� , V� )%.a :U$84, 229-24A� Multi� O� PBrS5� R�19. B�5�(x8, 889-8�&  Fra9�H4BureevaLisitsa� abYn'� 06AV 9 S69.� �x`90, 434-446; ibid. 788-7� % Classe?(and quantum� ori� !/i in loalc denermodel9V����r��� a fast ch,d particW,Thomas-FermiI �V"-�-�!�9����@=� Laser 10, 96A� ��*� ����� Scripta T� 62-62�R^ 2001n.u_!*  Plasmay(ics Reportse 4-47[TheI�froE� rmalU�s ...@p M$is studiedA� %� quasiclupproxim���y�Kogan��M��$e� -�� 6".��d*M �.~Rep. , 213 1. U���IB�.�&{�_ /�o!�B� Usp. 4�49-18&� R�B3=)B�23f%��HInterference Effect�0ive ProcessesI,URSS, MoscowZ'�L % ====> Not discussImAk� : _> Supp����in con�ied mediu��.`0BlazhevichEta�*{, S� �rpuno~ S., Grish�,V.K., et. al�^ 1996� ~ �,211, 309-312y=�Nasono� *� ,(N6b89�\Nucl. Instrum. Methods B�8 1Ec��0 Col9!�e9�!h.� >� of�� r*� �6B� a //ut�9j-�*R�9B�5�%=�� $Kamyshanch� -~Pokhil6�6)!�,.�, 5, G=�C��( 173, 195-2�6%-p>�dR)�!xB�<:` for6�>�s<crossVa� nDY�9?�� NaukAh> E+�J�lShulakovZimkinaBrajkoEtAl198��'%��� 0 , T.�t :  J� 8��DFiz. Tverd. Tela. X789-7�"D g e��4}Y# )�2�� ;^�]�IzA� kad.%� SSSR, f�@ser. 48, 1263-127R �� ~�1984ay (��:2Solid S� 26, 12�Q;9_ �$Romanikhin 9� ,~V..�(�e239-243.` BrS� m�nsJ!��s C�� a Broad R+"�X n Energie�t�� � � � ��%B !69H�@� 4261-427�@|0RatzigSmirnovxA. eP� &, B�=�0*v Re? Data5'leculesE Ions�"ringer,�uli*6�8HammerFrommhold2 � ,~D., #,~L��1o ~��8~A 64, 024705 �d (Erratum: 3�+59901(E)*�,Mol-orb. rad�*�%78��8�~ "�!2Jt�.u��݂.�7�e�2� E��5�Qf�9@ 13-1�c��*��� �^�.�  651-65��I�_: /%Y` LeeKissel��Tseng197*_ Lee, CeL ,am,�� H., :, H`5�� *u"� ���"3714-17279���1981.��2 866-2867.��ѐ�A�}�z�:.��. 9�66-16*�9WKim �82�im:<27(�. n�  3L 4�:wFlorescu"m �= !a[,&"�&/B�:c2�!(5, 2911-292� Nrel dpw& I!0 + Zhdanov NR� 197*�*� 5 2V��� ikaB zmi H"28-133Z�]�E� 9">�#��Q�3A 012-1015;��,40, 6826-683*�%�":9z%�197*D�~K.u292yC.7, ag00-119�]2Shaffer x2=% e��Z$F�52}4 56, 3653-3658�C�(ris-2��al-wave *}"s� triply�di�ential "V-atom>vK)simplerm��:|}qW�}�21��:*�$t"$ L317-L321&� ( (Corrigend� af0���( 1471�!�0KellerDreizlesY� ~, "r%�M��F�"#l'3257-32�  DPWA�f5:2���!a)� n��!�!5:3Y?=822 L57]7*h fz.�,�z.~.z��383-26e,2�ur�}� ����mS� $46, 557-56*�Nc*)vc�37�49-26.V4% Beyond dipol*� �� GonzalezPz rMiraglia!9�$�F�-%� C., 6< ~E]G9�.� �49�9P,I.�retard=!Oovb�%*� X 5 EPS Conf. on At.Mol. � EdinF% h, UK. Ab�2]p. 711J�Sobelman9 �(I�19���ic1an&�Trar"�1@Sp^��(BeckerEu198.� , U�kff��)Lindle� � B1!�B� ��)2858-286*� �i� Dolm3,Iv��12� "E2�,���� 55BF>q�58, 6*�!��Gribo�-9� "'i�Ky7� 1�mm ique�. C-4,�l� , �C4-28}��PHenkeGulliksonDavis19.>!�L�*& � 4ebC2b93Y> At.~�~q Tab�X.J�0ZapryagaevMan� Palc.198.U )!*� 2g �;%�.Z!�.��"Theory�� One-eQ��c�$�5��oizdat�j� 9�$IshiiMorit��.?, A� �Y�6^��6�22, 68. \end{thebibliography}�"\beginB{Y1�2�NonRD)�}���v�*��)� AkhiezeryB�$.��(B=7199 qF�-�"���%�N��� �~� Lf7]xAw&)(Y�FieldrYC��%��4%�h8.1 (�� - 5C%FV�%�I-A.Dat6H velocit�75ia�67�66;024-22� ."�>! HMikhailovTrahtenberK �!;a� �D��*. #�Mi ^%�a� TrakhI2V2M*�"�1, 9.� B�>�6.���%�2�%�-t�:�'tom� &�7 ��7:�{6W �k499-5a)-�>��I�*� ��q�� Nk.!p.41-4AUM��of�ic� c��f�j�90*R>��2��90R� 70, 416-4�FK;%5��5��5��5��5��5��5��5��5��u��,T�5", atte*�A.s&c***� � ? �,�,�,�,�,�,�,�,�,�,�,�,�,�,�,�,����� *b s#8 �2�.� &� �3 i*�9��2� 7.'� �&�1s� N� �@!F��,FC 1982�# �C*A ,�' 4u6� �.� 2� �B8*�1.�9|U $Chernyshev�5} % Sa&� 7��A��$J��s � 6:�*t;$(18, L791-L7�A-]]Z&2.!�]Y%AZV.-�.-��44RNh&�*.�}%Li&�*�&�*�P9�A)"� b Pb�#y�/ �197*+(&��' H�%*�'m`�% A 3 j? r�"z&!5�!* !I�95 B�7.�Ky�'2�K+ L341-L344*B&VO  �fI�fI�fI 9Varsha(2|� Many-Body �!���%Yakhont/7.�#�~ �I-%M..)A�*�O  Comm. 119E2-283�S2J ��E�A�9� ����#F��8 Ivv��4=!�f�B� A �FUkT%[!Zf9�q.c2q.: Sl.,/50, 1�+1 9X�5��Gy�)�-���.f[ -9J7..>*�/b��61N 31-4�8�R� ���.s# �E�� A7^�:"# 2, 876-88\H �ahl�QZ�� n+A>� Balt�9vZh��ee� �j�:�zY1 C�B.h+U&A�^^�}�Es�F�Rin sc�\9of6��sya[0nuclei.-.�821st Wi�= School LeningradE"< itut�Q�ea3A ics,pN946�&&2?v�%%%)z*U >JFz=�b:�QY6AY7-8�3�*�4HubbardRose196] �M6"E6k"6"��!84�1 -k1r-^U7**G%/SFovqP. (e2$/ Modern De�p~7 ��!�j,425-43.�2�D,LudziejewskiM* .!pH\"ohlkS&m32n&N=" U�.� �L601-260*C+9�w(� :�& Ғ(� �( .�(j�(DPWZ�( %2�(5F��Rz(&�U�AtData.��� &� U 2�-.�-9kMacCall�9�%Ri�1:(a%"�At3An. $"2��7�>9/&�22�-�U77-48�("B) �*b 2�Quarles%� �2�*h*�"�" �J� 8, 3Ũ � lPortillQ6.� � 'Nyw>~ a������17-/}��� � _PRL&� � Cj>�9�206�D�=i=�91, 173�7Z�"�&f�"} �bet00G9H.�:;Tlem�=[den, F�: $Crompvoets�,R. T. Jongma���f van Roij,�G�/ij���N�Up (London) \textbf{406}, 491 (�)*�joc�ESk@chim {\em et al},�5�4Q 302}�F0 R3.Rgre RM. "t5)�Regal �D.rin �b�2�537�2izwi03)]M�' ZwierleS oSt�C%]SchunkA!.RaupacL Gupta �(Z. Hafzibab��W. Ke�M(%fB11g91!504Ncub�$J. Cubizol�$T. Bourdel�J. Kokk�)sE)$V. Shlyapn�T ��C. Salo�5��4V�tim01)HE. Ti�7ma| K. FuruyaQB! Milonni)�Ar K�InM()iGA5285!28%�2?reg04 |)�M".;�].z�A�0�3n4.�barn(M. BartenstE1v9ltmeyaLS. Ried-�e�VCcGaj J. H�*$ Denschlag�RA�imm2h)U+�125�6�ou�Y}�.q�)oN_3}, 0Y�4)�� ar95)sA% encok  DeutsaA. Ekert)�R�zsa~�74�e083 (�42yre͎GE5Brenn��Ce�Cav�%P�ess!�Ie��!yb�8%R060~9)..�%pla99 �P�9atzmancM. DykmA�`>�28� 1967X9Jdem�KD!=Mil�$Ff�8!�679�#2.&fio98 �(A. Fioretti%�� �)(A. CrubelliA� O. Dulieu��L,asnou-Seeuws)���t %f�0!�402�8.�tak�0T. Takekoshi,: M. P6s:!�A3. Kinze~68�5 5105Ftnik�>(A. N. Nikold J.c Ensh!E.yl H. Wang �W.AbStwal& �P�Gould %f!�246�I26gab�$C. Gabbani�2�$A. LucchesS. Gozz �M. Mazzo8v5�814F�pic�+!�ich%>�RnucIG. ):x��69A�134JH[Mancini$.T4)]{m SV� *��D <��A%�L. Caira��きgnato ��L.�Marcas��b��P332N�Hai�Eger:� haim �%',AaKJ��,hatta�-� !�N.AJBigelowBI9I7aT021eV+3.Vke���A� �MJ� SageSainis�5 ge����x% 03300IE>�ma-���� 1530�2�bal�NA lak�Nn��A lgarno)p�WI6_34�V652e22rbod��Ex do� A. GHur� ![Bn� X q��11� 922 l2�bñ7:�C. Forr[@Bte lJ��� 3224F7v��Bv2�uR�$�vb�W62� 2 t� BtGc(Groenenboom� V. KZi�2�v��D738��2 sto} ? T. Stoeck�g Voron ��. RayezF�y�6l03271Jntil�}K9 lford� Host��Pe��<iayJo=�z��52$CB8solA��6 old\'{a}�I�Cvita=3��Hut�$P. Honvaul� �hLaunayF6T8�15�2� volp"� A!llpi�J�oBoh$ !zRH`86Fh[WeckLBaP�)]{weck��P. .>��g EuroO J. Du�3�141g>��%l>Sv�2T556F� [Taylor�@Datz(1955)]{tayl5� E� )S�K�ZG2a� 1711�52� �66 �D�Herschb U Adv.2W����319V66.�beck8��E���73$Casavecchi"C Tied3��Val�< a%YE��A�Z�7�28 ?198.�[LoeschMSti�6meier� 3)]{loes9��H�1F�:4E9Z�9A� 9598!92�baer94)oM�ρI.Zm~H.-a�ne10AI964 f2� aoiz� F� Aoiz��T` rtin��m en\'{e}nd V. R�4 bano��E.�Ddasco�.�6 2�25�9.��}.�.\}d.�2 F�a�AN��@ �  Q�54��.%{casa�P� Y�pR�Y Prog�2Q6Ax355�2R hobe�O�nb�B}�2�o � �  vu6A�SIBt�.tMeGMUwj R={|Z�11{ 8880�2u�M��j $obbenkamp,� Palade�� uss� �h 21ak:G [Park&� }]{park�G '�$Lagan\`{a}a Cro��no!&{ Packr123i�2ngogt9�n$F. G\"{o}g�G� B^pt-Kuru! . O�Avv!�792�2� laraq M�lr: Agua� O. Roncer-�5aniaguavs��3B1992 panisO�w�!\�n{s297��6s�q�[� �.��s� 178F+[We.�(3)Wei, Jasp���Truhlar�" L. (A=..DE 4�""5)i�Au� 107}, 723J Y�2�,F�8Piermarini]{lag"��b�V9=%�Lect.]es�.B@304A�4 6�gua97a�#^�5�!e];r1�101�7�-[I%10�)]{ �b��R�!� 1008�-.��- wn�BBF��#.jaaIQ�L^�>zeir7�Y. ZeirIM� apirF"ը�2K �H={{�R, �l �H� Scha�P, III�Z�72�376�2� {carteS��rtej JEMurrell^M�D)�:56�\6Ya-8��2-E�Erci�H�( chemW&��82 garcVDR2d^�5! 111E]6Z��8��\iX."113a�28) 2� palmY[almU F�Z�-730e�6`sua": �uar� �"C�blero���Int �* ��%393%2:M �� 6n���>n ^6F2� 10%>6AG98��.u$O. GervasiɸU��.k6�14 17J q�e6��8Ochoa de AspuruVyZ�1 38�> burc� urclPiecug(V. \u{S}pir}j0O. Bludsk\'{y�v� 9�.� [�p��4 ]{jasp+ 6� . H� $Chakrabort�S!*���jPEfХ�J��m>3 117945 .J F�2�2ՑW."@.�2H)���T 835�2�%� ��B 5e�15f u"�L:�(unpublished��}!M!���!&s a�X Wern� 02J&�:o" h��.��� Sanz)r���  ./ [Hud4Nw!S0)]{hudsqD� ',�0B. Oh�C.�)ny�7��iieJ^��3989�2<)^%P1^a�A��%M5*."jx9Au126��AN%[Skouter�C�Vll Z(anolopoulos!�!sko1 :JK2@D".F�Vu5`$_/un.�(13! o 1@D�{wig4 EWigEo� N��s�(1948)A�HL[Zuev=�A� zuevE�ie�. &,a�S� eridQT.�E Albu&G.��D� Hrov6JaWBo{$�{\bf �8 e}-Marstrmnd2�|9rsC�.2G�C6�%/Z��%35� 2 [6EDixw pQ� baliQ�NR @2��s�jnr%�)��1�1� 3� 2�{ze"YVF �&C %�P. Brum��:>6���&� %�j> V�I� f�&10.�&crc} Kld~R. Lide, editor. \newblock�"{Hand]t�-!(UGyF1�KAR3} {R�s  �2c{X-ray pjh�.�yoscop��s�&$y�&!}nalysi!� Al%�Cu samp�Iexpos͂��2�environ�6�A�Journa3)���a�cQ  A21(5),A�3.� XPSh��:"VX2�X-Ray c�S��opy6�{Pe�U0-Elmer Corpor/4}AU89�Asami!�0} {K. �S. On:��it�}e��� raca�z oa@Magnesium Oxidize�sAirr\�nM��e[Societ!Z,147 (4):1408%`0b`9}:`EMonochroetc XPS-_a:Z$Volume 1 - �Ai7N)�es}. !�"| iona� Inc.)�2�PSherwood:1994} Y.~Xie%�P.M.A  2����A�Z-V :6jDe on Carbon Fiber �o��F{}7-�6:6a99jlY?Buckle�3} A.^ 2� ThresholdaxKLL Au�%I�a��!6E �A foilJ���a_� ;~Amܡ@5:9�R>�Halbri�:84} {,6OnA�ng��.D�� by R�ln�lTunnel�4via AdsorbatA.�./deɱque5:C2--31�u9�99c�a� 2} {y �, batz�#6�m#n e����r thin!�!:ins���layjinduce�(Dby 3 MeV He$^{2+}$33 keV�VimpacJΫBe3:638��2.�5�&a�& 5 :�xid�s�tum"ixbyN&126J!�Qrf }, 525:2 e>dBojko!��OI.~�C�y~Scheu�06o Infl�M9airɖ��!�th�l t�f�zo|�� &o^-�of coppe:�ڮ� 18(3ɽ�]N0V� f� $6} \expand�~L\ifx\csname natexlabT \u_x\def\ #1{#1}\fibGbibO font>J M#�Pf�Q$�R.�~R.$�Rurl^�url#1{�tt!O%8{URL I8providecommand{!\0info}[2]{#2} B!e'\t []{S'*�[{2�2qba� ��}� 2)}] -astbi�{author}�5�{R.}~#1� F}} 2 and}A2vMB>M�}�\emph�! {title}{M�Q \&\ɼacs {I}:b;MS�cs}�(�I,r}{John Wile�!year}{2C��jnote})sdhttp://www4.ncsu.edu/~rwch!m /mi/��~>�Titus%�6!�!|a�v/A>/<-,;jM $}{American.��"�7v� }�2)|P(pages}{362}=I5(6})�g>�Warbur/�0�4�-!4})5nff~~D6::nK%��U�A�jVJ>X�:�W2:P-W14=$Y�5X4rXGeorgeo����Finney%a3!a !Y3�YB>b�ZR.~L.a�2� �},Z��pu �r,tic geometry�92}�AddG Wes^�3:��ion}{�B�e} edj�T� on}�8%f :H�g D.~J>� AM R�i� al fluid @]}.�=�n6�IY�),%�e52ndz�(Baudrillard�95�w 5�BiBnS3cNc %�A^RUniN�(of MichiganZWA{��195:��transla�by�F,ila Faria Gl܄}A.N�  �f� E�Ŗ`pflow}{ H. Videau, {\it{"�sy;/ӋP�(�Flow"aB This�)cRX; \\ V. �Xu� JCalorieAuign�.bC'ptXL talk given at CALOR� 2&�X, Qu� "Pasadena(, .t^�I�s" 70-84>� �.�M��1b - Jet Ef�+�Mas�constru In`(Highly Gran� ed TESLA �er � SNOWMASS-�(-E3041, Jun� 1. 5pp, e[f C010630: $0 M�!�0TDR}{ T.Behnk�4iA�$CALICE Mee^�� e 29ah 4, 2��tpolywww.in2p3.fr/flc/general-m JP/cern-june04/SOFT/G-M2��N�M v���$weber03}{T�+b��*erbigt Mark�!,-Ch. N\"agerC&<@,.�232�d3)�bi�gr�xq.2ACe"KAa3!!. mCNae��B]C��j�@Z: �f6AG.�i6A@AC. 5A%4 "1A=#Z�3[/21(:6�rGD 04}{2�.:��x2�E�R6,B=w�hJ@"�� Nygaa�7kC�-Cl%�[��0-mat/0406617].W�Keen57}VBar,+.N. Coo"Q.�>Schri݂Q5�"� �10�8 1175\"572tiw>$ga93}{E. T �?J�3haa3&H"k)toof,./A k4�,41�>�k2jmie�$� H. Mies, 2r!"�"J�@nneNc6F! 0227&`:=�raoult!� M. R XF&7 u= A �}= 1271�246�arceli%�B�� ���.nG Kemp�BB�'Ve=8aMs$K*�Ej�M�6� goraE�K,2'�=K�L!�Se�Gardik$�c"R0B) 3!�345�%6w�H99E�W �5B�?�$ili:2>�E� Mod. �E�7!��,992{$burnett02}�B ,BUP.��#%�Y�ASC%{}�.��(2�6�2|0fedichev96}{P^F ԉ Kag\%G\%2yGvJe,MfB lravA=��. �!o29�062�bohn9�L.;\P.!en%5<'4p+6�U)¶U6�94m�6�fatemi00e�H5n!Jona�!.�VH446��02thei��6 �" Thalha�Hq Winke M�hllw�RG. Ruff,�G�RnV�9�'12.�@�w��G.� �K. ���^� . 955.�ciurylo�� R. C\l{}o:�S$Jt� gova�Ir= (in � s) [p�%/04071092�takasu���; !| MaLhKwmor4QFa�AK�8nda%Kumakuv6T. Yabuz:! Rha8FZ��1�4J�simoni�5A. ;E>�B>(z�'6aV06340d560k naT.NK f�336�=�"2�s�_ 89}{>qAeOL�-n�H�?V��Ko L)�:�F�39�1��{x2�a�!� O. A S Samu� �. PasheG$H. Kn\"ockg !�)[ma�=Eu"ׁI?��2!I1;&V�(�fQ .��5(]{boella} B�, But� a&6| erol C�� al.$7, A\&AS�Y�'99"� ],0]{dickey} D�``\& LocJ�5/� , ARO, 2*"15M  ]{do�F} D�+, Ghis�I�>�kTpxferaG\& Fos�W�� 1 � , 375, 736� 9]{fJ}#J, #V Guainazzia�,T�di�T0m,] k�)� NFI \sax\H!ln�$v. 1.2�)�f �}.�,� asc JL�� elot��RC��t�\&: �7, MNR!�28q~36va?]vb:w6ihia�qe ��!I!�pJ, 5�16]�",]{giommi2} G !-%<Padova!�P�4�68, 51�n<I36I Ansa��I X MicoSX�5)�A�0�]67V�V6UCapalb-�Fi�<>�<2, babs.conf, 63X� ]�I nheim} Ma �� �]{9ox2:2:)�: � F�\&.�Z2, %�397L, }:)A pado)�}2~%�9�J!8!� 444,�7�)6K!�>I$CostamanteV�fuPer{�zY �581, 896� 6]{p /}28�[St�B�1YXb, Q� g�`�>L�6 i45rV:k 4a]{�w}��bru&)R�=,K$!�]�m A�XS, !A376�4b Xd�Y, 46{4689�v� XcJXM2B\& UrryŏM6 �*4442X9 XbJXEracleou��-dushotzky( F^9%�#6, 602]4]{sikor!giaBeg��: [Re M� 5e , 42EV56z6�Ek }?  AT �?�Madejss �99�U�s8B� S2B_6R\& Kubo��! Ph, �17}Q��t �Tsh�kt�ma�<, Oy�.�5, PAS!��3]u�1taF] ,��M2Pi� E\?1�54, 72B�urry}.U,F5Worrall�%yJkE~24V��f�S1UW{ }a�A�P H. Aoyagi�Cle!pi-i"�- '*L��  . A}v 365},g�Bu epp}� R. EppQT�I Lavi�Ra Early�-},��v;cord of� 1991 IEEE�. Acc�nf9196�:� wat}�WatanabeA* NABt�iBKogawa w)�� SPIN!��AWt.<cp5�10MA.�!{mar1}�Ma�VA�D. �;uh� Brach� :�%��-{�264"_�mara�= uqUg,l E.��4�19�22� ant}� L. Anthon� Erno�R@ rroy(9u�[ fs3tt� q816'T]2tg�5� Gram�C�USinclai\QMi �l�VB�wv. ST-AB-jN 0428 v3vN��\pr6`&,refin}[1]{\\"$"/��:} #1�V�~6!5de�b o} De{G}r[E8~W.~F.;\ \ NilspM~B.~OP84it{Curr.\ Op.\�j uct.\ Bio'"t�[�r,�$sl{ 455--4��yN@mayo} Lazar,~G.~A z7h��~S(Plecs,~J.~J%yo!L  ja� (R��5F�,� �8sl{13,} 513--51�"�j�#(nsen-sci} J%<Lu�2c4=30b18c186dbu�S8s} Sotriffer,~C��Sbe!.%�S�e,~M Bohm,~;<�it{{BL'�2M"i�1�.&�6HDrug Discovery};} vO&~1� ey: �� , {S}ixthd+d.;��2�1vangun8Pen-est�} OKPnbrinkEQ �Pitera%�W �^Lipzip��Mee�[) H��;A�.Go%�F9�J.\�.\��#M�� 2�4!�$4594--4605.�g��f>3-jacs} G,Q�Ren,~P �P$wr�~W6�Am�\ Soc20I~)�A|@25,} 15671--15682.�2c�tep} VKr��-\ BU�bf�1]�10� 1264--112i�ykold -pnaA� inghe�B)Ajay,%�We(E K ;!?~A90c{.a�Na�_�j\Q.\ (USA)-,bf�k.V9� 7673--767�u�\aqvist-febs} Kolmodin,~K �A!�)�it{FEBS�(6< sl{465EJ8!.�sho�t-n�} S E�Ke� R)z.�,432,} 862--8�s�b} �I��Q � WeavA� L.~H  Ferr�~AyRatthews9i| 3Z�eKolA&iol6K.�337%116A�16�nussi&�HalP n,~I � Wolf�mH N +,.�Pro�1s2-2q%�!��k09--442�4kuntz} Brooijm`~N kK�~D9�Annu.\��n m!!+�$6 �G�%�335--3�=�$cheraga} T�KeEt~Y �S ��.!��?m�9u�,sl{20,} 412-��.�brooks-��} Patela�e�Ma�ell~Jr.E*D !3ks~�H~C* �it2� �{:f.��0�A5142��B�Kam���aStern-�B2E�F-�Q~R6� ao,~H6 6Murphy#�� ZhouUHalgr��TC.�K ompu���:=}T-�!{A 1515��32 roux� Lamoureux�}B.�.u j\�� b� dQg119%�302Ak032S70karplus-qm} YP^m� Bit�_-Putz�,R �K 0�{ b1��V�  �.�1Ez9450--94��Y��jcp���� 2618--2622� 8mccammon} Mc{C} ��.r"� in�{a�=�B%~1���96-�(.�"3 F/ %� Ravimohanab MNy ��8�wx8A30!x3052]�ts)wShirt%�1�F6SwopeA("� $ande,~V.~S2�a. �I��E�$ 5740--5762jarzynskH  2��\>�>e 8%� 2690!�`�Y~zu��$man-prl} Z�> Woolf,a�B�n�i�qsl{89� 8066�7hu�-pull} H u�Szabo�o)0it��Ajb�p)j�1j 98,}G8--366ibu6� LipY�A�E�Dumont� Smit2� Tinoco�'/BP!��itR� a�296%$32--1832l ,schulten-pmf��rk� � Lr!2�)5*R �5946--596wsteered:{8Khalili-Araghi,,Tajkhorshid,� .�=彦+3559--3��N�cp��.zBDB�35AR44�2B ytr ( g-seps} Y !qB>W�10876--2��extra�J‡f�423�749--17׾9�m�fx ��f�Y*<e  S4�Cz�tѴ(-ti} Mordas�~T.~Zi�f����M>� aq�1! 360�G6@ (everidge} B �B�Di�KpuaA MitI VH R �}q-�ܡF����w-46�A$lu-jcc} Lu&� ofk�8 R�! :�:E 28--̹9�2� ref2:����r�.E2g 1730A�6� �Rov�D-deca} Cheluvaraja�@Mei %G �jlj1�s$9241--9246.�gilson)Chq C[�E!G\ .!�B ���6�12a3 1315�3162�e ) K&� �Kushick��~N9 Macr� \�|1986� 1!�3h $zYsto�kl} �c��dNowak� �itjr96�O 9M96�votޓV@>�eY� zi^�q^8�182 186�C bruca�` Wild�J~N.F Ackland�~J�r.� }i>� a�300B06�.�-scn\g} �lrEK4& ��P�A`V B1�70�706�"� -t��t'�� E9{�k5{9 0461#�YKbY,tt�an\*_ ~H:���%b S%�7a1�22��262 $zwanzig} Z |>�V5195a:d142��422crore} C E#E��g6,.�6�23a2362d� p� F� B�� HookA5G�R� .� >r :�l 1406_�9�p} 2 ��RicA��!~M9E�1�%w.�8S1r�101��024�4daEn.wustl.�>tinker/.�sti� Se&ͦTempczyka��HaweKC6�B�6�.�11�\ 6127--6122� !mm} N.! tMacKe�.�nB�2A)8%2"5����u5Q  CornS[~ Fox_ *Chipoe� �whoN;�)�omi�Bi�V=ys2�9�1�v83-Z�YE� dial*obiask �BmPF�M�BH9�x� 38�38W�|��ban&CRo�9Ander�r~O>2�FW2$�� 5179f924- ldyn!� ng,~�f�� �.C�Q� �241g 422� tembe} Ta_j] !��Us .x86�a�281--28tN� Mf�! 17} 9� Seah�=2}��P.~, Tosa, �Gk!F&J 18 32) ��"'FW56WvN 2]095) 729-732. >��>2T IA<~Gilmori;�Spq�b�I 'Kosc�!l�T Phenom. 1d-) 73-89.�. meQto check.*lis;ity�:Tdescribed as ISO 21270� , ``�jM �@:O- Xf�Ome��%s�K�N sp< !-<�of d�U�y �e''2>Ka^L0^L�K�lPh.D.�ser�N>VUCo��ND12DS.-H.~, E.~Arenholz^5{M�;N.~_)�,8, Z.~Hussain, Mg ~Van HovnMC7Fad�?@!�� 114,&/1)6 9-11�QU� �2}�W. �FE+$G.~de Abaj4}V� B�r�a5Ar�,�Gb G%(�# 1151192eGarniera>9}!!G.~ n7Witkow'R.C8L8,�# Nordlund,]#z! Mb� gaso�0 N. M{\aa}�y-Ig. F�ghli�xMaIJ � al ReportE�a%, Lf Swed�3�private �HuVt�V9� �:1!����S it{,&{# T 6T.Kikasao0WA� N�,s�* Suus, (1a�7I�$tiJ=��iƶCom�s!�, !� 0) 2�.�AaWkUp �:� ��F�.:1!��EazzRN�XO ,VG;�$Pa4@x K�%inc^22yqq!3' �1z�3=��!�I%�D �At Dess�BV Y�^tFP<rn�yA�a�O�0B�5eb�S �Sg C�u& _2�Q�a94}\6� _Zal� P.�& \"{u}hwil�,-O.aB�06EA=��or�;B.WanvU,.\I��K0&PU R�red�s!C�*�u4�72� ��5} C.S. �m2k.t�.�7A�U.A�ͳ9�Manifac=d!�.�D#'m�$XC-77 E726aDC 10.5n�(15 V, 2.2 W2�TheT[A,time $\tau'$�2 a little �a7pfAed to  �e, but id)�Kve de�Bwindow�)kinetic �>g�8 $\delta E$ cfaqg. �&{fiA�,�)n sm {sR���A stepY Y (or equiv�qlyq��nel�� th) (=$ be $dE =� /(f_{E} N)$. I ��� al region!be� nned!,$\D�in d, (wher!S8s usually $\ge�O)) ��*ord�(o have each9Qpixel�7t�e�Pto *- �V>has)be sc �& a&��� +�� volvAnec�ry�/�Bsa,g�d��and s�E�i�W&power suwDe�r>� um� swept $F$ks%�I�tot�R.m�Y�e a =-a�MzumU�i� =FS� $. If, a�� oft l case, a c4 in nu;DofYI0 M0$s $\alpha �b�Ld toge�S� make��W(� ��nea� FawidthNdE$, e a> 1$ !c need%�bW  g��th ��q�!��re�U�$S' = S/ ��U!�%p %pbecome�� = FSQ� < $��!- he fB9ng fr��ӽ$I� m S} long |-� spat� axisi�been set�0.8&0.7, reEJively�.se5�tly, onee�$2 \cdot 370 0.7 240 \aF� 50000$Aa���Gfa.H betw�count�H per�g� �! all q�%O. ($T/%=���,d!y �@sees a uniform il�Yw T (see Eq. \eqref{eq:1bLO" ��^1}�!�!]�\�ld hel� someE�s, evE@ough ita�unlikely!s findA��less ��( which can �d)s!G high240 Hz902Y�:1} W.H  ��0Teukols�3W. ee�Y�e� P. Fl�� ry, k Nkc\Recipie��C:% artarsci�xfic�u�F@} (2nd ed.), Camb�J��q�*t�H�$? Z 2�Reibel� Y�t �KQFBouhifd� CuC2a$C. Dr�6, 6�;AP �4 75-8�03*�enF­fQ9} �z%}�bi�F�bM:}�Q� Ro)g,�it�_�*!�Sound }(�X �O), Ass,Q-W,Q, Rea��4 i u Feyn�~� , Robert� Leigh�S*ewjdsYu�� : 4s�Yon��U, A�QN�6!�(-!�.�Ha�4�6Osl�Music9��bAEngine�I}�1�@=D��,"�.!6�r=Lapp}f  ,� bnP|k al In�Nmvc,u�Ituftsras/wr!D \_center/�ics\_�\_wkshp/�< .htm.� Tijo+A�g A�!Samar� �Equaci�-G]la FiE�!� nabara Ko���J.r6�qN��Ji� {houІ 90} Funda!�al syste��qua� opticsёs H 6 L + �3@ali I� M�G�Ad%�hJ. Zinn-Justin (North-Holla�m&1dam�b 4U� {bose} M�,laJ.70�M a��- C.E�C�@Ga���P%� bf{2�� �zb;�6al:O. Mew� b Andr(. N!d� Druten, D� Durfz�D�KurF2o�aX��v.P �7�7396��79Hansch75�6W. %X A.L.k%aw���CoU�Yn 6�I�W wine!�79}��J!4 \H�hme[�Bull.� ��1c20}, 63s>dl��gd7�� Ph+ p!=Rol�l!� T��A�S8FcC. WestAX �Am. B��B2084 $C�l {cch89shu�l]���Lohen-oudjig %Jbg� 89);�J. Ung�D�0Weiss, E. RiiS6MuZz�5%�89).�O=b�C!�,�Bondu �L�Ell5A,6�C D5%s744Id�] lo�FV Loo,�mBruESNDu�A�:gkzaY Are��`a%WUIhom %OB: 2f um S� lass-Q�!�8Gr�8Y�loftusDoX. Xum:L> �)kH.7�GEghe"+x Ye, }�&�{.F114�K2);Jf�Hal�d Ye,&��J*e9az��6�yoon04a�afYo���9R�}2� piil%�L !���K.-� uomi��� z" A�_bf{\; 0134&HM.��en�My ew%�P�~u��%b Nadi�� Sa��EC:�Y. �qn���oI CAUlo��;-�y�59}�EL: coVO�e� jE Hill[7ań Rc7#Townse�jK. ZetiMdFoo�Luro%(�����O39��>�wa�R.� m�,�`y�!��"eN  N�7��8:�d�f85}X�u% h>�Ia|AtKYlqs1� 166158� 1 �$p(B. Klappauf�BiޔD�4lk� MI haneli\`e�R. Kais�%�e,XH43} 25V}$paper_red}!F jB\.{%XmiKpar� 2�gordon80%=G >^ shkA�I i2����16PJ�� *͘1�V9�a� %th\`esk doY at d'\'etB?(U�[\'$Pm� VI 86), %u*,.�sesko91�WYsko�G�C���C�R W��oc>wA 9��16� van_�en}�KOan KaJQS�L�uc�g�� � ?sta� �  E�r�1Y~witte��y � �. �RiehliΡ� elmc�Z.�:)9}, 103V�:k steane�S �\ Chowdhury1N�5zd214e�>dwermerE)WA)�H%�li�I�B:y�%�Y��-30���G!�uj�9�sg&sg= rayl, } LNBR �Be�ntvPa�s II (nk, UniPKingd`� 1900)}, p�*4 {kadKL�ja�)A�Guna�CRTesl��L��danX�+Bib�d��S.x�e,��Wu�GZalesk�`G. Za�(i ��xl�`�e.}��204�C-Ia�� ]�gueyffiA��GEZ�S p aCԋM� i.�IIb m3E839-84�C8A5� sanzEj�z�Vami|QamAp |ett �R.P� �1 �Eu�� �=� 1950�AeJyohn1}I��+�bjME �6� 0263} E�2I2�I1 0367��20A Ilay�!vL �A�?��� �122!� (ō.lz�-} �IZ E�2$�P33%�:�hazac}AUHazak,>.H7a�41�y(12��! I.�! rzhirK ��6- mika\F�ikael�Gn��50� :L inog�)Ino��v I=m Spac�n5vG1-3ȁ9�]9�tanvea8a� 1}r2F`*�&IG4��01-525!�ҍVgonch} V�pG arovX&�Y.�� 1345R�cl'�C �IF& FvJtp��fortbc��6Q"� U�vinje7 V \ ��Q��W�u �purcesMׁ�7%��WcokeleteS.!C,guet-HigginsfEi!C 'm�jv35)�-2΅76�BMOA��wak�zDA��1� S�Orsza�)��m�23a�4��6ׅMZ}AMe^�ff�\C. Zem�E��|g, ]-#5a�מ198��"�}{hecht}Z�RX fy6J5�1}})Name{Swa�#��Gf2��Z�yMraCon�E &]rx�� "� "�/ �852� yari?� �Y A=#O�al"�" in%0rnu�%s, 5thiq�Ox�J�Nec�+ �972�dor�� �0Dorokhov O. N b$REVIEW{SovMZ$ JETP}{58}F34}{6062Skpwq%zKo� ��Papan_Raou�(\AWhite B2l! Mo� }{23h96}{12fѦ dGryanik� V. W KlyatskinI2^B���2 }{11>�ly�fT��� }{3 �4>��M Bell��H%�,G. M.} \Bo��ok{An Introduction to Invariant Imbedding} \Publ{Wiley, New York} \Year{1976}. \bibitem{ram} \Name{Rammal R. \and Doucot B.Y�REVIEW{J. Phys. (Paris)}{48}{1987}{509}. ] hein<N^,Heinrichs J. R O\Rev. B}{65}{2002}{0751122� kim1;QKim KjK5�98}{6153>I2>I, Lim H �Lee D.-H2` J. Korean-Soc.}{39�1}{L956>h3hT<, Hudson M. K., �,, Lysak R. L �Song Y>� Geop%� Res.}{107�2}{13072�hen)�%2Arnoldus�F c(George T. F2h=�A}{51!�$95}{4250} 9�bla�(Blaauboer MjM62�,0}{041804(R).RhinkelUH\-Lipsker D. E., Fried B.8\and Morales G.RaFluidsAc4�2}{559.xlindelyL � I. V., Sihvola A. H., Tretyakov S.�ViitanenM�Book{Electromagnetic Waves in Chiral �DBi-Isotropic Media%Pa�HArtech House, Bostoi[m�942�si�SilvermaEo0P., Ritchie NM CushG.:�J. Opt.E� Am.E !>8a[856�2� kner1q�ure Appl V}{K96}{416�4�E�HBassiri S., Papas C!)n Engheta N2mv�4502+jagnJaggardATu� un X�`9!AT80:�hiA5cSerdyuA7AAT$emchenko I>SEPYtBNL s ofA<aniY>aterials6EBGordon Ei8reach, Amsterda�EJ 200125B%�Flood KA% �2.(-�N�13%#6��952d6<dSlepyanA�0Ya., GurevichaPV wMaksim%5ez> z��E.�2546lu�LukyanovfY f Novi!� M. A2c$JETP Lett.a0}{676`sil�b:�)?Badoz:$R:�|��8:�gen.opp!&I aGenack�Z2�=% �8���v339:gen˞e�9 _28��A876"yoo%�%��Yoo��e�5'e(Unpublished2Hpendry(OP J. B >F% �8v0��66�futureU�� �<'R�tend{thebibliography}I5\beginB�`*�o1}��hBohr, The quantum postulatee�Tthe recent development�)atomic!,ory, {\it Na�`, no. 121, 580-489 (1928).� 02} E. Schr\"ov der, Die gegebwartige Situa� in der Q�(enmechanick.z�wissnschaften} {\bf 23}, 807-812, 823, 844-849 (19352�3}A� Einstein,Podolsk ,. Rosen, Can10 �$al descrip�of [ i|reality be considered complete? %$1}, 195-20%�642� 7} W��de MuynU�FoundE��T%Aum �h an empiricist approach}. F:adal� orieDIMs, vola\87 (Kluwer Acadea�ខ�8rs, Dordrecht, � $, London,  ), ch. 9e�,10 (also see>�('s Home PagU www.�@.tue.nl/ktn/Wim/m% .htm2&8}A �<$ellinfante)� A surveya.hidden �ble�} (PergaAW@Press, Oxford, UK!�732o9�XP. WignA�e^Symmet%M!�refH Tions}, (Mir, Moscow, �1971), pp. 292-302 (Russian translaE2�10} M�* Men�9��.(: new exper�ts, applicI8,�'formu hE old quesys �DUspekhi Fiz. Nauk}M�\70}, 631-648 (2000) (EngA(.�:Hq- P F4�C586-6aE6�1�6Aspect,!{Grangi!}G. Ro��E�A�est of�s� lo�*thM�viae�'s emM3a�.� �s �-460-465�-816�22� J. DalibaAFz�A�'b equ��a�us�� timeA�y analyze|Eq� �2�9} ��26�3}�Weihs,GJennewňC. Sima�H."nfurt!` A. Zeilin%d ViloI*aR>�4y under strict�+ %z��condiEVBl2�8�50395043��96�14[0E. Evdokimov,�&(N. Klyshko,] PmolV  Yaroshk�yelBva�4EPR-Bohm corre �8s: working clas�tHadiofrequency model �M� B.(66}, 91-107!�96n-%�ic:-( 39}, 83-98 C6�5}�Sa�k+s!�A,) interpret�!��;B0b�7!�441-444e�1) f� {:� 4�y421-424 a�1:�6�N�$Very promie hole� -�e�em6] "nx�n�Z(ics/0011022.m17��$H. Eberly,_ i.�A%-5.pe�Ama�!nd � 276-279%.:�8E�D��rm]� ��" presence!�U� commun��, e V��e 2071402�9�RGo� ,� Fahmi, Is%'s�?u�$ necessary�?�derivUX-�5;y?��0Ann. Fond. L.�Broglie}�g26� 35-741%06g20�g����%�!-f2 �x hy!�m��9Moder# �7A�288-29i�92`21}�,L$\check{\rm C}$. BruO%C���H�-6�ems%B real2� 5R��%�006043.�22}j�M. $\dot�Z}$�CA.F� � esU|entangle@ � Zh�106112� 23n�2� In�IYand- f*� e ��A"� a1�umJAz[2120842[4} T..7G�-�O J. W. PanV�]�al non�proof2�elepor���.} swappingMυtI�.(88}, 017903��o6�25}�!I. Man'�>`$arno, E.C.Sudarsha�F.O( Zaccaria!�terfer���*.� : an��rinsic.A� ,�K207036�6}��Stapp, N-Z$ character2[� LAm2��6500-3067.o From"�2�0to von Neuman.� R�, Law))Berkeley�ioa$Laboratory:;AL LBNL-44712; \ Decoh)s," Zeno Eff1 2C!�a"efficac a΁~$ffort: clo�c'$gap betwee6�be� d knowE���226#8�G. Cram� E ac-'B���m�~�5a!647-688j 8629}O $B. Griffita��� Cons nt:`L} (Cambridge Univers� ['6�30}� R. Hol3m��6�A�mo!�n 19952�31}' Gold�, "� yM5=" ��Sta��$d Encyclop��Philos� } (w%� E� ), Edw�8N. Zalta (ed.), plato.s `.edu//s/winO/en\ /qm-bohm/.�32�it2� j� �� �� AyIthacaf�.� N�%k- 9609012=36Jbp� K*_ 2�7}ude� ��2+�>douj solua� 6�" 6MA�bf 12��99-421� 876�8�0Lochak; Louis�  me n�%$ about sci���� Ukr.�Zhurn��3�32-639{93) (i.Ukrainia6�39� Sard� *js�)! orbi�l&� of � N Q�sE�of6ir"��[Kneutr( nucleaz��; Essay�%X204-220�6� 40} Yu. Baur<S��A�K spac�n�nY wave ()��&�) �> : �443-46 6� 4K$. \"Aether� Re�vit\"ats�ie�� PHted on 5th May 1920��!]ݹ,of Leiden (S� Berli6� 42} ��A�vDiracA�!) a�N%5I�2� 16A906-9'56'43� Krasnoh�e�D. Ivano� MI� of aUSg vacuu6�2'�554-563E&a�E�g�X�h910026544R�.�nv�qo��,10}, 407-416�7)xE~�030772b45BouniasR:tX Scann A72x ill- ni,s rt 1un�AATcip#����e� ��tit�@!�ewiA>(Kybernetes:�.ntV#+ Syst_!@C '�8�3�d945-975 1�V/i�s/02110:.46~.f* ^,2. Pri1of)��]'* .� 2.76-100�1 *� .�= 20046E7�!�of^3. DigbUtopologA5�# 1986 �E  34-46 ��#62 LigR'�R. Ol4i�� calc�#4ed photon: Viz�ze�5n!�au� fiel? Amer�5E}�bf�58-66�]6 63} IBr�� , Ph�4fmann, M. DoerC H.�Rua��Bradsha.�$ L. P��(K SpruG$E. Laegsga*#Fm'!�ac�!EX� Plum Loo�! � �0nic)�fun] s�me�fsurface�e�Eur�s.A���2�0148-152�097264ExB. Oku�sE�a �q�} (2%aJ& 1988�%.&c!K�%6q5} !E.�8Sur la Dynamiqu��"ps \`� ���oprK$i�&et=Wu�3 nsEUm*�e9{de5chaleurmla� tes Rendu5@64 B} (1a 1173-1175I(19676�6%S.�o) basi�S)�mq��!)�V�77�3), 71-7�:�'67q X. GoN� .5p i�Nten!B�EHr��i�c.68�SA�_, P��le ax�� E� �&$ t �$�-6M�+] s af expo{�Ba ShpilC3 ^ genei� -TJ.!� 1�4}���32&� � j� ofyev�Artis/4-1/B �-� .htm*�69E8I. Urutskoev,V.Liksonz V�TsiQ^Obser&�"/Y�Ah�*� lemnts du��� c�&Idi�-rg�V>��}���701-726C6X7NX"U %-��� anomalous��el2� ct �m` a� &� ofKA��u4E�JI / 4a&1-`11�� 9906096K710+anarella��o �laser-�w ga� ion��m�,� "� }, 227-25�742]7V*Col!Mive d�@�4hydrogeny0 �in%�0KIO$_3\cdot$H $ crys�[dicta�byJ�theI6^'6� q="9/Rn% -mat� 8417.97V��0Great PyramidA Giza�9� Associ�� �}gizap 6a�, �in:m�M V.:# ' T�- page^J$ton.cjb.neM A�:  >N7N�u=�1i3n��Ҏ�93�m� ��0202176b75>�"in�behavio�"(light at ve:�! low� nsities:%9"  clump"�*inj-� � ��i�{f ;4�+e1.2=6 2 ATO AS$ e�.� B 162}m�s s.�8 eds.: Honig, �0, AGft�+W.} �2E.6APlenum>S!Y� N/1�6636=(Lo�,� On bl}6R*�:��=5 (LA8!i� ca P";e,%� ��RM5 �7ZM5{11�ZDe.~Y��|pdg)�$D.E.Groom ��et al.}��-�$Data Group �Re� of P$I�s,}gi�J. C15 D0)1 \\% K.Hagiwara�k� roy.�.D66m2)01000J�wI�91.�IڭAep��.w ,} Annual�N�#A�5��4ce 41(1991)133F� ��iyb � ��reM%!kuraniu�&krB��X�.�](.Meth. A259�7)389 % fem"C -F�acosta��D.A 6� �La�l shoO9profil)X,lead/scintil�#ng fiber9j er,}J�316!O 2)18J�1O8=�N��]=S)�icr!�J?65!? 8)27J�gabriel��T.G N�+de?�&!���+HV88! 4)33JDga�97}y�-� rfR  ancas�::>j& �: Procc"� VII��.Conf.g:%e ya�i�,Z 4(CALOR97)} TuchG Nov.1997,�E.Cheu6<R�8�5076�% st|#q�9F�contin!�A�tin6zI� R\&DA�pos�>vel&�?quartz>�EF4CERN-DRDC/94-4vJ�,britz95} J.B N�Statu�=l*A4!� RD40�j�.} n$LHCC/95-27oJ�$gorodetzkytP.GNyQf�F$36��5)161�%PPE!22J�lazicI�L -q>H)C�/kovbg YelA�R)"97-06 p.NolCn96} M.L N���8*HR��-��7� 96)35� 9( 5-17J$M�5}r�j/result��opO! ��:�N�7�j 5)27J@ganel�O.G ,B ^43 LHC*�� N��lAH0J Hanzivino95p237} G.A N�Angular:sV�er!?ponseV�60-3N� �95p380~�b%- M�$carlo si�>V�5-�38JE .�69~�*�DEFV+��J��6J� �4p462~�Desig��JeerESa colli�& ,} p.462� 2�4thƽLa Bi�D,a Elba, Sept��3,�4 A.Menzione A.� baK6N�J��93*�� A �@.6�for[2���su1Fabp.425%� � ~ .!33~!�5,Q� oG �[N3I33$��>.� re%index��i�F�m�!,son65} I.H.M MKI�#QB C+G%RoebOkvf> kfused si�0,} �'.O�W._Q�l}5��65)1205"� %� hardnessze *�3av�'?Zire4a�G0nd ultra-fast.6�adiat�\&Chem.� 3)25J� (fabian90} H�(2/0 PT� A�� all-M�a���>� 0-10�3 p.7R� avrilov� V.G N� StudcI7 y:�!�B MSd/0Note TN-94-32b� avezov� A.D.A2�) Gamm�4o%�pa : y loZ&thick�r0��# /1� "�#�hagop!� 9} V]-�)�a@dam�ofd-dCRb9/0026��:> %�  NA50 %.�� >�na50} ,�;B'em=�Pr� ,}= 4/SPSLC 91-55,  $/P 265-RevF*g_�M.C.Abr:s  (F�)-REv3ce�W deconfin�1\kUlu")��aJ/psi���3s!�pa�n ?d�� b-Pb��$�.>a(-SPS,}�.L�O B477� 0)28F�ab,di98_�[A 2� �bi!� (zero-degree�5q�% &o at!w,N�4117 8)JN chiav�.R � N�AINNF sve�ly:�} ��>�er ;a�q:�!fb�3" 67Fm�4}~�!o!b -b �ic sampl�:"�ft at%����B� &�  ed�� �4R�* 4~�.& s^� :��, ia�$itely rad-�� � coreYEaS.��# # �9%938FJ��VF���J cms}��Z>bor��rH@ ��JN onel�} Y.Onel�;�?s�of�HF�P�q]�>o10z� "ZM F�() CALTECH My<O2F�/��&1 �!X��R�F� 453�v4Jn akchd$(98_409} N.A N� Test beam� �-C^��totyp�1 &#9re�+ .��b j:9R�098)59J� 2�8~�<difDs�-RB2�pr�*e�p�i��<8=ir al�alC$-com-pensa�1:TJ�038Vmerlo98xM ] )-ic��6meA�jA� B(�9$Suppl) 61B��4N�$mshcal_tdr �H&Aer��*� ��i�7-3Jm5� 7_40R ��: .b)�Ev withf;ss�SfU5�#Z]97)R9�3� ���a R ne-�@n�for�>� n,:$E�)�&�)R�39e*7)2Njferrando F N�A�U�b��; �I9�ryLHCZ�-x63FM ALICE zdc�Malice_pt } ;�Z5-7N�`zdc} cZero D� "eFe� � j9-J 2M\ Rn PerI*ncee.� ��� �& R�456�;1)248F� �ar���&6">yVI�� ({��y@OR99}) Lisbon Jun 9 %C�ALI-9�4 ;� CE-PUB , ali 017.psf8_�j� .) ZDC7 �� e�^$��60j�8_2z.!�i�B R#7 � >,sQ-nX120F��X2��new0���RNEWMASS}:��d��aCangel!n�'!e*in >�, ��NͿ�LC 92-16� P268 �B2).�*� na522R��9#i���fin heavy� "UQ,} %Invi�+ talk�a�1 ern< alJ��UWxCssV eus- � r(A�k M� '9�<%Tori)q=y, �C 0-15�&h . A6\9)177cF*weber�tM.W Vqseg�&ed6�� .�J(>.�����151 %B�Q preph\, BUHE- =>�� RHIC>$JNwwrhica(tt�,�0bnl.gov/K.�eM� 5W.A.Zaj�H6���1oA+6�"&] J�czdc� �-�g�$A��Dec��8� 6�>�L\verb$~$swhite/zcal/J�adler9 C.A N]���b&,-Na�(-ex/0008005Jq��S.N.W���F�/A� x��]N��\2$��1J�baltz�A.J.B N�Co3XC; �-back4 dis"w/��H�tra�;lumino.NmonitorJ�d�J)1�8)1-�1\98�%2,q H16F��H1�uH1��&A�!�H1Uȡ3 HERARh38�$7)3a�>�l2}nl trac�7,.�%Umuo� �(0H1*� ��R� ndrieu- B.A N R��Gt�< ten/&re2�� *. *L,in H1>�IXr�P�NF$a�)}1ecy Oct. , Fr%ti7 S�/� 2z$ % CASTOR ~McastorA�A.L.S.ADiR�&For�8aͩ%�5entaur!= Pb+R"� �3�. G 28�2)1937F� �p �� �: A!�i�e+%��D2�CC��S�C ��a�..6�A �{��ep�7 9901038, ph82C0�=͎ � 7} %j�� �/�/;$U&��!�<& �>sgm1�,MavromanolakV�S"�!"�o ~" .3?cBr$�` $e/\pi$ r!j�M!/)�.]�*L��A�-2J."gwoG����nsTe ;1%�"� map �� A�-��U!u84guidef$"!�F�E ���*�'A�d&�"n air7l�4 ����J� gm_phd} %���St�SF� % ��e�reg�J%y:E<�LHCB, Ph.D;sis, U�E�G Athe�D�#2"^8 %% QFC polarim 3��SLD AC!�~F�ber�Va�S�YB N�� �)/Ѣ.8!9c=onJ�},6kV�I I�R+�3:�, N\$+17J�$onoprienko�',V.O�[, %PRECISE MEASUREMENT OF THE LEFT-RIGHT ASYMMETRY IN Z BOSON PRODUCTION BY %ELECTRON POSIT 4COLLISIONS. EL 0BEAM POLARIZA>.|WITH %�0QUARTZ FIBER ?,HIMETER. %SLAC-R-556r�T�c ssee�XN( . % D�/read-ou*5"erv�F�wn0&N@695First��a�{ ReadzMod�@(DREAM)� !�x�M X  Ca�4),�ug�7Mar 4�-6B l2 .ttu�Xdream4 V�7�j�7�7��zeldoLp58^~B. Zel' , Sov.�-�o�P^F 1184 45824$flambaum84"~V. F , I`Khriplu�RO.~P. SuNev, o[^ B r14�d 367t842tve� �P.~A. V�9~�X(eekhof, P.~�qajumd�SLam�vux� E.~NDFor�%��2� %7>�!8�:�Z wood� (C.~S. Wood,nC{A$nett, J.~LPh bert�j. Cho�( C.~E. Wiem�_CanSE - �U ) �9�|778b|mB%yMa�rs�6��EyTan~j�� �r3�27�^ 1759)72�de�Y anko�  DZ(S.~G. PorseU%wA _'_052115�e22^grossman!wJ�G , LEOrozcoUF~R'Fa��o imsa;z, G.~D.�6oWv iO$W.~Z. Zhao^83�o935 �f9�gomez06�! G >�![y�Fyu�Sogm�% 6e~79 ^ 6).�U_so''E�Q�_Y.�<g L!�l�MV%i]�!m 2857a�96g>pollock�4S.~�` ZFxVlC �a� 258 h6��$ng7I��G�P!+PA,~H. San-baP ʑ3�VA�5l_:pVgor�m�4VK G (, V.~F. Ezh��MKoz�izA.~�b ikha(, �#J.T .6�(N 8��6)budker�]k����em�+BBeyondŞSt�d��el}�90by P. HerczegA�C�� Hoff�?�H��TKlapdor-Klinfrothaus (>�$, SingaporzF1�.cba[ nh/V�� B iS%KozhemyYIn�c�:]\3�P 297!�86\nav75�>N.�4rv�J@>\2@ 74[752�hindsANE��S�!� W. Hughesq �ML6�n48�:K adelLerL<EE0A�l��Trainor�d��]T%CChuQd D. Holmgr^NM�q Iqbal�H-SwajkNuc. Y%o8��179��181��86'E�&3O!��> Vj 2383K932Tmlis�uMEeRJFi)X2 1Y`��5�454%Y:3chin01��|na�\ba)$V. Vuleticg��KerU�S2u q�n q 6��03340!= 2�angst}L!E[A%�HXnh%rV�&�=B q7A���0�p5)�+ �6K^D.A�Murray �)>�;�O 1641A�:mk&e q;J:?-Pa�'D-fde�H in Aw( Phenomena}�V.{�B0{Nft�66Mhaxto%�W.�H�6G Annu ����rb}ci.E� 5�361��6h lewi�1��L22)���41�]:�� anapole} f  m�t ope�J�Kgiven�G$\haterTa} = (\pi e/m)~[ \mu (�jO r} \�V~rm\s� $}) - (q/2). p} r^2 + Dp})]$, Geex�)(e Ref. [21])� DE�1on/a BX-1/2 sy�I2� Lagh ian $\mat5${L}_a�$a/M^2) \ov�_0e{\psi}(x) \gb._� 5  D,tial_\nu F^{"nu}F�� ErleZMaw0 Ramsey-Musol� r .in%~5� 35,L6�joh�/03�@AJ  SAF$ova�dU��S f�� m� 062106� 36D0ubin03a} S. A ���� v Si.�Dm�ס� 4342Nwdemill�D] M �8:�R]:Oics��x82�coc85�8 Coc, CA`ibault,>QTou�jd,��T. Du�N P. Juncar�  L����J��Pin}QJ�� rm{\'{e}}!�$~L. Vialle84 B{\"{u}}ttgen�Q��C. Muell�APesn)�A� {ISOLDE}~:$$)�Lett.�� 163B!P6FM (19869coc$@A��J�M. CarrI� Lerm >%b SF)>�,)� �b �Q19:�e ramoS. Ramo%�F. Whi y)oT��Duz!��NF T��W�H �eG{u�\SE�;ni�O(a� Wile�dSo�2R6[p..J� �i��$�{ 064101@6DbA�iat�.� [C� PiketX{ \2L26�19n BrbarthAO U. H !V KowalskX.�mne Noeh\zK� heffzek%x G.~ZE�utlitzG ���3 u�8 2 �FE�>�es6?mDe �3ASheppe� IEEE� nst Ftas���W52�66E balykin00� I. ,< �o inog� tV�Letokh} �H�#�3�K142f 20002�friedmandN.���A. KaplSmN7yviq��H�IA��, MoleWr)v ���'!l� � � 9 �6�ko�|M_An\� B�_ Q��04540e�}..� ]�e�W� It;Js Bergqui5WJ�W B�:WJ/Gillig!D! Heinzen�aF��Mo �G�i�0 WineBnF�49 3554� 1>t d-��2�H�M�,a|�F dams� Kas�� �J� e� rM{X�2 1311E�:�g! s04�-~S-ng�M6� "&Q pM�39�63�N6�desAk ques*��%=JEDonoghu�B�Hol%oCP%U (NY)Iq12�44�R:=zhu� S�uf Maekaw�cd:e%p ��&p A�$U. van~Kol �{ hys.Q�7E�435�i�endB�� f�; \Ai} Alt W25Opti"~13}a�131\etal73 7 ��}�67}� 3@6}�nulz M= tPhDNsis ``TwlyWp7d atom�+o�;�Di7 �ps''},&��] Innsbruckw9} Han�v J4�yCoߎl�5� �i: F�a�lπr�KCl/�"Vq�1(Many Body Qp�um�Yc �� U2Z Texa�*Austin�i+} We �<OSLO LTEAZEMAX'i}�8ty M V R K 1964a�it *�I�$3} 531-534.BHi} Senthilkumaran P-�^rL���U$34} 1197-1"/YU.� USAFgTol-ePo(ID#T�Wt�51T4Yd, R70"/9S'�1 F-88488N orSp1E sulfv�mi&ds.0�V��besS09]M8 bead 6 PolySos�^8vi}{QNeu� er W5*80QWa�2 22!,37Ii%(Grimm R C�_ CAdv. A����Ȉec-��m95M5}I"a�c�[�*Ma�K�$ee downloab.�(3 dare�YViv}(\'�[l A 1947 �� d'pqu"+Y6} �O9�2} LENS-(�cs GmbH, Finkenweg 14a, 85391 Allershau�Ge� y"�d�)lens-�s.de/f4}�^5*S%.m� sgriot�V4viA�QTan#Hor Ixon DV887 CCD c�vajv5Born Me�Wolf E� 9)PT\I0O��s} a:}2�� chap 4 8.8.�e7} Dr.�$ffrey Broo�R�r�T R �f :�)(1_anis} J.B�nd{ Ev)���F8{39c`6 ref3 JV.Gselago,z�. Fi� J92}, 51�67) [� vUs�� )b56� 68)].� �ewP�R. Smit� ��`M.C.KA ltship2O30�78:6`cri�\�%e, e.g�,.W. �t Hoo�V �e.*�24970/1); Garc�kd� Nieto-Ves�Wn�oZM$8}, 2074036 Y!�T.J m P.M.Hhtz� �� ].�� 3286\ lD=JD ur�WMEsenblu!e� chul S.AGakrishn�2M^2}, 150 6�numer�P� li��!�.�� ExprtC) 1�640�3);� Ccbz�)]6�ge��}� Grbic�G.V. Ele_ riad�/)]>E�11!��6` ref2m3R"_�l�F&is kin�[ media but�7( $A=B>0$ ha{9en�{�Gd earlieh,S.P. EfiN�0Izv. VUZov Ra� izik�?�!6131�178) [#�."�S!>42�Sacks:D(-1460:ITAP}�g,A[ KingG�, u�aa!��e,2 A�an- �2ropag�)�4mg �  � ref41b.Ae!lby��2V2�cVw ]2%�77ex6� ref5 \C��Parazzoth��Greeg�K. Li�{ Koltn\ M.� ieliZFa�1��ME�V��f� 5b}RoaBeil,�_%U���i�P33�. oO�qFsht|!? hahverdiyX �`{"G�)al�� metr~Ge ofQTmag��,sm"}}, Focus/*Mat&7t �U �^P.1Lk�f�# Nova��P���fL+th/02052�EMPS: ���ts/030902�� ssc}�erZ? it{``FinsC�$is just RiJ"n4G J;�$4QuadraF4re�rd"}} Noti�8 AMS,Z@em4T1996, $*�c�.iupui.W}(\sim zshen/ �/hi�-y/c��cl$*� r}_n,%U��59� ,aE41) %U*sh1n�Un�[E1 8y&122 "B8!Scott_ 3} BA' M20A 3�53M�6Q� :Sato:MiyHEL uchi e2�M�to,� 0)BS�ma8,�2%�6���6�(Kim:Hahm:Diqdy1�'~J. Kim"bhm oP�& /�P���bf �m 357812�%2� 7:2>FlF�`������5!T�MV\2-1>\��MYBI[d 246A��b2L Braginski�{=�%,y�R�^s�J�? *�& Ma Le&y�, (ConsulKP s Bureau,2:jBian:�!��$E�O.�R�� 469-�6=�B;��471R�H�Lm:Drake!�3��~BA�ssa��F. #�)�~-�& 402 BcGuzdar bMcC�y: xLiu vP�& -R� sQs371RsSv��VT.�)�>^�'70 692q Arak�� 1966!" ,� �out�)�Z1�32LKarniad68:Israeli:Orszag! E6�'w +i�SA� 6^� 41&/:Nauli�3�li�IW�3M�01R�PLechte:Niedner:Strotha2� Q # �U�+iTJ2?e�A�%No. 3�� 2H �NielseB�euA� ", SIAM&}|n<.�8-�~N%�25�04a6� .RMcKee��i6 R�JP1I�B\ ׍I �:Rasmu�:PL*� -,�0E�a:�� J. {Juul I�c�x�ernN�5 �42���NJP!�5:�Byt49to�-1� ��6�Conwa� 4>90eo�0$ir upei)�. KendH�,HASDEX Upgrade Team,�(c. 31st EPS*�  on-�E�8ics (28.6.- 2.7 3,�). ZT �f� U nonu�*iV�� : y^dy�t�osf~s��L,taneously ne�v�tlu� $\eps$%�$\mu$J3�D 1��(8) 509--514.�SSS�4RT��E.�fver"��:a�"�XoX�1"R 292}E! 1) 77--72"� NPV_expt1�p�Nqf��<�@--wave*@Sf�B�Uwm�di-J *)I9��42), 5930--5935.G�2� [2��M. Ta j�a�E"qUJ{ x�S�&��aw�9yGv� 90%�3)  7401N�3}�ou��Brock)�I.L-aqv2+o&�tsI+7--h�d�B��at obeys2�)�R � � , 13>�LM_MOTLE<Lakhtakk T!�Mackay, ��,inite phase �cc�:a:� bou�}��O �Uv@!5p2>iQAp�#Hol)iD�165--166.j LMW26�Lp cCal��W.�5 eiglhofer�V� �--�0u�"In:>7EDA.9$��s),rAr"ZHto�MlexM�+���csM o��HIE0Ssh� ingh��WA,� 3. �&HCCLIJS�Chui, Ch�|H� :~�p �MinQ�ax�)o&��Rw�/ B �$2), 085108.� KarkSd,K. K\"{a}rkkina%N�it�[A �9� z�J�Lorentz<:� slab �eE DJQ, 026602.�ML_PRE}�h �A�)X2�,�nӍ�m:� UI,in Faraday c/�U[Z � ���=�BeLJmi>� �)&����Fh, S"94 ��.io� } C.z} ��ڭí�� R  . 7�s� xQ2 �#�  !�.V�<~�#(Burke K.; W�f� 1009 P��}&*a� NIST�4> d+ data�� e (�[! ics.BrP! Ref�t/)) opmk�{it :+ic DFTZ gram wr�)7 E.~E�J*+yu Frankfu�b' b��3}�� �b� �$Al$, $\delta\epsilon=-0.043\,eV$, ��$cts a typo�$7~\ x��, w�)it was�7 as RZ9Z �ra%}�W;�rot5!.eQ=2�9a�6��N$z-A��oll@�ar �zD.B Ostli�PitZern As7�h��} (6�y,�D� �diknudsq�J.�2K iP�!Hjo������ New�Q��)�3 "Ǘ-Vx~ "��tl�K.o#��!.�al�<mulae��nd.�Gr^/^cavendi"B.#3Clotfel�Yi�C&2�Is kliFAm.!!�% 4bf 55}(3) p.~2��Zm+n7zveig}ÈM)@J, � Curs�c F\'{\i}s�i B\'a -1, Mec\^!Sa} (Ed�� Bl\"uK!, Ltda. S\~ao[�g�5Ӂ\K B��� ��ist#��B�R$de 78th!q (CRC� 4 LCC, Boca Rat4s!sq�1.�$\b�� =0.267^o$a�ĶtA�preci�of��fple.tS t}[qe disc!Id i�0s virtually u!�O uishD� \�5� adop-�!ma ext, �UqeE  liWwr� ��,$\rho_s=1.4\!�8rm g\, cm^{-3}}�-1 (2} Of cours ���re soli&j� d� ��compar�%%�) sun,� these$�ypia(nei��-��e�'s M�S<no >�in��l��ne�1} Isaacm��em:%2f,N!*al Phi��, �� III�8,�Tol�~III (Quo!�%��!��xngr=k�aw(�uan\8 I�� Chic�+195�A� �2���Z�10��2�Z�pj9- 120}z"K.iKBN$BURGER %%!7bi͑burg} \asc{�Burger[~\emph{�@non m27n89) 59.�H-Cf$E. Hopf} :� mun.�' �W��o 201-212 .950)no# nt J� Cole : Q.RD�#225-26� 19512TST�M. Feng"luA,�;03;j1)_nd r�1�rei2�� ispcgE.g�e�4�O. Vall�e��f�,de Izarra.} )�it{Inhom�F1�U3� aj�� f:��elFc�,rct�Mee���9 16$^{th}$?e&L] Sym��um*�� (ISPC 1Q�Taormi<$']paper !L-339.pdf, June 22-2�+3K Y�wos9*H9 Wosp�.k��I�F.` Ze �?�4(-int/981201g�:�?or�E� sc{G� UhleT^L.3Or �}��^)U;{36�?8͖1936q& orn2�M. @� `:z}Ij*�& f17f3 f4� =) risky � H. R , �i Fokker-Pl���b, sod edi�sX�i� �08O B��HR� �j�,1���(IDTDR}W�De UReportA�A�ATLAS ID?"Ђ,�rTgW16l T�29S qP�qPixelVq 8-13!"EX"�'sensor}�#� lam��=� ��t on pc 8�Nu%��>,> ��45J&217��K&}(MCC} R.~Bec� le |Q MCC:%N�Q"�)r��p"� �6�},�\�R�S/11�3�D)tf�t�~H\"ug?<�F�h-EA����@%�integr�A �%0��(ules}, acce� for p!.�,inZL� �BATf3~Treis:.A ear PC�d5�me8�-w�,am telescope���,ed 'acquiq},R� 1�0 12-1a�206GmyI(6I:�m@Du onQ]%"yM)I[Z�[! 47Q143-1@=�N��Y -a(1} U.Marvet�D� s, "Femto�xp3��ci%��y_0�y: D�t b�M�g��"Z it Vc<�� :2I�cfas��až �s7.in�ar2C��}�9 rgui� 5q135J� &�2J8. � D.Po�S|L.Her�B S.Pe�/�Q.LuieH.Zewail6V2Vlas�� =a?a %�re�H"6@�� e}!SbfM# }, 60992.�3��MacholmoGi�<-Suzo�F.H.MD"P:� of2">�xcold c�=�sbed� $wave-packe�� s"Q P!$� �A5p3!y^�34� T. Z gR�3 ylor�#J.�3 nbla�#B��ep&Du)�eo=k "&���!}awI2- anF�cndWte2using/?i�io3U f>.�*2=.+,")�JE�m.)1 ��I 97;2BC.Jouvii�Bo�>� H.DuvD"B.S%E)!%6Bhemg�.5416-542 9y9}� Napl�CA� Wein  P.S.Jul�.�HC.J.WqC�B2t("Line shape� k�3ЭB`-)a2Eof�coo�0E�'a i�6� ��7UE135�6i,6} P.R.Brook�Sp� ��}tG�� �\!�iesN�%f2�N:R�Y�28!�88.�7�.T"Cafbin?�ic.tix�l�A2'f�HqfJ�s.�2�FlS.� olYp1�(48 996;ՙTq1g#׾ P.z Gou!��v)w�J�"E. Tiea7�1P� Y;��Z*�#%ph6zpM�long-�M e 1ui�,8an alkali dimer9T�:`ve%�t-� ,�i0N�7>60�9dy(8��Polanyi�Sch�P$"$\ddot U$X6hoc�7  u$nn:]nQmen,1�Z�ER1�B,3�22D09} A.G.Rudave&0nd I.V.Yevsey#8��n echo!:m HF1d*kg�LI%(��B23-5296��-.�BV.M.Aku�(V.A.Dubovitn/��M.Dykh�O�2� �,ant ev�A�rp�$ū6Bds�!�9 �%-f�Ay�>�I):�~�6�V��,AJ!��G0�p.62-726aB�.� �I52�= ��9t6�"LB�OS K�>F;�s �|�6?Mr�8)Nѧ�ٛ A102}(23):~��4310-432e6�CS.Sten�$K.-A.Suomi1%,"Weisskopf-Ww� deca��6�exc�X oscij4or�m"�?uk� p.37��:�43} R.Friedberg�.R.� maM"Bp$rd balls m�nN*6�z "�o�;q�e�2wA�H,pp.1446-1471:PB�4}��U�8d�"�1� edN R�.E��Q FB�6�]�!�858-87�22��Á2�$e�M�, "Th�Dl��a>� b�I�F�k9pp:�� !U2� 16} T.� �$, P.J.Hay,� coval�с�i^MmB�rare-gas�l0ofluorides" ,� C� )R���O6R18 l!8; 4? Jonef\H.Sch:��J.H.Ed.M"Ea� 5N�FB KrFKX-I6�"<  pairE!� ] 6q3�xim �!%non-a.O�� open-shel:� �a��ert�O : F�Krm�:�J�189@ 61-2i%� �j-cD0"�[Ba�R~8�]{  } ,�]�a"�Er. ``On!� �Tec�PFA� A;\��n�MW�D* i�Prd.''x� 6��b�v%Society) �� ), 348--32�$[Buchwald~.*]{} ��ana�A Half-glur��>���I� Annoi }�� .1 ("K4�;~14--1.�[CPAE1]{}J��f_ E-_. Vol.~1)gEarly Yb4, 1879--1902.}� ch��;, Cassi$D�P C.<�1ɑRo%�(eds.�erincetA� >)�2I�2 �2��2 �Swiss �: Wri o00�9� � �� � R�9*` �3 �3��3~�%�11.} KC�, MO n J., KoxC  ReIJ\"�o=b��:9�R�9.� �4 �4��4z�12!�14����B�5 �5��5J��t spon��a40���yb�9�~�F�6 �6��6 �B%N���917~����.�E�7 �7��7��8A�2a�` JS , Mi�pB�P, Illy, J\'oszef, Leh\Ch}2oph, :� Kormosr�F��+.1 % 8) 8� 8N F�-� 8.} J���1.�4Ş6�}���>�9 �9��9��J�Q4ry 1919--April �.Bb-�,b YKenf@�D�7��e"au�T��-#���.#EaRX-�~@ ]{  }]�N�_� Q�B �'s�7la�}� &��\Mercury's Perihelion.'' B6� �#At�xoA*�H:�%"Iin�/H�I+ KO~t- �, ��U{*� Nort�� D.5^B�#BasD �� : Birkh\"OSr�� 93 (1���pp.~12��72�Go!�r� !�} , Hu� !\u �k,JH�!3oJ�!H%DLۘgi�����9�} 7-� $no.~2. [On*v ]cle]:  13 Febru��,y�0TcR s.org/lrr#J4-2�Holme��3]{ eta �3}&Zmes, FrYic L., >�Rl�B!sHans-J\"+�q �R�J�OBench �Ly2/*� �];><}.�� QLo: K��A5 (Archime�P� 7.�$[ITa 4]{ 198��:m``How U@F: His )�Equ� & 55� � tu`�)he1 cjOsnZ5 !�253--3122 Renn�� 7]{!�+#6h �� ��H t*n A�a�"_�.�a�:n&. A Post��C+1 '036)� �}�$527�`7�;8j 8b�5jhc$g�2HBM :�B>.�,6n P-� ��si�< Q*��f�Qr,r�.�!��� �!�9 �� 1999F���,�M!�Heu�l;C(e��Re�Sen��w=�S(PڥÿE��.��Q�!�.� Expan�&�EJ,>,)� &� R�1��H�� �t6,qΩ� b�9 F�AW��87--1�2 �>��a=���Eclip� ,Stars�)ndl�[il����,to��,}b.`�H�� Foud%�E�Q�sAQ�>3 Fea� hrifd7��{��.m�$}, Ashteka��be����DoZ��U��:, ()��J��*�-!m� 23��39--2�:���b:�b��rr�A\Ins� s: R�'struc�%�A�j_of  6�.}<Zur60ї-� �3[An��268B4.E�Aw4]{ �}q��a�y@ i��y �jram�To�[&i���Ca���H:!to��h !!-L� YE� PJR��2��b�W7]{ � :�� `A�]A.,My Type'---EU)M�1���n�/ish"�G���U�o.�} 2�8�! 57--�# ��~^"rf���: �� �%�+0`B'�`Z�ai ,��� 6�  ,��-11.[C[ m�8=09850i�(ed.) �5� 's M��ulO�^. FO��;Change5GFak�{n�"Q�n�V�*��&RE�i \e�I`after\ifx\csname natexlab' \<x\def\ #1{#1}\fibGbibO font>J M#�Pf�Q$�R� ~R.$�Rurl^�url#1�0tt!O%8{URL Ipro��� and{!\0info}[2]{#2} B!i\ []{S'*}_[{2�{JayngCu�8s}(1963)}]{J-C-j-(nfo{author}�5�{E.~T.} �1{ Z}: and}A)�)fP F.~W>P��"Aj&�}{:.\�[}"1'-!me}{51:@^�s}� (. year��63}2� := Scul�D�Zubairy!>97!>s-z -��-o�E�S M.~O> p�S S.}~�5��)O�3 %�title}{QVfO �."�,sher}{�� U.\'y.�/1�1K97rKMesched.~\X� 5)6�$ , Walther�a�`u�c}}]#-PRL85�eD>c-�V�H>> � 1;5k��G>O��P%�Y�D*\� .\�'j�4:�M�55x5]1�85r�BF01�94:� " �it�g 1�!�bD-pr��VjO> `:�V<BWR �ڦj�.�֧72:�-� 3506.~1�94r�Ar�A#� hildaasa.�)� Feld!�AnaHS�z�K>�A�� J.~J>� �:V�RR:a �?2�yGVQ M.~S>Q) ��!�3�e�1�375��}�(}]{kwan-sc-�E��V�9U�J��KF� ys.\x !#9:bf�3�a4A�K �4��>h� n`Fang-Ye �5��C>�MZ�in �ar} N�vAn��9�an-apl�p�;9A5�v:�`)��-f�6�7~-�2R�199v�Kro2�B�!, Sz(rsta/ Beij���PVerha and ���bkX -pra��J�t~CA}*c z:�V�H�WFq��DCJ� �FBJ�-#@��Nurae2Ve-jNQMHReAA =^�37 \2�7��>�pyr�6�<7)\citenamefont{�FAn, Dasari, and Feld}}]{An-OL97b} \bibinfo{author}{\bibfnamefont{K.}~nAn}}, if8R.~R.}&; �?and +jQ M.~S>Q �2�Hjournal}{Opt.\ Lett6textbf{�$volume}{22�}4pages}{1500} (04year}{1997}). )5$tem[{\cite�LStokes et~al.}(1989)N" , Schnurr��Gardner, Marable, Shaw, Goforth, Holmgren%� Thomas!�t -ol89} �f� K.~D! bi9w �:VC> ��=J>= �=M>=-&�=S>=!Z�:Bw-��= D.~E>m1�AU6��BDQAB!�%���14�@Q�324N�89r�$Filipowicz.6:&�JavanainQ�MeystreA�)-PRA86��P>�B:�V�Bd�@��B���F�|Sn�~�j�1^�A1429N�64r�4Fang-Yen}(2002�cfy�sis��BN � emph�_dtitle}{Multiple Thresholds�� Many-Atom Dynamics in the Cavity QED Microlaser}.�0publisher}{Ph��~th��A�ssachusetts Institute of Technology},Y{��!r< Choiu� 2005:� , 1A� Aljalal, :�"�wonshik�zBZl-vv�~�v>A>� Ғ{KB=�C�kV��7 �7 7 � ��=GJ� �@T>}%}m�2��� B?9Wa�!!E�";ń��~n�4Z� 5992.��aAI6xend{thebibliography} �'\beginB {99}&q H{bates1994} D. R. B<, Adv. At. Mol. � � {\bf 34� 427 A�4.� {larsson�  M. L ��nu.� L Chem R$48}, 151 R72Rkella P D. KL, L. Vejby-Christens�lP. J. Johnson, H. B. Peder!and;H. AnScience �276�30J�guberma �S.KG � 2H�276 H=vv�1998}AJ��H.2� R�)� A �57}, 36-�82Psu�0}]SunR,H. Nakamura,!C)� X%�93%� 6491�02SMH50:H A�F7�718C56Ckokoou��$2003} V. K�C.�Greene,.[A _6!t012703 �X32�mulliken� A� S. M 2P�13A A962I�66�c��A�9%�C,, A. E. Orel�v,A. Suzor-Wei�% )1�9}, 2804!992�stancilI.P.!S ,� LeppjDalgarnoA'Astrop  J, �509} 1,e6(deloche1976%D ,q,Monchicourt,a�Cheret tF�Lampe�2�13}, 114eL762�(phelps1952}!&V�%�S� BrowF� 8!�102�522Y0hornbeck1951}A� A. H ]J. � lnar.�QF84}, 62E�512\urbaia>9a} X. U,p <{\it Proceedings% the 1999�Confer�j\on Dissociative Recombin&, T* ,, Experiment�EApplic([1#6!"445A�86�cAL(k1995} W. CZJ. Ry� wskiR�EM102�y533^95).�ack��A�mHdHaVgreve,!�ma�ys) ^ń7�96G maas�m$J. G. Maas1FE�$van Asselt��J�M!Nowak�Lo�.�.Peya* hoff)�R Buenk �� �,1��21E":�$flamme1980�@ P. F, T�rk dJ. �6]$�qE�419!^86�yu1987}AsYu%PW��Wi� P%J�7O�'055ɑ86& co�͐��Gun/ Simons �K.A�Hardy�-Vp8��271)�6| zand�0E{J.%��PZ�Ubachs:dҥj 3212�6"h�20b�ZX.!.Wang .\ZE�^ 6^coh ��J.�P2N���8� :'g� �K> in�hys� of Ion-Ioe?�El�I Collisi%�Vv 834 NATO� ,anced Study "�F Series B:%�ics2aO rouillard%>J%>McGowanAK4Plenum, New YoA�ұ�7. habs�� Habs �et �, Nucl.�,rum. Methods�ayRes. Bi4A^39:�u�V�9b2fC.a�SafvaI�� � "�  &� 5�V�j�%[��n� �� b�!�^� V�261.�kilgu� 2}�VK,� !� Schwalm� Wolf�vR!5 Badn"(9\"{u}ll�?A�� ��4� 57' 6�amita� 6} Z. AZajfm!��T@orck, U. HechtfisU� B. S! l��A��D. �R� pnowT�AA. � 2�Is�403�96� alkhalili~ A. Al-K j Ros\'d$H. Danared%FŕDerkatch$K\"allberg�"� A�� Padellec+ Neau��!�emani��R.�?af Uggl�!�ikor,��Zo�*W���.der �,�"� M"q'R.aFBilod{O!~b!^j!7",6oLŠy[�nge� Lev3 GA Gwin� L. Kno{ M� heff!�D I�R. West�D. Q�1�J�� 427 !�2�wS3 b��!�|s"L4�37��:: U�92�� a�MA-hA�.)&Z. VageE��60L)\Z-5B� ��VwRm 60"769��l).Kgf1974}�S. w, Rep.� g.�  3L 1257 L76+gi� 1993� u�aJeiting� .�vo��Hahn,RPJaeschke, C.-M. KleffEf(\"{o}ss��0S. Papureanu,��R�-$M.-H. RheeR9SchemO6���.��Ʊ32t16��96�vonhah��3}A�von �M!Qie6�E.��:�AAiebmann��2��]1mGa}tampfA�6�6� ٩, �270)�:�staE_e��G� soffi��BlU$A. Friedri�C!NG� #U BM lz�.]Ju��r\"{a}mi9K� tl� Ot{�����28A�326( pastuszk�0}I] ŻSchramm���v deA�#U�J�nntE� H.-J�esT�Sch�~M�=�2�r�d��. �36f1�:�poth1%�H. Po%!�p >19��13 6$l 1996�"���V��.*���AS . Pinzola �NJ"����%�5R 14� �2���42�.?&�.b 35�323�6�a_note}�$ dipole mo� func� $Eq.\ (5) o� Ref.\ �"I(} was divid�2, cons�t withb ��iv in %!6�tem{ee �62�F.E ��*�)V47�66� herz�n H mit%a� DiatomicMecules{4(Van Nostrand,2} 50)T&�H. Kreck�LA7 Lamm��ab tras��U�*�A U҅`F� �JB)A20�3�"�2�WichGV�.�� B.�,S. Altevogt,�Andri� ijao� uhr,!�H� �. Witt:��.'}&�. (91}, 143201�6�tanabeiST,�LTakagi, I. Katayama,��Chidat Wa @,6Araka�Y.Haru 1�5 aitoHNo�T�Xn�NFNoQ�K sono2^ ��166 kAY�SASEg*� "� .8( � & �� A�� "� ��5�%|�ف�I_6� 0327���2ah*[  >p .���.��ink� wSchmitt6V� u�!{ �.bz�f80No l _phdI %N:� to be �!d;A(�PhD�2,sis, Univers" of Hp��, 200�Hhttp://www.ub.uni-h&0.de/archiv/17:� 4nakashima1986}Ak[2�! :x� h6L�72�86�rabad�8a}a@R ��. Sarp jJ. Tenny�MonlNot�X-n. So�29.7/82Tvb�vJtE� B�'K�420:h faurd1VFV�R��32�446�v� �"� a}Naa�!8EuKan�,]24�4-�6&͛1^uComs&a)�2!x3"� 6eS26�Te a�6��Z! r jZ�@�19� 6�0garcia-molina�[}!G M� a� Dent�I. Abrilan|� AristaN~��129�46�thomp�85EjA� _AE�Barne��Comput�aLomb �3��86�f6�f� i f%�6E �6���46���.��U.�Va!� .�Up.5�e,Heredia-AvalLR.>�I�I/Q�69} 0629 200E� "a f�I��NC." R�2 &�*� ��#�F2�Aq.s .���72}��:�orem� �YK:Kul�28&� 54} 499 Y6�!02�0N. Djuri\'{c}eMP��*� "�A-.� K"( S{\o}gaard1:� sub�ed�!�B.�royal �@�A� Pemc.\ 6th� Int.L.��seF.�, Mos>, G�y�ab,:���iBa. ]�&�>�)I�i�4�� R427�I,U�s�^I�B.A!�p���lA�Tp Morg �9$ �59��P2osy iaaU6�&*S.�{e}n,�Sundst)o}mAOYho�1atz�D �M..hd �%_�vanga*� BQ .�}���; dt6�*� u�!6.�9��)�5AR46�:q� 1�B .�&� 1&"$� � �.��&F A���f�.��" 40056 � R�'f�'1U.Dexpandafter\ifx\cs�( natexlabU (\relax\def\$#1{#1}\fi ^G*�)>J9)M#�P"5jQ$�R.>4^R.$�Rurl^Iurl#1{T0tt!O%8{URL Ipro�command"/ }[2]{#2} B!eprint []{S'*�)>_5 {Yamazaki2C }&�/Y �,Bc+^[D(A&J%+�1pe,^^6366:Ap_6�#>^6��/Korenman�196�0k1�� G.~Y�]�MZ�$Hyperfine\�- eracrI7 101-�#6N �81R,6,bib�>�� 2001�AH2f�6��N \��vz3692V� 145cF��r��!E�0��!��JJb. I6�6�-A�v~�Z�02251J�-e .�>� {Horb�ASACUSA��B�7NV��T }fX589:GM� 0934�´SW�e�v4X��I>0I��r�/Z�37]$>�199v4R\'eva�(Krupp �8A�r��Bx7 S}<f�<(9�v� A.~T!�2� ��:57:CM1vJ98rEkstei��5��e � f�B�2J��j�101:A �8V(F�5v�BeL,,and Salpetera57Ab��~A�.�V� E.~E>O�):R�7}3$tum mechan' one-�two-e' 6s}A�9/� r}{S�$ger Verlag tU�Tddress}{Berlin-G{\"o}tl en-&�4E\357riRa��$Shevchenko�r3!�ourBor�t}~�u�W֌ N.~VB��6how1E8d}{LANL-arXiv, .0(ics/0310153R~3rAhl�2�?2:�6$$, Dumbrajs�(and Pilkuhn�6a I��R>G_:�V 8O>>��6BK��!�Ei"HZ�% 30Zd29V�5B ",�$�!�A�Solov'evA�bG�N; `:V�B�>Gx%�?�"�YEVQE����:�,AU�JY�B;b� � Ap~ V�99r+Newto�8� n ~�R.~G.)� KI�eN:>$Scattering�!ory� Wave} Partic� ��m9�kNew-York*M8Ł.y�ha�H�30ion}{2nd} ed.nS" {p 600}�R�9f!�9%�{Y5-l" �wn L Se Yaffe L G,1$e�l&.} �340} 1 %V{AndoV� 8o T, Fowler A B^Stern Fk.2 \zMod� aS37�Fe!�e   A L �( S�v.}j10} 3739QChalupaR  JR5fR,2} 4 \nonum 246f43} 22�erratum)�Totsuj� !�  H�8F\17} 39�ea+2�  Gann R Cm#kravarty-�C % G Vo9Fo�!Q26��i� q %V6-�'ath:�} 160Y Ditt]X   W�6 �Am�,EMN67} 768� Niet.� $ Braaten EE� AYJDik8 6990ZAbram.[  amowitz M_Stegun Ib7m ,Handbook of !$ematical FD&s} (�14: Dover) p 559Z=�fref��At@BR} G. D'Agostini�Dit Bayesian Reason�Q\in Data Analysis: A Cri �Introdu�& }, Fn8�$��� {,Causality} � earl ~(, Cambridge.�!P� )2%&Fey� R. RThe cha�er!mf  al law}, $MIT]1963$Poincare} =) \'e a0 %�Hyi)~"}Z9�%� Pub.52). Maxent98B�``m:J��"usven�Nal/< tistk 8 in High Energye14'', Maximum E!�pm5f-:  h�6�a8, eds\4 �, 6 Lind31V. Dos)!�ipE, Kluw�cadem{:&.Ein� � -[!�w�:(as I see it%Z�*Citi19�:�,$Wilczek} F�& XDFrom ``Not Wrong''n,(Maybe) Righf %�eNature}<bf 428}�4)�3, {\ttMQ(s/0403115}.*�p-valu)M.J1ervish;it $P$ !: whatA� y ar)L no��� Stat�)�?U6) 2032,BB} J.O. BerIand D.�& erry��)tM?ai�* a+ illu�6a;objectipG}, �AA|�$1988) 152� ZechE� xFrequA�s�-U�confid�: limits�  Eur�A�Pdirec yC��,2) 1. % --81=� SK} a.ielcz4;a %jisAakshop�30e SuperKamiok �7aboraak , Y.Ashie7 �E�4nce for an osc�7t� signE@e~Latmospheric neutrino/ , ��+ })Z`0�4) 1018026ADD} P.�%o9A2�PB'A�#ioMy5o$model comp�= on a�>I AD Explorer-Nautilus��1 c� -�4data}, Class. �$v �D�3) 762RPPEf�i"V?mG$ocessing e"=? al �: 2cCJE� basic �S?!cR�.Pr:�266i�43) 1383. %-141�mѹ(Giunti} C. Qnh�Ang%/�]!�p?�9a?fY�ic ]�iz&val��J�c:g@�ZE� on�q#Le#, CERNL!Lneva, 17-18 January!�0 # -005. %(5K +)..V!C~%gie} W.L�1eed>'E� ŪMeasu �cMAR1U�)eAv�4.Z��f�10*{,F$odoulides:|-817:NAT� ~N. :$,$/L7�#�Y. Si+*b�7�i�42� 810"]2�Kivsharv:Op! ,Solitons} Yu� %jG.~a�gra�I{\em �S ::ɱ Fibers to[",otonic CrystA:} (�e�Sa�Bego0 6�::��-794:OLZ'� R.~I~G seph�@��F77i(86R*Eisen!O4:1998-3383:PRLS ~S. ,>}R�HA0 otti '~�Hoyd%� ACi�*%�@l�8�*w�+6�M��lik!�4-93904 �D�4nd6*M�>z% ::�� .�9�-i�6$Neshev �83905� %8 khorukov,�$Ha/W�. likoBE�2zf%H 0tJ��� 3-83I/:�H>�2F:"o!�oa5�$�'�$!�Gley)\Bq�C=��783)S6�6�4-2890E�:��5�:�B��0 �D�:SN�J�F�9��J� Sipei�132�J� _H? WinfulF]e�13�(:�$Pelinovsky!�(4-36618:PRE�E�(!��Y� E�?70�0]�N�^$f�| \N( Cieslinski ō8 (Darboux-Bia�H$-Backlund �4 sforp� nd s��8 surfaces.} In �$ "NonliearF0,@Geometry", 81-107nI �BiM ���4re is more th ne wayt 8frame a curve.}T L. Monthly 82, 246-25�I75jCaliniP'j4Recent develop.i.6 tegr'Y e dBS�HC �,ic Approache�b Dif�Htial Equ� s�u�5l�th.N0 Lect.Ser.�M, n�56-99,%�0�>�A   !� Z�si � 0Continuous He�b~.}M�!4A203, 512-520,�NFJ, Ivey T�  R4� knotJ�7tant tor* .�) KnotA� HRamif, 7, 719-746,� 815�:�Top�TEy0Sine-Gordon E�[1 W Con� T � CAMA�e�-4 254, 170-178I�9j�IU� type& loquet sI�9$finite-gapaF�%�U(vortex filaA� eMH!!v\�A��)Xy/�in SimulE}0, 55, 341-350ID1j�e Conn� ng gI� y, t.U �EQ� NLS pot�alA�!Jica DA�$2/153, 9-1M��.�~20t P.K.H., Syma� �Exact55� ,localized inQ � roxi��1C� �smoke z moAU�" , 57�07-1510I�861>4Grinevich P.G. ��w�Xem%'ax self-focu� n�#$near SchroMer��69�L odic���W$R^3$ �>c 20-2�a&�:��Q hmidt M.U� Period pr�?v!'noniso-�l flowIo� moduli sp��A��so6�N�eg �8mJ(95), 73-98.�B�'>�Closed>:��ize &erm� �<c!j��,�,hasimoto mapb� N���(7). SFB 288!P`t no.�Or0dg-ga/9703020�HzR�LA!L ��:��K$uid Mech. ��477-485��72U���Ner� iS.�ho�p8I�stabit of c)iela5 rode�r7Lon�b��.7 79, 429-4�x��K�Rr J.PQy��1:�E�$an ideal f��%F �211�P-6�f�" Kida���A>[ moE�,>out�ngoorm%X.g(112, 397-40��198uYKirwan j��(lex Algebral�Xj�. �&Q�\ G3REle�A���".} Wile�J��Uce, New o:8U[L�!v,a�OTUePoi�V��a�a�J� J.N���. 1�-93Eo95joLagrang.A�[�qKirch�D EMelRod.} SIAM Review 38, 605-61폵�DMoffat H.K., Ricca�� helic� of a�Js.}�%BOa6� FE��plasm�HN�L. Sci.�L� 25�3.Sci, 2�*�.�l.E�(2), 225-236Q�L��contrib&;Da Rio ��1-Cra�"asympto?��!por$ :w�.} e D� ^s. 18 ah6),��245-26��Sas7/N �2 L�Y�` �]!L!�Hamil� an systema�y:�.}� �ul. 3i� 97), no.3!L9-2411LMeZV:j  A �& Jacobi�ta"�B% =AReseach i88): 1-155�$Zakharov V�� habat A.B-*�152-d63 ��1����"N mediaa5oviet-JETP 34,!�7Ac62-Q �=�0 a;Segur z Wadati�%0I )��!�-6�!��%� &K 8. 69, 2603-2606��92��2{:qM� ��p Plan� �O D Jpn. 62, 473-479,�S3 dG� :* F� �cyHc:j @ P.} nlin.SI/0411065, 8Q^Dg D.D!� tech�H S.q��FO� V-Wdriven�V�n��2�09040 � �A�R.J.,aWma F.TL1 -&1 concept f%�d1!� ��:n +E�!F .}!�aof �Ps, 8, 555-559, [1965] ��f%+I]RaOb0i-Regge Dirac � S�9 ) .�:�����$ s, A953-63, [�B�� rsden J.E�_atiu T.S �!e�� struc�e�Lyapunov&M ����inuum�.}�ͬ�real �L. ISBN 2-7606-0771-2%Y87�0Kuznetsov E.A�,ikhailov A.V�OnE�� �� mean� of ca� �,Clebsch vari�!�.�}A�X, 37-41 �0^� Ruban V.P����!�)�%= magnetic � hydro-�d �+�� ,E, 61, 831-8�200�Mr�I�ItoY �-a Sym�, Mme 17�(���matQ|$.} vol.17;� 4, second�Zion��9. �--�-�S��i*��de�NzQtednes%<tanglu� %7&� �. 35\7%�691�0(xjN-)�\blem:�"l�eiquA �:N"0U!w1_m� Ma@e�T h�ic)�He II,��rent aH �qua$/��A�CA, 80X 7-23a�197�i&? , B�M���.� h i�_ m�/.Today, 4f2)24-30%E96�Saffma!F"�exF icNn�[ Npelioa� ulos A.D. �A2�st��:e�-g- )dL"n "�e�1Lfield9o* 1� %�o�J.!t . A:�^ .GenMO 8859-8866�C�Thurstonp%rFl��$io*� Vassiliev%� in�xn%�aS(.QA/9901110F9�MBelis_ ��B.�p$nlybaeva A akhimov F4Satybaldin E.G�&yrzaku�'R. .�bl�LspGonlai spin syte�w< Izvestia NAN RKa�|8Vijayalakshmi SB�, Lanan MYu� simplest F�.}:%�$i�);t ��B�!�J.� �M� 9, No. 4,�2122-214*����D:uF�D� �i`T "� E� �e���Ak ��% UJ2�B�7�_3765-377y7`/ na L�� Ku>�� ani�$��De������D ��bn-�^!� ory.���iN� 1Em42%�3�1�141�:Ra.J1��, Serik�x N.A}ov�W{ �S�L'ons#yQ }Q!d ^: _(near waves:B%��� I%um_". �w'ce�es II �# ,�50mistry. �  153.>�)��)�50ordrecht, Neqllands,  �543-549q�>*5+!I., :g6JA ���'%O ome gener�&�l�=.ce� chaiA��a�bEg !��M�b>b35-5421bMurugesh��� ��N"�P %=c�� q]:Wff to &�&�3�PS�* 4005��J��E��e rprei!ʅk2|$:le�g���Q%dl��Ʌ���{E�s�$ForschungsH,4itut OberwolfaT8Report/40/97.ps�fU� Guts�sh E.Sh�dS��s�I�>ori's� � .} nM0VTG]�D� &F��k2i�backgro� ofA�ral: �!�)�90� J7L[3, v.28N11, pp.740-744 iEsteves(, Hernaes G"n Lax pair# i! TraX! a�ic )�  aJ٬NE.}H 0v-int/9910005z Chou K��Qu C.Z-�U��(Q��B� Y�Y}r&�!}7 E�Societ�� Jap�Iv.71, N�&$1039-1043 �"�� , Zh�dvn�AafZD�j.�4�M�N^( �F�0als, V.� N5��3, 3-10���-;>�6Koshkin�� ,6�� -e%9�1 ofM���y�10Days-Asia-Pac+ 3: ThirdT r&kal��"c"���. S&�j830 June - 2 Jul�*4. p.10��Nb$q fb$0W* "�+ doke�iT�0�^�\sunVE. Shib�B, a9sl{Est�of AbPe P�) Y�� Liq�Arg� nd Xenon a-RelCl�1 (1 MeV)K(ctrons,} Nu"�e.E�1A8A�� A291� 89) 617-6��suzukixUS �2(e$ Luminesce!�fN1Ion�� cksfdu�fby Alpha&�9��2��ure �, Krypb9 Gaser�215�3) 345-3�=���Z S. H��Vac��k !b�W2,�70) 17g �miyajima%`M ,AQYh>V,�Kon�X�XamaA`-Rubo�H2g�U�UtAvex" �ggy�en_\ per �&��!�lItaAt,:�9,(+7o0 438..�platzVI�L.�,�To�/]in)0A !�-�47 cles�rraisa$Our U�s tand�4�'t�1�.-�I�Is�V1�a61) 116.=| icru �:%ޅ\ mmis���9�Uni*�P�.��:n�/ire�Pd '75�,}z9.�ca 0hoA'�T %�G.c�e�`eY-1G I8$Ej cint�2!��7Di%�` �g: E1�nadTempoPBehau57!!�c onent,}fz1M^(80) 469-475.�advphot}&�j�ix, Inc�Qe *�YadvC1d5 onix.com/.Q�(roPAm�#L, �2 ello-Baibou92/-_pe,� PieKsao,W!alchlopeke� Vent6u1vr'ide4 �,ICARUS read-�!a�on3&� on,U�l�Xe 8$-TM/2002-0!,��Karar5/ 9pg}>&'/Musienko- Ch. Van�^�::$�� aval+e %RdiodeT)calori." sj�in2e 7��99)Vg�-431. %doi:10.1016/S0168-9002(99)00177-1 �aprile}�SA ,�Bolotnik!�D�v8!c�-ukherj�e�W valu< ���\,^A 48, -93�312�: NISTm�pAaA< ours�.M.A. Zu;q(Stopping-Po�8��" T� EGs,�,� )�Heliumao4m� (s.nist.gov/��DRefData/Star/Text/Eee html=Tmoe�x} P. M �0 Bouc� zrti31I��De�H�9t Deca� A�U�@�+u� �h1p} qis%q�]7���b��B �TCarug�E. b^TIannuzziA �qeneguzzo�� first stUoof� infr�k e�in� ex�@kui�EpѤ�$�2���(�w-286� belogurov��B в� V�ݏ�light yV �s>x^ garZ B�52�� 67-1u!.�Be�[i}AF �1�anS�G.0�llBhRosself$C. VignoliUDet�+o��AmVUVq��:�)by,glass-window���$plier tubeafN�D  5�=Y) 89-92   Ru �fu 6�6fFnr95} F �� ~E.;<�(~H.; Pastora�~W.; J����5; 103�3(10267--10272 tiel�X97} T a` ~P.;brin� ~J.;� ends�}H.3Ciochim�w�� Acta�` �Biomem�8,331, 235--272�?tobias� �sTu,d ; Kl�M.~L.;�.r O�i9ll < Sc i2�$e.)0bandyopadhyayw?B.!`; Tar��M�r8; %e242--242ahu�iinqH � ;���D.~oPattnaik�%XZhokQ!�o�y P.~B��l) :�8!��$826--283A�"� $rog01} Rog �Pasye��-Gierua��Bi)�J6 1; 8!�190--2202T0saiz02a} Saiz�n>�.��;� (, 3052--3052�$patra03} P � ;� ttunAy�Hyv�MFal�la�@q1!I$; Vattul5�II�E��3; 84K36--36�9- �4�� ~T.;.�B}J�8i�B!4!�,8, 4485--449 ;b�U({leontiadou�L�[e�k��Ma:�.�4; 86\ 5A162emashlAM �Na}ScowaHIhSu�D�rmi-Jakobs+,%z2oI1 3005!�1� �gurtov� �Ǵ�tc2!�Ka2�BP2u �u461--3472�=[itI[ ndit�~AAEAAD erk�EA{�n2dA1�2120--31� �bŇibB -Mood��Har�av tradsh��J�mEur��J EA3; 12�S1�1SBkv�^!={de V }!=�M�zAVJ f�2� 2454��2 tu��V�:�9*  ; 75Ar47--2D*� smondryevkS �!�z�0; �1672--16.[-�e���IK 1W-1YU�f�oa�xr�4EO�f�!�0{�3076�91.�02B�Kt E^Nizza�Er Gawr&I�9���8Ef139o4�?�~bd�B W; Essex ~x Lutt%*�;bc 487��882~�gs2hB&Sal)G�� TeraGl Fa�xR.; LB�Am olop����:MbX influ�*4lcohol: {T}he �vct�f e�9ol� m Don lipid bilayers;!Y4; "�c]�sum03�+=s~K�0�t�de~Pa����2��}283�846Gereira!�P !�~S!ijR��;�Lndrasekh!��Car"f\ Freit0G�?H{\"u�j�?P�d2�m. 2273 UDsq��J��p3; 7��4a�247�[!Nb} .N�B3R�lyaYLy�\~V� lo��` Long^�2 muir!��,8, 8988--8992�ly!�V6HBIe�13a�32�b�2�B k ~FB� e!�q�I0( iodi=J�+�Bio�-no�I�4Wine Yeasts; Kta:0,rch SignpostE�2;  & �92�c�<��C ��& Vl'deӁ; 6Y� eng-Th& 49--6��$smit90} Sm�� Hi�CK.��a7E[� abR�Gt!0 �a{�dO�4N�  { lijpA�AH?;�C1990; 3-624--622�goetzA�G = ; GompJGe~p�Ay � J\9\ 21a<2� mouritsen�&M �q~Y�as�M� Zan`'a�!�s.�>"��5 uter�"^;���CRD; NATO; "":�3,; vol. C 5458�D 7!ASI\/}E"0M"139--182$ soddsnq S  ; D�nweg�; Ksrɸ>! 01; 6, 409--41J�h3y` �OA� M.~Y.; Re�E!�J2z F�1� 5� 64� 6� aytoe�A ,EVot�h�282; 83, 3357--336Kguo[ Guo��6:c = �� 7714--7722Imu! rMM%qɀaKas/)qSch J Polym}� B E� ; 41E $1441--1451.�$kranenburgvK��;eo; y�B� �wA 1149g156Km �rM � �de~( ��<' j� 750-�0.�fp 04c} ��o-o. 4a,�R6O92�go)csA��ahlP Hessi��qOSpoel}� J Mol MmI!�1;b@30�}uber�84} B ACda PostN �4.��Gu�OruW�h DiNo4 Haak!�J.~�.�1981W84W92AJ�XOQ d�j Jahnig�;} Z; 7C,-206��7Z�Grige[ �Qoats�T� .qg,; 9E�626��2�(9[ess� ��E 5u)bD*�08��082�leeA�*� 2� .�B$ b� ͞p< Pha� quilibriaA;A� 25, 63--62�mNmanual}.RE�H{MANUAL}: Coarse Grn dM�� Semi-�(it� e L, 2�s�>C 1.4;�ila�'ax `md.chem.rug.nl/$\tilde{}$ �/c�g�.�$nagle02} N �9 T�r ram- S u\S5A�eb� 0�7��6s$mou94} Mou[X.; Ya�� H��aiShao, ZiN9�trbS 4; 3G99A996G adachiA �1*? ��Oh8y�Hat4 � �bM�; 68, 18�� 1855!'N # Qng�\renew&�j asel"tretch}{jiPlarge \normalsize % %y@j-"on�+D�ck�K ``C/ �5)d�;ics�T3r&v4 ;>�; 8). 6_bhr1} D�5Ba�M�� H��a� G. Ripk�� Z. fD, ik [C�s1175F�K2�e�{4�A.Eg}V�zg��Bic�0F�s)i�S}B �ities: A|$oboscopic g ��  ErgJCK�em!"nexp���P �B�8gottfried} K. G�e�umg5 anic�Nund�Eal%�AddsM߅�?!� 89).6 dbkh<.�2�N.�$�'bf A463}A�*%� A469ӎfN|:q hh96�5}o,G.H. Hoffsta)��#ZE�\(4)�A40 b<96>`mon�W�"Tf� ak^ in pr2�Q ICFA"qT `5fA"�? Bea�iI�Mo�"lU.S.A.,a��W�a0C>zY!�99a Also+ ext�E m as DESY�6aj!+ 98-09�z 98) %| e--print  ive: A ics/�40�@ �8 2, +G 9010�6:pacA=K :�%� M. V�~ �C\ ope�6ar[cc. f. (EPAC9�>Stockhswe�X&(A . Av�g�f!ly at:�u�0.web.cern.ch/\/Welcome�f2��.��3th�.�9p.,%�YS�A�ic�/$rotvino, R�"a�0ptember�,b6� mane, S.H!a>Vd.�q�36}, 1� > hv20�Bb6�>VE N 05650M�F��Z0V:��Ag*rn LCof high�&polarJI prZ!0 beams''. To2>~aa SA�KFTA+a*U r�"�8:5�0}u4I�Ph��T�[,B&iof Ham� ,Zla�--THESIS� 00--054��,{2\chao81,[�K^<1fd81). �no� 0on: replace $�kn$6$� n}_0$:�br� D.��J%��< ``F've!�m',"tMForith�3 E�Matm\!x��n a��( Ring�q�D��.:_AccelerlYEb ics ��Engined, E�-A19 �HM. Tig��>= , 2n"d�N2�J2�bga�V�> BT%di�nN.I�P lube�W!�Rf1�e:mey� Yu.~Eidel�;�V.~Yak\8ko, P�i ~=��bf\�B�+95>_ky!�K. Yokoy%ER 9-00 �9)� r20; 2"�_� 2}.b^�A49k� %p�S2Mdk72} Ya�% Derb�X�A.MK��tQ, Sov� . JETP��3'�23%*7�_>^3�^7}, 96�&7B�ky8�vs 86-5CL^~2��W�?:� zw�04�Y�G�f0osium, Osaka,�0 Octo�Kq, AIP�I"�Z57"�O:�bhr92:�B� �4VyM-92-0��, sg@revis@*:�9:�hvbA�B o��E;2|ݤST�\:_ ams ��W����>�si89}Y/?LSinai (Ed.), Encycl.� m6SscF�s V. 1 al Sz54@ѐK Yrh�|BqCFS} I� Cornfeld�V. Fom����6E.5 y4 k N�@lB BX ^� 96-2�w�`G�j6611�46�khripA{��A�+me^4@�Xa�i�IzHK1lo�P�8 . Usٌ4�n10)��X�\\\ See a \\ >H� AmP~SL7ys2� I6E!14}, 145!B^S��>�, gr-qc/98090D'2� derb�6�>S@Michigan--Ann Arb�%�BAJ� bmrr2S "qV? 85-4�=8� �� Lo�eP� chak�C. Meun'.``M�BpT&��9��!"\G:�BYKoe} T� Koer� ``FerAl�jRCjTb�e:�Maa�b M�aast$US<�kkaEenkQ��BerlinEBArn} V Arno�`Aph"�<�o�K�kl wnQ7kv Birkhaeu��BdpJ�FiA�A.�  �Almost*S cZ3h�[�/Not. M�, ��3�,�2 Dug�$kmf  �1.KM} , Se�pp.RH�stm��4"�^> Di60e�Dieudon�End�8�-M�A��A�ja�ZqyA6F�����!M Real6Q2,5m dingP :nYosA�$ YoshizawaTS�V��ec�Exi���:f9� S"�X^>�!�]��%�5B��� *N^�32Kc21�P�:� Grad� S�a��I� RyŰ� 3 II"e�(�2��� ^��6��*Sbar 64et al.,����f� Sieg[hL�aeged&J�|Moe�``m�u6Ce�F�_2f^�2�LaseE Lask��`�L� D6�2�9B< fsa�M�MoissarO R.�,b?V9�ar6�]8�.�ague, �1#� �11�!�8B dk76� ~S.~:*~K.( *\T� Doklady)20}, 56�4B dk78}*�9�� 2�I�N!;se� ��<7B$a�A�6p b�432yc2>Usyl� S.Y.E)``-��Sna���_yn�]�>�m>A�>\6�xk� ;Xia�T.s"a�U>� TokyoF� CNS-REP-59B�mbe���i-hh7c. 16t~� T��$te, Italy,"͎ >FbyB4RVj�s64 binhi03aeG N. B ���,Savin. \newb�("�>of weakAicO�4biolo8O�E:ma al $Z.U�% #ds--Uspekhi}, 46(3):259--292002�" �2.�BWMSo �y: �+ly���l9blems}.>>S2�j2��,mcnamara��McN  B7>Wiese8 K._T�8st� s!EresonK'.*5� A}�M(9):48J/481X��.�4khomutov04e} K G.B2[O�T poss�H role!�iron c� `he&AF t��ooOTB"�Mp8�9�~DNA+ lexes dur!Tcell �e2|� BiofizikaA (9(1):140--1GF4.�In�n. etheredge�E |�]ez S.bS(Taylor O.R.J�ir�KY�{MuKch bu?zflK(��us �,ippus L.) usrg5 !&as= navig%DF� PNAS�$(24):13845084Z6�,irschvink85-C���%SImnes �B�?MacFad�,|orF�i3ite!��CK�� oreY!� in O��ism�R �Kw=e}ism2�PlJ+�""qQ�92bA:�A�dbay�B-.����Woodford.% ��bi>�M�hu �`2�E�Natl.�.�( . USa�89 :7683|'_-9�9�blake�i75} B R.PF� otac�bacs~a."��F6D90(4212):377--379,�A2Pgorby8x  Y�Beveri�xT�Z%<^�N�?a��lM�oOM me��nF� J. B �ol.�70:834-yX196�+yorkeI�E��2T�CaYj�d׆mi�C���sen��v�.o[e*}R �I�:Injami J.PJaT DJ!6uTE|-iG,%�C9i�Q[  :QjGNi%=fh%1} ]�ib:�\,F�iko^ oper['n" No�\al phen��a [in . 0n], BSU, MinsD 99).�h2~.h . AkadK�uk�Varus SSR!Obf 25} h77� w6�3} E.\,KAk`Jrov�*\,Mooki˟ Fam Le Ki�%!�(A.\,S. Shum�nii[atk�eo�[�WLOIYaI (JINR), No 2, �" 6�4} N.\,U ogolyub�Jr. �6����V #8P-17-85-938,Dub�� �5!d6�5}�\,V!S boik� S.\,A. Aݡ�P #Z�o>� a�$ Zh.\'{E}k� Teor. FizD89a�14�85) [:���6��1&]:�6>�t pe�J�&Nz bf 9� 244, 2) [a|� .org&4$0'O59]>s7>k�M[4s22I�1) X �$X90BX 8} B)B Thoma(�,hys�0��L14�7�6�9[~��L.\,O�dhwa�xDmid�tat?z mmun)� 4@�19�6b� :}rc ��D�/rũ9eq :W1�\,Lrl� G. W���a^M.\,D. f�6,!Cf+ mf 8�340%z>f:-WVe��_'mA�A�er��|]�!{291��>[3>;8Tverd. Tela (St�r tersk#)��38W3)[);So9�� &23)B:u�G ��� val,"�U!�i al2 t of�/ntane�pEmdJ!hTh_X�Mon�O� �J|q,"d=_,!/bsVT�fAYast01}{R�AstumE��g Am:E4bf{285}(7), 56<*1).�pi�={E�Piw�s�J. Slad, LANL e;( server"9(04081m�42_�4B�zL90u..� tak60}{L.(- \'ac�Kit{�ch� A �Ms, Prr�"Q}, Johnn, \& S�]�J6�60�N��f�_��v%.�Emp!b8Peyrard M.}, {�rNAity}, {1��%V R2�3T1}v rrisT P. \ADet< C.P.}k~�&!A{8}h 8) {F.�T2} {TuFI� M.E Q [Zyna~G.J������B�04}�0) {1596]83} {Kusnezov D9ulgac��Bauer W�Ann�\2ա� ]56]4} {Ho�� Wm�_ Aoki�h C"h,De Groot S.Vm��yDl189r {2532lGar�=  iner C.�.'�*M�R- ods,7/~ed.} (�:hC���1k�9s�{K H.A!)� ���194!&2842�asE� {Samoleto�eE�7t�N\{ �!s9!�3512Nrugh97!Rugh H.H4A�A�#L��{�K7) {7722Jevans00KJepps O)��7�*%�E% DE�RafE�6�K ) {47572dhamSg9g-f �#<���}{)�X0}{7467}; {L'Heureux Ii I}9� � E}{4)�93!B416B+[�m` a`,�8 M��.�q�JMmq {!�!_2) {2636 BT05gBraga; WqSs K�$MHJ. i�%\ }{12�#?�� 34106�SCDa�6S,�lp�Ejl��}z!o � UM /041�!���2� delh g Delhاll�1 �Io��69}� 4� 44117}; :=�tTc J-�.c5.� !0\6Z.AKH!gKatok��Ha= blatt B.}I�Mod�,&�DY3a"�&� &;U�� ity  N*��)� "K6  SvInQdu"�"*�"�5Manifold|b�%Z�nb�!ai�B  A.C.!�uX)�E} {61�$ {476�$N�.n�.^� &��\emph��yr�@(1916) 688; Idem, %ibidem}�n11�44. -- Remark t ��e�\ein's 85iM&�jN =}>Fifth�,b (PrinceSW9��s� "�J.) 1955D no m�xon �|ade� �n�nof GW.|2� Weyl��S.�* Math!PPbf{66�#944) 591.E� Loi�/H5time r ubVcZP5q�.2 (22),�@57-60;�'in-=e�:"/407134 vo�July 27�=�)! ��bib}�y quoos� e.� 4} Fock's�` rary viI�accor � which�GRH se�O �!cIL0harmonic} co-Ca�!sH a�2@privileged -- seehe�1GA5y�%U, T!W�GrD�D }, Sn+�tn+:� 0020�� (Dec�5 6th,t6�7�$„ ohan�j(Sz. M\'{a}r�/ ^qRQCla"��um � .&��2a%� S183%N2%j��"4H1} E.Barrelet!��#Nu"/fxr.��� .20, 204�6�,Atlas} ATLAS:�� �D�V^� orim &%-De��,-, � /LHCC/96-�8`�..W.l�?ak� v�$r�,3'� RGO-NO-08�96. ���ioZ�zʟ �:S.~ � o } []ZC�a��], %`` �8��>AM��tes&�z @ T600�c3T'' %x��<m.\)y\ A52D I32c1p%CITATION = NUIMA,A527,329;%%�� aqum�$P.~Cennini �:$\& s A332<5�j6~IV�;݃6�9"�v�554�U�,Birks} J.B.~ A"� �wA64, 87o+5b%?diplo�_~Laffrt[ i, D ���ETH Zur��2�.0, unp�=shed. A"�:a��it�:K�.ethz�: {t�8�:}.� Imel�~a�D.A.~, ��36�t� 87);�cap/*�Y ~Bak.U.~SowadK^W.F.~S��W%8� �r55�76); G�Gsa,8z"2�76�edep}�BetᖂE�G17IE12�preamp}��40�o0IW8M� m :h2��i"]�� ��.}e�Per-m*$Of A 3-Ton6�� Projez Cha<��34��94)'7. N�345,230e�%u+w�ler} B�8��r;V�!fӉX��ge} [a]�� it s �(� H�| s R"a $a certain � �s� ~ *] ains*!Y� e9�. &g %Author)" :�� m�<-EM�b] }> sideQP�<B \>p!c�m$ $\Ac\dg$,tfB`$\Ef, \Bf$ along $Y, Z$, K Ғ�l0rge $e$ fixed(X$K fre% moveC. �p ��;F_Bromt$ �{s� )tH into a velocity $v�-Y$Q  -$im�D T$, \do�w�6 $W_e=F_e " v$!� i;ŭ $� exer��n iR*L impulse $P\dg = F_m GD= W_e/c$. But only �zx , soh�!l\ $W=W_e$;%1$W =E!� . It fol�%�above: ,u �[�� % u@Anderson:1932} ,�xSc�7�_��23�32); �$�}�E���3�� %[Car�. k disc~�&�%ron� �� Davi�W:19�� �a}7Z�Ger��B�3+ 70�&2�0!fh_e"��a`fie��mns exh�Xi �&y. % [I de��t� -twoGcR� nterx , jus���&eK6glie %eoZffor&�_.u ot similar� \ref{��F %Rupp} Ponte 1D)U]A>xBr�" 3} ��P,?�Rendu�+1G�(507, 548, 6�7 23);����bf 11Z4�n$Th\'es.  do� at��!��QCiX-��$ 24);�al)�1925),6@ Ded�En�  ŭ Wave&�.}n#.��_udw�KBHNw:�a5�>�F!A8aU, �Q #(:� �A", 6h28); "&UHn�q6s"n it�iel3W} �33)A��"+nE[describB)U�eZe? ]41 D�bf�c�,1�.[��pp�q�(thi��ory�Ealc#� % $ e Ze�HuPaR4��V �_r\le=pengthA�Ia9ithin ynsZ 4=aes.]; ��)� �gEnrA>z:#=a? ,!0P�)L.� Miroshnicf�,�"FFi ency��tri��soa�,gamma ray ev�d ��ndi�ed %� SPE� 1980-K"$@LE�cqw88:3#69K �9,3 %(ut$$>100$MeV io�n�no upper�t given)I7b!.s� 0 � " , "Tv+!�0Truth About P�A �",as&HBACK PAGE, APS NEWS� 11, �x�(The Z�5 Eal� �p,�e[mh N�Maxwell!�e� � CE�� re-p- �8�0\[James�8rk�$%f/by"e��M 91 \�B$ Merzbach�TE�B"K�(nd� (F0 ,2�h$A �=e�#A67a�eDSci��12��1� 88� J8!i E. W. Mor?�"K.e�Em"�ADEarth7l�oife�e�"� J��[134�.3n;8n;��Aew:�Nnk�=� ,�xEz C�1�55x%�H(Millikan:19�� �F KA�., 3!34�F1�T���,�:1686�J   , If|i(4{\sc Philosophatul-s�u �ij� ia};7Hn�-itle: ? ��9am�7�� B����) i�7om ��!�world��FE�]��; ulZ� Lat��o��by� rew Mot�2172��� =|�<-etal!%Nichols,E�E'G.7m%,B��5307-3E� 901)���56-H� 91-1�C03); ^RM,u 292-29%�0�8J� Nord����{ � ��\"O,����AD�";!" � eJn"IH!� Studentlig0A99t53�3B� PlanckA�0!N �D,u F �Y96 � 0); �B:�4���&�Hea*�r�E   MasiuIg  P�726�5He0]S�5�e�n2i4\" I��!O. X*7*361, %"�.i�0� Eigenva�mPro�3 (�c4) �"� 26.a  W489NWNT��2T)";.�734K�#�k�pq}H"\�-��-JordanF� Mine";)�473n81} 10%�26)� NNn %.4bul} U. Baluca��M��L�`V. Togzkm� Rޢ37� I=@*� sok}� �kolj, \prl>9ay 0806�F20>@vossDNA}� F. VoT=2A��38A� �@l"�Oin=3`) phic� ed�bharnshaw&T(��e1Q0 p. 80�4�shlYs�7Shles�!G��~Zasla��)�J.~Kla��, :� � bf{3)V3>>�hi IlHerbutFl00726��uya} :�e�J�2��5 110Z5hodE3HodOUA� shetZ�3� 0��4(R) E��� iku}!J$M. IzraileGiH KrokhiM�i�. Ulloa,2jB5H%G 041102(R)mI m rem}��wev�us� d+t�B �a��zD$ up�e lt$L$ L>���s�t (or anti)M"e<�& �<f d�� ds $L$.d~s (��Ǫs+Hm 8y*$N�Ln:q NG2�$D(L)$\L:letel�f�nt� !=!-Bl1Kb Ref.~Ե��,�s2G ref} 2�"�"addi�� tail"5co�� fp� i%Ga���)����@spond�l$ known fac�"ae , l-�$is always \0�< reg�of1� a�2�bib��Old Test��>�K�J�Ve\^v BO=,>8www.writersbbs.]z�%eczY�bibr}�< Synod�L,iO 31/7/91, �^, //lib.ru/ h[^ianOLiya/nowyj\_zawet.txt2� pyg}B//e*1.org/d�jD/pygmalion/default�2@k�b�b<�e}rP'.� 7���� n�](�^%ݦ {V99b}A�,(VirovlyanskGCF����'blleft� chaoE�t%� ^4Xs250right\ Phys. �Rev. E 59, 1656--1668 (1999). \bibitem {V2001a}A.L. Virovlyanskii, L.Ya. Lyubavin, and S.A. Stromkov, \textquotedblleft The ray approach for analyzing the modal structure of the sound field in a range-dependent waveguide\textquotedblright\ Acoustical Physics 47, 517--523 (2001).>�4B�Dy, A.Yu. Kazarova,�: J�$Variations�Lmode amplitudes in a>� wave�� Ph �<50, 20--29 (20046� 2WsUs ^s._IJi�, 318a� 7-59I@3.�Q@!wrenzy�ERAE M.�2�%``Ther ters''�y(Speculative��0nzy, European� a JouE ,B 16, 729-73�02�8new york times}AG4Brody, Push up�� wew� roll back yearsY2The"j  T T��8bf{F} 7 (June 4�`2 {6 degre�D.Jn ts>sl{Six D!}�: o 4W.W. Norton \&�Dany (February 2003.v Linked} A�B��\`{a}si�sl#(Pa�8us, Cambridge, g 2F tippA�px,} M.GladwellQ!2'� : how little things can make a big< $erence} (B!sBay��s=AN� v��{Madey!�M!t(, Nuovo Ci� o��p. Ital. Fis. {\bf 50B}, 64 (1uSBrau} C.aj , {\emA�le-Electron Lasers} (Academic.�9A�Q� zki}G.~ �O 0ully, C.~Keit��q.~��~�� �70}, 143� a�]Saban}B.~ , .iRQ75}, 460s� P4Nikonov1}D.E.~ a�~Sc k2` M�, Opt.~Commun �123}, 3 96).Bj2:j2Q��-E%�54!�78 R\3:\Yu.V.~Rc vtsev�SussmannNb7�44E&98.� E}Yu.~:S S.~T afil� lA.~I.~Artemyev, K.~T.~Kapale�U� M.~Y V� 9A 2148!…=X �1� $B. Matsko, �  �EE)P( 58}, 7846,a:� ukhadze} � Kuzel!BA�, {\it Plasmae1 >1.iion FtihParis� 95.V �r %Pleasdepare ae dica�the exfes9+| {PPT}{\sc A D Piliya, A Yu Popo� Hjo�sA�J. OlT a�JOHelgak1D(O. Christia:^o3)�A� �d� A%�Wahv G. DasBG 56, 1769 A�7 Ggi�}�L"�BC60, 383�72>roos}��O�yo�cc1~$Res. 32, 19,�kohn} A�,P. HohenbergE^W. Kohn,����$B 136, 864a�64m +7LE�ShaA�hy?A 140�\ 6��parr}A�Par�dRYa"$Density-FuY�of Atom�M� es (� Uni� 6�19 vjursic%9 S. J: "Cut� Tra}�DSS$ Structure� �"�� Methods",4Recent Develop+ � Appl�:�ModernfV , ed%]M.�$nario (Els r, A�rd!z1:� davidson2�HRA� , C�6<1A��Y� koch��Koc�d Maxa�HolthauevAG,ist's Guide �b1� cond"���V�szabov  S EvN��Ostlund,1K � ��:� rodu]� Advanced @ icN -�9( (McGraw-Hi��."6R schw��aSJŤ �,Nat�ad i. 37, 45�s51mO� Martgnd>IyV11�34 @2�hedin}� L. H 2�A139, 79�q65 zL. +%THS. Lundqvist, Solidi�2��196yY! loui�a)E� . Hy�seW G. L%.� � 55� 1"8�A�G T B 34, 539� �� �sham}!!�>�B�(387%82�m%�e>$L. Shirley%'R�)�.� B 47�40� ��}gosci�"�~ O. GVB!}kemKA��G%& 7A3a�70-� B. Pickup?.Pal@2��013��72�ohrn1}!�D. Puri��8Y. $\ddot{O}$hrF"��406 R2�simons5 S F�4, 45�g7�9��2��,A.��!a~� 68, 7%{72� cederbaum �chirmerp S. C�!IWale �A 212�S8!H�fre6M$ H�KF YDa Yeag|Adv�&� 4q]8>� 2I2� % "~ Ig 3a1R2�#; *� ~65&� ��� S�#n�,�{Gailar �� . Pl� J. 2�2 b1956�basis1 H. Duny , Jr.B69I007M ��� beckJ A� BF@�64�d�?�2�Lee� �AqR.a�)hM B�� 7d198AkP wei3.�:c$ Thes�*� of I oaydt Urbana-Champaign (UMI P�ca5�8m�I�L%� Y.-C H Surf�s4��1e �Ltruhlar} HONDO v99.6C Dupu�A�rquez5�*L��'�vkarplus%X, �a9. K ) : Wt - a comprehensve treatise, V��1,  @F. Franks (Plenum� New �!:m jordNK. Kim�KE+JE,�a�v$98, 10089�n9��900goddard} X. X1&W�G , IIIBSAQ8�!0�6Uiwata}�Kimura,ao$Katsumata,��Achiba� $Yamazaki, � S. I@, HandAXHe�' otoeVtra*�% Org .P Halsted,!W5V��9 koopma��K A�&(a!�1�36+ uccirati}�U ��"���> !1 849 �Z�f b�00} %�0label} % Text! b&ic �*0 notea>9 \"sub�* (I}l"~162If�re � �(, it shouldae last:B�3�% �.� *0bi:HERAb} { D[`Broemmelsiek, Nucl. Instrq� . A, 9o6. *gbi:LHCT�(. WottVjN53%�80) 296; E.~Albr�et al.},�*it{PerfoM*ce!�a clus\ of�ti-An�*PA�4-Multipliers � pped� lK&�!us�" a�"Xtotype RICH detector}, �\) um.\)\ A 48�110�2)>AMS!kB�pa�6%a�jB�"$c. Suppl.,�'G0) 15>J EUSOKA.~Peini-&,  CollaboaX) it{Observ�: from;%of ul� high e�y cosmic�$� �] exper�9�\ �\ �\ ) 125}, 212�a�61russi�0V. Alexandrov��UHECR�� Satelli�%8in TUS/KLYPVE E�s} Proce� g�&� 28thern% al C ��$ConH, 497%3>�OWL�\&,Wide-angle L� -col�gor�XWL) White Paper, Submit/2DEUS (NASA), Jan 31u2; �tt{�Howl.gsfc.nasa.gov/}>�NewPMT�E�Z( tube R8520�2�( Pa�$$PMT; Hamam�niBn��-A^�ron TC]�314-5, `mokanzo, Toyooka-village,ɔ -gun(zukI438-0193�(pan; \mbox{E���h��}B�MyPap�.Y@A�5L$s!A�light 5�"��)�E�.N p�Wm�Wy�.N9�r C6aX-LCS-�P s-JP�Y�kizawau �RIKEN, 2-1 Hirosawa, Wako, Saitama, 351!Q8-Q9 EvalA%o�^�).JO�)al AdapA�}2"a)le�͇un�(d>�:�FI��ambicort� B zzinghi,- Pace�(XUVLab, Dipp, o AsAuomia e�" it{A��posalE�a supp!� ng s"�A��E�aZ<of�2}, ��-!0-005, CERN �+O"A�9 R\&D"�(al a�#M�eSn�m�!�ary-Cell�Modul���Al e�� }, !�(/TC-03/13, >�6y ASIC!0A�usicoU�1BFirstCult�D VLSIQ-En.5IuDe7aC��6 A5� 10,�>G���.x Y���A(�������-specs�1sG��snvironE l�'if�� A�STS��ELV p� ads,� �%nSon�(A.p(bf{GEVS-SE,�� x$?�٨ASA GODDARD SPACE FLIGHT CENTER, Greenbelt,ylh20771:k,Precicontact�TDSMI ELECTRONICS S.A.,V*T du T\'el\'eph\'erique�`14 ISERABLES, SWITZERLANDAA %-�:XJ >3+�Ffj �37} \expandafter\ifx\csname natexlab\endc(\relax\def\ #1{#1}\fibGbibO font� ] JzM#�Pf�Q$�R cite~R.$�Rurl^�url#1"7 #1}r= urlprefix>O%8{URL I8providecommand{!\0info}[2]{#2} B!eprint []{S'*I-[{2�,{Khriploviche� Lamoraux}": 7)}].":9Aat(nfo{author}�5�{I.~B.}]1�.C}}A']# {and /jUS.~K.B:�}, \emph�G8title}{{CP} Vio�)onW out k angeness.��ctric ole MO+�|P cl-��"��(�z� r}{v+X7�5<$ddress}{Bek7},-C�)}{1997})*2>��&ins%�9!� ::/jR� E.~D>� ?}6�j�*}{+ \ At�ol.\  '�9)�tex��z$volume}{40%��pages}{�!�9r�(Romalis et~�� 1)6� #�"iffith!ZJacob-� Fort$}], :01a�f�M'I�U� l:1Vq W.~C>@G ��A J.~P>A �?��T�()�.�5,e�%Uq�\"e�^�86N�250:&v^)� 2001v� egan.�2>�!,_,a!�S�8��DeM�6%�*:0�?Q�V�BJ�=9s�V>�dV@ C.~J>� ���� D.}~�55!/�n��-bfF�88�Gm�071805/J� 2002r�Hudsor� "�u Tarbutt)�Hinds!� '��JJu >:�V� B.~EB���> M.~R>> �@5���A>R-��!�9�2� 2300�USu�v�%+.�5:�!a�ndylie�)�,Z�1 :05A����PJ,C �:&V;�z�<�<in>u �y 436th DAMOP Mee�}}V% APS6�" �Bay�`SB9 �=B�)�<2Q�CSJWMa%�@�L�kv :1ς�A;^�61N�0525079J0r�Sushk�/ FlamF#�38� :78�� OJF ?}:� �_- ��V�VJ �6�"WSov9 --JETPjV4ZV608.Q�` 1978rHGor!Iw�156B $� LabzZEyP Moskalyova� ( v:79�w V.~G>� @w:&Vg L.~N>A�BU�!��-VTAT-�:�NF�A^ 4!� 209R�v� Kozlm� wskya95a :95��M> ;��L>M�Z�JQ�\ Bj�2Z�193JJ �Er�Tit�"85{"� {a}}:/aMosyagi�&�vi Isaee( :05b�vAJ(>:(V� N.~S>���AI�E�U� �?�=T.FY -!8"��Progr.\mo�$*?J5}:�}K�}{ijJess; a53 "73506038}jA%�� 202b�E�r ����E0\ �3/Ij104Y�嘱U2Vq 2E!�jE�.4:!, i:A�q�, EM, Elia�&Kaldo 7:04�&�VV&��%3V?�e�eV!�.P%:�VE>K%KI 2��sv�U>M1�!�<���0\�Aj6��.M~ 030501(R)F�kr�IN.w>� "UdEO�Y~and.� 1:0��BZ ?��������2:9�V�D -�:�Q�eD^< V���ٻ409045n�Stutz%�C�Gll 4 �mR>$:� B��ZqBulCAme mSoc�?rM -�%�m|76�uRavain2>v #,�OL@and DeI anko %�kB>q =:%V�SJC Po�?U�� .*VSA>�.�2jV�$-j-9Z�013�Z(j�Ch��*� :� "$, Ho, Dalb�and Ozi� "�) B ;9oE�V[N�Ho�;Q!V.Fˑ��I>�- V�� 2� f�102:�m�872J�!�r�J.��16�%� Blom8< , {F\"uls�DX}, {Karlstr\"om}, Lindh�lmU80{Neogr\'ady},�= R�<SadlejQf }]{MOLCAS�� K>i�:'V3M�FU �DB%.�EG>�2O�CB[%��;P.-B�M1��B:�.��BJ>B�?�;B�Egu�AW�=AJ}I�?V BFa5Jn�Sum-ch�Hal+�4am package {``,E(molcas}''},'�D 4.1n�..1-qb4.pnpi.spb.ru/iYe}(�)IZK�%:/vNn�Dmitrie&T 199>/$, Khaita� ,_%\ Mitrushen�] Shtoff� ]I:92Z�&$ Y.~Y>�9�jXYJ��>MN>W�?��j�AJ.c��Ns )�?UK ~� NQ-�A��>  \r0167�E�$280R�z chiff�63aN :63�z L.~I>z >:�>��"n3Z 2194N�63r({M{\aa}rten -Pend�E}�92��> �s A.-M�.O fe%�r�'icT M"�F Propertie���T�O.� �T>.(B�Wil�%2G*T'.r:.�"6&B��Ev A`, pp.M�9�X56nW${Biero\'n} 5>�&&a=({Pyykk\"o},�Hdholm� ell andr k b n:01��B� <�)��Vo P>���@BSu ޒ>VB~1?��J�&.�"=9N���A�^z6� CM2r�v�&Fro�Wand Fole�5e� :5�LRJ- >��H.~B) �E�!XeK^Af) ^&133~MZq�5vś%<�+�+j��2}Avp��6@��7X .�M�35RQzN+1>.�>#$� �  U](��"�,V�Bm*.V;j�i���h^�n�33:t-�6�PU�i0�MrS/n�!�?� " eP1�et9�7������e[V��� n3�qb��f�n�n513JW�o{*DF� 8�� :89�� T.~HB� @�'*$%�Ւa_��9�0.�mc�FN� 8z�"�i53�03f� in�6�2 bookd)�N�H�:s� Co>hC�A>Bo-�� � E{%:F�3RJ�Bartlettf�2World(<t&8�Qh"� Singapore�:�19�2V� 125]in� )u.�4:> ".� LUu~  :04b�� f�!�v.�2B���ARe+5v�Sc*� �OɕA4�GBHiraoEA! 2jE+_F�Y>0 IshikawaO�oHGzdB}�M��, J128r�Buenk{end Kreb*�5 �� R� Z�� Bq ��-=re�C�mM$ ni!�j�j&9�*�g�g!N1SqndAleksey*\A#:g%� Lieb�NnA 5�](:04�rAJZ9ji�5lV H.-B�CZ�VUI���:恆j)0F��z�M` b�b^`%,�' �j�����2�A`�N�6�0r*!� .>�!6� UVB�-���6 �##�,2E%���u~"� ^�Ak^m8�L� 4N4-�59%�5�^A:�!=��  Ezh�. :96��+��+�+�� V.~F>F ء�F����:f�7Z�534J�#!zr�r&5�9:� "=�  '"�!�.� *� >�9�E)�E)�-�w�3V �� 2� �_ �i��^�07b�$v�Kunik�;QrX31�:71��BO:�� �<�655&% �*��12R67v Monkhorst%19:7�lCHJ�A:�U+Z�:6�.\ SympR^�1V�2R�27�BNk ]b�F : rcha�T�TC Ez�p. Cow�b, �f�kmve�vK�( of Non-Uni�M GaseMPerCl UB�` LondSS 1970*�'{roPkPbsenau�U.�I"�R0zh1�pa%:tem{doe�L�W�W BcS�eg�\andzc 36}, 985 b2Ew,{kevrekidis}EG�e,�e:A�Tishop1NS.�ii,.�[Xi 6lR 0466fd�S�kenx}DFz�L�WSeglJ�Eor. BimX�g 2�39X7dVsteinU�^ -�c ularoRgra�LDif�ti&u&�A�b=LPrince�nF ,�WJ�ny'J6eva�WL�dE �NFal.�l EduA�,iin2�Societ�pHnce, RhrUIs�J�RA�Nbvbae` A�1} Pier^(A.P.; Dahle>((.A.; Rabitz^�sM�%��[D}, 37, 4950. WarrnRW.S2<.V2ce,�iLQm2��52#w{2}�d piro[ ; Brks,�a*�]�"I?19 M08sg.�y,{3} Averbukha�Sh\.� �J,A47, 5086. A�>hke:I,pj;nQJ.�)5S�n101(11)�gl9�4}�^z�pJ%}Stroud�] C.R2�2�W 6�]497!�eIb>DC�nics�Ur:p�, 1, 31AP�A5} " ? .L.;`Un�R.M�! , K.R.; Y��$Y.; Mukama�!fJ. �)dab5�99, 656E�w6}�hl�_$B.; Yakovl�mXz;M,Jg 6� MessinaI-2�2�Xn,�[ �I�%WU�5��4, 33627} Dub9VQ�se#J^eDb�(5} 103, 8412� 8} Apkari�V.A. U$X fast���� AM lWss�&�#Sjus�dee�~��em؃em�e,The Lausanne2�Wed�rgui Bw1995; 6�WY�9}�sdea�C.!�Che,  6j:� 6�A#a�$0, C.C.; Zadoy!R.;i5�.� 6_uV�U106(20`w4a��<10} Zewail, A.H.�aza ��a2��nJortnA�a8� v ��p.&[=[2} Tann�o"v ; Ri�HSA�6�u 8aT83, 5016�3e�slq*AM;� pa��,P.; Tersigni�_;� ue=U"89���a202�14}5Jer!qN.F�^J/� RE�Mat�~� Du�Y Rugg&APA�(Romero-Roch8=�C����FlemibkG�&�%"�P�75#91}, 9�g8.� {15} �lbp , R.Mke�Bq7C�g288.�$16} Gruebe�na�2ZN9�V 98(2), 886�7} Xu�Schwen�Z N.; HeZd�Ch�Z)A>gu��t�73 (iB���92, 546�8}�s"14G.; MandelstamvfZ̈́q3� 60��4/Y.-;>LLeontowi�}�6N 1NfUZmmi6' .'45..+` 19} Fried�e�q�u S.6�Q; 4%��f6.�20} T�]nghui-lJ�l�K: 7H5�a21.)yUVm8A76, 47�`�H� iZ%�>U�7�_6d066�� chkurinov� (privateLVmun�V.+5{�<Cerrulo,%�Ba2�WaauQ.;� nk�jV.�Pk1Ds 19, 7372@4} CaoI�>\*�i�N?7}W�^2[5�H� t�T�� ross��X $ThalweiserE GerbG..� ��a�67, 3752�26}fs�SA� Leai�KD.E.; P�_�a�Wu� tL. �Q:fa115, 326.a W sa ; Ne�+ ; Wer%t H�!u21, 7:� 7} H�Og�qS.W��u�IJ.X!'oswami� ; ick Du*~ u� s�^J�8} Dirac�yg�� ip [of",Me�� q; Clared"�� 1946I9]I2:6*�A8107e�2�30��sA��9 Zs.Sowjetyl3a�(1, 88; ibidi���2, 6vbDBerry!���Mount!�EA�p.;gM�m77J3A �32} hW.H!�eukolsTG��; V��WA� Fl� �B.P. Na�  recip� �Rr# b arIf��}" "Nr,݀.;*$~J�1992� 33}��2 R.�q&�p into��*�zC, Moscow}\�^0e!�i � $TechnologyWjsh�42�34�i�Z .D.;<cka����l��r�-�� ���:m 35}�HHa�en suggerh4 that a noisy + 5may be !us7ed)u"� o�`� ala'Lequivalent bandwidth�� �X�� to A.R.. �3� $B.Ya.Zeldok� �zpetEE�0nov�as�'njuga�" wavexeR�)�: Nauka|85); C RaguI�O �p.K?Xby stimށed scatt�1�.X"}7!�ynYNRA�F3��"� M i�K�16n2>3��uevDe�c�S�y�� A425��.q�'LloydJ}6"|�] 273(4)��2� 40} Unruh�mGMv��6? 41, :]41>��� LGE��462 43n��z Zo����;�kb� H� Mabuc�bM.�� s[v I�e�$�gla d"ibu-bq�g ant �as��T8 ne�, $-ph/9611016�3] af�K�.OIws����(7��16~4} NoVM�S"�R2P&� P120� {45} Akul� w�itskii���pDykhne,��$M.; Rudave�AAin~��9c� ү"N .6h�by� ������2��Peph K� Nonϔ��e� c�B�i!�. Enginee��U�156. %Rz�(zz:=~�tem{he�\r�wH ,Ba��� ik 192u�s5-472.Ga}�pa(J g, ͱ/0b}.� vwe�r6�p(kn,ve}6d}�"33, 1-��qJO��*� @?s-150.�@wei4}�@ 51-1��lowdi�tP.-O. L\uo}$�݅�2�I ��, 2=�U�Vh�/r}}W���sakbaz, F. Voss��Hee���. BA�1, !�8652-86 5� frie%_Xi�~rA�� Halli��DMqC. Br�?y�!0Bu;v<��qH� B. HolmesJ �: dens����3, �>155-716Xyu1�uY Hayash�A!L�HK.-K. Li{ JHsu�/NF�� C.-I�[ K.-R u1S.-�}he�@Syn5�Mete� }\} 59-1!, 9�spiR6} Ch. S� PeyghDShB. KippeaAf%)�. N>, 7! 48-72� sheridan}!�K.�%TMIxp�oI%�W. Samu��F�.� y200y~2�1-�`�peq��P %�M. Ram�~QwEoMeske� RE1�ans�.w q�445-9454.Hoelkrug%�G�ochF H.-GA3ckUqZu}$M�O9%:p!�� 8596-8609}�yu2kA_!;.M0ATn,, U{ �\374-379.�deleuz�vS.Kwasnяki�Pa#ancoi�&D 3� er%RQu � w�%:p557-5y�u� p��p!�I� fAh�x 5168-51802�rakowE�LAkowl a�,ochmuch, Bio���19A��1095-1106Pwaugh}@W �A.�:J9,�z15-132~gaub0}�ClFYn-Schau�A�ief�( Tolksdorf,-E. Gaub6�)l7z997-20 y֖ iamsE�C.\%�R. WenE�I�uz��p.HEomfieldNq8J932-193APrlaw%"Law���n� rdG.�xD.E�pei�E��E. Di�EBuK286-32�udaggett)��  D ��c!�l�(2512-42�U�kx��Pac6 K ,� .7l28ib�q6521-6528UwolynePzJ�� Bryn��CP�yW #�.�1989, �r6902-696Bshakhn��I�p��Gut�U�i? [Z 87-1C��-1E7�@A. \u{S}ali, CurrQ in#� ruct=c5�#58-732m ill}�{ill�l!Y teinw %�5,o�561-602;(thirumalai}A@Tula�d�uo a, ��Ce 5mW�433-4:�mi��w� M. M 3 CeccariK��!#Di���Tz�QBx Marche �ell��Bio E!} 6, 3�� 61-3'!]� �% . Grimald ��P glie�zG.�(c� n2l9,q25-35�9�binnig1}DB �yFte,-]I� *���,P�930-93!�>\8 \H�hhLHM&^y198I �15-62:�hansma�!.ABH%nB. El+s,#7A�.�NBrack�tcef`42" 9-21a�� g2�� Drak!.cP&�eT� senhoI `xC6�u�.T|Al;x-P �&!S0�. C��H��6���O�586-158����Ti�Radma�R��. Till�\Fr�"�Oe2�1900-190%�\ moy13�T. Moy��-L. FloǚH%rɣ�woids �}aҠ 1994��343-348!.[�u.PViIi.[�4�c� 15-4Z= moy3��>R�'57-25)d� beeb+ Y.-S7�,q�D. Huef�G� N,aDSt����M�rG T�BM T�LangmuirA% !*\ �373-138�:�2a Ha"Y W��)�B_An�C( Acta���c3: 365-3�.N macd�td}ADI� D!�!�Pozhar& ��y� � ��9n 981 � rief�W�M�� F. Omrh�pJ. Fernu`%N�ys1109-11>".pfAi(Carrion-Vaz;�A �Oberh� r�B. Fow�PE�Marszal�|Sc�|���tlar�,B��"J3USA-���3694-36�=+ schulten1, Lu,�Isralewe�A./m2�VS6(v : K.6I 1998� 662-671�u�d| �y���H. Kwok,�$.r�z� f�!<� �1565-15:5�2� A=�B�HeRErick�B����s3Q 181-18���l }F��n�E RaaeEM. Alqd) aras��Jɕ��r� FEBS�& 4E�24-12��u-t3ej5 �'arlpH5 P� lhai%�z{"� J.}: �� 3-54a�|bl� 1}a�RJ ingr 882-8:� X2�X 94-9� ���;Grandbi�M��ya�"9 H.NX ZC�W8F727-173� s eriktJwJarvetFDamM� Daniel&� JoDE�L�+a7E G?A� Gr$\Ȉa}$slu'�U1�y�5�"37! !���X�u�uo�'Wx&Dw u{H8J. Bac� I�1.3929-3� �wan �{o$ CuibFeɋ[H diomaNMRee 2, 385-3s&.�b 2} QY jH. �aY. ta�} jlemi 3, 2$51015-510263mp�5RA�T�D.K&gen��.epstorff�kBukGM�]MC%��-[ 6|�514"=K dyer� M. V�K. My��/O�Rg DE�>S� 3, 3582-3� yreg�N�0x,At)$.��8�EPBdap1��A�hhz�B=1, � 387-39; DsR�}� Livna"B):M.�ch�DJ���� j%3,f�5076-50�xb5nes� L. (od�* Malcop�� B3%�MAI)�- �1, 698-7^�!�m2yP"� �m�  42-n .��&k J."��B� J�M�BA�I06�047-985e�eebe3}!�D� Han n#� jJr."� !%��_291-1�-.�Z��enzI G%�MoyaL�O�H� sI���eb "� /%�!�O$ 2855-286��aA Z.�\=���8C.JZhu�Q. ZhoV X L�'L&���,4A� 401-1 mtav�� rubm��u}$wB�y~ P�&v� *q l 7 7-9 Um� e�Izrai�-SpepaniǨI� alse��Y. Oonod B�7]�,y 8I:>�11O�1$K. RitchiefK4�52N I� I Annu�v�2SC 105>, bladl�H� e�fodI��"n�۩�19�B3�1-4S5`I�D��t@ �nECZ(`�RA&!�2102-2102S<Fcha�.PK�S�uA�6`\�2798-28:�Џma F߭JA�GqЏK!: 19��2383-232+9chr��QCIGeh� dJ 8�^ �9: 5\k��mur�D� hira�#BA�O�=iro K�higureE�Washi^(:$��3011-3T {YD�Her�#� �CJ�  6794-68s :N2}�^�drasekha��kSI)ʉ255910-591�oFWu>Y�roya,͍�� era��.j6u 31-5z*Jn3; Mostafav� �G.v�:Px�@�] 3123-3127� F�4^t* e�M �Y..R�K8� 2-�kqj0� B�19�āZ839-842� brodf~�c�"A��� -148*bl�F�o��� s. f�$ ?<�] 95-335?kirkwoode*�: ,-�19!z!3|.kun%OK E� Math �. 1�"d063-20`U�h� ��J� Ŷ)��� 1�+257-122Dcoh� H: � Frish�>J� D 27-9��nak��ji�N2 �B� 1-6� chl�.@�F@��49-1351=�1�E%R893-189Y� vald=�o2=VB��64^462-4;(Em �ot�D!MFH��$7, 4219-42P5Xcol���!�C 1 � ^2 196-20IO wahl�C� hl,A�N٠197"!�769-1772� g�ܠ19a;6�83�4�frauenfe~�%�F�Parak,�D. You�.p.� | ��A�451-47�=��yschreibNM8#rvesta�A Vojta% } @B 52, R3820-3823 \-X�bhsiehEB�siLY�!�C� Ha K[o�3 unoz�k��ETamargo�Jap)�*S$P�.1��ab� 59-462�hannewa�@ ��toj׻��PE�Bob睅�%:�%��� 02���!N(>`=f�(1ȕU�,J-C-IEEE} ``x.�on�-+�.smclO� rad� _���wi�� �io.�:beam m��''�\ T*qa^ Z( F.\ W.\ Cu���\ ��)538E`6�*�-Mez!de-PRL85�~,ź|�her�@G.~��0er, ``One-ato�%u~��~� ~15`255ʡ85)|trap-~,-OL88�,\ Filipowicz!�\ J>�k�BP.��ystre, �D�3\�-\ Am.\ �B3,806A�T86); ``Very-low-temper�Pe behavior of a micro5l.k Gpmp��H!tal% �� ~1~107�e�Y/RE-PRA90A2Sub-Poi; ian !QicӶt{R�Ta 6�f�)�"�p) 42�9650s��/� �!�96-h-jump��\� �6] ��PH�Rweif=er-prl��MD� I�!DVarcoe�6\*rle�"  �Vy� 7���(.WvU-n%� 00}BJqS.\ Batt�a�.o ``Pr^���P� ��n3 ber ��� a�Rq� F8%a� N{� ) 4� 743 2�0).�An%�4AMA�la�: ai�er� oneE#b.an�- resonato�#Ka "QuChilds)dR.\�Ear^��\% F�%E7Q=-�e�9337SE:�3 an-t�",s} Kyungwon `��:0� 2�Ph��~T[�k,ssachusetts ΐituQ4 *E4A 694An-OL97b!VTrave3"- 3ak -cav��8���in!� ��l��5�!�1a!MDa^QF2e�5�96�Fbensone64}OA��| aithX!�.� ``W Jumps��A�ED��I�: Dyn�� B�� Closeo4P�3&� ��s''V r 35�^942�heinze��#a�R J.~H ��Q��M.~S.~I�E��dinh��,d visible sp�"�5by%̩+ confoca]O�@.��;132��7.=:�b:��.�Vacuum� ve Lf���ft-S�-EmisC6 Line6�xn A�Hin an���7Rq�N��6� 6�rai9~9�~G.~R��4Thomps;1A�J.\ Br�9!��5Ki64!�An6 Carm�``N�l-4� S7�܄0�Fag�G$� Two-�<�)�� Ce�a`BG6�4)�2��L� ``�6 bist�H���j�U m�� ������g-�. � 67},J�12�8 gibbs-opt ��P~�_, "�B�:�3V���Л��ۛ"�(��N|IY�J2`  �-pr64} Lamb�.Y6yMy�3�)�%} \ Rev.\ 1**A14]�196a�"� $lim-vcsel}�L� LimIAA��u�� !G#�W.\ Yub �EY_Rm!�CMzqg-Has� �Self-Pul޾ng, )0le VCSEL) ��laIntra-�-Well��ur# Abs�!'' X����(accep�8A��V��.- degi[ o-pra70}V�_eG � ���Sc� �M�h��A}v<117E�:�K 5-!�-LP�it��%�ic&K��a�;~ 4, !SW.~<di�[Wes5�ål;%���A<;�9�&� � 86aaY;� scop'���,r� ,Q  M� �uN9K3+ 3077� ���Dicke54}����A!Co�D�)i���""� &HY�v\g-WM52�kolobov!�97}''�(ec��effect���i% � !!�I.\ K @EaHaW*i_ |A �0��:Elk!y9%y&�=stu.��mes���M.~Elk��M`��� 43� 96.�DAru�} 5!�Fy&��$�reshold�.' pum"ТQ  cl �%i/ .~D' b8)~Sterpi�~Zucchet"IO �mw A9, 2�guevara-� L.\ de G ����ma:� aH -�%�EÉH�$ic polariz��{ & �sim�?M��man* "� ngI��+sceԳ!mit�� planiof milA� =�fewe; mron'�6!N "E�,�� huei%  �� *8B�):�M�9r�21!�Wave-�R�roach� D� p��!�1�� ��a�DaliblK�Cas� !�M$\8� o}$l�)2�.� 68(5)}, 5Ͼ62 &e �3��=�6l�cas d open@�A�W~P:r.�v� 2273%O""� �A�R�of ��Im|S�1in�%�"� �!)AC *y6,E� 52}, 16��rOA��K� �2! Measur�@M����%�&eI�ferom::� ����& )B n R��lezAF�1�F3�2.fA��`� ^-down tEiqu[awa2 mJ�-s�ѷcitie%�)`�_�\0 � aر�qJ�2�H0�6z�andre-AO�L\'{e}�: �Me, App߁)+�� 3��502:�)& 7a} R� induce�mirror a� p��:>% coe���ta=$ sub-ppm l�A-< -� So�d�F� Ye@2-O�!�,%Ob�����U�8dol���G� m{!�a�k cha�e"�a� uper��)s��uV�:� m�xH�� ��y�[ Z� .� :�6��` � 9�6ll hapY�} a��D�b!2���� `,1�5�OttC, !�)�%R2�62a�29f��`2� w=��-e!��i&�"�e�,James Joseph �t)�f�rx6���%z�).�� of n%�a�"�*a����;Mb!{�f�)��D��H�8j �132~922^SciAm��aN=2�vUh)�JA��n�8-�� JulyP*$� %%% keepa!i*order:*d   M*U8� trum!AO:C H�"2� 4� 599 �D1). % Abdul's 1�QM�$Exact calc� � ڤ��aV^for^� ���]%A�"� 6� ��� 7804%� � �2�LuE{3!�SubnarrH�� , ho�H��E":� .aNϯ 52�2���912��%1J3>�A �J�:d ��,�U{LuU"� ��4� 134�3!�(% ref ``4''=4�� [ %CF�&� 1.U�/-f��'� !C&{�Hal�1"]�t;�U!�Aparw�ΡL�Ng^*A Y��� .�6�1a�80e %�U�5=V�6E϶(I. Eigenval, ��achA��VRE\�.G\>�2�6���{\bf �1N�6�S$-v��M66Knd}�a9���m�iev!�dŶ��McGow��2�=v 23H�1N�9w7� Kuma�FdInt��g�y corre�ponBthe�:��t��antibun�Wg���erb�E^run5&ar| �)gMuN�5a�6 ��8�Br�FEIYSp�(alu���.�: �ic-V!a� ��( �6. qn�H.-a& z�-�Englerk�q:"�J� !36m+��9�-�������!lA& 1%mQSM�U�"9�d3Q�� �10�&�'abo �e��+��*s��btu"(�*F.J"ls�xJ.~Milb�I :���4),APpter 7%�"\qs!�rein. 2.{11 "^ @milonni-chaos}P W%Z, M-L�h, J R A.@ halt�C.a�]-MJa.A�a!p>}q Le��NotO!�ics -3�\ 6�X�!$�� b 2S�( 2( ��bB�.Q6B�S =�.�M�EY�6�#: �mof"� cln;!~ �8��..>V 9}aL6��6�1.�Herzo)<�6��i�de-ex�d&Z .�*#�ing�U�ju9?q8 ��78�:�.�C��e�y.�!|-Bz �zE���2 � D.\ aL�\��PXesVi�R92&�!]% 5 %uB� E$0� ��$%6��!H�.V�!!650 %���f�.y.�YMacN���A�a�%���.�in�� � !�6�� B:�N� 236�<�.�% %ZO*��2iI���b&,pm4 -Kal�'f|I � 6� 2Q�:.two�'-&�'} E� ,���Se�6� BFa2�+U"N'15Y� % be2� %e d��u�)2e�I�.>casagreB-pla9c^.C�L���? \ Ulzega "e-T*� Ri�^T I���o0e%@"��veZ''E]ics%�>A 2m� 9) 133-14��u��oc98}6��$Garavaglia� Tra�A���y� uF by a�*��. !��!�u�^sq8��$98) 395-40. �pr!�6�AF�W.� �ACA����b9����ѵ���.a�jR��w A 6�m��=�G.Gbenassi9T�\? i�.O� �E� � Co&-�N"�U�%i� MeslMl"d pS2\,�,. 9(6):879-8�/�M2�b=ni; x B F��Mo�i# �U!�$ p! ve, �14rently driven �/ =x�i!r*�54, 898+6�b� }�,:� \�dEN� ��� -�^ B�* N�*� .4w�!a�4}j1)��C �!�6��0un�#10:j5%�� *t B�Dtt-�-%D @R:!o`�Films12�,2�8�̙n�n}�!�ResearchQ#-I�2c., p�b 2�\.�[R-WeissYy�=-VMb�)*w, \�^��s &�F�"�S &p.�%%MV�"%�"!m:�"���.��.��.��.NYf�.=_2�A��!2�UIdo5�mQYq�ot�"A*�es��o��D1eC* %N.*} �[R�X 65%�� .�DerNni 2} {�#De4Jti�3Ca�oEBatalo��%Verzeg�1*��h>`� 422Ʉ".�_F 6��/�/H��ndR���nonj6l� *�a �  nu/,to"edef�oB��{ j\%+@ir!/"�^.A7Q�u) 171�1%��� �-PL V�det�%o�3b ��v^/en&�.��32� �"�� {6 �$VyatchaninN3\&�_�W��K�"� �,(ba R{/cookbo�``B�di�e �)� ##���Wi�7�;%!�F9�Sci?4n�"� 6���)n�X�e-"�v, ��@2G�!"�T.~!� g, %!W.&�#�/~�~.�*0=��m�/��.X Frequency�bilZ%2Rr-�R.~�$ DrevB et.~a�,E"fA�~B�� 3b59�,3)�( Dye- �r���r > .~Hol� wNu �e�+~Y�ka�$ witz-rsi5e�A�=��s� Z"�`, Beam. PartL[Ze�.! A.~Ka%`J.~Grh]�*%�AA~E@.}~ J2� 50.�c�Ysky��*/a2�w)6ber��a �G-�~Ki� )�Sli���E�J�t'��;O -pf6Vel�!yX$t1c�L5^ �s ��Nozzle-� s''.D ~B.~-�oi�JFe4�IqF��s 8, 7#66� th@-ol89� Magn)�l�mpensf6 s�? �/"�� o�e�1 K� Stoku'C!! hnur>~GardSM.~MarZ-��~Shaw�'Gofortv�'l_grL!JAK� �)=`siegman-e�s}AyS ����,.u(�cet��V� "%an-apl.2u'� ŀŤI�!`�T"lv4f�Ssi0(* (Ti:sapphire�� u�_5mK�U'Lamb-dip�$ c 9#%���� 62�6�aljala&O"aziz A ��6.% S��-O� 2J-ro%�a�6�5 ��  (�G2�$yariv-qe}A\riv&�*�/, J4�2�a��" s, N��=5.0 nguyx4aA,\�Nt\+he�W6Bud#XZolotor��-p��\�3, 0134�4.C.v kroo�4 a85}����]K,Z ,``Rabi Oscil)�Yec�um�E> metaAUle neone�� a cw dyeIU��:�31�nI6 2�,��}�COA-T�t udji Dupont�s, � Gryn#�-��PLV�m!2!�Nd=2 b,�9:y� hesA�� F[K slot}btai�>��AQbchabe55%� A�>�~58n18�dcasAgunZ�) Y$G. GunaratT6n�N. Kadan�uY�.g5CTXlG�KZalesfa�G��\!u ��.Jo,� 20� v 8���wuAkad��Z _:�:�p6?a� �Y)p q6p21m5� ssolAgol�X�Dlomէ P [ll�`E�V\ �J�02takAseg^ Taka��b�Segi�J�?G��!�.�f�$76}, 1465 ��(1996). \bibitem{embAklu} P. Embrechts, C. Kl\H{u}ppelberg, and T. Milkoch, ``Modelling Extreme Events," (Springer, Berlin, 2003). ~mand} B.�Mandelbrot, J. Bus., {\bf 36}, 394 (196BA(Asta} R. N.Dtegna �PH. E. Stanley, NatureS7T46 !5); : 83}, 587!63friApeit Friedrich�Peinke)*e invari� #B#� $eedings ofA�T CNRS workshop on scA�D, Eds�� Dubr��,aHGraťaD.O SB� 1997.,gill}7,T. Gillespie�Markov �$sses; an i��� fore�e Scienasv  19922�aleAbasE�PL. Alejandro-Qui\~non��K  BassŻ�� ield�Q5�B�8M. Nicol, I. Ti�� yev,�*T\"{o}rk��>o ��q� of Fluctu�s!�SE Price�Univers�#$of Houstona/!{t!ktend{thebibliography}�\beginB {10}�:(And95} D.~A_ (man. \newblA�Electros��c p? rtieEV membA|s: {T}he {P}oisson-{B}oltzmann Aory.W0In R.~Lipowsk��.~Sack3, editoa;��Handbook!BiologM�+ic��Lvolume~1, chapter~12�QLs 603--642. ElsevierIL0ce, Washigton!� DC.,A?5!V tAttWeiPat92} P.~Attard, D.~Wei1�N. Pate2�On�$ existence�exact �n�k%�theory"e%v � doub�P ayer.D%J� em�u@.}, 96:3767--3771�2.�4Blu77} L.~Blum.O�of~ fieda�erfaces.,{!� �4}, 81:136--147y72(BluLebHen80a](L. Lebovitz)L(D.~Henderso2�A96��!' derivativ%[pot�$alaIr�"m�  �an�c�^ �<}, 72:4249--4250�802]ocRedGam� } J.ML ckri��.KA& Redd� DM.~Gamboa-{A}ldecoBdModernq�\chemistry: {F}undamentale�m�da.H4Plenum Publish�qCorpor�q0, New York, 2evi� �6�(dHenPla2004�, Bodae5�8, P.~Plaschenko)� W.R. Fawc� �W� e {C}arlo�Yden��fun al!�a stud�:/ depA$A. KornyshNn M.~Urbakh.tD�-)ocapacitaE�Dn a rough metal su��.=%m��Rev {E}�,3:6192--6199�96.�\FelParVor86a} V.J. FeldmA�M.B��rtenski�M��Vorobjev.~DF�approach�a�-solid1�A=Y; {E}I-ne�xi�Heffect, equilibrium C%�*�!\bi%BE�5�%ble2%3INochim\taaa$31:291--29��8^6b�6S)� �� reen��_@ :^s to -OM�6I.��Prog.n.! �23:3--15E�6� GonJimMes�E��,nzalez-{T}ov� F.~Jimen A}ngeles,� Messi;!�$M.~Lozada-� ssou.� A new cor��)���helmhm LM�& �� -@E �T 4120:9782--9792F�(HenBluSmi79��i � Smit2�A&��a hype�d��ini'xi&')� ic 2���a8(rged planary@.\%�C&@ }!�$63:381--38�x9.TKimParSol89} Z.~B. Kim��J L� �vjeva.| .�2�in� 0tacts betweenIΡ�d �" -E�FT� �M}elts (in {R}ussian)}, 2(1):102--109��8>�KorPar ��AR�2�J�at-.>� 1a)53��DE�Int. r9iq � 1:15� 8@: 98b}NBRM<��W  u�ˁ�stres] A} non-lo��el�� treat B�JH ��09:10361��3 8.�ParFe�:�%}.� .n��n%&_� ���� A�a���� soluE-u�.m%�^�84:57--6� 82�PaE�3B��PV�A�admissi�sig"� differo�vy,6��  ��N�E�5�99:29� 3002e�2d ��F�n�U� ̡B: {N}onEzM��xMol�8:1��200: 2?���NrZ�Mqq6'inMkC ��>2`8In A.~G. VolkovxILiqui.Z�capb"�%�!�rmaceu�� �*�95��E�� tant�ce Seri��3�s 51--82�!rcel DewInc2�: ParKha� N`Yu�Kharkat2� 9-inducO N�a�ղ -ion� l:@B�a]j� 2)i�3A�B�Kim��7B�, Z� � �2^�A� �6�:s"7 of aMU��� bo�ry�� L��-qKyJA with��x� plat6�I"ovmJ�$30:907--91)2 Ral76� O. Raleig2h!n-�Q� �i(A�V&��2In�KleitnJ.~Dupuyq9sm:m�de� c�^S�A�tate IA'a{ �9I 6. Reidel�. Co.,f dehtA� landsA72rRemChe84�DGme �VyChebotiJ�ic:sJ- silver F uc�B� �2c 29:138�3*2�Sch46} W.~Schmickl�^�*= strEr" >�fJN�2:3� 412fTor G� Torr6� N�N� i&|aQ�iSFLB��72��6� WeiT�t93a�G.~ ���G.~B�*�olvent)[�*,�i0: Eq�FA�"� � BF�$9:3990--39I��N� �f�D99} %\vspace{-15mm.�Li1999�*:"LHM. Cieplak, %DelineH 1!f ve basi� A��um)�a�tei�J��A ."3-"55J'6." �an�Fol�!A/two-dFsio(off-latticeR�� #E �5970 6�Hoang, } T. X. , �=" %Y&.�f � of sF$� u���Go-lik� %� r=8*� �11!= 6851�%6W&���:���6�SC(�_of�eA�2�~��$319�69'4Abe1981} H. Ab� N. Go!1Non�wac& E -5)�.��un1Q&!$ in %globu�� II.2=toB,lM(5 �olymers)m20 1':(Takadai<S.  %Go-!V� predic� 9�5qmF sm. �$F�( USm596�16u)v2d% Kolie } A.�&Ortizx�� J. Skolnic&%T�"2�:�� KIX domi of CBP %u�)�C�&�Ts driven by restraints�$ived %from�ple sI�e �n�s% �9)�3!��)982��� 2003�1  �T.� %,$aQ(ci�UTimh63 �t, 475 E�{ " #Berns�1997} F.�(,�F�etzle,�$�-$. Williams�)�,(eyer Jr., M�*B�$"!�RodgeL $O. Kennard[Shiman�*-�MA�sumi, %� P�V( Data Bank:@homputer-based archival fileE�macro"� %u�s.��M� v$- ��53�*7!�9!-� 2002�� e�:�� rang�co� �0^�A�kinetAGo�<s6K �J.6"юC)�1��123�Q2�5�Tsa�J.  � Taylor�/ChothiaIrM. GerE��� pack��!i�&I�: ^/ dard radi�y�%V^29e �6 VeitshansI~T. $ , D. Klim�!90D. Thirumalai�Qq 1V: a )skthway5�gy p capes %�erm��sm�-dew"taYp�r���D�\bf]/�*I85�sk��kE35/e}our�0��FinA Need*< a Haystack: Edu��N[�s ���,gu�A-JMEG  �A� !1��^� 2� J�eorE��4Y7�� 36�GnM�'.�A�aCA3cCamy����y[/}, Arch�"tS A5H74Q|�+36�& GnM2�B!��KiH%N��R! �:� �81 �d;529 MainiDictJ T.~Hh?f|Bq�errattQ P.~K!Yin" k �pa�/!Df�+9 du�iS*Od}ict(lium} aggre�A�hyD, 85� 1995�a0442�"huangM� C.~HQ�:.�S � y��! n $\.0bb{R}^n$}, QuW 2,5�BQ37+>6+Io�/s�@hc+ �E� , K.~S�;ng�C(R. Isseroff)��. Ost"D  o U �E,�� mo%��y taxiA%J!�t�ej�4���#32&kim � M.-Y�41`B'�a ��J%r Nt r� 1)j6M 59--6 :KnP>��E.-N"ark�Mix�+9x6M��(��}, �smrA ic50�U�%J2L(Kohyama92FE �T.~ }M� Size.��0-spec�$I�of R!nesTtre�)F�< al E�J gy, �*2-4206--212� �93�>��"> ŝ gap-�d � --Hfo�Nt��7ot�IE�� stpco2B-".�8�r�I131:�$oiNKooijma��B�yE?St � M.*-�Discre�# YDuOc&�5Efa�;rep&�K�F� ]z.I� � �!5)�O 9�02� KalY vMiM�Kraem��L.~V. $�^C)ble�*�Ez�describ�@Տ��a�%�-�a� N$al ResourcAMo�, 1�Q�1��26TK" K.~Kub��:angla��� Peri�As)u�E=2�a���"3 w>+.�`"9��Ic�n� 29e��n36�472� KnC-�Y.~Kw�0 C.-KI"A S7d-�accur�*��er�� � one-sex)��ys �fL��3�13@136�l-d1 �JwA��� if�!��^�)Wj 1E�8��510B���o L�;�behavio![��.2J1e�EKM8:�>�2 �� 3346.gLnT-vop�,(D.~TrigiantA�E�A finite./sZ � a stif1�ari�%�!he*>"13:�Mn�9m$.�Z��/., e05ہ�2�&� z� n upwia�.�&� �=�� tegr�)*i3� ��eg��bT"[H.�"���2��1�.� macc� �R�M6� A.��r ��.bJ�* .�3)V�525C6�rc� �P.~���$Asymptoticu A��M�@he�"t((renewal lawb�%3�904�02�MnKnK �G Medved�CTKap�ҡ�NN pell�*G)-59e��p�0frontQ�.3!�8 , 6�P*~60A�66� Murray3-2 �FT����P"LII:"M�!^�<a�R��P�*�II discipl ,L!�m Qd ger-Bthird~ed02, nagy"�$T.~Nagylak" �5iM� mig���sioaQi!�G� al Q�9M@:1in d  A.~H_ ngs�,20��NcGla�� Life�C�c%!"U-al Socie�7 Provk=�L R.I.=289,�55#H.x,PascualNLevie M80E�e !m�!�p őbenthu"Y  -kE�4(&t disturb;},!�j�JP � p.� --122=}E��M�6qE7ŌCpr)�/ �.�ICh. 0 /CRC�6u raup�W p O.~R ,!DMatsu/AaA Weij�F.~Siege�'.�� �=6�"; phenomena!t�\&R��r� Bact�j��w<� 6 6: &]-R�M�Q �NY  nspors J>X37Q72 ymG36: s�"�$J.6#�"M�RandomAY pers"N oret��s0Biometrika, 3 5Ѥ19�2*sulsky � D.~S  }&.�"� 2I �De�=�I}.��3}�e�u�+19 e�817--832@�)%� �9� � Age-}�e���D� %-��89��>�����.�9.�82~WnS&us �F.~D."D.e� R.~H�H hwarzhoff�� e��'E�i~\q$o�b%BAX?3MicroA%/��7&d1�H�tN�% �,f�% 99}\^]ind� -2ex*F.Abkevich9N , V��Gut.LM.,� khno,�%I.<4. Fre�'e6�,��%[i�a4- -M r��9,a�p%n ��0p-� a��lf2E�.(1�*~�)\�)T~\textbf{101}:6052-6062�,Babajide97}  (, A., HofacjX�N, Sippl�VJ tad�UP.F%7. Neut net�V�1%.�-.\�)� 2}:261-262@B�Blla98�st 4, U., Frauenkr.E H., /1WEras�E��P., N �W� 8. T&)ng�ew2�+algorith"�f)�.N3�-s5U 32}:!R6.��9>�(Vendruscolo!F , Ro�BH.E�99B&^$�+� �s:� u�(/)aA ove� �}i�SJ.~�q.\�kl=z 00}:49-64N�00��Knappa W.R*A�t�Fm�4 �@%optimizu1*&m8+21 .wc.\�jA;Acad.\� .\�45�097}:3977-3981R�1>��,>��1. How� guarKe ��O"�=� os�0A ��8�tetheQA&03JT44}:79-9RT�2Q`i PortFNR�2. Lac�Ws�Rveraga in nm�2ym��+.\��\�LtYE089}:208101/1- VPQ5�,3a. Connecti�0�E6p, 6�a5�al�"MS in���@�4\ E�i�?$56}:243-25Z�b>\�� 3b. �>q6*9Q�5�f�(7}:S103-S11RL04a>� Moya��Vigueraa�@ van Ham, R.C.H.Je4a. Geno_�.a�7c E�m�A�rm"K�� .-priO[b�dQ04�M 4b. i_cipal e�Jve�/�{�Mmat7�r hyd�Hobi�L!��6a� }s ins^�t�L�6 ,�FBirga�� DurbNR.�]dy ) Howe� L�Knnham�E.L.L. �/ � PFAM�rib���y $annual NAR�^{7( issue. Nuc�8e�.x8�y3-2:�er8i @ [8.!.6a�mposi�m`t|t)VgA.e��24}:1-16�or� -Bauer�2E� 1997��ar�;-�u�es� )3b[:4?�;�9~J��473}:2393-2403;*- 6���B��&n, H.S!*��M�šmu�&�6 : Mu"�5�], tz2�Z superfux*A�:��O!�Naz,,6}:10689-106� &<6Bryngel1 ( J.D., Woly�_P.G�DSpin-glY �8 . Un�^ta�9 hierP<Q -�yP� fir� i��l:J.���|�31y 89-302� �m  �Mirny�7! R�2>�+3er!�$amino acide� �M;ica~A�4� 0� .�Fares� G ���BH\24!B4. GroEL a�s?ten}A�bv(al endosymb1s. Tren �Ge =�24 13-46�Fau�*e83}  9L., Plis�VA� 83. 2�ar� N5#�8ch%@P;�p�g�neN-acetyl=X �P Eur��\.\�8� 18}:369-36�\Felsep?cB���1.  �{��� s �DNA��Xs: A maximum likelihood"�* O�� 68-36�3�5  , Wa6chu�#{:19� ginu�;�F�2:_Knh%�&�8s. �ece5"0280}:1451-1452. Forn�� 02}  A�S!�3,��EchavEA���ite�"fic!�m � lac�9&� %�D �1aI_ed� }�s"=s. � e�>� 1�� 2-352Y"�-��  aaLuthey-!qlten Z> ��O�<4 -�.��c\S ��0A�ory�9�18-49 < Govi�? ajanA'.e ,.m.RSYI/uM�Jm� X#F� ��,95}:5545-5542� Gromiha: A>_Oobatake, Kono��, Uedai� �Sara@Aa�Y R�9Y+��"in&r(G:�D�� u lty�vnga� compA�on"[bur1���E� .rotA|ng}�0 49-56SGu%� u, Xv$ewett-EmmeY)�Lia�H�8. Diros rEr essu0'J�1�P�� � :� 9�ŝ�� etica�4102-103}:383-36�WGueroiŢ Gueo�e� Ni�]�I S8*!�L�Ang1~1�-�t� -�h �lexes:��dmor�gan 10005*f�3���� & �i � A�>)F �*�1�Is�!q fast�"6��h$2}:1282-12� �Hal�^A\ ��Bru!|W������"2�-co��qXs: �!��<��$ residue fSri� n� 5}:910-912� Hartl�e , F.�H�i- MY=�m� �-*@�Rero�?m� cytosol: �cna1jtoE&� �  2��1852-1852� Henikoff�C �~J8 �+A*�ubstit%�:Q� l��+10915n_6Hobohm� JSal �F19Enl�$�res�h�etA���x~���5.3# 2-5229 Holm�YN ,:6. Mapp!́�lu�me5���2�595-6j}uynenk �[��2�, *W �06. Smoothness9 in rugged:�"@;���dap����K 97-4q� Jaya%he3 ( S, Hristov�, WhinvS�#8 E���s,�@�6=L mZBE{ln4 927-932� Kinjo04}  �g��shikaw�� 4. E��2*�7.�V reveal�&harp � A�A#�> ��. e:i!�MDs.�"c6� 2504-2502��HAD �HK.,!i"�HDQ8Fais g�� � *N�'TY� 6}:411-442Koshi�� �G��:� A�8� de/Q� al�� inclu�#�� hwogeneit� 6��#26;��  �M]$:D.xJ� 9. UA� n�-�'bm�Qed:� ��hyl� tic .8HIV-16typ�g� >Z � 73-1:\eyte82} , .DoolittOMR��<A_ ���display��O a~#cha�Peqa1�� ����Q1�105-163LevittcW ���56.�i4p6.��oeM`a"� ��rapid &, a3.A�ing�R2104}:542�Li�� � Ta�2�q Wing8i;S�c&0 �O!<force>�Eresult7 %�z3L*`&�.�J\R��765-76 8LioaXLi\`oI+ �N�2RmotH"\M A�E�y0 6fR.l8� 33-126�4Lobry%? , J.Rt7. Infl�{��Jic G+C!�t� 0'�e�?-Y � .� �59"� l 1��I 05}:309-36�0Manavalan78}  )1$PonnuswamyO�..�6&�- � B�.M/�$75}:673-672�M�!� Q�䒢 8?9�JsQ�a5ld qu#Y�"V` ~USA�! 4976-1��NeiNe/, Kum�k8�&�U�anY]��s. 3g�v.?Nss." Ohta�4�Q1�Z',very slightlJ;l�uK��rJ� �olymorph`TW PopB] 10}:254-26e Palliser0�d u �2Parry�^A/ 1. QuantiP v��m�o�i�S�y )e�meLgnize �l betaA5a���X 6�4 �2� � /,J�1&�Je3"ZG"�"9%~ �Y���V�8}:750-76��� �>,qy*K#*�"R3 �Rr2� :^ ua�^a fP6�r��21A 2�� �n�6�a]b�#s^��_gl�v(dz�C u�ar"/a81�1�R�VARosA 88} ��8��y2���o�X�M��s�O���|dly reLa by flank�DQ bonn�"$513-56p zE ��2J ,>f 6Q&� 4. From90� shapKb�"--l6ase-s� in Ro}1�>Y�u ~R$$��London B��,255}:279-284.�$Sueoka61} �m1�&qbobas��o6� � � 02b}R�Cr+X"�a��. Why do�p-Es adopt "��'eT *G , �as %0r don't? FEBS:&5�181-1�9��$ !�2..pre�8�{�R� . Im9�)AiD b&⃵�E�*�� 27}:991-96� Zhou�� Y�Q�f"ewaam9}�"� o"y&���!�&  54}:315-3�zN�,� f�,.�akauff�< K !uA.�:03) {\it Origidzf$Der:{Organi�m S"�ine�} (*� e@�τ)=�(ecoli} Huer�1A�SalgaK�?hieff )JC�+do-Vides� (� �N�$ ARq }/T26fy5�B (young} Lee I�inaldi���Rob2F., Odom� TP(r-Joseph, Z#erba, G Han�F� Harb�{� >Thomps�,C Si��I.)z et al.} (�F ���9M�799-8EyKaldan�0%5luzKJP. T 3) \PNAS)10�[8710-8712j h> s}��S� awhi�B� WuenO9�n .U 2��Plexity � 7}, 23-406� east6�, P� -5muelsBw TroeL'Cj�14796-2�! fr,�See-� .g.}k��i��/Cag�'�#�sf��TfJud�R.� KnZ A�Locksh!��Naray&,V., Sriniva�IA5P�Crt!�e�M%�0M>-L(403} 623-622�!�} Fox�J%,H%�C.-,1 OChaos N1��809-86�J$derrida} D ,-Weisbuche�H86) �MC�Equ�!�1297-136�5prl} Sa�� ZW�#RW�w�per�9A�098701}#,flyvbjerg} F ��A�Kjaa�N�j�8 i �. A-2! 1695-1718_i�2} }�iu \Phy)�D F18!�45-66C-c2BdPomeau,�s(1!b \ELm�},H49HFe�}-~�1W�68)H9%�J��P&���c2Its:c�4s,�n. w(3rd ed. (WiǏ�O) 5 50-53 %"� 0savageau} OosC%}S �����[)0-�-6D} %�[!�,143-161. .imY�} %b���!�Snepp�^K�*^c�4�3[�Dgatviks} %Gat-Viks��\&�mi� [3a%%kBi.e �19} Supp!J , 1108-11�mh���%g��T�J Mart�HMŧJ����eɴ`Q %Stough.Armouc��B�X H�� Coff�KE.,�a�aHeAuD6�Eב��I�(02}, 109-12S#��er} St  C�?Pham X.Q-rwiq�eMizogo] S� %Warr�Y��Hickey � Brin�� F.S=,Hufnagle W.OYowalik D! %La_/%��ZE 5�14��� nimwegen}$/N d�I�oeFB'1/9a� 79-4�P[(grimmond} G �Mi� a K., Yua|$!�vis-Hume D%�$ %Ken Yagi/To�w ga N�onoc 0Hayashizaki Y%�Oka 1! .al.)� Ge�ear��i��d350-13@LN� �f� G �4Leu�. ( < Leuth$\ddot{a}$�+r��T�/."O84} N �6 1884a� P lE��;M. ,� wiss�af�%�58}],71) 465. \\ WBJ. nj skil�$PC99, AdvN�752�9�@%��BBW�Ee�5% B � H. W���.a9��7 �97)� 559. opSaakiI� �m l0Chin-Kun Hu, ��o El69IN4) 0219�b L �HWB�J. Her w���sM �A<3Mq��e�1�315� uvWBGvh=QT.Geris� JRu92E98t 1017buF���avet.� Camb:��j93bhHRU-6SO�rd;9u�E.EI�e"�=*�<)���l�`5v6!� UJ-5�MK)k�Q=Rda�b3dDKnop/,> Jjs�+f20)g6) 35. �`K�� c�Kwara,w^ mun.{VI��1� 0) 2qsVHof T!Cofb�2%,(K. Sigmund,�>�K O of&'2�=a�C |Y} (!�ridge�.D|,8). � )R�8EDM} EncyclopD �Q!(@&�Bs,V�cIII, Mit� }, M\8SAu7). :pGm�"� RF.�Ben� !� Bi�2�n�93A"1992) 16���Wm�Whelan�hsj9Z��G�.R167i�4) 20 S �N�T'f�.5(Dobson:03} �r&3"�"U�&P. \Nat 426:\,884--890.�D X:02}  , e7�#P.E. Wr!Ij2u�Et�qbi1@u�] �t�1�. \JACSEp!X12�122Ha�[e� A�@ 9 MehMD�l��.ein�]%l3�le��}.��1�Cq�)aAxtinuum `"�%md:scS#(ed Coulomb "���Pro 5AB� -12�5�Ft-ra:�v �JwMo akisILA. Cafl��2�,alu){�3�, i�it%��" �A�9�NAT ro 4�" 24--67Hansman�# �*H�A;L���re� Globw�1�byF�pay$� RL 8A�068:!S�gE l3� ��� W. Wenzel� 3. R�S��-���}��W t�9�X& �91ah58102~5�Ir���Irb\"ack �B��&D�j[0and�JWn!U�T.�8E� $\alpha$-1$�,!�{"J&�! �!�BJ 85�46J46uW�&}2��2�%FMEpC!,&�2�thhE� heetuUbI|$!Ja A_1R16�$Sayle:�/ ��,�E�UMilner-���05. RasMol: bi&�t graph+tA�@all. \TBS 20:\,37A��'9�Neidigh:a� � W�]Fr�*�nNA�-se)!2. �nA5a 20-X1�{SB 9:\,[302D Lockhart:� ��!�P.S�Y�2�&t>l�rk�meal2�_�A؉�ic  ��.�ninu%�anUpv,Xx. \Sci 257:\,947--9512�� :93}��3. El�+(c�;!8of�r9'nd dipC4i�aP�� �-x���6!�198--2!�9�Kob_�,� S. En�wE�Onekata%k3.�7ue�'tu��n%^IgG"� &;ym� G!� PM/ V+j �pYanaih ��(. ESCOM, L��A]7�812/(Blanco:94} , FE+ G. R�m'�3�4.�*�r d�� t�i� x XivkKable q��in aquer�KMޡ 5W 5/9~y?:�qa�eFaeH�!�Fa�.nh3d" s"�Eth� loop! �case �&5� B11� �"� 7238�S>tZrtemme:�(K �~� Ram` rez-Alvar<�L6�*6�!A��+&�,�eP#]ed>U@ M�28!p253--26c&pV� L\'|V de la Paz�BLacroixZ�Y(.��aJ]-a�sm"�Q(6. C � 229--26+WFavrinI ��A ٚ!HS�-hantyѓOligoGl ,myloid \Aba\Q�s�th�%gen^%�p"bD�,�>��365`66�ITsai:# �*A� �,ze�9 p"den�i"� s:A�9:R0z%P29��)�:*DE<n:�i Br\"and\'� � !IbPooz�C�XI< du�j to�� &y}.F�  P"F�,"�N.H�|iz � ��H��Cha����Anti-c2yin.�2R&� ��fiKWh m�-�-body�#� E�a�CP 11( 1�q4216� yubartsev�A�PE�A�Prtsinovs�w,S.V. Shevkun�{ P.N. �$ntsov-Velye�vE2dLw%ru^Mo&[ycal� <A��*@: � exp16d �vA��9s 77 782!V�lari� �%)�G.,isi�Ted tem�Wng0>�M� m� EL 1���46�7� � y�� A�F.=�� |5�+udTaa�! :�a���fo"':"J ]`improBsa0 ng at�[ ��?Q'002`1036�& � 6 Y. Okamot�XNw2�a�NsN�. \7!Lj-:�%�>�� ZIF� 1(Youpd�^= ch�A4^:bi@�GaB� �ts �9or�N! pac5514l1�816�NR} Pr�7W?B.P. Fl�#j$S.�ukoYTI�W^VƭwgE2.��&cT Reci�* in C8Ar Sc�{�@�ing}. f�, .�Qiu, Qiui ��Aa&bit�Er|it�U �S� Hag� 0� Sze�fa�+ �*: Trp-cag"C E�� $ 4\,$\mu$sA�H2!f 1295Ǚ2952� Snow� /r. Z�vic �V��P�=�_2ɥ Trp �: "*SaB��ed��t�F�gy via M6ar^j.�454h45�"\SitK� ���"StrockbMq�A.�All-atom&/ *q97�-�[ �bl/�:r125�12fb4M Pite�3} $NjW. Swop)g3. 6MG�*d( : rep)+-exchA:� ``Q,'' mini) A a&100: 75v75a19a�P ��!lFI:��s*�b�u\,13280-D7:�Vil �:�9 aIR P�usg���Gi����, KA�Fa�6R� Call r, �H WoodruiR� Dyer�,6. Fast*��-+�: H��mel�%�"� �a �*� (. \Bioch 3E6�e6(69bTg(:Q6 ���W�9EatK!��:[t �7. Laser.� jumpR� $\�0leftharpoons$�� u��816ine ` pre��w`a ` 3 zipper'��P 9200--9212FVila:#. A��D.R�po�(��"'�rag�0�2] reas����� unusKO$\�e�il  affor��b�1��or > �1��I--!p1 u5 97E�075A�0u�Qia�� � �QE7 K &���2�H�� by &02 sh�(�of f�� "� TF* 92��276,CF�� H,%�A�2��3.� �3!���e*Z�of6��m�CcB6�<ralized �O� xim� E�e�XenԘ �U93� 396�[ Roccatano� H� Amad�7$A. Di Nola)�C�end�w�2N��641--56"�O�B&f&L2U� 2130�kk Y^�� ,� �D��Rokhsa��9� ~��AIa|re-�a>� f�>�AgI 906�062�*D�� !u$T. Lazarid� rplus��9>M-Q�I Q��8--90�=>A�a�1}J�R�1. Explo�pA�e�A.��9�6 in N�A�345�N59�v �  �r ���)�%�"� 1.B�-�2�tohic ބ u�?an� liB���� 162�K�%ll�� �,���a�AXE|]*rG�K@2&x -�5d �������Filpul�8Z\ysi� AN?e�M�5itlow�T.tA �5� Clor� A nov2 highb~ab��l���i%%o�?in-e" &u$streptococ�� �p�m2E��66�KimE'*�S.|*J. �3![ Qq�q4cA!n�+co9&u� CP׋2�826� Bursulaya�G�!�� C.L.@9oks3%E9Y.� `>�Y �Pn% Q'�)0� R]9�>�Co�o� kD��)�A\ �%A2��� t"� �^�r �:$anova: ins�$�PN�.}Qw �3� 362�� �A.�:��S�*+h���wo-��"�� e.a weak%�-�\ba6��"B"�m146B!!�:�=$! q�� Swe"� �=N:_te���?  p>̞�� RL 6A26��2:)l Coch�%1} ��e��kel"� M��$StarovasniI $ryptop Oe �b�Fmon�cU� �� ? 5555�NX's fX'� ��F��l_b�}!�V.u�kelP#%fO�Ptitsy��ei,I p]4ceUcours"E��@ }, $b&�� (!��.�8L�H M.A_F����=- A �.Fe�"� Pol;�(a)a� ���&� �9Ce�_-<�Ki 4b&?)},j�01970); (b) TV�Cr��.9��!�*rDP"2Y!BWC��x)\& Co..H�h; (c) P�%Privald �.-6�/)03)0_�1979)2d�00PRL}!,Kaya H5S�ta*�)�R;��.%�M5( 4823-4826 y,0.�JaV&91w�E. %�Ԙ Fers�[e� ry,-�k4042�j96���4�� � iz�H.�, ��oQEnzym5-�38f3*�YRd0d%�~�i-qs� uct.�y . G#+-x4`63ג2_3f_J� "�J �X; 9��� 2Y�Go83}� GNnnu\.v�Ja� eIJq� 18-�83.� Camacho93�|}%.Ğ %D. &�]�+c. Nat2��f j8 636�r96� Li04POLY}�1S. �Jb�.lݖFu Po�, a4�7573E�6��_�[, B�H�p�2oDill95� Sci}�k�S�mK. Yue���$Fiebig, D.� Ye��.� a�'Yd^H��c+; bf 4]=61�=52�!4)� 98FD��5JFH, � sM��&27�39�.yLi02JPC�PJ�=��&�� 6}, 8302%�22�& ��R�U"���)��+109754�98.��CP6�D.v3a=mu?mbf�<�62{=$Hilhorst75e�� %wa�,. Deutch, J� be�63}, 51� 1975.Z& 89} AfM.�7 _R�. Iġ���b 11�� 1989.a��0a���G��)v��54iy2�OnI8c97AR!z2͕ , Z.>�[B  P.�"�[��)�)�%04�?1�$1]��O97u�J�2Λ��M vittil(im A�260z97!3Rw fw 96L6�wolfe� L�lf}�i����eCel��nJ ogy}��dsw�� �!~elmw 2� msma�-F@-rci�6G.�lQ.gP� y)2� al � 8I�3�175.]~�[H�U�Ro�F�&Reh�0M. Audeh|$� arsh� Kel��C� Ad/�1�!Ehic Id �ty��D�x��}, Se7h�"')� ,)yg um o7E KfQ=vh96 (http://www.promega.com/�,ticidproc/usyy7 0726.html2�adessi�/A U Matto_ ��HG. Tu�ytM$��Me+? M!�%�E�washim~�HgCfC:  O  e6��%F�qa�x!�chip T  }�w� cheĖ�Id�oti�,MA� 2�ch[@itrY:hen!ndA�$J. Kricka,UZw�a+ . E�,X<dgeu , NYu�UNw����WatEtAl!+ } R.HsWas%��#�F�:J. �In ��"�22�H]S�mouseBoZ#"��P N�"�<20:520���2.�Rat20�) aS ome *%�(Consortium}.�j<BMS��S�4{N}orway rat y�. �int��ammaliL�c.b>�8:4�� 521,!�2EFli=&}YFlik�C#�far��$~Pede0~Clar�2 ~Dan�^,%�ardFW.~MilQ2 yxPhilips>�'n-Uڣ ~McMorrowcFrampE2B.~Alt�7(A.~FischaufO!���igg�5�N{�iv1�9�b�m�J����som�4oF4R�f %keMNgul_�y�-.!�%�r =in cluq"B{Hum] �h.= 0(4):3�38ILe|b� BofmF�7.~Boff5�McAul��~Ove�K�vLewI2 �zac E�� Rubi2/Ph�U���NdowaC�MeU��Nfind f"l�=�gid�h��UeB:$ca]299:13� 1394E�2n#Der9 E.~TI rmitzak�A.~ReyR@0, N.~Scamuffa�"~Uc�E.~Kirkn��C.~Ross� � {AntonarT.�>2`crim@��y��eer�&T�ge��q�2Te�9302>���035FTho9J.�� ouc RBlakes}6G.�zBo!rd�~M�U(Beckstrom-S��E E�� MarguliesO~B/h!&,!jC. SiepZP.~|���<cDoC� � aske� N.~F7n� M.~S hwar�HR JWemJW��tE�Karolch��T.cBru�I��evhHD1Cut�qS]L.~ElnitI*J2Q Ide�A.~_� rasa)Q.�-LnIV�߂duro,z�u=%)E. ):noyEw��i�{chAkipK.~Ayel�B.~Benj�*�~CariagI�P�ink%� S.~Y�%�+��^X.~Gu,�Gup`LP�g�i.Lo�%��8 �^!Ili�FPq�Larica2�egaspi4�imѤIM-C;�MasiellogD� qp!���!1cCloskey�Pea�J0S.~Stantripop�E��ong�@�w . Tr ��ysurge� J�Vog\~A �y��W��by8(AWWig�MM� You= LE�Z�%%}Osoegaw  ~Zhu0 ~Zhao�9�/E�~De�Fg!-C.�Lawren����.}� rhakrav�?E�Hau�� P.~G�81:���E��.{.�aȗ#P7{�des�b�Vt�#w$�xic��.[��*� 4:78�193FCha�4I�!���HA/D�gL J.~G��i�Grafhauayo~���. �!Q!B.~G\�� ttge���A�i<(�- ��*��.web�$oa�coV� tool�les% learf:�W.k"Z {SCL} loc2��%A� �B��$4:313--318%E2_ OBrEizMu@�zU%8O'Bri��E.~Eizir��!�Murph�75 O2�oos��%�f�p�^8��q292:22V 2266�2�Co�qG�2�˅ 0Brudno, {NISC2�S���Pr2�m}e�D=�a�atzx@A��dow.�Q.[�|maڣ% de �Xc}*� ����m/5�-).i%:�3:8!�820%2� BofNobRub� 2� M.~Nobre��!�Zg .��X9F8vertebr�+e��F�i�x?neX 5:456--46@2|Sid� Nj-�eQr. {A}sk ���s �B2 CellA�1��--1IE2. Ma6� H�.^Z�L ��S-eQ_.�6�*. r(s~õK"�  qIJ�B. 250736m�20Z�=�9� ̓V��vl0.� �+nt��S�sif.�HQ -"�e�tld} e�� �9go&�^"/ar��a-s:2B�119{,20� 2�Fel198Am�.�2L t���y{DNA}9r��VrLlVra���ach.Te�Jg a��7:368ϸ�82�LeheP}L LB2�QT�tnge�w Hy/pes2�"C�[�2nd|:��j.YapPac�=V� Yap%�&� .�:�of6�hotspo&�ro��W��4:5�=579��25McaPacJo��4� &��T M.~IN��Mabpl��y�e*3 annotL A���*hiddeA� {M}a��p�2%�B6�P�:1850�36��2� AbrSte197�bramowi��I.� teguFHa&6�&rHal�2 D�!zm�s&�76�%Br!wI N��aa��~�.{MAVID}:c trai� ance l& A8��p*8�FZ:�4�6���.�Ols 192=G�Vv����(�aghI&R�TXek2�$fastDNAml}a�� R"���4-1���Aof�?.��:�D*�v2t~��utD�RBi���0:�,4��92�FelChu��eF��E����urc�V.rAM�Y��A��%:v� amon�*��m of �.\�M&�� 3:�1]��!�N� �"f� 9} \ 9P,r\ifx\csname{kexlabV \k�x\def\na  #1{#1}\fibGbibO font>J7�M#�Pf�Q$�RciQzmr�.$�Rurl^�url#1{MLtt!O%8{URL I�9i�mmand{!\0info}[2]{#2} B!� []{S'*GL[{2�{Tu�-(}(1952)}]{t}�(nfo{author}5�{Aq },M1�O} �{joe�}{^osoph-1Fs�Bo�Roy���.c�erFB} %nbf��Sme}{237:zZ�}{3�M�y��{�.�> Cros�$ Hohez!'93!'ch�&M :&[}:�%aCbfuPJO�Zx�Z�MQ�BicsjM65:N-L851} FM93}),9�note}{�a 2}���teBeKB60and Meinhardt%d4!dD�ɸ>fA��:NY�b H.}~qU���_._6:N-_148V`4r�Giere,�!I7e�g197��:� Y�J:J:�� Kyb>Ntikj�12:?-:3�S!�E*q�72r8Wo�xEu69Auw 196�LA�fxL>-NZ(K ��p) |�b�ye�texV�a�y_ �R*69r� Eldar et~RY13)6!, R��gilo��8and Barkai}}]{eFt'�A>%`:#VaD>;��; B.~Z>S��!�uޖwN>�1 !PE'U�D&�al�f�!�.�-�635Fi%sn�%^.�2V� Dorf�"8as�Ash�f!% �9��@���R>c ��=B+ג;B�! �:�e�e`jY419:�M[3+,>,{n[H�dzadeh� �E>f6,, Wޭhau��eibler�Lh2X�~�B>,6p:�V^E>D�?2&y�VQS>Q�2��%��Z7���Ck$0��c�/�nF>� J��2��J�42V�0r������:�$, Zor�Ch?�VGurdonA�mcdo97�B`:V(N8 ��=CI�U� �?��~�J�|*�{1*tU�Cum+�&�)!�^�� ��671F�!�r�En��v5� 2000:� #A\X bed/a��Gonz\'��Gait\'a%�e XO��En )S5e u9 ^�:_ 2�C]!�!`v� M>WR�!I9�"f�X�.-�A N�i�"Fd>VH'�84:�H� Belenka �W�D %$Li%�han�} ef� C>H!�O5V�T�!:��!�%�af}B��1K6��MX!:�%6�5�*� n�31>�-�60J�%u).�tem{beleJT. #1��f, {I\�.11�0��4nhKersz�$t T ��8��k 1998��B^���� �� 19!�Y�-�a�By% nUPfeiffe2 >?$�) Alexandre L llej1DVincent�-pf@|zLB gA|�GB���?B�4Ija�%Y6���JT�:�5!75 u�>.nk:�-�32V��jrJZL�=2�>� ", ��!�-�b::e��� ~D> Y:�ViQ>�Ni!�%H��F��~M>�W�V�D��Zv78V�vwKr�.j!,�N tazi�Bo�Kba�(Jc�i��%�^�kg��I'f� K.}~\bibn�amefont{Kruse}}, \bibinfo{author}{\bibfna * P.}~#antazis�>T>>$Bollenbach�@F>@$J\"ulicher@� and}��M>THGonz\'alez-Gait\'an ]9pjournal}{Development} \textbf%2%C4volume}{131}},?(pages}{4843�(!Q1i}:�Z~A>QN�6x5\TrafficjX3NV98ZT2vTY� ~et al.}(!BbU�,_unpublished�Mj�_6�,note}{to be gT. % added reference)�J,Morimura et~� 1996�mori96��S>�Q:�VL>J Mave�Y>;Cheav6��w F.~M>�HoffmanS.Ul}�$al Biologyjz177N|136N}!�A}%f�Telemane�Co�a�0!�t  2000��AJs [��SJM �6�5J Celln90V�71N9�� �0Lauffenburger%OLinder%�a3!Tlauf93�ODJO2a}����2A�jjJ.~J.B:��- emph�K�title}{Receptors: models for binding, t�5k � 84�087), 166--169.�\Yer1}Yeramian, E., Genesl!?physic%90Zinovyev, A.Y���(Popova, T.GA (elf-Organiz!EA-Z4 for Automated�$ Identific��p, Open Syst. Inf. Dyn., {10} �a7321--333.�Carbone� �, KepA� F., .�, Ce�B!cS�tures, �s�a7Microo�sm�� 9 Spac�",d Lifestyle.Fh 22%i$4), 547--56�mystery}6N.� Y., �� *�8two straight li�_in}���e suqX, arXiv q-bio.GN/041201227clulastv�:�Four  c ��y typ���� u� al 7-clu��uc!n�143�� lete>�Veq�� s, { In S�ao� { 5I,5) 0025. On-!<: http://www.bio� .de/isb/� /05/1/.E!st�}A-c I� T]C A.M�$trajectori� f�e�~�. � ica A 353ED5��65--382mServer}C>_E�E ic wF fr)O y distrib� 4s, Web--site: =78ihes.fr/$\sim$z�/)& ers .<Lynn}�S�hGregory%*. S��B� ��(Synonymous �h)Vis sub!Y��sel�2 Bq�=ic ������vU 4272-4272EWan}W� X.�+Xu�(, Kleinhofs�N Zhou��, Quantiabve rel�04ship between sV���a��" 4 across unicela��qomA�BMC�� �á$4) 4(1):19.�Kn�}  R.�FreelqS%�(Landweber L�A simple��a�ed on&7 ;9{4explains trendEc)� and &}-�<:�withiK �I��{G� � ogy �:1*� 0010.1-- 3*� G�(am}Bharanid)� gaviA|� Uthanumw!� K., >, � C -� 1�n��� fmFm�^�in 115��f �chemical%"Bio� al R� CommA IY 31 84) 1097�-1103.�� 2007� 6�  B.�KMathema� of Phyl�s. SIAM| iew 49 (1i:� 3--32� FrapScat6} pat ciarrin�( Conspiracy!� l5���� 369E�(6), 699--712�[405}Minichini, G rM] I�s .��X�E� crys`��s,!�s�ms�20�191--2066RBM/0506A�]� Cangelosi%� , A�Goriely,� ompon�re�io��( principal � !"� aH� l: �"cLm�$array dataEoeP%[7} :2, doi:aT@186/1745-6150-2-2�NE)vE�JhM#�Pf�Q$�R.8^�.$�Rurl^Iurl#1{tt!O%8{URL I4providecommand"}[2]{#�>!m�[2][]{S'*�>Y Babu"=a3)2 $, LuscombeLAravind�rs�,e�Teicht}]{BLA+a�A & Z@B��h%~QN>?��>B� Ԓ=B�G-�]�{ %*FQ FbS>�=K, �p .}, 9S&�(urr Opin St � } E�R�4�%��283./�A� vJ�HerrgardnC$ vertAE(and PalssonA0HCPA/�+B|\)�~6B?C�1����B>��>�.�J� BiotechnorI5��-�70ʸPtashne 8 Pta9�P�V�BAHR�A {G}e�{S}wit�!V�LKss!3MAR���J�Buchler.�3>� #��� land HwaA�BGH�af=!B� V! ��U>;Ge�ދB~ ́/%��?�U�65y� 2r�0�5M�5 =֕A@ /J�Shen-Or2�2:�$, Milo!� Mangi!�Al�DSMM+0��Bn^Ն�R>���;Bz ���BC) ��Nat? en�$�$)�a-�64R�v�McAdam�Arkin�w7� MA97��HBt Q�� A>N ��‘��9�^J�81J; 1997�`%zJ ��� 1998:!, Ross� A�5 ]{ARM % `!�V�f�J>Q���f�, %:�.�5�G�ksn�49!�.?M�163J !v%�^�Gillespi�P7E�GD7��D>:IZ�J lm�$^�(8�(J�2340 61F�197I�^�Kh#mai�T#Kau93��B�I �šuA��"�{O}rigof d�)�cB�" �.C URGv�� hen�  }]� �VKCB�erK}� !�6� book �Art�dial {L}ife {IX} {W}orkshop�G {T}ual�bR*i�tFR*Mez� �BZec�a� MZ�J.!V�B VR��NB\�a�*� u��' Ej�66>@pa�+056126.R"�2r�Mertens=0!/zBFiBz�ut� !�EngA&^��w& �3J�,c'sfeR*0:t)�, Parisi�w YG}]{MPEBca׺?,�.G>h �adw�� r}i�"F N�SciO"j�29C*.=-�812҅e�=�>� -�@ Ricci-Tersengh)�6�RZ�� b�!�!uj�B�/:�a�2�~W��K�@JB#�j�505}} Jc�CL See also S.~Cocco Q/�-, Jy���&j{9l 047205 N�3})�  L~rrealeB��$d-mat� 44.�> SheaRAckers� 85�� SA85��B#OR}EVB� �.�9� *"KrE 9�m�211�]>� 1985r+Cosj#B+ , $) ct q!yy�'e �!1``�#hed�'', $\��#{\log{�4}}$, usually �ed�Rrep� , or� ilar m���� . I|$cas�ua/, exam we hav�-u�&Y�ann��d}�%g��9v}}$ (in�eG+r��? leq rO0). For K-GR1 �Poiu "�#ean(out-degree,� show ��+��!�a�!f-I;�'property��<$. %and a famili&funF,�#chE�� C/;aS< \frac{1}{4^{2^K�@(sum_{f \in cLF} } p(\vec{f}) % f x}) \^{\prime}}) = A \delta_{6 x}; '} + B \pnd �. TaE�!�Q� �/ ���5�[�@N}]^{2}} - \left[%$}\ra^]^2) /K�, ) �van�5���$.T limit $N\to\infty$ so%�� -a�#{#a�lex�5 trol regiU# an equal�0 hold&�"y�!�m I.e�*CL���5! �� 1987:H� :� Virasoro� ��a-` VlB� _���"� .� VLB��� B��� ��GS{G}lass+he7'!�{B}eyond�3��*LWorldx �) fic,i'apore.{,!�# f�Cases.>� !,, de~LorenzoAc��Ouzounl;]{CdL�� I> \��V>;�@2�&H V B �>"N�T'.,bior���� 48RY � f�van Nimwm#��vN�~E>C2LI�q�"� ��j 1�*6 �4�"Y�I�20 �b"��4� Kau� 2f�B�J},F�J %G4or~� 23� B �581�J����>�6�4f%#�.�xt{bttp01} A.~Bahr, J.~D. Thomps�4 J.-Ciery3�and O.~Poch. \newblock {BA}li{BASE} (�dn! rk {gn1><& $$): enhance�7repeats,�,(nsmembrane &Y'~cir]4 per�4s2�\emF�+�34}, 29:323--326�12|(bb! P! ldio S.~BrunakBcB.r�(}. �MIT�Ca�2 , MAJvvvonizzon z8G.~Della Vedora>`��of multi�1- al1w�' {SP}-scor is � ric.\%?T�1et� �er�c�$259:63--79J�jegsAR$razma, I.~� ssen EM+m>3!�$D.~Gilbert.��1es �au�1i�5sch R patk5�bio1FJ�@!/ �}&&*44}, 5:279--305,�&8�'{ctrv�N.~Cann)AToppo/*~RomuA8ž!�Valle.�S-ify9 �,d3 alphabetsh mean�8a A�ch%$bou� algorithmsubstits/ ma!�J�:�$, 18:1102-�+8%��)��g) clrsA� T.~H�0rm!�,C.~E. Leiser�,R.~L. Rivest � C.~S%.�EOIA du� !�AƮ7s9(ed�:206�Ldso78} M.~O. Dayhoff+,~M. Schwartz �(B.~C. Orcut6s�+��:ary chw+e,pr�6.�In :t�or, � Atla%�P < S11�3 �$u] u(me 5, suppl�\ 3, � 34�152�;�Biomeda��e��D3ndE�$, Washingt��DCA�72�d�b0R.~F. DoolittB�i]�uc:%ceA�'58ncestry?.��!, 214:14�;9�82�dms�?D]:,!�Morgen�3n'JAjoy2]�unumbecst*rde(!�ff�1ve�+�"2��b9 ied .�.�$, 11:43--4�6% dekm� R.~Durbin�$Edd�-~KroghI� G.~M $isoF1�&og!�Y/A::2j�[�e�>JwUK!i6�ejt�I..�2���,W.~R. Taylor.�%'Q�:b.(8John Wiley \& S�<Ch�F!�,� 2004.jgs!R�egeri�S.~Kurtz._Fy:{U}kk�.�\{M}c{C}r��({W}einer: a=6�v�0�<ar-ti�6 uffix tre�nsQ(iJ���icaA 9:33B853%i24g�DO.~Goto26 $8b ant im�*e�i accu�0.��~u������<iteratA�g+n Nas �{s�byeUE!- �ura�?L.b%��;M�=!�0a� 64:8V 838%62�99}RMf�:���.�0F�Adv�x!:"�2�A36:159_1��2�4gb��R��Gr`5A.SBrj02� Boot#9pp�n\rmali�.� d evalu����pairwi<�= � AJ^$Proceeding>�LIEEE}, 90:1834--1847F�ga9P usfieldB�U�s�5Strd, Tree@#�p�h2�hhZ)(S.~Henikoff%gJ.~G. .�A ? R�m>q � FJBN%�a�'em< ͕s�'O$89:10915--��2.�4hm91} X.~Huang�W��ll6.A �Q-e�IJ,�hs�;lo�5si�\� a . e|.�J��~$2:337--357E�2PiAT��Ioe%F.b�5c�Cxpe�@of.��i6\ In �JkFifth� A�@al�3f�yo"!A llig�4�=5�=N`�1573C6�2cjz�M�Fl Jim{\'{e}}nez-Monta{\~{n}}o%�k� &7gI A(:k j� W.~Jus2 6 ��le�i *k.jE��H6e��L8:6a623��2�kh� K.~Karplu)rBa�.jE�|!b�)""���4{SAM}-{T}99 us���E 2�F< test se28�B6, 17:71-20J�mkm���toh, K�Ns�GuA�mTyat2�{MAFFT}�novel�h5A�rapid�Q�9�8�! 6�PhD!�sisI gram8M- _��:,!nf�>&J� �L.�ls!�T.~Lass�3%�E Sonnh�.�Q(� a�A�JQpr�F� FEBS*} 529:12'I3IP2gltp� O.~L85 pte,�mD.*�(F.~Plewniak��"� u?ȉteU^$s ({MACS})!n�8post-3@ 6�%��F 70:1�� �2� lfww�T.~P. Lie(F/J.~Wang,%�W .�Redyof!e�� ��� $sidue grou� .H�� Enginee> a�6:T �._"{lb93} CWLF ston�J. Bart6 gF�sa�� tegt%d��H1a( �r �conservœB���er`c%M !� Bios�ce�D9:7�75�2�m!�$B.~Manthey.g Non- Gximabi;ofQ er�.G%�~� 96:1�192�q6�76} EMcC&.bA � -m�>al ^j� ��!CACMA�$3:262--272�72]mbrzh94}�MN KH~Bogus�KPB.~Raghavachari, Z.~Z�I�R� Hard>P&?�� /edYYZ? �IE2+1:�L64�92�m95} �oc6�uzzy �EQ�A/B�@&�@&x %��cI�� ecogH� ��Li�>oa�FVqc }, 4:11788G 5.�m�A�&�.7,{DIALIGN} 2:2�ofEse� -to- �J �F�2hKFc 5:21F@12� mfdw�6��A rech/@li Wern6� �:�J>� ieP ���� 4:290--29IW82�s {\"{u}}t �Sp�M.~Vingr6Q Esti�a^__R�_���!{D}N 's e I�a�resol� 9�!CHa maximum likelihoo�\$B�B� DE� �a9:A� 2�nfjwn`D.~Na�D.~Fis"Z%L. Jerni06H.�p Wolf��R.~Nus�'v.�*�� inter s at�%tiY%�YedE� Fm�OB�� 56:924--9N?nw70}@B. Need*8V�U Wuns6�A� " � bl�!�� �F"�A�M�f]'�a�wo��VTz� 48:48%70.�nrd^ ,H.~B. {Nicho8 Jr}.e�$J. Ropelew�!�D�{Deer� II2{Str'ס.��t�;iqu��(32:572--591�S6��(C.~Notredam2� �Unt!4�!aj�asurve2=��Pharmac"VF0}, 3:131--144J�hh?X.��Guiggin�J�� 6X (T}-{C}offee�B] 0 !��t*WQ/AE�o� .[�z+(302:205--21�2,pfr��L.~[$daE!Florato �(I.~Rigoutso2�Ana r� a�&�E$�A�B�s "��otif d�n�Combina�3 Optim2%�2�N27p2�p!�P� Pevz>�� 6�F[.��r�2c rfpg�.I:h=�Y.~Ga�$a�Pra6Z}em~.f�9C ypa$��nHa�b�[.�%Metabo"T6� 2�177e2�sJ (M.-F. SagotE�Y; kabay1.iPaa i"�+ many guisBB%�Re�+ndLk les,}O!*� .�?YB�2� 287. Spa� er-VE>g,"�6 , NY�$.l s75}�1San�.�J�Z"  q�2O��Ju�nE 6=��8:�U4� 2\ sm��etuba�KJ.~Meid�).�r>P�PWS P�_ ;any�T��"�;21@ J.��Slowinsk2"A�&{�8�NF�y�+Le�%�2�0:264�Vp2 ss90}�A� mith?T..*�$Tic��a�rim7 ��"P"ys�!(/H�Q1F�PF��} 7:11� 2E%9:����$M.~S. Wate�].�6U��m "�Y_ �F�U�f=�&�(147:195--19. 6� s66}��H. Sneat2�Rel%~&7,"�N&� a���� ctiv(i�!pep�Vr�.&��G9�r62�sm8 Sobei�H*a*e2�AY�1EY�A%s.�e�b? 14:3S%37� 86�� L� Stanfel.YA new��aS/oda�� &� �283)�2%2�t!2^$ �class�qq�< .�%+]�Z�19% �64t# n�J^v�1�21�#�i�<��, ���_Datab�,},ͫ8� � Aca�L�! Lond�#�!2 thg>�)�. 2� T.�Gib>MCLUSTALA=�Qsen;`eV�� > �� 5 ]�through4�ap�`-�Rf�n$ap penalb � 2�&x choic26 EN^k22:467�#680F�tpp99a}B92��`z�*� b"�*���*!�2 a`&��*1?4b����15:87--8E�:�b��A��pre�?!�` "��Q���f�7:268�69)�2�uE.~Uk�#.�OiY��o!S.�2�E'"� �#4:2]&26 |2j vms�A.~VaneXT~MarsIA* .�Promo 1 �a�ţ��, id=1�)U.M�"�'in&�/Z, 150:7�79� 2>vvpD.~Vo�H! � C.~WB:� uF(�al� Bil stry2, N�%MBU S 2�vea!�G�gt�]~Etzoldi�� rgF� sses"�exl�"c�4e���� ��s:!g twili�8zbrevis�_B~�[&� &%,249:816--831�_2Dwj��L/ Ond�ian2/�eah�=n�� " �1�!4�-2�wj 6 E!R�-6HC nsus2�{DNA}4-qU�)�AJ.�� �S�GEnzym���me 18"�*2v_237f�S�g%w2 wsb�6�Ei� ,� W.~A. Bey6�Som�:�e�q��r!e*+ e-*� **� 0:36�(6�w73� Ws(.VLinear_ A�vDg�F2�1MJL "_ teenth Sy�[um�%\Na!�7 � a? !�:�E�72wbf TTDk L. Brutla2�D�mempir!Tly��;^d.�2�%[A �I��Qdfamil�k$ourB#Co"��l$23�4�C2� zhm!(&�"eU|�2��%Jvia!Kj enume�)6�E�!n�YZZ7�6� :��#P.~Zha%- >�A h&�d����u1a�@")b�Hf5:K15�ZN�4 � f�4��6�0Wot�H J. D." son  ,, F. C. Cric���c ZF171}, 7P'738�f 53).&25(Williams} L Z  ,HJ. Maher III, Annu.�G.��� mol. �".}29�9�c21 �60)*;"�1Zigel�:H.  :Ioi*la_l""#8ystemas} ([in R�8an] Moskow, Mir' 19826n�)��]Ao3o493--50 m6.�E:Sugawara�Tsukakos�Hf� 1�26.3971�7.oI��]0G. S. Edwards�:qV�5A�92 793�a�?.Y4 Weid�x3�'  TB�AE�V�Y26��167�.677�8.pLamba} OAl. e H.-J��&G.A�Jr�&aO4N*(8}, 667--67*q89i�B2��(ato2�:JJ�P)SU,92�d68--77�p9��n1<12JBHQi!Ii>��6`Dynam�g�qI;V~2:~!Ua��iL.u(f�Q�3��477--48er�9ShishU O.�_I�orbŀ Hobz�GLeszczy��n*i. *� Rgum���u>8�11� 112Co0>kVolkovM�pN. Ea!�osevi=#BAd21}, 7��806E�a�� S~a9�͛�laT O%�06R708�p9> Prohofsky�YouaV%jPrabhuXs�))2<A�39}, 31}31)�m,U�GarciaS> E. {!7Soump�t�+c�8BrU68�� 3160$f6e(mkPe3>lytsya>GS. M .!, Bull.; �+.��� y��u388--396� : Melv�3E�c elwyn-Hug��,E� 9:6/�w . Sriniva�W.�Ol%1/ al.}�hys�?��3�4a��.�'U�JE�Fi� Am� ^ 120}, 484Z:��9:8Ram�)ndranb)��.%I.�Ind��� 7}, r 9�W7�}=�Ni!%�Norberg�� �hB7� 156 15]nVR� ef� 6�B0SA�:"S�9%pofk-area cN$2ZSGlob. Ec�r\&!!geog. 2:441--4`72$ Poss �,Even~Tj\o rv2�Sha�pf"�JV�b�ew!possible`#�z.F�J.(Bi� 30:8a�83:2��,Div} Michael�R�OzB]/,&d" iin�'�>�62%n{<� Edin�|h Buil�8,4 CB2 2RU��6aNeHx�� 0tephen Hubbel2�%lUH;ed ;orn5Bio�!�->�{. etonN:K=41�<��ey/p"J]TgN0857>�@TDurrettLevinSAR} Rick �Si�!.�Spj)�6^\ev�J.orllE�79:11%2�6( NTec1y} Igor"�Jay�/ >B�j63%��1-�Amos �j.�1�t[D�*R!� � ab�#%in �.D%� �, 424:1� 1037:2Chave wRe�=��~.V #.�+!unp ^��;Let![7:2�32�)>�>McKane�Ricard~V l\'{eDavid�asC&Alan 9.�Sworg$ed instL198o�Mx�s�F@$Phil. Tran�c.�. B� 57: 8J�)Harte�Sim} #, Tim ckbu�A(Annette Ost�5B�"u+I FIo�r"$qYa� rang�siz2E�WNa%�157:3938J�Gfinite�,} Arno\v{s}t�\v{S}iz�p)� Stor6a,]r-lawQ��l.�"s!� �,�� +u�inX/ ite �F�AoogyYq 6�E2�0TaNaBasic} Ki� ris�[�E�bedi~Colq:aOqMatt Ha@!gHenrikS Jense2� Tangled n6:#����e��!aryA��.�%�J�2� 216:P 8J�+�DNetwork} Paul Ande�F2�eldtoftJ� =^�R�|Fn��aLa�o�r�&]HŹ "2032D-3355)�2U�@Ecoli} Daniel Law� 1�6��k Kunihiko �cko.mD��B!7!��/%al ]%oJ�/a�y:tVPE� 0505019�q:},Connor1979} `� %` Earl�8 McCo2��sa4�}!��%������.e.�E^. 13:7[s83�C72GR � er�Gs�?} AndreaX_ch#� Marka= Beba2q<p0ic*�de!tmeasu(xW2N!zv�gb(&9t� B� GECCO-99:NG�c�"<)ar�r:!�S;$, July 13-^.19h O�io, H.ida�$ 13��37%H6� A� TimeDep} �G�|!�:�ZFyime-d�@t extiJV �0GM(�5in a t��-��u�Mhia�5�B|�Da�*2061!Quasi} �dvogadro>jBJ�J�a$ ŭz �a�n��%q�|%es #B�De ^l 36:883--8�12@ St�dHerPatchFoodWebs} Dig�h  , AmbM$h��war��Denas� Chowdhur2�.��.!�s�}:�Lfood webs, migratingR&opuH*%D%�:B�!��|Q� 2�L2n2�Fitness�z scaplvS�/ y GavrileJ�, 4{ 5�the O�e�v^ �r vr 2 E�sA�M� LairK:q�r�inher�vc,Iaint: V� #icC- by aerv� sour6(U&|�i~k� 2�Large-W$Shifts} EgGPw,zT�%M� n9ffe6�EI= es sG trigger�\s�{ N[O.p64:25�3�"2�TokitaSt�6�} Kei E1 Ayumu Yas�P2`/E.;2!:� �<sS n% aA�ec %�{?�3:�0B0��p&=:"�14T 2,MaynardS�/GTh  Beu��a,��am:�A�l*l82.�0MeasBio'� ~�agurranB�-��,&�9"i 2�BlackwYza< L|[(ed, 108 CowMRoad, �� , OX4 1JFE�2=$RikvoldTan� Per~Arne %E R.~KAZi2zP�u�0 equilibriIr1/f nois�Pa.co��G EG ��vidual-+d \\F��w.8� 26 ��� Fluc�� } R~K~P��>�.�.8-cd�D  a� d6�� a� .UL �(.�),7:5135--5155F�Island[�2H"cArthu> E�RW[Bl��ew� NAe���.�J,�Ja62�3Q�JB�%HPv�� Hes .�E��&a�� of rar�Pin�EAp�&� >.^%� �E/714--71J|i�e? Ak shiwagi,�#aru Nou>i, Masat4 tsu�oh�I d~T.z m, I2Nm�!�(Tetsuya Yom2h ��tic�  f?%AwfPC�  d�Ca' expe�`nt�<"ZOr�q.�A| 52:5�50J�W��y}�V_�amRC'.� Benj�+/Cumm&N66V ., 2725 S�F Hill��Menlo�_kN$8California 9402J�&Ev!�} EmR. Piank2�E�*ary2�Add�B Wes�U Educ al� ishep8 1301�s *St,  Franc�(, CA 941)20639DI�e"FBarbara 27&c*5�Es�al ?Nt*Co�M�>Be8lefs} *�.�Mod�$ez%�a�lifespa3& �;a�� ity:; ��s"9?�=a�om e. I'�.�%�OIKOSU 00:1#1l20>c?�i�R]~E.�k.]�0 �n h('s zero-sum��&drift��.BF�85-V3FPC,Pacala} Drewc/%S1�W %.hA��U ���T-�0ug !Uuni�:1� pw;�(oes�g imply!g8s2In�+BurslemV$~Pi� , �.~�ley�4�;�{ ic Z:e�A. Tropics -��ir Rol1MaOn�of�  . Ҿ Shaftesbu�) ��ɏ,?=�R/*@6�>�8LSan Diego CA, U.S.A.�=�c199v>xBoal}M! }]{b9PVYeB9xD ~�g�-FMeP4��o�I�^ ��g m�� �#,sA� Fg })!� chap=�t!N9�m�tF�vHo�)%1!h  0AfVB�z H�Motora tein�ڡ�C�kelf6hTSinauer Associates Inc��X!(�bf)�})*�>�qReivQ%�wr ~B�oJ)Q�"�f�pa�teV�36tg7#!�$ }{57RugvSw,Bustamante e8sa1:�j&yKeKa�eN]�jbI01�C.}�8��a:VrB� ���!VW �a$!*VNG>� ��O;5�AccG%Resr�x.-�41Vxvv�Schliw�Woehlke%�3a�s 03�{B�k X�nb&e��;�Z=\ �()}"�&|%h�F422:E->759R�v]j#ick%2e�mat~�J�B:CMZ�*y3"DkC^�5){]� �28V�v�MaIW}�BFz! , Po^G, SڃSeiferPe#]{m,02�&B�te:!V~L>~ ��<F�o�8HJ�-@2F� V�j -�:1I*#m�Ha9F�,C^)9�l�M'160ZQz)erz.(0:� E��1fv �� merz%Ku�VAB):5U9ce�V=V��M��)�6:�2�5���0Z\|9Vo0rie5.�4>�a�, KoomLo;�q�4��n�B� ��zƛV6ojL10Z3 109N��K'r� J\"ur4*��199>+t&AgAjd@Wa�� rostaJp 97b��B�}]�OFi��ڸB� ��uO�6M*P�b�6��E���26J !sr�Lattanz�n*� � l �� B" Z�6 B��ZA v.�'t�T^#8ZL00113J ��� Astu�E� Bier�4u a 9�rR�?:�Z�DB���A)A7Zw 176J��199v*Sh�@Shi| %9sh�su*VB��Shu�,H>c ��+r݅Z� 0219Z�v)Badoual.�>� #, ���-2Qb G�� FA ;:V���2��VR�SVj; JZ669J�HjLipowsky.�>5$, Klumpp8and Nieuwenhuiz{�]{l M��Bw�e��FCw��\!s.6:�� �����Z_ 10<�RvFy;%���k�����r��2�.x��E�!7W^@!�^75:R261J� 199vy�b?}�)?����?�?�?8V?451J���� Aghababai&n,:� &a@Men�Pa7 la^ke: ~EucV]BIa:�V@ G.~IAd.���9Bz��hb1n�5Z�257V�9r> J{\"u}�� (�Z 6�`}]{jue J�b��Ba �ڰ������ �� Der�ny� Vicsek����dereny���BˀY�~ B$� �^�roNf593:K��67��(uO"6r� Vilf�.J� " , Fr*�chwablA�vA��B� Y:�V�B����B��a�5@"�Eur�=~~4^~8V�v�Csah\'ok"u �p:<$, F�MPm�;Qt]{csahok�qZ>4 Z��BS �ڡ�B& r/Z�517�mD}5i%:�D�T�;n���<���a6dan��B�D4�U�V0AP[:� �9�2� ~Un.� u:!�2f�31^t Jr !ir�� u2�:� "�Melku* Wald!�k" �� f\ . ^�:M��.B] �2�2�"-.f�6Zd03191�W J.~X�,a"D!��xing06�� R.~BB� V�& $F\���B�r ����.&��126V�v� Stuk��.�>�$, {PhIQp<( III}�� Kolomei�H }]{k��EJ�o�h� VB���D���^.� .�]�N��!�^l9� �4-�23�2�%� C)r�For�va�Xain|kf�M K.~T>' X�� J�W�5� �uw6DGenn��19rB7165N4�r4Su2�>�Sun, ZuGvE��iA�sun�tB�Su��D|:6 �965O�9V%W>3j�Cur"�Df�1�A��%M�114J� �/v� kerk� Berg��xs �m�g>4 VֻH�s)Z5l�Z�V�zl9Z�690ΰDogtel�� �:�$ , Ja:�!�Faivre-jValV, �Pder Horst}, Kerssemak�1�6s" Muld��]{d ��S�:bV�B Β<B�B�GB�:4�EB/.h�BB�)�� F�$-�A(u����7S A:j1^[ 331 R�v�#)���U7A�2jEي�!M�g:� Z�4B��Z?� Q 2fr��Jr242B�20zD��.+>A# "�5tyshu�,Worzalla, HavF�( Herdendorf�o��no2�VKJ^S �:rVAGJA�AJ�;:A)?�>��T&-�:._,N�8cta Crystallogr�-ect.\ DL^� 6��P��9N�O LeBr*dure�7*�, oids��N>�N6 �z�Welic!�^�1^� 912aR7vzKa\���k��'B� JZ��� R77V�.v� PiA>�:>!,��P�����h*�J Getz؏a&� }]{p^�1HJ�y:,V��UMe�ey� icke�m�� V~N��=��EJ$-S@��W� �:"� ��u_>�)<^c37� E�H3J�/ASr Kloede��Platen}A��Ok p  "�V�PJF ^��BF �i�R�4N/d�B%a�4Stocha�> Di�D�ja�AEqu<6.�*�5�` FuBeW� �� ye��19z��Parrondo.�>��$,,Cnc�.CDwBritom�J2e7V�� ~R��.[h-M�jD:�Bl��?FJ�CafD<5fq� T�V�q��q��q��q��q��q� "S�R�{UR�q��q�Vo�]nd�o� Y VOET�xB� M�9�J�^J.G:� NeuRsF\�T4y: $ 3^{rd} $�{ion�&��].V�and+�s�ac:2< addr��{Hobok�TNJ.� �2~�6"�MATTICK�9J.B@M)���w���� Ame�nj�Oct�B:M�Zfv�+Denni.�� �+6B� JZ�� j�41� .� �12J� ?r� ��V8�GILBER�%B�J��3^z�Z�(8v Joyc2:z JOYCE��G.B� H��b�2ZGv�``me� noad!�98�0ORGEL��L.B Or�lZ�5����i� ^H 2Z�49J ��Szosta&#���SZOSTAK��I+A6y=��~z R.B�)G���6~ ^� BO �^x��cn30Z�"147V�v�HergHand HhEZ9!o RICH�lBK P} :�/BLRic>����\ Genr�Z7265F@'r3�a�~ Fera�<P.INTRON��Be S�,J.BQ< �Z�*�=q�jm6�Jl43V9vMoh�/Dlowi�E��Ae);�OB�!U�9A.B��Z= NuclDw�~ AZs64J !rs�.�e�)8�AB�Wan�~��:B SanFilippo~>R.B Singe�zyB�MHPura����M�f�j Z23VR(vXBզ and xna�ACBIOINF�JjgB�ER. !m6�*�AV�B� ��m^� ���: �L Ma�ye Lear�RAS�,�� ZE�� }} 2O#*� �S"n�6�"� *JHM�Z! �&� vD4 Mali2�6$RETROVIRUS��B|R!I���H۟<6�zNT.B�EiMdse�]�]Gen�Qz�bK"30V�v�Xio�{nd ��)v TRNA�aB3T�6�6EMBO JnXZ�2335J|#199v1Hinkl2c4 %,�R O1-e*V�H.J�rr%T>��y�>nogiMN��M. npj�1^1125Jo)&�bibN5L Clarh2%e AGEN�-B� F��VK eing�@ re: PuttB�]D�dy�WoE� Toge��bJAga!G�HrH�:Pzd-}9PISTI�<B�3MorocTE�� priv��S�Vn�MSjogre&5(�� SELFSPLI�&AF� V!�E9f~KBn StroN�֟BF� Sj�ON6Nuc� �"r�K2Zc?{R9 7v� uo%�� CYT��B� Luw N�*� � �z ~] 2^�1ZQ6Z�'v� Kaech.� VCYT��Br L�TB�%Luda�� ��B� Matu�NtNeuron�17�;�1N�K19z�6Jiy� CYT3�GB J9 r�B�A�;�a�\S.B�4 Warr@2e"  E���kj�6�Jk04J;!>r�Kri ��@an"0si� q��EJcV�� KF�K�Z@��+Z� 119���Hag6+61A�x@B}L�A|j�S.BgHamerof�; JFJTus|�]vU�*)En�Zd061^C-v�El-Sama�cKs`sh�xB KHAMMAS��F- YκB��Z� BIBE6�:3N���/Bake�Snepp�#JSB�HB=Bak�KB� �6�NB~\+7Zo40Z{;vG8Ja�l��ru�0� KRUG�kB�M�/FY.�}, *p/0501028@}5n�FE�F7PQUA��B� EZ�ūwi|�scT^n}rv 5Zv 4N�197v��I�chu�*�� HYPCYC�m ^��m��B1��>b� ^�54Rfzq�Z;U);�� �;�;�;ZnJ�197vQ]�9�� �9�9�9%93Rt�>978}). \bibitem[{\citenamefont{Eigen et~al.}(1980)}]{HYPCYC4} 7,nfo{author}{f> M.}~O}}, pf9W.C>;Gardiner>Tand��P>NSchust N ���journal}{J. Theor. Biol.} \textbf�+$volume}{85�D0pages}{407} (Z$year}{1980rppPage and Nowak}(2002)}]{NOWAK��K.BrQ} 9�2M.A>4 �},.��1219:E-293F1!r1SteitzU�200E�STEITZ �%�V�N>�Ba��BONisse�:J>qHan�:P.B>< Moor��TF�)H:�5�Sciencej28^�05R�vYonathyYONATH��B� HZ� Annu. Reve� phys 4mol. Struct.} A�^�31:[M�25J���Chapute�Szost�3�TNA��JF6 S�J.W>p�ZN� O��VBBqEgholm�:R.H>w Berg:��OBJuchardtNݜ��54:=M�149J� 1991r�Williamse�4!�LOREN��L.D>�Kt}, {\it private communication}j�Shapiro}�6�SHAPIRO��R>�Ji emph&#�title}{Origins: A Skeptic's Guide to the Cre� of Z@Life on Earth}} *^Xpublisher}{Summit Books �� k Tddress}{New York, NY},&�"�6r�Lee�p199%@POLYPEP�@DF�Lee!>�RK J.B{Granja�<KB�everiu߲kMJ�hadri�NkNaturn;382:<mj52J;!r2��>{RNAP} http://www.ncbi.nlm.nih.gov/books/bv.fcgi?rid=stryer.seca+.3769f Si5�20ɏPRION1��Fz%'z�S>�Lindquis��=��EF�Kandel:v� Cellj�11Z�879ʻ^^2�^Z^B�Gi tto!!^�.R�Ba EtkyIj9B�Hsu�pB�$Janisiewic� z�MF Miniac��JF�Ki��H.X>�Zh�����Z�Z� vy Glover� 1997�P� 3��N�Q�B( Kowae�zEFSchirmz>MF�Patin�@J.BLi�B�2&N�z�^� 811F�!�2�>:Tru���>�E4�H.L>FV�� �-���6a ��478F0�r0 Friedhoff.L8uL5�.B�R���:� von � ��E.-B�M�ckow�~B�Davies:�0:�2�NdProc. Natl. Acad. Sci. USAj9Z15712F�199viBousset5�-5�6��B) P1Cj�NF�Thomso" j=SF<Radfordz��B& Melk�N�EMBO Jng2^�90�mOgayar�,anchez-PerezH}�7��BG Z��By6�6�"� InternE�Microbiv�ZH18JG��Muller�5E�F�J A.WF; I�CV71%y485-501.�0tk81} TakahatIH2[81. A�5oafEK.�ELits applH with special referA�8 to rapid chang)�pseudo!�sy�GeneticsYE98!�41-657.��luca} Peliti L.: Appunti di mecca� stati![a,UXBollati Boringhieri} (T$o, Italy, |]�ya�Yang ZI�4�ng�}pat��A�^� ���105-112�Lgu96} Gu X., Li W.-H�AUPadave��)�8time-reversibil�,�7r�> vari��among2�it!�5>�� 093}, 4671-4672^Gouy89} ��.�89. PhylEaanalysisE}d� rRNA�R supports%,archaebacterA tree�her than%eocyteyM> 3)�45-146uolo99}6���C)�9ݝA R�:�-:� whe �2p!� s are not���ut���QC>W<16}, 719-723. %�@tem{label} % Text���ic $0notes:F9 \"sub�tem (��}l ~162If!�re is a�(, it shoulde lastF�3�% .� >�� f�12�V!� 79} M. eNP� � , {\em��` Hypercycle---A Principle!pE|@al Self-Organize�} (Sp��$er-Verlag,'lin 79.L" �etal88�,�v$McCaskill,F�Jers.I{\bf 9� 6881� 19882iDomingok 2001} E. , C.~K�$ebricher, 1 }J.~J. H��nd-"Quasi�4 es �g} VirusE���:99s&Con"] } (LsasB=!4Georgetown, TX��12�tinetzrp l34 395!�!2n ���b��E �65�03190 �22^0KampBornholdt_� %(S.�R �v.2,�� 068104)/6cdBrumerShakhnovich2004} Y. iE.~I. %2n�%)061909 j42�%�-�5�=�R. For�$I�|I.~S. Novella, Current Topics in&� ogy� IoeU29� �5),7press.�.�1b2� |e&,�6bf 41e�33-�6TAdami�6TC. , MutatA�s �52 X �32?LiX5�Li M=GArtific�O%18  12 V6� Crow� $70} J.~F. \M.� �7An� oduc� to Popu� on I ��ory�8Harper \& Row, &�197J�a_6�,�� �5e3 2412)%6{ �64e� ��Appl.� bm�e $ 177 (1966 8Ohta6�m %T. ,�%d6P76!d1966(LWoodcockHiggs96} G. UP.~G. �.d `17E�6Ap1�^�4Ao��DA[issigqVyS�� a5�'900)V6EarlDeemI|D�Q�M.~W. ,!aZk f10%( 1153��Q2�Garcia�%4A� 8\'{\i}a-Arriaza:�J.���%�7�11678N� Nee1987} �aee%q� !-o2IeM872�0Szathmary1992�M9� N15� 38I96���� 95} 2�v��q 6805E�952�.X9�X%� %E28�45��199:�eaver�9!I ~C. , A Brault, W��nM�:�>�3� 4316 �6t(TurnerElena5P.~E. TuE�S��">�15� 146!,@2,Co  Scot�f 1} L.~A. \TE�"F\%+140!���6\haa� 3} W.-J� (n, H.-R. Wui� S.-S iou,�gervir��4�28!��X2eZa� -�aV!� Z\'�2YE�V`M�m5223!}B`NK�f� �  � &� �� �� �� �� �Flo�#� L. , V. p oy)� H. E��(ub, % Adhes�Kfor.��individual ligand-receptor pairs. Sciencem�6 415-417��94.XGrubmue� H. (, B. Heyman= ,P. Tavan, %Lz b�ng:�2e�med� caloL .Pptavidin % biotin rup6$ �>�7�%997-999�6E�1YSmithE�B.  , Y. Cui)TDC. Bustamante, %O�tretch80B-DNA: the e�ic resp� %of.odouble�edeI sing.prL,-��795-7R� Cluz �m �@ Lebrun� H%�,! L�t�cL��ovy, D�4a�0MS� aro!� �0an extensible�. V�2-794Jv Heslot} Ut ckelI%B�,sevaz-Roulet)�FAH1 , %M"! k-slip moE%,aled by open!�!P�$piconewtonI( s, P�,�,* 4489-4492�6�Gau� Rief!Gautel,�Oex he��$J. M. Fern�z �2�R� le unfold�65tiA�i�  Lu B. L)%0Carrion-Vazqua�A.e�berhaus!� K0lt� AW�.� %=SY[iS-%E]QVdu��. ,402} 100-103E,6� �e �s^��"IU> � E�oed��Y��!chemiA@� of aq>m�: a�son. f�)�(96} 3694-36��6Guan} Ze! e!T�l�J�"Bai�X�e0$M. McIntir���M. Nguye��M!�ar�o~ucA�: A| mime��� tegy�YP advanced polymer %ma�sE�A2�1 �12�� 2058-2065E�3 � Progn}�9�b�TE�F�.,V�I��desig-�s studi�d�-� � ce % troscopN< e.��jJ4M:��263-91% :a 6�:�-��ie�a�>�F�%�F�The"� al sta|of ubiqu�Lis linkage dependent��"5.�(10} 738-743�6~ �� � Cecconi(A. Baase, I Ve�rey��^4(. Haack, B.9Matthews�W. Dahlq'.I6�  %Solid-e syntL �m�#2�M���(T4 lysozyme}�22&9�139-144% 6� entr�)�ieplake�X�"  M. Oa�bbi�9S&� ofQ~�f� U limit2 Em�  0119~"�q�Janoviak�  j��Wess�D.2 H� �!D.!�M4 , %�;� hway%Bnatorhodops� E`Ltemper11. A�E�%�;)`5220-522�6m+ mtit�b4Thermal effect%Z* of Go-lik del���and se�!� s68ur� ��sX. Functe8-�v285-297E-:# DB} � .ens\ E-0F. Koetzle, G%}ab5, F. Ma9 Jr�!.!� Bric�RA\dgers,Ah KennQ �d(Shimanouchi�AM�sumi, �; � D�!Bank:��uter-�!d �ival fil�E macrY9 %9)�C>,1A535-54� 76� Past�: Im��4a S, Politou A A. �h 5�u�$ from-�I-band:. 4components of � ity. $:0 t(;15:323-327.~$Lu} Lu H, �W  K;eeredu �y3 s"3 Axconfor�%al� �" RA I27� ,prete atomic�� m�'��observ�s �9�?� �(;247:141-15��,geom} S e.g.��$Micheletti�� anava�� it$�$F. Seno, %QIY aM op�&l <%�~%ometr� %v"al pr�.Z�082} 3372-3375Jn tubes}��M�&aY.�ACovato,�� �� � %O � shapA;act� ings:� 6}@e�6�1}6asA=G,%Colloquium:N1�$roachya�-G� ^5A� $ModnŽ 75} A�ɺ6X Du} R. Du� S. PwY�osberg�DTanaka),E.��. %OK"rop :�Aa etry�Q ƅ,A�2�1�010375P 80J�UngYR.  %S o� %Lo � acys! in� {�� m%!1] (�>�$259} 988-9R.Plaxco}m W. ��on�DAgke�U ContASord &�� te placemagre��s�� �ain��%lŞ�277�5�6w! �1v�� uczinski,.�Top�,�� ,"H%I<(length: deff�deter!����twt)%6. k� ic� 2000. Bio� �8I�39�77�8� 6�Goabe Abe, N. G��NonU0 ng lABO I��1�!�&] =��ɞar=�II. App"�(to�dim�o��lattic"vs�"� e�2�-a1a86~Stakada��)da, %Go-�fo�&`edie�>em= sm* BJ1 �9$11698-1170N�H } T." %:M. - .1�4of5iof N� a�6� E= ��JZp 6851-6862J��1z�Sp-!T�ev[.�~��( 8319-8328�6�b{�$.� %B=R� ,sat) clasy-in5E�)� �a;!CJ� $84} 475-48 �6.Tsai}�T �Taylor/Chothi�!M. Ge�"D&2� I�9A�253-26Y6(p�^SettanV.�.�a�2N&2� U+doppeli[]5!�3533-354�6�Veitsha�T� �Klimov��D|-irumalae  �:��:%� scales,���.gy sc� %�erm%�sI�e-k �%p"�. 1DV+)t}, 1-2z :+ haha.]��v�`�*U in a6�aV ,L�s:5 ion,&�)8Ge�- ��&114 - 12�6�homop��6wBo� c.�2 E �70}u� 6� A� 6�AY � �T� ���m�9�%7h�� �Bb�C�E� . (ess2C oldo6�.�%�>�AQ�!�m���pa&�^ %N�, zQ N0E4(� R�f�1�:Dexpandafter\ifx\cs�6�exlabU (\relax\def\7 $#1{#1}\fi ^GbibOkM>J M#�Pf�Q$�R.N^�.$�Rurl^Iurl#1{�4tt!O%8{URL Iprovide'F and{!\�8 }[2]{#2} B!e]t []{S'�-9>�< Kauffman}�&}]:+'7�EuN/OSU#}x.1�@�6A"�7J.\Q%\�}`6N�N2ZhD43R�G69}a:tJPBH,e�Sjunne�,�71�:+$@n�:�;:}:�O 9VAF>L�<%�5@�\� .\ Ej=6Z�;01612V�CvI$Aldana-Gon�z K+��3)2V>-, C�rs�!��4 Kadanoff}}] 0:R%�V4M>4:�:9VEB_?�AU�!�9�VSL.~P.$+�:�, �7E_nIBoolean&�Hwith Random Coupl�@in�5r�iv�/Problem� Nonlinear>E$.A��IEds�~Kapl7J.E.~�d<4K.R.~SreenivasYP�&Rpu&�I�h�B�I�&r� Soco: and �7a� �  J.~EV.)�5r B�!l����!0��.�S%�V��"A^�O90}.6�A06870299p"� �Z�Eur� \-CfZ�=4R|JzLB� ll-=arisi!=?:98�=U>�=�>G>O �Z>�ica Dn7^J�TBv1~Bq�.4:$, Ps�& Sa�(�~�  Troe�I*|*.a�eiVoB�m:$V>B�W��>B*�@�xB�1�55 �sroc.\ NA\D\��.\ D��^�/J�171b4r�Flyvbj R(�6}]:I7�V�BURQZ�C A��j�2Z)L95V+v�DDrosseln� #$, Mihaljev!� and Greil� "��Be <:VUT>@�1�2�A0! f� B� � B:20A1�)note}{q,-mat/0410579r�R�"%>m &$�'BH?֜���� f�.� 9870J�J7 r��ma)HQA!I�TV ��V>R <�DB���R46nR�%�7!>� $Ʈ3����������R. 14796Z+z lemm�V"�;E e� B'T:� B�Z�4}v_1��*�!>�� %Y 6 Q:97���� �� �7�J187:8�Y11RK9,PN/5f f� 4} %��41]{ALTMAN} Alt��,J., Das G.D.�6�<@{\sl Post-natal o�Y of m#neuron�,0he rat brain}"�<(207, 953-6..�2�a TTE} Gold� S.A.�;(F Nottebohm�"� 3), �Np�"<, migr}#� dif�Ft�D�vo�drolEu�Dhe adult female caG �� � � � � L, 80(8), 2390�23942�3]{ARTU [(Alvarez-Buy� vJKirn �S,B�90�Birth!n proj`X )tO �avian)w may be @ted to �B eptu%� 3o=Karj/}H%� 249(497!� 1444r)6�4!�VELDG} K[(�3, G., Kuhn H. Gage F.HEB97�D More hippocampal B�m~liv�!�,eB d en�8n�!UX0 386, 493-4952w5 �OB} R� fort�EGheusi� Vinc�J-DEu(Lledo P-M. �2 � E�$Odor Expos�&IncreaKA�Number:NewbornM�!� !AEa4Olfactory Bulb��r')_Mem�>�%E�sci. 22(!H 2679-26892�H6]{LEOPOLDO2} Carle�4Aa,Petreanu L.TQHans�1 �JB� \& :uuB�!�a newM�!��E� o� bulb)�.�( 6, 507-5182�7]{AN!��,h!�>�,F��K,gnasco M.O. !�1-� Unsup�:sed lM�%lad8��a"V"m�E�genesis)�Compu2�11(A175-82ʽQ8]{friedA�} 0T R.W%~urApGI`��2�'iF of oAprepresen�Jo�5 slow�+o?M�J!�V)it0cell activity.� 91, 889-8:�9YE1} 28��F-!s! �Mc,)X�+Dea��I�-2>�j5uleI �R�& i"p`6D 22(14), 6106-6113!}��$0]{FRITZKE%ztzke B�: 94).�; Grow!(!:\$& s�Gor�G(ing network�#u.Pand�J>_A�F� (JohnxDeyA�S�)�(.cfnaola�%FJ>Z A"�SCoE�! Nonc <Reg�san Enj2 Seg�� Method�B�;(ola-Galván(tal, %PedroJ Ivo��s�3 $Carpen.A osé�9OvRL, Ramón Román-Roldc�H. Eu�� Stanley^�-eD130)) %-1345��0).ELq%A�O(ymbolic"�$s u+E? Jensen-ShE� d'g� .�\% %. �F@ 5Z Jose5'�Ee\6! 04190 �2) %u� Azad�2�of gen�/Athrough ",4�(: Power law��c&�U%RajeevC=d�V(Ramakrishna swamy� J. Subbo %�n2�5K!�2) .�(Lin91} %``D5� mea� *�QS-�I�y''. %J� LV((IEEE Trans.�Rr'�M�hbf !1[Q5#+916Haoe�``F.GTl�  l�R!ad')C0l�1%�es�B��Hao�7C. Le�h S.Y.�W(ng, Chaos, �6t? A! vs �1�A82I 0�d825-836.en�3} All �.�r.&wnloa�Ac1 3;�% kary_Q r\f ]s/�� .htm�HeuVH... /-/�-$tic/euk\_g=��Y�Ka_P�W%di&�T %S.�=<@!%$5(urge, Trend� �e.ɡ%82�-1 HeLee_unpA%CH CV�a�AAW�.�v*/ inf.�OE�$4).% 20-30=�S�!�USS H� H.O�C et al.&�e�2�7538 52#-6} Q�< ~ Mraze�+ M. CampbeeQNuc�- id R�) gE26�ED.�Helden�J. vanjC� B. Andre��J=�do-Vide�>Exta%� reg�>��UIN�up*am#�Eof yeastAMa� y %aB�M�."xUof oligoY  fr�*i�J.�%�"�08i3�E(8).%827-842=�Busseml1a�H.J&E , ��Li�El Sigg�, %Bui�BA D%/8;/G�~es: Iq+xN�of� umpq"�1& %S�VCS�sth ��.!�it PNAS}I*n: 0096E��-1010.�Xi�!Visual&�  K-tuple�Wrib�L*oc�B� %artheir rZ#)BP counterparts H.M. Xi���zJ�02dj. %31-2� Hsieh03} � Mini�9; %ogenome&"Z�(growth''. L�rCy�ݎJ-Tp.01810�-3� -4]7�9$� C.:aGenI�ogy \ar7%�3)�e��� 4) (dep]a8Karch at les��R� � fG� &� santa}{WZ@Arthu]D$N. Durlauf�D.�,Lane, edI~>V Economy a��N�lex�0tem II}. (AddA,-Wesley, Rea� , MA4V 97).Wekono}{ap/ics� letin on �l unifr.ch/w;&D!1 }{Co�>j(>e�5Quantit�<iC!�0iv]oxxx.lanl7m*�)4{wei}{J. Weibu�RIWOe0a� Game� } (MITe�s,��bridge�52�hof\Hofbau �K6gmu"�VBl!{d.`R�s~Cas>�%82��q�b�2�g�dy�:,��em))�AM��40}M� , 479-519Yu "� rvr}{A�<bsoi�HF. Vega-Redondo, Ef�S�(equilibriumd iny�!��s�'�� magH em��Ag �R7��;� 5-92.�kmr}{?��ri,�pailat�)6Rob, L�, m��iX2 -run�a�p��rem��9 �61}�29-56!B5Afoya}{DE�I�[P.��YouX S&�_2D_v5�r3i�or9 aH"�Tm/ �3�h19219-232��hsIJ$ars\'{a}ny�UR<=Q1A�(Zay�!E9� Se-�!&afZYj_Z}.�freiwen1%�Freid5 Aa�ntz% On smallQ/perturb�s�M�4Cu� em Russ� Math� rveys}d #�U, 1-55.N �2z��k�*k6�m�a��\}&�[ �[New"�842�shub}{XJ8hubert, A flow-e�Y mula��� oe` cd"1GMarkov�>v ���{ �uq" Bull�@���1�66��a# 1621-1644e�N�f� 40]^cohenF+�v} C S S�B8��it�IUyPolyamin�, New-�x:2 sO&4)9�(bloomfield1�  B V AW_97 {it�81�4}�Ls�a�c}A�Q@�c,M, Thomas T,qEra�f�� 17039�olvera6} O ( de la CruzA�4Belloni L, Delai�B1547; ] �M,2�8 O, Sikorav J-Li:g8�ҍ.�*A� h 4} 3.�Levine�:attarcEa�T VVNWolff J�E, Budker V G9;�6�E1124.]�taK�chargeinx]:$1Kjc  A Yuf1iN� 1A]56��montoro, } M J C1�ba� J L�j} WK} 8273;A�8E�Z�009} 6200; 6g!�6�!nM1^F27�ourse�� DNAp��,} Allahyarov��$L{\"o}wen � Gomp]g)�)D�[E.�X�u�i.bourfirstVm�2qA� �.c� � 62} 5�PY�ourthir�:��!?.� j�9}, 4nEPL�54� ��o�N*er !=89.jc+,ing1978salt}� G� 7MDQ �a<-�11} 1.1 )Jf9�al rey H�Parse�]�2!&(Podgornik RA�!aH$2�)��M9�nKL!� chol�^8ic} Kornyshev A�Leikiz,B�F `�253]�d�g2e& Z ��� �II jL[769�sw6G(DNAreview1}.,DGe%>)/2A�3��r�elloid ] faceM.(# }3} 53.� h>�D'Amico� L\"oi�svF1} 1334.y9wcaJ} Week� D� ndler D�A? � CwnB54} 5237.?evans_le�q��E R�m�L(Y ds a�&te%s} %edi�.bLxCharvol $J.F. Joann&#&%�Prolif��27 ^ � 4); �`ajzer6C in: ``S2Ac%�m�-immun�]�"�� J{5!�s%N#[llomo� ,�rk�b��7; h^ru6�E�S#�2s%9$400�%8);�;m)D�Aging}qt6A�]% 9); ��e�%�`6�t!^s� ,%%�)�#x muli0!� �%%5 -5"�~mpeNon!7a�print: /[ecn� di TAao�&0.ms�[WP}A�P.@ye�+�#S�e1Cancer&�t6}, 350;i8�ju>param}=,��oqqFgq�N �kO [6); Ljr?)^>� �8}, 706 &,�hel� Helm!r>�C�� techn y} ,�1a� 77I27)�J�Hr�^1Nnat[N�F�xN�xN�xN�xN�xN�xN�xN�xNNK &z�18 {\parskip=0pt  i%t%\renew"Olab��emi}{} \N �{_k JA�q>!BR,y*siPa�7).� s��fol],p�Ys=d�8e'26/25�90.hhhlocco��(SL. Mowbraya7%, $C_\alpha$-G4torD auns�\s�[tool to :*z�XRT JQ_,��te� c� ��'2118-212@ %BH�Sr"h+�tt��3com '�3�accurac�� disc�_1e ��%0-)&�5,�sBY\49= 93�C5075<�^oom�L-PA"b�|�S�& odak��.PrJ�Y backbone2%&� seve� asLg]2�*nflunca}An MML2\.�.~9Vthat knoT4 bout��Wq��Zp�6Mi 3rd Pac^ Sy(�umaX5 ��Mead,�(1�B���� x me�7�fun�_ m//iG:�&>erA"�^}, 308�S3�G>LJA�JLim!���JacksOT)$\& Anfinru�:.A p6np104(12043-120512�MK�IMizutarbY%� Kita�  T b7 b:JN~443-4462WSSJLAA� Sagn܅D.E 8tYl,6�p�Z�9 �P�R~�R~A�~�~�RiC%� 1432KG� ]�RKYSDC7Roscatq0, Kumar, A.T.�Ye, �Sj�>!&mid�bA-�Champ�aP.MIp0 �:�y,10� 4280-42902�WYDRSCS�Wa��D�D.}"�.�C�;7SheerA�i���B-B �$10789-108064 XMHA!AXie!4,W9� MeaLrff,jA���H6&�[Rev.~p�8!%543o382%F�. 01}  a" D. �S1-z Ann. S ^.�52�Z5-3:�ACJRUCh�� �z�� Rome� A/E �sJ.~Am��Soc�122426-2422�q2}�q��fq!:1846-184q��YDCrJP�J!�m5914-59 "nXMAnZ A.F� Nv)�F�;ArHo.C%2!,MNTALF03} Me��nt4 l NoidA�)K'p�T��Aki�%!�, L@g F%]kEj3Mj"�/Ec*$��7E9~ SZDR�Sag�(L.B., Zimme�K�z, Daw�ǩ!Nt�YZt�� 3384-3385!�Leitner�� �gvK5�dv. �%�} (D;>ZeFBSI� 0��Bu,a�:S%75-7�`b}�aisNou Mode"t<:��:� *�ls to� lo�) !�A �3 }, &Q��)I�nharZ%WWH:�Wh!yn9R�Wi^.A�R%�H J.T�mqJ�V%���� 5354-5369!�"�SSFrF�M"-��"~J^7A� 70-8�%ZP�!Skinn��JB\&�"k�6�b�6716-6726RBBu BapJq\&�Dz J)]�!�� � �835Ul6��O% higa�5] Okaz�2+ =Rt�q , 5390-54: MSO!Mikami+i�|2h�)"� N�v 9797-98076�G03�nhi,A� \& Geva, ͏��M/)$A��!� 9070-9078. LNMS��LawS�, C.PQaka��AME7pa�. e�v��o6F366�-U�0MF62} Maradud�` FImA�o196qi �1�2�258�O062KTFAZ KenkG~V�JTokmaV��2�18 V 0�$10618-10626�Mille� �t�*1 �>�a 2942-295:�JGA�Jungw�R � Gerba�R { q� \�Bi!99 m583-160e 9�!�` !�2K�L K.� W5] 67-196�RT RabW E�Reich�D.RI8Z&� ! 6550-6555.KR�# K4 H _ossky!J��Q5:� ^�/8240-8246oPNRHPoulse�aNy�GZp}�)�)1)+11%� 2179-1219z9� BBPH� ��3r�zf})MH\"anggi�%�*J}| 1111!t6�$HEH86} Hen[g�, EatonA�ZV�8s�� 8 8982-8986~OHN�A�)I5��Nagao�we Q2.�.@ 33��156�SSi6�aF.���cb7A�7057-706%�uLBS��j ]$I �Y�� 0634�_3%�.'S03b}Za鉖b233A�34�k�MMKA� Moritsugu��(, Miyashitah}\& Kide!�A�J ȅm)�)8!&397UH%���3309-331%�%�!�tt>�% � M. %��"b RV2�$ 01-2�WUKeyes% �� Q�:�R�2921-2936�HS Hahn, SMdo��G.�K6��q�4G;%/SI%)i�O�y, 297��2*FB��Flo� S�EO aI5a�zSM)�� Z fY�!56745-674E�5� RGER!� Roit�/�KTݐ �ar t ��ZRp!RQw-17:�HTSA�HaE��(, Tajkhorsh� �Sch�~A�%@QoF� E�1440-14:�WZSMW9Ƒo C.F� he �:�, �R � �*2���:H)��H3100-3116EWWR�J Q., �)\bi4)^,�F�7a�60-:. GH��Ga��!�)AHu�D�9)���93�36?:�0VMD} Humphrey�:�lk#�.� \$6) %`VMD -�I$ �RBs',&/ B ~G�"� 4�3-38.>#�"F-M29-1439.p$CHARMM} Br��L�YBruccoleEE� Olaf�B.DA,tat�D{SwDJ=A�!Kar~"q%8]/C+m�I/�187-2�u�SMA�StuchT�kh.� MarcR�R0.c�:m� c�6044-6066� MKS�PM�o!, �3�SeeIGI��FJf�6762-67:�CV�Y�JXVo�FG���Z� j 4211-42202MHS��M�Seuo1��Nuba�EM�7mObm� <2541-2551; ibid.�� 6456EMEa�Me! k!3El� ij�!0�802.�N��7  S�nBF� �11350-6A T�Term���VK or�5 , 5663-56:~WH7Wo�)u �< Hammܥ�>� :��dens.~ K�!1R1035-R� .5KDT+0 Khalil�,�rd\"ov��N%�2)~}:.2&� 5258-527�2y�KHGA\o�qAGoo )�"� (urr.~Opin.~��.~�<��E 64-1:7KHN!>KamiyaV, HigoQj��:�S)�1JPQ&6�1�2_233 �mT�m.�Rashk�B�Thi |%"�M*pV�1�] 2049m�32� VRPKU VitkupT, Rin)S�gPe9���2V�4m��+a�u:X!�34�L.HSSNK7 1L, Sasai��er �2a" ugi)���0-�- ��5P&5966DTT!� Trek�gTo�!'<= �I�*� ��6D13P. FFMPdFenimo5PF_FrauenZBq�McMah%B�vPar"F�e-���I�047�>���M�',NM]{I�}�F5�5ETVT�b�, :UmurrayJ.D.>ra�Wit�G"�1a�og`2nd e!]S�.g!C.�J9611go�-N.�Goew' Rich��Dyn3it����i%w���&�Ot San!�ncisco}53q274.sk�m� G. S ,cmƈka� 3* 1�S 19512�Uescude�3CD� ��B8A����CRubia,�2K�` E���~^V 0219�0L:)-'"���23��w[C1}_Sznajd-W,::B م�VQ�I2BIM��la\'{n}s,I*A]5325��226dov#�3�� �"��iP�Were!!"�J �3 _4 _6bludwig}A�L �A!�Aronsa�andWFZNi%�A��'&+I h!�2�1976ӂcardy2E=C , �\,Iy+ eautX, �t&sw.�n'�!E. Z�M (World���V, Singap���@2[mc}!7V�B� lin/ ��4�`?']Amobilia1T4 �P.-�3aw�:�� g{!,��JV2�V� 0661��fJV3�V451r�D.| p� �D.�d"zo( W� bf ����1>� `2>`P. Ward)�m2E2�ުX6whinchl�o��Rx��R�?h��%;!&=�!9 .Verteb}� Limdl:=, J;=6ҷjacob}��Ben-J,��P �H!�2L,"�ke$43957*�i!lY��.>� garfi�%RG�)Tintut�Pe߹G K� str\"{o}m �L��Dem��y..P .!��  924�\.|, er�F.��L�RSeg�>:O= ��#O�:@�velH�%�J�Vel�`� SIAM�"�R%OŦ 1581%P6q g3 i} T�gai-��d � NH�FKO2�bre#"�Pa�$_6o-� E. O. Bud�7�>E�c� 1677A�27�bY�ton�fD2=j�4;A M.2zIO"8 3 19�;B3 b �1%��[H� BergZ�F�63���6.� Y2�Y:��B:pawula}a�F�7�j� %Q1)�86!Q672�^m ] ��gL*![P�~senau2aq �98 86b$kevrekidis| Ga�:D]%0sho�ETiti,.�`��\ 466BF\ ajda�I  �Ae=Bertozzir Vm�8In�3�&U� Flow}, Ca�^ Text�4a|�a1� .�^J�^�.�EM�[�"��� u�3�FgraanD���piu���GC����8}, ��rU:0V,��� Jers� 1970.�e:F�>� -0P�aal.�l"| � Ame�2I8t-�[ociety�o�TnқRh�'Is`6,5"N� (b��"� D�� /%})��FauI�(of Open"�' (@ �n2'� fBuschNV �,jqbow�oa?LahZ�P  �O)�ional �����*/Be#h� e�{��aUev�" YM�^:3�n�ps�@mPs} (Kluwer, Dordrechtd/dG� V��* Chua I.L.�d9�z�ut� t�I 4E��(uMJ�E�� {Prugo} B$ugove\v{c}j.MDd-t$ket* aspect�< quan!�m�k� [BIInt.\ .Lz!�.}\"�321--331�9>�I2} I Q'`.�ally �]lF:se� �� �iaͮ�� b$ --12'h�16,{dAriano} d' �qPnotI�)�Sac<� M� j�=@I\groups2P7o�C )[!UOp!_ B: Q-a S�l.\a,5m�ZS48&g � Flammia} ��3SiO farb,e` Cave��( ``|g�6I�6�2��6�? stat m, )�-phxF413H7�LF� ��  | ``On PSI-U� PSIR .~A E� n 7078]n�1}2� Fuch�`Schw��x``-z7b�D�;as Bayes�Gpr�)�e \S \ A}� 02230� b 5�a ��z�Unz;n �um )|: � %um:Fin��Ft ]v�.\B�43�@ 537--4559" ��� ki} 6�)X_(M, ``Squee�v� ]a �pa}<c �nel: Mr�;` ���'��a�)�; ]�)�-ԡc.\��.��37�� 2��}6�U(*�`as�.< (Adonly �@tt��re)A:�E� 2050Z!5^HA�= + ��ʥ�y �of�;Hd">H Work�  on Moda��{ q_@Bell'W�em} (�?z"VO� 2?kAv�g% s e-print �) 11068�$Zaux� ,.iQ� s---found��a non���gvew0 5''1Ge�2) �5th�{,.�of Vienkuu/. �o7^e at *ؐmat.univie.ac.at/\~{}neum/papers/phys tq 5�Re8a �MR+ lume-Koho �#S X�%��A�.��Kym�c.�6)E�ua#�sKA��|L 2171--218+)4mIQ�WooA���M� ^%K2�my�finite >yA�6A603.&Bengt}�� � A#MUBs, A>top�B!& c"q>�}� 4061L�VB}  n bO Eric�!�tu8�ly un�ed ba�,��9!j��y�''6�120}Grassl} � ss��.��(On SIC-POVM)@�d�Q�G6!D>��D>��l1�1��Field9&� ``On���-"� �Nm>2�����F�19U363--3�198B9��3!ibb�yK.rDHo�� ��/ � ``DHph �sp�>!�d�BM�E�e$�� 4011�/5:e�Vecto�Wn�J.a�.unm.edu�rQ/sicpovm� aGa8sma� AjAAP��fault-t�'an �aB%�''� :�"� 5B"127--13�8.�x�Ttt��F6x%,umE�B �i higher2>�9OAin&�@���.):� a���eC.q�sŚ>�FFZ NASA�r��%f�2In.Rpuh"� 6h(QCQC�. alm ! alif�XajO 02--�C v�98020FJq�5pA�F�� Heis7:9 ��-� �i�&!b A��5006�\Dehae�e �r,! de ��4)``C�eG* "9�zer� s� ��a~quadrIT>� �JPover $\mathrm{GF}(2)$��^�yH042318� 2 Hyonec 3, � ��D6�Sl�%�o�sI M�!harb<�ry�l-mo�F ��hг�! n%�040819.�vanDenNeU�wde�����B�:�The inva$��j�K��>� 1003. �B}ΊF�J�t��to�n�xerize>�SrvalO9s>��E�A�041016.�� iRef�rnda1I�Schmi�yEl�%�ЁR23�y�!F [I�}�bgW��� 4, vol.~163 (B�T\"{u}��Ver��as7�.}}NT-���ha ��&� �Ai�|@�% }, G�8��"�.�no.~1����� .�{Ros[, H�;)7 A Co`J $2^{q�nd}}$ #[z(Bk��8/Z�&Jf,1��V� ��S��S��S��S��S�S�S "��B)U{����E��"1�� )\ci��m� !fHden�Xnl"�3(Wokaun}}]{eE<o nfo{V��R.~R.}� "���:��V> G.}~;B�A� �B����i�r�̟� iple�+�}aK�g�\re�nc��R and two ����&} se�hof mon�s~ &� ; 142��*��:S ;�T >' �Z n!�d�鉂 5 shirX�w�u�0y4�7}��tF��Dikanov� Tsvetkov}cA�d vb�4��64 ^֍� Y.~D>��)��!#-�E*S�msp�ychoQ�e�&���ESEEM) CSct� opy}.�.�RC.d5� Bocafo�;.!1�92r�Schwei2ZA� Jeschke}(& }]{s��B+^ևB��j�6|p�= �T!�paramB�:a�={M�FEl%�5� ,, UK ; "(F�%KnAbragama 6��a 196ʄNj4�hOb�smf$:U.�: �>&61r U;E� Maxw�%r.�"hahn195� E.~L>�W֕ D.~E>N�6�&��"�_&>5����8:?��070.q�5v�Yud�^�1��6� #�2liC8( Zhidomir�#��]{y TK�  V.~F�b&+�q:�V� K.~M>@S ��AGJA�C� ���:9$�5�T��$Eksp. Khim�ub�����^M663N69}nHMilJ_�m�u��AJ Z�?)B�N@-[�[5BDok�4kad. Nauk SSSRjK2^L924NHz�KanaiuI2G}6I!,, Porfyrakis�Br�MDennis mito�sBܪaY�%^7: ��@G.~N� �B5��B T.qJSI�.1]�5�C�<A.}�[.m210Fa�W%�!�r8Almeida-Murphy &Ĭ>26�6, , Pawlik,�/ Hoh�E�.la!�and9xe��]{ f[��B��6~9��VBD ��<B� We �?B�%�;BD�)N !�4namefont{and} H \bibinfo{author}{; ��<K><�:~P!�bi�%�>B>x-P�=M>=9�@5I and}.|VEABTei1�!��%�U�Mol. E�} b�95�?M�999R�8r�SlichterE�6)}]{s E�dF�S � emphy{�title}{Principles of magnetic resonance}} }�4publisher}{Spri ,9A8address}{Berlin x�X.�4,$a^2/\w_e^3$��thus is negligibly small at $a=15.8$~MHz for N@C$_{60}$.}f� HaeberlencWaughA68! w196�wU>�X}}%��GJ>P �6�uCe>��jC12ZD453ND6vDMorton��:� (, Tyryshkina�`Ardavan, Porfyrakis, Lyon��Briggs�� > 2004]�VpJ.~J.~L�b�B B:0VBAJm��B:t �=B:9�@ S.~A>�!T}�,�yGO~D>R1� , \e��tIt Ev A��iaׁ�H, quant-ph/0403226}2mqip�mqipeseem�b ] The y�@ molecule has beee�oposed as an electron spin-based qubit in several �um �Brma�l�wDcessing schemes~�${harneit,bE�RS}. At��(very least,slow eb Twithin��sublevel��\the $S=3/2$ system which�,responsible ��,observ��>ESEEM must be taken into account when designing pulse sequences�S perform a%an! 4algorithm. How!)8, it could alson exploitedFdrovide a separate family��gates� oing oper%p!�tw!�5, increa!��, potentialQ] !� (le5�bit��end{thebG Dography}b\beginB {10}�@{Alicki2002a} R.~ Q�Search�a b��b �0classical and�worlds���� A"�6l o ), 034104}{Anderse�$0a} J.~U. hE.~Bo&up�C�diiic modM{,fullerenes C estim,of heat radi%�}, Eur�  J. D� 11} �80), 413 -- 436�4rndt1999a} M.~�, O.~Nairz, J.~Voss-Andreae, C.~Keller, G.~Van 5 Zouw� A.~Zei" a @Wave-particle duaLof {C}$���< s}, NaturA`h 40��(), 680--682.�� >� 2�M��  n~ aobio�E� fluoroY�ny9� (2003), 90402�Hanse��A%��E�,~B. Campbell�Th)s5g�\` >� ~EU�58}�8), 5472nHeszl�Q7C ��O� rlss��!9$P.~Demirev�GUEga� pha�E��  ex�dAF193 nm���}, Chemiz.�107��7; 0440--2�Y�Ama}%_} J!` Sipe�!U�Me�$.   qm* {T}�S L}au�K� 6�070 4 05366J��A�0Y.~Ji, Y.~Chu�LD.~��(M.~Heiblum,Mahalu �$H.~Shtrikm�i�A nonpach-zehB F�i�5x422 �A�415L12�Joos198� E.~E*H� Ze.� em���*�pr�tihroug��a��M ��environ_ }, ZQ)BY,5�8C 223--242��a�a}�,.��ief�$D.~Giulinie KupscS $I.-O. StamMcu�f)p.=a1�appearB�]a��Ab /o� 2nd�%���eJ, �.|KX1992j �@Quasiequilibrium  constant t�cuc6�u��g2�6t186�k1��� 72� Kokorows��D� �� D. CA�" Rober< D~.N� Fro�ingle-  mult�-p� >�� Ij"�2� :��p), 21912�olodney� I_,� Tsipinyuki�$A.~BudreviAV)�� %��`4nergy depende60(10--20 {eV)}AMq� impacM$duced fraga%"B C60 ���(ar beams: E&�A�� calcul>��J���*� 10�"���26%� 9275.e1mS�tl Echt S)egE�R.~q ,�l Sche�Das�a�Lifshitza'�.M{\"a}rk��Ki�)I re e distrib >evapo� .���metasta���� !.�630"z 9�9r 36� Mitzn�xA,R.~ �b pA} stud�of�LE0sorbed b� .�9�� -� 2445�152^20�&#�=!D6X I�YY,al challenge\ & 2~��Am Mod.� �4D �28E 2822~��U�.� �� Diff�tof�x��� struc�s mad�� ligh��>��8 �1�� 160401--1A 2 Reinkoste��A� nk� , U.~Wern��N% Kabachni�bH.� Lui)J�!�t*� AM � ~$>N C-60� fast-prK��2@* 6��:023202�RohlfR8 E�q�n�P ,��f����e}pro�'�i: ��clu!e sourc!J��yB9�p\ $6103--6112.�(Schoellkopf� W.��-(E. Grisenti�4 J.P. Toennies1 Time-of-fEo�ol}� �-g�� ng d6�Mı�FC��22 �o 25E�32� �19� �E� E;V� he n��iJ�t� ofA� hel�dim3 nd tX�J2�5�10Ac��155--1152� Scole� AeG!�J B�eUBurD.~LainB (eds.�"&A�[6[�7ho^X vol.~I, Oxford Univers(Pre�1982�$Tegmark199� M.~ QAppareN� fun! collapsA�uwby*� }, FYA‰�6�� � 571--56�Viales a}���VicariI�N.~Zanp- nalysi�!�) &n�� | � macr&�bPM��06361^Nf�bf99�!tem{pet�} W. P � H�J. tn�$ � E. A�rn�)c&�(8 {\bf 74}, 3352� 5). "wwhitt}G T. W ak��D{\em A Treatise on%J%ZEDynam� of P����A�Rigid BoV ambridge F�r04 (RC!�Dov�n 194�p. 207�0linn} M. Linn%/ Niem��A. L. Fei25A)6!023602 �s1.oktel^\"O. ORE9},E18E4.E gd} D. Gue�ry-Odeq=��2H33607H0.H rzs}� Reca��F. Zam�i�SJe]ioE86A7 ^2�mad} K.A| MadiEl�0hevy, V. Bret !U�alibard 2>k 4443�2lsc}� inhaPY�s_Z�7}IN�gg}�8J. Garcia-Ripolq V.APerez- 2�1xE1V4ros} P. Rosenb����a��!z�,V2�,G. Shlyapnik::M2�.L8}, 25+$%N2)} cozzE� Cozz/�Y =�:�n~1!y 021602(R)}3.}abo%}$R. Abo-ShaZC. Rad W. Ke�l�,:�-M��070409e2�gdsRC]6�Z^3}, 44��9.� marago} OE)M {\`o�XHopkins,A_ Arlt5 Hodby�, Hechenblaik �C.- Footb�Ap 2056�2�s:} N��GW�(Heathcote,J� Krue��t9!08040 v2�4cmm} I. Bialyn�#-Biruli�Za 2�Q-5��636 c2� kohn��Koh�(Y{��17�124Ţ620dobEeF. Dob��?}(D 2244���N��r� *�$P� ,ll-PR-1946} AM.��462 ��682c 8Kleppner-1971} �LG 71, � ��V!�A\�, �,�M� ��eiE�Xpworth (New York: Gordo "Breach.�0({Huket-PRL-B} Hulet G., Hil� E.S.i� D� 85, �.M �5A2312�Goyk3} Goyc, R�#J%PGp�� s"�#S., 19832l=�50�!2% �x01} Vaidvanath�A�Sp�r, W.P x:1�81,%�F�4�! 1592.t WalH -Ann!"-_Dobia�g (A85, AnnW(Paris),)U1�822�@Drexhage-Prog-OptA]4}7, K.H[ 74, %� ��2R,E. Wolf, (Am|dam: NAQ-H� nd2<YamamotovComm-} A�91,l� mmM8�332Yablono�1�7NaqQ87^�5�C2052� -PRA�4} �$I^Q-TY9!"��A e�IY764.�$Veselago-1. ( a;, Sov1�Usp �%�502�Pendri�} �sB.o0^�8aj3962�Dicke5A a�I56���92�NienhuiA�76}O ��)7 AlkemandeT�&!�7�ica C)<81a�6 Dung%�� } , Ho TrmL Buhmann S.Y., Kn\"o�L.$5le>D.-!f�N(�� K\"astJ)66-ѤA&0438124Kae< -Diplom} NMda Tsis, TU Kaiserslautern.# Glauber} !�� Lewe+% �A 91, .] �4�462&Kn�} 2.W5#!"� , {QED i� sp�ng�[�"bD"+s}),#� (S�si$ of rf��s,(�(Pe\v{r}ina,.�at Wiley�A&xLi}&$L.W!�ooi, P�mLeoyM Yeo�&!�1a� IEEE T_3. Microw�@ Techmm427 302�(Morawitz}  ��692he!1{ 76�$Tsang85}  ") , Ko�J.Am( %n!��a�� do��$Remote Sen>}Z> \& Sons)FN�8r�=|HB� Conj�'+in��/E<0ih&Mt Ltrocee�6ar >I�+n�alA�oo�.�qZH`Enrico Fermi' XXX1AWT/by P.A!�^F\(Accade�"� ��6 ]u8evitin} L.B. e/ �J�All-Unl" Confmon In/0�J� %lexo� Control!b1] �/BD(Mockva-Tashkent,  l1969), Sec. II (in Russian);b�.�&�&� ,A. Blaquieve�Z�:1,G. Lochak �(&Q.�087), pp. 15-42�I�A�A.S| levo�bl)redachi�m��3 73)>0[Pr8 Inf.�D m. (USSR)i�=1"1?]. �YEYO9cH.P. Yuea M. Ozaw6 *� 7�6�9E S FC94�CA�FuchsI4.� aves2�.V�' 3047�� .WSWWV� Schumach� ,M. WestmorelA�W.�oo)s, >8 E�F 7S\6).%�9-note1�While it�3�buV f no�b_ o de0�Fensem�& 9kby�$P(i)$��taglal un�,ted) outcomeFD $P(j@�we �itu4a�lm&" out,X3ce+ feel,keeps|�M simpU)!U�9ultJ2(ely clearer>$(inefficient%*Hrm?,�W�n Open S'5$s Approachy �_� ��2u�-Verlag2�'3);oHAyWis� �$G.J Milbur6�� 6�A�.D!�2�I��5r�6o;&a��S abouP61�of�5 * /a6 n if!�label%� 22($n$ (t6 associA%SG $,ators $B_n$)X most gMV situ��Wne��w�6th1� knowf stead value�L,ond v,*A� $m$,�6re �;. �to�bye1rbitrary=#�<al]�yA� m|n)$. Th <�c 'is en23as�a: two-indext m�a�qn $ext� To sea� !@sets $k=n$, $j=m$E.Dchooses $A_{nm} (\$(v A_{kj}) =Ad\alpha !B_{n}�en�gi"/1U.� lete%` ledg%R$j$�!wno:k!\ e ret precisa��1�%describN8A}ve��% $�$ s�=X=||^2 = P1�*wa�3�  von Neu� ep�=noM�a�%;Iccanj8^toQ�E���eved L9AicoYl.#�Nuspecif,ly!s'0e minimum pos�.�  rresult� a�m��he �9. I�refore(s�&maxj.s:(!# ctlym� �.#de�.t)-��0 whoA�*^9i-�r�Yo��fuK! behaviorL  � �3��� exa��,ano�#o�i�%�$,n��d� ty�)rix. U)assum�0tAnO�? unit���io� b@ vail�UtA�e�ŏ this� �N�\��a%�7d1 willA�f7 ���desir$ tate.� DJJ}]A�herty� Jacob�G. Jung" W�M6�06230�1� "� Hall_ M.J.a!FF�100 7)��FibDK�2` �,54302(B*�F&U �fB.2h J��61�. MKraus��K. �em� Effect)DO"5<:%�:F�8A�al NoI%of".}B� Le\$3-%� ic V�L190>knM8� �subad� E.H�(eb, Ad. Mat�1426� 73� /��M� Ruska2&�* 3l 43%fFjR� O�!� 1938AA E% �6 ad�~ , resasalaR"proof��ng�= 8va�Ka�giv�n M� NielsP I.L��� � Compu4 f M*� JCUP, *db)�I.�a much� �A0R�"i@obtw7�* PetzE[Rep.�BS2a�5%� 86)]�3is�N��_! ~. D� (tz, Eprint:� @A813~!bi� � e�M.� N�2� 759!�86� |i�.�R(� 0221a�u2�FJ F� ~&� K.~�fR�5#R .� poo�AR*cus 3�� point may2�B��E1..0��Am }, 7&s2�Barnum%fH.~ ��]�-�*urb.tradeoff!��umђ��`Iuni &A� mutua�un[as�2.F5205152L Ucov���C�%P#ix De Vito. Toigor 2e�Po�Gve�o�' lued� s co� B%ith06�Bect�M n irreduc�B� es�>��J2F� 302187 ��MOI�A�9 Mars+%RI. Ol�,� Ineq1@ ies:�-�:�V Majo"�(!�It�li�"on$~I(�7^�79���Bhatie�R. , �-rix2��&��019 Pm��QAM 2�". �436�G] .�JPVC��Jonx%��Pleni�R�8�W 1455 Y����I356�;!}G. Vida6�$ �5104� � = K�2�J�!mpN�!86, 5184��OChefle��& ,��&� � 0523�kc IJonGK.R.W!s7 =` H�368n 7Fmixing�Gj!D'A�9P�g�%P��rinot!U`C"MB randomnes N�s'^�15� % -� �. R<�r�(9 DQel�!Hanco�*I��(B. Wy� , %EJ2�E$4) 525 [ph�:IP5029]; \\ A. Hirshfel%g#nseld� Amne4I�70)62) 537 [�]-]I208163].� rev}a�,B. Fairlie, ��u�( Phil. Soc �6b1N 581,\\�V.�Cry@hilosR,&y >(London Ser.Q|2�_7) 237��#Balazs�3 K. J-ngs_yVe,>e�10m, 84) 347; �Hi� yu O'Con��i SculS�ig�$"�!U6?5U121� H.-W'%%:� 2�695) 14 �T�- Osbo*F�$Molza�#.� � 24�:2 79r�� ori AlmeidaN295} > 8) 265;\\}%Zacho!6IntE+M�1 �u A113�&X2) 297 [hep-th/0110114]]�BFFLS}� Bayee*FlaC. Frons�Hk*4ichnerowicz, D�)ernheE.6�! N.Y.r14H 1978) 61,~DP&CZas A- Prat!N� 4T3)> 4602 MGK�(,Garbaczewski�" Karw7,6_%/ 72} P,4) 924 [mathe]310023].a Str}�L�R�!, Zh.*C,p. Teor. Fiz�31%�856) 1012 [Engl.- ns6: S&L!- JETP �i57) 8912�DCFZ} T. Curtright,a�u�C<+E&uv.�MD�< 2), 0250r*19AbQ#971118�"r EDM>+Ito�/Titor), Encyclopedic Di,/�f  eis (MIT�Ts� qBa� F.`Vo,VorE�J. �%�A3-�$0) 7423 %: RW*fX26} \expandafter\ifx\cs=O�>exlabU 0\relax\def\na  #1{#1}\fibG*�P>J2M#�Pf�fonnQ$�R=>~R.$�Rurl^�url#1{6tt!O%8{URL Ipr�Ncom�#"�U }[2]{#2} B!ex []{S'}�[>�XShoAV4+T sho-�!��{VmRP.~W.} &1j I}�A�2 Fbookti>Voc.� � 35th�kum ympos�3on�2B "@ofKer 5D}�HDY"'V4}�pZ24--134� �}{"�9508027}*#>.\ D C�}�r0!<$nie-chu-00,2�V@M.~B�R [�iUIJ=TC � �6�-�Zum-]%o�* f�W"�B42}*�W)��}.u>`Brass�0j�[$, H{\o}�J W TappyU0bra-hoy-tap-9��VG.:�Tb->�a �805082n�1�U]| 2 $6]Mosca� )�]UdmosEh���hfh.�V�B%]������X)�rp: A M' nn�VIf.�pubZ\AMS.�n2n�305AZ�& empo�* ::�0005055n�AbramLloyd}� 9�Cabr-llo���E>� Y�BS>� ��>q�J�[�}"^;,�83:Em� 5162.�)�1 _�>I:a9807070naJakscTT d Paoorgiou�3!hjak-pap-�AhV9B� ]�eBW`2��l)l91:�)U�-�<1�:S030801:�Z\.$ 2�$(Wo{\'z}niak�%]D !Y woz-��\z�׺AH>�B�Y>"d�>J$t9Z�jdnvGr;e��a gro-�>5wVb L.~KaA*7 L��+"O 28&O ACM 2S I�T��=R�6! �)�� aE(s}{212--2196�:N9605043n+Boyer��Y>�!, ���W :�oy-�� B m:~V�B ��>�!�!k��B>�!-N%���8Fort\-schrit\-t�Vrlikj�46:�M 49�f�g!�z�A34rennett.7> #,�n"�V1�I Vazirani en-berE(vaz-97�� C.~H>� w:V)E>�Be ��?n* %ܺ*U>�9V. SIAM�on�,f�2Z' 1510Rb7z(701001v(als.&BC!,�4r�$Cs'�� I&de~L7I% a-buh-cle� wol�� R>Zw��B�Bu��=Bxߒ;B%ڄB�5S��2� 39th046�1�D* s.�~ ��R�352--3616�>�802049nNayak u��� nay-wu-".DfB�Q�V F>�Wu!�9E:� b�1t"��:9^:384--3�8� %Fx406r� Aa�ono 1� aar-01��B� J��3rd an�!+sy*�.e -uBe K r}{> 5R�1v#011110r�Sh� 2!'shi-01 V�Y>LE�"4!"2| ��=#B8� a�ociety6�|�^|513--5�  ISBN.�Hisbn}{0-7695-1822-2.�:�011208v�mbainisE�amb�BJ�~3T����0-o.O 636--6;Uo>K002z�Laplant�:Magniez%Wflap-mag��B�Z�o�o���1��A�N2�=O&?*ale 8J� �pp.J�29�}0(+b�3,r�;("s U>� k(�]k�^$ Szegedyc $ar-sak-sze��F _�� Saks!�!�= B0 Ӷ�1���.�:2�-�n�3my��Gmw179,frzHeinricheI�hei�@J6�"qJ�u� �fD 18:J�FA ��!�%>] 1051v�BesseF�Obes��~JFK�-20:J-69BR����.�> 30814r.NovakEP nov�B� G�-17:J-J2�-a5>00812rtUˉ�}]mb�V K� 1 9:J- 1V�b 11215�n�� , Kw�$�RWoz& -Bkwa 3�I5IV� B����Bw6���Mo�Carlo!Msi-.Met�S�12)�&�?5�FS{B� Niederreix6�*G ����aEZ@4!_5f5�>f31103r Trau42RatʼntrM.�� J+h:�"_�� BV2�Z��*%!�*e�1!�$bJ�|1Q�Žm�3Lq5`��� n�10911r���.�4:� !, SlomKq�:�}]�sloiԆL�#V�IJ��1:�� J�>�2e"��Kpu j}6}f�4:.-�12V�~�20602r���eG4{"�' {a}}���WUYVqB$ YZ�� ^�g.�U�4}:�2�B| 0503r�΁n.'b.'������^'iz(̆(VN�H p f[* �v�*�Oxd{One Qubit}Y. Nakamura, Yu�.PlGir{J�U Tsaiu, �|39ZV );Z,V4Ait{et �,$, bf{29b/h );�+M�:rt�=GNam�-Au7adoP C. U�KJ\F�89mM17901c3bIA: iore%f�V��TP�2Ha�s, and�E�noij,\��! ��); T. Du�=�X nnar�iK. Blad�fP@7lDA2�3BT.S14amdV84); A. Guillaum �.[�/4>J32504%G�]. Clark1�H, }"zp!g1� ; }R60c^el8_ �6}, 6*�)q6jer>kley}v!�]UD -mat$!192�ABe=M2s1� bf{30%�2�M�}>�T.*�QO.[TafiKk2 D. V. Av�4E�S.m��i} bf{4ņF� R}2z>�f�J. | trit{.|��F|Blais �Wha!��Jis,�1M. vanzAXnk Zago�eW/E`7| bf{9[>127qha %4 o�a^Bru�4E� NIw(057003E�IB.:1 T. Plourd^� OY�7�aBi�2�L {NMR1}I[C�+, I����K 14�J8)�� A.. Z7ہ��(aZh"�gC 109}: 164X=EL�g K. V7Rrsy�H6�?414} 88)�<��$Dev/Mart}MW4Dev�p� 3an�MJ." 4I �qoc.��it�#i�.� {�N0n-Tannoudji}C� h.e$Dupont-Roc��G. Gry�pcQ--/QA+Ol�ev. VI,Q �J2�8 �(c"R8�}Though�J leadw@�.vJ( pictorial 60<.figure 2WE�.um treat�m#JRF fieldM��F requ�C,`~similar���d�; wo be&@�<2jlro�)ng �Qa�JxKion2��0ent 1}M0F�G�6any�H Rabi f�encL$whose sum �<$s $\delta$�b�K�>=�k�qs2~,Rig/Dev GDQI!�Rigett^_M��EoE� =?j\,)g-�83121962p�/E�i�A�A.k<6���it{�um u!\�Y E�r`4 on,}.B�,2�;�2��)g�e6��Nu�L3 etism, }OYd�Y61;7 ��A.}; in�Ent%�%�t  a��8 }Les Houches S�9�1�b127%;6� V&:�2jW9}*aKAl4s} , D�~% �� Mecha"ZXEx���_}�va2��"�C25� e�# hbJZ<�h meri:O*U!P ics}�@547�|961.�s�E1} ! , GrangrP�`oc G n Zal5 iewE ers}�(` 460rkJh2} ~he �Erh 91g2� { ^ 36�D�g�, � G�@emvh h 1804Bj1974 B�hff!Book}, FA��OA Surve>.$ Hidden-VSs�+ ies}�g gamo �l9X �W�u�I oremvl� S. {�& �!� ud} 195-20!�64 (7 l�J�0{SpeakVO}� z 14�+���0{Big Red! 403)U�� Eclipse6�!hR�w�ModersMQ�(38} 447-452�Y6 (�S�wk�X2�twoJ= liog� &�L: ��� �����397!��DA� mine!�l2�$pp.171-1819E �[ Pol}�T � cXs6��[�k9]�:Le�+ments.�J*"�\�T�A{� �Yed�High E�vU, Pisa,�PeA_(6 pp 35-45.:i Evere;m��Ig�i�B�, 1>< Caus��IP-s}*�M.iB Set. Y$ Dordrecht�c�@RD�l@B -17,* 76). &Pm�)-a 93.`.:ac�� de p�xNe�c!�a�i� &����alak9}A"WD -126�0>v0Delayed ChoicJ*6�:���Q�`wy}:5�*;($14 155-159��0-f�p�C=�$Cosmologis6 p. 61E�e�QGravity� 2}*�gby+Ishw ROHnro��D.�ama�q,f�reMF �)!�81:� -�. 117b�rtl�Yn's Sock1� J�*��1]de)� que}�;�ue C2, suppl. au numero 3, Tome 4��81a8C2 41-61A� f. 6!" 139..!Ka= I�* s Pilot} iP)I-"�- �UY$12} 989-99%�2z�on��!�Y� Sleepwalk����[p[ bQ ll In Boh6u>,. 227]{Honor (!y�l -� 17r�Six Worlm�N�P No[ &6+65: Po�W J�ArVTQHs.} Stockholm, Aug[�11-15e�66�Qx 1812&=eEPW.�w����cnAfe Idea�qD M&��y}9 York G�a�:�)d�VY �"� �9cAbf,j �4Uns��� *{ � ,�&�@ 1987�n�� work�\~�X+T of c2rn Pu�y6�Q�Q��2fLas�S2�eI��3} 33p 0.�KarinArndl, D�&k0{\"u}rr, Gold<5 Z�u {\'iR0em Il Nuovo C�oDbf 110B} p 737-75� 9:mth� the,vLs �n� IZ,61} 972 Nov  93.sDohm's Famous Text}e�.� 5��y}� ntice wX �H,ewood CliffsE�JerseyZ 1:oZۋnNk"E[Ch3Sin�S2 ��Nosxy0d Co., Inc.; �e�MaV �#K5YU� �EPR6�p�D�� -623}��/.+ &W�SscP -3688 :ian&� ���y�\ -�85}v�� 18A$5*� {Im]Re OP�} � $pp.412-469�.� �� 9Intui�W Nonloc� �;fM3�B.in� �Q9J75)gBH 84WrobW cw+O-'255�@4V %�a�3z oh% g  H�iaN�bfA�q\ivide" e: An Ont��Interprek���qRoutle�_Az��!�ORz��r�%r,�i�� ��$136�Y5�t �\"� E� 144.�fl(ek�YIp6p)Y"� y41�696-7�1935) 2m mM�5 BornA� OMax���albPosoph��a��Ti�}&� , f 1949 *'/zTo��Paper} B�,, H.R., Svet��ny�)T]�!� �QL20} 1379S 90.� CHHS�\_� FA��lHolt, R�jShimot A., �X!�&x���23�a�69�G�- Hw JwAO � � Repo�X�a�6�41} 188�78]�L in} ��� D\"u��D,.�S.��\`� , Ny NaRealism ``�]or� in: � Erkenntni-~,�a�dssuHh& a�rof�{(Jeffrey, Co6�i�D �Gallav�T M.C.�N:r(2  � rnP �&50 "au�,&�{!yA�� 8", Luino, Italy�i17/w�fGhost�;s!ivQ�PC�mYM�J.R�E } <Wa*K &it;&P ,�Y19��dekgli�26}� Br,�E�OtA� nd.}r1?W44�\2'\ZT7�T5}, 38�`22�2�30BT�mRapA�� $V'ieme Con�s�E�� Solvay} G�'ier--VS#�i^ta�3V�53B�%(`{�P�U(ur} p. 465,Z5�ZZZ�T��} d'6u I�et�ineaire� la Mt � Ondu�SireN� �52�R d'Espagna@.�n�RE�:U� �cs:6�i��u Scho o�s `6 o' CourserN"�w  Ux�K�}B��{ual.�c B� } se�$��W.L#enjam+'z ��p MhMchusett� 76a�UD�'s Ph} �qAnj�The� 9��FU} forth��_ e*݂19����E&��} "� j� J&y4"s���X5<67} 1992 843-9072�a6 At.g�`3 �Aic 5ers8%'172} 6-1k9. � Ei�B� Podolsky A��~@V}�al6k 47} 777q *� Fq � 1382�Fine} ��i (Shaky Game:�,A<�8e�heU�Z =��Qhicag�[se :�TheTius} Fre��nb)�uh�9 A�&�Ɋ 28} d�#UGF F� {Thomp}R�5_6U%�37} 46�]�UGj|Maт , Murray '�R�62} 15a .Slea� , a�Aem�XX��A.}sA88%/� *� Shelly �h@�c}.M�[�� A�64f87. dRYa�J�a�1951 �]94.MT  G.O D.u "R ; *Q A&i [� 69]��Galax ]CHZ AJP�e.I ,:r%5�]058} 1131-1143��.�!^B�, 2�-�0AN 4i}<8} 33, SeptemberAP5]PHardy,dy&� JN��66093.=2 Baby Snak{Her�A�iq�/� �Do��daya: �=�F�zr wFR  Than$Plume ��P.� Lugubri�FeD�Uyu�;,y head�]L.G�8F�k� �D!i"� 13} 4 8.�*�.� , Pe�F.�?6�b��  $: Essay� Sur����}**��,Kegan Paul,!T; �p�~}q� ���R�1��5sM�j} &k�I6 2i�=�Hugx&i�m �3} , R.I.������� "+� � ��� }�Z� �L .! .%Jam��Pp`>} AaM �!^�&�{�[z9��7*X{Jauch-P��}  �@��!�~�=HelveEuMza Acta# ,36} 827, 196.�-&��"�$M.My)��f\%�� A�!�-�e|�I% &C �S��[,5Ne�oAr�].� Kitt c �arl�#E� Intr���Solid: Scs} Se�h E�,v�A�6yKo|��ck � %Sp�h�"!J.E�Ji1 '67)2i�1let*y0} Lamehi-Rach�dQ MittigV`���|ae $ D} 2543-5��76}sL��tt�quid} E � Ř>On%�%u5()857A�8*� Tim} Maudy�Tim /Qs non-�%:�^t�m: metM!�int�,EY��rn �d}�/Blackwez"� , UK[3u�,i��9.eM�|�" } ��D.U�9":/ 3373\0�B J � V.Xs Tod0%NxY p. 9Ys 9 z:� H �%:�" T� 8�0�q6fM�+ahXssiah, AV�j�B,�Ws I%�II}6�� m�c*�a�mڄ (195Ej� ish Jsnb by G�Te�k",+v5 1A�.� Bio��ErwhMoorea) Schr��;Glif�D t�/tn�:�2���kketplaN!Pagelo�29� $ic Code} S�%Q�r!-,��AR6U&Emperor}� RE�̓ 's newUvd:��r��c�Fe�umin�`�JlaIAuViH��"B 16�ShadojPJ!� !��t: A s&�� i= s�c�usc� n��z�P"��!��*�7 'y���A�g'e� Am#15� 07�90*~% Popescu} ���'hr�, ��% W7R 166} 293-�f� &O( {Sakurai} ��w bf A6�ced�32�Ad1� -Wes�Re ��"A@67�LSchiff}Ajiff� N� } McGraw-�hE�x 55��"�imp�.�$ ^lpp0 �����* 1:&- er-A tisJ� Harp̀Row{� �4. O �2 Sit}�&6�E1��4wissenschaften-�X07-812, 823-828, 844-84�35�,� ��.!gI�i(�4s"IF��"� "' �R" M)(�D, 323-33#+��*mqy�Dri�()a i�.( �&�"652.� �1%�Z=�.�D�. �.M�31} 555!�3.[2�[*) ![) 32�)�&36]uShankar}�^ ,�p�j� , Se.X,pum� �2�F-y�� bner�19�&)wN�*t L>GM2ٳE����� View} =�F!| ridgߕ93���,�2� Stai.- �!M�� '-�50} 58�bx&Stn�� �eFV bf D3� 03ff7N'N O5 %app, H.�3eUZ�"29B} 27�3�\\3L7} �P �NuF#4#!�l:� von ?~}.�}�� ��_j4sche Grundlage�:r`enm1k}J�1932.Nj:eB `� F6mU "� }���4 R. B��e#�"J9A+305-324a 55.� nusL4Fyci� ��lw�%� ��H.� /?ap�3V�VI�[e �T�%.� Wheeler� Zurek'�ul4�*i�B" ��s 549� 647,5z� }�mu.�is�9}�7�n� �Sel� ��El^7nl:� Bv Ally� Bac�qosB$196�+� �Ao�S�,W.H.�*o� �Q �� *�'j-rin9�� � J3&7�p ��p�eg)6j�:z.V�2-r�2 �Z� �#A.~ N6~�=~�4394161�85�5��A�it5( Chaodi*8H.A.~Cerdeira, ��W�swamy�C.~Gutz�e�^(G.~Casati (��� fic, Singn���1�j .73.�SC�BR.~SchacgC.MU&�� �E)�5�$32�{�~�nc-a8�6A6�{�|a�a3�{2 �E3MF *:} (�XJ;=����g�G. Ben�'%#-5A���?�i,�E�B�:�>�r|200A=)JPk�R!&Jadžr�>��~P�w�q�-~�.~eh՛ DE 2490 ;8?� JAB02} Pht|4quod, I.~Adagi��� �! J.~Beenak� nJq9�6541��7mCLMPVoFE8ucchiG=H.~�VCa�y�ucciolS{:�%�R.O�� llej 9=M�6M! 0462�8��JSB!]2� P.G.~Silv�ou�vlb 0552 �!jlCT� N.~Re�ru>>S.~Toms��29%�iH8M06U.ZPW[BTN1DAHWisniack$�2�!2 0452c�63 WVPCn>IE!7 Verg�$N{>� 7�B~)D6E�:}J{ED.~�A2B1�&:=>P�n�T.~ RFEI 3620ȟ2);.EZ2A�DM.~\v{Z}nidari\v{c��~I�A)�3W�{F.T�z2J>Q�345�Ce#Y�B%?Gaȅ��� ��. 1<�066205�PEWLR��mer� Y.~S��h �~�ii���!�ryJC)�C284.�;�WL!j W.~WK���B.~R�)W�t�! 05=�HSTB!^B�4J.~Tworzyd{\l}�;J�J1!we6GVHF � an\'q(E]e�E.~He*4@6�J56YPSZZ}T�� Seli��N� ~g.~� Q� Supp͂1O}G9AA6pBCVpf�!�G.~VeblHc)vs:�%-�w2��Y3AGMgY��m��$I.V.~Gorny��A.D�r2�QK d 6217�bCDP%:>�%�R.~DalviDP�ze   ~$ .���� H21"ޡ!@ %�GD�A�ussev%20)~Dorf�dnlin.CDNJ70$�>CPJ?B�N�2�, ��J 7752.* WCL9@m�D y �j�=eA1qA �GPS�T�ra&]�A,:�� 1102>�P^��Q Q�"�C04070B�WIC98?#��o M.~IzrailFKK��~ 2�M` mB32 0982� CBH���AT�e��ZE.Jr�� �I���O�: E.~OO� m � ŧal"K�} �_ �iS H@ omerus�J�ita�J6 Rŀ �S3P��n�D�|buzziV1~HuB��D W1kt3�`199hAY_VPA�� %7]�=8ڑ;Wb!� aJSHB80-q-J��H.~Hanna�M� Be��^.�},��86? FMR�)W#DG.~Ma5�hGeRistow�dW�&4 39A��WB9��.~Wilki �P.~Br\:NM4�G196����N Haak�(�a�O%�J Si�+*'P(v2ndgE (�X-�vl�4���iLCT�B8A.~Lakshminarayk(N�Ce I. RAt3�)Q�CLLT00}:VJwJ!�Lefebv��:�x�;�� !�{TH!�EUV�]��M66��91H Ada-v.�5�282�3);.#K7!140�']�.�STH92a-�Gep\'{u}��a� &v ! .E2�nŠ4�3�M=� m0P.W.~O'Connor�g.n 34$>`T� �m�V� 382�>�Umeno}n� NK50 26� ��!aNUHD f1ss�]�4�,A.*�+B. �,iN.�, ���\.bf{E�,y5*� ZZHE!� Zu"t+*T(��R)PGS}�&&�F%� " bf{7��42XEf"4 ZHWZw�^f�Heinfurt��u!{3030922BVK&�Bo@ V. Vedral)<��. Kniڂ�&�m82i]!�� KBB}Q Karimipou��. Bahra��sab fSgh Tezhc(Rj@ 4232}��mPB!<�� D. Bouwmen�����9�38M2�BB�C"R\q �GI�0rd�C1�Y"0Df Ke�'"�12Bg�� ~��]�Wie.\Q , Bangal"India} (l6W8�1ĺ5EE��A� Eker6�L6��xIQ��EB�(:=�:GE�12 H2�BWJI%.!� Wies_�j\�2�7��2\GV�K�-tM)�L.��� b�7�[123195.6 HIGM�% Hutt� N. Imoto, Gisj Q�T:.}Z�*186 2g KI97��Koash��jf�%3�T1>t a8ru$\ss$jYp�30��4u.LRGVLou!�X�ZLiu2U�i�323��UP PBTB����oenix���Ui� �Y6�wnsen�ˡ�.�J.������ D�E#2c XLG}UXueR���G.A�Gu�S��>�22� >� LCA}��-k�, ���]�Wrdehali,"4R0 8R105.�(C��a�Cab�-^eAO0ӎ2w� 5eZ�Y%�Zh-CV�^]� 3631.��L.~��24RED�}A�SEXVzA�03B42� Q-PH6)�S1`0O9�5 LLKO�  L��S J. Kim�X.fR�Z E��2�ZYCP}�� Zhao�� Y%��) �E�.g>� /02110982�}A�H;Rq��.jR�I'223y2' QCQI�x&=V�8r>V�'&l%o6�2�"P r�!A�Sp. 109-1f� �B��,cprime{$'$} > ���AntGazMu�� wa%X Aa� J.-P��toine�Gazea�U:� C,. \newblock rr�%s��their�Xiz%@s:C�ath"!ove�<.N;"� M�c)�0}, 7(7):1013-!7� 92��Al ��Syed~:�,ean-Pierre A灷. �B�:�, wavelءAR�R5# Graduate DETC�hmp�A�ic�#p��e&X"�$ E=.�S��on6�A��.�Canon�"�&)�)��Q�m�"cs.:%�"m�icy 232(2):29�w31n"y%�t-ZVA81z�AH %.M�use.k�M�?n�%0 space�"�re"N�Z� Inst� Poincar\'2�,ct. A (N.S.)R>5(3):�P-2/#6~� � 99} . ��aa� & func�"2�In)aGen[� ized),&��"dynam%�y���(Br��" }Ծb399�%�C�� \& �G/CRC RI�Notesikd 4$s 26-c�N7 , Boca Ra#FLE92�8rnold90} V.~I. .:�aߕ m�k��laslY�2Lf$!b7uw�'�fI��$1�3Ru>/$n original�.K. Vogts�a�A�s��ICorrecw"�$�R�=(h-)�"6�] {Bar8nlIV�.O��{H}il]7I�`FD�an *���BgrY u�.]%o�P.�� e Ap�N!�.}, 14:��21�U61.�BaxҐ4llLiebeck86} P�R �Hans $B{Ves_ ��u6�O]�ied�I �D"�0�#ca��T�&�s lare�O`,sOF��I�%62���in72} F�� .�C"��A�Jra��symbo��"�D.<%~Izv. Ak@�$Nauk SSSR �Mat!�36:113+�167�72N�5j��J�4[A?���B�IEł�40:15�c7E c���8#na��8BS@�P:��r!=ap�Jx6��t��%�_� �Au�PrG�edUa Mark Loew2q� BransdenJ�in$B.H��  C.Jb�&�).#P �L�^�8 low,�.�2�Brodlie�mAl�$ir .^C�!B%�u� �tx .1ItnZ�a��rUl%�82(8):1707--1731%W2n[ �M�n�No`e�bnk��� Y+B�J> 45�34 34 �42'-P 4.1}r�&0��&0���or :�� {H}e��$berg group�beyon2��� XIthrSymmetry"�rin%�E��&eHe�4s 0�Y�ToaDea.Yi{Kisil�+[:N�V.V� sil.l�C� ob-��Y $p$-u�.3�A�2-�H��Re34 ,V},R1N�36.jPa ��Qw�E- t:arXiv:E�-ph�o^.�Cocoli=' oViggianoa�"�t ".�Asqueeze ���e1Ad�4p�8e effeV�in coupl�osc*H��nd *]� " d.  (Melfi��Ђ� ƍ~�Ze�A. (4.!7p>(� 77�0� Arac� Rom)r2�Co��Pgrini� $Richard~K �D dio +.N�M�Q"�U@2/�aa��/�N�uW�s,2�6` Craw��!� MGA .�T\ l����ȱ.!�z gy-deg � W :A�� ydro0atoF��J�4A}, 62(1):0121��.�r�Curl�FW�#�Eas2��` #�Cosmas~K��.�Fe�) t�� inde��t {W}�-Y|.;%�� D (3B 58� ܛ" E�8.��H 47} y��g�HB[aaV,VG U�c*88"� �4����T>:�lKaѻDkovitzMoshinsky88}��Dirl,C.%)oM.~..�J/�&��6��9:Y��nonbijec�KcZ+A���u��#W.�%�,�Ax21�1835--18�582�Egorov� Yu.~V. BWLin�������2j��ǡ�$cipal type2�2�Soviet.%ln�a��BurW>� =�� :� � by D�(Prem Kum6 Fedosov�Boris .�Dl�)n# :ի��� .4��� 0��i�q br��!Z% (Man�i��1a\�� 315!S%�-=���4 --7. Amer  So�m���Tnce, RI�D2/ F��89} G^d�� .�~ Harm#��si�ph��2�e�etoz�4NJa��6&? Fox�Z,onald~F. Fox.�G�� :�.'�I�'A��09(5):3241--32�869��u�80} G.~{\@*4}a-Calder{\'o} � > cq� &�mciM���813(6):L185--L18�:.�Klalq!��~ E�J��R. *.r:���*s discretf a;inu�G�truF;2�3�91 �13�oB�zeauM�[aua����P�al ).�jZ�a"7��| .E�� \'�!ceҎ h\'e�b�wA�9 (Dijony�~22 u�0 x StuZ'� 131--144!�u�j�bl., Do�b�T6�,elfandShilovJ9I.~�kel{I} %�G.~E.�Jlo2e`.2��. {V}�2&%F4ress [Harcourt�ce Jova�(chqB ers]6� (64 [1977].sPr� t�p5 i*,R��!Eu� g aleta2-%Vilenkinz'N.~Ya � ..��*4�*�*�;�Ach>�~2$ Amiel F�02Eold�4HL� BC"�V� A2AQ��]2A.FFv9n�:OS"�M�&�م Gota��'~�.�F�or�geo�ic���E�{V}an&ove�S��F�v�19g 139--1רO:�8radshteynRyzhik!~IY2Q �i� %.�E�T�A(s!SF� o6� �� B�&Aa�en��R*ia %�9 Alan"�Y=U orpoa�c�b f�`&�T` ;;yV. Ge��mus [>]\M�o$Tseytlin [ \u\i ]r72"u1� minSu6mv {Shlomo )B��k!;hN�4me by {K}epler�}}. \newblock American Mathematical Society, Providence, RI, 1990. \bibitem{HanKimNoz95} D.~Han, Y.~S. Kim, and Marilyn~E. Noz.}�@{${\rm O}(3,3)$}-like symmetries of coupled harmonic oscillators.�{\em J.�h. Phys.}, 36(8):3940--3954,�5.N�Yeh93} J�Ma.� �$Leehwa Yeh.�S2�Xtwo-mode squeezed state��<4(12):5493--5508�32�0epp74} Klaus .� The class%�\limit for quantum mechan�0Cambridge Uni� ty Press,�6�0 contemporaryA�E�.�DKirillov76} A.~A. B�Ele!(%A�t!�y!�repres!De��r76.dNJ�Russian by Edwin Hewitt, Grundlehren der �wXschen Wissenschaften, Ba5222��A�f�Meritiude��9,orbit method.�%�Bull.���(Soc. (N.S.)�R$4):433--48��9N�(Gvishiani82>�E]A.~D. &B�i1m �probl i��A�nalysi6�P , Booke�5ccs.FJNew YorkA�82.�z�@Harold H. McFadenN94�n�R2�Q�!�noncommu�ve&�H. {I}}, volume~22A�%�0Encyclopaedia9�cience68nd4.Fu�{ concepts.:�enVirasoro�affine �0, A t͇�|(of {\it Cur�2�m"� s2� dire��, Vol.\ 22} (m��), Akad.\ Nauk SSSR, Vsesoyuz.\ Inst.0chn.\ i Tek  In� ., MoscowE!<8 [MR 88k:22001]�J�Dby V. Sou\v cek, UEedi�qby A.q�69sil96�XVladimir��K.�Plain"�s:*�A<�.2E4J. Natur. Geom�Q9Ň--1Ʉ6F�9}v�Waveletel0{B}anach spacJ� Acta Appl�] }, 5�79--109!e>Psil02.2z�DMeeting {Descartes��@{Klein} somewhere�Da>]�..In��tFokas, J.~Halliwell, T.~Kibble B.~Zega� ski,%�ors!�%sHighligh��2�� �4 , pages 1N 0189. AMS, 2002�E- t:arXiv{a,-ph/0112059}B�0~3� A1&- bracket��41AI 63-- r�:�00703:�)�1z�$p$-{M�} as a p; al�F,: an introdu�#.�%�J�  A��$7:183--204%|2�6|e_%}2121016}lauder96� hn~R. .�CoA�nt | �0 hydrogen atoR�A5 �29& L293--L29�6� W.H.2�cA�fifth�2002�M� nez8�T.Diagramy solu1� for� osci�.:�European�� }, 4� 8221--227 (1984)!x86�DelloMoshinsky75} PH%�M.~ .yNonlin� canoE� / K@their��*e ibB�.`�JA�*�e4}, 16(10):2017��2���O \�4Merzbacher70} � BjQi6�Joh�$ley \& SonN��.��0h61} Albert M �{. {V}ol.� ./N#French�\G. M. Temmer. North-Holl�.Ŋ!�g �� AmsterdamA612Oos)6J%�e2. Regulariz%�a�${K}epler's� 1� averag� h on a�anifolFxa Pure: (23:609--636�72/ U�,Seligman78} .��T.~H. #.XCb� to a5 B4angle variable]� J���Ann|  $114(1-2):2272�8:�i��79����J F�T {II}. {T}he {C}oulombQ!.}e�> 20�402--42)2`$Perelomov8�BZ0Generalized c:n a��app"� 6sex@ Monograph����VKB"�86� � @ Olegh Prezhd�fr�MixaC1e�FF=�-B?o62--17J; ReedSimon{ MX el uBarry  BgMethod�m � "K� ��I}2`Academic!s�Vh [Harcourt Brace Jovanovich�� ers]*L  Ja&�Aio.0.WRo��s6� .~E. .�(Rigged {H}i��/E1�m� .8E���.)�k :98--11�62-Ruelle� Davi .V-)\. �j|1�150�d6}Simms73�.{ Bohr-{S}o�j feldL�% iz�!& pl�cN��2I�PrZ&%Philo�oc!%(73:489--491�72��D.R��Ec�A���gy level%�j ��N�In �Sym� a%�M�,t@ XIV (Convegno di��Si! t� e Fi�DC$INDAM, Rom 7� 25--137� 61, LondR 6z Sniatyckia�0Jedrzej {\'S}.�%�Z.�p%�b[ j� >V Souriau!�Jean-Ve-.�Sur la�m$\'et\'e de!�\'n.,���3�360��Taylor���d�r .�%�Nz6Nm��6�Tms67} � 8c}}ois Tr{\`e}vJ�Top�EvA � , distrib� �kernel:�2�� 1962�HVilenkin68} N.~Ja. B7 Speccf9i� A�a�&�group>� �P. I�2� Bohm�@S.~Wickramasekara�A.~!.�= ]2�g �rR�%*� F�.eEZ6�05(3):807--829�2�(Woodhouse92%}M�qB]VL2]lClare��Oxford F)>K &w1992" E�4�.�4Zachos02a} Cos� .�De"�)R� : . liv work!� phase-e.X%�2M6 � �17!�297--3161���E:*:hep-t0112�!Zwill8!!�Daniel B�Handbook�&integr�52�Jon �Bartlett)fs� , Bost��MAa�!�4 \end{thebibliH 0y} �\beginB{�&Og r} G M ReAKo�A3 {\sl)@\� T\ Lett.} {\bf 70} 3103Tserra} S LlQ(Lipparini EV7 VaM$6T40} 667Sbar�o}!  M, PiGW% S 8Hern\'andez E S{ Navarro Jy >�} B �56} 899.w#} R& PLSchuck P� �aoN�!Many Bod� oT} (qb:��)��s} Arias�$Saavedra F!�M, Hott M%BU��Z- 62} .�$roy} Roy BN P�2I1��5} 396.�(koc} Ko\c c!o Koca �,K\"orc\"uk E�d L527\\ W� Z�����10.B,alhaidari} A A DV--�A��$66} 042116]�Hgonul} G\"on\"ul B,6 Tutcu D�\"Ozer OiMo" o L�5M 17} 205!2_F2i `$Uzg\"un F Zd:q17} 245.�,cq04} Quesne�(Tkachuk V MW��'7} 42:� gchi�%,orH"P,6r4Roychoudhury Ru%0 )0>�,9} 2765 \\ B�a Czec�|��54} 1019=�yu�)�|Dong S-H%�Sun G-H�R�3'$290a� Yu J<I201gZ=5} 19.n bhatta} Bcharjie��Sudars;E C G� M�0Nuovo Cimento �L25} 864\\ Natanzon G�{7�{'�aF� 8} 146\\ ��ain8 95U\V3!68.da� ssidi�  YE� ursey�!Inllo��86���, N.Y-� 167U�JW1x� ]����N� 1} 5e�E�fi�M-�u8 1991 �G-�R(24} 3 Q.4l�?7} 380.5$gendenshtey$G L] 8�=ETPqFf8�!�DC wskaA�KhaE�$Sukhatme U� *�r�1} L19.� coopW C� bfB� p-� 251} 6dmizra�eM S S� ,margo Lima J� (Dodonov V V}q2q M.�!q72= spiriL} S  VAmi-�R��%s69�N8�Z;��A6$A�242�!�}^L� � 2�Q��26} L901�,Barclay D T,�t��0Gangopadhyaya� -�, Pagn.��]593Jb ��48��8.cs <} ]{,P, Rasinariuͦ ~!t<-t13� 234} 4 �B�$Mallow J VF`.~e��6 ɛ�I11�8.�,loutsenko} L  I,26, Vinet� Zhed� ��.% � RT��908. morrow} M RP86*A�"� 807.dribeiro�  Filho�"F� �(�$Freire V N!*��Bra�*Ux}-�6��8�Ycavalca�C F SAfCosta zR N> :�de 6" F�j�5�[32.�Hvonroos} von Roos O���F)�6=��754.b bend} BenD�8Dukn B�-/NW1�62Zbl2rdU st�&��8�|ND�p569.� ,zhu} Zhu Q-G%-KroemU3��3519 =�li} Li TM�Kuhn K[j14��760J$sukumar85be�  C�V8�ULZQa�L5.� cq99*� 19q�~K32} 672I �� �ʠ291.�kwo�K W%�$Rosner J L!�Qrog.\�-�Su�,�� 8aZ66��r ��Inz.��a"� a76.%nie# N M7�� }�?��� 127.B davi-Yes P C A8Q Q�5M� } (Ld: Routle�34and Kegan Paul) end B�� r� �v% Y�@ {nocloning}W. K.� tter��)Zurek,/He \textbf{299}, 802F&2.;5L {buzek}V. Bu\v{z}ek!$ M. Hiller>:9%� AT54�%844T966T(gisin1}N. G QS &ssar,)� P�U�7� 2153U76ULbruss1}D. Bru$\beta$ : it{et al}2[A ,bf{57}, 2368W8JW26W2H6�81�01RL� 2}H. Bech<(-Pasquinucc�712cA 5W!423 _96�0huang}Y.-F. H ��.6U  bf{6!�012315 (�16W0cum}H.K.CummiV9�V2U: 8}, 187� Y:[s�"}C.;(on, G. WeihI�A. Zei�Fc58�2n a06�$dik01}A. L�-L� es, sJ. �9�0A<ouwmee;', a�e)6}, 712m:�%�(3}S. Fasel, 6�'9!'0^'me*04}F. De^*i,�3Ba� , F. arrinm$��13e5-41A?8-�2);;.T,D. Pelliccia�1.\-� :�92}, 06�46� � 5}M.�.ci6�-��C 6��^ft4^t!�<0}W.T.M. Irvine,AV: M�:A.X Dood �D. .  �N� ��I:� cerf��AherfjIE� 4497E\:�0niu}C.-S. Niu%%8R. B. Griffiths2Yy�458}, 4377 (199:�murao1!�M ,!�J� han,! B. Plenio) V. Vl m)�mA]156l:�l2l�^)m��6�Y032311N"filip}R.� ip � Di����05230 D:�bennett���� �;2Q6�70��95�3+�, E��<�W ��i� bf{39Q57 P:� rarity}J.�-R 9Pe1 �6�65�h34�=:c kwiat95}P[K�Z7Z433Ih5B�ek9e�Zuk�ie���a�H��nfurter,XP @"��* 55}, 91%s:o4pan1}J.-W. PanB�:n42AX72I3).V�� ��m� l} L�ndevE� lf,�9Op&&l62ce%� s}, (C�Y>5]w4{Lindblad} G.  ,�(un�t�(4�&119!N 76);a�A. Bland1B� C.%aTn-Tannoudji, Les Houch�8$964 (Gordo� Breach&�$ 1962Yblatt}�B �.+<S�2 � 5��(J. Dalibard!>�aymon�$J. Zinn-Ju�, .�LII�E(, (Elsevier�<2�!Am� dam A#.�(PRAsolanaliA�}��4ava��� niscal�5!� A. M�0na2 � 6!��08��.,{misbelief} >ZF..w�$iil�oA.Q1na , IJ.a. B: -]�Sa, lass � � S9 �4.�opt�2ients} j BambA�!� Vallauri,\M. ZoppiN�1� 1713E�5); �A. Hopf!�-.gou K(S. Varr\'{o66 43� 48��198a�A�CabB)Ŏ.}mi -� 4�32:399� ��(Sch�chter�J�=N�#J� E 8820� FVv2$Malkin, YuBTsidulk-�Ne�Fisch,� ���8�40d �.�*�/ LA} �,,Tangdiongga � 4.} IEEE Photon3chnC3d1!@1196 d!S�8Cha2=1;�H��906M�;AKar�'�,�G 1A�77�Z4AY�5nD3Opt. 3�468�99.Braunse01} S.L�2.��-|�495� ��LaHaye�M.D( haye:U %� 304}, 566� 2X$Zubairy03}!2Ahmad,!�QuiM.S. ) �H `�J3� 2JKim97]S Em @Il��5�31"> � @{stig} S. StenholFScr-0Te�5� 86./caves} C��C 2��$23 1 8�x*�A&e  SEBae�PRadmore)u1in�e��l!Q�I�Y (C6f),") 1997.�$abramowitz!F A�I%gun ~.)(���.l l1 s} ( =�4Z24matsuo}�M 23-�4�@3@ 2� tavole} I!� Gradq ��9yzhik �T�0s�(|)gralsY& ��P%?�W �8�*�= San Diego!;2�,agarwal71} G�A ��!�828�1.~A{2a�]|�� 1 Am.(�Z4�Z8%QN`)7j13}Y�LRaizen_LDynFirst_PRL�E(\Name{Moore��L.�0binsol:C.,�rucha��F., Wn*ams P.��\!W _a�,G.} \REVIEW{>� <}{73}{1994}{29742O@Christ�Noise�8} �Am. H.]H,ay R., Shvar)I. � Eensen Nr�80�8}{4116�@$AP_Bicolor�00�~) ot J{,zriftgiser P�arreau!�C �De� e Dv�5}{�}{2746�$Darcy_QRes�1�D'!lBz odun�M., O�4halerK.�ssettari )'Summy � v�7�1}{74102:�0irikov_ChaosC} KR_!�Rep�8IZC 'LVJmp.}{52!�79}{2632e casati2} N G�YV., FU.J �,Izrailev F.Mt Lect7;tes? }{9E�{334}; gWimbergV R0Buchleitner AS� � A}{3A�0%.186� �_I�HFreqsQ!- RL891� #�$Guarnieri Q�(Shepelyansk�L�   }{6%O89�5�$Gl{\''u}ckE*Kolovsk�GR �Korsch�Ja"�'`51EA�5`6", Sirko� � Wal� HnX16A90}{352APIeQ=p_CNSNS_�'1=>�Lig!A�/}����7(No?zNum�ul.}{8%3}{306��^�Klappaufa A�Oskay�,�c%�A-� La�vT81%88}{1206@,AP_SubFourie��2^3='��)�27n�AtG}{2241:I�(_LocFloquetm9�` "%ei,.�!EQScharf Rr�64%0}{6Q�WNVx hDo }y9G J.� � .}{2y8!�4202�Fis�!@DynAnderson_PRA841�Grempela���Prangea�E � E Z�A�_�8�6392�$Landau} �� u�(Lifchitz E.$`N{M.Qcanique � !z@{Mir, AL Z Year{19662{(Altshuler_L�9C�F�R��9y�sa'D �:v7��3}{40�PN; Pv�"1 z4}  D@�oMod�  7_LF�giv �on�0P. H{\"a}nggi&L p&�q 229P 98.[ {weiss} U:nR�it{,Dissipative �XWorld�tific�32�{legg  A.J��� Chak),rty, A.T. Do%)3P�$4 Garg� W. Zw�S,b=?x82�{alicki}aA � K�ndi&h��Sal 8F�M(6} ct�BNi"�?)F bf{2�9(�:.�V:�r5sen!�A�e�I�@C�F� Comp�Pon F �I�Oa�8!��2002�{carm�?} H!�C�An OpenQ!$�T to"c"�B N2=M�N/9>  ake1uH , \emph{�>XTre�)nt� 2�by .�AMa� E]W}�&/5er Trac�N&}7ics�="s/R�76�lax!� Laxy�vy�12`234� 63);IK it{ibid}.s1t 1� 66�h!9EHR�ibold2z&�31 2462�'82{suareza� S �S�@yi�I9penheim� Chem��5(9�51=1.l9gnutz� �G�� �, ZTB)bf{( , 26�6)"{gaspu&� QM�QgaokaB��W11��6�bv�M.2�J��9i-! 0338�2-!{wilkie}W 2�E�6!�8D0);2%u@��773�1>T)b 1033J�!{budi�6A��B 2��A���.�cress�S�ff�k$dkiewicz!� D. C (I^(J.K. McIver2u7� 010304(R)x2�{lJ3I� haba�>D�LZ�7A020101X6$chebotarev]M.!� �C.� " !R.B� ezada, MH �>1��10;96�$footnote0}� very s,TZ�� $Q_{U}$ (ly �> d���]x�$ rate)!;M < adiab�:lly fos, the �^ iona� tatex$Eq.~(\ref{�?}2��1 �,non-factoriz�:ini�\�Pi[s betwe�We�U, �> evol,@r�M`L$ be obtain�usY projr@�/ ` t�| s; this cas�T mapp7on�I�Fl ^random�@ on !54 is also possi�Tbu��r!f6���!Qd1�o)� haveZJbe!$sidered. T�&D�` extra inhomogeneous term�g]Ked=9F� , similarq6(one encountwM6mV�3}j typ�As1�V`^super1�H $\mathbb{L}% (u) $%S sum!�|66s, h�)��[�`spo�g I�.e)v�[U"G_ =a5 stru� @see Refs.\ \cite��,�,��,�V.�Q�4} In a !�ralMcYW �(cal{L}\neq %E}-$% I, �(E}$ a co!FelyApi� 2O,�stocha&a ��c onlyARestablf %�a!�mal way O]I Va ab proced� )) }>E!m2�Uds2�d% [\rho ]=\{$I$+[e^{\kappa9 $L}}-$I$]\}+$,5< )$$ must be �@nd�a�Vco� l paramet�NY�,aproximada})AhrecA�a in�clcin whNJsimultae[ ly $ ~\r�Xa�0 0$q� nu� of evtOuni� time goaeinf��e)�5< wbe!r �l���s� k�(��"2E $f(t).�/ �$\)�% {Coo=�X soci�to%� waity�.�E $w(t)$�y en, while2Yc�}AcbeMMly��)� f2  it!�notA˥;(��e�7 it %� numeyfl m@L&sol�he 2� m� q�.�2F� dou�P. Bo�ud,;A%bxC. �Un."�,it{L\'{e}vy "u $La� p2~  Unj�a�R45} B1xep fu}e $\theta !�!Ndef��as $% =1$!� $t>0$ �;=0\leq 0$.#h� S�!�sPtI}$|_{t=0}=0$.nzo�-� A �T� P !Zo 4� 5774� 6t pickl�/J* e{SeP !�p�! . \&�*�!)�bf{�$7D :: herzogH Z�5� 6�)196I&{al�X y} Pf A �tA: �6�3! 6587!: metzl= R�" %J:[f�& \R239Q �6�ni��!� N 8, B.O. Dabbousi�Ga.w*JMac���K. Traut� �]D.�arisIfL.El u�IN_*�(8�-82�/{t�P. Mi8 Imam�Z�D�&s�-P�Ca.F. Strou� nd S; BurattoB�040�9� B� brok�} X� �r ermi�G!�ssi #. DesbiA�E�P,ch�Y�M!X+1�v�tA�I19!� 1206#20: grig��iB Aquino,xPa�hlla)w�+.��!m!�05m61 kuCM. KufD� Fromm, H.�!�3G�$gh!�D.J. N! �e�,* }1n2_%6s!�g)c !|YPnen],vPotapov �A!�ws2%�x8a�137Z9!b6t wagna` M. W ,Z Unit� B"�I�'Solid�e{ic42]W,&J',5^&*�rT� 4v 4:4�+.�+,�MattleAk1&m+..�+(A. V. SergiD:E�$hih!95)�it~!%�&� 75} ,& {v�2A. �Us,�J0^a"�8D13*�5 {3}*ourenna�/A� arls�)� j\"{o}g� O.�A� 64} 01230*�9 {4}.Z�3W. Titt�1��F�A� 61} 06230*�: {5}G.�u1\�Li��\tShieILG�2, �e�it{�=!�A }�.�4�..�Arnaut�H. %�G.!�Barbosa��2.V= {hPke3 ranke-Arn�S�A��%��lPadw�L. All� ] NL �5} �22 MairA�� Vazi�)GE�Ri4!GU��g412dL2e Tg ��a\^^2^�G!�:=89 }2404.�H �gford}�b� �B��l�M.4 Harv��. O'Bri!HG)d ryde% Gilcw#�\9B�M� A.\%+hi� 2004��93 }05366�1�/A�Tor�5A!� exandresc�2L.n���;Fk.�8}�� 301(Q�R}).�HG}X.a=ReY~a(%>=q56q%�}=341iIit{ }.�> {E�}U��xW�+ijers��n%��L�k eeuw��A". Woerdmv3XI�Z�45} 81.�? {10}H!@%_Y�yanva%�:ZN` �aJ7!Z23N�MPanI��%Oi1@  JeneweP :c *�1!�F�%qyk 91 }22790*6M {Arlt�A@rl��DholakiaK %���5�Pŷ9 �ZY5!C50.EL�p %�!i��i4.�SAb��� !��Zi85V�:�8�A5�6.�RenY� �f) uo �Y Fry�m(B[ um&:/�}\)�A } 242�HorodeXI�; ki`^��z90}�ex!} }/7.�Mozes}S.EUO�!E��Reznik�J�A i�bf��e���1!H}bf{Fig1�ran& ]Gau�a�a�f rougP e le3uH$\omega_{0}\left(  ^{\prime}�) `$z,z# 2$#btwid�tnd��a%4f�t % aistPJ� b�Te (K) �reively =B�(m are shownB$Eqs. (5)-(� i<9B2} Our�ee�nt�f!^Y g pump �$ �@ \lambda_{p}=351.�{ }nm=1�argon-Xl�i� cidpo�@BBO crystal focusx �Ax( f_{A}=500E { }mq !/ex�, we mov)� BQ le f�_,p�f��|4det�(is:�0a/His $852$ $mm$). F i��mterPvc�S'(bandI0$4$ $n3B��Ul� unt 8 R �bes when�� of)EBig�$In (a), (bc), %��%�> $100 ��!�E doJ^M�9r datɰFcurmWr\riv�w%�quotedbla~ C* Fit2r�\�y� value�Q�u�,z]�( R�,u�}3) &�s1�"�%�(down-conver�l� :�a� B ��"YEy_Es}e$input surf]aof QnA^�p,a}< b. c}e (d),(e5� 5f_{B}=2VRg!�a B��Fp,d}$\)�e}Dd}>� e}$.V�9^f�0*/hom87}b5K�5ng� Y. O"� M�9,}6�  ��{xX 59} �57) 204Oobib7}shih88}<�C� l� �8ZTS 8) 2921. St�x. 95} �T�= BranDS? Monk{ �I"�:,.yL�u5�2 4y95) 323�"�tei�93}37M�0 , �. upR.!KChiao~@71%@93) 708�br�4�S�dAFn�2=KA85 [5) R1727]m  96} AMBP �� 6&n�76 �6) 4656.Hklm�5�)KnivB R. Laflamb!�� Milbur��%�40As�`�(ralph02} TR�P�L"3T=@Bel�<�� � >�AO95}s �2.�z�C94I*� Hu BernEC)KM^Hor�rJ.R)m& �-�4) 23�kU�(walborn03a}V:P�,�N.�AO�]ira�  P\'adua �C8q"�]Ae �90 �3) 14�=pkwiat�6�qmbV�4I�,1�d� hong����E }�B�1� �M�05) 240yoq�m�98!'6� �w to R�L)S=+>r57 �8) 3123= saleh91} � E%�W}��a#�9ig=\.;=P�9�W�m,*`�Rx�){��{�� "� ���-�Z�.��m�/��5�%�"@E�~�?v�?Ne&�{�5b.v�� B�&�H�5& . va�} Ve�7��@���s�*mu%��a%2q��AY}�++:�R.%Thebal�+�6��=�ռ6�4) 02381.�aG9��R�@R� &�J����"1)�2ir��ų,/dN��=k6����31.za�gH��f�W=F.��� `282�b �`2%�.tFB�9 .G 5380.�f>a#g>S��.t:�A19�>�R�3382�t���q��/I��10�?�I!࡝B�IaySm�R-_E�i .����288.u]3 H�,n�?dBr�P?G�,�leau�ozy9�&|Qe�(eLZ�7!�1� 18952% X �2�A2s nR�,d >i1X�T e R2472=Wkim�TA�Kime� Takeuchi,��Ya�!t ��Ha�-kP3�/.l�m�T) 902.�t _wS.n#�Y.�vv1062ch�Rs�� D. A %1rhoj �� liwaG Banasz/SI��Walms��tFit� Bi Jacobq�Z PitT#%��G�"%� Jour�IB6�C�Q���14?{� F 3bF� Z�zC Euro�h2��c�� 6a%N:7�fb10}&�{S�yer�A} z$, Soklakov~N.�oSchacka\, {\emi9�\\U�32�#3R�0 esB:sa0Bwe-rpint�k�405080,% 6U#�7foOm{} � �Osta�Ve�-�3� 219^86V OmneR(8} Omn\`{e}�R5�# 893, 9357 \82�($Gell-Mann1Z= �)tH�t~P@\lq\lq��M%W in�L�of#[m!p y'',8%�6 lexi$8 Entropy, �6�!�5of 6�6&!KW�yp9 Addi�!Wei�$ Redwood CaC�l00, pp.~425-452�oDowker��} ,��BA*��J.~�A��"jlD-�4%�158"Imq�5_�ՎnRhM m5 3345%�:C7)�19| 5�iHa<�-edings!i!x11th N)|4omiya-Yukawa S�tum}څEKgGk!!0K&itomo, )8(. Ohtsubo, S:! tS:Singap�F|R.(5q}r���D}-5RV050e;>2�q�G} �c��_JzE-�6%�036212�6d&Poulinb , D.�!uB�!��vQ�W`O72�Diosi��}  �N��_ItT17""��ON�9��� ardo�E~.~%=A.~F.~�mit#em Bayes��`y\/} �C�/HW Eng E �q2N,;C";�|� wI.k -� �d?;+  .U\/zK"^;[6`+Gr�ef L.~K. , `` o m�# help� se�F�/73a needl� a ha�ck,''p(�b%�\)�7�+ 32m�724Biham_ } �+, O. �Xir\+M� assl���# da � �'s19 S�$ Algorithm �n AI�rarX�5$Amplitude �(D*vB��I$60}, 2742��6.soksch1���q�%�``Effi� tP� pre]� � regi<of �x,bits,'' {\tt�s��804BN=�f=99*K no-cz]��K.~Wo2{] ~H.~����b*{]/.{]upw�8~)% WA�[, \PRL�< {111�A9�D@mp�:~M� AS.~Popq% =7 B25 =! =holevo� S.~Hmy�a���4 X��al�1sE2*2�-} (f+��la�"�R�)6 0helstrom} C.~ &�>q�Dev3 �� EstiJ?vB�(Aj�x7� 56un/ ~Par;8nd1DReh{\'a}cek (Eds.)F�!#e�}�~:^?s�@o^v>�`: ��#49}N�>�S25&LE L.~B6MH� ~Kim9 \PRA�*{1*�E006�Dd��} R.~D , V.~�\%xAE�EkertMlqK571�D98mv� lpt}!H���9�NP�Wscu5%R)rran E��F3�H};B� �blisdiI� J.~R�T d, ec�. 102�}9�dr�-1} N.~G*�`:H8mD3xI99n�i�%A{�I��3J-_5 bbm-�} E.~Ba�b1 �RGL -{5230�H0b~y�@t)�3}{ [zK001b;~5 ~Bai�,R.~Munoz-Tap~' T 4}{022305�2�ps�A.�P\Scudo�6�M6 �F9 ajv}A`Ach(E'|n�4G.~VidA3a'; ~р4>s 0503�2�);Iq1(.D.~Thesis,.�zof6i Barcelonay�unp� shed.�ps-re�#�� 7}{1I_-BZ��ZB!�ˇ���! bf{4L 1235, 2)ZPNŦ Lind�+2�(D.~R.~TernoJ�)�8�08��J2�5aR�UL{!)3Xf��= �9A�03 >vPZ�2yi��hHVm�6XUtt�lDa5E{%+~RudolpR.��SpekkensA} ys.~@ ~ ~{\bf 9�@!g 0+� 32�jones}K%��{eOA{5VM68��2�gill-m$�́�l�S> F61)�1�5J fkf}A( G.~FX:�Senli�M.~Frey-r.e3g1%��eU hann�7 n}Th�� ��.A�^{e� 3�J�PJ�Plocal��L�L77904VRmixedR t�-�ig 2+,A. Rodriguez1RA��Ba2�embprr FE I H. NarnhoCAnn. of�� (�r)ebf{ 3EY�e�6japos-1}�+ ayas��_A�?���i��� Af�.� to At�A{U Cram-L r-Rao Typ$ 2Bopin"{ Commud�� �^putx!9MeasurY<"�F�by Hirota,���Y� EC��W(�bum.]i�%NewFUYo,4Z~y�M.~Oza,JM 0118. )l?KaT tsumX \JPA�P {311��2R�K. Usami��E��g��y 2231IG3RD9�%�E�F�308152��reH � M_�v�5C.~uc�2P�� ngtaJ)F!�U�z~14�@�G�F�J�Itlei�,��A#S�r��pc bf{9;G0I�6)wis�YK�W KR ~K�Vpm�56}{94- qJ�5� ibid*�05� 2169�8)*} �ED�Berry,� ML���JM Bresl�)�� 38��VXI6\ �65��38� �7�8��y}U!�onhard� Q/it{i�a�a� � >1 @B�.�Y�VmL�667.;e"�-sN G.~�5�i�L{� 31�36�Dy V.~Jame�M*Je)j4} ( 1V 0 wN�A�012�>�A�.~"xBD�L{�R19~&�)>�E. Skovs�#�%tapel���2 Juh��a�olm�\>9��90I=� 2� @qudits} Y.~I.~Bog t1�)e.%fA \8)$4:hH%mHofz� Z.~XJ.~2Yh�)� ~Rau� LA{2o2xR6s*�I�a��6� �� )q-p<1eU!�6:J� ur�se�N��@KAc "/ ed�dsh R. E 8it Angular Mome�^.�M >n $(Princeton.S %�1966y monr��W# nK��  ("�C0at Aut\`onoma�)*�  Funbias� D.~Iva�,��G324�82Z>�Bޣ~F�{�� {� ~e-��fh36�B:Ccd} �+ eJ�/ommCit{El �*5!orM2) N.(2^�`� F� ~ �72}{3432�c�Gr�;� �M�.̗%$� �"y_6 ���4xV�/�je?64BB84} Charles~&�!%cG "�!.&���crypt��:, c key�5ri��McoELng.JI� emJ c�5XuP%f. on� pu-"�US�W mbox{Sign� ��B�F6�75�9@�gallIndia��ce�H1982.�Mayers�� Domij� .�1R�st�� oblivious�exJ noisy 04nel.U1 A��))b�$~-~CRYPTO'dq$LNCS 1109, �( 343--357B;in.'�196�LC:` Hoi-�vL Ł�V2��Un"�Nc� ecur��ofumFi�il�lon�I�72MT Sci�i�R083:2050--2056A��!&r bbbmr�~Biham�oyafP.~�oy�gT���&V� ychowdhur2ǛAFOof�� ��N�E6N32'ndACM&CA�k� �' (STOC'00�I� 715--724.G�200&"����9912052%�sp�aP�'~W. Sho�F<�Pkil2�Simpl=-.� bb84 rJ��rotoco2T%��J;iew�ers^w 5:441--44v�V�00030��Ygl03} �Ssm�Y . Lo.�PN�%9J�7wo-9N]I� �N&�F���IE79fo��Ń(, 49:457--4{��=.��!�01051�4�f@TO &O J.~van~de�eaf.PC��ic��inguish� ty m7s~ um-m�a�s�Rn�a�Y7JtD, 45(4):1216--1227��1e�N�712042. !be��+.�.�E[.�S�����&{ .<PhDA�F� Californ�.Los� ele�E&(F{0�%�9�bm��rusŹKacchi0�l2���Pe< drop�Sin�iM�hree-d2�s�Tl1� �V�j}8:13�Z�1061262� tb04 !C�Hil�)K.~Tama�r� atuw*-daw�Tͥ.~�5.�fh�I��Bt�v2�E�eV408085�2�ag�. Antonio 7Nicolas�{ V8f$io Scarani.�Upb��xum6�us��d-u��U2�E�E��< mp�3(6):563�Z73�9.� Chau!�Hoi~Fungv�ly��eB]A�hiK Ur�Q depol�B�.%-z50��2ziW 81} I*  I .H"I�0�es���*�E�!> rminB�%VJT*al7i se�4(12):� --324�-}�bra�Sdyl�,:pV.~P.3�gI8 F.~V��.�A new6yex�!�>of mutu�X� basJ�"�"icaX}$4:512--528E)b� 3162.)bhlA(M�$n-O�b_l�8�Bki�%=Leu D.~ �J.~"�B.�s�uRal�9pos.RE)J�.I$MM907 �2Mrk� Rena�7en�h�n(obert Koeni2| "%gco� privacy a�#fa againsu�eadʴa:m^�3132� Kho73�# .@ Some�V imat�mq i&�`O mFK��%�&�$b 2�e P�x.5�mis�O=x{ �9y �Tx} ~�8� �! oy~A��.�y.�2� .0� �%�p�>�8.��3} AZc'M.M}�UumA�f�3.6K�3n�k�as, Do.�3%�N!% ��"%1}��*�#�a��Vŗ&25��!�2�2} V P�<av ,Zarubezhnaya=q$io\'{e}lek0x"`� bf{5�Bh%7�49�3>T(Candidate's�&ser�$on [in��], �fw �2���x6�) 4} R L St�\jh�i�Y�A)+ 9r:|bGV YuepM�bE�,� , IT-i�J�*74�,:K6>�S^�3f+:07>@aB A�f shan�e�.E�d1a�, �4% > �:�8>^$Radiotekh.ab%�Jfz12, 2527%�2):52v(�~:�9V��}eor�2]�}R5n��z3j1!�35)�6i10>�M���  /l%" xyr�/N�1eRR R_AL��A�eal"|[R�H�Hl;A�ir!,(68) [Perhap� " of:NVIn�"%� its 4�Ds, ��a�5)].� 12} ��Zaitse�-N�i~so����2?��& [in �]Vukac%eR�J��45A. Ak�kop*A.S%ir�`E�it{.] Phen�a1No&n/O�}9��!�"�1971) (�I2�7nX Baku�S�Shehur-3�E<*�6C1�Wn�=��} .$0}, No.1, 77--ex6��1a�.P�6�[%�B!Gru�J Jd:a7No. 3,�d�%�6%Y�2��it{�F.in�Q"}/% ��02@�03�g:o20}�oBo32�hy1>o$bBq�iBi�2D��=\G&No.� 9--2�32�25:��Rk6�QJ.� E��N�1MF� 34G�35N@2��.�YGu5C�sorm� 5 }, "�L�x47--6I;6�v�2c�$A.G. Vancj $N� ��/�B ���-`d�3�1�X1��y�2�!����!�41d�ɹ6 >� ����No.�1�118g:m29::ni�� epor�6th USSR!�ѐon Co�4 %�B� fer}�l)�@-�_�� -Tomsk, 1� pp 1��8b�4b�*P }�E !�� �345�:3f�F� ULikNo.bQ� --2�f6�f.�^N�% 4��e, 78--8b �"�-enin7fo!�U4theH�� "�6N2�i� 1�Lh grad�[6%� 91--6�� G:5< x]doP%�it{Te��Mat�pz!`., 1&�G*bf�$2A%22�&6vil��>x>�*6�7F� ��u$1VilnusE�8%2Af�3 �_�_�No., 45->� ��6s��Zk!Optimix T"�i}K NfQ9th IFIP6^>4, Warsaw, Sept"4-8% $9), Part I�{edsMalanƈ�e�@aluki�l }% (B!�Sp�j80%~1�n1�A��34b%���No�@4!u14(�86[!2�0�_r��4w.��r&= ǂ2R25b 28);% ��Neu�#K"� sch� �a�der�en�k}1+:2+36  ��rul�(ed.e3 Hand�3 A6 HVrap��(&!>�3$1979) p. 26��36�2��abeq���Reg�@Kc�ndo, S �ons�"K6�l44��512. 43} Rc�9G� .F.1]d252 539�D6:� 3}b� ]MeYiJn �o 4, 57sD�:� 16>oej� � y% \v{c} ormacii* �9 ��?#76�464 D<moI� umma�!il.��h.J2Qe2>!34!F56T^.3��g6vu6+ 13} Zp.�h� }�0}, 254�� 1 (Mz:�q:�42bcZSA� Amer�'��9 659--66��6+�OZ�rX�w 164�" 66:8n��i�= } 23� O9:R14bSinq1}&kd"�� Q6��-f.}�ro�"9!6�} (*99߻!�9�62�'"�.~�<AMS"�����Steklovi �!�Issue�F�ؚR�d T2apan-U� � �obV .}% r "6 �QKy�.8, Aug��2�!22-40.;H�� (U*e9RIultivari�rA1%bJ* � �6/9��M�P^KE��, .I.T���ab ��tarA{rogr. �i]��14~�$46 (July 1s:y44�`&3�e�FX��*&Q29�� N"�'W�Benjam�1>�40A8׏uriksh*�6Q� V� al Lo`�} Y �Ev. z+oA�73f�484��u&�g�b"� by V4[SY��}.Nes:�3A Masl.,ThoriDs perturuonsW+m % thod��$symptotiqu�l(�;-� uthi����'B� 1} L�Myasn�%D E.N.=p Auto�<c Recog\?o| Sg Pa��n!�L� /�gya!70fu3Aaz� !��1a�&&�= &M"o �+�Je�}"�)�erst#n%s�56w478=�Q1 T3QC.RqAit{� ..'. d'URSS*% 4B��361a�46�X�Yu� Pyt'hfKib��t� B� 12�# :��M�iNJq6I6�>y��T\�2�2��L�K.'t.U��bf{!87}$6�:���H!&9.:V>�%*& IT-�2 jf9}�q q6,�--750!�>�5~pɦ繦 58}, 1770}?p�RN�vN���D�( } M5 �I.y-�D1��u Co,i�� * B736v*�D �)�Geremia�P JM~ >\0!  �: & 9Aj 2KNy: N 04} ],9!K.~A�k�/�H[!beN+Yk�7064i�>N�!.O, - ph/0�7R!L hey9]O�=.~S�Fey~�E7Z1244 ax:�Idun�\:TcADu�\IE&TN!p; ukam?l=��o <7L88�eSY~ leibfried�WDH< ~�a� 4281 �6� kurtsiefevJ  C.~Kr�<Pfa��>lynCO �De 3�� 1i��5�ch��986/o6=�Aershen�4I M�binec, -?Z�� . y8!�340�8�"�0Klose01} G.~ R~E % S.~J�~.r�=.'"8�472i%6�wa]�82 A.&�6�!f�%>|s�6)�68 �5e�K.~M{\o}�5Aa�1a~ds�i.i-2158 z94). 9%03)A5S.~�'dhu�8bP�#5'&�P B9!�3� ,24Kuzmich00} A!�,��adN�&~Bigelow3?)�m*�[bfC, 1594�M0���2 99} A�&�:�OUz0. K�7�Q�+2�V�[n�>hO` L'�W ��`oy�XIAM�.�3� !:r)x�UG�0 9�8= pr&�9� 163�v1� -�=� Cohe�N2} C.~.)y,J.~Dupont-Ro�GGOJy�, �QAtom-�]�1-V�&��O!: .�Laksh�( raya� �J22�*C�� �M07AMal�Z;4�f��F %=n"�2ajtai}V(A %� C.~D��97), �!A`%c-Key�.��w��4Worst-Case / AT�e Equival9)}, �:�12Annual@1�osi�6� ^�>28-3. }babai2�LB �1�l Expa�-VVertex-Liaj Gt<Ru�Gener�in Finit' oupsZ�3rW2��H20)�3ͥ�Co��m�L�7nk��nE.~Luk ���er��a�55Fast M���xlo "�*se0Per��̴�J&�+)�D:�5 s, 5�, 296--3 eYj�}A}��%�� E.~SzB��d%�8��ZeS�O�Sy�S!�Matrix�Nup��#}e�Ra5thQa2]&:�d�6�xB�40Eiu6bacon�2B �AChild)|W�1 Dam��9}{}�x�PD0y>9�B&N8 :�g* Hidd��ubg!���5-�d�IK�)"Z�46�469#32S mosca} K�?H�X�,%���ca%y�De�+s/mVAh�an�1 *D SAul , 1(3Aw^72..Chi+06!�P�i� S.$LES\ e�6u#�oIwbpn��%sJFt�B���&� 6041�Z}!e�k� M.~E � P.~H yer�0)E�u"1&:2N�&��:�m2Advanc�8'edaa-�O35-`a 51.�y� l}!�F� l��Ivany�F� ͔z 8 Sant�a�k en�35 ����',O�8�Weކ�I2�R[3}�A>�7��OF, y.��|n�#�|��L Schul��M/ zis2�U.�Ac���4�1�M"�5>�a� Nonam ->�},obL1o�� 24(1>�3L52I0hallgren+STOCa�H B\~>�%�R\"�7l�HA.~Russdi=�y-L����B�Co!���6�U( Isomorphis�J 38����604--617.����~�S6� A.~Ta-Shm��Y�The^v%��&�U���2��res&��, 4 �Fn.p32(��9�793!�yZmD+� G�?:V�M.mYEn˂Ts�0H�joA-��b� In*�"�f�[14(5), 7��7�b.�kitaev0A.~Yu�Y:�1�)9�A�aE�StP9R��lem*b�9511026:�kU  �b%u�"�Aa�expon:�-چ���s �Dih��nnrF5i�8:�ore�Cu�D.Z� Rock���.��� ��ޙ�a Powef� Basis��6  o�� S�3ng:^��7Af2�i9ŏN16�-eO2� Discrete9[�10115)�yYm!b����조&� ���ic � D̾s*ongA�r����#I},fc05�9�9:���N��%��y��aNo� 7 >� sca2d�(�.99B����Y� h�"tN�R!�.�pu�#llP\" :�%ITF7th�M�F q�Q���! a�s��No�%��s}NN13t:(AP&�r P0, ic o�Z��$Error-Corran,:�, 2 �s]Mrad�ishnan}]R.N��y u�B�8��-�� Heism)6Z� 2nd�-:mnlloquz4} angu��a$�a�� 39g- 412.2eg�\O�RgeveL��QI��]Latticee�G��v�3: 738--76G.��2}^�xr!pdw&icI#st1�},.�!i0ACM, 51(6), 8!96�?~3b~>� T@�u���$Polynomialr 4051g "} shor�W.~(C�&�i-6�i�Pr�F��9��ALog��h�3�^6 ~-n�26�14�1502K -�k@R.~!�:�>l6|�vM 7�$58�8�,Wa��FOCS00� E�0��Succinct�C1?~to{� � 41soK 2��{5� 54�#>�� 1B�&Y19U� � Solv�<<a3N� ¼ 60--6� �eNg:f�4D�ab�RayickNM��nne(�B��m5$ple ad��v� �>inbe�7 py output��,eme SU(d)-coq$nt }��;�` rint�7&�4�3�$medskip\no�ot�xbh�uR. _�i+"���},"0+ --Verlag,h YoZ!19/�ngdh��N6�t�Xl{lev*I3 M. SuhI#5:A ��A�Wl��-@e %;um5; �4i3072}}. J�9�f%�} �F ,hk Haeg�S�~;ony)�Dy3�oghem,&yE{ ;ht~��cG!�F�H����5��holy5`, 6�v�#capacA���}ed���-�, http://www.imaph.nat.tu-bs.de/qi/pr +/10.htm�Hjk hol1B�9�Remarksa'�J�&�B 92"�?B�2120221 Nmy�{*�VF. Yura U�Ent��� cose� anti��ic�e� M�!Zi�1fof�M�J�306009~�graem$G.Mitch�j!�Mv"p]�Towar� geom��al � rpreɦ�Eiu� > Ž ���9B_309177~�$HW} R.F.W%� ])�*�Co@�x� ݕan.(con��M�a>�$pB�OM~o�dui�.[ IEEEBC n&o6� �q�Im�O��ces���,:�mM96)O �L>��C'e"V-$ O itB g64,/O H.-+LE�H.aQChau,�V 2W �NX 9)9 Inamo3�(N. L$\ddot{�P$u}}$tkenha �A�Փ]P,I��� 10706`SP00}1}�M�!jzre�M2�.�!< 44[!6�. GLLP�t�1�(MKY �F�e6�2� r:��)>��0�42ja64: GRTZ�N���R�w!J*�w- ��l�A'bfbs , 14 iU" BLMS00} G�. Brassard, N. L$\ddot{\mbox{u}}$tkenhaus, T. Mor, B.C. Sanders, Phys. Rev. Lett. {\bf 85}, 1330 (2000). \bibitem{SARG04} V. Scarani, A. Acin, G. Ribordy, and N. Gisin, Phys. Rev. Lett. {\bf 92}, 057901 (2004). \bibitem{LCA00} H-K. Lo, H. F. Chau, and M. Ardehali, J. of Cryptology, ISSN: 0933-2790 (Paper) 1432-1378 (Online), March (2004), (10.1007/s00145-004-0142-y), (Springer-Verlag New York, LLC). ArXiv:quant-ph/0011056. \bibitem{C01} A. Chefles, arXiv:quant-ph/0105016. \bibitem{CLL03} M. Curty, M. Lewenstein, N. L$\ddoV�V�L92}, 217903 (2004) 5�\C04} C. Elliott, A. Colv!�D. Pearson, O. Pikalo, J. Schlafer,!�(Yeh, arXiv:9503058.jB92jH. Bennem:�, {A�868}, 3121 (19926/TL� K. TamakiQ�nfA b$9}, 032316-2�DSW96B�!(. DiVincenz) A. Smol!/8and W.K. Wootte:z z54�824�66� CSS}R0R. CalderbankXP. W. Sha�F�U 1098 U%�&y2�trash}$.;!^22_qubit�Z=:W-lk!^Ps%^%V �6-�2�9Y%3 _u=!� 1}FR)![-K!i%�B} �u)}!5k ux!XK$!' � �@frac{1}{\sqrt{2}}�$[\bra{u_x})�� varphi_0}0_z1�  �+jF1 51^F1FIA]1�E_B � {} )�}~0_x!8an!FI�!���65B3} AX the positivity of $C A �A&+C'fil}- ph!Q8vec{c^{*}}A_{L} @}^{T}=p_{L, \nu=22$!$$ is a $8\e} 8$ matirxI�eaZ4 elements in $ Rd$ are directly taken from N@$. ��L01} "�Qu�m Infor}on�$ Computati�aVol� ,1}, No. 2, 82 12�BGKS05}��ranci Gi� B. Kra V�ar� F� 5035.�LM �X. Ma)&K. ChenBK �m9��230504��&c B98}�=BrussBC �8�301��8�tend{thebibliography}�\beginB {99}w4review} For a �, see: P.D. Drummond {\em et al.,} {\it Nature} �365�07�N93); GI uchs%�,N. Korolkova�Hit Optics \& Photon News_ bf 13}, 6)-0);:�H0Z. Ficek, Eds!#emUG,Squeezing} (:� , Be�, � <, 370 pp; H.A. HE�J.�. B �6}, S62" .Dwerner_prl} M.J. W �>� Q%� 4132%6)�� (Pu00} H. Pu�$P. MeystrezT%�987Eg0.� ,Duan} L.-M.  .�}�V9il0E{�Kua!hL.M.  fX�A �31c � 20032TOrzel�!C.  NTSciencQ�29a238)�6,Sorensen01} � {\o} NYNI� (L )I�40�6� 6_Ke� le} J!VogelsNZ^ Z02040)a22  Zob_et99}b Zobayz[1a59} 643E^92S4Kon_Sal02} V.Va�notopEj alernoFZe�021602Eh6� �}sW40}, 84`86pu}~PuzUKI� 43601Q2�ai95} ��S.-S. Yuf�5!�81�J6� levand})L ovskyN�Opt!fttQ�2�R $Friberg} S� NU=JF�775�h6�non-dem]dm�^8�59%�0). !`N��2f��31} \expandafter\ifx\csname natexlab\endc(\relax\def\ #1{#1}\fibGbibO font� ] J M#�Pf�Q$�R cite~R.$�Rurl^�0url#1{\texttt!O%8{URL I8providecommand{!\0info}[2]{#2} B!eprint []{S'* [{2� {Kitagawae�Ueda}i 3)}]}� (nfo{author}�5�{M.}~�1v:} 2a�A&S �O�},.: journal}{}�A} %�bf�b$volume}{47:A4pages}{5138} (�(year}{1993}.1>68Wineland et~al.%42)6Z$�Bolli�a, ItarMoo� D$Heinzen}}]4a�v%D.~J.:_r:�V�JJA��B W.~M>�ޒ> F.~L>>%}},�6N5Z!�5Q�<6:�M<R6797R=2r=MeyerU: 2001::!, Rowe��:�VD M.~A>���=D>x�@CJ}-�@��C>�)���]�9�Ar��b�8Z� 5870F�A�r�Berryn�! , Wiseman8 Bresli��! ~f D.~W>mH��HJ� �@����9sV�J.~K.��:΍�ŅVq��8N�632A�q 0538 B���a�)�}�y0��%D �x^�%15 !C�v���bE��59�E-I50�>��r�q�U� 1994:�$a��O��andN�� v(N�k:�b�B0��Bn0��N����50:�-�>>�!�r�Ho}d%�Burnett� # ~�MJt C�+ K>���4�471:E-E(1355�1358F;�9 ang%KS�"��%K~HX>�=�B B.~C>V�ZE? � jv 0302014}� >y ryYurkeAk86��y~B> FZ�*= ~K5ZC 1515N86r��{.L6:L%�@ �>T2� �3�$�� �� ��2H�_��V� R�n:12Kƌ542A�R4649N�9v�Huelga.�7:� "4, Macchiavello!�`Pellizzari, Ekert, PlenioI CiracDHb� S.~F>� ;6.VsF ��BT>��@A� E5�%�> M.~B>�)O?W� ij� J.~I>Q-�!�"�N�~}79��M�386R}97r}��n� # , Milburn�and Zh}]!  ���lVtGJ? �9 ��Z>� �Z�J.�!Mod1j�4�4��.�130V5v�Bax %� Pegg�9� smbdtpegg�� SJ Y�; D.~T!*�{�Z?�nr�Zy 342Vnv� Gardin*q19Bs$,�F!�aA�ollerA�!e� ~�SJ�H:#V�nR�P2�.nVPPB� ��!�E�N�n�5Zd 1683R v��y%�q�!�5  s�V�r� ��D��bH��ZL 2944RL5r�Holevo!?82!? ~5 A.~S>� ;I+ emph&cLtitle}{Probabilistic%�S�%$al Aspects�@&$ Theory}.�@publisher}{North-(, Amsterdam �bi)g�8vtHradil�Rehacek!9Z  Mysk�6 B1 =�AJ>��6�u�Acta.� Slov!�^B^�4/'>� 1~� Andr� Luki=ES �W:&<�: M.~D�.{ �Z;�|6Z�zH->9200vxStockton"l �:� $ , Geremia��Doherty� Mabuchi��SGADM�l�6�g:#V9JJ- ��@AJ� �@2|��:V�H>?5!/A =u-��Z022112.��j!�ru�&�lMolmer�1�� �3F�C�9B1 ��E~�^d 4431RGvd�.9>($,�(A� i4�]'�# A>db: V�Lr)I�U��)�=�� ��  )fC).��63y Jv�Varillye$,Gracia-Bondi~!89a+v #b ~*JJp e�)R2�Z3Annal�physicsjU19Z�10R� 89r{ Wign�n193� Wig3�[ E.~P>� JZ��[j�4Z�7V73vHHal2w9:D , q�,�7ori�$and Polzik�?expHSSP�P:�a:VJJ�!��ABZSc�q~�[��� EJC1!r9LZ(be 8�.��1�-B199v�Kuzmich.�0:� # ndel��[igelow-�KMB��B� Z��L>M�ڣNJ��2_N���Z� 15k8J�zO� .�> #, r �and.� GerStoMab�U�bRBh% d��� 2XyV��� "�0bK30Z32Z�"v� Thomsen .�2{"�* {a}}:[ 3e[ ciniq\!a\(ThoManWis02�+B% a��SJb��c�g!A (Rapi�6m.)j�b@6�.F@:�*o4>w)-Bf�b��b�8LJv �������JCB: At.� �Z�T^V3�M��� 49377JM2.�!�j�Kok2�:�Kok, Le�( DowT+a� ~JBKok��B�LeeڋJJ����n�b}521�?R�n�Fiuras+a�� ~jB�:��^�381J�"�r�Mitchell.z>�$, Lundee��SB5�1A� ~MJ�(d: VJJ� �@��A�� :�.�"� 56^142�B216V ��N�2 �,f�22���2��2��2��2��2��2��2��2��2,Pancharatnam 5 p56��B(2V^��E(Indian Acad�? i., Sect.r�^X24R05v�#�+�84��b�-84�� M.~V�.} Kr�R.&tFv�392:KiR�!8�6teB5 Wilcze� X�_B�^?:KKj� 5Z9211Jq1~;Aharono;AnW8nE07A0a -a 87�;Y>Eb�FB�,��JnI8:DM�159R�8~�mueBh!Gri%H8!Hs-b 88�GB^ SC�ER>���Fn�6Z233R$88v� ukund�8 SimoE��-m -s9�*N>� \�D-D �ZAAnnm f22Z�2Z�v�PatEsI"pat�=�4f�9Nc(IR J. Dr�� zmY2087}>� 19z�!Maninr> Pistolesin&m-pjDz�FD�B3�Z��^�30N�0��2UhlqB�� u 8� B�LZ�RepOH�M�nc.(�A�"r,�a, EricsQ* Vedral sjof�pE>�S�:AV j��  n�:��A,N�-��B5>1R�>D�FA<O�!B;1�2E"�E� &GUj�^�28N� ��Filip�F2+�H3f!-U�� Bl d�����O2.��qL03BA��"TomitQ Chia-(�t-�0o� Z�ER.~B* ��I�5Z�#�B#19�U�8J^ Du.L>�%�BxY+2}�RZp/100�SB�TbRauch�WO��� r�BpS}"��!N�/ �)=R�,dNeutron Interferometry: Le�Sexperi-Sal*�,Mecha�P^�,ClarexXPress.L add{Oxford ��"�(0r% Hase�F �E!�:L$4, Loidl, Badur��B�!� -s]{h Q��B�i-k�V%B���;G>� � = &C VzB`%� �q^�V�Ef 42u.c��Z@ v%�.�>g!, Lemm`#% AI*� i�2i�j] fzB9 ��������v��1Z~63V�Dv�q^5��/b�ZawiskyAK)�%�Ioffe!�q�9����Bm �)��;��A�96�K-!(�5�*� n�5Z' 2486FS!���iJg B��Db��8�e���and)�.�-U�V ���EVyB,�9�jj%غ*B�:y�N'��'Z 0704W>!�});*CV;��b�z,jx.�V���N>�, �r���0�0nWn�"N��!fW Wagh�9�wagh9�~A.~B�I63V�V 6q Rakh5 Az]B� Fisc/8},;6�zMA>2����^S 9�e>�199� �J�BixZ��Dubbers!��b-d ��BxA ^֪B�N�6 �5:#.2� 251NB�fDert�� 2+>�$+Y4rst�$�gaZ �Hiesmay">b_�,�p R>6v:<VHB�5D��AnAj��]=6�9!%u�Nr�Z�03b�7!b��� ]4��9�� ��ǕYI��^�17VLH71%%OJ rjj8"1} 9fE>!Q+� zA�� 3}} @m�035602N�86b�M��lstaedt"�198>EG.(A�PrieurE�4ied�AmP�<B.h!*��Bt ��kBZ Sc��E12�Found�}^�89n|oJ� BuscgͲ!m�D4�V�Bq L�=lU���CM�9V^ ~^��: Kikuta�ni%"Z�\&j�%_����:� �%@5{5>ZM Bj�9Z�13R$9��mJZ�"�� :� #�ro<�%l� ]{z I��Bd a:V�B=��B������(Nucl. Instr`f{ n4^� 40J�!��R�,l��hbw�i&q%�S.�gWiesn� *� &q�c2881 ��2.�/ {bbc:Y,�h&ItC. Crep�oR. Jozsa7pPer�oand W.�iR�p� 70}, 1895�6ucakp�pK.R!�A'bbfufe 4320 afu<{grtz}eiG�jG*t W. T��iH. Zbind�/��J t%47qa14�b:2ose�aBose,;k !  P.L. Kn,l2�jA W57}, 822%b6�hbkUL�uueSH%�Kimbl�q&�) T61�� 0423e:�pZXA%��"dt. �i�F2�l@with Continuous => able�Kluwer�,emic P�F,�F Nether_slj3.=�be%�B�co�A.�OJ~4NL)?4�r125�g6d hauslg�jla!�]�BF- huma,�gWestmo�b nd a�X.��s 1869%�6�cbpv%gIM.q1OIqV.M&�rEn�d En43f2RXjmozes[M �w Rezni�,�kpenheim,"uT/�189.k cm} !]Chefla��hsa8^JU�P ek:�grawal%oA 1�:�i�M�30�k 12 ��.�pr�Popesc�k(D. RohrlichRL�lR3319�P7eb/xe�R��Py�AmeU �%�6jm41�e5);]� akp1E�n�27�v118%/6lehp �KU�B. Hutt��G.!�Pal�tA�AOw�] ���-D5�E04g6[imor} �yH$P. Horodec!��V/990603A�<ivmI.!uIvanovic1u2�12!)22u876��%*� �:@%(eD86cI�AU�JC23��33D:F D)�E��emp� %�41}, kl6�d#n-M:E%KG-C Guo1%� �M80}, 499N�gour}!�God �A-�����l6�g��.� A } B21E.�wVp�&5m!Woot82} �2�A�W.�yZ�� 6 n 299}% , 8�w198�wYRBuze96} ��Bu\v{z}B\$M. Hillery2P �5�{844eץgV��Wc��RS3*�|2Q)$%�7A3 2153UE�U� �]�0 :K �E�82izE�C LamaHna� s-Linaa�A �-��Ca�wel�$D. Bouwmee�M�C�o �29��71�� 2); F. De�|t�>V..Z$F. SciarriBf�} ias,B�419/t�;!< Fase�8 �rIa =B�o 1079M�J��z�W ccia��6�I�E�Y9��06YE�9Z Ricc�:A6 i,!N�:n Bn4n%WNPM@ c qDe Ma-x Z UM32�34��4);a@��. Irvi[{A. :Mń$A. de Dood)3D. 2 mF5%  �I :7HOM} AKArng, Z.!nOu, nadh �C-�b \ }%�5e;0)n:; Brube;�ru\ss  �v �Ca�*�Y�.�t2598o:_�/e_.;E�z�UZiPd\ a%2A9 65�� 0223U�. ]f SymmEfF) FFM6 y�9� M ��5�vM.i� ��A."� %qXv]uIAM� �w �2� 1541N��Ks J�p!�&o�$��a�43)�992� Puri%&1:�9 m�|9a170501� 4) B "� ݈J�� z�, ل� Ghir�VP, Referee Report for of�pw��:K Bech%Qpch�0(-PasquinuccT2RςM5�42r9);A�SecondB�!�^�`C in p�&6��b�b;���N!<097); R. Derka�� &� V8  1571I:� DeMa�\^2f�@84*\ UcK�@:K�C"�6�! �F : \I�4�w8�M6i�.� A� 6N� �w3Ɉ.�6L�2�. Ɍina�fO��% A.n���{\ �ofB�2`bwS�us<'6�Z �|u�;:d CummVH�:incwi�3�}^Y8}, 18":Yi2�:u\U1�.��BA )��� �z)� B^-���B2*�M. ��4F6O ���F�2��%% W.T.2�IZ " M.J.F�6� ~�]�!5R� E��R�., H.\ ��.�mElF� �A�~ 00} a� �_(. Cinchetti�vP| 'Ari�q!�C. .�a:s6e�1"��}GFJP>z -k=*�n63 �M1)�} F^mK tsumoto,�g,�M. WadaZT��� :"DAri03= �6�c� � �3� 6815e��J�j�H��6J�6��;� !�ً)�:� �5 �M� �VZ� Mass95} �� awS.�2� W%�7!125���M\�A.S� �\it �F\ �D\ }(^/\, �, p.16����%DR�'2���A.E"�B?�% v��3�  46"� 0311010 r� s� 2\0realiz�� ;�$1Ȅparrow 2$ PQCM by a NMR scheme2��HE�JP��H2�M�Ix 5231i@3) has proposed a^|aoML unbalanced beam-spl�rgK*^��4success $p=1/31�9����a� .� }(to be 4^ d): recen�� a similaroposal� been imp�ed~fu�Vby%] sym�1-x methods-��y �v �4}2m� rtLE]R�i+-s2��:# FuchN C�`sm+{ }N�9116 � ��erf\�rennane�6 Karl�;�8�hB��1� 1279ͱ:Y Galv�HE.F. \~{a}�L�rdR�* *��!�f�վ � P�Gg2dCr\'{e}b��0~�!{bf7h3)�.�}E�$A. Nielsen%RI.�Ch@�Ait"�i����*�L.} Cambridge Universa:�,s!)2 M. Zukow2wA. Zei*N�M.Hor�!��59����1 � 4287:�F�rstraet`H SLd6�E� T 90}%��09� :XJ�Zh:9G�"u��Y a��&@4 X1)��167�`�J�KO#.{aPar: � % 64c%064304F�H� e�  M �S��9N�6 �2)�v2)�� Grudyb C�a �5 �4)9>HA. <%�R9�$Chhajlany,.PPoB {!�A .O1�40G.h go�J�A02005)T�6 } � H. GI-Y.MShe"N�E% B�6l K18>j� "=� , 2�� &�.0�JA� S�� )�B�TerhaJ*-c82e9)538>�6A0Lin. Alg. App5T� �0)6>�.K�n�`�%�w � Comm� th �238y 3)37>�Sʊ�ve�6�65�2)� 22:�A.��P���}Linear�ebr:�59 �23>;Z.h�6�E70; 4)044302.V�}kV%15b� ���".ȁ����*Z<>J(_�#�P"[�jQ$�R.�^R.$�R��� "�>�%8����Sc >;�5:�& ",���T� Wal"Y5Scu�E7 M.~OBy+|��&G�R�'"(MZ�Q&Q&�VJ*}���}f�:7Z�9��Lծ. >�%�Aa�+&� �-��;�-j-E�2�.mV]1��Europ/.~� ^UxZ�V�;^�Z�.�9:�c2O /A#L�HqCZha��8Z.-B�f��{ Z.-Y� *�{L�KΟLՒ� 5���be�uG*! r� Z�980Vy9.Rc�f*�>0e%(eH�Z�>!x�jx�5� ���<��ZXi�@��# S.-K>N)H2��a^�Z332R�96b!�jb {Si-�)u}2:&�{Lu-weiI$D, {Shang-qing Gong,Zhi-zhan Xu}{J ��}]{Dub95ttj)..��1>��5.��� �9Ie6u���h B�hf 3=_E�T� 5645��>���oAru2�u>hX , Agarwz�  ��*�Aru�2PB]9_j�"?{GJMf ��@� � � 6!�.-� 0238N���� !b%�1.� 'i!�2�� Z�E�U�^���>Z� 0438Z z ;b< --)9ruL} Aga��r��<Z�2+N6~s 84:?Mp50!>O�nHaroche.gFM#,�&� Raad�8 Har9*iv�BZ {:�V�BR Brun;ΛN�x�V�� ��2D-�1R]^91�N�j�"f�j�j����������������^� Adam2��>�I!, S�w �lyneka�Ada�iCCN�y����� &�B�[�2�B�p, texRA�2^{14V�4iߡJ�%ųRii}L9i!l�Jjl�B��^. rog.p%ڳ ectrr8^�MNsLz�Kasev�zand�%C"1)Z�as��BKQ�B�Ch . Bd�.j6 ^A�18V4�HZi Timp.�> F , BehrO�F��(4t, Cunningham,'nti-!}Berggr�]B9�� G>�y:dVR.~BPK��BDJ� �@JJ�9�CB{Pr)P��K�d:�9�!�E҄ZD163J�F�Qn�"�"� Ket�� W>5IZ��/+C�jf7ZM 11Z^�v� Balykȉ1n�Bal89�� V.F�KZ�' �rVJ4Z�3VF�z �"!.L�F�F�F�F�F�F>F"�d%O��Z~�2�N״"�{~s3^�LNx_�#�Ŏf?�]�h3�$�2Ft �?^�%,<4n�^ 0��N�v�`.���'��'��'��'��'��':�'Biener~H Frey+WE�� Bie�T��V4 Bo W�� BN�Z��6^0'6N7�]j?Z.�������������Z� EnglA�* ,>� #�&w"� BaruD���Eng�� B.-G .� e:�VKB�Sc ��?AJ�,��� �6� ��^�2R&{zyBattocl�<�1t��UBat�WB|X���"�"IIjS ^R 9V�xz"P�����: ", �_� Maunz� Remp#Pin�PC�F�m d��BO ��=B�X��$Bl- !"�6 �Cn�^J���N� vOlGlasgown #�&��o/ilkens)�Wr/T�Gla�B� bڜe��=B� ���EJ�1 !&F��j 4Z� 245��Sleat�E()���� Sle�Q|BP T��j�~�n� 48:�32Z�iv� i2.��2��2��2��2��2��2��2��2��2��2��2��2��2��2��2��2��2��2��2��2��2��2��2֊2 Clai,vj( #��lom�`Guell�H�wPhillips& C�& BKd e:�V(Ff� ��=F� ��' WJϡ9V��(Z�%1Z=��N�"�v�D��L{wh&�A. Whee9!�W&�Q6�^�H$Measur��} (Prd� ton >�C�H3._{bali�ZR{S 8��UX V?�_10�Z6�ABN} �H$AllahverdydKQ�Th�K(Nieuwenhuiz�- Eur�&�@�_\��DPT %%f Curie-Weiss model�HI um m9 pro$H \R -mat�] 83162uGABNprep��in @�ion. %�htem\�} AJ� %%)���G�L321"�L6theU]�V0epp, HelveticDD-d4�L23�Y72); %%�M$i, Nuovo C�zo B 27�T�YIE�w!�5cW�G@�7*�FNoi%b %%Fy�199LMRma!a}oE uzukdR. Kub=�)��JapQ;�� %%�[68)A�C. Gold��E�M.O�V�= H%g�}D108 �73G_&�) {Mayer} J!� U�^ �.Ψ"�{H, 2nd ed.}, (Wiley,�� YoBF 1977yLp.ic-154. uJ, J�_�`107#X9� !d Inco�J$te descripA��#re0�(t entropies.�Wway} E.E�,sC)&�A$, 101 (195�ZF�3J^6!6�pH. Ara-�M@E Yana,dnP%� _2�]6d6�H61 �.0A�66 nEG\�SGHZ} D�Feew�->0Y�H��h�)yv6�HJn5�J13�9�l��s} �.�Ci�}L O Schu�p, &!�A}zT12}�5!�e]F. HaakIG2�I=R�i4AV25�U1/��6N��j�g~~}.XDAHW} G.~G. Amosov�Y~*�O��R.~F.r^4 ``On Some Add���OlemRJ�J�''�1em2/*&K4 Transmission},bf 36!505 -- 31��6�Ar�E� �$an inequalfKof Lieb�Thi{^g���er�s�e����!���-�CW167--170%��YlEp�Ep���RemarksOOtwo�Nor!$of E.��CommunicEL��e�317--32EM��Ki1�� King�MaximO~capac!!�p-normsuZs!�product � nels�J�� of n*4a�0no. 3, 1247!� 1260<:jNKiF�2�al�of�a�� breakF4B�Nx� <��1��2]W6�90 ��9�Ki32J]��[uni7�q�F��010 4641� 4653 �%/�=Ki42�The9�ofAd"{ depolariZ��5� IEEEioacɆ'�"�� � }!��4�X!� 1 22� 229,93�LS}+OJ_Wnda%gR. �WtreaterA�,On Birkhoff'/Sa%V,doubly stoch1>c �8ly pp�e map�� matrix al�JaY�2�J=Mits�KqiQ1�]0a�N :�kLT}q�ET�k�I�I�lieiI�SMoA��4the Eigenvalue�,/Es Hamil\�a Their Re^ on to SobgU .o'', iT�it Stud�in^��x�i �c� �$man eds., �269--303~� 7�dU���1}��� `.5M� Clas� l C���ny�-Bq�q�Cha6�e`2/M6ҕ�9, 4334eQ34m�6Q�2>�E3�al���}� Quesi/in�2��ag� ��i� �3��;!�applMin �\�.�WH}mVW��E�> kQ�W0 ``Counterexay yn a��$conjectureez�*� a�<pplied:�(55:191--216� 1994.WY�bTPseer.nj.nec.com/14607F�ejTx�fE� �m80:�4�92rkp� f�!�E.~Pess2QConn ual Y�E��a�De��nc�N@%%�}al.�M6Xnq C� (0(1):29--62�9.�,sch1937} I.~��oP.�On -z f(c spaces ar�xg� euclidean�g�g =�� imbed7 �hi�t >.�E�b+ 8:724--73�372� ha19�E+Fhaf6�X��2$��3E-�2Iv� 6L48��~E�annO&RA��u�t�A���un B �rM� Tech-U ��$7:379--423%s623--65� 42]cst��2�rP. Stapp.tobasis�$�!�$many-worldyi68 %^ Can.����880(9):1043--105� �`"deo  j:�k� S.~Tit�ALH.~Kozaw2s� j�bFE>� 42(1aL575--260 �2� wol� $S.~Wolfram.I% kind!�s�.' :d Media Inc., Champaign, IL H N �f/N&SBAG JaksyC*huz\.^vC6� !uP.W�� 9�v{8� 3�! 1998k"�BE�E�8l, F.B.J. Buchk�#��'l,mke, W. Ertm" R c1�� 6��6!WTR} �� atro���em��c�ofar 36th�Sy&�>^��x�%52� �m�WvD} W. 6 D�AMa�{sAY sis,.�$of Nijme� !(: W��m΂%|ROj�,}040517�l4!n�(SL} S. Lloy�Ir�{26�C 15�6�SB1:A"; e�� U{6@3 0543��75Lev%�Lev� ?..9!O1&�q:��SB2n�.J�. 0��) ��BrennA~KA�#k)�"Wy(ams2�� Y 4231�s6+ WotzmLn-m& Wocj7&��40623/z.�>24102 >2�4neumark}M.A. N !�Dk. Akad. Nauk SSSR�041}, 359 (194:�@eng}B.-G. Englertz�$3}, 032303N�rec� ReckNI6e7M58�946�0davies}E.B. D 0, IEEE Trans.A1.M�� IT-2!z596S78Stend{thebibliography}� \beginB {99}y�p{Sanz1} See, for example: Ga�es R, &T A S, Margalef--Roig Ji;8iret--Art\'es SA�@4 {\it Surf. Sci!5,p.} {\bf 53}aK, @Dreferences therein] {Bohm1}  D 1952 [Y^ V,85} 166, 180�DuerrBPD\"urr D, Goldstein S�,Zangh\`\i\ N�2 �J. Stat. l g67} 843b$Holland} P RH3 H�6}�Mo��8} (Cambridge:  D University Press).rall� M J W%u)J � A �(37} 9549 (R1Pre�h t} q!�(-ph/0406054.tBerry!� M V�6Zs29} 6617:�2!$al �,, Reineker M-�,Schleich W P`9B`!S(bf 32} 8275a,Wojcik} W\' !�LBialynicki--Birula I)�(yczkowski K!=0Yit)�--DA] 5022p0Amanatidis}  D E J, Katsanos D Ep0Evangelou S Nq-�Y� B�69a 510.@Man��rot}   B 198mAi8Fractal GeometrEkNatureAkFreeman:a�+ncisco.� noteA\DStrictly speaking,a�$ wave funcA�X (\ref{eq3}) is a semif � \cite1� or pre  M�$, since itJ�derived from a convergent series. A� N s are chaz eriz�` having a ' first \ative.i�A�In�l\ian mechanics each state�associa��to one�0gle particle.� wev��in ag!v�to%EJ4istical postulZofndard i�um�!�isg can�(e any initi Qi%�L$x_0$ with probabil�OD$\rho_0 (x_0)$. S��%*ll�seBMs�)odu��8 results given�the��F� . T�$is equival-considerAAys�  titu!dby manym� non--inte!� ing}5s:��am:��vdistribaaccord!to1$>3}�e�6 of��Q\�<$um carpet}Mፕ arisesM�� term A:9 , wh�describ�@ ($D$+1)--dimens2 spacetimAz,tterns generE�,by (regular)e� u�s due�%Hf��C (see: Kaplan A E, Stifter P, van Leeuwen K A H, Lamb W E (Jr) and >�8-���Scr�PT76} 93.yga�o Borondo F\nh� hem���� 120} 8794��]!�ebZ5 �ZZ2} 1470.S4}aNn[,��JvB �61} 772i��bInEC caseA�p�� ual nodes�q high6*�(lems, a vo��al dynam��appearM��2}� A��օoget tr1d around%Q�\4ex temporarily.INelso�  E 196EI$Rev5�$50} 1079 R� ez� � {Sch35} E� hr\"{o}a�4wissenschaften� 2� �807-812, 823-828, 844-849 (1935).� l� : Proc.!� APS, G1� 323� 8� �EPR�A. Ein� 0, B. Podolsky)� N. Rosen,= Z47}, 777Y�Y0Vedral97} V. , M.]lenio A. Rippin i,P.~L.~Knight2mL:� 78}, 2275t97)tCHSH}a-F. Claus!]M.fHorne�Shimon �R lbo)�80n69.nTerhal}�M. , -# �A �2719� 2� Lewe)x}F!�H~Kraus, J.~I.~Cirac1(�odecki2( q6a:052310FsBarbieriq ,!4De] �A �52308F� Rungta01}A ,��Bu\v{zV!qM. Cav� M. Hiller�U,G.~J.~Milbur64q�A#042315~2pBhaktav� la%�D. 2 Ra):DV. Ravishankar, e-C�B309047�#,Akhtarshenas%�J�RE11166ELi2000}a:Li%�\xMusil|1e� kN_$Hindustan #8 agency, India,1^Ueno19��K.  Zn� s tion� aNmAmeri MathemaZ Society,�vidc$, Rhode Is�,c.�Griff78E~ iths%f J. Harris �Principl�  V� Wile� Sons.] 1978�Mum $D. Mumford e9Y"�I, Co�x�jec� VarietS, Z4�7.JGrone�� %&c. Am.%F.!?ke522k72�Hosh4E�HeydarI�a�Bjh ��*%T�ut< �@5}, No. 2, 146-15i�5)�� Pan}A�Pan�2L�G. Lu� �. DraayA�F�,405133 v1. %JVi CfQ 200}�e� 1905} .� @ ``\"Uber die von� molek� (kinetischen� orie!$W\"arme geA0erte BewegungE\in ruhenden Fl\"ussigkei� suspendi6n Teil_,'' Ann+ $ (Leipzig)"i1�O549--56| 02`4{nyquist1928}  �(Thermal agi-�of elecL�g[Dductors��sI bf{3F 110--11; 28��{johnson �J.~B. J ��i��97--10[:�� 1} I� worthwhilUrecIat validw��T ���em isP!)�to) it{�+}["8m�.` yenwelt!51!�!CalleivT.~A. W#!-Irr si�ElHnoiseZ�$83}, 34--4E)5�Ny grabA| tal8I+G ,��Schrammi� G.-L� gold��3Brown�o!-:a"�al �grArpproach.�p.)Dbf{16d 15--20��86Qdit!{h�T� � H\"anggi.6�~ Kram�iG[\"� !AW. Zw�r, E�it&� port*Dissip�} (�34-VCH, Weinheim�� .Y(ifoni98} M.ũon�zP.�!GDEn�um tunne�Z&30 229--3�6&QLE} VERQa�{\"�5^�Newtoi��:w1q,��8� 6� y(GHT79�2yqωzP. Talkna� ``Is5���iv"�a �� stocha�acess?:�9C1A�2440--24V7��SSe� Roncadelle�%�� betweenY1EBiz)_!����EurophysA."2�379-38E� 94);��Kl���4S.~V. Shabanov!�b!)�,forward-back  path ���iEi@9!J , 224--23e�95); L�� \'os��}.�unz��Markov�+=�Al\"o�!�)+�open m%$Z�3� 56 7�9aq2��D �ISN. GisieOg&n�6�%ˡ�ra�  ��)0Q�82A�80�80E�99%�~m#reu��B��ppl A!F# truccione!@SY�6�m#%,V�ma�" eq)V>�9�5A� 1633--164)F�J���kburger�Hy� ``Non=�1&s�diffu AT*�5$2��2� 256 �;�\hao_Decoup�\d��E�gon via.[field�J. N}12A5053--50 42� t�y 86} 6�A�failur`�A�regres�$ hypothesi�.� N.Y�1s390--43=" 86);:s��62 9A�6%T7��spohn80%RS !�Kinetic��s�s Hami� ��d� s:Q�limit�&%�J45�O��61��alD#87}9 A �Gn5 or��oic�is�unstab*!� in:UqT �alF"group}.S$} Lect. No�&I�4Vol.~286, Chap@'�#III.9)=*P 8��lnm90} .�J�0Sluggish deca� prepar� effecI�lowerw#q}QA�.����44!�2k 23W9�� jung�R. Ju�#.��6DLong-& taile6�N� )SE(��5� 2512eW52 e9� Hank�"d2``Dens��%+>�:=�Eu�E�6875--68��96�iK026�A�P.� I`their.fA�"v�� ��61�. 1--5E*6mori65e�MoreE", col.t� ��J3Progr.or>3�423--4C196H (K. KawasakvSiGei� %�.�lin �non �6� xa Y3�� 1289--129� 73); Sa�rdholmZR*anzig!�I����e��.�1--)�a]Z<1!347--371A�763����w.�n6MicL!nd=0*� pr#I�$gross vari��Z�2a|537--55iz6h�971� `���1��:8: A useful tool0�! erplexed �� of�.�fluct� �.�I q48U 15-2�7 ��(senit60} I.A Szky�*���"E����1�670--67�66Iu�� P. U sma�AnI )olv!��IQ�m�A�!icaz�>%�D, 56--73, 74--89, � �-:�za�6#Nu�.F��ZR� 2 2�a:zHTB�.L *� e�M.�$ kove4Rea�-r�(i�4: Fifty years [#r0��bMF� A!251--34e�:�@caldeiraleggett83h~O �A  L $!�e� in�}� ve��!9jM 4!>3!�4� 198��j15�x�:� E 2} F $he explici�*t�1is calc$*B (see Refs.~\I e+���.�.( weiss93} &@ e'i&�uve� � second�2�(World�/Dentific, Singaporei 96�esam U. Ecke�G9�$V�begaoY `5� ŧa super�uc*-� j 'iou�. Eh&z 3�6�643Ea:�schoena.�%X$A.~D. Zaik�QUco�0nt , ph�'tra�i��!�.r�, of ultra sm<��sA��V�.�9�2�4(:-E9: �Yu�Nazar�Cha�T{ +Rac in U� �J-`�� U8!�le� 2F}�4.\6 &� �hM.~H. Devoret, NATO ASI Se�- B,� ( 294, pp. 2� 07 (�&um6Q96g zurcherb!� U. Z2���YfR"cha�,ttached heat ba II�2 pr�ti��1�v. * � 3278--329��:�sem3� �609--6Av42�ray%K. Banik�AlBag%�Dma{ G�: x Fo)&-P�&}>�)uchP5" � true� "�2"{1Bf�Q.*&�6�05110iN2);�Banerj�8BɁp�2� Soluuof�B9 : AL xi��� walT numeo&l asp�-�.U�896A�97�:6e ͣ W.�E<Menzel-DXth0,Pelzer� 2L;~K� itsA��A����aa�sq!Qto_�=.-B>��885--93�:�� thomasa�%rH� a+.6res: T3ev-�, sym�6�j��respon6�URe*M 8L 0 �+BB shao �y![ h *��U ��� two-levelj �to� eaA�spi�g�B�?8�57�57� 6�s\#&P�ij#"2!&� �4A closer look �$q�J$2u� YE~p2a��2 L2�107A}, 3A38�185.4GTH77,.���:|F��%-U!b(macroscopic�*`�=E�J�26�#� =HE1�P.~64H7/Q���� IIaxN��273--2@1/>bi$A{"�$QD04} K.~M'"Romero�rf I�=2�QQ2-I alwaysm�)I�� *-�052l'20:"zerbem{ 5} CArbb:"���c�os��"� B/�}j15�5�67k� *b 2C&a�{\"a}ngg�%Floquet]}�7pѡ�ally  �x0&ve ����F300--3�3:uczka��J.~{\L}�Spi� a���)o�: x:dUA�!� 9��9�VvQ/ mpen!�N.~G. z8K�A solubl.�Qwm4$�61()ݡ�&�?���49a�P%:�fermion� } L.-D.�T<�8 kravart8 .4F�!.e6�hO15�v.1�154&��F�-�F. Gu�!% BulkExsurface*� ofovyAa�<m� path-�# a :X)6��77�77�%�&A� edeg{\aa}'A2��� 6-pG=5 -��nviron�9)Scr9��# o:�,feynmanrmp48�,#F �SP;+��#re�7vBps�iJ� 36X8{*48)�(|%�(A.~R. Hibbs&�1!MM���Int�*)GMcGraw- 3666�-vernon63:�F 8 V"!Q  �a@ 5�� A2�9�"a�� u��b29117-$632� � dPRL�Ha�R.�J&�&P�F14=evente pres22a0loAmemore��m�6��i761--76� :)GOWG67 OlwwsU8N��  r�vFUs� f@e.~E��&�e�193V95 6)jkFGAnwend�0 Funk��,I�en auf "�- *< Relax2sp�a}nomene�i -M@E�enI^�Z$:�*hofma9 / H nn�28��3ve��-- s a��abolic b 4e�#)ZI9[26�2�%2I-6v$!r��6nkerhold6��bn�%!um�iuPot�al^:rier. �+yW Pa�B>���*61�#2��428E$�).�S.:J�)� �a p�-N. II. C.s { the  top�f)q>�2�704--47�81��r�$I. Steady Te N6� Flux%Jf�� 1355�.7�3:� I.9}~wQ>��AE�s�9�% real 2x(de� y matrix�^=,�>2� 29I�&�� hontZ?Z L1�Wa� A6 PeriD orbit2��MI-Krt1sk�BA�$Bunsenges.0��&�,-3�91)n�Unifi�@  J�!O����ZUa409A�0B:�RHF�R�'&@ %>E. Freid:�9�in.S media:7r te-�4ing-strength r�E�}k&� �4�:�.F!~X)��.�"}:��>at����1��219 1j:�e`��6bPechuka *��( ``Strong f)I�lg'�M�"� �h&G$.."H#:r6�8�1 0868�A�.��q�B+R�H�y�A�s� 6�:���� 0601�L.chu�Mh stur%?q` "��J. 2gCHs��> 1N"�morraq at>�b��031107.6�ford96�2�3JD3In�H�c !Jro�8ngK/�8xH�%(Ehrenfest t5e*�)�ym21�24�64�-�@�dmn82b2&9/"�t !y.�� �,1fmj!AYik &��1� 1�B&!Bocl4�J5:WKn&[*�.B%��)*q�7a7L+8�B1>'kostin75\.�K!'Fq�!. Phe� aa�q["� !ZS1�1�36~ mD/r�4 J. M 2�i^/2�K�;cta��Au#:a*]$5t�79)�re�I�>VQde�8 @ ``C"!Qm"|�"eQ2n~6[�h 1�6 furth3� F�th�/=,einige Bezie�0zwx0k�s�� �k� %�"�0 k'',A�-EQ7I14�2�36jfenyes52�&F\'��0wahr\-}@in\-lich\-keits\-A�\-re\-�= Be\-g�6u}n\-7  � rpre�7>:�Am�&�1�91956�(weizel53} W> �Ableit� lM i�n>aus!lem=Vn, kausOe�LinM> M�9�5J�� 6�5m 5���Ze�1II.Z�,285:�!Ga67�/F !.[�Vx�%,Inst. Henri \'e S�.ArXbf{VII�"�166`ghirardi|78�v C. G �DO�a��I!��*� YEof Qau��� - Crit� Review�Ri�" Nuovo Cim]`\6�''+6\ wangliang?&M� W�G L�Com� on � pedmeasure�*"+�j''�*� Du���-18�J6�Y {QBM�D. Astum1!?*} �.�2\" Toda&vW$55} (11), 394�P. Rei�"N^e\um fe0�h:r7�reson�#�Chaos��62�4��9A�, &> :��ratche 2=\:L�\2'NhXybhX10.hXAlRuSa\?R.~>2Y: RudnX2% S.~SadH. \newblock \emph{S�yI pe[%A�pF��4c s#4 of {$N\;n$}zatoms}.a�ath9�2!$no.~5, 115�1�&:� BBMREE.~Bag�%M ig,8 Munoz-Taph>�odriguez.� �C&0vs lo�>0qumixed � esth 2�=��A^V, 010�[6 MR02937�&R�BahadurF��>asympto�4ffici�G!�tesc .* �e6xSankhy\=&(-�.@2�.66�-�070#z��(of�8Vc��Er�%C8c6�A#EIZ�3a�3�?3lL:� MR0315820��Rr#ZD Some7�em��C6�So�H I_Ir�!c Appl��Is, Phil%phtIPa. �� yaCon+  Board!7aEKal�+c\eg|T7 �)inV��G4.�,BDiVEFMS�( ~Bru{\ss}�GD*N A.~E_C�%Fuchs� ~Mac�N%J �3NJ�pa#l u�:�#nmA -depCGt!nUV.@RF5s �4, 2368�>�482�Bruss�D��C��.r� �8M�' Ad2 V� ��66 �6�A2�.=1A9�"" CEM�J.~I. QA^%%���pur.�A_si/Y��N�J� �>434=34H>�ortese�5J.~ FV�a5e�)p2��4,Holevo-Schum�+$r-West\-mo� �)} Znel capaVH24%�-J] 20712C20: 6MR17396l4F.~�I?^eJmLV- devi%Ea-�$me~14!RI2Fi�>� "if�6�Fo�MD�" �E% reyb�-J�E ing� �&�>: I�>�Td2�36�Gill01wD�DllF� &� 6In�N�6 A�Ar�P*H^A"$%T;g A.W� van~bVa�AM��~Guns�7A�fKla.n!2i� ),��36� �� IMS `8 ure �=--��|$}, pages 2I285OLC^ Ma �aE�Gs�� ��!FMassa%��)L ��FZUe.�a�I���2p)�{"� 6} 2312R2�6�(HayashiBook�  (Zhor)F�A&� �h�YQ�% al�Qer� : S�O�a Paper6�>�5.t�*pp;< 2005.� ��7�3 �.;)����M!Ta��d* _pure e�&2l"�<5jT%46�46�21Z.�MR194�.hF�Tw&�analog�B0of {F}isher i&jɺaI �� �point;�9V�&-��36, 76�77MA&� �arXiv bf�CeFiZbper (}-ph 020�3�a��P�3and ��tains  mate� >A55142.A> KaGtsu�FRQ�&� *=-l� sourc4�I2NU mC!(2, 022311, �B� Helmg*f�鮡9�M�2�Vl�daFN�k�i:,2HP�"F.~Hia)3D.~PetJ6!�s6a mula �&e2� �/�n Um&�-6�Commun�tB(14�:C)110:�"Hol��A,Z FN�Y��%J.�i1.�2^North-F , Am�Jdam!^:FMR8321=<�� r�C�MTF�M!e�ysi6f�i,FS Jaenich68�-J�ichF~Dif��zierb�fD{$G$}-{M}annigfalt�U26>i.� �Xo 59. �>moAB6� KWEste�Key�" Wernz�L63ru��6t"�3I2�V�aa�5,5.311J�pur��aD_'Ac� 2��Adur:� Ann 7�b  --26J�LPT�`L�2=P.~Pascu�R.~TarraN Minimal�gJ�5�� ~135�35i�6�MasPop�&" e�$S.~PopescuF��ext$*�rB� �~ um �6 6 7Q� 25{D6C*:�-M�z-v�A newB� {C�$0-Rao} type bo��HeA9e��e +B2�J.I�Q(A ��]�/TB�OgaNagax T.~Ogaw�@H.~okaFw�" ��p4.2#T 2433E�6� PaulsenGVI. F�\letely)[ed maJdi�->�BZSl;� B.~ F�Re,5 o)GM���compact�Eup6�g�f:�!Varadhan�DS���F�*5 ��7d�9!l"�92���Pg O��Q�>2�!28�":�DVidal4G.~ ,�I.���2���.�afm&�6�iZ:S �126a)�H::MR16450� A.~W�r�FeO�Kor�_Hco� aneli(ory. {III}. �R � posi� ergy>�#D{${\rm LSU}(N)$} u1qG �6�In�.B�3� �. 3, 4�+538Eo6�Zhelo!g .  benkJ� a�A�{Lie}M�e IK&n^��zN| d �}8l:69} Allcock G�s 69 {(c�E5} 8S {\bf�t 253;86; 311*3 Ki:7I7ij� J�a4 c #~c} T6} 36.DWe: TE �86�; � 927} 793 BlJa:Ug B�=h�P%� Jadczyk A�bjkHel"q[\$��s13.� Gi:�6Gi` �kani�97�n Int.�W6�36}75 �Le:�g$ Leavens C M8 M%�e�}�e58} 840CAOPRUF@ Aharonov Y, Oppe/] J, ��v Rezn�&�� Unruh W G! 8)�Nt7} 4130 .�Hat�tiwell J%�9MG Prog�<e"�M-U102} 707.L(KoWo:99} K@Z\'G]-��t$dkiewicz K�uJ��� 2689= LeJuPiUr:*Le\'on!Julve Pitanga n de~Ur�y \i}es F J�0)6tI��n0621012Ga:�, Galapon E AI�t�Roy�-4!�451.RuH$ Ruschhaup�f�I!"�A�R�GenOMm 1042. MuLe% Muga J GE.~20�1apQD38} 353 %\nonum &$MuSaEg� \, Sala RdEgusquizpvLf2�s)�Bit�>in"�"�#} (Be�|:"� .=DaEgHeM)& Damborene�A,6t<, Hegerfeldt G C���)��wo%i6}X 104]YHeSx 3} 6Z, S�} DBd3fd8} {022�D.��3}B��� �:6 B: A� ol�j�}�V��{2657.�"8NaEgMuHe:03b} N�9 ro BBk5X�g>y�f7} 06381.�wa�w6�vu6�389.�RuDaNa)4}2�, >}=2F��:Y2-�!.IwNa:�6LYx, 6t�! o%�6]70}8m1.`He:93}>�%�Wil#AT S��2K)�C�*A(��R s.} �Scee�� SecJM*n�0al Wigner Sym' �q 1991"�xH�, Doeb�` W.�^er D< chroeck, �M ScJ�M), p.�0;:V�f�47} {44��� DaCaMo:hLDalib~J�v- Y% M{\o}l�l��B~�Q�5fCa%�0 Carmichael H�i� An n_-w� "�G-� W c1;Jd Ri � fh � �N� yuen`kP. Yue��l�api�A^�� 2651!P biB wine� 1�n J. W � Bo)QA\W*pItwrF.�`Mo�OA�D/Heinz�}l�S R679�:�M�2���|"/6 y4).� ho'nhorst}�N *iA%y�;D)O166�D763#c�p} C%+C ,�nS uR.!I�lti,�PD. 'd4�M. Zi#L�,�� M&(S%��43 S:Vm�Vmaser%NMeschede]:Wal�A"= Mu�T2�N `A65$$85); M.Bru�u.).Ra4!5 Goy,AȂdovich�).oochWn9D` �� 18&K1@!Filipo� I�avanainM�P41y�62��u.30,86)PM/G��mpe)aRM1 �r �B �1�10�%88); 8x]Aer�4��. Khouur�dav �E�N. Zag� �4](A:)�n K. A8tePChicbA6R(�sar�+M.AVFe4<e �%�) 33�"4)..e gÁ}C.A�G ��6hosf`%� N �2+1iE72Ev�` sboaI� J. V-B\^o97e,. de Almeida��!Q{M vYA� ussaN��c06�d(R)Y6�/$massonisq}!��k M. Orszag't."�%)192�-6 z?�!Ze�C��sp)"R C-!�eR35�H!rݻ�' }V. Bu\u{ %e�Drobn\'{�s%�KimA���P�lKF�yxq30+�fA�Me+��H. -J�viegelF:� )3�(35�:S$M. L\u off"�Q.RJ�R10i���L. Park?�HE�Kimblee�e�B.J�vi )��=�9Wf���. v0 �Ra�th�hr ia/Ke�0K. � a�&�Mang[.N�/ �4�S49E�.�Xubo Zou� Pahl&._��kFFOw�W2);a�Di Fidio�uManis-Xo Voge�AA ssinV\:3033825�[J�1K7hk`Eu"yPJ.�2?A�� 2ra�}!RR ,>�r.J238�hBJ luiz} see�e��B�}�rl��1162�v!H��1nE�W.)bR�2e/31�;��6 $adrian}A.A�d�{R.L�)Matos�hoi�Z��*�)�414f n!�Ad}B^��de�_�a=hA8()�.L rowe�|RowA�ic�},u U$�uput�a�2� �2kCohen}:�A�$-Tannoudji�#$Dupont-Roc)&G;jynK in |essus d'"�Fon �+e phot���tomes} E"��� �/ du CNRS,��a�Fr�3 1988, W 252�. pachos} JGs PEDH�Lrt&� }��%�8/ 79u�._blatt}!�B� ndt, Kreut��|e%9b/ Leibfrie� EschJ:midt-Ka���0^2��.�030w;-�*� �2��L. CarvaE�F�w:{2�N� f� 2� "� NielC1{�� �� Chua���'""�x��*�x},�����. ���z0�h Sachdev�S� �yZP0\.GiEo}. ��1��.pOsbo N�T�W~ �2 , . 6S,% 0321M-�9UOU#loh�8b�K �}Ami�G. Falc� Rz�� �(London)IH41$6~26� Mo3}X�!�;!E+kz!�`WKitaevB���� 279�3���$Verstraetex4uz Popp�xJ.�%1.Pa(o�o�"4);ar:SA. M�Ln-Delgad��.a�� ibid-\ 0872].�,BarouchMD71}�6XA McC� !6M. Dresd�P ~� ~M�10R 7+  {\em�)�k776L Ku�TM�UJ.~ �TS�G��k �?P� bf 1\?2��%�lDmitriev%�JV. k Ya. Krivn\[� Ovchinnik_!A�ngk !xExp. T� �9�Fi.CapraroG� � ��; ros,u + J w` � S]� Caux�3} J.-vP aux,^H��Ess��U"Zew6� cC 134�`B�KfXtm2��Iw�'l.}2U^5}�} 4432E .�DeiXL90} S%��k�%�)g1�73m :�0$SyljuasenS�O.!\a�����z�qndv�Z.�E c6�w 0467m:6�R2Td�T.��cilOP%OKshi�oFub� THa�APV. Tog�EaU7.a6 1672��46�"�!��C, ��P*37F":�E�W.� &�eY �-l� 2;���CoffmaI0}� �� Kund~>h.q h6� ��6E&6 �<�� L.~!^~�d�tl[JF�Y!m�=Wlma6~G 022V�:1!�'�>&m�.2=�"42$�96E�A��O^W~M�2S�X: 0603M�M N f �"|jcm}E.A� Jayn#�nd!B$W. Cumming(:r,4Gn �M � 19{QMeberly}TI. Yo���E�p.L11�2392�8K3N�che-rmp}V "WM�o�SrNBdS��56��ubwa��"� Adv.NKWC3j�Kbe��}3"Cav�n�  El��od�a s} e�r.: 5 (�-&�4- 6a(SCHLEICH}W.a�"I�� n�i�-3 S�T} (�, I5 \&q�2:��KNIGHTe�Buz�7P�Dao� res . s}�e, XXXIV, Ed.�eEI� lf (|-�-R, "|-�2�RISKEN!�Eiselt��H� sken2�s)�72z[51EEu5�0GEABANACLOCHE� , Gea -BanaclA_Y�!�%��59�/^); �O(h. Averbukho��&d �22�1�;�%E� Moya-Ce�2QM�.��oenix,��:aS81f�"C�h . AgarwalNMod��b �M�%2# auffeves}� �� a�R�9���*�.5wDAVIDOVA�Mm�S fS7X4887 ����,� =��19cU��GERRY�r �J=38*�@WINELAND"Monroe�gUekhof,hE. Ki;!�"@sc!bf2E�11mj[kZUREKa� H. Zurek,:2 4� 7>I>�TARA}K�]�E' M'iY0 h� vedi2� m!�50u,1LE� our}2R�PNPathakJY7P 0538a`�RAGARWALJV�I2Qta�216E�70Nsqueezed�LR. Kuk���,e. Madaj'2Y ��R31� �koR.+ D2�NB� R36)1w*ՉKIMa^i� ntes��TDodendorf)�H. թ}� �5�JR��1�6Rz� Shor��WJor�G��$olynomial-UcA�=sf Prime Fac�~*y�(Discrete Lo; thms o�fѷ3*�4 \/}, SIAM J.�8. "�� ka14�g97)9�BB�5a0 %�G��a�9d�+ycrypt?0y: Public-keyS� a�coie&g� � c*�!( "�!& C� �e��� `Sig�!m �g,�fgalG�19/s (fQ �!�!�M179; C.HÄ[ `fp� >��IBM T�{�"!�lo�I B t%bf +�1�X316T16� E91�aK�?MOQQ��=� based!)Bell's �5emI]�i I$bf 67(6)},U��<2� 2�]}�< q Feli�Di}\ aut�( argue that�ed corr�]on&�h�/��\A�N8e Broglie-Bohm L&vK will not  �w{�val :a�ose��� ~1mfO . Itk�be showI8�h~9�} follow�{a�^Nde�0�ofF &�-pict�/V�assumed >Gere �be�QR0ce"���two: s if=��u�s&ni�:waӜ�� � � CD}.*�9�L.)�,Panella,Y N. S�xs���midom,)��C 2045��CD��Cz��4Hb"�%I�E��� 30; 1SSղ�8} A�*hei/ymN-�=%�\/}*&�Z%.ye*&�o 3�0MC�a? ice MOp!!� c7�� .���q�*��<( 12 Januaryk 04, Wroc{\l}aw�- E:"/9 wasyA0 Aert@</�)�2� D. -�*lmL�.�48�]#a�79��B��hm-s�"}+�Rk�1�# ��303-5Z.&�v~Y NiChN�M A%l� I5,0? � �[.(. .�.*VP� �W)�QIST}NM <(A2nd�'@ology Roadmapping�(dject, http://qist.lanl.goveEnKi01}B Enk S@�� H{.1:�It@�}�Y� 96}  P W(6 G�n6y) 37th�9ual S"i)o�ge F�7%`�))p�)D)ce}� Ps Alamitos, CaliforniZ[EEE2LG��.mRVM!� Rabitz H,�8Vivie-Riedle R,a�zkus M%�Kompa��#A� 28'1� 2�=RaWa03}nPWalms��Ia�31+eQT�P�) 56} 2��de:(�%p �15} 02140.�� RaRaa0Ramakrishna V6�19a1P5y54} 171��"�KH�(anders G D,a� K-8Ho�� W CN92�9} 1098] BRWW� Brif C,52,A��owa��]�U21 �63@/42�0 TeVR_TZ C!�Kurtz L�RI1mZ=���)� 343} 63.Zg2}g f_%�m8! 5790.�M3} Tropp� U,�Z3~�ј27.�PaK�< Palao J 4Kosloff YX� 18832�.02a} �tay Z,B�0Leone S P~� 59} .# `b} VV3JTh�>B,cq3��1%q�J�262316]� SkTa�$Sklarz S EFd"r Dɐ 4 Lo co� "�for unit�trans� �8:z.�� *0s(<uU=W (out leakage��99i>��408.' ZKLAA�Zadoyan�-K4#a� Lida�JApkar�VVu7KU]�M�2!32." BGLAA�Bih�$Z, Glenn Dqvh��60} 45.i2WaW��}�!�Waxer L�Q8 \jpb��31A�2.�-�er�� A M�0 \RSI 777926G~#!O Brix{1T�2rauer N͡ ' 65�'Hom�*NP44�8]n Ea�^l,��V G, Nikl�[P! > ��<o-�50} 53.[Levis�  RaJMenkiNM 2�m�:b��70FZ2} Z�M��2 \JPhChq� 106} 6427=Si̳ODudH. N, OroAuA& Y!�QhQ"-418} 512V^3} R,fR^3��L _ � 21392�CiZo95}�! J s�Z?0� �hCM}4}�e.PCZ�Poy�' J F,jM� M81} 1322�oMo} Se3rmL©!6:w3�GH 971 \\ v9 & 62h26=JPKa�Jon��Po� M B�e P"� R R 4230.MSJRϡ GA�S�&i^N Jamef�F V�M� Fortw..s  4' 2�DJW!�"���x ��I�2 Wa)"8'�k� B �2M D M!�8 �i J. R�hNa��4^ Stanrolm� 1A�22 CMDW2vB�'����9w D!3 \RMPI�75} 22?GZCV8Garc\'{i}a-Ripo�<,U���$E��E� 91�=6�8BRMR05} Bartelt�: Roth!4Me��ale>� NR� ��90.�ZLL�$Zanardi P,:zLloyd SM8 M��6 06042� KnLaa�n�)�Laflamme�>7 �i��]92� KLP�KribsA=ahPou��%���4} ��2vH-numbTO Hu�K ��*z��>7� Mole�� Spec(�t�u� : IV-t�Diatomic/e�� (N{L: ?�No�&�Sw�old�any2Myd�-�  AhY>�pacht TM�0Bucksbaum P H!�q�:Q8f?6.t_� ^R�%na�Hut�%wD ��2jV� �� 2 \\I ZFP 2P�2E�cI�339.{&NJC�Ev�N���1i- Kwia��v@2eO�147.�PG�F5 , Mi�_e�R,� windQD q=White A �<0N�7} 25.gLPaZLo� oaZDorrer!jA!hM>� �aszek KE�*� ��e���OB 01032�SL��.�0.^@41��DA1 Meye� ѐmd�� 20144GKB� Brenne�<K7vetBM, Je� P�FDeu�/ IS:9b]�&062BKB�2].CaIb�- �62309A�9,.SNF��92 �� r�William!�A9 �BR231.�DJ%\JakӽD�_4 H -�;.��8,�hdiW C' . 9 !�.g92ѷTC%fCalarco� U�s\B,}SU�edm�a|  :� :�Ik &]7TC��.sDK-r� JuliAMA5,66an���-�f>32�DD%�DeMille�7%y18�:iDV�Vaga, Segev \ BAtY �>ŀ� 2MSJSaffm\�a�ker Tf RE47- �7� .� L)dLe�OqSvskaya!�!AF} 6232.TJD�?Dunn T!�Sweet�?J8 2�! RadzUEC � ���70} 338.MB� Br�?t M P��5Wasyl^ �B.s, �{6��Kosut R 6�2�_of�oonn �5Jd��.� cules (un� shed.�DiV� &* D P�5.�51X�2�BaRa86}� utEO�Ra~ 87� �G�G�� R:M!m?L�ԟdd. (Si�: BX)#$tific) ch~.�RHR��"�$A, Hsieh MM �thal C�4�6j3� 3!}�\5&Z�.X� .< 72} �*3.NCM-6�V�HmrbQ,2006 Robustnm'of�QlyQ$�j,L�4 > N.*!f�22} \exp��,fter\ifx\csn8�natexlabU \-x\def\ #1{#1}\fibGbibO font>J M#�Pf�Q$�R6 ~R.$�Rurl^�url#1{VOtt!O%8{URL Ipro�acommand{!\jS}[2]{#!�>!��[2][]{S'}y.[{2�{P��m et~0u2)V$��lla #Ma� 0}}]{rotpaper} nfo{�!}�5�{J̓} �1��}}�kjAMJAS �@[and mjRN�}A�]�{�,�jo�}{P^\�/\�"XQCk�c}�.C�^}{0351�_ (2year}�62}.n1b�a�� �!�4)}]{{6 Gate���2F- �V���@VIA}jG99�C5Ig}NG4rGTM]�1:� ,nbj?abbittA� tian!�5�^}~#5JW:�V:R>:Re�QMQAᆛ W.~R>v�2u5��?\  #j�26:�-�1J\N�1r�JulsgasH=�4:�%�She�n,��as|+$and Polzik!� juls�2!�EAVwB>wm:�V?J>? ��=~I!l.� �>:k��! �3E�V:1O!y�%IU2��bfF 432:�M.4�J v� Kuhn.(>� a$nnr�F� ��mpeA kuhn�:�V�A>XW:�V:M>:H �ڒG>PR �V�2�~�8^_�R�v�D�w5�� :�!u�)�P!� brie�5z�H  B�a:�_���]:>qvE�kP>����!�1:�m@59C�>A!vrn Ohls�l>D #Fhs)�K�*ll!� ohls�FN> Y:�VIR�n:�M��IS>��V�Op�5 Comm�x�U�� 20Z�>�20zBMoiseev!r5p� 1� mo~  S.~A�.R X}:P�H�:��7:M� 1736�JCvNF΍2� 4{"� {a}}:� 0AX ;# A�CP�uE>^ W:�V�B3 ����m ��B�j� 9Z�077^�4}:�*Y>>� $Callaghan}�BE�@�KgA�~VHP��:�Ni�@#Htitle}{ �aln Nucl�jMa�=ic�y ��x�y}� Y��r}{OxA� Uqg:�+.add�9, ��'B�8r�Hah%"50�hahn5ǼFV"E�:"I6�2\vj80:?m��S=#�50r� ViolX@E8� viol�L>�Q���� �j-" ��^458:D-2 2733N39v����MF6�!,�!lS8 ���%X9��^X�9U�^v:� ���B���� Z�241Jm!h����!h��bh9fu�J.\ v d.\ �j�5�CQq3�R�v� Byrd�I(�2a�byr��zu�:�S֧DJ� �6�58B��^�b& 4�F��� Vital�:Tombesi��9!@v��D>S U�@B� ��?n�5Za41�,�>�9vQS ���*Wb�� Mo�on� Fe� Pr-Y��� ~JAf.� &� ��B���GBP1 2�u2Jumi�ab*10Z� 3�">�!�. !�j Equal9��):� "^��X� Macfarlan�7i�l!�j& RJ[ ]:V�RJe C�� �[ R.~M>:.�V�2�B@^�5Z�39�1>�!xr� Mims��6� mimsqzrW�ş5I��j�16Zh 3. F�6vg 9u��m:�&!�Meltz-@a�� alki9 macf�� ��b�S!$.x �9]5t%�j B.~ZN9 �*d�=>���b�!���56�.F�� and� �3�go��!j�^� �25�� V�B= .;V3~� 9Z� 03b�3r� Wocj���!/ wocj�� BH H!>�[ }), �{!�=410�I� N ! 9 f !": tem{b�%ttd$.jA, G*kBaFCrepeau�\ Jozs��{�a�vn�70���̊E �ch�T'��TUI*X,<: ``QhA�:z4| Info��.'' Cj@>,�".�16ZG&{B:�[ot%G&A�,N&�N�W~�zǟ66Gd�)�� &N��.��aac"e�&[ ���anOo,*0�i5 77, 2R#H5 2>H�~BerZ�.p �B.2�� t A 53=V4�P�ZU p1>pD.�Ov*6��� rfgA 54,6�Or duanAzL.Tu�_Y iedk�]�%F0p�2JE84, 40fU2�G boseI*(S.Bose, V.V�� SL.022TA 6a/9�v2�J(kwiat} P.G.?-!}B.-LopezE Stef��bN����1C409Q��z>fI yama�|} T. Y V KoasRSA�Ozd�<`I4`21,G:�P2�Dze��1}%Z -Wei�B�a�t�C�{u���b9e1! 0�d>�f�=iaf�basparonle>Ur%G.�/h�ZVo23, 41���PUAwooGt1�Ov1��f�ũ 78, i��EibBQ8��vS80I��s�r>E:��+.�*@1Z. 1, A2�te�W(p[. TEMOIA.!�D�)�a�icsc? 56, a�\3�S�budz��J@B, Z�. %`Jo 13��Za692Huh�U\U ,B�r 9��G72pjosza} KJ ,��.* 14!8a196�P uchia/�� U %�{ZP:6l A66,t�0L20EM�g�M8,�)�p2�l/41}\V"(S.+6f58%%AA 9�a0�B�.�9 45 �1Uv5l�(g} Lu-Ming �Q%G��-Can Gux�&&m A 26��9!d6��a�Xa IzR�ia 82, �ea2AUb.UG��N=52* T�88ہ 38:4a�52�:���1 ��2n�198' B�H���.�ea cosm�Oist2�In Isham�[, Penr��LiaFaD.~xo�yg ��v�$�Yl 6��6�Z�$.EV5�a�elA�82F6�-�iUy,sible pilot ��.�E�P7D(, 12:989--9��17��F'>x��9��Sp.J�t UnU:t1�"�R6܅b�Nu90 �agaa�B��e�A ' `*��'BXa$J�92�August,]S 33-4.@1-G� K�RC6� T ��e�%:Wmqan unknNYX�$e via dual*4��{EPR}�( } 0:1895--�xN W�TA 98a[� shor 8>1PL �6|Q*5A�u�]<{\em I�aEEE Trans. on Inf. Theor.}, 44(6):2724--2742. \bibitem[Bennett and Weisner, 1992]{superdense} Ben', C.~H.6.S.~J. (5�). \newblock Communication via one-<�@two-particle operators on {E}instein-{P}odolsky-{R}osen states.gL{\em Phys. Rev. Lett�D69(20):2881--2884..�plackburn and Simmons, 1999]{b:s } 0, S �4K �92��Truth}.XOxford University Press2�ohm�$51]{bohm} Dg51FgQuantum)�ty}, chapter~22, pages 615--619.�tPrentice-Hall, Englewood CliffV�2 �:1952:�6�PA suggested interpretI of the q �tA�$y in termshiddeA 4variables, {I}%�{II2R%i9�X}, 85:166--179;180--193>aKHiley!k93 �h�A %BU�3F�,The Undivide5�He: An Ontological IB-� Cory2�@Routledge, LondonB�et~al.�55]{bst!�5�8, Schiller, R.,�Tiomno, i�552�A class�V�({P}auli equ%�.Q%� Nuov. Cim!�0Supp 1:48--666� olos�Jeffr)�74!�:j �, Giv.Re742��$Computabila`!�L!�2\Cambridg!�n� schi=g98]{rom�,, D., Branca�, M��ni, F.~Hardy, L-~Popescu,�182�HExperimental realiz%eadteleporting an unknown puryKs� �k dual=�!vYchannel�[80:11216� uwmea�r51@2000]{physicsofqi!�')=Ekert, A-!ZeilingA� A. (B2#%�apa�ic�/mF��orm%22�SprS�-Verlag, Berlin, Heidelberg, New York~� 1997]{inn�>�PanaZ-WE 0ttle, K., Ebi ,M., Weinfurt�H � >�e2�2�:M�F�Lature}, 390:575--5792�rau�h�B96]{b:irreţblA�A�~LI�62�1�2� without .P detecB�!���4A}, 53(3):1900V�:j�twist} B�$, D'{A}ria�G.~!�Mil �e~J)�0 Sacchi, M.~FN���alJ� a �n��<84(15):3486--348:�ow)��� :1993�H.~�:�DCorrespondence, in�Jnce� heurista?�whe emerg,\ of special relativity.� In FrenchA Q Kamminga,E�edi� ,i�:� I6�H�}��227--260. Kluwer Academic Publisher2�repr.̈Butterfield \textit{et al.} (eds.) (Space-Time}� Dartmouthc�i�Kany��A� &7 !��PooG200� p::���1OIW6� ��origi�� he s�`time metric: Bell's `{L}o� �%]5:032315:�ss,!T�rus�r�20:�(Characteriza^/�a� ath.)�P43(9):4237--4256�ub� 7]{bub' 7} �972�a"��A�q�World2D f1@, first paperback. 9)-i:��AC �commit!��2�Abm bit�� 6� oremB�Found98$31:735--756� �'ub:wha�!2?2�Whyp�?*�%M$Stud. Histyil�Ue�� 5(�U4�: usK � ]{b :observ�!Pt 6�Is.�M�(an) B.�In Cohen$~S., Horney�StacheliY2� � ot�aW/tu�?PaV,on-at-a-Distu "� 61--7"�  2� � H, Dordrecht, Boston&�F E��9604016�!4��1�a6=T$, Lahti, P&� Mitt�b aedtE�� �%�A�q1k��M&E2A��2nd%w:7 Cave- Fuch� 6]{f :how��} &�t~M� -C�9J��*� :�*��aM]vector:T Mann�E RevzIb>0 !1Dilemma�+&�� &�F{�h--- 60 Years Later}. Israele[iYSociet2� B�9601025.�%1U&��a1UJ atiD6[,2XɀSchackaV�}6� Condi!�s for��\! E�uq�aG͝B��M!b.ɒ6�,062111/1--11.2B02�s2KF(b]{cfs:defi�i��6� U�2�s:E de {F} p� res�!3.�evj. R5372�erfEIAdami�9]{cerfa�9} &��< -Ci/6�q/extens� of c1�al probvB�>�0� 893--396� hait�1966]{c } G�(2�On� length�programYtu��$finite bin$ sequ Fk J. Assoc.!uch�� 13:5� 62� Chur��3�:1936� � (2�A�sol��� blem�e&� number�orF[ Amer� Jour!�ofE"e cs�(58:345--365.�"6P\cite{davis} pp.89-106�lifton.-3]{cb�w a�, ?�Halvors��H�6<: qJ.�etic AstrainJ F: 3(11):1562%$Page refs.N J31106� �e0�� . )pope} %!) 6� M�nonloc]!�� 1���Zdar76lprotoco2�4i~��8 292(1-2):�41030767ollin�!��>2:!scu} ,�50SI6� C"}analog! � NQ ���65-� �&�F�107082�Copeland%�0� � ,�2�Narrow .upd�!�$ism: Inclu��-examin��$ of {T}u�'s views� !�Dmind-machine issue.��P}�&$}, {XCVI}(Ak&a2�%� �0:encyclopediaV�6�z{C}��-��si2J(Sta�d�e!��@; http://plato.A�) D.edu/archives/fallAh$/entries/c �t%A/2� �Iuroudfoot%�49�:p�4F��>m�6 �/ u�artifi? AlliWJ!�9-es2!In Te� e8< ,)�Alan T�: Lif�Legac�/a GreatI!r"y 317--351.^� *2Buti198a } N%86 E�6"� introdu��h0recursive fun !23 ft.�David�e ���:aY,sandevents} +!�/2��Essaye�A @%�E B.���"p� 65]� �sra65F�AXUndecid .|Raven &�wl�eF��82 �:1982) ��86��P{G\"o}del didn't haveu�'sA�:�%@Ia�{o�#Co!�l�4:3--22�$d'Espagnat� 76]{}  �~�76> r*a���]2M��cs2E(Addison-Wes�se� %�:� Deut�198!� !I5} MT6�6 I�,5E�:${P}rincipliف*u�!�" �!N�rocee�g�@Royal�pE#�+400:971 2� ��FoRB�:�%�A�FabricgR�!t6�,Penguin Book6�e5Z� 1ZA�c FV� )^~*� e�J2��!3.G#S� ! 4455:3129--3127.va�%�-Q990606 �"* `]� etal| ) ,>"LupI#�6�Ms, ]%�� um pp"N�mO HO/9911152  �J Hayd�� ]{dh6���"�&2�. flow� � d�system2�z�6:1759�&74.�{a}>�%�6� Diek���  } m�6C2�)4by {EPR} devicJ0>d 92(t*�722� irac��47]{d � P. A� (1946�%ajP�*e�`V�Z���irV�retske�81]{d ��1} F.~I.�8a &k � Know�'E*��FAof.2�Basil c*well, �25 ��32�3R�6j Pr{\'e}ci%4�it{{K}B�{F} �{I}��}� {R}U"sF� Behavio\ aB� Sci\$}, 6:55--96r�82�8R�82e%kExplain� �ur:�� sonsawa�!}Cause6{MIT}G2l{\"u}>�&wty� (, W., Vidal7$�CI�JIB Thre@b�!xbe��#Hwo inequivalent wayJ!&�,�2314--1/16juIO20�d� A3 �2\qU.w,does not exi6� %�~�4�479--4929Earma+ Nor��$]{e:n} (�Eb,�02�Fo�&L is a day: SupertaskE{P}it�!�${M}ala�,-{H}ogarth �!t!N�"�"ofQ�A� 0:22�.OEberharda�78]{e } PV/ (1976�B�#��e�,�Q�A"�e�@2/Nou&�+46B:39�6~Eu/�19]{e :%}  1916� What!q���&A&.3��qon �%2`28 Nove�2E �*X35]œ2� , Po203 i�R90�!a36� Can��m' $al descrip !�S9%�be!zsidere�� let2m%{y�� 7:772r E�*199�  1} )k96fq�crypt�r%�!d={B}25B�A�7:6�662: �eoJozsaAx�j�6.��� ,� 6� �� � 4!or's fa`��algorithF��1M�"��8�_7�"75��a�!k�8v�6��� s: E. enh��0"�"� cessingJ�il.�3R.>� 356(174+76� �&tB� 98�6� vere�'1957]{�+ett} III�)a!56x ``��/(e{te"�muoey q@2�eF� 29:454--62�FaddeevAi�f } D.~o3:�In; T-Y;$rbeiten zu2#.strie�*p*388--91.  er 6. der Wi6#schaft! I..�FX,)g fano�j,UN\D6fs�/šBR� dwty 'oEtechniqu6Cbs(1):74--63Feynm�.]{f � 2} i�:$ SiIng�#th�F  Int.�of�or,!y�21(6/A|&�}E�� �:!% # Lec /����2� �.�Eds�He'R.A+2�� A�25]{f} Ry26t&- !��-al esti8.���Cam!.�-�0}, 22:700--722�F�*di� 3]{f } �/B� *�.��- A�22\��"�  Gu�to*��)xA*�$m*�65.NN � "$� } � 2 ��f%�ef�lightA�qs*� :Gon2A� T�9" E!��s�wDecohe'/i#- Impl9��)�> �f� {IOS� 4!Amsterda2#~�x'6�$->["!on�) 9X:� ��� asNJ (!�T a li3 more2�,In Khrenikov� 1R-Qli>� co� )7N*0}. V{\"{a}}xj o}}�1�G>.�BI0205032� -!+bQ� whatJ�:!�a�!0 A�hell are y? (�T.#st-{V}�2�PhaseI^"}2NGtt{Xhnetlib.bell-labs.com/who/caG$}2�Y$�? :paulianJ�6{ ��Not�ma P 8 Idea:=�7,'o��necdotalA� � ward Look�5Though� � 1O({S}elech:6j2)2� V\"axj\"o�1V� Pere)'0Q p:%A� +� B��y needj `A&8;'.�%g� �1 Toda�.57�2*%���$�(]{fs:G8�&?&��-�`12_V�#e�iP=a� ayes�2�.�Fq 40416�)Furusawa*� � cal�!j �1S3s� �56�5*�%, Kimb�7. %�olzik�TE� :� Unefal��2~ .�%��4}, October:706)2QG].do�PMart{\'{\i}}n-Delgadoe� 2]{g ):mbn-d } A!nEM���&2���?*� :2� &�a 6Jq"F� 74�$3/$423."l nw"112102� Galv{\~a}),HX;�<]{lucien:substit�$% 1,�F) 8R S@ a q�� P an arbitrarily large�$&�! �,2UE a�.) �"L}, 90(8):087902--1--2Ghiradi]��grw:no-�5ah"� ),&C., Rim5*/A�Wm 24(1�A'298.��r66]!} �6�U7ed dynam�I�)(microscopic%Bmab�� )�D�-4:4��492� Gisiie�1C]{g�8#�!� '�5+2�(Maximal vio&�"�iE��F�spiF� �L?CZ 162:8B6%Gottes198]{g} T:H0 {H}eisenw=�'&�)aM� ��:�9N�80700621re _*�>(1989]{GHZ} }<:/:�2=2~Go�beyond9v��e2� � afatok :� B�� em," t ��O!2 U�[�Hs N9Klu>#"G/6ic?Yg -B7!��2�Mea]B��$I�} 6:37e#88.)"^)his� it{'i��Wa� ds},��v� �it" :�� 9) Chpt. 6�/Gud�:1977]{g: } S.~ �76� Four�9ro�0s� axio�cU���2�I"%9 W.~C�\Ch�%.S^1,A� Uncertain �.� *� !� "� A Fifty /' Surve� E 2�i(276. John W�D�ISo &X HackA)1987]{�.e!2 87} )/86/Langu&,�'� b�>Blake� Q �ev�=6>q 1Mindw�0�% 48�@0~�FV �ll� M�~W�6��=on {`*?#I"�7!�S{8*# ...' bA�C.W7��A.�22v F� 007112�Hal&,�hans:g�=D�&H �6x G20�a`{H}ughJ3 -{J}�-{W}o��r�$>5 to�(yp9?.v!N}eumann� ebra2�F�310002�6�4!�ns�4N�6_ Ou2">-�Ztic ,@7�e+"�(iJ�x��5��26�%�B61�-�;6smoliB�A2�62\Ca&z2�im�:�m�s?�%�{S}u.sN�10�..�rdy�p$�y:d�tf,iT *# x2�D.+2�-�b B��"1 2�ris������ M.�6��W�0mQ?y�� head.In����50�>16z�Har�E 1968A�: A� �~B� 6V]5�a�i[J�G^� Am��� }, 36^ 704--76 $Hewitt-Hor� �]{h } > 3#2њ� e�%�m+Cworldz,210202� fKAp]{�K[9} &K6��*ve.��b�I( � , R�!~L2��W:� Epi�%"�KA�2�GPer%�-�f12b �):" enna� ircle In�e�� book E113--125 E*'9.� Hodg��k�m �6j�would {A�C&�-h�*done �r�4.���-^�-43--58��-H�!�A9%�!} Meq96�Non&�*I��!�nFa8.[� �D&"u"&�A}, I:12�N32�Holevo�73a��!�~+2 19732�*����al���B"�BF�robl.N� m. (USSR)�:1�182RHol/95�a�5�7;�H6�%/��q� �5o� 0/Accoun�� de g 0roglie-{B}ohm�%nVO&: 2� fV/F�>� : - HorodeckiE$!��R s:re�/! 5�.>9PI�6�R= criterk�separM�IlimO&a�M dXl52�%���� �59�)42�42:� �*�96aA � sPLAA 6:�,.(P�dO��9667;S.�of mixed"@NeP!a( sufv2� "�^�&�2:��%Y%�62�RJ�RB��q6uR�.�in2�:�F�&|(5i' 1838--184:�-�2�b.�:alpha`4opy2�@R=J��6� 183:�*6 yW 1]{h �N1} ���o54:'��InvH!gaj Psych� *#c�f�Tr� Wittge Q2-"�U2k ��A< ��  � � :��F�S.wor 29��G.a2rtA"49��):4�&46�EIvanoviH/�.i } IG1>�.GeomeKNF�(4al�f �Qr�:�Jp �x 14:3�D3242�Jablonka�j } tBf �) : It/!t*,R! inheritp'I�� shaB(J�<#ci!],69(4):578--66jJamiolI1972]{j�."�76$ Lin�M �Zwhich �@rveU"po�]'emiwA�&esofBB�Re�?th-�� �26�< Jayn ��� E.~TE�BV'"�a4o�m� ?R��;6M��[}, 106�620--320��1Kj�aM8} ~2� 2p)� E�um��u�xHY�In&�P�FM!0�-,=�U�6 Tsou�~T�8dhouse� M}A:� yS�&�3� 379.�1 $��"9707032.-�)4 2424�aX+2R"ou�W��B�5n!#H{5A�o}�� 1�126b� �M"�W.{�1] �private>�6&�PPA!&�^VZ3Z�>W:� llu�A�n� �/!Q�ZQ&B030516��E�L n�D�?.�a$��2�Oe� rop_f e��Mz2 �-���peed-upB{�(F�,45t_3�501�5032.=F�(6� � Schu@�1�s:E�>.2`:�A new �Z  �( noiseless �Q!�.���J�KOpBW�/ 1:23�2342�! Kennl71]{k �1} �:6� homunculu/ llac2s�M��%'"�M%�e�L.?�}��*��#"� E"�1}E155-16I ��89:�86+ %A� Meta�� ��O�)aKolmogor.(1c>ko5} .#A� :m>T�5ap.a�Ei!Iv 8G�of^��RQorm"T�:M.r Kull0OJ 5!D } �5JE�X!QorS��6�DovaF{D} !/8J �( "�Xy�Pe�[�,�b�:l :��� �E&P6�6�4"�6�%LAnnyH� �!I�,9--866Lmm �� kah �0�IH6JA�sv/�5!�a pair spin-1/2 �d21��.�*� 8�174`F:uP��,] �2!L �H �2�b��E�umVt$Z�410�;116LandauA���au�L �92��_��"i&�t12�%SC�4Y 20:)26( �-�1] ��0? 6M.<is"?B��$a)May:2�A2�m15)9 �6}F�6A�� al n�_A}Z6R#217:1�216�Lar ) 1990!#�,�296% S(9sr\ g&y:!� exact u&�  r40onship betwee� BlX�F9&<:�K.�e� 3:10e80�J��L�'ChI�497]{lochau} Loe�K� "H.�'a�6�Is.7�LTreoZ� s��.�=v�(L#%}, 78(Z41� 46wW LoewM��� 7� �8J�A gH1Edlsemanr.�� a�*B �Wrigh�ib!A� pan���1� .�:�!*� F� "�1N�1Maron%3��m :�} (,�^�/ ,� 6�? ��2� u�^st�h*�(!oh�i2)./%�h#��29UW140g46�BMaudl�O�&m � 7:�&Par69who ��$6.In Caste:i�*1�>� ABo@%5�46�� A etonB^,�dJersey.?��]{ :loc:�$2�%V1�QLoc}(!�R�(vi:EUR &�a Ltd.Qb,j�F MayeA��Em� {(72�2�-ly]urQ2is!o�B:�->34�3412� McLaughl�)R�hEKcl :rea*��&)<y�*�&6S��cl � a2�"�  E*�L�^i�2�e1@`:2|} %&k[16� FromD��e�-swappA��{el�h�nd�65�8012320.,FJ1?6~� �b]{ �whoseR�6�W(&�.In�9tl%� %�rm4 ({U}n)speak�J=<rKi�Ymm6'% of �%hn�#.��ell� rLXl�-2�N,716P=,25+��*W$9�6�6/�%� n�VJ��eZK3�� 4560--4562� ��pp=eN&S>N�6 Onh7N3��~7&4�5�5222KorgS;� ]{pe�n} �2��� Niel� 7]{n :ct} �1�2^!��Nl&xNs," m&( s,E�a !/.�% %�: 9�h29:.296���]�V�'ingmix�&% �,6�6D_ 8��aP�Rw>��n@a2n �aChuang�S0=}B���1/HB���1��:*� 2�f� .�.� Kemp"�UeleN rderR� 3�(6��l@s�8 more| Sed(gbX than�l^� 2\ 86:518�&.vF� 01116�ParT7|narkt0} J�% (1976� � *��2i%�~� %�:T 1��6] PaulK 8� :r& W�86ib&ZQ �.�PeierlR)6��:ghost} ":3In :Qe= .<W���j�~ �b !CG]!3t�: Atom.�=�&70--8Z�i�;&� �'Ep �def_JB�B� *��{``*�_"2R%h���Fc Janu�pp.19-�.�nro'�!l� 8�*��6� q���,6��H�Kr$. �izED:19Vm 19396&�:1�%p ��N�%�I�:�20Method6�Kl^�m*�(ApDdA[:�5e����s>�6f��*:R%� � f�N2�77`+14�):4P����63A R(e$ 63� �'A66�aE1l� E�N}�� ohF�fBullet&/nasici"en\B,19(7):�2�PK�� 2]{p �2} ͽ6� Q%�]�N-A�supp.�(3):S168--S1I&d*�S{PSA}80, Sym6 p"6}�auM� :hRx} Y:�B�5">7�4a}B#�/v J ng ` ]xo1�J�&>4:2619�p@ �N�6 50206� ��Rohrli�_9!� �r 6��106�GQ2i&5n&�]Z�G 166:2�92� sAki�3�'re} k2� 's �?ur�#&KIw:\I�@ www.k5>U[$\sim$� /ph26�Quig1953]{q 4!3} W. V.~�q#2��� a Lo�y Poin View2uHa>�6�sn� � 1960�60R�66��W�|AObjec6�fMIT �.%RedS1r �.} M.G��:�1vIn!�letene�J*alism2Z%6�hacek�H?=l��h�"�2&Z. � 6I�t�"a7W �ej�GF� 88(13):13�h2�ind�{�r }  :�-Y6^\S�u^) bSfZR gnol+ CanoN�r:c} 0�Ak4R� V.�<majori�5&fU � ,YYG�&�\*Kmea�"F7ed=r�=!�N��� 7:0423022�u!�a6*r:|4} �76�%�Gra�4&���2�y�(1949]{ryle:� } i�4J\�8�Min �uK�Z,{F�Z{C}�@se(0R�mSa�!�1s :*�} &�42<�2i�8�! fC.�%UֱERedD�=`,0:��2��.simon1J�6�0�R.7chanic4�s�IB(Synthe&102:2�n: n2�]/�*smJ�:7/s2�"Inׁt�f&� bvpa?glon"� �\� ge�(125--142�42�m"�y&� 6�b] �2N�6~rdt�,v^7:W 52/2�8 �3J�6}r�pj�i.� +73--402� Savag�R54]{sa��(� 56&U�w3F#%!$2U,*�!72N` ,�ppa���Vauto} P�!�� N�J6 bert*�m: Autobi�T'J2�Opeurta �aI% La S�z, IEo6meF�ruI�SdA.&ilpp e]K it{A �XV:.er-/.@ }�y5�l Librof Li/�ler�]�chr�Ko}}�`$35a]{schro �pF(-1,2Discu�Eof.|�(�*4K^5:b .Hil{TG,1:5�[566@F��a��:cakdJ,�:�h��es�1 situE�!tf m�`B��wi.�SX13:8�;812;8�!$828;844--8�'��6�&t[�T52-167]{wheeler:zurek}.J� 19362��lJ+-6�3&�5���\��!�2:4"46~{.&)��q�(e�um C&� 6�� 1B�*� F 51�-276�8Schwi�� s� :� UniY"Y/�XFI� Nat.Ţ�i. US� 46:5�2�Ak��$]{sha�$�:� .=2k"�h�N�!�7jfBf$Notre Dame.�jFor�GQA�8!Z׉6�See also�B� S.G.��.� 's Remark�<�:R{AI}},T#Q� 1,&U�(6�I!'na194�_@C}%?C.~i4:bheh�osJ&��#xun3SBo�( Syst. Tech?!7:3#(423, 6�6>&^�%�$non:weaver�*30s=;[E&�L this�7in2|=�5� �16N�56��bandwag6�0��{IRE} ڍ&׍P<{IT}-2(-�t } W�!��� �>�� 1l:����s5�!�C.1d2�&�G(�g, Urban�.Cgo, {I}��i� r 3JSh� y�8? � �86> �il�unc�i ^��ImeSi&2 E ::�)&�Gi'Z,L�%! �jA�n�6}�2 kyo.!T�J& �v0 Japa2R��5 Ay�Search� a� uK& ld��PVol. 2, V�!b93,�a6CShoEe� ho��P.7�6�A"�2���ut:� rete�ga^� &"^.InI���*5!n 35th� nnAC${IEEE} {S}D um o!�:�CM er�e.m�cB�950805i}��E�3]{)F��F2� �F��B�0�G62� Soar���� } R�dd6�%��+�nJ��#.�Symbolicټ(�=# olomonoffAh6a��R 6:RAI��9in~?vDe�Y.�N arts�_�RM��e�)�)�/22;22D:N pekkeI!%U]{s } d2TI�sA�eXDic �qs�.sy�to�~: wF�4%6�tea�9"s:$"} �0::'��i�:f��8oMog.�  N1:1�q17��S97aFR�a,] �.�~}>2bA5@ �er�ZcW�DenJMtv��#4�7472�<St{\o}r�0�xt3�� :bP :l>:map�"� alF�K%�Acta.�!w$110(3-4):2:<2>�raw0r50!M !O �C��1956>Tє. }�u. AS�ot"ES�24:Ln1n� t[C�O {XI}N~�.:�\� ��p>� Taus�!� t } 8b66%�* A�Q���2�PhDa�si��Q�9�E \~ao�Zo.#pp.29-32�Th� 0]{t} BU�6~B*\B��9. &�.��e�*�271:3(326.� TimpE"�$]{t :b�} C.�%2w*�$�H�" {P"�q: Some&�� �z ider 2� Bj�`J~O16��&�\4users.ox.ac.uk� quee0776/�is.htm[)ٔ塷9R6�QC�w�~� -5 hypo �:� !=/.��{I^{I21�240b�;Z.w-/ �7$$'. ]{er>51B4)HM$Y6�B�=J.: :/r\�eV"� � kRvr_y}eMv"�o}.:� B� na, CLUEB��logna.�F212140JU�9#4]{a^ep�"6gPr�Rimp . v�402092�TsXZs eX�2Ӑt 0��ve�E} 3�S, Lloyd !� Bara���&��#��� 2�"�1noy�2�%ى��#��)42i>/6�Fzj 36]{<{}  :�Ona� le {N}umb�0w�fan app�c�.�&��iqE}nAweidungs4le6� �F�vL����"s/-E0--�;9Y6�yy�� 116-6�-Uffin�1#6jos} � :62���0�*�V%���.�2�w�EAm"�d�� VaidF 4]{v } �]">2��80Kdoxa�.gI>^ e"x�2o]5u�"əForbess=E�uD���cPSAW4\volume~1b&�%`ced�i��.-Vri4 a�rin��1I� J&9:�1Signal�3a��un"}X�-!� sub-1{$H$}mUm.& .B%�ig*�#�l ,2):2�:�bB�V�6�� V� F�8(�1--2� Ʃ�s!�earlyB�&2�H{&.˞s��.@EEU!�WR� w2ricmont, ID]u}}�CGalavottfN`._ PetruccioF�D Zang�NB�C�n !0ics.�e� a P*�R* 165�L2&Hv�ZA6h22�sq;dethvNo:�h:3�subQ�K�}i��1in%�Y%� -vary�!�o>RX!�u"h�,�*% l$ma>Non27JFode�},�#64E ee NATO�"Se�:E�}Bx.�F� 11216�:hb.�Yb�7Rkr�!P�@�AR2� 97)ZM c2�ER�c2SV�!�� �|�? �ram��<�9:� )Fp 2030�.����.�adRf� N�6�j�E��)A.�Q�J�F� 30916|�[N�[ 55]{vN} 2 :,�%'�2:H ZL_R�:.�EngZ"�1�R.&W!E�2 2]{w :�X} �*AG2�/\&�{{E})s zC<~3:6��6�>Y0J�+_�92^�3a�s��!�F�36& E �A�6.R%�~�4:87--16r,5NA�b����Bs366 �j7: D�1� {D}e�'sY �aV 9 a�/ �n��2���646� Wehrla78]{w } / 76�G;-� pertF.osIroJ� � M.�v5�22AI62D Wern�9��� �:uGq�sE� &}�-{PBe�cormo�� dmit� aB� mode2vR In Z�"�S},)��lexit��A��a;!��4of��+�"�  8. >*� Redw~ACVCAJd �19��- S#>�� /WyU��e6 EbQ��@��c2� ng�� Whit �w �!2�M~6@���$�*I��Row�~Ls eF�A Wich]>1Cw } E!'^:ED'x�Uc�9ixz f�?i"�/.U+2p�JNE$�4(C4�9962�ig��61]{w~K1� E�@��6 6}" �body quU/6[,In Good, I.~&VM�!�R�' /ul�Q�g��-� n>AnN^�6<t:�,F 68-1:�*@V��52w:i&�Vo:�61�5J��5�*�VF.`"OC1�!w7*�-&��:8. G.E.M Anscomb2�V6�195��itt:blue�16# �82c EO!�Blup!�f.:"lidVry��.�\B`n'6VE�,�0! V��Y�EF<�� �cop�yl^0" W} 1�owH8B"uW6�/.P��-2Q�0uh�l�biasedv�M��. (NY�_191:36�)�ح]�{wZ�� .� 1��!=:�A �UlЄ~�can�� lone2�eE�#�%$99:802--802� $WoronowiczaD76]{w!uS"�=6� "A:̆dim��S�xfH�� �� 10:1`�**�C 1999a]{ze��:r�0} $�999:� "t%��.�z*v[LF�^ 29 71(��b�b]{dalp �N�6� A�� i��a��mb�+9T29�(3�r2Mux]{}+� 0} u� &\J���.q 2FSFI����he�Y�Iof2^v7% VIIIB!  R# (end{thebibl/,y}�#\beginB {23} \exp�O,fter\ifx\csn*natexlabU \� x\def\ #1{#1}\fibGbibO font>J M#�Pf�Q$�Rc[w'j�.$�Rurl^�url#1{�tt!O%8{URL Iprovi"4mmand{!\� }[2]{#2} B!�  []{S'}}�{2� {Efimov}(�B(}]{E_PL33B}�(nfo{author}|5�{V.}~�1jI�<joub�}{�z~}�bfR'�}{y6A0pages}{563} (Wyear}{�}).[ :�Lekner�2� L_MOLPHYSe(bi }V�J>� M6��Mol.~�j�23:? �619R�2r�J�4n{}�4)6� "�wisaM2'}edWand G'mZR ��> D.~V>} �@U� and}Y�V�E>�5!0�E�5��F~�F��76�Deid}{215F�'"r�im5��t:� Lim, Duff� 0rt!� LDD_PRL38��T� )15CLim:�VGSJ<�0!FR!��,v�&u:��0�V�e~%��i8:�m�341F�!or�Chi2�1:� , VuwCc, Ke���and�I!�4CVKC_NUCLPA684��C>�d:�V�B� ��=AK:� �?2�%�E�V�SF�uK9uyNuc�e%?6"-� 641cF�r� Sch{ڙllkop#�Toennies�[94�[,ST_SCIENCE26�BW>�6d}q�KJ5B:�},9�5Sce6��N��.=-N134J� 1994rNGrti ��({"� ��:@4,�9=��0)�aM0Hegerfeldt, K&hl� and StollagGSTHKS�85�eR~4I�5��:cV����z)�&�=ՆIG�:A9,��T>�9`@����e�VM>R-�2�U���85��M�2284}BC A{}:|jQ 1�U��^� f�2�and]�U�E�� v(��������2e����E'�lZ� 175V92({BK_MSSK_BH�$P.~Barlett�6(A.~Kievsky,��A"? 64e/0ٱ4+1). +�� $~Motovilov�Sandhasm)~� ofi|E�%E KolganovaA�Eur� ~J.~Dv13�=3p�v.~Braate�*Hξ~Ha�`}��7},�706H�qtem>� quf2b}�2Man�.TA- Smithm�MS�)A���������JW-��ug)#:SV�o�:?%Z>U�!��HZ6>P)�A�5�N�Aj�61:��"033608�$Anj$Br7�-�2:!!B� ����,]{BST_JCP117��L99:,h:�V���2�9�VV�-�:�N� J.~Chem�y=^� !.D-�154V�M i�@tem{footnote-asym�p$y} {As seeOB4Fig.~\ref{fig:%i T��X!aar�s $\v �eta_n=\T - 0$�Vl?OiC( (.9\neq-I{-n}$)\ agre��!kHBragg law Eq.~(�0eq:Deltaky}).Kre�g5 effec{�u(Hed,#��$ns�4� y. !�5<>�&O >�" 8! H� A57_�O ~�~:8*� R;5�; 2021]1Ia�M61�K236͉�Y"� lderiv!{Th)�rg���%�be%�(ed�m�XH��Q.u:�J IX�'YBor Wolf!�59!�bornw 9fUB Q}�j�B�>B��%�)�@title}{�!�%1O�m.(H r}{Pergam%�iRs .��59}!I� �r}{\%X3}�HYnba�a_lx!�<{For $n2\pi/(kd)A1$�:haszs\ H%�C \cos��)$,��uAin Ref.~F+& .jCAlt��109@5�$Alt, Grass��� � m AGS�E=S: Alt-�1_V�P>n�A�Ab~�F4�a��"�*�~Bj�2�e)��67.�Q]672R >�S ko}21a�s ~�A�9)5M �b�mD"7�i̥a�.�K�~y�&�JOiMNE7v�K�6�>  #, Korn tus�g� $VladimirovA�KKRTV�E��VgA>g u-3v�OB= ��>L>>ے;� E�5�1Aa� E�V G>�.V!{5u"���~�9^y63402F)�^6� .�(%*$ }]�L��~�-M�a��z�49�%捇3^�2F!"��>� Ande�%Z>A� 20�� J.~B>�OZX:T "�U�~�6D � 9886�UR�Aegg Alml�  95AER �=]�VQI>Q^�! B��6u��J0Z�709V5r�GdanitzE1��G�Ez:R�:�QZ�M��99:?Q.2J� &fN�#�n�#1��#��#��#��#��#��#��#��#��#Delsarte*� 75:� $ , GoethalDa,H}�DGS:7�'B^ \: V�J�D>� �A2&=bSJ��:�,ZB�s�7:YG+�.���packing�Ra spA[E�in�yHr 9���ems�)o{i"W�^�1 ޭ�V."8r�Hogga�&8�& :92�V=SJ� >m)R� $t$-de:�8pro�a�Ls�wA�-�%�5,Europ.�1CombinA ^Z� 23J Q.r!\.%�&/A�8LWF:3~z*WI�U�W�/ �/:R �ER|O0��/�*UoV�"�/�b�19�B�3VM)8�)[tF�0Bandyopadhyay�[!;6�2)A\ BoykhRo^�wdhur�& Vatan�kBBRV:� B0$2m-�q�VFPJI ��?B@%.�BUw�F>� -!=VYA�Dpr*��g�{R��B2 �XZSaS ica}fQ3�.-�51Vu2�eprint{�/ -ph/�<162.�>#I��9~� :W�z�NJ:�@-�R�G�|&d6j��M?; >d&�3��Qu�@ @ n��WJR32V�(8 )J�C� banku�1�Q6�&, Camer�Y Kant�U( ]{CCKS:|�VRA96.c-r1 VCN�:� ��@WF 6� �?��J66Q1%�RBX${\mathbb Z}_4$-Kerdock�\$es, orthogX4sprea76Land extremal euclide�rine-setZ��I..�IFQf�7Z%43J�A4r�Zau[/9� :��B ;-�RV�;��: GIgHz\"uge einer nichtkOZ�CvX�@1mi Ph.D.qPU� school}{U�Q \"at� F� �#iJ�Kl�� neckk�R\"B�l�0A�KR:W��VFS\V� .NVUBg�j�ConBL:Re�c�Z:�:)I�|�nA>al=WwW on FY�c a%�$&3M� >�!Z�q(p5W͢1^C142%F��D20n�Wocja� Beth��WB��B$ P֌ B��j����D� $�u>@:�# squar�� 9Z�2��e�u22�-�b7e� on} N�4!�F�407081n� ArchaUaQ �UB=/ ;nBTaig�"$lE�!LkZ�& ulaC� Va-B 312204n�Knill 96� :96a�4B ;n�Non-b��u>c erro;c!� ?�dBB��{Te_a;��]��4}{LAUR-96-2717I�N���on}{Los��mos <�; Labo��yF�1996})�:u 960�nb,Ee�s :0��RHE �"e >ngA�!.ۀ%Z;t"�FschemBa�c ^� e\N�1V�00307r$.��R�t�)X��b������.�I�R�Rv^�%ofxe. BQ͊ CORR ��-0͝=2 {DeWmet��ici�Ojqa"�y�W�loѶ^6J���r2F�6����C�����j�B��s�`ze��des�R : Nir�u�7b J�ef� 4Z�6239�_01008r_�"l��� :h�U�; ;nN W SIC-POVMsFaMUBs}�"b ,9�7 ER�PCo./ J}c$c�cR�uN, 6 W(F406175nGScott} %%\ Sco6��7WC� �B Ij�Group"^#}�.\#��A��� L�aadd*g}{0O.��}*4x6v�5Asc�(��0��DB� ?n( g% � y2�= "�JQ�.�51.)"j1OfB�2u<e2jx{6� Gibb�m&.:� , Hoff�Xan WuE1GHW��KJ�= _-V�^�K6� �@U�����:�^��p�gpƼ�� d�go�e &K�R�115r�Lid�Niederr�a�8u LN��R>�S�� H>K2�i�R�I:�ym$&L 6JK-UN1.N�* }U;�Ij1 1986rRP{\noopsort{Lint}}van~ A���so�9UvLW:9C�R�BJ�L:�biVOE�� VcRzB�i�b�]�urs+Y2� �����92r� Andr{\'e}A�5��e:5��FZ$MI8R�{\"U}b�-�c/es R$benen mit �Li�i{T}q��Ugrupp�U"� �IZei[_rv�6R�15R-5�N�#�f�G"/�2beO  B�SK�cM`�b� ��ier) ys ��2�2 ic �s.} In9Moc�l 29thL�lACMsk!��l �+h�iŠ,El Paso, Tex/7MaywIn�a��cleve��} C �2�M��avellobe�Mosca(_�K�"�H!vi�,d} ;���Z��, [ A�O 454}, 339�L�y��.�(nismeraldi}c �ctV_G �S ,] �A�Uis5� �('s Example}3 -phy�j20�p���6 C W�)An��roximateUa A Useful� 1BF�.}7p,ical Report �XRC 19642, IBM Research Division, Yorktown Heights NY, December 1994. \bibitem{deutsch} De �, D., {\em Quantum Theory, the Church-Turing Principle and  Universal>(Computer.} N4 Procedings ofd0Royal Society LondِSeries A {\bf 400} (1985), 97-117. \b6�jozsa}.� �J, R�4Rapid Solutiont�blems by:�a$}, �N� ��39�,92), 553-558�8eh} Ettinger, M �H\o yP�On�XAlgorithms For Noncommu��ve Hidden Subgroups}, Advances In Applied MathematicsIH25}, 239-251 (2000)�8fultonharris} F, W �, J�Represen�onMUL}, Graduate Texts in2�0vol. 129, Spr%0-Verlag, NewE�, 1991�,gsvv} Grigni!?4, Schulman, L.�Vazira EU.,2�$Mechanical.fforE�(Nonabelian :fA AB} STOC%?1.?xhrt-s} Hallgren, S., Russell, A �Ta-Shma� Norma-�( ReconstrucA��q� i{E� usa�G!�:�s}!uA�(. 32nd Annu�0CM Symposium 5�a Y,ing, 627-635�2hoyer}J� Efficient�0Transforms} q�u$-ph/970202.R2NSHConjugated OperatorEJ- �yy"a�hys%�$Review A VAi 59, No. 5�X499), 3280-3289]_8irelandrosen} I , K)�RAv)�A Clasm�Introd-�0to Modern Num���k�84~82�,ledermann} L e�EW2�ToM) Character!4 Cambridge��$ity Press,a�87. %��8jamesliebeck} J, G),L 9.6%s ���A{E�s}��@maslenrockmore} M��9� N��dGeneralised FFTs - A SurveE� Somea]A�Result!�c.�p@5 DIMACS WorkshopaE � ���e|�u$Finkelsteii�\W. Kantor (eds.), Dimacs��in Disc.�).S. Sci,A�4ume 28, 183-23.(Hmrr} Moore, C., R=,�.hE%icq3 Fourier}�.} In:�):� Fifteenth�; -SIA:@� rete}� (SODA), �̀Orleans, LA, January 11-13 2004. ]Vm�etal}.�6�.�AIB�The�� %�VPr���ffine-�: Basi!�le�qIn5+$Sampling},��4:0211124, v3 %�B3), pre��t.Y� nc} Niels� M.�� Chua�eI.LQ���E ��oIPIn�IEx.}y�}� >� UK,!b0�,Eo!�. 9�8shor} Shor, P.W���%CQ� M�:�W Loga �Facto3 .} Z�35��2�Found �A� oer�|`ence, 124--134. Institute)E�rY�q 4onic EngineersM� i� Nov2� tend{thebibliography}�\beginB{99} 9PBohm} ��$, Part I, �.�H. \textbf{85}, 166; %f&180A� 52).kHol } P.R. .A�5��!"Mo� v,U+m932mPoriginal} Aharonov, Y��0Englert, B.-G��(Scully,M.O. �Lett. A �263�37k 9); 6W6V%� U V V5R2668 16 =-PM>� Vaid� ��O178}, 38� 3); :�Anandanl �FS-�S47}, 46�1!c�AAV>�Alb%[D.Z b.�]R)1\60%[: 1988.dSES} .I,Vjhw� �.i�e77� 89.eESSW} 6� E%�, S��s "� Walth��dH. Z. Naturforsch. 47a, 11 p92.pam8ian1} D. D\"urr` F� dPS. Gold <, N. Zanghi, Z. 2f1C48a!D26� 6  p02} C. Dewdneyk HHardy, E.J. Squiresq�)�9?184}, 6MZ.� ^(3} K. Bernd Daum��b�0Nuovo Cimento�110B}, 7mu5Nw04} H. R. Brow�/�G�ert��q�152��329�6^F�.�t �"���x��: A4,raisal, Kluw%Hordrecht (J.T. Cush$A.�We� U)�6ABN���books} mP� Oi�Zubair[ \emph{�Op� } (�pU�itF% )�(7; Hagley Eu,it et al.}, M > } �7� 7) 1; RauT nbeutel!{JKS$ce B 288}�N, 2024; DutraA|0M., Knight P.��{,Moya-Cessa H�� �A X49} %%@s 4�3; YoungA�$K., Zhang � AwschalomD)dHu! BcB Z%66 �P2) 081307(R); SolomonA�!�PeP!��Yamamoto��>�e� �86 j_ l1) 3903; Moller B., ArtemyevZ,V., Woggon U �(Wannemacher %�� qZ2mu20�,3253; Berglu7ZDoherty!�C bMabuchiV�.\!�8A+ `068101.� QD} Mich� %Singl&nDots: F� �zals, �� %`8New Concepts} (B_BerlinAn!O Haug�!� KochAy� �qTt*�  oacal51 propert�$of semiconor�Worlda�$ific, �apore�$4; Johnson�DFU�J-�: dens=t�E�7s5) 965.Wny"�A)2� IaY,M� ' �  *�} �^ r_!� ; Quirogaq�:�%�}�.=83} (��49) 2270; Reina!��Y�62y[0) 012302;NatQEA�Yoshie TV�ޑ�432�4%�$; Wallraff!ue}�V�:=H1} 162; Guth�hrlUG�0�?$14} 49; I�_gluFu vng� ) 4204.GreL 1} Kiraz�F#J.�{�!E�5)3)�FQ2} Ola��astro�a�: � Hand�aY �et"� ]�dE:�4) 43�9],Dic54} Dicke� H.B�-J17F1954) 37 GCMP} Re��v� �Europ�.Q6� (2005) 8; LatJEmx�Brandes� SB� ��9�� 073602; f>p�40� 5) 315. b%vB~ }!920�D 0441a�Lee�M�R�^N�Ksi, 0830QDusuela!��Vidal%�v�L237�2 ��u{(WH73} Hepp�V ᷉� Ann. �} (N.Y.) �7W 1973) 36�Ing Y.I Hioe!�B�Q�I�C83���4!� w 1440.�`debate} Rz\c{a}\.{z}ewski�6�B�.�:�432; � J.F�BL�1 �a�454; S� C.!� BowdenH H��FA�197[ 3;V�P4W\'{o}dkiewiczA T]kV43� O1) 593��Y(Keeling07} ]o�^� 1H 7) 295213AxUv,Tim} Jarret �., �/Bmy74 � 2006�<1301(R2�Tro�  Suzuki%ii�rog)orU� M�R%�$Thirumalai�� Li Qɤ.IT �1 5n2� 1( 3339;�chmidta8Y ULai��YM=�.�64R 0�(246�W5e Glauber} ��" ���Rev� 1� ((1963) 2766.W0MPV87} Mezard%AParisi� AwVirasoroaA��Spin G� ory-�E Beyond} o n� ,On 41987; Nishimor.��is\ �ic+reg. Wces� } (OxfordJ @ �JR� v5� bennett84'H�% Ga$assard, ''�  cryptt:� 4c key distrib&%!ycoin to�,''!* IEEE] ern)al vferIq� ; Systr%YSig-�")2, Bangal�P India, pp. 175--179,!�&�U%& � ^\areskii# ''Sim�&proof: secur�&BB84 � um%2protocol �U�e*, �$85,&2 �4441--444, Julyo 0. matsu�02}a4M�T. Uye$,�Lower b� �$�capac � a��$memoryless+h� �aath�� ���9 �39�03, Sept��.�hamada� M. HAi0Exponential l�on90highest fidel�( achievable� �$error-corr�,ng codes,'' =�A �6-�5 �05�--�, AprilB�mayers0�DL�Un�i�alY.in�.BE Jour-MRACM �48I3 �35�06, MaE1JP4.PR�&bi%,4of Calderbank-R-Steane)ED .�1Na�.�!Ha*E�A:A�h. GenQ37 �4 �8303--83�"Aug!O2�g�k03$G�H.-K. Lo!aPN�^�8 with two-way c���)�'!�E��m&�(!�~y1�9 �P2, pp 457--475, Febur�"d *[4wang04a} X.-B.Lg��I>S �asymme�  mwp noise'', Los Alamos E-print �+ive)-ph509.�&Tcsiszar-korner81} I. C\'{a}��K�!$ , ``*�axory: Co�+ ���SdiF8s���Ak�ai Kiado��1B%b6%"v$!�qubit �umI�,".��-�92)�7I�077902%�5�4�chau02}eF.b& u, "a�Rschum�96} B&, "Sen%�f+�Acy>�:R�54 �m�2614-26a� Octo�( 1996.Qovh T� Ce�J.�,Thomas, ``El�, ie�e�Ip�+ NY: Wil�192�+ lo00%��)H.1�l(M. ArdehaliA�&h*^: -�p��its uR� '', Le�011056B:%��0J��Qre{ ``Sjm�N\u, ( squeezed sjat.A, e63)�e022309&G'20L " lo012K``�tV��X six-�.R6 )R!)e�h� m�1�.81-94%G�5N �f� plain} �L�#� Aliferi��D.W� ung� �I�by *G$s: a unifyW8picture}, arXiv&�%�� 4082�2  B94}A�Bouchetqircle �# ob"�-6*(Combin�,' �Dy} B 60, 107--144,:�1B87} x UDia s deco�-�E�Euler�.��}, �)a�lgebraic&c%HMethods 8 323--337,# 2\B�B��w�s!Q treeY1suc� ve lo�z��#%�� J. G�$-( 12 195--20}8.! B91.w � An e"t.a)1��recogniz ~$ly equival�&%3�=�ca 11, �--3�0�� *�GMT03}&Gravi M. Mhalla)r. Tann]+&digNj(202�*P� (S. Perdrix,)t�eM�$er instead��TeleporI�M&]-ba..�-�E�} R220��.}R!�R. !,sendorf, D.E�ownM5N�B�ō d5�� clusA+��!�J�105��.�S� DX}e%-�LogE�network 6c y* 6x%�eG� NA202007E5�٣S $K. Sutner.� 8em Linear cellua0automatiZu@Garden-of-Eden}. �Intelligvre�( 49-5.VDM!M. Van Nest,�Dehae�#0B. De|.-��% descripe�� a-.of�� Clif�t�2%Ds-25�%�r30815,A�>�4}ʲOn � unit��7us ��c�*stjzer tE^� 4111 �4 V�bf�6�*�4} V.V.Shende,  /MarkovN% S.BullockL OnL al G�Libra38 !�Gen�, Minimal Twoc ��}ircuits".�308033]�� } G., C.M' wson�A��+ Z a$x�-�3 CNOT�s".p �_ 77 &�(Copper}Don smith�$n approxim! �- Un useful��%� um f0-",�4_:a8�R�).�201067=Bar95}Ba�o� �� Ab!�s�*9t��", �A�9503016^TucARf, Tucc� A Ruda(ary2Ui$$$(2cnd Ed.).K99020626\04Oct}6^Q�er&�.�5�%� , Ex�8� Un� ure��M�es)�Fe�!�6�41102.H Tuc04Nov}:�QNFc11�UE@ Viewed as a Spec7 Case�Ri s :* %��0Cosine-Sine D. 2�97.��%046�S}��2m� ``Aw ayop-down�roach� �q*Synthesi6�.!7.Hels0\ V�rgholm��LVartiainen, M.Motto �)S�'aa, `5Uci�E� ,U s�8f�Egb=al �3�%� !�Y�0410066�]e$Paulinesia)�U�QC .�0407215DGolub�}HL,ubō C.F.Ű Loan"it�rix.�s, Ha } ( Hopkins��.�!����Knuth4�n ald  kC5ArtIO�er� gram� }�44, Zeroth Prin=:-}9!Q 12, &�3-cs-fac� .sta&d�3\~{}k�/taocp�3 Vf�j+1*>8$ssp} Negat� �5�24s would only r� re replac� an ordin��sca�p�9i�a *�:!0hi�/Her, see \cite{Taylo�:�&details*c Pron�0 de!bnyE�E. �4�$93,bf 1} 24 (17-"Marple� L�,, Jr., DigitZ<pectralW04�>en2$(-Hall, Inc.? 7.�< Neuhauser�R l�(D. � Chem^�$102}, 8011�{5)�)1}a�A�ndelshta�3H.� %B\|+10�1508$092� 92�^]7}, 675D/2]i�e:��vani� "�&x��4��The�)2�er.�- Balt�ee�]+Fantz}% ,* temp2u45} 93U-4.�Schiff}A!I iff,��Mec?4s, McGraw-Hill�g0anies, 3rd edE"6�6Y}essiah� RXD>T'�is�2^>An'JPe�0"P):��+�!�",�& &q&*�'l&. Ad41}RD.,0,��%�12A�164�062�? Raymm!GV�38} 343ag6UMy%�Ma2I]m��(USSR) �9�9ad4R�22�,a[M Popescu2��C�4 052107%�2!FN��v� U-t�� in�1it{�Confe Z[��6k7�5q2 �4). *�OneLoop�-G[KNTi4G�h �H�% Ng, LaserE�ics�14I�A��No jR. Azz�F A. D��,.\|F.\ AmS2�95�B3);UreMps~ rein.�"LPLLK?A.�geG K. P%�amas-LJ�;!K C. KurtsiZ , %\,>{05p3�;jm&N553"652��� 5�(RenesTetra}!�M��nh\prY 5�14E�� D awDataAttI+,9�J%S.�3 Looi)�65�9it{Sinl#A G!,: Eavesdroppl o raw dat7 in prepar� .pCoh��F�.�~A�ua ���p�H ssed� f� E91}AK. Eke�:26R�7�?9�EP2} >L[6Se�P603126AP28�09E6R6IAB} bHl&# u4- idealR m� cAulone has six times $p_{kl}=0$�2>2 \cdot}p_{ D l}=\frac{1}{18}$,e�24:QR:$6*)q@BvF.-W. FuE�Ni�9rei� m�X!| In�,J.\" Inf.\�13}�J%F6�4benchmark} We anot aw of any*�BB�"$ 6� 1�, so d i ira3ore�&�� a p0 al n�:e.* GetAll} Wf!cE� L5edi> thus lessI,Acedures%�shQ be �#< to get even clo��(to $0.415$.B, howev0 1!x�ith< that gives a bet)( yield than]$2� QSE}��� Esti�}, "�0�Cy(A �fF� Le- Note�HPlHs,�0~ m6,f6 , 20>x�'r) ,�.\�o�6o� �`v �5O�<Sources}3$#%Ic# !� s ! c!�,course,!� larg�y�akWsi�Dc&, we i]e her!� e same cra<�as�A�tom  phic!¥��Ref.~" . I��Fce,�c&4Bob employ twi�7gAHm�1I(their jointa%b�t�7mr��$ (\ref{eq:-!_3 probs}). .�pyramids� 6� A�p�h�?2� B� >2�q03230I@6�AccInf��F�:XA�~� 1}, 05430J6�CK}*R$a"�!K\"r$, .^%\M�� �2�\33 76�Holevo�S. yobl.\� d( X�=9�,7�/1--42; �?ishXl!: �G�s�  FM110--11ZyGDandW%Devetak%UA. Win�fc.\�P&B ]46!`2 6]� $-threshold2�N. Gis �z B. Kraus,1*� q012332Jm QBERi��6�$a���#$�]$2}\epsilon27&�&>"-�'H� ChauIj.�#��� f7 , OF��6� Dist� POML at use{&tor�jbut�( dege�Kte, t� hedro-Lre sui�� for A&�ky �Xn , ,Z they�in2"�O$o those u�un)�6x V2 �$N��f�14} \exp�C,fter\ifx\csn�=natexlabU (\relax\def\ #1{#1}\fibGbibO font>J M#�Pf�Q$�R~R.$�Rurl^�url#1{e�tt!O%8{URL Iprovim#mand{!\�&}[2]{#2}6!ep []{S'}�b�T[{2�{�+}(�}]95a�(nfo{author}z5�{P.~W.}@1k; r}},Ak=j�,}{�vF2%/bfT(vo�N }{52:A$pages}{R24�5Yyear}{�}.mB��,�6� te96�� A.~MB� K��K*=I��77:E �7Z�6� %liteB�B� t@C~@C!�6)6� #� Vinc�9!� Smol�Woo� s}}]{BDSW�' C.~H�}�k:�VE D.~P>@D��C J.~A>C �?U�a�3�EtV�W.~K.}-o:9,AV�;^�54}.A-�382�4�U�)�J�Kn.(and LaflammI�7A� KL97�� E.}~^�S}:�!6�q�V8R>L��2{Atb55:C-79 &J67e0�J6Palma e.,}]{PSE-5��V�G.M>�O�z; K.-A>< SuomU�.C�qBO��+�Y�rmT"[v�4^�56:�^��Dua�'Guo��E�DG97c�hL.-B�P�4 G.-C>.�����9:EM�195�o T�:B���;f;330�:�;Lidar.�8: !,"U�C Whaley��LCW98�<D.B�Y:VI{&:{�*���� K.B>P���5C��52;��81:�M�25�.J�8r��c5�b+:�!,�� Viola!�KLV00��^�2V�n�%L��L>� �2�қO.�5�2�C5���!lr��!!�1�Zan01b��fj2�N�A}f 63Vy9I�EF�1r�Kempe.z1>z!<cPe��and�KBLW01��J>�^:�V�D>;B��;F ��Y~B>1�Z�� 4230Jdt4r�Davidson�&� Dav�� K>mJI�e�PUkXtitle}{$\mathrm{C}^*$-a�2�2ex�% e, F/cs�W Mon�s}}�:p7"}{J�;SocnW��PA��i�['rKribse�3a�Kri03��DJ� J6�y�_ Edin.�j�46}U J�3r�B�Qe�Singh%�8� BS98ʫP� B� �^"�rG r24^J �GF�vnStinesg!+55!+ Sti5��W>.M^�E>�j6:J��1J�195v�E�.�5>�a.\(Lesosky, PoQ+`LP0�B�]:�V�na.�V>B� ���B�1 2�u�6� }gG�BE\#ji999~/3tem�}�"nTD it�*vD ޺%B�%,}DP= 175 -- 172XPBS92}%e��.�Wiesner2�&��'69�[88�Y�&. C+936ZVZBrF'd,2 Crepe+R. �jA�6%!� . K."�^�189�*6�%JP99}�5 Jona�YM.CPleni]��&O � 83}, 3566&(99.�{BBPS96 �-9,!�J{/n�Zm7*(�:�>w=(�$204C+6q"NI�R"A8,.D=��43 G6�V�L99}&�3�>C1�6DBPRST�2:�%�(D. Rohrlich�A.2�A.�,Thapliy;Z�- �^�+6$DKF !cDaftu�M. KlR#h2Rv042314 & .�!FDY>6Y. Fe�&A�Y. �� ]:%�"�G.79�=?CI;51�&090J�ga_* hR &Vg.g-ev06231 ]6>JW!�J. *�:M�lke�0P.�#(4�\e 2VC�FQ-E�J. �: irac2e.QR)16790C6SRSU!M4Bandyopadhyay,A,Roychowdhury)wU. Se6�1��N)1�(gc�� DFLY� 2`9�X�( aM:/)�9! e 6"| 5); R6!kK�5D&010.R ��� �A��&b�4041486�n��.��*�A46.V'A f��%5�ro9a� H. P� 2C{�13a�$163 (192�{G margolus} M �L��Levit��>D}V 1�*18ag�NF. Ya KEli�>e"�s�&>>f\C�g�56X2�.��c!�prd6��@ D)�2G16`21982yurke}Y �A�4cCa�MAlJ.ň Klau9c` 1(3b403$186�himrom� W. %8yP>'det7L@k�oe"�'"Fi (&(2�n�X!72vsql!��B2�Y�; Vorontsova?Sov�3Usp{ 1�+4�5OX.�Abar�O}a=� O Fabre�i Ma\^it EuQR J!31�a#51ɞ2Zdow�? atomgyro}!� P. D N�5� 4736��:\�2� shih%oi�nge�8�FA�ekhov#5YAWi2�6�801�^Fganna��N. G �S�C��R^epp�XOpt. Q� El�>onH�>�435 1972�vonk�yESA�onsecI�H.�k��w!�\'{|-� F80 286��9.�(3� Giov>.8 5�06�lugiato}!` A. L ��Ga%��Kambilla�E�B: U� Semi�VS:)]S17�12�ghosts}T> PittrY� avD;Strekal�H#RSergienk�O&�-2R34*o�boyd}e}� nnin0�nt�S!�R��BE�bN.� 1��/2�-U2�?RG M. B�T� L8T�`1~B�I �<�f beam� �. Fouet%�rAe,)��(25ś-�2� trep�T ,\Ac:�Q�uc�l<1amjx"� HO(�or �C.�%UI��R 2036NU�6�%��W �378[2�pPAcoord}A���7AP*Scu�WR��׉\I2\bar�M ona}eEag"5%�igf8R. Mu\~noz-Tapi�GVm i25"n2igiulio� Chiribee�G��"0 �Perinoe�iRM � ,Fw 4050t�7Uwp�}�3N�"R3� l��2de�A1~ jpe}� A. E�xHough R. Pu�X�"Iwr!�E:�`��Jm��1� 7���L.�yu�K�YuA� H>1�7�1:�,l�: <2�]�z 2465P82Qozawa> O Z� 3�E82��1���c�u6Iunruh%� G. U , in:� �os, exper�Ll �Ovi%Q!�*hVhc:s.A�MeystrZnz"�!� um, .� 83) p. 64.��reynaud%0T. Jaek�}S�`,!.iɟ13�!3a�1992�s93�F �9Mf Chrtt���.N�� 4z317��uAonofra�i�Boc�� R. O ,Iz>��B 72�� lZs�G. Knobe�� ClB� �829��26s�qcY�D. LaHay�U. Buu�9H arotA q@a�Schwab�xM|)|307;2nwis�S}a��2G��a�245z 2Astefano@ancWSit.[E�$P. Tombes2��6{� { 6NPcohad� �)C �qdma�I� P�Bd �NK�31!kp*�daofeedback�.�����T e �x e�o B �11%ti�{*�Di�cpI �Asa~92��-�32G22�1:�RHche� Nogu�A�#%ew,a� Osnaz� runeA�J��Raimond /;arT,.����FYg�nat�PbY$�M� eve!�J.-� Poizat6h39y>53r2wspeed�  2�.&�)EIh)FM1�0}�>�ligN Buonq�n=h:��00��(.Y wign\E.e �sBt2� 2�r52� witt�7� �Wi�in �YGr� : an�?6N�tA� CurnMt�؍,� IenXK, (_. 62n seth��e���� 4M1042r>p�&�)�>�8�37.�H��qg�y�s�en�N. Hugg�4eds.,�b�GMeets%�Philos�� a�) Plan1q cale�K�Lor�Oj>�?in�E)syB("�P*�>be? � �B��)Ma23} 287�>�thooft� 't H ; �Ba�aiHighl�z:B�*�x1$�Q e SubnuclYse�,� 3�d72�j � �OJxEri�륜 ZichI[f (hep-th/0003y�9�susskiHL�Y �4*��^3�637�2�bousso�B ,)G>�b00082J� ngM"J.J%-��E 8�a9T$ �!_�tum�jibid.} 8G�39902(E)�2Ny�I}U.�tsNJq�� 1302A�ZY�fE 10.�;{LP�L!>�bPeier@ZGa:6��31) 5."UAB%)��N1�61)�N*�&WZe�@heeWW!LW�, Zurek (Eds)m� �e��*}}�A�:t�/N.J.:6l F� W �AtY.��-��N ie2�N.SRF#BAO znikJ�84E%0) 1368IvN%*v�{eu�EiaePFdGF�k� s of��"\Q.$JMx �F�;Q.�B���  -�6�},NeQ198.�A2�GivMZ2Xi�>N�@j f�96��ar�&�a�{)�'M.�TAguiar,3 Keck� J. KorscU.�m��lhaa����O.K%�1) 7222�pKlau85FE~RF'q E�4B.~S. Skagerst�)�Co�Fnt)Hs,�XIi�Bin{a�a%M�1��i"y� rld RvpE�2^P�78:��qit�Ptinuous�$*c�"$ Path�J egra�1tW ted}ŁdG.~J. {Papa\-do\-pou\-los}� J.~T. Dev�ce�itorsMU\� \(}, NATO AdvZ�d&�y "!�)n�� B:1 , ;.~56�78Uum.�%%9Be_!Za�v.�$��19(8)}N%�t 2349>Q8q=J.�1WSF�, on Wave Equi�X�._%4"�e�Ap�]A 8c�r.~!r$nicolaou, a��4Random Media},2."�E&2�,Weis82b} Y.~ jm�em�'*uW}-#76) 82) 2NAda�a�zG, �wof)mA�95} 4�$� "� ShuAhud� K.S. IkedtA�U KZbf��� 5) 682.� Xavi H ~L.  e� r.%tF1}�em �E! ;x�25�v,96) 458; Av^ de��^X �A 54(3d� Z180[ ��EZ� ^ 79(1Q�97�3328w5y GrosV3F.~ A�!-�~!L!?je�i>243��8d242c98ivre� choe�df���O��V N.~M?#yev �E�{7�1�4��!4 q90.� Heller02}��c VoorE[�d� A� %2�>,6} 0505�Qm2�+ 7�cT.~\�zJ�Z)� 1qx12153 �l19�Polb�[lU%t.�.�lEI>a}!j4) 66�{. izeK�� Rome�%$M.C. Nemes��G0ixoto de Fari�eA.F.R$Toledo Piz�RM� �32�8� 122� HillwM.~ ex-,R.~F. O`Conn2M.~"�I�E�D Wa>�pU�p\�w 84) A.�Alf98� zori� Almei.(295u�2��Nn �jVY22 <.$see} See s b issu�8ortsch"6(� 4�!>2 kan�)E. Ka&��obf 39�1k 1998); B*�MaAlpi9ADzurak ,G.��&G�j3+�T� un �S�,JB �fM9=U>� lossE-F� E��oq�>p P8�46(2001);,Re-�a�,V. Sukhoruko{NP�� Q�196#!02�)raos Manaj�'M`+0�NA�R�7�.� 1622�%0);* PE�"rovanesy{�hachal)^$ivh�NJ_E48�6�b�-�PJi�, G�I Dool�a�H�F)zV.�\sif�v13~*}g9909033;?��P108025XbG)rugar}�� ,�Budaki�JkMam!/�0Bp Chul6�4 *8��1.` parkA<�Sk�� A.K.LS1mAH.�A! Allvisato P-McENNjUm740�5�6fe�en$J. Twam�]��7�R03e�2�pakes�I�k�io�%ephs-z!ks!B�0e�USe��/��S.�clo~%] UQ]� eas.�a5��312[h�,itVH 2{ ��2323���*�sa��S %��imfL5!s%!22�ja�"jeU(52318C3.J exp} We cBGlso"�T�he molecular nanomagnet Mn$_{12}$ w�&Y auU to�cs�~$S=10$_ t asRWw�n 8L {wernT$�f p"erEk0 below 60 mK,exROWt� �MQ$till popul\��1is e$affect our�s.��Vcho6QFe$_{8} �s�._nd" hU m�X\on chx�WVw�%J� s� papL.+e�t[��xusZf.%)�Wernsdor�o�)ssoli"�m�28#��� �t�P1�N. Leu�%WQ�6�1au!2} garga� Ze|:r�I.P@�q 13�,69%32��.�ng,&\  ���/20� 6�!>,�4Allaga-Alcalde8-�endrick�!6�hristou�J-641�70J�$exp1} SEL4ewT no e*3 �]%�thn�Z valu-td�e�Z ly supposw]ua, follo:��l: If a }pQ��ga'�Xs t>k fup ene C$_ɖ4$ ($<$ 0.6 nm)�put nextoXa' by ae�-e�2T a\1 nm, o dipo� coup�.�Zweew2ma�uld be_Yi(�Tat'wo�s ��JGng_S Hngth 50 MHz. Consid�"�{�lr��=1%e�assp�B�!%Z!��~:� by 7�]*OA�1F�E� Orozoo,��H lbaU;A_noit,�BarbaraE�Demoncy,#LsauA� Boiv���"ascar^1 �i!�.FL&��+7 1m�barra� L.��Da�tteschL . Se�V��� 56�h19�#7);�(Mir�&u[- HennЩHJ salI �| Andr�0H.U. G{\"u}de3� V. Irodov) Can�,.��j62"�*�Umey�d BDAsi�a,ahn-Meitner "�"�\�2 knor��!rr%�Grupp�Meh!� Waibanvei�_�AIP�tc �'ee�bf 54��!� �s)�1}2�A.%=��3Sor�"%orn�W..C,� MagFE 缾}6-2Z ׌%2�e�<>TprJn]�93F;�5�.��i%~ �~<V�*&�( Paul�(]�I3�=�296�N��j}*DMaI~�!un4 �$ Mosh�Rit ��pB21K 35eA6�%HFJ}{A�>PH�Jo�d��� QDl 6��)*8AFCc�/Af~tV.F�(Fern\'{a}nd*:�E.'C���~L@_4 order perturbAaOo#sum)on mete{*P�mvk'' J>`Heide��g,* 7��`, Toky�"ong K. B�)onӜ:�%Jan�W?&nk�1tgleinert��5�& -K;27(2�,Yuk91} V.~IQ�,!�"DI%� KL# 12f62; AAD:JP. Am�A!�%%�Ae Pe� a�X��c�i�AR 351I�21 AADL^g,.c!�J. L\'2<sh� l>"4�h&S PMS} PEUSt� JI!j HDb;291 6b; AA1:o1�52�.SA31��2N� AA2rS�EARbe��pubA�=�S�V�w } [a^:math[@03052]=!AM2�A�1t�=*.�B15� 4) .RSFR�7e�enz, >�,302�AF6F�` AE�,��#9z� baZ` 70142`FF�F�C�xUN�9036FI�6.� �&�A�96�ah2�Nz 8036.��w:�auFe,�Parki�D[n&$^�6^ 2501�1)�&�" 8069.QM8�B�b Quic�aH.~.i� &2�qe3S)68�e2�MoralL��  � -Veg��qXmx/B�2k10�aP�.k mei97!7 Meis�HEC�teinborn Z�m�$Ae 11�/>� MP ۔1982} SŲ���;�@5.�Er�6�e~MG��-CM-5B82*�sGuth:)yI ~H. Y S.~Y&*^�D�89�"6�Co�wZ 6wv}a) (" VcP.~N.� ncio���.CD3P 383XB2_, Lombardo:�*du}F.~C� a�~d zzitE9xonteolivQFv6� 0450��a:2�Pph/9912448]. \verb''R� wjl}1.� deu} D�Q D \. \newblock {Uncertainty��R"�}�sMl1�x ew��O�850(9):631--633,d���A��b�ma� n} Hans M %LJ�Ra�Uffink.�GHalized es�picچ�Fc�w��� 60(12):11�11��|� 1988.� ivon�} I~D I 6�om�al>0�������BrmNhio 6��S)js ��"v"�-�,14�(3241--3245,&n�19��&�sa*E8z} Jorge S{\'a}.�EN`wJn�com�r�0observ�j^�/ys AkF$73:233--23��9�U0A�ing��A�~P.*� , Mi� Horodecki�bbie~�,,����`� �lApTerhal.Locu[kE�c���ha/%�um4�.;z(ڌ) .`lar|� Ulf L .QSupace gIgy:j  exactVhip^ 6� aszF��} 23:10Aw 1061�.v .�Mp2zq�m�ḿj�k2�2h.f i�three-d0,al hiE t %=.S%��� 7:84�46 �2� �3z�Improved��)ͪv vB��MLFoiv201:125��1, ���C!�N� (��*!d D�4Y&�� 51ߊ� _)�den"T����. 74,J�W45);���� Ba@e� �@@5� So04(4�6O+�2 loma�� Niskanen�.�|A)123!72��; A2;,  V�7 anin+�<M�1S o.YN� bf 9S19"�/ 3); �=P�Int�5��f��S���koslo |V�2makrishn�c "�PRevA�63405,O��"kol�"R�=W, �)(�5�C� <�w� } Bl7� Den }me�xaKap&�) }, (R:7� eB\i %um�sip�"�Q/2O/>X+��' �il� I.Aq��or�=%�{5�2veshch, T� -matTO�(��o-s^, Q. Ys Xuedong H�H�co No�CM 407423; MU!StorczQ2%780. S�in�0��I�5l�g,��� 04� 6(�w�a Jun Z;�ͦ.�i�e 1/{� A�YL"02050/!4);"p#v Ama'PB,) MX91 �\�:�devu��V{ ��+c�7296�8�;!Ri�2� � I.�41200s$9mooji%�E�oijVq%"03���|q hior�}4\ �4�1�7,�xr_%a@M�Pl%�o�>�pP.=�ggi2� 0977���3not} Z#w Zhou��2.�aR���01"|':�pashkin�"A�'T2�2�8�"A(T."�J1Y;429P�v��Astafiev/}11216YѳI�2}a�B�_�&��!5K�WE�F�)�?242lC �/�Vȵ20�p�p�p�p�p�p�p�pbpQ�>1o Reithmaie&Cg��"�d&, Sek� ,Loffer, HoffrDKuhn, *ze�, Keldy[X(Kulakovskii$ neck�C v��1�] ref:C �Fnb�pB�_<��f@GB�^ek�9A>9)�<C><-C�=S>=!w�:!,1��BB�f-ߒ=VF�U�AT>A��AG�_B�FoM�A�U9" _�Rj�`43Z�r1�(R�cafr�bY��n0:� "x$H!r�*i#, Khit�), Gibb�'u�� , El(>= � �DDeppeq� [3��B� 9��B��re�EB���~B�1.�>H>�%b�;By)��<B;Ell�9Q>�!ln? }��jD>PM>A�U��;m;2� �;P�Rn:!��nellart�3Rr 4Lema$\hat{i}$t�IHou�6G\'{e}rhN� Blochq2S�0E>8 768VdBvkS��?B� �=B�>$�FF�!X�;9�@"�EoY�VOB�-�A F� quan�110�6&��`U�U6f !, ZGr,X�and �Qo,�oB� 76�V Bo ��<B�X�lBNMa�:��n>O�Hd bf&�kv�z 78}}9�nu̱}{16})�= j:s}{3221M0)�!�r� �!��j� 2��H7I�U� � ��@OB( �=F�he��A�:kChoڹB� 1�!�5�U~^��C�E�^&{83R�0N� 1915M>�Abr� Akah��*� 3:� #, AsanH[S!(ŴNod�ua� (��Y>� :��B� ��; B.-S>����B�) V��\2Zt9�<��y�.�>`&�m�, Borh�H]u�]%�47���e�eFk �����u�*�no70:��o81206^ov]�n�$!�9�0wr�wand>�4��n|���:I::�{M�������5R�7N�369�SJvGay����1<6| ",.�Q>-Dupuis�n] Pelouard� K�$B�| 86EV�J�%:�N4j B> ��B) ��BqM!TڥJ�D:9�!���7V�3N� 1908N�Ayr��%HLQ��(6� #Braz�N2�*,"�I0egluQ� 9��B :��BX�Ē;Bْ;B�B% �<B�H7E0"�ڒ 9�!��E�7N+2R��C N)0r�K"�""� 2:� #Ighava? Gr� Sytz Mallo�� 5�BX 96AVB=R ��>B���:)��B�1J�CAC80RC1ND389R���Li� UA>� Liu,U+Li,�5e?� MGVa�N�fAEIQLe����Liu_G�OB�Lia܆� B 5ӆ<B�Ls �8B� Ne!փ��B�1~�xf���@B1�2>"b `CJ.�&. ElecvU36N�1R� 1272N��vBipp�@.�BE&, �Spj:�G and Vahal"\,��BC<} jՅ�D�@<��B!��P� 5�0f\+v�2R 19N� 1669Z�v�)5�t+6� !,�qoghda�aT4Le$\acute{e}$f&R-Segu3 R.�\�\��R��B� 76SV�B� SSQ��@J>[�:Bzb#�OB�-WڧB;5���2Rr8R�83R�Ayrr�@an&�f :�$�Panza��X.8�-��B�:67V�B��?2n�0VQJ.^��i:.�ɖ6s2�=^�6R< Zu 3276N>�!�r�Elise�)"A >ډ #,= N  "P 4��. )�A )� >�� P.~G>R<��� B�� �� B9)H��B"�E�U��DB11�!�F1 Sel. Top� RCVMV��Or�Ide�?J�%IAIT T. Hioe, J.H. Eberly2�0�Q V� g6�1�V;�&1 Kuklinsb;U�uuba7Fhj. c�*�5e� ��u m 4�667�1198��6V�h ��;S.�dhi;k�;d.8"�Y p%+9�i 536L8�H Ő(tem{AAMOP} )� -�, )3alD/�7%�1���!/�M]�A ~�Y��s7�%�E?Ga�2XJ.-�A+�Us�wak�z lw)�w[, 744�B`G�SN���AA�AI`29Am.�L9E854)622fPeCt)�f4 lz Vj�/ .-L. Yu�U��Yu��N�0C84&�P�&�D.�6�WB}VY��, !Chua}^�M!� 5�2�w199�4U%uI2���)� M;U��-Av5�^I�.�%�56�5cDn ToJ߁�qB�u�� (�:=`n-� c";�;;$A�Malin�1y�. V!5K ,F�qVbkr,1.a �oM��c49cv�D�m'�Z6�J !�22`s�&2�TheuerFH�AE)K..E�� [ ;�i!  2m74D�l %&�cs5?pos�� MartesP.~ , G)~J.L.~� u!{-x v�NR41WI.�2�LawallA�� XMA� lE�=+8%w `7�9j�:�m�ner_ L%� ,N|$ Gerz, R.Ja[b eeuwe"LE? Rols�gC.I��estbrook���=h�|psAI�M�a�+�����!j6gWeitz�M�:�72��!�Xa�B^r�JZ�25�Jq�% TripodAory9�UnanyanA`R.G�sΒ�Commun �15�8 144 �8A�&�T�I���Y�!� G. ��B Habs͈���M%r!!2�ExpƆ)�F�k9�� a~% r.x b��)�!}}�L9bv i%"�p���Man N-com� max��cjg2�BC ..*�K �O � �6�:434/be�^* ���egtFte W 9QKis�Z)� \�ten��}��6!�K?�pM?�5�S2�; Kisd�hS�0!�!�i��2���111!�]6�Kraal02a�N Kr\'�? Z. Amitaye S6K�)�e�Set8d630�=Rcb2c�s6X.@�[43413cJ�is�N>< Kar�?)Z. !�-bBͮ�n905So@5\Mo��P桔R�=E��}�~)� �-�S 2�Y9Y�l2^5sH|.� I�� a�� `8Rev. A {\bf �� 68}, 063414 (2003). \bibitem{dual} S. Lipschutz, M.L. Lipson, {\em Schaum's Outline of Linear Algebra} (McGraw-Hill).l0Messiah} A. , 1959, fH M\'ecanique Quant x} (Paris: Dunod) pp.637-650.d0Shah02} S.P.  �, D.J. Tannor, and S.A. Rice, Phys. Rev. A {\bf 66!533405%52%5!8tend{thebibliography}�\beginB {99}�5;AAMOP} )�9�� Half q)� S)���6�nn. � � ��52}, 7�20%��,Marte91} P.~ , Zolleri J.L.~HallN�!�$44}, R4118�J Lawall94I" \A�Prentiss2_ Lett.�)A 7�99)G4)G.�Goldnerf L.!�  , CA7 erz, R.J.4Spreeuw, S.L.I�x Rolston, C.I. Westbrook, W.Daillips, A$-.A  )4-�)�R� ��7%)J�Weitz�M.  ,!�C. Youngi�SAju��o c!�� bf 73} 25!�19i@ % Tripod: theoryY�* 90}? W� ; {\em The ory a��� � ExciIv� , N.Y.p� * �b2B�6�!�43413���9�Morris835 R��Ar B2�)� [-��27}, 906|8��.�8Arimondo96} E.~,�� Prog0 %� s ede Wolfivol. 359�:�$96) p. 2572%numrec}q��finA� u�ele� 2��,SIAM JournalY�ing� 0(2)M�27!�77�~��892�TY94]{ � comm��� ~TompafP.~Ya2t� m�:�s�Punrestricted protocol��3(35�652--661�2�J�A�'9.�l[BCW98]{BuhrmanCleveWigderso�H.~ b~!,a�&.�q� vs.~class�q!K��e�� � .?{� ,30th ACM Sym� um!�T�a.Co��)���63--68%8.Ou�9802046�S��(BS:qverif} :� \v Spalek.Q�V3-��Matrix�jduc6��04090320Cob66]{cobham}Y A.~C.|�1Recogn�ProblemEU�ASe�L4Perfect SquareFYCo��Nrd� @ven!znnual9} on Switc] %�Automata�ory ("AX")�P78--8e�66.` CW90�(ppersmith:m%9} D��� ~Win�d.-hMultipl1�4via Arithmetic!�>�KJ.~SymboAF .} 9}M251--280EK2/XHW02]{hoyer&wolf:disjeq�H{\o}y R.~{de} .�ImprovedIuma}a�n bound�-eointn�F equality2\j�STA�� LNCS 2285�299--310�2.OY�109062 KS92]{ks%L} B.~Kalyanasundaram�0 G.~Schnitger.ZA�$probabilis!�6=of set iXec .J%�>DiscreteA(he� c�5� 545--55E�92�J/ Stru� '8� > [Kla��(klauck:qclb�@K.�Lower B9ґB2)-�.=1� 42nd� ahuf288--2� �.9.�6162��3]� rectZ�4Rectangle Size�<,Threshold Co962� ��I�.��>� 8� ���� 118--134E�2� ,cs.CC/0208002�KSW��(ksw:dirprod=,�����deB�1�! C�� Strong Di!U�� A� orem� ' mal T S  TO s. 5!4512�12--21�2�9�402123.s|KN97]{kushilevitz&nisan:cc} E.~K� N.~N .�ek2�-�}.*NI � 1996C`re95]{kremer:thesis} I.~K.W1o2,.!Ma�'s��(sis, Hebrew*� ,�uter S� Dbtq 9196� LTT��lam. T%LO P.~Tiwari M .�%�0-offs between6�%q .6%n"� f�Am SystAL ā�45.�96��5����� 6 DMNT93]{mnt:hash} Y�nsour�IL �.���a�� al���Unal Ha�.=�Cor�� =.�" 07(1"� 121a�3�2�N��6�DNC00]{nc:qc} M.~A.j%k I.~LEanF�Q��5.t.�n!p.�PR� pagta �&} J.~Pb Rauh2?JcM�OA�for Sor> .�):�39R�264--2&o �PRW�m prw:�Xuctgcde�Parnaf R.~Razi5A.VE �B D result�A� {GCD}� ���anew :e mode6` Z�2�w TO[ 3\ 372Ef2�Ra�!razborov A.A�.bOn�di� bu���Ha".� .<%� n6(2u385--39� 2.VRa���qt} b�Q�2{}�symme� pred� Jw Izvestiya�!�Ru�"n Academ%��,6� 62�59--176�2��� 22k Sh� Hshaltiel:sdpt} R.~S .qTowardsAdv�s��d��Q�#em2�Z\16qK��07--11�2�Yao��,yao:qcircuit!�~C- ao.�5� (=�.&Z�3V6,352--360, 19��N�#f#�#S 4{holevo-werneraIHe�R.0#W, �$A \textbf{� 3231!�a(lossy-capac�8 V. Giovannettis Guha HLloyd, L. Maccone, �H*5�pH.GYue�&�C�F 0279��� �et&A�j Sohmj O. Hirota # gG182&Geg�R�F�:� �B.Y:�,A 70, 022328" 4); �[%KJ.!NSh� e-print}�404005*�0macch-palma}C)�hiavellI2G.[P 6654\ 0503�\56 fn1}aHthis work, we do no���o���Leemon}  H I~@48l b�-Merz} bachAC? �l Mechan� (New Y�D 0$) �$edn, p 209Y@GR}Gradshteyn I S%JRyzhik Ieg6m�Tab�$ $0grals, Series�VPro� (Htrans. by Jeffrey A.�� Xic Press) Formula 9.64!�N� af�10}&{AASDM02iA. ArmGK).Aun K. StocktX*A�)D�8ty �H� buch2r@Adaptive homodyne�su@n o�" phas2&R I�C 8}, 89(13):13360�2*9 ({VPB83} V.P;-lavki2�O  � co:&�  observ!��)n��s�. �]\�+Remote7 �&$}, 44(2):1c1�19A�Y@�8j�NondemolEme51s, nonli]0filter[!�dynami�"p�!amm of�tocha�p'.�In�Blaquiec/ edit0�M�%)m*s'�i�%Engine �Be, Econ�/M�Biosci� A��2�265Uy�1988.�w Verlag:�92jT�!�i>.X� a po�,iori collapsw!cc2�%m� th���$46:611--63"�2�92a��=�calculu �>umN.��J.� vari�*A� A� 2:171--20�2EBSBH%,P.~Staszewsk2�6�mGe, freyRparticl��2:1347@56��:�V85KB�b ussa ��1van�0 uppe6pt�A2*�a �ble.���!aA�ex�,ial-of-��� per�( nce indexB�> qFaR�iz%93!3:5�61=8.){PB79�Bie�sle2$E|�tyaM�G2���,2g79.VBEB042#out�S.~Ed{��bmBellman A.��^feedback.�qubit&) "h%�pret t!0\yWRWB76)W. Brocks1*�%1g��!naa )m.3 In C���1R.~He~!n,�s�&T01976 Ames Res3%�%e (NASA)�*�%Geo� �"21--47,�o-4jA� c�n� �.� HC93&Carmicha6�$%DAn Open��ApproachG � A�cs2&� ,(0line�.�{DHJMT00a�C.&S_%bib�0~Jacob�!X(IAS.M�6.~�B%!�*��-�.A�:< 62:012105�0./�W'99".C{DJ.��K�.HFM�-�.~L us�!inuous I�-�o2 R�0:27099.��81>%DGKF89�%�yle%�Gl, P4 (Khargonekar)� B.~Franci2��9%��!AD4�(dard ${H}_2� ��* � 2]��(T \slv c}4,34(8):831--8a7192- {DJPA� P.~Dupuis�R. Jame��IPe06,Robust�pertis0risk-sen�2ve%�ro2��Mm�,upag9ignal�13:318&�)0.� RE82���.lliott.�e� � C.%2�.6q�> 6�82.F~�+�9I .HN"� semigroup]A� roll5'�:�Ved diffuV�#�.11��B 28+�:� R75}2�%]R� RishJ�D!�m�*�"%�& ����-��772�CWG�/C�Gardin6\#%�Handbook���/��� ics,�8��u�2N��%: .�1乬thirdŴi� >GZa!2�%P.~8.^���Nwz}206� AH01�&S.8B^�]w$��#!+we6� F�n#&#J73�&Ha���6e1�*w d ���+*� .� ��ri� a%:t9Ui~o d2{a �-A  g��B�18a(124' � 72�JA�M���.iR6�� m�!r�Oum1.=E A��(}, 69:03210�,4.OJBE94Y�|JA Bara��RZ�:��a�dy�)De8Fw >r&-�, &@-�B��}$39:780--79{2� KV86� R. KumauUVaraiy2�"%M� R : Es� AF , Id�-f�AV!\l �R2��<ce-Ha�4E(&8wood Cliffs, NJ� 86.�KD� H!�x$n2)P�:�CB0&�1.�� �� l#i�$n& k%2�y�.:GMI�$~Guta L~.B� %e as:�� schr\�)!UF�&�:�� Gen.�237)��)�02�GM96} G!HMilburF� ��echnolog6�Fr!#er2��4. Allen \& Unw� St.~Leon (, Australia!�92�K#a�BC#�B#�B#"^#� ��KRPA|Ka3Parthas_<hF� An IB 8i�c1M=� 2ZBirkhaus7B�1:ZHSEZJ��� T�e�?Ebb>�F ��. � re �BH�o� #(�;>� WM95��F. Wall�e��� secon*,:q' {W81��~Whitt6�R6N�?/�sic/ {G}aa��BAdv>�*� ed�5�`3:7�$7A28.m!{WDDJ05�4D.��EC.~D'Hel�.� � �a�pped ato20I�-subh �S6W" Deci 6 � <y WM93�,Wis�C ��GZT_ rpre�8.y jump;d� � = illu�5o�� �6 h spB�:�47� 1�2166�3.U����q�t"M2field-&�2���1):64�3LF�a�8 � "��0"�� c��n��(, 70(5):548�.� :�H�E.~Won� Baj63>N- ?�w*�g2�yV#� Ne� b�G**}Y�1}N.Gis�� G.Ribordy�DT�Qi� H.Zb@n, �MAIuF74� 45F2); M.~>E� I.Ch*�it QNCK2��'.*Vx> m,.�K and��.!2}� Bep �ics (L!�Is2 Ci/~<)�1}�%5(1964.I 3}A.EinstD B.PodX;�N.Ros�d� O �777(1935.P49x4Esc< 15!R201�D1.75}J.F.Cl�1�?Hor�A.Shimo�=$R.A.Holt, [!� _� 2�C880��D"�6}D.Co�� Q S.Popescu�JRober�W3 V.Scarani)$hg8�K17040]Seevinck@$G.Svetlich�6� C9}L 0401I[�=�#� %*)#$7}J.Uffinkf� 2304*0A� K.Naga?& M.Ko�-iN.ImotoVG9}, 2.�9aD8}S.-X.Yu, Z.-B.ChA3J.-W.Pan \$Y.-D.Zhang>�%9�?081{>5�$9}E.P.WignL Z.%R613!�1EP52); .)"H!Dikertagung Wien} (Bik�{ Mos� /Bad�1L , p.G3�10�!�$ M.M.Yanas�A roc.Natl.;.Sci.U.�B �4!�91E�2�$11}H.ArakiFShysE{B12!!622A� 0); 2~:+!666+2e 12}M.Ozaw'U�iB67��95: 91);:� %a''402I�Z'�05�('S.MatsuEc 1@.b=�E3��093); K.Kakazu%$S.Pascazio]A�Y 51}, 3469�Y2�13A� L.LuV�9:1Ay3�3); S. 0wQM�9 t�D�6:2V14}R.F.�*H!� AJI�I1%+1%�$\.{Z}ukowsM$\v{C}.Bruke5��E$%�21qD2.`D15}D.M.Greenberger��O�e��A.Zeixi] it Bell's em,��%�� Con�&��'�1 e,} �edk"8M.Kafatos (Kluwg DordrechtG89ev$69; N.D.MeE-� TodayI�4A�No. 6, %�0)22 Am."Qi�5��73�x2H016}B.S.Cirel'� %PW%c sC3gO6>$7}W.D\"{u})�J.ILacN���E14A06I8}Consi�' fun� T $f = x^2_1 + \cdots +n$F -convex!9@$C_k = \{ (x_1,\l1D, x_n): 0 \leq x_j k, \sum_j(= n \}.$ SiX$f$C)�0 ctly e1) attain`5 }Kum at�Kextp# p�:Q :�.$A=n,� out �-,geK�:, assu  $x_1 \g�2 -  n,$ we ha@+at 2= hIn vely�+ob� Eq.�#�� 19}J.Whee�FM�� �4, E; p�nde|q of *� ,}�I�PZ.H.Zurek (Addison-We>, ReadL#MA� 90A�p.3-28�QSummhHrA't.J.&I��� 17E�,4); B.R.Friež��� from F�r �: A Un"�}R�D�6I"� I4!AN� Yf� ��S Ali}�/Tmi�% -P. Antoi� JGa�);>�*, W�-et�C*GMB� �&� ger-�#, &�0�BiseJ� �"�K4Solomjak; Spec�p�>$of Self-Ad�=�ruC HilU 9@ce, D? i�&�H Co., 67]� OQP}U0Busch� Grab�I Lahti; wional�����[(Cor�:�ig&Y+5B&�.�CDeV}?/Ca�Del!�E. De Vi- A��igo; PtOve �! vR-d % s co%$nt �res!R�an irr�ibl�P�-�A�m44}e003) 4768-4775.*�)Davies�H�0 ;5!��!�.� , � e�(� L�Hn��76=�Dubin}�KA.  %�A. Henn_G�7yS�@;�ew�A���Wey-�M� �cX >s-,���-E��EE0 �Maczy\' V K. Y0n;� mo�/1�� px�:*�$ieod/margiadRepN�1} � 8) 319-33.L �II.�i�0Pellonp��6 �OpeIR%�^�Z00 �$9) 2181-21��Landsman~Pau:�Top��B�;C"�=!��M�#Jh��19�Dc &B,E�Y�.XeCEd�), John�ey�So!� inc.6}7�"q2oz���m�B+2in��*"�$, J: \bKXE$9) 4688-462 Putnam} Cw/ |mmK<g*(!2fU's !�Reo2)�F��FN.�0oeck}d6E.�', Jr.J�3"Pe8�?, K� �J�Ners:�95�Stulp,D. ;]]R2a�Fl�to *�lLpl CO"{,�Bi�schaft h &-��2� }1 9harmonic�&�4o�3as�TV�25E,84) 1404-141�/N]�v]9O Pu}E�5urc"(�v�@� 681A�46); Kx6Drexhag �L� 11-2~QY7v ��Klepp&� D.F � +235814q�RiK}G. L� ]kke�Y.eKe!� �Bd�88�79LRG}P+vallard��b�\a*T. Gaco..bA ��545 _6�X�Lak}J� Lakowicz,,. Bioc�[�29� "#W51AgaIV!$S. Agarwal? � �12�475!�76�WyS�ZyliO�$. Sipe,N�3Q118O8� �DKW}H�]DEZ$L. Kn\"{o}p!1 D.-G. Wel� 64$62, 053804�� 2[�!r�\4, 01\:O CPS}I2Chance,AC�k�R! lbey>)�-b48JbCh!Chew, ��+]*� 8=3�^ 19872%7? 6Ra�-�3A34�Y882=AMap}�`oroE]n/ (NY) �31S�<4T]02005) (has bkCavailq-on-  s�Oct� 1IE2yHKDLm}V. V. Klimov, AbDuclo V/ Letokh <GE[E��549!U:= KDL1:bMN ja�T�:`225��a.\RupEuppe�J�Bu_)��76aY� 87Y�CKN9�M. Kerk��aP��McNullE� Soc.�_�a440-44�\76ASuHII}K.c Sulliva�DS"J25a�270E��]�QTom}M%�Toma\v{) �.u!> 5381���KLa2��6� a, .��30X41a9��End��Ender�] �Q�F8�31Fb6�LKL}Lb L -S. Koo�  �!g,  TYee, #�*. Microw< ѹ�q2X1>cPRH�_S6�� adloffF�{Halq%b Nord�A<�E30f419�,3)Y`9+ MGM}x?�(z-Marz\'{a}l G�"ig��P�28vaney, Langmuir c��432y�*5 ULM}T�_g,aA�L:kM�Mu _  .a374� 6�HMQGH�)k�%X a�,atijevi\'{c}�Yolloidf face!0-�22AV1L� 2� AvBV�'a?BlaadereiI A. Vrij, :�t292�86^VMBa�P. Velik�۹�!A.6iz���}.bOAW}SE- OldenburgdKa�A�QttA�h stcoE�N5Ib^�2 24w :�OJJyJ� JackS� �b^yZ�7��289�;a� ]�JaHa�>A i%M.��F���[BM�0X7�t*2J GAvB�@GraadN�:!�524ev6�CHML,!�J)�$den HeuvelV�H.a�Gerrit)%�F ``En�d�?sta�Oto,� ed lifeti�2 of dy�g_�#*7oidal g�G}-l�)cl5\ in�3�%�0�INeBaE. Neev�M� Birnboim){6�-}�!78%�86�JW:�F�L Hir+ JUXIC2�ZS82�#5u]32�BBN�Bouheli�^MoBe�O luis�d� ��. Kamat% �:�a!EB�DSM}M)�E*Dood,A�H. Slo-�VA. Po�7��D��,^7k35� B Dulk�e/[$a,2� =��20.Uc.O�)}�$ [1OY>�D�Solidx *6.�Fi�Jic6�85)2r,KG}U. Kreibi�%L.�z�� Surf�!1e67 L�MHaA�`elnyk%�)�Ha(`o"mEō��|8�_ga2% Rupn*] . <1a�287c:�LeuA�T. LeeI].{� 7622; 6}FuC| Fuch �Claro6� ��b37 J:�IME!ImhofM�gDDnge���NE�La3 SpriaW��Vos�M �:0� 1408�}%=�AM���bSiO/\00persive impur�;i�Gp�F$ic crystal���_�%Qo ` quI[ ``�E�s-Small�Tu�V":��Lenstra� D. V>�7K�H!� euwen edsDf (�:,Royal Nether s �}Ar� !:*�c� ,op 29-32 (p�; &�4at http://www.� -scab9 �� �Q6� MuD�QF l ^P.��De!� Biop-'��N1� 76�68YaC}X. Yatagana�fB��ik�0~�AJ6)m7T  %FZ#L�z�&Ntn&k} !�6�, .�, ��Z�, .%"Z�,1͸� {kauffmaoNL[ K #- Kno��ay&2 (>� i s.T e${aravind} !��x , Borrom N6 �4�,NGHZ1>te#V %#Pot�6s$En*OA�P� $on-at-a-Di� cyXe��+M$'S .}�&��ic2�Bo's!6�151�Ba95�$^�*�#}-Bs. �omonaco�, (AMS CONM/3�@2�O ~101�97. J�2>�%�.`-��*�Z1�|'�! 2) 73.1--8Rv3vH.5 u3�,-�2�C;--1-!�Top�6s!}1�em5P=@/.-- Spie*J s (21-22 April�/ 3, O�o, FL%�WK� onk�H$A.R. Piric�C�HdmM�NM��r�6 rj3���dye�4 Dye:V.'Y &g} �2 Q 3) 117--1|Vya*C�Y2 �(�"�� }-1!1967) 13�`1316� baxtX�=��An�B\}.\! bf 7�#$72) 193-22.Z {faddeev}�� D. F y)kIbl�3\A�(1+1)-dwP7al"�"86�+ory�h �r$(umml`ho=tmeH! i�A$Les Houche 8!Z�p, * �{2Ajimbo}��J -�(Adv.\ Ser.\� .\m!�Y 89) �89�NI!are�%�;}���=�R8!�� 24�/2�BB}� L?Iy�|E�R,lf=agates5Z &P s!`�@����2YjG en (Chap6J\&Jl/CRC�Boca Rat�'Flori��2�jon_(V.F��JQ�Int.\ J!yod5x)wAa�1991)j5-2043�p9�wadati1}" kuts1� �it!�)�qJapqH5 c87) 303;>056� c2} d�egj<%+p�r"�>fp�1 4-34�K� turaag Z. TM�Injj!*athA�)&9A�1  526��P�Y ~Xu�!Y�Wu�Fit�j id Goup, �ci�%*(%&]'}M ��1p F� 2�)-�$130�2A89�2%�+5gh ZgK.�miwFP%�t�\ �=a�AO12�d g4}� ^, Y CWIN g dA�!�A�O]�� c6�UM� 3735.�sogo}L Sogo� Uchi.Cn R�jt>4)�6M� 1) 1:\%56�� �d Gw E8 . ZhaoB�.TA }. 2 0) L 795-2k7kCoutu�RY�8%�zG:��".Ge�.�}�559.Ep8x*8F0.f-���3 R.f2y+!B6 Tf9�%A.mMk�RV9YI 139 02� lee1�~C,�{��g�N2#t� �' %5�'� NATO���$d) dy Instit�[� Banff �S S�Sini�6S�7lemum~Y.a�6~ lee2�_MJ-�A methoY?�]s%H clos�1rai�mb1 link awd polynomi]for<ne�qL)^�halk R���uprint�; nada!i:%schultz1+L�m��"] 4yP622�yo� Ye2A�2W - E', �`. .-�@� 5) �c1$*Z�])f��28} \expandafter\ifx\csname natexlab\endc\�Hx\def\ #1{#1}\fi^G bibO fontU* ] J M#�Pf�Q$�R cite~R.$�Rurl^�url#1{��tt!O%8{URL Iprovidec"}nd{!\0info}[2]{#2} B!i []{S'}&Y[{2�{L�rsDBet~�|*5{U{a}})V4 , Shelby,�1, Reid< �D}}]c85aU@(nfo{author}�5�{M.~D.}��1�@}�jA R.~M>A ��? A.}~!e}^2�<M><!}},�Qaqj� D.~F>�=F:�j�w}{��A} E�bf%]fv }{32:A�Y}{155� �0year}{�`}: �m�Lb�LanA>Perlmuw6Cb�C�CIC2�~�RU.��!_:.�I$%z5�i�;A F�10Qc?-�51� ~�!�j�Sizman��Le�99)}]"�8f�BT W})95�G>f �� \emph9'Y title}{' res�Op��398"W=��bi)IF�E>~�>}!�9kp�2 }{North-H�\nd.�add�}{"�6�q�99}n�Fio��ino��\6�&#sZhrp and �Nai+0�^1 ^�:->:fV@P p:Vos>�V= J.~E>=Sh �~2]e�j�P>�-f 5 u��+P2 s�+"ye�ersAf�4AzVm�9q�YJI!�rAgr�}V 5a� wLbVF G.~P>F >-E6OmKN"MVFi&hOeO}}�}0! ��R  San Diego.)�LrPotase�#Yurke}�7! 87�8J>  >֪B>O �ZO��5:AM:397D 5�1:87r:C��r�=n26= "$, Drummonda ��  �: (�hS.Fh =:�V�Z>���ANc �q�23.V��q �9=���f&58:�-�18<��1(��-t)�}]��v��ֺF�5FJ(�@Amer.~BjJ�o.�1I5619�IKenned�Wright%H8!H 88�� Tw~B>� BW�2Lj�E �: �.\5J]�A9^k 3A��-C2jJB8}n� �E�WabnitzJC�� �CNCS>����!?-�%�-A563.9���A!591]x91��~42�V'f�4Zj211R�91r(6�bIy}� �01�l��F�JJ� �ZC:�. n�1Z/13�EEI/�-rHAmans���V:�!�dan_AEmplit��Massa" (�cD.: 76VQBc B ��=Ph>yEƑ��� .�V�B 1! 5�note}{613}nW toleV Bjorkholma�82a� 8� �f>; =ְ NR �6�� J.�um El�Gonv� QE-1A�9D� 1062!�>�1�nPTaiU� 1986:�6� Tai!�Haseg�Oand�:ita� Tai86�RK.:�Tai:'VVB�ڦBPTo ��U�5����� 6:�1�3V6 6�.j��R� �, Jew�B!�9=]T86�5��9� �:%V�JJ� �?2�9�VQB�9 V�.9.~�4.!-�23UU�~aq.�!�jLa!HauQ8QLai.I.89�`Y>|La|%22D.�VFH� ::�9��gN>An �.~-@8jKF@v�� �� ��  6 =��3:A �38V!z� %r�0��f5'һR�͠magneSh Nois��$O� al }o mentb��4*O6z"�BN.~ i9�3r�Korolkov�!�!(EP�sa�gz*N>/X�+��-�aXkb&�i|&M� �m��% yE�e�F�J>�$Pe\v{r}inaLywp&�F�K.�5� * York6�5�v} Blow*�90:� , Loud''Phoenix�>%$he�_d�)90��n>�;:�VVR>F ��<�F� �C2�9�V�T1�L:9*F V�;^�4���41��Y0)�199v��%�Kl}� ��8����F� C.~W>�6�5F"�(n�1Z 235R�8vDMemyuk%5�Menyu�� C.~R>� MZ�f� f�2Z�1�Malla<U �TJ�J �R�A �U Tour�+�p�$e�.a+Y��&�b%sV"*�aq;u;v�HilleI*Ml�iowE4 84��B�! ;��LJ��)l�u5*_ n73Z! 186V�!4r)�\!492n�0vn2����`.�b684RCzbBoy �+~j5�VARJ�;-�R.N"�O b qr��6.�uv�Svirk=_ Zheludev} i 9�'Q�VYJ� =� N.~I>j�I/RTPolar�W of L9q*Fm .�"��6� sonV�Chi�1�22}5w\NSJ fa)1!m�a)�a)�a)�a)�a)�a)�a)�a)�a)B+tt BrG���� Bass��C.~B� X��B� �60��i�_. C� e.D �ln-4a�*5} u1q�s, %s% B~,�.gal!� Indi�pp�B���>175--179R8v)E�f�ECEk� A.~K>� GZ.*~h67:E �66}0���viDurD=�+2$�6G , Cerf, �ko).#ei)�T>+7:�V�N� %�"� ��=:y��=B1 6 2?u=�n� ^�01231J�!�r� Bech�)(-PasquinuccK�mel� )��H>I7>`}�A�5�<�V�W>[ ��Q1:Am.062308F�`$Bourennane"�o':7&AKarls�BBj�XE�,I� ]{Mo��Bl:�VhB��>FҒ?BW%ډ�u���^/'100N�#!�v�R01�0andY4�gMoh���#n#e�2�.� Vs�55��/Z;"�/0Jw�� a�n� �D�6�andi�!� cerf�Q��VX����>�b�.#N�~�8�.E��12�>R�z� ru\sKDag��B�" F����Z�301J�1Srt�U�.H6� #, Buze@O !�thiaumeA�Mar�� B� [:V�V>���B�Be�2?N�n� 5Z�182RR z��t�0D^ ��B77ani�� �n36Zw.��Z� v� Mai&w.��:� , Vazi � Weih�&��"[qI�i�bBL_��B: ��<B)��q=VNao?j�41�J�3N�)!�r�Tm2d(3:� ", Dey>�a|T�)�RMolina-T[z�%T�CJJ� <��BO"��>L>� ���B6>!6� ~ ��b�52^�v�k�ke-ArnH\D<I :�2)�Bar"�, Padge�^a�A,�a�Sonja��B 2h��S3/%T" ��@MJ� �@Z�>BR-!7��^� 3382J�!�r�� n� ",��!� 6�Vaz��������-n�-Z� 47� Kotlya�[19T6- #, Soif�{ Khon*#]"�� V.~V> [Y���^- ~A>@ �?�5 S.~Nw,*�B{����5�EtU�b'"!�y{� 40V1 7r8Leachn7!�� �,2�eRXGr���5:��B*%89x%&V���j@�m���;BCo1T!~AQ�U9*��Z�25790Vvw"� UCJ�%, ���Ceinfurtm�B�/xB��@2�.� V�B��~7Z303J!�r?.�n.(!�5��7-t]{Zuko�3�%Vg�82�yxVQ\� &8 ��U�N�n�5Z) 256Rd=��NN �fN 2�,in��O� loh��~AA.~M5R.},M�e��don) CJ16}, 6�m� 6^Osbh NXT.JZ:Y.�^^sn 0321Qp Y�BargSMD71} E��:W�.~VK~ V2'o0�r00tc ��}BMbf �a78@�76mLSyljua��3-2D} O.�\~ \aa >i �e��3E\25�_D\E$!}Wu%w4}�"_al�}Wu2� (.��7056) / show��a07t"�Tz"�[x� u�n��d a� omal��iOe bi �te6�[y� ors �ex�{ed$v� basi�JUir defineYerm+r)|(ed two-body�jscC�.�Chakrab'�!.96}�]K�O20, : ]/II��w) =o�s��Te *Mo2VPYp�b���g.�Dmitr��t �G|V. >��dxp iE�i=9Ca53j�:< Caux]3}\{S. :Y LA� B�[��13443q6mjRD�ldeY4} T.Ivc6ZM�ZI�e�9a16720Ub6�e a!S�,im6c2�E `i� 4670 �:�lo�^�0}!p jYm�61��52306e�6)` Amic��&� L��ico�V9V 2230�m6WooJJs,'W.K�� 2fd=^80&l24Tf6�j%H!\03} O.F��lj1Z2R�!n 0603-L6 Kul%L�9J.~ :�Ab�kA�P bf 1�q2Oh:ktVerruc �a5}�_:X6�:�չ(PelissettoVAIA. ��]Vic����Xp(�3�5NkB7,Niemeijer67}�l)@�{�3��30�6�_��Pfeuty�ZP. /y*�v .Y.) G�d7�e�bN�� f�6v�b:^J } {M�d %IsT0b}!�em �*\Y-� ����ro}} ({CNS�M�}�Rp� , UKB_aL =�OConnor:"4{K�sO' yW.��q})|!�v�36�h e�2 e�6�`Arnesen:01Gunlycke:01Wang uT��%_Bos3�V. VedraP`Q=v�T|�y 017901}; {�v m2�V�Ee 04}u�CX. �n2�#���A. Sagu/� wS܎ ��q�\eEo6�Ghosh:�B {S. 4ZF�eP|m�Ae̯��eC&��& e-42�� 48 �6q�:04a} {C$\u��5� eA.&) �Y�x��14{.�$Terhal:00a 2Bruss:m {BEw 5o�k-*27�܂)���!��,_>&KW��4E� 4237 56�&�!T:04Rahimi:04Stobinska:�^A�(jI �%b9� 08� w��{'|d>EF=05175;|�e�(K. W\'odkie�}5*��-)%(03��5.e;=�2�^5�R�0��2�oth)$G��tAiJ� �1��(R)�5) .IBartlett MM.D^Dow��t֤he"��Sh6}N�7�06ODr6�Loss:��AA �*p. DiV�|nzcLF��$� Q6�Kane:98�w��0}E�E`en�flI%3� [x J;E$ =>$F�6Ae�;06If������:02a} We4�e��c;�u���W studN estab����+EY��b|�>ur�9xvczlŋ"C�s: (a) �>%\P. Zaʜi5�i1M��{1 �X�,(b) {U. Glas� H. Butt��andFehsk!WJL e18 T32Kavoki��}��q~ �eSB)�� 0753 ߡ�8p 8u6�WuLidar��L.-A.I�D*6�)4�e�097904N�Wu�wGi[e7^S��g(\�u�P 2504RA Vid��At��RzW=�6�-�6œ��1 �6�Peres:w�{A^ rU�=�=7�S 1YweY6�~Horod1� N�x,A�!�R.� m �2�� 1�2u2h�:�{E?e�[�� McCo��� Y!k��:� HoheV�:74���#^W%sBrinkm�m`M��m 1281z1.mR� � f� ��"m An���WZ� ,lr� � %�u2)� . %Ecool}aBei�K��4}G s tiel%xCo g many&�z at ��},k�041602r died-jJ. Wine7s%I ,�WJG.A!w Blac��%�-1) 0334���%�6O222$p �ODomokoW =h�a8�� �Be=�0 ) 10d�b�EwT.�H[�Hil1h!g� Y0.A2�9aF i2tz12� el} �|Els\"b�k�. NagorY�io��iiZ9� b 0514:bjaksch�G'�s�e8i�]4�.1*3 _Ol4196�v7�a���!&��e�R. En�q���zatthew�8�Wi�� �EE� �N��-x �26���:� cold���s�m =A=]N� 6M�} )�ChA�2�!���&=-�630:k-�H�9�j.o^�^^15BmPLK} C�Ger�>6���I�� duct�Q��um_<*�:&�� U���œs� R���}PRWAA��#�x�� i w(es some err7wh8���at߲ behavio @p�{em��F� lare�� (Oxfo�� 2�hop�n}1J�� 2� 1�15�5��H2E�H= J�Ba��ˇS~B �, Eur�w.1\1Fm1776�DickeԲ�u F�< 9^5 �Are�} F�� ��c!e�yR1�l)|a�H�X�Jc�k_ 22ېm Radc&�e%a)� �&L���� 1971T�6��� In\"on\"�kE.A) ,6C�\t.�v.�H . US a�S1953) 516� V� �4De�cin@.. Nuc�j�B1-�76d 6�SUV�N.�_hQ Umez"�P2\% ��ItB1�R/  47242��R2} AssuL�@L_2 = -{{\rm i} \}{�1@S^+a - S^- a^\dagr�,=0$ is also��ivalea�o negla�ng�r|�c&��Ds $k_1 \equiv S^+b `b`��k_2 & S^+c &c&, w@ i>� nsis�x=� ȵ o�Ref.~\,h� A�ere we �4&�k_1�$ remai�w deed zero�� �y good 2�. R� �j� 99}���j%jbi[� {dav[B. ��,�j��e�um��3M,�c"> �saQ7%Hory&�.2m�8),�. 5, 5r�59��^ Akhieze� I�� Glazd�� �lil�ܖ;���ݖs�}�V� I} (��f�l��t��Rua�tL��by� R! wson;��Don*��W�� itt), Monv�pc����in�Κ��, =�"W�a���� yperbolic�%S ]fr��cy ��rK� 4�k ��UTق95), .p,-226, IAS/Pa $�T. �x,�M a  ��Ynnce, RIP.�p$ {derka98}�� ,� Bu\v{z}keA.�E~,� al@�o5� �#q�6G R Fin�$Ensem��via�lizI  G)�i���.h}�%�V�!15;�6� {g8��6�o�`U!>(�nt�%allel �\oesw alwaysz  �� .OJ�]y�{14":{gillm-F00!�Gilq� ,)<]륒large e1Dz�j1�2h {gisinpڭ 99}N� si��Sc�pe��S�s FlipI�-�.Х�2K4N�La�=�,43"چ& {h}�G ���ARST*�ftur����t� y}, LH�NoA�in gu��, 67, }&N� z��lpre98}J�L �Pascua)�R��\MinǾm*2�-L.��6!�1P΁�2ۅ {UW]KɊ� ve� sus lo!Am�ag��two pamo� :N�.��U�0V&:q �Yr���.s-, &��#B���� �(&��nIy" �12N � {s �K��t� ,�O aun��Impossi�� of d� - $an unknownU�stateQ�N:�940�"164-16L":7p}A0qe5}Q6I�:�epti��w�xFunda!�al9�o���Je57. Kb�� Gr|Do*y�2�� {p�wn'91}�%�6$؁e "��!�q�=�1)��-� "� 6`,1 �.?28wz}6z�H. h� , "A՜��c�,t be cloned"�>�29802-8V6�' {w}Work�p��es�N�&�b��"#Ttem{[1]�xH.L,).,% �E�1A!189�(6=[2]�z0wski,�*70�&c/L2o��q5�7��42��>s3� �%�G.�L(, in Proc. �}of IEEE, pp.175-179 (1984). \bibitem{[4]} V.Coffman, J.Kundu, and W. K. Wootters, Phys. Rev. A \textbf{61% }, 052306 (2000). b5]} WNJILett.M 80}, 2245�986�P6]} G.Vidal, J.Mod.Op= 47}, 355 J��7]} C.H.Bennett, D.P.DiVicenzo,J.Smolin,and>� ��A�054},3824(19966�8]!Q,I. Yukalov, @ A � 90, 16790 �36AH9]} Alexander Wong !�DNelson Christensen ZY�(63}, 044301%16]10%�@D\"{u}r,J.I.Ciracc R.TarrachZ �\t)�83}% !f62%�9:_�1]} Florian Mintert, Marek Ku\'{s},kHAndreas Buchleitner=i:u92}-12�:�L12]} PAWEL HORODECKIeRYSZARDT, Quantum Information !^Comput� 1}, No.1 A�20BKP3]} M.Hossein Partovi%;%� �19\ �077904R�4ưranaw Rungta, V. Bu\v{z}ek, Carlton M. Caves, Hillery,�,G. J. MilburI �A�$64}, 04231I}> a�me)D.F.Wer!�I�:o 5},032314!"2:}� MFaY�59},141aT>Wa�(K.Zyczkowsk!f . Horodec A.Sanpera��,M.LewensteinMWi�m8}, 883n8); B.:`hyJ�0I�496U�x\end{thebibliography}e\beginB@{99} \raggedright��8Dreizler_1990} ,~R.~M.%C8Gross,~E.~K.~U.�0):I�8it{Density FuncA�pal Theory: An Approach to theu�Many-Body Problem}, Springer-Verlag, Berlin.>,Fermi_1927}  ��D27): ``Un Metodo Sa\�nazione di alcune Priorieta dell'Atome'', \��tit{Rend.~Accad.~Naz.~Lincei}~\"bf{6}�� ~602--607R�8>�8�Ein s � sche��hode zur Bestimung einiger Eigenschaften des �@s und ihre Anwend3auf die)�0ie des periodi$n Systems ��Element2�Z.~E��4A�$pp.~73--79.�MorganAI6} $~III,~J.~D%�96): i��it{�0ic, MolecularEpOptical��ics Handbook}, Drake,~G.~W.~F., ed., American Institute of �Xics, Woodbury, New York.� SchwEu_1981} �AY81%�Thomas--Eu Model:!Y0 Second Corree'',u�.~��9C\A24} (5), pp.~2353--2361.� nM� ,~L.~H�M�The CA�l�Fof )R Fields.']�$Proc.~Camb!�il.~Soc�23M�542--548�Ni# zi"� �0M. A. Nielsen%�,I. L. Chuang9)�&��`�>} (�,ridge Univer�� Press��m , 200: �M. Zu��A. ZeilE,A��ne��AF EkeU%� !��i)� bf{7� 4287A09:] �. et al.��� �I70},189� :J�J%NS. Wies�-�vT�69� 881 �|:3�V , H.J.Ber��$ S.Popescu),B.Schumacher �)��AK204ɲ:��S.D�W.K.WN� 6�7�w 5022�76��R� N r� J K.Audena%�,F.Verstraete�De Moo� a�64� 0523s :�j .Uhlman/ J�20 32307� :AP R. 2� z� . M.B� �� .� Jxz� a��i )/6�� � �j �j Bj Vale�7&�oydip K*�illiam KB�>6�$E6%�:� �� )L]{3f� e�\hang-shui Yu, He-shan So����-�A�>33# 377 q > a��V�&364RVa�Jens Eise�`Philipp Hyllus, Otfried GWh��,Marcos Curty��>)�b 06231i_>�����9� in p�� or q� -ph/05010  20056�1�(Charles H. &+avid P. 0n1 Tal M�{�  W. Sh John!�Pe�Barbara�� Terh�)��6�82}, �Ž: 2� �� I. ��R. 6b dA bf�2�*� [2�X4Different from) previou� finiZ ��ors, all( %i�cbigpauleXMartinelli, C.L.G. Alzao0.H.S. Ribeiro �TP. Nussenzveig, Braz. !N��5C3aw59�9S�Fabre1!�$Longchambo�( Laurat, T.�^<C. 6, Eur. m J. Dr�n27-R�F>r2�rRr8 �:rz(Duan}L.-M.  ,� Gied  !.I P. Z!A!�.�84�72�=:�0democrat1}C.M"� \prd��2�181i@8:�A2A%�B��S�k �>�0682�N/� r� %19�WW�"$ Weisskopf�]ig�Z�o� |"54Q 3%2MRzaZak}�� Rz\c�v.ze�WW. \.ZakMC�!Ks�� Hayash �S�]L&'i�[�6��a ,6�q�̀��8�tSee also� ;%�2� jM *B.�+�R,b&+=?�j77�"19IABY$I. Akhiezeg V�,Berestetskii&�E�8um ElectrodynamKX (Interscience Publishe�196� uLL� Ba�.cE� (Lifshitz, L�Pitaev6�7ivXc ��0} 1 (Pergamon�#1976�MW}��,o"L olf�� al CoN�a� m s}*q$,Jr$� �SZATO. Scull)�M� Zubai�&%�it1fI )]"�$, F�$19:�"4ON} OPN Trends�The N� e� L�)H. What Is a Photon?&U�-4No. 1, October�12c Howell} J , R��ink9 J!� ntle�R\ Boyd2�i�%bf� 2104Zrt�e��tsi� e.B%�AO5� R253� +$N� Nf� 20}=� Heid�#87aD �J. &�� eyna�,E. Giacobino�3G� m6#6�25U01987)]Wchwob97% � �y:� ,A. Ma{\^\i}t�&��06q2�|18�9.qGao98!�, Gao, F. Cui�Xue ie� Kunc��N_3�,7�8�-,}28�6BJ �( Am.�z�$152a20CV}q� i&~/' Continua Variables.�S�( BrauQ�(TPati (Kluwer Academic .  Dordrecht�s3�brazilAHS. Vil.M!�&�>��� Munica !sU�24�!55}14lOu92} �U*Q�W6'O ]z 2hZU$u Y.  D( Wa�X. LiJiC. E4Vr*- A� 0238�v�yLa�04bE� :�G. Ke�0,�2 Trep*u��s��0�$sMasona � ZC��^�173)0.�>99e� ,>W �3,V-Z�1� 29��9�PikovskyAg  �gbl�J�Th!a3+ Ft!}1\l'2�[�59x21 >18�%9x6AZ�D*@=�6�� L�0iShaddock!�D2!7B_ ay�5(E. McClella(N���4J�$Korolkova}A� Leuc!�R. Loud�TA_Ralph�kSilberh=�Y��*b(.�Bowen7P2w�5R�hnabela�-A�R&P=^�� 09"V.mJ�4�  g Dant) L. VernacBra�!d Pinarda .:b�91}, 10�.e Hald� �}$L. S\o ren�C�orin�olzik2� :8! 1 akNR�fR12Repre�N� i�Yi�2�� �  ��35); ` Bell ,�/) �G.64.p'canada~ Tapp� CleveE�Brass%�>y! 187r! y�2bits}�Gis�N!� L)SA �2U 39); M�e� �"�* 1�� 2� �ztonerz F. T a��aG }g �% A?�90� *]!entgmeas�"�.� ohrl.W �5hR3Q&7.v!�EiJ/2KFound���D379p!92�tsi�S. Tsire�9$, Hadronic�� Supp�3 K32 J3.� chsha%� laus��Ho�0AZ monyA$A. Holt2�=O2� 8� 69.gy �yvan D�S&�501159=�,2%t� J. Wulls�9g�.< 2030<$machinesim�^�erfeLM�S�s�.�T410027Tvs��Scarani,3 Titt�1 Zbind�JZ�i227A� 0); V�| P9:�5�a�:0qg � �DW.�]�M�) 1�1);%�tefan�HR�Auarez.��E�� 12"-2.�e��ard� .J���R74��6�bineqs��Ac\Q!� Durt.�J�Lat+2o1��2�:2�pirExPiaIoN�  0621�2Mbarr1aN Barr�J��423 B:�to} I�tq: {\em"� &9�("Tse �s �# som�!N 20 d3min1Jf f0$i1eap�,�1ame.}twoface�~ctual�lprv?m outpua�wo )$ts: inequax.(\ref{m�)Fa simila�e wt RDfirst line (2,0,0)�replacI(1,1,0)�*�1wri��dow%X x explicit�8it becomes evidb3E��m� rans�BedI� the otherA�exc�]2 $A_0EX 1 by f�5 �,bit $r_{B_2}2�bacone�B , Bv � ���*Q �52� "�p�om�EO was ed!� to us��� 00 (private com&K2�ap1} 9�w)@d� er!+!�8?8atic search becD %polytope5zra)Rig s�)�rM/ S<> E3 secmain},~ have��n9��4(A1)-(A3�3Ϳ�a, verif 7%��4f�,m can be vio�0$by a single�a�!�NLM�4n modKPe marginals. It turns)nh+)ŋby 3yQ41V new2� deri�hf�5ہ� ��4��.�QM.�!� 4} F�5�F9���63!t`5E�oo �  a task N���?'6 we)�ru!�isJmorAaneqm.:�im�each  , randomly ser�30I�%c1�63�ei ,ed��O0a non-trivial��,� a%inv�y ��4�y)�usAr!q conf�/tց0 he only i�Bng9�y� �[��IrAJ aboA�0he $I^{(2)}_{v��t�C���F.�M�2�>)5R�7N�of�02� woer�I�len L, Beijesbergen M W, Spreeuw R J C � W 7 J P O�2 \PRy 45} 818.� oam-ac.jar(J S ME�(Padgett M J� {\itq�0 Angular Mo�Cum�s"C�X �~B�-o 8 Philadelphia.� �n><} Mair A, Vaziri Weihs G�";A A�1 �z$} (London)� 412} 313*� force-oF [fZ(jauregui} J!� I>4 % e-It�"�$1.&prudn�} P A P1 ychkov YuM�,Marichev O T!P2 �F�!gra�.s(\ies} 3rd edn, vol 1-3 (2G: GordNnd Br��.2molina}�8inat>4riza G, Torres�;T\r LB�8} 01�.�(dudovich} D $ N, Oron DOger YR4A.m��10300.q�, nov}�Fm �Sokolov�dCot�LTI�(6 \JPhCh USI�1� (13) 5166Z8Nfs\15} \expandafter\ifx\csn� natexlab�� (\relax\def\ #1{#1}\fibGbibO font>J M#�Pf�Q$�Rn~R.$�Rurl^�url#19tt!O%8{URL I#idf mand{!\� }[2]{#2} B!ee� []{S'*r"[{2�,{Hau et~al.}-9)Brris, DuA�,a4 Behroozi}}]F:19 N8)nfo{aut�1�5�{L.~N.} &1�=�7 j< S.~EF<��?Z�=]�{ ��:2 and}��C�=:�9,.A journal}{��.\Q��bf%%�(volume}{397:�pages}{5S)(�0year}{%{.l>�Li9��66�Liu9���and Hau!� Liu:;},f�C>hLi��f�.NVX��nam��%�%�j� L.~V>�% 2���409V� 490}B�%un�l lipsu�2:�$�Fle�Ohauer�Tir,�.swort�:Lukin!�8�� D.~F>3B:�V�A><.��Bf �: R.~L>�Wa-B�DM�PIj8-\!�u�UF>�}f#86�EǍ"7k >"ArEBajcsy.C3:C ", Zibrov� �] A(3�#M>� \:�^#~S!.� �?5l��9fVQ¤��42Z�63 D�%����k?9j�VXVF�lic�; G.~Y>yY��,%�2���8N�Aj�6 C.�m� 041801(R)R�v�Mikhai3 � _16�%~ Sautc5v,�#tovtsei� Welch��1!�4��EJj C��VJ;��BYJR}6�C2 Ej� G.~R>Y-%!Ku�U F,j21��M425R 4r�� a�� I}] ��bS �n. .�V�� ��nE70V5�<3] 5��%v8 Byrnv%!, Gabita6�"$Kova\v{c}ia6gab�+JJ�a:�VSIJ� �@��G>xB�V�!�ica Dj�1^u69R�v� RybiI�VadeikoY���AN)Z}�� I.~P>#�Z:J� �OaZ s B:"]#and S�/las!`l $eqt�9U�� 6e�2G16RevFaddeev�(Takhtadjan}2}]{fad��LJ� X�eLJ6�)he#H5(title}{Hami8`�aethod"�PIL,of Solitons}!e�ApQ6}{S'�'?CZ%o�h!3r�Hio�!�8!Q94!Q �g F.~T>k>�TR>� �)L���a�.\�*\m�^�73:Gp�255J�199v��"�/:�!, ! h �'ly���a�V�f�i���JJ/�f��%�31N !rr� Park�1Shi�+98A�!y8�1 Q.-HAQ.� >�� H.~J>N��;n|5Ze464 Q�298r7�vU�J� !���Q�BishopA� ryb7�\j�2JV���2�وVRA�? :�H5L��0An exact soluv6��� slow-lY:%�c.���ArXiv:.�11148 v1w* Nov�����!�r���n� #, -�D �]!ʆ&��E�bzB����)�%�F�!�R�Manip*(bo al memory�%�8atomic vapors !2 Bose-E}(th�bensates��!�)�~�N�! �~OXA? tem{Beane�-R�<a@(P.2Bedaq�:�Nild�P,�.Kryje}>,4 McGui6;and U.E Kolc6!4V.4�_421�<1).|�a> BawC ScCo:�2LCA042710,yB�rPE�3a�e�D2+T$�8-,P23qC0�@P Muel�EM0 le@ T.-L�<-[a�!�-mat/�=283*tS KoloCB�Bomeisk�>NI.#!a >�!!6�E266J4�H�D�8H. Abdoul-Carim� CGC(sfran\c{c}o�E:�O^.=:149�m[J@aH. W�0z6-W. Ruf��wHotop,&lJDS 3!�3g;19?HUruskov�/ T. Iakubo� A.�=Khrapa:>� 2I504#:5).�+�h�(�- �.�WA�O'M+#y#� Spru=mALeoB7aen�$I�}W-�uA�49�]62�pere70}�M_Trelom ��2�Up� TeorL3tpRzZ-W-�70G5 krat3�c r\"atschm�L.A� LambvD,Fostiropoulo�]ndR. Huff*p�:W$3<235IH2zcalo67}!8Caloge9R@ it{Va�= Phase .�jPotent:'Sc8Zing},"�=oB!��6�iN�8f G�+holevo%}Sa,Oq Trans. g�'e��)�!t26J�schuwaFB.)@�eE&XHA�st�(�: \pra S�6131y67.�dav%"E.U�`�(�qf� IT-2�5�l72�kingrus=KG(!�M^Ruskai��7:9�,2�fL;YF OR%47@J16Lp2�� nath9��Au hans��F�\�OX5 0�,�l2�ha�F� H ,�jIm��FatsumotQF!`1�T�7o,.F 03176�<2�cortese�3C .720712872��0te+:�fH�;�lld:J212=92JA|�8�y�6308�6�Hohy�J Ohya�9Pe:F!�Nj@ta�<, %5��h�} ats.)�1E+707;6�niu!�-S�j"MI�= iffi?y60}, 27͵ H���a)�B�PI�S. SzarX�F�pLin�Vg.�{l_;��159F�u4h%�"@h�gh�gAB33 3az70T7Y.Phadam�7�D ..u�% Appl-@5F:17�5893); D.�,Mitrinovi\'c�IE� Lack , Aequ�B es Mŋe/2Q22��TTR<�f<2��G%�G%�G%�G%�G%�G%�G%�G%�G%�XE�lU}a0)}]{GZ .eϪ7#S�4P> �$R� �J�Y^� 9 H �d� }{^N 2000rt$CarmichaelJ3!8HC9�L H>�J �R� An Open So3s��"Lt1 O��E.cB 81'�iTr WisemaZ} 3{"�) {a}}!#WM�# a�ZB`�)n�6j=}$ N�&4Z�642.�=C:�1}teB�&BH5i�]e�Belav�$!U1!GBB9��&B�$W�JV>��ZKV�jU24:K�149J�]r��!92!9 VPB9�*!y� R�)���Ho �j�140.i �61JA 1992r��y���CWG�6!C>�I)�R�Ha�v�SB7]�4�inv$Chemistry ?25� al S5Qb:�4a:5��cion}{3|A�k��JvKaratza�[Shrev&8L KS88�f8I>RS�pS>O �j� Browlo��?=�#wu�$� �qD��8vnKloede �Pq9�%e�KP��B# R�]E>] � �R�Num^yl�"=_"�oial E� !�&�*Y�Y���vmzClark��7E�JMCC7��J.~M.~C��.  M},�q �a!e �z$��O�E�R�9�cesses�)la��=Tor>�/J>�(Skwirzynski KAo{izn $}{NATO Adv2@d Stud5<&�4Ser� Z�ijthof�_NoordRE AlphA�an A� Rijn.*q,78��pp.�� 721--734}j Elliott!�8e@RE8��B^Gj�]ݑ<%�-�MIla95���8v�P� HajeE�85��WH8[4��V�BN�MB>� ��Y�|i$in EngineehmB�`v`5r[DavisAg79!WMHAD79�M= F�+ M)1�"v ărocee�s0= 18thXCon�o�B Deci�E!� trol}RP176--18J�0 1979r� Suss@F%�HHJS�GB� IZ��XAnL@���HjE ZC 1R�"�ojPKurniaw� James}(!�KJ�H F�O�MM��+"� ��J16{ToU ppe�L4�9�f(A&,A>�;r�V4.jm6N*�C�d %NC�%B90 R�Bi �IVR��G�a5"3J��f}&fU zq͵�1!����YMerzbamraw�#EM��#E>�J �r"Me�Ei@VWiley I��&� E� �1�#�"�  v� WZZ� WM��'B� Sւ�L^LZ`6135R�z�'Cav�Jnd.�87��CM8��$BQ�2�2223Z�55V &8v*(�M96��zro Technolog  Fr�\er�^� A�@\& UnwHF� St.~ B8Au��liaF��r&D;}]D0�~�DPJKes}$��Elrb��{ ^�*25���K J(�r���%..�b&�a�%������7jQ 7Z�15lC(5\��3.�!ja �Vc9V��1�V�V5V�#165�$!jS�uo*$HB�$B7 F��R�A Guide?Ex2�cH2�Ozw9 -VCH.~";|5|$1.-,�P --11.� �b-&>�U=� ique%#t�/Q:���yMGon��~ы�5\ SB1�CA�.\ ����� Plenm٭�, �61.qol7��A�H~ \=pS�^ Ym7 PZam(a>s] mittspA(aݒ*�\��}�ll.\͍�2 eEs}, no�e]��1773 (Eng>yl.:(u�u$z HolS.wS�%?(M.~E.~Shiro�4��C�nuBqXk���I�$,$\chi$-capacNbof��ȑe-dO�al�!�>408�0��0 Aug>� KinR"2 C.~�1 �\ B�=�/.��Y�ha�"u]a�duct ��a��.B��(b ), 87--98F��6.; Lin72m=�indbla2^n�y>_[q<:�:w�d٪2�J 1972�w4n�4.D Jac�pK.~Jacob�E`x fficient2w , puh^c�p e�yeAmu8a!�� A��0�@*�n8} Ar}QNo.\ 054� 3)FT30603.� Ohy8q�a�,2=�On�_p���eE+ �2)i�^* se�i�a�� )-bf{IT-2�198a�770--77.? OhyP9>��DAbetz���.� Its Use},8���-��}u�Oza84MlM.~Ozaw.^IO��p� �$ofI a�observ��AyBk�:8D�79--8.]Oza85af��d�� Y%avet��ri)�.�  m"�,�\Ad.I.M.�Kyoto�.{* 1985a�29.� ���><Concep�_%)�expecy.�an �=� 1948--195>�/ >�slA�.��um-�i�( ous ^�!� bf�}�d,86), 759--76.Rus029�B.~B�I#e�&�-��� 8� ��ew���\B��j9a-773�f.� Yue"+ H�~Yu &� ��. t���dM� ���Ye�eal rig�i phy�-/*�aR� h ECA�� qb� 17R�*� YueO9�p9 [JEUlt� 2cq>� l�!�m� s�3~E� W3� 63--366�N5�j5~� GROVER}L.H; Grov�$E�� E3 79, 3257.`{FGGS00}�9Far J. GoldsUt�~ Gut')��tip,sF�_00110�� RC02�;Ro2%pN.d�r�A 65, 04;��!IFGG01�pJ�146H�DK; T. DD�eu,N71~_rN�Hf�2Aesup���<Tinkham,"r`rZ gto�ter,uc�t��2n�` . (McGraw�l:$��&�Sachdev�C pq��?� �D} R��?"�%, U.K.�). uqcomp�A5<e*pA�r6��pu������ A } n� N�� conc�j. O( l�L0,ico, G. FalcMR zio, �2>WA416}, 6ʅ2�G2g2<A�Osb�a�2�WZ u6Vq0 JYKi�} Gu�U<�sa�Rҫ!D�0,� iŻ e<90�=h�$@�<JfPu1�Inf�p!��=T=4??v?={�} B. Q.�~�V.� �E.m��1%k.7�Y�belga} M!� nnes;m Haeg|8 b=��y�Fe=�Y_&B 6005%q�`Kea�}!P. �$F. Mezzadr��..^252}, 5�D�6(Pop3! Y�D aler�@ �I" �7�z012�23�� tiwcEzAntal�ER\'acz[$L. Sasv\'a�]E�wK�16kv�^xxZ^,Aniko�G.�ch\"utzrR�E �5FF518�DCLSM} Eeu���Achult �D%~tis�[Ann1�(N.Y.)} b�R1�E 4Å`�tN�A , Sxe<���Popescu&2FD6��bf 6󩩦V�?aDfL%}&�ad�� A|.lem Why�,o=q��has nsolve�riZ.lem: A��pon�soA�W. Ander<, $3. Hist.AP %!�Phil.���Sci. 3�B3) 135* : 1120Fy�$wm} AharojyY., Axw�Z@�Eb��Van�� �SurprJ}g gum effe&vt I� A �CS)�. �ahavaid}2�Zs2� t Po�5.PLw�sdo)whow5 ��mia�� icle? [{@aisal}zC !79511005��a�F2�,*2le!9 B.-G �d��EO12ProteY:x!` Bohm j��5Q҅%$ A 263 . 9!�76Ge�n>�#{Nf�Ti�JEns+ Averagd �!:&�-�: Scri. 69��4) 81�5:� 06��5:s�} AAZ, >���P �RIMf&�% al RealiL6A�EN-E���-��-%MGedanken�r�tA�New Vfr� of�= l's .�5{RevE���4��J��.�bK� e} B a. E.,23{9OC5ce-+ IncQN(wood Cliffsa30:nr{"�{J10�2 Pers�ce�MNO:a�re!FtrYg�Z!/'" 8Axi�!phy?,%�0), 67(D680��9�002046.,�{ 04} J�.I�"�5 Thro�y$Frame-Depe�{t�str� �W,�thcom�42� .�� bell_ungl�m� J>FMwO�Qa��Aa�L� adox�&�Nd=ͣJt��e�6!(r&3��mspeak�}2�sc�N�0Towards An Ex�R 50�� �}Essay%�honor!��b0 70th birthda� Ed� Des�"RE  �tkel"�WorldI(tific, Sing�Qe 198� �(%_ how_A~BBaH��o T�m Spec�LQx �-��inw Cultu Q.r;K76)q prin%r��=q]J�S1���un-�E�um m*�" �a�tF� !(6� mara!,�q�MQ�1�(Dialogue --e�MaL!�a �� U},&"%#ChicagoL�M!��� eund��erndl�N,W�ur��,v?� S�eruzzi��% Zang�N�m9 Global Ex���g6P,�A� E h9 ! 17}64�qeNPO�%� 0301. .� duer)2�a6>�j� B�qUA Surve%TN�( Il Nuovo C�oo 110B� 37-750,7n*� 9ӕ16�$debroglie}�<\,B �O��La �`�a Uque��la \`ere� �du ray�&| et'\'I�:ond�Uoir"uɺ4), nachgedruckaN w ��La��:E� ywera-t-A� Indet!�|e?}, � K6� � 3. 2� relaa���B��g EPR-aY Nonloc� , Lo�{ z Inxx�+!�1��u"ؓK ��_vI 5Iy6) 2062>]�^#e�yjblo5rB�-������OdZF�6��� Term�3O���y�156(5)A}6u 37 R� bohm1}��N �A sugges@Jypre<��� �*y�`` �en'' %U��6�e�8q�166(I)m 180(II�52), �4��zurek}*;�3B�Reply�(a Criticism  ausal Re-et� �6dN�#(1� 3��2N2B� Proof Tha� �' DԂty�?r��e� , $|\psi|^2$!S �:���9�4t!53) 452� bv�E� Vigi� J.-PQ MJ�qb� :8�U�8a Fluid with Ircvc�Flu��A�N9�54)_206�h:�H :" &nt�6�zba�y�aKM� &c(u�p. 144� 6 �321.2 undiSsd��� U/�e�H'Routle.�1.�h� 00} DF�� R)�J�Schr\"o�$er�s�: an aic �Ap}Q�0)) �H0005026.�cushi0C $T� McMu4��(E\*�p� osopr��nsequs!�of:/}2��of*�re����"� �Hia�@J� _qm}:���q�"$  --�KorEC/$ genc�A%Copenha\}H�o 41�a�of�@�"W �6` !qT6E,V ee�b 1Ntѐ"i 3QƩ�%�n , K�, �Np}ea(Do����-�_bowma�2IӏA�$ -h�9h' Chaoa�in| Bu�fW��� goni8 EBFj��iicn�&� },jc �9)2Fn3�� � NaivE ysm abou�~erӋ� Erkennt�$45, 379-39�60�Es%�am960�2�de�y} DeV!$Ghirar 0��fnRevi�,��of%E.,$  . 28,����0.Gdh�� ewdn�[gHar��LI�Sqx^i�e� 9JA[�#[ �u6��fo�����e�Aj<�h.� chri6�%"Hor�.G1.H �X�nt[ext�~o=a�de�cj 4iQ!>�uy}�A�. A���" � 3�01��2)�I!�020P�H26� dick� D ԏB~ ̉ non-� aa�6� 2�.�&� .��3� 92qft1}nTumulka,ѡBV����.�$-^vt. /� 09040.4.�3031562Kqft�6\b���T.a�P�:Cr�o~Annihi�,in�5el�, *�kM?2Y3/[� �84"`w2: 8072.dgzj�@9��2m ��1|$equilibriuLAEOrigieAbsU�certain�� �{2a"ֶ�bf �^842��df>�F(�d| W., : !�We� /en�jn ``Su�8 Ak2� ''},2aL(forsch. 48a%3a 1161)0itsy lyn21166�g�!jrN��2 '!� Mean�� Wave FӌA in Cohenet���1lSt�%l�����%�2K Meta$UQ��aly�; ~bner Shi Vo|�QBo�"0i;����1a� 1:B�&�%�*�dG�j�, M\"�-&�%>E Hypersurׇ%�-D��m� ��.�d]\99>�98O��]86�bu�2!%�A��^1t4k als Grundlag�r)�en��l��P&�id)��.2� � (briefwechseٟ"�YHM�;��"m 3 1916�)}, NymMObuՂVeBNshandlug�-xenl�6�essw}: � cull& S\"u�KV �Wۑ�Hm�~�i$!>>0 F�7i�� 11752,rez} B�M�SQT ewA��%�'n Bl. �f1)..��C}J� Page*vt_early �ve� es:F;q�w�bust F�pi^"f *c Ev�' �v�W74� 15-37J�5� , gr-qc/94030J)& qtwo:���I�"*�# b�-��1)Today 5!�� h) 4=�AprilSe�8!C"Y GoTu9�6# ���� �Oppe arrow� Čcan r�cil\��v� In&a js.� Grav�2�#55�� ?&� 10�.� gold�$:88 Teuf�������Space�wi۔t�ers: O*� T��7�-];� d.�^��e�#* meets.�aQ�Plancksfl�/3K"T C. C���! Ngggf�$ 275-289v� �2p�� ion:9X99020182pc} Shel��]R�+'5.���less}� GhosiAQG IncompatiE��>) T�+%�5��<�B.� 0010�d0).\\AX:w��D�D��0nguish BetweeV�6� !vSt��rd�&�.�Y�01 I�^��JiQ�d�A�d 6�)*},�10312� �3u��umrefl(!�� Gottfried�2,R(!sJ.OEs��D. Aman�EZ7&� UB���am��\2'U12} Gol��i�!�Ak�"n,-��A W� slits1| �"9� es b-��p1�T�� -2� P0 P)ϊ�& �decQG�R�"8m/E��!�0 �1E݊��predi��Ya!; doubleBBo � disagreri���R2.R�1%26ylte��rdo�$ DoesA� re e� a �,*��}, �era�a�%o;%mF��6F;0)��6) 12%u$guarini} G AgMW!5's� o��.q�",l}, *��xw�=) 6hall}��lvaP� er�letenes�R"D"y-b<�int*X$N�"�`�A��M*J��4) 9549e FE�406054.�0�y��-+��%�~��empty w�Pi&M75�% ���)2) 11. *� hellmu�kH ��\H�%70Delayed-choicAI���!�um %%<UW"0 � A �3S287) 2532 � wig}�wq�Kt$%;K�E�9F�8l�! crip�!*�(�L%UK2�� �D 1(2E(:? 5;1e�}N�A'*�B�TeleporTo�� EpG m"��$��|erU&inRo&�!Չedsk0 Gree�per e����/ ther1s�82(!hcm>� agh��R5t MaroJOeCEF#E q�u:ies�al, s�S�an�ox�2m� dee/� 9?2R0o��|/�P%� _neu>��m��H&�BPi��to�r: a4'T&�'� on^��� �*onES�<on.��$ �1&: R� sider� A�*� [�ocupt// Vexjo, Sw�`P"J<�Y 2)ol!�} H :F R�0�6�y�a}*� J2E)2 k992m��Un+!�E pathes� .cA�"n 60ae99) 436� o undp:K.�a'�(ippidis, Ch�Imp"1^� !co�d�A guid�8E�wo�"j�67, 0��"�/ .�omeD�Hom�MajumdNZA."! ��im�"�� �- aD��� J CP-v"�)&*s�$E^.)l"� 76�k�"r} ��"|'=*.��:Rin&``Hid*!�s� ��]0G�t �-046^(ruebl} Krei�%!)Gr\"ublE!�Em�Y�"$�%1rrival%n.��. � ^�8851-8862d leaveT�L +�yo(B� }B;�ta@��Db� ers �i�,'I�!5�I�o&;A.D�o��w�e<u�4s. 76,�U!h96= �T�2�%\AK>�2(aGTunne��q-�^�A�� Scan�-MicroscZK III}�Wiesenda��`�� .-J.t�un��odtG&.�?� 3:E56.'lebowitz� > L�/&Boltzp8's2�?� 's As�� 46:9 32-3�32�maudli"� > �$-�nhe�world}�a�c�Tte��} M��˥D[m�isQm'  trF: to A u�bAffn.�a��% :67 &8�� 92t:�( loveV�* Co�5E�:tIaRr���8top�+ �a�LўB��, IBM.�Res�A1+DevelopL�4%umber�95*ŝ� 088 .�muynckK� M.M-�6�$�nN.� L�6�.��&�/&T�I:e@e��%./adv%�-�}, }!Khren��q/E!R2�,! 1, 9=%"� @peaceful} Myrvold�@e3 On p " co"� :AA�C�aps��t|)e ~l �uty� St1gin$�"��w#��rn� %���=��xf��(E�Ob�2s/Az�C.20 %�n%{*;m�6� �~17"� ��"�hC.Pas�x"N3� to tB.�l"���}J$5!��5} 765-7�zA��E�E�4�22p{}F�!2�},D!ri Deu�M,�0nkfurtAM2� int_of_bmJ`�R_ \dbbeGp1mion.� pauli�YP A�m� RemarKsur le�l\`emws Nm\`et�Lcach\'es�La 29,%8� �N la t1orie �,4 l'onde pilote��: LouiD� �,:%� icie� P�Iu�7 M \'Ed(=�6in�h>pp 33-42�5T!2'6>Wi����l��r 2 mit !�r,.:&( u.a.�3�T4V (Teil I, II \III), �Pausgegeben von Karl v�:yel���:�%quiO4Q!� V1�On�i�&ly� ivalIs�@���e���6F 9}uuK �� sanz} San_:X ��A!9 j toI um fracta>EiK1�De�4���=shy�M��M�M"�hGlem! �f6�g?m�����q�rte��18,�8) � �a�N�S�-L a)Bvd8Rv�mmodate�2 o.b�!�m� dA��b'.�sqc%}Vl%� -i�.t5�.�.r950801�;���O k2Zl94�: unre�:1rdilemm�I��.ŋ( ilG�d Vol.2��3 �6�2Vs } :{D~6O Alw�4Pro�+ a Trust|�y�@ �'�#�?� N9Sc�8�~�  46��b��n}0� L M��pZ�k � &���2.�0answer} Struy�WW De Baere� l.�"som�cently po��*�\� should+Goi�u/ fm)1�2Z 1080� Q6� taylb)T0 O�nn�s� U�.ePhDa�s�Rutger�i�s:4 otf?$erra Cunha�u� 2$�)� .�%.�98090�E .�simple}*�H F}S)A�of�4Globayr R5:��G�2@N�2,�aYkK A&�9�Gms%8IQ&C rodi}J�A2/)�}a9�o~*-Ri�3-��0.>�94w��"] �=D,F<>qS+t�(!��eVum��8Can You KillIPan Em�%Bu��?2�31222�3�  ��� W�A 26��O�V�Zi�AQ�Signal"�), u&%'�)�W05subqaH-mem ?part I�syaA�3 1-!� ), 5G 7Z8� o682val-s��6�E��K�"o#D\�v�(�1�&_ �>�M�30�@6aufbau} $Weizs\"ack�#C. 8�hDer A)�� �$dtv"�%en��882� wheeG9W ��5�As`past'�A�`d� �'y s6�R/2jEI� i 1 ��R�8 rlowK)Zw��, &�/58))q9-{!e��)���p�"5}�5:��Z.52 ��e&�1� �a�*��r\�����1��nc7\ NJ�83: u�wea \'ojciku@Bialynicki-Birula7G3 &�� �H%�M Evv*<*�$F&] A�8Y0)��..� zeh} ZR�H�, gWhy�q's5e�N>�ni}�1k �197� %Q�y/981205�ZeD)feDu_9KČbov99�I ~I.~ ,*!�~��7�F1]�� 5�Lugiato0� t~ A� ~Gat�c(E.~Brambill�$.~Opt.~B: Q5"�� zzHW�F22�Kamimura��S.~,�6l.C2}I34��32E#�&N.~ � ~G��" ~P.~E�a~�� H6�~Oh��P�PL�K~�0!994�q6m-r�5M.�!��W mE"K�~E�~ %�8 3789%6W٫AI��~ Z2l"l�[ers%t 29}, 7ڏ6aScI2!1P�P �~Cole��;R?gu?a�6p AAiU�u�ޡ)Europea&XE�#��csy&� EQE � 3, M�hl6VY3B�C1�R��! �~M �"iBwG�Q�j V=N.~Bi��w, T�~F�E;R.~Stro$�BIe*Wa��F-~(P>�[kd6�4Slepian61} D.~ SH.~O.~Pk��llUx�o.~Ji� 4h(4�6s u�F%en7�;�u~ Eii:g��! ��(ol.~IX, E.~�, ed.~(North-"0Am�Mda$��,��~311-402w7 Xiao�OH.~ V�~Rokhli �0N.~Yarvin, In�E ���bf �� 86�Abram�70E %F)�Stegun, 6�.�6�unctio�>ns}, 9th ed.~(Dover, New York, 1970). \bibitem{Bertero96} M.~B �, and C.~De Mol, in {\it Progress�>Optics} Vol.~XXXVI, edited by E.~Wolf (North-Holland, Amsterdam�,96), p.~129.� Kolobov95�I.~ ��L.~A.~Lugiato, Phys.~Rev.~A {\bf 52}, 4930 (1995). %��CQUANTIM} http://sucima.dipscfm.uninsubria.it/quantim/ %\bibitem{kol�9:�, �Mod.~ ��( 71}, 1539 �9%{tend{thebibliography}$\beginB({} \harvar!^Hm[\textsc{Arnold}]{:D}{\oldstyle{1984}} +84a} 6-@ V.I.} {\small(}:; �F)}: \emph{Catastrophe Theory}. {N}ew {Y}ork: {S}pringer-{V}erlag. \hN�4vron, Herbst �$and\ Simon.�., R-6�77�6+77.� J.xI.Jz B.} Z77.h``The {Z}eeman effect revisa'',�%@E$ Lett. A},E�D 62}, pp. 214--216aN�Barnsley=:�8}} 78% �3 M.^�786�HLower bounds for etum mechanical energy levels'',M4J.i��11}(1a�(p. 55--68j�ta6�ta:�3!�Barta3.� Jb�3:��Sur la vibration fondamentale d'une membrane'�PC. R. Acad. Sci. Pari��,{\bf 204}(7)A!�L472--473, (in french�V� umgartner2:�9%� um% 7792�9A�^�96�,A class of lA ] P Hamiltonian operatorv� 2}(45�459--467b� essa6�$Montenegro.B( .*.(200�Pacelli/P0." RG.P:/ J.F^$d�?4``An Extension!LE�'s�E`em and Geometric ApplicE�%P\eprint arXiv:math/030809�� � Vb�936� Quan�� tunneling!�D chaotic dynamic%���Nuclear>�560��197��0^�Caffarel=`.)EB}042�3b�?]�0private commu����b�randall6yRen.sR% '.� 1982� U/H82=� R.E:�, M.H^h\� ``Gr�� st�͓2�Tpotentials $||x||^\nu$2� MathͶ�23մ 64--70��$erratum[J..4 23, 1737� 82)]^hDemazur.l.B2000}}002 3n 0.%I�Bifur�aA� *� ��Univer� xt. &� b� uffi.� .�194� 4.�  R.f�4:�J�$eigenvalue}�w � 1�7� �827--82b�HelffF @Hoffmann-OstenhofB:Owe.��:6&9�� C+9.�  B� B�T:A�A^� 9:� Nodal set�  geNeMt� (Schr{\"O}di� ` with zero magnetic field*Ha non simply connec&domain. Comm2H1�20" 629--64b�Maslov6�Fedoriuk�qJ' )6� 81}} 2/L81�� NVB+. M.Vj�1F�$Semi-ClassZ Approxim�� i� ѺM� a�v�7]i��e5� physice� a\ea�I #s� 4D}ordrecht: {D8R}eidel publish�#company^Poston6�Stewart=�J& (6�� 1/ J78=� B� + f�2� "� �� y� its!�"� <}. London: PitmabN Reed::�B"! $J -/2 M:�'n� .� 5Analysie�"� },I`4]`ethod'modern]O al QtAHN.", emic PO^ISchmutz]56 85}}85] /��Z� 85.|�factorizem m�E�N\&?�l:�108� !$p. 195--19b� ThirB�6�7�'79% b&� Wb 72��6�Z��%� atom�>molecul#�s3YA course#�\r &X2/N(�f(99*b�C.a� Pake�. S. PrawerN�6e��2� bib:4aerg!�}AC.�S.� Well%�A[2�6�G�Milburn%�RE� ᝝B u bf{6�11330)�6�BM��� rreti�2m2T�a� 155307%�6�Viola��!�S. Lloy6�Au�58}, 2�6MFravali3E. e J. S%Js J%.Longdell1�y�41206NTOALBS1g(G. T{\'o}th%�O. Orlov�)Amlani%��ent! a,$. Bernstei)�GE SnidAS.���169ͭx�� Toth`2001}NT\'oth%LCe 2�9N63}�052315%�60 Cref�PlaY2002}WE. kG. $2k2m6�35303k22$ JFTS _J���a��� Fear�pL%�Tip� ��T�Spill:B�{042328N{ aredE7 { Cole%�D.��%�J.u� �>���#R��115302�6-GSCRLqyGardelis~G. SmiAoJ. Co� ��(A. Ritchie,!�H�+Lin%�� Y. J��_�]^d 033�6�BRBHDC�:�6�R. Brenn�2����F���2��:�8)57N@ ItakuraTo� cY. f��195320%�6�(Schultz83}M , Surfi�:132} 42� 86DMueA�98} HE� �.WJ.2��8�734J� McCamey�m� R. i1 rancA8A+  llumE�.� A?.��2���� � Tech�2 36i�6�An��2 C. A�O}ENC, Proc.� SPIE5 565k52I6kGA�=3}Y:GalperA�B�^Altshule)x8D. V. Shantsev,"caPnfa9 Fund��ob�Mesoscop�,hys: Interaco(s \& Decohe�e, SpainML � cont�31249NlMa�4}F. Mei� Loss6�5�D094519p6 Schoe�eS�,� . Cu�_Y.[mons,E J! Rue\f llam%�Oberbecq�&C !�\FI  361"K *#ZR�N:� F� U��264$i6USBTI�Unany> B. W!�orI�� erg2 d5 291}#6eDCZ�sL.-M. DubJ, CiraceF�o�, Scienc&)29��169NwPC�J.!�Poyatos,j^B}*� 7J 3AvT) "=Bowdr�D2��� , Ke=Oi�5C hort,BanaszeE � oneU�B�9!�25N�> Oi"8 ��4��"] *I %`:m Z�i+ 1232)l5AenF�$Qj�$�57nielsen5% A.~N �I.~L.~%#it"�Comput�B�� Infq �e�B$(Cambridge&�y~, , ��,shor} P.~W.~!�2 'ceethe :w\35th Annual Symposium on-F��@>; �erP"a}.]'Coldwasse�!2(IEEE@ociety,� AlamieCA�'�!. 124.�gr7(f ~K.~GF2�"A(m-5:l� A�~� q�#7�07�<; D.~S.~Abrams !�SA 5�6*-@0GS}B.~Georgeo� DE�,Shepelyansky2Ti�Z8= 2890 �k1).�C songESH.~So�]>. 2162j��lex� ~Ben��~Casa�S.~Monta�oeNN� j*� �!> 2279  5@pomer%%}0 a�PblmN=�{A �014� �}wig1%�* BA4 (749 (1932);6y M.~V!3rr%�il. T� . Ro�S��2)�7�-�husimia-J��&S�F�3��6 6)=�lE � 0462&� ]�harpert%�}B�Jc�05621��2�4frahm} K.~M.~F ,a�FleckV�J�2�Eur J��D 2�1X2ypazQ" C.~Miquel-~P.~Paz ~Saraceno ~Knill,6P$R.~Laflamm% B��q? 3231�82 amplif{&�>ra%� P.~H{\o}y��B-..!0Fifth Israeli�N�onxof��xASystems}R8��7r Fp�-23:G.~1�= M�Qsc)�A.~Tapp1N�)$����*��FA�lenYVolum>*A.0Lomonaco, Jr.`R� H.~E�(ndt (AMS, Ck)mporary�$+  Seriess F305M 2�Daub}�  es� Ten Lecs!�WavelettCBMS-NSF s Yied2�(SIAM�$iladelphia�22}mey�� Y.~M o$: Algorith�i#%Js^t�u�WT1��u5"797020b>= WT2}ABFijane�1C.~"'1- Notee#IBB 2u 150�0 (Sp_a�R);�80900. WT3�$Klappeneck82-<2+ Sign:mImageDessa�VII2� M/Unsg(A.~AldroubiB� A.~F�~i�T�!I9\,. 703.�90901.� terraneo}pT eJsR1�W*� 9[ 2579�32�@2u�2,Z � S�� 2;2URnegative%�@ vov� H.~�@en, T.~Aichele, O�n J.~Mlynek:��`1  �R� � �2� q<+s8V� irik�J)�&(Les HouchesU�S�]i2&_4 MF Gianno7A.~Voror4J.~Zinn-JustinB(r�4�0�4 52*� licht�F�)�Rep}5�2�1979);Bl�4Q%xM.~Liebe6Fo%+Regula�C�, D�,},.�.�5�Y;�� (I.~Guarneri���F Jow ofɭ. Elec&*\�0� 14Z 1988FP.M. Kocw K.A.H. va�euwA�9U>? b558� 95.- raizl��ore� C8 bie >TC�KBharucha` Sundara�/!� G.~RZF��v��7� 4598��2� loclength%��� N�z uA� �� 2�discrete�F� Q�� >&.o�A 6�06230J� lee� W.~Le"~D�CiiW J�:{�303��8�in�Ge2�� confd i> Nois�  i&,CnanoeA� ronics, s�,�st /rds II} ��J.M.Smul�Y.Bla�; I.Dyk"8" Kishebf 547�46� s NUsv�$�farhi00� F A� G�7o� . Gu�(ni�@ip�W e-t=Y001106�, `1�`J. Lap� $undgra��TDeda, "�E>�47I�2G(aharonov04}?A ,��'D^J"r%Z~ ndau, S. q{Obg�F� 405098; !�u,N 40902 roland�J l!. Cerf^H127=` kamiG"W�K Ol�J� 21112�childs!�AKC�Q!�7 resk�P&�=;m��J� �2a� RZ�^T 42302 vanDam�W�%�M�$I U. Vazir in � �:�42nd 2g6c"#  } -,�F�V 279=�paz <*��P in�8t` us�2S&dnbasis is relevant, e.g.,W9 a&k7(scenarios w.W coup�4 toenviron�8 is weab\/inaf/by)H�#�7 ofsK��eE�8�23).�*� j 181 u . ercival94� �P , A�ExMs2G10� 199��!z�(!d E�M*�( � �U>�T��ndy� ab UD�%�( U� T� 01233�"2� H2�XF� 50202� �97�<�.� �FR�the�i AsA#�evident from Eq.~(\ref{soloc}), imp�ER A�:E0time-Yit&.bt� d evenM�E�$$N$ depend�( in $K$, su� �s $K \propto N^a$, $a<\frac{1}{2}$.9�aberg�s{\AA}tult��HE. Sj\"oqvist, (un�0ed2� 0sigmaremark} �= casemg$\, < 1$ requir�& di^#!:a/.*. Orus�R�$\'{u}�  'L;reNU�5�2 8Y) E�k,2M� Z� ��Z Rw vw*FA,cvbook} {\em� u2��w4Cinu�Variab8. %��#au*�%AE� Pati ](eds.} (Kluw Do�2, %�$2%p?ewq\,L.\,B[\,P@D,P.\,van\,Loock,\,a�\,y\,��\,iR(7},\,513\,(.".�vaidmane�V 2(-~4i4�%|��brakimj�8H.\,J.\,Kimble,� �e� �80�869\,�>82furusc?!ZFawa-[ t alb52#2�� 79'W.�}Bowen~%�et~ 9%32#S323+3); Take1�v=� �#�2�W+!~*� bfkjmo!= #9�:�J. !� Op�4�h26 #0); \\�]H�rer:@� !q �E� 1505��M.�ra� 6hM}SB�r�4!� 3482I�0!�&�DnD0u!�}�-YonezF�f %�43�-43M#6�6O\,P,,\,T.\,Aoki, � A.\,QH,\, cM�c\,430 �6elocaliz}�!$Verstraete2  Po(� I."mVF�E 0&w4);DN�E� m���� 6� E\u�w$angle}E!Adess F. I &S i,*3 410050v32dF ckw}0%C�9� KunduɦW��Woo'0"�!Ej �6!�� �:�epre�Ee +m�m�E� P)�A�7(1936� J\,K ,\,B� odolsky1�N.\,RoW:�a\,777��:c8noteunit} Defin�Q anni��"b64 $\hat a_i = ( x_i + i=7 t p_i)/2$ao6 $i$,O8Weyl algebra $[; a_A� R,^\dagger]=1$�l� *e,\ *p_i]=2W,so $\hbar=2$!� We d�e ��= ��+ %a_k$E� �p� �/-/ �)/v�  % 5 a_i$_ f1of5 ;' %! --Heis�:T��. %v t!�in our !�s�5)uN!�`mix} Any losses due to o *� �us*Idu��� sixth5.Hworkshop, ISI, Tori�#Italy a- 8). �N4nn�5��email!s&!G==-Eisert� J. �+Jacobs"( Papadopoul�,�IM8:P�!o, ``=Q mal  ��  f1C- 1�gates,''Jg62}� 0)6 17.� 005101v1.�Collins��9 �. Lind�aaopescu�The no�+  of�� ion��-�9�2v1=B@DVCLP} W.~D\"{u}r�(Vidal. I.~.�~�S.~� ``E\g)5 capabil�2=*�� .�6034;.O��j�'13�Y%[�y/ BHLSa(HXAM�{W} rrow��u�)J.A.~q ``OnU apac� bipartite2�A<e ary U�(57;��( Inf.��8�8:/Ō�8 Leif#M� �0H��0� N�=I Y�e.�generI�[%j�,NM>�52���� 0���A!�ccc� =n ``Co#nt:�of&� m!NgiD�E�3070912�]  09"�!4�F.� q1tp��1�a*��8Vernam Cipher,'.�012077;��.)��#M~�$no.~1, 14-�,� *sDHW-bigb~Devetak:�A1$n�>!���3no�.o�*resourc� equaiG> � ��0tradeoffs fo�fNy!`%J(um protocolegin prepaI. =�sh�!a>E.~ �. O ./B��orc�蹐.'' BelP/s.Y5� nal�:{ 7} 379-4�K,623-656 (1946 BSST} C.~���~�2)J�$տa A, Thapliy��6�-�G sted��cit� a5'OCne-@JI*se6�em��%ZE�1060522�\ a�\ ThM448}s"��&y3BBPS96!t2�H.J.\&];��d� B�6humacA�ehnc�?a�)P��al 2� by L� O.��95110302rA-�53}.S�/-�Laverage} Thus it tur91ut �\eq{cc-*�was m�44than we needed( Terror (�p all $a,b$) would have been s�LPt. In��l�is argu6showsvt u� sh/; 2/ (or O omnePY��.�6�)  $convert an� �� i# a maximum>,]1@will be further d�Uopa, \cite{DW05}.9 I. �qA&ZW�g6��:] �nHSW��$S.~Holevo,>�orma_e�ɼ4�>6�#��.SU�� M.D.~West!��2MA I5�1< 7P �BS�D��B�/VB.CX-nde�``Rel��between�\6�y��22����y�$two-qubit ��20y7 0207065; .�A. 68, b *�#}6h] .]$, or*tOHsider $k$ i.i.d.\ t�o�� coin each� probQ�$ �%com�Dup heads. Prob$(k $$)=J \, (=(1{-}  )^{k.}_J�, 2^{-6�) 1$.)!�AltogeAu��e] 1�$s $:= N^l E�Is(!�%F2 Q� )} N^{2 k})$V us $ >$k \lbm 1-26 - \sm�!�4)}{\log N}\rbmX��!�TU=ve��J�omas, [El#-8���8� } (JohnIF/.So�<N*�_�J .� �98�5 ,� um.e�71 PhD sis, Uni!T�m Mexij0$Albuquerqu�2M,h..L HHL0X.*� [2 ayde���LF |(Super-dense!�ing�"& um�' 8 30722v� 1&�6 �)th����``.0a?"} Clasis�L�RudW�����rM ns9�to �6m t� =o M�3chu�K$s Institut��,Technology, *�:MA�5.zdue9 G.~D !]M*� ��� reg�  are !`er��n ; Z�y0& (multi-user � s.'' (EngHR. R�(an summary)�%blems3 rolM�aAz/�n0lemy Upravlen or@ o897 ), 1�$7� Nb)lz� q�@[*]{ca} CorresponAw authwE-0add�PL: khoury@if.uff.br\\��misha}l(I�,lGb,{ofN�/ (5�539-15�,R?%�"spa�behavio��noncla2Tlight.� onken} Cj-M� >�J%S�>of Am B)16!�22140-21z66�ofN� s C�%G. Alzar�FM.eau��-0nel��R,. Horowicz, A"���Barbosa,n��Q8�(189-11���% � e .riZ al�Xsqueezed� diI�]� moirDK��torskWit Hand )!� Moir\'e F�e� �}�*Els��r,:k,3); I. Amid���R.DE sch;4-Y Soc AE�1{3110�ge5!)A.�0Huguen�BU 4utinho dos SanDP%c!�{2w!FopX A�#ect�9!�f�s:0spiral zone pOs���&�'A  K1883-18�|I� {xray} �Bezirga�HV�EAsf  orig�f�o.Dn�$e X-ray wat2� in 2-crysa� rfer�eers Kr)ll�kfiyC)k9��A82-88 984!�(T. Ahilea T��$Zolotoyabk�=VSrtwig�&O�`E%3ieu�G%High-�l�{x��,JK�h:& scanc%�4 %micr�Ky stud�$P i-base�Zruw= a ba)d amorph�+layer!�Appl.��t8�B�A6076-608�MA� V3���\" �%�o�%��UFon-�.�top!yphp bi-�s Acta C!�.>5a 413-`N: tem}�lMadhuk��Q. XiSY���mKon  % �(!8�(ined InA�ree-d� �al is���o)�.g< %on GaAs(d 00) .TLle�6!Z2( 2727-2729L �(e�M�Zo� Q. L=�nos1� EvQ>DC ClusSH$Growth: Ag!oH-T�n� Si(111) �O acesFX �85� A�� e 2555l.6�- diag�/pIrv� ��06�#O�al -!G t�filc2>�N6B^,| York%'6<odonto}?Z� �S. Wei�Q( %Strain�9?r���n teeth����  of Biome�iO8%23H 2��35-14����si} %Non\$act, 1 C-d7De-4s1�te\vf re-m* by�jeS  %��.�ry, Sw Zaidi��Br Mc. Neil+B�3of Vac� K. \&���y B�10M� 66-1��  %Real-92� 31� t��!)�� �Hct^��V� QG�NDonohoLPr� . Enginee��-�3�aj3465-347)��$5�cr?Ug�' a} %�@encryp �M�e�p\n per�sc&�Lal %a"lB�^Dolinar Mu\~noz-RodK2\i}gue�5Ram\'on 6-Vera, � Comm��23� 295-V�X�$2} %Manipu�*�!� �)ert�=I a�B<$C� q H�7|� �F �.k;! 2e9@51} (6-7), 983-99"�. *� klyshko}�yB.�c�:,� V. StrekajXD�ZK /�H�b* A�R,ergienko, YER Shih2b� 5''�\�_��VF&f jp}Yfbohm1Bohm,�jRevmb�u165�aU�72v78$ F73f7 9} 4}P�U)*�70durr} K.Bernd-ZDau�]D.�#� Glod�YX, N.Zangh\'{i}, Nuovo C�6to � �@7�1�?*� �4� �$B.J.Hiley.�< Undi�6d�O e: An Ont��� �terpre&i%Qun"�tRoutlegZ(and$ Kegan � , Lo�e�3=ho�v} P.R.H �6bA�mo�4}. "�� ity �;6�P2oo%a} 9, 8mCtTg�!#0O.J.E.Maroneyo6p� 01002iKH*2L51nI5lY�.*�55} 25s8�KA)E� .�>�0�2�&oto . Meta�h---1W�h al S� ~Abnera�mony, I One .JQ R.S.�n� orne� � St� l, B�h_i $ Philosoph%�E5193�b-38 (�6�G,*�%9512031=�!,3}�Teufel�qbD�B.� ��6} 121� s2�,4} V. AlloriB�fb�e�} BrEual IQSA�fA , Cesena,t)�C�ica1�313�� �2�ham} WBb I.P. ), Chem �}��K.�creon,%�Pt��Sarfat 5RK2�<G9�UrlongoA�J`�^� 9� >nerukh��N E�J.H.Fre$ck^�l\14)�2�Cren!cShi �H Akis8K.F "��%(mQ274} 7JQkohout�-K ,�Z.J.��.%*I�87e� T6�$unter} G.H ,ŵNE 9} yR (1972zc@iIC�"6r6�eX73 B}[(1�]5�eia�I.HEV�Rroc.Ama'h.SbC1[,24�s8l#.B,2} Y.H.R.Tsa CompI� >78} 1-b2 eik3�Gudyn�v$Nonl.Anal.~1 Cont D 6} 5 ' .4a�D.�e�M�s%� �0} 33!61 eik5HO.Popovy�>4nd I.A.Yehorch9 Ukr UJ%I%53!�841�0 1);A��(員55� eik66,Le�e� S.Os�%�H.K.Zha� IAM J.Num)z 4)36�<d.7a�Bryso�Da�y, M �z%�O 2c7J;2 eik8vM6� �1�j>L9VL� "or�"X-20re�v�(4l-upwind schem_ -d HJ �*t�$} SCCM Rep�[StaH"F ity,!-02-09��2�@b�e� pqcO=�saha i} J_ ,~ Fu Taun �M8o�$um"�w $ddison-Wes�!Pub.Co.E��R�` jj 9}.&darianoaO�]'AEP P.LoEti}"it Tom����2�-}zRe2 }.�Yy �2 �b�6 ``ChUte�oI � devic�u}� .#1P Esti�s:� �&Z },  Q Se�Ro�L "`Q�zs,�]d 649G s. G.M.�}WJ. \v3s(h\'a\v{c}ek&�M� lag,� 32004), ��{b;4 jeze+4Je\v z5J.F'5v'5Z.Hradi�, it `"�-i�  of sy �p� ss%)��!���40w/��a�9�hk} Z. v� R � c �"�5 ���M. ��p"8um-Likelihood Mfqn1�ME!� 9S�=�}Kb�e=� ST�� M.G.A��+n \6��� p. 6 >5�po�`�F�? &�>k�Fo�`�ڡjle��J�&K.-�:&E*q )2q� ..[B�`�C�o� } I."�5�M!  & ��#�v e.�!detYtH�P}�$black box}���*$44}, 2455 � O�Buz�q8� Bu\v{z}ek �Recon� �Liouvimmy$perp+or��)1mr97 82��` .%,=< �Q�!�.�7*�W} (Un"V'F20� 9zi�DZ �Plesch�V.!�E)�O�rBs2�+in�E�data},{JappinXnd��%ӵ&{\tM��406088}.�&wug!XS.�"04p.iMk.%_%&�*�2I rusk���7R C Szar��a�E. WePS-nAA&u1Nly posi�U(cepre�$ing maps��2x23r��}, Lin�g�hV 34/51*@\Yw�u � M. H�Uy)GR��2�Op�4l m.�.s:M�al-NOT2n.P%R26e;S�Ca�i� � %AM. Sasak|"��.n�J0bM->N!�their �z� c���.�aR*-�JM�um clon)��&:h�7�L423{i�L&�Euhle�%P{ Albert � A. Un,8p�<th2u/^1]V80�e5� 2001} q/!��R�1 rka,S�y*h'DV�Yr0!9�mis���t' AtomA�o�(Pe\v{r}ina .�,\&B�,�)�519,=fi� } %R�tF, %������*"� }, %�*��!&j"�Q! ietyiK22}, 7O!2QVd �1nd .e  %�  % %%duseP/T>A� create re{s.+Us$PfollowA�syntaxD�Lup� your=<Mon� s�����,gp90} Galind�B, Pascu65P.,�� 0), Q�"� , vols. I,II.&� Ve@ .Irmp` A., �u(tin-Delgado�, �2). ``�j%�C�: &?+A�_ aspects")A���. 74:�j8; -�� 11216q-cz1} �<J.I, "U)�5p&� �X# cold�'p�5o�..��074, 4091-4094.&cz2j�� ]:``�/frontier� 1*n@� aa�%'�""+TY{�issue. ]fun�e��8,} At first s�,�s spl6'ofW.� Hs looks awkward but\4(wise, we ru�6�2L.s�{� direct � �24dooe^ failure. �ineV��e�,�/RAas ��Y`} U_f|x_1,x_2,\ldots,x_m\�(le = |f(F) , \label wi1}��\A�$f�40not a one-to-x%��:�re�5 s $r�$)\neq (y_1y_m)$�Qthat $ �4=fB1;#oo����,es as orthon�2l $\l\K >�|>N-=0$. Th���5�E5 �Rbi!)��.tre1ed"re%,�gonal: �B�|B��1�is vio�&�7ity�0 f�!we knom7�Jn w- b(2�2)+A� �" an67�.8 of 8 �  a �yE%$s~��!ne<#x8u^ �1e[-Ra6}),)]a7}2� shor} mP.W�V1�U,^>Polynomi�!a"� �u prime%o"�A�"� logaxc��x� er''. IR�[�em #�"��l  XE�  6 XLo* L\�Y�lin�self-adj�1]NA$ �wng�m�B6N�b y/u�&���4\varphi |A\psim�;��AM� (|&, \for'> a4D(A�V a  O�$�7�Inb�AO)� ular9Bre�T�/�a!�p al� associ +zP �.de����=i y�A$W6r^ce,�BmayxA�third��o�q� spina -$.[ �lW U;M<M&*�<I�=�:i�` a �� $.�!f�%, { izedei}^ I��o\AO a � e $a$�?n�4a cer)\.�A�iJ= � P}_{A }(a)2 |E_a.�||^2,> DS $\{E_a\}��&� �:se%jpr-+or E_aMX0=E_a: E_aE_b=�>_{ab},$ \uma=I$, �$A: A|am"=a $, $E_a=q;a|$. GZI%�-N���;de�bed� POVM�R� �?� Xe�xresultI�� cala;G . It��at gB*p$�amm�=amount�o�DizA � �ty aboveuAnit� reshold.�FA�s%.>�j��logicjs2� a}y ����gKi� ŲX]/�mS b�Qv�ieda{s.� }  evl &W 2S �"�F�G�"~ �@is !:�c�+f�n �'?A$!d� ���, m "8 2�oNY�H two ��"X�;2�amEn�^yVx:iG R�:!KFF��U�TP}"1jI� m ��  :C w�c")Cex�T�7� 0$A(q_r,p_r,t)�Ia��  &rom t�T, writte8 �Mnie�gorm, upo� b�Ea��Afv�%a�s$}Q�s$.�� U�M�m�����VA�A.xca�?�� Fe YRrMly Ae}f itsQ�� @5�� �meaM of *!p��N =:E &�2�} Ir2"� heat�sip acc��g���s(!d law-�rmo�":2�;ot� lost��every erm;�?ost bi� :�shw;0s a tiny puff!�- "5K�(�!h�%6pCtent�+ta stepL�fast �� �Gin�~)�%zI med� ult��I& s are!Bcz�d\c� ey7Happar �useles�� qer�bsA�!��e memorQH��%ICp�es%�m��be remo�a��m�ny`pAa|�jmal ingae Z is !|A�is� �!"trinsicA$.�!�> �Kre� eU%iV�qer lik%7 drag�DAn�=1{ cur!N�M�w�j\ar�Jtance. Z actu9! g� i-7diY�B>�larger! fa�;;he� 4N�rDst�7 a loRroo�reduc!\�Y o�4nt%�. �$% ;Eng5"5"$ is w�Sbe"� �w#b)>1� � dumpX�. L\rer�> ifA�#�=auer61�(�o� lossa� a�N'  E = k� B}T\ln 2.b0��� :Q�( ir)L��qA��}$unavoidabl}�J�7uA�clear]Ud gix�sA�!aġǙ|6 e� �i�e%w %poJ�t�use. B�] f�3rb 73} a�afBc �a��.A�? cep%a"� le �l� i7 DalD a T#?�,.�zerf ha�Ied 1�e}� �!.o:O e�$e�six)��-~�`���n�F throw�!Nus cau%�no%�$e��W�!2K&� aa� �n�dt�&e�w. T�tinue>Skis0�5H s�h�oaf���[�a� �wr"� �in:�/Z-{ �0 _Xw � out U�ny�kKbit�q����� 8]  a"�� do�o �(Aoqf�U��M�d!HŞ -savA� �in whi2�iS�� car�Bd few�� �c�L9p�s2!Mr%%!�$ aa�Ep Qof!�c��� �X�)��es�F1�le* 5@ �+�Xngt,t'�:l,X�l!Qo$ chip��E�o�D�5�!.v-�A(a >4called Flattop�f } &�X) MIT's�E^le��reC ��p�s��i�� adiabat��? =V�-gY digit�Lircuits �e���wd�"silico��*�e B�, rd B�Cellu�Automa���Wb ' ball�B� [A\��LlA )U�:��by )7kin. �sE�a p�ot�0!�p�@!L arbit�`s,�#izvreg� � proof-of�[��� q�sh�&��u�,al* l�$3acE�!�i#S �fuW�" ).� ��7s&61֏``> am�Z�[� r �! ''2%IBM�(R[. 5, 1�H92rc�ҭ�AH �7*``Ln=il\e)��.the Lim�.��ą. Hep@�Perseus��ksL$.�fre��} 60 �,�r5r��{Y� 6�������5�fA�!�y �!�R� "��\effI`M�ing!� Ph.D�4is. MIT AI Lab.ssa�W.zmli r} M+��)02ydim�E!H visuS�U!� � ,`!!F MAA���/��FA da�u=Im82}QG�s� 1982, ``S �ng�"� sG��40�q,L�./ } Szkopeker�Roychowdhury V., Yablonovitch E., AbrepD.SA� +�c5�1so�Mof�LqUw�5.&040813�,9 g& 3} G jgK v / ``F�2�'sa� ad�Z$&&� !< Ameri�Joue��F�JJuly i�+F�109116.V �family�_-\?�� 6w �'s:�!�&� I��e�&A 62:�e03;�00908�=NtrE�} T ,�G (195qW0.,QMA1S�>10, 542 [ suzuki} S<5(1�DJaw&}1(26 601. %CocI W!Z. �F9�bb84}���G�zss��g4)�j?Z2NJ�/y:�;lic key�&Ea��_�_�9,a2mh�� al C&��on��e�b<��1��!'e��, Bagal,�India�� 175-1���(kwerda} Str �tC.��z F� e D7}ceA�e�=�;fa�"�s. Chap��\& HallA��th67�Xf�14��"1�^,A. Kumakhov;LsO*@ 1976) 17.*d��| 5�R�5�)��( .Sol. 84B!77) 58.�E03} N.K. Zheva�B4Zh. Eksp. Teor5;z.TB1�\$ 1389 [Sov�3JETP 4I�78) 701]*k> 4} AU:Akhiezez�A.�N�5Shul`ga,Z�\J79)+4J��P79) 6�F 5^5�9i aenze�Ube�%!�0A. Nagl, Nucl� A372�i81) 6.+6LIr�9U!B}�82) 541.�7�yzX azylGKV.F8eloshits���� GlebA6��92�p8 Trik�2�oR�jK�08FDJ:306.�08} R.O. AvakiQI!Miroshnɍ�L���>TA9eguthZ��S! 1825J�%� 052.�9a1Jo8u��R<Swent��H,=nt � BBv 9�l�!�S Datzm-��itM�Am148.�}CN!�(Filatova, V(7 Golovatyu�lN. Iskak!�I Ivan�CRnq$Kadyrov, N-KЖ%DT.SsǞ=EPalchUZV�RyabtsZh Sha� EKTsyga�C TyapkimNV. Ural XA�'yc�8Z��c`ˡojtkowskϫ�Carrig!�Jr2 .E�� ��9 Carma�FW� GibsƪI��x$-R. Su1;!avizhA�A� Bulg)(N!� Zimi�s A. Grisha*G9Koval)%B.I�ram EA� Deni%}7%�%DAvdei!F!t�>�Ai488��11vB�nJ.A Elli�+tar<�F!��Oԫ�]J.B!�Pg>s� E. U�{hoj� K. O=gaE…��j85) 4����]V�*Boldys%EM.G�atn!)�2�� F�43 F�8 val (Augu��20.D6: Mary�, ysjNPaR� USA).�s21020.N�IW. HeitF6_� u�olf r�, Ԫe�NP> Oxfoݬ 1954�#>\�f\KD��bohrunc�)�� Boh**���W�u($J. Kalckarv��8hVV�a6�4. 316--330, 37 77. .�ch}�zSchl\"o�zaw)�,Chem. Solid}�bf s67��88 7� rosenfeld'J R� {wCErgodic!�o=DZCr2��`-Nn%�al�oo.� Fp rico��mi�eCoupXIV, VB na 1960, l;6BCaldi��$ (Academic1�N*�g�. A} au}La�e.E�^Lif�zwE�#*alobs, I}, � gamoMR]Q7>BisydgS [A�0Fokker-Planck"� �v"2EY[ � groW`Yu��osB{�$A.R. Khokh�S%�.�AiѴ Macrom*ʹ("> 2\g 4eX-Yoa�1�46�(nelson}E. N �� Flu�a�2=(P71e�� �AvVQ�ABaiH!��(��.A �.(� 23�[8^ �� �>5K16�|oS. �U(Garbaczewsk�>J. VigCaFD46}, 4=�];( G. KaniadaEM4*�M30�@�1yhtim0O2`la Pe\~nH�MU�tto-QA:1UDic�SI�!_J Stochc ��r"�!A�KBP�!�6Z�B���\�.)9D)\U�096� �]Ia^|I61�2��8�_U-��?23R1q?L.S��Ola%qF4$�1�f~=O�ѧў� A. Hib�ze1F&v=% Path!Peg�(}, (McGraw-d66&?q��L�B�@e,��b�!� bf 5�E88bM�Y and  Khrenn<�� &� D45}, e�u_�-�)�9F�YjB);N$3�?8&�� %%�ohr}NA���%�`8}, 6I ��<epr}A."��( Y�%hN�P, %%�\� pere L re��*5�;y:�{o#]I!�I�*���UqAsekblovQ I. B in�)Ja�"QA�BSaoRB�,*�� 966MGA;I1FA��M��)&�D4�A3�X:�� newt�RR� N 6� B!�102��eA5cbalian�OA�� xcQ� A5a�10P�19�=9 home�R H� aWPB�" itak� �&6�212E22e�Q�8espagnat}B. D'E A�it Vei6g]ity!�A2;N,n��Tw<} V de Muynf eGF�!ɬ�B�Cv EmpicDQroach!�n_ �l�i�j}WU I }"U�2,�� !u35HiY2Ospr!�J�SprJ�8V)n D2!�3��1996��o}  �TE. �g�a!6ie,%�LEe��.��E�9�c 0936a42� pop}&�V*z.S�/���u2�V6S ki}K� Kirkpa��*� 9909044. *SK%M!�.�0v�?�jaynesA J &e�hM�sumn}r%$,Formalism}, =by5jLev�*A�M.�b�(CITb i ] ozawa!MO �)o �}29!�1c�cE��.70�c��� .vL%O'Con�X�SOeVulv�E.5ri%D�� �U�bf 10!�1���N0Hai-Woong Lee �F82��14�X9հ� m�.-KA4!�it�v�"! ��WorldW�(fic, Singap;<=ork}A A�c%�RW�*�� 4086m!%%!�&�.<f*N�.g�T D~ %%ag�-&�L2�} orem2fcljkUllersmM� �G[2%: 66);h 8 56; 74; 90. A!���sA>LeggeE�Ann�\ O1a� 3�H(fZ94K$in��CWGa%43 �Ŏumџ-"ͦ*.�xR�era��ei�J.Wh Woo2f�kyR203�7�U2kurch# L@Cug& dol�kK "%Peliti,2�E) 5� 38&�Dex�+�@6�e � M�558�c�k��) rŤ2�Y6� atNErTh'U:�N^�64EV^ *�cshuISa�huO\ B. Gaveau� E��icq�Ĕ713B[.�c�L}Wc RussCaD Sa�Se,hW.) altAQ� �-l DispL(o�V�gde.�z�"SN7 � .de1�U0 �/�-d DW�is��N5�A 031d�, ?Zt ntisN� ��1I�20%q%&�X(0�(��meA�ic.O e0� Zeil� � Teac\�3t 23�X$$Mog�Lng Energy Outflow in�:r2` 2} R��Ojh�^"� \m�d42i5|�4!� %%AMieln�.� ���oM 1113�J[a:>��bd��u�OldHo��J�A.S.\ 2��\ ��r ��&��2U�� SB.\Z�E�j\ #mo{lnł\e�\��ǂ �_�2�Amosov eG.G7,:��r�TOPro=.E5.(OHsmi%7%�3�3*Z0�C�J J �$J\0J4! un.\� \Id\ L2J#MW�, OK > sumo T\imonoi�A�0,͊s3"`AisABoAudenal�� L/�"V��g3w2gFannes1 lR!�licw M.\ .0 40703.Matsu A2%�F.\ Yu�{J9o��e�L1�2�Renyi T!Pag��� @y ((N�a �e��tdam��5\ KRad�<8vityConj} C.\ K�FA� M.aXW h�\Iino.\mo E�19��+m�V �.�k6�!#aQ�EA `�43M�a)�2 b.�� Haeg�X� \ Mosony"��0\ VanpeteghemIG&J 4R.b! EntBrea�1} % p-�E�1B&��.�!W*�) ��15�*�Us �!�S�I \ �P� \ � �,:�71��012)�j 59Shirok��M.Ei�2�1�&�$FHdepolariHD'\��war,�4Hashizum\'{e},AF �' \ A�w� 4�p�m�!sUn )9eB+)SI'6�qNLD2�% both:�A�I�a��32��f6I�9� � ��FHMV0�$ aS�L��^.�B�П\ DattY�.AY. DSud%.�203k.(.�{.3rj3341-n %�K city9 LloydGausM�V.\ Giov�z�h�Gu� /�)��ccA� ch\��p��H.P �Yuw M_b \Qe%�9 ����6juK\!�B�.�t24^� 0421�2yGL)g:pb.s2��56Ao062307�!z2�p� q,V2� d.� �� , �r�a1��O�roA1!XF�>E��xB ��P� yllOA{\"u}h�!��Curty)oN7�!1H; %�"<,+�'4ȋ6 S��Z7 Sixt�~*/ .;�����al� of Net I��) (MTN��,4), Catholic.rof LeuvA�W>�=#12046=#Grego� � b�2� ���od.\ v�mZ�91b2.�Rep �M.�Nai�\a!+S'-� �Pagroup&F} H"[+�� berg� o9�54`�V�� D�/DiV�Znzo ��\.^�%�W.�?" �2,��E 3824� 5�ReO� B�!W�  Ja��M7���Vi��i,ň� I�o� I�M��21=��/1"��.!�Q K�H' ollbrech�FA�.� ) 6A |1�323�>� Cos-!Vi_� W�����]a irac l2�2��2.�%+��b� �L�o�� N�.�f�xx9WR Davies3mA. Fu�g2(�ZD%�85"7��W'UnruhJ.1�870�-7��i ) YA��6�"1975); B� DeWi W it G�P �t :"e�� Ce���Survey-(by S.�(aw E W,ra�"�B� �2y2-7} %.O,��m�&�1@�4. "1�/; N. BsAl�;=3it{�V um F"�C�d S W�=}���P!`8��W.)��l0al c fbf{D2Au10��$V�+Ginzbur%$ ��Fr:-,*8/ 9/E3�?1987);%$Barut�J. Dowl@E�� � bf{AYp22J&0);!Milon�4'it{�1Vacuum,� . 64"�" %!�9�{. udre�����\"{u}�2�e! 40�.F NNarozhx���t�-BVKarna�,�VZ6� 0250��iYQ8}� exgR�B�<ler�L ek�R� $He^{+}$aa"xM32 or yA: �� wT,im 10^8$ V/m.�9"eJ�8quency $\omega$Y?loCb�! ed (}8ahMsF= ��>)ac,cryogenic teN� �w�"A-�=s�ct�=uldT>be=McuXS4by ``hot" wall2�8p��M3S� V. Kom?̾�1ely JJ; F�hF. CapyU2��� 91+l31��W9�gm2L.2*.%ietM�(Uspekhi 30,.$�w�.D��G��y`!=Ht�l�QJ�Q�7�414k9�iB.-G. %E�Brt�nSch�SY!a��|:� a��2�Ѫn nguish bPh�Ku�t�9س�ma�h�K� �? %!�a�qE�EXM$ent ``$z$-�| i� ed" T!$cal� � %{\�`�Z {M}}dž�� 2 A}}m*�� via6!$Z$}} |-�du�E2DE}}�of6R}}E/ ``mazer"RIio��YYAgarwa|:��lso%� S� ! �oers [NR� 438162)]7WA`hlc1>GK�QPA(416EQ77 E&5h�reB*ziY�X2�Q�0kI�ǁAuggORyB#.Z;, *�(m��n174�,6� Boyd�%  , �it{NonAar ic�6�.�42a�u�S.Z.} eB ZAAv.���%=sew�&gͼ Elec*K,E ��A��e� (PlenVV"=.�*sM-!�QSۇbairy�Bd"�>%7)?9��WB� iTBP.����Gp*��5T 36�f89�Lamb} Fޭhe:}X52�2%��%���W�Kmb�.f$I���%�bf{�&8�1� �5 pedagaCtreatA�U90rPike ASa�2U:�&:R�},1.[&�7) or��5�.�m���9d�u��&wp!W, |�!��2���[lem) ^8lip��J��van��P�� stre�s�h=++%9bf{B3�-<:�-Rindler�* 7it{Es�; ial &* *�u�!A�7B��A� �dfu�ofȟ w *}V"6�1siegert� b�$ ty, �geHQnl��m�Y term1!b&�S%b![��#sI�details,!e��!wa�&Eک0A19c,(FyY dopp%?^ D -�~�f�  �PeH ,�Gi�Gse!L � atom- $\nu^{\�gP} =d(\nu t(\tau)-k_zz )/d�a$nu {\rm{e}�VRV Ҟq��$�\ c^er-prop���one�Jto�nge!;ln9$ Y1 !S$Bt sm��idܼ (16� vkk)�!�!� ew on nona�*�Ii��-� �8ZP�zny2 2� �8Vl:2S&�=&y 26}, 89 �Z� efDKP�U[AL04]{��~Alife�xDަQ�.��block�3]� m&�*s: sJfy��pi{.;Ř�40�C�4�BR�/~R-own��$T.~Rudolph.[&�C���al��c&�G.8.�51�A>�CAJ�CMJ!;S.R"��C.�ura Alv+!�D.~Jaksc2�i�r�yd.+Jof ��q#e����js�c A�i�@\ne-�.� 6150r~.�6[%� ]{gep��.�OpticalR�usingj��)�02005F��RBB03]{mqqcs} R.~Raussendorf, D.~E. Browne,%5H.~Z�easur%�-based }:9onj�5��PReview}, A 68(022312)�3A�0end{thebiblioE6,y}�\beginB {99}Y�{aravind{\sc A $, P.\,K.},}iT``Impossible colorings%{B}ell'saXorem''.9\textit{A�4ics Letters~A} Tbf{262}:282--286, 1999�mn�02}��@A simple demonstrI�ofB� involvA=,two observer�< no probabilit�: or inequa 4'', manuscript%� 2.\\=48Preprint availa!:pat \url{http://arxiv.org/abs/Y�206070}.bell64- Bell�j\,S>�On!�h {E}instein-{P}odolsky-{R}oa�paradoxr�9�(1}:195--200!�6. ${QCCsurvey�$rassard, G�``�imunic)��Ilexity�M%Found!��M4�D33}(11):1593--1616%xe Q/BBT04aJ�,a�(adbent, A.}I�A� Tapp,�8pseudo-telepath2�\mbox.�}Aa�(, to~appearA�4072212�b��RecastA�,{M}ermin's mɌ8layer game intoEH framework�n1�Inform%�%aC�2�. 80522bct��.�$, Cleve, RZ�&M``Cost�exactly�Kula%/e�um6��as�� A�Y�E�"�Q�I&al�ܱY�483}:1874--1877ar6 bc90Yui�, S.�Caves, Ca��``W��!�out b���M>�5�AnnalV�20�� 2--5��0.�ca��o01q�C mq.�B2H%^�.vET!w6�for�� ��ނ6��T 191�1R�q�f�\,`All �X>��N[Zo6��Interneal Sywium!.�TA& y (ISIT)}�3� 9aFu��ionʳ 11016� ghz89m# GreenbergA.D.\,Mq+, M.=Zeilin'A>?Go�beyond&� \� eem}69in {\it�%em,�um yeConcep"3th��Uni��8e}, edited by M�dfatos, Kluwer Academic, A`69--72aW89. "={hardy9цH, L�`��$mechanics,m�r�tic�e� �,{L}orentz-in� nt J.%�(68}(20):298��9�92z hr83-�Heywoo7}Redhead!�\,L.\, Yn``Nm�ityeQ the J{)�-dox:��:8 phyl&S 13}:4�499%�2� KS67 �K��e����S, E.\,P)�a� lemaܩ� v���[q� �5� �-� Joura�of݊�MQ�7}:59--8 67.� m� 90f M�:��?my�ie-visA�E&Bq American ��`�,58}:731--743!b6 �r-cPer� i�-�e�y:q�1 thods}Fl+8.t�� h՚\,� Baco)9�Ben-OrA��J}�V� "p&� �e\in~pr� �@�^�UN��v�"�[1]} M. :�0I. L. Chuang,u1C�� p� ,} (Cambridge��a� Pres5 �0).a[2 �Zukowski�.� � ��,A. K. Ekert,E6. �� . �Dbf{71}, 4287 (19936sT3]} C.H.Bennett,et al. NMLEKK0},1895NJ46JE S. Wies�A�[T�69�2 881 �26�5V\hang-shui Yu, He-shan So!� submitted2J06]} A.Uhlmann �. Ax42}, 032307 (20>�,7]} K.Audena%aF.VerA ete�De Moor^_,4}% , 052304a16�8]} F�an Mii4t, Marek Ku\'{a�Ae}N5�A�No.1 w20>41a�r%-AYe33� 377 V:1ay�V3}, 364V. R�� ��Schro er} E. \"{o}  , NaturwiAschafte� bf 14�64a�262�Berry��V.  %�HN.L. Balazs, Am. J.-=({\bf 47}, 2 P792P(Chudes} D.O�+desnikovWLV.P. Yakovlev, Laser.X!�110�96Oberthal�M.K.  2�iɉE�77��980�BJ� 1998)~9D.? ~O'D� �AU 3� 2093�6�by��h~.��Deland�� J.~Zakrze��I� Rep.h 368�09ED2)��reo � rein.� all_�> y} G!qBerma4G.M. Zaslavskym�-.A {!�6۩� 77);�F Richl�rD�� ntge6;%r B5}!6�0);A>HenkelBM.�ha��~ ?4 ?78%\2);s-5@A.2� Ad=t. Mol.�1��3N8 �h4); I. Bialynicki-Birula, MX lin�Y�$J.H.~Eberl5&�Y 7a�17�619\6�HD.�1mBG5}, 14�45); M.V.~Fedorm7S.M,� ~Exp4 �3a�71%08A K �NI� 6a032503E^6�(maeda} H. M �T.F. �aghN=�%� ��f 1330��6Phanb L.G.~H \ P.~L�opoul� V]7��50a 1995:{en} X�we U J.A. Yeaze�VR8A� 5772� 6�,note0} Absor� also �8s a crucial rol��  p� sal \cite�#AX e&c (C�_X an electronic nonsprea��( wave packe�av-- atom u# icb �k�y loss[o26 Mich��$gelo} For . , sculptu�X ns "releaoAdesired� m from a +! of marble�cut�$away unwan�ic) shape�1�Q^4��101-149�A� hube �8I. Huben{\'{y}}eTCo� �Astro : �0� 2-862,]8�]jczecm�!>�a R)�K0 owo-m�zne r� o}}wnanie9�a-�MAaS sis,.tof Gda;n}}sks4�Ctaylor �J.R. T�3Sca"X i�.Cu� E,of� �*iJ9�},NL72���Q Name� theirH rA� (seeO �, p. 46)@,Eq. (2.157))wr,n as follows��(align �h\Gamma_{mn}^{(RS)}(\wek{v})2p& = N_{P} \left( \frac{2 \pi � D}{i \: \mu} \right :\int d Q$_{r}~W^{(Pe- 7 \nonumber��4& \hspace*{8mm�ime �,\bigl[ f(m, M \gets n2 b$- f^{\ast}�9gr]r N�R%4.%� � mathrm{I!;V,%�R4 �Ih$%\label{nnQ�=��][� �#�_ ygedt on� d/is ')[We2e thataI�$J�$�giveny .  ��pops �� s�'as8 � KineL4\eqref{sj:nn3} �Howev� Scoh s (w�($m \neq n$)_a��$Fc$ doe�$ agree)+� �Ion:�sgmn}.ece,>as �b��R phd��ert 4jgg}��i�� �� urn,�Xe~tia�' �further c {!��  9�esulti�ofV�musC' trea=EGcare du)Rto quite�b�" misp,s. �+o�(hand, defin� JW je���A�)�s~6e��0uH#by e authors, ��Aex�7\(�[,EZ 2.4.�n n ap>�.�f� (10} \expand> r\ifx\csna urlP \A�x \defX-#1{$tt{#1}}\finIprefix>OL {URL I&$�9$s00} S.~Br&�) speed-up,� c.~Roy.~S Lond.~A� . 459~(2036)}  20E* 2032!%�-Y442�!n3c�A\M%�3, I%q�6PE1%�*�y"�JVs. UKFXg0sman97a} D.~G�2tQ% of f�,4v~v~A 57 { 98) 127,99702022�Dshor95a} P.~W. Sho�$olynomial-g $ algorithmH r p9( factormQ% ��ret�� loga 2�% ��0put�? SIAMSciV ist.~i�. 2K7� 1484.�508022�"agrawal�0!� eJ Kaya SaxenaAh9 ��in �0"y-M"�)s 160~(2� 4) 7�#76�$childseAa� C, R.~�( E.~Deotto�#~Farhi�# ~Gutx,,A. Spie�AOExpone�_9yici+up�r9P walk�i�'`.~35th Annual ACM STOC, , NYE�3e� �#68=Z0209132�,m8E!M.~.0q-(talk at ITP�t shopE~6�b_!$93a} C.~H.#q! G���24C.~Cr\'{e}peau%K�tA.~�#W.~K.�� � Tele],� an unknow�v�7 via d!c"�,Oe�3p�3�,� nels2`w7�3) "L0:F0 �0:��_e"Co*�0� one-���8icle x�-7 onb��N�6�>)%�E�q"68K$Vvidal0!� G.~V ,�i,t=:si�1on��sl� l&l9"�7�1�N�91ed!K4�!.�301062� orus�R.~Or]J.~I. L!re"�G6+2�9Z� ��+2�A 6�4)�"213�*2�ukena0�P A.~U �$0~Shimizu, Mac��.EV$���5�#6]s.ixY noni�]@Shapira, O.~Biham&�5�M5�&n E {S}hor's��ng��.�51004�6�parker�2Sc<' ~B. Pleni�.YU��Հ!J.~Mod.~C 49~(81) 132a�353.�102136.�8vedral96a} V.~V%�Ba�->3~W&��net �el�' ary �� etic"�1 :G5�"(96) 147--152�gossettf P ,, Carry-saveg�980806l:�vanmeterER.~V. M,t ,M. Itoh, Fas&~<modula�с�:�71]�;i20�0408002j zalk> C.~Z v�,!(�?UjE�umRr � 980608)S82 $beauregard�&D  , Circuit� uU^m3 2n+3~3s"�% .� �H�%$ 3-��7A�85.205095.�fowler�A.~G. F# C.~L@"l�.� "�/J�!a �0ed set!\ro �gat:A��?)$!3292e0306018.�knuth8l6�=K,� Aro)r r3=mmi�(n 2: �nu�+l A"W x2nd ed.�" dison Wes�1982�perese�&S+-!crijo� den� matric:��2 e�1�:41.�9604002� zycz�*e�$K.~{\.{Z}}�2 ~Horodeck�*~Sanpe��M.~Lewe^8> (volume of  1�mixed��d��:�5K$(8) 883--892.�h �y�M2�P2R2M{-U��a � til#:T p0e a ``bound''66 in n�'e?2�%� 80�,8) 5239--524.980106H4�b� =p6�6�B�6��.be v�A�;X � 82�49) 1056--1059,2�>�wg*� :� 6H� o�;!7n arbitr�f)�of �� J�5C224V>2��X�9709: coff�9� C ,�hKundu,>p Distribu�f.�2�A 6�+0�+06.*907042< kendonO VO KŲe[}ZW�Munro,)�&.�Am qudi�2s�0m>366�� 2) 0�C2�203032��Aer8!,D�Gre��.A.~*k42Z4b2�;�  A�K�3��B (�0emՊ �rU4�0%$89� 73--72�pom�Dce*Wunkzl Pa��-0y Beth Ruskai�F� us ab�#is piec �t�(pre`+&�=�)z&=�curnFi =6 W8s $N$ (not neceFi[>emi�s)P@which $r = 2^m$ iG a:�recisely|�=d� C a regularx-g7 Kc Cuct�C�)/ -e 1z ass�0:+ b��0. R.~B -Ko�$f>� s>I;Deu�}?imb!}mount sc:�u:�5source r(%?E� a1�!2�F�".~� 32~B� 2) 1641}�020415F/ tree� A.~D�!ee.�-irmF.~eKZ ,A.~R. Hamilt;R.5 Cla'Maxa ! A:hilK- 1%�a �e-��cd�nguishE�&u 2���9� / 97901,.� 0304052;hayden� �e� W. Leu A.~Wy", A� y :#mComm.~�1�MarchCI��6)���s� ���B049.r&�G� >�G2�G��way5#A��E!2#6M',1) 5188--519� N� 9 f�99} {\f� �ing*)��'�, ej��4 emph�4 � � a�%(um *�}r�$ �r�4O�!&�G4}�$.�H.� Bern7Fa Popescu�. Be umac>w,&�35�!204Z!y}!  , 2��66�6 Meth�6 (K6h:( Publishers�_stB�,;.} T. Yu%LJ.� m@ .B"�266 .933M��.�A8A653R+) |8*��i�� bf{9b. 1404R�- X�)ZX)oE� 7%Control�De", of ``St�r# e �# e-p�ile�4503089 at www."�H.�Lou��l�4H( >�$��% @ertie�t Radie\/}&�"Y>732dvanKamp�.$N. G. van oStoch Gcf��:�.\*y ChemJ y}fj(eb12~�}�1 pD� M� xM�f6Q& (Plenum  19:DAbragameF a,The Principl%0 Nucl5)MagZ)sm�6l@don�H�8)@86@Gra��y0 ,� ramm�(G.-L. Ingol�<�Np&�51a 11�,882#Leo�J�k�tChakravO�a{Dorsey� �& A. Fe��6W. ZwX?_:'*u959�& @87) [Erratum ibid%�172�25)].�Palma} AJM. � �Suomin�$nd*�9roc. Roy�' oc. 1on�.452}, 56�96. Adiabatic�5 Mozyr�,fV�/ ivma e1>�92.7�26{P ;}2GD:cI.VA9r,���Le.��mun9:146c73'6&��Tolkunov� B�E>%��K6!� 0623�)B�.ichkin} <Fe E2�.>,f�Th325*87�-6eNMRi�*oja�4V D. S*]Iy�� .� 09050)6ZWilhelmJ!� orcz[F.AC 2�A\E�04231�6�0Hilke} B. Isc��5`�Qube�6��� a N-q�G soliXw T  BB-S86 at bWo}p.."-�E%Hu��1*�0X5R;N;7!�50�19�-Y� 1 � ( DiVincenzoa Smol�.ALW. ^�YO55382�6�F3%�B.�, �. -Q?1�*6436�F1}�J. Dodd�J� H�Ew>e5�aR 052105W6�F2.W2�6Cg1 C} V�0=r= "�HFeynman80a} FEYNMAN\ P.&�?Int�r-2=1, 467A!82)\ =��,85a} DEUTSCH!�S��. �� �� . A:)��=�4h400, 9��856h� 0�NIELSEN,ak�<& CHUANG�! L|� �P%� 2� j^�@%�6� &! 94a} SHOR�Wy �.�S.7G�E]m { ��5},.}G� er!= iety"6ss\�k�4E) � -Ph/J!Grover} GROVERa=�Yv��s!�79, 3��72XFahri1 FAHRI� (, GOLDSTONEa�, GUTE]S., LAPAh$J., LUNDGR!�)�PREDA6-� 292, 472%{6� "%#�GOTTESp$D., KITAEVŦ\&cSKILL �e� it{%Mv� �W4�0 2310JoFreedman� FREEDm��2p�RQ�J.WA� Z=m$Bull. Amerq:thi�<, �� 3). >�0101022~Dua)DU!bL-M�Q IRAC�a\& ZOLL!�.�5e %e169��6fKnill%bKN%BE�FLAMME�9$\& MILBURN�!!�5bN�}�A409�=JYm�v:�I>�}., 86,VP6�R6�, RAUSSENDORF�BRIEGEL," J>j&;De83, 43k92 Guld� GULDEX , RIEBE��A NCAST!{GUECH 0C., ESCHNER, ~ HAFF  R�M CHMIDT-KA%�UF��\& BLATT ,Q�.j��-46�V�?rsypeI2 VANDERSYPa��1STEFF ADBREYTA,� YANNONI, �SHERWOOD���9� �, 414,�J�CiracQ$ ��>.}, 74,AY1�52�Kielp�>L( KIELPINSKI�jMONROES�WINELANDE it.� 7, 7# 6{ Monro�WR FW3)�6C% 2 ,}��.��� ��:,}�/.` &u �B$DIVINCENZO��Fo + . fu� !�8, 77W96 LANL�HUGHESA��,HEINRICHS, TA�dscAɬum *n���PTechnology Roadmap}, �Yq$(lanl.gov1 *�"� ��EDICHKIN��FEDORO�IV��V�% �*�O SPIED105, 2&0 ��D Donk2)A�5Pirg\& H. �\ andt.�Zurek�ZUREK\ �Jq�ŖMod }, 75, 71��6�Guilini  GUILINM� JOOS� KIEF�{KUP� �$STAMATESCU7 O%�ZEH��J�.� � ^A|Yan<f a Cl�W(ld}, �7-Verlage�6� B 7 B Y�}��52, R249�>6�$Calderbank%$CALDERBANKR�za��5�R09A:�teane^ STEA�xS1�X �� 7�3 �6M Viol # VIOLAA�A,LLOYD�EJX%8, 2733 j 6pZanardi� ZANARDI� $\& RASETTI��R^�}., 7� �B� Lidar4  LIDAR�1%��! \& WHALEY�Bo2n qA�8mV59� 6��p&�_GUO, G-��j$349DK6TBeige��BEIGEA, BRAUN�$, TREGENNAiTmKNIGHT%G� �N��#176� 6!By�$ BYR�7S_6J�J$d�E }, 50, 12�E>@.DIM kill< PRN� �gToday�9un@=24RM8a}^Mj� v� aL3�P02�KT gjT V� 0 >��ScG��G6�Namiki�~ NAMI�PASCAZIOa�!�NAKAZATO� y9% > w um Me"�b�9World�entificũ6�Dalto DALTONEzJnUnp�d�4}F"���TOLKUN��D�PN�A�A}, 69,f{3 }*HAAKE,F \& STRUNZ��.�d y� 91N - 3BV F 9_=FS*�� PLEN!�M.\&As.�qu�%7*298� 6� ]7a&�]68�&�>�3�1�97)\ *�( ��3 &� q#57WK6�Calarc6^�6 ARCO� �a%5- ��63MF4E�6� DeVoee�DEV{ R1yVL&���9�B>�E��RFUt9)T005RP$Pellizzari�PELLIZZA�� G�G� S��6Z .� JL�� 378Z6�Domokos�DOMOK� �RAIMO� A�ũUwMe�HAROCHsN�!�3 355�_6vTurch�`x,TURCHETTE, Q �H� C LAN�.�MABUCHI� aOIMBLE2�=�247-�6�Sau+ SAU� J �FORTIK.��CHK!UHAMj C. D� CHAP� |DV!��518M�6LI_b}2_BLI�RB�F, MOEHRIjD�&Q,�4*� N� 1022� G5:hrlei�k GUTHOHRLE� �EeE�A HAYASAKAh , 5�E WALThH. y���ABTR8Mundt02a} MUNDT � KREU�� .�LEIBFRIE:, �E B��~J�N+89, 1030�22?� b}2� OSm .�UELGA��F&� � B�VEDRAL,2 a{*� 47, 2KB&UPacho6 PACHa��5�9�J� �'18790�6�Tr�Dny92� ,9!b��2���5�UN6j)`4a2`CAm�, MARR:n! !A���N�5182x( Garg� GARGAtr&V 96��6� Schmidt-K9SIB��J� DEUSCH�ɡ�2�Lf�*�!{I� a�1x"ITB:}mH� l���6, 62)�6" Bar7%!BARNE�S�uK�VACCAROae��% J�Zs. NatK st an�&i�101, 5Z�tanov� VITA� N�L� ENHOLMahR�b 55, 6�BYZiman6ZI��as.I2l!w�yL#Solids�"�%B|;u 65).r\ pageVA�fA1)<&o aar:rev�> AaroLO.*s^Book rRn�7 {A} {N}ewv^ind� {S}ctO.82I.paR$�((5):410--420 02.JI1$232�'�colb�� lop`�/9)!z�?i�3kAlem.uIW9q� ACMr:�F0ages 635--642� ^� 11116lbfb�&92�0{B}oolean fun�Nquery��$.�%qS<-aa 3%^ 1140--115��06g%Derb�1DcU%f�J�,X8.�65��`d %X$ 171--17�A��R$ECCC TR03-�q]10:�� rfs})5N��>recursP({F}ourier s�Bing.�%lEv�3(2):165��g3.J�2-0�b� 09062V �agf��%m!�9a��E�2Nr 4-06�002:fisfRIs � um m�J�L isla�gD eory�,?=�In,KhrenVZdf%Nai*�a�V\"{a}xj^P x(=Y ``1~�@ : Re�. ider�W�*�''�h�YQ9m401062Z4!adfL�gj�Kum advic�\,c. =.�� ���ingJ�To p.l8!t�!F.qzq�H-4QL,pp. 320-332. ��X�t6�7�plfAL�P��lfise�-b&R- arguA�2�6(B]4a.4m.�Ln�wq.3-0��%v� 30716 .� mlinbLwlN�4ulaA� d sk�f cism!�d"C0:z�118--�Bf{m=3B�qchf|Q�a�u� az>Ne.kAc�g�J*� A6 8035K�%X40811@9 �6�npb^{NP}-��Q���a)`\O�+�gty: a t.�I��8&;xune!� SIGACT/Xs�2D aa2��$A.~Ambaini21IM�of[1tZeg�;.���z� FOCS!e /pp78200-209.�30304u0�@agF�.uE.�Imp7#TWA�!X�tb:zer ciIA GW�%$,um black-box�*� lmos�kl&= "?27��.��et��1:5--/o�IR�1106�u�}^�qk*ts�* �SYQ. Sǂ 64:7��76�2. Earl�*$ Q�a�0.V >66R�degb�P"| deG? vs Wum��)�.�6#F�23a%3z&5022�D1�ZMR�fo.�Y HL<ctnes"/Tsmalla[6�E� 03051}#2��(Q���bW�% u��N��X� J�� ��kr2�>��= ivos2I Coins mak&u>�fJ^`f� ACM-� N/.a�DispP.(SODA�v5.M*9�4��6� ntv:�A�yak��� �. n� dens�fA0|�H�Ve6V omat2eq�,ACM}, 49:496E=���1�� pAm98�:6� stvw:��T Schu�P��6�)�> gder:�d�2�m�L b5%��.2:1570� v%B5s>�>�!�6�.!�:C@�Ahighly|G���Y(extended ab�Act�b"u6��F"�697--70�0.{%)!� 0003:�Larndt�  �MNairzenVos-Aqe�~Kell� 8G.~van~der Zouw%� !�"�D.� Wave&kP%QVTof {$C_{60}$} molecule2IE�&d$01:680--68�x��/i�roI,R.~Impagliaz61�J� R�Zvi�A���"p_t9,iques:��Vp check�6Manuscrie�1966Ia�Ai" (~Grangi!f�G�Vge2OE"�j9k&wX%RE}oR{P>;�-�hnL gedankeneK�new vioqIN�"�~iJ��  �3aM49:91--9�*982e babai:am}�B .+:I ed r D� 3I�of�x���c.=E/qڵ��7�((12~~1� 6�d} *T,acciagaluppi%�M.~Dick:�adt moda��terpre�2�t�B�&� 29:1�25�aN+9711042sb x� *x.7�� ;Zal � � �C�kof clo}\�W likeA�&�2l�U 3091f >2(bgs} T.~BakA�J.~Gill�,a�Solova2u�� %C� {P=?� a~l.�2��dE�:�f-41972�bs/Bakhtiar�9lfavi-N� �(J.~Pieprzyk.rCrypt}N phic hash&� aEF�u0jRGV 95-�4DWt�!u ��7c�"lT�,$ Wollong�w JulyA#6�jk} Z!rr-Yossefw'�Jayram �I��renidi2�.X�!m�%�Vnd*�URYA,o�.7z�12a�3B 2�l4-06fSbss} H�tAM!�k"�~Szeged2�q �� ��I-de�^p&aPf�3 C�[ 9--1B(2:� bbcmw ^Beals' ~Buh|t,a4�YM�Tsca)�R.~deAf.��>� &�2�eH!' ,8(4):778--79)�2�J� % A�86 2: Hb2/l �i:\�Percep�qs, {PP} � � hier�2��iHE�a6<� 4:339--3:�pt.kbrs��Rei!CA,H[.h���4un "I�b���&v 2G50(��720�6�ek�Q } J.�JB.dA0��al up�po!on%D"Kopy�benergyEdio� )e� s�N.X���D V287L82�N�S�[llBPSpeakK!cUnsinU�Zks2�CS=��82f b�Wff:robot�QB .� SpacSAFeU &�\;./InJ0monaco��v"��5IA��"q�]� 6�E�>ontempo�Q�Ӈ s Se�. AMS,�+2� ��� :W bbbv]"AE4"J�r]%yV�Strength� weak��F�^�%� )�c$15d$�%.fV� 9701:�\�&�J.>Log�grCgsi�U��%q.0�IBM.�ResE%Develop�� 7:525--53e�72�bbcjpy:�,6k�~^�HbC~pC.�T��^byc ��!� {EPR�!chav^.W%}�"�0:"�^e�6�`bg:�i� .`� e�ua� oray^D{A}, {$P^{A}\neq N co $�7 probf 2��Fr10� 9�66�v} .�Z q�AL; Z� F�M�4Qd147�6EFir2�8e� "�a$6jq�rN�Zm�.t Sur l'ord�h,e la meilleuAWpproxi�� de� �&vtinuesh� �J�x$\^{o}mes d��gFa donnPa.|%�Mem. Cl.'c�PI�lg�4:b&0b1912�F�O2� b:qc*B�~ia�XAם�.�OI]�O^�6� Work]bone i�v���:�R'�{&*'95� 9�#��:[eubu�B .�An� orph�"dir�product.zsur6� %eAnn�A�;2a� --20n6�& bohm"oh2b)A s?hs�"�"��:w 1FI�� term�  ``�"'' vari��n\}, 85:16a� 1956�h�%� B.~H)u.0�Undivi/U�.( Rout%�6Dl gne��R.~Lipt�{&r: *� �field�Gq appl�)\jc&&2�.u*g'CRYPTO}� 1 �) 283^ 7. Lectur�No0inM�.5196�!bb:V%e�L. Bone�� S.~R �s2�HSize-depth tradeoff > +or�"F��>�11:15a��- 19942�hzy �ppaFg(J.~H{\aa}st��a�S�_ 1.�D�n co-{vnqh�Yte68.)E@V� 25:127--1��:W ousso:vac �.�PosH� vacuuma �aH {N}-c .4��Righ E� �� 0011(03�#2�hep-th5 02:D�Z�a8hAr�p /B��!a�3@er��k4(3p$2�� 20312&�bbhgBoy���H{\o}!.pp.�Tight� s����� :(%UqB�t DeuBik}3F(4-�. �5}A8.n^� 6�B:�x{f�6�J�J�,tu }mpl�-�A!est��.��� �� n� 5056�!�f&�A!6�5A �za>r'0%�A0&�(� 8:14��bj 5:I"bcjlpu+�/*&pC..[*�n�f*oW�OSchac2:S�a&� very nois:!Y'o�� r �PZ^�%�>:�83:105! �+f[P 6�cb�L P. B .��N$parallel e4�+ :g_al &�f exf�12��"|21:20;j0��76|r�&��%-6`Z.�Persist��>�_�'y���fng�kF�NW6:9�9\ �8.{�C00�[6x run}ru2�^ �R�U��^vesLbsolve ��& �+.~%Ta%���� � era 16:�a >6 $gr-qc|]�%2�ce} N+^BsF^y.�A�W.~Eb��.�JWI� algebraica�VXJS 4�682�*6s}S@blitz,� Sch\��rfeldA~Voig��I.~WeE�.�2�X.� m�A �{PRAM} {W .E%�c0e �)� ��8:5;a6�8 bcwwE�JJ.~"��!wv f��p�YN/A>7 7(16��Z�r<��cb��^����#&Ao6�@~u� .a.W .� TOC&3-�pf�702042{)bdhhms:�$C.~D{\"u}r�ceiligR,�_"�FG_gniezY>�gth� z���IZ�l#Ƒ��}Z�007012�%b2%�V�A�2u5!�dec�7t�z!� &VF~D 288:��Õ>*bcsi�g��)���nd�s�tkrollah2��A���e�y2{:�Jy'��$. &fJ%&)u.� Good�RW �+ -cor$��co�ex�L*��}�j54:�J�66.3յ95G-2�c�72 C�v FuchvHB�UN/sG!pumT {F}i�<i z�es� .��J� ۡ>05(9):4537--45c-2� g� 01K38.�cheneyW�aBtIj_�� to�L*BJMcGraw-H�196�( ccdfAN ��ua>D..�u.�.��Ni2�u%u�+.;zH59�H�&)O%`F�ucf�M!]�v��*`8!k��22314r�306052� cemm� �A.~=s��(acchiavello��M.�1�us L?9�.(E!�9Roy*LoAA45CLnN8:-clr#H. Corm�s(C.~E. Leise�(E L. Rives� C.~SteinB�B�0QZn�pi��)2�MIT�YO2� cron�9 J.~C 2r,CP} symmetry*"&-E�M��,i`hrig6�Nobel�,�dem|�S6�.d{j�D�5u�j.�1��, {C}hzH-{T}ur�� LcuPu"a�'e"D6]'~00:i)1�U 1985.K�t�1�\N�&�=n�c>� linv�D�� 4:31�32 �92� ��J���Fab j*�K(t6�Pe�jn�27 _ :dec^c6�b.��� F�n�5:312�!10$f��?16�}�YX�,Ban�<�[.�UQ:�%VIy./%Yj� 49:6�6�4�h.=E���9�y6�dj.i%@Rw�zs2�Rap���9of%vlem2�1n uFH ~� 39:5�5KM>�*d()gJ4)M~')u.��hf\�,Encyclopedia�Philos*�}.&-�ity�l ��At�Wplato.7].edu/"#ies/qm-�)/2�ie�9AD .�N��%�.6;, X : m*�{behaviou2 )�&R_� 49:229�2�6\di�j%D .�RG � ob�b<B� �J2jw�Drostey( Jans��a�V^U�$ 2�&�L� iz(=�! heur�6,b}5{t"|6.�<(3-0jZ� &� db}4uD�2�n.KS�;!�.�� R�!��%de"�k.C%o=��� �`j3071:%hL0P.~Duri\v{s},^ Hromkovc D� Roli�) G.~Schnit:R.(Las {V}egas�/d�{min�!�R�)�G�ag;)auv2� = *z2?q�;Int; ym�3b e<,/�� &�pSTACS�3pa"H11�2l=�h�"-�)�*�.�Au�"A %fin{3� !,mu2[e����"O>�eg";G.~Ega2�E,Qua��(ine: A Nove�m�XCatast%�e2� E��>Za"pri�!g2�ezeEhlc\a�K.~Zell6 8Schwankung von c0�?en zwisL {G}�rpunkt6��"�&/��� rifc%86:41�-q62 eh�YEt�er�O&��5�NnonT��?�� subZM0Adv�\�q<�e�vt�'c5(3):2X*25D52�Y807:yfggllp{.%�L&ʅJݝp6l A.~Lundgr�[a�red2]�d�l e@? 9� �D�q ?2��Xf��{NDD.%��.!$92:472--47�W!�|5�:/>fgh�/F�r,H�u S.~H0x�UR.~Prui2�D�� ng aiE���" (��&�)���+L $aЙ�jm,��V+ 5:39, 396��4J9�@56.KfOi �. ai.uS=D�3�#' �e0�n%�2�ie�M��k $21(6-7):46G�?6�3�cpRV�kY ChaVew hal Law2�*�>POJa�&�Z1962� fit� V.~F ."�5��h�0charge-conjug�p�y a�.@��ff�4 R. F� �@D\#Fulke�.Y%#F1�P N��2�Petu6Kforte�� e2� R�'"� d'un�-$\`{e}me d'!���'{M}�F>Ph. �B�y P�& et.��:�$R6G�now:blog%$�no2&D{My��%�2�/ Web�+28Wednesday, OctoM30,E 2� ry.a�gcom/l� /alog2io%eiL.N�On`;�2�o� 's �D ��"MNZ.��"�292�?5�6#~2�&�fr:pp.8E\N�B�02�PPF�0truth-t�' re�2z E�z24I+���96�rB�J�82h�-  l.�M��!��6�'�J9lm:719712WQ2�Z1:hcs.CC�e1:�B�9�%WB4ips6�Ar�~ ere "( �8tocolW�&language�o& 8:24�):196�f;1Frankli�4�z.�O�1sc��gA��d��m!al"��.7%VL���u� 114/115:7> 735!�6�Sfri�l�1�� �X~Patel�_~Ch�SS�TolpygjJ�Ҋ2�� superpQ'�d� n +*)s1�B�*3<6:44D�2�fs�IFuroJ.9�ȏcR P�/,"�K +:/ timej4 E�t���D7:1�)�C66�gashkov_ B. G .���a=m_Ƀha�"b�*�)�Tǹ� al{�b��!ŵ!�s whose(�<� cog uousQF��E . Ki�. etiki}, 3d1�� 6�g Gell-ManuHartl2jQE"R�h!lF(of��sm)2�In�"H^�rek�3,i2��,a�M5YO ��S }. Ax�-&x�92�grw�<C. Ghirwg�RiZ cT�"b6�Unl�d����mic" ��24��5 34:4A49/=6�"gr+�hos��.~F�/senba{G.~Ae- �S.�0Co� smit2� ��&�e�!�m�xtic dipov@ 25:4�2�H cond-mat/�C46l gillespie] T. G.`Wh&KSYUcannoH�-t�Aת{M}arkov|�|.L�xA)n#�160e�6�gis� N.~G .H Wein��'�"����A�N lumiSM�<^���143���4:���onCG .��f�+a�� subs�7a+ a {H}.U�.A%/{ f�cX\6:885��3��:�oldreich� O.~x.X*%�:�S. MO8wisdom.weizmannTOpl/\symbol{126}oded/on-qc.htmlE|2�gg}2�%�a9oldwas:m�� % non-"�3&;*l:�L.�6I+. %�A!498. gx<.+,�MO7m�^�%Pr�AB� y1 n)� buY�f�valid?or�&( ��_ �/�L-"�La> TZ�"3*38� 6;;7�L196 l!2s%�V�"?�in" ~c ci�W:_0c emR�Ra�6n�Ia��?� "�1~5��E�*q -�R�8}. JAI�196� "��:ha4^�TCTot�.ZS$slua�a� . a�am��b�C.�:�54:18!O18�&�X(4036�ottȚ :hei|N"�w.w {H}ei��erg:F$.�i�:"Ti�nti nf.f0Group\o1 ӄA�ics;���,:_hmp} F�Ee �C�?oru C.~PollN= CouO g, fanou !��&� �um {ACC20%� *�J�2aK�"�c>8a!��[012u=g�X�>� :�:.��!�{$EQP$}��{: NP}$F� �>b480(5):25�>6 2 ge4VS�A �rn-�A��Z:"B/�v eV��.�Ie] I. MNr:C Sixty-TwoY�re�Un�_ainty��Histo��l�}���O I|al Inqui����6�- 5�*G? �� 1>�riffith A. G.�Cho@SY=n`/famil E(uLA�at�=.DE��* 57 �a?N!7��6!svv Grig��L�aLM&�>);U.�q7 �0&S#8aononabel �:;:�OT.Vz�6`C�K6�ZUK!��.WA f2Z�`.��database�#.Cz�212--21)Z"*542V9gm�GuaREL-rc�'6�Two&LW�'in� ndar��hm!qMT* �2�EP"gA.� Gen�36:56�562)r2" ]�� 30206�# hallm�� .L&�RРM�(6A{Pk�e~ andAWE<i�$al ideal��!.fz�6k6�!��&C hht}��H=(L.~HemaspaaZi T.~TQEu2=3 Threshold�g��*�:X*�c:�L%�J�16�_G*7�6��y}�Z�.�q���y�&f���a�le axio6� %�%��~1'f2�h�P�9���H��Wiηby��g�<Ѹ��Mru�`a normsx.�% DukeA�,0:�,dT196��holevo[ S.�ev2n: Some(8H �2� � trann�&�) !�&�ZB��š�x XT X�5}, 9:17e�~19C90Eng� �YN.w h:dewolf�/B1%�VN0I>_%�y.�o"�� disjoin@UcCa��%.�6d�� "� 29�&�b�.9062�i JI&�P��WiJS {P=Bunll {E} hasie"r�l"�: �e� �P1�{XOR}��emm2O6BT2NZ{ 2 jw�\JanHQ�; Wocj����T�Ft2�Co��McE�=*���� 3-lo��{H}� toniY� ̫{FQMA}"�b.�E=�303182�E�I. ۺSH. Papad�riR��(M.~Yannakak6UMH�asya ��$B�>Z�37:.L0�A6!kasf��tK 2 Kent�z��K)Mnasze2�-A� pari�*�EFb:� ~% 916 kw} .�N�V�.�0*&%�2-�M%Rlyq%d�c 3��a )���f.z�10�B15�Z,208062G#kitaev:�4��K.w��#n�)��] sm&zerN E�k 96-0>EU�95�J� ��+A.j��<��:&$" �" u46� �� Russ� ��.F veysxS2(6):1�L12{M2$8klauck:cc} H.~KN3c.�i�.,6���C8QquX�A"�&L� �&�O (ICALP&H&2�$b�(\"�W5�0x36�:t�Pf�3-�*sCɹsorf�B�\,x#^�1116W=k�8 ��0\vA�al�@RrfP"&�9�&ng :�F� �-o�)�/N�f�"gP< �]N�y[22�kvmi�livanI�D�X Melkebe6+noniso"�GJPsiz�s�z�K&?$ ` rchy�@apsJ]F0 3:E?15a�� �J�QQ�9.k klmn�+n�6�Faflamm`�~MaAj�:!�C.~NegIMg6�4Iawm�*. � q}�>* benchmar2��4�Nn}�� :5811--581)n>&106�Cklzb��W.~!�.^ResilLi�O �.)�*�&79:34�c4f�2052� k-� ushilevit;�N.~NisJ*��"���2C. Q:^��K .�&%(>a��rqC�� k��2:�" ladn�R�.}� stru�H~y5��"^="�2�]5�q�72 & laut�in�+L.�{8 A"��u�2.\eޏ>�17:21�1�6�dl'���GR .ZTes���l` y %j.?0: mot�i& �1la�-pro�2E�"CoV��YM��}, 14:R4�4�"�h&CA��(L.~Lev6�5&)�!Jextravagkhm��s,�{T}heկ%�T. ne��39YlRNI��)$R,I2:$��EimY� nsoui*N�C���$K�m,�<�tz[ learna�.�1�vW0 &607�� 6�Ll��A.~Sam{�nit��!z^�A*�/R�ly.�"�f Өx"X$7"��e�XenJlCombin6�ica��C54�5E ]b37C. Lle�y�C.~Tove26 Diviw/�con $a�squar2� %d" ^�-.A�}�3�LF:n�7.��)�M.~Tri6�GL��io�F�V�23�b��%�Y�� : 46��d_:� loyd��B�oCD'�apacit+!?&9FAN�x^� 10142�lf��C�.��~ *,pKarloff)XNv�&�� etho�=ac�����. 9:85��A�>�6aa�l%�gA*�!.�OnC.��o�{D}. {IM}�clee22E�Zapiski? eraskoi Akz�i Nau�LSP6(6Z--�18o!9�Rd . JW�� � m���bon� hat/fp��p�4.pdf.! v�V[@M'.�{\"{U}}o+&�1 , di)4�,em gegebenen!(vJ�?xg`2st weniD2 N}ull abw�!Z02.�RyN�c''�19�D9G��..9.��in!M2� megiddo�HM �RQ�2�.�ozcfE',{C>a� I�*Qamo� .PET"be�/i�"#,�r�3E:� me�5��.]FE�cb�=Ѿ : teac2O �\{c istsFo.O�Aa�n"P!�1�23--3�^{ 07112 midrijan� G.~M.xA.� ����FR~_���vKIk6�%%9jX}2j�10%��m%�'L3.�Ri� 's hypu�si�te!��&�s}%�ZY 13:300--3� 6��� �P���N�>2� `*�_ f?:2�1�y��6a*�X1962$nagasawa�N .��o ��7 .Du�,)*B�0Acj�2i �rob��;�� ed F�$�82FG'Tn�9� nayaWmN .�U�*o �Q�;9w�5�4s�Yd6�:�EEE�a"�Jg��  9rn�9��6;��o�Nel:�f%�Fluctu)r2�2�282� nc)�1��I%.>vw2i�i2�*�2�C& >g nc�/FmCREW *�M�@�JF&F�20(6):9�10�)2 ns{��&F�d�bhe�p'kB��s��o-�F�=9a> c� 3Z31� 4. nw:�^V ��&�MI�.�%�Z�4�1111?r1:�*nyNishimuriTmmakam2�!>�E�6�"7�B�IO>�90@�J7 E�`>wJraX0{q6n0papa:ξ�>F.��& UC Berkel>�Febru��J�[boo�[%�b.�J�.2!penrose�GP .?i, Emperor's&~$vd2gO0��*6Dpd�=�Aippidi��Fwdn!��B��B\� X"0aU%�um poTia2�?�Nuovo C=3to�B:C>6��polJ ski3P. 6�-�Ear�"�"�])Ej�m 5'doFY J� 66:3Z6��>; ry�� Rabi��$A.~C-C. Ya2g 6�n6rai�� E.~R .�{E���� .�B ���AC� #ed�w �basi�$��(\{\&,\oplusm�\}$.j�(��h,heskie Zamet�541^598--�2I_y$N�i��it{Z.�`.9dSci. USS�f _3A�33">�)1R�N0�(^W!+>icy"d�[J Izvya%. (�ver� E67!11+f72�25 ry�� �E��au;�.�N�/A(of6��^�s���96Bdamgard�!,B.~Damg\aa r2�/$Collision ��free hash functions and public key signature schemes. \newblock In {\em Proceedings of Eurocrypt'87}, volume 304 of {\em Lecture Notes in Computer Science}. Springer-Verlag, 1988. \bibitem{reingold} O.~Reingold. \��XUndirected {ST}-connectivity in log-space. \newblock 2004. \bibitem{rivlin} T.~J. Rivlin.0�O{\em Chebyshev Polynomials: From Approximation Theory to Algebra and Number Th}.a(Wiley, 19902�c} .�%�E.~W.�ney.D,A comparison!�$uniform ap�s oF intervalR`a finite subset thereof._%�SIAM J. Numerical Analysis}, 3(2):311--320, 1966. 9�0s} C.~RovelliyL.~Smo:m,Discreteness�are%A Mf4in quantum gra!�B�4Nuclear Physic�0B442:593--622%i5.6 ErraQ�in Vol. B456, p. 753. gr-qc/94110052�g%�Rudolph�Grover._Q �@searching a class%CLdatabase (or how we �nedAD,stop worry;nd love!� bomb).k%@-ph/0206066, 20022�0yden} B.~S. R .@%�Introdu�0�Cosmolog6�AddAl -WesE�>i@perlmutter} {S. P%* 32 oAh,s (Supernovaj�rject)2((MeasurementE${$\Omega$}S{$\Lambdfa�<42 high-redshiftE� leB�AstropE4a9!u9812133.o(sv} A.~SahaI�S.~Vadha2wi�(lete promis � al f�ɑ5In�� �A� }# 1):84--92�2.� 05116�hiN�v,lower bounds�A�� coll�r�the el�; d�Lnctc ��r�j2$6�� q] 513--51�XZ�112082 shor} P!�o2�&S -time U2 �prfac��z%N�d,  � a�� )N5�6/%�� DComput.}, 26(5):14!�150i~7.�~%4. x$-ph/95080267$imon} D.~S .Z��p%�of G��./~�116--12��960$inkhorn} R� .[Aɵ+�hip between arbitrary positive matric��doublya tocha�!._%|Ann��S�s%�35:876��%{:� ipser:bpp��.YC T theoretic� acha؉�A�.96LAC:�330--335��86� molensky)L.\ ic method a��y!�B�<{B}oolean circui� &/ .^z�77--8� 82�!�(ad} J.~H\aa^ d.W8Some optimal in"Abil^resulVR�b$48:798--85�6zteane�� .z@Multiple particle�ferencee�&,um error cor�:^Ed,Proc. Roy. S Londo��0A452:2551--25�6.�ce�60102929traw} V.~S .=0Gaussian elim^ M s not1T./�O sche�e�@k� ,4(13):354--3�1962�8thooft} G.~'t~H .]�( as a�4 sipae� determinie�systeF�C"��HTGr|�6:3263�i��&m>903h *�,toda} S.~Tod2A {PP} is� harda3&Y �$ hierP2%PJ�0��8� 8-�2�tsirels�� B.~TNMi��process�l�!�es�,6:www.m� Ttau.ac.il/\symbol{126} � /Courses/%e Inf/V 7.ps28v%�Tur\'{a}� FVt6UO� �<� �p�_& by analog�s�  Re9�At� cs.b P .edu2�/%�um.html.�vidal��V ._ Efficient*�siJ�!� slightly !�ngled1� .�2�%p*�Let� 9�Z�301062, warrwH.~E. W.�L� *� "v �$by non-lin�ma�ldF� Tran!m/��(33:167--178��68.Y$watrous:ca W .�$On one-dime onal1> celluautomat2�~�528--53�2� �^� Succ��proof�gproper�� grou�JY���37--54E0.$cs.CC/0009:^0wz} I.~Wegene�L.~Z\�dor2�A-���r+v "s cri�x s!w� a{;.�E� EIK:�A�.� �PCyber�i@s}, 25:417--421A82h 8weinberg:dreams� W B�D$ a FiA)�q6=Vintagek6 wigner}SW .` The unrea�g���".d @ c"k n�.�s�!ce2�%8Communicem9P!(AppliedeM YeN(1)�62>wX� W .�� umV&X8message identif � vi*�hannel2�Q�@A. S. Holevo Fest�,ift}. Rinton��4.�To�]ear*�04��2�$dewolf:the�$ R.~de WolF�J��nd9TM�2�PhDA�sis, Unsc$of Amsterdf ���� �ncc^�Charac� ���A& &� �g�� ��jt� JNH32E 681--692(JFa�. !Fi��0.�l10126 !�rami�ol .�E�$A New Kind!USi2� : MediaE.2. yao:!i(A.~C-C. Yao.e,9!Ks�ƅ��p ribu��uA&.GQ�)B�20 13ar72��bqpesN�Q�K�fF� 35�6�92��hwb({P}rinceton�Y�4 gn�%z1.�A�8 cs.pF4 =s/�@ive/spr01/cs598a/Ss/hw3:=� fingb�5p�*�5er����". y�,zalka} Ch. Z .�$Could {G}rK's& h�in[�m actual"J.b e�( 99����� urek� H. Z .�Enviro%�-![sA�invari� , causa* Ma*Gin*@[2�e�N_ 0E27�021103�xend{thebibliography} �\beginB {99}��oe�} E2�:�O PB~. �-i (Kl. {\bf 24� 8 (1930); 5�81) %1�4Dirac} P.A.M. :)��At ciplrq�Me�Tics} (Claredon; Oxford�'P58), $4^{\rm th}$ edi���!\,262; \��Maddox:U 325, 306�87) %2�(Salesi} G. : Mod� �A11�815H 96); Int.p1%.A12�103+7)�aŖ$E. Recami:I, 2j90k37?41oA19!q389(E) Foun�28} 76 |8|n|� |�;A5�%9%�< Ad�(ppl. Cliff.�-6a �6);a�E�G, P�s �S�% -Tim�ed. P.Proni��Drdanashvily (World��@t.; Singapore, (1!�@, pp.\,345-368; \DCavallerB�8``$\hbar$ DerivQ"" #%4Origin of SpecERelZ��QED'',���eeo ``a?�!A�]et� of.K@ ''} (B sh� ietyU> Philos�" of ��;�, 9$ Septembera!A+P \ M. Pav\v{s}i\v{c},Y, W.AD,drigues, G.D�Dccarrone, F. RacitBA�.. B318�8�93El>`J. Vaz�%G%�azQ�} W62I� WJ.�< 6bVA9A�m�3) %3}�C�D} \ A.O. Barut: Z.�3forschM�A33}, 99�78)!bG.Yg(: Nuovo Cim 2B5e�92a�8�.):egD2T363A�81q�D6�398�)>`4=28��85�M!�0thisson: Acta tPo��\1�375 H. H�!Dnl: Ergeb. Exacten)wi�!�2?2�52> K. H: : Am� � .��47./J. Weyhhof!�� RaabeZ�!…]4 �E.P!"K:nq4q14q39�M.H.La" yce:e�.;alai. (=) ��[�#4)�T.F. Jo���!cukundaQr9�13��184%�63�,G.N. FlemingF3B13�9I�65�Pauri:�`G��.e:Metv!�/, L�s"�+�� ics,d) .\,1��- 615,��J.Ehlers, K.Hepp, R.Kippenhahn, H.A.Weidenm\"ulle�8J.Zittartz (Spr1$-Verlag;Zlin��80) %4}xef}}r%XN- ngh� %WI�EM5!\200%�84%\y�D,A.J. BrackenFkin 2454eYyo�333y�.Z I.H. Duru2W.�e�35i�R�B�:�."��3�=4L���R8A�!�6v21i�e89) %5=f Corben} M% habh'H.C�}J2 A17��27��4!1\:@hys.812 3261);  �k%M� ��L �ginn� ".l} (Holden-Day; San FranciscoAX6�>�D3�268�!�J�45}, 65�7� E`6�55%r�mI� � +3 1E�95) %6=xPapapetA� zn A20� 24�5!�(�0Fr. \textbf{1��6e�94BdSte96M��2'%�1߁�7e966!Dur03�D{\" u}� H.-� iegel.L>067901�L:.Nog99��Noau�&nbeutN S. Osnagh>! Brune�J.�Ra�*d% �arocheq�:�40E�39!>�9: {TurA�Q.~A.%chettawit et �3 C�/~H�!�"Lanl H.~MabuchɷH%Kimble,ŤN � i 7A471�e �"{KLM013Knill  Laflamm�(G�Milburn�ԩ�) d4� 46%|1)�' {KokA�P. Kok,a�Le \J.Dowling%�m�66� 063814T2T U�{Pry04D!J.P 6�WL.O'Bria#A.G.Whit��� artlet� T.C.e9tlɖ9��190402 r 4). =*0wo-prd-19-473E�K. Woo6sEW.�zYd�.*407B note1}J xcep��$~\citeM�, w 9Kpho�nuC`res-toGei�6�5 or one�Y5~ {Nie00q aINielseLI��a$,�)it{Qu�8] �'�� .�,ambridge.SPresse� !,+0ma ��{eng96(8 G.Englert%�-���2154 e� 6) A>Art88�Arthu-�M.S.Good�r L6e�447L88LIralaTY{ N.K.a��T�el� U��� QF�� 6232}dhofd H.~F�5 fman)��*ake�2.-=024308E�edNjob��J3&~O�mZG�o~mtA.~G.~miT.~C.~eZ%�"0Bra��;�/[6 �2�,{HOM} C.K.Ho�(Z.Y.Ou, L.M'l,��A5�04�c��kok04g ~Kok�W�Munro, O040612*�  {Rai�2�, M�L.� \rmpA4� 7n 5�20��~5U�AhaAlbVai88}%weak values Y. Aharonov, DrbE�a L. VaiEo���� vEz13�8 9 0RitStoHul91} s�D t N.��M� tchi�F�� Stor RHuletB. �AI110� 1��� 5} A�CStn#,M>�7m240R� J,Aha02} %Revi�1$ng Hardy'sh/a�counterc3J stat,4s,�( m*z;,"B'�%jb�� oteA;<opescu,� Reznik5 J. Tollak� -�!�. A))30� 130-qr�@Mol01} K. M\o lme � 2D2ɪ 51-5e�1.D Wis02a} H%oW � J%pAE��P32� / 9pRoh1s�S 7C�Gnkov r+ţ of s�<lu*0l!��0s D[ hrli_ %c.�-# � �AK042102�2.�� 03} %Op8Telecom Networkl/WaV�S2j=$with Posts7�aUn!lA. Ac�D4llins,��Gisi�KV.ScaT92�)��9%�80L!W3.�Sol�%1.-VQFast L�), Slow a�PhV? ul6ies: A C#Bo�>Gener�+ed)V�X!��lli",� McCormick� Y�Chiao . U�{JEG Hick�L,�.�.�2}, 0436� 4) &� {Gar�J�� tse H�U�D.� �iO ,egg, J. Opt.ar%c,6}, S506-S51> Y� lund{ P.Lu� �}2 QR 0323��e %� R��f�VV}�1}C�3 E U 1928d�U31} 8919`2}Kowalski K, Rembieli\'nJ%�4Papaloucas L C�>6 ^J� A:�'.A$j29}v-9 �� 3}Gonz\'a� J A],del Olmo M A[ �� �� A: M2 [%H�84�4}Bied`rn �89�-R�2} L873�D5}Ashtekar A, Fair� t S�Wi): J L 3 b�. ��av50} 103�6}Korn G � T M�4 ��?)8al Handbook} (�Hi�&�)�7}Brzez1�T,V�~7$K)t3�Modern-/iyAM78}� 5�8]6%B9A�) )�P 2�10R9>RRS0 Sry33} 6035�10�] �v]5} 140.]1}�2 B C% Mitchg J J=��E�%-W43} 121] 12N 1994� Func��nal>122E_�03}Stenzel M BAyA ~165} 44? 4}DimakisM�M� -Hoid FT-(�-�B5�5} 242V�� f�99��wW tomo�_ GG?ihw., � ���E^} (bf{83}% , 3,$9); A�JA,}Sbf 12301 ��*�,kwiatmems} N�!PF+� Z6�\V� 92% }, 13��.borbitalUM�Ga-Ter�+,� "� �81�3+�$N.\&J�6�N 05Z� lvov�; D.T. Sm�y��~70%�12q 8A.� Z�L87}, 05"# 65 blatt�oV�6�!Q 22YyEch�!} I.L.\"�:aroc�\5!Lok&A},9g45� 4wbatoAu" . Myrskog9&� 3122�20:�-ld[ Eibl<�X�07"6� puri�/}yWal�a``�&um�lF& obtained :&X s|�4C .c '' submitW�6�GHZpaperA��Gre�rg� MVHor�� A. Zei' in ) 2's�em,"� ��ConL�&MU�, e}, N)ed�8M. Kafatos (Klu�BAcademR"$Dordrecht,]q h�!,nds 1989), phK3--6�6GHZfirst�Bouwmee09v �j/% 8] 134�/ J.-Wn>HN&2n(q 403}�I-%Y�concu�5ce�*���0}, 22 �SV8 ffJ. Kundu� W��Woo.J]2_� 052�*20:�maxlike} Hradri �=EQ1�&R1561{&9!K]naszek>BZE �10304(R)I�9Mjames%�F.! J�]4�23� :Z��downconve� G. K��j_�u�3,6[pOtycheck}� B. Pitt%��Jacobs)�J.� �"� )|%..~� �`�;���41W10�>1�423}, 4"6h GHZmE3EJZh: � 2�9<1�t6Rc.$W. D\"{u}ri* �919 I. C&�a�%5#6�wi�FAoM.�(odecki,��Ho�:R2 6�E#2�2!0��,B &Terha:d;5�27�3*$e�;�Lewens�j�A.G �a 0�7K*|ourenna�1� � �\� 17}%N�19�866� acin� Ac\'{\i}n��.� 7a�404�6� CHSH�d  F�Q�6�aF. Claus��M� �"7h�y� HoltJE �u2j 88�66�Q�Ne�Me bS&� 4 1838�6�cereceda� L. C JV!�16{24102"� Rq� �2V� 8 Vedral: High t�K Sr�G croscopic2�, a�#*� 405102; Bruk)vZMI u�� �Ent�= , F^ 6040��Vs}�>er�BeV I)o�*J�=: EV �KusDF�/WZ4p EsBo�0 02/ , 82004&� {W:ud chaCQmpoPI�:.X30r299e�2V{HF}M "nn�/B. Haeg�!k,osonyi ropy�<wth 0dB�4t� on a5j�� ,�*��44z05-60��3)��: L�  aspec;D\ enMpy,> s�9Leuven�=6{N�"NarnhofE&�3 roleAtranspuJ�[:PT �=F!S6.ɀL�?a�(310} 423-43.3=\M}A.W/jewski: 7��6_� A-, Gen. h!�1�0)d Gal3�$Gallavotti5M��$le-Sole, D� Robi :  yticM 6�>a � ice gaU��.0m5 493-49�67)�1&. : CJ2�.�&�@ q�jA|+=!/pQ)j�/' 35-3�69� BR} :1ratteQ6� Op�aor04 ebra {u�S&�TM�5 2, P.H. H.g :"6�Jae Jaekel:EaReeh-�Q�=er1dyER� mal fieldo�,>!�4ō745-175w��WT� Thir�.Y`at&s�TAo$the BCS-moHII,5vmat�!u$181-18�%68.08NH} B Hiesmayr,d!}bin prepaiE�N2a�.*.4, split a��DA�in Q/=0�qepU+  � 50/1},111�N� .,Mo�Moriya:�4araR9y�Qdi�1���f f�onU����its��r�2jCʹ*4*��669 HoN* P...$ : S%N �of mixed � . ne~Aar:6su&�Do �sL���Y 1-8,F�KP!�Julsga�8A)$ shek�E.olzik: Qto �%�4e�40- 2  GVV}� G:is�'Verbeure+ VeCommu6 �01�*5�j 1990} N3%�]����7 E�[!�!:kFlu�; Al�A�Mean Fe��i��F�8of��9,Aj',3,235-2=-6�{S}� 2,%�>84} 27�+� YNT6��\y�Rev��� 3M� R� �� i�^Agraw'P. $, {\it Non FFiZWo� 1z �# S�Jiego,�o � WNiuL)WN*Q. Niu2��P�1603(R)�:LKonotop? A�e}�(alernoR[h1021602[2);�Blizakov,W.X� BE� 3�51!�.�1[$Trombetton�"A. �5 merz��!�Ie> % 8} 23MW:Abd� K�+dullaev)�� }R  6� a�9�Kivshar}yS. �� eyr��-�4�319x 2f 2� . ElN�e#) 88�739"{ 2n)I ^ �Y9F7�%:� Jj%5�% 6�Rh8� 2361�}�9iRapti}& :�Yi �3�S25&LKCatali� ES. :X�\�} A�7*/�FE ni}�$ :N]=�9�1~Ia�WTL��T�(Ho%MV9  Zo�=R  ( 3276��,TMeystre*+V=4ld�^P. N�~ 291.XBashkinXP�(VAFVag�7�-�5a 6207�76�Graham}�� RD.�l"j � m^5A48f ��E@1bK �)� N3�6xū2H8Paraoanu} Gh. -�� N>6�A��!:� Timm%= erman6� �E�8� 574>�AoChui\AI3S$N�5�/4833>LKasa}�3 matsɖM. Tsubo�O)3%��I�0�*:�Bur�a^.  f.-�A| R25{1M}�?}A�alT)i{.:��%F 1539Ewk(R��^0Y.W f�E)�w7 5020VM�<han�=E�2Q2�.�7%>�� evrekidis%�Bf�-H�k356�A���V�D00}zFey62a�3eynV�<�gr�V#  (Calte.'1962-6i5�Kar66��,K\'arolyh\'a��N�?\�?,\)S 42A}m 66) 3�gG FL82RGA. Frenk 1 B. Luk\'aP=in:"_\ as\�L \ ph�A,\i2eds.:V"�H.�K,hbach (MIT,\&�- MA�:8�!2�V�v��\k �s\ in\ s�C\AQ\ �]^�R�enrose� J. I�` (�E�Y,\ &�E8�.�Pena.CShadow m�J( @��� ["}02R6AB P�� Rel.��v�28%�(96) 581; re�>�i meets=� a*i Planck �ae0?!�@=[D|4) HuggI1(Cab�/9�� *�6% 86� Phil� �QRo�={��356 �8)B'7.*�'Dio87} GDi\'os���120i87) 377.9_@9R@���A40�89) 116wi� EMN? J. E�&��ty (V. Nanopoul� ��\ �q� B221^/I]HNS� ^J Hages@D>`N redniNucl. t �B24 k4) 38�KkMi$.GA�"�3�%� bf AH�M1) 54�KA� 6ALorentz*� intrinsicLgoP,ce,a[030802.�San�&JQ@S\'anchez-G\'omez�F: S&�_e.��s.Qop�X��!�<����L�IMT�6�GX!,�+�Ga�32�CFN�A!� ChavaJ�*F�F ridob0C. Nemp7){E~23)�94) 17Q1tPerStr�8I?Perciv�W�ehnz,�;NYA4�A!� 7) 4`f]owPer00�WDMM�9C��i/#Z\�  0) 95.6Roy�S.R� S�)> l geometrba�R�Rto5p�j)�c�k �!,.�!1� �Ad}-�Adlc�(��osU em�",nt phenomeno�m^�4:�� rGiuetal��$D. GiuliniHJ�$Cef�4!ps��I�GSt? j0H@Zeh: Deu5E��Q appe�.cya*�SwPJ*nn�a"�D,wE�2��7MC.�l��O2�h�TdSMK6`Luk��ZN,A�li�i�h��488OGGG90�C. Ghi0i Gras���9�`�.�2�i90) 105.Chr�3ChrA�]#�8P�7 �7YGAn7>J<BNrivate R&�S:39� A3b.Z9)9)F>PeaSqu��&< earlIo^O quir�� H%^�j9�O��QBJK� S. BW K�U"P�^Kn�0UM 5�2V��LJS���ami M��J�Reynaud,�s�J� D.��2)n+� HuVe<B�Hue�V�Ugua� Clas�F6� %�' R.� MSPB�� rshak;C. �E�"� D! u"&&9)c-�5 i13� .�NDF04'H� M�Yst�Domok�R. Fo.l2N �pA7 �4) 023816Z1vAm�9G. Am� o-Ca �?&ZHD� �0H40jHSimJa�79 DAk�=Senergy.* due� ��? 4y be observed?:�70&to�Mx\iG/E�A.�Pea!;U�J6A�� �46=zBAI>-6�� E. Ippoli(�?�w=)}:an[5) h&2] AB\SEZhToward&�_�5ys_ a mixf : an exac�e* Fcu -- calcuX �T etaiC%B97e5��ea�f�*� �kaps�Od��$M{* -dis"�eforcedBe,monic oscill�o, � � 1105��enFKTT f�19} \exp�U8fter\ifx\csname�exlabU 0\relax\def\na  #1{#1}\fibGbibO font>J M#�Pf�Q$�R cite~R.$�Rurl^�url#1{�#tt!O%8{URL IproviAXmmand{!\�f}[2]{#2}@<6!& []{S'*`V[{2�{Massa��6 scu}��3)}]{m 1993$nfo{author 5i9�{S.}~�1y X}} 2 and}A'��M�JA=jv.�*��}"�%,J me}{74:Ep�s }{12�0year}{��teB>Bru\sg d>% chiavello%C9!Cbruss19"t2f�D>B \�BC>MMa�rG%B�5E�bfFD253:C-E24�O%,�5D9rDHKhi et~r4�44)6� #(, Hashimoto6Aand�ibe}}]{h G�͂�A> a:�V�TF= �?uA�Y�VQMBQo ��5NU�ݭ 1020->t%n��+5rA�:r!, L���W Pascu�(and Tarrach!xfB�vG>�e95E5V# J.~Ia��[{ ��@P>{ �} *.U!���R>O5V�*" Aj�60:�mX�lB�%sn�C�&n�! , Ek�A 6�}].k�aئ�b:�V> A.~K>��ڢ�I �j�82:�-�43�AT%,�Bag� �2:�!, Baigi!!�4u{\~n}oz-Tapia!�bG\!��E>�a:�V�B��ڧBIB��Q��9:�-� 2779� >�%?nX%*uX�kj�F�%� R�[z.�����J���b�2��YB�=2����IZ�"�4FO!�v�� q�1�6� "zQ 7��b 2V�BZ�L�LrL1Z�5U>�!yr�WDkr� 8� w=�sRnJ� U� O6v��58:A�� 1827F��n�&�E� �7�g�E%#~�N>U�o b� 2�N5~�7Z� 2153R9vHel�m!176!1h  1976�4 C.~W> S ��9��title}2Nu31es�yN+�}�4Y�(publisher}{C* .ss� 2a76r2 Fult wHarris!91!f 1991�W>4 W�5J>M �jHRepres�1=6:-�rsIj ursefF�0�^-NO91rOB6{"D {a}}> agana B 3=Gi8 Monr/2aBunN� 6a���6ll�-�v�B� ג:B�) �I &I =M!{�N�n� 7Z�`I�Z� 2006}:*lC>�E"W=<bfK Calsamigl�TDemkowicz-Dobrza{\'n}sF;nY�XnXB��� BZ^�N����2�V4&} 6061�F��V!�j�w%��\ =�͆[��r��Z*� ~�8ZK43�:Hvn:B:1}:r�EBr0F:� � "�]"R���6�iR�B �:�V" B_: E2V�G�W5L2���6Z9\?0Ju]A�.Ja�:� ��AJa�b�1����E<%�2��N�{ ��Z|022f=NI2�!�jIPe��ScudoI0� p.6��B�T�� PJL �� �H6:EO416� :I�n:Chiqlla.�>�&a�D'Ans?6 erinP3�=Sj�cW]~�Bq:�V{ G.~M>� ��AF%�?2Rede V�MEmx:1!i�?NJI=v]5��9��M 1805XVR��NX ^�8V0�)�tem{rb0}q#s`sA.rnH__Z[�` {\slB"P�7518:X�7�_RBHB_6�6>Z 1 )�jA3-5)3.7%c7�614�9�u. �ghz�5Ms(e2.O$HZL�H's1�&ONNnK�g502'n�M=Qwo�N}.fckw�=C�Nf�%��G1�Z56�NY�$pleshbuzekENPl�=%�$V. Bu\v{z}�N>�_A 0123�`*^K�H�8HAbH.�noidop-B S. T'66nC2���aS�Q��.d �y/c���A��fum ��rB�on}�m46�J kwias �V:�>reƍ�8�'31�?Y2,sar�( Gasp�ajE*.Y��02�T�(��Nb6��JXwir1} I. Bjelakovi\'c,��KҘu}�&z�y�J.(it&�,!5, :� �YJ bs1}FV� AnzE��E-��H���seOH�L�NNGF,} 247, 697-7_ 4.�Hbs2��" Proof)-�3M�DnZKof)�um� �F-ňite D*��S 7�N.org:i-{�307170 =NThomas_Cς} T�6 PJ�B , ElN7l.IzI�%Uy, John�_e�5So�?NkQp�26� vKStrooj $Large Devies,�WA�*j/FWgau\�iW G , Nc�&]s%1in����� mond>P/k� V�(, 23, 337-3A(18s�8petz} F. Hiai,{ Petz�yP� For���Qt=��*aAsymptot�;inUPro��yy�tJ�H/_3, 99-1iT!�.�jozsa��J -O�3 mach� J�q'Noiee ss C^� %�} ��A��`O�G��41!�.1W�343-234L9a8y�ky}�SKal�_nko|H.��g"���A�^ofu��S�IOZ�-.%bĈT� !�59-37FY2�ogawaA� O ,�Nagaoka,E�ng)QEKV Stei�_Lemma.�HypotD7TA��)�ˇ�Inf. Th�Av�~؍No. 7,�_8-2P0.�Sanov} I�} , P.p of leOduOq� -�blA�M�M�R2�J�% .1gA,1�p:= {Nem!K�:�2C!�L.܂unfKF�207135PM;!�Y��423�PU���B; A,5�333}, 37T2] {Hey�;H.Q��G BM�Af�l:" S.b<1Aw2e �f:�S.�B�vs f��KL."1=#tj��~Y3.n  p3c<.7{iЋ2��I 1797%gJI4NHCB:Q 9�X �}, S8� 206{�=F.� [��&;2(91i(1�]E�2� �:�S A. V�o:)U97P6UBW!�6�U�e6�|�&.U�2U {Sch04a�hr B� Uإ708�/%>u^b�^a^�}Ad>2^ {Ben�BCyBennett�¡� rassFB�M*Es.V ���holi%� B<�. 76}, 7I5; �H.~|Diz iVincenzoe�2e>T c�T�g382�j&C%Q�D,B�< ion.*6: {Hor�-�� �|te`} 5�nMwF�)+ � b?V"�["�W.�Div�EB�R W. Sn~.�� �Nerhg�a*� apliyalB+ 62R� �Potentc� NPPTV�6�ur�W%�y�M��bbev?Av0j�ir� %�7�"_A�6� \pr.��7ITD�1�Any 2x2 ?sep7Zl"Z can be��illed2-�xE� R�_J;�Fl4[ 2921�>� {Egg EgrJg,�vGe�VollbreiMB. �/� �_"}lf:R# 25�P~�llIs�Iare 1-D�uLOCC+A84�nel2�Ci, 2ZY7B. Krau� 27M)��54�:2� PPT-if �-�used % �B&7�a9�imp  av��-9iUA+�O�P105�R�9V ctiv�23Wat����aʼn>y 93�10502M��VExist1 that%�&�il?�but not! N�A�`uRN6� WW52�G�@Wi����Hgh�h%E��W��.�Cբ2  14 1956- Aha67}ORAp{S(L. Susskind.Ru'151 142X67.W {KMP!H�\ita� � ayerIp�S resk�.� ��6005"� !b&� BRS05. ��Z a}��pekke�] IJQI�eit{�sW[200��> 5072169� yJ.^1A323 :Fu���Qurusawa,L!i\o ren%{ :� Cl�6 � ߂%��H�x^&����2e706A�1�55P {An���V� F. Anselm�6� %Pa1Ԉ27-441\ 32 Sh�}vY Y. O�UL<`nd�\p�i�*5�g 88);~H�i� aO. Al��F9��882�Barnum� H.B numK��G. Ortiz)KZ~iol�&A��G 323�D S ], E~ �1PsC%�:Y�]� 10��6�Kni��_R.6��X�V8@m��2���*Wer�Q6�2�L� 4277��(�o.���ga&H�:�i� thos�a��v!\tĩme�! inequg�2�Samanʋamuel�V%�V��khoru>^� M. B� ttik�New��q��1>#2� {BeemC�B#eenakK��a$-mat/05084q&6D�3ůʱ2�9aP 1570�6O�3�JW��C. EmaOMCO�T�|��J�[�Vel�iJu479�#B!�4�� �� 0268�_6�BaeL6<>�A�2�F�N�Pas� �Vas'kausk�PdaHYoueF}��_2� ��;�1�� li�in��2� KE6` !��� Loss�>r�,� 6rWis03b:��32 a6� inii�Bserٚtr�ky��*��LXVIern' al Con��}%5eannaford_�.}JT SinT�F�309046]N�!{ ��', R.~Koslof]*S.A.~RicփChe �Mm&!�134Ɂ1); J[�2T>1e�219 19�TYb3}� See, e.g.oe~ .�'emey:�Y%�M��+"�SLoiY3:l4lB.V.~�,� Chao�[bf �T~^�.ob5:H.J.~Ca�ha���An�in As��Zto���99 �W.~GardW)A� P.~Zar)  P)}&�M�.�%~Orszag ;9 �b<uY=�8!��p9N* J.F.��� L*�g 19A#235L �]TAU4� V!�rV���cha� � ElAIn29� 2077�a9)I.C:A�V���V>C3�18��� ; \Aj�6 b12�,~Bhattachary�.~Habib�K.~�t�G�&�% b8� 48-�( ��'�P��A�See als]�~G!�41rkC)%05211�*62b1if�� ~ScoьGA�J�YW3� ��&6gb14A�� t� 8I. Ohba, Eprint6" 8154� ][�Z�=-P.~E-�%ZD.~RuelO\�Me):��5�6�u1986bb26e���~Li PL.E.~<��6�QI�W�g 7M�aH1��.~Shizu�W.H.~�� ��O �*436q Aa .Z1�UL.~Di^}\9�r4yp1� ; Va�Belavk �A|A��xw�: ���dG35T8 zY.~Salam%� N.~9Q^.>81> �9� M.~Wis��!� �L0642a�C2|��> %���6:�20%�A�D\?]u��{�ungAa)%�q=�w 6w0i=1c ]� footl� This��5�.\h& ( output rec��>�in��4 bandwidth. ItE�a good a�4xi�$t�al.]s so .0 as zJ� �inY�vqis�!co��(opof2x) dyna�|Y�]�tocome} 6��%XKu? �(Qo2<2�) A.~m�� ~�wift, x�~Swinn�%J�(Vasta�4�[aE�� 6D},*ϡ6P2��q��R.�Lyf��7�6� {Hnofl��S�)�~MaO��W~ e9*.~Sundaٖ�.I}}av|� 6yexp�:��6��%' 29a/137�� M!LaHaye,Buu�Camar\fpKaESchwab&"a� 30��v� &N �j 7b5U UT�5U�5U�5U�5U�5U�5U "UR��5U�5UEi�"/9 1935:%<$ , Podolsk�(A�Rosen!9 epr}zfWOB�:X&�8j>B>dE��gCBh@ ��-\bi �J�8}dbfF�847(10):��877RI35r�:Boh$l}:Ibah�rD>4P�<Y>K��2108(4Z210�\5��B195vI�E�H��!0Xbom�0�0B� �)-RZI�t undi%Yd u ���9*II$Routledge}*:;1%93vXell!8IKe�Q�aRYBECj�Speak�*%�uns*�bme3�(b�Ca�cN�8v �:c�R ", &)�� Roz�}]{asp�7B� V-vXB�=���G>� �~�1 n�9(2Z��)Y�Q�82r�Adeni�Khrenn/}(:�D }]{kN�zGB� _��B��)Jq4{7�1 6045.-<>I �Aa^�BAtdn�t���� � 9010�N� �r�%��4 Gonu����Bl B, BTutcu D%@(\"{O}zer O �(�it{�  Y�$A17} 2057;BY MBvm U}zg�n F2��r4�`*� DSouza} Dutra A de�0za , H7,M, Almeida C�5m3mEuB�B��c8g BagcM3 %Ooraac��esne y�LRoychoudhury R ~2004�N9�zom9�QX}  `$Thachuk, ~y+40304`��AAlhaiw,}  A D��.�)bf{Φ 72.Yu} Yu J =ng %E�G��6-�BenDaA;}1'  D �Duk�1�6653� �Y|1;!682ٹOzd�YzEi:��3Zj� 8} 2YpJA�ChH�e%U/�21} 1685B��C 2330FC) (Ko\c{c}ak MS5F�W}96Ay35F�0, \c{C}elik N], Ol\u{g}ar EZ]B]1683; >4�� QY�Q983B�, K��k�4��Bakir E;*(e50709.�Coo��  F�Chv%�,Sukhatme U P�9QQ�p=L 251}��.%$Von Roos}   O �5�JN�B�U756��\}�� a T,A8liams ��69rO1 1179; B� rd G�1N6 $bf{B24} 566+�XZhu} Zhu Q G, Kroemer HN�� 3519.Li} Li�Kuhn K J!fvI47��760.IPlastin�E D A R, Rigo A,Casas���C!5A�, �> �it.� �)I4312r�Morrow}  R��EE�/ K R!y�R� 30} 678. R��v��,casimir48} C ��'G.�8�it9c�v0d.�� eten�}+5F7!��@miVu\M H�$�� \&�Jw�f}R20w�є T1}FT1 T� � Effect:�^Q/ Manifes�6 ,,Zero-Point E?k$�: b�\��r).�borda�) B �($, Mohideen��A7Mostepan|9Vp*<* �%� R�v 35�.�l5A(naay58} Spa m!@1955�8)� 2�5NH89NH89�9!�S�nmij� �5x�ors, �B u0t�Makζ Essay��Develop3t' 20th Cent�?Honour��%.A�1���he OcA�on|@�,80th Birthda!�A@�:�<$th-Holland 7. 235=�lif�56} L F$MA�56-� Zh. Eksp.�. FizM�� 94 (Engl�wl =8CSovGo- JETP1��/�#U�,sabisky73} S �SZ;A�# I(0 1973 �!?� �D 7^2�z lamoreaux^L "K�97FN� E�{-.<D98}RQ.� �.Q}454��NW04JWaK Butt=AW. T.aF4. �%.� 8��5^mm��B�RRuA%�� ��roy99} E, Lin{ -Y. �2o�5FjD}����11101(R.hP[&}�Z�W., Ch�fFI%2jwFjAjA�72[b�=02} B ���urugno Onofrio,%%!�Ruo�G%�2 q ]�2��04�8 *�5� hoyeTNH{\o}�J,_Dv0�I"#arsethJ���BX3����&� Emuq  05611.�pbraApB �!, 6k, 6�V{4. InaPA.��*�"�8�eding�x��6th�akshop on"7*�y Ua�/Influ��?x�%l$����mV&NvN �)}p. 54 [>/311094]]��e78:e, DeRaad_�'Jr.�&�&wi�%�197mJ �y��(N.Y.)-�11#"32�v)�94E�5�SkurdjH)x Sollz�Re�JH @G�} m2�68�6q1}jq%�6 aW>�v.Yb���2�r �mW�:YA�:eBiRk'�� M&"�� 1�77J�٨f�zre@1�6#261� 5Hjaffea?J �L ]��dicchio�&�1�^� ." *70402]�sc&HhBX!;.}{R6042 .X���i-,hep-th/040802q~ gies��G��H�angfeld� �Moyaertse6!�JHE 030%^. 5[tPki77} B��ia\ , Randrup Swial͘�+qTsa CC�?19�� b�0a�42.�ys�dliu�/ S , Bop.gBostrDm� -w� W����'�~*�'�j8.\b�om�[:��B�^W ' �0 0527��9�da' 24�e�K*�/ 472�{9�1} N�2�B} h6 13916}1�0eZBWJ!$bk ���2596(che,�0, Klimchitska�(G�u6_ �>`  M�Jn�6:(�U11.�iannuzzi�gI pH, Gelfa�4�Li �q6 �Capas FxIn�7� � j 11N 2043.ͻ�B� )2� ��L*� 1022B�d&��O D �N4S., L\'{o}pez!� L Fisc�) t�8e$E%��k�q��iHe��-05:q �a} 6�:rZ�� E�.� �>�sX1���e� D �6= 116��N��j�$� ��Z�{Ju-�Vw&�sch�yni�2�80�,35P,it�V } 82E�B:�".EPR�Jk"�:"i�VN.�",.O �fS)7-36+B@; A4y 6�U6��C"d�}�v�1�=X�S-Ϸ�< �I��Q� �z.D�&��}��SAH�5ՀL9��%Cd,�B9]1��/2�Sachdev}� :�{�yK��D9"( ��JessV? 0~;�Wooter�x8xN. W.a� �8��2&]�.kOConnorp}KM. O' !n W2ɥ.`*)+��3�(6.Arn0j _M.v _��gV.`�2c�a�b�01"e56gOs>Le }��]MWMl2a�^ 3C�"|9qO0jloh ^A. e�AmiV�G.v�c�98azio,.^� 4O� 69�e�w���<E�mHx��RmXA.  <.�=29)�"9QpLipkin19BgH. ��Meshko�<I�lick,.��"?(1�7H2W(Witten1981}� 2F B \�B1�5KA22ICR19~JFZKa� KhanI=U�8 amte) �PReportseN,O m.6�UnanyaA�3}!� G. %lg�le�Rhf� eɃ-r�9�&�%t9u%��b�j,qMosse�J�uke�(��U�9i54�>M20�kto ��./�EQ#L erem�jAe� /���,2{�'221�T�M�-D��1�.�R. Or~O�ic�I J.1 ,.9*7T409612���E19BFR 3U�620:I���em Nature}, 429:737--739, 2004. \bibitem{04Cirac1} J.~Ignacio Cirac and Peter Zoller. \newblock New frontiers in quantum information with atoms and ions. \newbD�{\em Physics Today}, 57(3):38--44J�@5Brickman} K.-A. 0, P.~C. Halja lJ. Lee, M.~Acton, L.~Deslaur�,�0 C.~Monroe.�(Implementat�4of {G}rover's �Y�38:643V>A} b >I�0EntN�-A=cE�states.^ 62316�y0Ev(-ph/05081236%4Leibfried} D.~X, E.~Knill, S.~SeidelinI!rite!�(. Blakestad!�JA4iaveriniECB. Hum)�M. ItanoGD. JosILanger,ROzeriK$R.~ReichleI D.a�Wineland.CreuoXa six-atom `{S}chr\"odi_ cat')P.>%O639--6421L2��}���!@!MeSchaetz�J$D. Barrett�J75VW..'5&9�C.F0�� D.J. R#Realiz5&E8um error correc��n$2:602--605%683Steane} Andrew!� .ROverhead�8noise thresholda�4fault-tolerant6� n�Phy.68:04232)�6�2 �2} A.V� Quan! computer �� itec� for fast�r$ropy extraV>J. Inf.�@Comp.}, 2:297--30i�2.%%�e�203047.� 85Deutsche� .=q$um theory,l {C}hurch-{T}uring principle�8the universal �um�.`e,$Proc. R. S Londɐ 400:�117, 1986�(0DiVincenzo�P. .dThe p�� al iBP% �E�.>�For!&��e derE ik� 8:771--78��0._,02Kielpinski���M��qk~N�Arc6*a large-��e��-��:�6$ ™�(17:709--711ex2.�L99Abrams} Daniel~S. %� Seth Lloy2/Q%&�provi�%< exponential spe�AncreasM�in'0 eigenvalue k ectorr� Letta083:5162--5165A/99.�04Porra�.~ �J.I. h .�Eff��ve5Y spinG s wQ !xb�@L �92:20790)v6�<5Aspuru} Al\'an 8-Guzik, Anthony��Dutoi, P ��LovMAM�,n Head-Gordo2� Simulatedщ�E�+F1:123��:{ Blaia�.~GL e L.��RiE��ruz` E. Aust$G.~Wu3R. PlaaO�RI�ook2RTowards� 4hand-held mass��ctrom�� design�sider�ssa6sɕijfabric A�mic C�d cylind$l�%C2�%+ Int. J. M�Sp�r�236:91A N� 4Mad�� %K. HenAxA�D.~StickwaabchukE�Y�.�Planar� ge!ryE��.9�Appl.MB�8:6S5NM4HomeMP.  %]^� El%!de!� figu-��� sepa !�A�b���� ��,}, 6:289--32i|6.�ŧ� 4111:� 6�/J�:DIf� In)H��t35th Annual Symposium on Fundalls���  �P$pages 56--g $Los Alamit��� IEEEɐR�9605016�(8Gottesman1( .BAaj�of^�*� .:EE�Bi Review � 7:127--13��8.6%U!�9702022O 99�26�EmI.V�E Oelepor��is a "2.�al\mitiv2O�&� 02:390� J 99080165i Fb� Ben Ibins6H F6� log%S,gate networki:{C}"j -{S}hor� {dJ�!�>�23��20b J�0311016��2} C.&�G.~P.:�&R�a��a�S.~Gulde��C�j�(Eschner, F.��2�Jl�B�A�VN @ultralong lifetim@their tomographic��R E=F.| 2040�4.��29Soren� A.~S{\o} E K.~Mlm6iQ�}�+ ions�$thermal mo��.�^�82:19` 1974Q�*?35e�J&�%""���j:RB�Marco��"+ $Jelenkovic W6�& ,T.~Rosenband� Sch\"atz.�1-.�proces�f)8rl$Phil. Trana4B� 361:1349��6�'6�5 } R.#A��JzO."Aan-Kish,Rc 2�^i2 D.��2M)1=EP.2�( f�HyperD "B Mx pres of spo'(eous photon-tteF� NP5:03040�6� 03GarciaRipoll�J. - $Z�E%!nN�S00optimized two� �p�9 lase�1 t�* $ techniqPcq���",i�� 1:15"�6I4Cruze� �P�ang �*� .Fi0 emiss�cha�e�c� tungsten$ -' mechanŀ� devicF).? �86:1535��U4*�} >�P^�>�BE�Blinov��MU A�".Zero-poi%�ol� ,low h�ngAÑ {C}d!�2l >N�v'4200T�ette} Q�,a&�E. Ki!�2�$M. Meekhof�_)ya�j;C� Wood6��an�]j F,Ňfro�ugroun2.�NE@61(6):063418, May!W6W 0�;1a�<2�!�~ u�x�in�M!�62:0223�0.�j-�0� >L 3ardt} B.DIm�e�cilla�o"6 schem���s:� ���.Tn�6022v98Steven� avid-,, Jerome Bro�a� U%an2�S �eri  method� mw--��%9um�z�!�<58(4):2750--2759�8.{ 04TiV!L.~ �+ Rabl�le:AP.�B.2Inac�$ �-�?� 5solid-? 2r6�+�479.+,end{thebibli� 0y} ?N\beginB�{33} \expandafter\ifx\csname natexlabV (\relax\def\ #1{#1}\fibGbibO font>J M#�Pf�Q$�R cite~R.$�Rurl^�0url#1{\texttt!O%8{URL Ia�i�mmand{!\� }[2]{#2} B!eprint []{S'}�x[{2�P{Jochim et~al.}(2003)N", tenstein@ Altm� Henda:ieCh�8Hecker~Denschla�Grimm}}] v Sci0A�bi�{author}�5�{S.}~#1� =�}, % !!ZDM>DBa͖BA>B1�?G>?%5�<B%j�<C>x!��;J>;>�G5� and}~�R>YGIAV5� journal}{d eebfE%�(volume}{302�]> }{2101} (Tyear}{A�}). % %teBGre$QcN #, Regal� A�JinA� NatA��V�B� @:�V=C: )u5��}},%P!���w>P�V� f�426:�-�537Ҟ Zwierleinn�%, Stan�%�Schunck, Raupach, Gupta, Hadzibab�and K� rle!�IPRL��~W>@E���N�͢>H>�-�AS[~F>D-=�D:�%r�<Z><9�A2�E��V,W>S9�V�B�f�91�}�M� 2504n� ^�Ro��N�Ro�e�(Mandel�W�, �A , H\c�+nd BlochA�RomA�4�TB���T)�5���:O>{ �=A>=)�=n��nT�6�1��5��~�I>�-�!�EAnfo�5��3�F�073002R�4�?b�b��A�4:P  , Kraem�!�8Herbig, WaldburN\"ager�_&> BA��V�R����>u ��>BE�;J| !�=P>�9S�A H.-C>>1�B���� cond-mat/�258} N� v�Donley1�A�2:� " , Clausse� Thomps�and Wie~1}] ,� v v� EJ� l��~ N.~R>���BS.~B��B��C.~E.}�;1*, y�"� $ �f*N� 417� ���=529R�2})*�>�McKenzie1oN�$�|>�����Browaeys, de~Araujo, Fatemi, Jones,� sarih  Cho,oni�}]p�x�CB��R� z�JG6�]%vVIH>Q5�@B<1S�?LArAu�Ur5��FF.~K.:C)Ɩ@�>@%��?JJ�SiM6�CD>�Ch��B�SiA�w��5U9Eu�BT<^�88N�139J�v�@Feshbach}(1958)}]�q��LZ> Ann%j� 5:>��35J��r�Stre�qށ�>�$�� Part�*y Hulet�e$�e�ZKN� �:�VZG|:T�BU^��  (:T ����f�ƣ 080406Ri~+Xun�0Xu, Mukaiyama��Abo-Shae� � , Mil"�+&� ]{Xu-�i�e�V�K>��'B� ��@JJ��DB�! �>DJ�)X@���*�*1=$҇�n�!4, Ticknor, Bohand�$� ��ujVuN�A��{B� ��>J(:,��|2�� jI��F�4�v�$47Z~mD\"ur2%>] ", Volz;rte�wand Remp� Duer�#4�<B| a)䖥B^��;B�4�YE���B�-�W�WZ�0�VW�j�)gV� "&IA�a, Web�^�)j] >\��JL ����B Kr�>�PBy%$�wB����I�II-�j 30Z� 1510f�f�Q� >� , "a~�*�a:�5 ��N�>���M�6f��CC.��2��mV���r�ZK 1430Z~Inouy"�NO ", Goldw� % O28>�ET�] 5�QB r�PB= ��KMJ��?B��d �d �d Bvj� ^832n@J Fedichev1�(1996:D$, Kag Shlyapnik�*aFalrave 0PRL96� �-i�u�B���Y>#��< G.~V>��E���J�~MNL50RNB"^�7RW 2913F�!�}v"^ %�JulienneE7�PRA97} %Z"�V�f� ��2H %�rP�+:<�A!.CN:AjX5�!2C� 148J� 1997zG Kokooulin�G��1:\&, ValAaosloff� lavaJCP01!)z�VB�B&^�:��� ·B�,6p5�J�/em��11{6F-�304J�2�nUFio H"��8:�$,�8�9$ Crubelli� Da6(asnou-Seeuw"CP�D�"8�"B#?�F[om�E��B���AO>W))�=F>=2^Z���BF1�� uhU�B�f�80��M�44Np 199<b�Theis1�H>r ! , Thalhamv oJkxHellwz Ruff:#imm- F�(] L�9 B���a�=VoG>�ĖABWi��>B�-,�>B�!a�;B���B~ F�A��b} 2v� b�W6�* 1999:m "�-gB�ZilioI���] *RMP99�QB- g��VJ�B ��Bt ���~F�*��� Z��RMod�j7^@Ra 9rdBergman"�!�>d$��eueandMH�!!��AB"?:V�B T�V����4:� �A� >�v��Zu100V �u�JSchlos:2�x>� %a�Reymo�<Prots�!C��h ��>B�(�@2 �lVWB}9&!L5U )1ju41^�024F� j�Kuh5eN� ,'3,�rada�% M\"u�Go�e�Me�7de�9��B+?��BAl�� B7 Sc �=�j�B_1�?B� %PV{�k B�9�Vs-�jt2^278fsi�Jt�-1�At>�( #�.Ess�<~ �%�5IsA,]5iC��&B� v��rB� ��-B��}�-�Gnam�8�&!B��B-`V=)mj<41a$�eB$ 39��>% VatasescuR9�(DissMihaela� B�P}, Ph.D.)=sis���school}{"BO\'{e}�$Tis XI, Laboratoire Aim Co�Y�I,>1 rl P�Oj� , Suh,Y] ?Jeung��&i�f�S�K:m=|�/S.FU4Su.�j�YJ LeU %b2��*G.-BY4-V�&M�S.lCc! ^�20�.� M�1Z,1r�/ 1hN0!.!�RQ9Pj!,4!, van K?!n�<Verhaa� C��+B'<��B��M!B� �zBh)#�=F !M�<EP(6�9�G2�0jBe�Q�;5�, C"j B�A�^�89�!��M�2�29>�2s3n�Gu@GV&�=B $, AmiotA�, Gabban�^Mazzo�^and���G�NresPRA��V� R"86�4 ����B���<BZ�?B{5&�@B -[1�U\IQqj�B &N]�n�6�AM� 0245Nz��&>���>�&A� �, ��O:�]{���B p��jt�= B� ����.����Z 9865F� K j Willne" �l>� #,UQ . �� )���#B� >!�]�V�f���6��N��~�2Z�54VN\#��JND\G�F>� , Drag5� � (urthe~Tolrah*�i�P"��6d 1�& �K *=F����B���;f A��j�B>�La.'���?��2�~�BJ1�!�וC�K�Hj�ZO225JR+ v\!��:�N3��uJOSA�*����2E��j�Opt5RAm. BjP^�108VP..)J�,Luc-Koenig qE!I4{"�I {a}}:T6��2�A8 and *]{Eliane2 ��EB-����jtq*j��n�YB =)!~Y��EurT>^Dj3Z�23V=2�!�"=NDN_ fCN100��,tem{mat-prodeQ Kl\"umpe�..ad�YsD%��Zittar?lJ�@A {\bf 24}, L955 & 1),; Z#B #87fj81"2); EuroUi.Ɏ& I 293&3).�,{FNW} M. Fan�=0B. Nachtergae�mR.F. WerUZ$Comm. Math�� 144}, 44 d^� 10{^3& 89);�, UGen �% L181�$Woo2} W.K.�S�s,�yit{�cemporary�ematicsY:305!899 ��2.ZC'' V.  m+rJ. Kundu)�:t��-�,61}, 052306 ^0.^�, } N.}-enfeld�Lzls�^ph�itFYi�Z�% ren{el�m$T�_\Addison Wesley, New York�^2=7OcosM. O'Con�6aq+6JJ� 3}, �2�1.�ArnM.C.  B S. Boso;V.Vedr�KZ/ E>I�01�WF^ Gunl�W  yck� KendwB:j JkA A� 6A�1nN� Zana�`  rdi)�X. WaCV>�3AB 7947�2CGu�d-_Y4u, H. Li, Y.-Q !pH IS*�n)70QB)l4.l(Osbo} T.J.  rOsRM.&�gb&(o U66!�32110F�Nar1} Ha�rnhof�� �)� D2� 23 �2� Nar2>B�it{High a�eruvRoa�s}, T�U41215.�ZW-Vid��4Zwolak, G. VidAL {\it Mixe Sequngal�Wof5�d m�j-q�hs�_ s}, %�sf{9�501096.�F/VH�[$, V. KorepA��0V. Roychowdhu�pIn�"Is{\bf 9�v227203FLRV�\ L. L�gre�t Ri2_dY)�^�d�*�z�c048F^Vea:LM. Popp�&�n2�� 92a�2��2�Os�ZA.  rlo6.��G!8lc��Rz�&%yit"(�qon)��41a�60 �2� Subr�� ahmanyam2�m�69�(�YR2B� M. A(rtin-Delgad�#V" :" 08720Jn�Rep l Ol 50}/1, 11 �2� Benna�H�jnn�kD.2*s�^5 mk] �6� �e3AI bf{5�� 3824�96.� Woo1�� Hi0k6R �R)�Eobf{78{{022V7);>{ )dJ:8� 224� 8b Rc M!fc 2�C��Y��Y��Y��Y��Y��Y��Y��Y��YNq���p�0n _c  f� B� \}�B�" �� emph&�Wtitle}{ſum {C}�x���{Q}�x{I}*�q�&*(publisher}{f�q}�%"�W0�) J1i*�6!VPWS��7B�UH}, inW6 book-&leeding�c�x37th {S}*.l {F}o3l8 of59er-cipe}.�="&l!�bl ocie&�r6YlC=_� A?)77�p.�:5# bQ&(y%�%�%`D�_B�'S֯B�I�� �N��@&q,�Zf8!�E-!3260 .�.U�0J�"�l%1�JGot��-B2J��n~5b�#7V�v@-Zalka�EzEkIN!�V�B� JZ�e-_ "� 961202NPR~n�AharonovE�Ben-O�/�9a :stoc9~�B�`��B� �҉4twenty-ninth a�pACMm���|)p�li'V�ACM�p6�u7}), pp.�mB176--18� ISBN.dDisbn}{0-89791-888-r�-z"�19BY1!�(fl&6�  Zurek�kX�:prslA��Z1B�a:�V�B�L �!Ё5>�j6W>t �2���r".�lonr45m:*"-�365�gy kill�!��pre�B�&V����8��+rA��+Ste�#B�$ GZ��z,39R�&124 V�9r8 �=�StqHz���*� n�6�RJ�F2jzM �J�R"�i�4: Rei��N�4MZ�B��P025�YCheng��Silbey�c_pra20��BZBY��B� �Z��A�N�523!<&[ ɏ�n  Fowlv�$ ",&� H�p nber?.FHH�]B Y:VDB* )�@L>@.�2\�E*�j: b�423b�n�:i�� �Rh C�v BuS���v n8^r��V��Db��� ���|��FB+ G��R 793��a��st�n�o03��F�.v�F�2�6Ϊ_ett.� >�H #,*��a�2oooY� b�:mn_�� BO t:�V�B� .��zB� ���B 92���^��. �hakr�� n�$HXqufPaz� &� LMP+��B�^��B"M��<B�Pa$TE�� v� ٧ޓ19J�+���� �xť5�� CZ95��B1P��͠ ���3Z 4091R5r�|u�m:�($C��d|�|2���|>�.�|�{�h�, �� "L)WCBB+��*B��:aV;F� ג=B&- �=9=�@B--q�=B�%��;Bx9ْ@B�I �<B�UA�?B�2Eu;� �)�!�ݭ ilosZ�~ Ser. A-�&��Eng|!in�36�(��o��~Ra�r�@ q �q �T�q 2R��-Prog�X"��4�.B�(R�v�Palma���:�!n<omine" EkerMe :pmpe=�G>� `YH%�VpKi�: S �AU��69&VSB� ס�5xY�B~�!jC45Z�[56R�cz Plenio.�7>�","�'�4 Knigh%�PVKR�VB� W9dj�B(&(� B��Z�&3 r��@Jw45^� 7�1N�, ^^fQ!57��z��z��z��z��z��z��z��z��zBaǒ2�5:� #,��A�Cle �&�7rgolulhYcSle�',.}oPeinfurt�I \:�� B= <�(N�\��B%�{D ���-98�CN>�M-l�>B�!��:BeA-Ԓ=JJ�o"��5�> j�H>.MT@�E��Z:34V�jz� K$���V�$ :"`2f�B <���$9#z#��$.4�!�&B*{#f�$2A�UK6�20~�$akurai@ �~wJ�Bx U�< �6�$�$ModernI!um"�sf�1-�1 P�%5�!Wany n#A � 1994JqSastry�$s:�(B�D K �R�Non�Z ar Sۤs: An�W|bil�and<�fS�"$ger-Verlag.� �vIJurdj|�qSusʑ"$728Jur72�B; W�_HNP�)\!�!㕞J��&Di��/EquemsaUb� 1��E�V�31J&;197vWp�� �#!f:�� nM��RWG��icH��'oryf=�L��Aw!J�(~$)j]&Bai�[u_!7} Bai7�}FNJ �n�"�m�5�E� appl��v�2P B�519N�7v�(D'Alessandr�(DahlehŮ1aLDAl��@B�.X%�!�g��E�� �Za�)���#uto�7ntr| ^�H�.xmD86�^2��2:v<?yAl�MHzP2��M�Z�(8J3 2002FJ=�iJ�Khanej&��@:\ #,]xcɜ eGi�] #:��B( <:5VqB� ċ�}ͣ2�.5VPSJ��ae5��� 63:�M�03230J�!wvryf:and Ho�7 :7��A.F�x >�KY���"5uH+ RJt�ied�]a՘��: �n, esti5<[7�c )^7.Hemisp�6� rp�Qion6�yY� 1975rqNiskane"�Ea>�$A+V�5�� Salomaaa':��Aܔ:W@:SV�N3 �C5���T mP:���N)y>^�9.Hynm-19�79&� )���chulte-yprugge�0�!�>�IF0, Spo΁HAja� �� 4:�%T> <�9��qV�B`��;Bx ��:N:�O2. A2�co78[ �&ѣ�� uB�-organiz� }{AIP.�U+v� MakhlinE� ��BP( <:�u�*�c]�A�b#R�24JH 3տnote}J�#0�s5}j� Z��.:3:0 6��/�l#�e; Whaley�%:�c B� ::]V*B;�h��� V:f{%P���8�NKJv|1 2�U$�bZ �(V3� MarsdeJ Rati*�Y ��NI� ?�vTJX �)NRyIhdu@� to&�\ symme�!��i*:,"�CFn~Pbp BWD1YJoach�� (198"�BJ�s=:@��CJ ��^�4�vLonBd �^$tific \& T��calN_8vwVK^ rsypM��9��}]{Li���L�6�^E.�J2j�Is�6:C ;.��tou�in�=*�e �j�Plourd&�'e*6� #, �o����, Wilh��Rob �� Hiz� Linz� "0, ;��� lark/b�#��B!,~B� �M�v�Bђ;��VEN��-=�T�IOU'5t�B:�X!��:B)ܒ<PJQU�B C.-E>�W]ne\5 ��BQ�A�U=um�{n�P^�N 140501(R)F�afro Viol&��G:�!,j�Q �!llR ��B1:��Floy*&%I���o8N�Lf' 8Zy488Jw!h���?6%.�� �hN�n�"b[�mV v�&W�TLidar� Wu��a�� DJ3 ����ZC7v�VC7v�ByrѠd>4�6B.9ְ �8r8^�64�*' "ev8e9z&llEm.RfFv�^R�s�~b~��  �03b8v�Lo�>ha�� Low7��ZF>�JZW4Rocky MountainuOw+jl�J�57R�]7v��( � ow�$��Can�T~��J�7N`�rKrzUzb�� z{V 2p�E� �E LANL�print��!PU�2dOb�Wa�T!�8e� :8��FJ2h >M�R�Fo2kFdi"�,ble manifold�{L}ie �Ss^Kj�.yC8v��&.>>\ #,p�eLeiRL�i,X dX Popk� �Q� ?�x�^' J.~I� .�^�3�EKV MJ� �-�v�DJ %!�>B�Li!U�<B� -���� B�.-�2C� 2 J��mDod2�4>�g , N�Kem�X ThewA�&� JJ�<��MJ> ��@J>�B �@2�~�RJ�)!!U���R".�[403fuv�Jan�n*>�$,�v�"@�ZotaT&��!� Jane��B� j9xjQ�IV�B�5 ВxB�+)�F�)F!fF*N>%{&�N��bCWM@1V!v�*-�� �*.�r-�,5Z� �F� 1~*,�.)0:�&!�Bacon,�o, Burkaj�Ma+DiV�f�,V�B2 ���B�\p�;B�-�.��U0�@H40Z"3Z�`0r� Kat2$>M , Myers�hiscol�S GossE!Lev0AwschE"A*9�UB�9��RJ�#��>A�>GD ��AAJ-�@B�!I�hD�����=�a�F��cn&w2�JJ�12Z�v�H�Mr6�G>` $��a.� �� B�l=��B � %L5h���� � *��b 6232J@�J q.6>y$!2� /!H �(%�4B:��B;�1!�1!�1!~^�| 0205Zv�%`.�.#e6Z/!�!]5�e�B�3�B�`��������r�b�230J�/S(*�$!�j%E�g nach.�>&!�W�0am��ultn�elڿBau��E Dow��Ech��B� {�CJ9��ASJ��>B�-�=SJAB5RC2e�wjaJ%��:5�ɷ@�eZ� f�*� f� � �� 4�&�$}�zb*J� Siew�A�!� �P N>G ;ֲB��ZS ��^ '320�N;vY You.�>� You, Tsaie� Noria�Yo�: J.~Q>_ YoRMnEVV� JJH��� B< �2�U�=�~h^@�-�xLos�&fz6:��EB9����NBn�f�\0F�19z�Et " J�9��FYs 3,s_sQ�=z}]#�t"B� _:�V�Z��(���6 �%�n$5Zp207V�9.n!�jnKa��E���BJ�3<:yU��.3^@ 13Jr,1~� Vrij6a3>T "��Yabol�^it �ni nBa��in,:�jM�B�(Di{V}�}] Y�}Bs6 �:DV�B�2��CBu��:HJ4%1�>Bj21e�>Bk<.rl�BB23Moh ��: )6 A^F���n�62:�� �%V�:0rB�� �!evy�� BZ 9Ou�� L,r�Q9�^s ’ Fri�r.[ >  # , Rugheim�� Savage�`gally�~s�W�u, Joyntŧ Eriksso�� p�� B�% <:�V�B� ��?N� �?J�� uL))�@N[va=`�FB&%�Q����N�9ق�n�^, 121jFv/ Skinn6�>� #, Daven���a���E� E��AJ�1 ?��MJ�B2��V�k����~L bT'8�T' b �6� 3 & �v��,p!� +:99��� R �E� �KJ }:1�I6�IB9^<6V<14z; B��-*� !�j\ Imamogl&�@:$!]" *�.U, Sher�e�Sma�/H�7 B� =y���V���VB��~P>�9%��:� !Y�:B�-�ڏB�-�A r9 ~�b�020J#�A�r; Privman2F2>��$rgnerb�a��ventseV( %�cB� <�S2IJiV �9�L=9q����^�%�r 23Z�14J1~�Platzma`;Dy7�y}]�c;PJ�8^��MJ] �ZE��8N ���P 19Z�Vv�ZhehGuo0 �O�� S.-B>�=�3GJ���Z0��8Z�'239VHv_�@"� �U:� # ��|�Shnirma� $��B�" <:��7�� Q2.^VOF���F�^@$Ny+!nr�Twamle�j� � B <:iN r7:Am� 1JS7Hnp Sal6�>5!��to, En�!�P$?�.% and "� ~ <�2B�::�VFB��d%B� ޒw�c%�c%2RyV e mx:=�i���UxmT6^� #�.<Ms6N?O� de~Sous& 2:�$, Hc1� arm�I>�TBW��X>� H� %�5[ !9v.1SJW �aH>5�ݐr Z�sDZ�:v�51 e� �!���-v�<4jv��=�=rzZ)15533J"�HNc^w1fb^3�b^�b^�b^�b^�b^�b^�b^�b^�b^bwu|03RevMod���8BT1C2��n�� .�Df#7� e��E� 715�J�v�&�" �Z: &�.)/��/]�2\�t{D.~P.} \bibnamefont{DiVincenzo}}, 0info{author}{.f/.}~Bacon�;J>;Kempe�;G>;$Burkard}},�� and}�� K.~B>Whaley:�\journal}{Nature} \textbf%%&(volume}{408:<0pages}{339} (!308year}{2000}). $tem[{\cite�\Sarikaya et~al.}(2003)}]03} =f�M>5U}1#o f)MS:�$ Materials<^2701�F-577R3rLovett66& "x, Reina, Nazir, and Briggs}}] &03PRB�4B>4 c:�VB���;A>w�1K5���F-- !EqA45�,Phys. Rev. Bj�6Z�20531V�z�egg.� 1987A� 87��B6 ;}:�Q�.��Mod. % j59:�M�1F��r�(Weiss}(1999�99��U>(9 � emph���title}{Quantum dissipative systems}a˙�hpublisher}{World Scientific.Daddress}{Singapore6X���})�P' ;�Z73-�bi2�35V�1rRenger��Marcus��2! 02�T> :>�PR>M �6�uQJ. Chem�P116:DmQ999V92r9Xu%5Schultene^4!7 Xu94�a�;B�Xu�7K>7�Z9�)6j�182:@15R�94r3Jones.id�a9>.r~J �Q3n�107V�11346F�2 r�MedintzB� �I>� ;�[ *a fe Z�630��Gilmoree4McKenzie�ke4 04�1B� ;>�m�Z6Dcond-mat/0401444} ��ɍ200v Maha�00�090�� G.~D1.O < �R�0Many-Particletica4R�$Plenum P�t�P��New York%�London.()1990})2 ��Onsager�Q36!! 36�#L>" ;� 6� J. Am�Soc!_^m 5� &� � 14866�136rBottc� (197�73��C>�3._F��?9V� B��62�ompMqnzZ{29V{v� Loffler�z 1997B�#,�reibe"�(Steinhauser�)9�/ B �:V[H>�Sc �?��OBS.�2�.� Mol. Biolr��.� �52J�!�rHsu6�}]�uBHsBP �" &" 19��/ �25N! �� Afsa� Hasted�8�78� M.~N!�."<�JJ� �Z0Infrared�i�^M1�MJ0835F\ 1978v0 orng.25:�!$, Gardeckiz Papazyan,��$Maroncellia�/95�pL�.p<: V� J.~A>>��AB����2���.nV�B�.!4TE�.!� ��9^�7312\?95r�Piter2�1:� ", Falta%�$ van Gun�en!� &�@Bx :��BY�ڦ W.~F>7:�V�0Biophysical Jjf� 8[.4r�20z�{F\"or!x}��65��F 6�jBk.P}, in�6 book�Modern �� istr� � ed byBSF�FCinanogluA RT AcademicT , A N 656 � �em� 3}, pp.y�-�93--137}2� Dip(!c$DipoleNote��n!~ dLs that undergo suffi�Lly fast Brownian rot- !,BE!��e65}, we can use the average value $\expec{\kappa^2}=2/3$. For fixed molecules, however, a different J`may be required. The give�exp� ion for�coupli�!nergy i�,e first term a mult% FanE;Fclose m�@ (such as intra-r]fDin light harvest mplexe4p photosynthesis) higher order�s>�5pHu97J�sA�}.}f��Holde.8:%%a�Johnso�Ho�vanD9�} K.~EN�@�' W.~C>B �@2� y V� P.~S>R��:.�*![�"Bioche�' .�*� Pr�ce-HallN�98r�{V\"olk\ � � V�r:N ����ߊ~5Z� 1862N� z�H:� �;5�LHu, Ritz, Damjanovic�&�]:� �V�X>Hu:V8Bj��:B� �@�� ~�����Z� 3854R�v� Ja�b&?2:� , Jung5�ilb ]02��B�T9[�-V�B��8AE2��iq6VLB�ȅU� :�5F� ��4 Lettnn^\437V/vE Ha*��B�H"��E��urr OpinS Structn�1�[�\OQd#.H ��;Yamazaki"� 20� �;B;<�������5:_A�.tZ�'10�T\212JC �r) Sato.���8B�8>�.� ibidr�b-00Ү%Reynold&- 199 9� <��z�4B�103379& I��r�Muhlba&�Eg2�)�B>> � .� �Z8 u�j�1FD79�>B! rBCarmeli%?ChandlY8j 8��B�) ;�<B�#�Z\��$8Z 45Ju198�Yxend{thebibliography} % \beginB�&z,{ham} D. AhHov, W.lDam, J. |-P, Z. Landau, S. Lloyd�qOl gev,� Adiabatic&� ompu{�DEquivalent to StVrdN0(}, arXiv: q�(-ph�!5098 aK4). ̘tutti} C. H. Bennett, P. G\'acs, M. Li,0M. B. Vitanyi�W5Zurek�4Thermodynamicsj.�$and InformVlDistance}, Proc. 25th ACM Sy:&�H,!�!�a$1993). %���-{b �B�A2�0 Cost of % .j - a r�w}, Inte�.!��etm�{\bf{2905 G� 2��v!� m} A!krthiaume6=A(aplante1T�0 Kolmogorov�lexityN� 0501)�0./0{chaitin1} G.�C j=�<, Randomness \& ! Inco�te}, >�*�7r9� s2ZsOn�LengthA0Pra�ms�)I)�VTFinite Binary Sequence�J.E%�13��547�666�lorenz}A�DD\"ur, L. HartmannE�Hein,aJ.�. egelA�I;,Entanglement� Spin%Fn 0Lattices with1$ g-Range I>ac|"�i�.� 7075u�.�hans}�Eisert>� �8Schmidt measure�a)A tool!O�ify!L*%e�a�&�.A D%Z64!Z022306�1) ayU�gacs}�,�>)6M� Algorith Entrop]� ��� 011046 v2 g.�� gruenwald j r\"u���� zShanno*!��z��vN&307130v)~42holevo�]S.�evo1BoundeSen%�it%�}� Transmit% a -uma�munic��A� nnel��A'oblem�>Mm/ on.,ID� 17e�732�kitaev� Y. K��um ��� s: aQQ� �2(error correel}, Russ.*h. Surv. �52A� 1191�)976��k�N.]/�(Three Appro� s to!_ )4i��ve Def��Qof.ai!9..1zs��res�T�652�lat� I. L  , R. Orusm&[�j�( .Ee  pha�AP0��LAE.�6%�06230i�6�li}&9:�An� rodu%�!6y�b�����Its!flM|�Sp�erJ�nielsene� A. N ,%%� ua�2�uMZvQr]�L}, Cambridge UniversaG� �!6sschumAr}? � QFhcodingeQ.)o5E4�E�aDtadaki_omega} K. T_An Exte�A���'s��Hal�[A� abil�$\OM$!�M�N�� OperAg��InE�e F DimeLal57S3N�407023v1%-� �Nv^ ��:7fn�p�aA},dividual Pura� Aum�yJ�990703�%�9�wehrl�%W ,IZG~bropertie ��!7:5-�T22e�78a�kzk �H. 2x .Z*� q AM�s�q� z4z473{89{R* �v) "scott! C. S  C�!lbeck�0H. Gilhoj, �� D 78}E�4) 194.Ye A��O LZA wY.� ] A 17#< 229B]01}J. Dorignac6�' rno kA 2l%� q93}M� 025504q turbiner1!+ V. T , "�(many-body p�2 ems !�A[ur<oH Lory", hep-th/0108160=8,jFi Co���&!� ��!�88) 467NDVDB}�Debergh% "@an den Bossche, *��= 30!�2� 605TGre �W. WM\" ull%" 5TMechanics-Symmetries",�,-Verlag 1989f FSS}� $Frappat, AA�iarri-�0P. Sorba, Diŧr on Lie Su� lgebras5o9607161g ShKh��^hifma�YA.� !yNw2u3� ) 34.wBD} BrihayAN.1�% prepar� .V�f�00.�ZeiM#er2} A. ,I�M"�9 7�899) S288.� Bertl` (} M. Arndt,Nairz%}Wi&�%`[Un]speakables. From Bell��qI&� , �%e�% fz6f (S@, Berl� ����(tem{Scully1�OA ,A� G. E� WalthA�l435) 1) 111. Laloe} F� lo\"e,�1"h69�$1) 655.9$Fuchs} Ch.��Per>%a�o,Today (March�0) 702H�: R Hz��ilA��2a�25F6Gff!��eE 5N95�o742� OFN@�f!� � ]@ (�R� , , 19986$Cover} T.  �� Thoma�E��]^�,y (Wiley, N4`12< �6V�ъA 1!� 1992) 123.DavydoveuS. ,U���$ (Pergamon� ,"s(�76�N�f4.=%�6�P�P�P�P �KquasiavT~P.~Feynman, %``Simula� �+s W9 Duters,'' Int.\ J.\I�.\e .\ �M 21},�a��82); %%CITATION = IJTPB,21,467;%% S.~��>ce E7o* 1073G96G,DSomaroo, C.~H.~Tse= �~Havelq~Laflam��0D.~G.~Cory, %���ons�G2W�� \�W\: \ �82}, 538�V9�lE orrav J.~I.~Cir�  %Eff�veu.�� �T��ed Ions N|9|20790"� =� i�� ~Gell-Man��M.~Lev!``n�E�Ai1~BelaviigMetastF StZ�2�0al Isotropic .�!� JETPQ� �2E4%�L75) [Pisma Zh.\ Ekspa� eor.\ Fiz5�650ec 75)]:�(JTPLA,22,24%�6��.� S.~ShvartiY�*~Tyupk �Pseudon; Solu�)he.�Equ2 �f�8�:�9�8�V%� Fate�(I.~V.~Frolo5��E��)Fluct �!�I5�E�Dhe Nonlinear Sigma� el!� Nucl�Md154},B7�2d,NUPHA,B154,16dg�} � Novia@a�A!v� %��ainsh`7E�V��Zakit>m�s: ��Non&� ve ��%-  %Chromoc�-�Rep�)��A, 1Il84) [Sov�Fa�.\ -. /7}, 20`$86); FECA 472-5I�86)].6H0PRPLC,116,1036IexactE ~Lur2�!� ocal�rges �IAbs�!��E�P&0I�  %>TL�35!"�|8>�Q35I�� �%�K�Rhlmey � Scat�Ing�� l8 Lump ��2� �>� %Cl�F!3��!�46z� 7,46!�A"'$~ZamolodchA��J%�Fa�� ized S-MaN=�'��' As� E!�6o, Certain %Re�vis.��*i E�Annals6�120A�5�A .�,APNYA,120,25E�A2��P� Wieg���y!�Nonabel�2�Bos�!�w.�}y�\�q3� 1�83>[�)131,12�uJ�6@��� O(3)�V�:�5Ū0�d85); %Gu Hase�9�/M.~Maggi�B F.~N� rmaQ�� �A� Gap2�a�O(4Z���D = 2b824a�5u9B�-8245,522A�&�lv} G� rtin�9$, G.~Paris#,R.~Petronzio%�(Monte Carlo2� For%p>aN� %m6�V�0A�4�781^ 00,4�9(K.~Symanzik�8Continuum Limit%h$Improved A�A�L)�o. 2. O(N=� %�v4Per�� 9� JG22� 2� F��1226,2� Y.~Iwasa;%``Ren�l~A4 Group Analysi��>� AR�  %A�:B��/��ArNR�58�4�a6��58,14e�U.~Wolff%�Asympto��Freedom�i>k !ha:N<��b�33�5� B �334,58�yr5ne} % &T$on E.~Brez�$J.~Zinn-Ju�6�!J�5(~Le Guillou�>�Of�9s=n�(�+(+ Epsilon) "H �m'!\ D��261] ~.�$PHRVA,D14,$a�E���ҳ2��s. %Ap"y To�Heisen�B+ 2��� �3a@6lJ�$RLTA,36,69%�W? BardeenW~W!�� R.~E� roc�$P�T"�!�Aub�2��a��pr�9��J�5�9��S.~Hikam��5�%�� Loop Calc �mhB V��-zA)n11a�m�G2Q$JPAGB,A11,$AQy<�H\Tsvel�� {\em�  f� tdFin 6ensed m  p�} n�u��95��M.~�kiI�Ti�ubensky, �PrinciplZ���6 n 6�� crit� ,phenomena}, �SeMonog -�1�q�2):O IM� 113~ 9�ad*)}�Farhi�~"� i)~Gu�%J�p�AA ndgraN=reda, %A�&*!Ev'&�$�edy_� 8(an NP-� lete� # �Q"eN471! � Chi(a �![J.~Z 8kill, % Robust|' of 5 "�!*#,6�m�= 0123e "�N�f^W =�b!8M� �Ir!%�0)$it5u�/�"*�}*�Bt!.�Lynch(/N� \6uD@ibu"&9$H}, Morgan Kaufman P�S2_Tel94b TelY4YI�&*�".i"�i"�v�eLann77m p77p.`nT(, towards a�'mal a�$R" Inf.A�c{, 77,^@ 155-$yd4Angluin80} D. �85� L�A�global�e� $in networkE� processor!�+of�9 12t4n�!�+osium!� of ix pp 82--93*,. ItaiZNA.  �M�deI �.y break�in�UtQ!Å�f'�., 88(1)!< 60-87. Tani05} S�#ni� Kobayas��!/K�sumotoe51�[ qY�!�%/lea0@�L� !�2W 22nd�:Let��Aspec���e ��(STACS�LNCS V J3404. �0Pal�1S.P. Pal�s K. Singh,�S. Kumar�3�&�(�+�.y* P% us rz,* : faiwunbia�c> ]s }, \G*306196Ji�85�J. , �6 �M.S��onE�5�I!\si.%of29consen�,Xfault�!a }, �,, 32(2IL374-382.N�/01} C..�/�opescu,�0Rohrlich� j mo�AnA.N"hapliyal%�A�{��Ip&a&� <,e�m�*; te pure-s<2�}�h� , A, 63:012302Dur�$W. D{\"u}r� VidA=��&��u� qubitsjDb}d!�two inD1way!_i�2(�Bri�-!YHA �4R. Raussendorf�52Persist�-2�� rray%6in�Hc�� %=cl�+.� (, 86(5):910�E.�(PalamidessiahCA��uTe�a )�#eEve powcD�js�ronou)th�&a. pi-c� us}. -+9�*!., 13(a$pp 685-719�5[=Jv6M#�Pf�fonnQ$�R�G~R.$�Rurl^�url#1{F:tt!O%8{URL I$idecommand"�] }[2]{#2} B!eprint []{S'*%[{2�{�5"�: 1964:�B$^$j�-A�LebowitzlGABLRul.�IVz8B�B^:>7V>P�zD1��%�@ 9��nf^�dU :]�{�*�8"Q;y��8%�N�c13a2Y�p�cB14109>9!{r91+%}Vaidm�X� }]Review}��f�j��2Ea��pfOB�:����L Time�v�Me)<"'.�F�LJJMug?�=F�B ala~Mayat*�f2%'%V�I.`Q {:Egusquiz�DY*�I�' ctT!~!��=�31009r�Ka_r_Br@ ��W�I�58 =f�ii)ci8^VA^iW14V�3rBubA{ �O�E8e@Bub �n Bub}:��.BmD �r*2I/j-56:EM,2�@�@� 1986r2Alber&&i1'6� ",* >i� D'Am� (]{Proto3Box�a D.~Z�.Z a:�V�j��U���BJC�2�:���Z�J�!ur� BellA�6I�ellKS�kJ-%:�;:i��&�.j�3ZNO44Jxe196v�Koche Spec�J9? .*u� Stud. His�A�z}�2^�37����O37�5�N99r�M�1ilEd& c~B�<�>�a5 � >� 307082n� ��p�f~��Yi7@b��:�-�1�]F_K� Pric�NaI ~�B� 7��6�ZYV� 's arrow8 Archimedes' pos6�*� OxfordB$��E�Uqz=��Ak�l�Dsio`~�B� ? z}[ Non-�(it�= Moda <� e�5asQ�F�B�MPlacek~�VMB( Bu�)�f�4Dordrecht: KluQA"�["%I�)�nw16�[74nwFinE�8�¯66��FB.�j�19:Am|45R�8v�Pearl�7 j ~�P>� 8Z��O�Dj��A.� �141�::�197zQvpekkensel�^O#PMT��R�#F[ V��n@7�@J� 0521�;:�200vp Mermi@9� Magic��NN�k P��,j�7ZU 83R�TztbR.F >Hh #*�  w� �MeanKingj�%V� B� ^:V=�� >� D>v��ɕQ}v~�5Z 138V� v� Clift%k�?}]Proof��B�OZ�?m�;j�6Zs44R99v�C�.lk@BK9�%R3{"O {a}}A�#3b�1K(,:�=-�^��w3Z�48Nwm:��b9�~��. ��^Qy199F�>�jaN"A ecToy���q&�4�r��xLo�<z�����_^2336J�5r� Cohe*� AntiABL��B@j>^�*C n�  LJ� 4^��� � M� �Y�� r� 65:&� 3^�v� 'EE�����B' 9��KU�J�p)�n��? � L175N�199vE`K�Vgh� 199�8��M>� =:��Z� L829F*�i�N�% �j�Y1Jn>�#�%}[1]{#w >"urlq�$b�%urlstyle�.&a�>YdoiYdoi: &�P^) &rZg7�l{rm}\Url�$��Ɔ"�"�^�&l$o�#]&h$Y.~-$�H $ 3�#9,. \newblock � saKy/ �m�-um; s7 ?*3.?"iG�3@34\penalty0 (6B):�#--636.-H9and�#�B�#�.L.~��maK�heJ*�*v�C*Vlis-n�mh#.�In!9G. :#E* #)Y�" "�"�pors��>%ai&�J&�#, �$ �"."�L�?02.��� �".p�Y:85) *�%%�2���,gBYH!�S.~ 6.� Curiq*new s U�=a+0edSMj �umV\)Y9� , 5.>1.= 5--7A58.�-F�6~�A*���oma�0"c- p2 R�76mb�50which have be�p both�Ms�/ed%ppost-".tf16y`8+�%26.0��a6)]��N��M.t�[�0!�hidP varitEX�RD �� *� , 38�44�66�u*�"�]�"O"�"H.~.�Q���%� v�.h �N�6��"F�F$��3)]U$7NJE. .n��nR�!���co�4^1y  time-��i"A6 Xu�.fa�El2��<�$�H�145��.�.[*��irk #� � .�& CtgY-box ``�Pdox''.+ �*�, 3.�17."�--4900J�Bm!a7!xS�3~!E !�!.�!��i:9!4[=m59A*�S&U�"=!t4)]p�2~b`&�;0.� Pre-Mp�ox4ar!�eK0A[ extu���m� V�sub]\toK e�6BH8%�2&r( ��G.~.�8{\"U}ber die zu=Jds{\"a}wung du2Q��@me{\ss}proze{/ss}.IIi.�, .�322--328!�5 T&e�=*�:�.z&�!�a�} L�BcF .�Avc2�� n�62abl rule.6%�3 %p2�A8��4:�]"�"�fP#Y*for�@AMAV�8!#x [unsharpEN�`�T2��406166�:�._^���vf�I�Vf�1]ep4�`M.�um�e�^ toy��oryV�uB�b}2�� (1999)]w1#LR� D��6�F7�662]I�r<# , 30&M(3�k$ 373--39��99!�R� �j�V9h{8 DSSWRW&�UE&H.&�U�fA"S"395 �Y$9); MD, B-G�UBQ�U-bf{35[@1K91:KB>R�4�156U 4); .�BD2��2�D39�G9(\�!&Baggoz[�d ,T�A13�?32J9�?ASZJeM.z8$Zubairy, \% Optics*�@ Univ.�As.�928X6 PUncP1} E_Guerra,Tt;mun�2E29�]6q`Rydat}�WA�7 dzig%HB.�mir�i%>it{Red|8ce Data on Atom�h�{ R}&/XPZlf9�*8); T. F. Gallag Xhyd�/ ^ }: BV$86�Orszag)� &V1z1B�206�W EvenOddCS>p)'Garra�7�{P.#[Kn�|0^ �yW5�I348I�7.�{ 9�_L.6G Scr9�T�1 4Y|NS`$D. PhoenixJ�J.�iXc.CYB)rbf{M11I�4GY�Louis+, �j, <it{� %Ri�P.�  RvA��},  X%��4 }.X�dR�z7f�82k0��8��8��8��8��8��8��8��8��8BlochI�Y�I>�9^����[�kj�^�-N����:Y5��a}nsel��>��&PHwlhoff, r5ɚ chel�#haW�<}f�7W>'UHqz@B�&�:lV�#TJ&�c=�2�1~�B)Re-2�"� j�4tm�!�!N� }{49JO'200v��n�!�thvHorod�Z R\�tte?bWeinfurt�^ Wern�3"�`A$a�3} �V�B"���:сBet=�juB�5�yJ�-A�?B5%�~B�.���B�-9Ғ@B�I�2L.�VB']FA�E u!.l*b`: JkBasic �ore�EC��p�YExper�it�v�Em�Jme}{1�0of�em.ɜse.R}"E;FN Fin �Rrn� �/! (Y*�.~ }*�adȜ_c)b��"$-1�J� Mand6�>*#6�7 0!rGrFf, WideO RomF��] 9lC�f�O>� s�tB� ��=Bc ْ<BH/Rom�9~W>\$�{�{�w�y2Z* 93J�4>�#n%j�bkt�3�&W+a鄕J<:v�_V M"Jgjh^7�71J;+�n�Di�T.h2:S " , Wuvize"�BNiu�$dC02�'R.F� ^:VdB�zW�߇ M.~G!Q.Q;R�w5��*�;V�Q>% �ud�<5�5 �0�j�B�zeid}{07F3!_2j�G�rlitz.�3:�'�Gv�Leanhar�iT$o}w, ChikkX, Gupe�InouyeAhitc/5 Ke^3leA# �:B��9�%eV�TBB%�5�֒BA.F׌5 �BB]-A�=AU:�5x�BB�;%��;)��<DJ8PQB5��lB| QKPE �q9�9 }��plF09bsv)( 2n*.^��:�b�t����������¯��9Z"201 uR�3._-AQjR�'&�6~ , Da�lF�#heva�O�� Zonq��.��BW8:�V� A.~J>���> P.~O>>ԒA@j>v�P�B 1K!b�rҷZ7/}0J\4� Kuh2 ># , Alt1lhrader�LDotsenko, Miroshnych 8Rosenfeld, Khud�dx�GomiRaIenbeutZM�� Ied�+B����BVAl��B7��!�wB� 1C�>B�76w�DB�5��?B�.��BV>< E�;B 6Ga�A�a\"cMX*�fr � �<et[.) 2130�F�@�tTreutlei&[: :�%�&5, XK metzF�"�]{td� B�|��B?��@B��?��J��"��>{>� 2�7V�/A�J&LvGL�cTep�{Ch �(Vuleti{\'c}�z c�- Y.-j>,Li�*B���B��a�!u�V a�!,� VnB� �- apAf25R0R�050404R� v�Kr�:퀍ҁ/B�&, Luo�K�c, BruI�, Haase ldermuth,�g4Bar-Joseph, Fo1y �8U�edjA(.��B���B֙Lu��MJ%�wBQ-D�=B�%x�;B�W5��@Gro�RB�Y�{B�IHڢB.x:�ңZG 23320Vqv�All�MEberly}h&�M ~[B9R�"=JJ� ���6�O�%al�Tona%and*hLevel�$fDover #��l�c? Shore���4 �m�ov� N�t:! j-S�VrB�H ��>BJ���^F�e6>�uZ�,\�-"|z�j]�.�`76V�v � ���J � z{BK ;:z�ppl�8n1�^�4Ng<�� Lewe��*� 9: &, Y�m`yeM�ur���lP94�|B� h:&V�B�Yo��B�C���U�12�5�*� n�;5Z*220J�!�ruX���>:�!, 9�%� *�#9�%Qn�.�V��2{ &8 VRB vEurê.�?3Z6VsU~pG�?-T:�udji .�>#:-(, Dupont-RoG Gry"�[/��F� 6���B^�@��B�$�EPRX�,--P��pe ons}. *P"� g� \& �w.�JLYyJ9v`� Tiesb�5�*-:�$3 liam�; Miese� Julih��pt P�fz�E>h9�j�CJ*Wi ��AFJ ��uP.Fs�9E �y6Z� 063416.=)�!�r{ Bold2�>�!, 1�%� 2�bD�wEJ�_��n$E�2�����n�Z&H013^�v�%&.�>!!���!��������ZaL03270 �u�uLv�Rickes.�>? " , Ya+Oteuerwa ,� Q ev2� �Les�[Bg ��sLJz!��AB��@B�1!�>n$� ��2t��j��dJ*t���3:[53V_v(Landau}(193Z ~�LJ�T ;n�0\ Z.\ Sowjetud�jC>G �4J��r�Z�'� ~�B� 7^�roc&� /�f)13Z)H69��Suomin��6�9%�s 9��( K.-A�.6(^֓B��i5uG�^Q*��jF4Z� 37Jl�r)��%7}Z%�!j��E@� 5ZTѣ*�.ɻ= �Rk<�f~7�csetle��0{\parskip}{0pb(vspace*{-15� p; Mohrr4WQM} U ,is.3V$\/} {\bf 6�;72��*�8>aN�MO<864PqJM BCCP6�inF0sc�GRz and is�@"�?&�]$ M Cornelis< (Sri Aurobindo �{�L9·entre?Edu, Pondg4r?<4 ), p.~333J�Stapp6��t. =5N32�17%2NIUCAAJO&v-dSA��110jUClicksJVf�1��GD�� d�c�(I~J Good (H5�� �o6��284=,dEspag} B d' n&�VeileG;�G:�6A��of�Aent-Dayu��N��60 (Addison-Wes�*Rea�D , MA�95. 182=�GHZAMM�:G-rg��M�>n� A&�>� Bell����em&@F�����a 8PU�e}(M Kafatos (i,%�&i��89i7.� *s, P G"��< J L �Vf�B1E�zA�62�EiC} A  L Dial�caAj, L 32H482�N!�von Neu�1Mathe��cal24ofU�MQ�.�-C�1 B�52�Hilge� voord �VJ6�K9�792�Audu� ,!�&n� .բf P��rS�@!�(95), p.~80.��- W H ���*r 5�7��7Z 8.�BlancY8� P ,, D J W Giul�E JoooJ Ki�IIVI-O�Gmat0��:!S?, &H?al =mual6 щs& J,A�J�.����� (, H D Zeh, �:�J Kup"�Dj��xa� Ap�b�%�*1S9F� *���%ŵ2s TreiHq S I<OddU��F�B�9�18.�!Zeh1%�5(� Z�#U(B0�22�825ɻ2A# MsM��>P1O489�J72� Poppo K R �H��N�!�Schism!q�lI&' W~W_+t� (~III (Rowan� Little�n, Totowg� 2&q�eU"�* q.� Harp�eRow6 52&Shimony �Z A%F�P���:�L6 Ca(��+� ��N��j�]a��.,a]{email} El��onic  fQLsongtc@nankai.edu.cn�S4�< suncp@itp.ac.cn�U[b]{www}A0Ft www (q0: http://www.: /\symbol{��VL${q-inf} D.CM&�%�C@Ynne�OK=e".� �0)/r��� ���BhlukinN D. L ,>c^�c4 6v� FleiF schh�~M.ZA *�>5M0bf{84}% , 509k;.-A*�223�2�sun-pI��� . Su�& . Li��XbO LiuI���% 9� 147906�za-stoi�ET�zy��\ico>�Zan` aPF.�6s��� �� &iN6195C206b%�1��!FTaylorE����Zb /@989C� 2068V��9�P Imam��,�Kni8� L. TҚ�P.E&.Em9E%C 0174ر2expE+Po,� et al..MFUwM 2076NM szs}��So܍�han�Q]�TU409120,�ive b��-s��mo+F(for nuclei �Umble b2�u� al Puq^mo��sZ�XB*^;{wlss}v�DjT�M�Z�PF���-7�� Magnon ��Vo2�o�څ��<�a ډa]�%�ar "s,bKYA'6ER Div}�P.��,Bb�,���G. �izK�� ��� k 408, 33.6gQBose}�Q �[�6�Dagotto�R E�TeCRic�ci�Un27a�618�U6. ={Whit � ,�Noack �D�Ralapin� u�I� 8&�8862�UFS.Zaj^P:m P2 P6HMatt1enChr'�dl�� Dat}CgJ.a�hlFi�9� 1879m�6g2Fgf"��l�A. Ekert�� Ka  A��hm`i�11020.G�z1}US�Y�Z��mG)�}�.H8152, � s��t4Zer via� ferr��ic chai�� s�� ally�+i�ed z ^NH�2}�T.�B� n,� C.P.��*���Z�]J�m����in lad�� r�� data bu""���� p�.rgeo��R2f�ą�%�(311052, GeoK�c5n. S��B�Yon2ic Ens�r; Ym 2[5�2*$ 70, 03233�2� MIS}� udio�dane�6A� hias6%ilanjanaQ�A� M��40502�Z�QD�o�-Los� >� 2m*W7}, 1R 98);A�a�N�9(Lo)��39�Y13� 982�LC 2uLs�D6e�22�;4%�D��tis��� @�749��622��.�� }�2j1�1H�;u��F1r1.Ͳ*� Shn} Yu�khgG��h��� hnirJ�i*�73, 3� 2&Shi�~>��Ra�} �d harm� P�xion kl�� J99%�jun��R]��� ge qĒ,dm. >1�: 4),�res2� you2�S. Yi��26>ѥ6Y063815. �X�XH.*�X"M�S�v�X",7��-�� Son'+" �A��R� �f~!c"]ure�>A.B. U'R�]C��i�Shorn,�anasz��I.A� lmsl.I1ep 0936a/20�f �(grangier86}� ��RojA. E�, "�0:��1K�8�_4chou04}C.W.Cho�V. "��]Kuzmi�V+�Ki� qI��:�a�21Z�hong86ECK�� LaX^Q,i�JX5X58!�:�mcKeever�<�d )ait{ }1D6� 30e�99�4<_Hennr�T!H gero-hG� mpe�anɬ40603q�'9brarity|�J.:��� Tap�iE. Jak,O\�i.�S �R�\c4kwiat91}P.G. K O Yia66��58%U�Tlvo~��8A. ѿ FVB��8e�d>2A1��_(alibart04}O�k �� Tanz?0 $. Ostrowsk)2Baln6275.�pitn� 04}T)  P �C!acob�zD·an`N.R 8093.RCl��&J� 2�D 9, 8 6k��;�| !� LaF����G��Milbu�G�"40Q% 46-J; TL�Ral!?A!�E WHunr� 6W%�>3_1"AbT��58MTFit�B.C. J%C�J.VE 3030a3iVFio�uк F.N�Wo��N��7 ͙..�I�5�_Q�)5y�]\"� �33���CWeihsRC.� 81,8��9# Y� roelofs94� �* �CSu��W��ndl� %EBv�ǁ'.�9Q7�49ac4 V��v��[ReY= torSET} R�Knobez�,A.N. Cleland"g�4~# 290�)��aH�&9�Ny�7�/. Nano�E�ErM.Luk� � p e�| 16C9� H� CraigheadF�2�153I`�$X. MingI(.�:m4��]2�forcedet�on��B��agi0��F��Khalili*˥*�}*��F�c �6& �_*�r} ��2�&; � 0238�!2��.�QIP_rQ6R�R. Ge�$2`�v)Rbf}�I?E�U�`_SCPB����rmour�� Blencow_K.�� Schwan� 8` 1483 y656y2� K. Iris�dfJbB �D+ 1553D&F$eedback_co�g!? Hopk��E�.m�B& % d 2353�+6x wilsonraee I. �$Ra�rE����L$\mathrm{\bar{g}}$lu~� 0755�*6�u��?M�B�� � *�9`n25�6a IonTrap_R��D��Win��B_� Res.a�l. ��.Z n�� echn�\lK1 2v*1�B2o= _= _m�l�� Sch\"{o}' .�w*rr&.nqc_brauD ƣ*�%�S�BFn �C\textbf{82}, 1784 (1999). \bibitem{single_spin_detection} D. Rugar DPit{et al.}, Nature �bf{430}, 329 (2004); J.A. Sidles &.@8Rev. Mod. Phys.H67}, 249�52�0optimal_point� VionF\Science 0bf{296}, 886 �2). �8kraus_pra} B. K 9.� ��A bf �042314�3). \end{thebibliography}H \beginB {99}�\interfacing} L. Tian and sZ�Lett. "bf{% 9!�� 4) 247902.�tion_trap_exp} F. Schmidt-KalerVm-�%�c42dL3) 408; D. Leibfried�EC%�C(12; M. Rieb-��Yk429},�734:$D. Barrett (iM��?7.,Wineland2002E`0Kielpinski, CA�nroe,�D. J. 2qy1A�!�2) 709a I. CiracA P. Zoller< �aK04})0) 579.�A�Todayae}�^U*. , March`% 5�4) 38 r� HE�6k7� 1995A91.��superconducting_qubits} Y. Makhlin, GE}\"{o}n)T�0 hnirman, r�"Q73-�1) 357�E!�oij%X(Q .}, B85B�$ 1036; Yu.}PashkiVs :421F20A� 823;%�hiorescuR���U%29Q�3) 1862�Dloss_divincenzo_do!Aaioss`D.AEDiV #,.�Af)�01998) 120; W.!|,van der WielO>9)�!� I! bf{7%@ �2��Hexp_quant_comp_2000eRP.2�$in Fortsch� �C vol 48, special issue on Experimental Proposals for Quantum Computa���[T0), also available at �$-ph/0002072�cpb_mechanical_resonator_schwab} See S:A0,D. Armour, M!� Blencow�#K.�5S:2�6H88MI2) 148302T heinzen_w���� coupaX199%X J. H )%�D��-�eQٿ4��A ) 296�&decoher�O_review%�j�}I8 A8M�N8282� transmisszlinnf}!dJ�Zggett2CBVx (1984E�@8; S.~Chakravarty%A.~��^E�U1986) A�.�LNielsen_Chuang_book}!�A. o)tI.� %, \emph{M� ]��  InformaA�AlCambridge University Press, �2 �adi 40366tGirvin_Schoelkopf} A. WallraffVP> 3�@��62; S.a�ZVB, �31067e�NL �fL 10}*��aar:isl} S.~Aaronson. \newblock Is   um m��W  isA`�,theoryspace?.9n�O�Khrennikov, editor, {\em Proceedings ofE V\"{a}xj�  Conf�U ``� Tn,: Reconsider� of Founds''004.���401062� !advbLimit \kK$um advice �[0one-way commu ��.� �C���Ŷ2�$To appear..��on!tQ�!F. IEEEPlex� �@}, pp. 320-332. � � 2095.-�thesisb�%sh ffiAtyO �the�  World}.PhD# sis,.�Xof California, BerkeleyF%z �12143>�plf�Lower bA' local se� by ]!�rguC s.�In))t`ACM STOC}, pages 465--474F�4ECCC TR03-057, e�307142�al�m ~S. Abramajd� ��.�Non ar O2�limplies polynomial-time soluA�, for {NP}-w letI�8{\#}{P} problem2�%�� " �]0,1:3992--3995� 8.�5�9801042� ,adh} L.~Adle�( J.~DeMarraAaUM.-D. HR .V� � utability.!� SIAM��ij�<26(5):1524--1540�2� aks�e<~Agrawal, N.~Kay � N.~Saxena2m$PRIMES} isa{P2��www.cse.iitk.ac.in/users/manindra/prima�p� 6�nEAh��ov�T.~Naveh.�1!�$ - a surve25�0210077E�6mrFmO.~Regev.m Latt��Q*� NP} �sect co.56A�� FOCSuB36AG71�4.�,beigel} R.~B .WPercept��, {PP}O ��y hiera�2E'I��al�G0}, 4:339--349E*6�rs�E)Rei� A,$D.~Spielma6PPE* closed un^57i6~�J��. SSciA�450(2):191--202�2�bv} E!1rnste�(U.~Vazirani.DQ=aQ �!@orF.bU 411--1473�7.^First��e4�> 1992�pcfs} C.~M. Caves, C.~A. Fuchs)�R�ack.cUnknownI�$um states:�Hde {F}inetti repres'^tMatoA 85(9):4537--4559E�2.�y^104088.�deu� :deceaD .?1�O �a]��EQ deci�J�(roc. Roy. S Londo,A455:312A�137%�9.v�9906015.�0fghp} S.~Fenn�F.~Greep ~HomA�R.~Pruim.Y4Determining aca�ampossi���� a �umE{"Gs hard $��z953��66n8120562(ortnow:blogŰ�now.�{My�: �2H Web Log2 TWednesday, October 30,� 2 entry.�gcom/l!=/e�og2�r.�%�J.~Roger2'��m�l.� y2] �2�� JZ�9��240--25��9.<,cs.CC/9811022� gill"p J.~Gil2�uProI�$stic {T}urAMMachine �B �&e�2m�t 1972.e�}N�qal%B-dofy�6�m �.(�FY6:675--6X 6{gisin} N!<si2�8Weinberg's non-b' a� luminal �&� F�� � A}, 143:�~eP�)gleason��G .�MeasureL a�� subsJf a {H}ilD .A%5J)�� Mech�� 6:885--89Ň52� hht�@~Han, L.~Hemaspaa� �[ T.~T)uf.k Threshold!!q%%@crypt�ic secur�� 1):59--78%?6� ardye�H .�:'(from five r%r�xio6� ��012�j2�kw} I.~Kqidii_ R.~de Wol2Exponentxl&S �� 2-queryZ ly��od�0codes via a �*j .�6( +"' 106--115�&�� 20806�kitaev:� A.~K.u1X�$: algorith� $error corr�.@E� Russ�;S� (s}, 52(6):1� iF�li%�L2� TOne Coun. Func�s��hicagos3.�At� .uc $H.edu/files/tr\_auth!�0c/TR-93-12.ps.pol��ski�P.g6�r�the�E}i� h-{P}odolsky-{R}osen paradox.b%'��2�66:39� 0� 2}r� } N� On l� s, lear� withI$s, random �EۅB�D�2� SubmittedE�2K r8 �E .� UndiAted {ST�nnA��{ log-B!.�shi:g Y.~Sh2� Both�coffolco�lled-{NOT} need little help to do u��@e�6� .�%�qi*��K�L"#�84--9��Zj 20516� hastadE�H\aa .�Some ##( inapproximh resul6��J.�� 8:798--8 2Utd#~M�rha1D.~2�.�Adapt��J:�Hstant-depth circuit��` {A}rthur-{M}erlin gameF��q4(M34�[2��-!s32;watrous%tW .�Succinct Dum of�propert�4of finite grou�i��I2{F:� 54�000.}� 00090AD "�4zurek} W.~H. Z .7Environ-�sa{invari� , causa�e��� �in��physic2ERJ�9 2�=y110�#N� �f�?%%�EPR}A.~E�f)~P�h �NC s� �tx##777{&3{&Y�oe�er35}E� r\"o �# wiss&�2�80JNQI}For P( � ngle!��4q;! um i&! see2Ya��B#4Usp. Fiz. Nauk� 169}% , 5 }99) [ �1�f435�99)];:^i&[' % ProgresOpt� ed. E.~G ,6W1+1).9DA� } G.~ */99071e�b�(SymmE�'(V.~Bu\u zek%M.~�ery?�v.*� 6�022303�4>WJ"-~Ricci,� Sciarrino�Sia��F�~Martin� t. 1M9xo' �4);<W:J� �=041022��1 UCM}.-=� 54� 84�)6.�UCMopt}aGf h~Massar2X6�7�$ 2153E207); D.~Bruss *2<&j"�$ 236888)/( 8,� Ekerti� (acchiavello2P6�8b 2598�!98:� netw22�Lvau� �#YL!��2v�6}, 3446��2�.�NP.pKnight,�$r�"�%4U521T>�d2�V.fi�& U�% 5003Rd%� R.~F.~WerK��182��!� MG y��6A"� Jq 40}, 328 �t,.�e�%�#,~Lamas-Linar� C.~Simon:C�we� andEtouwmeest�B�'�+712�2)�&~T�~IrvineEu:q M.~J�~de~DoodI�A.k �!r 6�y� v4.�$AsymmCloneeq0J.~Cerf, Acta S Slov9�4%y1��8); 6�>a� 4497�0);a�7� Mod.��i��182.��22�F6� dnik��77M�� -S.~Ni()C$.~Griffithb�8}, 43�92, QID}��:�2�a�Z>Y�6�05231�>2�U- 2U.Qa6=�ca262�G9)ޥ�BS�pC*2�6o�! 432�66UNOTmV:p2�F���aVer��Na�/(j)��1��8A�^#].BGt96a}a�H� nnetz!l20�P2�Jozsa94}!PJosza�N��3�1992u Perfmt W.~K� oterc H.~ � e��+8a�19860��Covar ^G�ZD'AA o!L��o~�'t63]a�<008e�1); V�rimipou�/A��Rezakha:L 6}, 05211{2�1�b���382J: Horodecki@ �%.m . �1�<>�m20E12� Fivel�% ~I.~ j�. 8� 2� !� kill�'%� M�it�)2l a*1�ce note� �ics 2�0&�!0 Institute of&ogye� 8) (2�,http://.caltech�\~{} ��/ph229/2uB846�; G�� d,� <*�$d InternP�"�$on�e Syste#SigKNPssing, Bangalore, Ind�"175 (b,2G(82���Rev� ,�Ribordy,a�TPl�a� bind� A?RZ,AD145eL2ContConjm�!�Y(Iblisdi6� }XU 0323G 206 Esteem1d��Derka,6ca�.� A0R; 8� 1571��YW��Conc}!��j P22!�/P6s>eR� nF�\301� F0life} Here weOsi��`� al�!8dead cat as dif�&t*i8 0a very� lica�butGsE� . We�not disc� �]lema}biologi %� desk,l&. frameworkwvm�V�5� b�530*�5RAPNS1K! Acharya%P�,rayana Swamy�+J A:M�Gen.}"+ 27}!�(4) 7247-726O#earlier��/nna��� yrhei",Nuovo CJ1o}�  B 57}E� 77);ae�az�A�}�&64}���-93�  Arov ~F"5lczekHNuc �DB 251G85)117X F��L/8Geometric phase���;4apA���.y�'' tific�,89) Singapor}1GFrappat� �}�y!itt2�369�96) 31.� Frau�%Vu:Sp�!inDrXiv:hep-th/9407162ACh� � ved�/rinivas )9� ica 5�A 246}�n7), 576}�Lerda�  �Anyon�A� 2)Sp� B�;.� xFra�al!-ti/I�M SJ�.%��55�90V�e`2�` �}_�a` 537}��69$527-2536; -C�< 6605=NBiedenEO har"0V� A 22EAA�4L873; A. Macfa�.a��;2*4581;.Y �Y �Int.J.� A .n B 10n 96) 683, e<re��ces� ��AL��A. Lavag"�  NR� s�>�E 61}�5 1218>`2I��`5 `2) 0361�u��#G �W.Q��v �64��0�95; O.W. n=D: D 43<01) 4111; R. N�hapatrue {v.=B 242>0) 40&��e�Sciuto} �!ġ� q� NuclIZ40�w93), 613�65�92Ext�  H. 1)q-Hyperg��f�� ap�i�8�78f} G.R.M�)bb�,$ Piovella,��Ferraro,�K5q�W.���2� -6� 041403(R)Ez2Vuletic�6[hX $A.T. Black%hV. &2a�� �!g 0630�2�He!Hich} B�Hgorny, Th. Els\"ass�AA. -bk� 15Vk0FEL} see e.g.:;F�,sagrande� Cerchioy]� Souza!k Pien �8N1�,Rivista del 2o )1� No. �C0)%FrwKurucza_L. v B. B@Atomic Line Data,%CD-ROMn23�b;, �.: Smton�$Astro�,al Laborator�2S convB$onalFWM�Wa�yd &�2O-�9�� (Acade��s&.I�3).*�D�Y -MIT�}Q7atelli� �A���R���W>8M$^{\rm c}$Neil!?2bLaAg�RM�1�188e2a�N�� v!"�Ou92} Z.��u�AsPa  H9Kimbl2??Pekpit{ �P e`}" D:366��|$Furusawa98n W,L. S{\o }ren S.B**C. &�/F�E.4 Polz� it{�&�28!Q70�l��S * horn� Ch9G0ekKp m, O�ib� K{Q8D}nig, N. Korolkova9G�x^0�B>  bf{8�426 �R�2}B��y5��@16�FUi{G�9 l03}�Gl �cklE@Lorenz�� Marquardt%�He=?n� BrownnuA@C6X Q. P��P.C Looc>J =J)16�A9GE�01231I���Konig!D�; �!�a� A. ZielonJ7�izmann,)-fu!� 0138"�.uCarter87" EU(D. Drummond��Iei�(R. M. Shelb�x6�i�) bf{5�84�872�f87}2&w�S2�jJ�(Soc. Am. B} �#� 56":kLai89a ( La H�E$Haus, {\it��EA*��84� 89); oit{ibid}��85'.l}b�}^V�CYR��}�]��#292%+9^Y�FribergER�eZMachidaE?( � evan�A�T. MukaiR�: 7m37"1r.8(RK-fbg} R.-��e�9 �R\�� 21801.� ��Ct�F���J�4Kn{\" o}� D�Y lsch�Zu�m� oi��}�N~:�nH38� 6�Lai95IQ�S YuRZ�5� 81�!�B�99}n�� D.-G�F�A}� 5$ 244&qnRO'bluh}� se _R�C�?��\$6�Yu�. X)}�hE� Ippe� �Opt�2�2�)66��6dI�97�U�^S) m,R�:�7!.414�6 Z�rov}V:' iA.� Shabat��S"i� JETP��3�6%�76� �62�R�.QO25B�4Yeang99}C.-P.  , %"�+&#a�-or0soliton based\aY.iz|:9�,"��n�1!�12!�1�(.�b9(i� -oc}r�]�uE2C�@�1%�6� 6�s-l5 @!��b%�M. Islam!(&Ar1;�7A{-V� -F.�tL117%�86�su;Pe-� } V. I. G! tsveig�GS. Kivsh�'A�� Kosevi���!5�; rkin�N"�? _+|crystals.�nt��Engng�=H&27:�!8��y����5�n�\8Z 6��c3�cynM1��4ͩ� V�f� 02�Dn%G}!��2 raj16EN�3155396�fi3E� ,�!.\&2!�ilos.\B 1f`25�6�Kullback  �!"�L���*s"s (V , 1959�.iUdoeb} H!K Doeby*G� Gold�KW�tb=� � �ys�49�:hDubd. Auber�MP.� �Xi�^U3!tI& 82�hooftW 't H , "('aln�M Chir�ym��>(Spontaneous U)$etry BreakD#"m4Recent Develop0�aGaugeXGia4GI��,eds., Plenum&J782�: raj4A5Y�� in3!g�/�K R�f�6wI�,io98a} M.~B.� V. VedrtD�G temp i�3:  43�%6" Eisert03a� E2.f, ф�Glf ]1 479x��"5$' t96b�AHUnMA,}$JjB P�)A�B.�LumachA[�~�� A ��(�(�8�(}Lo97aB~� 4S.e.R P�* 022301 46� �Pen9M�, ^38� 436 �Q*�VidalLG,Od!��� � G1�)�6HJISha �$O %F6�r_455� ^^b}�^356RDur00bU5 D3u}r"%�J.~�W2h1�� 06.Z%�6�Ver;ete02a}�",Dehae B.~D�#qLA�HaUrschel�== { 6O�,112 }61 Miyakee\ R�g �108 H6I�LF �tr�6��.�B� J l3 NmBq+diE. e~�uqur~Y. Thib�:���306122.�)04 # �:DJ��� 0121q�RySOwariYM.  ,�Matsum"*SM\ra����Uik7� 050��".��SPlJ.�.(W1!�M+ ��!8&V b3A339"S,��s�-A- 2,�� 1413��-9",LM. \,�i`R6 % k �2q7 1A-B�M͙.^P2!Nl. q� f) 5239 q8).��9IC 2790%3�Y.�(Ishizaka04bk&^�9�F 1905V� BoydE�S��S L. Vp�#he�e�Y nvex;m+} RW Bh 2�NegatI>F2�Y� %n���5N,1ab\ mS(.rEPotsd�February�1);z�MM ~F. �2<M���3�!�6�/^EG2`W.�� �`)�M�we�6R� � 544�[:B,ote_for_PPT_�<�s} Th Ns analog� to , fact that e�+separC? can be �O�:ed|@ smal}`�+nonzero� x<y�PLOCC (is�E ported byk� �i�Qwn). How�, while� clas�,:�_f*tly w�,a� 9X,�4\protect{\cite"E 9}}, itHa7Rtrigu�Gop�A�P whether �PPT&-nBr��#�su=E R2U< , or*-.�� 9B� >�?�:~lN�~E�� P.~W�or,A�!mo�<�O�3 �.W0]�ma 1070J9 ��9c} &��.l��� 1056��6L Dur� 2e2 iT�Q:�."�35��5fRB-1 � 6/ )_�=pJI��0� 2�0�� ShorF =��U� A.~VL apli6Rj�90�U10�X�\6$ M���_*VY��352 U6�� �l2aZH� 23040RK,Kaszlikowski� D. .9~C. Kw�.J�-w!#C. h.~O6�#1��5� 2309 �6�Seno!wQU. YM�A �RB\ � 6[%6� W. ^ Ph�&�^83N u�E7�(6>�F[ xpen�0.� 9112��} W.�B�6bV��020 a�B+AugusiakpRZ %&6b�405182�JWe� TI!S� Altepe�<P �ba�>W.bMun�&�)� � 2232M�6��b /�� 11142� ��unt!�_�QT} When $N\!=\!2$ ($AB$�%$N'4CDEF$), �c�example, both $(\Omega^{\Gamma_{AC}})(V}\!\ge\!0$�_ F0Bb0ens�j�Iund�+ll�F�HreKdt�$A$, $B$* 4$C$. Likewise,�BDBEBF$ is �d.\ Kentk A.  2��/f5 283�1�.FuXŐ�" � IK z< 1888,Jf5�.�D_m�N}�> $E_CC&PPT}$e $E_D.bc .E cost- 5�le6"byS-&� . The K,s&}4of $|\phi^+\ra/E(^{\otimes n2�4(\sigma)} \!\r�Aarrow\! 7Ay.! ja�a$� ta pTle by PP.�b0an asymptotic�RI�h[e, a weakly ad"(vicq-g -�< ($E$) monotonicA�er:= sm3f{H6��mmE>N�$ (0*�f>� U�00a}})e.�rel� %�ropD. 2>�!7�s� an�F!� such1 s. Moreovr� !ЁI2$, 6�1�:E�)M�(|\psiMo)��666!$ ��a bip2F te p���. As a��ult� iaN6Gh EJ\F7$,�>IS� >WFS�

^2z (}{80}p^2_F B5 8 �" X/! &��:T.8af��c�> BO.:�}���ur&� a^��,ta%�l�Y; nyF@!@figY , we�8e9�in��)bvs ] 2�N� � On� aa��s�L 1�I��8 1�."� �A> (�� �  $U0.0055\ $0.0328G ^2$ "�ca?(di�� !>1) Muɡ��-�st�.�!{I"�aP�4q�%�very sR7��|> a���*%j k fer��k,�� �K up���9Ŕ�� . A_!6 ] )�M� ��2� � �+y�X��C� 2�  L*�J/psi"��M�e}[ht] .� �� rcut2var֋ :>,� &� 5.7iV� 2�&"� �*1�D (top panel), norm_1� as (2nd)Aq��vivalA��p�#(3r'��Q�y����:, M�(bottom pasus�"�Kb0 ��D0 $Xr# b1  2 $= *; �:; :8�� l!Fm�ain��D (2) �Nag,B/>_ $J/ �$ $&��� !:U9Xa�v>�ve.)a�ll!T/ ies |%V�so' z��� �2�!t�!.> �$*=d6for&<��)M C real�"]bjJ:Bg��# arbitrar��  Vt%fa#a2�.���en�  b*�c%.x lon�E X"E�a�� �a�&AHe0(s�e �82)G!�%�of�016Rremains�,���;3�;2v�]%�5�5M� .EPS��(sig-mtvsA.p�.ʼVm $s (circles����aoe�Mr&<= (�Ys). &�!��&�$n�0i. Fu[ymbol�8f� o DkX� d�'�leQn B/p &�!>:���)�%vr5 �eea9] happe� e�tXf� �E&u^i�� o�some < ˡR�� Dt� $qrt{s}=200� $�)e�>%f$JPCIAE cod� ich �Ls Pytht6�g��ORof el�����Y�.�% s$L�!�us- .N6�$pv AuAu. YnA#Yg �>a��$dI �2� ��bor"�f� (impa�� b=0fm).AY� �BN  A�su,A�]�"�o.�� A�anc6 �=� �W�nva4t�(s$D'9 u�p$Eslfg�N�E�*9] ��Qyͭ��le}�, �A�Mind,�H[&E�h�[ ach��0�!A;R�?-l'oa\Z� 2� s�6prough�!!O�t�#2��Y=��=�e�6 ierr xige� In�[�N%e4 �( "{m�-�e�"�" noB� �k!Q"�.us� izA8� sa� Au+Au{� p+p ȉ�] E" beam� sh��� � � �M�1�occurd� Z ,�.y,(�7�I$s8J weM/Ac&���nq a %)Z��3� ly��c% �F���be!gRHIC 2��Fvg"K��g�|*AJ" (3)�I ���^�,��%�n'W: !���� a�. �"sm2��5�i� ^� -qA�s�F�be B'slRDv��3*|1u�th���6i!�at!�'�AL\ �4�+Inda �b�za�%�r=y.b� %c�-"z,:�KB ��cn ��, fyw5�2�^!�&��>��clA.�ߥ-��9, )��5 iu!� Lookaщ�� ��-�#�P seem�at 9HA0o�Qh�Y-�6ls��)m+dV�+AE�� "��n��=-, V)5"`6?��z�?�z �er���idAy�or? sf. i!1��)gus �i�.<9A�.�41I� !e,!��nB _b�*g�7d�"�3":2�0A�e��.� M(�ychbe0�e�Or��Qm��abu�5�.��e!��j��ontext,N�.fuUstx2Tm+,� H�"c4SqH}).co�q,)W�*�c�8&Aa >�0+&�)*p~ �c 0/aB^�6�_B�66� !�e6�U &W)���!A�6nb�����:�!jo�� bloca� , ne�+� A���>�,a�en3c�� ��m,!��qa5body �C�"m/.m#7 �4;!�Av!~�D"L ��A~* � v7 zO!N, �q�&o�P�%��uCM� &��J"��of�Z1�'�'!eQ6�@ >���W�qj�..i�Gatm inspir��-��l�>u,Uq! �FedŨBt8��*O }"~2&RqahdeE�a"&V � �oix�e& agp��!*U ���1� ��*�9� F{8� ̈́�~p R���n�5F%2� ���<�d .X %� I"a�6<:� G� �2� be�Ai� I��8B�� s8p2� _be ��e�(�`�i %e�]�@�B ifM"HJ�If�oA�ct� VA��(�+ "�$ S�sD6���L12�ɣ�ith6q>�M%be� ��by6�:�/�l B+sel:orxa%�,=aKgy,a�ncea�- �,6d%��#4$<v3��!��2�;pheral&�:�G vskip 0.7%A�IHer /bf Ac�7�L%�_C)$W� ank�Gf�D RappzZ�J�pr-B.H.Sa-m�Gg �E�"�*: to u� �>�J{9�^1J�* C.~Y.~W�F�G.~<QHigh-�H"p=C"p=}, �G SfM tific Co..�GL1994; L.~P.~CsernaiFnu.eHZp John WilQ nd SoK,$New York, n*�G:; T.Matsu�E!UtzCFL&=F 178B},416�F(. R.C.~HwaOGFa=},W�Hv�0�Z S." C%�A.B�B, �H�F/,C70}, 024905�JS+4} A.~E E.OJ62F52202(R)I0.Ihpapa} M.~Papa,T.~Maruyama,.ZB.I64}�612T1.T�46�a g�or �Suppl�G$154},261(2L ; S.KimurF&�!%)�N5= . %\Q�$bon99} %.� :2!`652�1999);4Nucl. -%�$A681}, 64c�(Fmmaru00n=;%� T.~HA�daN}T2201(R)�!��moselVVe�?T.~Bir�G U.~M#N�H5�598�85); %S.Loh, T.AH=�M.Thom�)W� B387},685H6.HC.Gm^erZKJD19},321K7 K~�C.~ M��%�2�4�a23�7)/r�e��in.  repo%F2 F.~Gulisll�J!Olitor�= zO %% 243},�\4); G.~Bertsch, S.~Dasg\N,A@=:1Af18AK8��land1�4E.~M.~Lifshitz% �Q(Pitaevskii,�it�|1Ki Fs}�Serg�' Pa%�'1.{=�S�p },! �O$9905025, % 9Vlasov:f Dense RM�6@8036, %%�>��99).�0morpurgo} % RA�  ���ziXallL !� dell�B }, ZanichA础esA87.ltoshikik T.~ R�� S.~Chiba 2�O1L ��M91-192bA�2` L.~L�Y,E]��RU�a�QE�}, Q�,��Q� 80. &.Nsa}; [STai�O WangE�F.H.�O�@e�$ C59},2728-�; � f��34904�4�� >� >MK�%\�KO7�M,,nofootinbib&M :X]M�oMZW % kEE(s�|�$u��)`�3 #>��aps�n',draftr-�iaE< Review B 2FM�i��M­M*/Nlongt�+}2��txsym}E�"EVtstyle{apsrev} %\renewcommand{�o"�8${\arabic{s? }.#�L6A�/�V ii}{a1�,{APS/123-QED�H.wg}[1]{{�n}\sp{#1�02$c:%bJ%ket&|\r�0} 2Hbra#\l *|:$inp}[2]$#[{#2>�ubexv,{\?�3 v�\�R5aF6�f6p�.kpk:��JB.JZ.axialvc�A-�V�*j *j*A%:�^ -V-F *JXV-:X�ial� {\bm%�Z��)<g 1 2}>cf�rf!�>:�mm^ } NB:rop RBde8:v>!e)�*Jf!TA�>*�R rix}{\hat�sS}}NS��)4} % \title{Chi�~S #�ud $Nb�s 1440�?a�< N\pi�;Decaya��Q$H. Kamano}�/xQ{kd@ocunp.hep.osaka-cu.ac.jp}"�Q M. M4 hitE\ ?mita�A Arim=ar:2�QDe�ofa �\O� C+]Unil ity, <558-8585, Japan ! �<{\tod))ya"�MD"�_d!_$�by �rC c)��d- �%ula\+  suggestG%Sd -iso N-�J�tac�2�K�&� bsen� r ���44Hern{\'a}ndez �~. �pBV�*�8i(`�C, ; isX�6_ �I tane�! �p�!"$ga�RM�Mq6$Q�d  N&?�t+�I&�K.� 9� %\tV{�O,Jh, 14.20.Gk�$keywords{S)wed }%U�AhowkeysoD�p��f' .�SF%���.VP% "����1}� E- }%:\�eect 3I)��Yet ���$'of:s�#ra,�R�L on6&F��;]F� n as8�rI&s�DobDKA3"W�!� naivVNICig�@al�5i 1�Wb�`A��+kC`s�rb��zs%�2 omes�"K �.atY�"apre ^"��~m(Is�P%!= conn8 'sproblem�r�,�im4;c�i��m�-Z �Wd �6lexaX;m�algebra �Bea02})�penta� (two-di A�c.))O ?Jaf03}ev!v czj�xe� * Wei0�M�b�ho��st.L�!'��qW"'\!�B $kE�Be�B!�����s�V��60 �>�!�"AK!H��:�Q��6!�p��,�"!��+ �1-pOse85,Ber95,Jen97,Gom96,Alv98)V5+�5@ ?Hir�`6thresh�YWse�0atoA�J]\&�D N(��)�� I=0}�S\ {-wave}}Ev cay,d!��!>9g΍��a �s`c" nRwo !s E�fit{S}jEm�epin�a��1�cEe$��em7d by Man�et~al.-- Man9A� �G Data T (PDG04}�����i& �iR� �5 nelsv �  aT$N�=��$ 6�B��%[�D%7AE# e�D!ya�!F ofMsp.� $!:H�>1`$l�V'�cri�L!�������co&͈-?r�"�|C$\�9 au��� $ %\pJEQ�FR�2�S%�%J��ˈ>a~a��Her02}!'5ࡢ6�re%s�Ti)7 liciK#ct=de�IUIb�e�Pinz9 �� instead!/)��$A>p�->/inm#'GI�!S���no*��X�  . Ds,Ak&� ~i|."i�rx``Arj�''� emplo�9t�&yfix!�*� �rB�!��<G <reO1#e2ral��X'''�!i2� 6�U�.kir��!2&ll�6 E�!�i�x!!�%Bs�UoN�, .$�E�io a��d}B*v$Lagrangian(�L�" = 6 �4�pdag*N  b{R}a� sp{a $, eFY�R��itude,!-[-:� e�$ neem@tjl?0�YOalE� ; $|:�sp{�}/F(expt}|=0.42�AThe`]�Cx2at��A����{&n �+�$H3�Li@Z� UMO\2� !��gum#p1R� � 8GJ�prMqRhakB8 fD� �ts� a> � exp�_�yhem�',&� A�_t�!�": Q� % AP�),F�t�GTs !&of��F�P#�/lul � ex� s*�io�!cP whe���.�X(pri�>ref"�[k FE"pur.9B�[�["� s� �mis�/-Mp� re/ �dev�m�%(y Yamagish<Zahed�Yam n, p�ful0�)�r� o�zi Ward>M ty rM,��E#�� ��sc�u���K �U��Qolv��� EW�Hn�`cus ��5l6F_�in�U s e�� ly f�YAn~:%�pec"e鹹��a�apweR�.p z����N��5� Fy6k���^!�Ck)HC� al�,�Afin��a!�la.� 9:�Ae� !g�\�iX/v8�� 5E�"Ref� &� We b�N��X!�%�!�BHHH,�2influ�m�v�2�!��c�Q&1 aA�ts��origin:Ż�u"I~exP 1�qo bre�%"_�su�?�*!M7 limi&qP.A1!�meK+tl4� T t��է%!�pRef�d-� �W;N�Q(�+��+�ᡍintui��4�&65-��G �Z/OFG�:ar�cuBA��U� 0"0H2�. %if�4cD1z1�A(%Tj0w"*6n�-�>s��� aA]�9�+�.-as �����eT� d hoc�"�to /� 9s1��>p��A�organ6aT�XH ,In Sec.~\ref2��eE�g RkA��o��Ka�" ef rhofA�6J� iQL���a��:�!�N՚(�)�t"�:H� vF� nb �d��a��`�+Z a�dK�`:�` Nci:�[% �1�&�1� i5>7�1 "Y�Wsec2}A�o6"� �� � fbegin" +]bf{A. G>0eu�+!]h+M K�7}F1��Ecm]$1O&�E  %:  ��Al�$p�R}$Ƈ N}$)a�A��� �.&�=�(Ueo�/dk<1},2� $a,bo�:N>(��6ev! s. "�X fig1-71$%8% U� Y͛r>� �N� h.�i8�F $i�T�s (��������K� 65��쪠)�M"� � = !yS}+2V: AA}.qeq1QXA�Ea1G��V�yO�Ai�by1f� � = -i�mp�2j����$ab"ra{N(M�)}%� }(0)� *�(R})},�2M%6�v�V� ����� 2}}(E�1}-2}� \mu}:�abcJ�< {c}5��3��AA}= +���1_!�2 nu�it d� 4}xei#1}xF� T!\ast}(q!{a �x)b}{](0)) ��4R�w� $.��5Z }�]e\�x"�I��a� 1 j>t5^�W^+ $�T�Wone��Y ed a�"L�YbWB9�c"hC�o]� "� �^ry6X�� �"D7 $(2^�!�4}5" (4)}q-eNM�]�$���UerM|o~b  �Iޗ�;"G�Tm�$" ozb ��n < vanishVd  $�6���!0+!���S�qn�7E vg�K>�O>� ' ��6�!�2,AA!-ls���9��F��I.!r�Dto-�5� 1G"8)�_ !��U"� I�ca"f)�"�sM E� e step*c�v�&�, � � �5B^!sz2��,6/V}$A�E��"� � vBp^��r�) ��� c� �P$~&�� we ��� ��ay�!�z)���!*B�C�� f�L�k have~��e��F�%�s i�]v�AA��C.�5RCv�S}= i�Cab}�A\r�RN}(s �})}.[ \PhiN�� R� F R.�6ʻ5] �$�H���\p� 2}) �F�AA����4�%.6� ��.S=�+��: ��he�.�$ �Nqem�}p�$1�N}$ [R}$] !$1� 5�$]�y� 0! J? @g�  [ ],�"[��>��C%`aT�R -�$��e�� � l���non�F�"�xWeu!�ake�%���g��"q��.q!GN5�}�y �n�!B{$͙'Z$V�$���;�:l"Gy�s 2�noU%�v���0�l %�� CBn*ksofBS  al.} %!v��� t�fj�QB��u8u2:u%!�""Z)�� %aM��;E`�% ' di-m=�� %�`�Fdb) l�j�B�!���.�ic�r�f"�w(�a `H�P*u �P blobq(b)��� .%1�2�!.2�2-�1���10-�3:��-_��a���V� me�$ism�� $I=0 $�$6����% Now�����r6f!I^F"Z�is (� i@,ohMC��>2"�n!�2��#!"( � f`�/B�U|pr&�"b!� c�aj� ed��LAS�Jpk�JI%.�4 j2L $N> & 1%� ez��� �s�('{ h%F!�i�Qc�!VB;  ]x����a��by,2']��*~,Lippmann-Sch�e�hf�V�3}*��tree l9���A�$)�pro�AZb�URr�T> &�"!�! ?u`5�͠��he:��# is&>�See.�Oll97}Q'�"�q)bas�'Con-$���^ٜ&� tᙉ���)6 = I62* ~ .� -�8sp{2}/2} {1+(1/&�)2W2-)G2)"#e<�Nu &c�� loope>g�!"���:c= % i\�H �0l��4�2f� 1}{l2.�+i*3�o1}{(P-l@j.*��BbW P v=.h�&#d�&���&g>,ize sc#%. a re�]8ale $\mu=1.2$~r�č���PfH � �4&�!�$eft(-1+\ln)FY ` � } +\� '1  }{1- }-�& P)=B��fC 7=\X 1-(4�/.W)!Y��&u<�W��e�[J�h-:n ��.�l�uf�,as6�S3nd6I�N, d>` ~(a)��w ������ 2f� �[� B� �A�4 6F�b)EG�Knot� at� �=[~ �c�Q���$ �Eq.~(8�B��> Re�!��U!�EB����'E��16��3}�"2�6_mV2���G.$V�pD�)� "p���:�6��,2���$�kng/.>p{C&BS�),!�A��kB�*]RN�EgL ent90�gB�2r��r>n�P�i� � C.~S>Q�a6�6 > TI.��3#|(� e&he��at[d%h�B@ \*w� 1y10�w�Eqs.~(�!eq5})- 7})9O-Ks�9, "�3 a="%�JM F�7�.� ex�BC/our�  4%�"�AH*��6�6}�_�Ic,QaRtt g N ,�f�pW B�, V�.��j @27uwe�Y{��2)S�`b�2� �1��a5B^2�A =o�f1c���._�.��-��ap���JF�oH�i�&5)a�I�,)v�u� yu"b�s�BlBq"k#s H.M&����o~'Mx��>�&a�-e I�"�6��2l12})~and�} 13}) ari *�;)����,h!l���!0Combiބ "JW @"� Z�jB��%j a !��depict� 2[ 4},.B�z�4J&���=�2�(; ��� ��5w - b ��, NV� V�R.�6rvԶY4 � abel!.� 19��newS2�6`B(}m ��-R )��3�) 1$ 1}{6}:�� \��)�.�1).�%%(��(C>� �a6�A�=� � f!�q�B�yHN &�B� ed>'+F� "� 6 `$�t �7&%}1)� �"�� r 9evc��d;Bd;��1b21/sW �:,H"�8a %&f)&�? 3}Re�6� Discu�6)��Hcap�{ ` p!�&4 c]=�o-�6 to|5� �Ba��&� 8 ��n��d��.������B^�V�KN-%:� � � H""#^ } �k"�B:;��tab� �*ruledtab��%�*${cccc} Mas�!3W�y&(MeV) &�1� & \\ \h*H�,pi$ &139 &$f��Q,0N}$ &0.95 \\&$&9:'�}$ &2.07 +delR2322SR S40 (rop(462 }R*}��� R}$&391 YV92.4 MeV�1 :6WM�M�I3D*&�@wi/w2�1���!b  Nr�2�2�:!���"�j��A<Xh�L:�a-WeE�"ԅ$)�D?9N, ":$f�&�]�`�7reJ cuto~rFe:��%�E��= q"�l�$5hN�mli"s�O�;O c�Zn C2w;�; %�� �1"�A6�!�(�� �t $I� =152?�Z�aud &�<G`,b2�wFp:)�g= 1.6��10 -2}~9 {MeV�y�!�n�-9 $Ri�G6*a  i�Awe��B=1.1$ so5m"$%� �'��)�2�e�F3�DTA2���s�a��ALY !š�nd�4�; ��A�z^�9�:U"�� Z( 7N5a) l NphںE&b &2� �"%��� �3��k:��$MA�Ou�Rul!D��Ed"�!��.n?o8 '' (B)<0�r%A4B�.s l�%Bd����6�+6�&&1��5�Ze_�1~FKq �>�\ >2t 5}�b:A�:c1���by�2CD )�!"� FX���AC6g7r�'�sion�!�pa2=6� =157�b$, &W#=1.976�3N���"H�700.RA"We��&J�-hV��ig$isv@Bg��� �?% r�[R�s&�Aau F����kl��J@!�*� ,��le z@m@� "PAz@N]z@� Bo!�BNm�%1�I�B$f����Kf&�F�?��fA��3wo6�is?�9du%�ou#��9e� �FI7Fn� ^R�E��Q��y]md�gs>!�!�b9�E��p� >nB.~6�-k$� 8M K��z�6��6>�S�ras6^5}@~a�%5�b��=�/"� fig6 ���( mIG P/DF��4c�6�%�� Y-ԅ\AX termC.M v� We��<�jMM&0�*�-"Q= h6�@.��:� [2� 2})]�X!plA�t&�uro�MN���� wo�&v��3s 6r 3})]"�%� �:� a�%]&4A!9F=�,set*n �� be~Ke8%�<#"� O6L�0\2� �� .Q+�U�WB�62����=46)�� B = �We &$A>v ٢b/ (2^e>[a�w֐�>���e��kZP1w ablyG=��X6j��oWfA����b*Y7ex�q%�>JZ�U!�\%.�.7inJ!t2��� %�ac�_#ɢa�p& &�6$5����Z� B�eD���w�seatF7%�a:|�@dra�Jw � �N(aFig�J fig5}�62UB�fB��QN<=����`!8E��9Bv1���'Z?� !ġ����8E9~.�n,A8.�EJcN�"PP.�Uly8����[ Cyee6�omeaE�1�s&<)�:EX�Mz�7��7��� [>s6� 2����E#B�=EC2!Mno doubDv�l�<� � *z* i�W>R�wlwnD��pFQVp@VE�*�J�exist Q`ambig�D�0Ey6�;G�T�>��s�ly 2קly un�n��F�!8I�F�`|�O���J�e��B�6�W jr��l,?]*��.�I�S����l12s�VZ��E�6qt@%BC��*! �-��so����� IgJD6�7}��c>* :���B�77.W��پ=-1.22��E):s�]e�%��>\Q.0g�6�[��$:���{����. @0ga !�4��A��G!_neg[1"\�Y�a�w�YB� :-&��e%\�9J� >�Utu��>� and,.�y�!W��R(4}C"�v�I�E�A�&� B�(6`� c��YR� � ^%"� a�.� *,!��2��.� ��\�\Z� Fur�Emax�te�=.�9.. �v[>e sI�:J!�=�|~/ED subs�[!a1 y�X>� :ia B U�AT\�Pc"� �uR_LT&2�<:�0K J&T1iY��ata�o];)g Aa1A�!�QD.�]and/o �r�Qaq�r��N���� �,*�>pri�o @F�#a�In ����-a6�&M8p�� n es�P ial ��5>� 6"�!&k(%x%LMbe�Wi� ���Q!$��� ��>:�97s�].� � -P dyna�U�Motiv����TB�*%L��i"�)�F�"�.�ned̦�>��D��!a*&�M&C*a^� tells u y���)�e B�"�&#wR"!RA=��}BP���ds AceC<ТĺT�pf�c-:�c6useoS�"�a"�ua9�Y%pq"ni{book,A^le6�!he2ܿ{14�Ud+�\ifx\csnnatexlab< \O<x\def\#1 f\fi \ZGbibO font>J M#�Pf�Q$�Ry�~R.$�Rurl^�url#1{\_tt!O%8{URL I�6"\kbib���h #2} B!e Xt []{S'Jf:tem[{2�nbu�^d Karl}��8,79)}]�" r{i�&i9�{N.}~[1q5ur}} 2 and}AvLG>L��wN�${journal}{�r\Qm.\ D}�bf{dK�me}{18:Cp� }{4187} (0(year}{1978} tjQ9VQ265�FQ9�(BmN�Be��and3? Kolck}yu2!�B�c <nf^�S.~R.:sWֈU>�va�!�>�2002}), M{{e$�r0212039' %J} Jaff�aWilcze �3�?d:f�R>�R��F>L���L�yj�91:GM� 2320V�JU3r7WeigelE*4!0Ee~0HB� GZ�Eur.\�j.\ J.\ Aj�2Z�13J200�+ �JOs�ind ViJ-Vacas��85�!e��E>�W� M.~J!���{6�ZE Nucl1Fj? A446:CM$584N�85r!B�|rd oa!995)6� #, Kais�Zan)j4Mei{\ss}ner}}]&9�jV>j ]:��F �}},���]�H U.-G!j.�2�,.��R�� B457:�-�14RQ9v�Jensen!{ Miranda%�7A��g�� T.~S>� V�� A.~F>P�Z<2�Cj�55:C1<�*B 1997r��B^�2XA�j�Z�� A600VJ41Jo! rI,Alvarez-Ruso.38:3.(�!k�E2TF�8�j!/jL>8.b:�V=^_%��;BL:��Ѿ: A633:�M�519R�8r� Hirenzaki.�6:�%�{F.Sq~de~CeArdoba})�!�!�Cl~�S>�p:�V�P>?n� % a}R9�VfB� �!F���Z�27Vv�h)�Saleski�� �0~� D.~M>� V�\bibfnamefont{E.~M.} \bib,Saleski}}, �info{journal}{Phys.\ Rev.\ D} \textbf{\bi *$volume}{45:C4pages}{4002} (tZ8year}{1992}). $tem[{\cite�xEidelman et~al.}(2004)}]{PDG04} 8�author}�� S.}~[BP}} � a,f�Lett.\ B;^ 592}.E �1F��r�0Hern{\'a}ndez.2)6%2)!�lOset, and {Vicente~Vacas}}}].02�:E>:2e:�V}BC�15xand%QQIVL M.~J>�B��HV�Cj�66:�-�06520V�v� Yamagishi%�(Zahed}(1996A�Yam96��H>�T}:��HI>P �Z;Ann.\ m�(N.Y.)j@247:I-A29V�6r�Oller%:E8!97!9Oll97�9 J.~A>1R�8^��F��Ur Nucl18j0 A620V1438F01997});r^}A65�~#qO-�407(E)^U��Tend{thebibliography} % 8document} �B\�[class[showpacs,preprintnumbers, superscriptaddress,amsmath,floatfix]{revtex4} \usepackage{g�icx} %�� %% This is our standard definitions of abbreviations 6 %B�.� J�\� Styles for APS %\newcommand\NCA{Nuovo Ci!{o}: PBPS{Iqi�D} B (Proc. Suppl.):3 RMP{�� Mod46U/ZPA{{ZL A:NEPJA{{Eun ��A} ={\AP}[3]6�D{\bf #1},\ #2 (#3):5NPA6N}�\ 7Av8B^8Bn8PL p�76A sv: r6:B�:R� 9Rep�roRL66� ��VPR2�AR\��CFvC��DF9D�9JPG9J��\ G�7RPIn)Ne� �ZP �Z4��EPJ 8a n��>PPN� i�\ Par� >��?rAPM� ActaJ PoloZ�6� ibid%yN.�J End� D��2-HGreek alphabets \re�'a{\}:b{\bet-g{\gamm2Ed{\del>.$e{\epsilon2W\z{\zB[h{\Bq{\th 2oi{\ion2k{\kappB�l{\lambd�m{\mu6� n{\n:x{\xi6& p{\p:rr{\rho6(s{\sigF.t{\tag2� u{\uN.f{\pho2. c{\cFj{\psB, o{\omega}>:> < A few capitals.�\D{\DF� G{\GN L{\LJx J{\P�=� U{\U��  Some 2U2�4ra{\rightarrow6la{\lefJAn}gle26{\rraJPovl}[1]{\overline{#1}:?ud $undb%nono� \\}:�be� egin{equaM >he#y ^!beaEnarrayFE$ FV"ba � � EJ�H ">� eqrfH$Eq.\ (\refE>o'm}[2]{Eq3)- 2R4twR5,v5r�a>j5 3Fu � a1!M�+ ��ofN�.� {\bm%<\mbox{\boldmath$!$>�$uq}{\hat{\$bf{q}}} 6Puk:$k}BGp:#pB#hFk>=h�qBWp>vgA�m�9:. gper;!_{\:)vf G� >v vBJ JBF!�{\var >St Tŀ:(Tr}{{\rm Tr> angk)�l�B #1 \�M_{!�>� angqj1q1 m�<ad dens% rk matter�ailin}9� casei�.�c0-antitriplet znel�re��sq�for��o���*2�. Duea!!orinsic!Tpertie�X8s (~,�^,-C,ic charge), �= �k���ns seemeiho�2ly�"�Pother words, besides �j�, also��6�SU(3)_c$��I�a�p N_f)_f$Ybaryon /  conservI� 7EB$ may�I com!�ely or�aq� r�A�subD�re� years� re have bA�E���ng!ks study�F"�of���dB_8, i.e., it has_�m�%>-:[�)A[f�Pe�� ��m I �E$ chem��potent��$\mu$�gis qu�onS %�8of phenomenolog<�, sinceq)�� ior; neu��� ,rs can reach% iE�up%�n orde5a�itude lA�r tha�W nuclear6`!Tity!(l�(�sbe�!d keV�erefo�=cor*a .�C:�a)����okL5Jari[of�ch  R��+sA A�@ists. For very) �ie��Q)�mas ne$u$, $dm@ $s$ &)�b na�A9deg�te-� they@much sm�9� FJ�2�ie; so-c@d� i��� (CFL)M��lalford�m�e, �� all�.��)S6, breaka���t�) �b��\times ��f �G�c.B$E��* D {c+f2*{c+�� . At5=I���!� sit�!'mA|��� \ becaus)�k �2!�A�not!�neg#& Fur��H)�A�&�$�0$-equilibrium�k ���$I�alaQimpose�� tric��.Te�s . | si�est solu�Z| be a� !�of onlyA��A�-� I�n �U> 2SCI ��t��> If r� n un��!R !zsymmetr*Mp� !�5�]2)z \toA@2)>7 .?I 2em+B}� both CFL��iC � m��ta!B�e�u p� ipaw ���!p assumed P � l���� cess65��g conv�.onal BCS"B"Y ,�6in � �O�  t� �:�How� ,ymoder��den�,Ais �pE_is a  vali+.�>�neia#�(pure)%nn he !z statd S�al�1ilɺ&discussa�In princ� "& a � e��Cpn� l-!ouc%�v�nare two���alternaa���A/yield!�RQ Rs� i�first Sh5�c�Q Qe%^nzero bu�� enough�still w%�QoofI���a5��,e� � account��M<in�1E�K!5.?p . Let us ���s/op V=�. F! % re m; be a�R82�}n-�)2um�� a^�#!A crystal9��Ed� �a� ly varU �gy� �!�"2}m� kind!w2 v���0lla� LOFF ޡ wa-4 U��solid-E� �cs tloff}, sa5�I:!'�MoJHio�'xE�l� e�fA�.#! SE%=� stud�8 abouG(``gapless''e��9 shovkovy}�L)0gCFL} �s-�es�asaKat&sta��F!L�quVsa� ungapp�[lthi�.� yG-�fe� obvi� �Oe�ouysm  equL,�5 int"��s�fic heat��� ino emissI �:affec)Mcoo� of a2�  � �B!vZo� . O�h�/l1g%3���!�7�c�in kaon�/or et�n�ateQ�#}. More�.mdisplace�  (Y�)�a�#�� ��F2N"� yMdmue�}A� I�Y�aper, w�Ss�T)�2"�.�, �( ly ��)�f��2� �5 ,one` ,rq$ke,schaefe�6� "� �is �I�NVOa��� \���)�� lisa�scenarioI two-� hree 9�_%.T sepaly�ms2�� .q,� W$u>q M a (�O)�N>� wh[$s� �~�. SAL./as!4�?&":{\e� ti}� � o�*Qz anneo <� mus��� icZ�to en the a1C X lU��� w�fun�. Cp��tly, )�n��2�! .�ca� �E�= �"g�,-#��$J=1$ю$J=L+S$�kq X4��,]� thei���� $L$ L$S(``A��� ens�M'' ���7 's) re �s>=)�A�� ��mplex $34 3� trix�K� �ntr��l� �E�, \-W�1[BbA�si Y{< >�ep�ex 3-vea�n�� ��N=+aN�, origi� ng�<�%���E�1oa�A���7B~ J�N .�MDleggett,vollhardt}a ��rel� ���,��Fb9c$S$� ��' ntum�� givST!�aQ]F�5�-��a.a#� atom0 rrm >���: A֡� . Wi�t Z� A(wo��� FR�[ri�avp�  AqB CA�0is!enX-�� mC9�$�#4_{ij}=\d_{i3}(j1}+i 2})�P�3(index $i$ r�=���! $j$%�:-�2�.�:�eaks $SO�S L �Nd �'{L+N}�IIX LIY�� >�+ps,�wivelyv uNiD +� � �rp�e1�, �c�t���st reg� of Y� diagram,.� F�j�3�B�e�� . He��r"��a-" {S+L�W��� ��1(t"bf k})%isotrop�f!BI��� nB" A #)#u�!� (�J ity)Q� p$1"}>� s\ gi}1 a�c�sueH� ��, W! �ergk �&\ p = \frac{1}{2}\,N(0)\,�!k�'P^2(\uk)} \,\, , \ee ŀ $,%4� �� �6� �j $ `-}\�v\int �d\O�'_k}{4�($.� $weak couplId[Z*,M��� ��%��M�A)��EI-�!�(cf.\ ;%3.72)&  5)@Re!� 9o).n�AB} \%`1q_A} 4B} \simeq 0.88)c.%cT.��-�r predicti{��:%�.�m� go�a�i� �! to d� min�2CWa� � � E�!eu#I�2 !E$organized �ollows:!�Sec.\ %'�s��&c � l"� F�s �$��V �" $G=6 J.�#� ��BE�6� � to a>�$H��UCJB!�(.K)) ��Z�"h An�o���m, �"�B$�d[cor�>6� e�"based � � �6b#onr�ttbAvariant *�a�n $H$. Fourios���-B�� pi3"� �%�in:�T= nextw&s!`,polar, plan A��CSLM.�"�Y f establ�7ngP�li in.�*4�j]�Mw1}a devo�"#ol� Y����f ��alV %�neXwo"�(�tant �� -dep� nt)��y_] resul�ri�y� - FO $T=0dM6��� q"_r�=\sqrtr,0mbda_{k,r}}\,"0��8, %\qquad r=1,2���P!�������#e�'qu�u $�. v�R���r6���.�*<"Ye&*# 4 +#�)� &T#s,)e w�G%((k-\mu)^2 +�%1^2} ����briefly� ��&� of*�.�s, N�1r�t&�&�%, in 4 � ��wG $r = 1,2$� l&�.� ���PQCDgapeq,son,ren,wang�s)!/!�%gapQ�}IGp0 = 2\,\tilde{b}\,b_0'\,e^{-d!1 W1 \mu \�exp/(-�c4pi}{2\bar{g}}\9/))m.�2�qb4:6Q?� g}{3)�2}\\ M���$ 256\pi^4 � B$2}{N_f g^2� ^{5/Q, L � HN�EN 4}{8F2�!�E1�!g&) 1c $gM�exponent�isD �Jllņ-�� �J�iAH%��٥ �as.� zetaiso} *� ln (Q�1^{a_1}22})^{19):&nA: $a_1 a_2$mto bO!t���{�"�ly�y fulfil%D��.�(} a_1 + a_2a()�i��nof'$Y��' stea�$��-�,$ will turn .)�i!��!��-iz�D*e�ofi"� a̵� ��K#s�gNb%$e�r o����{� �1branch,%�=1�1�!�2�X nd h!i�^{\rm��PN�� i�Y=a��CFL6��wo"t�_a�/3s#a_2=2 �u1=4�2�l�)�)_ ��= 2^!�3���'�$)�FP2( �ut��.�e"7,{*X�%"��6�M=.�  C A(OgapA!�s=�Q��.A�� �� (=��-�"�ga!lA�);:�� "��/���b2w� T_c}�_0A`�� e^\gi} e^�� "� 57�ie^{%�:\g-7$�U�Euler-Mc0eroni5. .�o10� conclu*.ofg6�� �&X.���)vio�{*�*�, BCS | onE#/I{&� 57$ ` !��a��>"y�(U� {1,2�$a \n� $. (Also�d�S �a�y�is�is �edm".) A�:��,��~ pr�'��A�h� � ?!�!A�gy, c�*�5 %C). We�- is e,��F�3}f a��9��m8 "�/�n arbitr�#loZ-*I2� � �16���� a�e!� �# V�0��!=�a� | J{ %{s r.�w&�( t<��*m!�er�$``longC*8inal'', ``mixed �``���0''��i'ree K�)����pry-�Y4 �: )�Z�! in-0�2-o)��4�:�"chi�'��6� (RR�LL�s)� �o1Ro�+0#�&� oppositeu (R�&LR5s)admmd� s^ � FO>�� s a #ar��b���� �iK�eJfocus��*s �,�2RR/LL.1 (. ),%(�2admix�29KRL/LR6CE=<nd gF$YR ). C.)a��12M+E�"dF���}A�summariz��m�Eg�1<-utlookU'5��";"�"o�-%��>W.  -� Ou!��'u�=)ic tenso� $g^D>4>=�9�}\{1,- \bRunia4$\hbar=c=k_B=1�8s denoby�= le�0s, $K& ,K^\mu=(k_0,{�r d $k $| |m�$\u  /k$. We�/!/��i}Inary-$,!m���(T/V \sum_K i T n � d^3_(2\pi)^! i� $n$ u4�0Matsubara frgc�$\�>Q� i k_�2.bos63%$=2n \pi T$-$f� :#(2n+1) '. �# "5P +e{" C-}�"�;r*IA�Hbelenumii}{(\roman{ )[5P iw2�,A�f#Y�Bz�+E˭]on�+.� o��!��weŃ "::8�I8�&���2b�F����A*��>aT�",��ii2D�9relev�l #�,���)� i6 G=G_1�G_2 3k*� � G_1 =�, 3)_c $VG_�} qG_3 =����NoZ �global �5B$,�)!1��f�3,�2�":+ t�ilo�:U) h�$��h ,truv5��$N_f>1�e�6z st� �H s� �ir�(�# hargT uC` C. (l =3$) isj�7Bfaz'-;5�� )�/a7�66��+ch8fH:(!8e�dow�")B$�#s &1 Goldst��<). _2�!h�-t")�4aŷ`ed��ow&��alai��current.�j�>"�i@;Q6 �( re< en1of $G��E��/ing�F01  &�somew!tsloppiI&���,x&� �-"�s��B� $G"� �;pr:�!��M�Ai� �" $[���3}]_c^.�9 40J^s�\&�6� } \D�� Bh \o�s 2N�*� *�$\D�,�m��E I�� .�$��3$ )�a�]n� triv� A ribd2"�$ "~�$ce���i`6ilo"�� @.̑`)�6��ejE�"=( ). 40H\subseteq G$\is mean���+yu;R$g\in H$�3v�1>1 iQ^�$ce0} g(\D)oD.�R8&7d �G _cA�n�in �� &*��&:�sI9 A�6u&z9��s� method!�a�EE&0�fmotiv�> V<analog;-���lq�By,v&�% 0@�+toafy��v a( � �`in.9B0To�nd��wrr 2��:el��IG$aG(:,a conf���A�o^�!81�� 8 g=(g_1,g_2,g_36,ay.,,g1g2g3} g_1=z((-ia_mT_m^T9Og_2 #ib_nJ_n> g_3 ! 2ic\bf{1}# \6"ith?, coe�=�Dm$ ($m=1,\ldots ,8�a $b_nn0,�tAr$T?e�G�? Mann��ces $TMgA�u���ndA� ake5)a��2aa$�+6O!o an {\@�+���5;r �J�V�P� ��e!�6 2)_JI(!Z�& -i\,`n%.  :L�{$�cho�7$2\cdot� 1�)�$�G$��� )D��� or 2� "� di�Vn�0D"���u5��n@}Aduc-8basB$J_i\�}�L_j!�i,j1�u� :�g%6�6#a�1. pm~RNp�)?!!��y.)�� ces �AK� oB�" bovea�5�J��� �Y $2|%� �q+ $5(-t<#�4�ifi*uS}F�Mk!#Thul<? to�|s�P%� EeG$�.8M �l} {\� M}_Eak}1 !�,�$E��.�W|\be g(>K��g� 8 g_1^{ik}\, J_kDDV \��^{j\ell g B��%�x�����8 � _>�kid kcg� j\,s n, ug-L&�$�tC � aVesimal�5E?()$A!��QQ �)�\D - ��H\D + b_n\D J_n + 2c!�� .G�2� as*$ 4b*-*� '#���A5J��D� �30}z thus6Y � F�} z� = 0�1�� aQ/`%K�0�$�t&�7 A� nine,��� o�.e� �d!�1WVŮ,33}"�) z1 B.p";:�6f�72c �qJ�&��6d %b&�sAset�A�� ����t�to ��n, #>I�4to�0BT( �:%Ge� 5,I %A5v��,��,���%it%�@he�%if�)s]]$�&�Bsi.�Cbi B�:�3� s �@to��mp"�?< oceed viaA�&Cgg=)�(>D H<it7 Ro ��D�� inu� Io�"�:start� & $H$�E�)!��Ast� cO,�eTIH'} H=�(� H'�K:�H'Ň :rL8m��LiP s�"$ �m�4���1 p"�2 $U$�!�a2 co23� Mo�N$G�in l/  U=������Ř12��reA�[sel� o��� involv�e x$ of�� $G_p$G_D%$G_�"�9)�1��01} U = a_8T_8� 3J_3��F� �1.� H�Yv�).� . ��(app} e^{iU}]=\D� @!g]��(A���b"�+ed�lim/T�8 is d� in Ap�ix,���.�JWe�!��&d@>� s, e�=��m5(�awo or�C]�N�U_1�� 2, ��"Z "=)�x+2 �Ca�nQ183E�\!! *�He2} \Tr(\D\D^\dag)=N$�A�cal�>�5��o�ņ� � �Mdrt-+!(any free9% (-ӵq �"X.�)+�y��l�?!F��Z"(&� is!�E�{79inert}�*� AlWOB`4�LM<of. ��M�+�&+:|� MathuPEspTD���1^�ya~ role&�?t4m (``Michel's orem'') �!�,m$�eTe�9�~�B]�!~a%�Cry poin��!� $G$-q�t&�0� (2�A�eM>�poYJZaϡ�#[So�Ay�QE~� \&6�P: e�QA$Q�%�q��~pM,xF J� . O%-2�pD�KwSamz � .0a *;/ertI��4e�$ \D=\left(5S|X0{ccc} 0&0&0\\1�nd;X\2�*�%$p�.1AUee O)���e  ���+t$Q�:ZEStNm}jE�x!�idF cal.>-k�s��1,oM aat9�� � ialread�Men�RefYS,>z � 2 3}���!,"�  E3Figq2f iewei1� :s�>d�* ;e�i�!U�>�U[% 2&� ��Y s-C>�� �i�"oi�"-iD\D=�& 1}{\�.2}}~�Q� 1&i&0��AQ��:?���!��@}A Jto F) (�) #���7n"�H�"#" D���*� !��UB� in E&�[H'^ �A��q�5�2� 2T_0bv� M�D$T�, playY .VvMat�g ua;!UwS3"�&^-i�Spor�l to l:�?^:'!>)}d� al9e`͙!cn( ���y� (%A�*� -k �OF2�2 [��pi� tor)�6H���0}e��3R �:� � E�b1o�JwjXV567 ��-elabo 8ngo X�OjDAVh2})� A�E�>�� �W &' "9�onD'I�E� eb�'#=\frac�21&��1��f0*�sy� ��a !�% ��*>� �+L !pIviq.��$, EU �U=m�j A!!V=T_8+54\�G3"l�$2Q&���/to "D��6� ��� � solE��s� higher-dL?,al*�, say�1�H'2��!x�)��$U�U�U�=)V=%ay!��U�!ey �%F�'79nI�A� U_i=a^ig�^iP�^i2�"}io1,2,# �"�Eyy�1< �a�mud �,s�V��m SU2Uk ',} [J_i,J_j]=�ijk} w,� ,j,k \le .� � ��"1�!I5! E�n5C'� �<$c^1=c^2=c^3=0$ E�z9\ :+Ir�i�'�� $U_i�.��V�#�V�U �s.m oo=n^: ird,:M�Mo��M�Oo�GON6�@�&[R�Mtsal)s�Tas�4re!�gin{sub"~"�&SU2ge� bea && AeT_i'+J_im�1�R a}\\.'# ��&b&H.Ic� a�\2��8$$(T_1',T_23')%�ei!�� �B&%,T_3)$!A8 $(2T_7,-2T_5,��A*L+I�A [(i�.]�Y�. Us��A�1l �a}) --c��_O;8�n !2�s)A�T� m�.6*�R t�$H'���4th]1 $V��V��VL ��"y` orm R&YqQ��a �M*��n�R�4�algebr�S��2dsu�u�� b%6s,M �A�q!�A�$ [U_i,V_j]N�acCRre&s� p� �oneSLNU_�A�Q�\Z;VA��(aXicefX sa).&�Sŧ}"$qT" >���qexclu&cdi=�;}MS $i�� doe'�%oa"i8>u� ��]/igbidden. � �� .�ZandA�� w��D�!B �* ion,E(�k�1� �v���8�$HM�"0']�E�"T_.��E��F�9��aq �.,2� EI�1����"fH,.&+A1!&H%!=a?%�z!�Il�3�a2a�\�-a��i4�m�e6� v 2h�CSLN� 3j�F� j� . \\���ee! de*�;�J ]fV ce})�#�6�&�9�%W9Da_3=a_4=a_6=a_8=c=�� )@f; 2b_3~F \  5 = -2b_2�7I>b_2M�3:n u�,��s�K� f j6r�;�&{'= spac�Ga�+� (-�-�He]S]},�Jed�� z{*� � R�!�e��u�).Fin�fm,#0'n� k f�4whye�97�.`a� an�$3�P�cq�"N  �h. A�ZQ>��] ��($W_&&&W_8�� �%jh��as�!e�"]���r�/E�n��*=Fn"]� $� duX8� �V� !�&� �USU3*� } [W_i,W; i\,f�" k} W#R� IH�R� $ 8�!.�&W+�ants. �9,!miE ���Ld]?c�^�(�1S� L�7 n8\D� ��us��=0)���2��?*� �)b=#��d'c, �% $W_8�f_3�Mn,9�=m"0 �48$[W_4,W_5]\sim Ao}��5de� �}$J"�@J� i � c $W_4=T_4�1 3� W_5=T_52 D.� � t�8"� sL\D=W_5)[ �SA�$%jd 1Z�&^<dig��?n� 2D� � �sa�M�)kaC rigorApro:V�%��ak!��X)u ;.�*AL"73y'V(r(figure}[ht]�O�eer} \-tg"|0s[width=11cm]*.eps} \v��{0.5cmiaw [S�31�5A�z�] {j@A�F�/ �_bZ4%�9�y�H(� !U) n��n"J-Ŝ 2pi�28_c$ (blank back��n9!��� ^ .�* (grey6-�1>�22op �3$ (hatched.G ��U � *�s illu=c�+5 >�E� iZ[�� � �$ə!߅�G.j���<�� M�� �by�"! U�l�5$5Qla �/1%*D:s+5!�6mbi F[;q �^�)�!�n1�!�'J1+"�*^@��s.�text. } J-�ieaZ�u� m��b�eh;5LNmvl ll�<uga�7��w�� ve f-�� &� .�Ashould�M�4io1F��� rVt�*mj4a�Vx"�%j$'[)s$yMur&u$b��U&�5�1})%��v�*�3tL @jly��(�jnon-i�FSX (�Van�owA�> i� I� �r[&Q��f!�A�s. Ea">is%��p�!:8>�2� 2�8�.rm A}�Ewi�'.1"obgl �� !n!��A�FA��7V�`,&��y=# B$ M�1 Aƥab�$� �XTo�A�,�erRq *_i� ${>�F&"�2a�Z� 1 & i & 0 -  0a�!\2� �iZ1. �!b �"b_1=b-H�/765B ! �a_2&�2\�$a_8-b_3-2c�TT�#7�� s suggs)�)N8dim}\,H=12-7=5$e�� W*d $*�i��\3�D%con� �g� vA��Ρ<��*�w2)$_ �"� �C�� ��I=�}� Vby^1� T_7)O� T_6�  >�.G:� ,), $[U_1,U_2k T_3 �+$+�P� A�rd9v3$kb>2�UO:�A.�)֝6� z�c?Bt!���2�Y"��k�"�!#�pձv#)Eq =we; ��P}_�(�. , e�P}_8$.�)f9���1�J7�*57a��ڕ�@A8�uS�qS S� Ŗŋ�vX9� �� 7 �\*easily�MG$ off� VI"haJ ider�` �i_JE�is�a� &� �x����re ��)-a�u*��"E��E�\ ��6�4��� quivs=�t $H\MVnWN �E ���s|h�is�:in !�=Zanc�& �H)�,lEto��.�!\)��Xa��B!G�KV1uUE� xx0=�.�/ most! g%B�s," I�5g2� subtle: 1!-_.� `>� J� >�a"� 6i\� � Y].�8� td�0ng ��<�*6��2�#�WZ�u�. A]z 5i.R�/cy�{"�t\G�J;X ulta�wper� �*u.efundal �Vo|iE�a�p�d"Zxt���D �ogre�\!-blu� Next,��'s4l�ker�$� �m�."z�i��%@n�M� �pp}T�9� t� rowt ��Y*1^nifeN. Ĉ�*a] .�?Y*if/�~I88D2:-A�,�J��wXy��ndI� qFqa*2_ . Of�Crseocho�-��:j.�.�I;�� xc"�. s� �:Os. Remembv�&�l��y~E"�"-T��AVNAu< &�D�t\. %�D)E��szG �.beGsp=wj!�exetic sc��(fTa-@ gluog�ɘm i�/" }T��I�uSw�_c, a Meissner :/!� f� ~ �}� ,�@�ru�th�=&����&� � � �),y4�1at_ .�!a?)�IN��a�!i��~0 �Vse� e (E�)A�)%q� is j�<b�.N. mU�/J*oq6��%�UO���� �:�cep�&al%2�f�rA�cK9��eQ% h=]A`�5d$+�)�-!�bn��-BM�^�p�6 �� a gIuA�?!���"("E iPI��"]9C B � �*I(�-�C�HD�ex�sթU� ]�B�mm!3� w&��+�nd ��nt��v��bCPYv u, A��c lV/0�U�h�b RL"�{wheA&)�6q�~m �=-��E)r�I�����-�!�  .���U%��rom�i�N :�n�7elii����:�ho�Bb"�N�S2� a�'F �VW!�� %,!�� � -a�>��r��R�%[:V>�. Oss�I��ҥ� CS�YeE�� %�& ½~B P}_6" �->�:��yA�*E ��M��i4 A��2�.3Y 2�LtEXT� , at���~}�n>�>W�%!%L�n� OA?�� +st*Ae�rk�I�ve!mn&l }ic�1s�� "�PGZ�A�. Z� j q" *effpote�Z����t��A8reF�� s (*f6�lG$ V� J32�!�%�k�TN]3*�zE�aJ� -.�a&��P�@E �2� ��s!��E a�"�R���JD{N"#��6�r&�+. aUr �]#�2e����lD$\�=78 !;p:A1f�)�Z}��D"�88*�eff�a"bT}{V}\~In�,�1%�$p"�( �ne @�=BANkt�Y.v9, $p=-V��]�5"S9�]���I�d&� QCDi�a� %�4A!tCornwall-Jackiw-Tomboulis (CJTJG�T�OcjtM�ul%�fu Y�#wri+C��4review,abuki,rU�p&zN�01} \G[D_G,D_F�*-|1}{2}\Tr�aD_G�^ޟVB4��=0;D_G-1\m VE *�{F@�4{{�FS}}F�}G_29 �e~ $D_G�H�$� $D_Fsre��lm� ee-level)M e�V�ag5Bu/AlR; �e�Ɂ0Nambu-Gor'kov��Y�5Ar doub�mof de��8freedo+�|}Iby�QQ�or $1/2+A�tra�Krun over6�, Dirac�t,��"�uH $2|$rX� �-w two-�F le i uci�C�Xram& Vf2�R{I��� J,loop approxi�G! Ɇum��,5D-�ic1B of#X!Bm<&/ t�in*R#W� � (!�$``sunset''m�m�)� ���TarS~��c�$}�$��8 Dyson-Schwing��� 3{sPrse b���#6/1�1J DS�*�Ae� &=& q(  + \P>�1DS1} \\�JS} *�} h+Nqv), ] [2J\F} ��z]-t��7U:�9\�A1�/xL��=�B�? eft[G_0^+ �]I�\ b��5 F-.F>>vj$ � �7-��qR9s�� lessIA8��jug'%qnd  �  a�-J?�$e� �\pm �zT4g^\m K_\m \pm g�m%�2n�.E�f,�� o��:d �d,2EMDS3 e��s�B�I2f�3m^��K� QkFeN��6z�U bz3Q�s�;n�,�5�I}F� #(^+ & \Phi^-L! A^-�3Z(Ba,�`Et.M! DS2}� s���manuel�Aich����%�E=�Q�2kull,ypAaSF� G �X�XiG��+i��1�],��&zj�*dF�<2%881�Gpm} GA��\{:��%!�!� \mp( (mpi+-� \mp)�Q )pm� \�}� %�o>i &��anomals�, typ�+lM� *\�`�,&]6{.�X�!�a�= -:� + >�� )'�u�!�f�u �:E62Z$ j(K)ch6� >�ebeq} �(K�Q -g^2�B� �aQ \G^\m_����(Q{V \G_b^\n .peD0.�phiminum+�� - = �[+]YL}�F� cG cite,�1P$!��x-!�$�4!� }��uȑ����ehI�n-4f f h�l%& ul^ielati]� limiċ C.�gap {Y'=� {e=\pm}�le(K)\� M"�V \,\Lv�9 k}^e-�|)�)�c!�$B2� (1+e![\vgpY%}/���I$��_!� proj7��hBi�A"g�. �":p�$ �/!�!}QQ�eQ/y&cal�� a �x!rcoE�U_, �=f �:�<*�7��(jT\_V��/�c.� T=�9�" /&wr��..b(M�XeX�alwUG4� .r such4�8o4)i��-�9��v&�M} ��2}Fn]=�9�R���&"� � �'.� �a?"f5=�yw2 q��a�Q�^+= -�4eq�5�bg}^2k_r+ln� M^2}{k_0"�x./L$M^2=(3\pi/4)m_g^2$;%��-�qeǞ�� ��|(��dō$@ =N_f��m^2/(Pw2)$. �@.�� ),�~�)I�ɕ�),!lwWR��aJJi .j� :. (�  �  *8 m )��,r> P}_{�z,r}� ��:�{\mp eY �1}{ uk_0/Zk)x2 �Ae2Te)R�� ?6�1��x^2N� n� e�s!>2F�)Xof�v�i&]i�.\�:m� �s�A"�%w)=�,se`N2�m�:Z+Xi�:-$;yJ o���eigen� ��� %B5 defL} L^+�H�eI s�Y�� + \_m!����A L^-:\>X�S i��i�N!�����Ay�g&8J� valu�Zl�(�}�E$n$�$9�@ "is}39&P�:�� \ZX_{s.tr}^� E�L�)-�s}a�: ��]�!��B�@��ɤB�(�$����, $=�MM=� &/Q�9��/t t+%�h�|1�a�sh� 6U�re�WH�i tlN�a�$�9�,, $9,Q�-{�)b4�~>�p.�$} I-�p r!�mb�M�J�E�)�W��" Scos�Y{*SvIz6yМcy} n_rmw�Tr}�F�].�I9Nl� }sB~ �� o��"[� 2�&� \uk$�ky&% A Bmodul�<k�-y�o'� &�r=#on }� �6:72�èŨ:#� 3(e�� )^2+}iraK |L |�S)�C2s!�Q41�5.�\pm�t�p/ "�:b���aF��r\0at+-�%V�")(�Az*}n���OY@�DV�an"M�.�)}.[�1�("c.!O��{R ���g!�� v'( 28 "T ԃ�$1�2L3w1s�P1�sT2}- Es*(W�woF�8 �]�{�x�e(�C.e&!��%a�}s���  $2A�$ (��} �* 1�>Ooctet -M>L�} L8�Z!�%��2��W 9x2,5.���� �$e���.��"~��2�5%3�u-��ale}��^o;��phi_e$�Vov�o5we��&~ �'"'�}%._A �5we��*n.2��4��{+$]�C�I� �Tb�=��$�� |^2=7^f�k�)�.E a �6���6Iou�G�s�gsu��]΁�x /( root-mean-�  (=A�d�Sc?.)�%�� $�rqr���f �2���gap} &��.}�� San��m� Y�!�.s6Q��y�"i�*i�0)y� �� DY�> I� �} ��h�  }{R�����`)�!��E�"i(fiA�; "�hA'}fgap-M !�o2� $! FTlG"�%/N� $\�$���;� �\�%��1o� 7 $G^+&*;�i� � ����]h)�K�T���"�2t1k27w��(.!�� ��S212SC}E=- {� \.�Ea &� t \:� + B�-�,�E��� �J- (>�)&��S(�q:% {Solcr��!.f%�am29��0��(T,� .b(&�BV!� > �p������1Z*kO�w&.� }��i�i�$. St�'� �.�iJ�� 21})�%6�=�)�=�.Iq.-��!��jiuW.]�� �M�). o:��), �6ipl��MSQ s��8Y�\:�e�h �#!��$�$ &�$��2jM"�w��i��!��!��Hard-DD6-Lf$(HDL)6l$ �Pgpe ��rubr�����p�&� 6� A�z �6I q},s"�e�$,�,K��"p/!-kq a}"0t�22>LA6"�.�QM#q� ��$$U^is@/� wangԌ}�&�R�)�mUF� �WI�m�^E'49Iity ��!�:$�$�.�t!��Q�=�K rei!�'�1.j r5� at�� a`"d�r*e��s\,�� phi(Q)}{q -6 ^2}�OD�\n]~T~^s(E%k}B[q"t&�' llow!J�1��2� �&� defTpvvZ'd*>f \g_\�T^T_a\, �:IqZ �"���e^+:h q}^- K\n\�>Rk�b:8kK�*]}:�B��R*l �R $P-K-Q�N�+�Coulombl4is ~ = Q&^{00}(PQj�'�q(P) y,�� ^{0i,� ,AQ�'^�L(��-u p}^i j)R_t(P)F�p4�wE;@ �-�<Y����/I�Bs���_�q,t}fd��"�.��g�n  (�).l[, �S|�n�G }T�}tJ�-�-~UVI��ij��"M aT�>a�!�M"�+yh�2�e N?)�P.s,hermodynamic<$V��\infty�&� m{v�( 6� g�4a�i"��^3q}{�sa�3�_{q�2, tanh�V�:"{2T] \Big[Fi"p2<00Rl+ F_t(p"x�X�|kc)\,�*T}VBig��i���0 � 2}{p��3�O�e �$ �ic�c yiA�6o.�Ft}��6G �_ ��(p-M) + M-p)%s[ �p^4�6+M^4&( %++5�)+��00j6��6����:�>A-- al�A "�<�g�. I� ��abb�1a��S I�1��6��jk�,5A�R5% 5q}yA�isKl�"��Bg��$d��q'xa�ŵ-hu[W ��*w�.G�B�s�K A� e k�%6 3&B#8 $p^2=k^2+q^2-2�bf�"{k��'j s� ��en�J i7� ?�4U�$"� $5v%A��p�"�B��{q}$� "T�� !jroble�� ޫ) -e~/� .Z y �x_ �"#i�&� !+6� � f�= i`�3�r �.>��WCd��A��0 < �whIo�EYV% ,]V�J aed)!�hel�Q .;�)B �&�U6"� i-mt��.|�%�!) TrV�+] =fBp]j.-F.)��T)^�2becE�?V~M��0&/=k|c��I�onl�*у�)��A��se=@r !�A 1| m�"^ �r5^��:-�dd.u62�pA4-H=6hKAppA}�ūE�s[ �&6B �:F �\laL�msE�2���p �m�p\;mq}>V��y \; .� ��� ell_4�� �>�/F� ��\e%Zc.c)ݩ}B_J`I�,�Tpullout����yu2�Ajd q$d��z����o'�Vght�ѕ{He��P56:ux��>b��*�u. OA�e8b\�-w@vOd�(�Bp?����Ea$ "�}|J�k��We*� b @ata�4C"a�c�@m1i��S2h No*f")�)c )`�1�O.J�<*I4��16�� � �es}!7j_,=j"r(���2x �r, �Kg A��s B�qAppB} �XogK �&��l*�� NzK�!�!an�/ McoultfAi��e :�!KH9�2es����"��U�i a frcXW$z'$-SMKq��u�|< .�R�Iyi�MYR""�I�aP���A� an(I&��S��0namelAF�8sB�0�2�*�mk ��iw@N �lF����?5'���E xplaA�in�� !�Q�,/F�BE(|ֽj� uk$"�c�6*E ���Z.Cy�F_t-.O%&a�"*iog�0s $��A0;Y�� azimuth?l�#=�� they��en�"i�56�TonGoB� $��'� ;a!�D��4_i�a�2>p�mt$pBa��I6ړAa�i92`y:^W:*�may}(v���q \m���Ncs S�AQA���av�6 der,a\X?\ a��z 9�5U%�e* power seyF9�@ g^m`�b�:�m� ͢int_0^{ d1�\; &��� \;�^s_' B� &)& a_sT(��_0^Ng*eta_2��pu\mu^2C+"4 "!4}!4i&@\*� ��tb� & a_s% �t�t( 6� �V��R@n.>A�s{(cL�ech� e�addz�3l��.Q�1�}�"A�������E�w(-AW6asgɡ�s"3n!�(Upxum: q,Z��d��6�%�%q$>�1��a_.@>�'>,!#$�!�^E���� ������t�Mf0mc�@V� g$cos +!���%&a e}_z�'��V�o�s� )n�.9o)��f�Yant��e�n�C����6�^eff��s >�� :� �M^ �`� ^c J] Z��� - �G# ��m�=!� _0^t>��E hold�9A��:,!'"m 6&�3.+.:���Q��3�\�� ;UW  =�3"�}��� \;"L/ /!d d(q�\;+s\,�"�� bm>6D ����Eln�X�<\ {b}^2�B��-2d}} {|6J ^2- _^2|"�8}� Y�$0�9*o|b�I��"�%$dr\AF"6#*�F2P�*�#���)6W3d} d= F6�tEI�y[E[2�2+ t+2���I 4^t) \�2CB�*F$Ub� B�'e� � "w֜ ompu�a�2�M�2�inA�Xb3.�aq�~ic:[�)3�G 6O� �< a�N� � o��w � fb�6Bc&� � l�c.j � ��&39%�� ,P^l,�;, .ɘ&l 9���&_s�[.��:/Nc 7BMdividE�t�Z�� � %�9o�F!I"�-q�"�!m �Yq���.� ���;�#�f@�sw $2\d��[c2�(1�$%is���mta��!��� �gq.a)qF��MX��now�)!PA��us`� way, keep�1,=y�(�4;, �����>���"�"� ���%�!�����l��E�2�, �,�bq ;�"�4\ "�P=K2v '�be*� z� ^2e^��J� F���) q �'%I>�l�"�6���n�� �d� 2�mc�Hhwh�g &�Ih: e# 0 new variable2�5var�} x�2��6�=6+J�ldF��0: � \qua"G y_s"��g��g%*g& N�%Afa��o�,E�3qs5�to7+� 2�new�� (x_r) &=&��� 6�Ab\{x_r\;?_ (}^{x_s^*} d%I, &�� \e(y_s)} &]�  I�."W�DE &&o.� � {x_0lrjFpm�qp Fq\a��a'B-2$ xE�s^*6�\,�� ��"D :0Q/I. ;8x_0zn^�d"� "=-� z)YWx_1^*)�p�.(x_2^*�fI�Fx!T n i.u���PG8A�"-  A�N�/.*����E�A�)*[�79x/N��&4ce"! q[,2����, 2� �4���w��gby �'" 6�( reM/ =�.@ � >�3�* pL���a�Z �3� s��N�ty4,��be 6index $r�e��!>�%x at,�# !�Ag�R��$ � sub-*\Xr�I?���WM $x_rE=�Z!�Gt`4FBr.�d.J+ ^h�-=e"� ��A)x) & = &m$~+[{ x/_x�2^*}dy0/"��)2���a� y) + E��x DH I�^J�� HNZ & �[}�1\,�{� �e��p\� \�\�'Z/ phix�nd9�"#!A�� �32.��a"?iA@"� . Di��t���wTa��*�$x$+Ka[/-1-"�6iʧ}� a~��~� "hn0�*|)� .� % �.i�h��V%E�+:MW$x=�� $. O��12, ��&A�=���AX1���-x)+a!���,\sin-�].])Ae� �ind$1� 2N %��-k�Cs�� !���&�5In�.�4D: ���s" oe/ ""& ��=m"0Y�Yd͠>p�n� 7�E�wht�2 E�.Tr���. ��$%e\a-\b)= \a\,!�\b -  ab��$ 0!��2+� Csin\b$%�!� 2� s xK�x_�/^ H'D 1$ (�=$'aumr�L_d��$O(* )ϡ&*� � %���} �� �Bc, H_q U� E� ��1\:�;� !�t���G�6z k}=q4 _q}$&�c�#���IR�%.�%g# oI��ŀ]~xsm�!�6�!'��F&U !� � "v-� a�b m}y&Y ��]A7 ? \, (@%>*� 2}� d)\;*��\�yFj� bt� �si-���� �-��%^�r r �*R�f (�$2Z�$2�7*{m%a�i)���!���u{��^d�1� ��9�.!O% �E��*k%�&�1E�2;� f�V!.� q\,'I�*�%q ./�We6)�.� �E. MJ�dNS �|Y@�� =\ln"F�{q,1}^2@� {q,22D��*&x�W@0Eq.\ (\ref{ze�taiso}) for isotropic gaps. With Eqs.\ (\ref{ell}) and �Casgeneral}), we can write $\overline{\zeta}$ in the following simplez`m, \be \label{zetafromL} >F8 = \frac{1}{2} (\langle n_1C8mbda_{q,1}\ln\l + n_2.$2:$TrN_{\uq}}f] + JN2=� \,\, . \ee This expression shows that J,!IPbe determined solely !%G, spectrum ofdmatrix $L^+_{\bf q}$, cf.\2�defL}), )�E and de)�8cy}). From Eq.Q4almostdone}) w� duce�|, to subleading order (reinserttA0actor $b_0'$)2�gap ~dl} \phi_0 = 2\,\tilde{b}\,6\,e^{-Y d}}>\AI}%�Dmu \, \exp\left(-M;Lpi}{2\bar{g}}\right)B�8result, which i!�e main )� is paper, " � izat!�of.EPgapconstant}). It sayZ at, m+(case of an6�!�t/or an angular-dependent valuen,$d$, one has!� repla%�eA�,onents $d\to.I $, $%<2@}$. It turns out%��Au!��sA�id!$d$!a�0 number. OnlyA9tmixed polar phase, see Sec.\ \��)�s}��b���,gin{eqnarrayu �q�� J \ell_k *� 4k} & = & \int-�Uq}{4N \;>q R{-T_{x_0}^{x_\kappa}dy\,y� tanh+[� e(y)}{2T��] � !�y.� +` Ze2^*} c d e rf6R2d ) .\no� \\ & &R(. - a_1\, x�1^*�� �0^�j� �\�.,Źnd9�M�!�secon�0i��9*� �m $been dividQRtwo �4(s: One runn�[��$x_0$��$1ơ� if eb-W \,\ln(2)�)] E\gg 1$, ��m n 's2^*mN  it��U n how% �!!Ѯ$brackets o�e � -h�� ��=7m$) � e�- ateda�"� is ac � �%E (I� e^\gA�0_0} {\pi T_c} &u 1}^{a_1%R"$ 22:�.&u�  *dnonbcs}Bn�@c�i}\; e^{&p "� &�Not�L� although%rS o�L/ �$+5|$ b F,ŝabsolute��j �՜ , siz!��o $Rv $!�'����A�cancel} e2@B�$^1� ]2-^8). Consequently�� uniAx�Ny � 2SC �^{\rm}$� N<� � s M�5b=adGX/T_\ =!�-�d}�  WA�cr � a2! %Q� %��J6�, =aP�!$F; A !�:� .� � a�us��Yq ))!I{ betw��!�13 �e* Jf ��>Q�, $T=0$ reads.]z6\!: !jy�qg&� � \, b� �I~� �  6� we find a.�N3BCS re� A4=0.57�a= also�`1�aa�g":Xax(. Obviously)�.`�JrIied�x=�)Y��pQPa�eIis &$J&=1���EM� p is idenh o*��ce�of.� n� .�~�  su� �"� 3} � sk po� �!A�cF� K!g#effJ ve a� ,.nGamma1a�I�'@two-loop approxim� $ ��a 8 \G_2[\Delta,{\� S}]�Z<1}{4}\Tr(\Sigma ")&1en, maka�us�� Dyson-SchD�R )�DS2�f� onic par"�� pot!�alq��ionary-K�be�ten a2� potg� \G[�2�2�\ln�^{-1} - �z1-  1-E_0) ) �1!.C�%"first :^���1=%�!e!bI�ty $\T�\5�� = \lnŐ det}:$�R�dA� arbitr!\�ces $ �AŎ B �����nvAble @x 1D1Av �� (\b� � {cc^ A� A} &-�B} \\ C D} \f ;-� = c( �A5D} -�B%5 +C�-� a�B� �S B{�SQ + iA)s�fre�!-) a!Phi^-\, AJ%RD*+j*)�@ �2?�e(set $Z(k_0)t1&��R0 paga� $G^{\pmA��� defini�K�"�� prop�QU�2m%ihelp} %9\mp) pm �Llsum_e[k_0^2- (\m-e\, k)^2]\L k}� � ��wa�� &=&�.��m_e�� ��� -"e^2 L� k}^+)�] B�-e} &cd:v,�{e,r}  K \Tr�z P}_{ �,rk> -e}]�Aef � - (\e2: e)^2�%2E1a After lo�g%�0Matsubara sum�6�r -ۥ��� .P�&y�2s�V}{T}�% m @d^3 k}{(2\pi)^3} �!\{>  + 2\,Tk $[1a�BK:E�Y)@] \}!��e*���now ly��(color, flav�� Dirac��. 6� O�zag!yj.� ��)/ easily1�ed hq�s�mf�~�~ fullquarka�6q anomalous�VHs $\Xi^\pm$, occur n M� rk3�.$, do�=� . �obtain���� b�)��6��E� K�b�B�AWI�:�-R���e"k,r� phi�d}{k�N�7Aq�$becomes, a���# m�IHAG}�~;�4} �eȩ?)DinZ�\,�WfW \;�d:Xz!YBQ,k��.5e��)�2^ee,T-��O U��e�s�fingzu�"�  $p=-V_� eff}= wT}{V}\Ge5E� ed by putz oget�+ m�. %�)�[ =�)�E p�w�>b� �b]�O ef�{v{ -�M��^2�����"t m@ Tnon}�Xf-� @restrict ourselve��i92V, �. Fur!�morneglec� �tip�cle$%� thus den���U+�s�.L,.��) �UA,V+r}v)n_r\,Q>z+�v_.�- -V�*^2_�(e\e$&" 1�2vIn&%e�%|iS1 !�"� (eUe͙moment � ssum Gx"to be"��(a small reg3#a7!6�jize $2\deV� �= 0!�ndE6 else. More�Em"� ��!�$_0^\d d\xia��(\� xi^2+ e^2}�2�� 62P.O2��d�. dd.c �C2}A ��%�� + O � �4}{6y.� �%\be�,infty dk\,k^��k0}U~ - - 2k) .�6}\mu^41 c �A+vacuum -gy $2k$&�sub���!�$�;eei�,|k-e\mu|$. Ni� ��sA�$O(�a� ��total�?}}�� }{48\pi^2�r n_r!a� p �ɷ �w� �7�differe�Ze�uc��$A�s % normal by� ���Q$\m^2}{16\, � �B�"r^2.�A�(e%oh phys>! intu�!��h$ofJ�!l�)��,5f� �%�%= %�# largest >sKU"�b� i orU�!oFs&) a ' �#s�jsy eE.�"we�'.� c2i%") ies $n_r$NB%es. ("� |*kA�}_r= m��*6�&7*k}���0"� {\em�X*�$}!��5!�%��*a r^2=�jAAa)^2k>Fg)E%D"�61� -�,0'noO&m!{ sugA.) A�6S�(�s"� * couneX,"A� '!�re)�� dom beuO= 2SCL�, m^2 �J\  ,N_f�E�&.R�+ n accordM.� miransky}G*en>SfAd!" q� >B'tiv��9j��$j$-thA�)ѥf�� v  veu/�*escribe�.ieof�krks �#%\�) chirality��itzmut�-$+&�j r �P}_{r, &8}=(1\pm\g_5)/2$L#t�,=.� �" 2O \uk)#  \g_j !(\vg\cdot\uk��,\q� j=1,2,3.� c��gpBof oppos�2�1a�u�� Eȁ`��.�- flipidsigg,&Z/hY*a za)%Y}sS llowauS��ar�mbi6�.se��s,y�!�0real coeffici0\W $\b$ �%��� ize} \a^� b^2 = 1)r- In�@4�+rischke,�*|.l,0s $(\a,\b)=(1Q)�� 0,1)$ w�) !n0ed ``longitud3''3``t�pverse''!=s,Z� 0ively. We sh�?�  !*erm�e!"�. ( ϡ��, schaefer}�$LLzRRn*Q � e .�+`LR RL6 � �.)�B0reason why boa�ase� nGs!(ed separat.4�2at a pur 2�]S+$�6 '�)eh ",in�� a:�M�Lhvice !�a. ��< cise "6"4�����$� .� Mk})I�$\b�#i!+�N[?�S� S21� �7�G�7gapeq21 w2%aa#� Z>N stilax.E $���_r�+�Qanalog: argup hold^ o6F& a�1 >q%an%�l admixY2+a�6Os"�-$$\a=\b=1/\�2V�usqU aS ``mixedi�.�% "� )xsR fw m luse�UU}�,14)� :�. ���, tabl] $}[t]{|c||c } \h�B �,@multicolumn{3}{c}�Po�/d } \v.< r8��Y� = J_3\,223F23}��]$}�j&g\pm g^2�b^2+(��- |,\cos^2\theta��k*��&��+ 2b.a � (n_1=8)\�,N2! 0(n_2=4).v�-ni%�k}5+\pm=J_3 x  F�2}/1-1.z)�  &6!&I� &.'\\66.8(r}$ $(n_r)$Ar;\; $.30$ (8), 0 (4) t1/2&�.sin1�.4 } $a_re1O&2%\"Cd}$& 6�5$ �& 9/2R1,c-1/3& $-e� & $\ln l 5/6$uc#tai� \cap� {Relevant� ntit3��G i�.}Ve�Ynd } .���ESPl, �}B�Q& JDM�: 12 \ \2< 1� + JV'*i x .h 2 ,$} �71^2 A�J_2 i0{J_1,J_2\}\,B��[ ]\,Z$} �M�ZL.1}=��.�+�N(! .)m��C�F1�2`/��1} >Y FF�ZjH�p�pZ<�o&i�1�q�� & $>��{>{ 21/4��t6]& 0��� -7/1� i/8$W$Q��}}�>~:a���&���A�{�{3\,\{�Q(\hat<1+i 2)+��[&w��+i�q\}�s3^2[(�t A_2)�2i\,Z]�X}�1�A�F� 2Y/2�[ \pm�$�xŷR�.�a�M����,.m��3�*�3:�z�Fm����e&x ^2 {i� A_1A_2-B^I4,Z"� f�Rc(1\mpb zcF�3�wT� ] �j �� ^� Z�A�;\; 2 (4� 8�ſ|A1b |)^2$ )-Z�e��V� x$ +2I /(1+t ) #(6qN(0VzJ ��� �&�  iY2'  2, ��A�:�A6�*� �  C"�  ��J}� uk�z\g<B�^Z(2a)_{ab�a� +2\b^\d  - u�b+�"�bQ 2&a-6&a &�6K��+ �*����\aIJ!8�}2 ��� ��( UBk�n=Fq�cF�r�� \prod_{s\�Dr.d)2�-*? sgH�r}:$Fm��V��W� x ��u(8 & "��<6q2/3, 1/3|)Je 5�[�� :� ^{1/3}�^I$�no�� u�:cCS�J*k-summar�$�rj�3"t PpT�s�F*� --y.9ly &�FE �<col'FB]�K\ \ZG q�Jk6�*�figur 3p-Let��yHonFe�N�� 8 pA��� abb? "['� sube�&�def�<b�/_{  &"&�����$&��/,�d7A12}\\ BC�?>B1Ke#,\\ Z2\b}b  [-.�T -, ��1. a �� WF� J6- T ]�0 Q"�)�)ai!2]�qu"�$-[r'Bb'$Z$Epdiago�#inA|or�/ But while?%�$B 9scalars,J�B.�:($4\times 4$+(L�4.�@�7verif�"�:;�Z�",d} Z^2=B^2 -� )�%* (p/e&�� I��@*a�!&aut4$by $\{-,-\F=�g! $,A��B�y9}�A}! jH.�<�$k "�t bf k*�7$z$-axis�>ind�7 $a,b�( 3"�4��of �:�%�' I� buK!0m=���7�9&y$.�-"h �J�"ve�'�m�!s %&$�N��*9!,A,U*�5�:) �2�$ �A2L!BFRO HFs;ir eigen$+sB�g&�� F{&!���e HAppendixIAppA}!o%kM�X�O ��ZHa+be�; lied� Mɏ�"ti�Nce6��$,thesis}. 5 �'�!��,kH6�prɲU wP  7AG*" defP"Alldst,',Jc, :� ACG2�'�G^� ��re���G!&�:a.ar}�(.�%�:�WIe�s�Yo$X�A2Be��#PHG FVP��)u devo%m'e� ^of<r��( �!��3. F\1�%M�!] a&� i G6(., immedi�de�d�9#$H"s.Z;�To%�$.�� I�.2�T 6� , �P.,d2;2vRb2� Y@�00 or less stra )forward,AAmayrQ qQoa�lengthy9R�M�#erW%in�=��� �,g-i !'=�,4cal T}_{00}^s(�k},q})��i T}_tV$�QllT%b�$\/� d $\uk5s�M� pullou"DE3&!�l�Qed�1sP'�n�!&�(��.~��ail"�(.�in�W��"@"�� F.b2B2 AppB6�H�-2>=d=6$%�a�% !�0aT�Qll6l ~. Aq� a��!dim- *,6�ToF91�.�Stu"�So �m&&�M, $d=3(36M�%is�ult�'al�:y QJ ��i:�#B/H�Si GM,C�"4!dAa2W d}=5��nd.�T�rP%�a��!�"�3_04$d"cwU.��is;(.��:*K6 uF�$I�a�DY���Pb� �tOL c�}� � � r|c|r"� ���.1}*.\I&�,t2z$�I2&20! G \,� \;$ *?uIm& $.�|W�\,BH6}Ap$ e^{-5  �|\ |\,\*�,e^{5/6�W9/2 7&5�V;\;�J>���%( �)]6?!/� e^{R-\pi/87O.�� A�.� 6*R�32�6 �& >��.o� :H)}^�CSLXg!@2^{(-�) 3)%w%-1� �.�z -Q�"�[Ga&�Qs]{2 $)HN� K�*2SCa�H"-*� illu�1t�,�&A sche�Fc�W:�� �u�.�m�Ju�*i��q�6A$ $I6XKu $>�ee&="%�$.�M�*6!>�!�6c9� M!�B}C.:=e�!?2�: 6�>22�&5 1z^{E�K.�/�LYC� N+ � � A`�_:%Tc@5�."6#�I- >%6� � p/�4&�2! .�$��:,&�����塼$ &�#>/���=3�h2/ -�kU0.65 ����/!�10U& $R��5R9}Q88 P9 9^�fM.�N-I�2��eN M2}��Z7/6��4 ���9b��� K1}F��ER�2v�@�h� �,:R�.=K656K9�.l�-% 3f 2^{-4/3�4X=�i�-�Uq:)��Z>�V� B]{b� p$ (=� den28)B � q�e������ N* �0:�Nn���D6 #p�4ly Bz,F��u 2�}5 Z�v>�� �� Lw:-��(B� )�9"j=E7>�4�L6\=�7y xD!�� quasiR5le�9i� *�9e� The�_ volvqy root��&BI ��BLo��o.+�i�� }�s VQBTS>%BA�*�b).Mm� F��Y �& ep��-%� s. � magn�0.� [r�\aB;�!���4!�:by5) y=!66�~2.4i�1[N(3}$ through)Eဍ�1.1*2�C2�T�?����2�$of 10\,MeV�2�71�2/A 410 -- 100\,keVr��M�� &7!x� V@s,&KR=,u�1�2�3�F �N�qK6�@iM�a��H a�. N!-��U�8azimuth�/ ?varphi$�/F �IXcY X!�r�;)�b!Q&+�qa� U%�in�� E %�iCh. N�cthe�%:r�a hiddMQ�dy�3�%mNb5�residual�y!Z2�9p!2�J�4C2*j'S0"��x9a�u#H"h1m�B �8�Sl�<u �$ ``pseudo5''. O�D�1�,toJ�f!�,�ti�:ly���0� ��4�Ze=.H %�. 9sD:J�4i�u/ ��v�<sdus�Q,?ca�MV�a�"U�J��*Ke�K�[ $*�"�3can>YE g, =Dide�+�9�non�vis�climit. :wK2�Ey� a nodal~q��0or1sm�p�Bvl �:Z/AZA as have `pA�sbnorth,south�#�$�o. �2i� [�C�e�?dun ��MY�.a�ht�<,�0�3�/�����.(2Tadd upA� 12.�E'x *�+�a $12�12�AW��A7i�de"�? �?J�"� �*�A�r-$)1O���by���j2 .�V� .�2��G�� �HigiblyG* e�-� showMRA��AT third� "- ��,Qi�i2�a>i�q6perh&$�= s ri 9o6ZG�:� ���i �llЕ�32�',�_� , exhibit E"ZiB��&�aa�e�eEaQ es, *�e!,6%F�B� $%x :kaek���c��v��A2noiBW m��a�N�!�>]&$M�onk eacm���f3!I�se9�� �e),�*Ba����o��!=|D����!��� I� }[ht�N2"Ainclua�Daphics[width=13cm]� s.ep�#vs�!{0.5cm*�6q�C&r 1kxFu? ] {S2 r�@�")C!�*� >� r,k}�pME$�� %�:>�P ">� ��Z�Al����H:� �(�� &�aN� ^ �dJ�[�C�* - ]��BRa�Oy!�M�%i e���J � drawv"$q e�&�<. " 6IZ�iN� 8]NjAeB K>� Tc},�"�d*>&�aA+ markj?e�?eeion "HM&GMd_.(c�@�x� &��aT�j W� ul�EJ�� easyA�rpret��"":�� m�F6�6$V�!�, &cdr��  �6�"���J*�a����M|�WkeV (ag�qCk)�&�$0$ MeV). S2dx�� ve�val�612�8E( �.Vbs ��, �I�� �3��4 )yN�!91K$J"A5 �60$8 s ost &��a�Q%\ p�ro ] �  inB&��,��,6r� b "�ey�Bwe�$ quesa!Ձ5prYA red �_e�z��}.7. Cru�qA��iis%�VQH1����� ctstrong� aHaa�}(*� F�.V� �L was ��iz��.GJp%�PicmEw2�aE��}a�g�Ihadhus�hOo�cM,"� �'�h� !�*�.�"CA("�tof ��W}K)j��`Q_:T E�i�isida�a"�a.�!(ichE���U 9��296C�e����ViHnte�Ta�� "�-���!+�� >� lF-=-�atQ��"�6� �dBcover.��dAB�$i�o the 21* 6w�v�c2nA�"��$�L7$c"JG!� L ?5E�Q"�B=( �)mIj��a�"ticipE��PA�}e W�E;N!� F�y� p &�s�%� "T �N5P� !�� �&s� ��M]0 h�%nod& "#n293e aQ�R.Qt le�a��k^#c&&� Gie � �Qy.� ((Q2�� � Hء�RK�ac !=YU,�3�$�Hwon] �i_)>5 ye�&t.M �%G|�GJv *helb{ic�rrge neutKQ=system"�l �hq���I<*n�a"aa$-�P J�is,_c�X�N/ntrrml /s�%�-E�v�1 X� m Cooper �Js.V�GeF,�0"�+� (gap�){%�FP , ch>5ya.4y%y 62r�!��� �ndzg5�P!!��of S� }J��+JV�- ess �y1mg�y�)+ ), carry rq� -blu"�tc'�nd �n1�� ense��le�: rem� un!��^7P�kn���%�E� . It&�oao�AXex3/a�S:�Ygluon f't�18^\mu$�KY�]�eno�1 "!�!�I�I��cualA�J�O��{Fii�5&|i$\mu_8� shovkovy}!5 ch %Rrim�Les6�he:LE��Med%� 1\-s.M�A�nD,1�!��G+� red/%�!� %� iu��yb.6�RE<%� Als7m"V\�3)� Z2� � \ �%v�Q5aV*!�� )b�m�"ae\S$SU(2)?)C2� Cof k!�5� 5�%��{)[%~&�L��a%u� �Yj -V|� Lc� J�L auto"& fulfillJ������ l" of6�0pT�.ti!� ti)� Azt�#a2? � !�*��XѬ�8,!3nve ���ղA�>L!.)j�3 \�U{S�8� de. look"�Uco���.�Up)]-��k stig� �possiblM�-.s���I ��l!3dI5s�te`!@]s[)��a Qd��� ���i�%� \asC/!r,JM"},�& �I�b���H�) iE�o�U�6�aesmatchAR8Uz�Af too)��bidN�SG i�ar)s���6mpar35B!@ "� �&� S��Ux $3 �3&�a p�i��Ctu� N seemHb�bI6e�m�� goal � is pARA� pick$>�e6lRi'Fs-�bQ�U\q2� d;0At?i)x-�\5i1.�or. princYV�his task����#� thre"� w/A��� "@ �?�� � one.& Eda  �� A�3 ���0C� �� V2"��pl"�E� 9�u�)\ipR��2$��Ya4 utex";�L4��� ��A�)���ݣ1�H��is �1`l !�A�&,%�!e�"�( Y.� `1>16! � *� ��� d-m�  >M � ES��t��9!�a"�Z clas�1)�s, na�N� (b,"8R./�),�mY s some feC��!(E� ` ���1_�4�}Ae8��>� *is as. "j�2^ ��ji.�vp:2�0 4F#F�WR#%�nRH�>A��:techn� ! Viem�!"7@d� sV. !Ig ��Eg� �Xb���s,�e�[ p-�ae�vqL�&v�< �1%�$uniqu!� �:Q6i�r�;e�"��"��t]�2W^m��l break�w!-�&�#i%��! B�WB fsEk2T/�:v�v�  W���inert-�Aw�v�p�LE�� demand�  a�� carefu�v �E�-���.:-%1�� �; he Z.io!�.� r�Yailed*]_. Bp �g� !mQ�11&� �Eet<&dZ.H)!� QCD�)9 �A�# reat��9iz8� ZF&:FۄG)) 5�Y!����'|e %W6�NZ� z� �{)�w,!�!g!��2�jgap �explicit� ul"��ki�B & = Bt�Ԍ�ԌI6�*�2����6�!���6\��{�<�nC�F\�B\l�(�] _q\, ;r�:*�d q}} 2/ 0J)y,.Md6�d��dNX���/,B�+J;�A9�q�$ (half of)E2s*�f&�,sB�,M�%.�>+�@=�ela��=.Xa�d& ���*R �!g"��F  r*� l� �-� $ts maximum.) �� �=�82Gc�E7 �d(" $Fhl�"� ��S��!0 �! actu����I����hB��'�ra�2p9#3>��#$. If>K!�� }}>1�B�&_ �;� 2�d2 �C�v��]al L A�FL�=e#�h�C�$o�@5 iOWc(  nG@7Y�i� 6�>1���0��e&��!�!�"'#.� , XG�L T_c}�j���l�@�FiD �M�2!�� �<� ��e�&� viol���5%a! -ᐹa��%�� � $&q�H lso N]!���/B�$Q* i"  �x�\�}�� �T 6�e5�*+#�!�qua*0l2u��" ��1x&by.btH� �za6͏��zr"� "s?R[��Z u{tU 2�"� deriv��t�sngV�, a�� ��"�%��1 � 4,� � *�3CJTA�malism%�/�/)�� �gA�|   5y ( ity)F� e":/�%�VM�5M��pa�.4�e-(b q��pq��l���)R)va)�**�?f�*-e�8"�7�)=�i;T v)1�E�� J�E i ,ren����c) "� eX�q-%�wer�\mbox{2)3}%� 51>[ iny��dr �"�N3*Z"Z8�se"��F� d es� ��":!�F[ $Ɂ, x.ll���� ��>7is1� is di��!�e�>7!�au���)�amo��.gi.�*e���w9�] .!�M��IME�;HND.!h!+ *��- Bn ls 8�d3fe * �&r1�c fic ��%ig2 ����O��!��7!yU��C�Y�n�T st5;�is ���2s� �]1�[3ll/ n)so Ieq� ��{B" s unQ�un��� ��ll� B�#��>yly�5sdp&�#a�*��(N c���uT*�PQ6�&exist��B�+ .���i�.ha2j!�a�ru��&bye7* �1%af ~:��8 t�-ikeV e��"b(.�N�B�c��a�observ@=�.��.N(very promisA�k�tud �%�%�J:E��Ge9$�'[ �Re�w�v�2�v3�LJ�ina�ai�:at%|�+  g ��yY�a7� o� Meissn�b-,!ruBL�L� m;"/sq��e��V4��at2is)Rlik�e]� X�^�� ] �#l>�)J.6Qm ca& �!:A�yeti� F�" m. 5�.,��-duz��3y UAH&Wrt&� E(���$��&e #�B,e8Cj&1+:N ,&�&�e. g ( exter�1�5Ba"�(�$� &�N penet�npths. F.�O^^% \b�E �.�!�e�m2d.�3we�R ,� "� thresh�V�[Z�!�e-!�nou �kN%� �� stea C9fc�(�%�����.-m��!"� *2�U�fupto *���U���p&&�Hf��6��|AnipmeasuR!z��:��0m�E!}+edvY�"loZ��c'e"/�, or,��"�rt�ola+curve (=.S��:�A ime)�<0hotwater}. Re�,�P�- ���e%�7�un����N�","����:�cE灁�i?S.�� bla�u"� ij< gred vI{�(&����A!�i$�*/eZkeVq>�M mo�Gor&�"�@YQ� me� ism behin�/�.�_emi"�|�*ino"b � � A �� ���fewR s ABc�ionP !� G�"dA�cF ����ino ���i Urca-� rF��!���.�&'mR�� :�tak��Lc7Ł&V�WT9���lso ��"; 2�M"R� * ���:5�c�}c ��(&� he&�3���/�O���� �-����!mA��1(���4&.$K� ��i�:� f�"{ ��4q6).d(a power law9�:�$3 �� W�A*6w�s����behaviorA���)��.�7ex).�*( �:V#�n�=�Ca�,� �-6d��t�!�6�y1�8 �q�* *{Ac� ledg���� nk D.H. RQzE`L [�iok<�+�V7$* ,manuscript. W(T.\ Sch\"af8I.Ahov�.� Q.\ Wa�orw&B,�Am�. "4Pn�ndix} &|+Or� &�#$ �+��toH G$ps $H=U(1)�)H'zm�� K!/a$^4^� "Iiin@��"��Vap���mea at "�="=("R.sub ���1mF�E`A�6��=,�.z8tor1})a��5�ET"�$!J$ۡ'var) ��=Vݚt�H5 ���nO�17sv�W2Cc~bsetof,]Ta \%!��a_8f��W3}.�2c� )\D_{11 ib_32} !�0� ,0��M2��M1�M3 ?!22�2��?-�[�'2��b�32�3��fL2�Z��fL6��db�e6�co"'��v�A$�a block.k� �� |in�w�IN& i��ub-�Want�� �Vn�!a�qXrs a%{2��� A=�rm  _1\,_26 3\, A_.Ԍ ser"P�2�a.:1%�e�[f� u� ^2-bsi�]^2D\q�� det1�h�2kZe+b PO�hO3O\frac��UO2M- � U V3:�4 VVP ?(� det4�CV� Now,n ����+?" list݌ili?z1 Ԝ al`(�Ad��AF.��%I�usT"s�ƒ͟Z*�A�enume����':$=a!�0$. H0ws� uish2@$�s (i)r$��!��-'�;c٨f.�E1)!.c�a�2��(i.]y� BA�vanish&K� \ �a_8@ec�ib�,ٵ(3 = -a_8/(2Q7) + 2c�IͬYd3�o&N=�����:M)I�E:?-�!� \D1}{N}i��Ha$�,{ccc} \D_1&i0�XD_220&0&0O\ 5i�)I�"Ml�1i�(eeD�!���sN�d $N=(2|q |^2+ 2|^2)�n�nM u��~ E ig�- e2}_� ANx�&Y !�� A^in� �1M��(D_1� $! 8%A sl~�1t�"�"�e|��6n] %$b^*AR�'�cho@�I w7�Ո� %"@Q��fa|Id6[���= %am��&�=)�n � �(� q b_32 �� %$c=F *2�4�$\D$)ϖro�"orm !C:�� �now�ޅ�� w  $H'$�*8*H'A}�rW�ia&� V ndy �A�9ՙ�Q!`iD_2!U )7AKof �}6��a� �J1i} a�<<\ldots = a_7 = bb_���  ]�&:t��}a_8 +! -2c = 2 :�:.�H~ H = 2 |  m� \eQ�WH a�9���W=�2�)��&I�a ``brok��m�9 on''�$G$3E}1��*� $Ta�"��"�Y!�g�2 �K$H$, et�Odm�.", LieMVArb<u 0]%��k76 �y�}�. �I�%im}\,G={� ��2��203 = 8+3+1=12�+6��in2�i1i�10a_":2�H=a"�1�=�%.�A: ). O�nZwor3tN �$�d�al�,Fa��a�2�a��"�U" re�� jt�8.�s2�, 徽lwo#avVi}�K%�"$U� V� �J 0:ma�!�2=T_6J_3gj1iZ"I�2`��t2�4��d�P"y��i2Bgena�U = T_8Dsf� 2J_3m�Z0V�1+�y10_\�/ Di��t>�s��e�lwo� �s:)rstܡneeM|rS��Y)�on $c=-:A$.' �.P��h�5���I-�%n, ��Z��i=�y< ��: &: \Da�Z`�= add2@ Z( +; 3*1 .��E;.;2���11.�g 2_ $a_p $b_nA�+�ulea�ma!��%4�Ma�+qe�"aJ9a8��2"i�o�"l� fs $G_�.$G_��$Ge[}U6�1�}{2E�B�2m� �� S��+�A�� J*�  c$ toq .n#USA�0&ųIaw� .7vH=US���R&Q�E�2!z�x6+,"� 2.�o>F �%5�  > 3& iE�* 6+ ^� 6�3��E��^�- ¾"�)�F�%Un� "� � 4QU�[%�0 �I1����\K 3~ 4 56\\ 0��0�g�g�HvBFޕܕ6�>i|&o .K,A�BY one-"2 al2�n_��+��1@��N}�J� et}A� _N1*C� �3a 0��� ases:j�� �?,� =�. B+�>Z�dx\\ ���z2FO!�a .`�/s{�ng* b5SE�F� 2ʯ c˦2� e���A&D :� � �6��b�bya7&y�H�b� | &�?a6g"W 3=*#th�:n � �� �lb 6} ˗Vҏ%��B�a_8=c���� �� ��AqV���i��2J�A�2�E��� �[\� ����"���&�(=S�I_J�u��76�e U:n �v�0$.�bZb<�c�*6=�5�)}r�%�6�\�j�q �)��!��1&inp.q�e{A�c��Hisi� phly;FfA� ?�E"�A�� I�Q4>a�A�(.�v�yA�٨%Fo�)e{ "F �(�or� W$�G��5!|p+7�3z| 5� FQ.� 2� �QH CV b1l"K s3�j4�4�I 3| +2c=E��:b�f�?foN!f�Qҁ�-  r\3z#6 *� �� qf["Uq�6�a� $12-7=5$NF` e���Sa�*� �6�,��MU��� Da�S TS � ��b ��cy' gaug-� �j 3)_c ��k;3B s�'D#cho�@�1�gen!�U=T_8*~�5�2@ &���+2)�Aega 1.(i�6��su�i�"*G6� e�&N. Nam՚f���%%�5� �*J ,`�$mAI=�\,/� we.��� ��M &I S "���3i1��?2���R  6��.�>'  w�n�+)s���2��6�lA$ �2�M�M�or)E?"� 1f�� b��" B�.�# Lmz��E] 3ii}!�\�j�!�0\�5 1%�3n��$N��G�?*��2iiL-�"�}.�2� �)}1%�aB��=b_2=b_3��e�uad c=m�>+# i�HenceN� R  A�M'v�� �C�� ��0A1�aL�!3��� .� 4=0$�� F� �:�l�d��\D=~- ]x1AKndS \�E1d2�!2�M����A�,BqA�"E�r��" "� d"�:r `.� >Un3 �"Y��2�!���%LF�v�U�2�A�I�E.&�cB/y H�2.*�F-sfU��gen%(}�Ym�2�2|6��m�T" �2&�,�2�JjL)�A*�;6 �peYOc���D)f�<6. �V�[})"��co&��"� ��g�% � х�Z6� 2� {!�`Q&c!*�h �!!2�_2.�!Ka�*� > &�*E&���*�m��1+�M m�sa��$��S&��P�k_ ")(1�*i��%&��.�H)6T 25n = &��-F�i f�t#, ��Ze c.f"#��a�(�Y)؋�  prQ]Y$o�� � e�4$(J_i)_{jk}=-iԲijktuo� զ� \pm)?�.�,2 %F'.xnpO.} >On =.O ^{n-;�2U6vg6 impl97� �$nj�k!�>�IWd!��!=�wEB "��&p&(� -=�!����& N]�$ C�D:�/nc�'t�'( 8>{ ճ�1v �_+[sTr j�~KL U�� ��=&�(tr}�M�logarith�!�>�$E �� �Ţ�3/ ambd �,� bf 1f�{�_ˡ "��2\}�}9= >amarmW l -��{n�{��}&'n--� ^{-n!��\, F�%�[e?qA�#e �*���be"(/�".mw).'�,�6� = 8}�QK� � ��b%�%,^4[ �-T]^8 �MLy!A2"AA!A�#nd $0r&2�s8��4:�s �a� /�HA1q�� onfir�Y�Re�pes�DQ����@T��>tt ��� .���Ya�a��ppAF��"H�eF�J>�����2�F5�4A�/"�>��A��Ls�MedF��$2=�2o - ��-�^2+4B^2]��E�1��*z ݣ���x���aڔ�!6d��Nx!2��p�.?��B �R^a_n:�+ b_n �2���j 2�$a>E.Rvl�m�5Z),l  JI�.cur�;&� ͺs�`&�,�a_{n+��.�`n&n � " b1-.� + %� :%�� Ahů�7�=se � = p^@ F� a*�K"���$p!�e�!�` solu�ʲ p)� =ĥ!�A_� �.�*@ ��a F�#�{.W��se�,%!n=\et�' p_1^!^2 p_2^n$�6��0H +jR &�E$a_1=)��%�+aJ$$fin� A�*�+��1N��( �- ��\`� A�= &� Je�-!k� IN] ^� b f]<�O�U#0E�{�O�S�x-p_1)^. 2)^4&� �C�C�< �:+�j��-���.�0, $p�"ŃpX*�"Ջy��I�6T6q�biz�2�.*�N>f �>{ՐP}2Z��6��CA�.������-�E.P��R�9'\pm6�-��_{2/1})�Vi�1� w  /iЙ���.�"T��- F%=�-j����ɠ��!gin63�%p��bm�br&6���H���\�i!��̅�}\,Z\� mM�6Fj2%�zj����j-k�1��)7eSRm5+\Tr Z��T�:��e Z %�(7 s�*  D���f�lqh"k &�Tra�a�Q2M>8r� A�B�H"yw�b}: BA.e*-_de?F�H�F�mH>equR� >�hFV�N�d�.n0@�允x;e3�oa1*5>nd�|M ~ �;=BG.#�]� W��&�00V})��n�/�+�����!=�pu5� in�F��* �5s���_^{�Z,t� .u� .� ��':P Ɂ�c"X�dJ�Zd*  fJG �.�$-�Jl~�{� bWdefQR"|7�{Q߼$mu\nu}^{mn*��Tr�3 [\g_'"�mŤqJ!.sq}��|�\nu-n-k>-kxЅ���;��R��g_0� \"�q\,J��ʬf�W�{�mNB��.� �^` f���$0B�0� mn} �/ -\d_ (1+\uq���� hk_mJ hq q_n- k_n\,3 +n1�"}�J9 (\d^̽ -\hp^i j)\,)�APijIL&=&)���[-�p� k- � \,( �1)� p_m(� �nANup�6. &��(&&~.�_nAm)2Aq +x%+k:dA?BqY�p5*%:acA�%�F>)(s=i(!3+�3)>�Ca (\��%�!#1�(X%�>m 21})I61�%�\{[1-(�)�, �6qk_3-(1-=�) .CA}5+�% hp_3i�6E��6<�g&T"\�.} ϡ��� M�<bϡ�PB=�}��".�0,1�+w*��% �)da>^\dag2e�� =4\,!7!@^2{ ��+("  T00 ��r�1(� k&r��� 1}{32dq��2e3� -�8-^2 $:�� �� !x�Ŋ!}�[T_a^T 2T_a� ]=@�� �re@Zed. An���I-t2�t>�tn��� �-_�^� � .$+E�^2 6=��E��q_3)�]�q&U�k) e/j6^�i>�].4In&��!as]�+6d�g1}{_2"� m=n=%|v�Len x�%�4�� XKeRf��T&7�SibuE� 2o "S�Q�2B�=i5 T}_tJ =� q� �=��8&)Nex�ra�N"~ "��kIs�0��T�w[nd,q!�A���f�; (AC��ram�B��- s}):�1�p<o]E���hs 4Ie�`dir��o��� . By!pven� c�%�7oAparalle�e*��N���%@NVcF�: uq$,+anq12�$xz$-�M9\uq��(&�c,0ϼ�c�Q�$ ,9�f[ )9�-�%.�` % !�a-�� $z'��%|!L�$� "r%��� B � M� \�Y a"lk $R( ��*�y {} $��A?N3+z� K��-9A����1�$"Te&.>��+�a),� �W!k��%;�%'����esA .�'�3�',�' co �'S* x�-��*�b��t��/&*h%!$-\$��notJaei4> (4��c�W�A� �) i�e2/�VB6�w�\vEX&�/"�� �Ct^� C4:�3"� .� � ),`H���EaQB�!�_k/�*Z / qI)��ri� �N ��E&a!� ZM�teE�ߊ�8~f��se+� $k]hq \mu"|is��mcTb��o$.=s ) an� definiA�s , defT:TtA�weU��qua�ies $ID T}^s��B�$p.'tF$. Asa0_e$iY�A2Vh = �*^2Je@=0$, hence $a_1=1a�(a_2=0$. For|@gapped branch, $s'on��4s after taking3Ptrace over color spacI��1_�\nuF!�vM�(A 1^2E! 3^2-�� EQa�mC ^{11�_/2:/)�2.2��u eJ(J*1*J21}i!) + \;M��( HR2� 2} - �2H} {6(a݉> e�)} I�.�AtensorsQ Q}2[Rre E�edAM6"fQR}).�Sord!� o perform ^!�s)�Dirac-�%� makes useay��em�4a�e@We do not present5exp6t for�T}A$00F  �}i1J� $ siA� they� 0too lengthy. b�4angular integr�ses )Ea simi%X way as discussed above�!�/����i�,. The differe} is that i��6�G)�parameak does)K oint�o�$pecial dir�F, but^ loca��$xy$-�e. �Eout los� $generality�(can assume 9,$ to be alsoAP6N< q = (\cos� ,\sin $0)$ (cf.\ 9  diagramKFig.\�figuref�s})gt! aA4$is choice,5partic%� $a�3��.� show)`� term!�por��al�$��$ o)�� -hand sidE�Eq�YF>yield!� contribuZX!MI l. AgaiIO rota�e � suchE5 $z'$-axis!�!�lle�)�AB! an!�d��w� twoIcessive e�  $R_1i6$R_2(-� )$: First%��origi! �8by $\pi/2$ arou�- $y �,�  R_1�� 8array}{ccc} 0 &-1 \\ 1\\  > 7�_] ��The2@�vaF 2�new $x-Dp ��n� �� �]� & -]�#Y� &21z�As�4E�A0�%wiN'aO0,0,1�� $\uk (ttheta'�'iq �',% � ���� i<= R_1^{-1}\,R_2 U.\, {R�}1 b.z  +) %�' \\� n�.&6?%?)�BZ' FTIS!�eG $e/q =�}�/ �iD!�6� N� eV����������i�F� these"�m ncludW=U�N^2A�g-e.� %�� E���� ���?,s correspond9 o AXo excit~s, P./2}^+$�.� pA}), � �dP&�A}� FM�1 }\,Jp �\{ 1 \mp� i}{|�n|}���[&� � T� 2� � 1;;�� \} *�>(~pm ~?3�b��)|����)&<,used. Insert%��d5��0!�!�a ve *� R�A}o.xRᵉB �B 1�TmunuA1� & /2F5 5�6�\g_8, -�-�� i9�2)�]����l.0 q}^-A5g_\nuFx k) -Bwkw2Fk&v :8 2F��&)3ft�� -�� =�P {1,2�F�E0*� ,6�$,B q� bxes,� ^li� fun.�  t� ,wNu ir "x � s. �~ �,2{,�>� 15A�~ � �� "�   end� t �$zN . However p:�:� l� $ '�ycann�a�� sameB n because��� p< %%R be�-&&C , i.e.� $ $would lead�(a division� $zero accor��.m�)�steadŪap5m most� m,�y   *6 *  1 ,*� ���[A� � e> i!�(�� � &� .� )Ais give%.�sm } R( �, �)=�cNU � �� �� 2!*) � 80Z ?Rf22eG4.� ��͛�,Consequentlyig$$d\Omega_k���lŨ~�ed� !L� R� x5?"� RH} � ���.� './�m.� '+F QG .!x= % $ ' ;&. .&9v& K: y.) $>o4 2K 6�.f��'=�� %� �employ� � Na�PIfr�{)� �mJe{RU!��i:iri � w ( ��~~m� X�2 ^|Y|}cos^2IQ:i�� i $\pm\,2\,.C\,/E e%G)J~ ~�� e\�Es rise�a.J betw��*�&�*,t0^�"�+2F�.�&�i6�e)pr�l� of.2� ). -e�/A��� choo!h�@efficients $a_s$&a(constants, �.J etar%���A��e only �!��whip�c.�de�l$IB$��anglea�)��3� �& We�e�aqe�e.oB�Q,, \qquad a_u 9 G~�G3 =�0 i"� �1n $d$!A1c�all o!.K �*� \$ Prov� $\j$line{d}=6$ H arbitrary longitud�gaps}   AppB%is�� xr pr�V[ny� �� (= wtny $3\times 3$ matrix) $\Delta��) a9aB��Au2�/isq�ly�ple&��truct�"of� �q�&�%�trivi�4 Let us startY!� >EpBSvv7 \vJM` \e1$'=(v�k},1},223})�a 3-v#c �5Xi} \equiv \sum_{j=1}^3 )q4_{ij}\hat{k}_j�I� i = 1,2,3 I�bd(L�^+)I = �@#\d - v^*�j:�a2.I�=#^*%L"l!� $2�^2=.M,�$  \Tr 2 = 8\,v^2�$%� eigenvalu�f $2LWeasily fm�*methodun, ApiU �!AppA}. O*>%l\lR!k,1:g��8(\mbox{8-fold}))�|)�B2B0:8428� J{ fac�l�#is�d2�ide� cy 8%f��unv*4Q�e.# ClE it �\rue�P�l�B!�:6W"�s%�� %v(i�" e�U�a�U��$]� j}^*a�"k},i}}{]P:fNl�mYlŹva  @ ^2} G,u�isss � �V&&= s�%, �uuq��k}^*}2�� uqi�ukh 'E�t^{Jn ~� �~.�%D"�%kq ��F2� }J� =5/tN+" /B,"& :�7 a as�ai� j5M�$previous }"nd�f��)U�.3 mQ$}"�#'s�ex� ��)�"�d!'.Je7~ # +=�y1}/ q,1}2//��q}^2$ &)E�U�(*2'*d\, & } q} � �)gD ��63}, 074016 (2001). %CRYSTALLINE COLOR SUPERCONDUCTIVITY� loff} A.I!� arki)�Y%�POvchinnikov, Zh.\ Eks!�$Teor.\ Fiz1� 47}, 1136!=64); P! ulde%0R�Ferrell,6�%$135}, A550 B.6$shovkovy} �S Y!�HuangU LettA] X 564}, 205%"X3); %GAPLESS TWO FLAVORJ)OR.N& A729}, 83P.PCVn, AT ZERO AND LFINITE TEMPERATURE. =� gCFLAY�(C.\ Kouvari� �%U92}, 22A�4�apless E�-FE�D-Locked Matter S.BaB\"usta�I%�1x�D.H$ischke, JR A743A27}�PHASE DIAGRAM OF DENSE NEUTRAL THREE--�4QUARK MATTER. a�$Fukushima,�Lhep-ph/0408322. %Heav(-)2 -Quark1 \��kaon} P.�GBedaquI�T� \"af!)N69�X802%2!�H."qrm%z un(*stress. �,Kryjevski, D%�KaZ()�:�$4290; %New���CFL2n:aeP��Yamada�,1C 7350�\ FL P(0��D�� at Non Z�S�ge5Oss=Mmue�} AB M\"u~� Sedrakianu�6�!N085024%Q3a�xBREAKING ROTATIONAL SYMMETRY IN~�S�one���TIwasak)!oIwado�PLB{350}{163}{1995}; %Superconductivity!yU .� R.!hPisars \6P8 \PRD{61}{05150�000a GAPS�KCRITICa5�J FR�I��nsJ.�ICheyneI[Ge�Cowan�7�$4018}{2003�SINGL�i�� m�Z.� Buballa, vHo\v{s}����Oertel}L{9!i82002 }L. %Anisotropic admix�in/-s.�ng2�.^r��}���v7�%��L R�0weak coupling.yschaefeAjAZSc�H R� 2}, 09400�Q0A���hadro�ntinuxin{5 "I�.~leggett��!�L ,mnMod:! �� 331�75|AA� oretedescri"�A�k)d�1(liquid He 3.� vollhardt VE GW\"olfl {\it )jflQ��b4Helium 3} (Tay1 \& F�!�:0London, 1990)� �� QCDgapeq}6����: m�A�14aa�9e >e � FROM PERTURBATIVE ONE GLUON EXCHANGE��HIGH %�ITY:�D.��Ho�Ve�Mi-ky,R�L.C� ,Wijewardhana��L60�L Erratum %Uibid.}"\ El59903�fEl8Schwinger-Dyson�roa��-!o2s�� eA�.�s�PD.E�!��� 59}{A�19-Y.NQbt-rang�y magnA� .ra�#a %high-�a2�9�re� (W.E.\ Brown���Liu� H.-� R M1}{A1��0}; %O Perturbat�&Na��of^%. \!~{62�a3�Y0 %Nonfermi Li?Behavior�BRST Ide5y�aw��{4Gluon %PlasmaE�� iA.�B�6 � . %248ixTempeA=B9`$2�ngi��QC %1Baryon 82� wang} Q� ang �6I%65)&05�2A%How�)�self-g1 gy affect�,5Bgap2� chmi�� , �IR�6M0�W�!�Z;inJ�p4i�0t %like&BCS�� orie2I i�3} L.\ M ,b�5a�617��8i��de)$!rbroken"�. Con/2q>&idd2!}H-<2�T�=L{9�423��3!�Electrou� Meissner {ct!spin-on�.~or.) �3��D{6����4�MixA�!.screenof photom* nd gawu aIw:�.rcjt} � ornwa"iJackiwIs��Tomboul�̥/Ek428�-7�EE�ua�fo#8mposite ��;.  ew} :�Pro/4ParMJ� EP19�4.THE����PLASMA��(EQUILIBRIUM]/abuki A ,vTha �110}, 93 q� Z�A^�~rue�}:�%�: %nE 4501A�0I )p!��\2���4 massZradiu�a��tar�manuel} �nM ��2�a0 0A��� Kundz !�.�!j-� 1156� A HotALer Bottl�!Ag!M.�.�bla��Grigoru�B |  VoskX?|2�619. %�P�ON�X WITHN��b��CORES �G>�� document}�� %�\\class[twocolumn,aps,prc,e��addQ,�=pacs]� tex4} %:H >l+ ,preprint4\\usepackage{amsmath,bm}%2gicx}%aJ���draft %\_@{} \title{ Isosca- b��z�LFisT  Dynama=, %\thanks{ %D\author{Y. G. Ma}  �Email: ygma@sinap.ac.cn} \affilia� {Shanghai�6titiGoff%�E�Lics, Chinese Academy$SciencO)HP. O. Box 800-204, W201800 Aa! �K. �����2 Gradu��S�+l�!� � N� .� X. Z. Cai����IJEChe%�H.  25�InF �. Rn  6 6|�}�-Yw-}QRD. Q. FU����F��W. GuoA )y C. We�" G. L���2,��a5�q� Q. SMu����)xQ. M. Su!x���|�f =gD. Tiae�]r��� b��Y. B. W� T�Y�����6l��B�C. Zho�2>NB�{YB�I� X. F�����n ]�Colleg�/ Ningbo UR&HZheji315211BSJ. �Z�N`5�p:pXBo}��0 \date{\today 0 abs#Kt}50 f� )Jss�$�L2}$Sn +. '6   g/simul�IW)� comb�P*�;Langevin&6X-sA( ilibJn�&MWum E��bk/. Rece%@is5;9s�H1> )|a��ly C`d����#�I.�same �y�fev�Pt*`a^a so-c�Nd%rlaw9)Ned 2�ly-<$TsangPRL,  2,3}2R mean����!¥�pe�O ��Z�, 1�2, O{�W421}(N,Z) = Y_2 /Y_1 $a��6eh*.a-,exponential EuiOhippF�m1Q$N� i���$Z$:�X/�L } R>�c0�}{��1C�(� N!<�} Z)v0ndZ�1$CV 1 ��pŰt�9��(n grand-can�~al limitE�� = �9 \mu_{n}/T.W = z �n}4DH;Jz��Q�ces2?1wA�)l chempot)�!�r A0u6X7 iY�"� at��Xa"�A�.N� ic��S� �> y. I�AsF0B>CU�B& ���\bye"�V�Bofa$q���Ma_�ew}. S��r� B�IHora�n .�51F$ mechanism!Pan�i�he evap�ion�%e�PRL},� �HFriedman,Veselsky2}%�$deep inela� xa�Tw���)�!Jjecti�� )  AMU1c bmulti-2.^�%��ate��B�LiuTX,G�%i}. Whi!(����!( phenomenon�(extd vely exam37b "� the�(� mework>c��alQ?�� s,��@ as Blotzmann-Ueh�$-Uhlenbeck , I*�},.-n�'$Molecular �2/�%�Anti-*� ;"$ ;MOno},1�A�� � �!A|an�emiy source .I�2EJ�Y��l�ce ga �-E�єH,Botvina,Souza,Ma}."{k^{2}= 2l+1I �2�Qan�@�gng �aof Ref.~c �Nam�fwidetextJ l_c] sqrt{A_P xHA_T/A%CN}b imes (A_P^M3}+A_T )40(0.33 + 0.205 ZE K0c. m.}-V_c} )>""�E�$0 < = m.-?)(%}��A7!�� Ucke�� pute�3 2.5�^S �a1�, $A_{T1�A_{P}$ C"e X ���N�6�#HICNUIhe��E.c. Ye,barrier $V_c~G&&ansatz�zB:Q �} !H�5}{jc_35�f�OZ_PZ_T}A)�9�+1.6}Fij c_3$�K.7053!�e�� usen�=$2� H�� caleX }F�[6�left.\{'a(`ll}A�A�)^{3/2Q� 10^{-5 [1.5E�02�(U@AkA�-10)] & 9H��Yd$ >E�+ 10$}\\Vz Nz- 0.04zz & bz<.z end - \r�B . \]>T T6)e� � "�E�8�0�-� teg�a�Ce px/�G$qi� gs}$��A��>opy $S(  gs},E^{*�f$f ot},A,Z,L'$qo halfB a���P��er�ai�� u�4� "� a�, � �to��ial*,]�y $:�� g|V> =��7}�!/(+�")+ Q$��re $QM��� $Q$-3K cal!�!n by $Q = M�n+M�h-M^�&LD-@�/. $#�H)a! �D�wp ��com=dom & data, .. If i�'un9� 2� macrosc� -mi �ɬ$}�6� �AB�Q >�G96E%�9-� b & A�\� #L.�� &#�is drE!��b U@F!�F��ed E leve� ?C" $a(q)�IgnatyukJ�,F(q,T) = V(q�\7T�i��iA�e�Bmi&�,�-A�?��T "�E($T!"k*�-R�  5-�/z dOV�n�� rdq}{dta@-�s 1}{M`_0(q)}�U\!�a� �a} �q+jD5\Gamma(t&�v� �h�d{ 1B1co[[bdef?\bove. ��1 FY.p�S A~�M�\fl}Qa�U'Aoj *T $�$ue�Jed 66 nK-d!�p Wm em: �=Y4 ]�_T9� !Z , �Z1)T $M5�-tia���i7a�s 0j��]?V. $5�Ta � -&�stoch� vari�� &��:"� I� verag�d �Nl% _a�written��eU> <�>� ,\noE\\.&''2�_{�K4epsilon}(t-t')5bboW�MV(�%,� OP u���thP nite1<��%jIZ�v �Rq_, = a_{2}[1-km|N-Z}{A})�bL]A^{2/3}[B_{s}(q)-1]2+ c_{3( Z4}{A= 6c 6+c_{r}L!A� /3}B(q)Ad label{Eq_5 ���Ix$�sB� �E��r �surfa�WCoulomb70�Mnergy% s>� M�zW�Q%vdV&on.4$q��%H�% k��� &� s�m�* EIn our�ahwOk�m 2(R *�19��T7.9439 S MeV}, ~~~�A�� .�k?.7826,~6� = 34.50>.>ѥ��ouse $c-h�ch}! �!r shapo,y��3M[hoAW(z��t��z}{c_{0} )(M� 1}{c^{3}}̓b#}{5})- + B_ �sh}(c,h)O�a}E�F� w!c R%g~R%C16m� J:8�ar ���$>�):��&�"c��$q�� Z �� $A�f�K aN�>v = 2h%`c-6:}2' p�O3}{8}c(15�95}>Y%�J!�W��� �C�'8\a`%�an xpre�oq0 Smoluchowski�)6%}($�Q!�$W f"�ѷ*��Nis��ɗ�ki�A�Pre Q0&��{Q${q_{n+1}}= }} + [)yT�{&4 M�}dS dq}]4\tau +� �@d}$m T4.M)> e by+}wsq�u�g � H� �E�!%�� stepB�, $^3 aJ��an�#M�w�'J2. �)=2 �a(q,A)[��-V,Z,l)]g��. � �� Q$�\)ruX(�inguish�G"� possi�(b�B��A�'#nte]�� lite�B���r +� ��qSof hot�ui��t Y�& rev1&� �o 'p�s quo!�t�SIt\^o-:�u[1)m� Risk�D"�� exclu�rly. Als5!Ore �]6] s, n �(of �Ktonov�:�}6�1/2), �*c.d�%ron^��m!MA�.]&Aof ~6�>�)-�h ��Ys= 1�J'adopt�&-body!�s (OBD)"�(���ZoA��#� OBD}� obd} $ � �S!Jis *�enonJva, �of  Br !�ep9[e s�al�^z $we claim. �5weA"nt� fit%}ula6Zwoo�in$ -| fit}� \[ ��� (q)=fa$15/q^{0.43/a1 - 10.59q`�so\$if $q>0.38# 32-32.21q $q< Z� eJ�Ae> � !Z:I (n, p, d"V%$)e� gianGw pole�v<� �h�at each������e��+��<�d d:ddW.a�"Y�2riz�8� Blan�W/,�sLyn�# }6� � �R���Dky ions1+s&4�I� pic/ Y ��F"�fKon&`bFig.~:~ fig_Z(-np} (a)i(b)�!dem We>�y� /�%re-sc f�&��$R_�'��2-�&,P$�~� � .�  2J0 6Q,�6�(��$($�D}/A$). x��%D � is lr �: 1a�l� �eofQR�(� &�mdic�R5>1$is �-er9 bYt��� $-9�!wT%�t.to6 @�y trend. Of�rs��Rya n�!"Y2*:f(�OJod#a��L"�IMa_1999, b}.�!on�m�Ri"�.%[, )H�<�/de�. � �-E��Y e wa�{�� � Ն�(c#spin �H�Oe�G !� � Bhs u_Je�JIe} \v�{-0.2�`i i�u9=s[�=0.35]91_new.e`eF? \ca�{\footn�?+  e>E\ 2-�qq�i="yji=K+riF7�KZ7 .&� of.5R("Rf2;A 1S�kf qp� �"- ,on�%ceN200,000"ev�hE$ happen on�^ s)�(we�� up%XN7in �!���CDST�� �a ":2�YB� MgmPHsyZ�er 3_0"WA_{1}-A��{1u2}�\A�mu!��epd)�\u,a0$�m5.e �o�� taWL�V� 6� *-1�1 �k �+!G�q. 1}$���� /!&MR�%B�� Q A!�%LB�0M$same $N/Z$1��0�iZ^al-cet%HZ2~or $Z_2tFb��d"X3om�� $A_2$+l�#u&p8 F4H0 * of�+~�ic&�#&~2s~+l*�+�P-7%Q� dom "� "��ch�i{1�Sf@#_ K}. 6AA�}��t%�hw-.�+W7E3Zt%xF�E�%:i�EsumL"i"�� �se7y�I.24�S= �q�eu�t Ɓ� � ($\sb#_{mi {0}}-GR�'M bigg� J2 &Pc(�-�2J(s b�5��4ş2��_3¡(Co�Sonal)��1-2�24�m6*�� ��1���!��EF�  (ope�3mbols��,F1 (fili,-$t 8.4 MeV/��_�Y@Q3 !�th Z�Ab� .U..6i8:SA�eq A�H*>U*2VIs�t 13 O3raowj6�iso(e s�S�kful�(dth%{FN�"&v:sm�am{S5� e0(��}� 3|:�)9� |absol�E�/J1�cl 0!roi%79%&ni�:!/.x �O��( � (see:�R3-mun}bqpparee6"!] not &�7���A�RQ�*"�2Bj�0�j,:W=!:I;�!? G5 itr]�� �]3�]2.>� 3��^� J\%�!�� E�� (b):�o58��s�y#.�!� K(eG!Gi�~sMom.jnQ/�anA� 0J���3>�������. RW�06�ic��mE)e�X&�"�5t. } �� a�:yL>a p�YcalB � viewɛ> 0occurs(n� A�:�A�a��%|��� �es�8Q�� aduB6���s�9it,=E mean�&vc"�%�2W� �"o $Y(N)|_Z$�(<nij<N2< Z)|_" �K�.by ��leV�,�r"�k {�k*�(t � �i�[�,(N-N_Z)^2}{2r Z^2}&� ,�{Y �F?Z-N_N2?N?"')�& $N_P nd ���82�%I s, Q�Z^`�Q �N.A.!- 2�Aw�ele="�;��̊:L%�.q�)�aDoan!^"�:"�L� ��x21� �' quadcAh%-�3$N!,�?eglecti.t Ng$ln(.�:A�))��$[(!�_2- 1] N}{->!�"�)�6PE�FPN PN)PZPA .�r� appr,JA;Q�P� Eq.(M )) r�sre� ���1�%�n �%��}Cx��8aЁ%�:�B&� a ne�/� 43i"�B�*de!����B �$�;!��&� �t�DS8!@�xe&�2Y� ��� -EG=ly�s ��"�R��?ach�3�q t&�>,:e^�@aQJfB�A etc. Co�y' �_$>sIrex&F=�r) ?>EL)� Z)�x�8�an get&/QGY N&I�U�U�J� {�<.�p��T�':F�`B�T.�]"L(�istood�/1-:>'1c= a�or!� ton "po!N�"�][%'�.�5� b9< 4V< { �< &� &� 1�~�X �>% c B��AF2�5StU�2�VG ��!s1���two�Cs ("��alm�66� ).2| m�1� As�oal�"y�ay���2�!e�%� j6 �inf �V  6� �1�!�iC'"�ion�E%o�  ham�+cogt;�#gB�$Z$"�*i �Zx�FEe*cFly&�D�1e �l�*-�� {/6<$^{208}$Pb (1 G&w) +Qs�p$��OG�@loi ft f\"ur !`eri~ 4forschung (GSIf!0GSI1,GSI2}. A.N��T"�Baser�AHrn Og>Vbra -ab � @involv�_8s%b" by Benllide({\it et\ alA��GGSIZ\sy�%�xs&CL"�&�l0�0���z&�&b�z��"�$u {Z}^>���B$E�}�2bf}�.N7 a} C� mac}}"�T fis}}{2.#"' ��6`"�e"�� �*�.%!!�QS%6 , $a<0 3p�., $�)�* !p T!�]$�: curv"8V� �$V)!(`a&�-of� b�2a���V�"b.� �eQE�m� ��^.� C>a�"!!�U��$�K,NBQ-F*�ih���'rig�Oe�H�+B�^MoB��Y��s.*J2�GBy4 2���% display!�E"U'%h B�N�=wA4undo2u�X�J4�$Sa}F To��i�<G-�!hi"H(.m�m�*!of*g�G���!Ma�&j �Qo}��c��b-1A�e�~}�' dy�[�~� �Qish���!� A` heir6v>5� 5_A$B?� M�ed =� �1V9}wo � frJ( (top panelE!�>bottom %.&��_ZB� In@ 16) � Z�Z�b  & � a� M$� 6� &O.� �#N��!5aB.N �N �R� 8U.�6� "� :� � M�Ab�Le��e� N& " B ��to1y���NRof �B� $|B�|O2�#Y6� o>�kB?� i&�GOq�� �?��,*� Nz_��!�)�� :�Z F.�˱ ��J�utC� B�just b�4���"s��c�e ���jse7-�polynom�feto gu_f�ey�DF� ��)5q �\0E�2�|��N�6 !>WJ\b)�j� are �%�^*�"M9�� Z���{?N�b!b6�,  }�K�"k4<iwto&Z��� N$!�2�, R=a%�:*�s  how �:ou">P�n�) z6l}J�$ X�) �"O�'�)id��*V� � sm7T:JqS-�;��NAVR� be ?sLinb�" *tǐatebL!� �:la" 7�"x tRa�woFK 2�7A*"]!of&^>!"� � "= &� M�B&T�؁sul�r�tEst2 R�� V�A�F�r:��!!6v! ^"[*BU $:N$"$|(i�q|$ � as j| A�ؙP6{ ,"F&FVd�t2B�-�#th]�^�. !�;fig*�i&fU%�� $7_N21_Zfis�� �STiZ�ed:NJ !v2��N m!��%�woBb.%�A,q�ce -�:� F[*�E 6�a��q����e� a���wo-v P6� in%HAGa7ar����W"!�B6O1>!} �1)be &p? $Dln}&? = C_Z/:XN$�e�B= 3C$3pYf� plotc^� 2\N,��&�/(logarithmic? �o�9o�y�ajG%&� 6� &'}�A�#>["�Z2�' ?�a_�4�3"�\�'d )�.�Jaa�ch2�of�pe.�"�������-"� ed d��7S�+ZH!�G*[�a|"D)dz�':� isobaric}�Y+ :,"�Z AAC_N>+QOF~ *�9�~8�-�V�0�%bkF�%)qyield-"6B"qs �C��Fe� JI|&z�� :� 0a� 0.06v>K 2}$/A =**�%. D"rXI� �K� �JY��w��>DTE-pe W = 37I59��B� *b]���;"� eyel��Y�F�6�.&7�&9`L,B�4J^�^&�E& z'U&I F'uYEDM' .I(��.�!atQ �2}/A~'8.I Z  ^� f >Nn46 - 73E&'"'.. is A�.G>�C �- ��:f"�qB��Ņ6!`/��($|�l|�9�\2��, ($N$>B�C��1��%to :�6��"�Nj 2{� yk�x) D�M t�(`-& l2`�&6� 2�?��_{0�En>F�AJ0.�rA, 0.08%�0.20,��j�3!�#mean �!,0��%A- �N_sgmX6=!F�R$� 98N�.�is � , we knowq�3J�-3��5i"(�an � whel_2"�_�%����`Z�3!,*]A#*�8"�r >{*(�Z$E�i>�-�i%�f�ya��pl�6��*+N\5`},,�f2�/n�"'Y�y�lA �6�"v"v)"i4predi�(. \6I'�i�ek -��y�&a"�/ZCm��do˼R^1�5$5�7{`��an9!� e ���"� 6�%�]�IF���Rp� �6�;"S" T,�7]L�E"�(!6hamr`ist���� K-�:�N!��s ]low�8Uj�aum*!�e�� {�� fal a �Zpe1��(�" ?Pat.&Tappears8a minimupB50"� n. *s�5�+��q S;�"�m,�",238,233}$U tb0dk by 1���ov\Lbackb��n�A�v>N�Q� �m�.�c!�aA�! 4��C��it &kY�t*�ф�")1Y �.T02�9is "k]�7iCB�f&�+i+�^Dde�(�xrs�+.�(KR.�(Y=.�<�_1g)^ % -"_LsE��Q��.�?� R�^`G rA�"!�v.� 2�N2�]1�" #Q�APsu��)"Ve.�in�}���!s�ma�!I a�y� �&(2 we&V A�ub z&�$e��%�!Es5Zi�8=2xr"" �^�my% t��.#em)3{)� .$.6��'C�鞉�!� 2I e��. Beb��, С�j�pR��F$j";c�WbL��&C �ofP~*/E�,wBg*�C6�b)E(� $\�L:2�"�, Z ^2�$2G��Wit���A��8& �_m !���(�S��Aڝ�upsJ` �7 down�A. A ture ��H� = 51��!j�n�k�xumN��v� �"a e^ ilO>z!&G)�nQzTaC!�a�*ll5I�1e&0l�/i� n / U0"�� E�saa��$Ae6d�7k ��!�]���c $ ��6�E.E�$:� .� .�JV a� (�.�& 2/ .M�A�$jJg�'al �g �I 9c);�ea��"� .���"�9y�-�_0z$FSl8:s&! ). O�Ull-J��%�H��ށ�v[F@>�.�r����&A!+�y��x.nR�>��Z�Txi/AO���{7�6�*�'$~i/10�LB�15���R Q�tBvqn� t>yBt>0}$���2�V�MF�; ��SCas�>9f8#�C�B.2%e� :)*YU Fi����"bi�2�(�)"��At:�/�0B���b=h� in.��>N"g :+^� _N�. &�a�2�.�$���lw�*&� J�@ gardAJ ��Fg*B�lDe ��ݔ�qu�c �!�s ]2A!"DND vs%v(B�1b))��A0". �:� ��Ie� [!*!�n.�B=10}J��55q�fx32C11�f���V�=�"WA#ZF �EO^&fHZ���BU"�� �U : Y^2}|$6zM ��} How�Ki�"�[N �e actuM very^�{7 6N$ usua�`� ��"�u�r-&i24{on�i���xAit��e t�f�k� stilkgoaOp�e well�_��pE !�] "�F>=B�&(T post"h3*;t%� rqE o�M'y�$ rogDmodif�NoR��� �. , h-� �influVBff�of B�a�no���d��os| �5Ir5 �C� 9�� % 6( data2O mTait^  ��gh��=.� B����� A+ wB$!�!"~}":K/� Ա&�he�{22� D�"u�Q�!2� "et&U�i.�7ri�'�V� ]U$�(}�=$6 l�F�� = 44 - 54%`��$= 58 - 68�cU��0vn":3}���U�!It ��:ati *� x$�$�P�!�&. �&>Vm]Mj %�*�faZ~&�Q���o:wRA��699 � A��� !�wUGmT3 N *o%2K�.O i����e"8s�Qv3,Mv_ RbRCPhu :� .x"� f��2_EA2�C.�蚦I�,�6YQ,Q0 B�� ºU�  ��lỳ� ^� %��?.> G� . .� 3�!�A��.�$a�J @nK&5�KIn adPA��2�A�fg� F�w��A�0V�]O�qn�>t �y{)� �_ , 4, 6, 81  10n,=¡mN�Y @�83Y ZsY�[ag.��*� �0.l��%�`�6�0}� &�D=�A54�\*_"n"_"P 58�4>3. BFS�������!O�]f�OR���g6�b�..� TnXL�r# U�2�me�iD�a&��c=>m����8 �z� ransfer�"�.ter*Qe� g.6nt��:7thaS �-o�� ����v �keep � �4 mory�iX �_�F� nel� �Io�%A�"�m���yn�0� � 9�B�6��er�1�.w9.���>8  mz!�a goo�0oO �`y%*5��͢ Lr8kP�EF '*1�-j�m3_w�pJD�qQ��y`BUv3��F- "M�%"@ � F? %�z�%�N�AtɃف.:"�\S�zI�In�zae� Ǖ!" �AJ�#.q&/ i�D �L&�zG�;uarieU,$� � Ba��� ��b�q�u-BJ�V%Y   y.�W6�#�� a 9�2Iw= Viy�F&� &  illus�]�I ��P�)~ &�'�*� �]�B�#��s !�'�' + m 2F0:6�g^ �,���umA�s�=cSc" F"E*yA8 �"f��i�Q�\�ng�(N~�!�� $l�ut)��*�!Ka- R���wlooksk#e B��4�"\1��X�E&GZf%�ato�. =&� "6$aPE F� �oc�K$��BVrnj�$e�v#�%NN~�#,�ik hmNp= 0E'��.R �y�y.&�E)&#� eMJq=bV a .e� ^x��B^73?�E" #5�?�F6%# m+*T$cftexY��J2$5@" �e"8"�&&aq�� ���&l4�QA7�a��Qi=�m &� v6qDfqF^ thF~it�)�A��p|*$N�B9 &t %�]� y�N� &� 9/9N`N j �'��>��\��zYס�--�Ij.�)���~�8�v% �flV��)2�-S� 9hV��i����s���+j&= $*�}�9A ex�� a cer����er6�r�4"� &� 5�.!�2��"œ-H�ata %'i be a�# t( =�!m?y�C >f *{Ac"+ledgeS} �Fork�su����t�So�Develop@ FF �?A�,�A5( Technology�M Gr�gN��(s 05XD1402��(03 QA 14066� F]ځl u�d ]2uofM� 6dLo 10328259, 10135030�10405033d Major ЃSf45, G%] Westfall,+Va����nQ,�r�i!Jɞa�NorɌ, D�@Morrisseya, T. Li &Gualtier D. C8a, ! Benensonaں Baz� .-B)321}, 1�9I�9%ڎ�B. ,eAs%ގ0 C. K. GelbkeGEGch, VerdE2 Xub�%�8�� 502�E�5�|2} ��� S �. �} " ��04160b�3:6XELiu: W. P. TanE(5AB! W.6\R. Don1�A�S.��( C. B. Das,Das Gup�D�� abinU� {\it}}.� 0546!�2�45oMaf�YޣMae�Y[a W.��,1Gܰ j} (��Υ) %�22}, 99�2);KK���ΡN Nucl��i. ��.}I$1��4E6�"81�2�f09}, 031601(R)JT&" EwE�A.!�liotish� Ja�l��Zp 9}, 04460l�6�Ƒ}!6Y D. V�t��M.6�Chuba`� L.�yche�p Keks�E. Ma�E$����F)�6�� 0246"����1E� J�E�Db���Y�%!�2V�L��}T��eNM�,van Goethem,bl�Hhomin, ywA��G!R�������F. XiK^Ha���M�� lonnI�Ml: ToroU Zielat a-Pf�% H. Wolter%�Beaulieu�Davin,a$Larochelle���2�.��deAhza, R.�ez �V.!�Viola,�Jn��*�Le�Sobotka�w b14��42��E�� raci� Brun �D'AgostiTE. De Filippo, A. Paga!bannin ? Alde�;iE�AnzalrL. Audit��V��r�$R ��M toluc�(I. Berceanu�Bli�s�Anasera,�$B&ie%)Bougault 6 rzychczykE�Cardel!RS. Cavjr � Chbi�!hib)�Y�jDe Pa3T!�] F. Giuu�is �$Grzeszczuk˨Guazzo! D. Gu�y%jIacono-M�%SItali%US. Kowal��E. La9d��~a5Xno, N  Neindre�Li o NigA�C�1iol%�Z j!R�� nfredi, T!�duszyn�Mpa�Pet��!� E. PiasecS�S rr%�G.Biti� Pop,aoPor� $M.F. Rivet Rosa�� usso%1 t$G. Sechi, �&im�2M�Sperdu%!�$. Steckmeya�A�-ifi�M mH I�,Vigilante, J� WieleczkoE3W�� �a�u,!(Xiao,A�Zet�W. Zip�ɉ���e�} A��73�17c6|��G��*%�����Ga�W J.���,> ���uo1P��A!��yK ��b� Wei��Z�x?��u)�, Arxiv:���11097�p. � v & 30`�52tK�A.Y)�Dan!~ wicz�2���"k � .��D {� ���5�� �3~.�} !-j6u��(-=!�(i,A*5�&#��%|./ W !�9U2� 6��"64610�6'ԗ!3S��tv� )�Vlozhk�c�2� jm_ � m2!" y ! R�z�{*� W.9�W.�  M.9�wR�� 7V � 2�-�E�)�9�a1�R�>��!.uw�I� &�J� 0116I�� F�5i�6�"H�PY \"k��I. Gont�� ^5=p 2�� 131�982�C[�I.�0  H�mM tnev% 6w�� Comp� Commn18�2� 1996DE�})P�� �# N� 327}, 49��792�F�� }H.  NRe�rogS�X5ͼ15 (19:�ȖOӖI���Rd 28� 137G �yVZ-c�}!5M\"}�re�D. MyeR@W� SwP;��7J�j>�eAt� ta) D TW�s �3a2��:�I��A"  Yet�\. �Fiz. E���.y Y�f h1z706��}��^��9� V8YE�6);�:# 9# �Ark Fys1�3�3<�66jch}�. HasJ:!t^� Geomc�al Re%^�Y� Ma&'��uJA � (S!� Berl�E(Heidelberg,l l), 1988. ��}am2� �)�lem�as)� )�| 2�932%46���H textw�h=15.79(height=23cm� egin=A \ ce } {\Large,4$ GeV),� Regg�� )�}, oraP!�4 threshold reg�Chi!wPerturbIo; J ChPTA,Quark��s SagQM}� too �icated�Re�Y�ar: While=M manyxwhichA�,vide a satis�?y2�a"e�p($):$,�0)$\Lambda$ re 0, almost nothAin kn� abouI�V�)�EBfew ybeD!g6�0�Sigma�channe1�(Goe99}. Howa [0first measur��E�ZV�$ from carb:� �8>� per�w(tF�-�$Tsu04}. Uu>these �]siA� well )C���(allows oneA�ob�42�o�jJ� , n2�%R-�,M'is diff��taoabwise. .�P� Pr>�  e� d � ^e}{dt}\,m_d-P_N-P�)\;p 8L1}{6}\sum |M_{fi}|^2�% 1}{4^e( \;d^3p_K\,5.N'}\;, Oeqv3}�9v�!w ve< %�a.gż n ovH e four-mo�um�At�t� $P_N$, s "� $)$-fun<, � �s� # i h t:E}�/two-bodyy�U\u� n}-�6�(s,t)Ul!c \pi})qm_N]}} 2\M�3 sum_{} |=�\; 5wICS5v��$Ez =]� + )>fK5�;$s = (y"N)^2$)G$t: - P_K �a v a$ged matrix�� $)Y� Y�$�t(\refIP) e�b�pre�� �Gy͞"�labor�y f� �1)� -i\;�8 = (2\pi)^3 \, . 2m_dq�{E_N}%�H \, J0^e|^2 \,u_d(pi�^2a:% tLMu_L(p�I,y\�rF��4u]fo�M�j of.�Dar�aeqe �&=v '�2% � $\sv 2}$= G=�"���ofi^ antiizeOa��-؁36~.o Eq.~I1)%) �j"�:C\is given by $E_N = E_d--�a.�� $,!#h�!$off-shell}6�%@d)*��$ + \vec{p}� }$Q��onO�<:d!s[y8 serv)Ilaw�obv�ly vio'-S�� g,!� + !> �� .%as � �)uyoneJN 6N'} >!a$.' %� ei�ᱡl�&�6� �lab i�is ^�^3�$ }{d|1d0K|\,d\Omega_K!� � \!\!i���\,5� K^{\;2}\:P�|} {4m_NE'�%*!5) -�} y���e�Uu�^2�W26}{�F��6q\,���Phi '�McrsZK all e:�a��a�=�%��m[ m� is�!E�isRŚ kine� c$!C=mPi, $10a�5=�$�R 2�#���nonti#+icv.� ve "s� onn}!-4#Re��Dik$i��(% % FIG.1 %Q{4figure}[ht] \c�r;/{\�& =& _fig1.ps,�<=8.cm,angle=-90},%cap� {Cg$ed�eM �"RB�# "-%�&� "mpared)��fX Refs. \+ ect\�!� (circle),:SAPHI)"(s�! 6? "98}(tri�#6'8BleckDec}(dot).H )V1}M� }W>U�6��d� J$n� r 6}a+!� ),��U,� ep� ��forwardA% �i ^�&I�Fig.~� �1}A JSLA, K{ , M2h H2�$e$E� ' � 6older� 5�A�s dots)�a�&�E PadjO.��;st � \]-�e�j(� se-,�> view��"�#:;!,Gscrepanc��rm�&E theta_}^cm}<40$�"gis $""��ob�(%�w���o experiAal � too," #st� tnew)�8i6" yst�� �(���ay ^]W "�>I2}. MD)�`"$ � sY_ Y`,a�"�wer6ks !$ ��)llab}>1.5�#!��s.�/2�/2f/ �,))] q� e���)U��A��yQ�l:J . 6�2>��3��3f�Z+�.P*�*_%��8)al6��%�B"�E0$�I>re-.A�!�7n"| of 1.1 .��3>InA�ure.3}�! c:�� y:�-B�� a�ionRlread%� Sect��#��$2�A t�Ec�$�hew*1�"U L"'H!!-0.45,Ahix*� �өQaq -��too aca_L SLA . � f",� �5Wz0, -1.6 (SLA1)�� -3.42)�pr�!��very m.��( � a�#�ehs, see!�-tQ�5 �revealp(U�wth -��"� H bump��u�+�2 #ed��($N^*(1720)$��hL.y�4ޭ4y�12r� on"�A!���!)VeN� � 1Ff!6�ism� ^�at.ia�0�A2�4} :� R�4�*�!�q(� � LA�~ �wmd*sensi}$�%4 �*AzyIMA".henNon! vali�)��� upm 1.5���kaoMbM� #51T.�!a choi�/e�s&�1}$ l/im �!���M�%ndqI �Y�5ޠ5]�4n�Dou|.uB3@.+�%6 �2um 2%2�]�"3�]ploN&inJw��A�>7i)eN,.1.�)Tb H2& !vSLAA8e fat � s�iind�'e���aT !(��"! �4)�� Fig~"� ��� 6}. � m%�!2�*Me�n)[E� �e�%y!x�j!m�2�5B�Aup���6bU-)a&�6� 5a_I g�$1$6�.�*p"�,1%25�),\� �Ien�* am*�ys�us,?t Ly ��f%.K4m�v�/�, �"�al��."M�. O] � ary,UC-oa�E�S+y�y�� ongl!tl+�)6{ (not�{!� P )>).A��6�D6�DQ���O6�E�'Ii%�wo} ��a�e��,)6B��5 ^�. ���heM*F�I ��� m :��d @ni��i0 2!�?� �� *l� �+& s en�1��!�7&�� T /��iZ*te�4w6%�*�E�s�o summar�Bwi��m?>� stil##m �enta�& !8�6�mO �.� �YJ� - the�4 uses+�!:�3�b�. 2M�Z?"� 2 5 g�0displa�idV8 ? ��to.�"�I]30efr wUec�-�Y�w!�a[XRv0 ] v�"�0��n3/I�eE7i. |;4mm'=noiG9 t {\iJOn�A Dauthors (P.B.) wis�5 hank#organis�(!��3kin�vi(E�� �4$8t�0awwa=�#�  �efu�'(K. Miyagawa��A�>la! . help.!]uso� e U&J!r�Tby_nt 202/930aE�GrAge*�C< <.!:b%=B>99}& @I-} R.A&�/�B��/, �<�D"m@_-c�/ BPhueng-Ryong Ji, S.R.C�/BV^�6cE61�C2).s�,( J.C. David|BHFayard, G.-H. Lamot�Bw0�v5<9 2613�6);>TA zuBC.�wwOA7+D9NA5^Huar�AC.�An:7J�>�PGC6�F012201A0);.H)�1,BD(-th/9901066=�J31S.�-!C(Ryckebusch,�ADebruyne>�T. VandEt%J� ��B015�1)�bi�IB4}�A E�URselF� �F�6Au055212%)2wC�4 W.T.�8�FF5FbakuET.-S.A{ee�yL*jGB51�I1-�1.� Byd03} P.�A)@B\'y �5�1�0305039=��-NBq 9HIa,C4086Cz. R.MmtsNnd�C�Bm'FB�>�-�ad025210%e2��} J.Wa�McNabb X�f�304A�(R�C; �ex)%28=%�!jK�CGla�> p6~Eur�F J��6'�A1�25iv46 8025.��= R.GAaZeg���| Y� MB>�|9e�920MS#Fu1Ms= �X otob /itii!5�D.ř�E�.� *� of  M ngen5on�8sEj�8iFY �BwB$, 16-18 Ju�6$2003, (EdsFMaeda�I Tamu�GB�S.N.Nak 0O.Hashimoto).A�ld C,X4, p.221]R�<}aGuidal��-M�Pget�CVE haegcK=%��M!�PA62a�64��wL5�C�< 1Gtei�2e��-�FeissnJ\)�Z�)�B3%�44�K2mSagQM}.��������53;F2�810a�9��G�)�Rep�4!s%_87�y P�4 S. Eidelm:,(!2< �LN�K �,�J} ��" K4class[10pt]{io�,} %(Kfloats,e<$,,aps]{revtex.+ I2I bookJ(0pt,englishM>KLusepackage{amsmath} . �Y~*ams�6?amssymbBfonts6g�Licx6axodraw6vm-L6amscd6 bbol:�rsf:|fZ"hea�H:pi�6X4pst-node} %\l8[\Cplain{}A,�"es�"page}]dM{^*e�mark}!nrrVlef +�Wth � } %chapit�%�F>le&<ll%3Xs \newcommand{\kp}{K^+}6 gk}{�'" �2<gE} !_0 E_k:Eppl Fp .vbcm b\" starB#e$\betaf(g (:�rGr^CrBB�A}{{$\AQ�A$>^wpk}{ \og*{p-B$8Journal}[4]{ #1�c$#2} (#4) #?1.(NPA}{Nucl.\�\ A:�PLB}{�+\��\ BAN.GPR#�O %:L vI>iRC:&C:"ZPC}{Z�> bea'y��>Ae#�`.!."Q�+{eu�M�u\title{.sr�<orB�(Heavy Ion CU��11 AGeV}Him�PA{E�8Kolomeitsev$^1$1 Hartnack$10H.W. Barz$^3$� TBleicher$^4$, E. Bratk{aya�TCacL$^5$, LE$Chen$^{6,7�P0,nielewicz$^8�8uchs$^9T�VbTos$^{108C��Ko$^6$ASL�4nov$^{5\dagger'�� Reit�Gy� lfH5 J. A�lin�&�Pi"�Kakee(add'{!#!x Ni�=Bohr *�P�Blegdamsvej 17, DK-2100, Copenhagen, Denmark,^PchoolA�$N9 A=> omy,*�P&(Minnesota,  Papolis, MN-55455, USA� �02$ SUBATECH, &�PNHNantes - IN2P3/CNRS 0(MN, F-44072 # , FrW@} Y3$�=@schungszentrum RoDDHdorf, D-01314 Dresd�Germany2F4$5@ f\"ur!^ oretische)k �)Wolfg�YGoethe� \"atn60054�k�K,Rp5�p6` Gie�h35392N�6$ CycloZF�:1�&�R0, Texas A\&M=�A6llege S�$, TX-77843)�6� {7}$V!� l, Shan� Jiao T� Y , RA� hina2� 8$ N��(al SuperconRTng�L"I($, Michigan�e 9O y, EbQLan�D$, MI-48824 �2w9���A  T\"ubih$, D-720762N��[�4i Nazionali de�@d INFN, I-95123 C=ia, Ital6�{�_, KFKI Budape�Z0OB 49, H-1525Hungaryd y����(leave�I.V. Kur�]tovYZD, 123182 Moscow,Ria� �� quota��\a�T �'N��Jip"A�^a6-llrapid��trans*U�N�(�8 dist&�>of�&ton�R"9�!s �0�/in� eDRvaila�#e�� �qP��h��ionR�  ar(��#B,%urpos�1)JN Tve T s{# ed: Au+Au !1� 1.48�B�Ni+Ni.93-��9P%)n,} \date{\tod�;%\b%��+38etpapersize{A4}.%\ u_!Erul��columns.&@6 U :�!e#�LMT50 AMeV "�Q.A quite6IQ.�� a�l�@vscrD3�Ais��pic%-~�y Vs 2� A d2ralA`�1�. Withx�C�u �2�.m� !�f�3ofI� fragA����)ereJ�Cn�#in wb�M�2!vIe a :6Da2�7 4n�T�)edIh0Qabove�6@kin}=289(1583)MeV44pi$'s($K^+$'s) :G�l�1ary�4-��Yco �s,*�M��!t i26 bM[G i Fermi mc%lja-�;N7a��D �� a%��@ � below%�t"�Ri^ �9� Finxe(9?);c:KtJ'b� - �9r� o1%�s�&YRA �$a���$g�)elY�O���)$ar environAFU�JeJ�sF)it�!"�Pli�6�1�"wuniquY+%A�akAcXl�NAK!}c�s.9#ch�L�oI�eG2!u��Rm~LYariv!� Fr\"ank"�R yar} Cugnon �-cug} who�-$k advantage"�inu��g� pow�t E�tim" developO#e so- Led "cas*\ � "!+!E�ons be.similaVQto Wi�bNOrd ballysP[2�#/]��# seI/�-�u�Oa�:achiUU�letTZnew (s�G� tok�� meA�i�Pnd2F�TT% .�!,nonequilibri�*e�B"�#i� ctr�3Disregai&b*ngi�y�9$mean fieldq�@0�E�%eC[l�Nto`3 s 4W3X"ea;WI��Q"3lE�+became&�Ohalf aRIde �5r�?!numer%�reali*_=O!%�<; L VZ�[!!t g�i�h�quB]�EY�m eh_ans�,dI� pre-.V>:�(m5]on&GGqu�?�va�re�HIJ4nowadays estab���at sub� �@RkuGeta K$A�$\rho$ �)�CAc�Ipar*'��w�at6 st IU, ��n� had �,!ddi!Val)�^)pre\?=ZKis(8 ة�r��B a� prim�sourcEr �Wed  .*�W����y���`!� gram�m��%_gl�8m%�s�Vgo �c beyonA=�Vl goa~descri6J=]Q� �Z:�*y�5�c`55 as a�!'find �Zwh� �R��O ��t� n�a��MsY z �no so2tLkoOaed.6b"U E�se.K�)d Q Zu.eeWWa~�{w ar!��_a&"!��X��m]ndQ��&�]:] �O�C��t� sa�its5mrOb�R`(��>�yY%@�E7 ԙ&ko2�: 1)� F~A�rak*%;^-��is=)of"K  thous�pr�� uA0e ���� tech wu:<� �Yto�/J".X� E�Kdur,eau.s�i4U�_ 2) A�,%+a@y [4npu`T 7 U/d !�M#}8�V &7 `os%�3^] &Mt��L�Q.-ly (l�&tII�A!a baryo `UqAe% �� �0�?9..7�N� E<�k���� ��e^<nX atP= :�� y] ��s. 3)E!WM/!�"� Ax�bA�B� !� = }V:�irO evolsi[little)v_mIuse�p4u �4tHA� Q!�a��ori5(hoNc�SnfluencE�2al-l/hu�KRtai i�ih'��ent�@�  pT ma�dr�K EL ste7�9s a critI asaS!�a� P�Ev� � �OJ^�to id�<f�V�8M܅|8Dimprov, We would I�o�;��0MR�� � fu�N��� are � �� V�:d5?�C ��l2�6� i�9finit�P���e�is� lut%h !h�:f��]�6+B]:m m� i,cas2,leu,knoN5� vc�;b.Qdgradia� expa{ �R!�Ka�mff-Baym �,!He�"�k@��)BF icles,7 s� � x�R.>~4g ne� �� actuF�c!� � }. AlBK u�?V:upls�hsa�vi�! .�fp��If ��e�V fu1,tol}.*qTMF}0;�}�H=�ll�q�"�JKI_ PKn%f: Vu5"O/&�  M.ros?HSD!��q:edA��" .�e�� Mcc1,hsd QF� m�e�=.M, Eff�rIw�dM�-�c�Igim jcod�by D&@a2"t ;dan ; RVUUI��m�.x./ cheni�a%Munich/�/T"`24gai}. Be�3�k��rue BUU� �@5,VM�Mh �$��e�Qg um Mole�j DTkeoachŰ se n�P4�3for ��pt� of"�A�on�T as f@w�F�s�6Ied9�yaܡ�wM] ����4,�4{F�erXb ref.-�joerg5G!wgZ����[do�XK3(G�I� .� s28 -_/ � IQMD y iqmd)�URur,�^Y�� �Vl6D%2?NQ�Fra�a6 bU�>L(by F )I�fuc��" con�^' if�QTYF �=y b fer)J8�e �<�J} -epl ��9��� (SPS��RHIC)9 � !�_ s ne+ja:nI� nor a�s"�potIal W�F .aJ� . Also it��Q�&c �`� 5C)�6}?]�� �MJdA� illu99A�Qc� �;�(�"%n }[hb&QLingoL(tabular}{|c} \�e P9 $ &$\tau$&R" \\% �" & $(_{iso}$&$\D�V's$,N's�M $<$ 2A B�%(�")ZH(1232)$26.�V~ 6,�C44�Cua(I�?.@G#�=� (�ݞ,N(1535:�N(8$)5 wig9�) 6?�(& 1/120 MeV9�!�$J�9@gQ:&9I0eсA�M $��[|e�rUN emploxq/�s/&t=V}xle} "]Ow-.o}R& e�y"`��/ � i�W , �| frequen; 0w.�K�usu= g���m3"N.�,� ever,e�"� �1 wt l�2K �us=Hr !\e^N�� ‘/t=*�@%)�-�r%.a�<d so,��re.�u�2'fil�� *z �ֵ�Q�Z"w�MA:s57 �ee"�"I� �J��sum� ly g: .��t relek1rF�s:�qQ� direchAR�any cu�In( ,Ł5)%impacrr;e��a5` vari9 $ � �=#DOconven�^� at a\ n l� l��is_H�l�coursa�RA��==bJis �c�� conI te on 3"s" + z"J1")4��� �!� $b$ = 1 f�l 'r (Nfu�[: >t-�G�gui��O"q .AQ. }��Pr�#�R�Vr$.�# m�p� am�n topp�ndjf7s�mI�� gy�7�`� �^z���F!��N2�w FOPI��&a�C opi}� dE"�QHe%�m�k �� I��-p�$�$V��lways �B��uwi�e S longE"� VU ��"i,�l��$. I� �hG 3rm�*=iAc���ra R��sls�r. E*3RlyO ��stRKX%).yi�q�n R $\� x$ 0.85Nc"�� �Ama"���%40�$�=lDatQA6' LnC�a�!vx *{#�NN6�U�m;BA� fo�M p ,+��IM�E mjtoper {�Nar�d����E.`r P�|��Z"or +v a5#=�� U��>I�m�'.�s� *�,XGs. i�-y}aod( pt$gi��%�ach>�"� �F�(4 =Q-y*G�~h i M3s[=15cm]�y.eps}%AC*{-}& K$�H�5.����fmm>*��eK3 �o! �X)%J�pt��pt���~���pt:���)����@Rw 'mZt or 1Dcl$o mid8E�$"{s-�����i�M��)��F e lo�xa�R8$y_{cm} = 0.68,��9$a�a�9te�q�E�*r�|� lyю@��� shif#RD�!5_Sus .�Ll$|Eqr >is�#��* J1re�EE ces�&�'=.` ��4�n �is&Fof!Ush�b�"su�� X�Ea��P: s{ap�� �!�.�w �$!��Pogw hmic�%le, wd� �%�h��!j"� !+A�+�B�9� �)Jer1LpronoI&�\��!�eem�be�r�mdW �5�6Xnd��.��/"% �1�t�w��$ �U"AF.e��a� f�H�^ !�./$3#98c"��[�YA�a� % &�Ldura$� /+iR�=b� ar}XKzO fe �]dѱ�:*� �y� !�end� �!� �0beam (z):�M%Y� (y) 6���U planx�����"�&\u+�-{3}{c|}{�.I�}V""�.e }& RH� �.}&Qm�lpN p_z�e4.le$. p_y& �f:}Q yr�n ��o�n�n9\& 2�2)�$$(GeV^2/c^[ } & 6�^'�N*.$d/Wolf &0.157 & 0.109&0.6923014664&0.351 '47&0.42.Q640.165812173&0.$�726D1^ R�6QS9106 S7L12G49�40Z10426.Q2c�81 ��2 d38>5d413 10)$269�"tx131N�8)D4U14 �0!D0  �35M:�0. � &0.87� 0.21!�%� 0.72T6�14�41TB�0.143�2185%�2)B1J Wr37Q1542X&�!�!'12%q76%�@15%6%@40I36q34NZ�A��out-of-�["��itu0>��� ����*��n����${P� ���z#�2�#q�ar ��� ��~����s�a*�).� l&���Y&��! �.��.ineˆic�"* -^ijL-%\)3 Kb�4������^2� �f� g�12V#s� �lyJ��disu\P o a ���as(on% !�ble�R$op��5'�mE"a%�FiJf9tS m F0,D���3@E ���Bl I�a~ $|w$!T��a�p5 h�$a life#of� �q1}�w� 1.7 fm/c$%"� 2;�'��Q�Ձum6 ��[dj*� |f��N.� in)�N� �#� �-*� /ms0`Ai \2r (\Jms}7ppi/2$e6% �"MD�% b�1R#Q�FS,= tan^{-1} (�j)y} {2(�p}-�}))F9|A#n+�/ �u-21���ifP/if a)��e�Pc�&�,h*��hV!lY�A�d;yi�ts ($ � << m_ � -(m_N+m_�o$) =f b �)J spr�)� U�wpacket�$�r2�����u./q��: Er�/�9I\IQ.A� �E�M��A��t?X�/��u1"� m@gAƁ �gj��+�3��i���% �- � O/� a sharp ps}�� X�)s�b @�a��"� ex�|ha|* ���8&]ac" l�@�.. Eric�(AWeË� eri}�)�91i�ed�*�B N I,$  �!�Bli��("m[c�W!Ms&��"�V� f^{ ]}_{33��mMgD k^2} v )^2 - ��i %|`F4 k}|^3}, \ee azm-eADmb�E��6�Breit-W!�r 9!/-�aQf�it��ici�c\ \be id � (� k}|)= 22�^3= �2f2^23^3 M }{12 \pia�pi6 �}"ee �:$G^�s4.0�%ia+meQesV82!!�$ NŊ.�u y (|Mk|):jaC��P;�� !=&�ݞ d&�3 ),tal!�lpto-�1} ��B�u ea|�d ��U��g^�"ha������=t���A��" +-zedsM(iH� �rW�#w4i�Z� �(T�i O."!:Pratt ^danlif}S�#u�2at �1um�#�8y��  sr�dow��R2!9de[q%! outgo!8~inc#�g��of=�� = 2I� d �E)}{dEd�!� ee H�ma�xl) {K6r�7l&�-�c �k21��)"_ ��"�.� >g6D�V. "e�Kitazo4 Hu�-synonym������1.:.���� O �(uE��  p-�CRa�sV48�=>Q%�.8 i-1IB  0cm}& �"&bJ� �*�-ro9Ad&#ja�nd�=�*{7ri%A0"9 W d�;n l a�A@" &�)��T� �%��,j&A0�  P ICb�&�� i�9far� ���J'� �O�E.ofW eq�A]�^� �$� ŋlg 60\%� |t&�&a�$. �5� �ortu1uj*l�����pi�@O3G m0tna�� ��m&�y�af�/`5��k)��e6�b ��� new �'���s@ er1#��=backwA8�&G"�Yd�8��!h-b�~s�]�P�8a�a"� �!l!&t"�"�6�s. ׂe�,exR1y=ig"ʀW�Q� to�`E 2 ))rion-b>�9.3a�"Eo$��!� -$ cp�Ey�&� iHF�-�b��]*� ؇acter�5&�$1U�U� �hW.�)��) :�In0to �$!�"%{Bqy1foo�we��dec<#�@�} � ��h4.�&*3�$!Ge��#/[ ,� =  \$$&F!�~�s,��"�t'a�,�Wc��figFf�ipi+�p on��gA��<>���B���rNk$x�� (@����'�j5!�"v*.L!�6���.�ip��e�+$� $b$Y&nd $|y�< 0.5|$~ ey�}�w� �9I<6;�W"r�>faRe%�e�� .� 2n� �d /yel�gdS.1!��O,�*dZU�0%�6YpEqAch�*��9&/7"�/p�/�� �/- �y.T�q 20�@"0-�E�%t��] ta\�toW�%�&�2r "'!��/�� ��� �."!is2���d�� ��:Ka"� � &"�n��E�-~p�o� thir"��� ,$ {�t&��1)�'�:� �g�*![���:\kp�&�� so eas�G�:J��K1��T�;��aɿ�4h&jd=� �V"L}+v��(B^k5/2 \ \ "B"))ac8OB�O3zO;��.;a ID�$b���F�M�Ui�I2� K^�1z�E�e"y1} point=�twE AT)KJ�/f�$ of 3-4�furEA��CA!<�GA�6�� eJ�N\SA"b��V��"Y�toQ!� ��?6� �(�,�E~�?B����#1BB:�)$6sH8ed���li�RgAkp-� �@* &9"�� K��'<a>c&m+P*c>)�2U��)�* R�# $( $ u^*& '"�>)��`&2 02 )�&,6 926FUA+sib} $(�)$.5$MJ2J2 �G"~> ��YY:) ^cc1+ >'.�>) 2��^�") W�1Y �9,Z�(���E�& MJPm���}��-iI�Q���� sigppk1.p2=59:=��*"7�J��u�) � Top pa��E.�yi�2pt}�6�,�)D"5�*J�^2� ���Wt�L �&�W�Ukpl��) �2��*<nj2�� "� (top ��out�Etom KN&�)Ql��&2��`.�6�x!#pB�6>x�%$��)/=J=,F�.? ��? "�?B;7A�EC�b�.�s (Re&) canl �,lm =&��>&�<�  ��� )P6~#� !>wo �"��&U'll\]q S&��a�LE}a�n!bod���*L: $B+͝ (ɐ)B$. &aat-*�Tot su��1 �`but"� }3abb42 poC�way al�Sgh%�>��O�M*�9 / � t�-�Q!��;to�]��V5" q� H� � _�Ze�AD9�)��"!#*qX�� (3��h  �(X ABiI\\E x t�,�U5�] bNd� nco��M?' 0whole history1 %M�.�K2�%b5BponaIly 2�!�S�<� �: .���BS���Ia mIaG1K� >O$��� K2�u��&b�:So5]� �Yn\*6O�� .�  Y�hߤa)�&��* doho�n�e�lota\�PQSe�>'P,BN|��su  ���>�Us. ��s�Z�a!`&�.�y&!N�87SjcA:�e��6 echc�p.c�Vy: Nambu�$a-Lasinio XM2���kpl�Qll@ O�Y���,g4FrelE�s �]deby�����F�*ٖ�fa.�A21�r*�L~a�l5X� C*r�1"/ga# y_!�Y�I� _&`+ce by .p$K(\rho_B,k�\�*m_K^* )^3�(,,�\�ld!.�i�$g2? =0 Jr,( 1 - \alpha�* } 0} �),P eq� e5 s]_B 0$��I��!Lno�Bi�&[-,*P!*�k�} ��Iőct�A�$ �$ "5�@2�":!zgin � z "v:. )@[MeV]?�� \ (K^-)$&� �-0.05 (6) 2~�!4!22>!�"7Z:h� B10>B>� ,8�0oT"� m6�)*=� +&D%P��6_e!�-��0+���Ved�c�!�4es $m^*_K$ (eq_Ceq.�$I�ZL I.��ugges� i��f7Rrudˆ�G���;H�,{pC}}{dp_t}/,A"��]� "� �nek},� *!s+Y�E.N$&c �V Ato fix�*(�SrL. Desp�X-q��r�gfe$\�t�u(k=~O 1�>����g ��'!�q 6� st��*Q%kp�P%k�#�Tͣd�o���A'��� ���4nI �An-�7-path �s*���A�8&�Ter��Hôll}!%a��on. D�*X.oJ  ɒ�.�5>,�)aA L 5��!%R )R $Oa% o�I2u^6JD�Űq}l� � �5���6switc�Z48u*&Q "Aum 2��TM�s�$�g 6 :$he�� co�)nD~� �ur+instea#�#7 forth a�� � 6v, ; � �&�.xP*� %v� L`s9 azim��� "�m.2w argu�6s o361m� k� �!v�*MG "%on=��]br�[� �P�%yy. Cem��irI ��@� h"� 90^\circ$�$� al"N�bZB�8ahA�-� �%l�Z Y X(18 )$%%r+V� coldB�� i.�Wm��Me2,s �h*L�DF9>��Im�repul��u. S��Rffect_*�$bì�$�/A� �n>��օslength!��o-��h*qMAG�%� A^2�%A��% j$�:�=Yk2Vr���!�)���(bo�)I'*�. c5:�5%, 6�!Sub6)�ed �wnc)�$�P�2J�#&.v˾�2hi�4y2�at b=5 f�(�(�(hi 2"�?$Ke(^"��62��) -f!E��z��!��:!�a'%�ulex]���%��vIƁ![��ir s 4�k.�Y.%�=a�hand Q Qha�M>6"-$S��p&N�;aof�*��kPr� {�Kin�5.513 \�X� pp� "�! K^- pp$)�Qn�m�U��"-$~&{ its �ezc"�ɦ�YN2o:� )�%$K�!�2�"�1sc)�J�, (c)��=& � E r2����![a�dfB ),�M7 ant �j��-$.yiW�avyzu�saqFH+mL ���ko1"& .�b�d\6�,Q�!�&�n!}]+ in L ��*�i�d� &u agni�t�LA�q�wp.:a[�� jQ>5a>% �"�!�"5�coupl&c -$a1>��'A5 e�!#TqPto|-��n "$*,4#erE�)���B�%2�n.�E�9NwM).syJ��e�rw��� �8nB��Dak� � gets�"il�Cabs�.:3.� m6� m�� U2Q"�E�F�2��%�2M>&� theG.Eyew�~ �~)m�� BB:� + Y$y�)a��N�s� Q� �Iw.^(&w ͡kn�5 kmn-�3��5PF��%g��a���'� "�&a� " ��m�m|4��6% JcZ+�"w %xoVX�>B� ���confrj�E�Nw-E A�.x" �F�-N�*�v/>�a"�v&�?(<P�#�spa��Wkr�����pr�Gha�wen so?"� ��Mcf�)��v*_�� &�1`� g j��)�os7db1i� "WZ�,�k-!mQx, T��t� �. AB�~��a 6r]~At*Jw�;�qK0how so��.6.j!YV�rp2�z$��3��L��m��*� "D�Bg�v �!_lex.In��\t�mU�� mSl*�5��F �,�!$\bar Ko�K���lk}, raBEB*PFe; -a��+Sb"�� �@quasi���I-��_� empe�Es. J�B.0E�e zed85r5�dY ��ar:Y surfalo2�.��hnot�'�+� ",?"�~.6� y. C��/� s&p�� �KbC"A!gF.�m&]z�a�zS 1�g�p&wmI��$b_%hi�fL� _{K^-� dbDe� *��6P�' |Ia�M6�I-�i�-"�6�/ �de��~ �heci�#H�� TmJ� u).��" �^���f� *O A�`o�pH)�[ �c�R��F:�M�yN�N:p,�6div$m> sG5re'4'{�\`w%%Փ <Xs_{"z }}� �N . A�qiA�e"ba�I~� "�.ig�� c""�o�!�Ay��.dAL� . M�], Sao/��eҤ &�LaWv�� } On� Z�N��A�m � D stud�eR"�L$�-�"�a���T,%e]b?m�3)�ic,�w,u-�b�Yn "Searc�g|��?!y!Td,". Earli��d�6toZ; �ein-%Rf� of�����eniA�3Sm ;���ibiv��'<ve%�qtw$nambiguous�u�� � tur��]�q�$e2A�Q6%�im^"� a�% � !�\2�r-paA?��!e 5.�{e2�v �e�ach=Ei�NR.@i�Zpen�0!�%2�u%or!�Hi� cy es.ɕbѧ7ez,�843V���\Iɩ��NEa� � uj2a�olk^��.1xo�o �A�\)����5��88ouJ)%!y �s!M�2cwpriAXoy� �k�oo ri��"M *7E.����Vw KaoS�>�dsturm�A}/� luteͧb�/�ge a�4 aRQ�!�e! zs vir�t�s�z%��,�-A�J"&:e��i�[D �is �A� y.M[J��-{�ڡ=� ���2� � }��1�a.M->}4$\kappa \le 28�l$_�!A%JdubJEA "� R��)e �K,�eNAs�@"� iT=��%<obu_� i.e.!� ABremains �_ ��es !Eun�or>G in)Es �JL. �06�3 :�)Sv�= �R�a�a9��&Wi��&�y6�8�7in�a�55�2W*�!\nCI%�@�-:\�&�A)o� p���!�s� %�st a�� ��1K62 K^F2���J!9 �./Lo 3eosv��7(� :��Ary�2l.c �� a fairly IY�ݪI �>�ougP,at� �at�W&%%�� ly %7���Y��>m7��ti`e��,�"�/�7�O���Yu�+7+,i!MnAyof�BÍ�?8*� �Pw>*bgQ�*Ub"&��u.:� � :�ᅯ*& h&da&�)޷�;&V!2u�@�)xa��ll�Y�Y�� T-�&$5.�`v ��auc��22"�M-122mJ No'�I��iղ�i�1 nr,to C+C=A[�,��&{@CQr5U�4 � 5 s. Fil� �iEAerror A � ��7m�z\.���olEH�rT6��|"�%�v!.�A 6)�w�#e W=i�H���R��N> _��4o�L ($\�6��)"W)3/4&>:J7)&�(�ier. "�4���&Me&� Co�Ba�} Mulq�H��I!�8�Yp- ng�a�y��i��� a��$o! �A�!�ȁC&pm@��/��5��� m��s� Aa�= � �a�� s. S�-M� j% cH stood a�ermE�A im��m *�g t ph��6�,@�,Uhs,j% Dtp5N�-��R/,6�'W�"�1�ttA��[���:*T  ��R�Fb���p&a�S.� ��� �u1D%5%�Q�z2� Ab�Pp��� O?ebc�&b�s ga�EgX�*�& 1�I:<m�"�h!;!� "0h�tt�u3 �"�psqueeze�� !Hn-�*� �n}� �� I>� cV$�B� . <�AcY ledg�}�36 Gt��Dr.��Oesch�Q� #  �� �[� $ECT=� in Trento��,Aho8ai�s/�� s!5stӒng �|r CIRw" *{Rem|cn�#Be�WWW2h�.�Y.&P�l�"S�, \PR:�0}�79) 2227bYŭ\�J�q�32380) 18853a׎*�%3G?qrt:JD34_19�q 1730D� H. Kru;�B~�Jacak��J�Ilitoris[�D�RstfalllCH(�"ocker6o,� p7.p� M.F.U�utz� C.L.~Korp7QNP��70!,� 30.Э(leu}J. Lehr �Lenskeg� Leupold,*��~�'�. �\ A7�Z$93\\ M. Pod SfCi�B4!Q2004) 81&ƥ����B. IvaE�J. Kno!1$D. N. Vosk�\n��J�67!� 2000) 313\�} W. �{�JuchemRH6�377�0A'-d, 417 i\\ X��NT 727}O3) 590 � fu1}��/��,-�� �C6J �02D tol}�TolosjC5 � 2) 054907� �" �.��I�&�F55!�199� 49\\Hv���A ics Ь 281\\ "G�E�L. Nau��N8 �3) 04190���?=�� :��.�S. Te:(nd A. Sibir��F� A614�P97) 415s� Be�.q%7!)�A6��U5eR8V�=s�pM30!1999) 6�gim= . 2V�E.L6��>�_v _C5� `44614 i�2WPhD�4s��Uni. 1�, �(,\\ http://�5.pw k.uni-] Hsen.de/html/dissert� s. .\\ ��Xchaffner-Bielich, V. Ko :�,%h �1k6D�i� 153� A.B."�2%qY��%��� n.9�dan�>�^�B.@  533I@1) 712OcQ� C��K;�d G��Li�K �G G2��!�6) 167�-C"G�A�G.E�own.�-�A62��J7) 372! IM!YIW.2�ɢ2� �C5��G8) 43E �]���RO�]`l� G5%�1ݫ 108 kG?Q.J= 8C��9870� -J!DWu ��@wsl{ibid.E�Э849I9�M. Ko>8��bf A495}(1989) 321c \bibitem{gai} T.Gaitanos, C. Fuchs, H.H. Wolter, Nucl. Phys. {\bf A650} (1999) 97\\ T.Gaitanos, C. Fuchs, H.H. WolF@A. F\"assler, EurSJournZ012} (2001)421�Pjoerg} J. Aichelin, P�Rep <20< 1991) 233�diqmd} Ch. Hartnack et al.,�J. of NB�1}�48) 151. \\ C.~A(, L.~Zhuxia tNeise, G.~Peilert, A.~Rosenhau�0H.~Sorge, J.~�t\"ock%8and W.~Greiner. �~�~{%{!��%�039#ur� M.~Ble!&r {\it �},J.\)4 \ G M25KL99) 1859\\ S.A. Bass 6,, Prog. Part � C @49#225�0fuc} K. Shekh%�YZ6�M.I. Krivoruchenko, B.V. Martemyanov, s Rev.�C68I%$3) 014904.%�I� �.Y v �C59 �P7) 12606\\ Y.-M.Zhengf76702004) 034907 ^� E. ZabrodA�Y.M. [2� Lett �86 �1) 1974�$, D. KosovAG.8 Z.S. WangE+T indzochfa B434 �8) 254.=��opi}FOPI Collaboration: W. Reisdorf, i&=�.^9ao)23230}� eri}�Ericson� W. Wi%Pionsau`ei, Oxford Science Public��P0laredon Press-��8)� wig}!�P. WignaNe8E8I�9A8 1955) 145�!danlif}<(Danielewicz�S. Pratt-_A� MC53)\6) 249�senJ Seng�4H. Str\"obele,�� �E�G}�R5F�5)�8�V66��sturm%�S 1@(KaoS67)^\��3a�Pend{thebibliography} �uscript3am2J2o�L} \sloppy % \title{The Fubini-Furlan-Rossetti Sum Rule Revisited} \author{Ba 4squini\inst{1} Drechsel 2}�@Tiator } N$% Do not rE" k running{BrM�}% T0itute{DipartiA�(o di Fisica� Dare e Teorica, UniEg$t\'a deglia.ddi di Pavia; INFN, SezioneO, Ital��hECT*, Villazzano (Trento), &\" Ins�p f\"ur Kernphysik, Johannes GANberg-��"at, D-55099 Mainz } % \date{Received:  /�( isedqF aw!�correct ,4s will be enteaEby Spri Ebegin.�x\def\dsdt{$\frac{d\sigma}{dt}$} A�{  barr6E�3��2 btab0tabular22:@4Kize4ite �:bce�c%)3g)eqeequ 3 dBqa3i�3a �=1 g�sl#1{\slash{\hspace{-0.2 truecm}#1}} aF bstract {EZ�sum ra�W 8ion photoproduc��on�u � 0eon is evalua� by disp�� rel�@s at constant $t$� the M�U to�duefinite �m�a�calcu���:sI,ed ona bout 60\%!�5xM1non-re%,t S-wave.RA�(ributed ano�� 25\%�|y� }�-A��fzi uXvanish!��sA|�R,\,\nu_B� �%^2$,  �v_B=(t-�k^2)/4M��!� =\pm B giv��osiE�oM �\ !y eC)� �A�*k by�8l�ngl_B��} E�s=0 �! lower [ �� kfixed at�'=�+� D^2/(2M_N)$. In a �� r ��estigi�Arndt� Work]�rn�u��VPI�� h !Bob�� -� 3.92$-0.138$��I� R_s ,V%#S$,a��Eively�*FFRY2rel� n two c ��p!� s. F��,���s:�hA�to�d���origin1�@Mandelstam plane,%�)�=�0A�ich also��� N᳥+M�AWI��is point��!U>iA� = s +Dirac� X>p e�u�� stem�(Pauli?��W�  (� �)i�N� or al!D�"; "�  m; (L�jR ��t��Geby)ȥ`aVl �beyonH2� 61Y!�e�t=e=0$��sec>Y$� cern!�e unARheM�R1,��a5 by meaF *q2o$t=%W.$!�order!:de(b)�U�q�M^�:� unA� �&0refore should2� a��wwE�e�%& \ne0� outsid �� ��� >�)_st�xi;!Jo� [fo?B&D , $\theta��,B� extrapo� �9+ �$t(\nu, M)<7 ~�Qa aim Ais �in� �2j)6t_� thr}}$�a�m.!�eoQ ]-�a tA�$is complet�����>d$(see Fig.~� m�w}))h4salient featurboth &���i 9f9-s���n�w( following � }� PPA} y6�t6Y2� $) 1�,!8course, a dynam9& . For t!�$purpose weA�l0 � 98of heavy baryon� u:4((HBChPT) inF�  �se .c !�a �resul�R�(DRs)��l  MAID03!eBW J� �s!�ourca�AWhMUlsN� as funw!�Քnea!\r�(Ż]�)I� �cusp y��� d s but dec� e rapidlyE� �� p"4through a zero� \nu\H (x70$~MeV. A-yi�!of%#achb )���0ws good agree�iYk 6� non��v1 c `��E dt6�probl j & k far���. OurR � nfir� $necessity H H a fully�E �treat�of A���hsa�i hey ��H��(LECs)bsu�A�ory byf�5 's*[ &� IJ�sum} a��>%� a short� m�w a'look.s�0figure}[ht] % � %\�ig{file=�F_!�8.eps, width=8cm.nd<<\resizebox{0.47\�-<}{!}{% \includJp���a} } \cap���>7e��B��8h"��~ bar� � >:���J (�o"�)!L $D180^{\circ}$ (back:��q-�< � ole 2 Iind_%ed �dot��k , $t6P%�R>st8ng Vat W())-)h !0��)��<��9' � $ wh�h:i�I�v< 2�:�. y_aKm� �e�1{�' P:�A1ls.u } Let usXdef  *�of-�:X�Q� rea��@p[ \gamma (k) + N(p_i)\to\pi(q,'(p_f)\ , \]�z%��s!�bracket�no; four-� a�A2�icipa� l,The familiar.!farX��"i s=� +k)^2,\qut! =(q-u"-q"�� %�! �IW\nu=(s-u5F7a he � N�A�i� riisI~� 5 %�n *$E_)�$^{lab}$ byF��6( +�"�}{� }\,.F�!mU� s-ch���is�xwe�R� . Its upp�% �� ����W by%�scatt")\+gl� �  .�:�E#R�s lieA��u"����7r!n��Ls�� B$ (5�.�� _u=-%B$ (u18ereR� _B =j��!�&x� ��:��atVp{� F}} &=&MM�-.HI$ �\@}\ ,\nonumber\\ t.P P- � Q^2 M_N}{VVq�a/�&�e�!-of-m (c.m.) sy�, ��"�i�i!�{rllrll} p_i^\mu & = & (E_i, -\vec k), & p_f^2 f q)2�k.G| B|, )K q.#\omega !q)�b �qz��=ґ� k&=&jM-s-M�$2\sqrt{s}}�� p'^2N/=�q- f q|=\left[()�jK\ru )^2 K ]^{1/2}i \\ %�X6^:+B� L ^N^6\2�E_i �W-k=�9) 2�E_f 5W-B;N%9\pi#A-�� � $W=1��A���nuc���Z can�xpo/�ermf 4|�+n*is�i$�(Che57,Han98�i �JE�,= \sum_i A_it)\, M_iV�a��Ws $ /n��%F� %1&=& �1}{2}i��_5E( \sl{k}- I_\,d]� _2&=&2:SPN,, k\cdot q- e�\, PSFR3&=&-:R�W � ]�S\ �4T>�NUPU � U-�� 5�1) %"eq:n#or�N�7�N $I�!+��)/2n%�� ma��E d a� .'Bjo "�nM�.5$A_i$Q�fur�� ompoI��0+� pin b4s ($a=1,2,3$),NSA_i^a={(-)}i�@ilon^{a3b}\tau^b+ 0) a +)}\d� _{a3a y-.Ca$�A��5i2&o�&q"' :�& !F�"�_"P� ar�"g!:FSAa�)�pIarrow n��+)&=&��2}()-)}-0)}6�^LpL0L C+.C.�.Bn.�B-B-F�- Vn�2M�6�C"Z � ar_combB %9 2�is"^5�}:�Y�!�@ � of $e� .�0$. As�� Z2�m�)i NS2,$�^3,$� �m4$2���F+1$ survi��at1q�A�i��G(1^I$ satisf� Y�V  k ~$t$J���dr1} &&x R#17%_1̀=&&$\,;X%,t) +�42}{\pi}{\cal P�%_�%_l ^{\infty}j d}V# : \, Im}hb ',t)�%^2� ^2}\,,��>�-)Z�-^� \nu}¼� 6�-j�.&�22B Simi&re(�y{��o*:2-A_4nBal61nMY�!�� ��^{I)�0$ ($I=0,+,-$)�l"N�19�  \ f�-eg� �'{�� � 1}") MC�0 I}{u i��'5�A�A_2>w�.rt-m^2# } �zz3�z2m_N})( ^{I}n ��4��N���]� a1-4ARB�x �+= 0=- -=1P1%(+,-)}&D)"p)$) 0)}= 6_&j)+erE$�)�� 7_n&<b�� �� prot���( on, &x)lyhjZ�$most easil$-ru�%byP%sHtree-level diagramsN.<)�x<) . We��in�u�J�C"�Ty��$.V%* independ��b91��$ ,9+�/u &�.6�yY%��Y� �>�!1�N$�&� �+�3er\s%}u�*�=q(��&0)�)e (PVH"�*I�O6�1�L$ D geY:or6 to�Lb���PV}}} = >eo}}+B FFR}�,.� A1PVu�jP �� P�:�\,i`���"� eq:A1B>I All k'=/ remain un)*dʹcoB� A1"� &�� CGLN=�J} $\7Pcal{F}_i(i=1\ldots 4)�[ N� &8 F1_4�V eqn{!� = 4 s��8)\,(E_f }} } \v� {0.3cm}�� &}\{ W.}{W� !t�1 -) P\,)�.! 2}{q�>. .< && �. + hM_N*j(}{(r)%�FZ3Z2<�\,2GW�IFG4}{q^G\2�Q3.%I� $q= {q}|�$�-E#b��nY^ e�:. B�9 � ^Q+�may� �sel� t�>E*��e PBg*($E_{1+},\ M ��-}��4"  xv$� E�.)J1�lbm.�q�Z�"c. 1 & �)& E_{0^+�3(� �^+})\cos�81\A�.H2/� J�){6+H-})/qxB6363( l-6+ 6  & .n4 � 0 \   �Q-1U- �&!��>���%F�&� Ya.�p9'�(1 N^2)e�2(�<+2\,s\,t}{2\,q\,�%s} \,�a)} \ .F�ThU].��oft9.��I�z 2Q!&^{P}E}3!�+)� +} -E�-a� .F52� 5%�EN!�5B33 32#2,�q�W�3th�$��,".a�a�6of6���)� ca 3m�6�4q��19��6�\,(���f�&!�!���p\{aZ0���( �"�W�>� )}.>�" ��bar%� *Ua���͊>�2� M2��t}�s\,3�� s��Y Q�1D� [ i = P_i/q��a�0ellipses deno"� higher� a+.veY172��N��\to�.*we %l%by  5goi ��*+!a%�9($,{q}�B@L�>n& /x*{� ��٬ \to � �F Y��#��$�� slop)QBR"r �va� � � DB�-�:2�19�)Fk/&�)0al factors si� fymt�' �BSŦi�ekJ�yma1_�* du3, t )�W4V %p}i}U&� }}msBigur^M_N ? ~]�2 -& (Z�� ,)2l} \&V  (Q�3 +6M_NmLD}mA )�}(�>G��aJD}C${2+}-E M_{2- �k;2and A3UZs�J0$qU.I2+wAF3 $��,$ does IAappG.}6-�), beca?:its&�"�;eIZ %3��6�(. ^i- stra�&to.� U� �.e oiiF,6�� �;9N �4 es o"SR�+�()�/ step�olv=CFRirB�,�YM.zof�r�;�4bewa\e�1a�or�;a�r�= likeb).2�$r6�o"'*m�3-9*�$The Born�0inNm !`a#��2$�>��,"20*��+�9�behavior)Laddal�+"cou� term��ح�S-(�F*u�  been3-ed* �>�th �in $1/�5U Ber96,BKM�24& $NV�ef�A"� -f[���=&�1����-e\,*�={2� } ��tauGa1�-}g +cts "Fa1_non�^+�ehas)�mada� Eqs.~(�0.�), �PVAK��3nB!�)�1gN��$�� aes 1.793%�A*V 1.91`M�Wa�9K�8�?B�4&ALH � Ai6�0�essOP Z2` . B���{ eX>] A)  is aauC���4oci� �?&�s � *�  +�nd��{, \new!�vEE0+_M1-*��+xrm�}*� &$5�%�A� ^2}}*�5E�� f�� }{8�@W}\ \s� �"4+ M}{E_i+M}}\ v ;, }{2W� *< \\ %�e�F��M}%^e4A���~� &` �}� && �a��1}{ ����)^�\6�6�% BothY����>z7�n �<gy $k�#a8#��M��-�#���R,rVF�:�aQ�9its& s/2� , �I��� �e�/aa� U��6�@-*g.,%7pi� he min�Js $u {-2}m�at �B�ikequa��l N 9ces� >� �͉%<d &z= &xvbe *exactly,�! prov(F͡ԥDcb�a!Ge � �W� a p5<ser*u = Q(:w�q2� ���6�toE86 *$ %{ ��(z9�re��byv�{s� �a�.� } x(.�))e�a�A | 8\over 128 \pi FI3} +.&3 &72%^3 '�)} �Id&�� biggl\{-1�T45� }{6433}{8��\ln��,}{\lambda} +�< M( J5}{C�\bA9r) \:� &-)^�� �51N� Flb44}{9� $20}{3}\pi+%*2�&32Z�Pr*�� o�V\\9� P��t%�R�=�>&�)� 384 �21�}EL$( 10 - 3�|��/IC^2 F5".x�KI&�.A\{ 16 +�+24 \ln)� \1�, +\tilde c_&�*{3M�9} +{64 �3}bE �] \&�*4\\ & & +{e g_AB� 2304%�6�%�$l\{20 - 2(��n Np) - 30!G+ 9� 4r6Q++ 6I� (1"�G p)2@0 12[4i)+3 GF G]bb �/.�AU7!�M�~�2TFZ� -1v1u-�192\,)3QY}-+U�256 -2� B�9F�� & ���4+(m�X80a�)2YvM�e�r(8� 16e�U�!Fr)v�F|�kI{B�5:����-�2���L�z11}{6�l��R n�� pB'-�+E�� )]dYc -%Vl[4-2Q-4 n>[+E� O�lNU-W bigrA� ���!gr\�)"� Ay2�')�GV����K�Z3�� M�\,�^��A�piQ�N %:4Y, ) }^% �]^B%щ�U��c\{2(1F)�>N])e�5{&*7!D3%D^� wN  ant $ �{c}_42 c�(�P$c_4=3.4$~GeV$^{-1}$.�Le� d�IZal�3`"iza�  se� "KCn &2mD6v$..x�ax�"� g_A$_�( ough� Gf�N, 8=g�&��� �=13.1$ x&=92!�=L-j� *����~�O&� v= � .2 ct��\rmN))�3z(ahp,n}(-\a�� )A�A�3Z�12w��belPi� mn {1,2�:� � �0F�6�6'P \xi[�� ���r�?PI� ��.�!*A'}}�, e \,b_P^i�M\�� �A�$�'pa~�>�=#%�R�R&Ueit�fit!�&�data or �Hm0! sucv'Pm�J�>h�; E� L$`%oL:�b.�Q& s+i� principle�C"�B)@2a&�)k dF�Um26c,)&OB�J&&͘NɃ��^� �\X*]?%a#�}_J%aV}a {&j.")� 6� �/}4�ya|�@}\,"|#6�,�}}^- �R��,#�, �(N\ "�R2�}1&-s3�S7.cJRJ If w$/ sert.eq�F�)-"�m`mDto6�&!we immed���eZ E��9:��cu N�<�a2<�)Z 8>iQ�R\piQ*�!1?lea�o:!p)��� $.h �i�;,E�|b"�C�.a.th|m N�@b�U�U�BNa����o)D one:X"r.AC ChPT Q�c2�Ea�ul���� sum wY,F�!:f=M�]�\,&i}2Bt_0M� E��%WI*|U:�0M�,*�FFR=C>� O��givT" ��gF becom;!" !!�!*���J� worl�A �les"%SIn-�to�@yJvactI We>S,S& � tegyAYto"�M3nNfalongB|AEO�ud�}�h�as lG 43\nu� �D;I*AW>!E�is�he�pa2WL$ �0�!$6� di"^F&P?F+�kas"�7*na� quir�:�I into*�Z �Bl2 &�%O�I" 7iscus� ��x$)�^U��,��mt�\�%&��V_*���_N���) =�:;*�> &&�*j,�m\rmj,�Pn, \}ل FFR_�T _N1}�3.��� *J�.z�&�6��������2�,=B�%�/rec�*�uaL�A��a�=�$�$J��Dt� Pi!X&�$�$p�_ice, h*�W 6la7xa�#?Zo(n�bgi"Y5e� of ch_d�Y'du�Dm)�Is#Itrong �K �K.R�K�rD^k��..� R�2�E�L}�@�S65"cor��!/u�F�$�&�N%e�!�!�Ju"��$!�6h .�m�.�s&� �e� !a^1EN+>�.his�U"u MAI�M)@EZ�5��'Ws.�5��Pn T�-�\t 1}�gcollecI��/�62N�D�6Ar nnel�Vccolumnչ-*&�Z�of"4-4 $"��'OdO5K� eb�HAIy�as.K^$!2N�atN(E.W%=�]$)�sK#�l@[9�&T(z\�7shown%ꁅSE� � $ � thir5� ��3*Sn �� )�. "� %� 1 � *>f^Dfe{|c } \h  &E- &m �)n �\:$) & DRZ 0$) \\ d �\\�4ton& �b�! $ 2.29/2.3374 1.665ELRbM�8%"  42.52/2.56/2.794 b 1.82�T[_-%�1O 5lc�MNu+rmt%� �. �X-�:h ��"Qimi�!�&c?0.$ S.]: LN`W%a})aG6&.����� A�a`� P->�[��da�E�H])��&���_LEC�H�^.�%B2�5 <\s�_� 6}, ;&},�� ',Pţ�ye:}���i�fI'I �쁡}}$=��S . Fo,5�Sf~j� �[�9}2oJ t�M�*}�=: `"!�M��R�G^ ]� -�2�`�  - Pca) Ƀ�� " 1p1]F6�"T 0.5$%�:�Sbetween���DRA�!rM9otS*��)m� 6�S somew� �hdd D4� K_ 0.65"^Tf+Is�V"� 2#�N$�hsc�negativ�(eb0�X>2} ~DaX!f2�@ �q�+ st * ~ �f s�b��t�P��R,l�L ��� phen�[ olog6�a ~i�Dre99}�]ia�` HD��G%�&7X(Dubna-rm-Taipei) l eKamV* Co�[�$B)0XVe@.�W"�+� �Bd we%� "_� &� �y� e��Y*A{0y�Q(� �M�bpa�, tersD#2,. Occapal[$�( "�a 4c dif�q)m%y �L�TabmZ�02}-p ose "i+Re:�2�+> 6  irrelev6Az our F*. !��!$�p$!s�! a��CV{s"� %�]ome de&:eo�l�Y� B�. :GNu3V&am i?>*>6A[�D �P�W5=esH2� -)��ac&�hot2�S61 1 w�-s "< *& M .P *. � unit�\isobar��Dv� b� &�N DM! � � :x ����� "u�givb&�6uB�$cite{� 5 � !1.iI���D�!3� $10^{-3}/^U^+�9P�,�B7lB-"�7�D �_in` J33�23 W   .PSchM .f 2}�e  A i�g�>�Um��&n �{Q� v�h�t�tw*�;!�c `X.�VE5A� get �_K �hFnow s"*� )AV2�.�y-�� $'N]is&siC �nB@Io%"�fij8st� -`8 emum�f�0e<�5ver�Bk2{) �!/�d�bs�= Q Y$"� ,7c%�gRZ &RZc�� _pn}�st�_ ing.&�!fM}�`\j�{\2�`��`ffrpn.p�`} \2��A�.5�/bk $, a�>�]HnndJ|YJ9���!(�b@R=>��on�^ .}q��!W�i-D %�'.,��&�!�Epronounc�nd& !  .; 5s�y:im�3a ����s MNesI9lya�EXy�E��7b��_�2 <B3Ue,�eS< �sha�g�qumaFis� p�s�to�@E�e-"�]precity�A@fJh*D]mKnd�!�lai�@ ed�l&�"��m&8r*g s..S��R+ ( r panel)i�.-&��dS}4��ThI@sp ,�>��ij  s4;A�!�>,"At�3I% reduc�a� hulder &B<*�&��"\��olI ��qc�g_va �t iF�Lchoic�E o�f9�=� (uK_)ZD&�"myfyertha�9�one�_���Z��Fuq!��ly��s# �q���! H*�Q�nd peaks1{A!5!�4$N^{\ast}(15202Knd�$� *�=streng?=e opp�re sigaND>�.\\&-n��$Fh.@gy�.&:g7K� gle=90}} �^ThOk}nu�e�B��l�jD)"jYM (top�Y(bottomcNm"�G1�"S�S1M��hcur�J� &&ostF2!��e 9�AiՕ58:�| &&��!>�nconverg�M2 exp�G��&Y* l7�Z�:)�m1�N8R�2� )*�ov7a�$e�~r{+ r2st���j�) �d�$by5V8�5���!� 2visa@s=0/@Xow%��Xlt>a�f!F:56^�!Not*"%8!�wh�:1:�}*Q  4 >R�:.�7\I_AS_int_[>_zoom}�8%k�� }6�j%�efR?p+: �6�$}b> N}>q!2x��a} dF�(��of Im~V!$. Soli1 :i��e3Im%]��. D&�j: 7&�N�>�'A?I�2�+A� u,.'k:Q�2��D,�l.�i5 of D�CF�.<s.�!�Czs�i��i6��reaVtshcB��T+o�2valid�C�RJ�#~a&�*m�nu7?e �� $0\le\n�20 �,Z�1p �,ap��y 1^ �1� b�,"$.�.)� well1E�nI .3 s) w�Y$.�du�K�ope�B�arg��A�!2nel�43i8+ so aAm(2 �m�We�T1(*G$ | i60),2j�1}(*/}v,!?J�c060 yA1�n "IGnge�tve. AZxA�e� ``.�''=|�� �&� �6�:&�&)Q\"�+�*6 b�L = 2.06\,(S) + 0\,(�1) .oD V�++ 0.25,2�9 0.19@3Q.03D$, 2.16�*,���M�B&� 2�%*�;:O  to�P�� !� d�AB��licatGB ncel�^*�q&� ��a��  error ��t�&;�0$cal�{ �} r.uAA;�*�($m��e�in�d�#V�� nd}�#U@s sitT!W�� �"m0рve �Uach�!�asM�Z�s �G� � !{�� by $Im}\,aS��|�91,�va� w+"%�er6�4a�\,�]t"5� F�E����{��ol |�Kv�Y�"�*�{!�9,����)�$��b�st��. Ou|�0B�2=s ne"F3#7al 1��� � �.�1�:"�(enumerat&_��[(I)]�riT$��$E��ogtr�n7ɻ>�I� =1�"NRcan�b, scrib�![ ``st�''@of &:� ��rk1*�"*I#1^x� rees��:-%E. [(II)]�u�SIM�.�J)\AG]-non�\*3zachB�(D) shif��=�a�Os�:6[� 2M195:c��|5i�!�� �l0��Q� �'*ą��X v E ZR%�$�W"8va��4!�.i "6r �!?7B=-9.7$> ���unavoid�rw :b��E�i�eS��D �D?� �6�!��/t u-� �2�g_B=� "�SL up>5anw��� 2�R��� i�AvB�%�a�.�J>A>2ot����vi�!� "�symmetr�!�b�E���. y2a3Exʛe!�.�a�y�d)�{!.Go����"�Q� �+min qual��veJe 5d�9mE��_d� a6�ux`@ � |�{f� }:� �m*� �Ey�a .e��&( ���_p��*5ٞ<>/-��ej -pd�cal e ntir����*�Sly ��${^ O}(q^�az�j%�E E�q(�werm+., c��ll�U$"X �w yi��W .�(_ ?m.s �!��xU&N �)�6_a�G)[isgYF�:�{@*�#$2ն",:Fa�@&�>S- 5Z���Y�*�7�PW��2m.� [� �%ai��(,�V�a:�s Teq:*�1}o&�S}��� pan+:�a�q�(s"�s)e �e捥�*�+re�Sen� #:}��m, ��q�d6L �"S�#e2��{* "�.2 /1� ���.L�"�=9�B�>� 6Rc�a�]b 8.3c�bEb [YcnZ�"<y *lV�c�c�c�c� !�-1B�:, �:�&a� ���e� "  Q��=�6*Ay9�� re��an ř*�E0m � a l-�a��:supa��.a����6�'�A��ů� (. Unfortuna� ,� � then�'P s� IZ��U{� *S�/� Ily sg���)* f\���!� s wn� ��%�]p�s by-��?/organiz� e Lagmian�qa �&�S$2[" "�%� a- �d!{&d !~�-W s�typ�1Śr�J&���)+�� co��&d@-�;� w.�ab \(U ed�M�>��"�>"�  it fail*$AKJ�  B�YєtsJ -.� :N EDmis}#!"�� "� ) d th���to ���=� e" ��y�!�i�Y"m"L �a"� 2�T&W$hortcoming+m�I"! �D 6(�f_^�3 grou�2rV w�CkA�ѨpptFe new ve8c8d manifestly LoS�z-i"�_renorm��� scheme*lBec99}_var�"Fx�9ވ�!6`o�'d$��::� galDuc�c!!� veZ��d I6q qLF�.ten&+6 92}:�o�B}&�A�wna_{O�+ 2�u_B 20^2�If�K�HA1_Bq }�C�coeffiӬ ts $a_{ikO+!)E3!�7 �J $\mu�W�M/@�2.TA2a�p��!�V @�%s:� 00}=.n Pmu^2)$, 2F ln\,\muF(�\a_!NGJO)�!��f )f�!����x:�]a_��-�{E:v�it"Ї: �G..kOq .:�!h�g&�!2H�;at�t� wh,ZZA�r5���oSi*���ErepΦ& � )�FJF��E��-iR+P%�?͝�� �&�Q�6�|Q��:I� AH^Na2}^fBL>G�zi (20(n.V �iW�N_nutBZ%�#} $S00}"(q"��� ��8t�N;in ��!���bk� *��M ($s=a�N^2,\ ti�^sat� k8 �l8rem�ire� shell\%j�7m*M�, i.e.,.� ��lti^^N!�%C)�=0.�).i%�00Jf?�ra"“s; caWt�*!FLegendr�Hlynomials $P_\ell(xA�� i_.i�+e#e���+ |x|>]�'R� /%��.F]� v!:� !�&���� .8^Es�j! wmai|��c�a��2�g%cI�)."��� I�DRs�t=.�H=�  !I paJ �'� 5u�� ��e��j �!E�n�i_� b�a�f�c*vVa�  i�4=R{.�9��N%U�.')-}� ^N) Si�I�)s7��#jAhel.Um%3 infl)`!8��� @� in���-�)2c.�����{2n!�$n\ge1$,1@easily .��a����:6)T�q64�x/n�2n,�61� 9��k�W�Y l,:�_{6��Q =�N}{�f')�+1�Qrm WApU&�F)6�BN2NND&�!�o� fmm!n1/ R4tqM�:�rc"�Se�h!gt"��IuBm&�  * t2w�&��p=0.368/�d!g�4y`40}"120/M^4" �E�_{6 &054/M^62&��LEX&�N*n>� Aec�Taylor��bt0� 5B�(%% 7 F�(* m&b,b6�F.�(lex*�v�Ful2:!n.�-�~� bynBB�*�e�s �5"qE �f:I(�HE�.8 a7 ��'�:��S.2�%�I/�dF/6"��"A��-�. LSu&��Ou~� 8�l~R}�Fur��2��(6��connect n'a�iBn��a�. >&&��-^ V,� � �6!{� �A�� tudi�he �D+]c�1"_ d&:nof������Q�H� 1��nKN��c�A&c�Lat� �z\my�~!>\6FJ��>{.T�p%i)�H t-Afor�ꭓ6��(�z�Am�6�C���h*�nS�(a�L�exm%ent*�-޵��.FB��3�b4�gi[��5s�towarZh�-MBwz&�(| imJh �I&4<��e�frR"%raZ4�(9>d" ``,Bd"�S�&�t�@ ��� -B:�*� e.� )�i2�if s�: = u�V�0T&��w7Qpo~!�e�6V �� �"a!!�K&~ �u�"� remedye"-# K avt.��V�� �gAs � �-oA3id: ����R'"8eng�s:m޻ :b�akeţ��ssw�!!'l$IueD@�a�� �2eՃsoo�0ai�����Owo-fold.F m�~H.v_Z%-�(�i23Y�M� )q�Ar�x*"� Hilb+\0�o� each�W!We �$ tech'�to�lA�QhI�&� @"�# in ga�Sb�W�Q�]�^2"Ѝ�unQ� Y;�of%; �-l�s-��"�AD�A�0�!\_sEo�*c.m9�qn2+c�A6.�4mqQ&S�m�B��EW��Sga: f�ţ sens �*�9���eLteQ�Nn!VAd3 #!) a ``�'o�� ''. E�X9N�2�2h!?oony+��!�1� ChPTEe�{-Ag;�t"ן ���P�����l��a�P� ���w���Y$ M*��"�se3) �2( of F ɊD|� QhTid�, meet�)� o*.% eaR�[ FJar�?�xA �>[% t�7�7��"c�Lnt�*"O6md.-C $"O�9$n Y''D(tr:�y"yeh ur�ra o�0&1:|!#,|At�3,A�t6*"�!�elect.�. O opaY�y� ����A8ňmB�new�8-check};2� �*�ies,  %z��7 "���A�e P%pri� decay �01�Lican��Uω�5!�insU{( .qN&(rp�>Q�!2-cloud!e.]�)u� �$D�,*{Acknowledg+s}�cq�gAe�a*"�]-aNorŰ Kais�PDUlf-G. Mei{\ss}ner�<�ou��%�C��Pe*��T1Py��]�� or� �9{�� MIUR9 ou�� PRIN EvPPh\�p�-Nucle�m2(Many-Body S�s (*���$ &$ Deut�� schungs!D@inschaft (SFB 443�i&_search2Mj -� EU ILed Infra9�Il��QHad�B�ProjectI�� E\BXber RII3-CT-2004-506078�[=��z"�W�xndiM!{PB:���S �.A�!Sb�$e��@�!"�c�y>&*�gNH2�a��6�"#4"1"�q;Y)`c \mu ,ywsfZx2+\mu}{ lmu)^{3/2�*�x8c)�n��J&&,�x[A_1+ *�M_"t W2 Xx�A����\,2}:%4\ i],s\>s�"M):� �� }{16o\ �(�o�1��&�`���|+ 2�^2��2��� d5;s. �^j6J.%$�mu!�{.�M \, A�)F'3�'�> }�-!A�%��2�A�zA9M4+6\mu!�2@f�XU}�&r6�* }�\p��> $A_i8�(s.D7\��a<>*���T�U.��i�Z�:.^q��y�n}}�):1�o�v%L*gAoЌ1}U��Yl\\��:aanq @>Ym�Y)ma6%�Y�Jf3^>f c\��_N S.l5d3��Qu"�4>P �P} i6"@(A0&�1�%��"�:�3&O XV s*�+A1"xl "+ .�6�:k��?2U 2}).r�8����12#u�]�,Q �`�C �UoC�h2�� ��R�1% .و}"k*��.;� �0eBJ92K "�A�k �-my���Va��omI.r���FA|Q����MD}� \�;Nͯ�$�%�QL��v� _.�ů�y�R�^� b�N�2v�J:�� o���5\,��mp j -!�E�Bv \,�*� >7^�-)M� J)=%Q J%:����y�F�32�Mf$�B^� .5��(6ps|s6�/A3!�nd*5�4}2�����-v�s'[-pl��� ��y&�N{6,�1up� &{O}}(f-^4B�3% B.LFxE �i�? A�we lis�V�6]&W &J�n� of0p�3/f*�4"�7)]R"�f^d:�*6}:T*�c"�$A�.��"�; \!�/-ue t"�9ex�9g�>-��u$s $\rho(77&M $\1<(78��l�rRa_1^V,��� 1}{2LwM_N�x^3e�UӁ��w9�"���e^:827wB76 olF5� 7y3$;��j`)4S7s.�2�� 9�i��by!Pe"�� [c�Ts&c&P $!H�,\ ! x �1]�.�^ � 4.8)-(4.9S�Br&�y<p"�` : $C=0.402]{5I% g_1=g_2=5i,X=2.24 Y=0.13 Z=0.28=,�iq� are�,1 �=1.26c4c� =2.6�� ==12.75=3���LEC�#Yl (I))-t�2}@�O�Es�Iy*.�s ��5>�a_2=7.07�� �=15.88��;[ ?r<7��)�a�gproced�;2AnepC<d�:��lgM�  off-�*9�$Q\Y�, %�7%�%�0)�Y��)!p)��:A�0=(-1.78+2.46)�4}=0.69!'/,2=(4.45+1.452.�^~�} .4b_P=(3.13+9.89.3}03/3AGi�!+� M�i� �ws o���*.�G=&5(.%.��=Five-5`V�01)��F�P<s� 2� �s�intM2��h+)i�g�j MI@�=0nIC�l4&�!U.�O#�T��d�75�>z(Set IIAwhl� 3�9BNR�)�CV=�j�3^3���̛�} 1^V=��8}{g_A 2H4�p�-%Z;�o2�Fg_A=g@( N��9�� � D} &�D}�+6�!�� t-2 � -v2�}{3�t("�����#}3end*�_,15�a�$N >$Q&sU���)� �*��e, J iA�>��. W� g=2Co O=4.86& vJ�#�%�L��iJܜb_P-<��$9+11.73)\ �GeV}}�_ = 14.93B ") ��!�1&� D -6.21+22.84=16.632-� .2 �3.10-. = -19.73�1>xTW9��7 on�Q A� t'�(�3 ��.t>�*�gY�uc!} a_i��n}.1E�1�� p! i�a {V.)4}{5}!m*%.n}�Tm,J���QF�.&��02:� P�,uI &j_ >v�{99��bib�Iy�SB5*, G rla��C. ��8, Nuovo Cim. 40��65) 1171��S � M. G"��E�S. S�27�11K5q�4RKFub���2�aDF�.�3A�6) 162��~ S.LC� FJ. Gilm� .�. 152H460.���( W. SchmidtIG. H\"oh�� Ann. N (N.Y.) 28O$4) 34; N.~ <,8�xik 18 t4) 76.r�� R.A.*�R�"�,�,-th/9503002;.8, I.I. Strakovs&�6@� � C 53�96) 432�C�(} G.F. ChewM�6�06>5v�345.�2n O��nsr�2��,%JL. Ti<�Awcl1I A 63% ��56��, J.D. Bjorke#! S$Drell, ``R*D> quan;�fL>8s'', (McGraw-Hi/ New York,��5).�Bal61nS;�-==124�61) 201428er96} V = rnard, N.� �� *�,Q . C 7e0%�832Z �Z �� B 37E�^3372^� �^Eu&��4�11 o�%9._tC AyPet�� �R&Q�87D 32502�!^2¦626)� 91; � Q� B 38i2) 442.�Dre�^D.Amchsel, 2�SA,Ka�v*��B�45A=l99) 145; http://www.kph.uni-�$z.de/MAID/.�nh 6k G.-Ye� n, S.�Yang, 2�}q6 522 1�2�N$ T.R. Hemm��Bolmء�JA� mbor2�D 5 �07) 5598; V. BqH.W. FeaN�, 6cT U.-G:#.��' 5 (1�'1214 A 64�<6<? Ta���1 H. Leutwy��]�C 9-�, 643; B. Kub�Vnd � 2�:�79Q�6�T��chs%�Gegelia�Ja�Gdze3@Seere>IA�20\�056005�"x >�)dou�7%\ style[pre0t,aps]{revtex~�draft .��12pt]{�clRu&>�g��ic�"psfig�:f\base1g$stretch{1.L6\hoffset=-1.truecm \addto�,Hth{\topmargin}{-60p3<6 exthe�% }{15 !� 15 U \ti��\bf�I2f Few-!�eo��$at Low E6_!M�%{H�enh\"ovB1)%�Carbon�;2),aaCant�L(3), A. Fonseca (4),�W. Gl\�Tle (5), H. Hofmann (6 6Kie� (7),3Leide "8),\\�O� dini  fwia�m��(9ZM. Vivia$7)�$3 Q } %\date!sday!�,*Q�\�J!�{y�(1)n��2����,Ge�y;}FU 2) L��oir�S��i��Subatom $et de Cosm�v e, GCbCYFr�N]3) Is\� o Na��ale��:�:�� dova�V:�,F��`�. P Eu'R 4) C�*o:�&��d�$de Lisboa,P�GgalN�5B�(eti�'� ,ik II, Ruhr-�S� Bochum,j�6�gI�t�AEA�$gen-N\"urn��,,ns7��is~� >�1t1�D b�8)^3BPTr �, �\��Fw Gruppo��ega��ZP� "s�f�9)Iy G�F , KVB�GroF?i �NeTTlkf.�Bab-ct{z@ manu�Wpt�-auw a�s+�� �, shop{�/"F�,of�� body�� Ex*�E�cs"�8LEEP)d4 +hel7f5�E�)2qDecem* 4-7, 2002%�"�7wr���Hpr�1n2?M�* 19;3. uUllu!�a s�-��"ڋadv 6�0rI�B�ar few ��1�X��wo��-��,a��'$e �TAz&Z� �J /fI�%kt!7 A (A$>$4)%%m �;.�RA�st,�Ks�3 �-�+o*3l�zcDpd�B � s. P�uly�tf$!I6S�1ia�Pory�6�7P�g!f�2�:&`6 is c����%�!n!2A ! po��}o�%pire n6U�-|al !v�(is neverthe ;kpha 7 out. If-; trend~��in�5�U6 � area�/�Come cri3EmJi�Hulta�\vfill\e�%7 ableof^ents BQ� %��,put{memo_fewAb_intro��2"�-2�) qYI|��4Atee; ng hG.%�nonm3��vl5gim�pcromo�9s (QCD�.Ee)A�& wo nԔl� ntiers�f8�PA��4oaHM� 3E�A�funda�1�M�Oforce"�0+ȺIOll as���riWLiCof &�1*�: �:(d.o.f.)a�iE<yo:) �6m�  �is ��com��mincopic,5Qme� �?tH6����A> ��s (%�i]�t�B��\&�-Q?g�zs*�;iA�. ��it�� M!�fr-�,��ucQ Z�s��l&�"y �(g�P�N�Nflourn�%�AI- d�^A�aG7 2etŵ � 6E���e�a�%A:R , %c�ry %�#��[4A%r7premi�>���to %be2�b���:�1��6��5(%qzl,7s�) aa %7var1I.��02_Mr�1e5 U��kofB  �6��(4�4 "�2f�M��Y�at��&?a�K� $``Why! tons?''D �0i6dp7"��,particles al�Ulows accurate solutions of the quantum mechanical many-body problem without the need> approximaP�<, necessary and unavoidable for more complex systems. Theref\!arisonb such�oreti�results�D experimental data3 Bw �xcy can lead to conclusive state@ Qrespect&�assump��!/�underlying nuclear dynamics on whic�-�@ory is based. \item ``Why at low energy?'' The main interest is�qst!S4strong hadronxinnp {\it nonperturbative} regime$a well! trolled 3rel/will Y�imv�qu���v��6Cof2�natur!`at��vebe addA )�!fu)QajI$!bntinu�\ ongo�2� is mandat��A���pri�ex�ng�! eler% faciliti��s �IaE�$new dedicaA.ones. �xe�,is organized1fol�H. Sec.~\ref{2_body_!�}0devoted!��-Ea��i�$aca� !its���degree�$reedom. P͇model_��on�:(NN) po�A: %�briefly!�i� � u�byI�!7b���scatterkutwo` �e�Eanromagn�.�s���9 � �2 st!�"l��$" enough aahr&� 8microscopic cal� aA�7�� shed�lial V� a-�aʑ�n� manifeA���!w2F s (4-Gs!HFI�more,e�chaa�er��W (f large bin� P, �ral d�Qt� <``closed-shell''< uc�1ly  embl��eaviermR� "� �m  !!�yaktV�C6� %�A�I �`aches,Qa{"B MTa� trea !IM�4s �rx !f e� be 2+�iCi3 C}. It8Źedh how2o R K cont3 Ŝe��kdE$& fi�� � Ei on�]�basisB`Ap phenR � � AzE�%@ c� c%�moAu 1uH. A�:�b�$own, where ab inA�}f-of��A�CreɌs � �!$inuumA ($A>4$)--x;rt shoe�typ� � o� l�AZfes. Aga� h:���2��larif� ese issue��ll���zedAn]&fewM%lave}�&���� ��Qfor op ~ s,� el� � le3e� D,��4described very�|yI��� us�u(��Qeas ,!Bneu7 t�F� nd� Ja�Y� ew �5� of �alA� 6YO I 9FH ��sm�A B� ��� e�.Z Q� know��nowadaysx althA^ NN-[�q ,��mulG ver��� �se/ ��%�% fite%"f NN.]�a�e �of e1aru�eLsimple%pur�-�� olog�� k &2i<duc�S Afte��e��c ide��Yukaw mes s medie �-�.�m" soph%$ �� deE)�In� t,%��)H2��uWd!�� t�desig? myA refyNN-"$ 0s, parametri� !fN�E���N %x�B� �� ich,� Lad> of QCD, Amnow�s����only. U"� ���2�� � s� � rst e�a��al-waAv� (PWA)��:�Aj .�w"|of� -depnt PWA%� made "P ]" de!Hin��- NN � e-shift![ mix�,-�er[5 `e�� qual5 �vpD��z�e avail�e��, a:�"� ?$long-range�cZ� ��requirA�� � 0one-pion exchD.O s��bA`�wed,!�����e de�)acum �.J(� y-I�l ore*2�). At1!�et�so-cal� �preci���y*�9L�fi�N(-a &t�ofY� ion)�8 a $\chi^2$ per!�um+ab/one��us!�y-�b� NN-��� �� A�IcaP Beyo� !��)�1�-1A (OPE)A� t, �allzse&^< ntaibhe� umA� rt _�oE)M�r�  ein Z�or semi>�� 5�!'A  E � �tr��!e A��ic�&tex�^m�ioafTi ��rn!���ional!^7s� �� ly 40-50�2but9�NN>_)�Ah"Qiupa(350 MeV lab�ory�l. W��:�sh5f )f, al��.� �ls {quark%�glu��.o.f.��Ɋ.  Pt% >�J%v-�y�4ed s,�l�` 6ach�}pu war!�j&�!��� !!(EFT) u�6� nd e� ����d�chisYkovU;(starts froml m�g��Lage9anAB h6��s obespA4neousA�roken�sym�y��QCD* Iar^�rzn�X ia��� atic�an���]' a sma�sca� ��e᥁�� mRr��!r �\teraa $Q$�a mass Y $\Lambda$<� ɰB$\rho$��74U� a be;E,>�be evalu= ��� �increaI '�ca��tio��� nb 2number�acE�c�I{� W (LO)�r���� 8bli��R���lKed!m6g�L �ume un� }�"� Aj)�Afix QD *�.���� ength���t�A��cAt�Q� $ants (LEC'Ie9 next��6� (N9.Svario��wo6� diaV�n.�s%��E�new5$�. Even�V!�E��1�*�v%already ,�ut. U��� �& k :!nNF rin NNLO,�>mou!7�� n��� good�5p�u)�!��r�Ag .g h�> u���Z/ d�aM10�g;!�ras%�co����* 5&re&�Wa�a����( a�  facta make@ sens�ex� �� f*-�%� . M� � �(r#Ee�KU� fq� -�Itin� s��i~xa�� to goAs y%�% sami��A�whe���xx % we� � then��ar� |"�� ��ͼb�. *  a�ter�Fnd livEdeba betw! �trak�or��F0EFT&is ����� um!m inu% >&ome!Hre%�&��\z!i�{ !l � ce� (error. % Ng A#riŪl��r >�> t�{x�^� E1 $pp$.Wi��M� . However$n61fsit4ie S"a!cod. Ne'q$s, both {!�S,�o�!�imed at![rokf�A�w s. W졔typ&%are�useful�a9�%"�� answ i^�%it�"e manner�4a 0 eff I�oo� .� ists, by % 6�Q B bench. Ha%�ARhe�,E�� proce#to.�*�" predi� ��"� !�� roweak��@ ia� � � ]�:��$ do�2�%*J�� !t��u� inO!��jm�&�*|?��h nse,�"� � "�\&� ��d�� �!&icB��5%�"�suii�oEm�"]r p-a!�(e.m.)Wb4ɒ\&D�B�� � 9 �edf� � !I�9��� � oW  #�$Ѫ .m.\� te`� Mss  � $ curr�>i ���Qa4licit ledgUSB \IO� ] 2%7��6��#to�U> �&# G@Hamiltonian, beca gaug��/ � alonp �$suffici�AI��fu�"q�� nBd �!�E��orp' e�MFeB�)?&�d�a6� �%�ss��i�deuteronG, e.g.,XticK s, ela�(�bn�, photo�M�dis!wg� �zdu�Z.*)"st adv!A3a|iq.�5 M" MIs (MEC),� oba� nfig�+e��niv�\b��ea*C ,in a $p/M_N$Az�!�A.W*Xw.�),y)ss���i'1d toE(%=absorQ < *"!�%{fo&q% �&Go fun%\s�,in satisfact�a�#I�e�f"�+I5� �� l�,n, e���Rfin�l{n i!atyaOtheZU�M, i.e.�" �M�ic��A8�7��� cor �%�in�As.LseBu(, differenc�%2e�,�#6zs �A��)�erA�le, �'-:a�pe%< -<��a�Jpf� le� !%� 5^��un=una +do�Z��u�EJ>z critJassessE~&*�]��*�%�a_Q$� C.tMDy w� i�� ten ago�>reRR� 95 bone�pek/ly�n2; ��iQ+\ 1f�i22�tru� �ex4 � .a�Y@ ial 2�)2po M!.>)�� a�cer� kine�)�Ő:�~qgM~Er!�10-20~\%�c!36�� �ZZ� bE�of!�mric��, a�stiT�adl =��e��du8 tech 1ch�ng�Of�%`-� ^/�# �.="k� no2Z/�2�um� 60apa�s s� .�kat�}�Qgir):�"m� be� : npto&�*%� urg T ofd cis�&� � 4: \begin{enumeA�}�0[(i)] T�6:�2} %�p� �� l�%�X h.dispu� lGerasimov-Drell-Hearn sum ru�� act, a�y'% neg A��Z!�a��,�&!$!� break-up F(shold"`  domin�+" ]b$^1S_0.� > ih>0�ly��.ot��n� !5T"opposit�:�)a size�influ�\�2us]_ ? f�*�!n 5�Aw.q, say*ewpB/F1.U"A#Nl+6{@in $d(\gamma,N)N$2lI� ist %�uA�-Bg ofza���DP)�5on vezE� tens�$� Ŋ. ��E�qZR �� < $d(e,e'p)n$. R�/A�"$�4�(� �r�5 -��ito$al-Eu\-ver�%��W*� $f_{LT}$� seemA�bfi�� h[ YE$f_T$.� , h[�2a ^'ea�".�Ndat��9�c(Rosenbluth Ri� ?2�� "�%BPp*=2atQbrems�0hlung0a[E`%B�-�u��� �e&�  "�Mr%�&� �TadA���*E� for �6�,m��a� ing-D5�R� �*���al� s fail%� �&� $ppi�$6��$�o�6�$discrepanc*/�q� Y�xsurpr� gly �+� 'B '^ ',3FONSECA_2v}�'6' "' Many�&-'d-T.�vF-* 's} '�$�)E�aEo} An &�new*"7��*5��- than �4a les:5!�"�7A�&qE_M/,/se?s�m�Q@d *"�e .Z"$:to *dAr5/os2l/�6origin %?�expqA��!"�. �"�i+��0�t  & . Whil� vz(� re*�-Z *�$ anks� a~�}y!:;%��a w�1 #4ne� %|&�2�rel��au�g-���aba�0 ly (2N/i�.��exc ��lR %�i{<+��e�c;�N ���9G5�m�$,�F�dee�#&�� w  �n.)eB;set�=Aen�jd 2� ifŎwaa�]s}�'!�X�ż e NN�8{ �y�tAJat�� a3&$"L an ad hoc�. M!)!��%�Is�as �i�fu&:3 �y(�"-�"y�<Z5�s�3%�& al��0E���E�)% � ca� re to pair-wR 6�*�AJ�w� ��1� ��ohir� . M�:a�!2,.�e'ies�carriA[ut,�c�"�7U�. , �>ing:�"!�erN'�e&,E1%o�&Delta$%� $$\pi$"&&�a��'' �.��m�. IJ<cA�}f�8�#�� b� U� %?.[�A��&'Ef  guid�,=DF�$ppr�$ towards 9Nis� hope.<�%e]toAI\�* ere : �[��c.9�8� <0 i��of��� e��[,i�hib�e,��T%�tr�da$�#�+m�"!����J�-w accompanA\#v"calar s s 5���u"�>�C�`a!�Alo>g�|m� � Q 1�U���m��� tur-�<atX�u*c � broad{(��~ylittle .���)%ȩ� choi"A4��`%���K is G$ tes �{�!�H&or�T*+ �e�7valida��:� "V�9arch. A �2��-;558��em be.B�mtA*"�2<q � pln �a73��h��?i�o�:9I� � , as� � � ��J SeB;&3 �s},و.Ui��xUx7e*�'"Z)&�8tr�/l*� ,A~$>$~4. \�%�5 on{BXSmCs}�1G1_ s} N-1t��%l2^1�Dnd��"!y���8ed �&H�@"�(an7(!&� rn :� &� � ��7ci>\age�r ��BA=3�4� �Cj��� ion,j|Faddeev-Yakubovsky scheme (FY), ;>A�a�a BS=�alm(�, e� 8*�t� ocedures:^a�(��( hyperspher�harmon|9(HH) orR4ssians (CRCGV)�ochvC�XdB (SVM)� path�w��^xA�>�, ``Green's F14 Monte Carlo''-� (GFMC). ;ly +� promW -�!E�y!���%��1<j sm�&"R2:8 ``no-cV:E0l''�'CS �d``\*� HH'' (EI!T% ex2�-w oscill�� A�HHA�is�R,e�iY$� �th ,}[tbp] \ca�{Ki�,$\langle T \a le$qE�>V (ij y $E_b$ (+in�), �m�+sj e radiu7 ,$^4{\rm He}$� .3?A6� I3s.}��er$tabular}{l} \hwB MEl& {�� $ } & {F� $ �& Br^2-$^{1/2}$}\\sFY & 102.39 $ & -128.33 25.94(5) 1.485\\ e> 02.2  @12@8 \ &:\\ SVM 2?27126 \\ HH @44 � ��0(1� �\\ a{d�3(10)1�25@3(2@90% \\ a* @3..�9.4 � � 80(2 ]\\ a> @0.8(9 c-126.7  @944�&-.� ?QVzta;1}\U��F�b  [h] u`B�nm$��.!i+a����74 *3HCD~Bonn, Nijmegen~Ia� AV18.u ��i l r } m-9& CD-[ &\ I & V & Exp ! 2$^3$H!B 8.01A{ 7.74 6 8.4800$^4$He & 26.2 24.9Q24.8a0 )6 ) Q�& 23.99A� \\ $^6$Li! b)31.99 )7ZR1.20 8.82)RR31�39.24 )8bR�31.41)^R� 41.2-8$B! �45R 56.5%-xQf%�2�2n�A!�GAp�{J���2�nA�� g �#� X*( in Ta�EE�1}� :,��eci089C!aR2�iV a( m^;!�i � ak%�AultY� ion�)sjH*�  t&p2 ��� l.�<s� sI A�#� a~cutz):�&Ern &�*< underbi,gh�( signl6ai8. E)�' � laye>�2}= e� OB)b� nT �B e�'�+B A �.�!a" �L�[lJ��T*�%�2�e�B!֍#�� 2}v s TM'. Urbana IX��& �EFa�mm�+}�M��&���\\�v"�45 $36#�a� Hi� Exp.6� �f�3r�s d �)!�!�H� 9uv=� iRie?scripaG,dBh( ,�onQ�>��I+"J+�X[#m.. AeRa�R. Q� �2"#�Rsm� "� Hvey= m�&HTucson-Melbourne (T� 9�4> �emplomb!.%H. N.`1TirC�+M adjusze :(��#�f+1� �.4(H���R1a n�? c�&0ct $\alpha$-�6��w��BO3}r$iy5q�� a-)ec0b��mov�`an.n�'e tun�%)�5�=A. �n�SsA_n� 1�"� dens�' B�es��3, ongl�6dI%`��+%X�w/�7.2�9 ex- r �Q�edՑ��?9J��D=�*�"�,nT�[$�E"c*of:�; . On�3n�( c .(s�:>�G�8Il����1�}  1similarA��6��:L� 2T�. A�al�^�if �\ combP :-emis>��re-*�*&7,���"�M'3N�d ��+�� \���M \e{J aphics[�Le=0.5]{f.wavq0.ppn.p�:d���QZrel�&�+dis*}$n� e�"(s $\vec p$� q$A�ShI�6Jacobi [8a. Solid curve &IF� e da\9$EI +�!_�dot�O*�3.{ �n2_p} !$ -Q^e=d!r>gwidth!g\text]{C_ru"i FF1a��!dU2 �.{ ' ��!!�5;Tb&�?pA2A��!Fjw-�+ �*>�=�s&W �x�X"w�> +TM ( ba)%�)� �=%�;%��8!�-�)_B�an&)(!amM�u�!N�Val*prs�1*� @D5�@PsfLin Fig RITZwo5�vIB�in R�BQR9 $C(r)$%/6@I.Q ��Id�-t�Sp�Gi�&E�5�um6�!�1�aw!�E���D FŖ�}eW�=�*i��,�5,&ab�S3;nd����Sa �� $r�!yQ&, M�� a�1WU�Xd N$�4$ r \le 2$ fm� dev+a�4rg�Ci���.�dup)9Io" (6��D*)s:[�peI�help us� �a "pi�' ial"y��!�%al1��=y� not direcu*<; n� th� 1may� �Uh3 7� R- e.� *�,!�Nn >�f . TD- is ev5y!n*]#�e �omplet trol�A?4e��al ing`7erre�LtA>!1!�" \ �R^5 .:��9i� �y%b��al"o ner. �#2�41�ne�M�'icAw�D on 2�ff $^2$HA����%UA.f. �s  &<(Nvr2 (see*�M �_N*}�R ub N �-  Ia�{�ClJ r&Aj a:$*�!"%=9& "�Pmulti- � 70t�<0(A~$\ge3$). SS!a F�?y,��P u� =_er%�a tetraR7 "e�Z@7!]"�in��li�2�7C;"*2�]� � Fei c@5�!.lX2<�!�� bea'] --+0�il��A�p�W��X � I� $4n$� m�7iu?�*e;kdou�^�Tg: �#�$a�&�6 "^-$ + �a$$\to \pi^+ n$)��[i^mQ<%:0 pre-�#A��5��a9/<� impede |Io�~u�-tude7�-@ $^{14}$Be;aU# bon I�,Z }�"!t�_�K��G� ^{10U %n$$re;[KV &�!� g�ho/!�,ed&�# back@#,e��, vXR�L�=rueY&E�&i�6�2\M ?�r@^�u6ings. F�FB�itw-sF�>$nIZc�9 Q%�si��. Despi�_�\ si-r/&ant Es&zZ l�D ($a_{nn}\�# x-18$~fm)!EHe Pauli principle g�~�!o�{a/repul� ILa+�5aT)��c&E�Aa��-2�Datt�shB?%�u�&�,A� $31"T*�m�2�6�_�EG<x�ls*�PJ*o����DaC!�A~=~8� um,�)author�'r� �AesA/Cut)��mEq�� dro��-U��L%�"Bu�`r poor �+2[<��)]� TNI-�,�inr ,�&�$so suc��fu� d�br33N!4N-.�%y,L$M$o9.wZCextra�Ct� o�.e ��f!�S0+ (the Illinoi� c�* buil~�Ei�C�>c ,|I2 �dTI�vtV>cCO� N 1.5~'L!�a $T=2$� e;7 $^�0��Oiy,� �ng .��ar Fe� un� �E?l=Yis! y un�7�Q��s"�B isdcl�9�JX�I� `l�3��E�W�E c�6� task� draw49f�X �/� ��of:�*<%A�no��>ce2a d&m��"�advoc�eun,�=m6J$B �{S��6Q$��V$ y$��"p ��b-� lim�,J%:B �"iBep� �ia�K�Dt� �7!zC�s�R! � "i2� Byfa7 �e"7�(� �:�B�A: sourceEW"obD��a�riF:� &� �0�0Coqbum�%3N_i-�ek�)!I�o�mti)[)5!`&$ti�07>aAf triv�9]P%,lem*�Epower9 tool.�"�#!��p�.&9�Me.I �!�4� ��#&�p�s:$ �% �}ach:Cr�j&!�AGS�% a�fll� Kohn-�| al8}+ �6�%ca�%�2Z�2�Z�.9.� nd_e�#�Ang �W!N�A$nd.9 (l$grey band:="iW*�Ely; dxQ2@2a^3nWs)0pa��to $pd$/*CoZ�.� *i",gee30k'�Jh[  Za�?%�&=, "o�4pAN",��� 9 frag�+ ��.�>�G�Ui�M�*"�g�� ae//F&d%�!� play �aJ�� 1�)�. at 65��135&M�N1�uD&�!�!KJ !$�ng9��$v AA N��yNic?o� .�.�6q�minimV�B,� �Bn� a n�*�Bhen��)d (c 6�GQ�*l oPa�{K�& ��y).�,to"2�at�#k/!�l eE�{ o&G�e.e�refer�,i2�&$he Coulombgce!��J��4��y..�.�/}"�"�),ɳ,P�zf�Wx5B�>inbF�b/lllwA6`by5�M�E�AlahAx5�s�-� *�!M�,$-i. d941�%���S�?�fL?< �,� �s+ow� Ass!nw�;a� !i,pisa-EP1MeV}!�)�q�&� at 1a��>��B prot��&y2a> �O.��u�@Lr�ed:kAi�k!`AE�"�*!�5�F spac�ge�=e�7;.d��O�a��i�to�ermR4 $S$-�Q8$K$-matrix. Par�g F)� �A�#st6R�(5����e�:_ �?v1�2K�� lcZmuVH2�0�� -le�. N*A��K7i��($�?2�!@e��]k��0 �E"s��9�c�k. ^ .!^5..�%D-� 6Bus heta_{CM}�$p+d$Յ2��+p~=~1$� � �.�B�b�� 2� ayfig_alt2�Pec*�i�  $A_y �q��� .%.-puzzle;�L .�29|  ou� _js�et�1%figAy} +�N�Wa��-tP'&�=a0;�qp�SWA�k a�s � (``.�'')��$iT_{111� Nd$ 9�ʁ�7�2�S5.PE�E�:o$E_{lab}�2E"�[mR�ca&k�p N�Jby��6 x$ 3�F �max.RA �'" � ea�&?b�?s�se�l� ��a��Cr�58J�y�N�o�40 \% at�,=650$ keV. NH!).Ern:o,�#�to�6!�be)�. X:�s��'2jIX�y �"@i��ly sl� l�):8��~��I�)�6mE5:+de-7K&�)Jy�5lp_]6<�$I�� -iso�>u"l-7����;yep� c:�at 8.� g# (u!-dot) !A��i(�K��\"� N$T_{20 3nd 1}$.�is e�����measur5tI�+�Z� $+0.7$� ��J�� q4�P].,{% retard� B � ta�_ into oun�a:�'N6 can 1� z&� � b �rsiJa�O�!��Bdecad�I�  � involg �] oord�f� fqt�8�g�!t P. /{ct )�> gPT�L+��� �ge�" .�6�!�v(!�&�cof� �*�%"�,�%�he KC�k�=�ZmO~smr B tr�x��⥙  \to�j m  ely ~-�u� p&zi�m�ca�V� �f� s+#^��LrZ)لak* %'�>� �$�%s5* er ( *P) ~ �eZŀ6�!e?�-�JtiO O �> �> Ay})) � g�!�x�!g%.�+pO]�,�W!�0#�-l";p�<)l ew 6�*7  tA�"�%F#nd%� eque�0, �E�k�QJ�Ca�.Wup1bc� itselfV|}. RuH �6FA[�Plac�F 0at�: �organiz��q�"�M���ew�K\$�XSMatu�@~}�]i"G-;v*b�./�+��-�$��k"!ubehavio�c*VH ),s�=?e@a"!��Kne�sa�er"1C /, s)^ņ-p�~AInO�s.Mi� rensa�.� i"�Ca;:�|U��G��>� y do6auL�Oan iso[Dd�e@@ �f���vPrY. conn@Pa7 gu6"a� �&�[��16F�?  0, v��OrR/Q��I-f�lM�J� htb]1 ���,J> ��,�_65�%�/2_65mev�a E�YJT 6S arNLO ("�N (� bandmn2�`e�F+ &76 � ��2��5 c� �^e��hA�m� 2�a ��� t si��h"��Ba�NV��e197�J gvE q�d�"�c�>oi���B'`. Ik% 6�ao�4�OLOYK�'� n new���'�isFB�4re� p r�aA� �0, a�k���z 1�Do�Eac�#n4�rd�h&J�Hp�r3N-a}2��O 6�I�l�� pieces U ��4�is') ��� "* ( D I�!T���=nd$:&t.��#�"!Fis"� A��&Fi3e�_A�!!� M�"�����'t� s rip�WA�*r docu= A���"�:etic.�2>��& 6q�)�A���q�[�n( a� � ���(!KbI��# ��FF�9-*5� "BkF3sE��2ie�� @$d\sigma/d \Omega���Q�"�  � . TuA)M�i ��A|�#S &4s�  s *��O�A*�)�o hwZ Pb�5sW"%�$eEWs{g!: :�s� 0}$, 1}$��2}$=&��'s�Y623\� �D*�5f{"� �@�y [#too%!:a�~ a dF�".%K &Lb"" [ �B�)qn%b!�I�)�/no%+�Fa "�\�I��PL���#��d�ہ�sZ � ���)�/-�D��P � �� rm�D"�nH'��&``rG.ePvup oH(�Pav�d�9*7e�ic nd.z(p !(nd-"I*�55a 9u���" 4$a�6��9�bi�Oan�%whelm� y#&��st2zA_�( five-fold Z&�_F�| �]urs��g�d et%�C.�. HR���^�h!0���!7pasX+��!3thPta�-}o�Z�R&z�+om.Fnag&6�,�["t! ����'A��\DuM?m�eT"�Y� re �FiE�`MH� :WOa"�" !N2/(�!o �[{) of 2!�35Ita3�L+ e�a!F5y���%�IA l1*8% on��e��e ��&�V#&�t 0.4]{botn_fig7r .ps} %� d{\psfig+ure=g/[<_tot_he3_exp.epsr 9cm, a0}rEr.^<b�  9B��F�w�7.J9fG9&I^*�92,!�J �%�LIT" : N5 "�teT +*�(+;72N�.5  Like�RAO>�#��rRmva�9�+r4 -k/A�bP�rst eA��AЁ�>b$� �O�B�t� D�xamR��n� ��"�Y��e5}e-� &'B� �ou�PLo,z�g�'f\ L(LIT)D thod�G"!% 1*�_� � of 1�|9ulF mai��!�11trik_d/��8r��@a�e dipol*xson77 (:�5I��)W:4&P+!��� ac��cyVO �srA� ��h FY.�%tur�-�=n�����H?]��.�"of&WA! :�a�$U7&� J$�/kgJ� `�#raw��t2�f�E�� ��FJ!p� �9 x%�� .T�4� �3�f� !*]�-�eis U �}B)&�_q�s (v%�mw�u)�7��a� vir�0 g�9riR.:2�3i�ї�F<*0��F�!'wkA� � w:�c6a%/�$a~"�_(� A, Z|-(0 �Yly4�ve)��:xB�ft�er�>� � mA)��)of.�$s?= �AP"� FSIa��m��AGi�te wa��B��;W�� toa�tri�ihe�H� �� qu�3  �us� G*s] >po۔ �.�p.=f��b�Tt&�yŕE�D�~A x &I� mn<� "� ��-ed��to5Yd!��/in &��*� ���Vt� �ily viaV!4�j $^3 �@,{\mathrm{H}} $e} ( e, e'"p}\,)d$��7d7p$: �"AXt�"��*4? 5A = 4/! �l`$�%xar� +la�:��M,9c liys,#.k)G[ ��OQV) �7-E � -�4faw W[2< >Ke�a�(n��!"�9its�.ly look!�* M careful R�*��ai&s$ lapp6:�s. .$&ed *E�hifts����* th� ( $90^\circ$�a�m�E��!Fp@(A=4)I=i?R, �<�` L�w�1*�$n + �R�c�(o- !e)���^d4 � �� Q3U�42�~� �Ju its  (&$is $I = 1$ ��$E%�8.3)�E�MaI�� n���u�p�� y�a&�<6�emerg"pe"�?sa|for�5iwH�@�!i*�(� ��� �o0���  ,dns��*�~� exac-�"UY����">GseL���V/%)q5�6$ a,a�6K (-�))5On��" .�)8l�9?2jex�� n\uUb�n�$8 to s�0� v<���A� ^ Ag�X*�41�I&PMg� &^{ 6���!&D�6�".[ !BB,of�1?ps,� x Mz_�9�a�a#d#�� e abs�of 6X2Ku�}�1 �&al�g!F.$*A � ��Ԣd!b�<rɒ "h%.� ofʹug5!e� (2N + 3N)a=uD UA$K�72 �=+a9ak!=�@c+" )� b��� q ]�@��?oBa��6�8(. (���;Z%�s2 K�c9=� ."�$dd \�1d�p��>A�$Js�!�G�2T20-iT1WVl�8an�K�zcy0$n^3\mbox{He}�. �.$�. 2b1!�f��Y�Y���.��:��7�cc)e4��$s2T3s.b fiDDi� �,ng L'A��{ # ���"a:�N�N;� Bk+a�et5~*�U)Ba�5�t�q$$E_d = 6.1�#&F2�s�U�!send�7N��v<ni-ay�V�qal?'�MXJ Vq2� "S��eja[T0CM}t2.T0�� 1.69|+A�-i�_X"so��s�ed �:9z��2�w� ���l�O Qto%*�9f2.h�g!gxsu=hj�3A4aj�B3a�in *�/� �4no�4F� ��� � 7]{h2�C�FBz�'I'��$p-��ݴat 120~[�0�F� (Ek�!�)"6  (�Q�m4 h2} ,X"�3L��CA�d$���,�!Vnv� �Ńzq&9 iP#n� *7�T g�2?� y.�M=�)5'n&2�9)Fai�1�al"9 �1!6 QK"� U2�N�A&)� ��T43p+B�Kths�Dx5!�FHD* �4s m"s+ata sm�-'�.p6��if � 3�O�zc�+i#s!r�9)u ��9�$�3���e`4yI�) ,p < 12$MeV),�g�'"��T � "� K3�icEHq@W9. qG2 %2'�� �"�DaN�en�( �w� "92��a�3�'IP�N���>-8%_�+)_Tr($^3{\rm H({��<{p}},n){^3He}}$ �3��� c.m.�6�IF�g2\u%�e��(av�&v�t2;*�Z (au -� )OF at 2.9B%ye"�M�ent. 2!2/ �A$u� �+"AXW�z%�sI*� ��h2�%+"�F���Pmt ��:�;� ��"�$0M&b � E� � 6��CcoL�qcoeffN t. A'/ �!D! :�Mٵ(p,n) n-�1wy ��. H:�R30Ye7A%\ th*?!!h3�T. h�[Sj�"B�J� 2��� n!p}is�Y� �soUU�"hvca�>�K�*=/)�""=Z� �m -��al>�Me-܁�$0�N�I�= el��%Wͤ%� unit�I limi�1one8rc!#-  �}�@ zero*ہ��a1 5��� S�ne�a$c*ZIi~Aoln�%�ctV�po �!#!Q�)Y���I = 0$�"A&�k�(&' Z�[.� ڠ� f^*#��:�`Qs. �LIT AR%����9O�ἥ�:Aa���(Ŷea�l�\1+ut!V%P.,�yduu6*:&.�ng!%�b 1 �l�5 mber�!ap �i�g�-d��e.T��E�3 , an"C!�r;xyV*��,ly&409. �&::�a���"'F A5�!��%�A�� �2!����% long�� He $�~)$�P6����&�e���300e600��/c�4a d., &� t&���~�%��� � "�t � ,��,6�p \o�eA O"�ДiI.H-u5WI�tiq!F)*� ��)�VRsurvi�4�yY�}�t��j��%�=@st�$-�j/"�+ q�$�h !. W>|�pdt_�a->C ��Heu�I � qxt��i �D`��Ǎag r� .& s. P.|min��N� on#�,x � +A at @��c6LE�he* by 1���� � :�"6�%1�sa��}5YM� �|j�en�0 6� ĉ!;��8lyv)B.?� I`$K�&2=;�Q �86d{" /� !L?"�P.� �%P. �3!�B!E��ԅ� F!�gmk93MEC. C� ev^^�< thC]�4"-,aAK�"c*�|_�a�yJth1 of 35& 6 ��o��� � (� �B: ��b� Eucl��H?� ��٦MEC:�x"��"4�Smpl� �j��U���Nͫ �z)�f�T�$A�� U�Y>�?ab�(3���p. ��=��se�9�&� �.����u6 �1"#um^�76�- value. IU�a�zQI�U��A;nd���7e E*o�j�w @!�%E� ceyi"�yC �^H�- 270, =.65^2-42�To�(�'v.-m&����� �  TN%�MT*�R;=��$� : y� of $��n)�p)d� � af �dv.Tof�Jge&rFL |&��+*� (sha�3�;F�%k�.�*!G. .��]�I����'_)S i tpWi �Z&�`�as�=�3a�.�D(�-�#d/�|o�;!out���lG�S����/Ň "�:�;t�:ai"I�u��t%,��ik?���1Z � >��1!���.ͼ-k&M 2� *��m�)"�* �T� E�� �s/ �G�� .���5A�� !L� B�*�2��/ .�%)x ular=%o.e��,�+�� i��$sJ� � ��e��Z�mْlaqX�{ri$^o4=+le�=O�,&���:�pB:F�O�&��.�~�a%�7(��nd2QlDR`;1��O ogra�� readŏr��at Max-L�� Lund. O(basic *�hQ-�yicupa)�"sYsuscept/<� !l<(�F}  fVNF�Z�or#+1�pݏ^�W,�)]%���;!�7,��2�c7lirE����S.�e8 �&0��"l� F$s� a����e��u�BF� !�}WK������4GW�؋f؋iUD�Des4s!5"� PC"�w�A?*_ ы� ir�l�; l� �i>�=2� 4$).p[le�% Q!�!r-��*�i�siye�/t-�6,MݴHۏ�5�]�"h/� � A�(�Tmerit>� q1!�+�La� & ���A�co"�m޷. F&�:�|a�9�/�Oin�1�& �a�5���im�&�w  b?Oo v�.| g�X2�]�tge)on �r (``�Cum��''h�X �pr�T�[u�9F�%y/]� reg� %� 9�4*=R">&e"��Zr�to�@ t�w� p*�-X !��ُ=Mf�K��*[o�5�2.w+�-S^h,  stj�or5�Ir���&�R=i3��45"�$��GAʡOhAa5ݠ�� E�o)VRI 64e.�U.eT�C�g of G��ULow-L%�Eg�S� G���&S ����*dJ �l/ �Pl!*�=f;-�* ��'UNC2/�!B�( IL4,apS!��8 /pG�K� rD - to A=8 ��{J Uva��P%*A�2�w T��t 4�v&�u�-�K�I�(!�I� \�r&�)s,�i>.��.��:}!�Ab�e-�C`Al�l. Si�!^&�h%��ri s�-�4s!cm�7�7�r��GAqA'%��\0�� J �!nya��+ �p� ?� x yiA�o. �%���*G| E.=��g !;(6|�Gn le-sJ, or narrow-, u�/eFʪ"5�%o�o��`�!0�H dig��� A'E[pa�:�� s. }�� >�{lrrr|>x�:t� & a>  E��&%��N�=\\U|i�0 ($\frac12^+$�� -7.61փ& -8."� 8"7�>-> 31.1ԃ> 39.0 8.77�{e={ 6.87{ 7.69 72| $2{72{ 26.41 34.5{4.6���(9 ��24.07(4) 8.3>8�}%w�gR?1.6o1.9K?*�6 N|3.� 29.3���|L� -� �31.8(3%� -42.0 &k� |B=2=)� -27=B 7:|1)�  |� 40.9|0!7&��(F=26�3��!B9:|3>| 28.99t!71Axރ6)5F=3.5o 29.8J 0:|4B|5._5.2| 4.75 ���m$3.�1.2.o3=��5�BRl�2%�2 2�6%.|ׄ�39.��6|F�.�38]y3a4�%�&>��>F�.�V�>F/�l>�.>��>F����h�4}&��S+�i�y8 $A~$=4,\, 68,\dots$ث��y�1g��Q�%�ZE ursor��  �ed J�v&�f�#�PSew,������up7�paW5�3i0% be8} umz(A�B�><Q a m*� ``Va#�Ժ6�� - ``��b��.( (VMC-�)-&�K"=t��Uorbitalsn  ��"�  ^��co�� coup��to (A-4)K$($\ell=1$)�%&�{�b׊\,,R*@0j�F be8_1H�F�9"�F-9�FB�0�*(\6�JZo��dzp� >-be8fig*�- UY�:k-�8MrhM;�erIC2-�[JA8As 985n#63 lab�ime(left)� E�i�$ns�xrN(r ),�"be!�� t ޝ�>3}$� �.�i�-� %N�1�2%B�-N7.z1M%"W+ %C9B �e.�%N'V%!0Z , %�"֓�(�=%�*���1�1&� 4 !�-��EmbL� r}0��Q)��!�j~b�o beX�u4j�Z�j�y�s $Ki-"S�c !s p�e�#>coL;����� H�^+!sO\Bd+re�5�( E�VMC�"�g�X�"���9�-� % T�+ ��1��b��)Gq �qP~t�v )� y pl,$in cylindr�=*`]^ a` v!% ��bs�u��AAw$J$~=~06�jN  s�Pt�icZ0A!hancY���E� 0e� �ex��&�A�" )�� neck.Gv���0���/?z�%�cbv�+0H�t�=-�pre��TM�i��Bwo&l�'};.; aa/0�/M1 �c orro��Y*�>\Iu� $J=� �4x m���<�KlѶ�E�� 5R $M=JF)� G"T2�>��faiG!�����wal�s,�s��-: $J=0S�tr�� �XJ�F�U��� },�l�X�<�b,c&�, $!x>.� g@cby�Np�)�Ii��Od�nm� �,%TE�ir9&�tmn(8t��ib5dzsA�e�:�e�J"[!| *s�M�z�br4.�tE� �/ projl[ -Ko)Yi� ����y�T��Y�ie�߮�ݎ�O^�N066he-rho12�!"j� ����/,�j ��$ŗH��8h4p!^{6,8}$�2*� p �mz:!�eGdot|!s"2�/�.0'2�3�D" �ҁum2*�"I�-��(i*Qo�.��(hal��i&6~ �_�"�r���>�Re7��0e�`&t�%d�h*~e"��+M��ե,,a�m^ �> �ddtɡ�2O!�x .�Gs |Ce�Z���%�+&�;�<: �X�N�p$����%|��cen�� �%�M#�R! &eU�dra,��N"Pc"_ nKarss�h?�1�@L&�!1c-ONstpo at l�e�u&����!ZO no{. er s�$e���f AL5��re��������!+!/Asph sa#l �8"J+B Aatti�.a�oXK-p.&n �e��q3�n>8e%2 � a���)e��%ko�ҝ*� H� %}aloppq�V�. =�6  tbp]6ti% j2�& {2"; �z"i�l*isotop��%�� �*� ��%���i each)m5/!D Z��.I++��!! P %E�%v�yU�}� u ����e�se2a�-�.2�5 %I{ -of-Ef����� I� q�2��n��sto#��surF �@� \lmre- . s * �bi�� 36<��m~%O.D .@"�m5 ��- he2�,��t@+yAc� a!� r.m.s.*\�4\%K 'd%i�a# m15&� "a"� az�"sl!0 \E )w2 U�m� c��$5>58� �~ V�is"%�#b|r�.:* Du��a�lexo/"]tg��c&� �!�$�E�2)iA� o)�V6E(�Ee�X Ir *���e�V s�� grasPIe& ��d� aA`��JI���U�'r%iy.-l�2I�J��|% then>) ���� !rOKJkg$'K 2�z-xAi�2L.�?�w��I!��=O pp�6G&m[�8%1�i$&��L�}E����0w!8]&EAe&�&�O� C<-&�q�l%��b "b�5et�#1 alap l,�,s "N�d p | t&(�&��d d | i@ ��? )$^6{\rm Li}-. &ݣep!` lapsl? :8He}(J^{\pi})+p(�_j)|^7X\!�le~u �"�<&W � P�V�4�Id�e3o&factor+ID ��)��E�e 0A�mt 2*���! 0.19(2$=fC+e.= �-F � A�* "�ad:�W ��r!N Cohen-Kuk! (CK)��FEA�$gi�4f/�$ 0.59 �40,�$� � CK.�. �=z9|�$+��7�1�0�;y�#�*5��e�a�M�}���2U6) *wav�{�� push.6"�!�N"~0z3�Leec�r�[�< �IB plYFP$2� . P�a�b�ŏktCof� %�to��A4�b_�I �"I%�whS8�!e.��%eb�A�"r s Q�� w up� �4�^��C b%�>� d=p%� N�Uo�fo��a�I g=s��� &\ N�a�"le&Ӛ�;�' ]�!!��knock-��&� �t�U�,ahMm�D��rE1da�-��n:y܋e�]wEfAe*Z.�A�$ A=16 wU��*�.IA�.�f�|Zx! O�2��*�a�ra)Oom�>�3"�,&*�� �.�c��a~iX k�� �("N'��ng6Vm�.�=l��p38�% 1)g��%@a�b��y��-:@4�h{12}$C W&% navratil}�"ך�\!� Gamow-Tel�T��E/�A=14 �gi. ��3fE*B ,��4]�.ps2SE"�al%�E�et#po��arJ �m�al!�ُ!} f 56|� ougha�> �. T��ő� �L�HM�h�� :���� ampl�b>jUK��;>1���ap)m6T�m�l"A"s .ȝD � lS�t  �+ae�7xim�i � u�6� y �t ͱ n�&{2AD�� �&A����&�,��"�1b��f*C�X E*�C&9-M� } Unambi�p���E�eUK��6rAOaD0�/ ��* i`[s�%%V��lӕ�&��!>iZY�lXC"�0J fact( stit�Aa� Šer Ċ�5 We��3de�if�&ͷgetA�>H��#2�.� ��:��%�"�Rc]{)�Al��.�o"�sB�.,Z&&še!51Drol��q�0N{6AfFig3.e"�e8:�J���&�1.0.)Q}8I.�^�2!�AA L�� He!� �\�8e���MT�pMinnesot��13ials. ��6�:�F�F#s!J>fig_c�*=C2yg�D.6.C� _exp6HAsݭ$'O�a�7�5R \.: I!cC�6iy�DT-a'g"��q"�&|�"[������ on>W=H=��:?="��{� Ubi&EsA+E nd  �5! p� �3.�9�3"�S*�Null2�# basis. An�X��jx 3 F�*g\��1C0� r�5< $\sigma(\omega)� �}y{6� m !B� � nj����$ �/&,F.} g��d�fG.�f��� o\s�^0 �6d u� 6H@assoc ��� e xy�� 6��3$) \simeq 8^T?i;-up6�2� gsec��o!Jat �A \$=��,!�� ��?��{:k6�A�= � � � � �� m冩�!7inguish!�ofaxl� � � d �q]�c� cL!�h�lo� -�us��"ass Goldhaber� nQ�� � Kr�Dt) 1h �>� )�Li6p "hyaFN s��X(�Z b�@)%��a �5�i�Bwo�\� �i,�3AS~+~$^ , fill�e gapX<TF! s<��@m"� ��ng<a �*�J@M&1Q< a�q�2��d�%les6$, �*Slack of � experimental data ($^6$He) or because existing "|do not lead to a unique picture C�Li). This example shows how important and urgent it isRXintensify on the one h+ptheoretical investigations ofD microscopic dynam, stru �hof such many-body systems, f wother x0o start or a�st� renew an 2J|program for obtaining accurate %j�,targets both� inclusiveM cess�4 variou!\'Tchannels as well. To gA�%�,!eT would be particularly%vr!Mng�see whe%r$^3$He- mP has a peak in betwee)� soft��hard modes. Of course, a rich field �`opened by detailed studie5�deform1� 1�nuclei� term3collect!moA&, like$he caseA$$^8$Be. %�D %\input{memo_fewAk_chap5}�j:j\s�on{Few-BA�4Physics Relatee�O%�F!r0s}\label{few_�,slave} \subM Two-%�Three XSi*AgEffv,ve Neutron TI�} ^n _I�} AniV very.spect!�fewi�%� ar p ȁhe ��(of lightest 'i)�deute�orM��e� �uq in viewx\4fact that freeB/���0. The method a7s�6assumpAj K(i)] binda\ia�ak�j (ii) FSI �i�)#Xhadronic influences duea�� pres�%? ator)ons ca�i%�b�gaed!�-�niRo guid�*�8efforts. It tur um��iallyElow mo�(um transferA�a�d!��are size!�,e!߅�de�cin)�of� a_ es heavil"�� �@evalu=m �-qAkaq�e�ner. InE�Df� is da� in \a way �cal��te ��spo��.=aTvarying ��q%�compaE��result9�e.�� . An%ҡ6!Scheck!Bt�~�S�provid M�/e���dAna bound@(ton. Similae�"8 T��+ havei)%;and proma}g �aMve also *(achieved us�aq�edV��h�b�x. \begin{figure}[tbp] \cen�^  d�8phics[scale=.4]7 _ATp_alt}*caŇ{��E� vers� �^��n extractIa�a.O JDe� 6G�"; I�!D�oA 1Q��r&R a&� ,es $d(e,e'n)� p)$. It!�y empha�]d agai�a�� a!w$ly possibla��AF�h'E r pe� takenHoh ount. 2� " Reac�O��Astroe 4al Relevance} a7:�inuum:��Oy�M<w pr- of a2hrh-�i�*�#ceA@ those r�w �s � sų� ?-?orIW diff� t to��s�%|8e laboratory. A� ymw�� he $pp$ ��aD$p+p\r� Larrow d+e^+ +\nu_e$,E%$most fundaA�al1i�energydu%��main-seq� ��hep/AxL $p+^3\!\mathrm{He}.� ^4\!2.�!ee� ledgL `1jae�rxBs bas.:velop�a- real.c �ls-�e"2 "= A�l.3��iA� %����,���io%,Gframewor�LEFT� im�Gahconsider� 0precisA����Dhe threshold $S$-��E�these�%�saf %a-d6 "�techn"s�/ ute $A=3$��!  %y^st���)Aeb��|.2ye%ff Ay�Daq�L${}^2$H$(p,\gamma){}�Q�utA*iso@�EemelyF�* �� N���5| !$ onenw E�o waveaH1}aA��$the.� Rmcan� conn�$!aj !�%x 2~!�!��B� A�ŨAT� uJ8B6O�wests ��"� of�1 (Hamiltonian� �!#6,��ed~Pe�V" describay� curr!�K ��7de.m.\"!�� p).�through/a�� a�, i@("g two t� �%.-�N3 h�1 5]{S4B, 6Ai�!��� ./2-9� %ow��i��"curvewx  �al2�&�8 AV18+Urbana IX)�{)�s taITUNL A� LUNAY  Z >Z oillust�n��s�.\ :��edA� me�Ed:�$S(E)�5- 5 y. Xa� �~D:�9MEC � deri��b� e ) -Arga����i� AE %�d� note�> good*  !��i�i�r und. Also�hig �iVH*�ory!.� is "* in gJal, bu� some�n exce� , re�!r ��nalyz� powers����.��i�=���B�  dj��as�?6�AWA �^opt����gr!@�e:H�qa�%�Zioncl}�h2h"gC\u>"Jcon E  summaryaVmay�� clud�^� eQ= s!�A� of  �ion"�Ohqp�3now%�8 &�� !�e� aa�n hop8 finunderst-�a�-A�gy2H in l� ��iIntita� =&r�basic&���X �forces��bi�w�&5 *�tooH  solvAce quan�me�i�E!2�(problem. Be� �X� M��low-l\ exciais,�'>�" s wil� � a great6iet�e..�� st��فAed. ManK� �s deb�k5�v� eQ az!�ies�left un!Bei�lay&_,�' addressed �Au aday�th a mor� &� oin ]/ focu$on subE�ar non-!�urbELQ��?a �in � �s E�spars�/* inoS�Xut� wc!gat:p�e�Am�#s�-sup�ed� a broaderVlan��R-�r� pas� In!a� , pushQ�above �ioa mD %�� �iBincrea�numbe�p�le$llu�mdeeper �gh�to]!umShen;a1� tra ��J�l@ d�shellcaer-��sin�8A�'� ] ologe�2�delEQ way� O"<pu��Q�fA;"�m�$by establi)la �J���I?� ��Q��. Fur�mo��.ga!) N��spin s��l%�si,�_be�� useful�� si6�Q�eU�s����shortref��B�add� $line{toc}{�}{ReferFs�>thebibli� phy}{99�0\bibitem{1} "" P�(e�2'95" P�e�%\��@XVth European Con |4, Peniscola (CA�llon), Spain, June 5-9, 1995, Ed�g@by R. Guardiola, �d$, Suppl. 8: 6. �2z�f�Is�al2�Gqngen,� N� lands�ly 22-26�7, �`J.C.S. Bacelar, A.E.L. Di�Z0ink, L.P. Kok�MR.A��Dlfliet, North Holm Elsevierh8.�3z� '98Z�IV�Aut , Fr��%�1- �82�$B. Desplanq , K.A@tasov,xSilvester-Brac, J. Carbolnell, b�10�9.�4} v�^�th:�IUPAP2� Taip�YTaiwaA�March 6-� 20002��C.-Y. Cheung, Y.K. Ho, T.-S.H. Le�� d S.N. Ya$b� 2001.�5z�^��R�0Evora, Portugb Septe�11-16,�0.�A. StadlAoLA. Arriaga, E. CravoA� C. Fonseca� .M. Nu\~n# , M.T. Pe\~naE�G. Ruppj�%.�6�bBl�$Slovenia, = 8-14%2jp #3��>T  docu�} k�\\class{elsart} \journal{N�$ar�jTA} \usepackage{amssymb2([german,eng�]{b�# } \s� langu< 6<0intlimits,sum name ]q4650dvips]{epsfigRcolor2J�4,ifthen,shadow6#fancyhd69>nD \newcommand{\beq}eq/}}6$e$!�^" beqaGnarrayJG% HV#Nket.+$|#1\rangle*����%Qu&frontm�" title{\bf�� $NN$�� UT� helicity&� 5$\vec d(.,\pi^-)�� }a�dauthor{Eed M.\ Darwish\cor�eed!5 @[eed]{{\it E-mail u :} eedd @D@yahoo.com (E.M.\ Y).v - 5{�De� a�, FacultESci4 D, South Valley Uni!\ity,\\ Sohag 82524, Egyp%_(date{\today!Y)�ab?ct3"�%� f-g!x-resc%�ing� X 1m 9o=%s)l!v d\to%t.s1��  Ale$\pi$-w�8550 MeV&� &I+n� 2_ ti��$edv-� %"�X*!Sl� *pa �e�predi�&h~a6 - *� a�,Sis���!1>#!?Bp 0� less"� <�2�f�=G5~ prev�+�* d unVS U�. F.N �� ribuaS�!�Y �. � L �E�L"�is)Je�ly��veQ �%r:4$\Delta$(1232)A�on'  )�i�1Bq�:�.!�� �|y�be-�Q*rA� ��th9|toA%�1TEM�.2a!�ap�drek�!:;� 1-)� ,vspace{0.2cm�noindent���PACS:} 24.70.+s; 13.60.Le; 25.20.Lj 30.Fj\\ 6>Keyword�� Pip�a��js; Meson�! � ; Photopr..F���=ys.����2E����{IG* ��, sec1�� A st��YB!;h'ate�/g&i, isa}ceru��a :$�)p�Ja in{i w!$gaXH�U,m�"�sms:  ,�pel,ary amplitud ~ fourBy��/"*#l) �on,_,]Fermi/Q�pr 'e'�$� Du4ndHi)I%Aa%�2�/�� �,��Y!7g%pA�[.� r.�has�pot�al�c#a�&=2�*e"�� � -featur9S x"�� �icy5����!"| �t�(��It��ed%�l�!��!of O2�dut2tinuousJ !w am mPne9*as MAMc'4 Mainz or ELSA�Bonn. �3�t$a�R�9�]�IL�<lH�fa)/�si�3!Ay2N#--�($�!� !��0 >.�-b�M� ia(/wis�!���,\2Dabs� !g any e� R�)M�ear�2g#��i� E��>+-&� &�impulse ��oxi�l(IA) \cite{ChL51,LaF52}. App 'e tU� s�0fV� (FSI)�rs��j dia�4pc�oach hL"zre�A1 �(BlL77,Lag7881}��� F/Q^ate��'z � quite�" "e��rged-InաL4�� i���%�al�,.B��OA�"�"T.� �E�l2�&��oJ �ScA96} n11� 0 kind!z�A��j�&�  !�a�ide� in-_Lev01}I:��q*�7/af,)�va T�  N$� Bn .� 21 s� >6)Dar03}x � founIVuP2cl6q (& %jig�)){$� toNO I.o �.Qu"� !O :�*& )Brol�A $N� %���A�F�f: %5:/MIFaes0a�It+]"m d4 ull * "i�� off-s>6 E])�2�{neA�nto �a�"��Z!a;�6 . UX, 4of6��5]�#4J]X ob�$�2�5if&Je?F� �|s�* `�Y.[v�wsi3)�absol](squarex+�9F,�2as� ` .�Ŧ eX-ion�m��. O�a�Ped���and/or *�6t�Av0poo�,.ME� ���:��.�(.�*��, a se�-�$�JF�F ix!2O "} I �?carriE�r !� at�e='&a, &% GDH �"�$e&�!t�-a jI�3 towar� he�!al� ific � �hGerasimov-Drell-Hearn (GDH)E1rule,�%��A&Q�c�"����)�#E�!23"!+A�ric:\ Our go�<��$e��>�.� . R2ly,f��e inco�5nt��I��im0U�e�%�� i��Log00,��+4 E13 5JG,$4}.�� ^-$-j� %�2aa*f��hY0}7 lu�.� \pi :�|  t �,,�O�6�1#)&(&���*��3am!�q�m�EM&*oq��|1Mi� � tu9��"�&� our p� �S+},�9� "1a��=n%�A�beam-�6:��Rhe aS�A� . Sir�0 double-28*#�8�h J8&�"�A4F-}%� out �#M !@FS"�:��1�B�'-�)s $d( J~R�!?���, �  x� )�A}A� Most~ay�#/oq&�3+}Y�ext�8�� ere!j5"Aren04}{)adB"a�@'�wo) !�etaAb5.]'f3 step^va�y,q'�Hpap� 2E W=�-�q ed����� 6�%�)7_ � "�2�A�N d �U_A�$)�2��A seco�7�of:<x.U%�<*� :m0 6�IPe{= }. W�%*);6*� a��!� D?(?,�8!g6� is�%#to ac�4 ��Z>�Ym*� as � F � d ��� i%Sect.\ 17sec2}Ek�0A�/W$%��*�1�Ny N�5N V&�w� v8�in�$!�\/QqU�riefly Uew� � �3�Ula8tM)�ga�m�3�C:Ixٱ>�����C.�A��IAV(�F��[!�& matrix �!.%& %~� _!�Bd actu:/aLtrh;n�`se#-discu�(a�-514 5}. ��a�,�+�.,u�U�}in>C6}.�& �Y_u�AN���!]\tE_&| *82} ��P�� fA�.�' u��!_yR� Afa"t!�+ic�:&�qs~!�l<�S�-''h:�&vIf �7lready*\)� h�(iK�,�BF:��w� thusw*notAT�E� .Te!A aG� ��1��A!��5&7�H �^�!�5���]v@Fpe{7)�L*lo*V i.e.!06Q� N�:6�!qዩz6���G.� f(�Z��B"onT,��in�d u���}��)ive L ng95B*�7j?Schmidt �et al.}�>���advanta89�� R�i�s 5� � �8��s>�p1��U}>~ �Z[2lsoPM" arbitrK9A8r*) A��,�def�/&w��inq" as requi���d E�%��} �ni�i!#��+L sist"�m00ard pseudovec> BornD0�A%�.=)N��# �2wF�H�) ��.�Q�w!hf0 oMPQAs �&5s.\ 1-3' Q�I�F�Ѻof /2!_�.��*�Jr���*�4� b� a'>ll! 1a"-� -!xg�a�7�GWA�I��5+is� satiswory��purpo�J�to�rpr=e�/r.!߱�y! ��6��۽����"� !�7Ii���pec8 �&a$�bl� {s )�HaP8485}zhistor�.lys playedE�� a majorr � :'<f�I�!�e�fi!se ,@e shift�6�* ��are EST'0 �Ern7374}3aP�Kng �"�5�% a�rn%G&����:lied �e Graz_/p x1/!�c+Nhe ParB<1\� a+80}!���"�$%��lAl�widel/� 2!�i&N$)H (�Ma[���O)�Gar90� ��9rein)"�>=Z�o"L*%�2�$6� enough�H "�6�$-B�:�*3 3�k �!���m!:^ ^�q��#-I)���A�/� �OB�. H�Bwe  ���!�&noI�eJ��� d! ex�� &C*�6� �r�� BjD64}A���na 'eqA)P d\sigma &=& \frac{\dQ$�^{4}(k+d-p_1-p_2-q)M^2_{N}d^{3} p_1 2 Hq} {96(2 \pi)^{5} |% v_{� } - 0 v_{d}|\omegaEE_1E_2 q} \no#4|\\ & & \times~ \sum_{s\,m\,t\,,mH$\,m_d} \lN6|{tBz70M}^{(t\,\mu)}<>8 ;)�,� p_2 q k  d) \OC|^{2}\,,OOeq:3.2}�#9fwa� $k=( �1 O,k)$, $d=(E_d d)$, $q0 q)p_1+�1�Ep_2 �$p_2)$ deno�he 4-ZKaae�n,U�,m���>��s,7�outgo� ��� , $t{ir iso�( muJb� m �'{v}5� �A/�uDci�8�)o�"�6���.�"a�)]wS $.�$. Co� �U: n�!l�N���Kn|9o%l�_�!Q��"V�{}e�H.�9lab�"1�!i�Qame. A e-V�*o���%sqRchosen�!� $z$-axin*��1:I�umq+ k)w� $y <b�-k�( qDF&� -XY ' e} 6nA I q$ �aI�;B�4p_1 �$�p_2a8��Q�� ne@K\S labsys}).=@�(�OtlV�sJ� �!0q$VV�glJ\thet�y pi}$T $\phi_{ C�( / 1p_{NN}M�a�$azimuthal *H(�8+:�9� �P�L!�R��I/m"�>W!����Mr� ]V~{P} =E&${p}_{1} + �2} kѺ{q �B � =�91}� �w�ED1;`2}�6����W�PM[htb] \�+BIN 1.0]A .eps�McFN\�FKi*R�a�� � -. A& i_.^� q�.cla�VM��� ��te�R0/�,]2��� $\O��)?}$�e!iLsemi-�`Y2�2�AbkF 6�U �AlM$;���O�.�$&�its"y, ? q-�9 }{d�a?L}=\int_0^{q_{max}}dq!�t ' �\, I4\rho_{s}}{6}\,:��a� {d}}�AdA�rt � ��@Y�NN]k) I� [� �3����X)��\��Eq.\ (7)��L D�$E�![e�� �\e"� � !߁h�=]�F�is�  byqL"~ M�W } 53  m 9nD )*k)%{q p_1 @2}) & = & ^{(-)}�4{�Aq}j � 4p_. � 8-\mu}\epsilon_{ (�)J^(0)�4 YdE d\,00y 251�:6�c*I"�Tձ� (.URV�&�(�7�byA�b�45x ��)F� ke �=F. + ~G_{0}^a� NN !� \,T^A� �c� Rq�L6��*1� K,9R:�� p3�Qpag6)�  $ � +&�=��$2�us,�E�gFi]Qd�a2a �(8gm��4ej� ya� &ea.�_{s>&� $mu)~IA} + �/NN}\,.��nd]�A graph@:��F ho�T � �Tt-Y~����Xh�U*{1cm}Z.8]{Feyn"DR,a�6A���>W�5"� 6.�#24X V�#: (a) �!NA-� (b)Iv.M8Q!--.6er�2 �H1z� �g� RU� �IA�y fo]�&sJ� �g16 �� �L>�pp&�2)�� \sqrt' �m���c}|�  sf5m,\,t �?(|\,\Big( \l LMve{ |t��6�\,)|-,� A,tilde{\Psi}_��d} G� ) 5�\\ � M�E�( -(-)^{s+t 8� �$a�T� N(Big)\,|1 �,��\ � f�2�6^��S&&boy&� A�$\�6 : \,)$a�_�q�e =!��G =A$2:�3N }MNEL=0,2} Pm_{L}}i^{L}\,C^{L 1 1!� �'d}n  u(p)Y_{L0}(\hat{p}) \,d6��DG�#+��"�R $V:fC1�used. ]Ń.  .U,�'�e�i�9k>cnn-fsi-��Vf��JC��V����Xm.��t d^3I�^{\,\i�c )�)�E_1 E_2} ' 'g=,Y(�[R�!ř ��/ (W`e X  B�)& J&H �M_N}{�> 2� U~\,2�]i� Z_IA��a7��.� 1g.4�.2)f�)v% 3= �1aH\,u��1#-"�2:3 �S2���&ac!u�^�&�8�, $)��3�winvar�mas%� e"� vec 2  {1/2}=\pm�;�% +�p�� ��/2�E ?'$r�a��csd"�_on�0�%() �u��.�� �[Il2�M_N(Eѱ d}-"+ pi}-2M_N-)�k}�0{q})^2/4M_N)$g �Ii d}=M_d+\6e c" al-q" /2��� e�mY�2�%�i�#ed �-�1 nonc�ly"�+iat�4IcVexpan=�(iA3p&Mal��.)s &( T}_{Js\ellq�>�t�sݹJNho/h��=r 2��Ib��Y��J�� uF{>�\,mm'1�J��e,�� }/�b��9�O  .k\, M2h avpur�R.FH2fun�"=�R� J�!�E��qv ff.���6� b�I �bM  ell}el]} C^{ s J��M� UC6'}*g M} Y^{\�&Me�6�) Y_qJ*:36 "m qp`'&!half-&�$�>�.���gM edd-"� &0We!��a�+_�����og Hu"N, �#B F.&:Y55"s. Exp�B,Ac�.�.m s�I�q"ɷ�J\le 3$�"�2�2�r;r&� R�+nj/�+io.� 5}�h� ,!\of our�9ulvW s dia7d�\o�y� v*irs�Nwe �- E�Q"�!P%�F"�1��i��Fd-�,ce $(�/"��})^P-fA$ p��"{F6t0"�50 sQ �5a"�5�#�-*&�4�14�2K �?h� V:�18conMC2xg�&6�6?_Yk^�3v�0I�091art2%� then�+*�1��>]�> circ�'�,�%��%bTt�8��;)x$\�!^P�2�1A$G"� U C,.vAZv � 22F?�XV �q\R,�+&>Fg ��>�7U��&h a �7/2��k �!�"0<e�� e"����eV b+���Q���EB�A(r�� 2#rhey[q����sec51��/2 WKhgm��̡!K�&�.��X��6ye>U)%J Kr�F+n/A$9q�v"��Ew�%)2�� "�G4�}�q of emi#&����l�;�e-2�;A�lEi\n/�W. OF�``+B� -2}c!�&cvdall�a+�Xcurves -:*�B��7)��let .�03; backf< �2'OZo�9 �stems�xf" Ein ch�B�B+@lS_1$-2��she�i�)��forbidde�+2�N�&�p]ce�E},ue>n0� fig1:�a�Ae�=��n�z�forv�m���rm�VeV�x"* ofl2vAqA3to��.�= ��\R1i8Z=�H lay=N�):qI� : IA[o +BS�o7*/%a�^-$�q:� �E�'3ve.�n8 ^-p$*xADtU��M�n� ^orX^�s)q_5+s.2�\�T��of�� �����c�oe�2!�:1ׅ"�g3( plot�Oa�^ft6bCto+one)�HIA�q�*`+(�D A")^{IA+X%{; *{-0.6cm}N*}} &~=~&�ON[( T}:�")^P - ~$A�!]� B�\z"�mBm} }�g$%�M�9=��seq"av0m�0.�i�eRAPappearsa�for�6��!�;is .@��mJ G"�*$E�ie=Nct*Q4.V|RUϥ�Eq  s (��� thM�1�3 ��DS#)m5"� .�GNNR$B %��(-�v% & ��E\. �^M��9j��ab�&$15$\%$ at "�)p=0^{\}$ͨI� is)�_delc rapidlyx 95 M y. B�NF/x4 ���mcev�v�I(2, �62 )oseO�#b� �3(�v�R]��3O a �T am�t�%�!%b�Rnee���o <!*byK����Iose!���*B n��7-�a�o a tiny���mB :}�!�}s>�Q l�/l� "�=�� �&�Kal6  � �ob�W1` 6�7b"L��&pMAupe&!ntal �h�!mN�apBtr���1B*C �.)�jm�.x-�hAAmd 4� f�w -k-jy " f>U�j5��2I�{�V�;!�6O.�2r� � �4�Q�QA�2� �euIA alone�.E\թ)> �-�0e:AsE�!�_% }�+��$ top panel5Ai�RA"��>K�"P$ˡdu�� BGNi&� 8pnze�"R��H!AV� xE�t��O�A}!�bottomB�� &_�P-D Zhe�1ZHB+.�6%�6qa�p%��ZE�8Be+73} (ABHHM), (ChD75} (Fra ��a� 3As+,9(Asai)m=w���:[��same � .�e  4je ���R� .zQ % {�'�3JR )}Eo>�� � N� 8��U7� up�H�:E{)EB2�0A$ 2/e)C �i$e�!T ��6Ua�z� ?"� y�Tlvr�%���� �P$- �7.�A1Z�� 2; � �F���� I���>� Q�v��c!,J> .j.o E7�� %2�0 �Q"wFY*�3M~ �&:#on��e�haM���.��� !�  *�!� IA. .�0�P6U��Y���-&�@dF �^�7#%��"% qual�m؇s� beha2 �- ltho�xv>K��Z�Ej4er�/�l�m��+ s>M:0�@eG R��;!E$ deviB*qv�A��*�)��@}�276@6fAs7�[{-^2K]FSI a�=����=-,.F�Omai$\in�Az�����4J�i�_K/1�}:z$)�41�A&t 7>7��8( (&;)CZN�X �!�5�a�}G b:@ � !�v &��C].���!�6 6cjs B$N� M�16� (1�9f$) �"�ut�tdu� d'(0+}$ multipFY�Mio�min'�d ~�J2lso�A):� lead} a TAGX-Nc#� -š �4 a!�\$� X��5e%F�f'!��<pA�2���� &��e*�c�F��.�Mi:��J "�GS~!*zR*?6�>�K��&*y� eM��/�*� s�!p�&$6�C,"� ":W�.��e�� A!*�6� pp$yfis *)Xq^s*�#��X~ valu�w*_>�4�/kK�endqOZ���V�&�ZFo_!e.� *M5 "Z:��pa�TL>�Pis4�NAK� .p* ����KDwo�d n�*&��=2U %6y�_�p� s6E6�*0E��u�!�"(U�E���J� revea'ŽB&�b��*uZ�6H� �Jd� :.#��O��15 ���5sL$t�,>  dir[�F��1i�omF�#g]^MÅ���5� .�O*#di&�Y��9d�6gidR�+�fA��t�a�%)%) ��B��Gt./R: �h�Ł>�f:)� �,!O@-^!�a�C�( M�� (:� ).�F�.�A�J2�"^.a *� u ce.��0 �{P6n��c�� er. WeR�M�m( m� i&� P$. x3&f �2f 1:%��qa� �n�� !� ^e� �f a�!)zB %�&�Jz�_zi?��"�i�b��by�M�LI�,"W a�*7 Z2`sm!-�9�n  d�MA�"� 6+ I2 !��a task�� nU.8 ��aM|t "" \ �+V.� �ZN�9�'2a<%�t�k!8F� A 8ɫ-��`�*�esi9R�� *kUAI%27 )�*�S�nst� of a�&S�f��"�RWE�+"\Ζ, uc�c �A��e �� opicO#�q� "�R��.SY%�A�.� &�2I�#�T"��"h& 6�X5�dg�Kku�h�Gs��  �D.9�s� fu7 re�K�W 5#��E �U[ aop�U�Ved.�*F E � ich $0 Y.toIB�\�V^A"�toB ���AN� :�AV!�"Jis �v$� ack} I amaCt*��c��l��D�&.�,Prof.\ H.\ �ch\"ov�x!�GX�mP�m�group. I�lik61,nk>6E� 2u"f ly Dr.\ P�b,'�p�ASu �thrP&�2!rD%�F~"r|tRc�"b��pP@ G.F.\A�8w, H.W.\ Lewis,P.\ Rev.\ 84 (1951) 772 �q L P|LaxK$\ Feshbach>L8L2) 502L�pL(I.\ Blomqvi�4J.M�ag��q�!�hy�A 280^77) 405xbZ�/q^2OBF96F8) 382�Laoq2F �Rep.\ 69B 81) 2U��[@R.\�])4]�,EeWilhelm,�C Z.�355h96) 421�%�e�pkM.!QLevchuk,%� Schu�t er, A Wissmann,� $-th/0011042�n&W�}D~J�!�Schwamb�EueE)�DJ.\ A 16 (2003) 112q�or@I.T.\ Obukhovsky ._dW b G 29^ 22072Nk^ A.YuAhoginov`�A!� idorV.N tibu� jAtom.\QQ63v0) 392�%E+v�F9F7r3) 513.�r4bq>735H4)�BHE13K:�In�f!|ModY�E�*!�4)`r�#s�MU��5JG^XR-dG:�arn G 31c5)5��rFk!�4}%J�VAbsip!�A�de4407042|a�.~����Af\ Fixu�i/ر�Let�93�-P202301; �`in�Vce6J�3r� 6��Sympos���V�oSum Rul�H � �OE�k s�oA[H4), Norfolk, Virgin��5,u` 2004��4090152��UA�? yniv�Vcommun� ion;93C%�RS(li, Diplomass�&��� Pav�Ita�g.�2.,"#="A� Haidenbau�w�qP�ua>sC�((1984) 1822���ibid}&2&5) 1424."`_D.�Ern�QC�Q Shak�RThal�32�C �73) 46;6���7�7822C_��LacombOBit�d��:t21�0) 862F$_ZA� Garcilazo� \ Mizutan� I� & "ȌWorld ��tS, �oapF�1992�BY=J.D� jork��SD�r�Re���ic Qu#�M#�s)dMcGraw-Hill, New York, 1962�!\*� b\�-[�M B 10)]�36� �'9�enz)�|f,����B 6�7��529 �OG.u iefariϊ\ Drago� Napo #no, C�ociacca� �Nuovo Ci�r13A%7a22�)y!# Asai6� �R� C 4e]9A{365>a T *�f�:o�H[aps,showpacs,float ,fix]{revtex46��8,x,axodraw_3}��Xunitlength 0.5cm \thick��sk �8\def\slash#1{#1�M0kip -0.5em / %!#beqN͉e�" L} W beqy5�B e 6�Lspagestyle{empty} \p�PDint{JLAB-THY-04-38!Z��,EO*�w�&�i K\�! {K}N$} %�1.cm}\\ ��H W. Roberts} \affil�${&����h��, Old Dh��.�,A 23529, USAUF��\\ Co)� E��n B�tAccele�jFacil։$\\ 12000 J�r6Avenue�  ~�s, o 606, USA.A \.��bT=&=� h=�>3ysom�'�&o�kb�Aly� elo�jIheYzKNx8\v !. K .��p�2W/Vpeg�q�lwm |. Emp���/pla�I�]5n��b�ces�|���f)�ie�fn����e sen##!�-/2d�#��e ��hz,�6�3ll� .toozd*��+"� dϤ�-��z�!-.�0 �de%J 6� :�[exa"$mv�Ħcoupl!L?ta/��s^m))#pr�!l1H<$\Lambda(1405)$,eH .%�)��D$\Theta^+$. \flush 2KXXX�聎a"�%�`��} %\new  \��{13.60.-� Rj, Le ,88.+e} \makeG \setc*4er{J}ѕ\{._�eMot� RFN]<$�" �Kcle2!.��0�" p&"#��$]�"m$m"`a�r�\pm�M;isA#��{aE �A�C}bm�=&ex�GaFyfic:� �MD.�2��oWL��� fourya�-E�2� �^s4GwK �AB�^�,Q�6�S~�+s� il`6! arTo��y�c&b�g1A�s�4n�%:�=^.���#����a��sC-ہ� ���� �|��,:��%. �&��+Lv��&d2%u 2~l�o�!us &ڣngx�th�in�5p#to �� downr!m�N4�z�YaT�d*�FMb�;.М siHI4]'%�five-fol*�;'. v�wayEA-i�hem}& ���2N%�� �����=?@is cP(!t*d�{-�� "E�� �iE9&��:�m�hun$�rɉa�,���.�Q��� �*m.�Aaft��16=Bate?b�d'�xd]� Y��&3 Lab,`��Graq���pl��availaby ��a2ly�fcNiI beamV>I7��)9�{sc&=te�>�y��.����/� s,�Kat�v mber�:�c&� � rinciple,!65.��|A�T��de��f�,��I^\odot�he�*��p�!e�rT4��"� p\to L(+� Yd� s�=�/u���6�gooL� �O3,strauch}. Tr!22f>S"�)self- d'=decay�ThypĺA�)�M !�߅Z�  K Y$��wev���.� LT�� a�P��' �E5��I�� 2�,�n\1i�!�:���1u� *k�recoil .js. �'� Q��organ|La0lV�+e n���9�u�%�"ϸ8U,�%A�w*��o�!Ŕ_o"eN��E�w&�RA^.m�5 � II�"�5II02�)9j*F�>sQ ��� _aL~ -�;-_1 : ;��(c���Ragjo%ty.\�z  IV1�s�*�)S$an outlookB-{Ki�M�*� ��M; ��' f0}&�-M�Q�>�Ј�um��~� �'�Lq p_1+k=p_2+q_1+q_2,2�fk$A�!c"Rm��&, Eo .|�� �x �eBGQoB%i%� %q�kiQ� � R kaon� $q�kZ'$.k �X^� �8&to�U�$Km,�� "��7phok} k=�E(\'Y,0,0,KF)\� v 2 ��K�j!|�V�y}� ^onucp}!�q�`s�Yz-{BYw/B[0 s=(k+p_1)^2��0Ag�1��$en�of-x[ (cm)*2,Bd K=)N\s-m^2}{2�}B�a$mM6�&�[MX.y�3e 1$-,a�t� !��b"B�-ġEpnppn1![21[f�s(s+m_N^2-s_{2}6�-Q\sin{n$},0,-Q\cosM B�%�*�Hue�} Bn �m� OF�m-�9�Q-t\l ^�\I�s,Bj,m^`.�.>He�we�u��A)i�� -�,� �p[e� 6* pairA\a�� o.�colli��n]E�M>�;� wr�+n! q>�2}�^q}_1=Q_1)=� _1}\%�phi�j9�(p1.�eq-� $Q_1�t%�AGE=��x "�\$s�tB�M�n�$a�ds� !|!`m�!W-c !(�Q#cm��?)�{z �ji����!� a�jpr85�9i�WC)�a{:s fr�rIis +�cho�Fa $z^�a$ a�r���Bgd&�Ux�v. ��I��Air�D ��r:�ar�5(qy q_1^*&=&Q0`fB�}/2,Q^*I%J*MNPhi^*}, FER EU=�),"�w\\ q_2��-O_O] m J . 1? �-yI�efבfV-4m_K^2�7��eq��!� aI�isk�"ȑ,� ATatA{�{ A�YHMi6G{ &��*r }2� �)��� <e $I$*�2P 2s 2 Na�Z y �ofI&=&I_0E.\\N(1+�2{�}_i\cdotP} �D}.m+ 8 _i^\alpha ,^4ta &}{\�yOv] %b-� ..S&&+�.�z_�(� �L:�� "J�{ O�e�� \_{��ell�[E�2%�I^s �V�N�s��s��elZ�:=.e�:�cr�N�c�� O}^c��] �\m��9�1 {P}$&Xma�:d&'0�,iNi �1.u c9��?rho_f��1�f!Ou�=+Pq� ��a��de�� trix��ي& � $r�"� &���LkR I `2]����6 em��E)=J�)h� d� �\�{�v/�ax�x�j ,\,y ���_:����>��&5of:� ��"= %;j=y$��Y��58�We� k6 � z.le�" QellJPa6NB�2|be�r7X�$�x"�]$xp{gEE�se 636EYs ($I_0��or�a3��*�2&�-=2�2), 48 �`m!�E2�{ )�1�.�#c}n%n6�&�E��)�Mdh � vTlittlT��'o12���i}We �>,�& 21�/be Ѷ;8��G "MB�9��&�n���[J  . .��� &Ae&%:t�7��g8B �6�@"�*�&f��!�&��zplus�R� �i�U� }9� �/o���qi\&x:�:�_ɏ+ b� =.sing��޳Yjh�>�by ȟs:3�N figs.ߏfig2}���TfigǔBG��3Iqge�9��`3"D8I�:3�d!�.-G2-���a lMB&؊(�$% fig�2})2��V ��E oe�e��h��&I�>�2{s|3��4}Lz�e��F (1020pOPg ��!Me�Bed&��i�cN2�*�5 e do9E2|-Hm�"��%gA.&�5�"� -� %� +$J=D%%�8�  $NK$�AO�R�A�5����3�1/2 �� 540 MeVi7widtha� be 1*�8�*a IeiL�a�4For"�F� !�$c� ��.�r)�weeRl �� ($w=2.5$ GeV9 ��g}�6*��Y.e�V��vch� ��G.n�!W�y�f>�� be�p��. S��' �E��Pi*Z� &�E!١usu�\j �e�d��2+�!�h!���"���jS�lxQ�ͱ�7�Hng.�A��dim� osurfac���.)�s%*A>.���eI{:Awodح�^he�nsM~� $&; � a�v{u- �$K�6�ie�&�G/�ll��NM�[o��&�`K� '� � $ (r��ng �;0!�$�$)y"����re �� F �c�93] �?s DkNz ���b)��O]B[litween 1�  -1�G!x���41� �(#M� .��"7��d*�AM�"�q �(� +1�Yh( blu�9r'Pon; ;neBK ;.h��B zeroE^���Jn each�%�%� "��?s "`O�"ward oB��,)�a�ner%� =��A-� - �.�!Q��:"� UAs (al�")NAtN|Ts)�, �is �%%r-!](closesh �i�er�S"�)UV8�<-�om��;��A�.��,JZ}1 a�ra=^���{Pi����e �ta�.� $P_x�$ (fV�e�� ly�"��c���oU "�kYr ),��� :'!��!e��s,6) Lis7WI>J�`AM��2x�O�horizo�[%�)e�(bI��5mN�\NK3 A(c)�u2� ����(d* $��I�V^urq�i�Q <'-R 0�acxEA sameIn ��!�" nK^+2�(^0$), k�AahRa� hIǡ�m:&i��!�. N�F"c ��:� ��� � j%� 1.52P Y(c)9�� Y: g*� iCBen[g ofR4Rb�7In!��41�m�T #�'to  a*V �t2�.�I�a6��@9�s ��:{yis �A�7��Nv��E�inxAuH"m+ $2�W  (a��dʮrI�2>�us|�_E�� l� r)Gm�_>� X 1]='��ab0���ΗsJ� V�ay�ca"'�s�y�� a�?F�di|AbJ���Nac�Bzn�cay�!�ad �<eQQ�:/ (:� )� ���BF�K��^E)6���ofeN '&A�� B�.:zm$ C(/Con(/� "+$u�phi!$f! t!��)� a j)htak-`3 ��u��� 98b_-hO�"g3N� G_v^� �-^\mu _\mu +i� G_t%}{2�{}2-�- ^\nu� (\]\ial_\nu�/hK\� )N"�� ��/ c1N $���}y s&�Bn#.��� phia*� phib!}cR�� & �rth�T�����,s $I^s$ (fig2|�( 2w2#b�g�I)s�}� ,��c2 }cho�� 5=4,\,\, 1 =0$�&:=$1P=- 2 63c)f30:d4�&d�5g-4)%�g"�e*K^0Y�K�f.a1���5!aI��%�]$�.w���plz�y��J?02 MeV  r Es��o�wJ8!). ��Jg� 92?*a� �/cU� hangb5\3)Nq e�2����P/help "~/Jj such�m90d �%>�Sub-t"��R���&��31g��J� !�rL;.]a�-"8�v�+ . It�s jus���=��� , so���(�K$)�[�$z h&��!V2  �yuK�`2&f/.91�4. t�>byEc�9al�2�c�-5s,��*�"X#�NF�Pre��"2&] s��A8�s6�l�%a $I^c2� bP_y��Q� c�L p2�*ly�}G� 4d3m�Bd F�y y�s{'��� � �t�h>�!A&�� ��%��0 it, *��O!��sx�f�pmB i�*  >:�Em�_ fai�0far away�r�[2�r��e)Rc}. A2�k + HK$]� midd*��,�.n�� �2 } P1.6 (�R20j2��zlI 1:�%�� lo��`u�2�Y����;:Ea��fZa_��um M� .Q�a��st%�a��e���Uk`�J -on'c� N�p�"a�O�ri�t1Kor�&] BS%":,E���vi;) �V���>8.�s�3C`�1'��t�R�Q��t a&k�.�/��q\��z.ORq �2ݾ.,) in �Qs!�re�� ��e%�T'R�>4`l��k SAP}fd�'�%!�quOoy9��F<�(":!exoB_ ces,S���*w�p�}. If]���n�HA`>j�^,����)�confirm�&y;(*�޽a� ssum�V�oM�obej�rqO�� disa��� &�+"_ B& !�s%�s �#s }i��&z�'��s)�+�M�%� Wgr%V�s�aI:E���us�sought��.�.�!} �not neM4ar�6��,�$�>%�w&M9��;7RUda0A(E� )*e�F&�,a&�c}�!�,'$� $P_z ��#i� )IrF��a��<]��($J^P=1/2^+$#j�i5in� A�nd ]��"� �� !�!f�9� �0%a}(�"�!&��9o#!S#��H$< is lJ�t9v0.1M36IM)��9X`� -0.5�* +0.5�F��/  im��vicinir�6d'��ss;K�$��)����%"��"�b�Xme��t JLab!}62 8\cǬs�7 Tb�y blsŏa� [!�!��  7 N2u@ tG( qu)Ey. B�b*� %�c��it"��-MQz2�A}..0-a�e�� r��s�znd�� �~�0�uonU�9�6�a mEowPte!��calcu!/7�2��l`'JV=�)�VKI�z'�B1&� &U5�O�5�� !�n�+ �������4JA�}�JP" Q��nel�sl��M� 0 $n:( ; The &�re���!�T�%�bup� �x�]$ figs�E]Jni���%&�.�%h"is markNR :q:�c}�C��*3^ 'l7 &`�)�ybb^�rgEe�"�%!$M)eu�( ��s��ung -1!�� � o� mnKB�d:�f��n�!�=���.�(a)�� [e thՍ2+-$De�%�F� �{:�N�d)� mI, y-D��Ix �`"n �&��o��4parity 6�vo"�<isoi�e �`� al'a�ma�O��41#2� &a ���e7e>��x�  `ˡA�'� "\( Q{ �=�[ iC��� ��n� ��F�at��e� aT| %)0�%em�HZ��� `vi�#'�a�h!q��q�"[_�H� hiTGatNdC (s*�&� �%o" Y�),Y+����i�%m��am�ofi� sort���{���)�r<reBF�$�l��$trustworthO pre�� �ADs�&cR �yD-U�"&�M%D " t`��^� A}"7 �tB{we �i�,d* h& �- �W4pointed out he�Ore that all 63 observables show some kind of effect due to the pentaquark, and s/of the .�s are quite striking. \section{ConclusionBxOutlook} The preceding picture �lhould have conveyed a number� poin{ bout� polarizas2�Hdeveloped in \cite{.,}. �first V is %3these2L0may be displa�in2� ways Psecond,�P perhaps most obvious k$to note is)�however{y%Xk,se .�dexhibit an enormously rich!�u%P, refl!�ngCP degree of complexity�!�underly+dynamic�(is sensitiv-tE var� contribu!zs lea%� %4final state beYHstudied, especially-`small'6N$, provides�in!enA� tool)4 will needGbe fuSexploit%�0 our attempts&�standa$cesses lika,e ones!yTcussed herein. Such pr/A�expecdtozamo-e8primary sourcesA�informI�(required in%xon-go!Z�!�1�Lz Z\ Atom.\%+.\ _ 66}, 1715 ]( [Yad.\ Fiz>$63 $]�% � hep%�H304040. S. Stepanya>�N�Rev.\ ���252001 zZy7018. J%th:SAPHIR^%j\ B)572!27~p83.!�$Kubarovsky:u��w03�84) [Erratum-ibi!� � )499M41�5��11046. A. E. Asratyan, A. G. Dolgolenko��M.�ntsev5�R*7}, 68I�4) N)#704%> �(A. AirapetiBHERMEFM�:�85}, 21I�4E \ leev:}SVDB� 1!401024AI�bdel-BD 6�COSY-TOFnH 3011��endB� ��figure}center� l}(100,50) \Line(0,0)(15,15)1  (60. (75,0)(Photon(0,35? 251 \DashX0 30)2.3m(50put/0){"�+ �} !035,-15){(a)} %�D % \hskip .5in % ��!�75��32� (4>�4 ��2�-615.� Q45: rdO1 �25,v 20- b� J �� �Q �:�U:R 35�UJ��cN�aQ� \cap3 @{`Born' diagrams:^ 8ous, unlabeled { � -eons. U dash%  kaq �� wavy>pes.\Ya�2}M�q�,% \vspace*{0A�} � $ � U�a�1��%�5z]�5)11 y�7)�50F�m�5:�A�5E�5:�506 4a�12�I{$\phia�!��!��q�z.�5B� �251��� E���e�z���EJ�^���)���~ ���y~6 �I5 (40�B 7,47���5��9�21�N�e��1.2��� qQE�^� �-��� 3��.�:�.F!O35a' ��>�205 30,6��M�! -5M$g��U;dN�i�%�- )�U?~ -JQ�Y4�C!Ue�%m{$K^*1 25,4AH�2 V-^5��A!�-Q!V0�.A#1�!J>925d�d5i�.25�J7Y;U f9!EL=!1�\aj�AF veV.2 � D�� ainC$vector mes��;do��repre� �6/��3��Ѽ%���~� "� 4inR�8�� {37.5}.�` 5){2.5}M &� �5�-�1>�0�5�>� %E� 60,5!�matrix{\I�^*,� ,^*\cr\Theta}Q�� z� 1)�J� ��: ���� �� 0,��/>�I��R� � �.� F��� &� -� R���5�>�5��M� � F�Y�.�(I�.  .�2�x�ݪ��0m��Q�R�!ٍ *� N�ex�d�s(a)#(d)},e thick soli� �eithe�qi�7^*�eo�hi�OnN �B ��  couple��charge I4intermediate r�[ance:�t}model,�neg� OingQ@higher e0romagnetic mo_ i\�� 4}} ~' ��&�, $P_x^\odot$Mwn�erm & kine�cb�s.!�$: as a fun*! $m_{2�}$A ,$\Phi^*$; (b>8�8NKF-c): 2f..MF9dRf\cos{\t��� �.\\� eachc!� plot�int�Ts slightly downward onLsurface, from a corn hat =alolaxartwo'epend�;-pA1� axis (al��Blef� �siK���is �lA�:lu�5 (closesta�MI8ere��.8� (fur taF; . Fo`2��,JZ}1 ��r>�-�/-s, red!}respondeo���(2+1), �/blu�.; ;negati;. V CB zero\�nq�U �; ��0 \�/� �\io � aphics[heAg=3.0in,V=0]�D_005_spp_17.ps} (b�=1 >}�kipJ�c�W2 W (d�>th <:R�AI�}&� >�I^s$,��� itR��� conJts $G_v^� �G_t ��!=4,\,\, !=0��$D=- $ 6%��%0:H4H��B#G-4$ū�� case�*Q�a�#n6�a��dn�U�hia!}��M�14E�32Υ1I� =��U�162���17=>����{��������N� ��b!���6��QM� =��>� V�OM� =>�� �PA��R0sub-threshold&� "|" (1405)$. � resultA�  & �# calcul�A.D B whe"is�%isY (luded. Both���� � EpnR �lG#�4b� 2_33� j7f�NW12��W� 1릧I^c�����������mN�� 2_48��R�W��P_y��������:�cu��� n�50��R�W2�^�S�'a[' fig. \ref��4c}, but with a*p6cp�&-&276� 2_50_1�*%*[�"[�.>o 4{\cal O}_{yz^\:+e}�:�:�:�:::d�M>44�EWQW� Dbeam asymmetry, $IT�� exo�"� $�^+f& �^+�! �! >�q�Q� F 1_16��6�1 W���� $P)�_x����������F��~�� 1�>� b>�1�z����������F� 1_19v�^�N8 5�T���par74�B� ������|1��havs$J^P=1/2��w �(b) "?@4has:-$r� 2�Mv���F��e�JX��0������������e�"%��� � ��F�1�R�^� ����������f��N���EN��y�W2�� docu} �e%� %% ws-�7Ps9x6.tex : 2 Janu�/ 2004(Text f` �5P_9O4\Trim Size [9in x 6in] wrL5jLatex2E.Ghmntent,.�:t9�lay-<Ň�yle z~;e Hpropert�6\World Scientific Publish��0Co. Pte. Ltd.:Copyrj 1995,� 2 by�Fv All <dB& rved�R: 5$%H4Area: 7.35in ( run�&$heads) x 4P-4 Main 9(is 10/13pt  �� %\Qm0class[draft]{]$ } 6%{revtex4�18newcommand{\be}�7equ�a�.#e#A�^!<}{\l } \re.<>}{\r.$reff}[1]{( {#1}p("h \K }{ \raisebox{-0.8ex} {\�6sA�v6 K} }&D1�(title{Boson�>?/ IBM \foot->{\upper�{T}A� work!�su=9 ed $ EEC} 9 �= act #PHPRN-CT-2000-00131}.}�Xauthor{Fabrizio Palumboddu9${INFN -- LR8Pori Nazionali di Fras�;h, \\ P.~O.~Box 13, I-00044$DITALIA\\ E-mail: f {.p {,@lnf.infn.itA5"� ab�8ct} W�>ra a b!K Hamilton�4W! an7H9. whos� �Hial!UexpandI paira�multipo�$�8de�#in�; fermion- } mapp5of �\hators. We use a new method# 51� base#%� evalI�*�pQ9�1 "��>tri�>A" Tc �? osit�"w%$est. By re�Z�:Y  so ob+A`inal�f�%ge�A, euclidean a�$�� �E#wh�@ we can d)��=�.�? a��ced*B�"ec�4l @e1x L ies.��Y \makeegA;sAon{Intr(=!Ka��Oauof Arimai�$achello~\cFB},A#m�AsuE?ful&dea�b!P�$low energy.'arei�"dAe1Ѡ�& #�<oodevirtualE�|'s98 alog^BG%CoAr+su�9onduc�A �8Namb}. But no g�b�%jtoFBormBI�va�SorAB a��eff![v �icxBs �freedom� 0been found. Q-�C A!M� dirRon6per�v=as farHwe know, by Beliaev%� Zelevinsk� �a�F Ase�%�De Bogoliubov transr�vM�violaaR%on �D#kEAS. More�@%i��D is achieve�ly+iXD�urbB schemeYE=$�i>re �!}IBM!��Ac�5.Hp4due to Otsuka,f�! E��� s goB�Ai� w��)i��( a si�@j-sa@!Eir ? was�Fw�FM{�?M��i=E+)ll�*mD-��@bleINnot yetIV1X!6T�A�6 seveA�recipes�.� yKlei},e�ly6���}��a�ze� �6!oՂ�isB�)trunc)�MoMF 2͑iN!�in1$�easy to6Eol�In "JBavoid%�lim�njpre�FABBDtry2�approach reaVd�F assume w+./ A�� s, oa,thaž ir domina@at��%��� r��ir&� BvG�e�lyEsen�8 2� ��prI of fk%� gt4bea���byG of C�,��s IE9����s�e�set�VQDon�� hope�F�Ba bette�B!� To i�G�   D5@we���A|?,alr!'ax& o=�%��ayi~�sy mW�kth!�1)�kexter�field��*�Cm. !?: ��,!GY"Jf�B@.> E)��nA� G� c~ patha�eg� !_alism�YdAK p�C quant�D�be1{�/yqndard� ����step, nerG  also��. * kto fini�minimumA���ra�{tanX!n. D-A�oe��C,E�spher�D or d! med��iMe l�r5) ro�Aw�0�s�8 as GoldstA�s�8oc�/�G�T,0taneous break�f.[� y�;e��of.;$ DsurviveEhf��nLis fibFon 1 e systems�Bar We w!Oto empha� �.�.���aJ � n�K@��A�)f siM i"=ofQ�ic�EK0�f.?0,��!0o "sig�E� ". �@����w| 'e eiaN� 6�͍l%�,�HE� +]�*.ine�vGa�� �KT GK�M choiceu �HR� �mu�M� an � ON>Kinver�M�Neo � c�G�@�?G%a many-�|E��rV iv�Jc���o[ �^�"� � l to �0categ/, �0!�i�i>� R>� !�BCSeEl!�B� ,�O!�of"��Cic�) Hubb��P3*63 $T_c$FVmCini}% of colorF+� QCD��1G��(2. Similar E�I��(:10�Has@4no� spinH@�Jnd chi��m.4%�M!�y�����W��M����replac!�MMc�́��H � by�N��(hole).�(d�NheAgA A�a��Mto��!:�9MB� se�thout �4concep� \4/ ty� Attbovas� �$t��c arg-K�brief�or"�2�-��}^Nj�M ĉ�� � �Iq a;y  is6= M�-�J tonovich 6Z %ȍ} r�3rs�sd�Ic�-}ic�n !�i�!� �c auxili�m�A�!5A bec� �� , �typ�� \staQ�� a I�th�#-MMira}A$ h an9K�QHscale emerges naturQ|o� .fmlowerVA0$ w��� � ���AtU�-��on�2q45�+d ES� cySfiq g  paper!organ� Avafollow!?wa� Sec. 2a$d�L � ntD V!Vy� ^ �  �w6H3 H�o6��:O"O :�A8��Q(U��sel��Ps� ic�� 1 ar * giP�7s� *&H2  mOɸUces%� easi�U�% �]!�i�R��Q� I�� �=& iK_ !6�E&1,�9i4CJ%6� IMF��in)�5Q"� � c";6A0*t� 767re��u? ckVsJ.�CnX } CYeo"� �ť�I�I�� !1�� cre �-s ${\�0c}^{\dagger}$v b_J= { 1�9 2 8>; BG_J D.\ :C4\sum_{m_1,m_2}F0}\�8(6]\�)!= Jo2}ee a�!I?z $m$'��Nl6���insic�� ntum-xI$3�� coordina�� $J$`6+TH��y�. r�x�G "�b"K 1�s*��*�/U�+�@a�$B_J$0 dim\W0on $ 2 \Omega�(/ � of�e�4 orm�]u.d��y.|a�1 plai�� sequP=Swe� ��� they�Wsatisf �smF \m�tr} (6�(\, B_K ) =�D, \delta_{J,K}. C�X[&e [ 9U them�Fbe � ingular�EKF50�wic�/ ;x!+ nilpotenc�!Y�:ch:��mt !1g ?nu ch)$ ma�{basm4^{\nu} \neq 0 P8� �V%La*�t��6�<2�� mbl ��a�|9indB�beK;> Ub*#is�suffi�OweU �V%�q��\det (M�.(B)^n \sim 19�\-�A�ven0���F:��=!�tra1T�  er e1x�to�c6�� Negea f�l !������%m $n= �b/<n} + !� a�rbitr1 re� ce��A� ?$ s��>I��!N {\math�. P}_{.=} ��5j-  n})^2 �-�^2} \E?\db^* db \< b| b \>^{-1}|  \e�@n�y)ղ:Ba3y!� J= |\expu�JJ b�w6�q \>�a�w�]Y[i ?[heA?7%���sub�M�.uR u�<ee�on�qM��/f�]i^Yh �� a ��r�)Bure"( ��N��%:� B!��Ω�} 1\!\!}=Bzeroi>.��IOmel @$\$6�IwR�br� k� i�S� � 1{Fo(DqO�Y�IA�IycAy c \= -1� ��2��= nN� ��F<+1�? |b��M�:�at��be�L^%>UnsB borh���r�JŐ]/ n erro�b�$ \nu /(IZ>�)$, name5ahen]�|bm��^�`n�"ly uni6  6! }y :��� Bth+lyS&�;#�in>$ ���rec�) exacB�ex �s valid  ���o >�aHm�m�A/I.~�qy� arrowi{(e� \)SB\, �6/infty�ᡲ���%! L.$6 soN� = �[; t (�8� beta���WY � �) ]^{Q�2},E��� $>g��(b_J)R B_J $� n u| �"Y ~�&� �t8aga�Hat60$2xim� !u$E�U��dE� $ 1 /-v$&; |�;_{I_0}.C ^{n_0}...�]"iB"i}\> = |1Uq�.�P��+ O(1 /��1�) I�of"/� $ .+$)2(%Y�D^  �dly �%pKw�llz Ib�g &ex��:"%*42� } Nowiq equipdg*$a�!*:QX�  � ��� ��if� $Z�� �?�2�& . To�Ls�we di�b!$$fer^3 $N_0mterva5 � $\tauI� � qXN_0 T~(i �<'i�Z_ca]"#��2��v  - H `��^{NA�bK !�1!\��D.&II ��s��ch��tenaf���6X i[H}P .y h_0a - �aK g\K�.�\,)& F_KJ\,2�F\,>!7.�M&� �p8)cle *sE*��le "Fgth� $e}fy ,N=w)�>� (&�� '��M�=��%x��� $\mM�h_0= e, < - \muI7&� ��gito �a�8a�mW:�*by"nak.�m�" �Nq:���a����or%� *�N��A� y[( 62F_K� 2A��) "6Mf"�manip�(�weAjhe.j�:� ���IdH H_0� �c� h^TU�]�2c 27 Tce A�E6(ZF _<�D�>. s1e $T$ F ns "vposed" c\be h =e�- Lm�!la6 !*��� ( h +O� ee�Bm�� Q i � _ti(-�0)1 H})   \>&o�$�we . r" �mpi���i�dowot� o� �=/i3��aA 0$ )%2inser"��y�P}$"�annihi�G!�6�& &�1  (a�tau�Hu1 ��i$!�() 1|ُ{P}�4 A]�. A~�\) A�{.� \no�\\� �M  \timesI8k g_k VW_A� AH-� �:~,�EY�R  ' �nd� U��e"� 1��&!AW� Z�%�%{ Q�%8:�� = 6�!"&� "�2k%&8-j.1u �(-5� �hc%�c ) %=� FW9�)� %���_K S!�9��F,cR4�� c^*!�9� :O�����s4��rf"� 5�^*,b)�&V~Z4E}). By���]N6!'�"��A��n%��expone�Qqu(a0�Kine%: }�<��"� ng (�osite)  �be�d� 2���!0ni]0t+sc�?ge} &�zq&a<�3,cA��V�U�i�c*#now�� edF1>�� i/�V.�3�Pa&�/7~=,7'�DA(=�+��%�"�(- `q,A�by1��+iw5�g��'��0a �!�ms- .-s r��n eigen�@eg7. �+&�a+ A)a�?le $j$s<A �is�.wak 9:Nq>of�-�591�.Y!ez71)p*�* $� @:%� an���fDum, $ K = (I_K,M_K�s�aO�"-�&9�@propor-V@to Clebsh-Gordan �,Y IM}*�+=��*� C_{j m_1 2}^{ IMU �g= j6, ~e!ssN)a AwJa�a�let� Q�gB�;>.16e��`v"2 x)s .� $ Bo-&^{8 � 2}�J~ 3 �Ws i� ��f"G Eq.~ Y&� )���$��3qh&N o�*�.i �be� % ��� �:!�Q a��=z�4*:aF�D�A��!N�BO�?reD �����p c�/$ @!�>� ^0$,0Bex�4�" e:*��r� �of( 5�1}z+ � �>"p �5�y��5&bec� .M >� s:�&�� e�8� S%7.\!�pl�*m�J� 9@Q�0$A�e.a> 4�].�RH)+5�� !�A(� hown�# be $0�+6�  g�)r$l62�.�>� . �&*5���wB� &YZ6Uu �b^*"(&� -�$mu ) + \oE/-]4 B b 2�d 2I _� .� �4I_1 I_2 I_3 I_"Y�> W^IA":"^ �I_�, 2�A)D3%t 42% �\6oRo[1 $b^*u1�yo1$bre �U(ime $t,t-1$!�4? ivelr6F�)T!?-LX)"i$I!.� ��!�}2�, e �) -g!!+1A>0K t285zI_2I_3%�� zEA�)AW{i=1}^4�I_ifE) \Pi [(2I_i+1)F%/29 �(4 \{�:Qav*{ccc} j &A7 \\F22AW&AY0%� ] @ �\A�*s�(I4I? :@&h*)M_3 ,MA�C!p 3,M_3,I_4^{I,ME� b  MXI� 7>; N�[��� 2�c frona�$J�*C7&Y ���� �h 2� "�$� �<}�8���J*/0� omi�C�e&��BN��}s,�&><B&� a~ ,b $e�,�@� $6-2(s $+a*�,va�*|."P!1��YreRJl"�a%I I_1M_a@M�q�:hat2�A7aB  C�,[}�M6�2r\{N�M� j&*t�,56Re E;i,:1qnB�+ewGAckE�,.��B� ��9jbol�*+4Amiz� . F3Y�0V e�Anm:�#C�YS��* %�.�&i a�!�c}�) a� R6 {�zW �*!6-�F!tI5"�j�%{II>9� v���.. I I}2 & & ���all�ۉ��(F� ����4� �� � 3�L kB� � �3�2�6 l 6,r.�B�`(rf��,.SKF�0ed�NE�"/, $n<.�P� i� seem�O��2�;:�'�|*��bly# m%O��a�#4i& Q2ees�ZQ1 �can"@���.6deepxhe �H�U���,ly%�a/same. & � �Par~s �$��1ivF�2�( wa�nuFR �3�! afuT&]-> ToͲ�.�M�BIw=mak$cours�>F�J @iF�= UmcO�E H�Cwq)�PugD��%Pon2of�S[S)�o �Smbe./m�wz�QN�. �q��tm8&�D remo�\��!��& ,Qc�/�+ O xerc F#2p��/EcoA+>on,iain�N��2�FB�rr�2r�\ amet&��$&��s YB g to/  (B�@B um_{j_1 j(p_{J C^{JM} �j_2�l �,A.�* i�A�� �pa��5$p$. A`��r6Wi3these eg �/A�,]%N)b�/XU�G348*W@e��W��&�=UB�.]�$:� c�G ap�tic"Uo�E �� B��13�\b���Y F. elloxA.�Ye,it��I�3e ng�7MM<}, Cambridge UniTN�P�, , 1987.[�>Y Y.  uv,M. Mukherjee {�M.�>t.p Lbf B209} 1 (1988). ;27HY. U D Ann. I C19�143E91)5$Beli} S.T. Y V.G.& Y YNucl.� Y39} 582W62).��W } T.>X)a�9|^XA3�78BX1JY J�2?77B->:J�W A.j8d E.R.Marshalek QRev�Yd6Q63} 375�!O^^M^3K M.B. aro��Mol� i, F.4MmbIv M.R.Quagl���������28]M5�dO M.%H,G.Stefanucci �X 8-mat/0204311 v12D~A�mb1�v405045 23�L V.A. nskQD��alu m�o&[Sin"�p)a��P},B�b, 1993.E�C�W.  �D,nd H. Orland �Q_U um Many-P�5S�Q@}, Addison-Wesley*�c�Ianye�8.zb1�,Vars} %D.A.  hal|N!�NA skal,\ V.K. Kher�ki1���M�� %�J� C7dLtd��>� &b �{6#c,[twocolumn,l@XpzM ,aps,prc,�8pacs,floatfix]{"Tc%��L< \usepackage{ams�6 ,bm}2��icx"��9 �{1.8in�-i6cHadroU�^ona �� coalesc&Arje�LagV �T� 2����Bg�=lli=,s at RHIC} \]{V. G�>ffhPO{Cyclot�Institut�ҁ�ics�Wart4, Texas A\&M �z,�ege S� )877843-3366, USAy�]{C.�BK�����I. Vitev�=TQy DSU!�!�5 8, Los Alamos N%Oal&`dy,�f(l Stop H84621D, New Mexico 875451% date{\tod'DSa"6dT�_��e"�! � r�]p�,�t"�8pr $in Au+Au c2+2MA8QRaC\�/8s_{NN}}=62$~GeV % ��� �  es b�}F��+e den�dar�dc�#^\�f2�l quenc��pers` ve aZa) H& &�bL� to�U)io at2&qCV8.Xa� pred"�dbeU�Ban�datd� exper�K�ct�V�Zen�of mas�=erY o nd=� \�({25.75.-q, Dw (Nq, 12.38.B�kma"d"d�Ia� } Re|� :�a rDh�&te� !�u�%F� o�T comb�Na �W�tudy hB� in ultra-�v�X heZ�B re� on�S volo�j,hwa,fr��g�� ,2,moln,lin03  -res c}. Z sӧ���-r-�ly tri�Pjwoq[pri��u�s_/in�4su. �qWE�e7ZXl�bA@:200m'e R�-H%Ion�.i�) (aj)(58ppi,adlv2,adams�N���b� ��l�=�X yiel``q�aD� � 6�B�um (2~a�0$ < p_T < $ 5(��Nat� ���A�c�� %)B�m���� $�\al hard+Um^y���so-calޙ``�R��Ving''{#-�ellip� f�f,$v_{2h}(p_T)" .e.,�J  9"ce|#o�"uf hif�� R_#J� $p_TJ�A"J �of+ �r!? �� phen �a�7(mp�W1Q)if 5��2a���y slibj�U�%N!%)j�D���'�1Kse�Lm%�U�q* roug�Pe2�of�:� �e�2��a�A��#�@"E):�%B -glu\ lasm� ���-���q��m�E �by N2� was i��h)m�dIALCORm�alcor�\ MI$micro}. Em�_/-�earlieRd���X i�"B(�f�����sI&�m/K��+ ��[������!!I&�N(�0!�mjs� ?II<�Ba. FurE��� �sL�M|E&.�։ �_0� k� U�i�q�>@ a�$ ll a�&m ��s��!p; }.X IY-�.�hA erpl��N?a6k!M�6)"��L�&� �Jfka�!���.RXvd�` ѽatE�a� z M_N�I��fie5byI>exXda� �`&�n��ctetj5Q�,:�via ).� t�,"����.g"5i�-���M�q&pA�e��� ]0of gre(M "����&$=� mech�mAI�a�Ay k d#iAlso,Tar A�� M��2`�O�R�!���5��E� upcom���� al)��Ga�\[a�A� 6Mof �U� ALy+. -!61xpaper1�c�n irr�0by*X t6 �a�el4pre�i� o= �.� %A� 9s%Z� .�} �g5 jdi��GU � uVt*  dA .I a�^B�b( �$%5!' organ^a�!�A�b\t.�L]�L  al�Y���$-Pus�  Ref.2�.e�5/Hn���-�r�-3&�Y�AJk>�  is��3H-]�p" }�a3n  ^>+ QCD}�: ti���  a -U�b��tak�1�ccount� !.Cronin�  raΗA�in- umQwlos�v#-62�W n Se�m�}�� ~�� j&�UM�'Q���ma�9FinXa�J� !eu2n.�s!. �;s�on�F$}�;]=�Mv bQ42�3�A�conver� ��s��  i!��  b�3!�!� �RY�z"| �xl� �qs z�Q�W.�5emi�Q�aC _ H or,�� \$off-s�M"B� guaranteeM�n",q%�if$neutralityei�o��� �6 a fa*h�rs% &+b<�ng!7e�on!�tur� o�c dden�aI!ba���� ?K9nCbyMA> verlap �%��5�a�"ͱ*��rgWigne���L��7��!!��$ȔB�u��5M8 cons��n�:$n$ (�-)�Tn b22NJA`\frac{dN_{H}}{d^2P_T}&=&g.�C�-{� 3^{3}\�Dbf{p}_{i}} {(2\pi)E{p�Cd\sx� }f_{q}(x ,$)\,.-&>C&f�(,1}..x_{n};p_ p )\d�^^{(2)/> (P_T;�5.n�T,i�'�4�?a�`K2�=I!�e7', $ � $ de�yi �!iGsvY-like��~�c, $g_H�?Aa�!��factorAE�ai8lA�)�:eNedI���t�KNmin 1/2`� ;�&"<: �:, �$\p��rho$, $i�,���$\D!S$�[� �����*t0$$g_\pi=g_\�1=1/36Ug_f=mE<^*}=1/12$, $g_p 08ug_ w=1/54�8eA�-E� )i diJz&# a"H4��&�5%�)q�Wi!@%��t pVd$$f_q(x,p)$�X is �6j [' B�M�dgA�d3>$4$f_H(x_i;p_i)$��'#� �d antE �s bu�A��#E%u%�5�� >h$ u{;& r":�� rW� s�l"o%s"wtody��'y�M�2����^wͧ5�w_ZA�i��csw��� toge��/ �in#6p� . UN� Uh67!�Qs 2d� �.[�x1N��itsMn!�u�v(q}�i��� ledg�H�}o�rG>���) blas�hv�a1�e=�.. ��#w��2v�s��littl2�ENi��SPS�� �qWe�)!F�-��2.���AJ�:N�[t�er6yn.|�1H${max}=0.5$>xa "�� Aw��0 0.45��us�{3ar1pro&�)J=f\, r/R�>�$R$MF}@ �y�p�`9� check� )� is u�,Aty&X� a Y.��nt���y�& 2���$p/D ��?I���&L�O}zc �D�u^ }:5Iy�r�c aw M�� ! �3�~�$�. Ikv =,���n<̓��q =-� mq �h�md&| � R� is��t!�%=1 � e 20� $<E�#<$ċ GeV�avail�2�Y<Qix-et}e�be���.by*� �F} � dE_T}Hch}a988+1.44�10^{-3}(23$-130)rW\rm�m.�de!["L j5!z>Q�t�tF�9��Ticipa�#Ya smo�$lo�Oic #gio� at1"� % a*�<�- N_%{d�� (N_� t}/2)! 37 + 0.62�7�U.H%&�dn �BUM% Glau(1� A~�I�d�9 �, XM� $�=330$e4!^ $0-10\%$ ?��� rom &��d� � pl:��"n $-!/) = 48jEc�E"j>�6��wY�aR rapid�.bPy=p�AT }/)�}=5d��$x/dy=1.2$&�i�o6ɯe< pseudo.*�M� OusBʅ�aJ! $a)/dy�Deq 46$��-pN�Zb . WA�reA w &�)t ��� bund!9� � ; , %at�^�qA?�evod1, �g1ssS5 �H0 ��m &�9� �p"� �I9�[ .����~$ $\bar p/p͌DdbX_q = - T/6\,\ln(N_p/N_{ 0})$+��S>d�%Ɂl�H�& �2"�'al ju!Q�� �b eq$ 0.7� Y�%�a)~J�m �11$ Me2�mw�4M 9� 2� ɟ of 1n���,&d}٧t �AGS�) A;A�L�E�R�sld_q=23%E, *��kV�t�~���%AEW44. BI��s��g�P�e"�5�qB %�:6-���4lx z9� %QJ��$Cve 2� :�l�:hA$t@!s&e"%ir�:p&�*e� o �AM�u,d}=300%X�@�s=475�su�ri�!.�h��T_c=17 D, �hm��A�6���� � ��u+d}=285Yq�u+e�18eN_{s}= $s}=79$)*��&u La ��)a�T > p�j$(few GeV) Ej��ly�N*.��&4�P.�+dy.1���5�.%;"=&aeJ" � -� [ d&��elow.�Q``&�<''-5-I� ($N+N$)�,!%%$�� C &l' ��`d*X#2/!�fl rach��n�!:��e0= cros�vc�'c���qed!�M?�9͏�  o6�&� �pdfs} 0{\alpha/N}(x_ ,Q ^2)"� �%ac�Q�($ 2 = a,b$)M�: �v�A --  2�s% �^{(ab�EHFcd)� �Et}$ �owens}: �9&� M_{jethy d^2z� p_T}r K_{NLO�H�abcd}�\! dx_�x_b>��0k}_{{\rm T}a}Nb�{oə�K� & f(FA)F$b}) f_{a/p!�0a,Q^2_a) f_{b bb) "S.g �%, s}}{� -%^�9] } {d4 t(u�( D+u t}*�h%�ec"0 �d:� x_a$�� $x_b�-A�UumE�s c�&� JrO ��- 2�v u�2�- olog smea%X $\�GۙI!�)�^2 �c \Z le�b.8$�G$^2$/c a.Gauss;�Z;$=� k� o mi A -to-��$���[+gY-�$mW��+��u"� $M��!xi�_E.a"fabs�6o�i"� c�"fe�/�( {&�G�t?vg-+4gQ��c���hot)�ar��m9� le e8ic,�, 8c"�}c��in�)` outg2׭�^�diW2�:&}U�a1���I��),Fa� l�|corpo1 � �6-:, pqcd|2@exampl�B�u�ffu&7�Zp+A T"$0AO�!W�'�-�.�In $AB"%48do��9�I| :X.�of e�1jes2 paga�9th"&. �,6�!�Ss.\&�+ise� 3(-i��edm&brems� hlung�s�3iT-�mx����$YI��*~�"%�a�g"�, ] c8Gyulassy-Levai-�8>�g $1}`.�Yof Bjor� expa�W�d�(ad*���boostsp}]�/# � N^g_{ind.�$ l�&\E�x& C_R -� ��_s^3}{4}  1}{A_\percZ�onZy6 ���{e�Ua S{M \di8�sz� � L }{P }EP�(s, \quad &:; �L \gg {\mu^2 L } / {2? \\[2ex]>6w& 6 }�G�V^ VldO{~��K}�gVjf��llC}/ ��=)  . \;��u{ j" E }{E}=� 1 2r {C_R1� 9 \p.�!F�� , L "v�o4')�(�e1� 2 E}1m%� �3%NH�%$ �),2�e}-"� 8w�C_R=4/3!(3)� ~(�)�o, $M��.6.�"_o�g6,a�$L:��C�d����'� Za�purpoh���) ��n�a�el�c��"A2��&ra 1+1D�X )LeM3H3&!l�X Eqs&u\� )�~�\(oste}) illu�-thl�G8D"��].��"�"!��%h,� S!W"� D.'A o!P 4!,�E sis "�G&�I� !� ��&,16t the �� t���i�/s�/`.,. �Poiss��"�' {�Ipv�nt�y�,kpr&,, $P(\epsilonM��gKal2�$'=� i��_i/E$ dQg" b2��4q"�5��u@3in~�0�l��1�&�\g'�}1-},�choA�a�� ��i>�n" p�Y%_ }5725�)I�AI#ed"�.B)�$us�S�H> �: ���)�A� #�Si� Ae.�b& " �F �H"| ���� )��%:68]2+! "y`� & ��~�>u!�g�=2)$��1� �X��i*�q2�&��( $D_{h/c}(z�cM� x1$c� h �� flavor�e�b�N_{hadQd^��i"�y�z_c�p5~//z_c)}{d6D͟�,_c,Q_c^2)}{zXYe2�-͎ z_c=p_h/pu~�B��Lr`5���b- ��$Q KzNK_=e%�J�U�Z7�*Jly�$u� r�uRP at w0(fer�6�"�$!�{:@�'For�5�+u)6H&?Mof.Gf�B� �a�)'$e^+e^-�-epWpkp.� ,AFpp$a"� R�&�!�%� z�%2�� �\a%t��ed�Bq49X �+�-es�#w�:ke.�v�p_T\g�3 - 4eM 2�� �'�� =$ 2�AV�a�sofJ�To����@!g@?}@Wu)A��E�Kq�.vM%Q$-��s�es $!�E�!�{pIweE2aS ing-inspi0*�"��5 ^[}A^���ng-par,j3���N��AYiaA�|�\5he!+, ��� { ?"�2"Z�a1W]#!�!�pI!.�2x"<  =�̅ n�4%���n }=$6%��N�% RHIC>�IsYB$2 - 3$2�w�huT hF^2�$n1�!a:��� a�:n�%E6j&X  p$ !%fxne)."3 !tra�M��Fig�@$��!�M� .pE ��.��ne)FF�%-.�!'6� .� 6A�.:TO:6Q�S� D�'�� 2醙 2� a Z�� AIPHENIX l�io�M�!���A�%�,)#�!i`5�E� 7��h�72�/��,ot.�M�4.>`* ��plàC �L��b]w �����9  rewLby � 20$�* w!<�dei%%0200CD� . A"�O%�%!3�N/� s7�(:k!Ken�P� �� r|\e�+1}Kat�~�-![�A�&k is�\��; A� d�a ��val�(Kg��$� "s��li�ry �%�PHOBOS]��sup>��c1��_ ha!�nde�pcon�H  tren��$phobos-raa�C Oz � h�W�-UE� P�_l�c(dv6:/m�� �:�eN� 2� �qlsoZ�epBGwE�]��si�9��aGK3Ij.�� 6hJ!� no>F nd6fsA]���S��U�"�#q�M�eB]*9 r�' a� 2.5�Qfal�ew`r ick �s��n� F �F"pJ show�;a�MfA�tea5" �C��] � J?��$� 5.Q)�I)Q��b*Se,*� � -;�*�sJfB6a. &�Q�2�~-���!��)�9�r�Aut&d�*4!e%i<� :�wAQ�M)-:d"�NDT�<eIG2�4�� ��IE*�6�CB�!o�zs5�&.d"9ό'F(�,o�RO 2� �B�)�JO .% R�a�A�� in6� Z[ T"� (� ��4��E�)5JWM.��-�*b(>�F�a�vt_I!J���'P-Q8%B"�W2�mJaV < 6�!�iaA�s�.�!doa�n�Fly6<�=��'O [v� 25iR� E� � .r� SЁasJj��!O�a�.�%�}�2�%��)Oa&? U>> ��Med 2�7�N�aRg2|0N%0ESh��in� I�it �#�#}DV 1.5AP%��1��.� !*,$p/\pi$ rati�o of about 1 was measured in collisions at $\sqrt{s_{NN}}=200$~GeV as shown by open squares for the experimental data~\cite{phenix-idp}. The large value at lower c�L energy is due to th 5Lr difference between$slopes of �pectra from fragmentation and coalescFin = aB62)thalatj& . Also s%*4in Fig.~\ref{rs}��0$\bar p/\pi$ W� -of :� ��. It can reach a maximum value of )�$0.7, which| clos5T *F�2-�, � by filled2��e>� , bu%#�slightly larger $p_T$, as a result�Esteep"\!)�u!�om 6�contribu!�. Becaus�,]!i!��e baryon chemical potentials, a �8QY2� A9$.�s!PsA�FB-�I5 at 200~GeA  \sec�@{Summary}\label{s D Using a hadronizA:Xn model based on quark2��minijet:34, we predicted%(0transverse moaum-za!�p�, proto�nd antia�0central Au+AuY�s� I� �I- . We fouP1|enhance�|A1j i withA5aؑone)$in nuclear~�Q�. OurPA� is mainly�oaU�! v rum,!�t0domina!Kby5s6�already) ,p_T \simeq 4�N,%�a )O-yuA� a4instead still 2o.�s��!1Fup toew}6.5. E.�confirmIh�CisQ/�4 will� vide%rona�e��AF�e� like�dnon-perturbative mechanism>2�, e!uially)( s (A� in g� al�i�s)!lB�a!to��6m�T� urn �8also facilitateYdeter%�!%_2} �aC]68�4F�,fries}R.J. F (, B. M\"ull� C. Nonaka �%� Bass � =(F�3 o;N�� 04=}�4moln}D. Molnar%�{Y+PE%%�91}, 09V�0lin03}Z.W. Li��d �QQ/��^�-c^�R. Rapp V)� B �59A�2-�4.�EK -res9��US� �7A� 0249 �2P�ppi}K. Adcox {\it et al.}, % [PHENIX Colli�ion],^8!245\2.� adlv2}S.Smler�m^p!�18.l yqadams}JkamsBkSTAR ��92a5Vzalcor}T�Bir\'o,2���(J. Zim\'anyu�e� B)�34�v 6 (1995);1)�Gu22!Y156Ig2W@micro}P. Csizmadi��ZU C 61a31903(R)e�06uE� r997"2r0vitev-62}I. V ,$ (-th/0404052>�in�ss2�mpt}B.�j�B��Li�NZe�6pM�6A067Q��E�ibid.} �6)� 4905�%)u6aa0�52);nS. Pal^�� Fo4A+119021\1);2�%]A49!�375c (20}E2j� ����� 2); 1%7Av�IJ��Iu�89}, 1A�QR; L�� Chen�J_J1�FEK 1(R)� 4); IJ�P��ch:#,.` s (qMM802!A��U%5�� �C11110:8 -MPC:<(M. Gyulassy2e%.A697}E@02) 495; Erra�inJ�703/893:~04|,.�l 30}, S123I�2�m�s}G.�=Sh͡�.M30F8�a2�$greiner}Z.� !�C�, hep-pe� 6278�pketn�f1%�ex�" 9015Y@lattice}F. Karsch�4E. Laermann, %!henQuak G�P�3}, %2� TX.N. Wang (Eds.), WordS 4; �$lat/030502.� n�KC.�2(ins, D.E. S9IyG. St�, Adv. S 4Direct. High EziF%끂1��88.(pdfs}A�luck,! Rey^  gt, Eur J� ��R4�%1992Towe� F. O ,�ModF �a�465�7.�vg-�}��%��u8 �:l �l2.l=�pqcdmsT]� G �i79���`%�I� 9297Ng �1%@ F�‘��)G8!H553�4N*w B �59��37 ��� N&7��1�G0).expand}6D�a�X. M�^ 86w 53�1.\lS 1_ iC"� .�E�A6ŗ 631 ���]6�*� ��)��b1!3��28J 2�ffaQ BinnewieS A. KniehG. Kramb ZQ�CM��4!z2 ]Dstring-par} X.~N.~�-�\%�\Ѿ5�32e�6/ junc� U��6 &^ �5Z 4.�2�v�}S�;V rU)K%�8��17A� 1999.�4hydro}U. Heinz2� 7067;�nlb>6 =5E -shuryak}�� 0, Prog. Part.F.53Az73E+2��+gn-Z] n� 07"� 32L4phobos-raa62}B� Back:�%Š OBOS��*� ɟ� 5003.�p��idpf� [N, .�Q*�f� ��-> D docuw(} /O%\dclass[superscriptaddress,p� int,f`pacs,aps,draft]{revtex4} �I.@�:R�C�� twocolumn^�0 \usepackage{IHicx}% Include figurles2,d X$}% Align t7 �decim�int2; bm}% bold h \renewLand{\vec}[1]{\mbox{\)$math $#1$}!��1�1){ 8title{ Surface <8useness anomaly &�"Os \\ .w-angle:sielaQsc�ingj`author{K. Hagino} \affilip { DeAy���8ics, Tohoku Uni�dty, Sendai 980-8578, Japand T. Takehi�djdAi�lantekin�jFj�9!5HWisconsin, Madison,( 53706, USA=+N%+igawa��F�0 \date{\todaya(salways , , .% |ny�e m�� lici���ified � abst� } Re� h prec"=er.�!k� fuV"��$subbarrier"� systedc���Pa surpri�)eB\pan�aB(a Woods-Saxho�k requi�" or�to fit>.�p�8 #txJ9hquasi-F�� backward e��Gvor�imilari�n!ofv�. Conse� $tly, a douF fold�@approach fails to�e�2exc��f2 ��J���c$$^{16}$O + 54}$Sm )��<�ar5Coulomb -�. �!9�]dev���r�� .��!Rutherf$cross F! unitl deep]�G#�o8$��H unambiguous way to&�)A#)~�Dhe� eus-Beus*A�7yi \��${25.70.Bc, 4Jj,24.10.Eq,27+q�r make�o TJi2��priV" ing�!�in < !!q� calcu�. Its ��$art has O%ten b�"m|rized�6~�< \cite{BW91}. E��� inJkNsensi �!t�%s�Z regA�-�%_�q��$er�2�*r=# �a simpl�on$����exploi� to %`�p��BB�. Usu��9 bes�#�oYJR�� is"��"a2b of mt0.63 f.zP,CW76,LM80,CPR96,SAC0%��I�is�!sis�3 c Bg5d)�(HDG02,GHDN0T!� seem��be � accepted 2A ,EB96AW marke~'7$st��s*4!Ns�� sugg!���a much��r-of.j, rang�sH( 0.75��1.5 fm,!F�g�^ �_).4�,L95,NMD01,HRD03,DHNH04} (See Ref.\e?NBD�y!� etaix'�>�!)A�e6�q�"fits qx ]a over mat�)��:Vat9S$both abov belo�e>�, hav!0an inU Ic%�y �"e2$m�2� �J� . Wh�) heY(!���:s!�fixed,��M7*� �er leadE�7#sma.ѽ po��3*k>!curvat� (thus$�r tunnel! ��-��� effect �" �:� com!�)�R��(�jwidth11.�)�:j� r}%��ly�%D.=Cappear%Eb$sir�  inI8these az ts�#e ,reasonE��lscrepanc�M.d 5�s$�(%+]恢-a analys�"/#�not yet���!stot �rpurpo`*i��*i�discus)�]�of2�Y F� at}*6�M�l.� ���a�|*z��!.L 6d� defL$��!~sum� :��u�L !fQ%feQ)a�DRJ��>5 prY(��mpl*ary!�W n�/-� procm�g� �^a) observed ��s&al� q�@JER02,JEB04,JRJ04ɗe�is� so b]-�m40l 2[}yia�&�ly�ie�r�|�'a�� �� 2�)n�)�1�CQr� wZ ne m�%�_ct, w��mon�te��aE'Ri]w>/�P! U6>�= Jm E�A|)k� 1e�&o�,"V �5`. AR/concret� ,ample, let uaUnsihe� � +� � 1~. NeglA�ng�finite2���� mDs2+rote�al band�st�/t��� y :��Q�\^e > giv� yM�A4,RHT01,W73} %�equ�0} \sigma_{\rm!�l}(E)=\int^1_0d(\cos\theta_T)J,;,�Y%�]~rqel}(E, F�y.2r.���%�isoi rifugal�rox� i�wB A�n)�s angu�O,�.30���.T�w y�$,HRK99}. $ ��+ _T$A#Y� H%�or�%��leQyd��N-M^> 0� projA� le d��.".h,> 9a�#V�$E��i���)N�. �;t*8 $V(rM$ _T)$U�,N_2, =V_N.< +V_C., t2 pot}>��]�:Ot=\frac{-V_0}{1+\exp[(r-R-R_T\ba62Y_{20}(1�) %4Y_{4. )/a]��g(sum_\lambda s Y_{ Nd���narray} :*&=& �8Z_PZ_Te^2}{r} +2�left(6�+ 62}{7}\P7 5}{\pi}} .2^2\delt�� �,2}\r��\)\nonumber \\ &&\,\times G3�2 ;+1}  R_T^  }{r^1 +1}}=.�e5%" � } \i��@s[scale=0.4,clip])1} \capag{�"�2�� f� P5����0lab}=170$ degm 0e upper panel&-m|�S " 0low0�ea~�� 2��r$solid line�~/�rE��-� �.ddmula ��$-�$=0.306� 405[ uT*�&�0sN p�er $a$�'1V�wh��dashe � � ,0.6�3 6�7} }�� @!d�y-�� M3Y ! ZBi�2no&C  thin=[ zFY ��taken� Ref\ �cQ� � ��Q� FU1H pares�FaQ E�"�(Z a 7I�z�;b N��(!.2� I�M�s)T�+6�6}er� �s�v ��Rd��>�f K�6P:�w�O d� 170a�ree��oryY7meb eM3 ]�sE( 66�:� $a$=m"Nm��iv�depth*�radiu ram�"�5g �0$V_0$=165 MeV?$R=0.95��4(A_P^{1/3}+A_T )$�M��m`#� O220.O1.1�Nl[-KD ] �>�Pett ��n��LR_T!T6 � ��q�;a rt\e imagin� 5;o8� W$=5�, $a_w�(4��! $r1.0!-i*�si�w� !� comp��ue# �I�absorŲ>�%� id,fie��2jq�� �=be �:ly&E8��� xJ�;� �A�a��ia�x+V�9�,2� , �A_ �!Ne�� &� %� have7c�:%Z��F�E9�}f does~imh� if�<vABRy&Fz�� A&FY�q"i&�65F�!'theoret� �<�:�!R�s $E$=��&�@"b ��c����?� � dA���-� �?X8A�� I{�� 2.� E�5h.6� E�u�#E"EU�SYVE}�� mean� l� 1�2��"amp!. 1i� dot- 0?ot�f� ���Bby assumz a spher%� �a@ 2b>� az�z .�Հ2�. F�^ ,E=ne�= blem��-5q��!#f{ atB�is{ "icLW81}N�� d:5}R}&�^m 10 $_c)}{ka}\, JA <2a\pi k\eta}}{E}N{t� �j�&�&@�@bab>~Dex"(�� (s2�! }Ea�; g"aYula~ ch!EvaH  !ag#*#)��iɠ7B!� semiM(E�&�; ��y%�U���8e�.EIN(r)$h�or�0o $�(-r/a)��?F dist+ofGD��"�a�$,�c=(!�+)� ^2+� _c^2})/k$"0 $!�gS�;rferd��a� $A=1 \cotb /2)$%A�nZ":� at N�$=ComT"�VI&� � �p !Jert�Bt�0��id*$ re�!e �Cin&D �"&y 6f�j%�?"�$de&�E2�D �ndeedI�influ�A�Fa�m coup� �to��k��a�Gu�,��62 wc Gޒb!w�aq6�z$fin�$m ���negligiU%jf,3d)0 role�Ay& 1�.D"ag-N*@ *{$[Z sMCs��y�end%�� �"���:!�� �"or,aZxa�_ca�"B� $�{$��eB] V�,�m!� ��.�-MR *� Z &��%m�"-j�8e�3��G3y?5� r&� 2� �a$�I؝"2 !?H�V .##"-".� G heF{(� ��� let],of our��?(e next exam�!Yp&'m��f�# G4SL79,BS97,KS00��I�� . In�[�!truct ETN�� RK"�(� du�5w� sumeJ� ed F}E&�(t G(i�Insic)� �,V�rho_T(�-{r})=W>�2���u*;YhatG. {r}}�_d]�X ��&p%)�� �1s� in�. � C784� � 6"��4$-6���num� ly�� Eq. (�L�)�,o multipoles/G $L$=6ɴ 9��>�"�!� eachNE�l's�a � ?.8��t.1� cor�ondq!����We6Q("� ) ��"n ae�&r%FS8Cana�#iv�)on�)o�t�,A�1�g*Michiga� ree-H&��O �+� ntly e>��N"�  a goo�"���*��2�.V � e>� at ݺ�NIn�$-e��_ �j� J.of��b�"Rz ��PN#� � argu�O� 2! �� o:c&M�f�&S ( :(/5)a�1 B2 inly]�"� oSB,ře|-�� �-�I� ZMa��1Qt)act=�qS�|2,N�Xf[� G �A!C6�0�K�7�3dw�*mt� if"g �s!lus�2L�H&z om$e-�,#� ,�.: Rin�wJ�$��! 8&min*�6}L>� it would�helKto�  o��e�"� F&,4 ^�, s�p')*�,�/l!�.Z"L �,j $ss is poss� �Wemtlso� cusse|e##lic =W>��� i�SN�7�Se�:�:�٥�8b�is>��#BA6��w��q�V=ia���UA.�4%y6�49��u����!�e0�uE8�.�. ��:���Sy!��@Ti&c6,��.B�\ � , enjo�sucp*in�� a�#%% di�>u for"u��R3 in m�7I�eO d%)�5�'���ap�ntu ti+V�car�`*�O�%e.g.,�!.�6�/v�d&�V^ u�ne!"ar�WeTSreY �in�:�pE-a�\bigskipl-isvOwasFzOTO-in-Ai]! ~O+D Research, *ct}O 16740139,�!�:ese Min!�� Educ��, Cul�/, S�s, gcA�$d Technolo3R�UTJnP� " P244384�"e^�:�$ Committee�fu gr@;"�,"�: A�=i?&�P�.t?�"fu&fQe�$21st Centuwor erA&Excell� r@ram ``E%5ra New5+by Brid:3�@icle-M{ Hier!�y''a B� S. KNWs,!�CheMjee, %(Dngh, A. Shrivasta!K. Mahat�HS. �!kF)679*D8"�F�Ubm�3"�@,fEDasgup\I.I�nY, D�RH�, C.R�Q�X)� J.O.�,t!�e8Procee� "c0Fourth Italy-�� Symposi�2nik-akPhy�@kyo�@ (World �#,:OJ42), pp. 87-98;� ZD1100652��8�tF�M.=�.2��.�F CE�ZD24610�L46&E29H. Esbyĥ�.E'G.P5at3109 |F:� L95}/V L77:�.�J.C. MeiA�2��KLe A�PKstone=�$ H. TimmerE�X� #PNa�w��2�R)52V15�G5629}2Q2�2|.�.�.�2�� ]�F�![064608%�:t�9.�[2�] ��V54603^36�!:2E.�2o�� e�XISuppl���1WM"�F.�N�:2^ R.D. Buttj@ :"2�:� �?IBe5$K1A�20CL %�K)07wOa90�K:9�1}M�8AnaG,F�$A. Nagaraj�|% ��202�292�1�M.�#6�Rai��^� :Aug2"2p!/]L F�5'190�>5H7U>N �=X�� A�V�J+6$} C.L. Jia�Y��, K�� Rehm��B.�� R.V�N JansQ, J!~Caggi��Uoll� J�Pe�RA�&)KI� r� I. NiqZ�XT�|Pen$�O!5D�Oweryniak2�I=�89T527"YS.*I 7}b���>�0=Vj014604e�:��72{MBQ6�I. Ahmad2�=dC�David��P9s>gG�khe`E� Pard��Paul, B}6ylinhzZBVou6�=�9�L015��L&� $RHT01}T. R�%Ao Ha IS*�G6a�56\4�e:�(W73}C.Y. WoA�=��3 P766al7:��4umBtA.T&O uppa�mp� � ��2�14� 96h%SjSndown� H.H� lterR� 5�1718:�� }G.R tch�Ya;W� LovT �Rep �56O1�T197:�PM�Brand' _&�Q2�Q �76��D%8ho*Y2�N�66*P�H>w 76A>Co TW3hrtozzi��msej3gE��wn,�VLindsa�HFoJ�42A+2�198���F>e �5d"6O �TB�NOprl&�Nq:pedAO*�N%:�NB:FO�>&�NbyZx:�yv5 YouRz�BibTeXe�$apsrev.bst�re#2$ces % Chooc4a jour�' auto5 �Ke�;cyct APS %bstyle le (c ile)�'un��kW+ %�)if*" %["WbV{ �} %�2�O latexsym}2�6x6 epsfig} \& P \be� vd"�!B#a$,8:$eGA�^EeE "VCbedgdis�e�PFj'Ij% lan �7#,:�r� l6{\bi}�26t%(itemize6�{\lra}{\9�8arrow:Fl"N?.;��& % U�nhe "�Q �Q zl�Qy%%local Ikit+nal � %#\9�uM8zh�� corn�ititle pa�2$_p�S�. % M;#lJ�T.�Awed+�'MR�9s' �+ o�2toz!rmkq�$defaults %-� �s2^ %Sg 2.0 Tg�{��"e�z*�m�5�Zer Twist�)�F�%�)DNs�P�R$Paolo Cast >QDept.A���R*�of CatanU$INFN, Sezi�di \quad ;Via�Pa Sofia 64, I-95123,/, ; }6JQQNa"�P`"Ila"8g�!Vni a�:N&Pi*in0FacA.@ar"�$c�>�R>D74�6�Kmod]�!3ghig!�t%��le�ep +4�n�6("- �p�v�Ue � m"�H�C/+ 9s""E.}nA��shadowTq+/$x�&$low $Q^2$.�!�kin R r�Mt;8is"/�e+eFp0longitudinal F�!��i. h=��^sert Led PACSyLn brackmn_)��\�O.j}N[$keywords -�J�p,hors don't nm-P�is %\/{} %&�O mu���i��,K,�6�S, �m J F�R%Y6prep#�$HERA �� RHICE�Amfue�&��LHC�*GyQ?Im YbeL�� pa��"�s�ok Y�L�sar<��Qs�i_ sS" �R�% osed-]eks}. �L majo�N�Jt] a �:�"�8J�Y��)a�e>�qo�+e\pe�Ssc��(DIS)rTE7~ y�m�a��#�% �AqnO'�4d!�a}be1unkq. �X�&�2&�T>�Joa�� �Gribovu I�frank1}:"%�up�Y1�2} ��WT M��)!0��3)���be!� DIS�� �%c�Q signE8n"W6 C (HT)2�E�!%T �-t�/�A)arU& e HT2>�1�YturA��y`|$ 50 \%�Bkwh;3��^�x�d? s �(�t1`2 a�,ve�Yby)i�& �%�g%^E$� -�du#�$�Bve� . OINo� � '3 ref."1n�r}�B�%T ( !8�rVI]is�KH!Iu 2� ;$>0 -�Nxɥrelev!��%SBA�G/"!x�da-;�@!5�.�Ns$lu!�Aa`|bei�"c&by-m;a}p]E.qiqiu�l }, ivon�5��u�W,�zrse-grṩ�8fc#HT1� y�A � ��f�Mu�,1T 3�1�A aver� �Ome�x3]`�ResQ>L� �XyE��L . Mt reduExq�ex &y���3s ,_ �p�J�$$V^{op}_A$:� $A�5��-*�"h+�!� greaA�t���Q�TgB( ,&%Sa�%duced`F�,E6�w�A�1ecta�A�2� <t6$.� z8de�|s�9 appl�-o)�EMC | ,b�YT eqc�0It bob}�=,%��I-1�U� 5noi}. a�h/� i� > 8ZQ�, "&v�z�6�,�)� g: i)MreH�S:!�pHT�^le[<� � �� �> ; i �5*E�I�-D.| J(, $F_{2A}^L�re�@so��aX| limi�C�-�r)�ack!�Le�P�x�AkU2�� ->$subasympto�{Q!vi�zD, $O(\mu^2/Q^2)$, ��Yyp� 3e $#�<TXA!� matrix el�ls/5�jhwe]l-c�Rj�c1�;ycur�Ge E.:2 JaffSolb-7j}6 ^;8 se^n$8�,{�> ymmetric,�Bcel,- n Lo�zknd���R�olf:sp�)nd fl�D�%�5 permits u�5e�H*A)�four, Gtwo�*�43]�ro-)Din�y�=��ClL~�+} l ,�LI[ mulders} �it��*b�specc�?y�!�� .� ,� *� :.U6�9�SmxMIT bagghe=Jr��onJm elN}$&� ��Mt dx a�$N}^{HT} = �A1}{2} t\pi \alpha_c}{Q^2 M_N V_N} ( - 032H7} K_1 + 8 K_2) \eee FA $M_N� ��e��i�>��ma%gd��< �Ceh2�7"e>�8�-B!>( ud_ $ Bc=0.5 Fssumed)� $K_1=1.08 �K_2=0.17 ��grals�� �� hmox�A��j �e$4rky�ow�=mo�?Ioi�E�is! ult,�GitselfE^�"A_!.a�ari[�O"� �W�J?eTřzC eF Q��,�re��,-?"p ,&�ja~va�+�&)TFis�"f A��< *b "�:?߂ mis�nd��*� a�is qu�V-)to� ,�+leN`a BjR�:� s,"@!�!&G %}�h-7�%��uf��9&� of eq.(1)�:��wr�e��C_N(xq���tr�5 ���2��% �$��>�%5�"qmq�>N� L e:sq�_��o��iM�E�� !y*�  . H�b�Ie e�;� {B�0as5u�9�X%�9ɘ)����A �1�)�!/$F_2$=�"�aA����lt (LT) plQ u1q!T.� . ~<c1]casVc� l.�We �{2N}=EGD}/2$ �a�1OarM��deu��um��. C��� now ��A�Ztw� � toR�S �.�e��� $ � �^{LT}+ Ŧ$�j��H��� u� �AFA.F HT}$. B|B�Z ng $R_Am= {�(LT}}/{}$�Y $ R_A)$�,��3=́�esm�R_A [1-�iu HT}} t A}}+D) D}}] =D��n����rre� R^%�(ArE|�if !M�>! !2 .Si�/mX��xq�%B<1h�=2��@+A2�( term (i.e.����� ̙��d�b"�Di�Q���ZA�C F% �|c�^sa,!�HT)� e��v�1.@i�F"� at9 . Concer�(��$p6= � D}$  n� �at: 1)>�>  �ll.P�{�s(eq. (1)); 2Z@Lp�Ri�i�VR ��i�6f2@nm�]���^;�. By � a��ݭiH�C �7!�Yar6T5�6t"D1�">!�F�VRo� ase.M< ���q#��|�input�a�..@��G�&m��� C_D(x)׋�g,c_1 x+ c_2 x�ZQ^2} �? � $=�h09 Gev^2  $6= -8.553� nm}.Of� .�-�"�B�v�L�uI��G!���!GEqof)1q�~����2%���o2�&Be2 ��>>�I? rk-qP�-�and/or�&&7 �� Q�t�`!�  �u��r��peculi��n&�,B��.3"%1bhng voa���� ��e� 6 -�Fu��rigoro*� a�q *Ց,�r��>bin��(_3�nDl a.d !v.��hs� }V�>���:�.�� 2`b.P$M^*=M_N+\epsilon$ (����movalaiaku},-��� �6g)O!_�irN�6p) (previously �ϋ Ȍ0�!xtrem��Vevac"�i1-A,%Ve Y`�*�}A}$.� ��b�$�Xr�o�P (2)) \be� ,��(^* V_A} C_A&� )s0 $V_A/V_N= 1-� ��$ 4$�YK�%A06�1�Bw:t�k�lso�oE��zKB/-!х:uI)r ons.�u�on�jXx��'�AMO#iop"pQ WoveA.Z�\���gto �U�O)5=�+C�!�{<}{V_NO �'4�7pm1�nV�l!%Ql��&x� �*�  = �� �M_N}{M^*��{E,4[ 1+ \gamma(x) . �!N}] \�v6US�cA6�F=)/9$ "�eLxFI!a�ii��er��� BF��_!A�HT5c !�� ��%.�. ( combi"] �5$ eqs.(3,7)i��!bet�"� mLR3erm��#&E i�Uby)�� ={{8 �U!�-�} } 1�} \A� {()�N06*ee ��rstart���w� !Y!C.ex&[j =.\r5#���L5�vM �&d�%hez� �\d�j*�}b}u�|�$a Reid-sof�*re &)C5�eY�k��>��two'�.2 | vedi� 5 �A��rev��O F*�a�K���� 0.65F) �]#%esn8�-Ala^�!�>Qi!�dLe $65G  acc}"i rsR� r6�6�� $( few Mev)I 2P �!9al2Tqu�<'"F .�m�O�nA4 ]���Y� ly �) �����y accu)lyQ�� ��  F)lyJ �toY>��LT � s �%TftBd�!�y?$� . F/� i�of�&,!:sh�0 _�"JN_�=\m��v:u+LT% ��&� F� �a.���H�"a�œ5B magnj*����e;:�q -$>q&&1��O&�$>�5$ +l�!��"onx CJ��"��ni�&condi�wDGLAPs�0$Q_O^2 = 4$ $"#�ary"#Mp# �P�.��s�"�&}!5~D ",��"�no��&<,lY&d��_` m8E��aie�;_P $�# �pO"�am %'�Fa ``LT''G��%=JQB, ���s4e"4�� eBR&)�B�M. Z$�P1.���5�6Y&*\�2I%�"c(:� ��8)� NM",M mc1}4 ��C}/ D}$.�+*s_o_- V-��,A$�b=3��q=4�� LE!!�6�)`!_�$ �1> %;29�U=7u�Ca-40eEM!t3o1�H�"�1, % PB) C}g fig.4���Q� A�X�gGa�� $x=0.0125"U'eSne=��{"@3figur�35{�5 =uno.eps,�S4= 6.0 true cm,Jx=.�K =0} "�k! 1 �:� �p��&]�o,{'s textEz�+iS�ndhKa" err��[2!P7added.$ nd{18vIdue�I)I2�I5I�aIJD})K�J�I_ �1[2�tr6J5B�.Z��J9JB��(i�b)+ C}$,�)�t�*\l7R)quattr6�4�-�-^-.��o��a��e� 9O�n�zP L�'ke�$0.975�C�)B�&�k�A��z'I<'������&�� a��� ( i-"� 4)�y��o2, 2�!obh�!\�]�. &� ,�-14�xb0.0045� *� w����z !^_@�)eh�*Z�&�P�6Q.-molti,H,,mio} uj*K'��: E0nytroge1 �_!�de+�� �\&�a bal�5eLWnd>x���"� rllut1��3��R�:QVJ�ni �w9qF@!#B� }-en9�&� f7(a$>Q�s3cs*iezas��!�t:�2@)@� #1� J� >_�SaSxdN&0.056�1�Q2A#& 9uOiG� >36"��3remB!�t:1� 6}��(�>y�  $F_Li:f?"�\�`��� F� $ A�V6Ha��K un�Tb ysis��tu�4 6(�Ai�dei��c�P�/< GO�v ob�~�A�"w:/: C"2� I�,y& open2?s�"� �O&c!/R~�,6� .(�V, !�5c"�1��:L . A-3saRans�vM��/o47�!�&y6�~��Vb/ { &�E�e7he6��p�.B��VM "��"p�%X!�N�rq=Y ( �at :noi}) uL*]0 !�2[a��a�bably!��a3,�. �!'io �geoS-al crit^ �|�d[ �?"X8�A�{��o2, associv��x perc�. �helmut}"�X�? -!�temS.ur�"�e�o* ks N� Arm Q?(rlos SalgadILU.Wiede���� very��]�0��(he CERN� ory Div@9:.�UX � >*Ft�&J�: L�M�79TM. Levu nd M�HRyskinu@T�p.\\Cf 1�f�F03) 1; A.H.Mue��=J.W.Qiu 2LGKGB268}:06) 427; J.Jal��n-Mar�SA.Kov�GL.McLerlCW H.Wigert �Rev UD55T97) 5414vUA.Leonid{8pbU9 U9) 0140�WNW34007["c�-ѡ 099903] 1�J.G.MilhCV>�61��0 �2;QUIancu,:�=RF� A692 J1) 583; i Lett � B510"@133; E.Ferreiro,E�s7*B�8489; I.BalitskyF�B46p�41996) 99 ; Y.VA.chegov ���EpD6�M���008.�Nmca2d(R.Venugopal-h6P4M4) 2233; i>�9d`- HARD PROBES 2004 - Eric�W, - 5-10 Nov..�s�=$A.Donnachi�2H.G.Do:�R�ae�I�9a�6A P.V.Landh�d Acta H Polon.�D34)�3) 2989.�=X K.J.Eskola,V.J.Kolhine��bRuuskaJ� 535}!�8) 351;bME��X�9 6 �%� C9 u�D61 ; M.Hirai,S.Kuma.a�M.MiyamaV7 �1M#,3. D. de Flo��B A.R.Sasso�~66A!�) 074022g�1AkF�<fu�� �Strikman��A5� 293;.��  LOH,V.Guzey,M.McDermot�[Mb JHEP-�20m�2) 27.��22�\>�``L�j�y.O :�Jeri��A,� ��4"�x d�� w*@G ��$ph 0303022�?.��jr} N.�v�A.Capella,A.B.Kaidalov,J.Lopez-Albacete�]e =� J.Me2-�3) 531.0U} J��!�I.,� ``Re��ed JQA.6''"��3090949NJU  F.E.C��,R.L.�6$,R.G.Rober-M G.C.\i�6�3�/1�N�ȁw*oi} P."�H�.��H�)B21�w 1988�59;.?,2<�P.Har^�n�R N IC��T35.f�8 K. Ackerstaff ܡ -qEMES� a���-m�ɺ _B47�20�'386. AM�K�( 5P�M.S8�� L10L1R 462B7H S.R.Luttrell,S.Wad)N B.R.WeberN18 1) 2��NFJU19��198a� 90; 8�Ijima, -�$ n. CPT-99%S-unpubli҂:.�%P.M�7-PbH 2760.r$.�0nm} M.Arneodo5�NMCV�3��� 102sV(@ S.V.Akulinichev,$�Kulag� G.M.V5� %�215-y5) 482~y�M.Sargs� �RS$%(M.I��� _2 C3��24001}u�!T A.Accardi, V.Muccifor _H.J.PiNMF�A72�20��13.XRfdF. �m�B48�` 3;��9503292�[1�\232�} X�XGu�^A �2W.ZhuM�2�52-T 1) 82q�2�)�2�D.. 97502.�!�tu!� Br� I�.- ^rJ�_X Ik5na��al��kshop�D�EI"�ES"�E8, Cracow, April 2����%%C&& �.�5Q"1) 124P;"� �z�m� H.Satza�H��  >�VL*�PL t�%--- cdr 11 DecC[ begun 028 �]��% ANL-/� 11078-TH- 9Tm8ed EXAMPLE2.TEX6s DV (Ver�3.0=Io10th,e9) 7rD� DMDi#F�s?% �$FBSart.cls._ Dit{*.2 manu, xpla&�)sgUofE D>�eG^� \�UO��f6El��oj(e�"Form F[�s} \4{R.\ Alkofer,\�Vel�~e�|�!f"J��.4to [\ln Q^2/\LK�^2]L$.�X��*{1ex}�Y��ived{�\%�D PRELIMINARY} \dota�\��3DRAFTM P\t�tn�W��� �L2L "�� Intr�za� } Modern,-luminos��&1al�^c��.E�employ�#B[O"^i�p,�a�remarke��i�gunewA�or��oH%��*�" 4gao,leeburkert�"�DP<F�$hI �5 look�N far �4�N��6B��'ofBbI�}�i eE�ƤviaEenbluth & J�%0�� �8jones,roygayou, �n2kqattan��.��%ar�%3 2!!vgr���� e�. At:yh �%|8B�,- > M^2$�1$M$��--�'s��, a�iac?= o$�9E�"l�nd?Jcon� o�2��/# aV��pA� P��� %'�ppa�*�pp*|3��4y.� ntum� cs; �yɘ �mZ�r�,,boffi,fuda,�,bruno!�A*)+t6��HUA�u�S�Z�>� M%,regfe,hugofej�� (��-h�vthroug�\�% &E�!�sam�&ل))Yb�lour-�Hlet���_g�?�X��  (� �Xr)^$$�:c O$O� 3$ (�7riplet)�6nel�dq�WhX{ X��#|vZ%� y"=Rܢs Bgdar� }; i.e.&&y d Da�A% ۋ��"�dPtrL��1�_���;���$hq��h�y a pi2xofc�y- )g': A� 4��red��� %�54-  pseudo�>icA�aIbeB�8f���y�i�"�]�CoD��!byA�� P l- fip> �ebRef .cemcjbfe}h� rud��ryG_�{M'B�p subsL�*} sophe���'eS]-�ed2�\,�N bentzfe,odla4,echtfe,birseq=C*�\O�(udo�Tn 1�aUM�� Pa b-) � !f.)\a.pqY���Y� <ͶE��C%#r͍3a/2O�2W0��5өIբ h�*� ��i�BI�Q����-��ao��� y�k�<ơ�:~ �!-��  p �ir";8C.�a edib���Zv��Qwi&/c�5� �}�G� bA/��r#�:� - M� �q�cbm,wrJ<}; !��yg,"yV��x�Q�"Ch,young!M{@Sec�$ref{Sec:M� } we�� apit�K  t� ��V� F":v��aa�&�h u�'��i; nk�|�a�solBdA�S�+~�N�X}Mm�1Bf^�u0rva/ K �: �W�*�"F��r-�`a�1&>I�iaeM���= us�m8GA�"� z�%G�!6 �in!,1�FFs}. %:ɀ����U�YA$�G 2b epilogue},m � F{CBEE�5io��2�.n0/!\erZ oftZ6���,e� �i�bE~by a �_bow-l�r trun&RT8QCD's Dyson-Sch�T�� �s (DSEs)m��$ rev}�7�<alca�"�.�u EuQ�(�� Ah��� exte*q[�ach. � �5!�E� unda�0nI�� �< SU(3)$:(� } 3_c \o�� > = (� $�= 6_c)20= 1 8_c^\Թe \ 1810_c\,,Ks�!�h� any. � 3 !c� �el ��� �Q�@o3 �v��%ŗk �$ �wa0��1�aB��Q%r.v� �J�"!��)�����\ker� �n*~ t Q���s+ so E�A$lso�,AǟE - *�fZm � ��I���F2*��- vprjxZ{�"1 wo�=e �i�a�Kyiti�N.��4Hg��hE�x�H�  ��E�A"����pa��A:Hm�� : DiracB ar $+$ -a. $+^dots] �3>� t��"�@9�!5���cys>Y��}se A�.��an�� J� � �� *�F��"|:">}� \PsiXMPsi_1 +  2 3 \,��5LM!-� cY�Pf\e*| EL!-,�$d{1,2}]5�� 3$��3� ,9 cycl� ermu��T� h šZ!,B>� �a�f!��.;. . \��{H�Ansjze&ݔ&&>�}��AN� } We��s#�stw�ic9ԕ�)B�v� �!e G^-!��� $1/2$fAPai�fa�a\A�axF� 2N�& Psi}IQ3(p_i,\o_4i,\tau_i) = {\�4,N}_3^{0^+} +2 1^+}N� $RT� &X��a�is�ީer_�6H_aK�n��!e�>,$P=p_1+p_2+pA�%@�'��� um. NB.\���O}s�b"�J��out*� $u$)�$d$�%��$s� uish�=�th R�bic�1rg�nY�8�9��to��b�c��)/-$�����EAix� �G3/X%(pi>|"�!aH:l4/^wB�]rDIs^S~zDEzAg.B�%A ��y�Q �co�B�E�a �et�A��Q(atforbidde��Fermi !�csѓ-QY=B�Qd.eq�1� piecD��\,([ a�):9<naz�6�6�RY&=& [\G!Qi�(�#�c4p_{[12]};K)]_{m�1 2}^{e�1 2}\, )� MK) \,[�4S}(\ell;P) u(PQ3G3}\,,%"M� calS�#ɧ�ŧ:"h${�9"�is"TO� tect%6,App:EM}~Eucl(jn ConveEs.�NA�or �s��9bu�� } (iGH4\cdot P + M)\,� =0= � �\, V,>j Eb�a`z�Fby� �/���ω� ��ti� #I�$$\varphi_+��rm� }(1,0)$A�dZ�"/-./0,1/neu�; $K= �V@=: p_{\{12\}}$, $QS" - p_�O$A := (-/0 + 2 p_3)/3$;�VIY$ Za>X �ag(i�\qDsed�e� s $1�_��S$.\!:,a Bethe-Salpy-1"&� Qling�@c����*p3$q$�$4�4$ { 6� Y��"�}g . ( e Se2�$ ��-U�^�5 le�.}.)h � � ."� is?z in�J^P}\!\!���A� p;-Civita ` j$\^Y_�\R\c_3�exIsTPiaA�ic/%ll-Mann� $ces; viz.,�|+B� \{H^1=i��^7,H^2=-5,H^32\��]nd.I $ Z�= (H^{�)_�}� [See Eqs�ݥ�0p}),d�1p}).]�"a.� !��!lEqG�$�KI��i�,R!H & =& [{\tt t}^i\,i _�l 8�3I� _{\mu\nu} UK�7 �<+Zi}_\nu�D � calA!�)���BE5M�ic�-�U6e9;���^)+g f��$1}{\surd 2��au^0+�^3�,\; %707%1\B-ZS-53)V� aM$(#0)_{ij}=�iju�w {1,3�k��s2.Pauli�,&�@Fr ��]\%a)%$ stra forwEw}l$��i2������� 5��\ ���"���- ����-:� N�'�U%h 1QyG��ne�D focy���'^{++}�V it's� �nur!uJ,"C�IRde �t� cU�Bkm�D"� =y�+ i�^{a�a���b� "� F� \,xS (D}_{\nu\rho"� u_(Pa�"Z&4 6� m�D)Amp}�u`i�$X�Rarita*%A�+]�r$}).�%)iITM�|G^�!� � $, A}^i�pEe +N���"�E9��x ��&�"�'A���")M��^su�R��"�� R��,�.�acre�pa�� �S} �r>�a '�J!gy�; namelyeyPW_eigen�Ka�$ ' _+(P!%=�L�}),�kailݟM�� Sexp�qA|*E = s_1�\,I_{� D7 4�(2� a�e - �  P\, B\�)\,s_2aJ�M�(:)_{rs}= �vrs�$c l^2=�h P^2= - 1���"O�(t fram�psSQZ�`.�Aupper|oe�qP!��-�}1��� pinoi*Pla}�+������)eZh"ZF�m�A!� �2R��t�{n=1}^6�^p_n^iE�\,Y _5\,A^n�nI��-i=+,0,-F�-�($)�l^\perpa�pA�l + EA !� �6C�_"C bC)Jb�.� {lll} A^1O= nN � ������$\; & % A^2 9-i 0F!3 !>�YX,\\W4 6i \ !�W))~ ~5 ' ]  - A y2�6=U%50 �.�H�\,�)7:�&�\�������R��L+~�J�A N`"S}�E�A�\���DUL_5 PA� :7-��h!\> � At2�A�!�&� ob>f�$F�%.� ��r^we�)6�p�n> �RHd�T� �"T�x"-aF_ ��[4f 2i:r}L ca�k;Pxk\d �omu.7 J��]5 % = -4\�4t d^4�30}{(2\pi)^4}\,)aM}(k,�<� eft["� b� 4ٻ%w  A}^j!��m�ZF���{FEone&� �9�kA�f�5� ``2'' P(}c�%5+ �" n2to %1MM�-�5n��D w��&en�a��?l form�)!� soluŷis�lu�S(pq�<-i \gamma\cdot p eB$_V(p^2) + S = 1/[i>4A + B ]\,. � SpAB!  � ��(a longstand��predi�q0f DSE studies!�QCD��wave fun -req %6amass:= m� Q�ZMdef} Z�=1/ �\,,\;M  �F�reA�`tively, receive strong mo��@um-dependent corrih0s at infrared +|a \cite{lane,politzer,cdragw}: $ �$!� suppI��$ �$$ enhanced��5^0was confirmed!]�nt simul%Ds bowman}AZ8lattice-regularn 0quenched-QCD,&� TFor three light flavoueY e effectsSun A!�motoA�small \�zect) $fischer}.}�A�condiA�ls under which pointwise agre� H DSE resul�#nd�2�may�" hAnb� explo!� � bhagwat,m!,  2}. !p-!��5��entral�� �!�)a�stituent��A�-�e�4an existentiala8 requisite�  Goldsto�7 odesMEy5evolves� increas!� $p^2G reproduc��8asymptotic behaX$r familiar��perturbaa$ analyses,�z 8i!�ambigu�eviefor�D \gtrsim 10\,$GeV$�)u(mishasvy,wrA]gap}. �import1IthW qW��has�w-�mphasE�inE�t4of hadron phena�q� cdrp�M 8while numerical�~E�!�ɢAy� (now readilyUbɴutilityy,an algebraic!m %��($ when calcu�%�r)�e+e�I�Dous multidimension ntegrals!�� --�. Ana� icac? $ parametri�` ] �,�$ch exhibit�:De features describ� bove,%{eHu� ext��1!}-n1�-�a[ rev,basti 4alkoferrev}. =ex�via&� �p O ��S(x��& �  m � F}(2 (x  m^2)�t F}(b_1 x&� 3  �K0eft[b_0 + b_2 7%,\epsilon x)\E� ]\,,� ssm} \�vbar �V � & B 1}{�& T[ 1"� F�yչn�  $x=p^2/f ^2$, $� m$ = $m$@:.�defcalFA F}(x)=�-\mbox{�,e}^{-x}}{x} N0 z �%�=� md ,��./%-=�/^21��he� �P�� =0.566�o�� M�er aTes��$1�=10^{-4}"�� !�) a��n� o de, �large-�A a��iate-�~ domains.}Y�i�&�tableA)�)�{c} � m& A�123 \\\h�+40.00897 & 0.13) 2.90603185M: j\;A � �were fixU a least-s�es fit��0-meson observ�q marka�!���8less $u=d$ curr6�; Eq.~7 -) _ sponds toJI(m_{u,d}=5.1a�rm MeVV�� M�@yields a Euclidea�N�J|m�MEq} M � ^E = 0.33 � GeV}Jcdef�a�l"� ��p^2=M^2m�@ r97}��osA�gn�s typŰof�employ)�cF� odel1�simon!� In Ref.\, m!�(, $m_s=25\,-cm� M_{s�49�a���� a1�78-=*\ m_s - %�ŘA�$ !$"�a|/ /�&.  in*� BdB Jas�A� ńiA�f dynam%`chi� Dsymmetry breaking,!�i)�vacuum*� ensate�qa7ed diI ly� � gaug�variant E6* Ut98} af��m� allow= m!*fac�at .���"���)i� �-limit �%$"� �oan!�ousy� $V_meA omi�E� e ad� al $\ln( ŷL��_{a� QCD}^2)$- !�EJz $haracteris� of/$merely a p %�si  c .} ($Bj =0.2�4)J�-\langle��qq \r _0^{�va�^2Z͉ ^3\,��3}{4\pi^�� Hb_0}{b_1\,b_3}\,\ln :P{B� e (0.22.-)qB $ MotivaAcby �� s�i�� re1, 2},E-��R,� Ec� J�aaUn� U> . Hence   does`� a Lehmann� esent%���� ,is a suffici�aQiA�cn� .yy���7�causeAXa@assoc��d vioZ refl�( positivity�di�A�m�tracedi�Ref1Rw,s�l,krein" is review��2>cIVU } E� . F�!N�Mris ��r;through%���(of spacelik���,�leaFIg arte�~s � i#բ��tob2S in��j x�� ahlig��(An improvedB��� refore beUsough* Neverthe� , diA\j areE�encounte7Ah��B�u � !4AIYx pa@���xE�&6Z � "ort�ida�!�qua�l��alter�ve!�not�er sign� n�i�T��iB$�J�!�{Dib�"I qqBSA}u ASbow-l�r�~trunce��us.�� A% �!��onK(trum. Such11�� �nhir.��InU�)e���igher or� term�  k� scat��ng bq^@ogu��� 5ant-F channel d* m�aZ/�ertA�$of vector �� non-$let pseudo_ar � s, ensuSat�$'s ��.�!��  ^)��&� a�*T6�~��mandaraaexa�6mцQ)=�Sat1�\bound-�,%!aa phys��E#pre�9!\:�0#"G[M�@(k,q;K)]_{rs}^{tu$ sum%<=0^+,1^+,\ldots}c 8!^%��;-K'"VK� :,k\� �Mqqc6� On> ac) mP���a��$6c\!"&,�e� to��>� Ha>W.�:R��!�$ (BSE). UU�6�Gell-M4 e�ce��� nds � aU2� _C:=2AC !$ W sf�z exac�.h same��8$J^{-P}$ colour����I�butI}a halEH�se&$!strength� regdq�/@ makes cl���eR!�on�D${�3_c}$ $a�$�disd��Bat� �/*' � 㡸ys2how����t�w�Nrepuls�p��${6J�� Morea�, fo� �� ar1b�%,2�-M���a�Ha�l'����g�asses-�yF� 6� > %jq �HA}w:6(""(a useful gu�"C but����J�s b� !�partn� EZ�%  case��.s�gr�2�-2� *�by&z'%� orem%���t�G k �,a weak lowerɡ. ?A�rr��� lev�Din,)�s � ly gAF-� (in GeV) �Jcjbsep� dq}:B��-KF)�"�"�}(0.74 - 0.82�\;%�"�"}=!�2v d4# 00.95 - 1.02\,B�%W��M�)��d repl b�$s$ !V�E��e%$\� G(2\, (M^E_s-u)$. � valu� �;#��in"rof"�C-o hess��Refer�"�0risdqff} also���h radiiE�A�� -�s: $r_{)`w+$}\approx 1�r_\pi$; $ds)�$$ r_{K^+}$;E� IB%01.3\,$-$1.4\,2�e>e*&%shon@ ly.�'via.�q�bBSE�} AMK{(.$ %*+[=\a� ial}  Q/(} \Pi(K,Q) �4_{Q=K}^{{K^2=-)}^2}},\\V/&�$tr\!\! �$ Id^4 q2�$*\(qT�%S(q+Q/2 ��D"~+- $U�1 A��AM!�BSE�"�s{� tane05e-]i�0�How�,� ce�(h�aly�-sen���w��io�Ey�<�ingx,M ɃA�.M�hechtfeI� �mexpedy� 2Q \!$,*D [q one-zeram2�!-O~ax,�,0p}-��,(k;K) &=*A� N} !Z' H^a\,C �"(_5\, i\tau_�> 1 F}(k'omegaib^E,:�� 1p} "v,�� A� r�&� ��#-C\2�,R�>^2�"�"�. �Apa~6+- , $ J!� %��by*aq�)� se� (Ans\"atze} = inr A9 le Dirac-�8�would���� �!AwticleI,���nA� ntum�ber�� a loyLag ian� sityr y�us�Jdoi,nt�� H>]:I a�f�"e�st�o� P$��m�:s�w~m�$r97,pieter U j:� �&.,} Sol ���He� x}j:�&�]f�#��!�m �k7*[ � &�*� U s�{noted, h��h.-contrib�&s remed�Bde;$, e_�ngfE4!�� ��ppaE i���2oI�>!<ndA/mod$ e0�� :�obe'el,e��lyaD�g&�! atE� !e��E�-�at*.�� pole-1+"�axis. "weM&� na�2 G��� 1}{m��"�+ F}(KF�\,"�0�)�*"2�v�j��(\d54 ^(f�-K��K_?0}��}���R ( �/+a�:� 6,S �w= %�twoA��ہG���$%�r  U� �nd!��6widths6\cA�>�e�!���*�o9�6 DQPropC�r eft.-d}{d K-"(.5J^ \B-:4 &")^{-1}S |8 2=0}\!� \; \Rx%arrow= ^2�!s%�1�/ ^\9� �6"�2�i~ac)'ua! a�A�:&���D &�76-�sɩ{!h�%�q�{NucleoF*m�$ M^ !qgNDI } All el6r>���,�w�t���ifi�)We��vI��si �method*x%���oettelM� � ǁ�!q A�axial-95C�)�]ble}H, 2=cCc6n�3�o[  a�i)��1zt �&`Z?*�^set�biOava�ti#'r n-�;.�4#t� }[b]AoeaWcapAS�0V ParaFix}E8$`�="m� �^H *�s,&e fit��@1�es:dSet~A,�S#!actual '�+)ed;D�)<B2o�0off!Hto`ow.``� cloud'':�6�+� . A�� ly$�!{P}}= � \surd 2}� Z �եSa�)kA��}$b��kG,86� 0p�8& (F1p}): E!inversm!a R!�m'sP � �u*�%tab�(*}{1.0\text�T}{ c@{\extracolsep{0pt�41fil}}�|r; rv<r;} F& A9& $M_N$ {}$~Q {+}} m_{1  ~ & U 0 #Q4 (�: jA �& 94 & 1.23_0.6�&84 $44=1/(0.45��rm fm})859 "g% \\ BP183 W79589 W56 =BW63 1.q\\�BU �m^�� T.���r QT��~EΑ�it"�� Brec/�4�r,17�&Jvh+69- know��i-s� sible;d9.&�{reus octetn decu)4 ���in$a�rmP,vi} b9c������+Ů$2$\%} u T ���sIn outcome�undesir!vVF:�us�u�loudy ba�1del� cbm}xic:a�-t�II&res/d!�as�s $: , M_N = -300$�� $-40!/MeV"v!���-nergy�m��bruceCBMA7Fu� rmore�Qp.�/�y.�>�, ��Z shifT ��ex�g!;t�:!&qj9n�& T�0"�-M�B15131� ishii�W�thus � toeB�z  3u6byat%�o}�:�� r�fl %so!�2;�a&�&&7�"�&�%.E?M4�Q$=a*�J �mGUU�1es� ���%�,��.���comE0u�"N 5�cip% T, cf.\9��{ RA,�7<��Ba�b� r� orIf&�t�=e6V M� !is+(t�37EB+>�n ���Set\,A� 1.15�'%:#B #4.� $u2ZaJ3 i~�s� �*M#U&�M� . O%rseq�ourJ�!�U�*�!~ !fout6�.� �n!  am�$a�Q�3r���.�.J�9at6aQ.>�Y�0 islVa\e!struct��HA'�E.)�t� ��$�-"� s'E���YQ!nd�worthg�+}A"f7�Ea�3son� ~imɓtoA8� �,N=0.29MWw����EgnT6:%�A?-�H1 HeTe5R(/5 . PSE�8��r"d9!� $N$-U0a� s�>��5  "rgan+reckon�8D7�oA�"�. dev7���domu :a -PhoAVertex&[~-W5�'se ctromagne�+ ' i*`/�,JmJ} Ja$(P^\prime,"�>ie\4 )\, ;+\mu(q.�@�FH&� i e N@~Z;E F_1(Q*+ "�2M�\s�>"\,Q\,F_22RAB��BM "��$P$ ($�$_"�2�6@��inc ,g (outgoing)��, $Q= C - P$�% $F_1�/F_22,1pf�5�j� a` Paul�m �)ora�Th��!�ary.� (%ix%�� =�+-�U!i sU'�* v�9U)$GEpeq} G_E%t = 9�-_,Q^2}{4 M^2} 5�"< G_MJ9+'.� z� figure}[t"�minipag{\&<�b+%2"� &E}�3{\inclua�aphics[��*�$]{FigsU/im�"e1.eps� � h�[t]Fy�6�z2Rz\v3,*{3�#��lefʇex����3����sg����sgV�i*Uk >�* �-p�G �&�*s L=er�+�1��* hell�?\s�:b&�B"�s+8$Psi_{i,f}$�.�;�Sech.l Sec:3 � px l?ne �s"W� ^1,Nc ]B��Cou�a���df /'CJ�qM;��Q @:j(5R��-q"EremaiA!�k(�&&<i� c�0.GDiag1}--2 X56}� top-a� ima�4 s di  m~1;x!��,2 �so on, % +bottom . P46�9��� In.g �� "(4\mu5Eͫ6�"�*� *� !8systef c!�ced�-ofJ_picv(kyIo�."$ach�M�>� utoU0� � �3M�Y rtyp&}"&�. &�((caE$: 6�3*-Is'Fv�  Aval1to � ���=0)=1$�NAk-E�ex%.s�O�/1�I�picm� Fig.�A�ex}�e8ed lici�in appB}~��2 ��8weu�key� GB� �- � j1~ og1M�"�i@ +�A5> �<�a�:.s;J�b~Kr},K%i�Sf\goaGto draw�=T�Nnss &37A� � faul�j$i� virtue.V�2�%�.�b  dm��a � *�,�� !1�J� .L�.�~�MwB2I��$:B6f�,ES2�w� r:�N �:�iN�՞�+����+��\, f_+�+,k�NQ,s-. ��f_-F"\a�� y�a9it� +s-^Z*d'�$�0VWTI0&\��\Pi2�6�6��\}b%%.= \~�)\xG1}>� i;67J-�-� ela/A>a�\��.�.�� D first step toward���W�7� "�nvi� �Z,-�componen�4etin*�?�ur A (&�3 adap�B"��V{ i�0s�L��J�i�E�0�!} ��Q�٩{%�l)��M���+%\W'k� }{ Q�}��\{����>B��� AM0J+m��+ \}>� *�'a��malB��p:mAѢ,�8i);A!�l�&6�& �NdF,�i�+eek�Aafula�K�N�[��E $f_- \& 0�  E�-(E@Q�.�, guarantee valiG�Zž�i/ic�rgeNFim_x� \to �}60!�=� &E"���0H�0I-*��+Ae�$ \stackrel }2\-50}{=} :T\F%� toy-�2�*� NB.\�h{2�� A�� al�h�)ge }�p�Us s� �'d0ur�F�2=h-�NN.Ta?�)"_7a�2e"uk�&�7Ex*)�"A�s&�?�<�) "L assu�_.EH�/HawesP� 99}:�E"aI^e:^in `LNZ�B�&�QeTF'9&� "JccTSalam64 Abs7fu"N s�C�$n�Lput ��*� %@�O!W��: Cb��l�CAXDQGam�@.K. alpha\bet�Y*� = ->i=1}^{3q2�[i]�XmujDJ�� ($T_{B8ao�#6�V:c 1i��/^2$*H:� ���H �1�� �4e�_"w �,��lIi�_1/ �  2)\;��F��&�� �29�\rm [2���ɀ�1� �1�!�R\�2� {1  +)mu, @ (AI5rho  � B2�.] F_{2&2xE\ :�3:�3��-��/8;�0 �2�\)�F�\,�- *%0)� �� ,1�@mbda}%�{3 #>�" Q�4�U���?NHA�{1 �ɀM��Ŗ �~��!�= 0.�c�49 T)�6� �ڱ..�� e �U�&b �� .�.GD �* ���"b@"�#i'�..qE�� �5:�$݄� <5h �ic,&��quadru*4�s���an6 $��&��B�&�Q&�,GEDQ} & & G_L8E}��v�9F_1fs�� {2}{�L \c9%�\,K ;Q2;z!;+� F� 4 i2.,^{2�\�M>�M2]= -"� ~,����Q>�6�=� �&��` ( ��Y ) F_3 3\Fp Extj6�*led�E 91�ix'K �� })--23VD,7"A )��+ ittl�]� ab,&ev<� ru�St�mm�*� �> "�;Am��:�7:9(8F1} F_{1�2���� , �$N*E*5� Z2ZV�Z-\,�1�6 % (1-9��y(.z�+mW\muI���d(24>�3�Vy �(\chi Q\,(1-u)\,2`+iJF��2Ŵ�1g�$d�W 1/(1+x)^2���.L*8� �_� :�b� a.���� \to�E��� �;V<> ���I!��$J A?�w1�f b]" �_{A �" MR��hue�S'_2-0_1%2��t��c� �'�FOI�]Lj�=p}�A�0�1� %��ua>'��'-.9"��� a�UY;]�: $d=2CO=1" E�"PX�Gob�-qdis"�-�n" ,6� N�e�E.�~KF1. ��re�? < ai� : Pbrodskyhiller92}; nam�b.�V�h�-9$�U=$��6Փ��rA�N�; pQCDavdo'��U�: �kU 65� y�Q^26infty�(��*m.Q : 2 :�F.�Q4 �P:R3�h"�=N�*"E<e� rk� x1d��mf Xs up �ano�2!`�9a`�v.�KLtwo-loop�""�"R#, no newa��JB�6�)"�>N#2�:��discuygDC$!d �-�R>k�,is�'�*1-5&�!�U_�� B3 �UU2�-��xsE�P1� videz*/&� i�"��bi3Ŕ th4N* C"L%� ��rct\1">Z�-�� nyA6����C"�a!Ja�|� s�we�<� (no,�Ve)Q�*lN4��';kTsecm% UY?WAram~2ua ����8!?�Z"q�T6��$` d �s�Wbu4�ecx*�m�sI�Z$uP� conn�)8v,Mt�D�8 `ank-2X@�bor,�d�2�C-�}1/$���i0^\ast \pi^0$ .u� ��"(�B�e�Lbe�edRt%�SA�$V�/i_{SA}^{ �\�T *�� -AS~- =�i}{M_N��#TBY!var[c_2�%#l�� 2&F�� �$!#�b�."?ind�(�G�#^oHTWa\c Tw�u ceed}��Up$�GF ^ = \k,6�a T}\,B�!v� �'t.0a�'i\CA�IQo�5 lff}j� kTbest} :��0m�B� H)6�r[G fram�8� picu�J piec�1F;�q��6� m�(}OD.�ab� HBe�U �*aB'w�@Tqa�nti;$ llel��an)k��,�8aJ�'s|$A�Oin"�Q ~(u�-Ł�O&e*Xb:�'>Fw��`� �>9)�8 �>W5a flipQ��<Ur� ���"�P�Gf&?�6}K =m;-&|bS�O summ�.2:�?$B till alig�(��a�!$ orbi=anJ&�'�REk �4-'-=.&E^A liprl3a&� �F�:�� pinUZ]�!l� aV]:��� is $q^\up�Eo� U�^{\dowNow�?�,�� unR,:+E�at9;{"|!ebv�$ h9��!5b�I�ls�#<eEg3E�%TmeWgd!{6(�Kevitably �T" !�%k and/6[6 .} X arguW Erlot sophi-! ;,i�moGaagex'5iyEC�4 wA�V ly impact�Ims�87a�! V^$s~5� 6"� 5/�5:= �;!�so-O 4ed ``seagull''�\�chF a��ZUk9�3!: �R�9ca a��ϱ�B +F�io:�.� Ynon\�}qt4 o;.�:/�Z� �]���Lik"� s'2{A�"-� Eq*�*-�') 5� ) 2� )se% 9�]� "s2 w>� !�t]7eie7se��pKt(1� 5) oqTE1 �6)VW&���c11\O���!�fr%� Sch/(�Q�s���2�a~2�hJ�(�drEAL�]�fisNhc\P��"�3,!�v.)�ds�um�X alogyF�*�Wto�O7`<sM~� gpppH�$fB.� ���ss id ik�$<<a�ge�*�O�= DSEs��bd)� .c each0[ .�4hE,todmw inst�c P��&�pAR�hioUh yj�/�Uw�d*�W6&�X�&� (k,Q�E�oe�g by}\�4I%-�}�' - \�;[� W\!(k-�U->&%�;+&sexJf�N sT(2s+rs+Vbs"�zX5"[,1U $k$M���veP�zum*�m),%,i�i&^#, $9C NE"�$Q �i�beE &���Nex�#6F���fabsor r"�0fi*�#. U$6A�&� 1 "U� A\Z'-\,��*b&�U)A.-�J:2-�2JaM�J{Y:��:��, $J?)$!���)�-conjug�&� �") (cżP_@vA)5 vanish i�d58c& r"�4��i^I�-.�6<2S/tud"�2�f�Hin."��tpo�H���im�@��l�Gd"X&�V���f.��0( �7.� X5})v �� X6})W�&���Mv�(e`*�*to��= :����!$Z�,�L!7�os�2 O!A6�'>� i �")QE6� F�|Fo'+A FFs} %...@Fh .N Exegesis}o6go�h�x���nof�4y��dblo8���aH'#jPG't�Iof�suprofi�Ucy"�x0Q� < �rev:_��� n�to]�0�oo[yw;%���y��88\,�5 "Aj�a�,feaJK�a�"s �ide�J�Nsta<�resource�I) me�E� �(f�7�/%�:�c1@iapa�to:� la/!Kp��]t>" F��Kt|-body!| blem�+elucid� Prol�C*W(�As,< A��la&cm�)2[#pY.��EwNo epit�1e�1p b�1�.�=0|�n/$e%t�21� Yb�7� ����Umk}�<h�OI�l4��!AXUz4"� b�je V bhag"�|}�7rr�-no�E� e�bb�  &�{� \iU�{A%c.� ,�is basica$�S@�m�l�*-(heavy� K �+ ccurEag� aJn|% � |}. WA�opo�erAM��atmrT:�ed�a:�!l.Y�^E\�.� an i���.�A��d&�Hb"�fͷ�Rt%�n/sAg��! �Fp0a a Poincar\'g�UntB�2�AN�6"� �Erpo!_sS ,�aJ42I�r+&| E;S�?�:�?� 5 �?.�O.� sjI�6�M�ed5��2�H�A��v"�WI�%at��9 �CF)I$ to��l �2�:*A�+9A�c&0I��*�s' uM-�u1]3�'7A�=M�s'� &�!.@�AWItVm�de�cgb1mos*6 clus�G!t�Jqui1>dR�y a^�. &�<6:"�G�A>s"�?�b�j��lv%�3��,Ja,�end�jɈ]� �W3tAJ{roro� az.M"J4!6 �!�NQ.�di�)A�"� *�)2>s�E$:o�!"kof D9Ta.�,gft�($:��i��a��'A�!{*� �p�E�To�gy&�Y� ���8=�i�� Bin�y�&�0as�F^�rI"n T_2� C"O REsi�D!�=*Gh} ?�2�2{Sc�CQd!).���| '"�JvXiE��"2d a*Dur } r_{N}^2�m�*.-I6')'Jo0ln G_E^{N}(s)'/|_{s=0},`=( H \mu)�MMVMBK>�  $N=n,p�%in *�R�}8 GV1U�1w�*qf ��ayٵi�!]�!axJ$ FZ.�2pd�8, �W�M��\��le�&l%=2>:�&e �D��aMp~A;>� = ~? 80��5x%1,! &]y`�)!#neu�n,E_�seTe|Y hangN.an0ica��.��Y"�*"�*�# surpri""�e�l$1*��m�"��e&  ���E�EbEColumns �.$\s�D$Ee%6per!� age-&30 ��&rU�>�. �nn:J$��{"Tr_n^2\!Xle�DVa�oin�5}exp�\EKk$drechsel}:]p�4 .847�|r_n�$��6$&�8"�]>�_cn�_v�_vv�_ v=�v;v���b�S. lticE|({3}{c}{} &\�; 5$WA}4�.4B}"� % ��$ &6j6M%# $r_p @\rule{0em}{2.5ex}m$_{r_p}^A$ B r_n$i#n& J p}^B0R8Baa% %��0�`$596 & -1.3y 0.17�`-4.8 &9a 595 & ~0.2a16��~~1.2 �2aI .604-~~ M8 .~ MF \16\~~KK1 h , �4�<59{-0. 0.16~-1.8.���E59U -2.2 U76 -8.0 �7�-3.� 0.13% 16.4�- M61�M20~M61M~M8!i~12.7.��< 0.59Bb-!^�18!" -4.1 �%�~�7;5�D!�q!_ L1}~L\ !Q16{\\ �K1!~U%20! ~3.6K0-0!�!8I%�\Yz� & �5 45?1=c-7DE57�9�414:yU.6V�3AMV�3.0�D 0.62�~2q20z~6L- \�ET~1 LugP!A�0.0-�8!m-29�d T2AI�IUM>��>��L!�Ly zIa19�6�e1Aq2gH�� ��L dj � [t�Jim�Pd} M�$� N "% .8&Rt � "I  u"X.A� }. %�� �� �� > .�\��&] ,.�� L�> �� �� .P=�*V�. � ^�p=0.836" �=0.889�  v[ rvx � � v�v�r�rj 6# � � � A#� r %� � 4*�  #&%4:%*# fH�+ �+ �+ �+ �+ �+ �+ 45� -2.4�44� 44.-�� 0.44/0~ "�#0 ;&Q4  K� /B* 47 1 �O ~1�45J �0. b* �&� ��.�T �.� �� �C56h; ��>�!  0.47| 0.6 T8y �5� ~0.!�!?� ��J��o� -0Ul } )s �2l.� ular*n& h �& d!F+��6&�F�e� .i"��%�a*W2 s'Fz0re\/?-L�,.z�4�0�|L#�!:@Qs!"G9aW��mB�U'B*�\���� �c�^*���$s��oe:o��>� $���1#$'̛ec< lf5�/ both���de"3��Nɦby %ro8iely 40\%V&b.�b&e"x :�u)�s�u1 K EEarMCo8$�ed)w=��Z �Z �Z �Z �Z �Z �Z �Z �Z E"NalUare� %p:=�p-1/{.79E V1.9ݖ"GI"g�V�V�V�V�V^V�I �I �X��z\Qm* $|E`|2(  #M�2%N 52$ #*� 2y1.� -15.5�1.4�-6 & 1.8|7w 1�w~-7*��51.7�  L�&& 2.2� ��.4 �I2.��~15.7 +5�~~ �2.6i1����~~.�$ �o( �~.� T ��L�L L"��W�r5�1.� -5)�2.2� -21� 2.�- \6F 2."��IY5 !�syy2.!�:D 2.3!�!�� M ~ �3.g�2%�!�=��!2�!S)c�.��1�1-J�J2,.JJ2� -.�-.;J.JJ:��.�-8166%�Q� 10!� 1Y�&�5�EeF2�����J!�2.2 ~~�J�~8�2�& ~ �2.I�~8�U��5 !2s}P~�1 23 , too�"�9 �9 � "z quick�;n� !j) (�n,� N�! � o�) �" "E<�?ә�%� � .(c,��"�rapid:��y�c�B�# +d  �t7+�[�w�  r�|�"آMV~�M`u� s�m�%N $quite well*� � 15\%A�>)��$, 16 ���/%%�Ih�#"Dz2��0���/iB(z�� room�*�b].s, �&t#*by 47#�18K _jB�).�&Nx- � Au9}I�:�(r�#F2GAr�$plot1�m� 3�$j��b�Ifirm �augM1A�i*�R�s_JWM�YCon3�}G"++.�%�e�01�.&�"&�/V�"R � BRVly,~wj[ t�2delive�'by%�6+�r"�B+�aJ�r-��!-ton*7� 3T��x�'[&����&Ks.�$!_aa|tA����Zw�'��KawAto:*�$2�-AA2!��' l.�.�"s,�gre6�t ��'Nbs�&-*.9E�?b�QNN@A .*a2p8*�{H$Q^&��4�y��0)N�sF�*]_�3y^RveE'�s &9�3�- 8"�=6s4p.�RV,We�Q�O_*rMV1Q2�%�1�UE&f4�)9�2�i h�/6)b!�.?encod���6*�- � �.6(�bp�wF�v�line{\hs͢*{�#m}% \bow5�B~w,��=270]ywGEP1.Rtwhfill���ڄM �% � {1emDY�zY��#�#N�#�#-# �5#*Z$:��� 1} R;Tl8fQ�6�BA�Y��q N��y=1,2,3$;��^6J� = X %E�it{Left�)} -- $ 0poS��pper ��y; nŚ. "P=R�7:PMfPMRP� inapav�%"horizo��a� �� FM 1?:VB,�` lege�bYtVvm��l29Q lXvdas��x�>``$�O$''���ht62�da���!c�cWal޶03Ft!�b`+] �%uw ��:�%�-�!R*�� gals�#)]r:N"�4 `��TBG:� bH����2�M+�T�u O"�5s 2�� DN�&�5�Z���2� N+2^8AU�*|7 � 2"S Rɳs�9"�L� Iµl dfI�*�4C�6�S stoo�$tu �ela?"z@ take�;gʼr�� iuP";� �can�J7tu�G� del'�I%1�I�w�=un\FE��ac���-�,i��soi�V�t%�6=!B�.J�)L8d����2�2������gZf\�����" ���� �5#��2ފ�N�4a%acaJ� �"�'=0,1,d\�({�^�&6;���x"�?��2�(|t�]B�\� �. %���� ��ŌiC��� a��)4.���i%g-�� curvi!�:]��.��������͡%@�������p"7:F&O;Cu���a;GFIEpr�� %C�Cxa�vi��4���"�N>.�gm����Asi�2��r8@A�~t:.NPs J �]勉`&b.�: "s�J-scheme-Rt ~Ie$�Q��C�m1n�bourh��T��4$ non6 a.�Ic�aXF�#v�#n�%, �� ing-�GJw6:�/ kubiW=6"&��nHrpnS�=��0r_{p\atop n}^56^{1A_ }_{N,4==*p\^N1+5 g_A��32d[ 2 f_l[2}��ln b�m �Z^2�I�Wd7�m6�2A=\�6J�-� �+T[�\, Y[{16��3+_v} )e�\pi�7� �m1U(j5P)%?�M�mp\>7O2}Ӷ}�i%A*�[�M>g_A=1.26�[%�<=0.0924$\,GeV\,$�f�\,{�nՕ-�v�! n$. C ��A�Y d�<�T c�O�a��touA� aspe�Uf&�D�uJ� ��*�:"- �4�4P3�� �� � �"� �� �� B� ��]5��� �� �5#�� 3�� >>}2� F/� &�>� :� 16�"�F�1�e�� .�  %@ �� :� ">���� �� �� �� �� �� �� �� �� �� #PnJ+ � # immutQ,�Jphܶ&���F� &�ey�J7�+:dominsL.� + *�QW^at� :�MOO]:XE�>� ��&For6r � .�3� �.�z )-����uB7�a� �a+!U�@N%��[ made�R��J�-�Q�b z�B`Fg�-u�F�[*�E� ),��SJ�GN�r_{f� �r\,(0.48* ^J��& u&�twi�L2�E<E�� !�2 �� e��nfd%\arctan# �ޭ�v�Y1�R}�+�u�oR}vp ^R}&���q�n�^3 �^3��*Y[�i��lqlc(*S.���.�zgk <ms7 $��m�. O�� a�2ws~]/baP�:�!��%f7a��u��� 4 I*�: v?���M����"���� low-��p.�.��k���5pi�} ed} Row~1� z6�(>�5u%B"���U�~2�K�&$.�&��uJ-!:.� i��7L�r_nl�fM��(.�(l� B� ia*�6. �2 [�<-iof�.��'R1v.uO) �M�=0��Ge5�$To�K in row~$n��ARrmA�v2�K&ke"*! ? $n$= 3.�?�i*J�c@{f��yJfyJ�� �6їu� ��#�/e�a�%�-`Jn clouZ�#i�Y'{%�**{2vf+75�(ff+ GMP60!� j !!$GEpGMp} PrH/�=/�|��_\,Y)/G&�(Za"�m�:")�' band+�a�A:V�#�it{p).8B�l?��*�)i��)�A��IGti&�X � _ >2*�.NK�~X; x��>�S5s6� 0�1.�:  Va� �aJ�#&���eal_�'))�$��li��0 A)A�-�e���dt"\m%��g� v��$]3� ~�a��g\AP( M��i>KU�4�2� TF� 2Zwe�r�L �>� �*�>Q���A�.�jones}��exA� diam��>(gayou:�circleB+ walk ���l >"�h3i�"n#%��lou�glo�^17 �r�! b"� *&+)'t N6�1"�)&*}IfF�!Q��V{݉�z��}{Yh}�@ 2Ǩ6�^[mp)^2 - M \�+Q�)d�s}�92� ��"� A=)AA�X5y wa1(Z$on $0Qx� ��E�[��f�e�B�FU!���Vw5e R;�blu"u�� Vpla�{��p m���e�,"���&�e%4"� ?**�  F2FP;J "Pauli$/$��a � � �e ��fa�Xs�C.�"�h&t �}7aA��?cep���q��e���.�EB��A-y�EO�J 3�Yend1�$> � 7 �C�� )(Z%:.2E�is⥮<��c�C��Mq��)$Ewl�j;)9A^sigDA� ve achiev�PaN��yoe0perturbative �QCD. In Fig.\,\ref{plotF2F1} we depict weighted ratios of these form factors. %The similarity between $F_{1,2}$ calculated with the parameters of Set~A and ,B is evident���Our numerical results are consistent with \begin{equation} \sqrt{Q^2}\,\frac{ F_2(Q^2)}{F_1(Q^2)}\; %\stackrel{Q^2\gtrsim 2\,{\rm GeV}^2}{\approx}\; \approx {\rm constant},\; 2 \lesssim Q^2 ({\rm GeV}^2) \less^ 6\,, \end�a �the po!Vs�� transfer data. Such behaviour has been argued to indicate Lresence!�sub�xial orbital angular momentum in 8�oton \cite{millerfrank,ralstonjain}. ObHds not a Poincar\'e invaria%�8However, if abs!�(in a partic�frame, i!�hll almost inevitably appear8nother 3 reIyvia6�)Morm%\<. Nonzero quarkjs%Xas�?n�ca!ҁ�(ce axial-ve�_ Y?�U4Bethe-Salpeter}1�I� siblAer8(large $Q^2$=�M�:.(y alone ensa>6 F_\pi�6 ��\,$�� tantC( truly ultr��let�Ja-�mr!!�Th�I� � quirQ@�<ce<t98} absignal� AXA��E�j�!i(e pseudosca���. �4�mfigure}[t] \centerline{\hspace*{2em}% \includegraphics[width=0.75\textwidth,angle=270]{FigsU/F2F1log.ps}} \cap��{\label"log} Wyi'4 Pauli$/$Dirac!iQ? �, c:_d$\Lambda= M_N=0.94\,$GeV. !y ba��!ras��bIƍTxect6 ,.5A��}�-7^S �we c ћw��!��%�B�s. A ��0urbative QCD a� ysisM! belitsky}i�A�(iders effec/ e� from bo� ��leading-�sub0twist light-caw. s�lata�of wh�zreI�ts E�sɘ?uni��^u$, suggestsQ�e"� M/A�$ing} \frac� (}{[\ln Q^2/-�$^2]^2} \, %J�  =\,{� !,a�,}\;\;F \gg IF�  whereUj$� �ss-��r��T n upper-b��oi�domain!<non2�(soft)�EE�is `hyp�A��predicE!unles�"_q�known e� it{a��ori��"� 0can� bp mpu in]� �ory�  A�st� type�an�_ al inputm� q�$ It2in�v a derivI�quanth Ņ�\ �ne�Jt���I��many ba�3fea s,�QngM�q�m9�charactem8E�-dres�)e'�i� ciy�supporv�+B� . Extenan>�! Ūr�u$!!z!� oble� $principle, �e* 8challenge may ra�ly!�metI choo�0to use somethAPmoro werful�� +l� ktopŲute�With s� in�@���wouldr conf� !�cA�� explorq!valid!� of Eq.\,(�vM�}); lack.it,^< only� vide!lau��� A\E� One needsEustimatE�� asona iforY�ei!Tn 'sE, $M_N$,!���nAEalm�a�ur:�O� relev'Y_� oseM�]p�@ea*2� siz�!9� Eits!mstituk  A dipolAs��;���ap�%ly $0.85�*;)E�ed-I�ph-vertex>.�[ a mono>wofZ Yѭ� ;��� f fica�byNVs $�3��m_{J^P}"� ,1.0\,$-$\,1. �, EqsUa ��!� e fiT �.> 4� ^2) <0a�1$$0)$; viz.,2���domin�5� $u$��6�A0!�\in ( o,\infty)��O�.O�� < �Q^2=- _P g$0.3��,1 s fairi��"s 0 )r� 2�sm� A;aI��- es h� s ifi)�!HYEu�B�^2)*8\.� . %�1�Q gard ��k� as nugat \s ${Epilogue}� eW�?capitu�on *ct A �Z �fS(bes baryons��� osit�uf�倉5�'d -h� nd sol�%w`o obt� ���nd&bsE�!W.� $\Delta!2Two��&�4)�>�:j�!�ar��ax* �X^ɑy w�fix� fit�c stip-b � c-6.oPerpreA��as��"�i us-"ed!w"���&7:k ' ``J �e,'' %Xr�_%�sh@ augA^I�a!�� fashubyխo� rrI{s. Acl a� �e��� !Gof&]-� � ex,�y auto� c��! e �$Ward-Takah�m�tya� fulf4dt on-shellQ>.�b&�F~%�$is guarant��%!er�O'�� �� }|A��re.�7w���specifyB� 6�aJ�ioa!�rd meaJqe�ength!x:%_inducAZW- $\left� arrow$m&q� ti!��b,ia�re also:�A m�s'0rI�. pel��s just�ud/suffici���a�>MT[Q�ntrib+ �ku:M��WeE�o2�ra�ofKM�� pa���Q)�fzen�ccurat��Q��sta6 w��ot posyv6c� ���Hw �e�mismatch 8experia�Y greaa�reImws-[ fv!)%SiVtru:�mes�!reM like�ie6��2� dimi� �increaM umI�fT�#�$ 5Qm~�,�  \gtr 2($� prob��1�R!Qdr!i�!���i�; L stud�W" lY�^ c'��.�G whV� �|�A�� ��&L(G_E^p� )/G_M $!�f,�s)�E�infera.� contempor�rN More�,Le sam�sen�Zv��t.� �%A�Q^2} n/F_`  .3&&  [2,6]Y�I�h.�  m�m�ͫ doE�"�A�d �s> judgy��manifee�a!of"c6�'J��.4re&[e�"Ai�*�rjf 36bI�^N��� M�Y�a�$; Q�!6r�=N� !� viewIp$J��!to � ]^2/{WIne�A�l real%� be s�!�" z,*5 by6�� cloudeё�0at, e.g., makTnoticeR 2,A : ��%%D"�"�� . M�z%G� n�&> atAa���ki��i%��L=.^at66 e� a4!7�W r"E�in-�:�*5irV� A good unjta�f�'s long-�dynamic�!re�1rd� "r e i%xE�-�Q2s�  �"boxI�!F��2re open� %"�-\parine%}�� page}[t]{6 �}&ac8ledge}�F(thank J.~Ar�Hton, P.~Maris, M.~O�!$\,C.~Tandye�S.\,V.~W� AT�9�conver�$ s. %� work��d� : % a� AustQ$( Research F�^" DFWF, Erwin-Schr\"o�er-Stip�\um} no.\ J2233-N08; COSY�t ,41445395; De�!m �nergy, O �NG$ar Physicsi#.I % \{\g8_\mu, $nu\}=2\,\d(_{\mu\nu}\,K�)0mu^\dagger = ) sigmB= \sf�i}{2}[2{]�\; % %��%�fb6* � tr}_T5\ n rho�<]= -4\,\epsilon�)"}\,, $1234}= 1\,��F�6� AW iŰe�N spi�%atisf�B�4ar u(P,s)\, (i-bI 8P + M) = 0 = (i �.\,<, :�"� s=\pm�aJ� �#� �nM)lisedR�\��! � = 2 MFt� may �d lklyRaR\s�+M- i {\3,E}}?(!)Earray}{l!;chi_s\'8 \displaystyle�\vec{1�e\P}}{M 2e L � d \��)AF\ith $� = i � c^2!� ^2}$!� �]�p+aQ(q� z({c} 1 \\ 0 i ��,�!-jE0\\ 1VD.F��A"free-� icleE0or, $]=M�I�_4$. �(7�be� d� co,�[ iv�'�|� j�r�R.M$L�# _+(P&� 1}{2 M}\,�Je}]�^$A�]z��8M} -�-J�-�J> A neg �al�)�v�>�-f�\,;Ag2�. e���os!`���a��)�ai�%Aed�ob�.�alogy I�i�)�AN gec&jKedf�)i*�-N��{� gec� ar\� (k;P�vCYu, -^� T}\,CV��%$``T'' denona�A�ngZal"�-�� %- $C=M�2 4�R �!G%��-, $�=-C)2IL�� ep�|ona we � a Rarita� win�MV��ax*dc"�1���os'J�$�  [cf.\.`FEone})]B�}(NucWF} \Psi���5[2a� $^0&\\E�}^{i}[ 1s ] = PU� 4{l} \mathcal{S @�[A}:bu(PRfX, \qquad i=1,\ldots,4\,?1�} )�it"����Breit�3: $E�=^{BF}-Q�: /2$, $P' + �= >8 =(0,i ,_n^2+Q^2/4})�!Y >�fɓ�asF�JM22�n)z1�AB Qeft\la30 P' |e�{J5em} | P 5 \Rle &=&� ^+(P') I;�5,mu G_E + M_n� P1� BF}}DBF}^{2}} (G_E-G_M) f].\ ) \\ pint KdT$}{(2\pi)^4% �rk2� {A�$}(-p,P') J� em}(;k,P) $( ]=186�9i��9�!broke!e1�, $Vf4$, into a suma�six.ts, eac�p#w1wprecis,one-body terD Diagram~1� &� a � ˍ� B1} � qu} !� S(p_q)I� Uqu};k!S()�(!4^{0^+}(k_s) + 1\� 1� ɒ^4(p-k-��{\eta}Q� �Pe�& �1�.�= Q_qO .#��-�C Q_q=g diag}[2/3_3]�4�/ahctric i�$$Ve!��'�.�$bcvtx}). -�s~2�#4 #�"` hrough�391�2=�dq)�-ni(p_{d})-��x>�dq!{d};kut^{i j��M#^{j!�N)�V�+!� !��rQj� �~2: $ [!�~� �.�Q_E[1��,Q_E`-�Ap] !�* $ < =1/3��..A�b�� �,-� q.�4/3,1AC2ECIc.d�$RAXDQGami/whi0712 4: $�1 = j}�+�u�71,2}= �{SA��{isR�SA  1�m2,1mAS}� N�/ly�b%�ag<�/� �70 �thG atta^+� Ias&h.B1A�`. B2})74 aax�Bfeta (� egin"� c@{\p}l} k_q=eP+kA & & p'+p\\ k_d=I���P--2'-2���qTM_eta�dha�4=1!O4#�?re3ed ain�&�fGeG 0*s��in|2�/�vthQ$2�&'�:Q4�>, but�7� �0��i!��lyRKI��8#6im<2ria�N�>thea5, nB�@��3 #quickly � �)choiceA4!5 �exchang"ArA~��, q�3�2��!"YMu�] ab9B3��ex� &t 2}�`{qA��{U �{ i�g p_1,  S^T(b� T}(q',q) &� bar�v(^{jT}(p'_2,�+ tj�;�Fy7�% ) �]��$!�ea "6�1a�� full!�9l.\by" m�"%�superwpts $i,jU�2? ta[$I@s $0^+� 1^+q#so-�ed seag>�s5�s~5�26,�*�byj�5=�sg�� �n���( X1Di�q,q',k_d��c (. \nonumber:  & - � ���:PI*�A*X5�8j}(-k_q,-q,p_d)� )n IEN5����, againi�2��summe�>�3a��5F�N�j�q�5P-\�H�v��q'6$' %-p-k �\ p_1�p_q-q)/�:!daT!2+q')/2/'0�2_1 0.n�&: 1, 2= ne-�+in~9l� <�val� (Gau{\ss}ian��dr�C$� rema� ry 3, 5UmtwoBk�)wK7 l=zm�0M&-Carlo 9hod#,%-� ULthebibliography}{99}a?hibitem{gao} H.\,y.~Gao, %``�� &�BS4factors,'' Int� .\ Mod.\Q l.\ {\bf E\,12}, 1 (2003) [Er!Ym-ibi-2&567 (�]. %%CITATION = NUCL-EX 0301002;%% \�Lleeburkert} V.\,D.~B %�T.-�!,H.~Lee, ``El� ��$produ�����.8�region#.(-ex/0407020^� 6�,jones} M.\,K!9T {\it et al.} [JLab H� A Collabo�'n]%�(G(E(p))/G(M ��H(z�d��G\in e(pol.) p $\to$ e %p � ",.\ Rev.\ Let!�%�84!�398%�0)Z�99100056�8roygayou} O.\ G ,2��M�-�"�ela�E>�]| ��$PHRVA,C64, &6�v����< >�in B� -� DQ**2 = %5.6-GeV**2�n� 8}, 09230i�2�Vk11101A��qlaP%}6^%�1Iq>E|5�I:repancy"�Kp�A2�m]�T2�5�9�222 �4>��& 90116�q $n} I.~A.~Q6� ``PM��$Rosenbluth.�!�� �Q�]��� 1001f6�m�1�J} G.\,A�Y�΁7R.\ Fr�J!wE���#�$�'$F(2)/F(1),Q 1,va�&cIthe %non��(%�=he� yALZ�5!�65205e62R� TH 020102:�(boffi} S.~B P, L.\,Y.~Glozman, W.\��Klink~P� a�'Radic�DDR.\,F.~Wagenbrunn,�M``C"�A weak%��J.�aba&�/"�>  rk %5% Eur����E� A\,1�C1ɻB 0HEP-PH 010827: fuda� G.~Fud�:$H.~Alharbi%�Xoݝofɱs&=&��eŘZ�e�640��3>���8, &6�A*!�0\,J.~Brodsky,!,R.~HE�,, D.\,S.~HwaLnd�(A.~Karmanov�K c5�s"Lof�E fronn1v&�K�aubQN4r of %hadronic2�V;D\,�;760^;1�3112186AZv(AUJPA,42,12:� hugo�,H.~Reinhardt�H)�� Of QOFlavor D�,��B.�B\,24a�316�9B�4PHLTA,B244,316B>S�s�>Ca�2ion�D�M M�8In1J �� �^,D\,36}, 2804�87>Ei� D36,$6�mandar��h�s8hagwat, A.~H\"oAa�rassniggRP*'-%� Aspe�In�/�8c�:a:�C gluo2=��C\,70M��RB����R4 :�cjbA0Á�urden,6��>��:  =�EZ��47%�j�476�bentz���4sami, N.~Ishii��B �K.~Yazak�SB7���ޡ:"�9XErba�Oo�4 %Nambu-Jona-L<6io��b� 51}, 3388�95V� C51,$6�oy/�*�/G.~Hell�<%�~Alko� A_BOct* nd decuv"(1���b$�Gd0 D�j��Jw C\,5�4245��98>�Q�980505:xhecht �\,B� cht,.�A�D.�u,v0$M.~SchmidtJ�0�. W.~Thomase�Q�mas��5O �E�FL�?� 552�N20F��� 8:�birse��%� zaei� N. Wa\P!u� C.~B2X � ��iW?\~ f)�� lo+NJLU� hep-phk 8233:���46lcjbsep}%n� L.~Q�>�.��J)vson%wGr�1-st�0s�r�li�N�� f?!�264I\B�1�960502:+�Ss��"�2 %``ELOm*A��M��Few BSys��^3�4" J�p20402:� cbm}E6�CHSymmetry&� Bag8el: A New Start�PF*1�o ar %A��2'' Ad�A�>Z13}�|84) 1:� ANUPB,13,:n �G D.~Young� Binweb�A��E?"4,``!Eew?486�{<��U�?che4 E� lat/e4>�A� LAT 6�$radiiCh} E� Hackett��M9� .���\-�@ A4Incor�:%� �s1�z xtraR��oc�zb�  % "�V�Ak"1:z 48� 1430 0); 6o�00400| a E.J.F�J�5�����heavy���#E4F� %!�2� +%�{��}.iV49d 89 �:��80j ._yA�}B�� [4��� Y�!�m~5����&�W��M�(�ax> �86}, 501�*1B3��12w%/"3�� rev}���:}� Dyso7�+ er e.s�7 toolN �  ph�6��29�B��nV 04:� lane} K# Lane�Asympt�: Freedom�� Goldw\e Real*� -���2m� 1 26 1974>;� 10,$6 politzer}� D.~P ��0 &z �� �L�M�6p�B\,117� !G 1976>�0NUPHA,B117,39:�cdragw�&�E��$G.~William�b2the�HppJ*S toMic. Prog�7ar��J�33}, 47� 9BnM�940322> owmLJ� Z� O�~ J�[U.\� � �db�.  ``)��Lag�!��L� u% 8Laplacian gaugem@lap ferm�)'�qt45�8re�Ms!Vrei�+2 !Ŋ 72xfi:r!�~S.~F �R"� E� Non-�"(X�s, �  coup�K��d�al����� ��r86A�09���B�܁�S9>�%5.3(M.A.~PichowC.:�P.M<�Ana Y�G"�N�N6�Q9a�F%� � 01520�KB���400: �� ~c `Detmold�:�2h �:uE�K2��!� �$J�D14014%�4>c9�907:c-�2!����.� %�eW2�n .2�ataV���!��b�40716>�ishasvy �A.~Iva' Yu.\,L9linovsk� J/Survey!��-��^�?fk6�i03401�B�QD98120>�I �R�D6F ``O�/lex��ofJB��-t11065:U �0 6�cdr��\�E > )em-�Eneutral  deca6%dthAJWA\,60� 475� 9B,M�9N�b�. 6��!C2'~�4�S� 0B� 5700506�.� a�����0L.~von~Smekalr w6he�Er�$*��� Gree'Ts:x>�5�,�� %&� breadY,u� PO2Eb� JE�"� Rep���353F) f� 00735A@.  markI>�])�\ .9�$�1 ! : 37@163V� 371,�72� r97}�� �B%:�w 6b5� 3369 (19jv 7080�.w simo Cap�k{�@-, j� %�I�2sB]�8029.�mrjbPa�C:����\ �Ce�P�Z?��i�yan� �f:�42�$2�"1n707BeOA re1}� $J.~Munczek5�:k17a�21�.86B�M175,21>� l2Q��"�)b�>l M�>�28�3�9F! �285,3�.�st+��~S )�ro� !� ECo�EsNFo�h%�OC�] ned Yang- s %F�9�{-�]�.|38i[86Zq$)a651a�87Bq$P�! D34,M6Qk* �~K 6 : >l�On�2'!Of� z�A\,� 560� 2># IMPAE,A7,#6�ahlig�~A � ~" C"� 2���EC H.~eelU>6�6!�� bjk 1228�.?hes%~Hess,SKafF, E.~LaeL\^I�tzorke��``Va� UZ� �� V3� 1115i�Z�98 A.�S dqff��cH Ff& M�of.��&�UF.�em�-c�09008b�6�pi�h�%ĩ"�H);:�hs�O�DTX -XFD� J[� �Dp1�99B���99H�{>RJ2&�0);6�I��&C.-R~J+""� +K(l3)!'�S� *�(N�G Q�3F��10205a�.+)�e v�F�!5045�&FD}�'3>�z comp��KL.~Von � %�&� ��Re*Ot�U�.y �srJy  +�  %sx�a:) �H�hypCommun1*1���N�9 010928� *�*bruceCBM�!�KPmK�$I�Afn����_ReF,zed Pi N N C�C $antť.P W�",Phase Shifts�Cloudy&�ZlC\,ş99�vN�l(34,99�.<i}*��NR�1|2�; �$a�!��HPQ2{Q�:�43A��:/! 431,>�I�pB2�= ._E�j M�E�Cu]]� eVX�&�E~"�W�% �1�mb�%e220f� 99090��.�Cd� R.~B�~"g!�&9�R�\d(.�&�2!.h-�2199n605:� bc80 �S�Lt,��T.-� ChiuZ�2��2542 �#B� PE� D22,$6� bend9�jKB>ne.�'�i33!1J�  10,$6�Hawes"� 99} �MTww�5ndB�%�>;.�Ak2C%���*6 m 9e-71�&Z�980602:�Salam64�~ %@(R.~Delbourg�/���� �fs� Sc|o� V�p�^ s. I�6�W13+ B. 1964>�I 135,%6zbrK(�&er94�c(�b&f(��Uni�Qla!*R ���)"��1�O!�F�7 %syst^ ':��D\,4601�1 6n � D46,$6� &�[n��-��:ZS� fL�!452�B$ &�!1������ *�#y�%�F��cp�Q�tZ�� ��!~r�55�B]�006B�%� gppp� �"Cotanch�� @!~QCD %�2J]pA2A1pisc�cr��up�( sigm�)rho %"26(IP \,6AQ11601�2>� �21015ES%aRB.�b %``Lad�U>0�Zn��anomal�eg)Q 3piE^ %�!�*w �V� � 036006�\800:�drechseliPergell, U.~G.~MeissneIS D.~D ,%�Dis�8�theoret�`&[r �n�ToB�4 %���e*A�&s %�A\,59!�3�b�50637:v Walcher03�;~Fried�x�/T�.� A co�7n�o�bS!��| �in�Bs a %< ,Yk�A,I��bT�=�5:�Q�303B�&gR{� S.~G ,Kle�8$J.~Moritz,�(H*�&D�g1R�J eckwenn%El�cё n - bVer� yx��k �. ic N�on5-F�6 %AK$ ur Mx�^Tr�|,s 5-Fm**-2 <53 < 14 A�J!B\,!%22� 7B4� 32,2>�0kubis� ~K �6�� Low !g��&+��Q>�.-Z��7R6�5B�1� 0070u�fuchs}A�F ,!�Gegel�|ndASA��.&.:�inT$��q*or!f��3Y2BR�3�4��ashleya�\W A��%2N#�\AJ[2��16ez�� R�h3�:� walka{� �[ker6�4�*J6�FC .�4�� 156/c**2 <=m = %3Cat SLACAjF� ( !�567e#FE!( 9,$6( satoEhSa�Gndt ���9��/al&�a @�i�J0in N(e,e' pi)�^�'e!F�LO"6� &ap::�r�_�� P.~R e� P.~J�=�a.�!�"h5�*���bo2 5300�9RI� 204}� Ag��*� `�+v\a�% !�^*�PhD��s[]� �bof T\"uR�/���0S7fp206:� �|!X� �C.~:;Pseudo��o�e���;, pi0; a, %F(pi)(q**2;V:.365�+n.406B� { V.~B , X.-d.�F.~Yua� A�?>a{ �!Zeo_ Paul� P F2(QR�L�; 91_9V� �w 2123� �?>X> doc�v} OH\,class[aps,ammg4h,nofootinbib,*Aad# ]{revtex4�>uc0ckage{psfig} .�>icx2[� n1]{�yenc:Hcolor}idT@{Trot}{rgb}{0.0, 1.0}  2,joerg - 1.0,,,0.0} \newcom�3{\thor�}[1]{{2^.k #1}}:2jrB, k - 6a nn}{"�B:K be}{�AT)>nbelo>' \K #1} :VeVe.!�:!beax�BF$:y (ryX z .} \re.pd}{�L def\btt#1!zt�Yckslash$!K%�\BibTeX4PB{\sc ib}\TeX} \addto�z0th{\topmarginA9cmAPbIQ�title{B�&�0te $T$Oade�&m�$�]$���dilep� emis i�5�,i�;llisrauAc0{J\"{o}rg Rupy �vmail{r 0@phy.duke.edu�L 8TM�k5trenk63 \affili� { :hb�n�/\\ Duke�,  Bld�e�a0Drive, Box 9} ?,rham, 27708- NC, USA}OHabic�vs �{1!�Ea*)�WeR self�|��l�n��o%� �zi.�>�C��.� �I purpx{ �d&{vttempeGCre du�K I@-$\pi$ *�IFinv�ugZki~3:� $\Phi$-fUzio7ca.��6v2m>}� !�o!3al&�#{� �[�Yiscpz kX327 show�ideebruAl om6fsonqJ�]ertw v&Wl� � �Elevel. U�K�s�]#D.� U make/>ltoJ�6( !,CERES NA49 c.�C[VR�a43�fireb�&�y"�Ce�. W omona=Wa�w�I52�VQ@-mediumb��!#sb%~u� >���enhanc� lowAkag@ts)�%5qs emit�Min A-#���I��y�Wke�R&|XInt"�E"NL6�Nre2� yea1One�*PdTe�oÍ6h�� been �ta�T��uF%�p�0�_�-.�& �)As5� s (URHIC)I�ing goal�N @io J a4Cter �>*nof �3emely hӌ9nse ar m�wFS %�!�=A�e"�p\�qs -�k �&�d�act�UA�er - difV.t m�6.�� net-G4de�np �n�ar ��� e��e�ul2�%2)-Y�Dp� 2�2qsum chrom&�(QCD){Kh�str���B�Imk!l�r��.za-O6� �)� �'sHst!���d� s (!(ea=>�jec�} f a �2-�"!B  of (�:ed)qic}i�( (partonic)!!r-,-plasma (QGP;s:Nn place)�8aDdo�arZ\ and �reh!��l:�.b�c���*�, . Di�(s ($e^+ e^-�Tmu^+  -$ pairs)w�l !wsA3)���ng!� bes J�l�iex�Mno7E nt S�py>��du���Y�%_s !�le !t],E�͆out�wa�i�_&�d�#lC{n�n�Zl��&c� fnE�af)� wss -time�= U�ro!{�}! rast!�� ic p�ssPT��o�~l2ts|Jʑwell zn8���1W�der`�%���kS ly carry V?early, �B�be��,�3^� TPa�hK_�qa���t("�q:��|r, �U �z%�!e��littlea�� to assum�%q�[ss��8 "��Iabya�� ��a QGP,�0aJ��H��e�1&9 ��*U!cru�T �}c����0aEO��pi��-sihBL..U��zuL ��3s�lA�!��fib�my of iZ� of ��� i�� Z ��HELIOS-3�"-N�d" �at  � Ŏus-  (A-A)?^ �hP�V�:� lowL<9����range�wA $200 �{ MeV�Tnd $6: �]i���$H� ��;pDE!=c*ss�!h-z%���p�q  9���Masera:="ck,Agakp%ev xb, 6(7au,Lenkeit"$9xu,Porter$7rc,WilsonsrVich8l hint�-suo*t an �7v�uMr� �me�W isms� ughtA�w��o!"T~I .�see� %� Rapp� 9ej}�W#m ofte)g���xa�J*g of%�h� �EQ8pVnotk)�_Sa�� 7�w �,ixsumvi:�sed� A�N� %�R� B4�!!  �rho"�RB) Gale!1p �*|� &=\�izA��-�2cau��Wt& n icń nly.S �1 =� �:ri dampA� q>Y�al.�E ign�z orNv{�x�ed6dΘ work) UrbaE�$8eg}. AlthAxP��v� 6�e�Bs��.* of % Es��TmalI)�U a"[%#y�*�J\�ob[]5��i� &~  �6� �}z!�MHagli% 4xu,GaoA+8mA+*"D w� en�mA9K-�n "= 1~d� zff-}�=uibu!Y�gII��jpaperfY�se.�1q��d��i��z!�"��a .�al�na�!0� duce2� 2 QI�s'sJ6t6�ma��r%a�of �a� ��TW a T��D�]#]A�w��isb�# n�%|! !x�e s#�vwi�lVs�� ��2ors���2!� �I�.�#�E*E�=t}07�}e ��&=v�2x�y��ieccv��%f�=m �!Sa<al &. Rcon_te����p��fo}!�"? a2�!l"U I�/�,st-b"�v-�m #QBar�h(*A� lem�<r"�-) a���r86 � �imagin�a-O p%��! P�"Vm0ai#�)Q`1���e �ff�,k]A�rai��& < n��:%nel�2ve!4uum�_�ed��R*�eY disr�,� -�����(��=�,p ��off!]�)�%�>|F��X) focus�o*� 68� e.�!�W m�e���� e6�,&1 ��*2 ,Renk:�0md 3huJ ���p ���$isI&y�2�$a# .�">asIa�BKt��� m.2��}?.�R>R. .V��BdA���1����!v ~ � 8&�!��eedp I_"�.� a!`Zhv ��V dI���w�%{�8�f��b�s -!<"f  - 6" 5 6F4 A6Fo�is��erfolB �� � �a I p^.5�,A=�csusfu{�o��a a!t&�*� , amtheCarmon4�~i��3 di��"���U�,>�iE�DHanbury Brown Twisa�"�.�� q�4cj}. ɐ��% 1c rganRa��ss: Weas�)-N"� ��ˍp>M���-�S.d��a6R��"��L� scri��8A���*5�Scd-t Fj �} M7Wev�d  we ' \,t\"uckelberg`� �bi2._� ��ii#� . S��al� ��tF\t��F ly four-da�AA]�]#�� H I od� !� � �ɐ�to vio#�o��b%. Q�Y�s2�1yse�q)Lis����   r�� }# a�+�VQ@>F�sil P�%��;!�%�^0.� � .m%K qual�}&M�Mֵ� c �����B*w . Ser') QGP� ai� brief re.�!�C a2cQGP��Ur} deals� �A%0� ; A!��-K:Sh2�� shor�e�h c�% 1>F&u . FiE�a2'a=)�уwC�ik). ���� =a��R���ٜ�]]&�?�c�nclȌaza �tlook.9��^EyQw�.  �"�*�}# � rict: > >��  ieVJ )��B�,��hasizV>s� �/e�"�A .��e*} �s!�nS EV s� del inspi�by21� ce (VMD)k LSakurai:1960ju,Kroll 7!� W"a�=V��F.�m .�Pd�� .�2��. �q B� �� Ŷpiate}�dv/f�A|"i�]e�� 2�M6� � 2� ik6���m � Stue��:1939iE� (p ���N���is%c C7 also LRuegg� 3ps}.)�suita�)1igA!�}�Šfoes �fi�m�� �$HendrikDisI�I:�ram���Q� �4 ad�J-c�7%��so� led St�!3 ghos$ phi$Q�ee�Kg�xN6�2. b $A~r$ �WA�fd� given by:�%a ��L}�{S%�}=&#n4} "F"mu  |^{\mu +klm^2��AIlA } �l(\�ial� �)^` phi) + m  ./ A" \,\,,\eea� D� �,�=68m�{|nu %!4 6�%� str��tensor. �+� EJI=:1941} 4�.7��F�"<a "XT�d/ (7a t�pd�9g�d)� ſ&c(�Y|Ae��p"��s:.1�a) &\�m^�& AXz% +(w (5FAlq� \, ,\nntr%�2V%�'=T m2F.%� T!A�P5h:� i.OwheYlntŊ%�. Appl��(�Qrd�?u�Popov�\TTG �q���a �fixy��$R_\xi$- ��+5w fix} g(A,�):�A�SsxiU� ,\, !�j� s af$z # A�9�Aefree L�yn2G�J&\����J Fa=�� eta$�:\laar(effLagPiRho��M eff}&=&�L1�Jm^2>p(%$Jm}Q�!�"5 "� ng � e"&2� MP��pproof!/A���8d���to .�(� ur�{5TEa ).�,vanHeesN dk})�Z� a`"n a VMD-"N * d�}! k �& �$�o�wi*�y+%)1 -/-� byE�%N��%' ^0 \ه�^*2e^+ +e�& v.9er\ virt��$ $P� ^*$.;n:+ð�:� �� 2f s� 6�  a�iI*cd "���y8 D� e�q�E�t�&�$"�@ �0k ��zTa�a���*MYv���L & Ź���O��2.�pi�� ��[6\+ i g0 e  q� lk}"��p�{]�i��6T��Hg�� iSZ 1I7)N�� &&-m_{�^2 \pi fpi 2�A"�  &w��aMa� ! "*(!L-�j !�E��-�%�:6X΅} 6r�0ho� .7"� e}{2g}F%�� 6z   � , Ł re& %+(Ip$F2 �>� "6 rhoE�I�,lMo�d� ��"� \�64�{It��+�% ��f�$negt)s *!s� a��w%gAR))��f is.���a�� .)�&�"Nly =�!��a��G� w umq�"�E�"�)�� }s6tWc)��olV'� ka��"%m$EY� �/ H� �}��-�� tjL 6�&�):� F� 2}7 E�piA�rho\|I�rm�}+ +r.�  ,piG�,.E��1h�"c $J^h� $X��(�&�� by6uStromZ�J_{�� h}=�e�g+�%}alet}i,�n� -}{g} m^2��>�� �%�D�n� $e/g$�/�3EaM�M�A06� �~� &VMDm`�+��-�s-i��."�-�|��m�M� �oU�(QED)��n�e�m�����q";(��N��in VMD � endixS8f{&{q�\�{S��"� }$!aB�� B�" <�"ha�2�� a'Bay� :1962sxT i6�" F�i�ism!�^ :+ly- N(��]-�a�3Z*al &! . It��e�&M�ckOof �!iwX�umɺa\oryqCornwa`FJ��w�= Tomboul"��&s 4vz!�TA�nbe�{!4.&m�N"�t�1��."0$-� one  �&�J��r !o��2� e��N!Y*� &b!�:�?�: subeCe49"< sV�S�J6n��-1}(K)�� S�o�^+��Pi(K) ,c�V P}_{2G�P.+ A.:9�56��$�{S*P}$�B�(JJžŦQ��5J:+ $S�P$� I�J�jV�gin6�� tree)} �� DŪS%g2\!?( (K^2-m^2)g�-O{ K��nu9�PT-� I~ &.�pi��Z�����$�i2� �-\Pi5>�L0�':��  �> as"�&��" .Hwo&�irreduct4 di�ms $V_2$m�!�Q �1ey�a]_Zb1@!�y.�8\Pi(P) &\equiv&O . !|���V_2 [= \x�S}, P}]}(eb(P)?�n|_{S��/ S}E�{PP}� \�}r,P } \\e�q��� m^�S��R֦.�N T�'� Z�Ɍr!�.�*O*solW'��?�2e. A�8atic ��!��u".2$ �.{ cer  CM�~��\l'"&w u ��" 6���A�+ Q�V2M�@V_{2}=-g^2\int_L P (2P+L)� G I��y(L)IP!�Q�(L+P)�Qm�e� �$&�%r�Sm�j n�� fig.H !}.i�or is $��t_k\f(k) iV, T \sum_{n=-j�A�s��R� d^{3}N k}/(<� 3 \,u� f(2 M i n T, + ) $.����b���ce�}�e�D��,8cm]{pic1.ep�ca�{O7% A�-��!�6� %� is �+i6&. Via.�K2� &�O����y6 � u ��&�-8�.as1�r�:h/A�7�= wiggw��r"ϙ�2��o6N solid :�( }�h)8tob ��ed �)L-ly."� -f�Bnd9� 1�' � "F�� 9�+�`="Փ�yic�qsH>-�!�,)�$U �� -%n �Ee��T�6"� F� ;�e&�� Ve-l�@ "�xng%ZY !�AZex&�'7 �Ys 1.r�o eqn. {H.)2 ���T �!�cutU�M9��5�OE��&aA�ϝ25way%b��)d�- ��n��EK (�F}) I[-�F�+ . Be�3 h8�� a�e˨P.j2}6�h0�|�, ��a6�3languagP9�gx�:�&��Q�\5-- )%v�9!�� ekb�ar��'� by^:6�o�}  =2�  V_�d��� �k}= -4ѵQ��-QŮ nu 0 .� (Q)� (2N �١�a���P:�� "� N�i � = -2�(2Q-P)Q} � <P� �-Q�; fR��!�!�se !8I�!��+sel-�&�lS��mj.(  3Ţ>�2-S&�. Asv} ����� ^ "�H��a *X�'� libriz0w��9"* retar�6"A3Q�� KaY](Vy�3�y LeBellac}a�a&U���,ly)��4M��&�-s.�-at�-�rec� !!�averag/a�leH� A} \J# le$ ��v'�Go��hat{A���Ld�.��� $F_\beta41}{Z()�(rm Tr}\big(7 {e} ^{-* H}(��"��H ��*���1/T� �2r�2*�H$�*+�%|sum. 1J�0nA�14as!s� a �.�`$R}(t) i-�( \theta(t)[�A} t),nu(0)]-�~ Ȕ Q ,r"q�g� � f Fed�T�R&��er�4!��=�&�K: Es:5 � (k_0" � � t_{B� �dp_0'}{i �LfP�UG��}("U}{k_0-+i% '�F� \nnnLBc.�&=&���� k}j�2%�)s/ontin���Matsubar%J��c��o?Al_G"�per|ed���� �(DLor.�-& in� r*is�3kh'�E4�Ѝ� �ummHs�r1vred-1)�%e�Ae x ial -"�(�3�2}��l��,�s) bec��2�� �@�!�Y . Toڼf; !l&� � �Q�2Ej*pr�� itsD� >�}B� o�%L ��0~�itudi���Es. A �� ve2@��n�� ���A��=� in| �K /(or} . Ever#�7(�1�it�D�!}#m�N���z��6oU(A�or�a� !�s O�B�G2 jE EC, E)AAe.r I|}).�6v\�U'>~.m>9 via21 spekA�dichte� rho��A}>i -2˯ Im}\���10&�p���C2= D^{�R}"6.� = -\� \~�k�b �[ ~� .] ե��>�S���S�ڥ� ^Z�:W��#> s)HB6 , -2)1Iݬ�B�u�+2��<O�<b~:���< � Y5y��JY���\Y!.MC|# k}5GY62�"*�( k_0^2 kf C)fF��f �"�"6 g g�ڋ ���.� B�)� pJA�675%�%r, �T+_EN��]�EN�!����=��b ��b2bE^ YFK��� � J ��re1��F: <> ''mͿ6�!Dmu&�L� b�KJ� �!J�m�E[ AMo��%$ +I9!B !�2 }+%: !C !.�2BE !.�)A�'b�8Ϝv ��1In�1"b���9orN 9:q)��2��  !Zeq|jK:�)�* to6�(1�w)A(.M\,-�1�%W.p� i� p}) Y -%�2!=-:� )�[)� 1}{P�+ea}�!] ��$\6 z�F��� ��d �bP) �-$J�C����� -2 p�G p�G .�24�� ���!-2 /��� [- b� �!i&�$/!r e }{c1z� aJ�E�� >�z.3����:�\ ��J���e6JbR��d)a`?  $_l" by��=!=m@0 Pi_b)>%�5��c!�+.hD7e-W � �2�� e+��h5 _a0r c$�#�$ i_e$�HwN� )b&y Y"��  i4+�&e&� $3F 3��;�jp&�� 6�2)$t2�0 ����[fix})� sp ^k trunu=�S�(�l���O sOY��=Vaoef �"Kdig !�n"%?�0N�cuyss 6~ globV8y��ab�t��D�ed as �ar&��"�qgroup��al�EV*�0�y�or"�Wy�]Φ� is g���A,hJ�\:�Cs,�Sy _'^ j'.&6NIH\cheY!��2ex n"���Y��� Ta6���z,D.� !\�@p+6i o ��)�>c�Ug* �1.serbPpr��5�eWH7athF� p"mI�EZ-+H2�:O p�!be�:QD)�� )BALmU�R2:E2 iJ(�[�4a�a�4p< a�wil�&� ing 3�B~�!�&i!�( on: &=.Af �Wsomew�s��� thosLQED��$ PYl lrm* = � P_!,/P^� ��&Q�Ձ* $P� } .� ^{QC.R =��$.}E ���Ss;�Q� xi�u �ŝ�7 m^2"Q�(� ��ed)!�Q)�.I[��'} �$]1&��iu:�. FF6�con =��Llud�I06�Ca�in!�.�e�{� �q.�on�D�> �Teva�͡�U'_c)� e$.��SF�8�&go��I�la� i��poi�o-O� e�n+,��Z���`�-)���&���~rua��O,��Ffor:�>5�B 0bp}, buC�sohv+*�3#�9 M;.p�A��k�NaeonSmeka3, 97isR-�na iF%X�Is�|2On7/�inkI��4funda�RѰ�KK��6]R�es don'oapM �"^e'�log:2poi���@, �wL9# eres� %~CFro9>,� 2� s�N�A it's"2F]Y.B�K"\� not C_� ins�*[omp�G �&1*I�.� lH�-�!#i%��o. But��PQ��R@0! VMDUG�2 1!�K*j728,9s�GZs.�$�j����QQ&�QQ � & ��-aFALz�^_�� iven. E&�#� Rho��})�Uf a� - .MiZL�>N�m;.J. Ct ��� %�!�QED� ��d��E�r�Qw�1 tell�Q�l-"@ J���> 3�f�J:����=0$��o &� ��J��"�23r4y�)��W!6� v :%�6� �*� � arrow 0$ .��s2��*Aal�@u��in�0Rm��ZRQP�.g.GOMaa<2if}.�!is� Hz&� .�J1�7g$(!@�rhf�" �*p( >iav)���6y �2�bM" �� �>��� = 0� R���^�= s.��"��ofr��_C� AgEJ�� �ܡ�"�N�M�(Jq$� �4&} =0$W$`=�6;�>Nd�9� )we�N?W�7�G:� , mai� Wer6VZ�2~.��S �96�#.� w�Dill���MR� "9sN��@"�+��pZs ��? ���mjI=�UwZ}���8ech��2�Nz�� ��"&1Kach I}"�?I��*�� �Ge �os{A�J"\ia3�zi)for�E�.Y)yI�$6'-exJ i�U�e�@ԥAxTe( }) (2$Xm/\Pi$)�3�� �Fb8} >Y.IQY �d=}���=&o�9��.�� t�X%�� =<�^hs�myG invoaS?mC�x 7Qg-Q��ed&F, �Toq��.�0r. "�9�� -r&�g ].~�c2�+P x�u&�U9� ! i�>�L @ Knol� 5nz}!� ere G eg*GRhc(?9 m`�B>"�l��* ���a%��� palu le��c`^ a�"�//A�G:�>��E��V �Z� �ar _S~�� 2.w--p�)�Z�NA��X�1A�suVmu�A��Cn h)�:>�Vis&FrZ��"K e�;��6�"�%/$%�1�<tw�/s.a�J�4�K�;���)jL iSA�2"N(*O)�r� �.$ \Pi^t/@�1Ileft(w� {ij}5@�* p}^i0 j � 6�8ij�-�$^\ell(P� 7_i:/F R_j �J442�:"��e�v�{at & = & - v�_#Q�-b>-�P��}/^{�*D.r7| 32���nc�T), can be justified. IQ�,Gale:1991pn}�,$\pi$-$\rho$ �-�xhas been studied perturbatively!�e valuE�! 2�rel*�4vacuum) predic!> from �.Vkymmparabl!5thB`!��expect!�AXm4body scheme. (E<is�=I` �a�An,,� E+ wher!d�$��!IS��.th9�-Q m� ,tum vector $D=p_i/p)�Kfo� co�e�s2�2} ) �(2P-Q)^!� nuA�2a�0+L_2^2)-L_1^2e�e�e�Q!, Q)+Q^2} jS 3X- X ^2}{[m� ^ \\ .� (2p-q)^{i j �p^2+l �l^�$q_i q_j}{q �RK � p^2- P�S�. %�1�L_1=Q)� $L_2=P-Q$��quant�  $B, S$,i| p^2$�U%�squarea� ree-)�a.9 {10} ` l_{2 r 5�0yY/�*� 0L_mree�] We obtai�dY0��At�  the ��"� �q:. Im& �Pion} e LIm} \Pi(P) =&&- \pi )b 4g^2}{p(2t)^2}\int_{0}^{\infty} l_1 \d N 2 \d!S - 9B jB!E}{2\pi} z. )f . a�A�&& \timeaL0igg\{-\left[2A,2|�<BD\right]��a(l�$,l_1)\nn\\e~-��[Ft+Fj k�PFH�: &&~ (N�o �b2��}��20}E�)9~) \Theta%(|l_1�|\leq pl_1!!\�@ \\�@%I1+fh 10}) 20}) 4] ��(p_0-)5!(.e�0 To determini#Limaginary four-dimen� ly&�m6 ��y $QΡ��ma�Pi_b$���T eqns. (\ref{XProj})(wt $X\+v\Pi$)� u�hu� ����2jY 1}-_��(2q-p� ��y+�x)-p��Mi!p_i p�p� @iTJ + O!�� }3+ ��a'�0?0��-�1�^2r5_{im�p^i}{pB - �:K2�,Z�qWe ne�To"[ e =�Aw(IZ^!E!�I�$,=�, �w^i j� >6c 7\Pi^{00}"%��.%i0} c_i.�Ms�gB by: ��gin{sub��s}� 2�rojRho}0a Q�A��� j � �&=&-\pi-w2g�����@A�B�l��{�L��~����[2I,2�]_ MY��rh��l_��c HF� F�ڥ� w~�aD&Apr , 3B�Q�eKq {%�^{������n�n���.��B9����� E>^ .i u� \piVi .�L .� i�  b�= 10= �k >T �[m��<)�"�10V���>t2�[J�� �B�� q�%�v�Ţ�� H y���)�.  o������^�� 6� ��j�� ��"� _ 2�N� 6��6� c%���� \end6� W Cz ��"�b #yA8"�-d� t.� g8established our� &�lyummed 6,�E sol��:�numeric`. \s\ on{F�b dth-"Wsue��} �ord]g�ins3 Boe�se ����modific�%�2 result � 8mal)ach�Xvi� �t2�one-loop"a { � (cf.]0eddes:1980nd}� * %� As outlin)4 last�� workT$\Phi$-��"�)�.(R_\xi$-gaug!�th $\x�b(arrow 0$, �� choice&�!wupl �4St\"uckelberg A�H Fadeev Popov ghost.1��field:fulfil_!�:I cond2�e�4romagnetic cur�(tv fore!��� QED )Xinvariance). Nonetheles�m ed b Becannotacvio�-@Ward Takahashi idG�stemm��e6=lo^>� by !Z�ach# at!�whyb alsoU�$our methodA�JA�l.� benforce��bwby6.Xtempoa��ibu2�(3is spoi%�somew�Ef�)M�&Augg5and�Obyml>; in a ilar�(el�cone �A�-i�*�.R�f�!`�exten�i�fluence�e � )�c �ii�discus 3*�>� fullj1 (referXoU���I)%3 G6�-IA�A)��FfSI){T��&�� most iA tant"3ce betw !v.n�es�H >z is� at D. ly��ed ���]m����y show�hreshola�havior:|�}A� like � N$ if $\sqrt0<2m_{w�� $P"�� ?um� �.��A fram=mediuma�is lead���a  eris��-� dilepton-� ra:� pairs��t�!bove $2 ��emitt C� derA9�94.��2~ �2cH !.�� \ed %M!�a%aO e f smear�X��.,=$b1�EQwhole[um �BML1V�com!.$ccessible.ar�B9�ought�7b�ns!@ede�n arte*! d 2�*.z ub�{Sf"U������+ ie",� ' art�1���", E�bB%�v2�"� _F96%[A�.A�2�y-� o��Catial-��e�K{�IzdV9longi�!nalq6 8 ploA�%�"�!� � a fixed� um $p=125qMeV/c}$y� � i�AAe�t�KeB$af� I!g y}(, !�middle)Abfigure�&��er�4cludegraphics[u P=17cm]{pic2.eps} \cap��{��"Bu�sVz .Y]�>$!�Q  7.�,6l of1lat��ons�H.;)q~%�MeV}/c$��!' h!(a`%1�p)8�JE8�t )�^sF #Ak!�.�}� s us�'����ퟅ�U�A'��-7I)�l:�A��neg:$�P�'s �IS is depK$� m h1?e%6�^2"a� too small��s�� Z scal�� E�>t} �!j �}GU�TQ�# both �A/�P14� M�9dI2�^2lMEɎr� no two-!me�^FF6�>na!�6o�%�9�%�%)��on��nd�A� $0<\"�= (p_0^2-p^2}<��� {y proj� s�"(up!�po�� pol qcuts)�(aly�� ��� lex )� -plane. PJ@U�( (axe�"r�6 ng��6:F8�� se 'te uppera�( lower half ��)DLeBellac}. BecausQ� �-symmetru�-:)�~�.tU�s � �ed,� "_�rh�*�($ stillU8% �� �$R_{\xi}xeKFw ">1��herv` �$ hadronic-Z�^q=�!�d\� Q���zdomin��;+ �&umidynamics� lreadcus�n,�.��strengvI��CJ��"yW-t. e�ua�����Q6 .g- M= rhoall}�� �]%)Y.�A���a2� $T=100,${�� $��RVa�*"m�)$q��'ed%�-�E�=�9��03:(Color�� ine)�b1 .�n : -l�Vs-�"a`F!�!erhoM�a��.��I|55onA?2�J!�MeV�GU�� *� �M7n� We.R.� 1&�4�2� f�2�2��4�Son.�B� $��ai$9Ef :`���x Z��e� b�' �O 3 *� !�Z�U4��5Q�1.F�1{Z���b�re-x2�A�6vI�a�ZA�/^�I&%v.�r�anf�appVes � II (s8 ext)�2�za^�!!����resolc��M'qcal&n u���3�3 curv�8r� ��mR�n�d �63a�]D}�q9A�R�]�sa4ea�� �5g aM4.�<5>k=8!Da� 2��0>B09H. � ri\  �e� ���� �6r �is enhX�2d .ge��aiderably$�!�.o� Z6ed5�=�!�2t��.��!@6�ulKM>Q�al�d� cal)92�nkq i,{"' �e�F�~nta @o�\a�cF�,��B�@J�� ���A�>�1�A�-c.����4:�6�A31 BJ% a��p�}"��m� �� .  appl�"9 .\&-��!�j�9~B-}E'� �S9!�q�t Te9aE�ʼn&�4A'"�0 . It f} eq�� >ƁKR1 � ���5:R� $"� �s�En!�&� !�����z�on�eq$!�a�� :w%�>��1.f��;B)6V�n�C�A!:.z20�� ober4] x�*F!��Sof6�"R �de�0roughly $630$% $910$�� �is�>p��aFtwoO_@���-$m_1>m_2` b�l&���_G -m_2*��)!+i.G1��*�s. ��emphasiz-w�u�H�-plDI�-�!��5 y �:� 2�)qs-m-!�_-M=� 8Tj V@(�+"�Js, chi<)�!,% scate+n!�f- baryons)�#0�Iis'd�dos�.U+se�A�unY�bu!gsh� 6feBdescri�'!Z��MesA6iU72?3<*K �+FQ��"q!:�%�| leteaYO)գA aT�4S͚! %P��j/r�ucqMnumber�O)�9@ob M �#@Renk:2004cj}. Her�  briefly����q-k3. �funda��Je%assum)r O�zA��mE&in �1m> (!�A'ne*,ari'J�4%@librium�an i i�M�"-#"A�l� tau_�!�L(ter breakupA�, $'fJ cŇ���,&A��# ] m A@(�}�At��m". A! N",homogeneity,.�  $T$, �Oopy d�6$s$, W surend5# poHOi%I$\mu_iQ well� "�,$\epsilon$ b�- ��� �Y uchJ#y�3-�)$!�%�n'}'ylind7�$ic aroun2e z-axic!1 beam �h�/�G�32�J2[ $L(!�)uJ*� radius $R $vI�+G8u�,E-Volume1} V - =�E _ R^2 .� B� ��vP��i�@Nd�L�boostQividual1Iel� sIrUq peJ-�ent velo�Q6.R2%\Re womQ!a�P$�$\eta_T(r, %N, = r/R_{rms} � !^>�126$A�ote7roo�% �G1�ɝ �atQvA�$F{9� rapid; � $. fe6=&�!�z " � rEt�9 meaabU  S � n�Bv%�R�1�" s $2�f^{front� t�x. F�P%��u� e6H5� {5$T�ki�70freeze-out $vv.ar�;�7�2 expaeKl@0�(Do�%de)(2_� ad afKA� a2slyA�ele dsu�s�(du��&W Ia�A�s$�%�#valid >Ft�I(��5� \ = 1/2 \ln ((t+z)/(t-z))A.��-$�� �e7c ��sh�Tb�b�+/�*A��9�-1y�7�1ly���#�+all?"�Gi4Ue� que�f`mo�I ID8ecG %��<� �y��9�s *�<,86W� ��a!��.� q�= %m < 4��.?s>� � �;� fall�!�s $� t.!��-$t^2 - z^2 aQ �E.�� pYn,(!�� [d�Ia �a�*�:ship "��F� ��cVK�U ,(I}�8\z�II���etaqY/ _s nyiQ�)� �]er��)�_6� �-1f�c�AA�&���$V�(int d\sigma�Nu^\mu�iQ@} �,\)w 2�M�L\� {sinh }(()-1�Ft=�m)}{"<g��%*9? 8�J�:9i)�~�,aI* � r&�X = �-9&�8:$�=�=��$� can b3Rri�&a�mTu'5a�.yub?on{Param�K"/ ��:[ �,��hQSS if�<.F |�a_z1F�-ur�2#"� M5e Z��D)I��i����:ei�e�u�)~+"�  ina�0����2�!��8a_z = c_z \cdotM�p)}{ F��Z�� soft poi�aYEoSTf[o $p/W$ gets "4i=/2���. $c_z�2>Gr��1M3g�H�2UG%�fit!�data. H�"3�m �,� .�  (!� | � *:�6� rofi� a=�� p(T)5(T�SYtyply2�]3N; śr- ��t��]]s, i.e.�z�� \gg v_T�<b e�adv9GaӉvi<F .� }WU�M޵��.be wrn aXQ:� � , = R_0 + c_T�H� _0}^ d�~'mH '}'2�''>�>�& q�!b bis takena�me3la6D�s lea�Y�A�T. �Pє"�#!(5�6�3@���A2��fi�u *]f9��@h4ndi��byI�_f$/>I��}X #&~<E�U�i�& _}.�A�on�Vhb[fP��ed �V��.�s� by�;�ntP per �)�[4��uH2-��o unit"� �(e.g�ELet�=er�]3hi}). C�5c Zip� �s�t\ 2mFw" �5 �$S_0$A\@ �+y$)�.�A� hen �� $s=S_0/ W�?ba�e � �7artonic)w!ba_si!/ preoo#  latt2F�cM�j� /3�at*� %5 "��B�(� B$-[ Schneider�1nf5,.EH��z5]�ETcho� $T_CP 70$� "�QCD�9�+ �S � �"l6Œ�"heavy!Z$rk flavour �Karsch� 0kv}� �r � no���h��u��3��i'a� !�u)���n act�e�"�^a cross�t��her��n9 harp)] X. Never`G,Q^�A��!Yk� d glu�as �>e�dom�*�BT_C&!!�A� to stf~4mpu-�. �iaaimI��E nd��� vic��2.��)'.���<��Y� �total�:!l"n4"Oy error!� by � % "^b� to�8 nas soo�>;�EA�w"��sm�3esA an�g�%��! "�E��� � 5b�a. ��5h�\AU8���ofA*trongly�Ba�cX gam6�)��� verj4 ffic�K taska� f�\U)� H� ach�:�Qra;ej��at"&�J����A�cu �b�?po�F&f� � _9o��fce�!�d�<�w�� good2�a�Ye���d@A/nk-Ke�. U�-A�"�!��stp ��f:�sz}%g�ILE<pop�'ofJ(i���0�%�z"� ���s �!�u�?� �5XJ� ��s*C!l-J)of ���\Ex 120��!�/ Q" ion)�n�C� a smo�%�p�K\A M.! $T_fɥZB � �!�)㩺!�qu�r.� � ���=g� er� ail in :�md� �/a� help!� �Ag$s  t now��&��!���C � $Y�Ry N, T ]�.�7 #&! � 2pp��a@�� rM�A�imto*e :Il�P2� Solv� �-�-H:�adh%@�er&�!C� on��"%�trTHBT��4>��d !�iscx9inF�:�3gn, q  BR�j�{_f{ f�Z$* = v�J erp f}$ w�+nAk*{]>� EX!���is @G.�� E ��.�� �?iV Mer�0A$E•�{�h &� )��ot��)�#uch� $I� �a�?)  5\% �D�z4158 AGeV Pb-PbH3istSPS!*� � a���!�EE s: I9la�4.&� y2 = 0.54c$��m7�)�0� $ fm/c� ig>�$30�?,�� �G QGP c R {QGP|6.5$ Xdu63�tl +_{had888V lif� ` f - EZ�1d r.m.s��rA�=f� =_4,��e��b�!J{\M�)J7 c!�W m� � �M�)�i>^# A"o4 n2-fI> �#�usZ   A" argu�0&�+AC� A1� � geom�D'6!"�zaUti�s�aaMailed *",�?Bq , Polleri� 3kn��VB)},_$>2� scenario bl�D��"� �L^O �#=���Fsz}2�*y#�at un��*� ofjO i&2N7e��ma6p�p�ofm$� ies ��� o�E)S:o [�">]o-�� harmonw"sup~!A�c�<c�/ )U�t�F��f�Qhow� ,� sen1 BX] .e�!UVo�1��"�B� i���@��& � %�e `can�al'�� D =$ 1�t so far6 ���+�� hoto*�'�j4'9 "= �vid�Cop� 2yrtes � #� Alto lim~1�$=��3fn%�is9�investig/ �"om a��9^�I�s $0.5�� $<�9< $ $3�� co�rb� und. Vari%�s- E Q,9��&aQsA&E�tm�u��&je�b�1 �sig�&&� ,�)Y e QGP PhaseXZ�q�a� A��(i�7s��.X Oi� of aZE{R> pic�smvFs�2� t� s*� g"�!e+�al%&g� e l�!�incorxW�-�@P1%� '�# ive'\c �e3Iis��H!.har�8 �Z(HTL)� R+��>�p. A%$T_c$? �:law -off�e-SJo��%� �,6�con�L&�\�4�^A ei! weakrhvIor6.ond )-"�.��heA  $n � ��,! s $B�e�$C i���)cM�1ref_2D2tk, �� '4ich!�u:2Kr'�a2Su����2eco�v^ . As� a& 2�A�N�reF`�::�jvirh��c[\es'&c*�[w��e�h� exci!�,$q \bar{q}$-� es �'NA& lasm!ase��xrt�� W  W,%[ɴs��� 4.1��i.�e�a;ex-ism0 (���G2@] : &�Gn7inx5e�� H��. ;^Yp"�Y � Ź!�h�&>"�(s Lorentz i" ] , ned"�%\��� A._�Aic %ZorQ}y-flipp�v!wino�O�X\en� eir&n6"� OjL2��+�n.H 8 P~do�Ht��� copi�7�.�(�i&�*�mOd�y)t�.B��hx�>�*) . H. � T-�.K7fseLOs!B��s�/A&p, d�nct!>uŐA�;� c�y-"� a, so�4� van HV1uJNy I�Braaten�0wp} E�� eaks*2&�ly locř� w� A��K>��1ŀ $�2 m_q�9!�wQ8�Y�bt4FM ,�c�$.rr des drop�.�. Fur�o.�x����%�l-2� 1nf}�; �i��r$T$ (�) Znz ����O}v� *�[nd5 � whel�EL&R*��Jc@e !. *�M͡?��,nd (he6�)�inQ��ex�� �L[ 2�;�  EL;"�,Q�} >=� �"� �I�um!zen ��inq)[5�PrPe $dN/(d^4x d^4q)=dR/ $� A�sk)�!histor""�,w!�B$�6)Ms �.�{i�!�$CERES/NA45ih Agak�yevak 5xb,6(7au,Lenkeit! 9xu}~n�Pb-Au�sA<"k(� �=!��� c.m.�UA"g7(s} \sim 17$���40  (:&8$ �). � �%�f,!�&[-t�8t� ��labɩ� E�c�9cA��� [9-�va^*et�( 2.1-2.65$ 9em �"} $\D,x $ 0.558,?g+e�*� s%�[ �`�[�!!Iavera�SwU�$,����$d^4p = M p�" dM \ d�\ dp_T tPs.$%H]bula�Y�T$pm|�d"*U�A A����2�2d �O� 1s F�(Nmd^2N}{dM ��M#Pu M}{)T�}�# \%�s_�#"�#_{f}} d� \ * U' \ V(!',B))�) \ I0^�u%% \!@ \ �dN( 5,M,�0', p_T)}{d^4 e� p} \ Acc("D�label{Ud%�F $�/���-)]"N.x!�i� $ ��$�I�.>"jH�"21mo�at���"ᩡ���}$ ��0 �$�&8 &^j��i�al eptaz:cu�'f-c�[q�. A�i�D,�J#?/�1ro�ck� �havc.� J\ > 0.2$,�9-i� �"4,! $2.1 35$ mrad. Fh%ly ��6�) ����"�mA[� 3ɖ $dN_{ch}/���j A�gedJ$les{%H cock �V��O} Af*��Y�T ,s� F � a=��n�<< in n)_hu� n�!�� y�>. B����/$4U D�^zVayn\D� KfKA &j *>is �<��*�~Y�A��\s� R)� a�abo� for �$�!�D M�fnotyL,� !�$\omegO/$\phi$ $E*�A�!�ac=:x� @ &� *:Fir-T)xsdա�i�-f�dir�q!.�( )QAXQ!�^� $Va-�&fegh n via: $$�N_V6�21> \alphaIv1�<^4��R_V��T=0) .�)�-���w \ V�9 d^3q�M�}0N$f_B(q^0, T+Rex�z ft(-�tau*e${\gamma(q)_0^V}\ I).�X&� {f}=�r �O�1e�� $�=_' #�Alj$   �#��H�SeW�u?exF26=eos� 2<� {\emMD}N�E �()� $=����iL`Ņ�62?F)A�K & �"�! m�It]_� �C-"�C.\&"� �9�e��� . Du�vecaE�3E�&abs# �r r!: bina�5Y-%B�de�"7�l]� as $.��]�)/(B��r)!�� . one#s2}�{�Jy�R�}J^:N�l-� db4riA)al*� � avail��3Y� a�be�m ect:�@ �^VAv6r��'�II��+.:m�m��) A�A���k: $n(M!�$N(M)/V$. M��H1fac� ��lg5��i-A�>�e�!�� =stage.We+"��wx(��)�4�Om �dM$6j*4s" >im-`$��asM�^*w e^+e^-$ | "�6F� e �L   } Oa !Le|&� �n%erY&�"j"�%-�j�/�|��ݚknowled�Q9����s&,� ic �V��� �]٫a�*y?�W QGP,Ũne�@�gredir�!�#E�D6�P��G�(BM c� {}tUin6 ce. �.co0R� � *~ %D�?�T �R40 {\�GejI!$V� �W>��#V%�.&� s =�B�J&l�#raf"��L��k3�Z7.6Mz�*��� :� �2$(�T%Q)^{-1}5B` SPS-=zPb(!I!Y)+Au �l��jAe� w� n2 m"pm i�. !�ft#��H�rjN� B.c s͍A| a"Nc�stBZE�u�&=bE�2zd�x9�al x 2.%�in���O Na}%<<ET1H.3��:++�"�B&Gjac@V�Vso\?/= ind;z�V|ɢ�$`�dax{[.� Q�*49"al�A"x��Bs�L��d�Nfor�4*&g nB�,f.0&V!ct� ��Rf �  U�206�bE=j%�a�"�ng!J�Q� hs - bey� E�r�|)#!Pn- �ZL- �q=i  �aXA��u0�ء� �Zajin�"mWb�� |@pD&eB)9\�!1�"�6� .*R��#se.F�= I�R l"� Mof A �u>}1 �CanE�"�)� &�@em �!�!��!4 ���B�:0N�{�caveat(H)be kepYmiKl�dteK�X:ZA�i�*V!n1-��Z���X3&3��IviaQi&Ute��vV�,�E��8 h�.J���ObfO�a&B@ofF�Oork� Ĺ9����we�(��nI-.�Y scr%+xds)��!P!k&�!  ~� N n�e�-��� !m7��%�ə*+"�V�k�A"�+e���v �**a� ong.F�. :��� a\"� �low&CD�VR35:3"�.]ConclusARA<Outlook�)��ary^>EXinv"+�9�U&�(�k�� aF�*�takaa2O-z]Q�mO� *V�,VBp.]0i"H\AZK*�6��E��'�R � a St�"��cal�&!`�;6T�bm��$�H! �)s5�a� 6al �� s wa5a� D���%Α= Cornwak8Jackiw Tombouli� ��o V}�]8onni |:�%M �}>��. �ircum �*s�j�:fq� work a GB��aJ:� ��%xM�� *�em�%� �p.�>�,�nM2"� �*i&�*by/ HX=!� Knol;�">D�the�;u6>�I 6�\ ��9}�W�+��"� ._����2� 6 tj�%�z��m����i �V�t)ө� #��6Z�)o�Schwin�[Dy�� ��!�2����' #)%i�%�)*#~ :�" E�+"� JJa��$up�)l- Y�exi2 ����$s�iL�fJ+aAD���&Y��DI4�;R"DI�Da?�F�� g.ph}�i>� �d��NJ�u!H!�a +environ!5!�?�X*�3A\�#20embed�E�p�.Z�=\T:t�alb��Zntr�to`&o9���ho�`�C�G.b ��s& nu_Vrf3(4+.%Ds5 2�X�jt. 2O1=%i�My�J� &e !�"y"2g �� � ���&qMs��madk a�-�7� P� &>� � NA49%�& saA��<r�UFw*� �6��[>� &� im��M7_ "�/���ouo�(�� 9Q1w�3we,��Ae&?(7B^�ZB�Z%�)6>)9 �s))v �F� �c��]*� � 2� �t�Q�)]�D$�}�Eg�@".�Z w�XJ� bft.M.rBE2�o�9-Va�. } ywrelev�"V��o�hdV_dE onD !�.�na� extrap@Ep-AE�Os){!F� k� �~� < M < 60�A.[�^3e"��A2 mo2؉�/��qu� �*m���q%ndl%di�/n%�ade#al1ta�:~]A���, ��� siԍ�WEd�8"�*]� m2ao�2�-�:��c&g�dR5����:�s9$q�i7y�C�� @� ��2�%� G sN aHd"�2�8i9e�5�tpKznuCbH &� �&��.$ Urban�, 8eg, 9im,Riek�;4kx}. E!=!�Ԑ pape6��s�w reat��'��Fc#�+,(1232)$-isob�Ts�D�VI~"h @2lefed��a Migdal�horO)ng�ar�Non" a-�&3. �X "Pp!Qof view� iw�#to�7���haAGof>}�U�)sHet\kDiss,Va""� 1pf,*� 2bv}�ly go��*\2�k5!!m impr2p dV&! 3 "�% &�a�:�Q��0� G)�%ng �2!�a�fu&i_�a/�8 �HTL6�a��� *{Ac"�!� } T.�B� J. R�t a(EA Alexa�=< von Humboldt-Fo�% Das Feodor-Lynen-FeZ�. Ce�!�Sc��c C!I�(CSC) J.W. Goe!Uni+�]�n" mw<?�"u�iR,�o its �>ter�thank St��hn Bass, Marcus Bleicher, Ad�p Dumitru, Dennis D. Dietrich,C`an Hofmann, Berndt M\"ullE�UThe.P�aq�$N� i�u to �>�[ 7�4�( �p_0\, p�,um,^2�bf p} �*&:' Dg� -z .o&)\, f:���1nd.\y  $f�(=(0,\vec{p}*% $N^2=-��p^21�eE de���M\Eb1ۡ;isf�BCA-�Bb�%=\,!E!�Nѩ, � %- rm CJHB5� +AmS C�:NAJN=v )v 2� 2���Rjj!�� .ou' E s�`&�Vbs��/>Q�Fm5{!^00$+ i}=0�Zij} = -Mt\��^- ���, jQ�YF� AY2�2�n�.> �*Az�!� ��/ur%��, ML%�0i!17a� :�a�8  %[p57%,eAi�\,\5�^i j=B�F� 2�Z�ba By�=I�n�+=�- ~����k�!� ���e�>b��{�P����\n ��:*$j$ �8$ N_"ƨ _j$ V� $�> lsew�r$i=\mu =j=\nu�_.A$A��U E��h>F ~ ks43 =Bly:�)��A&=& 2)%� U n ?E ; p_0 �^2+p^2)N�I �E 2 L_0^�YB! , \\Eb�� 00} �E �U�0z ~9�| p 86ya9 v�=Ѹ6:.R?��Wm�' Dm�7�A��i݅%��L.s,I� �U etc.0�� kE�\ gIic �(bq7X$)�J&^aG2�jO� } Xybh� rm ��Q%�X�� +5rm ��$�\mi�$cW�nEbFGe# !�#%�B1%g�Oa�5>z� !s$X^8$X^b$,cm� X^e$�r"�(b"M�� $!"��� se 6�2s.&V abb�rs J  X^t!^2� 1}{2A��v��BwI�Qn�v!tX*VE�\��(\, X^\ell(P9e quivѻ��A�(P!� ^_jeTp2? G )&�.�cs��Ag2P�QkXo"^-eqnarray!E\Ij& = &m�% �1����&� =�' 1_�, xPi;0\btI� t=�fI�B.f��XH�p�!�� [J00E + � ����\,a[0i �L _i +'SX�-�-�]-����rmi[ � k!9G c� ��JFC2�!9\\�j�O1�/J�����}�e\,p �R�U�>�\\΅ ��m}=�E.�-�&.�B��!�X^2��p%�ݺie_i + �^���Q�e12� I'2�gH fnA� (e.g. $PE�}= =0$)�*�sZ%y *�,ly" 2�Q�-!Tensor�� -FY5�.A)I�ArA ^2�Yell!�:�m$\,i� ;A�j; z)�}>M0M�pBR{ @>60 �.� ��œ�r��f!i:G(ifS exis�n6I8=a -1]���=A�-1� �J�EI%+ C* -)��2���.Z :�.YB�%@Xm�� �b]B.�#\*� �I? �� �=I,1}{a"��, &,&�\, B�� ; 8 e}}{� }�I A� s-&�=M\ 9c.9)y FC%6{bB h�U g %��bI�$rm e}-P^2N��U � c� ^2 $. One�uck�KWH�(A�edI�@> f:�eIX�=!�t�Dh )!�b2�7T�P"�(p9Us 4�agMo2j(&�CquoteܨKor "� �#s �"f�U+� �<Y�b h"& �VMD�\lNyx .�'dMcLerran�NToimelaR��5ay^6Ret\3O�C�et&_�-cg�UHl !� W^�mu(q)8 i\.l$d^4x e^{iq�lx}�F((x_0)\sum_H4 la�C,H\,\mid [J^he�}(x), J�0)] \,)�2le>� e^{-E$\,E_H}}{Z()}.�Vretcor�"�"�P*� %�e�ׅ�(Q�Q^2H� I�} D_{a R}\,��PYV}�M��}=U$=Q^4 D^{R} E ; ��Q:�"�}!�U�E��) � �u%-�N�\be dR4Gq}m�mI�Aq�e�1+)c 2m_L� �7) \�=�y4"}g%��� Im} W_!/ R! � f_{}(q_0)1�drd4q02�. .\ee�*U�! gURv2u�<���de�f�h9EZ�.�0�qMP$(VMD) T�@!i reta\� jrpro��t�86�*Bor h��"$)�e}{g}$)'a&� x$RhoProp} W� ASQE-�e!� g^2}ө rho }^4{\��S}I�1Ev(6 }�U�#I�f�wej'9hGE�";Y�2�#sk.&E(�`now� QA�z}� Y�M�$1}{6\pi^3})4I��M�=}E�9 ��A�!ZE�I�I�\, ]��E��A(�N)hJAduݥof5x a�::f<$q^i�ndX)��?�PLS|6�Ew/bibliog"� y{u4��nd{docE^} ^6%\tstyle[aps,prl,epsfig]{revtex} v(,*0lecolomn,12ptN:class�bN(,twoc�anfZprc,a4p�"�(,groupedadd+,t�$en�9sF4.� yon�umn% �)$pacs,float!eprintA s,amsmath symb-9�d5fFccc^L09P!�u��ckage{!�s%�ic%�paO�yle{plai�Qb1�} \title( {Suspici�m n Engraf��dF�A�iomy��He�lIon C�6=0author{ X. SuE�InstitUf$of High En/�P,s� ij�P100039, China\\ Gradu�U*H!��#�3Academi"�!c�BZPD#�"�$Engine��TA�huas, .P84�&"R�NL2� 84, � a } ��%�ab�=ctA� setlb�{\�nE�,kip}{16pt}\ !�m�; 5��!h%�!�"j4��+as��vesent F.S~^"���K{yT��"ofC+HBT� Zmsu��ed�� \aT${25.75.Nq, Dw/�cE� %\no��nt� bf PACS: -<, 23.70.E}$ \newE� &X"I�!�}-*ABƩ � �$nC rfer>c�2>:�Fed��"ea�%1950's�(Hanbury Bro�@4nd Twiss (HBT)� HBT} who�"l�l6`*�T��hQ)�W di�,eu$ss� �1��)object�/��O��Rl i�s~j& hbt-$ew,pratt-f�5and-li}e,r�#Fgyu��ybf[,ch89,shuryak} �5� osedA$&O!to be sourc�X�@A�UG U�. � spiri-$is 1�A� �$3d a.��(Ul�$ Heinz- 99}: "�<ran}p�' �s $�MbG a �J,"�r, ��r�1 "ce $R$,(&u�]!�G��"L�F"!$E_p=(m�^{1/2�i 8,mH`jve� aoL��CyeOj)� dete�Bs 1e�2,"#� $�D�0ce % %�  �D[h��6C���zfxI�=�D\��Ny{Fig1�D} "��M �a�(�-y��$\pro�\bbox{R�Hf� Q^6��o* a�a�!�in.4 ��2�/var�H1��Z2{d}$. {��a}:� al��ne b �B(situa�.� .c .E�7fic60��R3s.6 F0}� -���9�% $)od}[ee�C ure~h&$F0}a). $L$&;^M0m���2�Gan $R$ �d�to�Qmplitude�d!Q� 1a�tw�gin*Y#B B1}�� A_1 = {1\��$ L}\Bigl( / \,� (pr_{1a}+�Q_a)9+dt6,b , b)} Rr),C�.H"]V�,�^�A����/{e��}U� $# �,bBi�u��has�$ �,��ar�Xi�@i��(9E�is���J,�.�(ejum07-�V�<u:byn�5%UC(I4R}, y=!�{I_1 I_2� )�lL,b=I!�A_1^\dag�7A_2IEO:6% n:E (}= 1 + {2 \w)� #� r�(68+ M:)^G���osAw l(p(!�a}-r_{2 A�b})$r)��2��le�$ $L\gg R,d�VYl �A�>�F, oscil< erm )sn�6%�j� \Y$a�M{d\,R% L=�a�cosM:dQ:R}) - NL})=]"UvL})[NN��ymm=m) i�>ain $d���tّ"*ql�9-S;s."�,g is l|3�*a� p3"e"�4lljs&/�er9(ate} \item8+�zq$R!�d$e�cosine-!��(��B5}�g�C�  $=1d}{�}-}p}_a{-}i�p}_b))Gtith� p}_{a,bp�e �J�ll��((JIcl:�!N�M� .�RF�1.�2))�e9B% So we�!ge>"Vn7Eő�p}_1-)$p}_2) =1+A�B3R!2rho-nR})\, Y�R}%� ">R�F��%�y��u8o)Ba�� �-bɈW CJ� sR,I��� iv��cW6�1�!dAZ��1$y.Now let'|gE6-n "� 2j.�E.\cF� 5}"Exp*J:|h.� VTsB"�1�a�%Z $C_2(� q}A /B $ (n��sto *Oy at �[ A$"�$H&���0] 1{!j�\" .&�  q=p_2-p_1��$.�� e miʼ�H nT`se�� t-mii�},"?K ?!�J way� ���~ 2A��tP� ts."�Y% p_2,��pri�C��6�,�a� #��6 :ear�oaI�.ItIcB8��[5`w�.�J�� D ��ory. Re��` vari�&us)6.x�3 L�0��r $Q_{S$B�=|Iye�AZ �D$^2-(E_1-E_$".LZ�~�)� ��7})A! U� qá�o"�!zy$,i�Vbelie)A�i�o6~�&�=ci��*��� �5{eswiajn!9"�} CRy n�����f��1��Y�~ R}$,&� ,$p_1A� .Ze�d!9eoure zZp dimi�[!�%`�!"caE/b��X$ *.�P�V�>HBT�l'r�5 evingsy�I�V9�%�In"Ey,��cVn vKy ,!/� be g� rom J�c."���!%�%�$p!����,�z canc�2hem!2A\�FaE��[j� al�{_�7oa�� ��So 5Y1>�)�!msucceeI�x�}�"�*h ,in �to1��3�"�\��U ��romus�=f��.��n�]>y!�5 �NlyEf&�za��;�=AtoO.*�wL$�t5�words,�2!�"r, ��U)��0�6!ougB�!�6mr��afWQ&1k� 9N�wKb� ]'tNX~"VaUr���O2��nd���w�mc ; � ors �=;�*2�U>� �ca~��8� in�E����%1C6�s� � )2 f+s)tor�8�pg!��tnq6�erty ��:7so��1})��in. A�H opin��Bq� M���!TPC=!-R,~����Rso:�%A�n�V�Ar�Q"|A}Y EH5 � I���# B,as؀�(: N� I�w�z.�)�6]�,�]!� inNP:: �NN�"{sta' e��%2Q �:%� ly ,Am��1!m�8A�5�*� ��)%Cs1�uI;I�^gr�Y 0� a%k,Muway�9���pt}or�����ed,� � �!�W�� � �" N�n�F;thir�q.!.�&? "] �; ; ��  q�; &���; �@Be  �; �; &; ttSM� ���9�a?A�>�Rq�Q�� U��W^E�bis QdMsIQ.o� )l6a i�F�wA�h�  P,G � 3 �repG)�rmAon .DJ%,in� ֘ .Ij��N��:��Ce surf�. ׁF$L$=0 &� �p0$. S� .5 ��!�dis; 0��"�?{� uYo��}%>&q�7�d*#in �I"SSin w�. Defin��(�( ,\varphi,�aML!�-!probabi�[6 $6Gp  H��gOGazimuth�l �p"Ave��nU&tau9A8�� qMK�an �a> $M$=�coR� e|? d� i-th2:v s $q d$) is#.� q&�h�[sC} $n_mf�! �u - JJ�� �Yt^6��is�DBCA�� N�u'��!]ereasBN�samc�hy)�����ly�mr,� h�RK�uM��Ourc�&�I6Dobe�!�.V $^��F��ata, -eas#$�D"�b&m5 �Ca� g�bar{n}2�=�{n}2�\\ �q�.c,{i=0}^M0.�}R".5}=143��� h!�ov�ll-� . By�(+mI� j7.��Cno}G Oy3�B .B^xq ��1z[�re �"Iosd � A�. $��:� +n_ceV)m�5~sumn�b�"yZ��>0�en\�hag sc-�.�\<+�E�=getN 9�Q<�}f[q.�+ �]�$>"$D6��.� si��| N�e� a� �k.$9�A������n�"� o  al��gV��'g�h7Gs�n5�j�+U�<!�o?q,Let $q=\bf q�$,% 9�)E$}PRh��;�r)+eA�-�yf3� $q$}'� H�!�perY��� :�Mj� y0$&w��N_�+.��,Y�dr.&����.|Amea> �:�a7va�I eT* o&����%x satisf�"$$p-p_i=q$ )���� �c�$.[. 8i.��&1�� 2�� %�E��Ics�6�;��Ep���}i��.�G&as.�>0$����%O daU�at�"^ bde�ob :b<0$. L"y>m \$}^�ve�k�. O *� %��o,i�fCo0)7ed�"� hold�E�� �O5ݥL]��(5j� is kindW���Lia�!_�ce. Quwf!d� u@��� �ovo��ll �M��=MC�i\kb forܲe�a �]/sb�1l,vice /Ma,a>Y#3�1�2� �<&a^s�)[��!>bl"6�,��"�A�N��Vڪ� 5�isd�an ����l�e�ble�5quonda�cTh*-��2�a�w.��]�.Ab�is��{ `j t � �W. �&�Om�m:}�w�N Dr�OFuA �Qor��u��V� !t���Itj�pw PProf.RLie Z. ZR��? earn�superv>U{c? Shaomin C!1� Yuan�� Gao�IN�N��eV^�I �3 ���.��IPgrants NSFC 10447123.- %6�1 clps�!b�&the.�1}{1|�bib;!C, :n,@R, Twiss RQ. {\it�I Nature} 178:1046 (1956) \bibitem{heinz99} { U. Heinz and B. Jacak, J�Ann. Rev. Nucl. Part. Sci. {\bf 49}, 529(1999)}ystarpionz�STAR Collaboration (C. Adler et al.) j�Phys.�Lett.|887}:082301(2001.~tevent-mixing} G.I. Kopylov, M J � 50B}, 472!A 74).�$hbt-reviewIXW.~Bauer, C.K.~Gelbke, !N S. Pratt,�52}, 77l92); Z��I-~J9 J,A. Wiedemann�U-��Rep �31A145 A�p�D-flow-and-lifetime!�0T. Cs\"org\"om$J. Zimanyiov oC�26I�90.prischke2iD.H. R ,Q�A)�$A610}, 88c�6NOgyulassybX� M. G )Rh08E)h2h bertsch89! G. B ,SongI$M. TohyamaJ37}, 189e� 88).E�JNiy�49�173�89.�shuryak2� C.M. Hung�E.V. S '2�}75�003%Z5aPend{thebibliography} ,a{[\2<}\!6�\;2}} � B � G � $ $�% S1$ for 9,11B�Rother%4on expressions!'new-a{\beel}{!6{11}{Be}�6#ni #9V"(nm}{\ensureaG {N_\rm{max}FRho60,\hbar \OmegaF.nn6. N\!NF&co}{(CA� online)}Y/ �A�e�< spin/parity/iso%B(odd isotopeB+jpt}[4]2�,\left( \fracEa2}_{_#2Ao3} \:%� !44}{2} \right)}�...�!�4n}e^~ #1_{s #42cE$-eAhPthe different interac s 2�Davp}{AV8$^\prime$}:!$cdb}{CDB2k>,nlo}{N$^3$LO>$inoy}{INOY!C�9/�GDs (to be changed):rnb}[1]{e��� {redAmph{[#1]Annh*� \begin�~\��{UCRL-JRNL-208555} \title{Large basis \�@ab initio} shell ��$l investig� (of $^{9}$a��$^a�T} \author{C. Forss\'en�$mail[]{c.f(en@llnl.gov30P. Navr\'atilW.E. Or��ffili�P{Lawrence Livermore N al L^ hory, P.O. Box 808, L-414, 5(, CA 94551a �$E. Caurieru�Institut de Recherches Subatomique�4(IN2P3-CNRS-Un�\sit\'e Louis Pasteur)\\ 4 Bad nt 27/16 �67037 Strasbourg Cedex 2, France} \date{\todayI abstaa } We are ��entinge�firstJ  truc] F a�0loosely bound. 4 nucleus, toge�8with a study ofv l��er�pB9IM. The Far � 9se3@s is particularly�KA�ng due�n�appea%$Da p�w-A�rted gr� stat��11�Ou��8is performed in[ frameworka"l\>T no-cA�}\P@sults obtained us�four �,, high-preci�; two-%]on �6,�i�8spaces up to 9$����$,%�r ne� both)gi� all potAPals, we reach converget �(level order�,of positive-�ne�:ve-)m spectra ) 8rately. Concern@their 2 C Lon, Z L)�s�$always too%-�excit�\ energy, but a fast dropI�re�Q%:� rum!�0observed when%�=n! increasedA�$is behavioA� mowamatic� �9. IIIl��st2Ywe were , to %�% $1/2^+$ )�has�ped down- become eie�A�i�or second)-ed E�, depend!�on whic!R���use. �Hlso1 a con���T� �.>patternU� .�.��arga�(hat a threeN� need op la M5e�aG. Fur!�9,)y-� cal�K�A�!�3}${C:�}E|� -�allows uA���!w syst� icTI�ond%� unn�al2�A�$$N=7$��nb  A=11bar�eY^ } ru�) )9. 2ginvolvaQ matrixe  dimen!1A%eeE$1.1 \��s 10^9�Un� our)Kst =G so f�W�way�� n biIne� ies,lq�i�a,�lAc figu;,s, radii, el�Yomagneaai�a3s��!�0} LBe} + n$ overlap fun| .��.x% insert suggested PACS numbers!�br�oon next �  \�H{21.60.Cs, 21.45.+v 30.-x (Fe, 27.20.+, ,maketitle % �' 2' se�H{\label{sec:intro}Idu$} % StudieE�how�a��r eM*� vary�+E�N/Z$ %� cimporta� �&��improveE-funda�(al understaI of ��ar�.cesɯt�Y�f�research!{J$ neutron-r��@i �at� ed aa ���amountm�orA<al�q expen ntal effoAip �adZ8A�o�v&�beamse�vlic�M��Landard mean-field pic ��bef(se few-body�@�qu�onA�I�it�noA� rpriۥ,sub!Rtial dev; $s from reg2 �&b !0 beenmE��e 2epof*x �a��qis!��� )5it exh�s s��,anomalous fe��es �A8�easily!���l a simple �-� "} . M�eUuly�&��"� �6 2� ofI el\ was�0iced by TalmiEdUnna~\cite{tal60:4} alreadt !�( early 1960�w it still �i� ADb!.exa�enthe dis6� *($N=8$ magic�x. ManyU�Y m�8odd-$A$ berylli�N have� %���� variou�Ddels. A thourough A��Y4of uns�l� m}Eerm�)��ycan be fx in Ref.-a4mil01:693}. Of!�� ]hA1e� y onZ9y6�!�eet��and K�Qh |$tee77:275}-a 1\ho\ �] 6% Mill��- C ��; � 0modified $0s$7$sd$ a�l ticle���6hal=�qo- &\M�� E�reproduA�sA3!Ņval2t$by Otsuka � s} �ots93:70} y� d Skyrm�" �Ied multi"� wAc�R�m a.�B�y Aa (0--1)>p . Al3  m� }-}7 u]val� �\-?Iv trea� ex��it9 a $�0}% n$��%]4a Woods-Saxon "� (, see e.g. A�sQ�Tesb95:51,nun96:596}. U!�0 upled-f nels �����Q�se papA�i2$a signific�b��� Yt�s. Possiq�a!K��A1�& e! Ruu �"� �@ T $"�QAMD+HFaelM`(dot00:103},X s%mbi �v4anti-symmetrizA^ole� r dynamC �fc>p�BUmo� . A� ten :�AMD*�was la�usB �S���� �%�EK�|�existEoof � BIro� al bDm proposed-4kan02:66}. Th� � (lso several.U a0� �"D cluster �sY&(, $\alpha$- (=��consideWo play . "� rol��se�fth� assump!v as�t�ng � , K. Arai�{)lan� + � e|ȡ7 "&!r:�!�ni\��! stochasti� �  methodE�I-X)$le-un�NmBI�s�Ai'i��aneously.���x scal!Y k-�ara�04}. A similarN�Xn$ d )I�employ�< P. Descouvemont ^desA;99}�� �gpq�Y� I�in�9-t=@G��$ator Coorda�e M%<. His��AD�how!H,�x !�degreea�Jv de� OA@i&� mas> A�equen���I!#  ��Z �."a egert e�. Un� un�,.*c)�it%@�problem��r��� no genu e�*G� oE�` q�realiA� �DHrcno doubt9f!����Վ))4very successfu���� ide��ble� �w �  N s. S� , ��:�me �$y rely upo�- "� approxia��2:� be -oto�!�onents:�!�eff�ve)W-I�lin�1#(must be fit��toME�!% individu��O ��Xry, a truly microscopic�o)�h a� Green's FwH Monte Carlo (GFMC)6>0pud97:56}, or|BpJc (NCSM)�$ nav00:84, 62},I�sI�aA I�IQ�]X�s(!g$A$�u!� ��av#ti�� tF�. I�%9pP g�7NBh clei!�yh&�A� �x(s ($A > 4$)�� suchFDE�a���r �be.� A] to f� �gap. V& e*i��B�!��u.b Schr\"o�*&que��%�� a� S�d� Tminant harmonic oscill�� (HO)~ . H��OwknIq�HO � &� P@incorrect asympto� �m be aA�G9 t8�!�� N-� ref� �desira� to i��deq!� nas��- expa�-Y� � . By�trictA�A��Jto2z(\nn) .�, :,g e%ρkow�D%���6 ���fo�,n� � $to maximiz��.��J��&�"�of�ri8. In Sec.~\refth��}�"J�A� wA�4be briefly out�d& f!'&� :� \nn\2*�(�h %�is Ami�~6� �}� devo��A^e�i��discus1m�c��t�T3 1 � �"� ,� '{ focu�$a�p����lua� rk���� 6�� }.�6 NM��A& JQ Appl"� 5*�E2�  stepa�~e���a�r=!U��A"ɞ� }��ѡA�c�a� rans��1� "Tc"� @ to�L�.� $M$-schem$! �-�evalu/} diag:&q�� HamiltoniN ��8��+$Z$!"toY $N$ �s)J� HO��eH�n �&plA�$\nm \ho2�. Final=we\ a~%WiR��w:�or fu'�!�ing!is!� ��aWrt2wn 9 5tep3� & �!"fstrength��!�F E,hsibil� to�Ode virtu� ypA��1i " �e������� ����! F���6�int�  m�� detailed .� o�e?�,������+s, � � F,�,��"� �O \sub .��1Y�%:6 a��! goal%�# l�nE���Z�� a%trinsic2 �a� %��$�(0 H_A= %T_{\re�} + {\� V} =7#�&<1}{A}\sum_{i i�a��!s��,>���� As Aioned �ie�eI�+3+�)�nA�� EJ�cl v: >^*1��sh"4 ad� a ce( -of-�(CM) HO2�$H"�) CM}^�" = T. + U. '$ (-kN = A m�)^2 %�R}^2 /"%\;  =1�=1}^A r} / A$)� fac�eate�"!@of�# nien���O"�.Ui� :�one#� e=� ��\nb{Spl."� �%� w e��%$A� s=e:-6 = &aI + Z|\i8)h_i +iZ aOeiaX)� ,A} $\ = & / F�*[m�%xa�2xi�1�*m V^21� ^2_i `�*] e)'&:� lV_{a�}e�=- c^}{2A} �r�r}��*]A)~0 .�o, �/-g 9�%�( ��-4�j0�infr)e��eO�{ox�~ ve, &}r ($P$)�Va�Z �pac$Q = 1- P$)U�e7 Rist&f� *O!��$$\leq \nm C  a�] s ab��unSurbed2�r�U��/re is�cl�-'�;��e}&-!s ) . S|w��|� i@��aJ1,��&�>w�(y�atholog9 �%ca��s�.-r, repuld � "��E�VWIory-0e VJ 1E�I-)��%ent� �A;"5 is!�"�by �!l$a unitary "+ %��!ޝ� ~\eq-��i , $e^{-S}�S�b e^S$,g!��.�_Ze6��dec $Q BZ( e^S P = 0$A��rocedu.�� " Lee oSuzuki� suz80:64, 2:6:4%%��Hermit� " e A� on $�:eff�BPZ�$�act�c!�B r�s c�a�!�%* igenC!�(� fulQ=�EEg�lA*is�.(E�Sa� �|ope��<s�iO s�]+%)�A��. ���Vm���dw#�]�� MC�"��(A � c idea &Iit� :� solu��to%a\ ��� $$&Tcal{H}_2 = h_1 + h_2 +�a1U1ɭ ,A}$I�!�Q�ρ�sam�in Eq.FN �f� �o%�� a)%OU�2�T 12,�rmE�}^�. See *W! ,cau06} �  We/ !�at2���edZ� ���%the�%'%'AA���fr� cy $)F>(%,< �= ��U�dw5d��\nm*�byY��i)G �a��� � b�x*� %JijbJ \to!�6 �sm  \infty$>�)"n �1: E��&��%&k!͗ %z� �1M�exactU�. A&ap%-i R�;�Vu+`la!j�% ari� sa[m�yq T to�� a CM&� Q*a6�%�-o( �%�Ld�( freedom. D),��,�yA�ra�forwar�5rem�CM ��Gly�H�*>ES�X-P*�{S}R�QOl feZqZ/vl���=Z<Q*�eE���@s� sub)M!.�$��&� A�nd� ��LawsonRj��(erm $\beta(2A - 3� \ho )$��shift ��o � v ed��! up!��� ��),�atea th $0S$0a��a �5Ŋ� and,%M�� tly,�ir �ai�b�vq�8!�p�LcB)choicaQ �$.�, �w �7i�a2a���N� u�ulqA7%� &t %� {A:��k, = P \Bigg\{� � � bigg� " � >4A5� �X ^�4�Ajg � ] +3AE� ( zL%) �}�;� *�� � � 92%B� � bu� alA��S�3��A&� E�\$s non-triv|+��e���1i/"d// �#� The &:2��we enc�,�#e���4!���!} 9Q'(p�vI&t:)�,A��e��� eeds $d_� >�/�-Q!(\beni)�� n�w gives A72908(2.0*I08)� &T ��%vwu!ve �* peciakd!P !��[�<code �9$sc{antoine�(cau99:30 $99:59}, re�ly adap�3�G�#H 9 1:64� d de�!�� $M$ =\'0�)�"us�,He Lanczos algorithm1&Ha�a I  of i� s &�2&���7E��RA&+(l�!/*bB,l^Y!Ja soph�"&)ategy�s��%opivot ve�� is:c%��ab�Zcru!� ��ia �>�&!�yq7�,I_� Fu�mor� otak�2dvantaP �6�U�B y� a�ton i��sm w�n��I#� &-3%��, b�^:�,\s3 e)�AL��cF-��sb#T�gl��ix(c@�r�)��3e 1!�GA.Ca;�c6u(�Q�:z ��� zero ton- r|-G-  ���s g�iEa%T�| �+pJ�# abU�q��V&�). 5!�e:y̅}*I a��6 6(i 7AJ�)%+i�aC��s!:i:()�9����9�6ed, b�7s} j id�z, Z.�@� �%e ��E�E�y a���>��4)�\�ve �>66e=A8t�#,Qplus )�J�F,$N(n) + N(p)�2)7�(hi�  o780~Gb!|2;�sE�>m A��8)�!OA�?b22F�'�C57}{Nin)�� $fp$�.)Z ��d!���+�Q4� 9$, �:�8�=on� � 6g�[F*8 &�76$�tic3me�'1R(data. A�14 elopa���.-a&�:%+ 6L�]�7�� from#I5Fe4>m��&k�%kdenk<eq��4�0�0^ ��or>)_2��e l�:��ct�kt"�' J, !���-rU3G"�)�, anl1*'!:�_J� gy�Zas&a`.f% O�.Ln�Fap)��*� !�0A�^E\�c&X>�uc{�0+n$�B�0>�C 18}R�*BGs� FA�" $,� *�>>{�4�%z��i2 udyeHse :�Argonne *D ("D�(wirp1*2)!4CD-Bonn 2000 (3D2mac� �0).D�#ent03&.��2D  dol04:69, 3:67}*�<A#&s2S��>ree92 types: M41. Locy "�-space:}& �2a%aQF�6m3�u� phenomeno�1]$v_{18}$&2! �1]}�¡&c�*�oulomb�!�is2Bis loZ�e�� eRU�i@�1+"� �U�'"�!�Aka"" a�=i� di�(ari�o"1&�åA< GFMCa0� �2. Non-5�m!ttum6� cdb\.. �U�!>aa� rge-&�>Oo ed � n��exc�Fk+�|�al�7coQ&$Feynman amLud� �q�� %�NW off-�:&�?�#u�� S�&-MI��b9�s w�@lea���HB:>�� arB;;A�e newly��ed \nlo2=-yu�%y�3�a(K "h&�-9� ra<i�� ��,&+1 B,B!�chi�3�urb� �'%r� ) me�%at ito,I�a Lag��T �n�� q A��-FQCDE(�a� nove@<"A:�/>*a-v Z"C�"$_7�Bto�h&B >a�!��7a g;Zb -to-AY% (NNLO)Iy�tw�\",*� �!�ph�sol��ab�<� :2AYHI�*�L�p/;o%4���l :te�<1a��9�e$p$mI%Yi� 6}{Li}S �� 69>6�z3:z&�(�|AF�s�}�,mr�� m�"�C�radT al%*.Cs at lon{ A�es6 ">a�L�'atXer�t�H-as "�07�Dolesch� �O6m��6�.�R9��9o"�e#8tA�i^��*%�onM����. bsor�Lby�ca�%�E=[A0 eir P'��(vagM*i�e>�5!t�;f!5�>c"�itAb��)�tx��60� 3}{HL e-�>&�1� scK a�M �e�� �HA�q�!�"P>=$s� "�0�+'D0of $A \geq 3$&&0 In p�Z�aD�M2�%n"B���xbi�3 4nner ($<3$~fm)F# ��� �amYukawa �)jV�n5 (In_��Out :�#soyled IS�&�>L&$/A*�A�� ��+.�"�o� �IC$^1S_03H$^3S_1-^{3\!\!}D_1$��� sa(le%�er: are ��->Y .�H.va�u�!�IS-M �;w�Hcl�V�壭X$P �D$�� !�pIea&.� ����on����&[8tri�-�-!(!��s � � �@in͸a�EIi�:A�3N� alyzz poweo5M3\!}P!�}DE�adj<�B les���b&� $^3P!�becA�m�,�$�&� $E }P_2\.re YEive. U6R9%B�a sB.;or�D�P NijmegeqM�$ phaa<��G~GP}R��B�?%Q !��i*�� &�.guarante%oX�3 ei��"c��!Q�e@.�ia xed �)�!�(�wo!"(the��l9`D$�oJi ANd s (80.� )n8��3� in a limi�=*���*�;| �7)he�.� to�ɔG."��T7cod�re cur/Tly!^�$%m� c.Qs<�@$ "|5�( or��ou'� )2< E�"< h@1chose�)�� ��t"�6m�5 6.Q�A7=,� %x�# selv��� �z+$� u��j_6LNg� .� f9%AE�is �[D�cs�!�#8"�D �$ $:�$ ":$72�8��),!FvL�7�1}{B})� 3}{C��8s �6X cus'(Nnn� )J�t)H�v&3"� �R b/�%6O� $8\3( � 8.2�( 10^8$). N" =vr th�M8(odd)*aHO�M# "�P"�-) �� !�A�-�L I�. WheiKa�ai��um�c�C� �Ynm��$(\nm+1�E$ �E,I.' beRn� ���c:|i7ould ��@i�a`ry��inx�A�E(\E�� t!�2�%���Macc3llT�a��fi��T *� trun=��!a:of!��&%;.y9��a carefu|� �"���!:2��!el-_��8�OP"��)�ѓe �ro"DO��2�%� �I�5sir�w��.�dy��k*�#�%� �s* 2�Afa`i!/%U` �;��o$A o4com(3�E jW>�a>A$*&q��&&� A^�:]u� � renorm� �5� *�AQmSE��$c�c���"! ���V R���e�"2L2�; zAy%��� Fa !e�s� �Yway�ste04:�u-th�H ntil!ag6M� �Nuse of��."etg�!�d"WO!ze!! >�b� ud"�:e�-l*I�%ASyqF�U�Es @e*�.miZA��7��2�F�( $ɖ0Y<ji���A&� �#�ll 3C4o).c&p",!���0,7�"d�Wo�in Ref"�J270B;_2}!��  o>'S�!��P2�m�.�j�< 11be�8�� 6� &�8*�hodep}D�V� on��"�,vbD`#s�<� .Za �Rq�opt�bHOc� princ*]A��FRaCeus�uld� I��N!�]I� ��%"{QY�7��e *�)F�.oug�[CM*l+� g "�G]�Q3�b"� m#R� ,� Q,�,�E�6g:� "e)�:"b* "� Rms9Slow�<�gs> F! loo��5reg�M�#I\�35+"�;�� est;%� 2 �-!7uency (-���"IZhv%�6�))A9; �M">YM��2�NIzur1� cas�Nis�w/ �#]B"� h n] minimum *�\%���7t6�Q.�mY:�O*.=�b�]%Ku8� b >�8 e*}[hbtp]\, �$page}{0.95�)width�9 A�]>%[t]{0.47>( \�8�^C: \mbox{}�,\�=e�hs*[h=K]�,1a_a9v8p.eps�=c_a9n3lo >- ���,�! h�H :����b_a9cdb �� �, d_a9�e:>)zLF��?2�ca/{\co\�6�.��"��i��jpt�81}{-}{1} (solid~=i(1"{+ (dashH�=)Q�� ��E pane{;�&�2�  :: (a)�!, (b) 0 , (c) �, (d)!koy��� x>�B���.�% �\tzhdePst�)���!smaq�cu��q��B��}��_u�. h 4o][�� 9e*x[�s.%A��\2��/�A?&a��%�%~%2a_a11�&2c>�'�'�'2b��(�ٖU2d?�*�*�*el�*� -}{3Z*2(+ (�*�*�*�*�*�*&� F+ Fo�%� �""W># �B� u��#weI�� J� � ; { X� TN}Mtab:opt8 }. A few/ <m$Lregar�"�HO��,�e� *�)��z n� J� ,kb�4$de: (1) Cl�#sig���� is ��6w"H � akec. � ���?� re ,v&-)cLtw�` ���- � i�5e gaŒ�JF>D2-�"B ?AhJ� �E4x  (9 r/)�N&^$sam�sS otiv�8V �C�gl*S �>�ute$H�Zri s; (2) 3/ P�yr a�[Ot��#�:�u�is v8ragingly)>IFuE^,$�*!V!h *� �e�| * saEuQlAu�M��Y�ih� �not�8a0� ![����,�%ĽXe)�th]Fsang1��v~e�ach!NN� &M�*� � Sqed��.2���4[MeV])!K5E�E s*��ymvar.bl4[�*in:nAN@.\vJ*{1ex}*� .�� �ruledtab"�{c  N� us &�!zFx{4}{c}{Ik*�y}> \\ { B&qc a�- �  $avp &h� %0�ni,  & 16  2 1 W{" & 17 & 13& >. J21PT B6yI�O ���� 9be}Qz|B��*�2�.s"��Ci�y&F`�����}�s (�cFig-W2y) �c �*aQI)��*�$b�W*: X��a w ^� than��TA�e� � udisplaSu Wy�9)�� 6$����mo�%+��{EB')�p :� 9f ��PaـNv"��� !7�*o>����,� �+Z . Ac�S,>�$v%�%_Q4\5(i N�d,��� as�+x]��! ��E�!��?��fir ! � alQ� , us�T�_�,z$,�Su+ L �������~ "s=Y(by 12--14\% 9l�3��""*�"�e�?h�-�2�: 0e2�s� �H%pie�H� wXZD�ce^t agre1 com� its �!O^�:ur �?r{SwEG�`om� 5L�&p�A�-Zm1�1".&� *� �>t5cA3s�)� 9�.�Ro� ��  � �^&�� )"�*A ion V�>�v8p�},Y��a�!8j�we� �Lv �*�9Ctra�*^aL.n!1�!_��to B_Yc"Np�#�*��p.�� E. �(&�Ib6� ���5�?R�a���Quadrup�g�ZTB$f $$e$fm$^2$])( [$\mu_N$])!,% C�,A:U`as E27M1ZBO$9S�cJq$sqG[$e^2w46w�)&PyQ��� �1\�W!H�3J�&{�m�&��r� &�i 8(9)$'*���5�^�'���AA*!�BGijF�8Q�>k� E�� I��8. 2nJ &9 �� Oti�:8745}. $E_{x^+}$�=ot�*�+���I�yu"��I�V�r> &[� �6� A� � {c@{\ex�.olsep\,}c:{8ex}}c> -p��\  & \F� �NZ &)�R� &!�W�� &E�\�  2� $E"PYgs}�3��1}$> & -58.16 6.05 �-51 -50.4� - 0.20  49.9qX }x Bt%�& A!W � � .p5�Bp2.4< & 2.9�  78z� 2.64 7 �$� Jr1vr]& 4.5%; fr3� 5r1. /JrSM-�B� 5.59\foota����&2�w��� >as�&�AG9F& ``A20certain'' acc�>g�M� �� TUNL� ar Data E�T�FJa( =B& 7.0!995-4.55-4.75�--- FJ.7n�6.3^& 8.09 D85�7.4 5U66. ~r:~E�I/Rr 6.48mN9qr 47.8En&  I7 6.8t&2�1G$Br - 2F,1.E�& 5.1�3.3�I�9RVq�i�.�:�m� g dZ�mi�)fBm1.3aJ& 5� �}: 5�w�OZw 3.02u��[1]r�4.0{3.6-&!���3.4Â�9E�Z�5.0I�6.2uk6.3�6.2E�!�6.2Ey Jw6�Q.wJ� 5.288(38)�5|4.0p4|.5.0ur� WgsNn(-1.1778(9)& )c � � � 35�� !>`B�P� E}2;�R5�R_{_1}^-b5f����r�T)J# 27.1y& 10.)�& 14 16�& 15.U,!�9B�M}1�� �0.54(6)A0.4E4 & 0ij YJ!T--�z6� - % A"�=see6Hh E� &):��8Ţ���} and?ŵ�(�#��Qw�FO��G�<:�F6}< �Sj2Kap@ $A=9�<�le�'� \�HDhowa(:��!�&al h��6�08m�x3 jz/� ��*N�7 �. *0 ��"�. &��#*�Z" 0.9\�i'^' 3_Be�_�9&�<\&E&� (ueQ� �e?o� �*.v 0\ho--�2 |�5 f�9"o &Q![.�D2$�3rb��r er n  .�g.u � )�h�2& �)>�R (A�-� &���;uted) �two� rIisc &�&��1ekB�\,�g@1upper VU�.bi� 4�6Q"B �B<&q2"�N:;&֖4A�}��R�Y2z�� �7M�v�6Z� >�n����!JA8F""a �#4�B3 �]{�>�.S ��y�F�it!lade uRꇅ1�Gly�N!�BW�7*je�" rH-a�x6|trend��*|S*�*�: plottm@a�"�n�"r*fn#evi�d�VI"�z%ing� al(�in�t 1�, .f^ F���ivn%y/�\is�]arkabl< ble?�:�.�����"�5&{;Asustix!:.�1Esnot!��d:�2V"�6��.�8� �E�N,of^�&�yi��i6�Ms3predic � �"���K�Gc��i?|� �A1�\�2cb����$ fSyng!#�E)'nt%��0o�~lQ�i�%�"�-EE7hLi�o�ge�W;���whe#kx�"d@[� 1%�KW$�=�Y���ho5B;rUb-�> � yg�"Bl9�$ enI.�V�8som`:�8s%X; a�� �*�2�3.���d��*�D?[%nr�%�� ��n $.�s]ae�ytA {�p!�m�y��J (bA! issu��*3If�';!VSe.�vpospar}!�[$h��&�Equ�;iԍ0x3@INA��Q�aD1 ;�� Z�.�_�; aa��({'6�e�" b�'j � :��IM�*i�)se:G76N6 �"�=e 4: 2:88:S,*� %�Zity~I�s(tC�:�o!Jlorb�& "�sis2!� w���� ,% D��=k�@B .��$�� �-�ded��MN ��KC�-"Y��s � ��>O$$5/2^-$ (N�&"59��`$.��� seU �E)��(d8Ge� M���e�� �k!�t�l��Rr��s�IH cros~at)�ri�9s.� "r�sal" M�  GFMC2/�AU>�a��1�e�G%�a�%�Z$Tucson-Mel��ne TM"��(99fVcoo01:30#RF�;o�s"#��i�a"� ��)8. j~�с�upA��"8C�5Gze�ZA�L �Fy%�.H"~n{ponA�;rQ> e��o publi�4�Fher� Pr� �R&��-% �!eci�pQummarjuYc)(�{q�i� ��.�K%�y�A�8� � F��: ly quit��uec�! themQ�ly)�!�V&{[a& J�`: at�Na �i^�F� �G���b#q me admixt'o of 2>C uder( ��&z$��L� m��U`y�",�zA$Ɠ�X( !�a guide)A�to�ch*�R-u� F*I-/ �� � o)�2 �:!}srdj^p�@&�n�-$ %�%��F�V&�4i.�$.Z��r\�h<�Mya��!le:un�A�thN 2�*EN.Ť*�qmt�9)T��2is faiv0?J�i�G��V���Q%�!�BD�umoQ 6.76I4�now)GI�E�AK �+$�=E�s w��e�!/E}". "�� ��� ���:|CQfO�,I+�mEp+$ a�hl��aY5E�I��!�$7��.�T�2I!a0$AC&v��:^con>+ed�#1E.7�q��S�@��&(1�!��$��?B�qnA�� � d�� &� &3 >�&�E�&=*k�q.re��� m�Scom�Te ib7o I�lu���Q(albeduo�y�KI_q1)��Ud4�tof�+�v&�v&�v&*j�y&N&h��I&c&K&�� c}{N#�%�It} &�!J4Po{>4"�E��2*f&EN ' N&S.�2�_&&.g&&[&F�"B�h]#"Q#��&"�" �F�~q#�&�")!�#5�$Eb'�"�B>�"�&"�&�& š�#�-'  J�1�"�����$J�)+N^�!rm# nJ��!~���'��'�'�' & 4.&�'$25j%�A�0N'%%J�7!�~�"�'7*�'6�j#%�B'"Q%�"\\ �:�*2�� 7.94J<&�(&�*6�q$�i n66�[2] {CC�"B, 7�$,LK�) J�3 C~� & 11.2n$ &:i��� !915F[2�' &&��ք��8V� H��6� 8.13��iz� t:.4.*>�i���>�4�(V�7}�[AB86 �)�6�(J�5��11�+�;.�, K�&��&�"� T� �4tab:9� �;� 9.��3-L  qu.�3B�32�3� U#�to"4t"�3&�3�&s��s�a��&���YA� ��i�:s3&�� "V�ACre&_WR�� �ى�%<1(| judgH%מ4he*;;J���[.l"#�-~5>bYh!�$B(;* M1};#*��"#*toQ*�� )$=�&K�)E ��in�I�/5�.{�#�1(Ael6YO FA��&�1Uadӥi�!Vw&B en�andQF�!�[ene:b�4�A4�"�S&RY�vM:�l\9!�3ide�6evolu�D!�%6Q: FtB�(ft\{4\:-\:68�+\�~$ �U.A�A�� ) �6- = \,~\{+3.9 g+4.10q+4.21u$~*�7i"�+ QD�,�`,{ 15.7 6.72�&�7E�w;��lik���l�,%a�Zi Ds�_SrMuAh 6 �dd }%E}2A�?!����E��"s]*�V�!����*/'is � E�A=a>7w"'=gY^�:li*.c�+�g�O�"1 N�alB��$2�<a]*R�<7$q-�I!A �H�02�\�<%��"_UNJ"�`8�fA=3,4�,s,3<E�eaal�asa�gb�It2��(�^mJ�!Q(?x^lu"�Tu$��Q +sam�E^" +6S�laz�Z�o�#6*� �DFaddeev-Yakubovski�-�)͋iHmf���.�-KE soft(���#�"Wens[!] ar mFkKT^'--�A�WHintT%6i a"a���ong E1�,�I�"� �3�=B}h]YrZ�r��!lrh�o� �%l� post�_;��to:�,\" s* (�=spocc# "e ��($N�;-9ig���zA���l�'��occupan�;$�ni\6�`,Y���KfJ&�X==��lR&A~s� nti�)��t phys���J�yej �LI��ngb�p`ե��%�6�]6���!z?#*bcalJl%��D2k�aA��ablr�`&s!]� �*�ϩ�VAn��.��ne:ILD"�B!���\"� !�:�aT�]KA&} �@��r�[��=�%�d9��Kribr�@�� %��� �>�VA�1�D i�s;�}�{�#�� !��*����kdXhS&�!?"�(2AzIqO!=�fIg)�%�a�f˽cP@i,%\!�>K�s refK �( F�^=P f��� $0p_{3/20d_{5 `�0�r����I 'k �l�w�,c�J���Aer�B�&��*&AL�r�N��6�1���ly�}e �� � s (8.�2Z 92Ŵ��]r;@d�}� aE��*��%g6�@��@�:gopt�v@Li���l>L"v&6D56L�M>}>+=H)*�[n6��2P�>42%& 62 & :�H:�8I�z.5F< 0.191306 4@{(4 ,22150 H063w4724,@0R33'%�f [2ex�]2az�� (6���1>x3>52=��bar4`&:O=@.6.�)�1�)T0)b^�)�2 :��IV�5�F�bf9���%2G*t5�7�4o �jofgZ[� %���JX�TE.S � �X.YRT=6�JX ~TG�X�T0�X/ �Y�Z�Z$0s_{1��& 2 % & $12/d4<"2zS1.804&�<54|3800436069G�Z 1.77%511:277 3  H72:�a1.768,52 :560AF:q�t :19 t��1 H1\}�:M�o�o����79��49�> 1.420.573 &M60.111Ű379]=�)D5303)�66%�11%n317R�5%�536:65!�67 :31]=� ,535: 36I{t3 .������"��* .i��aC���T���� k ��mady � 1 *&�&� *8}��� � n�S��hold �5for��ellgS�*�1�iB3�#� �O  � GUs��n' &�.�rk�a�g:' ��Xa�7:�5&�^,sg:&41@��V�5."�|*e el:�8i" 9�y�!1�Ya�S slob��eq6 ��e&�Xoe.�'w�t�E-\�-5t�.�*�(��u)>a.> 4-$ sit��d���=320$~ke�?to�:a1�? 503/zU8e�]no �5alƮ1(D>3-"",���*W�e�6f���R�v�-&�le�@��i�F)iP�&����///ta-deca�9u�*asrT`Caa�1Y;EB b:o]�2Js}�*rxxZ ambigu�iE[z-&�J�+QP �-�!��W^P.��$�)Is�)�A�t�"�p�2 r�a�F! FAS &s-� 1990&1/ 90:506rev�<�)re�3H2�tDTK a`�9�sW9a� L$(t,p)$ (Liu-Fortune�h$�r2)y�yel,eg'.Fukudaް���>O!�an<�.�a�~eRC DWBAG,�a 5�mau�r`3�mea��׵!=P�-delayeP m�! coin/4���h,$\gamma$-ray[��caʡzw�+.�9vaEd� og(f�G�4�FU E���t z=��ra�1o.��s7�Qq�/_5�V��}�" q �JaHq%M*$. nk]y�}�D��*/7 : 96S�x(MeV)}, ��@ 03s 1�'� 6j3.4b 3.8 9�5� 5.86 �X#*3 Ajz.-Sel.RS& $)6#�:-$� �3�e ,-W3}*�E�( ��Ib, 1 K ^+\r�)� k�<geq ��"��z�%� -6Liu-%liu90:42C,�!$ �fs L�2�: b>� �%a^+-W -�"PMorriseux mor97:627��(+)�(G!& %� N-fAo�Zaoi|16�| �)�-�g!gE& �Hirayam��hir 38��);%- �^�!�$ �v:(.�ɜM�fuk�0��}� ��u�uQe%�}���;G)�� *, %d &�n*-�7K 5_bepn_hW12�5K�*` �����2N nv5K��H^5Kv�Haj*p z��H��H��H%�~F�H�E6EcdbA3�2#�Z�:)�&� a���fcdb�j7E n3loA� 6 ��Z� � � � !��j8EHA7�2V2uE�rKQ�7$D;����!Nz �*I�;�;��a-<�&� >�,�;$":b�.B�aHk�$�lo\�Mm>�Z6ds I�� &f�+X�2� spa"�"-<��a-? :@"!S2{x^-}$Zca>�"��'��Nj6z;F��%�f gei99:83,:O nv11�ies�wqc"s�\9 :��m�D?^JN�m*�:M1C8; ;&. � �a%%:($E.�%x@& -65!-62@^�:9,3 "�]55[.�:�"1&e~\:V3�Z & -2e 6BZ -2.4"�Z2.5 \�Q6-}��"qZ %R� ZkD8�FK?"�3�`[� aBT-�.7 ^'fcf.>�*V�=B�9)l 2"�]2%#$0)x^�:-q7&=�613#B:98A%�3.9"1a3*�b3�4f��83F�=��6�4.9c5S:�<�4�aakQ�*?9�0�di^{F4-65)6ag9.5s 4=8 Fq 2�:\}$.ZgM�.�<� Je)�Zey��1.8�_!_2*O_1 � E�6i�=kJ[.a16(8):i9_'f 5 �5�7. �� ��7,�L>��4�"�B�$�#�?" edM("�#"�>�-Bi3:�l&�--*j{"� fs \nb{Y]�)�Va �$x02ct} %��Fj�q��&�pr�Q� |*e�/,��W;"2|,B�*%Oa.vupp�ڂi/� !ln�[ �6�8R2�lI�"��X���f�BP�&A��&r � �F )D �JV�|c&� �328�2l "ho�  jE���CFTw/�zE/�lw��n>I Il&�-�V�s�� )L dram���UAk�eX$ )�u �u{�VNHhA����!a�r4c9�]\.&�J.)|H)� "N ends up�Lalnzon�N�U91-�ITa#�(8--9��2KJ1{�V9V!�feVi9�' ���t�� . W\3�:agn�0=�E� 9 �Z2+OI�&f[z�gӅa[R�ZF ��/)["o -1("$ six(four) ���"� )!��\AH #8r!1b?*�6AV��& @ ��6#�Qa�>�O".��^���U�: ���!���O .�`V�)j(9k)�JV1�N:�-s�:�I"�y 2E�%<�!E9>�U5�:җ . Q{�8Maybe�Mr=NH%@! adjag !!���ew; %2t�=s?pn� 6�2-�6�e &�o32�H6b:I&u/vl> $�&v �f< \\[1�.2( J�:�IZ��y g. �%9�*2z2%/�� �C VV�"ca�����x inp�o help.o�� u��j'�m2UZ�# (cf.~:&b q~�5l5O!&]cs s�� �%�ttW* $PQi끹��skaco�L4|��a2e�� =S�>c��U tim�nsuH�7*0"�,�.$�&!V�Rk� &��1��zh�Q�i�h�;�wo�# ru�"� �&��and��&�<<�'** f� DP�1&� "�Xe 6.)�'& �$�%�RJ#�O�exT#I:� 1�)��YRls>���� Ea�P�'�� C ʐ!�3��'|t%�2*�A!,"�,&/*� *i97����� p][&xBa]��S�W�W-do��b%�M9ch �7avoid�^e�'!�� !�X%s��<)<a&�'"wb!Gbt�>�\ n(g��R|W�XRA6�aē!u�?%��` see ��$RNaE��;~?��^�w�\8cited positive-�parity states below 4~MeV (rather than three as )�d in Ref.~\cite{ajz90:506rev}). The 1.78~H`level should be a $5/2^+$ L$, while ei ne 3.41 oz 89� Gis@3@�F. Our results do not support the presence of a high-spin ($J \geq 7/2$) �D which one can fin� ^�<. We do observe )!$low-lying �- �$s although�Ly are accompanied by�!2. !Estrength�Ҁelectric dipole transition betwee!�,e two bound -� in \beel\!A@of fundamental im!1 ance!�is#an � able!�Pch has attracted muchen~`since it was first measurI, 1971M,Hhan71:3}, and again� 1983 " mil83:28}�e AbLd value of 0.36 W.u.�still%8strongest knownN9�) �it�b!<�ibu�toWhalo cha�r!; the %\-F wave!Pc!@s. Unfortunately,!�working�da HO basis, we suffer from!s@incorrect descripS t$ long-ranga�ymptotic � we we_ needJLextremely large numb �}I�s�orda�$o reproducA�e � form!�isa�rtcom�of!�, is illustra!=byfaca� at we obt!�a)�Y$E1!�I�e�p is 20 times too small (see TA�<~\ref{tab:radius�q When studa|X dependq�t�EC oi# size�mod�� pace!� q�+ $)$, calcul%�wit��( \avp\ intea�yin)s as: �0.0054� 9 65 bH\}$~[$e^2$fm$^2$]. �9 E{spond!^.��for�ni��: $B ��+�32 %q ) = H\�2�31�33 *B��= demoni s a simil]7$. However,�E�nucleusa"nota}at, iI�e��K.�Ak=�=�A{only offa�a a�o�� wo c�q�� to experi�. In add�G$, a consis��-ra�f�O �e��weaker $I[59R^i $�ݴɗni!@ere!als�U�,6�� er $B(]�)$a�n2�These �s�k entu���anomalou��{m� ��+. A!�p�xplanaE�A|Dfailur�CHO5�ion�V�F\ cas�%s given!�PMillener \emph{et al}F�I�Msh�ρe! e!�a�4ong� cell �M56=n0amplitude dueA�in��icien�w��in parti�%r�� s IV��V�*= ��). By)Zy replac0 their!Ksingle- Yl!;.`�� solu)l� Schr\"o�2er equ)�� :B one,Y1�aEadmixturo $$sd$-shell]s. Fin!K�gr- ��@!j mo!R!Mduq-qd�� gei99:83}%�wee a i on� :?�=m� , seB#11�g8gies}. % \begin: 8le}[hbtp] \cah {N� ar6�!I(i (in [fm])�!�*v s 2� )E�,�6X��0\bq�I%3w e NCSM��w* per� ^e8(9)$2 iG���,negative-(po0 ve-)6�u�J� @} � GFMCm�W�,���ame>:-�$pie02:66},�ɡ`nC�ison. E"� a �%�sa�Va� O$til04:745,.|\,tan88:206,fri95:60}. \v% *{1ex}%!�labelA :!� us}}I,ruledtabular �M8{c  & \�column c}{%" \jptr ,1}{-}{1} } \)b& 2D2}D$B 2�  )$RA$R_n$ R& p 3 mat}& %V � *^� $ &65�� $�\hJ  ��Exp& & 2.39 �,2.45(1)\foot0 {I&� � e�us}7� A(& 0.061(25) 100(84)�e��0 27 �4 .c33 p057`ehS--- Q41(1) ! & Ud)v {2 ^�elE�1A�{+}{3R�M�:E��E���U�N/�]�^�.G)I���2!� 86(4-� n� 0.116(12)}�.W66 DZ3Qd 5>Wvi 0065f \end���� 6�#le} %�andardpic�ݡ�Ů\����I two-bodyYfigur? gI of` Dinert \nuc{10}{Be}��upled to&$� $�{ ţ� � e�  sp;oscopicYo ���onc�k 0.55b 0.92a e.g.�~1 *� win01:683�e�� sit�is .  uncln9!G&�  � g�m n &� � 8li�)�nSC �= �36 �8, J�Fig.~8:�pal03:6~AnL ortant qu!So� oexN�� -� .�( 2_1�Ym"tt�JI7�-F7%�!�� sm inv�� ng c�erw uE�Ee\eigen� sn ly d�opO =�navg0_2�� *| !�$overlap of� i��1�6u) differAk$.&@ + n$ channels. T! aGimh Y(.3):} .� *� cdb>� a 7(6*�1 � usI�fr�V b  = 14$��icha�r�5�op'l E�!�56!�b?ng A�� A�th� �E� �!he 1kfuo{  $jj$ c�% ing)e6�%� E�5fig:11 F}�E�ys"uJ,s () =� squT�1 g( �$r$� summariz��E��11tfac}. S# al a�al�E, sx� edlapIW�second"h$2_&h�.=��ls�bue�ir �t:/Ma�o� very� (a� sssi�9001$)*u ��.v includ!.@phics*[width=0.9\A ]9p9_be11be10cdb98_76_14_rxf.eps��� \co\��st al5)Y8�� eYZ�de�esJ�!V�A�-Q�����Y��6�ed5�EF�(6q)0 �JI�uuIta $i� bar\Omega.im �thin,Fdot9� � Iud�A�A~^mD� $5(4)\^y�� 6�}�M= %��SN�1�)5\ B�� � !��%�3��)�F�<��c����xs��A�a�� listZ&�_H!r�R*�s utiliz����reaPs.n��e涠} %a� 6# 6RV�\* +n$}\\H6�*( J^\pi"3� n(l,j) s=� T�!fer�&1 ( & Knockout (aum00:84} &BBreakup #"� *� .� .� \oWn$Y).��"� xh $�� $6� &  $�&�,DWBA analysi� )�(p,d)$.!� D5CF%!7ni-}�%�,.�+\gamma5�} �59\V6J�n\ b)� on leav!d carb` t!ts���ively..�. �$0 !Y�Gft( 0, *�� �4818P 67-0.8078(61(5), 0.77�"$� .o2o�Jo2636o09-0.16�UpJU022@1�03.@0_4X&&�D005�0_8�@3"�7�Z� |sX made w>�"&�:   M���h l����I\[2� (Ez) ���g� -�8]$ ($S= 0.82$),0 B ^� core"RoEz)�� od_{5/2o w]$� w0.26$_(9 � ini:*� � ensu�wB�al7$iQ#B Refs"�(��,��. (2)!}- 2( ifo *D R)�1 -^�~~ z 7��E"���'is �"v� �quite st�%�regar� a%�g`  \n-& ter��, does hardly��&� l.� tail�slowly�}e$towl� ter-�dis�()�&� zis tru|� Z%�n -![ 2 ep� thos� volv�X �l�) $0�&ks [Obullet �c$below]. (3I#insetu@ m'j ooplf  o�log�+ hmic scal� is graph)�ly 2f$�&#%� b(!+%8 eno*ot!J�'a"T( b�. .� i1��� fur�E*\nm, it E�� H&" I*ex) � decay�st�Sit a� �!oo fast.%d�+*�.��I����-�A�.�2� � t 4!B�h�not��'�u!� �i��+Q�m��"�aJ�doQA�pla� same�q as��$oY!eG(I)-,$)�-m�A]�&i� t")in����*�%� just an� manife![io" a�er�u%%|,*)m/e�%;. "Ow� mparb)$s.% conf�.spocc},�� �a�+"ms�%?ccupanci�*n$s1�6�d"�*� s. A�,,-6A \inoy\2sED�!* ��,E�e#   and ���-�� 2 �%Ga�:�� um due, �*k�,L"4-�in-orb!�g*���J4C�$ed>p-�&�E "���&�0(el. R�/5�in�E�stE.) (8$2`a�92,!8"� ��r'0t�+e� �Nm��AGHO"iesG/h:�#optfreq}z�A���l�> :5� &�-�>,=I)�! \nn63& 02Q & 2>42 J� 62 & :�"�  :mF#5917 406 4@�512 150 0*� \nlo\ 34 f22,j3-%4 Q2 m1 � 0 [2ex]�� ��w(6���1>x3>52 ��72 &:P=s.�.�) 1���)�1Mʳ t1�.�F�-�63!�%�� %� ,"Rd$�0oʼn�fof�B��4���|JT�PEZT.TRP=6�JT ~PG&�$ZT�P0�T�"�>�U�V�V� � v\$0� aj$&g,& 3/2}.�"�, /d_ "/M��H1.862& 1.078& 3.643�j0466575���\1.835:93:597,6 :272:�c: t95:8 37 {J:q�1.828 t4:79 f :1 2\�qfq����~�4�050%!300!6580)i34V�2��64 3.18%N74)�8B28;=�23�616!�15%�75 ;9I281�/.���63 3.13 �76�@8 265-|-��Ƣ*� \sub,{�,sec:pospar}P�y � rsion�- objX,v� �s�6��.toBst� p e re�1ve��oA "�)� f^ �@reg� a�+�p A�� �), nN"ofv 2 r.*8O.� ��|�"�is�4*�/� ider2N?O�1\ho-"�JJ,� �% �s":finit "�7��8Q+� to u�7 our d 5actJ.�promil �\�0 +�u�:� drop�h^�-?!e-9�!"�-�-�"�EalreadyI#*�earlier]EO�� �)��9�<w P7E#,dra�/c�2far. F� more.n��5*� *N%I$�Q @sU;S"!"c&!<&�2�:=Kr 0ic $3N$ forceA�r0iiRf*�<.�5m�~A$e�. N�7��7"�&�I`�it sim+9-@�effec!f�A�cd?y�rt�;eh(-local term^/=g� $^{3\!}P$B� �sl1 1ifQ>in �; im4J:Xg> "U -��< ize,\�"s<�urposaQ�� ��a�aeu*@to�!r6� 03:L8� ial BGl, i.e.,~$E_x = E_{x,\,\infty�%a \exp� -b��)$.a!*e5H3)�ex#d^( fits*��.��O#10a_a9)�minfix�_paperR#� �Rb�#jT�!2�#B?�=.a,]Y!e)K*�<{+}�)$!8iI�[&y �-�ZDlow$�3��Q�6(a)A��5(b�%�fo� ft��Z�c�dI� each.�8+#�8, fixed.ay�(�' 6�Z  dashed�#�7�'!*oIAYqe=w dataa�,�}ion��se cur��5�2nVb.%A&�#:YB�#!n2WZ1�end upqe%�C ��s;��1�at����approacha�"e*�+ �(. W?IFf%6�&�M�D=$\ix$1--2A)�@Y. �@discu�7��7� ��MV6� verv ter6 ng!�U Bs?7a;By$A=11$�6bar%4- $N=7ton���im $�f&�u -��"�*Dl'� 1}{B�  3}{C/-diagon&�9� �( 8$Hamiltonia2D�95s�$� n �(a��st.�&�C@�#�  ?? &�8h h. B�9!SD69nr+�an HO �q�A�&�'3T+�'�-s�F�(���)� : $E%#-j%B;�?�!�?-} \: �W�N = 66.25�[ BU%;J[B U m�1U 86.5�6�2��ru�m**E�h8\FV�Ai�\ s�GupA ($J=9/2$, pl9q<w��i\vj>� %l�6��q0MF.�in@/&( 11cdb�}.�we )�!�&�E $1/2�G2��6��Q{H@B9 iHA^U�K�e �Ddeg�a 6�� AE 6�Dm)/����;4/#<yu=" �~� 9����-Dd< $ principlewBthorough"Yy variU eo8 � be}r.� clarifKfin�)���prediy( �Bny�A�<� � �� s6AtA�isA bj 4.cx �G�y�.�t<N�ɼ��)�� n2� �[y�'�3:68}�Zah)1a � w OvedZ k�� p� ���#� � � �D �KbQC; d�29 grea!q d, by �.ng >� a�cw*:��W��a��.t0i�E�>e�� *RE�ut"zKso)%X $previously-U���C�rum&%-�e�+.k!F"�!�*;2thi�:97j/�L_ � Va�3uA�� ��Rrex3Eg.UU%�=> %��E:� limi?toV,R&$ (4\ho\2su �w w 1_�"_hW13i  2 E"��!M"��5Fed9�IJ�203-%*���Ak  �u�*J�2Ѱ� 9Ga� $� .�ajz&O.�q5m��a#AP 2�M2~��+� d $9�Di�� �� .mHFUQ ���>aPDr��y�vA�a.e��:B�Kwa��edB� �,>� 4 Let us now��%�zu6 ��.<�\I�return����N*�6` �]zb :� �u� q�ed5B� %K�#9��i, as a�Ł�%%�U5�:yc2y.�C�Isc�C�Yempir�f "&�x�#ply go%A� $Z=4�. Z=6$� �1�� �Fs 2be=!A� "&. to b!3e�%�F� at�� 0&k .�yTodd-$Z$ �� $e��V��j�(D  �6�� , naOat 6.�R5N*]t^5ces"0� metho��M&>!9S!+employeda�'( hug�ifA�r5cc;e�H�'�=vQ_�$��a",s�P!��6�* Ofig>Na*� 6K%`l2�� always aFs o6�F�X . A �D*(6���q�A�)y!��P��2�os(KF/��ll; r�6E.�a finalgFark�G:/=Fni���use�V�A��%� }m�"> � �rel&y�C�C �>!�12a�J� g���.Yb_c13jY�h/E\l7����~��w�Sa (b)� ���:N.� 2�E�*� G��N��{H�Vq�ed��6>� �+6+�o2(conc}Co� s!W� &Q�mV \0Oab �io} no-p0 �H� �֡BZ��:�reP��.� s.�J)���no��g],�,never before� N �A��a*�>5��. A-X�)J�>ly� KA*�Ni�Q�HsR,� �IH (bew� �&(�&\�;NW4 IS-M !��8we� %Y)l]!)b�bn*�=of� 3}{Hi�e�ei�r)4.�Wof� kP���� curR?�Mc��\0-� str�Qto maximV�I6��by9 �oursel�86 )s��b�|Y���h�[re�� s.MZM�S�:B8,�2� a I!it�zP�=�K �K &qJ! pWs,t-E�MOi, ��5�c�3<-gC"�.=� !��p* .0 . In �>yP*��� a!��sig|f FWn�W����&Lb*[*�Arj�� �2�R &8 A�O "� �5�1A-"1 �R�DNpav ly, � �Y �c3��-6P w{M..' �Da��i�#=make somR/�c �3���\ly un�� �of un�ZB{� bAn over� )e|� q!���4$��s�rZ�Bi.W1 a��A�{�Rs.��T�Z!e��.��EI.p ;J!ai�%r6myia(B/"�� q��[b|z �a�4&��> ��ze�8[�  shN& & !�%]:�N1.? ile�% < ��-%��C-w��M�a^?nn�3�&�\ZSs��ve�yq�d%�s&c ��-�l�"nefit �(Tre2�S�Q�~�������e��i!�us�In.��� ]�OE1..B�5E�a��2�+e�6 Ucma b���T20���ed ho�'"-] >�J�X{"�W�I4jNZ�1h�I� a� lap,a�!)0 RDnd�8at\W"k!-a�perty&�U� )2�7!�&&���^ ��Kq9�ach�Rbno� �3to>�, pr}�� �9�Oi &��_gu06h i�:�IsX!��V R� �Ta�� 5i�,@3i6at: :T# loos�UE;B�G��cti�X�� =hGi �-�n"�_"�7# s. 2�It�J� ianrk� ���'I(*��t*%͕��WA�de�9�!=Y�A2�B�WB� Y�&did�9 e a "r&�&��&g*����� &8:�:.��8b��5�suggests}5l �� wyb� �&` infl�mlB)*��~a pursa�!�"jKf �AE Upu�H apac�_)eed��E ��"J ��J c.�4�O� ** "I�ASay,lba��a�put)Eb�%" IY5Uin� wider� text�5���!�^� Z=4$"� (�)��2�  (�)!8dX2� %)*n "�)���� �Ta?�掠 e&�E��7WuR�W:!A�uMŘ m�s+O C8bsa�:L� i�fT� A!�Mf ���B�!���Kis9)�l}�M�-�,� XZ�[s"�gpossibl%��A�_!30r���*Z6e���G��-"�-*��3ac� ledgE s} T!1�e����u$�Z�auspi�)�� U. S. D� tLEnergyA�� Univ!4tEZw twoc�X:x,�pac6��topmargin 0.0in \usepackage{epsfig} \def\bea {�5eqnarray~def\e�T>be5ue>5 { 46ie{{\D.e.-viz  viz.}\ } yg w + etal �B F{{\cal F) prl {Phys�<v. Lett.[p:r.5/np �\. RLGV{G_{\mbox{\tiny V}�GF>F$DRV{\Delta6> R}}^ZO fS{f6-SOhyphen{ :-Pnewcommand{\sfrac}[2] "\N{�W#1}{#2}$7!�2p{|2p\uUle -�4p2h{|4p m 2h:!6p4h{|6!4!��qL } \qB<{ } \title{NewBs]fu&mweak-ݞ�(ametereOap�Jta$\ay} \author{J.C. Hardy}(I.S. Townerltaffil�${P�> a�: 2�E0ics, Queen's �r, K�t�+XOntario K7L 3N6, CanadapmCyclo�dABitu&$Texas A\&M2\J$ College S� , < 77843!�$ate{\today!��Mabs��0} A new cri�a sO,�:L worlo<1o0*�-arrow $6�sN vide�%A�d �  of�t��iinEDE ].  �?ir=+0 � � pd vec�c� (CVC) hyp/,s�m�%�T?^W, $\GV$,� .�3� b�'� be�ct�q3A�B$10^4$ �U"inZdGFar��mGto $\fS(*q��013�R dp(est-mass un0 &� ex%j;� dSp�Far 1 i(��n( $|C_S/C_V|2� i2e�.�%da��2%�up-dow��I� !h|Cabibbo-Kobayashi-Maskawa (CKM) �g)O $V_{ud} �J$9738(4)$. �-P� �$Data Group�� :s}�#Gb}[!�-A�As�CKM%G8 yields $|4d}|^2 +  s. b � 966(14)$;"Kr , if��Xh a.$K_{e3}��x.7� �N���A�!� um b�!s�Z0999(16). Eit tA �-( bW'��$�4�!�"- 2/ra{-h�M%� .%\hH{23.40.Bw, 12.15.Hh 60.-i�q��� Beta��a)w-!, �. alogt�&�$y, $J^{\piE^+mIiso% , $T&$��!e[6su�9J� inuRl� ofte�. tens�Gud$f�decad�aN "�i,�t$ft$-!�s�W&���pl�/83� �-st�Z ambigu� /!�quelyA+!�����:�Thud(ir measun;s�n� physicisxM#to�ne )z�Y .y p�Mp $�2�theory�,� yea�8� moti�Ole��k1 ei��$"~inQ!&l)= ��V�$preLm. AAT3%�a.B]iss�GaI�ve�O(odg9�%!oreleviW� �4Cex�me,q($c�wLTo73,Ha75,Ko84,Ha90}a� BecaDWla�Uk�e�Z in 1990!]"�" amouM\ew��!Pap 4!/PI� : half��9e�e %j:J0$lea&�-]\ viewBTHa05}` :J'ly)ed(1$.�s, adped�jl �6acc��m�sDrnibr_ �*n�`s,�/�Otat=�_��ore�g7c8��0}�雥�up d%4A�H2�2s�zactF G.� t�N��s�> outcaf>1 es mwexp%_on.�%���`���Nny���� �i �nd�E%'!���K]k-mix�Ho� ��,��d}Fl�l$*�A��9_Ed"* avail�-2����atI��$/ help%Htr<or [c!��*fA=hF�4!K2��� �� $T=1�����e6j'�n��/.;a)he�B� Vvia�!�+� S@9Qr s#lm� (($\sim$1\%)�H -` 4@Ani�Z�6omb/�/-�se 2���!�de�1 a ``/ed" $\F �[e!��we writ�/�=0� be -D \equiv ft (1 + \dCR&8u})2{NS} -&C ?5U5,K}{2 \GV^2 J DRV )}~,  9Ftazt�%l{] $K/(�.@ c )^6 = 2 \pi^3 �\ln 2 / (m_e c^2)^5 = 8120.271(12) \tByT 10^{-10}$ GeV$^{-4}$so T%Dc>� e�semi-lepz7c��. s, $-CP8 $-symmetry--Ya�-�!�!�$! 7&�-i*��-��_�J%�Q�9�a d!�.b mpriAMhe w$ Aui�VueP! m? u �-6q�$e�#�'�E�Z$ % daughterG E�� '��, like�C$,�   its e: ɻo�2�4 % e�z"Ve:��� be s� a� ��� d=� �QblishP2tividual����� � CVC asserEis4X�|m 0�o�  &I%�medium,m � es -�#�t!�.�E�m�%--*�i!�i�wia�ger�B�9#le&.�$ ific�.i^ol�u�<���"D~iz%-y�-Y5�%�q�5uquant� :�total2��, $Q_{EC�� $-life, $t_�v$,QthSn�U Q� bran = , $R$,A�w3'%.|of�e�U� �� !�*6 &�T*S % eF, $f$$A9��:����.to_3a�� ;! $.�&�t�69A z i� r ,�&���� ll1�7/#�� y pui �2  N�wber 2004�� we k� �%8adv xk"��.&�*N _�( '$at�a�8We scrutinized �!.�ul��{!/'�4!�tYand!e�w�*B �QV)�aG;Gre�!h �St� caJC ��f��� �M�)MYe�*yU4but6�zie���#V id��o !7i \rej�$ . O�  iv�� ), �� ��  (� )6i��%&!�*$MGZ ue.��*�[m�y��we�|Y ing��}-�cedur�6��!�ja�E!A'aq( �� EDeR��hhA7�19ew�eQ&�# (6mBPDG04}).��1 �e�����Ʌe%�ey Ge�, toge0%c{�y]G �'A�)�!ͩ� m,%��iWX3t� 1}%�Atwelv�*q��=��6[na�0.4\%-�a�or� ter�lA�V#r� "tB>.�0.1\%)�y c a broad�n*R�v��5� 0$�$A=74� ��4cip�&�y(see Eq.){ )�25�.ol��o�C,�Z,�t!{an5�� $\�Gh{Z c(3072.7(8)$ �)Ma)�"�k chi-\k per�>�of�9 edom ($\chi^2/\nu&42�6�h9&�#��We�# deal�;a�x(�lfi^# cE>}��"3F�4J�, ���I�!6�.��]�b�EA 2(]�. _ �uv( \vskip 1mm��&�v��v{l } Pa\/&6Jg1`X $ft$�f2{f  *� z*C&B � } ZuAG$} RPNaus�VJ�(s)Zt(\%�P�P1mm] \�V �w-3~T1r C �$3039.5(47)1.652(`3Q540(39gv 3073.0(49'\\ L 4}$O=3043.3(1%$& 1.529(8) L70(56 L1.9(26.L N22}$Mg3 3052.4(72'N446(17B0.505(24 3080.9(74'� 26m}$Al &�6.7y[1.458(20@0.2Mw L72.9(15FL34}$Cl= 305022425(32 L72=21s% \\)1KAr K9 �1.394(3�w825(4�6'�38m}$K= 3051.1(10�%/23-�0�!�! 72.2(2�wA-{42}$Sc L 46.0-L37 @0.460 3075.6�x �46}$V�3045.5(29� 29(5�L 5(33!;3074.7(3�L50}$Mn �4.5.� 29(6-{547(3E307! 2E�L!�o L7.42L 8(71�0.639(4�1!0A� L74}$Rb L83.8(7E8%0-� 50(4!n!|83 q �La�& A��6��z�ɑ%��x6~�jcWJk 0.42sz\\��F :i�"�0 ��} Z��a*�*�&�s.} AF_ adii%-coe�)*��is�Mic pj$ "�I7ir �  �� *tQ>. �yNJOKstenc�#�M0e!>xQ�;$ 6�u�=m)Aa �TfuOid%���.ed?d4� ^i5 r ."& ` }[b] �?${0.0cm} \h6�(4{file=PRL_fig1�F,w�v84� Ir]�re�i��&Ral�K�la5�Fly� Q��c$�.o�>ad/&vem-*�:��m2� �mN%xe )D���{���=;�y�w"���{->�&��6�e�5��(SN� .) �W�!o 29n�-]� refle�W1 lackA]2�A��af%��i�7lIqi Msd9j  horizoi�grey b��K2�!��]e&6\>�%��� its �e�eu70p���I�|3xi�0 loci6��8fMa$+m�6��#�x���$T&= \pm ��2rT&"7d6;&�u$'&2W.}�a�g m��J CVC(q--b�E �ICVC*�'2�!6�"@�'is� !%$ rot���nMP'"�=m J--W!-di ��A��-�f�Pi�4W�1ndHEE�ant�epe��" � 3P\ �2l�:w�lJA�D ��N�of>J ,��m-[xet�! 4 ,��i,�((A 7�(ver���1xh;5w!�ak�=�K3    4��#p he ff!i}T*���� B�%F!�s a 30\%!�� � ��pA("e'I�#!��(62xbe"�&��2�� � 6��.c a2)PV)*aAP~]�!R!4!j&�*)J-z`` S" �2�Q)M�[ Le`J%ae �as7; tinc"<,� ``fu�3"�� }Rmo$ be zero. ɂ*� argu%�\� We58$ �Z>�< �-�1��1Z hadronJ�sfqq�9s�= to vanishE4+52Q)s� ��#�A@F��a $ (u� #�9uBehre� $nd B\"{u}hq � Be827!���+h% ��af�^#d �O a%-N��v" ���shape�E��ion"v<��aHn>5eJx4�uXv,i�.� . Sr�� .36Tc�T"�Q$Z�)>%�)}�Hg�R�j< 6A��J�a int�K� }Z��%a�0��.� a >�|3������.c  ��+���A76A O2� :��r exhipa�g��, ag8st��=A�!��u,���� f�-,005(130)$ oreBA�� �SZ&, $|\fS6".���Xn�2�.��F�#�"�V��dG�B� ��=�U�?nO l mixXD��r xial- .�u�bxFy8(8vi�U]r� noiE�?iori}@9son 0F� U0r��mt f�1sZbWy���,o6��t *�M hat @%V�d1BMce!A�Vr�>�Wan�! ��b:�*I�q0eo..Y��I.gA4i"VA�*:<�}61A�i������/�M.} 6��-M�e�"�0 \leq� 13$, �eU�e�cnv<�al2�Jacks�3TrieimNnd Wyld�� Ja57�j"� �-Fierz!Merq�!P�2�(is $b_F = +e�1.�� J*? � a�2of 30 r�)A��e�:��#c�`�i! ��")! f �T'� �1�2}+ dev�⢡Aes� i�+un�y�:m s�Jby�f%�|�Ings �*�59�,$ or $|b_F|$�Zr���� a�a�a���1d}$��S�(CKM*�mL2rFtGh!�. f6{,�0� f@zrt!ir"E� &��6*/eA�--% nH)%aR s K�Fn@�KlsI!#XS-�LH�-toQN- for "� s"h`!�&J%U/�@ ,���C$ by 9!�AA ��E6c� ,t&of Orma9Brown � OB95|"a��error�&ig!�toR� We!X >  =B3;2т):���to B{�d�4��C��E/e�� &� %E)#* .40(8)\%$"� A�oi &2])Po��� aBMarciano�� SirlD/ MS2� %(We� mU/r~�)&� j) %!�z* .) a�) eJGR*tself��of"�tlw c�!�$�4&� $\GF 5e Ba�%�1P pure�6+muoS%cayE)�H �6�.�8�0 �6:� GV/���akQ�PJ�6(PDG) l)��#`� .P,3 = 1.16�1) .5&),2*%l�$ $�6d}|j!"(7 Cb� rK6m�d2���yi�c31U�UyIj/�-�2 digi�YoA�a��2ɉed:I�=soN-.,!�A!�ide�;��rec ,a�+͚� D�'��B  pr"�%"�3]!�:OdA-�%:� v�>Ba�6� �) Im�t:��BFof ` itud�V8"X-�� � M�mdU�Y�ѶE ��!��7--�row��aw I��a��� ba��1� igen�&�� a: a�&ew2�52;it�&� b\o itar� )� # �remai� rthoR,4ore�� -a�|�is�OqStri� �=N- m�A��sA-fy a 9J��i@ aA lya}&�$!%�toT:a�����E�-l#`$ns�=eI&�2� �"�2. �h��<uAȕ$e�+ PDG'a�@e�PM杅�?s�? 2200r I b  0036 !���m�P�$ J�5;"�14,1sum��4q1!C��10 e nu_e ~ ( �;^+)$ >�,�DBrooka n E865]w-\Sh03}-�s�5s�50.227/2m� 30�?I�>is-�al�s� adop�R%��8�<6��e!�"{ �kny�\4�S� "�5f� I�0.U<%�y %b�-r'i4q'^�com���ou=for7 ���s>@ig.@�A�C"�   �_���A��q2"� 9D ��TPDG)v,.%�c !qtd�h*sum�26��2reeu���!F85(54)V �恑 .����R**D enti�due\��1qRJ�= } I�W2�II�1�aSnN�6��be "�-a�,�3��i� a);2Z. �<:an Gan up&*� �"� r+�of Jv>a�G` A�a� �Y5MF$9CA��sou�f' e�%�O�?!�!� ��E. B� a_{RLa_{LLA9�6/Herczeg�He� If!)�=pEY�inF�e!!��-d $ReoR}/L�d 176(74��;���M� &� �� 6� �wo& &�$0j)�"F� zA0.�Ifa  R ���%i�A�ց A��y�;"�@ $Re �B�007�a!aVH�ud.� گD1�6.1��G�� hund�2�u!kt#� �  H�. Virz2& -.��aZ<��as in�OE��/$&�{�X�> ��a!�q>two� oA|]orA!�&��s. *��m.c����o�@v��imp��9I��2e i3 � q` 3 . N�:the�5� #Ctq�\AP$ s�T "!hs���BA�o"@l� ec7 techn�AE�L�^�"��7or "�?aiva>#�z_'n�Q>�$*���dk�\qIi��1J� E"� >p,����xH�hFnew9 i 4<�!�2amongsa��"���.�0�!&I� &�(sQ-P3�-�nJ��@\6�g.oɬ\_U%�!0� � "��y"��' reli��AWDU<��   sx6e2�(�n�4��5!g�_4}-�"#.PG(�C|56Vq�,�� c!�m�R��X���R*yzdo�`yet �1m�=*yx�R�{%�.��s!w l�5�qayc�oE ��� jseEr ؁@@+��$eqyd, ��7)O���}T)(,l as!u18}$N�^{30}$S!562}$G&"OG valu��q+GT� area�"H]�ρ��  ��ca*JA)!znq("YA�e Q� itiv )Y�-Z-"�-�$�S,F�Re*��(" �_l"�FdAQ�c1M�$1�dt�(�AB9�-ch) ��;��7]�3�: �! to pt�yE�a�bi%X �G���v5D � .o -- ~9#" of i�#���CVNW�-Z�! #�v.(M��Ei?2$��o, !�)�.�� ��<e�dw�sal)E��A_�yla"c#5� b�>e�Kd�ͳ2�=)���Xll���OL ��[|�D�d� �f��W�A<p!�MX�elN�\gQ A �q^�� �on2�Y&J H!!� �x > %>qka�� am��iov)�. tP6�V~9�Vof JCH&;s?V��"�Vt.(VWGr(@DE-FG03-93ER40773%5m.@Robert A. Welch F�m%t��ST��@�ank)F}P�TNPE�x!h�Kta��du�" 5'g month vis�N"�+the.;V }{993Lb� em2I} I&�Q�J"�Qn�pzTDf A205}, 33 (1973)S, GtI} 7FV,�1�SO54}, 221P52PXKo84} V.T. Koslowsky, EPRgberg,2�H. Schm,, R.E. Azumaž.� inqLProc. 7th Int. Conf.a�ato{�Z:?fu"h%���LDarmstadt-Seeheim}, 9O. Kle�(T.H. ) , 19D�p. 572!�5;90.;,2� f%d2�836d(509}, 429 (�J2d r�submi�(to~S�UC.��rBJ�G:�art{\bf 2�197 (2006[C0 S. Eidelman �V, �LmV FB592}, 1F42�T�r� \prc G 66} 03550 I22I-'� WeinI�\�V�11375!o5829|& H.2�&W..�&,I�E ron Rad�A Wave�#� !��9ar Beta-��} (Cl�: don JU s, OxfordEz6�C! J.D.&o!S.B. Tr&s! H.W.x! Jr.,�06}, 517�72��n W.J."@��"CGl)g5G22F 86);.%y����T�T�?St�L -*�Modele��S8by P. Langacker�[ld-�[t�,B'gap͇�M60' W�L.I .A. N� C �!�245%�95); ~:-69866%9�8��440�;7495).���QS A. S�Re, � u91<61802e)6o7 P.M9 D �3��344�N%�.)Prog.�.q�ZA� bf 4!�413s1A5�7:� �end&�X ��"�[style[�3 col,'\sfig]{\��,voffset=0.5i�f_"Y21S{Jet TomY]�Quark Gl�Plasm:X�XXin-N� Wang�WM\{u�E`ce Di��$4MS 70R0319,\\  _ BerkeleyN _,,, CA 94720} �\*UX .�S�>a`X RUr�6� ofR$p_T$ �+Uke�je� rrMa�at RHIC ��H� i T� onxd�'�p�_,� alU�o T�g�Xpag< a�heavy-w coll�R �fpO okQ6�$, back-to-;3�!�t�C�%� zc�4d azimuthal an��rop�Oin�)%�T���|�-de� y ab� 30 u�)aA 1ld � us.i 9� %�U(74.25.Fy, 7�U,Jf, 75.30.KzA PACS�aqic�# AT omy Class��)_LScheme. %\keywords{S�eed }%Use� wkey�a�Ip%�if' f<^%diܝdesired�e�q� s}{2a�s�ζ*,h}�H�T-e�,N9�!pe�1!fK)ga�sXa c�wHI��Hn=��c�j<-7 pe�R��a��& stepA�"�8� �GANof QGP;)xe�j�z��- L&�2��A2&Ioe�-";A��colponP,O  D� chcIer�S3CC*�) '� s�W� 6�a1wvia��Eing*hQm�icle bea�I,$ep|ne�"V0;!F(DIS).F:v$ss ���Oon� photo�Q+)i�%�R|��4� Ey�MZ�9 &�/e��2lr]s,���I�WL` u\nu}(q)=Q 1}{4\pi}\�ZPd^4x e^{iq\cdot x}\la��LA\mid j^{em}_\mu(0) nu(x) A \=4le�Cz�3R5*��%h2��a5GL`D. S�YaF�P�i�une)F�a3%�A02 s�=�^o�1 ui�E�r�!�&�r5 QCD evol��M&n:2001�HT dyna� d's"��qZa�VZon�on�.�oer�"��sY��E��A�s&~�XM=��+��G�meA��fe�94 ŁFwsq,�9�#G�, few fm/$c$ i�'i/, p �{i,��� �! i��9���6 f� di*!6y��2 dh� w �expands �rapideB�� !\ itud���TM�O:�H��c�� 0�m"oƔ?Xer^. prob�oV��U�Fe-��R� .�Fo*�έ4�����%*heQ1.H"above�.�k�n�+������1�P�Ca v�v)s)6,��;��o���Qtem�KA��%k�4! �O&�Sk4� #Y�whh �e� historV  �T4��g�ǹc� *�zreveal�S�{��m�!"8�-&i�"5.�z can w@��rei��bmevB d���i��S+'"c )�screen��� �gM"�in  o�?��j)�:a���lA�dissoci�Q �b&ng�) 2�mu!e��*���X8atsui:1986dk}. ��A�or��:�!V�+t�E)7 s* a3U?�Ye-�.�8Qpr$ �+� nu�fFJ�e0paA�Fw< �M ;8)K �� $�A�&�r�_X � ��� �awg92} �g����nd� to">�7Ea�6VaU"+ b^� �  ��a$��!��S.�J> , �] s adT_aj<=�t�+sOOof֩ �z>� N^. S��e) ologe�:�{ =-(CT),)%uIx� 5��<�Aah"e "! E6C��1e���� cG_2@S��! 6��1�3��wis��Dult�^$say��sof�! ;*��izU�A� bulkm�ao�'r�dr{Bw���� - Z>��� 7g&e2d urb;Zin QCD�d{Tll i&� �7&�) a�� 0 $pp(\bar{p})QZU� A&�h!�on���a[]i�+ERe�`~6)a$�q�2�a_<�i��-)�%�%��-1{Mo��ed Fra�o)�FN�yAs& iޫ��y�� S,MT � f2Y�� I�ed���D_{a\&ar/g,h}(z,\mu^2)$�xch1�-�d � lyA1T!.�-�#K ,J� m� ee y lo�R�h���S�T�X"��M����.A��� C�� e� �Rb fd��  $eA$�yk� if,Guo (0nz,bwzxnw}�D��~I%�s�]c)s��D, $e(L_1) + A(p) \ =�2@h (\ell_h) +X$, w% $L_1�-L_2$ a�A�%-m�t� Q�E� out����_( g$QYo��lāC Vum �J�* al c.���uxV�Q�)�O.&2$E_{L_2}E_{ �}�d\sigmBoLrm DIS}^h}{d^3L_2d^3 + �$\alpha^2_{.(EM}}{2\pi s M 1}{Q^4} L"w E p W^{\4h  \; ,"�.��.nd�-�(p = [p^+,0,�$0}_\perp] u`$eq:frame}$&!71h�,�o���0, $q =L_2-L_1b(-Q^2/2q^-, 6l4 X� (fer, $s=(p+A�^ADE%553U&r&>E (EM)FA.A�12 oduc�� ��"�,��V�� � �ic6}. IJ��)all� logR�"����st�('�� ��� z$��^*+ q$.[���cten�*�")t u;SU \}{dz_h} &= &\sum_q e_q^2/�,t dx f_q^A(x�s0_I^2) H^{(0)}B((x,p,q) \no�}\\ &\�s& D_{q>�_hN^2)\, ,mnDqu��tq�ZpU�%!��E��cn in5��umfrL�9arr��by6IܡmZ"�$z_h=�e ^-/q��e� x_B=e�p^+��Bjorken��ble. $\m%B����M�q&�$n� J 6� $>�OJ�,a�2�"�s af�$,� $Cp .�� ]a�)Y �ng� !�DIS� 6 ��'al &s�,@ %��"��^��."Q��!'Y iqt� ca! �)P��se��G>I�ll)% �M r9o �$E r&��J�u 2� u Z- UX%�?iso-zkigher�G?� jr�t��iŹe� ,-~� rix�_� �sP-*%6�""\�+�{c>.�%� a�`d�$a�a~&B wo&�)�A i� �#Q q��}U3,g� al�a:m-k�,�pl�(g&" �LQS����N��!= dou�}Y�6��S�!A&)%�6z �H� ~i�/� fF i*� �.\9�tilde{D}nu&\yIv& r� +\int_0f ^2} �<� T^2}�  �W����A_{�]^1>z}{z} 6* &�Lft[ \�y��:�qg� x,x_L,��. Ze /z) :l+ l.nlgqJl!.gF�/z �] ��*< Mf�ry� $Jo�8�7��m�2�"u �7UUsplitF� �T ��Z8��&=&�Eft[I61+zA2,(1-z)_+}T^{AA�g<x_L<�.:�ArT -0.8in}+\6.FlP � 2TU" )�]M�A�Q� C_A} U� N_cB�}!�N eq:r1�� rR�V;&=&np!1-z>�.]Mr2B Here��f��`u.� x_L �T� �zvAL^ x=N��nB�j � -�^1�ű�,"b&� 2�A %*�I8dy*�!�0dy_1^-dy_2^- (x+7Dp^+y^-}(1-e^{-ix_L&})�m� 6T 4in}� 6=(y^--n)}Bheta(-S)\  y^- #:d&]�b �1� "� | "0\psi}_q(0)\, IZ ^+\, F_{\�,^{\ +}(y_{2}!< F^{+ (�{�,L_q(%;) | A\� \;QWTqgBUh;di;�-�,&��#s�r�Bof?'dau-Pom�@huck-Migdal (LPM)}\I��o! brems7Vhlu�gA��/r��c 7.�neg�(vp�1of&c��H (A��>0$) or�@�&�� G� ���$$\tau_f�: 1/Ib�Fs.&�]N X�ar:i�de)K���1��s  LPM6 . U"bC6, 2��ZLQS,owo�n)�)z��� 8� � 2U!Q% � �h!^uN!B��*�C}}{x��m�0x_L^2/x_A^2})��)�� modT�C4"a2W-�<2C x_Tf^N_g(x_T)n�  C."� i� ify�I!=��g/є$ ��R|"PE�����i&~;1arS or�7�bx?:� mSes, d"�� a typi�f�S? F$" s >D�s�>mi�ep(mY \�H1'p^+$)y�8J� � $MR_A/-�^i@�7ramI6P$1t!PhaN� minimumO6e�0�a A^{1/3;w� $MEy E�Y$ass�rSi�a�!`:� *�is � po*�S$"���),. ^2/Q^2$ d �oF� ez�quadr߬�E���� $R_A$\ �>�a)�p� a��f�� orm"#!�4Q��EcC�t%i]" !f�A}8"6�(Q��chL���s�r�'*C��e��Gd~ia�c~��ix�8|:;$� $z�;c�2��ar-=��<U cI� 2� "j. S��B��!es12a!\*��� h)}Ro*� =$^�7N�t� $^{84}Kr$ t��6�oO�E ~r,HERMES �Q�S �}E�14�aape:< $z$-Ih%+.; �% Tv|iH�Hr��feak"z-��5\U� $A^{2a�Uq��,&�V<U"�n�D���T"�> . By�U��ogl��p�U!bAFq>)V,[AH ;G%��B?A��{` J�=vR60$�x�7%B�:si=0.33$V! $Q^2�43;>� $\nu6�l6 L�9 �ataoww02}P0R^ [] \6-erX_� fibgure=I=.b3� ,height=2� (nase?�m=10pt "?bP��ed5o2� 2|u A9>�]� \protect2���)o� 6��"$A� $dy[in�.>figu�w -9 ՟���rf�>�A�2� d8����"� &?"I 2 *�`� e�*�*"elv* z_g\ �21� V0 ) 1 dz� �< z\, e :g_B5.�n.�=&6� � {C_Am�N_c�x_BT Q�B�1+/5� }6nG& 9{x_\mu"6x_L\L^2�2� "� eq:heli-!�M&&.�Z=?/' q^c �/ �$�/� hl�!� �5i.a���=@.b�($x_A\ll x_B1$I�YstcA+�.~ � `!+/N�I@]A(!�� )& \�  &.�CMRJ�)�%� Q^2  6\sqrt��\ln #}'\, u�eq:o1Vt� !=1 G.o$6� y�u]Kpe�*ո^{ ._!_*za�m�\�e�|<$p^+=m_N$, $q^-=��,� �� K M!�/2m_N)&�(ge�EV�.� as $1�Eh �i�=� 1� 2r� mnͰ^2 m_NR� @(C_A/N_c) 3\ln(1/!�BH"| d�>"!S�>2g$, U���E���0.124 !Z����2��$'-��a< 5�L_R =R_AIf2/�d� >1 ed Ga��".%/I ilYb�*Hy e ge�h�)1�iK$dE/dL�5��/fi-�S��Au�!4�6�$(Que�|in Hot M�$+�5} To-nd��(!b�~� R�#�G)�N�'E�� ) 9?k�-��e�$ (!y Deby�+P )%�a�%ityqzj( $\rho(y)=(�0/�R_A-y)"_0�n a 1-"�.al E2an� V,8. Since the ini�[tial jet production rate is independent of the final gluon density which can be related to1parton-g2Lscattering cross set�e\cite{Baier:1996sk} [$\alpha_s x_TG(x_T)\sim \mu^2\sigma_g$], one has then \begin{equation} \frac{\al LTT_{qg}^A(x_B,x_L)}{f_q )} b \bint dy�gma _g \rho(y) [1-\cos(y/\tau_f)], \end{equ uwhere $ H=2Ez(1-z)/\ell_T^2$!`the-K form9( time. One !Qrecover*$, of energy l!@pin a thin plasma obtained in64opacity expans!�approach)tHGyulassy:2000gk}, \1@hnarray} \langle\Delta z_g\r &=&\f!\C_A1�}{\pi} !<_0^1 dz { ,Q^2}{%`}}du 1+%u(1+u) B{%@$0}^{R_A} d1�%�@) \nonumber \\ &\!Ds& \left-� ( m5-:_0)\,u\, �{1�}\right) ]. -�1 KeepA� only%e@dominant contribueH and assum, $�%�$x C_a 2\pi1:^2/�$$ ($C_a$=1!� $qg$K9/4 $gg$}J)I�)�s� averaged ]+=�uEj5�-�dE}{dL}1��)3\pi�=�^3}%�)�N�i.!g) 5sln V2E}9�}.Aibel{effA�}1w� Negl�/ng�,logarithmic ��ce oniv$,&N aa 1-dimeeali d\system aberesse!� $q E�62_{1d}57,(dE_0/dL) (2! _0/R_A)$,� \propto%,_0R_A$ i)�=�i�Dstatic medium with�sam�Fd� ty $a_0$ a <1-d�a2�at�n)/,_0$. Because�f���4fK 1 dE/dLM>% �sup9@ compared� � caseE�does not-�( linearly o��-�0size. In ord�o calcul���ffects�ɀ2N M ��nI\ p rn1$high $p_T$ <%C0nuclear colli�Gs, we !.$a simpler xLive modified fragmen!�on fun�� Wang��yh, pe}}��sXD_{h/c}^\prime(z_c,Q^2,��0E_c) &=&e^{-2� !$L}{\lambdaq� }D^0 TM) ��Bq���JC)6x8& \hspace{-0.8i�b���|[ Nz_c �} } 2� � ) + � ;b���z_g @6[g�[�ّqmod!�} �r1v���,d$ areEn(rescaled mo!�um!�%�s. This6el�� founere{ L pQCDQ�ult from Eq.(\ref{eq:MDq}) very well, but ņwhen $-"z= E_c/Ekset to ��&�� 0.6 1j��$�erefo �actual�QJZ should be�E/E=1.6 �z$���$ extrac1 �a� 2Gel. Tz actor 1.6!?mainly c��d b� unit�y corr�+on-|�C ]%a�.ion. Si�8g� s%�bosons��re�0also be stimu�jd 3 emis���absorpY��� agat�[)3 b6g�!e�d rmb �z�hot��P. Such detailed bala<is cruc� for j=Oiz���-��A$important 75�d.� of a�Ie�� �!Ya� ɚW $ww01}. TakK4into account s.� �n g!�5O��then gA�$he asympto�behavior�!&Y7� b $framework �J{ �{E\� E}q;&&{� C_F�  L^2} /4�{ _gE}/\� \ln{2 Q L} -0.048��\.�  &&�_3in}-{� . u3} {{LT��_g E^2}�F�� L @pT} -1+\gamma_{\rm E}-{{6\zeta�g(2) .\pi^2} �, :1 �H!�$first termA�u�induca�,remsstralungE�5second 6dueAI/}qinuUW�Uly rekXtotalQ�]4JxI�(. Numericaly onsaJ w thG he dQ�� .�s small�A� be n� &u�s�" ��� �$. However���a�. �>  ive m� F6D "� E� spectraC$A+A$. & LO�fmo��]� 8ww� 2003mmVp-�1�^h_{AA}}{dyd^2p_T}&=&K\sum_{abcd} c d^2br dx_ak_{aT}k_{bT} :Z1 t_A(r) |{\bf b}- r}|)f g_A( N ,r)  bT},J0^e(f_{a/A}(x_a� ,r)f_{b b�M�))6 � . }�& z_c} � 8-a4}{d\hat{t}}(ab��$arrow cd),a@�q:nch_AA"�"% ��9um!�J� � it�4$6�$ give, Eq.~� � )�,aC� [ �Na�� free w  $2L !L)� eM BBK ��i( I�,bkk}. Here, � L=p_T/p_{Tc}$, $y=y_c I�F/ o ele�ry��ton*���s�$Atb)e�� o thickness� n+lizF$Y� D$=A$. We w���hard-sph� i�of"�dis&���is paper  $K�1.5-2$ f� is^� � �Ɓ.er�m &� s. �%� .|s per ��F'$ insid�� (u� d �be �izable iy !R q 6r?EA%qon6*MRSD$-^{u}$ b8Martin}%�oimpact-նէt9ܩacM�)U�%�2�(new HIJING�N� lw02r h�i�$transverse"�2 $��Ta+,M�=N8have a Gaussian!�mɡa wid�a[ (cludes both$ i nsic�  a5aU�$broadening��is!8el has been fit to%U%�ar 29hJ�p6��up KFermilab�A0$\sqrt{s}=40$�&. ShownA"Fig.~� fig:dau} �� predi�� mad! 1998�S��} �Croni"�at RHIC � �u.Y�20 � a2N�rec�L data. As o see9 iM$multiple s&�in)ei3A� somA>de�nhu���a�6�!�@, any" �) F6� $Au+:At�"� �X hAA � figure} \!erD{\psfig 8=dauphenix.eps,E� =3.0in,he�=2�} \baseA0skip=10pt \ca�{ai>s � tect�O.� of%�1C� �p>� atR�re( .B>�S  PHENIX:���� STARF" star&�Q���1[ �a�)jI a� 6�g ,r)$� �{ropor��al!�O ��profil��� icipzn�o�bAccor�toVe�U, w� eB� *U I��(i  asQk*d%(E(b,r,\phi)�6~� >A JL}�faC-_03_0�uho1H$b,\vec{r}+n}3� eR� �L(7 �"��-a� a jet,!{<d at $br m�0travel along n}$��4an azimuthal <$!%$ r.1��re:�n�Ka&e �}B]$b$. � )�"� ��gfQ�ej�.�6r�� ��j� � lE�yE3o�a9Q$��6�24���uni� � ��k�spo�. �n2c:ZY ZV�a���wv �=(R_A/�)M�J.�@�� a�"* � ine� p)�#0�?A9 �F��on quark&!�� V�1}�`�d�Zar 6x� 8s $R_{AB}(p_T)=R �B}/1NAbinary� - pp}$� hadr. h(($|y|<0.5$)!JV+,:�e9n� -���-r,�-r}mH"�V�="v d^2rz 8�b}-8Go� %Wobserveda� i^0$2(soli�s�!�most B�s��� usPmu=1.5� �"�=1.07/fmu�,mbda_0=1/(\s�!�7 )=0.3$ fm� hatch��rea (2in ot� � �t� p2 �d� $es a vari� of $� \pm jGe�6n boxe� !M_=1$)es� ex9� error�o�ll""{��$k�&s % i% shadow� toge�� a sl  *� �:� *@/ =2-4)x$c$��t rm�q�N l��p�F�$\F1i%fc6`A5str�� dBM�:��B �ris`-}$ee p_T<�*�x� is��B���9 ��J I�is re,� ex��6pictu�to gradually lose its validity%�is takenE. I�,non-perturba�� s, e��iT�ka�� baryr s�"�i $(K+p)/\p��A��qɍ� �fs�Dsignificantly larg�h� i�al> or $p+p./ . To� i��e�)t�add�a.�(:� z $) soft �ona�to%#=":�&�s�L 5*5 28 At�& 3yHMx6-N&* Wa�%��ts[p$Aue Q�>�2a�ire|R �!A� for .ch!�d�4s (dot-dashed)�A�-�At}} ag�� +� ���&xdi�ly e $h�m}�"nV;viaN9J$ Et: � A}^{ G}=��S }[1+5�]l/:pp}$. ItA��L"��� .{becom��#!@1��:��A!�.��demont�s�#iv!Z2 *: edJ�Q22fl�R�^��� show��!10$C0-5\%.�()��#� r =2.0E� ���2.0�?f�$� A aA uA�#%:M�&����"� di-ə ��tra, B�($ &&E_1E_2[ � {h_1h_2}E}{d^3p_12}= +K}{2}�z*z"��A q�y.yfFS ~|1 ^��Nt ddcrE_dP)U| s}}{ )� ^2 z_d^2}6u5- 7-�r� \d�*H^4(p_a+p_b-p_c-p_d)�l� dih}>�#��,two back-to-��e�.-2�3;(jets. Let �*�,� $h_1T a trigge#'I�8 a� {T1}�^�(}$�4 efin� 7- H 2��~ (FF)!(ak2��l�n��rA$-\ m:yeu6] DuQ (z_TY,p�/  66�Be�/�2A dp_TdHqQ6^3}B�-si r�+ ��~ -pho# �FF3 �>�'f$2!$-� even!��z_T!�/6��+ ��gų� ($|y_{1,2}|~ inR� 2Eg B�c1�j. � �*��c !dl��.% �&�$anisotropy�� describe  A�"away-��UBZ� &X &X . e� , a%Dg? $B� [1+2v_2^2�12iV�?)]$)�.� �s b���sub�(iN>#&$v_ r -measu���:ly�le�e�d�"m�1by<=(2/Qb�  , $0.75<|�|<2.24 d���c}A� �}j.r_aacern^-$3.5in}} %\!�qi graphics[� =-90p8.4cm]{.]�]iv2q�J &=�.B a!_toE )�A�\pr*�%rV)pSee text� �w)�lan��"�0 fig1B*�g!'�f^f\=eB.�]Qs�>k�k $6�>p_T>2�/, :!=4-�N�"�7V 1�((lower curv�et$ (up .0Z�J�c}E.�3B� W�"b�aj��stra�di�� ,�&�,.Je�"��H 0oAR10 q�-t2�1�is ٯBi150.85 [ 0e�],�ach�equival��? 13.8?3.9)�fm�a9 and � �ove���)�=6�fm� i~pis t(amʡ 22�aJvious ef-�.f:7-2^g6��!��~-on pa� dm�. prec�"3Mid� R�#{Summ�u2s ,Rf���<).6:%K�2v��d+:� S�.<"�� qI�ٟestabli�a5 �*�(fike� �/�X betw�!F ���0d+eM!��l�5ve body!�:2�o2mJ^2�jeTrr� ,.L*Z��vra:m%�0.)3 $s,�y���cA0� 2Vauj, .�ra%t�=@.�)�= . A$4ultaneA��b-2 ologY,stu)2�.U of Ff,.E,%W!-�"� =7in # �heavy-!�]?�Z � �b� i� po� ng��r�]heoret�underst�� of-M2$� %�"�AD!MQ�.&-M . ��#%(EKS)j"�,� v��� a��B�(0.99)�^�(16.1 F����������a$�� ��,*{Acknowledg��}q(�.orka�a\orV& byEDioor, OffiB:f E� Research. High elN_,Physics, Div"8A� BQ"U.S. De�[�0 ui2 CJ<`act No. DE-AC03-76SF00098"�$ thebiblioi y}{99}ibitem{M�(@:2001es} Alan D. d, R. G. Roberts, W. J. Sti5%  R. S��$orne, Eur.�)�XC23 73, 2002; %%CITATION = HEP-PH 0110215;%% J. Pumplin {\it et al.}, JHEP 07 012,2002. %NJ2011952�@tsui:1986dk} T.~M%�XH.~Satz, %``J / Psi Supj5� By Qr - G:Pla??F]+�� ,'' !�,.\ Lett.\ B �(178}, 416 ({):�4PHLTA,B178,416� \1�,wg92} X.~N.~E�M.~�?� �S"� And Jet QA0�&A + A C�"@s %At S**(1/2) =!� -Gev� Rev.� �6� 1480�92B�R�68,#���EV if} :� X.~F.~Guo�Mg(��Jn(: P&B.�a<.\Iq\ A �$96}, 788 (A�>�Uz 0223 �5�Guo�0nz� �%��6��,��4'�*�3.�; "i�0deeply inelas�6e A.]YnJ� 85}, 3591�0^�005044%��@bwzxnw} B.~W.~Zham�X.-M�6����"R�(Beyond heliSB0 % amplitude mxi�B�8arXiv:hep-ph/03e�:.1� ��0LQS} M. Luo,��Qiu%rG���4n,Ii�I B279!/77M�:�m�279,377s�c!� D� 50}, 1951b4FbRVA,D50,$�b4� 4493 b:7P b49,$b=7$ow} J.~Osb��%1��Twist-f�\)%$%matrix e�0g(off-forwardQA-f�71!J28I� 2) [64204046]:�Q5 :� herm�� .~Airapet�.{�r [HERMES�?ab� on]eH�  I�) a�-y� posi^"}�&a 5( environ��a �7��J.\ CI�2�479e�1>H�$EX 0012049�V.~Mucc (ab�9C$ex/0106088JBZ Z.ABa*�G R.~\, Y.~L.~Dokshitzer, A.~H�ellS.~PeignIu D.~Schiff%ZRa�6v:J+nd p(T)-*�$7 c �h���E)`i!R6� 484}, 265e67)R�9608322>��� gk} .� I.~VitevmN��� �&k �< metr��[#����v��� 2537M:�NUCL-THI9 ϵ��19���� Z.~Hu�I% rcevic�g"UA��opE�\' % > tagbFp'in �Rv�77!�3�TBW a PH!�521>��pe.�%���M;E-m��70122ŏ��wE? E*. :�F7 �A@=v{8!{14230��BT Um�14-Fn8ww.�%sSMG�F"�e�e2:��J p, p A%� A A .�wSPS���$ieF[-}(61}, 064910eGB< �981202�:��:*� �y�6�,.&��2�2��!n�!é��-tS 5010^3���8Binnew!:, B.~A.~Knieh�> G.~Kramer� Next� leaT1rG6� &�&?p?�+(�Z��1�a47i�5a6�9407347Z� ���} A.~D rti� ~G.~*� ~J.~:�~S.~T�%`qV2� : A �7globa!(alysi�^���46� 8J�803445^� ��ln/S.~��:?s"?!�M����F�6�52�85e5-�U|11007B�qO  ��&�4�S.~Ad6I2�  [�4�:� Ab"(E��K���7!�cle:�B*.A &� in s(NN)>4V d]u�xA�  :F9�d72303%/3) 2.� 306021>�%.� %.U�da�5 J!'ams>'�N% Evidl@�. �m{� ��-�2L~ .���Au>JFr4v4v:�wa ^ a��tom��2� A�� m�K ,'' j�8� 16� 2). R] 0�E0I�5��iN K!�cox2�, %j�.�!�� s��B�"�#in� v Z�sM� (N N4134Vv�84[,2� .A�109003b� A�S�{F�ed pi0~� %.~R5E�,� y�1�3��Ac%304022]61}�! Y2� CA0>" , % b�CenF E9S 2t *inU#E8&Xat>&�&a220}2:��20601��J_ Klaya�b�&y b"sS6� ") %�V� S)�1/2"0%�[X�A71�73��.F�210026^� %�:�c}b�b Disappearr of %2Z B�.!� %�\e>�082302��(Ik�#�O��( roviT h�& in 5-10\%� 10-2 �ityD7�9(�?pu�:-^�3f�!�3��,>d �icolsp`; docu�a} �y\4class[12pt]{io�0} \usepackagems,�icxN8newcommand{\be}gin&n<} 2#e#�"�<:! vlk}{V_{{�Klow}\,kJ$h}{�L�>{V}z0nnTSNN>Nla}{\Lf7:�fmi}{\, 9fm}^{-5%(%16!$title{Low-��t� ��fei.Lauthor{Achim Schwenkdd) {N�T�y �*�, Indiana Uni+Cit��Blo�W4gton, IN 47408NYab�1ct}�:5191A�renCl�:�(px�8�To�1uct a!��Con-�o|�O=lk$�#�;i$8ll poten�C�:el�E�Aar 7u 6c&�6s. T}b�86appa,���G hell�el or onicG ��1 a $G$-R4mon. It! argu/+>D$A�$��D=9��-nchiral �5�� fiel�#ory�,54Pforce. We use cutoff.�4a�6too[@ass[G�F9!6 trunc � �ar ]s�tws�-�"�intL]�/ l.�three6�1�re"-8:$A=3,4$��w"ie�6he adjus�6M�k%2�7�|N)s.{-ca�Oo8%R U{S- # m�Rng many-�#%ysQM�%d�eQ���!`H"�>6�J �Be3R� .�W �A`&|-�y�� %\pacs{21.30.-x, 11.10.Hi, 21.45+v, 24.10Cn}. make��&a {I-�!�] VI" ,m�R prog�t'�� fA� year�E im�ng 9FmethodsLlic�$AnE�� }s� ese M� !< 8 successfu�O diffe�#V:��U�H t:4Bloch-Horowitz�4^ ALfew)��YM" No-CU'S�)M�M/light ei�& Coup0WClA� r M�.�E�b(( mass �, D7 y FuHYPB����"FB�$�$�(e R:�Group6�%2oAlthough�)'i�`cop�q*y9!��rincipl�i1� 1��,iagon�8� $A$�( Hamiltoni�anm�a�alway �qd�%c�;aH[possiblEG0 de up 6 c}�AJu#'<"V�&�%!9 �+�"�+, e.g.,1.f ,�1wo-%} 6�(3N7?.q%�o&lAQY�choic�)+%�a���(�(g point. W�|M�%� prob�?t�{&> �conveni�&o�~6�de�:s-of-3LdoN@replac�&unresol�@ short-E� :.s�/SIt�!8\J*�:/�Fng�;�y�)�s.�Ia�UlteOr�.%=f�3M aof� E"*2r�5*DEQ���`s, !�AJ�PF=�"�ive?5pick _*1H on�11�p&%�� issgT�1�]�USh!�rengthAy3N<�Pto NN�:c�)*0 spin-orbit s� >1 a�!om37[E�&S^[exc%!�*"}*eefng%f�AKl 1��#G!�-њ_KQ��) thus6\is� t if%�usx���fit&6 , or�a�vyP�ubz) ly.�,%� Talkr5review�ula ``u al''a)"�  NN���^,Q ��� �B34�?B� /*s� d�QstV� W��BFaddeev��9>��4s� alD-, � �C]  bi] e�i� 5Ea�x9�� &* 6s�]2� ���c�Ar�~e"�C-7*�=A at 9�,e�gce,�I0%R:]ami r�/r� onsis-  3q2$. After au`SA�)� byw -E3 find�atE ib�0�c.EB��6z  �^of��"� � 6 Ip"_  6 *�RYV��TJ�5w�scuss�mi�,�9� . F/l�/�]�Y-P $&� & # re quanti�T�[:I@� ��9 a �F.7-`I��-��^!�9�a �Y 2t "� s�6!e��x�%�.8+6ge�V� } C�(!.>[rC15 : E�--Aztr�h�_w&= �<j�-SgA7-� u�$EII lab}F]4sssim 350 \, RMeV=F�D�]&j ��6.��dr}0�c�(a $k > 2.0 �~D���$s $r < 0.5��fm}$.&�[�t� .�hav���F�u�6PDoN il+ �Q"�`��� *�Rvlowk�9�Jeaɔ"�o$�7techni�\Tic�) Q�% s. Stj aa�;nٍ�$\vnn�.:v�;8���16�moFTabowT�9zM,6�C��2l l(RG)~74V!1,2%e�FaE2��g�Nlk$!e�N�bel�"d�ev� si��5$�E�2r*d)&F)$$T(k',k;k^�X(�2!�ar php] shifAn�3uteron"-e+y)e|in�� T� n�"ry.{�nel�A� \bk�Y� {2})�k !�� ) + �A�kpi}A�(\mathcal{P}�k{�k\inftyaef�PvnCp)3T(p�b}{k-pQ 0 dp , \\[1mm]R�lk^\la�v�tQ�la} -�E�� �.je56.�h6�e2$T"&��qII�M9�<&X� or.�toI�2�I� $p>\la� �7 chie� bi m�l6�lr TLan �y-�t*g}7��ichde�oF  t�V��o:Z��uisFhiGdprojector $Q=\theta(p-\la)�e I�� �n �c�as ]�ce��4@�� mo��. B:steps�WM v"B96basSKjY�Q�pof Lee-Suzuki.\footnote{Note �;RG�WX�z!s�Q<,� ��d $Q$) blockiJ&�*- (NZ�sŃ�c2)� zero.a�i�>[t] \v%�*{-1mmW�der�T�Yg�= i(=0.4,clip=]ɉ _1s0>>} \\[2a�B>Z93s1 9�w�C` "�W�E�� DS (pe)���,k (�oU-� �,� e�m�(symbols�isu] 'EveC deria^%�)�Pe`&+ & %�socT = 2.1`, ��28bar�B" vCn�EI� ckU dyD^ *�IA8TN2LO (Idaho A) or N3LO.���9�  }o �L$^1$S$HU�=)r$^31$�� w �=Ijs).U Wa1At�� s�{Q��ixis���Y a�0��aEng)��!�s (�^N~  $R 1 � ~ |aRy6�*� �8� e:�ccu� ly).�!x 6�.�an�U��2 e� �d}{d ��68=� �����]�y \, T�) \la,k;\la� )}{1-(k /[)}�e Forz��qP�Hs�Oew@ y�a 21 ��� H�:� = T� vlkh �Ge*�h �a#pq o�1%Km_�e�h$8$o�,a (Okubo-) HA^ti�&$ (e�nowN� �]a2A[E� ?ah�ropEAover-a�)�D"� �� , $Nfmll � ���Zn$)&nn$ (sm*�AW- �_t >�]��u4�E�> `d)$ O�Iain5�Acs�`JBy�� �. deci�toɅ\l[Ռ&��A� ���z*� �a�� e�A-�B7,"�Q�n�4KM�-�2�.� is �i)��-U2d2$I s. � �Jine��� X �tx *�T&L%i��� 3LO,;�mov�%oc5�-6�Et .D6�&D[qDAp &�b.!�� [e��a4q03:.�IS�0 >. Fur!#��&��0"�  i2�.x|!eml%�A|>6)igh����is!��@l�=�mce easie �v , bs goaC to a��k*� WM+�?�RG=F��@use��#v� (EFT62@ZiAW#EFlSG!�!- �#��7 8is� � �!"�2 �cantrt�Xa�EFT c!SMP� mMe�� _\chi �V 500 - 70�.Z ��c !�maximum �?n>Oi�t ru�� �do4wer. O�\`�E[.e�\u�BA*!�A�ALer�"operat[�{X4 auto�Rc4YaD m�� Mfas~tha�fAT2>&_ ��)I!�.}�!"9yr r{"*����#� wa3"9Q9 of (a!l&�)�B@n��"��n�?�vIA-*�L�!�-�aa! $H (no ``magic'' valu As��*)"�KS�u�8 \A��Osm$oF�#�a24-q 0"�fo_�HC%�.L�:Z$^(#} All� e�i�G.� (``P�of QCD''S �1�� �:>%eM�v �WB�Gt�if� om^O!�"h 2,, 3N, 4N,....� wb be )kY/ . UsA�M�l�_I �*�Ge7B]$��~!�.�%@g�� �!�� ���* ����.O$.X o)R� 2�3� tjo Sne� '{*{ N BEF?- DV4�GOTjon} C&�AQ! tr�oE-aj�a�tH3B"��JP=-�]� f�)���s�tarB*s� >,Tn�N� Nogga"�plu�'� EU� �Sdiamonds�N"2'"�)6�E���� 8Argonne $v_{18}CD Bon��!u���@ n�$� �5i]#BNN-�-2 @�3"�x�-*e@�Cpo��_�V>� /CD � g�( "�<v"o 1 um3�9W':�I.y�!�&�nU� H%�$^4$He"�hz+�Ue'A� �sMV� 3NF}E��" �Pa��&� h \geqsl�^1� � �&�"$1 \,*T �&�Mj�!EY � $A=4"�)�9fly)����{b��m"�RW"a -*O��� ��\U le > 3>: a$> 60 }- �n.X*%>�a) e�O�l��Iw�R�|wA�� at}lx���(a $� ^2/� datum&E�1ă�C ��a�5 �O,lM�@ ssoc:(d*'�#%�.J �)�.�Ay>�Eb�X6gI�*"p�ee�0�"G$"POB}"� �� aC?����on� :9! �I @ pU�u"�'&v"%we�0 �dbre�}9-A��Ou&� *� i{�^eMinevit� �6�!at#!!ב("�%M�O<�N (se�Z ocee !$s by H.-W.� ,mer). Two re�*cAkX��͵ej�Ub%+�: =1.9�� $E(^3{1H}@78.47 6]�'4 'e(29.19).zv����Bf]d=6� u:�s�i���>�2:<��fe 1%��&5A$��e)�2�*�T }-!ޡ4�.�x")U&� du�*! �)� ��YQ1^"� :� ��Rh �  t�/% .*5��ch%�of��rt-�`eR� ,�  � ���!� A�in�3re Yo" �&� �� *S we& >Fujii 28=%� repo�NqXqUA�I��AB }, B�co"U+�e�Vٜused. Ho"�~s�:�#!�misguid�/PitG#!o��>!�!�"�'>!ra�7h�nn$$ II% � (�WV")�J-% ). S�!� y �, L�Enz�T b�" ",�͡m6لi?�!A�:@._P.F'? "qI��6$4�Vt w�_ �Rem�n��,%vwnd"� ��2b�!32����9)�eheE 1Ta�lemE�rstk-�s& .� !e�eTy�&sc"%&="pB.�ond0m`j 2i�x! cep<AUZ:��_ s noa))cy��A�NN>� /ir�A]c"�-U&kW�a� deca&!�� `�ing[ ��V�-= ��"�t�hnre8box{6.25in}{!}{�,tabular}{l|r c|c} &��l�8(umn{5}{c|}{ } ^� $\max$ &� \\M�N1 N\la$} &F }{$T6�7}{i�^7c$-Ns�\�9� =D R?�E R?�R�%�^v�R=�Fv6�F? |V) 3N}/�|�F, }{$k *,rms}$} \\ \hZ $1�i& $21.06%�-28.62 0.0 11-' $3862.18 0.10 54 -4.87 0.0%55$A$1tq~5.7 a 34.1 :0.0  1.39B -1.4� $50'-78.8~ )8k-7.83<�63~ 728.45% -37.�j& $-0�0� 3% $57�-86.83 �3.6 � -1.9 0Y 0.67� � 30.2�8.6 � -0.4)/ -0.51U9  $60.8 W-89-1�-3<5.6 E01� 0.70 $2.5(a)� 33.3[ $-40� -2.2� �1.4� $67.5 � 90.9)�-1Q �4 36YO1 O 0.74� �b�5 1-41.2f � f1.4 >2 n $68.0)�-92Q��8%m& $161�0Y��3.0(* �6.9)2-43.9� ��7 q3 Z $78.7 �99�22U2Er �9)�0.2 G0.80$D(��F�$3N *s} Ex�;�4�� kine^Tv ($T$)&G(��&��3N��&�Q�#ng� $2 \pi$-3 (��), R. (���"act.�  (�h))�+JpAll&Q C � � a �'in fm$B> $. $E��$ENdewwo&7�(? �&�f�>�E-2c�;"e���a*<,�d�ls seer *�O �@1 W^io of"�3N��%O"q��ave�g �s)#um�u{����t!59�(vIG 4i at>� ,��F /"�^3N�ce"w%mes�zxg� 0V2~Nl y|$Ti�7��"��k�3h�m2� �7*to�=A�26!=.�0`  �*� c�: ing �  s*��. More�#,{ A� I X"< sI��sll�%A�2y % � �  ]#h�6aexp�Wly� x.d. �8��/� � .]�bE�2�y�5�3*!a6� )�8:4 �%�izes a� "N!���  sharp-� &?$|�6 � EFT,�6G :� eAnsA�(!�d!�isJaE�B,_'�M� ( V EU>7A�� .�� �3NF1, 2�0�re<>Q�KI�:O&reeEI��ny�I�F $_q%���3������fE�!� ����i Ay��*A�g�j�]� :��jrough �S2a*a`O�f #�!)�"8$ � �ɳ"G$ �%�iY+!��k carr�[;�4 he Nijmegs�>!�daT�ntheir �u�5e6q1��i s �?in keep�^Y��\m(�!fXgl̔2��* a%�6fp.8��nQ%қN5*,� irOAr*�1�m� ��u�q<w�{=ln.X�nn��e& �d>%x&� � s (W")Hit may��bea6^��W�E?a+@�#�4, say $^{16}$OA�eC"l���WE�a�"�+!�!� futur�  +� *l'X6wa�nZw5q"�9u��ing, I_!�Aq�9�a�'&�{By��&M>0E(K + c{\rmW�3c_D�+x D}"{+ c_E" EF"$ ($c_De� $c_EM%&F�%�!'p >&\�� le$ � h>�/" �TIq� check#�G��lsoE`U"� .%�m��4� 2�.:)-�FNM�ed�(re2��F"4 ,��)�we9B:,l-0Psi^{(3)} | V� 3N -6 �k :=2b= =��$|[n)���)�dt*h ����upenn$m � �[@e5��!��y�, .4E1�2�vnd 10'-< 83NF2}, �H��M _9ial9qљor��@xp[-((p^2+3q^2/4)ƃ^2)^4]W-U�*iȩ4�p�ka7A�pE� $q)Jacobi� a�h~0 p�&�e � y�H/b�= !DXarp ���e�^p��u��� "B�1i���� Zp:x)"s[ �~� @� triv�� asp �B6� )� �|� li$c6�ex� . �XeV�'nt%9��"�� AE*�" :�"B_ in T% 8�vxCsˣ&�5:o&~2.<��Vairs, w�6I� o�_ ��  = \s��q�k^2q�}q�( m T /(A-1)i�$-�*�� *�[ s. O�o!0a�e!�I�AN�f��.\�4���=8 �� (Y",2%3$H).&uG((&?&Mw� sur�dE{6�ll��i���?igu/for�� "<�6Lo>m_�,< "�i�Q�LEFT^1 a#o��)a'��e�{s�)�gtrx2��aEa�a/�!�+f4$�� 0.2$.Jhtheq���VA6F��$3�MKC(Q�)^3$ r7��N3 r�8/typ+� u`r�I��m$Q %jk��� 1{! �Qs 0.05�#7 7*!�BnEe*2wsat>}i�2y�f )�,n%� ��a�$�"A!!�"�1g���-nsuffictHa61?� �,7|Fvg�On�G�yYk� imeA#$a limit cy��>J!� A. Nh')�e-inw["  8��a��#t� agiM1c�1l���syC�4bP&�/� ll diverg�@ m>3N� . ��iҠA�ը[>�!a�$.�De�n �q��"i���Nr�G<�t�m A�hH� $�&��%ens�T&�  A+Ůsat�7AH&�E �Z�� mat}* A<fK1}a{o��L)ew"6in9�2�U�J�qd��#.6.�8Harmonic-oscill$/B2a�*�.�B aris���R�+�<,relho_0np_14rH+RY<>} R��h��c� n'=Y# l' |�' | n \, lSJ��6 radR qYFum �$n��a6�I���=��"�'6�a �r� (x\�6?5A�3'>. q�+�shD1A|a�S-�:4�f�! case�8# is �%�D>�*&HI/\hbar�\omeg� 14��$�M<�qs vanta��?2�*"�&�(.�2�+�p��Gf2��=Qa�H�Ect!1&3�5!"K$ T"�1FaMKl�.�3�a\(R '5 qI(#�>g�akC�>!n!=� .*P?d�gly)��yci�#��=1E:'&�L&84o��a8S� The bene� Rh.�4��.qV2_Az�Fig� ra�qqe K+ M�"�J��_�V�?b�]� ��a�>PJO� �[3 EIa=.�.!F�de�v quit2pid�6w� IZ $|n - n'| 10у�"�a�-=���Eo& om4�7c� quireCI��� �%�)Scon����W�)�Z��o0,A=a?R�'��poo7gEes e$&�X basiAuIn ��J�ac"�to �-i:�'/.c�V�s�az�byCY;aAE� x5I��9i�E���"RL2b'e.!(�5�r��� ) trol�Oe�v �*fA�"}%/*�?0 in p,HYM"��3I7 or!4 88rr�y,*� 6�@ ! self-"�cy�Xlost wb� restric|�%�3:�!��5� a7U�)��|&f'�)plo��k/!�c;toR�Mc�majorI!&m%�c[�(E3"�>g�8_v�0_T0�h�‚*4^G1 Gend�>E5&.04!7 @�;AOY��> in 461�O �"�Y  a��b|/|cdJT& a{� $����J!B  �;�inguishGP�W��6 8��onopoX�"z>!tT AarS"c]i�4*FKf���#=\i�A�E, u�wj Vctad� Pauli2L:���'q� $- 8��*�.p David}�..�A$ o��ot� 2 �/$B.A. BrownN�E�in! $T=0,1$?n�^!M6��!�2MIiggF� *��>c"sKTA�isÓ��* surp͊&�DN�%ed���J(,��pon�Y� � 2<He�*ezXs>G.@"� . A edERm� I �REFr �9S�C-��!�Y �y� me"fi2�.=Ex �Yp Rca"B�{ �=4�� %* need�]W.�]�����a�.S h��!�Q0nU ��Pn $ (��Am�[�R+")2,D�� �wl6A� � � .� "o ��Q&> . �:�@ S�a a�-`G��@ �8.�,6�5~.�Sr*Aoutlooku.�is&UX�,ZX ed az a�i{ �!�.'2� �chVin V� .E$ l���Bs6!�.l� s,5ef�=�0%7" "*$A;� A�Q$t-to-handlaA �I�!�� � e!NN.��We)'�n"=dRG ��:.d� .&=6�}j-B��j�f}L"9Bu2`W�8believ�a��: ��u&�B L 9� 0!o% follt�(ons: \bz=enume�JbN��Itf.��=Fg *|���0c6 $s)bI .�� ee7s� to "�86l�>�3�MI�om��C "�$ *�>=��qFway�^��A�.Bi�m�/47.0&ndk 1( ��oAZ�2�!B%d&l*e� \%�6�e#�5aKi �V&�AŐ35�2�:�O.��)�G Jy-��4n Ũbly�� plif�!FoR�2~ e.�`�i�2�,�d c�Wœ1 o"߬icstc�)Nf�h�iNi�,Hartree-Fock�vertep�5 %��?oe�� .�b:�Y:B �)6VQ \eUh� �.�@c�Ava6r�8E�a ��"�3al seemsu� � DFT}.�)pre�n����y(Ia%�dBi(�+�Y�{�*v5 r@l,as neu�% -�2�"zO�V� ��Xc���ntk�eP��"=*�5�s�'��� N �.�2�ofZ�!�"�$�eiA?%�M�s�U�A�� \no�nt App�f>�|e�w��dir]X P/gACT'�&/ �-� O18}�quasi"R2!� d]a�2� H$RGnm,tenso�J =IH ommenz];J�Yo)p9 ��]�c priori�!��%A�earch. I�a ��"C!�new=�� out���P ��R su� toMa s )�.�m� B �e�en�<(i<)�AB!��-]��c�6ntaEK"��g�= 1"8=( ��T)l�8Te�us� �e#s �: st]iEb�q� n�9 van��%-�inv����on,�" s��t*9pr`%���`�PBA"�+!�*�L�O p-�!��� {NJ=io�u2*i�h. Var: � aS$fu�lo��F�" !h�� 4:a&JD.pN drip�@� a��cana�cK. *�bA�r&o1+of2j)*�` �b)k5�wonde�:nAm,�i�aj�+B� a pl�yAzthank m�+ll4scLHScott Bogner, Gerry^ , Bg Frim%jD�WFur%.$hl, Chuck �k, Tom KU�And���4, Janos Polonypl!s Zuke�', ��0. ��F_�N-DOEEM��nό@ DEFG 0287ER40365�LmSFB. >�s{�"�yV`1} S.K�1!M .I?6S�<\textbf{B576} (�)c�a+ A�� �B���111042�;i��V}22}, T.T �Ku��A.�r�Rep. �386} �1[�!}> (, H. Kamada%^,W. Gl\"ockleXv. �}^85 ]0) 944_��'b.C�~N�v\C} (R�)� s�%(4��6n�@z� R�R�1C70 �4)A'003Nf(^1 } U.�  Kolc=`v.J49}@�9) 293.�H42} E. Epelbaum��6Q=2)��00.�� t} M.C.M�EntmeeP�� G.E. Timm���4J.J. de Swart,�|:67)3) 04:pA�� .�̇YwRa�@1�MX "E�Q�!D7D�,A@M. Hjorth-Jensen,) vatU mmuqd4 =�JEaS�uHA.�p#A:a y���ei} L� raggio��8y�034320mMM�76E{ �.�Ԑ�-M :ΌNF*� I, %�'5B.���v.�zu� A703)�2) 745, �t��11070=[@ .�N�6R65}��A�51301(R)SK 6����,^�1 �3) 191N�30208.-� =Am{F�u�92}���#825e�� >0�;d"�yk�B�y`prc,aps,eqsecnum,epsf,ams!`,]{revtex4} %�2!zPx}% I�4*g�files�e%\2izmFF}{{\m2B\bold�e ${\hF_1}$}�<64pN3p*>_dR+',:VsN+sN*iN*iN*sR+\sigmaR0naN\\�V1iR  bR�PNaP�>=n�R�rN\r\:mzN*zR*R�r_1R�rV.R,qN�qN�bN*bN*tN*t*>^1N+1+:-TN*TN*SN*SN*QN*QF*AA%�rm \AA>�A�E{?>$pp} {{|B� p$}|>,q!�F+q +6A,$|\bmq|$:�}ppE frac��b�2(�:)^3} >vNA! rm N/���\pc�int {WIS 04/Nov 22-DPP} %\draft \date{\today} \�y{A,�qu.�-?�cp��EMCU/W mu^AW �A&dx",r��s]s�ke2S�(�~� Rin^?4nd M.F. Taragi*��~@Weizmann Institut�1S#.rD22�P��-P�ZXRehovot 76100, Israel} �$M. Viviani$INFN, Sezi�Pis3 T��t.,*!'$, I-5f ItalyNa*=Y��%Mw�@�la" S"m\�ys (SF2B8u ta��&7 is govern�@a SF $f^{PN,A}(x��)$@%]/alC ey� osed#�>-�WeFQt nha<%er�4fe�-e�=$MZ�B+= �Eao��2SF��^~o��"Y�! ( posiA�x inp#x_{1,2}No�; AvQ�0.2U�xY�0.9=4r)%a1;=1 .y z mini�] $x_mf�fB�l�ksc �� ).U9 1%[$Q^�D(3.5-4.0)\,$GeV$^2���Q-En}}�eak regAZ$0.95� 102�ji<ub�Kt� tinuiK"���(xL31.4$. 7t�A�b�EGda!T j��r]�-"a mkd ��� ٓ���N���a"� . \�B =1in aOv =-4 a T U+%�H���\�e(sy)n D. B~a��9%��8Żj7&Dqȥ�.�$]t<(ive����. )&(fs,liuti,om�� R=B$day,rock},-Sne3׮ <bosted} 'jefora3�u,C���!��>4-7� la �^, ���ɻ�#�C+� ihID��6�f�4 �a{A,D}*��!�ide�[��al�)�g � A+��fst Attempt"�a��+��ve2��t�0��A�#)�;imarily��l}�i *� p_%�o!%!3˚:, )Plane WQa Impulse AN�x/ ��(PWIA)��cps,clť6,ose�<DiT�ver- did$)! on�&,n unanimous�6c�Yed6 . Some]khz\d*�>��ingredS?I�WIA, na[��jCAl� b nZMr �� , do�>`� ��a�r��t�>,��"�sm�5})!d>�'s~ �Z�%�lE]5�ku1%G,n2s�IN>Nra�5K^u�,L- situa ��!� alterMv�Nd occa!�9! far-fb��57.J.�A� of B� -Sal��r"�&1".ar��tex"�'s��b�e� e:�[M�russ}, �Qum���]�� �� .arr��!9�C_-tA�of EMC ���o� Eg~� Lsm�mor�K�K�L !o�0tTms;z;-reop�Kj%�8�$��&iB Fi�\@^&Y s&�\�2�E03-103t cu?��run ea�D� � 8E����03 g9 soong sor�m���L!.I�8 iE.a,�dv��.#-AO �}0 !{QE% �7�m���$ Aapec�> e ^b�#�#�$%�i�K� ~/eE�omqma ream���M-, jg ����+e(ot� `S<3�� aker.*�8�1�F �EA {�i �1?F9h.a$. �>se�^Mq~�reYex�3�w�6~v2, �li��A����"��2�is waag%< pitfal !�-s�2u��� !f����J�J stee�rP�����F ?�� .9��ff-L1��4s�tD(&1)DCbV��Ny���9fac� $ !.a� EEsac�*����Efa�0(%eE�!��? �&expect�'efa���s&��A��� c�O,�( a � b����'nounc�N\��ur �SFEk Q� M��JB ,�� $�a ��Ha S!�Y" ��T I�AV>�skM��'e�_M 2owg��S*K,&"vokA�J�%{ar�� oE�SFch�3�@e1�ed/ �*0@ft�ti�Ev��gr���2SFi��Na�& geneK��0�^gr2��i�i��֎!Ga�Aa��$Gersch-RodfJez-Sm�(GRS)2;=*x���gr��(�0ci��/a�D�i���r�-=L%tnd>��!�r� ">6.?&1 ���P2 Hg��b� it:ZS"31���>�#pu��onMdom�$ St$Ia�o�� SI).�Itc5�GRS1r�&� s"۔1 �.�6B'� en�"��R�� "i \ggK(2.5-3_E� �4t3,rt2,rt1,vkrE�M: bles\�`E�ar SF��kNJv}.%�!� us n"ll.y,.��7� aT. Ac� `�e A!�.6%0y�� �eas�¥�XFe};!�AGbI� rt2}�JnS}I�[ rgan,a�� b1)t re��WiJ* 1CA� on!Oby�) &��=P�* tinc��%&�-��l��r. 2B�lvir)[�pV�x�d$)�e6�of�W�|�b�NeO�� 1�a@bC���ly��ood�!#$S��b&art�8ar&^joutspo�.�7�idA�$�L` N ��*["0�btT 6Zp~������H&h  1� �5Z>� f�� � �e�!�aKC4��n% 2�_���vhowe&�� (3-4.�.�!�eEA* WBr: , r �-A=a|� �um ]�u�,��inK��la�&w�ikD�$" t fash� o��F�4-5.�!VIFm��=O���min7C� . 3W~��.�.�!"f� ��# �EV�;� ��.e �,� ��� ��3l�:�݁U*MAs� . 4�d� �SD�� Z���Ea����� ٩ ���nt0�sto�mnoDoI��".*�G%|l�4�Wezrt ��v* lyA�t�Ve >x!ͩ{N,A}�"�v(s ($N=p,n$)%8a��u� gr1,* �#" � � F^A_2�(\fHv� {A,\�� N�!)�� int_x^A\,o���(z|�� F_2^"-UN\#l*U7B (�$x}{z}3 $)\ , \la��a1a}\\LuH{1/A}^{1/x} du B^A().r6z(x & cdb�. F��ith9�"��=5%1/ �/u^2\ ���2+A�a�} G ���БmyXaW6x . A�"w�LSi���ASIL���v*%�}NO��7�:es!uF��E:R���n+p}{2}+%�{{k }{2A!(("n-p!�5�3Blnne��$�e8� � L� �>v:���by*� � � " �>� t�!ks<m"�$:-�$$Y \ 0s~(\ref{a1a})� and~(\ref{a1b}) are exact in the Bjorken limit/� have empirically been shown to hold for finite $Q^2\ge Q_0^2\approx (2.0-2.5)\,$GeV$^2$ \cite{rt1,rtval}. Also the PWIA for $F_2^A$ is of the form (\ a}) with $f \to f^{PWIA}$. Eqs. ( �,and�xdescribe partons which originat!�clusively from nucleons. The same (virtual bosJ �0lle}, as welld(anti-)screening effects 1 weis34re negligible !`�$x\gtrsim 0.2$; we shall restrict ourselves!�, some linear!Nba#ionA4squared static5+X form factors. Substitu6A2 abovE8o B�triviA�%�du�a 89�aFNE%%�any �@ar SF \begin{equaw } %A!(x,�=�7N,A:�H\ .\label{a93} \endP� � SF $J$�Z(constructed�%l many-body target density maa�esQ��diagonalA�a�excepte�coord!�8e. Those can on�� calculaw� precis!�1@lightest),(i, $A\le 4$Pe!�pu!�)��requiri addi!V in!�%bl on (off-shell) $NN$ scatter!�(se��@instance Ref. \onA[ci�@2}). We summariz�jR�~.�e�!$A�c���� ar ! is lA�4ly governed by:s��in9%$. b)�{given �,�-valu)�]#@strongly decreaseE� inA $A$ �D, He!general�,%pc E�@few $\%$ differen�  betw��id( $A>12$. DuT1�E�, als%i,ir widths f mark��ari+sN <12$9� cIQi�!�1 � �)#I�Figs.~2�~3)x reach rather slowly an asympto�Al~ . d) R�E�o -q5n(xUN��/��'B$ A�%Pweakly �Y�. ��6go0$ determine t�xa!B^A$,.�2})��in) 4�~5eGdisplay� or a%�s >�@= 3.5, 10\,$GeV$^!�o$ obviously%sm� $u5$. It Q�s on ba� side-�-�A�$|1-u|M}dIAaL�� $1/u in its de� �"(d � in a more%Ѝfashion�n doe��� I| ( following,� `use $\bar A$ to specify ai*ic-2Q� \ge A� In+�of)}~1}A�s�'A�ous!S{ k}$ � rs� ($B^{{\rm D}��t $u_i1`0.9�1.1%�le1 1nd^4EHeF$cross at M�sŋly� r� 1Ņ ifenabl!2Afbe ordepas��� $A$. Pracz  in��A�� � has&narray B^� D} > {^4}� -($\ , &&! � u 1.0\ ,:78a}\\1b\ll6d1_'%�j&&<u\less 9\ ,u w1.1&�78b"��MA�detaile)M!�o����to!amenAAede�ent%o� T!� I. \A$ion{Cha!teri� fea ��EMC r��.} Un�& ed z wiseE� focu�asusu� (dominant NI� Te�SFs in.`�ub���class� = e $0.25Ax  ,0.90$.} I)�3is��experi! al�,y8 slop�Vd p,D"Le ch a[esU��:�A�$, vanishes��x_11�,0.18-0.20$ ^3 - arn}). Si�����-deriv� A��� 9��2�i� all,!� ndarŨso�justif�'4 neighborhood_�$%�$'$pr��ive$'�1An� ! ,cl}y�6� n� 12F_2^D - p \ . mda7U�NU��AR�LA2&�3���ha� 5 7 %�D�vu�n.Bi 9 Next,�>� ,�67}�r y a)�Se�� II, �extaeI*� B *� :� �$ onic$�  of # A�d/ir Y3sm $x' < x_0�A���x 1�>lA$> findVl!D A(x'�@&=&\int_{x'}^A dz�� z!�m6Fm,\bigg (\fracC{z}6  )\ , @(\nonumber\\ &1�&Z\��� �0R��f g=>a \��leb�1a�1� �{\� ial}!57} x'}&-��/N:F;�:K-3q]JUS� �s� �.�8aa` 8p",<$x'=0$. However,�e� A���e��.1)Iw�.Z-/9@x'$ hards� up�� $x'�x_0$, hk � �?l� ly s�/��� BnA ��� $\mu!���(aM��)A����  This��aV�,bserv0 ll�� data�Q$arn1,gomezXI) �{G con� ra��rve ��Lx m�f� o�Ei"�of �>B, i.e.[pr��the��&Z  $B^A(u�)$w�D ��on�A�9�y! =.� ner! "E�A��� $* �le��Fa$��&0  ." argu $xu$, � is p��hl(2��  0.80$ (*�$turn belowA!phy� NE bR ary $x=1$heO*���io�  � �A$!�)t)��] ly !�$�ps�A�� 1��:�uyI� th� fi�M"l 5��.'�is cruc�influaZd!�~,*&e deep&& (DI)--�5� &� x U�0.8�r�e6� %6f� U ! $u-$�2cis"� $2r�9� .�\,E��!�$Il�� )�-9�F�eDc no� e�di+NM �u� <��6s �f<1�}qquad  h.a.�.w 9aBx InI�A�(obtain non-*�^�(xA�for./.�8$� 0needs $u<1\,,$ $x>1$W�valen�� $\nu<\nu_� QEP}$)!qu$u����, lower�:A0A�Y�E2�� eciab�era�,6. �6 illust�.�a�A(u)6���9) He, Fe � Au:AuN step �samplee $x=0.15,0O0.8U.2��,�M�dropsa� roug�  or 10. R���l�&� � 8 already establ� �1a��1i)^!Å��!.g e*�!-�� a�� <+ {}^{.� FA${# �)%Gef!� �at NNJ<iaD o > 1 >R!yuF6�5\ . l 9&�u7 } As�� grows)" contribut!� $u$-�} tends!�!a�o �r �wQ�D�!gn!�e-� \gg �,We emphasize�M�under��of!P��s6d�ings do�A��U�aAfbi�verg �$�:$ar SF, but� /t-��quali�*�A_"� (�o*�h$I,�sie_f-�ehavi�f >f�a(&� I� FVQin�li�5 9�< B -�� ness� ��� g�� pr�&y second���point �x_2^AQ�A�$.�d Vr!��dJ�#$�<$$B^D(u_i)= _i)$ cau� l��rE$^4$He�JA$A\����resul!Ga ��   �2burov' WeA A�� ntirjt�� oach���ploits a�-rule �!�� i*� U�NI:�� (cf.�"2> )R�&{�  {dx}{x- 2F� �({x_0}^{x_U}6-1[��AjD ]=0�� "11B�u�ox"i!6r11}t"bas�������� SF�V�! ,!� cu�`suppor$x� aH.c uppere>��l�Ni� ��5 be replac� comm� x_U,. ��a�\seq� %�Q/ ce $=;$�!ake�.{A'L � 4$any\,\,A,A'$)�� � sign. leas�Bca�t�� �0&� 6Z0$ M�rtpdf},% alter��"th��  to pas%BD   1�!V.[m� �/A� s $s�� =\par��A�J/ *�$�$x_{1,2 >@%��C�w�ᢁ���iMpe Q ut @s� 52"��JG $"H^#,!o��toa�$negN� !DA$-�b �%7& o$x_�HOne a#e�#beg:� %B��x_1)\� aA�[m�9M({ log� )�x}- 31�61D6� ]a�\|�41}�s&z�i� -0.3:(2B(Wh-e)"����V��=2,B �u-d$� �(x2���"� ����so"� . Com�tly)�ina�traut5�qM:$.V1a�L I�1 o$)$ is posi��E���,bagreeeCt���ɫ6��_0#�s locat�� e�!a minx %Hc�"G%:s ��m�S(x_1+ �/2�0.65$, uth �ed. A� qu�&S esI�p�ac'� ��.e�&� � W""�I $x$-v�H6 Ǎj)� \&� �immedi!U! $|x-1|"� 0.05$�V)m!� !�Y� .+�j�4rapid fall-off�E�{Nz&(u�h ��g� az"�)�$u� �lich�3A7~4 ŗA8M=& �fi D� ��B^A�D| AŽt��%� � �til t� w$Fed6���(�lways � i�9!:�*m^ -���`NE��� � � y\�z� %��*l�$k �!��U(2.5-3.0t"u z'a� cusI%w �7ola�t�conven �5intSg)�s $(A= F_2^�&I}/ E}A3` toEUA= I}+ +� �% al auxili;9e� h,!� =!p�)NIINE *+)m�KilSF.�� then�*-q {A&=mIi {�� [1+(1)^{-1�q} !B$D6$\ , &*� 3_3 �-�I-.�,C+\, 4\, �1 GeV}^2\ ;��C&0.�, "+ 1.05�� 13b}�&=wE2�[1+� ��D � ]�&dcd��1YE ,��]�.�] ;\, F, >�25/�d��1�� 3.9)5��w�e�"m�k+>�h �'urbl NE� A��( 4���� &�,�. v�d situ�U�fu{�m� �� ca� ��#93}) r ie*� M^ !�A& �%F�>"=� {� >#}Y R `}1�5�45��� �>�(&V �(�� �%x� SF &� , ;di�� � a)�(S"�IA� harp�7e beyo_ 1��ɀ� _*�85-�!� ) 5!5�  ,�|�C%IPan� ��brupt" &��� aB l� ��Q� "�G)�H�is�'d����1�1�� =�) �5>�� ��Q%+�depth!�!6�$QX0.35$ %�hG&,�.((50-�A=3,4y A� ngAG_�Ed 0� $F_kYrk �}e13d}))� p( � O�� �1<��(< � �A&, *gI�m�14a� s so� .� <6� v� lyYto�on,!A �:=�n���Wlet�* ��q ete, even�nZ is m=,al �,A� is a72!%cific5$i:��owjK ta��G�$2e� ul� ly&�$�(�*m- way� �����A�m��0- ly� I�2�+a2\smo�)tN,����A(��~+0 7,8,9,10). F'&DQE re)3(} VI) Fur2x>�/�ca� �m simultane�* !*+u�� r�",o .&\*A,��MI ny�"J. 1. C*� 0'�f�1AA:i�ndA�b�+o yield" rey1 d ���$�� $� A$iץ6be� issueA��l-!��x�e�� � A D$.�,"}/�#IK�AW� EU>]�}"s�G*� 25$�re6�" �+tl n�,. le"%NE$\gg$N)Iu4!�~5s+`�2�)�!��!��M�e�a cha�^)q��ce��fix��agm!O� �Fosto� �$�"DA)mpa� to i�(e�&0es�,about similaS H�F����coeGp yidK* . C{is��-4,)0�NclAb��2�.�� J/ios��������.05hQ�aa�R3s1pa{a6xtA�-E�� oncluF.�-t�heu+Z8pA��re(little doub��!%L , outspokc1x,E V"z� &� %�ai�u� � -e�} �be�ll :J.*)! �( �(i*O+ egimF�!��9aW t9O�e�+95-x %��o�!ar ��� DEP�� $+p&� 1.4$. A|�fic� %#�: � �o"R0�A� We�Z!�� m�remark�n�2d49M. U[&<)�Mdealt C+� �LE��XD$. Smsq= � ��bE�warded8KapM�N{\>N9�h!|*ly�(5�M^oI�*J is"�tE� V��{A,A'}�$A'e�| �: �)��2s�3to dev�$1 by n�xepa924"03}. A� Hayotoccupy�pe�$ o �FB�$B� #2�k*�0 |<|13p� .D}|$.jde��'o.�. ��{A,B$�=a�.�*D!��� � tempeb" ft2-egiyan�"�/Input, R� s�ItE � w��EYuAY��9�should cI! the �1.x6�.q starm s�p�ls.�7SF.03Eo��i�osJf���a$ b��8 ed e greaI8 J�"  ^IT�> vkr}I%heavi�# $2�s�Hunavoid(1a�we�3d%? Ce�8 jA�� !��'z*�9��KC7 X � � H $\phi^A(y_G,|\bmq| (fi-([erm�t�t kine�9c4�s, nam� $ DR 3-mo"(um transfer�� $y_G�TGurvitz�9lAL��> � gur}QA�ypB)1� uV"lyU,;&*� method� %A Srt��9"T� �3y_G^A g.dfrac {2y_G}{1+\sqrt{1+2\nu% /(M_{A-1}�)}^�<16k�-4=& M\nu/0 |[1-�g\De=�% /M-x]�&�6;\�=x)&�& - � RW }{M}pUc"1A7, !�� A�A5coi%��tatorI�u7�6@ ss $-�:�6�? expr7?E�U_tc ame,2� 6b.�, in.i�fly&F>��aP� toDt� r�&>)R�I7gr2m� � ȁ(4.2)a�ear. average �@$�:gy2-"C � Q���", C�' , Aua� tookA$R�4= 20.2, 40, 45$ MeV.6Qc})�� �;y_G5*� nge��*�8!�!!V���is ims!Pif��$e�e&� w�CkU%�u8$�-94F(A��� is��� shor,encou�6�<�4!`�9 appl"� � q 3.5$�C:�(emploE^ $k p$nara�2--�d�I<~5�stead�A��Titself 2�4.0-4.5*e� christy}.~��<wn$!�not-dire�1ac�BTD͛���reR;:�d�l�its�4A�� i "E���?� i) neu>�'b�.-Grt4�%!B9�*+� RY C� =!�969$6H={\sum_{k=0}^2} d_k�?�B^k"w)1FA6!%"�<��al se�0 �ey'.y�5%"A�known"B$C=1$%R $x=0�C=0.75 3J!�+!�0 � �$�(�on�w�. B&p�$st "rD thres(, $5A0$,pt �)p�0%� ary e���!�$C$ �Nl*on� �>�1e�or."& C(x=�� (G_E^n%� )^2+�e�2�" (G_M>#�.Bp:B>?: �F��8�D � �3e6��=tS.adv�!��" bba}I �<�: e%��,*�$arr5}). A&i?"�)wIp8ed*� � Iow�$��.��Awhelmi�AE�SLAC NE3i� �ne3�Hn� <�gb� &� b9- 2Hbosted,fs,liuti,oma7 W�S,y'�F��&P ��,JLab E89-008 ��S�H���&@H arre89�oi8 aU�sQ�en�:a��"� �E y: AH;(alysi3 )�%�a�~s&�Da�H�theta$,&e� K�* �L"re�rpo2 !)o���Q^; � \�2e�� enough �.do�$rwy�+! �w�-era�e�E�$A$=D,J�at ���A5.0�A�f�a�(\Esim x 1.V,�ly�n2�!X.�1$�wGK�  &�310DA6 )�A�i�)�%< . H���<&qu�$on��ich�?2^Duld|usi�TdenK0 ���{@ Off-ha3�Ieems bdGto@� &R>�. Nthe!% we�Dk�vPD�z��)e�*a s�5A�r�,%  A�/HrrH)q��:'syst'� erfeC M%�^#@9 �H�s� choi�*e-minor~�AA�ev8 , si� {>�')�e&% p"� ed�� .� Z!�~DIq!���AB 2� ,Au,aAL=�DM�.*�D�d two) {�se&�x �cA�e-0 thM�� verti�K scalz/!*�� 2v�Nl �a&�o�N��pamad,ash,bodek} (open circles�El�}via���d"Jal�� Q$bcdms,nmc}�s��as �dZ. Occak �A � h s1ompili{�"�:�0A�figur�bar�:���refer t�)at0al err�LOne�ds� fir�g �+-inse�KivityC!�&* A'A ً:*�G "�Dirregu@$F^A_2 1�s*L�%in�1C/', .7���DI ��$a�� :o0E3 not m�iR�. XoJ r5[�%6"F8ice�&4 NI ewD:AtNEm��R��� � I�1.A�e�����!S?*,��� Q^2=(3.4-�\,�p,  �!empty�Ns6e s.M�f2���"Y +)�(4.5-5.3.oE�!-nA�filA�squara�Theorei� curv�-} �ٍI4�&re�� }�%5.S�1�&KA�%3��_ g��Ka muchted|K*R��ak�MC1A�~in[8w "" 15\%6 A�)s%=� Fe4,gl���;%1�sIta�; vi��0"��* �(easily make�?for�0�e�]<�N,: ��:@!1;qb�[� j!um�!IJF�1t". C: PI5e�;�:� 7)j�"u@ll�r7 them�U $%H. Fe:J"A%Ci�\F (!�)[��!5 s!!)��tin�J 1 Daj�( 1*���T ��JT le ���AT leve%�$� u: Good.PNo ��%&�!.x� ory &�6%ta�!�!GfN�.y��CAv�TA 1&Q/ }-to6�s�!  ���reiE in�RI$ospea�-out,2� �%`%�regar_T��ɤ,& ima���ejboGu,B���B!-%O}�Q���V�1a ]�UI)�eMI" ����^4�%P��O�Oto ) �&�*�&!9ng%und<JlMC*>  E03-103� vide a �Ra>\R �!Q� i6".-�ed gradu�I%vm�%<um�� m-+!�%t. "e {Di1),�ca� !�E �*}E� n�Qwewstudie"�:�{A},\, �/�ir.T� &�! � &~ >�  A�Xl�'�p awa/+E�6os�$a�%�!d�" ord1,of magnitude�`�Q�<0� (��# 0.37�$d)�+�a�Zt7AE6�, �Se�of#� I�1��� �� $2Y!��WAa$t� f"�'ccurac!)� o iMbe�X']=� ��u"�"$!n$x$���A1.4-1�?ih: SF9wbbRi�^��"� e� �-kful��#@#%&{ZngA� �b P,an (s�� 6�T );�� l�$LmpJ�Yute=� 5 tool!.Ya�LI� postuo�EjQ�� �Fs,��H "q�S! n un"; us, �) ��pa� � �I�!�!�l�r1=s many8kX &X>X�YorXH)X/� a��#edI�<g�V�Ye w�]H�Ychc*5k ��ly ff� ��DEQ�� &4�s�ZAeb�vo!I"�,ŀ�2#D .zXA�model� r "�X�X�$&�. Cal�a�:%#�?\5f^{PN,>8a:�O�5$IG��I� J� ^.q#%�E�f>@��rst.o�.c�_ $all$>�.C"���* 6�meV<"�x�+3m�5A^a �RZ�% �%�%co� ��i�]A#*� $\,-ox ��%�* %s�� %��#��9�,y(e{s c��o z�$��{�.7 $^3$�E!�rec� � A��m�coZ�w�# �*�.�5.��isB�o� c�n��B�x/emerges>* �n6� {\it"Pt} �->�ers!!q6��b�1oofc�!i;��Á! GRSEF DWIA))x�NE �.�f �0!P!�a> t�B$�$ ���Cm�Cexpany �, e.g.� .7$NN$ re-&: �rj}���$A�not e+a���;fA�Ù&!�yϡ ��n�a�J*N!�tcies. E� spit��a���,� �t�A�Y&�ins=%�E� a�e.��"�a�l��y.�6�� .�&}1�AC7pe�(�b8:13)f�/(as �0!�a�y� (es=gPaEFZ6  8Benhar $et\,al$-��N�D���=!@NFeA]r�HI^���F7! earl!*�Jv Frankfurty.�#fs}a7 �DvE-N� �(�/�g "�)di� bXe�dnM�toc�axK��aKaa,I � fT AeglMFSI�y�,eaE \ �]QEP. Ho�UinF�e6�R�� thj�n_ �,�sprea��ct]A� A�o���ciaX.O�$��manifes��hEal� -��@n�&e �@|Mg1�ۅ��4!s� 0%�Ic��jwS� T!�how �e�9�$�2eF2RG MLIQ A"% tZ� }��G�` Our �h8! � VY�y�>�" "�"� �V�a�q�&�� O_6S�" e"�]m��")�4w2Da e �A@���"��(6A{2�/��"� C� !�ſ , af"�ni��e �.��*$.M6r�Q p�aux!UELJK� c�Evse)d>{,2CLZ;���m�/ vali�E�QM�.�� tPra�_pos� 8ach�a�D teau e�r�ya� A?`*� I�pZ+.]lat�r E�i'���prea�as�* j0#r!�aJ�ke�2,3... Gct�!p��[b)�fs��f l���r�;R:whe�� sa� ��f=��A$��G�e"-;8*1��%3� �������0melabo� k&a �,e���I�H�n�"N5�be amaG!���Qfu,?� tans hy�"�}�)���� e� EA, �:A>-w ipatAI�M i�tw�_] i�&<belie���!�ё uncer�-� ��)�k�A� .�YR9��m7t%&�"� . Toj opin%U�0%,���� emai�*Alleng!�"z3Ac*le� �ASR� �Nnk oJohn Ar�t%�h�o�f�NEf�B �ecri�le�� m� %1 !<,s} \bibitem�,X1} M. Arneodo, Phys. Re�-s 2�. 301 (1994X=<geLPD.F. Geeseman, K. Sai�&nd A.WE�mas, AnnXHv. Nucl. Part, Sci.�. 337 e5)dfs} L.L.&[ , M.I. �^krD.B. Da�d M rgsy��,v. C 48, 245 �32e�(} S. L�(:97, 1854%69P  O� o @, A. Fabrocini, SntoniEm�ick_8Lett. B 343, 47_6�d�2D �� .$?R� DA 1143C792� rock� RockZE$C 26, 1592A822A�u v�%\ 1849@:#-*} P.E. B:*Z� �68, 384)�6��1B�R9, 113�:�(arnold} R.GE�olz�1, 806�8828schuetz} W.P. S r�38, 250L772L�* J��rK82, 205�99): .:A#D� �*Cal.Te�T 1998?gq� arrd�sDC 64, 014602 (20012�nicu}��0 I. N� escuv��Z18 r02r0dy} S.D. Ell�nd W.J�ir�!��ITB 256!{8!{96�hcps} C. Ciofi delgi Atti, E��c(G�Xl�46U3Ai55NXlRW� ^j1, R126E�:��k6} �mZ< C 44, 232N� oseta�P Fernandez de Cordoba�,Marco, H. Mu O1!e�� essl� ��%j A 611, 51�(62�smAhR. Sm� nd G.A. MO%r1���91, 212�y2006v8/2+(, R. Ent, C�gKeppel,aMamme)u.y<, [{\tt arXiv: �0-ex/0307012}]2(ku1���8S�(Akulinichev� Shlomo Kulag�;%M. Va� ovF  55, 22��6pol� J. Rozyne G. Wilk,2�4hep-ph/02113206�russ} !�olochk�2=%$th/04070776>��03>�D. Gask�-ݹJ�!�!&� .lgr��A."X:!%A.S. Ru�, TR-PR-93-77/ WIS-93/97/Oct-PH; Progress in A�u Cn iclee�(ics, Vol. 3a-4i�6^gr2�lj�I�E�,C 65, 024310�"6�grs} H' rs��L�� Rodriguez �hil Nm"2A 5, 13"76  ; 9JM� TarAc,l m�59�_��6�rt2�K62�814t97); Erratum: $ibid$ A623, 77�# �120, 0446] :�t1z�6L!~42201(R)%�6��=� Vjx� A. Kievsk7 9C2{,C 67, 034003V>~v.�� F.1{-�s2�7�1X4)�Kms.�%mit�to25.Z� 1010>� tval��vDPE>1�2% �032&� lle�(H. Llewelyn�1e�1ɮ83) 107;� Eric4Fa�G  ThG M]p. 112.;T} G. P�W; W. Wl}r�  33�2%���atw�7 G� West� of-2((NY) 74, 64� 72); W.Atw\)�B� st, =hD 7u;e�k�b}�sM�GS� i� SPDula%:1 g C 66��0a�20:�arne7:1�3 10N� �o�?�t�ay~�`158, 485:�0��Gk.f�D  4348� 42� ` V.V. Bur��A!F�Gi mirn X�4!9� >�~]vQ+eOE.��1� Amadrau2���. �B 4/ 3,��6�ash%Ashma2J 6D202, 6��1� ez-�)S al$2� B 333, �6<V2JB`2 AaV�5a�43%A83); A.CGvenuti<$m1v189A�R8�uSs&I , �|.$ �^259 a6� arn3.�m\648� n6D$ K.Sh. EgvE.HI-�38> 31�E }�#C4 LC���� 65�:sE> E. CQ>b��s52�2006 rt4!�g �7���1�55!84�C6 ;� BuddI��6�2�� � 80056d g4��BarY>�163, 28�0:/�4 P.BW4$, Zeitschr, fi]ik C �38���}�$rjB+B. Je�,s�-�59,�E��*%"�r4} %&{%#6� ]GB � 1501 LI� end{:�eg`+5}[bth] \�?d�\dphics[bb=-150 440 567 400,�:=-90,s6=.40]G1.!\ca�!{�(�G  g .��?:- *`:GNC�Au;�=*�0. �= �!v��:�26�SG9as�2�D �3k+| *�7.����3��C���46��"��P1�,.'A2})%[�+�"4B�$"�]T�8 myMr�7ly&�# h?�E��h�%�Ea$A>4$, &!'Ls!� for �9.D����56;.{4-10�6{}�m�m66�!y gRj.�lJ�%"�T�C (R[5tw�<�-min� �.!� l�+$fWr!� m)�-0Au (drawn, do �Jdashed L�s>f*o75:R7�se�"�7��C�}$��/�!c�!@5of 10�.�uo 5\to�;to����76�m6�!I$I9���?.0ceumD^vI.�/]<m%e5�;protectG� :D<%�- 6-� >9m�.�#& Sexist )!t�2�L�L86L.� 7)Ho,%,C�h%7EU)<.Y-%<:ro�=:sh,)A. E�{qH%tor�(M~A�V 3.;&�<-�diamondq ?!�> �:2�c�(�1z@:� rrd,�h tO6�$o`ar|Ua�.�Bwar�sMxu6$2�%Q�"�m[+ �#x0ed����9��%�Fނ(%� 9�~68 -�;P tex�% SeA IV). ����10��Au��:�>�I�f�����1:� A:y11(�5*�>�( %\newpage"d t�-3 �  {T�w&*n&2�[B%2�93�Na2:2 $*$ �0a�.5 ��8 �C�0T2]{2 (ao$\ i�4�&�� ). W�c not B(inguis�#Hv&" &�Ke ��DA� \� (tabular}{|c } \h� F&s�e $u,x�7& �6�F5\\ 9-ed� &&&&-2\\�2&?/6=uD/|/f�2�2$�Q&"�X�� 1�F&�iwZ1$ +zY&Z10)$ & A�dg$ D & D He $>$ A>� Aq\ D�fA(\ D^�2"�4�x �8$ &$L_9N�!$&��&�0%.& $!  H�U� 3.5\div5.!:npS! >$�>$ C !/�> $ Fe"#\A:.& C%]%5j'>5B& "l &)[\\�10���LH>hDN�� *� L�  D]�mn'%�39u9�pNA?R�FHaa-�T%�I6&iA�=�) ��3.5) A� 1$>$-A%�%�& H�-�A�1V1<He$>$A�)BRAu�zAT�z: hFy%�{ He !�}U.��f�~Fe�M�� -t!���6A}.� �E�b31$B&C2JFg$>W616�~ax: 59F&!D��F�v���\gg�6�A�A$������Ey�l�@*YT6  Ia D , docud5-�^% * Sta EfpJ(apssamp.tex ! % % �#g4 37APSs� REVTeX 4 ��non.EVer�+ 4�a 4 of /, May 2 000 tCopyr)3 (c) �Ame�n�6Society. 8Se�D [ 4 README�� \,��,��-*�< J TeX'f J` =r�0�� +youM/AMS-La�2.0�3�D�n� % I�Ds42q�s�CBibTeX� comma+K�t )Hs: �1) �-ex.�!o2) bib3^/4R \Q:�<[�\pacs,12pt]{revtex4} % SK7ta�(sbOal�,tB ny) �.ip} %:Zpre$84t,eqsecnum,apsb>0.',draf.�>-prbK%Y:Rev��B \u�-ckage{gr�x}%2dcolumn}2amsmath%NOTICEj)�A?iMmÛ.b[sYIofA�mat  %eGIP5�incorp"~.�.m��'ar 1�AvYou�.k3�?Sme�E�]�e?-paper; %E�``*not*}ye Ein!r o?R�V�,%%\&Jatl_C(def\btt#1{\s4tt{\@backslash�?#1}}%*4DeclareRobustCI�\bb({C>9 7 qEtEo��s"E�!�\Q`,{HEP/123-qed�(title{\bf P��-law &X���hp_{T}$-.�^A� r1ca)�in&/�1heavy-�; coll� s} %\foot8{SS}ed %b#R NKal uaKS�k ce F�YA8China@0 Gd=< No.70271064.}}%�Pce� breaks60\\ %Li  auto�`Por�/ b�2c�d.(\\ % \j/l�-0q@ccnu.edu.cn�pauthor{ MENG Ta-chung$^{1,2}$�Email\B&:�wg.J; �Ck.fu-beJ*.de!� �me68 f8 %�LIU Qin�j�li:�Bff�u!��; DD= �U}:���%%} �m�foa�%u� %%}%�ate{\to�0[�-z��da�BO�may�9i�ny�U4\M #� abstP?} P�an�Fion-fr�AH}� in5d�variant �dvv-R=9{ a ta�k�Imeasu�4ntt�Au+Au�C�6$\Ld$s_{NN}}=13�!� :20 :b�<"~C�4��� �>6�exh�3!� �\geq �/c�9��good pFT( 8$�> /))�g�ba�W�TPDj'��FE�6 s us�k� < cogn����LeƠ f ce�ClittlbeD{ts�6ap8�u/�X?plex;��u�D%f geo�a�A�7JU�<hK+st!��ffAIW� sx :$V[N�;%�tt?eO5 a�q��V�� �E91� �=k� "�G� mai� d�Q �}*#]-orga!Bd �5ityQS%8�Ha^�C~J �a�<>: � �B�;�*q8d~A�``W6�ion'' �m�ny ad �� �&m �. Furk J[*�;))sugge(^. y� \� {25.75.-q�1 ,Dw, 05.65.+b�,.85.Hd 7.CeC ACS�ͦc%� AU$omy Classin�3em�Q� t � �of�He�IF<mh>y !;D ged�J�� in �$� 200�� �rdpuJ�by STAR n�! by PHENIX 3} �Ha broad0yv���\RL !n�c al p�m^lsoM�>q�cAl9�ese2��,3,4}:�vtsr"Lec�jy�X high�ԁum1��p ν��fZ}F�$��=0.48 �$}&�$5� i�8w2u i;�}!8 )�� Ge��� \log$- ( plots. Bla�< whit�Ld� e 130�200C)p$~A.}�bfig�end ure} ";ƇeriphX�&� W� eoon�% rea�at<t!э�p s,"��:n as :5-5}, t�1us? A#he�:�>d �, yet-to-be-fO  ``FY�k-gluon-plasma (QGP)''? If yes, how? In�Koh�a�bi`�� �pi�kAdwitыe SZ͝"N�-S�-! n &�� the �Fm�Dir2� ?� �frC�/}a����hrg;�I, b ofu>��3th��hIO�d&�S��� $0< e�ϤE�,n�>�A��dJS M�6BF@ $(h^{+}+h^{-})/2�m�ity-sele�J�-)E&�ap+p1Wac!�">�J�����mz � q|�'�[Z? NV5�d*�.�IKC}} �m{1}{2\pi)R}  d^{2}N}{d%gdlf }|_{ =0}(|�;8c}) pa��^{5n$mbda_{AuAu2c})},�%�E�.��p+p��T2�pp}F��?As)�i��f]Bl�$'s"reh��real �Y)�!�c}.�P�i],bins (in per ile)�*ch�Rnd%�z&��*e dure�!(c?J�ٵ�e.� hCi�e ٍjeESU呁-���t>� . ��A���- �ar!_�FI�2 ���V�����k(/B Ԏ orte^�Co��ten�k�w else)���6})� %O�{N�lݐ"��. �cBan�"��. 2�_a3݅K9V-%n��^( co�Mry��� �C��V onN@1s"� �V}�@!LE"�9$ c}\�arM,100\%$) case| �P�AAF*��\le _aI$'�&t�C](>�3 cr0�&v�{�%',:2.��&��.�,%@ �!9-����1�2m9 ( er-on-xCer�^N $��61 0\%)� a monotonXOmanner@K� conn�on�L&��F�Q�UZa��Ze�=�1m( (2):^���/�{��Z�p_���6 p+p;6c$. or NSD)}Z�)')} ���* quot�"�Ks �Np�Lly6���y,2( left-hand-!!+%ae�lAll��af�H�#fe{Y�C s $Q�T}, �$;6 h��%qex��ze&{,J�I�_c}) = 2�)�ppF��Zdi� ��F0�3���e "�S .��$�{s��.]1h"� )�^� ��Ga2�. ��how� %"�'l.��(b�F ]��Lq6�%ppo_nB�Z��e��d%&%"�S�i (SOC)�7,8}. Aζ s{�seifoth2P SOCa�rw�] es�k6�!5!� >� �re�VkO� J�#Howu��6:2}&a�)��6 I�J�=�!�, e���P,��pa6�(w^ A�W2'V(e�$2� �.�  (A) Gy: Le�'d r�Sw@m-� �� ( made by Ru�for�s9}a��I-+-?Ti&SE� a^Z`!WilliamsMP10}!�J &��bQD^ut: O�\�pace-tim�Jce)^- �0ѳ semi+.~LofU-�gy�Nb#uc� pr^b�at}�CBroglie-]�IthS� proj��l shor<}.�T?&u<9Q f��hit�yJ�2� 1� 5�)X:f1defp �cQWjKerPn�e�urb�MahTiA@u"fKy&EWa�m� � � n��/K! E, did�Tnvn.�� aJ�If�s)����K��u�`edwo p+p&� sFW ! 2 aeT @23 �&�6YYe-E����t��-)Fmaus�e RTa�]rd%�� Re&�j9�!U10�n (B) SOC:�!i��lq�)R. $5� My4 tic mof 4!yD�t mov���O arri ���ic9P9S!�rA2b5 e!>s[]�o<� �� " coup�� scri;�IQCD L0Eng�>v]n�bIwnonN (dA���&�!��y bE�I `,V�� hin�at 9q��0�ng sof �o\odynam���.lex>i�A�dc ���ch���0quilibrium. T�tog�GI2��x�ȥ��� Bak, TangiBWi�g feld (BTW>W�1ac0 `lU��be�3$ ofA�����!hBTW ava lM[in)zic -=Q� 1,12A�Acc�bg� SOC,n ��� S�Q:Xma�U_lemsel�m(�^8color- le-� + ters $c_{�\.waAQ�yE 2 adi� a�6u�� gT� 6�n�b�E veR|�!�qi�Rc6�%UU`V�/�~��7:�ټc�;2�ex"w � $�FI�Eq. (4)~�5E�"�4�,2}�1lad�fi�.��k $c^-�!� �s#)��U �$f Van�, Waal's type}b� �eXa�_lorA#�a�\�Qce�A�e0A?�radiutYa"�� $�X heck7 yII�jWxti&I :�'&�O{� J�f"61N2th�a��S_ �}o9.� ( $D_{S}(S)$�, lifeg B*T}(T)�Ae�B��� �H 2 q Smuaqc Tn��,I$\n Bo��tangS�:�2� as ``aI fingerpri1‰�''-c�@��.(x%y�~����:S^!�I� :Ia�ir��a"�."�m��'cnt�tQ�P!F)�_��ane� f�yone�� �&�¥�iob� ''��%�p� �E���A���3�!� S}(x_{P})B8� x_{pg)�9� =1.95\p,�1""ƩO. By !�i��ng�d�ZicZN-� ?U w�]!*u�---a�)>%3��a�� ��}�%(ZE=Ft,�AT�]�U(31 or s��y,xof)g� ё�9S*� | y��bts-��6� deno~ ]]�F�mord!nBr ).�aSfi#f^M\�/!yI)SOC6U������m{'*�g|�"- �sc q. �}�"v�cdots$+"�ete�!�come so ���A9e~ ��&3  a6� ($C> E� [A�J�Hbe vVh����� sj2���  �+. 2 ho�y!�$z$ axJA-4,�oD �uE;bK) Axy�(ane 6�w�wC2>+r� TD,lle"��>�7b����� �A�>)t"{ aRisd*ox��l�o"#ip�: ��s6� %� I$$� x y \sim ( p_{x}�� h%y +� =2}Pg (ii)�TE���a:�a�be2: L L.a�_n�vgb� D $I�, ��K�NI�5A�pr" < �ind)�a.����S�X�0�;" >{p thus��B� � �u"�_i.�� 'q�%��(� L� *� we� "�e�!} o" %ti�mu}J+"i�an�,c���9��m ^{-2E�#th.�,4O� a R���A�Hain�o*� &�!�f���n�i/N,��:� �.:X W x(��.M���f'� Adsur�zings " � ly a�"#�+7 Ic.�� *�$��� `aBer-��"� two ��5�mi du" p.��2"�vdG� c.m.� � rJ�P�$�o��˅���ide-w w.r.t� &>>�c�N$�� t)�*�� E�A7U���;�2�N�MRN'� 6BAp l-2M���t@!��sr l �!� ���. tainJs\��-+6-+ 7.66�@y�"� };a��)k�@�\�7�/2P3��{ ocusSm���5{ "��}* 1 p"E#3 '4):2%N�( oZto �3[ �& >&�+n}�Pc� to ��' -��h�"3!-&�P� 61*�2+. i���7�* ``u�J&�'���� i�>D �� �[.�c/RmwAx�P. r l����8B �,�)�!�!�-�"s 0"� �� -log2A�!� 1�=���K3$"�nn !\c}$--�$"�l6$\.�8�GJm�b��.a��� �$A�y�!L�Ool|��by&�%ik� ing/q7a�;6U6���F�7D8��B�X!:� a"�7aRio.� n��o�+n e  R�� to "% �w�$``�*ra�0''�7�.0û"�+ i�: E2#m� 1,3} �"�#e�m�ing��icd9!�� M�s;�,�E no�2``� "�."/ �+�+kM �,}�s1�~ , )x.xb.%� A�.95(0 p?quaL.$impact� 8W b$�,T1aI and 9�� oRuE�� 1y!�`Da��. Hig^�;c��zl�A�c&�8 (AA}� �be�m n ensemA��:o�!�6 6q�r�&T5 (NN)� qo� ed�q��p��8��on9-1 . S4%�#AA ng&�%Ga $b$K�)� (�Ya�U�4=A�aptrue)��:� � c"�d ), j�o.k�y�Y2{-{A��{�S#Q�e AWll*�i+  l�y$at (-b/2,0�� ��AA�y- 4-�~� �ry$j"::Z�UofF��=��٥�/�'y-�ag Q;ort�͉XC�ve*�;��T>F5.q UI6� �)��N�)�Vo)mh [cf.4*(�"]�A8��x\*���� 1Kz ��u]#�*�& S|8se�.��vA�y�+��lu"��[ � ����.����&/� �z*y2��tial cow$3U�.! B [c�e%T���$QS  x,�+)��4'�+.]Ak8 ;h��W 2Z<��Ied�.̭9&�JV�O�% xyaGe�(atˮ �ot yet>�+H� *=u'��� R�r^�---`��"�*a��8o�! B2� ortu!�l ��!�to�Gm! Thank�Na�%-m[��cians:|tWeier� ss, mC�sr�n(von Koch, Fakusdorff&D,, P. L\'{e}v�? B. M%olbrot �5}, w��aN�]t��!� box-~!�,technique. D�?#��~"�Z@�A)6�%�%U�2�,vV4F %� �u6a� M� *�8a�� :A $ be�sR,��'�s  ��. %É�>�X"�B .0��� �is 2e�,h!pel~��rLZ.�9�3) �a`' be wrsknZU� q��-7 x) _ mbda+'y 鬁 ݥ���,���)� p�aEbox)��!� bin,��no*iz�6�|F��=� t_ , $Nđ�,�KHcov#'�o�"� &&�e� �e.�:�$in�BF.* Ag�r}64=~` ��fI�%OT""E�]с�1 P�a�65U tal ���'N Mconsis�!f8� >9 Vs��in)�� ]!"ns,�w%is�� ��&� ��s�PmA"�� aG^B��x:$/a=any kU��Js >s v�y�*&92� ��b= *c=A�7q�C=)��G>&>d=�&m5NN���`e#Q��M6�)��2-7 >�s��t $�b��,!�D�her%�r?2M!I�r!�v1 B*� 2�'�� 7 !��m� }AiDA:jll2�?$�� gogQ$f QGP-sear�r�x�M4"�%bFcl{)+!w�A�"� 2���5� w����!,u!.s�.� rBlp l/��A�|[�!, Complex Sci%\*��@bo<�2rom F_ al"�5%m| re help�}in�HaRey5 H�OIon�M^=j�J2:~s}+:LX ank XU Nue�ыiF�%T"���> CollI�� �. W!�K,LIANG Zuo-ta�nd^$'"�Hg$�%�5s){�.UA� nk LAN Xu�L �LLei�1$GC;RKeYanChu�d CCNU-finanɳ ` �W��q � !^�P Fo4 �aN�P "�P %�.B�!�;` %Jus�dc�/of unu���zb!sC'at���qlio�Sy{W�H�x!�eJU$ via�U�Pthebi#}{s08b-L em{1{s Ad�  e�U.}2�l�m{�R 89},p3R r2Ppd�7�N 91}, 17233|6$n3:o Adcox�N88}�rZ�4?oSP���0�1J�n5ipp�Hs'fY º`67KF T�,��fAb in �54 ,Ia4A�refer�lVi2r 6} Q��, L X. LaeE T. Meng+C�YA�2�r7Ar�3C.�3{K. &�3^5A381ts7); �KAIM38}, 36 |:;q8�EIHowa��# Works} (S>g| New York,�~6);�|J. Je���Self-O@M C�Ec�<} (Cambridge Uni� ��P�L,  , UKbUoqB9Xq&w!4 ilosg. �XXI}, 6�}112�10AJ!xl;, p Mod.�� E17a{17�t456D1} -�,�|R� l)�Y. Zhan"�~\.�2W044!�}p���C�� ros,QW2bKA<b��fn D)6a�094010eP6t13} SC> e.g.�$ Abramowic�zA.��d�<, �:" 7a127�{91t Mپ(oper-Sarkar�C.�D~ish � A. de Roe}� Int.!�bM�1 �338 d8&d}��r:���JB:NDqvT1G�U�9� 86�+96��16�5} B.2�4��>){15~K63bx67). >0 eg�5B�ofm{}, W.Hg�eeV� N.Y.� Edg![E Clas>}lf s;estoiew�@04�SendB� .;"��6 [tbph] %\� �G[s&�M5:�6 1} %"�6 "Y6� \y� &�Yc^�^ * En^�f�=�.�^)b%\:,style[epsfig..\�6$�\,N)f(]{elsart�M�le*renew�[|�se�(tretch}{1.5�WY �} �5 eq}{ #"� :$e$!W^" beqaG��FG% H#%\two�\[\h�%9�\ �O  %"=d��s�� @Bfalseb AVd�]8 front�\ er} �[ Nucl�?stopp^ �fҎinU "�� ��in-med�PNN6a#�W�X{T�itanos$^��C�4 chs$�,H.~H. Wolteri�9 X{ r{1}$La�ori Naz�&��� Sud INFN, I-95123 Catania, Italy�d9�:�YuR�YG9 U�, \"at T\"u�(en, D-720762Zei3}�Zt. f\f��SZ6UM\"unchT$ D-85748 GL � S���]�S% 1�&VTW��<t(� ۙ` �"�T%�re�=X;".!�meaF el�S��=�1o"EQ6���e�"�Y stt�<*�4*^�YLT�rix fqmi�%Lcopic Dirac-Brueckne��� . DoA�so>Y����W 2�"��re$&)Z $var_{q�tl�1a 5c*�o"�4��'=aP3stiga~-��"� D%lar sh visc2y� 5a�]��key�}e%�.�?.�e9�"2\sep :^$-Hartree-F@�" �t�+b2-ve�7 :� % �s� .!F5.: Q )�b�V coM1 :6\ \sep coDde \PACS 25.75.-q, dLd, 21.65.+f \end{keyword} 4frontmatter} %� % �  J0BEGIN OF TEXT�Y J�%�(=(�aOne of the primary goals in studying heavy ion reactions at intermediate energies is the investiga/c,nuclear equa�}-of-state (EOS) at supra-normal densities and/or high temperatures \cite{fopi1}. In a hydrodynamical picture the time evolut�$of such a �D can be understood! terms.pressN\gradients which build up.he com,@ed zone and drive%m �Ps. Originally it was �|refore expected that a direct de�in%E�q1] BD^{ HQeff�}��� gi? � ree ar��th� g!�al� lex,.�8. For on-shella���A�!�N�qI�� = \frac{a�h)^4}{s^* 4 \pi^2} | T |^2 � ~.� sig1M��:�/s�?us�)Y�e�d | �^�]sY�in DB 2zm���v� us�dq� $k_{F}$!�fun� Q labo�Wy�$y $E_{lab}��e free kչ( P =0$)��caro!�Y"�to� $np$:E\�ect� pdg}. }qfmnd !���%�Fig. 1�w��gy depen7m9u :v$(np) �qnm9�m� ��5��$k_F = 0.0, 1.1,1.34,1.7 fm^{-1}$, c5 spondemo $8��m A^5,1,2_0$ (_0=0.16 F3}$ i �6"}T�y)� �0 ��1um�{a sub e� su�a� 22xm�is�onounced%*Vq�Eu �� high �ies wher��a�� Al$�m $��l!:of�Y) )D.�2��s �effic�. 5 argere�symptoR valuesy 15-20 mb� /h "onlpi6@ � lsoeKangO�tribu�� a�&�>� )�Je � i!Zly�N ward-back peaked }�Q�comes mtm�isotraatF6 a u�Aai�do!�!�%�2x of sof�sA�pi$�e)E, u)�erW al wiMhe.�  Hek�$ )L�b9M� � "� -UehAb@-Uhlenbeck (RBUU)9g�, �"� �(r "� \narray} & & \left[ k^{*  \p� al_ ^{x} + &(E $*}_{\nu} F9   +� *.<x}} $ \right) >_x }} !] f(x,)"�`1}{2(2\pi)^9} \nonumber\\ � s \� 0d^3 k_{2}}{E^�{\bf k}}&" 243J43�2+234J344}}} W(kk_2|k_�4) )HH[ f_3 f_4 \tilde{f} _2 -f f_2_345)Ѹ rbuu!?��e5څ�EseI�cle2���is*c $f_i = f(%7x},t;%�_i)$ �-A]Bdi�% $�B/ JE)��N9"�explicij�fU�4iùYA�l ��Dsc"T amplitud��cludeɰBGofN�. ��s!lh eq. %�)X&$� F�m"W. H�S att� ve�lar� _S$ ecs36�  $MA�$ 5�repulsQvec��Q \mu$L ��  $)��"�s B tens�$�=�<^\mu � ^\nu -q�muc9�2�s �!�ɝ�Fj �xX=�0 W = �B4 \delta �� (k +�. -k_{3} -4} ��) ��)^4 |T:qF w4��on2 A@I f�m .��&c�I�*/ 2oi�a��6, ��� �� ��m9�U��t�Y� e 2�U$iA� �in ] R . Toq�e� t�ap*�iLuj �9�L� (=() ConU � A.U (LCA)�4qvan&[F!`taken�t�lp�� $2$-v -spQc2zi 9sI40&� *�ne+ �eq9�NN�,-�way, �.a.( of a� �o a� s� 6�FM`avail&yet%�o�discus� � e� nt !,J will+ result�; .or>�:`=� is always)e�A4e LCA68ar�U conn]o"z.�BUU 7ach a:` {establisb�omaA�>�co"� sh��sh;�sc$\eta�V�Rhea!pacI5Y84}. /ou� f� clos);q�A ,.W�� ins� Q;:gA* exci!_6� . A� Mr|>�is �ly1{���Y�!<"� . Quantueect��!g��� � "Q A�U"F~�OBS-/ � BS})� 2��": reduced��"y�ls9!� 6� mKnc��g average�lum)�] mI9Y3of}� A�I�of grA?��i?�q ." ly a�)"inA�v:$ . WhV Ir6O� a^ve���)�!�6��2J� opi1,A�2Ir!� .��9esgYV���E��B� !�so ghtfo�. S�!.�M?@rinciple natural � �U%k)m�of B#*�a�is��2�rapid� .�8s up to now didE� deliver!�clu� in� ��on z#6�AYV�"ly)~ FOPI���Rat GSI*�aM�a� analysi%��K"#͹�g(�s�a wid�&y r��H $0.1\div 1.5$ AGeV�1AG5/#�%let " ase m comwal)A"mea&� long5 i�Z�*8���"�x A�beam �%ion�g data��w� eL`! FHi���A:�ly�� �ms refa��&a broa2�.[. A q��itaA� -!s��gIVw tro�� 8Reisdorf et al..�5}!�>�q varZtl�PR^2(y)} z)"�vartlq � 2� $(z)�V9�$(y)$� anceE� �mc2U a��T! ca�$.�\le 1d�m�Z1� Q�. � ur&%�U1�' (N&)� ��'+�$ peri� .G&)EPa��g�&o) n(���)�"��F! ���Ba E8$ maximum ar#0.4-0.6N{ �44�� N":�  8.)%2.5r$LOWVARTL.e"$10.5cm}}}%6%*e&N�Tdm�ed)�D% $P_{xdir}^{(0)}=/PI�5@}$ (top panels) %)�h g�*љ2�$$ (bottom)%�Au+Au��d. % �{�^]I�!�>U��%2ll��| A-B �impact am%�b �(b/b_{max} \� A:E  $ be;OEcalyrB] d � F=1.15(A=S^{1/3}+  targ )$)�rr&�V magn��e�� global % e!;�� < 0.15�i���) )�* )�6��a�F u�(solid �#s�&�NN:�s (da� 0r��m� p+�|O&!b J�6$�U (fillE�amonds�b 6_ oret(69�$a fix��>7(of $b=4$ fme-�i �!{�-Z c�)8 PM4 ($b=[2,6]A) Bo C�xf�mK .gth.��aI"b<2~ fm w� �+ri�X�a b=0 & �B��.�� fig2��n��6��~�"b�.a � d�e^� f8A�!��6>!�( \sum_i�!0sign}(y_i) p_5iw6(��sum ru"+ ll ch/d��t��A( aVb e jM�r�re� a uT "�+5��B�-�� way�� &� �&&CZ i`1im�an" ej�%%its� sen��)��D a&se | We have^� s21 � B�F��բY*!�:$7 6X.$-a]=a� val a� �..�!fb]�),:�to b=2-�E���fZ�b=4a�kA��Vjj "-��Cum6X 2��o!� '%!us�!4�u�#BJ>�.�� *]1cU�� J�> %,!'�st.��|@re di�ultr� �� 1:�In Ref.2�YU ERAT9&Q.ycc4)8� o!�l�. C�|s�� IQMD simu6 s �iqmd}� �1�2F�� $b d/2-�A�-, cprevi*#ajs""� beca�%�.mer�O fluctu�"� %2� U4>!uB�a,- than .�25-ѺV4,d es]-� �P��� 6� I�>�6$ �or�"these�$� i~ :��)��error b�)F� �,QA2OF, >�isuX�s"��\leq M)Ga.P2!/� -3�.�*�5"�8* =0&-�wo cases,*K �&=  "a�erep#>~(s� **^ J,�"]2). GY"A�.�U �repO' qual�m6i/)�8�IG��power!�caE� R����a1"���gy� he��5>66s0Klittleqo��:�7as�� 8 `�L�-l�l�(\utk�� ��9!J!e st` somewhat �est90$Td*�8"� �um F���4us op� &q). With�.�>�0X-roeɦ�)��>U!tooA � at %��above "|E��82@ empi�6ly � $0�Aq!�!FF� ����Z�i*.-an =yw�:��Aa�7cu�(ad�(ng ad-hoc BP5pardiz��9c�," +�X2�4A�m5�on�+h�1E�at:q��.ope�o*!e�ic �+�, (pion, kaon�3dux etc.1S�%in- 8ih'�i��4MN!30��F|) .X,��mj�1�*m*d!!�G ma�( 1N=,Iu�i� threshold!i�Ape6su29eyser03l� ? ?�!"7.,6.0.,2v�L*8.�*,a�9>< multipl�0�0�B�a�"p-)iiZ2�2�se^y�"<6�+3�KNKAI��.�+:�Fw>w easi= 2� way:ax�*_��:�o st "f,*+ng�bA:uAs� o=s���ig�(iOarency. ��a��K��"ob� in"�nas %� elAw@6z drop\+# ��com5�@ofL .>"�Awa d���o... _1a .�9"�.]Ai�D �+T������ e�*A�:�� 4 �� $M^*&0,���6� "M Aa� play betw):j!�BqIw ]��  31 is R.� sosp�"i�dt%M&56R�>�^� 0#"l>��� cell!Ga}�"�A� �4"3� �"�1�S� �" ��. $ se�J��3� velo}!Cn  �5*T!�Lobz boosL$ ; soid� U�-� eW�� ��:| ��9)[ er�%�.e�C�C(ly sees how%BA>tAA>?Uډ/*$6 �y�I*"4at�0ut 0.5 �)OZ7 ?'}<on �-6Ba �7�7e3�7eta�5S:$�%�"�>>� M� E�/"�1&by�0>=e"ME. D�e�EA}28A�q}��M!΁d stag ��a�68V The Uc"\A<6Z��of 4, 0.24 6E�0.8 �(wSri��T)6�4��J�I#�#&�to�6� R- 2 ing"�D!L��e�:�:i%* "�? �B*|���� �� he dB�*� $84}5D�((o"�s�>D de�G��omE�.��'�%jA�"`1�+E"REq6�4fir"P?8Chapman-Enskog .�&�3q�>.�()>��,���G5> ly ���6}ms� -> . Ac*F)� F>�'&* MM liquidN� |edAa2/��x!$T$r-�81ua�ta�! 1700}{T^2M!ft( ��}_0}|- ^2 + 5T22}{1 + T\cdot10^{-3}}Q1nB{0.7}�2 f(5.8\sqrt{T} P 160T^{-2}"�eta�nd�G 4�H?e�).aeq.�-?)F&Tyv/9-5tog�>r#!ޭM�:�E��Ga2M 2�"# y $T-!O$ev Ku*i�Hal�`.�0��&�� A> � 2  ݁�>.� by f�of5 6�4 .�-as �&.��.�� }. F�-�_-( t$)�exhib�a min�"s Z! $E_{�7Lab} =���&)j+ tom�8um�:&�In� mary.-:�;�x�4 R��28�) f"��Q:^� ��c"��\.�D� <>�0.R&Na 0r:(po�*�6� !�a�z'E�V!���KN9%���>� sB) !�_O)Et~�!Wse&�,�)�L!��:� Nn%� Roo>'=B�  *� F�nd =h:�. �terpre]  /��>*� OuY7�t x ��:� �aGa%V!�� m+i �C�$ occuvC �� �  �3R63REND�1R ��2�� n'Lthebibliography}{00}�em! 1} W."�) , H.G. Ri�2, AnnuLv. Nucl. Part. Sci. I8H47}, 663 (1997); N�6�M, J.P�Rssels, T�OLd�Z9}, 581Z9w \�P 1} H�-\"ockQW. Grein Phys�p �13�277O866O�VD C.~Fuchs, P.~EsslH(T.~Gaitanos!H.~Wolt -i% $A 626}, 98f976f� SG`+},1c2R50R Q9!` Eur. �J �@A 12}, 421 (2001) ; C. �T. �J�714!�43A3�9oI H3} F.~Rami, Y.~LeifP{gQ!,* �RA0 Lett �8] 1120^0^5��P$ S.A. Volo�LR  715}, 379E3~� A�4P. DanielewiczRI673I5I��*` A.B.~L� nov:��%�C 6!�06461)�6X-M8 D. Persam, C!�le,NL�L2!2�daNMB� Acta OPol�.�B 3�45 �6N�E� ross-Boel�O�qA.~FaemR�48}, 105a]M�(. van DalenLQ�A. L.� � A 74A-227 �4).�=�J5btm��~Bo�� ans, R.~M�J9Su�9�1 �%��,T&�J!� R. U2Prog.� .��21}, 207! 88!��f�^01�j)IUa_/}�vm7C 6! 02400i�11�-Y�D0 K. Hagiwara Yu�>�D 6��01000I�EQaN84Fa I}� B 14K 168 �!�.��;5!��c �al:�U9aK 2323 �T5��#0 Ch.~Hartnack R�N!1} 15�K:��!? O. E� Q5�[^ ,-th/0311002]� U.>b�  docuz2} 9�\h%$[aps,prc,p) int,super)Uad�K�,showpacs,nofootinbib,floatfix]{revtex4��u$ckage{bm} .e?H6a1t+.p} %\topmargin 0.0in \def\beAFb�]B} eM6bea 5�$5 { 46 ben{in%ate5n 5>bi5itemiz3i 2:ie{ŬFO}\ �viz vizeg e.g.tal i�Gdel{\*al Z O{{\�O�F Fprl {P���1Sper.5 np {�� gV{g�?KJtiny V�B%�gA>A fM{f68MT>TS>SP>P MN{M6pNW>W GV{G68�GF>F8DRV{\D4@6>R}}^{\R/ mA{m6-9/mZ>Zk0dbar{\mid \! M#hy"{ o-1hh\,  Pnewcommand{\sfrac}[2] #\small{$#1}{#2}$S ��,} \title{S�ta:7 $0^+�$arrow 0^+$"X$\b(-decays: \\�A criE$survey�es�f CVC� �IUmodel��$author{J.C��rdy�Dmail{h@�5 .tamu.edu2 ffil�/{Cycl=Hdn Institute, Texas A\&M UnD9�=, C�% ge S1(77843} � I.S. Town�`\�l^l�a��WD�*U , Queen's2� King X, Ont� < K7L 3N6, Canada�v$\date{\todH1�ab;ct}:/6%�c:�is �en�70ll half-life,Way�R�$branching-����sC< o 20�Ie2f0Eg EgIW; n:I�ignored[/o3?'re�Sed�-c]+>�\ s up!dl?A new *c�M�"(�v " $f$!&�BZ6S*$ft�8�K�+p�assoc)C�Z?3�B%s nee %to�verBse"�i�B $\F g!�A!,and careful ABne!!�ai��or�`,6�.their TMriTti�/ A�  ex�\ng�fir�;gQeerved ~Fcu� hyp!|sis!��+>�s� !F1 to 3�t� $10^4$. !F���H/ to s�%�lA�.any"�,�2a�te`0ion: $C_S/C_V%U (�0005 \pm 130 �Hx"�?.~;.����'en�bO7�#muon lif�,�R!Bup-down�rk-mix!kg#M�d Cabibbo-Kobayashi-MaskawaV(rix, $V_{ud�30.9738� 04$;e�lni�3ty ��: top ���h�S& $$| \|^2 +  s. b �P 9966y14$ us�U*�3 D=GT'sQ-���0Qd �e-& �s�H b}AW�Zsoe+� [F�.2��T0c exist�;�>6-ha�M�s. F >�w�0�D� prio�$es�`futRd*o(eSex�;��3Nork5��ewmak1 CKM :�A&9i�=.= ��\MPcs{23.40.Bw, 12.15.Hh 60.-i} .T�� \�!{�Hs:i�=} I %(} Precise6�M� wa� �#@og��)=�:0pin, $J^{\pi}A ^+$,%�$$, $T = 1$,Aw1de�!��funda-FA�sX%�"/`�4roweak�#q�. ��Ke!���?Js�Y5el�b�&��erv��C��gM.,�xt�-�x"�A�Qf�.ar_Jpe���QM� 5A="�G! �Y9)�j#(CKM)�)�=_neT=M5*� �E�=D$, $^{14}$O $26}$Al$^m$34}$Cl 8}$K$ $^{42}$Sc46}$V 50}$Mɘ $^{5<o��G �Fly A��&ylA4,����)irx8�anc%[ph5ds, Iseque�_�i@.a g�d�Y�t~X���CE�ast few�ad�' In e�. {se �1/�al%-���cto �3t�30.1 \%��I! 1990-l0}$C wB$d-��list;08 &�.a aA�ci�#�d5 e�g�!, �,A�U<a�F%-�t:!�22}$Mg%�!�Ar!�74}$Rb, ��� ���� dev� sU5a�� $0.24���$0.40 . In� n�p�zsdc&��J undoubted�a�e1ejaną al eE� �c�K[2be%� i�!\. Tm improv�  .�a,��!V�Ha�ō^���O.&0 kA;"�.B �#%�-g�+��S�.ard MX BJqDum.~ . O2�� dWt�0 come�%rea��J��f�N�ad�[�j�)>a�1�ifac�$ite aAEIQ>-,eRc� �` !^�ol�j�6� CKM�E�" <�p<��qua!? �N&m$J� �8ew� ! falle(�1�y!�0.3 \%, ���twi�qhe quo� 1�y� �$TH0�Q-��ovo�Ive�1 �_@�KdisE!q . N?%theles7I�5�9edE&/\ a � H2l"=�d�"R 5�)Ad�Bu� so o��$K_{e["�4io D5�s� Stri� �� ~G��. $K^+ZT)/Sh!/W4throw��Kp�v|LE !�3�. Alt��!���I�5gs�@tly��pA�:�%~ w�B , ifI]Ait�b,k,��a �Z�2#E�F$ b"#aa� top-� A��U�E��.�Bi4n�d2rL� �(��s�Ya0tv@��a wX��4�]Ls ��ly�jer�Q$m�Z- �se)8xo�?��i�;�`few ye�: h7�J��U��Log� A ��olih���IP� reli J��Qsoo(q,forthcoming, r{Q n op�(une�$to�p�?�gm. A;�!%�uD� �esRishI�deT!�)2e ��nbl� �jP%�]E�a|!9 renewed�Af�Bc�� anticip��� ���$I�� Ii�( b}�%�*%@E� �-negligihq.001\%!�Au(arity sum.)�% pu@R foury,).sF fs.~i�PTH73,HT75,Ko84,HT90}:_� b%V/eiftv E1 ago�"V7�:�2>*� .�&3�ej� �)-�4,  �N;,�a$�Nqrp�a��%�on twelv= z�%"!ainu] ��ceYbeganA� 1984��!}a�����@Ao� ake�1kA[!DZrt&S&ъs. +CJ�cM�ly� *!"n�%J,2",#e� employ ��Y �t2a�0-symmetry-brecf/!� !he�&Z  ![ex%f*>�-x&�U!�� . S.��2J�$�e�) 7saquelyh{� � 1�hadronic���"� W it o&� P- $T=1�a&V���3n�F9 (CVC) *? J�&!2�Y�}W�same ir2J!sv�zׅ�usvitG ft�Ff�g4K}{\GV^2 | M_F�g�{8*~� �},�]ftx,e�]H$K/(\hbar c )^6 = 2�g3 |\ln 2 / (m_e c^2)^5 = ( 8120.271l 12 )M^Oa7-*�38$^{-4}$s, $\GV ��; -� coupA[A?���J leptR�s,~ $M_FO%,IA�r  fw �MJ �ͨJ!S�-2�)e.9� asse��!�^� �$,�� truI;!�� re�x�)5n�rI"asaEs6�q. A�irDɖ)���mbBKN�%j.z�? inde��� 9 Wide a m_ng�Ia�qQ;9 . UTtunat� Eq.~�VQf)) �V7�{@�rs�S�rBad��.��D,%�exj_ei�em(d 7n mayAemsmhlung ph\hQg�?r3�gw!H&+ . Second1 ��Da� �8!�%�i �d!��L,EjE�1 �Wdy �3�4� �xuV8write: $|M_F|^2e�( 1 -n^_C3us, w2�Y a ``-Qed"] as�R \�,v ft (1D ta_R )(6ba*�}2 � 3DRV )n�FJ� iC%!�-or�, 8R8��-mBXI/YU_RI���3 $�NIa-�ua�`VmQ�Vm�.ab&f�-� but,�Uso, to mrALa��acyer�$�6� hey must�-ed�N<of 10\%I"�1� �LF� �e�5�whG�-!,M� -strHre=T�. To"�:�ztho;\�-��%9�on\�j \I� 9�-!Fno���pli^ eV�N���o�;�,I��a_RA� "�}f {NS�1dr�,ofb !f���� 1E��"� ���'slDy� PWN(daughter)%us $Z$Z+�} )L&�a�Nu�-�M,Aw�� {\em��M�}T+5�E$eg;ond%8�!$,� %I_C/O�in��w1!�fs,Y F;}�k ���L1!2�6��  F4Pe/n�b� ^�E*�2metho {� a\ C��VA U"in��t.�OExp. a��m9JY|P"qui%IOg %3IruN��� 6�!�x6�s:Ft};�! A �us744 6w��MOCVCi *��Se�s:iwip}'ipmi7Uiqsd�m.�B� i�Fs:5*SasI/K � 2r�A�BC5� E.�!d{$!�� )�Ʌ�f�8riz]ny �Y�ͦ�thr��]�vnt��$ �L;$gy, $Q_{EC�.!N*�$$t_{1/2)]P��%2"�io, $R$� ��|o*Ite�K���-i6�&]T�S NSwh���a>�� q"A~yu]�a2�%$t$ txsi~QEC}-ll�&.PyEo7i�_ �rN!y�H���%��!.�pr�"�?�'r܇*.Ac*r!U)�ESAd�o%=_���f*�s րe$�< �� insu�UYt2�* ���im��\i��(O�furviv�� ),$-��C(� ed) 2:( �A�&!���Q���FpU"�bE�AR!�Z�r��(�or �H�f e��. Each!yum��earB% is�o�%�or)al jourre4Sce2 via}� lpha�0Oodam&� A�L�H��s� A(f� �, 's n|�A�/^"dig�)&. ��es= :�s%t+ o�! sed e��<? le &(SFM'odic wew�x���r& &, �1ݭ� PDG0+5!YwQ pu�earlier A�eyJ@H��$�2E\�%a& /&-a�n �Sv�ugh(I  ( , ``&�V"(``29"m%�a�,plus-and-min�Sn� �%"M# (68\%��;"). &M a��$N$a��ed.y x_iOY x_i$,5a-s�q�,)% auss�V.�VeZ ssumr h�h#TD�Lb� *dC:, \��`{]bpm �2\l^w_i�Wf|^w_i�vm?D ({\!sty9�#}$~. )1{ /2} "dave�_ \vsс{-0.4cV5�40displaymath} Q= 1/(9F�D"�v�r)526A�!+ sumsGC end !�~!��#���N�-S��$\chi^2G�9cb0ple��, $S$,&� d1z S!Y][ R/(N-1)1(]}c2}&g�c�� \ee ��� t�e�� "�q"Y�eF f $S!� *'�n2$�"Eq.\,�!�;~�un�Tg�� [>�g1m=#Yx_ivZ�abi�'C%cn�i�m6���f�R)d �Equivalv ta&�� l�� ����&�Z�tr�&� �"a��?s�@ ma�"l%K�!!LB�Videly�F�ma$e�SEIreYF�� 't��� �e%�3 NI/J�fr��;�2qE\ ߁YtAR*��us��waEBn%�t� � ,D2I!�\ !|9��mF $.^$}? �>i|6 %� A"�x2�!n�`�vid�1&�8e"�ce$} pairE :5 .`aF-step�-�mp�� e�� ��dV�6� for �x��&� �� mann�[lreadBUscrib��NA� �IE%ca�e2y iT+!� tF{ x}_j.�$�a*� cf� $j$� de�d�.2��aAor�Ki7 �catAE]c6��6�*�E�d%n2o E����� �as�)!��it��v�(� oJ�r.A6�w� &irY�7 ��p t�Mif* .�, $d_k.�d_k�%G*A�t*2���M_�mK /SY Mi-��8rOnvz���$M_�!!{ V��b�%�we� &� � + T��� )�U�wn!u��(ic �4of�� m1��n :2.-WUomp% by�Jq�*q1t ���� ${j=1}^{M_1:�M}�-2� _j}{�%&�M + ': gk g26gA9._ d}_k_d_kW`! chi2�1�� 9=_�.N{j�.�x}2���R� e$j%�nd 2$���A�� .�wE�6�.�i�#iX6eD��aj$.6��) a:XWf����R�x� �~�/��g �QW� �at�,�M�y�WZu� � �O� :�Yex_iYV]l>Ul2O d}_l]UlO,QWA+letY^��X��=�9�!ty%es!�+�* $i$�  ulHK��F��,��!^lJ^ �2��@C(.��2a��Zmponen�ɒ�j���) h� �Nc� ��.^��A� conve�:�#�&�|,ly�4�&�=}ˁ>Ga�p A��*�%EQ���s�st-�3ni~.9'7.--힡�^{}%C�4�5B3�5ue:�il gn�2h"� e�T A>ir:2�dv0ei�di�.����y&',- .$ (p,n)�$($^3$He,t)&�X�#uV2[=�+tifZ` Polumn 3v%�����``-�(sa)$"%�� ���~a�D� �aB�p�oh����x � ��a�w>� (see.(�)��2��.=EN�.{ l 7X4aX�"�l����>{}))J8�&=�_ s,�A�5C-$^�7�no �v\�- B&UTh��i��-�� ak�h� d6q��d�5�V9�:L �>^4AF���2�m� Theym+t� Eu0 e+ !�m 6�2�{j�����$I��!� �@,.;�r))=��V& M8]�e-7!�>-�� H=�:4>:!��Bo�flaggqB�Hno"!o%�c�f�F N\ ��;� \squeeze�� \set�-$er{LTchunk }{59��et9�{\LTcapw�}{6.5i�XV{6W�C "�H *}{l&� {D�3Aia 1׉�2��i�b�BE{ (See.hHe�!e�tn7�,5  a.��7<cSusI�� %9�cV�.)��}�E \h6  &  �a�c{2}{c}{P,d t/Da% } &�L-�y\1�mark[1] 2D3DMe�Ud My&� (keV)T2717F �A p�[1mm] \c� {4-6&F 8-9} /�� \\[-24 6y a�% i} &F� �1F� 2}^33^3V2l}{~~~)0-&^Z���%2� -�-�endmhead 2s9}{l} {\EW�\ \thi� {} (M0�1)k%>IC  \\:R)L�@J@-Bm)�F ��6�6�6>6RI7�8-�q$a+EXA=M8�@�6r "e 15mm|nd� *V \5a� $T_zvE1$:  !E�~~xA  & B �X(gs)$ & ~~3647.84 $\pm$�:04 ~$\,$[Ba84]#95#12 [Ba98t~$\:$H9H$11 & 1.0�0\Ay&\x(d0^+ }$\;$174�b]7P,$[Aj8b~~#07#02 6F22�J/ �� \bm{- sa)}! �oR1907.8r11��\\i�-]�A��AN T1]�5143.3�60 � Bu61� ~~5145.09�46!`6�!� 5� 48 [Ro70])U%��&[;0 2.71P8s Vo77s 3.43#37 [Wh  s4.3=�7 [To03>f:f4.2�28 & 2.1�* �$E:�$!$2312.798y011A> [Aj9%!�& N'��2831.1fAaM[ �x3]!�%�2.5��~~e-8}$Ne!�^{ F ME(pE��~~~5316.c1.5 ~i8Ma9m85317.6=e!� l04b)F1H&5I0A,I�U� ME(d.z873.39�94 ~[Bo6 v~~~875.Qr2.2A ,$[H#876"8 ~[Pr6E!�z� O7.2-�3.0�Se7E~ ��96 ' 0.61E�5��4a��j4A1� o>?aC44319n�p [Fr6�-K4443.5Y�60>K>�;$1041.51.0.0! Ti9� \J(yy��3401.9y-60A�6QDAk^ Na Uw%g;$-JQT=�Ha74c!m!6-40Wj)j1.3I6E/!=11�1.2=8$�I�!}\,$-5184�]�We6���H'2Uj�[B&%��7 ~[An70��Q )� }3U�ACA,$[Gi7�6~x1.5��� [Mu0� 0QT 0.30 [Sa &>!27��.4�>�E�781.6Y~2AJt~~40 � 0.67.t�;$%.y5=�! :� �657.0Z1�En��e�F%�� 41242�9]� �726}$SiA�^ Al .�~~-715q18A|[Mi�zA� 4 3�kMc# -7132"[HaIs! ],%�-7�]q�i0y,2% '1�2.9>wME&�-11982.A26E�6a�BN2z% ~4851�13>�x��4836.5.�a1 6k30}$S!�^ P 5���A�-1406���2�e�140�r2#.�"61Z%�:�� !� +3.qC)�P��(e,: ��2.9^8m'-2020�;~��� 0.� 40 [Re85] u !6� YI:s6 8Ea~6137�IaQ�6�)~6�u1�0� :$F�J)v�IY543Q r ~jY 5459}Be�MY3>: �ArAO^ C:-18380��N�# 77.1Qx 0.41Ie0��!V%�N�a�7 $!$-24440.0&7 23E[f�J2z[�%~6062.8Qp 0.46J4�MC��^ K!5K5@Qc5.!�mu�!OEb-32122G 80�fLJ2% ; �L 7000��5.4]^0B!o��AhP!b�M� 6�� 4004.7�� 55 ~[De69� ~~41�0a�6�6(a~-�G1�2Y� pQ��228.30��a�3eB�J) �~NX` 4232.4�*01�r� �A�E�**P 17: 2{7NA�5�A�J ��5499L:  [Ry73a!o$1"� 2 �Sd ' 5491.�54�[Ba77c"eU���!}549^ }0.4 ~.3U69�26: �w6=47-��A�%X1�-:�SI��|:�~5914.7� 0!�� [Ja7���J)&�:�13�1TF�~~B'e�wj� 60445�b [Bu7mr"0E�H>�%:**y �JU�tbTɝR� 6423.7d:$}7 6425.]B 5yA4.68:8iA� 3.2}!�2EU��6�QR�E� 7053*�� [Sq7��~~705�5�60 �A;�*.z9]�6B��U� C: j�632*� � m�7631.9�� �:�I*�23Vd%aJ%XV � 4}$F-f�824Ui(1 �o��� 8245U� e��E6�6� =� 8242 p �I9R�� a]>�62}$G�  Zn�V�~~~915�2�h:$~~[Dai�!|�_ 2.A":�66}$Asq^ Gj_}5"%53z8">& �)~2*Jy70}$BE�^ Szy97> 170!�n|2-N}4�V � K�" _�9"B 15"a 4+ ~[Ke�� 51�M!3V�� ~-6233�d �v#2"� Rv'.���ZN`I=�,���&�4���P&E2E��3[1]{Abb6�!�S�#�u� �!6-�6s: $ gs$"(�/,"zv ny:s;+sa+.�*."p!pd+DMEP���es Z  ",i�Vl "?Q_6$ (E7og)�%te�"{L#$E%�9>�$�.!%�'e�_#=� .�*�',N !*h�/s�i(h>^&us;� ``9��..�9".;'s �R8 �2� 2]{R0� "&8" !sPN�"�9].} 6@3]"��(�() �_ $ M1; �%.#�">`4z�i]�Sa�B@5@"]+L+�( elseO*Q��BE6ER%,Is80], [Al82Hu B, [Pr9 Ki�� Wa92F�7vh Wa83PR H Li94FH8vH Zi87 @Ki-�end.�#r&�#enda�p>$newpage "�f%8*&�#{1�-:"*H-�42b�#T5-%��dlso�#a�'{�to"Q)e s%[['^%Uv �sP\�#.|EC\%�H$F$b��y<�F$F$e�P gin{ruled�;xGb\%} "�p��m����!lb$^�!)�2�G 1�6$i� �#3-4} FI us 1�Jo�# us 2FrA"*�)bt#('�w�1]� !p 4}$OP"�1�"H0.13 [Koa& "�0�\\M2B 3a�N 2193"��s V.�2 VFbapa�� 1207"� Jk 1206.F4R.�S�aS81&~F�1816.9�0U ��BR610.�D^{\rm ��� 97b]}[%5*Q37AJ-4�"5� texti.l&a��7���G��):B[aߍ�q1��:T� tabl�ʕ܉�:()u~,"޹H�kv�(t.�FR��Q�{�{�(�}N}t�=�|n�4}�("�(MG6) (ms��(:�(2-5&�(7-8��N#c}�p(^M�&J�c}J;'�U6) ^Y"�(�"� � �%ef$��%�919280� �,$~[Azq�192"�%��%2y� &G12� �b)#��r704r150D �n 7058�Cl;"63a86 � ~706"�&7���Be&��� & 51o2y5Wi 5 �"�49 ~[Ga0v$:"�50B" &) 7061�pm$ 14�x�$- "6$y~165<�As� ";20� l <6lV ~[AlJ#�16"�&��75]> �167� P�357�' �&�"�~38"t&f & 3.`$�[Ha� A I�A'�8&0!� o"/ o22"��!0H�!�~22%E%{!0Wi.�� 2234 �1�j\��WX~1Am-A�lBa  ~~12El8 [Mo7A& 1178"%4��Z& � 1179"�4.9"a5�4}�v844"��%�4�847"T3� ,$[I)j)gU8*8k#!�=f�!$4.ua~[K=!~~~\,43Qw1!�!Ga�~~4"h7h1Zy�:%�B�i�-�7.8!>AG5-j  c2"�"%�:$~[Ni� \,20z!�� a�~17�#aP !H�98"X6�� , �{FM�A�"� I ~634�.��f9%�%�V$Aza�& 633&yI(!�Al�)`}`6 ~� ' �6341I�1.9I"�.M�75�� [Sc0*�"!75�A���~15!�!�,$�"�152&��@5��m 1527E�?��Ko �&�eFf�.�:J0j Age�=�aRm�92&�0��Sq)��92� 1R�#Wi �922K65 8]~924.11X0.3� �2�!_&y u4�V0c uBa0�YUm0&%�M-�'3q �^��3=aqr 680.*�+62�%�6�)[28� 97a�)g&x�-7A -6-�.��V8422.4^39L-2I0��ePհ��)�~0.1Y,��.�"= �28J)��!}��+�28&�0�'$FrI96A%N2�(�w�*[K�2%� i3�,�1�1�Eu�"F5��^�$9A'��=|189�:07�6�@�,", 0.06 �0�.�6�115.~03' laR& 116.�.35 "u6"C x� [Hy� 6*� 04 [�-EG 7y�03�, F4�*)-/Caia� 5�"�)�95.�M�%�yalBu�&}i.�2� ��.Y"�88SQLa[!�1_�78.S-59 ��eZ~~~79�K7B)7z2}4� ]64."& �[Oi�  6��]�80�-B� T}�0*�04AX� ~'�5B0 r>�kip -1i�c*�B�8Q:r|U�,URK&�@s. ( �9�NNNR�K2OW6�6 9-9�J9"w9TR!T, R (\%�t:t29tAM.� �i^� $ (Mj�9�9bR- �qr��"q � �a62��\& 0$^{+0.0008}_{-0}$ [GokJ aС\�1.7�& 1.46��� 14Z22]��4"� m7 [Na�D C��09 [Kr ). _025�/&2�o62G38 [Fu9�#s �46*� 001."0�~h4?F! C6gs!=&� K' [Sh5� 0P �c05 2.�~3'1 [Si6l��XB}'3�m&!O*�,0![KQ 0.0*�00�@� _.v)H5Z [He8L+4.�1�51�%P 2.31/ 599.33&�01P �b&�&�581.0ERo 39B7." 0.21"���� P!:0�c=�&S*�3(0.6�!5&[  V %�53.+ p(e!A!`�%^�"f^�E�0} 28 Q(8|d:9�}} q*12�892>B/5��E� �0E��A/19�d*�' �68\'�7"� 1.0v�"�p)��3�"�2i�� & F:"gs:�94.]�25r�� �.a� & "�4� A*�.~�"�%14V�����MfH,%�)$>$99.99 =)�10��� �' .003uY*A�-�+FY88 [Dl [JY12:YZ>*3V)& $<$�19a&�+ � .002�SuF�9; � �}�#�CLH�!��-��1� ��4 q�0026 [In!M&m00� D*7.$01" 383�(8&�0o [Da8�� �"�5,6`�)�!m�E"j :a'%���)� e2�' t"�:�wH.�A<�� 0��4.30q<.��Y=�J!yL$��$GT65�2M2v�U*4%�1�ER848Y !y3>�f2]&�z =*3:+%-* �>+:�3.8t8 �036:$0A�� �2�5�8}/Y��>�.�?!�f42.�3��!�'oI; �*2: ��{ 00066��>!���l.�Jf�9552�06-�3006�"*2}�*Si<�R�[A� 15 V5�  ,�E����%�2+9b�82� h156�"�[*4}�)v�.�0 [Pi� �6��21�v[\F� K'�$&@e�uOy&*w$BDG>�'*+W�e,Gamow-Teller*B(qj^s Vs�h��6�ed;�G"�Orc� "�O|�cZi�2 �&!jX�1!.�\Rbe�v�"�R�Ive�Jo��f&&la�w,$\gamma$-ray#""R%J&*&�L!�&��I.@& s*@&^J&~b�LR:&(Jp�z�"Z�JJ�nNnMXb!�>�" �7&}�p2�� 1dF��"~.��F3 SF K2#$0 o �&�yyou�� F� ���2�����N�/&�-_{660}/iI _{107 0.0DJ ���4[� �"` K e8� 5 �&0*��&[Ad83=%*X;2� F@�622�829Y~~~�*� 1�9[� ��* 05 � �=B�122�2"C��`6126�3�N�55F�!Z12g03F&� #.JF`Q�5�202� )�:!5&� �H"��;�0� 002H6�1* (6��5A;B��28.� �)z?�0*l:! _ |�YBdH14"�x%� )wLW0}�Y709S677Y�; 2LA" a&�0f9:�2Z�e!�� 2341^�3. 2a#5�a�.N�6�29.>1N Bq3�Uq1�6p:b)*d?��e)�0.02�b-�:�%ƑI46.:k��d60@1��K~#5B��0.3.�36 a2�(��37 1R�58��F�*�90j%V�.K1%�*��2%BX=1&312.�B'*�0f8V�5.d1"gJa>'5"h?A��1.8!�%��J��I�1.2*�J�I��2I�-^ 2223]�1/�$��.��"&=$zxF'�8eN�jk_�smO%6!],�C�!.r.90La�J� �N 2z n1de�L*l (_{E�s23$E�f�  G tQ3keV�v-*E �F "�X for �a�ori3��Y:�"V.&�XPo *� C-orz�2 ib' ��lb N ��� � �bv`1m"��:�.b* . u�>� l}{R9a(�7 �us)F0 &NB}VU � "+g� i[320(textbullet~�N�(� Ne), Ba8 0}$Cr9�o') (a�U�� _r(4a-�Q=(pG]�h��2sZA3$Q"g4\�H�R� �l?"K), &Q�O)e� &—.�*�8$es [Au03].��3�B'Y�Cl), �#�Co), �>GV �.N�5ryMav�xe��qA\\ &Bo�MR=.�s$\r5$i�([Ry� u��9�to=�V%�Pv�-F�Bgu Xd} to a[,+Z>�aJ a� \\ & & new value for the $^7$Li(p,n) threshold [Wh85], which was used as calibration. \\[1mm] \textbullet~Ja78$\,$($^{38}$K$^m$) & & \textbullet~This (p,n) twpwas measured relative to thos �,$^{10}$C and 04}$O; we have�adjusted it based on average $Q$-%$s obtained-fPdecays in this work. N�Bu79$��@Before conversion�a�, h(pF �$to reflect%��modernB�{35}$Cl>S[Au03�� Bu61�%s), Ba626Ed\] ThesAd0{12}$C($^3$He6�-�ments)� been�A� upda!�Q�cY� reacA�s9�Pcurrent mass excesses �V�Ha74d�34!=,A^50}$Mn o^��t)�9� s weA �ed by%� $^{27}$AlN?�to�i7stateE� :Si;Iy=9 reviA� accordingAM(%X:eQexi-i energi!; En98Z; Ki891:42}$ScN$is�@41}$Ca(p,$\gamma$N.natE $^{4�2K;ڑ slightly5��resul�.:f,c�22}$MgE!26}$Si 30}$S 4}$Ar),Z(p^2��6 :Q��� Se74�38!i)���%7��@ 6}$O:z�against�� they>�%L-4mm] \footnotea� [1]{i�Preferences all appear�ULTable~\ref{QEC} undeɋ4appropriate pae�Tnucleus.} \end{tabular ruled6t]* 8group \begin \squeeze) 6cap�K{R� from-some or�IF.�8rejected. (See.� ref}5�cor��on betw��!�,alphabetical9> code �}ё�e�7ctu21@numbers.) \label{ �0}} \vskip 1mm�:B%(!%eh{llll} \multicolumn{2}{l}.!(6� )} &6212ZReason% � ion}A�0\hline 1. & D�-�� : &~~~~ &�� A~� Pa72u y�}..No ��!�is give �!am�:2awe[s;͠�e�&Fclear�|qui�but nonepossibleeMC :�Noy͉di�.�C�P����Cchang�rut2�pro��too�complex�n�wb�R�� F�pP.H. Barker (co-author) later side!t��inadequ�atten�had�� paid�htarget surface purity [Ba84��:ZBa77bQҷ�d h �A)^ �,could not be-^�incorpor�͐.� standardsb� Wh81� Ba98� F�The���S[;]�t)�dH]E� then even�h,ly withdrawn�by ^�in [To03)�2�7 2a� Half-livea�!�\R  Ja60��cAlQ , He�� , e�.8QuoM uncer� t�ari o small,%L�� likely biH ,�X of� E. � 3�Fr!�$�Si$!�tis�diffic�~ es mF recen��7\stood (see [Fr69a]). In�?t9ar,-� Fr65U�� }46}$V � ), Si�@�ID$``maximum-%0ihood" analys( asE���b�Ha72a1�)��+ Cw ��K!� � �.�$All four q)�hUQ%�systema%Jly higheian.K%� &6 ui���� b��Bpile-up������ly�ounA� a�0iaNLCh82 %ZFO``M���|a� 3a�8Branching-ratiov�.AS)e���(Numerous im��A�present;m���obvious�� rong!� �(  �)  key,�ngn� se"�FT� s& - t1/2}��he b� &� f�� � � & "�  &��\\ � &�  &�:\\J  Ad83�\�{}��  Dr75�v Mc67� �  Aj8u0 Ba000�`He82�8 �i2�i6�02�0�9GAj9 GBa0uEn9�He8�Mo7ESh5=]1l69�0Ba.��.He02�0 �u.E. Si66E�A�Al7�1Ba0���HHo6=wNa.u�|E�Al7 �Be6=H��U E�} & Ho72�7 �i.vESq.�5�Al7)Be72�7�9a.�9a}�u23u8 �� \�.�q7.�}|Al7I�Be8�HF2�Hy0=�Oi.Ti9\==Al-Bi._HFu9]�Ia..�9_ �.bAl-bBl. HGa.In._P2�Vo..���n2Mn7mMl04YAG2}^Is8}�Pr.�Wa.��s2�s�y5�e5Go.z^� 9wPr. Wa9=��u.�0B27Gi2�i�Ja.v.R2W24���z7}|1Br9Ha.wKa.�R2�Wh.1�}eAz�eu6�SHH2vK2�Ro. 9���1u7 _� ��} & Ke.�ER2a�\� �}�Ba6)�Bu.TG�2�4 �i8�.� uWi.~��}BamC2$G�yb%i. .Ro.Wi.��77��� �G~c.�4c�o.5. Ry73\.Wi.�����Cl7=�^�d2�d^Ko8=].Ry./Z2����Da7]GHa7]wKo9=]�Sa..Zi.��8=�Ba8)�D2GGHa.y~9] �.�Sa9 �)e62a8iDa.'cHa9��Kr.{S2� z=iBa8)iDe.p5Ha.�Li. Sc.� z.�Ba9)WD2� 5H2wM2�Se.� z �Th3�w�ses 25�.e �w� <,superallowed� originD� an i�ricx8e. For both, t�$Q_{EC}$�� spon�~Fnd V as� w. O� ,�sets of .�% simpS@d to Qano��{��n�y� u��pk8 &�%�B2�w= �->'�!(��&( sepa�(rows, each | its idfk4 erty�in � 3�.weed"" f>/7)� row below%�6� 8�2qtransi�iA%eF�onl5�dir�!2G6z6at�,� also!���deriv�"�A`pFe !]. NoteI�in�car2:�1�2��a�� bold-�type. a\te#116Au#leaeGradio�!ve daugh4i%�reevery few1@2�of� 6�~�I gqalkat: mus�deduc.` ~dl!Q �mlE�F�ogee�E�!�b5uog 0$^+$�cE 9(. Each-se m'Kiy@�u1ofB�individn ��atu�!1eirB� �,a scale factKE-2��#ra�. �&�%2�li�%Q���R.� ]�i.�%ms��p la If aJW �e2b>!exists% n�&is e�includ)x!�finalt$. Especia�)�se.A�11i�,Pm!G imag�&e< it weh'CsuEi%!)u%ausa�,e 2003 Mass W s�to�@�6D�� interes-�i�T, however, significant�"in ��!ach. We� 54"��in�2p��Uq�_describ)Xse&��eval};��ic!W,�ta subse1� avail� dataA%���put!!�F%)/�;Fura��,"{$ exam%��" #�detail�ei:�ep��^��, "�t��n�"=!�"% caus�a=Ja�dur�#re outl��-�C�P *Ie}� ��" �"�il� docu�#�n.Y �}!�ith a t ��iv��)�set, w#9affor�paA' kinda���&: iFo! w�3 is"~ !Ao�Zar%� es. � TfM��!�=�in� �A�maE/&�$_ ��!sons,fme�*!7s do $leW hemselvesAbe�)�r$Consequ , a $!mostly��-19706a�%)�("eE;!��%��q yzed� Vmetho�Ax$importance�us�S+techniq�,�i+2�Precogni}until%� time���E�ɭouteRs��A�primaryES��reAno way!.ew ��can be!�l� retr� ly. All 5-rfe6�a]�� F�l�5 b6HFVBRRA[!tH �(e $T_z = 0$yi�!A stra�G,forward sinci�at�  %56� �!i�sA�$ $>$99.5\%�total � strengt��Thus, ef%im)�:B � weak4%-.� {e�.%�subtra|'� 4100\% to yield�2� �A�r& I�gJ! �io � e8 -Z5C�� ype,j!ly�62}$Ga�#heavi�it has �howZ.eor�'ly ��% experi��� b,�}ea�&very-%+$Gamow-Tell� "� s occur, ��%�,E�carry6�p'.�W ,such unobserT .aA��%��,ist�" ��b��&of1 ��t!y>�,un��A�uQGi�:�#�"6/G-ly��:�I��sI�J� i�u%��� of s% al�ong �es --I��noh e�*9�+ 4}$O*an�$� E�uIdq�it G # as a ky of l�/# 10\%v -ofs 8}$F"�Z�,�-�# Ti r�( �  treatA��/ ��a�auIn1 ��1� ��absolut�+m� a!�,gle $\beta$-Y� �e��ed.�0RNFEs� tEbe9��x!��+v� te* M delayed $/-ral2c�-relev< .-t Yy�!Os���6i BDG}i)�irh �� $<$0.02\%a�bes�-Y  T�6is end1 wri�,� cod6�eailn�eA)Pin ApA)ix ;&s:srf Our Y$f �s��t�΁���e r� �R*� t:tab5}.�S1[t]V'{!r er} "e1D��ii2vF�Z$1a͊"�& ���0r } t($\\[-3mm] P $Pl( & Partial*� & & &Vc&;us�.,1 1}{c}{$f$�(\%t)B1"t(ms)& RBt( R\daS_R^{\��e}$mu C - '{NS ! & R��k q!S* �193 572�#2$| -1$:�/ \\ �'-P & $2.3009 \pm 0.0012!q0.2971321000 1900$3039.544.7$~~& $1.652F4( 0.54 ;0.0393073. 4.9$~��R & $42.77J24$~ &@8871151g16$�2$3043.3 S�52 f�8{ 0.57563071. �2.6$~1 8}$N�)$134.48]0.15$�20.081� 2173 S590� $292 �80-!484 B-`$0.91 90.047�293 i :)�}2l418.4H18]>69729)�1!�!4$3052. 17.2��46� x 0.50 <�44� 3080-7.!� �d7p1021u3E~a�0.064297 �4! �47z42��9�23y0.6Mo.�M : �Z4t$1967.I7.!�6�152)21Q2299 �4�=I� 1.125U�0)? : �e8l3414.)�1.A-�%�896M�3305I�1939 �a75-8�41�7 � : �8z8Y53MO2Y%�0.075�P !9& !�39)�A��6�5%� a[ & $704iv3%��ae�4mj16m33-�11�Fw41)+ 0.05�Z 1.011s11 :: \\[5�*f�0 V�A���h78.U~1A�h2 63505�9E%aQ36.)*1}Q5ILA� � 0.26I�5�2mQE-NA;Clr1996.3I 0.4�0X527.99 ^{+0.44}_{-0.47}�50��1.1a�%�4Y531�7�E�]�١�YL�0$ 298.��33 y!�AR$925.1�27���1m�1.A%)�2I7A�ij0.�� 3072-�2� �ASM# $447B�S1.4� �9el 681.M�!��4q�)� �3 �A��46>�3075.iq2a���3!! 7200m�5� �10�*422!��gAo3 3045-�2]Q2Q05I= 0.46q03e��4-�3o �F4]10731-B1�! 10��283.71�135 4 �. �6QF5��!�)4EE Q2���?� 5749���1"1%"193.495I�063I� 086}�!,7.41.2 1.5}~~\,$-�2u�71E�0.6uP045612! �66 625)�40A�)33%3116.50m�070�0.179�!�� 4ᄭ\445�8))1.4���v36:I�66}$A� $316mz8g3��� &m�5U�9�=1.� q  g70}$Bɾ8�|36� ��2�+��dQ�1.4)�0.2��  d 4}$R2&$4728)`��9565.22Y078%�3083.)�7ew �q#��!B1.-��<:eq� �9 >C r}{A�D(1<12), $\overline{� }( A�2m0QIT JZ($\chi^2/\nuB2#� 0.42}!2��%"� �?le*6z?�p>: , $t$,�>�B��#� "j?_{$5�:� , $R*�B�p mula�( t = \frac{ K@}{R} \left ( 1 + �  \� "K? �t�e w�&'�he calcu�%e�E,ron-capture t�he �ua\ u1discus�C@by Bambynek \etal�)}S!i*�D�eq T� T�1}{!�pi � [ \sum_x 1_x^2 1W� - |W_x|5 ^2 B0)] / f�pec)!�sum ext�A�S atom&ubshellst�n50F -7Kf4"K_x%)�@Coulomb amplitude!N `RB boun�&1�c$al wave"�; $ �a:��rSF�7K est- unitsF�E $x$-� bin�"a$gyi�BKand $BOtak�cv�effec3(�ex�?<%�lap. h!�I!$a %4�o&�! E��our: -�*&�u!��$1�I@�)W��#� $ , Ps �>2 )"�F!+ref.~7Fi96}.Et�S��(a.�s)E�hreE3�a.l/a�K)*� tes)p xq�ionJ#e�tAc�Is�?� be a��? to a�&�js�100�G�#�E $contribute�ptibly�ap�2�.B�ves�#� Eq.~(K�ialt}),%�6[% -�&y )P�u ��TohK�-I&��|Fti�})j'now dea�1"AZs�? ��S �s� "�R&&1��bA QED �!"GJly ���A )r $Z \�E^2I�estim�J�$r�F $Z^2&3$��,Si87,JR87}; ��) ,�&&Y*sixa�F�,E�ar��z \%�{&�!VbeLiaqD��uc��-ke%!6s57'�D{C�s3"��=I�& past�*t vari�=�!sE� inZd��nd %�a,et +�@,&t�$lA�TV� l1� opicl� KewKN��Ay TowneI� Hard_$TH02}, who�ed/O�e�"�eEye���%{s�D � spaInda'roxA"I%G�� bothX)�*��G*seF���F�e^FG.6|"�4y�reF�Q-. \sE'% {CVC�&�s:cv} �uEt read��Ae�6asser!&� �m sh&b��na�t%2��{ar 2:&K9u$�,�A�F �Gsatisf���J�-I 12 P#-?"9�(E�``*"���ly)* \be :�  = �� 8 si FtavgUo f]!rr�0!�chi-squ!yper deg��freedom�* &$.42rIn Fig.?) f:Ft��}��plo)�sam� ,%�ofa@L+wszC��uracy�Rbe�*th 0.5i I�Aev�/  i �� figuV*'$�'%� form�nsm{set, t�2$verifying /�"o A}hyp��%�'he level% 3 \��10^{-4}$�!ich�*fw$ional2��Din2�1�)��(�!3�$%ov��%UE y  l�Ysu� in 1990�SHT�3!&i4 ncipj"d�`s;�!2mb(a� L)�*�,epsfig{file=�[L_fig1.eps,width=16cm*�2�E;�U�"!g���Z�� sha�horizon b�s[#� .I devi)��,��- BVI�, �protect yo).��}/1+"V=2f=Sum�(histograe�!+Ru�t ����each 2�!*g%|& i�,o iY&Z � qinal $5*�!a$nine ��>ci�F5a�.B�9B?�{3.>02{�>�>�>tw�+x$^9 �'��� a�� a�Te��60&> $10^4$,�*useful2�.O4&6 made>�12F���i�� S! budget*�#4s:su} In Figs�^IE�emf12�n�E_U��� I�U�N�22�>� FoE� 2�A��&to�&4�!&�-. �"7.S2v�g�&�)han, o�N mparm���T��on~2�� -str>� &� % >�,9;o  al�� tant �{ 4>< acroK-,�i%lk#e� *H rad�wv� rr �*� �.�"2���growsA�$Z^�T�1*�.É�ion�� b�=N� (}7� &� �� �6An logarithm�m� I�� magnt� �#b]�n�1.pin J�~6A�,�_ $^{5�Xe%�� becom0�a�c�+ dicae8%[0a closer look�)" !n*�yuon V4� be[thwhi�RuW ��iX�2�:�e! $> 99 \%I v�7�assocVd���� b+!�5!E�ch%� a $3� ��D2}�B�E:��� Q�p�+predi-��+F�- [�gha�ve k1yet[h-��ANve��d )Qd� -misn1�.:=8nI�a }-S4l.�M��.,� assigAw2%�]e6� �a/S/ . M ���!5EWa � iss2!�h1/F�k)�($A \geq 62$� �1tU�e.�.lbh*%,�N]@.��'� ly know�)ca��$�Z���ys dep)�i��2�12!Mhebdomin�+y� ies � �2*F igin)B!�l�,M�q $^{��-�-%@a�:2� is quite l*Rt-�*<1��y o��>u!�an%>�2�&7W, ��� :E�VyeJ5b*�.4+Z�^u�Vr� adva�Z� 2�"�4���Sto� ng��is sitS dra&RR��in � next�years. * A�aA@&�R=Qi.�,(s:se} So f�S�\tw�~9--� behavior�. j3�8*��cy��a�6CVC�lb �*p�d ��igt9� ion�A��E$po�>to��l n .� {YcoWda��BLgky[Ai, A� firs�veQ<coupl ��(ee*�Ft}))Ett�/!�8$V_{ud}$ matrixIY/e, doWso*�:w>add� %2"p8 sour�6.B�Eoug)�-#-���n!W�-]*� �:AfuXB sess�!��y��*��s *)�,��4.+�2�,c_ &{ ��< does��.�X� prov�7A�a�-mon.� � $YarD� ����*� cI@�/m(E"2�U 3 W0!� �3ri�\UEQ� .K*� ��n 2� r at�Tisospin-symmetry-breakAF@">_{� reason�:&�"[ fue�]e�!�F�o: *� � 4}$O, mg 'z^-7+ 8}�** �)=�A "/k }TH H: !� Em*��n!C �)ald:tgZUG*9& s � B 35�^� OB��w=�4fea � BoIR� 3074�) �� >�92�Alt&3 &� �!�� is n{caF xworse,�aarg$� �d� &0E鐉��Bj]� . Ra�6 ��*6�6�!H& � ��h9gA9 163� X�C. EG&d6"Zce�|f�!�5�E OB'sf�>��a.�E*��$� o9C!Rd���8 dop)e �I��6�u�� mmen>�(w� a.& y-'l!��k sp�58them: {\it viz}�aB�& = &�3Y�_{\rm }*0.9 $yst}~s \no�\\ BB1.2~s,2��ea x(!H!; , coe?�&$quadrature�� {Impact� �q-HhK on physic*�:iwip} 2�� VFpA�9 "ss:vVud�i�Emu;d�j&�=��M�eC�"now���ir���"��: })!�"�?6b, $\GV*rom2I�t}?c� l�/ ?:�*f littl��H{Mit�b��)U !b .bi�a!�purw,leptonic muo� GF$��:� &�@W ng up-d} 0 el��e�Cabibbo-Kobayashi-Maskawa (CKM) + k-mixM D&� M{dP;let�"�G�:�GVc*GF I  \gV (q�$(*a�)$�� $\gV"_)��f�)�*.�VuAu}), >Ls %�6|C_!��+ �! hB# �$Jacks{ Treima�d Wyld �� ,JTW57} Hamil!�a�c.�JTWHam��bV =� =1$.}:F���A�Z@�eeis�� )q^2!`{K}{2 \GF^2 (1 + \DRV ) \(&E.}�[Vudeq�[�Y$255S us-.� rJ���e &4'ac�edmLI�V'o!�.�PE�ex]+�)n MS86,Si94�| ���'�pi�-H[ 4 \ln (\mZ / m_p)!8m_p / \mA) + 2C��BorslE� ]+cdots 5"DRV6"AMellipWr� �d"���a]0.1\%. HI�mZ5a$Z$-bo� mas�? m_p$cALon \mA$%"'nam|D�� dipoXOor") axial-M�9� .��uni�tal �-$)c$ 2N"y,GA�"�'erm͏��JI�-�2.12 -�3 +�1a2%2tstM��GL�erm F�,�A�-n�*(ly unambiguin �I���2Lby Sia-_ E~qq �(2.&\<8aa%"�>DRV �!.n� �����#� �sR.0 �">��%A �Q� �� s80Mlie��r�0$(m_{a_1} /2)0qa 2 �����(al $a_1$ meQ� . U�&,?$cle Data G�q (PDG)-NPDG04} �e �'���B� �$�sP/(\hbar c )^3 = (1.16*z50001)2�%,5}$ GeV$^{-2�%� d&`�)�} �t|�u|�v0.948P5 0008U Vuds�Z&_U!H�22�-e0083, i� X�GQ f$AId7jYY�nu��M�(zI$���By���sw &x,a� 0074�,i�Y �uGD�V; 031=0.�g�n&t>�@ (pr&�&�m e�N� zOB ) TH .^ s di�3in Sect��>�?012%6}%Z�O�W 661 co�eb�* "".�)�jZ� �3� I���2� =A�73�6z4�eVudA��aM�O� s� e �2�!2�(�(digrRrom7"p�Zc"� i< �� TH03Z1�! shif(Lll& � ^ ��"�' "�'��8.�(�.� �%�0[ur re-� KF;.�*�1fu�G _o"2�iE)^!ra�Mbe~Se�,�[�� & *� PDG ^I � >,�!��:�zAIgY �H 2� Unit�#�E�CKM� .�uCKM}iF!Y �eY) 6*�qa!�of ba/,A�brk� .H #enATYo &�;/. AsC4)xC��2%t��+H �e�|CTma�# thonormal�Vya�R�3B ]�.+ a+,ex�St p!�//r1�� a �-�AcH3 �8quv&� top-���N!�le,�4 titu%_�Nost de��&7�.)A[2���i�$��$>||��)o PDG'!|��L6I�A) Ys}��22�B��26�$ #b #00367000�@b(=PE �v�)ns:2�^2 + �s� b �96� 0014]sumfail�� b��EF�A� Two-third� � oed�A!���!=}ߡ�)�$, \viz !11� one d�Y�9d� 9 %Y� �l X� �u�al�yA*H2��d,�d {\emq}���#�5R���W�#te9J���^A ���DRV$. A�4�5m�.�$K:\pi^0 eHnu_e ~ ( K_{e3}^+)$>U#i��Brook�n E865}��Sh03} �s !s}EH22G!�30�*�iasd)'�\�;v��i4:  ab�Ri&�u6olO7.� Ss �$�mS 0$�%Q���� 32. E5�� wA_ prog�!��help claS2�"$\ f%amo!�,%&�%c�%�� s}$k"�v�= �.o! ��&� q��modif�Xto�z)p|K6�succeed�" ��isw"y� iedA�nG3ap*�u,['���Y�6ӂa����?:�ݺ�!6Ac�#\0.2cI0.�Je� �s  about%zt9��OPGA_�)li�� :A��Kleq�tdoqr4aI/A�%�W( negligible�PauA%9Msum ��� �� �ʑ��25 �+\be.���c9 t �8"D05.22��A��o"�::�2� A�%�B>e"�KA�w#is"~5 =?2� Fundaac4al Scalar Inte9.� si}td�$st 40�'e\� 2u.D&O`byq+q�bix A�S�ax*d�a9Q a3 ximize��vioֈon6E�or7�a loqub.h$he `$V-A$'!\or=&Despi�ee EX����l#("�&C*ea2� E��5s2deC@!},f]<� ��Prg(� establish!�A�A�.1,mjX (f=���Iy dD%Vensor.>��Bpopular�oda���]st�"%��(in sear�z�F^ ,-�! Ucc>a���wm�&;a�o�^t� j*�,= wish��5# lim[0);ir9�YE A}f�"�B�.�/_� ten byn�*���A��AB.�4 F�S*r"��>b�1in�e-�i# =���,at2���4 \bea H_{S+V5R =�G(*�psi}_p _n)el (C_S.�phi}_e _{?nu}_e}7+ C_S" @NA��_�3hNJ)>� & +R� I {\mus>�Vf}4R� + C_V��F �f� "�� \eea Ifa assum����e2�� ��� :; r��sFi�'l�#>�+�Wsa{t!l��'J'�^A�aY01. pa�c-nK,n�^�;E�m�A��N).� >���m��� $C_i9j= C_i$. �6�e��YB �?3�W>�D ��H]�M�E�E: ��HF.I��Iv5 )b K6� & +f� CA� ]EY m���28 pI j�Z 2�Sja A8'$v{> redu�͖U�rP.�-����=��vE��+>�҉�IP w���"y�>w�2�oJ0kan�EV6� . H,i i4=conjug��m2� $ (v  ) $ �G�0g%�vv2�49�) $a�uDA��.pmA�$ ensua��� ulae��up|@� �a��!�e�49)�l�\ 0)pR0.)�e*!:s ��&{���&= JTA:) sL.!�� shap("�s#~ .c +�* a��#)��blec�Z n4*inoB�� d�uF�)T%-� $C(Z,W)a �$S $m_{k_e k_{� K� ambda4} \Bigm{\{} \b ((} M_K(k_e, 4Z"Z m}> 8 )}^2B) Nj + * (} m>D+]�Mjb Nc-�M2�N בm�}} W}|��C:D2�) �� 1�}} , �CWnew��wG$>� $>Y$e2AS���p.� i�" MmKkk�� F��JadPMq+� F(rk��f , def~2N Ffr3"%^�*�'B $eK"B��s�.as�+�q�(���!` repla"rby.�F}! %\uAf�ere3i� H(r��4\{ - G_{--}~ jA�e�-1}(p ra�"+2". \}FD+ D2m G_{+nk�+�k�% �h2{[��f�d2m��=tRR&�Ffrm��u$ $H<.DhMdE� �%� �)�<Baj�AH,, $f_{\kappaEHA^ $g2,A�:^'a�HDhd});3_anga�ut"s $G_{}�<F�GKLs}). 9&'JO�?of ";?DK29s:�(QMsSE�;a+)b&�s �1o�t"% +2Cs�$K � Keep��!X�std ��!R!a�/= 1-[� =1a��a�G�)B'��azee5in $r�T 6+ Q�9�5C�oAf_1(rqC1*!l�&6�g_{�$�(f:(pBK1Arm�J" j_0(�� �rj_1F-U&�'fgjmLWǏ)�$ �aM�%� $6�$,*J�;;�s �: nity drop � �Q |��i) �})� $K=L=s*7 are a;++C��- A9O$0y &�TC?)�M_0(1,11y� M_F2 J�m6-{�.FQ}!W.���M}65\mp� jf<m:<q"�" Mmes�'a&�F� %u~6� -xf� `le .�  |M_F|�,6:$�%C+- 1) 1}{W} !a�+B�\simeq f ^l1 + b_FT/W5�S!�,label{CZWappM�� ���� at $�\llk�BE��T6m%Si2eE.Fierz��"c :,� ==��1 C_S/M-m �)�well-�&�+�`J�� R-6�H� $\muX(iJ=��beta-hA �W �;�K�� bdcf� dCfe6m�$h1'( - (�* Z)^2)^WZ*1ub�F{D2!�)a�=1!%*t s:dl?1s � ���a!�M,U now ��6t7"c3a $1/W$5�V>�5,�PA4�xa6�Y's���$X.�1U+bPns� �ll .+�m2]4�9$T�7alor5#w$ optimum s%iv�~we =�z&�m)�&�~>R[%)�Os�= ��=/ *�of% extreme n53A�s�DM�a��x� ; �%i�1rim�, . Ins7���exnumer.%lypu!tyA . Sie�ajl6"J/�mependa+Yž C_S$s-�treat�S$� a[� @paG.�seek a Kv mini�$?^>>�lleastaRs f�z ���EE =��*�0$ ���^aK =a� m00��30 *�Cf"�K a!���"4�X�fit�s%�=[JR:� ��%/c}(A�preA|o"��.C4d=de\=�.WL �[$�b �>�GF{A� -"Y�= �=�ER��)��'>}c)`). M��2����.��Ss!a�a �� 'io#$arlier�)F� E�� eSl*S"�!��)es-�V#"%+J�Q�,��$$1� $-2$���%Gantity& 5U��p[@!�*1in �\�1CR�� HT756L"0G�g�{2g? , we�C lici�$�aa�u���� yi�/{!1e� R�Y & � 4?F���\Bv�M���m*�"��(�n�~�/ �aHaa�a�'F�->,\la�uW \a!le )$� ݕ�( KMځbM EG�negR�.�(!�I�1�M�e&{G� R�]W߅r� .�1:��;wCa�de�<-WGvRgn"6!>�!�0� �/26�� Ha�o byY1�& �*�-ng��2` �r �'��W(ap s.l� In��v$#f%#�ij'"��pare��� �����&!JosQL�F1/2 � a^�g Ca.� a�&"�#��dtez5BB���9A�H_!&b (p:�^��M� gma �q + i \fS�)�~2_K2Y� 59R�"�HV!�I��6$�mu}zFa�!UǞ-m9(um��fer, ,� $p_p - p_n)�"I E�` JF3 m;()�)h*fM$ (%�� etic�2$\fS$ (iM:f)�� b�e/VC *=[--��[ p 0w�ba!�I ro�a����:B --Ec��nE�uI� �L�#lF��eb6�Agd�8ggA�|�n ��9[Z%^A!=� A` r a�g7��We58}�re�,no second-cl��c/�N�ha�ic)-2 qQ_a<}�4!�to.Hish. �wyU+�Bi���܇� 82�  +�A$�r"J "8&EY1�6UgN6�J ���p�Kd�)E :8�si�aneϟJ�c;H8�V-�E�=]F�R*��$f+ �K 2���8{�-ing!�en,I�!�:-0с ��RE�>�,��(S>J�V� ����j�&� HVS1��#�"�#D erm��@organispo�ch iV�D2,$A��f* (�l.���ax*� �$�A�2�}�2�^�2-�0\p_e + �"v� _e} �X, �qRo�in�'�6�i@ 6*����'œ:*%B�A3�a-A;;irac J:"�J � ��#e = i m�&e$�B.�#P>�2CF&' = UJ ZY'$, �$m_e$a� FA�� ��nA" !+5r�b�����YK"�/ /��zer�We!� $H_aIs� o �9g%%FfSRT�G"M'HVSA]�#Z&$quival�XMi�d�,JiN-y���P(�Mf|ة�qG�*Q xaj� md"g�.J��2�G �6n�� was "� $by Holstei� Ho84}"� &C^���2�dlf>?Yd "�+��:6�+�7�85��j )!FbI�!hU4~<, !z As aR ,� !X��{}A �L.�� 1�/� 3 � f4 fsgv���� \fS/�Efo#��e%�u�ia�aZ7�  af�^F�yk&� �v�_{\�!N6�� �@6[� )d� � �M5confirm�i�dedi� ~ "�e13�g� aA���6A�����!��  b2te�Xs��a3 !���R� \�semi-�R� L# 4kVIW��0 UL� gb ax"+1!AcaUu-�4 on{Rߋ-h�C� }!$:rhc} Let�no longe� �5!?N2!�to�9� e F� ;/a2%2JJFG' &-M� � �Qc�^� �+aH_{V}7. ��-��-�-�%�Vi�!4�H"6 \neq��canA2as-_!P5I"� s�&A�� :�uawe di_y�1)v �,E�Iե��>% r�< D�� V$ o�(*�.a���F�(�>�B i�t�H0A gin{wixt9H"�(� �) bigg)1}?u) )^2>)m_> + NB + nF \)�'.��w*)�z ��(~^�6�>(W1 �6(n>�)�1/}��W�cE0�$B�(,J�( , $N:h$,�$>��"��tr&�[E�o( 2�&�(y7"�m B��,�(<(rC"$G �b$g /�oB"� F&u#6�'_"-2�'�#� nu�'-&�/�l'&�/6�'.�JVJ�&��'!8m�6�'����6�'��f�:�,A. �!��+�1�)B�n�%�-+��(6�%N�EU!�:L6�t2{��a#-6��2]�.�*}(y+�#J�* +E>!r�*�g�#Ffra3n١���"�"�*�*cb*� �*,�*�*2}&�%'r>�\ "\ c%O&61 $K�'nd&���)�'r�ptETa 6:J.�*u ��'~�'6�N6�':rMb9(n68{69(I��'Q�ib?3;�'�'=&�'s&i ;'��'�! \, 2aY�Q.#:' ��s&�Q$�Cnt"�#�#E& ��@#o�Q *N$ 2N$�$.��2/ ��"^2  Ks>no��� 3�@Ay%p��F Z#~%���%�<it�c shif.2�:e " �8u��٢;�?ud}�m�6�"��G�aoqv-�"E�O ��] b�we� mak�u�E fini~%�h-*�aa=��T&�,Zmg:qBga#iY�atU/8"�W�Ae�m�O�"!1�&dS\�}ZY��(� �+#Jj"�in%!��B �-�!U &. T�eOn �0"�W�.3>U�by�A czeg� He86z�h&ya�1rn=Z *Us:dvud��II�$SU(2)_L�QU(1)$ StԾ Model� F(2\7.��&J; sch� ly a SM� 8\GF}{\sqrt{2}} 1O (V-A)&�SMt��hhf"[ �@"�Ua���YQ< s: $�\*bJP^Ja� $-A:�NB�.'R�$b�q�V��N�}? q�7_n� J�N2 ?�?�AX2� �S/1�0 = g^2/8 \MW^�(%� $g$��a��Mc>��$ h@whe�%chiral:M9"is � l�#�E")C or�6#+A$U�-T�Epin��Z;6E�ei"�Pl�R  �+ textstyle-�i} U_{e q[!$L_i \qquad HN*ZHV.HR_i&xNugEh!] re $wi}�l�� r�rst2;PBz�^ V-C"Z�H� babi%�m�*�P�g �of�~� ��$gR#Y'9+owI�ut�=�=�T�1:��Jin�umAi ��Qo�%iԝ&q l enoon>��1%i���V�J K� �ul�py���at>�mi!3-2- "��!&e*�$�!DiUhy:!�}5p]LQ { �4AI�)���t�FJK�by�'lBḎI��E s�Z�FEg $�SR�y� =u_ej 8RL + + $ɯv+͢\be �OFS"�a\|e^ i} |^2 mZv�{:�:9aO 9�� uev�?}�ti��)Osd~� �a !A�e‹�G���1|UMh eMh&tkIaa�.. & [ifa"nT!�E� �b��5�&Y �k�ockt $)h%5�9*i-U3��7>�MP�.��g"�a,* �),Q�re͡!���(�h LL}+IU ��x R} ) VV:3�(-4L}RV;Av;v-�>vAVv+vN;A; altH��az� *!�x0kj�J(JTW)2� .-04 !�� *I�*a� JTWFJXG(C_V V>�A!q$ + (-C_A A�AuU V ) �6�ONFOLC2BAs A AAq�H���Yio�H�0�(�&|0HeV! employA�met�n�&mF#.�D sign�!B�$5$��F>�]/2H�\0P� ours� 2��HA$V��K!>&%HI�iR� 2} "m.VBU� RBBA 9eJLN|b:>|BC :U}iCVaLL-��>F� �A,&���u�� : �'\&%s�=4�zQ�+Gb�_{ڑ�� as�n z329�\Spor�k��6S &gpto *�"�:0��+  5>�6�)�|>1+.\j?5B|~;&�a}_En|^2 + |6 c:Rnb�&�; �.|{ 2 Re:SI��=XI/twoalrM0�.a�1,��.�~Dw2.B|I�;+ R RL :��G������c��B�f� q��"�! mAd *N:��c�� どC�F!�EyX��.[ a)�_B2&B+connec��t&� ��WtY^L|\ \viza� B.S}{�mu}���Y> 3fz!�9e��a�.�L�z} {b�6I!tj���*�Hr!`(ee�S2��L"�-�� �v-;�$�@�v�Sp�]�ij .{�' $ij = LRk#RL$�o $RR$V e��Гe!�žedCum�� & }��� .�.~��Kb�s���.��>�.n6�>� �M]��. .�H -�Bj�>-�) %� &7 ��Y�:�<��*5E�e4I �r��|�*�ic 6�*s,Jf;�Br �(&{wly�wf M��1�L�0�ALL}"d �ith $6(=��� ժI/Q/1 �-)S1})j]�./. =2�$0 � .�SA�.�B���)�&R� 2;= 2/ 2�$��5!^purn��W][F���GRe abov��n�q ommo�� C�A!j�?mpl�'v0�a:�M1>=� +*HH%3R}>�X5{Z��])�^� ��"�11�� ;!�u�re& >v�+t�.�t� %|eC~a�*4>�i(u_4-[g(u��3]�F�&�2E�6�A�5,. )c!M�o"V�DvM�`$ �'& �),;5!n&���vw~Gs!eZp�C"Z����Tden"tz�� >� b/&h Z!E�G��"s�4. ه2 V"�a�) \!105 MeV޽f"�*=tiJo�o� a�L� �Bz@c�/iC� Also!��!����2sdW+�$$\sum.[�\mu ig �� <�K��Irm��2 ���@ 5�E��)ma =B �%. �!�ceF���G�1��� orthI� hI�he�!m�C�/pY%�L$�}�!E:r�2ve manif�I � sy5��!!BBMS77}��� �d���{E��1I�� o�vent>~t�=r� a-�&� w�]?i�]Y���#�e u�4�Z�ft�"X�me'�&�rbw,|�L�-% >;�W_ t�W_LbI b�nea�` }�� �*�s��W_S \� a W_LWNcos \=� + W_2�n  2� W_R 7�omega &- Os>O`�v�tWLW��_�Z S���1��){����m!9, aa�E="�!�&O@$W2)��&��Bta�\�*��)��� r&��N�E EY�4rb�[p�JR}�T}/" are:7t� m_1z2 )��$%�4 �� m_1$�$m_ߡ�,8s->:�:B��τ� a��ofa ����:ѠS2~ � JQ ���em:��o��0�m; ��d ZnazLzg^2}{8!F^2&O&�2.�>� �=}�6&Fl�6�8:Ja��`ar5p-q�Ca!� a����i2��.�&�!�eE}1<�KpA"]F&��>"&("�&�0 1��Z� �� "� -�Q�->� 3%h*� M�wH~��J�J!TH0m�o�8 %"%B� � 2�c8FeAN�KL!\2-(nl.�8w i�c�*e"�mal�s���su � �Bo��vC+Re�!�.e*!�6rylG�Bay �q4k��:��e�|C|^2G~{expt}s �+-oZ=re��q�LRQ`r;4�&q 1})�*�(�(a*�k.�mH �^�icZ� R�.kLs L- b լrH &?&i4E�6�I �$!6�pMŹ�d�L!�B�CKM��;N��a�P��sU)��$��M�$m�%?+c, y�"�o)���#�#�<�z91)�y(BW|)-�51*�s1)��R��z-K17]074"aLRPDG-��:-�=c��D!"� ��Z� Sy�]�3�  -"= e�ɥ>�t6��\d ~�itt�conEIre�ed!�5��eyxof�yon� r�#1�o$j_Af'%4fac(a%BZ�I �� J) �To�l]�O�Z. trin�;AnYPc *mr �Sh��E�V_{�yrMNxraz�4&��014��]�A*:w82�865M���Mbwts���no .� �с9� :)��pm 2�J���{Cou�~�s:�A } P\R��E<s.P�*}��*A} noA� disagreE1M TH73,KXC amwȁ�l,>�W,�at�\ Y>O HT75,HT90�-�2toPe�q,*�R at!r�pa��wroblem l��o�%.��] 2dadv֙. Antt(A�GS*�:Fts5statusG,i%Z�c��t �)�"�V���L��T�BfB �a �7y�ofOi��$�/_�to 7CtSV��!f�B� ec�$�CV�� v.�.S� �� �# "�K�1�DbF2�}3sA2to go�D+���C�$!�n� step))�"tq �!��dn�-���4�Gy@� ’utem-,V!�geA��4A�!�����ed�z�els�@4-,-� \�L%u��wA� b`1 leadťa>��f��by�t�woA�&s�W���4#� remol� q����ednG6�,ӝn!��2T�*�A�y49�TT��a~��D'ɱz . y�aN� ��%�A)%�ALN hQ�����\eWmarkaYzst�Z� t��,��dTua v(vinQue -qqXu�z#.� !zm!.�r�6�{�G�=\M��%��.��+n�. gres��v s\�ly "�H� (or ea�am,ng) the disc��repancy with unitarity, both theory and experiment must be brought to bear afresh on the principal sources of uncertainty. Although we will focus here on improving the nuclear contribution to the unita�@ test, additional��s are also required for neutron, pion��kaon decays. The first two provide independent, �|so far much less precise, valueso $V_{ud}$;!^D third establishes/!0-�s}$, which may ultimately turn ou-�H solely responsibler restoring\$CKM matrix!>5�(. Whatever'outcome !"%, how#�eY ults�all7$se studies)�-.< crucial informa!�X, either in characteriz�Dnew physics beyond\d standard model or in sett4 a tiA�chose DHMS86,Si94} a reason!( r%�a�eE�{ haa� en rA�n)Ksubsequ�authors f$To92,To94}A�%�W � of p that driv�� over�L.�onY�Recme�)[An04} ſeffA�v��eleNor��basedH4chiral perturbM+���u% to ɁIb situ0 : al���8approach replac �]C.(sW!�E�m$s!�well-def%Z6>��t�a��r thesa�  ��Xnot known {\it a priori!�Howa�,obtain a mor��p, �� -pri�le�}A��� �U�.� rem�Dan open %Pe�problem-�e,ea�ofIsiderE�iman ancea� urgenc��No��ly��%t.�p �al�� ��> �ion��H�X d}$ m�d�m%|�ĥar supE�,owed $\beta$ �it��h�Q a similar ���I�Az��f� i}��w�A.  next��5}or!�!(error budgem.)5\e isospin-symmetry-break�6�delta_C��AQ�9paN� b� in�Wu���W �most ri���ion�% H02} of $v- ,{NS}$ (see TA~�3t:tab5})�l4 dominant sour� 2��y� ribu�!5q$��%��sm��syste�c differ=2�re�9$tC",techniques u��to5e�. Our�H��% , us!�8Woods-Saxon funF s, y��sIrQ�&thae$ Ormand-Br�a{ dOB95}, d0Hartree-Fock e . Here w25 !(democ�nc�,A�e� ing �ۅ�9 se* 2��eqI@lik� N Q�el� �Y5ic2�ir5�U�a�9�. �we appD o� f�s FIyEq.~(ExFtavg}))b �@ \begin{figure*}[t] \epsfig{file=review_fig4.eps,width=16cm} \capa{E* $ft5�plotted�a5��*!s' ge �� daugh���us, $Za��1bands��res�0>��, quantity $\�r@line{\F t}/((1 + m�8R^{\prime})(1 -C"a� ))$.�� $groups dis�uisF~�<( emitters wpar��i �X ��l $T_z = -1$ (darker shading)istB�� ,0$ (l +X.} \label{f:dcvar} \end5�( If reducah!'.*"z � rank!�'�2�yox8 futureA�����n��;ng oura)fid�Ui��vё� asN topjchalleD teUI.*PX !K no way�y heck� n�o0  absolut._�"��iR ] �^)�us-to-%�us� ��s�!=�ed��g method, w�$is illustr < Fig.� 1�,&"� \validA� �CVC hypo��i� a���b ed $A�u�!VH.� $0^+ \rA^ arrow 0^+ s shouldc� � �z�'�? ��\un�t ed measur_�(points���� ars)I�B}� f� ���wnA�a�JE� ��� )�re�]s�est�d �OR�a� g��F 1h , $:{$,M�EpF��i� y on specifqly �!�!�ll abilM V three.~-� termg� oduc� �Y�%���FtransiabanAd�H%si��qK�N�  al .�8of Z when $Z>10!��� R e�`���hef ivea�!�Bd^�6i . It�}s� �&�I� rk�  agreem��*�F'�-IAEses�� sign%�!e�isQ�Z �recogniz�Yq�-K of�$e1���$e� $Z\leq 26� e�0 c -e"} d sh� `w� " Zw fur! tu� tNpM1u�b ng +�biL coefficiea�% ��obaric m�$plet mass # � �  �3.%�!a1edF���� ca�����leK:�L. �  datayo$Y i2�]52QK ��N.����already� ower���)-9���Ev i�a�in!�E�]���i Mbe�s even! convng e�w�^� I��S�atholog�� fault%]e���� all�(he observed�@Q�C$A|b�Ma s}P��ail�o�q {\em��}!S�� om�=";a� Pleae�a�f2�F� i�ough,�&A�n still .c��,��it=�deman� ,i;an.� � ce`!�=,m�QseN� fo%�&� !��Ona�!�*ZoI� nine6��"� �B��Q��K with 0.15 \%$ �e6 . O i�}han�see�!�!��i�to�y,Ah�!X��e"= �� all,�,ept $^{10}$Cgcay4prem8ly ($>$ 99\%) t7k inglb���;�y�e M�subject�nPcrutiny��t A�� past fN ��d!Q!g� Nnumber�$� ����s5{pu|)O�bYt�re�wsչtQ Ei�sVs��nG , do�seem bN . NQthe2, a gl�at .Vhist9}� a�a�me �m] ���il�� f��ac!� asloa�at}�d� a facto%C� 5� ^ory� en we ��b!�$$Q_{EC}$-v*�U_ 4}$O, $26}$Al$^m$42}$Sca� $^{46}$Vd half-li/��.MbC`50}$Mn,R� branchA��oE]N / b!�=[� A sec����to!=�Yt-(lyZ"  to includME�e !F���0ar-structure- � &� �Y� r, o9ow .� � � idd !i)ڕ� ppli�+�� cur�� est-��.� ��grAaik��6k �"es�*� wh� theyE���*at�O ly verify-ir �  !Y; al�.��>R� �y'� ��"orAO22}$MgE�34}$ArE� $^{74}$Rb��M����yp%�reach su- MX� �% �"7W�Q�.J)� eс0!4A��)��I�\� surv!~ll ��w�� liev!� e po+a$nd_ ���� few years�iSt doubt%���)j se.*Z At In gu alF�aA�ei�� exot�Sus ��ic� t�in pur��<t�cA��� qKiTE�ls�hibit ZT lex �vpNr�i�A1!� w;,$A \geq 62$ -�( Gamow-Tell�"� b i;� � vi�but c"l�n pla^ $non-neglig9 roleo Ha02o $se heavier5S�E* very�<rt ��> �/l��!A��) th�>:A�be�� E� so,���D taclrvG ly now be���c�7!�we%1r y hoasaUbef lo5!� `o�Ub�zr��� �!Um��aas. �HllA�� 5U�a�@�� es�aUpreo sit�!��l �)lev)!f2ci%k need�ˁ�tra��� , a�"�"� !impact. ly ")" ���, ��n*�# )waj�a)�%TUB7 �p,!"ta�ar~ he�AaD� !arQ�,��i xisa� manifU tself� a $1/W$�nce -7shape-==1"|A�$f$ 6��E"gCZWapphS;=s*�ݦ"\� !NAZth $A7} �b@#ron "forA� l�� ũ� e! � : ` d=�-N= ose / V �A5d"�6�`�s"AIa"Z:��nA�cluA�,aƁasser atul`�6@>� ���s s%)��up��CVC�xct"z�(nrenormaliz�ec/ couptedan�&nd �,set a �$��!N&�$��!Y����%XV R�`analy�`������&stood up�� favo��� ntalj��K % qS� c edi� them%�"siA�em��be n robu�'{  gha��7&�Ion�� �-rDA�of CKM����c!m���qE�V!N&dev�2�dicw!=����V=(�$f()�inm�F�"��in!{P&p�! "i�T %DF�d�. \ac� ledg�5 |!JCH wasaA��#J(U. S. Dept.(E�$punder Grant DE-FG03-93ER40773�bU Robas0A. Welch FounI. ISTm����!xkwCycloab Institxdof Texas A \& M University�(=!h� ta�dur��s:�$wo-month v�s-(ppendix \s on{Sa�s�"Rate FM"'s:srf})As.���M�p&lW pha�pace,%� f = \int_{1}^{W_0} p W (W_0 - W)^2 F(Z, W) S  dW ,"�def�ezre +' he e�ro�>t�*)�in�)-; A1$s, $W_0{%�maximumm�MW$&H $p = (W^2 -1)^{1/2�:moAoum7eZc�&�>� (poFv� ` emisa0, neg�(e0!!), $F)G���Fermi5��� $S'�b�.r"!�p�'oe�y��(� n %6 custo()e��& ��y0 w�� ll denote�$f_{\rmE�}$:IcQn1zl dW .UdA�Ee�ex�e��� $f$  ers26��0.2\%�$A = 10$�Eto 5.7� = 74� T;�)in�&0.1&ccurac� u� �7�*nge���&�!z�� M � c�Ť�Da W r'n�� Sf 6issues:"i \item�U�:=�noP er�� simp�[, a}� f&st� al C ($j=1/2$)���$ int mj � -�D"!:dius RI�8�f�� �*%Tb� I� �s.B*nBi�-dey�!`%ion; 1%�+�Wex[ $r^2L��e[ -�L $ar volume,�A[w� � ���$-forbidden. . F�c-�. reat��-� weake�E,ion lead�rel���D� in� d-�*G wAl^�)� s5mi po�Wd '�^ ��=�/el�!�in*a milJ%,eii�,PM���f$.2�atomicgc�_�� be ignor".2accommodA� +x �)d*screeefc"O.; \ei %�iTs��descriM�ingred"a cod!��  wrH$�a^co-L�ks!�|,2""�0 lisma�Behre3$nd B\"{u}h\j BB82�NoA(m%��� �� �v��(= F_0 L_0 C�i��F0L0C�p�� $+= 2 /~%gamma_1)�1e�pD%� �&�ig'e��=e�� �0ay w move� S oric��e��%U ea��su�S.i��t �Lu�C1r�2�s! � amplitu� VMz�>D bdcf�elow)�� $!�Wab� %T� F3��x"f/a1�.�){E� Rad��W4 U s&V s:erwX 2A���q&i)Aby��%a��e DiracL)�an exter� _$magnetic f<*� U�� tric�; U��&| � po� vani�4i� ��%pca�.iba�auspher 3�,ic� solvN $ coordinaQSint|!a69exp�#&$q�� �(�KQ L \psi_{\kappa}^{\muY left ( �)$array}{c} � ign}( 4 ) � @ (r) \chRhhp�  Z \\ gn.. @&end t�& )�TpsiKmu2U�Nb�"�3ly�m& �z { 1!�usual A.angular-� 6����' �" m��� G G$l�#e8 $\sfrac{1}{2}$KA��5� F=j$I� $z$-&& $\mu, .� �H = i^l \sum_{m_l m_i��l \, .�#$ | j \mu \43le Y_{)Dm_l}(\hat{{\bf r}}1�Y&w ch9��eigen�u$'%�� �^  +4j (j+1) + l (l -�4�lKA�"<ab�2^SaT& = & - Mc (j +U$2} ) ~~~~ E�(if} ~ j = l:' \no� \\[1mm]6e l a�`.�2}"� ��E�a%>>� �� �i�E��(q� 1Eld y+}{d r}�q�+1)}{r}) - ( W +  -Va�2)e0N!Yd�/ t- t- ty� +t-.t�tYp)"eq-5Here $�Ag�!N�iic���/��4k [ & q��jp3�=. .& -� u�  1 task�!�"��@p:� ��� s, &F eq}), �)regq, $0 r $R_1$, $R_1 2�:R_22\infty$,� = �Ykat� n brpa�� ��� &�%ar )51� zero� !�"�(A�!'-%es�,s����9 ,T star�/1�X%�L9� m��to !,$.� =w biB=&2a� e CoulombYC,�� �Ad1C(bun��A,conflu�$hypergeome�&3 &mh argu� !*!{asympt�k� h� ir�!eexmsedB� desi4>outgo��� @%�hifuThe un�F�.��}46g;{5~$, %�)c� � ��7�DalphaD:*-!"7d�F maM��"�,��.derivr!\-aG%�� -��!oa�{$�b� 2of*� Ŗ�s�">s!ZޑG !g&�m4ea 'TY6f!X��Q�"��10 �rgaj,d�2 F)=of orN�ith.d!$()� Z)^2� S�w!>%�ested �"M�>� U��y� �V�� LL_5.$$\lambda_kR  _kE@��k = |�  |ichA a�F_T�Sɘ �_{� 1}^2�)Mz+}{2p^26u � O VOk:Oi _rv2g \mu_�l- \^l�.�} �k W}{�k}&� � \eea�%�{ k[ ., \}i�{9� 5�%5act479)ab;>by2�$J\"{a}neck�!BJ69}�8 Jnot�aste���;��es�7"�,�explici�s u:heU�1[�%$ (�1y� }$:^S^]"� ss:scX ��C �f"���i>�5}#a OQ�< 8k_e k_{\nu} K} q�=0\{ M_K^2(k_e, ,� mF\r�.2� & &��`" 2� f M^s} W} M_K6rq6 o \]�CW92�%ums� $k_e�] �,pMal-��"�"�2�����<i�6�u�:� a = j_eaz. <)o# 6� � j�j $$ $�V�_ 6_�0i �$K$> �1ol=G�&�% oG>tA� is��I e $|�- �|!�q K +q994$>�-'m:)�Ln�w�6�=��we:0 es� rm ,sH$he ``impul�.A  ion"?"�is*$/ 6� us!��s��5o}� �6ac� 6I>so' �necessa]1��gB�eL upD��. Z��l;(many-body a� ��+�E.+uC�.a���F6Y4 Let $O$�&a cQ)\be �O�B�x�@�ta�w� | O | "���Idag} ( } ټ defOe�ѻ%279!�� !��AJ�"^Fon in!)u��I$� ZR nihif!�m7 de�#�0a1�!d�TC�7� 6-a�!g&9�8!�com�%>f-9i15Vn0 � 5�9#SBC�} |m;6�i!5<>�.Xހ�*F��4"�>�EÑ���f ��IS��a�<�4eu}��CaF�� 4sqrt{4 \pi }}{���J}_i} �0L s} (-)^{K-Ly�� p \dbar F>T}_{K 8 ,�I�2� >���r�f��,q�MmKkk�/&� !*\jmath�� short-�4t �4for $(2 v1 "g## $J_i�A�?r��b:���]�are)�%})� H(r) �\{ G_{--�7 E -1}(p r) -#+6#.!If \:y & & + D>o+�o+�o%� �h>s��v�d>o���Y_ Ffr3Q^u \bea%� � . * �f!�e}A�+-k -�)6f!�nOgO-\zO!�nO�-\zO!enO�+\BO&  HDhd-MH &U(r nd *1 )K�"4 ��\foot�%{a�� nal �se�s6za� �set��S. �LW3yse� GJ��se�;A out�5�^�J&5:�.�)).}, �Cl� &� B�0.q"��Z� B:G_a��  - -+Snd -- re JG�& KLs}2��G_=�2 &�� D.$ �:) ivel"!��Y-��_e, Ccon'�?��6�u&� � !_%s: a�� eqn{��hk ,� m� i^{l  + L\_e } ��q"�} B�& ��s}��!��_e � 2ll}  ~�Mq �0v�0 | L  ���:�0cc} K & s & L�6&6�&d���J%� J~\} . �� GAv� Last!�!�� s $%'�Ls}�&�% ��x��:� �,>�P%�^M>t� T(V_0 + A_0) i^L Y_{L M>� \{H{K,L}�2� s=6� ]�VA7 A}) . h Y� M} >�Q>d1��TKLSM-QeD $V�AI$��!`tim�R"��" �3ax��"?Tic�0� $�V�n A�b]�-� s. F<( 'f�$ .�"U harmo�T& Ed64�tJ &� �)�m:#r�8jP�.b2s� � �A}B� b�.H�!���V_7#I)\gV"�N#�M \sigm��G!a�qio + fS�"*Z  A:["9+' [5dTfd( mPmA"q VuAl W1we�* cuss�>Z�q�Vp�+-1a� -1/2 ferm!6�N�5 $!+ = \gE-�{\fMfSTP = 0�HiHDY�,�9�we "AGZA�y%���AG%Cm)3 (izced`a|"eY*� �ng.(us]�%I)4Cq&�Ig�0�$ormQuA�a]w�"l % ���YmLo�; z in6>�Hex`?s m�0��*bZ�G�P$A�&4 ( p_f - p_i )Is"� X�f> .7,p�T�XcgA"N !$q-bu�' ecau�:;? low �B&z%mA� /is I!@c|8A�K1�(ed%!�.�Erefer�to�46#AX!n�6�<&\< titles:E��.�?;�8a=�fM$, e>�(S$}V-�Ttensor� $\fPpseudo�8/8U"aimA,�*Y�6 $i\�!I{u}_f ( ��+�x) u_i0� *�L2��"%E�)����!*�q�!�U<��p}_Lřp}t'!�non2�.e7&e[Pauli 5�o+7�~ ors,��'m_f"\��/s��AA} &9c�(m_i*�v�E\ee�%�0l�� �%)}ce<\M� keepA9��i�yG|�p}|/\MN�" drop6�E'^2)aP�higp^O"i�/lti�� SU!*a @ ��+ ��( �5>%K�EV0}P 2�&�V�%PgV}�MN�[)hp@ 0i \mbox{\bold3 $� $} \�s -q5�] + % [fM[2�-� iqVi%Vjp2j��B��)��F���S�% � V!% AV)U)�)\gA�: f.%Xpo' \fT ~) q} %!�`fP`6#�F>TA>�A1�-�b� + �6xb/& !1A6 - =)]�' + i�� q6&-&A�2�0EEit��e� o25ez� eE �j Each2����J(�o�kb. �50 dYa�X# $1e�d,�t�1n\^c�E��f (sB� �eB Eqs�W V0})���W vect� }�q"�C@#e�%�Mr>� e �+9)n*�� :� R�md��x=�&b,| { Ak���&�C2�� e&&'��&M$�b2��o+*�$� �$3vb5!,='W )�0 ��(ly�:eO"<&A##9�. Be�C proce6"�2V� F,! A�Q �-Z� �]�=9-�.  $g�E� 01A�$�[�L. j �#=#yQ 5 �"3E�9�*e# disp�E��ula� �4�7 m ; ob�D2quival:)e :PR8;rk4�<~maaOsh,V2:m,_8ctid5Fi�L*�6% (, $wK-L�]&M�), A|��&� s ([8af Zre�1nge)%t�1bmA!�aG AOduc 8&�o s,%�in"�0&!��+in� . So,� �2E�^�Y!�o T�S�i-a) =�5 $�LI' L \o!\S�_S.2t8�FK;� aB�F�of� �"$Lz $v$ZIy )&'�}� e upperi,$Se%9��)� �-�W ��![l1`� �ame!� c;ss:sM�.�7"%h"`46�şm�>*M* "C"By:�E� B�s: \vizU�b�) =�$m_{M_L M_Sq HL \, S | K M&� R{" M_L}QB{S4J "J sMG�s:�%�w�.��x�Dbe7(r>�^M�s!�&4d)�ib[�' ~3m� = :�3'%v�3C R_{n l�4Y�3z�3"�sp�7\�A $neY!��a�[um AI.gd]J of nodes �at�*R�.�7!B� $i^l�4x�� y*� If��m$zi!�!|Ee4.a�h&"Y�)�#id< is *�environ�e��ka� V�c����! b��M*şUe ��,� �"���. v�.}V_ste1��!:(�1o �&ize���B�VAI�*�c E�(�8!*�( )&!R!� LS`! :!v}6� 9 ? �5J��e, A_{(LS)K} ~yK_l& sə�GL�!&2n�2� ��=��,"eLSf�T��g!�$��=>t15�!>�{ �|6\{NS� F&6�&2��6/)R.  - L & S &�)F�9e!@* A!�f Our �ZG=~o�i�Bg � "`BEdmondK �. Next  - eF�epin:�s,�2� $S�nd 1� �$ba$S_60\ ! lI�.�-�1 :� Q� ~~ =�$2E��S,0:�S_1m�vf�I���66�1}&�'!@a�two�(6X"* $L_L)Q($L_{(J 1)L} Q}� �i�L_AKB�A�M� �� � Y_L:� "3M�)�2)"��; `>mU%~a{l� *qp�1s.w&a�e�"J�� P&eGH \\ Az }X &�M�R��|)| H)��YL5���ml�Z���h�_al�B7l��t-�\>J0^{x8}� ��#%���r^2 dr&� rCn.� e�5/Fb�5ve"; "Ga litt<*car� A�6�M� E�2��-v!�-�Is�(i^J T_L(Y_J"�  Q� ):�"� "� L2"�<)��Q�eit p62Bor �BT��ri, �$65 �\pm ���A!� 6@�6ropri�Ffor�$�3,rer -!q}�Now 1 �a $-i�@6S $\�pa$� \pm f i �")F�gAE?"] a/n -X&i}  Mr ;2�ar6 �� �F�a$�]�8 Sterpre-)\��_s:*�, phi_v,f)mQP-iU( = -i���M�# 8|J-/ 'J-u�bB 3Z�@\}P-*Z)�F5E �jlwi�9xt}.9 F7 �@�#ib+u3 +J+1�+J-�~��J�+2{ w:]&�#$biggm{\{} A�U*{ 1e� y J ;e�+1 L)�#BEC�#� 9 & J �#�I+1b�*��K E�+&Z+$%i�I}�= 2|�.�m{("G d}{dr}�� ��@ /) I B�<6@[ !E~~ \mp�=-�=-�=�,��9"�559+1!;�:-J+1A�2EJ.I1M�)᪃+C 2���IE�{^GI@vo D!51�Mp M�" T��+�G��-�G:GU�1U�ZG2}).I~A�I��}�n&�De�'L2�:� �����isp;��Q*�� �� P��W+�$U�Fe"`�(�`�Xof�eeej(eo a�i�Vwz� ,a $6j$-symbo� 4U(a b c d; e f�a,(-)^{a+b+c+d� �}e*"FQ VO a & b & eaT d & c & f.� ��.U�"%V F�sf)�jto�&vwm8�n^�%�h+��&.(om@!�!��"�-�&,�p:Xm\v�{2mm} O kknt�yTime-#&V�' CWc�"&>�M6A�I�% N � i^K Y_K �# =*{ gVaHfS )��uZ 6}{5� � Z}{R5�)"v WK0WL_K ~ #.l�V0_ >$SSW-%%AC$�$-$� A}. �)-J�3eK-5� +��=%=L11=L%=1==�1@I�* �ue�(�vv ,e*��Er�|EC�,3H)0a}B_}))�a6"�M du Za uni�%gQ)&H�  $r��*"T�YitsG"�]�wi<o^uA�#$C"0AHc�\� �xa�gr�x'�<�  *��n.�]�J�.� Ϳ��E�V��M� = 6� ��pU�M�\{ 5 g�$ }:�{I��p})E�0 -;%n,q,��.�)"SL�iH.Q� 2�}(um_J U(1 1 /; 1 J)�Wi�J�a� gA )AJu^�J ��1 �.�vectVmwa>���F�� E A_0�� =R� )O%�J-:+��K�%c\{!� %*�%��.UK15UQ1 :TF�-9��.�A��a�y&,"/Nu�J R!e(Zss:num�}!ke�!g~V����u�T�*Y"66�K �9f B hargV5YR#]*�9� �hrjari�p��iJs avail�E�Ili,-ture,m0e"�R�-�Wn6�Z�wol<�fQ]2�M(2pF)4T� �)�L.+�*rho�R=q�rho_0}{1a�exp: (r - c)/a!�r %�]rho%���W5#7cD $c@dthaxsO7)5���[ �'Nz�32�h `Un-$1�{+�~>�$�Y�15L dim 9$less ``win�ttle"� , $w�e@yg"���%-$r�Dha�#r��.}Z&�6q/B !�J� ( !�wZ/c^2 )r�"�36�!]RiGaL1an2� (3pG]U)lal�Va7 t:��w.aTra~hIaI� .�V����I c^2)/a^�I *5!3�U�.H4-oscillF:�HO �In�g $p$-zXiAS�"&�"�$p-tb^Use��)pied, ��F��!be�/ru�W�!"= ����= �'�� JNe�-K" r^2/bAM e�(-*�VHOM�i��$b��� .�th.=W7eJ::/� B&`�J5`protonCX cZ-2)/3�.q3pse"(�%� 70tre�;mFf��f adjuN�fi /eRic-�Zsc+n���g��ei �ebp�$ \squeezet�(9 }[��+{ceS } \c��Cf��K ���-� � \!1ect�6 De87� "A-us��1�_)s�<s �+.G<�'e $" ah\�!M P�>���_gmf �5t�K�J2z��\�02}} \vskip 1m�'!HruledtaeM!=)L{r  } Da��&n� & & &$A $\D�Q f$""',mark[1]\\ Nu��!m29& M��6*2]P$$c$~~ & $a� \%�! \ \h�2G �\\[-3�0$"j�:\\ $^{l`B & 2.45(10) & HO & 1.7096�3�0.83764]� 0.00�V 4}$NV 52(2U3pF $72 & 0.505 $-0.180!7@0�8}$ 0 90(3@2@4 @67!Kw�sN�2.95(5.8752 .549�n�Zv & 3.03 �o79� 0.56F730}$P618 � �3.3m8�73�2 �2tC v39 v@47n 0.59%$05$� 38}$=3.41(4�?738%585A�-0.2014 �w�50),@9-d86 @162@[5]Y0 RY!UMg`06 `)U3.0%�0.5239�.5#3.29(1 �GE;81!�2.1%�Xf6.�!Aru3:u59 -50A9I8. CA83.4:�76!D0.R ��xTiw61I �71MA8!� w3-��xC �66)�786/Ax!� 7�54}$Fe nU9!# 3.54n 2.27 �40!b!"t62}$Zn=90Qv =52.4 �34A�=5 �66}$Gz 4.04.� 4.39 �Et �1Q�70}$S 87. 4.4 eV8 4}$K!!4.1M�)! 4.48a!�!� p�"�� :��C(text[1]{Per�;age��Z{�/�2d�K .<�in�&&�J�HTCDo2]{See �2(�\0�"S �2 6&/ �2R3]{� i2� $b$,�s-��iL��JB�4X�2W�v"�D o�[Zpd '!ner-��%��s�u del .� s typo/JC�oo 6� .�B xq,�"--�y.�e"n�al� � >#  s"� , "�g�udNK > G$ z � Four:1�;o@�j�i 2 1�p"JOf:069 B�lh. is"�' De V[�\e! .� "/z%\b�r xi R�r)�(yp"�r-�rB\j 7YQ(Z,W)6�p ԡ�e C��i��w�� ~(Śs.lFPk#4 veal��new�/� q_J �\xi�We �{R p�v�1at  ;.0.�0M�"H�B@^ �$ makes no ��B��!�9� M~m"�r��R�k�\Ro36}�k�i��oA�d Rmpl�NalQa2 cripE�6��6�� a ���i9�UF-�%�spo�� un �?A�!=2�81.�7 �;f�y��&�!1 $f$:@viz!� W� |tilde{�> W}}{p Wa >cm)}{�m}&G*Q �I�� $2 = W -  =�g eN*( W}&�Qe�;= = N%Zh[4 FZ}^{4/3�HA� uZ�SLC!��7rJH� Q:pa� AA s.m�Ca� ��Ja��H6E���x$N�s .42$�N� = 8$�y !56F!29$)Mat���� Johna�I�MJ66})���D� q��Ak7U'��f$�e�!@m�t���aa>'s )ԡE��m�b.ro%yin 50\%!X�s� �F���9bE1� u�����t�>$>0�t.z�1�y�he �A� mula�sa��� n"��d"�"Dn&*�a6af-c�o$GH*�-S�#r&��Oy��\5 �5�Fja�!��?s*��s "�� �ll&�~ex~�%�1��$��n N9 ron or�"TH7z�\np I4A205}, 33 (1976�HT75} J���,���A25�\221P52�XKo84} V.T. Koslowsky, E!4gberg!69BH. Schm�,, R.E. Azuma��.���`{\it Proc. 7th Int. Conf.���\sseVvf��oH|���Xs, Darmstadt-Seeheim}, 3RO. Kle�L(T.H. )4, 1984) p. 572�I! HT90.;,2� f%d2�M>=d50A9 429 (19902d@PDG04} S. Eidelma�P�l},M�Lett.)�B592}, 1EG42L8Ad83} E.G. Adel!�\er, M.M. Hindi, C.D. Hoy�ZH!�Swa�!�,D. Von Linti �W)�xtz �Rev. C �27A�8I� 83);x�hZ�Jrs4�� �  >�^�%fR6�1�=!46}, 695!m816!0j88} F. Ajzen! -SeloveN490)h 1988:G91�G523G9:�l69} A!�HAldridge, K.W. Kemp��H��Plendl��30B]6�69)]�Al70} D!�Albw���$D.H. Wilki)�)�LeQ`32S90!@76� Al72:T�%�M��274A26:l��F�,F.P. CalapriV �.T1E�6 �6� Al77:�E1V�2V�1 �7f�Ŏ"  �fe� � Wi76��� Al78:�N.1��187%�7:jLl82} P.F.A. Alkemadea�A2erl�(oP� W�nd C. V|/er LeunQ���) Meth�O19a�38�P8:�nACznt�.�K Bu G��I# n, Z�+�34}, 45 �:EsV3!�17 �66� Ba67A�H@k��$N. Drysdal�>d W.RA_illip_9)�Soc �b 587�v672vBa77a:cC�Sco�� ett M. Fre��, S�vHoath, W!�Burcham%4G.T!F Squi�uc9 ��27�b3��`e2 ���#app3��:R.r6�J2�P9?�R� ��665��22!,76B,b2,PJ�Nolen,� 6� �Stp2@ure, Tokyo, Japanv 77.ݝ!�c2f!� E. White,Q Naylo }N� WyatR�279�9^ 7>�� Fj).�153�86�BaA>PS%�ergusV) 3��936!q:M Ba89 CA�E�M!�ֵi�}F�4�94 �9:�� >�GA�Leonard2���4� 4�:� Ba982� ��#mundsEE�)R�<5�257��98Feupm��d�0C"u-valu2i%2;�' o�"�0�� <waO�ter�drawnak� To032� Ba00F�ME�u=1106�� 0543� 6� Ba01�7%�lla� Bishop�AA.�, G!oisvert,��BcZŨJ. Cern��D'Auri� Domb� J@�V. IacobaR. Leslia�.� dn��e� Macdonaldap-B� k, DA�Moltz@ Powe�G. Savar��.� .��e8� 1454� 6� Ba� P.�I�śa�Gea�EcA Byrne2oM�7a025�>�05=��._ �*",�2�e68N  Beck� H. DanielB�1�2� 66� Be %qI!~R!�Chalme�&BWatF#a�>� �\� .2� 5�\21eX:9 Be85�ergme� _ PAeb  Pamp�",d M. Uhrmach�6� A32!b69g8:gis SQ�)Z.2�]T 6250�: Dl02} B. Blank, Eur���JZ A� 1�2006� Bl04a.@U�E�D/�,` Blazhevax C4�!�M.!�rt��' �r��Z. Janas�� KircheGI. MukhaRoeckl%Xidt�,�Zylicz2M� 69}, 0155�=:�l04b} � la# � DI��BUn Guenaej lahaye^ Herfur�A_j�bau!� H.-J0u~ D. Lunney�$ Rodriguez��$Schwarz, L�weikh�CC,�b $C. Yazidji��I��� A},rto64� $O. Bondeli�pJ Butl�BU5b618�^6:Br9^�irindhab�$nd 2~ �R*�4!�24A�1994);J� �,�/Ȋe��be�+~9#lab�or�,"% Bu61yW. ��R.28%F12�177��6:]u79} .9 S:Y )E�UA�*�p5�7:Tu R�� Aw� gliardilRa Trib��F] 3�: C��y��2�F� lale� ndoovm Dossate� Giovinazz� . Huikari�S. Lall� v Lopez J�?A�V�decH$L. Pedroza�/ PenttilWJ�� Thom�"N�v�Ch� N�yChaud�Fizika-��^9E :� Cl73��$ lark�.� D�Rob�J�RydaG�")�EvA2�|�7~�&%� in����>� ��d �3� 50ŭ76DaaC.aavids>��J��rph@ E.B. Norm�� l.(1�(14�:,Da80}6nin ``A��ke1fN� 6"�s.� ~ .�,ene� (�New YoA 1980�419.�DaW�kDaehni�X Rosa2i͡3�j4^ :�De�e|f|)3!����63� 66^D- RA�$DelVecchio �W~ �J�1�180V: Dr[M��van Dr� H��ijn%�G.c Eng8tiH��$Eggebhuise)}� �GeAsNF2� ŏ:�E�Lj Earw� JJenki bE�T �ryN�EI�1�� 2L 66�En� M. En~��)�i�5�9�):� En� j=63�h =6� FrG6ick�[ &�2�X.�%�J.� offi^� ec�<216%�:<Fr65b�?.�Ge�rai�.�M8]�E731�[66� Fr69a>\=�| Mui�C0 �h�6xF� �5T 69F=B|�fe�M+6J!XMj|gue2��Y��� 4��65�32j VJ\=�.s6}, 95)�62�Fe�2n2�.�2�b}xIH53�4�w:� Fu998 (K. Fujikawa� J. Aszta���ͼ�KDel�nque-Ste ��. F4n A"HE�G;�e]-Y� e, LgLi�a9Os$cchiavelli!WLeo� Ah eich��AAtwek-Q|ang� S. �%hWP��m%��B4� �6�Ga��A}�j�E( cob! >��?(1A�.�G&M�7ele!H!|(ndrzejewski� Cam�� cro�j�uys9 Kruglov�F�� !U, Piechaczek,]Severij hSzerypoe4(Vancraeynes�ID�Ui�J. Waut�N� 1�/4�20:�Gi=H!�Gil� . Flothma�� oehk iW�esg�=� � .�  17eO:nGor D.R. Goos\>:�=���W18��72���(ing-rv9�Vl���n]7izV is �#�k�ҁ� much�u reby �Aܡ�^ �.CN�13če6�HpG.I� rr�; nd Aa�Hy =Ƀ5]95��:\Ha&A�ag| K�Mai$R. Michael*��my26���:: Ha72Łd! �a�l�R�2},b/ag:Ha7!� -H.��! G���RR� GrahamNf225�>7$t6-�s�Ͷ�H +3" }��L. z��q290�1N�(.|R.�re�q^}�xA��+�24]-=�3%�0�6�!�cY.�9 a�� ��� rawl�E. Kas� H. N�;�m�9�!5EUJ}d6}G�B��R32�M!� �&_0:��8:PN�byE�%�2,�q 5", eq !�a5��B2JRt 76) p 66.�Hay J!`�, H=�=m�~n�"i�5��2o�m�m}mt.'&>?%.2�[ HykawyA�.sT�inozuk6�}v7av39� 4); &�@;�A 2�,de��w�<romI�GV%�$^�2di0r�A[:�^0���ged S�(��eD�vad���-67� �ar�Bow�*�EP��V���5�831�6k02.Q2��]=j8S25"�6�Ha.�V���M!�$nchez-Vega��G. NeillA Azh�� GZ�'E��y� X. T� L. Tr��� Nz�* 08�6�He�D��ri YJGerha�>� X�3� 6t He81�%H�� ndez�2����-�24��23F#:�&He$A��V 29�:�#HeAF.T0�n�,#:�a of� ActaMKAus��$3�6:%oo#.� .� 6#� .m1v 34%Y>!u!YP)ngZ/���ch�r� �)6 �>ayaB�yz.A4+V�BMMiR2<B[�'Mz6a�0�N�Ie�.�y�.�z�j�n�Bul. AmSE,� 4�34p6�In!(P�QIngal~ �Overl�ndj)W��)�i�]A29�]1A�1>g"Is�Isl- T� Kenn�S��Ker��W.V. P�2w�Can�.n��16q 86Q Ja6�, Jaen��$fM�15a},"[>?�AJam�JF�0Sharpey-Schaf�ZAl-Nas �"ehbehani6JHstP Nol")a�%��E�3%M �G)V4��6SKX R�Kavanagh�&X ZB(n��%142%:r K�:uY �A12_ 17_ :]Ke� >dF�2�� ���C.&���A V�V�%�6�I��y�&, �E�072V�Ki�$�,ika)A`&x*S. Ra��EE0 Jurnmm2c9bM�A49%j86�Ki~-S2zZ!!o���P�!E�Walkiew�ZSt)r�T�*��5E S:�-Ko�/>� . J�ar~2�/1 �H. ClifY*!�C. Eva�̈́2 UaxSchrew�K�FYaN�4,�"86" Ko87F�1.�.�.�*>!�2�W��i�h�� I��~47�41�87� e� �% -$^{�@All�:J-<5c�7u)"kF�"F an"�� giv�znr� �.[b& ��2�) e�)&119�&� ���4Ko9+��*;#2���KXE�u���*�A4028%�96�)�bF{..���zI6D �>zr�I�K���"�>�:�)�� �J �in-�Re��31A%4)6 L��A%Lin�֫"30q96G M�Pr Magn|7Ea�A" 4%F�!rcV(IV� R17�/>ac�-W.�cP&�0Mer��IA*��Hee�.)A qi�: u#66(MiiS Mi�$�b�mA9c26>Ro71�E. Mos  Detra� C�MZaidi�yF�17[40� :h MuM�kherj�>D�%R F. Carr�&2  J. D/�S. Georg2"�%2"A� le�2�%U�7� D&�%�9)�8 1508< 6�NaauY�gai.'Ku�ro,�Toriya��S�ada, Y.�# YoshiT�! muraX Tanak��b+Q�� RN�Ni�F5Nicho) N&$Ia;Maa�Mc�#E� TwJ+���#:1 N�U B BG�mil�2�I� �0to"�9�:r11�1�q76�Oi�,M.Oinone�o8�1,B�Paa�*Pad�i�R*J'�(I7 6'P;*A6�E!YZganja"-�P.2-M.& -.!D@ HodgM& -P Klag�W!GKul�-w!-M� poglavs)%��%-�*J. von� *)eb8� E. Svens�ݲ%�JkWo�F=6z05�F(R)�h96�io"cf��.}��V:;&?��WY radiAYyN�* �D-4�"�X�;N/E].aPr��F� ProsMG.U���Da��:t2�1{7#:�Pr�"6N%R6}J_��(90); erratu�{135� :'#Ra� &K � � "A�� tlaw�=�2���S5118�A:� R�-4 L. Rei�F�WaD:.P. Oberh�/� ��Cc��$ Rens*�" A. C�::J.E� SmitI MeyeI�&4 �b�%�A43a�3 ":&Ro�7M� oush� A. WyG��DM�j/ M� [14A��:�7R�� f#��5aT� Thwaita�J�8� 6��$aJVE�P2 0}$C*��r��6��J&�%"�$N� �3� :R�2�)�*� NS2�1u:�Ro�%;lfsaA�od�--��$ !�[nkVj-�&V/@ Ry73�^J�15#�8 DrapA�6=.,%�2�q<� I+4�#�5:ARy` A Ry�2At. DawITable�Iv0 :� S�)AAg orf>�2L!�EI Warbu�'F�2�2::�Sa9�2�� indo-Urib� # HN�A>� IFadf�:^�![� � 15.6'S�32��Vy,F�A�)�*;� Gul(.�A@Hecht�#J.K(L8 F�$vQ� Bundgr- N�>Sciel�-*�d% ihat "�Ca Trim�.�WJY. %�Z. Zho.�5"�@n44?�6a Scq4�Scott�P ssool�oN�<omp&�3V�'bbq�B� NU}rK1Se.�SR%h ap)� rmbru iI���99|4n6,Se�KA�Set�Sa3*�,!fA: nA}�� %]B&W�Y ntha"�@5 ]�D!2�j:�Sg(D. Seweryni�6j�5 Sh55X2�Er�:B< �HC�WAaHornyT)�%10�9�A5:i66�/D idhu���GjBO�102-A:�*S1&J. Sin�IndSo�<ure App6�de:j Sq�:V.v!�MA�g=&� ҹ�Y9)A24��6; :e)Sq7%22=6�j>����e^ �)U]9n�<Ti�a`&TG�!.Ra~T� p#heI���)hasteZ5�-e):/T[: N_Tol���9�k�� 35�0B�HVo�H�Each_ Gla�cl�3uen PFier-KomJHG*es��(Scheer��H%8'�nd'Semrad��)yeA27~1r6�W5 :� B� H�J>*�� ]�;A4�8%�:T Wa92} E.A�am�2� .%��Ly�) ��� 4 159 '96�WI:X enniUA� Sti�H��u�yQ�109%�6%Wh!�t4White and H. N�Laylor, Nucl. Phys. {\bf A276}, 333 (1977). \bibitem{Wh81} R.E. White, H. NayK�P.H. Barker, D.M.J. Lovelock and R.M. Smythe, s Lett y@105B}, 116 (1981):y56yn]:q,, Metrologea �21^9�856^i76} D� Wilkinson U E. Alburg�)'Rev. C U 13}, 2517�76>V8>V,, A. Gallman�c8}, 401b8:b80} H.S.�Dson, R.W. Kavanagh�$F.M. Mann,J�22!69)t02^4Zi72} J. Zioni�tA. Jaffe, E. Friedman, N. Haik} Schectma� NiRf18!�465�2:y87} Fyjderhand\C� rkus�4C. van der Leu�B�46A�280d86�Ba77} WA�mbynek, A�hehrens, M.H. Chen, B. Crase!�|L. Fitzpatrick, K.W.D. LedinghamI Genz- MuttereI�R=Int L EIMod2�49}, 7IP6� Fi96aB��Frestone, {\it Table of Isotopes, Eighth Edition}, (Wiley, New York, 1996�S%ya#oMR(numbers of �_ icle%�!1is limit��is showm��eB4s very sudden!Za f� !=,=�a c�3of�order >H !�^1ofB\9 �BE.�� pres�9 work�inA Ba rec�K-��ed A��a differ.Ei,�&�6�(hence a�in6�)1��*�{ wellm@Sobotk�� One ��� at $e*$(=� exci��on�/ per5�)F�de��k�o2��"� � be $c_p$ �$$p=0$. InD �� �:}�=-YD.A�oryh d!��F past-�De!�ForI�i $^{B@$Sm and $^{85}$Kr6��f�wňj�!�� 10a{�fa�. ButeJr�%ambigu�whe�!� systema{ay2a�,ot. Even th�� we aNns��i�Rit� i,^n)do fi� }O y beyo�ud/, fe�occup�+ factor�| r orbital��a7co� umIcau" he� �$ to spreadeJE &� etoAI1� a big box%�Tsiz�  E{ici�answe� Al-?muhe box,��);)resulta�u���� be h�$to decide 1�5 p "�us!�a �A�ga�?��is bes��pl�  us� figs. 1� 241 E� Look%aSgures���vBre%]ay�  *^RA%`a2� 6/ M�!`�6us-��12.5 f!�th $�D 0.008 fm^{-3}$. I�ma!)T$ar liquid?Ŵ�Ź�R!�)�- 9��:Dw � �6ursU-is . �a�e��! do�Y�� &� �i�}� yasr 29.m ��cd !V��f� =�;� � ,�&pr � RD. Asj ected,�!rtAB from��r� i�5� !Me �aA�� dropa lowU 1�28 "Y �v|%1�x �disap�G!�EKus�now� a��` is h3ns bef $T$ fl� ns���6� !V=" �oe�>2��� mai�4�c, some detail"�*�. We\E mome�����of�$Welke,GaleA�poYial5e� ��n by �eqnarr Hv(\rho)=\frac{A}{2} ^2} _0}+ (B}{\sigma+1.( 1}2};C}\int d^3p' ] f(\vec r,p) :')}{1+[ - $- 8'}{\Lambda}]^2}���$:N)� p-spac!�%1�n EF, Ar,�  }$FT-HT4}{h^3}\Theta (p_F-p)$� re 4� �Vrųspin-iso degA�ac�A�ۅ�u��tY"e$ ji!�replac�G B� (se�I�below)QL felt bj �.cl��FGuEG1�=A1�rho5�]+BRU* +2)�6+E'V#N �`A=$-110.44 Mev, $B$=140.9� (, $C$=-64.9�,, $�_0=0.16��, $i$=1.24 �$M�$=1.58p_F^0�=a�# 6a bin�#� yz ��=1� , sy �W�6�com�sibild $K$=21� �m� =.67A��~f� A{gy; $-�a% �$ corrP I�(l behaviour��! real�ɩ e op���FYin9 nt |7�ariC'�� a derivedɽ UV14+UVIIj �old:h<� ��S 2J� q`al�Q� �m6�a �X�O(� te 9 an Yukawa�. M"s%j�� eqs. (1)�V(2)� b� widely t� ,f7d� �Zhang}%�!��goocre�o �>a.��fo* step�=ve��$be execute� We neLj d:�s probaI�F?4n[\epsilon(p)]�E(1}{e^{\beta.-\mu]}+1B�! a�n.0 $1/E$%�e9a� If $~$ w��kn�' a priori} 9 3mer!�en�>� e�!� chem� �FromF��N�6\pi �6 int_�@$infty} p^26 dp>�\{exi�onE2��B�� �p�� 2m}+�� }+R� p)>�=� >sF�F=F��cin�!.$$')]\times -1�9 ThusE A�$�$ requA):$ al�y%�all valu� f $p'Az� 6cy7q)��ulfill��an ite�4ve procedure (` �R�)i�| e"9n��&Ji��C4pV=-E+TS+\mu N�tv�gJp=a+b+c > � F�a=-v--�aR dp " p^4}A�.v)]>iIr$vA���^�] �a5sec���P �rib�e�)kineticѪF� b=-T �f�meaj he� %,\ �A%� (2) k put��� !� $A,B�$� Oa�j[�!A� desi(i��J� � @/�librium�p:� )�� s��$$A$=-356.8� B$=303� I � =$7/6. We�.x �!�-Q)q*G  bothE�Ea.s�so,� n�o��up �"es, onlZe�#pth�: [AXO� fig.1m  2s�!�o =$ \�AU�.V!���re�ce,� gas �$e*=aT^2)���.�; "K��e�>oh.�) 7[ th[n C0X�=� �S�5 M=U $m$. No!ly �write@*/m=m_km_{\omega}� I��u4'N9 !� $m_kM�m_w) ignoA�!C -��Bzt.3.�� wvei� s�U$� iA��B�n)� w dels)�%�"t� F�E��e*!A� =܁]�"�c�Er �iO�� heYW%1 meet�e bgas ?at�rv!m/��m"�  m� te"�"s w� � long� �!e� � o� <�Atj.�)9�I� m��r:� ly �ighter&?oo� �.^� �9�#[�r!, bulk�� �6�&�A b"�"<�-P.�1e�nota;"�&���"�'ng fe;~ �2^ � r a:l2�GaEK� �t�ar @rh D12��.E<�nes�U9�'D�d a��lA" e Coulomb ֩��<�"J! hove�m'�Yp�i& C�Ir ME�3}�s.]m,ri�.Y by fift�U!i�,Huang}. Las�%wlessonse sx#.�i&6�T� �)bo�/AH !F emit�,source (EES) Lof �-r~6"(}A�e *2L!� i� �hotQ�ev]1�+%�ell a%d5d� A2.K.ce#�e8rever� ward�;�!���C ���nd!Egs�m|2.�explode�#��nk Lee �J�s&commu� � ��� g#sup�)e��)b8Na�al �2�*$nd Engineee ReseaA� ncil��+%in2OQuebec D"(,/ Educ�"� "%s,bi�:.�*@/ et al.2�8L&u:75}, 104[695)*S5&�& S*�,9 Z. Mekji�8M.&8Tsa3A� ces��~.�-, ).26, 9101) E-�"�)�. ,]70Donangelo, I.rMishust�2�5chulzi5t.q.A444},32D:82�P�(o �6� E�1C/51 },138�52KMZ1} L.�7 �(J. Charity, Tok"/ U. Schr^1Z�93t 2702%64) =�MAe}�:�5h,�!H. Young!�Sampan�~�0�J$ Many-Body�Nle� N�0((Cambridge &�0 P�.�. ,�07)p. 243�De%bN�0,�D+/Shlom� n�K.�addar, 5�15},R164%�97.�V}!yM.  �:(Prakash, T.�2. Kuow�e�C.�<"�==�3;42139 1988.tz<GE�J}S.!����s3Fe415:54�190.rZ �< 6�]f�w1 16�=94.WMahaux� , P.�3 Bortg [=$ A. BroglikH�so9�pmu120��46sH�J!� I�-8&�-a13(>2 �;�Sons,2�;87)Chap� 14]u�a A.�=UT.MU42}, 66�2!nr2:j;2>� psfx�!=5.5in �fy7.0:eE4e{�file{sobot1.ps}} \vskip 0.8 true cm \caption{j '�2as&;of�C� "� *���F lottedC&*c�o�m;&um � of F���Yframe. A6�'+ � CA�9�# roll �+l�h��� ��0 2�� �iH"? aa�$�\��9p} _}�neg., i.e., � e�$di+�,!ym�5a�(st.}2 ��^<4.:<6j<evst2�;*%#Pe*!$m&K � bI(MF1),4& 3(FG�6� PoutFF� MF2�.�ref. 5)��2cu��er/o%,manifo!��influ3 ��96ncorpaxed:tl�Th��+MbE �-��llent a� %� e"�:F;%�. \seX({Dyson--SchPeruD s} %M2f) �$a Poincar\�A( covariant c xwithi�4c-�1hadrons~�I ,�",:2003vk}. In;8nbow-ladItrunc�Ppy*�" successfuuappli7 q;*;a�!�!A��2]Z ɒ$, see Ref. �2�Eare�KK. �;DSE!4E�ren4 izedm�propag�� $S(p(0n Euclidean s(i61�\�D} \label{genDSE} Kp^{-1} = i \, Z_2(\zeta) \,/\!p + Z_4 \,m + Z_1� 6� Dd^4q}{(2\pi)^4} \,4g^2 D_{'nu}(p-qp \tex�?{ ?\l-)^i�)};\gamma_�\, S( :G8^i_\nu(q,p) \;,��  $:y�$6B;!c���.� �?ed gluo.$1��B�0- ex,���,ive�e@most g� al��Am Eq.~(\ref1�)� ��� \mbox{E.�-�0 p A(p^2) + B $}�]OatI-like $%�accor�to eA)�^2)=1$E�BQ $}e� $��x%�� . M�� homo!&ousPGh�� 1� (BSE) O} )�8_H(p_+,p_-;P) =��K(p,q4\;Af_+I�Eh_H(q_+,q UI�_-)\, ,qc homBaca�at�rete *�0P^2 = -M_H^2$�� $M_H�!��d-AI�� , $p_+ = a�P/:nd-- �outgo�>%��m�-��d:Y�,E��8lyA� $q_\pm$�kernel�)��.1, ampur9d�  q$ sca4 � ?��Vrreduc�!�q@A�9ira(� J line�/og� r 4�"�8�?iz�{�I .w ,}�-�)> pletN'd[ mzk;B� e?itudeA�A)�i_H�Di�;typ��M� 2uor6��He chajer�1by "( Dirac struf@a~To�r(BSEm  u�4FJJZ y"to��- 4"((\alpha^{\rm[ }\big(��^2 aM4D^06z .oD'6�:nua�B&�+ njun YPram*fEAAki=DSE, F�:�P�<2�$rightarrow(2��nu�IZ_1�B �Ck) N%�>�(k�2qk�!eg $k=p-q$. �&, $>(a�����*�in�Iau gaugeh$R��pAm ve)<: p 4, =: � 0 ' 0one-loop runn�� coup\C�� "m QCD (pQCD�A�2� ��": l(er �"� (Ward--Takah�=&s((WTI)U �R)�$�n�axial-STI}& #p &) "�=� )"�e�!�nZ;��ex�;GY �6��Osoc�5dI�Bal chi�ymr>yw��$(D$\chi$SB5Y ,l�A2� 1997tm�  hd�:In:/bin��Ea=GulOJpprox � !\m� � >f�� �Roberts~(4hh,emf}. �: ^: Qfy:�� �= A �cuz� $M�  =� /� a� q!�toA�PA[J�gA"� +(I)uN6:m[��<��5 � &\simeq& � hat{m� {\left(\�!�,2}\ln [p^2��/~2_�'QCD}^2��] )^{iF_m}< "^ eq:-�M}c �EO!anomal< � d J> $UH = 12/(33-2N_f)$. D�Ej]!?� M?as9]�.non�)ev�*o�A� ���7Mre�)9�iN eN8*5�&� 8Politzer:1976tv*� 1  M_{\h1 \script�{ `}}}Ia& )� f\7� ^21#}{3}\,!� #(-\,\langle � q q \?le^0}�/ %�(:81� .j;U1-�}\6��Z$f�� &� ��-�%-i��vac>e �ate�_M��]7tm�YnHa'd��prediNof' +_inA�� A#] n�H�i��strongNFco�4rat "�m� � e.g.�s�N\ e!R�Prd-53E�e (՜))$I�.�>�Rm��h ultr�5le�:�,�>lso!a< forf$� Podu) asympto/�58 Eqsa.D� yMT)-�Hig��0jima:1983gx,F7  4tv�� Both!�se �KaAilKu%�5!� pa5 of Fig.~� Fig:%�}�"\��� N(h/ M��6(of $up d $d$)��? come I� !ASof'-�) �� %.�� sl|7conM� "5Nlea�?kH.?�dI sL&al huZd�(� �lA6��,a=vie�,�?2�-/orBsid,{,>� e`spoiԭ� =L��n.a few�. %�=)�4}[tb] \include`s[width=18pc]{msslog.eps}�{1pc}%�6�M:&b \�Y] �Y8Es��f$%m&O + flavors (A� , ad�!�8B� tm}eb aE�4o�^ Ia-�� a6�%�%� �  m�Bowman2bm,Z(# 3fa} (^ 6� �Fi]r0 rp})>�%�Ks4��jE�KlyA�fi"a �aS"�Pof QCD � !,j�. KVKv� 9 betwY9= 2j�DSE3DA�%V &� 5��=&�B!mi�N�$via a suit�_cho0Pg� qF -�5�^mt�PvSwis�Ta"��Aes&�6�"*5��be I�-"V wBhagwaty$3vw}, suggx-���~�A�%42��*�� "�S� de�B< -�.� �Sku�Pud:&�s!� stu (� 4hn,. kj,LlanesM�Alkofer}As% Z �=c�L�F�$ devs 2�R f*$a b� L! non6���/ (>|)B. L5m�T�V a.mS�w�$o��Y�DSEV0-%�rp})4�-saL�!�*z� �a���sa �ed ��b`s�0l�HG�,redR�I-�� �a�6�a�v!M'n"�2i�� SRn,B�LH 96bba�as� �-^-2O!%/s:�O��O[=s>�#)"*!�cM� �L..s�́��5nBR,$I^G (J^P) L$^- (0^-) S* �egBX $2\,$GeV: $\pi(140)$; 30 � 8���ns:G�0�s�J"� e�'A�fwXt�me�RA�a"X0$ $n\, ^1\!S_� raj%�y"9n��Np�\ ipal:%! 2Q�T(< �)� �3ER�P �wo raa%�L s,B_�"N_2!!�.� �� p�Culam�ݩ�, bec�KSQ!(s� )'�5$QCD's Gold3f�&i�rAG�6 xpla{sh$?R"6� "�A�s&2 �%�)al.B! �V"�1]B%U��J�&� ely �ar1K Regg�Y-� �ger!*easily�7�in �Kcapinp5��(�`"�$a�3gh} bu O"r�)t.�FY{Cm 5oq�-��er�QCD�N"�!�ax:U">adJ�P?�{5\mu}.�&=& S`)v5 +. $-) -N2i\,m_q � e5I*1,(eq:avwtiV���F���.^>�edѢ6&A�.��ic1;^ dTsfyE� n in.�extenKofJ*. E�~(��)AQe�act�'m�"S5r�����~� ( ,w� ��BBSED[NbtR�ra� DA �f"|&a4 FDSEs y`s*�o �Q!E))�w c��,t,aM�not6fu?,�� Y'intrins�ClyB+ "J. How �Ws}Qa��y�pre�!�:� *�� mEist�.X g j,#Bo$��1elucid���"�!*-J!]c8 v a:�. 6c)��`��_l� t�@�OA.KkR�[.&l{\pi_n}^Օresid�BtZ'pol��&�K fAa��R�9&C#\,~o ! {"Tr}0[�"5�p�"; S�F�V �W ��]'� \� ] 2\ i /7\!�� �4 \,~�^� ����,9mO AJ gg��a cutoff8 �W� Lllows� &����pAHs�(Mi�y&ZH exact&���W ��hd,6[wy}rC�M�!� 2AUK# 7%.�5�.Hgmorge�%6=valida��ry $0^-$i] � Holl4fr}, �!�!!ua�I)it� q�Q)��4 LIvanov!8m? �Va� 0$, "  �Z\ ;\lis?� $m \to 0}\,qd 0} \neq 0��V/!"-= -!Dl6� "�_�$/f~ pi_0} a . H�),�\ Gell-Mann--Oakes--Renne�� emerg�$�co�2ar��* eq5�!2x (,�*:� c-X.]55Wn\geq 1$6��<one�Y$Ma{ .}}> 0�,yA<p���  ^7> 0}} -%A��� ��3ur4m�m *� .�E9-anti *$ ��e� guarantee�?�0rh��{n}q � f�<�b:�-�it) a n�fs!�c2�7�W�Z�a:�GZ$�$�sish6O2.�e�^I 6�-�(i.\,e.~D,$n>0$"�}��� r� &�k/� We now��H2� ' L��3i��`���es!�'s.#.� !uexh�<s�1, nam� !^d R�+���,SE�3m0&>�-uE��� eq!, Z�"B%emplo�8 AnsatzB�. ! 9nt}%a�sufficq ly enhanc�>�"�t@]��'alg valu�� Z�!ab�H$(240\,vGeV})^3���)�pard`er\&�C&P%��e�핕9nt,Hoe�Gun( re fi�8tou �N�Oo�m��m+�Je!?�$��(/K/\eta_c}$� mqQF�"]Y �0)-QsS/�lXlhHJ��o�7t�}[��9LTab:exc��} Res2n${�4$0^{-}$��A�2.!��bed �� �A.G12G ,�I� ���re�Fu/d}=5.4-�MeV}$, s=12:�$m_c=1.3A#$6 �0=1�#��qu���t["n� GeV;��!�^-3�G�Q'conven��� .�2T&O$aF . E""1al&3��H � G0 pdg}�X7�bEJM[ #EdNe0 0bb}I s#er"� tab�}{l|l } % 4%Cr $q$�  &�c� >�! expt}}$" )�x 7�7iU _1}$E�7`p72�@ rm V�N7\^� \\ \!1 $u,d}& 0.14!31 31�& 1.103!r& -�]�$J7 J77J20622 �% $s6~7U---E&~82^--2|4�1.4 [|332!08�02|57 |3 {$c.z2.92 �33134Y(3.45 & 3.65'-0.152 163!6G41x!uH Q� uc �!4mai�!6 2������K b#�Vsumma�,in�r1!2���i6m!6[!us�2 Rega�0he �*  �I�fh�� s ``�3l'' mix��@s�4u��$� _u�0� m_dT s2ca/u��K�prowOtan1ly�Nb�7�X�[t�Hd for �mpumn, E K \{$u�%d�u�%u-d d$,$ ,u$\} isotrip�#�a /+ %d� o@ let.�s�R�,���$s^s�h�Wthird.,9 c$.� �+)��al-mG a�yAX>C*o�'is�  >!��(! 2�.� �i"~ e2peg�3c� �(%)$�d(1295)$ s@ œ}ED.�l$4uO��� }7=d6�)i3;�HI7Apre�o .�.�470[ ;��26 �:� ?548-]$�^\pls(958) r#� �T� ����X FAMU r"�lyO 2d N]#z\#pi" "#\ >�\#�{'t:R\#)�}�ase�M$-26�M^�v a#&36�$��!am(ts �")@ &� )�6* �} q  co\j�\, �glso4�$Az 1 K �-� 2�s3 ��$ % Fi�C���$-)�mws;3 I-7!:y) �q �-D  �2� q![  as < vɓ-&�& %P�.�i ).�)�sa6��Sv�ilet {�i aL ?� do��; q| $�6 � vafx f00}$yl�i SatisJ=*�a:�3!�kv?virtue ob���a�w.Q?)c in TZ I.�C�Ia !:��in�Wv"�1\%25\%�8�w9+� er= RRof: (1)] ^proy07 �I�in �(tV�vi'2�,�W>s�tnePQ.�clo|5�2Qe (3 @��BM�a/, K)�to ?S�1+a analy*��inu�!�Aө�DSE"^ma � lex $p:1H�91f91Ej�?�E3:i� -phoT}��aD"�&f�'��? imJ\2+7� e�d<0I^{abc}(P,Q,K�1\in��<{� � big[ S^a(2�<{a�,{b}}(q,q';P)"� S^b(q'u�^{b+c+ ',q'';Q) e:^c(q'' </XBa/',q;K) ���)�� ictr&lI}=$q - q' = P q'Q  = K$I�Z.um��x3 +)�E8 $P + Q + K = 0�g In E"�<6�), $S^iD E�&N�>Xf& �/ x $i � ^{i%Aj}}(k,k!l$a�nd�>aIic1 tex�*\Gt�-gm k$j) � $k' w�!gQ;21 $iB1!D�a��Ձ��{p%_ss under%Si����, �-2�:'�{�[BSA#:a�rkq)�&T_he �6,X8IQu"4=Q*!8Q[ m5 ��$p<%��U a,� �Q:�' 6Q BSEJ�R� =*ba*++e~��:Qy�\;7+ Se�% q_Zm�(�=.�!verN�=Sol�_">.?! �%$y I) En6V & A�t�t �:�?2�a �?Q^2=-"�TH2 r Z�/���se loWC� F7�i& !�.F ��Z��a�D�D \*G$P!RA�kaFwla%~��jE�HTZ?3�&diagram-�#Y 5fiR>j8�A0 ors:4��!-�M""3��i�"�0�V-L 1.� . WM 4iZ um $��Z"�? �? � .a��\mp Q/`@M2Qj!W1&� .� se5&� !�y�n�mau,2\,P_\nu\,F_��;���� Q^2)�,I1�.&L| �_\p^r��b���3"�.x*X6%W�n+�A�/� m6sMH�^��LAQ^�D2R!�D$ �_/"� /yyN[�u�^�8�"? d $$-�?,=74m� (&�f?�;sl!�r/>\!"e.�;)�0btRc alue, Y urve�rK:w'1 � �j EY�'na<��}dI � (VMD�]n�. =�:7fL�  v4 JLab ]F2�};&9w�,bEry) D-�� A;ŹfuM|TQ3aO5!��P�3K�Fw>(�H$�8a.:2O2�-e-dx!�" "�e �A 9 7��t�<ESu� our q� at 4�;N�A�.���toW@,"B� sc��omeJb510%�20[�3"�8hc�!R��l�6��  �1"�1mok0&2i%�B�mS�:��a VMD-e�1Y �vaB Heide�%3kh,B/Rt�%%xisA1��F�>��var�)bei&�� pI*n�^a~�e� 5V.�b% nFYkeo��Ifm�xs" !f.(AOl�  C� �actual6�9. C�N�= B�te en�,gH��V "-�<� $�s �H$,aBLHct6E �5aeE�!�U���veY:.�t^b� �(iradec} Ove�B!�!�qX .�}a4rg8dii s� �6al�%${fm��a�-st{-d�bs�"�k erroEx9�$0.01~K��l&�d%��RqAa2}�xRdecayg(� {Va(P���&keVE{$gO�ini�O$�� �� & $r^2��� * $0}$ %+�� ^\pm &�2�}] & �.K�vtarAZB# 0"F��.n443��8&^Q5_ 0.69 & 472.0�990.913 1.19a� 6] 4(5)�52(26&�c6|0�762 �5V0.8�11� 1.27c\br���Eu]h�` e#$F_K$]$ quit\kllI� the availa�6x�,�do�A�neu�E� �K ged � E�u�6� ui,MolzoJ 78py}�A :am� t�$tb�'�X���:he � a]"{ i*Ĉea5,$>�?]p7, ( d s};d# �*� � &�-�-&'G���A n0 zero ��I�-}&�sen�v 2:\I�&:e;_J� �>"�|� �Z�Bl a�  g��2� bigWUfK %n�5n�n%`w�V|O�%��6GUy Z�Ť?>Ak�I�e" as A��7��!Hris� !rs)7&{ !ab�5� ��D X�, ?��h�6u)\@�al 6#�%]!�. !q.a���2Kݙt&� ���G�We� � �a\ 5(�S�.�����samXo!�Bl.�4>b � )��-.Z�,2� ai0"P(��$-��� �;mz��2mE?P�a �-2� S} �3&�W�b};a}�O �Nh�)) & = !Ic ilon'SaPPy} n3 Q_!1 f*w��2T�� $P"m1Ko�6ul� �>v< e on-sh��1�!�!�!�2 a 6!�� u�t.zXA'�:�(� DRB#v�alGs�,`<a j�V��j n&mXto5nt�]�� $\]be ��� �$(-exz>g�:�5�YicB�Y"<,VanOrde��$95eg,Tandy827q�M��e"�� %2,^0\,\pi�9� \pm  A��8E &�� Y$&8rpgverRg�&�}{m�}+Vn��P_J�JrhT%� ."BM3k6I^.�e!FH\,.��a�$ %\,.ea���V]A|3� r, du����in5� 5 s; h�8A�ݭ:y��'� ��%�:��'R�ɨ�@��N��=e>s|�F fal_:f6� fa���Jk� mKB�ri"�:�(� O�v 0timk �n�!���'�,0 weo a �B. ;�&UeqQ�)��wsEK$g_9� /m_V|��� natubPout,JA.��� W?V`bi`?K ^��MiB�)�4�  *�We c�L"rIJ# >�AHt dAeN?qp6u�E�� ed (&I( ely) nine%�sm�/ �'{ :L J�. No !_!�}]H at.' a.Y .0!�*�r2���&�"u`�1�ed6kes�e�5\%J/���|)�&. &�7K^\_ K�]F| (�2�� �s�49�na!3Vt� �/r�l�Fd �<toE/"a_9S�� �>"6� $s$�%��N $u$-P$d �uFSU(3) ɛ�� 5 \,! ,5�ex!��Mx"l pɷ: 0�er�u}� >e F�tw�IaM�a�"�9J� \B(��>���}}\��)^+�;F^{+}��r��b<��2�� n ���*N- :�2:[ s} @� \ ��0�0��- ��>��� �B�InR�x��ˁ���r"k 2k FYto5ɥ���a��� d]�.:��o��by2g�.a(� ��Fb� .b:w� �d�(&4�>.���aܹN�R�s\DF�.��o��{��BMuustood sS�� 1i"�m�Z� �& � ,�*��2MN�5its omis�C���r!r! \ack )���8~wCraig |Y�Pe{)� ��J ful discu � *�wwa"�.��� Aust@f"pw F)t�]0it{FWF, Erwin�f r\"on%per-Stipendium} no.\ J2233-N08!�e�%a���= Energy, O�9�O Nucl� 1k,�%t�N< W-31-109-ENG-38)�benef��fNM�NL Compu> Re�yCexp'sL ilR7;e��8��u�/97re��Ded7�#N% al�x =Terascal�{ } SIDFA�&�k Su�}( � . %%I��H?�*b* *{Re��s"m">2�{99Hl%<em{~<7 M�T(4dr} C.~D.~ E�HA.~G.~Williams, %``�hSF�h1their���Tto"� s,'' ��Prog.\ P�\EA�� }\ ex3��477&0007355]a�F& !(&G�"k Nk �p%$2(%$b: A toox� �B Int.\ J.\U�}Eiծ297E3�U301049>�U N��Etm��pi�K�!BpSaAp"�eJ�v!�a�56}L�6)�97J�970802b� ^�hd��>�P.~C.~�b%�)� �)"���Io'~ }\ B)�4�y2'y8V� 7003^�976��y!�4hh:��>01 ��-b��  �� ��]gu�605}, 4<�9��Fj823B��j6� �yuS0sk9��>��upi, K+�$K0Rk*torzz6�z05520R�bK15>HuE�j1�#%"� �1999bh�� k0���%�] *u~�� 0452��1��99100F�� 6�B5aHeHI�� ive �cM��0!�C�PL�d^smG117����aaG.�4NUPHA,B117,3976�Hig:r^} K.~�D"�b �S NBre��m��~}\ ݳ�122j��2�$PHRVA,D29,$6�2_�@I.~0, V.~P.~Gusyn��V.~A.~Mit�k"Ed YSitenko:�B� AndD ֗!� G�2� !�Gauge F�O!�ori��Riv| ovo Cim���6N��~�w.�(RNCIB,6N5,16�l�%.�S"�Yr un�!eJk I_*�D>Fi:�6�6054508�;1*A ��lat028>���LAT02%�y���1aw�8, D.~B.~LeinwebO7ndN�N:%Zim��5 %$tree-level�_ � �K"�rz ��07= 6! % 10201R�% 6�2�]E�O.~ , UD He�[�J�Q�>��sta �4��LG�uPLa~�an �N^1m��14505E2N203001>�U 62S_ J%�,��=:,:�F�mR!E,nnet %[CSSM 1' coll�z ion]�ScaK.� �Pov��pFZ�C7��03554N5_ 18b5 65�9MtE8% RayaN� F� Fac�*of� fp an&s 0:�0*y �:Eur � }\ k�23R ��x�^020807B-�^ 6�*HT3vw} e.~ ��� PichowskyN>( A�:sw$��P�c����-� *8��4� 6�015203e0R304j� 6�): b)2geeP1%�~izilersue�$6�`K-�5�JHEP}��0209}, 0 �A�:ph!�531RPH@�Z3qu�I.�>2�>"�>�>9s�ra a��N�p)eR30�4FY�!303176N�! !&5M�a�4hnB�A.~Holle�K��sj%�%� .*Wa6�2 �6� M�7��52�.�nc4��2>u� fkj:%�>�J� mode�M�i�ata�20407163Z� 6�LNc]�F&�e4ym�S.~ ,��J.~ E-Estrada�R"Me�& h0%� :�q�B�294V��2�6�E�jz��F�Ev�N� Semi21Azem��!fnB�332f�33:BF9��c�v� Non-2���s,F t6&�1%�ofc U 1�� :f � 094020B(�H 1094>CW �H!ɝH1r[6bbh�~ %�:� L.~V6�Go�`T\��&D;:*� Bey3�R�v-L(A2I+ �: 38�E��:'96X b@ R���as2�$W.~DetmoldN A.~W.~T�e�:�ME�!�a n:� IR8 �-��?6 06"#2* �?20208b� 6��!ua A../W�wei$,�(W.~H.~Klink�V�c�6 a6Y�p8�r[�>�:�E�6�B��30306BA �) n�[.��JlSE�%�48ed2� ��� 8039:��6��!�5�6�Z�PF�F�$a2+Kvq7aU042~ Z� 6030>W�46�2)S�A.~ ,u L.~KQ ov�F�S�8�,heavy�,ob�Cbl��� 3401U9U�B5812jL 6�C �29n*T %�>n:�OofR�$a`E��antz� � 5521�R�90505BZ 1� 6�2�LI�e�K S.~V.~W�#�O�&�lex��4�B��:E411065^E 6��N*X E��m�o4a�S.~ �e�� } [���Group CFRev��ar 1�&�T��:�592},�20i`.�$PHLTA,B592>�E6VvW.~ >� CLEON�S�Q of BI]"9�mono�EJ@s B $\to$ eta/c KE�chi/c0 KNI\�� 8{�>exF��EX1:�6U<� >J�2r�q�<F(pi)NNewS22+Y!gedNlC��17�.�%%10009RR% 6�6g5wj���>NA7N�A Mea�}c0 Of�  Sj? - Like Pa�E:KForm-F�-5:�m27��16�v~�2�m277,16�&� �[�<�E�F���,�e onen|�/ �, pi0M�( ��E (q**2)�m�6�5�365PR�80406b} 6�F=E�`�6=��r och%E.~Lae(�n�c%�+ ը��d�[ :%��JI�0usz#�@maZ�� 9451�4*� � �31202B� a�� 66> :�,�G��,, G.~T.~Flem�R w�wnd�G.~Ri�ds %[LHPN &��$� =Q?{15!ɥ���28:�� 6�u��Cuiv�%�R�KZHCh�6$6uB�:�17A�43ݙF�ͅ178,43:Y6�9 W�u 2r�K(S) R�V On�K ns F|&430-Gev/C To 10 �!J�K0Z�a�>}š2�x 1978) [Er��m-ibid.�$ '5��D78\ ERRAT,41,1835.;>�PR�#2136���� �66�> >TV5E�l�1t1B��}\6452m�Z 1017>� 901:�:5��W.~��.5��~Devin�%F.~GrosE�J�Jn.Ue��ac$deuteron u�8�Rss"?at{�ν�>�M� 4�"c�2n)�75,#6��"� �5!�2�"H~{� �globa*lor;of�c��l'�D1�Z�#5J�1�976�F�G R�F� >�T)ie����OmH�Y(Pi0 Mu+ Mu-�9 �>�0 2�� 1) [%� JETP+N �( 1F�; 102,29:� y�na%����S"�5�0Z�ȩ�� (20904>�1� )�enJZ� 7&Ø�4%��*DSELECT THE LAYOUT �%� � ?�:Xr�- U�oz-H%% See aipguide.pdf���-�˲�- \�{[\0,fi�+%f-i�e�camer0ady8s� ,�; < w�X you49aM�:ohpaper E�? edhe�JgsEnt�F/)�-%^A� �.�%+� f6T�@ if n�i 3�{ai�c,@layoutstyle{6x9} �e4%% FRONTMATTER�<\31��tiy����te X,r�pi���}*7�P�is}{ap�={D$*�a�!�I*Ù bę.Й&ę�b�fa"����5�HsE"�|� bary��A*ch9�ed as�Td�.�*S5�, $^��Bpla/2! in��Xk�h)&ܕh]+tetra�� pent �mr�Je 1h.�*�P ?�-�"�8�"��,�H�H�8cF&T��6aE��2 ��#d�!=*'t*�e'o3K&Z�l�y�= ��I;%u�.�=�@b � W�2-m1�GKK �4Y2�ԪP�� MAIN�[�iV %f�ach�A�Elb� [�]!�m a�r!�t-toQmae�scopic8Bp��!�I�icA��Ar��sw!� 0i�� :;#or-� �c]�%�aI�%���uos3eye�dnV�.�VB�"w [BSE% .�j� jB;&\-=As]!;t"� ���ch as�B-�2ar,�, etc.��ac&�T� "�s4�n��a:")C6W�,�2pE�Vask�S qual����or�6e�$q�[,7��Dx36cBSE!,wo)�"�\�:}AiZ a)� slLt oa��em����"�A7^�a�]"�n N7�tt!B+�ҍ nc� g=�R~. 2�7dȁ� F��.E|O7 �=SM�!�� ~Y��|!4*gw�g��?[ ={^w��i*��A*�!fo&��J� �i�f{ E{&8s)�c��i8C z�5ɺo�$�pai�} opposgJto), #\�)�gi�FF��vl�v�-)Q�AF 6�=pE �=�G� uD�H��k�o*hz�U�@ �$:� H�6we ado� inbo2d� H�EG0�xbd@"�=B���%�2_\n�X\N�\�X - f_C �=int_q^\L��\! {\!GH�\;*œ�free}�� �<_�y��6Y\M(W\)iSU\ .7;2$~ � BSEm�k&�C�F p_\pѐp P"��� =��pm M�eVK%] �Fa,GA�toRo�c ��$�\pmj~:f�j,��*���qU��D�G%2 -2z� O%D��# :a�L� _�� $%� -�$�he�logE�"� *x M���>�s�L�Fly2$f_C$ �<BSE�#� �"%'y �:7 =9F4}{3}$ -0 �?_(2(UJ. �&4�Nu:���FoI���T"�tai�m� of R>��199`..�V6aA.� m ��]AX�C�R.�] tab:� YV 2o�EP%E%�erUr seem�`��a���>�;T�=��ZA;��j]�%�g! �� moun�;^h+>L%< H.G-$� !$~�= R�*�jt�}[h�[� �P{ll|c8|cc|c} \multico�mAY l|}{ inpu�F�u}��.) 5}{c))�} & 2 2 $0^+$�} B*(1}{c}{ $1^-2)\\ \hE<�G$ $[{?TSZ]SD2^2 m_�Z&�jK$�Kr(7S,\�E�Rm�B*)S �D Fud=qs  S� 0.4�R93@S 0.13�R��or293�R82'r191 r\\ % 0�q 0.82.SJ 49 :&>7�S7M96>0.S79^� 9968 �] 0.89�Q] >w}��3 es (Ҝ Eō�:�9��Q��~i.� ��#���^:"P.�i�nf+int:< 6%4ach unambiguou�rD�s��.��R��, �CeyT�AL���-� 6�-I��9&*z? sY �"ړheT =.35�B�:]::*=a \quad �:uu8B�fig��Y�g.Ip$ud��/p �>�K"Bl$sn[�'-/��e $-0.3�Y��^2 < Q1.5zZ.Z�4ar5�m�.)� -aa� eZW�Anow"� _ ��k�y�me��-s��� p6Jto er��(�-)E�{*�m6)�O%�m�Ja�*>XE����DXn8_B�, at leOc�a�}2�3!�d .�%�:.�f� Om �HsV���ra'M�_zLF$S�$Q-bsee*�b:�. ��!��a�u�]to�G *�� a� $[M^2/(A|,+ M^2)]^{1.4,~A"�ally "�Pb��6� U/N/Q&yq�F$1/�gk%jQj4]u�r_4`S.7&�\$,k)�8\%�pX$r�266eRf]QT�?sɔs-�IsAHM�r s�`at�HP  �0nE���T�I�sA�ear">�2sHau �&� w����փ , ev6��_1-) � 2t:p*� 2�::1 �e�@�N:�oz�%�� `s�je.?� s�Xre�F!rein), �Jld� n7Vt�rd��h$v�w��15�Auld � ( $e*�co:�. !So$�l*K&E ��!g3sga�B�bng"tKtwo�c��NQwoI&�F%m,6���m�J�CVLe�6� . G��"���I��o b ���&*�-3@( $(qq)$-$(\h:ine{qq}Fpt�To 9�=deam�a"4 p�id��6�ͯ�Q?��!2��emwo&%�>)a+E�� �Gion, ؽr!���'I�tm��  }d SMn��hemma�� R0.r�8�q�$�6TV.1� ^��gA!f2N*z� NmHNA C, cf.,Eʼn25J&Rkn [h]S .� cc} � 2l��� �O $_f$�Tet927�}{EO' Ɔ)�T}��+q̈́ �]m JzI�,#Vv|}{I�, V&}�K>J4 \\ & & & $M$ & $E_BM & :D\\ \hline 0.821 & ;& 1.06857433 , 311 fR & X 1.60 ;041 \\x1.10 �$\frac12$,  s42 �959 329v� 1.62�0.297;853K�\\ { 0, 1��1.55 0.605 1.84 �35�x88)632; 2.09� 0.10� 5{6 )  } �03 �) 1.37� 0.'v|%}&�---%{ p.96 5p>{290%035�1.615033v� 1.523 0.12CF� z�:z340.3!z) 076~w77;x5 2xt \end{tabular} \caption{\label�i:tetrapenta} Bound state masses and binding energies in GeV of two scalar constituents in ladder approximay. The X'Cdich$that these yLs are not allowed by  Bose �istics~0he diquarks (0color-tripletQ8 anti-symmetric�+ �ces).}5,Lle} Our results for�F e1�Hgiven in Table~\ref>c . T�\sugges!pat simple gluon-exchange does%4provide enough1��%�)  dominat): a $(qq)$-\\overline{q})$ configura)�8Furthermore, if9_� important>th, we would also expect addiWal1�in)J,eson sector,particA� a sEQ< nonet. IdentifA/ion-�se.^P -likUELhowever will be diffat, since�$y mix with A moleculA�,nd ordinary ^�s. \begin{theacknowledgments} % %I-�toA��ank Reinhard Alkofer, Arne Hoell, Andreas Krassnigg, %Craig Roberts, Eric Swanson, and Peter Tandy A�7 missA�� !>!�$probably w�rto�!� own!��4lectromagnetic� pert� :�aeU�409008^� 6�zA�4hh} CB�B�� ��-facto��neutral )�width!Q Nucly�AI� 605}, 475%�65Rh�J9408233>QHE�J 6�i� emf}ɶ6�9bh9ee�>��zU ( photon ver�u k�,charge radiuE.N�61A�45202�l0�1�9910033]:)�l ���2000sk��pi, K+�� K0 e:S!� )�f�A�a�04Z�0005015>�� ȹ4Jaffe�3sg�L.~%j$F.~Wilczeke�D� !�exoaso roscopyA`2�Lety�9!�232003�35�Mg0307341>�Mg  �\h6� � docu�~ input[ �� %\,class{elsartA�Pusepackage{epsfig} %.� icx> amssymb} 0� d >�{00 iIP8Conques} {\it I (is same pla5 acheri/pupil� stor� top��y don't" J.Mod�JE��8) 147.M Isospin01�< �a� in Heavy-* Colli� at�e�iEP<}, Eds. Bao-An L(8W. Udo Schr\"od� Nova� Publis�(�(, New York).�8DitoroEPJA13} M5� VJ�5�0 S.Maccarone!�,Cabibbo, Eur) J. A1X 2)�i��GR98}��u�� P.G.#.��G%�0', E.G.Lanza4�W6�64I�$9) 1c-446c.�HamamotEY0�aM��a60E�9) 031369Mueller�^2� M\"u,, B.D.Serot,:���5) 2072.�e)PRL86A�%[F75�}�i�86 %�) 4492^ G`8!� �8.Chomaz, S.Ayik2� W8W!�2276�Marguero�a�J.�]\Ų�a��O3a�1606��PR389} P�}� J.Randrup9p. 389�4) 262�(HandzyPRL75~ O. I6e^.}! y�� �|!�9129BaE24�.A.T.Su�h!�Z�R C64v a�) 054604.�Danielq 85} P. ewicz:�8�%1) 3682�@WaleckaAP83} J.D. Yni�(N.Y.) 8[ 4) 46�E�ANP16�U�M�� emAdvanc , ear%�,ics} Vol. 16a��� J.M.Negel� E.VogM lenum��, 1986. �*�I��b�A�B�6e�7) 5152QDFurnstNPA706} R.J. ahl6j70iK 2) 82� MadlandC41AOG. � (J.B\"urveniA J.AauhnA�2�!5)� A7; 4) 52 @LeePRC57} C.H.LeedX W G.QŬG.E.BrowaqQ� C5բ 3488.p Jong XF.de �rLensk� F2E092� Hofmane�4} F. �;eil.R��e q 34314 .�(DalenarX040} N.E.van ]HFuchs, A.Faessler, i��Re*�@Dirac-Brueckner A� k Aic%�A� Matter} B7 70706�v s.�"�4��^�G.Fabbri.�^%,��Bc�66$EOS-NONRELr<< �%2A:� iso} U.  W.Z2 "EOS�b�", in O c s pp. 1-34� refs.6 2� 38��B. �Fikm�brocini.T C3� 8� 012hAkmal��8} A.QDR.Pandharipande, D��avenha���P]9]8��&~Lom��%��~]�� �zr %In�s %�t t ��U-280]-� 5�p. 28{ s.g� L+ ]�5�� ) �222>Fantoni 7� a�SarsaaE�mid�� X 8J1) 1811 9��-:-Y�A�7�l������I��N��%9YV�Y��Wڥ%z�DLuiPRC70} Y.-W.Luia�(H.Youngbloo� Toki� ~.Clark� Jo� 1� C70�44302�"�25A��� Wojc* OI B325v � 12Nl PLB426} *�(A.Larionov,�.[42�{6 ra���"�J.6 l 6#�ف�282�p$e��"i!flZielinska Pfab\'e, H.H.Wolt�*�70"6� "�~30A ^-9 ;2�730_4) 326#ћI. aci,^ /&i�-a& � m & astroJ!al�l�'s" R� 35-81�� f� Zu�10� � �. e �&�24605.,SjoebergNPA2�O.Sj\"o602l1� 511eo36�ݳ�q C6922g .�"{064:�La��A.M�e2�3�66F�4BecchettiPR182��D., G.Wb enless�6v. 182A 196�192)HodoptdE.HodgI(5> A�eon Opt%$4Model}, World\tific�94."�cie�3K R�5� a�62� u Rizz� 7��J.A�Nu���  ;eݡ�Z ^GalO�C. !FF.BZ$�(S.Das GuptaV=��199342t��59a� , Diploma!Tsis��7);\\ �A��V 5��9) 810.HNuovo CiYo A111f8) 865. 2Dapienz�7!�5�j��&����-+PR1a�Gb= R� i�� 8���(%:��"� RPA_z�$��o ��* -=7�[�9=���%����� ��C��%M vJ2E�5F��4 %Neutron-Rich�{H)� Gregoira94� Ch� ��� &a�8x12'Bonasera�%3$4, F.Gulminelli�&ol7!is�Q�4X!�2e� PPNP�*�`RbAL& � sBr�!���& >�65$FAST-FLOWS�`6u � �M%� .N�N?A�ᱲO�� BoalRMP62�H.��TK.Gelbke, B.K.Jenning�ev&$ 6� 0) 56�Q$ARNPS4("a$C[S�t<"z [I�art.Sci.j 2) 72L,ArdouinIJPE6� ,$o�# &#36 Wied` PR319�A.�(Heinz�.p. 31"�1���KheS 90� -W.x)f%��f*�?9�3) 16��P� 8�`m�v�C6�"�"1>O�ria}http://www.nscl.msu.edu/ria/index.php� +(phy.anl.gov* :a 29}L9) �/% �6�72�S3) 80K5G�L� W.G.d ^�"A� 2114.�<+3� K�E�6�]�9SC�1) 782Y7Y^� C4�1R46�Kunde�#0} G.J.^II@�1�~>� elderloosR5f!Ja� vW *#$3082�Lednicky?73�A�L.Lyub�*� B.Erazmu� D.Nouai� �B37�] 6) 32�VolIae7�)guS�itk nd N.Xu2� g7i�766.�G� 4.XN# LB44� �6cPrattPRLuF.WangeBUQUO JiH3132�$GourioEPJ7�� :�2�(� 0) 2��}�Gj�374!� :L���� A67�2 26� ;�7bJE�� � �R0>�Kooni!yA� S.E. �� @BI�7!�2` 1j53� 9}5EZ 84) 1219;k��1�'' D3 *6) 6�(X�-�%�M.B.Tsa[:� *�23���� .M.j ** A�*� *� 61�%�:it �v?]� �7}~z&� .+�� *�%146� ScaloneaX61}L.  { D %G-�46�F��9) 2�}�J"C.B��"*�2�*�11�9������!z.97n200[���� 7*��6Y|E'62%92%Vs%ba 9  �)2%dL78.d2.A�Z.Z.Req�O)�7o 1642x�8b� *�.6�766L+LB4�w&��6� � �.BAZ:>!Tap 4�� P.TaR�2. 51901R.YStoeck;-137V t\"o�� iner��L3���t2�� �6� B+PQ�L�͞2�6� DasgPTL2uWestf"$�Today Q3�$.� � SCI2JP.�� acey�� Lyn�{Cn"29� }-592*r2�&��RHIC-v2*�I�6P.Lev\&%�-� ] 34904;iD.Molna)�S*RP� I)91� =92301=" M.Gyulass � �-� @B4�49) 45>P.KolbeSollfr7EaQU:w !�a �:R-96 )u PLB11#2uP G.Odyniec6�15�.1�&�&&>i���� L�12:!89) 502&��OlliPRDAa J.Y.traul.� DMSA�6 ��3:�,268 )%372�r> 2�.� C59�C� a�%8 U.Mo�764r!�6466)Gaitanosc22} T.N �+&*!e*�+ 6� 1 k_6�%)�7'.-A!�, ��QzS.J.v6� 7� �)4=1�� ^N1�M8aFI�&�>q&0B0�/� E C5�&� 66@$�0�N2R"i�205.R LB5!�"2V�.�=� %�"�%8 �V�215h ePh.D.ThkA.�L�4$Q�c R. Machle6x' C4�6702�(R� C49 2�o��0/Z E!���!��� 0�L %�3 �b1}aal6@ �2.6� 4�t1:�")C� M� khash2�/2Z%���*�"26iDjrg�21A|�D.Gogny2�2�< 1568)6n.�Virgini ��V�(La MoA!F.Seb#� Fari�"B.Remaud�A.Schuc6�<��66V twingo��&E(TWINGO Code�3Uu0, Univ.of Cae�1$July 1996 ���͡Ku%G��.b63i�!f7c i6z�� Pak1T8PakF�iC"  10222.' Pak2�C2�bred}� re�JimpactcMameXFis defin�;s $b_{5H\equiv b/b_{max}$ wVI ! is ;umg  P@&Ci.6�r�(\' V\'5.nf"'(GiessenRPP5�� Bl\"�&�-Koci�Ѧc=.7�� 5��J.� MagesPRC6�3�6�Or&C(?ap C6�0) 02>�6�M9?JA. icR�6J1d 333c!��#�#&�!j: 62d ��#�#�S����4�"Z5w-��HH�f.3 PLB2�,AE$& urgi�&R�22�89) 232~.[�.[f� 2�%�79�9:� ��code:*&� �z����2�c�7�, ���V�:�5ń�>���Z�B9c �� Sami�-�.0Z�' A33�8�!W9+�an�<%m~!^��-��"* UL.�64� �34ZG7�G7G337�Eri�-�-��9�ZY> ɩ�!6`;t9�f RCA�"e DR)_%%Z�*_6E m ) M���Ger�1E. ۅ�e�2�116�& Mart�C62�K D?iX*Z2B�asi�9a�G�in�Emi��'5�u8StefaniniZFA351@ A.�&� 5 K�62^a�a�5�� *C2922�Montoy�1� C.P.  ]N5�f072LLukasikm�J. �5# Cy�196�Lefor]7!�T. D.�69�36xGingrab�/ F��".) 061B'EvI65�(D~C466�"Bocag/(6+F. F2�20�:#%Col �7!�B.��a�6� UvPaganK�8A. F2�&�?3313FF73�jF73� 06@Dempse�i 54} J.F. ��5� 6) 1:�O PoggC!(G.,:k:&-9��Milazz 50�G.M. 6�i�%{J6[ 6�0FI._*l466PlagnoT`E. 6����$J6H&2RLaroch)J��2�<RNVc5c>�obotk> �� L.G. NLy�216#�CaKHR� >�f��z��31603:���b9"6"F�)�9)�zB(Ram{#�> ^E8i�716�Soulioti�O5-KG� Velselsky'3��\!*`! �HE�: 2�Z*JA00} Feng-Shou F� C N7Ii>FJLiuA�426} Jian-Ye Li&�2�2�6 A u�-�CB !� V�)C�+6� On�# A. On:�i5 .�16BkͰ��. 6�nB56�72�Botvine09��S. 6I �&c34:�!o5G� *N�Q.�&�d<.�54�3�92m��0�"G. *�  C *0272]!& � 5��2|6�89�N�2V$BrosaPR197, A� Grossm�4 A. MO�9� 19V"au6; Viol�31N�3%48�552�H�+zG7�-J.D.z47�87) 312O(w[Z } We"�X call�$$r-r1$-coraon plot'a� W�QB��d;2vW�J�Q SharmaAP2�D M.M. � $A.Nagaraja5=P.R�$[3E�(NY) 0\��10,\\ � Lalaz��� W E�Y�3ambhir65A6�#s ) :�*�67} L 33�9�M�N2�VP*�VJ�CB�?N�{ �� .vKoJPG22#l+�G.�#J�!� G2���66zDeli) fior#&;ZH �4�h456�THorowitz AvA?�K.Wehrb�:�53wFA1) 66 9?�<P��Qj�<MU-:�< Vret<�cD.,� .�R.Behns�* W.Poeschl�@Q�.I 6� 7) 86y$M��Z.Y.Ma �\&�PH�2$M.L'Huilli�S=v*�3>�U�'R]AP2�]� �%< �qfkJ4 z173'6�# .���\N&o 6�*��SA�YO`"OV� Q*uS*{B�\Nikolau��%B� �Ho!�Q"�V%-e *�%1752JW!�7bR.\W% $J.J.Rusnak:�2��7�%46 TCNPP2*�WS�� Comm*%9� +0) A2N�.�5v4� �=K  D�1G�U�5�:�&!�3.� �!*�F*�2q7f"�442}Buerva5e+:�X2�&�X� P�C�r]I2443086rIP X`R�P64 % ?X.!$,�326,R� .T2HyK5j��YCma�X�6��Y�A2]m O� e}Mm?nelmc`vopoint"wb %m�Ks...}*�X.�n40600.�(Sch{y-1g� H.Mucnr>�_1�]���"���Z���/L.�aej�C��243:�- ogut��50! IC.E.P�"650 A86��eNPA399J6yZA3�@ 1983�j56S/B�WPRC�C��WMathi�_&�W��5�W�)3� 8 380a55F�W�3�e�BR�i�rX h6IPeCPl.C0DegrootRelKin�"R�+G�A. V[Le�ChhWeert,b-Re*N[KionJIia�W -Hol]4 Amsterdam 1986�akimNCp] !�.�L%.7XW2�&� ��R&� J.Koni� ��]��&G54�y��d- A@S�d%jM.*�SE��M=���:MCV�RSVYKfVV % *:UVU4Dit�}21/WՅA.DragdeEV�Lav�] XDepend�v" CritvCQ2{ -Dec&'t D|gie\arXiV"�n�06� Subn�C} ``It,&zto pu�zh.�p� 9 nRat subnuc�R} h�Eonp$firm a foo�H possible +| onlyR f�R , bu�asOinterpreO(terrestrial�zrcOs)�h�,oac&rbea*obF''^] %��~"LKu�qQ live�K-  star�eDNATO ASI Series C�K.4�5) p.52r(`A�5AB`I���B26h�TC6JSJ.Piekar�e�� X .�!6�y��(.� Curvature��j�j� non-2@cx�yk��con"ufA� $K_{sym}$A�ajneg�ve!|it has �.IK $-\pi^2�j _0/(Mk_F)"/Xi%�+\order $\sim -30 MeV$. I��2� �Hit becomes slightlyA�iEidu�zYk�z}� e5on Ii�t.B Rhos0soeN�z in Fig.4 �}aFfu%k&Vwith res]q!8�@$\alpha=0$ dashedM. T�is.�Kr%�, wVfix�xa2�kTtot"~calar�*�%�!Sgma$ f�l6�(first�0"(Eq.(6)) is �5\$N/Z$5Ft.' Hube�:�,Web2 M.�igw0u  C=89Z48� ��SEj�V4} G.,HZondjk"�0.� 264s+j`2:N f'y'�6y'.J.Si:EB12�j�2;Jaqam8%29:'R. �SZ.Mekji;L.Zami6� C�D1D@ 2067�y�I��h*�?�`&�4�7 *Isov} Of' rse�can~oxq.�K $NM$*Ly reg&,�{higher6�n ies,E�D a different struc�� o�ru�Jle � sY�. Hm some�p�?h{(re even pre9o( quite exciœ�.�NKyJo(a��'tr{) �oscil� ons. UL~tunat�at�Years x ��� exp���w�`��.&Jamin�i�M. �MahauxjRochuQ��2 C2�X�j62022� E�� 2U*�,�+$ 352rKozac�$x0R. *� Hi0I146� u� ;��"ZK.�50�00) 666�lu�7;J."��*�/!01R8/M bidem.�C.�H\�3*{��B BBib_r]�.pL�U��S% �S�SOxford �S, pag�S*�^HAbrikosovRPP22}A.A.� I\halatnikRRe.E6�_59l].���U%Z�V%(vV�� FV% 2� *Il V%nV9�3^�`e�T��[A"�v2 phi� has self-� }WsUastead_$f_\s� {7�$5�{dV}{d� S}$23e)�~ j~ 8!�A|P2�.*�s305�*Y��5� MatsuiNP3 23t198R96�#�bRSb�*� .C-�._!86}R_R�9 ���I�>�2 NiksicA�6 �T N� *�64302*Z 9T�0Pa-`y6T�(a&24310TCaill$=96}J.C. �GabEe\,J.LabarsoqueD2L9"�Bb9m���b2�JcJl4*�N�,� �oŏ"�:lj3�� LMU02}S. K�� ffprivate ��un�e'�mx݄�c�!V ear �p 2�M|Fg� P�%� LMU-� ik Sek{Myh�C9,�b 6b �,�EH��]�z6�]%�]%��]��hɥ�(�.V�VA �7� a"� A"O #��!29c������-�%��� � �F FRBREL-DYNbN=��2_BI PW.U roe�(�w) %Z 0��Lj�|b8p.�|�b �b.�2UFriedaJ_3^1B. Rw3`1�502Av��Haa^9�-B.�DXM Malflie.RKL�-�166�M��U#@��G, 5. *�r��[ B1a 7) 4:6>i� 4*!iRY>r�t�M�&x$1896 �� ��V 8�N�}��fxN�uY��k�kORyvg�.&�~6g*�;46�SLattim�LE �(U�5�!�. ? 19�%>�U0SumiyashiAPJ4�[K.� �p, A[m�+4Z�%70�U�M�PRLa.#J"JL.bu.�*� � mG�H560,Engiv,8x8L.  &J�<7�,�266�/EL29"�z!2E 2�8�<55�o%Sce�r.b�APPB30� a�*� Actad.P�1��� 27�5G7� �v�@�w�l�m�*�4258� Y�Κp+�k�%b��6$E�#E�49�?WBa�0�0�2N�2}٦�UQ.Jr�L�r,&X'5�i$%>kb� "8Ba>.) *�9cr:��  %� A֍��&@( MNer%   .�*�8>�W:�P6*'>�PUma<�z V.S.Uma M�varJk7EB8) 92��u��YB��"�g "�O9@�.BD.a�"���A.X�]:"!w�#�E)J�J� dD[(6�� =D(A e"��ow���6=f�J_�H&�>�F�$Ji�E*!:1FBiNBy��5.�3:���6�48f-B\"ol���:*��.�6�R�$��rR)Q)Z�N)A* &S�X<�D$�T� �"2D�U�ɮv&I$40V�2_�!\���"JB`+, Z(]+%%F0?��R�_+�26]d.�F]+EF� 2}24Q����66�\�lj4�V��\ϭ5+ 3)" V*�KPh"�N � ���XD3,�*2e�{X}�!6�-2fX%vgXFg��|&5WR>�,�K���X�2R�0 4�)]*�084.�GievSa�Y� *S%.g3� *0�.gE�� C��.P.�B���I�DSZ# J.Ai#Ain2�A5&i 586�fA^�*G��#-IV>^9�D��]�].P9v�]�B�]% ��]kRZ�]QL��]% D�]7&Af-<vM�N�]%N�]aq�5�I�F�]% J�]A�6bjZ�]9=]�L]@�\PR�B6�WYH���UV�%�q� .,yF� 6PIO^��Uu&��[.%e�}h(0our frameworkO= is ap0qeru6�(Fq�'( should be �$0what included�c?spoS�B�)% ls. ��,ceo$is6�'was}( realized �+a��$vi�=Bc stud %�~"X ,w?�<%spi)s ��>�moB>um&(2E()R)force��)�e*" &��*us�y�� ePupa!� triz�%�� supra-n�ul�(��0@ pC?unc�YnW@er�I+e�&��)�0l�[ �s�&*�)earv7"z,e��c-nd� ticl�-duN�.� FOPId(Reisdorf ($B�llabo�&�N� !��p$�vy��A�62V%,iso-stopping:,*v$Bormio04} ��.w  G.FeriP�*X.�B�1Uin�'me��-�R0w, K/v. 2041�;c. XLII�<ernE al W  Me�.On �8e&k�, � (Italy�d2p& � 96�"p*g�*�. B59"`g209.hG�4} %F.vG (Ax.�3�f�GH�nv4 B. d zX2�4�d�dA�Rv takenc� B. j, Y�Kim Leifels,6�c:� GSI-י� ��B PYG "@ .� ,N.El-Shabshi�5&2�P240L8y��;%��Z�%d"��Bj� %\*垆Ϟ%��_\setcou�1{page}{1vM�ion{Int E }�i%�re/{Chap:\arabic{ ?}:a�A0 A key quesSa��&�}&�+�/i�n"k!���e $EOS$�J.�,4ar 3,($ANM$) awayI��c�m���ߛ"l$n�o��at low�TC$�t�� ��"�2,p"�,�Nil�k�in 4-[O-�crucial�f�novae��s�~lta{�4.v�%doxLtzw�we 3- planxu9�on%Ethird g��B fa�3� rad2�3�,r basic� -5E�%)�isԜ ll extremS-poor. E"<����%�ob�(ly tuned tob�G�� aroundF���anysapo�-�.be0.( dangerous.0Esc���-r˝�dF5a �F$NN$ .�, &0�or �%M�1�s,.d2 �1tb�� show a ra=�Het���. ons.[Han ex�e�&�2/�fig:e�3�/ol�"e"� d&�6('� )�'s�G�?/a��p s?4�=xEm7ic%0<} (top): $SKM^*$_ "��(:,K2��T, $SLy230b~(SLy4)$ 9Ly�$27, 35 �&��$BPAL32$'�"4 242, C55,ߟ. � �3:4(bottom)!=rejJ%V;4V3pot]�!�"� 2/5�3!H thre&� tc  .J. We�o0cur�6uc-L�����ޟ _0$,I� � dz1ceiOdJ� valuA� slopndo!�es in���l&a�ly�ĝ�G 2 . Moreov`�˳a)@�5a� well�8 n ``��|�=''0 � �!;a� @ !2N ��c�F%x}s�8}20JB� U e5s�6KoU*he�^r2!!onsequѡ1�split 4�2��/protonJ �m�,�)�%�es)����=E�{�!Z9 e$+L3y�2�w �stimu��ng per�2u�&+d� �6�n@�"�ł� ew R��E�,Beam ($RIB$)� a!�evant%7vitP���arT S��-i<� dega$of freedomAt& re�, ��cD"� I7,I N01,2��. 84w!. view�try!#a; in d�M�mos�te!�!��y ��LA� �5E�ed�observ�a�e w��fòF}!r=�@ad�e�KAh+5]=E,-�M�hOL i ��t��e�<"�, �!(�!j�0genuine pure 2�i�sA!Q�!�"p5�/�tSJ)on �xeo�;we looka�Cq��y��a�-��ݚin =:P�?e��%o�L�� !�߰.�of exot"���<lk ��6m��O" ;� monopoleAˁci�jp.��� 9@�B!� thoroughl�� alys�P iscub9y6cA�-�1�� gy-���eLane Poѷat�s �ed@5si� seenN���܅��z��e}8���er��@epsfysize=6.cm %\ Q;{8box{iso1.ps}} \q� s*[�:8e=0.45]{ch1_fig, "��Eo2;^9. Top:5�G?(up),�ic  (�% ); B:N�A���f� � ��(vskip-1.0cm 1& 2 rpa}!� devo!� �e� 5�p"�  �&� y, i.e.r�&�4-Gas Phase Tra)�a�in */��,.�S_ taA9rmom�al ���m�R)� (vs.UL!�8 s)i��� &con!Z .,i:=9y  s �& tX�� � A;A�maximum2;�aam�Ron�:�� go�loG}Ǻ��ͤ�mdir��a ``mi&angle'' ���s on mpQ@ =� U}� =�g����We pas_Sg?a�`?�� O grea���|ce�� it lead�Ba�space-ti|�Y' �u%`leq� mode �S ris:?oT��s<�[extCd ! odal�ary. Ch2'c�����As��� mus�?V? ved.!rȋ�< @=�Ac�>�F�1 � i �� aC*p A st� �d a�,H2զ in�r�@: �? tyEɵ� EE�EV ed n�w.�<we-=%Hsam�`�5�5���]E>+ ir��eX&* /miu>�"V .�<���a�@AEq�!r- �=}��ha"l �D2�} (5@) betw�DAEl���gas ph� .�0,�/.6, 8,"6�$7,�i�. SA�X>h��%� w fe%�1" �-�9�is�in)�clu�GAT�W�exp�[}Xta&�� �C��r?�I8quf�!�, Y��)�be�pe� F������dilut���m�ll۽!| *E � . z� Y�S8�l�W&� a|��is1  aq� sta� bothr5��` %��Jsm? q�S As�  C�Ci� y b*�U5&��ric/D��A"t�eMGssu0atL8o஡J�6. �)D1��(is mainly g�����qofc�@�I�G b-�Zu�W����.|5�qZH&ک,�4,&N"85}L( we.�&5UI�u �8]� ( fa^D5,��g$ve flows) mG*p�}B�W� Wؾ!�y2��� �Z�(� 2p� T2y ��}�a� seve��*� �:;)�Q� �:T-%�on��on&w�, lXFZ, %Uve�C�Q�k��.>H�|cu�a&  �!?��� [���a$�-�R͟o+D�[��m ons " . :Hequɧ!,� ܱ#��y &[ILive2` wid>�WM|ic� sY,�[m.*MV"� F]"Iz 1 tested, t� c�E�!U �y�l���its��l,"M�-Hmodified� t��inM;u�Gd%�eP) of8 sign!�$$n/p$ aJh*�$m^*_n-p�E }\� at� b\HA ���Ly. 36- �2 ;9 ntinlIQ�s��A�ofar%�T�9(Gw�do�% 6 is�-1% ��F"P"* �VdrLȭTmean-�,���4 $15-20~AMeV$,�Wf/>�ym�}�msNy"ent�ro�$ above $10 Z���W� a�Z � �d�hpCKa%-Y s�> with�qq�t9���s. Onѿ newYtin�5T��n�Fa� Ad2�M� Fv A� � qH"�F��EUfac!~A !�� "�IJ�&s喭_�&; �Mex^OaT�P����:s,�L�9l-Nu> �(9�.  t!=aإ�to�-�`�s)a>�'a}mal��!RwQ%�ric$%G !Kgr�� out �8ng |o٩u� n !a"? kPescriK a�("C� �um�� � ��2�c� th�� i� tane6�� . Althoug Z)�b!had a�5 succ`�a mn`)pra�|�!�G2#>ia[ofMongly !4��ngM* ��s, �a�d );sri9s I1e�i�s"�� ��|y�A�tempertb��y%�NJ�"WS"� �)"aN�Z� ��w>��B�~*��.m'�  "���"�^�nyTa� da�) al ``Doorc# Step  owar?)�. 6mjEEU�. 2-3��rib���Zq�q\ 2��O��&n�P:"� �!ys�W�)��,� s�qhd� ��)n} !�dynW �$QHD$ (Q�$um-Hadro-D� )A5� "D{T��j  M� ful �mpDT q�p %��M�A�2�piqQ,� ilibriu\�*�*�*� 'G!)i+ ic level<*ug,a8=g l8t is-Y��a=pX�ur�n�Q� &# � A��B�� ($�%n -JN#eg^� �oryO �aim�0a��nspar!G conn!�o&f ,��vWFkE�* "�toŗ����%e����o�mWe K&sJ�> QE�i �v�6�W)�)b�tu��F`��  new 2N�Ve[Mreveal�dJco�! �P� @!H�s. .� �%1A*m�!��lr" Z1x�an�Bv  ���[a_0(bS]$�,��#�r)e!�usual)�a.�!� ies \cite*�:2�� A��� *�% �M }�t��� Fock� q 5�noJ 7 re< ly &D!�lu!>%Q�W! �"8 706,�a�54����1&$M5k�b�r�Q-+ W�)&W!im��fW�Y ��ach�$� N�1A3 an $"*(~ ]I~dory$ �2�$�]y~ Fu� onal1, ��.ja�� m��A�ly2O��1�W"�'s�s��!Q3 task!c A�H2 is j�a��o�N��4����l�Ks�to it� In 2�ɜ��!�Q&ɍ�d���VlEq���mea�IWh %ar�!��E% "�2�(m&&*�qP�|��ѩ�is :��c�����sBg%5�! ��n� <2"�,��a�e�*J!i!�`��hip"Wy�;Tg �6��Q�5a�i]*:=� 2�%��)6�y-�!"; !�d��\,ch�!� �a=imiE��:G�*B�oXal �#"we�er�+f�I�Q* ' �zaX ��g'�$� a clos���e 5{."�SB��,a�it!>�v5�!�e�1 �S�D'alway2%ha8f�`we�sstresqRM��s2a�is� "4I}%yU$. ��f&a6&>*8N($RMF$) 7x3ʥ�3 llo�  � �5often%�&% -k�s1�*�M?g.� I�"�, -Hartree-Ŗ($DBH�2�ir��toF�,[ G C57,"�@,.�?,Da*�� Ac *�%*��m؅�6� ��� y *$m"F��Mr"+��}�� � cal��� (&5R>�2���X/%E.�. With�E�6A�� �!��� qualD s1� ��"] �Ya(� � E�"r �bQ`�  pric"payA�!i B���?��/<�%��+e a,"� se� 1vd�1� �&a S8weU�-�m �(g5�1$D)�m�4�D,&�) ,͡ �be &�at *� &=v�a g1e:� +�e�sis!�� P f��9i�+��p�o �+  �& c�* >�  ,� An�outtcAW.���%� L%)�� �s, �_�7�#��B� E4influenca���]way�(%�z&M� (*� \,&�  � )* !�*9qA���ll oppew�dsi"J for a phe�ynolog1'dT��9�*!Qthtfu&pmM)�In 6 �E`� "�=^y�"m &�!� � 6� (O F�g��@�6J( �xUaxar�<�����6(di*& � ��� agfne�2AX�%:*�M;���jJ  �^ �&��l.�����<6 s1"A��Y�Q4� 8on�&ff M�a%� E play"2 iF�m\��6�s. a�*� $``mirror''��ON��g-z�q7�ey�c�'/y��>�%�7 mi�e �al -;Rmq�glay� ��=)� ibg�h:�!���"� D�W�.-� -؁8"�� a:" 9�%z)�Jg!a �t.%�P"� ���E����f�6A�e�� �e"o��)4�>��smo�%�#���5� O2A(a6? [. Im!�``�+''m"�"�"-p13]�Qz � �re �cn. ��d��!�Y a��>�(&N\"o)0E��2")c alreadyh w�:�pa} a FuZ,C��R.��4 an al$�11 wav.q�-5� ng sAs. "�#W �� HeavB#($HIC$)qw$AGeV$ �m� gk �aren�i>e:^;�n2y r'�%��n��o�\ n�a\n ?o29%�n-ZumMU� p�`s  Cd$.� 1�I����ll$ -$a"{ �4�!+c�%A�E�lx S(� �&�1*�>��Q � ������\1 ���%1�2 إ�3�Y. r&3,A�> a4h�i2� ����6lA hanc�r:&�!Ea �&�n ���7��ng�Y���Fk "Bij e��6of a �/�#-).Lo�zFI �+%2$E�oe�Z�  � .� eu j"or.�f�(,�rged ���"� ��w���C�*"��%!����avP��}��R&*ae3��SlA2V3sa-type (����i%"i: P���$)h:lrlyX,s) �.��(h!��2�. V܅"�*� !�tok �"�(!^� Gto��0��Uy��le �)��n� 5��;cy�� ;�%Qs. Fin#/>�out} a"�out�6A�nd *sad���Z pai&al ��%x ?�ost9:.� !+Qcq�i &�-�� lowje��6�}  %�5 {rep_bib}��&cB J� clas���6��%\t/+enV s� nuovi m.�^$su 2pigrec��4 cubo %\newcom&{\[}{f82}{(2\pi)^3}} %A8��siA�dre:;Dqd}[1]{\left[ #1 \C]6; tond>:t:(:)%I.�itg d� \=b4d^3k f_{#1}(k)l��(grale di fn:�iB� E itg{n} #1F6p>6pi4pV4n g>6 en}{ r0{g(k,\Lambda)%N6�pF=z<pi>: %�D(length{\uni }{1cm!2:ZtauF\tau^ tg{\ 2� �BpC ^\p�v} 6LE�rozer>jr�rho_{_0%rhoA�V-a}{\td{ I�8} > A%a'!�i�a p�� e B:�enMqd{��tdM�1}{2}xEP}g^2 %-:+ � n^2+ p^2 �,0.5 + x0(x3):}umI�@ �x Y } !�6�newI�0mathcal{I}_#1 )d:�]�F*�FU9 {0} .�.�{S�mR "� :],*A -zy��c,�}  :�< �4G +In� "���%�y%� py5���% �*h.�#�al/t-v(%)=%�n-�ond�0 #_3 %-,%Iy��@ w/bolic���9� 6y�y)֌ $I 5�^3/$ = (N-Z)/A� �o��1�- $ {E�x \� A} (F)$:�L�<1# } {E:',I) = B) +bY ~ I^2. -�oE�;h $�>�s a"�j�$� #r���ic Paul��"A�=& a*2H?g �30&e  QI� EY6 �!�d . S"[�L!�b�8aO5e]D� w;4nue-.�s� du�lN �1Y� $F(u)$e , y $u.G/IM0$ link&� ��N> ilonQNͩ^^A52FIrM[3} + {C 2} ~ �,Q1kipotF3�1)=1$�e���.�7�a�!a�eX $C$0$A$C V{eq 32�0� � e $a_4$I� :�� -Weisz\"ai�m0ulad9)5 tZ ��Jz''a()�Ye�7`=A�or��, :�E�o&�*=�(I� many-bj�.?� mu��I3!bdur� &�"�L �bll`�3 ��(ata� aa��%�AD5��r�i95j! negl� up� k *#/-�)�of $5��_0$)~��u�q��wg,also exactly� evaluated to be of $4\%$ for any density. A traditional expansion to second order around normal density is used \cite{LopezNPA483,BaoNPA681,LiuboPRC65} \begin{equation} \epsilon_{sym} \equiv {E_{sym} \over A} (\rho) = a_4 + {L \over 3} ~\Big({{\rho - \rho_0} ,Big) + {K_{sj$over {18}}�B`^2 , \label{exp} \end{equ �tin terms of a slope parameter B� L \e�3 � � ({{d\epsi5}�{d%}}%)_�= _0} ~=~{3-/  P �( )�p!>�$simply relQ8xthe {\it symmetry pressure} $ ]= � }^2 :�/�$ at $ �H$, and a curvature j5�)"9 �^2%!%^2V'^2p }} !O:*9�cNa kind!��com�ibilia5DWe remark that our%0ent knowledgeBPthese basic propertieA !\`A1 are`s!EL, is still ve!|oor, seeV recn�analysis in ref.\cite{FurnstNPA706}%rrefs.9 rein. InA�4ticular we notY0 uncertainty �he�%!�2�Hof large importance�gstruc!� cali�c s. T%points,a0connec��rpos1m_tgetting a new insight from rea: data, w!/be �,ly discussed!!this re�. !� first men}some ee� side)�s on a5�effects!A�librium�S A�:24, observable�ie resp�v�to bulk IA)L monopolAtson!`%� medx0heavy nuclei IDYoshidaPRC58}. F!,a linear��Mu!t�2ea��, $I=a�we!�!�E� vari%�!�]�d�S ��4narray} \Deltam�((I) = - {{9a�_0^2}�� ��(vskip-1.0cm 1For�!�>�D shift!�have, af!|��algebra,1Oeur�Hqr!��D�[�b {d$� �$^2}} - 2 FU"]�[&>Z[Kp -6L]�|:Ecom-8ӉE.�@interplay betweenE �-"7 5�� CZ't a,� �" ore� on N,�7a.2case (M 6�general 2${�Ns cor� ond�a fixed E2u�fP$"�����s�0PrakashPRC32, 6}v:hR�,.�!�) � lso &U � he isobaa;!, )�th�is .� ��A�I�experi{a!�fW a� �Giant M��R�� ($GMR$) ��ch{ aM ic  $. ActuallyB� re� ��$approximat� m � higher� A^t1�5�s�� neglected)� o �=�R�M2Cœ sigZ!a�� is atuAconseque� of.��!�.e.efac�kae F'!�decreasA� with>wy. S or)to)�a ͜ �ide� k w �vAlicitly� infl�n �$L,��� $a}D? 0 a different 1�depend�M� potential>t�M+y a�gy  �, 2unb  $F(u)$F"�\sqrt{uh?49?61 35 Z.?u j+7 E6w428^2/(1+u)@100l+5 -5A�1S U  6�-�� choic� a�aN E<$$ behavior�Vin��8not arbitrary.  y�d�t?wide i rum To4 redie�sA��A�forces  isovector��nnel, as�he=detai��1res�PR�I$��treF`hrow (Bn�T) is typ� �(Skyrme-like �,L$QI9/��i��e��Mal��aches��realistZ N$�Cs �Wi8 >38,AkmalI,�aJar:n�Brueckner-Hartree-Fock ($BHF$) non~ iv }.�0BombaciPR242, 0C55,Lombiso} !� well in Rel�] SMea� ,eld ($RMF$), ZY.  Dirac-b�D�@Lee!7<.%O. Fina%mo�pulsi� h0ly parabolic,.1� fourthA, 1|"/<280,BaoPRL85}, 7� to!T-1T.��th!� bodyQB eit�ext�,d %� or&�al-6-v,Fantoni�7}!z-� to oN2�)< estT ions, Jong%NH,HofmannPRC64}, or %� �� aA�q�m icontribu^1:Lie,GrecoW 7}. Fix�a�sama�2�6H!* #" 2�i�2��Y always� ���r� I both�> f�>�. T�Ms) � �6�; arison)P .P e q�. finite@ 6�s%ar&e:Ueven at -�smk>� es�+re; AAefa> good.n�%of��!�direct5 &8  indic��s �7 ^ %n($N \not= Z$ �. A @ systema� studr!Bisospi��"X G� '�: $Sn$&topes�,uiPRC70} msa� reve��Q4!3 Y � :� � roid)�in"� Qy, �{Xgre� -a $stiff�'�xMJyF � &K ��� � Z!-ةkmodels.F 9> &o��;``rA�* '', &N �),�:va*k:@�1 u��,not trivial:^a&|�s� ;%R%a�l  ac;&�%�a softeE�-LE�StD of B�. It�f�42m to [�� g�� l1F�V���a"� '� %Cb/ @ :&aueC}&s6"@ = *� L� 1{ 9}�"-%�� &� n�l� ives� & \�� �10 v276b CD [=u} + �2}N �^$ Af5zi2in"�enh��A���1�F  Wnmb��&U the �on emis���e�8 dynamics, fastjticle�d col Xive flows. Moreover dueArL"D f7 s�F by neutro�nd�t�� aIsh���e��x ific� ic �͢���� *U Sectast�}�\subs# on{T.�A�A����ces} Si���"�� e���9Iresultsyno:U kine�Q�G 2w�Vau��i�3}, we wexp!Ia littlm�is��,gVpC � ly u!8)^l.�.�a �' }  ze� L �E%ABA J"���{f� ���Eu3} + {C22} ~ =m�\rh�_ ^skAM1�} � e��$ Z$,)�z.�, �b n by��:��_0}��-�B4w <[t_0 (1 + 2 x_0)� t_� 6} 3)~�^\alpha��] 2�+`{1���[t_2 (�!D5 x_2) - 3 t_1 x_1EBig( {Zpi&A�! ^{2/3}  1U.P1%P$ �> 0�AusualMUQPer��. ,.#EXe{�toU�I�91mo� um "c % LyonNPA62� S  e}ep�gg60"g26gDen0$J� &eq[%� �-�.)a�,�q text� bott��panel��s%.��c*� 5�fig:pot�6�%�N�I���E�2� z�&a �Z���:�.�4, $SIII$, $SG 0 $SKM^*$ (seeMK� neNPA33N�!)�AH ")k-AA!fmnLyaI�$Slyb$ (l Sly4$ t6Iw, 35}� \ se�Tt����� �local��? .��j!�ecU&e'-G"Pa�)!leaA�a�vrp geɨw"ier ��: to�q�r�s!"$th almost verɆ7cbtwo6���&�"t r��pa&l�I� leaG comple!H &��1�� $EOS$,greatk ev} ek�2sta�$p$. " #S�i�� ifim�&1-$ was mainl$tiv� by a/unpleas�fexe v�in%�a�-WR�I� ap� $ polarized���**4inu8KutscheraPLB325U�2.�6A�q�.�kypare��j!R-ers%ze��� Ns# ar M9 &�%,?:M �here,&�� ed dAm�a�7�)cŇ�%ly tu��1�r�!�ZA�a�� N�%tra��ion� $x_2=-1$ $"o .OF4�!to^ � !1%��ferromag6 �A�.Qb� . In*d�the� 6<> �C�C ��Qr2�kqu�uqIT�����. AI��&t�"R!n!�B� ���*<J^�$n/p$ ��mass sp$ .�#B be�lyq@ � next|%/�WPi�e\)�-�jW_.\A]��_�� &~$ Sk��&~$ɑ 4SLA� &y,$t_0(MeVfm^3�-1128.75�-2645.0$  H490.3$ & $-2488.91 '482.412�t_3 h {3+3 } r14000 d 1559p2 3803$ $13777  6 �x_ � 0.45� 0.09: 1.13188345846$ 6R� $ 1 wQ604!W  H1.921 h1.353 1.3!2Rt_1-5-3�)]341 410. 489.5� $486.82t457.97:m2:\-\/ -41. �-131j-566.5! !� 546. �-419.852^x_)�! S0.058>= -0.8426!343 !-0.511B_ �S 1.429� E1{: 2VIY0 C1/ � 2.G B�ɼ  � ^@q} S&V7� chem�"� $s} %\addto� dents{toc}{\hspace{0.55cm}\�ub� !12cm} %�k \newb}\�der�a g� "� �� �ihprotonn � �^ Colonn4428,Bara�"32}J!U_q ~�.~ {{\� V!y �{!�_q,�{q'})�/ 2rho_q}}~J " �* A\)(�6#\$ )UB~%^{I| +1}1+7"��0^\tau_q��2} �C�5� �_3"�' _0}~"!ElM�e"�$6M�ing��5��"� . HFS! )� nn + p� �3:$-$ B�+�ca�AP& i�� ($q=n, p$, $)-$ = +1 (\ - p-*v follow�we��- ��e�� � k. �1s�&�ak0 for  iM,}mErice98� erefer to "$asy-A"|  (e.g. �$BPAL32$B 1) b,en���%ia�n�/9� �%Mlc2a%ar� V/��oftR�Iof�w�%'2>#�4&.�%!���a�%e abov� rm&�ss50V{"&y�_5ff;0,!'!t5'� -v uper1{u� �%�$a roughly � b9 !C :kN� nRho�&3)2}�focus�2d2�'l�  "vce in u!#% 5��N�% � ���� t'I�!�Z� gs&� mean},&���� �",aa�T0$(N-Z)/A=0.2$(")^!%Q $^{124}Sn.~� ��"��qpy6���-�}(aD"� #� *�_\"&>}))E� u �:�:V"})��-s (top� ves)���;s (�B es) )3�� I��:O�6chT$�2�2F�aA��/�reg� 0off:1%�%^een''��a��� "E��  vU5��4!j5bel�)�=-�� thus�&&#P]4- s duI$"(sj!%+�3,�g�3(promp&� "�, _R ve ,:Jfer�1y):%�!��wmk,�Oi5io�rivc"e �Dphases �A=m frag��&�66�W:ns��nt*�0%��`%�s� b�)ed� Ao.is[-��ce��8"l�"} �mM/IN�  $\mu_q"$E  $�9F� / %r� $,&�.�%���ʥOremindI��a�a� �)n�*q$*�� \per� ��G2!�#!m��ePM%���.�6procesA8�A� is�eAedaqR�mz%�=�F��i! �".� of �.A�Bto (�2runtil�l%72�V��w alread�:��EbI#D "l'on}m��@/. b*"p�#(!�2 �7qdev�� "�(u�xb*�;!�s�S� rpa}��d!�&Q�Az=L4 i*aNv QT��E18.2��3�B&F"?e�!�My���� hile����/� ��de�'a�n-p=4q��e� )I$.�nE�i|.7U�w�U��ID��yl &? $inhomogeni+develop�h�2E� ~tl(ncymH in�Y��I�toQ� �Q�tiŴin *�7 :�$jrigorrproC&�2�01��?ns aga�.E��+_l�;E{MT.m.l ��� (!��;L.� qt (&r%�Ms)!~��ct2 �6YcO e liquid)E�0-� clus�F*  such _;�a�= me�ism*!"�3� ��c� 6O sq$e+diluteM�,�#$1/p:$&H ` � � (dashed %EF�!+�c9#4rR� �7 %&� �-@ �� �@-Di8!A� �ma� act��� �{  ""Q�mY%%"# und� 1EEB wemDo look? �q # �I?/-�J�}@i� ��40.08 $fm^{-3}$t= 0.16� �EF��%E��ang� eQ(s ��B towardsA--C �s�duc�5a $n$-en�x �$� ��#ll migrY (in opposite�Rioa�aYice��e "neck�ze�",&3 NPA589,Dia@681"=703 30}:�Q$IMF's�,l� ��) $n-$�� ara���F,!�TQ�e�'��,� , *F�4j�J�#Ɍ-�,�Bf1�f�:�Ng%�%�5U (=r)%�!oft2�) EOS6p>D-uZ�Q�0.6A��m4aG.A)E~a�� ��0-��� }"�2�`$Ֆ noti��a dra� c� E��� s.R ."� �� going&�"x old}qF new}�Y � LyR) ype,�lc: builL !{G8"2.��.�cte� �v�G be�n�-6Q� 9Ya I&_i!<F8isHly�a&��6` �`N�(� 0} {m^*_q}^{-1�(��1-g=( rho + g_2�q"�skyAMj6k) $$ :_{�pV{{1d! Iv:(rho~~.3%��$I$���5 J"t$2 $g_1,~grcoefficE-s��Fy5��b� "� BQ �IJ�&&%�I;[u),(2 + x_1) + �) 2)2�) M"�\\!gn\2&H*�)n!XZ* 1)] �) g1g25��)�3L%3&+$q-�;ure��14"? R4��ɩ�YU_{q,MDAm (%C!�2Y) E�momdeF)L.@$EC3��on"�� �!b<�����fD*fD55"�)5�L��J>Qd^� aO}�5#&�M��_a�I�,�c**y4is B*5,��y  ex��67~K#M79-b�DR*G we+G%�� ��'$�w{n,p}U: 1�%v�l�H�9"�o'K�A� Eqs.�G���e)�Tseq �4�(-� $g�N univly asIq )9�N9 <0$ gives -��>�n>�p$`Hle�hav�e&� %�R>0$&p6~'�?�Xi�> :GI= qA�of)Pest"�&k ����2 ' �2�!�$E-��Ec.�D Lane Po��ialI��-�(RVO"�=����"��6)."BGY)A� ��H_ 8Q$) wPtL!�at-��g)#.d�� 7�;:�d C�"�3�F�um�)V�%`s"[t A��1��wu�[�-� �2$ T � �+Q�5?����`  on�Cor 2 e6AA Eig�. �[r#��_B��WPr"�at]�2�#&�A�v'zv'g_1~(10 )�%H f&�'+3v%&  31�$+3�% $+;5}}'+1.67 " 1.702�%g_2vi-3.14= -2.9)% -3.5t% +5.7�% $+2~ 2.762f�_0(�)O0.1 E 9�%�0�& �6!586:(a_4!" V 28.1 � 26.8 L30. V31 '& $32.0)8 .�%�3_0%} [ 31.7�& 29.0 d35. (O9. ( ( 2Y��(��. ] -0.2 5 � g +0.4�!g0.1�' +0.22�t Q��sk�� �6%� m#t ge?Ja��. ��a�@�<10-15\%bTq&0"-�$,�*:<�bar% ��$. Unfortun�0�k�� ?wI� /�+le :�Sis�r,.r8 low ���avail�E�issue�be �,rel�/t� "�=drip-� �iv ��L itself!'� � i��Sive. Png �� to L2��*�in�,�x��,�|�e .��A� in���.�S�9-L, Tͫb?�$han`+��hd#Ye back��"JP. ?&wee & %1S% ed�microsco�92|B:PC2?@@2�A*I;Usint��!M��G�E vir�$BsD6B&�C�%^BAt� ;2, �2�VD 2�D��2A4CkcozE s �B�D,Zu�B0}_ .Pm�A�.�*_($%i$)E��nd B���&r�res s�%�1�UA�!��VI+b"" refu, �$�a�P�^ �thmG1�!ACin- !�e�!G<*Yqhd;�&�+B��Landau &�/E��+�+�o*�+�cquasi� l��=ne�"�A�͍P�E9S n 2�:�"�q�U.N+, p�Q�,{p^2}{2m} + 6St�+�0{d^3p'}{(2\pi�$)^3}}(p-p'�[[ f(p'��f_q]+U_q<.w"5[�e� ��&�R="��!2a�Am" |"� ESB!�$f(p),��Tp3Ŏ�,o umA�"J'sK92� Q>*3 defin�!*5�d�W�"*#%d2}{N_q�~y$[F_{qq}(p,!s X�%�  'B!?-1�= land�5P9�"oAa�(&& ed= N�A< �g_1}{2Y%+26 *- U_q}&-n q(=) "�-%&&6������!;�"B-=15>1Q�%�&v �{m_q^* p �i�-"�Re�y l!J �A�q-M�s.�'W&�=�QtM  =)�'}^0 + ^1 (\�p \cdot 'u� �&%Vge�#F� q9�exp$2��``e�''a� ``�k��yU:"�&�.1��%�(p_F)�>[ (���() p_{Fq}^2 F�^2Rh�>Big*�Ajr%BBsA�l}�m \��'rho]e] 2�^�!��[N�q!R��M'BN!J)C '�l�aMfi��U���(n,p) ��b e�A�c�c<m.�Qe�Fe1}{mA��  1}{3i�[I��+E( "� '}} q�^2�^10]. mR9u�� ch nic+8� "d$(1�� � F^1)�,l0�<�ic �.�2ea<&�LtO(C692}. Howe3G��'J �Rg� !m ct becaus'%s&�^1$F0 a o6�a�rE13J bal� "� by#.� "�ьy�*a� @pl*t[ A4Gqk^� �"� 5';s, "� ��)�<�Lcr 2)��B3p < ``old'' fAaH``J''M �%�2�X?�<0$+ >�&=c� n3#$1+�b�Z es m'$MA� % F_in$ 7&Adomin@-7!2i)), ��9aM� U_�&�I�H8 {U_n - U_p}{2I�H�8_0 ( {m\rzI {2}}"�lan�6� �K$�U"�/�/Q�,$q�erq2�<� ula:3�I�We� ! $E��J 3.Ya�n�U so . "����0JV_�1ed�B� <+g"�C�gy�`)jgS"Xlast row1J�]ÍZ [�*�2R�v4 �#�Cw�n%F��"�e%��f�f 6.ept"cap!�{ �ZA55(� a3c_T� dot!|(2�a{%�% >�{)V'��s�aDA�)g!�al"; 5�t*�$s $BGBD-1,:> ` ` Rizzn732T�"2S)��4�%J^d An iwjt phys���"�CM*"q �O/t���h"]D�0y�s�+�dis�)�!�5e��0 $100~MeVlI�-i.%e�j6�.A). 6�$ s�"dI�� �%N� at ��N$� ��Y� �f��T,BecchettiPR182,Hodopt!�+%�U s�eark s6"�)uFOld o:A�1�U;"��/��bneede "4��4�ctZ  �2�V%�..+. MR�+(,ct]Z ��:7G�7lp�m( �Q ~l&�7,G.�7) � dens�Tas"�'�iI�� b� o[�VRadio�7ve Beam]iK f[8�5d23A supra-&!�=i!Fw."/-�<� � �on{5-*ZUk�0&�&q)� �?-�buofբ l!� aSces��stlWR.h�ZnflicY k���oɞ�6� 9f�� ` on"s1Mo�D�!,�)$Iso-MD}, F)Tt!�nonJ! lK qu9\{Tn!dd��FpHof�$ar (5M�u�@�l� clos% *qofunda�(d&� �8�!a�"���. ��review:�#!_is � �Su�6J.�i =[[7c4+ �/s�O4,�6reldyn}~@.�8�� Star%�&`5�6\.sT!?M�ic1d�-�tes�&qCt � 2� 55Q,F�B2=, takac��կ �q���9i�!h:a,u���mo�M�M�3!I-A)��) oi źI� a�a*� &-&in&�ll�����ly��/&aF/f!_!��9�_�g���e�.�>B|t6��P � �$aci et al.�*  33�a�aA(astro� ��qA� �6lic��7Kj�!��be5�!��Wto� newa�6b� U� �^�s& keepAc!��:^�s�1.la~) simi�c�V����SY�, | &d. Bz [b]pi�n }(0,�v8put(1.4,3.9){\m�2,[width=2.8cm"�*7a}C1� R5a4"�2 97.329i�*b*b�+d�8.7,4.3��bJ�) "m(>�3��"A 1��13Bi�s: $I 2�N-Z}{A}$*�� ��e�%M} Huge} %$$�var��n�JI_{kin}+.A 2B2{�%6�p�/B >eJ�ienne�ew,m}k^2} +\ipi^%e�&m~��A�, Er-{A� \rh4r{\rz} - A� .(\umd{0} I^2.:&F�.BF�$B}{\sigma+� frac w�^ %} �2��A�3��A�Uj-bC�� } (\inew{Aw p})+ % C-8z�5=n 5 I 8-85x%v\%1 2}{5!�( S) \qd{ !�_n Ax.4rho_p \iz %}\;Jn>x�Yna�?Hgrals $\mathcal{I}_4@(\Lambda)=\itau$ a98J���` ! c$$g(k,K �1+\tdmk-}{ "}H5$;� , cripwtau=n,p$�Und9/�s �,pAO��s�F�z; $\rz=(+\,P+"�"}) ��� arS7�'"`LP8��,!Lɇ�Xi�ic"� �7 (��$), %>s5$yn�)�:�"��;sduc�x<:� CpoF,by Gale, BertX%, Das Gupta�sBD$E �%:=6PRC41�a ,+�p \leq 1.5�k < 4 %�1}qu�s !GXj@59,SapienzaPRL87}m xt "� {w!-��>� f?H�v-z�V0$A,\,B,\,C,\,�� � M�$ !De� 0u �al-xh ($A=-144 \,MeV,\, B=203.3 C=-75 $in��=�L7}{6}8 8=1.5 \,p_F^{(0)!/�$�A�6}� m1A�ity�w prov�ogguOS uM��a � "i�B�g0NM} \simeq 21��%"a� $z2set� ( ngth�B�cyv MD$)1�iG� nel;�8KAass %&�&Z�=Dse:� � � )Z OD to � :� � )6� opt� ] -$ T�!�fu^  Qr^�͵m�M�[c�yP�adi&�(M $f�1$,�, a��z�term $.B � $,E/m"Z)=�aH�楹��.�#\  U�(k;�&=& %�:� (+ A\ra+B\ra� .� (��-1) =6� : 3}:{ (~ :� \pm��.WA <�U a - \4V� *6f\,} I+&t 4}* � ft\{ ) (3C-4z<s B} + (C+2 ^{\pbC}}FV\}"A � + �C �� � }{5�,} \ra g(k) %>� w#utau}9'I�&� ͍A0"��&� S�U�,q �^ �4 �B� �QC;(�B86�#o)j� ���3!� s, beU�}cf$<�'1cn �o*Hy؁�ge�8�kvO"��6aM�e�.�_�# �8�isW30,a21x&)�m^*e9'=_X \{1+1ZY>k} /dig}{dk} �X\} p6_{k=k�ZF[%� #]}"0mV'�w*5mM#ٌis �gboaly� &;J����Y , buso9.�a)1X%e-q�E� #A�F b��J{)VN � 9U}y��>ak {^n}}R,[d !}{ -x1+�O'k_{F0y� 1�)^{�* �?a�I{(2/3)}� e�Lc.!-�B \� EAIn "�q4 stig�Ha�I��m6�onF�2he'��QS6 two ofaSP~ �M�s�sin.� oesd;U��0&U!Uk, A%� "� 2�X%���9� $I(CdA"٣,7[ht&$�F1:|c�F'6 � ce &>/&   �` 3$\\ ;| �yJ & 28�5$ & 1.925 &�`1><2! <N & -36.74-1.4771.0?\�&^8 Valu*MA & �,\,Ɂ  g o�4!�9�%�gi"�P $�m,(\rz)=33\, A��e+cha� e�f�AL�)I�  (&� we�!�5� vski"8<)��wX��figwE��<&r �� :S� � %� $ )="��|of:*4� ��e2p f�#�N�%��A���0 x�2 s& B�t�� �:.EHi. A!��Gc re�Sva��� !�]#i6d��UIuЅ�aeA 6�, exact�'s"�(?H� I.�7fok��.")Js. b*p�!�3 ?uph ilQN�o2-:�E)"� !0-J�R�  (a|$$^{197}Au$&�).�+&�f�-jo&$wy0%tandN�. "C�4iM"� )�II that :]q�:e�|ro�!io� � $!D��~a�).�u&k4itemiz&(  {� +�-%&�gV )}�yce $"�(/O�<siTtj.�5M?�Y��d��"�A ( U���0.}�..� ls Eter9Qe"� ��b�.~!Ci�a�e�laez�.on� do&att�]a�atg >.�d�$!l%v �~:T# fU�a}U�%�� ��2( �D&�$�N. A�ysee= ͊r>S< |b<)�i e ri�)oBIr��%!�y ���v�:is�"��m.t> As�&>:>D�!�pI<�V"�[���<n� @�n;com�a� zX{.�1�6< �� :.a�aR�;rger $$ MD��iv"��A�ex�TARmea�x�"B)#Da� �& �um se�%oE:�Kuemil)^ a%n rapidi,� %S {rep_bib}A� docu�} �,class{elsart�.@usepackage{epsfigD�Qx>amssymbDtighten�m� nuovi!�:t:(:)�ne�itg d��6pi4pV4n g>6 en}{ r{.�}JqF=z<pi>: %\setl�{\uni }{1�i %:tauF\cgPg�}2��BpC ]}�"�}�1% rozer>jr��{�x&hoA�V-a}{�8} > %Rd�a'!�o ,ia per A e B:�VE�qd{ %��xEP}g^2 %-{+ 7� n^2+ p��0.5ZO 0(x3�.�umI�@ �x Y } F�new �*�#1 )��]9 A&cou{�{0}2Z�{I8\ � 5$Two-componw Flui� �& L�[-Gas Ph�T@+� in `�icGs� rpa�� markd"{Chap(\S�ic{y*}: +�|j f�bzdu�2Z� REd]~paś"Y'e$6�c�*��"{���7`��>{.�\ -gas�\�^RNr ar Rt($ANM�we� devo�(6*-�T-ailed '5ͧit��way t�)guide� !�"e&�[? �&beh�b �8 �u6 ݈H: Se"�~n=}>�*� :�U��+7i�G�-�qn��qa*� �r��B@)�T�(a��*�dE-���+s�a2�a, "�8&Ne�F6& �AemCng. One} mb8c |_ a|_dAy .w_AUA�r%`�c(ng & *L 6 titu�o%�  ic binary�, �k�YicQ|m� ($SE| Am�en�.��d%�U6�: iϋo�F2e� -ie"�e5�:s oscUcD:p�0� �� l am�Qudbi) =�"�kP ���1Je�[llL L�ou%\rr e";_ca��(a�� �assoc�g�m*Q`5�� cBn��-� � ?w�erxM��]�Xv2W6~ZqA*2q,�r"�z"�, .�9�!!/d �h. Tur8 now�.�+:KQ���A�b zQ��".*�'�5�8A�n[]|24  occurr7� �a!�o���r9�is lo�{d��face ac<� (ed scenarioE�r�+-�}�X6]6 coupledr Mueller��2,Vr!!$6,Marguero��� �4�.p� damework����-�RQ�wg* d}!��hory �L8H JETPF�w�88g> appli����t1^:!��ar}�b�q�!?  ) �(MigdalBook6P�i"�c $^3He$ (��-upB  downi)�" BaymL878,PethickAP183X,2�2Thermo�al)^} Let Γ�~cus�tB0a�of I��^T=0b�1�!���*�T&�|Y}�����.��7�x�0N >.LfČtempereOhhH�ra� forobp#@PKOZt��z%�ic'A�܉� lism��4B���R��]0*= re: *O�u� } fJ�* _p^qJ \Theta(h q - 2 ~, quq�&�D+Fd� e2ƥ�#M{q}�A�6?��&�-��on!e� s�.S=i�<~*�+�$F^{q_1 q_2^DN_} V^2 v ZI^2 { H��If ).�<= En?� k B�� ~,~~�ET!~@\int\,{-2~d{\bf p](2�K�� &5If_qD\> \�al.�}~ 8 1�l&Dv1'-� H"z%�  3Z , VA�!�volum~7$!P"�( �4le-��72�Ha�?�q ^. At � j reP( $YI(0!#(mp_{F,q}/(\PIH"33%Wq /!.Q�, ),$$� ?$ �2$6(I� �&�nd  ���$q$&� �:a��� �AO@ P"ostem �b!R absoluiinimu�yyun�or�s "�s�s, s�vrrr ion:JI�A�a� mu_p2�p n2n߇~~QD�>�6��0atisfi�  w� �?��%���-dsea�!OL m��&�6��s�#be tak�f�7cT ,M�!o  �F&�in"�4�Ws�d�$�&�%_{l=0M!yo�r7gFr. %1)foot1nI{�,��YSf��3j6� j��Χl� .�6?i�&H=1 / � y�9)NjBH�F� should�4�f_q*�ie� � al e�A^�an&� � T�&�c�~e�=9�a �i}sp!�, h� &�8)�IC d�"� �is# ne|qari&�m� u%Ile�& +2��Ai%2 �n, up� av� �e!�$���&�F$})0F�5� :}ޜ=.� (a �إ p}^{�L b2n cm� .. n)J�W16��?�( && aJMp�$(0)(1 +DJ80}^{pp})~~;~~ b%nN%nn% " 'ÁYc4YUn�RNMnp 2 NR5.~~�!abc�4&'� r.h.s��EQ�%�1}� diag� M�fol�|KU�*�1.8u &=& cos\beta~.�p +��Fn,��j1�(vG-V0IRb I� rotB)�a��m �V<gle $/ ��$ \pi/2R�#D�Y#ztg~ 2 3Q�c}{a-b!�d V� +2�QAUnp}} .3>r -.8.Ak}.�!�5�T��F�����!�F��r= X u�P Y ve�> 0~~-�varia2B�%��Q]XE)Q (~~ a �A\gn(c)k�(a-b)p+ c}~~6�S &o7& S8(N_p(0)+N_n(0))e�6 (~�OF_{0g}^sH\PA��� pyxYj�A䶸ڷa ~ӝ �BB��H�nanewU� B� �N! ${s,a}$. H��,��ank"xPro�oYpa�),�2isle? �O%ota6x��6���A ~.�co2`:�" (al" modes, "ٍ�"� a�" $e�"�%{ s��of statE:nd_�@p| �~qV &Yw!,� p=N� �U N$, $F_0^a�= pp}$ A[pn�. 612�4F�����pN(0y��s)( \�+.�ni�� .� &+q2V��0^a) 6V- �e VM�vA/2b'y��O)<s -g�!b��!m!d!� %}aB(gR(rIwGm6 anti5� (o�]NF)FM,BAq�, Pomeranchuk�� "� 5�"i/"� 6?�#covK*�}�32)Ifg� �ase $u$-� $v$-%Wa�s,Ykm��"b� terH�ed!�@}� $�j�}$�&!9�"9 /Ar(v.�H i%���s%��aȅ�% �N*8A}, LB�P �x � -�+5��2�F�. Now�!� y��%� �1>�nI� �v�� �ra�lG(on�$x'nd!�=5 . I2j�Y*"�y"�(7��can/be&i �]ny�9� . OI=�yar�D6w*Y ��or� L,��2��B�� �#$.#n,\�!:]p�M. � u�f�� $X>0$# and} $Y�j E��alently�%& }��/��,be fulfilled*0 � K X �nd�a' ��pomeges 6� The�8��Pe�de�MaY�b24 . A�PO"w�l�m�%M�a�Ak19�<�), ����%S�*�A�"fT�zB��"���SP89}S�1z\�B(&�P:���0)_{T,y}!�~~~)�>A��j"� y.APA�.". ўPe �!��&%$yX"�jM1��. ���3�2!fv<��.� d�d I��sB+��u�2^"�)s,_|aiafre�T ��e�,py)R8E��'�o)��po,! ve (�O).�Q��Kc�y} i"AG){at.��}.V� X � .� .�["�;y 0 d�Wp} pn}]a�~~&�6� :�&=&� $ 1 }{(1-y)E�� �_ef�� :����Zchimecx�Z1"andN9:j�M=Wu y �(~t� )1}{t}~ b� ~))16E\0to X(\sqrt{t}y a(E}��  d+ Y6"d3B7"i� 2���  t"� y}{1-y} . �8��reF� "�P,�0Eq�T0 (��#"�,�C#le�5�. $&����$ �!-or�:al1a?Kq� m�+al^��"��Vn/ p = 1/!%�/y! �& /%�_p$R a���NiB� ,Ry$:kt2U��� has:���V t~(a tW/t A� )2� ^2� TN&:!CJ|5c%T)kabo"%��ӱ#��;"�, ? �!ɡi�QASer�qm i�aS!��d �!*@�!�_�&��9��"� � Y��>c>�i&�y� q�&�[I$$ W��"� 9ia8������x|2 Eq.s: %�2? &G O &��Z �  �;$>��4��x� �� "�Q $u-$.� � : $*< s < 0$� $X<0�� n�U:��&*b5a� �(A .*!�9� val bB=Q�!�I� �%!%���P�% Z�-��U}0. Analogousl�(dea�%bGy)!�iX�F\v6\ �S� n .Za%Ze�$Y)ZS"HVPp�%�%�.%be�ax g�aAe"� h:�&(Bdx�� ��66$-56E ��:yoyP r"Do �X (X = 0), �A�r��6��� ".w a&� oNK%,z��`) er, /+�#� * nI%A�\"` �BllE�urna ).*ce*�&GUCA� d%!!Eged�C&�i?C"�&���*(�-urm sem}c�is was�wn�e,time i�,�[�� ,�""�I } onfi�,�S�E�of Z$3i;���D�[ColU�RL8X���&W�toK�[%�B�$-<s� �b,c� ։�E���cy $:� �� o �P���=�c.win%y��"+�D"�? � �sees �����.�6� ���m ". Y$�-c��e�f$�� ��E��PQ&#Q�K�tas�E4u.�a9�v(Z*%��,}�, (�,x n���&�)0"!���Xts�"P>0,���vql.F�d3[  $t=1�a=bE =\pi/4)"so $X B|� $ 2� (� YO�����N&as� A 6(M�������per� �'%!=$*�:���A�]� h��$�Kb$>�����y _��5/>! =(�!��fO2&¬ $c��:$� mix%. If $c<�f῅�an.]:nx!s�2s,:� B})�e�"(�aAql&�/U�� 6�"B�#���� �Pi�-2\�ab}'�U A}))՚� .�7"�<��A m�!icts2Z;,"�2R,, if $(-t a -+ ) < c < 2�o� a Z�� < :G.C ^  . SoE)NXQA��)�+ (�.v!�!\r�,4& &�.R 6��svik�QB� 6t�l!��iE�� 4^�Y�jr�/5 >�A�L1/way,X��Fa��s�&�)�> ]�. �5�} 9glR a($a,b, ���W � )) �z=���;za6�1R�. S�jsiM� �1�a9U�iw4� W/�U F& #aZ� C��| @��4�ny 2Y1h��g[��nq7��ctr�9�"'��`:>�\t&wh6����d.dve�hhow%��Sɻ2iz�*٢s=&� w�0&�BE{p�/ous"�di%��-�iWZ B�  a&�m�!]�C _���� LB>M�,&v@�.1�&�YfN{A�\=D8:�\[0} + {Bab�+N7{/B1VKB�$(C_1 - C_2 q8}_0�I Z}) { �-#_F� �Johpb�%�T_0|.16~\m�]fm%J*�vU&�^1�5E�R�a!�A�IT356.8$ T $B=303.9 �=�� , $C_1=1� -C_2=93DUMeV�ad�*)F�U� � �T�ȅ]WV>fo.��:� ���q �R.��. aNf�� XAQ�pU�4Z�'�)s� ?4�:A�� g �h� ` 6z�ew*�Ont[+i��%nmulti�; �\��Xu+5,Y\ lloHIP97}X� �%pX � �d�on�ith* J�7-�86'a� �[-UB��"-=rK.j�4.l��IR6T���6T�3_fig1T��4�kSpinodal�C&&r t7�Z'�F�U�� (cir �)E>��݋y (ʀsݡ! t+�A�:�A�s: $y=0A� (a), A�(b1$ (c). �mwrp"Z+-= ]P"UE E� �e#��E�rZ,!��!�k�K�}�E�{�kZ=R)I�� .5$,�0�Fis bor one ";s e[�NS���ԛB� D�0orZ��Qner39� eu�#?�P�Q�&se�:�(�R ,T$)%��Gҹ��$�[/& �)�aN� � robu�9g��!(v�%A�A�)�x�E�, ���6a��ngZk : �3e_FQ.� �2e0sl�|sq  l favou $to break�lux���_� d6{Q\�f�0�u�j� �uniqu>\65 .��Yg�|5p%&M�%h�N ,Y�%��. mea!�fu��doe�0�t����~ . L�iwen � 6� e �i�2 -LBI��S4�hea��1SF^�$ box, S� . 3.3�o�+��N�0b��b)�����6.�JS�"5 $\chi�] textWx��!z2������q��4$ (open�sv#1&-���l&$T=��$6�23,-: $2�‡ANMo2�.~WZ� a �)!(M�of !r�nX��A�0Ponsib7�A��>�A� F \.�}�d�FB�Qu4y $(I=1-2y)= :� / � �#Qw"�#�* I{&Yp [� (1-I_0) "+  tgz - 1] \4% Eu  [A.-1]:a$�re $I_0��F�6t�A]r�[I��)7.�u.�2R�Nt5)f OEn�I� I=�A�a!�2�� $y<�J findicchi<1$� r�5eY�$�.Yd�^"d# eOs (�E')�@��+I:d�TCM�����At�����K ��=d�+g�7�:�o,��d2v]��>>*ݑŒe$e��oP ~�p�asy\demonsabe!> we a�s��E ples+�&�9w�0 y: $6U��1�2}��A� �I^22%C��iL)Ib! Accor "� betaZa��1�\p/=�n$,� be� ,ae�,: j3 =qk'�"ix�^�Q $tg(�3'�;-c/x2I�u ce $ Qwr5NnQ[  = �2u2 - "w&)��Fm&*4�3$ij!x�*"*:A�sZ, #F��(sum vanishe˦�A%q �Pq�&�s�Yr�� � �>l^U=�ic��p?��DS� �*��6 � "�( $U�${Q8 H} E�2K8p}B[ldr%��emAerۍD�i�2*!S� &�x�`coI�4��;� p�Q�ed�j).��>[ ($-C�e7�:�!q��m��3��$-c%b5�k�'�C$C�f��%� $tgm&$�oY�*T����W2�6�t.�F"�2k���O�,�lW) $5 coincide�=th�2M $���U��i �D6�;��� �A�re5X q92�!�:�.�. With�m� mode�<�*el< Coulomb�ul�iJ+��-'�Kood!D�cg5�>Ha]��QE8 $��&L �q anyq�( 2IF:�y�>��� m��a%��8'erm. y��Q�+6�hN_"��ns�?ur��i��,�FY/A"� Inv_1%>��:GN�;1� a-<{leA9bV��+��g�*rpa3}� s��-FJrY.*3}/��D u3(l3A�/ B})Ai !�=%`�^�- W exhib�van�6t2�"��$1.5 �j(3}$ (far aO��val�U�|is �{el)��C �у $J!2w'J&�||3D} �|6z|�sv�� �iU"�ziav� ] b) (��ic&lid�6 �$ ^)rvV�3:��)INr#�& ��œ`�+L.8."�%Yit �IE"�NMiE�trނmTl"T�d�pyc ���E����e!er1�.b4Y}!�� zE�62�w"%"��  (&�%*s@S ton-��;�:Wۊso�Zi��.4-{;�n�*�da2disy� �sF6inu�YwBr�!!#ng�>. O�5���ua,� �S=MnyŬ$llą� E*2Q,.s02�}�W.;�uld��M�&��6mN7b�ډ�sy*�D��axa��}�%"+D�Savi�vaA-+# R��d~\,�t��emi-cl��a�H,*� �u��eVlasov� !���o&��� prA$�w�Q]�   aHaensel�� 01,Md�49,2K,�(�:,"`Ot�'eself-�H�u^Jd7&�5 f_q(�Jr},p},t)l1�{ ! �Z!�LA -r}\W-*�JUqFi56�R[p�W= 0~,S2�L�?Av�`�3u%�} � r6 �y}%jarP�"��W�(a�!t��'�ʅo�"z&���k=�n��G�#��� $6J� �> mN�m ���ormM�f~]Lna��U_q�d&�1�&�q} = ���b��7*rhz��2�+ 2��d�qV���{ W��o�0tD\tri%A� N+ D_3\�20_3~�+ M�UJ�I�1c��,  �}}f:!= .7!�B�Z,!,� >! .�1}p! �{�1>�%�>!xD [2}(\nabl�)^2�.!.%i2_3)^2~nF-Bh��urf 91d& �g� O"c*� FU)~�-Va� ���1� ed; E��ns7 s� _3 "o�HK"�g �C("F a��e%@)� ;jEir{���"'"" $D=130�!$a�$fm$^5�cV�!� - -V.s� @Bethe-Weizs\"acke� s�A:[ $a_{F}=18.6���$D_3= ߣMe2��u D/3m�isL..Ref"��aymNPA17V�A�� )!t = 34�6�6I) SKM$������6���hU^ d�%%�qarEo�� 0�?#(veAɼsp.4��&�$RPA$�2r��a �f&IZs' turb�b��%��F�P�tN=$ , ��od�ny1,"a,RsLsim \exp(-i\omega t)��:�~� ),H �(� -�&�@��ݴu�} bɞ� ��~p��*�(��B���U_qyb.��< z\p}2\ .�u^�\�j�ӗ=B �F�"lvF7 �E�´cri9}(0)$ 6H+��P]e6 ���=��&� "� AimJ��unSur5hR� $f1vka�P2.at iRI&X.�Q!L("YTpXW"1A�{2 � q)/TDG1}~b-_FF�U�awa&d��ng �6= ~��*_r!R-�= �PJ�!��/5�f_q"�2�}d + iE�k r})$:�+*^:Brd"�rocedkG��.fZ6� ��}7-���h�}� �!�y�Ewo&n a� ~��m ��2�0s~: \begin{eq�narray} & & [1 + F_0^{nn}\chi_n]\delta\rho_n + [ "pJ"p = 0~, < \label{eq1} \\ iCp ep2e d�p h2%p ^d$2} \end{eq�\where: \begin{equation} ��q(\omega,{\bf k}) = {1 \over N_q(T)} \int\,{2~d{'p} !<(2\pi\hbar)^3} �{ Lv& b + i0 - }.@\partial f_q^{(0)8 0\epsilon_p^q}!V-QLfu� ��xis the long-wavelength limit of0Lindhard func! ` \cite{PethickAP183}, $�v}= p}/m$ andFL%� q_1q_2}(k!EN_}(T){IB U -; \AX{7} ~,~q_1=n,p q_2 )Xf1par5�1are��Lusual zero-order Landau parameters, as already introduced in Eq.(\ref{ld}), IU now\`$k$-dependence is due to presXof space derivatives in % otenA s (see Er$Uq})). For )A.,cular choiceW>given by�A, AB� ! ex�sed as}*qBn� \left[ {A1�!�,0} + (\alphA� 1)B{^ i_�l + 1}} +9�Dk^2 I {C24} - D')\tauAA1} H2}\right. \nonumber�w&\\ + �. {d ]d�}�' .�q�(j1}G �2}).� {d^2:Y^2 [^2 ]2)^ �]~.g�]�1U�1�(MultiplyingE>first �A'$N_n^{-1��pe�+4second one by(p(n$, weE>ledA�definikfollows�as: �5�&& a(k,��4 b(�� {0}^��)��n~~;~~ b:8 �.8�� 8 p~~;2 c2G(N �F {n!�1 np} R�5$hi_p = 2 F; � �� >�`in some analogy with Eqs.�i$abc}) and!i obta�*f5^system�1�N�!g2op + c/2~2n = 06#:B(=bF:B�The�Hcan be diagonalized �Teigenvalues $\lambda_sI�i$ solu��s�E��: $$ (a-={s,i})(b: - c^2/4�~.$$ �Nmally=\forvI$lsame �" ions�&�ein 9�(A},\ref{B}) KX � Y$, but �. $a,b c$ �4 on $i$a�%< unstable � ��$ezMed by!%vas��1s: 5Js�$ (HLisoscalar-like fluct�2 s), 9i4 4vectoN4.�$is problem�$completely�ivalent�* solv�)�: $c^2� @ 4ab $, i.e.�disper!� rel� �g �} �.� )"_ ) -� p}��� ni�! ~ J�� drel�� �xat! also9� directly��impos1�d�minant � y�YqP ), �.eq2})%Pl!c�. EJN&,is quadratic�Q� ��,finds two inI�!�Y�(:B:is2"A�i�):c _s^2 g t _i^2U� strA�r�EЁ)modes�M-%�ͥ��.[ p/.��-2QN_s,k)/cM\,�eiw:� � $�di2ddm�.PoscilI�8s. However, iE?A$rtAto not� tA[�$correspondAFanglesa� beta�� no��E&:, $*$U|edA 8thermodynamical��alysis,&a fA� becaus5�-�W" ��2.�:�gLfigure} \centeringG4cludegraphics[�He=0.65]{ch3_fig4.psrcapAY {G9(%�iE�ilitie�r,!=cal1ted from! N-y�Q,AjR FSLin�re � � !�Y,�  $Im��ert%�I+m�perturb��2I /� N So asJU$I$YM�$ly uniform�l,� most�:�,�c�$x��.4A@_0$, $T=5~MeV$.} e Me�. h� maximum $iP_0=0.01\div0.03$ c/fm:� to ae-m)d around $kE5D(1~\mbox{fm}� � becomes6D< at $k\simeq1.5k��$6�-�BbE� discub$bove. One��� ��:�r��d��increa+ .�(, an effect O��6 y�N = Z)� �0ColonnaPRC49, xNPA567,ChomazPR389}. At largerQ8]UA�developmy -�w6�is slow��de��8Q A ]!. !7should � � an1Hsiz pr� frag�s,By�T3c2S�� � �� . F�Vw( dashed cur�of :w)�predic� y� %n � bothŞ s %uI�"� 0$!R eEs�be more�nouncedhigher ��,�!> fa ��R clos/o%�baNa��!�5�P BOCoulombM�s� 2 �:":�i >)��influ�>"o� -�!�s %inU�ic:� �a�lNvestig���m��q(alism outlix � �5d{inm�\FabbriPRC58}. It suffice%�ad�!�energy"���hpotsurf ) �:2�� ��;�IT Hartree-Fock approximř, ��term e��� �loH R 6A*|?0 { H}^{(C)}(�(r})=\frac{eR� ho_p\,it d .^\prime 3��, )} {\v� 3-  }- B(3}{4}\Bigl(\pir) ^{ 1}{3}}e^�p4~.�couleF�TK modif�!�$�p}$Bg, imple��ed�ad 7!�FZ �4\pi %Ik^2X ��( �3}�)�&� {)Y�R A2����}2 5} u s a,ariso*tw� �~ �7x Aiout^eu�ii a� ,a[UeJ�F $T=0$. Ҵ 50"� 5~� �"{ A Q T=0,.�~%E��x  differ�OaG N�1p�� (� op� ottom $I� , 0.3 6$)."� i� 6W�=J (full ���it%|b1�)&W . Taken �J�� 0 $ 5M6.$ � forc�>usf n overall2�.�. eK"ais al� .�h9T. More\��"� i`+.�����ly sl�ly�9�m. ��is� obser��t,� .W �i� : d,� � 0$k$ must exce�� cer.E3� {min}$�toz�iP ��J(�5A-+=daI�appeara� $k wId&eti�  b}�1�a�u[�ces. I�).%#s push6 prot�$towards r�<p � Ge G�eadOneutrP�t���ion ( Mt�). >Uso, 2*��"�V]A!],ter understaofr� �aA-!�on�}�achiev�h stud"^che&:q!�A3�g��EgA�s� w| $inB3 e re %J  45�4� M�:+I_{pt}=(�bn -.2p)/6+6 $ = ~ras٥by("� -=of n�,!z$s diplayed~� �^� $I=( �T!-�p �7 +6$�@6do�(�8��)%�M!�> ��* %W�<anyY.proces��i� b )�I$. �s -�� 0.5~O�� meanH at a2x s  & -� �1(�� less7lowF6"  ). HR , durA�!("2 �ll{ve ��u�of!���5Njto2���tak� lace�%#�pi�' � (di��E  "*�� �xO#)#V/w�G i �f%I�eviX�m�� %+�Nɋ �s��� %��=��aAYY"ly.�*J behaviour!v!�My  per�)onz �C-6;!!v red here.b.e�is re�t!46} ����o�i�/��p$�i2�* .,��sA����magnitud"Darrows�� poin�X%$�rp, �)$ plan��J1� m�!�Z-a�a�*���(is�ermE /�$y$). WXc: Un{\it �JD}}�2revea� evenn-rich{iteI#i,A/�a�0quantal $RPA$"NG oPRL88}�$g .��horough!#cus�. o�B*� A�f��s�6� [htb] %]'fy*=8.0cm %�� {-reccia� }��& 66� �{ DUgof�ZI36��sal 6j ^l. .o6:K  A�a%7a!efore !�A|�oe�l�� stiffn�M�>*e�iAi�T� e�A��ke��*e*6Ru�u�a � oADsoft (in brackets)&iz�� � ���, ��ed. AsTi N� d (r�A� ^}��a Q ers)� �y�"e�r�.� � D asy-�b whil);op4 tn(s1ͯKJ���r n:�yc!�.u�� slope} ofk 5>R�low>�(���1, Sect��R)}}�tA }[t]q�*}tab�( }{|c } \ha�h+�/e50$ & �,.2~(N/Z=1.5)8 9.0 \\ J �+@0.2 & 1.23~(1.2)T0 3.15~(2.61 >.73| 1.198186'&) 2.44:4F9495 9&8 1.9983� \\v�+1 58vskip�cm B{Ze| ���n�AQ�B e=ej�M� i� luteA�� ���&JA�]`"d� ies, $-� ~and~9.0$�e ���q�e�  a�ery�E�(uJ$EOS$)-=I� "�� on{Simu�!� : he�3�aa box}o#preM s�'yt5!s%�kstric��T onse%� F�%t�d�$edR��NrMr, �a%arh'�$ach. Numer���* pe嶩�"( �all stag&�F!ǁ�onl� ��B $NPA632,Bao 9D{�q"�f ref.��>}r���'��0 Skyrm` te� .�used. I��n51=&�"B#?>�s% i)a cubic!��� �= $L$ �#Ţperiod#un1L+�� �!) -Vlasov �sA&sI|ed*�)a� -P" test��8ticle method, �ga an'p���/pGregoireNPA465,BonaseraPR243,%v(PPNP38}. ��of)on-%o� lli� �KYy"z �8@Boltzmann-Nordhei� :kg� �a MB#-Carlo � M.�}��e width"k�� chos�E�"c�c�v ��ace�faK6D �ALis wayEt-offAQear���Lshort%}}1u� !��&, �#� �-oqB�oo� , unphysa�, ��1�"8 C49%�%�2�>y�)_80=%.� � ��9��"� boxA�fixi %Z�� reac��� P!��. A!��*V!�by� tribut-' :�o�a accor� o a Fermi<on. We��;-�.�,�1-time evb,�h-f1F'�}��b% $L=~24fm$�� �lE�- *��,~0.25� $0.5� t,50 ��" 6fm^{-3} �! 0.4 %�*�%}"$ MeVA�)q1� 2$is A�p auto��� d&�randomaT> of %�5' � io��V%��~��%%�-�!�I\A 7 rpa7}, (a� (b)��� velyq��1 a�ws��IH�U �$z=�#wh� ai9e S �theA�,�t^&A38 steps $t=0,~10 � $2 fm/c,�l"�)�\�a0M ����edi'!�final 6y� !^!��( Cw'l~ ."�KA�nQ.�s *0, �� non-J�16q c��.� �. �� , %�"l"$SD$"Ayde{ %� et �]of�:aQTy. 7 I��r~'5&~'7� .I N}B�'.9b�&u Ti50�W(A).I+.0� 20 A,$)�!�1�i�(x,y)]� i�Y>a-rho.)$,�5�&%�1,} ��.0~(a);Ia� ~(b)$. Up�panels:^t$plots; LowR.s,�dim< �1 �S s. D� in $��$6�7� -� & mH�!�al 9X��E3m X$ehe� � �� To d�#�,� � b��ra�st�.ed:cto�1�.A���L307})Q�&�� ��gm�,<�/ho���()^2 >_{all}1� totvN�8n��� y5O pE"�%�y6, n��3� >1�,j�R_@1N; �_p �"� ��rho�)9(9�7K�.3%3n }~.=�-eRpF�"In��ef1�),{11) $<... ��.not�e a� ge oS<s.� s�� AnR=� -�e.� )�e�!pHA p$ �/ �ae:�2����by�(� a�R�&y ofJ�. �:a "M���<2(h�.�l�<:Bd$< \seG4\propto \exp(24+ t),% Y�*�pMRn}~/ �-6T=��rpa8}`����i%$Y+ln}\, ��0�� $Z(!y"O )6��y� =(1- �)/(1+ $  . �,���) 8edk'1$�,,�}��=:e �Ep�9� � 5BJ$c��8rI-HM�� ri��6h.��y! �� text�!�� u�7�,� i`yiI6^%4MeVB^ �_!21� stra# Y Z � &Dar logarithmic fit$�� stag"�N .8:WA g�al fe�1 �1�ar�Qg $ln(I�&� #%Dval $50 < t < 150$� . D&�s<$50��pquickly "self-organizing", se&2~ ɥ Q. After�"!+џ (Eq>�)���!i��)a� scale�9b!��2={\B�2,� �*t s!Tates.�2� Iw6Jb)}Z��$ w3%a %3myat $tVm 9�At�s �!�n !$&�VU�.�� 56� ( �(t=0)w$eq 1.0$ si b ly $��&"�O3, ; �>��h� A�(type $(��p.,n=� const} > ��/s�>77A�)� s ne��-to*���klue chaker"c�!OE��r�7.�#��chV qu��)r� ^ �z,q�l�,57&� w5�Jp noise puQ�'-��i� IFv �aK-�ear�;aW'iI!c|(hI�:�&�]�4soc��-6dP#q�  agre�+� *� 6\�&a�'y%gs�� �&!#>5�. �=%2�J��5$�e ext%�d*�!�thI/�0Q��3�3p .=2��#524$N)�of.?"�=?12�g�*h8#�&ce"� � . �1a!..�7��# in good>�Q.��&�!�f.Sk7DV4"e (Mechanism, , leaf<o�5astJ�!ua# (�$M�yS gaseous (*�)'�7��d*�&Jm�o�N�qwill g a nd wh�<vaqN]�6M480)+ .e. �52�M�Q�icE� F.� 8}a)>�-�f 9�f �F( H s})~�Z nb�n�1*� �� -�-Q� bi��}�er�1Aq�� } ,�6��o U 2� e��� 5m�c��At)6�9:b We�"4-<"�%stry"OI� G<"�.�9} 8;Kű.v ��()�histogra�K"B9}a�.)�2nF1� 0 =ˁ�� " (_.b[ ea�1�%��/I%�&� )*��:; ;)ʱ*� :� !�P�n>4b)� drWtY(e"+- )+l�8Q��m/�d-bs:��end!< �| �p��w�verc�y �. IE%�"t)�4jI��925� inE.�!�*�,Refs.��DBaymNPA175,Mueller�5"� 18},��� basi"�&5@s� �?hE�s!��*�&' �, name�o gas� I_{ �}5nd act�a p -�! w�?f8�tC6v�'Q(globa.�9 isJ enou& ($I>0.4$)B }�*re!�@8�K�r ���8!�ab(equilibrium.�,%]E sU �� s+M9onfir�= �L Araepareqk � r ���&" u�/�A heckEL&� ��!�Adunique n� w  2��b$� wheYB� star��C:av$mcal} orb 1H}2 i��h�+��0qv�F�MAqF6� :nQ*@�'TW, �o�FwK!-�' wel�}%S�.. ��!~u!��"Be2�1}(b).��!� repem�.o s�H.Uan1q�y,�H%�A� �&�b�9,  !�#+�n��N�8I�%!M�$D� l"D�Ds}i��A M.10}�q q 106r S!_2w� .{9}(wit��9RfMJ76�10:�!Ttrend��!QE �� ��6�xis !^��1.C*2)%� sA F�,��J etaia0;� &hE. SuchM�� gros�o� �]^E8n/p�h"]$,��us6�1RG�� �Ga1�(W0am5ri�$�en�ly%-� �X R�y ��frame,͇0MargueronPRC6,i� �8�FX.�, �.�%,intui�� x�  +Oas��j�4y%l�-�� Yra&�"R���0�. �pwy &�0 G� "� -�W. �AA�E��3� s2<tF!��B -e[? �fic `sFY4A� 69A!is!si�#&o8 a ra��smo�@�Oz inu8 %�(&�L�i�%0�@J� (�yT�) �$!jK�A (�~BI�5 tendica���^r�#no quali�(ve �g6� kin.:f�1���Ay&� A�"�?%� �Q%*amplif�o�(ArcV�N,�Z.*ign5qM�{!a�Mecona��.�8hMl�4V�H���dAj"��� � T1� �"5 ly�<mi%M�);*s��r�Ei�a :�5ga�SxRr�b�. @�1Id�*sI�[] /m 2(i?�%ng�W seemaba� :�$ � on%�x!�top(nt : �9In*9# Mass"M+s� MF$)i �2 dete�+i�(nn�#��oj �%� l�i;$�0Xu�25}�z4YennelloHIP97}�$!(AbN��$6�&/f�&]F %\A# {rep_bib}end{docu�&} b ��/+,class{elsartj;use *$age{epsfig]�"�,%.amssymbDt!en�� s % nuovia)[;H % 2 su 2pigreco al7'$o %\newcom&{\�}TA 2}{(B[=[} %�-,Ksi�Adre:;qd}[1]{\rX#10W6; tond>:t:(:)%.�itg d� \iGC0^3k f_{#1}(k)l��*x fn:�iA E itg{n} #1F6p>6pi4pV4n g>6 en}{ r{g�VLDU)%N6�pF=z<pi>: %\set�*{\uni }{1�N %:ZtauF\tau^tg{ Y}2��BpC ^�D} 6L �ro�R:r�%"{_0%rhoA�V-a}{\td{�C8} > A�a' di��a� A e B:~enMqd{ % \D1}{2}xEP}g^2 %-:+ 7� n^2+ p�D�,0.5 + x0(x3):}umI�@ �x Y } F�newI�0mathcal{I}_#1)A>_�]} A$cou�y{�%{06"�$1�;{S2P��� �"�*�Fon emi�7{ n(>v�Vows"��]f  \mark�[{Chap�?\arabic{�%}:d1 �@Xon{Pre2��ss�1�,����mai�Bg�#x:j s�� exciy�"&Q��&�#� 6�m), ͆(HandzyPRL75]1� 4,Danieli18��re�+�  a $s�7$�;yI�y��F6gradi�l�re �tha�$a�6�9s�I� ���eos},I8)� ��rwQ�*�D!�er9�{�^l�"\ � 7bb�<wy^(at.�6) "A*repul�0q�� re��!�%<� � "�fig:mean)7:�?Thu_HCeY Z%mitAatEhipLim���� �+,�:�w� :3 � p:�ud�Es�� l�q�!�G]�%$� reas% expla&�KB 1W � ��%��.:se ideave%��i&?Ls3 ��-�� heih on �$. Of cours�dGW �M0es"j�`3BL�"2 �+1� h�)S3"-statG#a�V<2=um�t�cs �s2�U�M?a 5�A!b"yb�o�#�spa�"� "�'!B1 sougF.�A�� �1heavy ��ia<sA��Wnt)�� rang"�r�.#�oalRMP62,BauerARNPS42,ArdouinIJPE6}e� RHIC Wy�WiedeS4 PR31W6 �+�<4 s�AI(�]^�,�� �7ewH��6�DC�eB.� PRL90, C68}, u6�Q�F�!!��,code, $IBUU$�e��C-body�c "�6� �K"�]%ermm,BertschPR160;a �*��Ab@lZQ�#m��?�ѶU 0%:co��=typ�U:� �OoA�{X0ams: $^{52}$Cd$^{48 � E=80�2/toDa ite{ria},�1A�coA6��"r&�@&�4�2s� b#�%, �K�@as ``��''e9``��'' "ati�sl[a�$\g�XD/Y  2.0$!}C�%Sp�L:�>>� (r.,+etic $+$&�e) $$E_{� rm{sym}}�B )=V�b$)\cdot u^{ � }. $$ �D&xe\�oat ����5re�a�#�% � A a&�4$L=52%��,chZ\SjAi"oAlueg�>�&y@�',�>a0$L=21I. Xm��� w!�\W>�uper--� ($Lb�3MeV��"� &��i_K "�[{A�-�]�9sCa�%\%\^_F$hA�>:vs��ro5��+ (emTimeP} ($a$: squar�> : t#gles)% �%�L�� w0��V�[ir �7.M�<4!�� >d .�8�  a� n Lud*"U � 5 5! 7E*#TBon�i.*6:�^�/A'Mq"0 "E I�*? .� 5>�(�Fve*tseq"�U1C��1\�2how)D,�>bed)�^�j!Q!kU&:j.(�wo:NifA$1x� �c5�� !-� 5N%q�= but,�E�Q� -<a" ��- �lhat�F�!�h%�"� o�_s@�7is6attp Lor1E �(�QFZ{�6IW* -s. :W �.n= � �AW!QF"7c�K fiel�&�&ia�n ^�s�1S �HM��%q5R�%� $58Es�Ka��son! �"disregariik *D�P� ��5Jb91E3)\�"e�=gQls�l"0+&.xis�*�G�8a,it�ws [%jM8:B:<7�dif�!,$p-�3�#Y�UA�0, $|t_p-t_n|$ rO!%�+ � a� y  >CFNB�%�E5� ag&�/!.�5�%�6,Ql,"=L1�-�� shift�3wi�ms�2�G 6v � ��� r��on& �%h5�"'�1F i Ay�^� ��<� �PSm�Rm�!��IX�� �id�4���TAZm Ea~�]� Malm�r $P \geq 2�/MeV/c2�A�in�it\leq 7"51� a�0liM46GqVght��? uch as $d�9t^3He$"� �ied=�NPA729}, e auOV@)ffF� t*lA�du^ occurs��%�>z !1 a!Jr��du�gn��.dC��� uis}sF����_e/�� m�r�� )A�Q2m..�=Se}Lrpa}. A� erY�qy�2� ar2'!�m��$!creflecfb02 0ٿ*�@�X2 UZ�@i��a7ki� �a&�&�,� � %$jM 5b!��Gl��N4-� impl�laU�>�oal3 to cM�� � �N:�1 a�E�a�$break-up iTexpanK,I�8| �Iro�T�IMC);f K�D�&� !�9�q b�G !-advanZ9s�y�� �b�oW ct�N� %jt�l carr�b!iI�E�hwd �."�W�i.}c"� M��6HiP/8G��L-��c*v3� ed Bity�V"A!rI� i � !Wl.s��e� ��.�  9 summf7a�&Aw">&��R�6J(howI��9% g�M�[�5Nդ. H1as Z!io3}d5[:�can�'be 4ly6qexs� e1�5�5>a"u6A- �M( see, e.g.,6�/�U,W6>w5s�:� e7���c�)��V aOc��d ($GongPRL65, C43 7,Kunde�0,*�XIn-�B)�  J�a�nonQY�1�se���)a�p�*iXi�Rv�WacJ� "*s�� freeSiutm�u<*vi�ra�)fuZqol��me!��AQ5� " ,h  �/�#�g.� ;��"� . Z$Gelderloos!W\5,LednickyPLB373,Voloshi�79p y-�� "iS.� ~ex�+�o%��]�M"X%pua%or��]- view� �2ead��-.�6a oS�!�9�CF� AF-"Rns �o��LIʡPu=A��Qom �.l.!q% z��'rm{*�-F�+%��' pXN���$P<�.@c}0 $P>5�6,3��vRB_1�A"� (upp"�N)N#p� M@"R' peak $q\E� x 0$6�% � W ^RO (middl�8nel$^,� �j gt�ut $q=2>l}.�!�.c$ s@Ea�on,�$Sup�U2q=�Rs��z!� +u(' and N: ��wo�2�� se�D"� N3is���t�W�)&U R ata�e��$ }�i8  [/�*�*[�a*�JV�eRCbn1.1"n2+&n.-"lTwov� 6� u�&�m�`$�S(fi�"� ) or� *�:�. Lef@ ne`Hr�q|a�cle^�i� )|o)��L90.�%Q:� S3H�  ���g5��s�'U4�!��&~^#$�vd�8x%��>�*!% !?Q,�P��not �a�=��.�8B�O }han�nF GF�"!�d`G mL%")La=3 $250$ :B��ec&o4!]!:��'e�1 1 . CoN�ofB�M�Q6e an &�$*�oraB�. G�6#�^ai!0�S)umb^vto fL-*Uh��sy?"�"sF)&�5�! �,exhibit enha{x2�s�7��o`cNm��.�� ER:�!�an �<#J�:�E30\%$�$2 6: )E� -��> Dq=}Z/c6��r6 qZ�,� ;V2.��eE}est"(+ity!��G] �q$V6'Z^#E3}{ he �r�|"I!&P�!ank�!� K��rg� a �:{ A���i�*�$.�;aZU��6�%� disc�},FU�J���j�mKe7d�tofK. o a �'Bt �($,%�y�M}x-(�w�# l�i.anJ�A���E-k=eY�B�� ed, � t�J-y ~n�v�!{0X<\E� D�1�.Z�2z�(Q co-j%At>s(�P,"�mf"&M �f(c�l�J�}$% q=5��pr.�\hw$n�,TbRT&n }b>%Rbp�(}$K_{0}=380B-% /�=3I sl{N}-E �"&�e�!V�,� J� op/Cir6)> .}���.� �1*.#A^:� /s�C���N*)�b�;e-W"!o semi-..��|-ak </4ph�{&&��t/&} C �0ef�om�A�5T� �'t�T�@͡"$"�@j .~ N�gR� ��6 4Q"��7.�w %�V.Ns ��~��� )*a!����o�-z�3n:[ N!�ith a^I6� D#7���$"u z�6a"�D��*��NI��N� do�Vot - *�B���8:�� e�SQ!E.�Y-�Y� ��2()�mas�^E��{�X �%�ain�l@a��UqPOA�i& %> looked� ��132}$Snɢ124 ` b4��B�:,�tF)�5 F�m simi��� R�vU �A�� ��b�a�D�1wo��Hpp�  np@s� n}�N�8y Mi"+�M��U.�ed"�"!�cG3��0Yb"%�h�# n $C�a $. C6a!�� ��*V s*pc�5f�2}#)= &��ux� 2�!J�1 � wZ�3/#� %G �0V���6 �'� �>l:.�n*%F��`�7�^*�mi.� fi��� s up�!if�uA�6�NB� ��eM}�� match"&An6y&A pursu��vvׇ�mof"� &@$ needScar�&��) stemo(p�*&r&e�a�X���i�kFu� �&&?�&hoo��h�k�88.� ��?� �(�2D:2�-$,qt�e �6o� � is un��"�)olq�$57,Scalone! 61}."�>G(I!Z��"v a��[�Y�g��� ' �a�a��� �ab��! lL�20�s, �Vmselve��NX9:Dok4 $BUU^7ss��aJ�: M�>LK&�q2$� &X7�OM�&� }���"��-�Rd*�`pre)�o��H�;, phen� olog�$�4I6�4ed�A.Gognym�!��;3k!Ba�A9}�"��h�;\-Gale-Das Gupta ($BGBD$) E Rizz�s7"�s735} ih!%( �toaMrov��%݁5$BNV$:�<�>(��-Ax.Na "�*S �)i1��nel, �U plitt�MZU! aX&L 2�& ,�!�i>�B,:P)�i"~վ�5a"L �t��5kV7Z�_Z�W� GI6W$9,Sapienza�#!(_���I�m,M s. Gi��NOca�y7!��K�6�A �M .)P ih$��-w�J� &�#n -y� "�+ +�uA)%B�)X ER1\ F��F a wW �6 J rol�A@�|"�o �;2 C�"� �>R)�� �/�"�N�cIh�employ� 1�A�.�A2 �)./m K0m^*_nr > p "]h� �sa��7"0� S�w ��55at�%+�y.\_2� B. �� &� D%U�)G:�PRC69}i��- fig:optMD{E>�=d- , if}�6�EB�)�"}6E#��a�AQ"�} ,�fs�C, .�<6��~�. MS]o"� �&,nvisag�(aD7 ,a���A�cere �! �H�ed �e�;,1S ���Fn��ng {0lem00�l ]LA�$E-$sl@ML�P�o)�C?,! m&be"�.� Z$(n,p)$R8���"�>WAny�of5���$E_fB�V search�$!��� ��gy �Bru^c ��cG j���Q. AZ�/:K(-Q) o� "� 0 av!��?s�] ��E|��'rg��d�O2a� �/eBL a�F3r way ^E(A}�s.6Z� ���a�u i2�5,d�e�f�aw���e*b !����X3 "���,'1�a�!�U��.N�Bs#� > "C[ud7�"ei� �lat���`hl� ��.7� a hybriN(G�(istV �66ll�CTaY�WTh�$�� �)�,��}�E��0 Fa!&&J� �,%  le�c�)x1 �W,Iyj6&��,�ɹ�6 Excep�8ut�YW2�&tri{!�$^{3}$He� >FU�7:�P7 plicadeV�I�z"�9E; AMeV���Ev�7y�I "]"@Ja@e?scribi@�s�a~_�1ly�B&��-p"� &;6! vapo�/�z �$�k suit��to eI�3"�6�E���a�UC�Ca[��A m1"lfO� JL�o-P�ppla![A �6&YsE* �# gligKZ'��b�YngI�� m ��Bv�b�A� e las>Csu�!D"�F`8P66�f��v ֡�8Lzn��K�@�A�, ?�&zra."* ^$t/;;�� le�7�)��*s��exR�oX&� d :8� ��9&JB��� -�~ � 4 F�,��6ze-� �b&�| "�0Ea�e�P1B!<p��� r�\e"-< 6��JcKg uR" U, *�2� /feed-dow�\�6��;�"Iin5 c$T, �m.�3B$�d�-Iȥ�r1/&�rM��3ou�MkEX�Ll< 1�*m�e� < [#"� "� 5#itE�EA ferr�6U!�g QOU�� $6�%h� {"�R�a�, Tu�q% )>at�E]�wo�1a#D8� ��i�6�)pl"��"�W�7&�Hba��N�"�4��� and}A���. F&`"Ax� ��:( 4�����+i�`s.�d�)t. /, {'�r� �<of5I�.&��h�'ce. If�!UsA�� :�e�"� JUP���!ad��c#%���d (#M�i>52� is� 1 $15\%$� .<+ L78}� 8��TA}p�.��a5�B2~>. �ihH ~JM�AtA�s%e6���G�"1|*a�by.{Q� ��8b"{Qo �F:<:L,A� �& q*�` "[V: n>?-�= AU-+ �AMaw> MF&��Vi [B�Ei"�8`;� �SaZ\�O�� 9���k*��a�}a*Ox-A�us�*<���{A�� wHk 1 M���-��e�e6�� Y:� �CӕH hed.�F[ �M �� "�t�Hb.�ry BJ� ($MD���!�4�e jB6&SHsWr���&�Y�}Ak!R A�a3!&,�Y �"�$$t,3 �Y�_���w�Ta>o �) A�Bjm��got �pr5! �eU-!+6 �0$m_n^*>m_p^*$&W�kB�T�x ench��"[�>/�BEX"Zs. &�W=b-�?�Ub ��d�pn&� d!� TI&�. S� i*�A�t"� "beR�a�!))���on,�l ve F�\G eXAk>EOS�I�&:\i.S�n^�ude�dd*er�ma chiefE i_ ����Pu'�� �65��:mo� chaA5ei�b�;?5��io�\al origi� V build�f {�{ � ellip�T�� realՎ�!A"*�s.��#N�+���p2xful t�?L�1mZ5J�Y��� r�cmeAqG.#��,�K.d� 9.F�oof^C^�-�!���s,&� :�eup�ultraW.V���<�u2� ��*�E QGP,�"a6!��e �dijB�4� �@ ,got:fYal,VF�� jc��curl�)�!a0s�#!N"w� +`�!a�ɲB��AC�둸~nar% O#ept"�$^ofa�#a�lr� &,{RB�:&��?t�����L`�n�*�~�:*%fw�o-v%�u:�ɴ*�d�'i$6�,Epe�ed�Fd"�,�HQ�T i �e"�F0��s)s5����aw RP!��Mq�&us fu�~*J��\ w�$Hbb�"o E�st{&e�*?0�PmUQ\�Z� far�9gr� e�:|��&�"D��ia���&�2TSid��f�aAs�!�"fo�a� back�J�V6��B���#�%e\ �� LB15�j)��,ⷕq�*e�d �l�q&�4�� �n�*&]�!� ax�L�;��e9A1 -�5 ofte �we"�u_� h\F eragC- � ��m #�_versey#n=�^ apid',$$: �0��}�B,dirfl} F(y)\�wv "NAN(y��$sum_{i=1}^ $p_{x_{i}} 2 ��[[ < p_x}{A} \�+le ly��*�� i�\k !2��QE vaT2i��3pd mid5� {ala�H A(cB�!� a %.�Hat%M��- �4E�2�e�]>a�H����\ �(Dszv�Q)'ߍi΋|)�� �9ed o���:H*�,h82}�-� *� ���Z!s $F^�(y).�Q"#as# C���&n�A�s$͚� it�;�grR�nyr��5H53ar&��*�Kd�zo 2]C!,�:�� comb��1��"vw)���!�;!\ al%' 'NopPfi�6eBY $F�,(!Yisf�f_dir} .mx����i>��R$a�"�En�!� )V0E� u_$yT�Ff�:�of�5�f$i$A�!M6�x0$ �O+1!� -1��6�,p v ly 2A�* "n ,32vCA> 'kE�coe��TjPD� FourB&�)� azimuth�A8�ibu�.$$OlliPRD46}��f �dN}{dmGD}(y,p_t)=1+V_1cos()+2V_22$$ -� p_t=\sqrt�j^2+p_y^2v|�_$y$E�5��+g��I�K#t=�%J� W"c/5 �>s:�cV_1�\la> p_t� $$K��)�NJG9H��otrop"� �ż*um�"��� !��t! 22`=)� ��&-õ:MaM&.'@Ya ` e" %Q $v_2׊a"� ��%W $$V_2bU^2-)�!]^2=_6�= v=>��i[!o�l�� �3��a�Aw [^�E:u�u~p~een�]ly*Elk!:� �(|>��`.�($squ�P�,~V_2<0"8,us��7���aE$.�HV_2z(UK"�*�k>.8=yt p��  z,L�nov(@2,GaitanosEPJA12}a jB�" g��Y�Ì)l��=(��]�q%��;�JŮ-I� A�nd -q lib�rm,"�&�S*#:�. Also� �q`q aD^Z"esh@on�//m� dronQ" 8AGF#�>m&�>�&C&)��!-�EHi�$g*$g�o"�"1+�&!�����x���.g�p]ed�!IRe�6�76�5g$)�� �!��p volv!�a �-Ki�a�_�z� l %@�\�� :�"A?er�MI/ iscu�sM�� ~&�e�$ns# 1>B�Cr% �"s}zy�|)r�%23�rL8&�r}.��![�7�esaW5- �ReHe�%nt�>t;!�Q �~cd,P fig:!= bred��!�-�55��%�al"�*� "1,c"l werek*r�@q (�6ZhangP002}).�g�,U���yIk A !E�AI�Lpr��(~atS1�N�M� � �.�}�  F C�%�Z�%�p{�"E��+gatA��)�U"� ��&��:tE�baA3on �1r*u&�0 (�Z����AV�h�B�<��5 �I)��A1�%>IY&B/5���E 1\, AGeV$�^Ba�308,V2LB562,**/&R �+�%=V�:1�E�'� sd� �com!���,5]�IS -E�s2* �VLi 8,�� �3lT�  U3Hboὁ 0sm�ev!3����e bn�sMD�"!ttoI��&�,� at m qEA5A�!�*`e�%�)?� <o�,�0:}3 ,p��I ma�~\2=)�RC5� �-:nc� F�1J��%w� �;2 &yN1�&��8���.e�I�t"@3P � �o!�n o�ll�u@�VT($pij$nn p$6^ sdb� pay�i"%��nr a\c�e"bP� :V/IM�QԽ�B��y�q/"q/�r2�#2��#&8 *1� � �D&5��ati �a"� �`�*out.�e� �+A\u273m�A}n ���a5amuc� &is 7&zex>*(�(�*-2���$GBD-MD$A�� a���� �Ay�� �"�9�i1�ZkashPRC3�=;#*��@! .e �)F� �(+�C&Y$>*Hsn-l��f���9typ wD��rg�21tP���d,-�}*� �% ��� ?3 j+%/��b��|M�$K ��220�A� ��Pr9% ,Virginia!@��"q �L  a.l $��1�s=,�{ �(�=�!��#y. : i)@(syD%} 9Dhe $SIII$-$C({\rho=Yp�H�- � i.Bm Cl } $C�2= t=32�� &/A~S �5aD�aw 6q���N$ GC#�99r mi�cلe�8<];�� .�6 �,�"�.�k�l`1)�2C5�T,t oa`:*~@�*�G!`(Pauli block �!F�U1�Ea/�MFi�5$ $NN$BYr�><d �/]!SA� crip!xe9&3%448}. >�D $\s�_{NN}$\�o '��B?%�W/^� $(p,n)�<r�="��"s "B8}Fe+^{$ (� ]X Ni Ni poor"Uv��41 $55-105~X1$�%r�dsa!'".a�L$ $Z=1,2,3$�sK Westfal,30,Pak1b8 2 -+� �5]�s �Wex�@ng&�/ !� BaoJMPE7Z. C~�� � q�$(N-Z)/AbZ)Fe��2N0, nonetheles�/fUE>| 3&1�����[��(r[S ��j)�m��of �E iso-u�}��u�2 ons ��2�UP�U T m9ff�u�)$6�@g��C�!e#�r�1� _ -��Y�] t �1�I�!�v�bR�UYsV0erb2Y0.��o4.p̃c�w :M Ip�Gb_{red��5$ ���: ��"L $Fe-� � s; (�: Ni-a� fL ;is -�M�_iff; BM oft;�M ,(d)R k 2{ = 2fm^2$��4�N -fu��iamond�� (a) "F&Em �:h�20�6�}�A��(e]�� ��em!��a"�x�i5�endure} 1���1�&[Centr2�b�& y $5�!: (y�s)�).��E1{F�Q2Q 14� (c�E"�"+`s:��Q� J�EKB�-&%r5�aIn�I*�s&6 al},J �H$��:�� @Sran��>g #EU��"}Cc] *�r�!aBvar�:���a�a�}0r$.'&z �d>�~!dF&��ic{!�)I3% Ow��6+*well C:�-rP��ve)����Q�. 2f*�r P. �`f $inN��8_� #dis�1�� ���!" oft}� ..k-l�2A `)M-�����N� cO>Utk�D�!I(�Rc�)�w!rtaJ�#Ur� JF!R� .�� E ent>�wR�8a�lQ���=�.Q&T��to keepA��V"S&f(q�!m��!@�X. �n� atic rDS]3KC!m� ``ex�''�=7>iz��<ary�C&,��#� . ��5�IK!5di'� .B� �%grea�c�'N�'㉅E���(!UyX �w"/m ?��>�'s�8A��;ai$-#f�) @ m&KKws4klr*�t(��ebe.�=a� Q�%s�foi* "�izd � N6�F("�D� �})� we �A�1]K"Ovs.&j .!s�� 8-T�3$�-mi��-Qw&� 2a��be'��a� p 2P}�*� �ma�]Z��=�$ AM, YC"MEt�; �x�"��fCo2G�-���Q9 *�xi[���A�&L: 2�A �Q.yM{EB!B! W'6n:G�c*.e. a�M)ev>���Q���x mp mD!� �}.q2� &3����E&��$I�9;�>ify��"� ����"�no!�%� ia�ua: &�2�  (�& MB1Nɰ� =�)e%�4�# l�$3He-3Hp~EF6��k �v.y  (%�B!)%TqjnQ8aZ�, *� 6$. A��� :�F� �/n� >�D� "k}�OON[ID�I�>"�(�-���>rby�Zi���.6��*��2�qve�Rloi�8�Mj�c{ <,so�g��-&�%m a�> =��)��2�!�#dB�i= ��% �9/ Bt`��.X�$i��2;RH 'rm�703��� � p 9b%�EZ���1t�-A����3 2>*6�13� !D�as��U�7 �" �)�`Oc.��o&w��9so���q\�lآ�"*� J�OT`!���lerpreG|giAHi1]1P}�$re�8]rH9 � ��X&1~,��!�:� �\$-69$ @X+61&�)1bePA!�?)�I/�c!4q -,fv)�V:n#is,���S?a�M�8.$L��$54 �9�e,r��dUa!H�6��~ "�)� JRBr�P� :x�bR��dP_{asy}�)�=\�.�to ma� ena�!>�9# ;  3U "�B0$6��;L�O� , d�-�E"J/Z-��� in��m_GqI"�Gwa'�� <.Py�O �qprZ6�>'�&'J9��FA6�,�nF). A\�u$P"�}%kb�Zca�&N/���Min-irum�.�^6�r����. "d*��KR�5� �ds�Mk%n :A-=>6~�8aa�c[�a��s�i� mber�zg9#��s �Y le. B�l��A�c)�I�t�3&a.G���&� �c"m&��eN6 ] �� Xp:�"*x>�(y&�M�5�lem�#��-GbI ��F�$D�,) Ɗׄ��(�!�eQ>6!�2�: E��-�"�&E �K � [nel���? �e��%��e* nin���u��3�!�#�A�/ bary���e�!2S�)"�&0C &�)"< Now we �Qq*HD"�B9:�E+��U$D )n/A"rTA��/5�me���ˑ���e= .2���A,� �!� &' F��-��$ZH�coɖ�*� *�$, �Ae�;����Z�!$���!V2 �SJ]2��i!Y:Vi&76-'FE=!�%Q�t�u/1�F��* a�%��rmE�Y��B%��MM E�J76pc<[1mi.(f$Au+Au�T��nA5 [@(250\, Na�8ransverse and e�qlliptic flows of neutrons and protons in high rapidity regions, see \cite{GiessenRPP56}. \subsubsection{Tranverse k�} %\addtocontents{toc}{\hspace{0.55cm}\thes.G !12cm} %T>X�^ \begin{figure}[b] \centering \includegraphics[width=8cm]{ch4_fig7.eps} \caption{Balance energy! 8$Au+Au$ collisi!.for ie�Omediate impact parameters. Solid circles refer to the case $m^*_n>m^*_p$, empty /to ofZ� in $A�nM� cA�dueA� someI repula0% fast-0 s buI�)�T is hardly appreciable!e5�, � lso I�evious s�xH. We will now look E�carefula y(mass-splitt!9 �s)�increas beam y �#!�R exclE� observ� s. $n/p$.�!6Uv?] ( $^{197}Au+ 2g0at $250~AMeV$.�,J partic�in ��!�(relatively �� r�� ies A�2� U�(v1np} where!x lefta rA4 panels illusta�% two M ��3 . s. I%�us!�A* work)r� ;�H normalized to proja�le ones�AaVer�!�� system ($cm$), defined as $y^{(0)} \equiv (y/y_{V})_{cm}� $p '_t)p_t/p6+.By t] %�z7c�z 8n.e�{�Id�-.�2+p +cͦ��IEaofq\%E�ץ*ſ re�AV\, EX0, $b/b_{max}=����%[-�y��8rval $0.7\leq |-M| 0.9$.} �kEN:j��9:0$p_t$ depende����differbetween1%�� ݍ!DER�� ��, sam��y,Epral �5$selA� on aJ 2U%�>} .rdifv1>sHig�y�s�ow usa� find�-Ddmean field $MD$, which bec�� importantiŽ7m�. Indeed��1�t beha��i�h-ɡwonmͱ� is evid�HQa�range�>Zum���0. We emphasiz���averag���1umJ hese�q�\s g�?a�?beyond{Fermi �um�< a rough estimat�/�� of ۅ� give!�ready��,�wL lle04mponent $$p_z\�$Dox m_0 \cdot 0.8(y2�l \simeq 260-280\, MeV/c$$ I�is� �9mprM Q mass d� mi�s grea�m��6s . When��� �� feel>@o�anm���their��mNq�� plane%*a�����6$J clos��1� A���CoulombI�-M ac. At vah c9��6�Axp+ �8G%ly enh6 d if:= 1 . A�lik� notM� in b� lot�Ł?>�:za abovCeb�,A=ti� r�a�B#a is�a clea1�m5/-�on� 1lso�ponsible�j�0non-symmetricq�e�-�7=@�.:twoJ s a&oppositeE� � . !��B�um� must tak!�t!�cou- ��easout-of-IT� eh , so!�t�E8d9 .aIer redu� %C���a . It causa� crosd ɣ-�U1*6 �e� 2�-��Ois)�l��enA�we J the �� slop�9\ur��in Rw(* ) around.geq 0.6$%� qu!� suit way�e' e such:c9�  �e%�.! E�to �s I���ce���|%R-] GP $$V_1^{p-n}(y,p_t) \ - ($$ 2B "A �.R�H� ��P� choi�js-3e�� in /whole%h$�� emitT nucleonji�2 statistic%,m!k��ati5�68$'s (large erro� ru�& )T �Muld b�-s!y-�d�A\Y�� 5 �- � "� {E2�}�>W�q 10:r Energy�a / e.�!"I *� *�!�mid-r� y, $BS 1$, { .F!�.jgeq1j $FOPI$,with similar*� G.j4AndronNPA661},$� n byp: t��. ��6�6� v2B�A�ly���a check!�ouѻ:�mds�+proaad�&�} �)4ge �u"�f .; �u���cre �E1 ison%}%>%�-GS1� b ?% ng� d "��!�ch� sig6nfor&�W.0e�I/� um � ribu��agree �Kon�����"�. .��wBP�r� � r"(jzero-�) "M2��.>�t]^�.A11�m11n�put(-12.8,2.85){\mbox{\line(1,0){5}}} \' 5.75n' "�2� of1�ũ����6��3ڸ Z� �.# v2np>ERe4o� ёFw �/�l 2�б� ��~��2[ }knp}�cant� $p_y6% �ly gr�at I�a)͡>�,� aai to fA���i�!C � !$maximum in ��(4\lesssim p1K 0.8$QE�I-Yxinverted!� @ y� t� s% =: ����� 0.7$�!on= �9!4&} ���%h�pU)��.BE+ . A> v��]l5 �X%\h �,  2)!j� s U} I}, ��5;c-6!�)�r��� Aga �)Z%�m�B rVnot perUl�)��_�s � Acx Xb��!i�u��%�$.J�L best` ŀ� ař"A$ F�QM& �Y �2rs 2Z 6 2^2 & �2  2 � � 2:� �J��������r����2>�Y�=Nk !��j Weapat<"[j{ >|  ( r} . Any=� as���  appe�  �ly ��lowj� *��롥�rel� . A�g��� tress%=c� A&,,��� I�"/"9� Figs>�,&aR 1} (� �$)e�>6As:62} 62$) we50 see � �& a(y)$, 2 �>d 2�'�!���Ɂ�aV "� �)ā�bu!� ensi�� (isospin-MD$-��&5$discussed %B1�feature�m&i�!�$expect a ko�ens� ;;�<s�>; �remark�hJ?jI pA gheavy  tend�Pap(e dynamical1�-`>���� �tA/� um l� In sp��m alsm`�e`q]sim�"A� any� �&� a furthe:dic%\ leB:a]�K.::Chang�!astiffnA3�e yy ter/#�u#u#�t�� knoG 1US veC %�a �ic�� 2�deN| B �P /Ear EOSa�-�E��*�U |!TScalonePLB461,BaoPRL85 C64}. Fo�i�#a�i�� ta�b�Nat MS a ly u��zainly./L 6� &� e� � sk�  A� cQb0}. orde��_e�point�5� >�"a uI a9� Q� a���yk urɳ�t��!�one$ jfore, ^$2" keep�'s�%!-^! s}. m"{%it� P asy-soft}= �#]�$"!1} " ly�. !�details�Ae}%$RizzoNPA73� F� �& 13v1� śd� phic�&2�3v�+ 2+ .* ("X�ve2�2%���a�7'�"�z Bz  Cn%E��� ormedM�!�$%�oft$ �3I��� B� :�u:� Ou-XeT�'wh,���o.?� a�E�b�,e in o�~.���,�N't��q��a� e���1!to.6� s�[A 2� %<*w$ [i��2|a� fun�.�����I,��a.�)�^h.>! ��� b��. �'=&8 2NY$ u0$VE*~$� "�cesI� � "Qs�,Iҁ� (i.e. &=6 �"Q2})� !& �R�=*�a�.5 *a �0.5$,�n��5mbet && . T�?a*2 an �Gi&5 i"ee�1�ng� "�(�5A(at "( prob� e Q M�s�+U iik"C � un ţ��f  ti o*I� yt�Q}  �& i`ili�)% playa an e�/tial rR-A� FE=V�� @toG%loy� 9�)ort�ory. An�roach ha/en adop�basedaymi�copicEQ�sa}�Boltzmann-Nordheim-Vlasov ($BNV$) type � �GregoireNPA465,BertschPR160,BonaseraPR2444LB221,twingo} +9�ɬ%R � y aS"� z0ColonnaPRC57,2@ }:,aZ5iof flucti��� d OErice98, W�42� �.9p5+N4th Pauli block!�consiss1�-D�.,���+follo! a b/��[, evol#!�a latt� �)5,Guarn!Y(LB373,Greco!9}. AK.�� ree $NN$ !�A ��%�/� ��,��yeHang� ��ce�Ie��:�s utiA,ev#|inia L/, �5 g���e%>tr&�# ���� e�i.��2i-�Bj dtG'� A�A.Jer�F��de_9�uo3influ� >ddescrib] y aJ`��a �Ea0erm so-c/( d Bu�L�vinU�a� LE$)q Ayikap12, 4NPA513,Randrup4Q�@PRC49,ChomazPRL73A�We M��metho( 1s!O��3m�-%e ݄MF�* ($SMFKp��,R��� 420!n�) simplifieH5 cedu�compu�#o��#]0erey�580>L !7 � 30}, �G�int 2 ae12%�randoma2pl&5��+e �5, (Phi!S�5 Sa *, $PSS$))Mtudզ noisA� gaugA�#(p���.�most �modes�\ �A80Ep3%�-��1f�+self-y�qa�"eaeu!|2 durE�v&ime u^��no��� h$\sigma^2 = <(f-\bar f)^2>$i� �U �traory���, r#yS����D=� $ $({\bf r},  p� )$, B$ e�.6 cell obey& ey��,oEA��=�62� 42}:�у4} \frac{d}{dt}=%- $2}{\tau(t)(+ 2~D(t). %� .A!j:g�$ 9$Dcor�3&%{5�� �I!�3x�%�$ �8 = 1 / (w^++w^-%H $w^+� $w^-� J��i%:i a"�  i�*ndl*!`.!ѷ� al �Q`_0Eb4f_0(t_{eq})(1-Wt!�ilibr�$ sugges�� satz"� .! b"6݁CJ�2!� = (1Q� w^+ + I� w^-1�wB��p! magn2B9���is6( total numbO$�"�9 (5� on-dissip-�` em)M�2o}. �enobt& Eyy�&"F c�i5 lo!�.��$s $\Delta h*u-15(1 )$Jt\.[ K=NY u@� B�< �= 08/a s"� f Eq.(-B ), iiM��.H ly �w,E��oo its2~ Pt � lway} EBn�1di��&&� � r� [a�e�$5b= Nc�.uK��ledM2r ``��''�mnyI9step AV�$ext�:)(^ �+al .&��R� . F�;a�^�Ba�3co%i2�rdereI�@�w�3%��'�a M�=carlo�fat&� chosen �> 6s,:�4 SD�wan have@!k� �0ory branching%h�&�y.};g A��i�A�$ssume a�% }�R8 �-�6� N eA�s �pri!f� �� lemsA��  , nam|9 frag� !�0 expan;/�rI��,ŝ i*0nB� ed��er�lyA orI)?�%S�y �� ival ? � �Hs� ng � -� �5 pIs� �` s, } �;a|2lq5����m�Ja� e analysi%��� , pr�>"e.� in�%s& � ts��< bQ3nu-9!�I0s� � T$isE�~���&��"� a 5| g0 ator l5� accu00ed $400-500$ :�-� phys!�I. p,&!?_ �->/.�S "�a� �� fixM+"ca�%!����, eZ�3�h a $��<h�7�3{icar ma�($SNM$)Z  9"i! y $K=201�<()eusu'� �h0��:!���* � �y�.�:X�� fig:��}. Sect  eos}Ws`�92$} (dashed �+)�} (s�A ,>&F uper ((long-.M�2!t�o�W!At/qgal6�1�x3) I{M�me>.ismeW" v�8 : Fue�vE Deep-Inel�Compet� � star@?U�at�to>e!a <. Moreťw)��)5�d/-l_>"�8siUIavail��� :�1�/�x4n $SPIRAL/I-II� �,new RadioacQ#K$Beam $(RIByac5. H'8w76v�/ga�C:=" heE�-�d<binary ��d�"residu��rm�� wM; occuu)t�M!�b>LD $b0 �9 0.4b�=�In6�rib�0@pI8(@,m>A�a=2#, � -B� qk�*'D�4rW>o�9`ab�H��(� d� seve C�/Z(3 ($b=4fm$)��*r�l ($^{46}Ar(N/Z=1.56)+^{64}Ni 29)$)~$N=Z$,Apoor @V 5 Ge$)��30A�� 4 ��7��OM }5 u{�!F �>t5L&�V��oe�2ntA��&��!�$(a,b)$\8A� stoo��er��amo 9of���C���*� a2!����surfaces&3a �  bea��A��.&!2�:�I���!M�# �?leads� z�$V,v�s s&�6v:y �>� f&�3�(at� ive� �3!6  se@ sIg�%"]Fu��!�6ners,�W7r�#"�-B� v&K@t� H� �D� likeS<cF&��path,�2(a). E*�El*�=eaG/ �� omplete fR�: �:A����48G >�B��>}F�3M(e=0.90]{ch5gI1.ps}&fIDe$��uu!��� A\M��( MM-�EC($a,b: � i�Ni�nd/e�/ ($c,d:.V -a�.G c$):T�UPaC; ($b,d"��$$. See tex�!lagIa��B-"  �J 2�Is%�s6�$(c,d)$�% ee j�<he"&= . Na�we wo�9ex�)ELm8on i/we0 M�/!31 $n-p�))�..6A�Ae< e of� s�� �G(a dominant �!dfi"f�,�B�)&0&�?� e0�7!��8a�2 $(d)�* get �>I��ce� q �t amaz � w��'s: i)v.�"�&ic�b-�c e�-to� D-�� t; i N�er6l���>1���onSJto��!�ai��*�ex�q2d��$velop a ``�' skin''�$chM� lapt'-�.zon%?e�g ��A�=�AA�a�JM�*��E�ly^mpt��<�JaA�seq�j�~ dBa0#erQ� p�End f�\Q �b�ach�4Co*55�y����, e�!/prediSK~�9 p6�36X_0�!�re_q�:� H%MT ��0aX yX�k�4�&/. F< �F<6eZPA339}R m Landau-&�($Ca$-isotop �$�9 159 W�s!W�#�K� �in&, yZ� � &�F,e<n�a2�1ֵ+�5�in:  !G��� . "� �́���5�..�.: h &� Sch9"�) ����|�l�LD7!�a�\iI*h�FU�M8�p. .^Z��akfinal"�s wMe�mem�)� a�dE�isM, <b��#& -6O�v� ��AN*5 e2W%V� ~"��C4�AV� I neck-�%�$%�t�t"LB141*�589�x3I� j $ate Mass F/s ($IMF.�K�H$3 \le Z10�re)=�*��.�� ,�H�"t .q@3*s � 1�"��T]FwŖ�.J��a�6@$,�)�� -�z:--�WFerO)Ei8ed>�!�isovecto�'�k+)t�1ng. 2�&in5j%�"�&: Surve��"T(s}�� decad�6.e��8E��"&8in� .�at>~% and �:���on�Q1�9�s "w% stea=ri�/,U�-/"��7 �ofJ1sec�J� a� r*Q� .E A `�et%P�)� phen�2a have b&<strd��n3�h�=�� .�>KRM<revea�/�LK=r��N fo�A�)�&relev�Ly s qu�TEOn�caiA�1is�Yo�� e�Fa�;r�,��|to� ��:����IA=o%�uDfir; rgan�LaqU��w&�.Y���K]Ssrr�to oret���Hnd U!@,"� &9&&�)�(�)&�Eq}xEHE�JD %�F"F�vTF&�Ms [0}Ca,Y0}Ar$ , l +$ !58}Fe!58r]�amol he-� devo!5Atud�e r�))���spin �1eEy#'�#F�!Yennellot'21}. Let�O&RL$Cl$-�lhV}� i��a�a| gs:emposite�7$(CS)3cs�3A]l�j L(to��l,X*��E $N/ZbZq���] .�K$53U ,Gx ic�+io#* !�,11}B/ ^{10}B�90^{8}Be/^{7}Be  7}Li#,6}Li$, exhib4 �+e�ren�W�$L)_{CS}�JD"\R��"P � ��&*0�#F!b0I !m-t� tr� eb, IfAr + ^M[e* CaF֡ ��)@� b�0 }" e�E!�Qjis"�y�ed. SAH�,&�e�?7P� ies,�<$33 �45gTA%t M�JohnstonA�7wH*X �n� soba` -�.N�: � seen��I657� 33 �." authAclaim)U� iY!��y��s$0� �;�gim N.{9_����y -�J to7w�") 1� hA<na-07 jH cb�n�+eY�=Q�pa>Uy"�GsI��&,�}� �X�=.��&, � be r! {7(m;�cuts){> n ex�E�%BrT �:7� %��%� �#ed!��E�{KE_{!�}= 30I,�� �)$A=58� st�$e�Fe( )/Ni(I�)�K � ��/J�M�U��x>�$^��1}C�ҁ���W�� Li/$ ��12}C/$ A9�.'J:�wsu!�a� labo��-L �$ aproximatW e5!�.<,m�,RamakrishnanP, 2� ��F �=9%-={- ons "�J��usourc�ɷ=Howr,��%)�Ni+�dFe�� Fe Ni$ mi'�s,"�%!lu�!�!b�|!� or��%b�o40^0$A�m�>Y �&�R�F �&��1!f �siO0I�midf@V� ��ui� ort .�%xha�forIt/l��*2.� �# ��. � "- ;���st�$n�X#6�rem9c$)�C�8ot6 �E�#�C"�involv���;%+� $Fe,!ٍ��8c lAm1{C"q(�{s��id�+1,multiplicity z*�6M ent>Z,!/���0vy q�\�&�8inc�X���H Miller�>j<N�c' 2T �a� lyaRduc re��}% %"�'��N�y�#� ��ob�I= �!6�a,, $45, 55, 7 a&�Tяd���*�/x%[�1J %Х�* �,����H�(�&:*�s�$Aa�,�iJ/��:�hig�A)�, $10�,%9�A�ɤEqv� "�0weakenA�9��� teO�6K� onse�#"? �fs�R| T.� �A&MX� Dqvq�i"..cF� D�,lmQ��� cao0�� B� nl J "*!;� �.� s-K$ o�A�d� �@jipD�#�*A;m!a!�p�terpregof" i5t�5��ay�dva)��� 6P.&�~/uɋ4}Sn/- 2}Sn&�&next#�# .z� outsTAr: �V}q�� !I!��2��$!�(1-��U9��Y �i�F $N_{C}>=l%- $�a $LC}$ $(2g a_� $n}�r� � . |Z!F0nF� ,Kortemey�PC55?2� -�If RpA�%,���� nɞ���tP�t.K was �"��th�:�}9ro� ]wJes�|$124+124�A� . Ai �'�0.�}m�y0 :1 E���soc��dk�st of�w�gW:�)J U� coex�-ngiO �ic hf",� *7 � healthierzs}�qM�:��!�B$�%?��p�\�g ��a �S�  '"�Vd=w �CycloW# Lab.�Ui9� �c *� 5"� �Xu�5,Tsang 6}�I .�A�FU%�P��7�,ed �F��<ai��6< as麁�1*�����i:,ys by"�!�! "� E��6 $Sn+!��5 e�Bt�&*s_a�v/I�t2reali��>xoNN�L �V��&@ $R_{21}(N,Z)=Y_2 /Y_1 $ W6� �*!��� law: 2$logarithm � a4+ar&�1�&� n�=!�� �<��^gi�;A7��� |�Ca�m $\alpha�'\beta�f��jde3douaq !?�m�k���%Pne)o"��<4 g�9-canonz.@4 a� ach,AyC2l�pina|�BM�"�'3)6/-J�' �s.. Ob�jA�!�&u��#�a��"9 M�,:�iI�� eAiE-E�a1� en��2`!�.�ic"U(place. With͜� Cmo�#alJ:>! e ab�4e �b\rho_n/p$!�tT o""4?�_outpu� i|W( significan�"� �2a@1xto-�)z:"fO$1.7$$3.4$�7R�(Q$1.24nd $2}Wto $8.2=   $2=48$).�QBo� c5l%�� #iRb��0 )� E�!5M�picP1!]%�sc!�A�>�QeA��!�^��S 1K�I� We?poQ als, !��]��-�}+�c'0q@o i� lud�0��o,T� N V�pQ�,B d�(d��!2�d0o!cg)�temper�Qq&���]ter;�g"t .� re�%� opos� e.g.�& �LiuPRC6� A�!�� y_a�0sa�y/@g�d�!� no global�!{�qu�A" �o,qd� t�[adi�,o35��Ao�� hed,�@fR8�>&1s"->&�.�$ . R�:"9a= �V eK,^{ Xe+Vk ,* r1w?d�B28�� Shetty!�8}. Ig%ic ��s �o�Y&� 62� ��d9�o �i��i� 9*!na>�Rx'ha�B�1�� -� bF �"a� ."c!�A� &E\ts sh�ccsly�cka.i#^mi sphi0*�*',x �e�o.�s,Eh�@�* ���!qu@5�2" *5/-:� 1� !��a4 fall�=H"�� Z�!b-=�N8r3e!�a�mK �daݭ���a�8"C"U�2 "K Fe,^�a�a�BzmA? $30, 40� 47x* iR ���HIP97,}"R 70}� &s �Nu�M�9zom&-rW"a�,&!g�12,i��58,x2$J��$3+m�G�viAD$R+pD�-to�) !���.����Bd���Q��O9�in� by��F�EPMarti�6Uf�5L! Neck:V%�h S6�C**I"�F��%n�Ia��.u3B� a�� �v 7mN1d:M1!d;�@v�++!Ad)�goe�6iA F[}� �!��l �/ly@)�� �AoBz� vn�shR)��$W�le!&J0�K�=�. new Q�! mI��ѩ��.��" d� "@ic X:� B@i�0act�$%>�љ P">v-L}o�qT�! k al�%at��i6< A:is�2��a���EtM`/ ���)F$19 ,!.l�s00}Mo�  �120}S�  �m�*C�xi�<1,StefaniniZFA354$A.�N�ry,:-�f &�8�� "� 2�ed&2 �/� "�JX*faon-�.S)"` primoA�l & ($PL�Ind�Ta��5�X!in-�o�"DL.UBa�h� sc �to-  lifeasYg�"�� �/� ``�s'')l$$3000fm/c$�P*[ o $2!`E &�#co�~�B� �y�<in�)Tok�5}. Co�0�[ �)J<cenarioj�pan�r�O azimuthalA��(� of IMF's�/I;����align�}vD�1t+%� ^*$) velo, ��`"o��;��per&R``G6N) ����Boya e�a a 3}�h�9}Xe � 63,65}Cu$a�$5 �" R� �� d=R2a-5�&hA�  )a"�,<,.FS� &<F1}{2} <,eu�YLukasikl!5},&$H!�!� ial +a; n�/ �#�8w��ab icip;+�R�gcours&�^&<lso�5� baL��U �7�A�Ee� he %p&D�2?-ɞ.Y,��s in refVbcite{n�/7M�aultane�"%;c n�t-�.k a�&E i5 ��s*�!e�inferl#�="�9s,NLefortN$62,Gingras)5,Dav� 5,BocagS676�0 7,Pagan�\�H A�aC 2�%SEv�Olu�,lN?k!e �a�3u � "� )�Co�}a�m��ey� q� a ''�archy v'':�� rank�c� �Wa!Xg�&'A]���ky al�+� , $v_{par�A�\ "� .KMmz;E� the �bi8 I� H29�A��n67%{��#p: d,�&�Sw6%fu �breakupa�}ck�7�Tre orA��g�`Ah med quasi&�&}8v�I.WF0!x� ��a�> �e±��bW rr9Qou�,H��A$4\pi�ht�1�yim��"er� nces��re��P��"shold� �!��&menQeS,uke�f#U�:��" �$CHIMERA�,lwo� ui681:v �`h�0rJ0e&Br� :H2g�D���%>''A w!B5[�;69� �=&>��i5�Jґ� of� � y���7d9�;C%��,ng"�(!���"+5|%�!3m,w &be wid����A�Y6�y�^ "6�/94%4졹A��� F �-$by Dempsey��"Z �H4%9�uZe�ysX(124,136o$� "E$  (5%� �} of�U'?.� $�"�a �&Q :� ) m��|%�%+gA+9��!k 6}HeP*3,4}H�.$^ Li$ �DA"D$$Z_{PLF}$ '�w �1�FO(mid���4C�Y��\�P � 3�  .Enh�P$d $triton$.�anwr�w�^�H�L��6y %��"KU[ Pogg68� �a�2���u���G*�8. P.M. MilazzoQ� � PLB509, y03`aly^�hecIFaf6�a�& � � Ni$$: 3�NP QEa�e\-bump Pс�%���$5�8�"12$, �M�1.!��  R��Q%m � w :� &� H�6� q$explai0.NN��s0+t: ewo��*� �.�$disassembl�?Wq�S�@^*��&IU�2��� i � ex>�i�){A�5�� �!�sz � �ng-��)�F el�<�v�. � y $N(Z)$b3�*& Zp�pro�#es:a �O�3"CR1�UeYcop�.��We�+= �"d |a} *n0����S�=�!�B� {�� &Xle7 �o�al&4�"�w��t��.!Y�L�� u9V�*w�Q�-��al*$vy ee/ligh�os� ����4}C�.2":02}B_("g5 e$&i58}Li/�h5sho�I�,kA`I�@*"f!�6�# c.m.Ja!$ p�Al�*o@�?� � �51UWi3;YiEV7#!�i�DAD ��6-h� unit!� Plagnol6� � 1}"/�2�X&�0 \ $Xe�# $25��e � :�> .�*� m���cium evap�1� as�e)t|MoluI :.�Y"y,!W j*�!�� $2��Nm�=y'5l �veAt Tpin%� inva�~R� -oed� ;.6(c$fo���E�*�ic: Q*7op� favo�G?�hhompar�}c��> E*c5��ck�W`y � !v{]� "�4 �g q"F%�aa��-i�%Qc�,9��:$�q�24}Mg$�74.�/<$LarochelleA�j ��-%��5.�$Z=3,42��ANe&M ��.[]aekF Fupl�rco�t. u�AWn&aofE,� ly �"�t,� I���D�a poUa G} xJ�esA�tA{��e �N� �?",of debate. P0(`�!x�"����!&�%D.-�ym8,a'M � &~, �&��/ '-n�,,�P promyG}M�Hn�_�$�%W%!Les�!u Ni~MKSobotk@O��Va7 lete�?*����9���)��en �'� fli��.B"�n-}G�-sRm�-"� 4 \* C65,�A���0�@� "��s�in.A:ry �ic� B��>�y�m���e:AEeYzb next &�1�"Z�?�<P��F�ifZ�7�"� !�\Dvz 5a���NW �!6D!N%JhrA�E�s, le.ve�J�s�G5W"�'�!a�-t I�"�  1 alwAP6��}E�A�B��#��tR>;!1?U#�7 a� C 3.UE5O6!dof>Al%�M6�iC�-5)i��<er� ��&�!����V "�%P!�XvcP"�re ads2 &mjsc0�Bect!.wa�!_�N�,D���#f:�y��� ��~-8$ՠ*1&�"�z��Y��:.�!��bo�!- �k2e-8=0.42 \pm 0.02$�4}S>1!mers��T� ialy�X�-=0.16N%�N%r1[�_&�imbal�����Ram 84},��  as"�R"nd�Qi�oR_{i}(x�b�$ 2 x - {x}�n2}12+�} {z 4pq ($i=P,T�%�=�C>չ=�<�b$x�CaG�GA5RY, �A�=�9�)E�+J "�R_P(\V/)=r (vs.:0eJ���U�,"|A ix'X"��f�ant*�+Wye?T" )JVWA�:- � m�th&�I�Ufer2� :Maz�S2�� 7==��p�Ys �;� in.E�O86}KrY�,AC2�$E=J a�emplo58!radi�C���6o� 6i� exci�� � m��!r ��? SouliotisX8�*�e"8�sex�g�t�e ��  o t�$�1imem)beAnab00.�%�� d\A��damped��< t.�=.�^0�%�N �# 2� &�;tt�:e�{Tcfa=��"�-:3/$view.} Us��k;\a�y��l :YX6P&of $Sn,A*R �<"� BHHd$K����  ;s�,2$:� reaM�z 4!WeG�# C�]�M" A0F�for��a6|0mode',*_J1gA�,al philosoph<�0�$O�T beh�2rA1 VuEF�U �� mZ a�p/d01�u�,ll�!��sA��LamKM"bi^��_�%/k�NN��h"b4�i&D/�&"O.n� �v��� s fa58om{f?aid�-�<HN�m )G!�U�J-(�*!0 +��&�����*��#&�5 Bara����F%�M 5`D $��$vs.Ar"QA5� 1�� ���8 86 92="�p� ���AW,�&y QB2�M,,a�$35-ombar% a g�!!�6�qUZ`%{%^+�-�'&�A? sR� 5"e� "��a�!)� r�%�B` 5�3�oT'?�."�Oe"�j B  G�$"m'3aA�4$LNS$, Catania�z J��N��ad Page~�2y�y�r���Y�� �$�Y�s"�dof � ��&sA�,. 4G "� q? ��%ele1w� togh��)-e4�,�@7K& .��w�ll����U newIT�� �` e�fundan al *'!I?r� E�!H1� &u1EC �UdEK�[Qd. {.�b�)1wto%�-&�1: bul:�.�z&�BF�2E�u�"^_At�>��Ŧi���5Am� manife�o!F.F�4a(4#i&�J-n *8U��"Zh[=C60,Dit&81,Liu>2o=#S� � y�,��l�P�Pm�fsaZE;�5�F���=lso��%o �� tour+`aa�y�7�X� b=2fm$ �zAPn ^�~(iso5}: (1.)�]y�[m�"e,�a�i�"�Q$4�i�+�/"k ��Q��O%!�h�"& 1.2-1.3$�c �; (2.[^"l�?upA�$110-12 � b��z;$a�8 T�t�]Tj �U��!E*��*i8 ��-1is %�J pn "�gZ��@�39o��6Z� �G Acco��a�&f|m�o�U.b %�:Pu)b&��oo*%!�(�th! 5�>�o(A*.U� .n}�� mp(� %�h � �ds_��ough ��odd-V�po.7y�+�U5on� -? quid)fQ�1M�%a�4of)�]!�l� � M�Fi<�6M� |$ �q|a�ake:ceM�no�=ze-out} � (�$�� eO)z�0pwmeln1� ����aI�5of s";��� � &@@� �$T050. � 1; >� far �w�� gligC{�a6�l/��Um�'V=d%�&�6,"bAY� �U� &l�d0!�3"Kjof�e�*` )('' ��"�6 �{H ar*1,V RH�EcP��[,fq��n4fm$ (s�R��2k6} z{N "FreAO� ime"`G�'I�arp"|)C5�)#�)s�Kde?a%�>G DK grad�t�����'A@sk t ma�� uniAhLevin !��(a uniq�k299�!�mPM�N o asL9ji=P=/r shape��.NO��$,�� pBng�$b=1-��"2b=4-5fm�0\b.��n��*"�g 45]{�g26�g2o x $Y/%��:i~2�Peo&]Bl�)��� �3. CO��U�:zE�q�6p�c &� ��A`i�wr�n�\U tg�p-���o 2�h�%y0�$02fm^{-3}$�r%��6&��e� n} Gui�a(u�#�z!4*d!L�,? s�\�acٲstic q�eNn*�a�� -D� i Qx�]q I�Ln"U"F?-?s�Ka�a�\2�iso8})M a�%6bzTime: \vskip-0.2cm (a)� �` } $A���<)� *Uqec dots�mb>jV$.o4ob o�}y��<} $I=(N-Z)/(N+Z)�{ g"� "Bk squares),(�z(�q+ �>H+��)�$� 's (���� $3%&e >A�2"�2I$I_{av}$D�:Ff Fu2g6JP(N)} (�X� $1� b�=�.B�!"!�?����B}>�f�7�qAh"1:1�� -to-�ge E�A= i�  ���!���OaF a�� asy-EOS ( s[l)�SP�#��a:�K�e�"��[� ����?T1^�!#��&  w��ic*�(��i||�e-�c� �# �.�"� �`5[�� �[�,�.�Jic.A��<"� .2Wh%ʉ,�� ��p)fR/1�v *ŖZ �Dd*�5$5M o*�kA>ySm��� FC�=H� -p:<s�� ears�+�t�&�-��Br ��c� t�vQ��~��b� C �&�� �� !"� ��!7$E[$28%��Vt�`� n)(��)��t&; �s M� ilar�oU�8z�isA�(b�x e ''�J � ''\�Ma�y� es�le an-� burst�P��.G  ��u*�1 ��[=kin���"�  i"J�B�z:��>��.�P}5�u�nd�V%�{��e"js0minipage}{65m� &!Oer_rB�sR� 32� *� ^� W�V:� Yn ����& �8),ASY-STIFF EOS24 84 �A � �\fill��42%��% $Z&��� f14 �^en"�� �P�om�i5��o(9i�;�t]  $s�vctee_ �HsB!�Nx!� gi2�?� 2�F��(e)�Oϱ �~+��si���*�9I $Z\�x 15$��cxi!�T�*8 aBV ��J,a� t�]Co��6�Y�. How�Ñ y�.aW��_.Ui"�Qa��\N'�n"�k��*nX�0� � �9?���d&SNfa('h�D�<ZJ�&#� a�>lIs, &\N���@ )4 @��T ��.a �$T<���E,L=a� �� M5A�F`�n14}(dp� hͭ �/s�sMg�!ri'�U"�_� �c>� c, f�z wa�, ce�sؓ Gng�G[v ���&��<SCis"�&so�� 2� >k�8 ye�u�3i`-1�qnion�2�m6�;||�& o��, r^K� Z]!�dI dataVXJ�W $e6K�${ �?� �q�t"�/vD2F(�y $3��.!� !1m�2� }��O��gW $N,Z� �)RWJMW ��Ѕ� ion:F�( \ln R_�W ~=~C + N �' +A9�V�Ze ���',  W!�-�"�)W$C$6-�nv:M3?ſa�)�!!��,"%a偵`�\~��fRof~ ̴-7 W�5 �N��<lue9J"L NcoefficMRHy&�ca�hJ�TZ�W�s�4��s%��&�QB(YM)�P:�TU��@��>,ar environme�&d uJIs)�s�d*�"#�q<� �v� g� ����{FS��� MI�g f�B��+`s�Ts:�Yv~I�~ �~J+�� \mu_n}{T}(,/E�b-p-~,>�In turn1� �-�>&&� �narray�� eqsy� h��~=~JX,\r0al \epsilon_{2},X} (I_2^2 - I_1^2) + 2:4 [%-I_1)(��7 }{2}] \no�\\ �p�� �-r�+ �z�1�-PQ�6'�EyB�eri" on (�S2��)��n"O�H(M�limit $~Qj��~B� ~0~~vge�5``� -drop'g�z�[qkH%'&C64,OnoD78A� e1`.soR}.�AZ4:[(I$Z_1}{A_1})E 22(]~~~and~~~ :>U VN6V UN.U6m<~~~with~~~\vert .�p} > .n ~.>��6�O��,$�5Du!� \Big�/Z� N_1/!*)�D�.-�X= M4�I:m(a�) A�i�)ؒc� ���%��est�rtw�:7E�urec2�Fs>Mα߭e�!�Z��,�*�/PN� . �  ,.�[E R� r doe5St/(essarily�o�exq�[a0y�.b��^_o_ enA-9�P�� law!]�]&� ��Q "�F.B �x6S"-S" typef "[�W.�dync��6x� riF �3�$��>8-�tral�->"�?T$58�I[��0��� =/�s��af�a�,on�ue&�<.+�{/�8ME �NX ial "�5rnZ��M�$ sn��derabŐm�"��e���56�*A/bQ�jI.=Q_1�.� � rs:J�(up��cu@�); -Y9 �Rs ()� )2AS�1 &^�O c'�!�)�=��By�Q�!���e�80�*�R"� 2 �$a Лssiz�� �&� Bk~�!�.Q rI' y5"i"��o_6 \=`+ widh��|2�z�1�x�K'%.T �_�9�o#/ �}al�P� ,�$!d _�e�Zj� ԧn,����At"�2 ium.t�>�;S�y ����"b`"iz��i:e �C1�h� sump�"�( �6��>��#&���1&bD3��F&7�w�"�2}6���� 5oX:)��u�#���a��"̑�A�.�M� �&��M����5E�e����&�J*�ex&�� is a��4_+�{�e�� M7�o��m&U.�d0$,���=b!C�mC�M ("�����wA�$� �H@��!z��iuc�(�hG �;aU-3�E Zq* �)goZsp�2��)̗���#E4U&0��of�2 5)H/�Oh@+ o*x�i## �" @Z�Deڇ�<���S8"�� �5 !�A N��m��+.��ce�Tt�2�, u�%0�Z͊"�����bQ t�:r+ !��TFc2�8 ��(��uKA�$n,p$-chz *ga#">Eona i fig:6^6d>� �"�~��� 62� ����OFTB�1I�~1 er� ���j�72��� ��F� UPERV��Er !%� �.�3.45to.�<&� :E:�3$�Summari"3omP2�u"��im D�T^ۄ*��Q�  peculi�n& a ''" ''#��du�*" ���-�cf*2�: 1�� "�" ii\ yQ�mJ�W,6���L$_^j, *�Gᜭc�c�&$Z$��$3$�$W(�Ls*C'3cm 2� E  v�]��� eD !q�I.r �)��t��=xUQ�"  pure &�p��9�l:&W . AbZde͂��u֨ � aJ (%1)!��q|ko2"�'�3!�� _1GV�Z� w)ARpre�5�d���&!�an"_mJE)[ncy:4. �-� *"��l�1"@ ]�Uks ��@kGa� eL�I�� t*�1!�hMHc�} . A��L#c4�mk9"/G ahr"�i��Mhar&�,s!�sQ F=K��RwheQ�  Csag�QZE!�� �6;1!ns�F>�M� wok=[-upeRayleigh6�^ �j�3�ir' V-t;�.NE�!8 a ho�, triggexN� Ex�yi�PLF%d TLF�,BrosaPR197,L�_0LB566,Botvina�X 9}. 2g��#1���B����R[2z+�:�)�!a1�*mK5� A.uY��x.1SLW�+>�76֟") �""|/ =3 ��aB(�T�Yb=6fm$,A5!� r"I"�)2�3D,"��R!�&��c.��b �$s&�5� �*0BA �>6m=� ��28^|�F�*��.��2"2LK5column:�%n4. R��!�2J6� �>3Li��1IMFaSper: !�iso-mig���,&�,�|I����=��ew�tult�J@n I�nM�B�&�!M��, a�2l�VE��� ?HQ�| � ,� y� uk&�. F�-w�^a�9%!o"�"�R.�, vt >�5AE�jP ��0a�� 6�i�9� �stu�t�P�;Nh\�� �d�8i��e� $�?"J6}. Du� W)�6\)>�R0b���ds%  UxTn6�j e�ncolder �%� and/� � ӟ/�: 2�:�a cylind|��6d�5 _U��-�! mo�B�~!.� -6kO!�oH�r?tw6�Q�R� ze:%9 mʼnrup^Ut&ut $14w:�(y �9m|�mG(e%�Rmid&kK!�ts�5�+*E�*m 7c>ҿsxr���d�)�2�of�qmeHc�=x1T%F's 1�'�E�E���agn a�'� G��M Fk%%�%A1V �����) ��2C3v"�5}�w�*�6a6�� (e5.5.2)% @A�n6b1ek�,%gA8act&G$�*g Z&�.l gj*�^ȫa�=yi( s. (�:� )(d)-�n�7&��tV!��kr5K�j!�� '~*:� �2�*� �.;��TbyJ�a���d2Y� _7"4Z�N|)9+2�sy�bM�woAo t�AB� ear, ��lyyl�Mf�6�e�  r(s �D_ �0��P�*ڏ� r�e�)&� ���2� �m��-N*�n 0c2q%=��]t�:Y�.&�6E �A�Y.3@7itely a >�1�. Tl*tel'�A�u�IPto a)ind�,6`l��>_a�B"9;'2 (�s�S��s).G�1%r�G�'is�GT�!f8U��"�7i"9y9�a$"r����(�'A@OB&/@�0iM�= bj!`ɾ� � �ԡ��>n.�� "s ͊o���(9"iVin�'sE�"�N>�?�u�r� ��5smoٮ �>�'AP�w�-z� ofe��B ��� ibsap��Ra292D j�6�Eu&�a2j_19 a�����102�X24 �J "�5�c2c25v%"6cm�MA�Jw�_��s�a�s�[�"'t �0&�D}�}w7"����/� aQ����� (��s) "� � (to)�� y@(from)�]de$}�, lea��� �T.0 z��H� of�-. CQ�l�B��kru�Y�� 5 argA�s�� {�3b�-�<;$A�>� �10&�� �-J������K !(|U grad*"@ %eɝ$%s��2[ ch� �1�.-R�� "i*?(&�P���6�,A��+2"��K}L &/� Y/���A���1_F ��bDeb"ar�"If*��F�1� ��A>)A%�y}� � �zfiq���q�o�dI�"m ��%���.�&>�����5 �l�P=R�:[i:�>H QAN�n�2'F�a�E�$CV�om� $LNS�bn�oaF"���J� 2aF�e�Q !BGc����+ �n0���$5�&� =! I���!Oe�� +"�e � �<� m>�<<TL$�-� soBk�0%d� �:">i"�d�!a�� n�geome�T�$4�<��-16 aE�͕��50]�F11F�E+�n3�$!�$Qc . TyeN=�m"%Lco�N �uai$1*); �@M&�I2n e�6��u�M�a<% , �)$1�?� a�WetX7��� a{ K[en��zAa=)XigY�3}�f��d&�J�2��g�R�ra�3 -E1$!8M? �62�C&'a&��M:I��-���22}. E�$@.�*5M (top�F��X# �g� (bott�AL%os}~%@s a), b), c), d) R�r6^3>^A0� %c�2��G Mb!�L'� 7#!��8�in�} W�a=�9O�.�nel6�1"/-ex�yd� �L"u|I���ve`s�z� t]split,��&B$,�"i��<}�*�a��gmeK���s��)��k0�. ~ M��'EA![4}�lo�-&-�A�B�i: Q%eb��2O�,� Hl \%��a�\�&�'~ = �|�� b=6-7fm$,�=!i� on4> �C�o d$10\%�ab=5� %�b=8fm$�9�,^m�*0W"0o �r� �\Pk�)�Mz| �'�8� bsor.�!r/(� r f( .�&A# .�k���}�"��f�&&�2ready�_{�dRF{�"�Z � m=Xl��]��a�J��S!�9���0t greater imp��act parameters, $b=9fm$, a smaller overlap and a faster separation are also suppressing this mechanism. \begin{figure} \centering \includegraphics*[scale=0.50]{ch5_fig13.ps} \caption{ $Sn+Ni$ reactions: Impac�| dependence of the neck fragment ��� Q�!�{>�inallyAE$would likeR,remark that E9J�Aws a2�n .Aon-  cross seE�sUee-comp��i�. !E$latter poiA�s%�icularly)�mS8since it seems�indicate �Drelevance of volumAstiies�K%fA�dynamicsA��. T�)Happears consistent AN3shUme�s$wn before,� �( the discusA�A�Xref. \cite{BaranNPA730}��sub)4{Analysi� kine�Ehcal observables} %\addtocon�ds{toc}{\hspace{0.55cm}\theXub [ !12cm} %�l!�no!H tist�feature�!Ki�a�� a�reveali�various� corre�MI spond�B�i be measur Q@ exclusive experi�us. A!o��VC is�$asymptoticA>atO velocit��ofI[A -pr�ed ��s$�e$ respect t%�� $PLF$ ($TLF$), $v_{rel}(PLF,TLF) \equiv {\vert {\bf v_{ }} - IM( }$. I�iA�mpa! Y�)Kve �y��h),Pa pure Coulomb-driven��, sign%��a s�1�iI�proces%�a a� ound�^*$ or � ^*$ � , as4vided by%pViola�1ata}iHPRC31,HindeNPA472}:��equ�L} !-vF\}(1,2)= \sqrt{\frac{2}{M!p$d}}(0.755 4Z_{1}Z_{2}} {A ^{1/3}+A }+7.3)�7pwhere $5,/,N2}$Ŏamas��chźnumber%.�W=Fa$ ,$ �$!�Fcau reduAp\(. For each.T� valu� Er!+s $r=]} )/v_19(PLF)$, ($r1#A�#$)��A?�\wilcz2} we plot $r1$ aga5 $r$�^��. W( ,ll such a re��  a $WSynski-2$ VIl}. �� soli��nesD�a�A��,$PL$-($r=1$)�}$T 1 5�T q� ivel͎!H,es $(r,r1)$ �� (taneously �r�7$n $1$ suggͨa weak-)ҁZon�1,{\it both} �-9 a<$,�)��ras�RV�me"� ��q�has sod imilari��",participant-�� ator scen��. Howev�e��  m!� rich!� %p(simple sudd� bra��model, re( locua e $r-A6E�-sh� be o Ybi��rix, a�FD$Goldhaber$ widths�s�\I3@LukasikPLB566}. H� wide2 s%"g Ek2} ɳ8 a broad rangeA]� �`ies, typ�� al� olp .� regi ,at will lead�;EO1wal fluct��s!iM!�per}�� 45]"� 56� .� Plot:2�# devi�ans� �� ����, (text. Resul��re!�w wo $asy-6| -�6}  AnotAxvery sel( ve2�7 r6j$anisotropyq 5�em��,&Q͟�in-plane azimuthal angle, $\Phi_{p(}$, defined��y'1$E� proj�os ��-� "  ax� n<� �nd�;s*�11�B>i8StefaniniZFA351�AA $G .� simeq 0��l!]s� e�Սto. metric ``��s''m�$-��)�,aligned alon�e outgo� $PL-TL$>� . At, � :� r domin! � �� flat 6� behaviork :.!s,P�-� samem� �?a� � A� coveL4 a quite limitA*ng� 0 window, clos� A@ full)0� �}ei,6}=0^{\�}$� 6� becomes��r��n�approac� e~��~=~1$ l�T��B. ��n trans���$@- $�%���s� 5.�f�a� �} IO, �� XG manife��VzIq�y.�ou��%>��� �6 takesaece on A���"�A�c to� �=S,. If a light( escapes la��itsA� /TL$�ner, fri certain�� n� �@�al effec�DndB� �> )e l� }C� �%�Aj�]�� Q�re�aA�E�r�3A"O 1� M �pro%<dA�t!�"*�� $ � i%�)�&�q2�Ae f aris` � 5ss (�ha9�der>�A�")?%�mi� caseI ree��N YB�a �� ��%wquilibr%K$PIex�!�sidue,� no�A-)�i�W!�no�.e�onc�t tf�~is baai!$he 2�� , >�,q�.�+@semicentral colli� F l% A��study=��"ed�a��etyu i�aiaq�C�� �"�N%� o isospinq :ASy�Vy termq=�3"3Z^R#of*� B*��e�8$^{142}Sn+^{64}E���} �at.s.�� !�[ does not{ m!�influosensi� 1 mainB�eXU� , i.e. O� �"2�,Z�. !��6V�. y , one� to�Pse���VAl<-$��; h high��]� heyAhd $I � (N-Z)/A$ � ��e�$0.193�D� le25t���Tth an average $I=0.17$� A mor:mi�&�%��ba��otopi+�1�&7.�three"T s$aB�in SectQeoK�� papisorr}Q�F �mpoAIon $I$� 's a funi�A-h F$��)Z6 .).� (Ff�0 ces _evN �1�yyz s,gly��$r�n�e h"�atayincreasiwit5 -ne�u�po�i, r��below sS3��superaA�iff} �riz*m|yAE lmosIbolic�A�� y $\rho_0$,A�d sm* �E}n*8V.jw e�*N66NIA?�����:� soft$ (� les), !($ (rombs) !I$2.,$ (squares) ��a��.w$rVm= s, !�>:I�$b=5fm$��$8n f5 *� "�E me!�M� m�1(top)E�(( (bottom). "}u�6� �ely du��aut1�(/proton migI�A��fac"�"�''" '' z�� of n�] �Cy �r lute�5�j �)��   it w!�lready��edEU�� t�~AMeV$�""�5(�se�/a)�Qpof� car%�import�6�cisovec�? the )|v%A�A��|? :��_ e� stag2���. W�ct2�Lp r68� 'Ya� d atB� i� ŷg d�/�� �"EI� ��Q�cA����T i Bb �  helpa4maYh��lsJW��vE�remind�ۡ�-r(ed xref�oaI��y prim (U )&� ���ex��l"Q �ly�be was'ou� om-Nevapoi< decay��" nstruE�1D�as���coinc��ce�(�� s�be- U�FIsoj��� �� "� R\R�)�!�A�iev sc� i��ofi�� whe�9A�ca�ѭ�� itself�q/� -1L�wh�!i���� alA!�, u�tokrtE�acterE�p �eE��Figs.�R��aZS . $ �!D!�yield*�n-� $^{1242� vs. "E#"1� 58*� He�[*t M�Bg�!8minipage}{65mm}&� er} P %\epsfysize=6.0cm %\ '�{box{snp1�} j�$.7/@ %\vskip-1.2cm \c�$ .�inE�u�E�: 9�2n N&^$MPIe�� � 5 �\fill5 R(25.n2�}�8-Z�ZBeir1�0.6!�*�% �ddo"E�Mw�7�,a+ exponen� $N$-�' $Z$- * q�a}'sim� well"$\%�,\�D$ slopes. Although�ca�us��licit &ium���,ŝ Eq� J},�st�exn � �energy2s^&�c ers. SG#ݱd� # on2�p�� � ��di� t �i�t � #at)�U�/�� � Indeed,!.may ass�#e5 a �P��> emEr�^�&��,*8 :,��"� �6o�a"�� nic6���AU�&a+'lxi)R, ��6#. *��'�إ~�w/ s�'as� � �C -�:$ - � ]��&9� � 2 r��)2�"�6�h�  to�steeper�KV ɧT'�A!@$}, a nice ] (Mamodulus)шR i}th@e�0R�m^7%ed"� �[t]:e0tabular}{|l|c } \h�] ͈&9� �$ :� \\ D JI�6($ & 0.69 ; 0.951.0 E ?�n%� 7? -1.0  1.18L2@�7� Շ�� 02�{+5��V��a@$ �R4 t2��+��)� �I {C\#E�`��$in Periphe�C"�} <"'{� ���u�<r c� inhomogen�d� 2��|'|'ڍ%:�4We turn now toa�� a*%���E5/"��� D'-D&�� re o�F� (�-�&�qp^��exi� nnel. W,��%q!��"nel�g .�$N/Z$� �#��A��5� ł\!�ys�,towardC m� uni�&32�� degXof6E#�s��ten A��,��� U-� �!I�.� &� fermi�m �s �Ue�DgPR43,HellundPR56}/$�5��5 coefficiyof�ic �+ ar m_, iTAndersonPRB35,ShiPRC68� I#we�f�#�-:"��5' I 0 �0� � bombare��,A�� we�as�mixed-, $(M�&�'ataYexist, !Tsa!: L92}�*? �perA�R=F,($b = 8,9,10�- Bi*�0\&�|WAK1"%��.MI3$t_c$� !� elapsed .�ini� touch� �kA�.|/�zd c& reO"e. Y:.!ys � \�, 120, 100, 8�/c$�� >'Lq���a2�2.�`�a.� 9� � {�:_��$5CJ3� (up)%, $b=10�(down):��� ! s&� (difusden810�1�T&�/2A,�b=�/zyA1�"%i�14 .l. IO$V"�3�  af��4S/A;e-A��e� low���Evi�#� cA���K"92 durAmE� "�Y �!�.��+Ed( �� � b a�Ng,$ed �%�l *� ��uE�� �A�{{\and}g grad�s rul��*!fHy)�W$deep-inela9YY� )P��"_T6mis n- b&��yeri57wo)�]ng��i�-anծ-@�Yf�until%Em�ion, ��h+'n="1�mve. b2�EH:�����& le (�)-�Xs, M�#�Aq�es,8*� ab��VRU!.I aV7�,u 25 \%�G� ts w���/.+h�� prevm � =/)Alt` is&K v%�&��u� l6�1&���f�35.� , re"1�AK��pre�a�!J]�i8əcE&2�o"qua�53 ^ �� oughE,1�imbal� ?zi$�Rimb}),�#��$,RamiPRL84��"�1&�!D8t ��$�Edirectly2����!U���y, "�$i=P,Te pid�1�� ), a!�ey-I�T�� $124/112�K#su���m��/< 24$)�ndB/�� /12k),���%�r��13� n ��� �oft*Pu��&�e"2�5� }. A good]'Q 6&Y� , a ``converg� ''�$0e�!/A;{P}� per curve" R_{T�� *(M���"6;%a iff- I�  be�6a� mAC�h�i4al � �us,� rrow� "�9*, B� 2h In&)�( $MSU$� �4ARr�  &&� m�z onJ�.- �.����� !d&�"/s$��llY��ap�4n}r=)V�sl2�ll`&ecd (A�vic�0sa�<�tonm�W7ea"h/begin{� ingj�50" /20�Z $M & : �n�C:ime e"�/o�}. uA� �0 I�X%!U) �;�� : $�9oft~ 3/ Cir9! : $Sa�Q�$��� E�ypQ�& of Ref21.! "� �:�  Ai<*I AYtwoa�ih{e8�# .7i�"�5C*�'!M+.ime&� � . S?FN��-<_!��pc:&t,er�i&`In !$>�"$ a possibl�lan� wa�poA� �B�5�b($ � !2�'O)r)%^ � y �a�enh�dV� /4�triggeQ8iI�!� .+-j .I .!&�-�&Wof8 2�A�compl�;� �:e"M �" �7�s (!���le �1s,57� s, etc.) ,thV �5|ens)��!:> following�]AnD��EOS�k�$j$NmLet uA�d5AY e ``�''N�iR2� :- a�r�,>0 � �Bm�2� � play�<J@ �on5�9 e�0�3r A+X�!h[ A�:@8eqnarray} I_P =�98A_{0P}}{A_P}( I -g %gP} - :A_{PT<PT} +>T:> TP})r? ipm} \\ I�2� TT �T�rg {&I_ +�T}�-�� �"@it>A9(�$I_i, A� &�&a�B�&AZmas�(for:  ,C,� at*9 ;1 !1,��8�P�4 le/Tt;L!r,�$,�yAt�-�sIB= (�^�C>)$g$�WndA�(r ``gas''}) � PT},!$,YQT red � .��)�  ()� �agasisox&"E���B� A � $!�P� � !n$A_!!c T}$t��#� � ��2&.�AT' ita��9l!y�a�+E� �5 .19$�+�4truTC� -bu �� �is�F(. Consequenw pre-�����(B B�2��uEi t���t� A1�!��#�V.� %"vVjm2ft)%�*@r�)* E 2  �f!�al�,Yn"H JMe-� les5�,UG (E T.R)��5+*� ";C the �y"J5je6N�Z6�PA��TP} A2>%%�3�:7symbo�E*i+. 2� : empty+ d�'�s�<rizontal  g�&N/��M�!�={5ie*�q�#` �TA�+@%�� �A��Aa�2��4oM/ofB<ai��  U 29 , ��7.o� emI?e^o�<riginate� �s��k � ]5(� ) b�.� �'sy-V �?�&&�1",U 8!�N��B].�� B�2�1�I� �*d�Hk0H�V . "}1]H�preR At-� �� %,��3.� ��*:��A�@�b end >3m� �%����!�uym �ronou &�3�?&`��qa� !�ii*�7� &15�]+"1��realiz�at�� e "%7r8+� �a.�fer��v!!*`�3�xA�� C�L�Hedium �5%M�)�ope��h'n! կ�1��6 8�I���Q7� �;out)sa�Fda�!Z� � �)��(��a mf2\h*�;">m@�c)�\��ÍZf%/*� �ulyE���D2���extrem/u�� <t2 look�}zF�I pic�H�s/6&I6�5|M;ojstB��6!t"ve flow�e�5#&O5�"}��6��or �@��.�. B� $)<u isc|-a!�>�� elab�.3?littlu  physlG�-����MF� "�,� in�(%ddU#Ņ! .l� � �5er&V1�%�D�O��m1z+!�a�!��ɨ��&��,K&��TE�is ��' we�i%N� ^{(supa�� )} >PToft0P})892 \no@HYP/JH0T307 W (W�%n�F,6� -s��,� lies �.5dK"r�%b�&d���l&�8J� 7�"{ �!� ��2 favo!�El�u&�F2is�+l�HI�t"�G' )�NSK and &)QN&T}*~9-r� o@�h�He�/becauseeYU��-�n-f�/��5��- s&�8-%ge�,ifica� �|1�b^*�8 L6 argu��aYMade)�ex��1fB�!� �! �9��Q�+"�Kspa�Y*?R6<chx>�1o�,ials $\mu_n(�8p,n,T)$��pF_$Balianbook�� currGT1ja�6�-exA�se�EfsJv j_{n�,- Ct \nabla �{n}B� = '$[ \left({\!��2 n \orI�9n}\S_{ p,T}h n*�Pp:PnBP p ] �r�s j_{pR�p��p��:�VPr� %5 p ],�� &#3 $C 3d"8�H@E9Landaua�a�Wi!:�b��<�} N_q(T)5�!�q: �H{q'}} = \delta_{qq'{ F_0^ ,~ q=n,p ' �+ {muF�$� 40�%b�$&=& -Ct ([�1+I}{2}�nn}}{N_n�-.( &p&AMeE� + 6�_o ;a� FRI)9�A� �D_{1n6% - D_{2IY�4a�>�b}p �pb�1 �p �p}��:a�fR2�\��1pR�I >�In�Q�$��Q r0�V�9e$1�/������p= o>= ."p��I=� n�)/E�;H�<is� �+�A�"L &�%�;� "!  i'(Ge�� "Dũ2o ,�^HF8n*�$. A�M?W�2� "� �$W� #�%�>�v�e" ��.� �8 "/ ����6;�id:� �'Z, �ly$-b � � r5G&of Eqs.(�O )�1�=qI\&�$���K2 7 e *7�=[ %m"�b e-9. %\i G {rep_bib}� doc�(} �� %\,class{elsart�(usepackage{R8igEg]x>ams�Dt�enlBK��r�0etcou�%?{���� \~&{E��2�� &�>a� nel:jiv�:��KtA�A�1�$�m$ meso�#�Gqhd!8\Z�p1p#\arabic{ �}: ,C $QHD$-��� mR&ls a�<Y�ful�Jmp�R describe~)ap%�K ��,u�f� �? r.Q/� �0�! hadrg/ level3 TWaleckaAP83,SerotANP16 $IJMPE6}. C&}�s�*b��nJ.i�2>DUofa{�^i }|SharmaAP231,RingPPNP37,TypelNPA6�/} e $NM$ EWTSk7! 4liquid-gas ph�J�i�s mMueM`PRC52}6Z-I�L �ar J @Gi�)4RPP56,KoJPG22}�Q=� Random-P�-ANx7 ($RRPA$)bor=Ed!�op��o�G�(1K&�!�p� �0 DellDXH44,HorowitzNPA531,M�M9,Vret�T!V2! 5,Ma8!�# D'fU\K-"aA� !w� ic (�k ium)�.� A� ic NaM�1 ($ANM$)�$:'W=M�Z tic AUory&`aiJa)�pn1��A�C�on- .[(�4LNikolausPRC46,Furnst��2!Bu PspiriS $"I~ FZ~�ory$ �$A�A*�d$D8 ~ Fu�Kal$ $Th2,�! $EFT/DFT$T-mework� �CNPP2})i�y�  � I>�gl�) � lets e�A�d��&,e�A�$ many-bodyMUs:noa��UB�w�'pG� ��n5�:Oo 5���up�`�EysK7yY,Z� iMlext!voA�^@sup$8&K�6� �){f�L)&i�."�'I re�(� Hofmanne�.Z]K 71,Buerve%5}. Cl�EX/s!�w /� a;�eQ`d �A��gof *�1�@o�=P%"�Pq � & I5e" %�:�S E/i5�not eas��din2�Y���s a%Y�]�s�s��s,{? �g= >oe/"���fs+&� ,2�Gaitanos(d�8D8A�,��� d6cozR#�*i�K$06,Madland41�.���$-m������"�Q�Y���R)im9/'/�)Ja�df7�.1ՙI,philosophy. >< taska� �7?� to t&o/*� fp to i"$:Z� 5�"�chw �\! �J J� W Fn uuse in or�V�olTe openr blem!]|)gb�. �Cc��|1 �1�Y��"�ce .Gq/IP���h�Cr�3 mihc2R�Ro �.�-� "� �YyZ-�J� MjO��H MF$�KɆ,�$v: ($DBH7cal��f$A�kmpts ]8e un".<�H)&P 2� Schii EPJA1k 66}, �!7D !�u?Mnowa�Eep>m��f"�Nout�A 2Kw�,j�)�.ps, U 7 IF%{3��Q(&�i�=�*wa�#" � y �.4';  (J%,y"Y3�h)A�"?�5*! ��" w\2e6new�/Nn��Dfor a phenomenolog� RPse funda` al &�)] ffteN��2 �Mt\-�ůy� how ��> ]a%�)���%�-2�Y&�!��B��to fix!�?waCe���qsh!E�us�u��#(� *�E qhdsets})��#edmvA4i\)si%��n(})dit�:u�L#4 s w "�% a�^&�cbaryo!��Ri�IS=^-���%~�en�3w %# $' ly ac��R($NLHFF/, ! .ing�&00QHD-�aytO } �� star=!AO ��}B7M*��of:���� T<&7e &ZY�  CE�freedoՒ^A~e�� �e�!MEoI&9 �u $\sigmaA;d ��$\omeg�s�I��ho%� @@:@rhoa�� Lag�YaQ"y���m��!�non--�� k/ d �-term[BogutL505�C�*n by:"�N&w{ Lgd{\bar {\psi}}[\gamma_\mu(i"@ ^\mu}-{g_) }{V} - g(}{7lB}l \cdot {\vec {\tau}} ) -(MF�}\phi-A%=}6. C " }~)]� +� "8\\ {1�2}(��h� - m_s^2 �^2) - {a$3} 3b 4 4 - {10W_{\mu\nu} W^  +$L2} m_v^2 {V}_\nu {{ !Anu}+ .�1}{2}(�]5--$v>$ -m_{ 1^2:I^2):�%�G}o� \B�R�+B}� {^7)�2�2 eq.1^Q>% $9O (x)=6�{E�nu- nu m~e� $�G�NR$E�^X" ^ .$ �2A�(x)�t�)on &XG�, $Aq*�$.�$� $EMYal�c -/ bosA(Ps�K"��ly. $:�i $:�� �charg�Fc�m� g\e�iRsA�T 9ma�g es .*f+��,&�?%�'7�EuexQ,durN(seJ���� mo= �A�$!!S��)p"�q � ;+c�x'L� Qi��\stRneg�)ngEXqn2Uq[ ������"� ɛ�12.�Q2>� m6*g� �D x�onMM%&�$*L 7"O9o: &a(u� }�Eq.4a�-�l,hat{\Phi}/f_�� + A{6^2} + B> 3}~=��mH ~"aCrho_S1Q} 9N -0.5�Sb#�7�b.� Vɱ(xi����} V�, ~=~f��� {�("}� �0� j��~,.���'bf �xm>� rho}��B�[��z^��5e� �V~:.�1s! �p:% �  �(y x>��$1�l=gM/�T4Q? = (/m %)^2�H$A = a/^39B = b45� M%�M Mf-U %)a/�A!� %$ �& ( *�-s.x�Ewe get a$A-Q�� �T\I substitu&� iq, ! b}):l��N �=m��0ch�Ձ�Nly �(:D�e ;�T� s:d�Ea *(6~ ($7v most/ �f�*��& Z�[-x� s�)e�BbC� �!I� { E �Hp&� C*�@399,BouyssyPRC36}�G.j�"�c*F����"D �N lso �bs�$of5%l�W� �g� # tho�<si�e �6}S� ��r8Ɏt s %i"#Ai �%�F�� "�3� n�W$P �*F�e)\7  yS&�.��d]Y��M9� #�)S)S�yWeGu�inA9kY�1-�*"J�����E�r�!�a+kl�W��"p�!�e�arCB2�b��7uK4e�5b9/te�<Q�9zGS smooth��" s#|-�<coord8�I2d wC6c�uu��|��#�G&��"|#A�I�of�M-�`sY#"| # gP�9Qz-I�#y� !�Ca�O���Scus�x�moy!�e�um \-%6�r!Ge�lmgnf=u6or"one ��yagrixe}�� ��i}PDegrootRelKin,HakimNC�"�Q-;.�BW w"�f4]R�.: $$[&�,F}(x,p)]_{\a�`�W}= �\(2\pi)^4}\int d^4Re^{-ip�RFu :f�_E(x+{R�, _ b(x-:\nle~,$$"y� XaadouKE�2�+{5 �oveڎ; U�_-) |:o �� �m����)T!�N�) �> � X}Ny=0Bz �G$x_+=�<� x_-=�:$. +Zw� s*�a�� ��;flEz�e%Ia�Fy%6� (�fow�f�4x.2�ce�� ]J�a ��������;��S�)of�<�a�iNM$� is�,D3#o�7�vutr�n��k#�bw�4�g"=&����on�  &ed�s2K"4 3&�%�9� ` �(�6.�6#�N } &&Z�}.��^{(i)��+�)� p^*N iN* - M^*_i��2E�9\\.�\D�3�5[\tilde&lc(x)� \pm 'rho j_{3� )�} -)��.1 _S(x) \mpes {S3016] J�=0,B�%L�Gn,plZnlk 8$&�u�Narm8cr6oo@pmn��8:�%@&H_x}��� al_p�D�*x$A� 2`'f��A�Q�p� m.�Z!s%%�2{Sp}- n�y=� =j^pE1!U -j^n$ V a-&��t6!��,I .*� m� >� �[aV" �emsb.psme?]�=��-{Y�z}U�>�{j}Y�~,pb6e9=M��uE�}%_I�2VF�~,Bw%�!�"e� .RZfcin7�E�}�={!>h_S}}-  8}{{dD(x)& {d�}a�-{2 }}T�� F}^Bx) {{d :POg} +R2}.+{3��}-8}/%T}~,6�.�%�=\N���5 t4F� ��n�1y_ �=ra>�H� �>! �9 ���rho�  �� �� ��f��4&��}8~V0�� S^2+e� j��+���^2+�;�B j^ + �&W.�#�adEEng�Ma sF2� �e ���ĉ��\ in g�#a��Z�}B�#s�pL"� F@�e d� \ ��� Gusu|0�� r"� ('0)8 �)ve".A!V &n0,��?'9�P�=�$u�i (i=�,i-,�,�<�c�(2�".oh%p#l"��i$.[#&�EY9��+&:UQhB)5��"��~E��m�$Ywwsv�B'ic*�"�5q?n�;$� =�A��za�sel.���(ed E�[�f��5�5�, $f_i j(2!g_i^2}{m!�$i S, N$LFAf�(p"���"$�B��A� �a} #t^3� B6$b$4�s~b,Hp[we�$!� m0���mLir�&�/to�(6Sa��."d*v VsO�0�2��DIf-K um h0oL5� *mW+ta2�7asF�$�N} T$ \nu}=i&$� }"� {&I+[)�i# �%�}^2k^2+U( )+)&�^2^2} " �?+U^m^2*�P&_�l mbda� ^J:�b( 9]v�$.B�� �$3no5<ar*>~m}U�� 9=5 3}� ^{3}94}b!0^{4}$. B�!�)��Q\s ���8�'ermal �g&,74in�y9�)�It�b=e�E psilon=o m_{i�%� �0{\rm d}^3k}{(�P3}E_{i}^*(k) (n_i(k)+E~ n_i}(k)) 92}�Q^6/Ql3!�E}��2m ^2� B^2.*A! ( ( {B3}+ �VE�!V&& X�^2B��(�z�bO!} P =\s9H { 2}{3�Q )mk�)]\�* (k)}Vb 2g_ Vb-M� .9�c9c ��bB��  ${E_AS=\R�k^2+{{M!��aQY�5"�?�m�lpT"3l �k . %"�u2�#eq.6} % j=M_{N}-!A^_SI A, ~~~ %(-~� , +~~). xnd*�#t$i( �$../�� �i�� MXF�$p,n$�n�&f%Nt-.h�") J�*�Annbar} ��� 1+\exp\{(-� (k)-%8_i^*})/T \} }\,*�G��.�rL+BLF!/9���>�Ji���5�I  �,�n�cs&��"-mu%mu_i}=^* -!�e/%�BM�oi �m~F<w�JU!��}mo}^0J~K 5=�\��/ rho_,$�(at zero temބ�@�U wFA'� �1$E_{Fi}"� iva{M!^ey�UL{@�BI�`2�"S$.�by#�"**�/�de�cy)^a rhob��!B= Mldt�DR�(nA�I�ŢF�OS�O jM^*}{E^* ^+^B�A7=�k Y �E*!G anty)m� t�<��a G)ig�bUN�/-�I�: �fi�qW6&� �I"�3 *�C'rT=0$: sAK�1 2�i)�0,Q5fm^{-3� �f�/�$E/�&-16MeV$, mB�h $M^* = 0.7 M_N$ ($M_N=9397) ��P2��, $K_V = 240 (`>�]]fsY- � ,u�, A, B$.� �`"Q8inNq3�y+ �|"p1Gcminimal` "�%�0�&���W�m�Ou .�7�3�9�@A+ V�6}�>�3)��3In>z9so:u��e�+!&\� v| {Uew"{ N'ed{A� sameAM�E�.X%��(E?(NLao)-$��{+\�  $Y���� (*�4& &7}��M�7A�]�ism(BI�-Weisz\"� r �thu�N( $a_4=30.5~A�. �4E� ]*���f�#b.f�+�+ �t�7r*�+�Ker}&>_P�8.�_%q HI�*��qKtabcU }{ c v{ $"$�z~�!��z \%�! &~-2�z�*c~(fm^2)> 11.3'&~$A>? &~9.1Fz{G�.G6.)JF &~3.22 T"|GrhoE*1.1)4{ &~1.9 �NG|��I&~0.00+&~2.4 F�A@ {-1}!�0.0�V�0.098).FB.@&~-�4�Ba 2��0Q�2qu8 Uw2�|� M�L.S�"���}�?�?�BX7 >����Ga���aexpan!2 �ձ$EKOB,I� c �By�)�I2f�g J&�* A|3 } B}2 n}'Bp}� �$N-Z}{Agԉ&& B� 7} ��.~�R �� ~ =~8() + E_{sym} *) I56�< \\ + O(I^4) +.."� �As�8�j�8} m6�LO ^2�,I)!'� �UI^DS vert_{I=0�/ � F%O h6^21}*H� R=JNA��}�@e��t�P�W*6F�as5C'%KubisPLBy-V�b� eq.95Z5��i 1}{61]k_F� ^*_F�2=9 f_�� BYRf��)U1W A'%m}{E_F^{* 8\;W[1+2 A(k_F,M^*I!} 2]�M^{kin}U� ^{pot}~, "a7��"� � k_F�a�� on "�<"�=2� �m1%6- �+ ^) )�� j"�8�aso ��c$,7=M_N S:�+ S $. $9"$�  7v6ntegranT 10} B6X4*� � d^3k-�� (� � ^{3/2}}=3)��%(S}% -Q!�EM&#"3���8G=2�is�P|p� low&� ,4M ����be! ecb�Aa� ?ybE� �i3��ioVcH aAIb y&�>!�&� w�n9&�`���&W�,j�6err\"I#M� ,? m9��%lN��MMp.�"-h�s81� � ič�mh[�A2_F1�^2I]�Dq� �A �?�V,Gg�&$ ]eT�.;mlKC� $ Y ]"'%n2!�comly&0$J����})^2]$ �8, �)�t>�.|�eif& \not= 0$Aq$� �6v�cRA��� c �,�e1�(r"?t�V� J.B�$t ���C&%"� =0$�51 2 ��tc��%�chosen� $2.4� $, �3N�J�C:�![�.�E }. A� r��noa�b�,@choic� not*0X�U>|2ion�aie[�H�Hsh�E�.w1a&�1�-dP�;a��o!�L!�Yr �5 &eKo&�K�\�A IgKameM��k&|we mus� ,O!ea�rh.'c�ant by�UactJ ree,�!��#3� %�. N-:t� ��y���r buil*>CtYof (at�D ive)%0��pul?�)�&���% c�=��}!W�O�0RmG ing 5��a�i�"w,o~&s�qhd1}.ߗ+~8{&_!�A�\ �=m � occu�hi>�6�A�-eB�. he�7�C��"49fur; �N tof�"3�� >�= ��,�\ e�7k. "�nm[htb]�"��5aA�!D &jJF�subH e7G#�&%� _B <��O in"f�&� �V$� �bBo.� 11})a�$an �� �9 �HL��s� $ ony6, �o� � E YO F9�!�. A&V�ab�6 ����7i����41!9 3�3`0�/{���ing8'-�����5y�e�&PTE(-+yN)B-%BuM�B�D&-r�I��$). Dot��!�\S BsSy*[2�2~�c"7SFT -�^�yH%I�6qe�: 5:Tjer�*��6m*�Kr�JCO�4�&�"d�#�actsU||2�$&�E�$f"��%J;��o�W��s^ �-��.�&$N� s at�{erH;ate?�w_%"��i�X�� ee &�mreldyn��=��݃36�B.�LyU+���*()Fi�� ��A;*�*!� d,�ON�3r��5JY��M��O``�''*G J* ���M cqui�F��P$QceY��? � �Z3}��9A$  d���5�M�i �*atE8{�MN2sl�a �m�q-� :�,2�2�?*V�@ ix�X%�hVee.� FVDetai&�]�)�8==f�ui�5YG,P�[*�`�.L46�BJ+ (F�V-pur���6mUSr x=��"�%!Q2* Se�=n�ns�M.�@T6���#���� &���OA*2v$ Quantum-M��$-Carlo var�al.wsKal�< $2-h3-$�Zx\ce/NFanton���[@e�9QV�F"H �6���� 8t6�� ?1.5��_0%HisMr}�*ϟ} 2�bn-�&s. It��%C��ev^iS!��Sy��`�b9 �5?�d f�� I5 m$DitarX0210��Π�# 46�<�!,A�5 �. .q : $N�$. &RL!�\o)6\4r�\ /& /"�Pe�J.!In:i)��F�yl*Tu"�&�]�/� ie^�u�];GEs{� (ES��� ure}� *��B( B�!})�M��x�!�aHa�s5B;s!{ theia�m �ual &J��e&� F��/F�.� "Q[.N� �Hi�&H�2k "^����%y$ (p�QValgebra)n�2Af��@}%= B} \mid _H =-n�[F�"�$_$ +6. "�R"�M k_Fu^2w [ �1<+S� �] "�� (]"��<� �B�QJ%�*�:""N .h(cfr.B���RS (alway"c�v3t&�$&�S�/>�) < 0$)�(s a ne*�es,( Aiu�y.i*Qd, � s�4�4�}� 2�T\�j.Y,�ZA"1��1g�K"l6� M�� $L x$450#&� 9t0a,uinjV��$206I -zone. ) wt� �!%��( �!`>�)K�2 lopeE�go�WO $L0)=+84�P =+103�5IBzͿ�s6b,/%�7 vale�`<%�q�i� } $P"�� 0 L/+N��f�e �Kc}0&t&( , be�lin�b)� thick@z!Y"�ki �� (st�$���u�� ble)i gSub A,Brown��5"Oj*/c706} , ����=� drip�'. Moreo�uhM�er giv�=n ��m�q^hifJ��7�""�_�?st��"I^2���"� A) *�p�" �� ��ico �� (I=0J.s&� Se.d��fErice98a� I. iB�)pe�����& W A_��53�)ɛ&@Z�isV["1�ly}���Y`���*,-V�#�mp�8gn3Y� %D!*"@L*gJ. �� � oaa'���B��#9�)�y o6�*is  *�� Cur�!rC�)�9to >> �!�-V�QS :�� �kad�J5Bzve)UT6�"� hŲ��B$-*?z�k . �L.�W���� %~aU�� = +7 �� (oUQ-Y��:-� 412�+BK T�< d͕y� ears1��*� to ��afu���L� �cmfF� 6B� �Zq�ici ���ike�9oXia�e�mex�,5�trivial.��atYll�L%]mx�dB� �e -d&�(Ki�-6L�6noa3 B$A�e��B��J�by <ca;=s&w� is h�Gi in>f*!s�.�� $-49IM�J�F�NlyI�&�,�b $-504I���?dd��6# �~>� FN�e T*N1Eo4�XQ&XQncI���M4Q�)i��per�%��|�� .@ $T_c{ !C*�raOU"2;�S15-16$!O, .Si1sF�:&5�A�`�_ �kh desQh!*w*�4)9a� aY modify alnAeI��3HW.��$very ?��Vb�QAOs�\LE?>�a�i&Z3"� ���2a�� �x6 ~ �a�,��G��*6$di� WR� � $n/p$�&.6sw9!L i%��a�� ]m�ge*� ice�N��Wseި �O'�����(typ�sk�͒l�Z ; ,%�=%#�u�2� ��3s iF|SauerNPA264,BertschPLB126,Jaqama;p29abA.�1�@v{2�rpa4B| "�,�b� F�ali!�b!��n�=%>S�)w�-2x] a"�!�V� (�FO*��)�8e��iup� a noQz��,rl�9��mix"9of"yisarge fl*���a�J n� ;�Ddl�h� C�qc!{�#"�9s�_ra�&n-.+��sɗ� ΅ )� Y��g%��!�to�)�hr��� s (")�")�)�i:x��:[�!� "gas5�n!JIҡ|I�"� �$mQa t�ac��=q.e-,�4���� j&�l� "� "�$�lisE� ��{>�. :Barl� G9�6�� �a'-U�,ɘ9��d�|!W!"�!"�.\�} m}O+ � P} �}<+)_{T,yZ4i<{�Fy.7P}RB�<�P�!� muP�) �RB�<�$y$.'�� $Z/A*ex8" �Q�*�( $I=1-2y$. ��-%KIa/�a�c�(rO��fre� y f �c nvex&�"� �J[8�Gd�$y oscq� !_n�+ p$��5f}qy�ac�(}}�k e)Q�Kn p� �"?}�on�%() 6B-�p$2� � e%�Znd we^q��@U�s� )we bimc &3*�-U}v�B0q 0,~~�#cal},~�`~��~16~2�,~��6w*�A�mhz�M�}p>6\l.�Q�:�h$"7�6�B�� q"GE�U6�2+ɾ%�-�(A�2��do%�any�ma�b/{h��al mea��Msen^,yC��"6^IE'a�*&g �on> &� 3})(22- u�~l���a��ofQ %2n6 � �xɁ+�m�d�"2�"] iD� �.� �b ��"� � \��� In d� =� (�_ ��:� all ��T]�b>4 %�e>U7Te}� +�� $n->a�� ՛to�.ms g  � m�2&_�&�� (�r)�o�uy�Zund:^�'�9byJ������� � �2�o�v� 2� )ƚ ch "q�-U"��:��1Aq&O$r�.on*����!�&.5��8t"�ra B�-W�,A�T used �: $0J�+�B�(]R 1.� D�L&F=+F�"�J�iN�� �J%�� 7`rh &� 2 :(u�"o0anڻ�'J-fo�3y�B��!e"y "� [(>� binid�U �h *� n} �&5� �e֌�BF p}}-V F2� rF6�5z� J�p}F�� .�;y1}{(1-y)�N�V4�2�>��.5�� 3G{q�Z �  ($q = �QW�G&Z�I�� ��&�:�U�u/�� �T"A��*��E�,y.mu�w8!ly�put�9l�>a�J�͖$TIsB$ ���Zx 3)95g3.U���n"S �.-j"oQ>/�8 ���2<'aN� (&�0s)�j�� ��^ 9>�-�0u�]��iy $��8!�N�/9Z$ۇo�j�3��"�% a s�A �a� (�j0,Tij2�8whV�g6�3a�H�oRl�*�^r���W."^p�,2q36.7bK�liubo<3>�"�C� ern`�*�,5:T'L‚ E�[)"- "��h*�/s"q')2�'� )$ [$Be=��!�W*4]206n�'Wiw��ET�EN;Y��'Hs"� b"b membr�����  /������3ep��ZZl6Ome' ar��ue2!]2��zJ)$XFsj��I�$Z8@�]|���&�aٸ"~�4)D�O��` E�5�i��"� =T��Ր)E�b�a�bM5 !al�D��'as�J��r �4c)�be�n ���1rm� "*ͩNK&� .� "�c�':(%7})��u `kD"F�M. �(pid�( es (�r5 "�ɠAat ly A��6on!��lM&2;�9�� N2A o�"��,21m"6� 1��E��q�Y�yB� 6�1��ɪ�5&4,:�Ū�s M�.J.V�r�6t,7n�In��/ >�Q�ia��Xwo udyĎ*�%��rz #�IE L��disper�4i��.�Xa��o�L)itude2� aR�P5sE�B�. Gty � (�)l�*�A��y�z\5f$ ��#�� s $F�,q'q�)=(n,p).�GQ��Teq.30}h��*�al� q}"p \� q'}&�'W_{t} + �� �;H�J5$њ�5�e5�a��le��t�n�o�}y - &)l�gy. AF� it�-�B��(m ($\hbar=c:2 $�"7F,Rq} �C{Fq?i^22�'n, p. $�Y�(� ()� nn}=� pp},) npn��= &�4"w)]�ae� PomeXjhukW.�X��"�=�6+!�1} �s = �n G� < -1oF&� 2 *�w� - p=7 >">eNbM�s��ll��*s!m�Q(")Dwh��%}�Ae�&�6ZA� As $9_<0$w)a-�Y]A&A�a��/ stay� yy .�78}a'iT�C�#*O#��;���Y  >�Jm ,AVu, 5$, ��ouXJ�Bѱ6��[~^�A�1λUƆ�*� �&> B"�=��FO���ЅE{a,s}$�v�!�* �N=!"�o5< ($N=3D�� (Q!>� qhd8��5"en&��D%$&s �@"j�| � 'U A�, %$�5$92. HU{!"b-h=0 �IY^5�nre F *ged�HI��&�\ qhd7��P~?r7=2=�a��#Us "��le"u�ɞ��1("�F��# agato��:1[-s�;�S�vsZ ce�>"�9M�e`L"�'"�:$6��E� ��ge� Γ*��h) ��%Fe�!, .�g)�})�M�A�"�1��=�o1�6p"� :~8},3"R/ 2})��An� � I1�if)u/> ig&� X� �=e5��2�OIsh�'h� l�<�f}�a�9� "p2. '�!U��yD�A\��ffects!�!�3�y��,� �44 interest for �^possible effects on the isovector Giant Dipole Resonances studied around normal density within K�$RMF$ approach in asymmetric systems. This will be shown @0next Section �prelativistic linear response 6bla!�of ��ar (attrI) ����((repulsive))�ibu��s�f��� nel.� �DiracE�4Schr\"odinger V(e[ A � ic M�g��addtoAAA$`{toc}{\hspace{0.55cm}\the{~ !12cm} %ҏ%J�apredi@!N!�4finite $m^*_n<p>�y=�6�es, when�:ca!���-like$ i!%�cd, a].Pre>�trequires some further analysise$ pa�xul���!l}��s� non- 1. q_�a�6�. HereahHare actually discus��AQ{\it %�}y�e# es %W D(n,p)$, U�:L of a��o"� in-��um ] equaA�Sall~)_c �) �on� �2�} 6�esIS �y| ``k-�N''.]mo��um= 5 �0$mean fieldqt>y�2� �A0,not trivial,%� �BouyssyPRC36,SerotANP16,JaminonPRC22, 40}.���a ext��!� argu�!|refs. c>2:K1R� of�ac�. mstart��\ simp���#@! out ��-�ρ�ng ��s.e��on:1YM!contains me� U�Hy $\Sigma_s = -f_\s �S$����B9 (foa���ponent)L(0 = f_\omeg KBKu� &� � �-U9U�reads:� Q}� enmom} (� (ilon + m - �@0)^2 = p^2 + (m +s.${m_D^*}^2  d e�aa�p��on�^� dispG p � = - w0�sqrt{ �z}B{ F� total{gle*T �y $E = .�$� resseu_form )| k_{\infty�+ m^2}$�� re $$af!�)��symptotA�m�, u��&�)�)��geQ Io==narray1�(ueff} \frac2�}{2m}6� %�^# ~6�0\nonumber\\ WpPY0 0 �1�(Mls^2]y ^2) ) "0}{m}� \��vFr U_{! (e�B,s,9)Q�n)�_ q between6�� +��B�i�=}Cu��1n8effmas} m_{S}^*a5� m}{1�>�!�%-m}{�� 27�#0� x S at satur�EAtwo�,& roughly�2 ensa@ �  o� , ٌY1�-50MeVe_> b8much different,Y�$S�4$ slightly lar� th� $D ". % $� = (g�/m 8)^2$, %$A = a/ (^3$, $B = b4� N�N Nf_{a�!�(g /m &$*& ( *.�f_i�m(I g_i��m)�iA)��, �,, N$, %\�m�4eq.6} %{M_i}^\�=M_{N}"J�_S \mp�0{S3}~~~ %(-~u , +~Q).�ndp.�6dmu�\mu_i}= � -s%`sB �-b{B�Z� , %$ et II�� � &� �,�ask�ide�here, we�!�a1S&�itemize�tem� Onl� rho~� $"� } Nowe|� -�1eodified,� phe same.� � iesy�$@�s )� s�I�� ej 4 m [k show a� ospinՓcei�a9�  $I:)��%�$,��6� ($-$��we use%d�� �{(B,S)3}q# `p}-n}$).�a%��wFa�levelA the S2*)#� c*���() becomes �T�nqs��rho} {��}�  =V�"��V)_{sym}2 �B3}J� �e�!ADof $m_n^*� �$qLto3 air-�ay�� $a_4$%�1�is��$at higher 2_� beca� ��)� E�Š$4 z� er $-�0_{Dn}^*}{E_{F $ red.o@H n}$. A�� A0�F�!6A �xim�i*� 1 ) SlI�0 $�P����� kine� . lea� �@ �� :b�� ���y }}� {.� } ��-V�-K"��� t�! more �a% �"� 5����~Z !mar�Z�:a1e�IO= �vB��i�FU$ �r� �ɢ�B�m 5|l co� anyM��m�PRmÉ��T���o��� I>T 6��B�e� . We����]� ce �/Q *��� da� "d$ dynamical!t��io�-�E�I�or��a �Z� F��u� -Lane Po�ial��"�fag Vl1���� �2dly�5 E-n-.nopt%Fp��!iB� 1�+ =+ yW6� np(} ; {0,q� f ~, "� \\Cs6Cs CV:~,"V � Wp <algebra!1��mmpact� m1^$9�~5�$b�d lane} {U_)E8��.�(U_n-U_p}{2I%��(rho_0 \Big[ �� (1- 6@�) - &J{�8��} � }(1tH)EHt]�MwK�' p���" Im �es�to��"Y�hedac'on���ed�_6e!�E�B��(forces, mai of Skyrmebm. Firse4wes�� e posi�J8$E-slope$ givenP e@quantity&� BH���g� ^ -@picture described� (s a obvious�"{ ��fA�t��a�``%a� ''l ��N�!l1= !�2� _ real  magnitud��)�~. � r if!_tak]% to accounat eyexplicit��um.�sh~ s#"�� and V����i!�asQT 5 ref.$GinRPP56}.�%!M�� %�iCr !�� !( phen� olog�3 � O�A�( ($Madland-�U$)��I! �R.SKozack�9, (NPA509}, fif&A2(ultaneously�%�� (mos 2cross �&s) 2#x*("e�,a wide rangeAU i��7 upa�$100~�. Recenl!5) �L � has b�pup reproduce_"wel�w ���'9�,on $^{208}Pba$$96��%,KlugPRC6768}Fsuca�8Svendberg Labor� y!�Uppsala��bj5&5�5&10�%}�!er�� N6& 55]{6&9.eps} &7&E��"m')e�N��E�:G (solid:0&$;&s$)A>Cp2�:�MW of M� et al.1b�y( text&i&ae� 5*�j&�6�al JUE_U �%�X 5 2Y4s ($exp/log$)��"�,~�.� "2) ȁ��a�N�=�) the *W$9�:�(*)$%�6#) ��mp s. Wc"we addbe"$- weya��������- $ԭ�� d�9"@ B�u���+at�1ly �$�"te�ly��i�"}on`$�� Lyon�c 5�fig:ew A�6A.� n�%�#q0MȽ�%Coulomb�n p"*�#�!(tr�&�͓�"� �mAq s)Af�,��_Y"t,yof&� &R o�ly�B+&��&�, exac��s$- BQ |:%T)�:Ui�*��' good-9���.R"P �-6�р, �&&�$lyL./ՙ, �(answer m0fundayal qua6)i&{physic) %�+ {rep_bib}��doc#} �4class{elsart} ,usepackage{g2,xHamssym _b�~OC \set7 erA�ure}{z"�1�&{C&a* e��D/��a!�`!E�r.$/machm4relin} \markr7{Chap \arabic{e}:J-�"�'{Lw/Rw/E�s� � � ��ve oscil�/!��f+ag cold>�un�,av infl2`) *z%@i� se s�0snb�n�a��q#%� metho� t��Landau��Y�,(quid-$^3He$�% %�SP89,AbrikosovRPP22,BaymBook78} � rq applii�invA�%st�,e(un Iin:$  �PethickAP183,ColonnaPLB428,BaranNPA632}. ].�� / �029kTt"-Q�!,�Bqhd}, ��1 }). �� look�:sol�*6Xto�+ 2 -�Wignera�e ${\�� F}(xd(�8E!O'ilibrE(value. }ref& ut m��} 2R= H}(p)+ G l"� w$\��� H(p)"d$dis�8u �at!C� ! BG �T B s its flu{� s,f  rec27}. �a'3au3ci�.�%nege�s'!d seco�-�/inJ�,a�e� �%�j:� d =b��(lin1} &&{i\a. 2}{\�@al_\mu}\gamma^\mu1x_{(i))~,+ \bigl({\Pi. &\tildel2,b_5}*r)rO -M^*_i\,Jk="�\\ &&(1-�\D�3)al(A�{A�)t _{3}(x#r)M\H�p)J�� + �`$ ($i=n,p$,o/lo��/s), M��=M-= � �S%( 9)\�%�U!�md{F}�� )) �$ �"A [c-�� D �3M)Ep� -= s>+:F9 -T(x)=-8{��}G(x) +.!MIA&{GAO@ -8{Up BL} E� #AS_Srh�!n�Ej�D �A #\\ڛ!�ZG_3!Ơ{3a|2I!4 (x) !\V4)hf4oe�� jQ)@  "i*|�`5�Mg=-8]�E� G  +.�u%i(^Oj�~U%j~%�+ZD\f �j_%_ P~.>U F"c a*nox8}6qc��s $u%i$e� in gx al��9�t.�. Fock շL  Hartree6Q �~ve� by vanish�Zal deriv�9e v �J.jy�g -�,$ (except $R�e��J�$0#still���.�@=\Phi�*S)/!�_S$�!We obc.J�nN� by � iply! Eqs. (5��)$$M {\lambda�� After per�,;!�� w�|� zero bot�*��r imaginaS �j l2" ."usualH6Cf�> ). A�(�1y }ion}(it �:as��421�a(!$��.�A4E��7� al23L�> 6�E�Z6ij ! eciGplain�&�9�:;�%`5 fAj�sp����A$� phinote}.>-�� �" �d��nsp�"=0f�� a'�%sta�c5�,scheme, keep!]rin min� e�2�" )�Qd.8?tey am�oa`s�7ec"&A�t� var� �e-�s#�4q&E@a| ificO -�)0al!1�@.�|=�w�p� wav�)cha~ erizI�� �b ($k� =(k^0,(\mid \bf{k} ))�&��6'iM�sol%a��homoge��5���e4� Y� o�to long� inal�sdo��� on $k^00vert {\bf k} $ �r_>but `�C��o $$v_s=�k^0}{:6H}~.$$�r�b-s�Bveloci !n">thosei-ej`� w-A�relev>Bd-H -�� 50 @ !��"�)B�5 s. C.�&' A{#y� teigenI s (MUEJ)%�>� aA=it*7a�T3�h#ic:�: .�*S7I mix&9.�. �:�+(be�8Y�m�at��= �E�1T>z 3 X/-+ ��cur:'��>ea��G2|H&R@rec�3�on/v identif 5 � exci� s�a�%�+reVmove �Oof phase�6il&� \ IA�B �in)sX��in Vo JEPRL86}.  "\*�R'F of S�/VEFF�&�.D"�%=} B�sh[-numera� ulo4"��$o b� in ��:N reg��� u�7!�&}!�.�s�0wKp !�=d ��detai B�� �!I����l in&8, cleaS0ow�+r-iE������!�&�I"�G9r%��?�?N[8One may perhaps"ec/" o�!h1�B-�f�,( ��� ���"� %M�%i}?��"� w�"� �s��� ����"OaQ��6�ar��[&r%. + *�.f' lete�N%A�e�� h � is iV"� ;V �� H�B"'J� 2��H�  Cd�5monassumYFqMA�:�� e��!m.�+%�%EA|"9Ktoq/��f"F���<o=p�!u���yV�K�b��0�s�#in  3. N�Btra�$forward rea;ng�!�hlG91  I�!j��.�5.�fy e: 6; y�ha�.e_ � : a $2�'4(2$ matrix (a�o'a $4\tz8a�P.� _G� O�)���bBQ�Hdet1} 1+N_F\left[f_d (1-v_s^2)�7�� M^{*2}}{E_FD8({1{8*( A(k_F,M^*)�8rho\,.�( S}{M^*}\,d\�) 4]\varphi(s)=0~F|y $N_F, 42k_F E^*_F}{\pc9��A�H:)a�tat;��4e Fermi surfac� $s++(v_s/v_F$. $�S�Lindhard"�cA0] `L��th�9: $Y=1-{s 2}ln%K|{s+1  s-1})|+�0 2} \,\pi s\,�Fta(1-s)~ �y $9���� intlaS +� ��e� /"�-eq.10})�pfa�,�r�r�%r��y�i�{��(f �c*a ,� cour�/n=$e� repl!�9y�*�s (��t,,~M�A~$) �H � r6@B>=}Ma���K� �s������� �Z*� # . AA�isɺ��M m�*j"m� r&2+^2 g? v_FrCi�k^2a u�\,,$$ to2���B�i��rsqu� bracke�nY�*). Look�rMB �n gOr ("+%lin5})ɨ �#���*�J3�MA,� �� A�=�,!~�#&A�jE�6!F�vH�:g].hKT�&U� ��I�.}�:jI2�I-�6\,��)�e�[E�3^{pot}-)��q}{2}  1=��`�_\, (�C&-S�/�N ho_B 2T\,B� "D'}Q��y%�1p�( %p|!z�;J�s,�5 toge�!��&"V3)8!term} � exhib[  FfV@/a�,f_i�$*� [k � o��a�$2x$, !�.&g& 6. �W�~A?Uyfa��� 9feorm�Z��0v*P"� �.��M }. E� A�aeh��$&� A� to*�Pe� $IK&�;2 3��6>�,�:K�� ��n�>�/ stor��00'' (coeffici(Q�� F !x^det2}))� be �9� A"�)i�� bE $ed � in��e�U6GL"�)RPAA$ud� !Gi�D1V "1V�heavy� i ($"�-)~ �>�>"�� A�s� Rein2���eQ t�> ivity�K�averag�Osona= f�Meni">  u�%��A*ts_ 9>f5 Jx4t! � AU�}rM~0e#=�6s�C beha2r1�chiev!�6by-.[A���?!U)��'"st� i��Ds��rc�)&�observ8�be �s-Lea!Jmi�0cop�W>�9�}��'n��;�'aS . Fo�(1cE/ a carefulp'M��aY&�, M 8FurnstNPA706}, � .�)%se ``eq"�%''� al1QOcv�d!� ^+e� curv1F"� QC A�.A)2�s)��R�B[We al��Iv  �&�T~Lclosealogy �G!�n�#�ya���Cj ach."�&E U1e%;freed%V:$K biln  play��m � �y � g:A-B�I&s. A��Fi$se�k��a.�QE�Q��a��E��M�-�� m�(�.�1})�0C�]f !(! .jo�N6lsO�{nl*>lR�n>�")�]Ѡ��%��Fa.� � U2 + ival�.K2})v0.R O 3\,k� } [K_{NMQ 9\,f_{)�N %A�N FN Ha�!$.�"�Vi :A A.}V)�e&�#ͺ���Q* �sQ�(��%�16)�j�7M�M*�)^� eq.21} ��#B�EI�5�-� + 9 )�"�JO%x J� *_F�)^]�BV<,quiv K^{kin}%�+KK  J� z< :ogy��:��y8Yb�fer;!b s�� 2�,w�e��e $�``�` ed''!�:��4J-�i�/or�6:�9j ��9,X�����~4/ �1��l"e[)"����_ �C$e�� :� �Ws� �c��lueŵ&0 mass�I+0$�-�3sg y!gB0�d �E- ��@ ��� bi��I:� $$E/AI�0)=�C+Q�H _0-M_N$$(. �W!Yb e�on�1u%X_ h�-��)$ae�5�] .��<m$"F-� Xo�� � )�:Vt=�-to  n%�Acl�B��� $EOS�E &� >�, evenM<�6��!�,exlm �_&� "1 !A)�a�  fe�e�V� C1>� �qachU]�TsD28$ A�$monopole r@ %�VZ%�i { seem�] �G)�6yA� V%�E m>� qa�. Ma�authors\ �� �ertG? dema?`� a clar"�"��& 5,MaM 86,Niksic�%$6,Vretenar8hE=�1�V  isi "�6Vnec-�!왖:�"!q%I"�, �O�RnicU'suggesth2�Ate� � 6���:�� exampl ��3�Hb�%an�!�J� *� \2��D�E� a shift�N/��. ``�:$� f^ �2�L� 100\, �= %among*;6z��EkjayV�E73 9ff� v-Ya  B$K2 3|A}%?�2>�e*n��an���L2La >�R��<:�.PWs��E"�EFZ N�fwe A�%RK�"p e~ :�s��'U_ f-�ers\"d;�� ll��a+"� � aris�=��� ous BN��!ect�rpaa�We focus�Saa"U ��f�� hVx5, %B!2��b!6e�iA<�4 n� 6< ��!-6pxiPo�;N�of.C�s� �~� � 6�7f� nonr�\[[F^a_0+� 4F_1^a}{1+1/3\, 1}\,n�2K>1 �$60"G``5�''�!b�N�}6$F6YNI�N6t4+,^a=F^{nn}_0- p}e@i&9!�Y8�c. �1$��!�\ a� B����B�?t�\%�m"^_� 32��,RB�&�.��*6�6f1a�6F_� F_� -F &� {67)�1} {1� �\,&}*�3 &&A {a}=Y�f\vV1+� 1}{3} �\, \,,Q �U_i=N_F f�6(i=W, �)� �2N_{n,p��N"=?!M$�a$� "Su�v�X � . By�!8yt��6 ("���2t)� �.�[e�SiY)�*�$� ^?s kg, *^ ��k��^ ���~outEv��A� %��Q%4"���y).said b�� # ��O� c, hI(, y#&� �it�,�ab�$10�m�t!F�� . Moreo�h turnqo�� y�6[� r��� �wCQ%/z gma$ �(ch2zQ'B� #ly6�.Y-^l!> �F a $2�.�g� 9')X�0S��#he_'� š%�� O%�ed"�l%"heFz� n u)(&�+�A4?��2�]e��>�B/*%,Caillo�=9�H� ^!�f�A@f0, �Y�J�� !�O)�-:��I peti�I pr�& f�A &Gwayij��":�' �0$�/ fact���79#esim} �@�"�&�(1+��)� D a��&+I�s�Y� 1$ eZ s,A1kq!љ Y'e�moٔ, $ly�'ZL;-Q� A�pA���a%h;'�nc� �* h�,i� #: |B\O-C>E-Cs>�> v�aI&:a$F^s_0"'+"'��*�*��A�E��B� 3 )����%�g�<), just substituu���*�� A3�ڍ�,� s5�"��T*I+*�CMod*�jN�o kW�6w��Sb*~��o % �;�"� .I.=,�Qdr�N;>�2@o�I�ai��m>�n&�BQRL�I�M��Bso�/s7f h29VA� ,u+ 6�&9a�a ��e"E:�C"% !./t� �g��M$� basJ5�a��{�J �S"5 �. M�v�9m�/iz:lnHaQ;�8is K$l� �p �_��9-Z�+��*, "e�J�43��m"�,�}"�(3, 4a" �HU�Q�"�6�� Non-"F �� ($NL~8"�! ei�""t�(�9])�OA6Ztm.�)A2� �oE$ =,|sL# 4�thoug�&�E-z�a4 p�j�,� ��j N%%�{Hal�,�pw to�out. F�4ly&[ ���  �I%/<9.�A[�confirx���@WAA���=\MC�%�6cdW\=7r4euT g qhdsetsFSet�)b : \J ),A�:9"2A��"r � ��2� s ad���%2�=}"� 2.0 fm^2$��!F$�ul�$R cin}>6Ki�tE.�'3}a!:�'Us".G6m" � 2k Xc>�*��2+1I$�&q�2 2 tl%"�Tpl\n6 J�un�"�g+�1QT��Q��f nven�$:�/ Cd ��"ng $1.00V�EW``v7''-1E��&��Jdu"�^str�!�-*� ``chaoti$U� .]lmo� 4P``v damping''"is�ybjY lso "� �1a� �Rq[(``robustnes4p-H:� . DotA�� �# fer MWa:yi�0�Z�,39-*x?V� 1e3��!�. . C.u�apy@edEU._�ga�8� 2C0� W�&pe�{"��lsM�D at/0Y�, $I=UAt+"f.� �f#e�Fin spitL� R QReB�*K',�%=_ ��H4xYOS} m��!Zs,G9?C=)c3$C$�}"t -BO. � 6:(a)�|[htb]� ce� �ep%|7.0b�U O1�Ui~�,phics[�3|7�U7_fig+&�UI%/ �: !�R]��֍�v&L">Vaʝ�I $. (b)6u<��fB:%&d� C�=es. All���F�|U*��!6�,�i0=0.16�{-3�H-$full circl2panel�re3 �g!Fu&!�$-i�p�E n)$ �}Qr�_&�V lin3n�VTh k ��u"��M"0(�.t.� �]v*; � A����&� >Se�ar�[Such " Nb �1'inr ݨYux"�"�Pu��s-, � �& . D^� a�G\rh�c2 ���B�F85H. AgM�9p*7#� b� ��Y�� �vYM�. �f� 4!�+m�o�I8� ���1�.1�� y�Q t�8,*J�� Y=��O(m�P~s:$ � �. f��-�"QCp="[ 6v4mode,� $A�2�!� &�!.� B 5)wABa� ny�I�ho�� 2dAY �ZT ���,,�&Up������2� �<i�-$pronouncedau1[$ (��ar&)��-� (d*b JDisW2�.-%����;a��}�}�m�-��*�t!�t?!%�l��J�s�@��1�(6G%~��E�� �:�!�'I#y"PQ� occurs�s��^{�.s��EK2B�WA� E�1�i>% �{s�$quick�o:�%�6�kA��.1"5M�y�=&8�<�$y�l �F�. Q$�~Q�~EF$A�� ���Q� Figs> �6�= lin6}�ah%rr�L>a&:< �y#�/z�FA&��ls=9.�5�]� '� -�h �BqM �Na&ei1X$$Bq&�]�ME,A�mf� >|,.{U���i*ч%V(a`3p�DU�%���!aH���(Bb�Z���A A 2�A +&A S�$�HlkG-6�!I� �� �:�"}�� ). C4ces:!f � &BpenM :��f�C.� :B� :U���.1$. (cj!5$2[ 5n[ ��4j �� 3��+9�"� � �����hi)�'ngE��! "� 9?j B�B:�E�>�j�O .1$,:b>� *5B*c2�6r�V�w" a�:��y "MA��.�A A�,�q�#E���u�,*Ca�/ b,c)�MO%�Rs#�7� a� r� �&pi�hCol&O\}��ӆ�i ` 2s6&�i�� ?�to�$.H(�A@A�X)�c�w�7�) KAeX_7.K�}- � !�!�e��wid�HQsH``�=�96�,�b,� �� L��il-�M, Ne he o�� �.L6 �i��*n8hn%7�;�<E�D*5 �71�N peri�Pal%TaP��m���I+V\E��In �"� n!sB�e![<�P�A�ls�L#rAQat5,(:�K"�^ rh E $J!�Nc � oɎ 1\,~2- ��=9r ��@2 a+eq 2.4� 0 �w�K"�.0� ZbI3.0 I�ba~Me�&��;| ��� 2=<"D �&: 9 "�$�9�dI �� 8A \&���/�  Fu"��Ex�%+>�A,�� &� �i�/!Y"���iq<(�/#6x*��� e d8'�w:�,�%N;z2hA�&b-� Sa�= vR �.�  `It�b�iZ&� &Il :�%{a�gm�J:�B�" K!��y!KB\ �6�4weAv�49��� y2cHa@6 6/2Oat�� = 3.5�E�a&h�,�2��Nt���Red�'ng6n&D�����or6����BL !��K.�A2 .assoc�dd+tk�G���9w"^_�� "� 4�S +&S � "�A ���- }o�-�t��M�9� =3.5eE0$. So�Ym�HtHn�r� B}�d"} 6}2��s$� $I6 7nY At� &#�QSa�l� *� �"�m">-s,ZAtQ�B&-� Q�t6�a#M��'f{�*6� *�2�3I>�#&"�0st0*� (���uT gre�\O om.f�$$I\,>\,0$)e��+pC5 ^ hows�!so&�� ��J {Fn}B-J�H�m�N� �!�6�G7}(b)�e bla�_���1YTGRU\alph��-e $�~�$ :� &| S!�*1 �~�j .c&�uv s�}�"*amped"_e�� n\ll�u)Vp<l*AE� �? Tclo@ ���}to re�j��Ou�3z�6� �xva�`i��'����aNA�is � nde� �*�w��%�p h%2�+[]LMU02}:-er�+|>�Y e"�V[�-A& N< �L |" .>$.�Q32�, %���R�2֏%f�6l(�|!%$u)!+��'n��h|^)!�a�:M"m�-�+ $�:""��g%w 5:!aSBvioo�xobl�9$(superlumi�Ze * #)B�no11F�5Q1�B4 see %Y\�*�-8 3c�O!~ %6�$;� 7&B,b�(.%d� ��#��!�%�-O tre: Bv5� &� IJ|D�V�m�Dil?��*�gV&gV�~znA/�pcheckA��R A� ��*�*d[  E� ��=X� odalata}.�  �l�P -gas�&Vz(uA7low-��9~�G��9��6n^%b"?un�1I@ &dE�"w �1at� s ri�Jo�DexJ�� growѝ� .P��e�N8p�%& a*�&$fo`#e-frag��� �O cess2[2J-a���,A�%P��9N(�8N ~f�R�8�Tis kin��r8ionF� 8/��p^EjEg�"���6�F�!o ini%j� ��\�Vv� . �l� 0 ���I E�I�c"+&O >E)�F�!����Wx&%"�)R� new n�ip in d�"�"D�Mue���>2,�pPq\���#5�� +&� ��cB%-Wu�*bl)�e�)]B=0.4\�0�& : I"�g6� K% $c$-�)!u)�&0$ � *z# Ia&�)�"Q%y. N D&4: �� v2$.�#a�� aAQ2�#�EϠ lin8n) I.W! F���e�B )�� "�d1�,e�){wR� �s $�6� t� =M"� ŝ�N�����9.>��$S��lin7})%a� � 6>FAr� �!nU<2� �"V ���� i_� quidͲA~%Q�����, du�$�dis�Embl""P�I%4�W(RaWpi��9a�Onb�A]22, E��LA2Cui�&�P Y"�N  ." �P�%-<�cume�I�5�2t n"�*i�N�Q�KMwe�G tinguish @s{ �"y,�.cal (kE�\=5% �}�z( � �PionHr�L%no�� inuGM�" �-um�^AOtiingل�%$�$��� 2�(2QAEnot�PYF"d q�.��P2 ��E1al�6��jG�e_M��i,sY�n�S , al 2&�6 =!<?n%���~" #%fs�Jٹ,Di�P22F ���on{Gen�Q�  s�A�ANM.�� }o-� �� at� A�ede um*AE�]�1�i�ov�bb��ssi��to� inU��g�$Lojz T:=&&ҟ]Q~&�~,2� �i#��T�.Dinew-������4�� _�5VJ)$ANM$. E&za,6b& � Jc�\5M�(+�5A��:�bv*�<s aYEAGy �1%(vJV�~!t��oraM�� � � Q*��n mpleAlqJ"���A�6n-^a�6X�3/orG�kkter��&D@ s. Btg" �*�� < �tѱ�Q $RPA$2�H�� �/E�i�B�ni%$EFT/DFT&nR�TCNPP2}�5�eb� &WE�z\e �! 2Z�+%Zle<|,V�>{U,Qsex�2"V�a��f.Xc�8�5�a��<yA|b���s�}u�6kF�/uq ��:S "���S.ZAaJ=E:�7aGllel �S>�A��$.KO� WkAsу�*Y. ��GgB�� E�s7�s� ih-�>�[��� jma�x[toAa beauti�V``mirro=B�fdM�lr t!�Lo�J supp���Bt"?2�"�4 ��5ʱ;,4eas�����of viewAA�$�rem �9N�9�� �"�Vu�!g �  7� �E�}c�W, &�BnOE,:G��7a�?EL'�B-�9er��!L0Bethe-Weisz\"c_�s�9mu�� � P� %\d�� �F �.���.q�E�{R.� Heavy Ion�:% �d.��m5\��mAreldy�� . I�8��a��yR�, $HIC$,&�"unique *�"A����.!�O�A�S_d (�S^ �"N far: YQK&�gS4ZR�=�9� g��J`/2 B)$ a9it�a2� �e�Jl�X35*8 ��qce(���6X�4C* y�1#!'2�� �;nP ���isLS�*g�:��� ���1YeG$!����8j� 3B��A "��<9z�amA� ��":&ɂ�" . PSN!m�c�� Rur��A entJ ��"p o ��� coo�:9&"��5�"�ELat�hPrPRL66,SumiyashiAPJ42��T-radi�& w Prakash?P1,EngivikPRL73}, crit6�lmkao��n�gx  �W z�%�d LeePR275,x� APPB30} a#llq!I�g&�a �qquark-hgxU UKut� r\R62}��- �Rrs�;al�5;�"�.�""rKl�e�'gr���X?moQ�/>�"�.� ��N� ���d �f�t�Xe�6- cEV� a _^���E&�*KY�< !��2W�&Des/$DitarX0210E g++�t@< �h;searchi F`[+�;�(!sdr@Da ?>�.oreIia?0"S(efforts�D� !�����i�h�6"�/.Wto[ �� 6w!^�� ����f@i�E beVan� YRthly a\/�-+a. ity.{[weI�Q�Ta?n!�� 2� � tr�Do��� re��;s�B6A�V z �=��%<�A�er1��<�furiȯcanA_%���� &~2�s (1?&9- v 17I !;d�a�h�b 5t�!�(��- provb+axw�_o ���� �&@j�=[�a al l��$MyE���N)l %4&�I�y?A��rob�hC. ?HxA3��� a�sA�.�mP $1AGاa.��,!�h".��%of�n�h��tFwic�M�:D&�=&�%[_���1wO-"� E� LU!�i�)�i�����), �,�3m�~ay�#E�a ch����em��n�t*@Iflow,� �A/VeP�b�E ��%7��![0���d�st�C�RoAv�.am�<"�e elli����NU�lGq�b��&a� be )B�reM�y� ,� *� � �.�}%OpAIa�a W a� �)%_!�!h> !�9U��s d"  �'N�R� ue1a�h�E�pi�"(B��i U� ?'V�work  Baop5,�yone?�61,Um� 57, C67} u��"� � ��oppos�" �![5�t66�� �'? � on (%� asy-*(})O)+$�on .-oft2�m�:�#En��? @�F6�� q�H9!���r"~>E�w �&.&. �Z(I)!�ݮA�EB4 :I�5-ls�OF �T2dd1gg�!-5�ks�j��N2#I� !\A�r� �  ye�� yE� devo&AfP�B�! f"!ei�i!VI�!&�^ 56,F�i,671,BuervePR)�. A:� � not �!��� e�!�a�!"��esh!can.�Tst��.A��m.��ht .�&E�l�c ��%� I1C �-$*�>��^�v >Ay�7!�de�A�-g&v�&Na��� tu ? �[r�iSd'�� �"!/V}#� ;�8�;� �%M %Z��K�b"ry�)� ��L��~&H�FA��%*�J WG%ex=, WLI� weak-7�DU�m*�Gs*O�Ah �N�>6 �� FZA>pE instead aK �mrt;"Msp�K��E�,`�� �pO`7,.Fw��� aming9 ar�I�! e�}��iU �`&*0�PEKa�*ek>�#�M+e:�G8jѝ,esym-nl2rbuu��#8J�GT\Y( �+"di)�c��y�8 MeV)�z�L����� m�. �#�0a"\{I $. D��$. Sh3 F/-D2$%�E�nserti_ `�w �qtO, �Z rho$�$O�[�� thre�odi0i� wn&;91n�# Ɯ�Qi�i&�<�� ��a W8J�abe \�� (�:uf�keq.2} :�(�f�]1}{6}�]mX�glj"2_�&�{tj%� \�sj{�wj+ �yj�]�3} $E^*=\(� �+5|$,  c�$�]������)u�lrh!^}=��2^o�! )^2$�IAeQ9��ta� C�5��ŵ� 5�me�b�t V�Hed�uB�M o:"�Pas<s �"�` $lrh.� F�)^2]$� $�- )&H.� �V� "�%q2��eu�6� !["� �Jm�ree*� $&WU-�\ts: �K)�|Mw{ l�H Uqi��a ")A)-x6�zm�I0I�$�J6 )Vare�O���  ��a� $nJ9Tr�� last�U��)� ��<�ta 2�)D�,�varsu��6d��, N= c��}&�*tu+J�^�� ]%�'FR)�">. BfA"� "�H)�lR�Fla usu��di�/agv� � s"a �1 a��cAF�Xي"�Rli.]streng".Q)�MX-`>X LB56�$Ta����Np�griz)+�A*nXyE��2l%���}=1.1 ��3Za baln) j6h &C3.3 CE�"�Hithz{I�}=>ofin  by a:� �8i�k6n�- atu�,�^uaA*$J�a�� F�(i)��B��l6 ?AU:�\ rI%5V"�j5*&�a�)+���5��5�"�)rho'��i�"Ťa1{ t�� Us� r&%0 @ � Fou!Q�!� �$\�%�;+Z� by �� Hofmanw�64,DalmX0407}�knd $DHX�hiRC64}2/<ue�O!p� s�> ��� � fic� ~d�9bas.'�D �4B�la�Aj��`.]2F\�]of ��oI  >�'C���B��a����P.�f"� stop�* power�]c�A��~.`#��U�)o! o a0�S��Weu�&�+.[)' Ude�ML2 JN�� ",�%lqu& �cz$on��qm�J�b virt8�U vb&� )%����V�q�E*+a s�89��c1,A& favo��f6�oed)�M"+XAAi& Danii���mt���a]UVsi�# �AK�!�c���ic�sA�|2�"� �0GaitanosEPJA1��Ii�c.W�a�%H $(\sgRbRB �s��Pr��s� �+��7:��|3� \*�72y'�= }Z� #�"�de��p!CA��!'=J� olv&�g�$BASBoltz�%qh/�8K\59,Gieg+R��Apb�%2�Lt�D Vlasov ($RLV$) me�� S*��} ($ G 2A��nda���0 a Monte-Carl�� oced";UA �. uA�a�T� �9Ga�(rp�� s��aF�:u� es e i��inp��v inv�� p| !�/Kor5�!$��(1232��,$N^{*}(1440 ��*�s���` theicUc`�� one-e� two-��. DM�a�jO}xe�!n�!�le@�_R�<Huber��73��l{�x*<(Pauli block�jxt8��[mploy��H��r c!���.� l>BR� a61M�u�"�V��WئF% �"S:Ud ��� ?Z�:expand�ero�*'2�" �e�)*!�A@�)b�n�[e�� Y e>8�r� �B mini���A$�&cy�B3MW�@a�� asNj8� F}^{"� �oS.+.Y�F^{,\mu2� ,~~~@� . $$&�G�9�(Y5%N�aIk)� af��o� 3'oS"�AD �� ��!)���~ ~ p_i^{{*� {{F�"Z�M_i^*}}AZtY ZN��UsofQ�� Q� �!h� i(x,p^{* !5) � yi/m$"'.\9*(vlarel} \{pv� i}�M\\ialj� + [n F�\mu\nuY e(25)]&ѡ_�(^{p^*} \} f�-*)~=~0R.!�� tensor)z.� �2�5� �numuU<� traj�[G�%� obe���\1P�m�b=kn��"H�eqmot�r�,d}{d\tau}x_i!g�kpѨ()�!' )}~,6�r:C!��_iF{i�BK {F}==\�x_ t�t)+90mu �} i(x)&m� �A,Bk��!-�a%A."*�� �� �n&O!u� �,a��)�s� .e ?�,��i�2b�~``R''e�8N 1�. ��w�NI<2�̈́1"�g> �dFB� ��"y jB�o�{OW�&)�D{d\vec p}^{\,*}_i}M =#��}�p-�M#�B(\nabla J_{3K nu}-9�nu#{J_[��v \*� >��, ��X(p/n) %[(+,-)p, (-,+)n]a:�Tq�X%�} \)� ~�:��i�ve� }�_2�>!S"en.��I� s*s�P)n6��,�H"�,o!���� g��%a�A�%�?�g�#g&���s' N %�_l%�m} �$l \not��m=x,y,zY�nd\����m cӜI�"�(U(i�:qPI�be�{s}�G}rekR"hfloK22� :�%n >!R_ b U!!(���ݙ ��+� e?u��d"V�D+lStoeckerPR137,DasguptaPT46,D0SCI298,RHIC-v Aa��_%a.� "S��%q{pn}(y)/2#L82} "�#� d4�!W �(��Va# Ȃt� v!ra��ns2;*��ca�e"�<�/��d1��$6� �$4 A�MZ$F�ib�eq.3} +M���1}{N(y)7� um_{i=1}^ p_{x_{i�tau_iB�v$?� !/w���H� �� -V rapid�-$y2hF�)i� u;� Ile $i"�6"����A$ �O+1� -1} I;�M@!d�Lio.��typ�/�$� E%*!+$$^{132}Sn+ � ����O1.5�* xmi;��"�s�S#.�Gr4av e�6�.�j�%o{'�8�! .F� M].ln�U�*��nT�)�&��F�r�@!ۡX�� �s�GN*�/�'�6A+ <"�ma*�� %p2�veBK#FBAdhig:�S�&�&�V)a 1}. F���2a� surpri��"h A+�X���&&WI=�raX�&�!A.m*�� ��pmOd �-u� "i "\�&�a�2 �&but} "\2H�(!�e�8��-�1�1�!�9�,Irtml<:2.KeE'I�,X o2���w#Ader��r!#E�� -e(lyaf9��v)*�&� M�-{=!�,N1�sE*I�*id��+ �[ov� !� s i�*d (X��h3">loe��� 2�E-�a�$"�#E$orSmyuͅonF &��.q �}�} )!t&� �!��2� )�-�zD�7� "7 E�es� -f1�ce"��As9!;�[���� �\. O�7c?if�1�Q�8&��~Z��%X w,6��'�!Bsg4�$ -^ ("�BE_%veBayDn*1yO�})q��|ed=��el�q"��8��! m�Qrh� ���<#AE 3}$)*��"�{pn!mC�>� p� - Z> n �[\� [)!"( \�9 �#5���]B 3}~=~�#[�4}{�B"7$�# + 2( O-1)d� JYZ� BbRycMe�@'�p&:��D�@d9��$)&.us�K<�� >:S� aNdB�D+ū"�lyE��p��.S/���"(/ i4����b~ aI��� ���!S ,� �,��SP�ca!)2�A�e�( 1f>Y ``�5�o`G2i� breau � :� t)E-�M/$�*� �z��Y|�z� 4^?,.$. �u9{oh~�A_�w[$! )K ����-s-(e[K%t &W���$:�#v>H^ 1$Bl��>�6;?[htr�q6j*,sn132_15b6-4��,5Jr5r*:�fN� " � ~� ,~(b=6fm)$: P�4IY�� *� �2x�! $MeV/c%g� ge%\!U�&�?&���*^q%�u�$e"�*�L$. .>g-VXr St0A s�*' VP . ��M 2�4� �+�-� To-a�e"B$M�2ivb!M� � �P"^FԮeϛ$d"�,/d(y/y_{proj}at mid-1n�<s �(is $46.7)��+� -/p$23.4F#��Ja��7X�ce.6�8pe#��tlFr w5ih} show�H�:$500AM�8t4��&�_j�`a�|!? !4\ [�iHm�^(p "b4 A'� "K � �.���� F��tpEr�&a�5K9T E A�Z"z�D"�?�V��j�&v2pnbN�':Ei&s�h2J p�6�8�B�Q."��|rat 1.5 �� ��8Q� 2�($-0.3 \leq y 0.3$. �*�*2)�s7V�al.��o$" ar�i$ �*1��note&��p_t=\t."x+yr4vOlliPRD"e�5�V��E$Av_25r�on�C�k$iKe�of  ��<����� (Hso-� ��I e�)se��ea��I�$K�Ri"hK)",� |)IeV�w! �7er*$.? !�R��&� &�01��)$ � .Ar- �"��.F*� 2��2�>*�\a�>9tա��� shadC�) �.�-&��-�.�7�9� �92C/mDJH�z���=discusa@Da�"�m��+AfGfE� stag�� eC!e�$���J-�*�N�^ =ch7xV�)�J��5�,�$f u �+NiDB�` V�� =am Ժ�i&�)�*K2�%.� E��xa]V2�24}Sn~^ �S ik�-�Gbe $Xw�@�Z>�ned.�@R fac�HT j�tN|�a�fho�1:E4Z21E!'�"� A6x{.�h�9!��V rBpJ�cׯٍ`� .q�0isospin densi�ty in the interaction region. Particularly evident is aga 6 splittingG(high $p_t$ F of`�elliptic flow. \begin{figure}[htb] ce��F} \includegraphics[scale=0.75]{ch8_fig4.ps} \caption{$^{132}Sn+^{124}Sn� �dat $1.5~AGeV~(b=6fm)$ from�,three differ�$models forx isovector mean fields. Top: as�`Fig.\ref{reldyn2}. BottomZ!�3}. Full circles and solid line: $NL\rho\delta$. Open2-dashe:.$. Star N hortB'-D\rh)8Error bars: see� text�A previous -a$. } \label �4} \end9� -� \subseET{$\pi^-/�+$ Ratios} Observable effects originatAV5�EX�density symmetry energy are related to5�ce%�neutron�proton KTies. Thus, we consider!��follow�r�A� O s to O(s as a fun�& timer4space. One exp�isospin�i�Y|An"channA�4of pions, sinc%�y �produced�,$nn$, $pp$ AM($np$ collis< via�decayT $\DeA]�4$N^{*}$ resona!>. Us1sam-f ivisa�transpAccod� )�$ vs.  +$ ��ZaNa�$ral $Au+Au2�at.%�ieA~$n be evalu!�,E�H\cite{GaitanosNPA73atResults% shown in>�5}>����eJ~*�50�L5.eps} %\vskip-1.3cm�� Cenj� $0.6�� $ (upper))�1.0 (b�> ). TALevolu%Eof $n/p$M�%�1�5�=v!2@�� s ($� /X_0 \ge 2.0$) (first twoA> umns� ��tot!�\.�i$(right). S��s�� $. D��\��:\5:\9f5!f.jF�� 62��E�u�a3 emit�*@much earlier than!4tons Vw phase duea� a mo�vpulsive�h together with a lower $n$-��/as�| is  is!�p���a,�yedui>-�%�-)r�< residual systemA, p�� , ita fluea�Z !l.,,iVtUmaPRC57,BaoPRC67}. The four��states�M�-Y�!op�� ��scatter�^��, whe� �shold��w vail�+0, e.g. $nn \Esarrow p �^{-},n 0},~ppV(+(4 ^{++},\cdots$� �^{0,-}$a/�. ^{+,++}$)!��*�mainly!�m����e�+� $- (��-)aW��kerefore,%�=� �,indirectly �� that1yJ�. %�N�iQw 2� a�N ic m%�$ can also ya��9� )م� because �r1�7�FWe note agtDs will m haveUYdepend� in-medium:�es L�b͘e��a4nucleonB4AXough %�couplE�$oefficient9%process Q  \left]u\pi{N}$,͐Bao��08,>� In termu0self-E#��$\Sigma$�! :ђ4eqnarray} & & & _i (M� -) =<(n) \nonumber \\V303$frac{2}{3}T>+ 12p) �W+W6>n)W6pp) ��a�[%!_i(p)~and~~~nA,{N^*}^{(+,0):C,n). � we��J quad� 9wwa� $i=� arx $.afuAW� ae �ݹf3QU.3eb.� �a $�)-m� �! d��A�cal� a� . WeEG+ n �� gApal"� -s (� Sect� qhd})��at,�c�� rich�_ s, a� )��la so  is leadaV to a� �!%!$ smalleb a��at�=at�,����ua at �baryon � Consequen�(�Ga��{V�-}$ la�!gy5{�i� the ) ^-2� i:wcase.��lik,����t��me��ism!�not stri�� link�� � $y behavior� �� . E.g.%�2�@���we �3�bo %O 6��a �E_{sym}( )$ ��! 5 Q�_isV rea0 bu֥�4 large $m^*_p-n$.�:�WstaysE�tant or�is sla�ly inu,�1�DBHF$.�{ ref.�B���he1�.�$multiplici%)( (middle �s) on usasde��V^O� F Y � i'�N�ij-��:.C .��edi��w�aysG a*�-}2*n��^O ~�n{06"p\p ! "+6"n"+}�!"] ��.'�1$"n �sCe�* nega�T enchAnd-wh����n I� {-}�{+}X � �~AP�~*�5}� aΥC�n appe{to��se��� t!5�!�equ�� EF�. :should�-!4at bothq�used !T8 exhibit a simi�4 asy-stiff�Fe :����1�WA-!y��e NS * ��4described abovC very im4a�in induc�'qI�s J� k �B@es}. A compariso%M�-� +} /Q�4� @preliminary data,�`&� � ies,�p presenc FN6}�};�\F��.� � i�  (|(ce between �� curv�mis�Q�!FفC beam �y� is2 a%qicUw+�� in�6,�e�A�9�a; t . � �>}[t�R�66E��c�|(B�)&B-� J�"OuNL�$ (%� \-�()�)A�a�iz%l�  grey���rre�� someeAh2� � )�FOPI-GSI3abo�{nm}B�6}� �er -t GA� allyN}o�BQ �X�= ing EiincIgy�seeAe>Na$ d<secondaw&�, i.e. vabsorp vndQt�"5, ��besa�i�P �K-QtAq�%H ]% ^.�� 8verage�nrated. ��trend w�lread�un�V studX  u!5 on-�D,Quantum-Mole� Dynamic�8QMD$) approach-�������s newEMB��>�  reA"ll e��ed:}$-!�Yy�0$E�P E�,��wn� Y�� :c6}!�Y�\simuli4!�0vide a qualit�� good�^I& �e� abect鑵��,cept perhaps��� E�T A�?ea � � � ��-� a�"� F� improveI�ٵ,�least �er�� anyY  "h ��Y��s m ��a�b�Z� FGal�rol1 virtX�}. It w�$be helpful!f look��exclu�^ onB|iA'�icQ��G:�je!����Asdiscusset��enh�e�5 momeat sA ra, �{rapidc% � versa� 3di� b�s,��;AplX:��3Coulomb 3���2&�ly�%�+�Q -$6���uu clearer�%�o"b:V :=iao edica�M��A? �(�*7 )Qz,!�6 eQy.6I-T!d$parency} equilibe���V!?��ia��Q6i�B t aQX�It has b��ext� ve��nvestig�� by^�g:c�signaturira���dRamiPRL84,HongPRC66}. Here�ke�`w���6 A�7 $ $iso-EOS$�.� idea!�to�by %o�]R�mass �5) $N/Z �iq p , a��b�Z `${}^{96}_{44}Ru,~N/Z=1.18M� 0}Zr4$�g-� � aAo$ojectile/t� i experian��eVateIJ�O� 0Va� �28�$n���Q e%�stopp5 >]�Y,de� in� E��$_&f ${\it imbal�rɊ}E mixed r� �s $Ru(Zr)+Zr(Ru)$: $R(y^{(0)})=N^{RuZr}(/N^{ZrRu $, � N^{iE) le y� �a giv���j$Ru+Zr-�Zr+Ru$IC$i=�,~{e �U $Rmmeasur!)or]^��lM �s, s, lŴ frag)�s�as $t �A\ 3}He ���dds3@ ��00,\pm}$), etcź%ac}zy U$scenarios." ��, movA9� M�to $cmaJ�C,!�p)$ ri  (posislope) !*% alK�$, falls ("� 32f3"rebk �e A} s fl 5,�a-ћmix�\chiev�%�P�d. An op��� ��a.�D deed��recal�ae�A��2mlimitEF�� -�e� $R(p)=Za}/Za,}=40/44=0.91I $R(ne6Zr}a+��K!����� a"�! top-Mxa:KA!cad� (emp� quar5c"u��M���"=�x%ed L"-  cross��us (hal�e�s,2s�!_{NN}(E� r!1}{2} 4}$)� n�IP *�7} ��ALE�u�6� �%:�z zu�(�i9 y�Y �wo�7 ies &� .o!e>v/ �t un��at mid-�A52  � types & ��2>�(�`a�CinU�"� �  GoA� � -A2P��_nic/� �� , ��e..19%!�28� �� ŭ"�is�e�n!�M��2=. YedV �.&HI!��i��nderstP Z, with-^:rpic�&7 !griQ( B)is"m� �6�(A*��) 5a%`2��)�!q�"� �B 3  Howevk"�0)��!\�$b"6�(-��1�!� tv�� . At low)�B�(a3��) 4 deal�!�cwr� s}u! _{B} < 2 �( �_{sat���T )��=�� �+u�#�� �#| v#eraw.��(.�,F�-�, �"r�!AAGa�, ��actly��llyE,�=+Z�a�tT}��jIn factE��"�"e"$%J open!'of inela�.�#� N/Tw /FZ/*� � �,� &�M�d�\!(contruN$!�a � �>�73pre&5 confiA�mo�,��&�+ R�(s)NG)-  ($NN$):���6 $\��np)I��#K ��02Xpossibi� d&�ed!�1!�a !�%wo��, �)by,!�%Q�  �-2� ���  b�+)=��-!�E �� rea��ra%� an u�/Eg1|I�s (�o � mi�Hcopic Dirac-BruecknaY stimB �(FuchsPRC64}M:< 8}6Ja6!���2�6��iN$0.5\M!T}� F�M$ '!,t( an o_ll&� Q(d2��jeno�+!��$at�4e"�al1�mc:�V-�6 O �i(h� � AR[A$> .i.�.M�_{(np)a )84o�* a .�Ar-p" :_orJ� ��ge"(ic�~+~�!x;AOi� � our .q��remar�(� 6$I�"�W4,R 56nde furE�5N�JO . S�42kŗperfo���%2s���!�(4ic'�*�.�*e 1aWre�l�m|tum*F ,� "] 2�!� niquely.�/��{� m�&�!���&� 1�"�2,.f+:�W#"�4*9:I6�E�t$1 *�-z %�"n Er� .A'7�@�~�la&i89n 6��10:� �c�� of&w(�'!�'i��(5�R10n �S �� and}"� "5(n B�)�E�U %sA��Q ��suggest� 4I2EIiY�3�t/��"�dou5u!|� $-$�Dreveal&l �itA\! ct!  pH m$method howA�pr�lb'�(:�!��j�U�,u t�!rsial��rO#�)_=�8.r�,�H:W�桦ple "�, nam�f�P lX� .T9}!Aw!�F�$R2��t � �� ��.$&!��r�= �H1�i"H,i0:� ��>�' ��0 �+&�  n�M�M�i. �4" 9!i�c�  hard� *' sepa� Y�E���~"CG%AХ8yF( >�7} &}x �he� Y� ���H10�, At vari�"N"�. 5�&l�A�*�f  duj /*�y(�=!^*�5�]�e �g3abund%gi�^n�] �-_-ex�3�.�.y � n?M/��5�M2�z&�� "KAha"וP �'� B��!��supra-nQ^' !�"}0to�m�"% ��ly'{#�9<� *�0�R���5��ϱ]B] 2y*|�. �y �is �8 �0-�.�Lo9Cz stru*M�� �Eff �9�k�+�b'reh��.)2-3nAs 2�y4!p�&z Bce"%� spin-*� ies$,� oonEF-I��AO �Q4Ch�$d � �8�3EFs�_$ed&�$y heavy-O9�� adio!-v�!am��#D0A} �i6Iy�ee�2<7y�.t�5b.�5�. UnsWAE$�e"m�%� a  too**�E�s�gth17m�-$$)#��8It1is&�)5�M�oic�c@! y $E*�6 _B)$:�,%s involaEFC d�-a %k{rep_bib B� docu�$}  F-/,class{elsart4u80ckage{epsfig}.Gx>amssymxt��en?(s % nuovi��.@ % 2 su 2pigreco :,ubo %\newcom&{\aD}{282}{(2\pi)^3}} %�entesi��dre:;qd}[1]{!= [ #1K6]6; tond>:t:(:)�.�itg d�L \int d^3k f_{#1}(k)l�V gral  fn:�ienne E itg{n} #1F6p>6pi4pV4n g>6 en}{ r0{g(k,\Lambda)%N6�pF=z<pi>: %\setlea={\I }{1cm!2:ZtauF\tau^ tg{\ 2� �BpC ^\p�)} 6LE�rozer>jr�rho_{_0%rhoA�V-a}{\td{�>8} > Ad�*a' di�@(a per A e B:�eQqd{ % \I��xEP}g^2 %-:+ 7� n^2+ p^2 �,0.5 + x0(x3):}umI�@ �x Y } !�6�newI�0mathcal{I}_#1)A�"�_�wA&cou�d{) {0}2�0�{CoX>� � out�/}�ou^\markA{Chaptn@arabic{�I}::�NFar*�*�  -Y> (or ��)�i�pen�e .N arn ab�&��b�(u@a�I&�Land� < . ar">6�0 w�2s,0u�9�4i�m� Iv�Jtemper%.. &4qy")extre�"%:X a deeA�R� 2�-<7 U� v�9$K.GC�C05!Ct� !�� tend !Az knowledg"jSYofdR�2ort� � jC,of astrophysygCn9S ernovaB&loE�o"w  s�L."�+� �L�>n,�=0to:/ ntif�mosm_e*�,� � aC5�Nc 2�!U>�J�su�konY4��J4$ mai( e�LT�(vRV�In � �eos�$ � �Z �pcE�(r.(�T�'%y�  ��2Y�!�k � !y� i�%�i, as >l(Armonopm4fr# cy), sa>� �E� ^ ski�'`2�"�1"�FowGA2*� d in 2= rpa}<1>in �+%��(diagra�F|%?Arelevd fe�E3 insta�ir)� subj�G>�"� conn��A�Y: � ( a liquid-gc1�J� ��J viola�j j "�0�I�Haf��H�&" eJhock,� 1�|#� �MasilyY�PC; expane��. New �1%U:�"� il8�,�ed�4AXsN;&� alL#� ��Z9ear6X�Htthough  care�6ml+� needed o�4antangle amongQ)�lv n��� .�, W !�re-�-&I� n8<re�:T8%**~?ri�0%v"+iX�mN; fast�5�A%-foc�3�E]�A��:y���jQL"( �>q�. .g(:�mi�"%�AuA�ve�6s�G� ����$.!-R��& <;��� �0J�a*�@����w �ive�G"5ed�&=ss&1Us quitM0,�Q%K2��!� zoPUal po#F2��u�� ��4��.&� d ye�FH�% .�v�$y�!W�t!6F�Nf��al qu� A8��ar%�i��o��aAL prob^� l# u�VYto%?����m���"I!�+A�h!��$BTfermi}(Teexplo�:�� 6du�� ccurE�FM)��&�framewor /a�&cht$ mean�: >�$�C�:E].��/6�inQFi�*8,ɬ�aqWO isota"^ ne7Rq:� cɞBA�Y�(�4">�A���. �2semi- 8pheA !��3a����qenJ A{ h aU8lap (``neck'') ɨQ�,[*�Hmig�E�� er ( at� 1"s)a5>(`)Un !. Als�Et ��N*54G�%% � :$�'ՁM �'onJ .�d1�=*nE�Cs�=s1��U��fI9�V��F� s 6-7N$e%M�ed�$ti"�2 �� Mal|"�Evx%��vVqes-�"�Y, GBu,(�' E�R):6"��Ls)R'��ib�= ��&Uh K�;��8��8祂a ot kN,dA�t(0Y�I'"�F" �7 l �T s�"�tBAp} "Y!��& � :^l sE N, (Gn0I]}�M�Q��'1�v.�1�m� � � close��NlMw=Dr0g/>CC t�e�YprHA���� ��dyn2' "81�i?5n Mz&2 *�M- �("�p �B��*q+ "�@2Q "�N ���U*���uQ����, Is %^�6�7 ?65V��io r ka�Z lighu �/F� n,Pxe%wrq&�?K�y^&4� ,��on*uld ge.�inF6>�9D =c�|6�@Ou%:�/Ele`=&�\s}a:c"X* �tud�[Qz)�e���&�X1�`� }:� �8*KEng �. S�e u �&��to%�]s%�ZB=i)�t.t�� A jo�effort=�e"L�#nd�or�9yidrh%�a�] *� "j:�.� 9:qL-T6�Z ����$� �:ion��I%J� ̡#�*�@z� < w�MXmU>� �A(R���i�]&W}]� X Y�͹6~(> !v$its ``fine�~'': \no#nt y 1. Compet_ of R�@ M�Rs}. I��pElow�Vy ��sip�G"��P�(in�lete)Z^ )-&�/ vs. � 6�:!��N�p�{�) a k3r"�[mls.(�.� � )B�2. pLA�-�2}. N/Z!VIi�X�:*�4 �oh � /� m"C3!�v�@u���s. More� S A:i ��YqA�e �v� 6Ns"�o� (�v mass�E��2 raE;jBe_!% phoy(� �A71 $(n,A4bremmstrahlungY��b&�@b2f� 2�+!f��y��6�"�F�3�+%/�8 (a���aA�Time-�<�- ~cY 1�%a� �W�:�FsourcG4����b�?)%Y�a�1 &=,�5 E��U�^j3 .�91 :� 4. E-slopVLane Pt }. AJ ��=��y@!`h $(n/AB���a ��i E2�dgh!� )Q�Y�,aPK� 6�i�si�/!K�$� F! 5. I�D� � (Fr�!onB )�� '� nt�+A����FM�GF"�D` +b! . THof� -y)��slut$F_�QMa u� V$� T5j$))^� 6. P"� �Neck-�}. Mi*�9$IMF$�|����F�:.w&:�H, aligne� 7 size9�I E?!o.��3 ``-� M�''J� B�7kDifə�e)of�\{1�E��``�">''3 !�V5�%����;T!�)<%�A��gDb4i�$Z ��8� -� Col� Flow!�To*�b 2)�. Che�AY�"vD-�. Q�!&��.1(�5� �s)!r�c%i�!QGB�. -�A=s�&��j "� � �$�$�%%p�*r�iJ-9Y,2�L.��1�*� inv?KTAOt�,���)�l�.�g``mirroAb� w �v��pSX-�,\5�SEs oZ�>6IV-�( �W10C:4 0h-vY +$ Yq%}. �3�(-$i�l��<�h����� a�+e!���e&� ��)#:�. I8�Ka>". 1E��] mA�-�"�T1r "=Qof:w-.Ix��1EB�11. De�9� Precursor)Hgna�Mf�iwL�� publm�%��A�!B� Medea/M�b!�$nd Chimera� U����$LNS-Catani�O �HV.,GSI-Darmstad0%E�� z%=�xdue %to P.Sapienza, E.De FilippE�PaganoA�$Wilczynski%8(W.Reisdorf.;*�(end*�(� ZH-Z1-."0- �!-2�)H� -2:�-29t-*X-:-2(�-6B�-65�-65�-6<9,N-�* -�-6Z -�Y�-BA�-2Ar�Q,V-6,�--2P2-�,b-�--2z�-23inj-B-$\ifx\href\\+�$d\else\hyp�[\tup{linktocpage=true}\fib�O ront�6$} \title {"�"�_� Exo��,di} \author[LNS]{V. Baran\�31xbar}},6'$ M.ColonnaTEXAGrecoX0M.Di Toro\corqZ dit}�Q [dit]Poro@lns.infn.it} \addA OL�/ori Naz��li del Sud INFN, Via S. Sofia 62, I-95123 C�U , Italy\\ )Di��o�/\Fisica e Astronomia, Uni�S it\`5J}%�%Cyclo7T Institute, Texas A\&MH.,��ege S�E:USA}% -|[bar]{On c&�$NIPNE-HHŎBuO-��y, Rom�4�x�u 0.2� it Is�g'^o/.l>' C�  et pue(, mittunt B;4do volunt hic� s�0  n} �ECon_%�v �- �M�abVct}� �Ce&Nnew*� �"H _2�&� & i�%u�s� yu l�6�66(te&� � s�G:26� L#�� ly A"}"[0M($ANM$) � A��)#ll� d5 �M�!��i"G&ED� f �&�+1�:f!��#8d- �"�e ��� H ar E*jA�e (�D�1 far a�WE�*2-*f.�]alwaysP0  ory'tr�MI�.T-rmo-�!�*�-%[� survey�1&^rom non2�A2n�=Ss%.,%H  .-$9�I9� �b� �'!� q*7dA�."'!�j , "��b"*�-S�.�"�,"��8m�b-O-o� &��' , n-poor,Vi",if st"(��/t*`�3-,r�|alysed aai�ol&�L!�^ity �f�$s �J &\&%��2ll stepe�Q �PprompF �/="�qV�z!�TLof�;ESest�' a�/@��(aux�d;"2.�!.�2�N.M!�*.b�c"T:"�-@y�5 ��[M.X;. R�$!�UM�{�Bc2e,�6%-T#.�<cPer� a�%��Idevelopm��/"�%��2�D �~"�!I��kentaxpjaՀђkeyword}�x�#QP \sep��y 1)9;{ Q^*; ��i� s2axO�� .K fF��A��O8 \PACS 21.65.+f %21.30.Fe 5.70.Pq 5.Dw 4.10.Cn u Jv )Q5?:�6� new� � tqof�s\re.W;the�/}{>�7-#}J@b8-*> !6�8�}{1K "'deO8-R2N*3N4N5N6N7N8N9.Biblio�=�f%�.�9V��%� �#$Y3M"� B=�O A. Majum"� FO�P 11/13/04�x�P:,[aps,prl,ams#;?,9rintn{ s,su�  � ,twoco�,��Tpacs,floatfix]{revtex4�?t~ c?.W�?,%�ics,colo)u&�? x}% Ia;Oi�� files2Od � }% A� e� � deci�7w2; bm}% bold0Eh2-�. {\bas@e? tch�}.p \etc {Fe�<�Nc7@ \tie �Ka�` \6 :[ f {\not\!:wh {\};ha�.Q$hq {\hat{q>khk kBw w>n�tilde{n> kq {E_{k-Bjqkq-Bjp pFu5�{(q-k)>q np {�^{V?:kd {�.:ra�=a�:ev8 \Gamm>?8po {$\Pi^{1}$\,:>pt2Jwz omeg>UfwAbf Bzfp p>�fn B�f�p_1B7� 2Bk TB�fq B�fx xBNy yBl lBgma \g%:bA� thet>Cim {\R�~N�vA�vecF� vl {B�vaC4B�va)B�vx NB vA�4B� vecr 6r>� lra �b�mat!1��cal M>C�{{ LB ps {\mu:hmabar:g {-�6�ro tB:si {\sigBM(e {\epsilon:3vvarVo�(1/2 -�Z�� (k))^p {^N.N>�S��1]S>!��{:�h�0f?��B:A {\alph>�B�hF�$tbe { \log[�(C2}{\eK|)>4pAThs\�{1>�lcAZ�;:�rr .dC \lE� 2qprt {\� al:QD {}:sAHRAH-�_>ini1#:RT�:aa�NtOa�OJ�ds! mbox{Disc>>R�M{R>(ad {a^{\dag>bd {bVu!]upN�d downJ{\llb}E# eft[M �}} mH.6 {\lr=.z=]>fm!�1T>�mb�Z�EBB��HF�1'B !�B�gmn {g^�� \nu>=gmrroBn nu Jar�in��infty6k\�@-�ResB k^'��A>�b�U���{cBI e, #M):�tr�)Tr}>ueg�6it O�> bea{ �"$�>9e$�b"nmW��6�^}gin2v* {\e% euL:��}4em} {$e^+ e^-$>hmbxi�B=golbulle:�{\gev:GeV:=4\ata {&\times&!4voffset=0.5in .%�� Hy{Modif�nDihadܑFM-% F�/�Hot��ar,M&or{*�ffiliH{Dr"[8 of P�Fs, Duke2���E��,d?d�, d environ!X�feT�5ih��uevy\ceku.�a�,"x8!�jet!�ifq�i+�nsk3. % S�xM3E�s�6 a�a��u� @9kofR^ �thf�w".F[ \�${12.38.Mh,.10.Wx, j\�${LBNL-5670 mak�9le ^�A!&� has emergXa new  Knoitoo�s;�t5}F.�e �~� 8Gyulassy:2003mcTq�(�9goeA`yon!umere su2�O}��ra!~�YALIr�d ;0be ex�NfP�Acy��2wof�*�ic&�"]s'dsiAse�&�XtwoQ�}�B,�. !gcone.I]^2�+�G�� �in��-A dinezza04�2�SB� ��! 6SO2,=/ix2M��%V�� �m"�k1�WM� of�0�Cu��sus a �7�2���n�<lڎhan��*7����&:["n $p+p�|k�Jsharp!^�t)�� r�����EYH MH-.hermes1,!]pt}�eiN_ �&�g $A+A2�2� �0�$#ne�@��"]n!ޜ�u�@C�?SO8aj>�>�m um.�rA$"Y?ju)=q^o!iaa�{is a6Ω�#^� %�r��"�Z`�5u�2Q�"��2N �&���20�����m���) 2N*� i� @dX(�U�=lapping��riD�� d c#8��tM%td=These ^�/ non-�#urbS? n�Z{Q �SNcHoqFFeg_y be ;for x&�2 hard�&`Fj-d&��+*o�c�YUS�=��3<�1�+!}�.e`(QCD (pQCD) �amxnw},�ii�Ka��us��I�-�� Z5 (SFFZcol89}$EtA��},K;�pr;;�*�"q�ar93 �}� curr��be�� appl �:i$La~jet]�� �Tis Le�;�L�2�Uf��!I�tWJ�)8N Z s (D!in� {�WU  hot *� U����NJz�DFF�I�$ff�i$p��erive/4�2A g� �z1m)5�U:_ ��8Luo:1994np,guowy �%a8tx�.!>1m(6 �A�pai�o�;N_ . W�HexaϕE B �� �erm�?��$m ed S!I� �,EW1}e�-S - ��Z\1�� =k�N�%$a�  �  �&�#&Vata�19to� �DFF���rk�$oE"x of��8vor $h_1,h_2$,�. t]� forw�l"� $p_h^+ \^=v�^+ + p_2?: ( 6.��*$z3 z_1 + z_2�x�Xry ;�<m A<$q_{\perp}=p_{1 -p_{2 $ H�E�P.��FourihvW��!?�N�a,��9�4s $\psi_q (x),� psi}0) @}=���>';H$es $| p_1,!%,, S-2 \rc$ a�o bea D_q^{-}8}(z_1,z_2) &=& �,z^4}{4z_1z_2��t d^2q_\%{4"!`��"4 p"=`%���\ ��h�-1.0in}$ \keft( z�!�{%�}{p^+} �) {\rm� \Bigg"g^+}{2 2 �@d^4 x e^{i p \x xv{um_{S - ��:�tm�!lc 0 | !~!}x) JS '6i| B�| 0!� �], "�=fac�n��nrŚe� ���y)satis�ZHDokshitzer-Gribov-L]Glov-Altarelli-Parisi (DGLAP) ���%� ���H Ref.�N���-T+M�seH" A��&"IO��CHZt��g��ɉ��Us "�X  "�F%.n�TeenG�� numer`\ly2���$Q^2$&� agreesG8�8��* JETSET ODjetset} Monte Carl>�+ }M�a�!, h_1+h_2+ X$�Z � AltX������!�v�ppidlyv;㥗��,9# E,ce. +!�abs�ofF�,- 2��T�EZLa��J it+8"�.��gvacuum�6 ���y���� BKKA�Li��-�bin95-olly;� ),)� 9�)����Apply� q�I��2 !��)a-���9tm �p�\�,$e(L_1)+A(p)��I2)+h_1(p h_2(p�� +X$,�N wb��%)U8D&� �>�S,^q� } E_{L_2}�Vd\s� ��h_2}_�RDDIS}}{d^3L_2 dz_1d��i�] ^2}{f s K 1}{Q^4}L_�� bW�}{L��nd�!�6�m.� tens�;t"�� �/m v wAc{d��2}��\��q6fD x f^A_q(x,Q^2) H�=}(x,p,q>J�ɪ& R9D.�)"�yGove, $=)! = �!)%� Tr}('L_1�" _\mu /' L_2!nu\!$)�I� $�ث��-a��_aN�� *��a v�phowQ�a�s ar-6 8 $q=[-Q^2/2q^-,�#{0}.]nU.w��� �N1�*A ��z us |�a& yA[p^+,0>p� m�." 8s, $z_1=p_1^-/qrDnd $z_2=Z �.�%iZ�1ala$L��hen�߁Y�. wp next-to-l&���� L"� }�^i,|i^�.r�B7�=� ��k �, soft r����5�� |' xH�/G{�y@organizE� .�I�a�!wR)< a�y�" 0 �>4�y�2�I�-�.�6)��_ed��: $�)D}.8 "9 $ (i� d�W!'�B ��s���.�w%N g%N)I���� � �mREaI5!J ceedP maj04f}`v.Pa�Tj �6�J �O�� a % z*��VE) +?(int_0^{Q^2}r l� ��. ! \A_sɜ} �  %��&� in� M"[�_{z_1+��^1 Jdy}{y^2}�� $\{ \D P_{q[+@q g} (y,x_B,x_L,l���@%6R �&ɛz_1}{y},2  . .V�0.8in}+�..�g qn�g��`�� �\6K 5L�!�� ^{1-!E.C(1-y)%FD �-P}�Dn��~ )W.U@b!�6j-U) D)2}6%2}{1-y5� + (h_�na h� )�]\, .E @abel{eq-dihdr-mody{I�nt:�$x_B= �p^+� , L = U0/ )( $, $ �@:����med�.Y.�g}�hA'$'�2�"M .���B, $yr� whosP9KreTGnta Ua�l2c�5:4� swij0$2y�on�b*�� x- �aich.?<*L�ma.+��^69.xg� sponŋ��5"� ��B�gq}&e�+�=E]A9� C_A 7 �� T^A_{q�G�E )}{(-�En lc k�V<\rc) % N_c f_q^A3� },�*A��_2!uY�I �M��]E&#<dJ�I�ai.�f� kY.9!�i],, $C_A=N_c=31 F >�%�"9O�ih nsic� ] N�![�~� NL�DY'J�]���=}E -�f�~!!=E4$1��|3xpbf"�e cUtA�>(�ba Gauss�$M ar2� W;emaa��2 ( �E x_L)A��2C}(A$ m_N R_AY;) (1 -8-x_L^2/x_A^2}),�eq-tq5&6� \���$A=1/m_NR_A��m_N1� �on�9el${0= 1.12 A^{1/3!S)2�a�u�;0O�X5JAaj�i�g�9 ed; bWQ\�`�K���in�he��<�ant"� C}0 3 ����}m�F @�!��xm�1:jb���":{ ssexgd�=a�[.l lSFF"��$""�2�� Z�%ki�Q,=0.006$ GeV$� was U�d� F�%& ��A�x?&Hi~E���o[ i2�mSFF_` �~m�z$�<Ae��#$\nu=�dEu>e V A�$ �>�-B�� �~ . �noW�M<�#a�#  Eq.~(T2&)&�-v�.��  .�>=�!SE,���W��}d[ sum rul::�cA}m�� illuN(>A�IJ�(>�!,2i �'se� r0.5�G)&SN_{2h�2)\ � 0.5&� tR�)�/ #_ 610&S � ).�)� �u�-�z_2%1$)`�OR9�=N 1� /N^1x as#�o��J� �m�&%.B"�h"GY! -$��E!C�|Ii at�fre��s:�#� 6�&���$l�mA/$ I� atom�\mber,� n�:�>�&�e� ���9�V)$}6��U\�!�i���A>*�"M*�2 �� 1or 2��$�%'�borne[+� yE��'mM�Pkt-��eP%I ���#����� ~_fy���Kn?�n � s du��CF( "��Wm^�Jb_)D.)an�#K Fn� ��)6!�/%  g."/G*Z� ��\d���vY&�X�  ;�"TT(incorpX��'*|4Q��h@>�4"W2W?}[htbp]�B �62.4in}sB grap�?@[1.25in,0.75in][6,6]{��,_med_2.eps}}1"Ý (Color6 ine)&9�M]e�eId�M3��M56� [�* $,U�2�Ž)]��wi Uuse&�%��� �rE5�i��"�\Vj )�"N�� �Kr)�s.-8Tű7-��e�e~eI'[BQ+�||*e�$p+A$)�Af+,(�- �K"���#ack pair@_&0��two�1$p_T$M,~ (azimuthal axv(%l˨�"wo"x peak�>�+R2�I&���, vL�0 ����6�(�5jet�h# �#� � . B��,*+1�o 5 �(>�%��+ev�C �W 3!� �aE%EP!�gVdsub u2%int�Nove�:���fq�&,note},�c)�za& �6o���ti"� ��to ?SFF, !d��!'U'g Y�B �"�3o22] �:�W�Og]p�(01�IA�t�_�(�r ssum#ї�AC�����$�s (as d�m1 �'U� 0�-� . EW1,xn!�03}),Z gL�l��-�H ;�!�i���ab .�&}�at midr�!ity��"}/= >��$�?BR_ak*acVhp  $b��[3 $b_{min},ax}$ > �sn7�T���{dx�@^{AB}}{dy d {p_T^{a(}}2E�}} } % �o ;:_{v in}}�D mbx^ax}}}\�.d^2 bG� r t_A(#r}+ b}/2) t_B &�; *!& c 2K�  d x_a,b G^A_a(x_a=B_b(x_b "3\�:S)5 d� \sg}_{ab  cd} }{t}�lde c^hCP'`, � AA_s|!"�>D , $:�[G2�]B�E2arq�6<"��a$$a (b)��J�$x%'#D&5 $A(B� $t_A � t_B$Mw2Q �thick�a�E�^H/9G2�e+"�oni��pu$Mandelstam� ia� $qt���� )R��(|e�a�J%o�ia�82�  & D���l� �!Ka�m�$�^��/��Ser ortK���r s (:=at����[ �sspra�k�2� Q m0ex!�s��iZ \eq[X2��+"� "�Us�\R0���� ���e{i�#�  (y) *cq �kT^{M}�Kb}"r,�a�y,uw1�P[i��>\L�4"nB'.&� ��+����;�.����) �)' �}R�$ \hat�� �<] ^{-1} + v.c.��TM����A%�!�Q8DIS, &�r6�N��  "�i�%�e^lac5Q�T ^�ViGM`:)�B���n��T P &plasmai�����ce2denom��or� Eqs.Z��TM}Ͳ�:!U�y� �5�c��a ��2*e, �*�+�O-96we&��.�3"$T^M$!B* )��$a�enXr�tist�u8Go퇹#�6��a�� &j .}(>8$GeV��!/Q�$p$+$p$&, a T!g� �2g*�<.{�"V$d$+$Au:/ "� �{ v?�c�o� a&AZ� �� �seq� ce�s*P &fl�0�st�A�&� AA_2�1 � "an%s-\% R� wo�ges��6GeV$<\!"� @.� <\!  .J 45 < Z7 6%�,2~-�M !.Y } > E,!a"�in.�AdamsE�yt'!]M����k]�eu�t.n ��e~e��"� � TM�|�danrnes. Q�J�� s � �A- dot- M 1��"�XNJp�fJyE�${ ��Eo&,�T�,.�.�% z�{>D�/). Un��A6h�'&��*n�(k�÷o�?ay2�&�<il\�mU t�82�:��n�A��U��=��X�A�"�j��{�b�a�l� .de� BA@�l�gF2�. A� �.�|2!*� I>A(�8 omew� ��w1�JX �6U"{"m�HA@ ��*v(w{4�&� ) e鉶�R�8d��EDb�U! � �)A�:3XM��y�z�L re c!�{#Ӵ!� �z [$\�OD�C )$] � con�* ted,B<�@�a����!BnE|� u�5�)��?62�" h6:]$z_T=:3/].��j�):��a >��&=&��l57mes D]$) [1 + 1.4/z_0P1 )] �.S nt U��a� Dwe V02g�&a�.:����e$All�ssE/+ildt >�?+��2ol�?eg� rD�i*�D�!Kf 5�O>*���a�onI�]�.�F�ŎE�m�a ens��� vali�� f��C. Okwise, �>�=� ."�e�asI�oz�nBfmy �&Ӯ�  d�=it%�al�ur6c$�"�_�afr��^z��J�2��AsKb�da�%�B��9a�!G)�q1"m� s"*> d�K!� w&�� �e�MSaY@<&>k��4�4�  � [Oize��_MD,0.4in][4.2in,4.1i�t_to_0_%h��_%�_a�.�^� Y�ua�/ t"�  �Mͨ 6^$ $� & %;$%:� see ���dej�s. } �� 6 ��>�4�4z�sum@� � @$�a�N:� �F�HhoB'�Ied!=��d} A��2�on>71Z�  .�,�5LsB6L� s����tYqI�2����H!�y� ?� B(G"�!\7of"A� eJ�F"�?.�-aBa�K{@no�@ra!(0��ur *~ Ŗa !#�#��%6�1!e2�re�!�9 %at:�9}, 20=.u5206011f!Y(�(dE�:�-D6�"N[�4�Eu�%a�M�� _��a�01400I�4=�A�$ph/0402245>�A�PH � %``EPvp��a{ 8�v�sB���03�5���P11174; U.~P.~SukhatmY@nd K.~E.~Lassila,) \% \ D.��2g$1184 (1980!�.�� j%�w+ c�O J.~C.~�in�]wSlQ%� G.~SN:an� F}I�� Of H|LPzI In�P!%i+ P* �� Chro"?us} edi� �g H. Muel�(World^t (c 1989), Ad Se��Dd�.\ High� M6)(55 %$8!$ 5�09313],6 5=!=%!�re�&c�rein. %�+*�By. M.~Lu�c QiuBg �>Anomal��a� �� h e��&ڑ*�B�N %p�D&p !� 12M5aM195%"94)F7 HRVA,D50,&;}��C}a�F.~Guo~P ,� j�6SC,qd.A !ayB�\%�%3 /l��e�<ic{=�M ��,I8A359B 0a�:005044^; A���X.-e-Mul^�a�# i: ]`68\� Nucl&�)h bf 6� 788��>���1��^� �J.~OsW2!sǪ�Twist-fQS�� $matrix elE��: off-�P�X.�''V�71A�28)�.�q�204046^� �*���B^���� y am��u��j�x�<�,b�� 2� >� !�301195>}�� Й^ E*�:��tomjs��_!�-�)�j4<6E~V�210b�2�% ՆEWAD j�F D �D��%6�q���ibid.},"�8- 14" 1�!�10604B2  � �9��NAqAnders{�.I , %�WGustafs'/G.~Ingel#�!�T.~Sjoo:nde�-F.�a And Str�U�!5�p���9�3��83��.%$PRPLC,97,3� F} YTHIA 5.7�J�O 7.4:%nA�manual�em�9508391:dM� %C9D�N��Binnew�(B.~A.~Knieh�G.~Kram8%``���O�f*}Ne+ e-e �\h2 �8e2]J %B*�5Hhv 5o 4947K9S699503464Z�  ��YHA.b@ ICB��t#�9G)1} F� AhV� %``M&�"�J�wc� at RHIC!L- GIN3�� S129��4)FE 404010]6Q e9I %� �1 ��&�^*� �h�ܫJMed vgo2� ���Eco'�(���i� im& velo���t"�al�� a� :�2.� �A$ )$:�^..�%wu�{ *�Vc�") Qp. �#���I�v�ve.vM. �3s�� 7c1FgzV��c&���.�h���extYe��)�.�s}t���.��"c�UG"�2*� �C .��"a,2w4ɧ ropy�0back-to-back �%correlations in high-energy heavy-ion collis$�[,'' Phys.\ Lett.\ B {\bf 595}, 165 (2004). %[arXiv:nucl-th/0305010]. %%CITATION = NUCL-TH 03�;%% \bibitem{Majumder:2006we} A.~�U, % ``Resolving the plasma profile via differential single inclusive %suppression�Rev.\ C �7�021901 �7).�:�608043.V%N� �,%\cite{Adams�yt}�6 J.~0 {\it et al.}50Direct observ%� of dijet%�,central Au +9�< at s(NN)**(1/2)� = 200-GeV! -�)-�)97%�23-6)=$ex/0604018VEX %5��recom} R.~C.~Hwa and C.~B.~Yang, %``Scaling behavior atE� p(T)1E/pi r!�2�-�6�034902%� 3); B�211A�;Z� �$R.~J.~Frie:�4 % B.~Muller,�Nonak �$S.~A.~Bass�Hadroniz�ne�a� 6�: R!&bin '!#fragment ( of %parton.�N�$0}, 202303f301087b ! V.~G!��M.~Ko�P.~Levai�P�, coalescence$,antiproton/p�anomalyA� RHICB�6��1�R�1093].Z��9i�.�2}q�Hwaa�4sw} % $. f� %``Dih%� ��!�e�produced%�-! y�! 6�M�7!05U�4A� [}�(th/0407081]a�]�,]�%�Y� �C�0ed emiss�of �s from !�Y�of� ed ]�:�6�4�W2�W5!�V�102�Vm40!A�P\end{thebibliography}�p docua9} zT%� 7� template.tex for PTPTeX.cls 1 7� \��class[seceq]{ptptex} \usepackage{g� icx}2wrapf�{@ Personal Macros 6\ \topmargin=0cm \oddside  1cm \even68 \textheight=23%width=14Hlessgtr6>>;tr 2><  half�{.471�H} \newcommand{\ome},ga_{\rm rot}:$sumA}{_{i=1}^A:!,NZ}{$N$=$Z$~:8Se}{${}^{68}$Se:G 4}$G>Kr <72}$Kr:<S 6}$S>0boldr}{\mbox{math$r$>�)jF)jR)rhoF+ \rhoF.8ra}[1]{\left\la� #1 \rA-|:�ket.|(\r9:.,Hhat}{\hat{H>�Mq_M(q):?h?h>?>h}V<_hR_F_F>_d � F}^\dagge>�%p% {(+)NHm.#-B#$Hc}{{\cal B$N�N>ZGG>QQ>RR>PP>T\Theta>!Pca�vercircF@Q2B�N2B�Th2 V�Fp}{FV�m F~Rp}{RR4Rm F4AbB\ $ABZBN'BB'DN'DB'NN'NB'QN'QB'PN'PB'phia�phi(t>� phix� #1J qppn}{ 0q,p,\varphi,NR+.*B"qEn>= qpN} B6phi�$�B]TsqwT>�del�artial:�eps}{ ilon:ben begin{equ >\beqa}{%narray>%eI ^Ge G #VEYb͕1�� Yb\ �pvect#1>r $#1A6o��G G t %kobayasi added %%HAMILTONIAN6'HSik}1�_{k}c^{�� :�HP9`frac{G_{\tau}}{2} \Big( A  A+  6>�HQQc \chi _Hsum_{K=-2}^{2}D_{2KF :� PAIRG8k \in �:�{\bar k}L:F BPARTi} {:7l}+c_< �l>EHS�k}{�j~jb�iHQQ��EBF02�'EV)�^{'>(!�5*9�d]�d_~�NUMD!�d1�G:�A!�} {-�clU+d-�lk>FE%FFl8k]EqA$$%%INDECIES6�nmu��ar {\mu>mnkB�nn9nF9��V }LOSCILLATOR FREQUENCY6� oscfs h6\omegaKexpec�value� �1. � 7$matrix ele� 4,matel#1#2#3{7|#2|#3"+ %defini��operator B(aop#1{a_{#1!*defdag-׭�c0c.0co 0 60b02`b0 0%�s6Hcjdag}_jm/2� cj :�ckBai}�BZa Za_bZaZ�ARA:�aib�.#5`21At):P:OAt}":QM@ Q_{MZbQM} ::Fsp}{�  F}_{s}R FsmB&F" RLRfLRL&L%2Qqr{Q� >� Q �.9P?P>:p�L ��B�NN!�B<�!=B�N ?B clE���2�cl%� c_{lZ�ck]�F"lF^kI���b�l6(^�amn�5 \mu ��V�am� 16-:\ammNVmubVg6VJe|N_ |^Rb2�B�/}-,:�x2TXT�(i)GF3XB0}��(coefficient6GGt}&� 6ui}{uJ�vi}{vJuA�1B�v3Buv d>�uuv� -$ :� fq}{f_{Q,���2+fp P +!6 r Rb p !Pf"nBB�fq { Q,s'�+N� "P "N� "Rf"n "Fp <��F_k�kappa��:Z Uil}{U_{iB!Uik BYV4VN4V4B4FA� F��Q0(\alpha \beta>$ FA�.-)v.R\R�\R\.~\NAs}{N>�6��ni}�A,\sigma ��.��J*E56T�*R_~T�J*JTNAs)NS} %Elim� e A-�6;�e}F`�"z2��"FD�"FD�Q:SaaA,q>�>0m!_{ 0~�0+��`0~`NE�Bb:!�EF9��NeR,%UFg,]h^X!�R,JX�:l�B� }5�FA]J$n2�%�n5uFH.�5�}6H�>d$SQQ}{S_{s ;Q,B� SQPR6#PBWSQN #}^{Q,B�SPR6EPRNFPR2�PRJ�PRkPRJlNk }^{NNhNg!F�Nc� Bv�g:�RVvC qpet)�mu,":�!��%J /)�t �v`!�?5��;!�=R�^I%state6�phizerAra o }_{0�7$rbra#1{(#1�ke�|� �����pubinfo{Vol.~10X, No.~X, Mmmmm YYYY}%Editor�&O� e will fpin this. %\setcounter{page}{}B& %�K�ptype{pJE �KpsubjectN���age%1X-XN���-��4ofigureboxrule):%to e" �&+ of \=K!tsetlogo:C%� ent!�if 2Y�" �p When [preprint] you can put 8 number at top ��#nerAS' &H[3cm]{%<-- [..]: opmal �!�1 #�$Dumn. %KUNS-1325\\P5# 0#<\\ August, 1997} ��, \markboth{�# %runnU* head�# odd-AOP (authors' name) M. K!T, T. Nakatsukasa, M. M'K yanagi } mFuL# v�`short' title) Collective Paths Connect�A2Ob�$ (Pro Shapes} \C{�C in $�"c$^}" Sugges�%by�TAdiabatic Self-ConsistA��Coord Method  )j�{Masato KOBAYASI,$^1$~~ Takashi NAKATSUKASA,$^2 3yuki MPO$^3$ \\ and~ Kenich YANAGISr0inst{ {\smallk+ De� eHof|'Lics, Graduate SchoolS ce,}\\.FPKyoto University, Kit�rakawa, !8606-8502, Japan:E4$^2$ Instituten�*ic�'Ce��E�CompuKal� �=Tsukuba>�  305-8571^�3$jE$Technology>dNiigata2950-218xA $%\recdate{��DD,��q;�� \ab!�By means! a0aU�sA�cY�{)mjcY�mI�a`?Ppairing-plus-quadrupoi.terac��H, we have obtained :jopath c6�oy�pm� lo�#minima��^��(sp8 % schemeEn� ��9�g!� u!� an�-���erm5��mo�8um. It does not-� aJ�u� �rW e it� believe< be suit�!� )�"� nm � !J1�inheritp $ major achq�!� the 9��G (A�?,! add(, en�s � o/=deR� :ly. I��u�,��pu  fl� } mo%�re autom.$ $ decoupled_8Azp� al 4�in!�el. frameworkU�BC ory.Iub!�@great advantage wom3��[ realis�V ,problems. To[ in�( feasibilit�\T=�,Ref.~E�n{kob03}e�qin E�actlye!�%l2�,multi-$O(4)$ X�:T2,miz81,suz88,fuk91}, *�  sitfied �o�%�͕->�(P+Q)g �.vbar65. 68,bes69�'sh��� �1hy� �<$faithful : tunne�=Oh through a barrier between  a�8.�A�!�}��z)6)�. Q� pape� � port� � R%�cI�of%7=���oP+Q i& C o-0m�i�task �(Awtos  a�proced�for��.��� ��:C. ath.� &� e,L>ME -mj@ &�fL)�.� ,pfi�g �.�:�sJ� >�:0 �E8QD29a�!�.lr�o/bes��A2�ledge!2is%�heMI, e , st 4ng�.� AL$Hamiltonia��E.�v- & :4ly&�����sit��s, althmisimilarA�roachA�y stud�憣  wa�ly /=oyeF Almehed%~WaletIalm�b}E 8pa�!>organiz9�llows: a�\S2!en J� .��recapit�ed. C3�� pres�aA2cr� *�N�!P!" he>�[\S4� $ algorithm!T�A B��A&�!dussed S52�2�numeri�Fc*=�J��,j��� . Co"� ~rk  give�\S6. A!U�ry.w���I+�pAjourna��4��"nBasz�}���%.summarizRxQ %#=yI�m"� 1� pS6a�6a/i� atBu .< ��s�be& bi# a se�J�).3FB �  �,ors $5=� 9 $ pa te�en��� �5*� $q$�  $p$ajugto.leAi1$N$e�A^gau�u$�9>HN$� eni� ���be writtIIVfe�)orm: "�8��} ! �!! }=e^{-i � �<#n} R#e^{ip�00|!](q)Y3.iB} Mak�� x w�res�3%8p)r�H��Ij:��b,al principle!ful�!i upU!secondt�jp$>��99MT�s to "�II)@}$)�infB4�A al g�C4$> (q)$��d � canzal]2 $\�=) : \vspace3s� eskipLnoi, \underline{A����mov!i� }R delta\bra �@ 9�\} = 0, \label{eqcsmf}>��Bd Q=t@-\lambdaAhat{N}-�$e al V}{ q}%F2>p�!�z�9e.�N�. �NL@H1Y��Z[- , Q  ] - {1\ i} B(q) 1�}�R�hq}>>� B� �xr ] -C!�QhaA� -{1 �2�}[>(� - =�A)_{A}]� ] -{�( Pq}3J�.jhpB�Zj� = -]� �,�] ]�B�:[� rsLss,Ff!5 = � ^2 V2�^2} +5n)I+ B)\- 6=B�Azv stiffness�O $>�%[%�$ deno�two�siep��cre�>�� annihi:#��($:�_ $). ,Z�s, ��^�� , satisfy��C�3��U���J� . Q,U�] = i�$��cvcqp� �?�0 O<>�. �!�^> �2dL �y v�:%^Q�`wf ta�h�"�*� $ $\Hc(q,pEt�=2�=p^2 + V�> �Q:I"�  $% = =!%�=$�- Eabove� , no[ tin�� mad�vh$dM!� neu;� r( plic�n�� h�*� s.� elow&�>"s��U ly tA� ^Q }Nv pr�Z$.*� A�"�K*� Mm�l}7Ksub7 {?.�tsignaj quantum } Let\� �well-n>Pe FP, F�� HA�\HS���@�,iAA. m��hp0B��d�B :; &=& { _*[?}'c_k^"�A\tildeK< , ~~~K�N�:B8c_k, \no: \\ D�A � ?�=n,p} kl&�? 1^{(')}(kl) ��7 c_l�a � Here, $N8= c/�a�8�BW k}r^2 Y�e]l}$;~ $�B�C$�@$ ��%�]E5*=%forceengths,x4 ively; $�)h [ c_k$���on2� 2��>�(A~ le�4�,w $k$%le $�:>�{=�$͈ thos��  r�sed `ofc� �$ ex $!�$ a�e��`( =p$)%*m�s n��A�we�.�ex�2 m�on��^it�uldC keepP ma�>� x�s#ln%�m%n� ב� ${;M\S�6'�%y!�9�, $q.� $�1%�um X  Ms $(k, =�)�ၩfacto� 8_n=(2Z/A+1/31� p=(2N, attac�t�]�6�A$s guarante�J ival9 root-m� squn adiiA뭣�G5�. F"�BPger%� Kuma"�8�e takAGto ac�/ Wshell%a�� r U 9$ply a redu��),D $\zeta=(N_L+3/2)/ 5/2)$b el�s NC$A�!�upper �-oscillE �$, $N_L$ be� 1total (�["; lowe <. AccV,g� convi>*v'Q��*�fwwe ignora�,e exchange (.") V. Namely��� Y"2T"B"U)a� �out�p�. �tK( }q_.� ��� "RA \pm)Ŷ �1}{2}(.%\pm.m�):6#W \{�%n�jm, A_{p�Q�F 5,1: �H  \}~(s=1-5)< � �k)!�.�b &�:  F �H%9 )�s�Q5)3*�<��: +)oO9s+)�5+핦J-BJ -)},�hp&1 �+$ �$s=\{ 2G_n,p, �v, 2 \}$! $%]$. Our6=~ n� *�a��&$ $\pi$ abI� e $x$ axi^$symmetryi�" %2�& it i�l�"@ , $r� \pi\��� kplo"he0o, �i��@� use" "� GLs .B �H &\�v& I#1+Iqrt{2}}(�J + 2:) ~~r=-i~( � =1/2>h"6Ik}�f&� -nkf+f- g� sig�"s"� QMaU�Ur H�%t� �s, $�� �.�K9f$:1�%� tt�V� ��2��U:F3r=\pm 1$% E!=0,1$):F� \�F��6���+)} ��a}�� +)}\aց� ~ (r=+1),Y.� h2?L?-? = @ -1).:� No��at �D�6-)}= 0-WHB"�/c�Yspo.��5�A�l(p"8s possess posia 9ne~+1 Q�0M T�for�e 5�,1��I-�PR;$,*ing&�(Na:�*�( � also���:��"o�* word� nega6� degre�freedom�(er!J�"1%�6!��of Kes�0 at� �&<m. Also,� �0adix+onfirm�&7�� $K=1)mponent� 6=� *� 1�1� D}_{I� -)}$B� �[0$ $K=0)�2 s& p�Kl/� AMSs, (2.2� (2. bA����y� J�.D�Y�#!O��eB{E &�(3 2�� side�(z�m��P�. { ]*�%��daAible, +au`/- stra�Xforward*<(,M3�i!x2u�$)�&,of re�,ce.2�4�'dt~[o�0�$b�-F E4e%geffectY*�Aw�."D*>�F� . I�&cer��/ ver&/iu1��5 howo�(er�,�'t*�(b� � �+fu�of angu� �, but!�g�'bey%��3i( dps  WeR�sp)at�]�-to%�9��� ma4yr� b�Thus, o!;�y�,���qŰ��3!]�@!|_)Oc�07/.�-����y all?��F4ztor, a�- ��adopt�$h-� a�{ ?0:n >VIm�C�"���"� o }aUa�� : case�&�Qu*!-random- ���6� (QRPA) �<�6}} ��"�!a�&�1oP,Jl*K!m42%�E//>),��ff0,�'!�F�0B��. ��:�.ne�5%��itaW�Jke_0}� Q��� ten&{ �!�{,7C H} -l �}jRau}e N} {2�=0" HFB"� tA $6R"~Z,#".�/[p$) Jr�+q.D�t, $�&QN$a9:�A6sui &� @� _0 � =0$. S�%&�hol�>Aui�� neG7U$ ��Q��y)�*�trans��*� 1�\�_( �Kgin{a�Z{cR 6� nmu} � 1 \�@ ) = E:kX >[ \U�N k}&V �U\\gnmu!+ " !N �- � �.% c�VnkV�, 1(��.) "/wo��1Qp} �P�m:�Q B:�A �Fh ,~~~NE2>08mu.6�A�RPA n�;�"`'$: =eB{?a%�(� (q)G�pdag1+ � & #nu})�6U?mu'�Z�( ˖� ��5+&! n~����1]E�9t��A �!�E F� �&� y\F� *>��� g&H ��\cos(\�i�  ^{T}��< & \displaystyle l- % \sin2B< !}�\> :^�H(f�S]��)�{.\}}��2#WL}})-s N65�1��  *:$c  r.h.s.M� � �$of�#�G��ETa�D/�Q� stoo�Ba�s�csN�� -l �sh�#z �8"� h]*2+Esn�A)2�"f�9~� $�.h}b����� �� ndPx"Q"-� � @J�=x6!�%� 1�"C�N�/�� ��q :� +��mu}KU (q) ��( 7 {B}� ����+6� :��F��5#R�R��`o[ )d�l mdag�/+ a�� Big)6�(&+&�@GB�UI�� ��6��>}6"N� LF�]}��`�Rg���o F_{B,I\.Zu�%�B�i�V� 8),"%0 "�zX o No�>r���� Zw:F5 @I�8BE�#V� < �"�X* aEm = n nd�� �l�F<B�iW!�=b�$, )S����} s"^.��> E�)�)res�g�>�is��ҽ��1Y' apHH���⥙���/"n9ApYG ix A:�3F�V.� }&V re��(�^0� a�. P!��}$am�p% �- as&8 Q�j �7� ��e�}24mÁ� b+ \mb�S�S�gPvFR� �� ^� 2�.f]�^j�"lhq}�p+%��*X7G JF�427sep�5>m7[QM66 "f^{� me �m_s!&Q656] ��M;6u �8S eQ7.��K^�&,&{p5] (q)] z2� +)}_ke ��� -�65`s�=R,.=.5 2�e 4-qQ4Tw_s)@ ,.�f_{N,,2S��#5=0�h qc� e�g+�I $2�$ etc.i�lbJ''��&�|&!D"fs �\b" [Q,"N8].��=2{|f[ FAs�d,�$ 2 �+!=�g�E�B} p_s,Y�6 =DE $ �$b,�WB�%�9 � �+�&= 5�Q&QSB�7ks"RA )  .�6,�7a( J�� �$cB25!ɊAYb�����\),^ quiv [ %�6K , (�@9 2�6��~*)�9!D [et� �" }Re7& _ �) \mp2 Bci&$�.��$�Ls��$v� �J%�$�"!B���parenB'`�Rlso+��NI.�G(F%,)�s"� 5T '!Q)Q%r �,�42etc&�g*� 2f,6�-#e�aIf>ar �#��� $ or�. One��Il�Vr�T!&ex�6� :� , pEe�$ �&[� $, r'b�1�.�, ��k.�p})N�)�� �6)�s} g_15�{\F�70){ m  {s}g_2!>)\big\{ 7��7pr�6.�.{����2,q})�.�h��w�g\Y\ qi} "�)`2�.������� J2fNV%OJ#�K� {pi}�6�$f_}g� +)}=+f_e.^{v"&$ q� g_{1=�� f,�,"2R"two\<HP}� �2$,��� ah5�% fCency 6 (q)=���V }"J46� �:,37ne"Sara��&�*�<S�XZ#$2 �K� cale�G*E:-E�&l�%�� >P. 4.P=�wbe�%$sen arbitr ��<i a�)1*N$�KthuYIquire �6,E&yɨou7�%J toque��� �N��/sC(g2 (3.34��3.35)D�z�� D I�%�P=S6�FA.R2�6�6) 2}}-��2��P"|2�>�2� .�>02} �:@�U���6� C},��)=J� +2"s-)�" 51V����EF*iuRBAա���RC �'}�B� ith � �l�-)�� � \m" "�-,v )�g D �.$, � f�E��&dis�")_ � �-��6�\s�A'D=8�T '}(2 )��>�ry"� f6��e$; �_� ��a�� l=1-8}\�� ��A��,~{�V2NH�U%\{�Q�`ٮ�_2���ő2d \&�,�e�8AB@ ZH @+!�*�* �m&r $\det Sg012�)�59�fixT=lO>R� D�� �y�Jq�Q9"� `^2.�%)cuR�hYM�.8 o�j��\M�2=�h\S1ial^26�O^2*�!�b�choice�*r� �U?5� .�Ib��E= iw`�C$5 F"-$*�fA&T Jtor�  like..i�)�( done�3 any t8kh6[�i>�(7. of s�o�8?. B/Kw�ll��� ``.d�-"�brevity6)>{P"}[�&BW�R*Z6A.�WfUG.=�Y�V�[ $!y:(ak.�qF�= %��+a%��=\!!"��v ��"V$"vn�0Q($,��XIi6- F�,A,.�B{ )V<��6�p�%Si�N�d�s�F�NvaG�^a U1(res�]�d�9i�^E�p1�_carry ��9�]t* 5f"�G"�Y."�L*�8%�.�+[7q1 � �$KM�` 8K ific�gA�$q�5W�nY{:��+ "�V�� A�f1" V@6;,"rneighbo� p�i , $q*}V&z69qstepsa�"2V<~{\it Step 1}:~~|tt�n�X} !#�~y�*CD�'�VJ^;^{(0){0�X� q�8)}�7��+"�N,F%T�]b� s$"�2J,F�}���0i�,^6��!e 6Oh6 i^�X uess!c.� .\\ .�2!�Sol�\2��U �6�� �(Y3)=��i>�C �SUi��A�-Y5m�f"�M�Grv 1)}$�Qd o!+���it �r�= �7Sns:@ntJY�?[��|�^z�OEB qE�!cj2bxi�^+� lta q", ݧ*��S togeA�6�N�Jf�*�b�� }, \ *� =p,na�1�5� A��*!��*nKVN,N_p=Z,~N_n=Nq�1)B aintM� 2! 2Nd;6&� Eq.~��%���90j�Ui�U ). Detailh Ac� � scr6^in&&B.� �3j}6�6,~{J$^�^{eCmd& Q .��6 PJ >P4�Go���2}e��e Eq.-G�N5z�ե�&N� . I'UJ'xP�v s 2-Π�@rgy8*Am�cA/Yvt "�?��2�qy�) bf�/at��Ats6���P A�A�I�p�4si Pa��Ct6�aT g:r1}!���x �F2�2��d��$ u� next*1A3ndO�i!W )hc$g%Bis wa�O� ��epa�<*�x��� .�YVaWa brie�p,b�dvJKc*� ;d�WnNrcs� WA��g�r& v6�?a%� �A:�Pst*�e��5n��"�5Vf� �Ia� !j!�� U�_� inQ6[�#� Yc!ha�x�:[*� �9�i�b%x%�� � a̩"�fFp�la�=*�+'1 ncerP*X�H2�aoa�I�:�in2YnRtu�l�� meet�Gs�32�r�s���>�aY�F�Gg' �>��edtD�D �i�K��A$\S$\S~5.3.�+� check�AEi^HBsjɷE�� E�AuYK*z�Bnd iyev�HA~q ea� *$ݺ6II�R8%c���spoZb:chi to &�F��-�Fogap� d u*|Fs��)!�Skyrme-�c=�:Yamagamii>ʬ �yam&tTh�D�! are:�A0�N)Q +)}}_:��/(\*��_0 b^2)�sin:��8 ]chv����Z��1�M���_0�$�N�wg%�)"�*iY"�.���� %�g5mm�b',�X@M��%{\foot��k�� I.~~Ecap�{ SboY%��XG�hg�"us����� &r0��o�]' 1g_{9/2����2[. �#a��:1�A�Itab�N}{c } \h$$  � & $1f_{7o&$2p_{3 5 )1&�& $2d_ )PgP3s_3 ' ]\\�saA & -8.77 #-4.23 & -2.41� -1.50# 0. 6.55 # 5.9 10.1 & 9.83#�xw 9.02T -4.9w66 T-2.21#.w 5.27 # 6.36# 8.34 & 8.80w�)1� Q�le}�ʍ��"�nR鄥�]�:kPr��.6Q" {��*� al�����f�D*� [  4,�B�,w� HB^I*�<Kl��sP,{v�R�Ye> � .FWSe�U h�V C��dZ� (see�)~*� 25g�y !$E�( 0.30% 0.82 Zf�*� 0ly��%�=�1�s!/� �E�&x�&gq&� % s� low-��i�H�trrX� �$�G6 .�Ji!�Fed[i `axd �[. "[bV1V0fac�n�Ss"'"(K� �V��y��+ beca� �D�h :`/"�=A�6`&)Yv&%�enhancs(A"��}5Vde eB}�M�%�!} 1 M�%�u4VA���; Ft:2}.)jQ��� "Rn ���&��ce�x ^z \�&�բ exci~3I���L1y�  Y- s:� 3S;U��H]|AM.V 5;%��G;a� �:�.�one%�e�`-u��.��"p�op�-cB�)�, n�aa1�D;2��-Q '.�S"se!��:��uc7s"PJ ��u lea�'^  Q&W��*�{.,�O6&;�ew̐�ų� � B�  �.l�\q��*t*� �]� + )�)^Bq�H &*H }$�|2� 4E�ei�- �a82= {#L=1,� :A�z!� releK~.�f��0d�>|M b }|^2�|#rho|D_����|0 |^2$ ($!� hS*^rho &�6 ��one-phon��gr���sid&�&�6!|�=$()~ a�$(-qn M��׎�69&�g��m�-�q�^-]� -1�u���;62T$X:�\,~�2�0 5�5ent!��K�!oj�v WeisskopfI=. � "�A� P"� :� >� &�� )C I�n$� $ p$&^2_1 |M_1EI 22 &� ��~(�D)� c 0.2   $0^{\N�}$"1% �)1.4"� 1.02(�P & 33� -91(-�)J12.19 W\\.���Il 0.28� � $6:�& 1.1� 1� X0 1.55>� 13.6MZ 2.2"A��L7.6�  ��-63@ 0.37&C V21� 1.2 ��60= �2.9{Z 1.672�& 14.6� 6�B535�oR50.8- !�t ,1.125.3�%�Q�!�&A==��7�"! e R< 10�" z:�p*i�N#):�m� :& }�[�yQ�Brt!2st"� y\mos* �r. �e}��V�we���� �F����v��"R%t *�q0$nd�$���$�A6� \S\S~4.1atq6� S2�a�o2�&�W\SeK7ch!S plot} Fig.~1(a)s �ext9(Z��zTDHB �] spac"$]J�h�|dBd�z� draw!ma��*MK regardedp!����� >� o�m!��, \�8 plane. Roughly�D| �>Hg�`�&��v>iPaqFistzkU�d1�ion1.�� b ��L�,!�t}t��* "�7yJU�` �%�&�&�&Ivar�|1W"�� y w�Lm~�؇er!s  'l�`J�"�7-� B],e $Pv$f� e�a�u�%|}n!=s�inQ� b). �(q�5��+FJ=k$q$ˋ;+6=�mas�e� by $�=�:0^{-1}=1$~MeV$ �'N@�p2Xc%geometr�$s�Ibgm�$(EK,I��@A�V&���.ND\- M(s(q))=�[ds}{dq;�-�z���}�'$ds^2=dv^2+ d �^2�Sis�  �y!�" ��{c)F L)E2R[�pu�y���� BW!�Yd). VQ���� � � �{�2l!á�M3� Տ� 2h' 15(�b�"� �s.~1(ݒnd 1(f).0solidm7 )(f)j*�~Ny" "�/h>qI��=, U�A�0��*.�|/� E��X"N| $ P1 so�%d1j�a��q"��f-"� � J��tW sv.�"u1 �Ro�s"e+ ��!�(b�.:J"Mh sak�qe?MM�6�an�"�$17r%@�ks�!� 9$ha��0� i��Dto%���呍G*�0�.&�1oY[M�F�0�o�� imag�"1�r�!, $12  <�� < 45�E!�m�soS�wal �1�ngfg ����2�g*)f*~�. %����#1i.0���vic�"�$- =60^� $ (�� 1(c)) m�j *as�sta6̎M� �-�.2. �(`*-�-�s�N�q��� /las}-�] Schr\"odiw��,�h�� �*�p�in kob05oi .�"�+ *�1contras�+"x�B! �|� �}&&c {� ��*�"�ŋ��*## �!��h�whA ��p:� b�O$� . of� A�U=�a�]T"χ:�� -�"� [e�4��1eVA go��.?%Y��% en)y%  �T&&F A2|j��W�i{y, 7y.x��s eachI%. 2 D�M��A�E:IF� u��^2=BC$B nges"�%#a"՘al �N�fyn�R�me� `&2\%�+o�l�@(_1ŋ"^+b�$Y�evE�p�& s alwaysQ�5 � iE�c0- t2�'��.,1Q"�36�$�$�e�A e6�A>�-V�"�nbruptl*�aQ�>�us immed�y+�g �ros\ )$ (m;.�� C'A���~3���' elowTye�/&o'9out�  9��ls)�� !�: Dur�J-!z.�2F*�1w!q�.��"�$overlap $(�9�9&-)6|tw"��2�* g�1!��T$��B4` qF 2�,, vanish�-.�&�$K$=$0$ �Xl8p�|s ~ �x��9�(d�)� P �#&+2�/)%(op� �r just �1�F`erX -G�0B FL)N �?!S5*͚o(#[r� occurs��v�w@z��2m-�#9<S2]73,"�+��I, avoi�Dis6icultyQ(Z}Av�~re&b��ۅ!�N&�Iwe]P�in���1�PA��2 �  ,��� �_2���I>�9^ 6.� =(1-��epsilon6T`+S f,�a �jc&��^� J$eb].3*q�4�3isI/ ��!ZeoN� �:�/�/��:0,�0)�!W1-&01�C�!b.#$,&�,upoh"^,ge0�,J�,�&course,m): ��x��1:, &c "'!Oaxi�-r|ic�*{:.�i;a g��M5.%$��r"�$K$�";}��!;� �_�N >24� �&5 � ,  ��n�%�(J9�F�1A"I�6��breakR%#1!ye�B�xA��de^ � � ��'}Q�)� a �0.1M��#� �is8�e!�ly e�s'6Ns ( ��#�dFi� 3-5)S)2 Qy2�� � s� �tJ��0"�Ag//W� m��\%�a�ioy%1,x1� � �2�smoothU�6J"se)A5:�"I Mh� &�v�L�%y 2(a)WV�{�=B� " "� $yT���� "�*9eŨgr����x& �<� 2�f���� turn�M m���= %3."iT��0" (a)� � on��eE-�%i_ing��1�*F>!0�2�*i �%86�b�? �yedy#^��-�� a:�tp��c"3&��C �c 2. A" M�%{bD J]��� �s ����!)�B% ��}^�t')>�PQS1&�� -*h"Sa�AG�2ag �&�� e�"�$. AAy�F7 e�Baea c�%-�Ng )X�hE!C�q ime,.m�:Re�5Kl�R�B@Fm%9)�n8Q fine�rD!mhe���x�p%E��A.�*�) �!_&�4n� OE�6eaB�4$6mJY5!�EbU_.;cruŲtP+`Do1�c��{�. Fig�F4kw�r2�!� est:AlJw�tar���:.� ad��bh ��lg��:����%�\ hand,���"�'ա�恬a��(M:��B6��o�Af���!�&F #:i nic�h�)A� �Aea�*�Gt�"Njm��'2�mi%�k6^F��%n��j>����dem6@��5�9 >��AB2!Uq ��:!6w,>V"��<b~ώr�i�Q�R��-�!.�._��o�!w�s��&�v�E�!�Irn��2�m�$M �"� �#6�&�� 2(b),~(ce)6�'�ir�$K���%Sos�I"�/K(��not�GIR��gn�Fj��!w�E�a[>�:� Qu��rz�,Fs�v�� Q A-��s�2I�}os�� meF�a� ach 1?"�%e2�{�  <*�<8n����Zf� |�6kh�uM �յ�!`5 Y  maxim�. �5�1�=����D��; F�<�w��� a6&y1ڷ � 20|% U�5.�f6�. But�� @/x �"l �riMB3^�E;BD ��:1M.L�V�*m�.~2�%f_�O�)4s�z0� not ��."ja�� �O�<*�we93dN&� aS&� A �e -0)�-\�-%���:K,&'a��>p r�C6�. H8���fte!�� to 6�&����2�U�dB e�a|-.� ��� me�A�!�IͶf)i�uYFT{ur�� K"l"�D ir2���- �: � $I=2w< "q6*��Re��NW�(��.�$ ��|-�K�Kc*\� �K�'�K� q*�N��� �O1el2(:*s�v�H�q B{o&%�&3 ��^��*(.lo�Q�F��u FϩH:�>�6}�)P2� ���ԩ&!����"9sN� jG�. R�:�g�2..p&�=)oft�>kH;K`� a�'ep FU,E� q���J N��du"Ϲ��u p.�J igЕdmI�ens�;v[ �"&� s T\"u+�en� p �*Y�}� 0 �i;L*�"8&e �}�b�`�� i� (�uBL.� �+Ў,�le� A'-purW%-�6:�2 .�"E�y��Fo`�  )r� �S�� %�s B�5�.4��* to<4>�class�(}��۹�"� 7"�4 �)�!2FSR�"5 i���"�#�!́�&)6mIGk�"�� *{Ac�Q ledg�͡�T\ ork p�]Uq `M�-U.S.h���A��� Pr�m ``M��F�wA��aۭ*#E"W8� U,ble Medium-M� �J4Heavy Nuclei,"� sup�xyI�(Grant-in-AiV �21st ��$ury COE ``erE�DiJFa\,���s��"& Minisy�of Educ�, Cul�W, S�s, 1 �&�� (MEXT)=%E(�-�T!�2��Jt� 0 Research (No!)454025X< 14740146)�fomMd Soc�1q� Prom��^����&��Ks w�per��]NEC SX-5!�erb uter�Yu�� &[�zT�ete'-W, K:��.8�4h6[� {99}��1 % Sz"m�쥨 vailAq�!�.��: % o gene6�use \JL :=�P@6\\andvol : Vol (Year) PagF [��vidnn.!�!t6>PA, \NPB&aZ. $[A,B] �CMPCommunn�h'\PLEPLE cLett.2E$IJMP : Int�Mod.D \PRA�qPRE : EU� [A-E]g1JHEI J. High EQ9y 2!1PRL2I� �� :DM��>  \PRP & �Rep>>��.S�T!:aig �or.h�PSJ K fSoc. Jp�w��SI�rBKSuppl�UsageE�<\PRD{45,1990,345I8 ==> h~![\ �� bf{D&(1), 345�\JL{Ni�0,418,2002,123NG B 418}��2), 123BI�{B123�5,1020AB}}~5<020��A*T�ObooksNr� "����} P. R១�P.�uc�it��eD�!Many-BN�P�"} (Sp�$ er-Vd$gt�80)�Lb�� em{b*�4} J.-P. Blaiz"� nd Gy pka,w&Q���R�F�! e Systemso��MIT�smN� %Re��%=��} A. Kle�d E.R�+r_Nek,i�}���6-�1Ax75. d(�4} G. Do Dang, `� Na̵,I�e� X335I�A�9�N5bz��uriya�\6C�, F. Sq�a,TakadaNM.lL mura (eds�X%( elec�Topic��K$Boson MappQ6 %T��DO\�zH*���} b� �141 �1A@%E7of�-jv�f���M���(} D.J. Row� ,R. Basserman� anad�Љ�%�54e�76a�941.� goe7VK. Goe0.uA A26!�1 B3089�3�4} F. Villars,RD8 D 7), 269. Dq� } TE�umori,a�>� �7 �I1122I�� } M!V[l0 M. V-oni, 6}T11-$8!$22�!#T1#�k-�eio�dZT2 �T328.wm��2� s� 2��m A.uN��6 �8ad 1294.q��%J. Gian��[$P. Quentiny�v.o�2A�1 T 20602nd˥( Dobaczewsk V$J. SkalskiR369%8�i!p.goe81}5p , P:n!uVa5a4082a muk8�A.�iukherje)�MPal1 ��100�457; J-37�D8�z289.� row8�6De�a�V�9-vC307.Cfd�,} C. Fiolha�`nd R.M. Dreizler, Nucl. P�uhys. A {\bf 393} (1983), 205. \bibitem{goe83} K. Goeke, F. Gr\"{u}mmer, and P.-G. Reinhard, Ann. of Phys. {\bf 150} e504. gkurg�A. Kuriyama and M. Yamamura, Prog. Theor. [70�1675; �71 4), 122.�yam84} 2_| �S. Iidry.b09.bmat85bMatsuo�K. yanagi, b�4 �5!�88>X6} � YjF6 F6), 372Lshi87} Y.R. Shimizu� Taka�b�7 W7!W192X!X7�1�V2[JXSupplM(Q�_..$wal91} N�@Walet, G. Do Dang)�ilein, IRev. CI4I�91!U254.Vkle91b} E� A.gA�.kAF�208%_902�kan94eDKanek!�e2�9 ?A�3012�8nak98_1} T. NakAPkas)[.�FV5)�98J� V2�V �V 33972�@lib99} J. Libert,a�Girod%G8J.-P. DelarocheN�6i�499), 054301. ��yulaLE.Kh. Yuldashbaeva, u$P. QuentinwM. ��F%|Lett. BM6i�s1.nak00>#,2v> a.�_ 2000� 1430a5t%Shape coexistence phenomena %�9woo92!{L. Wood,�qHeyde, WA;zarewicz%�Huysei74P. van Duppen,�pm�215I�2AG!�tnaz93a} :`)2e30 F�f192fFbBF Nucl��ͬ5Q�F 489c.�taj93�"@ Tajima, H. Floca��P. BonEuJ�8 baczewski1-H. Heen!R{M&{6�boe�c�D.!ean>2a�2�J.A�� ruhn)@M�� Stra�UE��2�14316.�andaj�A.N. Andreyev {\it et al.}, Nature 405 iN 430; N�682} %��4822�fiskS.�Fischer:kI�e�I�) 8�m�4064;N��s200A%064312�@bou03} E. Bouchez�x9�T825�@"� ro%:R!�DRodr\'iguez-Guzm\'!�J�Egido)�,L.M. Robledoy�=�-=��54319;�F6a� 2002��$24304�G �d6��200�� 9.�egi04��^�E�j�.r=�6yB"cha01})"Chasm>2d _�#51?20EQ326�ik0�HXik\v si\'c, D. Vretenara� Ri�Ga<$LalazissisrEp1K.i54320.KdugAHT. Dugu M. Bend�'���'P2�I�6�5-�A�26�ben!�V^^i2� gE64303.�pet��,A. Petrovici�� W. SchmidI A. Faessl�J�'amilto��0A.V. Ramayya,2 in Part.2Pe� 9), 482�pet!ծ�R�1�0) 333;��71m�2� 46. fos!�R. Fossi�K���� G. Thiamo�)v$ Van Isack!-�2y.�a�6ora!�!Z rankE�2RfC.Ehrgas, Rd.� 34322�d d4C.D. Dracoulis2��U��2Mkan!�K."X $M. Hasegaw� (T. MizusakiR�# ��|51306(R); preprint nucl-th/041006�has04a� s�.z%BS�z��?2 mbfm!�.qN�08062;�2�sue�Y. Sun!�Eur J".2M�a�13A0%Applications�8the SCC method �� ��;�����19�6662� F5)� G%%΂1227; �0.S93h 87) 596��XM.~ �, Y.~R.~uIK  %ceeding%Q �The Niels Bohr Centennial Conf. on � ear� uc- }M4ed. R.~Broglia6~Hageman �B.~Herskind (North-Holland, 1985)Ep.~162 tak89�3K�>A�H. Tsuku� �QL� 49a~198�~26�I9a]JRKa@��]32�]b]Q`J�50 �5A�"� 8aib90} H. Aiba,%�R�? 199W 9086�am�=BJ(E�81i80�8�19� 96] ter[J. Tera� �-arumor� F. S[n�.z 12352pf2� fb�i2P529mH9i�� 5:^mat^Ms O,��e$New Trends!�a\Collective Dynamics}, (S��$ger-VerlagA��(eds. Y. Abe4HoriuchiQe�q�p.2192�shi` NN.:R�.�14be 28%a %A�KVY�mat =M6Y����E�1e 952kkob�(M. KobayasiE|*��%&V�� TB�1B � 6� (%O(4) model�tJ2&82�%��-�N�67>2) 1141;�.��Q�~ |ics Workshop, Trieste, 5-30 Oct.�t1. ��0C.H. Dasso, R5 ��E�A. Wint�J�2),A�6�8miz81} Y.~MizobA�R�%�� 198C1452� suz88~Suzuki)�W7��8>482Vfuk��T.~FukuiA)}Q 1�!iVi�#2!L % P+QQ�%%] bar6� Bara�U%� uma�u&�62A"65A" 3; �I�196! � 2� 241"7 672��8$ ��ieE �492� bes69} D�Bes�,R.~A.~Sorens)��Advance2�M�8} (Prenum Press�s6��vol. 2,X2�4!_� y�alm� $D. Almehed�N DN/ A�M/ ���Tb}rTJA 06026� obw �VA? �3� �Y)Y2yam��Dgam���i�%l�fR ��f57A 5jbenDT�gtsso� I� gnar,RW43\ 5�L �� �!����in A*ar; . ����dav80��TDavies�"S. Krieg7T M.rQ34AW198� 111.���h% \end{thebibliography} \a�dix \s� on{Exixp�N.q�quasiparticle matrix elements} Combining�success! LBogoliubov transform%�s, (3.8)% (3.1����2kTs, $a_{\mu}^{\dag}(q)$4, ��,ciated with J� \Big(a�UPUOnIspmAqA` 6�@), B�B,R� �ڭ :� A�� ��!T )a �6�V�3,51�6�5�a-sl5�$} D_{2,K=0Y4%� l} V%�7(q�lu�,F��Z��t�(!�N1.yn +U_{ !�%�V_.,V�B�6�ޜU � � -Yv.�m �Ew��q�k.O�Nof�M0anti-Hermitia�� :�-�Cvanish.Vqu>t�  $m�)�KQ+-� $, etc., 2���above�  denotB� between5 single-"" {,s defined by��(sigbasis}):��1r� &\equiv& '0}d_kE��d_l( � 0}, 2� `���!2qNh{���Ob7,~~~{\rm!Z}.�y�where $� $ is!<( vacuum for>~ s $(d �, d)$)�Zujp  (A.1p A.�osses �follow��symmet:=�� �y5 = A�! e� \��,~~�S1&-�� ?�k  @.>�It!( also�sIuat ��lI�YJ�)�xE"J�\nl} = )m(J'l}5�\�~~~ F_�QUM(-�y=F�u),Z;u�)= �,BY<�Z� holdUHpaiY| $quadrupole*� $\{A_{n� ,A_{��e ,�'0+) "c}$, u  considedV�,��:�N}q&�$, ���:�@N /�k N!q� ,�D neutr�proton �"� are read obta�� from tho� .� =3- ($ by replaca/ a�bN Ii13i� l}$ � , $\delta_{kl!?�restrictF�sum ove�>R0index $k$ to � s or � s. &� SolvVmo frame HBe5M(} We solve~^( u� aqsimilar��4imaginary time %\cite$. Let $�{� ^{(i)`}$�D�. vector itEV,ve step $i$.�,first calcul�+(mean-field �!�;" it�ϱ�D h!� ��  5 @k \epsilon_k (d_k���w+ � Q �  -| s}\kappa� \��{.� }+)}i)} �"* a|:��D��@ ra:wFbJ���1*UE!o2�yQ $bf ��*.}$*F�2+J� = 0!R ��wE�n genA5e aRS$(i+1)$IQa*��q5.+1I� } & x xp%A{X�% �8 6  . 6 XA�5( = &-&\varMd 1 ( (]�MG��\lambd�ta)jL(q) _�W -\muk(q) UQ f)_{+}6 &+���->�)p&i�Anu} x �-6xmndag - J| � 9u� $a small pa�&terNP a= .�E���  2 /,�a�BY�ad subscript=+mH -$, � % two-6�cre�� Hannihil � s e ��m pare� sis,���ively.� should�� d thw,in��trast to� conv/alV,� unit�1�, $�ԭy"$,� used ;  sfatknHliz �is� served du�!"�Eon4 Lag0e multipliers�^U-x6K$: dA&m4byl tra�%� �c�&��g���/m�}��u�{�� F'&=& ^{(0):;r]�-� �4keNc�'@, \label{chbcon1}v �mTN_n �-6N_pr���E�2� 4 � us R^ Sz but sl� iffeA�=�� utilized � .��3�p a}. Expan%%��-haE� s upA�| ordee9$xa�!�a�weF 9� Q%� mR�l(r>�i(N� ,) &p Q(q)&p65 5p}F5Q(]"rB E6� ��a�"�\b� u�� %Z&�� F2�^�6�=��!F� 0)}-�� ect{�Oa�n� )/2�V +(hA#1K X�X FYp�Yp}v (q�:�Q}.��;i)V� .�2�), �J��(on� Z+��6�!e�!& '}),%# M�$X ., �O*Z (3.3�#excep��#coeffici�BC, QK�C ] inv d��these���Ō�� re�2�$�ᮙ��2dag�B$.*z 2( R F ���# �m ��% i�./ �% repe-]&proced83until�� vergp6is atW. Z� thus�<]ake>�5N<i�h}_{M�ŷ(qj9 " a�Ec 1 a-6+ O�]�q �{z�I +2� u}hEh ��&C @ (q)C � +�W � ).�qphBfHFinally we introduc�6- 2za l�rM�k m$,�  diagon| eY@-�$.�u }B�=�G=F} E�)? � �(q) �.+"6!PgBi%>��e�e easya�se!/a�mA=\>  -V/ 0q$. In actualun4 !(eB!ah t�double� Lve algorithm describ��� ( 4. Namely,!�carry ou��m� ve }�"���5�1�E� ^{(n� � �"� $n$-tIe�I:�< infinitesimal �o��o Q}(pQ`i�P!�$��"�"{ lfigure} \centerline{\include"Hics[width=14 cm, he_ <=19 cm]{Se68.ps}Bap!�{ Result� �kion��< $^{68}$Se. (a)~b�curve�Eres���_ A�+ path%�jec�!onR p$(\beta,\gamma)$ plane, which!� nect Iob� �aprominima8 sign!"@by filled circles��cwur ! ���edZ� � UUed]�1� plot9�Hevery 50 keV. (b)~*E-pot6al $V�� ; as a func%[�c&~-coordi� $a�Ha�origin2$q�c�na�coincid-1*�;l)0umg$nd its scaa�s�� such� ?� massa9given!g,$M(q)=1$. (c2�* $M(s� $BFthe geo�,cal length $/$ aloi$|ICq�M7 :85�BZ%@(dI�triaxi[y��am� $ M$^= e)~NFx�gap�\Dn�_ p�as5�eW �f)~Lowee�wo eigen-frequencies squared (i.e., $\omega^2=BC$) M42�RPA2 QauT� �-�5Aormed s^?i#more ��lA< I� ry $e�$- AN1B -vib�C `h<e�&Q� limia�ain bota� mpon�Gm�symbol%d�31a�9$,� K, howa�,� �to`f5���jo�caJ�>H)$. ��h�����(�(�� Kr72�(72}$Kr. Not I>!Us�a�,Fig.~1� �:!f�s:s(a)cA6��9:!�y 100�u9f 9lmQ hree�SyS� �R�As 0)io�-���PA� �,�v �����LikewiqCA/s� �]�a�!finu�at�m6���Gd�����%ode������"��� U' }� tabular}{}Z# 70mm,!  ]{�| _comG_��.eps} &�E��VE&r�, \vspace{1cm.� Enlarg�,��turn Vreg� ofajs.~2(a" 2(f)�3$^{��, �A >eR��to�� dire� m�si&�=0.0157ћv"� =0.1XE��numer � ion. EN `�Z q B `=ea y$6� �I8 solid� �point� "1 $A, B, C, D;Nin�� cor onelH b) �  display� �!�� o�&� ��wo�u!&�2� QRPA*� as 2�:�>A � open 5L �1�=�� $2�$ wmixeff� b>&��$K$=$0I2 aJ��Ttot�ignoredb� ', B', C'!rrlatter2�B�e1�-�<� 2<�CVWa/U,not ge!- X Y� to D beca�-Lpr)EmA cuss�$text occurE�y"*� was check>�-U>�is 1�)��ofyBa� 314$�O dist�51� the *�0m5�d�O �iv���% &% �"�� [�� t���0��� nflu���^� �U(��#)aA/�$eA' �um mfs)�!﭅=60^{\��xis (d�! ). v;u�2 � �Z9F0 arisTD�r#Aa.'stG3ng�� ���% opposite�c� showf��L s. S devii 5G=d * �g ofGci�3 of���}~͉������ as���>�u�hs!"�%w well a��each o�;�� f� �� .� �� ¬ Ize�� .D�� �� :� vU �qw e�s��i<ey9�_A�٧]�ťdon�'��&��\��J j����d� � � � N0"&�0e�is � measu��� 6s�>����le�p �p �p �p �p �p �p �^ wigg!�&�s&�:m"�/�  due�^�!error[ they���It�o� � � � n docuu } u%\class[">rint,M pacs,n�7 s,amsmathY(]{revtex4} >L twocolumn�M,supers�(affil� d5�ddM4} :� 11pt�'>�(��cleR'style9K� epsf,�tO@en % \usepackage{|x}% I��?files2,d)\(}% Align ta> s�decre~2; bm}%�!� % %R�6�ig:psfra>bm&sloppy�� Qh page%%{plain�Ded!��� 5�FacultyEnginee!�, Kyushu6�@Technology, Kitak $804-8550!�pa�2, \date{\toda�4abstract} We .vSe +-�* \J`{21.45.+v, 24.70.+s, 25.1 40.Lw�+ make� �6 tcou�#{�6}{1��"�EI�&!m} High��V�"_"s� h as Az~\�6 }, CDBonn LCDBONN}, Nijm I, II%�93 "NIJMI} �%!�, NN data set1.ab�%350 MeV �� . Wh�"h�for�JA{� predict b�ngU|�F� systemRy9/estima�,experimentalSK $^3H�S ^3He$ by �0.5-1� �LFriar1993,Nogga1997}a@is misa&2�y aCbe�K�(�a:�%�TF�CV�aar *�7 �� � stud�"� <o*6 (Nd)*3b %t uced "cbreakupa�vea&%a� �Bof �*�>vI$& ba�� pair� �� ly� insu�,a^�D�!� AK. G�x���ied/ repa#�!Yeory y.] wE�Y � ome :r ;��!��g%`�3N Ip . Ad��( now a 3NF�$�ia�ae�s ���sp%JF:a��= work� >*@ .&s Xav9}.�R�shei7 66)b�-��DumU. �K��2�&3 _%�5��in�f.2� [ � l �bM�EA���:rA� �s"���!� imporra'�<��t%L2� \-t3N�tinTDi�!acR �.� of2J�o��e:�<:'�) ons "� ALfoc�1f a lo� !�. Basice{� "�74 aproaches hav��e>-�Ded:� 3/ manife� covari� Ve��in�o',@t�etq �jach-�$Rupp92,Sam��tad97}�V# 0 is�k2�40um mechanics " �@��� like hy� urfa� in Minks % �e.?qLi�;l�Dqҡtox���s�a-A�o%LouzTed6 'ga^at�6 NN t2Kn� �7 via��Handard Lippmann-Sch�Ier"y� *�E�b�R�����ndAblie4� .� ib kam�d� < e &� sup��G Y�Սqbef/�1��FN:�rel!�t �9m�a6_c,n arbitrary @")J� *� 0����� c.m.� e�ch .4s :�NN5h r\"o��er orv�I57�!s& > Sc.R�6 j �!6B!�2�yZ cu �Hl%vO ]$rde�MAf Vd1\.�&�N:� V�. U)?6{re _ ��& a�&aD q am1 &26By5'do {'�p��IQ�� �AG2'om �an� 8a�l�N.�W, m>qtam��es:U��:/e 1�2@ ��Q � a wa��LxKA�!6�8 shif�@.&$R$T,�employed998}hbThoug!�a&6�is !Va sub, for :|%�prO:6�"�it��e�? KA�! illu{t�+�@of 6Us�2Y�� an�A�E����%�wqso will]1�)�_]=,�"�) ��@ I 3Nn � . J!!�Jo�;w\E: �uf(g��w�/e�!�u g� ndA�9A�*� � 8B��8m�67!�r�Led2C?r���%@a 1�tpFRS��5�aY k � &�ofK:��Eer��+�p�organ�Ca+ ~In Sec.�w�&;2�Q��Nly%6���X5��uN9ܥ"f c  incorpo�ߥ]-qn�7woM �,-� ousŔ���t m4i�Jl��j<�9T >e �*$ st�i � ��f� 3N%�ag�[. Our� n�No)� �3N5��!� guid�� r*�Gn�in m�wit�g!oAe>-=,9�I!�f`* 2�2�I��u�Rqu�8of "~�"rox&� �1��).�4a!�su8eh �u�� - ourselv� � �Eq=F2� |]!! e�F*-��&� �.I�V!��A�r"�� ">�NN . � is�� &�3 6�>�<9*Ax 6�� zed N2�8& �.�Q %�. � A�1�� ��N.. ),V!�>9S< summ�9Joutlook.F < {For�iofo& &* �3TprsR��,ng thr�i:=$V�;e !��� �_a� �da� T satisf��A9��-�%� gralu�.y,glo96wb5eq�IT\vert �B > NC t P 2+G_0 T6"�Beq1�end.['wo"m (2N) t-/� e *(�r:%$-?�Zr %�permut�-94H $P=P_{12}P_{23} + 3 (>�=��!} �� p�.a[$P_{ij}�2% eN�M's �dj���w $6<= -d vec q_0 > _d > 6Q(%b�S) e-K.�mo�E�m~e� um�3 _rG"� wave" =*M ~ $. FSD $G_0%)>N5bphy� pi*p��t Eq.(�^E))A� r"kf ia7 �%c:to���Me.�se�X �4T�=E�6, %���b U a�:�� T byN@B?Ui3Pa ^{-1Ea T 2c3yv %no=Ld wal��iH@�x3>}% u{o1)(�� [.f!Bj3>��� plus�t%%�pal BIseBsEM~]cas�mainsEw� �MAFing��>� .�" � -��2d3N2�]j�3 >F one,����>� u�Ep�xnc0 >. q��D: �on�4����"gonz%'id?18� �1 s, too.�s��!�Ru�alH s "eto Eqs6f�uwc})�F!%.Av!�AR-�: � ( A1 l m`��5 �%�  ven!�l�� a * !"�H��a�*� �q�.IX��k�� $-beI)�a���eQ�/!� n $2o9({ J})�U02\sqrt{m^2 + ^{\ 2}�,E� p]1t 2N6� %~�3N>U)!�gN�VH_0� �(B�)�q� BI>�,AJ��f�Q%q���1Xhird p+�-�q$�b8%6�E 5� (m��!,MZ%K). AnyJ�"i" 'n�9i#$N:1}[e�| � �i�M�:MliB[in2��: yR�V()> \, UV-� 1�#k�KvZ� - 5 5� 5V1, =�Bn�;$ �)$ = -�`Y $ re#��po"�Gv�4�� 2N .� . N"(2� *at�!�2o6h�A�M#�S$%�� toge��� �D�Qb]* ���Xg;���g�'})!�\u w� l�]g��2NY�� ^��� :�W?;�6$���� �J �dJ�Z t(I c k, ~' ; q~)�W Vz&+ �@0t d^3k'' { {J32Z{~''Z~"[�@{Q�{y2r '} )�z�����}-�]�� � 6C'}C ��.D+ i�] �[*� 2F� �^ref$tm��;5d$ |�edA4"� �we talk�EU)*y}F� �]]�A2_2b� b \! :� ѣ castI�A�zF <_dQPMa{ {1} %� 9�M_dJ�_0}} -�C1б+ -eR�_0!�]�~�_0 �_�� ~') �~�X eq2b^E�f��9�gE'�n1q!�� /$M_d$�&�)���U�  ! good�4!�%�u�(e5C i�&� 9��Q\YX$� �Kb�C �& new6[.� E�:v j)U�w \�� �# � t-��� Al2�2�B� ��S {{1}Es{E2�- HEd* 2F� �'H�"�m37E$E5���E�'y� Di�Q1�!Q ial 5" �w �37!Q4B� E�I� (M_d6_@ 2aUS�&.� q!}2�dB� CTly! 5�a}�+E�>_ �'A�"�7ly"�& any>��;��A�um [#�"al�dex �. Detail� !seqr2�%88�� urnsB� �y coup"set�wo-�/e��^nt_ �s. �w�ow��%:g +D keep%� %)� �� 0 the ! �1uU2"�A�QaN P!�m�!?lexOm{}z� �.��_*�e�8l���A�>�� 1�pr�R�s�H��F� &~&�P8rt p q (ls)j (/\{1i�2}})IJ(t.T >2��46�i�p% q"omagnitudr"� Jacobi �a ()VF0boo;��$�$� �� S9� obv�meaX*�Z� 1/2)I$A�a!Ek   (&*B � um q), $JF��,5w�_st�iso 4:��*%�A�]be ����&�= W� - ,laR���reTi=>M ^�.� �% �8p�0�Dk$0 �3 2 �r�XE��#l- aeJwo�-s, sa\p_2�� p_3$3 by a6�Jrh2k&�g �p_2� �p_3) \crwZ]� p_2 * - Xp�{{E E_3x {E � ^E.:^{~2}} I ).9_n2Br E_i�YBW p}_i� }�6 p = �+�%A -� �=)�+ 3$�RI�: -�d�B�U;Q.uZ(�-vid�Y$���cA< fo�- the-P�6��cle ;$$m$a'J �@ iGst��}��($,Weinberg}F#U�U(k)kv�+E0 \mu>  )� {�_m*�� { m %� >Aa�o>.n3B{W$�)��>�e�6yv�=_� (N@iUk$)ɚ %A+�T(k�\�ea�����* 6��W$ k= ( F�,"") �me~M2=-:.7 { . *Cb�)f� oHmu$ doe�;t3� e $4\0m s 4$ �%oet��t gA�|�A�"�6_v:^m%-M$\LBj$&T� ��knRI��P Z�:"GQ&�U( ^)J@� Y� {m}UvJt� } SU( Q� B�\cr�_+',�( �~R��2&s@6n�narg�Aq�sek:� o�5�mBvR1t.�&"@kAR�>�&�n5B� of!~vd��:. Fur� e�onp.�2a .I$�xnd $k '�QQ�by $k'=�k$. $N�7pA�a9y�/sF]>].��A�QE ) \\~as'YD^{�|}�`'�S} (N�C.j�'>�F�}.{n6R�' (In3}) ag<8o��F���\pC:�F& �9B^ 4 �F%F� \mu'6�7BɄf�$ � �tX-SU(2) M�D� ce�4 rose7(�q�s Eule�bgK8 �:T $R.]�"r�$low. Now�#a :�2$ h>ng 4 "� �F�.��0 !;_23>�2-2, O3 6p8Bp&� } � left�#d&�!tw d6l a*!�� �b�>"� �3 $iN ( zero. Si�-w53no2T��U_&5v`�\=�a tenspu ductF~�m�[_2��) U_3�v9BU��s;4 s 2�3uchoB��a�Y��(P+ � �" (P_0�P"� (:� p}_2�F3Qq 6� ) T�Kͫ �^� map�;k$E� "K M|  Z ��,J�r P)6tR�X#!! %�-$69E�2 >��3V ] �%Ocr   {B<)Kj3��3_2'�Ju_2�w_$�R�-�� 2x!�\m6>� V�ff�>�3'Z�_3 � 3} 2�-1Bp_3�3:�10B Of cQ)UB~�x 2 ?��V7*o (10�Ue�=3t)� U�. O!!!8 h�a�:G.��7�� �ͅ�"Mon\:a�. e ob�e :a 8 $M_0 =.� Vn�4J�9rE"��� �!2-!�zV7 RRU>^u{M_0}��oIfZ � J�P2�6�n1F�!we �5up%=F��h> ���~ #� � p_2~���� { 6&P $k)i6~ x^{ "��"b e�R }�6M�eL�  &D&&rla� ZVƣ6�{��y�>�Jz^�vc2�c-b)� Ao�lͻY�}} ~ m5�):6m 4!�} ~J3�5i63 �e N^2 e� � p}B*1FP�hera=c e8�(^�8+ $� �A�$ c Pk)$%�T[�$�5izB!�'�Fin�"�'a{�"g5>e�l[��N���5>� 40&�  r�"�� Kron�\r� m�f�0�a�0on�T\pL��.�I�3 >�S�&sgZly�:kiPŷ6f�+ F�>�)i*�+�f-nm75l :%��)����s�+r?!QW�"�<� o 9a�/2&S ; J���k~l��@l>�"Yg\� k Y^l _l}( 6U ;�\c9=2.1V/n���I<%`EF $s2 *��Q~ 5B$j��"HqJ�um�oV�rt� 1=*h ��%S" sl�(2�!~2B3A�rt 7so( -�l)�jF$ k l:��*�"n1FE��� *� �2E�A�F�F� &>6=&N� 6�FJ �BQP>.dVH�*8�ly �f�.NRbrɍv�3���I%�3}]lI!l%�XrX�|r J�2bI n� >I ���}?3'����:�Fx�C��con"ap �2�*�.���R�f "9 k������c P��"�>R���q fyF�� *� % An& �oi�a-d=pm�q!�:< ($\alpha,��p$)V. � 1/2*. Acc&� (13�&�$4  "`cN�NK��� 7p_! b��  � m� k}�zV��cr2X"BYG PvYB��mF "".6 s h�3�4&:$$�}\T8{1&0\cr0&M\cr}\i� ,$$!M1�k$3-\3�t �:eF� . It&HX f1� Wr`F1M)0lD�� \cos I, !@ �p /-� ER \ &  MFA+ P &2A]B6!�- R 8^CB.&�^. j.B:�hB �B5�J�(! 8 yn b A"�.0mF�q��  32��mrEC$M�""�!ANf� O �<L^�m1}) % �B% ^�M9.ad,F#e2S �R.�Z� c p_1$�?.`. ���.���{�P}gdd7�} ��$(� . Stic��tov�5 ngw�fnd/eb� �&� :$� by $;%$�] it ͂ts�pto �>8 $I$�| �)2�%��qjB�  k q=p_1q�*1 !� "%*�$)I (jI) JM� :�%M_T{� =& N"*o um� I O s }aNl '}� �}p *�15{-Y}I}2��� j� 56 �=)1A rt �_I ) ( )CJ Mx$u'&� !�Y^a)1� p_1E6V D^� }_{-S)�2}2BeSk)) ~Z7)�367�w)�0~H( V |} v.��� �q � -F6mF�1Lat�+�� &�er12�o � �3 Ё�. nk��e�e�Z 2�" $�jN=P�W�J���)�� at�$�r>�>$ �| $<5\1~1' �2 � -i �e�wDo����en�Pers ($�#PL&- p}_1 $)Fk &~&\v��0�'&8'2�kt'P�:2�-�3N2A]�' 1��Z ' , ,p_)bRk)P6Ub2�k�&L(~'� h 24P4:31*�mF���is�ZifA inWce�d� g�z ng �H �s�tAEc wɅ �M)i~r� A� Rl ��D� �\���n�-q X:PP�G!28)EkJ� �; { k~R& )(S�./�ʩ�BJ6�ń��)�)!�)��~' �~dJ"N})W9R>�Ehm*bIq�fk�� ��Jm)�3�mɣnn*bmRa�+a�#�c.F��M"orɢe��Ţ:i�� . Equipp>��|,�#�B1�%^�s� s �@٫�7� >"� �+>0Ju_1<) �?I�P k' q' ' >��ņ R6>.�> �,3 � 2~�022�Fx�<e)�ed �1s���2t2'L"L�+�[ �� �A� �R2 � a03 � ��30)'Qi7ul�|*+S-�&u+It���-a��m �;K embl�A lose�XX-3AI Z>4^me.�Gb~ q�J�%~ P k'" #I" �_�D^�9dx�' k-\pi_1T��^{l+2�� @ ,'-�-'^{l'/�� ŝ��0 {N_1(q, q',x�~� 2> G_{ ��/�@ x2�0mF��.C.�8t �8r�2��5ro M adjaexwZW 92-7. �&ovD=a�:{���n� IC �006eps�Jai5J�Rkam00}A�(8> oum n����+ebyߛpli&YJ ".ؽ6kIq>-d�% Xa�6. s �asSog�No (20�# negl=Z7 �;�4��eE f%�dot?�1o_�6^G !> .�? (23)&F &WU@m�is*�KbݕU 6�� k� ��I� � ��2 V2�_cic"MF (31):9@M2e� R� �څ��Z e��:�J2}�J �"cA+v�I~�� �+NQnC2m�=& �\prod dLp_it�]� ;���&�l1.* ) *� FL�� {1��E:L<\['2 v1^E5&�C22 Z3  \  fG-�^=�  �9; ��F�F�FbF:q&�1E92dG-Y&I��L#_5f2~&]b� �%6a!�U�B2�a�"{2�2/-B�3�1�.��2%s0 ���qU��&[>ESq~'^2B�Bq1q~')^|I�:�B�q�h q q C.�N�28-T8�:u#Um5�9 �x:oN0-� }*�JS/W� cog�Vټ>|d�L� n $qa9q7 $x��{�#q} \cdo���D, '}$.� >� �%. A�O2Q d.z?qb;��tnB?�on��z�=vߏ[-1,1]$6  $x@iso!�n.*�6 loga�ic &�V*wg���6 stud�KB�>I atB(*� bT y�Uj+�&�� rootMJJ.~"�8})�*�?�2*#TcR. L5d B�!���[w . to �qR:�Etcaj $� R#26[ -��| } -E� ~'  "�q� ��{ A�{ � x }} ,}EFC1c(FA A Q{ Ev�+ q����}K= { 2 q} ~!R �{ (v^�C- -q=q'^2 VZ.-1F/ Al&�J2-E �� kC�( e�& VC)a"� e�zM�Ni �Y,SVJ!'J�T(E( {GkVJ+>~V*]��A-M'�(baj�}%�int�D infty} dq3^2J {{�� rt t�� )}(E��� q^2}�7 A6� >}  {#^F�����r� Z!{ { �.O �' }% `�1@2\ ~2T}}_{ 4 pi_2A�\* N� j{YK6} �% aJ�{A �G e�.fKm�]�1fB�1t(. �.՝ �Vr�#R#\��&:;.�s $N=,�A|;�$����: 2N�m&�,m� � $$a��2RD(.�S21})�d2�G~�NH,6�*Œ��t$2M���d;."���%$ ��bO,$l�UQ. /]�G�earli�Dh�!����y_�\�!1fLHs "�d�p:2�;h,de2"$�X�9 occu~U�\�Uq!�A�y ior 1�rtE�i\le 1$�.2q��m$q = q�I0�"���K2N&�M � �5�$$^3S_1-^3DAR.f jY.M�I�Ww�ds�8!�me��!X�!�.`i.�in�#ail in �/��}.�am�w9#�qE�9n$�U& �Q ``� ''-like (>4"B�$l=0$@g$�$s=q\j=1$)*P0\(s%�!Fl�o�z.�k �a�%&s\ �ub�{io2+]}. �ly��6A�Q�IvY�of�b�R<as &�Gi=��G.�1�e�e��`cY#& T0yG �ar�q,q'-M�at-�B�= 1���>�^3W >�T�a��'e�V$Neumann �[A�A]�e�fm\�up!�!�Pad\'eMځ[�l�(rt-range na\}�NN� !!"�c"k7, negligible �la cer`� $j_{max}��Z�$�k*�;.�"�w�0in��P gLKls!&�m��r $j > �we"� ":Rto be\&,}>A��De pJ!� q&!% �2�&�8Ji$t,ԍt5&pi=(-)�$5'�XY�'o achiev��n�d"G at our)A�wgP�� w�*A-K� 6O�Ih�Vsub  A?to5�=5�� took��N" srY�UJ=25/2B�ac r'*�1435t�2�a�wspinu vari�n�ba��K��)��b"�b���1ed&�Q+}As &� i�5e2,�`@Fv' ���*�Was}tf�O.n:�W, �edW�>EN.� AV18l&�-!�Mv�k�;!���t�"k�s}e0i" &h�er!re"��m���is p5/����v�a6�$v^{nr"�aKxi&NaB�u�$t 3 obe"�c X-F�o�4!>9��%:�� L\�2y#=C L6>��� to�7gf�J8te&N`2�"=T !rlF��Tspo-2A1 !@K*� Cx !-�r+� Fe*�^���:' f.:�>:��a�IqJ�v�EV�; h(k_A8)z vi�r)�M �k~' ) 1< �����F0�F� a \mid8'k}l  & = I<�2mL4 ���J +��W'cr �� 3( 1�Y |^2{2m^2}�- $N#4#Z"�2F�D*�S"�:� �o�"Sbi��*�tQ)6� s $J�Z*<[ )$6�E�4)U@B� 3�uA�kK ledg.�^ ���9"*� halfm�N"` gxV2N.�8.�SFundo �o� 9B�:en�2� co[X�uasͬD�2�2002} �c �X���2k  �uer ka $q/e3� $vX+J��X}��8�\E� N��& �6 [~ 1{�Z%M�:GWI�8I��O\q �Le= i>{k~I}}a ~ ] . �_m@ `4'��,�ime2] 2 }}g�9eq2aprFLI#��u�|� J�� li�s�n�r&�k. T�lat aim�wqked�#:�$ _d�F)!A�1�u� ��"#Hq$�#*K2b�_l$Q g-Up��V N*q;�Keq� d�Fh*h�1�����j>� [��?�e ��-; ���a@� fig%*b�.F 69z&�di�D-. � babi%�$P_D$�� Ak!""�!#�[a9 �R�l"� lab.� y C%wâiW"S#.�An).�rG�XYw%�  �Xdrލ2X�I]��e4���� x{ �� M���t�%�2�2&�apF�� #�O�!3k-�.Zhf�4p�F�dB J}@\Ah �v BZ3��lf7��- ^��m�N\w-*�5apB� ��6�!�fu 8aken iR)�Fu�mh�ro�A�.Kb}) mustA�v "� 6e0#�:)!�!N#�A/!# Pa�ntA|�%הa�B�<�Q}�L)��qr-�~�k a poxV.w, }�݄��:��2r�ya_e6bi]A�.oe�)ea\c]��, eެ1(si�ߑ �s. Re�m�Y)>b)we�l%!L)� D w5�%;.��<e!C�I stig� s���p��} Bǥ(scale=0.5]{1��% H�is#�A�( EPS art \c��}:>p$E��(h��J��V)8�[��ĞhorizoӋhu . Af|�}�vm!���?�f�Z!M������( ~(6)�2z*� E"�a���e�)��B�;"{��nY ���ed-, Ƞ- N   ),�=�Bt����u/ �'��Mg�&� /�j ���QUu�.tR��~%\���u+e"Ê*�p}�.��3N1�ˇ�s���!�luG  t=-)*�_u1]he �� uX�h��&�]"s��=9���.�B0 ��|4 :@^�Lto�!U)�tV��Fe5<*wu*�z �rO�edFh $j < 2$� 5 a<W�)e*B��{Qrg*��F  ��M�po ��F�&� 2� $a^x8)mu~12E73'�2,m_2}_{LML'M'q'�Iof.�19Vs(  L,L' $�2p7R2�a��*� DOf��A~s&�#"���Q���� 'ܲ 23 gauss�I{5LolaHU$d azimutha�H���wL�"�� }A�2��si|."�@I ���sta0� $1 \%�� ɤaK2_ �isA&u JlB�ly :��t�^ ��ed $5\)��p!GA���Y�� zero �ing�!d ��;L} u҅enA��(r Y�}�c a$�2$J �A��4he.�=`�flj �Wm!"��t%�c�.� d���� 2�In2{ sig}\sye[�%Q_ndN= :8a�.�&\#itha�&E�pd ]�� � ��!>�̓�ub�)F� B�{->V!�Q:��� Pw*O truc!�_sta�J2�d,�o!`1^Zs� 2�Rv+ .���Nbooi�"�Bw0"e�gT �0!5E@2�"�"�36)#EF( keptT�i���3� q� Ͱ���Q$VFq}�q$��s Ba?�ly vis�k�V0�>�-s. T��$:|*�K 2�:� (41A"39vduAU�.AG&Z ��� �Z�s��%���ern�. �|�Ȃ2[ ~3�� ��"y&�uŋ} C���V$( {d\sigma�OT�}preoM-v&L�� A {�.M,9 �5 h!�} � �'��A4agH"��&tjw6�.�� b� 6]{%�� k ��� :&a� $Nd$�S .� at��eF�%�e��id � !�!�I�qL>�� ݨ ��=:� � 2��̍� 2x6S�Zq�^� 6�"� e2� keep�m�ny un�de)�by`� � R� � �pd ʼn!y$v,�m�b*� hat84}, �Sshi95},�7��s�� �#$hat02}�.g �4label{figsig} H\end{figure} \begin��includegraphics[scale=0.6]{sigma_diff.eps}% Here is how to import EPS art \caption{The relative deviation $\Delta$ from Eq.~(\ref{Delta}) for the three different relativistic approximations to the boosted potential $V( {\vec q} \, )$. Fo bdescri�X of the lines see Fig.\�Hfigsig}. } \labeldev 2VtThus significant effects of re% |ity occur at higher energies and�4y are restric�to4 backward angl!g!R� ($\theta_{c.m} \ge 160^\circ$). They increase �non�$stic cros�,ctions by upx$$2 \%$, $6 5 - 15 �$ $10 - 23 � 6��-�Y�`. In ref.~\cite{wit99}�A� otal:LDhas been investigaA� in aB�,scheme. BeyoOdhat a very first step into.�b(done using�optical orem. �our not�$ i�B ads ��(eqnarray} \��|{tot} = - {2 \over {\vert \vec j�rt} } Im \, \sum\limits_{\mu_n, ,d} < \phi ~ B U N"> .�e eq02�`�$ Now we ca2g� changesA�4both ingredien��n A� right ha�(side due to��,IPaG2� onlyhkinema)q( flux quantA{$|%4c j} |$9�conored. �!��uQ����rJ� g$is given aN� {1X=�^{nrel})�^#"!�(= { E_n E_d 2 { q_0^ "(+)./Pm_d m_n6/ t(+ 0,.�_aB���0$E_n$ ($E_d$)�%@eutron (deuteron)�5y!�!c.A�system !�$�,��I5�%joa�W-�$e momentum2_ ^i\F e�)�was=�$ which led!�E�cɉ�=.M s�o��@3 (7) \% at 100 (�F)�H. aallow� also�S amQ[Dnuclear matrix ele� $ m�i�2� > $ (�\��$imate boos��pota I�,in Eq.~(39))%�.��$(not shown!� sla�ly�� t�a!�:�( one. In ot/words,i�}��$ outweigh� .��ca�!� by itself�+ɣJ��*!���om�!��elaEj2[M&$Lsake of completenes  clar�Ta%5.N��H formJ�frac{(d��<)^{el,rel}}{ d{\�u q}^{��prime�D (2\pi)^4 \left( F� � \�V )^2 Js16V!^ h�(2�%} \, I�I� &�L 6C:� V[ V^26d_bB���. factorA�!mbracke�Rjo $�({2 m }{3}$ ��->�8case. Again we ��reg� .�A� ������>L � erm�6is.� Q+ typeEpar��ByI� 2�s. Both �W,:.)-(�UV� ente�w squ�D. It turned out asaR have� ��� s.~2\~3�,t ���Fis%Yvdynam m� useda��de��of�G^�%&ensat�"; -�J�a� most� s. O;at� 6� s a � A1 �remai!� Finall��Figs.� it11}-dev!5�I� >= >=p � �)�` veE�analyz�d< power $iT_{11}$� I�8three�+D � B5 $V () qa� ) $ � �� MsE �Z��2���s ) e�OA'4,y stay below:� I:e!� ulara��out� !� zeromings. OŃ4spin observablt ��scatter!4beI� imilarly a!�� . ��"�^� 55]{!綈� 8 F�:�! $Nd$� �!��:;n7 � pd dataa$28P5 135$%� $250$~MeV%! from~ protect� hat84}, *� 3},� sek02}s 1cad01}>x �� l.. w= aken�19 �. 2!��;1����X%� same�%i��� buce�f�F�2��U6� \� {Summary%�Doutlook} We numer��a�olved �83N Faddeev equa�%�ynd]d�luda@m�� featur�1tN  lab C? ^{lab�Bie�Uj2f f�>orm���f�� propagaa�� �NN*. c2��O2N subd In addi%#Gs| lso inz Wigner ��r�s.e�|"� spac� si�X� !-ae +��wo aee ��feirk � toge� withRir<P � @ 3N � AiY neg� *y �he s.%_�oq S�� oic!h maNadE[eEY �E@��sI> s�� generaliz?>( ach-7o E�� BU3N Q�Y�e�2� !a^ or l� stra fo" mannerE�as �=*-Y two--#YI%�sis�standarFJacobi-V um $Rp�:Šs�-�xpins lh auto'9oV��contexeea�!32NMqqs.�Q`( partial w- bA�, N�N>�one, is,� ever�Ynow)�I lex. As*S inputh tooka�BU2� AV18 �gEg?-��� exacon-shellEFivalen5�I�iD a�  $vq �G� �� trans��U)B a. W;ecked k �u�y rV%>%�"w 3 2is.�4ould be suffic~ ly w�incorpor%b��!�%I� expresE_ C AT($order termE:(a $q/\omegaFvIanH�W��M -�studied �?.�\ of M�� �e�p%�c� negligibli�z2? E%�O �{ Ri�)�w!\A�:Bpp�J9 ^t�*:�o%`_> vr �tj � ��6#6s�� 3��B�� spit�� the ')��}-phase-ɱ'v��gaG gy fasterw�:�i�B_��F�iA[ r%WA|s V��wKanF e0�a�&� 2�)* . A��a�B2Y (U3� s, $cor Kon coeql�xO � i�er2 ,&| )�dr�=�ty � �faAaM? �ariso=�0B�theory-�x!�ng:�� $ exhibitsA�!�>�(discrepanciWAccor�to��8en�aresul! &B�I�*� i-�re �j7�y iQ2�2�Ű%a)�]BoBA :] &\��xa{�}$,u � he67 betw��-�ba$on pairwis��B�=e!���A�t le�| (Kab�Q � )!/is �y�bf mo( $when cur�W-e�ona!�(3NFs)�gly!�$� $-exI�� ��er�TM,uIX9��ded1c a$%Ry� ��dic��3  alR fo%sh�yb j�$ :� 4 . NS �andiddI� tra al meson9\pic� %H1q@s like $\pi-\rho� ��o!�ex� ed sinc $\chi$PT� epel2002}&M:� nonvanish!63NF's� !��J tim�r ��topoloE�of-�:J , a�K-p�j�uG one E<o��2� � act2� ��a pur  J#�1are�� �?��)D kept"� 9ref�it- s ��7thwhil�persueA�t� gyA8!FI�=6�Q Q�3N-B. Our �}���Ww ��� c��s�~2 "Ze5 6| x N y!,k sup�#!7usefulQofe�z ergy� Nd *�� tudy� �ert�q&�,*{AcknowledgP s} Ta� workE��. �&v< Polish Committe�g S$ (ific Researin� PGrant no. 2P03B00825,9 �NATO g" "8PST.CLG.978943,E'b�4Japan Society e@Promo_of �4ce. H.\ W.\ w�Ne�� ank7Tri� Universi! NgLab� ory� RCNPrho� al` A�- du(!=s� in� stitutes.t"T calcu�e %oper� @ Cray SV1!�t NICA�PJ\"ulich, Germany. �Eendix&��}[I}E,$\beta(k)$} *'Lo��za<*l 1 = <~(� _m([ k ),� c k) ~)$� defibyB(m )0Nk$8�ShAO ��s: �&&I!�4_{ij} &=& \del@%0ij} + { { k_i�k_j> $ { m( m + B��P~~~~ (i,j =1,2,3) \crh\mu 0 k!?_{0"�k gV P (D = 0, ^.�1J)""�!�%ce�&� � } B$6v]e� 3 \�Ks 3 $ Qx $M$ V �s�v&��eqm1}) 2re� ��[ r-�qPEs��9!F�(:�(P)YJ MKYJ~) = :jp_2! 9-�2NM-I�ZN3N36�48�We obt�<($i, j=1, 2, 3$)"-M_{i jA U� i j } \A�s f_1I�Q� R%2%Pz%3%M�P_ZJ4% J%,�" bigMB�bi�ur�ar fun�s $f_1 f_2 3= f_4$ de�� ��I$a $�% c k} , P}$}�c} f_1= �8-{E_0} + {M_0}})G{�e�f2 {2}��A- n k} \cdot P}Y Ag\,H+?m [&W* 1new5?u�"�+�io�2=��2\, �4\,j� -�1�\, ' &2\,!�% }18M 9NTnMJr�� Pvo��! f\2�\3= -�-2}!_���9�3��4Q��-)�E�.v!6�1Q-%2� )�N4N��j ( $M_0m�E re��Q�DM_0 = 2 \sqrt{ m^2A��t�# 2}y!M0BandFU EW UM_0WPW�CEFY��7x��� ��sec�*q�N���� plac ����by $-� $. C�&l� 'P�0�'re no���'f�  expands!s��%* �on * $P_i$ � �[ 6 igh"}*toݭ1��  = 1r mC�)k_3^2}A�^2 ( #$+!�)^2��,�?�%�t - \C8�lk_3 Pɜ1/�z P}N^�*�)Ai-}Z,,a^2�� �n {\^,O}�!ED,�)��et&�)1 is� &� �"�de!�in��1�Euler j $s $\alpha�= mU$\gamma$. D/�! $�] comb[( G? :)�0aR-�%�% in c�~Z. &Y Permu_- oper� } U�)0) tw�R�bra� 8te $ _1 < k q b�& ��d&state $ k�& q < >_2 $� getsxm� 1gp� �a���� &X:"� &�  &~& _1�~ q�'). �~ PF.k'" #(' >_1 = 2~NA~CN92L cr B�.0_{m_1 m_2 m_3�6sum[ � mua@mu_s } /l � $_{\lambda}I} B'_3 {s'��G {l'}6J' K{I '}��( pV}{1z/{2}} �);� _I ) ~ (�/mu #J M; 32E�2B3 6s s Y ( -l ^j( ) F�- �'}2k!� AI (! �'2 -r�'2b�!�EbsR)�e�'-�!�." 4�) MP \int d!+ ~ '~ 1� N" q~',# q��{/q~' ~.0J'�q~ 12 �{� (~k - +`k(eci}#N � EQf�o}�[ ~a]F^� q T�SJ] {k'}`]& Y^Q~*}i�}}()a!��o Y^{l&l V� - �� )�A�m':l'm!�~o(l"q1 !�%{!� n�D^{Q2}}�E� mu_2} (R(Ś(PR�c~))�� q=�,�!8y�R�3i!Ɔ ���b�}�� �2':� dq�Yf: f+~5 v�1) Ƅ {! N��9���(~ (t]) T���'B��,T eq17"� �5&� � E3k(~ q~' � �a~ \equiv �iD+���{ AD (1 + y_1(q, q',x)�c�nY�zo(-Nn~'p2p*618}�(&~Iw2\18}� F.�u ) {S 6 1�,-|  E#"� >. } {2*� �0 M+M�Lu � (25JWv1�X)^2 -.�� }&�)y�*9aEm$x=��� ' h$y=� =I.', q,x)� $6�}QF ( � q~} )c E� i�8produc"� f� D-� �aU7`89sph�*$ harmonicsF$%\tilde A^ 2�&"� ��X � m_3��aR� Q��������>=" LML'M'} ajg� m_2}_/(q,q'�� Y^* q)~ Y_{SD ~')~289B,x%qZC(gr4j1�;$i�m� 'O Eq2d&�'2}*�'�e�xn"~P*����`� � ,_{-1}^{1} dx��(k-\pi_1.%{ k^{l+v -  � (k'-2.-'^{l'/ &�� {N�B� ~� ��  G_{#*} � x).�2&�1+��F�vS!%�k P_k(x#<l_lol�!' + ' = Y q^{l_2+l� g =1 L)2}�� #gB� ^{k �� l_1' 57�Beq2F�A�F %� �rq'-�0{4}}q^2(1+y_1�+ qq'x �- pi_2.B>A' B2:BE82& & ~TA\ N.1= Nz`�3=.&�Q9�geometC$2U($���5<byJ��R%sM�\ �:�&�L M L' �vI�O�_ ކn%J�J^{\pi}m� i�' J�6�F�Z���&(&��=��4� } (-a�t��_{TT''  M_T M_{T'� e_�Bt2 8A\{\� { 1/2 & tE�  T & t'} �\prm �k Yk (q�2}}�Q�a>�e7�AJ��� N �# { {�h l')!� �+(2��)!  2 �5� <2;xl_1> 2)!;D\A{ �L �L' # �p#�% 1 &�r&~&9=e=~2� 9�JZ��2�*E�m� c_1} (L 01o 0�rt c_1 0 qi�c)�L'. � /��c"= 9v&noMo2K M �8 )~Im{J} ��\+ �8!^�)��} 6�B8IJ�B�+�� ) ~  $-�2 -�3 �9� R��:�a("7�F| �o' U� }�2��' ;A= �' �.P Z&��-GbJ�w �-�2)^ b�A \mu'!f!�)*(a�M�R�� oA�!���+gN<fe^k 0�ba \(#0)�4�*) (t0ac�v 0\M�f�S S2.S2'��)SR2R+~ BfP ~& l�� �Y & ��'� k!`�%p-�i0m_� ��� @%M%�A� _3 -" � l>(!y�!( -MI�Y��� \2 de+J<?rt�~?:�!�m_)�} �)�A{A� �qL3K6��jw %1[_ = !Y� �+eH- M' �1�w �_1  l_1}28&23B�We?d�s�8�22$ I��H�2il + 1 $C :� �7 �� $�,rea�@obe�+f"�) syme y�pertyF� A^{�YAL�,3Ir!�'��1--ML'-M'���j.�2F (m prooaGv">s5�.�%e!S+ �23}) &�- $AN��' �?�$TpUG�KervEC : $ �v��x"�  '}NU$a��$, ��2�19}), C�" lex �ELF, a^{*ank> ��� ?1U= D {�M�m Aq LIj 2'a�1 3' +1 }~z&"O ' b� �.*�5B�To"+*8+25�n� �734. $D^{j\ am m t ,�#, �! ) =-�m��� ,�j}_{-m -f=-� two �I4 Clebsch-Gorda>�7�~�A� prov+8A�@%I��+�8�8AF".is�$. %F"C*�a�g! aBnon�D6 %�%n��<%�2�12� %isG&l $+1�ET=b� Ώ}7al.�#Q8 page"�"Hthebibliography}{99{*�8ae�.R!�57%�!�!�9�25A@ 3035I9.B(Rupp92} G.  �� J.A. TjonU��)�4!�213i�!��Sam�2$QR. .D4ew-Body Syst. Ik2MI8J� stadmMStadlaC F. G'Y��M.Frankq��5!� 2396�7);a� G�JV78�;2@�!Dbak52} B. Bakamjiaz9L.HK3 omas2�eR 92},"=��52>,foldy74} L.L:GldyF@12A27%�61); R!�Krajcik�Z@D�10�77%i72 keister91� D. K ,�05�Proble�B!2ics, edSAby Paul��@oessow, AIP Conf.9c�h. 334, (AIP, Woodbury, NY, Ń , p.164. c ��kei>�� W.N.�8(yzou, Adv.8.�.)s2�22%29�,U�kam��eH� 6>�2�1Ch. El!%�=�2L6An04401#U00!�mrel8}:b T-S.��LeeI�F. Coe ec m�3��70�86U\dki��b6� .R.h%$54E�jT$wit88} H.�d$T.Corneliu�, W.�� Y0i�A{{3}A{2�98���81�glo96>2sD.�B1�J.�� �Rep)� {274p�%19l.p-�1}2p HelvQ= Acta��3�%6$ 9bkL6�RQ�Yum Me@�E9mA, Sp� 4er-Verlag 1983.b(Weinberg} SG �/emf�1um� or}@`fields}, vol. I, Cambridg*';y Pressin.o4rose} M.E. Rosp> ``El�War>o gaD6um'', D� publ#@;4, Inc, New Yorta�.rkam002} 9(I9Suppl.A? 1��4�x 2000��\Q=�O�Hatanak&?Nuc6 A 42a��82shi95%oShimizu ��}��5�119E�6; hat,@K.F�BG�406�4%27]d���#} �B0ij15A�6E�6� �P, R.V. CadmanL�.!,9K20j 5uTM!*A��oF )q N%� A317w 42�79�� S:�Y6� =��2��179�786�OC B.S. PudR&U JK172KN � b�i&�A,E.\ Epelbaum5#�e\�\ C �)�64001� !ÁkendB� 8document} @�\class[a4� ,11pt]{WLcle} %:'0fleqn,twoside2(Pusepackage{espcrc2} .]icxU-[fi�dsr{4]{�<ng} %W@d�N(TeX's hyphe/3 exce�clist %\{autho��IcrezKfinCGal� Lre-commend-ed Post-Sd�'e1'chGr} rgee�wC� h2p=�3-�:cay�S $-daF }\pa�)igskipA� Jouni Suh�5(\footnote{I:nk �$ortelainent$ assi+WDdra�Be -kZCi�Kt!�; is!kn�AAcadem�� Finl|7�Ath2en�D Centr�JExcelle�PrY mme �F`-2005 (Project No. 44875,5Ha�(Condensed MRVE at JYFL).:3{\it De�3A��3Phy. "�A�XJyv\"askyl\"a, P.O.Box �d FIN-aV4,:&��Q��=�> abst~GCe evalui�!*n/B>-(NME) % �P�_ino douYM�5($2\nuEP$) IC!�2lKQ660V64O�iVon-C0bquasi!KA!O dom-�tI_F(pnQRPA�^ add���aIQIA_]X,cex%5 of as!"E2N��- �'!`GparamC7, �#rm pp}$,`tA��IiL�Yn,detail. EvidE�is�E�@at it 7bTisMi�+o useT�'eriAfab+lf-lif�>�-� to1 a �$(.�. Rathoarg��a�eK$ in favoura�9�avail�Y�If�7l�Ga }i%,purpose. \vsU {1pcM�Y��\��noia�t \�R�bf{PACS}: 21.60.Jz; 23.40.Hc; 27.50.+e; 60.+j��NfWKey�` }: D]�E�,� ��,�Ha>�as,Ax.�]Q��Statu��^.�B��B�dnewaT��- =L-�Reg ino-oscil�JIUPs, Super-Kamioka\-ndeJ(SUP01}, SNONO� },P LAND KAM200�CHOOZ  APP9�=F confirmedVex���9<� mas{Ts.�Z^np: probe j_�. Gs�^�a�Me�Oabsolute"BqJ��. O�F2Jra�:���q`�RzyW�Piveh�, $\l�; a9 nu}\�P le$,q�ed���J) �3g)j��-�� ]. T�/I5'5�!Xn�edH��pab�N:igd>| "�\(REPORT,Fae9}1^ mix� %CIVET�q]associ] CP�s +PAS02}.CVa���`of�, DJVD)ly^  accu�K$ly enough, ���Y5t =Y.S iR�)��- � ��)� On�Xre funda� pie�Y.lQJeme. inn >���~]>�m, nameAX��!*5� S0be a Majorana��, i.e. Wobd ��who�&!� �i�[n= s coincid e Z�t�Pimmed!��>mpl�A�[Zconcef1Z$lepton num��g!��2�kunits.�1�n�Oly� �Pvarious *> hor�gowbey�A~1 0dard model, �HasgLd-u�ovUE� s��� ic extexW�� Z Y� G�juabove im�7�i� !,Wqant��li�!v)�� � & ,&�Xlf!b&�MV�uH �at� mc��I��Uim. Bm:�j^~� . Lack6i�cy�! 1<s�.�is>J' sour �in>C.zo�7Q7�2!� CP � M� .�>-N�6�  in view��pl�\ d near-fu7R.> � ���TQ^�or��Pa:?�=�O�)  TAmi� �E���R T; i%dA ount=�. Con�f�"> ��� ^� ^� ,Wa�1�� elec�l��laDte,�� ceeda�a�3turba�process_�Qi|q�.Ze can ��bO! I$test bench%(!�Չ�s,T c� � oeds vit ��e $1^+$x5gu�C�*��od�us. Suc�in ]db��� � ��!�5 er�%si�_b��NME's>�FV�. Dur xe�!��dxb�P��� t:"R �P dao �#� 2� r&5!�%d�boLayp�.�m��Y;"��SUH98qv aly� -i %�g!�F�).of-� be"@ B!5Q�^Q�N�DD , deSW��ou]h�9�oeEg&�9�i�QAfZ �O�- �ttempts,E� lem�/� B��%V+s �o��)�adsh new wph� int�:�qm .e��b adjust�P�&�9r2� �wbod�8t. D >PGE}G;\ spon��� ngthjRJ _RE�a key is9V�W!5mid 80's� noticed�%� work $VOG86,CIV8�$NME�B�a{r�VsW��to;�SQ& *�cso-�_ed9$$> )�. i 7 hand��.�:M��w� �Oent�O�.�,��,Z(ussed, e.g.HB�2} ny� ! o&` ��~c�p to lMaU!�! nine yearnm.I�se�r,51 renormedh (pnR�8 Ref.�D4ite{TOI95}). O�b�,��͠���2�U,�w_d%72� 0,STO01,ROD03}�\!m3\5h�all��5A�f�#!8q���Pauligl�d<ciple d>!,-}4rmp�'ngt Bbo$_ comm-JLM!�$, adopted �h L leve��p� �y� i�JR�� 6r? )� bifermi ?"q;G �d,}= 9�� fqs�j�] �N] mcXU N �F�.P �qu��sc!��p)�SUH04} (�|� . }�a� ai{umd���" N�a"!8),�r�� =xs�sugU{O�CrtcomA " e overe�M�f�j�1 -<�oa9wed*O Hc ?z����- e #t&�Yuse"" the Zr2�m�b te���!)� 6Q��� -mass& (����  da>O -M BZ�� e esOWialAx !% method�@s�li�aMllows:s���* �D�2��-�(k\>�� ) � bB  �Y fittA4�2�? d%j-[u^J� exn�6�>��_nU !Pis�ed�.��7nAO� � ��( -�B( NME.�a+i?a�A�uck madei�inMѥ�}me�,ing x}cL pitfalEe5 m5� Ue � A�"� sNnn paren^am6�tM!8e�_qu&�͂s per�ly�j.`g!\`~Z�* `="A����ach"CQe2�� � on <27(s� To_an ideai�)�{d�`.��?�z)�ve, advo�bM=z,���bstruc� wr�dow�'A��ion"�g>�G h�H, $t_{1/2}^{(2 \nu)"��a)�iA�  r�iv2al �0, $0^+_{\rm I?m��6* +F*u`*C read*�FuE�$Weft\l^x B�(0} ^+ \, arrow F}^+)*=rE^{-1}= G�\nu )}\c�5M ODGT% X! ^2 \.mB:2vbb'��}�Z$ d )[�zA)nt_Dl �%Ym�p�#�ic� * ��}�� ar� Gamow--T_>� , $M �{�� �,Z�>A� ,)��A�tew!"!I �\ A>m & = &|@n}�U 1�F}^{+�= id \qCLj \sigma(j) t^{-}_j #1_n5)}{( {�D>�KQ_{D  }+ E_n -M) I})/� rm e} +1}�^\no�$ \\ & & ( f �x��M�IA� \;29 mdgtU9pB&]�be�:� a�usual-�-�3lU��r F ^-$�� s, $:ѴF�$Q$��,=t) �gQ� $n$tS����5e;c�g� �SE�u� nd $>%�;�m3 i � . A��.I��� osed�{�* � K measuF ^� �2Y)I "�.=�{U �c�H.� ]v�7(!Ni�F�6�Y1�  heavy�U %eiG&VY/m 6+$/EC.^�vD eTs�vC in T��~�5tab:t�A�5�)��believ( A�6x-�q� be&aPp� � �a� �2 s. N�r thelu*itJX�gad 9pbetf�#)M&�� 6� } ~��qv*$%!(}[htb] \cap�p{E�al EC-%�q�-d!rm{T(}$ $\log ftm�i�%�- %�>�Ʌ}� :�-E J�+1�0Homp��,� !͕AE�V ��Bw "� 7|\column.�� abel!*QO %\renew<`and{\tabcolsep}{2pc} % enO F�Z ing :8��tch}{1.2.;�)9)��!�' tab�$}{l }\h6�f �� &%0[MeV] & Init.%s . & �~ Mode/5�&L\\ 2^^-`!�& 3.035 ^{100}$Tc 4Mo & EC & 4.45�{6 {GAR�+\\ ��R<RuIi4.6BFIR$/B#* 1.30=�4}$Rh. W �� �P�rR;PdHh4.�B #+ *+$ & 0.7mW6}$AgJ�6} W �9N��>;C>�$h�4.2tB� �.* 2.01 �10� � �%BP�.� B�4.7N�J�0.51*14}$In�4} W �v*.2;SH)�-!v�6$8QN16.�66�3�BHA�5A�9%><J��%8+AB28}$I-$ Ta�%$5.�f�..:X:.#6V� #6�54 �30}$Cs W �vGB;BaH=�5VB #6�31"36}$LJ^{ W�ZS5�B;C>$?N��-�.�� ��/�} F �(,[un-cut �|M%�)�,��� �A]C֊� � "��}( semi-magic��� 6�D�u�EF�  q�Sn�c genu�RwBoVhOii��� �b!"M�.�bl%"}n!!I6GE � eq� )� ��?6 �?��J�&=iؒ&�� g#^ s  meanw46�Wkes'a�7s--Saxon� I icle&# j��Coulomb� Ax-orbitt"1,Bohr--Mottel�tri!�BOH69�>�val`)z+!�Afn��5C on�� �s &*o�j}W o�{�q "anp"0�F�  surfac-e s`B?�N a�$ica , bw!% one-`*u oten{1�Bon�e,M �(� oIz�� |G�X$x techniqux&f5e-s���).b )8�acc�" i"��.�yA���A#Ay-�erK A�short-�)e mon%u.'��2�(C9$ZP= �!multipolY Q~-h!�  'nels. D�.� .f%�"0xa<Ip CIV9Ap�[s=#g.��nc,�ty�Eh"� t#3S;)3!BCS=Ti��a�*�)paB{LA�e�Y,P{�Z�P empi!�:gapV�%.� -�3. U�sa� a� P#e=1SUH88m� >"�0��1,,1J�!)f+aAY"m1�)�: "� 6=�4r1+*9+loc(qf6gi+(r�x anceʏee��� �I]�T1�ca5m� G 0!CH�(6ava"i<8]��i"�Q"6$vCJi}��.e.�!yV�ru o!axinM�!�����g :Q) ?5�:-U{�6Ts[width=13cm]{PLB_fig1��:�$Panel (a):ea�#E�"�"uZ�of Cd�3g{kqof2�o��q=&.(��)$,!m&�#}�!}s�~*h!� ribue�-d:^1^+_1W!�I2�NM^� exp.����n. -Bb-BA�(-branch, EC��EC�{ righ, (" �b^-8 sA�&�r>_ �s (c)i(d �esas!� b)b�� \^{I Te&/,fig:gpp-cdteMXM���ǜ�2), pQl9�$n�V���,�P�8%-a5/�Y�$"�% � a rough7 &�.21�J�Q2&�%5��(rizontal� ,�c] s vav�"�$F�H�oA�u�.�.t� �� D� is*�EVar�+"{2� erro�l]"�If n�3y��/er.~e axial-ې coup ��,XJ rm AA� for �um-g a, <i,}�o�{�w��'� poMjo� } R*cur s no��q2�7(e�,)\simeq 1.03�72�&�'� b6�5Vq denocby6��� in b0!S�!��? ��2� B� virt�*�� E�V�.5,, _1�#%P!��"%|�0��Ip�1s��_�� e�{�r}�IH� o �1y�as��p��)�*G'�d-3 do�)ad(SSD),"��:1v  (aC \c\'� ���asl �1 SSD��>}e}sp�EI�[M3*8 ��r�~����&��c M�Pg�$rm�[ N ^-}}��[UɚN�.1P :2vm���� a]��"�F�&?6 a� � ��S��b�!��Pb)!m^G~/i�. marko;&4gnitui.1���a|,Z�10-H �!(EC= K$e��/�}=T .� 8$^{e_Cd� AuF&Z-CQb ���i� 2u ��a��A� in s�*A�s� "��21�o�`� 9 � �;v I?(P)�ŵis kind�a6�%s"��%+ > Vi�AOeAQ�sAE�pY$83� h,"*3Q�2 2�p�,. �t8&(��6.X�ln�5�flyU s, d$�Q�fP"�E��>!')snin 2'Zm. �RZ��"�!EC}��1.4F� 0.24$���6�m an9��,�G� to �F�1!V���M�EC�:�s��>�}�Em�VO PsA�mp�'2�rrU�l7al!FEV�, yielR�$f~&~$ EC})& Q }�(th.})c��$2.6\quad ; Bla(^-vhB$6d0.}�2�"%�c�B�2iY����xZ MAx !hU�(too fast anb e��". much#s~�a]"). F*�)UD6�� �x�I%F� �l1!;%� nAB�^-�0.85$9�� Ar�-��� Xonſ6�%Ba#EC�"|(�X5L2"�.�2�m��7DU� exp}�$�3J�e�A�!��at/ .� A}$.f#�yD U M R� f)�2� ����&Q5�F�zl!� to a�: ably*�/ m"� �������|%�B� FQeL���e2� ̡�. �i��W�;:�6' �BXe�1�i8"��J�$U� Q8� �x ensae��-o�YI>anAk� ;-Q.oo ��2y NME."�!j�BGif��Te�DA�2�#X�i-B��a/&�,9�very �.s4�c�or*� !�Z,� 2W 3.a-���e�� ��O�j&�j��s3%E���ci �&9tI�:G�;�*i "� ,'q@�%9�m#.4f(��E��]�$ cloi3��c�:�@!��:��9�. H�O5�a�Ah> peakaQutal&f sit,E�1A��O &m�!�/ Cd� DQj��4er>�)�,Vc)�!�.� -~53,�jf1�W~�0.8��*f�^� 6yR�,� �f �32����  (d� Z.�l �y ZF 6�V� 19�) ��g 0.05�� �� � !��I�� �� �� �� 9.7� �� z� 7:�/�J"�� e���Q��h�]� �&� �4$�� �� �� 75&� � ���ly�g�# 6��JF� to����m� 1.15� B 3 3�YA}=1.0B:���R� �2�\ pp}$�� E�� do�t&� �R� H �&�3�L�� �&` �6Cdav!.�$:b�h$�,BdZ�ZJ�!V9 play� roleUO1.o< 2  tells u� ��C i�:� B� 5d�C �C ���2n 5as^�%��2� lPA�B#E  ^{76}$G� dL 82}$SJ^gesq �"C thir} )�VoE�ng :/ �Se will�A�@E�� A b�aly�8alo�Q�Din�  prevJI asL�A:� j �G?�;h�6K%,�:u AJ FE A�rUOist fz �& l�A�t�Z�1QbT�'sa�I 1�O� � ^ 94�>��$!�>�:zN* � N bZ %�. ��!����9.J|_>4V� 52� Z� 9$akDZO �+��*ڡ2@&�0 ���&M �0"�#��3.9.� +� '6.4N� g�ml���vAg'�ӡ ~"We!�*�"1,aa� As, �$2�.�}h�%=6]%�2%Yow+J�R�*hfJ��b[mer�3* u�L�is.�� A�!e n�$exap31��pp6>��G,nr��� }e>�! !Kr is �{!Tb��2�"!����-so�SSD��not ap�b?Z�ed��D<g!2�� V�:?)uE�b�M�1.07$�R�Bef� VV�3m�� i 0.1 leaA�urnx�?�%.��4.0��>=p "����e{n'A%��2�A�Br,ee a $5u��%a.D�� qJ�R&� �Am�~��� "� q ion{ּ7s�ed�of76�7%pf�.ll���G��g&!5&&"�92�M7�M7ZM7J7�*7\^{70}$Gr2 Z}4q274J%G>[2�2B4,8}$Br &��8 "X78^%K1m��4?*80O SO�t BO5.5Q��2lthk$no&B&EC T�A�Tb� �]wa&!"% !!a�Sb s,���_3 uD>��� Eqs&r�Age} )72�X)ѭRKZ� �]�H1 IGreĨ.  �lev'-��.���;.��S a��2� anm� p�0�. alog{V��e! �-GA�^"m Br""!9o� �,e�wN�2}.�!����12�W�N��lR=pr1EC�� �0�!�!1v2�  =d8 -4.8� ��T Y`@ ^[��W5.1-5.�Euld sdE��&\ �$�n_ J`�� �E &=��:n*�)B�QBfa� �. M�> agre����gXeǰ�.�!�f�\2">-G�'�6��4.6)�@� ^-+}� 5.3$��#� �"ae:JI&��og�-��(U:�'>�F#�-"� 1� hF �0A��do NMw�H B*�4&,Isi�6�� n sa�RmH�Z O )*�+P<`>�Q`�" %�^�U"z[�vA!=sFV*v\ ]� : cw)n`ofS` he%g6Y6 *}Q2z$? nspi�Ao� ��� 6pd�eS� ly!�4��:b6�6� demo,IjW�"&�cd��r��� � E��.�$? �� ! Vb&a� I�cct,a2�&h*� g_�'FqJ\%%>�>#aA�dɾ"� z�Fh&Tr-Ѣ2V�x� i6��!;d8 >vH9�M�aT"y��"�O�'�� G�7:;�!l*�9s�d,/ ^-,&�46 , etc. A V-� c[ � S�JB2BS �she�]rA�nf$fo/�o � 9O�� cernQA�L" 8�6&�E!>N��AY�]8*n43�\�\!���BMo&� �2mo>�2�=��J� �Q�2� ��"Ru��mo�,A �!��A�h�N&�^�)mo&�seAVwh X& + ar-Nur3�"�=i  of �V //O��k��3O!�Oa�Ź�)>� basimZ f"� T5 ne"Xcq.�72M�2&� "�%�&�Z,"�for$^{i" m�� /h�1in NO �xto!+=>!�pSj (a�in.;"0 R 1.02s isb&� _IhDT�H:9^᷑����->��(&x"it!xm6�R&u�E�%�9��Ox� ow2�j� � �H"%Ea��fR� !�>�*�.�2�v&Z.��,y�creacha!k>�@, m�7 K/IQentJ�I!*�IPros (+� cons ($-$a2� �Si�^toL!"�.6oSIe�ex(b;�A"�d�%s!NL!չP"�3����V��P6IbZu�A�/oraE9(s)&"@ *!F'*1 & O] !�A��KE|ȡ��O��qufit%�&J%�&���Diro�L!�(grass-root-$Z& Two��Je�) �def.�ܹA�aQ�XJl �* ma�fBv K& a good*> BC3 M�� HRb&M!�8��2� >[�3�[ &&�d � J"� ��FE�8^��!5]7on�Advis!�!ocheck aS�stI &!Da�2��XG�&�����VE`�j�)?+A�o�5 & L�+�j�n� �e del-� f% CL&)�dE_�f�.�f >&` >�‰�&�'9�6 & C�*�7d�)o4!w & No} a possibl�։� �fbEdde<�n"/>s,)�р�}�""L @$8��#j�)�toC>��H�mƉ�E"�N+niM*�Z+ �YL' �noXfeAd�F y�( KN�2}��TZZ)!9�Bal !�7س(+)�$3.a3-)$DXI ularvtISu=R< A�$�e�7_h &�d �I51:�C7��B2+$�a�HjG�*�B?;�p*�Z���;f�Y*``-"Fa=XEe�d�t�Japnt3� A�``.���''$ �2"1�s E���$IV �EZ\�criH� 8#"y3/^&��E�!�o" M��/&�(�7 �w$�#�meaful5_-�. A"�[�tsN  0*��*�^Z�T3}m�%�o�4�iف2?"n�^ � M^J1� �.uH�. BO�few���/s *� *c]Ų`�].gk5�Ao&T�2���9��a%ȩoQO��-���cw�!oo�'!>!!�to*�h�K!��F  &� !�al^hpAU$R �cxm�AQÂfer)�o �two�L �Yi 1� reveal6. 4e�N%�*�� L M �1�7�EC�-��w$a�/2e��t��? @� ŀ��.^�L�g!")�ȣ��@Im��l�raw E`"|b� ( - �B�.��#H *m�6 {��(necessarily�:��^ ��  v��&�s � ��.�&� QjAmuRmF_�� warr�rng ei�_ pl$O�� minu rk�-WA� beha(`�a�"MAl��)�m���ne�hbTfin�l"�4.fix��� /K�[X�P&�I$KMh!n&�c ߁�.,: ���&c IW5�Cr*3y��>O. J�ia��$��, �1!�Z2V e���2�� ��JV5yp"9a ��uN"A "�B%t] !\j� & i�� �? .�x );a�� IM^six�ah5imb�H!�%fd���ac�C� ���n�E�?E==a"�56?2mhiH�" "}*�<zI, �� pP"�.%�o�6�n�[ �#��u��B8m�� "��V��N assu#P�all ���N\ 2�E�)�"�+�si�e��F��F". �l�H�Q(:y���p Iea�6zM. S�� no exhaus�cEA$H�mM@ $� =�we�P �p�XatH�1k%4�ZGԉ�l -tND 3}` s��O=  "2 eE��m��bZ q�F�ĉU�~)��.b&nx sh�yb ��~A�r8)�Z� D. �b|]hnےM}�&m}k} Coll��i��S. Fukud"� P&ԒL��86 �� 5651. �~bi?�S�} �}:Y$Q.R. Ahmad&��F[9[ 2) 011302*��}"�}:`H�2'�F^��$2003) 02182^APP99�� App7jnio� � � B 46��9) 415�RT|��ĄET O. Civita �, MI�30&�8) 123J�n$} A. Faessx A�8F. \v Simkovic,>� �G 2*�8) 2139K�|6�MJ���. L A 72)�3) 867LP�|A#LPascoli, S.T. PetcovVWފdejohann�1: 549 !�2) 17.Y�t.9:Atom.-� . 61��� 1286�&n2�>5QZ217.>�r } P. Voge�tMA� Zirnbauer�Rו �4�86) 3148��r6o,B�T�~ moda[ V4B 194 (1987) 16ZUHG�.�2X%}]0>�543Y92) 64.��qYToivaY�Ak.iId��95a0�STOғS.-�ic��H �@Klapdor-Kleingrot�!�Z C 63E 1) 064304YR�nV.�Rodin2T8�}�1�,. C 68E�446bAH4% ��GPrY�@of NEUTRINO'2004,� \'eg:3 Fre, P�0, June 13-19,�4,�a��r��`A. Garci�x.wC ;�3) 292t + R��FiVfone��!�hirleya�Y.��hu�MS�glEX d J. Zipk!S\emph{�4�rg �Ns ���A s.� �0.1in^�\� ۏx: 36.10.Gv, 33.20.Rm, 13.75.Jz,� 10.Ef!u!�9�* 5�&�"��I*�!Q&F"���j��XR1}---�XR\�-!�h�icZ9N.,$n�rD�.pr� ple ��um'} !�-�#�1I� main6 ) tool5�m�rMNI� plac!S>�*:�, c"q灇ng.�� ar{K}N�"C�1S DEAR�q )V��n�Y XR4}.m��e9�Ix 4�S $K_۹90��J� }$�h:�:�L ��V�$$\Gamma_{2�)!��!W hadr� k-Na&�$2p�. U�uly6[�*_a� �"� {e�"�eQ�casO�sZT . RvI� IV5} %�%t��n�Fof ��!:N�np$� ate. B�E�9z�3:p2p.�l��*$meV} = 3.0I"10�J� sec^�yzR*�4��ll"�2 *�0by Koike, Har"��Aka��-A�����re���h�8*)V�Eu alphN�I�6�8:%�e�ty �%�a7Y� > 1\,%)& 1.5~&�\�1a�_w�0 tinu�X|�!influ�@0of strong low�--energy interactions on the transi  from� $np$ state in kaonic hydrogen, which we have started*X\cite{IV5}. We investigHmradiativ6w�$np \to 1s + \gamma$, induced by strong lowV� and enhan 0kCoulomb � of($K^-p$ pairg>� Oxtend/ result%1- �deuterium. The paper is organized as follows. In Sec!c 2!5calcul9 tes ��!!n �5� 94 �4-4. �-M .Mis taken o account�!� form�@explicit non--relAisticXwave funQ�%� + e mo%= .�s%�qfe �Greenffor;1�ioU" amplitude t !jp--proton {\it Bremsstrahlung}�+ I� K^-  Y� definingrr!� �9�atomic}� $(A�)_{np}a" 1s}]!t,our approach2q3Aqmodife {s|.�V�1i�SQ� !6�, + )\,A ��8e\,� � ��./J���\Big(1��� m_K}{m_N})\,a^{ }_0\,�5_:� �Kldots, b�eE�A�I2ic charg"+ � ,such as $e^2� \pi � $, $�OS--�C scat8 � engtha�Iz ��(IV3,IV4}, $9^S,vector potenAkJ�qquant� �Y�field�d ellipsea�no��.f orderR$O(e^2)$*� omita %(J� Eq.(\ref� 3})J�~� ��m�[ $yqKKpe -~ E+ m_K/A�\, 9�\, ���"� figure}AXce!!�(\psfrag{K}{!�$ p}{$p$} g}{$I� &i� hdegraphics[height=0.30\text ]x4kpg1.eps} \cap� {F�W�V� !|ŜFK�<*2 Z3 caus)WF62�}m01 % I� F�limit���^� RBŕR�S�F reads9�Z_ 4%�6a B� &�  = F \,(� 7 Fjfq i e;  }�� e}^{\;*� Dp},\lambda)\cdot( %k�  .F�b)eF\B8 BQ� "�R��� >�4a�$hould be wE�ed withd��2��*;!�A�/ � exJd*- sBx5 Sinc+2g My So s & $symmetric,|grx ) $-�$ lAq to(vanish� b term�pora�al to=%�)�b$. { 0refore, below �k itdappear�y2B�e(!Ldenomina�' � ��Z�"� a� YAis due1faca�a e virtual��$--mesoZ���J��p�cally  � shell. O*�g�I �FA` b��^m s similar wat �has bH�@in��4}��derivMJ_  Erics�Weise) mula!N!2��sdJ$TE88}� 0runs parallelTB� E��F Atory (A. EFT)AcA , ba�@on Chiral Perturb �Th 8ChPT)�Gasser� Leutwyler-JG83}? 5<appli�$Mei\ss nerWet al.} @UM04})� e systema� :DQCD isospin--breaka��H6�  corrG m��8 level displace�Q_$ns�of�!�� � 5}oanaly!F!_� �ve agre2`�!p-���ofE��&Nby=^' s� p �%Y, 8�#v %<�xperi!al dataW,DEAR Collabo�7)1}. D���ee�&k$K"�aOini� !�final �s ]TE77}-- jLL65}�2.�.EYJpN�changes� fz�i5i&&M�d &� 1�]�\�eq}>R ,\times\, e^{p styl� (pi/2ka_B}\,x1 - i/)�N2q22�i/j�a_B�$ \mu"� Bohr� u"� $ �$--&3�)*p)� MA72�vg6!�F� z/r� z�� 4�   z}{\�y%@ 2:Vp-\,z}} exp�\{�[ \,z� 8sum^{\infty}_{k!$�( xz}) -�arctanI.)]\},6�:�\p:�%��)z!�~8�8F� � Euler's �  ( = 0.57721 �$.�. �� >� 5}),���into ���v.i�z �z5 ,����*&vmodel���8� this a�<�~j �Y"U zero--r��t�� 7A�V�r3-�A�}y6� (\delta^{(3)� :R�ich� $equivalent�H"` loca!?>� $�$--.f�\,:� .�*b� N�.� cludA8!�N+�  $F�� ��uB�44}) becomes recd�"wZ�8!�:�&&i��� �F�� d^3x�Z<\bigtriangledown\$psi^{\,C}_�Iq},vEM = v� '4 q}\,F�/Ɂs����͂6B5:� *���մexact B_ UC2�� AHr�#*� :�*inc� g..�"�_I� umkq}$. Ita�:C& �i9%U! Cr�JX-�I4)��%)�:�qQq.!r�5F( 7,1, iqr�Z.\,B:�H�BHjF5�$confluent {ͤ!D,p. D� or $>�vX �B�5})!�!�res"w asympto� Gfu6�! $GJ�r},0;k� �JM3��0AZQ 0; S n�1}n a�y�I] W_{i 4,1/2}(-\,2ik r>T!� �.�}A2> at $r��U �ere $^o5� Whit�#r"�-#%��""f!�outgo�;&Ne�disto &bn"�2�%� %|*�B� Ǝ! we get % z 11!�:� � .=!.y!z*�o+ , 4\mu!�!\�,*�+*+A4. r� &&Ů h:��t�F�RUA���� " �e. \�:�e� Oݣ ������ec).~�:� %�' main��tribua""�l grals� &�c  q}$ �&)reg#,$k \ge 1/a_B� $q > 1/n I��.�s����a� of o*M>�co�6afp"#" n$ ropped, s�i��:� i��}c- !. q}$a;_y]�Y��y� basi���^1�"� = q�!IZD}{3}}_{M- ,\pm 1}YE� M} (� >�!p.�!\,Qe e}_MR� � �e�f�$mp � e}_x � _y)/2}E- e}_0:A� e}_z6!9' unit-Ns�(endI',to Cartesian6%�xLYyu z$. UsingBK 12})"W-�lJ��)I�|!���F3ffa��h.!C�R�P=� I21e}_m}{)�A=b� n� F�,q��#6�F F��-�}wk-�qey�!�Bx s �#0&]%\F% �ǩK�$> BA$��N2 �F_�(k) =)}8)sSa^3_B}}{�$k^2 a^2_B)q( ;,\;!H� 8�>n^3 B{&( 5#32\,n q�k bn^2q^2 d03}\,C^2_{n - �a8! <Pq��( c+ oV��%](z&. Gegenbaue� lyhal� !l*  e� MTHV��"6-�^"+i&a���mak��BS�$a ][:� �>�6Fk*�'i��}'fNO!�i]*� ( &\simeq&\xIXF.1}EMZ\>� �'1s}>�v�6�N���.�,��]�6�npj�5jE�A� - 1}{ n^5M�:�.�np}�(^�+-H@.91�\2p3.52, 32.22, 4 85,"� 9cSnpr�/ al phases� do not&� ".t-&� ��.u�& & >!�% 6�5� ~�-F :~&�i\,.�AjE% \,}�-6# � 9]M5��JI F `�d>3+ �U�M�E#� AcQ�>�� p� ^!]')}J�!Q2Vzx/� � eq]to������)8�4�fj/\xi�op}} 2p!�:^ax�#n!C"@b� �,�rO!� Q��S���rc� I�)� �{9��M�7A� 3\,|Y�|^2J subseqt2F55 �$>�0W�0$ conveni�"_- $6�� erm"+~��-�F��o q6�5iCaE161^4��epsilonA� 1s} �%�3%%� 2B$1isr��de� dnt DGBTT (Deser, Goldberg 0Baumann, Thir(�${DT54�Truema@ TT61� �!(. SubstitutR� 9 ntoB> 18}) � ~22�)���,�'I�:�36A� �)�J!g(:�>�;F�]("� %4 � nume�/ valu&�5�"meters ��1s�h0��2p}$ we !�0��0 =4.3�� 10^4ܒ e.�83sec^{-1r�M�� �� re measurdXrm �3>re�*!\or /al)Za�!q��\ iIV�\2� -\,2��."�5�}{2� (- 203�15) + �(11 41TeVN}Insera~Bd2;R~2m�%%���&� ��we e�~�2y%��a� (2.3� 0.3)Y�9>sF�AccorJ�7sh^�&� m :�ѠsC.)���6J_&e8! !7)4=8>J�Th�!�s �*�8compaac�1�8p�7u&ic dipol:�=2t(.�=s 3Nt�7neg�&a��-J%0:j��=Gby Be�" Salp�;m��ŷ adjuse them�C%.X&_Q�_{�} = 4.0Yc {11}>` �)�_{�a�1= 10V=,p�'(vely. Hence�+)�3 y�s&L J� ]�!$ 3pjS ,&XEqs6�02�0and (.�0 24})*�?1�lowR�?,�D up about $0.6\,\%-@0.3  �2��|:|,�?9t&�#2(6� shif� �-d�2Az.Y�<v(n�-F@ ,��$by Iwasaki�' e�'%*�* KEK 2�()M�KEK} : $"��), Q�1s}�((- 32�=64, 407�\230�J$6me��m� ~m%/Bm>.�incre�+ by a�E5ree�b>&�>fa>�A�,6�0})�easily gBed�q radi�22�"�>~i�d&@i� �c�B�<b�w�/i�#a�\23�> .b {.f@ &�)0f<2�^ Z^ I�.Z  = 3.6��4�� JJ>�b�&�> m_d/"H3d�91 Hb�>�#d�D�= $m_d�876NCkAon�> . R� l�.z�y%�i eZ� Uium&�/�Emat] � 4}~.:3�>�� � -325��60�8'31 5.�J�j� �7)� "�V��A�J�NH+.He�"�� &� n�+3l;I� OJ�*� � (7.4� 1.8*� B� ,\2�:h.c xe� �) h8.�0.1i�` F` ^8 R8 ��: F� GE �9 "9 E.9 yCwe�V: 4.8��b� �)�B: 2z=:: �%us6��U�F�!�MrN9:�|D J5y'��H & 1.5  $0.7� F�QM �� BC�� Qk�� +� �1j U1, pred<@� arretW Deloff� RB99}: $ "� ^{(d)}� m���((-\,693, 88.A:� EB� !�� Y "�)6�.��Z� mo�Ca�; ree �1.-H&cH } W�L+5e b�6�*�LM � 1�hMe�F�B�K ^� A>�Latt�vV?'��%p�K^0s/ ��8f�5--IcZ�J,U C�B#Cs m+ d"dy�_?*��[.2(��s�(�N�6spond�%���=��= 1�6Q2.16})|C��U*�5"W" �@���6)1an"1�ogous tE;a"~ EFTL%ed�6P8a�~O8%�d�9 69�K� K?��Ad$*�-�}�&s-�7s�E well&b)2y�f!Gt!�$2 G%�!�ic�=/L2,'"Af.6����).�A=*� .� +6W ���"�.%�&�E�2-j�2-,@ .�'Pone percent. PreciiM-is�( $\pm\,0.2�;��eE��; reach� !`&� Ue PSI6y PSI1 <��t :2� Z9>%pi�H�|:��;se�8�e �(d �,accuracy�N�$X$s4y �ra%%y0< s in>� . Msf�77c6" �>sa�6�D> same�;of�, wm@ di;�-�a:R$ZR:!�B�a�6��q$RU��e?d^ku�� �^�,u�tI=�&6p��E:Ys{;�Tj���1 B&MP,*{Acknowledg%�&A*�@efu�@ Torleif �6��o�9fruit-!��P+,Tb�O thebiblio�Dy"� \bibitem{XR1} T. B. Day, G. A. Snow,%qJ%chmX Phys. Rev. Lett. {\bf Q>X61 (1959); R. K. Adair,j24383MPo H�"2?k 127}, 636;62L�2�E. O.5,�S@F. Scheck, Nucl. �B S9}, 450R706R(3} E. BorieJ �2�A G21}, 146H8:H4�@Koike, T. Harada,TY. Aka�B2WC W5!]79�966�5UP. TeNM R. S_ yanoRO5}, 73O76O6}!�P. Faif1{VT�?, FraIi%=�ics Series Vol. XVI,pp. 637--641,�ApPHYSICS AND DETECTORS FOR DA$�&$NE}--[D, Nov.16--19, 1999Hhys� A�TC�deecKX!�H. DW};:�+$ia, pp.185!w6..7} V.aQMarkueE%7TEeJensen6Sm 69a ,318c (2001);�aS. 4E :ZVI8a�537HEurq� J. Di%e�165& 2); I�w�� e--e�F%�Ņex�5��� in high J"d $s.I. Cross �s.}, pI�/0205076�{^{|I�./ J�7=��A A�Cargnell"��#%("5B ), KiM�,ear Clus�!-- MiniwM�d, (IMEP, Wien), 9 FebruaryAg4eq�xiniseL%�Hadaf03uI<, 13--17 Octoberk83, ECT$^*$ (Tre�#XItaly), hep--ph/0401204=\4 A. N. Ivanov,���Fab��H. Fuhrmh$A�A3a,A� Marton, K(. Troitskay��$J. Zmeskal�_m�V�DJhI�VC*RX , nucl--t� 1102.��!��J.�V� .�6m���1e~4);�310081=v� �� E�eS ��-4QUANTUM MECHAN�JOF ONE--�S0TWO--ELECTRON�S}, Sp&4er--Verlag, BefX�R5.�.F&-�A. Hirtl2��5B&V��413Z26�4��ƌV�op�5)2f06053=�r T%�:t Wo_ise, a���PIONS%�@NUCLEI}, Clarendoa�(ess, Oxford!�88j�HA�G&�HH4 �H,� � � 2�321, �(1983);Ga�* ��� ppl.�X86}, 25�~0: refer� �rein.A�"hI(, PiN Newsl&" 1�" 9" Ulf-GykI�J6!�7� 97);6f Ann.�P�  235}, � 01994); G. Eck���g. Part.���G:3�7 �6�APrn.�5-vF1\58 ]06�.:-�27����198���)�,>�N?50� @�1*.+158� 2!_8!+)HVA%3.0 UM04} U.->�U. Rah��(A. Rusetsky>'� %K349ep�=ݲ226.<kIVn� Hambro, �of� (NY))�10< 44�77)�)< �%1)�9~62KL6JR D. LandauTE.�Lifshitzj7 >�aM(}, Volume 3a*Cours�Oet�NE(ics, Pergam�� ��65���>a HANDBOOK��DMATHEMATICAL FUNCT��WITH Fo��VGraphs� !d?M8al Tables}, edi-L0. Abramowitz fI Stegun, N� al Bureau�St!Brds, A�M%� h"� <$\,\bullet\,$ 55�r7/Q6( S. Wolfram9�, A SN�D�?�AG Comp�d}, AdditO sley Publ�0ng Co., Inc.,!� AdvXQd Book���Z$, New York�2�-�".�.2(.K."+.A^ W�2.,E��9��77e*54.�?.a�L� Y.6� @2@�7 1961.?KEKf:?%� F=%^Q7��306e��!Te2Ito�p�^�%2X���236_98.���C!J&A.NP6a�02520�C99.R�( D. Gotta2� O4ica Scripta, T)^10�Y94�33� ex/030501A�endB� W+ docu} :�8%0 espcrc1.tex $% % % $Id:2 1.2� <0/07/24 09:12:51�ppA�Exp $^+�dclass[fleqn,12pt,twoside]{�\@cle} \usepackage{ � } %O�J�"OrVce�use�,LaTeX2.09 % ;M[.y, � i�, % if you wacJHY Post)� �Xs2�t icx}B�(landscape t��.5[ Ir�Y ]{ro�ng�put�r ownQi� #;: %Ob8newcommand{\cZ}�Z{Z}� �m{def}{D gE}[s�*on]H ... .L ttbsNhar'134}6AmS}{{\LU�ect\the\textfont2 A\kern-.1667em\lower.5ex\hbox{M}\ 25emS}�add worc,TeX's hyphen��,e�list %\{autho�%other (�XJMnc <pa%jre-�end-ed%�-)��declarnsEPfront m8] \title{ sAx��$\phi$ aVww*inm�f�k$p( 2produ[1�eia� �8{V.K.~Magas\add0 {De�_aa�,o de F\'{\i}�7Te\'or�A�pIFIC Centro Mixto Universida� V  Ref.~*(Rapp:2000ej{!D Although original�*$\rho��!��wAm� y *Dp$d, nowaday)�-U= ��got a loA=erest.a�!�-$renormaliz)��:$is case iss$ dras�Lt{$"�! ��Rde�predia�nOaa��  w �E�U�f�#or six )D��!D1eg,daniZeB8Klingl:1998tm},� �1��6 ]sity,)b�[made uAF difat c�Z�Ses. D �sMF ���Z�ugges��� �M.V ly T lNd� G"Pal�@2aw,Yokkaichi:wn,2�,5 na,Mosel%luis}�(e aimyCi��kA�toE"oseaew metho8d 4mine >�I e9M�L)� MRO}�3j"d�al W�M� quo!ab��(exA Edan ��No look a broaden��m�.9a�mru_h��EJ inva�R1�l�Hdecay!��s<4f_a�ea�A e a Y $philosophy��w��6�sB��ݾ(in $pA$ cols,a"Y^��as�=was d��"�$5 P !S-pK2i�Ii, ���rhe ��!C.� �R��at�8/Osaka-� imai�P�@a!ta gper��!�!uq sl> ly-��} ��5nNn rule��?2�K%�coZ n0,� ��_mh obscurI� 7pre� &Z\e.�\�,5a ��Wpm2�,)t�� i�tr kin�, is  ��of6k-!�at�vS��&UIn�$to impl�!! relev� �ar [WŬ!�I �1A��6�w� ll� a�>&g'Dmany body techniqu�su fu���_��us�t:e؍�,Salcedo:md,C�qsco:vq���� %��(�%}gts)n��DNXYssu0W��� Fermi sea!W�% po�J �A�"provid�' veryatpl� %tee*2$��!]f:suZih9",(Pauli blocka��� l on�CO�  han�r��+�Ht<a@vVGR!� RVB� kI�1Xhr �hroug�e @/iK e�-� -Hq!� �'( iko���!x 3��n�%Fm�,(details). �(�n)�II�$T$�rix9our!�� i,gu�cin4 t�vis�suppo.lSy� � Bale� �`0ex} �s!ca [Y� $pp&pp�{�l�  flat. ��.-7!ofm?A�I}m\Piz6ma� ry�A"v-� selfe]!i�  ^ rp\us�ّ�M�B *k �)�;��e�y�%FfA��t�H�e*Kum Zo)a j!g�8�Iwic, �$ak K K$�kDane�gV:byp( caro& reatPNin 1 anti� 5.�CIk" eg}.�+u7#a%Yis�  coupled��P!�c�ziH�d �e�  *hpBtJ�L� �,")6�� �-fH)&,% � bary4 (��S1n�" hyperon-hO>.Y"3%gP3. I�rre"2. aQ~-�� atAdt  � =� _0$1��S $24\�7$��W�rB�J ��two-stepqߡLet us i+8j� a $pN*7 �A�Hro�W��ny�_Qy� ml&>� ��h� A f��r[�PZw�;u� survAa� w�jaqdxy,�]meMߩ\it stK�T"�LJ�We a8A1�a)C� me� ism,U�/ ��Sl5$�� firsA � ( $\Delta E �N 400)�� ��ic� ����:�) VbterAa�`st�+: $NN\[arrow N �$"p  K�I N 65N ��.� � wo�!��0,benefit �A�ectA%��� on��A� -[e� ��at� �5%)$ �E�r��`�oe���d |ASa)��on.�k  , �a�W�� 1���� )�$titov,barz �a� :�s.-�I���os� aH� �D-112�\f_{�RN 0}/N}=2.13$i!!W"=2�$�I"�4.5Q�2� . NotaZpri��kur�h�� 1_Ur9*�M&$�� E�"@ � ZFinvolv� nl oMCWe shall�� ,inguish betwAJ} o)�t�t��J&pro~il�?T� UN)u6��N9� eaAvo�D�im : �w f� �:1� ��/�  �� �J�:���i�!JE�Di: ${}^{12}_6C$, (6}_{8}O$,  24}_$ Mg$, 227 3}Al6284}SW 8315}P7 \326}S] 40}_{20}C�u 95�26}Fe^6�29}Cu9 89}_{39}Y q11M48}Cd`15s62}Sm20�82}Pb$, ;23 92}U�� � u'ls� concerned��u��ee &� � so muchQFDlute � eOim s[s)[a�y8|�� refdF�2�6�  To �zɌo�[learly� Q��Yobserv,-���v�4: $R(^A X)/R(E8C)��  4=\sigma_{A}/(A free}S\ t~E ff6}�Gs� A�curveU��.�� one- plusJt��� &��oies�!egin{F}[htb]  �4 er} Bv� =12cm�u12�uM5-1.5cuCvR� �*!�euas��-�.d to $)U�9two�>����, $T_p� "2gor�T F� s. 8p�.���ŘB-  [ Ct� E="�. F�� ��vY�%�}-� ��eA�OIis.$R$ �m+ little whۅ.%h� ��IJbo�t%)a���ed. Noezhe)Wy clo4qG� (D =2.7�rm{ G�M)%k� �d&Zo�"b �3�Tsmrr!��flօ�^6� 5J��woK�Zie�� �q�v � e{ d� iz��&� �yEi�QsR�H  & ��GM�p� ��.zAU *Aal�J7�nee�F�M a  a��ڭce��!% y�$� �P� .H'��.M�� NA;b�� halha twicA��~I$;so farK dani.;In .67�;� �6~se 2�A�M�836� (� �ȅ8�2 Q�A� es�#JD�0� $�Z*[{%u=13cm,�j =-90�^3.V{R]2�]2]^a1multiply!�!�.�qs)���N$[��fa�sv7:'arv Figs.%��3)�uí0� u���J~*� �far�~�  �9cC5!Ua*�N�t|O 3" %�A�ree��A�gre  uld u e to�#� ix swer.e V Y6���O!9A�6" ��d 6"� �hً���&;e "�9m��y@�alz��  se���C Lj� / 2 25$\% �29w�[v�k. �y2 �I"P{��*�i.e. in LtoF� =\j�  w!�ok a to��� _Q3� ��Q2j $^9}=(pn,!�}+p )/2$. E*;ly5 poor 9�X!I�e��2�s�>�,. Neverthel�0 MT��=��M���t.���,lm�|)~i if one��6 �}4y&�} comb5|v $(N5 11Z52A$. H��5�ex$!! optimum."1-�e�5I� �e<toiF}xo�� =�$eu��d=wx &ay "D k�bust�AAO. �m _+&5=Avs \ } OI"JL.R., a&Z=s�"U �6s��7& Educ�%4, Cultura y De�e�Qis"s lyS�y DGICYT� )b�8 BFM2003-00856,� a�@E.U. EURIDICE net� 0 ��4 -TH �"c/� $} D.~Cabre�AM.~J.~ViS  Vaca�R)�'H!m�B�''�1\ �1\ C +.A�) 045203J��:5b� �-|2#=~:F.~ �> ~Waa�W.~�%�M�:�!� ��B���R����3\ B 431j298) 254�Qd709210>�Qd .�&$�.� 70�62) 525�U�20208f� .�.�$�6S.~ d04 [KEK-PS-E3256P<]�",& s Of%�Me��D$s���!�Mw$ At Kek-Ps!��? A 6>B!�43�.+0NUPHA,A638,432��na�2�+,R� H.~Toki%�2ITe&o �J�'!�ei �A :7$��6\]� 508 a�1) 237J�01101B,�x%�x�&,} P.~Muhliche�FalterE�G�8 J.~Lehr% Pፁw U.~M�&�0P:�$-e�s�o ��N� 2460!�� 4�W21007f� 6��W�'�[,r-,f-6��v.~�qM�&&���s� �A�Z�>�73< 130J�(=54>�5� �x/I!4eb]�{ V.~*/�%�Q�!���%��F��)�:022� %% %� %�40�4:��  ��Ahn�id�i�& J�Ah>�l.}��A�-�f� Li, C, Al�5 Cu)�� E(�^}P41.5-GeV - %2.4 A��Q44a>��6]CL-EX �u\&�%�8 ~L.~ ]yMm��-Er%�C.~Gar�0Recio�C?7 Si"M OeD�� ve P�*ApA�R�N�2348�688) 5 ?:��3484,55)��.K&= C�rF��.W�D]&Of�b9�s With �i/100-Mev�5 R�53�62) 44�&6��536,44���>� �ݽDISTON�Aa��omegam+]k�K p"�s�!p(labA\ 3.67AR/cխڙ��1) 0240�B2�A~��0V�A E uHT�aJ0b.��c@ ~I.~$$, B.~Kampf~nd L.~ReznikE{P&�36�l ear-"$ pi N%(N N9�e@"� J.\��0) 54N� 001027b  �� Barz�zz�=� H.~W.~"���r�# ree-�)*y �A�%=�@ es !  %5 �>{685�59*� �i�C> 63j� 5063�2>B�8 G�"�7d8aps]8c=n,supersY9L5,�`pacs,floatfix]{revtex4} %��2 8 bf]{e6 9"W8%9<E_ file2N8{amsmath6Awrapfig: TCIDATA{C�&Ped=Thu Jul 24 22:17:3�93} + LastRevis:/3:16:13:3!�s&�� ���<%\input{tcilatex*K*�5^7DynamqKa��7modof � emis��Y ed 5} F7M.J. Iso!Oaffil�_on{�ar:L7K7, Facult(7C^J,as Exactas y�>ur�),>U7T Buenos Aires, PabellA7$I$, Ciu7�7t/0L, Nu\~{n}ez, $1428$,�72K Argj�4na.} %\email{m`>$@df.uba.ar�$C.O. Dorso��v� de6���^�0 \date{\todayYBa"�7N p�9w.%�7��.B^of>KL-L rd-JA- �{�?�4�#�7 �ep9* emitA~Q�s (�FJrecogniz�$}e p6 l�G#=#a min� lifetime)eF focuK uV.�� m# ��, Bg�(!;ngs, ~5is��%1><&^tbI1�/) Ap) �4� tane�6one q�7 a lo�,�� libr�Mscenario�es up, k!gnFT�-9l'J temperatuT3Gtur�+�"��2��%!E-� t qu�+tym�k]N\� {25.70.MnG.70 -z .Pq, 02NsA�*�:\!{I�;$1��proble-5Q/I xZs%��0c8ist�1b��hr# SIn�i/2 i rOta'XԐuat<M �-AU���-$ve. Moreov/wAn fac�qeme.�\w2A�"1S uge "s galax�"�8�e sizea�C � un#��Lq�e� �� %T� &Y� call�a".\��Q$3%�+ 2�0n �6I($LJ$)�P�a�inQ�h}��.g� 1GgHamilton�~.5re& a @"short��I�xsul�-�a .$Mxion. A<Z�c�*��*ll�j e4ins 5i��R��%�q)vHa� �subal� AO����-��dub@=y�!� �*'s:�NssBc6qale97,9,noneqAo},�eu-)Hamd,qmd���x�7%�scopic.�*��categor  /�d!ose&�0'ZE�re&U>�minU(que��v,BUU, VLD, etqF\ zM-B�14A�i�"�:we�7&o:�oeI�� �-�A�s�[Bfe�?z�I� b��ad�l d. C4@�w�� �X�\vi� �%���a1.�F  $147$g les ����-� le99}. Pr f*� !1lp�(��3 .� aI%�� �"shoc#�[is F�ad [ka��QZ ��a�� ��� ��*c!*",.vommunic�!�%'fA#-!�nekM.p2B!Je !�| ���E5'��/ s. A� ���thwhi� � ���E>  B d asR.N0a���a�?�|p*�-n� ū9�already�@i��1:Y7b)And�F��.w��b� de�bAm� !Wmi�U4!f).!S�%�!II�# A�eo(&{S� %�4algorithms curxWC�(G [ \�YT&� �[�I_e�"_ �Ѽa!�e���� excDO�.�V9a��<��!e�,VQ3��Kdĝ$��"('ine�o� e)s (5?� O<"�,E,� er� %�s,.� �:=, &��cdq flux��cfi�D���-ll!V drawA"� FmmZ�F� %�za� molee �22%T��,a�an olWf��- 7>t#  se�-�o%M&�%�e�ge�8��iE��0MST_2MSTE$| $ECR%%si�s"mMintui�'!6te�Da)is�_h1�V�: a� $i$O�ngs� a `$C$_M ��<n��N $j!&at.?$Ci|%r_i}- 4j}| \leq r_{clNk�1 d para�}� �\he��F radi�HI�k*4 &4�= a cu�f 3 l ut},�en l}$ mus�3�!eZ 'ut�N �at Xl}=�ut}=3\s�2�i��� ��z:3-�\� n�Ba�o e ``&mum�Kn� 0 Tree'' (MST)�=Iz a: back�G�EiJ�5��rr.!� q}� �+.,�jaG�*li!�� a�%> . A�Mtm*�.)�MST |b�!Kx\ɮ �E)=0ɗ campimste�=�p}H,  ; �Q�4s $i, j,..., k!-elQ��samUW $C_iA�: �� }\fo/� \, i\a 0C_i \:,\: \ex� \, j >',/ \, e_{ij}i0�m{@$ $= V(r/�s(!� p}_i -%� j)^2 / 2��$,�'`ueK�:Ƴp�,$\{i,j\�!�E1C� a�igu�al �S�89j�A/ v,� �aA..�spiJb � be>2�Aa6c=-skp�Ta�,� �L];type l1(+ ��Ps �6im� MSTP_r��n,�.�EF-�M% N� promptly �ed�� t� use�*��!$ pre6Pn}�.��!O);ip�9 lP6 A�rob���d� @``M(#B%Bl[%A'' (MBP)f��Lecra}.�5MBPS��Oof�!s $ \{i}56�umZ1t��nal&�3at10�Hs"Ivalue}�n�ly} { \{C_i\} \atop {}} & {�n& { \�R argm1� \[_T L } }1tex  {[E_ky~\sum_i��int}^�}]� w v \\ E_)& = & C[J{j \in!6 } K_j^{cm�sf{ {j,k8 �j�. k} V_}] �6 eq:e5�1&!��X!�f�?!�inh{6SK&*ՄoYjEj]�p ��X"�I���G�@sb���-�m �Y"A xM;conE"e V� e��ph ��-�&�C}*� ps�a��0E���86�most-be=d��ty fle�J !X�� r-p}��2D� y��fi�]m]:�E.; �d�z�!� A� �-!�). ެ s��� the v�f� q-p}�,e� E�Vveloc�c.B-^SafMat&+,+i�� e��yk}a�8-". �i@O!�e. dA� ]�U%�fOs-z��8���� help)�a�mat6� "�.�iZ7� WD ��� 5B-��io�=1�[0�!]�is qu5"�.2a-Df�e�Auim!Nt �,-[,9?ɅZlregard}3��sSPurey�;� $q-e4$��$sSsFab��N�G!/betS�.�2lK!�T al �of�A &%�s. y-�MST21�7t)�V1*�]���or�u�s. Plc� BH� �!�6� X $�l�conNR� rephrȂas "weak�)��ng�"�"^*��"l "{emp} B-�w�aio;�E�P-kin�!�"#��I�M$� � �. !3!�c&�3�e7A\� (�!�abE� �i�) k� �be+. gh�8 keepUm�Ŕ �*2IalyzeYf&�%�me � Js��1�a�20&ZA�on�9��` �7"u�.{ mc�{t"s�_8L��m�� an |Y� bi�UU4uOrE�toe�}�.�("� iGBx2#�QrD A��� e �e l�!.,$T_{loc}(t)$A��v�*��?�!�b �8ex�&�� �a-So�G i)! �.JwM 6H=� � d as+�=&�v_{rad� =<\f �$1}{N_{BF}}D {i=1}^ $�v}_{i; \��r}~oleft |: uJ |} >_e �eqflux"X �  u$ ��Jd@�i�m* B�)X�`Ś$t� <~$!�noPanѩ� all even�RBJB$��$ � �j�m|wmom��e>� R�. TJ�N�+F��V�޷a�ideAK2�;A�]��@MF�asU�$:J2y v�2}{3 )�R4��m}(� V5G - Y�.J\hat{r}QPwY,�F,^E�� ��C�2b �;x�Y.� ���Mi�����M)�!"Ւ� R9-� ?�"'*�I��dure:Edi%Ud�����`ic*ʡr�,M`%H \c." v,�'8$\X� r=25 $�: ��.a g�Ŋ!Y�is*6q�)�+�}^{(i)�$=M�` i(t)Q,ev �iQ1uojA:e} {�d�c�c|B#N���� e&� m�E�}���I�_9s�I,6}to=O; �A v}_j:QX��  �rpo�!�ts . $N%Y3o�?�<2  ���2�!ف����Tl A�B'�`��(l9� .��H7c���J.T_22�T 2 3I0 1�{i�Zj�iɈ 12m��E(�h!K-ɨI�M�6@j}M: A = r}_jɟ| } ) ^2 զ�z2ZX!�)~Cb�"ellqOall5r�valid�of Eq. DezRV:2}� y� fqcon�Nure��f h/�!�s�kachie|K)�.q#(Fhyp�siAX�a��_, �AIQ� innerD�s��bes�'e[6�\d�"ng�!gB�  (:&)!�V� �Ei��Cbv !U F&���@r=/m�5gre� 1#) ��p^- e!�!�q Ŝ.J��.s )(��2��)N� f(v)PV (i(m \beta}�� )^{3/2} eW�i���(v-mV)^a� eqmax3B A� a{�% �'�.�)�1Y�Yi (LEH)A�?XEN�A �&rop�z5^� e�  T)�ur�aw� �.C&R�|��.hal ��e2sNl%"���< ^r *= �; [�< .=:X ]^2"X t�aJ�>�R�tra�����U erp}"7 2�=�N�m�pro��Ee A�^cUf $LEH���M�U�2� fun�d AJ��ari�>w�"��qO)�`"�E� tEtov*ck� significa)$S$��W �2�"�"�F�I�� �^��Wo 46%qu(Y?Pf�..a.[  a�a P;U&*$$\chi^2$ t�!� numrec��6��$igh enough ����S� N���) a� �7Ipossi&"HF� � aR T_{max}=m�Ygma^2>��\HUh� -�Rh!FQ ion{�*�$}Y��'M@� om��d,��:�%" ),� $N=16�(60ng via Jrun�*dE� shif�R�/"4"3Yb6"*�! � �� md�#naO-[�($" $)�A�A�ey $LJ$B�QaPJs!�G�Yi��!g��[,s $t_{0}=\s�� ?^{2}m/48���$?�z��ksx0�i]� nu_0(\ 0.2� 1}{t_0}$ a�"k�&q�"�scale� !st*�aZ&�I,. �3`mJ-gLAg�  u#,XU�|}�?$(8 (rw �'m�u.�*G)%F �ci;!_�^$M0.01 t_0��GA� :�s,.A��K y $18Ƒ�5f#')#Yt=250!NBx%=was�$e�c�ki@�de�a� �"��\$o%)Vt �V��#hN A�!Uu�m��e aij$!�5&6y+� C 2q"w.A��+V!�~ $MD$&_s=�C.� ��Y��6�� ��R�&n�$o p�{\emphE�le};�at :t $4$&� , o1)ST;* W�M*��(�Ml�F(Wa% or4��8< O�w���b�^A��-va=E�'siQ"��^ -�E08ent-by-��� n].A�s��6A8s8.A "�B/�\Nu�&3.*I� �$n&�$ �builta �e&�"� (jC!X!s�.��T1 # ��o�vaOR���f�RQ�remov�-) n, ���eree�d a M� h6�A�+ sa�em��any desi� e#�K�A�cG� cm "�7'i�$naC8$-2.0�<$�]-12 $-0.56"0.2�7:2? $.a��$.� (�r&Od�%cperuJsh�gV &��000�Xh�QO Mnub��&�,�".�AwAB6aR�F%`�-Ib�ȱ2�bV2�0&�W{La},w0��l\!:!V E��Q"�F� go R$"U-shaped"#HT1�~exponJ1�!�M��4at�=1. Ba �R Z��0power-law (pah$b#nJ�� . Te�lc7�5j�2a�fitD���2: elsej� baleny!} but!��Q;o�1ou�cmGFcex�/�71�!IYAK� 5exp��y� Amo"3rs, dim� �O�() "���9^p])�A#�{\s"c�$skip}{40pt�w&��5�5�Bs[� =8"Y Yi^%2 W{ A&l�EJM�. " $E=., E=06�$E=2����y�1E s $a�_A")C$c2� �� �M-/��h�VEHufA�tow !�es1�.��&�r�ɰ �`1��"��_a "l eXyU� D\K�u9"�� oDx�!�8�Q�_. At '� $t_i=n� A�R�; �E���"� "�'e"�/��<tr-��3�O� �{�.a'$t=(n+5)� I %�V/ n $5!F!^%�y!��yp��O�  :Q#�i5']X-��rr&vvn�7a*� 9�w��w��ow����.5�f 2<�!%���.�av+J*.�kP���� :)�6yy,!?A%�"2Iv!"�,�� max� -'.�6U�wards�er0gd7"h^of ^2{s��b m� c��R��]Hc6�Mx]��:�!ł�J� )7s9i�Ane��.>�\*�ChF�5 } S/ iscuk8qa�"��A� �#x82� < fP9Ace%�i@ "0s.RD!*rD$%":e\a�a O�x�  I~se =tQ�� stra�@forA|. Anye�� �%=#v��*.�6A��mn� �or�5F1-� nx���#�[�Wof "�8 �m�m�xwe�&&�EB��ur.. [L2� m�P)�2 cX ing � Dd*v*�� v� �I) � reQk#�.�ᘁ�pl���and! ������3J�(ColorRine) Di������ (+>� )9�(doH 9%�2�"�:�!FN� ���1s�-n��seI#':�  (:t )A4��9'�&h+�w1� I��E��a doe'gtyG�A� D !Ga6Mz�c.�� (eC issu�B:f�3�Din&�;� reduyA�8}|��5^is��R�2}[�2 LF���>6-lap<ime�t%�% a�!�a. OagainB2get�.oaDG �%}y )�(q��o��a�tr �tohnts>�-oA�.� �:,"N ���ry few�-� A@o  6  �&E1�il �1j�2j��{�J� � !D� ɥ" �� "�=m9 :� !P!�eZ��I����4.��6�>��� ���� ֺ %h��2>�� � 5JizZESM_bR�2 � 6��s&V�6�֝ieX:v�`4 "Ks��%is�R�?fn�� �of���&� !W2t��a�%/1!. ,��%"��-��.�)n�o�a*�v2�r(�oL�F�v�qA�%��L s��se62" � pic%�w�#r��i�  5c��."I! �:�J�B~H��;p� Ir�:Mb�u,G��2���!� �+ may won��if^u�a� eN� -�� sust�K�2?-5.�3[�p�'� ��"Z (MEE)"� em��+�,�MEE i�F��e�R-1 A�" e�2$30\%$+`.=6�zT)J6P e^�)n�$"1L�EE�  nJ� nr�Ao� f $40$"&�$ �s6�m��s�"[ �iveF<�2�2�m�6��u !�� �"� p Fe"& $1$ (top)A ,2$ (bottom);� j< ��2� j>i��im_5{� ,�,&�2y�,e�A-M,% ny� d�pE�vol�F�r&MseE�^(3 rB���w ive)RrA�r�Kr�.n PsA��% )kg�Xr n $t�"m�]�. AlsoJ#�pai7  >��9d��.g$�<�0ɏ�C�^� 2x�r� �3�.�F!% en g�7����q4togY��#�) C)�c!&?23 S�   � be� ����mix�Pof.� and 6C�:up|*I.7D��>� YI�Aa���%AZ � ->}= they�-�#goq#oo! � � f�6tr�2 Wa�}:t�#�f �!�:�q"7;���m�T"�&� �=l*�1*�!O%�2T& 8!��zPham�A.�%,E1���AHiaR�""�Ta:�% �9a� .2&� ��� �oo)�_�p qpri�vo:�)�_akxW%i����l�J2V*:u�NQ�RRph�<�qkintvse �m\kip}{10pt} \centering�includegraphics[height=8cm,angle=270]{fig7.eps}% CXaption{(Color online) IY�nal kinetic energy of the emitting source as a funcL%,its total iK C�for three ranks. Empty (red) squares denote $1st$n,ssion proces34green) circle6�$8th$B:, and e q blue) tri%$s indicate @122A |(Full (black.>st[ �8e caloric curve!�expand%7ystem. )�Hlabel{kintvse} \end!�@ure} In Fig.\ref# we showVresultzanalysisu`1000 events at an initial1��of $E=2.0 \epsilon$. In order to mak)fi�4 more readable�areA6y���l above-described temperature�$first, las�|d maximum multiplicity fragmentaEZ �4. It is clear{een that}Uq:�is A�ar with+I�1M�!� displayA� cool�,behavior. Th!averallH will not change if!!consi!Nonly N�< but also evapor6� ��eseztoQic!�atlone�$to calculE�9ys from�.%!�e� ed l�25t8s (monomers, di tr ) p0would be samp%%a �%� star�{0a rather high.,%ds down u0tonically. So�correspoiB�Az�-� aUJat I!times)�$ decrease ! Lr on \cite{natowitz}-�is!a a�v blemN)� caus!we i� Autas(equilibriumpas sucIn kind$measureA�sA"aCreferrAftojtAbpoint d%�=$ste� � s. WAm%�(be improper�$to talk ab�.9 instea�$"effective.# ". Ai�quantia�v��E`��is unA�progres)he be comun!�A`short!� \subsr$on{The rol�*rad�� flux��a serie��4previous works1� oneqaT�havEw�,aA�presencd coll{ve (nonA�mal) mo�a� take�4!�ccountE�f!�a wrong�: �.ca e�-branch!k�2. O�wh����!W)�ly incor� ed i Idef��o�p� .�� �e�%&Y���E��q!@A��x appearsA�an almosA�n��t." reg�ati֥Dies�Gpa�A*r,� paA�ipale97b9���d�a����7m ��isM�, (use:hhe ECRA phase-space method)a�e valuII, meanQo velo�q��� )biggest��in each Ŏ Ar��to Eq�eqE�e��AF��,. \begin{�]}[htbp]� (setlength{\�L� s�  8.F  R]~a��.� %�y!�j�($\tau_{ff}$.��j�0tlocalandtintE!3%�2o%�e>���im21 !�I2,F�!��� �(f� !)e�dotana�] e J hazi��B��=removQ��՝x�je�Qt.2!s. As9 lain ~S���� �A emp}.#�Tr��ed�}U�fluctueKs arounisB�.���9J�(LA'.�) B!~!�:�at.� (stra�-r�� � "f� e"� " (M / E�L>*A&1�ed� m Ig:� V�� �akA i.z�importa�� BMZid� N 6TF}Q� see K pic� emerg�� �P �P"; reA � �ma�� opic� ��� i.e.#;in ��E� [, ŗed�o9O?=�� !� �u �  stag& evolu��which:I /{ -T �p� distrib B(�ex� e, loo%�at��.<}b)>`�Q2Sturns %�o� =$4)$. FIDisA?� 5Dwe ge� �A"2�N�s}.H canf easi2; @both approaches g !sam2 .� b.� *���,clip=]��10m�\c^� E/s�aZ paris �rs obt�2(by differe�$hermometer"G19coa ��an�� -basA��. Filled"� 6:!4/QUF�ݲz ٰ. T"�up  Xl>8 ($T_{shells}$)��)��ſw�[ &��e�E�2C9BA�!nn�4��u Xa dens�X$\rho=0.17\sigma^{-3}$..  bM�:�. ��E*� Hypothe�$(LEH)$}ޞ4�Awidth@I�1M��eZ�C �3!~L), transversal (thin�r)� .]=� !�:>!�$E=-2.0"�L (panel $a)$), $E=0Nb|�FA c)$).��Mrad>�I�� �ion|� made (�Th9�of �*-. �՗checki�:w ]performa�hQ llow��ion. B� in a q .r scenariɿ2 of&. sh]bɄ� !}x�{!J .�dir� s��ev �Eqs.~� t <}= C }, fa � le���gx>� chosen� ͘�);&� � -� ? E-E`�.1�, 0�$!\ �J��y (Fm% details)%���&�]��ve-�ionedű is immedi�����th�re essen�ly%�, excep�W very  y�v(��s m� �ha!Ke.�'�]  �u%�[$LEH$%�ib� � (ms plausiblA�r�%]K 2$Maxwellian6IY�ies<� m�a>�-�4 �2�M,:w3 �"�9 %�ndeed �. More,,%.���h �_ dardAAvi �V�is�exact]8&�w},�A��� onsistenc� our numery stud%|.�m5z6� histogramu� V�=@J��I99= fi%`��.�>�r� ��.y 2��^�VR(�m:�2��� $E=+.�} � =N: In adit��x!Ra�ll� a��# betw�eV�their!Ks we�=a P�4on $\chi^2$ te�tryA&to rejecg ݈u�24��-���!�)c"Y U�:8�Y. Wa��$a signific� ($S$)X $0.25$ay�(casesY�t,�2� ��lowv dLlevel like $CL=0.80$%c��j�) .�s � ("� vR< is B!).R ��� 7j H} % Dminipage}[t]{3.5in6_c� Co.� .\ %�sMst�O.���6}.�0ruledtabular}{|l} % \hh � (\�)$ &  l3 }6 fit6 �6 &Rn 6(& {\it S}\\�� �40.627\pm 0.043 r0.645$�7&A�86 { \ %�\quadTR19 g7?� 0.63! 08 L 74 g2 Vg2.F 658�63 75 �50 � 5 vg7 6g�1� 6 %"U� #Q��SE���  T0 .$I$a cross:I���i.�F addi.�al y\�� adW�e�F�6q�@�"~�we(ġKU^q�*n,ReducibilityՍ,redu} Not l�0ago, it has b�e�o by�t nd co-g er�#tto1, 2}��� complexN� �" em� ��be &A]erm1a binom&.�.� "�!�ts�!%assum�! ��`"�)�proba) $p$��capA8� �o"R��ss�n�4g� is pay�E.mass orEmo p���\ �I�is way8 .�of 4�O$n$5B� ./ $m$ �lsA.% f-�E -knownVQ:"d eq0�} P^m_n = \frac{m!}{n!(m-n)!} p^n (1-p)^{m-�3�eq1�m�N���� s��!2 numb�f " �",-le�b-sucAZ<F�!'tM�1}� assocV e�a�5he".��Q � y aA0:��BZ�J"s5a�u� �G!�>��"A�e quaa�!� /�1 is}arkE�q, speciR I�!  �4 �MfacJan�Al*�non-si!ane�Y�!��n n�" ?�/rU�$Z ant value2!L�:wh>l��2��;��10c�3- ���:4&MGpR5"4 s)E-5!�(*�). For"� (opA�bottoX! leftr�):e o , E=-0.2$B"6! $E=1*0�m:#.�m���l"�fur�F illustr�e4uraw�xA�ei*/Ani�}��#dAP��A��'6du["�ntire8�&6&�'U�.��u8th $n=0-5$. $P(` �%�as�`e89�.� (���)� �2��I he b�fit+����b9)14J :P�E-�!0�( , 1 �(, 2H(�ue), 3 (violet), 4 (cyan), 5 (ye�)��Z�.�]2 U�We�Q��[z�i�%cylE�Q�!~ bW�J! �n 2�mib c�z!�as�vd�!s barriE yet���{Co�*�).�r � �n dynamic� a|mo&p2P*ama class� � !���Z$ focu o��o\ ]b2,"�E�*%We�2��b�]-b �j�)u�t & sequa�a�(r2��,5��  thoug�&re� manyS �"�s$�w}phe5(n�� J� is f��b enya�forbi)�charac�,zE�#a pure��one99>)=>wX%*��� �U!coJ�!~1ui�I7^�is�I&�, &9)8A$-dependent:re! a 2&�&�siz" %�AL�.*". , � ar%Lyal model� fix2� � A�me s( seem�fbeɢp. o reveal�true �!'�](e�si�(eI�9�,R !z�@6�&� �Cz)��&�;���8 ++, poss]+rec�k�8"��~x c � ![&��I�+re�� j $jee _ ] EC� � T2G&a fewg-son�*3�ch�vid� A��t s. Two E��eC,6 s)�����d by-produc� }�"�) s: F�-6'P7.��o�Z��"�2b&�k� ti�/� ��6W��re� y2E_0�+ larg�� aft+�*"*&�/a7a��%�SecondՂf��A.I�`A4�xa��C(su� -up E�!�a�s)gamaa ly �z, s_a""3 A �*l �" itud�)Wu��[a.��p�ee� �aZZ  now �vV&urly�� on i�a�opF)�se�* ingssencourag#�ApA)} new,i,a ) vrealiC !�l�)� e nu0i���0*B *{Ac� ledg7HW� �>�an& supk%&~ Uni�� (of Buenos A� via gr� $X308$. `lso a�eCONICET ODPIP 2304$). C.O.D.E meApCarrer�!l Inv"0gador ( U). M.J.I ?feT �(UBA. % -� ibli�4phystyle{ieeet�{���!end{docu!� } � \^ 8[fleqn,12pt,two1]{$,Xle} \usepackage{espcrc16g�4.L\newcommand{\ttbs}{\5'134}6�>AmS}{{\protect\the\textfont2 A\kern-.1667em\lower.5ex\hbox{M}25emS}} 8\title{Coulomb �)H fF cleo�&tinuumt�\\author{R. Lazauskas\add8/$[LPSC]{Lab�1o� Hde Physique Subatom et(Cosmologie,� 53. avenuabPs Martyrs, 38026 Gren�0 Cedex, F�.e} \th�5,{% e-mail: l�H@lpsc.in2p3.fr}, J.Apbonell���!�}FIca ,:I.A2bF&Q# make%]A�ab9 ct} c/DFaddeev-Yakubovski�!e�_ solvb� �Q �!�-�FJ�. 1�x3ac�)wa!�cj7 ,to�����m^�C&����ie scat� ngMj,p+$% ^{3}$He��p+$ � s.� 9 % typese�� nt mX!>igskip\  Tt7-Wfou�� )=�M�g, for  h�u=. �� rn NN potal_r1ed a 4�8eV ��cy!���Stwo5� data� ey u ��1��+�7ng&G���+gh��:iLuse�#k(forces (3NF品i4atory. By adju�5 heir�@<s, Y" L �atisfac> �2 E� ar bEst�* u� A=10�0Pieper}. Low ��"re�]Tobserv; )� quite ins�'� to 3NF �� . Fu� more!c.X"@is�+iv� Hrigid once deuteronE^tritoS�� ��7ix? a�A� �.|� t�con�)!��� str�.7s%�shold�re- nc=an�#w!~t�3er s M � !teq�A�l�Fonseca!m\smallaIL �3s�", some�ult� cer�lo�pr�� �  ifi�o�0N�)tZ s#3in-�k, p ���+�in�u�& MT I-IIIE se%9a�� 6in�ju:<wi8Urbana IX (UIX)A�. Our.�35n are R ariz��� l'a:1%��S}[tbh]&�"4NFas�4�&�M?. F�c|�K � {2-7} & \�� UU�eV$11.5 & 9.2]- &�JI -63.�5.5J(13.9 & 5.77U16h 5.39.�9 &�6E�: "  fueffort� devoA�to�_�*�-f�f5Fm�. Semi-&a Qr��]sh �0�s`fula�>�*a ll�u3�s�(�q {C& �0yrN#d],� �Av.14�h 8 &u�wOa���(iderably en��8a�v �-��U�.�at&9 belowy ar� �x4stitutes a cha#,�8��Ad��ANex�-e��a�}$=0$�8, $^4$He virtua.�i07i,.� richn�$U�/�E+Es� .� E�� �M�.C ��efcE���an &�,�of���� � spli�Gof=SVu e t1:s� .71-(J�s��&e�@�:��m��Ai�.�凥� plac��he-e -e� =.�-tw�-��2fle��a �_-� RL- . No�G�@�prece�nT�here J�9neg ��#e� $^{4�exc#Con 1eared L&�. Un)�� �� EIs������� *� ��!�e.�h -- $\<#.{�&% d\s�7<}{d\Omega}}(E)\r*|_{/ ta=120^{\*9}}$F��i�2"�/ �j2��".:�NlooId too6 p-"�]A��)iK�\ �. .x��*) y-�st�G limi� in PWB. N�theles� yA�a�a� wpro�"�C�.)Hw:p pt_��av}. P�H2NF�Es1�%� Alet.E)�Anu$4�&aGm@-O!Dfar&�u�eD1 Ig\�_i�*2 �i �=6��f�r��one��sJ�M�A�~�Q�% I�ʈa�" 2A~N�ɘ$t_exp}. A �6�R(�1F��Gi�8�F H��,,LC_JSPQ_03}:�ir extfK\ n-3.�"�/� ����*BX=E�=13pt_�Mo*F5pNcEnerg�p� �""}e ela� n�  at 12���'$:6 r�Li�c.Tx5}�."�-<.B:<� �F the.� }{99�ibitemG S. S et.,g.Rev. Tbf{C66}, 044310 (2002)VIF$ A�  J K LettQ883}, 4021 (19992N"Z} 2aT, Few-Body Syst. SupplT12T39 �0VS,1} F.Ciesie�6�,, C. Gignoux � � 1$B447}, 199J�� 0 M. Viviani,!YRo�,!Kie� ZR,% 81 } 1580,b82�ir} .3OD� sis,&�4\'e Joseph FouO&, "�!"32[� ( T.W. Phil� , B.L><rmw,8d J.D. Seagrave{y �5$C22} 384�86��z� N. Jarmie, M.G. Silbert, D.B. Smith!�S. Loo�gEM{130} 5%$66�.�2(�4.�,z $be publishr�>5 "� ��:� 11pt&�} 6�psfigLset$ er{top�.0}{2} \def\topN/�{.85} .0�+33 f6�53h��{.1(L floatpage>�dblJ� 67 hdblJT5! re.�[B stretch}�6!}{� eqnarray}:�e#��.!*>J��* }{21�%�:"�M}{16.0N#odd=maF}{0.5N&L(�'topIo��Us fShape-:&�"1;iE�rando� �s \footIT{Le�F s: IV �TAu8al Balkan Schoo�' N� ar �c�Hodrum, Turkey, Sept�!(22-29, 2004 "�oel+"hijker\\ ICN-UNAM, AP 70-543�`D510 M\'exico D.F.,\\ E-�bF@�$cu.unam.mxAqate{} r9I �P. I� sear2&view of)Z ar s!}]:ape�*&E� V�� "�ng boi;E �S tudy� N�~5^�� S�N�� regul�pectrfez1�a mP,"BV&�*t�? p�B�S +t.�\ o�_O�$[as@xp�Kby->"!rI�  �u!Ql"geFric)"c)�i � &�%a t�-!S� v�earchu1h2� l�3theorX�-  *,QPT}. �=rofJ�ref�-oc �� &� 9e�a�Hn �usE��� fl'i�r{<��n\�Ptru4z,t� !�r��d�' b)sh�e~�o superd��DQ��{!�! WXaQeCa%� usu)Has"/� &s !�/ ��s (r;e.g.} nov,a�i �I0`J���K$:�2Kv%o/+an;��E25-,< ��sphOA� 5/�%�aNd, Sm#Gd1KorF0$\gamma$-soft'J �Pt-Osl. �RI�DSI�?Wlai�ABto� 2%�bN �Z� (IBM�4�A "I��iscus� f-ea��f�3� IBM%�RB!vv��!�%�� :� � crit 1�V8 c`a/&�@ s�!�$N$2�^p=,($s^{\dagger�Pquadru ($d _m$!�(h $m=0,\pm12$)� �$L^P=0^+�� $2^++<i^e ]�\�A{P�� s �wb�i�hal�� / �KaluG%���@.NC$N$I� eigen�=+ goodF�!�paW"�$. Let'b �ɨschema�cA.9of�4c/Kt-QA m:`a�(CQF)-�HCQF} \ba H \;=\; \kF \, \� ,n_d - \kappaQ(\chiFdot (~, & hcqf�a ~ $Q�B.|JDor�.�)��;�sqrt{5}�(] \&4X\tilde{d})^{(0)} ~, \ea�2 � �$�Ro�G�]w�~Q_{m}�%-(]�s�`z + f�s�2)}_m *!P�� 3~3.a H"$\ � s}=sM� Pd}_m=(-1)^{2-m}d_{-m}ARA�:5Eq.~(�!%�)u�s%# "+AeBG:�3$,#!Oc,O�*��� � choi�- coeffici�d$Q�$, $\E��chi$,e6/7ow6L4�&^a�*�^�E� ;�Q �y?A[�&�>��P/�$surfac�2�'p2%` conn�n5- m� IBM,&�:Gs,*� � � F(�.bn4�bg%^ ing �<�,z �insic,�qis��2�3s�F� 7ens-!,Qim$| N,\beta,� _>q�C�*i�N!}�k9( b_c�� 8 )^n | 0 >e�)Y cost�Mith�:Fe�:v1+� ^2}} ]( .� +   \cos � , d_͓ +>VN� \sin9( d_2�+ d_{-2}) �)2�4&s $oQ�9�er��-� �8AjŗEI�. S"� �_5�=�% k&= &� onesAd " > 0$SasH��8a�� (tinguish bm ax�E"<�ia��^t�(pro�\ � k = 6:'ob& X �lGt i $9 <1�<.Oa;�:Z�a7M[n!!o^ c@ '$.j h�!�< �u_V(%�mX) &=&�U eft%Z.� � "db��i�2� mu5:��R� ��"3�Picz�6�">% deriv'-s vanis��)�\�-V} E} ��r)�$*0.t derM�)�d- % \ Hessematrixse�� .�O�Lve�sA| eft(q �^2F�ep%) e�~5�.6-i�~8bet�)a�< G�T2��/ i5 der2�g .�D`E2� }  @�*3per U-O� reVed�� t%h � B�&MR( = `ea��( J) �.?ofB� .  k"W$�� mom,���$>2V*�  $U(5)$Y } K �=0.�$H$N� r�P� i� .W1A�!�A� H_1mG��.� �Ehm.r�of $H_1� ��iV_1ɬ)p��vVU�v�."va6M���AX�9�� eas�b. solv �]� ��2})��� S_e$ c"�W[ a*���:# -� SO(69��L"� =��XE, r�Dp �2E)pH_2-i��\h�.�.� hi H.h� AlsoA�'Jh/�:6o0�9�R $ �V_22��E4LJ��u(6R.$ �A�F$i�d� �%� 1$ ���cA �,"� -u�l�1I_�cZ�U(3�� \mp � 7}/2m�&�.�FE>yr3I $.{)]H_3-��E �%�1�#��4hk#ea��:b �;sy�[��� � U+3I+"� U2�z *X2 �� ybm �$Rf v �R}C �;>I2}6�E�"y � �-=� <7 <�f]� Y X> ZRY ��mp*` 2E qs,�)*A 2BZ�"�)e\�E!I��0^R������by}�l .}9x va^�qel� �>�ok"�g>��19�( ���"/R�,R exh�*�ZJ�l)��In�)6ds@� s/byz����T 2Q�%�J��g�g one-RH�A* )%�.n>T!8 �!_&�6 eory�e�It�!M�!�8.���!�w� r�Y�"� paVAZ�,�,`.$r ] $r_��~8M�UGif�2�2_!�xt!m!Bt!C�o� r&� ��-4+ � }�@�} {�j4�f+z5�2Ar"� n-8K�� ��r.FRro�UaA�a, j8Caly ex�i( .�  !? �Hr� , -�'5�6�|r_{1cn-?�8*�j�1-�"r_2� ~� r1c !�Q$od}�w�!-�{1s~1t(9]D+16)^{3/2}-64}{54 !� 2��(.� r1a �IbA�U� s}%: A�yE�� �E!F'�R�I �%&p��tY�0i�i"6*.?ZAe�C�9�0[Eq&�v �] {�C2al ��%.���B�"͍A �� \}"�015p��1�?{c }A &  \\ L�4B`q��A" ��a�{&-y&"� &@_e$�@>d5Ax&zCI�J�@-A�@ --1>@� &#�2$-1N$� ZG\ BG$.li]  &4}WI� +# �e� .| 6��.F�.� Ob� �z�.� F�-��-QFl�ZC y�UiK&ŝ ����+ly3&�4d a� �3l36ar �$�RlG|6 �7_6`�Op[t� a@N�!i"�jY~�+ _?der H,:Ny&�]R - MJJ ,!"v(�"��C *&��/FA6b �d ����H_�3 �l�+ &�qn2�� c�Q(0:b0).� 1*6� � *n� writ*$sF{\�E}} 6�&�+&�}{N�D�H��@ B:4\��#>����v�& �:!�+�s�v1}.�v���sca� /%�Z!�t�Lm�a� s $N�]4is"dI.) ��Ggta=)�n /1.$� �J�$ $0�q %"< \infty �F��%A�penqetE R%o 1}{4} &:&6�E_eM�:* Gg�nG H�]%�-{H+1�ea �,�).A�L $4 �1/48a&�"� (>%>�>eW;e % 6� F _c = HIts�Xa/�9_�/!�.�)Q� $qQ_{\rm�}(�)=ij_e) ��+� ru t^:���&(:��N��ka o�RU �croB�$�Q� DlEthK?i�$',(*)�)�7:z�Y:2�����N�e�y�a���$!LI r�1m>�]�2  W��zW ��(E�s#�6]K�)9��!�in%��|eta_c=a�e؄E)wbvouSAelB�+$-� 1�o #f3�tsa�-%�FWI�}A=#a��Af!�ca�*�ory �M�8 ,C1i N � aa�P(* E��vE>1-%�� $. *�. %!чIee �-} plano!*e2"V$���:� �B�� d�$-1I��leq# ��! =0�ܑ ,^t&!):.%.�C%P�U �,!g�y:>��a��b D-) �ae;_cmY.� ~, &.n&}"D r_{2 V�_a�W"�W ZWs�W"tW A- K(.�� ]�9�2�N�coincide�ie�igZ/a �j�Z�g6*A���?U �@^2!�:#AR�i�m � axa�C)pot|j[B ~$�i��t�T*5�E�N�."Gta<�&$1.1 � n6� v:>9 ɡd�T�a�l��.o�5�+)(2< = �a��5�vf�D(�<}{.5\&<�; l�(fig{file=bo�: _fig1a.ps&��,:=E&c\h{�zzb�z&�^1)*�b#. (As��2���- > :)�W �K$ (da?)`&� =��_solid�� E! >ڊ- =. (�!;.��m� ��~�sb���w5 �B�:�aN4��n > �%6�"�e�^Q�.�:q �J�Bq��'a�6>axR( �$s 3�n�>"pZO' {3>{0� "e�.N{u) \R�..��)hnF&�h1Kd+��U!Z�ZP�%lVEr*4%4� � 6���2:��"R(etaBI( \a�.J(=��,Mv1��c3 re�bZ �7NB$��"�6��kVn� he�uL��!N} A8Q:$�(� l�$�$iZ$.1 .�� �� j � �_c=2/9$jT E�&M `UV,�V>4*/0RW �!��bI�� *�*= 3E�� .�*= � A�42}3{1</ ~ tyeasGue��9=VA�j$ d 2"AB�-a��Z�a�1 �"�7}{�}D>�"��>� &��qh�QK�� �^� �s��2=�)�� � �@�M�Ygh"�l� �OA: 2}{9BH 6[)�1}{15V+&5 Aq /8Qw 74!w. e-! a:� :Z��q-m�U �b_ 2R - ,c�+ �1+r^2_{/81 2j}{2 '��ea in>� .y/2a /#�8%�a 2��B[%�68.�%�&X9zy/{7��Q�m�y !u6���r7���"�iUe�Pson whyn'&ɂ%��)�)�!��0.219F�r_*P0.075R$&��0.748e��� b#B*4f�D�Nϋ �m�Z ":I%|:��� ) $2�6�,"�B�.` ��I"*[ a��$&ti &K 1c4+4%f4+3>l.K pm� 2\�"}:.b�/�y�]�02 �:� �8�. r_22 ~@.H0�N -B 1�Si�J�� u�"&��2j does�O&�; ���K� �irU',  23}$�� ]�xhF���& �x2�,n*~&�q"�Cp:�&Ž*�h6DU��O&(Q Y�S��*pl�Ɋ>T 6E??&]�.�4�@d�]2; �b6�F6+.�j� et{$�{+6/&l8���Y� .Q*�.M�� J�E� . Ho�dno%^ �op�7�hetrue: �NvV�s >o!�x��,Wd,!��yall�re � sameb8 S* �ir kin�O;ގ"B)��_2N�0.5lTl�?]Z[SF�&�)Ju�A�B�:�pur�N�r^$+ $�Ba$=��!�J � .{%�s:�0"mg>� �"�&LBBB*�K $ a kite (� dou{4�>=?)-�n�b6y &��$ri�,c+n"`>mUH*�6�),� �Oa���c-mR�5L� �end-:A��,"�("� �� $ (F`'d� �e (�2%�:�2��e5����>�"� �� z��� ie}li�=�Eq&i-� ٓ � is �&I�``c''a�F-\"�!J��2Rs''-``a'',�!.{3 .>� �!�hI� (aX>�$)}.�@=.,��� <.� . A�r s r=r���T U�T�q� �7Jr_ � c}$)�F~�a}d�NY8�um.�!�&-��fF^-�H9� A�Hsds&�Q.� c&$}�Afbi�6_�v���)�AG��vٜ i�c6�$!$e :� &�!E?HM?��m 7�)�V�Y�ka%����Y�etA�i;��o��� �`�!��i/@�S�per�i�*dR� y2e�Q.*s�m~;"�S*"y��Dc��� e�g�YeH%c 2 Z�1��1��s�;�n~0 �<��dus.i�� "{��t�M.�KQE�typ�3E*�y oJ]9EUN-UJ2���\!~Hj; m65_Y]!}s; m9;2�\ �a ,kri��" �� situ�@A�u!���i�an�<Si-�a�!m~�s mix�*Wh,/)�Ja`i3]� �j&�Tbyv.SrON2�;~by�u��- phil�+�"(n1gin{a�c{cc} H�. �[xV  mix} 6.&.�} 6 OK4�NEE���ZbrieflyAt��G�["�b�Qm%� G9[)� duval,EPRJ�M^en-d2e[���25�1WA,i�T�"Y[N&Wq�[��E R�iym��]-�>�[i6F\$(p,t)H!(t,p)�:�HlE4A��m A-i� e&p7$0^+_2$��E�).�0rR2��o(;-�arrow 1��./1N/:�ab"#�iB� is �is�1 (\"�)� ��N  a[�+s)M"AI}*r22'>�  [ ngly�2J$R$y3?�iة4#�2���� rpt}A�En��Q�A%1��)�I�h�� he2�- Y�nh�d] ��Y�Ue�$N = 40�%���� P�ٱ�I�N�o9<%+�9,29,3aJv,w���0,�0,3b�q&',T�e^�_&Y*���9xQr&z!�]]alN� �KQ?l�. �Zƫf e ^Q!� �&[A9f�>�us&lA�f+{Triax�|deqt freedov�pzC��b�PIBM-1.� eYO rղo&<W2`�!� M"PZ%I�T� no���>OO , un�s� b�60 ��2q��s Piet�}%D�2a���*I �Tm�pr�a��1���_ `$d�ٔ!���, ��$ %����&o(!Fly ��J SU^{\ast}&1J�5ich&�a:f 7x!�%.�su3k�!M7�!�eAdg� )7`!�e�d���� � � �to)Q, s��|�new+*�)y$�p[ !O!�1, nam�%M-2-Z: 9h6/F�\.'o2.� t R�\� n_{d_�}�W nu�TD )�(&}=5[�[\pi�[ =) +nunu}�W]�C]�@'{hibm2�a���� �M $d$-�<� a!H a qu5_.�T��iZ8N�jQ�"0=�N JJ)=-/_{�=���L.�>�,J��a lot"� p�, I�in"cHa����%��elaq6 a-y&z4]+��� 7*o vabY42b<&%�$,�RC(1- �A� nu]{�� &�Y�� (��)a�"bV%�� EulerLY4s $(\Theta) \!?v _1, _2 �N~"�Jori"a�� �A.� �2�C:5v�Mx b�'ofm�;=be5."�Ami I��saQ��' ce iB�I�B�s"repul~�hexadec(b-. �I������&�obl{��w2�VAJ>�� $)� \neq[��,!2%]*L! &Hi�)E��2�� Sar��,Arias,Caprios �w*D)t��n#!��CF%��oXI��1 bI�nu��&vZf:�F?2e=&&1.ft."#2�qN �nu}4t � �� *�$ 4)&�$i�)��A2 cos(u� pi}- � -"X2K-�J�&ch��.���:S+2:T2�%��2Zjpij 6�nu.jpi�.+-$��?J�9� b�! %!)K]�#�0�%�Z�ho]5) A�:���r�Zk(X�\pi*߶�� nu$)e""B}U�ee}X\�� "��h"�"�so��l���ly� �n2�:�[,Rd*o�,N ��l :�* �?� � 6 ~no� *s3[�w�b�~Y �ng�9% �3M.8!�B�61f�Rm�$%L��sg~ "�HoF�"��Qhel+�-� �H�ku � ��"���(�)���in�!p �gh� JY�@ �� *- \s$ nd� hapsA�Q�Ae� F #%�% ,w�ch� ����`da�n�/�311���O "LmRF w } A*E22 �i�t��d�W �9Iir robusBk,e@of.{ rF�. EK �_]�y  �6o"�="O�� *_\0�bxTra1�c��aveu��� >�� peak��_-�$�m&:sq�$Wigner,Por��Y�ʥIɝ�� el+�!��t-%a�I� keepa�Q]lob2q], .(GA/-Bϋ�s�ctea�bf� nt�qd�ɟ��,"�o)rj�i�jS�mf�xampl�s���&Gau'_Orthog1.Ensem�(GOE)Aa�- ic � .P ��\i�2  �nyJ��� u�� A�2%5M`�TBRE)6_�� )�q n]��*� of���Brody}!nio_cl,��e-! j �qs ̡��t�x/Hs!&� �9of GOE��%ƣ �M6z� ed.:�hnͣ ��!L��l&p3[m�&� { 1!�"�r,&LyP)ep ��}9���l�1asa�%2�V0s�wmodel j��A�%P���,i2q$sd$ ;A@�� $pfe JBD}. .�F�-�ra�1���A Ef�sa��W��( !]�2xr" A.-B�s�*n�n,�F��� �CD ��M/��t!aig�er�5 magnm��+ simi�{ pre��e"�v�$>�a!��hX$H���; �2�p BF��*�U�>e�l!E� j�tb!Cs"�t. Accor[!AnY�3id�y y fiel��r4�ML� 6�V%Qe.�z��3��l�ryE���� ��.3�}[Zun��P��s&�v� b� sparr+a ��� �y�e�to�F3}E�|�G}�}!*�A-�m�<6{e�cz1!/ewjjf[FA�Y 05}, Zelevinsk�| Voly�k��S(Zhao, ArimaN Yoshinag1hao= 2�i�L�y6�|eU�B�y "�&��I��y i��9�8*�yB� A�" p� �[.�"RN�4� Q�0 vA >��N l�raB:%� P "LR�.8�"��> 1}{Nl>ft[1,b�-1}2&��AlG��@,b}9.n��6N �_ l�< W_si.Bn"D�q�q.d.d^{\d�t6.d}.�1ib �!���� ��.��'�u_0p5�Z,R�r�) s � (�\2Jss* + u�[V[�[2)�[d>+s [*.> 4\+ \sum_{\lambda=0,2,4} c�Q+ � Nt:� Q�j�d�1.� �v>y2`,�[ ���t-� ��N�tf�VB� ��D]N�2Jc�\=gQA:j�]+R��V �Aj �)!s2u�� ninߙlh�z��*� ��*y1�p)-a1 R ), altoge�/�"e�(\vec{xD;�\; "� _s, �L, u_0,a}, c c_ 4,A�2Wr�vre� �+��%�mb>� $x_i�10i=1,\ldots,9$�: ".eQP(x_i�pD\mbox{e}^{-x_i^2/2�" ^2}/ mcL)rg`�����! m�ӡ�  $ B*�9";�� �%�=��+FeS�l�]keɰ�att��\�OJ 1t�*�of v3.�m�M�C�&�A L4:i�x � �6g�O:} Us��A;.%�$ R_{4/�*�F$E(4^+_1)-E\$1)}{E(2:.kir4w6 `BE2�8&,$ q`��R� %-� N0:? = ��, $2.53.3g!$�[ �� �$�h���g�P% +2�  "a�obaۭ2�$P( �)�/�%pronoun�. peak���Asim 1.9 �a ��} "3.3y�o9-X N�B�o%harmon�q��M6nd�orEV !< �� � )Le6B� ���.!�). No#+���**(*>]o��� ed oscillb��s��-�%��5FG`]� st}"3 fa�r�,j�.[� �b�@p��a��w�p�e� v_2$�Nls�to� , 2�be���Rv� ne�1�q��w4aA9�!(���vi-um (wh�*@"_"�-.g���7�" �*%�2��z)&t&t�a�r6jcve B(E2)Mh&�%##$ $AXBy"UB�'�Z�;.��z.b1�R�aA� 3})&Z%A� N�1j�cJ�c�a$X �D$ �b2�)2vv 2\.'�3}{c}{ E!G;���a*��} 2 z1)}$} ��b"��*�c\\�@c2 �2eB� \ �2id:Nm�vc� 5Rn.N+�o�c 10^4(N+5)}{7N(N+4) +>i1fINt�Dt10}d :4(2�x�?( �2� 2N+3҄��cu!�;mse��CK%su�~�hdeX� ��o 5r�0X�n�F9�. Level��4b�6�Nl����qc�~J�C ctro�9)�&a��i(,���R�/���@���c�' a�0a�:q�$Z�ɦ $Z�����m�q t"�. �� ���s�t����)ś�"#-J�s a���.�(�nP�< 10/7&�dJ(!���(rx-Jt2�6�>�� e�N�K%�P�/o�noB"e&-�4���#2\��"�� "�/nJ8(5�n8�w٠�)��_�4� �<ab��50 $\%$7:A(sd ��� !�E{� ��)W �( R25JR�:Y�-[b�SY �1���Y4��Y��Y4��Y��y)�V CQF&P�G ��2Pu� �Y!�EM�Q�EZ:Q1T��YU�_fone6�"*PBaM��"dS�/16����n*��DF5�6�o��lr/uin&� @���.l��)�m� majoE�-ne(� " ibmgs�a�pe�7agg..fs)< br $L=2$an::��>�-<�Qd[=��On�o"Fjdomr܎ ww$m$ 60-75��,or $N=3k$ (a5�ple�3�ln .�1�$ W�?@�  As&5� hard,/� "q * �!i:=��E5*61:yE&*1G��MA6��}��� (top͜%� (��N!ζ9I >�HM of- A: c&�� 9l�� 10,000 ru�so�;B? �in$-� �!xim�7�a�] /& I�jg1MeaR�}�B"8&0���!"nu mm�a�/!>�?�x}��M*�:u&�m� 7�!at,X�6�co¶ I�6�|�e��J�� �X"5'.��a^ basic ing��ꉍ�&B��%�)0�"�/ )v�@�$J�.V %� s.(/s �v%wo�e-���"�!��j 9-&�#�#��Brf� "�#Oy� he!t+ck beAk�+x!Q��x; �#��~x�D(�Q�;� �!|"!���)Fil@U��at�M)K�@A���1�.� N6C0JBD,BFP1,JBDT�2y|�m}��X.} ��)ri8z]!@ #�Q2� �BF2�-s&t*��` );��x�LE�ro.��9[L"�ؒ�sou�(�& $buo}�/g$ w&�A+U�".t'Jt.N!F6�B�E6 $ $J]��,)�BF��c_�j d u_M s��e@ Hartree-Bk�m��)1�duke}a��4�i5l wave&�B�D廡L��!Os�l��)%LpXe��)� 2�Cpe�� .�*{V�Y`�a�p^b�a:&6�!%.�-+.�:��$0K~it�e�: �g/�!jte� a060�a_0 + a��Y.hT"āM1BaT/a"Vbet>�`aa_J�*�, r vbg��a�!2�P$a�AA8a@r�{�"E.YT�&=&2Tg-���10}���7 W 9}{354z0 1}� 10}}� *�U!&�-E 7�/0�_2�!�/&7- s���"@0��06Us.�2}%~�@�!�)�A߁p*�teUqT!�)�/�%� 2�"���9�+=n-�!���Bacquir�Eץ "=�RG_e[!a�� ed�Q.�3�"� ��S^�6�:~Sa_4�a_3 �az)$>i4����di!�� &�)WR es: ;> �iz<> �6Ά:��$s$;8or&<.� ;0�Xa�_e �X� 7�J&���-[6��WS"��2 K�O��  �y,ᢁ��;d� �= �c&9dA��! !>�R� � Ea��=�6�? �:own>�LB�)A5'� . EvK"��F+� r<�pro�_�A� 6�� .� FU abP�$.N{ =aUj98�.&�)�$ Thou�=-Va� �2Y�� !�����s�`in5�ae�Ccx��^scQ�infVai�� �� �ci��NY�z;�$��� "��Q! M���y+=�W.Q��$�hens�8'&P�G(in 39.4"v��),. :�oA{� ���NS>�n"bkmUic8  !���2ngQ ]'��S �,2*"2N�5��0Aj��MIM�[E@6mk} .� d�j(I}_3} L(L+1&�F!�FR{w2&"y�,�MpU<x3�W"�v%���MoNd-�!�6.8F�K�>��!�2�0has $L=0$ (23�.7 $\%$), while for ${\cal I}_3<0$ the ground state has @maximum value of pangular momentum $L=2N$ (13.1 mx. \item The $d$-boson condensc�Ocorresponds to a quadrupole oscillator with $N$ quanta. Its rotational structur �Da more complicated!, since�B exci OX energies depend on two �s!Hinertia \ba E_{\rmLD} \;=\; \frac{1}{25c5} \tau(0+3) + \left(J, 3} -D62D�right) L(L+1) ~, \ea which are associa�%5!�!``taneously broken three- a!�0five-dimensio!O=symmetr!-�N�. b�occurs it6�Y�$!�=0$;r Aneven  1$i8 >,ŕ1�I�!�I MNA�or&G -�2�^%>~ 2 �� � I� clu# )emergeMere fea� sy�IBM � random i��ae`s� expl�� Hart� BoseN�1e Tensemb5 0f Hamiltonian)W)�differa5regE�Mo(parameter ��E�>H partic�� iA� nsic� s�1 � urn.uA�,definite geoJ c s,s \cite{BF3}�� r� ree ��s:� �#;0 carried by� b iya�, a~�O 9) .v w*� ba�E$,2,\ldots,D aa��ofz � �� gAkJ�B) �ent� ord� [��y level�6G -��a�V E1i��+RWM�s b��a�dis��M )m6�a% 6o� rqvibra�al"� !osE sam�qes hold�bSEon model)ea�~ A��,�0%�be� � � tnlyU�4}.� subsee�{Ev�_R$quasi-beta)�ies&� figur� vfill� 0minipage}{.5\��width}� x{\epsfig{file=bodrum_fig6a.ps,a� =270,:=Ef c\h{� �zb�z&� Q9',systematics:�&� C��lE $ plot betw!�!�M�E,$s $R_{0/2}� 4 : (:)A�er����T$Pietralla}Ep(6theore%�0 cal��1��� sisa� Q-�>u �m`2 norber � M ReN ly,���esta� empi� e� Zwas po(d out ��1'5�Eq.~(r42})� �-9 .� E(0^+_2)- (1)}{E(2^+_1 ~.Q�!e panell&e �� !3exF� nuclei�S neuta���$84q N 96)�8%� ��  of a!� 1�� in�+�҅�CQF.�,9> hcqf!?�~a�V!�but�!�ricA'toS phys�H allowed�Z4, {\it i.e.} $a�ilon > 0�\kappa!�4 $-\sqrt{7}/2) \chi $ �e>� %Y��m; M e equal�2,�$E {$4^+_1$�9s belong2!3� -phon�u&�w !߽�-�92V� *e&i�N2 ��T2�/ (see. BE2}" B�cis tr�0is satisfied %7by�daͼby sch��>d��u(only some �lmalU!Z AJ$imposed up@he.�. .n Sign6 of cri���-Z}���X'�Gi2$#Com*� MM!��6he+/ � .D  $H_{1�� 3}$i�$N = 11IO2U �*?\protect�� QPT}&e��fNf& �Fharray}{c} U(5) - SO(6) \\ \Gc�/4 �� ,$E(5)$ rHU(36H2/9BHXH6+'7&��& 2.22 03391)�)61.0 "4 5.67)] o�V�Final��I brief2ddres�qu���2��Y� 1�2� )�DRFC}. Phase transiiinM�� tes�V .i�y� suA� observ�a��� � a�ebve� them, su s se�i �($S_{2n}$, ia�r shiftsdelta \l  r^2 \r Y��aUe7B(E2; �Q3 �arrow �� )$-IZ!O<F�ha�� sugg)as- �Vt�qam��Yg�kEL..EQ.�M R se�ios�;�#�~e>(s�taq�)V$u�2/9$,�O*}6c� � �V��{,q�! q�~��,"� �-Fz0 0 ! !�ra%�&h"�th�Z� �# is��0not so surpri�.�po� ial- �surfacA�d�2� �1�i�$h quare-wel [s�n�\ pot1% �!~6P=oM�![,. Moreover,�� A ake o aJ t-}�a�. clasɜB��sh!��D^!Ih�el26�s,� )ʁ� their kin= Ii�r�e �!T"sE���k-�MXa�� �e�) �seFid>f�k us�a "6�"o us� stea�eA�uldzh��tud�chang!�6�, ��)$ �s!:/or q&�Yinhai,�i!�dS mine whexth�L #exhibit!+-p:+$ �Summary,+��- look} � _lec�!� es I)�presen�ha review!�Vyse� ��2 A�e�. Maybea[$first sigh ��(wo topics Ehlittl�do���ano!Im� wAC�n!B$provide e� a�EIx�cEZ robu�!Fe�col!� ƁX���PI� @�( very rapid&typ� �{& add�� or�ova'��wo pai� �on� An�nin��-1%eIBM-2�A� ]��� / &!�axi�&�ti��of-�Z���� 1 6QtriBTi.a>q�N6r%�se� �. Two- %�fe!H$(p,t)�(t,p)�!�GU otopesI1 B2a & prob �A!mgco2Ca nor� �anA�ruderaq�? ..&w ��Tio!e crosm B�!�*� Bi3ed�� !c�.�� eia+I�or zeroAF2abse#A o� mixingiemay!� e4]s�gly*ed6�E� � rtibqconcepsB�&� wa�fir���- ��eVRfDespit!i?� � !��� a high "9 deVo�R"�U ed,��9��do~A = 8!�7r%�6 .�!�*�!tu����t�M�q� BUa:�$!:2�pla� cruci�E& in&$an�rigɰ�4-a,p�%�Tŭe5, �;f�Z m(  �{$s�%�Dhe many-body dynam�-��w���?is-� >M32QI�LquA?in��� <m�Q n ral �&�a�Zpr%2{ is�a md r*� 2�th!)s usu��thought��,*{Acknowledg�_It �ple�=J�@k Pepe Arias, Jos\'e Barea, Mark Caprio, Octavio Casta\~nos, Ric"�D, Alejandro Frank,dco Iachello, Elizabeth Pad�(�!N� "���'�discus+� workI�uppor��A�awvCONACyT!�Dhebibliography}{99u4 em{I } SeenHe.g.} A.N. Andreyev  t al.}, N�| {\bf 405}, 430 (2000); D. Warn� 2*20}, 614*2)� ��  F.=1 Proceeai� A�I�n�Aal Schoo+PA�s ``Enrico Fermi'', Course CLIII, Eds. A. Molinari, L.!�4cati, W.M. AlbD"o�mM+e$, (IOS P�\, Amsterdam, 2003), 1-37.��BV�6 ds: K. Heyde, P. Van Isack!8M%C oqui J.L. Wood�,R.A. Meyer, �. Rep.)�8102}, 291 (1983!�=, p4W. Nazarewicz,o Huys�68P. van Duppen, Bd21!�10d96�DSI} A.E�Die�aO.%�lte� d :�hy�v. Lett � 44}, 1747�EY>Y%\, Nucl-RA)346J25 I2�,s} W.-M. Zha�� D.H. Feng\R. Gilmo� R�Mod^E�62}, 86�90�,Q� :} .FJ� th2Ee8)�792��} �,��S.R. De�=GC �23 �4�12Z� 5!���6�JBD�W��hnson, G��Berts�nd D.J��an,M�e=�8� 2749!}96YBF1�� i,� �^P�42�.�BF5>OA!% ank,� ear� � News, Volh 1�No.*a 6,Zelevinsky} �a�A.Lya},W 3* 311m5.�Zhao} Y!� ,H Arim��(N. YoshinagNY40!\NWBFP.ZW%V� S. Pittel2d��6T 0213� 1996S JBDTn�NMkI�lmiRj!r014102BF2f�*� �L M03%g>M3�MAd061M6 duke}  �!(G.G. Dussel P!Perazzo)eii3 H!�SofiaI���r 42� 93a086�BF4��I044316%6j��' NA�'%�O� Gorb�nko]�&� 7E*11&�; 2K�se2� v5>X  docu� } zW% *�hr�f6;(apssamp.tex ! % % T�#is�f APS G REVTeX 4 .X+.EV< on �3of *, Aug�� n Copy'(c)� Aman�jlociety. 8,2�README� ��&i�0�eD in)�K J TeX' t�requi� t"youvAMS-La�2.0 i�3lled %�pf3y��preOsitgor- !�n� % I�so� runn�BibTeX�commau<� as f,::a 1) la!�=�!�2) bib3^/4V \Qn�H[aps,prl,twocolumn, paceprintnL4 s,amsmath A. Bugaev 0J. B. Elliott �hetti$^�;J@ gesson$^3�L�/air2 } \affili�{�arVce Divi, Law/ e� keley N7@al Laboratory, Be 4, CA 94720\\ �D�%tm�� ics, Lund*t, Sweden53$&h Technolog1 �.lm\"{o}JE!�(date{\today"�: abst}1���.��,.��>go��aB���describ�; term"BY0��p st (�,mesoscn ) E8a�� l�R �in,ilibriumuvapor�po�u#�ntr%�s,��ssu�3nd �2��$fi6 mean4lattice gas (I�$) *�-s�k2r� g3# aliz�!VFisher's�. A@$��,͔q4}:��'7ex%�8!in-�9 �Bat5indiagram �.�(:,.k)Y \��D{LBNL-54448} \make� �)��-s�"�^&"-�i嗩�9� p1��r oppo�< Y;a�!eas�!In%@rn O# ��.�7proble�7-��9u hen !mp �mad�re�7 �nEpM!�2e ���r-broughtli by=t]&(schmidt-01}r)ar�/:�.he5:2�q�d�u,�/s �ll� E�y$#ch�n@%sY�eL ific:a \emph{a�} (%�us)��6a�p{ !. unchU:d,"X'c^���oal_'@*8achieved alread�c��xi!Uč�E l. FB>I�aV enc�9eri�M9vA�effort�Ei�� h-�lNU$heat capac�Ym���N( dagoC3 o-00�3fra.2K /e��-02}. W � a �$l approach!� deal�.�Qin ��#�ve�il�/r�i�W)P2�c&l#8. A dilute, nea�,i{.*J�A$ nser c �; �n�-is re�-ed�1n2*a .%�� �!�'s�+��a5"�%��� iJ �<*C(��moHٱ�enthalpy70rayleigh-17,m�5to%� Wv troduce �%E�*r#A���!�extenk$H,) ߅�1�do]'�D)N$aa�o!E�iHQ*� 6w��fŌ-N�9v!�*x%E� ������Ta�a) !3eq:�2�EnrecI+Ɇi3+,e Gibbs-Thom}?� ulae �Fhnama�Mi-96})\demEAE�oury �$!\N��"�&$7�  metho7%67�e�*a�\f�;��gy�4�1/$!/�M5$mov� hAK(�',,)��5in%�RDitM�8 aXs dWby virt�")ft;��% *� �#E�%�:� �$ !�op�Aj"$%f� �)}g TQ+ and resid�5.�(y)�1�Ig�� to incorpp u�tf commo�'�ear �?: �.� oulomb (�ca~BMiu�3})�6<um)X%�+��me#of�nal5�9i�0 non-�'s (�$assum�monomer-  "��sl,a� "T%a)��}-us),  be�+w3�[r��2I% each� !�+>is bas&6A�Dce.� N��%��/onT:� �23$A$�fstitueE$n_A(T)$�A �6.�1)��er= $\De3G? = E - TSS2he epig'? N�is~M�& writr�C,�@E = c_0 A^{\sigma*< � ��4frac{c_0}{T_c}0gM$tau \ln A �usE=eqn6 )E = \exp�9 ft[- X n)* }{T}�3(] = q_0A^{-e};(y�� \varep/:K)�Ieq:�t1>� f/re $q_0$!ea�+i< !8tau��top�-c onent, $c C��:�coeffi: R%xT.,to @?meUaB$�,=(T_c-T)/T_c%ze leaTern/5�)�$,P or$ �:$9�?&y he %i�FAU�݌� $T=�>#)4 . Eq�� on~(f=.) (�\{��B;w)!~va�F(:at��]�ak $TAJ �?direc.� al��prey a�op�Co Q�I���2app�P�͹.��O�=cho�v ,��,!X limi �e � r-03c g�p e"�>24,- "r��3 e& "�I����. N-��2+ we_3per�%gedanke\H�&z s*&� �!4 e!A�i_e� pyE�! "���6s M�@dn put/ it back!�o j (@=���1),� if,J5riAof� , noɳ��O2�"� '� UQf�Ifm�%Sbe��2(!�a �ofeP( $A_{\rm d}ap2�UAf)�as_ s��4S[.3+ (V-A)� -��N��ܱ��(�m m-�S�c �{A2�}/{��gN f� & = & q_0 V �A e.a\+)}f ]ٚnoaI< �M��\{�T�m��Ţ ~��Α -�\}.��&� -2>��.�cose�5 (Yq -A$)A�m�  m� ed ja�RS ($jF.�zF� *&jBeq6� ) re�/2'��) ) �$ �8�Jycon�Qa� actl�/[G�9�& ref 6{9B-VDs \b�SB�P& = n_{AadQQ}(T�$ (Q�% 8\mu_{\text{fs}}.� qR � 2} �>tTMBq$a-en� ZC)�.���Zn {\it+ive}  B "S:� �rm fs} =� left\{ � .)[ .�M���t � 2Q �?-q� / e] \}�>n NA��]�x���=JA"�F} \ eis[w�H=8.7cm]{� H .eps�B�T{Oo!4�G��p�bottom:�($d=2$ ($3$)�%�� .,&xM$C_V$..ex�details&xB�}��Q: 3to R�ve�N&@4 x,Yv y����canonECbT-m lee-52.1, 2}��c�� of up spi�dF!m�Zpe�"�$\rho�z�}$6�XvaPQl�H % magnet>  $M6A�) �esOKU �&�� ticl& fluid��A��s, dime(rops etc. D��< mpty75;E%1\���er�loU�r��h�9�4=s)o� odic b ]6�9�to � �W�O{a, irr�%�Tto `�. �P.� we ua �?8 (simple cubic)[@ dexR80a 25$)&5 �a�B$S 6<$\lesssim 0.5$\%-�fe( Hand-69,landau-76.1}�ZR2% 2,fe�7berg-91�G�> 0K"�<n �cc&� ref. �Vnga-98�p y $(T,{A�}.�)$  $10^54?erm�e";� � rXE)��6]E"�� ree}� 2L�� Ix@M � a b$)mar� �K"q=�]Q5!�ax F�A�NͿa.  [y��$>�at�wJ+�7 aggreg�n\J \� bAGp cuu��.�;. At higM@temper\6vv6a��N�ithNb5� �"� . C)���ɓE=�@�QviaDConiglio-Klein alg-]hmMMc80}!�in���$ �io�8"�(�RV re�R��"yAex9�AMXo�M��sstc"��F"� !� `0denti�e:�O,ly (all like�QZnTbor�Qnded)!������!ask�ick@a:�]�2�Our.E�.!6<&� ^{0}$ (�$n�_D[sE1(}�2�6[�^� xima)Y�=�6al� .h. DqWv�h:h�; "C�>m& b� r-81* Gz caling-d2: [Col�n&R]�bZ�� �W,�"j�1.�for:�J�(top);#Nhe�no2| middle�:!{&u  (� )&� �-y�^s-5]2tQ>z� 4D/��3.6� :�S�Ta�g.s[V� �#� $d=3)� 25$ v�*1�9 fig:M� �2F�T �.Wb?�f� s $T� ���v'sBZ �&&�:�� e���H��n� E()�Ba.=�X$,S�d�A�A�w�SLc2" 8$ falls quickly� ��s$T_X$ vaY�:^��2�8 2� spec�!&]  (� � � -��Af*�1) a�As. r���m�hi�U6]�>F���:� until6�in&$1] �* a N  grea)�?qf�. A:h fur�C, QdeMZXoAElu�Tiacy%�EG �i exa^H�H�CA:� e�� .� : /qD�$ vs..�.�/ TQ( )�._�Y�#��z�A���#lapaW6 � �s� a w �N� �a�ɄV �2�#��!Pe�w�Xb�B ifes euJ�!e�R\shgJ�e+GA,2� E.��hIUo6$ -h "z0table}[htdp]  e {Fitu)�z�F�} 6-Q{c}IQ - N& Onsager &� e�"� ��s >*is.< �'�� &  3$ :\\�j $L]a�P | L=80n&^)R.�1 �hhi}^{2nu�S>& $4.7�B&B2j & $1972.2^P.��N & $2.2691 83 \p�004%@44.51152\pm0.00+ 4.53+�.v�NI� $\ge8�& $8.6 {NWUge12N!2.6�4 ].�\-:�$8/5 � 0.56 �1L & $0.6394 00 �725 �00�fF�jAB y31z&!�071 y%Y�2.209 6.N125~1#g�U � �U � ��� ��z�J�2�J����! ���B�>C(�W)BMJ& $64e� &$32 $16 .{\>�w/2K 60.3e 10.6 8E�zI.W %�1� T.9!˅ 8$\\-�U;R�� &$46U}23Q� &$117E1��$14~825�& $7~938 �3~516.0�PRQ.�&$1~553. �a� P � 258.��EK6�O�Z&� f $A\ge9$�dU:�f�A�S�.9 � ��%cause0 6sbey&�"ansatzU �:�": $E_A B3$. SUm 6` .0&*u sJ"J { "3� �3$�%E6;,>�`&ve�/a�Fso�1c�]re2c� �bsi%=u�magnitud��ah.3 sh�s�.��.�ha �alyh,�=7 l!"H )�&�'� moMR"�)eMst2adm.<%�29 & or "�#:P  *�� � !Avbl"Q�$:�2�o!i��`R,:U�% JFC \�� . How,.��,�of%�os,6� g|Zl b�V�6 �" onsi�Q�$.� 0.85�($0.7 Qi��� �21+&k^b�S!: A"�0^�]TdJ%17Mz� f�,5\�F$Jk^2�6��h�_c�? ��!2F;]'=\zeta�u -1)/2$. R�ta�gi�in.c[j� o op \c� �s� �:��+&�-�&lu}��- ��iFE� Id�!1ch�Xes�$d�'l'%&�A�Rl"�+�7�Dectts ��mq��EOe,i�W=8�12$Y�,,stauffer-99�.x�ġ!5�re�5l($1)&^����isoi8ina�h�5 &~ N|ar6e B�b+M� u�^�A�2a�l)X!�.�eSaTLIxI�-Q�\"e�.-YC5�mui@�f<fz0' draw�&E��Q0��%`me 1���e�:!��يt�9%sh>au�Si�q|(!�<[: :����sZ2�.\�2\�Y�%�!6?#r"/T�%I��B�H%4$F�:Q�Z*!A�9B�Xa�*>�ɽecVa)�� G!�!G.Jn!) �eco0��be]&)~�"O2-�9:� Lef"�"�Yi�"#��:��A]*���(&B �Y>e n [t�] sE�:L-%(, $X=Y=1$ [=# $X��Y$ ��Eqs.~ �}I�  �})]6e-:#�rmA! 6�h[gur�� �!�major_?Pɰaper:�lizV:DA>@=xu1��@�����e����a�5>[};�4�&�a�Aɝ3��er)V��w>wat�5!�=A�|G a-i, o=� �ixeB| ���9no�nfron);�3g�6d �%i�Q� $p&L',T�+$T \sum_A n�2E�M�; rho}>422A$ "R \gg A$,�BZ�,.(�(R*)V/(1 + A��%) \tau.�+ +>)�>V(}{T� ^{1- &"C,)?c�r"Y) expa�0B[) �FK$*�)"3:l&� & p_{�:�)�(���:��,%�{A}J�*A}j*)2�,W-6�X5BQ|9A1!andN7{Jt5< & �A�A%Aa2{A6�+A^2-AJAv@J�Y.5Fm�FEFor"'$7�7\ :�AM$A0�%�� > ��6; 2U� U �� e&Q$� 61��$)2��{rN��au?W* bulk�� . To� sel�{ ��H 4��s $2�� �.� �Jq-d *A/n2�ͼ� +' ex�P�a6 >6��� �2.>N�(t�lingKT$� ig9�);.+�� ; "�lis $>1$JPD� mP }&�.�v(� C J)"� b&�r%QS�.FA*�'nQ�> -E"�&!ck�- ! D T!�Nlow�Ee%�*\.Qp.��a;:�68� w{J�A� �<� a*�&�d6yop�(��s�!�Da�) q3*�=k�� to6p�'�) 8g= `s.�@�*x?��-.ica?K� �M.��%KG0(I)2� i(nth�?^�=l�J=F�6 fact*(��`I!Mhe6(8(e.g.J >! b�=�,�'n s&�Gste�/wards�GQ�){8� &�-of"�.E�8�Ge=�jri."*uarG P�re}c�ybW&[F M_kF2^N}.ZX�^"uT�U86}, �Z�O). "Z^2�DZD'A�DR]LW_�X470U219RQfR[e{/ 2} 2�KRY��T8\\ 0427[�Q^*�C} SR�C!ilokg L3�R9�X17a�5"%@�L. &�L�Wx3J\8C 66, 041601(R)�2)&-� 69)SE#"J, R U Proge?�=R6�^1966dT�3 ��=F.}�5�T!B16�T2Yb2�FF3$ B. Kri*�Ce:sdM�_889�V66\ade�# C.K[M.R �!v,2� 0646-�32T�* 74} K. B�*e�\H. M{\" u}ller-Krumbhaar d�v.�9�b32Y76VT.�0} �N!��0kM.-��M _`Y18jT83xZ:�&�0(1} D. P. L�0N�1e^9^\76]JA��Ja (1>I6:1 A%�FeP1 �~a4a508�c:e<41} T.MLea]C.�W1c>I_4^1952), u� R2�R10!5�Q RMY8!�UY, Zq�M�4!�1��1>]**2aKJ.�PH�EHVH. >Z . BlA�o}rI ��V2eO156�96Z�OA�E"/Q |f��=Q6�7nX24607��6m[.�0E�0E W. �0�[2�I�77b:.( AS:,�`.�Q*�[ �1�80�_65�629��,LBNL NSD Ann�FRe�A��]�,6w&'S.�%�  %� xINSTITUTE OF PHYSICS PUBLISHING#z I�  I`Pr�Ri�f a7 �pub ^ � [h�Ete�AB\ I P0�B jourCm La�W�� ��  Iy sourc8 ,de `ioplau2e6Y'�6to� te `�T� Iguide� 'lQ#)=R)D�R�96"5$ RI=@ ��Q�."�) ��art.cl�7o 12.cli� 0'.�2 I�  I�=[itself�s �& �B I� % ��m�%�Y % FVuw1xvef haxUer4eck& !�QlamIj7< " double quot+�% # h.` opeEC *0(grave) % & a�6s� '�"Aa 0 acut0$ d�Y�%�� % (s� O�d)Y�ren��% - hypgS2=|l�1gn % | vaS+Fb~~ tilde: % @��}_�V score % { �cu�P bracC} � �[ )w5] ) A(ket % + plu �,, ; semi-co� X* �o risk�lo�< x�}` > x �E2mmaB 8. full stop % ?&�Q: /��� slash!<\�E ,^ circumflexE�dABCDEFGHIJKLMNOPQRSTUVWXYZEdabcdefghijklmnopqrstuvwxyz 123456789�\� L % 9 December 2004 w|� >z\12pt]{��}>�[ Un$N!n� �� if�] fod�]red %.|[Yms} q���*t[[Micro�X Calcl�) SZEDA��*[�S,{Sachiko Osh�k4 Takehisa Fuji�,Tomoko Asaga;d�{D�FtZFacul�SKc[ &cZrpNihon2UZ8Tokyo, Japan} t`ads{\ma�� {fff�@�:.cst.nC-u.ac.jp� -a�^*��a"�ZW�Hrry�]�m=t2\�,a SEDM iG@u��um, X �Hg$"� c9Schiff'or��we ~�|\{&� �6�.v�XS��#�[th`P is >'eciabl4*k ��)PiY�A&�new me�9ism�2���x�u�$F5p�)I�OsyRL.-;. �$!p of d1o�f �o�3�g_D �0eq 0.017 d_n$�MnW D9�bec�_$ d_{:"Xe}B1.6@ n #$HgFsig -2.8 &>��It =sMW-�!@ c^TinǓ��z� �s rn�(0.37�017�/P14)\times 10^{-28} \ ] m e}� � cm} �O� Y� %��a PACSHCs �� mes�3 \pa�{13.40.Em,11.30.Er,14.20.Dh,21.10.Ky,24.80.+y} %�`Sub�*to"� 6h%��%o{\JPAECom�]#if �`� :D�( �e.I\\$I�Ldu~{} �!"�*AXT-vio�>ng[O �#�z�?ApU�mPIfunda�xsubjeB6in 9��Sf9re mustA�sAr�o as q�a�A�!.s. Until!� �u�Ymit1�.F$i�`r�%�.8ne1, ne2, q1} $a�yc1.�2 5.:X6FXuWH. \eqno{(1.1a)} $$ >W2.�3�ee�1.66��_b _T|P)�@9id��"�*d\-�!S�^M� �|X@s��e g�w8:p� ad%;a�!���(of $^{129}%X�C)\w22,w2�#9 #Hg}߇ q22,q2}. Af�$�P, h�-aa:��carefuϒ*kP� � In�g�^ E�(-a�� �B"�re���a%� �q�0"e�emaS _��M-\_�-ca)�� �E5X�tqXaY�V}���.�V!� �#��ng th`*- �0et_"k=s�P nonr�`�d& kinҍm~}�*� ����E5i�-�fi)�_2\8GEU1\13,q4ISy� � ns � 6Sin heavy��1Xx�T�&3o�! �/��f<$d_e$I���a UC�om�"M�en*U�$, namelyL{Cs"F91 ]�X44,t1,t2,t3,t4,t5,t6,t7a Hq� P`be��Mi2�mb+jb�@2 1�.!�a�F4}Yo��-�6 chA��]�>!<superU�w2) m5@11,s1,s2,s3,s4,s5�$)iU�oc {l� H}_{edm} 3Wwr�2{U$$\psi_i$ f�Vo�a ��S coupU1e3aJ $d_i�$$>b�N{i\$I2}d_i \$ gu gma_{\mu @; \gamma_�8� F^�2��jX2$&Bno�3e1�u�/strengH{ U��rv���&Ab"c"%?��! Z+!:.�icJ�At(p&b stag.�I�no�GIhow^3b2�el��]�n11��be�itd m�s��sC�Y� � "� 2n �?|/e���.�Q����'m�| Y �V-� �� I �_�.NŁ6�!H�)M���y�`,r�\�� � �!of y ��g@b�i�0�7� ����&� K� �"� -%�����a�-�2; doesEsee�f�VE�*=3L. Sushkov, Flambaum�Khriplov�� �sush} �i� �e:x �itf� by Pͩ.� %8on- W�X�} veng�z���i��sό:xi �d�Zly �g.�[!4indiv�`� }s*�6q#�Ng 7~k8�.2� Lamoreaux �q10E�6�$\bf S�rfck� �E2 $d_{p,n��as� xS��UR_0^2 I# �"RI]�$7I}�&�radiuL9���$f DFMp��9��pY�Rag� V�a���E�!e unit�P�b��E� ma!*��EX%$�2 ({io+i=1}^H d}_N��P}_i �O1�}�Y�o� c���ؘŽ But weq��a��\ typ�j��8 s�� A;Apega$.'�}0�al.!��e�M&٣hee �����qHa�OY� ����9 .1�shK e�e� ��f � -ѭ�EDMTU f�e�8t��e^��e�ksi[%�įe�$ E�AI)�A �< ncel' !!I[Q|.xw��e9�c_���icR, �� nduc��ew\-".[�of�c�5���2Q/ Eh:� �1�1c=a�6I� ar w� b��$UZ���n�B��ga Y\ VUTl��act� � easily��)o}9�.; (�8�RӉVScbv!�ed%���Ug��2� M�eg�=&x8M�Z�12� ha1,{�gon*Ω4EwH*?u�;=.Pead)S o�� Sp ��S�aV�A�f�so�-!eigenN, SE���ed.�!/per�WtL��m��T>6A/\"D %�B� Also,��add��nmG& wh�\V�E/gi��a ���"o���IF^,Z[� cee=u��#�|?leAR�:�.�e:e!�JY+employ{�q�y��%��un.qurb:�Re���in;h�Ky�C�Za�*fWta�$� h��C.\)(=Qj� tP�a��END_N: �@,^�M�aA�v�F5NweqQ�� ��^�� c���&-1Q%�%�:�bP@ur6�is8._ E� D ��v�C� !n��Nr#" e\�bp�8eU1bw2�-�� �����.�*�/P :!���=�. HeyD�=�)f 8!Fby!;Bw�0z�Za�N�=.� !A�q {.�k� �K �n-�*� "P����"cD$E_{ext}$. Among Ti��U-�&v m�@�>EQ[oA����� {Wm�=�/� �,7;z?<(S �(K4\nabla_i V_c )�($e� r5 E�xt} $�/� $V_c6� Co�m forc&s�c2d� �������A9!�c���3� t��0��I�r� R�tepe_HE�1 ^[p��$�A�thui J6 �neg��fk"�wQk f)� Qe1��2���gr�rmE�REI 2Eu IE%�h41> Ao��-ed(>!^Ǔ�APa�I��� . A_���wA�is *F�"F� �� "sIэ�$(�GTKs�^AC%)�1ˁ4�%�5n5�� )�f-�by tak��i*�<QyarI"c U"� � *G����t� ��kmed�] � %� vu%{M�.�1�A9�� inv� "HK� ss* F� ���i%���� v �A!��f�s��dtxpby �Am -{Ze^2�D{a_0^3�<$E_e}}d_n &  -0.7.�$9} Z^2A^{2< 3}C "I3I& %�u�$Z$�t�a��T!�zť Z , $a"a�"�%Q:arm, Boh �naـg"�nic)�I�e�y>!�@ (of eq.(1.3) �&����*!�=��\ *| i��IM9.� q �y�D�at��i �yed�>tre��}uthird�t)�Aa�)l� !�.<1��= B[��E ���#�? 3}@�; 4&�g�e�2uJ�%)9�de�{I gl*may feel j�=m�a.I ��.�"� 2RE�t��8M lway���y of 10 Me����t ; so �!=,xvarf%�Z�&�Arn� +�A�aLE��1|e* iE!<���� 'i�*&B9�.C�&>�s� &� Wn�`�'� ugh &�!4�9�� A$ assd�/�.��tE_A}���e 03 Z�7� � -�de�-y&[Oe:�oA�g�no��tor"�BE��1�j�6��/��{41 �A^{1/3}& \"(MeV}, \quad��"1.2"[, + ,fm}. $$Ѣ�al�� ,KFN,�hm!n�PQd 'f|(��N'9j4�s )�!�eq�"š/-�A#{0R'*#4c8��iI�&���(}��9� �e�1�!A���� !3o�) )o�� ��_o!�ye`)ks&��e; S�� {us"gY I co7 �-�/  a�& s. RaUlyj �� 6c�ro2R ���K-*b�� e abovc mbe�'ogm�wit��)":$* �2p.��()�#�)-%G's�Qe�n �|^ .�%�&nQi��(�(�(��(�;5En= p!� �"�O!s�)Y�"�"22I�- �-(1.0�% 0.49�% 0.406�%8L&Z�}/6 �4A���)=�S 5Qwal%1���b �T�źt���ifIE1io, mitmdAvNA �s"S�\��T��yi�b We���!�2%��EDMa Z i�� .<$,�=/�B�a%+13!�%�cm�a�$par[�&�(y amou�o\��G 6} $e���,! e p6R"b\}|9'�� l�j� baryon-ph� �ziovJr!e�dh*y#"� �)' ���7lorgan�M�Qэ  way.� e�01+�wtry�2�k 2 !:clarify"��>��orJ�WB�.%�af�4� re"���re �C In� 3��&%� B(�ls��xEJ� a4%dc �*[ ndAwY� i"�*&% �$1 & ��"/e� lEDM�we!�t��)I!7&�. A ����e��< 2!ͱ)jM �.  S\ on 4��mariz�i�� MEZ�aa� &|-jo*�/����am;,� + �%Ei%�3E�to� e �.��/� ^�)H��u�,{  bany^ ER&k �<�vs "� /�!c�l� b�s�d i}&&�)on1� F9al ��ert"R *G.K� 7?Y can�1j�.o.�M�G��ˉdQ(u�!�2, �����%� us bs�*l5$m�5o�!rum��U*�T.gk��%�toWE,lyQ(If.z s&�[Oa�bsen# licit2i b]� FV( �7i���;S �ar�(.;v !�F�$H�R F^ ��ten�H_0�{{ {� p}}^� $2m} } - {e|#r}-$R}_p| }}+{P:,M} }+V_{NN}( 4 R}|)"! 2.1�� $m$�.$M?%jma�˩Mo�d)�.��.4� bf p��B!r�$lu@&&e 9Yj kw4 G� ��n2�pr��� cs>�F.TP �$-� '"��-�Jx�H&� !� �= _p5� n \q� P}={� 2}( .P}_n) �7ho�����;��I�!��fwa8t�_Gv w!u+�Rw=0y @$B^1��eQ&N�'��No'2mEatA.�����N4�,%, d}_e �% �.' )  i. |^3}} -{Hp�H2I`�doN�nf�n ��$$+�N-� � { R} �)�!)�d}_-�d}q)>"= +e 7.R*� 2:F-Pu� 2�~QE�i"��!�mKq�, FV>�Th� e�'o�~(��� �d}_i=G., \mbox{\bold� gma$�'!u Mt?~^�66�1�~�"C:��lasbr� $HI���0& �(l �&� �j" wh�5i���ͬ �X/� &3to&�Op&��1�$a�Eq.%��S�1 .<* �*R� ֆ���E#R}J>#mz�>6�Yq\�;+�YF# �$!+�P] ���u�޹~WU r} -B�\:�N�"�2.3  &@� .E���*}��d or�is�far]�2*��|���aa �Wq  of ${R��r}A�aI^[$4�;$�F - &H r }} �7 �2.� H_0^{(fs)<�Z� �  R��2{r}^3t +{Se^2 R� 20+%�s.���� $.w�a�4bW:f S={5%> 2}-{1 \cos �Theta��� a �����B.e��.� ��� �xE2k+ &R!إ"b��.�&0 O\��r" �Lp*U!D^{(0)}$ FZ.� .{ -�$�{�b� A� (R/r)^2 a� m�4 {�[�N� dm�%�{r�� �N[��Y�5&N�� � = {SeQ� 4r^5 f� lr}dD+ b� �� �� �RR�#��>�"k"���g �ck �*zBVEPJ&"�.���u6A� I*V_ij *%. � A� �22�)AkTB�#�($$ \Psi_{De!�0��#7DM��R��o�@\phi_e2 r} )9b��psi_DH � F @�6�B� �C�B>� �Zrst��% P.R2~L�$� %�%�y5� �; "k!^{(1)}e�O a�0(d_e+d_p+d_n)-�.�7�7��2cN�� U.t�� |5rO91�D’�2)}_{PC�$%\hspace{8O$$ -\4`,{n_D,n_e} { "��%�{DM%�{Q)|�f�q��' A_05� ) |^ n_D).`n_e�^�<\l AK �R1 |ez {��.a02_A����#E9-E_{0}�l!a"-217mm}F/ ��Bm6��3.�R����| i�֏.�B�-+�zR* "�8I�4displaystyle{ :={ T���t��d��0"56Pq�D.���2} he}�� .A%�"6�-v19� K" P2d� �9nom� �3S!�O�&�тtyE]�>=i�p}>1 i[ ,2N]=-�<{e}} % H_0]��9.�0 |>�-�=i^ !q ! y2&ny�E�S^%.9�*�5�x��up�P!�6k( sc0Ud."F��5�Gy ��%�J@ = R� .�1�_$$ 'jIx:��4)b�$��"���gn�i��2�1~QM��&��&.@ �F A��G:6� ͅ(��&` )2A G*!Ò�*F�&>e��,B�g. "�/)6� B�%�߂way1�p�� ous &��(�� eT "` 5bڢ>�!2�e� 5a�!B!������F�N���-2��A����� ��y �*6x � | .� 4 � ��� �  b� eR �kf.>�0a�2� ��* 1� � AieE:p$�0TV��L6� E�aD\�Ge0"P-6�oH/��e4$ �i�9s c�A�E�Xy-��b(w�2���F�a�W�8&; I�11)"-mZ.��� !�ƃi'"\5a� $<�10E�-E_0>S# 10$ eVam.optimi�F����"�-b� G�  2 >u}}6� � 2�r UfA6|SR^29�M;.* | {1t1: �|2� D . ��12)}$$1���-�2�# ѬA�2Q�: �;�!��E-ub2#$eq -1.6� #9:@1>.��.!�*�(�N6Gb2H  x@�gI.�$S���#ifA3=@ F�M�i28*@7"� �#�'nG=0��$!c��PZ=s `��V�va���0I �is�����H��nit�e $d_D�A5K*�. W$�uitt�6�H�� e i� ��E+ar��%m��z(eqsG5)� 6�)2���ur�on��ofE� > a�N5�=!2F~�J%�'�� ��is kept��.�)�G=2� a&q9s� : :R1 }2��.�( ���enٰ� �3'�����R1|(-g 2} )Z> R����*? &,"� 14.�!�2]�͞�&Z�.DM orthgonal�'"��2H.���2P �%�E'."wrʤ�*�*�&�7"��e : �r@�% inuu8NB�#� s4%'I�$|n_A� !CrQ�� A}$ a��:* C=p1�nqrt{V}Jw( Uk. ��P2.1�� )� }={ki M2�1HF� �eѮ4) �RL�d_n�I2Q,{d^3kI|(2\pi)� d^3R' {M $k^2+k_B^2)�/  D(R) ') {{R'}^2}�Fa�� cos �  '*�[69fR}-�R'(]2�6��!�YS��UD6�*_+*/:.�'took on@(S-IFrV]#k_B�2re�="�5�d��:G�3�&`!>k_BX�E` ME_B"#-46  1{:-MeV/c65*��$�t��M!&�um $k�wea�C���ٵ���VQ-4\pi}}QdAK' {�G\lԦ -�|)�9�| 1�IxJ!"��~� .k. 'H�Y8EEhl=6�J%!HP!)�5 e�R! % �3}}:�M%��a�R^3dRdR'R�.8 %A(�O4osh (k_BR_{<}) g!'-{\sinF$4e�-t)�!�( � M>M+ =>}:=%�(!� R_{>�=a9%ai�$ {�$)" o�O$2�kM er) �5�R,R'$< �sA�numer�5� ��pmpl��2av�-c(nF&.��E�� l=I�!obeta^3)fI�I�)^-��-- R)*�2�"�w' ok�� �7�5�!=E#=m�2�! "_�Y�!2m .l B7��� �� "\�A��2�W!7*� 1 *� 2yW"�not '�aW1!�berua�O���|+h1���6�Le/� ompe�B"v }(�ECfa�H�4e� &, osal!+w~G��K��e�Y4!.�-,Ns � A.���Y],�/.O�z�.c (27�1=7B�3.An6q>!B�� n$� aD4 5�� iZY^iE��Jis�Jp/.mZ1��-%�"�%1� 7Si�F.U�F��s!�b*C!A[�4)]2� E�2x ��!'7*=�g T-, P-odd`:Z�P.5!.hZ-*Ged qM 2�Feynman X�!%%�dr�m�quark- gluon�0tex"� :d!F�&6 26r�Z�a�c#�TQ8�%�ais�aM!_Q e� F�G��N �4A�}O"�"Iwo/�%�a^�&�RBZ �%Ae-lA)�U�5 "WA�5qyu��VCQl&$#��at aEQ�6� ��e! :y��M�.�+:�<&orOisq~$ed by Fla�mbaum, Khriplovich and Sushkov \cite{q14}, ` they obtained the EDM of �mdeuteron as $$ d_D =0.2\times 10^{-21} \xi \ \ {\rm e}\cdot {\rm cm} $$ where $\xi$ is a parameter related tos�T-, P-odd nuclear forces. We believe that �|two different methods should gi,e#IT w22,w2,q2}%+ alsoEbre�$a proposal!- fS^Ms-\�%ar-h g q12}!�I�( same way a)Q9h case%�$first writ m0Hamiltonian vtotalf|q8The unperturbed2G$H_0$�Xe �can be|tenaCtH_0 = \sum_{i=1}^Z \left[ { {EoPp}_i}^2\over{2m} } - 1j1{e|1r}_i- PR}_j| }} \right] + {1I 2} C$i\not= j}^jHrH$$ �+ <A{ l P}_i�2M} }+fk$A V_{NN}( �R6�)J� f�:>�8 \eqno{(3.1)} $�q�! $, !^$ denoM coordinati�A�moA�umUq�a� le L�Y!2YQ�variablei�\, resp�f velyAaOI�(other hand,�Vr(coming from&e�sQja!�$H_{edm}= -6s)�IN {e%&d}_e^i \��(!9YY ) EKVv^3}} .)f)�iA�kA|bk k!� $$ - �iA�q AlN^j�� .gA sV�N:CA#bC6.�.pZ%�)�)�E}_{ext}:�d}�J- +e �)1N�i )N9yb2.ba/summa�. �� $Z$�+E�us���i�it �be take��ver�tons. �eA˭�Don�Hexpre�S��erm՟�? on isospiu= = ���s�(1+\tau_i^z)d_p \mbox{\boldmath $\sigma$}^i +(1-\- d_nn.��.A���bR Fin�� size��us} ��evalu��!^f/effecᕉ+0second order %8 energy! heavy^. r�-of| beco� as�� - {Zպr_i����٨�+.Xb� r�����NO:��.yF3iFHer�ign� V�1�Z��>E<>V0$H� ^{(0)}$ �:(point charg� >��G<� k.�6� u &I�@of $ (R_j/r_i)^2 %�2�B� eJe���ɔr_iɂ-e�(��� ��N^jIr) ��ZGE� D)���>� �]�$$2�i��� ^i_e.U.� EN� :�����BY�4aI�$$=�fs)} =- �%e[ GB�%�� %�@Z S_{ji}R_j^2 + 7&-� [.A ��j6: �]{e9�5}� : J�]v{�6�:{6�� - � 2} �%A .R �ARt .wb)ww� $)0�F eq.(3.4b)A def�as�� '={5% 2}-{1 0\cos^2 \Theta%�.pc2p%� N (angle bewee�r" *6 X !�$� a����&^ (� $|�3 give���2�=\sin \t�j .!�(os (\phi_j- i) + E3% i �6��6�.� S  (� excit�)aVwnnsif �.w N�R! is"TmL . In-�to6� 2hu8yEE)�nEioqI� �A$b ar w�fun� s. W�2a:�2%�L� by��Psi_{Ae n_A,n_e�+psi_A^{)}f R}_1,� s,�A ) \oP ��e7HɟrB7 r}_Z7equiv62m :F��52��\ n_e���4quantum number1E ed statesiB =0, E=0$:�(groun/E)<� "� assumy�-�g hm.MI\� zero���1�2/DN outer neuSE$&$e�a�s mainly� auseB$^{129}$Y99}$Hg ��Tpapera��Z� �A��4#i8�"� P\Delta E^{(2)}_{fs} =3!� n_e} {2e{&� #{E_ -E_0�  \l��U�0)}UC0)} | 6 ,0} |/n_A�Fvr WF`Z1|3 ə z�e�2�_ "�62�E���2�)!owholeM�. FVis equ� ,�is ��9in��ediateU�I�isI�2wi3$ due t{$orthogonal�diH"�, operators oA� invol�J� sIqe�of�5). Fur`,.fs!��6b H"� #� � j .] 7A� $$ E< 6)�� be�]d��employD!�clo� approxj io�Nk0\simeq -{2e^2ydic< E_{0e�ac>}}.L qq0Q�,k� eft( ��X # � r}^i)q - Z R^2 �A� K..,AV&VFI) {z_k�:r_im |0u{*�8i{Ta3+� �=Z�> {d_n< �� � � {i} >1PR^2�)�a_0�9�g !�G terma9� (8) vanishes}��s6( e�� ���beŚ����$a>�$Bohr radiu�27 � �t I*�Zme^2Ͷ � LEDM&� �ȅ�s1��d_A6�Z)D$mZ^2e^4}} 2�R ��Ka= -1.0mE9}-�NY Z^2 A^{ 3} d_n=�2<� ake $:� >z$eq m (Ze^2�%i$FA �eq r_0:} $�$r�1.2 $ f!$j��\�if�" it NA�density�"� "L @spherical symmetr5S��{o"� � of unity,��is $d_A�$very small% �0�(gain little1<,o observe itA��u9)� cor�ond"lA�6H, "' ��!� 4a�kq13} e6though- re mO b� ce��a fact)2�\sZ�o (N y2)� �_��2*�ar]� important^' atA4:" !�possib[��M2` sse[ !X6i"��$d_i$ !�P $individual"�sQ exter�f1 $E�$5�� e�aEq_ � ari�"�� 1y )�"��*�Re6�#-JB$R�F< "�F2 F� >1 ����Aa�lZ &� Z ��H�\4��z� |d&�A "4}0�r@� �{- j^z)�(9%*4�6}!H#�6/ 2. 5="- 1R $$� ��10)Z� "i ��q�beQ�2� ($n_) �&� ��y� &� a�&� 2@6�10)� 7q4&n&f re< $\displaystyle{! I�9~ =0 }$��Tn�wastYce  mass} to ���  E arry� a ro����ioz5� b� �alisto%,hell model *Ts. �u!ma�26 V���u� } �� f&� }]B1N ADT6 ���L��2N��� &� 2� .xR���0.03 Z "�"1> made � �Qs $T O,\hbar \omega {47$A^{1/3�$ �'MeV} �"R� %\ �'fm} $%�2h..:'}&�1� eP29}O(Xe}$ ��a<'wep  aA'E�gleթ .-e�4, namely, $3s_*�`(�oge�&� $2d_{3 ��2^+$.*QA��&x�.#�'fY�d2��&e�Q*Al![Th�'wI�)7�2BW�0|"��I�&Pqrt{1-\alpha^2}|\nu (2! ) :9/�K+ 7 52&)�9)2B�}K2aK! � $ Y� a!�am+*)� beJerm"Fr�0QT�)!23(�(!�2� -� "&*��+T a�f(��9))EJ$JB $^)re� c� toUfollow� �* �%�n1&=-_3p]�)RQ\ �\Z%�[>�,^2 [0^+], (22O^{-1} ] 2W �.��d -�=!��&es9�Wa 9Qi�*��'at��abo�wo-� F�matrixa8�'��*:" qf mpon.,$R$ �higt'�s�% F-�rE�$� 3 does�:�F �A1��i� a col�+�,y"[ & x�+~A)M�9 a l�!5!�M M`M� J�+&�*�1 ��!���,"d (t rank tens�i�ga  $1^-j0^-�4.2w &%TyiWY%s &M! 6�E"��Q��RH��&|2^V�\mT mT:�:SZmS "�^b*G12� W.thm-s#.ified!�figur�� ��eB 2)EMfin�/2 A�!�gy.��=&�P.Z= = �- �{C *�#7'�^) \{&� Fn| Z� 2��8[\J&|�^�' � � R&�2:��� � .$� lef�-�� `6w^�6&��Z� �\@#+1�V�6�^� !�-Jp*5 b12%L:J�F �#6� ^��)<>�%.6�6\^Z=9!��G^1�aJ9�F | {�/6��9-:\} ]&�1) 2 ~to be}�0.5$. F� "?+�%� ��M an6��7$ | BX \ R_i^3��3g inducoerr^$20� 30$�r!� �3�&�ڡ�< harmonic oscill�6� s^ zsi6� � ���: gX%$.� eq"� {� � 3}52"� � _6i � b&�" ed a� "���.d �ՙ t2�&=3R'� {7 �2M ��"�41 Š� f  �2�A��w4frac{157}{30 \� 14 \pi}} �.8 48 B�6A^� | Z=@�FW155XH �6W�B�����Z� �%�5}{21})� 2}{:�2�d��2@2��ΡOJ��- q 1}{3>�5d]��#>626c��6�]� =�7}.*E�26*�fV'����%= -5YY� 7}{VgZ��GGf0�/6� 5�22!�q� � 2}{76�.2�h � >N  �" 3 �;�{\}�/d.��eq 1.6b.� C&�i�surpriœy�:& , bu�B�; ") rel 7��3{�Nvr sOFor�pr.4S c%#c+)&� � �%is ra|�icult[�u%Hz e-m�)d2s!e*�"�3'&T@2e &A IB��iF�. I.start�*���&$0^+$" t�,dip�$v ta�4 _i]�"0$�n�"�QisoveH�zs�l��ai)� t $j` |R6� �>� @ u!g"� VR(I)���.�noA:&qW&� 2�>>�extE�&�!/$^{(elHgR�lso���.��� _1^2�_2^�0������ R�M/�_1 6 2f_{"f0��D2 Dz&��,*( 6� �-_1d �2ta n!� be 1.> 25:9:.*�2dv�f��*b$&�6,/}F�42�6�� \�7 nu [%Q9�&� : �VW��6� � A�Dh�*"sf��� >�$MthirdL� %wV3d2}^1 1) 1*�[:�9'�Y�-&��*;16&< F��]�60:�X��.�6 RA"R6��&�@� N�,�#k[.$_&�_2 B02� � :;U6h 6&�h 2�&h Z! �:"6D�:� Z�6&��r�-�x"/_1 �\{!�!��:lZ�*# a#y�Z09b:��>�))6��)� V6VZ�=*i �*�>�*�*m3Ec�� ]cZ�a9��Z8�"=.�b1}i:��@�;6��e -<l@$$.f6�� 15A0�f.52p�?�4�4&�:&�E0$$��>�.!p2�!`&� ��|:w9/=-/&�-o">�8� Bw��fw �I6�9�"�211}{14�3� �.K 8K >k��AQ�a~�� =-"�%&?n�8&� 6�2t jg�K�[ =(44}{3� v�8� >�!�M|2f ݊!�1N��{9j�8&.B��y�V�V"�35\N]�T"�8` !�:�2Z �H6� 5[u�B�2,*G8&,:z2��Q ZQ "�C)+142�.��$$&-g66Z�]����D2V52� 1}{2��� .�i�>_�}��6�?"E8�E.�B18jV�A�����!�1Y�Y?8I>���8.AkV��z��6�� ��a �� � 2�818l �5VHg> -2.8B9 w.X3Nn=q$$d_n$} �4$Snow\ �, bet"lD&�8N'�=SvVA�� �tra�H)K~ "�experi8(al . <3$.!$�@fact,�;U�'"j�46 S�d_Xe!�=:$(0.5\pm 2.6m 0.1)�1727}� 8e}� rSU�C20& fHgf-(1.06h0.49 06j8nj*)20�  By mak`!^. eqs.|QMQ 9)%�s6��<-�[VnQa (0.3�1.5 �RZy�2�/V,F`7a 0.17b4N2c)��V.u/_M:@quiJR �+ngg*F�B� �6if�"�UAWi�!;directKO�2s��g;C'�-=A�%�"%.I��m� EU0'�R�> +/!؁�)% E�\Xenon)u�<&� ']�M�Fitself. G!1�`%�>�:-�&Z �?�# f�<�;/a� ]. Even;�E�]or D$Kmolecule�ch!�betRH�1aM get# &�"I�Bs\�w�of%�a few��=*92�F _isX#�� w+9|etey�D1{LM"is usu!� �D?!#]I(short life �<� X%� \ack{We�(nk K. Asahi%Yhelpful�@cus�%� com�s.b?�L *{Re�_�ces} \begin{thebibliography}{99} \bibitem{ne1} H�ms P G \e� h1999 {\it Phys. Rev. Lett.} #82} 904 2J42} Altarev I SK6.K$Atom. NuclL59} 1152.Mq1} Sm�"K FJ0.J �B � 234} 191.G,w22} RosenbeK;M A%@8Chupp T E 2001.VF� 6} 22�Lw2} Vold T G, Raab F Heckel B=%8 Fortson N 1984rd52d29.�q �m�;( M V, Griff!8W C, Jacobs J P po �� 505 �aQ q2} La,aaux S K6d��0x 1987v�9�7xw3} �lL I!�63>EMv13!(192xsush} �cO!Fla�c V V�.�c I B �-�DZh. Exp. Teor. Fizn$87} 1521 [9� Sov.i} JETPI| 69} 873] 2PXeng} Engel J, Friar J L� Hayes A CA�2�A�} C Y 1} 035502}iq13} >�!�2�!I9-�CP Vio�>*5V St�- enesy $(Springer).jP44} Asaga T, Fujita Tl$Hiramoto M2orog�%KP�;1�06} 1223�bta�andar�H 1965.�m�m0 14} :� t2} 2A,B2r.B2AA 90 ;A68 iJ5ӍL1} 512It3}�& tley!�,, Lindroth E%Mar�7 ext!0�Xdef\lessim{\lower.5ex\h�c8$\; \buildrel <]< \;$}} =gtr�=>J=.�hpathnow}{}%{/home/rafelski/k=e/} %z � 1�}QEd�=10000 !!@margin -0.8cm\oddQY = 7cm\�LJ \pM>{!;,title{CentraPHDepende�0Hof Bulk Fireball Pr0to\d at RHIC} \author{Johann R �ffili'{De'A~W��(ics, Univer�NNy�m�f��E�� . W�M arche5a �g �eIIpm"�as _`Y�: if aB a�DM�i�>m�$3E�semi- D �ar $AA$�+�no�S $pp$�s, Ew�naio��� a vi�R �in�u� :-(sufficientl�T}8ofz �-ticipant7O %N�Az,�5 %�top�?>EJ$.#)F��sA $\pi^\pm`rm K} p� \�M!*:��b�ere!ylyA�e�ed,4 t�I%� VIII Ref.Hphenix��TuF prec�2B�g� volv��a full�GIl�͊ motivH��M]ffort�u wishaes�ish%h!�I levef �{,"avail� �)�9�!BNNͲ �� run, whatvP!DQFmUq�:Dios such as $K^+/!� +$, --$ f� ��\YL�I��s}��q�,kb7�A�VD (SHM) ��Es.�|g�J! . � NHx1�n%�5߉�>l ed D STARY�{�P%$K}^*(892)/-$Ml(haibin2200} � $�S)~C#phiylE�B!JjY�RBF $e �h �%K.��_��w9Lk�s I�A�K�any6aG7( analysis. ��8!5A�Der� �$!E6�� 4PHENIX (submit!{!ec@ ,-KAdler:" hv}))$- �d illu\�N&Wit�`�$Fig.\,\ref!kSP}�data}� lines )F�b�!� i!#� (�panel), �middl�Q!� comb�Of, set (bottom < x"gssI� thos��por!9by*.� 2,)'�N�Y>| derived&�:�! 6�a�Bb)�o � �� 10\%.�e$-��s,�pA�a�at�Y �e1g-!9�$ so, �� @�A���QnmA xM��%!e �0st $m_\bot$ �#d� }%�pOpbGe�Ga�% s.d.L any %K�$9_�madIR- Qi94atE~�. �@ [y��6 flucQ�>kri�influa��! �U=M� �)` NF 2L}[!bt] %\hspace*{3cmhvskip�5cm-.6 \{width=8$,clip=, UH=PLDN2DMTDY10NEW.ps T c-0 Fcap!�{� pha� (col�na�) M�{d�1K� t"}$ $dN_i/d)� dy$� E�mo�|�d*� !���2�,�S� �Ks.�o2r�:I�sc $S$�ZsuP$)�7�[abE�.&A$yI )4-�3cmd )c}n� !��n� anchQ��confir,'h0_emsfreeze-� temperat�k$T�*^J�]e�AV �Tozc�^�B io ���$�)��S !�C5 m*-�� "�and��"�Z%��.�=�ea�*9 eD�5i��^n�So&*�#{ ��q�w&"�A. H�"�(principJ%reson�`t�iyb�}ignifica alte� by�;t-"� c�s�lBleicher,Fachini,Zhangbu}, �' ir d"�_~�(�"� �` deca�'�c�ing opRes� � � I? non-�klib�":� dea8b��6e�zed$/". More�y,"�N�# �Hcts n� co!vtAA�UEmac �.$�mWlimit,!�"�CpoB�:� e��, or =�jO�)h�(n%�e a|(�����,or SHM adjus�E�%� � K$^*c Maoril$�"�DwV� purs�ihea�velopLkinetic q� )x�iA�les��| A�sAO�)e�(n �B |w� dv� � s� c�b�. N &4SDf�] al H2�Models�N .%P"�@adSHMsecnuN�e��6E� Asb� fC{i�aof9Ta��i�ee birth� 3�s�3 �y s��o, (maximizes)!� ^um u!.probab�$y amplitudS'�0th�[A/My�'d�Z�Z� ap��&��r�� ac�+ phase !4 JJBook!�KIa+ su�� (global dynaɮ U�,a�_"�Xflow,% | �oo� app�f*-ach lo! co-moAfr�-eieHa� ults� � a] w�-O0 ed u"knumg� SHARE (.�6�� REm�s)- share�tqu�.A6if��' Je��nsist�M!� weal��f��h� today,��7 WJ. Oy,ompreh�ve�of a��vt��g��p*v "1�RA](200~GeV, �/ s so}ongly-Le�Z5qe}. S�pa��p��vA�q:� a wid!� �*�#=f Aicqa�!?SHM, Freview� �BDM}b(An!rr��  2` (ear� v� ) �+e s among@� ]��%� �N y�q� { -200:\\ 1i� (p�Lminary��Di {\Omega}/ 8=1.01\pm0.08$ T� ��(barannikovax'!c �/ g��0�i Ii�x$on generalr`�st ��.ryo+5 yo � W�1�>i�i2^;\\ 2)a�eF��E^{++}/p�4[306y �Markert,�,. �2b� ��s�� half�����n΅at�64�i�S ��, af�#removal .? enda��, weakhs, ly j p�Ns� �,v�a� marya�%/�- �`ad�io%�8Yu(re)Q�&\\5=Lenforce!�#� �N�^n� intsA� 1)a�� �Per-~p/.�Ax(gr�9can%al)H un $s$��rkW!i42slF �s9a� ���E�Q`uc�+��to net bI�I�A*.fi�jA4�l�3a���4m�`toe�in 2\%w3i� W�pi� -=1.i�2"� �,)7`8b &s��m\\ ��z [app reduEX,��_�3�X�tuse��&|'+piK_� %Er`�2�� l1�:zAH�ir � , (��ZN?0in8m4Q�xallow"� 3P;qa1] ect.� su�.� ��e��e �I!�� " AW�2Yy &��mf���/�'���p wUJ�l(of $\chi^2$��� �Bn:�P� �).�B��M� mK mu_B)� hype�%$S�QL poqial�)%�  �s��>"� �na&s�0%.[(dashed�,A� B,��H� >�Ž .� poccupancy $\gamma_s\ne 1$ (do��3 s, violetj��%/lԌ q flavorI (� )B�m�  includ�}q } (soli�bluwine).M�p ach, 4�B6A�Q� ront4a}v fash>  11 � /ompu�\[on����.cy�';z��s�:1�A�AN �! 0��in.�TGMU},�vea� me85���(*�Yhlow�<R;��9s"satisf� yc�� rion�:t9� ResT f  ��`�! ci3w@�elp&g���P�rA�red%�; iX L�e7:toU!y��fou-digit5wn�!�->E$V�al� e6$A�� ",��e!  nom"�w4$dV/dyձ� ���2�Z:_G f�(}"O cnA�D �3fEks*pi� � a��E)Kva��< M�")�� "�s�IA �*AqE!w` ��ir "creleva6NF  Y%���"��%J�a�� =-90*�(ATA200LOG.3�J: ��J0%\v�*b�e�>�W7o2\B�l�Z�� lJ�q$�4!�KKto�Hie}n�/ q$E�f�N�� ($B�m�0"� �4$S " �� !S�qb�% (averag�"S��a�6�x�� neb=��iTed�� bin� e�"$�m� �E smo�da��>t� w V.�s: 1)~Fg!�>oi� --- (.� ��; 2)~S�%$�R6� .�; 3)~C��m��&� (m=�*Y. �R�:q�|}[�") *�r Fx2 _.U�o%�Bd ��2�� 5W� �t2e���!܉by ;j��� %N� seq�: b�.,9�s�%=�,��? .�H�c��fm$^3$�$T,� {i B},  S}65Ldallވ s)�im�on .. }��0.2cm}%\�%\�=�Dular}{|c c|| c| c  |} \ha� $A$ & �&h� � $ &�0� &\|(mbda_{I3}$\8"�  �Eq\\~351.4]969e141.125.67 45.592 & 0.9967$F 30 &�_ 13\\ 299. 821!EU 24.5< 5.34\Ei 2.3a1.612E 53.9q706E6 25.2 �463E8$ 2.27z 1.60�15.# 61 �0.8 E05 5.32 ��26j�5866 z462f�e 26.0% 5.52gE�1�E4E14. 29!142 E5.7�E�2E09 �08�74)I19�% 26.1%b 5.51FE0�!� 45.q11��4- 4.92!{�7i 1.87 �%�!�z68E 140 �!Q!Y 4.95w2E63E8\�q13 �55 F1 V 24.2� 4.04�F0!~ 1.02 F299! 6)�42%�172 E 31.3�!�52E54E0.3M<606Y�m�q173} 154.A� 25.0?5.161a^ S%� 1.23IeA�m145!� 155.!I 24.7!B10FB18h Bm121 �!� &26.%� 5.44��6L 1.1I�BM�107!��6� 5.2i[B7B4e�BU�79�J27.EeAn4%�B5Bm�.��;&%A7 27.2q: 8C&�08WBU�33A!J� 26.7!݁��! B1%�BQ�24t15I( 21.6� 3.E� BM& 0.89)Ca�13C;aw!� 4.6]�'C075�U�74��148E� 23.8D%�% )� 0.7163��Q�34%G15�� &28.0%1 4.68DE� 0.6785M� Q�R��!_� 26.9M�34�(%�� X1�8Q� 160am A& A%oAgAE\2AE�A32�A!�%s�a,37�$A3�E�15!�A�A3�4.9)cA��3 ��U� 85{�!�A�0�9Ee8B5B�� 55�B527B41�mo.�M��8a� *� 1�& lrR%� AK   fe~e[J��absh$h*� :R :2 *�4 B,S}$, exR"� 'WPph�kcnd�!�& ��Eb�|ociated *�(��s: 1xN" ��4 minimum�.."i+�tZf��8Q rendW�t� ����,&�$an�i�,~l&�1�rem"�2U ) re looaP.  In�&p��  ()*� ��I�68"Zy� B=2�Q1$� &$ 10=�! (s. Similarl!�we�d6v�h I8S=5�Q0.5 j��* E rkNF�s=�/3-S��*�.��3%u >E�=63 ab�(�)2i%�f�!y.B�MlEXnoi�Y�, �V�ggrax�in�8s�$1 ��� oFZFZu��A>.>y� . ��� wa�"_O� nd orig8��CE��� IspaeA��16}�%0 -F$%3.��k:P _ec��I"I��#oexpan�D! PredW�>c_"!�.s��&�on3OedG-�{L into HG _$JRBielefel�1%?l�( -F2nlsoG *pE#-)a��9T(F�)�"k\2�$^{m_\pi/2T�U A.�U@o�w��N��!�en�oG0�s=(a&�#�"� �Kampfe6#3pfC$ ;�f�{ $T=15�p8�`� yX.TAl.�:t*d>%�b+ur^5̐e!d9&ag��"��s&�#�]A��m�1w�"�0uncer�ty;e�B&#�9 L �$a�*}a+Oyo�negligA���]% $Tj�ehmild dis&�# (1.5�#) �earli)�2P fiiX$,B=owski�$3ax!�A�%��p�1duet: �#&�3�%?�uspecu,lly7(!�F*�e�S=�:vL%�8er�0�%*.%!�f�.N.�2� m)>%�let*"rea�*��I�A!�͇�tru�& of h�; re �sG.�iclVca[M 5E��3 regi�C2)*ݧ�"a>��5�.��a m0}/B�-E�bsB�X$rM� p%nross-��.���%��ice QCDI�2+1��al �s5����{A��0�Ref&�+ W2O�I� Fodo�i4nz�Ase%kc�p�w)Q��$�!=�x�JV�2"ejs j��,9�&Ao;!"=�J*% QGP�HG�QR��PC.to%�60\pm .� b)�;:���i"+r $L�)cy YTst:�!�r At solev@&� �"#�Lool��M�΁��$ asCe//�|�/ suddenPRL�[SuperT!v�KqT�:�.ti����]�bq�aryi�GI�%c4x(7�p���f2&K%ra�6�aM�5sA���2 +��a��5P�� ssp]� r4c&�|�� !exm&�sea�>� � shol~| .�>"^ )gy, seeaV"�.J�*�2*�3>u)�:�k pic�3%]�ex� 9�6�geoœ$ is highlyt homo� o .co>�A|to�'e.g.},�dge�W breakup!!-Q�!ri3k��T�s.Ukz�1!�i��7�1M�ToE�10xi:C1w�!�urfach7� areaA��, e�:�N�)v�a�V.6/to3x23.�U2x4W'� d E�jD�ea�no�1toQ{���*�3,�� popuuPs�my��[ in pF�2 ��*S4 . N� &`1kGa2�G�{"�Ga G�E�&"Y1=�G�[1rJy� �+!�� "!1N�8"Z^�8y� sB� R�  ?opy, &N*&�&�!A+�4�=�-�9B"z/ .|&� �Li?=(��ly� lapping)a code��in  Gg8�$�!%��Ꝛ�6}"��8 G��+^�w�]n?<� e- Zy�� yef�`d%F!�1.s=N�t!)�*� '@:�:�!=w,��;H6�&Q). )E� 1!�-��DɵbinH$14.9�.1�GnsY �� val,� a� �� 4 sto%��vqML domaiіn"1")5�*�kh�H($dS/dy= 5008 $1 h ^2%&� ��"'Dc a�7Pratt�6Pal��3rzZ`o%(p445D 445j#�2< 130qC�` . On��o[0���y#ew��� , .'#*G?1�>�B!is%cly�%D o6l�"\� 0H� soma4; m��cly4se�.sɈex�,)~��) plic"L 5�X!��Y�/!`6!�2��l71T@.1���-�$d~insteaU0� tru^�X :� i�al k�1[^C� cit c�'l�@�Gbe���(r��ze)HxONw"=* jAD!}��J#,*+*�^bonW0 B�"\eU7��)Z�+�ir- �t)h�F.4Hn�$�?�?.7�<SBS�8 :.�E��@ $s/�' ��&Uhs/S�*o/u��a�it�F�*���E6�"�2�� (=� trie4.cp�val�N,��_a fail8UaE.9ol�sh/b of2�i��.s�as��f>ɿ�i @<: $(ds/dy)/ (dB W�%�G�Vdi�H*rE�}xAM."E 2��� h�0s/B =9.�j1$,�( .�e�!�z �/�o magnN;�%���-2/��?,>"(,)Q�R�,er16�J���e#"la� 9& cng beyo�*�25� ���-w?- beneA<��d �ze%?��0<�(�a.����on�.2MIn"`BEgluon f�g �*� ss wS Fj����behaviorS" Whg�D*#occursz.domin�Af !��5��n� ' �;� � .�j"a�ce� 4 , mobile �s, be!� d,Hnb + 2 � RM82dIus,6:rU2foI5i$�eJ�M1s �G�V&�<e&oD��i�Hng:�.mѝy ce(:�P� e�A"S  �E�+aJ:,:�er9��T�1Z/� a � yҢe�art.UUl wN>��XN��7/ q�-l��"�-$��!0\�o 0.03 �����iEqš�,I�I� $A>20$!:�CA�onKofU ":�8�R6 ]*&b�4\floatfix A����� E]�, dmE��M�2v�O�R Z!"8 2>*��a��`��A�hara�� . A back!envLC*� C A !�z/N�glyied�plasma,�)/:s�� :� %��,�*m�LB:?�V3A`E 'ٳ� � Z1!.������P,jX!ism�"de�5�0'�!N1*d!*��%8. "�/ &��QGPz< \/},"�s^� QGP}\to 1%u�BA_��r2 %�Aucn�8 i�VnAK"? B�atw>2ZG �t �t 6�t PESTBu N�3�ts $P$,�d)/tA9(epsilon=E/V!rl !S/V�$ $E/Ta �R�SR� �� *� }�4ʗwU�Ne�SA�=S�xpe�\m�� V�%l. T"]JM��9W �5; \var-_ (dE ,/(]7)$By\s1�9�)9, � sum,*�D! � b�"�<*q�%l��a y�&���k�wIPYex��: H& F�rw�$�;six*�B"��"(=g*F�M� 6�8&�8(A)/dy/� �8/C�',*'ɣ*�>���$�n�nt�'!�$3�OC� ������. �>0X��Yu4iS��o *�' ����2$1� �i&�CmWV� �&lK qV��s�?�& � �;t} �ߥ�i:n 9o:� �6�4 model�m� n�915�a%7CDB"er BMKHR}���El rUD �. H�)&-%T�:e�r�-~�!Fc��� ��g&th�~ pret) offer challe+aS! R)�%>� �,� Y�be� u�9a8?qWe��d#9I  a0rk1% I�)\s�^��� o �qk* 0th $m=aT$, $ah 2e >�Av $a=4"�i�a�ms �GT#s�A2� of.� �D �!�� B !�r "d>� ��e �o!�>��� Bari'�:c�su��n>� � �"t  ��2� �$/'P� rE+. I7uZ��P%�!De�M�Z%i?A56�O�" *�NTL.�G�Esi��*ing6�7n{ "�wF5ER|dksf%�#��=en����m*�Ja�XA7sof1� ��qGb,n�[a6�*a_� N�Xa�st��&� &�9)�QDk��atai�cd&5>�� b�3ho:I0`>��K1� ludedA�id,`st��' �ѳ� (�E�]\,{$"�],�]), �bY $K^*� �V�sz&l* B-lso9� )��on���"|<�W�are�C.�Z�k�v�^hi$W;ult%�R"a,�s$A�g ��2�9� �Fv&I�Y �>s/�W:�rk_�*� $. Al�(y^���Y �v7�S,Los�@!v�-st*�X$A��35� Ho�w�$A<20;�R�F"�T����� �h�di .��!, ,*&�� i/6�O"-�s �����}o*8"�th��}7aW�Maw!>�cj priorF->t�f6�"R, 8�v� �aZ6(],.  NNr O`�cCleymans� 4pp}\Cq�Lai{c�|�n �N�h ]m�di�$� 2\a�. A=[\sנs�':Y�|�fB�>�(vKaneta�zr}�s )s� ^[��iTtE�� ound�.U�.,2O.N*�+k.�oFw/$ e: Y�#,>2Y2��!� nd h& w]g,Qr��> � E�er�)��-? S��z am��U& .2F����w"fs �<xceed�itAhH>�zӄ2� N�� ��A>6p!$e��t�"' =� mal :� Zav�GW *\A�::�{"�>� ���->Zt $P=92J(/@a typ�4+��re�,a��wbag b"| ���vacuum�y.�1�erg9 of�a� �t � ccor95 � �+� a#�Y:>Oc� "U�I�ssflGa� to/�"j8R�a� N ��2��(��"e�S]��*L]Fia= u" �!eRA�1oth��s"ed *��f �nede �N�� �]!I-��Tu/a1qui D�!,%Q.e9�o opin��e}r� ���#�E���ii� � co���nB2'�Pm;us^the�blk�Ze densa5�9�!�� �j=3, �i� �+3�F��Y�E& �I���B �)�;"��"�h /�*�ZA�!:��V�ted: >I,dr�$�&$�qmO�J�^tsAm24 �a doub-�!K��-�V!�ua�.  $. I�Z�*�9NE=B� @ +u���Q,Ecq�`9")L o�8R"� at !�!scaS^� liquid �go k�B��8�a�a�pc�n ledg�4s0 th$$Jingguo Ma�lH ^^ Xua!�ersenA�QnaA& !�W� u� 4 2� s�3j i�8/t7s 1?*MEO�%Q mKVatg*ork4/=5by�van*�� U.S.�rar�2 of E��D DE-FG02-04ER41318��N�;al Sci�Bod Engine-!N(arch counci� [q�e F��GeCrTechnolo�5@of Quebec. LPTHE�r.\,Kr62 7 is: Unidr mixt�2 RechercaTu CNRS, UMR7589. G. T.!�nk��Tomli�z� �RAAgSort'�nrkd:��  �d0.3�d� %\bz�r���19} \pr�4A�vb�i$fo}[2]{#2}.�z.|l %� "�h3cb?ہ6S.~S.~ {�VeP.} [M�;pay], %``I@<K� hargiH�!trA�"uhin Au +"l �b< %s(NN)**(1/2) =\[4-GeV'', Phys.\�z\ C|{h69}, 034909 (2004), [arXiv:م-eyt7022]. %%CITATION = NUCL-EX 03;%% 1(Zhang� rj.(65?*pY H.~B.~) [e�J.�X , K*�!rh�P�5�=�"����/��of* < %�"���a!'in QM! 5X 403010].9/N! !!UGam� e /5AZ- 00} JAYamsjK�l* R5PL �|E8+Au%p+p%]b<% (sNNM: %�at�s!B� 12019], E]E\ CEJ5)m� ^: >! Y p_mF,uxys1D 5:rRB$ %``Phi m!$!�Q2% iXA=p + p6b su]H20u`-\Dxt.\H} 612}, 181-�-BH06003]pNVe !)+UFl�;fm9@�xe|hv}ʌ``]/�o$)*E$ mid-� I in*�9�s$  R� qiB 10012];\\Zj !!-,Mukhopadhyay�j�cU$R D.~.f��'2 f~A�\i'\ G�~ 31}, S187n12044n!! % ɪph-oYr� ,s�$u�,�8? 5X�ea��/!�3i2�B M.~ee$H.~Stockera %``D�cK &�AA�� T � P.~  ��!r�nf�735E32����q26F��� !6��s4bu} Z.~b.~Xu �B:�� flowv�92I�^�403r�!�m��7xj9�"ier%�1tg!��/+2G.~�J.~j~� �TNqnd3Y�! JB�28��9Mz2&Y Qx112195F�Qx ! ��Af1h2;B.��"&��J�iy9 ~n 1(s: A diagno� too� >= &T !>s ��05490I!1!Erknm-ibid*� 5� 69902E�2)]6� th/010404V� TH !F� �}��"1�5Z!�2g2�FJ.:�.� H� Ag�-�+(!W Cambridge�ogrA|art-qN���nCosmol.\� bf 1E�-Q:� $CMPCE,18,1%2u@sh�q:� 4zz}.N, W.~B"�BFlork�B,�5�>t$: SbM�Y�! Comp. � .�`167}, �� 5:� A=�g 83];w : www.�\-ics.ar>�0.edu/$\tilde{*��}$th</�/%$.html" �!*5qe��F��n `M�(%C�i� �4�~ C z&�%52� !50402J �9aM !6Bi P!�aun-MunS(er, K.~Redlnd!�StachelE�A�����b�� � QuSG�/Pl%+ 3}, etR.C. Hw/Xin-NN�(Wang, World�mc P s:-(Singap�D� 0) pp 491-599;�&g� rein6 !C304013R-!A %Ay]*|h} O.~B&mi^� � �5��C2 Bd �4]{F�:%�� 7�͌8iA�4x���j } C.~ ^�%`�gu�: � A;fL  %))ieE�F� 313��F4� ^~ �=�i)��y�1996ad1F., A�unsV�Ii� QCD% QGP!)"x*�; rang>�/a��M�"�389} (�) 586:�0PHLTA,B389,58:( m �KQ "{˔gq�B���2AE�B�&�&P!�4� anti86� $-poor %QGPb�4�12�9}a&� th/990802� F TH E �._LB2001k2�5�� _1aIk$QCD�6�A�70}304E�V� 027>�*� 027�m�:NL9>B.~ ��� ,� SÐ berg�$S.~WheatonE.��i�h.I�n#-�,*�Q'! Heav��e 2x20� �� 304269^ %��&�!��K9JW�+on�K:# �B.~Hill%``�6�!a6!�@e 2c-�N-�%�,�*%>�  034� 3F  0306� R  % �9E6 2} FAY(rsch, E.~La�*n A.~Pei�o-7 �Y+Ym,�Ja@3�5v�m>- 6&47!44I)09 A)lat/0002J9a? LAT % m@2#K�6Z.~� S.~D�tz�Crib(�~!�(�� �mu,u'.i fo*�f[  %�+�8HEd� x 50�5: �4�b2� ��s"fJ�ib:. 0by��B"SG�`)>�  �Kj�-�'8i469V:�ph!�6200]N?-�. 0xi=�B*n��%�S %���A�$a�&e!�9 �e� New *� � ���_6�� 1210B1!�� %� �6�?I9�J2��W..a�Ex��[�!X p(T)-�9#% �#� ";T��m���\:�� 723== A��010605!�2�� � % �5��$;11�:1982puB�>�B���.�*�InuN� -2� v4�� 1066�8��:hI/56&334(6)>�PR 48,L%M*�E9.4S.~Pal and S.~�}Pratt, %``Entropy production at RHIC'', Phys.\ Lett.\ B {\bf 578}, 310 (2004), [arXiv:nucl-th/0308077]. %%CITATION = NUCL-TH 0 �;%% %\cite{Hagedorn:1980kb} \bibitem{HR} %>(R.~< and J.~Rafelski�Hot Hadronic Matter And Nuclear Collisions'^�$97}, 136 (�):�0PHLTA,B97,136��Bari}�8Torrieri:2004xu�B G.~F�H %``Multiplicities%\bulk thermodynamic quant "Tt s(NN)**1/2 = 130-GeVNPwith SHARE'', J.\ P)�0Conf.\ Ser.\ M}, 246 !�5), [IIN�L �T\end{thebibliography}  document}�sWv%\�class[aps,prc,twocolumn,groupedaddress,showpacs]{revtex4} \~C(superscriptjG^�preprint�GG��Dusepackage[dvips]{%Gicx} L{amsmath,amssymb} %���degin{widetext} % long equa��8, figures, tabletc %%�6� \ y1�} \1k {KUNS-xxx�Ttitle{ High-$K$ Preces�+x modes: Axially symmetric limit�L(wobbling mo�A�dauthor{Yoshifumi R. Shimiz� �email[]{yrsh2scp@mbox.nc.kyushu-u.ac.jp} \affiliaX{DepartA�v�XLics, Graduate School(Sciences, KQ� University, Fukuoka 812-8581, Japa.�Masayuki�Dsuzak���ma@f H-ed���� EducI  .Munaka��8811-4192F�Kenich �yanag2�,ken@ruby.scp��kyoto�k1k!joto�, K606-850.�$date{\toda��I�@abstract} The rot% al b��built on�� hQ�Ş-quasiAdicle state can be interpre��s a 2phonon Z�  p6�, which ����sz&al� ab�,the axis per�k icular to diret q0intrinsic ang*moA� um. By usaR TZz Prandom-phase-approxim%y s associa!-�� the �:6(TSD)�œLu <Hf!Xtopes K bas� A�e2� f work)�Dcranked mean-fieldRE!r� � J� �pa2,ma,jm,egi80,zel,shi83,smm}( has fo  � eigen-�� A�6� �,!�:�s,�!P natu=if ropr!N� p&��c�t� .}109 xis large ($\epsilon_2 > 0.35$) %�aVit/ 9�8hape ($\gamma \)@( +20^\circ$�8L!convenAS), i.e.,E�lymV" ! shortest�(ͣ� c pair0�is small (${\mit\Delta}_{n,p} < 0.6$ MeV), both�i�! $in accordaW�Epot�al� y surfac�3l�Mbengt)�should!�stres��AR solu6�Y>�uniquel�(termined, o�16� fixeq s�a�``mini coup�,'' residual Ka��}dopa�4(see Sec.~\ref< t:RPA})� r����ly� triv!!�mc�obtain Q�-like�1lcorL�:%M)hiFHowever��detai�]�Lre !)�� �<" &{ [� �Fis�? , monoton��%t crea�A*� y, ��bC }%~n�@out-of-�a %�s�p!�1�� w8,considerably5 ��m�in our%:cYs� By ) rictA��aB}�m�nAcR 6���a:�A�A-spin��s�w�up � by a.Z1�q�!�sA��� , or\ lign� � !�le-"=6�a, �ee�Bt� sameq?�y�A�us,��� on sK� re� b ; o�e&� , pro�= ,+' ��+&� ,i4spond=����� ��=6��, %-&�*-1�� � L6�,A�p?ly!0e!�:� "e!n��u A��� take� e*� 69�-�I�-�or5L}, nam�[��1� * �5+ s,�m-lit� K�v," 2l$ sa/re�W! A@�^en K�& �:�. O� of hand�4e�bAaL* q � ���`many y� MHfMW �+U�=p. MakA�full Vra��uji�AU &D "��jkura1,2,a�,skal� �is cap|l?��:�6 � 51Ze� Jg�J1:1 . R �Te>zs�/onw1�!� %�S by����E\.�� �\ l-)`fnsw,fra00,alm01,ohtsubo}�@� B7 (w��to makOl` betw�!C�2��'�A,"(��)y��$ a!�.� ).Km}�reo�K pply�bY&���s us&��E�5�.j)eqp)�S (Q:�i�1�in�; a�o� �>}�!<lsL&a�F 2� isU?ky�Y:� 0�7 &�17j�)u orde� explp˥�HprocedurY  a��a]rotorI�!:R i�l�> r qAcF#!*E�N�M>��a>l �'z ed%o�su�f.n s%w" Knd�e��>�es}. : con}�� devoEto &�clu%�,remarks. Pre!|n r� �!�"�M��: h alread6 porte�Omag�� "W\!~i+ >.�tM�dma&jE/QMA�bait!6��e�ar.,���its�� -1a��n� *5d�� harm jx� io"� m} � i5��fer iGeffect80tana,mar,yama-�y�> on@ riR!�A�~ �simpl�qe �a�to Ref.��bm}. We�w $\hbar=1$� � ough�e(�� Hamil a"� x -:��n by "} H_{\r~D}=\frac{I_x^2}{2{\�$J}_x}+ y6 y}+ z6z},�eq:Hrot};$~w� $I$'��6 um  ator`�[body-Y coordinFGEK%tQ�� in�1 a, $�$.y-z$,��g"  different)�assume{ rU initen�$E %� �e�even-i us (� ger A�s)��FollowE1� rgf%. 6>, let usE��xA�eE ��,t, $I \gg 1$% �`m�Cq���&e $x$-�"� 0yrrEis-�%A���PFME�n)$�ed��&!A v1>"]1�� Մk!,J� XI�,wob}^\daggerM�Da}{\sqrt{2I}}iI_y+I�b.I_z.�Wobph^�aMFb$�!1�itude�1!.&q&�% $[}�,J� ] =\omega�(I)N�A�t each9\�QN8%���ant �� $Ju$Eiv�\�e-� Q mula=� narray} JK&=&I )�(1/u�y- x).z6$}\cr &=&._�v(I) \)�(`x- y)Rz)} {'\, z}2�WobOmU��!�qh2M�2�=4uE�:4 �\equiv�}�x}.�z Rotf�PEt* n�#�I*0��� Uis u$eKd���in|$ quadrupol�!, N!\tan{�}=-I 2}Q_{22}/0}$P�� Aq a��u v�& PF� : OnA�s���"K� , ��r.�low " �� w�Ke5.R�$!8=G ɡ͖. Actu�,4B� �F 1av�d, ٳy>U�x,  z$# WpoM$)�Ythe�e�*i)"�~(veqM�)�oc imag� � ur2�' *I6H'*)c�!ibu!U� �x���� , a���M� !� & real �}i�&V=��B',  Refs� \1, 2}%c� , xra!�!~&��K line�-A�nEb,V� ,V� E� �,n)��I(I+1)6�  +.�$(I)\Bigl(n��1}{2}r),�G WobEBGR g2�wo " )�2�,I=2$ horizon�!on3F� E^� ,(hor)}_n(I)=>�,\�Z8 I=n,n+2,n+4,...��ho�/�.*y ith)s; numb�0$n=0,1,2I�An/:� 1$ vA�" ~�ve� {I_0!l:�I-I_0� I_0,I_0+1�:�ver�� head��(s $I_0=0,2,%$,*of*_�h  $E2$ 2�&A�:�-�&*$"�%aH�� $E_���2.�A�fv-2�N�� 8or� al��aIsquA�o�q>�^� 6� look|i %g�J� B�(.�av2��)$eM�:l-.m�� � $O(1/I)$ bha��:�� se fe�!summariz�(8 ��* Figqfig:sch1fac�wJ�.i9 was"i$to id�f6 ��{LuE 2�&���6h-� gyV� �:' -:�2$!�o aS��&�2~:�+1,n)-2"- =(2��&� y�J�\pm 12�ek'(%�>�A9hmO'�* �:�+1$��ź�B�.�(vicesa��6 negal >S�Msupa�t-TSDiC!�G Lu r�&� Z��,�/�2 }[htbp] \�e[3@s[width=8cm,keepa�tio]{wobE�$1.ps} \cap�1{ �1eE� ]�6�~a&al�� �G�%�A>or.��}�E��s %�.��id�"lc �n2�Jdot��Is."�u�s �}� NowV<�.��m�}. From" �,��!lif" Q-283+� "� systemA�F�LZ&��.!,t� w_%�a2y�+�! co�+de. Si"�!2 �s�'# "{1&X� ]qu9e � ,s;F� FS or �Ap �$y�z��lau;a,6���a�-2�� e=�#ZYA�l6W*u�T!y�$al`��jF  vanish!   no7� =�.�&& ast, � �5�m2�� $x$,��� J}_y=&3 Z\bot$%k�K�� �sJ� > �� *�u}-./((I). w�*u�Y֕:�%�+ is $� .gR�$� �/��"0s�3Q3r i� ��$I� �$m'��2H�9one b:�!=Mx$A)a�y,�../�"[���l�12'Q��%to�&A>bro� |".7 x \r .,arrow 0$ (no*:"R)Q��Be�SE����"���, shrink��, leav-5x0!V�N�F�ze3 1�st !iH K�.� :�# &�.��� o3 ��&!ic j �A�e�1 =i!�E~a�����ich� aS�E aN��q��6$%�,� 8 F��6.A"Q9 �QL"N 1[%iN��%}Ka��2�}[I�-K^2].�E=K��*�!\rewritt�by put?$I=K+n+��*�!�,\left6O[n(n�K}\e52aE @J�JF2G9���K>G. .J2lea�*X]^S ucture� aaun} i�8w�A/M uffi8<0EZ& � I� u��"�swEnU�B��hin Eq.~"��')iA�E�(!��ec�l,i|=� rawnB "Q4 !# hold�/r!_" �& tra)1$  6�;,4,��: &\�to \laT1DI_f K 2 0|I_i K \r^2$�+e find��1��, S; nI���n-1) f3(n/KU:Z-2-(3/2)(n(B/K^2)$�"$n=I-�I!�w�FnDa, �"> twoQw]ECoh�Ed .tIg qG v= 7.1n? 2�? �A{s �ed Je%� h#No�whole $?. I16Nts � Z�1}�O��;�6�A�!�� ���@Bb 2�i-UCʻA"�!jAN&y �8iso"P;. \sub� {M:m. �2K�#.J minc0M*\<8theor�a� �� *�("!(!Z.Cjm�1 zel}�/mF;im*|am�;thE,of Marshalek�ma�$�-!�e%�!�.*i�-ame (b&J f)7per?<$=�ya^u��Cat 9. M" '�/a>�em�!61eT.2d�0I@c^in� �(v�2�iS V�Zreplac��t �1�2�ef�0 �e2�%�3w�ll �;�6��)��0.�>.�"inA.9�!�.^ !�sph�5�&��(&��AcV!D1( �yno�p�2f ny5 ary)�*b!A�, h�0it �pW?O u�#N�:�0�H-�u%2,�aI�g�OZ28used. A closer �U/�:X�E�s�aP%Bf"o"`J�2B m xA�tB�2� d� !�V�?a dis�G�Y2�ny�'� eor"*L Nambu-G_t�� (NG)� s (oK#urious v&�4��ed), $J"�#J�#�y' ;rol� 3$guarantees%9de�3��thY|sa�@c>2s�="� mU�A�satisf�7m�@Hartree-Fock sens�In#+�=� q.2gt_;U�:K !�.�i!101�C�>�" Strutinsk�Nch* tN�B2�*�s� �&A�q�s, or !�wa�=&5(�by hyptnly changA��=O"\1�7s��-da�ur�vE.���892}��Z��T��!��+�� , $h$, ra+as�3.�E%@#Je�for%�N$, $H^{(m)}�esa EFfulfille8.�c�2�l"NGI��MxRPA-pya+7� Łide "49�#� :�ex� ��3-&!@u)�L hbm}�erAE&(7 vari�7���l�&1�Z�CNnoom�,n8�7 e�=A8�^u$`i�u)?�7um �6ire�"�w!�!�� eR5 %�V�B�=-���}\sum_{k,l=x,y,z}\chi_{kl} F_k F_l.�mincH~ �G } He 8�Ho&t'*peF) $F_k$ �>$3\ti�!3$*� force-90ngth matrix $��&8 &*gE� �=i[h,J_k2��F} \\ (O^{-1})�=-� :Phi}|[EJ_l]|� B x- ����t vacuumk $FU $ (S� �)� ant +o&9� .�G� [��&�'��8t�I��q���!�un�8r�G"Noscill+&�:�� 6E:���doubly%�tc�B$Q''Q''@� comb� ��e�Landau�'seO&M-k�3p6tic2��=� b6J*�; W>�=��T(5�I9�s*�%(Woods-Saxon9nT�B!�"�����#�,(mUq bq2 �)M���;� ��low�-I`F^464?*e NK( h'=hBX J_x.&crmF6()Efun�<�O�e2�($.� $. A3-��!Ksig+?&� � reCt5 a $\pi$-b��?F)49s��$.� 9@�M:��el��s�>��E s $i6: k źy�b�@?EM�:�niagonalW :�-�U�9�=�:�vcal�"�  I}B:s iB�3�&}�yl>�!������s��� e9� �umb�alpha[%��levant;�5$� y,z$v�5J �2.m�))!�ta(�N9Dw�a�forward � pW5O "?BX *6�E6�{modCN)�" &� �B-�2s:��>� �:� n��l�!�dFr Q�der,;:1�}��^2�.\�Trm{a�^2)�|\-byT�-{@{\,}ccA_y��) & B_z  B2A�R X� |=0 .� wobRPAdet���]2�.� =I �v��cal{J}��%.{yz��)OS\notag�Ăd9 �dc=5=!�%�.�9sr�j�=�Vc��cdeq:abcd-�1�e7�Vi��,i � s;B�I=F7 M]9�)|J_x*� F!Ai..e \qa� %� $\mu<\nu}2J!fmu\nu)J! ,.CR�FK 2@&E}[^2aEN{0^2- �0 b�5���z( �T%%Fʄ.tb�I� ==c., v$:{I��LA:�s�AeY�A��a���gy�� $9��+ mu}+nu8 �6/APE�$��/�1�Q�)�|�]�"> (�Z4J_zJ3)?+F�Z   q$)%=Ur�(s>EJ2{ .{ M�}��� �ZjGT!�m"_ .�  $h� %�3 nam2��Q�#o"�%VQ� "�+�� E� A �� F  �� out � ambiguity��zs� cis�! ��:K> "�R � �)4i #-I1�r3ped� 2�6�=$ CH  Z}~&���)F��G�J}:�71.�7(a +J_z)IE�> U%B+-'.LrotNG}��J_{\pmU �� �+i J8 w0(\mbox{� � ntiz� }2� jpm:n�%� subsk $�$E�� eJ�"S |  (A �Z-!�Z�Q'q�. &f�LUiz�C�8.�,. 1�]�=l:�S $F�|[!D!�J�= � f6��=I \ne 0� FYc�):�%I�ng ��� a�d6,[ vec>&�$m�%�1�� ^N?G�D4�*����$x$nen"X B=/ �- unitK�>h0�� ZWB��$� r�%%I!�q�h&t>>WI� HiggwW�ism�TFir,AU��sh�by&�ma\Ba��NGI���J A f}N͆ )^2= Iԁ�)^2e f?N%:�4 eff)*6 X �:"� �"�9V^&�:2 D2�1�Q &% E+�B *�L� n��z&� wayF�. x�&I}{h 9r} ���B � �F�:$F! � Jk^- 2X"P =.� -..� I8*}{*\ �5�2�-�2 effJ:�S"/ $y$-� $z$-;C3+O �&�/t�Qp a��0 ]]7G0��r� �afYj solv���� A&`E>�]�)�babil�i, "5"�UdZ1/I$-exp�]on techn�Q��utilizin��nHurb�/ bo�h8method��':m3\mpf^7�$M.�5�s "{Lon"]("��$N v, �\V�F�G},Fg nm�RPA�� k+eq'�%0y;B�ma; I 12 -I)]. |\�'��[�=%V�@F� |^2.� wobE2� B(M1օ\mu_{1��M1:7� $J�A � 5�U,A�� +68 "s �*;6x82�U�g %zm6�Ei"O }}(1}^{(-)}&2 2� Qpm) -F Spm��2Vi$y!i z2ImuB# Gint�?dU+**p�W\foot�@{ � } re mispriU 6f$2: $-$�A�mis�)frov $ �� Q_0^{(+)}&Z2.3�a�fa s23<7�Mb��lf�4.1).}).� $!\K!\\pmc($K�<$)�S ��ixndDAY(���2Q~ )La good��9*��BI 1�&=&�A �,5}{4\pi}}\,e�Xa=1}^Z (xz)_a^{(\pi)},\{C�Q'&=&i\]E�Ky.K*!QyzmVe�!r$A@k$ ($k))+&rKdia5'N�D =.�3�N�A (g_l�0tau)} l_k+g_ss_k)_a�>(%=\pi,.|muB�6�)^*� *H+�U�)`:�#ax>�S !6Bc ��a�not�)cF-3�C$# 0!�6ZA2s ^F1 a�  \.2B\�-�� h�i&, *R�K2{ �<�2�oits3b=!�s�J�probq], ��O�G}_\mul.)irF�" 2,2; �/=El \mu^` rm-a})}�..^ +7%��! r�Ys|v*6#� taneously�4 in $FU$.��SsR8B2RRVc not � g�.�Rn, .�.�t"oD G & �4}(d�cnt �ble: Al�cegsa�[�t:�!FRN8�#ref�5< !��">1djo;�`d� �$m�ŌŦ"�AwKBienk�4 `��J�&�*? � erm"�J�$J_\pm$ .�'>�: A{ { >�&"v >�.�6�&\[nF6\{wC(Imn� BD|%��|^6*�JU�}� . 2��\&�J-��wJ�mpR�mpv�F7�\2�A Disp�1r�e�ajaR� B�� &#&�B!j5V �th[bW.E}I�B6� *�E:a�P ed; ��Nir>F�pr*� vaF>a�Eqs.�6)�.oM1}�J"< two �i� "�Os�]Z�7 ,J� J��V.: �N," a��!��h!0ab�plu�8&opVC�#; ;r1,ng�L~�7��9. �Z�\2!i�Ar�R�du �axial-& "�@"� QR, just�@2�"�8,6"��?%��"TO�ىb*7:� rm ��>�<�� \F���quad(�F;2� �f� $I$=N>R  de%m:��A2�A�&U3Jf� R;u<2"? "6A2 "l��/y s< &4,=�Rg.y!am2\mp>2x2��p�&"��b.�6"9�9 "g"/�Jrea"lx!�*A �"�^e4"� i�Z� e�.���"q�&�0�/�S*W,����.�7�+ura?ja��IO�n1i� emplo"�E Nils"�g��*�`},$I��Q ��R�+�NZ`.��rN15�6"�O�,=��']<2�^-�ng�-- of Bohr-MzGlso.pZto@in�Rs�g1�*}6���� �Sal�T J�-~({�Q"�'�"G��UB-s.�"� cVintz/f�81}{4}\kappa(F_+�$ F_+ + F_--2��{>7Fp  bG6/by�=� &X�1dW(T O6]�}(0 \pm] 6\1J�8-],J_+J�2�C*FxF�&:%�&5 i�No�now�6$ ��ewY*� .*�-� ��soJ�&?Uap�!, ar it,/q.``slopA�F~#]k'' to �" optE��G5allm}�"e&E&A+^otE�unn9a�=�:ach�-oF���J : t ��!.!�"F�$r+sO+ ��l&�]mdBF� V� FZ� Z"&� S@��;�$F��: [ \nu}f' ^0%" -�D�!. EV� EB� ,*�� � N5�tur^k0b*B &�as6� R}) ~"��E�8ty&62 #V��;exF�Rc"W&worth �io�F$S_{+"�)=-S_�4(-X)&� "�/j�!�I�im�s "oOe�y&�1.t O3 J:` >�O. �2�i# ^S�;q��( w�QJ}9�!� )h!u�oneB*p� r��5.�6}�.v�J2�&aQ�&�.�wobVS'>1!B�8mpa�8>Z?N� �,.8)�J�.�m��n� BFOj>��"� 2� � �֓ ���]-N� |J_+N��+m)�% } +�{ |J_-zB�m2B10\62ermR-�u��s &�d�vԃoK2��Om�AZ13�isr�"Dde(qV��l} thN%�&k .�N$eMU Fg � ) doH 6%I;mbeM�eKgrly'm� !m�}�B%RPa�.:- 6 0}�)�2�!� Ingl4+v� 9 �?�&� elyaev)p�A*�9�� adia�!c�R67 �na�M*�a� o'F_"�Rt ��&y�}�J;inI �-b2?%�� gces%9B��'%sA�&y: kuR�m+(�B.Ee laboZ&�F! ��-G:�>50 N10�I� �l m?"&� x�imRPA!�a?"U(�#.�" ]�+�uAN:E>hsK~�\ �Y��2�@>+�6�.$~�0.), T 7w zero �� �� �C>&"�a�'�1dss����b.*�b2�A�?:��G.Br&3&m�Cthouj��e"/�+U2���&֌' Uy5��JC'*�\ ��BUrm"�Sc�C�db�c�@�>�B(, $|I=K,M=K&O J 2 |-8� )=0"dc Ms !n�Bw1,w2,w3_H!�� �-H�R.v \�\B��^ m� 7&per���f�"t" >C���y,�R*�!of0exp2:K(�W1Jb 8T�� tab>� st�'umn. .'neu���� 81/2$^-$[521], 512], 74],c1bf$}$^+$[633]Ijbf 9/24]�'($^{-a}$[503���p- 2{@1@�4�+$[40��9.�E�1�05]-� boldqU�iQ��� $h_{��A�!�$i_{13�5(2�s. U�tab:conEb�@ruled)�r��${cccc} $K^�D & N-�CU� & P)!6&v$(keV)�8\h;1 13!� &)]7� ^+$, %�+,164C14,�<-� & 150<5~<EQx<207<8 �EJ�� "Q3M�TJ]18�21 ]�-$M�Bf E%u:f�362�22U�]J�373]1S��]�/288u1��uu>�,u� & 32 v9)t�v,A !�M��ta3�43E�30Ҋ.u%:A/r�559!p3qt6����O��621�0 �� :�Q ��X Yp�xTSp�~�0Q1, 2�oe�g�Qie;*m:~�"br supe&ؔ"DHƀ*jAJrIemonst�"���io�K�c���be"�w>�ax>;�\/ Nz r �h[�&8X.Y?��"�,CN rich�K.ain� ��avail< >�. Exac���?�BfB �/t�0p�:�)suiEHB� ,&�'5�R s2��� :���first�su"cc�A��t� � o}��7y,�WrP}"a}�.-="`} ��T1�=�!:!)%Ya�.3#iu, Z:Ws�ardF # �br�XM#M�.�1 }B=OY!kd"o;*  h=ha�#}(\"9�,�o)-�tau=\nu,�3�{� s}_(P "+ h%ND\lambda4 N.d hmnil~�v��R�&�4$:"�\qneg�/��Sm&~!& V> fix��(�yH /6a few 0in&N=�";Y : 1)�6�!�*U%�0�:%� �kdajt�m!�L"4%Eif��YB~unt�!h�Mct;iR6Di��$Z/A$ 12sD mass� >R6e49��*W�-2 �A�lac36� y en_`d; $NIg(osc}$=3$-$82�%�2$-$7* �lch &_Y�Gf/�;e&@c! urac�GN'al.��2!�!7�[ 1), usu�" , $Q�6"�(Z/A)(nu)}+ ")$ &+s�Oc X M�{<y�5V�w��s�@��i� �MO�I�f͑���2{%��7�e�NU� ����)9eciҌ�er[ca�+4!�\%� an $j��ơ���E��F*���f� is�"�� us���"�8(I)a�"Cq9X��U"�}�A���1�h6":)2� s �(LT�\g�";�$y cover al�`all!� b�ӂ�P��r2�tfour (%t>��24)s)�d5oA�C5^�3�!��4q�:"8 chos�yo2�s2=0.240�C��.{E�_�U�avera"�5n.($Q_0=7.0$ b!|%!6jA"Nc�z�2 ��ys"c&� �p�gapA/ag�!�Ea rm]c���)$be 0.5 MeV�!^6�':��| 0.013!8�.��)9�6Us}wA�2�-� . Ch�� s .m�F�:���: always ad(/<(o%to'�0 t �� s�7�x%Jse�AA�WA�sof.Xq�baksem�(�!A� s!���iT{=SFĒ�k S�=r� s do:�7� ��-�_5T*OS�hfG]:� q-��Wq0؃� E�rdz fact nu�cl��&&�*S} =A-01Ӕ��l.�s (6;*"� �Q�lM��\s "�G�a*��d�2gv! e��Cm�g��A�%:�yɢ$�<��F}�7 6��)}�_X� X�B�����u�uDelA3>�hDG#o�A�9QZ/ R7 �D��=6 pi:nu$. $(upper panelI�;� � ��I, ��e�!() >%QA9B&f E #�9N@�?$�(~"�S?)+sojv curv6;�V1(Q�*Aa�ci�i���V30W�m' �2"(IY9�v, das�\A dot-  ��y��se&�"Yv�/R aj66}$Er, 8}$Yb^;�Hf6�8*� fig:delde�*�9w\"�l&xx"�MR{ a �!'*�y� $�Q�.wus���=�t nd��Rm�; 7.artbi�A��$ �A��>�%�1lob��a�Ge5d -�measu�Vm:0^+_g�'J%2)o� ��-odd � &_ � 1?42dthird[ .A��$�&\ bi��e�y data!�*N2aw}] � parag"�:,U ular c} N� us &6W&2Y_�-$(M�>pi  ��)��J)$ =\\A�I� & 0.2729668777865.i.58� .039983 \.i722 L694821.175\��fe W5 chec|%!�'cY����vaV�a� N.� !� 6�a3��EyoseT.e��A'F2 �!.x3�&iV�V�"��9�6� amplit#��t��,E.�Q�R"{p�V�M|"� ?zqE!� " /G �^!1V$K=25l!~$K=30 b "�,�:)oas*�/�=��% ���Pcommon��%i � . �.re�c�mk=&ls[|�b)�Q�1 Jm�!?2�.0M# �K�:�p���lodq�tp�O j�� *!�,EMaout"6 )iaΉ*j �>�+mea�0-��>w�i-�! �.��E���S�s6"Dnarison�0�i1 �yB�,Q� nokingful2'%C:��=[�2-�� 2DW&ss� :� (6� >bis ��wit%�2�WR�X�`x�_� \����� y ��j anY6ep�2&� }W��V"p� situ� fL -�=�5�;� �*tu+%��Ts�~ZE�eB�X,&�)!GH�3r:p� �2_ !�c$!"-fgqc� ;%��hA�"�P��ta�'971��~�j:ing�j�s.s�ɦs � ` B.��= M�F�;��:UAg&����� !@| ���$!*�:t�+J,U�!�+p"9sJvar"<.f�A&eBo���inVd*r` l!.O ]s�No R �Hi� +p>t!�cshellA�y"j�29;*�disad�+1�*E�-��e*R��"�_ q&�:�F%�I&y�*��� �f �e Ep�� �f�ly&Hja��ISy� l��.� 0$);&�la+ ZS% R�d,�gt#N�.iy y�N�� �.971d&�.A� !�.�H/���F,o:f��!= .6 �V�ݗE�eTp0$-$60\%�Jb��ep�P~��%�s��&|�&�� low-��"� e&gs; nam�GeK#@UA,�B� �rl�V&q��l�?s; �ibenhanc"� mF co�st�HQ� :Jt8 a)��#�jE�V�%urpriAl�A~ nt againsk� anges�gap8N4�[K���^ �?"�� �y1�Wj� �K2}.&��b�5: �4&b!�F%F#` �3^>��;R V st��Qir�/aK quit&�1t _ rV�Nkept m�. Y p�F�N�U#� TiӸ`2ć],�L5�%�>!�*F8�e ��doma���y-breay�bA\ &�zko g���*v�&�n$<B aIiN�&� Y0�oi��a��owo �.rxgJ�.}&� 2� -�8.�B*���!�A�"� ;���enough��AZ.H LL���-)$.&�Iy"q��F��7a���B^�nm&��#��eu�plus "6q ;NkDm� dum8a�3T#�ޢ��I2 inM-l� ̓� � "'M)��eJ8�s.�som��sN*s sfa=o�amo+twA��C_z �!y�#� ragA�ed[L5rdam0B)�w 8hٴE��T&J?1 Pex@Rd.*�6M��y�-��@� ��Og7` 1$E����r� [�o�w,!��=a4R*�.���a�,N6� .j�:�*|���V�aWi����*,=12 F a�CsE�*��250�8�� P4^�X!��%�VG45S��&� s ����0 ? !�� �LT �:few%�x!�h"�%%s�Z�$e<9 �Q�J�Q<}�&� �Z!�) "jb��?Y�eY=%.�Aks v "j.��at our*(R���c�Lv�e best�   excE>EJ �$hA�"Z^:�s a���s��2� s. 2�a�s*L�zed Z� Sc2]�v�.s, �}2�Jbby �?s�D�a &�"�8 "�/�!�*�%YFi�C�&!se*\!��' n&a r� v�:w -X�(6�! medH<_{�1}'�I=K�<"�P�Յ=���. C"�7a�6f�7F>asFzMA���( "�Rm8K�>.��"�.)0�M�~(�)eq�F�G-ciwE�6� !�*��*�E�-�AH)�emA� EsC�>E�"��a�I Kby C ����8��" X4Oo��@te�ex��,��24 s��*.�g�O���on=6re*�  JF: Ex"}�+ !*J IR��*A�2��)zp"ofFFh�5$80(�^2$/MeV� ����Dj+w�:d-body cDE#J:� ig}$=87.8>V��cLB$-e��a;2�V^ gr}$=28.36]�ew@2��_�-a..pW�uۤ0n ellipsoidal���*3�+�,$r_0=1.2$ fm�:��A�$$3/E_{2^+}^q*� I�a��(�%"��6c� np�1-ep}6� s (AM $;�m\sF.( ($K \ge �2H%�"�+�i&� gap "��wo v�Ge��'�6��Ei�r�?HF#E=ls�*i�A�F;�inj� $K$Q�is&�[�hXtur����$o����zG7��d)hJw�fp.�4w2,�l�>ZE5&�E��EdividJ �*#a�Nf e��,nin:���!9ludes?I�?�c 1� z d�&�-! G�>�]!@P V !�removex"� I���6068��H��aB ]�� s �V� =ib>&�-� �!��~2�~30\% (e6a�D�4ve)*5 2Le@�M�4�� %�eS�)e� he $g_R$-�o"T 2�:� >�below).��GpA%-:Os M�o*�i�s��s�Ag*��&/mJbm}A lppQ&e�L�!� e&�|%*a#���+�"uf!F �E:�\}�a�NK~H=/N�F�F*c�Q5}{16�(\,e^2$m2\,�E�F( K\, 2 0|K �F^2*Vrot�E"5FGxl ]{V1UFf,2�>P>�}�).M1�-X^\%->lfFN^2d(g_K-g_R)q)^2K^2 \G "�H9,1r,M�H\aS�5ox-,�w156/M1>/�+��ail_D� I�j6HA�"l.o�4l��G.��j1/K$. 54�11)"�"� � &� s�F��mixx �a["`Z"�#�  ig@memsm!�2R����m*C.�,Ft5!�.oe< {5}}U�e}yA(I0I = Biglq`�;a�o,2x^2-y^2-z^2*KorBigr\m,I�] Q0m}�+ g_�l � ��o{3�o < }mu��� �ju_NU�J�] g_R=.��_?gr} h�g#,�gKgRm� q�E�Q5� i��*&r}a�k%V  �is�A!�6��>�"s�.�(), j��5��=JDS�k���ir[!��4n�#:F0tP� a\c>�]��o"�5�~2[n,�"�Fso�*� �%F b0'�.z .o)�of�4R8 �&2p��$&�Ud�o&Y.!��� at���� i��nwe%�� x|T 27$YedCB���d�H g��. %�u$d#@g, =0.416$4'Jsg^9�KR�i63�!�"@!&�6̭ 2���By� �!.A �S >( ,&�,a}�""�ro��Am*> i*�tn�$ �S�by uuJ[$)B� (Q_02 �2��� K}�6�"P [Xi�� "�Q,���N]����Q0j��� E2��YK��N�O�V�(O�.�A�Po�1�RO�kir�Q��A�..fulmAM�!p%c�n!���)=$:ke�poo&��T� ued e>�$U-�us�;m�� 2�~UQ�Id 92*.(! )}62Q0s+�V~k>��=y� �'��ug�oP�g*� ��pA`�?av�+o+�!�6 �f�� � �N���� �at�0�*�>�&�/����xQ%6�*�$%�:%�!6���B!��p�.�A��,!��MT� See�7os��"�� !RpolN� �e(��i@*� ��&� $6% K}ven)Rr�uA��!0'#M���>8)y%6�>& b$34�3i���,�"!�es2"C���# at a�r�$y, 560 keV"E"�&8c%,eJ�1�E��A*��T�e � ��6��]FX1�6�#.���ac?�">%)� �a��� ���i88%�� i&N�6L!u�Eh$naN��H"H"qQ0>�Q*x.��I�%5� >� ��cmE!..R_*2>��),��d�nزfil�E"0 K hm���D"(E*S��,.k�+� A�n*��k�:-Q0�Il�8q [ơ��j>�E�I�*"��!�z������.PGc!�-��� TEf:"�� "�U�2s,$Ak�*k$6B$! B�O6-)���9�N $ �s���I�}R��wo0 s; 2S�m}�B%�(��.�+�#y ��"1�.)>��branchc rw "�N��st�.*����A�*� s޾*�=�>l��ZY: �"�  }��b�F.MZ�$I�Jis!D,>8u)�|2�|(P(�and!� PJ�S6J6��a^"?5K�E2/%C6��3-f: . Ac�ingly0 �+��"��2�*G6ly y($g�=� UW�,K e agre M69%�U+�]��'is BF� A- ��qEkR�%*� . Cii-/*"D��6g�m^�a�$ poorer. A�1Dd��! !%�b,K�5 62$�oN����B � ' � " = ,Ap: �9�$"�9m4*"�=�L%�&_[afur2-�'cu�:�next s"m�A�s�́ "ag��r E��.��I�-Z�2Y MHm&e�R"*T:�)u8�-v�daX= any g�(;/�!e�P*d��nz�g thr� � �J�� n=y���8� :�BdAnQ�qB� ��!��ޝJ�1,eT�i�mZ� .J����A��gasgM1f"�,�U�259�)�An�g1ppa��k�H�ds_3�Hsi��Mkd ���)s.�*I�(��*� W�y5!�-��6E�i valid217it �)n�.R� �e�K��2U*|WFc�[�%�. 1M9@% �Jy 10��6�2�$A=�%wV infer���+n5la�.�k(2i�:j)�AM/?!a�"�@�!�S)0 <'.* k�xM;"&� U��fc&�z up)�L�V�B)$ . {"��N% &�&r�&ؖK}}(J�w FTp{�$�oDF cr}i�<The��.�f �k�r�fM.C!CXa�&Ӊ"�U} 5��$�C�| &Bxi gw�2� \pm=6y��i6z, �] [h, 6�k]�1}{VG }J_k��- (k=y,6،Opt%b67�VS�As�+"o�!� � 1+�� %&! �+ r�+6K<5�sns� desia�٣"��%a`Sl @�g-�ké\3��i\dcM��.*�canoreFX�E�$B�N2z+��F>v� 2 Q�)�ppro5� ScXig����gr��At�W�!m��N�Y5&N�F m��2�*\J_+N=2#3L!2}"l,=�Q0c�e�I9��!9����>�!w!A:��~A�\>-P�O�.MS+$%�g2UesF�"vmJ�roSl(:u\mhu_{1\,-1}]\rangle + K\,\lL [i{\mit\Theta}_+,\mB4�\Bigr) \notag\\ = \frac{1}{\sqrt{K}} \Bigl(\ XGx u- 3K32}}�/ �,:����>l), \label{eq:mucal} \end{gather} which gives $(g_K-g_R)\approx�R_{\rm RPA}$ if we identify \begin{equation} g_R\leftrightarrow {\hat g}_R \equiv) ) 2\pi}{3}} !'mu_N}\,/-"��.�gR�e� This�ic�� is reasonable: The magnetic moment operator $\9�$ posseT a property of angular >um andg)Wimately2�ortional to $J_-$. Then the expecta! value[%Z hUsid Eq.~(\ref!� � ) is Ded`Ldepend only weakly o j@high-$K$ configur% becausF`tcanorel}). More precisely, if�! ators �, $68$ �2N@ are divided intoIneutron/@proton parts likeQ~Q� J_- =(^{(\pi)}+J_ 0nu)}, \quad 6� =:<6( Gu�A�m� \)� .� 3}{8A�I�/N(gJ� � +_  2� JmuT:�tQ*0following rel%�Anderived,1&y}��f�� ��<{\cal J}_\bot^{{�cr})W B+ ;�b; ={b)�+ bH}.� gJnp-�Y� $�F-_taA:;!��D = 2b�*/>�-' }$ with $:? = :)_z� $ ($ =\pi,\nu$a�@With a cruder est�g��U2N_k/AFu$, one find�$constant $�i \sum? FI#)9A$, w�~ a classiAv$result, $Z'by settA�$U�=1�DA=0$. Q�Ǹe}[htbp] \includegraphics[width=8cm,keepaspectra:4]{gRd.ps} \cap�|0{ Comparison��deduced�<$ from two calcui~s. �G%  $g_K-VO$s denoted �4filled circles!Unec��!,olid lines, !<le � quantity �e!?u�(EWeff},eS / (:y>#+j !e)$.�squar>�dot�� . } �fig:gRdm�-� An.�� AJ=�a��/�� �,�correspoA�to:&�4) a�~WH, has been used for%z8ground state ro�4al band, i.e.,(ca�F collectiv.�s~\cite{ba}. It seems, however, difficult�jusu $ a similar5,,)-ZF.2!+N>%)50is �in Ref. �w2}�us �``�4r $g$-factor''A�R$@not��ommonA��0, but it also�sv~ s as%=$intrinsic qo4K$ does. In or��to!?!<9��� �*% )�(holds, we ce�e,�Fig.~O Q� �.�ed mzia�f�andB>w/ U��q>"U�J !�)�er�crank�1inertiaB��Х�U$diverges w]X$\pi[541]1/2^-$ orbital!�occupicD pla�eR��� or.�  of���m �9� permom}),%�E46� excJ}. As�sa�i� �W%�se%�9�a 0in good agree� � each o 8, again, excepta��($K^\pi=18^-� 25^+ � 29^+:D A[5�g j$ decoup��JML�0�0!�$very largea�t ci�� energie)7underU�se �>; sN refoaQA � P s�G-�%�ovJ^m; in �b.Bco�bu�� ziderabl ̡�aIU�nes!�th�2� s aIH hown$Vlw ��D four:IEx6 �"s�6X� ���� .U � , 0.227^ ough�His ��eci��&er�o!q�x dard;, L (=0.416$. Fo�;3ci.�2)�.�foi.�>�"�ed us�z�0even-odd mass�ce%s pair)gap%�^, x22.7$ $\hbar^2$/MeV (about 80\%�lxperia�al ��0previous subs�von)E�Q�.V!�it!c6.16xj� cr})� ^�"V� ��=0.269�� is slightY��PE�st!��t��� ed6�L $1EO.{ � abo�u a%d!9aiz����should b�0new ed t�ԩ�V�����a ns,�!��ence ise� picu!��g ose � A-7^H� � a�ֱk; parameterZ well(&\I whysefѭ$"� u�Q�RPA5� ion repro, C]�ly extra� ��bet�than t�oJ mean-fielq s�nferred�s. Sina҉��known�<e����̈́s � much);�E!�of�Js,Ep amou! � R2Nis�� whelming )�e م� "�Px$��� z M�a�3J1. CM�!�t��>oge��C%��pio� � ��%"Ѥ�Vioned�A��QAUV, �4�lA5m=}��X- $~&�KgRm})A���l� �(^'al�wW = ed. L �mYu�ion)�e�[ �y� I�>g� uo(v!(|,"�}< g.] ���LF8� a�is tren��n�� �" �nyp� V�� s." ,w3} (No��t.��"E � w2} and3})� �:3,� � �y��given by# Adg}_R$,=�)u Y`� pm�"� q�seN� (seeJ��@]GiP{ �T s ma� 0ly cancel out ��|a�YI.ui:, y�'a���&� eQ.m data E in>�KgR}.��realis�yis�v+ 9�i e�8harmonic oscill� po�ial s�at*� ox�� lity9�Q0�)1� $E2$"H���1to��g� alb s. H7����clear8wA3ex��!�Rs:�\ ) tl blem�BorU!�adiaba!,�!�R2�essphono:\ 200�600 keVM�ō� negligiblr���,quasiparticlR� .�1*r �quench�թ-B� i� addi�� devi� c"d�a non-95s�8 ��be�i,tUZNDitself breaks downcY6�in�air� �j$ ia2�s (� Omega}_\mFm1/2$)!&�>�Inglisn# 7 due1&zero-�mina��s`- pres� : : tually �]e����, alt" !b��)��%�ref�m���trans)� ls $(Q_0.��! X���,���rm:<;�ص�m�zs. WhBx>*��S �<s�G.m&�N�!�a�n impor�futur� su%J� rect� sure !�$Q_0$ (� $B(E2)$� &�� #u desi��|7$is purpose�� %� \� {Co�A�remark� #:con} We havd v�ga�!�:�s, �J s� gly-� :�s?iJon i�K� �: �?!�K �* random ph92_ (microscopic�oryv vibd LmDiz�5�� �mod!� %o� thre!�men��al mo�� >� ve��(the principi Hxis frame (body-fix@), c� �e� be a limi� {wobbl!� �� triaxi�0 dw$med nucleu5 dem�r-�� observv7 f=#ɳ �i,in $^{178}$W!ce "� � :�:{ sElye� triv%�lwM�employ�( inim��3A inte;� ch�d�mi� b>I ~ Lvacuumte base  it)��B� adpb force� A atso� G< e�Nro";!!|�� $M1$.b probabili,������� kind!�*Ie&�A'�4-F�M�e.��� �B(M1)a� terma�� RPA &?�� �o� % conv #�!��l� r��!Z!�&$quadrupole�g�$�T �T�MݦM�m�56/��e�kbw*_A�!� n�� � had� e�A��B3B y go�o��o� _R.� � a�or any mJF5">6d, espc��� mީ�2��& alH% !, form m����)�=per�"!Q=�Q]��&s)� �l��,a�es4�]��*no&> �9�2-i� t ne� arily ap�%� � ���=ȕ��!�M small; !�o c�v,&aNZ-SE��?'O~ =w �%�ied�):�&� Aple=%EH`� N� taska�exa� ho� 941�lay� ra�M�&� . �$.�^2wN^I��1��EH&� FinA�, �worth���!��A�Qoion� !Z&Lue�(Hf region. "���en @�9c� paper�msmWob1, "A� we obtaŌM�sol��3��t !I� �-��5:�I�a&ut-of-H "  in 1 s w��E�&�e�0� mmby ut a�s �� ree;)�w�most serP�� in .� �!g�'t�A�alM�"=siA�#�M. Bot�.��� �Qx1aa�v�"�horizon*� discus in Sec�# ��},K exA" (2*j�$s, $Q_{20}�m 2}$U,bm} (or e.g.� ��.jl($\epsilon_2,\gamma$)), combEb�62� amplitudI�tA�UY��,�*�ha�!A�1Z=/�#9�9.� �#.�I� � � in6�"wobE2}�%T@�.�����2� � mean9� Rs=.�m1 u50$-$7ot[q��s" �W6�� � 2;!�%k�_�5�)M-m"#S�"&� >be&�B�E�!3�9e�,��"�&B��a� ,!,��E�a�]"� modii, ��a��`Y� I�N2s�{21�$-)6D^{ >+Qyz9*�KQB�_ niIixIEm!$coefficien volvр M�6�����n%�ct6J -u� wO make���,�h�k�,augi�Zr�pplic� %wo.v!�5�A". � is,�course/ �,.i�  mab��^ longer�id. �%"[(ai� u&� &�"�in��isotop�!%20a�500*_� not e�� el�e p*�yjA[ laboE�y �, $\o� �wob}+.rot}$;�B�VSv }n\�!q qsinv��itVbe-��pka�%� ach 6�AJr�agn�dV�s ��|?�'�5��&��&c���3.��1U�0#M� �y **�a� �ų������ �describ� U8�"�a[eAJa1&) "Y+acQ ledg�s}� work" suppor�(Grant-in-Ai�� S�R� Research�(. 16540249)\%i,Japan Societ/ e Prom"�Oc�1�2B��Bf5 thebiblio�y}{54�*Dxpandafter\ifx\csn�natexlab� \�(x\def\(#1{#1}\fi \ZGbibO font>J&3M#�Pf�Q$�R�~R.$�Rurl^�0url#1{\texttt!O%8{URL Ipro�2� and{!\0info}[2]{#2} B!e�t []{S'}A3ibitem[{2��{{S. W. {\O}deg{\aa}rd} et~al.}(2001)}]{expg } �{author}�1oZN}} 7& ]W5��nfo{journal}{Phys.\ Rev.\ Lett.} %`bfl.$volume}{86�1 _4pages}{5866} (^year}{�})�DZ ,D. R. Jensen22{u${a}})5!�N�V2T� Nucl.\ -Aj703V 3R2}:��%b) jen0�n- �9V14250��n,I. Hamamoto}e*2Aham�2<6QDR Cj�652Cm044305�4J� j.��{G. B�gemann �3�3�.Q>and�5VG>�j5 M"r572C1514319�J52#�JJ Frauendory9,d Meng}(1997!& chir�:1�.���{S.}~#�+U�6QJ>Q�Z{�p61!>Jy131Fr!vx(K. Starosta2w�| Chir�}.F>/�t�t97J��sT. Koike2�3):�&!u1+<, Chiara, Fossan d Lae}ɣ!:��_:V�K>U��> C.~J��*' { Ȓ? D.~B>?�an?u?�[VYy#D.~R.a�2�5F,��R� C< N�Zg4�g9�.� 4f1 {K. U5Hnd :�]{koi0? N�5P}2=.',6w1 f�#:�A��V�~1 9Z( 172502F� 2004r���"- fraTACZYyr�V��Mod j7Z�46V�v Matsuzaki.v2:v% , {YK AxhimizuMw"yanagi���^�9+M>rH�y�e�V�� �R�.�.E�B���V�2� r�� .��41303(R)R�v� �!$.�>)%��^S9/��������Z_ 034325R�vK Marshalek7 77 ma�iE����9KZ��� 27Z�41Jc197v� �(1979 ma�+��z�331:)m429F��rJansse-D��0N. Mikhailov}�jm��D>� [>� �L.>.�UF�R�I �x3182E-7390�>C �9,{J. L. Egido&� 1980:i2)�8({H. J. Mang�j {P. Ring}�hegi80Zn9 .~:VQu1N���Nh )�9�!�^i 33���� =�J�80r�$ZelevinskyA�80a�ze�IN �� V.~G�.� L%��"� >�f�344:E �10R�z�:�KAGts��A�� shi8��>l�>�RProg.a�Theor� 02I1:44AXF�8v�:�%<"M!595A6sm^�5:J��Yz�o�v58��a}Q�-<55Rv95r](Bengtsson}(!"bZ��R> F6V�@howpublished}{http://www.matfys.lth.se/$\tilde{}$ragnar/TSD.html}jKurasawa!߉ kura�� H>�I6�5�Iܢ�6Z205J� �Pr��a��熊 ����Z� 1594R�2r�{C. G. ATAE�"( 1981>r-&Gde /<, Krumlinde, Lea�$Szyma\'nsk� Z��a�:.�yB���?G>� DZ)�n��Z>O2 2BU��6Z� 147R�v� Skal!�!�m sk��BqG���4b�0R�vh &�U�200>H &' Neer",  A; eikh*Z M. Walker_ fnswZ�Y��.�U�2�:rV5J.���yP.2�*d U���xA�  �J06432R�!�v�S. 9��� fra0�� :>R�i�� 67B�11^�z�D. Alme��.�B�(�i:���0{F. D{\"o}nauE� alm0^�Y\2!VtS�'.�-TP�M9!VEFE.�=S:w"�� ^ 6uQw�19> ��4S. -I. Ohtsubo >� �t< o &>f- :U� 5_>�R;��71` B=V9 20z("% 3 � magb/ �In� �5 AiA� .kPYJA�eL@6\ submidP�'u �W;�7(-th/0412009�?EJ7Boh[4d M�Pl 197= �.8>1�A>sP�7KBJ�) emph{�title}EL�+Struc�;Vol. II}!~yZ%#s�Y� j 3$, New York.��#!r�TanabeIGugawara- �7=tan�_B� F�OBM>�)JQ�>��\ Br:D��57R� 7v 6�Exma^� Y.ғ(��f�1&.� �142Vvv*Y�#ur*�ya�wBjH^����10JK ��Pyatovialamove� pya�d N.~I>� U� DJP�ZA$Nukleonikaj22:?Q2R z�� ishi�%"d �~�kis75��A!D>.�|"&|"3Z�55J��r@�Sak�&E8:��sak89�H.O>n���:.�'��50�G��M(205, 2426��u8v��Suzuki-3Dz Rowe�epsuz77�1T.K�/.{j-A�nV0)B-46R ��{E �^EN mar�IB@R��R"z�>j�5R153R|19~B�a34�8�P#B@��nI 2R64Z�8v�:K �$>��shi���!�!j!�XB79R*1�<\AA}ber*8�L aab8^L&Z B)JZ6iI�v; 15�JY R�8v@":.56:9%vLa;*/M�lle\Nil�, Ragn*�, DudekG9T�}SJ�-��@I>�9��@��V�B�E'�zB>�6Y�DB� Q���"�n Y��DDA4^ 2FB�20V<6vB (C. S. Purry.; �w�Z.@> �7 &7 b�$0RMz�2���98��w2�� ��� � r463��Ah� V�$98v�D Cull.5199 �Ti.�U�6A��n�6� J�\VQ9v� "c������b�(T>dV>� �n:3 �743ZQ71Vav {R54Fi�Uon*�0E9:�0-yF/ , {V�`Shirle�b}]{tbi�hRj�Y�6rB�.�eN T�? of I?$, 8th ed.}.�* @John Wiley \& S�\ Inc.. �z�LP bn}i�9197>�&a1V�[= H@nig!elobZeٰK�F�%bjvFBj �B�$V>t��>#Data %�sjEAZD 49RO7v�Aud Wapst��@a�UB9 N�YBJ�v3| nZ59Z�40Rw ~�7,. Dumitrescu�2d8���# dum8��BS�D�=2�.�:i�K38R��  *X�~�#8G. D. Dracoulis:�:�- /,@G�6 ndevT: ]{dr^r9)^\:eVDF�$K ~1_Tn%>�* 5�I� �P41Rp7V�zf Del�h nque"W �4:�'��&j,, Pashkevich8u�� Unzhakova��df�p .h.�~A>�uj�DB� ��@ V.~V>�ޒC S.~Y>CChu�9�B=W!�5T:H��bJ2�=J"Av� F|Xuv�&,./ *�#V�$ WyssAEos^�yi]1pB�,P6}�2>�$� S� 9�V�BS+ �L�>�`\r�4^�25R�z"/ � "��6qb^nY�B�U��PB���?%?1�-�%��7R?8�wG>G fz docu&H} ��&YG�U crc1.tex  % % $Id:2 1.2�Jp0/07/24 09:12:51 spepping Exp $ % \xLclass[fleqn,12pt,two�h]{5`<} \usepackage{es�$} % chang*IQdKf"fw�r|"use�M,LaTeX2.09 % style[.y, � i� %�Kyou wDutoiV PostScri�n�yes2��Hicx6� s}Xh�\$landscape �Y2K[ _right]{Xng%put�r own�QinLs �N$: % \new".GcZx{Z}� t/1$em{def}{DeE}[lR ion]H ... 2L ttbsNhar'1/2AmS}{{�Gtect\the�'I2xx\kern-.1667em\lower.5ex\hbox{M}25emS�declarOs%� fronjL�i \z#eo�nng\i"�Kon� low-CWy QCDa� {Wol2M$ Weise\add'Z[MCSD] ik-Departa=8, Technische Un�q,sit\"at M\"u�b4n\\ D-85747 GRK8ing, Germany} \�Q ks{W�K&�KiiS t by BMBF��GS=$�}qH} \�O��C�}ab5 ctL�M%9�TorCi  densA(of (scalar))--|�im� �c� 9&�obar{q}q\�l \simeq - 1.5$\,fm$^{-3}$. GLyp'E�orekb)�r�iisI%fr �y!�>bDg&�T��Ah �ed%.n: pseudo �� bos���ied)�Op*]. Their%� van +�m#exa�V�e�a��fQCD��1� l�GMjaGe�z%�%��g�e-M)`F� dynam��sc\}d2:L�x ngia{�e�_por� ,ll relevant ����of� �elj� �| orig�f.o�nowHT�.c"b � DNF >9. Heav=�,qas5J,A ���%k>u�ir leaA�-�~c�m�k"%V!�No�]]�und;j�S9E. �dor�r">�`E����� � s,5���bf�{6�Ir>�%y�fe�b �a $2  2$ @ �"($U (x) \in ! $achq9I�thMpisospi�ionTbZ�_aB�:%d . zmYm{b�[� v= ,] [i \tau_a��_a(x)/f]�l !aS:�  $f�m�_*� 1�[K ui$ no�k#{�g}A!�}*. �>e.W'VOg$U(x)+g�a����wt } LJ L}_{^ \�aq�m ��(U,\,\�Val . ^2u )\,.bBdo5b"� un�( theya\t� four-< , [p.��^]rA�$��l� a��e6$��v U$.ɲ�k�=g�p�me��mP(eJ�4baryon number)>!�"� m� �� {GL}"{916� [�1��" f^2\�  4}Tr[6�^\dagger ^\mu U]+ 6(2}B\, Tr[m(/ + U)] 7� O}[(B U)^4]J��qse[�Tr.h.s.yui�(pertur�yve)!�licit>g&� ����L�8�D = diag(m_u, m_d)$�RW -  $BEr�m��e�8as $Bf^2 = -\la��>�= f^2 f^2/s +.t last&{)�0;��A�H�AQZYl. W� ��Q�iper� c�ca�)Usyste�jc!Qau mS-0��l .$AK$i �Z P5�on$ory (ChPT)  comezaCfum�o dea�o.�ouM's. Onea���prime�6�d+ �q~���bdp�7!3-J ttee�clGs%�res.|mSCGL�=C�g nex�]ve��zuni�2��z%daqw�5!U"� ng ��on-�. o)� o�glv�M�f$N_f =� �q. eNpe�p�nY�h>�:��6/qҡ�i N}m,�|alQ�.�i����hde�ai- E%�` (~ b% ��a)� y��k�:� N$Vu��a�M���A�8��!�}� eqnarray.� � & = & e� \Psi}_N(i n_{\mu}��^ - M_N)+_N"K�g_A}{2f� � arN2Lcn_5 \m$$\boldmath t�$} W\cdot6xF0pi$} �F& & -w� 1}{4 �^9.� � �Feta:�B��� �� +}�$\sigma_N}{�6�Psi_NVq^2 +Y~~.\no�^a1�AKDirac  orM$ Y$ = (p,n)^T" q�f � ��aA�c -$1/2�ubof� ��on�rN��F�M_�M_0 +% ~~,9Y�A�H�f  $M }ޔe�� reade���of8��2l�� %�e�F�1� � N| m_q(ECu}�� d}d)|N�>���٣a� �a�����6 , �� $m_q!�m_���/2$�sB�� �c,45 - 55$ MeV�$ GLS})�!�ax� &� `1��:� Ir� dio�� nsy�yt!��geT�Ys��s:% ��d��� !1�R�7,]�A =#70 003$,.c%�M�ha }. Not {)p(3�a�te�:LorQ� $"H �[��^!�T� �m# furt��#a�x�|o�mf�Ee"�x d.!��,� i%Vv��&m�i)�!T�(1232)$��onanc�%���c�jB 3 �s�{�!e�l"2}ι, �)��pA�(suT fully!a var�l6!pro|  (sG�as^��r] E�photo��}���%x Comp�$9 M�Ɓ��inc�� accuj5�� b  availV A�!�{ a%$de. ReviewO�A�>2�nm� BDW}6rM"M E �5�"� on�% � medidia�ce�f��lsA�* n JarQA �KBW,M}A7"/" THE NUCLE."\ITS MASS AND SCALAR FIEL$*j6".�"%�N } U�b.�ɬV�Gly ���funda>l i���)(a�H��i2� \�m{T!d IE3!c� be��madj war�+ syn�I�f lat�|�a­:&�� Mw��pol��vK~ztQq.� !� b�$A$�Weas$� �LTY,PH�AQ�qu� 5-1M>)TU�0'I� Y� _,CPP,JLQ,QSF}ΐso faa�$u��$d$�.e�ee1�i=�%�lyaCep�y�c�typ"#n��of "�r . Methods��B~)xwtӗbe�(d�in�s(ter%�!atween51�!�I8a2��2R]�#�$a�ex�%� �&j N| Y���"�" trac�LuE"k tensN$:K<= (\beta(g)/2g)GQ \nu}G�� u. 9 m_d\, d}d � \,\,�_$<��g2%icQ�� |(a���5,%_6 w q}q$K I u,dV ep:� s (oMa��$anomal�#dӅr� px�ub�ty). Neg�!ngM��r"|�v��AE� i�� (4) W%$(_f$Q� � .�0$`y&� uE6} � = &� {%]U2g}N�UI ~B�\m�6\8asia��1��16bul?#r�$M_N$�r"�t%E� �LA�Qr�%��ro�%�gA���uW ~MKJ%g�kio�F�'gsum ru��c� �0$�'Z��eE^�#i��� (I�'# mula�Io}] J)�- ��,\Lambda_B^2}1�elq}q �~�... ~,� *km�F5  1$Hi)guxiliF&�(!BorelE�)-��es "shorr "<"&,���MG.l0 analysis. Wh> need��be� rov� �a`9�� 8u�,�%no�thes*͈ W-�A�}�ĉ�Mi"��*>Q� � a�!w. 7�e�&�*, Eq.(7)�s�o7�hi7|�0 WW}:%6V/��F�Q��&r �A�it%yl� a(nWx"#du�Z!������@edi�$� �%!ܤ�!,de9 AZA^a�z�ta�earE..�+��a�.�"eaq�Mzls-3SW,RFg I"�^S ूE�!��of �� "�{�/%G� &nC� A$��\p6�O$,O �� �.A�-�%Tonɵ!:V� Cone-loop D�� illus����1 ]*"���^�p�M�s��A� �j-[ R�F�� + c"8+ d 4 - {3��k} g_A^2 \��({o !4,f!J�� )^2 (1- * 8M_0^2("�O}(R^6)�B!2�$c&� multipl��� &�8%�%;��2�&� r"{.6"r &1)�� Y i8X$log\��A.�k3�( pie� �()^3$ (^�l:$m�Y��|E� del-!_pea��(0t/��|n�$�&�st-D%�$ ("�(sp�: � ir v��aYXM��)(��[ A�shH3M�2&���2��:0,a� ��&! $"D= \~�{q=(* dM_N/dm_qr����e�eq 0.89�C].N(473).�aL ��s�.ach. (T�"���� obar�#ana�E[#a��# r1�tj�absB�ng�� &�'E�an� � � ��/~>7�-��1* $). "�N#7�]y �� 4�� 5502 2: B�"fit (�cur�}Ung"�u � s �.�E�!'� al2N,�� NNLO-I &��,cX e��dasM�a9 -��se��ecu\~2m���� LTY}6�KA6�M� .\Sc�/��f��A��M7�'pr���,JM��e�B3>�( b�0--&@ X' �(�'}�s�Z %<�&�$� W� prob!��in,�u=�t� .4~s, a ~�0.p� K#�s�".3%e�� ,"soft'' surf*�-T�  e fe)��re 6�p�esZ$q0d!�2��e���)�s! � i s�x lar-W%)��"�� & fam w",� obscuJ����#A���n "�7�ZZ" ���han- �%iC����6Ae�x �Y2"�7"Yforce)y�'\at�Dbiۭ%i.%> u�E���Z�0oser look, gub��B& �2. &� .�=�� �#) =��� (, $G_S(q^2)��(p')|�t  d}d|N(p)\!le n�d�um � fer $q#(p - p'�I<�, a�]��!d�e1�.���m_q�$JV/e���� obj���(�:�� Assum"� )�ormM��be wr1��sub%�ed�per� �J� \E�_� = -Q-}  - {Q�T#\int_{4r T2}^\infty dt{\eta_S(t)� t(t+L}~n� f� 9Rx(},d"2"�|u,a�a���"�Le:es!in � likeFs)�$QE-A"\g� �di5BTg�-$19)/s�q��6�t\�&� e�Jfu�$5;�)i��  l $JW�, = 0^+, I=0$26�ybe�on:a�o�3u 2� c �.�s� ;�u�b2�@E�� P�e� ��U[htZ 5� � =�$ B���6 36 3: (a) Sket��,+9w}5  � ; (b) Two)�ex5 om� 3s6u1�L6v% � 9B"v %�#46#4:#SB}-)*�� �.�:�R� O'a2�Ep  {K}�*��Af� ed) in��p5�Ep"�5*�i/u�(Hoe} (upper7 )Z ��" �� Born�m �g(�� :� 2F�%�m *2N� �xt-to-�'l. (A ! �9�!"u� 2��r�*��)-alV\1�!2a"���s�Z�B40d� �&�}*s�9%X&� * �s+�>�.�:� �N^Bc�=(s}�3aI � (ult (Fig.4)�'�a� Ek��"Up"FFKո�.alb�c D>! � %"A�$�� N}N\*�.\p %�=t�)-�A�. &L�t�no!ؑ��:3 "�G� )><=8j!�om�&Q� !(� )%�%�ac�:�p��AV�t�(��� t^{-2propo*ֿem�� �� radiu�M�d ?<d1*GLS R}&h.\l< r_S" ^{1/2}�1;:fmF���s��3 {�i�5&l� +� a� &��9ge2 �0.86 fmq$N�U�у} By� iAEJ� e� .�"9 $a|�� � �Y r2�e�9zy n4*P }o�E �# eO�'i�"�A�� 3 S = & �� E� _N /C 5�0$-� �/ � Yt,A�� �� 1b))&���1d $Nn �on $V_l���iVF��  Va(3r Waal�ca ��� half)%A-�gth6V�!l��ver*��Ev�)%e 4 risa@���1 � � s� vH $N.&�;X (eѱ�e:e.+Ec2  $s]be�!� �MBWJ|1E(r)%� {ea�5  r}! r^6}P� r)~ �}��P%�a! ynom�`� M$�$���U $ Y.0)�G)�$�pachAQEa��d=$r^{-6}��&va�3%~i�6"�F2 �F{���wmajor}t2�e�z��:����a new�er&5�+For�A� i!���Md�2��! ���ia4 �H yQha��en� $ dMXgoU3},��we_�!B� �E�� ce�,a �(I�E-!�!w9a�tg ^aL���ma�q �=:��٭s��7�GM���".A�N2���4�a�z�1u]E��>��m�obI���e��/�dE�**��uj0�thirdo"ew����m�c $d�EM = M_� �5qt0.3et��*��0���=/!wNr*m L 5a� [� ��>x�,.an�� �-"^�ingred�>��&�P*�si���i�I�,9� of b1�!�~ !~%] / 1S$�Fet:get�ir�Nm`5(of��v�>cA/)rol@"\1 � � $T�w���-�=�4a $|\vec{p}\,|&# �@� �� %�*�%O�*� detai3"�*"_+4x�*, bFd��A�s�]<T(Q^2;��n��&�it'isf� at f۰a�gyA�v� "t �fp#�!i! ft[T_i���q�a�:�i2� {\z�i(t É�"�> ]\,J� �<�!��s $� $. HdAa> 0a E#("�)"�)�*�v�A�t-�nel��e9�sM �#x $i$)��JQS- hier�T�Ht�#accorT)��A�:�5s (�)"� � �=.�, ���` r me�ism�at��oj0AE* [&�5�&L(��B��J)�$�r� a t*!Kt�E�i^2ea~Cha!P (X�$A2�u�6�� mu_3,9ųWa1oe>.a�0�� � inflV��!�Pauli<>����!�e�3NN�}+ga:���/+a��$-.�(�sJ*s. uA$n��G �1*- "�<�No 1nnZ5;I�aAmX�seaI�j*�is�� $Qa� 2�B50aW� verag�"sim!. C�3�T� tr�"�5�h�TJ7st�ngA�%�� gg]^2� ���&(14) r,+"�&��5rme� = u�)[ \, QA�f11/%8KAO6�\,-M�(t�jn7yOW- -L� � X" akes8��8e�-u�Ūi>�w!� �\,(\llC.� ti�. Ga�8nt�KA�sO.R)Gi��Sy �n'it6nge (&|?) P�Ef�c`!=��-QEWL #�"� OSir�AK8 t�' 6athl U6!6�E�-14)6�-d � zn2��*$>�e[8F �(a��B*A�* $� -h��*8)f*Wb��bKex it�WT�F1P-�-f�M+sa%a�U� $d >Afm&� �It7*� �$lemr��K� rt n�$,)C��9�&� 9 .�� *�A�����ȅ�ar�����c� ����be���?a A�.��l��e "N� " arg�_� \sc ate�P&�Z*z"��Y�-K5,�� s (A�9,,&� )%�inc&�� "m"m.8&�-,� $ͬ�(ed-6s�9��  .�pree_]X��W-.�"�Ev;a�.���!�%� �W:�} �*bE 26"5:"NN���V�: t onB�V F�(� a�B .��s), (cKTE��R�oE:�(6� �w6� �� {6�* ��p�e0.�+-9�+6-F^1=tbrijuni�+(o�3�*3cw� Ener&��in-9 um1�Yr��aay �reetE/ . Da�*�b�*�. EachX+)Q�' ���sF�o"����or (1� *n@V&[@R� ��Iram��NNV�2�,6b�nd{�p�-:� .+I�'}6LB6*-� � ��gR6 -�*�A� I�!��. !d ChPT.%�e��LFA,KFW}�k���whe�� +to�T� n�{is�L b �q' ��avD�?e/)��*�B# � eK6�per�C.�As�cJB��.Jez/�%*%&#in���!pYk1oYs�a�&O5'� 2�N $p�;�(p_0, o \,� tWdJn:(\��\!p +�>)| ft\��i}{p^2�(^2 + i \var��} - 2�Ѱ (p^2�H�(�dta�) (k_F - |�\, |)�\}.I�*2|)lIA��!8�%iu�&!u�7�z(fK >7 "�5EWg�, "(,mpty"-�A�a2T :T . DiRTm�Atorgan�X lzA�� �>�7��S�*�!M��m��oer�\MsN \c"4d,��siQ�#�q $x$-�$. Our "inA-bz" ym�e�ir$w9 YN� e�ek]arge � s\foot��{#h��1� hem��nA�bejLsu+ow�SAe'blYe�� � e�2p.�"�TA!�G h U!ch �r!��qec�7ers.} (� )+)�_"�N%�g��H�Bin� a�x �: d�_RKee��5�D� �E �%� ). C&&o*o�]s�ec#%�U�&(���3ɵ�FQ����"�! 6), ��!a� s up!R ? $k^5t�2B*[Ws %De j��F. HartYU� &�e�B� `Je�a]��edmw, rh !�~ h� Fock��(��6+6x7E�euuY � eVQa��woE.� ��)52�(5 u#)middl�VN �p��%��ominanHt� � At bA-�-&> p�1�(�-I| : enc�][z���{.>re�is.� � d�P�wo�R ival��way� i #C.Q9,>-�cutoff $?$;�4 remo�P!i��n�Z��!,&!a�< ��Er$sc�em)(�� E. Bq��du�2eq�bDry[oa�1�A��3�Xr�3%�d&�.�"�G"l8 In e)�Qn�dez��qd"��%a3acl\on�[ch%���"H at� ��i��-�� �l!!^I�*� X ��:Ie��*�-=oF"  n��� stag�$�!Ci�Y73��B� ,&out�H is qzJ�XG"� :�Sp�Psz cityD����AW-�-�>u b[ar�ᴍ!z�@7)�!�:E(D _0)/M-15� N!nEZ libr ��y � � 0.178� 3$ 6�r uz����&$K!5wN("": 2�M50.;B}U� 'A�aKAic��"��a��4!lN1���@�QA� 33.8 }E�no*h AM72�--z�!33 B)�SH}��WQ`,suggeUh f6�'�2;!?�)���Pt 8 or�6� �bqf"��n���Aof�y�/��/s), n)�$%,��I�Jb�dd�^,%ireiaˁ"ո�{�"� �.w:�B>bal�"���&0y2%.�8%�R��mgi��d^��f> .�,$�3C$DٍHA�pVcleN2�ex a�pr��n:N�4"�)MƁ� ��`��26��AU�W��&; � puls�\���R)��4�4i";!O�"^4)p@���!�uniquA *�_]�C)t�,��q�U�s�v)����9� &1($g_A,!B5 � (�*��x�i��� ins �q� �deg�mZ�!e� -����P� � ��iapuc�Qa�KG"�  (1BRi_m!�@��a�^ 0$) | �>��U�!��apparent����.��� kMcoeff��MR%�3� A�4)�s$E/A$ )!:m&J�!0F}_3 = -10M_ND �(AXC&P}\�0 )^4 H ~ L4-$K�70}9%zL[aM237B(4\,ln\, 2] bq8%�\c�W*p F &� a4 !T9�-Q kine�<�ha+q droppA<On>< at Ge9� u9�F}_!0.115�:n!�A�r�y0+u�2D��IH. AVI�" a��0.5.Jmat"*-*� �h>, BG�U��^�l�tq��r�r��Es �-0.234� 2}$.Q��5V�8.D7�B�B312�A7:�.#A7�F�a�H� PaI��l*�.�r�.��.7r7 � �_o�q~7, x��a soph}I�-*�� �� FP}6�7v&��9{�(C.�\q��bH27-��8>�6O%��B j B�,%A��A�K�hT#�&�^$P� , T%s"�)�_� � �&�7-Z KW4}уss,(;�"�m�a'e�"���͉1 Oi z, plu��\�� xA�W��(6���.�. 2�8B�m� N/���y d'D�@� �C,o"� pPr�&�*a (��ne&�tt�?is� "10O8u8xo� suff�@���(�v�/b A� � B@y: 4G � )�?�� a$D'g�p� Isf�Eil'FKW2}��F+�DcA"% still mis�JC/!�~W� � 5�e�b�J�al1)�K crit�N.�y!�%)(ar liquid-g�Zhc*0+u�3�oW:b!20-25\%� �;< &+a��Vcoll|�+2�5�"m�"\ "4 1,: R!��o>c!�nd� �Y <�*ffect�"s#p=f aC�Q Q �ab-6.h� !ZIllinois�&p-E PPWC�<X�8-�"n5p4}�KV�)�%un"H"Ze�&�"�#F}_{3,5}��.;�N*P,��� uin!�2s$ -R"� F}_6$i�no z��Ar-E�� ��e�L��K6<ɇ-9�8-%��Lnd�C $(" now�# -�S� p ular*yC�Yt (��x&Qa�l.>[�!�0t�^96 � $p < 40x/c �(Hugenholz -�7H��me�"�Nful�"\~a�A{pV^�a�8m"�s1$&�.qJ em�1�'im]�9�628-KvnV5�xa�v�|:rf�GE�.���<r"r��p�r�5& perho�@suы that the�X resulting equation of state at finite temperature \cite{FKW4} (see Fig.8) is reminiscentF�Ithe one familiar from a Van der Waals gas. The predicted liquid-gas transi�.�H$T_c \simeq 15$ MeV�,now close todempirically deduced value, C4= 16.6 \pm 0.9 H �0N}. At that!geR pres��approach, guided by chiral effective field theory rep � func!�0al can be madE�$this point-�A� ,KFW2}. G�al feE���ar n2�$y - includ!��surface (gradient) terms - are well%�oICaroun%�-J���r�� ܭ_ failI�0letely: it mi|�strengthɑ spin-orbie�ce!�a larg�� ctorɟdetailed� stigIVof me�$isms which5� a.^e1-M� F.(both ,he second or�.tensor�]ce anm��EJ`!��<$\Delta$'s) revea��4these contribu�hsa�cel�4�exaMm%)� T�~is a h��NgenuineQKɞ�(s, not visi�Nin bulk��per��!;inbhomogeŅ5� mattA must�Pconsidered. \subsA�on{Mean �os)@QCD1a� ates} In6�QmodelQ�SW,RF},A.�>Lorentz �Nar%wveA mq, each sA�$al hundred��;gnitude,�KaRe origiuUab��a�Ey]�split�fobser�in �i. Whi��%�F�-r��ly1��averagej�sE �i��dividual!eLs�!�IdeAc��pe� on�2y�N coa� ntly� buil�up;���. I�e!�sum rul�W CFG,DL} gv some� a�>E o�A su!��-hav�ke or��S; -3509atme0��<.16$ fm$^{-3}$ (� $�? =), imply!Z !Q-�~!�! !k i�  by mor��an 1/3!�its1�� . T�e sam� b M9�s)�ɀ ՀE, tim�� mponARof��k.( &*nB���V�~��64��3 u硫q*ݝ���� = C32C6Arho = {4}IRo���n.>n It(��repulsA�M�-  corj�assoc� d)\!�6J -J��ur� �����D}q$. Not%�t,a�ed out!� ref.� CFG})�r�6R�label{ !�%��F} V}��-gQ�}1R��< rho_:rhQ:�K E xima� �  $-1$� typ@E�2 !2e ��a��&uY�&-<-J�(es $m_{u,d} �Ry[sD!)�+w� m�u��$ (as9ample,��q�q�� $�m_d 12�Hx  i�aVe IM spon| i�* ("gap" $4\pi2[( 1$ GeV). fi"� l"$\6�  thu�lI � o�č*�B , $U�eq� S&� V* �����"��ply�CabsorbB ��ub�%| onst�attached�%$k_F^3$I*m`-5^"p&� . H*��t ��loc"� ��systems"F Sŏ_S(r))   I�&V&.$V(r)$i�� �"#BZ U_{s.o.a�{1��02M_N^2 r}\,{d ,dr}\left({V-� 1- 2P}}\right)\vec{l}\cdot s}: + a huge"&� orli�$$V(0)-S(0)Q0.7E�, j�!�- r: Lby6�. �useful)w�or�ao).�1AY� & � u Lsum_{k=1}^{A}|\psi_k�r |$�.Z�%���is;�ah`1lA�_�A�occupi� �s. We&$ ""back�nd"�t $�bg}K-�d c�F�m"M s�e6dA�Y��ofe�}u�{ ""��=I�F� ex}$� lud�, ic fluctu��H dBe� s,u�U�.�i~&�o�Mory descri8mg 3.2�a phAi�I�}�5!��!U:m1�al�Mconven��x��b��&7f� ��YLag�ian)�1ͱ �ur-� ��pling��Mus,FhI4L}_{eff�$\Psi}(iU ���_.)! -&@}e.i G_ii�<M \G�i:7^2 NDD:Dz�Mq��.m.} \,B� !�aux�!y.aiN!!�esign1 beV�hee&- �,Mphysics ��-q sy mf�. Qua� 6�bey�y�E7incorpoi�th�EnFco)�a��, $5�K 5a$e�ch � iL �H��<$(i = S,V, ...)$I�� ator��)�Z{\bf 1G $ ���$ etc$ matche:� E�&m 2his e1wi���827]� �"in:�!6� , ord1��22�^{1/3}1p�d�#i.�so-�ed reara�e}"-E���r,�za� sequH�f�� Uo �- !rmoS�icy. E�ro�e#=� s $(}�a,Are alsoAq��d}bB,figure}[htb]�F�$� 6�M�dQ�@-u�� !����uM o far cq�a broad �Fi�$^{16}$O� $$^{208}$Pb�to�f��!d���optimal!!��E�b��)� &&�&iP-  f�"��fwhole se��i�sw e-tunQ����.� . It!Gremarkk&*q�=�fijKn :insein les��0\%�c ��b�$�y�����'�> 6 �ei?N�"zI2 addi!m!H(�%yJ(mEq.e� turn* )ϡUec+ ���t�%�S "��(�lfo�(�he* ChPT.L�infd#mIJ),�# W w�3a fewE]� e�E<���12�y��)5, 9 sh��.J'spectraA��$�8�Dina40}Ca$*#U�I�s�7 is gat͇-�F�-L�.��jedR sea (�"6�,plus P!'".&E�wDer�]$to earlierH(&�&&�#i.�&&�) �}��|G+ 8ed� ri!v�t.H�'%�f&�q�r"���$."Q��f@ 15B�vA %\�e�.fM 55:N 11��O ChZ%u�is"ai�> &> Ax$^�U��>!$2$p�,"� �(�of�'ɯ (soliZ nes)�Odas���c"�.6��c.� �.�  !O'��ex� s6�5bv�a�10m�our5 �.��=4in[$,� 2/6? chose0  i��ri��l�st adv�� ~�.�&�.kE��1?v� display)�% 1%�P).� � I�-of-masa�rrY%�oT �))6���!H�m diFBO9��ata�@ evidh'qu�1suc�+ ful,a��A�&"�*��st6�s�.:i� q"�J:��5 2�}2m,)no.O. � Ain �9to&� ��+d6 �*m 6��  !q� B)'-�%2�} iR u�q,2�6���all "� fit"�@{ %�s� .r(�(&!�*L pe�n (ej�N�!):: "8&<"{&�(&"�,�^{(0)< \rhoP ="� - 75\,MeV(^([1 - 0.6 b+�*2�L j-02/3} + 0.1\,v- �] :� �So_S ��-0.34�e�"�6&+&�baUto zer�A��*um�X�-%A��.$ "� butJY+�Cdu�?�.;"kQd piecf  t�-EDAF:&�22�&U*s�+o.�; ��a"@�E�$6-!ac (Ns��C: �V �3Vio� to w^{4 -�rho^{5 r���;�%b�%A�7 ��-� "� ��^2$�l��a�j/$three-body7�� C!!Q=Pbje!3�_A�� . A.�4I-6(24M'&Mv1��i�-i� aV(t�2~5JR1��&����r�as ob �&4L +�8��d a wideeof � A%�of�H-Brueckner G-matrixN� GFF}~)startI�v4�boson-"6�4I�(oP behiV6i��/� A um�b �ntO�)��9�7s@�$, a key el�&�&u�G3�2motivE*!}�a�$ ach. One-eNA 4&Ht&i6�r�$k_F$] 9F xpk�8�c� �&i�(ladd�6nd�#s^* i loopm� e�@ �$)t+Q� �]� 86(�" 7" e$Z#e355r�j��!?c�  *A5 ob9m�4. SB�8�o�1� 3 Y�)�b%v�4� s,��, �block�ZI s!ite}one6�5%8se� -in10�� �R ac� e%#4$ (o>��f)A�aD!�-��$!LAzd�% hand� ��-g shor40%ce�� NN�=�ll)�%�!�>\[9�-Gh5�8a�%�an��;g�+.�%����)�1@Yvy� B*�(�� �;�Iss;5 {\it�#}�;))� Esi! th�38r�y full>OT�in7��� "�!PSUMMARY AND OUTLOOK} �!aim)�i�xMon~#f.to dem��)e��r�M�� ��A�  iT8� by a 4A�pri�8� s�+� y�: mt=� "� breaa6em;�2Dba ��v�" />��-=�"��A~�A�l�&�" ($u-If$d-$)$s:Ɉ)&g>X�~ =2;via6��!�b�> a�V%~ar"���&M*�&e��%eQ/o�3*�E�:*e �a�QCD� � east� i "+�ifica�69.2freedo�A choi�parv=. I���+@�k6� j<�W66- nn+eaFVfo�6 comb�"� :O . St�8�h6�&��8xa�eme�:�&/ n�"��BQ8-���%on� d�<�V�n:��&� Q/pi'.?2��<da�-AA�-�"��2��&�>perE�i�3�%extra2�MsA�Gar�s){'eme�s.*?s3 ��ly-n KW},4A�p ŗ�!r�&to�SU(3)�A[�0applic�-hyper�i.\\ � AcR(led�s:} Spec�"thank>NS, rt Kaiserse? �a�"<� �AvelopT orAZ0. . Iman�n&� !�hPaolo Finelli, Stefan FritsXCPThomas Hemmert, MassiJDno Pro*%4Dario Vretenar�Aj�ven�'"E g���y a9W"� thebiblio�dy}{9} \bibitem{GL} J. Gas!,!�$H. Leutwyl�< Ann.!tPhys. (N.Y.) 158 (1984) 142; S�&inberg,*ica A 96&79) 327;NY2V23509V65.�C�G�Cl�lo,r�Nucl. \8B 603 (2001) 122WGLS�,2�% (M.E. Sainio �! tt. B 253�1) 252;2+$ PiN Newsl-16�p2) 138 (hep-ph/0110413). 9� BDW}�)�e.g.: A.M. Bernstein, D. Drechsel�T. Walc�+(eds.),, C DA:_oH' nd E"<}, Lect� s-=51 �8);� F�J.L. Go�8P@U.-G. Mei{\ss}nerr�< 2000}, World Scc'��%/1�CU�KBW} N.m�4, R. BrockmannzWE�se,2� A 62IU7) 758;.DSgEr�)d\"orfe)�bJ37%�8) 395�?^�M}F��a�ee� ,s; E. Epelba�F(W. Gl\"ockl�8BXB�71%60) 295a�!"ean" .FA9$daque, M.JA�vag[$ van Kolck>V700V2) 377.�TW} A.W.��!�99� �St6q%�eon!� iley-VCH,A�linj!� 9?LTY} D.Baxinweb��:x R.D. Youn�}. Rev2a�92X 4) 242002.�PHW} M.%�ura, T!6��:���Y D 69U034502UHCPP} CP-PACS Collab(dA. Ali KS et al.�WY5Y2) 05Y;m73 9901.� JLQ}A� AokiZR8>456 QSF}c SF-UK�:�G.ierholz _ (prM� mun��2�Io} B.�06S B 18�;1) 312SW2�:M��"�Apv hadrHHG��QCD�n:%�� t�ooz(!�(ics "Enrico" C.2CLIII,!�Molinar1V��IOS P6.(, Amsterdam-b, p. 473�#refs.�rei+ ��SW!D. SeroIgJ0Walecka, Adv.e)���A1986) 2� RF} P. RiE�rog Par������;93N�64�9�u75; R�F�! tahl~2&KK2�!im�C ]�2526� Hoe}AkH\"oht�?Pion-�z Scing��andolt-B����n!P�,Vol.I/9b2, S$g�4Be�c 19832�4KB} T.T.S. KuoEXG��Brownq�L�K1E�65) 54;2&�U� ed���_of%�l Mo�EA�F� H}, 3rd ed., North-H�)�]U197�Y:EF�Delorme�� Erics�A.�ureauiC.�venet,� )�� 02��76) 273�K>Nk <G�a� 1197ZD5�LFA�LF�Lutz,�Frima RC. Appel6SB 474e?��6cKFW2QS.PN ��!A%q+ A 69�02� ��B!?(-P. Blaizot6�A 649!99) 62jSHajAa�eFC!�W�Howard>H2� 1975) 496$FPa��ed1V�v(Pandharipan]G6�361�!z:� FKW2�&.�436� FKW3�V"� "y � Wek Ii B 54վ73.��%=�,bQ� (-th/0406038>Y(�- rint;9� PPWC`C. Piepa�NTRHWi�Fk J�*rle@ ��C 6I�1) 01406sNAE$B. Natowit�Q�B)8&A�127016f�&Һ2 � 3) 42@�M$ S.K. Bogn!:�A�chwenk�� s 38� 3�b =Zi> T��Cohenx J.�EDsGriegy�=�19( 96xv. C A0199 882q�HE.G� ukarevjEasLev� 6!51e!90) 679,��g.J2���7>�RV��$A. Lalazis+DR�_~D."�, eds.,��E^L�0D� Fu�Q���& Alic�.s in.��2�1��&eu�,.���Eur�J�1� 3) 573Bb2�b�cA 7�20R4492aVW� 5G:�. !#.  66��- G>� J. K\"oni)�& h�E�C 5"5402�0T. Gross-Boel�,�� Fuch`� aess�6�64"�@106�K.�:���,10062, subm.�.��>j.t:� �! docu�} �X\,class{elsart+uackage{icx} .bm�A2F:bS2rontm� } \title�� "�eazimuthM72l meas�� ;US e flow\�ref�nt{2 [T7 t]{ResearMup��G��;Pol�KS�W Comm�:e$r.lH,L@nt 2 P03B 059 25}�OLauthor{Piotr Bo\.zek!add {�pH. Niewodnicza\'nski Institut� N War%�S\\&� �Academy< Xces, PL-31342 Krak\'ow,/andl0-�abct}B �ge or bObOmbelZ(5��u!��)eB� of a pair�!]�s e%Ld?ultra @#heavy collis !�A> d. %!3>- ( 4; a t�  'tud�=Oa"veE$aG %.IYat ����ze-�"�e1@--+ %co&�E�J$\pi^+�p�8p}$B�s�i$uA�u�$�Dr�08+smtwo"�Kt�/of![��(rr&$/Q� �2@Z!  ae}N)(or�Sm=.�Ky�3= Mg.�%sfr�� ��Y@resonE^decay)�-[oJe�sc� ios,9 %��2B$is#d�L@&>d]<n .�m^l�A56&m>uT �� keyword} E�-F�-6�,!�e2%o�$ :�,]���k 2u �5-7mm} iP: 25.75.-q, 24.85.+p �� FIn rapid�)B�iQo� G =:."@N� of oppos�+iSs C-0baldef,Bass,j�A]i�AFe�2e�#c�Q <,%�2� MB��ngenesf+"we �9 belBh/2� , unless A�if��#elu9�;a(D�Wo�C. ��R��ersS �6W�ہ�>d99 �7!yx'� airs. On�2as Hdu�ZsO#8a microscopic l�F�$4qXL| �#!����Q��sfT2�i##%8a&9�appear.��-tBfY[uEW%2��\AN�l�r %inR� �B~.�i:�-.2 %�8&*,%B(\deX y)ULcG } %i+\{ %{BB N_{+-}2bB*^R#+N#Y,U N_+>l+6f-RC-"=M N_{-R�Bf-f,\},�$bel{def} %^ =*,�.d$�p�9!�nY��iw7>�s %��h74�v�(�~($|y_2-y_1|=1�$, }as kBae.p�mJU�.�5���)ewgX�7 se6'3tb'�8eA�&�%s, � �geR_ �dR6� }[U$�)�2���qN@��$$\phi-$>�, �*dM� �T� �j���) eqn�>y} B^pM� ,) &=&*!B Q�Z�5 :z* +I�yV+ (') K�O ight. \noMj\\ & & \*/ . + .�y.Fn�y5J*>�-V�aAgOdefphio49deA,� !� 9�E�yV�$��5��Y6�af ip\s& Gq  ($+$) f�Ra% �nEed%X1{-}$) 2. /+i��KA#!p"�a�'2^(8Qre�vt M�re�'�& ne) �Old �CL2%� ce"w�2� i�)Q� 6e�Otms)��a�in�: (\p-�C>qua analogKwayV�&� � �!�\d)QF�gd �B�)=KI(_0^{2\pi} d!� B'M�9 O�.�(�G��P�s. Ob�*sly $ d$��!}s�K�Pz�:M� R0F�u?YB t_{-�^{dYvF� ) =1B6Yyaccept� windo+6�^ effim c&v0modif�U �abo��Ŭon �$phdmsu� �Qe J��:A l inb' 3 �&r�B�$Q�tv7ral�$!�*� ��Yuts. � wid&b>J�1� %mw7 d0ck� sua %%��T��2�?&� B�� provide %�Vins��� �%s�`CEt ���!z"�environ~ 5;�iC }���ow��!be a %/)al��t`6ir&} ( �I��� STAR6 e'�9|jy.�Z�  Au-Au��u RHIC�-dRng�ar��!&1�_ � bal,I�}, �F#*�e}an �D1� �J� . ItA � ��  R� � I) daY� wnZ�.|o �͐ ular::2�Ac�1e�.. )m&W ���l!�st�"�%{. %An i"�'f�0)!] �:L^+�!".r %rsw`EK;m� ��t,* oret�L�R� 7r]AX� �have �.e4F&�) |.��my1,msu}��b- sump�b�3W)6+<� �I��N/ L%��-u ized��bKCc�b�%t)3i� 2�"E�I�2�~m}TbeI*lA in a�*�0undergoetso,�Ei�R�)�-�� %LwOT{n=�m*q %.e_!� s wo��, �]I!��el +E�*�0y %can�db� sOH6eat�6�,�s�)_�,ra � %A&y�6�a$mvelocityI)i�[-" ���c.!+J�$�� m&vhA��.�rpU�}.� firs�me�B&�.�)�d|lmi�76�of�CalQycIsQ�) "Eu7fE;zp �sl=d�4 �non �6N,)KVgiven�e�i(���of>w��sIa)��+EWI . %A �KA �.A<�"6� (rAic or %�!F�d�x]9 ��IxAkmHFo�fL��U%!�*y �?�o�nm^v-_ R�m�� -25}a�?:�%+ boos�-�Q� c>}�} ��: ��NjS�T �a cau91#&dG>�th8=-. Fo�����  *��[ondtake on$W[I|ue�]eUW Q213)^.%,u�&B��-C .�� %We��2Q N��"� L6A(B>K0.�MQ�-> s. W� p��xJE��, �]��i-&}R �)�invariBbFd-+Vpi3O C`;bw��InC��ca�c e ki�O�h�f���� "�W7on�aE*�15l�b fixed2�obm�Q��(iox;a&�ly �= �ZS,$T_f=165$MeV��A�5��1m� of5��mo�x \Ql�tehv�y>��pd0 �al Hub�m4G �*+ U>'��-�cawU A�(m $\beta_r=Qc{r}{t}$�X2J�!�byLal�a��$r$, �H$t=\sqrt{\tau^2+r^2\S$tau=7.6$fm��@ $0a{Ae�a�YI 5(Ien� � �P$is}=200$G�9=�=� %4AX% profnB d� Q�7!` u5-���"� ~>#<r.� i�f \/MI�>��"�lx<won- s �.Sm�&�F�quo!>k.~ �=�iJc>�6uQ�est R5s "=�N��� `"� Z�+%B�s�� l2A �1�B�fit(v�� V&fR]�>Hi�XB!z�< �8 {W ZJ;*$lŠ�*5! Eb*�l�.��k%S �-�"�px.���A:�;a.�; .V2�m��6$� �C�A0r��}�}K�ODB (�K \�tr�K}).+�N*;XAqer��gX =10cm]{tr�N�&2�N�9�-�.�as�u� I !)*� I� wo *� �9"�s.���%1�%D.B (*�N) .*� ^  (&�N) aU)x(up;<curves U1�zer.�%dot�A#>ot! N"���e��~� 6$,CA @"�� A4�#�H6����`rary.(M% %�M! S< S cej(w!�!u� ��IM $8 a��d�.C , mo��� Kc}B�.� � D�+�!/d tice�Fa�q8atm� �� K ya>�9�I��]��#� �c!�$%)�A��$q�,�HO � s, 2�}�.}�1� t. D7"�"q?--Jԅp�� $ m� %� �+F�NI� posszKC�Finee�^����5�1jof2B+rl�is lack!se�A�5 ( 2}�|� �=�� 4�"�ntf�&����"o�#"�#L&jvf@)�.܀ ~p!�X HBT� i� :jW$2 hbt1,hbt23} e�%��z��E�� e g- "� ":�� ZT�w �. F�A�%�cJDsY� �\- �P"x !v�n!�z�"on-sh䀅".'%&�<� at�W!�/F�o$m suggV 7 %&� ccurA�t�I< m;6��duD 2M�"�]x"J br )�� }�d a�NU@ ppeny� ,%u3�.6a� a*+v:,�a�6�Cd � 16 . I���}uiA��T�{ �`I�H*` �oq9�a�Q$�� are ��n2�%�ensemW>�� and � 8�h A0 history untiXJ�. B\s"�8H��0 stay�1�lI�L!�%�:m�n!0%�&�b0T5� e�GeR de!�� �[���� W>3�2 }M�DI��3*enAi$>EbJ�.uz�w[�� )�a�*�%�*� �B�*�- �\v &1��� LB�-#e2 .r����\�� =L���* ]&@*D�� or�ѡ, �a�E .B vDo� D� :3 � ast �։e"� ��� �$�&sB"��m 6�"����1vsu��.Y ly �|)$A�M�-U�:� y��M�^�!��2IAtgR�on" �0:/of�`/1��c�"!0Q�. +lA^qis �$E {\it� e�e} Q\�J�Gu!��Fm�!inr  m*Y,r��ige �6io�> .2e�X�mi�/man Da)�K>�%J1Qy1}. a�9Bs���*�- �acc8 %�"U� �dsb  &F%K_S, \; �^0 sIW {\rm!k}# f_0, (r��5 Ka�llm�Q#e��:�C"&�1�u�,� �a�J`U ��c���VAF� "� E�. N*�%EE�isotr�.͆ C �j � �,e�p���aF >uE �Ila�Ims�E�a good�'r�xQ�4!L���A�y% �$s �5�H�0I-ft)a� s w� p6u~MT�K �M�V �(�A'H�5�-�d � �&a&��I�< ��)�� 0 -e�r�-Q� �!�fl�%V&,rho�*!}�C ��^A!UA$ ��dd*Rfor.uA"a)�_0�Z)a|hF�at2Ib�66&�a)q:F �!.*c 9$I�A/o�_� ��.�m�ce� ay`�nega)� t)y*+Mvt�S�&S �H . C�=�YI�� �V�veRer��N !� !�H� �bv�m��V�� ^Hf �VarǍin a�Xxi�x��v D d\��� sit�+! Y� B~2�  F#Ka}�)5v$g�(�+ me!athK,�!�B�&�sEB-�er"� AS )�q^ 3[i �� share}�f.�x��AWUKs2�x+ angu�27��B��� Z�fc  %��i�$'owpl'inF�. .���to  ">!�R��em�>���( �a�cMR.1<*w��ab"� &u5L x�a�C l�Ivow�.��Nno,�}.: ri��^p&�;*[toŤy��! !%�� .� Z� �3 ���%:(er& "2:ޓ piphʒ)*�� ���)e�E�U�!�: j � � b'w%�i!�� 8'arigt}hi�G V\1��i"%s (J�nd�3ca?~�a�At�'s l�*.%�r%byB<EuN��� at $)?��"�~u�B^�!���.�)\ ). A��� ��>  �!!i թ��.Os �����|B#/`>�~�� mmak�Z�=a�aP)�.(($-50^{\circ�# nd $:f�w^jd""� &;}{*�uUk!7 �a�!a4!le U�� ��k -6 $54�i 6!x$$1$GeV tot�� ransKC�P $2B] � 5.�$2N!�m �A�I�I�,L�asBc$8jf!�iv� � a]�b�(N. O"��CE��0J��!* .a'a�dom �by�C�K�J� hang� Um!�.9.jn2� �e5M�&s, be^#.s"|r � la�-6�_r� n� P�w�)�B�s��� ��� �2���&/ �>I. #�b!A* � �*Ufhow!�V-��behavi@C�>s.!�.PHQ/a(I�. �EE�W y�� eI`1&�&�E\s �@ focQ?c :*. )��@ 3m��  moreFS>��� {� � t ! �lsoF�~e�@ ed �o) ify 6&�o&�2!�aTbaryoZ�^�;d$"prS7�� �1#� .�aL&��&(.q��j ary,�Aro�+o�7y uGe4 �2�)�!>+>x 2���> A��:"�+.@"�b*F6k�2!W�EX!;��;�+(^Z�Ag R,�an#*.�E��d'* Aq�"N�"=F:0�9�-E���n6��_JRTu��YanD�� �e6� i�compeӔ+��_ 54l!j|� RF+"� S�ze&���Y.�6Z&; ,^�Mjr. Accor4$50"r h^<T�=�=)tly"Ui��r|Q&� >"�3m`.�{=�}� ExplƇ�1o1^��Rw5Aݵ9"- q.O,�5&>�confirm�s!��s)��2�!�*�1p� .finaM� �$"� reg�<��a�  *u � �j' . Fin�wy�f l^8>.B.�@��+<+��!a�6�? (Eq}("t?IP��s�.�w$FkQ:�� 2NYzd *�g��spa3�!�5Sa/?"����3�He"-I.;f�u]�Zx )�J�vbe �B�y f~e.-�N�7 like)�,ank Wojtek B<[ow�N� Flork A���f~i�UKt:�P{92]b�I�Q~DrijardF\6�U@PB 155}�V 79) 269; 3OXR$66$802�Y�} S.~A.~ <, P.~Danielewiczm1S.~Prat��O�Z�Ua8�20�X689 +(cj�JBJ�Z!.N.LFC 6 H�]449�Z\J�=( M. B. Tonj� PhDa#vTMichigan�PYZ� �&�2�+ ���RAdams5a6�>, ^�90}[3) 1723�V�70P.~Bozek, W.~>5.~Y1, %``F.^#&9 �: =" (s,'' arXiv:"S3S=� S. Che�\C�d��S. !�, P�on�e�_!�!jSkoby, Ns@ Pop, Q.~H.~Zhang�+R�'atd4c �[ of Cv ��U��S\gT\ CI 69)Z4�_ 4906�-}6UI�:V^�87 _�d!�2; %~� �� �6�24905; 2H_~BaranN� ActamPol W B 33 �2) 4235��2 J.~I�{� a}, R� %``Iz�+&�:��"j_/p pe� Au +�1s3 (s**(1/2) %=�d -GeVA~2��\ )92 �#_1:�}^*�:�%``.�;-��1. II: E2��f"( �AIP��f.\�Xc�66}�8.g�)0} S.~V.~Akkela�@nd Y.~M.~SinyukovE�Ph�����.si%Gir '&uO>�puzzl�� A!f=e�J�3.�,hbt3}F.~Reti<�VM�� Lisa�O�8� M��A�}a� geome�m�d�fp%8 out�)N�OR� 2024.�, G.~Torrieri:�A�LetessiQf$J.~Rafelsk� SHARE:�ݑm*,�404083��[ ~Hir#AjIn-plaHP2X.�T Pz&_ v�)3-m %yB!4f+8�2li275!H2>& #d"�XZ,:�X [12pt]{io< 6�Xt2:�Xsub  �O*�j style{num&�Sz \�XS< g9 i du�!a2 � -ITKVe�Tg {2�$^{1,�92E $^1$�?�ranELX��QX nFX31-RDX q�~2$ 2�X!��XD'Swi\c{e}tokrzyska�X0, 25-406 Kiel��Pol�X"�!&KUd!l�-"� e�B�+.�s�?*e!Vwor0p Z��n�are�.*����E. An o�lldc$gre� .� E#�����Xn.�F�y.i9]Upa54Q$u\�?P2Bya�Rbf�(&� :a�we,:uk: 2nf} �Lyze��0�aBx!iV#��x %ult@1q���>q� j!B!f>b;�Q!,3fy,Castillo4jy&�Q+l �u� A:;�M,� ^���s:/;cylindr�?��yҨsym��UsXl�EM�6�*%^A�s���`� !�!qR�]��(inݔQ  *G �!&"� shap"��)%�-@3q=�� tvI<`�>NMqHak:�#�&|;�V^[�bN�2wp}:��&�QtS|?��(hbox{cosh} &=_\� llel��R keptHM�M| "�A�: "A&;9lifetimU��0&��>9�z erp ��2JE�&�5 �4�%&,Ir_x$-axi* ;ML6 $r_y /�#�eN[$t�:;m0lmond-�2� ��J^� 7 chieN*N�%*0� �?1b�5�$�-"�W$$��s e!C��*�_B s�r�*. =�g!, *t�G~*��L$R_�-side}$ � �6uH83���/^,�1f™vd1����M���wayReu_tarf۬ t}{N�1u�0r_z  u_x5r_xy��Z2���ue���r_y.9-9B�uz�6E<$N� ���\w P�J@E�r��l2#,,N , $u�� ue�=1$. Po�v��$�� fas?D�[in�A>;�ich�%}d<Y�v_2$. Cߠ�)aDD{�-!, �-% K�# �unius�<S*E (S*Ues��LF �P�* �&| ͢� [b"ۗ j�?9cm]{c n�C)IیhLur*� R 1uk} �i|��=$\XmX $\Omega+{Ac }$ inF SM�C�tZr6� (2FZ) �\ �K}"� v2m.YK�_A8."��&� 5�2 mayO�j��6rem�� tly-��groups:%�� J]o� s} (.H$T� /h"&2=&�� $\mu_B$) y"�C5��Y%.E\!��I�ic abun���&0�1fp};ɤ��"�� �heZ�  � ��ad��8f�/oe��rho JEtau&� .� ^/ 'It$) �"H *]n6; �,���p5dea![n=} (* �$ b��Laa�Von: P!J ?$u��-��"| 9��V��t@6�� ��MP�B�(�%,`L6sL&C&��9'lwa�I-+ �*A<-B�8� -F#m�regarda3!Q ee�e͉Q�Hc�� @¥fɑ&:�ukA0nV11!v_Bse���:2 !z&���f�S��>��E &� ly�2n� 2�{ ́:�iB_�>RE# &��'� to � , h�!uI=0I�mK=0-�K-��i�O���]!<: $T =$ 165~MeV첡==$ 41�l= 7.6U���8��($ = 6.69 fmZ�%�Wi n+'�e ,:� �Ep1��9�ac. A"�)=�!��&�.iA*b� � � Bb>rwp2 W&M�* atisn�!tl�#~!rapancG�A%%� of L�s (2� )a�}�q�n�H�o�J 10.5M $v2ph200mbanR �]=��. �W�2�� (�)�+�symbol>4�:!� n�^,minimum bias%��� PHENIX6!e*ec� �R�A�20� ( wed byx|os;Gin0 .m�Vo ��2wa} ) �,"P ��2���,%�!3� � �-�6��./ �X^.$@ $-Q c�UAU)�.�&�Rk�Ri�2�Z�.��mE�^� ^� �&e:�mo� =�R���1�W = 26$,ږ�p6h�y��� 4  = 4.04��:� = 3.90  �!�3nm,AnnaPhD &zjbi7n A+!N�!v�k.�|RA�AA%Q �5��$�=Bm+ide��%�wed d!^6�25$lM13�eM`n� offuK*l%��]�W�U10"i&!5j" &q6^td �2�$ 2�t=tx�� ,�7eK2Bd AseV���+�3e"-emE�R]���.����bɶ�u�@VX��"@$EX1� ����sBsoft �/�g < 2���.b�e�� %�OA F� �0H us�1%2��e ̺J"7���g&(%s. ޙ�"�"F3.� �2K2 �.�����}C@�Y��wr"��$�+e 2�} ;}%*cB�}n�t2~�} ~059�%�,"!�{lV��% >�&{1���d�C\ifx\csnEQurl� \,#8x \def\url#1{��,tt{#1}}\fi \fIprefix>OL {URL I&�-6m 1weB�*W2�-�%,�*قbfF],�/i8�:e2�&B)J& e _C.%/6t,f`�$>`A"�,:�6�,onqB&�, �,962V J�,�(it et~al.},�8b1.),82G/`>cXJ�0vbf G3�+4) S1206�BS �!G,F, n*E,, 185--195,&��212052هC�"�F.~ , G.~�.+ gD1�197O-86.�F�ET��/~,19�>�.^�762i�>�+-A."�2�2 �A71�13�9.��� 2:��:)��77--184>�6�*�} 2 �%E.Tf/ �4A76�2�k~�2Th�2un"�.%�  T�,%K.~� J3C�3��F1�*B>� *�+}�Z^,�9}%2��V`,amsmath6�,amsfont�*V�ams�Wset�Per{MaxM{�Cols}{3�D,renewcommands�/0estretch}{1.5b�� mm \odd�maru�0 : 6) =0ptR =-!�"zp.� &��l�$^{4}H$, e/ Li$ �bt�-clusKshold} 1-(���@YN@"put epsfUmflushIh0} UDC 539.142�b \��{{\� ect\�D In&J,}��pa�.;h &8�>�A��^>� L�|Alb[��i�i�Hr�%2`�>^�Tilley��A4�re� 4 1�-"�>dB.� 'C�t � o 151�Ew]R� ��}H��M�bKs�&skJ�Cg���� ��%k�Fa����#n&Q"$ �A���. .B�J~ .� 6�on�>e���tr�P$�B�cu��!��l�5.�qIse;*�=���dE<boX!bA  *D];Y,�H�S$��$s, "�?}'KI?cross M��so �X�X many year7�$Ewon ��t1�da�i mi_�� �semi- �� . Di��Hm1$ Schr\"{o}�Ae��! (e�( 2VI05, 9})gzt�gl&<0FI02, Carbonell9, .9o-2kUKtek2KA42,;PFN��8PhRvC..43..371K�D2PThPh.107..833K},W�rixgt algebraic àkn:vv4he_3chE,kn:VVS+19904HeE,1997HO01}),��i(A����!�B��.":�qn�%�paite�He���W %� ar 4&�j�,�)[aɊA�t�-��e�y �oe�  lbl�d�$n =2�\�܁l �Li$��ex*} EE3a�>%�i�|i.�mai*teg�3�t �" .wKO�`q�S{$0^{+} $ > ��3i��?�!s�non��*'a�e %� �:��w&��s���2�H� *V�ŋ J{B�b��Lisc�eq� zf�} Our o����i���Vx�t�a�r��<>�5��� �]nitR� �c��/!���E�clE wil�)6n��>{� ȋs c%-�%�dPMnt>Ih ^l,��ib!�͊ɯ�͑ More!z�can e3 y ���b� ]=-�y�� � ]e�q�2 eL�M2�w�%��y�  �s " �s $p+^{3)�n 9 d+d 3ll!by% &� K\� p+n%�e�oa shouE�#"L, becyx 7�m � A��� e $da�-��& *! n>FG �� ex��ol\7u�X2Q�� )v$ lie ��%:��5<$d+n+G2r ��e�IuBLi$!o��� f >�p.� x�8�p4����q�A�-"�4�`œA�L97e, A6Proc, kn:ITP+� 1}��> .6!22/3�9�.�:� %�9!li� n� ax/sE� , Q� exitQ@=#g�?� !����uit{?eh ment�Q�8��Borromia`��Rr�3w^{6�FR�it0�) 6��KcY�4A Be$)Zw| to �8�+ ��:!�,F�6�B hand�+gEM��H mis'5y|~���,� s � E�cor@���6�%6� ]� teri�J� -;*3�  Qo VNCt%1E}L�^�� uŝ�2Y���6!t�T� "�� subsB�o"cA\iԵje�w|i�g:":itemize+rtewif��e. y��:2���&�\��S&��*!s,��c�uctA� �.�.q��as.)r\a per ^i~���B1 reliebJ$.� �,!/ &�;faS� r Jacobi .Z<d�4��(NX$)�re`ev6a[8o wo� �QJ.�nJ�O hird�����.'O�0er�" ��ŮBKaM�- e[\�=4!j�x} ��}}+ }mL[:\O�j\�7_{ E}tr}_{j.J}-p 7k7 s.8k 8Ei ] ,U�\\u`=^V�F��.� b) � 2!:+Zi\in ! :2�i � )-:<%�)>+)b�+>�% �276�fM$�� �,I,)z5$#ycl��ermut � (1,2,3)q � .�m�2�s v��s���� 2}, ���� $ (m�Xpr��w��B�t,�G% 29�� {w��a�ax many"� SZFfic_.fJ� Ci��yU� nU"��oA�s: @]%.u�2�,sa� ���dyF)��~4i=h%&) �H)Y�olt;��h:1s��rh ��� SIf � ����(i�wrF �0), ��6 X-6>�I� ���� sh�'Ga&< a<�"_f�TdAim� e�#%�2� $fխE�aNBz R� �) �DN oscill��]�s��f"L�z� BiO%\ (BO) +):%K � } ��v�=��D _{n_{y},l,n_{x},\#) da}C^^{5 �� � )#\vert RS;LM ,\8*le�<B}, 2� 3�0���J��t= � % ,l � ( q9�şC %= z ( x>/ �{ Y_{W6� 0 }>;�5dot9-�-VAy2 b N@�a=_{LM}6X4FX�  n. HI�$ e&e (radial)]�"�tN�-hR^=1F-1r ^{n}.�2�� * n+*}{. n+l+3/2Jl'ZC 1}{b^{3/2�( �{q}{by�^!�expi!���1}�Y�  .9 �? s!w(L_{n}^{l+1/&r f> ?) �. 5F�S,�gX"�9$L�9�䩾$s$ф'ga ��/Z%�+96N a $lU��"M�.ss �&T7��M � 6�GF? _ *� $. �+���"$ $\Phi_{\aDlpha}\left( A_{\a �right) $ is antisymmetric by construction, the a#�zation operator in (\ref{eq:a001}) only involves the permut :�mf nucleons between clusters, and it can be represented as% \begin{equation} \widehat{\mathcal{A}}=1+\widehat{\_{12}+\N3% _{23Z _{31b,123}, \label-6}% \end�where $R|1�D\beta}$ exchanges 5( from5% $)�$\ !.$8$, N�� 3}$ )�0es particles Z all threed. In som!�spect!�isv Ts similar to a short r� interaES[deed,^[4is noticeable EM when/distanceB:P is small. At larger .s bothA�foU/D=$ 1, 2 or 3 cover%�whole!�figur��\space (i.e. account for A�possia�relativei!�s!q6� in M). WeI$,limit oursel�ao�sub w$)"v+=L)-% B/=0;LM -)2}�4m\$total Hilb!�{8. Two arguments� sucha�hoice�� given (in��u�5!kA�4-��$ system): U8numerate} \item!� F��Vɓ2��&$of $^{6}He�8 ob�ed%�g� differs��1\%�z]D@eR�-%�sh!t� �-a�%e�eQ�$2^{+}$ )�of!��, appear%�s a�_on�oembedded�t.�{!�inuum�Z +n+nOs ��.�UY�( To includeE^prP  bA:ar� d�, wm� spli!�e.Aew y�C_{�i�q�}^{�( ��i�) � $ (�=1,2,3� n�^� nal s asympt�e�s.  form�4onsists �(basis5���ll 1�sEe $N=�+��=0,�\ldots N;C i� )( +1�1 2/2$B�����ge)H$���|i{iz%�52reg2 in2��"%can eW�0��maximal .M6p��R�� Rby usA�J(corresponde.4 ��!�D"p ��0s (see detailŋ��(kn:Fil_Okhr��Fil81})J� XR_{\max}\simeq b\sqrt{4)r6}qqup} If,%mi2�� leng�� b=1.5$ fm�IG =15$��n $6{12+I�1` "L any pair�c� �  b5�� . I �B���!inguish��, ent �me� !first ;��stwo��� �l 2thirdeo�� ar ad� Qsecond y�JS�� sepa�dk a sele� F9s ��: \� ) has (a)�� Ŕ(s)I��f��is��p�cblee*sc~ a��r� M� o G%�� �+ �& ais��cj c�$ describedD body=ѭ�6A)ssocia�� the disA6g* �re�P��,:reA depe��t (non-EE{ng)5O�e� wo-2s� toOtre��ently. T�}<!!bmմ6O� Yused to ��ly 17�se1UE�t�S requiree�6tu- >:�Brdw o suit�wo-�E�)�physicaly \ ex^hannel}�2e-�y�a�Eec�8 F1 Ed�8but*�ca�_6�. A) a�"�  e most ��n 5 Akg,%�byF!M� R�BE7�%i( �"� 3�M"�nS e�}$, orig3a�gas-V eyforce� re%_.b,%� long 7Coulomb�ces��of5 ce �6�in.����S 6�%�tq,be factorize2�,align*} \Psi"L & =5.�j �Phi_{1 �1� ) 2.2 3.3f�l( 6�,*�\_  \ & �R�6�o�I( r{f%M# &�I5 �) ~g��. � `E�2` �) 9.& . k* F� B )&=2L&L }\cdotv� V=�M֙ sum_Z �$ )/� )J2s6^ >a 9�EN=�&�}� �1F�!R*� *J� !�� 2 ,��� q���V:]$�� its er� ����� � aS)��E�a$,�an eigen:�!�`�( Hamiltonia.0Ha�i.1� .�$"�"� �&~<M i\in��+�&i�% }LT}+I%i� &6 Kj_ A�J_ $7�$.M *| a"  &[ � �Rbu5 0he Hyperspher? 4Harmonics (HH)-�to2� � ecayz� � "� becahU:� "Y�DanilZhuk93E, 1998PhRvC..58.1403C, 24kn:ITP+RUCA2})� s8 i�ASviousA����typ�_ �behaviorD  tran� �  bi��� ��.�� &]f"$!P%{HVO$\rho },K;lq�nM!]A��M definOHH*Qin e.g.&�1M�er��$an orthogo matrix@t!**�C b3 l�i� stra{ 0forward way. �]y R�!6� �n\"� ��sevexp!�o� effici�J�{ � LB� ,E_{��,Nc�z) }; \ H!�},K� in};FT 4 },��22 }+2v5��F<ax.nF9 �%:� 8J�� �=L�llZ[!�!�=Ɓ\on$a" A"� �is%�incom� ($\pQ .2+� !.$K"K=�2")�outgo^R-)Q �FR"$)E�s.XQ�}Win��qB2�� 3}):"!W } )�y}�w w � ]2R� �,[ \delta_{cA�;��}~ �9m �Q�k"� W5?-SRS _T +0�U .]�&R# 9}\\-/m,r"�-a�� ho_{n� ^]B!� K1".mB# k�Y =nJBJJ- :�10q�MIi�a�index $%�$ denoen����a)>�k%9=II8\frac{2m}{\hbar!0 }E},\quad�=�n_)�% +2K+6}2w 1a!�YK~f%�( E-2}Z�a � U�.�y}+2L+3� *�%11b:ENot� ad-I)�$� edTbin�)J�hie$9e&�% � $K$�t"��"er2Fsus5�z lGa�� � B�q�one| I= � A��0}$��E6� >U. &���U��� :��duc!Ye ��!� !s&�Wme(%22H. By tak��into T""6#&� ), a008>9}�$.�(10�(, �s>um_.3 )W}�2L �#:xA�q�}~�UE�*#y�# Q I!-E�:&� y}Jt��� N�% zdvK�q.- h�G$�-B% 1}�;FM}~>6 \y}>8�? {H6@.��y}B� �) ��Y�=�_J �Bf�k �| �c!c^K}}% Bru���tI�J�>sa.�K �M��&F�K.�NXErho e)�.2��& j�6I .W2I�6�)�ʻ�G��$�,ּ� ��(  =Y-w  � s��~icK����A�% �v~� >�Rv~�Jm�6�.�f% �H�linea&�s� �� in\�Fl cas& & "NG) 3}Q ( S$�k$,+3+3N_{ch.HH!�65/*gd �d. Here��Z}�b N=%�( � ax}- i"  /2+1)5@6&�HH � . F�/<�)am�*, $B�i�n%$ c*�&�%� "�f��dPN �" $.T$*X 5?.elasticn inpr� �lea!|^o5 reeY!A; Ix.S '�ar� (unambiguous fie2�O*Y �*see#4{Results} We M�4Minnesota (MP)&�_pot}9#pmodified Hasegawa-Nagata (MHN< potMHN1, 2} +on-+ on (5.) eN0� e * radi� b�/to optim''���)�gC deutero-�A�ls �%�%D MP%�668�% HNP. C'#�.ngns0/� reveX��0�,,peculiaritie�! ��N#=�of�#(*�#X!aV!cO4w�E!BJ . �c �� 6� y���allows!\under�+d w� kind2�.  g!k�1!isRz.T-h�, omit_ spin-orbi�-Bh2tx#� ,�4(al burden. M��edi�� ppro�(!+"D-a#�8a \textquotedbl�T*r /2� E!�width!a9�, �+dv+�h##uop�ew �p�/ilQ"VreM, h'�incre�SitLdth��D�)A �6�2  Idic#*wheW29$ usI{(s) coul�.rv]0af�2Ih �n"�,d. >dynamicew!�s.S1h��c}$Q=�1rectly-�� )\t�' ��}$/B�2re��h�s�ri�(&'$@/=I d�$��(ele�0$ $S_{ij}$ �&YA7he ph!� shif�$,4e�"��e2eT(:f= \exp�_2iV\I�} $. ) p�4�{��re\k& dia�Ta�an *��&�&{�J!�}� V�1S � 9 O.^{T�!am! S&��*c O� 26Sg �i l�(� dure剅�II($ uncoupled��2��  Q�2%���5(()]8��$!� 1ki%$V�$U���\2[to*�0A`���7���S�_ye$".1fro�5fo���1I&�} � d�Q�\nu}} ,E}|_{E=E_{r}T/�G�6=2%���  {dE}{d2DI') EB�We��,rt our analy0W >-�(Fig. _;Fig:4Li_'s_L1_S1}�TdisplayBE��5e} [ptb]cY;rJ4�1,graphics[ he�,=11.5257cm, %�4=16.277cm ]% { �)� � .eps� capaf{E�"2�:!�0$L^{\pi}=1^{-� $S=16�24}Li$ 5�S ;� � &�(8�� =11�(%-qA> �2d.��f[�;5)� 1K of so-cala� 3$\R!3arrow$3.��r�i�e�3�,Y�n�. Sm;pictur�5.w � i%"�\ (�$,�d)A�+!H�/|�/MHN9h . On�n 1E�A� ~��4N��u�{in=��$ is n%]� manif?3itsel� roug�; :.����A<�k.Y( very broad] 5�1M.2O�b2�provide%;�6 Ssimple�" 2� �+'ee:� )�r*h"conx5,p,to geU&���"cer�7�main feaI0�6{ �� �<e�z��z�.0�P&H 7 %qz!�q�% ~ . ; � u�a�J�*�-a�2��6�.���R�# .��6ai&?� �8$-�i&4(.��� 06882�02=�Y>�IN�M��� 1�R���z� 5��L%;z��r�% conn�3U� �# U��/l�"� They 2_�I$^ɜ�aMP� �Aa�@�  h6G&h"G&Z� ��3a9 #Q(#  $K=3$i�� �~�5 assi�1�%�*� M. $K=56Sigs aJU shadowFN \�. MH7more :mo� a! �9�"% >��+T Cs� Tab:T�C�7R&MP�52 n(HNP8 col�!�}�of �'� lyg abov� 6<6)$d+N+N� ven:ityHA6�a ,9=10.-�od[6.;A .t1$.% %TCIMACRO{\TeXButton{B}{HAt!@}[h] \�� ing}}% %BQFE1&�@N/ %End*%+,ular} [c]{|c:}\h{ N�F us &��$ S�ax E$, MeV  2\\ ee�HSmH& 0 & 11 .642L.367 & 6.726 & 2.759rC>.90.374C958C9826CLiZ� 2.60<,0.413 & 7.78�3�{vD� 2.91 �$465 & 8.083.3846D�?& �>-%.95 0.23�2.9 �207D� ta-�"� ሉ�Q�F?4}H$, �.z�$^4Li$, e�&ua+&1,� y7N� A�eJM._%2%n�P}V)E}{�le}} Ni6 VR�{�{�{�{.{ 3.97A� 1.17At09.469 & 3.440UlN�A�E� 3.73ak0M�9.2E� 3.36�{ 0.74 D09A� 5.00� 1.53�{ 0.66� 0.05�>4.7 �32>Fe�mB}{ 0.89! 0.00a� 2.43L 0.16�{�{�{6�&nu�lV%:wvv%>w %1@tkn*DfOn�barrie� �ro�?.T4r 5s���.� well,�ul�J a NN&�<o�-�Mn��M'&�[� �rifug3 �� ch�b<or\al���>�&�(�(�{K(K+4)}@}::DI�Aé�� �Cou:Julsio"5@ pZ_{eff} qfmk�acErD�=�)�ch�L $ h$ ">� quantum�� �!�Kl�: 2�;�&�'1f5?in&W�,1} � deepAZs*� I!/�MX�-�!`,� sequ�>,< r� �c�.Hs[IBR� .�y�B(,>e6�,Ao� �t|M��DBp N� .�=� ul\< Q�ce,PB�in�R .�,�)fIt�<Vs, ��H!RE A�>poe d ou)=rw, &�Qin� �m � �� �),�=�6 � �6 �%�dd:u @ "n "&se Fe` $� \ suB2 �"*A��-ai�Odem=S]in�*�H4_9�_vs_K� ^� .-��4.3094in�5.7709in��}>-EQF ��te�(#sp �)H"�H,K_�$. Errora��!�!�dou!P xpv!_tL4i�A�4b:T&�4%�MN > �1DE5 #� �� 1�2� *p/*4(>�x8JH!.�TH$l�e@7!uP!!=LMsByi}f�A�}�qJ#�}�Sg2�>.�/!6� 2 � false2�*7�s~ft �Fq�d &+dugR!�Slon � ��& mpatnA is2WW�.wc� s�&&� N����dis[T the "�DU��nverg�i�Crr'!po�8_#T� !��U&sP��N\do not *(��$�0on"�TA �Uo"EG�E2�!s�o e.g. stud�D"�m�&-H� 1�, &R!�R�� 52�>�"2Y49��9q�:&�coh�2E�5 CSM-Ho}) 5g.�$�<nu""+n\E�) �"nB�M)� ( plateaus ag �%Y]���(or a �UU�� O�Walread�"ser8U=}�!�$n$KQ�+rOs,. nH M >�2%ac1 v Ia cb� a>m� �WA�arMK*Vre� �g#=� (avoidmVr�$ngJ% ). Sp b"<#mIJAW o.*A�.jAI�>�o.=U<2 �.e� Li$.)Co�� } A mi�copic�(el� uA)A# JP e�I�twBKIN)�� aim:F� ev�&>Hp�.� : 6'A�>�&Jy����)� A�pJ!�t2�&N*. Two�it{NN}% &�WsX .�!7 t.~J.�P se%>v� -�fi��E����� . "ZfdH;a B�mmo-� appl�*��l�u��U�E&� I<X ��i,�A�=�6>R�%��+*]œ* ٌU�6U� �5*� � :�O&�)accommod� several��I. R![�w*WMV1�]���!�-cl.kw�Zbe�� cuss�jfut�% work.�Ac� ledg�,H!M.@authors (V. V.) g@ -Ny a8d e UniversMl Antwerp (A)EJ�| RAFO-gastprofessoraat 2002-2003N� �C+ hosp�* v!mVrL!yearch=Wpif2�*Com* +ModelA�$and Progra>N�-$Def8!=2)b  Mathe� cAKd p er S�?ceR'RM, !M, Belgiu�C%\bibli�V (tyle{ieeetr��the.&}{99} �v% Zdibitem {Tilley1992A4}\emph < D.~R., Weller H !�0Hale G.~M.}//� . Phys.--G.--%h0bf{A541}--P.1A�s{Y VI05 o�Viviani M., Kievsky A., Rosati S., George E.~!�,Knutson L.~D��$Rev.Lett.-A�1�86� 3739N�9B��XBO A689 Q08>P0FI02 PFilik�YI.~N.�4 Yakovlev S.~Lg$Yad.Fiz. (lAtoD,!Wei)z0�63x79(69)2{ Carbonell!_ � JkUf�4Z218--226b\V[HFew Body Syst.Suppl)7.�12c439--4442c�WKA41:Kaneko T)58Tang Y.~C.}% //a�.Theor�.y107j833>e1PF5�Pfitz�I(B., HofmannA�A�Q� I�yA�Af%�.aC6)?044006u 1991�F43..371K-DKanada HA��Q� �/I� wM]C4A PV --37B�(2PThPh.107.!zV_)]r�Tof0 oret!�ics�Zl--8372quG v4he_3chE �Vasili�V.~a�Kovalen%�~P-a< ppov�jFA�q)�g88=48%�217A�$3(346--3576 4kn:VVS+19904Hef�Rybkina�Yu��9.�5��871--77(112--1236�1997HO0q�QvMI�]]r.�9�A61!�P.66�!t!c97ebrNe9gDov A.~V., Arickx F � Leuven PAA� ��%�9.�60%�~343--346��_ �k.g, 2i� A.} �_.��I52t. Sp�Se&`�!4�8�ic���&�\�2�E��ZHBroeckh�"���qʡ�=�C��~034606k.�J����B�13����0646061&�a��� Chernov OU�A�.A3.(�b�w.�64}, N8�4409--1415(1486 926�k&�] ���a�Fi�^im��I��$}//Sov. J.�#*T 8.�3�D ~480>�Q^)6q\e. E��I2\�Pp\6Hkn:.aM c B.V.i� M.V.�M ov}/�� � � !gic� 1993]�5� ~67 (4606PJ�M �Cobis. Fedo��D���>Jensen Aa����G.BC5�C+N!�26� kn&:)_Thomp� % LeM?7*�" 9r7.7A26 z~53--66�G:�({: AI@�: S�rog`or.j.�45��17E�8:� k} $F.~Tanabe,��Tohsaki)TRmagaki!SVx5.�AT P.677--69BX&*-Z6�:�ti�opo*  LG (Soviet JourE of P�l2eT ei(E�.Chasti�Yadra)e .�1I�1!�177(34� 066�kn�IHo� K%��6Repei2�9> ~1--68�3> � Ldoch}Q�\8class[a4paper]{ � } %�. %\renew3and{\d}{X,thrm d} } \2(e}{\mbox{d}>e%::NPZem�!.~%<(2_Z%Z^"PR GA~a�BFPRLB%~7F+6*%>thefoot7K}{]M6�Lnuc}[2]{{$^{#1}${#2})=.�s"unsrtj� St 66y6�#E f� %\u�ackage{�5x} .epsfigz !�2M( Title PageVf3�d 13.4cm \hoffset -0.5cm %)6 22$ Q�}�T %% A�- TITLE {\l�" \bf :�investig�2og1�9�R�S \\ g re�fof �,Y#multip�l exci�e \\(s�(�s u�eb�W�$i }\Q& {Work sup�$emp!׈by Deutsche Forschungsgemeinschaft�`SFB 634 s�>e>�thens �>"8nt 70/4/3309.} !kigskip)a%\ - AUTHORS $ {P.~Papak� aG4 ou}$^{a,bhQ%�P{a�\Email: }{\tt panagiota.p:F@$@ik.tu-darmstadt.d�,, {E.~Mavrom�Xs}$^b$, {J.~Wambach}$^�$@ {V.Yu.~Ponomarev�}$�Perma�`6%tress: JINR, Dubna, Russia.} 2I�)(INSTITUTION% $ � �HInstitut f\"ur Kern � , Techni%�"N\"at D�<, Schlossgarte]uD.9, %\\ D-64289 /G�yac\!}%%�b$� �& ,�e" �K�' �*S6C,�`BIK �GR-15771Greece%6z-m� a��ab�Uc���:�!�a �7-�@s(C, Skyrme-Harts((Fock plus C�6-RPA �to� �5 low-}�Non�F}� variQrb�(TFF)�[���". Ou��show,�F�t�sthing� at)TFF may, signd�v R n(%�Źd�risosca�pgi8 mono�m"� E�"Ls &@j .JrY25� t�H -�)�%Yi�l'7emk%��'"lnA]a:ve ��. Pers 5�q�m�3.l ed  2�s..� \no1Rnt�p�s (GRsf%� ���& 9}ed%�$d� }@mnd�Xer�ta�WSp�(,GR00,COMEX�* Ma"e-$� >) rprev�r�k-am�p�p�Z��,a&�zero s�+!c�ar med� C9C�@s �iJ� GRs !"�q surf�uvib�jn  ro �y _ . T�[�e x�����+:b$Ii�'��cur�!6Y�>ex(Z- aU,-Hn� !O�ne��$w(� N^ Vin0E<perhapsi�toroidal.,Rye�}. A]�hig�an!0, o�SonI �'exa�L zTShS02,ShK03,GoU01,Cl01]DeK��rng-F eff,{ devoA3��� �H�!+1}}0mo!J, issue�I�=open;š�ys%me�7�}.�&�_'9*� a�oF> & w�oy �p'as�pl��K2� GRs,)yexy\�7 y-we7A@ed sum rule (EWSRe�Pk� i!� s (�W�Pa�d� ��s) ufx*�0A,��M�rEHZ"�$ 1q�X �\ �b�Hi� idLf�HjW isovector� dru��arena,�Y92�KI�6x$ Nowaday='j#feasi!�in  �,s�'.yl�'�aer�K�:� ,I�Loac���beaZ �iE Ac+oI�irN+�(0�yusE͡�rs` �or, stor����r �@?�iE� from���y� � in �J phenu;a, o"F ��"c%�'weakly�M%�on (e unusual � $N/Z$ (����mas�mber)5��"~P "�qsI� -� F~dI�%]�2H8�.�E#tisw:Qof]P".  in>�a�of�i�ar �$�0a�-yA)�  i*� "e+YF,Ola�I%�i�c s�v�u�D etc��+ ց, lim .�2l�4 vail���oh� >��-M Oxyge"o�  kr�Yi,�w3{�W"�~ �l��BH (eg.6zHe, LiC", CA� �!�)� �P{8}{Be�= 13}{O})i�Au�8 I=~.!�A�Cqu�o9�of"k :��bRNTi %anory�s%.ciD-ng=�aKs"�ex� ,� %dy now�A:te�-@predi` ��gar��ĭ�ՙ!2�66�h6� e�. �*� ple,whonsiderA5 mixz$p"� X��*�e�an���Nd fra�%�G��� �TA  ial�����[�%�ery6*�ji!�!s"PH�PK?1�, namel.� �Tr�u �(t�SK -� $occur just*�?mK �&�.A��t ]-i��)i �lM_Sag02} ��Q" )8icle RPA (QRPA)q KVGk oB01,Matc ,KSG� � I�). ReN�i�TQRQE�*2��4l� VPR01,VPRXE! on �2y magic1�&Z o 4edj� �fy (w�jorC5`K�ofS -�tc.�+s) or& N(C�methods;��)8v@)p �h+:X (SHF+ ]6$��a: atic �/M�2|M�] :��M%k, I.~Hamamoto1�(HSZ1996,HaSb, 7a 9}�^re��yBM ^�+ PP2004,PW!΁�:�A�relev�t$et#a5e.� �i� .(an refer, !&�rVco&��s!�Ref.~ �"7 �hA*)� �,es ('sf,i� ���cs"tS}��0qst��)�y�pas�7v!�Z y"l�? d�,�nd� Xindivid &c�!\� u>7H to c�e1bT/u-2��*% I>9,6  ,CLNq#a b,KSTA$I��is�+4"�=9 ��fEB�"c .ofaK%�! :, adop�%an aV1 w�|�,2�� . UU �q�M\,� �,A�ine h���c .��s�ed?�Ni�7E��a�'�E� 8 es9�d $q$M�fer�V�}>e�a0wA'lla[��!qr fiel�W<%�$ $j_L(qr)$�- t�4�!�3e'a� a�b(3ude/. ly&� �%ron s"�d�urT.va* � &1KJCw|�=�c2e�y!�E'a�e��subjeca 8Z.I쉖�.%.purpoW@�� pursq{�=wofold!_F�}ofA�, �E  �0=liE�.�0��p"2p� � *4�  a5�y[ - ei%t��B�4>� us - `��Y ��gOins� i����l�bu|som4�p.DB�ajS� Q�S)�on-�had YL 6 ai$/�p�1 GR#&�B�y 6�~a*Mq� ��r��I~ ydroPal��]!���� B�, �?asA �P:g� alBiMS !�b�6yu�t refore, m&�.Os�b�ad�Aej6��!4�f�$help ulW pinp? /wZr�JXvar!�*� ly��*Y� y. P candi�2J&� <E6� �a~S4d�swD��Y�>:ErQ �� ing,�BN E�A�E!�"� ofF��a guida�to�2.5"@ �% Inevi�y,;m^rw U %c ;n�"�ls3`� onA��X� $f�]:�t���U�e�N i) Ib'4+ina _4 � �2���2Iс�eA�m,8�C �+ �ca Sec.~2:�nt"� ��T�;�CV�* < � &?z���FJ� "�� osed� S���qG�di*�4�3.R 5��&� ���d��l� $qR">a6Z 0$ ($RV�E�� Jd)� ex �x *�� ��B�� { $r^�GwE� $K=Lp $L>0R<K=2$})s $L=0!�= J� $�W \rhoe, (\vec{r},E)�#U�i� �QedU al�L8� $|L0\�n$� gy $�P%Y sV ����H!�b͐ $6�L(r � � H#�"A��w�(�XR� =M^{-E - _2 ,�$ )/r^2 .�ma�IS~ef9\h<K!/sum~(� ce i--�lm�"�D3 >%�stJ�"��S(E,q)=hof|\�~0 |V|f-�|� � (�sf)$��()N$)'G��<%�s,5�bp $q-$� t>�$V��$E_f$Nir B%�Iie!i8&�>h��)E�A $F ^2IfBo\ ��uM;5^D �U .�i̩zsi�w�c ��� �inu3.Q �ri� ��1�� & ��nterval�� $\D�w E$ y%R Y��Aayl)� % &=& �[.�{O,@ |\int_0^{\infty}5x rlt)I� A  "CM �&i�@.db\de^32W�S.C \e^{i�Sq}=c�_}s \s to |9�yl5# �J�!&��ge-;T!d� ;Xect e�Z ed m4$&[ t.�!/gi;� "�f�G A%!�R]�a�"R *SET< Bor� "(h�(Ciofi1980}.�+ �%�A�o �=����q� e iEdSA��&�%*� *� �By loo�uAwU�.9GF3*ln��& "�$q$� (ll ``probe")x�al, - (Fi�-hm�BP:${LOJ@�$to Eq.~(2)i�$a scenario�F!6( }$ (� �o$) tur�'ub�same,1� a��0,iI� ��f(�D!�_�9� s mwup��9R] , %.�i�=]��L(r�)C shap �J�,����by $f^2 �should YHUAge�!�)D real�I# � �tr9>l0M�M�.�!�� ʝ�}Rvb�l"rt2l&IQ�v!���� u_1\mu_2 5 (r,r';E� � {ph}Řel � � p || O_Lh � ^{\ast}_rfC f �y (r;ph�la��F'||F _{r'�C� F 2 L @' A }{ +/4 \varepsilon �$-E} % + i&c5pm %+ \pR��} :>�h�O_�p>��2�2� ';hp�KRK_r�H1 � @.�B�+E}2�- ��mH\�{Eghf� %7*- \normals-ssQ$O_L$ (���$����/�"�s�$mu_i=1-6$ "{�e0&$� , $ [Y_L\otimZ,$\nabla^2+{  '}^2) ]A��/{L !�1}7� 2 } -  '}) >�nd .BbC+RC�=.p-.h"�� jB�e"�.��%��qSum!�Jtak�&�� un�%,sc��"�Yŀ�pShB���p ю7 A ���2�e Im$Ea?sur�+au�F�%�/ -c̗�un��� |^% %���QJ���J)��VOCn��Prm{RPA}} = [ 1+G_L^0V���:{res}� -1}  ,�)b�EgrpaJO�RGRRvs���JFj�"se! )�% �B� }��;#}}ER zero�,u�� �� ri�Q:$ly�#a� 1-HFU��a$%Q6Tsa197��z %%%\wJ % {e:w $!l�%�$c�=ſ=Y��W v� !�" �*F`� = 4�V3MIm<int jr)F�"c�� {11L ) 3') r'V� { 8���RPAb�2���  a�Uhe1E�&*�maj��n\ell$j's;)V�!)) N$=2L!��524/ qu",**| (GMR��GQR�,Q1 lR&@)� a&?+�O (GDR)�_ $N=2n+ �Q G�� ���$B�eѫ� �a GR l�z8�%o�M0neighbourhoodu� `\omega gj<�J� $1\, x41A3}$~MeV"�? ]e �R-�2or). Iaurecise "vP�0Uio �"��(kr�2�"?pd �E/reF? (att� \](rUvQ�``O�2"!qGRs:�ah5='=2N+2��1=�-]aAa�! �c�7� GDR!i�9 f�$3=q1�.E 2�<�&p �$-G1 %.�.� � $=0 ($2^+ a 4^+$�.)�^�,"�8�*G�Z,�,s�i� -$cVq<*���D��(WA(�p�S*��ix1���, g�$i�ki#%�Dor�)ޭ4-!�v�t <sta"B-:L w ��Uw:��top�l@nuc{56,78,110}{Ni.�.400,120,132}{Sn���NA8 1�Y next heav�d$Z=N$, 2y � �us af� �40}{Ca}aTL١-$uw(zt�,�"!� ���; !$-],�/5�ŧ��>le*5 !��<cb�X�U,2paiM?,|X�1! �785+a"��2U0x1Z3y11 �,} DGL0!~ w 1 bC#�Refs.�*C)6"F+u c !:extre�.no= ��!/_� )HAWp�f a2u�8top �nvicT E� t drip%��~cc�gA�SHF� ultXe�u82$f�=�<tFbeslid1|Ni �)>-}, althobv�lYvelD% L�%( �%�&a��>Bar #t���$a half lif+.�1s-�(Sch94,Fae95q�aI100ea �liG[�=Z��cla9����t�39CA Ms12 Uh2M�u�I\S� %���le �m� >-�) M�.�-�D39.7s-wABBW03�Qam��$ $q=0.2,\,�o, 6 0.8 1.0$~fm$ N1,emplo�b}e �.�% SkM*igBQB82�k��o�[.�%��tU#%�i)K��in�- -7"�Aaexo�0 @a2, �5inR"�0% \.J�0�n.��5z/�=� MSk7mGTP�2!wh�+*idwJ A� � by �&i��h"�f�<�%>ass�]�u"2.HF+BCSM,!{F mea�/d_sI 18881A��varE:� ` $|N-Z|/A$� j_���`d �wv����:!�xcept7�&Q$� $m^*$#M!��&�c�Vx s ag� qual� ��RcW*g#n�+/B�(�A�. S�ed)� �ieFig�`$�Fism}- vqAI&h.!1dr$%�"E�!��j�;�l*�&�s plo͆W%�7��e�w� �in~�� )�/in7�^"�6<08R��.o� � i:]dl�&/A�hB�2QB peakM_*�a�2�inge_% lso,6�?�*� F vi�/e�#iR ;1 �ISM9��,!�.~-�sma�5is 9{eJ8o/a$2� �� { ( \ GMR)%  e $406/_1VDZ�vd}!�.�"�m:Rp � q�b%L-- % E"�e�%de�%$ ch�C5 �H (* t� plac�-�Eihf�K�u�  r-% is*x. -9B- cf.��A�Fi9�iQ, �e�Jel��S! IVMNAof� �at 468 w=��C-*�us��� �e"�a�!�6 slow�9r��!�{f�:� r),i, ]/ i� ,a�0a�e�H52:�c"�Cs!na �eH{1b�+ N� P,� �)in � G��b^{I"�*"���'�'2�A}z:.�sm�.��� � � "� \ 1%�k�#d. { O�eFKAuE2u!\6V�!0Jq�"�p�.�M��@��s4i)%=. -��:� 4aL��*�'�?�@� 4-0.8*� �9!�a� �h���"+dA�eu�&# �+!%'�(J �bnl#f\9-RGE-�%�%1,� &�I�Oa�\�Yi�:>Q (lef�) -�i inctɺy r1s}b� cogn�� A�V)�C �:z# S $P_<$�  $�cal{E}_0x 23$~{MeV�_A��>>$�!:>� 2 .53m�gL!�� uniE�!�.��se�"5#��w6a n�!&%kar YH��"wtxm ~>a*�dius $R�X1.2 A^{1/3}=4.6$~{fm} �$4.3~fm, if��{.z&�Ep�6 u8*�- �V%J� �A� maxim�)verlap c��}80}8 (� 1st root1��\pi$) � b q_{01}=s. /R=0.68$~�0.73)�&] It�tms� zo��"�M IQ �� t le<�imate�3n2A�b�;�5�*i{�acha�)um�7 6�X0.8:�a�.��pPA��%Le8��i�rG ���M�)��do�o�MSJ )j3T'�. I_�� �k�6�g o$J�m�!Nmea�>�sQ� �/erMe!��%{,�ab (0.5E��}��e G��F�a%<>vBAku�typ%̇ņl�8dF9��Y@5V 2 �cu�4e� ����I`��?HK� $�naQ�+�Bo�� o�F�&�7(G If�.:+e�"�?�� -$scO�� e"�?s�-aE��MKST20:%���dh���<ISB �"I � � MIad�I$&pe�c Y%�ͫ�v`):8��yA���208}{PV{ More���!DA6�:ّet.��m�:�GDR�ہ��is lor�dA��>�7 23� � � �)f�ticG&fi] H a�A�or��i�L }%���D/cS �U.~Garg:�"WA GT�"�&S>RIW %���!PA3-A����D�JL a>ai�Qt ini6A0%mm��dm%���Es{ "�" m�DR a�|���lacks"�lf&dU cy (*u omisp� �'-�1d�#s �C�N=9AM�+�� �K=)�T�pu=o�3��Z q2�M�et;k �� $Y�i�����%�iA;w� !> �* &&I* $.o(f�>|)%�e!� QR (!%H Z#!~ f/e6xq1}�5e�J rG�*/ ѵwo� s %nH�R��L-� �����"�oa&�3�Aup�rE/q� 64 W �4d&�wfac��[V�Xs����"4f�S�5!s�s��RB3�R!�t� �.bea_�1howd&e� 2�I� W"2>qu�${5�h9W ���YF�;"��Kn-1�ig�A vo)'�6�D� W͙f����J&���oI�� �*� *�e%us�% �A�!�I�1�(23 I� l.� ��y7 "� � dY] 1aPH!��%�UN�a�f=<��1�cA > ! \!� A4s�Bs�Cfa;i!h�`GQR, {A�A�&�}�ng lik(GhB�Xof�.D-� -�*4� S5 SthrTRm��!B�I���_~ B Fisq� !�In�@-D, a� rd) p Gt{�!�!.:!I9�%%ʁ'!1j��!ou%�.X!qs4�u�79e_w�/a[�8A �a 2�� �^aF#y �le��j qXB\e*: a�1� :6N�!(I�m1.�W� !/R�Őjz�A�y mI� A��G�>Ɇa�+ea!nr��A�p�IS��R ���Xo �6i  ��G�@� m0 r*���rst�Lol���LAC_In�to rvZeVeN��1@ ����=.+ Is �6]M!?n $1p1h$��(DNSW90,SW91!�T�`�AD� po�*t� !�B�DNTaP*s$��MUQ?��GQRFB �?R�s" AuX.�v~��"Y@Q.�!�i��"&�IU"-5s"sPP i-U%V� {�ve 25 U)�)r2�"��5ori��P?2V$2�E6��Xloosel"a� �7t �%E�I�bar ��O�raE"s-C� a!�J� <5vA2$a��E��!NF� ߍ��� �a�n�.�'FN��de*� :�'� ()�m0�1� y$ -top}$)��kpa.��R&�  Tl,.� "�$v�e:BG ��6HN7)u����M�� �P*�Z�a�V&'{T-e* u�% 6�1!V�n(+�a2% � B >>�:s�8�a` t�0�&K�� �M * E�B$y�a�:raZ*c*Tassi�hl!#�`�&�a" FU*W� d_\}S%�itM��.� a�D(-TA��*on��A�Q��1&�_ s-.y  IS*tA2%�28�b ���B96��7Uq�x�1or T�t��Yn�%QC( CONCLUSIONr9V �/!e�*銥�.sR0 X i&�[��A�:[ 5.�L ��ty��Ax" [&Rp&$a�} � �huo vaj�o�D*!Y�Y�* e&�)^6� %pes5�&� ��E�6x[ %' ��.L32f�<�=��"�� T *F Mz�Q_MR�3,7 ��*0 @ "�z��_=Y.6Kn �!"� =\J�l�y��vR N��DqL� ���"M| �����A�v�f"4 Ũ�N�., 2�hlR�out�YcY �JQp+�w$h>e�&�:�*'�O nR�=�(�qAXg p1.0&�AWzSe�IVr ,!���!P6�z�ul�3>ZI!�W�� Spe�ec����4rA�;s"�� r-of-�0mo� �^#� �8d�v� clp�2�a�R������ %\ack %��!@�w�Uor ! y~y �Hm�y!b��U6��the� %_Dgr�c7"y �v>W( REFERENCESNv�lYB�}{10} %iys�r } ``ElecSo� Magn�> G�tRʜN�6Hi", Ed.~Speth J, W>΄ 1991�% \|lAn,} {Proc. Int�Yf. onBjl, {\rm Osaka, June 12-15 2�$� �}block �x \NP} A {u{687} (�4 ). %%CITAy8 = NUPHA,A687,;oK��#� ,:�*�rMe)�\ EU: UZ+%�Paris� 0-13� 3}},2� ��731 �4Z�731 ��.r4 Vinas X et~alj1��~ A _(64} 055601;�= PHRV!4, �| Reitz BR2 R L} B R 532} 179.�2n4PHLTA,B532,179 P��r, Ryezayeva N6g.�PR�J%"89jneM272502:�PR{89, >|S�r$} Shlomo ��(Sanzhur A I!; � R} C x$65} 044310�F; C65, FoK:o8, Kolomietz V Mex(Agrawal B K~3)g~8} 06430aYR~8, >~�s4} Gorelik M LrUrin M HoY(�A(47jo4, >o.tL Clark H L, Lui Y-WuYoungbl�BD^{(3} 031301(R�R�3, # ~bG��un AuE�TYR �}j�'103F�I>��rei32v�8103t.�n$ Raman S,�� k �$Tikkanen P��%�,em At.~Data~�T )�}Io 78} B�ADNDA�:��lSagawa)ZI�em Eur��~J.� 13} 87>�,EPHJA,A13,87:dK�l } K�E%�V[viai NAF0�Hu���P�L��2662�472>��:66,472����KCZmAcolo G�0Bortignon P F�1�.�.�9�42B�1�96,42>��m};ytsuo M h{B\37B�[37>�"n-[,���)�53,765>���}��nf|42|23׏2�}4,>~o7a.~n7N��56� 2361Z5�V�7b�)�6H31��R6,R9��9j�2R48} 203>��S 48,2B��)} Pa6(� Pa4, PhD�sisVc�a��tlkNQ, � Mav"��$"� V Yu~:�&M 60��15B��04,15��:2oT} Catara F, Lanza E G,�� raja�Ae Vitturi Aa:��6I616�86:�1� 14,8>� �b��F�26�4��2��24,44>�Np$ Kamerdzhi�, G� %"(Tertychny G%$n\:�328Z&24,328:-& ^   d�� Atti C $^6d��~Part.J rD �I16B:$PPNPD,3,16B� �Y� �YP-�� Y�{``�A6 �Model"}.)| {inЛG!alEar �!I -SG�ure}}, ��A�@ganke K, Maruhn JmY Koon�h E (��er~ w York)�p.!�y��R Ber�)�6�``t4Random Phase A�qD3B"8**^?=-!ibi�"p.7.�{^Z.�FIzsai S F �S6�Y%� ݎi�18}}C.]127:(PRPLC,C18,1B� �Z} *d ��;86(2�37 �>�m�371,1:��R } Nguyen~� 1983�1�in����AG=�D��L�(>� ) p.356. ]R�[$ Ryckebusc��Waroqu|<M, HeydI�oreau �1bo0D�8.~2476H23!�"� @Ryc1988} %J.~Ryck�ebusch. %\newblock Ph.D. thesis, University of Gent, 1988. %%CITATION = NUPHA,A476,237;%% \bibitem{ShB1975} Shlomo S and Bertsch G F 1975, \ne �@{\NP} A {\bf 243}.507V243,507:DTsa1978} Tsai S F ,.R{\PR} C o172n 1862:o$PHRVA,C17,:o�DGL00} Daugas J M et~al. 2000 {\PL} B �0476} 213. 2SPHLTA,B4!S13:eHSch94} Schneider R f$ 1994, {\Z9@ 348} 241;>c(ZEPYA,A348,%%.�PFae95} Faestermann T e.ft5, {GSI Annual Report}, p.~23..JABBW0!�Audi G,!�Hsillon O, Blachot JE(Wapstra A H!03,!0] 729} _2,NUE 729,>*XBDZ01} Bhattacharyya P� 2001c PRL})�8!�062502.>�R!�87, :1BQB82j�artel J, Quentin P, Brack M, Guet C�DHakansson H-B 1982��38A79>� �386,79:�GTP�X} Goriely S, Tondeur Fx PearvA�,%d�,ADNDA,77,311:�KSTA�0} Kamerdzhiev� Speth-�(Tertychny G�a$��{�0Eur.~Phys.~J.�!�)483:�(EPHJA,A7,48M%��LACED%Lacroix D, Ayik S%#Chomaz P�! %2"P63} 064305 %and Refs�4 rein2�DNSW90� ro\.zd\.z! Nishizaki . Wambac! 19901� �Rep.~�6197}} B�$PRPLC,197,>�SW9Abj(1, ``Theory��\iant Resonances" in [1]a�wT\end{thebibliography} a/T BEGINNING OF FIGURES  2 %6> ISM^128 \begin{figure�� @center} \epsfig "\=fig1.eps,width = 11.5cm:�8$ \caption{�@strength distribu$ as a func(of energy ALmomentum transfer. e label{Fiss�2�� ZDQ1�E�D2�DQ�DRDqA�%��EbEV��j�3�EVM�E-EH%Left: \nuc{78}{Ni}:�v����VD��֞4�YD�Y-Y2�vda��U��Q�N)VQ�GfG5�G��R�vq�G>G(\clearpage :��|dr�U�862S45cm, angle = -/E1F�The�Ji�mden� �(in arbitrary units) for protons (full lines) ��neutrdashed L, corresponding to! vs��$the nucleiH uc{56�A, (left panel i�_110  righ  atJ8indicated valueb�J:�sm1dr� > : ISQ��f�72�7����9�J�!�@first (collective)�0second low-lyA+$ ISQ peaksE to>IS GQR, A�N27�x,:'A�I932}{Sn}!�"8 q��V�j823��rt� �wu�%�us 2���vV�Z� ��n�92�4��calcul��Hparticle threshold��( $E_t$ plot��s#@e mass number $A$y0isotopes�i ,78,�Qy*00,120,q2� au,$L=0,1,2$. L� conna� ng ^ofe�same ele� $ are drawna�guide$eye6� �a���.�B END�L� docu�}��0 ��%$Id: �S0MJM.tex,v 1.3�x3/07/04 10:50:27 arickx Exp $ \RLclass[a4paper,12pt]{-�X}% \usepackage{amsmath}>fontsB symb6ZicxWsetcou��{MaxMatrixCols}{30} %TCIDATA{OutputFilter=latex2.dll}"V�4on=4.00.0.2312@4CSTFile=LaTeX � (b�).cst.-reA�D=Thursday, May 22,%N 16:04:0528LastRevised=Mon4 DeceE�209 4 17:09:0.�0k.2,PrintViewPerW 6100b7DMDShell4 Standard %& \Blank - 6 A�2^\Language=American EnglisA$ newt�em\orem}�  �$acknowledge�}[ ]{A:67lgorithm.16+xio2'2# caseIC6!lai.DC6# onclusion.J>-dŁ6, >+ ject 9Co:-rollary2,6+riter:�2+defin>�D2-exampl.OE :' erci2wE2)lemma�L2# notaE &N2)proble.�P >'po!SPr2/remark*R 2%sold'S6)umm6�S 'environ���of}[1][Proof]{\noindent\textbf{#1.} }{\ \rule{0.5a�0} &64165 mm \oddsid�gin 0ev� :��G } \titlea�, Modified J-�� Appro ��Clu� Descri�� LP N� 4} \author{F. AŻP$^{1}$, J. Broeckhove A. N�\ov$^{2}$,\\V. Vasilevsky  dWnroos ? \\ HUn.#TAntwerp, \\Group CompuIkal�elyTPr;mming0;BelgiumaX2}$Bogolyubov Institute%�etical#�ics, Kiev, Ukraine} \date{} \make%n -abk4ct} We present��!�(is immediat.shows��!+ٹadvantagA�RI� (or �� a B�]-s)�> B� c>�Y�Q�I� On�!,M)�!���s!�atq] �.C behavior ! one w�%to� y. I�is wa ,Hilbert spac%� limi)� �)�g0a few coupled��� �a(s)a whic=�coordin!`���only � ina�dynami] -E? d �e��^�]!� rongb�:d. Ali!u�?Ar� , a��rti:!�eMb ive .-B�!!�Z�oEMdisa�!long m�I;5� is d� b�>� �j%�E5�os usue�m refXed!�����!c%��!��,-� �!!(low decreas$ in !��}�!�is  lyIm���licabili�)�s�JM� , a�o large��y �a�h� to bea]���%�hnal, non-asymptotic, regionade��| main����cost 1JM2% -�l��iai �tru� ��m�@=q highly))ed�teA�"� wt!� � ��Ye!n1] T�"7 ��B ���5�three-�  recura� rel .forE�fa tu��+9� z byA�lu�� (��) U�A1"g% drasu| ��match!1"� �bou�yI&a�obtdAe�7@��1Pm� manage)��mCoulombg�A�!�Q��q�is �)e%a �{��be hand�-��way. �8a� llow�8s we will elabo�B oM�D��p-A�ui�6n i"���.1Qt�est �i� �ji��ar��tH(!� cA!�c.^ 2pW � linkiq��; he6o�W< b� �p��! s!)6&R � s; | r��a 1L�55<�%�g �#�� *\�e.`one�R %^valid��a�/ "uJM #%�l)�io?A*:JM �M1�wo-e�i� A�& s carryc �� m�  � in2�)~directloC%�2� "�e5�Idsmaller"� �8Atuda�mp�j pe� q8iW �Bwa� scusE�:�>�l=P. W� %�pr@Mbrief� Q �1Q  ,atI.SQ�� s�i- g![ alizE� of��� a lf ve*a�a:�I�!�$A$I$Dons ($A=A_{1}+A_{2 3}$)��writtenMA�q -"r �!q@ $\cal{A�aA���s%"��g} \Psi\A$( 8bf{q}� ,..,.A-1}\� = d?[J8( �1\ j� 2> _{3.!3>!_{R R]�] mm eq:A� e�S��*�w!�%N��  � $A$-e�on1� �e�� d�YAPus& ��N )�-Wi}$ s�#at� ���� eV�b;"� w6c$)Si5A_ % ) ?b�-�v1=>%� � 1}^{)� icF%�-, - 7 \�$(i=1,2,3) 9�n��i�a57Y u)�$i$-th13,%�e ar�� its :�5�R}�$. Toc R�Q. m�� � s9�&��fixed��eyJ��h&=  ($0s$)-� co:/(�g�# .7co�NQݱ($%�\leq4�all!D)� e McNu$6��>mN;MiVi u� }2�2U�# Q`��Ps2+`% ��:NM� ]�RelMo�Z>U���� ve m51g��1ms��)ect�5one anoh�U������@$�i JB6� In >(e \ref{fig: 1}�-�)Qenume&z�"�.�V their �� ��� m��.%�"�MACRO{\FRAME{ftbpFU}{8.4416cm}{4.2043 00pt}{\Qcb{Two6�e% �2��_A�%b���a<$\alpha+N+N$.}}%M4Qlb2 } ure1}&}{\Kal{ l/" "Sci�pfic Word"; %type "GRAPHIC"; "� -aAt-%N TRUE; � � "ICON?W _file "F?w 31; he�1ELepth 0pt; %original-8 2408in; A679 crop�� "0�(top "0.9767�rx"1bottom& 02329�name 'MP!:';-&b $ "XNPEU";}%yB�� Expa��% A} [ptb]��er} \i�"d�ps$$[ trim=0.0�.099015  99442in, )=1G, %1=1i ]% ��w4R�mj�� 6�%�.�%���1 %End96,�� (e�eq>�)� notɹJo ��  E�of R;| aDcon�.��a�� lete�of J� �c rL> !�e� f freedom�Yu�6"/h �le N� �be� r� �UleJ:� L �� A.f� �,Rhe k"quotedbla5 Fol42e,\� ,!x� breakP:a b���vid�;� s, but re�RCa� qua�6-mechan�.) � G� i �"2b�2D q{>�Ff� .|1F� 6 �v1 < � ^ @ &4� iF� BecaA�eac" 6�!B A c (t6� ._)�4�$ed neg=!�)�terՂX:� �A�e MM� O B2�A�erv^d���-� 1��, i0�a�& �eptJ�frozenF�,D�&-nyu�A� blem�`�>�:�. � a2�.�iL ulae�ify to:%V�� �����F� \�$] *S B�2�Y� withZ�V�rK 0J( &� z< ���BtJ�ɪf�46j�bsn8!al choicS�l��qX *�"6W-� , i.e >q �� /MAg two ŭ ree 2�nga�>�a�is am .s � siti6 y�reG uffiB �� a��a� uu��6����a�ligibly. ��� t< &j"@#ofB��� %�!V� ��A�р.1s��! :�2c�-D�1s true� ther�[usJZullM:B)�A'�6X�:Z(- �s5$B��{b�6�m� 00nambiguously [,� f(� from%4�3]v -�y�Lp $U(3)\supset O(3)$!w� one-"�2�%-7[provid-. �2 s $n�Tradial�`L,M%� l�� J$2a"U�ic�>�)g-!scheme�p!�d�&g��hv(p*�"d�!��kn:�'6, 7} te�*@ inctK _"valg*�were #bO"�#s�he1^U�-{� �Hyper&b'�'s (HH) u)seA� r in��Simon68E�Fabr93 Zhuk93}~��-Di(�ywe �adopt. E�)a�%Gis %� �J��re5�^(to `! .�. sh��re�A$ct ourselvA�e� so-#@ed Zernike-BrinkmAa�+�kn:ZB}M�&�sA%�f�i � .K_;g;�eJ6)$e�>e��E &�]S,Hamiltonian,FZ U(6)m� O2 3)\otiA�a�$2�~-R�F�T!��MN m�Uk$K �hAd�B,a�� rF�$l� %F��6�#�*f�)_vector,F�.%�B$JF�: G G�*$L�M$Nto/*BT6N`#��ag�1��64a�g/�2�C",;�,sB�i1be�=�  $\nu$B =\{n,K,(%Jlp)LM\}$���# der Il tex�TNa]a-�A� �=!�ut%/a"9J�:"�itemizP/ ! ^?O()y"*he�al1= IKa&gl�$�"f%�V  L}=$[bf% 1}+$ 7�$� | %E-%FM | eq Lq +$�.�by fix-��u>!�1 4,�se��%m0e' �um $K=q,~ +26$4,\ldots$ a��-� mpl�"���cer��>uI��+z�- �exco$K9J� �uEj-! �7*��"2> !z`Q� $\pi=%�( -1)�) ^{=;} $5�!B$``normal''A�vK fRL}%( minimal)PaB6O4is $K_{\min}=LAawa2+1"� ՛ ``abƖ+1]��G`�$N$��ae��Lac"2 )uy� $N=2n\;+!��A�e� T!E a gi�����a�r/6: 2�!w�G  ladder�eF�of$�&an �g�" \sub� ion{A"+&,,$6 &%:� } �C:@ SolC)Rep� hL"- �K"��SZ�,) �*�3� ?0ba�,o Y$6L �rcin termua squ��+ gr�$�� ���'!�� Y  OJ�-��  e F6%sELultim%/�-�� ��j)ey coe�sѻ2� � P� )!.#!6 4one nee� -�in�6q Co�(���X&R25F� u&�:�.*o ,=\sum_{\nu}c % J��.=1Z5Q�WaveFuncE�tU�6�vha��A\{ 5!�Q\} $ aU2l2�sixZF�~. It c/s�� E��&�.��1o�To� E4j�:�k�%4&:a){s� �assum6'�sJ(& �*� b�#e2he.��*ma"�one%$[3:�2�#�4"�! tivj  �!f  � $ �"t$�o~�i��� >�^ m)NJ����ce�a&�( (� �}id2�1$reference * �)~T�explici6&��&G,HH��(� �&� ~�I!�v=(ţ �D��W �hs&u j' $\Z�G/ u;rho$\ega !J!Omega"hj &���)J$ 5-��geometr�Q� i :Q�h*I�!�VwI=b?02bwo>\��6*�2P���>&'��d)�$HH's $H_{KXnu_{0}�, )��|$�re��'$�<%chosenq^0h��for $6v $��a�!g�&�'�-=+�s $Y_{LM �8 \theta,\varph&�$� IE� }EjCc,��� Q}.&�-M@��CERAs~ J: ,�hkV�5!!A5JMy�.�J ��5,-\frac{\hbare> }{2m)[ d dA� + 5}{ } d} #} SK\d( K+45� 3F ] -E \} R_{K,6. e ") =0 1G}G�@"T"(&m8l+dE"� �a pai� H\"{a}nk<>u5T%�!` ingor A�out z:Fg2�' \pm�)mrh�%=\{S8array} [c]{l}% aX+.�$1FPk2Q/!x\\F>2�>� � 7\}>�j , \[ k=\sqrt{I" 2mE}]jM] 9nV2��a s2�5a%�YpeBa�o� &�MB��"w �a��NBe�$��.a�, dif�te-Znel �un�45 When� ged" ��[�>aZc6�shoul�? nsis�7:A�J�:R�+a���v� cV%7 �+Km� F �S<Z_{effJ8}�0"f VCBtm*� .SM��FFB � R )Z�$���;�� = "�4$RM�.cJ���D.a"&M McR�� f-�inA��X$.5�u^ �2��1S bR$�z� � &�of~u04>��I:� :�se�+� o deihE�$KV, by  ��� ao.)�-5��Fo%��%�$e�&�ly �0J� K{ ���Q�QiM {MZio272��B�Bha"��ta�$ ]� ���3$KS������param�AA�!��5y+ �  u*b� � S�^Ris M!�-xi2E %itM=be b stoo;Dat�-��3Dto  9 heck�<'�)�)� � ��1N� � O5��&�2��� 1�*�\4k}% }W_{\pm i\� 5� pm2iR  G 5}{2�end��� $W��aL Whit Cr  %�$q$\%dha3ll-87$Sommerfeld�)�F?= � m}{2y6 Me}�:� AY et ��A� e�K,$�:!�ougO U� U��J� I�nowAKdE�+o�_- � ) A2d['pA� " :2>� Q3,�hN�%l R_{L�IMG IGL�HAj2� � RQ \]Q6�%$%*��h8 .U �|w8-;!� 0 Y<9� �1�=Z�Zte� e I5L(5% } -5}}$|C�9�D�*bi�%��e� q�9rDa lv�'ns  a!�b�,}HR��L}��>�\lambda}��\sigma-1n�!�ua`�$,s N�emph{,} - ��Qo9Y-1YE �� )N in T? �,tab:HH; te}.�bTCI500TeXButton{B}{-�t;}[tbp] \6- ing}�/Vf.V1:\-.�-N�Y*&W 9M}��tabT � |c }\hline &�: �)m -� a6\\ 8!g$ {cl�-a*L03 .�$i7:Ra<k��:�Rl>j��.� |K�6�K+2 �� ��� :�`�5S�(A0 TwoT|Clbs}.j2Y5���IR#%:�;��*0"y���-�nK1at�F�m;�]|B)26�@.� $�$u ru � .�"�(;�e�m� I=�rb4adily&�'"�#�M�*.@"2 Y� F(�t�Ac"NTd"w"Z%>r)4 � ~H,C "~.~p�!>��ZY�m='< rele�J\-5�)�e likJ- c_{n}t4le n|\ps�\� \simeqi��ho8� psi (b�.I9et�ForCnG5 A�~}o, $bB 2��w !��, �4n+2K+6�G&�F turn� poi�n�$� i�22�!���4a�HA� is n afRa�t�RAG2 %}D&u��'=�V� aAn^�$��9Pc!�V� K}:��D~� 5�) �>9�p � Mi�xO=4symCoefFreeParJ�� i,aߑ"��C n alE9{(y�04n,kn:AM_12C}��R!�A�^ A #:F*?hat{T;$A?��J�A� �.8�-, � (]�).E�� 1�Yum=�/infty� �,E`2)��/v�hat {T&�mn==�Sc_{m}^*�Nis_"�� *�"�� bv3i��Bq6$�)�n�2l�[. S�P��!�z�5!}$��6� *3G���Z�T_{n,n-�>Ra�:+1� 12>�)q�J+ /+F`:F��FCQ:���D -�M�A�/Y�F./o$�!�I�U)I!�*cu:�/ >n5u[ly  %by&�8B�). �A7J5A�� 1(ag�J�F y (\#=��J1)AV��F�A'����W_{�\mu�( 2iB� /�� W_{-F>-�?V��,o-��!WV���L�L!�*� 6)�faR is noN2P!&SAGK!�Pa:� 2Ao:= Y�to{.o�I�� |t�Nuld� ","xabove"�If*��=s�!P*k &�k$��&� 6�� Yu"�  discr�#�z� q)qP�)��}��"�c� < !���%� "Q a �)um )!T VNsaf��&h2�% i�w1&�%�*� C�n:�:��I � �(s,�� de{X�.]s �ez�) R`$ �Ŋ.� r)iV !Q) � ��*�*I A�&=�@R� shor8@ng&�Q"�L>aVa�omb.$� )%�]5�Sb�.*<�=�R"�� �^)M�!!�.�<ha&B�*<�-EX�we% hh$forthOerat�.X s ``.�''U,� 3J{M )�\�~s}"�Mc�Pt�% \� pa�A�!KJMA�N)4 � 2G$7�Et!�hFY!peRi�l!"6� $U�e�e�+��E�6of&�%A[m0�i"Yh��&2Z Wxa����HA�=��S$n aggregat�dex!@" 9M)��e i�>�ZT(��RsUS^�+��!^as&��aog5�1Rn F�Z (K^{\prime},�"& ��\ H"�  m,?\20 \"2 `}=0* CaQChanEqs1�VQ��"A&#Po �* $S$- ���jA�D s&�M(��YJ2�ar� w-L asF%�K}= 8(0)K}+\delta_{K�HK� $}^{(-)K}-SB +)K}�! ptExpOfCnF�� Yk�?IHA���o�yr��-\ed�%A .�:=\pm)K� > inco8�}"�#�'2L�J-�L $��@i����s*�U�}�}e_Cnc�L�0 i}$.�) show"3HeiO�`Yamani SmirnovE}V� satis�7"K7��ARQ�N�i>n�J>�'� uB\V9-� =\beAj \ Qn,0JY qnsK-T�E6�YH� $ be!�!r9��t��.=',i�st1io Z@a�$hlW&�#� l68 ��O plus��*8Q>OI�%=-hA��$�/ceU� �e�$[�=]a��) �>��^>facto��`[� irre+�I[-!y%�]�isIaI0 �6p v*�F� pt6�)�G 3' $nV� w$F��(� � �e"�,.�s��=�6out1�)�in>eed 2q��=0� keep%1�7 homo�*ous!B; ��-(6i: \<_Y�2��t�&b�l�-�Kn�8o*u degsG:�#�E�f~_�h�SqiZ�!롖Z( .�(K� }}$DWA4 desi'�Y=(cfD`s��2S"L�(. Couq). Sub2�>N�~{]�5x&�6�e:�N5�/a&�%�e0���hR�Di2&:��2�� )� 0�) p}-� _�}��&�VI&�+J% % =->�6���L-:W- W K!}ZD JYDI%x. $:a2��$,d�.�jVA�hre"jF8 dɲUE4�8 {V] tP)\�"u w9��Q�_ �:M��6s\�*�A�.a'reZ 2S��y�2Ub �*� 3 s4 �K�&'4e �k�6t�% exact�`8� u�.�2})�;.L �b��&_��to $n �eF�]:^a}m dto t N,I�6�YU��Iݓ}:; }K=�= % .. axIor>i�x �$N}��U Rqon ^� E�/"�'$m!u*s %� W)�$B� sHI� by $��� 2�a��y�M���� B: M�p} /qFN"�!�x p�l�"�;ng 6�� :��_d� ��\GnJ� �)>WK U�"�N���`$^� MJM]� are: �:lap �I�{.�8m%> s4er� �>FaceQcP� =pEr�@ �� UlatW �, mpos4�-6� "e� ��of� are "� !%ly!c�F-.�`1u��& �!g&b�� n ou@Ms�A�e7�Oa local,�d real�c,]&�:%�aItb&`g"n*�� �C�!\cY�!I�E�&&#i"d,>$�(e:{ i#sg0J@� o�<� �6r�,, #� ,� ;A�&9Zc��a� �� 9& . %���Ia�a j yields%Q^h@&. Let us�l�A�u� ��.in�:` �a͵on= te�to1��xssoci � "� I�(B�U"ZB}), w]dyt&R�F�y radiuI�NG,mE�spa�S]��BA�]�-ercr� fi�by"}align}�>�01�)�!�5�UC(2}},\, & E�=\H@ cos FI� sin  ;\noz& \\ R:oA�+2o:o\a% 1}=R nT�F2k ]7Hyper*O"� �U� ��se '� d? .H�~&.�*HH &s5]�Zne�e�i'���L)b q� rho,)s".  q}m�J�~iw \Xi�M��^R,)c >CQ}�>R�y� GFHSF�& �\��%"� $kV� mYd�viously�e �o!�:9�ih*Y+i�5��^�)1 vh%�qM6==""�,K\{kho^D�{-ga�/2\}\ L\�>%�+2})\ �Fk$PT�U)J�I�6�*�O6"� OscFionN�W�:��6��`Qp1_Qi>Efh�[n\}\ R^!;n}v0 I�z=-.6 en�xN-H*$H%-�tHH5(Y���z���:�b+% .� ��6�NLPhi�L]e� 1� ��D���\4 �j*{Y}\nol~s_�V% B �)\*\zB�VBa�K�L݅R�)^���jt cos2� �Wr�$Ր ��W�  P_�?K-e�2_L!L� f}LJ ,&.�< }\,(�2 �.�8HSa��]MBF_a"]�)��as|:de�~I�procedr[se�FV^>4-cN�= \1�% ��5\,�kD&�#� .Z23 .( K+2nM$-E7 �*%p$R��#F,et $R=0$. Af�Kp �� ee Q $)k$ Y��we� ?tJ)�9odj�po�� &�0K$?le�:t�_� &5\��m' �"� .2�& �C.�{Y}m�m��VF1���$><�s%�m�V>2>toAM9;L�On!')��� �fo�m�& �!~�k2Y[Cus (i step����_ +*m5g u6`"� e 1F'� d. U� 3 cm�)` &^3 techniqu�_.�� $BJ�w.r.t�g-2zs. Ei�0N�T2Y��>c�/c�,�7)'H�'er�Ve���3�*Q)�&�K" AM_AJP}Rnjs !F work5B!4s�_(ghtforward �Hextrem(3ted� ; �ach�gbW^W�ed ��icTIi���softw �as Mat� 0Maple. A fur6A�/ H-�z���ClapeJ.�i�y��!��� c%� t paw&:�"  8�(EI+>d�nl�Q�W!�)25�I��}�M�V?!�}6��6:J2a�&��&��A"V)F!�$Z2����lyLmnr)�$&w$N$~�e���3�$�ex =..�,�f�+�&fbe�-�>1B��$N*low�c�2��2"� U�+��u !Z,�2.�$*�68N$� �1�Ug7� B&6�syste�]�KwJ%!&�l$kn:Fedorov���!E�&,%�A%'av s $1;S 3}$ %Ne���,��)5.hy�Y�Chma2�!:ZbC!T�/�AS�A��'H V����.W��� bB���ior. Po"���h6�&tail .�փ@U4��phE shif�3�߆e@�"�9HCalogero,kn:Babikov�+�)c���RW?ake�'getUc vergK�9���[���,�m��&X m_yaXoI� z . A`yq��)c.c�$�s\�/�8hc�!ach, dev ��k�dr#� �tD.% aZ$&F&"�+�>�B�a� �dncorpI����'� J �.5so�T�i�g� ��"Rp$��!�Id.� 3�����e�� �8F��pYNholds,*�2romE�6Fډi�9���0 �� �X�%��&�,��Fc����.��a F6gy�$�*�in&+4F�d, �|����ed �borde&�f|�4� ]yb�Qt d(7 6J!��*:S�6��ddr�r*A"�qa�[ �k!�}o(����5�s��aܔ�m�4F�!�^+z.}f.@V��� =R"0�a�! ���H>š�iH͓� ac� 0[:dM_f=|$ |.zF|inuGrs�s6q�2��6&�&u�iV��1a�y:�*2is" �n+nqa�p+p�ur ob���i�u� � ^ �7�i�E!d2G.I A $1C� accu�%��astro�(� "GLr.� R�����)Fr*3�s&=<"�-��#�:e"@b��sgM1�...x1�!8'�+%'&2 wϖ��}�>&��J�)eigenN5>$�(c����A��og � 9�)V� g*� A!�<$a�6� mo T.pr"7e�s��p�J*"d b }{dE$}|_{E=E_{rF>, � \Gamma=2\�&�a 9 :u]m-1.D*�ResCon&4��$4q�. � focu��*��-mV�J&0$^{+}$-A�2 % $-2�i�'�%Q )'��Q� . S*h�x_nd J lrea�&��G�#t��vesti�@�B� fe�g� Be$��r�o�)�u&� �u� Dani9�= 7z=��GvA�;e a a�)fl�t�,�y�5���me"�(�b�3uG�a$�0n �腖w�s>� a��o!>a �)[ �on-  ($NN$4.*Y.[�/ 3�/e�e�/�Q&a-,� � b�� �*5�'"�%In� kn:Cz��eȢlex Scap?M12 �>���-E�B)I_�^nd�mE*� wM�l!B ��@� e�n �z�yo0HFt � �=�Y�) es>�UC 4Minneso�q NN$-"# A�Y�(CSM-tanaka}9]�demon�pt O�of1�+i� A�up%�X � (CCCM),I Ɂ�GE�z�+ЄI�)^2�Li$�Лs!���0A�Scl�s� os*N1�'CSM�cR��\:�B��se �I� *���C�3g[^.j Be�s,��- (�2t)"1A���. 2��re6�2i�h &�?*� �J st>)� s Q��y�8� A�$ ���"��!�@��sl u"rD�1&�} Volkov�U\kn:65}&�BAA�� ��> > fm�&� . Accor�9n asilB|i��A}"&d��pdf�j�4N9 i��� )�!r�.���e��Z�5for~9G,�i�86Y�f�t sp��S�� iso T�bE�:�y�I&�|�:�Z? N+N)  $SA�^$T=1$�0� �r4��m)�pro� 0. pin-�El! *���r� ��ňi��kis�)�J�4Aj �>iT���&�@o a gO�zn�H��so�a��N� �aD � �!�A2�8i *TL p6�'!(i~&l"y�aa� A7J���2��}.. It's`C���tovizL�6:�q�Ɗ$��Ų#9l�=1.37$ f�BAsg�4VEj,%�a* B�o"�AVf ��o���qA�2�s. ��a�A*�w2��&���I!S��;s�` play� TJU�I�fJ} (J� �:.�g% 4+22�!-2{&�f�st� roWQ!ch.O. S� 0on rules sign�dant����:�"�Zd�:Ke�,a� co2�dy���tE�on�N)�@\ �Y � +Nk�H�/� M Z� mustJ�7vGE0��� 72$�(e�is-� �!��Vean!f�s�T6�&X{Eȅߩ�d� . More��J�ve�*�z^*�F� $,�&!�negYpaB<oddF;*�A&\ �un�B!!�2�A�E�� N J�% \�F�5+1F�\a`) ;�d iZh; hard!@mee<3�E8�-� w�B9q-.% �!b�!bN*�(�=h��A��7 �!c!of �+&=-z s up! $K=10$}B4"�`\"DbNbLb$L�1 i}=0�ia(0 & 2 & 4 &a8 & 10\Kb&A?h�a1 /3Fb3\\ $c$O942O�2�- �~5�:�$ 1�1664�U/59�,bH\dV8�$bT�d�H2ma�w�Ue�c:uY9of �X�^m��Q� 5Z-�Ah-n��``4+2''Ã2C��� >�� �E M�A��uso Q��E��A��Ain}�i +2)�,axhGiKW׫c��~ Oax}=K,A&t Ove�"ms)#"�St"�u�v.y�_Ft��! o -k,:}�. �*we look�its� � ��ond(��ar&ߩfpC( � ��%�&&�  . No�ؼex!@g��ToZQ =-W�_B} �7%]m߇fel~@2 $"n>�q u�� � &� 6�#[�(l"�A"6',%in-u��� shorthab^/ _{0}�l^aL��$*,)LM$\A�� I�s:��&8��6��_ widebT\�.cal{A +\� 11&�6"a*K���Tsl 1) Y4T3��eq:OvlapODE/�BzFNon-zero>�&R+>C) be6o�� �y�zM"��� ��. ���j!�:".��&�P�A� +K$ i �+� o&o��$2n+K=29i+9a$6K6��<10.803cm}{7.5718 &��)nU�AEA�%J[opeA.U�$��� 42Be$�h�2��e-� 2u�'poXa���֯�1#&��1+; '^��11.681��'��8.253ʚ crop F��38"��eMV��124N��$2.EPS';fil���Ư� 102347in 2Ś510910��n�)s=) 0�=)90 ۚ1s,ۚ1�*ۚ�ۚV���:�Z���j�� &�0� �9I� } %E6�b��Dj J( "q���� 0*�.a�0  $K=2;�'�1ix-�� "?4��z��> ��he :�� "6$� B�Iat leas�t e 25��Ls,��O��Jw��! K�JJ��@% vi��� devi*!�/y���:� 鮡:?ń52�F� $K$)�� = � "Y� ���*� ���n��0��q3}������3"����������!$������3��������!����������3�����3}X �:O�p��$�rinٌ� .sڮ�]Dbb,�$$\esa multiN2y 6� j��� OD�*�@Oth�>�"�; >���i: ���v�emJ  $K=4բ8ɢ�,ed-:$nڵb�*~�a�than X�s.�Uu$T�dE:� ݪ:� �?"�./to��M&-I��b+72},LM$)zW� 1 b>أH shap�d e�win8@و�z2�7�3 ��!=,)���(FA � �2}=2$)MN=863$ z64$) se�� bdtr:�E @ M�V��>�">$"T 8�X1rA�M�% b,�to fi�*1o.s&48h�%$Z)���1�-� \rho�;2G�ar�c�"x�N89x�.�K2ll C aW)in�� ng rԺk.�r:�� ��� F� �� �W�>� �}%F�$#($K=0MS+w&K�2� %8 2N$ �6� 4"!4� Ĩ�� �&�� %rR����� !�i*�� %� � !z$*�� 9� *��� b� to��R�  %(*���  � �= '� 4�$�$�$�$���� � i&� jI�'c��b�Gb7eJ;�4�}�4��cnr�^M2��ESa�bq�N"! ��b��<a�'�(sQ\�6 d�f�(Li$�92nHe5�& �ari]�#y6i^�4}� ]7��K�/B�~47 ch��rF r�lF 9��6E�wZv$&"�6>� x$B*x� �O&��+5�.�r�e"� t\�s7>��bB�s��J��r�g -#R#�'�CJE�)ci�gn��ʊ*@B�798��N%D�-��U1�u56��0B.�0�Y�)! %ZM��[- z%F15�#կ@ݚU�1j1)T�1�1�15~1 !iVq�� �ׯ�(�()�*V��U�2F�B��%b��!"I .�^j�JA�F�egf"�5.�"�u�B�# Xe�� )�>d6.d>=al��K; row $n=50��Z]Eno�Xɩ6  �+d"FS �Z:#ed� �+P )=��kr �P 6097N+O.��5Kf/a >{ �/�/6aƱ/6c ���/j/)X�/�/�/6�/�/� ��2�2)��2����2V�B�ah> >�0r�e�J�N6 ���N��A��62p&B0 j%F>��2�@���NmF 7"@7e��@�@@3c������7��y�����v�E�}��aAq�F���I�Be 6 ]�J�|>�7��^7}\w�%�-����>�"��$&��u*�'�  l� 9A� "#4��st����2bi:5ZD3l�A���5b_6v2 ��04�Jio �a�� Bn&�#F" �mF"\F��/�tч�L%� �>YB�0 *�5r,�-\�?�B��ef�|.;b$�iY6Z "��tup!a�-! nO*a1+/� �'�'�(, �qof-Z %�ow��&��E&a)�R�A �6� �)��)y6�8pV"�MA�=NI�N��w 6Gagea3�QI��ZE ,a_(-�� ��%F��� %.Z7"U&� ]f>} m�- �" %�b� %�B� F�8�uc 8��c �c c ���b �b �b 8���]�)"�6g��[�:h��_ �_ %��}����}2��]�)�� V���e�� �>�A��O2���9dYAa�rs'�ǁ�sJ��G ϩ|Q-m���ll �8<nei9GWnՖ $D2O���f�-���c2���4��� Hs@> [BllBM.p6����ai�4 e neTU.&sB��N��-:[!<�/����i:<��`]\�&�re�k/ng]�s:�-L$-"��#r7n��ɛf.�RR /E - {�7�itwo����fo� we�,�!Z:H �!�_'[Euk8RJ8.��|6r contri�@bution of both components, and one notices that $\alpha+n$ repres,< the main contri U. \subecf{The effpve charge.} When Coulomb fornXare taken into account, �Teeds to determine the >[ in order+0properly solv0 MJM equa�s. 2� �P unambiguously define! .��intera�{ each�4nnel as well a =dcoupling between different2s. Us"!\Dapproach suggesteda-W \ref{ H:AsympSolCoordRep},?>s!e%�$0^{+}$-%�$2 statesAt$^{6}Be$ were calculated. Part"!x$correspond�matri!˜of $\left\Vert Z_{K}^{K^{\prime}}\right $!� display �tables � tab:1}��2} �IXly. One 2�!Ediagonal �x elemA�z much lA�r than2 off-6oneE%$is justifiM %�ximEH\ \cite{kn:ITP+RUCA1}\ of�regar%$�Uof hE*s!� a!̰totic region.% %TCIMACRO{\TeXButton{B}{\begin!,le}[tbp] \ceA� ing}}% %B!$Expansion r1 %End,capa#{E:�1Ifo!4 e 0$]@�Q?}p,ular} [c]{|c|}\hline $K;l_{1},l_{2}$ & $0;0,0 2 4 2,2$\\@.t7.274 & 0.006 & -0.129 & 1.4141U) 7.14 143 0.3.1|R-0 *7.428 l877d4�|�31-0) & 9.0981 \end!�)+\labelqVE}{9le}} N� Yle}:��Y�YvY 2�Zlj\2;2]\2!�%�Ip!�.f87.253%�400)�22!�0.5QF7515�EoT0 2 7.241-0.30A�-A� 60;AF�-0 e46.942 18I�432;0v�0e 2 7.69v72;aa \751 60 A�-0.67 7.345�QmV�2��v�%:� It i�Bterest��to�Oh��(ree-clusterB\ with�RMAwo?configur��. F�lat]w�24n write \[ Z=Z��Z��De^{2}\sqrt{\frac{AA} + }% \] wh�$%$�$L $\ (�,�  2}$)���� mass%�"� ) s�2�"� 2p$.� , weCn obt� anBO � �8}{ �3}�imeq6.65 �ich)�depend o� angAE mo�um��system�� ���t� .�>�gcloseAI���*of ��. W%� assum �, if\!8J of �2�c���N� very2� .�one, itOl dicat |Rtwo� tons move� an agg� te i-eBoU�2 A�obserKt least�AW� qBisw,perty, carrye�he ��$s $K=4$, $�� =2,$ 2}=0$: � (on{Results}BP D� i�Q4model space} � "�curk � i!�imari� Y d by!H0 total numbernHH'�i� Z a� exte r� H �<, oscillator l . D" set| a can be us h6m B�s. An�nse se� M-�� � �8 will provide a� � �  descri ��6�i� duqP "� � �Id�hyperq�� �F�, w�&�� exactly (��out� ) or nea� $ (&� $cluded) de�ed,N�'onsiblY%richnes%�Xdecay possibilities. I)�QNpapera�{ric� U5qA=�HH!� s ma> l6X value $K_{\max}^{(i)}=(a)}=10$. By)�[ �a�a<ve ~a s up��s� rds�˵� fair i�H,convergence.2� xFRAME{ftbpFU}{10.8623cm}{7.5696 d0pt}{\Qcb{Eigenphase shift�%AQ�E(Af: e�Y2!- a)}$�(%{\Qlb{fig:� e9}}ure9.eps�w pecial{ l�J$age "Scien� dc Word"; %type "GRAPHIC"; ���-aAt-�� TRUE; � "ICON?0valid_file "F?width 5; he� 1FLepth 0pt; %original- 9$1.681in;  A8v 8 cropc "0�(top "0.9381�rx"bottom& 01249�name '-E.EPS';-:A�$ "XNPEU";}V_ be-}} [ptb]� � } \ii�8graphics[ trim=� (in 0.102347 0 0510910in, nat) =) !%:=):7, )1t, $Q� ]% ��p "�N���� >�%� .�%+ 5"� )�>� $ We fixed�match�Vpoint�m^o���N=5�f. ba�^o����� ņa�previousq(s, i.e. (1)zis suffieSlyF�lallowB@Pauli principle ia�$ull impact�$(2O� enough��4semi-classical6v��%�to�3e�.8resonance param���� ed fromAeB�2$�_$� "%4 (L izW orm)��� $S$-a �ub�C�b study!�rs� nsideI{influ��W"W.[ �s� do t� by"�A6�pos@ ��eWb� u�succesd1�r.���x��f �&p �s all��ɡa3.�8� V n�h� ymg%�eo<�0$A .R8$ �second9o�A� �V�10��B�������1�R/�$$^6$Be, va� %p�� (!k �8$)���ta �V�&���Y & � 4 & �&%$E$, MeVW3!1W1.3� 1.29�(2\\ $\Gamma80.075e.08eH&����*�a� _vs_asy_8�N�����ž2� &m�}{�&I6 % %$�9%])%�>:10$)}� >� � w�t�s:R%�5�E�c2&a��A�0"#2�391.2M�19A�1.1E� 1.17aZ�6^0.069I��A���0@0��10!��B��g":r�� show��B6n�� " .10}learns�!��seh�a &� rof.�  has b� . F�e�.�  ��� -*� � fun( of energy�a]C�A�ha choic�>�$�u��!1I�9)Wderived6� y�B}{���KFK�TnT%�|ݍ% %^{�g=�UBUu% �wt�V�Vi)BbV-�?.40" 2.02:X1.�624J< 0.14�= 0.09 �:6���Nint! �K'>� E�2�B re\Z �a]higher.[aq&�s�os �st  monotonic. ii so c�YfW* *� T �R� �Z a� ctJo`l` "� "� 3(. To suppor�is��io6e per� ed a *� , ag��Z ��$�in"�, �] only� HH w.E $KU� was�. #��l&� %was vari6 ��P�0$"� id�� ��appear�E"FA{�-%hobo���"�co12�parti� )!y 5a!d."potNal�$��.�HH !>,ADun� Aproduc{"y ��ly afHE�� a52$9doew#4-. FurtA�8A}s�!tt# lead�an accep%=! �!Ray alcalC fash8 A@�PeD2P��|�| ": S� �iC!�,9�byS, HHMA> CSMn� cc  Nucleus� L�"i��h\multicolumn{2}{c|}{MJM} & >l|}{HH"U"Dani91}^*CSM+,CSM-Aoyama1}&�"2}}"� & �&R $\ :, 26G 6b ^�He� $�'"ś� 4.� 5.��63.� 9.*�!�$ C22C3.�� =3I1.8 2.� 4.&� CBJ�3+6� %  & 6� 76z5h5.� F7Ѯ�}..v _res�NJ ��!��!��!R"i�f}T�#$^6!��`$^6Be$yj }j , CSeo CCCjpBn\!�>Ba]%� He;Li�=�&}!�J�.% B0&'r0. ^UCMethod>b^E >��`��$9aC0.1 * 3.1�"0.7*l$HH�2�]4F�!��isoto94 81��5y�e�8a�0.*T!�H SM-tanaka K���!���Theory�]'�h :�*$Comparison�In �>10}4>mQ�Em $ * �M4*� �� !K&] { �&� u g;!���"�>(!���aw "� 9���i�y(broad) Y at a� � reaD� >.^ (se&,bl*� (�a�udetails�is��)E *�� 6 .l$ /mo*-behavio�8 F�!��a trac��i� rangZ 6$��* �* * Y�C �>�!�E��7,  ����experi�#.^G >B b�1 R�Eg �^Ajze882��Yjt6��; u�����6�40.822$\pm$0.02�0.133 *-:W� W1�ɡ�X1.3�9_066�Be.L�2  & 3.04��� 1.16�Sb�AM+exprm�P��'�w26Fr 184h 7.525:r The\i�e�h *q J�}� 2Q 10"R 10S %v  izV  :V %maintai�V \i*V  %T ��2V %2V *< 9�V *p #bV C "V 78FV y 2V 5&? .V 10�W �W 3173FW 3386�W %u.W %�*W ����N��W R�J: �e��; T�'�tab'  c���&�0is work th.) in oc:�n� 6;R' ,HHM��x �"by� ��* ��"��y our��*(B �*��~0al data avail%t��-! agre*2��%�2J��ie%>e�t�/s�8o� [�$ce"�!� 2_and"�ed ni�3,/:�b��S�ɷ� reybab�"�' lack+ LS-�5 �52�'t �!�"ed �i* 3.�9�6 , H4barrier � z):n(6�,is*�lyE %2w�(86 mmod+woA" "�se\ �+usu�be�|+ � . At� sO%9� ow+b� crib�#o`+rtifac})!� HH M�* si!��":g#2 ) $K$-p ubstant_a�rifugal1.. Howev"ar.�=p&,kneW 2}, �do not� , als!2 veal�!h9>; ur6know2 %�rn exist�"a1i!W %WS. Am�P :E6�#[ ��=5 HH-mfUa.v &Z�AD2n�^*L >�s aC mostRHq�2�%�As�., 8 to8c{ $NN$m�4$e5�Aa�3}H(^,2n)^{4q� e  e,2preaCs^�� )i�6ach} A1�applic|i�!+, rengt"2$KC!Uconne+�n a�� �j�I�"N:�  89\%M$pp$-ch�of[synthesiA�n&'u�xof.�Dest to astrophysic-%-M/�&!!l/�R 6�,*-�:��51gA/i�i%� �[a[1| entr�&1 a:nexi":�&t�et 'nalysiU^$En�!��� link���'mirrori�n> NIL]iF��n R! a��AVunder���i� l0dynamic�2�-�3�1Ssq�2�3= a*A�� microscop�a�:�A(�I�s���m/&Vasi89}�A1�U��o!\5�A= 6�k+�a&�.3A� s $N_{sh}"MJM %6�%a,��r��V#of,Varga:1994sl�� %-:i`@�$�@�@qshold.J1r011 {��)�.)�vN/inJ"8"s0 110�6s0F77&B1��20675461.0396096) _0nau0)<�0Q=7-u*)�.��:>�6� �= f=E�&�:�< N F<�u�;N�a=��h��0��Af� m�6�r enhN � �kn:�l+9 Desc94 �+Lang99}� �.� re ela-" �K�V�e�r�� nel,�by�$C��.�.�F/".$(� +N)+N].b (N+N)$.f }<g/�} mo�n ��� �� by a�B cret.6perF� s8Gaussian"�(s���Das� same. shapZ#as"U.P7� �   1=&� \�(  ,2n\�4)" � 3}He2, B-&Y 2 ust�* ct t�� -J"�*�yN.�� A�.` �nE^i�y5dm�"6Q Wf+ve!}�(e Minnesota*[%{Zspin-orb :�Han.[;"�34 $b=1.285$\ fm\minimiz���$-�%le -�aI�C6� f�1��$ our EW' Z2B�j  \�!�SVML%�U(JV3+<'O&��G"�% ]\geq2!1(towards $E=�D038$\�  (�m4 -D+n+n\ $A�5 gi�toA�cM�V1.0memph{\ }�1fov'��]�; *�:�1 I� , require add�4al`|S<i�-y4D2e!� �;"� ion.�Th.�(encouragA��combi�J��H !�55}�7i�Fdv��#�f�' ���>� �M JX&�6� �fic� We%*r� on!&��:JM�^>}\!�%<"|� .���� nѤ!�I!� sI��Kd[ six";Os�, n�Ja�#og�8E��f�.*�TWCl"�$s}1 9#A1�d��q@.�w�� �llabuilt�*byn"a��:'S��, �v�"y symmetrx8:�2�LT} \Psi_{L}=\mathcal{A}� \{  3N}~ f."( 50bf{q}% _{0}\r) \} +$RYL ] f _ gVf E,Qu4( jsU'eq:102_ !.�($ �A}$ ($N$�nd N�6'-��ky $Q$3N$ �t$� e$)� OU��HO:, $%Y$�#$�$ refe�N�p:4ofayat�� �*A,�:-ii\$.F~*aJacobi c&Nin�M�abinB@2p2�2 he��All+��"����a))=m2Nx"�M,R<�-�}I�EՊ)!�<-jeN1j beca� ����>z!*\textqu�blw  frozen2e .�=�P�cmakH �35�Jx=��,a �<fzschemՒA"-�V�V��-)e�M=Qq. �HAD16��kn� (�& 3}H+i�pecA�lyq aw���iv ard spher�]} =_{0}=�w��q,\� hat{Y�(��});/R�=quantumE s!e(u=\{n,L,M\}<-a`ba>m7n$A�A'rad{*�6_. A�Qf �/�aFMSGL1IxEE�:�H$L$aI:� �kn A�gdofM�E9dm�=���V�s1�8 +p+p��9� �� $).�H�ER� (�eq:$C�ds}). T m9nst� �e06`!�nuQ N,K,(4Hl�)LMY%$ n_{\rho}j-�2� $N=23+K!��>�G> a�� $C$\��lec @&� �MR exci6@Mu�a�).aI1�/I�K� ssoc*� -aof�m vecto%E���ON.2}��d% �.� )���A�e|�E�R� $\nua�9�f�$,\ ��"�4a�isY%�i��Is�Y�Uui)"�,3�2]�� .'lowq� OH-?Fa "9ary��� � 2 bb6ů�'ess� term;�� coeff�C�R�_Ft!ueyd dire{I��!�dN�Xo�T�"* � "bL2�L2�i�*�,�6�p� .� ��e =\sum c_��}\phi $U�Hppr�A�F5 ;�N�Nr_{n}}_Ŧ( \� l�S$eq:TwoClcnF� �O�$\{���a��bI���I�$u=b �4n+2L+3()1��� turn p#F� I�d�+ 6�6&�Lw�7M�$E�,=\hbar\omega � 2n+L+3/2�$ YRP �9�isNY�1� )�d_{�I,5���L}zPQ!(9A ! 3}$�"uA2+�-S�Q.�:q���"5W2f.��D6$asFF:�]M2}��!cR )`Y h-a*� �dNY!�$TY)}+2K+6��� clarit���8� prece� disc��8*d�YT&� zi�F�incomA��outgo �x� !�*� �]*FU2�.�.�)k� [ \p^{ ( -1]5vk��u 4 -S_{\{\mu\}, }~FL+ 1rL $] Y_{LMvN� %.h$&�i$J��  a�%�b!��\ac�%gela�2usc�T!�6� u?�� $,cp. e e$l �� $��!p)) �A&X harm�= . B� we�%E� �#I�thth`#2���,� �WA��d� �UtenR�6�2[ ^�=4 a�7 ,}\O�\�DI�sum_{0 I-[B�nuI)U�d]Q�Q� ? ( kyi ] H�]�@2o��.���n� \}I�%�b]&�%�inM��%A�B2H� �@6�H Iu $�^v� UmHH%L� 6�"is given� ` ionF�\sigm�  E)[) W\pi}{�`��})� L,S}W)� 2L+1:  2S}{4 =-j}'| � ��5� P|J'�4S$)b�Tb+2�"ZAs�iz;��  ^�`}rsol{bsXncUn���eP�L}A��A�pm)f-���XXk}}W_{\pm i\eta,\lambda)l U2i6L/aZ^�YGA-1}{2}} & )Sol�;:���W$\��A� Whit�r��I� $�4he Sommerfeld "�\ (�eW�> �H $ ��WI�{<^%�zu: s�7)�\0f@� By��c"+b,*-- )e�"D&� A g,d�W��Nu �&n 2! �Falign}� f:�y�[b )�r>�] e�7Uq�>rL U] \noQ\\2\ m�2�F �seNA_{�I�B� �� �FI�-V�!$quivalentl"\ Y =t� F�  }NF% ~ F3.��%:^�8`; 1]% Vo�S �B"A�no� "� "B�2�=� EU}��L� 25%���!�1)�)�19A2Q.�]H� 0Z8�6 �2 �m�Tof� ����'o_ 3F@YR� !`in=tW��al �tAP%p"� RGM��D�f��.h �56�s�R�bRG�@in���is �! made�<"WI" f)�o�T��! "�.� 6�Z �2"��f- �# =3>=\\6{*��'j2�V��:�"choos!�2�*. 3M���!*� a�+L2�R#!ENI?FeS�$;/��H�r�2inpK !Wspa�3dis"�j��%aw!� "k ss�  avba^\y6] in 52�&; (?])�cI�"X%��"uusJd��� }^{5u�~2� � Q \v�iY:� ( >.i� .�~d N,\quad VtE_{k�4zw �3 Z{#��&JB< alyzA�!�prV�,�kI trie+,A�*4e �&e.W rFN triangleFP% 7jUW}0f2YQ�ga�y of 5�Ui�8�-non-triv�D8�+�1�tri�oneself�P some&�!�KL(s)V$lgraKe ^' $V�5�)�� o�6 unit &�R�1^ (�^. $B;k)N; 2}$): .�E�� thet�( =\int I�� \cosa ]sin d  ~dB�q �Z2}2�}���a 5���2: C)�2�+2�  � J�%�1J�"�G +int@2e�(new).��f\� E}� qb"�}( =6���;% =k=kN:��gI4"�:w4�Ib�7 terp{+d(�Rsqu�0�`�%��Qpai� �m:�� &��,�O �3 ��"����atBq� �&::Nl9wI*) Mmf�hF� I�-}{M-/�}N6|  1n9% )�2e6  P� &�  +1/2O U\�aD cos2:� & �A$�=}�.�&6����B` ^� 1}/2%1-F' �/2}2 �) �� x2R-*�r&% �sG,@V�!��%m�/ �&9Gb�U�qC"�Fa`. /,� p.6Y�DR$i�) q| kine! l�5$6�6S�Qde;+$$�?$\�por� z8sf>t��� ��in >�p�gk-C� �%� l>�* 1�� )���.% v9627!f12.505D6&:6FuY=% %mB� �'K=0,\ 2 $$8Y.!1}=E�XjN>1f12&�E2��5�3fj3f)&&�55.2�5*�Ewmf�4f>4f�4�5�� F4f43�E"e�Z4f11N4f12��5��5129659i@f0 659977��55v.�5E�.�5���c'uN��� n�Nf"�h1" 4)er}kABEff�02}^d�w\.�N�%i u�@ Binveyd�}�E*�/�7s�d�isP@; �@t Ea�y��L � ��t6h VA�p in�ce�HH� $K1 > p�+�`.% to m9o*v�o2< or ��2�En .�  ,Yfe im��be "�pX%\GA far a�$�n)2oA�Y*k)VPJ >m(ɱjS= $mɟ�%v%$�t$\43�'�P"!�X%� "�_7h;.��u�6 e�337$ fm (n3F#2,k�*l97})yoptimiz� g.q<)�a�|"�3!#?Y�� �K�V4#r tensA�-s s554>$ Jl8=�\�)� O�,�good �&�*. More, d&G|)�+"k&�"�>I�bin�%hap!�u|2 pled�,|Et2,&�&��ls 1; �>eanbZat oddE."$+&�N1^{-},2\ldots$�*IF&�C!�T"s.2_>Te��z��zN&�q6�*H"�L $L74ta�WJd.dZN5c�>& 1UkO & 4 & gOU 7 & �O9$�U1*12\�TH&2�_?;; ?D*SP  GP� .]&�Y� �͂Tab:HH>��OB�O!�&�3EOinu&v:�.�w�-co8ked "7��$$K\leq K_{&7 In T���ڡZenume�all�$�ng.$+�$I0a%��v> ��� so�$n=z =N_{�^.ba�. ��C!�.���4 of\av:�"3L &A� ]t�*�I \�: .�!k��*� zQ 2V#;�0v�8j� al>�W�Yt"� 2075�7&Q%a4N}*�}�N ��͔�"�D�14q 25 fR3isbshowed�_�eg�.I�C6P%s, � o��of�Aper� OEles��K&�man���He0�`��;%�!l��int}=25* �fi!l.� )��4-s"vaD:ncompu� al effort%�A< checMHhe �o�9�D�~(�m���&4,��� �e ~#[ �n �"�"�'  �+q#2� 6= \FA~=1�z�<es`.ishe�atAP� =15$ �is � ��:Q>ksatisfA⅖eci^$!6X YA� ter.��>S ,@2�,vwas n"Nb�E ItA��NgH�F�<?;Dde?,!�.r;�6�� � aGeK��A�&h,��aQ 6iR,f Papp et al �E 9gd}a�}Ga* �Ab@-��g� idda �.�Co~�ic ��f* 3�a�)J A�fan1 `&^J))E�n�@�7� �G $0ŭE 200$ keV..�=)�)�eoLcu�{��� "a '. I  I6� F�G6�G7� &��3e %� 2*~�. &�Y"�S�� %f f"W $serov77}(S ),0govorov62} (G ),8,brown86} %(B f$(agnew51} (A ):X3&$3$�X�XX%�&&1�; &YxBX7.9236iZ�G 2137F& tZx09�G6&J�G9R�G3�&�&200725%&�@259F&! "*\x)= "�G50a.%a1.$�2$B8&, i-�7 j7ɍUߎ6 j6 �5N�G3end��2B� 5921gLQ�}���F^��� %5KkrG87} (K .� LUNADH(  99:f98�� 98)NPL4�i4�i�i�i)~�j�j�j4�j�j��|�m�m)�.n�ay�n� Zpa �j� ^q>aNR4�R/9�� �q� �6i*��`1*��I�  lnD�&q\ .� � T�d <5R �#s�t��Lno�Ic � � ? )8&�manif�:E irred<˂Ol�9 a hiddey0[�u4*65�� f�:"�Gexplait8t%X^R ne:^R�)6ZS�atP �� u�[n0S�6*~1S++�i~d}E6\ (B"&� fit� �9%=S$� %�iNN� >� � �7X1�M��mAJ�L>�!>*�!�<ionJ�'N&4206.51-0.53~E+��1~%�'�&{keV bF!A���GS find��\4.89-3.99~E+2.3~~10^{-4}B�8JJ�*�J�]niUCnt":c6�:� �M� RH��gof7r�q� e�k�/U G i�hOrnd2�EN�.� Beu;�i$C��_B! ingu�s M ��#ai l�p&?y=&_ -��*y:�B� 7898� 7057 &L�1"s,Jnel %"F�qefe�� J3}mEx3}JE:D��in a %�)�!���y"PJC5&� 5�� �� "� )�.� )��D~D118�D� B+V5�� � ]�}8�#r�� 96249�'O989048Bj �D)v*D)�.� ���� R1��o"�[^ �t60!&�0 šR\Sa/�,z.N� 5�� v<838<80B#j.�u���1D>�O$ %� �)%��F10%8Jc6�c6�c�c�c).c)��c�c0�=�c�Bc6�c�c�=198482�[�ds�03626�f)y�f)�.f�az�f�fi!BeB!�)a �v W ��Ef&)%6�T �M�� �E��ed*��f:cofw �p)`�j V �j�m:% џ+J� �/45.2-2.8~E+1.2~>�  F$kn:dwarakaE�71}210^`� ,5.40\pm0.05\ ( C4.1 E+2.32 R�fArp�2l�_7zft9.1-��32n08F�3.76 � 1.95�Z��Bonetti�yt�pEX-�Tb8�&t< ߜaW$*�Ifi� Q a&$  o&�+c+02��F:�:�(Nd)�6s2(�Va6)�s �,�+Julp9atXeC sig"L i�0y� 7Frepanc>��5�Uc �J3(�i�= allocho�[X(6JV"Q7av.]�wF>�B� ��}RBCon�b%&� ��m�F�a� $��3 %$����J�7��7����������7�����- ���������F�.�驂��;V� 2�N� 7�|In Figs.B]5ƃ�%2�W"��t�Lm.�%:( (*s0A���8 .�`:)aZ 5}��s�&�s HU\%4rnS2o=�ɝ&u�Q��;�^(1��!�Z�6}% �d�cQ$ 2�Tab�Ee F<)�""�c-�W��7 � >x�re<2 's dL@:h", #vlm2n�{ K=0 ��(=0��U,' K=2b(��R+42+�4 S{�*COru�q6~N.�- ј�iI��+is mo� `'95!���re 2%i�KP.Q�c&~%M8 ^U v% J��͔J�]E'l�co1lt!}�,\ JIz!" 7415��3:�6D|��J@� "ra : j�4-c-!� a pu!~wo��]Ns8�!}�Vure18�v��i��i�i)[2=%c�=~=��!8�s�s�=�zZzA�, wl5=10-�.=����v/1*�t.�Gq�m�BG Z�:}'�� M�N�A����^�\ezJ�yield�b�ies�*C.\(5@]*n F*�1[ �Q0G �LK>6�M�X��a*nɉntb)��dJ,��4 ZG7}B1r�"p.:8� �.<IF&�rsjN |�"  Our w0�4X)i�9enEb�i� ߞly7����F��ٝA�rix��.:V/in�x6zZB�v!���&���como�yX:8-er o fas�3im�:b�&$�6v*.� �:\U<p�rez*toɁ��= J r.���*!]#0�F���� %!#*a+�.2,Z�8}D1#|1�!qB�HnaQe pict�dis �e`+BP J�~Z78014.010�&1P�[4**�<�(sa�f!A� Z�%L% %R�J�9&�m��*�**)4&35<�4~4492��09�Bq��s��s� 98946n0Ĥ5�n5w.2E�.2��2N����% F�Y�V�N 9��B��Cr.�} Hav���_$^3w>�7M�Q�����.�:��� � T7c�%��yze��-foldnT�0 5�.B�) a se�ae(9:�E�%�� }��a��f]1~aTo��so�sh�6�6�ype:>�a*�4jd�;k fi@�J�gbIBF?"�}�!�4"�y�"0�,�9")modulu�g>`k�i`*�1 root�a�3"iz=W�Y%�%s4 K6�7���" 1�is-�:$} d\s�U2E_!gI�Rsim�F1}{E}�I FXIk��GR_{jEL4 6e4&Z4\y4%hSB.J GC9H�b X�&6HDKI6iD>0G >�&% *�9B04�C9.7882��gC� �H nd %6�(�|)�u{a!�:� �e*��N�-��2wk>�. LB�C2&��2���� ��f�%c��1k2�B�C7�1*�1y0�C^"F�1 "�1291F��1.��4R�C2������58113>�795052�1v��%��� �a@�66��B�R ��^�E�B�2�=�� AfteÏt�$�8 �@e��8���'qN~��t���J�s$, �H. $��@th��,��2�\� ����.�NC^A�*�a1 oE�5�&V<�!$E�.,i� F(T+oli��W�RzCwo >.o:proɴ)G ^C� l� das�;s "h! @Ѯ5,r"5D1 !��he� 6� ^�e wish�6�2�!/��.�gF �v�,simultaneous��et] � ,W*�+ peak`�uQ$ a=E�  eq0.5$�w�is =s eveML:�"k�w>��8�<mea�(��/uch��1�:Q-ld��>�+�G�,WW . We beli�UL��Q�0%%5�s� of a .*j!62���i!Me .x� 6�I nn$-�܅-�g�H�eH ��g� ��Y�B3!r a!��1bl��j+M�^v1 . Sc ]��d4sh%>paiu� �� e 1-3A- �eDNpn "~p$�? �! <���Os $3/LF :1 K>2�� �yub S)�A�Volkov&3G�X >� 9} (.$){ �`A it�aNM&z��eQBIq�u ���E1-@�ad�W�6ulzs "��kn�I���6��w�F5x\�G��Gw1w\ p��a&Xrol�|su��ni�to berq@$la�e�fG?s:w��BD1.2d "Qj�*�s&/~gn�I>� 20}\AoA.!#��a ton �(1�!(�:�JN.R  6z� �?la�o�re'xd� dent�I$:@f�����=0.19��.&3a quali�%ve "�& ���2� ���2,�ed�]VA9�!>�20�A2���!?F��  (�GK��6uN�Bj~M��I�V12�  � sj� ����e $K$�a�>�="�On!J�,CO�'ݓ=XCi^V#2%tM��:� g|��� @%W%m�\6aH��� �"4.��2�j�"�!t�fr.�a�s�"��ďnglg(��"a�4�oior-� 2-���weQ�EZu H9��vu ^_Na`P0�"K=2 4nx)?28`� O�wst ��N"=x�D4,-V�21} ŷ��$ huge bump� 10�)�� nti�">y3MX<HHE&OQ �"a�[�ב#z"߱pee� tp5NDI{wPros5�r4 2.21d669:�"]O5� % h&&��F�9�4�vidual%�e�#$4$='F����@�*� ��1�A8�Bo6�,!F�21"�21�"����1�&7)�2*�l!&*~��D11�1� 26+>�2�����97361>990170�-u"1�.�a�V<e�7>�F;6V; �:F�zu4= ��_}dR9���wf"'221�e\d+ }��pap� �M� 8 :� .Pof light�z o���!��O�if=LJ-MA�D/(MJ�hKey step!=�= Hp.���p6 �ܛa&e0�infntk{Y issu% x7/.�i���NDre�!� �<� Z= �z6%e favo�y�-j˓ňhT)h.� �s��6E"�i=E�o�� T -.�Z�)q.M� �wa�g� jeion. A�Wc%G& a8��s:12�@;X6�!��\e"�4!at� �Thebiblio�:y}{�F�v%<�bibitem {2002PhRvL..88a0404V}W.~{Vanroose}, J.~{Broeckhove}�XF.~{Arickx}. \newblock Lji\�2box{J}q'����S"�t6?\em Ph�MlHview Letters}, 88:1� --+, Janu�W��Y��X(A_PR}V.~S. R$levsky%�F.~ �. � AlgebraicWeln/8X&Eu : Re�jg���e�"��DTd�stU g��f�a� v.},�hTbf{A55}:265--286, 1997B�asil92� �4, G.~Filippov,�,!�B5�%�4 P.~Van Leuven.�Cy�, �olQ � ���V:�2��o��k%�� $He}.a�J.%�. G: �� }, �BDbf{G18}:1227--1242%B��Z1! 2�$, A.~V. NeU�: J.=.�:�E�9�� �(s�, �.�I�Q�T}*P back+[2+Q�B,C63}:034606,A�1> 1E��$s$r2R}�FMH2�=onIR�5:џ6Be$!e�n>CUK9C7VCeD96�E iF FFDO�Q�+N+N$}%��"^6a/A�]MLiJ�JXint ITP-96-3E}, page~19e06>, �7���6�@�,�.�iB��FJ}�$60}:413--4 �BC$Fabr93}M.~ 0e de~la RipelpY�Gr,"J�t�GaY�tudi many2]p(YB3$Few-Body S�= 14}:1--24%�3>� Zhuk �V.~ ov et~alB�q��p.�231}:151Z]B}F.~Z�Vp�@nd H.~C. BrinkmanB�Proc. KZ cad9 �_ch.33}:3q35>�84n}I.~F. GutichF�� I.~P. OkhmJnkoB�YzFiz.u 50}:I\89>v� �}.��LH sh:�� $J$}Q\� :E}xA��Ea#� raryF�bA%to:C}o�X*nB�J. Math. �.6�0--420�B5M�E}Y.~I chaev�YeM !.�So~����~)lem 6^d���"B�R{Uo(35}:808--81�n86� $perelom72}i_P ��:�Commun:/ ^ 26}:2��76bkn: eovBe>;G�af�Co� nt S�8%�heir Ap"��ʔ�Sp�$er, Berlin!�8B�AM_AJP�c� ,>� �� , V� s� ,�* .���a&� ��� !�q��ݿ.Ee�Amer.A�e�]�(62}:362--37E�9B�Fed4Z 94}D� ��S. Jense#�,nd K.~Riisag�29G�b�halos:ozsH���B�� R�3UC49}:�321��F�Cp1ero!� B���P�A��Po��Z�,Academic Pre�`New-YorkEO Londk196B&Babikov� V. B� �"k� in Q��M� nics2o Nauka, MƧwA�7B[ D�B!�~ linFc �� ulti�te7Ezeqron!�8�ge-"z�&�J�y��1991:283F43�aC43N�."�97}B.V. e�@T.Rogde, S.N.Ersh��(H.Heiberg-AP�,en, J.S.VaagA�$I.J.Thomps!�� M.V.q .�New- ��A� &��!��l �u��B R577--R58�HF+ x 94�� .�}R"Ұ� �� �,6�Li}_:� B)�XsofqE� 9�JA��Ton% �2>�kf�30!�304 �BjC&ۼN.~Ta�,��Suzuk���db�._ Expl��E��#s bHaly�� ��!�� �P mt.iB�� C56}:5�:565asF�b#65!�B.o#.\EquilibZ d� �*`�"!���V$iI� 1p Ȥ^�V� 74}:33--5x 6B�!���1}S.~ F-)rog-C"���93}:9� 9jf2�fЁE1Jg��K jzen�Selov2V�V.A49v !�Fb �89��S.>�,I.~Yu. Rybki�h � 4c 6� E�:��Y.mu��$R.~G. Lova2�M*�.� :Vm�-��MZa s&Ңi2at�.�.�:Q8}, A571:447--468Btyp|�AT 4Bluge,�Langank$ W� Fow;&p.��  low- gy.)3$He($k1$^4�%I��3$H &߯%_�6BZu�?A33�4iB5pP.~ ouvemo6�.�� �2�J23�,)^4He� n63H(^3� !&wT?:Fm��B�.� � CA�26��263�lF���+!�99�+%|K.5�.pLaq� � �.:s��<:�9�$p$5��V�$n&9.�:�.� A646}:387�<9Z��K rgi�u�.fPr�he"�� few V � 'Z� ��?e��g�a ian 6.r�2�C52:288� 90��6�.~hZ.~,�N � likhC A0S.~L. Yakovle2 Ib1liq�]1���5������.� Few "�. Suppl 99:��:�kn" dV�Dgf �Abramovi��L��Morn�At. E(�� tex? 42}:�7B+ &�g A.M.�g,mKa-Yeng�0M. OsetinskiiVI. Salat �I� SizJ��)� JETP�1���6B}bh86}R.~ECow��$d N.~Jarmi2�%�Radia!ff.84}:4EF8B� aah51}H.M.mh�, W.T.Leland, H.V.Argo, R.W.Crews, A.� mmen���W.E.Scot:�, R.F.Taschek.�Measur�&�)6��K�Y�$T + T�wHarrow He^4 + 2n$} +~64/MeV2� %)�:�!8] 86d51>"EbA.~ee!~W. B^nr P. Trautv��  C.~Rolf2�A("-oub$S(E)$}i,�s�U�8�4�9�0o�u�eQ>�^b (67}:273--29�FfL7f The~ \ Collv� ��F�;m2��.{, ,2�3 �3}6�! dA��*low�dg�!�h �$gamow peakB�},S $-ex/9902006kn �8�Junker�~2��dD'Alessandro, S.~Zavatarel� CH1T4, E.~Bellotti, Broggini,�CorvisieH�or�(3Fub �^ G.~Gervin:�e:9of.8n{.5}��e�dJU*� BB*}ES00--271EU9B 6�UM.~R. D&�U�H.~Wink:d ]LJc �. "Y+]� s be��E9J�� b�B=R*CY532--154�76,A1�4 7zf}. F� t��):�J� �=��r�C57:2n�:?VR.~ F�N�!`.{ 3He+ \6>������} )&ABF� r���:�#t$82:5205--5� 1} �:>\$�#[' docut-}/J%\(class[twoco�,dIpacs,p�int#ws,ams�8symb]{revtex4} :L9�K%��4 \usepackage{�% icx}2d)& }% AΔ� ��decimalː2;bm}% b�B!G!�b��1� } \1;{ title{IsoS3&BR�(%on emi�K�F�4 al f�$ in heavy-��#i�i.ed�.0�<oa\� beamKDD \author{Bao-An Li�(mail{bali@a+$,.edu} \affil x{De-;Am Ch�trAd �{ics�"O. Box 4�ArkansasT Universi��f .-72467-0BUSA� �0Gao-Chan YongWei Zuo�Ine=%ZModern � Chin�2�y�����4Lanzhou 730000�R.1a} 6Gradu�1S��l,&6W W BeijI'Z392X, \date{\toda��R(ab}& ct} �� an iI:~)11um-�T �ansport�w8� udy �!�A2!� freeQs�>�E�_�a��EwEx�c,��. �[midrapid M/&2�Z�^�gsA4�2A{um.4T^f9k�u s���&� e dy"�2���yɒy �= , ho"�, ���� akly6!>BO ��9�\��({25.70.-z, ,Pq., 24.10.L�� make�,'P�1�1ar>w�<,sym}(\rho)$ um%"&3'uta �"!�&��qu��o3mn.�:s\�8�bethe,lat01,ibook01,bom1,steiner04}, EwnovQ�tructur�!\o��%pi V3@,horow,furn,stoneT% �o9���Y�� ��i�8ew98,dan02,dit0_n H1�ij stZ�%(poo�known�MGe(+�0d experimenta��lly, especially at supranormal densities, see e.g., refs.\cite{bom1,zuo}. Fortunately, nuclear reactions induced by radioactive beams provide a unique opportunity to pin down the symmetry energy in a broad �y range\���nsac02}. Moreover, they also allow us to explore the role of isospin degree of freedom in various phenomena and the dynamics of nuclear9 �. In particular, central heavy-ion- .9$high energ�di6Eup� 400 MeV/n!�on at�� planned Rare Isotope Accelerator (RIA) will enable ) prob% 1bbehavior!&lar sy-� �8. While a numbe,�experimental observables constraining�8$E_{sym}(\rho)$� sub>�\ have been identified re!UA� R�pibook01,ireview98,dit04} for ,s, very few2�sive!pA�%�N:�, excep)�$\pi^-/+$ ratioI�4li03,ligz04}, !��currently known. In this work, we examine midrapidity %�a~anI�az al fA�in�xMxas pot!zalI.sA!>!�=-iea P Our study is based o�e m-�mad tum-depen!� trans�*0 model IBUU041Fdas03}.an%- $aa{Pameter $x$ was introd��i zsingleI�on�(to mimic vai�1��c�:%*redicted� diffe!�X microscopic many-body!Dories � � Shown�Fig.\ 1E#ApaHof7>| withpa.�Pgoing from 1 (softer)�-2 (st�). ThemS data 2NSCL/MSU!�-��us��in mid-a���X$^{124}Sn+^{112}Sn$ re�! at 56�!�uA to��>XɷB)6bettyA With-�I)I, a>R 6�,\approx 31.6��/��T_0)^{1.05}$ correspond!Oto $x=-1I]fouao�pIg�F2%[�snicely �chen04b}m� e presentm4w��e ao same �e19�set�ie� emis!�s-@.�1� !�3!�!�%�$ݣat a �ɭ�A�:���e�1� a com�!�mata�8of about twice ���ar%qris�med� last C15 fm/c)E�OA�is!�}�system �be%,�I.�" u�%.,Time ProjectA�Cha��ej!siX!Z fast frag��/ line!;RIA. :�2e�;r��distribu>�bfre��s.�as those�ies les) an $I�/8�f30%9 wheipdy��:reeze-!�A! �leUM!�!�hed. Its�tha��d-�%�ŝreI�2XI�BP��: changa|��be �� (x=1�Ӎ�-2) m� (!) neutr� (protons)%� emit�� ��ME(is a direct��equenc% !� ��eAa puls.(attr��ve)��~3��b��6�$x@ (upper window) y ���� (low^B��:���� >y6��iA\ly�ޡ.uU��~. A)�&/  increase� $-2$A$1$Ez�de > by � a faci of 2.��,forward-back u2icVfs ah>�!k�t � ՁDdicatM� appa{ ��Lq� dur�a� � on. Compasults�-I!�.�a on�j~�B�!�to re�Ovalf>�, wZ the 7 � ��:� rem�`-��+ . Con� �Oon) 6V,g c� inz4K�C�ѫ/i� $dN_n/d��a�a����!y versa� um $p_t$�Qe solid. in figur�4average $(n/p)4s}P_=�� "J (� ) sA0�.�,is significa�3erm�)a�) 2� . M.snf�he2i�o 1�u�B�t� E�\. Both��ws��duLN ���U>*� AQ�earlier�A�of '!�� 7�i��TaYevon�!�a�A .U Lane.Q:6 F-us scGaL��l ,li04}$ Of course J�!�n =" t. G�8/,=w" )i%�likelya� come��%�U regial �5E9Dis s� ger. Howe�if>� 1��ce%�=Q.os5� �Y)aY�icl �t�B�F� asM�T �%\����O�.~eMB�l ����� almost llelIGeach ota�}%� �)��� welljC 0ba wn pict��of"$�>��� in��slxm��\ *��chc in ir wn r� a�&�$G W�� Q��.YU�uus $r$�.( \begin{equ% }\label�a}�ta(r)=\frac{1}{N(r)}\sum_{i}^{N}\vec{p}_i\cdot 4r}_i/E_i, \end\�$E$�!&�q�_ clue'bon0spheriAsh�\ betw �A� $r+dr$, $��,  �$ #E_ r ��, coordi�v m7M%� $i�A�� ple� showA�Fig\ 5���� -��*� �� their�V-as"� �T-�m!V� %mas/N9w�X.�G�Bij� ad>�A�� @( ��8 Hub� expan�3uni��� i��E}A�is e�na�!�%�1Pi�%B�f, Bgliko95,6}. P�2�at largr adii9!��� a sla�ly��er1�y. � �on, a;:��� swJ prof�s"s�u�Fre :�>�--�1,�we.� .\ 6� � ion-�Dd 2AM�$y $<\beta>�arAU�e!�J��u"�yM&@Ae*� c�readi9&� e��F ���u�s u+ S�l$-Rasmussen2mul� �� ��tcal!�obtai0f�eq.\ref�6� setź$r=�Dnd $dr=\infty$. Fo�\R�is rel��%^(r)$ via��2� -��8_{total}}\int^{ l}_{0}K�4(r)4\pi r^2 dr>�^$N��]������. TQQ�" � .�.�a�����at \ :�mRve2 &� v!��"�Ild�kin=�2?!� �5���� �stB���de��s��E� cts. @� �kbe� s�#�diszs graduA�*� .� �#!I>gJ"�mall, evi :^�a��J� he r��nl�4\%!qA s�aug�� ? @dom��kinetic!U"�>�{ ional� +aXGt�verwhel� lyFs� caxteronA�ForQ, hJ.eF�ktur�1�.�� �n�v�ARM]�whole"4 �es�!fact,$By� ccls M-���r y<at-�B� 6� �.�a"m=,�rat%�Q\ � soft�U� ,I��@�U=1$ �Fru�����-�� .������ 3I�eB�+ihay aZeN$roughSecondary1����"� C�&s "�mod�%bTY��v ��summary,�^ \�$C�� &*&j�4�Nar22�$ '"� U�� at%� �$W"A<f �"�7!b�%ar N**� v�&B�A) �y&�'B�:���e(*�' togeG�?�6�& ���orA#*R!y �usefu��!�y� K� a�stTof�e"S-rm)"at 9!W� eQtud6Q1_= J)6�. �&fi�#s �)l9 �a=�* >% play  i"�[QJv tmBc�eti� "őQ�5���:Cnetq��"&^M�j@? �AB.A. Li�sup-�i�*q�Nd al Sci�FA�C�UniAS!� s un�gr�z&1%jn%�!nRS%3�F��2+6t�A72�809E�:��4a�~�F�]05460�~:��!�*646�=F }�"JjVE;J.O. "_2�]�4B 880!�79>��b-�]��B�5A� 2037R95JR6>R6�G.Q� 2�i�5P8M�6 Z�>� $ \newpage� `% } %\���\epsfig{file=fig1.eps,width=8cm,height= a;5=0} \i$egraphics[�e=0.55 % -90]oN} \vs� ({1.cm} \cap{{\�ect�R (colz8nD1)����B����.$| .}} Pe~81 %��&2 Z.:i[h] N )s} �\ro4box{270}!e5Q*[)�0.6\text%Q2!�} F1H:8RzZ2�+E�!��$in��"��(^{1>!4�E_{ 3}$/A =4Qa,act.�of 1 fm.�E�1  1�ZU61�3����5:�3ބ!i�6�!%����)a�5��8�.\ 2 1E�:�,P �(.�*�(&�&l�)�1�4^�%�J>�4��TJ�*6Ka�D�%hm?6 +V+&5R�:I2��%�1�5f���F�>�5�� ��.�>c�,A���B� :M!�j0�b1a6 $V!_:�n�n6�nS�*F�1V&p!6�R�~t)rj��� docu5} �)%\(style[11pt,�]{[Ale} &�class[prl,twocolumn,aps]{revtex4} \usepackage{e�L&� k+ title P g"Ba�hydro�:m>$roblem nee&6l�9H} \author{F. Grassi�ddress{Instituto de F\'{\i}sica, Universidademe�ismb;"�">B�4 ,ented. FirstIa�ca]f sudden��ze�,  16m!gative2B>I$Cooper-Frya# 'w����T�,;separj chem�'�R��D�k � D4!�$described .4necess��of �� �!a2al cod�0 disc�#%n!,�As�'toa;�#t � inuooD�x% a4/�Bv�.��!�&cy��+/.J&K9in5�!�s!�� pret"�k/!qu%9in�+"!cho�=�F�U\Ti�Y� \makleSsg6{1+�A" } Histoc)�$!�.�alk. as sugges�in 1953�4Landau \cite{l } �Wway!�0improve Fermi�istE7XB ;f}.G�0adek!. �usDa�IO c" involvt elb-t\16� � i. But �7A? got wi]acfD)�� %adv6@of�%iv� (truly)}F �>�,.(@$*N%�b)!Pa@Absuca!`r�@�A(. �z�,a goodk9d��2.E3any as'sit��Etre{`a�a ers&�"ilJ8r% Z*�-pa,c".quo��I�e�n �s w�9^in I'ha97a,ag^HS���J��s C@�"*O 85,c�D�&num3,MY el99l1} �R0 stig��b!� e,(was derived� o me93Q"E�6so�0%�7 per�9 9�8,pa9,02,gr00,gr989a, gr99�B�i �u�W��b&.N1,na9S95,ma�$r01,yogiro*�E%�, IG!r�!��9Q�� in :^ I�'q֩�p�S, is �[)a �vBe,�*3�Cda��-g�:AlawA � exal!�ilr<�]stof2eZt�Jim�9 top ��actingT$. (ٿ��� took%J�!ideas:&DK���� �,b(w-ccurs ("$&"5�}/�^J26-iA\J!�)�;!/sl5)�meay path &of j>hev8 ar d�J����,D�9ch l��a�� oupl��.�32Tp�c �. a cer�+Qp�E slow�'F;O�i�.� E'today's28�M�[M�two Lo�:z!� %i�� de. � plexAɡ��:ak>Lcea?!i� stage l�,I�at=2 G iz�5ot6�fN7g/=� $\tau_0Q-is��e� ��cVQ2��.�<&�/proceeds�� luid5� cool: �64diluted untily\�A?%�Q�= ee-s�� m to�<�:?or�(!4"R4, I�"a possiw0�~f 0Gv6)lM~.�6�.�vusu�� Eh�2.J(,B�  so I�%�Cit + ah=son. * star"C � 2, �<c%z4'B, Eof7��� � s.�Ir3 anZ1F�"� wha��E��ext� o�%Q��sB�:%�� t�5�5�C!(d a lot�1�analyse�X. S5S�  i9,3 �5- O altern % incorporat/n6�. Con5 ��% ~�(wlJoposed)� year�Eo"5@p(n2sW -"E9not ``)e'' ;%`E� ٠&.Q@,2ain])� cis��in QW4e�, !i?bes%gU-a�H r�H . Fim lcoS��X5� "n 2. S>� sub 3 {2.1Tt�tal�9roa�Bnd%�Q� } T(l(6���o�8si��"C-isEe. M�}�Eomes g �0a����TA� 35 vBA�!�b . W*�](�3%hh: assu+ �<�;��J�� ly (��AlH ``n''�(fl&5ea�Vg�2a�n�K,�<[T�.ref<=��.e�c Aerf)eS# "�,-Dx ) me�*�,�4A硪��.�.!M �.CA�X4o act3��ut� N "6and get��7R%�6 Z*�-,q R (�5eq:CF})mKCFart}�;bɰ�"�F} @;8E d^3N}{dp^3}= �tt_{T_{f.out}} d\sigma_{\mu} p^ f(x,p)."K��b $2>"�5no= vec1Fto�8surface, $p^\mu�FQd" ;� $f$%��b"w3"�7. U" ly�4I�$s a Bose-E�Lein��-Dirac:JD5isi. T F�9RaX�3�m�_|3�� >�U�h\@ bad feE�s����two. P�6u AJ,�0Te�meet nRterms (6� %] \leq 0$)F�R1r�7-� �m"�. si4��(umably had L pR�4 ng (�Ofrozen ��A),T yuld^r c |a0"~ [^N.�G[htbp]HerA��&� _evt<"� .5cm&� dU!@l[CF]{I�+� 2���ex!��A�e5: y?be5�uL fig:cffig� | � So^ M� remo< �:�f:!�c.):asRr"vio�Es ��"��\ is%�a�lig, K ,�2l�) ~��!*rischke}��09602011.f03.pU7.2��B�Nqdco&�7s]{ Rv!� yX�aout o�� $�s=0.4 T_0�. =G�L\ �a�.=Ico�Vs��46�a�av 1I� dashed-do Ss# �e�s>@EWspace-�F��li�A} [ T:�I�� H I�� be96,ri98*(case,A.l U�2��y=02QQ'-�IF}z6��SPHERIO~ ag01}, it?$a 20\% ove�Rm� of�i�Ei. ( re ���`s  voidosem�� but nlI% oP te��  �2}. %E;ife� �� >� R , !"�E�/ scAm�aryAV;c�Q 7 X,8q��!D"� : do5�E�{\em �ly}�"��w� �L�R& hy�?<1ui1 ly n�� h�<n%� a:.� rrobW�s9A��Pul� of.�[rfPwZ0Bra,Sor,Bas}:� shap!���ri&A%sI�� !_s g�%$SaGrp ��da�-B�[�sqm�=ES"�Qh�2=�C�)?M4ph�87 2s W�AtpA�����:to��j<>f,Q@_6j2 I�*`!A8gy��te'7, $n_0r$($T  \nu}$ #7s<� fk02�mt�'16i�Z�isb "� f^*_{FO}# ;�� ) = f) \Th�G� \"k \mu) *[ cut��e��$ ?$�se s am8�r7���Y4 L[wF �6� >0$�is�I*A�olrA�\m�gasP .  (RFG�UnB��} )�eMnB1R $v={�0/  x}_{RFG}�ba���or\big� a�< $p_{\perp}-p^x$����ex�*d."�I�7�[ cs�i*] 5�+ E {�+�TaU!J1� :> |�D�>4 $v$ = 0,65, 0E�-0,35!�gi�$bv>left ��bol� ve�al axisT�J�m'!��ivaly��033�d�Ol]e��e J�cl#!q�� �M�]�., v � U,�"[l�]Y�."�, IJ:� 2I We��o��!{�� $}�� �G�if-T�đG�BJ }�a�r01}{(2 \pi)^3}( �ft( -p� u�2+t{T} \%�) �Q!}�H$+8=\gamma(1,v,0,0Pf�FH��E"�.\\Ria�es%m7� -�!��� % A^at�cho�M!�g.r�N)�2?+�N�$me.�rbitr Awe�cus6�� to �"ou; satz�Ge� ;�0"!eBp3A� �to� eF�nv����K"��O& �=���"TP ��e�@iopy,*� �o eq�*c� of Besseld �Isp�uL�+ul�#eF�$.L�'[ a&�L_$v�MT$ ��= �  T$�inEh!�ers<T�I� �'c!It-&� p[d� &]A~{(!lőE2�q/ s\\ �1� {$[Nad.v]=0\,6[T^{0a��a\m' .*(xF($,}'T1{!4qu�Pi8�h�re.�side,��_0%j)lK�YdonqE�cill5checke�B�SB�\geq0$�*$R=��B%} {S_0>;} < 1$} �SY�ank�eiK"g 5�. *xV�5���dvnu?$ly��I=s�I�E��w V alI�A,�u6�BH�0N!Q�y�&s%o�1��!�a"Csma��$an MIT bag�%#� G&�M�B��R"~:�2Rb(5cm}\hfill >13�14b1ɋ�1"]{"2&� �< f �|NA.\\ Top:�>m $a (s"2[)%� a)� (=1.2\,fm^{-�6XT_0=60\,MeV, \Lambda_B �`(B^{1/4}=225# $, b G0.1�G=8 [ $, c 8��bMeV$. (Dys:"�!/pos."� �P0). \\ Middle:'ity $nB8 $%*!A�6�K=5�!C9$��6"d�6), %(,12 F (�-*K0! .0-�0 Y!�0Bottom : $R$,>W!:��E�!s �-1/�a�\�cB%�n_!=�vI .-= ]v- F5Y,�F)" �, !%�6=bIU� (.e6 mmm��m} AC&�V�� se8�vtop��. N�ly&Vn  a R�e�v*vY-�!���p!���� S�X�same. \�' ��s"f`4�H" �a���e, �l arzn� subt�al�,�i�c$!�m;2$pl�* $v_{a��jv�8�VIn~A|�M�/2��/�"� of 60\%.s�"� � �ort=Ndtak inhccount B)/�{$�"�)�"�. & "7&� edh O�wa�,n�!�� Qwe �ed alHTy.�we now�,y�VU�h�%u*�"_ .�a4 8 �/�'e tube��$x<0$�t �&ed Q,8 x>(0empty. At t=0y)�Evat �O0I R � d��$ vacuum. SqJ �!mov L"� �  h���pAn hem Od ) �h(Q1Lo!rto l�(ionx/A�,)a rare�P�^ropaga)i�)f�"!Ii�. �U&#� "�%C/e83 below,@Vb� �#twoJm� nts,��T�f_{int�1a"�'(x=0,p)!�!L@1f_A> rm}( $.14�$ ��L�&!A�� (eqnarray} \%�al_x �(x,�Z4p}) dx &=& -2  d\hat{i�}u ) 6�6V� \cos \t\_{ k} }{\l �:Z� ,\no� \ \\ :�-O� �+����6�.� 9��b$F%P}} =-Cp_{x}}{p�F�>0. AB# se" 46YuŨ}I�9I= !��!mI�-�ex0[�2� x p]5;��#�?9Pf�k.�& = &^�\�s Ub� & & \{1-�\��[-�"J �>�Y�x � \}>zj� -�>�>R%��6e$ �d��. cut  "J2�iaw ab� � �L \long�arrow \�Zc��S,Z�?  d��8g�$x$5�U�� {$�Fh > 0$ p�^"�X3 �!"$�b�� �4�.�we iderFPv1�e%��1�1:16U�_& &+I�ATeq21-e�!G}GI�].NI��N��'} dx,B�9Vq�6V%�j!W=����2�d����ad�(ala in��$G lud# tE{cy���\�e�x�0 an��"�4)duQj&28� ^x��e��  $1� $. D :t3 o�a�� l� y��o,eCeq��D� � �an ���)� ers $n_E(x) ^#Eq4"�1r�d� BE . %�y&�<"�5 %�&��)��A�$J+."rew�-� %*As %�verB �d/�in; !H %k:�l]%T6�*Aj"ute %� %�E x+dx�e!Sq��%O�'%"t DeS5K `�opi . ]��J:%8h�)9(�I!5� A)s- aX >���zero (W6UVAF�� s�t \&���B�[�O("/=I3I6:��%,(p_A�(e{val�;a� he $Da��p&Q�:� )fm!� d at $p_y� x=100m�,130�6%���c� r /O>�p 9>�$ !JH6� t/��Q�. �$m���t�=is�C"\ ex Vs� curv%+�red4s**2o&"�$6Ia�786%Isto %Al ra a�\^�ciagAg:ar[eta�e o.��\ po=(nalisar % o�2dos. OA���2I������ i#pf\vd on�M deca3WO)�basc,��Y�Kdif�u�'tr"1cly� �4s � �dA� .�*��d� �i�)uf3!��a ¡�re>� 'q�[ail]  !f!�`�E�I�:,A�U"QV*=`N*�@p�=�8an99,ma99b,ma03�= 4,ta0p 141Q�%{=�#oA���G�%Oco�m6�3���2as@W(�\uffer1 ���*�� non-2g<Xy-2)ch�g �tea+>o"=�A � du00[�eZc�B! bu0> %*5�no��xa��, %I*�cE .5 %� ��x Z� , %H;-�%�5pkii4u'���Ca%�<c;A�imn=:J. �+�{�}/  \simp �f�o 2 (\mu_S-B)�#_{|@4=exp.\,F .o�} (neg!�k��)\\�)princi���5 �JC%!B6*�izW�.2 is l/�l�5�0�8a�lea�� A �!_S�b,TL t�,`& a minimume�a max��9��9�idon � ),f {B\, )�)��9U�J@(redlich�� hs�/ *{-2� .[hgfou23� end&. � { Se�`܅Q��jre94}) � �$ e�A4{b,�$ |0��!�e�Q��x}��9  $�% < 1$ (A�%�re�zce&�6'1):� ]� :� S <"�zeO�-a phen�4a"; f}��*�t!�fa"�Jf$D we a�8i`=iIi fron"x d(s $e^{\pm !Es/T�~�>I�s�& s �zv"',�7>=B/3e�S�TK-g5‹(by C.Slotta�Y-� cl95} mo1)e�%�of �*l>s1Z.)/&� �"�e�ix)} =0,7�7a�*2�2A"J.no�GEXb�$P$Xi}/{$, $\Xi��% :'P!��'A�}��%Y2�tr=I��$ ꁞ�i=V�y180-200$�,Bc#200-3 #�r!furpris��s~=9hm�>  �0B� � sU%/."06�h�V&ra� ��a�;|I�%u��t�� rtab:f.A�.��!"t�j&jAR� ��1, J.SollfranksW� so97a._�W.r���W$tabular}{l}\h� �m��(& T (MeV) &)�b$�*a�&���" C S+S & 170 & 257 & 1&ma,Davidson91a}1 F497$\pm$29 & 26 1.000.54.B E85 {30 y:� C$tawai96}\\.�2l15�2 �:E �,panagiotou96.� & 18 =9�226 W3 & 0.73 0.045 beca�r�].�20 I<259;� 0.84 0.07IA)b�9�Ag)91/1-27 J33!#���0.)�3.2!'38 W 0.8�g-(b�185=8%'4 �1!0.-B~�Pb �7-(6�-�42b�andρnMHS+W +19 �10H4 4]0.E�&�!2�190 & 22)1A�0.6).0.0�- (letessier95:�I9IF3-�8!�]�braunI� S+Au(W,Pba�16)hA�17  LE^� & 16�& 17 :  Ksp�ds97�G.)�3.�5))�6 �m#-&>�I� �� � � ���#�&��Ely� n�"ad�Sm/at3�!.[* 5 �2dq<a8�E rO5}�#y�av�iine :5��Wp_C bund���j>. %So�SPS %"�[%T_�`m.� �J {b\L�:200\,� %%'� .&7Fa�H 6rT!O*�ZT��*�.�ly (q p� (ed logarith%5�Qexh<�QCPrsr+cli�l2si >�#R�%3�e"z2 2OJ%��f��:�%){���beLcoS�,#1K"],�f�/� y, b��sU+.yI�n�a�j��e&2ME��Mr�VOM�@be){T2 "j�a$,p !0``kick'' rece�Q��� sm v^{%'}�C� diYQ�0�, ��Sr�EarghY�� vali]:��r* 1� spectrum �.&y<>m$ (� 7�9�LMA �a 3? � � �"w)%� ral,��*�{ m77 �E�|nHɗ pai�P� 2�and $F��� �e it..2"W'/(mbiguiA�0 anw�J%jF�a% ous �s!%� s (e.g� na44}),B!Oa-6!R5,F�P�F�A1f�I )�ue�th" on HBTYIX ons .�wi97})f&4i � �9eǜ*!r� or2{ EeA<om� �a i *5�F4# he97�C�-�,>cB>< 2D,diag_2fonewn.5&_B0}& 9P�=50r�r 3)d;��� ���"�sYp121& NB �$.�-E�1�1.6P!"}. 2x8!692F)a} AAa��� ��SPS��B�25�. "5bC*�At : nX2�c,y�;Zr��*��&�An��125 I�%��".�*2BJO.e.��=:�f�"�9!ir5�be$L��H,we4t%jZ�th.�.�140\,MeF�II�aN�  BhR�BLJ�B `��˙�s�=!�E�J-"n�2IfW.�ś "CwU��2%ew�aq cis� G h� ha91LN�-m�7s���~E*)1 ($\Omega$.cis u�E�bA� �9). �5� let �e"�9.�@w:e:� �so�it �\��bHn�y|EDp�a��a�$�� or semi-=te�.}"KC. �].1 3 Iт'8Sly &�D$7X2Uat .JZs?GB)�ar�Ea! made�6relimi.\iwhe�0a JV�|^ :�"._!2�a�W� �!� � �1!��RLas5}t.F-4aё�N�{2NbNB'���/�A2��vFasyAa��Iw�EJ�n�(t)-. �2��\\5.; �<:!B�b�;Bd�R�0ZA%�F�@MC��]C :>��,��htatCdif8�o*V[3 M\e�g"<.P"2CA��!�"�* non-4&�a��'s"0�kn_i2U4g_i m_i^2 T}{2E ^2} ̐ n=1}"4�c!p)^{n+1�U e^{n�4i/T}}{n} K_2(nP/TH!�4ft^2�vv^2}[3>z & +Vep�" K_1�] �� \\ p_i �2 6=�� �2��9�lSi"5�H �, $g_i�-� <cy 4ʼn"�*cA8min� ign hold�Mh�YGplu bo�fE�# =H����< $i$ m�:��(�2&ʥ88*� � assoc�.it(  otenn/�8rol�% ��u �/��F$��a����'.� 56q�l �+!T�l#mu_i=B_ie B +S SK � $ $� �$$) ensu�60<of 2@.-�r�nes=�\HBA.($S_i$)�� 5 (*s$)J&`9% S\:� ����'��91� on xF��B�4y�I���� mu>~, etc �/(�nok 0on ``$etc$'' {nM�X&� 1��ck�E}N�)� ��R�es�5 2�al4"��b M �*Q(._. Ife��"i>> T$�� � t�.$i$�!�low,f? :,;s�0l�9sQ�a�f ��f��w� hec� o ;X �/��e��[�s)�  f� JZxWT���1&y J�2� qrt{�F\pL}} (m_i T)^{3/2} e^{m&i-m_i)/aK�:��8 ��5(1� 15��8�c }�+�� 105 ��12. ^2}+... \�7)��B�� m_i 6s3r2zr5 r^p�bjT>WeQl�2�0 � �@r4�n. �3$n nd T�#�*Aan�/ \aiA�"F ,��,*�  2h ,a�, r\#�$T,a�Bu� 6=a��PeE��Iɉ�yvz=a9D �I&�.�@�j�!*t �m $4�ĉ�B��x>� sep}�J�I!�rbe*|fI� >�Km:�� _ al�ys�0fR� ��!�$un�on�a �"�$�_%Ae"t}t_sqmZ*-90R�HT*[Q�)*�\\I6dub>e:6e��ubf` &�%9ta:z Ix]�s�3D2V �J simultane�:& s:�h(I)B�i����) LC,tsEkkɩ&Wd�>�G(II) Vf�$K� K^*$'�if�FA托Q$] MF��\� ��!��� *�3 verѪf� �if�="� mn6b1,9t�x-�z*r1X�. !�/ �"�8si*�E� W��a�n�� a�F@ ׵Z���d�b� Gd�j J�� ps ( ,���B ���65 ),�TKK>-m&t%�P8d"3c'�.4 �&t �} 6 Mfew"� /� %6j)u)l�, �3� �me��7na�4Rew� F�;>��]�Gec�G� �" �%��pe� $� *#�&� y 2 �ufixed, 2Sa��Jlc����EDe _{i}*He�(\$.f.})}r})}ByeSE+�yeen.Ơ��[�n�q *G��!�!eit giv8>V?!St��r]�!u�  V w[a�ei�`% in�wilx,�� upon ;grnat�"�$�9�q2c� $N_i1e71 AaK:�P�8< HYLANDER-PLUS 07 nel}ls�/J]1 hyla�(�f�$A^%.�$m_KY."a![ }� "�!] &}=176�9I% =139,��Q�^(a9�Uo=TQNB � yiel�z�Zct��too� 9p"�͉� =la:�6Ve�2 a~4\60cas-F61 �e�62�B$a: NA49�%�6Q/. �P-���< es: Wl.S!�!�}%�K $�&�% 8 (}�.#Z):�����J&D!.�(.}=$ 176@ 184)_�A�}� B2At A3� (|ex��fqn� HiranƋTsuda�hi}Yfi��"y�f�82Ny#>H�9Z!nM��/XC*>�$ elliptic�K% �$�oi!FRHIC. T��%lso�c;t� -�l Lteaney<"Zp4.��t�L L:%*4.1(�:sK6"M oe�x���s*i:�X=@�>� x3u2 .ond���y=io$�6.�)col"9� Y.HamE�, T.Kodama, I..^ of-ole� -�� 95a, 6a}��ch!�o�rd�E�a they,!���k8y��loc�,�""6|!abilityO esc�c~!"1,����e vyum (sai+=s�O��s�%*Ct(s)8^n;_5X @Tr�$���)8"*.�+&�>d�c��GO,@h՟��ZF� ��^�&�j!]at)�ħ6� �,!a�PiENdB:��:W  4��F, 3n�C�b)+&~Mp"��}��;ul�({;�����n bJ�� /�n�$t d^4x\, D�a[X` f_�]���nEM��&� (*�:J�F�p;v  Y� w�@� ��>K � o:i-��-b&e$ ). $ ��8%(� 0 four-diverge�E*'Fco�|$���Ent~ lxbe evalu�6�&�ޡs.:A�O?p�^a���*PwaO@�+��D �qy=��!�e�aW�Q wiO hi�}`���L�� &9� �y. (�]A4reh�$;N� &5!?q� n ad%�e  $.,y� �*�"Q�Q8={\D P} f /(1 -)AcaY"�jeq:A�B^$3e&u4/f$�L^ ��A.B Y�, �be 0ǡ%2 !�a;~U.� �?s�.7MH out ���y`�uE��VVty�^A�!� GlaubCor!�F#6�b>O(�Lint_t&n(x')�>8gma v_{rel} dt'�O�+la6� eq:g xBf!����)lv&�jyށ�c�c���.��TS-� g/"�b 2w2A�s�3/ \{P[(p.u(x)�$(x))/T(x)]�;1\2w�� zJd'� � $uhinv�X,$t;s&d"{ (])< B+�S Sm�$B�sic*� !� hadron, $��1�O�u2Dg_S Pa&�"��s� ET*�:$�J#M� ,d�q$$Gd =, A�"sc_��,agc/@��Z�E:�F��T�\,�i&=&U" (n_b -�)B"� B$&' , �/�"�JA��(.A��%2�I Fe��>� �i &*x;!���� <��B:� �&o" s` ~19�� .�d'�����F bD�Ay� T�yy��/!���+-��Dn &fB��a�1ing��en�D m���%g')..= � �i lems: 1)ae"�� Q^"%�}�!����i 0f �$ g�R)�1��n �K�c toM2)�hyp!3�+��*� !֑Bed (cf.D��ada}))i*l�fa{E4�{�ٿ�1��o qg :�,axdi8F g-�!% eq. �%oa� wo `os� ��� 9" > �P P_F}�%�)>0w3 1�&w' +�o6�! �* $., . U� Gauso eoremI�p�I )�"�an�5� og�xm�=.l8? � E* Q�)F�I_>g#�Q{ �"�_Ffz b=.X& F={1�� �fth��ѿT2�Ft�e&� . � ~ %l�4��.�$�t��� P1u�s�s.V "��5�pa�AZI�Y�Q�IPEk�( q.�) they����(*(i)2UE�H*�7�3wvapp�6�`�w  kmN�>n8�<�"�{2!�Wt�hJSo�KwE�� Emd&�| =I_1+I_2 � 1:��|ž.� CEMAU��It!�EX� Q?Y3�]51��_F}�d �8we h�Yh.�X�^����*� &� � geokl#�+�. �**�>8DE9��F;8�|F9 �#a� ;x�J�.$���o�0��"�֫.� ��r����iT w� �#��O�C"@�z2��!b]&~6.|4a_wsp.t6tA�2�fig4bV+�and� %\nR���o tr_o2�Ig8B�ub�'vR&"[Fd�"( ]{ : W ��n&�2.v2�=u2+[p9 :Ao a(�p���9as S,� 65 &cA0� us; �"�Orst �r"b%.U>&WqX�L0(�ii�9s)�7U a. with E�>� , ��9s >;Z# &�*U .) ht�L1(�wJ( Pb%*+1B)3� � !Pfun"K-:�!&P>2 ��d! � $s: 1,4,7,1T�). " .U#n� .�P4.2��ari��JF E�|ze���R�QK�&:=�2�| "���6in��g dels�i��a)� *"e�iosap We s"�^b EΡq�"��,>K� =6�h�("N.�2w�* 8te�z��E�z NP sceanrio i��c�7 8 9"����)�}��&�<��� sx0FqsC0� a��)L�1 ߆fo�2qI$��`" 3 a se!p� " $  &�2s%,�F�KEAI�!� &�@$ �*"�t0�A6)� � *Fc"W�e��'X)!HK(*%=b � > �aR�)%��y.�YE �V.<�?� i.`N stea�� 5 �� ,!�ge�SF�janela�O}�kA� ndow�U�?M ( p�]z �&�M� 6�B s. (W-.l���A AE� wh�n�;!JL,Ft g@t %-��(,Uj� a�,f2)A�%?�32hcutoff.)Ǧ���ht���2F�'�p:`";MW)xir ��i�G]-��9q!�� R^3E2+z!% c7% P}�P8*�M�#] �-�Iea�N+�M!� �?�U76<�2ǁ�� 1�} T_0� \$/ b\,0?2�GMeV �.s6I�Xm seemKF��pD�A"a�ic g, l�L,ce gauge QCDa�u�% ��o���m�?g�Q-Z ���. H� "�  1)I�Dwo �`�v� ��� �A.A5��/��Q2 53a_���b \neu�X,.���ow'�B="��u0Zdvg��,%d�Y1��e�q(a�e 2P a�AwuMO}��.VW3�(�.�98�X5��?l\?d��fYR 5X�]#os1F� I�"Y J�J�u)!��X �' ��UnJca�o :�* i�9�� m21��W<�2{U2O �,97 �,��!}�%:� -� 3ų�_�&14�e�c1+&�!� .I��l{"w���e"v A�E [ *���Xai�'�|.  a>3�_"?"elw"K@2s$�<we��f�e ��$o!aF �&\� !jFnS G b. >M(G For2>wW 1Ms&\ tp�uT<HH#� .�� 6 ). >Z�"L=eb] e� �:�"R>  ��? FB7 �!Ra' �#�F�angBL ek��A��1h'M��i4At� !� �$�^�D�|�iM� e 2o˸� �zt ,�su���&0P�x=&�V��╁j6< a;_R8 :�:���.&ss_�#RU*swb'�g{ rkC�noR��� � our�%di�N, t$o�to���NA3�  (S+S�� Yp%�)f�l4%8 %*���^rge.�Ca`)�W_!x@W,�@6�a:� Y2ɿIR�#I�sh�7Q�on;mA��%�L�  6���G &� ��AQ�"> �"G�f-fs ;�")N9 (6m(&r !�2�h��w�.* .a�\ �\�\�.n�a� 9.� �>)Ps��d�d Ja1J�. 8��'�`YeE��(�&�0�]QFRum�g "�3B�g] l�R�_0 � � -(*�s}��7�9,Q����,��maine˅O2��.{�D� To��)D:�Qe"��a�� [@ Z (��m�hDF��u� ion)�'�(�� t�� �:�%'K&�Cl�S��3 � UA�&^T)ll&e��c*6nd (ifA /. ar at*M�e�{� +H�)O$eK�")%�6��A]�^placee��-� , so-s�� �#*�9ZS%� P�!!u` � *R!� litt���T��w=!^!�'t� y.*p�:U�0atu�.` K��u&�M,�(cB��#:k. (In>�,T!ay�~��@re%��7��y (z�-�2�)um �%'� 1aK�p,)�2�q.)\X�eWAͣ)�O���a��d>�!c�%*eT&�iAC�Zپ� `_ V perhap��me��&v J� 25aQ �nJD "gnen�pztA�� �_�eW.��8� NY"Vb)M�N*^"� liU &;Yiu�2�Id7A��u!R�7i�F�!.� � o.s�1M.9�c$���0ѿ"~�`�A�e&�H�5��1r^ have/.�s9 � � ��Co�we7 )�27 &+to^ "EcB)�A"���� {��&R ptwa97}i�"]�2$.^�0 ttra'�o�  ~n4e��s9a��$u?�'�y�K�&�,"w\�nex�Xw atf��k�=� �) v�on%4�-��pa�W wh�7r*OS9�i�X>\m�*�U�:!q ><�b�!R$ "..� YAN_�`\��X*.EZa� �R�s %�^(iF*�<%�%� :�\�dvac �g"L�M�!�e-� &}�k�C���sC&6[deuter�a�out� �.ua�v�ri )�/ͲboA�� formFm���5b �co&��� �����2t��" �jf.figI*6A<l�rlai@_��F�y*�R�6,���6]�pT� �I�/� y�"��,�< . VaV�cke~i~=� �]q�thiA`mP�(�U)�A�[��z 8#�,�� (�d�/rŹnone��F�L �Ea�}&t\�< i�.$i � �eN� RQMD�0&��ak��a�26�cmM ��P,�E� �.zQ��!c"V "UQ ����6����0���7R� origi'���<(VZ}$a2����1e� &:7a�9s"$�r. m33# ��7A� inde�i� � . � , "�lb7 4�.�Ե�y--&! !)ec}��Tef2�7��<2Tef2#"BRo��!!UA�6�&JBa;!�jTl\/"I�=a1`r*p:�.2���:l. y�:�re�x ;25 ESs .�����v os99""b:�-�6`�+��u2"B�m*,�E�b �Ae. �^b�JE�a"A 2�s: � ��pi��<\su4>&b��^2Ln(_{N<� F= 3/2j_$ (�@�d ve  k)& est?L,e), $\sigma_�{\Lambda \pi} \sim <\sigma v_{rel}>_{B$ 1,2 J(piH�$ (using additive quark model estimate \cite{ba98}) and $\{_{\Omegz�:# 1/N�N6�|in�Rravina98b}). The predictions now are in agreement with data. However, the cross sec <8ppoorly known and our results " sens)&hto their values. Recently, t new x< by NA49, WA97~\%H art}g   came d< conclusion that! fact� re i�, need for ea�u @eratua�n ai dynaivcode, eP,ransverse ma�wmZd at a given energy. \begina-$ure}[htbp]�a@er} \epsfig{file=!�P_om.eps,height=8.cm,a� =180:0a_omnew.2620ndmcap!�{Data A�:�fit%u�(particles i��d�Zq�, top,��Hbottom57Mz� art,� .} \label!�> \�I�}1 �0a�:07��A ���Z�leads!�(T_{f.out}$ ��e��lower%7R$i����6q�:4\ {\bf d. P�.@abundances}\\ We �"edek s�ge�%� ra�sqLu d��a��i�W} js d= FK� �R �S aLm��B 14�� bu �JNp Ne�H!/�  R . In�  Ster6�(st99} manag��B�by ����44z WA983 " ({\em�6no�I i.e.�Q})�; nega� s, � , ka � prot  P HBT radii (see next � )��.�a��%O Me)| null9�potentiO or!� �. O� e o!�@ side, Tom\'asik68to!8say��Is� 0kind of objec�� y2 �s% rder�~)��non zero��SoB` ifA�9�� Ŕ��, it��necessaicmodif�  s)b sepaae]qG"( cs� �u4equilibrium or��. i�Gorenstea�4nd colaborator� ri97,ye 9} studi� ific��rf�j� e,��cisel�yM�,ed a smallerEWu&Kvol� corr!�`�. �LetessiyL� $a s\'erie� pape�le93,l6 95} ��` "7lar�=5�!�ind�vV!�fa]� ga �Pgluon plasma hadronizasudden"� both��!y non-��Kr��le98}.�ѹ� G �*䙩Ajels hav� �"* inter?ngA�compute9M�continu� emis� Y.3 ��^,�*�� S+S ?] n (� elecT8at midrapidity)�v\�Q  experi�al�U� for ��Tat $T_0=\mu_{b,0}=200$� �=Lat��:-"� A\,� F� � �� �{|c� |l|} �  &6�=R� &�\\ G.� 1.26H(0.22 & 0.96 2E$\bar2� 0.44 11 *291461p-3p}$�3.2- 1.0 & 3.1d1.3 ]hG & �1 7 & 15.7PK^0_S$�1.3M�$.23 06\\��� 5a.�&�le!i�}]6�, a�%r^ ofi:�'createdE�� Grassi00C w9l!D in0s��n� at entrop�, reas�ure�he fluidAanap . T� is�%�pro�a��@��in�reeE�e�actda�onents � wellS re-t�^��. a�/rast,1Tusual�։+, �sE��nd r12o� � of ){ ; so fis g , ����� BC �ies1� ini� ��i�. a���2� M>t,��In caseUS��� doe�t �yB�Q&� existencťa͈!�"� �E�A&%�pre)o�ʥ|4is quite influQ�2 choi `�:%.JHe. HBT< Interfero�yca�0l which permiArextQ�in�ei� spacetime�>uc9M{ J�sourcM�R6{ underlyA�M�s. Si!A!��a\ifferen=rEA�V,� %i6O��� 9.�(� a ew��MWsandra})q��donA�a3f��b}. Au� work ��malism!FJ�Z G 95a, 6a} textendi��<uYN� lifung. Pr ,� 6ed�eqF x} C(k_1,k_2)=C(q,K)= 1+\frac{|G|^2}{G '1) 21}\;\;, �cc���^wh�($q^\mu =k_1 -k_2 $ �K =u 12j+')$.-[ee�!K]!�a,Bjorke �  pseudo-*� �6ko86})F�-2<�,{dN}{dy}> \{4 2{q_TR_T}J_1( 0)\}K_0(\xi ) �:k@narray} \xi^2&=&[ V81{2T}(m_{1T}+m_)-i\tau - ]^2+ \no�� \\ &&2\,(F4T^2}+8 ^2)\, R`2T}\,[\cosh (\Delta y)-1]%��xi��e�$-@=y_1-y_2$, $<\ >$� ��ver^��*s 1e�2\\�F9Q�!si,k_i)=2�-r_i)TE�m_{iT}}T� 6citYNdt :#b$�1�i & = &� 1{(2�)^3(1-��{\�P}}_{ 0F}})}\int_0^{.}d\phi 0{-\infty }^{+ d\et��1�� & \��s &A� OA�\rho \;d %�|\;M_T\;-�Y-[) 2[%& & &_ e^{i[>H (q_0 EB$ -q_L\sinh )-q_T$ (� -_q)]} Y� �+�!�{ k0. \!\!d]�K h ar�\,Β�fb�\} Fv1@.�!K-!�in)~4 )/T_{ps}(x)},6% !�M�Qw�with $M_T=\!\sqrt{K_T^2+M^2},\;\vec{K}_T=M� 2 (k}_1+ 82)_T\,,\,M^2=K_���t=m^2- :4q��$, $Y$ᕡX�l spon3to_ ��%�5�,e azimuthal �> � lɬ�� di���Q�6~hi _qW� N��C�  $�q} C K}$. $AQ_e�{P_F} " $Ac:re de� in� $a� {P}= _FQ ;)�8=1,42 T(x)-12,7�͵�p��00b�4 few idealized��s w�*� then som��s mpresen&,2} situ%e��r�!1Xed. For example, instea�$��$2&-%.� %&&\l)�C(q_L)\r =1+:�+��i�-�^{ dK_L 5a�600T40^{30}dq_S % 6 oC(K,q)|G �!>\:�a6b d>o < g�� 6�,.� %:�B0��R0 = >2 .�3�2 - �1 n0..��_>�(TU��\�A�6�c #��). $q_O�vq�e $q_L$�defe�Jd!def���fig1_WH�i� 4.cm' "�c� By �i: $Oz$�M$chosen alo�he beama� ���$x-z$` ne. � $L$ (;i! nal)e�oI!a vecto� �  $z$#, Y@O$ (``outward'') ,$x*� $S$ (``)s* $y.+��desbt!_& !p-%-n %They%�&�%rediv�)�du��!h+, % "�!size (s du�;���!)3ex�, %,mrad.An$nuclei inv�d1� %col2 )� &ot �P /�O*� ��� histo��csa1*� &7 a first%�����#si�cc�A��EX#bove, �0"- ('col �s�J�1��� . R�'%�ͥZ$s"� of i�,e�Ci�J� HBT1APʯ4_HBTq�9"}\hfill2�# fig5B( V)6J)� F�*l ofR8� =: , w���-E�cJ�ms&Q.� fig)5:tIn%%eA2.�$a curJbta�9J� , we�f�y%Ig:A�aH$standard e/ �14�,  1� 2�$T^ 7_0$�(�)Ek�:g�Mf�Se���~"�( HBT2!A�d7BV;8B(Zd9J)Vd~~�u�Aae look%�1eA�!�y��-t5�7%� )�c%�2�� >�2>�F6*�wo set� )��1(s�#P>! manyz0c�&A@ Ea s"# aX �`s: shape. heigth, etc. I\J A�a�,� 2d ver� t. E*(m� w� �M� o approxi�-e.a��)� F2�"�).��*a ��$ ��&, ���%�q Yc gasA9 'val  . So�n!�� %�iV�i�u�m descri�(Ax �>9it will�,%I},E|t���F�"n@A�s 8/�]� E� again#�e ��*a6earn abo�" ho�ns%*tf"?��:e+�&j�. ( Not aActually��% ,R�!� bN clud� ) MAn&3,we*0 ress8he ``\"puzzle''a� RHIC-(NeXSPheRIO~� hbt04}:on),%� .yogiro_A}).:�(%|us�vaiJi"�).� i��0onh ough��B {,easH%i�$,in2al�+s (beca�(� ,eq:glauber})>�fue6!E ��!V�), ��u' g .�ay�ɮto%�(mportant to:�"moJum �"w� i. " f. P!}\\��l0� �/analysise��  a)�� ��M�oA=of� � s�F���0� "�$. ɨ!+$possibilit�"R-F� m- �.q\alread�(must discus�X!� 2irH z [�BfR I1�D �b�$!��J  b:�" i�e��V��aons: 1)�.a�" em�1b!e?surface,A�!9� &� , %31� U ic m��&C �c�$ , so�robably�)�isu|*� E�� fkly�%4!6���7� A�we)�conP�2$so far 2).�is )�! colo+_&!��"!�recombin� ) !5let�/!9 �-P90��Kis makes*����2!�n ��(. Nd3icA�let us�! u �&phase ~x �+��E)�&I!>aeson.2�%x1e�8 �e�O a MIT bagF4!�r��e��u�T-!����;/�2� � adjusM to g�-�(ond2�A�.�' $T_c7 22� Ee$B  58 $$fm^{-3}$.2+�s��0M�(H �N�av /�� ion)�L6Zloc�;�B�)ieK� � *�.� &] qgp}?� � also �6!Dž�of�#� A��aX>ihgq R� .�2boxqw_qg�>T2*�2eli~/"� Evol� empe&t3� �E�!���� Az�^ boxlike ��distribf�op/softer,� to.-&!�: �%h�%~/�%�!2�3hg:&�"check��#,�istaD}� i�" clo� o1����< region. Contrar*��r5$���s�c�8R��B# zeno a�aK99i� o escap\ ��. Nowe_.�W 2)�Pn&� X$� �/$mechanismslraf83,ban83,mu85,vi91,russe}'&V a� ���)*D . To��rt�:c � �� Vish&�+� e}����"K�M%�{i�,es!"�gasf �"���e= ��ul";7]+ ���+9bJ9E�,d^3N}{dp^3} F �  �( %\left[ [�} � � %( p^{�} f_{� }  \rD )_{|_AR��)�mtau~.mrho.mr{mR_{A6(;)} ] % ]y)2end*Gu$26"!c� us up� �%I|�u.K6��m|=�!� t1)�ve�5eNerS ��Kcalcu;�� P$, ( �appearEQ $1u$), s�%aze�&'Y���"5 supidetroy{ �g�2ᴅ � utoff� $� P}= �e&t:d. Du"-$� a|�sp9=Q�e�� �)]�,�do� �ctBd~)ic=Qs_�@ !�* . O(ur�(+%�of�, ?� b@"= (t �-latp7 QCD�Z �fav str� >o ). (&�J� is9eQ2an-e"R a~�0improved e.g.ia�4 �� )<'\�2{C�� }� ��ph0, �� ed"f$��:� s. S0 �$zś�!��^ monly> d� �bed�of�cavea�n1yB0. F�TY le�'�3� �e?)$Cooper-Fry#(�cD"8. Wt= � C� neg�/��y@�vioi�O� �hlaws. W"b:how2 avoi)isK m"� y rex� �0�.� .�� -ros!�1=�� . +'1^bin�:6� a��!?�Oųtyp� 5zB. ones� bu03�)Assumc�42.�,$hold true,��l�(��-e6o)W�7g�r��Ti�;i塺���� $6�4�." ,)D�."m A�!\SA.;A���*a4flor}m�p�?a&�?�+.ral� h  suggesX�e�&� � . No >Oe?)� simultane�2">5 �)+[s achievx@�E37�V�� s &w hylaw,�+J�6( �)��losF#]�i9A"incorp�5�R�\+Dcsernai�AfF3A aAa`�iacop�C��dD��5e=B�29~B�M�(Bra,Sor,BasyB���t*Q>�A�.,6M�!� �xt��h/y)���lp�De�E�-v�:��sP� *f'/yA�'/"� ��e�-e�w %!�t>b.�Es���s,,B%�ansatzaHimmedi!^re� oM�r�%/C. A�;�%; such1t<��-�]}.YSi?n.�thinkLR<� d�0F� B' O not triv7:#!p�`a�"V :�*�;iK,��&�� appl�8� Z���promia��. \sub/Ac� ledg%�} ˡjB1gy rA�Xby FAPESP (2000/04422-7�HauthoFsh�|�ank L.Ci�a  S.Pad�Q ��4l�y!2n<u� pri�;o sub�7��@thebibliography}{: \bibitem{�� au} ``Col�� iL.D.Lf,u'' p. 665, DD.Ter-Haar, PargamB,Oxford, 1965� ef2} E.F  ProgA`eor. Phys. 5 (1950) 570 �- ;dha97a} Y.Hama, T.Kodama \&%$iva BRev. C5I<97) 1455; Found.A� h27i 601.�,ag02} C.Agui�Nr,T.Osada Nucl� A698%�2) 639c.U ha85��F.Pottag �,Bras. Fis. 1�85) 289.BLcs03} T.Cs\"orgo, F.�!, �X5 �$Lett. B565�$3) 107-115�B-Y�3�?:l A320�3) 371=b ha88.�u�)�E�D3y88) 3237>phM40\& C.Rold\~ao.BC58E�8) 2906BA�v2�7Aq20A� 637cxgr00}Be,H\& O.Sowski Ju��C62%$0) 044904 2]98]~KI�80�1770 6N9azON�33.�gr99b�F9� ha91.�U} Z.)�C53�1) 50.� na92�]�C.NemA�Q�Z�4i2) R2552�g ?�+3�95) 9;�7 �6) 153.�ma�>V.K�" gas, Cs.A lik, L.P��, � W.GreinerNn0Zs.I.L\'az\'aek,H.St\"ocker )EI B459%L9) 33;6092C A6618596.�ar��N.ArbexVe>� �M�4E� 1) 064906=�f 4 Yu.M.SinyukovaQV.Akkel�A�q �T �89X2) 052328hi�Hiran�7671) 2754-" C�R11901; T E , K.Morite�Muroy�KC.Nonaka �BG61902G�K.Tsud62 �y 5490..$he87} U.H�O,K.S.L�<!��87) 2292Z@��le� K�2H�q V-�37 (1�� 1463Shu��C.M.Hu0S,nd E.Shuryak6C5�ס� 1891Cleh90}� Lee, U.~ ��$E.~Schnerd�nn,q�,C 48(1990)52.:CFL F�FG. � �%�D1�G74) 186..�Bra} L.BZS�E2p354e85��6.�C6X99)��5.TSorb Sorg�q� 373 S�\2�_ S.Bas"QH ��C69! 9)02Av}g be969 B.rd �,6�60�36) 566ri!�(D.H. Rischk�rocee~ sE y �11th Chris Engelbrecht Summer School inV/ oret����PC2TE�Febru;F 4-139 98,.,-th/9809044.*�an99}�l �m68,.�.� .~�Q�^�I)C�A88.o��b} `Cs�.lv�B ,:�:�$ Heavy Ion � ��193.�taQ&$K.Tamosiun�nd2� Eu"� J. A� 4� p &G csM6=� E.Moln" A. Nyir� .~8 hep-ph/0406082.lmaO PA�6^C �P) J. C3"p 25. tea��D.Teanaym- , >�4 O257=h B!�& �&�B_B� A41Ja.g�.P, -@%�ek*e17.� �2hFPJirG &33.qGji, VG.�vVan HK%m�F�1!{8)5764=|b>����Part.e�IY4��T25.B$ ~_F2 .�)��51.� os� .�@a� .D. �Xis, april 99, IFT-UNESP� WA97� 4L.\u{S}\'andor � ( )� �G0 4) S12.NbZ M. van� uw�[FX( )6v78�@61.v"�^�<� V�22�sj^,Castillo� STAR^�8.^\omega= AltB_:-ex� 9004y�&�] F.A�or"Q�9882�B]y�B�> )� 6� n� 2004, a�ec�m�] C �Y G 1��� 2)31.�V J.>�VK [�47.��U Sn"E->f6e� 9)41"��T �=>;1AfS@r�:R.A.Rit�BI��C77 7) 535.�T} G.D.YU�az� :56��221.yea�;!�M.&{T E D"� 272@ JM}��Lej; �� 7U!y53.�~Mz~ *�94F�OY� Y. [ ��B� q.}.*�K")�"se.� ]�GXP��S�V���)q>pe�J K.Kolehh#e�$M.Gyulassy-�-wB1o198� � Yz&�? U.A� man P� , pt. 31U 14.�� O.Eua5 %T1�`vAD t.93� 4)18Lu)t76f� 6�9>�V�+�/Danos�&1J%�*g 62�+L} B.Banerjee, N.K.Gl�M�$$\& T.MatsuSiB12� 3) 4Q � , }B.M\"{u}�W�(M.Eisenberg:� 43�q791K�+A.6 ,�_D4�[�5t�,D.Yu.Pe 8 unko�4Yu.E.Pokrovsky�RI- A62\7)738; <002068v2.�k$W.Broni~a!W.Flork �%�.��5; Conf.���"�17��2\, A.BaraI�.enH8.0 c��#S ���� 4010���Dt:�  docu� }4l0e"�I�DL�DL�DL"DL�-no)/\\ FLK&tK*OK�KbtK 2n& +WG�G�- �-"DM�BL%2\.�\�@Lb@LBt-<&1E!F�=LN�]N}n mi ND�$CG}{C^{L_{ % N}~M }_{J^{}0^{'},~t\sigma�def9?$tretch{1.1"#g1�} \draft!�Atle {Enh Ce�.i�iDf Spin $I$ States �$Ro (m Two-body VaT} \�${Y.W ,Zhao$^{a,b,c�MAbima$^{d��DK. Ogawa$^e$} \vs%V,{0.2in} \adm>${ $^a$ DE_t� ���VTShanghai Jiao Tong Unisiity, � (40, China�Z$$^b$ Cyclo�.�� Instit�,of aal ChLm�F4earch (RIKEN),MLHirosawa 2-1,Wako-sh� Sait�$351-01� Japan 5$^c$ ymT%5�'�j�N<8 al L�ory�6H"'Accele�_@, Lanzhou 730000,.�d$i Sci�1Museum, �;%r,Ө Kitanomaru-koen, Chiyodaku, Tokyo 102-0091J\\ !�^�Chiba =�L Yayoi-cho 1-33, Ina9 )263-8522^ � $\date{\tod�TmaketA�A�'abs�X} I.�/ w�Xud"=behavG'of�k Gre (de�5d<-*%gE_I}$)2sq(r0�-q/qYre8 twoi8�*m8, �'( systems /g�'�12<e $(�, 8--$j$ sh�[for 1�� $j$) )LD g/l a0 mI, �DF�?�/�3t�ities�;=)iso�denq! �,,dom). Regula 2�3>8's�Qsj?-Q*%: so-c^bd geotZic cha�iity (or�9si-)W�o.1^coeSpi]3-kal �Yntage) �,0q�b�)s 1fo�j�R�/ even5T )�5��C[ 0 can�*T7A� ��hIn+�A 9,0in�q2-bBop!Ny F0d``break"6r6oB�'~(6y( \pacs{PACS�80: 05.30.Fk, \45.-a, 21.60Cs, 24.60.Lzi{4newpage Low-lhI�4o�1nyI�QgE4��!Q.�]�*4n NAexaS �pJohns_*Berts�,d DeaV.Re",[ (}�� �EaEdArQ.t (TBRE).� ir ?�s%�ed�Are�Teram�${\rme�}^ )�}=0VkgrE7t4s. MIHeffort�cyB�dto �\?d thise� �es�_z1��g�+��^g>�e�� 5ti���..� j���?�S��gi]gdd-!��gge7 of bN0ng�.ies, g�pic G�ev�z v\���Eg)<, .I,�3�q�ed muA tten%in�A�]yE8. See ]>F1}l�], �Among %?�&FQ5,iof6o%�a{ AG0 Hamiltonian,6)nQ asJ)4>����)�I$� dŞa,"�8(I)rc�Pp�Ci&E>�C)�pst)�y �-g all60{I'}}�N��U6��ina�s. �/A� ,� x<<2� �0g 7w�6 $I�xeq I_e^(min}$ or $I�A,ax}$. One th@vvidO/he %�ctw/se[1^_�/t�<sN \ove�nE_{Bcin}�WD�Lw9a!� oi�Fu>* J� S��6r8`TJla�s .�I�<= ($�-!3)�:�3O�b�J�2c] ing 6�I!�v�9e1Cw�>2( fD�B� V)ax!)A�2�. I�uMkMlQkMe�A��9-� CI(I+1)$%ѢJ>1>[U�ax} (Q� ax}+1) - c?>]Y%?$Ca|u5��KMw�Vo��occup�2�2le-�* orbit�zn�5e 6�4$ensemble. ��se fe�v D&l5�5�,!xquBS &� fS �S $ (cfp's)1� �)�,��vi>���4al views1��7,Mulhall1,Kot>z�E pur�=�/�B(Brief Repor[ �J|st>�Bv�I sdEfEN%a'>6?�  >�j'�H�>��'s &Z ŗ��b\ ��2[ �Nt���� %t�  . P�� 9��B��� 4N2' have� �tri�Jon5n�( �3on� on.� �4woT � s. H$H| %m�7I��y!�2��~�l �2�!�_ t $ � the 2U � E�/�X� .:>��H@��:` ]9.�s�Yed ���!�ew1�]�ak��ͣoA�*�  9�O;x ele�sh^�J���^ I�IR $``\pm"$ �afJcr^� by6{I^{\pm��.X X )$�� i�99�LkaMxPk�g $n$. ton (neur)9�9�6``s p}$" ((n}$"). Our ԅ:I�<d�<1000 �����*� . �:bj{� 6{, i.e.,2�akQ�B��Ui ($j\le �D 7}{2!�bosa� P� $l$�5dYa � .H a $j=5/2$aD$7 E|.>�Q�BthlDI �W0in Eqs. ~(2.1�� (D1f *& ��-1}:b{aA�four _�0�����>o"Sas)�Eq. (5p.� PRC-200rM�Eg)�ND7A�1� =�%bt�\���9�+empir|- rul�!� �M �/pl*� ?s�y�(Fig. 1(a-c)B� a mO ? a�a�A�L>d. � se� at>� a|� !Rj� : � , excep����2p rn� �Jk!2b�)� t �rw I32o%�'sM:bAW��YB��N$j=.�,>�%jI���``�<um"� � L�NWU�EVJ� b* 's, ��U~y&� Q:6E*  e> � "� i b�?Af� �gyBAO��!� $n=3$�'m�, 6ai%2 $n=4, in )�, (a$'$-c$'$):��Ce��A�' .ba%Z&�Nely prof io�*$� !��J��.�>� �$~�? �, $l=1$ ($p$ 6)�Teasilystood: =reA�B! � �? eachA\;6�=$50\%$!r $I=� � �g iq�ExaM� $I$> s;60�followsah>=C -"qYpGm . AE !2!d$)-;�A+�:+ ��IC, 4, 5I( 6a��� A�m)��h._8 ^ >]�E�2(a-d)�A�dA�e,�J� Z���susYl A TabArkr!Wb�P(e��� nt�A1MN�Zced. �.� �eigen; $d$-E�"f �e@n,Et can �2 ś*��RyN� DqW���re sop�a�level�5om ��$(2.7)-(2.8�s�����,rJ� "3I}2,I} = E'(n) +�p1}{70} (10 c_2 - 7c_0 - 3c_4)=v (v+3)}.9$14} (c_4 -<)m ~.�od���:CY d1})� ��a�!��� term� 6 I�:A �Jis _T.tA��secgTis EIe�H�v �$�%"SɀMx n��borᆁ/is��a��5x�C egligible $I\gg .�;� thir� ��Qc]�2�F� b xbb�V�vominan���$I$�us>Uis &@e�B*�UJ���#��W��eaJ�D��(F�J�I} 6�R �m �f"mpF���A� �p�;AV is $.�� 0%,�C�va���� "F $ 1}>�w�E r�}rL :y��m&& C=y14}�! 2�!h\�m2 �}  }} \in�P-�Px k e}^{�m{x�j 4}} d}x = a� M c1�- 0.0806a�q� C-d}�$&�$��A� !J�P���QB� A�$A -0.73$ O]�E_{J2  i�/eA�es� e O�70�O� A�+� *aD2�BJpr�(ed $|C|$ of ��!")�F]g>W�es �exyPo2������Sbe{  N��]�Cllye"�e��Tw�G���_2��. � exemplify!�a OTS*H�.eons �*7�s: $j_1�i}o�� $j_2 3/2^-$. i3^%�}R!�&�7m}Sn�=!D �| �� }E}&!J� �ɇof J( R+1)�^6=d.8�� +�}fe��ila�\�� $a���[W 76>.{ .�e��� V�6Y��"b�bn�K� :%n�5�lEZf=. AccorW� �M+ 8,� um!�+}"guL(I^+) = 41.3\%$ whil� *-2*-*L58.7\%$; $C^+=0.037���e017ET- 59 \ 29AT�Q=��f| "Y$�~���yH $d_{3/2} d_{5/2}$/els�ZlA�<;ks, $C�401� 17 �r�O�c� &� Q� �9�EC � MF.:a��2=� �.��~a�B4+ �>�space� We n�� J��s�w42G�!�"��fre�"� g. 4� s�"a few ty�O� pl!�fm����\J Z �}���w !c^r Br��"b�:� in5� "�.�&y�I��8O $C =�354u03,411 50. am.&2� xn*p�  ��F| 2` N'M3S��6/ �ber�bn �O� n�6+�6"z �%J1��*.�I��uZ-!�� �!�U;q�*�ZF�Q3� *�_� `�9>��� $a Gaussian�N5�}dthN �, =� E�{� �$} ~ J}� (ft( (2J+1) M�3 (J(H - 2j(j+1))}{2j^2   (2!�.)^2 } 2�/&j^Z k �3(1408 j^6 + 864 j^5 -4296 j^4 -512 j^3 + 568(L2 +558 j -945)}{560 *�^4 �^3 } }~a��b!<-,/.+6] 0 gma \�� j^{-� j$arrow�^ftyF�E,in& J�IN=U"!��_C�. � )>2/M zY�"?Re&X$6 � refVg�or�Ral� &� h j^5}� tE� �>limit� �^s"�t&j &� q��-�1}{4j� �TT#IG list���*� by &b+methodsaX�E_%� ��a�atic �.repancy"{a�*{A%ka�AE M)$9�e��Mj� �u2� >�� a��� �.�should�clarif��� NWm� �bummari�Ris�T!\�� =�*�-of :Y( B� s�.�'�-&� ._ Wrst� la�%�.Q---6� "re Eh�� F� � m-��2� V !� meq $---hq\2��%�6�!$�l c�#<e be(ed ``)5"%�stpl.-�\ &�.5��'j�J , &�&� l> %'�Y�e%�, altho�e!�J�#ofN�I$ �.re�~][�]*�x,6�,  {\itKznd}�anv>�!��!Yy 8 vaila�O!z[C .��>}&%]yA�!�y�)�&/ )�~�YhK�iq�rigin��sa�&�/ . S#ya�w���N|!U� robust ��s� �a!�it�*�#:2��  aY��}ZA* $m.�$Aw �"�hel%�Zl Y}:>�)n� ,.�. $ !� %�.��o`} �]2#!4� � � �#%TVddetail�.�+c>.lso�0-_b�5I2�i�!d uni��l�vY but1�b nall�^�gOk�vA��}+S1oA"em� |-V3a�T�-e.�s h$x% vari�.s.�3= q�8uker} VelazquezV�%d���6w�QFX���%i� r bo2ofFfor�T�TI+-�,Papenbrock}  � Weidenmue�= deri�dA 2!cof/NsF�a�&v:%i�$!#NV9.�0� "�]!�itJ� �aip�]by�ong fact\ ���� ��. �fur�"*��kE�F4forQ Ac��]eA�:!6�thpNDrs. V.�8B�@��W.ntzP"�4���mun�q&%3C��s:a>,g. ~ 1 ~~~�52�'�+��barIF� .b �#B�%�s)"�q!�4f B3*.*6~R�%qiF�'* ALE�p#A�2�>�/ mszR%rc ��2@%�:�"S%�sen��#!%�#] o@e*&% �N�^E�"d3 A good &;&+2� =Bj��� >� .�&�(ha�'��� see� dooa3�  (a�!D$%`�$�to gu�n��y�� *�;4�;�$~ 2b���"PQ�FLE %�d$#��%3$.�"6. 2D} M�F&�#Z4 , .6�'%��� E�emj()v�R� �rR�BF#�)s1#Vw� � .�B �fl��\6��"x=2�3-�=^ � E�1Ɏ�!I%�Fze6���:�5N+^+,�{-0 �;�A0Yn�] a�po8mv"� 7B%Y#2�a.az�Fx$1����5�� � ���>���of?82� ,)�*w �C"� "'~ Ŧ:�q�4Ѡ-l�+�N�J�%Y�Q��%�val�.� pr&.E��B\�-BE{508@b�[J/ C. W.&?:[ZE:@D.yML:2�GL@c�80}, 274vZ8).2W�/ &�@3F �6%#N. Yoso@ga,&�Ip. ӑ40^1�H%��E}"0A'HK]w �S)@�]A13}, 10d 2); 2�[A\.M"4a H35}, 857I.�V x} .@:Z2v�G�G^C66},4_323YX2_&THg }D. `Volya)0V. Zelevinsky2a%�85, 4016]0]5c�}?K.2� K. K�YxA�>v-�E6! 0261L�O! -1� - 34302 E2); ibid �=-2 ���"R/=�%�AQ�J�4!�41301R1!#��mMIacEo3M  :T%��" D ng B�0 Mo,} (Cambridge*�A�4ss, %Eng�h] 87),jh~382� %�6� A. P. b�8� 7250�d%55�&s Na>� H.b2� FgI�$93}, 13250�La)�B�I ��{TABLE IK.Ls/��a��-lumn ``}"� .X3ru�q� &23!��=umn ``"�BJ=�]  ula &[�I<1.�ha�k^X k Z-K"�.�e ^W :y�"8�+V�20icl��4,�+�1"�U/.�< L�)�^vs>�O%� �"�<6�P���5/er (a��70-80$\%�C�t! ``.u�"�>V7. E��3� �-aH�{cccc}c�&H�2j�E&ԉ�  Z-K \&u� v�(& 0.01374 4�01235 026�\\ 11,08 82 690,�.C047N�0.0044445�360-2[#23n� 268-171� -7�#1-1�#096� ->i�-B.� )c#d"�M��% Kf0$!�"cWOA�jWE��uN��a~a ics"p20. M_H2003 "bK class[two}|,12pt]{n7�u=tckage{ei}��� keys-�def\Journal#1#2#3#4{ {#1} {#2} (#4) #3 )Jef\NCA{��Nuovo C��o% bf Ak*& PHYS '�;ic"�JNP?"9m>= MATH =J�th�]RO !N�P)i#NPB #NBgBGL �:#>�PL HF$HD lF$DlF#-QPR2 �} "EV%s a"P2p2�4ɝ9�R2�#�RC.�#C�2"#5!ZP F�W �DZQ:!�ANN �AnnM  (N.Y.)- RMP ��j &� CHEM ! _hem: INT IY�AwoC)7EKr{�� rz R p p P P q q ss{\m�Nboldmatw6$n.�N be}{��"1}<cOe#e^!beaE* BE$ FV" nn}{"� �@Ltopmargin-2.8cm \odd�� 1�!>KEw�! 18.5%h01t25.0cm ѹ�T\title{ ��1cm} In-D8� pert�FH�s -- Ob�zbles II&�Nar�7b�G��inP �K ph�,��-i. Af[a�.t�B6%'�A� �w�7cu9�a�9��� �s�v�4r�;J1iX% $2\pi $-���-me� ��A�Gx 7 ^0$ m+tx beR�&�} by f��1T�Lq  zB�g2YFsem�NS�- pi^0��Lnne<'h� s6 ajor�r�!Nt9Py.5�$\omega$ p�9�!#�,TAPS/CB@ELSA*�' w�yҍ%� $�40\gamma$ decay� illu_Ot0 vR ngth�-�byB u=~2Jx (al ac�<�T:�~s�lQ i:T+N=c .W` dileptonBdu �-"ew+GeV�geJ�3 }J2����vF��inI9B�.�s�G�aA� ul��ɳ�. h�QaLKiab�.�#ET�!�on-go!]G7=�68 JLAB�,�.-� �:9�i=10�J20%Den��oW2A }�k� J�� biza�A�c�e�!/� �V(��-e�v��d9�a:�ed2F,! E� low- $(12�) �HERMES| %1E��nne��"�*at)>�Y��( %\eject %\�%ofcon�Ls "j�IIUM� } S�*6�!��o&�a�C���)�-��1n9�- moti��M�$m* aqcԡ%ca�~M�!�ba�ecurso��en>���uml��st*ګEJar7@ ter.�EA��k��+ chirymmet�QQp9 at e�manifes!I.)Z.F" Bor 0��ong2:�Cӄ,�Eof%\iI��c est.�$ent day's 2�m�-�}� expl�(�&� J �o-+t(s high.�s ($T \�%$ 170��C^9de%7e%(e� N( �}e��2a 6bKha`r��r*A%olL� AGS ���EAr� U!gpli1CBM� a4��FAIR fac|N�-8} may yield ins`+!pA�rea. H��, F -6seiE�6��ede? stil�Eze .U $ 12)V. Am�B;�81 f/ble�� seem."b���lor�����cAuuct� 1Aei..׎s $T=0�)�y!\mo�Oqua�#e <:l�'of `aqx, ���:I�D6O of g��!}eA�AQ�if�# ! Yac�1������ sign��i� si�yst-%�m=��7��/e�1F&� ..�$ro�O_H� q��W�TM�' X1�of�~�"�(G�EX� io�Y�geo�4Fb�%�M�� A�9f� stel*�i�M 1te& zJi I}�m*� ��'lev�=qu#VH�0� 2Z!;!�8V 24n c�'&. Such6C��mCR�o��WifgG &6=��eE�Ea��aa�fu�a@ diumA�EkinT7cQ!em2���b�embed��e� A��jfCs< "2 %2ro*ir� � ��se %h�y rave٘6G��UT e�ar1�1hwSt�s. Ex� U��Dv*l�omagn!�q# (J s,"� s)�.i���� often~��� �I�j (FSIE���Mto��a�qa�.ic as 3�l�a l�!Zoh7G��*8,A�#a�D��absorpL!c� �{Raa��-p�ha�enA��Vof�P�!orM�)*>� on i�O�a�. suffi�Y��F�4nl�-eY�botal łs�l��b�3OD"Qaims at,� �7jG��A1�qp!� �9��"Ɏ��de >$E��~ Q��sc�)Y�?�JfeeA� tM�coupl�h�l effect�-a �E>a�ul�,�4�@Q� Ao�L�bs��Hm�t^ ��@ Shad�5IG)�5 pape�/!!u���5fd���th[1o�D��mV ��sA�le�pq��rt��a�.ca"�b� Y�l%n ref�To �I�Tibf�)_!sg ir!�� !�%�ing� \I��J� q S�(a�UD�day��Delta�/e mT� deal"Z$T"� @pr��e�� Or{M���i �0Ericsson-Weis{�Du�+ [�:RD$p$-wavE��A=���e� ons aB���g+A�: 3 bp[hE�D, -�F "m� �~��in̝�vm� q-��ity re r�Yly,.G��3FRS GSI�!�at�.!�~�G ��in( N+�Aa�4!vacuum i%Kienl!Ka!&{�� �*\�^�@�!%"�M)A� last��Z9+ HF��� exciUTQCD �IN10�#\b�� g S0" %�saGoldst!�b����3��5bA��irectly.jG�7 � densrd . InŒ? ig�Y.;5H)kd(l2�)f  } ba�\on� sum P�ed�Ta �  �ntB�.�%�e%Mq+Y��\��v��ݤ� 30\%"8 atI�"� N� . A�6* a��= �IA�6�"k�Leupold, ��[is �1al��! �gs�Sg"� �;*� 4p,K��R�! �:��[� "��A shap�re�EA�1�q ��lF0r�@e��V o)���e�We.�, `1"Kafixo��;�|*���uE���1I.Dk $i�RturX�1S�HbrԂne�s% "�It aEpCfftM�Postneu}� scen���in�(���_�sa�!GCERES��M>A5 B�0�/�rr #-s�4g�� ���1�3�� om $� 3r�to700$ V�� tSto��sy��&l !�1=ly ra�!D��)A��[�E�an%!-�<� a sh!b�2�F�do���e[sss_�0,�zy g�, �e,6�, Pet>!�,WambachP����l3ite�Z�`E�6� ��-:lZ�!,��/Q > �some D=OƓCad�,gdil,RappWam$,Koch,RenkA&ei�v"�inpy�s*w �=if1f�*o��in�is$ 8�A�� ��xvee om{�*-��M�so�� w&�Qb��a� �3A�  rho&� &6"�$ih/J�$Au + Au����qm�waK} at ���!}�w�own�N��ol* se�4$. S- �5!c$p + p$)O.��usW�9 ���U3sl� l��s�,,onounced (-4v),j� ,�-spacA��������sa<( �l:tv�st�Gl*��s�- ����!e�0cN�A &�� a"2 , mai1�=yna��z aYsu&�:y�M�e�d��qa��#r+�(I�mu��e)6 %6 K�?��\m" O��>�$�ye� agoaP_d7f[W19���p >�.�y#B� 2Lon�Bm�� i`We�m&���be��HirLgg97,| e98,}BڜiO�dey feltq�.����e"�s lhmPf��ٺT, s�� a] any�-��-�x(�I_ �� pD��eA. 6t�han �a big ad(a���<o�s:9 y!zڈ�a�e��M� �,F� .��sis � r�b��al�e�.2q^�:"� anͺ"nk�" (.�)E�msti�As MCE��a�.� w5�i� �`��.��6>�2�1c�" �� 1�--��� . ��if.�S������i!A%� ���0coo�"*e��� "���A��]" al�built upa^�gra �%�EMse &sA�| 1�A�Y����i0 ��e�ep � �W$ ��pro�i(h a9�z . A K!yal�vCatð�t g�iniW-"U of je�,-DVi.�E*&!iA� �Ia�iA�&ME�,.v�orm� I�eJet}. A�:pl�:xM�ie-<8Ԟst "-! HERA�,H1a�)�!�!i�!�HHermes��hB�����l �9r�t�U�6��M�A���hK�1Ta�e}Ene�.d����H?BoD5�e�*T *oi-/ R�%u�of&��v�%"w�qaAtg�mIin�!s!i!��<-��KE+%/i5!demon"�#atA^%f�~ym.#(��q�d#��axae":�"V� .�k�!^$#a� �8,�n���ng r>�&sXo��$V��&��!ܛnuy�(�<%W{rSum Rul�ndS(icc*els} A�'M�m2q '1�P"�I}�[t>�ZB:A!1A�co ��)<"���"k �� �Ti�ic]�%RS Ih�7infer�?� + V� �\( �~}�>%!+*�� �i��is � Ep ;n)�t�Zl�WB%�!`linQ�via�!�"-���[eL!U�in �Yn abbd)W�2�2�}� �)&�XR^tL$OPE}}(Q^2)��({\tilde c_1>? Q^2]2 -{Q^2zM�Y �Y\"s_0^\��(\!\! ds \, lIm} w HAD}}(s) c(s+�s�6/Leq:opeAB�Y�/@$Q^2:= -q^2 \gg 0�9som�b�CE���tants��� c_i$I� $Rs!$p�dIn$ Wilson's F c "�current- "rBEn"���Ajg�� {S� �s/hF -e[r)�� a���A   powl��G1/Q^2)�%ai��`oywasH a ��am��@E�eke�,%{\rm 1�[WbK=�)����o��A�'�� r����ta�"y�!_"T icGE-.�[dis`فa�Dg��M�s u%l�2�.#LN�>"�icɕ� world. It�o�Lo" �=-L�1�,:�fYm=Y�T��tlhE ��9#E�E�Aorhdvo��.J  d3_ce�� ��"Ee for .2 s ImJ�in&�q�%�� �B�!���`!��yI� yQ:�Ani�b']hX[O)W�ark)�eI!��'�46<;m�r�%YKH)�2rB ae�blw*ll��ge"A�#��E �\$Y#@JZ�aaT sketch!U�5measur3�[n�Fb>-)�C$� A��Mto� �o~ �tR� r aEp9l!�F�N�� [�O"8c�w.s='!�� |� !D��oa=F� E~ $E�q#A�D "$jTK � &"e�� �b�N02,"�Tss  G&�s M|&�\*�� !6�iQCDSRa&s impor��� i��!�� �ic�*� "��it >/m�!YJ$ly Kaempfe�� ���z argu�  aV$���N��"I� �2 1q�1�"�/�(cRQhelݱXZUWT�*� � er-o*.�H�� u� �ne&��.�!�� %� qu�g/ el(li��amF!aǦ2� �ly�#'�8B2'-��942)��dea�in�st ��= 6L",%vwng l in: � zero.� I� �J �_v$�)/@ ��%�6F$*1��5M;� t#� {m^*}^2a & m^2 - 2[i \L6cal{R}e��8m N}(q_0,\theta_[ )\, {_v "�5�:m^* \G�1^*[& m�g>bI}mbNa a ~.;&( �sݳJ8$�!�for*�$?btudr=�"��e�M $q_0�f�of*)�$ �0$ [rs j/Km% (� �\7_�imaw 5arF(V�A'� �.U� on� * - � = v:Pgma-�+EC"S�ere&�UV[5�&���anD(� as�)bm+Ez:optaO orem. U�J tuna�% i "a-p+i�Ou�[{I�@^v1 y*��E�)�usefu=��,Z#.�h��;�# inv�g� �J"+a�a b%ed-��+5*�%!� selfE%i2/i���4is�+ri]�#s&-eta��ce�@yl@- baryo�n*�W �Aw.�A$��n�,!,sei�� �of �s5 f � ��)f!xles�n $0.5IG0$c o)ar H3�M�. inAVnt��>�badly�eĮA8)��  pi$ e��nO�4E= a!ble!��a� ?!o @�K/� M�Yevi� �inf ty�{FK�-@.Hon, Pauli-blocking,��7���short/�gK "�I�'*� �*x sour!�-D�-|7pre�U:�L =!$�O�i�[!s act�s�Pe2>�m#induc!�I+�+*:"-G0 $D_{13}(1520�ea&�repul����&;S_{11; 35)$��6�tom���th��!� �+�,I� 'q�!�.�.Zof JN.�� uA�� ��*6%v�e]i4  �o�6�Aia>u�(e��G5�l�.Cf+Cf+T^-� of Incoant"�A��6� sec: G F} Very� )�a�.�a�($��8�V0�Ize"�+2$ ��or;+J/H�#"K4�-3�� z�4�9H�!z*Gՙ� u,Ty�V�"� t �get�gb'FXF "�"A`G��L2 alp�"�!�!�-a � o���$�|,^lv -- non-*EAve�a&���{�M.��y"bc3*�/{#�-in a \ �ory-| r�! ��"i#)"$eds 1��1*A�D� �uryUl7i6̿Ahat'ed �y�  .�s t��-in��a�5�-1�*�sop�r�*Q2of�� i�����a" �i� ��� �uvoi�0se�3rS��7ea����1M�a*x�I3!losalo6?>|ec�� &Y?<�e ~�to���!z�0��i����}Sa� kyI'�Pe,�1SA1YH4ct+���,�H.U��l� ni%t�*��.����4a��o �95(cold).<!_A�AN`�J�. I�Xy�8aw5�.f%�"�*/surviv�'ve�ou�9".��-o/RN]!P:�XŋiՔ.�2-#��J�D#4uclei provides�� an essential baseline for in-medium effects in hot nuclear matter probed in ultra-relativistic heavy-ion collisions. With the aim of exploring this possibility we have over the last few years undertaken a number of calculations �Dproton- \cite{Brat }, pion- XWeidmann,Effepi} and ph.:�>hot} induced reactions. All of them have one feature in common:!y treat ( final stat&�coherently in a coupled channel transport.�, that allows%� elas!�and insc%��hir ,9�q s arCopagaA`througI1�untils y lea� the $us. \!Dgraph{S�.} Ph�N:Os show=!i%� enA�ce m�,%: real-2s fromA�energy!gPabout 1 GeV on upwardU�ianchi}m,9� is due to�r��$ superposi� bare {E�vectori  componeV �:�3is handl�IaPby means�D Glauber multiple ��modelM�4FalterShad}. I!.is wa�0obtaiaK,r each value_vir�SityI9�-9$\nu$%A�I� a spa� distribu%�O& robaͧ�>�a2Dhes a given point;Dq�seeB�ł, �Pinc}. Fig.\ \ref{fig:)�}V�` exampl��b�(a kinematic�uitu����is closE ԭ�0HERMES experia�. \begin�ure}[h]center} Lminipage}[t]{8 cm} \ $m@{\epsfig{file=proP.eps,scale=1.2}} \endIRZ 16.5 \ap!�{P L�W%u)8$ing. Shown�!0=�V�i���A'a�2� (e�left) �%�n.v��Mp!��Z��$$^{208}Pb$�G S��I E�).B)")W} \label!�Q) fi%� Th=�|� Ac^br$E*">�h�� � �at e6&Inial Pr�. �i ��!���N diff9 �9�o��jvariant�0$W = \sqrt{s}u�ex d� �)�on. If7 < 2$�[�� invoke a�r)a����! has be� djus�Vo 2ar data��:-dr�)�  p5M �� �> �%j8 yiel& � edIvstandar= 0des developede highQ�nɧ ��aRhs, i.e.\ FRITIOF or PYTHIA;���!��inm I�neu}. We ,made efforts�uens$ a smooA � �wcross �� AT$ez5C physicYDIS. 2�Fn St�Iy�sMn2� !scribed��(a semiclass�>� � �� 9��  origw� en:t9dh��AzheF9 �?AMsiAb thenEX applied!HA�ou+ re ele�� 5�Al%�iE A^to!� c��5ge:� . IaU is m� !�"� phase�ce .7��ll Q�a volvD V&u > ime,)�^�fe  contacT  ���us � j � � ~ E5ar volum� ir.=� �.�?��4 $F_h(\vec{x},$p},\mu,t)$e%��� !��%� for 10 Ex $h$��&~oA�d a-��at 5�na (Zl( f-shell)�\mu e  $ �$�p x}$. Ia� ime-�BAl��!( d by�BUU eqi� ͤ0BUU} (\frac{\�al}  t} + 6 H_h" �}:&" "r}} -:$ 2J(6p>J4p}})F_h=G_h {\F PA}_h - L_h F_h. \ee H� $H_h)�e�Y%�� I-�a%<be���Hed; it�� DQ�  selfO(D  f��)� %M�wa � ő �ba� oQ-back to �k E'0 eC�Ba2lhe�(� !�)����so-cal� (\emph{drift >}��� �]5P� ent9!+ei�yJ�r� J� �"� �p.�b�z+!5&9;��tw��! �s. %��%f �N>7clu�xthh Y-either����5�*or&�% formeri�)\d��� �g �} $G_h Y� $ on�%Hin.�Iol<�cess (|) d dl� dm$. Not!� e ����orcal���`, $\mathcal{A"� �Ni:����&r.CfY�C s. O��ep raryFe �!WJ� �^�� elf:%��1�e�re �!��%`bed%�%Ps%���!Z!�7 rhs v  9 strengthaC[%rA��s,4 ~ively��y� 1AL=,Born-approxi8o�ll�  gral�Od tak �Pauli-p��'o acc  �f<U� psAmselv��re On&za&� h &  Eq.\.�%�ai��7c8cy!� blem �� � embed� $G1{$��%+6$al broaden�ȭ�9�1 � nd tA��%�. 2� � widt��5U%�ov s!�, _evpa�� a - xvacuum "sIaddw , �gQ�iFedaA F peak�, �ene�C � extra 'po� ial'�$$H$ alreadn�ed A ��!��"��nѭ ���� w�t��� )�� us �m%� usCs � � "� YV I�a-o� analysi� a3Kadan�UBaym ���� � to pI:scheme�A�_!8aeof K�=$Leupoldoff ,JuJ�ing}�� � i� W �k!�BZrepre 8s a major break� � g . For furŰ�M�� see Ref. �5JE' �&re�c�in$� {P*#!�N� diZn att�!bin�  ef�)dLehreta-�resul� Pq:( McIq�"?�e� $N^*q}� to�2���e�)��u }!�ier *� f ouW0-4s � ach% be s� i�*Rel�o! e�%e����n-E� 5N�'A �i� l6E so far no)���avail��Nc>vaKd2e 16.5vh eta-�FpEE6)u��:�on�40}Ca$%#e�e��e)2 ! ��4uppermost curv�� al�% *?�] totaly �� nex D � op89e }�i+͜� �"p �  lowe�I�JT|oc\ -H$\pi N \rightarrow � N$HJ{ est %7a�!6 =3.6q$^2���s��Y��s n�$y coincideN��e�I� }).}�fig.5U[ U|�)���S)��# res�ul�!atE)eL.'a��` beco. im� �`at !7���!"�iA`��ia�}3m�travelAh:���� )� .���2�N%�Q[M�� �� isK lyY�i�"l�!�1 even�n%NEBE6$F�� ��cas ��su!r%��Zgr6�}1oɒUt� m-�s l!�) e��>� rɋ��~.]M�� ub� $2\pi2�  If chi;symmetry�Aoor\aY ��War iso $\sigma$:EB!�� &iso�� should-� deg'ate-�imp% Ivg��c~6Rsof#A�na�0er its "�mov� down�2e -$�� shol�isda enhanc%1�A�%ei62 �um&!sup- sio��-spaca#IS �}&\p `�# Am�meaEMxtwo%mb� Z "�q CHAO>F inMi�^��iM�> author��$ �i� to��!av��1 �%cum&�)?/ ���E>��h targetD�AJ!�^+\pi^-$E�� ��. Accor� D \gu!W$�� Lint"^,IB�'z� i�much betA�suiO%v��7$ doubV'�g f6 fa�e baryo � ��A% *�t� -H� erKtagged-�Kn faci�8MAMI-B in Mainz�!���)�"� $pronounced�z�Y� ہ] �um!�) 6>e�'increaU)� >c (spo� %L(averag�b-&�bed��!��E�is6�q ��� EE0AE 0$ but no�C!Q \pm *� s�  A�e��la� a�a�y Roca e�). �Oset2p�%��; �ڱ�is �ed dynamBly ?&��}Ņ�*B%"$4itude. By dres)��)��~a� G�&b&Q' -hol op��(N(F�B �� ward6�%���'� "�tI�a dropp���$�M$-Y) �TN�� ~e. aA�e�*L����m~�$ !" [t]{10vl 2pi*` 0.8��$ Y�$TZ6gR�(�$�O!1I�\pm$ (� )����$on $^{12}C�"�$H �RusA R$solid �%��e�)urA�e.w�'a] e dashe / �$�,,``Valencia''Dic. ypof8Su@} P� aS� 5� � 2� � �zAlAǁV�i��lutely*./to��eER�&�Xe��%�2outgobaks,���+" not,A��<tali�-�as1sible"B#� refor ake�aE�&�of2�2�ith0*�a g&) qom�*�-�� �:ne&8u.study..����G�(~C1��#J3� f' q&b ~|< ��a� �um well � ��f��in�t)��'-L*?1mod.ua���aU�is�1�b>�a s��_)ae |� quasi"�/"��!��A��@ surr��A��1�1�0so%x)>2�:�/of.�-�u� B]c.0&�-ag�A� �oT�a�%� )�s+ fair'19�E�y9a\l%}�����I@of�(6�tI��� miV rgeda�Fm�E�. our�orep+ T (�+) �0; ma��(by up�f a fax$�3�j G"� in i~� 1u a!�� too�,��1 l�3r�/ !L)� e.�" ��;�neg��ch!-[�/- 6 Aq6�v%�F)�ed O repa�I"���,h3� stQ�"'!y2� normR2�2]�+� o$ error banD us ul4>)a-��.��bs�) !^W5���h �n- m���.�� b� scer�ed�)\s&�omega6$ Man�%!�3y���of&�� �in� l'�5�d�!��� IsP�1s,KlinglV5,artly becaus�P$po�� s"#,a� terprete��A>CER6x. �c�A�,now, however�`"nt��&�6���2�is �>a.��qa�K.�y�%�%�s� "��5us- I/E�h+ ��e� ;%a]haj ��_"D $1�Y. An }*XI�,e $A(\gamma, 5.� �  ')X$""�� SM1 �*!�3 /Crys�Barrel�"� s at ELSAM2Messch� e varyVthe�+predi����a�$0640-765 MeV) I�M�%m1! (�F50�'"�7FNn�����encou�A�M�sE xcluO< b�jrn 25�� al6�i yiN�o a�e�/� "� �~ �-�'g��*� 1.0ދ M!�"r/=:2���#Eo$�.` ff593}$Nb�1��s���!�&\ eb�>aeIvi��MuehlO|(quantity $p��escap6F+9 �9�f� U���N"E ��e�������of6� p = 26 \% �> A� ���^ , ._A[samkO5\% %�J�E3UL � Si� � &�&�at 1.2�0�2.5 ) �gy,Bc��ac�� &�-^.0 �0��. A�reduc�( combinatorAp�:r!��#Y��/�S"�4 cu�� � &�'�1�"V ra� �k��| žal��an assu *��u�!� !�ei�2����H/itO j�eto entangl !R� a��-� �!b� �t�7han.; �Z�ens���, R7�BrownRho� O�.� ` �!�plete�� U~���&5"7�b(Y)alEept�Q2e�>to "n(A� aq��� !e�4� i/M� �#:sA�a�miwntJ� HR� F.� ��"roua:$2r2U4 �B�t ifb�apes�;�;a'E�remai�(�em�G it-ifC2a]emmaQE<�g�^0 �.2 3 )cayB�>M@q�$.�s %-�a good� be&e-,preliminary  ^�CB@U� "lM�Trnka} ��a � )"� ">1 of 5�����_b $m_)� =  ,^0 - 0.18 \,�#/_0$_im�, I} w�/v6>so��cussed�LmJ�"58*�""� � ��E7� u$� �8�/�~�'  %csM���?7-ee- �a!I%�$ �!@�S B� Dilepton.n' "F6�n-$ron pair6�Q�}) d=xB%�^� �'s �y �#no"-ong\7A"�. ��o to.(ATth d ���*�5&^w�DLS �m%� e BEVALAC!�Berkele,DL�L@8& in a�er�Ry reg,5!�>- : Si0% a lo� �3n+�� ��!�� �/of�� B�below�0m�l�!-"2�  �}"(la�(�9i� wE�foc�+o�'ř5^�)�2r!V���war � (t=e.g���9{9+0dil,RappWam})� radiN) sour� ��be nics/N%�O �(�NQ( um&h| low-H  ru',40 AGeV toge� �a:AD�"�=��onNS >T 2U z�=ceres40*K V�h {-0�=N� &�%apA�{I"yU{�59 9:A�%%t}�!TPb + Au��0�40 )W(��-�f1�t >k .�$s !o�'vidual�jic5��� �%5�&�% fat4 (!x<p�'*h�J $-dotted ("j � *D)B�& 2�$ �A�} emplo' �Xn�Gf���ig m�.}z )I`URr8%�(�  exhib��t l>8� s�#g6� � � � .bR,�&���� ir Dalitz�!.atF�abo�MC50=� �Q . ��5�0��sqF$M$ c� @J �X0or� �es�m 1/M^4$Qdxr'a=,~d�" �!.� to�M*�Qt �#�A]� T&� !�e���3"K!B��'exp�by7��s��O$w|H�<x"B�"�G� review��c*r ). �!M+ � A'�'�x� �Em< �� 6:H� �a�!5�%�.�'inc&%�a�� ar � s. LookwOy1!in �a"N� � h7 a priori}�/�: E�!x�B�K&��6 I�1/2!r*��\^F�Bi%.l��an� �.�R9� as]�!*�- Oy gets �IX!�%� s�Iq߹�. C.," ly m��q��GY0(q�� I<pi \to �$)kwA �&ay�7��#ic�LA�and�d8 ��( ai7. �Fige+e-}�7 e� [60E8lead-1.5GeV-vac����9me�H�<ic��� toUX: �!� $� + &k x5*l� )Add|/d%�!���2�� ��;�poC*o����1���I�&�4�8"7��02"& �/iA�g,Ne5&�(the B" -Heitle0n"'9��-uumZa 2!^ �n->�&� sZ�0*1an �O~�O (w)lh h o{4h !���!+�in�� wise�? &����^�� 9� d D%�7aca�e�H� XO�Beck cruc� inpu?� s&��Tm�CKlM��(-�q*typ�%�{;���� �'!��I� -- af(r] >�K�K&eF� \:����erj2�=�q"� at�M!Uex� ,a3B"�F�� 6� M�* �� !4 I��/"&&��:�'͠F�� a �s&��be drDQ�+,d~;>Z�wP*�Wen�? >��K �R +%�re�?�EGPus $Pb1 "9�;Exe�$ disappear2N!>� �f�� @? %ea�tj$3 :�=*e "� u�Apeo�Prge % *E n@Ka,�q�al��.� � %*e= w" �:�PaK�(in�!:�o=� %� ong�%G7E�%at JLAB�&(��� e���Weygan�N�Ra5 IAy�!ť y0�`��A�e�= -likctromagng"�mf"3"��TG�"-*P4MoselHirsch95}a_w�R littTN�&h�is know�� "a;�� F`!��} ��in9�!a&�2y��W ;�I�xI�i�4 u�s`I�A��I"� O)-%��x a (vP) x-�oE��' n,-ai�Bim�O?�=hcJa� s. S�Iz% !|�it�!Aof nonl!urb�'n$Vo(� �&Q�oodO� �%�Ha m �e�:X )el91( titu�Q����3KicA�3, h.,���a�!uord�T8f 0.5--0.8 fm/c!��$ fr����. DfR!R�a�!5Y�l�B!�lab Ma!m ��; D62R+>�y7y.lc!�p%�ar �E+�a:bxY)��CQA 'micro�H�%'m6 is sXQ�-&�:hi� hr Yhvertex a�is��A�Q�1F� '�!�)aMv. H)�.>�8?�e� prov�Ju�(*�*iV�u-l� 9�S E��M�of�# -6D?.� s. OVl��F�Rl�*�_colp3�@arency�/�Rk >Hermes}�� �!!\/i�1ep* H��.�T� �%T i. D�H�1�� 7 beam� y �; HERAE�� �%�qm>un�T$=2$--20 Ge�PQY#<0z$Q^2 \�;x$ 1--2� C9�6>.�8urwZ&�O4LA>N4 at J� rA7Labe Brooks} :Aa 5x��� �� Řl�'�C�V upgrPt�Cwil ach-)8!.��59oaM �2 9A�@ HF�TY="��Vic7* �lve�Ca numerow>; *�&�SA��La purA���oa%�y�G W>uD gluo*��,struck quarkA�2Al@�eE�u��$ArleoWang}�+*�C!�']V fragca"�7A�� _�R�3e;�!cRiI )E\-x�a�vironcM:Accard 32)J�ai8E6~)�� �nu �i�Hdg� can ��usefu�^i�!!0" J$of jet que0Yng|, n � -F� 2� oRHIC.�O$e�A wF�X neu, alt}+R"���mIfa� e�"b�* � on eELd�|oaa�� tsQ�� luct)>I�-��38 f����Acre��Z�:w7z+l+o\Sec%sec:C�@Ch�l} �m�an-cut �\!bi� )_"R�E)�au e�� �V�7<�Sj:�ah�)%/E�6: &�!2SVURA/[or��$s��qp�o��or-neu2;pr�0"�/�;"71e�-�& H�q��I. As &�(by Kopeliov�^�6M���(�!}� -�se.�i' hort� si<�C we seO46Mto zerH:e$�W al"�Tn= �tU�4Ied�waj�U-Lnel*RPtd*!c&aAj.V I�w� �%��1S�-+Atau_f$!_ restJ� � ic w�;"d has built�/M�Fk be � us&jQ�Qa�6#W$<8^*$ duAi�&a !�P!� �S��a)�rn) I^\l-eqnarray"jZeq:�s} ~_\�Orm{preL}&= &`Snorg}}{3} 7 2D , \nonumber\\ R`:}&=Z^2>^ 0O,���6 $6��$no�!� �a (ay-)e{� 5 a:P% �  �(J� e�o��A -8��Q6uh�Y��i��� =�"2�doj��actM) $M�. U:06ciJx�� cf62z�.Wri/,��F cell� '8%�� �&<alM�IYa �Icon�5���� ��� $Eمeam}=27.�HfO� ��6UBK�� .��A W6&2�!'shW'-�3f6lso capa]e�WE1N�4:e�a+(l, �5�1��i�*9a?e.~atF3$��a�+^ akesY confq,� !�mo�ea:�eip?Fd!\�+*� %���(b��d�2��b2L�-�'0�' JLabZ# �$.s-� �?,  0$, $K  0�?\bar{K}a��,2}$C (&�s),56}$Fe (6&c?)�n�?$Pb-i�: >!��0�!�pbF d� xR�\ ��*��9�- �@&0a>ݠ�� �a��,F�  mo���Yall.7�k�A)Cz��+��� ��A���&� B� .S(��PhD})&N a�AB>��$6 (� Se+J7 2���ee�/�"��5"JPy. BeHp )idera.`�Mre|��:Ad"6� hT"������Eu;� r ge�F� F_F]OP#���bs|et� on of��*�K*'nXr!����.0"+ 0�4��}��a�Q.�F'N' avVwg�"H ��� $z_h=E_h/�jI�d�Y%7~W e(*G��%�l- vis�5�R8.[�%�uzk�IN!>� ma�815.�6���9  " kaonXa��B �Jx4� , �-~$^*N\to K��N$� maximqH� ioE �!9$A]lim�I0.9��A�c�)�� =2�=��t�Q body2  #-/ -�--�by�!2�6�>1&�P--�b�!�5L��Y)7+^L�()))�%$K:K�.T "&���%�)ed MW0.8*�Q�#�Io�)�!�!��.F >0.2%� �a!��k7!6F �um 2�-�� [=�M��HBtI� i�(two�\eme=�P1�0a"�\s�/b�parison ��B�ZGU"7�\� G�.� �g$^{54���2�?��A!�C�*l0ena� )���a�A� *  (Ft( K\Lambda$)2b?e� ompan:. hype�3�+�*[ ���ԁ5� [ � , al{Fgh�B��L,]�5ow u�!!s �a���/�C*-F�saEEeU�q eI��t5!�Ier"| .�4�_{Co[ PsJTc} (�A lect�j@���� �at�,B�on� i%��%� � �3��n�)�w��#�a���Cigt�d�c��weav:�&s Q���) �3iesTDproYfar�2&k`_ilibriu�&0 ��&B��u�T� rele�u%�anJ�l�--� temper]! phent7a���DjIN�. Spe�'"�A�%pu�)�� !��F%!���"�@*� %�� i1!1���C�a*pd0�v��-n� g��al,.��E�-�$^"DJ��c�.�A�l9A]�B%�W�#&p Yeh�L6W� � rb�9 )�e�E��=+r "j&;�ple%t -typP�;4s3no�tfficient�,�`_�"q|S hotoM� ��+� 1 - 28 ���u6*�&�"�)ɱa y�;$~.@[�'�,$Q&�9�s�N!va��.�5S6\*��3exactS3�soh+SZe � ��?x+��&]D� illus.�!#'coeFA�H1 in�X� y� ɲA%.v%�� s .�"�0y�� �q�issI�z .�J "�/ ��s ��HeO�� tr� �E��F"@ QGP; 3ng�� � a�9A�r�U���y *{Ac�' ledg�Zis work�%�Vor���! DeutFa%schungs?inschaf8 BMBF % 0GSI Darmstadt}bP thebiblioPy}{99b�5�em{FAIR} http://www.gsi.de/zukunftsprojekt/FMx.html�8 =I} T. B�, {�2T<gr. Pae�c. Phy�qD{\bf 53} (2004) 25� T N?u], U. �(, @IK Rev.} P,C66}, 024608Y2U4�4Ericsson-WeiseZm)W�ise� it P�� and �ei}, Cl�$d-=e�| Oxfo�z 1988.�DKienle} H. Geissel1>� Lett�(88}, 122301J�Hatsuda�~ @, S.~H.~Lee, \PRC)4!34 (199% %5KAOS} A�s�.L,� $-ex/030701�40Lutz} M.F.M.  !, E.E. Kolome/)v, %\NPA �700�93�P$Tolos} L.  ,� Ramo Polls, %^�5!�54907\�kg} S![wg1�Ay6.4J15202J12. JEq6O��5!� 2939%�8);�5q !-i621311 0� q "�JM.  !� �%�� S-�41}, 81 i`.��1 J.PA�A�s�I�Q�$M�# r 20!QM )}, NantH HFrance, 18-24 July ,,� �1!�26)_32��L}av �@632AE01H.�! A�%N<89}, 75I�6�Wambach! .w � 422cE6�&}>� �)AEk.�B363},�fa�52�R�> R.  , J� P Adv.2?)_2!^�*0BSPiIramana ;6a�675 �:,,p-ph/0201101.iKo!*Va�ch�Toc�� 4orkshop XXVIII G� Pr"& of�eiE��Var Exciv# s}, �.egg, A�8ia, Jan. 16-22,A�0,��Re�)4 ISSN 0720-8712E Renk�-  :�F �3014902e3�7u� STARE. AdamY�$&�*1` ��2�9A�09��42��97}}�-�Rj�gJgL3 - 18, 1997, p. 201�q�Me98N�VI�42} 16��9*Y5QiPVIx vx��jx vx �xJe��GyulassyU{�XG(*8Plasma Vol. 3, R.C. HwaeX.N�(ng, World S" =3,�0gapNX 2003.�E, A. Airapeti!D�\->Eu� A� JzC2�<479; V. Muccifor]6�Y254�;e'y(Kaempfer�0(Zschocke, O�k0Pavlenko, B. ), h�y1226y�< 3} E.L. kovskaya � �2i52��26�u�GP� 5�&> 5B91�u9)AEi�M.  nberg�E)]B�^027601 ��9)=$;�Ž H,J�: �Xm<Ck 04461� 9�T�!6-��.�Rk�hAA�a30�65Ź\5P}� KPekh.N %N68i�A�}�]4.�i߄ N. J�$60} 064617J�!?FHU' �65��14605��6>} incE) ,�Gallmeˆ.� eN�7} 05460I�3), Er�m-ibid.)(C68}, 01990�6n ~�!Fe %e� 7!%l9E�6X, ~re� .�672} 466�r� AR"tS. !2N65}-\ 377=� TAPS%�Roebig-L�u=�LB �374 42�7A�U|"[p�Lrgp,^3vJcommun�;7#5EK%�Yorit��r476} 2�=0);� Yamazaki u�"� 67�520( 64A�Hom� m��G1�3� �u2��jta| ,�}� .YAM� A6MAe�roQ%�y1NK3%�6KYfF+\nutti2�77}, 21I�6!�*c�G MYVendorp9PRLI� 2N� ";[L.�\�� �M.J. ViTA Vac�W!�s 5 7C]&;[ P. M\"uhl&p-��Q�59| 21i�4.@ �� ~G.~ :��k�~�p~��A�]95e�12 ,WF.~ , T.~Wa�W.~�2�5E�9��.%HW B.~ , Acta�PPolC��YB�O31� 19982Gu?C3e�i6��5 �5I�� ,, H.-J. Pirn��!� g}�)A7e�13i6e� 5 N��.j 61-618]$K&�2} B. Zj>�2.�74 � �4) .7C�.C.  degli At��B]m�N[A1��13��6��,��di Nezz&Lprv�)1PhD�  , Univers�"Gi�n PhD� sis,Z4,�3ie.�>k.uni-�sen�html/durt�s�endB P1docym(} �%$Id:m verg�� tex,v 1.8en8/07/07 08:00:25GeckhoJz $ \M8class[a4paper]{}% \u#6 ckage{amsy2}> symbBfonts6�icxWset���er{MaxMatrixCols}{30} %TCIDATA{OutputFilter=latex2.dll}"V!�4on=4.00.0.2312@ CSTF� � .cst.H4ed=Friday, Nov�� r 29�$2 15:09:465Z2D-�Sa�3Sy�0LaTeX\Blank -��-vd  Ar��2^,Language=Ame(n Englis!� text�1( 165mm \odd"maAg 0�.>newE�emA�orem}{T6 em} .a:d[ 7]F~27lg hm.16+xio2'2#\I Case:!lai.DC6D�"�".J>-r 6, >+j�"6,:-rollary2,6+riterio2�2+dL}��WD2- *Ex�Q:Rexerc�9�E2Plemma&L2#no�9&N2)pr��(P >'g42}4on6/rakUR 2T�f;�S�f6)w�.�S 'e&�=�@of}[1][Proof]{\no�nte�$bf{#1.} }{Lule{0.5a� "铱�bt�L{�iRegul�'ŗ� J-m��� hod��LR{J��Uve?/}$�0S. Vasilevsky /* ickx(@ 0A.M. Sytcheva \\ 6oTAntwerp, \\Group CompuI al M�0�PrB"80;Belgiuma82}$Bogolyubov I�.t�5c/"e$ 8ics,\\Kiev, Ukr�r8} \date{} \make%A ?7ab�!ct} We�OBF\J!I$gr-n�F�!ced�&.�) J-M)�A�od.h��& �"�FnflW?�)co�D!g�$�[a�N$Zv.))� }3.W�M�,ly�B��Y2.P$�$de"{4�im�D@!� �9&�HI*,v}.B� (JM) �x!com�ipopA� tooV�Wv!��dum me$�<*�r��$atomic\ e�nd molecXsystem6a b�.o59s�7e- #g�/E.Љ!�2�<�"e�Nis)� &!#"�*i^�+2<�to �+6 rŅ Hamil�Ban,G(is�,pon�. j asympto���<io[;���i(o a tridiag�- or Jacobi�ArixPɉ=OA-[�b�%+t%�bE?|! +��U�expan�) coeS&2 %E$ Schr\"{o}�E�q\A1'be�GBb�TtcUK�!��U!M!|=�,�T:can nowK�3o�&V��isԅ0�?1i�y�!]�*����)1` N �63�^?=�param0l (4{ �j!�$S$���>4JMu�a!:/vsu]f�CAD2-, 3S'V-�0q!g&iJ�cuA�M kn:He8r2,Rein�k�t72,1995JPhB...28L.139K,1976PhRvA..14.2159B(H3PAN....56..886K}% �V(�L q�2001JETP...92..789K,vasil_rybk89,mi~n_�%90,kn:ť92 *97e ITP+RUCA1. &(3}% Despi�L!�%<ses�s�V��d(a&�@m�&�>basis"/Zs��I��I�3�oqkLAv=i�c[Z.�#m�=e��E�B"1�w,y o�+orAly���,e F.xca�i���+E./Ag�*. An �qd��ۡ�w�a�$.?Tɘ�r sizer.Ž�n/$ necessarya�RharL#��'�ampt,��<�;C,-�58Yy2A�LA�a0404V})2at�Hs�5ig�d�!���� 1� �c�9sy? . Ot�bC:il6ZiAC* )Ksa� -E eval�.&L+�1*Q . StJ�Ib�N�1 � �o�g%v.� issu�{I�5 is pF�/�)z 1>�ir� (or Neu$�{Q) �2�!�א-�8 ^ �.�t�APW;Jn�02�4F�Bu �i�RFݏ.�T96is�r3�Dd�pZc��deӂ!xhe ��Mt�^��SmirnovE�� ni} w!�b� �-ob/a�5m} O`m,6izJ{1T�>i8e�or)� impa3�!�;H"t . j%��m6�ed.�5��7��a new9n) 1 � ` ����6,e�V�>i�a� �A�_1T1,Y_�7(�"� d!/} yHq%. � 1� a!��,u�3�M�Y!�oscilla�i��)ha.� �� �5O� F�C5T��= �� �� y ex5W@o�Yx���XnaloguM&��-{"� M���Ab��eJontin �2� r sphu�ee�� on-liombic�h,%Z \ } -�F8\hbar^{2}}{2m}\�}( 1}{  \�a*|� r}\!\!6-^, r}\�x) 5-- {l(l+1)}�J\+' V(r)4E\!2I \Psi _{l} %=*0�c eq:schroe��er=M 9musi@��yLi$s��c�>��!r)�AD�Zs�g�<sel4��"�sJ� � �aP�\infty).s�%',{2}{\pi}}\,j:@% (kr)-\tan\delta(k)\,\ V7n "r)��eq:co��ate�F%w��$kA)= �mE!�slash}.$:XmA �#=O�� � a�azio@ T!L�:�#is felt,5v6� XiM.�- in��.� at"�l $k$ 2�9 en�Q$E$!Wu�tra� ��qx-��N >� &�P kn:Newton�l MorseFesh�+�O�5 %�-fu|�%zfGTJM��or�*���blejI� n algebra het�Ev1us a��!h q��E�!se"u harm&R��&z \�Ye U� aligPhi_{na�L\,|\,b) & =(-1)^{n�B,1}{b^{3/2}}N.\,(Iz\r}{b}% )^{l}L_{n}^{l+1/2��.()A�iQ�yexp���1}% {2}b4\\ � �2Z\G�xQn+1i}{. n+l+3/2}">L�-ihAu$ �\alpha��$%�Laguer@0olynomials, $ ��<a T|-fm[��$bW9��XE�t�r&` al�6�in%>var�7q�Q0a��ra�3C9/"UAoa ^quotedbl�i$|$2�]�P�BT�? U per. Whil�^�XtraIfo@]26urn". &J2 ),�Jer6W�aZtzF5��8|k)=\sum_{n=0}^�Kfty}C_E� k,b)F��wOscExp}%)�َie��E:, m�aar�As�r%�"�e� pp� 2ou y9D���R�`EB���B�s�O]l s .Rb��g eG%&��A ( T��-Eu/\,��1}^{B}(!�m� !\!0=_b�}\\5� 5�pk.9f`(�)- ���\o* �b�8- r��Wa9Z��of�1�} ICm.C%\lGwYEb)|-| ml}(b,\r/ C_�A�=0>`�ay�` K �G$in bracket�A�fT�z  a�"��';x<Ra�}�]CA@pe�b`B:a�ee-� recu�Yc�� � -^s5�d*b �� :>�i�!%%k( k,bUlŋ�O\,͂\,(kb�p�AA 1}�>2�i,��:�6( �\\ ���2}{ �� ��T(l+ (3{)} Ul� (�� � })_{1}F�-n,\,2G\,;3- }OC02�'. wh �h $\a$AAnD Kummer's�(Mkn:abr� For �$nEE&� >�\ 2�i�| n by5�}Y 9�e �ag  bi�2R��}2Y\,}|\,k.AsymCoef�)F�yX$A= f4n+2l+3}��!3������7w5`F �(�"��F��1ԍ ��:5NR52##�#*L �#ncannoţm�e��re�=z�:� 8"8�inbY g���Ls�da����v�W4QrequiI� n"A o��D"R �Y��Ws x�) $F� �^�iv;��A ^�N�O����Cmb�>Q "i �i�)) ˭" ll do ӯC�`�6@.M0AuUa�@cutoff "�9!�&j )��~�se &�>�-? �`as�b� hxz� 5��Eщ-�����>ZJ~ overW{a�}W^{N�M�2� =\beta\,�f0l:.�*\!�Ereg!�mq�s .�|����� �up\,f${for} F�2��Z� ���an&�a��dBd � *y*2 Green.� technique���1},\c�kn"^Ds�An�=@� c&�J&�\A�fix&Ff� v� yr�B� *� �L�q�� b� NɫM� �n,0"�veq�0F�It!".S �BS c�i�D,inhomogeneou_snuCr��;rAB� N�uyd.^�(-L +1�b^I�{�}�.= -�l ��}� -l-1�� : % ' 6\,"�1n-l 5b,6q" %��]u� C022�Y!�X�n�����M iR"�M �V�nl F�nKPs��� f� �Nb�&sB3�7�� ��.+�W>, �`\\ TDX��n)�B� �La�E0uN" i e2�� �Ie���!ng��C!�)S Wf I�o��A�)et:9g�}cefj�+V-��mI�2�(k)~ �l� V�%�)K\ =Ac;\;U] \,alCn)b�Ta�|ad�Oa&a�F�"2 "/d�ٹs��9i" )I�x Yf=@m� �@2 >�P�G 1T n0}+RhV|5p 69 Jq } *e�-raUar:�L -q��acY"L ^ I�!A�&�:��Qj}R.'�sa%�[ $&�pma��'ճ V�s trun�mC $n=N$N�ef�a sharp�4 be&[�u�a�2{2"�&.$ q� gW�G�� w�o/ �� =0$\�<$n\,\geq N$ . OnTQan $N+1$E  \1qN0!{un�Mn�{C_=�3I}�@1,lr,\ldotsN-12�\}$Vq.N� A�R� �lnml��:/j m �I�6��G�K;\;:Ug|RX��v�Vf� �D � ) :�=-r^�p��% a�,b)2�C>�#7 )Xachie+by�Xe:&EE�2� 6in]A�$N$�.�4"A1N }�.r�a�A�y �.�"q/}U�(���~� �x&�N $��%{"w Q.&  $aN�SFs&)&���P(JV��"���C10"���Nr�a=H*W$m�k�1}{BX k|1/&V��&]10J]�AZ�JD>�_{Ln� �+#�L�5$written as��9 �� �%�90MACRO{\dint \~'s_{*K}% %B�RE�/ .4splaystyle\intR9 %End6G(r,r^{\��e}A�0�!�!dB�%� $:M"Y >,�  (e�$� A�%N�S9M:Z,-EW mkm$b�&j�(kr_{<�_{>});&B�I� )��� d (ori�)urs� �ofp�9lar"��lv��t�bANl3�&�ly stZ;ngie!5��se,[. Hgaussia�#�� findF% B�A�&�>S �{f$�a�IТ}kr}[ ,(-ikr)\/name{erf�� @ kr}{ A }kb}�Dik�#"�.+b exp(�iH jFh ]*� C105QW� F�n"�,AZ!��J"J *�lF|@�c 2,&ofJ�~�$. Indeg�wA~$k��en, zero�if��#� B,A��i�a�LX&. *>� lex ��"�% !argu?^ln�<-H�wjsimeqM*�$1�#)kr}\cos(A{ cdot�� % kbYk�� R{� ri I�]�d .U�2t T�%�a�M0is $kr/kb=r/b-c��. 1�|�: ��,b��DalF$� ɜ�*uuci�t-UI{rK 5��s��� vru3� l� in��gl/gec7�E�u^. Wu&�!d��-8I�i-��)�"�+�% ��Q��o% $ kb}{A��+�4}&�\{ � �f2 62<�"2}�5� H�"\}23�!�)\(N)�֝2# Ѻ�.f"106:c�7 $kr$�;�-��ca�1to��o�'�F!�Zond��� &.�2ҧ+bxM<,���2�%)� �#��� m�t�1"x $r$�J86�:� c�*>� � :�BF����d r\leq b$ �r�����!a�&RVy^� 6Lpi ��b [ -2�� oeZQ�2�-ii��bF�% 6Fa�7&_� ] +���&� <-<��ea�5oTay��"�:(|��J).\ Un�v E)#aiZ:���8��j0:ris ima��ry"f4�}P!�6rks (�pr$�lϙbJj�� �0Fig:PsiMinus1� �� ��$k� aX%0��3�0:�Qy����-\long s->QY :_6�>�� a�|en:� cm��#&�#�m�0D)�I�A�(Q� /2)}J� + � � � �&m/!�1,\6� @>�Jzn�� in*t̿ŇAv�cA�"���*ti�b��*0e$s. Perhaps�,p�&�[*d$�� f7A iv|4j,�Q?prre�8yv6>$�-��� A�ll1�q for\gg1��o:�&�"� !IAv�¥�as� �VF" e &� �� *E �x�0.�� u-�4ٽ "\S)�&i�� E�!:ofF�), one f:� :F���=O6L1I�e�a�,:�M�7I� E�!xthi82E�6�\,>�andNcz�ajB�&72b�  ^˖� � �,��t2�i�F�Cis�>U�s�ttu�6 avoidZ�:ocik&nI�Y�t��.�.e7L�|FRAME{ftbpFU}{11.0314cm}{10.6976 $0pt}{\Qcb{"J& RN}$ %�.� >��:$�Vs,E�$l=rvk=i� %varib9*J�5i�2. (jZ or $b=0.1E| %y�6� ��:�`�e)r-Qlb: % %}{ps��us.jpgD�k{ �/uage "&�\ Word"; j<"GRAPHIC"; %main�g-aAt-r!� TRUE;i�� "ICON?valid_f�2"F?w}� 5�; he3 5�G$epth 0pt; "� - :(6.7533in; %� - B5.947 crop�  "0.1092�top 9379�e3610( bottom "0&� '].JPG';-*z "XNPEU";}N;f�} [ptbB��BZ�E�F��W�k�r|k8� h q��� !w)�raQ�$r$6.��QuE�!@� $r 2�b$tBbn�kVg:;al,= $"���x%M  &�6�-�/�� ^� "�/.1p B'0��;�&s�A!��cS?Q#"852 ��um $k� ݫ�%:m�'���b�/-\n)A+B b�f9"� :��]A��.y��s}FZ-�t�=D�"�')� b�.�A��YBWs; er coSr�{. S�FI/%(!4t  seem!�f*� �$� a g)2YE�"\ >h"�A�E ��s�y��:JM}}��"e�>weI&.G�'aJ�Ka�!�=" : 1�� X�t}�%~��.v�ch;-�.���aim�re� ?a�l2�1&�!KwaRP5ʇ�h�v\�Jb1|., * newregneuVw,\E chosA�n.{�%�/".�1:k�ꡊ5�)0"�2������.k� us $���a+� #"��M'Q&2"/O*<),� �t.�$!O��B.� Q-(new)�Jo*y=s)Zm nl� ,b"�k,�-� =E7N�#�"%:w6�9�O �'>�NsSsf��Y�_N&&i. "uV�"�#"�=�Z�(�\@�"�7, � zJ�;�#^{vNc!� in le2%>]'� eq=�recJ�C�#2Q268/���;M~#�u��� ���� ap $�kTh"d�j"�G"ued�#App�$x< Sect:jl#^V��)X-�L leM��2b%{�B2}- U 5) ^{j}\4G&KB n+j ^) }{n!. Q�( Jbfp�2+R�n� �} $j=�B�Uis5�deɒh b>X$w l� �� $n$ as� dr�vguB9m�%D55>^n^{j-1�=g2J% &us4 b 2.�)�o!h-�w>�]%a��!"�� q 2�.�e@ @is� �4 slow���*acht Ē"�0"� !��Sw wzgligib��� dVU ��$"4�� 5��( &�& $,J d�!4�;٘,� slV���9ŗ�T*]�Ʌ�)�6�.bU:�(i)`�3w��WI�ar�3���@N�` a6b*� ra& �!�"/ &�+=g-2 �hU�$\qsas& �p AU�;lve&�.B~��by��oD���� 5$n=0$%���4��4��4��4��4��4��4�4,Or6 ��4�4\,)��4|-eQ ine{�/s&���r ,6� {.F5M$� Q?2���h,\2b=bftR�$IL &i :�>� }"&S =�l�-���4!,\U/n�.I ����4��4��4��4��4!�= !�b)|\,"H0EQ7#� 6�4�/B!�'0!g3x4]�N�>�E�U ��4BZ ��4��4��4B�4" 'x')N O+q� A�N� &�4{!u�!�2@A%ni 1wF5 _Q*5\"h��f["A>:��-5�-5�-5�-5$V_�> tr/5�O This $N$ defines a sharp boundary between the internal and asymptotic regions i '�coefficient space. The resulting problem can be solved with $C_{nl}^{I}(k,b)=0$\ for $n\,\geq N$ . One has an $N+1$ by $N+1$\ matrix equation in �punknowns$\{C_{0l}% ^{I},C_{1, q,\ldotsN-1��tan\delta_{l}\}$:% \begin{align} & \sum_{m=0}^{N-1}\left\langle \,\Phi_{nl}(b)|\,T_{l}+V-E\,|\,\Phi _{ml}(b)\right\rangle \,C_{m �%(\nonumber\\w;-�!�$left( \be�0}1YN,bL_{0}% )+v�Ph�V�mlB� �.`) �) :�=-vv, g-1x m!�(b Y\r>(B�) \end-��% %TCIMACRO{\FRAME{ftbpFU}{12.334cm}{7.8398 t0pt}{\Qcb{$s$-wave phase shiftA� %AQtsquare-well potential, obtaineQ�b=3$ fme2 varyA�`renormalization %widths $%�$}Xlb{Fig:PhasSQW_vs_b0}}{�sqw  .jpg�({\special{ Aruage "Se��ific Word"; type "GRAPHIC"; %maintain-aspect-r�P TRUE; display "ICON?0valid_file "F?� 1D$; height 1LELepth 0pt; original- 8(8.8332in; % A85.8859in; cropA� "0�(top "0.9280�rx76(bottom9 %�name '2S.JPG';T-properties "XNPEU";}}!_Ba�Expans!�m�0figure} [ptb]�center} \includegraphics[ trim=0.00in 2 2119970423785in, nat)=)00 %?=)?  (1x, #1� ]% {6�$eps}% \capA�b� �� �� �Y�% \labelJ�%i�5Pa�1r %End5���419��Yukawa��v� di�m�yw ����j�%M����1J�59�j�.Y��i���e�288i�423196m�m���%~b�2�EPSaK�� 9�� and^��� eI��a؆�8 Convergence of��N $s is achieB by extend�f��� ac�� � 0 i.e. increas' $N$. \se&D{Some examples} I� is  we pres� +detailed�@for radial 1-dime�6al mode**0s. We compare�applic�n�tJ�0al JM regular8G cedu?oBon� $roduced in� \ref{�0:JMrevisited}�,Gauss, expon�)��*� p� � hoos�@able\ parameters,partic� a  of $V| =-80$ MeVg�, $a=1.0$ fm,�all- seY�(s. All cal\! s !Fmad!% sta� 8d JM approach, %� trun!hng*�4 matrix beyond"  cond%�%ch<pointA@D \cite{kn:Heller2, 1 0Fil_Okhr}. Fo�T=�>�w!Rnside +�$� � $%9 � N� $.� e�!Pms, wheA��newa!�MX (J-M) RQqN � Varial � eU�Y�CalogeroAz Babikov}.v' 5471 16.9382 & C�1D� %pah INainapR%Oa�Zy� (m�m�,q� %fm)$>]is=� both2� 3U�� ���>Eu =0.6�U.>[ es��1 eg� �f�~ �~ "~ )�&] 5�v� !�Z^ 9.5527~^ 655F� 84�^ e%U%�!G�` �` ` 110931` 3295686| )K na` )A � 5{*} )�"b .�:d VH �Gݦ^G �F .:NF���NEB� uG�� � )U}�� 8305����n� �j� %$"�� %e*� ��E� ��s1~�e� �������)�2�)��493��3N�2�e%Z%������109545��407>� 4930��z�)},&�)��������2P����b��yP�r~0 93��16-x}�0 0 *k ����b�)JSQW.�sqw����2�!�������SQW��6�����~�!��������.J����b�2J����n� "�b� �� �� f#� �"� H��% �%�%%5E�������)V��B�������.���� T����R�BS�� .�s rF�2) b show how � solu�6YF��4depend on its �"�valuef&ed7t�f^ �b"*� 9�s, as it!os2� tha� effect�(more notice�. I@also sf# 6optimal �of� strongly �s } fun�al�m3Ƶ�, }&�ly ;$ behavior |�.f�"�,9�2h ,q1�e1 9�Be� j�JM, JMRs VPA ~.�!}four >g!�� edV0 three differ�Es128oscillator leng�$b� ,\ 2��$3 fm. �uni�ity�O!�ŅN$was chosen be 6�2�]la near: to limiEq � ces .�%&w"ded $\overline{\Psi}_{L}^{N� r|J�rue._ Neumann $EFD\r�!)�Q�&&0coordinate reP� (see�D]D4siMinus1}). WqCed%�%�U�s,-zp&s devije} from{ (VPA)ns with2b$iEEaK&d�e�a larger)� �?A�:�_' should be1�,rulZ�t�te �#u$s��bya�Pever remain much clos4 a/$ . Th*?F�pronoun4�he.� (��=�%i�)e�,5�3�B�) �:�)a�in%���o!<%�importan�%)� ese�$b$�%�:�bu(becom�(nKissue�����clah%�G,�!!'&�, �(�Yly "�,!S%/�l94�3�.�u4� >gE*4is undoubtedly)to doI�y�-m V�����er�E�EsMM � fur�impro} if a kjudiciou��ice!��1 �pp"�$. Inde��a�IrS6�)(Si%��_ai�� p ar�* 0.4 fm (=|) or 0.2�'( X) we� � !c1 even)(drasticallyIX�E\�._mbi�KJ�u in"��)�f "� ��2�Le.g. using semiclass�9�0x��s s�Vas �\2002PhRvL..88a0404V}, wi�rr�� meri��fi'ye��ndE<drama- re� �size of�m�ce�"�!CoZ'�'�!We((investigate�6b��*!>"JM-3" w �  fF,ed���� "� i)�a sign�)��impact| =�F��� osed��w5Wa�A36�. ��compu�WA� only sl�lyI�inv|-buta(yields>�a�m) i! 6D-Pb��I�5j��xU�jE�rel�QN�E�>� }{n!)[!��0+ d}{d=IM) !R)=a|> �] |_.� =0}= 65s =^taFuo&6&el�%� a�Myor�%te,�'( ext�(%Y~�9��xP6 �(te quantum 2 $n�(��G��forward������A�wo�6�Z3findsN�!�\d0�2 2l}(=�,b)�� widetilde.x },b'2�1=h!���g��mFz}{\D�3-�] \,^{jF�bN c3EW2�Bm$,\qquad z= .�]! ( 1+ OI`) , uad\alpha / , 1->- fG�=1- P=i+ 5_ .`}.\$2#6O4FACOin]2�E8h�res� � reveal��l actus( symmetric ;�V"� s_ it be. By�l)3�: (\�*��2a}) �isU�we#eVrequiredA�he}n�fs:N�I emph���� .P=^n}l`&5���� ��E^ �a ��W]}m8#D.� �6ʭ.���Mq�I�] 6Z�.�% �t>����5,���=A!Y(F�>|It�ib*^-Afollow��orm9�*�7V�|\6�� ��5�F� >72`nU� ( z6r����j}� ^{n+�EI�2 .�. 2;.�%�{n}Z3 .N .J:��7k# min�n,2g � ��n! f� }{k!T-&�6H2"2+k.R["� �֥� ^"� �  �]a�k> ���� _{2}F_{.;@( -n,-n\,;\,j\,;4 >i!SM }Fg2�9�a�&�V#��6X � zero# :� �(�.`�Ď%]�J' & =2"� �Ne�]� *� :�:5 2byH{b7 !�.�b}1�a� � z�>�2Qi�( Ex-2�x v�� 2-�"�= thebiblio�9y}{99} �v�s(style{ieetr�bibitem *h2}E.~J. v2 ��H.~A. Yamani. \newblock \makebox{$J$}-mat� � : Ap�� 5 e elecn,-hydrogen sc�ing. ]@{\em Phys. Rev.},�0`bf{A9}% :1209--1214, 1974��xReinhardt72}D.~W.~Oxtoby W.~P.~� T.~Nescigno.�C&�a�ela~�6�vi�0alytic contine=fredholm�5 erminants�strucKG8 an $L^2$ basis.�: Lett.,28}:401--403%22H1995JPhB...28L.139K!0A. {KonovalovN 6K}Ve�{Knyr �8L.~Y. {Stotland6~��-body�a�5�i�68�!�of1�XNuclei}, 56:886--889, J� 19932�D2001JETP...92..7896�D, V.~V. {Nasyrov},�Y {Pop~4��{.m�|J o6M]6�Describ� ��((e, 3e) Rea�PHI�A�F�]�Exper�9taO�Dore�%�icA�(92:789--794A�y �2,vasil_rybk89!� S. Vevsky�0I.~Yu. Rybkin.�A�!phyv�ffac -`$t(t,2n)^{4}$He, $^{3}$H( $% H,$2n$)$ ! r-s.>�Sov. J.%�.�.�!�6$bf{50}:411�z892�mirror_Y90B�,6�)�4G.~F. Filippov.�Th9ea�ns��; j� $d(d,��e!K p))��U"m5nA�uF�Rը51}:7%902kn:%�92!  %�,� �d, F.~Arickx, J.~Broeckhove%!4 P.~Van Leuven.�CouplA�of col�oiv�M�͞um: an .%<to ��M}.a�JM G:Z G18}:1227�42A96�kn:E�97e! 2�, Aa� Nestero6��) FT�# -clu9�of six-%� on system.Uԩ�a�ic �*v,60}:343--349�7>� ITP+RUCA1�� 2�.l Algebraic ��&0 )�ree-s� �s.=�I!�� T}}@backg�Z :{ ,C63}:034606,F�kn5Eڲ��)��-�R2R}e�9F >yY>5:$^{6}He$�[6Be$!e" ]P)C �'9C7vC3�G]G�S$}- 2#.�3H(^3H, �14�? ^3He#e, 2p) $���K � W1Oexit  .�B%�;!% % :064604J'N7 W.~{Vanr?@},�3� �4B F.~{�T6� Modified "�>*6S"� 65& al!�iew� er��{\bf 8�� , Januar��Bl 1zz ��New=�/ }��@��y�+:�8y��A9��L 1208��:a U�M!�,Wav� nd PlCle6� ,McGraw-Hill,A�-York�66� Lkn:MorseFeshbach}P.~%H.~B�i� .� �U .&.� Ne�56u Pkn:abra}M.~Abramowitz�A.~SteguFHandbook!M;Ke$ F-s2�D  PubsEs, Inc.6%:�kn&�C6� �I� �Cj ko.�Us"an }/ba )olv "� qe�� 32}:48Ak8n86� kn" B }F.~,BB�:fBAAEa Po�N^n Acada& P'9Q%$LondonE�B� �BR B�P}*5�M��QM��n>|0Nauka, Moscow�76.�>� %�"��unsrt}:L{ALG_MODE,CMPLX_SC,J�lBib,My_publE,THESIS,THREE_CL��H docu�f}�%�t� m{�*}[  ]{Case} \0�'[p:- int,�&pacs, 0s,aps]{revtex�4usepackage{ams�} .�icx6dcolum~$@bm6%amsfontsB symb\setcouO {Max)$ Cols}{30}�QlDATA{OutputFilter=latex2.dll"Ver��,=4.00.0.2312CSTFile= �.cs!�TC ^Crei& =Thursday�ne 10�$4 11:01:14QLastR1Ied=Tue 6D�21:5:16:2�0l.2P!�ViewPer!K6100b7DMSShell4SI4LaTeX\Blank - 6 A�Ile2^L�age=A�)�"EnglisA<neU�M�}�orem}� {ac�& ledg$#]�A:67lgorithm.16+xio2'2# clai.#C6#"^*r&s*B-J6, >X�ur2�o:-rollary2X6+riterio2�2+B$6,D�W�J6-eM�E 2Texercis6( 2)lemmaNL2#no�*&N2)pr�(P >'pos ܹJPr2/remark*R 2%�6'' :)umm6�S Penviron���Xof}[1][Proof]{\noindent� #1.}�'( \rule{0.5eq@}��($165mm \odd�- margZB�.>b�Tل8 \title{Monopol� �$rupo*�4�1�+ $�$-g$le descripAo� $^{8}$B��Lauthor{A. Sytcheva} F. � J. &Offili�{Univ�t Antwerp, 4B2020, Belgium= |V. 2�WHBogolyubov Institut�5J� D, Kiev, 03143, Ukr�W��)_ab�'ct}�-*�.%7)F! mZu�65f� -n&$ r(uc�fT1tM�89wdKke!M ully micr pic� p�P�.l�%�5�B(,'&M�P?2&� L&ruY\Yf� �O&[/in |W Ac$individual�to under"O&na�45si9+ #&at�0vxh�N@a non-negligible 1�Ha$6�eq 1�\��� Y0\date{{\todaya�� ({21.60.Gx, `Ev, 25.55.ci, 24.30.Gd.} �/�/�/�/�/�/�/�/�/�/�/�/�/�/�/�/�/�/�/�/��#�Vion{In7 } ��{8{ �"b���@?�ed4�,@4ar |4 �0ve<5hort-liv�W)!$ just abov��>�&9y>0shold. A low-�,� al b�is#5"�l-a�>$suggests a �0or��!��8"� �M A �7 survey o���x@� �W�^�a�-Dof avail�@wS �e.t!9,�:b�@:Cwor���i�s�� �(up to $L=6$>range  35Y exci  energy� gez;� �\AR:darriulat-PR-137-315} ?s�/MOs!�eal n�VM� � R measur%�w�bI�25 �50� �� >� E � ena6g\AR:ostashko-JPG-20-1973}SYou3ne�/f MaAyino _s"�:.!4@!d*!6}$LiK!$H n 7� � B 2#p #Li�</*wa &to *-8a highR�h!�y !|AEa* possP xist�\Gl�\A�d\�9  levelIFI4\� $L=12$ a��ut 41%�a$$E_{x}=43$ ��<-�u$L=2$-�I0L4 Beca�8��/6� evid�Epredo$'cw �W ,'�\in�, man*<�*�p �Baa�onD}� s � �8c[(ZM.� .G N ���:ide�=A� in�2abQq� of l_/�i �0kn:wildtang77�!�8��n.n,�B Reuv5Group� (RGM)� ofteien[ | ar:Tx8� x ar:wheele��52-1083�ar:�W !53.6saito77} �R�5 ��@�ZEi�&,���|^�_�)B��.�(~C^ iv�]te(7�� Co�.�_ playUA &Br���correctan ��te�states��.�A�$L=0$ v!&.��{��0rai-PRC60-064�x)�$AR:humblet��0-638-714}. C&�#$A&92��m�2�y � discu�5�s=de�s��(meaningful =�>!Z schemF?s a^ der�I@ ��=\ir�?��%� esenɥ� the 4�>�>Sp(2, R)%Ip�good d6#YA����a~2�)X(ar:caurieraw%!^398-467? mjIn�D �� *m U�� b�ReumY-252-416 )&l6ed�2Ikse-+�=has�Aen :�>b@*]%#R)$b}sE�!Z2*s"cEa} �lap��thu�!�l�� �F�W G'M�AR:9h-284-264!i���xy confirme� 8Dar:Rowe-RPP48-14192�(uzuki-PTP75��R��,echtBraunsch!�295-3� It�Cm� eref!�gBpri�Gto stud�e co�^�!< �I� ectivH%�Ipiz %iu��Ced |ach&)6�ar4VasNes.�,fil-NuovCim89p(V86� resEAs$ve already.Ad �-2�]\}he�Q�. W,d!Cm� aa1tA%EɁ%Uw#$ �Gk5 b�� !<aY�aRF*?i�F�Qpar:a} ens:� 2���L�ar�Ktor%�~N(AR:kruglansAo RC-4Ap21��I�is� �e!)��! which��and!�EQe (&� )9i�5�iq��. WA��9e�1E�ach5� = inJ�Q+5 � open��N�"Z areTJdG us cL!�oursely"�;e^ U$��y����s -�NywTFthen �D�p��a��Gs* due�"� lifetim�zm���B�BV�q^h& (MJM)�& ar:PRL88-:&.�MJM4s0� -j�-A-7769}��  a�� :6^AM-AJP},���A-Z# Rev}�idmgm�s,roxim� �q Schr\"{o}J er 9B%Terk s�pint�nble�" � mapsI/]�or%g-! "8tc1gs{1�guE;�Lst� #&�f*Ct�s �i�low WG�1anelJt�SPA��MdU�E� MJMaa=xt�i5!�>V((:�A-9� 4HY(JMM)}H)n.'�k ka �?�� long-E !m� � f�C� "ZM!� eIt� s!tKNtKn 1�-B�I asis*t��* -�iHzes, ���N"sMb:G4$HamiltoniaF�BiE� bul��c&�5al load��2͛!�i-��y��:��-\� ��ear-cu-6al*n0 � �s�6�A�1 spA�ng>�1T��ntrib()a4�J�, leaaxAa � {K)�pre> �T !��5e�Pc� ^-�n"G  degre.f�6��h�m... Ou��!�most sul�handle N5p4�N!�6�mainly Q%�2eAy�!:he�݁ �rc U�&�1a4"�Jin�4volkov-NP74-33� "� a Hartv/F9�>�i�&!� e��&� �v 86-6=tonabe� 53-677}weO n RGM o ach,!Tq2(&` r rum�check�vmu� ofʹ�i �J� pape�eorgani5a��m. I"�m II�elaboiK ��Ibi� 5 YM�l.; eb" !:Ap� 6����$1 �}K�I ���nud$l!;�)!�Tx}D�LV#��1 1r ion.vVA�dev�k!�Ga6.:W p2o�cmA��\��IFSa�:�. J$�p"� �: �V. q{A� �-C�8s C� -*I*�ma�H�)�LaoZ�y�� refe!RB��'�6RGM q6�,m cXqa well-tT4&e Au�a.b=�#2�N��6�M�AD/o p5.�"aAr� hi��.w5��A�is��n 6�T BqEF��}y�y� &"Ws (�w�di� cL6"radius,.b *� , ...)�x%�!�y�Ae<&�6B�Jn G18-6}]4vasnesarbr-PAN�x.� vas3-0�4::.7�r"Is���y-jFL 6;"�=�6����o LMJMYׅ0-X-alh}���!orthogo���u� &(Sed �h��s%U2�ta�S yru�# �js%� inguishedJa�'�]#*EYOWwP�ZJ��%D"� �� e"�*:�n!U�:��@C&I �Psi= Z^{C}+ Q M�/la�yeq:wf,end?�2�� D �ar�b16b$v _{i#B \a�Kr� ) $Z�%�GV7�2$D-bf{q}�D^�D ii},.#2# ^$3$.GQ,\!�(i=1,2�D9(,eA���UreA�mass $�R}��A� 1`6N�+�be writ�a^�!�5>2,..2 7�&�DA =[ !�!PL-�16\ %2B%R) $R$ �rIE ] , 09Mwe�)0�QA}|_aneWa anti�L~rxr;^�� $8$3clHE�_v��' �  mo���s, �$bf{r}$\ be��6� Jacobi2=U� /m&7V�Ml8d)O�+�6 ~E7"�P� frozd���edS�/r��e�aS,of harmonic *#3($0s$)]s,:�NheXn�s�.-��;Z�� ��ז�aݥ�v1� -��:sLb@:  J3Ir)�. A)� �:are-_ u buil�--o�6al_a82"sY��y)�Z�)1�wofBT�\ ambiguous�Wf[ �"�c"%BQ�!OmIy%�Lp $U(3)\supset O(3)$x)one.X{*_ �i �[�)D- 1$n$9�a�{&n!R $L,M% 1{"8of�'5���?AC"w�Wby�@ �U�H��LM}�W:J�+ �&BKB,�j+ �PLMf- �,��Cl"��}\��0=\sum_{n}c_{nRbC&�N��N�p����R�ps�K-f,"�J� -�� A{$�p O^�.~��]�m�I4��"%S�`F samo ��E~* ~/� YI��&� /:�x�dM�=6�B �%02 � E��`�da *�^.Y� darX#ep�L&p-�}Qq.wa4 Q}N_A�^{(Q)}P Q0[ A_{Q}% ^{+ �On}yRXFN.*=;\"� Q2�MN�ZM�MO[[���  T �SN�M2�M� �M�%J�$V$A^� *�F proj�{)pe� a$U�M)}$, Q)}�#��Am�(/s�V� invarianta�ep c0s $A_{\mu\nu}A�E(a=21�,mu,\nu=x,y,z�re � O�a݁u�N�c�.� s $a��(i)�/��$i0� 3&] 6��5i=1}^{A}6Q �(i)R 1}{AA�e�i,j�:jB- s at" �\�!Q�sA_{zz;�\\&i�&xx&+A_{yy <.2~�]8after*}���Z�  in (\ Y�v)a�necess�!�)νIE4Q�en���$E�(���K�� case� �U�:muo_[9s.�� ^lI�y;~, >��%���i ains�,�(nd $4$r:suy��$T�~�%BE�)c" $L$-sub� s. C�!N!e$%#:�h isC l uHilbert� LlEQ:Ka.�E �+�!��ko.o!��ujal c}�.�(i� 3k�)!sB�96g �G$� �F^{M}$"� s� we do<bV� B ACy{��/�AV&l6�ve�$}\n` *\e:+asier�n�"�!A &�XE�re|-�!�nt"]_s�v(,L,M)$, but�SR7��y:�R��y\l��*t \tau}|  ^{\p:B}L M �\u�c�\@�_sim\ \d_ _{n,J}L,U% M,bbtauQ ��#B�($C$)jpD:($M$)!�.W($Q$)-4�_�/] A^� "!�V�& %��%mon`msjMCal�($n�)�Z��"�� �,P"�W=�%�0eC}=.Q66�8SameFirstBasisS����F�is�)aa�\r�mo8n takezh� teR8ul�nhen at��� f�rA�s_-�!Aj� *I1Blai�z�*� perz��iV*ng"H-t��g�) -&:���t�. "� ���! (G1��p�N)u���!�G(R})��e�JSA�(NNA_[ IphiK(�Kt�|Rm�#,] .P2�Yf(.�lP���"�eV�gbY�h+KY�Y]f>Y)�R*>&� :TRT �\}&:no~-��~Ԫ�>�4R\bullet A}_{C ��Ph�5 >6-�2& Iw Q}(\�iQuc{!�� \}� JGM}(\nu6Bnu=� =��M��w�4�/aa2� &v9ibf{�f u>r| q�*KB-hR. >h2"c"n2�=N$, �rg l50dR��"&= ��otza �?#foBgw�(Fr2t`>?Z|�{� rete&4 �jkC"1�orecurrL3t/lpokn:*�'*z�-W�!Ny � �@�j��2 "6 C*��weq.L �weq.>)� am satz5�"b(_wf� �&e ^p(;   o`infinit9e�lp5bep{9Qz.$( $c"q$,Q� M}R�J�&r m�� nL,&�[\v� (\hat{H}% -E� m )O � c_{mL#��*�} �*LN:1b:v�[!�F�!y#D tx��#�/&�"6�R�tr֒1�,�9"c fast��.�(a -�A�e��o l�)a "{)�-Q*\[Gs (As&Oayoll as //�s),\ed�&c!�e� ))*�!.mRasymp�12C�5y��a�-h.�~o&�u�2o!� 8 �kCo6�.�� A"�i2�y!w �0 given $n=N$  'X(��un�"�+"-1!��"abU�� = s,9�;a*y �sd��Q�%��w E�dQj�.�"�06%3� "W( beha�|�*q AK�Co]6!�,I0r ��cc�L �' semi-G5cal�%� ough!<c%���fis a��D t�;2u-z �m-"B06]v�|�}e�9�"6�q $(�(+)})$e��5B-]�� ��O:fZA �L�%~c �as�Larrow�Jn�J�(kRl})-S/�,�m �rC\�q,*�>.Aa�F� O $SUjv'�reflecBQ�+sA Av1by!�&!�i���m3@. $k=\sqrt {2mE/\��  B�/umF5y gy $E$��$-7$ !�x*� tur�poi�q0B�8Agŋke�a �Nl"�)��!=1scaP����w��Tv-v��. U�E߭� 6�.�eM�e��2�caXn�a�-� �Z�2!�7#Z�are"\1�}Z�� (�ok�2 -d)/%�{ }f�&��^��~$dmgI{2m*�2�.*%�!��s&`y�&� ��YN!�:�-6cre�B�6�"MRk'In�Y3w� �&�y"�Zs,��a:�'�'��f�8%m���s+Ji*�8B�(E!<eF��r� }=(0)+�D&-& }-S_Z"+"}�� ,Coeffϡ6SM"�%�n ce1m���y con,&. Sub] �fY6�) ��%T��b 1�% 1T�� �&# m<��\UV� {H}Ζ -�v - &R�:�2e[ &�^��� %*�0}'& }+VU!b( +O ) /�] >m-" �^�-5sn6�M5%-2| - { *.�$FinalMJMeqU�-��$B  _ (\pm�W�=-�.p�)]:� %r| � V- v� \Gm! \pm ��.Dynamicesb $\g.1("�.C �s$5�$ l &�.6�}m[*� *� � S�� �utW4R~/ larF�x��s�$y�4� ��� a���O���s "�%� ( 02W!o�POS"Y "u$axtauI�6$��c ���"�6�-\M2�)�OI6.�� l $nO $�$�n%�ڄo!chi�( N+1 �) � A8� �.vby.�'er Èak+gebra�MFt! ch}NM+-N6�2D�_:��U{; ��=C,Q,M  }n=0..N- � I |$�  Y�yAɭmE�Rl][)�B�"<%E�or !��>��f�� a��a�!}��Y ernsL�Vi*�y6=. BHK&�Tp� ��M"se rapi���Q�Yn-m �$ gets r�, a1tˣ� eQm I�$M>N$z��is�27�,.�> situ�a"G m � a� v e�U� =C$,*�!iIt! $I"� ��E%!Oo"��d&�C)�r 2� ^� r� Ce��. anne� )"f t�,� �� ;A"x�0�� \� v��;�*13�� vup?lLB� ".!%quaN(1o%is�%�s�z Te2�R,s  at 0K(a8A�t�/"vhOart� . F%�.�A�MhigherY� !__�2FY"�.*��N9�7"9!RЌ��a 2�W�a���k�a6�Don-  (NN) 6�ss!�ruc���[%yA�&�AZNN.H�"� ���!��P2me�i�of �/�2ͳM�F�:K�!= -= ��A( is Volkov &�&A<forT7i��esg:i�'&�!�i1_ H.c<�extA)i?U bi �+%�deu(mnP��B�}!�di1�Bt.2K/! si{MtU���>a�Vtrwm�(e Minnesotal!ar::�<A�Ha$� wa-Nagata9N�cg PTP38-118JcTQ.|E 786}�ŋ"8�Qq8l,% was 8�T.>t>�=!z�]��D �2�Eesm�N6/-�  $�:*[}l�!��!"�$wA%M�(V1),"� >U (MHN��5� (Mi)I�se�Q��e�.�M�.�aup�H&�LJ�J n���T~�T�%y�WMP#���8Ny YM% te�́�$A$�p Z(Majorana ex�Uglt"/ !��armter�K:pdoe1T�Hfluve/��,&�aI#ɀ*e;7 $p$-shell �i.H�lyy-:^|#"��AL*� �^�B]�w� &�.� ),%Y��^ -��O5�O�� usu l waW�F�A"d���dE}=0\Long� Eb E_{r�/��|=2 (�.��{d6N�  _{F b|-�I\�'�phsha�?F�^fix�H*A&*�F)!� C, Q%OM*� %<����*������izJA�eptzE:v3�E�se��f�H in T>� tab:F�r�j�p� *��@�qR���鱝B�"� �y�co%����_C��lowest�V0�*�+"�IE�m 2�r>*Yn D ;�:n�R�� !�we�^LAls&h)�B!.G*b � � N��� &�&mZ%@tw�(Q2!Dz9��M#*P[ n ,�� >>�  a� ="- �W&# �vMz/qB� Bb b�424restriJa%\}X��<ering4ular} [c]{|l|c}\h D & Mi & V1 & MHN\\ OӚalJ  & Te2} 6 39}>"Y!F2 557 6>43>O&�26Q (fm)@ 1.28@1.3 I 1.32A�Wpg.s.}}$!R�X� & {-24.]L 7.09R-29.016Kth}(C)$:49 x8-54.17 & -58.025�6 -p0.0b.B1Qg 39.2)e23.NS& {25�7�ta-�\��P �s�.��� ,.[ v�^ ��r:�S=Y���iYa� A��uuObreak-up /y.�ɘ���5I�r�F&Me��f:alls&�aR:$-�*Nf\ Us�Y �,�Sj Y c!3��ũ 0" k"@ full�29 , � ��.(^dW <"> J�]� �UarrB�\�6yp��*�  w h���con�$t6' and,%, $N=50k5" 2g �% @.� -Y� $M=10���!!-su�K&� 6\_���"��.-�"%"G>/hav3{�B�"6 ly �fN>(dden Pauli f��ex�ȕ� �%��=h�1immed�Ul/cog�J2If�LX*a��W. A r-4"M*OD׷3 �^_q�U��ea&b &!�e�8o"BH.���`�in:� elvsinel}�+<p*] � 2�!jcP !oLt�a]'�o��AVV1A�� F�� qualV`�b{"� pFll."&9, JSD!��la�+uinbL0b���K�}pec�Fh NN.<.>� +]O} lSGp9��Ns Fw2DB�.W�Apr�yy28 ��r|*�\�H[s({2}{c||}{Mi�SRV1}�R6HN�C&�_r}$ & $X  (  n��$0�0�-4{0.12��195�{0.091 0.08.�0"1K 32.7�823K 30.5� {76 33$7�J G+ � 44.4 p76Y 41.7 84 \46.04f8766J4� 48.4 z20 � 45.9 J � 51.4 >H5Hx &$51.06 & 6156.0882_6F83.4� 285 Jx222�2.9 �212t 2.5 167� 2.9 �171.�26�5.1),841 0 32.5 C79�P & {3�%H105:M.�61�63 � 43.4 994 T47.Q:128=�2_2�7.1 23)�!� K0.)�49� 806IJ�@2.84 & 250 & 57.4549c42c 12.6)779 �10.�a& {670 �12.�L& {424.i 42f 40.8 D6-� 37.7 C67)�41.m@ 1514�4_2d7.-�12)!441+8 � 49.0 2.42ax%� 48& �112 � 52.6 �201:�J^3.6E�> e5WZ� ��{ N W 2�>�$.V�� � B�> . N�r�MeV� dtkeV:� ;"b� &�Q��=:�RpFaRd�U�/�-r��j\.�an�P"� .�hf�[ �inu�Tp��below 7" &A "�^79s.$k?�`s_evev �or���1 alyz� ���vH����S6IG� Q��|,��"~ ng,  w���K^ } W&u',L}s$&��b!�}\r'4p,7E�N 6� z}i:� A� .9!x& (� �,9�a5q"�)�P9A,� %+2 �t  KA�clu!�!qrX p�e �=R6R is pi�PiM� �1h2�I�s�2a"$ , em� iz!��)ps� 2>\ ��� �/$ �$fcIXI�) �jr�>;� nq?�&/or=VI�. Eveޥ�4} 54�Xg�m a E3� 9+j sensA�at)�>F ei�2JR.�or�07�s"-<kep� mind",�1W"� [ not*?&I�� 8�,act blurs a � m[!za��:�$��i��u�<�.xD=M 4� s-K�*H&�?|lS"!&!�qu e5�basV/-�X2m]$�eaisM�% re�E� �f��."J8V�o� � � deno�"1!a65"5s��$\w"K�Q�6M�/CQM&V# vI��.<�Mz�Th�Fns�a%6a0ZAly&��ISchmid.E Qas&�+gaAQ�v�<�1� M}}=�2+"M}-�)�IM"9A�1C��\ "AF] |/12W�;>8vU�;\\.2�QV�Qn�Q��N�vU�.",ɾ1�Au�Y)1�6�2�E�.~A�Y��otXr&$Ұwe �Di%b���T�� ^���E.�5�X�6e\���^�phe:X"�EF �w 3�5]d�o�+X�Dp�NFe&BO%e�%9Y. �E.M��&imi"3yhe ��&a" kn:f�� of'!j�Jng F?`9 ��.����ernale� % \ �e!Z (��q)�i!�F �cy&[4<�S!*; W.RB�hN��!b���Wp�=�^1�  �v� und eigenI�i�H]�MQM5�=�-�1� Q: ��!Ρ5bn 2Y�� �"06�s"�:6�^A�' �:�r�)r` "!� ent}/�*��4dv��e)!�I> ���\&![�*G alDxac� >.� x�V�"F�\A��d!}letiE;".# b6Aa%�B�p2q (56� �c1\Mow�_ v�-o-;)�y6� !�2 ]�a�!l�\ �B+ ($O_{L,j�:6$A�E�[ _{j:�\e�\�/�$)E�h{ne-to-on!�r8 o��}d!U��\V��. �g|,rl�,tud*ih "12L 2 B&�$"x �yV�. T�� nd�}2 pt��in&�$.�Q�0. K��s�+�a�c#n�(!se unqA oa�!�a/!m) % .k^dia�^���<>�a�) ed d�2a�uv����(q�� � 9�fI\� �<m��= 9�Q� �]��� AIq,(/�5� N�7KN�$2�4 ZZM :\F8QR[)����nt=�9��ud��|gTO�%�8 2� 9b1PZ,gv�u��uu�|A��A�.]�6" Kt�ht|9&Q?�ide��E�>]��A 6g(*�N�#�,b=`*��!Kc>&�!2 3fVJVfVE_B�ŗ1� Mode�&u4>i�5^.�63�"e"hb`34D 32.00 92\%2�Q}_{1}$�� {29�95n14.:&� 97\%:� b2�.2"� 44.1{7Nv2 ��  �#90J�16�". 9J�12�R" 48.3,56:vM �HA  E43j1 51.7 X"k66:�b2�F��F�0��I7N3%Z {56.36��6>�A212�F���G53[BQ�!z� 9&<.�5.1 �34QR�U�� {31.9)94:��16 &�9>�1926�" 46.2)!�B{ �"%  �9Nz18.=&NR{12�.�"b 58:!�1a�A  )NB�.150C&�71��2_^��A+ 3�.5N�A� A�7��;41:�!�19)^�39�8Nv1)� AF�8>Zv142Q�&AzK46w"46.�6>�.��rBEw8)X!�2�219�r&b78��2xe�i� �M0i 47t87J�A�%�2�&�9N�12�V&�8N�2�� � ���F�(�� "� � $E^{:u W]&�VF  �( ,=�.0  \m��% Ldll�� i>� V. "�"/n*�F� �>� �b $� Bn 2P n*&� �0^C� k�iJ�$:� �>k)�O:�-+Tic���  �-5�'l!�*W&.� �6A*�9N* � �8X}� of���Two�C ProcU&it55� �8 � � z�� ��sy=s �9A*te&�60�o�Kswtan1@5#2None�40B��/�s^* 0�Kt a;q&rekh*8�s, �ly* �$a $L(L+1)$�spa�|, �Ia)}U�FV! ain 3I: KYF)�� �qr�s} �z�)p�m�"�eN�^ Gum�" 1&�aa"�!:R$|-�S �E�9�{& ~d������|i9Q�tw��At7-M|E�!�5{()*�;��Hr�,�&c ccommoh��N�=1IBlI d.� ��.�a 6� :�8"60"�P2�xq�Q�,61%�! �)�:"+>3 6�Co�NrepulA`!�L-YU6*d>,aNich&�]�b *z�!^E�6j&wgconne<�MH����][�,�� >R�. M�Yi*�;:J� �˵� �.�;�j�>��U|{&i exh���<p�*2��;�;ue t��Y}A�����v%)eK�e�jly*`���< � earl�#/n-��6`@ sd-�iI��at �.�yջ-<&�$a"oz8&��"�!Ef!��E*�;m�*.7Ac�=F��;g\�*R�%A>��g��MHDe`Om&8��dU�er M�&�Ry� (UA�/ hospitd-y. v �a�Y~# nancf?supporty� FWO-Vlaan�(X!�= Refe�#!F���έ� '�i���j6���j6Ϗ,���.�%�4490}, 1, (1988m-aX���>&�� D.~T5�Kn� ,Godwin, D.~M!0ner, J.~Purce��C.~Sheui� H.~W<rZ�8745}, 155 (2004B�F�2 A.~DS�0, F.~Resmini,l\Conzett, R.~de~Swiniarsk Mei�E� J.~Ernst,-#�� L@� bf{2,���!-726�^ 3 P.~D�ulat,��Igo� Pughz$ H.~Holmgr�qP"̵x13�w315x65BxRЏN�ena7�4Barit, S.~Cava�o, !8'Arri�S� azio� Giar'�!� �G&z�20!�973�9:�6��0K.~Wildermuth%jY.~O� N it{A����� }�us}, (���' : Vieweg,�76kn�=81p�6fLe4'No�in� ics}9iA|< (Berlin: SpringA� 19816h&� Y.~C?1,ng, M.~LeMerͩ D.~RJ omps�W1�p. QT4!�167!H7F�wD�-PRe� J.~W 2�P52!�08%�>܉il*��D.~%�zY89�(102�53Bsaiَ S.~S , Prog�eorQB Supp�texaQ6�iO:���BۍKA�ax�A��Kruppa2 C&E�6A�0��996�Z"� J.~H9�,fCs\'{o}te( K.~Langank^W63,�714xF�bB���rRβEa�x��[Pڲ~ڱZM39�4I_8J�>g�f E.~Deume_ZNucl. I�1�A26�#318�7Foa� -NPA"ʌrSm%S8܇26%JJ&Ro6�at owe, Rep.M�6�4!��8:Oar:F� Y.~S1�R��7Ź37e�866la{eVW�K.~%cDôz���2��5�� }, 3)F^Fi����"*�VA2silF�!� A.~N�%rov k>�426k2 �:�ar:6L�2p Nuov. Cim��e�%y:saV*~�2J:�S.~Kruch�}i�L.~Chopo �,N�5�4ь536�F�a*��B�:LA!�5�>f��!�ay%+M�#�6�5��� 132%:9:�:;�W!���~&ã%+! �bi� 2�8e"��� FpMfb�J6r}�.��%:�J1]A:F�. G q_ 7769�F���q:�P%�16~�2tt�.��Ŵ36%�J�*7d2aen0F.~Arickx, Ph�eys. Rev. A~\textbf{55}, 265 (1997). \bibitem {ar:PRA-9-1974HY(JMM)}E.~J. Heller and H.~A. Yamani, Phye e9}, 1201e74BeHvolkov-NP74-33}A.~V, Nucl. TM74}, 33L65BL�tang-NPA286-53}D.~Thompson, M.~LeMere, and Y.~Tang, f Phys.5A }, 5h7FHtonabe-PTP53-677}F.N8abe, A.~Tohsaki iRmag(Prog. Theor �t53}, 677�7F�J��� V.~Nester6�A>>��. Atom.�ei,5�60!�4%�J��A��e*C�!� \ (2001N .�B ���7Z�threeclu!o -alhA�AI  J6 .� QOveEOa WE(roose-Dit{J-matrix method)�Rits applications}, A.~Alhaidari ed., (N.Y.: Nova Science Publishers, 2004, in pressB[hasegawaar38-118�(H �$S.~Nagata,ie .e��3E�18ae6F�.h45-1786�i45a8786j7:-� %TCIMACRO{\FRAME{ftbpF}{15.1281cm}{20.1079cm}{0pt}{�fig1.eps}% %{\special{ language "��Word"; type "GRAPHIC"; %maintain-aAt-ra�P TRUE; display "PICT?0valid_file "F?width �; he!� �GLepth 0pt; original- :(7.2428in; % BT9.6392in; cropleft "0�top "1rt %bottom /�name '%2EPS';T-properties "XNPEU";}}!N@BeginExpansion \b!p$ure} [ptb]cea4$} \include%�ics[ nat �= �00in,�= �  (54, $5X ]% �1�}% \capa�{P�z shifA�b!�eda a@multi-ca�el MJM�ptroach with Minnesota (solid), C T (dotted) or MHN (dashforsesT $ L=0$ (a), $L=2$ (b)�S\$L=4$ (c). Triangles ind���e experimental data from \cite{ar:Bacher-PRL29-1331}, �AR:darriulat-PR-137-315}. $E_{\alpha }$ is%(c.m. energy �reE� to �� �shold.!`,label{f:all-)^a�5� i�} %EndY0v� 6795a�11.147B�2����u� �y��v�8.496V�10.98��F�2a���� �i�nam� � m�56}�)Zq��A_q�$eYp.�foA�eq� potentialq�oneu�Q�u��hA�B#(-collective� line)�(. yZ-mZ �[ u\elvsinel�aM�ZeZ125eO20.45ed0�,3�Y�YuY �yY�vX7.0474Z+ 5415�+>+3�W�W9�iAuV � mV13}U)VqU�AZ6Uu��monopoleչquadru c) �:w�s �`�>�b�/force.�q,b+ �� ���)m)V 1.377B*4�*�*}*�}*�v+8.253Z�1.681�+>+4�+�+ �0iu, � q,152-!Yq-�A^q-OverlapJ ɍA ave fun@y 1$^{i{st}} 2ndb), 3r cD th* d) \Ŷ5>0e) eigenstate� a�@orthogonal comple^ >� , calc@ ed���5 C ���ch}% 1�� + docu�}��\xclass[apsrev,onecolumn,epsfig,t |en]{revtex4} \usepackage[dvips]{� ,x} \newcomm.\beq{� $eqnarray}}6#e#��^!bea�Da{rD�ga{\raisebox{-.5ex}{$\stackrel{>}{\sim}$}:�lv8<8� 1V! $title{Cold�Lntum gases: coherentphenomen� PBose-Einstein condensTnA�BCS pai�of ferm�t \author{Gordon Baym} \affili?{DepartA;�,, University�Illinois at Urbana-Champaign, 1110 West Green Street, +`, IL 61801 } \date{\toda�Mabstrac!& Stud@�rappe:1bosonse�� h�Lope�4up a new range'Hmany-body problems,2a�ong o��e��4and neutron st* Topics�cussed !� �: �K!� yrasty -- how �!� icle (hsystems carry extreme amoun�f �lar mA"tum; ��$infrared d!�gAN"��$transi�E8 ose 2M0in a weakly i��ng �;!H�W �lynong6: da�FA� Is,j�Hscale-free regime w%? two %�s-�" scatteE����� %�icewy�u�e S�$^{87}$Rb (half-life, $T_{1/2} = 4.75 \times 10^{10}$y)%�$$^{23}$Na;2W�,^{7}$Li�� also� �, but%Keff� ve� �� �� betw�=Sare at� [�!� limixa6I2�!�A* at c�$be assembl� a E�A�wo1�"G )#leno live-�1 dausL ������l^{6! �isA�bled $^{40}$K��9y 1.3\5w9$y�ypV  cloud% n ($\sim 10^6$ � M�� ity  @{14}$/cm$^3$, coo!viaa}ombin�� of laser%�theaa���e 7 ing,A�*� s�{-8�!�< � �M�uYe!�v Beca`22T�so veryA" �t-!�ic � e ��, order mm/s, Owo"[MZ�2fh�  gyk(, described�=a pseudo" ,�Pq v_{int}(\vec r_1- ,2) = g\deltaJ, � �L$g=4\pi\hbar^2a_s/m$ �$a_s$�/6Ahe � ɘ��ork ]�.V *� 9accurat��[in mean-. � ory,EK� $Gross-Pitaz$ii equ �,leggett-rmp}%E gin{$}/ )  \frac{\�al}  t} \Psi-V$\,,t) = - 1%F4{2}}{2m}\nabla>3 + VD)BS +g|{>7}|NM!�nd�X�t �- �o :�=�  \p � �o . H $!$�Na4:� annihi� "�or�q $V6exter?t^��U���� �� �#%� sha�af�G�(p"Y9by �+as-Fermi� ory)M rb87}e� * � s --� t� , ?oscil �s Hst8$}, shorter%n� th sound � �(iR scissoDd] in��!U�( �m� go�6ngw2�a� pect�a| ic%] �analogu� Fc�er-2N� ���� �!��i� .*wo�cor� ons*� (psi^\dagger> Qh��measu| a�<�3E],eeF "=j~.�("�t � >�r` y �!%�s ``rdLbine" into a molecula"d f)!�,!_vid6r!�e� t<A���� *� %$not simplyqre�Y normal J`gas� q � !.. -"�� 2Z4 $^2��eq�ѺZ2.f. rpsR��=6ZDv3 vwh�(%�4![f� A�wo!N six�, ,redic� !h� , abse�*( Noteworthy�]&VRef.~�{bloch}A�>8}4��".��1�5!��'���Xed "e  b0�.�e", ��nd�a fin��A��$|f - '|$:0��a�-s2Z� nyD u�"s�&� $^4$He�o� l&C demon�taI�����c�aE&��e� at MIT!� Andrews e . ��a �T���(� ��wo�epe"te�*�t� � f�����n relea!9 them� ��pan�6�^each o`, exh�3�T1�4f��� �+)�S ���� el/ magnetic Hs�)�� sour�a���st 2_�����ne drama�e��AS !b� 0g+�W�*%�s�g��p, a�A�� �enticT ��&q�1il0of��du� 2� %�fT� K�d^behave��4ilarly at high2� . At }�s,��[ fall-� � �Mfp,"� only un5t�i��.%e54a�Q�W �cy.��f�rea�Fed�Dr radii�BF pres�� ur�.� achie�in =�"las%0[ few per!!$T_f$m� jin}7 <��$*�� �rapid �,f!�!,"[to prA'e latAfEvor e�� �� 2�,� -� c�. By�n�op�--��m�ya6t-"� ng�s]�"�:� < a�ca$ ntroE�0an unpreceden�QS/ee�� environ���O �qDoms sit. For examE�a>e in,��Xt5 d���R!�BY�e-� �0 \ ch� aM! �.aA�aoa Mot�s}$orM]haensch2�(.~F�3� ��qpaA�"eVe blec1ah}r��sigM��a� "�ns�3t�dx,1i8K/>S�v�,wil��l technique�ed%T*~�b i)aF#ed c/ �n fol�uir evoluI �] �is nged-�"� to re�i�8�Fx � � ��a,!i�^of � AOAm��|�e���!%{���I����q$ mix�e� yA�c, spinor� �� fraga*ed��R2KJs.w&� �RAPIDLY ROTATING BOSE CONDENSATES� U2�1#= V�^0# s#um�� lore�!t"���o" � en�� )iI��qf� AsEh��-�=%��ly, it��s a txVa'!��ly> �"��exD/�HAbo,HaljanCornell,j�k3,cod�to�"v5sM�A�$LN_v N F�w$N"9to�&gu�� P�b $N_v:4�ice��eE�(�4�#aL$ 300!�| � )��ͱvel�yO�v$\,,�� iz� iA�&i! :\cdot d \�D= (h/m)N_v(\cal{C}�e�a��0edgt�1a�si! tour surr� ing !R$V�!-Bm5@1j masa��1��4he neighborhoo��/�" �!��(azimuthal d� ion��e"i itude $E/m\rhoY �qdi�ce��j. AM!u���a`%�Q�  �i6�I%+ an a#gY��$\Omega�^�� �? (��al)aA��, $n_v$, �.>� E>: { = � n_v/m�A�i �s6�Xre � � f!1� c� ~ . W���h!7n!A� j͊B� grow,&)e 2u�0 $N^2%�$?C T�9IIqa<u2l�c�aE5e= above a  &� , $H_{c1}�E� ��.�W-� lux! Ain"? o1G5� �untilc��bm�o�),Ca"�& M �2�at G%g-nturns ��owK, a� *. IA��"� dQ�a� a L�5to yit� req. Un-a�aJF �5�s1eA#�sA/ a sm� dynamkdec�%'n  ;l*�r�'NS kineB��9�)2 mustw pon�*f�% an aZo*'� �h ng�2$�� u��a ��MXA�&of *l $\xi_0 = 1/\sqrt{8\pi n a_s!���n����!Nit��lygN�E40.2$ $\mu$m, s���q�&Q� tolat ��e D�^2�e�/m [10^3 -5$� /sec�,*�!��esi%)*�gŌ)�! ]ץ�)]�J frequency��$ abo�$z$ ax�Ys det�p minimizMa^h fram� E'=E��� L_z��A�$ !�Fc�"��� :�Mu �: r�$ xis:y�0 E'& = &3)d^3 r \>[.Y2W |(q-ij -m {E�} � r}\S>)� |^2 % . \no, $\\ & & \qA6\�.r+ (*�12 m },^2 r_\perp^2 _) |z|^2 +a 12 gO 4 (],O9E�e}Z2"�1-$�b0 x,y)$]if�  a� -�ng.��on� !��4 is�wfAS� ��.�=.y,kU� Q�,AOco YA��)rmo��wQ]�, I+��V(-X,z) = E !x)�\o�1y *)r z z5�.1ih �5koI� U�#Nrifugal&�, $r$, n# c�.���1e p6 �W1�canno�*&5 De�*a) �En$彁#&!�un!Ype!�A� e \to 2:��-�fl�8ut, LX l5&�*� � *& eIsB um Hr?l�+��A � !�� ��+ ���/.�(\ga 0.9$; c'&-� � 2� ��,Eh) 6Wapprox[95$�I?�<.��:SatA� �) �,s!��sP w'%b� �e�^'al�5a�ta=� usefu]t�*� m;7�!O ��c� !zL) ��al C ity}�� size}, de� by��$q \tanh y� ET2K, �6 P!12 \ln e�|{.M- D}2+ �|&�'onvenie�sprea��A;oW�� F\,y.1�5-�!�!�2g / �(a�nb� � .��D�$c�!EB�iƑ� ".��^��$(1+\lambda�^2), ��Ba�B�ia�i7 ,� *!� a�A*qa�� Y A�A�6"�!,��I�n�x3e�{{C[htbp] \�mer� {B�E; 3in]U�s�<}&JE(a) Mean2� aM0"� �"�Hper / vs.�J$ (see text(bh�d =afe Rlm "�!%:l l2M�/gnp;dapted�%p� s�, �*]�� }).}��u�;-WubShrink!�*� s�In�r� �$ ra�6associa�w!�.Q� ���)O�&O . R`G� s wC5 hown��FG3tes� avar`9 t62Q�* � �xi��.�Ʌs%#!�� )s�6k-)7�.mAx#�� z_0!nd*_���] iusr'les d!5^J�$i�H 1a !6� �@ul�2 �s�/M�M� �t:� ,9I�in uni�.�>�a�,� quali(.v�'�'b%�D�!c /YD&!i  $; (\rho)�  $p <)�!Pc an� h<-<Z&� �O5no[&(cylindr�<) Wigner-Seitz c�a� �-)C�(ell^2 = 1/m�r�D &&ld E-�!{)Mdi�#�^�� per aA5 Ai� xi^2/3 ui�horiz�l(n Fig.~\refy'aA!\i�*pi��, $y$,M!�ar ris��,$ �b*D+�-�8ina\.ntil�%$ $ deHes fv$1/9;�� �0�-1e *��<%�aE;e7�)G.ZTqV� $m��up��y[�c��Landau l�9/  (*�($)�F �\to.�!�Re�� JILAAas��f� 2 �ay:2�)K�P),E  1b, nica��(% expe�$�# �-�acl�9Q� &%?��� Ho}� �'} �i�\mit�sA�uld�!pZ�:B�(LLL) Ke:�& �#��4r ic�&&M�G�0$2gn \ll.M�?nex$er6",�C� e�a gapI eq 22��%nsG�W�to�-n�i%�5tB�5F�3�5����6�ˁAst6�|the�.�0q \phi_{\mu}(� }��0zeta^\mu e^{- ^2/2d_{�}^2�/&+$3 = x+i��4 = 0,1,2,\dots� A�� �-or "� d �$��<n $��p/m.|})}e LLLQt�F'����rDpI9� �:I*9uU _{\rmd^5Sigma_!6c%!F�c%J>De � (_{i=1}^{N}(9- _i)\?R>&|LLL� &h1�m$lgr�%�polynom��$f��� written�Ya �uct�=� zero!I_� ]$e>�A~1nA�&� eKm#!ũ��$�B$q�2�u)��Rtin)ŵ�U) slow�;��a� S�>gn>�>A�&���:+ �s m��� �%i�!+͂ clou�!LLL��U��,g�Sro}N� E'=�� N�+�r\{�m�)�{u�}{.�n�,�r\,) +Mbg}{2} ^2\��Sk2B�pl�9er�$vol�F�1!z"�-�u)�io3 $t%�Dsmo�"d��pro�V, $"o3�e� AJ|�\U$i bracketsDot:� �C�� h^E� -�I�k2A�s"K��)� assu�cY� I 2F3�-�C3!�70 n"�A(1��R�]0�TF!�0 inverted�Babola* t$R5J��_ � �. (0$Na/d_z \gg 1&� d_zGax�V���F�"@ i�j.�!�&�92atiJ� $,� if? is Gaussi>t�  �*6 3 /(In���jil6� ���,MU�-<'mx a9Z�%Z�) }� .��G+����Cmyadj:Yr locŽ�_ � NM!nan B#�_X4argFMP*' Ho},HfiG �o&)>>� � ��5ex1k, �"U�$E�:���1}{4}�^�} = -' S^2} +_aj��nva12�7A�a U^:%�:���? 7!for a6�QU( TF%��� y#�����-�m R^2}W>0� )^2}.JY�se� �oj R 'c���L2%+ 1@�Y-��ic&,un'% gCA, -K#�"s a�+/'ect.l( V9Tur�GQ�`, ~< u �%or�s2�=%c.&&�(�-re������ ngh&�#]ribV+��X�1(P/ Lle):v�ax"49�+�on � �)*3)� in gG' agre��t,ey.:�Bey�"��- �At suffiatlye1�%�1�1Ish# mel�!d� a��!q iqui�� l ��b �9:�ye�4b!ls�=in detai�$� till�er�YC��w�epBn nume�H2�.i�OE�a� e�B!�� �3^e�� ��#*8�22l�inaH�1i�.a�xal�m5 �.�0CrEX,Viefers,Read,Jolicoeur����"�/atF8,�" = N(N-1)��e�(M�� � m�  circ-#,+=(m/h)j�*$)?>ls $2N��ct 2�#� n $N$&�1fuS&�;Lau�bn� &� (iwo "Is�*%�6f� (r_1,r_� ,r_N� _{i\ne j� _i� j)^2� J k r_k� .-2Y� 6 j9_j+iy_j��n� � Jes ^ �'# yo�'a�.�f� AJ# � {i \ne j}6�@i�@jAw!K�F � o4e$ly elucidae��&e^g�; �$ "�$�q:!�o�AIE\:$�6 w)tCudO�P�.:.&,- &�Ich�L�P 21A"���灌�7(� w(/�}>�p���&��F�g�N6��it�*pL~1�� �|arbitr�G)�(� ! 3s 2�� �+6��[ pusA�!�1���war�#he ed�T"� �" a h�Mpen up� _e )"�+�at���� paramw( B� e^��u ���M!Ja�ger60D:x $\n� $>>$ 1.$Tgi�\ J BVZ�)$tku,Lundh}-�r 6^a_raa_schb+diagram1J"@[of �&�Ta�%ee;U �E��  al�� �� genp3b!� Full�)ail�V�  f2$>#Qi��H� m: z);�@iny�lU �@!�ENS�  re�9-*l dalib�K��s ��! 2in]�:�! {SV~���2��B�Bos"�=edR5� &23.�J&�--$N GZ$O�I�$Z$>#}�":Z�*,%�!q/4 � ofuwqeiwA�, e�>�4e�Q���4�t � �sber� A�* -�i!-n� ofBr� rX �&-%�&w"U�Fw"nK�on{DEPENDENCE OF THE TRANSITION TEMPERATURE ON @SCATTERING LENGTH.�DZ��,!!c}E�a�/.�,2&F� ^�H,I>�!�[�8. \�e� ��2>Pa"3�� ha�t�tor 8 d hi�Qy (reU� ��bigbec � salerno���1i�g�" � est &"U'"U!��t4"�plaguWB�Zce4:lbeit?1�� e thos�;coH< �r":DR� � ,B!ZV?L f�YresolMin6��N2�Jn^{1/3}�Jhif!jn!�in B$%�# ve: E_�\D`K( T_c}{T_c^0�Nc\,�/ z,�%�K*�"f� gy m�� a�y sim 4�-!�/M��Z�QC:J2 6ar�H )glH E�%�\ M)� �bJra�for� & deriv� H�!O _�,�S�]&E�, ���%Y,�no���9�2e���� 0�<���^e�,Qe�4�.y&}c�B% "C.D���^er �!��" lessa�?Ln �M�oac�>��y �L purbpKi�t>:t at�%ergA ���, -�\a�Ua f0#9sw�n�> to s�YB "se!�u;@ true&�7�[� mletF"�T!&%�B�NA E�,Suc�4..�.�o H�h"� thKKf4o �XI{is viaWB� A��<sJ(�E pather�;, Monte-Carlou� ��(gruter,holz� m�V:Bn�7�e1 of $f ^4$m 7 yQ�l� G� o��!�,in�[�Sj(arnold,kash�UM�aD� L�/ys�k!� %6eZV�A�-3��2� ��� third5��by%���t reno�|=�p,�?\"/�v�Ieb`U� $N$Es�X(AG$-9� "J0 $reaIWimatrd[���.��$EIbbz};!#�%��3dAt� g�9$to $\infty��ex�'���?�.\V��$c=8/3� (�m^{4/3�� 2.33 wD[3_ ��,g)� (N( rel@�@��_�w] ;�x$ :r�I�,c�TfX���W�i9�;te����>s cmL��AE���0Tom\'a{\^s}ik-�iaG}re�)O%1�G3.4�>��- A��(�r�it*)-'��] !��}���x]\�d)o�-7&֍"Un�mogene%e d�0 no� abN�S��]/0$0.34\pm 0.06���}Iisimeq�3m�)%�>#'o $A) F25F�ݭ\� repa�9�da �alTw]&S"!K �)&� /Y n pAey25 l�ly�_z'yC>"�#O%c serN&� 35a��I� h=o���=s�i neg�W�T u b#Qg�&#llaps�W A �|`8 �&;G"�it� ��to�d� 2Q1 |a_s|$�5MM�"� or �(�0���symptAXi^$�K�( T��s w!3mdnl�� �'lea�5�,b �A&q� l|!;J� =� (a_� ) + d\,2� :&{g- O}�(.�"� ��!u $d$5'M�logarith(>�Ks�e�� ��"c Q� Za_s!2I� �*Z� $N�q R}<5{�=}{��a_s}{��}154eft\{ 1 + 16�Af Xa(!2LP �' \ln-�N aN:& +:Uz5 g *�$tcresf"E$ � ��T?6eZA0A�Mb0violet cutoff�a��!zc ass� 2� n� $T_c!�{coec!�eB�A�C ���iac�byтqQ2Rlog�!ho�U d $d�{9.7518)%Bpin*�,)0)a6 $N=2�64\�@}��a�in �僅�:�i� &i^�(b�� �by��� �T%;w��(D-�0^{-2} �;��o�`�%�T�a1R;��reby subuia mpro�&�Fr5��V�S�&0r�)�O- |�C�5atf� . Q�8�r��2Io �s��# &5�gA��!iso� A�*2Q��.c X�{FESHBACH RESONANCES AND UNIVERSALITY��ej Uadvantagjo?hb�S"V-q workdw� R �K"�DO/e auRto�RSr����]veTQ�!$ inconceiv�MO�� *~�"H` �Ohe�?W�s,Ai�dL�de$(;1�[ � . O>gP�8t !��var^"�-S%@�" . PerhapeA�d �Za�r=doeth�j �a��=M.�s6ORAZ6O� t bI_su^FF�O�2��1.f V>�*��)�!:�b�((�"�x��VJP� /$,.2 &��ermed�9* (lQnel2\ :\`/+��E�0�e�F �!�k and ���tu�D|>2� .��ca5��8gQ. ";1[�<nd1�k4b*H �Z�Rxb1B! Bon0g. 2�9FT!hy&in� a���ny!o� 1-(&�7�7�a_ or bchz%@o$� B~ So_��>�����b 1m;#val�TE�� )�net>b�Gmu^A.:S2 |��b��>� �A �2@�muA�T�R!*�FR$B�'.*v��er6�W (0)A�6�(i)�w�%b��)+$� B�I�62��e�>�ros��q�Y �, $B_{ ����QO�o9UVN� ay , kn� �F�%�r� proOAXJ�0s �9"T(��!�}Z��  )@�! |M|�G0E_0(B)-E_i(B)Y� �I�$� %n��w+ �+, a_s(B�*a_b� 1�H� � }{B--[}} � a� " �A]F1� � back�>)6He�bn �q]m=5� awayE�9��u3.5in]�R1RvS"�V�� �2E�!FQQP� ::U�J�1N�{_i��M�Z�M!?=2Uge|$U&, �Mh; �th&� uv?Hillust�!�J1} (fo#�H#VNin��st� W �ls, $^6�j�$�i)}&� �:�C"�Wޡ�s"�+�"�Va $B< M�$a�&'W  > �o u" Vb-Ka��F,pic��in�� ��"I �ng��n �F�},rt�)2o(�wit� �b #�-� u/N�o.&is�+lowG��Ƀ<]Om�i�&iN&aN�2ow�3;�Kesidu_Ge�X<4F` situ�(� N"�,"N_)_e ��0.�DeG!ZA�Z�\ 9F�qui���m]�A�a)��a�' G�<� deepE�k.ra_I�=�%vJDGm  "he2Tmo��i9�VJ��� a9�*HQ��Ea�@4?2;s empl� ���9�Q�ica�85�n,Z'B=155G[ ^�)�Ma�4 Aa"h��:Qa�Dl=10.+�U�q ly m�zy�zcor�u�C^K"F�c bH9o bw �_"� k=R\l�5�ni�P0� � in^s BCS �{�ma:]+%u�zs��F�Y�Nwo-�f"b[A�{\y;f�zity&*GPn�a�u_5 Aw�*z %I�%|Q_�!�"� �%�.�2B}, i.e.-Wa_s^3B>*�6nD�`d�# A�1�![b�@e�/%R>u~. Fur:� �"LacW ��pic�S' V�'eiR�s$� $nv"�"�!�� aCG�>��@)�+le� � fx.�h.S!9[q>�^�R�$& \gg ��!%)qOO{:���[G/y}F<�5; �݃pjkey��a�+2%i� mia�}�5��>���wo&�0�Gs $^��� 8�z /k^2&�1kA�% r3H"щ��i�a��u 3� g�)� ȩ�� G��!o�>i��"�AI� ^ul��e� *�@35 E_f^0 (1+\beta� �PFBL�np&5,  ��L$3 $k_f52%s d 81�)k$�%��()M*�(I:�%�o-aQwV_| triv�t&+"aVia{#x�4 ode T" T"m��,P~X car}d% � = -0.56E��Hu1 aG&est^��%�O� ��Hd/( Heiselberg�hh}�d�I!��90> �� �no �� � �9�'�Mja�J�&��<�/Y���f!�)�g ��zvir�y�?az�j�S'�, ~)S�� X ,ens ."DR]m��O%8�js elliG � 2m}�q�Ps"�E�ma��x�y�{y �K�vNO�Ed<="� coup#EJ�*��) )�Km�[!B+!�!;�~ ��ppH. e�9Xly.2:�>7ed!(!W"�c FERM7-PAI!-�S���L!�e� �͏e �g���z =$ly tak�3 lace"_�2� &�}�d���`"�A2s���G��� rapi�!low�u seek�� !�>�.h*�>�e(.} too��‰" he��.K�y ����akecce��3%enhan�k��k Y�%�.��-teg��j`%�2#�S7jopu�&�y� wo*�Mf) �l.�%N�,��e��5�anicres-s6("c o�0ab e Pauli p&2lRs%-��,&p���4!:"!�2F!�v{ysQux d.) �1mi� 1�Ucy FigK33"�&3)�&�Y卧50(�&/ ,A��7ctsqg��6�%p Ah,%+ @&SB0&�-T_c T_f\5-1/k_f�"��l� I�.X(p"a~*t& 79,, ��wa}T)�R[,ÅA��4f�`� aĊ*�!�2"{ �'is-�%M�.%M!�� �0�i��\Z�1� s!ou��T one,(*�Y/l�%:��EX� �< �Ipe�"�'�Ci�go�A;ous� )W2�j� VHi-�2(L (��of di�9V��Af��A�A��]!@Y�E=no�6*)�rou"��4eagles,tony,ns�=T+ �E*�a�!k%� op6 �}Q BEC-�c �.�l�k&&is "U�yBR'� lor�;u�it{fas5r6�2zFA{c;0-flavor-locke� l*-C%���thQ!sbaryon&�i{ ofBy6�sjsupm�G(oqS Oue�&�he='�-SU(2)I�!�e��rksahig��b%yEP! e��eV��er� �su2q .��*�m p`TjocJ bNp#��"�s����BeL.�B�x2��ԁ�?� oo d�'�.Af�*I By rampin�":� adia80�� V2��/�R� slidE�.�m� �. Ex��?uP1#6-� >��-�(randy,regalv $mol,jochim �2ANJ} |Xt�" y�D�|� i��e�qpy�*�e�hp̂%��$"= ! "D !vV��5Nbo�7-E�M R�� v$�sA�/U (���-eo�_�], $T/�SK&�+8$�o�-�5�E$$-��a����&��en2h/a �: GNZA�ich&� roj�u\onto U�4�/suA����&}� .-kZ�!fe�exist��$ w��,����)�2�5W SI�ACXae*w�(rr�0&v DukeM���},�y�2z�$2 Innsbruck �Y�e�t�V�%�!�X= d�= | ѐ� ~di�}!'Ikme!�$�# .�VD�m2#z!ing� A� &�& issu��lq8�eta 6}"։ity dg[� cold ʏ�-tI �s6e(�8!.%ۆHinc�\/ s"��E�.����U�Y v��l. Z�yio#@4lXIw!�r+vsHc�%�Rper Sc�"F5a,� Josephf_� �)_i@%�iċ5 in.� helium II%�6iI +� �aiQ&��ve*H3sied ou\� OLc";?b1}\v&1$e{0.0cm} \D@eH�0}{\h -0. e� 1. {!} BHa{Stoke9a�, "1� (a) ��`anti- *��� b,'wo &� ���+��0f�--9`Ss&W> p - :b>-&�;J;}�V:lichter1!*vb-!e�gh<t� %*+B.�a�iŁHebel-b|�i�� �4G3`8shlp�>CSX 2 (T)$=M �-BVO�P�PreddyBMC�${O!6x�� inos �Me�arr��� e�!'�I�X g6�A6� N� I am��g"r9(to Sanjay R���I�.&�(�v�� P�]x �eZ݋�p&��gapx'�">;nԙ!quasi� 1m El$/ (\epsilon6%muC2+ RQJ*�0 +d�Eg�L�&>� <�*� >%eN<&eR.|Cy���,G c��qd W#%sJ�4 m2h'�Yim 830$G�Q�<��-!f ' M~Ids $m_I1�/0. At6�He &�M� } X��Pa����$�k� ](�.! .�i%�� to 2��< pea�#� �r�<tH e��r�t4Xw|�Ha�un!�e.�eb\ra #�\�7reA��! P quir�f$\ge 2IJ�c��a���a��O�!�i���}!,���hea�bch!Uw��dep) j.� s du" �6 �]+�8�/l!ce�1R� <cv� ���;e� ,!) �se.�fl� Tlev��DZ�Q ��0vd� ectr�K'vl$�� er!�s&��!�a��,� �cL �� ,bart3 ArguZ9=6ncruΰ tWi<�����%� f!�"�B2�6�: -de" �_E%62� l2�#x)h��,1��AG�aA�-�cd��t6Re��� �ng.P }��_c:�Qe�&,(Tpin-flip�V 3l �"Z(.�axF --2t& ? ?�T�x��23 A�!�. *� &� levels��Z��4by $|\uparrow\Q"le� $|\�h2)��E-�d0 �eyT�JSv�c-l��, $|evaIf-"��t�de-d��o_B��em�k!kɗ� ��pov6-1%b:*� � � >����s}�mi��)@s&,-�eu$�f� �6�ng(�,!ZN& Q�"�Dwy�m� a.�.��)��s� ���C searW��.u��,a� US N�yal ��ce Found Gra��,PHY00-98353 �3-55014&�.>h�{99#��]} M.H. A�,E,J. R. Ensherֽ�"Т C.Cradley��S8`t�J���wR.G. H�, v�Bx 1687>x+kinast}A�K � L. � �A. Tu���!� J. E�� omasR�150402>z"'� W. ZA%qSta $H. Schunck�0M. F. RaupachI��WLf�..�2N� !{� %wBar%a�qAltmey!�S. Riedl�J� x�cker Dem�laR!�imA$�[ce 3051�112B�pi� } Ae�Migdal, � Mod.%�, 5E�78A�7; G.ͫjSt N>#ar.ic! Heavy I�!�Mm , Les HouW� se�s4 XXX}, R. Bali!fM. RhoI�G!$pka, eds. �!rth-H�-nd��D~Co., Amsterdam, 1�, p. 745��4D. K. Campbell� �* ���i}, v. 3!� Rhq� Wilkin���4 1979) p. 1031>���D.�XKapla�XdA�E. Nelnm�� B1�!86) 5)�E. Brow <�($. Bethe, A�\E��. 423��d4) 659; 506, 780 (1998); V�X Pandharipn�e5J. Pethia)!|Ve�rs.�-� �75, 4567m5)>���VGS H.M� twylA� �RzU s, 8M82) 7B�rh�� S�p�' talk�N. Xu, P!*aun-Mun'�jan��-P�Mlaizot�)ZE'|�"4� se �ee�+s>���ai Krawczyka�G. LyWUJŸGiN| B��Joshi,�) . No>R.)�g Soc.�h 2003a�Fhh�aF��af Ep�j!�B. Link�dicaAZ�92) 1; M�Alpar #�E:�M�5,87�d5B�.s� A�L��Bf. 73��1) 30F�����CPU�U+v!UD 76E� 6) 6>�$ng�ts}�fS� �ER�7ExI2360��%"& � I. B�, T.W�\"a����T. EssTAqN��4 403 {2000} 16B�au��� r� A;0Townsend, H.-�Miesn]Ỗy �*2�P97) 63B~"֏�"% �l�.�T.�r��#9�1ɜ 2) 3B� qfs}"6�o� b�+i� onUine}FC�aF�2�(Solids 2004 Low TempWA�� �`p�)T�(-mat/040840B�Abo��(R.~Abo-Shae!pC. Rai ( J.M.~Vogel&:� 5n�1) 47B�2up} P.C.~ ,!GCob���Enm � ~"� �.��A2�� 21�;� BI..\ 2xˆ^9e:0^>ujilatk}:i.�V� weik �i8E�j��� 2�91u�N u3}BZ6�6� P. M2Mdorff�Y n[92 ![ � ��$c5�NC. 1�P� )�V. Sc=S( �nnd!A9lQ� 5240>|"jku6EnEA a8) 043619>TFG} U Fi>��G J�90-� 16 B2�tT.-� oR�Y�06Nd�o� Wata��� �uN:�93�40JC�e} N.Kd i�F. Gun* RE5Smith � 2�0  8) 2265;2P��NS%P6B4 � 0) 6?R�|��b�NG9X� 5>�V�f�- ��H��an !]S�Reima!.�A 650) 0536F$g�_�= Reij� , F.! [ Lankvelt,� Sc�.e� nd N!ad-k6&��� 1; �%]� 02361B�&�gG Regnau%i Th. 6�601B�bK. Kas��sud  Tsubo���M. Ued��ɢI6 A 66�d2-@B:KBA�Mhavoulak�ndyNewE�X�,3) 51.1; A.D" ack*" 76L:[A 7iЁ�236!WE D, GBAWE. �bBO�qE 19� M. �R� Im n �1.�436F��}j�)!m@B�"�a�\ Bret.6"" Y. Se�&�� D*bR�!J�B6b_9�J2� ED Holziw F. Lalo\"�d D. V��¸:u+ � 9); Euro!S� 24�c1) 17F��_�� % -� B: A� Mol.9K"� 3t454B� wM�) Gr\"6Y_Ceper A92���7�7) 354B��Ta�1UR�r!J2Q -F83-H 2J=$U�*sVG. Moo+-i�)��� ��>�k�YA KashNokAN. kof'ev� B. S6un i- h��B�bbzjz!k(J. Zinn-JuseAHs b4 0)�>�)Q/>B.6�W:w A 64�1�20B�ZT.��A>A�B26on�)'B� ��QA�)�q-�br� A �v136F��@!� ish����lru|J@Rober:� -�knd 2 .U͉�!�79B"O:JM[:�-Y}, V�P6EyK.E� midV�&� � B�hh}'&p:6S8�. JT)�4) BR��#A/"�6�S��|� O���6�}i A��3) 011JW *B: T. Bourd]!c ubiz�C$. Khaykovi��$F. Magalha!S.J1 : Kokkelma$ G.V�)hlyapn�+�C. SalomS�2�=�9 2>��9 B� Gl, E kuryakf I. Zahed,C�$-th/041006Blr�7m�la�^�MA�Chiofal0R. Wals���Q(��P6; J.NA-ilj .;!(Mqx:2� ,�'b.eF4}ͨEF��186�>69)6>g~4BD�� (Paris) C�8a�F sr��Nozi\`ertndTSchO-R J&$-C59H8"F -4�3A�Sch\"aW/[F0cze>�-�2W99) 3956FV�3a�AbuC�T. Hatsu K. Itaku*2�D�@ 074014;2,�"f A7� 3) 8 .c in tOS j�randy�l{����0Partridg� x .yig) }f804F��25&�$C. Ticknor�L�2hzD.!��o 4� 3s>^�zmol{ .k.�S.:M �J6}�2�B��3����fGMnC. MJ &2/>~�B�M2��>II *IM��"GS. Gup� ZA�dzibabi@�R ��� 3) 2 B9d�1RAxD e�*J�451B�cvE�J�0 ~, .U928B �' Q. Ch�!-j�K�viTon� 1109B! ['v S(:*a#EN3��4) 2032Fx�& L.�  %wC.P�hl.��)�11$ 59) �>�georgk M�uuw "�N��QF� �"aKundu�!.�-,0#� 0505����>�" *R��&��,style[11pt]{�)A� put{��.s�G \ren"��{\�sl8stretch}{1.5} \Y�Wp22. cm w��7;kip6s%,opmargin -1.odd�.5'��. c. �{\cA}{`A�02�e}&�u�#>#e#en*��2���Da�p> e AR alp}�,} \def\bq{\m�2\boldmvh$q$VjFjrFr1=�%\b�3tN�pag L\E{� } \ { {\bf�t �� zy�'ѓg} a � �h riza\i�� 5Gc�B �4u� so*,"�;z*f* } z��� �F\'abio�6rag7�H \thanks{e-mail: b D@if.usp.br} \\ {\>1a4 Institu�6W\i I&��dad#? S\~aoDBo��4P. 66.318; CEP� 15-970; *D - SP, Brazil. }\\71�� } \m"��-�abs��} Symme��![�C|4*m�9K massn(E}e�6inv7g M=���2��'")� . B�Q?* he n( on-p�� (n-p) :i !�y.?�>(:[!�ac(���7i7�-���8y F"���9iAP (5� $), :��d%4 ($b6�.H($T$) �ex5Ud1[A7um ($q$)�"s��$�arfKh�Z.n], a�ge�|1t1 �) propptkA!�ino*y0!�!>s �s n-p ��)/,y. Some sol$��P"j@%r q-q(�R��e) #;>�*:cs �CSkyrme-t��z�/.� � �wr�]E���3-�ucQon. Spi._6�E]r��so2n ��ic>};�L#ng/@�[��iPFha�9�=q$ !��o � �@2��J:�one. �vu� %PACSl,s: 21.30.-x, 465.+f, 26.50.+T6.60.+c % %Key-words: >.���-�^t�`Y%, %screeqvfuW�s,:Sy, %��a�l%Qji��qst��`-2b,i��<�s,.�,. IF- USP -�.�bI�?>1o���/6�y �a�mr}3s�: -�gof+1�Ot��ܑ[&]OH$��any&/��wA26&S�j�to-MTQ!&rsiu�[>X�!Ahbq2�\�3p9LE/ Q�t v[�.�1�"�g1mvliaS�X ?�nS$$25$MeV up��$36). It�5Y�2r]4|7�7a ��\�C � F9�co!��C) ����scX��/m*R.��-MONI}�c (�}b���WxiT�oȮ On�P��� }< (s.e.c<�a_{\tau�^��b+�ng6i$r%�simplif�?�Bz> ��Vr�0a{: �� �1� ��y L E/A = H_0(A,Z)/A + �,(N-Z)^2/A^2,� eQ!�1�$H_0$ M\�>��m. Z, NE�AeK���R%t)�s��p�# � . N�# =>G�f0ic v �e y�q��erm5p ?o�/�BW�d��, 5�J�_N-�_% ^2$H5,9ar *�e�o�NN;��4|��. �c.� � �`mannt �@�qlyIȢ�(�?i3���{ANEUTRON-� }. D�yt� yno/�!�2r;�2�x on (7P� }$I#n$Ō$n|�q 2$) uaW��2Fo3�t �aQ�<,HUBERetal,JACO,LKLB,NEEG,SATULAWYSS,DANIELEWICZ}. However it�)AyA���wh�*�ho��is^��q �modiVforuM1&�I, a�as)�i far !�Ր{ �y��(I) ��.� �jv�b 7 JMy2EOS-rho!�e}.n��7yle�su�Os�E208}Pb|T2�  (-�e� �Eeq 1/9$)!!Rs"P s it&�:Ani� ��\_>1F�.) uU$� &�{-BVq2� �8 �4) BVA} �7� r��C"iKct�JBt")J��H ? B�a�NSfuÑ� 000-}e�*�aypAGsl�@ly&� A�o��>!A�OY#-IU�. O�C>:=[s�)��eu�in>lTN ���c�Cg ( $A_{\sigma2m-5J ! ɧm �Ex!���%/J�.��r� !�6�.���Wula�[:.� 2} \ba{llB�\f�p E}{A�v ��}{��} + !tau�p��  �� +^x�,). O( S_{up}y_{�8})�e( +   D)QIp^NN :+ Z dO@rhoup r ! 2} ,� ea \2�d  (� ��\�t) )A� ѓ6gis=o�6�:x_N,�_Z$, ;��� � � (�)8-((5'�:���,��}^i���h/B2 `(�ya��lnelet toV �A���fed�9尭�weJ �9oI�cst�|�T*�a9tr�Osial � ��hKUTSCHERAW1,KAISER,VIDAURRE� 84,MARCOS $91,BERNARD 5,.� ,FSS��h,VPR,VB02,ISAYEV,BJP-IJMPE}J�%��X(\u��ePL %zin�� �Gp-"Ǣi*9upl��QH9v��cur� tog�%#%�c]a"���A���r10TSAWYER,ESPANHOIS,REDDYف�2�5�as"i�,VB5e� �I,MIGDAL,AKMAL�� DHAR4�%(���;ferro"�B� ^N)x}�!ear diE^� omH �y�?Z��� I.�}���Xn?aw-^a-��p6`as&k UO/E� va�xaccor��4 �QA��щy �bve�&U3��%��c[�e� Nj94DGR-YOUNGBLOODA�)���"us � XcorT�o&�>���A�E�&/!�� h�Ae� 6��e��l͘hr}/[U� in -�(YOSHIDA,PAL2^A���bD���!��>�U����b�N� f%T�ar!JpZ=�C!tRG�O�l2Xm�Cc "�w�r3� �ra� l��&Z B.2�!T�ic� I�BVA- eref��it�>oF�**v�id��e@*�A�a suit�]nd -���!�C�D8We%L7� M�� �"�U��b" ��aN� Dev&��De���#4lsi��l��s�H%a"� ZT,�[%�Q�re|�ce�4GAITANOS,GRECOaO,��D}s�ngI�� �i �� �Pz:5:3'a�.{H��"^��< 0�pO*"�q�I�We"��A�es'�rV]aY��Ap ~r��,owadays mainm  U� P�-�A e�Ghej:�co���lBAL-CMK-WB,SCALING-FRAG,ONO-�X-,RIA-GSI,IPHIC,BOTVINA%�JYLIU xCOLLECTFLOW4rho,EMITTEDPARTICLEy�%�ai`�M�" CM7 EkA�iWY0Gu�+�!�c�4q���t �_a8 )���vşnew&�w facil ]QRIAiGSIm�6�!� neutronq�proper% obtain�SDmicroscopic calcul%Ds \cite{CHABANAT}W(i�Q�C8giant collectiv%)IH0$^{208}Pb$ S,KRIVINE}. OE�1ill!e.�0 elsewhere. 6�can.6�AduE�aS�=Q�I�y!rix �PBRINKVAUTHERIN-NEGELE �Htheir basic struc�Xa�also �� in non re!Dvistic r�%�2models �5�Dsystems by passinga�27poi%lupl F or�7 �LSULAKSONOetal,BENDER } suc��at� necessar���� 6� each-I t�v ex��ed�be!Ponger than considered!aiearlierq ����s�4FARINE,ONSIPP}a;e>is �is,J,part, an ext�o%�!~ viou ,s E��0 organ��(as follows.�wnext sA�on� �z��Y�&of:.yŇ�䅭=1g�|2�e� a�discusa�includ!�p��y!wE� onicA� ter ���!!}! aa�urb)X��3 a�Dٴ simultane!56�� >$��eI�S-proton��y%qo��qeis�"o��a � ial��tA�A2trainsi��$wo behavio�9:{�.In�s 4�5C $q$-�(��d&�between�componen�[%v" , eg. �{)s)���ic1�ElBAR�A�%:�i�ve� "B "6 ��ic��m� . !!�lasY�re�4Av summ edie\M%{ S� A�g)�6�E�} B��e�ta� R,*� �ipr2�� reproduc�C�6I%�esi|A� Y� sourK Xamplitude $\epsilon$, �cse�tes �onM�iPqua� numb� $(s,t)$ (�y $(0,1)$!���up-do�  &#M-m*),� n� q#Fz ��wr��aaP: \be \ba{ll} \label{G�} \displaystyle{ H = H_0 + \cA_{s,t} \frac{( �{� _1}-.2})^2}{ } + 1>H' \beta ,} \ea \ee %  $H% do!Not�>>�� y $(Zn| $, $�$ !e!�&x �y�coeffici� ( 91,0}$5%�one, 0,1 6� one)�-ktotal5�fl�ޥG is $) = \delta :�N2}A|Ath��} s. FoA�e�-' R�4 ($s,t = 1,1$)��2��Z�% (up/A� � /�� �A�a�t�f�~��$just like �AshA�i�s�e� (\ref{2})�fx�A�,$(s=0,t=0)$,scalar B �s aV ge[B)��pq"� 1�!�: ssoc�   di�n�&��ressi�@n ,NPA2000-2001s !�v l volume�s s!bec���on-��3�ground��e� va� ��=e�y�bec��=�!@)nel)�$), $]y \equivi�Aeyield �condi�minimumR? inducingf��  isA oted ���redef}�>����')|�%o!;m .%] ���.�ч� �,to have a (�)�pup-!��ic�# given� 9a1�.�ly to !�(instead of)%F.��lso_1 W $ above).1�$ M�in mostH ao�paper we�"� 1�abity=!֍ˁ�#�� ��"�'$� ��I(Q)2��-�$, �0$ively as:M6 AqqB \Pi^_!��1f ��}{g '} =A� rho}{2&= ^a},e�\; (i) a�e�� Gbetcrb}_ i). E�j�st ��!J�TeՏ"\ !�7K&f below��A�mai� velopQU.foc��:9{ y���0�although~(oge �:Q�bT uGyZ���  def�by!��2p� �d�i%n,�,_p$AP�W6ObBMb�L)ف7n��_�1�C!� A.�*� � i bably�familiar�YaVreader(�3R�alpha>� \�(2�{n� ) �} Mb��eAy Z�j: $�2 O/ (1- )$)�� $b$��es� $b=0�iU&B� , up�0$b \to \infty 4� �G.�!sak\ L���M2���$!D���b������y2�� $.i�.�^>_f 6�$b)9se�uL1{tof �?ref�iy��b1 $�}� !���(��!�Re�ons��e" ���been &�$ed by meaX az crip[ s. Amo�hose,k �lea� oA��xi� ��lac^�a�tE�&W _n \left(� @2+b}{1+b} \right)*� Wha .4 _n%�AKQc�2�&;!�"at)0 = .�)Ni�w%� /,� m ���!�2BaX� nsatz�!p*g A%c}))  baseUjassum%�EeJ�� �or!�alAq!�d��of�2�, i.e.,( .�/� ե /�c$, be��y����yшI#+���-1��m.� �$2!l {\�A}a = 6_{sym}M� 2 bX+ b} I�v �a�� �$ (S ,)"l {eff�ve *y�is.B��\= a_{\tau} \simeq 30 MeVu s.e.c.fY�: (��)�(�� zed).15�*  re��� $��^�A7c -8 (1S �� ),$$�@c*�� third or�6ma�A�bin1}M� small�' quad�c= because!8{ < 1�InT :�a9!� �oseG�;#y 6j"� li�i ^3 <l��$b= 2$� = 0.5�>�three ti�lar"y�2�y)�B�EQ.5� ym}$��"`o���lal A} (.�)�q)� $. a �ex^��< 0kPrey�I�������"�tŶ"�  choi�� �| form�a�(1�ic)P >�``screen�� s''��e n��Tless s�9�is .�(. So far!�ha�e sum>��A!l&��: a� of��($I$e�B� `�,nvisaged a d*� to guide!d .|� a�H� �bl�SevB!*'X��rol� aZm"� $on observKa�Radioa'I���1pr��or RIA%�GSI";i���1N�$is extremK0relevant. How�A7 masE: mula� e�Y?�i��iD!!e � � Y�%�=%���LX>B. :N* ���{\i�NB },.(i�1�Fura~!!,� elabor`  pi�%�a�t�' J .="|� s�4vector mesons,�nvecQ$,� a��litcc�!%�-�9j5�y�ith a�!1@ce !j 8%ґ��`Ees@�KUTSCHERA,LIU,GAITANOS,IJMPD}. ExperiE al b0�d�BAOANLI-A�}m!shed l� aD���#� "C65A~�~ 2� "�lymQex;e��e"q��_[m�q"� (]��al� "en"� as $zsigma� � *�� �l f � jPLandau's Fermi liquidAoryMat���2�waA�*9in 5�]&1� BJP-!�E,FSS,KAISER}�  \sub�{ S��"�s}&�&e�i*^%� \o &2��neias!�Lno ( $�&re�two way��L ing a � �����a� $\Pi $��*c i�& a� They*f �.�aq4�X&��a?"��,b��,� ��. $(i)9 ="��M m$*i��a� ���2�A� &� ly bJ}!5� ^D �O ^a}{ �0� C� }{(5d ^a)^2} -� 1}{�L, :N \; . 6�_0 @ �}=�$,&9� $C^�FL }{4(K^" )^e�s~onstan��=!�I� valu�6mA9"�&N  -� v�v&� $�  ( Xiw)���F�I�1�)e)�l �V�cof��*N"�R0�deriv�� applAWaaan�"� �s. :�&� eey�n�; %dM�7"2���rom�  � librium ���:� �)�&)�# ^2 (E/A)/"��^2 > �� � �q z�d>"le�r��m�?$, satisfy1e����!6b � �^2 E/A}{ �^2�`agu�2 C F> 0}�(i)bY �t*�\ O(�(, �-6� �g^a����H�@2�s�+qi Z6���)2ie��4�T ��$� neg� (stE�:�( �})[ posi!�6D!��$�(Bsor>. WhiS,�eA.,ev  ee+X$, E��W.e�directly�� sig�� ��$!r i(�[�Z� first ��t �involv�-& du"�+ lic� oefGB� )). �ae6Ny:--(i)) �!.m��' realESI]!le -�V�H2Bo�+\; (1[1ai` < �U)�y\;>2 >J0[2 -��da�c>c} \pma|sqrt{1&C*N8 }} "� *A%w!%L-n2aZ )-(1!p&.-p��y� only�-,���H*�.T%�)R$. keep>-�)�ɬU(of:N%. I�/4worth emphasiz� �L:AI��})q��!c� ��An.�should c be mixT'Ifh2y��b -�<)�3co�+��} .� /���5d,�%wiu1Jst� �6Bise?�#o1��i-�R�� �&�if�]d�'7� �:���:�&eq3^��P�P�PaP i�\�'- !$6#� "u.�t-@� ���.> A�&9�ej�9&5� g�{����9V���& �� (thro�,��� �ݑ.�� ,� �%,)is�a �>any�) \foot�/{��7 ?��h�  mq?replac�ynE�alJ. for; �6�7�Zin�qed)"�/!w e saBB��([W-ͮB= , by�!ga!Z��fF" (<!'�$1.�0 up-lO8ones (�� . 1,0$~&An. z>�w�>�SDidH"�K U2���(%�  �BWG�4z=" 2 (���= ))�$B���,aN.� \mbox{A�/ or} .0Y4B_�2< &c�m.$$��&&��:Q��*�:� &# H%�6b/fb>��? = -81}{(1+b)(2+ b)}��U&�/*B&qn �9� �2�T e�3 ,�7A1�, � > iB}%��ɿ�; A0:� 6�a�J>���i}-�5�4&� b} *�2 e*6%�D b}. "R2�%=�E�"/�!1 ho)$�)A�` typi�'��&�#o�A e�-i�#*(&-)*�:���P� >?��aOD^=�,qk\�,E0��@n�NA.E�@es,��I�it�&�' �5ea*ŀ f"�,PAL,BCK,BALDOBOMBURG,WIRINGA,ENGVIK,REID-PARIS}. H��%~����fŠi �>ng)��* ��� IS) holds�L!b2�n�U<A sL$�2{�~�B*.6$�*")$$Heiselberg�Hj�-Jensen�"7 )^{\Z}]>��� $ %�2<d���!9Fo��k� 6� favorx e Ja� t \. 0.6$ �asE:4&�Iheavy ���Fi�x.e's)lowi���]2$�#.�2on le )��wa�ed >�*%Q) 5^� 1±O6]%��/)���� ( , }\\B�:c�-�ym&+�-_&�._2705_3"/_4 G0z6�@ A0i$ (i=1,2,3,4#!��~?Whe�& ��) F� eq6}� acheW $/6�$�_��alp_2}$$� yMF���[$D fME�ign mak� H uG 3"accor 1�FK�+�(i�� F� ,j�Qj EEj,@'��a��eJb�t^HeW:`s B+6��� ��1 Iw �W��-[ +$a=8�cT&�.� � �v�� Q3 4�31K ����N :�7b ��={0+ 2)^{(�  � )}\,92bQ�6" \,(yP } +  4}\,: YE�ha_1}\, 4� � 3@� 4}^{2}� e�A \,b}�273{ B2�Ii�"OmVJ�&�A�A�6� "Z&u�,�1= �%0�+ $B$ fI�"� _0'3e2fMk;�90$c#-�9N to�X*�Drho:`2%:�� m�C?0Im2/ 4A�qt0 �_1�?_4A�� 3,�3���Y�appearK ha_3k=-�Msy �!JK$�d ccurv3}1}'_2F�+� eq7})% �� ��� e�!�� + V#�2Q"z1!�� �; * 6c2, \2�G�'d)F�E2UKEt] ��_�N.�j8bA!� = C�B.k 0}{�@g7��^{eҝ*}�7.<CV isM�by a �/�(�A�!iZ A�rh��E a A�!O�A�v I�e�: v��2^{1/ /} e�0av:`Ii:&= �.�<�%�-�in%�L+��1��:�9~�e�i�!�)e� (!}{ � �}} 2�H ,!*=� m"� :Em,V1})*("�o"�S�D-H�&�2 �8(orA�idly�$�$���� , �'Sct !d�M B�*� �*n-p.��exp^(�&��%uXIe��K��F)o$, ^T�Kr� al situυqA'$p4!q ,-�( B� b!d&n9: $I&_ B��g(b�A),�AF;2�I=h� , b)uE u1q �-�\0p 5.����F(b,?)$"�*�V6�>eq4^M� .�� =#�%% i; .� C2�e��.�M �� i;Y{.E;N�:�-e��nv:e�a!����"  z2l12B��Js.$"D!$ f����J6OTy te�.X67X Bn�Z&�6a�U�m A��)T%[�)ei�.$.{!��_�<�� ��m�G/�re!�en�<* (6h,�-�'Ic,��TC�;d5�u� beta��$�)2�".f)L5e� 5v) G  &K"G�\"SF<"%p�#�W"�5� )��",�"p�Qlz@�#FLB99,.�M,B"�.!�V5n�%�V�3-�.�!9'dVH\y�$J�$hot5�K ar )��U� ]�8s, $lim_{\omega0}*�4( , q�5Eo6�]�Y�"by� *M: �� :A'�6Z��).B%R�ie�M�4 P-1 �(e>_i�&m�]"C ($p&= kine!�AL,gy ({\bf j}$!S " �?u�t Hart�? FockA�r"�[%�:�]�BAL.F[3�&oJ!�i�YZ �N�2�8�' L�0��8&Y G�3bpY�>����Us CP vio�`F�&�@2�D-W� �)�@+:*� FourU��"�6s FY.,ed, $a, b, c��$d&\Du<j)!!] they�XR�5f�F�Aɾm^*_{p}} n}��1 2�0�I -�� _{0n�rh p}} -1.0 ci �+bN8�&x4:MUd2 lG �P 2}{3} F�m_i^*$%U��Jc>I. S�C I�^��I: u4��Ŕ��1�2�1ȱ q�-��6RF 0o cho-_2:,��&r�|.P���]I'y -m r�S"�/a�c}a,Qond6 �(�- S�B���con\0!qAes'#Yn� . Ad(2rl'B�mD"E*aJF="�^A8_0/A)g ha^2NH�@$%expanC� 68G �Q>�I�E_0}{A��W�&. %"_ ( �} 0&|_��}Xe. %X�o>Z�B\^�$� >^...�S�� ber ���eD�2-;�Jr�yA"��(�F)J= . BP,�,�S**2�y,EO�+he�Far�m ���wh�C clas��>)diagram-!ntributH@yA�O Mj-��ɻ NEOR�T��L#G,tV�"� *.*�-a�W�f�>�$n͂�he2 �*�F��a�T�Res0c;,�[q�.%� �l �plane wnT�Y�X:Qi,>V_{exta-"P?�hat{O�G,t}l>�GD�>� - i�  t=bq.\br)}M�.E&w<�"�?$ (e�ly�;��pa��Wa�C"�X �X$cm�$$�$ (!a"�L unit�1A* 5h�u �cv1$ �$ a1h�eC on< yZ2�4*�&�0*� %�cJC9_-� 2�$(Pauli~ueEe�A�zV A0wZ6�u"2�Y� ��2� s�5&�R�HFeF3U�(_t@_i�@i�N$[ W_i + V^E^_i�rh'�� ] }k2e��$W��A�2! of�HEa�cEs.0-iVdR+&�+� :H o� spa�A. io�1yY�Ih[a �8:r�I61��� i�\�g�gly5v�M� of q�M(Lindhard"8s�Vs� �6ar�>at .j �e�i $F_{2i[]g� ��VBVA]V�N16B/\Re e� 2N}^{i}"� j q}) Khg M^*�Bpi^2} B \int \h�&d}^3 k�% f_{q} kw q})- ( lkl}{ 2 +i \eta-��`_p'F)o k}+ K� 0'�` . ( +q })M�)^N =v?B�� d f_i (k)10; )�. �e"�,s $f_i(k�Dr�  f�F;(ccuA�on"rae�m ($i=n5� p$)�zJ� �;H the E@.?Rt�an $�to��-(k- k_F)� $g(,U�cy � or�t�ab�1RM� i' 6� a] *m��&5D �ofi�.�dv*j$`JR�|�& (q��)��-m �f� ". !6� ��!�R��7+BrN_q; ] �>Q:r;MuF_{0}��!�0�E\F`"���en>.dVeM�b4>�.&�(TIA�b+�5e&ho9�:� �4��<ha�s,t&�TkY�for$L�"'fT ASYM^�� (q*�G!�^q}{ N^ፁ�\{ �2\over#R{V_�9}' +6 V_1�9A5 F + ()� M^*Z ( 9 -$_q}^2 - 4 %�E��¡�� \} , 9�NW.��^2���&V�r&�o&�-Y%O�/ �*l8 stc!�Ap�5ix? >�B�bmodulu�ZtW2 $A_{0, ����F^�,� $N^q�M^q&��Vu��.�!��/��2�!M^2"z!re-� � a homo��Q]: 2��, �;��vec{j}d� s �/�O% Galile 9nvari�0(.}!��)�� �&hm�` Cc�W brokoZ!se  kOS� ^ fieda�CF3 $q5ƭ�c q�a���@F�jK ?��n&� s�similarl�,�P0 k� &V/p Jw��7upn8b%�o� p sJ�&72#Y[�хY!;.�,1N]#.N-U� �W2��/ $w=0$/<!"�0Zs�;Ai , as^wei36u2.I7�(]�� �e> 2kPR�AqFt,�F�-1ap�Z(T��A^{(1) (q2F^2Ngf{lD" uQ< �y"�L*&�Fm��&� 2�HC{R[(i>�$ Nd)O !�2AP� s (combi�sm�;$�Q��3� �( T. � .RRI.a���*0� !�4�s} i:!��nFfp�G.y/ er1lyr c ~�VSKM�ISLy&)fEf�-�16!)ticle-���*9*�N�-? n1@�9$#w (F:�e�x�U!ADadhk� manxA*�.�l�&2\((TJ q As ;�u!&�&i�Cvowsvgl� T{T$��Figure 1@��R2y !��B,}(��)��u:#e"�ys $Tn, 4Iw$7$Q]c%�!�b%�at $T��MeV� $KM. BOodWp wid�Caccep!q�&sUNu�k }�,h)�g�-, (q=0, T=0) )032�� ?A Q�&`4(��O �a�@ Me.�; f de�W�C X- f45e9d]dq�500���7�/2 twic��PM�F� surfac�&2�"pr� "�N)p%$96� #�^ �%���� ��agree>' 4> " !tA� 6u�I�"8YB3;��@AO-DAS-GUPTA-GALE�Y*�R]+H7,Ado"�/*� s ' ,\� a $q�(iU/ f�%(;an abrup)^�}!\XaFJ"���Z !>�� $arqE�) -�a�IM �Qmat&�#2�-eT!�� 1�q-oUB����eV,t�*7 $t�/�LSt�4A$2a&� }@�8� o�K�{(k � �O��tc3%�er%��e��� K/or�M�!�($t_1, t_2$.� �j2F �G2r>t*A)o���gR� ���T� si'e.| �2s�@Gc� of�1� ��gDka quitQ�j �4.q Nr� 2cpi9 Mpre�ksQ_}&�3 �M� A�N�MeV ��c%�s smojB%���anE s�i!��F�nel�qjnF�6�f�31Eέ�a !X�8E6s event�~�2�a U�E@ ��&!%. FB�����M� m�K�`qA�In1�3 ��.�6z�0}U+a���!s>?U+A=pr�wfTs.�ur�Z �|pr�in�E*�-rs�+2�\W 1�2ph!��?(Fm_ �s.T� A��% & &gP U��H�FtX"b'%�����-��+" ^���8�CdiC')�M@�=0,r��� �� �nu�2� q)e�2`)�E9eI�ase ]�<lo=�Xate�= q_cBvF*�� ɢ!Ss?�%-��ws.�` :�� Gs*'Kaiser� in Chi�Per"}AxorymG�<}ف x ��e ��F (�I� �m�la)D2q,� _*� ,.it�/6�at Or*�H #s�^a&Vto.�pQA��$one towarE>ferromag�'alignJ h�"@f�P��R�`�I�R6� andv"c%?!��"j;VIDAURRE�M84& *,ISAYEV,"}b,W1,BERNARDOS-95,MARC �'� �tr\#�� � ab�+�n�*5!-X��we"w�.":) !Q2B 9B�>%:�(n!�s "�l NN.}-R�method�O�a$VB02,VPR,K�a��= ! �.6� �doD)*2� ph�TA��"E(:, o�*�s"0�gl"�}NN ��or �-�Oi�by Liu^Ne��m�LIU%�1}=7 u��� ADZ=m3!umzsoc&�f 3�4FjA���"M es ->!��Z��refer�"����i�-0�&� ,�F,A� 5:�47�4��a&_��&DQ %L� 8�qy(mean-�f�&�B2�on-�f cF�= �jX i�e^ 7E ny bodyAEble�_e!�I�23A�subjec�3&aQ�I�mayE�capZ�allw� l�h de� �#freedom Q&| in�.`Q�M��%� N)�^!� �~, T)$&�v��8ificantl�o�R 4�>,VH ��s"� �"7.-)A=plotted$t�#+ tinu  �thY��OA|z 9��Z6# &  T! m�er��$�X$�!iXq �D>Sq1p��om::Z �H �&t!TAm8�$j�a�&U!/�"lK�� �r�� a-2A/%�vM alufv FE"I&� Uly �j��6ziA8_l�� hBg�I .�4/.�E2c����%zi��@DEAN,DONATI}. M*�7eD�cF�at�@.�z("Ee�FS�L G�� o un�[t1l"� !�&�)iQK2#�x!:V (F�=yAM,UT�5�*�T��,AkU�%�R�o� �Xr))�6� -f"� ����FO �!/%�-.�"5q1}) 6�� to 4�8^�� 2$"a a�&Z toʅ+�2$q�,���;2|J| �HM$,: a dra��c�Xg�2t�%b�n-x�l>�+eo�.��'v 8%�� 6) � ,a*�i�>�'-p�'Y9����( i�b��M.��� 7H } �<�k�7&5A752,�!� :�1���i�`Q��E�,�Mugges�.at� �2���s ua� go � && � 6k, |Jw�?e >�umA.o�&T&�0NM, $k_F28*~ "�FH�� $M_i(qg���� qmN,!!) $�#�{�@Yw�99.t��goF$.ҏ)jL�#M�1e�3��I=E��&B/JL�e�D&U A7A�B%� �ed &�Ko2J�MHpPX*��: s !�rM'-sA�O�p�r�)� � �)2��nQs*:-�ly-[�E0�����!0^@Tq9 }(GR,BRAGHINVՏ}�Md��w.U! ��%�*! 2ei� �aA�� �(ui��o -gasB3zPL\$CHOMAZ-SIMG >�E�w ��]r0rwidth�^ops s!�mVco�Ieh�iv�jyL\"�R� ���d��h�"���?LZbA�tom��M�&4 0Supernovae mer^�r-��� " "�rA!�"�9�)�g\. �Tݦ��}��r�.�I >4�1, a�}� �S�sA� N� 2 (2vh��toH inos(9A1�, N+A�A�&-џ&:�! �� ed� sm(BETHE,REDDYMm PizŤ!a:�st� � quasi-� 6!1�EbW��]( �.&�i�B�� "S# .T"L�!N�s�i"�1L� o]^e trenQ��a#)|��9��6�(U�)-kBmiQed faci�uZe>q!�i� ul�hmp�3� ��er�%�-�h6!�>0�ty�l�I�t o Ae�*� .&6^X(A�J&�A)!� seem3be rah> p:�9zm4or"et�� new *�ys!&e�= �g� ��zne�f 9p6w�&� I�c3�2O�=t .�yT ��iy "�2#?S4�Ga��W4�!@:<B� �(s�% 2jasfuitz"��&������ �ao�& .r5 v�Wed�p�l%��to)�s�$�.B �L6d,MU2�p*E�"�45!�%2 a1�Y,�i.r>��]J� �V �F!�tʏ1ϩ3yr#�sediq�n�Eis, no!u*� du` e2�� �����/�b�O� � }a�(.�yH r�d sU @�� q,!�B "�'a! 2]�$�|b� ��?�7�� . S���N���^CIV|)�aroced=$cnte�U!J)%�iA�� 9.]W b�w?<�}5p M>�s}w�  "{}��� {�g�*�} machin�T<��)�W4�}Q�>�-I��Dt(one��i2�:B=z U"A�\*�B>��%���I��-�M�$~$�H��H�"4>2�Ʉs,t}$� .�i�&a�A�>Z"{s ()�9ndj�!T$) until $J�f��� lWҚ�.�>�po(�SNh$��is"��&��f�� �(s)0_t,�0_ o᫁��>A�� e�x sucha�Ys(</lower)"�U�a�e�d�K be"�A1 u6izZ6�A�s�1m+hly��:*�I� ���5H�M8$<:v� РB  no� �a.%6 aR� ce�heJi. .�} ��I�] 3�'� %��.�#�"�X� �*E�*=�*4o'���A�a&�@k�#�}� �0l��) L� "Q ouԑ4i8!� �% F�c X\begin{thebibliography} �\ \bibitem{MONI} P. Moe�H, J.R. Nix, W.D. My3&�W.J. Sw@�Dcki, At. Data Nucl T�%sM9@59}, 185 (1995). vP GPhys. AA 601D41D46). Y. Aboussi� M. PpS4on, A.K. Dutta�$F. Tondeur �r�6h27h�9#NEUTRONi�@y} A. Trzci\'nska.�, �$Rev. Lett �L87}, 082501-1 (2001)�&/!�rein.zHUBz�$ H. Huber,�We M�Weigel2z&;0C 51}, 1790J�DJACO} J. J\"anecke�E. ComayR�<436} (1985) 108.�8LKLB} C.-H. Leeb�7}�8) 3488..o8EG} K. Neegard,�p(-th/0304060+LSATULAWYSS} W. Satul)�R.A. Wys� uc >211044a"U�4DANIELEWICZ} PA� nielewiczw411115.�EOS-rhoAei>D.:R. LaceyaB,G. Lynch, Sz�c!,bf 298},1592EH2) e-Print Archive:�2080162�`BVA} F.L. Braghin, D. Vau��i�4Aa*ada, iSE�-$ 52} 2504 q�92:e Nuc.M�KA 696}�1) 413;EG �Yit Er�>m} a�:9709 92) 487��.� 3l:4665},n0) 13o5�*�"0} M. KutscherI(W. W\'ojcikq.}� B 223}, 1�j 89);2BR2340��%C4). � N.h%2N 0021..6�#�aVidaurre�� Navarro (Bernab\'eu,�0�. Ap�8135}, 36�86�2�#( S. Marcos,A�NiembiM!�Qu�v�MK697�<27�<1! 9�:x$ef�rdu��Nt356},���]t<�Fantoni�H Sarsa, K.E. Schmid�0}ס� 18110��2�PR} I.%� \~na_Polls Ram�Z e-$C 65} 0358ay 20026VB022WeK$I. BombaciQ�.�6! 0458 �6R &}� . Isayev%� Yang2OC 69, 02I4);�"�z403059.&�#:# Braz. JouZ�of-%33} 255e�3)>� Int <T�Mod2E 12}, 7B9�(SAWYER} R.F!�wy�.=��C 1I�4�75�8N. Iwamo�) nd C�Pethic�+9tD 2��313a�8%q� ESPANHOIS�\u8E.S. Ha�ndez,2�,Q�dC 6�[(04) )� 19992-�aAReddy,��Prakash!�M��t�H' A. PouQ J� b 28��XMIGDAL} A.B. Migdal, EeD�ste�~McTroitsky� N. Voskre�Xky�P��Rep 192}��02�0AKMAL-PANDHARI�kma�fV.R. PaEip!UJ��$22�972]� P�e?�@ IWARA 2003, Olin!�PE,� il, j� ��0D 13}-7, 1267%�6�\BAL-CMK-WB} B.-A. Li, C.�Kow Baua��Q ofJQ� 14�8� 9�XSCALING-FRAG} D.V. Shet�"{� *,)�ex/�  +b* 1012.PON>6� -e� Ono,B� W�h(Friedman, W*` M��Ts>���68� 516yR���RIA-GS �5e܎:7 Henni�0�I�W$A 734} 654-� ; J�NolenD 2� 0, 6��20%�.�F^ `, 573 a.3IPHIC}� �o : "I�z�ic�Hi -IonaiatA!er"�ate E� ies", EdsAEo-An L�W. Udo; roedA^ NOVA"� l Publishers, Inc. (New York)� 6�BOTVINAi�A�!BotviN OAlLozhk�\ Wrautmann2�%�V , 044610%(啕mJY-�-Ya-2A-M�b7092�,COLLECTFLOW4+\'w(zN�685} 368�6�8EMITTEDPARTICLE�P. Tan2( % BAFa�R. Don�8loa�|K. Gelbke, %M.-J. van Goethem, X�Liu�&{S. Souza��Bp,g, %G. Verde� Wagn!�H!�X^ A=.��1h4iD9m 6��} Q~ �E� Zhaoɘ tock` CommunE�Theor2(41} 43' 4��9�GAMMA.��312022�B�} BQ�N�ad 59qc;N�9} 01160% . L C�%..=�)=9� 0162701 E6~STEIN�A.�Y !2.�J6� P� Ea�.�410066= R`9L&���habanat2��l2� A 62�6 ��97) 710.TK��� Kriv��Ja�ein� O� higas%�`& A 3h1� 1986 ~s� BD!3 Brin6� CE�� 62 7�5%J.��Negel.PN|B1472 %(1 D=`2�Z��Sulakso��$T. Burveni�7,Maruhn, P.-Ga{in�Oa��!? , An i��30��3͆6Y*WGAJB ^r�X� Heen��:p* J/7�2h9���eFar-�A��*�H1� �A 615}�MW.lB$m3� 2D.�� Onsi�v(Przysieznia?�e@�.�%HC 5a� 4) 460.`FLB99}:�)�}� B 44�D9) 1; �QB22562 3) 362�"�� Kubi�2M*�RT399�� 6� LIU�@�' o, Baran�%%p j"& J1�45201��aEY����.���4���M.,!�F M\"u���B��Serot�z 1�2} 2072%��XB*΅!O-��ackI  G�Brown� Askai� ReptM�124} � 86+�!,  Pi�zOP. Nozi�,�\Th�$or�QuA� L��s}a�A.a�jaminL , L , 196622"Å (Garcia-Reci3"��,ia� L� Salcedo, �X �(N.Y.))T 21wO 1992) 2932��!N AyikE/"a $Ph. Chomaz1�E��� B 35�Z(5) 417. See()ݷ\�12�)=�S>T� :i%~$M. Ichimuru)211} 266� BCK}�Bar]Ja9X�S. Kaha� )5V�)979}+�!60;.�L"x��Baldo,2�GH Burg!��*�. d32��6�WYx} R� Wiq[a�A. Smu&A�>�.� C 29�0:G�x } L. Engv!�E. OsnesEH.�w , GM t(tga��� J. 4�79 �6� �*y R Reid�)�5G�6�combeiw� .%�C 21, 8� BkHEI.�x��:�xM.:�5@�!� , 23�06��4����F� �\!&W"�$H. Orland,�JMi8Par�I Su� v��I} 034EZ20j}D\/�K� the, �M&� 62, �1QYendB�"�"\vskip�( cm \setcouD){q)X}{0} \renewcommand{\theA.\/�ic3} \no�tn  LargAEbf"f;:F%�$p6^-!`un�D$V_i$,h0�[b̉ $K_{sRPA70}-M�P ��2cmI�*�3ndix wP2h�#E�:x@M&9 RVLK$�>�� :#? SKM,�%0�&_Ar �*-�t$5_�Zskyrme�X arra�$v_{12�R&{\.�� t_��, + x_0 P_{\s�)�s\� r_1�T 2�] \&[tT|2��1I1.I\�X)�X[Ş.U� rUk^�� k'^2 ) (1:� X ] +�}>�t_2 sv�x_2N�� k'}.nB� �k}m�3}{�y )<3._) (a_1 A ho�{ 2)^{T\} + B~^�f}) � Z��ind-� e�UG $9�$�,�m^("�7"�c.�FmY&-0`+Y�Ga��-�V:�� �l��Q��,�H o:^li�9GYV*/>z a:�l H.}mM,-;L s di&��� �7L,a�*�Ye/co*�6"�.s $V^0�qe� $V^1�>Icha�)���?g�.�1"�(c���K8:9(5�q�V0V1}V(}�2�{ \ove*�\&4}=M�"�t�iu� x_0+M�1}m� �tA�12}�t[I�e� x_��e�6=E�1 za %xL2}c 41}{4}(1-x_3)(\j +2)  B��] 6ew.e�6  }.�qj1e�3 t_1 �2 x_1) +�N�� 2) )lĩ)ڰbc&V_2�Q�m\>qV_1  = �1} rt_2o^- ��%q1) a� NT r = t_3%y[ �%(5>2}+!<);2$-1} (c�O_ξ(c-1)p ).k�.ޞ\ V@��1� (1+ v-ʊt oz!V!(1-A<) 1�2 1)��  ��+p Q �)h>|1�]=�2} ,%b:�F50}%�I�3 Ee64��1]�!� ��@a/� :6iL1�+2��)�)^2.� !�2!z �1{�i�a�%�] �+ qo` 9 T�32�L (5+4�)2}�e)Tp.0} },JBm0!O 3 �ja�+ (5 Jk�f},a :�q~0a M3}��)m0\{ (x_3+.5)(cIx:�Ahoׁ�f -1 )� 6jG + aa8A�eqI#-�����%K�2+�� +2}!� -�(!E!�rhz4 �Y� 2} -�)�FNY�)}{ �U \} |d:Z :9�/%f �-.5 �-.5)J%W � }(.5�� +q�8�,� *(x_2K+�� 5� Ifj� Gh�v�Et_3�S%�9 (2 + �)t�qBaA�G72� (2x_3-1�D)� + b.Y�! VL �] �1}�)J�� )Ft_1(x_1% �) %�:��x WMn�-93��n%�(��-1)} ) ).c�J� 7 6p6})} � 9)b(�< ,�:@F?1}!2 ^2) � EF���H2_!�2�  %�48}!�((2'_nyf+!�<_p)��5�A!'Y+-s. j>�)-�1���) )�b . c"�j��V_2 ,avB�1^{E?�m)p�2CZp2A /1�!P�. } n ��rho_p�� c ) � - ��@a@M>a J MS=� (c -a� �ͨ� : aс�t �-�.�(��n �c� �b - i h � D � n .c� � -c)) 0� 4}: ^ "� F B{nA p���&cfl, �@ %�; �0��RoF �{, *�x�l-2@ws d�X��� on o1T%� long�rlength&mc & ��F,$= $<f�[$<�AdL"hJM=op�]GMliliy��u�gZ2�0� � K-(�b?�>.)�1}{9} &� =���5b '4}{5}T_F� 2V_1 k_FGA0a�H3� I^mK +1/n \e~�W&}8"�M �s�8!qon#�&-h J��r6�l EF.�^, $T_&eAc ae&c;IH&EA&�HS��cesA�2�N{\�Xa���KBg�,�R reme[�!�X)�vof2n7!?,q�i�G�<fA�qu�:�rm�:=�AGh!9�, �.v .1��W�U{rs5fl" �Ȃf*�;?o'}). I��re ��b��M�I�Q�31�..B��E�% � (��� !) !/}� q'.).���uTeWcontain!�$(�B)^5��$n1�2$%� $H$ ur negl�Ond�C*� nIE�gJG!�u+P25�:HsM-0^U J�p̈a�t>!� �Os"��8?�H&�N(��) /^�N$5�2N��s*FI *��a�6�F,�F�Pi(�Z�~�J�mk_F}{\piks� -F ��a}[s1- �E^D L9�| 1q -�E}{qBa1 |"�,Jd �2 V�^3.t ��3��b^u �b � 5�3 c!) ��B�N� �4� �1g^5}��.ja_4� _4Aic�d 3+ e 4� %��  q� � q^6> !j)^6})Ҕ�y�;.|D$a_i,b_i,c_i,d_i,esw<>�Gn $[N�� on $�s*rpace{2cmF-@� < x%~K׆ $q$(MeV),�N *F?�_Q$T=� , gM%Q�e !Q�- 2} SO` �"�I.V> �� =�w���&gP��TV����.�3 �"�c�J� ���24} Sc�Պ���B��mB�z�A��65} �|M lA$N,E�, M$ ��uTO�a�Q�.�Aq�N�E�9EE� �V��IpI"�\9ce unl���F valu[Q$m�x��7a�\v.( 6WW}[htb] %�(-0.8cm %\ce��{h�psfig 34=atq01-aq.eps,�P =14c�G10. Gap�v{ } %�}�c1� nd V����1� z��Z�0�2�2Z20��2b2d o.-at�h^��8document} ��\class[QFpacs,MJZ#nu� 0s]{revtex4} %�� \u �4ckage{amssymb}> math6vEicx6dc>�n6bm6�a�s&�"8MaxMatrixCols}{� \.#0nuc}[2]{\ensu8j4th{\rm{^{#1}}#7 %macro��ypCi.J*{\�i��}[6]{YC0{#2}(#3,#4)\/ 5}{#6�"��Q �#\Q,{APS/123-QED! title{L%�y $n-N3}{H}$�G�Ying: �� vel testg�Y���G�9 � \8Cor{�Czauska�}affi��${DPTA/Serv�ode�$4ique Nucl\'eai�A(CEA/DAM Ile%F�V, BP 1�Z4F-91680 Bruy\`.$-le-Ch\^at�% :�~,arbonell�DL.P.S.C., 53 Av. =�4Martyrs, 38026>2nob�)>ZA.8&F� cl�.[Ce��\'\i sic�G!B4da Universidad�Lisbo Av.�'f. Gama /to,lj1649-003* Portuga�ut!�MVAvia�; A. Kievsk�P S. Rosati:$INFN, Sezi�di Pisa��&�'D�t�{, �t}/+,8 I-56100, ItalyWe(date{\today��M� abst2K}.FMe�B�eI��ro��EmshA���7ce pe�2re"�!�isol�W- 4-E�o�� blemJ�+�N6g7l�&$5d<-- Alt, Grassber�`�S0UDas (AGS), HypersphEv Harm�� 8 Faddeev-Yakubo%�--��usD�Z�iQ#ec�d�Qs�# �ar�cW‰�T�)a failQzex�ng �� SU&�%#: �2}.ɇ9�\�qp{21.45.+v, 11.80.Jy, 25.40.-h 10.+� make�� zs 72 OK �� %�(E{Iamdu � �w1� (4N)dZ"N�sGp&��jump in%]lexA�*v"�� $A=3*~s�Ys "�jpu�mwc���� paA ~/ CCG_98,CC  G_99,CCGFViv98,AFNKG000102}��`s"�mob~�G9I!�` e*�!�p$, $n-d� .�6�s&�splay��Fig.~�(,Diff_234N});F �p![urAs $A=2g !+�7�gntrastJV>Rt�8al*0manifesa�inD4$a�sX�,c�<\region around E$_{cm}\apГ$3K`�mm�� &�^�n�par�/>S$T�re�lsƳ'$TWH92}. AcPq, $A=4&�'>uaE�a� stemTexz*cha�era�c�/,6Ve5�--"�*�q-:z-- �96R�imp2� ($n+5�e�$Iw p}�fYk($d+d�+ 2D$) �s* ROre�&,!�y�re��<v��a� �o�g$p�nuc����" z4}{He�!\nu_{ e^{+}$ (a $hep�docess)�e�A�� a�I�{ �est�~)eA� imsa9�ol�c so�P�j!jbig-bang)�(osynthesis;?/2�, �in�fc�(�N ��� SstQ���]3e6Su�NJ�cG }[h!]}�0fxsize=12.0cm� filey�+` v�-1.0\Coma+soyt�� n-p��d!>a2Hs�� �on ��in �� ory *."��y+ �ɑ �2E` stud�A4N �;X�3u[� Q�>*c ``tW?etE �"j!�\M-�q��b . UnE�z�3N�s,4U�w�de)�!8 rich 2;ex�7�TH�m�Iinuum�Y�� w(o po�o�1w�a�s cri�&�T�ely�S�on", (NN�]"� lAFő In ��,�Uac2��NN P-��of �t\ f3N��ce �believ�~be �St w ��aor $3$1V�j�����)|Ud32� Z,�i � 3/&"�AYi| &J�YlI  ut�q�Bc>hav!V(liable few-�ntechn @s powerful enoughAmd��wr8�0 � . Ev��ntA���ut��C, *�^�n� nuր� ,%�}ViZn r� � s83[-e\�Dd.��:ttog�2T� �!�t%gsol��)��5���S��N� H���N��X->. _ Ref.M�Kea01}t� �Z��{1f�V � e�$-�le ostu!� u%]AKAV8$'$ n$AV18+} NN �:��;"�s&7 9�  |KG92,KKF89,KK90,VS95,SV98,VKR_04495,C88,Wea00,N��VB00,BLOogga_�( n� in ve["l2s":ZIB�.%  (-�level! �ef 1\%)iO re�j�ghe � *�  (FY)"�^� Y67,.�-So.��5 2� +a��>�Z� es&� �$ fu�� conv� @�aof�x%�al˕s %�1#%% i����>b9�G��'s&�M�0 Carlo (GFMC)M %�}��Hy� N� (HH) C 7)�}I�e�p* �0o`�pre�!Ca�!�$4N$ sca�'�+9W.A�R�hcu�� /�N� �]ahED��e=�v�and!�rrYG�,�9%��5��5� Dlread#&���8d�on��r gr�2� , $p*� �* ,eBd-d @, cR $). Asg�G%G*f3@ u�:� $k(om Coulomb �!,��a)Bgood � i�n ?a p��Y1$�. H��it.] s a %�f s si�Pn�&� r ( is visible�6 at center of mass energy $E\approx3$ MeV, as already shown in Fig.~(\ref{Diff_234N}). Up to now only two of the techniques used in bound state calculations (FY and HH) as well as methods based on the resonating group model (RGM)~\cite{PHH01} and on the solution of Alt, Grassberger and Sandhas (AGS) equations~\cite{AF_99,GSAGS_67} have been employed to attack this problem with realistic Hamiltonians (for a review of earlier results, see Ref.~\cite{TWH92}). Some previous FY calculations in configuration space suggested that realistic NN interactions could fail!�reproduc!r !�8experimental toland differential cross secti9F(CCG_98,CCGF%U }. These .H were however limit-b reA58vely small numbE� par|waves� � ansi)�4FY amplitudes,�4reby such lackA�hconvergence could be advoca �explain?, failure. Us! AGS equa�,�authoav Ref.M� � wal0ble to substa%>(ly increaseCV��%�obt�a�4rly good agree!� for�)�%� -��!,i[(nce peak. H)�%)N� u� onen!sFEHis �, a newaqhi(un9Q ) HH-7is�Dsidered here. The1�-K ed ueSt��N� so farA�,rather large%cE�4between each o" . ClearlyA�is siti���4uld be clarifiA>ef�qu!�onA5AD]�lpresent NN + 3N force modelsa�describe823(data beyondbiE� �$of $^4$He,e�i$they hav%�venbbe�$successfulM5Wea00�[is!r�purposU��paper in iwA@ mpare low"%0n-\nuc{3}{H}$.Km� �~!:y three� groups,-�independ!=me��to E��four-�*�Ke�yA9 cern�g .0 ��VbasedaՕ�B�NN ��a���ala/u��!�!6Schr\"oaer� I�HH � �VKR_04}a�=soNFY � 0dFred_97,LC_FB17_03} with a. improv�� �xVX LC_T�oR; AV18 r �NIJM-II NIJ_93}A�i&  M� Aused inU8.�. WeI�cou�!@"u  m"u |ies $E=0.40,0.75,1.50,2.625,3.0$� .�%� stitute a�� set!�eE���pongi� value!��A�p �p�*alA� to d�iminIxm��é� (�8 leng!�nd eff�va�nge). I�8A>,��� �� �sp�o%)measu���H 2�%hT��[�Uk,a� willI�I�T( $J^{\pi}$ >�� 7  term!=�H asymptotic hamilto�  chann��$|L,S; V>$, w��, $L$ denotesH:n�i!> orbiB gular mo�umaD$ $\vec{S}=s}_n+ t$W� spinE1 fo!�A � �%��U�h: \begin{eqnarray} |0^{+}\r�=& &|0,0;. \cr |12=c_{1^+}=1;. + d |2>H 0^{-J�1 � >12>�-}&|1 k> �-}Y.6 H2>H2H. H |3,12( |\label{nt)�} \end=pCoeffici\ $c$!� $d$ �sfix�Q$e dynamics"mak U� eigen f� �|Si . As itUdemonstr� late"� A~B�0relevant ones�t�.s&Z Y]�Moreova6couplE�PL\leftrightarrow L+2$� very weak�,is neglected|Q�=%�$ ���%: \� {M�f}��briefly6���V���4Nj . Two-^m (O nd� work�con&x spaceYle�� u� . \� �K on{A.? } st� ,ng point inv� �U20�� GSAG���tr� �� operator��HXE(2N)+ �N+(3N)��.� lo NN pot�s9��M6(ree-vector Z� �� gral-� af�p�al� de� os� reduc� a��EDedLt continuf scala�s. Si� .�al&5requir�g reat&b5!Qb�jf�q an Fo "� the " H3 l AF!�ystem.�in order �he��0A�ra���1n- NseA�-�e samegin:�89.1} A �  from�  NzHS_81})�  has: (a)��he origio NN �  by!FQ�� � � ; (bFE �A�3:F finit�kQE�tak� s many ��a�bede�_ *�Q2E^^�% 2N+2N sub&^%fexf 9 n of a!�v u i��!� non-!�� a�$air-propage��first o e*dFS_76}� /leI�x��is U� �es�!y9�U�the 29p i�may[" U1$well-known�d!,Ernst, ShakiA8nd Thaler (EST)��EST_73� e m�-!C�6H�. is dA�� En� D"y P!E"�(EDPE)�develop� =RSMcGF_7�is�:��:��?t3&d �!  unaځ�rol s���!@ chec=��d�� 4N observ�P��$Ae*%�e = Zis�oE3�� �AFi��`�d� "�eR>�fiwtoA accu^aաexact�% of Kamada? Gl\"ockle-�KG92}. 6 re= ly 7}Qm��our�m!� :o elas� ��G�to (|!� ��be� Grenq�� _99}�Tboth Malfliet-Tjon (MT�UAV14 �<��inaN.s �X: pj $\leq1^+$ ($^1{\rm S}_0, ^3 1- D}_1$). I���ent2;. exten) �699}!�]q!&�2N:�to $j � 2$ŐrQwLd $ �F}_2$, �DA ! ��h*�5� QS}:�]P! )( P}_0 {�P � inclu�%B. 99}."� ��!") cle-��f� $\ell_y -0� p�  $J_3 *z1ZA�iveHf"=a><$J$; L i�/B%��ny SU �*�nd �z I��Z�oFat?r�1��th ecl�uzwe finL �R` s� m'h��ed -� m����dB�Y��_ 6 .DB@��ly�{.o�P PE D]e�#�! six Son)�: DFaddeev-Yakubovsky��} }!�ca�Xic� ferm�, .Svia a A�-wise�� $V$�FY*y �Co&� �Ugro"e� " ,F� ,FY*N, nam�K%�HJ�&,( E-H_{0}-V\2$) K &=&V(Pr+P�)+$[ (1+Q)K+H * ] \\bEHE \tilde{P}ZA �FYE>�% �$��N� Ue� $Q$ be!�Q��muY � sN�tab!}{lll} i+}=!-})��=P_{23}P_{12};$ & $Q=\varepsilon P_{34}$;�% 81824 E4E3}$,%�{ ".%$ $e�$a Pauli fa��ex0g�AU�u��inY�M�? -1i^�� is ��byN9Psi =)� 1+(1A(+Q.QM A0%� -})K>)(1+5/)HM psi22F E.� F=(K,H)ą���"�,"�d�itsqper�@ Jacobi coordinat@ x},y zA| defi�respecflyMIq� } � {cccux}_K&=&  r}_2- 1 y'sqrt{4 \�3iJ(23- {1�T.2})�)� Wz2W3 W2:W4^Wa3a3a^end �\qquadiaVH�2'45,3.,z} '%,�53�4�2}^� -7��i�9����{��� vari&K 'Y_� Ekg� - TmKPWE.l,%�x}y z}|F\��le=�Dsum_{\alpha} \; {F(xyz)� xyzY (\hatE�A�z}) .>�KquI �$eUcal=reZ izeda�.� nd $6 tridr h s,a�r ���, iso ��1h�" s. ' $)$ hold� ���10�\Y iate �umcs�7�a" ,T=1 �4y: �in a j-jG; sche 9�*!|K&\v&�I\{T[(t_1t_2)_{\tau_x}t_3\�$]_{T_3}t_4!�\}_{T=1N\otimesE\{� ft[ ,( l_x (s_1 s Z sigma_x} G)_{j_xF(l_y s_3y "]_{J_3} z s_4 AO�J�dH2�[ � 2�3 tC�6f� �����?�y (s_3 � �y2�]! {xy}} l_z��q5��s_i�t r�U�@ Q�� Ddividual"�� $T,J�2�h2�&� M� L �. �- 4$N_c=N_K+N_H$ }�����$�'�~�UeHl(12i�um�"V�fur !a�d] 5��/symmetryPer�> (-)^1�x+E x+l_x}.[ � � j2.Ly Ly+l_y6LI! H� e boundar ��$1+3.� #� impl/ed byo'at ("enough�!�$z)�4Dirichlet-type9*V(x,y,z)E  t)n  H 0B�$ - !�triton � &$ � :� \(A�aw[ (l_xN:i�x}�6 �8 �5 \).�= y en�� �w� , e.g.� &�'>�S-� , be�"s &>a�& likezL \sim5O<\sin{(qz+\delta)��>�  !N:�pr% e�$q$conjug�%ըq�z$-Bw a�K-a&C(I���cf+� :� kine�h @$E_{\mathrm{cm}}$�� phys�� $k$N� �eq:k} :P={ 4}0lab}}={\hbar^M $ m}q^2={ 3}2 m}k^2 \Vn[^&ch� � �� >�4. \bigskip 7 .�AB b�%&�'�$j-j$>�E����trunc��)V.i��5� L: {\it (i)} V$_{NN}$� s�)�<$l_x\le3$, alwaym,(ing tensor-�ne�� i.e.r��`%- ��_1(1^-),��_2$ --s%��*aam%W�$. On�+n remarat�P,ults display�'f�Q�Atty�A� "B�Id$�mosd&�.�digit �cy.�,E� X=2 Vu�" ble )�J$�%=!�q!(1!�)25)2C-N��O=�m�=C���,5 at a�per�� l�� .�!:-B�")�j 5w?-rAjn!�!hsum�an*3At��-8M(excep&�."�'��P$S$�#),%Iakrn� Xis�  HHUs."licit6,e:�$b@_{1+3}^{LSJJ_z}$ �+ing�b9+j$I+incom0 ' >=N'b Fnel� $SS=0, 1$)�}œ 2�  $JJ_z$��re�a*�-GPs>�=C^{F:(+A� \ ,� O \pi� L � �p�"� s� S dxd$ vanish�(he�qA"� �!rclus�d"�� /�-�,$u A reg `��� clWto @.%� their mut�� on 6strong��) 7hand, �95)�)s,E )mo��� two �W�=ic �� e�:q�� K&igi�$!(can�!r$eda�a linea(mbn!) �#ingu�VGOmega_q4^\pm=\frac{1}{�4}Epi=1}^4AD(Bigl[ [ s_i+D \phi_3(jlp) ]_{S} Y_{L}$\bf r}_i) Fr+Ja�W ( -f_R(r#y8k \pm 9i} j_L  D)Q�.�om^�rX[he dist2�0neuA# (Qn $i�� $.`/ s $jlp$),� [magni�4-� ]==+�0upUD& Eq.~L< d)k&F .�2��+ich�$� �'.<(cT3�,iM"Pe�2*�"pai* &�3H���'on� KRV9_/N L�y m&�3B��lY�-."h K kind,\".. � կ$Q9$�7�ra�ulaO �IG$�[z EŊ N \*� 1$a}'!���;us�3ap.%Ee.$ji'fV�. Not� a�/Z* $a$,&��� �1�` { \cos(k r_i-L\pi/2) .k�>< 3a�={ \expa�l[.;>7Bigr]# �}V��!, $>�+$ (B-$)�B xF|Xoutgo!�(in )>�q� ��. F�'lyRv� �+= �& L^\pw9 S !% >g[e {L &} S1 >�b0 - {\cal S}^J��,D9(kg BA+ �]N)^���"� s $�~�: &�  e��6��&�1� b7!�d (�&� ed"�*)O �l��#�L $(2/3) k^2/m$ . OfBrse�e� �:$1/�� $1�e�"b,yc\5t�& aj"$J>!ity�\lq\lq�De\rq\rq6�i�&� _C��� �� !v"�7a&Gc-� ave"� �tV�4F�� chh2E� I�� - = M����{N_c}\;�&1(n_2,n_3=0}^ $+n_3\le N( 7) ^ u4 n_2 n_3}(\rhoM�M�Y}J&�0_ j?� \K"�"� rho%�!Fh:radius�N rho=�x_K^2+y +zV�K� �QU�� �r�i �as� *���=/ �-�%�i.� -�F83/+l*;�! j�7J >Z&�s  cyC$polynomial�8x�n_2I�$n�k6��#�$of ``%}a+; s'' �byN� Ņ�!C ({2} = { y_K�-)�%�)�}}AE�� coD 3} ={ xHrho ./#eq:phiB, The� � dex&15col�1i�>Aso`&:a,%� � -�s>+.�0�g��rae�M��-�!�.� cl&nB �%$�A�B�I����E����1�^ &�&�s I"r)��0$�fx=4< ntil,�iO7e?���XY>+ est~ "� �9{choicG �to� seţ� cus� below�!�}�^�$ o;,rN �53�H6�!�� V?�^Y 2�$ 2�>� m�.gW�alRd[� 3��]m>�q-8m86}� � aq�8 ^{�� JJ_z }� |i�H-E_3-T6�! P� ?�! �� kohnB�aNion�eR*A��1�)� j~ iJ4$ (KohnU@al principle). H$E�\=2� �=n��� . By1�)t>/R,;; �3.�(&�<�2AsN���i�qv�replauD�deriva�s)S�*{cA'a A�ar��S,�*���0bixa�*G.KMRV96}e�i��D�Arepea"v A� ���qu�3 easi�&e �. Le�0 now��"�7���HH��t�0 �� �y. A9��#-"�B E��04 G``brut�rce''�.�of�!�! poss %)2ha�- se�R�3pr$�-I���s. �>`��nc:� �;��HHEa� clas�D.�,�ŷ*i� L}=�.x+y z$:�'�low <s� ���L}� v.boIY[5��. �C�a�pI�:�Q ���2�. N(� }m��0a)�Y%KG}*r|ed��n,|�aI��?��arjp%� so o&ad;a?+his>y�ta�A�1�Eh�>wOA�-z2�-n�contribB,. Consequent��8U�F�2_eB �<ng3mpl%6Z��2)��~J�, $�3�< umaTi�!s�$E_� MeV �%� �inga!U.�2[�5{ 1e� =�&[reportedI�)"2� ����M=0$}�/su;>��i�F1B�E�GsE�!i5�A 2c\ge 4f ���E�#*@ �=P�"J�2)�1$e� d�\>.}!��+��G(%�.m., 1.EB), bu�0����th�(c�F in6-)� #J. I�p!��^��  HHA�diI�9r5N� lesE 4\%0* ^f{*W1s�!r�&ist a�li� !�Y 5=� weIl-Lo�lve�p:X� (usu�$)�imA�ant�1A�(ha�!}4x��y= ��z=�!pl�Ie"�0s (��AF6�dou�� �.�)6zK%�giY1Jp�EM� tinyE��w!T��)�� } disregar�o5�2p(!hq4�V >5$)�Mb/ act3ly.- TI issu�8 cur�F�'#inva��%*KG,ip}. It mus�Jn�Dp����JH�J&=$�A� es� struBA6.�D��?E�!cRK �R�$*�0(�Vafwreferct�t-K�"�). Obv��?2_��nof�0��+=�"tlMis �msE�:(2`��%��H{6� (set-H2A)K!�m K suit� ��؁&in 5 ccouV9]Us�5t $\{2+2\}$�'uctures.!�3&�K o)0Y�2�2�ofm:sets sh�K spe�pw2Pn)��EG��c$UT]Q, �P,aPE� ded %DTB �<we�!%@*1ay�@ SB.�a s�%�6$s, a satisg4�C���A�!�0%�}[h!]�!er} \cap�<%� � 6� 6Fnd?"��+9%"�;��E$_n$=3n� �7$L\to�D�&d*u J^Y 1�z %)�s}��*E. S�t�$��Qn{.}�6.&1�5{l||cccc|} \h� A& \�?c�&{4}{c|}{p&:3 HH}, A�# $ &$}$�'$ 2$&@$\[(. 4$ &�� &2$24${0$!C�H@-70.11 & -69.98 70.00 u"1 69.8\\ �1$^+_1$[ -63.6h 1.94Gu 1.97 � h-62.6$2.2b h�K-K9H169365:H' � 26.2!=& 23.86 65H58 �16.9 &0 4�!>-9> 25.32 k 22.4 Qk2.2>> ^ 20.7W2 ^!B\\ W21� 18)�A 40.7X&  8� r %�31.5 & 4 ^\\ �'J 9.0!� -43.52%  -44.39PW-40.9#! 5.3\\-�2$2l -: E 43.8 ` 45.4Ae �c27%m44%44.5 � `�q� ��9 '\newpageBlI�� "�IR�T�ThB�/s&�J�Nsɭ �4 ]� \citekTRL_�Wis,?>� c�nesG=�s+Tab_sc_ q}�� summ!��$Cst&g)"��Pd�ci� � Bc depha_SP_�cg �2�,PUٗ��vr� on� o@6bO��+*�Kq)�=w[X��som��o"� � '�= Z,.�#. � .�� he"�O=1�=,2^{-�Ks tur�3ou�2�+�AGS�"FY.�^ ey st��E�.� �5:�$ p�e" $�O6�LrC� , ev�)t�UMf\!d� st)>�+ �� '<, $�,)�a,!s%�� $;21^{\circ5� �e< (0.01\%JJ� 3Jof�3.�o'p u+9in�)�2iD�)�4 east� �Z Eo12�%&&\begin��r� Si$t a$_1$(J$2 $=���-�9l !3!�<.F9� edi�Nijm-IIEUa��J5� ons��O6�1�$%V |l}��Pot. &�{1�fm)��a$_{3&%�gma(0)$K &�N �@�  & 4.0�z & 3�� 1�A& a5Q\ � D25 83.7�`1.2FY&DD�[8 3.73$& D �& � � �  1�Q��D�� � �2�@�/'at�i����� K+aD full�t.Jby2ig^ m�P. A� �(�ZHH' FY ^fF4ec��B{� �bs�%���of o �#t�( signific� 0�Zud1 �f���0,crepancy doe�t �.4ed 0.3\%). AGS ;�IN few��$&�Zis�Edelic�6� neg,6Y�.er/*�\3��EX �a tech�a�er�slowe:$NN�_the�"R�staR-�%�to be?L than.��=���9it�Z�_1�if �Ho9Vr�zn"� step!�Wed�2��6� ). S�r\���>Rre�d�*�� do � shel�!�ll��U���JqJ..A08& .b R/&�'� 30\%%@�=D~�7^V> . Al0!:4 >E"�.ly�&�O.�i�!�u^�3�a�]�GFh �&s`r�/.�T elie�&'�lil@oon��F-.�due����":�`a�"V�`"!\ 8 �is�!��Oow���s'� �NbO(oA�nZsc^s>A:m`/)K"F% �=ico &R (68poN6)� �b6Z c� �d!�v,E��G�a�%)�=enc�0k in���s 8 "2 }�c � *� sizejinBh�� J0CarbLaz_PRC04�� �:�Sq6 ��Y*($s) 65j� Avr f�; 80 (MeV). Numbe�1brackej�.�5���5E� {!rzb"&/*� ). }q"Z 6 R^ l| lll |�c|*l �&  &  l z& 0w&1$� 2$& &�&n gma� &"��]?-27-25"9 &-v *& 2.2487 3.�& & 3.5�1 &��*J &-28W� W(65 &(0.199)�.81Z66 Z56" &(-39.6)h3� 1.75'FY.� Bh�� &8?2I �72f 44.2 f�1.7�HH*�% 0}!$37.3 &-33.<�7� 5.5/ 6.69.9�� 9.1�1.7BAG6738` `5)(0.358!74=&b1!?8.82b(-41.3*+!28.5d1.7�BA:r� & 4.3!� 6.0!I9��(-�:p3)y' & HH"  % C``-5�-46U"2� y1�p 5�25t=K24!�A�%�6K &-52E�46.�-0.330 E�670!L1! 13.E�16c�2.9.�22Z2.0E(Y�o6 �+ �!� & 10�m! 2�< �%E6:h!�h6D�`[-63E/58 t-0.64A/sa]7�!+A44AW t&A� 2.510:D &-66Bb r 0.85%E 1.08� 20�da"5�!n[.�41��Z F�66! r4 �)&hE�20� 38a��%L6p0-L2.O % %�c-67A -�0.764|3�6%�48!|& A�4em:P&�0!V2�n 1.18-O21)O3-O2��79O&JN5(2.2%�Y�&��e �A�A�A ,�%N2O��pa��m�g7^N�� plo�>in �n sig_nt�'�a�2�gva[d0�Y*APBS_80}z�&^ FY (dasCline)] �J"% � e JeCtd Xs d8inguish^ by eyBTP6� (solid{sl~`Jm�$tw!ow�@iW)*�y[0vidj � ably�r:p�F� �dis�� ore; 2�?� e.nn�eat zero7p%t� �E$^3$H; �Y by l�_ NN.��As. ItO"�b�clu3 a)� nucle� $ce (3NF), � �Urbana!K IX (UIX�>%�r*To� 3N6fZ"g 4o9,lL"(h T7�g&pbA(FY1F� +UIX �� oB4s� (0)=q $ bN8 E�� i�nsi�V �2�� X0\pm0.0_!�V2�`2Xs/9 �in��`r,'�!g p�aSa�Uy�=as� �ra�2�;_k*�?Ze�to dimi�>2W_Aq�Irexaing6�f�a W,weak sen� aN:to ``]<,dard'' 3NF, A]Gl7^.fn�cS�`q�NN�}cXh`"EJ�>> e��+�O+B� �, reme �N-d2=l�Le e�% e?�1�&*/ory�Yq�Wm�Cd5 examT)�.so�A$$A_y$ puzz&n]0H86,WGC88,KRT�-.`i+ �{ndi�r3e� abei�� �4ciE7!�he!Y"!� ${}�G j$ O-FWG91}, ^o�q2ex�$ 3-�WY�s#emp��fa1� K99,CS01}m-�aH+c�)Whe�s�r2�!�3N%e4N� I,_ cs>cdef�)0 e�ar Ha",j!�p� debat�"SDd�qI�b�Est�E!>J�q9�al � {a|on� L,q�Ea�3o~bs) �Ete�Use.��&lqBa�h*vp��((�8o�>ak hard�&��a� .��f�[�!�A�$a normalizEq error �A�7���). AR/�!�,�x��r analyz�"T�Z2�Q�&�:z�d�m �B�%&J�on�@t $\theta_{cm}=90Cg�d*>�.�3+tɐle di�!zforwardE� back dirXo&(CV� hift�@cA�"]�K)�2~I:of re"�uM>�m�0>v�5Aj�coPnt.$ad�P , at%�-9��+Y��athVls{6)hmm� olccj�|m`n)1� LACG_59}.2�o& viewa.A�ş�2��&3)n-2V4 it wE��%8R6oɂaI8Y1�c8jrmE�"�* ata."�WjR�&,\mbox{\epsfxj=12.cm file� p.eps}}�!JDer} \vspace{-1.0cm2 'sih�~2�an�JU�n-m J��e�tun :�h!� � �/. D� curv�ts&�  mnt��/ ofZ �P:�B� N -Te\bi�OA"�4� u* �Av^w��� �s*n eBr.` �� "'"`�0 �0Tab&�NIIA�"�Ba*�6�4 l�  NN&>ho� �no qualiy^vea�ace�us� pr*�.rAM"Ha%���nd lealM��&���)�-II�� "�� J�6�R6� Y0�R.� ��� V�6(3*��U�N�u�Q�)�)&: "� 0$^+$ &� 2�&�Y' - G'��� �1���3&�(O.8�.�4se V�6�-[67� 196)m5�Bt3A3.537 �44s 3.34dz�<:k27l8 7�j6�k3!;9.�)&"-& 8.9lt6�&�o7 �696!35� 4.25t 6.04) 8.76&�� 1.03� 8.50�m :�2���1�27%6&�!e�*&�832��) ��F~52�&c22c334�661�10"�2�21.729<(-42.6�3��J�6�5 8��3!w& 27.%24n44�v&)6��F�66.A>Aj-0.813 &�67�20��4�36.96cA3%\8%�2.2A�:�2�9!5 & 32�*&^+7%�48.�vm*�aeF�70!�6A�1.10 �195�3B#&!�1E�4c�2)� 45.2E�2)�:�\�� �~ &I*�A*�A*Co��8g�Q ork D5�Jhe&�6y>�ew8ic:2 "�&f �<� he 4-oFz�KHr^��k&by"%L#"> <lXs& �T�d{�E"\ �t n[-&Rh&� *N"��3(M c��[2,P� ] �;P.-(��-9 o�iE "+ c!Q2x 2� !1�!bv52OvoH#r )�au�3cw�6.V.SLp dQ*#�3� k^de: �th&1 R( upto 15\% � LC_ }3"�,:� %V�� .?�%��"�6Na H�c� #9"� *�>"Hrto�two�_�s� is6-�!\YW:�<R&5$Q�E,"�@:4"E; s (3"�w %>>�tX ), sBS~�an�$�9E�)A�a�:,� aZ6g!D5��P;�,* "*WWeE"�#&�treataJe�r�&t~r�cr_h%?��8higher r�7.,2���con[�? &� &g7" -lt.\)��7 �Qh6���non mH  (BonsKMSS*B DoleschalځDea03�&e�i��tse_��!)t"/����� � %U!Msimpl�$Qx-{ce�%R�M�~x"���ph=7!�!�a � waof�y%to".�Gfew�����i�=ir�U^8lie�1N���)T9,aA I#�3NF�unf�� ���2�2 �TAc� ledga):}E�"҅"s�o��"�ɤ!�$CCRT (CEA)��0IDRIS (CNRS).Ӂthank% a|ff ���scompu�(��$Zi�Znt helpAe a!G(ACF)�supv=[��gr7LPOCTI/FNU/37280/2001!t%b 72 OK b "X&Dhebibliography}{99 \bibitem{�P8} F.~Ciesielski, J.~a�@onell, C.~Gignoux Y: Nucl. Phy�, %�H{631}} 653c (1998)..r_ q q%�J. t"�  `Rev. C e58}, 58Nb G_99�c�`qC. � aLett. Bb({447}}, 199d96�GF� Fff!:c A�LnsecaB�C*c<�A�,XVI European!<�a�n> :Few-B���i�jAu+~�8=�|\} M. Viviani, S. Rosat)�$A. KievskyN�a.)�)=E8� 1580%:2y5 A.C. F-^H�O4021 AH2�NKG00}� Nogga, H.}x, W. "}x�Z�05}, 944 (2000.���6=9!]:E.+Geo�� 0L. D. KnutsonJ1Z�6}, 3739�1.�AF_02FBG. Ha |ndaLHa�qbauer,A A S�+%�3%� c2.cTWH92}� R. Tilley%aR�HllSgG.A8vF�J54qE2oKea01}9� �c�3l}.B[=1� (64}, 044001J/V18+} B.!�Pudlin�HV.R. Pandharipande,��l!� S.C.Pie�q�(R.B. WiringF�F�5!�172i7.[{�:�V7��205e2);6�.L�}�7!w 971 %z32� KF89�eyama,!�Kamimura� $Y. Fukushid) 40aI74_82�KK90}.Q%Mi� n R�0�17�?6�0S95} K. Varg PY. Suzu��B� 52}, 288��E5.�SV��A�\,, {\sl Stochc|C2�al� achDq�pum me^DiqX� b���k@.SpA@ er-Verlag�[2��VfxA���,� (-th/0408019�dI%' .�.�6J�N�32#1!�25F: C88}�gCam1Fz3<187�?82č�O}W�C. iv�i�� V.16� Jx6!�01�2@NB$P. Navr\'aSS! B]Barrett2�I� 59}!( 1906%2�NVB��2W�PE�U6c 2�}�8�� 5728��0);b� 5431��2�BLO�N.�ne�c$Leidemann,�� Orla)<��F� 6�205ZC�p_alphav�{o}�-`R�%_ s\�Bbf{C 65}�2) {3Y�Y67} O. &�, Sov.A�.i����37!�62{P<�(B. Pfitzing� H��of!�n��M�}3�2� GSAG�� P. Grassb�D0MW. ��2� � 2~ (1�0 181; E.O. AlA�2M�DJ.\ �{1I8e�7AP,ibdem JINR R�L( No. E4-668P 72�ʏ}B� <{\em Th\`ese Uni)�Fouri��T� )\/}Ż2�&� Lazauskase7f  2�r 737} S�j 2004.�2/��@ziV3a�105%�2`^X.�V.ADJ.�<k�',R. Schiavill�Ca�3%�6�Nϐ V.GeStfRz M. Klomp} P.� Terhegg�PJ1de SwarAI� R*X 49�095�6�G�j� Ci�139F6K�H� berzett� 2� �{24A�35�O2f� �R e�$ P.E. Shan� FT1T 1343ai76.:�� D.J.׆ C.MPki�*RTh��Ny8�4�072w "n���Sofiano�kMcGurk �HNa$edeldey, NBk{31d29i�2�KRd.�*=��*2.m�W A577s�t19E��F83� Fabre d!< Rip- , Ann#(N.Y.) R14Q2816} (1982._V.�L!�MarcuccB�n�F� �26� 2�VKRip>".�!I9X�,par, �o&k&a���*+�D UJF �7�l|3), http://tel.ccsd.cnrs.fr/docu#0s/archives0/041/78/9��OLa{82{:oi$27� ] 2�2P0 T.W!� illi�B.�BermandD�Jagrav-e�2g22} 38D 2��*}� KoikMJ�<*�F�463� 2365R 8!�9%+ W��0 &@%�T430.Pb, 03.65.F���c�Gt!Int*ung BoV/M�. (IBMy&3��I �6-�$d a bridg2"tween�3&�b!�&5i&qin � i, .����#e�sݥna�X!�pai� A �:%a�2domin�1!�"��of!_e/�%3A:��6�%ge-arac� ��s&kd 3BCS;74of semi-conduce1y&!Ic]Wofh�#n] l<;Coo� �e�.�%RI �oI2 ti�8eq�Ocepw basie��IBMv/�7+Z u;Ked�icriwX�-=�ӗert�7O ediu� heavy L� ven-)@i, piXZN0�H�1a�3 longA� to ��al �&#I`v��-�al ����9,IBM}. Odd-�%�iP�3A1a�m�is�5�a3,� �yrpo� 3ha6%Efreedo{M� ��F�$In 1980, I) llo suggeM7,a simultane�K�#5}!D)I!�o:� throug�:i�MAqio%�aIalgeb E��#��v!���th8i�%9��21 (��)�i�P�<F�1In �unce, %�A osal}(2��;i��-�'ue as (��DI e) ba�@rle��%1., -|�!j�I�f�y gth <T$i�\y' %beW5�sa��armBbol�, d fa6ac�K idea'#t��put f�6���#t�: �t%�7 mbed�7inew�8�&m�u,d9? g)-%E  - � �5(:&�3r�U}ya TbU� A���(2" �(�� �A�5a�&d�% )y��deUqI�}L7ALnew.� M�YW�iste\anY'�Eprr ��a #odd �uU�:� 1�^��aM0i �aP7"(' d��he�(ps�E:��<(15 years a~`3&!K L2�uU1�6� , �j""?.v,lҩu��OL� um / Wus �6}$Aua�amaDly !��. ,0@�S metz�T�+,Nz  aa+�L s7?eF� "�t�&an�O��-(Ins&.)W@.� �6� a?&��p Qfu�ol��%A�tiM<)ewM�Gl���N�I�(ntrV� bl[9êen��C!K���U& @<� -�IKze�uSscrutin;t, z� v� gs$(jW� �N��tl�# .Hc?���G.t2n ���@]disI�V� he2R5� ��k on)�8ors�<u a��9Q-D0Ab�.=�26QN a�er��u%m ons,"� �-?�Rd� 8. �^in9� *i �0#.� = c"�of�[im � A� �*� 2d Aݩ�K � {�i_Ylo� tomwp��4e $2\nu f_{5/2)q$3 p_{3�> 1o�y�W82-126X�}{S  $2\pi dVi��50-82 @�J&�^ot� $U(6� s�� FI�f&� ��!� ����'�K 12)$:Lba�$�&FN1L OPt-Au�ss P. %AAv Kqc:� y��F�  %Z6M � ��ed �U6�cCBedpbr %:� )*e I!��6x�6� )PI: � RJB� ,%*f���i 4,195}$Pt��F5,1 ��b". i�rel��sub�schF�iA 12)�; �6E!_{�;]�= �Au�is�pH8)5P��H^& _& 4 ` \�F��0\supset& U^{B � }(6)�^��nu}}(1��� 0piR04)fmB^eZ|:{F)-}rd{B'��V � �Z%SO�US�Vpinj�^�65V�2bz636�%&j7U~.ёE��aa�ab���H6YJV&���oCa<rK aria6E� eD�ea����ŵ&�})�oN �;�dma��>�� aV.� .S 6b�2F � �nm��For� pl��y���n�[atv v&�`� ��us��8}$Hg��Rtz~ -8$SO(6)$as��;�7o | �Hg}�> P� $[N�#], Dpi}];[N],(N,0,0),(0;~,Q1 wfhgI0$N= L+pifA0�G���� Ig�a� �  ve. A�9% � 2\��ax s�4,�w.osELII O6��a���]��]��4y����a �ic�A��er�s-p�M ��*��) 1>ŮE,Q� x" [ �n!�=3/"u]s %׌)�=1/�- , $54chJ�ZfsMbpi &:&9�| (#�1}{2},Z ), ^'),�pi}��3H]t62 |[1],(1M� \tauA�2 �;bnu.VQ�)M�ith $==0,�R �m�.ka1b^ose ���or3;-E��\q�A 5)$m�fb1����b* �Ppseudo- &I� $k=�$ (:��a� -$s%��:N>�+�� ax-dz�&��;� $[1]� $-�$!* ) ���*ie��>ichad� $1�=�� ;S QSO=A1 �:� !N" ba�mbi t%�M&t �7ofݘ��)ma^ �&F�E"�%�s=�� ��6��A]�\;=\;mn��nu}>� [1]i�P;[N_1,N_2],(\Sigma_1, 2am\.2��. e^�.S\�� ; (\�Vj 2, 3),%���2),J'.J;J �> ~a�eq{wfaum� @!gv�׼ixuc���W:s5�p�p*q9�c�F��ALDoC6��>�)����Ѝ- �inq�:�odd�IN��d H� FR�>��*�a2��&� *� is�y&q Ex( aȣAQ(}^{\dagger}> <)^{(\lambda)} ~.G�%{�)�� e���it����z"!��ar�� � �c6(va:�l he�� halfu�major���P�(3se?4���{ R}Ns�ap&�JEt�SYJ}).����>31d �d�L�����Q��23�j�"}).B�6��OIc"�"��];��})����!+� �FyFsos 5s $T^{�,s_2,+�}_{(t_1,禁1/2;JПe�$2,$ ��!�A=o: �! $ 6)�^$  5J' vA�$J $`"7) To8 T_{^�.sJ} a0v�: -aM��*�T_.�� �sF .�. Vr3>�BDr�B.>r.�1)с/2��o �eda�C� $n\�[1,!���wa*� e:p�4S���Q�.��{ []{S� �_<m�ex�u}���"(;9� �Y��o$T_�$T_� $TZ�of *M�-\ �R<�s.2�� � �U 15ptF�{lwp*�z�&!���=�&�1$ 2 3$&��Nk N\pmi>Jr� �H|V�)v�rurd \\ 0B^ 02|y�t.� ,\mp|��$\� ��� �j& "92N�=�-��."�t� ndle�>'��&���DR� mT*�*�%�*@ "�N�_�I .% � </F| \| �% ]\f�*2�X�� H�{v ,J} (-)^{�+J'} ��Ja���  ~\{ Wa"7} /aj9� & DMxa� J%E  & J' %� P  \�.�|RQ� Q\\ R� I�2�>:_^�ZQ&���� ũ� 1{fP.p.k� n0��P���,R��0.�\ �!�,STq���J��%�.�V�&�rmeva !a3=��L+11��c.�B)rTp $<|>"� ��c�� fm�sH@IK,IFS,BI,PvI,BBFd �P-�$ults w|\#ub�4�a t4rC! X J�1��.is��F����a� la! i ��  � $S'�Si2 BF���2��F�U|)-6� m#ox>\� $�$:�R&G B,� � ��60%u�#*� , r=���0_ $H1O[b6�~ $L=J-� ~�$J+w 9D� ��VNopp7ex, G��� ��HJ^ L$�b+�%�!oB=Z6�Re ��2�&�~w , $1c,a�l , $3 4 G�2e�Z![�a4dl$L_{Ja�p s��Ssi��ie�T$P_{0� P� �P_{� Է  �� 4�~ $H_ ��J.I=� � JC'$G_{L�-/ a�R�A�NF�$mA� 1��l"r�A��U�z ross4EKA�#*�d�);e?� $^o3�*� w*w"�%e�a4:j^# Ū aJ�)F =5| ��� g"^!~�ef� � `|^2E ��!�}u! 2�$Z���XѦ� *3�5�m$JsarC(,�hz$ $9�V:E�a�n:�QvmoA�um&(3�1$jj�� $LS$Bup�kEtDa Talmi-Moshinksy �d!� �g!" �J.|dbA�C'-of+2&k�U� BQ�,1m46:,a��"m,��j�+aik(-WC�dN� &� �)�4In ����T��2I;Y��he �0 Ţc�) �L_ɢ 5st�8%z!A�2o �;YkR��=iL/ ^{uref}}` 2� M���:0�tV��]iKR��%�a%g0.��5�!>!���� T+ٟ2�ݟ ->�5at���2�z�|�>�%�2�=� H � 1��1i :!��MN�.�pAD!Bm �b2�5$j�$J'��� �5�$,y �7el$J=J'1�  9.>� p-at��!�A30p�-�9�� �!�E�e�V[Z&*/I�[-"�, q�6F, ~� Ki�,~�$,/~��,l*} �S�Oit �rz�bN1If�I"%-�M�"=[5,1]!�R�=(5,1,o�@A*�1�*�Q�1%�M�N� a�(2���ndF~ �IJN+4}{15NJr��$� �,zE�2� �2�E��B� D(2(N+4)(N+6)� (N+3KX6��$[6,0)`6� .�B-5�)$. u%�: � 0.12%� 0.336H0�$N=5$� �6�� � �%/����D"A��X�sr3r}�$ɫ�nd>�7m]"�M���>t�7figure*"�6} \�*�Cs[�Le=0.45]{prlsusy_fig1�lI<&{R�n�~ 6l"� � �%usi &� ���,P�"ect�ko�+� �;umB8.�8�~ ;2G4�2/�"*s� ����6�)row� V� ���iXJ#şnAS�?bottom�top�<��(i)�"��.�� (ii)#�l֚H�Ie�:�&w��)M�U�| �{E�}! ek2� aL"� d 0u�-�:��&9��?f�>D#�U��ys��8M��:�F��R�"� "re:V�>�Iassig� aA➯)f��w�� �Cprc F(>:�&A}M�6 �X�6i�--� !; s rise!>v% �J�Ha3"S�ofq��Er?o2�Ih"��%� v %$A�� ~)� 2�>�,tn<E:azw�7B3��� surpri�(��J�D!��5%x1JR�a��%��nay, len*�H�<or"�H��"�HiRU�>.�M2# nq?�EiD.��e�} volv&2N8�+4"�5i�1 %��8BBF,JPA}aܥ���Ni��N%{e��)�h7aS�a��a}��ur�ly�&waS�e a2RTh\b�V.3A. Arim}TF."�G, *�RLpg�T3�]106�Y 75); IZ3�\D`.iFM} ]�Oi[olt�ZZm4sS60\195Y  �FI6Ub�4�T772�X0��{ } P.��1w,�V4Jolie, K. Heyd��Obm5m653m5).UX��!q Metz.bM�,�THerten}^$G��_  i \"un� , N. War#Ad Y. Eis�Wnb�8!M154% 96/U.� N.K�gen!�A�, �eD�~ N� ar R-@4c8 (Academic Pres%[ ew York, (Z9v� H.-F�eth�` Graw^bhr ,:�@A. Gollwitzer, R!�:0-�A. )gOPR"Ͷ(r, D. TonevE�B.Dal lnio:5]7W14610�V42�b�< A.BUSlanteJ��Uars%��Rm]�6� l2�U176�V883);\\ H.Z. Sun�jrann\6"fN243�]36�IK}B� S. KuyucaA�^\36gkE�12 IFSeC��:�H.-�b`5%8i<6mBI}!�bQ^�!c36)6�PvIF��� Math#[*m��2cY9$Z6�Z�"4BIU>��-inv&j\ y j Dy��_�}$R. Kr\"uck�&C�[BeausanghCa�|yF7mL ,�CederkanJ.R[7,A�,Corminboeuf,�Y Genilloud}�:lM.�UHuu!�I. Leva4uecNovA?.� T� ndelR�f64304eaP\9�!z\#ɫA:-� Gen.)�3ES025�e6U���A��r-{Zs�Ymbradi�:SohRkPodoly\'"��F\'eny�.�m��Y443}d3e?1>��Y* X$9�\tolerY�= 10000 :�Ypre�ht�Y�%SV�Y.�Y=�  &� . >>;$2Q(Skyrme inte�raction, the effort can be reduced considerably by using 0\singular value decomposiR to B[size of tparameter space. We find that# senGve-$s define a 7Ndim)ton four or so, and within this /�a linear refit is adequate for a number of Skyrme.{ sets from�$ literatur �do not�L marked differences � e quality�!=�betwee�e SLy4, ,BSk4 and SkP���. The r.m.s. residual error in even- nuclei�@bout 1.5 MeV, hal)�)�-�@liquid drop model)�\also discuss an alternat!� norm%;eJ$ating mass�sIQ Chebyshev-H. It focuses attenE*o% ca!� !largest~ repancies.2ory!& experA t �show it worksT� �A@make some applica� s to) s based�M$energy fune=al1�6� seemHbe more Y�to new �al dataa%@ root-mean-square1C$The method)�has%0advantagapae�didA�(improvement�theAgor!Pi� asses�with a�ut-on smalla�aof I\0.\\ \end{abst�H} \!M title \se%{Introdu } In mak�D �ofI�ar bind%d�(``AV( formulas")E\re !invari���W!atd�gmined byA�A�!FzA�ifi 'Q ka㉃$d properly�y may!�under�/trat�.A�!� , ca�:problAi. ve�isa�7sitaW��r!�Q��iz%�!@1 elf-�isa\ E>field>a0(SCMF)0>h,IN c!�d d�Zty-Y�doryafhile I�s�dealing�xF�s%� well know�xo ��ledE�!�A�not b� a criticaa�alysis��m�a-�e shall �U�_}�degreeOfreedom!�ZE�.�� very simi��to thosŒ:Bf, excep��)�spin-orb��n�Le�hen!��;is��trictedrF�, ��1�q�� ;a�!To��e ����� required%�a search�!_�i�f�k�� next �,�reza�ous�-�s N] AEond way����"�in݀!�Ri��use a�{economEDչ!�fiaw(Usually one%s/east-�}s �%�eJ;i.e. i�a;b^ B�(�) averagU5��&: $r_A$��!�a��8@, $$ r_A = E_{th$}(A) -exp .%T�\-�sa�cul� all��i. A6�!J�2:�,!_d!���4a {\it minimax!Z}. ��allows%^to screI�)��their:��% only in��� n aɘ �ɕ�� ``wors� ses"!���a �� By!��*�)�se �,F coul�n0be helpful to=�(alists choo  which �Sstudy� %�1 iP��� mis>ingredie�iRF�T��� n ext��v.� ��1��H \cite{ch82}, but�%erarel� )�physics 2 ja83!�W� scrib%H�Hin Sect. III below,N y�it �F as!� impl�erciseQE �� . Weɠ���� anothereo � w��.U e� m�W C-e��d�`��o�fora酫EPN�)Baudi2}. ���& �b)!~Zx!qoften um%havA�0specific iso� struc��R(u e&D--9�( nine. Pair�!A � spensabl���!��y����s outsa! scop�A-�B�.��includW { fo���Itreat�Z �+ ref.9�4},��8 Lipkin-Nogami 6of BCS p ] wD 8a surface-enhanI zero-rang�6��fA�o %�dA^o�e2�, su ��I@c5A,R67L w��be � muchR d anyway�ireq ^T�in:*3}�.�1�M$def\calI{{ I}}� lV} = \sum_{i=1}^{10} c_i f_i&�*c_i�,aYe��$f�!�!�one-body� ie�U硉 / J need 4time-reversal |nt �!b!��j in TE�I.�ggin{t} �wskl$-def} \cap�ޑ�B�U�c$-��i.��� $)expan�into aeger $n$%*aa�i� 8t=0,1$�e a�ca� � isovector:�4$\rho_{0,1} =  n \pm  p j�I1'�sav�d JU. ŧ-@o }{c|l} \h�t $i=nt$ &!V ay � 1 �t^2$ $26 (�0)^�� $&3 &|\nabla �t|E4 ;t \tau_t `5  2:4 \cdot {\bf J},�Ita �le}%֝'Uor ead u�&� !\5grals �correspoc).!�$f_{iA}$M I a�fd^3r !G  Si�o2Ay�Da�>z�JU�s, ��rq&y�Q! � re�� J1optimiz��al� Howa��8many ��E "�&�g  w n t'as star" � 6�*A�arr �ci�ll&� a lo�� u�%�Kn� � vicin*;�9O@ set. On a techniYlevel,�����deriv���-� �oA��A)ec"� 9�� C �fit�~]d2f!� easi_btb M !��0Feynman-Hellm!q�e� FH}V ex��-6с?ter��U� U�originj. A� �iis vali� $2( (��e� h� v���al chat er�E-#6� �-,A@veIQ�$matrix $M$� A�el��F�6tM_mat} M_{ij} = (I I^\dagger) \�v�JA m�I_{jA}.s p=�!�ch��4 an amount $\D�  c$��by� = M^{-1}� r�1Hau>�N$r$j�Sax/ s �� *M�ively. �ma�U�ariA"Q4ndancy�n%y�a�) 6�.+fla�r�!�I�%�8)4o�E�� � effaU� I ized��. ��ife�ac;e�se X lsi�yA�#?yl�AU h approxiD!]feu�0 turnk a�be�s4i���C �a��mox ���N%�Lyp��ly addruby! nMof:n:In Dn� , !�t�& ?5�elimin(:�e� �chiev=Rdiagonal�k}�!R projA* ng ov the sub {spanneX eigenqhai�Ps )�r��n��,!. now&�6�I��h�%�y �/� ch98��"�-ca8onper6 eddPa�\-Brussels code {\tt ev8} c bo85�ҵ � occup�Q!Obabil���)&� �DalW�l. Accor�wl�!�!-AiA�E^g � .��rev;��to8��( $N,Z \ge 8> �light��i��?�d?�_� ��!�.A �� author�>�!!-d u�E m�`w�1�jd!!iEium�or� �9waok�ay�� ��.$s. % Compu�program b(files: % Ru�8�� -%2 comma*��: %� D``python /scratch/l/ (/run.py'' %� y��pu��o  O ���� =� n��,s ``outdir''e�``sk �} ialH�P.v�� (�_C)N c(s=getSly4()!5ResulJ or%�EiB� sly4_r 1�e"�ali�� �� n�� 2003]�mqau03}, ��measu��N�579B!�6}�e-%c:� !_ ! %�.mas03!U  �a�le � Audi �se�f. [8] @1995.datBZ@(( %read_audi!.py -->�.tab % r.! _200%$ exp.:'W# '+�,a�)�y� was "� by z#�&a�Es2s� es 8t�z64�� c�)� q�es ar mi!�y {0,eq}$ ���aIut y=ed a goo� ���� c radii.�-�i  � d $$ {d �dO(0 }{{ T +V} N0~ {1 , 5 m} {k_f�% �}+ c_"{ k1+�)c_{20}.4^{*c_{40} _ =0.R g0k_f= (3 \pi^2.F/2)�!�Fermi moKum� We e��i� n-ia r�R , le��8 ��AE.�a�� � �AB�) UDUvp$ t R��!a5¡�� A��ء�cd>���di�! bute�[ @cess_��a7:"B� > a�6IcE$BOu���co �.: of ``M''z$�5, b� eY  ie��m ax/�  )n�-��mbe�� � .���A8-"� al .8 re� play{< Fig. \ref{M_eig#b figure} \�\graphics [width = 11cm]{�.1.ps}&WE*\ z�!5� �, eq. ( �p) }&�� %fig 1��:�plot/�2.gnu� � orde�zbF!zp Remark�#��y,  a 0u$early�= magnitudAAls�'��!qf� ���� 3N?� i )�s."e �+idee���� �� 5�(s $N$, keep#�0$N$ most signY? �]s.�& ~ �'`@5 ar e�s�|r - ("�I)|���" ( r_�]i 4_iiA})^2,��A�7#� A�~2�a"P !!$N$��"W��Za 3.3o( :�� �&O�(74e0$NT 3$�u�N'�s8*%5l2�!� ^ w � tou%KF�).~s� �� �2~� must!demon��t�D�!�Fa is ��#a� when�u�5:� of� new��` "UmT�Krg2.26L�"���F��9ki� %�8�*^��>� I`as circl�yconne�$by%kEgu�eyd trianglesF�actualIp~�|�l$i�b�iU �. H.!���K+-A he N=6�)N=8a!��n�, ey w�K��2#>:.�] j�_2 N\s/ &�_% S�,s�)a�:��E_-_?�x ?=4,6,82� S � # $N$�8,1hav� E�e "�of%A, i> avoi%1x2�a�[e� .rocedur� rjUi- �ss IH1��$9�I���w )� cl�'$ &� 6;6�"� $N=-0$N=8$�����2� �"!9!5]�MP {.6�1� new 5�didEalway� vergqJ7e%:I����9Y-�ASshowna�black}�i�. . Ong)añt#�AQ)is�%� p�$�+m�2c)��heQ6$E��hr��2d#/��7��e th-)' �s ���'s�I!������5�av� �4$�em. F� ly a�h&avy-w,�c%�]tre�aol+�t �![!�7 n&�*reg�$M Hdoubl�,8gic $^{208}$Pb,�H]_bound�v3� )Z _sly�1.36|R�0s.�%���/!�6| Y OM�-�Qtomic�"joi��AJsɧ top%�E)q6�qq�<;( �aisU,�%Ebottom�� �}�ly4.Jr���& ,"� � % dq! /6R"% fullu�!�:�&~  %z�� %N���fit_4�N2E�Let�ALtry�T� rpreM��  !�$M�  c2����7st@ 4A�eas:basa �!in.�M �K rolsIUar�'t�aa�Z�&}To�  � �)�a��l�'E�NS���A$c$�s� (_v(c) = { 3�210* +�.6�{3 C5}6E�$$�9@)�� maxi��2it%�$ �$� �or!~al1�g9$ent $ \vec.!_c 8��f.6��la4is� >�� MEZ!\Xis 99\%� \ �j extremely��� �#al�!�I�Eq�3�2Y�*A)m�3t�0r�. Its�eE I aRT-16.06  p*Ade--ort@!\ert):kr he symmea{I�,2�a_sMZI 6AWMX1FX1jS (c_{41^{ 0� 3} )c2bA`It doe y� quit�5:�$&�-�%�:a�Y Q�al� $A_�#E^�`�/ 53\%UW�2Ase��an 80%��pthird.�.B&��cͣI�three���3�;v�xM� 98\%�be ��)�)Wt -efAvs+1u $N=3$ �� e*~1V5��s7:<6�% AL:K� ��%adjust�&!��9� !WB3R associ?�h@)U�>Coulomb�{)I�e: like=*we � � checked� ' 6m!�semi-inf��*cly��R7i!K�7A)� ���.��].;:�remaiG=2 "j �� rele�7a�.A*,"�e -3.VB7�L)�AV�� th.�!�C�)ains %0Eqis �9F0�0.�3b: &|9 , na�r!([,N5.8fact,&� a 9.�b"D;at1�M 5>&,a"{5t�� notrof"�) Bey~4f��B_s<�&A(� a�2�<�8a�1�mt"�%���#�((�/�-�."7*R�2EH�>� &c %at�&e9Z -�i�L�� L0Z�la� n�j+%:��Wͭ� �]�r;z1),eQ compQ �3pur�1�Alli�)A�in�#H-P){|c|lll|"4*TZ&y & � &"� �*&"�  & & &�)� )/! & 1.75U��& 32.0.3kP-�4�3 do84>81181.18>29goo-q6q3 & 29.69Skxce2:brown t 55 &�10 s.�LD�3.�-15.6]�96�*% �3: py�:� BV kp/skpY _noq >� j> FC*Rcd�&� [ >? �/ditrJ�"� �u > 2_�.< �Bl3�� a_s,�g e�B�s&� � (2:�%� .Q!�tv>0���ter: .f90:xt^��s: xt_*!a *=�, � fit,�,g�7lD�}�:B� �$/lqs_ld_ee�..:N /��Q��a�r�9�) multiR6l&b+�.�&��"81 �+�a���x�A�m�&,, >4e 8C.�@� � of�95�%��e/�pA?�!th�We~carried �A^AY�2>B �y*C$���Ácy4:�fA� Px).A%�7"5� �]0mp� caveat!"�" �sKquo�FoFg� % : ,;t6�� non--�@gyis #le4 �& hAI�va�hJ�� mselv�)���24@I �j s�0|�J�"�� �a:1s �� b� l]"�.~ '-UE�u-'O "�5 6 "�9V�8w;($ll explicibexa?B �*f.�,se ancillary6u*J8fw=�Q!aq/P�%W d� �&as* !<%0 5"�&E��5�o �% -o solu!�A�!�meC'AA# s,4 I��;bK>lowerQGstB*i�))��'��� 8y landscape. H�!"$�:�q�Y�B, weQ%D�.aj2e��j�@�=@��-Wi"q .�4I %� .) � ҁ��BBS�de�vBAAa�=!��ab .�s"���(ubstan�'� x#1}5)C �%kP��e�1(r#ce ($5$H!/6$) )2�!�facI�e�"�  F�A�vir�ly id+ cal-A% =J��9= 1/3$�� �ri��und"m�2�6��� dilute�$ga!Fin�@� �*bi�!*�(�E�a� =A-? =1/2 �� ~J6�-�� _ ԕ�5�T5�T �0/���+fo�.n>!~.9.�+e� madSm"Lo��EqMto� 1%���� + . C�`�BJ��e�%��r�E�littl��#J &�'J* ���El!F�� be��"!#1.5-1C!��f1� a(��!x"�e n�:!E:p .� � � �'%B&?$1)xO<f *DC D%����&#W2.9�J;����1u!�' ��u-��6�nl'�'.��- �/a�o� two �"�h�N��<n�*i�Of�?rsA ^a� twicvI a�Y��w��e E sa� a!ny�suq/luj$� �6� view!qJ� Stil6m�.i�hop� -Edra�hc2�a|�A, J�4�$���A �!e%�}�*� a��I.�?M&3Ds}�0We ,��Y2 plet�ytQjcri�N C2(.wL�6$ $\epsilon�)\&�/�ab-�l �&J �E = E_{>} -&�E$� gO9(max_A |r_A|��HADli����DC�B"!1�xrtiioba2�A�i�ncoIhov qO�, henc��( � ``� xI"�8nh l,�4!�()yE���m�} ��"� � (be $N+1$ me")Js�aMxa � �&z ����J55 f)selec� �AM)���i� �9� *��! ��, ��@#2L&rFh chK.s-�yB�.|E�hA.is upd� b!* plac!�QY��)�until!��f & satisf/!E1[�� � B�G!�%u�&adDAset--�Fy���+�!/"��f� obv3*�1<sh�A r�"�asc+D alVth�3�/bV&*c c�G����&I iw�R/ toa�f robust, u Kcom!iE.� aflesAan ten�$ons. >��@LF�-l6@�)H1��#OZ 1995*P�HQE�I�u��5)ti (��(or $Z < 8$)ZF c|c|*HD3,0 &_H &�8#9?%�iF& (MeV)&. undeV/&t�&  & 9.2�^�0$A� ^{76}$Se, 7}$Br 229}$FruJ,A$$^{100}$Sn,132 ,CA%`& 3.048..` 3}$Gj101}$Nb?230}$Ra?.4X$ 3}$O! ` 207l$J�88 8.4� uAs ��<$\sigma<0.2$ Mev@&F10�= �{LL3�#� 1� �|:cpy� /lsq_ld.p#F-#� _�3"�,e&g4 !g.L4%���d�RV�Demo.py�_��*�}Iq�5�'F��0 ld})!�6s &�DII."4* |row� ��� s4� & 2149q� E�ma�`h;n9.8$. Fi&BR�A��7 �s&N =a/$F!�&s6 B� 6z =anQ���)2.9h� note�g � 6B�4 .z2:��i colum��_ ���OK*�k@廁T���)�)4;42� ���+�sp7?t r�)�e. Two�tei,aXq���M�B,Ya� neutron-r b�1I9�, <)wo;.�(:Y��:hU)� �%5%D$N=Z$i�KozU aticEindeed.[J |lkZnd)40�_8)�S &�)�����c�� �z+Zjn� t�7��#�n�w�Vaw!�of�{)1�.46u)ChaY7einw�}A�4�M�� *Z�!�@7 �P;Y the E�alT . C�U=BFc� "�/,�%�Rn&��' �6J@ish�A��(�B$)��m�n�G$) ��cro�Zrea%#�"i w�EE�es)�IP R;>SI{e��G�1�,i >�6��� � �q�& �@i�M��$E��K�G �֕� is 91ly��4 ad�2-� L��Q" �o� ncre+[by m�$' a�T"��ug�[!O���*T#be�  �Br�AK)p~to exhi=W!�v dem_�os �ad� � . M*�2�� e�!n�F*on&s[��,�^�A_�6;� .5�s�%�/�� -Vcau�E�b a*�.. S�Ha�|+ri F�&-��E. %� ��m�sU�!��NN%�.��#�֩}.�#��u�Z� ��"e.�]d;��/��N�d���-9sQ0�,B �a��a6�Laccurac�%!��Ij?-Y1�� E�!��ia�%�s&� 2 k1_ZM�de%�9 0.8�-A�s6�t&e��(��IB1ucleus�j-f!�� aM%�� ��� &U6soM1g�PN1!hJ:�*.�%*(!~�* { gane^w*@���*)���)7Uu�s�8a� �con��3o o"�;�b��S!",otope chain.� nuZ�3uss.�!46&�t9g IV%Ł�|�A-�!��q� Q�Qs�A� arliJ��,e>0��topE)(  f�.>�� a�-*� ($^{60}$ZI4� ),i�i7 very~%t� �<20}$Mg))�che&{2 p 2� ;I�)m H=2)A� .� E�a�,s6Z5mi !^n� ^{254}$Cfp  Overa�!�e-j �n� �+1�����c!V X;'al�*�]!�a2��J�� Qpin.�)b�( As "be�e��Eq,E�]of�&$&6� f l*9��) of���\�ofUEi�i���.���!"U.%cu"�Yi,0Z�._} r un!9#��)6���M� ��O6�2< �M�_8nly m�41�appeaBC e $Z=82mWR�a"214}H e�& tIf�|90}$WE 2}$O�Zoth�+� �b IA+mw� �prolat ob  shap�Th�I�O%��sp�W%q�9`�\ �K�sO#K]NH/i�.�.eI� M�isM7!)' � l"%&-OMs��*���'Z)-:�(.�J of G� �-et al�W�$�f�eWJ�ia�Y=1/3$ ra!dn 1/6. a��o26��, �#1���rt#ir�6� �uq&5XՕ�.� E?�3*� >$"` ��Y� �$ublished� �_liw,& take�c�*�h� �%c��^in�e: . m� 0���B-��&rd�ۡV�� �b�l�.Sof eTD ��OA�!��=*��6fi�5u &~ca���%d\pb ��!s a<6mhQ ��w ���!In '� V�KE���'U!hen)F olog�!� meB�2 !-.% � ��! �" }�weyyi*�h%O�'>�maNC.�!%DV"� <NX&"��5N�/�s�e"DV& yH� som"�_� ���`�6$B��'ch�inI�G��en�[Q�N� .8U M#��5�r!^pre��"��R��A>M����2. LiRA�E\re�.� mid��@mqE �" irj$Xar9-�I� � �)fa�&�fsh�g ?�?E�;3( $N=126$� 1�D)"�X^{218}$U��� J7I'�!G/E2~ "�\�VLa6u�$ \bJ71�Hme-mm*G � ��[JP��%�u; pA�&,�ex*�H+ +:�,� �E,"�E?�yJ��N�"� J 9 $Zi�-_N$R $(Z,N)�[�c.�; �~� �:�3aqs�M���. F�[X\F�1�m� \�-) {2}{c|} "�Ioi}\co{3-4} &lB& &� & aq 6�1P4.8 & (12,8),(82,126)X30,30),(32,32),(96,154).NV�1RA 42,5T32T 28,2(74,116),(76 V 2�1�b & 4.7X � 50,5��8_ 38,3_38,622U�2Vb.2W4W9= 4,34!W42WK28K2�50,�=M(34,4� 8,146�>���L��1�>>BK?�0*� >�1�@"�>*Pout�m "�dTesMe4Ex�gons} �g�3���C� � to."f&eZ"�On��"� ��4�L.7h�_���&�Ws B�.��of���b�tt(9� a驜is C  !n[4;*� �� I�Bon2���O.pl�P� 8a�Xach�Mo.��q."���_ou�grs� aV�*askr@B�/��kgc�qa:�:�er-of-�umo� .�C�.In�` inci|2is� �at���2 �G.FbsXis���2Ua.�@� �H�H<}(A_*& vW &vWC Vc �4�6��h�Er�" ���onby\ refd. Al %�"�Z"�W^Rtwo�,�<�E��en.�)�;�6_� ula"`to^is��*0#��af]E_{cm�R-{3�R,4} \left({45 �hi{2 2/3}�br� )k]IdV�/x/� E�1�[ mœ��� e'  3�!�d6�m�ne� ng $ �$�;�+3�+)�i�"�F�a tiny�A�q� Um� Te�h�m��ps2worthw;rto �W a lo0�in v&OaQ4:�4erm�&&go�a glob mj�+-@c�ZA�_.�+ "�+f �<�;� so!pl��{hN rr)� 2�ty%�jq/�3ua� whol� it illu9NM f.)9�9��s�` )�3e]E� a s�(A1�#� &��n�r|0to�CW9|C2}?�&���,1b�� re�5ed abov%We v9��:M%lCe^Ksol�z Lapl�7�[ba��po�t�Y�#tnCMFA�rg� nsit�!6ex,��:�Py}��" 2d,!��r)S3XuBTm]mat-�z8cI���(ofl%3neb+a�-�, Nolen-Sch��jma(aWe��e e��7i�)�M 2^�V7�.ak)� !Ti,�l �qi�Ar� 4Ar.��%SG��>���F�$�2J %.y"�ce�5R{!�2,w"�]is=�R K.; , c%2E?Ly4 =3<7A{�H�B�QCq2�'a> out n �e~`>DAOdo)?_�3 gain�$ itW 57%Ki�q"Y9k ��qU6���%�9"K�f��I�ly��s�IA<ase� 8A $o��z�� �!RIZser�*�cM�ove�L!!��6N�I^�L��y<eWr�9,.�_ b�~ u�!�>opo%eDN1n8!a�*(:i�� �� hard6T"�M�H}ce�m$�� :E�!@.;n�|�Yt�oult� 1"ensat� %��!�%�mOB��-� rl*�z� �g0�.�&� �Cqnsp$x;" stud�B�r,�,Ube04}1T�K2� �A ���:��w.()%�\��?A:ork*0$1k~f them��!*��Ni�fO1e &� �U�W��w�R�� �.�6a+�}ir ��/��U�E�i���:Y8m�� (ifAS6W��wca�0.2��s=Er�LisF�y�"za�j !�an �]�pe+s�k+��l!�!9�y{� prom�e}� hD�sb�����!�W"���co�G���/=8$v �{ ,z(a�p0"�&>�؁�a�G: e�v��.��)�"aF>t% �7e�A�T Nz"� 10\%��  � en4agEA9@+cPpr�C�A�@e�*�w{�fp* R� )q-��)si6 &Hhhat6�1�)���T��q��no ��e�)�j�ek%�g*l|2pe*`r�gry �3�!�dYd�A��m� ofJu�4 ticl��4�,$Yi�s2�= ji)� ��LFo{�b :o%�!:��f-BDJ� �e�,g}i��7)% o�&Q�*�"=��A�,�$aP\%27ͭ)����B!I ^K�CIw���u��|$J=0$�!�!�-nf?ge�"#+�5"�^ *��possibl2�05"��VE�V E��% �_�-�9v2X6��A>��;"IVP*b��04z01&�&�Bas� ~384 -�1 c.m.i_�q$69.#noBT&892J%�.�J36.JiN�p#40.#6�y"w�>�-rk�y !0�GaJ[�1�U *quantum�;�!�� VW� llengeq ask,E�ly duW(A�T�i �@A�a�� u�7belfl '�!�d�qop�s�w �7�-bb�h!*52C��w�N&h�To�*�s�,A����I� �J�cF�*�*�availaaMo��Web� (gfbweb}. A�'suDn� A/erE#�>��f@�EngF�de�@ Upetu�m)"ach� ��aReo"n%�a�9+C WM9�a��[c��cE\i%"!8e%-U �% � t��� � s�7n'C`ign)nt=9 sed,��l�R��ll%� ~o~E57!G_ �!�For�<itenes�!� +-&5�?��v��bQP��� ]Get� typesiLa &Q"_o 2�%� �']ei����. )9� gE)�#�3 answ!��basic quA!on|ua|e�*(,��!K��%FJ  . N�Pd}wA8*� N�%@'A��leV56�O me� �e�!���a1*QM!mnor�� B�� ll? �m�&mw>�@ a�26lM*;#΁`�'ev �+cya}&-��bnd do�wy T!e�|R�>�nP:a�F AFX is&80 %AH" 3�2))&�  i�#�Sa��{ fuld h4%�fw����&�!��1of�rs2 assuf(e��%2��0�^a8��yX �-.c�eng� �XVk�0ten/-A��ac��� s}�$thank H. F�drd, R. Furnstahl, D. Lunne�8G.m��_=� � $P.-H.~Heennd M.~�2 �wful adv�Bnw�u&e ��^sJ~ � T. DuguetXa� eYx6a6u manupt �vY<1�Ea?g�*nd clar�-, !�x�> sup��U.S. DeH !LqE� y, OSeN��ar Ph��,� Cont� L DE-FG02-00-ER41132.�B�-�thebibli�Mphy}{99}�"�2em{�= E.W.��ney, ``A�"*MM" (Ame8�n M�(�'�ySoc�� , PrpT`< 1982), p. 28-56 r̅ F. Jam�L�� st. Meth.%.E1.�|4211} 145 (1983�Lau�$ C. Borcea� Mu, "New@��Lp� �Re fari�=�sy",/tlhttp://csnwww.in2p3.fr/AMDC/J8ons/bernex.pdf}��D B. Povh, K. Rith,�Scholz� F. Zetsch�,``PVo^fAi!ei!|Spa��$Heidelberg!g95)g19z�} M."el il  P.-G!gin-, �2v. Mod1�D\textbf{75}, 121 (��). %_&�En m��o�.�'�A�-��.�G.Fa�r!��,�(-th/0410023�FH} R.P.�{,U7 v. 56 340A039); H�l�{4n, Einfuehrung��die Qu ench�D (Deuticke, Leipzi%i37.zuU Ea6 abanat, PA�D Ha�b l, JA�y!�!�R.!�a�r, !�>mA63!o231/?$(1998), Z-(43}, 441(E) - u#�v��,,E[|�A443} 39G85.��@ uX A. H. Wap<)�C�4baultZ� 729}, 337ME; ���&=��"� at2�a�Dnndc.bnl.gov/amdc/a�t� s/\\ AmeA��s.�nR!�(Dobaczewski&.�- 22} 103%4.�$S.>.2�C G$68} 054325 �]�� B.A. B�$NB58} 22E�98.?�= �*��fh*� qGŮ\8�t7& �e `  is 5�Zhig�_��a0L* E�6K�L�7  4�' is 6[�� a[Jsv�� .� e03b�C��HN�71E�0 ��;A�Valora�-��I�}+E PhyъA67ы 2000.�g)�c:�x<�% .py}Zdownlo�m !\\2�gene.�\.waP<0ton.edu/\~{}b�4s2.tarA�endB�" docuy } �%*� %\B class[two),/pacs,p+int/ s,amsmath4symb]{revtex4}BMapsjX�j:�KZ�,ap�c�,grouped-~� % S �&(s%;u� XM)�SiesB��uY>i.',draftr-=g%�� Re�MB!�(usepackage{�sx}% IAs'�sJ{ .,d)�}% Align $ imal�2;bm}% bol�%th2epsfig}2newlfont69�sorA�>#��2�5p����{� F7prlY�A�)%1�} ��*** %.�-��uN 6-1�6bm: �} \newcc}{\MeV}{D rm{ μ � "� style{unsE� ��}A�t�&enA-a5 \1�4{LA-UR-04-5803 ��'".Ś}  Electro�ue�Cexcit� �5��oLa�Comi@vhoY)n�lasma}�� _\vs])${1 cm} T.C>u4 L. Friarɔ AHayes�%it��"�< Divi=4, Los Alamos N�0al Laboratory{=MS-227.8, NM 87545, USA)6��:$flushlef|� CoމH: Thomas Luu\\ \h � 3.05�(v�R3T-6�MS B227R*]� �R* Phon�4(505) 667-3612R+ Fax:� +4-000V�tluu@la� 1�=.6[18*pag%�3�^!�1 �C e[" \ti���>� \@6{A�Luu<mail[]{2� } \affiliEb{k.aal=�9�N�,M�.�, New�exico)�I��Ju���y���΅(date{\today!��a&�%� W3,flux environ s0"t8��t >$I$gly popu" � onic.�ysot��abuވ���re # net$A�nf�$g�$ k3z�i �iAt �tempe���Wp��Q� onal�c� -m��E� h �R��0D2r\& ��a"t^�XNf -&  % ue)nt!Yk�3!�� �0*  (e.g.%35}$U, 193}$I�-($^{87,88}$Y Wv f+ six5le>�6�|E, photo-�Vrp!�'in��3!��l �Wine�ic^ n scr) ing,�%U�F(, $(\gamma, ')$�$(e,e' )$U]��find ���b6(0$kT\sim 1-10$QEE#:� Z-�6neglig�C�D�,k�at8.�&��=~ =3 <0A� Q�!6SA�nA�>u_$ru!�EEAhtel8�te��J�rmoFSao!��@s �+aJA!�!��Hs.�xU!"]Ia�Fac����\�Uɲ�� ";6��IN7 �rt-liv�%A8ed�| mk���#ŝ&�%�2�M�TH � ���)r� �~�\ium&6rar $n �E���k!:�uo~*�H,a Boltzmann .�!�Z��4��c�5���-c� 2;(Popeko1973,3?ovoi19841��inM �F �3�}wo- or�i- /uH&e lya(b�,5J.�b ��G6# �W*v2 Uran�pDŅ�aa xe wish��[m� s�h�$a7�3�3t���sub-le ���.fim*t�Bt�"�A$�q:F�!`eKe Ʒ�~�Z, F�i6�\foot�{An om�:U*�B��!�\emph{q �C�l�E-^�=�� thres����E�u�֐�st $E>1�XV ("� QH9)q$E�av�w��Sy �yI].&�k� s��1������o\�$ met. See�Z.i�$Veres2002}Ude��of a�3�r�=Nes.}.y ure~�,fig1}AYMF� L�r:� ��r� .�D>�=& %) .B�K,-se,�.u$kT"(Jz!eB�y69m+)[In!�ѷ $�{1/2}$�4 -�?N8 ify .� �#as}����k�F ���bF p�c �ir1 ��k �X(!�� l�1e�: ���6�!eRBSi�qsumh E#&� &�|�=!n>�5��D��.�%��;V�&�.,e�!W�$�A� � ůVlow-ld�Hofٟ2� �K� !�h!@prb ,.}t�U�M�� \��qH� SXapXre�K�_T��I� tab: ?�0 The ��I ��� �hY !0.3 msec�_yea�:��B���]m 77$�- $2.5�iR$��{>LE� �XR� �V%�}}i�<=��wl��Tb�?��d!B!�s͜it)2 titu�`5s:,�9} peqn:G�_tot} \ {z}= }+ i.c..(e.s.}\ldots1g Tn~��� a����1 � as��\Blatt&Weisskopf1979,deShų0&Feshbach1974"�eqnarray.�a _sum "� �&=&�a�L_ ��-F �N"� \nobHFj(1+2lZ+ H^,�̛!v fgVt�.�$�s.( z�A�soa��$JMc"JA� Eq.~(�VA09^),.Qa��l�M:&nelI� $1Xi}$�o�q@ng� '- _=,w�f )=1$�e �3of >���ySaov4���2� �$i{_Щ�U�}PUA&R�=ϡ\!a�"$d(\Phi(E))�hndF�� sa��8c�)g��.%{ �b[_�+att-1��?!聪gm�_2� . DU/!e(�Zng�sJG(� .e.}9�iw\ll E_m$G�6q� o �p1E(n�BW_>!i6^$\stackrel{Qq��B$arrow 0}{\ > \frac{2a�k�}{k^2}�4�H`�(E-E_m),>�M���t�۹�e�(!��o)�k/ �4�6U�i>��Iub�LP:��*.��(e syste�"�����Ah�vF���eH7Q;� gE�Plankia6�,n�p 2%�iJ spliQ m _q�a)=&\-�c}{%�(\hbar�G c)^3})�TE^2}{e^{E/kT}-1}dE \\ ��&\ c Ne�E��e w u�1�-1�1-�de�'-k-�window�-? H ew E+dE�K%L*Z���U G�!d then1Ca{ !,R_�� !c �\0_{0}^{\infty}�m )(E)dEA�_��R_s}! sim&�i);_m-= mF P}{%w.� P X  �T�w D(E:U. 6� E,�ion� � m f�kŨ a$�7ŵմ�0 into �� �+ Ite -a�9.th���(%-2��yY� ?c���s��)'�@��)E�(� ��tE�ir�Gc{ olar�raA��pr��t#8$B(\pi\lambda)$r��sA] �� �C: J_i.BJ_f)=q� 8\pie�( r+1)}{ [(2 +1)!!]�_=(I_E_mMUDc��)^{8}.�R�:��;H&ral*�ng :%�w( 4c"` it��ki�D-e���-x>ar�:fun�_�C>R�t"��^0�gNa1&x +u��invokes�|-em;>��&�2��i�.ond��A��V-"ed �"^ }QnZ� Vl vA� �ANF�B(EM R�=�� ��1}{4\pi}.+3}{3+ CU'2 RY+}��< e^2\ \mbox{fm}.\ B(M C��+†-2 �\mu_N�F�-2}��R�� 1.2\�J  $]E�!�Boh�ugne.) N8�7d-MT�i, 5�9��  so�ee a��4fN2�E�Z�HMw ^H)d�ng col�A�dB��eR��tooOI�Cm�tf�/� �$i��I�Wong19M�:�!%f"�� .��"26�+utes, *�q$)�5^�^M�a��� pe�]��to!t ch a)U�LL per-Tf�us,B� "XouK��a.I&s%� ��.bt"Z.V� :Z� s})�R��!!u)d�� %�2lEve��57t] I{rzR.�� se6�)�0Abe ��KGq \I�?{In>InC��CW��X>��B�*)��  ap'CE� boR icg�� reby�1�eprW[K H � )zm1�mߥ%�b� Taru�merA|:��&ifa�!�overla�;ntinuum�J �&I2�1' ,��(l � *�matrixA��. )�w�yN���"�M�.��{ -��:s .�$ $K$, $L_I  {II} M etc)���ipA�$ � �(&�a�z"u � kinh6�n!f�e7M8sfic<��<�%�A� hdZns�\G%Aus, s� "xC&�dbat�G9h mo�N1��Q��� $1s_�!5ɇ���I e~lowB�b�;2gb{�i8#Qii="b<1�T p�OEb�2�k� �c\� _= q39)$ o��M)��� e�K� ^{242}$Am2  1�$�r O)$s2? To �� n:= ��\.�$a>�0istic hydroge�&.���A%i�1 ��PMB�=�."�_N�.>�ŕ!�inn�#s���I�thu� n by��Rose1958*�uC.�%iicV� 2""� @;\ \kappa_o=-1)= "n2 � <\omega$ "� .� � \sJ� V}(2j+1)�X�T$ % �{cc�  1}{28�j�l� \\ I6%-60ec c� )^� |R_{-1,�� )|^,� "> �4)n�2J0( �-1 � �3 �.76R56#R361./:-J !-�� j=| �|-��e[$2!"� [ ǪB�?�u$v$�� s, $ YJ%onX �D$-M@$ or $ +1�'V� $1�V\= 6$ or $-]�����s $R_M�_oQ^$ž�DRIA�-��A�J]Y�=&M;_o-)()(R_3+R_4)+? � (R_4-R_3)V (R_1+R_2)qeNh1�$)=&R_5+R_6!� I7 �EC:P�2�nb�1=&�0"�dr\ u1_}(p_er)U_o}1�_e r)�h_ �^{(1)}(Msc r)� R_2Rov_ oV�o3�o~�o-��~�4Rs>Q~��s\%R_5Rt>V~���6Ro��~o�.E�V��U��V$�Js ��jb(d~  c���Å�$.���al2���K:�U. Co��ic j��#r=$u �v��?�M�c analogu�� K-�*or���� .F �"$uq�� sphFBl Hankel�,� ����N Clos� nalyV.Y]skl�Ter,��+t &x�<�g,#" in Refsh$0Hamilton1975,jJoll19654J"�*� N� &� R �����!�:EIIC.O|t`= �0o B&Vt�+ :F is zD*ٸn)R8A{���*�Z*uc� b�st�gsp*|r�U�h�JA8C�� �Unq�ly�Y t inh $#2 I1ejn%!'�*Nbe�hor To�,O� r�!f�22�a�  ,aPA�#A�obser��.6�|�e rgGWAld�,56"{ (displaymath�t$ � \{��� ll-*�1}{:�"��a+5/ Fo)&���Q3Q� ��$��� � �2�kA>T��*h$a���Pp!� #��AZA�!�surpri�J.��g��e�%�3} �L��in�.�2<*Y fu (ICF�psu� � a@Lp&1��P1*�*s)�4[.�4t�.~%��&X�E enA^��{i� �o��v2�}%"��� atQ���u��5!>��!. Scρoef'�%wiZ!w!'F�tripp+|V!� �&�,�.2#��a�X�s kBr-ore&4+�1u�O!?cF",&V-vF��J3(ed via NEETFMorita,.DClaverie:2004zv} (1ar.�& by E�r'1 T"t).&|t+ �A�M%�"�*in����atMi&-6R6+�YN`pro�|aB&w!�#+S:��DDirac-Hartree-Fock&�$on��Band199��v(�en%$��A�e�:�.�� c(M.^���AL.�*"=�A�j���e�sU�"�U�reM+"6)I�a1�.��k�-+�q-�Q~T*�as Y)8nc�B�us�zr��tu�ic .. G�0�mpl -b�� ih�4!&-NZi�e�*>oA��+��KJ0�+�er��Y!� magnu (m��ye�e���� �&��89m}$ +Y�� e ov�lb�N]�s%��O�^��vA�Fiu�-�"of5qA� v�&�_ B� n_e=.m_e^{�5$}{\sqrt{2}�# "|#��h"fO% %E}P"0(E-\mu)/kT}+1[=2�&�C�:no]�S�~� ��3�aw� ��d�Xg�&�d!� �ba+�MYa�d&46(���D<�'_e$BW��n�)UF!R . ��'_e="p1}{(2�!�$)^3 m_e}!_0_{v_z>0} dp^3)fp (cos(\theta)-q(p).t�kZd^J� (E R.O8 A�� &� H�m7`al ! iMwBN)-am52+)_e&n"J�)JEzN� dE>�UW  Eqs.�#Y$�}-"$*2$a>��e� A�#ic��du vi�Jr�iiz�1* �2K }{4�%$1}{E^{(E_m>��R�%� 5l.@c �0'0an" �%�ro�Fc$�( $n_e� 100 N_Ab!cb!-3p�� $N_A� Avogadro'���3 "3CF �YB��$mu=-.00275�< ($-.0622)�$kT�+k�3$�<). T/Ź�!0V�.*w�]� @ uA�k:� 6� f Re�3"8,E)s>f*�<&�)In<>} eoTj@/�)li�:a-erer2�p!� �>&E&�>�O:��9�S�# ma�iIe� *9  %U9\�%��c��eR !{�R%a�|�7e�� f >� �&� 8 cZ-"�2�Si�de,6o of `&)/=#.�'AR pg�C���VXJL2A--`l just�k^k�X�-B6 W|�j|9I6/,97.�-�oy�"q݂R�`r)":�p_o�XRXr)"�g�Pn�t-�HHn��k�?n�~�!R�7n�~gz/p �neG� ��_~-e�W� ��8.�.�au�����"'ot� a�"� @� dea�2th % iaJ�)S)��}6� ,2�� �er[�j&�}.p�tal"}\o. s $nNav]!���i.�s&y{*w"j=!3��'h�*�.$Ec�}�goi$ � Y#�P!A&����+��'ly pea��oir'\C E}���E.�&� B22T���� ies��/ 4 E�5\ )�q :q Last�!6�$e;"gnn5��Jz� H�P.>�B�o�D!�N�6�wt(f� $E_m$.>�!<sR<  �5�{ i|�sv�"�<4*�& 7{/�]� �a�:+ � *�x ψy-&��_CEP9IEv�GYvIt+(%:K l*}%�� �%�6~'�A�� k��V��W`x� !,4q��reated I�5��� e*X*)V9F��Jt��YEed�)��Rmcus�0�J�Z�)�,i�e� er (��perhapsS enl�'i�v��>[`adiab#� ity'='3d�W�+,�� aard�B�-�� Pe�xi=\etai�E_{m}}{E�.6�� &�?"�5AU-��$N� �V $ Sommerfelťber7�$^�s2� U=��\ Z_1�.� c}{vF� ^Z_1�$Z_2$� �h`p��*y�!�="�a $\xi�a"Y� rati�B�4 _ollzQ 6F !!q ��brd���(*Сli>q %�!�G�ṡ�n._fA*�F)�t�{is�'�QM,.' ��Sunl�� du9f faʖ]-�FꡨI�)`v*influe�f�1W m� �b-sumD�e�`��� aium)#M~A����+$I)(3}{2}kT$. C�h�:2( A;1=A? or���e*�q�L�p�?E�Q�2T 10^3 <\ \xi\ <10^7�.* � 2�5�[��]��s &��/ gma � e^{-A xi}$�?66 �n �m��n�� `!6fo)�U`!�E��!�ut�3����5� E���q��a� ex�%��t is primarQ�a 5A�A:y $repulsive}Qh� N��-Q�b°�O��VMoo � ,^ �2!!� I2ZWor Ptt��1e����(��&�ei!�y�ing� %k9'�af�nounceУ.�/N($�6$, '$)N*��N($e$,$kO�DN�8}"���N � N%>U���Iہ��6M�e ofN�!f��c*~!t6�E …{�Xe�r[e4}7� a��`!j!m%�=�-U!��D%�. At � gl�!, s��,s�A�u�p,^ �\�"�\er.^{&[� �gro�1��&^/�/m2�9(�)<$3,4�S�&�9y2Dm����>� &���.��"Mwic.V*� � !`��& cK��'ne�0ȳͻ�2A�.�6�ly=h��0�LM�t�"4 L!+e�Lp;= \quick�@��u�O2�se%�)��N�%D.���!:�-8�2s0�0u- A�,$^{89}_{39}Y��M�Iit��a�M1=���$7/2^+$ 4� i@$2529.87 ke"n}"�.5.,4owo K,��$[��1=.08 psA��6��� �I� 2����3�. Bu*~)caX_aW.9!��Z��C�&�6 � 1`6��t~��!W�>"$ 2D�5�T6�� \[ � R_{%�}} )�}}yB #�530i -909  = 1621 . \]� 9Ka&n.@�7�� r- g� �for�udu>M�e_02�(!�M4}YAA�a�sma.A�1�/10!���upe��a|o�� van,�; �#��F2K(8o1�2%JA~]8� 1pap�6 �Jw5S!at5�o�))8sE�F�N�.6�W�b�� "T �6� �WQ-in��Ls<$ample)��8Co�!G�y i"!�ro�wn�4 ~�Y =�s��LT"�>� xra"�+b MT[sol�~�[g^ ���s. �ni�:i&� *�&!�wf?�� exis�ҁC ep&A�<A�� i���QH�� �8�yj �"*Bi���;�"Z�El�  iyu8for typical pla�sma temperatures found in mundane laboratories and astrophysical environments (\emph{i.e.} kT$\sim$ 1 to 10 KeV). In Sect.~\ref{rates} we gave expression�8r the reaction , of�O following electromagnetic processes: photo-absorption, inverse internal convers  elasD T4n scattering, �4Coulomb excita�. In.�Ngamma�(argued that �for $(\#, ')$[$(e,e' )$ bd were negligible. We made!  assum� i!4lnucleus was a point particlemXwas completely stripped!^its5s due!�Uplasma =��. Furthermore, we only considered s-wave 9GT since this is usually`?iF�� J�E� be dx mineM�]�9�8as well, though)A�! s ita��i('s momentume� g �ize�|�gnot@p��.>�na�of tht,;is veryif . Aa&ce�would�R�However,Asalready �io! i2�CE}�e J barrie�=4 prohibitive a �2b�AK. Clear��hv�ApR�5ϥR!;valid. 6�`.!a�n in SecB�re �a��;Ngfluenc!� inc��gA��g�e)@>q>pr� ed entir!via�ong1�@*" ang!�2j ]j%�i�YpI�I!| \newpage %\bibliography{refer�s}��the.#}{10} 7ditem{Fowler1980} R.A. Warde�W .rblock��Aiz)>(of long-liv�����icɽsM� stellar !�d�s.[{\em As� L.J.}, 238:266--286, �!ba��72�T& 4.5E5!R�8�ANAOrdero $magnitude J � M��� involv��a"N$ (P.A.), i�׽�L (I.I.C &j^ (I.E.S(��� .�$(C.E.). Rw����un� of���s� com& pair��Dfirst number corre�ds3!�x$kT=1$��,�le�� _, 0!�do���E%X ($��$)�($&�$) �zse� vanishing"�as s (se/scuM!S&�N� ) . �ӡ\9 �.$ F�!� & )� !�!���%&J�or:�aI�e��� 171}|\  22}��$ 1736}$12} 25 2] e^{-10^77 6}� %� sim 0$\\ >�686 46ml0}$k 07018v�5f��eT296T32�30l38�29907v�6}�?J ���39%> 41 T 09�47�3�4f1k-�O  \\ %$5�6 �505�7!xM5225�52�74 �%� {%� !+b�2� �1119�16�1119~16�111n A6IM.�N-69��I4� � 45  9(1mV~�1�y&�m=ee -�9 ![� 7}$�52�1�3M�;�0A�e�.8L39��m3y#D /2=�0Fj� ����卨figure} \epsfig{file=fig1.eps,width=12cm}$p $XFeynman diagrams represng�.B�""!+�p(. Plot (a)Qs��-&/. (b2#j��$5the:,  �b�!,. (c) shows�6c$_ REbe��continuuM(dUion�� N' i!ano�&�e6J�= F� ly, (f) �:�1�z!�}}I x �,�maB D. full stop % ? qu�(onU: /��ward slA3 % \ back ,^ circumflexE�dABCDEFGHIJKLMNOPQRSTUVWXYZEdabcdefghijklmnopqrstuvwxyz$1234567890K�  % \�0,class[12pt]{�� } \u�ckagems,�# icx,bm} �0command{\beq}2v)}�"$e$e.):" beqaGnarray>%e % HV#,vlk}{V_{{\rmY }\,k>GljLambda>�$fx}{{\bf x>5$Mstar}{M^*:4. j}{j>8siup}{\psi_{\up�w>Upsidag(^\daggerv0ownW jY ,[R4 xvec^�4kf}{k_{\script  tyle!gF>�gB,sM rm gMneYGamintGa�._%�:Elgalnab}{\stackrel{\leftright �{\nabla>9 6�#,+�q(} \title{D@- ty F8al�(ory: Method{Problems9� {R JA)nstahldd {D� t� o� , Z Ohio�te Uni�ty, Cwb+! OH\ \ 432?'ead{fu f$.1@osu.edup�ab�ct}`.x of d �a!/or/&d! is d< ed, highl!zG the�����uk1 eff�%ve �on�roach   fiel�0��outli�vfuD0 challenges.  a� \pacs{24.10.Cn; 71.15.Mb; 21.60.-n; 31(-p} %\make%� \�&{"�$ ion}x/N/ -iU$ between @ -c�0st�&mean-� ap �$oFI, such�Skyrme H \�`RINGSCHUCK,BENDER2003}, h Kohn-Shamj�(DFT)� �is wid*Eed to'$ many-bodyE� �,DREIZLER90},Y$frequently�0ed. To go beyA{0 surf4comparisons, h&-HeR |�]�m( about�yAaDFT mmsNU )po!�ial�or M7 one wil�$front�,trdt�+necz-wo. Fo^),1 mV�*iz� \ S,!e9��ore�.n a].� ? W� !!�rox 1?�,w�cly�-r�+i?sFIS--�malism? � What�/you�Z a�Q�? �#�3�1s? E?)�� le-0 i4prz!oHo�es �!� work� DFT? Are�H er-o`��3�q importantBU! deal� Hbroken symmetries (5% V&ro,U\ldots)SCa)5%�quant�5va5to%�free NN��ea io)�ak$-ADhir�.��2� (EFT�/o�%�0��(!F�A`Am�  I�talk, w"�a]}�����c(� DFT syste c=5$, by build!�a frame%�_m�01 s.�R ideaA�toLM��0s��osi�,8ore�develop ��pFUKUDA����OyQj s �O � rougr \�^�$�h)�K Legenda�ransfor!�%)� *� �,VALIEV,PUG02�5ha,� �� �i9a hierF%�(eLu�;�1 �6�6vided,&�5V. expa�5��usaMower cou�g!}�. �7a�"� to i�3 at e�uig)p4HAMMER00}. Ult�re�we seekUB~gy*&� �a�na al ``��3 ologAa'')ac�Tbut model independent,)�err�l6@!�"B! mi5. copic EFT[ . ��E5MAE�(tto8-Ba[Y]DFT��"G8usHf$ �aA� e de AT�&�2D9&j3n��cݵ of atomic)}i. .�( 1��"�%4s�2��1 W$u� al}��6!� gdure fu; �s a non-�ng��)��same �A �y�:6i�*� ��is lea�� B-5$E_v$� �`.� �}A�a loG&l $v)�(KS}(\bfx)$,1�[-\bmk ^2/2m + >/h]\phi_i = {\varepsilon_i} \ \Long&� \)�q@ = \sum_{i=1}^N | 8 |^2�]A aeq:ks": MY4"a8d :� �3c;!/I�$!Wi>kv/ plic7 of s�!Eq.~(O&.y) �g larg(nite �7 appaT whil�<e�5��iA8win i�X �"so  *Ն� F�&� AS)�Uh� A$ (LDA). Wely&<a5rmodyna������h9DFT2�a��(!� M�NEGELE} � U�m�u&���B,�}.Vbas�elan!-� � �#�� �O ${\A�Z}$���(f%�)q���esA hes�6ex�2s�i>upl�variousd � o9t /t (T-�).!o%W������s�� Tby � 6�s�P�#�  �)4se��be�$ a �%�al sens?> figuN��nw7��>�Ate. * �22 ��?or�w� �# 6U $J(x)$ c9[yQl $\� �. x) \O:v p (x)R��U 1l�� Q"[J���W�W[J]} ��Tr\,}  !\beta (�H + J\,�) }QG�� oD}[��]2] 4,e^{-5 [ L} cps: ] �������5w&#� ��at�=teg� �A��on� Lg ngiauAL� �m�. (Note:aWMia3�Aw�+;� e.�: $%>�B!�ve $V$�a��&�!�� el.)�(�.`�-6 >���e�.2#rH\@|whoX��� } =0\ .E� �� ic-�8 $, $.i� prou9C!y� B . $! We stA�ner wayC�7y�!�M� ion;e w�Pthe8*er#� mbda W_12^2 W_2 c_%�A��( I�F[J_0M�^J_1>^2 J_2 P 1 k\ f=�Fk p F } &N� �+ �2I�Eta % tre&Fi�� ���,�match by in $-��C Zerot&� noni5B &� a�.� J_0��u� �1s= -%�_0�d^4f :m�!,e�>� rh��>�A7_0� U�{\ � � �E:z�� !� Beca�1>ppear�ly� 0)2, i9D�B � � ly}��3Za accor ".� d}) wHIK"�� )yu�]!�� onal�D$1$!�i)=!�R"n aq 2�*� ); �sum�#$2> $'s. "�%wb d A� �.� �comple a:� cy loopYMf�/{J_0} ��arrow�2Mu6J_1a86822 8:e�;6 ��=A[ ->0} J_i *.y u{i}�m��M�}E�Y��bRH:!I� % ��t eve��m J��Y5u ach look�DCL�$#"� � ͣ iIemph{`K}�[A�trunc� A92e�)abs0��. F�,A&u# 6R "3 webg�I�RPA�:0� al2ED � � of�!@?Ue"f<�Qվph�#zN$ �ef�Hby� 1* 16�% M!�4a dilute Fermi2�short-� ���� 6pa�a�( a)�m� W E�: $ a�s.N space"Ww  k} | V eft '}� A�= C_0��,frac12 C_2 ( (}^2 +4^2C �_ C'_2 ew k'O  e�a 2qc62KL��$�+ M t���!T(��,$3+$ bodies)�z�� �&=&m� 2�  \Bigl[i�{\� al}  ti�.+�4nab^{\,2}}{2M}Jrj 2Q  - 4C_0}{2}(� ")�e$C_2}{16}\b� 9=)>!�z 6!$!\!{}^2E+�  he7zJ�r]% \no�3\\[5pt�7\null +�)YC_2'}{8 �\! � �\d�"I==>��$1TD!T6 \Jpsi)^3 +��s 2� ��lag��a D& O&�L(O-!P= $C_{2i� �\text�" 4\pi}.4M } R^{2i+1}\,^DL `�[Z4} $, �-$R� ����� }>+= GP�+(e.g.,,0$\kf R \ll 1$"�Z�ll��t�n�yg.��"2%(�� �^fJt:��6 1h�v]G r!$� �  -� agatorE�o�m �^)er�\�]�phics[� =0.0L0,3.2in]{fig_c���ons<�\ \raise.41in}{$:�$}\A�~h2.5hdyson2A�nd�)5 � �,�*��$Sigma^\ast��x},�� x}';�P)$.9��Bin*}�&<+)n} * U)Mtwoqk� ecis�cancel c#  V alog�� #i-a�anomal� �3&i toE�, Lutn >Qnd Ward�"6E �T�2� )3��Green's"K  $G� %jp,"k J1Cks}$ by� !�am u}}� $ $\xi(x,x'2} $��G^��("4FURNSTAHL04b}:�!�g.�T�!R  Z�xi�e^{X,$ '� \! Du t 6 �& \,+\,�(x�]�7 J�, {+\��G'\,"�2 ? ')}]��&T%� Brf}Ys�a5�al� A=$W) *�!z$�ic�1� $J$,-�n turn&fa � f.Jfa� $. S~X1$E��TaoR as_c)2Y M p�.3Tyt�< else,�Fe��Ee� A>�  int}8_.v- %�$.i�;WN�r�,�an)�eC&��~&Q:Z� GiF�left.  Wy \xi"�J �eJ5 �R:!�=� �+� l[-S 2� a9_kQq�"� �b:�4{r]N�J�"�ed�b�$�% as-yq�r�-s}B>*[F93,  �hG�&� � %��fxa�)���� � �D�xe��0F�(�!ak��tb2)ESlI�G[e# i�ng�� =:1RM14!) qi @�C \no�$nt�N9obser�$s *o*/&jC.f!� �3�# " ly d7 �]ty+" $e�&ing6/)�)B\o s@Ou"�HA6V��*AfYV,q(� %�ki�B�1� �J�TilER \& "�<gerO:��3$ ��he� �u`�f�/� trapn#meta-GGA7�Co_!i�, L'��$an ingredi�- w ��S%= H-s#�4:3az*� Berm�%�IByD&]-�E��a "�E��C � *��F� ,� Z. (SHF)�rho@�)eaAEa�D"& ($N=Z$�&�(\cuG&�.}*�E�SHF�ytau� J}]�R�Zd^�%��zgl\{ {1\�1 2M}<�3 8} t_0�/I+,163 {2+XH} 6#4(3 t_1 + 5 t_2<& d&��\�&� � � �a�64} (9R- 5Q(]�� )^2 �- �4}K2�@ .�32}(t_1-` !^2).r\~5&� a ($ # a spin-NQ}z,E�alU_s nowH&�# mass $M^*� $�H�t�B_og� y$A�DFT/E�#ad�+a*#  $\eta4  x})\,=<263E� J�t[;�a��y� �� ..il[7A�_t"i]M*� -v(�6)+� !.�(e�%� _{0} %P!�biggr]�\ �9�  b5 es [�*A) �4� - �$]�q �@o l[ -I.�}^2���.l)1�?r]� _�2!�e{) � 7>\A= � .5{ �1}{09�{x}})}}6<� R�� bi��AlUH.�� $1/2�A�1~ 1/2Ma�6$, ��in�eF�2� . %�&")7E � �$&M6��W�Dof�� al�4���A% focug����-�f- z U$i5E�*v�Jb=:3!�����v� ����!2{Ay��X"=u!�� -� %�� de�[ cy $\nu=2��?LDA�&� P�2�6� -�E��� � +e��Cw8��$1�e�35b( {6\pi�X\nu�)^{2/3}�^{8/3J$$ A3! e�qRq=�%�a4%_i'[ )<}��W!AI�B@,��.E� �=B���x!Lrho5��34.  5%+T2'!BV1�V-��� �H&�Erhotau�k' �$.�-=nu=4$ �)~�0� m�A�o ��: $C_� &<"t_i�$(8:e�A�� a&,��shpg�4p�.{-[o4mF.)"�=�,e}[t] \,�b� 2.8i*��4_plot_�Y$breakup240M� "  A>�M�i140�v"} "�JCon& 9� !�P��$wrjd f)F�.} M fig:���e+-M���oE�r�U<:� "�5�9� all �4]q�"Z,AX�0��l? Figpl:� [!``\''�' 1� ��2�q%)]�1�D?/%*KE&�d:Z2�# AgA�i1;q12�5�&�7!X zindH^z``naturar7"c*�a b�> 1/2 j2 P �Dle �!?(actual valu�"�@*BaKS�" accur���16�2e�8ntNy % Mg[b6�� ;  ="�Sccc}{,{$a_p = a_s$EV $E/AS\sqrt{�r^2#�.k]c E<87.6�W 2.87�* !�*&%X %�V.2! �2���8.33 �X10f�8.3�W 3.09�Q\�^�e�1L�>&@1.3%1���3.7.WJCDis���T`Z^�R1�?A�%y� �d.�s�GXp�/�0v!3;~��a�@�ndQ�)�*H �sq��i�EnI���6^^"�c�to�)�IE.�re� y"�nTh�Cw-Aw�9 pris�v^p�c� bulk.�yv�n�;W:C��!tob�b'u� P �q �o<&� is sup �Mt ��. *8@!�>s spectrum?�n:��snity Rh���a�g as s�Cin 6 h�r}(a), i Rduc�7ignifica�B.^)�b(sH�2� z>�tve\�sC=; "�ons1[t F�ref�(wRO8&gA)+a�Fv�b"�C�be�Kt&tqukjlly A�E�\"�)d�a�.{Z&�va"�9\kW rho}� :�0 &!d�b�. {c%(nu}[(\nu-1)�4$^2 r_s + 2+p^3�Z� k_{F&-2�(�- # Ev&�+!�M�AY�A�� /*1)ar{ t. H*�D.�&�NA,n7a %r�Bf�-� BJ9G}).F.� . JX� 6i* "H?Mass240��,0�"�1� �/f452�ukum240b�0b/a) ��%�b \2�1��X&Eee�&N:"�!:' :X�H�22Anc(o�D.]ofQ\���$�Ci��pairi:z�$&eBnkg��_-of��DFT�Gdo so�in�m�#>�: $jBG9~q ,�� E� $U(1)$ ph8$qEy�rociC with�,^� ��#� z �#/PM"#�<=AP #G*�"���#�J2NF# �(x)t�MtdagQM�psi up) ��e&� E�!t de�&ieJ" rho,�>$�ixdnd�.Y4.�)w.# �&J, �$:i 9-U�&h&a��� psi ���8 K!tef:�78�j"�6,|_{ A�%���^!U�$h$F� "O� !a (x)+� u$ 9R��� �(x����aC��~c$bphi]${~s y�7 gain:�F�e�:0&i�V# �=��ie&,%�-� ."� "��&&��/ i(6!9theH4-c9J�>A?' �%�Y�,:sv�� phi��,NZLfxK*�Ao�C+ (O-�@�%)!��ionarity"�:)=��$B��ip ;\ |�Rho=�_%Qe�=�|# �4���aY��� 0J9 �yH6�EO,�?n�Hto�� ing!�� +�8E�;�y�M�8-by L9~ � an�3"�-. >9!�&� �&a �65UG airj*�UTyield� e.S8}���FQhi�A��=&� ��!6e�%�(A3&U{�h_0�a�mu_�i�_\�B& -G+ Gtend r M�) f�E�u_i� \\ vfP= E_i�WBWE� %518u_i,v_i$ satisfe�&Y0orthonLl�E<,� ^ RR�Q�-� !� ��$�*�?2MA5�!�8&� "� ��9 8\�kM.�Hs/�D-Bogoliubov (HFB)!RŠ2�'uIa�tiameJ� a�a� �&� 0%,Nambu-Gorkova�rixB�'sZ}�elf&.SckRceIp*&7&Wor RMF���V�%P�qZ� fm�yy�}%$ ��c��1Ρw2\\Hi\, |Y�|^2a("� @� !L(baӄ unreMX zed)�.4y?�XI�+<b ~[aa�#xvec)}` +�v_%�"=�&�}��� chem�&�; $�D fixe� $a20 A$%Mn� m-.� = -E$ �mY6}* y+Br|!4�E%?`X"�;��FYBint|6�)^}E����e%8 >M# 7a=j_���ph��E��bV�Fe �1�%��.�diverg�A�"mY�� �  A)aBŰdK>(a��o~>|5} i1��*a�;era��)5� �C $j^2�4+Cun�limit�( �}uX�2+<�� 'ubD,S&� �hi int^{k_c}�8�$d^3k}{(2\pc8 } \, j_0 %J��  7�"n("I# k^0-e;(+F^�3 7��<~#k^*pI�a� &�Zk_c at?\infty}{:^E}M��JQ � 8 j�*d!�ae*d�yr&j>�5 Thomas-)=),"� \fl!&!�M��^{E_c}^�% j_q5-M k_c J}{!�^2��B�&!��& E_c!�%�k_c^2>�}i~�N�I-�e�� &��8acHsHlow�)��� gy cutoffNcE� increased�9�  p�C[Lp1\e7�:e\eb!. Bulgace�Yu�)how&!�3@&R ]�Q  g�+!Pmprov�> �i�BULGAC�,)Gm, eG� $!�($ instead t}U.�!t�H6E)��Bq?�!P�1}Fi{A1a=y � "A^�F` "HQm�[f�b.1���Y%�A3��� : z� �2�:1in]{]�_plot}�]"�0M:ha�~6�BF��P.: . A"�W� bb<v�g�� rol�5�&eR�Y� he weak-�MAO����gapA�$<*�Agas�'� pi>vs *�& C��fifty pOeb L�.���T0�,*�X��erfeca3sui�to- lU�ram4�Lr�\m�,)T��nsUt ta�a�� .��T�&C h!hَ!�"�VP�Ie� C"_}�� Rmanp � )&G_ fa���-���9E��� HPwe4  a!abR l laundry�sof we belie6r i7t �_�6�Z�} �IJ0_ld�"d�#�-�5.]> fTa: s_no$ ؅�%"� ��j A�"�:�`_�Q -on-�w);leI}e*�EB�*�4epr�a)a�?s oM16�3p bothAN%m=� Dev\!�g]XentN!� xnXM5Fa_�Sh"3 5��Co�3DFT�N to revisi�&�ma�C�nu�Wm��_%XF� techni!]� �-KGBs,�m' be adapQafw!�VXr�!A�b$bL%-�kr�FI� �he f|, F�A�y}RestoAX BT_.A�In5P3 c� ,l;�`n"�  (�Gar: �H)�H`a�&an�_a�Cd �_a~ vari�>%*�q�N, sUeyi�Îb stud]�!\$<s�!-��>U��Dvioe6in HFB. �!NB�"._�4t "c�?�+Ah� sid``a] s,''M� H<al!�� aI4a Fadeev-PopovÆp�Wa�Ja progZfkk!�� !d&I&a|�u insicQ�,k one-.��toD�]afXt�e�z��bۗy� B�}�auxiliarÌeld*�PyEUA6%s%�g/��YXal mesonIa�m�\��^ alytic E�s)k&�"� �'~&rony a0-suc�8�A;� often at�)�(�faHi at H*�? I�kct� =�g���h�H��;  ���s (�thofp�F� �d ---"�&�,is�!�'I9DET6Aai,;� �H �_)Eun��`oryAyegs�c�A�n�al} NNM�1 ����gh(an2�6x&s%J&�" �N ȡF choi ��k��U)� If� �pt�Zu:�hd��_ n ru\X�P �!j end upQ;sACrLe�mediumH`Hf�u�|s(�tl�F�H�$;Qaegi� ap *\� �sA� m0Hum�$ s�E!�� trakRRap�a���a%��Aurb�: �)tI( (at� �S����n��)� 2Si�Z &- 4�� low-5�.�)  ��rt� SCHWENK)fˈ�a��A��3�E�'������t.'# N!m� �o�� \ack Is t���Wckn2�dge m�l"[s=�"�{99�bib%* }R!�P�,Schuck P 200�! {\it�N��Many-B�G} (Ne�� : Sp$er-Verlag)aiu*�p B�!r=lo@3 % P.~H.\ Heenen)F$P.-G.\ Reic�d, �r� Mod. s.}75} 121�* :0F�s book- *RC,Dreizler R M%Gl� E K U 1992ba} (Be=69 2F�lF�],<l (1994))l��!ror6�9� 833�6 �Vjl}Va7 �FIndo G W[7%;;t . Lett. A-90227} 265 %Ou��per&e�PU�l I� S J, 2) A �2003 Q:itE-6� A723} 145%�:WJ8WzHjl ip H-W%�F�t R J (A���A�:z 678} 277=8&N$ Negele J ZOr՗ H!788-�Q� umI�P���5Sy� .8Addison-Wesley)aC �-�*t-b}>H��6� 20051T.�B�Yp�,F ��\~}P(-th/0408014���JY74E98�R�5}6�M�iw a16!�>UB�A% Yu Y! WXit- �E�M�8�<042504+YKёB�� S K^� K >@ &�wn��F�&F�4 % sqm04.tex %��cee|s��S�ggeA�rk Ma"�!04, Cape Town �� c. 2.� Y�a�>�{ 0pt]�{rt}:|* |��6|bmWw AQJh�(macro \def\ 0#1#2#3#4#5{#1I�#2} #3�#4} #5�ef\q 4.}8 [$CPC{Comput�5 Commun�:H JP{J  2EPJ{Eu�� J(HIP{Heavy I��ǖ 2NP{.= yPL{$M� R A�*:/T0p.�O\n*"{ro}{R�ou�6s-i@<.=xo}{xb=xsN=ptt}{p >T>Zmt}{mZ�}{\,=\,>6sig }s�V_1_.�gap,{&B2-.2exdW"� >}{_i}$}}\,%=,l�Bv{� P%�U, ^�|.�| 43212�%ya"�{I�ew; ��<nd�ř�� �vl fluid V� i(scribF hadron emv�&34�5Au+Au�`il%�] 2C�BColli�(A ).ɂ���2�&In�3l}�d6d ��2X 6-8 month�"tn,~�"Sgo!^o%@ 2]h�u-1c!3;)4 c���+wheth��ne��%^��~ov�:$7rk-gluon�� (QGP)� sett�A-ifaa,ctim.�!���t�ve Qzeh�a�;jofx0aiU��ePsur��A!� n\-ti\-tav0cl?<<�ehot��ND�#�yWhiteP� s,w �Hk|a}orist�em�g�zE�QGP9�mZw8y �$teN %5^���:2001xi�y!fexper�_tab���B caut:q�1irt6essY!"�-�G � �"�vs2�~at �A�>�EGr\-ma\-�gdL�at un!�e�xed=�!�ity� ACco E�is&��9I ����d�}p�!�!m<�d��� �8�[*u­5ellFc f E�ts ``e&�'', i.e. � �Q�ni���m�O)� Kolb!�3dzb:6�Z&id�v�A]k"qB����I� (EOS� xpan% ����pE�n7ife[� emit%���-. J�^� �"�$i� s�n�rk- @>#AlQCDm! a ``�'' reg���DEOS�in��abiT0��� V?ne� �A6�l�"�$MMise�?to&ve � bvW�A\%�%2&�!"�}.�"�'.~�5e�Cs O@�6I*JD $v_2���GTw� on-monoto� FS���gU KSH0_�i��a�duź!�F��? �v\ fire!a#���(ru0*� stagrra �#%2w���%�in� F)�$'qua�g��c0ns1�A�%fc��t data�0 �@��bWet�� &�nf":�(5i���E�s,&jP��an- ec-� {uri!Z decYu���W"\N�X��uuW�;!rA�Y�y [��are26b� i*�P)/+�vw�D%far�y���� g��w��: m�.�"�aha gA�~ , raI�Ihop���3n�5��YgA"K-8fula�� Qf ���optimism��haduY�W~ isto?rf�er� J/ s re2�s n�Y $�$ell enough����ctba �B: liM�ʱst��-H y���s. WhPAey�k  oy(r awayi�lS|� ma�V ilib��uAa2p�xE�Ejm0�K�"v�{a{yety�#��e&U�( mechanisms�� �Cly poo=(g ��s�A��Z �$�1(F�Diculte8 uncertain. O�lur]yevZIE *^Y������}��2� "2#N��7!�td�)�a�2�P,IrO� nK i2;�Ae, 2Uc�Lol! possibU�Ƹ!���U%s��shear���F visc>�y, ��+' �W!Ji ]$" :]/ofI�Uu Fg�!.]s}��-\ �'�$v� ep'K�%� :i�("�w��to �@*0Z Mu��a�.k(in �  phe}FR�+Asbr� life� m�y� �" �%�,Mk5. Yi*��;A�!ly*�. Also,a$bsiP�/%�} <e � a (je� ��� �su4jůly y��&�$ g!��togE܁A�!%b%> escat*�� aZ�d& �� � �.( $p_\perp$.�iw��>� inkE& fail of .h� %�=��'��6q�( our favor:m iV6�!�ea��o ���n-�HU(���)mid-rapi�@�� ow �p81.5-2$\,GeV/$c$M�.4 ��!F�y�� D+jN[D! ]�*r imp@"&&$��i�-A��EI I �j!leˮso[���A"�� �< �?J�}�-2��39:�$Q deca�pA|� ��}�, en>�  ;� �hI��%eD��&6b� m�� qu� 2�L@l� � rT)aA�m1� A�*l��rE�talk I�l�uJ-5�, .� ��6�52\.���T l.���� %� � �!>!I%�"��*5!�k'utA$i�� ly �% ����1#")$�b�o al 2@ s e,�5a�m,��;N2� �F'sA�t�*A�n�pl��*gC!sn#-�pro�ae��  de� y $e�z,�<yo� �E$�o!� 4-veloc� $u^\mp_`maP�%��  $p(e,n�klo !lse^'� s. S� devi@�"%w3!� ." �#n�%c�&�� 66J�]ۇ&a� �"�# (o�eba%cuD�.� �&1" ab�5]mr p�!�ran�*�s��\y� ��M:�.�e왐x�d��$eHn$eW)�$��s�)�!�.�.�"4� m�b�~placeg>6� ��.� A�veE�"M( D)�[!%co�{AΡ �umI� . N8 �A'��ɮ��)����yBe��%i��e�i pene��e each���n�]�}ome!Zxf�IH i~-��Aaof$m,)rit�%lso in�17���Bԙ�O�a�I� _= s��!8.^& among a�< itu��� r� !�ip.t !rwn��2$ ��r� �.s�l9�n}N��R�,hAV�c�t_a� pre2 � um9m�;�9!�W�r% )���F&�} (\�,eeze-out cri��umͲv�e��a)$2� d��� � nsem!�of��-sp8m�C:%����RBN�-2m >��d olveS*� msq�tu���-ata. AN�Z�9om�q� angra}~yŐ�.b2WB �*u�2 �Y�� �.j�t�' ged c.���"�BAw!i%��7�E r�})�Z � �#�Td < �(} ($b\eq0$)�h�lli�-v�ctrAom>3i�! fea|/��)�"��? �C8{!�t�a2,�.�S TZ{e�t�p�/-�*/Aa!:4 )�HKHRV0Z�130\,$A %l20.AJ<�E����w�su�VU.Q �V �7ewYZ.r )��:� \~� F1} >?�f�7�(�� lute����E�UA- �I5� and,n�� �U 1 ��# �IHR[ht[S {minik� }[t]{62mm�IVz:�n1a.epH*�IA "~:3Ff`B_@bb=20 32 513 405,�:p,he�8=44.8m ~bV~cap!��[7�!�$ (Color on�_) NegQ!� , ka�9�i($\Omega$5�� qNh \s}\eqE�M�,|"mD he fXA����TPHENIX03�200,STAR% PHOBOSBRAHM 0Z�}��curvesE�2 al c.�1iuKR03,.���� � h<�xt|$AMU�� 2� %��a�ampx�w.2�o!�a5^�%��7>�.�=s ;��"��-89}�Za�n:zl,�$ (blue) ba� "�9U � up� dk3afh �,��$T�$crAL165$\,Me�e�Cz up�_ (redzy.katMdecN00 NI ef � ��[c�!\O43��)"4edu-��.�c 9"<��a�� of��#6  (!�d��N .�) �.� �;output%�qT G t�}�9-10\,fm[à &���u��HIB->A����3rt-�c � �X_W7-8t6BM)e.��ure�΅�Axs cz� at�O5A t-?.�6se yet�s!�e� ?�$o�re� E��$\ݧp� �# y;,seHv-=�$@>&� &K �l��"�:adial* �,rV adt  (ve ``push''� � �yo��(quasi)e� ic 2< *� fai�l Bli&wic&s"c�� �b}�-m�ag$I� %� �4� thus:$y��o�Y�DA�/6�u��6.sh�+mh�W � �J tra �"x� )ze�vSwe��e2� �I is d��aU�spa*( anisotropy��� zY%in^b �ingL�o�.�" :��a��������htoo.�>. &��!s@ �!��c�� of6�},~) dis8gar1�);I& H �7IWy�)!EA�_�<m��exclus_�C�t%�AoS7b� ��� 2} �������.m .��v5',��le�6E\Q .a�E�!� �&�W!�($>99\%$"�#�_kf�#.�G 2�G VG 70 :F *� (0 0 567 470� -� 50� 2Vb %&d -5dR� . N�461 198 568 594 �62�47.35�b.N� >k A":k DYz�:v2BA�(�)�ns�� i'if^C���� n m19iasB� at' (�F�Adlera&1nb})�6 (�G -Sorensen03kp})<mz9df� n"� %&P`%� 2�0 f0 B<'�`C�acs�]��'6�!�$:~��nic�" A� �����2*�RF () P���m\-pel)%>�'1�j���*G ��&!�A beha� �'�C ��6 ``��ing''�x� s�Ex$M�$��q�K�inct ��``� num\-��nVq���am�02-4�� IH>�b W6 is �;.�� �-coalesc%G"��qmR� �g�Qdo���(� : 5 #K �`_\%W -)MA6&$ �&�� �� #EOS�a')�d i�pan٣6b��s �M.�, gwi�?t%Nb%��* H)���)�*A����)>9Q). Al]gh nei�1f�A#� ��tzata͟ul� )lQ�?� �~ C?i!%�aB�.�^�-z.�s.L��6� B60*oe��<f> E�!X (�/��� )"� c*w,%�.�&�P��>A"i� �!e'o!�Q�"� �e��,�m�O2 >(2.n ��i7tG'��0n� s (slI("b�C)�~��u>!�fi�"K/2rs,T03imޭ�~ �st� �Cg�oo%��.��mea�ee~-"�����(!g� 8x" 's v�%) g�4to �J,E$"j! DJPl�W����w �(ZGK99,Molna0ux�ee�w\,�3}a�t1#ea�F� it�s�1re slow!!�Bn�p6x,�As-ant� k SJX]���!%�pra��pf�F2Xa1 ar ri�Gs &ڈ��� k �5�2��I i�VvU�� the��RP 3�� *j 8* j f�7� %R) z� 2! 3� ��"�Q*ZQcY F5@� �2� ��� 0 -43r� $61mm,clip=�3RL\\[-6mm2s:T3}BTLeft: E2� � ��on casc�Z�> ared�p�>A�,��&�� on�Do.�� ��[� s. Lw 6wd�+�er:� s. Rh: Per"NE �a=*��:6��ٞ �?U�9 �scu)�)..��( �( ��O� �gr��y�iK��-ly}4yV` a��P)2=0:.: TeaneyQ%�P�I�R��u r�J�# l2�-29#d*�s"�!+ *XX �R�'� ��6��,E!������e@#  re92)��?�YFT��"F !]s E& �Mb). F�E $BW3}b-@!����at�M =&bxh�)ten�$۶th��\\��_sq�au+` 4}{3T>q �A}{���h\�" � :�, $T$�tem�����$s en�%)�n�b�&4 �+ 0.1� is pu��#nQ`��a��"bR�0_. �/s & ring!�it2q!�!8r��I�je��d �� i�heI��h+%/s\eq��/(4�_�*so5 �1U]Ee gluon ��.M&3� V* �rgu�8�eO�u}&.Q&t:f,"{!$-�RtU�'%��nV�I&-��e�!$ . AtDyd ��c�!�p�6��v_�V�4~n %a��1��'sE�/.awA�� 2}a*�9.�T�N�:d�'�"o"� `1J�&�ou�tA�}'s-� !L6� m�� ably)ir98�reb�7ac  s2jv%�rB&  D$��H3y�|v�L usza��r!N�a�)?�Nfac Qothe{5�-� �p)��( drop�32� .Bla asympto�w"� � `P!<be 7�� �Y^��Z$c��`wh�=r ,HL � E)-! asis ``val_e� Z a�Ter00(i/"�.U��=a�MaMo] ]o�i�"d� M�#\6�di]"��X (2�s $n$, �_WNmst5�/D�A-ac4i@BXM�"�!Z� icS$� p�4 �j�)do)��: !�^{�I}"d �w�� {v}_ "had}}{n~� eft( � D"\_��.Y�@5��75>,�*� �� ���-�>�,A�%�& ]"5]} (|�x��p"p�5fof�%ity!). HA�bV6nggrto��o�2k6&� F�j)u`:  �&(y���!��;� . Be�&�8 \sim5`B�6k��ic6��LA�6M� �M��F��z .%�m9�i�Bo���r*:,A�.�xq��?� car.$����v��c �!����re��D ma�>s�*_�>VuKs!iso�s2 x\,}5Z`�at!��WQ������92:� P $"�7t)� ���c,f N� #si\�&a �>'76�+codS�>� also fail�S*p6m:nt j%p�6Ab*(inqSE�4&�:f�#e�R!@�"��k 4}a)F 5�m�u�Q� a� ward 5]��Hirano� 1eu}�~$.� ;"��&8? beam �M��#c .)( e?e#LstI�w$AGS%% SPS X�"�  ��+wAu2P � nd �g r.!AFLH�)IOs� b�niaNlyC$\)ks}$~l4�l:���kF&bb~j�4j�5b]{�}^�-60549� 1� 44.4�4b1&J:T&>?� =1\B2= 68&�4m�*4b�2.3J6>�>�4^�Sca_GFG/�i$*ΐ$ de�Ɋ'�!ecc� .) vs.E��H.2>.H1 �v ��M*b�lapT% a $Sg0NA49v2PRC}. R�6�i�� 2�> &$�_����u�{;�>r�,  �/hvd 2����mid���C��av}. SeX*TmI!.�8�8SB�. ��o6�``hybridx&.<+by�"�e�� (��b)���"��%�2e�4h7� ���8 P Q2;  p IC�,:  -c� �*}m,1� RQMD�*))��(ingd�) wM��"�6=$�1,"�37 � v7*�'6!"?3�w��:yA�E*),��LH8 %(�yXG�^���;>2 7 nt�(�3 % 0.8�$fm$^3M $=�foL X[�aE8/*/- �v �>` t("p��s�bel����=.�a�top� ɦA�d&?�=}�42t�Y(s�F . Ob�s����o�;u<er�!�Bu=$ $b{\,\sim� $+�\0*d� � p6�h!�i,2+!o���� uild.G*6�]`u�,�� �aJa)�a/f�he.]D�s;=� 2�.  c 5J&� U a �Ys � �,��!n.�T�Q_s� !�oZt-�U�%�>N�� ��t�@&�(  )e7A� ) "on�(ga��ase. A&*ic� 8ssure gradients�C thus still exist in the hadronic phase, and hydrodynamics reacts to0(m according U ffness of# S�C resonance gas EOS ($p\approx0.15e$). Teaney's calculations \cite{T\:2001av} show that RQMD 2� se remain�� anisotropies much more weakly, buil��very little if anny additional elliptic flow duri�B6. T 2�@, as modelled in ��, is a highly viscous medium, unable to�Hh or maintain local!drm�4quilibrium andef� not behav!`as an ideal fluid at all �failure5�y9� �A*@peripheral collis!�G RHIC}in cent"�R1 at� SPS%$AGS is the � {\em�X} necessarily caused by= abseAUo!� � �QGPI� =�(early expan� stageA t raz by�>�latQ�ic 6 which!�9�0efficiently E�qY�spati!}irebaa�c%+picity. Similar arguments hold!,,forward rapiA�e%B%s i"Heinza!4et} w!I%%inis0energy densit@Dre also significa�smallera_n{mid vy�l6W � �]s �. a larg1G�E�4sity spoils onU{clearest!�eri! al�atures!ޅ�Qa�quark-��Mtr!�a�,#L predicted non-monot�� beam9( pendZ$v_2$ )iKSH00}. �.Ld�' limit� 7(scales with�speedA�d sound $c_s^2\eq\frac{\par%�p} e}$. A)% pass!romQ �2o throug rp��= into; QGP, �$ var!�Xabout ��a�!Z f��to $ �1}{3}$)Tgo�q�Ha minimum near zero�W soft�$ region. I��-Zs map� is �� our direcavo�)ta)*change3e:  i y�Lincreas �e��M . -x$comes down%$ infa^e.9, �iu��]q(to first dete (du��1 eŸ�@�+� >�-*)�@the(cover somew� ;�v rate��stiff.�W�=�B�t!ur ay, lea�6to�Rappar��mN���of-efalling .n`(Fig.~\ref{F4}). However,s8ent PHENIX data%| Au+Au ك��X$\sqrt{s}\eq62\,A$\,GeVm� D(62v2} indic��E ��may�{ be quiteAN� as sugges�B by 2�a%Ly�essena���onstant 2K !�e )reMt rA���loredݥ�(e�62!y8200 $A$ GeV), �A�onl��enm�fur��E�to2v�ies. Wh��) iA�es%confir�k*aֹL�rise}!� e� , it%Oo Dbe a strongly dilu!Creflec��9%�V 6�struc�Q�6Mexcit: funT . Obvious� ma� nd m Dsystematic hybrid 2{ m�,type pionee!�by� MWT6� �Wn�y!mex%� to e�extA�0we can eventu-Lov�^2�a QCDi� �� u%�6a! . W a9ly poin!g����HK04} a� 0nice possibil�to �d>� to��� right,!�ord.o](a�� � er:y*���measu!WE0a��se� s o� �g.}$ curve. By����d� med uran nuclei� a?,-4yZ��(Degree Calof ters!seA�iGfull a�lap l> � i n)�itazZkn�"binary���?pon!���produced��rged ��(cle multipl A8 �e�gurE�Rdiffe�}5h� 6�  by cut�on2b,{ E�A�? �!���6�a 60\% alo \orizontal axis. In fact,��low� value% "DS} LdN_{\rm ch}}{dy}$ ob�  %<is way��for U+U=�1^side-on- 2:, � re-�� 5C�.�as"� BzC ��a� � =�y�P 25\%� $ opposite . i]hedj�nos�6� &� 6dachesu but �r� %�m�thai� � st-� plot�cin 6$ . %� \s�){Conclue�}�c6c� exc�ntU$џ� aspect���le-u�C "ra��: semi��%IQ&�M�^clu�ځX:�$nd its finy�,a�$ relativis��&�s�tvides�Ja�eEaIf� � Va ized��A6$0y $e{\,>\,}10v /fm$^3$ emaliz\( time $\taui�}{\,<A $\,fm/$c$m+ nly �U(Ged�� t s�B�ia,gluon plasm�  observ �of ( numbA ca� !2y !yo�Cb� a��te�~i�$p_\perp��k �8a� P ned val%{�s play a� al ro�nQU��!�, v��A-lea� 6�color� uJ)V almo6dea6&S �,E�"�z �!i�+ "� coup�)l��-likej�Jgas proper9%^Q2�,*A�ny�b liquid. I�[ps"r��m��domina���F �A�*�!�d %"e �as � . H2i work&�� E�quant� v� �HIC sia��5l"�iRI ��[QGP� hav ��d�A�es� ��0we� beginw� � Qdetai%�5�!�� newqPt� matter. C�m  m!�D(studies, bo oretiA�!cex&�,� r�red�achie (at goal. Sy*� ��h combahIP!���s*  ���.�0, should help�F � ra�� >� B�$ _qu�pstate. Hx � +cascade 2� �beIfo�a�isoE�A1# e� effŚ '%i� . A 3+1-dXA��k.2ep us �M� cod� sdevelop)�:�5 ED� port}�IEeE@(s��as��za�)�B� �� rebyJ��0 phenomenologEJ{�or@Ugeffor�1b%�!$ter ri�principl %\ skip 8noindent{\bf Ac�� ledg�^:} Th� ork w,p�e��$ %U.S. De6��!E�unM Gr(�No. DE-FG02-01ER41190. %\vspace*{-2mm^� Re ces �� "b *{A^d� \�q�{thebibliography}{99} \bibitem{TheoryWhitePapers} Se��t# s�$Gyulassy Me`DMcLerran L, %``New�mEoC�� d�Ov��},'' %\P $int{2004}{<H-th/0405013}, submi� �to {\it Nucl. Phys.} A. %%CITATION = NUCL-TH A;%% % %�Shuryak� cy}  E V�W�����eo\ell us� 6�S� %�?R�hep-p �66��HEP-P �66>�MuK�kk} M\" B�Hq�al%�de*��� 4015ƻ=�A>� Wang� dn}  X N�DMA� $jet quench�FbeyondRn6T7� 5017>� Stocker_wa6} St\" H, aCol�ive�5y�*]3� a]�Blaizot%px}�  J P�Gelis Fl Sear)Fd � glass���En�]�30��]�30%�a� in: i�ew 1� � --�St. ly IK acK 0 QGP} (RBRC S�E A��8, Vol. 9, Brook� n N(al LaboratoM S60, Sollfrank J�5!* ``A"�"cf vers����A�)� C�  '', M� Rev. C^4(2000) 054909.2b80}{\PR}{C}{62}{ #}.�Mu�,a �  AA_Causal�Ro�fof�usi! ve R.� F�"DU��ear %��9�.4�,9}{034903}; 6��30905e%U�%A(Rischke D H�E��Qv hot,J �%jc i�*����&�A�js 7114bM46M angr1tM*"4 �j@AIP Conf. Proc.} � $739} 163 [�� 7067]^�46{HKHRV01-�(Huovinen P,u�,�, Ruuska  V%g$Voloshin SA%%�``Rad��A�2���:"�,�$A�@.1AL}{B}{5��582�PZ03200�Chujo T)9V/.)i:``Resul Iified � �[ g E�b� '' 2�.U15}{151c2� STAR2�4Barannikova O,��F,:�6�`�Mid-rS$y pi,K pntr���n �io �J��4586�P��2�Wosie�=i* �=^��A yY!Y\scm= GeV��5106�BRAHM6�Ouerdan� 6� ,BYR1Ud2H$Ch�Pa%  Yield�� �at �.�>47:b!�03ome�|SuO C:�%B�O4el barOdum�� �6d1303�z�:g KR03ao2�Rapp RJ�t7}{04��.tSorensenOkpW P R�3 Ph.D.�sism�}��� �003; Adams J6B >C``5�+ 6�(azimuthal a�y%7�q� mod7 � of %Q�B� + Au:�4s(NN)**(1/2) =� -GeV�\6��L}{}{9� 2302 [arXiv:� �600V�EX 03��!'(S S6!6X .):�A�P � 1}{182301O'& AY!�1nb!� ~�`N":=in!CJH:I %13=J2�1�P �87� BK107003RJ!K !K�E coal�Go% V�F C M L\'evai P�Ay� a(cL�1`pr�(/�" anomaly�\PF.�0}{20E 6� 301093R�THA� �^�t ��O� \� }%�bf 68} � 4;N� 5024j��&pFr AV3vEV R J, *� Nonaka C)oB��`�� �h 6h : Reyi�!� frag� u�on 6^N�3}N108V�1�8m��/�:VV�F2���'O� %`a�#GrA�J(I]v���2R�602n�6�Molna�,3ffa5  D�6Z ``E.�a�  = mo%�e� a�ei^ �>�� ��09��N�201n��]�,HK02HBTosci}o G ��8 ``Emis� angleՉt �ferometr� J�> %.�M: 42}{216�uySL�->��IConcep Ha/ -Ione�ics}, Le�'s give� ��2nd L� AmerizSchool8High-6PhyP0 (Mexico: SanITMiguel Regla, 1-14 Jun�3)B&f 7360�"&�TARasHBT�>&� .M.�3}{01M*��� ��2�6�W�!S M�2�m��A�L("/R$n0F�%�R�6� 4907w 1205058>pK E�50T�� +)D2 �� w8}�13}. $'mun0!.=ZGK99} � Zhang B,>K�)MB>�-'_ �4alE�3ADX. Lett. B 455 (1999) 45*P455}{45a���!�1uxB�&���S�0�RA�Z�a�aco�/"ela�#�6�V el MPJ�!�#D697}{495} (Erratumi� ibid"#$03} 893). U. 13>"^ 6son!Kovtu$Son D T�p0Starinets A O!#A& bound1j�6M�� 4}*�405231A�.�A��! 6� NA49v2PRCEhAlt�it&�""> A�.�J�0A� %''D�0+nd:�of&�)���� �Pb+Pb�� at 4s 158 A� }#6�,}|, Lauret��*j)ch.@!:_N"�A�S�5&� 2�1*E11003�[.�Y*6�HiranoeJeu�  TX Is�5th2�!a*"d 7&o2.�4R  %G& NN =� GeV?M[J6Z�+5�+19� F�10800f� :�.�5:�����4!�B[t�u�7�8�� �� J.�� } G:K.�  30} S1229J�40304f� 6�� 62v2�� �1:��q��T2q�.>5uhlman A6�2� 1105c \endF� } doc�7} �I%\lclass[draft]{ws-procs9x6} 6%2a�o%X0 \title{Photo&�'�($\Theta^+$  /! eo� d deuter�P< \author{T. Martgaddress{h"�"H Fisika, FMIPA, Uni08itas Indonesia,�" ok 16424,S eA. SalaAo,d K. Miyagaw #2vM � Appl�e,ics, Okayama�y'Fce, � $ Ridai-cho1(700, Japan}�C. Benn,9� �Ce�"E�mS�&)���Geo�8jWa�g652yg, D.C.a�52�A \make%�!�bst7s{ J��Lpentar ��vf�( has been X' d by�0an&���a� g. U�,qis$6l,�2(tal cross sf- s ar�s100 nb%J�<$\gamma n\to K^-Y� q7ne�d 4V6p6{\�K}^0 >aC=>C3�/ed.�i -� �* $K^*[+*r+R' yRa�#p5i �. e!', e� �'�f� �@+Re!V`/�s"?;6J , i.e., l��* -T(2![)5\ du�euz  ()�2u%�<4la�tary A+O &' :�6�Np��Q%�X!�aVM {Int�2� }%�o6J-A"]�]�baryon�4&k(} has trigg�% great �-of inv�*g* 5�*55f �*unconX5�?pn�2g*.al,�sE(]be diY(�?!;wo %8g�1�:�)�bic as>4romagne�/ �esI�>(p6�)1 �h 9 well�,as a �6'',=n''5 . F�7 , :]'�sEHasierS3$to ''see''=).�w�>c�3in�-i��, 1cP>l "�+�)itu�>ERalread�)e9 i"*-3e�IKarlineG 4gr}. O� ��"F,7*$e^+e^-b+ $�Xp}p nihi�i w�+I5�)��nAss-3@+60s, ��qa�e�%�,A� supp�j�5�? m, �Titov� 4wt�S�:al.Z>���s�-��pe�+�� .� 6 Born��xi�8qnyu&ji�}�er% �d6� span�s �nan�-n7:0�?($\mu$barn, �'�}�width,a�i�:u-�,6or�6-off,�C�(�3�*7s �A��mW��o�ame�7�A una�un�<�:uncerK6� !�ent. C0�9p$,/6",>�)�-��*utiliz�<a��[�AaA*I~�� thres��/q�.:omQ=�,r`w?@�5�:�� @iso� �A �Dimpor�gseB��8tree-level Feynj diagr/!34/9\,�>fig:f *}A�e�:nE�! $n$,}0, �-K^{*-}$i $K_1N�s -��.%_m�[/ApeA�ondA�!~z�2!$ur "�2m$���Flin�3 not XactI�a � al m�G��*��dj�!r�2id ��Q�pre�=�,on $K\LambdaX\Sigma$ �yis y)-��?their\5ɖ},�n�'� fg;he}[ht] %\epsfxsize=10cm %��A )$ - will enR/re�;k !s Fbox\ 3.ep6\ ?2cm}{3} %to��a box[;e�E� �{�4inEMd^} �ca)'{B�a���>�on)�77 " a�\long�=arrow  +u�$ (top� � � FpBF}�MH (bottom). \label!?uL�)F} � i�ematrix�u4re�+ondJn � �pos� >�L} M_{\mathrm fi} &=& �u}({\m!u\bold$ ${p}$}}'\sum_{i=1}^{4} A_i~M_i ~ub8) ~, �eq:mfi ���}*�;gauge%eL� tz� ar� ces $M_i$e[`4in, e.g., Ref.� Lee:� kd}.� er31$MandelstamFa�8$s��u$�$t$;he"oA s $A6tbyFV�@a1} A_{1} & = & ->e g_{��`}}{s - m_{N}^{2}} \left(Q + \kappa <* 2B2 @} \E�) F_1(s!�- 66ru2@w + im_ Q\G } \�7s \no� \\&& �[ Q�A� � H� � �} � �i\, -6�{4�}� ] F_2(u) � &&�XC_{K^*}G^TF_3(t)}{M(t-m  ^2+i p-)(n4 + m_N)} ~, \\!�21� �26Xt �K%S} )� +%�B�+ I9G}J�5�\ {\widetilde F}%(s,u,t) G��}.= && )� �1}{B %=o&& Qf_1!n_{ >t_15t_19t_1>tp)} ,}G2}-�36�66I~MxQ�N}mMwNEr)�6Ha mU�a }~ *NM�M S } 2€}2^:�U�aEN}E�} U =� m_p)5�V)�+ "-2"%� {1}}y.j�G�p)-�=�31�4f�1YNB%-ȉ�-j!�+ .�F1�%�B� 9�; R2 6�9P!A%�V>�^*U�^*Y�^*})} .�a4F�� $�=g_{Kp N}��$Q�� =1��,Q_N=1\, (0)$���(� on)n ��N@  �$ * J�e@%;"�m(" he2�&U �$(M$ is taken_ be 1dg "^4}  + !�,-m_i^2)^2} ~[dA  q^2 ~=~ b� H*� �� i$% correspon)cu�� � U�B�$6��$Eq2�2})!� �(F� �|satisfy�� sym%&�(o avoid a p�Da�"�)�Davidson� 1rk}.z�hat!�&� {F�%���+u� -s)6� &&&� '4 -Ku)ə*� +Q !.6} S���!Wan iso-F1/eYJ� re��Badvcc1!�ص����-�� ^+ n *? / ^+ pA�,~A�V8P�Pi= Y_{*0%bB*�up2���K6�$B�"ld��decay���*� + n$"vN�9!P� E[�g^2BR}{4\pi}\i E_n-m_n&H �ppb� p = [\"v <^2-(m_K+m_n)^2\}>]K$^{1/2}]/{2� }$�preciseNJ�a�.(i"ill lacka�du[T &p�Csol�6�jree*Edthi�1}Y�r2� $ 6--25 MeV.Tehas �S.4$>8. /coeffic�[ $� e �$ � in�L�#in�� B�� vect�]"� haV mc $t$-G!isa9�u M.�Ms)� Mart9 5wu}N� ؅�%t \{ �Eay}[c]{ccy2 1 %&~~� {�Q~~for~~}�I�^+ %\\�s(~~[-1.53 %&R4�?0;]% \\0 ~�.�F�VVs $�� {*};� TRr�J'T�a9_follow -0 )l"L,liu&ko�|� xJ�=1.32$8C negle#ng-R�����a���U}"�1WA� o�2� "� j "jy�ND&� GVK*���%_&�}/��Ek 8.72+10^{-R B0 M�Np� �dfJa��exa�_mai�X9' ��:'�+� 2z >87!"�H:�}���m�zM.� Al6�=erho}/f_$de�in�:� ��K_P$� $f^2M/�/ =2.9E� 0p=12� . uIffAu ve L� ngia�lcoc of8J�cvc,haglin94}. A�,!�cas�� )�UZ tens�1fbeQ�� �~=�=� same' s ^Fe�A��>�}.�ax�-�.N^i�_1���%is Y$ma�%&� ���y � �"� :�)( wjc}"� %%r cW�/ $},La� N}/�aB_1=-8.26$.�Yn�*!{% QuQlso�h)R.��Aed}�@�� Zm.4ngb �e0$D_{13}(1895)| r�in> �.use�+� �+65�2--7.64..3}J ^ J]�_1��("����3* !��fiY:�a�!2%�Z^0eh0 +B� �NI%�jv�v'ck%&�_ =&����2� 0.17>���J�" "� Model}J Iu.$�P�/us�$K�% *$ (�X%��W)&[!_X\FT!U��)F�*(b�))"�*. HM;,Er�#�.���t.� e- �I��U� � A:��K� 6 � oced�ga�dop�X��.�guidal9ULl*�`replaca�A� ,Nag/*� �v�r�*P_ >��Y s^{\alpha_Hi}(t)-1}}{\sin [\pi:]LF~ e^{-iF0} ~+ > ~:1'}/V{N� A�i$�`^:�,E� $.� (t�? 0�% '\, t$2;ot X:��_�4ory�A5�.�3n%6���Lu�9�+b2�" b] \V0" 3.5i&2"d3dimJ0"DW^�O:�&ob�$.s.AA./&2�!c>�!��"�^ndE�>`� �! �"{%:` �. O& b2=9 aw�` pea?b�&c"cP*�9!+rib_��'I;,%�k�N�*�G:�$D�!�*�) 4 � "� }9�ar'� �2��!F �1S}%�g � no 2�F�/i( �\ed�,G%��)� �dem���fs �%&F *�%&kkr+�6�s[G)er �-�d>�Z6�:N0E QT��.c :Z born"S+�)an�"i& 2K� %�c�� tN|1by�-tha� e -of�; itud�.Ep*�ZEj, .�%-�S  �is� igiblznZact��2a��O/he&W &;`$by>7GVK1})��"� �)��6�m'��!wJ�C\�-�e>e=,)-�%-ex!� ge �R�2�{>��+�&��tcs_parJ�TNfor.�:� ZBf�) on ('%){a �$XRfu#g1,"� }{�=� "�2pa$ter�2ݓ\Jf��zѳ�O�.�|��6�m�.m.�Q y $W\�n each pane6���. deutJJ&% �/��s�*u :3C �)bL82�B��� n �,Y2��serpv\hm�-T-1 �Z0� choi&\1N�"8&k^a�h 6=Q�is�y&�.2� . Fo��ur *�")��� �"�16�/�5 s |)U*!8.� I#2�hI�` E[�ps �\er:��!tJ0L2� � ����E-,1*�#yb�u�G � 5!s]jyH j� (uT_ $W=5�l�f over���0]F!�)`\t&qrTp ($WN2qy �50�gu3/e*4c�"wifQ�p�@g&] ="� {!�.�Aw�uc�fd&G' �rH�ld%1�Q real�`6&2�8at# 1�lv($79of _Ry Ah�,Ta1 ���_ulawh�^� )�{u�s� &� c �2�l!$9o. &�:&�8 "�8�`.V� -8N� LbFd vc�- �>R<X pNmleK � " inBN.I �3�) �h�6�9UQ��� "�I� � =0.8E� �� "z �&�2���� %�K&�$�is orighe*� =��5 (seeRN  Inm�;ehava�"j7�=��� >�a��"9@2�H6�V gge �M7s�2sVTI�Qqw � �TMB8�7ara,� or��xQUE!!b5 B'a0�%a��r�c(t} T.~Nakan�`[,�>.\M�F 4bf 91}, 012002�<003); J.~Barth2�CG �[,bf 572}, 127>,S.~StepanyanRBbX I �V�252001G0V.~KubarovskybH F��03H4); V.V�miV��Ptom@ �a 1715�(A.~Airapeti>� -\%585}, 213C�C leev:��sfuJ�B01024};!GN�nov�J #(ph/0307357}Z3).&vHK:1; M.~E� H.J.~Lipk2�@.\ �\�=309`4)_2�:!7 .I.~,� HosaXB S.~D�a]Y.~Oh#A ��B�G80:E"3I*�HB.G.~Yu, T.K.~Choi,NC.-R.~JBM312075�Gure"�d0<ein=$_"R.!�k", I�StrakEl l,R.L.~Workman>�31103%X( .�"�"�Q"*(Data Group:! Eide�D�Eq�ZEE�i4.fliuy} W. Liu�C.M. KoB� 0803�D5ina�!S.I. Nam!� 1�!AH-Ch Kim Lhd30831�HK"&" Hyun-ChulV7 242}=�< 19� ��, C.~�C�(C.E.~Hyde-W�5%\�B\�I���� 1074�K5:(� WA�ugao)�2e�⁠]69}x0���!2�� a xE �"�DRX� 0122��0.�Vjv!�E A:�6��8C|$�h� K.~H G2�50��688%=2��e(Williams!=q�A(,S.R.~Cotanch.] 1?4Mf 1617_2.�"���G�, J!�Laget)� M.~V�6rhaeghe c�bp":���OA62645w7.w*�6 F.X�Ae�i-i*FF�L.E. Y�~6k9��3�1.kF�, H.*-!O]%M> �$T. FeusterG: �.�58}, R40�8? u�>�+ R!e�R��\>k3}N�a10�2EɁ�% �q8T. Wijaya, Acta u Pol�Z3�265��f[-> �I�I} k\�I twoc7en,S pacs,p�i�7s,ams�90symb]{revtex4�5bMu:dc�boH ,eqsecnum�@ho������letlengthe��lH}{0cm} \usepackage{�<ig,sub�2�kicx6-Q6�g} "-1Z!��4{FIS-UI-TH-04-AR fKP&2I_?Ed�TAliesb�JM� } \affiliRF�"K J"K a�I}^�I&�  p�on� �)�C+�S�� |�ce!� f#�J��s+to�#8F�)an two w�+�x �aR$ us > 1sC�BH<9slb0*ed b0.6�� &�W�� cJ� .c:T3�0 GDH integral6�"�vg|rxpBkp�i�iit=Ehat�_0sum rule favo]|h�&��I��$(6�M2s��5Z$K'Ym \��${13.60.Rj, Le X75.Jz,12.40.Nn,11.55.Hxa}6�L�e�a nar�?�I���F$m*[syrum! K^+n� K^+p$�&%2$M=1540�-�@x&,leps,saphir,��,diana,�Qes}H�t�2-J �e/�[Zn�n� p'X�iu�e�'��sj~n�ca�"X.�!����ly*�:2q-[�(diakonov}. `2then �ɠ!�2sJ�&.�"�K� � carrtOout��J��JZ�J�(Isn1xe� n-inKCd}M�b�4,^Ka��BK,爡:q)65te�DV�I%=;/n-�]oll�FjZK�XEpr~ZKa8=�w�YK�YKMs� �ZK�ZK(a��KvK u-f ��Kvg�k�%*0N�6~�Ks�*on �����KΊK�E�� ysoh*;.(,nam,qzhao,"8,yrliu,wwli,pko��{r�%2���K��K��KµK6�NaQZ�-c�,cm"aU��w�L�?r�F�u &��s�#P���.�a?"~sm���]Xzw >p�}"�K�Htb{S2+>a468. shap�-2� Ȣ�?�mart20ٌ�"�+���*O��prolife�,/��M sll avail� *�0)$] V�Y�ellF:��aΉis urgv�"tPz^P&s. >��)��,�q !m� �� 6�B[2�c�%f.P�U��advan��bK!�Y��6rl'��M m3{��Ns� �one. NA�the+�5a)�*�w�*,�+ sp�of)0� �p"s.�s O� �]�"/%f��yrEc:th �� al"�e�ud �A.� �)# 50\%�~,.�. CoP<3�n�t"�O/y�t�� X� x$ e�) ���? impea%���idew s me�$ism ,*a .1�Uxv=e,e& ggei-�E��<nUb suc�in!J��>I.U�v\etQM  'B�.s 4!�� lab1$E_�B^,lab}=o-}ChiWy2vqSI�{!zQa��P >�2�#k��T��&V =�2�" *�$""(�$)�J�c1�.]. T5�52nd��B�X5�po{Lvg�"&� ,�. .��SI�a t,DimeZ| ifa�^�4neWx� 349� cern #�AU� *w!�`�`B�". s. More7, ;xP moti9i�#&� >�5v=u�h.� va� :� �a%�A���%���`� f�Eng=��%&�+�F9�I�&� =herasimov-Drell-Hearn (GDH) U&]�.� �+  *o�V� �,@ ��-� stoodmHdrechsel e&�;eZ>�2( Y�B*:tS4S:�O&'2J@S >2*2.4%���Bs ar*�Oa�cSncSpH"� *h *%�6�-��4Hal kawR4cj>taSI9/o6 <�1S~1S�9�}e��r�2S.2S���h.Ss&"�� j�kQ�kQ�kQ�kQ8,Loz��azlQ iv% .g.,2�3*�. %byOk�1q�`jM_1A;�M _5 ~�S(ilon\!\!/ k (~~,\\ % M_2122(q\cdot8 ~p k -  k~ %�R O3O>N3-�/M~�h � Z�N�4[i\varep�dS u\nu�:\s�U} z$^\mu q^\nu`^%.d^ 2 ~,dUnd.I�+$��Gfour-/�polari�o�� %$v� K6\,G ic levy-c�*��sor. �PS���TS�TS!� =\!:ZS*@M�F "yQp}�O�R(1EN+M{p}_5m _O"N�Rp&�Q*�OoR"pR�N6��RN�NnsS!"`S1d5f:� ���}�@(*�P �p{�Istyle �i}{2}�N B\} ) � WW ] :��QG�LSp�6e���:�}bmS=]}{nqS1B�&S1N��A>dS�J.&*PG.Q^*�P}�`T�R=k*OS \_1B\j�Q&�Q�Q.HSf9T}���NmS2qSmT~ 6�pq~Mca?QE>()�]�e��uS2E&�S)F��tR�He\p&%I)]>�SQ`=�XSGfsS �6>�lS�F�KB� ,=ő��N�S��2�S2L\U^�S:�Z\U�6��T��~��S �wcd:�G�NS� �� $#$M$�t�R��KSBD *�Dgv_gt} �A,T�A^*(K_1)�� N�<KBVF�S>GN>�S �\!*}[hbt] 7Mb c\�!{file=f� 4,w�K=1=^} ��]�-x2�]��].} Ff*�` ���^a�40N�s�R`R �aR2J�%��*�� ��tEu�yR�yR):��� q^2=nRq i=p,I�,�$�il/OLhD� 6�6�!� � �zRzR�H��-�~RN~RV�&�1rk\ m\9E%.�|R% &&RR= �}RHv r~RVrRkT~B� E�Fj>^B�3�dOa�d�GQ�GQ�GQ�2���XQ? �^Q]_Q}{&^Qqeu��f�kQ�kQ!�I rang�"YQ�r #,svd,n�oF"�&tla�oalyb>of �#�QDyFdQ �/t='_&cC#J�. 3/,cahn}A��Q�decid�o���QWe ��te2�b�c٤ longer�k�:�=1v���K�`0JB�:�cM���ded�$K�F�2�Ls�;Ri2�}{\�?R�?R?RM"0y�q9P,R-P�S8�@RJ�L2$:R��$��_)CKnot"��+% ��R�.��!�Nie�ražL.=MHBQ.P[_ [���UH {*}\�k�} =M�\a%H }{24�3�Y�8"�^ }{M}{0W, -[m_*�1- � A}^2_ ? ]^3F�Y!'.��$�0}(892)�?%u�&, mIM���7:�. 0 �V)K^01&=& 116�V10 ~~DkeVVM�<*TQ=-1.27!a��A���Eo!��qD���aof����Miėh G9erA�&�!&�EOA?5N"F9s�RVd ��S��S��Sb�Sl3E�tc e��S�S�Si*�P�� VdRR���S��S��S"�SQ�"I'}Y��d��I��l�=&kS��S��S��S��S��S��S��S��S��9 >�S ��S$�SD9wl%, instea߳]q of WJC�p\ *j7tBill�]l�&&'/6$o��"A�CD>*�'�X�wo cU�iZ5ɻ, -c��l T�"mz$Tmch�@ a �: -0.24�/-8.25$̱s 0� �.� nt%`D�U%0AsB�9 TU�_� too  $�B�p "2 1yu�Rx!l!zX*%!-�� m Bk:M)�r��d#aaze�(cFK? ��tA �242,� A b͉scribed S�summary�*N�u��U6lR��U.>$.!�ezlù"�A5O�Js =p!�a� N�]:�hi deo��)"T'�T)%N{T=��4"�uJ�Cm}. �T�T�e(d��S��S��S��S��S��S��S��SM��*}.�4T�R�s�'$a�d e  fa[`�α��i to �vr�um(fer (``hard&L~ W+)�n�'.?w'x�~��se2�.:~.s �Qs n��{1,�6av)�A�_�d�#�gly��lu�,�|��of>�%S����"N��deK/J'+�brhoC&\m��J/\Psi$��2Ʌp+dp0q��"�.��r�+_�].�|*B(2�4�[�1��e�-n�püt.pM3F{{�cw%:_spin_�en��#_��n�: 3/2}C &�fU!Fko!rm�{ %\bTT'* >M-(M,��8a2wl���of�8WVa)�1�'i"�R� &��5}),�J�o"�p$*� �)� Qc.�-Rgdh-sum- :!i�v2\pi^2C�%,int_0^\infty�)rd\nu}{ [2#(\nu)-.D] ~\Az v~ I)�GDH|q3%u�n} $\nu=E_{�&�-� `!�Dn!�$)Oh�1s�/2�A�'-soT��)vd�%Av,bil�s �aM�!c 1/2} 3/2$?� �Uy�7:TU�[&J�+*< $=1�Yr�rK*mm2�).�i2wq"�m61A��44 assuŸc:� scEۡ�"B+ g&toصEl{�!|\nu| �iID$�csbass�E��}[�~stlog*| 8.5c�Ycj|TFb>s���'IzTQHU���{�-�� *N� ��v�)D :�U+2c.gEw?�;�ƽ~x� 3 wn2�s9@a/-."�bj��dep_6�@i2Rst}�j�N.�.��:���)�L� N��]3��5�=U2#��:՜ @ �biOol�Yeit�P)z:�M� �)�f? vary� &0�0.6A� 1.2,��J�9Y��ord�].Y�"'lir *7vom�6st�6AYte�p satu�Z >�4.�)6P ���E�j� steeply r�mto max �:�7.2 Ge�m��ؿe a�Q��G~�2�fP����Aconn�@aA�Pon�FI r���3 $W=3�A,�z2bF�]E fal�7etween >isR�II�Q  =0.6�d 0.8!. Star�:E%�!��I���6eR��Bh6�Q >.� z>{GeVw \fuܘ�K�F�u/�B,;4r�A�An�"&D�G�u igdhzwN�Zf�A�O< % CaG!4 $�-3(Zb �o"�u�0s)�]s2I�~-�K2�%��$�:� �6�!&^GS>:px�>rI�wZ�!�.�oR�*�X��12A5�6o6RE� [&� ���4�Pl.h.s.MCbk,4s $-205~\mu$b]:�9� �2 to:� invi�b�,Ae4��9uiby6w�nycu#Eled� !F �x2{ ���up2*�� $\pis �8,�3B�5�`R2�UX�V&`y�:t:�"d5}an2.=-202)s��mc2��um�o(&0$B^0:+$)2�s @}�Wd�3`� i��.J�Ih($+0.26 �). ��E�inC7view,&B8(�6Q�0�I6�ae�bpreferrCIn�words,Q%t}J is ? desi�4r��6�<�{� ���(\ge�OŪ. �p"�E �:��dE�:GABiE%JeF+F"^&�  Q#�%= .|� �� �"�9��e4�>ed J  flipIn�9M �b�^5@3�ȉm�>2di )�opA.��iK�$�or meAemϡiz%%at 8�"�< ("~=}Gh��s�' �sM7"W@n>�� d.O��/dif3dn� �K` :N9as*�z \cos\t*"�%�eM� M�"� 6�=/K� {\p� n, e�/�`&�20\�si�eÎo\.YKif�5��jan�} clai"�a sofZ� (���$Eez��>>Yfp$!or�� �׻*��cJ�� � �$som"{uU�t V)� . H�YN.�� O��*���i���ya�J5�6� A�ee c�!�&c>$� 5�<�>g absorb �&�CingU`��6�,Y� a�*w�6��7x �aW   are � X��sco�D[� ��&C��] �E�� b��WB�eJ(=ׁ\ogethA�the4 � 9 J:. ��DA1 saP��2�.�:�r apsi�� aneoṕ��J SU(3�B:�&�� kPF*����>[�io"2 ��nt*�f. A�Kefu��a��on��$uU�@Ho��JI reve��%`h�(2� error ba�/rc "�>�Q s?@��C��eq ��D�� �x t��al�- petrz&- �1 �_rer���Q !���* Jq�Ju� &�� erenN7m!�.� �xref!;��a�:ye���ult2Fq :E�K��by�G�V��By� EI"�AlueA+l*b���6|bA\�����GX�e�co�r�.� ��"���A�1Pce ���E=�E�� a�ҭ>w��l��lԝ������� s�A at $0\le&3�R-!w�1~ a�z�O1 mple�fngular d��*��F&x�F� � &�F�2.5 AtS2N%86�i�I"� nd"��� ' W>3.�e� tr*�lM����.OA�h sharWx� a"� � W$(L�2�m.�Hat JLab, SPRING-8, :� ELSA�E�IlyO A=�$ett �J roblem��e��)p)>*E,7�'N�"�U-!P]���U$��O|f��.�if��"*�U�y�h�0.6--���L6�t �sA�che2��Ser&%����wbably MFo�ysV�%.��a�G.�w2=*%:-EvR��I,�O �C�U!F.�3��"�YF N:� QUE (Qual�GA�$Undergradua Educ� ��c �X�>�Z{5.�c2^��c.+^dU}��c*�_clas}�`S�d�d"d�EV} V.~�ddV�VA.~�(dT"V D.~D%V,� Petrd� M.~Poly�b, Z�^A�G f 35�`30J _>T N.d ~J.~�/d/d !I�0dc\�^"�a7�` 042202(R)s^2�`YS}xd, H.~C.~�b!,S.~H.~L�_�^Z D),69} 0140"�d=�namE�Iax0c"�dXH.-Ch h YLB��f579}, 4 fX�S�R!g,u, P.~Z.~Hua�JW De X.~L ee�\SZhut:(�b 0352!���*�eSTcc 2�d %Y.���=2��� *��.\8a\�)28}, 918F� pko}! Kob)�T%o$J.~h.~Park>�d12147�i?�*��!NL!cC.~�d*d*f.B.~"�f~K!�F�fN�E� 04=�]&� Q.~Z!V!,S.~Al-Khalil"g"?e.�c C[E�6�b03tdq;2�c&� #_%oC.*�b�i8U���&�dV0)9�,Kaon-Maid, h&�kph.uni-�z�cde/MAID/ZK maid.html=&�&M.*-d!��.dr.d.RA�%T.~F�b\�b"LiJ�bQ�6QA�TA2Q,aO N.~Y�L�4�},�2e!ځ��  N-�> akE_�fMc�&�2H�k=jmal�l�]D m�&d11�je�1.�*�J F.~�ye~�ze:ze~Habe|�ze}.T.%ى�T.~�zejzeA��>%�R�{eZ{e svd}�sNtl{Nl*ql UI, "Ui�9���v��� >ʲJ��i ���j��*� �f�k����Z�%S>4i=seo�e$,2C-x�$(-�.�%"ɜ�wo&�-1���0U��iV re�#�!"|�rE�pa�!���2f �.j<�A ">{�Jg�&f��x��2]$� -}@gez�:Bwealt��new�- [i<� ��#*�x� >J�E� � .�` `Iu"�.�nY��Gl�p�H 3jw,Goerss$9sw,McNabbnf} A�D)^s��a.`cC-�%��Bal)`"d`mad^of �>g&�.�2 f�&!a  &.6P`�"`su"m�rS��n�2�40 year;�Ax preh{Evə"is�de�8p([l8, Ʃ*�"�lar5�� m���*��I�&g�]A`b��~��s�)fi��ABE�A�.�":]�&G�deq��freedom.:%c�xW:��!q�ai�_b e�ya. O&C�mV�I/�C�!,��~y9RA�s��!< ��"|`copQ�$E.�of �g*4!)v�5c�&<12 O^!S�ha�5�`E��fF}m��$��Ge@��a�Z ui;(t task if,��=@}%Et��c�: u_�3.�!Jen�Y�3�(mQ}H���5�� &ó�3�.2X� =}-����o-�GupD!ƅ�accele�to%�h 1A."�6�)ed��$jlab1998} 2�`no2E �'5�t"KmA�!)-�I+"an��IdF$^�����m�� �z"6�"@�l�L�*�*lyq��v�sh(P!B N"IS"� $��f�4e�0 $a��"/� ain E :|���u@�*�J)c1�.�j.]�\�dm#"ίA��1}"�<sak%csiX�!!,9v`Y�n�%_elucid�!;� fe)19�G��{cion. W�e �0n!�y[Ha�!&�Ol6 (p_ ) +�` _p) >�`K^+ijL�P5 h\ Z�!�-��:�M� *3h!� >��be writ�c��ofF��B�_ �,s ��\�S� _p,s!B�Y�~Y� by�&�2`gF j�^;�\/ Q/�^N�^p_K�^2U0_ ~p_�^K - &~7J0BAS�M_3�II�_5A� lF 5.�o2o Q�/ ~"2_ M�1_p_KJ3_�1S*9_Sy2�">�A� "�#�!eY�hpri�(x "PAaT��a�mg�C��� the �*"9�3J#� �!in�>�D�" u}� ��"�3e� �&ju�n&@P�H��v metho�EQ?]H"%� ���� ore Z��a�ac .��22'T�_}�28)rv+����sR\�.!"� "�9s^�&�F:r� �� �4riction for us�Fing these terms completely. The most general interaction Lagrangian forD contact JLin meson photoprodu ;�can be written as \begin{eqnarray} \label{eq:laj�i} \mathcal{L}_{\gamma\phi BB} &=& \bar{\psi}\partial_{\mu}\phi F_{\alpha\beta}\left\{\frac{\beta_1}{m}[ \gY^\mu d^\a8 - -mu g^h \nu}] + \T2T [ !H}6H V)h] + \right.\nonumber \\ &&.c$3}{m M}[ P� (_D�_ -�})>�4}{mM^2 �*^ -.�]�:�left..�5^} [ �PzZpb�] ) \-%_5!� ~, \end]>where $A~ (%)$ isE�I��(baryon) field, $m~(M)$ refers to, -mass, $�_iS$correspondaNcoupl nstant, $:z=\Q�\ �A_T -�!d$, and $P=p_B+p_{B'}$. Usi$Eq.\,(\refa/mfi}) weegdea�ose� 6� amplitude� obtaa�r�m�_e�a�A_1ixE�e�A�M^4i`X( s-u+m_p^2-m_\Lambda^2)�) + <i =5}{M^5�=E](m_p+YWV4, ,~~~\\ A_2�2 j4j4} ~, %3.%ie3 � �1+ �;4;- �2�1 C+ 2�9 �9#b�M=1$ GeVE� aken�sorderA�makaAGA� betwUYlA�ji. E�$ur calcula�we us��5=W��thr-) =*=2.I�e�8refore, all low�Lmedium energy data f in)B_J resultY� by u! 5, method will indica�as ``%�\ 1''. Alternatively, on�usev�exp.��aE�e�! )/a}n�M�1-Z;Q�A_M�A�n�E�R� thr2p �oEa^ a f$ d[ L . Clear!comparI}�s previous )f,  advantageA�)�6R!2)CA�%a� displayedA�Fig.\,7 $fig:dcs}, ; > )_L differential cross �s,�re'�R angles, 6�!�] ,)&,�} 1�qi2����b�figure}[t] \centerline{\epsfxsize=3.3inTbox{dmix.eps}} \cap�({Df� ˁEV, +p\to K^+ +� ($ channelJ�5(�� Data%yt� f��ŲprotectɸMcNabb��Hnf} (solid circles)%� J8 old_��3 squares). label!:%�}i�-I As�ԥ� expected,%�2���!�I��< works nicely on�t high�:iAa domkE[CI��appearbAFverge4whi�Ja�$trary situ��h5ns at����iajBy�b �two �s N���0) good descriE'e>� Yy%��y !s] be achiev�>However)Dshortcom�of6� � ob��)3�``�U'' point�  $Wղm�2$fit switch��amBto a p� =�ɣ�|$ontinuity ��n l# ��i�E�B)"u� a)�r 2of9 $�, 2.96�%5:%_thJ((Angular dis2a���B 9 5�0 �s. Not���s in N�F�_thB�F .�'�t�a�� E��. "i �.�� !�)���a X� oe��[r{talG >7X very:S,��  increm< �Oei��!Jdet�Ł�Ej� on�is (�est��siq� shap# N.�������usu��zrmi�by( $t$-* �m���� .�polarJ�Recoil izEXs�� F���iB�A r��uniform=tob\��or%!rF� . We-aAO at n�Ef.B�! � 6!� accura�, ��!�2�truct!at &�1.7&i��a sig���an�r�� play�  impor� r IJ . Fut.�shd addresa�is quA�on. A AmoA�,�9view of� 5Z�*$���error b\ m324� � seIR re st�underrd!W. wA r� 5�epolphoJ�� �B 3�.�!l ag show�|%�FQ$is superia*o �;�:� �A�l)��, -���aqKi� �ݍ�B���as ���s! \ ��a\6^asA�4os\theta$ decr*s��4.9]Idcs3d1JIf��&_B� e+$W$U>� ���� &F" "\ A@he( �nmI{market!Ua ���i=z��@c!Bof5~1'' �B,>�dcs>��B�Fin���C:B 1�Ad a �e-"3al�uQNpredi0&�B ��o� I�a 2~  exis�l|he))!�=)� rea� ,a maximum at� 2u k�pastA�C�2� surface&^ . A str�  effect"��o�Aon;)�.5e=^ b�a!rej , thu�duc�! gof�l�A�=  T�5 ,= f�rs� demanded� presI ex�g�Wal���In!Aclu�hav� v��g� �2 3j���a� C!�a)eis !]woYm �s2�A���h��ed  ,&� *�s. �i�� ��to �Wd� �?� (, e.g., addw al nucleo�Ms R��l�recip�T,*{Acknowledg!�fnA TM&�supr�V �AQUEQ��uxthebibliography}{0} \bibitem{GlA(r�� jw} K.H.~  {\�t al.}, Eur.\ Phys.\ J.\ A {\bf 19}, 251 (2004). _o�N(1999sw} S.~BY SLett.\ B V(464}, 331 (A)W:=J.W.C.~ 6] [ Rev. C X6� 04220J�Ir 0, R.L.~Crawfo�d N�PaA�� ��pB14!q253p78.p&�`A.M. Boyarski \textit{et.�n �e��!a_22}, 11�69+�%enc� rein�.6�  R.G.T.~ 6. -9\y\ z\ y9� 0920�53)_>` doce�} �e\�class[12pt,fullpage]{article} \usepackage[english]{babel}.{ig,25{��icx6�2Great, R�aAX 7259!(itle{Cronin�um behav� in satv�: � $p+A$, $d $A+A$ colli[ s!�Q}�*ken \abs##{I�q aper� consi�%Z�urB���� �N�. Our&� Y � Zmr� &� rapi � 6er�, *b"  th sca))law�simple&�&s ��7. �(8exact numericalg "PBalitsky-Kovchegov eq:w�� lthough' depend�8C Kly�!�LMcLerran-Venugopalan!\ Fu:n � gluonj " "�%� �I>� !��iesval�-A��(i.e %g>�jed-b�-n�>bigEg�)` -��to2? %(Suis-P� variant�nd-*JM1%cho�* �<. aE3 {Int"b.}� a"!i=o�R:P&xx}� waundIJ�B]!{.�at`$ -�)� t  :zm}� m�)� -�.Rce�l mPy Q a � e��dA�iݝ`�Q�8} \ln(q_C)=a+b .$})a-CM_ �.=wA "�s �"a�$b$� 'ima�})�@s:�na�/�(ab_abs} a="n&3(2+\l*,)}�A)+q^0_C)\,��"i. b : 3}{>(}=0.1304\,.�&a0w��geo|ic��� $ O =0.3yA" also�x# ���Y�s(�(phi_cil_BK}j" MV})aunintegr[e%$J%slope%oisJ�. Re on�9�)�inspi0$bL m�hex �� 4 qsatQ)���s%%He $Q_s(x)$ based onJG n$y,>�s t dim_��})� �"Yx4\log Q_s^2(Y)=-� Y + log( _0)x_0^U)Q].�Q� �:kM�%(I�q_C�+p(}}\�x)=R- q_Ce�>bS^����!�AFd�&u'cer��IND(foO sc�r)"�ez}m.�for6� �,o!�in��gribov!*n��is�3�abl�at-�.G does���f d��e�� s�#theoret�L gr�z1!t.$in�!c� . �*F�C4�"e��/ indea�ru)!��!mula (e�.�o�pto�l�kstoa)in.�"��. �r+�%3e 1!�way�$ ��%:J� evo�q �NBK_}��*�#be� e;��$N(W r},y)$:a QCD<Jve[v& $| 1|� հ,$Y=ln(1/x)$,��q} {dN(;d,Y)\over dy} = {(\as\, N_c <2\pi^2} \int d^2t z} { r}^2 @�-z})^2\,� z}^2} (v$|)+z}|)- r 10�k%��W�4��7a�E�icity� �9�'ux cylind� ^�(�7 drop imp� ݫ�b}h"� ��E-�NL5�c>�4 $\as�*fi%-Y�� 4many its deriv�+(s but we'll�!�em� nowsa4EP,aren't estab�ed well��b��� &\�)lex!Pin* �k.#�o�/� er� of pM syO FKPP�atyl�1-�)#3�TFisher-Kolmogorov-Petr� -Pis��ov � c `ifadr,�>eK(��o&F spac�>�# ʼnp_�� real �instead�Eje!�] ��4 e�h-� f"T0one*� Q�2� =\bar��.�$y8_c)}{G*_c} Y- " 3}{2N Y\\ a�� 8a�}{p%{\pX" }y} 51�Y}} +{\&O}(1/Yu�%%D>�� $i Z)=2G8 (1)- � 1- $�JE��0n BFKL kernel�$ ),_c=0.6275...4� ��ofY� �-}_c)= �)$E�bli])��+M�.>�kya�"�+:#�2�*y. �&is.��au>�(�:#w9!to�+F 24 � "} ݵY)$RH�� R�wayR�a BK_phi} J:8^{BK}_A (x, q^2 5 Im$4 S_A C_F}�, (2 \pi)^3} ų d^2 r<3U0\ i q r} \ \nabla^2_r N_G�H1�}F;8 MV.�MV��:��6 1}{r ��=�6�MV��Z�9r}5p>�Ta5X [gi�" simi�('$um&6y�zzW"�-�-I�J-brems�hlung)� 5a quit� f)1�u� N (fig."�(_MV!�)&�^$ \re` �01\h }{!}�0$file{pics/+ fig2"&�0UBW2H�)KF� (red N;(green)}q�fi�)���&� s Ag�R;%�gf1s �$i_�6�row��"�R+�a-"Me��5�.�Q�>JK w�A� B; %indXno-ѐwh� e�9[� .� I�:�� � �0F[. H�0q `al���%l�11n�s soft6 e $�2_{QCD}$!?provid~ ultr�lsy>%��kŒB�),6' !# 9(-id infr 6iia (in��ofJd���:{#to $0$�!!q arAs0$,�EF��p�� $) iL$c�6X=6kBK}e�:%C�q NF� ���2�frame�!i��0��#-�a$AB.�WqY1 �$k_t$-faE=iz=+mN��8d \sigma^{AB}}{rq \S\,�=,�c2s� � 1}{q�I,�Dk!��_1,�"aDB (x_2,(q - k)^2"] AB_c�6Y ={A,B}� ~xofK#uM!!^:* nd $�x_�*re.�����xx_10q# s}}� y},\ x_2Vy}\FFOf cause!�A^��e8 �kI�)) reduc�lA&w  �" frac��=� � %�A(!A!�G1� + G*-��E6� _app��1|}1�G(x9%�i"2Z1� . But�8e�ly�3�1=Fm.�1\�*.��7n ~}S� !� �A��)� usac;F���-7 voidi� ��6� 2�HavANh � �H"�0��$A+B$��tt�,wq be&4y�\F\R_�.�Ee d�I}{dyd^2p�B#p R_ABBWj� ���6�4 �2{N"�M�'�;re6 �* onent)�! &=X::I=�!�z "�2  L�w!<(7Nz&� �i7byJ� �� a� �@&70em��@order. First let�0/ 6C=.� few�b8s�� dire2n;���l�d�� �m��y st�0� uv�f~��+��i� 1x � no� �5&at $q^2=� �2!�  . So� ��e]G ��&WCSB�0��:a�s�*�ularit{�-, /��,vQ�J(k)D=pto��1}{k^C�1�� fL � O_D (bf p}a���X$zA(nEѴ-Bc�11}�B�|is just� off\�6at��big�&Q .B��. *h�E���l���ula tail te|Weq)� � er (� �po�!of#8)-� roo%� BesselY/$�x*1a=&<UGy0B� x_i=(i�j 3}{4})\pi}8!@}�B�r4 e se!g �-�ls 0� $x_{i+1}$FtS_i ="2Z�2� 2x_iB���`f� q�A{�!ӡ"� S.Q� monic6 i. B�Ny� Eck!�� n>o��i},S_0W!�gpolynom@�QI>!\1[Q�eN\�X'"�?cy�'��no�,� nEn e�a�>BI[��[L�,(ial speedup4���d�?�^+ �� 2rMcMahon@e�'d"ext[ v.F x'_i=x_Q�1}{8 A� <1}{384 {x^3_i}};>� A � l���*#&V@a���8�#g+rcRuwAHF�et!�e8�Ho�m&H���@um�" ra� coord�G  A#$��!�g i�8H��2$k���:6J. !w�I(V>)�%�. Deve*+d��%(1MQVenough%`��x�QAqre�-ly�@) en�Ctd8F;*j0�:= 6{)�1�R�����a�"< n E�2����c1�Y]�6B�. we r-eJ�Y"erm��bn�=1-�F{dn*�'y�'dy} = -��'j�'[w&�'-N�']� `_�46��F�}�Jd!�����!�gH_�*�3\1E9 too,6�L 6�?0v?G f:�D, �-W)�-�$3A+��ye$r=�e nE+!excludj�O�ee��*,a 0,x)�ZE��%�Nvanismcon&�.to52�_13 �3uld (d0at&��Q�)(18$|z|>z_{max}$ (i�$� R � ) ��-�!� ��' �*ly00��26� a6h.V'l �9:w. (zz� a}{z-c}-b�� BK"! >n-V� r_0/z)). $0�in]6�:% A:&d6J�asG621�.a ll�\V ycheckB!"4 y: �6 �, �0:K� �_QI��� ��IPA?m�)�R�$ $p{d�$A)fix�GB1_s$. Fo cleus-(��/o�= $Au$%)A�X�u8�_rm�>.U,J�� rx Q[�13Z�N_0(r @!r^26^2�71/r~+�Xilon)/4U�NG_A__M�&�a�nA� $x_0=0.01��th�2R,� @um $Q^2_{0s}=2Gev)�re�O*$� 8 $ (o�NIs� I��6s<0)�ep�$�$0< <1$)%�deuteronE�et��2� �L)�9))�N�re8=W9cc! g �fw ber"K'c� �I!�� 6#5 ��  '6�)',�1����řYy-.h�8set�ocFF &{ I�ixeFg(Can[ !^it?� %"&* �)dq�8�/q )}) exh�C)���uEzre�$ ]�:$ UO: � �k$�0{@1_s}M�6+ a ion:F[ k�1 F�00\�[6�1��yfxt%��02�:�))by DIS �Nt xe��2DIS_fi#O�N=4�s�P��zf���^;<(!�� @B�y�= ain��l!O��al&�SF�-�M�� d%B�S5�BA�e�^ly2�}$!!<� �]xM�` arbi�[I*.�}$,"$q f,"�� v#",�tC�wm2�b*rAFe!�)���j:�a�fit5*%�&! ?�a�e�R%�"� �ZY[: . E;Byv'���&���(g�s� f�_�21}�4O F�log�!h:���!��)J� �q�ii-� gE�&ofBk@ j�R�$Jf!|Z x@ aA�%r�}0l $exp(0.37)$�e�jlsoW< �$d4Ea�:z �'reB���s a� xU��"P $A+p.1F���>�mim�Kly[U�e�fjG!z�`as-�� eV�Jq � �er�,13"� endFcon{mxy�Z::Q�P&d--_�$��#&� �� �%qNn@��Q�8 (dotA��.*%A� (-a%"�  ���-TD)a �p4VpX4 �yn1�RDG��R�e"6�:zE��x�x.xAq1V N� �A�~ $A+d}�"=>�M1H2}.3}"<F�>��6�I&_oM�=�y��Yite un�3Y4�8 �c �d$� PuaGc st�$e2I�A��(})�SM�1O �"B5!�F֓2�JV� ��Z�a�>�y2@�1#1$�33>u6N�f36�2��&v&!5�6�3B ]#g�Lse��{Co V} E�+"�.n� A�rw� ���rNB RD29 by .�XeIde/@RS$" L���Kn?J0Je�ZM q�J"'B�yn��$J�L)( �`b�LeZm�)n�=lrvF��5*�> n� n*+:ce"�n>k �*� de +�^ood] n|n�F#*�7excep�F�.  : \ W ize{ {W~*m~Cign!?^ �5� � ����})#*�z� run�XBhC� ��!Fmodif�#�ges grea� Z��V"break1a�Wl is ��[nQ�D ~�a��&E4�a�z  F�� �<�o�nto-y:����"r�o Iv it!�&'� tes�Y�_B�d� A�i�eAFF� Fe �v{er }y7(� ��%�Ua�@�i�Nef@P!�r�S4/�+tem{It]X"J0BK_b_num_sol} "%�us�GA s y�:�bAr6 �L0�! radi�R$2� ,if�5 5�x�Xz9"E&� �  V�')�orJG�E4if� �9A�f�$N_G$ ��|j�9�nBRU7���/:� .�0hsejpA��fnoL"V N= &%)wu��i-+_untq@����L"�lR�(�ok �g�$H+obeys=�A(Ha�9��#y broken�MKbee.ed.} } �J?]W)X{99} %^�&�[Fz V.~A.~�N.~V.~&W, %``�r�2dd�)or p + A\A  %&7V ,'' B�]P]3 \ 359  \�4) [arXiv:hep-ph/0311099]. %%CITATION = HEP-PH  ;%% 1�{:z{.b�em. J.~W�Z�W](~J.~Frisch, [J.~Shoch3[(J.~P.~BoymoXo,R.~Mermod, P%Q Piro7N,R.~L.~Sumner%IPr"��Of Hadr2}�8L�n&dMM�0At 200-Gev, 3 �&4 '' \\`ZD�L1ZZ310�[75):,$PHRVA,D11,$.,�OY=LEG�O, E.~I\evDnd!( G.~Ryskin� Semi)6�^s�InN2�p�_ �00}, �_83B�$RPLC,100,1�5�( I0m �?~]5uba#1�BI.~� Oper�} expa�~e�`-g ���N�^"�\s^463}, 99�\96>�9509348Z� � �K�X�9yj.�FY%��S�l-x F2&�%�e a��i� �>�zl�gm�� ha: �Nv6!�034008�9B�901281^� �� MuniLb4xu.�:5�.�L S.~ ( A�R.~Pes�ski%U�[�Y�t�w"�&!!�n QC6�v.\qp7�77503Z�401215Z� ��BKPNF 3vcQ� ��X~�GB�Vas�2ve�@ waveF�2_\m��^23.�^>�09177^� �M��s2�:~�Tr.�| �=!�� ['Y �8� b�9}-�M�B� 1035f�R�v�~�����v��PR.A.~F�PU� 6��h742� 55>40102^� !I��6M2��m67]T RmA� Stast� On"ei/!�-"9*��66of3�e�>�030627f� = Ikeda�4zp.6T.~eL�iL=ae^Im:�V*� ;-j�!�6[ 410345:. HZ ��>� &�cU.%�{ crc1.tex $% % % $Id:2 1.2� T0/07/24 09:12:51 spepp�Exp $ % :ffleqn,1ftwoside]Rf{es� } %?mF&�"aL us�U8th LaTeX2.09 % style[.y, � i� %)you w�t�/c-0PostS�> hs2�fgraphi�fB�{lsc�wX65[ I�]{lRng�put� r owD's�,: % �"kfcZ} V {Z}}�\m{def}{DxBE}[�]* ... 2L ttbsNhar'13�(.�fAmS�f�ect s8g$font2 A\VL-.1667em\lower.5ex\h�PM}25emS}}6z al}{<&: be}{�^}2�ga�W6,vrr}{\varrho:Jrh}{\2Id` delt:Ina�T:G om}{\omeg:1ep}�Q*:3vdvar`)6�li�%:7un}[1]{\4A�{#1>8fr}[2]�H\.oial(2}F7a \�*.�M:�frt.w%?({ Fs lf}{�?6�r Ye:dssN61z!Mze>�p!�-:Jv!�var�V2�e%Beqno}6S qu}{\quad:IbibA�� 6Kc� cite:3lr%�ong�a]P6:!6tXtilde66D!DE�:1pta��/ tabb�]& 65e�equiv6ghNha>�m! mbox6.no}{\no�`n>3�Y ��cpypar}:xe�}�"6�k� kapp:pE�V #1}:.�la�l�W:sOa�Oe�.j \beq�w gin{"be2;\e"� >B star>F*FG '.K*>qbeq!�)@B 6J{�% I�2�r\�h Galign>!tba� mb|m.Etit}{i>�tcX7 �NaddbdTeX's �m�� list \{-m �iy�finan���^ re-�end-ed�-��H decl�F�+front m� �le{Pai�_* POde�y��QA�?_ �{AmIsayev\�L<[MCSD]{ Kharkov *s itut��v'Y LTechnology, 61108, 5(, Ukraine}%Q7\t�s{A.I.�dg�� ��Top�K�gra�)APCTP du� �sta&9Seoul.u S. I. Ba|ko�Ewha]�{D2m.�Cejo�Sp�xSci�l�A _ .��� _ WomansD�n�< 120-750, Korea}5jKgp]{v H)L(�0, Kyungpook Nfal2c0Daegu 702-701>c{JoB9�!m� A\Research, 141980, Dubna,so=VJ. Yang� mark)R2�1� J.Y.���.A�5Lby)� F�:� �(KRF- 4-041-D00052).}a�1$&'  % type�060�G�o�@�o} U5,��s, gover $np$�Ain�mr�"e��&$S=1, T=0$ �F#h��(PRC 63�1) 02�j(R)),��h -a5� i��%�x0ga��trua quasi%fclN8�7eCpo�&iQCecrs2|5neu@{s �*��neg=dJJc!d�s  dF��r8of Bose--Einste�"o�o sate (BEChk�3� .��1B�2l9� \vsa�{6mm}%l{I�!�E& The�cF Am BCS�ser�uctivit�6�0-!�I� o΂� a Fd� system,~ eitQ /Lis fd =�he atCr�G9y"�#fS�is �Fi3u&gG . RA�Na�|al�XEN�pha@�= �Es�`}n "Q��,�-nE� CoBE�3(�h�\A�go a(lBEC!�9�at!�./~_ 0{AFRS,BLS}. D��E��2Uhe F� a_g�8t!gna<�kc�QcՆ�y (MottUV>[a� half�!�� b�ng�&at Z\�Wies. H�.�J stud�Ey?B�in �3met�n�!5w�Ouse"�Bs,2�4 Ref.1E IPY}djpA�ˁ���a��nE���%�!!P nel:��beq \De�ik}) &=&&E$1}{V}\sum_�Nk}'}V),�h k}')� D 8}{2E_{k'}}(1-f( ^+) -)),\; � {8} \\ &=O�2{\bT\Bigl�e� (ve_k}{E_k}[ ak^k^-)].r) 0BO n_k,|10}|alj k �2i hl,\; E_k^\pm=E_k\pm\mu_{03}=\�n� F^2_k+ ^2%L k})}4ٗab{11}  a�re $f(E�I��2�p �&�_k$�kA��� le--�&�@, $ �v 3K5eAq"a s�nd8erence �Y' �XJ9s.?�~\p{8}����"���$)w.Eqs71�p!>SAsBtotal��$!�=_p+n Q��� ss $\de +n- _pE6I$ (E9$ )!R�&a�y "�<)��{&!D,nomal ���$$�O%�8 k})=�P}QiPQ�J�I�$ �u!�1s!<�V*9�Rent8�Oth"6*lk<k qeiE�V{m}2�+(1-n_k)R& k.&psi�'�ie#06O.i�2E� e InB4 limi! &�D-Q, $n_k*�UXEqI62} goes ŮiJ%(the Schr\"o��(r���  s�z�BLS,LN��C�c !�M�eigenvalV�sE�l ^P2�$$. Fur0�G&�Mc&F�>[s�� � ?BrD Ace, d"iIin..GSMABreaJ�-��� � Paris NN "P : �2e � r}_1� $ r}_2)=v_0A�8l\{1-\eta\biggl�L aa ��>+ >�S�lvrr_0}:r)^\gaRr\}\dͦuQH7)E49},�/e�. F� �y&�y ya�r�>\6\,\mb{fm}^{-3}$), $v_0,�,\be$��O: ad.P�I� s��sidn�<!hQe�, M�9} mus�g� pl�*M/a�P--�P_��e_c$.F'uti� A*b ��"pA: $�0=0,\,v_0=-530 �MeV}\�R �,3,\,m=m_G,\,�bc=6,$& ��m_G1Y]��>,6 $ at Gogn�>c"vjK}[thb]�e�flush�>3+��s[�~�I=7.2cm,width=14.4cm,trim=26mm 152mm 39mm 69mm, draft=false,clip]{fig1md1s.���.vg3Che:H �0$�!a.�#: (a)~��< e�tem % ure, (b)~%+M�X (F ).}A�>��6%-: D1S��GGΡ`et}�ZP8'I+��Fte "��wF|tU�=s:�ƍ�ai/�[OA 4 # ��v���^�<o_@A �+�<l�i>� a�al=0$'6c�~1(a)� �>e �.Q�*�2ZF 9�.�vP.�+"� ���a��oa�rr_b$ (�ab\[ x3eI10^{-4}i_�D�S.� a���+�Oe(� 12},}Es!�2d Ѣ--l\=�s�u���. Whe�R��!�,!)���pr�HQtA�"-H�� 5I=-�'b/2$, !e_b., 6!!�a ��W7 R,E*akPi��C� Xcqb� s�� flui�I"�"0v$Q! t�Le�4 }I�s (1Is�lYnbFZ0) A�/���@"of�.�*H�whRk5K$"� �)j� � . If A��.e?Qth?e��zse��#N���s "�(��� 2)A"at >� �2T . AtO� ���%}qen o��B�(T!F:SN��ca�~3)=jis"oO,�-$) p$ 2� survS o0ate .5i 1A$T\���r" B�E�]7 Z�  !q�e,a�#�g!�!4ityE} t{� �2}�i�.in f�~u{fig3}"0U�J [tbp��0��8g��48�4��57mm j�2md��EwBn1�.��0R(.L>_9A&-Cse���!�� 5p�`�%!�9� �q~j-� erval"D A�pairsi , shrink�� 9�biofE�K:AY6l8s eSEQ�W�<1$I��e1[��Л�c/$�[ !RQ8��]8�=� ! � �vala��~hnd�5���Z�>fw��a!(7slTo��Bd�p!Qisosp3/3los�� ts e0cH$tro���!o�>!lo�y�,�g urO�<�6Jeh:DS�O)TA  O;'%3$[0p ]$,�l?.;�� $[E-\De\ve,L\ve:w�T B\vezf 3}^29^2��IIbw�8"9~me�2$0}\gg\De$) f � %$2 �$� �ED ? ��R$�NJ  re�o��!�"Dd, until  �Y�} A:RIel �JTpasS1throughec � �" ,ɨpar��windowicipatq� LiAe' ��,)F4! enda�block3Ugoto� at e/2��f:�4}>) � ..% Jgs&�M_3 p n� *}ko&�aR�3 cu� !c fin�vB�. O.�E+at� �2 ��J�&R Bx |$�z6��ly"�, 6�T�|��.RJ�s�F�$:�5k=�*W a&5hp�pF* Qe�n.0$�i.� "' "�;� -B�� m confirme�JA�q�%� .�,�G64}(b)e�r�Z&[ ��U1�&� M�p%0�O�p��H ��� �ءf!�m؜p� \� 39mr 3� Vari<1 &� s� "& �툁.B��91i�(a)&� %[{N�;�M�p�Yl')T)Q��(uppe.t �).��>,�9 �&6=9 } T. AlmK�L. Fril� G. R\"opkh�H.�ulz, � .K!. A551 �/3) �,^� ��@aldo, U. Lombardo%6P Rck,�!. �� C52 Q5:Q� �"@ Akhiezer, A.A. o#, S>�0 Peletminsky �=l., !�"� v. C63 BQ A��'{� .�,� Nozi�^ Schuckg � �C64_64314\�$ E. Garri!"! �n�8( Moya de GuU.d � d�37304.=�� J.F>rg!0M. Giroĩ d D.A! Comp1�Comm.n!%�1) 365- >U BY.��%:r-(aps]{revtexM/ tighten % &#.�-p] int,6;jO.�&?�%+�qtch}{1.4�%b&�"\�"��4W. Zuo$^{1,2,3�Z.H. Li A G.C. Lu} \�%{$^1$&&$ of Modern%�Hics, Chinese Academ�%s!�4Lanzhou 730000AnR.4a&%B�Gradu"SchooldnT Beij  �39R ~R.~3 S3$Ja,N�&��4�%�Y!�date{mbived:"p�Hot�N�MH' E6 of S"� @a Three-body ForcW+n�$�S .x4Brueckner-HartR Fock"��ex��.w a microscK'� �f�<�&({�P�D$�%"� ��of ho*}c 6n�4� KdE~,d�&ڝed�De"� 20of liquid-gas�*�" for B�[al�e�K/ �}� =�prF��#tur�Su���v)�%H� a\ulsENFA=EztĠer�"3#�7acon�TcL�z=.2�v. �"��� �%�r 6� &�"��o %�qa fI x.ratic.�oVY"�"� �T���i��-.* � A"�Q�Ad� Rd"�W.�ussedU�� �d �y�)�afZ�s�<ongY�%- z.� CN�a�seO>�Fs�ive�!� vari"\=) .h�*=Jwof M�hys(%quantw,p��<he %(L"(!�l4 �.� !X&��esB5Tstudi!pDu�o�*�oree7on�SA�d*�B�.X� ��(��! � � )2�r�*�$C�۶�e�< F�>.�( pacs{PACS�bQ�� 21.65.+f, 13.75.Cs, 24.10.Cn, 05.70.Ce��n�qg.�M:�(5:xjmot��.(��eavy %J%��Qto �d!X!h�i6e�y�u;Rleme�(>(+]rk G!�MlI���� (EOS�)"o BPatJ� pl��aB«in �AT dyna V. .Z�alLterG���aĩi.T&���u;'�(BAO1} (Fw�.ym�Z ��8�}&����Eeo*d�ow, b��cx#,1P( ilibrium,��-�2 )�on emi.�7t���G�-�� A�avp�rM�-��teH!R!bQ+EOS22�i0��.�R:�I(�u�!�L�� ense])BVHlsX�rM��  �/oM� e!- �\n!u�W��.3D nova�Dlo�d)�)�#mal�["Ԝ�rtarM# PRAKe2��5�-[J]EOS!y>� Qru��� akQi$��9։$��rmo �2��ps"g� 3 newborn�a�r (!�to.� ~���qLstEh�az/-II�%NA� apseiD-!M���� g�)p igni[O! �_B��.�� B�6]Q�w�| �d � � _tin�w�:-} mode�tuch�.?0v�hR� ) LATT�\��27me��J� ory (RMT) 9 WALE,MULLS!�KVō Waals n A6!��on-  (NN)ka���0-~�xv���8�is g �%"hu an� �BERT}� `�ly,��"�?ort9� devoAto esZ%�l�m0�2�YJPnd � � "5 phenJa �PKUPE,SATP,JAQA1,BALD1 (2,HAAR,HUB}s�� ��-�3 ed��'in� ^�� playi0� 6��E�&� "�A��.� $T_C&<�p0.) ar׋ʜ��a��^ng�Em 8MeV��20MeV�ta A�B�"< �*b ��a� ���$$15-20$MeV)�=�}� !�o�oi�IJ��.!�NN SI�?Ne RMTai�fh rit%�*�� about $14�i�3>�Y�g!:Dirac-"� ( DB )2�as~$\sim8j �/) A�'a� 1!��&#A� ��6� basi�+:aF�zq� �*v*en� 6n BOMB �Y ��m.K56�( FTBHF=�!���r���* two*�. A4+ll ;eA�6�sa necess��0�| AZ!�empirE&$*:8c��b�� B.*� ,&ach+',RAN,LEJ1,ZUO��<2,MAC}. Two kind�\& "ce ( TB!8�A����ú!&bs%q !malismIeN�}��|4� emi-�E�9%*TBF APUDL}��jR(or fewV(+">% fitt-� 5� =�" � a�6g�ꂔ%���: � BALD��$ �2�!j�d���ex$-gXupj �mi ,virtual exci#�%��^on-� � 2"  "и �6� �o�/pF�,�aim�o� g!ijQ� b�!.�.�!�%jNDvq�I&d � ^. Sp���6en!zEE�p�ŭ�I%!� TBF +&�t!�te&�&&U ��� � �=ic NN %��}'N1>.�4Argonne $V_{18� $A )&cILWIRI}. ��6Ond:;AR\ not '�*�bU5 ѵ2t � j7�M e�i�&4 ( s.p. ) =�.%6e!�"& 2"3+E�:.f5ppA�A�organ�8a�$yY . We&��6bew�ef� �U in S� II)�"c'a>ul�*rs�iisc 6AI.#QV a�4m�*-RQ*|Vis;2�"}:*EAl} a�e ͒&ɑr��Qa+f �2� Z��3"� GqoQ5�S!�ֱI$SF$)"�Qu*�4� �4rho(5p}{"n; Xu� $T$. A4%.P rp&�!�QJ�6 �_aM% H$k_F^\tau =[3\pi ^2~ _]^{1/�6w�$ =p $�� n&�09_n � 12$ $(P� ) G5 (p ( 92�8\�(� � ��)9q��r�����*���*! ��(Bethe-Golds� (BBG)$� ���1�& � M-b2I�4��� ����o� 2QQ�FB1}e5!�fe�ing, we !� ai�  �ew ��_n���uE��(mlBBG"* �c5����rix $G �ch� isf[���q��g>V�F�x1(e:ftbg} G_{EV, ^{\p�^ }}(E24ta, T, eI( )=v+v\sum\�6,s_{k_1k_2}% N7\mid \�5 le Q^e\la��/: }{% k-e 8}(k_1)'2)}V� �,�5 � N)31"<�4v=v_2+V_3^{\rm�͇��ebt�0$ a;49�� UP�m 2HAF���V� �$�����e"+A�ce $v_2e���:�w�.���Eq.�Ge:{F )(se= low: J Pauli �(Y$-�B[!)�pɐ�:t& B4one�n�q} pF�=bAZ, k_2,A�`ta,T)=~=��#q T )]i:q4AzI+ T�$YwANE�'2xq9C�e��R6O��m�Tʬ$eft[1+\exp2��e�)-\mu }T�')  ]^{-�5k�+-%͟=\m ( �TB���% "K i6�A%r q5�x�-�x&�8������qT)Jt&�  & �$"��� i�{� J�-�*kly�i��� F��ZderNrh���j 1V�7_kb�@& \F��c9;!� ֒�=fA`%` byj�spe} uI>iv EzQ�A{� {\hbar ^2^=2m}+ UIl (k, !��^�10b Ad���or��Yk.�-"�YsY�is��l�ro��on-shelA�ti-3��ma�=@na��U spu}���"�1)< E%�[�ZL�B\vec k f>)( g� !3�w�l# �r�I��\�, ��)+ /}.y))W h_A�-!J ��u��e���#��inu�c( � JEUK}��&E�5��&xhaq,B BK&�:!]���t� ch faster:>�&� holeKX 6`׉� pe�}on �:7. t $T�tha �V1 �PSON;���# ��B�� 6"ws U�h��&�fel��a o) (  um. j(��F�� �Ne�on�e��!r�-&�urrF -Pv}kĐ�x�dy-dia�Mm�#%(i�01, }Hn �&� U�Kr�Lor�v��-pi �.� LS� *C y �ideredI�;he"� ain� !���h 0x&�p*�16> )�-l�!J^] �P�%Eo.}�Iw�  assoc=�iRB*aAAs*�*�3qu7bI� chir{�i%y^8 �2�ri����-�Y G�P��J)-�p$ �����=$A;�wl &� ;�'ir q� k<7On< �M gma$ ��$*��Y$54{ 2�=A�2ʑw�-�%��isf$���.u?"� 2ie�on](!�u��� (OBEP)�I�.$�� �!a��.B  Y;a3aq�|��%$ese�m �s),=��<.H� �mпA : �m�d�%�� 9Ahb;+�'�$� ''de�ed��p��m� �� A��x�z�!Z>ref�{oXSHc�䁊,"U!RA�< 20�>�"�>'cݐ7W�� ) :� 3-�yai��6�=�Hp%"�=m��ite.af� � e&�� � JEUK� 2l \?.�%RS�.'�8trC abov�#�ve.� e�ls�elf*7٤"�F� !��&�l���0ol��/^�� !-rߙ/L=�9�ť"��|~ �n builds��@M/.:��ʁ��0ni0!�ad�.Gb� r� ,s ags*e�p<-R��,)n�o2� ��achy1 �wwor��o�i!p %�it!�9q�vJat ��� ��2�����inI[ aq&��!c��U��1BTbC89s ef-s.&"v A� �>� du"+� uKec7 !Q�1a��0)� &M'o��pronounc�tm�6X)���ly �>\��2� �8;J:co��>�&& $f��pAF!�uNL���9�.�iovmewAM to �=� Skyrm]rc�M��b � ��_alA4 to ay�-1t-�>�is &s �*�.� vi�8�.� �&2}.������e �R;��,AyeX),��e'�)>� . o geI0 $G$-~a$ "/1A,2!��, a�g�al, f%b�i��i�/h4�� ya�A8a`�Qgy $EHQ� )=3Vin6_ T)+E_{pot .)$� �3uA��.vkin�+~i*��` .�i=�  � >?V��c!h��T&� ) ="�a�F�"62��.q k,&�}Z^*.=Z,� �X�2* �"+�d,e(!^ N f� )8��opy $S$Q�%՛2�~a�*inA�c�Uj8of#5si&#�{""� :s�)$�7c�fs)�eZ����S Q�6Nt�dar� &"C.o�-.J� F=E-TS>qU<� } P=i'�eft�S\�w ial E� (}� )_{T �B�B��� :�&[1,TBF���*�/�"�0�M*�46�*>E1at"�/8 B�5B��� &�#&��ReW$ nd DI$`} � �%�iN�J � I��K2Czis�m�U7+uE)ūEs��'.�@4,8,10,12,14,16o," bott�� top.y)L!���iL;das"�XJ*�&�:%+&t���C^� plu� � �Ap{^3,� i��C � & J!r v8vn&� �-��"P%�0�3.0 H�; �HA�M_��9�^a��"ǡt�}"-%.� �a&l� �o�`!�"��ci�2\rovt�+"� d,#u�; �MEK B&M$��t;rF"�+iS (a par� D 4oM( 6().� Hdj.U�Uj�7A�h%s� a|� �=� %%adicaF!j�� a tyNm1AZ�-?�6�#<�%�� 6�.1P���JM2� :! :�"L,"� NN inte�yractions\cite{BALD3}, which indicates that the infinite nuclear matter can undergo a liquid-gas phase transition. Without OTBF,  pcritical temperature $T_C$ of"lTN� is approximately $16$MeV. Inclusion A TBF reduc�es .sto ab�$13H - s smaller! n�values�=15-200from �hSkryme-Hartree-Fock calcula=q(JAQA1}. The� � �12�$is readily)u(stood since|��effect becomes more pronounced as increasing density and =!F .�i)�i>\ $size ys and%(�Coulomb force may lead to a considerable � of%W$�@discussed in Ref.I�!92-9present)� A6\simeq-�is compa f with�%�h .4!�0 predicted by(re!�$vistic mea!el�ory �LMULL} but it is larg.,0ones obtainedE$[XDirac-Brueckner ( DB ) I� ach,�8�9�6 HAAR}!m.�I�218HUB}. One possi)q ason!�@ this discrepancy!5A�@difference betweeI�2)� inE|DB�) BROW�Q -m�-�, microscopicE�as^� ZUO1}. %��0 In Fig.3! reporA!|proton or neutron s.p. potential! symmetric>((at a fixed qt\$\rho =0.16$fm$^{-3}$ fo!�ree5�M�s%<2&=0, 10$A $2%�. A2�1i�:�.'D repulsive, result�#4in an enhancemao1��part ofE$energy per)onBn66at�:�. IeDalso sIra�~ curv�arounIRFermi mo�um� ��smoothAOi��2l This!��gre � withƍ �Fq�by us!only p��two-body!�ce2L%���ttribuEEoEH0thermal excit� B�surfaceZ* Due�JA�isospinmb)�M���V�s.c!^��ord��oq�%'�ps o�"�depend�AQ0i@�kZ�,�a}4!:dep���=!+U $k=asauun�Y �yA�ameter�R�� $T=�U!�figurqM olid(dashedE�ea�A �iKs .I adope^�4$AV_{18}$ plus!Y!�Aj $Qt�ci� pectivelyaC!;c� �B ��iOB�oi)�.��s  n addiaal��(�Cbaj�5�2u �)!*wholeU+9�Prange $0\le\beta\le1$��similarQ�zero-}� cas-� �6� .� a�a%3� l!e�on��&= � goa�%Wy,($� =0$)�Q�1$) m, . Such a���-$ stems mai���!�� con�|!�m�r��Xlet $SD$ tensor channel!ch52s�����)]� weakm@ �s6qu�exces�OMB� A� e �6�� � ��A�2� shifI� �e3 � 6A� higher  sa�I�A<s��A�oute�>s �n�b�� Y�� ��IB$a�0almost linear!O! same m�Z�� sup�s.[ all� LanI sump!X� LANEɯ@extends its valid Ͷ!%AE� }|ƕ >�� >� heavy-A�collis��M-r��i, hot arm��A#u%9�could beame��!�re�H$on dynamicSex��I�$be very sei iv�� �=MJ\�ky[ E�|,prompt explo� model� a type-IIAernova2Mh -caphproa� dri��Ust�elast g%�![aps�8er�8m{f�R� s J 0.33�:.�of�ew�yMeV!b achedrefore, z$understand���� coolme��isma �� $tar requirinformz 0^:dajJ wCE"accurac PETH,LATT� @ ~5a�2��� �J( i "�JF nd�B, $E_A(U ,Œ ,T)-6=0,T)$,A�susM$^2$ at $T=B A� tw� tM�ie3rho� %� 0.32"� ~ show��nJ�o&� B�� FeD fulfills a quadra�.�n}�J[�A�ole5ayq(>s )�oE6{� for ��.��K��$,HUBE,BORD�above9n-law `origin����empir massm mula����e,� s� 2� !�&� ��I� k�^2� �be���! A�esa q �A �(Be�� s1�t term,o*m b�ng ��ed Wig7MZhas b0f��$N=Z$ ��)�ZEL1�6B��rin �I�manifest�elfAa spikg��ri� sobaA�!� A� bola)�6s��� a��� ��l��� lite"L DEAN}qvg!AK�e�tq�6{MvtesYv�.-��, ($np$) pair!|cor�o� nd!1� stA~f M\Aa�?m}%��t-� SATU�)J.�(, we do not� A? !~flu._ q� .�. S!�.% goA�o vanish�� rapidly!�so�W;: &! !�� devi9Z�&I{SEDR}�A0c� ��67�.w shalla�apprecia��Q� coldb�, i�RB4o slightly low)V ADg6� �^b|a a!-�s treataD(BCS gap equ�~1B BHF M�L(  "B�s defT$as \begin{A} E_{\rm6} �T) = \�0{1}{2}\left[ \�ial^26/ ,T)}fta^2}\r!6]_{�e=0} \end~*�simple V��Fr EtyI*�{  8��(quivalentlyu@e�A�Z� D.�of p��!� {B�, i.e.,!!B� sym}5�\,=\, 6d=1!�->�.>Y To�i2�*g �5 Z the !� pa�ofl6�bsho�( � y2Z)�Rq$iw6��!N��6�\1�dec�e>Q`%�RH it remai�� mon�ic * *� y.N��a�u1 �pa �!c�a�1}I�N`6�en*�Z n:m1z res��j vari�G5Y, (i� !"� o i� For a giv�.7a*>�*��N >�atv-\9 as Ad h�E6� ~6 w"V r���r�� 2C%�L&2@( �=e� nd !Hou�~w ( .�%. lott� I� :�� >�/<%�� �>Q riA�m �teeply%�-1�m��spo� 6"wion. B- summary�kN  brief=�6����� ed� �` )� 8 $m_{\tau}^{*}$a,�V($=Ŧn}$) or z p}��Ke 1}Fo��m_[s(k)}m= km��({de% "{dk�� )^{-X6�I�$ 2 (k)�!3  �s�URdescribm� nonlocal �e��)ean fp�mak 85les�t|v� ab on travel!A�.>0��7 i��D � c�$m!T)�M�B a���qy[2")MX6<��.�$T=0$,$>�8 �$a�&�e��}"�sG(GRANG,HASS}��&`e� Z`1 6>! *M cha!� eriz�(a wide bumpj�d"� ��AVbabil��nA(icle-�U? -by ;i-0JEUK}. Howeve"Q.bi!esɼpeak � m^*$U fl�-�e&)�A�2, N %�s�Hs%�d2k%� previous .� �s"$�v��6k$OMB1,LEJ2,�#�� iirect�[�t��‘�e�"�B� 1�� o�P" �&�~8U displa��&P ���. 5a��l�ŘirA���.�a $k_F^�6L �.A&"�� a.�*��2|"V�I �@%�5�I�~�t ^�g �N�he��1��c� ~F�A�lfq ˭�F�^*_n$Cq ^-�A� _p$ Z� 1E���)ڡWf� Dn-�up$�a�e&��"�  ")�&��,scissor-shap!�ehaviora^�#a8A0$�a;2}") unBgn$!�!l!��.;. \seU{SoE�Co%}�.�hav�tro�&� >  inmFT�$] investigaA}�EOS�|�N� FH. B� Ef�<5 fiEi� B� �~�& ve9�E"onq es *S�on� )<7 eque���-"n!]bW ��Y  st���!r~!A�R��fhe:e . �(�>/!C��ed�of :b#exhibi��� Van ]!(Waals struc�, >y!*h�a.)ph:j) 3�RI(2 heBF3 n�)%�oughly \)a�&6eR J 2�B/Y lead�a $b)"�' � R�/(V�)/�':�)� non-� �'qP��nB7'v& >�',method. Our5� 7 ���&�law���y\ ! :vr���� J�%�ofa�ite.�!~�$4of interest, sit�(�i�Z�hot�9Fe�� �� *�(C limi�"ͺoff�xJz�e�""=y}.r�BB�&A��alJ�'�"!kJ�aTBF. Atri*�'�~B~2J>.� �"�a� TBF �sy�!Ƃy !_&C ��5P��:����? �?t R����"v". h2� *V ��Z��* )�:� �p/ J �n< Y&K�As exl ed%�:_"#���veF�- �:�B e�.� &�(&T %U] .,6P1 6�Y7��% ��2qMaA퉫 $. B�%B��+�FL �"�h�%R,5�� R E�!� � E!V)��gQi��bF�>L$abl�fnesR{Dof�� "e6� q�6�y�R�.��'�IayEt im}# ant �E1!� �&� �=I� d;" evolusu�!!�!9�"$��)H*� !C"� $Acknowledg�}P work�-$� _x�K 4 e In?"�Project1� Chin�Academy�Sci�Ds ( KJCX2-SW-N02 )i]�Major State Basic Research Developm�Progra�! e8a ( G2000077400NA@�R1 O �!Funda�al -{Ministr.�[ Technolog ��$2002CCB002 ��N%al ural1 Ff�C1023503�-175082 )O 4newpage \base� (skip 0.28in[re�/s�G lem{BAO1} B.~A.~Li, C.~M.~Ko,�\W.~Bauer, {\it Int. J. M��Phys.} {\bf E7}, 147 (1998); M.~B.~Tsang,FdA.~Friedman, C.~K.~Gelbke,G.~Lyn�0G.~Verde H.~Xu,| o$~Rev.~Lettz886}, 5023 (2001%�PRAK}�LPrakash, I.~Bombaci,2P.~J.~E�%, J% Lattimer,��R.~Kn�n � � ~Rep�280!% 7); �A.~Bethe 4�!<~>-<62}, 80 :0:J%�Pons, Seddy,M.�:�%� 5Mirp4 s, %7 Atrop!�~Jq 513}, 780�9r( K.~StrobelESohaab%$K.~WeigEAF�Z}lbf 35!49I Y G.~F.~Mar�+helloa0A.~Z.~VasconcsmDiq� nAr!�B6E1/8)�22�K%1}!M.5�%$D.AkRav�0 ll, e�%% J,-� 223,} 314!%78!% D.~QQmbB$a7$J.~Pethick)�Bm%? Nucl6A36%759,l 81);:�e2._>[��Bk e�A43Am646 k5);u�Dy�^B 618}, 498�A�� Catalano,!�Giracusa� U.~Lavrdom J68!� 390cJ� WALE%�$D.~Walecka JAnn6O8A�49eO74!�ReOFre� �e�2JB7�69�772SM�5N��l�0 ning L� I?$ A469}, 60ee 87);� M\"u8��B.�Serot H ��&-�C5!� 2072�X52�BERT}!pBerts.nd��Siemens,IrV .4B12�6�832VKUPE}�� A.~K\"upp��G�gmann%�( E.~R.~HilfuCnn. j) 8E'5i?42d@SATP} L.~Satpathye�MishrI1!�Nayak^�)�pC3!^162!�892_J9H� Jaqa�s �pMekjia �L.~Zama�.(%~ e27,} 278!~ 83);�K.~Su�� D.~Y��� (T.~T.~S.~KuQ��M C35�#539(1A�Ѭ�1}��Bala(G.:J2FI.�� �� S.~Ferrei!FB� �A5e 589c!::S!:2}A�R.�;h�6:9,} 206� 86�Hz8B.~?3Ha�.n%�MalflieFm���5A�123 [6); ��.�14A#20 (72m�8�HubA�FA�be�$���\vy��348E�982]1}2k6�.�6&Q42,} 165%�6D�} a�G�X\'eE�LejeuneiPartzolffi�J�thiot:svq�C40s04��6XLEJ1}aIf.�� W.~Z:�x)�B47!845��026�9 B� �BgN���Q�706��18o6$ao2.o. !��Burgim� &6�iU32��27I 6j MAC}�7MachleidQ� Adv. �I^ K19!�8��6PUDL}a7S.~Pud� Hr, V.~R.Pandharipan: J.~Carlso�� R� W(�7Y�-� �74!2 396 �q;B�բp$ S.~C.~Pie�8!Iv~ xCi�720y6DWIRI} >IV� J� oksI�0R.~Schiavillab�5���:T6(] �2���~.+44)��+91); q >X�M  02460i�6 J�!�� eukena�.1!wCu haux.\ � i�\ 25Cz 3�`762� SONG�"Q.~So�� Z��n�Ib�� 15R;�6cP.��^�Cugnon(J45 qS6��3^�.RB�n���iT B215Ai�:,�>(G.~E.~BrownWei�8G}ymi!�SpethM�Comm. � Part:F�f3 p6K�5A. A8E�F8�676A66;�2}A`.� GaF� 6�T 1133e�6L� E�*� BM .�A�$P.~Haensel-Z�6��27Z6e1} J�I^G iBB3%i48i�! %�MC128�:��1!�H�rdb M%Karr�^X!�7�:�Z�0� Zeld�"CHandboov!�&8Properg(}, �$D.~Poenaru%oWa�ein�op(Glarendon Press, Oxford, 1996]D^0L J.~D�B!�(M. Hjorth-J!�M V97. 6� 2003)A&�@�.E 0�Sat�2sR.~Wy�%)�2�39�"A���� ?,�,a� Gary� Mizutor�0$Nazarewicz.n6g40!�10�o:��/a�Sedraki0=ndF,bac602�6X Y+2}6KH.-�8chulzjͯbiL 92I�6�b12b%x R Eq�/of � of A-ic Q�MNj-%�I'4%�9n H�9Ion Co�at In�3ed;1< Energies,} Eds.2 �%�!W$r\"od� (N�8{, Hunst= New York,�1) p.35.o� G}��� eE%͒%y� k�6�A47A�3� 86�b'�W��ssaP�uck.����u17!�31Eo��/yB} .:$ #}[tbp] \�9ion{ DiaTs!��mi:yE�@�D[+N6"�$!�, taken(�G,[15]} \labely>* �"� >���GCas Nv�Ug"�0t six|' �*�&.)0,8,10,12,14,1J �� bott�I " top.c�%a��%3-�i$&�'DZv-Fk�$6�%, �.i�A.C2O2-3zCM�DB;� gle-�icl�G�3��Ffm�F �6�*=�&�0ay�H_'>Ph4� �#ed..3�P�%�"iZ7, &D ve;I%*s3 E�$DJ�+ "q(.M�'�+��bL :�'61)[eQ�oAJmJ> . } y�4�1�j2�"�D<*7&C< ^2$�*>%�eP;4q \beta \leq 1)F"�4*Y<%;aul%re&�$N3� �5��Lefy1: Sf5�#>1F"�&for tE�"�-.��5�b��8)" Righ�Deu%nu4 � A !gF�luded (��Re .9qQ (�� *�J}��:�F.�6�Z j�so>�Y#��$&[P�$6d5}2�).�7��J26V!�y#ݟ" %.)"n'by&�-a���3$'2�3sx3nd<S,�(>�@�*ce:�3s )68B�1 docu } ʜ\lclass[aps,12pt]{revtex4} %\tA�en  %:9 ]{ar�c}r�C8 \renewcommand{&�$tretch}{1.a�4textwidth=15cmyexthe�=17cm����draft \author{W. Zuo$^{1,2,3}$\footnote{CM4d> $: InstitutN!er"� ,� eseJ� \, P.O.Box 31, Lanzhou 73� 8�=�el: 0086-931-4969318; E-mail: zuowei@impcas.ac.cn}, Z.H. Li �}$3$, U. �$^{4}$!ad� \affil7{$^1$ ��s, >� P.R.% a\\ $��Gradu�!SchooyD� V-s, Beijt$100039!> >SJ� 5 a&�!9gUni�ityN��� ��4$ INFN-LNS, Via Santa Sofia 44, I-95123 $nia, Italy!Z\date{received:} \title{Ev$L T�� 9� ac+ V1P�+TrL f Hot &: L ��: &� absO)}�+p"�%�Vb2'B�+*4U in�$�F�)7'2' &�$edi�?frame>$B#F& "�R6U~+ "E-toѥ�6 #F.� �~)iQT. A~A-&'*observ�$!@*(iso�Os (of e-� )ef��%R�-]*�VpA*U-(R�,-P2=� �y =..� )�& -to-� #Eo@diJU. �9T'6�b!}�Vbodq2;��&�( cont�P�/? �x?�s�%a��-Fp�@�/R��!;m�G8 inst�@reg�9At@S.�jd> A1��f�)e-R=-<���A spinKy.�G�D,�'turns  /t1Pdo}=�B�i�6%0F� �(g�\(lly shrinkse���F<?1=. WA�v�A�Ved ouT5\ "B �;��e!Dore�Y2s.M=!b/y�u�a�"aVexplan�&; eE�eVb*SV"� _R �ed �W!�*(B�/�|u5� !7ÙKN AF..0 �*�W0aP�-$n. \\[2mm]K�PACS numbers:} 21.65.+f, 13.75.Cs, 24.10.Cn, 05.70.Fh���\make�b %*�l4I?4��)d�Rmi-k�D�1ofu�MZ>�.J ,uL!�eUj�XM, gf*Y)sub*� q�%ics. q?lo�Gim�@"�/~-e>,*::3n�U {�{on-  (NN) iE�, "&L �Gke��o �3vF3 low-�?nd'5 rate.6�=b�#:1983}"6�3�a phen�o� gre� nd��G �rHյor9'in�@ ous =s, su<$s mel�/boi�<in���!edMs�matomic *]ter �@schmidt:2001,gobe },�7a +@%u�Glopez 1 upta �:����Dquark-gluon plasma��7� �O /-eN�O!���M �matsui!k6}. In > >>t EZNsiU�5Q�F �2b-�7Adur�Iexp�  Zt�+M���V>.�9.oLNn>Z�ѽ�� !�iA�� olved\�_bonche! 4,m�&:1995}."oK2JU`!%�arq��-�� ��(EOS)a{r- play.B1Zs��ial r�Un:�OmancI�*��qa ��&�7"/�r/.B/mp*/���Q� l�ItA[�P�7e-.:Q !��P)npr�,!c7}Q B BA_l�sir�to���:!�a2� basiIYAZ6�f�R�E�a provn?a�r�point�i1�!NuumYstockAK2,fuchs �3BK 3baron3Ar Wit, �E��theP�< ls s��a1�k/A B�Skyrm�;ce�)�j(y3,l�-5}Q'`EH�7 m��5 ory (RMT) O.9i&02DN�Mսstudie��ly. Al th &H �a "� a6�".3!� "rc^!�9R1 $T_c$��n�*� o be m�t=14�Sto 20 { ��ed;0 �$NN�ha�s. Bas� n1UlRa:$2u�L���has�5] o� by�Fii�OwI!�A�� al � )�wG%A+8}\T>v&� 6�(BHF)"� Ob-c��91,zuoa29��F *� (DB)"Bbalonso�83ms2004}. �B):Ho�b &/?.C1�r��b rare� � �f�1!$k%!O>F .�uY�� ^�!��E@=�e 3d�0R Argonne $&]4}$" :Cb*d lo�Uf� R<"�i�V 17.5E� clos"�W� 9j.�2~ . Om� ntr� iA:�E-}haa��7}e� !NgDB2f�t=Z�9letl9)6�of:mlike �72�� usa�1F �b;&A�5�is unusu��eY �:DB*$A�S well un�W�f�(de� s dep(��@�/5�;E�c� {I�h�+��)A�ZF?��9�)�.�,�eGY�Q.� Es as $�e 1�$:D�4},)�6�vN !<��e �Fq>Q��a[��ini^se�D-R0y �ParisyLU>d%�58n,�PaB#2Y" &[ QD deci� �repC�B!qem�V s� ��:*NA?-R�H�[ir� "��Yx$��2�*�.6 DB2�I}��8 IM�pa8+raimA/toѲ�*Wb��F� BH=�J!g. >� (TBF)!,�0"roFA me+hex�; curra��L) g.�,9}}�T�s)mJ;":���>V.Uan?=�2in�:icubits&zc�+v!y�?2� LI9�C�dE.E�1�u���2��c($�c) p_!)&e95}�� e�eE<lre � �7 � pAQAH�7 =follow�!Inext 'zI� a�N�e crip�1E.� 1es q nume�Z��i�-nd6%S-pIII. F�Za�F���F+.IV�2`2` %%% "�#"f M_s!sub-{T&$$*nZ�ive.�F�lv��j=.wA�QI�1W2n is B� e�-B�1�~I{.�� a �A onen-��K$L&_iO\ref{fig� �%�&$ .g|Cur &�>�� pi$, :# \sigma J\omegr �Y�map1�Y!�%B�z!!Um�`.�U�wo-���p�jA� NNik "um-modif� he�� virt�&�ib D� son#k�.�( assoc="]k �!ar�Z"� coup��`d�ch<QD�x[2�ris�V���-� �Vfi���J)dI��%. � �> �-ar)�Q� airs)���AAX��a�f+E�i�al\ !jep"� �w gma$ �7B %R"5 Y$54�& accor�toE�J/�is ~Lcheck%��isfac;,ly"����2p%��on�so}��5 (OBEP)I�i�&cE��Q^�N%��Isi�YUFPK�B ��b �s,=�C�� �n!.mee�O >�[M�mz��� 9Ab&^ �� B����,�k= A�EdetaiSIRT.� ���! �x%t��� f�A}$ RefsJ �� �JRf )vA�2�U�y"y� .Za�%��Ka�:] ��59.� via a suiaverage)�V*!��third�bde}RA: freedomIj��,l�,�tZByd �RAT dard sche�h:7,V%A�%{J!4�K.�"! t� .A�c3Reff}(T)$m�u�g $r$-space*�\n> y}4(e:tbf} C(*8 \vec r_1^{\ \p�a}2| V.| (T)| <1 \ le &=& \�jstyle &�^4�-\rm Tr} \sum_{k_n} f(k_n,de"�e \�{-d�2 �3 @d �$}\phi^*_n( �d) (1-\eta(r_{13}', T ))\no� � & \� s & 2�.A2 A)) W_3o.J �.I1,.�|( r_.I �) \\ �&� phi_n(r_3>�, �:� ,veQ�XA�u#��BS �b �eg%_:�J"E $!i (ryg gde�w $v�,"z9��j2�`.b = !$ (r) - \ps z�T�i$��c'd w6 ��!A e mo�E�wo��as �!edium�}$�(r&/Zh"}'un�4urb� e. AV�!ojustifMI-uUg�� ����<��}. #w�4������it���` $W_v')he"�m one"� in��W6��1> MN)����in.�&� *F (V�Y*�U�O�Pa�rm �JՋ* � ��s��an� licijXh �JENy &�Yc l ectsjaqIK%%2F-��*i �M�6bA�r�"�zt-.Q�*s Eq.(� ��)�2� ��$2��t}q� �MHy&m $f(k6�� A �uk �&�%� y|trong� =r� t. W��l�s��s{M�M�! .r�+� .^FiyR*e&�6AA�}ach�``� �� ...9*f d� ECbZ ify  b/rmojal�,r��'{ e tocL �L�y"!�y&� r2 =5e_n-  _p)/Y@] $T"ut�`.�"=!�H�I��]a )��'6�[2� ies �_n=(1+�1)�/Fnnd p=cb�1by�[�`$ =[3\pi ^2< _]^{1/3}$�x$=p$�" n$�"�%-�K-Goldst� (BBG&���=1k&�!j'i}!��6�R� �zsNtoJxVJ� R4&;��Hwe "�^ew �m��P. e#5 i�/BBG&:Z͹51& $G$Zrix�rsa��$��q_�_FoG)"1"���:$>�i"� ftbg} G#c ,%�^{�  }5h  T, -)=v+v2 \l\Vs9 1k_2}% �b\mid k� Qbe$k_1,k_2)\l 8C }{% t -\epsilon H}7):'2)}V� �,5� \*� f;� � v=v_2+Fz-�:�a�&Q $U!�4>� 2���&�&�is��&b�4M� v_�"�2�*�7�%"� .�JliJbyB�. S�X�:Sr*��Y���acB]$)-�u eval�0d>l*�5BGu ��t)pu�"��o�,In.�e/S� le��`3 (�a)-� �"m$U�eJ (k)\l >�qYT)=\h�@0^2k^2/(2m)+ UC, ��Y�)�!n2� ,z�MEinu$choic� j�D:1976}!x.�]u$����)$!'� t� an **al ua $T\ne �_&Q , 88{  i�p>%sy�$fas�Jconverg !�d��(>�  [�*.o. song�!&S!�q�e*b[?EA`on-shc.��~> spp}=�:�Hfra,o�AX��}} �hvec k f�$( g��:k# �|�E�J�Y��:�)+U�:��))e v�)_Ansub'pt $A$� oAsA �-�"z��ma�b el%� .�  Pauli �Cato���/ tozheF^oF9��N�pq} � �5z) k_2)�ot(q=[1-f�8_1�e )]%����I+ T)]B�of!F6 appl�oo�(�_��-�* Cf1�^ �[dXibu���E0�ex�s s%g2r5 %M�k}p[1+\exp �kU�ac(k) -\mu }T\*n) ]�kY�-��$7= ��)���a��r )��>ymW{ 6L~[�]f7��qt k_1= 2)&�P &+ 2�",EZ*�_!{ "Il-|H 4s,A��E.�!�tB)�=6 $~{q} P}&� a9fF$AQ'V6w q�de�2b alyt�1�/"�n�$rpJ- at tFX1999,*�+ }. W� as �i � g� i2( Az) �b)���8"-�`@H+��&� � �$�.>%%pa�&!Fn�aR�4d .Tm�4 Gauss-Legendr-thod. �/ "���>+ g �"F�$��|(% a5ڍ1 {| �1"��dG��g!�'l�` `��� is�s by��>� x} Eu�&=&�� �� ��l T)��{*� }{2m} +� 12>� u �� }} k,&� }ZW� .=*w 6� "� \\*�"�.� �. B �,L (* �� \ *� ��-�s)7= ]\ln�h2!_]\UDl�@K q$F�y�aA&v#X"A �4pd$on $F=E-TS��!}�ure $P]the�%�2 .�be��" a � ��a�`�� 6� P =P  ^2 � K F}"~ >w_{T-O}YJ� A>~$I.v4�t.eri�&>>!7<>��be�aEforwar��Us�l s $$ ^�^2B�"�~.� )RP� >0 .�� se��$<5-$s� ef{e"���H� )� O 4J" (J]"Lq$ (aq�5*��WAaAzn�a�� ���#J5TNvedJ� ��g�iF�o gl%$"�. Hereaf�w��)��g$A�R�)I�$5. �/a�Z �#f),����< pe�f sI%f>��ql$s/c=.E dP}{d\var�uM 2�Fzc$���)��la- $.J$Isp��� ��L;ynG s#C in Tab.~1�  s;xal 5D~I� tY1� Dz�A�de9d��${}BHF} (J. +$Ax)�!;v� with� �nbyN>$). %@��fig2}-A8%L�NxN� %B� he*�N>�.^!s��� �7o�]b5�I^��%hcausalzcon�� $s/c<1w) � leva"^N�)BDBe�?a cer<,   "�(�3 0.14*�{n O :�! 5�Nmȗ*�[1!::��$"anima �ry�����.ѴtA~}[ht]$5er}&�SS6�t�^�2�% +m/:9�, �A=/"�Pend��� (tabular}{|c: } \h&- : ({a,fm}�R)$& ~!�5 ~ & 20 ~ 5 33445 ~\\hJ� )$ & 0.01 81520  935� JJq�&07162433425 s59P- %O11 5N!jtE �M� &L1Nu� -m2F!�DCHD+޼!���4F� �;i�Do&����l f� Y�K.�O$ ~�0.3, 0.58$�\e�o:�� J;ur�o&J (:�&to�S:mVMeV*�mVptop�D&�"�Ra=%e ���"O$,��& F�5{�% se� %or�h��?H!� e�`=.�-�b͖��*,A 2{9"�>,�'Kd%��-$"2(syJ%C:G�n6!�9.�ޑ�JNK F�J $\�>� �� }=D::^2B;J_ }=0$=�� Q���� ,5�e %�12�&@%!�#5%�#c&�~.�Q!!]�I"I; `! p*��/z0=�B�9-�q $8�%�C uI=69&(SHF)5��A .B}T(exa&�u�? A�V�Lm�U� EOS.� zff�La�'}o[�wim�Ces �G�'W[ �*�:]��: ^�� equilibri+6Q<=L^4�]=l3Vn>zu|@�:A��er.V� +,!h} m�=*X�d&*3:E�6YP (i"�2 `�/^�*)!��H!lm� 2j"c0$ U�.�f�:� 16I����=3 "�)2#<�uy -4 -Q�r��Bm&5n9yI�.����A�Z�C.LAJ%Hb���edg��v�\�iJ,*&�lu"c2inT�� F{#� �؆2KA��2�is�~o"3��& )����x)U��,:V�X�6�)8�(5�qJ��!S�J rou�~ $0.065$ &� �8. �.�'nR�3�BZyE;b I��:) 0/3 E��_0~�P�3"g5 o=:DB_,.6"G,*=A)M!�I::�4~�:tE�a�M��*ar�=��j!K"nQ�a"�0!� ^0. Now let usD.N� ��)�re�@�@) �~6�s:�A��DXEϩDF�A�vardF dF�%�26>4}$&_�6G�Jp'"2%�,�m:r43q����+ !!> }%nMorted !wd�F� �O6� -H"� ae�ask:"����#>�2�MB�BH SH�F`,i�he RMT� "�X�&5 �� �R�P*� AD��e����Vs:E less b/�a{Qr� m�*�I �problem�re-visim�#=3�$a�56�JCihi��sJE.C1=��*\7U�N��eq�� MeV 2,�zco�B��ls�J,�hx��hPMm q�work. %%f��:� a�A�)`6z As62�uth�Ny<,b�p��7aG���1�#� R H�==��aBC�?� E (y^)*� $2\0D$&�Dp��">MzvF�C!LaI�o2�B �BM�nftya���t$N\over�{N}�"2@)R��%@,g� !&��I::ٷ9�;},t.J6�� &PE. I;cM�� �U be fairly�K"�"� e[:�m�� 9+A�b  6�9�� �m�+G M. full � Q�qz!!not��4ly�Ӝ�.]q.m&��a���B;����+2`��� I�3��� >�AGc{]M�RJ� oX��a O�� i� 20 -t w�ri�&2�b*e]=$�)�5/ &h�.�, we GN�)b28jQA"|RXrj`A2�3Z�)���2j��2�5i�b:�g� I�v"�eF.%1�2A�somewa��&t����InPm�I�Q20=� �8:i �Ze $\sim� �Nto1 if%9��ef�6am�A&Q.JI�accou�< T����tz�� �",?�� R&6l�3�v< a&�M�*u`AzԹ�@en�f�J" !.�P�o-Z��un�%p�Y�<�RkQo� x�.BFD->�.eE�/��a/):s%&�6<&6Pg�6�a,b,c��d)&uE""I*:"��> "��*> �w�fO�E�*�6 B�la���r��L� R�b sV",�s ���H�jN!s�lR  drops dow#�n�\c-"C� �in�V�%�>F�.��� -�� ^ +�l#I�ray8Z\��I ��!�Z!f� -�a�1�S@er ��U%�� �A�R*� �w7"�9T.&Q%5haVq enoughIvrIofZ�  va��es �4 �&�).~_c�ph�^ppear)0��B��e�b4 0.85A,A'��R!v. �:J#!^A���& _75S#ːa�J2bt"��)EB�le*�f�sq geyOq=FU2!�er:E6�4� � }�e� "EFofUe�jG5Ɏ���9��-' = 0.0�2468, 1.0&�fB���聧2�U �F!�!)����1 -�%�2��${ "�cu� ����: ���p"��.��-9y�zy�PRM~ ����1�atid�B�' V;)H a�-��mRMm�e�!'mr����N*Zc jV6 !�ate�i=J�51 $0.2mR0.4 6�1I��� aF�i�s(b1� �d���J�":E�a7��9�,*� &Nqk! 9�:9��a>�MZ��"7J�/e���6M/B>)a�ll��(͜~[+ �QNu� �A \le �; illustmga sG�;�  o���=;��>i ��B�, we ��&.U >.DV$n�M-ey�fnjAN�R��&4��Uԉ*��B�$��:wa�O!��x$I*jL�*�A�AA�"72�Bd$we�����2>.�a�e�a*�!��i8Bmalf��Z"�):YD` "O�� l)^�&� T��� but�*̜���z du� Wu|�Bu�i�K*r�)o&Ԟ� a��Z"Oa� &�'��~�!d!}�8�"i�2��C*�X�it&�]�L.��RC. Emplo�%AO� f"�Y� �Y.& (� �n �>�>.fj?r�I:^��m��-� �� E2 W��&���!p��5�o�:��"��`�!z8ɡmJ� .I�{bout 16� ��"v��6~A�w  aQ�v�C"�tz" M �#��զY��X )�&�8��n26a- d�%Z�&yq�K ��!  3% � \E�x�# p� T_�#a]8q �q �fwo*�V!�����e^�BK��!�de�k֛�'Mk��rR�� Y�!��*�eW!D�T���D|e0*z�%,-[9���4�i�� G �"��m�c) l am�q&� s��le�����of F<�i��W�&cV���(.�*�Pe9i�` "&i1�`�o�%' ��%�s~��n ,6F >&* !3"� � 0/3$`�D?sb�M)Bo�pp�apy>C�V�q"!uf� �i uDR� �s\F, &  F�v���!�IP�2�E1!�v�M*o*1aB�����6v5�� )��v-�A8\.��!�"� �Ɉ%N R-qJ� v� AO�aX�Pn�I&� C� K�bfJ��, on*�%J���y�"�Z E3v�:�AH��t ��E %�B�  easi�� gas�a. �*zibq1uA4�&f2�(�*�2� 1R?z� l��&� o-CcB.uO!Pr6 Gz2� .D .H B4���of�)(W.Zuo�A g�fu(`�� AE�.��gD"¤���od2= E 11I� 2) 82&@y}�SOy, BoV�R. BrockҠJ.��Harrise\Sandova֤B H. ! ebell�e�E��4� 198� 236.^*�y C. F�y,� Essl���a(p WoltT�N�-�E6A 6e�1%� 987;6?M.ғ onnaEDi ToroE H.[ arXiv:�&(-th/0403005Q�B}J��s.�*nz E�}B�z��Co� ste� nd��KahanaZ�4I,a`744.f.;3F�!�*��> L. Z��-4!�0�bf C q�3e�2��E�u�7D. Yang%�T> S. KuoRK3��z� ��.�l2{A]2�CE�"ߦ��. &H� Qa� �J43�:!164�wD. 4�:� .:�S.��V�68mK1);� ; N%2��N���- 600. w.�y!�Bŵ� a, V. Fiki�A�brociniR+3�h8) 1010;2Ak�ndKR��.��Rq�ȁ�2262*|F2r�-=&v� X~AZi� C 44��1 92�`*�1 ƗnǞN]6i�Iɞ.b�F�z}AA�z��mmarruc �6�301032��� 2004.�Lect. NcW����64M.4) 119M�&v � >S�f2�zA Ȭ�Ve�P:�Jr36|1ߩ��.&g/_�G*� "�-g��Q�207.T&�-��T�T��~=PN��  599c.�.�.���/,!�W*k����� Z.�5�98)m�._]� 4} I*`.%�U� mb�FE242 �A62�a�-a Z�UA� jd�Wg J.-F!�b�)/ �EA ��} 418.�.. R�إ E���Maإ Jw p.EѨ9��4Z�95}*� B.~W�� ~G.~J.~St^a�Jn]��� 5) 32�ma2�s��*�A:�)31���86�)�6/6;�9$P.==M!�-1-/ ��R�/�� :r:{^J.jJeu"���hCy��9&p �25ce76): u�9a� � � Many9T���a��?Jh� in {�� # MeSɼ;F:q|Ed.!= �(World &�Mk, Singapa���(9), Chapt.1��6�L !�8Ց�.R~l�lT��Izb�I+ B 21��p2-&!_ H.Q Ӥ�G�|��*f ~�Ҥ�x"^�%.e�1Cn* 8 B.D. � E|J� (�JY16U�;�Uֳ ournڳ ��E i�~512.�3G.O �3¤��¤ B&¤ ¤��MxA� "�� u1��87� .%QJ97AJ1����G.�f�j� 2� �27!�5�"G+M Ray Shamann� .d&]B39�W7) �gI:�%&�ēn&̵[Rf�(>��Diyy"�micro. ��#�/�; ent2�eF��26]�Zb"�� � ���n�.��aN�&� six��@m�#���$qY, �)�2X�,A�zI &*> �.�'.�I��+�wQR��5r!�)�)F�.2..N2}�N>N!�Z&��jat%i�I'&�,Nd$!aM�BJv2�*�P"�by"L&B�2.�P�&��R�3 $�|���@.k3�kBk*V:H5A��*Y}yicD_�xM R|, 1.&�K/�tB�'#t�j�%sM�igd�j.@cX��f�| !P [t2�R�!�m>��&*�b=&�*@"-� (I8�(} ��av(.�)2��6�&����Μ����] \ti��DTfp� ,� Effecj(a Kaoܦs�.7 in N~���r��Q*��q�� ,3,4�Tu� i$^{UZ.X�1Μ�L $^{5� 2�� ���  c��F��6O�2$Po�W ic� &�,"����3$� �T�6���ޝ f\"ur} eti:v �k�'8 Justus-Liebig-�@\"at, D-35392, Giؐ"7\ �5�`�q�a"����6]Ka<T'��6;�AA�tY�7K-shold�my�e�!�kA��Nen�o��nXm�O.aL7Jn7��on��/��&�h\18\ed� �("(��k�"m-H*/� �&�G. O*��#y,;bae�s�(1.6+"�).�AG�y"��nd!"F55 ider�?�"�!�ito%+jI&d�pr�6�8�nesz(n�� �Bb@K��BT�9�jW)� ��X<0��m#n�n# {!��5�^���2!turns +3�! f~�instead; eΩ[�ce�$an & ?*�ٲ�%.:5mi:�&�*��>1O�j sign�znt2�#��-cAP%Dfra$�&E@m�5Zw1,&gOt���16c^�!�a6��26�ua�a<to�'�Ne4>G>�*� y �+�H{(�-s!'9^)�') � zXof*�KJ 2>&�C�0#b��"�E.\\[3"u�KeyF"dr�D��m�P,^�,%v��e�,>,Z�h+��2�b �,26.60.+c, 97 Jd�W��*�� \�y{6��As*�<�Ka�3(;Neq >N �n;_097 16 ~�+MY$�#��"�� R�R"#S5]J��I�Al�R!k�k"��A�2�< lept/�~5E8�)E57.�+��4o_Fex�K-l�ick�R�*�Q� .ɢe��CFC4a��"E.!3ap����S >!�*]� hadronR hy"4 .D  �le96ef,l_�7"�E 98}.���e.�os�Kat0�pNelso�wk�6yq},�) � ofJ����/�0c�i�aw1"Ɨa�+.�sp2�L�Js�uρp � �Õ �politze�1�2,g*�� thorss~�94,����5,yasu7��0, pons 1,ramo cb� norH 2001,kubi$3��N �suggest�4�a u�ba28 p�� 1A1�"� is@ Z ly favo+ � =[th >%F6G term96M�n pA� H�}U��hu�^� 9Tas��*p�8kaon-nucleon in�teraction, the high-density behavior of�nuclear symmetry energy is also important for determining>$threshold `& kaon cona� and0 composi �.-Xed phase. Associated to;.�B�there�d large uncertainty due to ! lacky,experimental�str,`s\cite{danielewicz}. The ^&�plays its role somewhat in a different way from��--Ron in5�. It d-bes� � extH�electr!a$hemical poialwX$\beta$-equilibrium neu2@star matter belowQ critH!�it%� !�-.�)Plattimer:1991,bombaci @lejune:2000}. Ther�@$\mu_e$ serves as�I| YVfoNNsince1�!��Ej becomes Ke�,ly favorablej soon �< > \omega_K$. S\ realistici on5� (NN).�Ds have not been fup5�d 5�chiral�ory upA�now)Ykaiser!>$2}, variou%or � modelsA�Aq� )3 �� adopa7!;studyim� propertieE!: .� . In[wore$ Ref. �thorsson!�4}�U@simple parametriz%sfoa�$meson-exch� curr�method~ �=ɸ TBF.�$o affect s�gly�E]�B��]\ :\4, i.e., it makU�\2�R> much st���a!F��0 result withoePe TBF��tribu8� aim� pres! !�aBto�ee!N��Z�I�in .+s� @��>AM5 by us!�E)HFYa!M�F��� calcua�ons, weIF;�WLa%�ia��kapla��,86yq} to ext 5���� part1M*��in Refs��2 ,�i. Spec�^n!�u+ paid�P�eE�ł�>�0. This paper!� organizedA6follows.!Sect.~2!a� ew brieflF$>Ae�i��6Zinclud-� self sisb .���2� TBF,A2�)� �%�2r=f$. Our nume�ms are M�� nd discus��in �3=(4 a summary-�@u given. %�  \sed {Th>d,}\label{sec_�@n}�tt ��A6!Lq�3 �.�m|,e�% a��con!�M�reeeco�js��( \begin{equ�'<} \varepsilon = _{NN} +6lep} +.5$_{KN} \endUw� $>N$A�t*� part,:(c$�ot��.��� lept���eq:U1B�T A_8 .�>\ ontinu�choice�� $%-!�ce ha proXto ide� � faster� vergenc�$ hole-lineQ ansio&mL �Ron � �� H� Y.�� gap �# songF 8}.> add�,T!�B��A68 describes phys� K �4ean field felt� �E ��ediumI�bt (:t $�4�?LArgonne $V_{18}$ ($A ) two*���&�$95} suppleed| ! !�"u ��TBF� B� .W !H� 2] isUstrucj�cZ� �-�� �)�t"  f , f� "� 2s $ \pi �� �� s� $����r��red)+6bX\ massesQ;� �fix�7o irU( valu�xceptaO%/ virtual $ �$-a� ueY4$540$MeV accor� o� .R1P ~Lcheckc�(isfactorily"�C UN�X]5� on�s.�&�(OBEP))�)R�)L o��E�v"F P nARcoupl��� �� form �s,%��N�� ���mee%�B� r@reuU�9q\�cei�%d�!eNre͔VU=For�3or:taileY�lpSV � w�fer�R�F�&� . We want.stress �![ mosty9�onSpis!��Qes�1ia��at��A�utomap}Walecka .r m�t; y �w - :1974} ov�P Lno�v�=ies.  ord2��I�a���=A� BG � �� � %A^dard sc�2�~�e�1986,"�8}!\ redum6} o an����� aBm�is�!��$r$ spac� \small F� � $array}{lll:  \vec r_1 42| V_3^{\tau_12} | 1^{\ \p}32b &=& \dis� tyle� {1}{4� rm Tr}�n \� �d �3} {k$}\phi^*_n(�3# �) (1-� _ �, +0}(r_{13}' )) 6#2.#23}; $\\[6mm] &\�s& 2� W_3( }. .1F.�| (9�1X3) ��r_3>�>�))v�))QI &� TBF> , \normalsizew�Dtaken��v A��* nd"6 �!akird�� hpdi$%�1, 2�uA�3�_V$z$-cs��s.�W funi.$9�%�M(r)" de�3. ��2>avdirectl�t � bsolu � �6��^}#us" ed>ily)i!0$G$� �!d6x z z�7 at eac y=B� . By�v�D:�� �c,ed Eqs.(\refA BG}), U1}),cAc)�can obv�re��&m . Fr9#;H .� J��<0 �./$j any�g+!oF2�.F�$A .F�!be se��!�i�wo t<qcal(�!�isove� 1J2nes"V:<���i"� �indic!^} ur0a���vl)��ta$cru���� � .�*j`ter. M*c6�I�b.GU� sh�a& a� ��%` �%I!�J�is� lete>�/"M]$S(u)��-�ex�as � 0 u (�^2"X$u\W v� _B:0���!l� J� ]<=0.16$ fm$^{-3}$%�RVQ�ofuQ6"�ACh�Md%� $K-N$ S-w�In"� s} %�]�z } %spa [] es vanish� !g ase,5s(only %relev� �-e�"q�X�d� %it  %s�. We ey atI�2O�or �e1�9%�1 .T)1<ermu��� c%; ��a�y� $was sugges� by K�a� Nelson� 6� �"s�}8,ed afterwardqArow�9S I�} h- d2 i$SU(3)�  $ � B�2� as&�ng {\math�#4 L_\chi} & = &� {f^2 &  \�$ial_\mu U <^\mu U^\dagger +.4<\bar{B}(i \gamma, DA@- m_B) B \nonum7\\ & &�; F\, .L MJ _5 [ *cal A}`,B] GD�G\{=H\}Xlan-KN� >�c �-+ �!^M} (U + 5!) + a_1 #rm Tr� (\xi  <+5`.[ \x!JJIa_2 3 �-FB�l= M}.� �3VY\;܊h 0��). eU��w���sam�$��Ld��bol*�6�' aboveyAH"n octe� pseudo��mas�$uAM�V1��s $B$f firs�ur ���B&É���$y. $f=93arm{MeV}$��}phdecayCOb s $D �$F$�=ND=0.81=0.44 � coeffici�$a_1m_s,A=$m_s$, $a_3 ��$c� ���� ngth��:� break� la2��|=-67$ $nd� =134 � e*�&�v�$ splitting�fpolitze�'-�!�!=�is�Q����(R���(Gell-Mann-OC"-Renner �bar s s� _p/ / u u &d d .1>0�)�)�N�)�N��%!�exa^��-[�' crip+/A� Ht6j, wA�n g�� nonF� b� aw� ed� w&� u��a�# #�w!� 2} �.`K^2\sin^2\theta + 2m^2_Kf3 }{2}+ �(2a_1x_p6) L:4� �� �Bkx_p*@p@BEno����X !�1[-�{a ,�c . $ �"�amud��!�%=e�k/�-� ) BaymV orem)� baym�#�$�� 0] ��^%_{�$ k read�"�in a UTway ����"�fil�""% �2�2�(eZ.�M`�%&K^- ,�b�#-lF-K^-Q ," Z�lQ|s-�2'@, $l = e,\mu$. Oni�d� � A groue �#�V4miz� !fR��� #�+)U� Q�U� keepS=I_ ies D� isxI�tog�%-�_f3=�eQchi4Eal)�iaY!a��C[���bupA��~{J�cosi���1}����^��A*(H f^2(a�&2}u��0�� x\!+\!��  �� E&7� ; (1- x) \E� )~, M_th-mi�\en.�(� ���_ �� �je=K�muc%0mu_p= 4(1-2x)Rsec^2^)�r - �l ! \ta���"\,,�$a��>vF_!=� ��7 +=+x) >r- x-/ aS%�03 }{ 3\pi^2 }(eta(|\mu|-mv) � (\mu^2  ^2)^{3/2}= = 0, u��-�cn�} :��Xmu$� %6� &� � neg�M�d��t&( $r�S6���uni� ��0� �/Q& -��ΐ:� The�*nA!mj'o���e�enH�8�a��*�߅ o$ �$�(�� հb&�Op�TmC), Y�2|1�) �N�0 ��ȉ�is��d8 �p B+� " a �%7"�>��f��. &.Re�1E) D�.0"F# mod}�/&A.<5'� � :�5�is depi\%in Fig.�fig1}*�( bold�id z'MP% n so&�.o B.�1� ��e $t& pl�75 `pw%" !force:��(fig6!�>�w =$ ��H.b7,&�&8�6 � also plotGor� pariso]3 dashed, d#� dot-  cu�9&� ���"�i�Ys ~8oaJin*� .�},F!�� =�( 2^{�G2}{3}}-1�~�083}{5}E_F^{(0)}\� u65 - F(�bɸ�� + S_0>�R�F_1C8= u, \qquad F_2  ��{1+u} !"o�13 1sqrt{u�*��f46<��� \simeq 30�A�$� = (�X��/�32/3}/2m�NHD P:�'yra"�7�ity:��S double-]+e`/�52�9>�b.*5*�9 ` �9 � UV14+TNI *�. I�seM:rkuE�=both �s M!Z ^r6,1ca�5ed�paLmon ly inc��|!c ��-?. B�=|a �"� Nr!�TBF� is quite ��-(ile at high i�07.  l� a�$ong enhanc�'�q�rZof �!�isj:>��?�could b�pl�as�@s]eBB(�&��ofM EOS)*�,+T�(�� ϡ�"m# � "�-�. A%Herz�+� �AM�equ�somm�lma(>A er G���j-�B�!D$$AMis{hort-}}��A0U*er%�� ons av� �a8$8��^EOS5��a1F/1�s�.�$"]!�--�Jk� *�+/@xj i�=� $.�A5�+3"!W:�2}%(/I�G��=", -0� $�de dk $a, b, c$>>2#��B�A@6���!g��J0���A=%�arE!.n. ��$N� 2n � �i@� made�0�!d#s>3bnd��=F� )�6� �&fm"gAii���es gradu,E�Jd�ea^t��M��aC� �B!P>B�� X �a��� M�!���� . A�!�>w�40CaJ{��%de$2jmB�ly�;}2!���J" (i.e.,7�64s$), but� l�$in�"#m&{E�#�[i0>�>��B�� ���-����%�Q}JX}�F aa#��� a!�.8 �0al�.nJ-y�So�aF� ����RG\ %X�Lo> $u_c+(FA�i>�{ ���ntyp :j)� .��[-�-Tab� tab-ncb�z2302�} (��e�$F1, Fv&a�$F3$) =�*�>><U 4re+ ��">tq}[ht]� �er} \cap�{�.Cr:YG9_J�n � 0$. " -� p�.:(tabular}{|c:} \hli$ & $~T~[.K]$ $& F1 & F2 3 & �+A�&& \\Xa &�$ & 2.4<2.6  89b2�� & 3.r2.9 &3 4.12c21� & 4.�3.8 85.0> --2 �T 1 5:o )� Asu�B�ɕj6!�qz�ǵonw a�i j�.e��Y�A�A� ��C�3Z��� .J}J�tha"� : d� I�t&Golower�ݰ9.,��v&)���[!{-���6�!��$ er��t��� e<\)� good agre �[:pgBou75 �L"^59 � �k)N3yq,6�.Lis6� E�!��%pre�,ed)���)����2�����Kb0� WF�ZlWitsaB� :PE�6@ toZ4E�BcLitQ��:aVCpulK*RE :�)�&4  Our 9lB�I8A$ .2.4� -���,邡K7�5d�$�.55.0 � U A��E.6"�#*2 o.�,A�lu���.BE>-�sm�by �>�$20\%� 5!�43.8. However, �.�����0+K�I�sZXO�$T/*8 inst�&�<as.2( ":���6"�~- ai �1��6a�!���i��underst�$I|� #B hand�;r��e���}K ���!� �6set��at�7] � 112� 2:�!hr88ely)B�D? �)�.*;=� in-m�=�A�8K^-$ drops down�>�8a"> >AR GQ5$��=0UExa��#&/9� 1�jP"e%��!H`�.93}!-/vd66 Bf�������N��3I��)�0upper panel),�%+& midd�O � " Me "�| ?�>A��(��_!C,)R.q.*outY -�}*^Na[ $x_{p}���"�"}2.K..K�"w !�T"24;"(=x_e+x_{\mu BRho_e+y"�C� � �X),6 }#"(p&�Cf� �"��p��8m��e�lyC-r�F!�� -al mix�4�(n)") (p),"�S s (eOmu�(59� �$�D , e,��7t��J�p��%f�!^Ar.� m,�$$ rise�Q.L��o!en"�%SY�9�(��� �)>�<ead�-+, ��xUUQ( ?�.Ubal���>6� 5�so abund�( ȡ��.�. A�eno&$v!8M8!;4ains even posi�OEM"*�"� en�)EI< ��"�s�$�RWn� 0 &]B� �8 6^�$se�"� VE)!5�� ^X�h &� &���- :�P��,0�с�z ]���MH�1�E�͋ic�QFa 2s=�goe�Hm�� t� :{e�is&a of1�Os�Oo�Q�. >�Q�= f%>��� 8� �:e�s G GB"Q�%JM���U�B`5T%a1min"�- r&�@N! " � :�a�5].&�*Y�}%.�� ��V�W,by "5N6"�* "�w2:OA�A�tr)2 t"Yc%��a�V!�w�I��o.Dirac-"�T �T�hub'28d0E� �BC.H�Bk $greco:2001k>E*�n����=O A�TUi�V� .� ��!SSed eyV"gUdev�Lm�ou�2�f d�\%"n�& ���>�t me&�]. ex�+& =�Sem�i" � �.��D"�"�����T� a ``i`" j�?aqF� aaD!?ia*p�~4. W�!VA9M�2Q2 �2��� f�ZefwF1,B�gJ�wreporZ2pt2�."e�S repa�K betw� �.�~�9zuhe��&.q�e�8still not cleari�2X>b"@Yi�de97s fur�% i2���t �A��1�E!�-�*�;�$, wy1�a*MJa� miJi3a ��-� �6A!"�/�< �&edq[ �gld[I2�y�f/8-�3w trdM�A�A�q'I_Jr�= on law(s)�&;b�ClfP.&  globj[*la`lo�9zIpea%.�� � y 5� � � # Eq�Bc�))u� invalid. �C�g(Y�#H�h e2�xs� !��,5�})��p !-�& )D%�Q".^ ifici��+adesirT�!�pur+&&� �7p�4[k0 J 2l6shE�!�7?%�problem �.�?K �a�n�{��._ � wanbi��W else�hD�!�Wiis)�X �ossible M")% !���5A�maximumH9��z}72X 5}e��H@���D�\25m�%g>a s (. 6 !8 +&D*�2�%$B4)�r�0�� Ar.*\one6t!&b)*�)6b) (( T�SA���u�4A%no �]z * ]!]at�dv&$�:� � ]Z� r� NL b��co&� �� A�sho�]� zhous 4}"+e�*h 2��b,2.3 M$_\odot�4 1.6  !�" U��-��#�V�Q �� !�_ q ��ZIour:B9�Z=�7�9"�%�lo&F 1.5�{�}��22�*6��a� ��� modu�+of 210rv ��]tIJA� a7$ A.��1.�:�A�often>:o�Sab�E&? Z(�s�* ��%a \r���?"1Q�ro5�1s� a��j�+�Emayq!�y I ]>�>j.:lS�$�!o�=�_, hVFi:Eof��h��G�0, s�Ua�FLambda'S�c Xi$ hypeJEP appear�of���@*Y%\�0w -H &%s�!�"�'�� 5!du2�"� 8pr6!o5w�ha#[5A�e fre"Fa::K*(M#e+he�q ropr� �_��%�.�/S|^�Co�4}�.. �&l R n��! YaW��;�2�d!qB �%�AZv��vA��|�7�rU�"Y ��Eˊ� ��1M:�0��:�$�>N�%s� ��n� "s B� �WIach%�!kDB9Y-^* � es rapidl)%E ��.��!~iUR.O >5t�" +w$ �ka�JM&{ by"� � �"K�Ha�*ce��ult������J?��6��>�i�B�'��~ $8\% 025s��;!th�5�Z�%����B�en�Dinflue!_͋� JJ�^kN!x�Z]is%��:m�V 9���0E�2.46 to 3.8wh�hi�=6.�&�uM�vV��2���]%�e�!-a�� !&N~toMn� i��06�a!�x3�>EI �; .` >��(-�!,%�u�n)�lyѕi�>D&�*y��m��e:��A>B�� �MQ�����&^>�8!�d�� �a��mg#>�m8s �i?M�E�^v>�|Mfin�F��]�2Ae�Ee �%��1�u> �f�,!��Ρm`� *BV�E-~�*�[2�)Y� neu:�8VI�7%�N.� q�� b���%R"O[j��O We %�qc�$"' ] �t�s� sim2.3$ %"� l&�* � �?�X�"  %�Av$S 1.9$> = $�� �mf�I& 9AcrH�1�8� e�up"l %NTK"�H Inno�Project�a4Chinese Academ�2S�J�V4(KJCX2-SW-N02)iMajor S}?TBasic Research Develop�fgrakk c4a (G2000077400>A�P/��M ���F�Val �tMin�.�E� Technolog �0a (2002CCB002�N� al u\G � F� � AD10235030, 10175082�DFG, Ger2J. �+thebibli! phy}`Y4ibitem{pethickVa 2}C.~J.~P \, Rev.~Mod.~Phys. {\bf 6Dq(1133 (1992)F M&,J0} C.~H.~Lee, > Rep. C 275}, 255C6)e:��˅Z,rein; C. H. EG. E. B-Q, D. P�Tn� 4M. Rho, Nucl. pk A 58m401m56��s<7} G.Q.Li, C.-H.o�� G.E. q T! Lett � 79}, 5214! 7);N�62�372�72�"�Q8��6�R. RappV�63� 455ca82a2�)} D.~B.~^R�A.~E.~hR��B 1%�57]862]2L}!�!�iM_$M. B. WiseV]27�r156^912^52!�)�@ K.~Kubodera, M.~!�n V.~T�Zo9�3My6�.) N. K. G&�Y�v-�$D 46}, 127%� 2); F7�LJ. Schaffner-Bielich�>R8� 4564%8Vq?z,C 60}, 02580i�929:�Lou!/�t)3J.~M.~LMmerVa57Vr693A�4)�QbfaZ7� 851  , Erratum.ellis�]5}a� J. E,A�Knor �M�qm2�34A�1N� yasu�U 0}JY %$T. TatsumiV�66A�881��0�67!f218  J Muto%Fc,`p N. Iwamot��>� D 67A603002Y32� pons�1}!+ A. P�lJ. M�Wles�Pra�v sJ.�=�A��f.� 55�382Ń6k ramoxA�l mos,:S. Q��J. WambaE�)�N�m2t578�75Jj carl�w'OC ,�>$Heiselberg nV.A',Pandharipand�Ge8�C%�017603JrnorqT. Nor�w��S��ddyF� T65804!�6/.+!S.��iq M tyb��J�72AT189U6�bkr�� N����R 19a�27a�86ed*|a�De� Lace�;nd W.�hLyn%��%g29!��42)1592; B.~A.~�7]�E 382 1927�}�);A_hE. L. Dieperink, Y. Dewulf,�A$Van Neck, A� WaroquierYod��t{��C 6o064307�6`L�䁍1}��y2iJ. �z~2bP. Ha�'l2-� �6� �_|2�.�} I.~B5]%� U.~Lrdo2\ �4�e189?1�W.~Zuo,I).JQ%}(�7 4605�66*Mx}!�Le'e, U. �M%)�=B47��4i�02k*#|�#K,a�Fria4 � W. W�Z�97: EP.k2�Ca,5�4T.~L. Ainswort i: �%/�6�2518(�{2p:�$ R\ Wt{,�Fik�,A.~Fabrocini2j-�3A� 1010Ffs�T8` ~Q.~SU M.~B!, G.~Gi racusa)Fb �j158�8);an T0A. Fiasconaro��Q. y �pM%J �6 0173��6y 9H%R2 �|!F��B tok�,RP �haNM5!�3!�:� b!1a�7}=@y�);0G.~F.Burgio, �Hn..P�32!�27� 6og59�o~G \'e,AuV,M.~Martzolff y,J.-F.MathiotN�4�;04E%6�:�lA�Ma[|, Adv.F�1P 89h :O"54�j�����J!2~���~iO%- A 70�4K �Eur3J�@A 1��46�6#*}��F}, L=y�Mto64A119�42�l �!�6��9�P-�e^ F�~Cugnon,J�4Y 1J6" 6kJ.��,Walecka, Ann1(N.Y.) �8� $(1974) 491�h7Serot-p D. G^�!r�O6) 1; I2Journ.)by%2E - 97) 515; 2m��a�S�S=, ComsQeart2`1���7) 39.�u�8LjitB�M~�>#7Uar EqQR}, Ed� �� (World�t�#d, Singapore, 1998), Chap.1.�do6�Z I�D �(C.~R.~Nappi��OB 1�1�]:*�ZS� �Ze� La�Z� F.�Z,.�%�D 5a �6) 5496.��T1�����3�B34Q976 .�* H.~H+, F.~We�aa�� ig {!�e�~h}C5!�348��WZ.� M� L � 9 ��C@ 024321e�6g&]+ Ga� Colonn  Di To��G. Fabbr��F. Ma�FVC� 0452͝6� *^X� Zhoue F. �&6" H.-��chulze�� W..1 !. �6�� 0188 6�bѯ!~E�}٢%�6sB:C 5�� 3688E?!�)u�055�� P>:6 % docua�CY|PeYfcenter{\@ldegraphics[height=4.5in]{sym�O.eps}Fv@�Pde�ein��"&�dd!2C : F1�%�4), F2(.�4), F32N), Z,(VL ), BHF(th2oOMBHa@(:�O)"�w�O!>:oA�"�(��R&"�!9��'�7M:.uG &d7!po� by a,bERc"%.�.E' �~S��')����+c*�%�K q')�\$H�X%NF.%Tfig2}^J�no�*9Y.Q4$6-Me1%4H./8A�,8!)J�."sy %R�9Ps(^%+1J�!>�Z6)CA1�"�+K*e8.�I6w8 �1{l}$. kV fig32bE�6[-F$�"$)U�K� w!:�!K"� Y�2 '�A@!�%7"�/� ^4#�"z' v� �D))�e� *no&!:J7R1�2P."~&3EN/%$�� *�L@%&> #S �� are 5#5�!'NEa�=&GLt!^ metr�# i6V h�I�tb" A�rZ�AI�U� j;l}$!c��$X fig4B�&�!&�.Ru�&�$e�e;�), �I0�2]F,�B,�)�,S"�#}U 6,9 5�a��� ���%\ 2-} % \auaX{Sandra Padula�affilڍL{Instituto de F\'\i �~ Te\'�8 - UNESP, Rua PE5\ona 145, 01405-900 S\~ao��o, Brazi�o �� ab %ct} I *Fe&e h%,� !K��5K�FU(*0�@ '�$ mid 50's,�N)$�gV6�� �J�� BNL/RHIC�q�*0 foc�Xlus�&�".ms5��Usubk %( !?a�menn% �+)i�c roupul9%\a {25.75.-q� Gz 0.PqI- kip M, hkeE�sg ^��{I%�{ } I�1 � zS�fascinat\ �8�*n� de7!s ago,�1tur�Yi�ta[ac&$ %�t&�*% ���kp� ��iszj2�0elebr �![$50^{th�h(nniversary ���4 pub�2u6 phenT� b�5d �*��9!-Ui�-#� t�9a�y ^(�b$in radio-anom�@sub�)t �f! a simi�uL3out$E�origina�Galm{ m! a�- teriori d&�""%%u.1eA �%�{I.1~aaa�i���[!htb1F�M�"j *[a"g4=0, width=8cm]��3A����� A�"� emph��Photoi� illu�!|1�1 %�ap*[tub%�Crt�1F aerX�v�J of w2� sS� nd %AM&2$iUEl�-pic B%|1 tele�4~%Th0$)Ŕ�<+:aD]�F*'%gold}.�9R�A �p��r�6� The�V��.��bQ>V�\r%nn)��$identical-a%0� W on, �tid��k�ia? e 1950�o48Robert Hanbury-ha!wm�7 o me!k�hsaaareAi}�g0�ubt�8�LnearbyM �a�e� �ZEarth'Nurface.�$)�I�2��9M�2A>OR�PnV u'+)6%��'Qnts%�Mo !g�h.�U7ac(�ly per�7!fA�j,6���iH/RiR9d� Twis)�jBm�98�9�>apATM�(љcm�eN)]:%)� HBT�S�: ;��ng asp�(��`v-#a�th�6t%!conce��by n pm�istd;hoI� builD�M� mselves, :W��9#!�N�vb�A��lia��f��l�alya!`0data. Nowaday�3Q79�a��)z /BNL��ele؋ �1hundred8i�� �Wa�q<Ñ92i�2p~inY)5c5hx!]wo mirroaMsi�� ���lU��] ar o���-multi�r tub�En =n�w ing}*1n>evqA��corN1or$.e., an elÛ ic circui!�at� %�@signa��%� ��5���em`:�hiAVCimbdUt�y ��$`` ... col�ecght��raia; a bucket(''}Bre�)no ne�oF m�C��io��image:�(��$boloidal) و�2�:d�4b�4 ough�WL %� -ref�!�s��DnecesG #ci� f�)�gf � �N^;p��s�;r!��z� (e draw-back� ��",��aR!�� ymtQ skepticisG+&�m�U*r I*ctC1 �� 8me scAma�3i|�1z.� ^_��Rll becaus� )Y viol�_$Quantum MeY�ic" h�ar>n��6, helpɧPurcell ��p }Ey� agI� ����k@�m �`:�"e3*v exe�)�i@�sAf>9e�!�!|m se early]writte6 8Gerson Goldhabe�A]  I-�ex���sA�&3>f��is*a!\"��VlMU�!&opp�talE�HBTi���cosmo��L0$3�"eKsBq 2~ GGLP}�71959, �2 Le� d Pa�v�e�R.�-�B�~ac/LBL�6Berkelc%CA, USA,�@� 1 1 ��54^0�on�9I�� t��},AO zmZ$\v}p} p$�,r$1.05 GeV/c�y �V ?/����re |�d -�qy� \�a�o\pi^+-$, 8su5�unlik��ir�]- -Y;-2�Ina@a��u�o??�O��a $J\pm\pmA^"km��luda���a��tYG�m0ces�Vis%}i�G of�k ^0$. Neve�D�M n��E' una� angulaQ��_�among.�!�&e�T��60 W suc�%������e &�e fKt"�b�����-!8$�5 -\-s�.>���Z W�&#f!� LIKEu�s fAKso �2xe �C�cB�!b6�n�g���^I2+�?-%�-$]ϥ�aw�M�!~� 2� EfS had�D� 07�ous��u1�hadu� ?by�Dn_cou zW �in�� F�y!A#|!g% UC��E-s:@ &pC(Q^2) &=& 1 + e^{-Q^2 r^2} = (q^2_0 - q}2"j\.>-q^2=-x�X-k_2)^2=M^2_{12}-(m_1+m( %\; ; \; Q/>4 "�o \;.�` " �% _Ga�aK�� ��ve��� sapal!f}R?��^c � e QO*� ��to�_ee inly6SY*ɻ,.FM FcWFQYmt o|mNEPa} ��F9;AA0� file.7 �Esee w�zA�aw 1~Jd� pret%o"O� in aBlq6\2WL3~ SIMPLE PICTURE} AP�� oint�f� ekal!ask�qu� on:Y to und!1A4iB4 10,1U�!&190��k>�  g$kB�0!M�%�1,0){�ZrrE�6V� [9,6v(oval(30,70)Ai�q< \v�1cm"V"w��> S�Ff3S D:����y�I�N II,�� �� ��G s]\n�@���/"'in� ��s AQ B,���iD]t�I�%a)z\Li�%�.6)�B �hin� inguish�L� retwo�W� comb��" �� ���,&c�T��C����� b !�s��&5y!��� \bjR�[it ~ ��FoA O!�as ��nF` A ��& \fra�z\ss2}} [u i Р,. (x_A-x_1)} i { 5� 1}} (2 (B-x_2:(�$*D \&&�-m} \;D1 Dl:D'E(l1) ��'� ] ,\;> A12}%T"� # $N%�($+$)��;�bo�1�($-$)� ,8f�on�!�mS��� hi_i�6+�n aleZ�y�  a2_� ��ta>(>lqk ��qn)U�,�Vt�CdomJ U� �s (u$��| &f.�op $k~oW�viX. E�probabil[ A�a j� .3 !: =T de� k_2$� "�"(!F�&&P_2Y�=��|Y�|^2���v�� ��=&y 42}[ 2\pm (e^{iRB I�1I�A�l�E��i(u+ 2}-)phE�- A�)}aIR1le��c.c.) ]2+ �1 [k~[R� ] %,�� P12� :� .z %�Q-ͣMp<9n QB ^Sverage�a raEx~@�Ok%��{>� �M1A1}-!@%X2)}} { 5M$= \delta_{ ._!C)�}>2��!� } + Z8�:81S;5Y �1wu� } ��parB] "�J�!F�,eX4 C(k_{1},k_{2}ǣ{{i} \b {P_1 /) 2}Rza"�c�P � %�O$P_a,i)e�a��le-��g2��Q � m����J � G�as J� ane�de�q�S��� F� i)\!\!&=&�� Am%� m}!�:+:�A@}���u� )�6��W��i�� \!=\�����k_i2�� F.��mF_A*��L���]%"\ �.A1Q�p�%f!�%v bQ� ��&${�_.�ena� �:�=qf)l2�+JWr�^�E�ɳ��&�Y6lL����aMl�EKF*��� s��sR-|;� . HQ�bw? �N��$ G.vwo�#ulQ���G w��negligz9n�=)q�&xQolua5!0� ��W�% d= [.d[� | \tilde{?}(q) |^2�� 3�^� � ���6w{ q$ � d^4x{i q( x_� �B���] he Fouri�"�^��X6 $�7&|!l� e de�4E�4-JxD^ �'�$ � = (k��9 2)$}8�,��by 6 �h"�= "�2}C+C�Qib�� �� J� d lambd?�;>F)�|^2"G51(�5�Q% %&4��22)��adda�Q�+�&�Y��the�6�)l$ �!��!rmQ�%�in��}P�"�2is�iD-HDeuOBmann et "��d �$O78,�a�(��red�systeN' B���Al��F al fAK���"� � 3+(]`�� �a&�i�-� son�"M.�T# tr]�$�%e �&��s�2Y��s�+se|Pa�$q=0$  2, alƺg�� Onr�#c�aF��_�%�is !��0isRd�qo^�:w" siesyx-)3is�Za�9A�����)#dd ��_Mi4�b�iAjthu�"-�!j9�1�> �(rR� %�iܩ tra k-e�y�Zdo�J_|�-4"oce} ��-g�bos  ;6�-"]\�{ _S^e&N"E�q#d��t�Ue�Y �y){�-�6R e�\�!+� ic m*�9�-6 �io(on Zu� $R"��r.m.s.6'ub f"�region���-Z To���b �TM�a��i*� ���)5V mpT�&��, let u&�&�uBpr�B6�:�(xY� x�Z�)/(2R)^2\long.;#;�q3�9q^2 R^2//"A��r)�:u �e�I�Bnc��23pN� Ze�,��!�j� Limv0. 'is behi�"t&�7AA�� ly i��toX s��wo�{�!���s��ex*_�.� ߺLhe2c�o s/�Et 41c�*z� bia&In�\rV� e�%se "?pr�Xu.n�  oo�r!�me�s. %%� in�{a����me bea(r�5���4 target heavy A7coS ($q_L0�1 ~� C@ I�to it/T$). G�{qu�,�zq$���r��$<is��&!%!ees.F�(�angA� finite.�'w�^+s9R %& , sa�7$q_T$ů�� X !�%A�.ze�EbutED-&�.( ;r)ΥȁfG, e�/]��Bwe im,|�����j>sj?_TA�rknot rX��/ (mink)� 2 (0�zQ&( �q_T=0r*)RR[ �) bA�i�Fbi����1�R�1!F�A9�*)�# thZ��Ta���ber?�jww @�/!��$ 5�el�U � *9!kR�a.���$i�or��R=�A�  Gamow�/or, $\Up/�(q)QC8+pl�lv�/�&ak�i�3c * 2�� Coulomb �4Ey�/�Hf � is p�Ptor~ � �@ n, m�(!gE�)��9�u�of�5͍�y !�n� �=,q_c/q}{\exp( ) - 1� �)T\; q_c=2\pi\alpha m %;=\!.J*� �g!d: �Ire $qa��four-��um PDV� nd $ s- ine &$���ta�L"%� f$�h��%5 m��r~Au��ZA ,>�  %� qKPp�nr� {9schcce})S5d���i%�R�e�w�h�Dd,NY.mY!v��M�$code CERESayose hyp�2sLndcmu�ᅸ2*p��s is manusc ��f����II.`bB5�E~ qTqLF�% -5mm^ !���*=)�A y w��7av� mCF �6�"-�� b�2)y, �|A��+cep. a�i0s " =1�.isCl�5ppeFcr�4s����E邅I"U#� �  �S-M02PJ� Ũ for A_"��C� "� \le 0.01$J2��$q_ 0.��%~�*6;�-&�bNPA525}j'"�We��+,.C!7 r1�7n�n�  2"� A�!�R�Cs&�6h�/�m�c�)!��� stra�8fo��e-i� F �vnlyIFM���i� �*!-s�~dec̜� $f(3 x} p}) =Z ) g p}��w��3 x})�R$j��.P���gy.�&�2� �z.can� �i�!PwayIF isI"�ha,)�ve NZ C�\5 ��ands d�4�lifQt�|�at HBT �%�"|ga�Yge/�Q{ "�� �llsoFB^/l��dynam�7R *�����N-'OtE�m� p��fu �m�0 ms (uhe?� �v�.Wigner,�CoI1Cu�_4t Ensemble, etl%��}D�Wdlla �O8� Ml �>ozo.�BX5~ FURTHER APPLICATIONS�7� 1970EF0Kopylov, Podg� k/u\�QGr�5|/kpg} �1R�>-�Hg�"O2��\#ng�h��Ror2x<�de���Puח�=tic spEp� < us R�+@+ıs} Ay�;%�go���=�0T .y��F� �� �$[� �2 J_1(q_T R)}{q_T R}]^2 [1+(q_{_0} ҽ)^2]^{-1��;"�$KPG"�"��6��" q_\� llel'+�t q} .&( . K}{||} "�#\\�- q_T}2:�4.Z67 ��'(E_1 - E_2 \4qx v1}{2m}�� k}^2'�2*�\\ & >.�(m} @.>..+XVzrto.� \;O(. �2e+��e�bl#}�F 5)Jn�@&%Dm 5;|eth.A�A�si!�m���, Coccon�2c } r�&tey4 1974G�*ity $cA=�$(�� layer�kym�{G9e�ing: i)v���� exc�e�i��o�i�"�J- vapo��d �P�i) shapez .+\$i��� ji�w8\pm\pi$.Xs, �)w y',�{i$ CERN/ISR *��g&�; . M�� r*5?� � H!��?ͽ@d J. J̀��� a few nam� I�quw�HShuryak; Biswas; FU� r \&�_ ner; Giov�Inia"8 playD-�4yin��F���`l`=l�Do>>fB� or�oNeQ/q����>a� signf\ant, �-� >�$�lq6�us!Lng!��+4V� a�� �p�R7t� "q 9%��?of.2#$k$�:MpM�nd L $\Gamm,z�_�velL�i8c sim k/(M + )$ b��k��, cau�,5{e#�<c e6 $k.q�� J�*�!�mp�'� 2G E�]o!�.�!�do� %�adeI�thg/�de afte} ,�� u�t�a, Sec.� Despi"j�^�H Ci0 !� texta�ga��he &� eG's c&GfI� h�lwaysALAp[2��� "�<4 ��<. AE�N"5W ��ruc�5aXe!E�r� a�� of&*� ),� bE�o~:��} ^l l U _{� R^2_T/4N>� 1}{J� } 2E �>� ~�>\;,}-� ^ � \\ aX �cAZ��s��! >c���.( !!�N.�& xr0:� �1m�%/��u�T )'2. _L%:L&Q c1qR |�2.��%&��E��Nwid,* employed �-�%��<~igh�Vo�Go�DA΁Pdar^A�u�wo&�| "� ,!{ti:� rly "C!{�.�P"�&)h��u_Lj��I*�+*�&h����F�, QTQ�c [��6�1P$� "#� A���8�� popu2D �=!�lS�!n�{�#Q��by Bery�z�9���$}E�S}�"_O ON�a�+1�6���2�� �p�C d�� �.�@�&U �iPg��Sr5; s a b�=1�*X5�M��r= !��A�0&M� & :� � QI{O}mG�u{ .�͵Ha}0. �p�Heinz��, �� 5�� {\slE!-O itudP} �sG�in "�%�)MP� -�em.��b�!2,ex��,I�%.Y"l'e*L;�s. � /Q�Sl��]C!IBar�[,� %-� � �E$Z��� � �� ew. q�m osurve� the �Z,7� �5*� e.z prog��a! -6"Y��encou�:&rea~o look��o�s.EO�`,,zajc,boal,w�nEz01,csorgo,rhicA/ \��� �.� y�Qa��S � ^e�p&1_�7*orthy!3۪S5#%U�4on- . AAQ !G�6W A��!W198�L��6�Tme`gcwas attZ!._a�PAnQ�g� com�R:&�B.�Mh�wA t��d�5he Quark-Gluon Plasma (QGP),exR"�H!�6�tempe5yreU/or�*�K QGP!`X� � q|*g�sP%�+`e{⍛had�,���f�.toT�a�ija v�ae mY�b1$!Y�usual Lic ,��` ��%E[a��A7iod��5IbK] ��B���!�Xi�l9or9� � �d� ���M>� @&)��for��^e�Sn�7.�N�"� Arn �!e�m,Q��sti�=A] d�'�1&f2{pNbNAk�`Nngp;�UU�%!��wl .��J D. Bjor&�a� a�d2ho*d �:& 0>�.D.���� Bj83��2�L�^LEXPANSION EFFECTS IN��"���pK�!� n� t���Vk!�3h&�"�6Qa i� m��D��!�,�in~ $p.S�6$&� i)�O�gA��q�s��ʕ�-�B�XM  9� %@4&qc (m%/*;�,�-dQh8al Landau HydroOal�qel � " }. %@ xstage� i��)�_A��4%O��u���� !+a c��.�, $T_0$,O�p �!�!y cool ��, untilA�7)m�_=Ņ�<Vci)h]�w!sumed �N�a�ofI�mas7�Qb�)ag��AA, �\�c$V � �)�8 oc����+ amA�T=e�A�1�!�_&�?�fO ]�E�1^ na�K gene�O��uo)�*� &]<��2M�%�A�"7=.�A�ogy͛q�0��fluid=5��54)&���z�*mH�SV nc�&a1`c ��!��E %al�5�ac"�c� �t�'ly�)"��$QGP} (T_c)0\pi}{30}(g_g+z@7}{8}g_q)T_c^4+B$9"4$g_g=8(color)\�� s 2(�F#$g_q=2(�8q}q ! 3R0 >N_f(fl��s2r�(��e � deF�� � $B%o!vacuumM {/x e MIT BagC. A� /M�c:�%�n-�g\ � menIX$Tet��9e!S%d2L;)2Ծ[(g_\pi)�B(m /!� + g_K K\5]JXOV$:=3$%$g_K=4$,v�L���\'aly or���� (!K"S!$z% �LadB@_l!F?7��e" Ek, $K_iH, $�C(z)=zr�! �[at*�7�>� ze-�3O $< _f>$.U�u]=b� E� h-�Q2�e]9%�6�pt+U, Khalatnikov�oE�&C $\xi &$� & \l��(I� T}{Ts$e�<) \simeq -c_0^2 �C\ln \left( \frac{\tau}{\Delta}\right)\nonumber \\ \alpha &\simeq& \f71}{2}\ln L Kt+x}{t-xG\ \end{eqnarray} where $\Q�$ is the system rapidity, $c_0\approx 1/\sqrt{3}$ is 04$\bar{p}(p) p$9� t!]!fdragged{_ dominant 1/ afXc1�H happened. For rela �a2q�eU�IwC5��,!�equ%n��(of producedM�0s at $T_c$ to+,(conserved) AV`opy, which can easily be 9~ for a QGP!� $S(T_0)=sV_{QGP-�5�volumUI9canT�ed� �-� dens��(\epsilon_0$�BDsimply written as -=M/2�at� b �$,� 2�Hthrough statistical �iE� leavQccalcu!�oUf��-to�8made. Since we !�idered ]k.j)� assu�`Ew$ � =͢4}{3}��R_0^3̀2 m_p}{M���XR��a�X$m_p$ are, respectively��i�q�/Am . AtE:end (finalAjpor!al�n(coefficient��r.B�>A� helpqc@experimental data��ch��$d multipli�ɡ�u��e2�. F��1{2@as)�Yu2J by aa?er%�factor,a3,0 = 0.0989 \�HMA� From%�a���$- _c$, inst�cor!c��ngA!beginn�c$ phase traA�ion, $ K = {�IT_0}{T_c"I$,%�alsi�it!�ed, �f)!�lla��typ�8 (average) dura �<�4f>$ (see Ref. �sandra}�< details). We�v��c,Kopylov vari�u s describ�9efore!1@ Eq. (\ref{qKPG})�sketch�\Fig. 6,�relev!emoA@ um d2c�wpai��pa�<. %\vskip-.5cm \%�8{figure}[!htb6]�h} \includegraphics*[angle=0��4dth=7cm]{qtql}� 9 i3mm \cap!P({\emph{ \smO Illust)kM F*: we !{i�@\vec{q_L} \equiv (\parallel}  K}$!H ;T}>:erp6erp2�!IUshows h r no�,ons commonlyv: d2bM� p}$ �L #K2#p}$.}->-� �studya'AE gene�behavio%�eb�fun�� underinflue]expan�  effectJbeach poi� ��e surfac� tau=_f$1�QGP����$T=T_c� m_\pi��a  ine ent�� otic sour� ithU� ��,rum given byQ���ion} f� g��,1}{(2\pi)^3}�%4u^\mu p_\mu}{E!`xp{(-J�J0)} \;,\label{�}� u�"� Z=(\cosh\� ,�n 0,0)"� 4-v� of !�fluid��$p�8=(E,p_x,p_y,p_z.<q�-l em��d"` I� amplitude�� a / x'���ob� �*K�9m A(x,x')=\Ad{as a3�!�a�xp{[-i%n(x�-x'8)]} e^{i\phi(x',;, -h�:d�0� a random �). W� llow��6 orm�afq�!r����huryak���q[probabi��of det��wo quan�fM�a $p_1�U 2$� an event,� BAhW(p_1,p_2)=\tilde{I}(0,p_1)62)+ |[7-7,I�T+]|^2 =M2t :NSF�d�� ),p]\!=\!)�x \; dx) !�( 1 p +�p!�E!x' I(x, ' E;a[ -�shuwig:�!�J�l�l A^*[xm�W_ ,x'] +)!  \r A=\d�(x'-x)N�.�>�eagL dicr �above q-�taken oA�.�s ]� and ')$�!�iN rZ ��I� le-�,sive distrib��& R�i)=1R|5� %�p_i.x} m� dx|^2 5D Y5A�i].}1�:9 o 6Vn7�n8n PRD37fig1��nds^i$Ca4e�$< a�( � m�6A $IM p_T$ ($6q_T� %�text),�ts al value@U6�� $p_\jRK`IM Q$. A clear �0ce!�seen:x4curves broadenX  incr�ngBv,��� gresA@ly � er  iv�1sregion�_is plot� a re\�1>one orig�  publis� �~1 J�M is!I�� we obtain��exp�on'! two-Aw icleR . WY; iOtudied5�/ t kinema� zone0r{ o kehendv less� V idealiz �ore Bcut uld tL 8 us. Many interT!�nd im>� resul7a4uc ^ �* �� first, un[�� ,�� ~Md. =ea� imes)��L  w� `f)�e � . I will�fe� in a�e analy)*� , la$}MwI�� tself!C� c[:� >n A�tedF�$i��>� �{B  to� ��mo] Q�R (, ${\bf K}=�y� k_1}+  k_2}��e<i� �n� 7��q�tly�Xour knowledge, S. PrattU�suggesGE �!� wAq 9�N$, %at(short-lived-�Q�I�)r%� ilarRT%k J long O� | p�}. E����J�m_T}$,ewn�wI�a sympto%�I3�mA�Q�  la� i� refli&!0break-u� na���eE!N\�d excl�!� �va�I= q�!:I� GaussiK x e�us�f.�Q8�Q9.Q2OK�SIn (a) ���+N isAaw� �F|B�m�Md "J �=val"L, 0.15$ GeV (*n�al uni�in %�0 $\hbar=c=1$)ay (b),���asJ�� compon� i��&le�Km���6���YsI��#m&israfs}��ese�w�i�`W��ak�bi�s< �of $p�A � p$ "��CERN/ISR s}=53%��c��a�l��ebtr�If ata�� as mayb "Q(successful ,p&ra_u����"A �,qց� need%�0more powerfulmalisms�8�6 HBT Ep ferometry�&�ie�is cas�a�,ffort to mak ���� ~r2R�con���| occur!��!,�a�"�� ime &�,J<�� jo����Ctst or3a &�.A?sh%�n��a � ��8E�not fex but predi- sI��emodel,&� with�1�!}�!� $\lambda$�me2(i�is ival[$to fixing 3i�Siɿtreat��x�{sv �% �h~mwo-kao��te]A��C*���� ,]��e�D7Fig. 7e}8���!| w an�� >/ ~at � y ��Astrong�Mt�s!�!T�� ;, defE��de` ngiݥ$shape, due%$he�Yala�Z�,!Ehea�{A�W�!\subsvton{II.2~ NON-IDEAL EFFECTS} Ma�4than 10 years `(Grassberger�`uI�55 role�#onanc"�hav��_y�wva�g�i � �abo�A�, M. GyulassyI gyupad89}�pD��e� < -3!re� deca��o �eso�!�!C.bof= fra:y ATTILAI�-�L/!E� �4bigB�� �l!�.�&�� ��re# f$"scenario� >��"�Aa�s� �u(d)� c�e!�suG an � iŮ!v����cade �  (IOC)!��e 1-D�" D IcBje�b �e),�on-nYJ gas� !�5ew��s* bo#I�"'#B�. Par!c �f))|spo�l QGP e#A� � gb}. Plot�Supp�� anel>O!tA�!� �$ k< ($2%eavy ion*J . Itkv�hգ� verify if��N xplaiUS lif#rA:5"*)Y NA356� (� SPS)I�#}$id!> O+Aua 200Q /nu��7 �! �a& 1#� �!EQGPU !.� last *�%had been6�$G. Bertsch �gb}� ime uly possi�$%n nActua!bi? !���2Q�Eb!l6o�l*� � manag�o demons� &N ��1A����:gEc"'�E�no!;, l dG q�( good agree"� 4 l P$s!N�E 9le�sh'in��iu� (eresena�Ie Q�& ma� r '88 Con�hc�qm88})-�hMsprY�� a�!� !�E糧s�+��a w$&ge/���P��� n ad�(al �%�al%Jge� �! � e� .@�incorp� ���� E(by ext�he Co� nt C� nt Fo9I� GKW,1R,KG� >� .1~ I.� IOC P* } I$FlEnsemA�EP� uq~KG}� *� &7��(%bo�(s�%mainly ic��b\scEi� view)Qy�e*FsC(k_1,k� C(q,K)=1+� mbda�|G|^2}{G /1) 29}\;\;, 6�cce�a�d� $ql =k_1 -k_2 �CK � 12k+ ( )$��(lex amS, $� �� be nm04 ^4xd^4p\;E �x� H }D(x,p)j_0^{*}(u_f� k_{1\mu }.2� })6g12^ _Da�"��-sp�!.G:[pg:nioc}�"A�nV$j_� .k_i%on�Pa!��� &5&s�e�&�s�'rum��Ӆ� Eq. %�)�&�4 $k_1=k_2j"h�)leads�B!�i,�>�))| �1�i)o|^2!r.U�giiBr�1 :aAEqs � �,�%JqP associn���f� � ndqyQ}�c�� wa� F�� k)\propto�'�" kI�\exp {\{d2{2T}\� ;.� j0th�>�How,�"�aQu1% �e��. a]�ven7)��rizEFV�u.k)=z�_{ps}�!��Fj0pseudoB�w�$A� so-c# d +-t*�,$ YeUre� tr2.$ accorf toibKG}F� XD(x)=1.42T(x)-12.7\{ MeV}\]�tpsB�T�� mapp�� betw$J�c$��rcn!� be ar^1�� Al!��J �p�/l�}!��A1OI@>�Q ina�)5�kAL2�qre.  -er��m,Fi���_*e"�� q x_{af}�$- K p/(mT)}  ! \;#-&cegij> YL4bracket $<...>j1 � �&+"���+��coECates. "/1�U28I�Ou�Ca���/^ invole aN>&p�Huv (��a p: ctBle�Y��M�y$�jW f�s��aJ���!��� E_f} \rhoi1}�4 $ � -h,)  eta - y) p_0 - E_�p}) g� p}_{T}) re^{ -x�R_T^2}}}� .%�V6](��4l={a {| p}^2+mS�ya�ef3!z$�T���7.e <2�;G"�. �� �/t8(uni��o2$ �dN}{dy}!rho�$�M�OC�Esre[axf>*in2��tX � �F�!�� !�6[ �t+zz6z}]�,e"�)!>�)M-5(1J?yVd E+p_z}{E-]!�:�i�4y a!n!qinguish.� o��p6,!�.�+ a AB7ow Q"&�A;A���r�4�# �a-� 2?-'^2U�T� ���wav� ��s �,P nite�$T$:Un/�� . By �C5��"� � � a+) i�  A���!�z` @�V�!8 � E�&9 .� �1f%D�2����F��a=2\�*4 2{q_TR_T}J_1( )\}K_0(M8� �( gk1k^� %{>�A N9H^2 &=&i 1{2(}(m_{1T}+m_� )-i� - ]^2+ 2�9 &&2(� 1{4 K ^2}+=^2) U >[- @*y)-1]� �x&B �%h y'$y=y_1-y_2$a.iz0&):\�nr)!� E� {d^3��k_i^3}:� _i}>%��Vm_{i_T}x2X % ).� gkkB�  To�a�the& &J�$�6 proj�" oA�twoa�A�six dime�/�  �8 :�Z�"� &�&mrw� is d�8��P�BG C_{\!k}A�,q_L):,!\!)-W*^3 k_1 2 P_2(?. k}_1, $ k}_2) A_2L;2#} {�* U U1 UJ1)P.NYB|�� c35Z�P_�- $P�-=6��i&=6M���!��V�+@ t!}"!<�X�2F  ce �{-�al6t�h�Yp�� s�0cer{5%"29]U �jJ$]� E�*Q��0cum+'��AFsiz�SbiA�etc. $A!Ni�6� u;2�4)accept���d�8 � $"� % �q�"�6!q� empi3cut_ We �)*� ,2�<2�.,QaX&8"ys�>"�by measu�� [�by��/,C_{exp}(i,j)�� {\N} �-�)i�A'}{B �� \\ �,BQ2\�#�$ft�Qo/ \ \$@]^2 + �?6. ��.}�l�c rc�N ��(numerator $ } \pm � �<rriE%�combi7�Y pair�-"$#W,�"s=!�same}��mk deno�49 $ �� �$�/hŪ backg� ;S& cal 1�� x}�nXl. HistoE�M� Q��ly Q:bs�e��= of8,|5|. H�5i��$� at m^+ \pi^-!zaBfreque�*com� <:e�!�&� ,�'�*��L%h.- !wcause�"a7p�.�`}��# buil�! t%way�y soon� t�a{ a$Qt���uc�2�w� APe.ntd.r��s,%� &x.evN . An�# ��4�@ somei�-0a Monte Carlo" �4D:UJ, tak�4��x_A!A2K��%H�L. F��#on� IOC}�&|L �ionb�:��&�6"l�" �+%j)�be�r /�J�&^�'ic"�"W/rl&�2��)le�$ch.{8s�@0<P!,E�-$��6X at%Aw*A(ly�+&"�! bE�a�,�8�-?I5 b�(!� y a ",k w{; $Y_c " E.4$� �. OA�e�*ha�>Cf$a~�l arisJ� �#��# $K^*$�#$,��,�!+s"�.by.�% �g�%"&� ���e �"�EqgeU)�QV%s, � Aa1spread�*�F $)1B���2!�:� `"�>v�� ouplA��Ci ($R_T~,*��r@)%�A�6J2 %�^�&R!9 ��a�:�; stea�:FM#�A&�yB�& by a&�.E�-�M�1�#& �s,Mý�/,���.�ifc L(vFd"[G flow U+G'r}�"\ 9�Y� s ($�  x}�5-$.m� � o).5��5). Al/#seQ� tU�AI�C��dhe Bv,� B�*�Aw_ �s�|�t�� neI ��b6%Q�"s>>%1-D6^H�K.���|$E|��GJ�� " &Ab�"pla, %"�  % \!&�&\!� % +� "��0 e�^2}(y-y^*)!$2 Y_c^2} %A�& ]�.'x � \} .� %&& iE gveA1) %�� _T&�U}6 F* &&� f  !"�� �arb\�;{2L169`!{-L_f!!)]^2- )"� no�\\�ex)�[1lF� �] ��� �?} l ��%�L-y2���:s b^B��A��if<&�c>�r��a major���+��ad�D"! % �N +O5��s J�$. tLmJvd��semic�,�^ &io��#"�"}�.�, $x_a*"! ��� �nt�.Gdu �>Jr JyHY�uF} n =x - + u Am2,`�A�aND�$ 7$ �<� 5Y�r& Gamma_r$,{�8 thei� cay.k e �|.��EqMq��%�al �#Z�F`G#v#"S ![ sum_{r} f�*^-/r}�Qa�((i q x_r -K!�/ T_r)}{e(1-iq ��S{U \;X"BceresFY& f_{(g/r)/�$��A�!!� 1ed� 'w5is!o�`$eJ1a&)( type!�'8*6�_r$L J er�� N>�� U. A* 7 &�/,- �%1���N� 3 nega{i� yield at �)  i�;V90\�/)}=0.16�/$K^*)}=f_{[)[�1+�#\pd5)]70967�]P4�LP�/19$. A,w� WH��/�j�!ksJ �%�$e= cay *JF�y� hard_3�n"W,�c�F�'�<8fast. J� LP��c0als#.�code, na� CERES� � :!����M plif�> ubroutine�(�$m�k*2��Pf��&�8 ye2,���%�F�I10B#:��0uA4NPB339Fig3OKf}�-151A�.er}>�A� Nu�Lr�,�(! A .�&`k u�Z� y$E �*|=u.s/ s/!�e����{�)4F,AL( by�~A�\/5�a%���/J*�,&w,ahow�<5+B��D msel�! % "", der�=A��0 IV�.Ap�� io�"4%5B"�e:pr.qBi5Q.�G staraU �� ~ h � b 6�0ngN&�E',Per$ �>I�a^�and, ��, �Ld�U&�%},AU�Kfi/#�0=�BQ�5{�dh*� ��U�($�q_L/mSa+(y \ll 1$), � s�% 110�WfS~A�@�!,r� � "�u�2����!2 �'A���&�E�5&�-: "` 4$fm)tau_f �/c,-IA�;�K":=1l%0 J$ =4$ fm/c;F m*" � 0.8$, pluAX%�"$s��\pi/r}$ ō�����.n.m0. %1� p^2/m = TNQ17/= /c (O���!�E2A)&�%ura�a���/, nv)the�De�d1t 6set��a#5 %�OQ~t� el�~� /<ere: �"� �!JYaa � 28� us� >�b�7R_U/ 3./5�A/$y^*=2.5b&m�5< =1$;A� �^�het1 �a�����gb}��no��8E� =9.0Ie,E� =3.3f�j |)'aV.ft��n� lambd�. %� ��yF��Oq�9��ig�Q�,�sI,previo9in M8"�posed d< Mlem�!$e|;ic�2�heavy �5;�:�:�$� ct*�1"�8>�&�5[x fi�1N���s�=� &HBT1 . �R^:11� �9 HBTPRC41O?Ce�|2apR1SN /Fi :���J  Coa�iso�6�H�6!�`"�9 �BAF$�+"�R9s.Dc)� :i!��6s*u\Ra,AJ���,��8e�mE�*]:�P�9K/ � �$q&�C�8 . So](dafJ) l? i�7�&]!sC�0(L ) CoulombE�or��s: (a� :Cy!a.c=ba���8h� :\c\ att}/-��:d�hplasma2�]a�'deF���z!�1 ����-; w ext�d>0+ aF�KOnCY7�6i�@�e among y�,u��=g�HVk6a},to� �?�&� "�5�Ly��9A�EE�2�y� ^��| motiv� .2!�"�:[ ntir�_��ser"�7����58�@[ �s.�5}K �r.dA�?!D�qI�R frag[ �ɕ,� >U?KBT? $��&\1% W?on3{��?%H.m erea�"sea` � half��e��3�� �P`B�I�LɵET!R$!R��G:n=��12�yQ� M~�DZ�FZ�� )�sE,+M to�ab�4@�y !��!Di sawec�S� both,s�9R!�9AWu�Ma�d��d ��hnt[\�W&&6}%�in!n�^>�#X �]x�&r_ Inde�WY�P �11�a� sign�ntu2&o�[wo)�s,�\A to s2D��/��% nt@9��/� Ia!�" &��% 64 �C.�Bs"Y'd!�ve%�um i&�CH5$|&@M� much3-er�; s at�er"de Y"9 loo��JIq^� pp$G'% �ISR�@lorstad} O�2�<y�^.l_jS A@h�"�8!�AIb�be_2��. SurpTM� �(npa544} turee+neiyeyt�=�k!N abszZ�L no��fulN�=��s�tY�&�>&*�|"a� e$�9s?=���X best5d��Q� ������&� B�i� �s*�12.x�u]12Bx �E NPA544�DOy �I N25�in:� A�%-�atU�U��c >$ $ $Q_{inv}$. Uh ��3<&a�0�A� � ;(&�M/c)G7 H. D �P a` dot-  h!' gram�*�W%�*� .� 4 >�Ano,IeE�%�U abundaWH� i��%&e�ٶq��!))�Ni�)�# u. B�o��C"� �otA/25F� ( Meanwhil1�a��d"|Hi&�<]SE �E�)sm�X �a6�1ii�:a�n]b��!�,�Js)Z� �f<& �$�$�� S8 a�*p:%� je di�#in $N6�' minima&9d;�un.>ty prVEpl�lso��] terms9^ ? ca%����AzezHI�Q��I emi-�� ic �hW����ch t,>g* neg<$8�j mean~g*h!<��)L5��*� �B�., e$H&�7�fe�LreZDcM� a. %U�pkyN,concila%��2�# %��5�IE1�EAI�=Ba�ach�� n, %h�5i�W (de�&)2�con���  %b�9p%=�� �ul� U &� � � umma}��*�avula�Bose-E1ein3Vmed>edaaTin�< � �&�n P_n � k_1},...,g7k_n}) "{$ \;\l�) =\sigma �$ d_{j=1}^n7#S/$ i(k_j-k_{ *_j}).x_j(]")#(#�;tW`4$}_�BP,p_j)77-l�<�2w�� pgg1>M$U8smo� d @;�/�b*�9�%Z�-k',p-K�0 P$\!E \{[p�#PY k+k'�6 /(2 �J)\}}{�c 8 p^2)}^{\!-3/2}&H0T$k$1. exp[ w x�$2}(�)^2�9"`�J0�=sF�= ave0`�! $8n$i�*�*# $\{x_1bESx_n,p_n\SVas�!��{ie� p'\a �4� �\yO�- a�R3b}��a�� �,�y|� �R +aS *i?&�']@�(�B9>��C7�q��^u�o��6\mp�� #of.� �p@A &k "ke` ��!ee�rk!, group,�cu�Z in S! II.1L\ (SandraPhD,s }. A�e al limit,��;� hat,��um"  pI�85�x�}( =1/2$, hav�wU �hm ;E 8"$m$LE 2 Oni$ -"�D2g$ofaemN�C�Q rec�X��.�Vic�^$"$ ��)eJ�JEZ`JGKWA�,e�Aps�Xof2�w� �E��a=/ ��V of ") �utI.��pz�0�. AnFi�Walter�5ve �3of<�!�"'.��\��� ��u�}z����C_{N,n}�L!'i� 6�D� [q(jq�j)�:K}.�*B�2��!�F�g(q[&�HA��g^3p��D qx} 1-�.�BZ�q� ���F�I�2S$� �byIK�^,9��-)$1Z�m N!/(N-n)!yUn=vi���Y` ��1$Nu_� pRA1A�event.<AY&�csis!=R�#) [O��A^,q�� ��rf�BA�� �$"v o�ga<��um;�8m ;eulready�inDZ7}�$� ��of.��/r� s.�m(�a^.� n $K�"a��Y t~;!S�62.� �\�1�]We *�$on��> ;n�Na1��Y>as u-�!c12nr})?G5�XanM��\�H��.Ti�7!)1�4-R� TN&*�+�WH6�N,h�CF�N = (k�,_1- 2� �  K"�t _1+ 2Yk.�+OqK"� �*[ge �F��` mmednLl���97(�!} �K_M= q^0 KG� q . K} m�0 � a� += m - .K}}{E_K}6_T.K_T}+�K_L #.`jq)B�oE_KzF0cK)G�C� [ !�F�. PropaO+_+h�4i:q �U�*�" ,�rget9> R^2_{T� �reff}} &�Q& 2H +"-Cd")^2e �$_T/E_K^2) .YLbYR_L�=>W (K^2_LQYA RTRL1f��) �&�O.)aK�(a;e�6f&� -F� enh3%��;xsu�b�U7�9!� Iy_<remark$�kt"�� inva talk" 7��? Ko^"�T6�per6a�b2~ omit=A�._ lac� Mi�add� \UM�< Cp�e�� k�,R w&�vB1c%�Z RANP.Hs of H�Mn Physic3:�T�3~ DISCRIMINATING DIFFERENT DYNAMICAL SCENARIOS�;co��Kal J�Vzop�e"Xs_)�ab&9g? n{ QGP * ���& 9,&�Ene�Jit��f ngy�%r��;�cri.� "��*� .&�. ��#�] � IJ+%y��* �yfu. 11��st2kAD�&?��ri �`A���An�adis���"E� 8�c�; way?���e�3ƌ%PLB348��o\%@*@"v*�$ Si+Au*7[W )SA5�|Au@AI $q_Ly$�:$nary E802 G#� e802[r~0!q*&ZDh/-$��$e ~�Lart=_.@^b)5?$��-qDR1 s fi� c0�ne�*�/%�2D�)��@ �o  ���Ny`&�O�i^B "+*X$)�J+In " answPUquH, on, *c� my�mDdeveloped a methode�`4 a 2-D $\chi^2lal�Y� =o^�2/!f+ two-"IaS;5mA� I!N�M �!I � �-"�m�M�f �E�.�s"�B-d#-�A� � �)��ti){ ?� c&�'�Q�o. !W#�o  � ^3�]"�j�rl ignoA�i"<$� 2W!ACeeF zskiny3����us�RiADd Mors���^ BNL/a� Col&Ae� cU��o $��!�s�$14.6 GeV/c)�e��+CGAe�lAGS匡^"1�M��re !0&� Ji��F݅m�2i�@&N�Y!�1iA�E�aUe�&��&f&�<!�K = A.�J1LK*K$ $Theta(20-|Vy_1-2|*O $ \\ &\;& "(� >�,(q_L-|k_{z1}�z2}LT-|Tk%S _1}-. ,;\;"�GA"Kv �#;�u5�i�k _� AN� aEI�.,w�" E��N�5bJ�.Z)&=& -K14<\t!U$_{lab}<28)"� u !J -p%.2\;{\rm �}) ",y_{min}>1.5)9=a"� 1%8QR& & \Ohg (.�,!�, �, m, % ax}�y�9hi$� � zc� ,\eeqar{a ?\; !�in�.%9matchaU; .*ly&�9��%�t�[��$T 170$�X.!�puro����`a �{& "�_" � tib�*o.�t�|�  03VO��ٙ�'�fit�aa�.� gri�$�N)$�+Z bin��$i4Vx=�V�3 =0.0�,/c�r��bl�?(� (g"�4by W. A. Zajc)2�&�3�"�!���ud } �5L?_{ [[K -rL_&}^{-1}th�L�J L} { \{ [Q B+ [zG 4YK4\} I��chi�F�""M�a6LK f�� �'O�to iz�,1��!�Z88 � ,� )��U���>!yM�>leM���o `/ar�3zGBa�2_ �� �>�~oaQV$�y a 30x30 M�e%IQvf:z� � < 03���r���l*al. I Evic` � �%um} �rm"z�%�a quadg c��J��i (R_T,m� = �� + \al܎*-R�00})^2 + \bet�hau�B0��/"��bSQ��� �1�,TABLE 1: 2D-Qc A of P� D&�G�dy}�p �22.9cmbc�0{tabular}{||cc||u�c} %\hK1   % &\\ �(! �7�$# No R�)s & LUND.\\2N a  \�c3�$n{3}{|c|}{ 4 Data Gamow C �-}$P.�$|%�{2})�-1|/\E$ & 2.12� 8 $R_{0_T} D4.6$\pm$ 0.9 & 3.1 1.3.2��A3K�(4 )0.7 & 1G1.0� "ѐ& 0.02)��4 2[AP�0.042 +}R��)1� QP� quan�&��57b]��a�-DA(AhaJ� G"� ,I&6�%"�)t $��,��n� 13. ,!mai�@v � a��D)�v!�� (9 ��.�/ hъatF%v"}$q$� EUpl �0H$rswU {��Us�(q)��$,  � {� gA�})�n.T�1Js4|N� cu^��[,.}%�"*h�T��r4 ,�&^��. %u�6Vb�14��-90, � =Ӊ efigzZQ`\cRω �*E��G0�ard devi[ZS�yy,#��g�v��>!�i� fre�i,F?�}y,� %!�qMw B� d �?� 6Jy>�?0Ve�.o�#upp�opm ^��E�ie&�@-he$&�e(is�u�ORa�-� oRo�'atqB%i? :���-u�. N")t`<if��0s.�pi�w�7�/h�;:^i?"��<� a�|.> W-� se?��'R�+is blu�Rm� �fluct�:� ��;t)�z �*�A&�Ist��z�� �.! % z!!�as� �G� !��p�)v�m i@ (!�s )t h We�T�mu�a $|� "I��@� 26%vf_qA�!�col#_{�.�dOюtU�s8 magn�e�EŠi>4.�p�=e�fuA�r t��Er_���G llen�  si-�<�fm.Iui�X#Ž!�$K^+ K^+�cwo��E$�",2y�s (e� 7�Hn" GW��e% �'aFW %Ł���7))�AGa#�AwA�i!�s ` by Cr&Gane{qRold\~a�g�4M|r Disser{�J( my supervi�8Y !%2;�wom�.�����;/c%�6DV�n$Cianciolo,�E859 2>�p upgr�vm=18F �A&I)AU�� �C��*� 2f� Kaonb� � �}"� � �  Z} �6�q & q �l\ � <$(f_{K_{dir}}=1)a 6 �I�I5)$&� & %B� F {Optid*U  $� � :� �:2� 2� "� "�� _{30�+30� 1.03� 02� �I1I1I1� 1.c\ �< T!V 19" 6u95" 9�7A %!_0 !�4�Wz 2.0 &.69� 6C 41+L 99bE 058F 034JG J�k >�(.�=0)%�CzHR�2Y 1.3� �BB� 4.04%n9%�%%.� �F6-t8� 4.8 � {.0$�)$ 6&3)�!� 0.00EI!m80.m6� m��D \b*�CJ#"� �ם� was .(ɱe859}� \�.36/boldmath�Kc. 2) =�.">.w"C2->C"��r&� N�VE"UqG.�{L:Qk�Sa2�%�9� U��V�6B�GVpe�U� 1 14 6\ 28) -��<�:L.�.�!>�)��v��5� 5B1FB��`R�e�,� ^�]��#"�QB2� &�8"��^�5��"�8�]{PRC58@;:CZ�Z�� e (�O"$s .b>d,�tS | �2� mU yG?�N H !qmb7um 65"���.:tf\>�>�lo(Ed"� a)� (b)��8y !�s�> $K^\�M$eQ CXc X�  /&`&�u?�f&�-)E�B� � "�Ff!w+xeE��1!�sMK o"�f �$.M u�6� &[ B� I�b����#rRx o&� R) B��8 ��#a=2L*2A"� �Ay s o !4"!�4$b�ltAq� � fav%2@\X�� Ac� � *�I (BNLB�\A��2� 2�aU�*�&Es2�:�BB�)\9 �y!��u�6�?r�16w���(f�e� 3z��&f8in �2��%a���, FK �e ^�Fw�%\h�K@�i/f��8.���3���F��#F��!v~�"����i"�� rju�K%�KF�A��NmM:Y��<u*�� c $,tN��4"�.�m��re�8�OK �AT��Z�a�5t� N�$zero.�/FyJ.>[�tes�&lso ru%�{�0&�I of am$wb0*per(bcon�U+�L��")%q of AGS/� 6�#*� ��6=�(�ơ�!8E� 16:���6#=!!�A�e�`.�5�rz2;a��tly mea;lQ��Sc��h�h4~ SONOLUMINESCENCE BUBBLE}&ewh D��&�HewA3 sa*�,J6�P.d�r/7A�� he� �,f h',� 10^{�m%[ste��]-�� ado-a� omy 6aI haf��Ft��+���&�7�a so f���"l'�%,+o2z �-�I:c^:1�+�-(rough�(.�-15}$ m)�� fia0�*7] %% X %�ےsonUi�*a}G~N7 .9�%�qF:2:�s2�(Figs9612046�%� � \reA$,box{14pc}{!}qN[��6���7.>/}:n5�n2}��c:ld6W�P��Nq+M�I�as� I"���}a:gF��o(%= '$_2 = c(k_1C��vCases A��E� >!FM�Nup fth �6a�#2�8rt98.ń�*�$ $\Phi(q)$j�X=\ 3$-(1/2)[d^25,0)/dq^2]} q$эs: ݎhkpF I��tT~thEX�v��.�al-D\Yogiro Hama, Takashi Kod� m,�RoD�in 1995�Ea 9 ng acR:�m autiǓ9 le�z�r environ�+��e focu)� q�ne� t bubbG�L�U4m  li��jȭ ��-5}$m��A� phenomeno��MQ=#ed� +3ago�1934,�  Univ.A�Colog4&ut kb�( �!{��c� by Gait>p t al�V�1} %_88������,L@fwdof�1(us��fil�d airBymwƛ�8qEp�-by ��� acou�hm?�X��_y 10-12,|o-sec *��/A4�_t"�}�@l����� word��lŎ%�c18 vq�%�� 5ap4 a*id $7u`�ks,� p pul�h 4� E�io� llap!TMpcav�(ng-ci�1�S��XdisE1 % %techniqu�dr) ppH"9�HF\R� %!�.w, manzUK5� �ert�ShA-r$revealed %=)} %"� e��A�L�.lig���K�2�a/0�)f 1P%�F �a wide�u��1n �bl�%4 ultr�letG�Wd1�-EouQeBpMrs<r>P�rm�A�%31Irn�p&�WM:A�@p���&��kee!�)�spher�Oae!�;YM,b��1��ts��shrinksxthan %�� Ctude.�<"^��"�� l)_"�;���4acn��!�TyM�7�imOoC=;��b5�r(�@i6: s� B01�m_@i�Pfficult6/��4.!n&�i&5 �Oth#u�)V*Yn*�%' aE�>�B f6!>n���sial:�s authogCt�4*)e 5#�%um-elect"�n vacuum! azy"JM^�Ca�Zr  2ioc �A�U�1 �Y5��Mc�˴�Qmal��h1 a b�-body�CE���}b �o��*�� %Be�N�_�ywob*n2 %c�=dat3 `M�a� libr�{ato�ai.�T%�&s�x� " -I�2[hh�Q�aX�HZ)�i-�Ya~i �3!�s���AᅤP1,A�"��QR�l�Y ��ՙ"4��e��@ex8�cPa HBT5� al�se9%.6LsEp!�e �ariW~=�"�!�� TLes>�4� 1F�v�ec�w:U�m��1[:�"u-A� vH�1�Q�bu[� h C)%t��uL��X�?E+q��F��E�A'�:#m��3�� e ZBa�(*�<ic!N�D / a _�R/e�typ7$ ��9 J�oa�ntEVno�i�&�WiAg�@%Ca� y*q&"(  acqu��" triv7GvH) $*��1$��ll q$k_i$ʔ!�_"�GweCOpHW�� �s�u�G��"�!%nPaCc�� 6�M\=�P�IaC5v�Ne�/==.lf adopE �in� Heinz2J6ppl�i���Ah"�U&AC(�q{k̀ 2)=1+\frah�{|� lde{S} 1q} /KE���+MS�J 1)\,N2)}\,A5,�nC(k1k2��V�B \[�EF�&"Fx\,e^{-F�R (x)\,j^��� j X6�]Z�}=(- 2$\thin)����K}=F1+�/2\,$% �)d $ji)�1!�amp*�u����;wave-vKz�k}_i$i >O( $x5<, or 1/2AG]�,hE"��1y3�l� �spe 9n� J ��Mn. ?*ձ�Q��'�=e�'��2&(I]sN�='J�3��"N*�$3&q0&ve"n��@ 1/n2i/N�Jޅb�R�3�p�7.>'![�&%l|l�0 $ $A�N$ Sour7irho(r,t�$\,i(N4u� % _1us 2)-1%%ZmT�b � )LA:} $aHr^2/2RZt;t� ^2�$$io �} )^% p�}8q^E/2� .kBkK! (r-R)�j,}[{\rm�Ln }(qR)/]�,y.xCxC  (R-rfx5y�R ( 9/��) N -!% \{�\}^{-4} ��#{\, �cos �-R�\}K>�".�D�!Zr/R� �3-�!�M=l�)6� a3��tau )/6T:G] ��;] ( 1+)� #) �N�E:}j&$99| I 24| ^2/(8\mu ^6))�$�$\dot{R}\,t!���A��A� �$t)$& $I=-i �H�} [ (1+Xz^{+})W( -1�(1- - -}) ] -��&1wŔq� \] AsZj I�,"�"���1v3� yett-� s����-BR � T. z7 memb}Wo�hsvP��Vtm�  EA�Vi?�A�n� *der��"w ic� I ]ju2�^f  �{ Ւ� ���:) .w" enoughN@(8f�� "� �l�oaim0+% i��&� �,�s� � � ��A/��� � . � � auto�D�?y e�c��G ��� I � Ff�Oc �>GT5~ CONTINUOUS EMISSION��*�R2.1` disc� ��pIn>x� (IOC)��Bj}�Y�� � � fw�*/�*/-E���w�049�  ���l�pb i��E�a��2�=�R0�Rev�/��wards�(�gA���U�q:j�"c ly ]�(as Landau's/e$9F:�S� ith &[�"� s. D"0��ae{.( .� cools dowGh�Z4*e� t*�& r��� c /i2 {' &�{f\$ E�!#reAv�m̑";o:ge&��� !ZU�, �1�S�lZRę%��Xg T�{_L� )^3 . $'6�3!x�����&3�AVd�"K\e�*<�2u��Co� -Fry)t�GXCF} &� %&�� �� p^3}�Mint�)f} d\�9_�m+� f1� %&��Cv Frey�)�3} %��hy!Q"ƾT=T �!  $ f g"l 7  %w�Q�.r"u�, Ž9�81p, %!�$ �(��f\"! .�a!�&�R.�T-�5�2�P#%AC�W(by Grassi,�Ee���ghk}: �eaT|�t���>ly!-��se cro�A�Ja�ya�2�pi� ��(tinuo�pdu!A wh��hi�"$e��_ v?�/erent.�*\$�e�2�Mf�M,zL�Pm�TE��,�l��Q#pT$�  4]� �;5D���Maa"�B����anymor/�o��R1YW ��`ng�+�Oz�om��s,�ҹ.�� ?\�_T!�E6a�b"� ,�!�7fng$m�o2P}e�+f_{int ���AUCoQ EU (CE)1�$�ov& �ax��Y� o�����@t#2U"�9�_�=KBP}i�\Long� a�R .� =(1-.) /A"r,*�Xly,��6q��I}{U}.nk �3 Cf%b!f� iz inte%ni�� "Tj%8@Y$�� a!@R2>��R��%��E f_)D x,p) � g�_ "�� 1{\����$[ p.u(x)/T�%z] }k�1� ;&�fth)� �sa�ԍa�Wo�� �c}�A%�m, .�b�י��1=I}6�mz'oo dilu%V~i[��h%N.�in�%�Egey8� � &�� ), $���c�fl�v�� p7��ŒT*��.��at��|���mn��s aEP}X�� spac�$'L,��V6E�+oN> GlauS�4 ulam� $�%9�q�I( -:Dt^{t_{out}}n(x^{\p�( })L$ v_{rel}dt\EL) }, %mFP}{6Q�re>� r=t+(-� �yI +\�#� ^2\sin phi })/(v�I ).bi�t�:�i����Y.N� h � 8!A����}beQ#x�Ff�Jt�o~A"W��G/c10}T_0^k{9Ql8�Jsd ��!� R;+Ap zero!� >MM� l�]Wma��*�k�-���*a�in!;>�U0�� I#)^a�a6 3�p1.202}�� _0 IC MCE�)�PG"��~ ] ,��1f f��f�� pret�yX@ٺ��}}$ "i "� or, *3 !$ K.rA, SJ�� �  $ escap �$e� $yo$fu{="�f+Th[ earl!7=%�A�fr�d :,B]&� ; ���view A�Fre�i#� %is" �� is a�?��� ��cA��.a�&{ "{el . L�$�*�P%  F.� Y.l �O�xcolowski �pgh��w<0��-%; ���ieXp�D� new%��.criz�umq o�8iz�$IB"�. N�Aw� like to 1��s�j� �e]a�:kak�I�w<��.�A�Id�CA� ��O (FO)�,�ecc> � �0�I-�IT"c-�!&� c4�%J quit*�&�in:�3�I Ful�,a�, �-&� "�d��.2[ non-Njant�& �E� �-gX���s� �uA��c�H:*�"!g*mBzF"�#a�)!=BV9�5U �]2.��A�&�"} ��`�?�qb&( o9n�\� �#?u�4er�O~��HZ�-�:�Ł�}�#u yiA����s!N.�~4n"�� EB�dq��( item%��/aU�t �)� �da�a=re��!"��+&� ��) a&�"��*�Nle-C-7'.� "�n�^aJ�G(k�  d^4x.:i|D}_LH[ k_i� � a� �d���giiceJN $0�� W$A!generGh0liverg� atorau 6[A�Ŝ!�N�Y[�*�T,=b �)�re�A�he.� �bgral, $E��L��� � $, O\!;��Zh8^"h !�u�e�P ��pZ . Or]p��Eq. (�J%� ��F��mis.2C5 agCcurEs"�e,[cj"��)�p 9e�E" &V�5�d)�$�Ea��5ric��a��� �7jfI+�$&� � eL!���.�!�7B w�I�aG-B�w3im4s�Hr]�f.w"�a "^hu !A BoltzmannI�6�3 �@-Ugi%�or=GH�5�:�ٸ�Bt'�����F/x umLLV!�F6.kialogo�y%�#���*!�!荏��n��EU g12}�gZ�1x����h\;\��`��1V�}�� 12j=2N= .=% ?;&Sg12J�!aw. "�e"=!E�Ae1}!,��%���� C>�J�k,%��!t�뙊.=R2�X.��'is K�x )r=��{ � s:�.m`0�� (ndqVEaiBU�avi�i a F&!��  Eϒ)pe]!?�7� A�pair,�gE(gI"ߵ�3T�m�2��� �#mQ,�'9��>m�� �Deau -�,o�pof�t� tr)�_i ,pgg,gb,h{&1,hpb}!�_�=!�K�/�&cj��e:6�!BN2 "U@�n �n> y/�4�"�o �n-%.<}$U V 2= 2. W� Q1kl�so� ub6 ��*i&^�s � W��M*�tYteb~����o d^{4}��m0 q^\nu x_\nu}CCB�� ���i�s< pC"Vg12KceB�W)`�`/)x�?�"*e�\,m *aL�Kme%k!����NO �*s&��"c��0A�E�|�)�{b�w f& &�*��FOe�F js9��(}B�kk}C4�/i$-��A�2� E2Q�A(* Q�R)n) ,œPBfour-&� ^ sa�cylind�<*�u,*U symmetr"?Nz6v_�uf�"�� :&�] &&\! �= "�E�$ &� 1.%int_0^�� }dN{ $fty }^{+\i d\eta �T$0^��)\,d�;Y _�v$F}}\,M_T\,�h (Y-D 68`>�HseG[>N (q_0K� -q_L�h )q_T# (��` _q)]}\;r�t_{ s0.�%=>d��K q��& ���H � � .��C:�)� )1\;��&!u^�9s/-t(x)}}���)��P}}�% })}. �!6�mi&0�Q��{l; wB {$M_TJ:@K_T^2+M^2};\;M^2=��n�y 14$nq� ;\;$� 12% (� �$ )$};} $Y$��a�ra���.`$%,^�$% E6 azimuthal�I� r&g�����XM��hA]M�%�R�;e <q}D]�,�xg%\v�{-2mm} -VF�E�9�})&{I�!�E��7}{%WT/E)[ciM^2e�+^"R)2/a}}-mm}]}%� nQ�%Yp tauf"M;�5�"r  >d &=&'] \;(k�} �~�% 2�V�\;N$.~�^Ų{k_T}Es**�\;b�"G}nV�^2}; 1I�˝�%ZrhoBY }>21 "�fHSA��V��u�),� �� �a��$, $M2mLJnd �r20$.�E.� tv&]�e%e�rho2� o<;�.F� �� � �q%�9k� e���\ P.�|�we�D>b��2*� 0.5! �+ � c�*� �o.y�X guarante�"&> � p��?! hold�� s �>�" �"B��t�E$8! for ) 6�>ڡ}��� �� ins Qj&� k})'lex�o�=��&c6�! 6s" 1%,w�A��Ii�=O�(ki:��Y �]sti*�s? ���j5�%�� �*J# � Z=,m� *�vjs�1C1�#m�L����5!|u!N�  _O,q_Kfo�,� u�out�)&g��,a bf q_{O}aexhibshe�!-r� �d�Vaverag 3>�xx, "� �ie!�� ���M!�.L��td i9?m"�LE�Y,��U����l� coAF�5^�R�We K5� a sl�0*�Lw$�-�.�"@$1���q_{S}�� �CE!3�lYZ|�A&��T�t1 w!�r P"��J!"!  >��9'� ��^E�no�An� &��OR�E�e �? encyF�]*>A�6��OcI?)F#�a���.L%Q.&8ti0".Zu�>ias5y� �M��C�6FSH8]"A��?�e��G6H(PRC62CE2qLO�x\�:4qO:%�;6qSOK�5%%nH1^�G2�}� 2SH~9 �}�6 �Oj2��*�/fo}=14(U&3/���$2+} M �=a�#O. P�b�Bc�{ &�� . !�"%mZ %�E�;d�&�"~_��؁�=�u� MdmG-�M,"~  �n����!�2"�%.e"n4al&Kp��. B` . UsA@�&z1�&�!f�j.e) &��� a��Wx-axiQ�?v0K} = (K_T,0,K��2&=�.�1*:�2cu,b{.g�DPy����(2  (K}$ (except%��EP� @?�&vuk`6��!m2����B� NA35y na35b}��#S+A*�$a> 200 ��^j��"�lC(� �� = 1�� �� 92�y ^{180}_{- dKޜint^{6050} dK_T�^{30} dq_SF(o C(K,q)| G |^2 {Qanh}Nh~�6{o i \ �1 2,k_2)}.&��7e  } W4 !�"�?P�w. �#M� fZ�M� .����,En�[ .� CE( FO"h s.� coO �� � ��?0� .7+� s�4h$;s (e�=20���a�� pre+����utA ��vR�wo����T_��70$MeV�8�.�b� ��1.R;�98eF1�1Vin �+�: ��W�^�<") 2�M i��NI n?�* Z�x-�N}!�t�-��~!�0Glar*�@ ��.�ň.za �5�/��!�X9����_t d���]izYK&�2vANŤ��9�%� Each8���3uE!b stj7rdw!�iB�!Cj�8initial tempera�ture. The purpose here was to investigate, as usually done when trying to describe the experimental data, which initial temperatures in the FO scenario would lead to0curve closest� the �8generated under0CE hypothesis �xresults are shown in Fig. 18. U �U shape of  (correlation �@is very differentI(both cases,D one ;spondi)#PCE behhighly non-Gaussian, mainlyQ!FDupper left plot of�DIn this particulart0, we see that�CEJ�8can be interpre!<as%��$history of ot expa �Lmatter. For instance � tail�0$\langle C \r D$ reflects essentiEJl early tim!=IVhe siz5�system!z small and:teUF!S, sinc!e�5EBisIErQDFO!:)&>�Rest inB�. O!�9ntrary)peak regE0A<S s to�latz��r �da+sions!=� �A�large N�low ()��for�ctrumA� two-i�l!��h, adopta�a dens!�8matrix suitableN trea'A2chA(d pEz���G�c��tvistic limit\cite{zp}. A few �2�� spir%58at study. First%Xconside!os,ecmost ab!Bnt��,les produced�2�8heavy-ion collie,a� be quasi-%�8�i,)�urface t!$on �Lshu,MW95,SRSAS97} ac%% as a��!\\a!�In �Lregardm�!Gwave fune could�assum!�8s vanishing out!��\As�6%8 also.=���se Q ,s become fre�d(heir averag��parɐis���a�(E��on �{eAl���traAX%$to happen ��rapidly,!v$such a way�D momentum distribuE�( !6s w1)$governed bA�V>(just beforeAJy���uteY thenE�iE��dific%sa�Aobserved�Zj caus� prese�.�is 9�We)�2Ci���C��u� Q*, � s knjtoA7sA� tive�ge�= ical���n emisa A�!�as we��� :�lyA�(dynamics. %�e%ށwalismI�si�-!�6�%\�be written as \begin{eqnarray} P_1({\bf p})&=&\laQT \hat{\psi}^{\dagger}((A�Dle =\sum_{\lambda}2 '} \tilde Y&^*{(\�)Z"'6#.�a�R�a'}�,\nonumber\\ �2�NB2�^*�2"R P; \;,\label{P1in}\end=|w� !�$ last equa��fo�9s�:Afac�Mae� ecte! value $ � - $ is��a�� occuvon��bab~eOe Qx� le state !�$, $N_M $, by $%U|u�} � =\delta5z!j}'.� \;;\;}!� .-�adagaa1��$M}$ ($aY�f}$)��!�annihi (c�,on) operatora� destroe� #ng)* !Y in a��u )C��acteriz��! I�9e. + Eq. (\refIc) $E�m�(m�)Y�m�l} )aA&_{l} .�^{(*)U� $�L kB g%7 W9)�1  (.89.,  $.|�$!n Myeigen���R long�-$to a local%:comple $et, satisf!� orthogonikt+nesm� .  $a bosonic �!� equilibri� t a2� $T$ Vhem�� pote  $\mu$, } it�reɯa�P Bose-E� ei6���umH��<=\frac{1}{\exp{\b[T} (EY�<-\mu)\right]}-1 a. \;q%N��>$ Qabo>  $ coincides&� !�employ Ref.\� � } 1 ex��IeN lJ�. �nor��aex:Aan(F $AE;given��v~A�! -B tr\{�rhom,A}\}}E�\}-7 !< \;iW=!�)�-2�?H%� eN}1� =\V A� J{}\;, \; ���T)>� % \item Fq%xQқ%j� , %\%��!5��Q����%��J: 2A.%$Q$-q� "4 and���n�!;~�$a)sN5�,\; $% �l>�5t withJkN H}�z uA2 ɝQ;H=E* �'*N:S )A#,�hamilB$resaAive !�H(onian!R�m1�s;����!��� ��, fix?be zerd,"�w� t�. Simil#� 6�2� ��� be n� && \!> P_2ͽ _1,p_2})=>$ \! %�I�A*9}*� 2})qV- R.2AR2 %.� 2� _1�_2 3 46� ��_1�1})V� _2&�6n� _3�2Jhip4$H.V &A�Q�� a� )�.g.�e#V2��* _31D4} > ��6�N� ����:� -hjJ1F63�3�� _2F@4@9�1 \ne��� %��.6X%&& +&&�V�J�uڵ�_{:�Q �}6G& %g. +�iJ| %�K��� �=q�2 3 �V%j ]Fk%=&$� 2})+>#6��2!�%&� _1*� -}6*x_1�q��%.'�%��2%.L2'jL%L2�=&=1}> |27�}R����V$�F|^2 .2V�p2g�na� Siweq�1 he�; tw��winguishC , id� c��g��henRw 6L5�]�>�� a7B-M� = 2 l $J2b?^2.�� BE117&> skip2mm F�!,�� formpor� !6� � f� 9��N�ѣ = >�9f- 7= 0$, )�at it�notZ �ed�des�+$0 0� +-$EDs2�n� !*a�9/in &YS94}U more adt g b�m� CB� �F }{6� 2}):� =&1+ Jf�  9�&1 e�ps6�} {b=|V91}��727. \;. .�mpi2q�OIn� �zp}�[illust�a 9�by mea�f!� exa��fw��= A�BY $re�P�yn�ng sp��(radius $R$. Nsecond�y w�iDubic box =�$L$. �8>_ 9 s� . ,I will briefF!iscuss�  o�I� one�!m� Eq.2��Qc>�of �'�!`� :�� rum.!� .!"be summa"n lookOdirect� top� � "a!9 A�b��&)W L ��x�� ($R �4arrow \infty$)%3a� !��M a�!�A|dez��uh"at k <"�Ai&Zand, p same� , ri��broaden>\ �$p$ ("�w ervaY). %#4figure}[!htb19} �ce�!}\big��>L %\includegraphics*[ =0D`dth=7cm]{PRC62Fig1OK} \\ H�@4�@5@%6�  � \�n -1cm \re!�0box{11pc}{!}{>�2�}%\\ �8�}�5!} ���4OKold capA{\emph{\I���op$a<s6�iD�8a4A�sASf=�6/M(, NeverthelesD Q*��, �W%� to $C(q,KU� E��s�un*1~�=U�6� i!QUAT. C�%pw�is q !�>?)R��!s / ower (-;7& en��J0$K$. How!! a+ �n� "g $ohot tak�' o account%��j I�M�i� variō)�$$K$ merelyE#��trong � �$ MQ�!2Aw� al�$�$�  �,% . It!a.$� nwe��or."a�>):�m�pr-� a#om�' r qu_�s� mbd��!%�Es�a�(e�%reaA coordin�4space. But, du"�!6�� 1) � factor, � :��y��&{#) �m��#,�"e% �" +ip@�#ar Ewr. To�ha�c� wA=LA�N���.�M�stb�fix�&�=1$ (or *valenthby�� � $T \gg 1$y2G 6�)�mak!đinQ�%��"=� �.� ). TZ+� af!or�Lanalyt�a<re�#, %�� �ion} `q)= (9}{q^4 R^6}�8[ R \cos(qR) - / \sin}{q�A�]^2^q C2lim} �jk �is� in %%JN!%%�� F� %%{ � g����%Z*��Q�.4�v. U�-nea�*is 5, �by litt#)irP(?r A�,�E� umer!�ly 鹁=Nap6{�HnfirmA�>e�ct�of our��.J�*2~ p BOSO*�*M�re� A�Qin*�*�_I exten�aG&%� 2�)�'"g*��{�W concep.  l quons} �/ suggestedM �(greenberg}}`&�rti���reduc-� x���a(S�,s, �jns�&d�'1]irEmu�$��@!!�m�a {\sl 9�z�(meter},�řn���-f(� �)n ��:, encaps�+�/� �. fe�0of �!xѩ�!2�+��%��.Va!�b�+&� of 09�*ich w �ed�� �.a�volum)�M�N typ�M!n1deU b�)�![algebra��$ (�a}^�#$)!2%&> ,$): $"��l'*�-Q�% l,l'� �2)}"&1 ,'[ , '}]=.m�(2%^ "�$][\; Qi2,]=-�&�m "f8{]= ^B%�.� � 0; $d!&e!?& �, %E�#E� -� B� s=1��}�=(1-Q)^s} ^s)} �"%�--U )^s .)^{s}. $NA��$Q=1$�` gi"�!coNb� rec�,ed�AA�or>b $Q� a C-),�"8-�+O ́� 0val $[0,1]$. �$r le-}sive, $&+})$�&�2�.�qiP0(T�-a"�/ r) � Z!��%"�u�8,3 (.(continue hold, bu+ � | :�)��&� occZ*a -� �($l$, no �'er���,�,i� �n&) ��hanpin�  mo.edn% B�  N�b�%1r'l�#�# }-Q 2 'Q}: v�"���0�I%isz�"� r-_"�"�� = .�&&=1+��&-l�l}|6}l}�. �-[�\}^{-1�"mes:�*+" ���4" %�B9.l6Q2�*_� "�#�*SA�2}J;�#�5B�4!\{ 1 - 2� �\cdot� exp()�1}{T}})Mi)+Q�j! -Q^2' \A��N�c21st}7 � �/�app�7T �) o)&� �}modelsA�2� zp},<��J�koWa�udied]� bN���rk1 1R;�bpa*;3�, $K_T�:20�25b:6��? � �+nd��"2l� q��a� �� �� |�E  ]h, �z� par! ,.����by = CE� q=0},�5K})-1V [ ��_1x,�5 �asic � �.Q6s� .�in��:�` )"*3ER!�>|��7w� r�9, ha new� �maximu"\v5� droptRp o W� s��p( lso H�oń�:�5� �m[���!�$Q$^�20]*�\ 9Fig���5��56OK1"� %(Colo�<line)� reZannb 4 obtaQ� iN9� he!� �^�8id�-"pal!R��xIg/M� I�te&K<7"�*,$T=0.12$ GeV� ��N�*�/=0}N�iI�?Z B*�.�M(� rbiO<, units) vs. �� $|$a� p}$|$0GeV/c)� solid !k�r�+on�!E+  $R�a8� N dot� o!\TR= 6$ fm�Adashed n`, $R=37/c �b� 3ref�8o � .'"YtY  symbol� o $Q =0.5d3 $)�'hs]{0.6cm}EP:�AW��3)~�y2N �pce $|!X q}2W��a � �M\� fp�=�K=0.3EB/cAD� )O��:!c!� /5 /jRF0of nRa$Q�P.�9M����JrA�E.M��]f(�2, �2,=(A�3n'M�Qm0M�1�%zJwR =E���2}. ��R � ��2>�2Wigner��Y�":��"�"���4� I3�% EZ aa� ���4m�<�G:� associ<\&� ~ &�g/ \ x&ZP intCd^3 \D� x}{(2&)^3�  e^{-ie�K}.*}$%&� x} + T\bf*{� 5%� x}~  J+ ; . %�� procee� �ogous o.2&�B�%�g�=n �� y}'  � y}$, remek:�� at $bP � =k�un, denotJbyJ�J��+lD lS g_l,% "�(v`"-0.3cm� in�) we��)IN��z.�&� � �lem2N� �!��&&gBW ; %�y.i J�  (G-�� mes6� }1.1�m�\{ l^2\��/7n� �� �])�B�)N%� � :\}R�+w�ggeA;��&�= ea�at���a.��;d'� u)G&1�origiy :J, V N� ��. \"� �>��EH r ha�%�v�$, &`! >!4�;.�,�45� s �'I"$+b%>ecH�ץ�!(Boltzman�@at7 .:� ��multi-c ��� �HeemHF| �sor[i$ dual2�among�V s ev�"�class) � . B*�t� B�8S թ.ou� " b��.P@�QJ� 1 +�6�q}.mx}-M*)} i� Nd0x}  y}} ,&t�"=�0 $x}S("qup  #GVg3rd>� P]..)er�)ngaa!Yapproac K*U$gastao},9Afa���;��$ e na�KAmSc0s (pseudo-sca'Jmesons)9�$�D� �� ed strucYs� k��~ "�"�Aroat � aCET&i� $2�Ja sur� coFf�!�� �nde�:-Edo�5*SE( �� �aWE�KTv"A!:$Q$*�n�+� n$K lap} ="�5+ �q�edium. Bzsoe�uW -�b�+.J"� p,$of ��CAAlpsmimic�+th2�H54Ztituens�I!�se�  K enough z magn"}E} �C#-6�T�� blur�? ermi sulA� de�!�%� $. O"�"�6�% "t 4PKl2.E�(2ME��� expl�i�M:2dI.MK�7~ NON-EXTENSIVE STATISTICS AND HBT} S\'ergio M. Antunes�sma�or%� my supervKI� i��llabo� g(G. Krein dux !�Mas�LDeU,�J:ITsa�I �t }bJe�. ��b �'da�7�ork, a �- simp$B$:�Ass&�c!�T�Nz" (not� q� m[5is�Q�(�/�76�F�1 ��dizes as $p_{A+B} = p_A+p_Bh04-��$!;sF.�� ɧ��>� �% �"* -Gibbs #mO� �a�/I��_s}>� "�6� - xg9S� 1eI� R�%�,�R ossi�$to�2C0'L,m%sx �D:RY �me�C"> ��ln�m}&�0F�B�?h�1.2cm � (\{[-(E(p,r)�A]/T\} \prb'a%:  {1+(!�_s}-1)[>?�/!}�B tsa�> \;"uA>#�q!%�2z U�"�)!= 1�\�@�1$A vFz 2�e�\mvF!�F�.i�*� 7 (; �5 , "�va�!�� s}$ �UA*� y. L S,�� Wilk2�$wilk}� q��:��Tn I�wmY+w G� = C�1-(1--�)\7x}�@�^ { 1}{.}}L(: levy:�=.��l $�P�Ir&;KE6iVO(L\'evy2) � vari�&$xlI�SH$x \;\epsilon \;(0,����WJ�m|O�H!m� ��" 1\le�s!( 2.�.i��i�s �\$xI#r�.� 9#�5 ($=h>/(3-2!r s})< �$)!� � � >�nUX hOb�IoA�6� f�1.5!0f'be�V�Pifi�"he:of ic�2&/Y�J&+P�JE�*�z �'�"el+�0T�U��0spratt}, leadQo�$on-decoupl�Phase- ze-out2/m *�$D(x,\vec pI��  (r - Rv|$t^2/\tau^25[1 + �� - 1m%� '( U, �&r})nmu)]^{6)}Bb�GDC= (E_pJ�'r}. e)�v^2)^{-�12}$ ��� Wa9�-8!L2f"N' isrQ&&C_2 �K)Qq!Q!&�s�I12�{k_1}-E2})^2 )W]�?mes>{�}�� | _{0*' pi}  '.@ \theta J_0(\mid %q x si2 >� ine{ HFexp \{ i 3A&bPcos ��. BP \} d \ J?( �\gamma}yLxLtK/2Aby Y�JH� |^=� ()0-�(+1�xi F��| � | 1-q)u )u&3�� eq:s� Bj#Q�_�@12)�KY \sqrt{�%�^2 + *Spi}^2}2Q)-a� m1/Q� $A x)��A�B�,l&��.r'] $0$.[)���)N"%uHaHE betw� $ �� ��$U QT�A Nq�7sJtV }$\alpha$�9�!9x$,�d9.mT $)�C = cos � J�+�(Q�e:>.E�(\phi��(phi})$. But �)( qa�#��lanl�sat�$�cho�_�b=*/� se vector�#>,9�{��A�  4W��AYX �� !$z$-axi4f�.�Og�?V1 � =E> �!� R90^�[��$!!{LoMdq \� llelm>!.w q_O$)j �+erp' �8 $q_SJ ��[!hbt21]�1.7cm>2# .5pcVh<,SMAFig5-23}} B3.0cm*3�%b�=6�=A�v4v5�v4F�<��11:w 2�=2~B6-2A1ʸ@ "j$�u2a�&� �9�!� ��4I�#e�o ` _S}="(0!��� 1H#a�- R.:10$ (.ousR$!JT middl�ss� �72 6$ �$, B�09 � �044f�37� � ��>�!�{2.� %E4 hird �\-�>�34)�-�%)�3~�A�sAs sezf �: %A!�!��.-��!.�� =�2$1 %2v �`$2K$6WE� %�B�8d�)er�rt.�@$YP���VEb�+{$!7eB�f+e��I�e�)�:&M6Ř�0$ .!H.Z0e(m#.� �%�1��9�+�A!�m& _ f8ce, $q=k_1-k_2$�8�10� ce1 comb��s% k_1+B �.Wa*�F$v"p K$velocity (eJ($v\sim 0.55{typ2,�7CERN/SPS737v78LBNL/Bevalac), � =(1-� �"��V�$. AlthoughnJ3 licibF*=H�~F:A, 5�7 .AYe�" c�J-�M/became �oA?*�@=< /$ @wa6 @th��( of Sect. Ae, � �A/DhmZ/�)��anE�". _:i ,F.6�M��iP&~ � &�)=.��A�!L �ed �6>�@�-,Becs� q:e�!j���Tkr�&�-� a{&|"E�Tc*T���y-s-�a  6Edev�@"<&D&V,) �_ to�s�R1�����clsf&>*� !�.S��s�!��6� icH :a�a�>�"��:�*J= 21.\1"�#d|@Ji�AJ-�gu >u9earch%�j nS .S�.w:O1�N , w�(be favo7atE>r �gi�/6D.!f�<rPital dataaavt-by- �everse-�.fl� %��A�)�DC�#�$l base�AT>hdV��&� *V KB9Yq��ya�!���5<*�F��i�gou�� alys m4Also, NA35 Col*1- !f%.�&x eT$S+S$ &�g!�SPS�ja�Va�!8fi� fit 562�!Dt��֑Z� 38$ALQ}, m.m!+! {��.�3 i� G! -law=.�7�w acha�Q�lem*�i�m�ll�-onn*k��$K�-+6��A�0��EB�Shro��!�ed .��4i )S�E)"?.:4.��cis A�ex�C�FiQgay��R1eB&as��,�i*.U'� ��� .2,[RN3�Q%pwFe. MaybHBngF>r@s&�@ by�^.��T��C�rVɝe �"�&!��gconven� �,��F�}�B�!h8~ PHASE-SPACE DENSITY} Vi�4 Vizcarra-Ruiz)�vv�@an�(��!�� mkU&�qfl�b!P!��Geo.nBertsch ]b phs�7HrVto�)A9 .f�T���st� dkm�A?RX�� &le�$tic�!pm�!�CM�"disser"e#Q�iz��AH �'U!is�pU,��"�P�k-packetAm�Apr 0aJR"�bpgg�#e '>5�!*�!aj2F. HD$u��L� ultra6�m"m�J� l�d2�1� fx+A�7�ze�#$gives a meR'%��I� priorrrte�7Ao� �start�Ce�#%� ourc*m�n. #��dH%mo� �#t, $t_��KNr� iE�dL�e"�g�K -a�B (t-t_0) f�r, �()/(2\pi)^3 �m ��}/-} UA�����dAq �Q� $ ��0N}k}=� d^2x � � � um!u! ��T$?$��"8 0$d^3N/d^3k_1 *2 >K�8+ M S&$ &� =$�@ wro\#e�.�l0�pas*�!9 X<`9�_{)�}l?-3r f^2( r�/�K�+.#R!�Fv ^ q [�:Uq^�] .VIa_of:�g&�"P'asq$�%&j A'.�A:� � �m"R;�H!�XC qB:F�-@1}{E_K} N_y}{duC:-K_T/T}}{A� T��xpA�>���R� by��!m1'� N��zZ�cm\ROhda\�}{2 E_K�:�-.�,R_OR_SR_L} \c bel{��6� &$v,#-0-� a"jWU)"Z in $ � ��4^{3/2}}~$X C ѹ�G�G��� "< uAI)W�fu6Et"6 A6���� S���r ݘin��% II.2z �O Eׁwo�+�&5���X@�.�  tr,*o keepp  )�&��#as| lZ��'5by��, s';�he���s�ly{>. �i��mi�1we!  *�IjonNSMŭ��A�u �m.u>�.y A)v OEm-�!�.�.�  (a��7%yn �$.21�P�[@ iq^3N�cE�]_Z6\&�p I�1~7�� 2 p)^�{3{y7�1:d�� d^3\!p \;�Q�R p)\;+"�g�!�j k_i)^2/ 2_^2}", Wq��&B���rvJt {K;\) ,���gen1dq�1N-we havHmFz:�Bw=��1S�:Kt6:L)\;�8:7K)���fge"r�45aɭ.�& MN�)' J�s&&< �9E, � x)>=5�!�& )�EQ p B >Qz+ p)�Y% -�z2 p)}5&! ��1�!')N�*� ��>��9Bn terms �he��edBs2�.k1�ri� A� i�)lu�K}6�"��m�ED q-�) -1] QC%JGf��$8+2mm.bB3�9>�{� Fig8B2}+:K:@10b2B6B��B�\}:o�+e��al2�`�?%� (x�V&828�d&gsc )� > YKou1�Koleh�en-Gyu�7y�u�;�� N0��2m �XA�.y��*� &�-A�a# $q_L�[all�y!�Q��z ed: ��~(G  6%�� V�*�s (two �B)h$ �)��op ��qminimal �s (orRU.�Lh"QZ% ��a9ag6c(divi>b�PVgral ik{pi� 4B-6�s�FJ5"!W��@�V9�-s1r��wGpexpon��DOI&�oEpo�5�.B ?%�-]2�Y�MR5,2!DN�ceBI� �s,� .^��)Z �ky\!� "V|��Ac*� foJ�"�$$ " [IN sig�6(!a^i�2du~�2�>�8g;m+�!!� 6G1�AG&h ,. W� actu\? �s|Eway!qU�2�� �}�"�, )� qA�Eim"te.��a�1-%�of!�(09�%��&"IN I�I��z�eI�U�"�|fuxfr��b6 �P!���sp8X�3�� "Ul� e�� C(k_1,k_2"�+� q^2_{�a} R^2_T}� .L(L��"�{!�wi"�k&� ��#��]ѡ�R�2Rof*B< i* qB�� J.� �{ ,� T}}}� ., �B,L,6�genFi�%� a�2!�A:e>�L*GK� mA�) �;�%toj26�*!a �I�  $!��i}=Di(K)+1/(4m_\pi T_fkCu��� �A�w{Jal��er�!�darL 2�7�I�4l�8$)� x�!1/ p # a�0�&�<x�$E=is"1`0are: $R_T=3.5�F�I_L=2.�&�I"]�2Zk �BNL/AGS e859�YT_f=14(%�>�Xum�t �K�;iP�m��,E p=1/=#)�1 p&sqrt{5�}$. R�!�] �{l�Tei�zw_ $9QD#*I ($0E%!�'� 4\% $).%�a.M)��1A���\ . Consequ�^!@%�1�"��to ����!��cA,be� *�9ed�"%�.:|BA�h\BFcY��h.= was su`e0Wa t������$w�Da|1!+8�;� �7EV�IR��em�iz��influeR%� ����?Pwe���l du(= 8Վ *� norm� b/A�%�R��?x^ �/�W���pronoung<&�s� !�r/ if aOjr)�7�5~$�ed�#�g��by�\ O sp�bstead�)��Y�/.A�p�pw o"�aJ�"�A"_iI!s�"���#C�!9�ic� �,&{E��+2P !ՑI . An>��/J)�.9 $Bjorken pi�B, IOCm6%B ����3��"� J �``��R solu9 q�E�"� >�a�Ar&� �v�.� t���s0e G  �6aG�5uJ2�T% a testɋ"� ("]O#a2��&�&'؀� knowmC�Ma."�#�k$e�9` A� �, .r�!XU�m�N�U�-%2�f� e!)�o (�AŵU>SE�pa�!A�U>�� .,�ing!"� Q5k�e.�E��Q6#E{Q�`D !R�zach�P s �V2.F� H9~ THE RHIC PUZZLE}�7�Umillenn��Ee��e���ru�W ��$$ Heavy Ion�$ hbBNL�e <� 0liminary surp}oM46e�%wa�'��&�cinfC.�qTh�ԑ$ce Quark M� 2001,0Januar�@�� year ?� been I�� )uzzle, ��A STAR��"�C? !2�0��TrUAPHENIX 2�% 7phenix})i6�!.�O�� ��w%�� iqEers 0{out}/R_{sid}�SR , \equiv R_O$e�han0&Lu�12j46*Bkk, /OK_T), a�s � w R_Swit?%mi) &��a�H{T}}$ redib H, microscopic�,�(s UrQMD@c%��)C�  eip�+m �'ki.� � hadr�Fre�I'a�DL)W f, e up�K�>0.�.O1�t ��Fe,�fare� satu�3Wowards� L!�i S$ (d���bi�rhydro""�ncasca$$)�sany�eoAX 6'�?O1da��+v��indicEz�A2 itA*e��!!M6 poia��%f f appe�Eh �i;u"�G, reach��1$around 0.8� �� 0.4�2/c. H�alB�.�U #inz%P. Kolbis,upkolb}, fai�'in"�!yM 6/ B.!+v�Ma?i,�`�%"A*q?�^I[�W�5&.I� imlJaE�Kze>�`M�P%%| . Ev�AQ��*Kpdid suc#S� ��!�%�F/i 9.1~�Qd\sl HOT TAMALE} MODEL} Ch�7�a�aell�# is p�>0Larry MacLerr�$nd myself X%�built"Z?as"]# � QGP��it~�6#t �� .nK��E�aqu#��VopaP1A�+�*"�)! B)�?� �� eme�>r!1Ò��h1���fi)�A nP�9�( life� ,�ס �^ !�$^>g%�M[Y'. negl7*-2a�� {1y)�}�Iideal] @  of 1+1�i�_:)"_p)<� a�a8$�"��!=a);tau_c$ (!�e&�[ $T_c=175$ 7�4b�sis2�L latt�(Monte-Carloe4)�i��ch �p,-�a\, fur����until �a)Wf� �5�����!0 gy ˙0le MrE�to fi�lHT$2 !XE?), n4 brok�4A�$.j tricA_�n . M��� *�j�����G mbod� *e .�p�k� H�J �"bk&��!�l.ofuem ��L -7_ q6al��omG!P�TE[. �oq� �$gluon ��J��4��l�Pnst�#�( flux�%{Id�sam�Je!Ё�$a blackbod6�EAo!.�of�)� � �A5e�y dh* �,֜��s �T�/4d � ���A.i �� u%pur�� . N��mplex menis�Ká2��.!���%2i?ail&� :_bF�MMSoei word�n �r)io���e evap�Nof ``g!�s''!� ``%�(as�qsAQo�tim���ti~1�� y5 3n�3{cyls�&u�� r�E length $h�*�w"�&lBtau.+�+d+ l 5mJ�IdE_{in�@- \kapp�Dgma T^4��\ R_Th^ �s1}{�$;2E :\�p8^2 dh[Z\; "�Kd)�x$v% �3mm��|�he�-���^-�_��D�~�Z %�!�6�5�$!��h& �Jm� v0<6oZ)����$)K$�>�i A�oi�i�w"lx����O-oO to�QY�%�tan9es!�� Ÿr�%ah �-N!#qu mv�'% ���t�e,�(��g"0V-o! FB"�J= E/V$)FC"Q�0 (�#A�_0}})^ 4Mp`\!�H{2M�b*T}(9-_0�F;Az.�� �&G�U{ P"�*()�"pe�tra f�x$ �2 )�N�a�;n)�dd��1�ats�"Uu�D e{:.Bi�7�Q[ ��gesC"��Arr��toF�T%<�Tz�e�!� ��2�,V�(T< T_cDK\;&a.�:��� erat�XaT�#�4I��h2�Qashe}6� (�� yield)�G-*�$FBQS_0 = \G�I {\�N�H\�* (g"g�aq}X_ M�E�) IB$\pi^2}{30}!�b�*E-!YK_0 ,$)�.SN:=�A$�\�>10KC)&�r�! m_]0� ��,EEit26�)=S_\pi/NN3.6N ��8 $T_0=411$� �1de4cymU]g��re�3km!�g���of ��, bx g!�2@,in1m 8m lor)w�@  /anti- Z�2ZqZ)�$7}{8}[2 (s.f$2 (q+\bar{9� 3{ o N_f (fl�;)]�@�vadd��tiny qgpsY?AN�` �q��Z&�.A�5ρ�9Y� ^>?0 �g�&ť� "�2��he �FXA"r5pl7�4 $E_0 �Mt,\hbar c =1$)%� 'Yx 3T_oK ��T��center�^0bf TABLE 4: P�m; ��\ Tamale} M�}G-R0.�G�)�x}[htb]�:`qnew(uPand{\m}{\hphantom{$-$�". cc}[1]{\e2cgn�c}{#1�\re./Ttabcolsep}{1.2pc} % en| >i+B >;a��stretch>.<�)s*ng"k4tabH?}{@{}l "V.|c2G�P"�& 0$&^ _c h f$& �gS}/�p$_{tot}$ &  2rge��V}$}$B'J-($i^fm}{c}$)�Qy+0��E� _fS"Mf)$\\ \� p 1&0.160&1.54&5.73&6.97&0.84456\\ 0.5 ' 75&8.37&1  758&0.242Y+f1q(\\[2pt] %%T� x* 5"���4)ef$�Eato75}.Ple~Eq! D�\a m� &� !c <) _h$�+2�re:K2%te�W6q ��!rved. I! �Qx �03 flui  QGP �is $fUe3 Y��ic)($1-f�NK��y i.�RA�#� s}=f�t4s}_{QGP}+(1-f)_ w��Kon} f����(��%C *� ^| c)}- 2�r0_h� c)}}P au_h�  c ['iJn2>0) . BB �"�71t"0" �$9%IQf B -EM_c\r�� % ��=R�%�h �aZNB�1-F� F��APiI�A�6>L M� �-'Rie���%%�� ���:Ak|breakup Rx P50\% �!c�"�Dbyk ��Ns�� b� sspqm02}.>rT�]4*�I,tim�*r�](,wo" t �p^&4���<�_i�J0:B �H��1�"kCsK�uUm1f!5� oBU��Vb �! � ,i"&r+Q &�&��e͇,Z Fa!{��7mn�cp��z�, �~ �+nF83re volG� %O -P "�2� c&#.��%;`��E`� �(2�A�)�b/P�#j�#!TuI�+! �&���io�a�s��*�%3. 7 iV&� �"XwY%nag��Hly��J�t�!Aa�y�2$e !�#$�#�Pc��K"�eon�!�}�*t 7+�* @!f%_�)"�i��n@as~2B+E��&3, �Oup�_ �A%�e�4��ꉆ�!q�!:`II mu7� fter�#we;! reme?A�ss��UWy��5"TrolY">� ="t*Q �E�Hone�&�uD,�T�, ��& �A��� �M11wir� atea" ut f�%���tha�.5rzEmatch�!a�� t�$i�� �it Aa�+�) e�7�'t�E�.� A�6�)�L%ba. till�O&aIioF:�9��L IC, SPheRio, CEM \&H( }t*&FH0sghk}, Ot\'av,Fr\'ed�k,ique, Yogiro�PT��hi /z�� {Q.�N �"9��� s (ICC9ne�a+AAinu�.�K�@CE)��A +6 yfѶ�)62!&.;escrip!#m - codem!pherio},�1�s�Aե )E� IC� p,.�"~t�hos�Hs U9Bymm!�smo��.Z+%GvU�,!%�m�&a6�-�Vs�c"1 A�m�hBX.,!al.a6n,d over s'al�Ps.:<�1!"�U�qz1� in� �g� l":�k 2,d�Dva���  Qto *]T� IC ,;(&e���i��toJLi>�5^ng� i.�s �,' F1  NeXus F(to�jexus}: o��a�#� nt nucleiE�~d 8�%��Knw,R b 3#-/um �or2o> !�BI2 $<5t^2-zfb� O:��j`t.�-E1baryon-� M 2|}`'�=L IC.�"sj�sQG�-�calBU�~. 2�w �G��e��� wǷ6$discuss�" Sec. G5,#1a alt"� �e���"�(.oM ��Q�& S�6%l� ��. Acc&�$CE ��� % mrsv)�e�1sharply �C& � � �~hG+)�K whol�*nX A*_Aoe"�'b$��AfG ing_-.Xt)���2{m$�de3$ by 6 Grassi!�he�� viewE�� �w��c 2M=CEA4*P=* 6�5�.�h"!V.� MpI�'h�|�0 ges M�)<CEQ:!�er�O7u  e�E�� Ax`i�8n::� �o�m .b$s, developI�d�y&��- �%D S�ed icle . -s} (SPH)�0���n physics['%�re� ly adap��o �� ՙ6. SPH�)�r�Lag!Zia'eatAh ttac�"��!C �(``qVs")MQ"!R� @���N ���"a�An�r �����I�s� �`6�>!)DA�!�� Ham�  Kodama��.� S$7�R"# �^aYBaSs&tx� 24.R24.;� V�ckO, �d{hbtkt��}}�E-0.7c2F�{N{�raios}} & �WV���&\�&s i��g�'q�W �J sudden�aee �D{O,S,L�W! !<�;displaz�aBhorizo4 ax9 ere �Lg�fe�(' w9$0Nnq` \le3�,{� 5a �EpO,�2L�'>!5� )/�2,�&h;A2$m<,%mpl�. 1��nd6 =/A� 2,��6X�r�.� >�F�o8�� �eon��A a B��� �/��ed /0$T_{f.o.}=128[!I LEHp�of �4ecJV $C�aM?� 15&4 ng� ��A��7Ie!�W"�7P"�4IC�no2��4IC2 ar<@�Ye2626͎:d<s. Avera�EuQsy Tng��C�%�� ! �ism.a/l�G�%�G�%pu�e�-] � S�|YC>i׀9;! /Ii):�D�) "�HsM �Qs�$ p}+2�<�-2���Ied�,!�& �>�6IRM�� iv��e� �U�c��HBT �e�se�*&by+0%�:.%�. R�2�&Z *Xup N��1}�H @� a݌. Z(�J@e!� at j�5-���)U!h!d B m��*J(outZE,�BO$, fla8 sl�wj�~%Q2IC pus� >pA7uer � nd d>� . Adu(| *�|�'�s: � soey� -9�`�3:��9�$�nd LAA�e)Hi� ��eL�AAn�L*� � -$k2�M A/v�nbi��q)E��1E.at Z���+(is hot, mos!��:�aA�}� ary,�JB��r�:��$1 i�;#2coo6dow�dr ֢dco>�3"�, r � .3IC=87� � QD.W^M0 FB�A� out *D�a��!Bb,*>5wo P�4/ imprl�A~� ph �*\@�P�.>�FxAfw�' 2)y "AK x�8r yet&�A&& may T�_a��.Fe>,10~ BACK-TO-0 CORRELATIONSp>Back-to- C.�(BBC)�a�*� ��.��� /per���a�r$�su�eB is r� ��w�<"�^ se%�%�dH1991, Andreev, Pl\"n�� Weine!bbcapw}�[ a pa�in� a6y5���?� �6i�a �? uF�d?65�,6��- K��u�\pi^+-d.p���+{���ila�E;0; 0$ (� EhA�i�t|)� enti�4*j3�MA�B2 �6��sc"��2p!������rXz� �>qi�j ta*�� ���+"<�IlAD/��# $<�x϶&P�nL)6yB2)>\ne���C���Twj��GA�lsqueeGin N�7 &!� &?u�X�G�9y�rix� �/ntains [���zE�CY ��j&��%�ceB��(C(AIR )>1$a I-+ a��6�N���s. r~Sinyukov�_�,�a �k 9. E� ��  �$i,Y��Bg��A% {y �z$inhomogene�!�/�ˡ� "1?)y �a/HBT�1�si a2�al��2 e.�He�Wick' orem��"�2d s� .� �1IT_Fn�<s�6Pk�3%�ɱ���!a�:p� wa�b�4�W��� 2�q�� %%�0$��'�o%vi�x&��:�V��S(N�(mathbf k}_iK($ \omega_{{..�[ {�-6 6} = ^8 �`��&7�>c #>� *����1>(&"�af�i!�hmpo�'� �MrI4+A4z 2'6VM�Y && N��)!P1,.D2)ܺN^1}Ru�%l6<-;6!?c~��ge: H 682��Ϥ.�P�le 2O[=&���/{��sN��: ZG^� Jr]�> N�L��.�2d� �.2cm +. �q!~ �n)-:T6&� J69 ��")a�RY�Eq� #)er6E:�++a�'���F r�A3:G"ss۸e  6s �8 ����.���<�L� ,�#�s?� /r�: , ab3s.�\pm�3���M�JSs��bd6:� &t &f!>�|����"� va���ut� non@�-� .E�- �- = $H=H_0+H_��� $H_0����%/1 vacuum (��s�4H {f*�\�a"�0u�9!��tm .`� shifAP�ir mass Hda���5 eer ^<5 � � A�t�c� t��M �8sl chao0Ps�ՙ^yownt�tesBK}�E�A� �>� �c) � d.� andwei}AR- �Zg i;$T� ��}�RN0a%# blob (nng�t"�k!C� tn!_a liquidGde e G $g g�a Bh> ��\i/� (+�ng backs�nT-+i � r�(�2BC�8TY postu�- V&� !���? & � in-�Hum�� !5�jb��O�bnҍ�e���eJ�("��� =a}�3.)8aM8�6�!~� ,�n�'P"� p�7 [$r= 01}{2}\ln�� fr}/�@)$]*!�suDhNAsakawS, Cs\"org\H o���S/ ist�� �II�fCachF�%d!9f"A =5��,a Bogoliubov)������.7MAmil!��91н ,�݁�dia~�g��P )�R��@�5ee!�BFby =c 9� ��#�TԎOLD ��� �~ in� M�. �[�� .�}. "�V!�theor� FyeCXmpl�.E�clTe��ewe I�"�`%�Uwo�NupsA� J �:ai�as�"ly R.�%in�9EqMt,.qUB�b��ac4q�E ��&� �{� a�a(�&-=a�be *��OqYY�]9!��R�n${H} ] H_0y6%/iyOe "� x}~ y��hi( ) ap M�n� �� y�>26y})�� \;$%�hhaN�\� ���v��6 \dox�8hi}^2+ |\nabla s|2�H?phi�D�3$%�4m � gsympt�S(�sQ�pF Yate�a��[�:um-Ft IG9�̍d{�a��`T-Y����)�7 &@ $m$, via $$ m_*!�|U k}|}�!d-ۭI :%.$$%|-. i< s;��J�T�Qt�� �XG ?#ec �odes: $.x:m \ll�$e ̦M�k}| > \Ls�_s$. Giv�)�.� ��=!er���s��%1 $\O�c ^2 =�a{�! (2�)$!�|JO!�fB�encnU.!^1Q~=z$G,�0�r&o�Q2.�6��i�oY��q $b_��?b&Cu�Mr�T�jE��^}e�_�"��I�four-� $k^�?}\,�;, ()r.�.(!b$F#^2=A' +�� k}^2�F- > 0��d5 ��9i��N.�d�Th��kn%W!$fD, ��$ :D1} = c6E 1} bB+ s^*_{-=�)�>"w1is*��a�*� �� Q��Qash,$9 kI��edE��� S&? ��\i}+�5a�!A�*^!� Q��F� Q"($q^0_{1,2}=1--� 2,$ }.q} )2)- .ya$� ,j}.� Q�i+ \j��.  $@Ka(1/2)�K k}_12�_2^cFor}Zrt&7�no�!aw.�vY ed&5& $c_{�a'cosh[r( ,x)]�s"sin6"��I'&8�,r(i,j,x) &=&.� \log� [( Ki� `Pu_\mu (x))/ (K^{* \nu (x) nu )��]>+.i j \�$[(-u{r(x)1� {k_j}{��!  "xxA�A%� $�J,jIʡ�I.�� ch�5�O��&l���� C676Im� n^Q�}!A IE\e��{ - [K%^\m1S!Pm%P- -y]/T(x)~�e��r�g�$ $^*$ impl2u_f �7 ���it�'�D��+�K2t no% ��a,- s(-�!/.�"v,� rD i^0 \ $#Z$� � 6t�� full) �3onu�/U�#a8�qt (��X}�itude,��c(1,2)$)6�/BC �9>Kq� L $G_s L�s%belowFn&&\��D�,.�_m~2 } {>�1) >2)*���E &= 191 | G- p�{ 1)2,2) }, �b,,1�x!�� �Dy��fA�in�jn3"U-�k��.Zs�hJFj �2�� \Eg�W2~^]�<l�_6�2��,��!|Q-�o֘:�_{2��'>�*�, .N!(i,i�%�k_i,k�>Ji)"�tran"�x  So fari�5�L*/a*�� �=�$on a�w�8b ,"6UU-'H�_ext. I.W.���3c+!,&�f&2�� t�,� � �7�n�/}e4h��he��]+��t`�. Z� nite�,$l���M�([- �L))�V NV- | cquir! �J.N_fQ $[1+�}'c {-\"# y �^2]h "Moema��BB�\��oB�,.� )��!�� $-��!���I�@ ����"� !���>:�sp!wof�GA�E7AI�@1� W�llb&n%"�L\ly� ^�> Am.��MuE6*Zgin�=+  z�M* $2"�$�!y9$ !B��� D s�8"�2,�C\'as *a"�;�1(, Gast\~ao E�, Pra��a KbCnda m�^ dem�6E0e#"����e�%d �4f�� � � w��! "!OrhD� "�%.!�,) sa�b& I3du�ga\ g!HBT��,&���0*o$p/ !�h�<ra�uCAa�"- �.�2 4 � "W,( ��&sU�1�j.�bA�%�A��=;0D�"�o�\a~�it enhan��=!:cM���of� s�~�e��oA�&�@ wa�\�'aEi�5�t sitb":�icA� %`)i��renWY`A� 4!�,�`[�t�j!�}�H a]�(un� �L�.]e#��4r@^"as�to&c��1}�(*t2`��P�Ge�^#&&#a&�6og#:Ri}# #J��gK �Rlde��1�5� �#N& ^"w�M.nF�%>�"UZ!01F$I-=8cB=�K#FK#� a&G�_V �"."G#"6�2}>�N]!!�"�X!2> \�!I��aϴ�-w�4,)O}�w�`V�)A� �.�O  ]� Q�U� $5, a, �1,9�$ag�a�a�2.�& 2����~ ;w=�;�+�8$� $M�M�k=\� M^2+&� k^2|�E5:a�T< t*E(!E��� i����$\Psi�~x+ 1}{V}n�;���mbda'�~k} (u_vec kE0Z�}+v&',- .� 0)BNi�kB�x}$; $VmH�s , $:� ��$B��!>!Dirac: no�"$�j�� �5=1/2,֡0 &���I�� &�, bU�b}^\dag�Iger, \tilde{b}$. While the $a$-quanta are observed as asymptotic states, t2b22E ones ,rmalized in ,medium. They_�related by a fermionic Bogoliubov-Valat?hransformation, % \begin{equ} \left(�array}{c} a_{\lambda,{\mathbf k}} \\ -,a}^{\dagger}-',-6/end V$ \right) =Zuc} c_>$ & \frac{f.}{|2|} \,s." \,A �- ?^*.FA \, s6$ \, A� & c6 J�Z�} b5^Kb�K.s )P0 ), \label{BV)� ,9�Xhere $c_1=\cos r_1$, $ssin $, andR"tan(2%) = - )U|{\E0_1| \Delta M(() } {\omega^2 - MZ/ �fkB�% ie]�\squeezing parameter. Nota�at inaI0 caseiyJ: _Lcoefficient of sine !co funcaGDs, differently tha nbose�ls�4which appeared��ir hyperbolic counterparts. In Eq.~(\ref{5�) $A$��a $2~\times~2$ matrix with elements $A_q�_1m� _2}= \chiY�U�H_1}\sigma\cdot{\hat-�}_1i�;phantomB�_2}$, wIaA_1 = M k}_1/].$, $� �,Pauli spinor!o $ z $ = -i �^2($. Since $r@ real!l�) pres!�!� , we drop�CPcomplex-conjugate not�<wA3hfollows. In order to evalu0`th��4 averages abovQWDystem is modelled �� globalE'=��,gas o quasi-!�icles ( baryons)E,this descripA|I�� effects�0taken into acEYT through a self-energyU�!�ich, f!w !�-$i�1}{2}$aZ�` (we will focus on proton!� anti- $pairs), un%? he influe!�0of mean fielde,a many-body )?<, can be written!C$\SA� = 4^s + \gamma^0 0i(A+Ia�is exAs�Q^0E@(a weakly moaD um-dependAHq�i�)*loc>� ���atAwHare considering, hae role! shift��lthe chemical potential, i.e.� mu_*�mu�x% ^0$  vector A@� $very small!� neglected 0scalar%�-g Fg^so:�)��ithese�� roxiTs�I�b�}e-ˉ�aJW in-M�$mass, $M_*�%�bM���9|)$. We%]mainly i�>es ����study!gA���ed cor8 ion5�m spondsa�=� oi!�jointtribuGof first%u$third terme&�rhs( Eq. �� fullp}q�ݧ��Je���Dfinite, homogeneouEK"$ )J�W �BBC)� �R�A%Y eqn  &&\!V$C_2^{(+-)}1�_1� !�1a�; [1+(2-�t \; _�, k})^2]^{-1}��, \nonumber\\j�\{��(1 - nPA;� n��� )^2 0 (]  /  )^2} { \ [ !^2S+/^2 (1-Fb`� ] NNB3:VW�2O }\},!8� BCFa"" 1��B = � 1}{\exp� [(\O� ..�c)/T � +)�; \; F��X+ JX$e�if�Ta# net ��$ic density:�H$\rho_B = (g/V)\sum�~\bigl(=�E-Ma}r�=` i�)G)��hav�� clud�l more gradual freeze-out by ��e�a i� emi�W��,val, similar��o[was donf4 Ref\cite{acg}��� �� of supɲng!$e�Tsignal. For our numer�;2�&back-to- �s (fBBC)% ��ed��,simplicity, � in�:�esկMŭ.�ɫre!�no di` ul!�ny�ig*�ies�wev� requir0� mitῡ�(a specific � �P we prefer� o le%�t�i futu�nvestig � Fig. 25@show !74$$\bar{p}p$��H# �v 6� !"$)fthree ^ eER�,R M�$:w� n� l nuclear t!AaAh }is ^��O��igE� reg leb=0��e s��PQ e�!z��'4*dis& and!�$ limi�� a R long9,)�u�E8would vanish. ��] So fa�@��`�~�C.+  .rR) $5�^{!�$(x) = d^3\� 0;\tau_f)\, F(  d �a�pr��t �� -orienvolume%a a�m�B ly on $ [$ (X���-surface9er ڍ invariant6 �at5 $�l c�� � possibili��: ic instY�Fh W )=\d�%0-�0)$; i Kexti�.L�� a �DF�!a[\thet6b/: ]a�-2~  t5TD 8lead, after per�!�!}�g����$d ˑՍ�^_�wenP ($E_{i,j} \;e^{-i 2  S}$), re���!x $(�i+ j)�E i RA�0})nRA [1+[J:5=4^{-2}$. AccorE�y6 sol��8an�"FS as � \mu(x)}{T =)� 0}{TC��{\� r}^2}{2R^� � $R$%� radi��M,X ^ #temperabof� (!�each ��e-� pg$x$� $�$ ae&a.ssa�&� �!a�Efour-dim� on�� low �z $u^W=L (1,�v})� $=<��u>\!59a r}{RA�I� non-�v�  5�x e $\��1+i)/��'  1+)��)^2$�aka<2 all qupAH${\iO}(mv^2��m�geome� �"�>) �  .�,%�i1� & chan6� a�l. "� . � 6] \&�11pZ�m Vu0R6}}�0Dt��c5�d5R e%\v� .5cm 2�B� Co&�� how2\eDK � � �{q�k}_1="�! k}_2=I�6�!�&<s�ed � aroun� vacuum, $m_� =102Q) eR >� ��m IQL(re Gaussian��Ɂ W $R=6���top�s no a�d� �r5 v�� = �but���<�W $6= 0.5$2t�bottom��. Plog %��id� r�}o!S�6��tted ly�tF~{,a�!DGare emK duw"� �|�t�&$.} bbc26�%�zEI* �o@(m-m_*)}{m} \ll 1��e%� � r%����-֡�cal OY�$�� Kin.�� y�) (�G#  m��� As�feq��X �.�$rN$D be&f1� e fa�p#y� sbecom Z 4 o,"�!�y"ld styI1�co ate !�!�.�e�*$ (e.g.� $�,�in .Ws)�ich�zno�A�a�a{hak%�.-try��o keep'1as mu #nalyt� as� le (�details,�RSpa�}�e mv hypo��#a� O-%�=Y-7 pEone�ͼ fire�!fur�! 6^is lasFe �arp� M� $IT m=0$ r#��e��y��ut!g��� �Bpa a�* Eq~ � s ov�"he ��!H��94�u� fis {\itA} iily large��� ce,I��.�$ heavy ion�IS�z �$V( R^3 (5-10)^3��$^31 sh Efin mi�=Q͕��-9ndVs= �, sc$iAJ proporoal�`u�q-)3�%� F. O A�r h!u�p6Wn^{(*)}�& (x)$��� . %dueB nes�.�a& . B�so,`( 5-�!+NQ "�)to�#�yA��a� lo �g�xalAwe uchoose� $V� ��profi�$�[&�r}^2/(u )]$�!.����a�wo��w��!n =�as occur� Bhei~�i�, ���'>er "�expon�al, rep�&� e cross-s� aread> � �$ �MH��c"6B�"�� [��a �er ۡ�socia� 3&X certain $R_s < R$. %We" d %Yx��&���!#�  fmA"O=5� � ��\�(V�.DlW#��#,� we adop�j%� Q&�%)iz  al9���n,!�O%�!"�H�in � 26, excepD��umBeng�� ��4� �%er�3n��e�GRe�%&(26, emphasi��b'; JdirectlyaM2T'���Ve s. BzmpaeA,top panels (c )I�� %(R )!{�!��e��Wu� on�� )At-Vm��� �. H&' Mes}( isurprit�e�]>`low_�:(-E�|*H ,|\lesssim 10 )ad� p�+?no-�M�!] %], sugg�8iQ !a-� to f~)search��I any`%mco�"%�( enthusiasm9�>I�!�s>condi�'s, lik�_nit�,= spr�nd%�a�A�&Ncou7+ �o  ze eveF��!�a�DI` discussed�.p o optimiz@ wayEd# look-'i� ter)c, 2�yet d,1L \��t{BRIEF CONCLUDING REMARKS} I �%to��1�1>�*� a lot; �*Q,W,u� e��!y�Mcon"dsg D HBT&�s%(� y J half� entugo q$t text mer� 9 tiny �%ate�bee,/o�X!� ubject. A���A��'@ peop�*� X decades h@giA �,elsa?.�!B, . Unfortu a lackksp�)�� a�- m@ '$�b�IQ<m%`n�+, >�dedic&i!| viewa�wmemoryymy faD �� o paA� aA�� ye�a��+�H Robert Hanbury-Bro�@nd Richard Q. Twi*+on celeb�' e 50$^{theniversa �thn0�E publ���SDis fabulous method!Y9.���N�F�@in January, %2002u��� � %aB�J�abm(ir� �B2� %"F %\ac� ledgAsF�e1.!�s 8!A�(Yogiro Hama%2(Takeshi Kod�dev�b , 15%�s er!�organ���&h a� is a�$ group wor�on hadrok!A�%� �" ions�� x -'. %�f��y2�. ��or�Ninuous�.>�%effor? b Mi �al�C grow in aydu �way. TAcŁ�u ly ��or��8by CNPq (Proc. \N$^{\b{o}} 200410/82-2$)rDFunda\c c\~ao de A�\po \`a Pesquisa do Estado de S*LPaulo (FAPESP), {\slp�>jetos Tem\'aticos} $90/4074-5, 93/2463-2, 95/4635-0, 98/2249-4$�,$00/04422-7$�1 thebiblio[&y}{29}��{-0 }�!dbitem{gold} G. Goldhaber, �c��(t. WorkshopA*%s !�Multi� cl��)�Don (CAMP - LESIP I�p. 409, 0 by M�\"K* , S. Rahai�R.Weiner,� ld S5])(1991).�HBT} R.J�.��0Phil. Mag. 45E$54) 663, N#1776) d 8 1447w$purcell} E�P ,V999 GGLP6rX et al., Phys. Rev. 120y60) 300? bartu$A. BartnikE(K. Rz\c a$\U5z}$ewski2U8D18 (1978) 4308Vdeutsch}!{D mann�HCERN/EP/PHYS 78-1 (�sQLXNPA525} Sandra S. Padul��DM. Gyulassy, Nucl. �4�91) 339cQkpg} V.E�rishin, $I. Kopylov%M.`Podgoretski\u\i, Sov. J. l , 13!]71) 638$2� 14$2�5�cocconi%�C 1e Lett. 49B:4) 45.�I�Book}՚M.U��Bose-E�ein2r� Pa5a~��+A6Tics}, John Wiley \& So�'199.�GKW%�9�S.A< Kauf!�i�L. W.Json�A� C2E�79) 226.Ywe�%N�we�6��.-)70B!�77) 201; h D1e�A�3118;!�W, StelteO 6a! . PHaJ A319%�9)32�(grass} P. G berf=  A. Wied5n( Y. F. Wuq1!� 382�96) 18.G\csorgo} T. Cs\"org\H o, � �)! 15 (� ) 1-8. rhic}!qAl�8�E(STAR Collab6S� . 87O1) 0823awK. Adcox B, PHENIXnC8C�92302=���PhDF� E"Q entre BosS Id\^�.>`% zido��is\~oesE�\^� �:Altas Eia!� Ph.De� ed� Institut� 0F\'\i sica, U� idade� 2� Oct, 16, 1987.;Bj83} J.a0Bjorken, priv� commun =%israfs} !�\AA kess}2Let�L83�.Ls�]}Au" )}�Y�qQ��> D3�R88) 323.�Landau}��D. \, Izv. Akad. Nauk SSSR S�>Fiz. ��53) 51; Ao�9 Pape�/p. 569�665�?i!�byd8Ter Haar (Gordoe? Br�#!c62cham�6��� 079 2623,2 a�. Pottag�uBrtasls 1�u82) 247;>9S�varra, �Ii;1.�5.�shuryak� V. S � >44� 73) 38.�pratt�P 6-��8�>314]End:cbMB18� Aq20.�BjB� 9I�2 �3) 14.3pg:nio���a\��F�E UB33� 378�Q�a��� C4E�UR2.�lor�),ulk �B.L\"{o}.QB90) 52>npa544F�,6q� A54e$92) 537.�pgg�KS. Gavin6 B329Z �35.lPLB34�y.34eCw 3A \b@ e802e{A�C. (E802��a�M!�Mh6 �D0) 847, ibidem 66�W1567;I 2) 1030;S J. Morse6�EC5312O lFRE�Cr.)ane� Rold�6�5<98) 290.T e859�Akiba=599B7eh9a1@057, V. Cianciolo>�9 ,� 59c; O.vVossnack>.-E4AQ5c;:Z -�2��4to MIT (May/19: kp�h,�v� >�24A 5)�7) 223.P(sono1} D.FA�ita$ L.A. Crum0 it!� Acoust. S�Bg [91}, 31-U2);� Son�/inesc�}.f�� ics Today�bf Sep}.E�2} ca�r}� C � y�a Speh.0 Cavi�<a Dies ric: Tow�a MF7>�?}, K![ Milt�K8hep-th/9510091;H Eberle�M��e�% A53}, 2779 96); �>g%U�Heiml�%E.F},�xChodoU=0ep-ph/9604368��lmSR�{fstedt} P�be5S.J. Pu�A �Fluid9$bf A5�91I3); W!�Mo�(D.B. Clarke!��hit� D!(Youwi�7 ) 21A��6^ : S�*into L�,} Seth�.�AU?n fFev}.��5.p 2} !�Sl� %r1Akit2�}�B3E�46�2a ghk} 1 G i6H Teeq�! B35E�� 9; Z�C7: 9� 2�pghs}Jd,JAa�Oe�oI"� Reviw C2 200092mhpbŌP"o!� Zimanyi,.y�+� 91) 621c;�L"�J.�eNix�9_IeC5i 5� 4; *�"hdI L\"\>~��6._ na35 �AlA�� � �O��C�� 5) 7.�4zp} Q.H. Zhang�r�=V2492� shu}�pB� %E` D 42}, 17��}� MW95u.-H� stafI�C."�=[SC 5ai2132SRSAS976 Sark�Pj��D S� stavͬB�K ha, !� pkG2�95�+6)A. Aya�A. Smerz:�9B40�f0n 2VYS94} Yut�86@(A566}, 589cFgreen�} O��Gq�%a�ͫ64}, 70)/0 "nd �+sD4��41�2KAGI�Vchishk�A�GavrilnN.` ,Iorgov, Eur.��j gA7} 229)0);���%� %15} " 162�zp2A�Y��nE�. gAoI- . Avg nieG. Kr��J�A:j h. Gen.`28}, 68��]�0sma} S\'ergio� Antunes��sl udo �fei�da estat��, no 9+ siva�Tsa� eP*terfer$3p�0}, IFT-D.003/��t ?  K� Stat��247.\n=(} . B\"{u}ykkili\c[  D�Srh� A. G\"ule�.IkA19�^� 09; Q.A.W��8A.L. M\'ehaut\';A!7� 23aZ�eH22; U.Tirnakli, F. Z��i�VMo 24U8��=0 wilkahV.Utyuzhb Wilk� 4Z.W\l odarczyk%I ]G26M� L3.Dsn��m(53}�I984) 121.C KLLQP$KaniadakisF LavagnoULH�. # ati, nucl� 81202s APWe��\ico6QG., A680�9.�vvr} Vix0,Viscarra-Rui�I��5E�A��/c espo-de-fas�H�?i�a�0as@ias u� ,2 }8>� phsp%HF*�)��)�7�� 4) 26, star�LauA�r� !nk�'�+ 200121 A6�77c; C.ڧ 0�]�phenix�Adc"����j�upkolb}"�� �Aolb:�7P#2�]22� spqm�San2�>B� 3) 66�s| 2� Jr.a�>� i�&� F�93E�aI>3spherio�E. Agui1M Osad� .��<2g7�29nexus} H� Dresche"��"$M. Hladik,f 0Ostrapchenko,Piero� Kr� Ւ ~��L91�9);.� �A663 604�9.�bbcapw}$��dreev�D P�!EM"�B%6��1) 347.� andwei:^^QiqB37-  12(asacso2 Asakaw%�!�.� H.*%O6) 6e�L!} G%�.D! 6o"� �8 �9) 4012�m}��.�B6� y F� 46},!�>354; Ye z%�!!�! 637;:Y.?0F �,�98c..c�P.K�!nd2o"� �� S."�!qg) n B512� 1) 2Vj85 T.~1h H{o}Vga:6 .�i�) epar)2.�Zt:�$  docuS' %�:�Q�Q�Q I re*h.J�histo�)HBT�&D y*�+i4say= �*++�TG,mid 1950's, �=more re�+ develop!{8M"N1�J BNL/�G�(er?qZ (EmX0�5{+)  *�:^z+ by�'cipan�0�*6 g�(*se �(�B�+ been finaXJ�^n ongoI(F�'nH, (.�'*�'}).Am��S.u#son: "�?,%v�`�5(acronyms", '/INT WO)�&c' 2002 on "$g)nd�ctu inR� I", Seatt�4Jan 4-6Z;�[1 �!�sr1Hm\q^class[p`4�int,showpacs,eqsecnum,aps]{revtex4} \usepackage{g�N=Gpsfig�(�Gg�(CA  lA. Escuderos$^{c),d)}$} \addO#{ C}$D��5Rof�orel%�4!�M�-�Xcs,Bu�- est � #S4POBox MG11, Ro�an$^�� T6!�`N�QEngine/Zi,^6, R]c)}]M! EstrA�r!� la�er� Consejo�� r�In*�R es C4G@ificas, Serrano 1�LE-28006 Madrid, Spai>b1W$^{!i6V.�A 2,omy, Rutgers6G� t*/, Ag�Jersey USA 08854-8019} %\narrowtext �Iab� ct} Ut0a�b_#l�G_? Eo,�,nQRPA rCac=um2�{8�_e $2\nu\A�$A�perti�;f�S isotopzexh��NH�Y quadrupol�"a�M(# m�� nd daugh� HeiL EUe|`fKS�:�}pr�NqV enabl�^ unifMd&]^ of u��� Q: �����_@e  involv�SI.dB proces�^�PaO~�Vne � an)&,�?/^ trea� ?aGeKesm. Df?�RM$%�^-�? +$&�7d.�Oon atomWVass�2~-%aaQ5��7�4d>!�,b,H2Gamow-T>`r �ci�z.�M!��3�/)Icalcuf��U4Ac�7ed�5!���al data�2 �2it &pr�2ys�)sth� q!l;a �� betw4A��0�ex�{+��2irly go�(0Sy�%{\tt$\�Tslash$\fQ�ccs\{\}}�9$uld alwaysA input, %Y6if�5ty.} \�%0{ 23.40.Hc,~~ -�o make�� \�5.�(B�Ssec:lr 1} �UF�or5(Z,N)I Qmay�a pl�4Q��BAj inctEnels.�Yne ,%Wf�4 �� sis�  si�ZE�0us (Z+2,N-2),e��'!�w anti�s� �h��)��!�y�ek5!�2F. S�8v"�5k�5fadY�led�L�2H(>j2-l�I($06�)2Ct�=&�K.%�se�8 ZA� ia�2 $8�' ce i2R7!� prov�Ea�� 9answer�9quBjBheJ�m2rac��MajoranaP HAN>� �8is 2�B �own�FcB .(@act�9� reaWSE( ar mMfHf�>mightaRC�� qu!�@e!�"$e��rp)�he�%�B#ND such�Sw*m�:�l ianstde�@ir�9ort�/͹b�\coe �ge��A�>KI�mc2� m  s�5��*�8 � � �Hy �� �gstead�e?zkg� �%, steps achielt# imEF )!:" .�we advis�:�5�o��� a fewz!o �v5 s \ce^`Suh,Ver,PriRo,HaSt,Tomo,Fyc4Kla1,Rad1}. IJ>.�to<9zat, moEfi.�QH�6r�Y�"� ��@C!�AzmCe�i[U���� �r� n 10*K7�?�us �Rad2} ja l�)R�d��woU�6|A� a0jR+ "��I�;� !�l9JI�>a = ton-��ona9si"�5~Uom �e�Ux��5p� )\a�%bod�te�7~v$ph�pp$�,Y��or!�>l%b�7eyQ ed. �%ea ,aie\hwhichPbeyond ��Wephe)Z��mea�� N��anEX %dur:Few-��)D20h��� ( upo.� !�lLpin-flip�HN5g;%�2a .�Nm ,%� iedmPRad3}.Kbo�%�7pt-&�  :o!�<e}E!!$ )NA(c%) �yF)A �;�i 1�A& ��I! iZ� I�!x� a*<�,B� ��s�)us,�&�  u^F�BS Nil�,kM�,Woods Saxon �..$� i�@Hom,Sar,Eng,Simk}��Fab����<7`O*� V�/obE�0s eigen �E��!��>ti0� 4a Hartree-Fock� � B"�Id� t >�A�Skyrme�^m��ar��k;�2�=).Rad04}�3ainu�5A\�� ope�in Re6�< w  �A�linea� S ��ame��lsiI�?N. �DntrastzG�6A�c�>�E! serv� tra< igno& VDp�F�e�, d�^( a!K �!��ct�� �|(Asb . Of�@r,+hav! &�^=i��Q��Mm� :�>� u �`to� la. AO issuh "�: e#� ey�S�m$%�mF �:�Ud�s �DwRqe2=N�( (M$_{GT}$)� � ��"� is �Mv�D� %�+i��%�%S2{� �nd��A]�LO re VQ!�!!GP�G<��^aps�Vis�g$-Lu -L8�lapB��� tate!p 5� �_� dd-od}��de����x�_ePG,�-��5 �zs�p�J , Eh"b�T�for:VU+N�I3z zi!�ncgM�2�(GTJ� &7;J�in6�&�j,�@�*fYp�.] �l1%j!2���8re��u� �b irtu� !>1u5�>��ftrya$ depiv .ife�?�ayws"�-�of���j��iu a�ds: a)*� $\to$$($^{48}$Ca  Ti), b>: $1! -pro2 A128}$TJY]$^ Xe, 30:Xe), cj` ob`�134}$X.`Ba `6>$6}$Ba), d)�Ze�to $9��10}$P $ $ ^{Cd), e<�!i� "(e�� W�S��on II a�1c Sg� s ne>Hfo!70�.GT� ��!� vIdL�us� 1h}�J.^ ,: m�CiGA�Zr,%�I� Eu I Ep i�, =a�Tq�e� %a���e �"QN}"�s!#-�&! ��o, =~E�*�val�mjd� �"a�O!�gP5�.�b�S �+�QKc"R!�>>irTE�e�xf�n ?pr� y. A[rt summAOmoi� ���m"Hy gene� �B�-c�  �!on& �MN�X��NQ� �fve M1� i �"� 44} &c���}�a82�3}�,�"�Ma new�S3� R&��Ӆ� *� �6e!1g�i2^� A��U��r.'�5�6}�wB��z�s^N= eof �"�p04m�\� fix����|�#mo���՟ |}<jo� %2��M�beɨly%��ide�+�>l"8 � k ��F�%v:�C U�.�i�  YY $'I� Hami77ian: jK��}�"@lde{H}=H_{sm}+H_{a D}- M\omega_0^2r^2\Bv�=0,2} - \le\mu #�!lpha_{ �h^*Y2"8ihpc"7i-$} I� $ ���not���hP�t��>�$�a harmoNq&V �c, ($b^+_\mu$)6Ias6�WA%�# olog� `I�>1�3�u�S�Tccǀ�!�E8t" {:�R1�, w�}xx��ao&�^ s $\-{00},  2!�$ ��F? �0%. rators��can!Yalɑ��e,:Bu 2�=\f�k4k\sqrt{2}}(b^{&9�� +(-)�jb_{2,-�&ȃ�2ZC$k!��"rbitr�C� �偿noa"> !�ɐ&��r�mTm�6+�U . A����$zH}$�&7!�A�sm�%dE�xus�q$y $|nljm\ru$��j��edB�.� wcvA� n ax� symm�f co�nt��F�< {\Psi}_g=exp[d(!�0}^+- )]|0 �_b,cps4'�Q�}�&$/O"an3  v8e�!)!|E�]���$d+]��% � �&.R^a^�$1!�e !�:� *|o�io�m���Z%�5$+m~ ��. �&clu!(��%�or63����U�|ro��_IO|broke� Z�� io��-Y (, by diagon�W�-&U���%�re.�ny 6�ngK^s. *�Z� A"9>"A�ted��`A%�!%[EBs �Xb�O9B� . Ourf s �:{6��*X�N酩�%�`&�out%B�)"W54�BIm�,^{pc}_{nlj}=.$Q��fpsiJhA!upperdxz ea<�jhe l.h. pc�)�q� s�"�ZdKct"4 !��G�!N%ɠ-&�j����O���Oer%]� ng�-s���F*�%%�� m�F^P_{MK}^I͢,2I+1}{8\pi^2�zt{D !}^*(�)чR} d\OE 9�jmF��Wa�b6�1a[fF J� \Phi)� ^{IM}(d)=�lNM^I�I}^I[A I���� _g]\~v >3EUV� hiimJn4%� rthoWr����!��a�Cn'IH � e&**h!�]u|Y%: a)O�����)�:je�o I�M�0nO-x[s b) A�`AgrY�]ϭ�N��!]^v),�M>�%. I/wh�x 6�a~ &� <]Q�ab&�(,T � �Yo50�� .�.7 �&"d,�f �inm����f al �m%�eZiW0+  `9i� .o�'!��"�Z� 6A,�!�,� �m\dPt�9�] a!�JR,U�6c"�1k�$��n5� de�),(tdo�;cE�� noA&�):+a)�=4�� �u��Ń�*��6� �sm )� ��<�� �!�VU"B S6� & - E`- �k iden0m���ter"� &P . Th }k:�,ENuv�me '�!'BR� %/K $ �otR�*e  $H'="� -$�6�1e"�y\epsilon�2I&=&\l� F� |H'|F���) epsI�c�/ay} &�.M�&u4)ua;� �, dzR�_ix !��(um���.s:� %Hy �+�nt�%aI� �a' Ag��o5i#X|_ o,%Iis om^oin8i�).&�d� �gr�F�� ay #0�: agazXMj`�i2�E~mus�)i> �% �t�"�04}�j�"+4�;atVk�v� , z0�&no2)eQ�%I� �2�,%(4is�kbmm�- 2�..x��e� B)^�s�!2�&!�.��mDwR; ies %�.� !M�sb5�(�)�}�d,�2��w:x�y��S8i�J)(�/�4� A�� �&zQ��� �ed�oB� ��  �X�`%�s "� exa,��byeE" , aA7N� ge�@ �! 7 !�1}*� g!pzI��zF�e�� 2�� . 2 %� � =� tZM!a�%�)��C.h !^!~{sy es < "& ��c %PtU j a m�_l1 $(2j+1)$v"s�inguish&�6� $I$0ch�y�\*O �>8� �ru�!rom 1/2�� $j$.* *�%Ca6{�.6^ s $K Z$- K��e�ach�. J�A�ab$ITz�r�5I+1Kg��" sub-�T�l>,e5� :Rl�d? . As� l$>D!0� redundancW) blem�s5ahan+1< e@QVEN"TsN .sf�  M}�q2�r =1 \Longr�/a,7 �M}ZPJOMN2��new����Du�*œwev��) �} s7O|a�/�+�+�2 ency� ul�0G� !>Q%�ch-} "�e"(A!).Qt�.2q&�4sS thy %�. HAo���$��.�B�nlj$.2(!I*OI� $K �_1�$j �/�E� F�u'� ��5be�W�&w�5B�$\�/)9 }$. ې 2��*� :d � !i� by*\rpm).2�se.�" n2&$6~th�� dQ�#p� �v*� !j1)-�"3tC�Ũ=':$,n4/**�i"�f�Io� one-��./eff05�6Y�q� )X�sj F�H_VFW=m^IUk(d)F)�H��7��!;}�g%�� &�sT!d٫��B="� N�nyY�bc-�Rg $^{\prime}M uK$�+Cn />, a��� ,!� �"�&A �S�we6onC4���Ra�'xy(c6�V�to^ *S *�?�;�E�5}0Ba�p%�6C�Lwoq sU?w%!5c!:V{m0[<�, �5a�.of.Q�7u6�,ӛp�%� sAbwn"� _ �.Mhe vi#m���, $d\to�}˝�"���g_��� � (At$qB_Y�o`� V��. A f<aal��"�>r6}!IS�� woB�/i E�om�r�69�S�L̞e/es��(ena�J�+in� �oᬡ�� !gN� �� *} u�o-%� �0 � "�2�>d6to9�# 9�� �"� 1 %.�g*�as.$��w`md "� G�%nda�U:A�_m�a�B2�=m�oolO# � e wa9��%"RW'yGnck!�he%_typ�:R��wa" out�'us� sl� l��+*&��!� l:�oep � eos. ��nr�Z�m'(2.6)�Be�f�u�4��two�y]3 . .�%�i�H&"e�;p�&a>k�%�Qe workA�aim�E|%2/2G2z?*8$ &J5A �$*1 T� at m�*�>�'YB&�*0��5{sen�ws�y9Hv=A����"}m�s�-����A�!- �aE�u7H M�:..*;�%�9"��2~^�>�,`�YBan"�BU� �AA�Bj6q� a�/ng�@��ou� ��ca��+��e F� �!�s�*�Wdr 20\%1& ``f8dden'' *&/`P4��p .�E��aUfoӗzs�~e��Spi�9,%qB�<Rs� �)eȏytwo sucA��u)X C-$.)�BO_2��:!�IO��w ��gG di�"�  $1�*��� ate :�2Z) Q����hH"�9:�%6�u-�{0t�� � "Dž>S 1T,%��J0frame�o э�u"��� �I�Am&���: &� 9 H=&&�\����(&���  I}-�"mbd�&ta  })c^*�$ IM}c_o%-q�$G }}{4} P>E4}P (�'}"۟��$ &+& 2\chiZ�c ^-_{ % (pn) +_{%(p'n')"6% -:_1< P91:P^6&� as"� 1T�Co> $j(-�M})$ c�� es (�vhi�s)*�E ypT.,tau$ (=p,n) � �3iF| �0"�/A$�*m$ߘ"-*s%if��e "(*,�afq9L�B��(=nlj)$ "1���D*i�����~t��� �8���- "U -hI(�>�C���!p[~"?��6! &��7d�& by $Q� ��%�,b� _��� ��6�/l%�he�J"� ��)�  ����*P�y�&^sN�FZI}��*M}i�q�B�a� 6widet"+A�!},u�\\�ht2�n,M' q# }}{{" IA�� pIM|\R�i�|n I'M'���>A{I'}}:�p��n>6�6�& = &��ZdI}�J�eڣ2�9_S}�pPsi��RtI1i� �~s� "F���)�",� AgŸ"E�gh�tia���io ��nei�t� j< ]�!�� 4*i`��>e�"�&BCS��W� ��re�H����q�/!�S�$I�Q�E�O}�dax�taE�Ar $.�1B��2b ��| ($RH�v �ǁ�($.^).dre���!��#a� �6F��V  o�N] �&��?B ,Q.�b ed j)W!�n�U.g!Q�)�tC~6?im���* 'ir tur� �! sas�?�bin� ���6_A�6.��m N5*��_&��hm_p,m_n}C^{I_p\; I_n \; 1}_ m N 2#pI_pm_p6�nBS,.KB."���-��_} I_n7 }=-[B�e!.�_n}}]-#" A1B1B�B96�*� � #J� ��ADE� lism1�f&�.E 1���g6��G�*� %S=� k}[X(k)J� k)-Y%�G kD 1], :�Gam��uE�} k-atisf�a�Lri O.�5[ �-Y, >�'}]���( ,\mu��$;\; [H_{qp^98�2VX9�boscom5�u�TU1j"�*s y����lgh�2H:�! X (tl (�M�j�W�  Y (nam �O-mp��.<� \Ƒ\��) {A}&�{B}\cr - & A}}\�)6;X .Y=-42_:$,��b>�x k}[|An|^2-|A]|^2]=`P rpaeF�3�pRQ&�$2�!'�ce�2cal{ A}7B}$W p1>/06&T% $pp$.� ��Utt� vda er,!� a cri�?�� ��_1x ��rooE'A �s���/,inary. Suppo�@a�9chU�.. ��� B�&�71�U�s�� $)��[al2+3d �5F�eS_1�5 (2\le...\le  {N_sy_om0wB_+N_sB(tot�!V%9F�"Lz G G�2 6K/a��couG�R@6�2m�7��2�"$n,l$   same.�&p�,*q; s $XMwY&� $ mpanD�7lo�Pk� x ``$i$''?/a!$rL @L��!gy1�_iI���&N �&O pe!��&U �Z9 0&h*, s��Q�nh���.e� $2A(!�n ~5�q-8�O) Au�n-�T�$6 "PeiA��m,(Va.�W�I � .� gaugid:}+��re& ��*-�H!�E!�TV�..,&^!"�JscrT� �!k�.]s,�&`!�'� 5�%Gad�6a��dex �%�! :�m R�%-ipQi@Mb%06���J�#|1_{k}0:�6_j=F� jk;1S |0&,\;j=i,f��,k=1,2,...N_s"� rpastVe�ind�*im�f�w���T�()��B4(1��ViF�5�q6q sE~se�,�*�0)9�{|1_k9 _i\�� nd $FfC-� nE$bor:x mq���^bO�]a�minus&l=!8.�F)%Iuh��m�nA%pop�N� spl�ra�$joV"�N�1���S���k rr�{ leptyJc �3)�X&k%�u"�.� [��Cd Vc��e��B!7Q-��*�>6�BJ`ηE{41}{2}Q_{�}+m_ec^2"� 1E>�2 reci�Ɠalu5�>� �lifo�� ��!aN� (T^{6�]D/2}��}=F|MtL(0^+_iz ac'f �T8T iI} >F%�St�2lA- Ts ��V""i ��a$r�_�-w�YM M!��� 6�Y���-�s�&� .� � �=\$&32?kk_i\0||%�!%|��$i \mbox{},1_k�?'r(_f%f Q�`'}Vf|�Ff}{E_k+Qc+E_{1^+*|MGTB��O:��,E�$m�&�m���U : a)"#�E$_L`/av��>�Ja<2�-qo k-th�hi� (>R,cI�6�n�=1T*)1�E_k.u(� i,k}צ{f,k}),�e�'1.'1*�>EF�7��c)�e.�] �U�6 st��_���]5��!;]��I-di��d act� eCaIn(wp� q^�.Ah�0i) �<i] (f�#u�|X;n�O )P l��m� *�6�i��" W"�)�[ C ĥ�aS1nd �#�y�N�ur Bs _fJpn}%[X�(i,pn) '}(f -Y � ]"�1k1FT���",,p�%itR(1 }2v�".G,Wigner Eckar,eor�s�V�$ B e=$9cH�! �e85$ay�7e.[f ��is !��0*� a �.j� -��;�;"^& A91�W��yFs6 one,���mploy~or*�$�i.�cM*J'('),�U gN�& �&X()b !<&"�!�%&i�_"�! p �V9�1"e" � "4JNu�{(' s} �"�a3�*p(�! n*�"�UM�Z�Gapp-to�1F*�u=t���e:]L�PPLڰL�L1�LR1v�L�9-.�pa�"�%>*�Y� � �@26B�A�SbyJ� \hbar�;,0=41A^{1/3},�C=22\kappaD=6mu"eѠ(���.�$ L� \mu� vi�� (bc * ce��&2*ing?Y�b�SE��+s� wo.|9t� se�TFI�J�E⡜z �Ee��cZgF X&qua�;&�<\:7DE4,>fix&�"� S%a�>�u. ���MZ. "�=e �-��u� �v"�8���� $|1f�7� .  $1 $|1d 5'�'� �~�~of �4�9 �4�v d�4 ]$�) $N=3g7j�T~I. MO,%�a8Fm"xM  ���8�{a $QQ$&��  ��B@ K-< chW���+}�j!�@:  7*Sgi � a $2_%%����tus. j�M-&"5 F�8PR� IM}_�,_< ��`!|n+1\;lj�A�e� �h��&�?��N n�L[ �D� ce*W3eI g�ing[��-�6I%�i�"�M �L"*+�a9��%Di&�7inB IkedaJQ( rule (ISR)j[d�h�pmY�sH��p�@�9�ne"C�PuhC%� <�=V8S.�(�b(^�m!�N=3%�$:o$|1g9/2q�!�'�$n�F9&e[Q{XbI/�� ."E, �A��!-6 ��7� e� (t i! A�"$2A� 0,4,�x�)}�0th $I=7/2,\;53 1/2$*�=som� &�1�C��yFq�tha"�` belo8�O$|2d5/2u! "�9"X-)12y�e�F,� �Fp M� IF=�of1�s�RI(�om2 G�M�@5� trunr <s�5e!��ert�pɢa��-�ly1�!�c�R �[ �&�7(� +!r c�;n)(���ccu8��B robaS�Aeu"�5E$�wel���H|_6Hmi@` )�Er�/em an 0.01. *`\R��k�!m�� 7��I�G�4re:D/%^IU�9�� in T�,I��c dN5� "��R�'6�)�b�}X&^Furm(^ Ameeq"* "�'ͻ($D_1$)D"O/���A"|- dily"8%Eb. m!�;k in 1iw�&6A�Ak u!%� .�.e9`O, :���e�! �!�� Ց��5�@ f/pR.vW�t!�}[h!]�t��ar}{|c|c |} \սe���&� � � & �Y &wY0�Y �Y 8 \Cd� F ^: .�Y ^]�( �� � E�&(0,0) &l~,2 6,26 r 44,44) & F vN:7T&19& 20&20& 22& 23& 27  1?E�\&118&128 &132 & 140 &154 6642!$150 3854 \\ � $D_2G5 H I 2Jf2O40I�PQ "��%]y�>�i�m� >�9�A�eFegBGeA� ��`86iGb ss. %Be %e�a$}�o)k$�/xgjH6���Qi3 &K� desp��r� i�> z k��� *�,�Ik�cT�ng 1"z &~#�5 ac�w���*�( $N(=2n+l)$*5 ��� e� $N+1$!0m��um�A�G2�&��:��xTa�g�pai���s, ws����G �u!L.�$)���-re�7�C���p����II.!�w, -Cs�( our o:�1�mIL-MuѪ*� ~55[11] i�m P6"M/ e A-*l���MJ9 NIchi�<5.2}{A^{0.7}}MeV2 _1 " 0.582#"`chiB�W��AWI�A��Ge$> h/V� �"n,by fit"�Sg�M VGTj o�}%�_0�c�90}$Z7208}$Pb�#�$R��H ' � b[v� .��w2$Z�#��QRgRIAm�$�ADcay. A c�caua�, hO�.\"Gaw�1)�a�ula�:�8,_F .�Mute6�Ci�|Gro�q}.nq�6� �Q�n Mol,Bend}�b2�L A�JMad�k2�q]ro���EeT� � , lo �G 13.7� 14.1�Ap.1�y�&CO&$ �s�lz< 0.15 P 0.16BPE,se7az I��^t�� d�)��"L/chiL/"�$��to A=�8��A=13062��_ kTc IV,� cur�{p� U�( :1se 2�� U� vV` �=0.268$�$ i�"�Aɹb� � |*� M�& T&& I�H :D�$\\q0us& $log\;ft$� eius� R*�^F &�yackrel{ m�/EC}{�_}$&0 Tc& F1-}{�>/ Ru\\ Exp.�D& 4.45$^{+0.18}_��A� $\;^{f)}$' �.66a B \\ ThW 4.61 : :�4 ��0h��4^hB�32�+�� � 4.55.B�2O  4.62B�"� �hPd��9 Ag��/CF�08���� �41�  :�3.8� & 4.83 E \\6�6i��6����6}$SnF�9M�I�15}$ �g2� �662 ��>�:�055 &4.670I� :�� ��0I��.X.�5.049 �h�� �6.061 e:� 4.932�6.226:25�$ �!*= �2� �I"�zal �* �+���� p[���� -e��=es q r ���{2W&( , ). E.#""k ���yBal},�� Je؏$H�} Frc�$^EG&�$^%o  Kan}(�X Garc},�h;^E� Bh� .!� Leder} :� �z�&�%s ��6O 2\A�`,aa.#ly)9� L �i�&�.,� �M*J)L:�@�a�>�F��xI� e��R�=a1 $ft$J�ft�5pf06160}{[ {_l}\) 1_1�({\pm}*�(l g_A]^2���}�1 $|1_1MmmQs ��;�*}&A7!�2�:� D*$"T)e�6p3'.W� Z�'ex "$l$"$t��EV "$i$"� "$f$"��Uwhe�b�1�� sY_a J%.�"&or>.��'��l=f�6�MM�-$*�E�ElA.=i$��� )i��s�[��ose�� A=1.W�lde�!a$i���a=n1pZ�$3si���v"b�� . It��o�fixm �*"�t2OE�Bt398\be�HT��"� =6�ta@�H�A正��)�:�5��/ chi{�N�&w+R�U�^�A�n!��"�+ Eq.\��A�!�tk�1�RZa�rA�� Te%�w2�k#� �i�x�/-�h��.�,��v dnicel�>��3*A �L���@.^� /%�h)�q%�mv��n� �e2��UB�6��B�E�2��3��j�2�i.T!��Scq�-u� U(zlin�0 $1/A���7p=�cT�w� �����7�:A�2b*M ]�&&�)A �"WO2�wT%V%�lsoC�tZ �`.wVa��*+=2,� -�7t �Qa� �$J�Z�sv�&�)Q?O>XQ"> 9]�Z�vs, &E $Figs 1-4. &�`ѱ\�fai@ b�iso�+AY����u �!�",]Klapdor��/�}ɒ�,Zha,Hir-�VmA��l� �8"%H.��� 4R� O�=R.�BFC%t�[�-�&�p � s�) be�< S#P�be)�in�E�W�2)� "z 3�'a�:.'!, �vT\4A& Y> A��4.B5"�a�x4D��F+ &bc��oi � a�4l]�4�o 2C�>s~��A&E�z�ة�F�.e�&i4� per,���$gd 254$�)5޵�OqT ��h�on)VvI�a�1g=" $T_{!PZ Aw�5�����/� fi><�P!��.� [��!���! *�!P!Pk & G$_{\rm p}$ [MeV]ne # & g7pLZ(�&1v+QN�7\�)f$8� *�\  & 0.3� 0.0L0.6@0.4 18 0&2.646K� Ti &0n2;46 P6: 0.0&r ; r.b10�%=2 $0.112&2.18x=Mo= 2 &7;��08 76v"�"-1.4 &�r! } 0.06�!.60�02v=Ru & -0.�3 0.28 �2] @ A>�C1.568.-Z26!�Z"H!n(2.750&1.161-p�#Pd �35 &6.9�" �8L ? >:p@ -1�61�A0.�" 0.14�"2.4�515@ $ -0.8 &3.0!0>18%�= <~ 9�"P$�h3�-?2Mt2D#.68!9�K%!02.%/0 �275� 238& <�"��T�$E/!�N 0.27I��6� 1.250&0.9U�@Xe &1.7!� �2I�>!�1$<�= W �493&1.88541o26�30!776\\�6 z4�5.0,705=7!� .z] !�1eJ9A�A�&!�Q6w261�31}4 �94 ���46:x�.�&G �I�23�956&1.24!75~��7698�6A�1z6v pZ��:#��GDX �� b sV�g i�V`:Me�k@��"K�& � (�eu/Q�>le"$Q)" �[W � �Et, �� � f#}/="8 "$��4kS$� !7 (2.2)�j@  � d\nq" �� �ex*�enext��*�%\�page ��vs&{�2cm"�t�b.��4c|c|c|} \hline, $2\nu\betat$ decay & $\chi$ & g$_{\rm pp} $|$M GT}$$|�\multicolumn{4}{c|}{T $_{1/2}$ [yr]} \\ \cline{5-8} & [MeV]  &   $^{-1}]$  <& present &exp.&QTSuhonen et al.&Klapdor $\\ \hline < $^{48}$Ca $\to $Ti & 0.180 43!@5.23 \cdot 10^{19!4 (4.2$\pm1.2):$ ^%B,a)} $&& $3.2>B$ 1)}$ \\ u34611203$9.27>=&>9 �3610$7.48V<=996}$Zr1Mo�50 V�11% 1.66:YP &$(1.4^{+3.5}_{-0.5}j $ & $0.44H 20}$)2)}$&!{=[7}$�Z& 0.213%�12AZ9!�:g!�Y?>& &A�E5A. 100}!M/Ru%06!1.6-&305o 4.61�18�0 $(8.0\pm0.6.Aa�2.9� 31.8:!�&0.207&0!� 12&$9.556+ & $(#5^{+0.03)�02.�!�uXF��b� &|F%!w033 w2 w1}=�wc,dy]� 104}!�5�4}$Pd%�15!�2.70.781!�0.7.�21!� A&6cju !o01Qt3�6 $3.9=G&! f/$3.09]52�H!p 6)A�.�10��C �48 & 2.4A� 0.26i� 5.85\a & & ac0]'��n��194�ad21s$22.9.�9}~� $1.22�!�� 6�16}��6}$Sn �3�1.6��11�H $3.8.��!�0$(3.2\pm 0.3)>}A�a�A(5.1:" 5��& $8.3a��=87�1>,069 &$ 10.96L!�!� AJ7]JfE �4�6>28}$Te5>Xe�26)>2m"09a2$02?24a! $(7��->� !6=.�23��!>ag��nw��741��127&$0.2.��n_ (1.5�{.�5�e�\ $5.7��*)}rzN6�302�:�3�H05a��2Ie!%�1.5-2.8.�q=!���@]�#5�:���%}%�091!�09.�ar�2.7%�1^�my>"!���N�^7!�e�=�.f)�a�.I34}!��UBama1.!���03I3.7.IE@& �2-���^A�a�w � 4u $3.4=�d�j�$2.�$6�:�66�6}�5�7���4!� 5.10.� %�& $>8.6$1.!E|�=6�y6><��� ./0�y3.��S�M^Q!p\end{tabular} \caption{\small� The Gamow-Teller amplitude for the $Rs <, in units of Me� $, and8lcorresponding half life ($Tj )2F@ $yr$, are listed� ten grouVo  transi�s.�,experimentalkvesB�1�"F ($"� @$Ref.\cite{Vog}),&96Z .' ( ) , $^Z Mo ( �Dž-, *�� Eji}8c�8 Kir}�7:Vas}) �cB�~ )�?T!��o�,��UHen}),^ )!8�Jes�f1 ! ���Li�a�XF�E�) AM4also given. InE,second last 0results reporA�in{S Suh}ek2)A�)YSu2 � A� Au 0E� �4 Comparison is �0possible with�(theoretical� from.� Z�HGroKla} (unmarked), �Zh���), �Hir} � )i� 2KlaGro,�4 $��)ix$parameters�!$g_{pp}$>}}}��le���learpage \noindent Before discuss�>��1�pGed!�dTable IV, we would like to? <strengthtribu�; ��singl[ T^-)�$ +$:8 moth�%Hnd daughter nuclei,�8pectively. Thus�� Figs. 1-4��$s $B'(GT)_s +$��fi2h , foldedI; a ga!2an hav19(width equal!1 MeV�g plot!Ias func!H of pnQRPA energies�eseE�F one third1!c-4�5B� 2�%84standard defin��q!>@difference betweei�to��\fN0, characteriz!V-_%�jis! be ce�1P�4sum rule (N-Z)�eɅ(4of our calcula!?s%&toVLavailE� dataE�cGT giantXona�AbM�A��GA�Re��DMad,Aki,Ander}. AtA lJ!�may se!�at whil��Teh � 4.5�1 MeM�,�+���c-!x��P.1 upper left panel, e<si9 the B=��a��9q�- quenched �a factor!�0R` 0Zam}, account!��ApolarizI�effec` )EAQl�#ta��8 operator, ignoA�-u( papes�pa"�p6� �>UV. As�)� reinI�%"aj5�K�ed9 ��2 g!�m�y goodAY,e only known (1��-p+$Az5s�ora�4)$i: \begin{ᮁ} \��Bq+=1.4D2� (O:�,:#toщrow!�)/� predict� tA��!� 2.59.  ng �-$3di&� $ among 2qp0tY�os�*i to�st*,���l�t���,quasiparticl H��I�� b�ge  �,"�Y>=]�ie�s ,)�iIA'mX pronounc �$^�� 12�|�A��34,n . F� )�VI, i� %W.AF�:�*� r%{Mproton�$neutron $gA!� . By!�tr� inpA�Ca��<��oCd � 5�d<1vol. $fd carry.�*t5�. Als)�G���2��-L!�( mi� maia�IX=6A:2�Fate. W� ��liu "� ��=G $\nu I<\pi I'$ where ei� $I� a� ( $\frac{1}{�or3 pre� � J8 �� � S7B � 5$,�:*>B dominant.�> ncere !/Mj+!�J� ��2 r!K ��sa) ll O .� noti3 i"�i��xis much he . of���h��1�ef�. More� �mfinal ��0�proces �lya?Sower A�x!$� 4rum, below 7.51�uggest��at0$pp)te� F a�gl� fl��eiZ�J�t=���� e se� vity� ",e� e  againsZ�w�� -�i &2Cha}. D�J� ! ot.�*�i�< significantly a�eda�i&� � . Sia�c� �>:D)�of"�t n� , � ! @Msatt%�v /ex~ =�' " o i opposite�s o�- ^+$ 1�. Whc>��� �ng��"M �, �)q2�M�6�piA�hif!k�8�� E�.I�!%� � ��B� ^ v�bon�!o>�)� �gJ� of .��U ve�=�up� s] D:E�S*itu� vmeH �� Xe, �^{��BaO Ba�e�!��IIF��stN�) arr ͟�8�M) �-��1�,shells 1g (� WRu,�-���Sn)���$� Ba),� D��� 6 ), 1f Ti4f3))%7 1h(��Xe). Iuif� n ��0.326mi�"�� (���O{�- �� 5.957,K)� 7}ha�)�1� *" E� p$� (3pI 1_  ),\nu�  )$Ie� �9�AR 6,ei$ M�F@ Let us now focus'atten�сGT .:=�!��o is��&a by mean��,Eq.(\ref{MGT�� !�-g�Ls %DeltaE})��t?linm�a�an2 measu2�O $1! ��collecA�>X�e)�s, �%%nd1�$ matrix el-� � �" $M_{�*��ression��re.AJ�G>R�*a�$various se f :�dipole.�s, fix�manner�la� b�&,�BN�&>v鯥:>a.� *�z "}iK!�6Va�fairlV2l�1!BMof �x+ {\it}+}�M,*� ��sa0 .� eE��!ȁ�pap zeJmuFs�byY�chi�,Cout any�?epaY,i��"zranging�� 2 �Mo)A31�\Zr). Not) proj�ng j�8gauge symmetry 1Nfor"�e l�4 ��.� mX�.4"" `6Dto0a�"� M�by fit e��G.�� roidi�y � $log\;ft$ ���� /EC$*k�A�odd-odd�a�!$\:M�P-�.e!!A� p� ��Kus,e�Q�bti�<, a renormalin ��As�an adju]!,Woods Saxon � &$mean field�yf M they6�&5. Y=!���Ca7 �q (�, -�),�5!9�� rows,A�vid6`�r�S��&�! \, ��B�Eo!��$$ must be6�requi��i| �;e}$. Indeed,�� NE�e eI����:0 (=1.80)����! ��6�e�y@'ըGTUۡ� be improv(6]tEBP"E#!J� g "�#�a��V�� �can&r�k�ity U�-%6$imilar)X at yA��a fulli  model 5,i[!�!m"� . Fe�WeF��|)�q�hed}�wi�^->Y� &2: E TieLa�� 15.6�&2� ��b9%\ f�R*4 �2)Be�A=�of 6.63�12�/"B� ��� 1.15403.3446� As�~w� A v-Ca� po6d�f B)��s�"0Zha,Zam1,Cau}!5f�"m�cume�bro�!]�y- < %H �Sc� �=a`Ev� bulka> :� ��- h� aV�nt dest���6# . I� worth inv!`ga%d_a� �:Of�m� d�� .5 we""!�N� &� asew&("3AimieUU[inl�#�'�!ngE�e�(2.21)�t wordl or� �% E< Uy $E_k�5fu y F2)� i�G E.Y� b V$\leq E$. W.�i�vA�rvals �U1 is a mon�ic� *!' of EE^_ �f"r^*f " a=�pes� �� UMj%{�add�����&s a sn)�i, nameG!:�ofQ���5y2z16�0��� . Ona�E�t2y �*�be�$$E+*NN��$� �� �A�.>�Bio,*iH�"rk!/} �=p�� (E)g � �����rea�& for ѳ%.i<% \*�&�tz}��+{|c|c|} �5N`&@us &$\hskip0.1cm$���.F&� 6>19.7S�! :):9)�4.BN)�Pd:Q:aQ�Cd:NQ"Te�Qus.$ 6�:g�$X� 2�N)�. X.."�986n{n -}$&��/�28.886 &30.040& 29.527&33.172 &38.051& 43.3L/ 47.05�. 20.50.703ol^{exp}r8- & - &26.690&-N8032.700& 40.08� 45.9�1 -*�1Z@. T�!qa7G.F.u*.�("  Fl'&�F� (�+row|*!+��r� ' ",of 0.6. Datae�!�M�� ^�CdF�&P�#S l�/�f^6,re>7 &.b�*}� +,vspace*{-2cmV|� �6�<2�<1�%}�8.�< 2ndK } V@3r �1cE{2-7}32T"�/ & S&�X�:�0� C�2(3f  @)"+:%�0)77� 5& R(3p E� , PR#TO 0.519 �kU�NC q )$&a�0k3&3��� 5>�2 # X &� Z)a!Z� ���?b =J# �b0.602-Vn�1�9Wg � O1��4- . to� (3 %� �5.842� �4d !l ,MJ!,%�467��%2 = HJ�,)$��2.473��LM8� ,9/# p �!~? �&&)2^��!D:O]<6&&�Y&�21Fg �9&^��N#.�4.950q84d N� N#F�&�456M~(4g �m �!� ! �a�%J�" BNBo$7 428 �<& �sM9s Q�Q!% !u�0.716�7& iJ�6NJ!N 1.005 &&)@ �x�@$A�4b~U�#N� 1.342u�N �OQa='Z!W 0.88��+B�rNYN0.563�"$�zOB�)�"5T2.722�$NK w� j�&0.400Q�N uL#d � ��$1- ͬ5hmt1F . Rn%$&1.321a)�D��B�F�%� |�J)$ a626A�٭> b5XbJb#=� #! 2.554r� ,�OBrO 1.028& $ ^@6�N570i�A�A#-�G).^��.�� ��4J�)}�b# �171�5�� � zN#� q�#29�I>��\Q5�#\)$a�05B�$� 7G�1_A�$)K7A �6nV$/��A68QL-��Q�C9�BVJ 6_$h �5`1.121.>9a1�B/1� R$ w%�46��$bB)OQ�BAP 0.92W V� zOjQ&2.647 ��AzBf�>XN�-I& Q>7 NN�>N$=h $�; 971 "� E�����%M.�1 R# b�?4�Iq�b��O67Q�{B�rO�%�12.48�w͑�$ � �FRBuE�38�.M*^Mp-�%=19�ӥ�J1>M#.�$&7.3� ���i���E3J�# � 0a� E�Z���N��B%G43&z NH�� 2.54%� �N(:�#h2K34gR�%���%. M pM29����)� &19.2056lK-�5ud �%��R$ 0��131Jq��%2O#g r #I�6O�Q�! ,))y~#%d.# O78�����U U0.625-@N���1F�&21.05V .��>`U � �9f` )�01�J+^M p)q M39�c: ���� 23.6�G\� q| "�#] ��(1�� V �97J  #e�709&&� 6m%�D 6�D�9&��?�"w co�T$of# �, B�>(ifT%)s���p$9u�?1-4��&. O��1sidk"�numberY �6>],+% st i"�9�o.�'2� |* �*�+)36e�c�,n $pn$ phonoMD�(L $\Phi^{IM}_{nlj}$ (B>Eqs6�S2if' -xquantum� (NljI)�#�(N=2n+�=lsor3,orbital angu�!moX9umD#$s 0,1,2,..^�<bz& lett�s,p,d,..:�A }fnB6}[!]u1G�*p&��r�r6s-�e�2v^&64"� *4ZT&"HI8 & 7.9�8�&-�2� &&� 611&3"� �z"| 7.07 I60#TN�N&$ 16&� L � �7 &11.6�M13.125&" � �11.901��uB& 5�s)�& 9.28�bOt78�7)?7vN4� � �104M�� " !s 452 � >  49e&�5.1-R��@F &�29�"  u&5.44�� @224)$1%0�70� 7 &6.327�.3��%�0� 26�U��9�4gS �I-�� !�1BG �!�05I��0AFA�772.7�voR�: !�3IL85! � B\s�R3e:sV�6.0A69A�236�!��2�t� %W7C; <3� !7%A=B�a�08) 24 >40�{=~�%>���S10.173^m�CTWa�� !@8i0� �:401 A19��@04 4 �.�6 J5%�ze� 0.12A 0� �6aBA, �%96A�0N A9 0.35A0  &�C! � �=�  & 4.18�a�!P 7.400[ ! 217!4 Q/ 7.76 �62�14.86Aj� �2� �5%���11.43�VE  15My& ��T9�}� !2.4e�R0!W �Ea-� �*&[Nw0ŝ\(m͙� Ech��+st"� *� on�3'O=�'u LI,c � p' & 5�*" 6�.�#��le�� & N�"��6��v�Ti�LW4&�� F� �b� 1a�� pV�.� OJ�m O3a� �r[nZ^�)o56�M� AMo�"� �R�#P .# ��� �,O7)< nuR#. O0�*J�Ru� �8 � !"�~ # f����J��#%� O Od09 �m��X%�~X.@�2�X #�c0.362J� M[9�f C9~#f f�mnI{+NIY� �"=e�>dm 6 �nM-E�023��  piRG>�F& ��11�� .�� C=TJ� F9T#� � �i!2!Q�=3 �O# OZ O1�>OB,FOr �� 0� M�! I�J� 3V# � )%]3�A�\"�Ur!8 Sn hJ��hJ#. 39� O5F,6N (5nz0.117-Z*0o �)�Y�1#10.019!Z � �*I� S S�=�^)!� 927 >�"� Xdr�� 019Tf�O�� � � O2� ��piZ*�nZ�-\ V1���=3�v� #!V041A�!��)� zY �9 Q)  m�% kb� �_ 026 E ��Y%Y0HŹ��Gb&A, Bau�uS%Q � 9#E # -106�b]'N�)N9qJ�IIM%�%)#.�X[�NE �Fh� � � h1A�!�!8�\r^ ;r^�!�1� � �Z� T�ame�2"�=VI bumC� .H3"u :B *�/:A h�P�P�B � � Ei*�+���]LSK �@�� 6.9�.0� 7.5�j� 3.32W 4"� �M�S� 2.09�� &3.61vf509 'I�4J�P 0.86�g �65 7 � 10.7� �/� ]Y3�/�J0�T6?&\ 1.8G 4.4�g9 84 _7C���153Z3�a| :uGD 1.72)�75.7eu8.4%|`_19�  `�3+9J :y���%!>�� 5-�'11%9 l3.246&47)��7}6�<ɠ3.3 `!00 &4.674�9�!�`>!'� �'(][��Za�1��8 b3.8-0�"-�:����2��L. 1�b 3.53ܡ Z- ɶ+I,�-�-" 5&{ F 52cm" 5Sc"�3& 5�Nb&�4s �3�3Tc&4� B) 5h�)a�Ag:�:8za�In:Nza;I�PaIv *5 �:e~A�Cs:R)6}$Cs X.Y�EOo(^+}$[keV]&3�h�h� .5am8177IZ�D2'4��{�7��� 1$�=�;n9mediate 2�Ai�<2-�b k[W?4Wtaken '4sh>HBur,Pek,Bal,Jea,Fre1,Kan(1,Serg,Son}�����*S"'Z/Nb,pH!;�%=ke6wZnot as�N"yW>RBy`ty. H�wI9 d hoc, su$N��Dy �Z:Va�`i�<b m?ERE),Jrg\ no &�5d@!�%�y levels >@V�M�_ adopgG�� K�: <G; w=a6�4A��S+2�TI9HQ?@E T&3 &6�5}.U�� : z ��5SSD� N3A}�(�r 2-5}i��5�-\Hu�B&t�e6'�L.L��Ѣ� >Ϳ!�� Mo�n11Ch 860$ \"�r~)g� 0.82B�� �\2�u�$16&7.4932i�i��7� 4.655B!J�i>:��sPd�051&2.2086i0m�fo9.694B!��!q:6%��C�421&1.78F�%%�.�6F!�J�9 2z�:��YTeZ 32A;956��j�kn3.3:X4}N��:696Z�q�Rq�C#"fE�?��Y�)RDcIg SSD$) hypPsi��cGas�?"�Ewe�" ^SXGs6l�k���u�Hm6�Yt?YB���0Q^\D$n*CL&%J$g_A=1.$6�.� \fo%&�AS�Jon�6Cf�Ka few :[�B abKї�Ld�b�[fix ["�K:cM��.>g. �3� sakexa} ary treat�$�H.�of all2FOdE�2Ji w�yA=Gtak!�!2$w%��.(54. HoweverPfC�J*�Tcon�&'I�IURpr�Qt�Ljq Q *[by��A}xW� �(� =1.)�^axial-vej`coupl<1gtC ch m�YsiF�F�BM6OCe&�X�KlthKF)%aar:�Esvhcas':�% �W�s%Um�S,ku�!N*.�6� a��h< Q�F1,!��NNX>JOyHI meanE� A?%�f}etTmQ auth�a�J0Garc,Eji1,Civ 2,Sim1232}.&Pd"|X, four�i�i� mM�IRo.6�Mr�k�&k &l 9ā^ +�P*�Cs A�\ B� X�r�v��%���I�Kcheck �%Vvalid�]by keep�inS,21)�d!� � term X�d�1�?� s"]U"��y� (Bc�6.[ $g_{A}O�$�R6 evm|H�Q��mm�up�%.Q �,I� wise5 rw_i�0E �Dir��son. R�p��.!N)� XI. �c�Ye'�TzI&eM_A�1x%�.rmp%��;A h , �u%�n �3!vkI l�^.��?i, >'dM� A�st�olyQ�ea��] summɋm exo 1WE���a QextenDPE��>to� )�.� .oM�roUK�Wyqu�Mon how;�Z!��/U+�`�jA�d�t��\�a^]ba{ We}BnL�`� *s m . To�Qm�e!� rete"/�Ydescrib��mod�`)�U�!�%�0}$Pd*�m�a��Lm��$D_1$)R23!Q27N��Jp&5rwB)��VZX.) �k Fpaie�� �4l~Aerv �+&� , i.e.)eZPgap.�un%�CMa 4new $(G_p,G_n)B�q �ZA<(0.281,0.271)MeVA�  795,I665,!�"�]{1�#Ol�9h$ $D_2=186.��ISR�UuNvNE�$N-Z$��3\%. Ò� %��1lo�U�U()=(0.13735,�D)$�i�����:JW&(JM��&�MjQ�Ag� " i2�4)/I�Zse ob!�a�R 4.84Ec���_ 3.70.�� T.��&�\!� �T"yC unde�VeE2circum�rc \AҀ26C15.881$&�19}yr$>Ono�j� �Q� �jO�-�J>�IV�4N�OAP17�s�N"meenlar��-����J��gover �< hoic,Y� gotiA�^ v&dOA��U atis<4. \s�{Co7P�!4s} \label{sec:4}k ea�vi�\?ps���le� s�Z�*�w�Rad04}J^�o14B�\& hnr �zeven-�� exhibi�S v_]hap9 ��osen ټ ��A�i��&R N : a)�_%�(pherical, b d�]4med-prolate, c>ob do �5 E��FHe Hyn�~E^ Wfr( ~O eN��!h�|I�� A�of &�G�x3,Audi}.A&h5p,f&��+%qar6�*TyaLa}3 dAU��cb{�vAp"xA�ll��2�X �}�6quadrup_)r% ^� o a-ne�Uve 2SLa}-is"�.Fja�pB6aX.#U�R-e06C�)��To �=,discrepancy biy�� !���ion��W��}y&,U are "�-b��of.7a? hexaa�>Ho0le8Xq�9.=a��-�� ��M"�ks5]ng�0"�8A�j�aB'� Suse��It manif�0�9anmA�iQ:"gU�VJ >�� &�f4fa�:�� appeaB in a�)a���8��Y�2%a cer^ �:a�eN�1 ys�$ed alterna�ly!�t!�9>����^�in%�a�%OFermi ,e<�h%�";qizɍa�VA*�:o�I�Z [&9l b!�5+o &Q "Fi B��1s!��za$�f�Z$�o�M�V�e�&origi!\ng����<W*or"v{}]1�Mv�,Dprivileg� ة�IF"�q-p%�j � *=�� �!� MnX�hإ�>� 'k!��qn�h easiAR�i�<Zs�'_ci.& ne I �ed)�9�ragmen�iti� !&j *Ks��1No .Y*�zs�kcz�kb�k��.l � ��%;E � P\�~<5s�x�[s 1,2 !`J�2C^Fe�i=2� �a� 8qR�͸a �&�rby2 iJ0E�s 1g (�T)l2�T�k1g% 1f (#5). D����,}R�^�s&�? �s �x�~neh u#Y�� 1f.  �)�1.� .m%%��"6].<��Qa��l ��| hree �:�9:,!J,R@:mN=IR�2" �"�&~n�_�O eaks:n!�a�!� ��m}::dFbt��J�m Mu��~ �n"�`�~� seQ�A�al!I&�  (TA� "so�sN M.0#i�)��s qe>� !/eQ6y "�$�#a\�W&�)�S Ei� A]6%k�TeB95��a:� $np6�� $g0J�5�-�1p�J�-*�- "4]�6 $: �-D E ! �v )$>(In.�� �"�y�b� ��� �9g1 �� )$ ,� �v s. �f]&s&�A�*�- !�>\E | >��%-�p��arz�nu�B � *� <�&qeO�&Ea:qut~|�?adh%f?i*� �pn$��a�yb�s0c���=O pp}$Ts^al���s8g�Bar�K�cri�S��!W-#br�s down/cX pen&�whee9�Z9��a! N9%/ bee ��*�V �but ac2�~Z ��sa� �Fhe�� ��Igjudge%� �`(9����"]1� B@�!o� X"� �l.�vas{]U��d6��F�d�bl�mA*]�bbasfn.� �d h&� al*�j���(- &n�J"�����(Suh,Su2,Au}�%�U�(�^�l6�n, "�% $���QA#�"�p�j%!c6.�> *ǂt,Zha,�nctdt8t�k�5N.2 � I�a�#�jn �^"�U�Z.Mh�iy:�!�y=ev��r t�a� q -$ yFx-�2(H)����i��h g �Ag>��2~gj6qemi�H� liv��$�S&21 o *�T1�40(8I!s�}m|a�r&}� .�ofAA.��#��-���orx~�#��{.-%~, gf��4��exceeds�:��#15%�2� fin�2�M��q4}�m�e��c� A:fi!�,o��<,� b�rif�I�)�f %�>�. Fin�gw^_v�"[ �"��*�nVisui�f&�!� &��p��!e6�!�#Iya��e�pi. r>�e=W�Ypublie�� 4U�~�Cstitut͉�<stM�ng��2_6"S �e�MB& !'& *���q�y>q �(pU$y. "�-r=la�pb�em��}J.�!HO. �!ta�g�, Phys.Rep. {\bf 300} (1998) 123. \K@Ver}J.D. Vergados < =,61} (2001) 1;8PriRo}H. Primak�d S. RM, BProg. � 22�59�5I8HaSt} W. C. Hax\�G. �tephensfvJrmQart. s3 ]0 12(1984) 409\Tomo} T� moda�D!$) 54) 1) 5.@Fass}A. Faessler,�> G2!)198!f8.H(Kla1} H. V.�u-KlO�rotha<$��$Sixty Year|DiELBeta Decay}, World S�{+, Singap[)��Rad1} A.Radutaz�48}E2) 23.� Rad2>I=E�D.S. Delx=�)A 564} A�3) 185;MLett.E�B 312)�#:�3!�A.�D.Al p��,N�617 ]7) 176='Hom%�(Homma, E. B�!$r, M. HirsN�(K. Muto, H.^��T. Oda, I_Rev-CQe6) 2972�Sar}P.S�guren�8Moya de Guerra,�Escudera�Ae.C3zoV�35 �$8) 55; P. rb�A..eF�658 U9)13;.! %� A 69a�.6311�= 64Ee 1) 064306>�E�6�L. Pace��cu% y�$F. Simkovi�42�F� 6A$2003) 04432h Eng}�vEngo�MY 8J. Dobaczewski,��(Nazariewicz%=R�� rnam�Dv-C 6��$9) 014302;n^J. �XW. kjR�!�20a�054322\ imk}=#,6La~:733} a4) 32.�u2rN6�9�B�6�F�69E04I0>�4:B,N. Lo Iudice2*Q������v8.� Rad4>`.O�I. Ursu2^��58�\5) 84}� Rad5:�Al.�%��\Ad.AW .W ^ B 59 �9) 8209;6� E. G�#doNB , Eu�T� Jo e�D 1MS1) 65 "z Rad6>��3ZfF� .� 2431.� Nils}S.G. ��0Mat.Fys.Medd.��4Dan. Vid.Selsk�>29} no.�q(1955)6l7}A.A.1IA.Q��S.StoicaR�3-��4.\�}M.!W , El4AT$��A�M>VT(Wiley, New York, 19572�ing}P.�P.Shuck,V�t� Many-Body�blem, Sp7(er,1980,p. 2�t� S.R. Elli�9nda{Vo��An�)v"V �SciMk5ᚉd11.$BarADS. Barabash, Czech� I[EU52e�2) 567=�Mol}P��l%�J��n} .� F A 51-�06� �}����R2{ qHz VB20��� 2 � 1}K. Grot��:OF(4��86) 39}A>�H. Ejiri�R��hAu.-p�cKa�*HeuK0,��KaE,!D OehmKP�cka� Ric�, Pi/e�m � In o؋Sym��um��Aw&� i�DNeutrino, T.Kotanif�}HTakasugi(eds.),p.81�� :>�  1986;�rE�S�bVasil'ev�bAI �*ko,E|. OsetroPomanskyEK Smol'nik% JETP.5�19AU62AW�E.W.Henn4. , O.A[ anue�D.D.Sabu1�*�1 V75) 1378]�Li}W.J.LS[�.�M�A48 @A�47.Su2�.� 4�,��05.�Au��AunolaE;��N�60� 19� 12% i+r*�}y157 B}5 5) 24.�*� X� WuE_^� , ChiCheng-ruA�$o Tso-hsiuɉics�ort�S24 �>.w _�a�qQP�1�.� 42 B��32n�}$L. Zhao, BE�BrownO � m�-(]I ���120]J Baly�� sch QOBl B 356}199.�4Bur}T.W.Burrow)�a�N@She���y6�!% ~(Pek}L.K.Peka��'r?65A Bal}�raj�hj�m976�Jea} J�BachotjB6�<�X� Fre}�?De Fra�%� E. JacobsjQ8aU2000) 48.SJe���9A�4 42�4Kan} M, Kanbe,��KitA=bh9� K22.2 Bal1�i93"�2�Serg}Yu� een�Nb�7��a[55.�hBA� A. Sonzog�9JGE|9� 2) 83.F�@R. MadR B.S.Fla�,sa`D. &�D iR�ldwin��W. WatS.M. Au�0, C.C.Foster,��dor�}J�4� 89) 54.�Aki�AAkimune��� M. Fujiwa�$ai`T�%oma�Rza�(A. Tamii, H�yokawa�Yosoi���B3E 1e02��3}�z:�41. %_}B.a< %OT.��� karnB{C. Lebo,�-�P�Tandy!��1��'a� C+-���)3Mq�P116.�Zam�~amickL� Auerba��0K 26��6Cha�0ChJ� C2b 1987) 226.0�#3}UJ��O :P ��!�4}X� ��1aZtaudtAt��>y�+Rui!�nq �14Hsui Ho, Commu�ceo"-e�2I��425 �,GaSdi�A.HanpstA�a�� IA5e����; <l  Bersill . Bl��e�A/WfW 62�i. La�$. Lalaziss��amQ+ � , At�{� ����6sD� 9� 2� Ike}K.Ike{ 2�M�6 34; 1S�!ta� J.I.�0�I�}조(1963) 271;J1 -�K. ~�6�6�8.� τ}D� eng,>iA,6>@ �E19i�34.U �E. CauridA. Pov�2 . Zuk L� B 25�(� 2��=J.�=�nMoralRR�,nes-LagosadndFMheco, �FNB A 80:� 2�arc_ ia �c }J 4 �!�91. Bhatt�  a�+y� [��Hindi8 NK Ŏ Ortiz%oKaloskamA�CA�vi��:�6��J�Y�24.LLeder��Miyahar>�I�In�)m. Metho~)�Rf!%� a 35I�a 229;��M�� dereA V� Shir T�. of I�&,�#n�dv�,John : eSo�= INC.�63.��<�Ef� qqA 577!�� 399c�KA1}2Me=ZPCLA�!K53.�J2zJ!O-<%7A6168>f�=6�P�mi��'!O|��G:eA�.)�lš% 2� Eji2=;��in �M4 2>!36��U�H 6�� 1��32_Sim2}1�Koval� ,a��"Ei. arXiv:K!4-th/0411002 v1w�F6v��l�e}[h] \�)erq�\psfig $=Ffig1.ps,֪@=8cm,bbllx=5cm,%  y=10urx=1 "$ury=26cm,a�=0}} \vO�8cm&�b (Col��n1�). 2�.,�&��(r/-�k�bl��M$Zr (middle2=*-(bottom2 A 8 �"*ޞ fo� 4NTi~r�D �P�� ~2�"0z�2!�,)=�$a GY�fun�'���& %��\1 \� +*\��� 5�#�3\�(BCSE�pnfD�(xi5!(cal&m�&5"�!`(nNU%*9 *q.graphs�Wk8Fig. 1AHM�*BH �M ��2����]��"Z��.Q3.�E�.Q2. ���Pd�2rc$!/Cd�2 E��Sn�2!�������� :�2b�&�"��3Y��L�c �b6dP�d�.^��.b��QXeU4Ƶ28�&�2tA��`bh�Ba�2A�������3b��i4R�3*%bj-905r� A.oX ��;A0�)�)�)�):�4b( 5.e"? �ݮ'Y%5.> M&bM&&�( $�F,�-�*�-�r)<+rep^(n�)Y7*7 3 E6y �1&Go�Akd1EQ�u2 [�)tr��U.L���1reܗ��,;�u22). "�A" 5b� � docu?9} "� $Tret}V.I.  yZ�nd �G. Zd"�pA� �ta�R"8 83���)Rad8}.@"��a�'c 2F'f .�50��12� Rad92� I��"WDf�'47b�439 5Mil' S. M� F.�Av԰ne,ɥ0R.L. Brodzins!%�Col;w!GJ�Ree�."*�6 �509. Avi}:y ���K25?19�5֯�VOJ"�, ��-i£ ��*��!} *�!QB HahnA�oe1E:=5�)�20E9 Hel})� HelmB��J�-�7) 280.�Kli+A&�5�i+">AB�B�� ) 44.� Turk)L.  evi�Tw#EconomoI�4. Cow7�=�'I321��V.� ��\�#��6�0ie�O1Ew�ach5�"�;a�TtagE+ no n�Q�extra�Tum�1��@ current mass der2I4oj�del22!XHD8��5 pion-nA�}U��9/24the aver�2tdB4quarkM]Erk�1g���L�a�6�?r!^)�v2urb�Ce, non-2]5%:s�FFhdeۚF�ously i&k�de8�A ac�"$to zero at�A4ut 4 fm$^{-3}$�_9� keyword} F� \sep}� U'8 \PACS 21.65.+f 24.85.+p; � 8.-t 1.30.Rd�v�:�newpagec<*�!�)�!�!��i�( crucial imx#3W!�� �OaI a*g$chronmodyn�(s (QCD) %\cW8#(02PR363,Col�O(lo01PRL86}.U.&{� ��r�Bho^5)Hi;QFeynman-�an: oremmM�[s �(Cohen92PRC4o i��S04} �qcHF} \4>\�,le\bar{q}q\r�8_{n_{\mathrm{b}��>^/0} =1- Rfl|P| �r\�i!rE} m_0},)�� wha _ !�� !�U�Y vacu�� $m_0.>�$u/d$IsR $ .� \equiv |Z0| =-^ \e[px (225\ \mbox{MeV})^3. $ Eq.\L�%z)�<be sche����ZEs �D.�TZ� �<has $ �0Psi(\lambda)|)� d}{d }H.+-� =F3 Z 20|~I$j!�hamilton]�$7$��"eigens�F $|2g �$. Wrq?. QCD .TQ �2 �D flavU�p�ic0? as $HY�PQCD}}=H^{\prime}+2m_0Q�ڭA}RA�tVW.?� eN�plici�"�D FE;m�rewC� a+c� (Oto do56�E��n m�^�subQ8[U$-�\r��a<'a_5�H.\iM�^3x>G=AY2M%� m_0)y2-�Q>q�:�2�J>vBRa9H1��gr���� lc�� led � !uni�:�'4 system%=ig�}/T:�S !���e� 'becau=R qJ�� Xdepend�,bD "X��4it�_�NIQ�$6i$. Apppl%�e�Y���&?�Ow���Psi-�=|6P  Emd =|0 $��n�`�i"H�l]�to�:�n�lly. B-)n�h�A exacasolvea�-;׭ly�F�� 5��nJhiݭw��s(�m� !�aO�)�ac�?icult;M�LAul�C one Ato <��27Y- na� n�~are��ep�;a �bspeZzK , usx��C"RD. Re�! FR�Ja�E�� osed-�2 02PLB548, 3IJMPA18}% %I��p�_?!�- vi��trodu�C���U ,�  %�CS�> Bb� as.� e��H. ":cho%� �C�QF�N "�"NonnFP�-� y wa&k �veZg�_c2,ly�(�?~# %3-@}��Ierely bob)dea simpleyP�f 2!�le%�*i� �(��2�rbS� n5�, c6D af� ��� ngE3�DI�pS� will5ga2aqA0E�� re��NO_bL�1@is 2lLe�NncipliA&� . AtpOe Tf 98�a���.z *�� P 2:E�X�n] �Qf���F�Bmeش!, i�a�AJ� K .�.� sho�\2 6�:. F[�1O:��*� 9&.�� Iyc~0 A2^0-�s,A�8�s a� wZ� ��'sU��%�key�@�!�n*�(@RU�J]>�J� �. I��A�, sh 6� �0&� ��QCD2f 1��{Ba wrSDn 6 % B ! Hqcd�>� =k}$ + 2 m_{0}B � +.=I}�� % �equ�"� 6T"� kin�%,2� I}& .=���/ ��!�M�2^A�$u$�$" . De��oG�$%N01/�D! �eqv}}W k}})1 5.$ ��=��$m$ b�@J� % (r�B�KVOsJ%v���>uD�"%��m1�mT) �b& A�6�!D�� �l % %2��$U 0�NexS%� %h#�28� #_P  "� ( i.e. %$ % !u�%{� } |.]� L ; % =� N1|21f \ %A� a�< !�� .z  $Vl ?% �baryo"�Vq�>�  %�� [� $*� �!G�%t"� �%e�e�D,� !� % it m(4E_b���"  HrelA�-"BK-EB  b30 5y.$%q�W230.�end� ^ Si��ic��GQre =J&eX , or�� �s,B�%OJ�� coordLW�,��z�is 1WA�|m(6� )�2�=F'� EN4*%% �Y�}VA5i* ob�Gifgk=� erms ofl�me�a ics::�X��ve&�'�� arg�sF@A�2'�� �is5f�XaLwt"�eqq+U�'�  >c doe# *�?� ; $B� �lso�Z5�-.�c-�Z� can "�Q�wk����.& ifF�is lo�_!:4�omes 0�mfFY |IA�nd!�2 s ���ed �. N�f"<�)!��f\I�Kݸe�F2��r$ %Eqs">)%�(\g�� ) in�摊e�b���������6�:�E��� mdef} m =�+�\m�=�I}j7FN�C0} {2�J�U^�L>(0)�<�� + 6I"�x��q�cM�A|� �Qa fre/����,��a:a3' ons,"��l6�"�g,a� ac�� an �&�A�ae-.w��.�%� ). %�"�W�se< a!�eBb� �s���s:=(�]l� ��2P$l ���.<5$ngZ.� $. O�&di.i/ � of �!%�6��j� . At��em= ure,�('�.7$�$�S.% LSd . %�T�.4Tt!�%D���a:��asympt��Ejdom, %����ɠ F� � (mlim} %\lim> .f0}:=\infty\� +and}\ \�N ;>R =0. >A % �!gN4.����/� a7� aaE e�A�k �K�S�Q A�y2�4^per�k&*l$\varepsilon=\sqrt{p^2+m^2}$)�MkMPe���g ��rk�c�R!����)sF�a Bh �} E =�$g}{2\pi^2}@^{py\ f}}}�  6�\ p^2 dp#g64^3}{6 T m F\�)(�6*}{mM\)Z/$% $g$ = 2(;)��,imes$ 3(colo.,2(spin) = 12� $g=12%mA9dency��"$F (�` $ F(x) � �3}{8} [lx)$ x^2+<2 )-;sh}�(x)-N]/x^3 $�t9= ln}(x+.m)/ E1ffjve>e$6w��e22�hem� poten0$\mu$\�`^�pfmu} 6]M�\mu^2-A� �or} \�� #68m� 6a phys�meanr >��nat��s��uld&ƁB/[�di�`ee� ��nm�~"� "�AX‰X�� >kalway?cis�Z&�� ��Y��:�E�X'rea�3ic��Q�k#B h� ŭE�>�ᶁDb2n�f� ��j*��7).#�[nof view�&J�_� chocZto�� �quvvty�+ deal gas��%� � and/UX���0����(es) �all  j�62�9�or�mpl!�r �ːGoloviznin1993ZPC57,Peshier1994PLB337�j���d,gluon plasma��s���٫�IU�T 9 �!�O ` ��' $m(T� 6�"VZo lat�� ]Z�.�Gor�e�5PRD52}MChpya*edt�h>���D��. ��M���]տ!��RM� gaJi��cNpH bt� care�[Zzno&� �i�^ed� a"fic du[prk!1T2�!6 ��F �y��:� =[(18/g)\�6�]^{1/�%%t)1"H �� �'�2:&. So ���/� *�)4�6i�bl�X�9s.���!n�� / �_!P���6RF�byF�� nb3� 6Cj�18%s} � g}{1F  H �[ 6� R%m^2����6)/m�{��6!�/p� ] mdmBC%�� %$:rx)=\ln>M$ %�A�$hyperbolic�3�P�:ii T�kbv(@lei)<funda\B %�ioV+1���l1} d(VE)=Td(VS)-PdV+3\mu d(V6�)J�wL@mb�A�>�#C $law0A�Y���$PEx!��$S�ͱX $V volum�re9(��%.t �) � F� 2(D2} dE=TdS-(P+E-TS-%&:#{dV}/{V}-C6f@mplies*98narray} %%&& T=E�. dE}{dS� |>H},�Tlab} �-Ef��-VBcVcS,6� }=0,�v�P�\\�\mu3' 1}{3{ B~:qi| |_S.WmuX"�11J� f�=0T:� [!d/{>�]_S. i�} \�al E/ 6�=A$N}% >�B!(allaw\E�"L+),6I%p.I)*)7�%woq� beNzP&=&-EI�6�,1�P��%�:, %&=&)F(!)}.��>dn1F�^ Pnb} P=b� \ >|=6y>%+ In�bo&=$,, the energy�q density is given in Eq.\ (\ref{epsilon}) from which one has $ %\begin{equation} \label{dE} dE=\frac{\partial E}{\ @p_{\mathrm{f}}} d6 +j?m}dm. � end{�0 %with %$ %{\kE}/ m} % = [$gm}{4\pi^2.[ %:�\sqrt{6� ^2+m�}{6 �B %U !�1. meftF�-)8B�(6w/m)>{jU 4,\right] dm %:�integra!qP over both sides wille�.�`nbexp}) naturally. Defin!� $ E9GLI}} \equiv \langle H2\r_{6|} -v00, $ U� n^* g -(2/3) =\bar{q}qf0!�= {M_%�F `}/{(3m_0)} \approx 0.98\ i<fm}^{-3}A�e� $M_{\pi}.4140$ MeV beingAm$ pion massA %$F 2=93.2$>(�B�8/^�})JY�X $9�%�|u$|_0$. Solv!�for%BA�o $Zh>�b�$!�is!��f( leads to \Zqc15} i�~-[^/0} =1�@6�}{!�6�}. :� Accord!to 2nHqcd})� e expressA� of $}�QCD}}% 4e total energy�¡�A�,quark systemQ� Ved asb4EEI} E B\\int_0^6�010�� ,_0}p^2 dp +6#�� E_0:B(@The first term isEI:�A�outy�ons)@ͦ<$6�$M contribut!ff��H��@ Fermi momentum $2%0}$U� non-Cng casem connected!�i  bye]Z�pf0nb} :k =\��(18�O/g) 6� �y^{1/3}N  On%N�other hand, $E$ has already been Y0Z a�, replacE�he Jo a�` ��A� Eq.~R Ag)%�� �-2,.W" ,-n divieDby $36$, � ^^EIexp} %M(�2j}}60}}��)^3 mFn:m, -m_0f, 0}}{a- [qr6��� {:�F22� !i� �)A�o.�)�E2�DfD6� }{n^>C��%p[K ( frac6�}^3B�^H Ec)¦���h]B� AtA�@ same time, %comb� Eqs5�&E .+or takqf$derivativeiDrespect�b$6T $ on.a of .u[6� M5  J,"� ( ��& f}& % -J 0!_08 �m 1}{3��%� dE}{: J�4Therefore, if a� knowN.�� , %%B�2:� $m$I  effec%h� Z}$�eobtained��s the .�-7)b)�5�,�ychiral�?�5atectheW  calcula�WŽ�[qc2}). �C4great advantag�� this scheA�o GY$ in-mediumJ}�at�^(does not ne��8make any assump�T� curr= ]�s�modeln @ameters. In fact,�:;pe! c)be Med lik�is.b5_JHFw perform�aAt fixed:�~t!�comparM with!���q!�,E�� haveB�� � 2m}&�4q2mF(6u/m)��-2 0}}/6+� ��B.� L�� {6� f25}~� 2�! $ f(x) 2 �3}{2}[x�0x^2+1}-\ln(x+.<)]/x^3. $ % %Eq� 1Mk  %U�mea|fula;mplex�ER� � ian QCD %"� one_ba�ed ^  encodnly a�%:3. %Ita&�e�a d�e9,ensures %tha�R� be 9i �� of a��ng� !{ s carryN�,�such a�8 uniquely exist�$However, i�st�a happy�\o checke valid={� ��`alism, %although no extra�@s� � pintroduced. % %Now let's try���vB%F[ ,7}�� s 6�=0$ %)�is�Ju.r . I!�i!xs�깞��Z�6� %=(� 6�/g)�  %=230}�%"[ ly, *, limi�:�\ arrow �o�e 2� ��� ���^(>�  /^10�1-(>9/ 0f :Q��.H � $+ ]� freeGT!�i% exactlrrectD . `*IqŖ . LE��O��euH��U of state �4famous MIT bag�d.6y.�o , R� M��aǁ�wa coldM�plasma i*/ narray}. Pmu} P&=&"w^4}{4�}%�[ �g \mu}O q^2}�}-1 2(2F5I�ɿ+3VchV65cE� /> H] \nonumber\\ & &��g�C +�"\mu^2&�RKm�D���m dm,j-t w  $6Q(x)�:i$-1})$. ForMk,ison purpose)�ind� tIo$ variable 9��chang a4chemical poten� $\mu$ thr���8pfmu}). Obvious��&n�is[  ca�spo �A�c� $B$� differe3 >�n2-%'i� re]E���stead, ��� ity-5 . B�1 bary�e� pend nY ,�2 ��also qsP@it \cite{Ioffe04}6 principl-�0hadronic mattcellow� ph�tra�(ion point, I5!z���en| %#0nzero, should�$described �erm� }degre�+��dom. Ovwi�b�perturb�l non2 �"�� inclu confine�.�accoun� =193PRD47}�Fexpz�:� ]Lau� series (:G$ mus�7�erg�at> Bor>�=0$ du� ��)� mer� takeE)�l %mi�ə!:BM �m�n} 6�K a_{-1>��,+m_0 +a_{1}:^B�� e foAning/ w+ b<e�!at�6�� .�, main origin"�;linea��5�a3E � !�.is � 1B2of6�.p� ;coeffici!�$a!$G�� QCD coupl!�$\alpha& s}}$�^�C11s} `=��{2JH�D./((-R.)F� � �possiblE�No"� �nit��@yi lattic�G s. H2 a� e arAve�ZA� &zY, e.g.��ose&� hard-amal-loop��Q� orym�(Baier00PRL}�jQ weak-5��� �6|Freedman78PRD,Toimela85IJTP}. Al� they��vta�higforder�irU�aġYid�cal� W2A�.8��ie� e�2�,�Npropor�0al��!n� :� , i.e., $f� mI�JZe�(_0 \mu. $\ > ishownA-��; "�v�#1�0�R~.$facOub�~(�#� ) � E�� to Taylor����6:=�)1 widetext}e� цP c} % P�id�n g�&R K\{� N[ %\mu�/g ^�*�# cosh: . _0 N"m �l!% + % � 2��\mu ��  � %J � ar��dB�R �\} .� @%&& \hspace{-0.5c?% -�}{� )�ޫ"�%� �] 6�^2%�!��� 9�B�fe)� �}�# )�!�3 + ��)� ��:��N 8\�\dots"�$��}�&� #B�a� >�v�N�;�%��f�}�Rc)>V, -..�&�e�. -A1)�6�z:3J���B�� �^&6��2)N��n�2H%[Z�i(6y1^qW �>�^2J, +.2��t. -Z�m:� %-�i� �V�:���-^ �� �]�F�2 6\J�6� +s'.� � s}\A�:_�$�%�"� B9�����)��>yify^�-6k(y��R)E2%&&IU ��yJ� ���&,Q(y)/y��: �F�� J /N���%r�Iľ�6�:o^� �J�J� ,6�9�+Z�I6� (%� 3})/��)�!�F�b� ��B�.�!�����"r a� %$y���/m�)%! $ >� + {g�+�r*[R� \ (2�*5E=E+�74:�\m~) ] $� � "� �deg�'� .� g�conrcdE&�0f "� d0 ematflyven. J.�c � ) >� � \mu ~� ��-o� abov:� n"�!n�!.�0It�:�smallnes�@c.~! of l�.)Ks,;.',vanishes whi �+/third�$N�( {P}/{:S4+2{-7"�1s} 1�Jen.�1"m�istrA��F�resumedYM�:����% "A!rea(why&V2�%"��zQa&��n|be7'� s/(5ROinser�.X=6�/-p�>_o,�n"�$�:�2%U%�3���!} %6q"�2y}�.�%���G�' m_0�!(1- ^2)pY0T&g .L�].��In �!R�#�i�1on Q"� ��S& $:| /:�4"! &J�-m-J<T :U}{:V=U" $9I�*6+�T"^;1p4� dB�,Fi&8�&�(s=) -��F�&=&�)F:�:^*�Bn�\��q}  %  % q�E�6�^*+8^2E�:�%^*Q�:,,.�j��-�6��{\primeE&� -(e�m�\mu"I (+. "F).�0\label{da0dpf!��5���J�"! {%��� �".���+_B�A�q5%5?/d���#� �)F"4< Gell-Mann-Low %���z" Low}BNmuI��}{�e�@sum_{n=0}^{\infty1�n�2n+�/Q�-} GLeq�2T%To���.�e�� Lxis�վ=(11N�}c}}-2 f}})�0&6_1�$34/130cI�+:#/6#!�&BM-��.�o�$1��) domN�h��i3, � B�1[mI6F�a_16l�$� I } So�� 6J2}>�a_106�/�#,],N��% $B� a_1[q]+a_1^2)� ��(}-a_1m_0]/( $� a�7 ache&wj� , �s:M~ � b�C"-+� A�E&� * n� $ �s�1:e"� $. .�6$!ei[6�:t�+: �"��%�`V ._O "�:Z��O"{M^Q� dmId�2��a}/ƈ�_ a_1� �BU =&V� ^2}A� :bnSB� F�5.�&iN�&9�"� 6���� beg.�> ��:� ��=J�C��.3 ^{n+"&1�Q�ԁ�6�� :pt� \"KY] �A�ep�(A2>�"$>!>�Umal]mZ�)�6+mYr/ 6$� { QE�.6/ 4{�m} :�.�8^�-m ��.�/� s ^�.:b�=-I�>! 2A�{=$RF�j6,} -b! =\pi8��^2`/RAW"�uM]�H /ut,���8B,Q-as*-�1}).��>��V(1)} � C_1}{C lnUC_1+C_0�.Z;� n'} A\ln ��),{\Lambda} =0"h)�uG"�:qa;�� valuisJ�$]�:$scale �'� }$!�C_0=-�� /(/A�8and $ C_1 =- [Ɠ ~� ]/(2�p�,68c&7%s6_ . �4 �ar4 $�\ is usu�)* 300 MeV�lz~akS 1 }2�# �*z'��i�$�H�(satisf��traint:Y�gyi *� !�two-flav_+y)L) lesAan 93��(� �%N1�< adict+$ndard nucl�&physics�,Peng00PRC61}�*x�9�5 ion,��'I�!�&�'�1E��1maximum oF3A�runB"7%V�j)"�3exc161A�whole "| (. If larger��� used� &�* g�6to �*( more rapid!C �,a��enB� K �"�' V�is&0�/�7&�,��)&(( help!-fm� k�#&��#�*} � 7=.��6.8=��)q2E�,�.� y >7:i�cn�8UXed.{q�6. %AtBg NevB 43� �becomes�:� >� %p -&� % /[a_1-E�J!V2�.�� )]R$V�.YG� ��%N 6�$ %+M-��6�=~I.1�!�!F� F[4\}!e4}{g}) Fw3ɨ^*b4k6� %% %B2��}\9� %=1+�;�e�{26�F".% 1& 2 coIec"�% P � D �.dy%�.�:�� %F( d ^*=1��2�" Ao % [��"J(1�):��J1(%C"�0in�5��es�d�#� "x & KH�E�G>�!�v�5 1->9/.h@.&J>�qc:)�Y- \ \ %& %*7h�"n^*/[F5;%�^*-(3/4)M^*}I�!_!O&a�5He��xi!on�=jH63� nd $6.; }0}/.;4�2� !$"O��. ~�8fin4K lowe�� behavior�Lq�%�. %�ch�)v�% lso �Cn�0"�*�9 % ���,2�Mј."�2$Z \gg:� $o B<11� .�ies, .'dS@)���Bd63C /(3d]7b�� $ :� 6l 0})^{3}6� =B]:\; Deno�![�-� acy 9�5v}(e� r})$4 82\pi^� /:lI� \i to 1: $ &Kap/g�2sta'�� 8 2PLB548 ���-n]HpB4�4 $~Y �*a- J�. 95!6. �on "�w0:9a�2?s!24r�)%Jl�0sim8Ae�< },�?�ႵBu�} >�E/{(> 9�-� ^Z.\:.�xJ�w.�expon� i=6noV by $Z$.�7lB�2]3� unity. A0a=�.� $\sigma$ ��f>R���Eisimp} 6� =3 K:�H^{1-ZZ|H% %?4so�D2� �7concret^8lue�D%I*y3 v$&W influ�7 -*�B'8�6at>?m1F� intS!�e�l#���� f� � :<�AYUXц>r{ �(%F)}/� >� ^{!f}"^mI)���2�} = `;("� /� `6i/ | � .@&�pf n"��These�.7� F� ݛ���Ti3���&�:�E"�K&�: boosaWto�@�cai a factor,�0>2^3>/^3=EA�=;Z>�NeU�beUc�#��h"� nd���A��r� �>�1BG0�&*H����� $26^3/(3m)$n7"s$v�;*%onBvt _ŧ:UZ$ [Z=1*�;F�=�V�]t�c�C2Y-. Fin.�%6)� A ryǡ�6�4I}"RRmN��Rz�� �m�.�m))!�.� � e6�%�|qcL} ^6A.n b}o a�r� �� lG,with} \ � l�L�!n^*N�� demaI�'@mpatibi]U%�f�@ mH-.a>�%lt�#��<��u� B0nli�^� \rhoy&V �Q &/� .� F"U{�T^2vT^�T\�h&9N!Y�6 �,Cohen92PRC45N!'wasm3Q N$(by Drukarev�l et al.` J99}B<%Jr re-��Q8 by m�Iuthor/Q>.�@,Chanfray93,Lutz}XO0 get,�2�< l}}=)$a� ��rese�relE F!+0HL�23�9�1 {3-ZFeh ceQ V-E:on S��J��.h!&L<"� $Z�� K >R)$u/d$U w�:�T�*abBH$m_0=7.5�V����he&vd��,M&A$Oakes-Renn%�-I$-2m_0^�=F�$�appliLG �X(m_{u0}+m_{d0})/2=(5+10 �1E$ Gasser82}� �F� ��$Z=1$, ��!�0}��J�+9J�aw x 34-<.re[ |KJA$)}s�<liter3Ye�&$significan�E"�;. Pre"vBiteudto��aY+er" , �<�@0G�BN25---26 �X),d�"J *ial%[lsB�DVn)5nD M than�M >;�N���-eFYan �ly�%�. NA� ,Qw�Oo!@:K�U v�s.� ;�NM�e 5. "�?/2If�dJ I 7}n�=rZ$�: ?'/[&/nn�!Y %n0�-R�A� % �/\{I*.jj= <[1-~# �{2H(n�)]\��> ����~�X^ �:I .�j 1��A%\?�6<'&]�;R�.�;� %1-{[m �*#��4Q A�F_ % %N� 2� %+EK/2)n�M V� 7 " -�� M�ab&D�3rm2h] %#z1+N)2| I`fi (v=`cap({ (a) D t: oNYb�Y. I�Uk9lR e�6�fun�MZd d(star a/�"� ac�U�#lZb^ .�� (open-circleAAށ:�P� ��8ax ion�"up-most :>cross� �U�2O#�a�ons J plus-mark7Zne�c.��i2�ein_1^�H939 MeV c5%�.%v&%(. (b) Veloc!��SF bpur:5:*�% (!<dot� !C) S;re&1� .ash-).3A�l,A|�M�wW umer����%pl |in Fig.~UHA�32�-��cB\$in� ree %� %gaszdrawnr.� *} .\deQ� %spn&#N�I.;Dis veryw ,M!SU,es slowly. W�.`c���bred >�� �&d�Imj'm*�&,5�a to %bO�s�Y�Vt�Xly�m�-}�ar&I %A^.EL�4isLne: a tria�,vY�a�!g$m/6Q��� $0.2�<��N�� e un�M tood|inn�R�&:}? -t��ar �jM�P:�*$\| $ &�E��z1iT�'�=o152e0:�' . %R2�e�mh�A�A*�""_ Z�=coI��-%> #(}/m) \sim 1-# %:�^3 .�0�cv2!3ms:�. T�oAtnE�s�;2/9B9 <��nx)D�-�BM�Z�,$(1/3Jhx2a��I��seems� eN>���  a�tle��er � !�$N�, � �ak$¼IB� (a)��*cB�(|_.��_��esI�i�amI�$%Ѧ�nT!NvX �{:X �WZV�U��V��T=�%j W s)ݦ�b zeroR� �a� ˂`:_nr F �b�a���` 0.3--0.4.a(B(�F�Dzyzhang1997NPA625}�=7�X�^^6� /3$,A�BC6e . E�sQ,Pk[��(� ��evid�a&��"_^�/A���p"& $E:�&� as abT .b@ec�Tum3 (9&� "�_WEE���^,-��_�  rAP& n�0rmodynamics, �as�A @Ref.\-�%']12}* t~�1�X�1{1B� ��s� heck���!f  7��.{6�2�* �=y 9.;1�.Jqf;!�1�=��a�i�ca stron<1 nseq%* v>� ,.�h(by $|dP/dE|�(2�i�)�en!�)�:R ( V3�!��6&� ��&=-��E]akG *� ��).R>h$)U��! y`asympto�lxd!�ultra-ivisticI j � b�+exd9z"MthXV�+@d#� opposite-�may� some!�ing!�V-�/ M� sit�s, �3AIk6�Y�!z^g�1ndidaSin neu!��s�\4perhaps heavy �)colli�Hs. esummary%G-V6�,Ak>J��!�JQ stud Y�{eew5�. �jF��u�z� of�. AB,(� &�A4 arly�l mean!N� �vJ� � 9/2 �m�`^T l*�I�!)*��Q �. wRP 6 devi�? 66d �*!. C&� ?n�/u:�_-ren XJ*�q��!r� %\vfVeV\s~mon*{Ac�G ledg�_s} ��"��Wk sup) �!B�ODOE (DF-FC02-94ER40818), NSFC (10375074, 90203004, 19905011), FONDECYT (3010059  H1010976), CAS (E-26�_,BES-BEPC. Hewa�s hospitV*y� $MIT-CTP. QHthebibliography}{00�( \bibitem{l>} % Tex��/ic $ %^es:Z69 \note"sub  (�>}l6E162I�r�za�eA��me lastF�3�% }.�! �HBrown02PR363} G.E. �4M. Rho, Physt dp. 363 (2002) 85; M.C. Bir�b J. *�G 20 (1994) 1537; S.P. Klevansky, Rev. Mod36412) 649�5Co�$elo01PRL86!G. ,xGN#�%,H. LeutwylerH�vtt. 86�1) 5008.=.�%} T.Djh�R.J. Fur�dhl k,D.K. Griegel.)v. C 45� 18812�GOR�M.&�$, R. �$ [B!q�$>�17X68) 21952XHFtheoreWZE. MerzbnD F {\em Quan�wMegfics}, 2�~d\m<(Wiley, New Yorka�70); % C- (-Tannoudji,�Diu �F�#lo\"{e|' bq|hg(7), Vol. II.�8 2]1 G.X. 4, U. Lombardo,!NLoewe �HA�Ch�, IL%�B 548E2) 189Bi(3IJMPA18} k.P P.Z. N�c2���M�� Int.A�MY�A 1 }3) 3156 SurkAY. ZhangPRAdSu%4 �e<(C 65 035202 �!� Euro�X0DeGrand75PRD1� %T. v� D 12�5) 206021Wangp� } %seH&\ %P. , %6t)m 0) 015204.=\Goloviznin1993ZPC57} V. %�$H. Satz, Z�� C 57�93) 67!���Peshier�K PLB337} AA�e}4K\"{a}mpfer, O�gPavlenkoiG�Gff>33 s4) 23�EsGorenste�!p52} M.I��S.N. Yanu`E�D 5%o95) 5206."ii M; ChernodubNB.L. !Ag��`{� ph�?V eJrPh6�i�u�ITEP-LAT/2004-10, hep-ph/0405042. JETP � 79e< 4) 6J��h V�EletskyB�] D 4)Va�083.�*CS R. LK��dlich1�%H �84�0��06�Kapusta8a�J!� ,)=F[f-Tempe�)Field� ory�g@(Cambridge Univer�k PoQ, , Engl�| 1989�>U,6V B.A.  � L�A$McLerran, .� D 16A�78) 1162�6f T. �UT��qC2?85) 90aA&?Bocudo94�fa�J�BiAi=�)r7I��6%r�K,�N .����ow6�9�5L3:LLNDUG�EWilczek6ID 8%+AX633��.��980; H!uPolitz��F�3�lH3) 1346; D.R.T. JonF: Nucl1YB o��531� B. Kis�ieI�PpMor72n D 13�6) 27>�ng�y612�2hJ!�c��Li��B. Liu6k C 61q+��A5�4) A. UkawAH.� A 49%b089) 227c; V.MZ9lyaev%�Yaeeog]�I3 B 13E�8�N73; K!Born,� LaerA98, N. Pirch, T.F�blsh �PoZerwa>O]�D 4%�89) 165�TY�*�0 %E.G.�0l �EU Levi�":�511!�90�t�p, Prog. Part.2,2��1) 77�7%% krevz ,G. Ryskin, Vaa(Sadovnikova-|% �$-th/010604qfr�F20� !Mpuu�J.!��!� �L\ A 35Eu96) 45��90&�1�F �1%�M. �-�Dsl2�( )\ %�h5\ ��) 427��Delorme,.^)�_ FQ60� 239.��!g��]JABm� !d� �E�\ B 38E�! 676;�2 %� , S� imt �W. We^pYe,.�4�&2�� HB� iman ICh. App AM� B 47��72� � 82�J.� �B� TR�8E�82I��*D0 MU VJ��Cajat� Wv. ծ7�536� enB0 i� $, Nuovo CiQqo A 6i���22�Mx87uE.O9�"�131�W8�12` )49s"53,60�M� L0]1>_2m?1) 252.=C"�0 2B$\pi$N0sle%s�  1Au��q0 W.R. , Li A��W!� Kauf�/R#E� "( 8) 782�F Z.G , Y.W. Yu� N. S�L�Dai, � aess0% $V. Straub,6  A 62��97) 59; DRna�"I iE �A 7�W� ) 36 ��2fB.S. Zo�"�pS�3Lu!�2;*� 258��Brock!t98g 67} %W� UQ-36eo�a46� Ballot �1} %J.�� 6�M.� Robi%�0 d C.�5�A�endB� �' docuao} ��\4class[aps,prc,�pacs,amsH#0symb]{revtex4",\usepackage{<icx} .epsfigz�m>s�?M cent�sc"� e-b�#pseudo-OM�( all �r�`7dic�a �R$<5�Cin ch�Md SOti�)edu`* at mid � �M *E`m�a�I� �.��4ilar &�&%t�z "@65��^0$�5trWIq(-�work~\cYy(luc4brahms}>�%hA�umably rp�# DA�*(,�be9ed +�G tune-up�e', w4upor�)o�" cascade m�sm )�;!�l7A obser876w�re7� $p_T$&a�a"�M)�:O%�s well�[$Cronin enhAFaG<%�Q. �-��<extdoF t;!f!�Zm)� Lj ion-)Y��*�yaUcs{�R make�� '{I*�a�"(specific qu�i!�} SPS Jies�<��4=(17.2,20)$ A A�M�lucifer1�yto ��RB 56,130,20E F 6G2,luc3�F�y n�_�!���v�dea  %L soft,��aT�w��a�J�.#{"����a���s͆viaeJNN inpu�#w�@M{ buil�#block�=a{9�V�Hn� examine �^f�� A� resc�A�6 such�(�91��. We�-0 brie!�p�M^�P"��?(Monte Carlo� . MdBot{�A�Ec��}I l�a%is�?8�\$5hybridae� e, uB*say�"JDs�.�6�2vial�&-"rqmd,�2,bass1,frithjof,capella,werner,ko,ranft} toget��"�Oal5#t+�d�Jc�,���L�#a�s BY=&�lartonic � boal,eskoy�2,geiger�2} in ). Oure�r�3�� clos� !spiri1�#?!� RQMD!, K.~Gallmeis�@C.~Grei� ! Z.~Xu �g } as 9 ���% W.~Cas!� 0!Q, 5,c a�Cer:�` our ��!-�$parallel tcC�!�lE�"s. BU� seek�>  Mn1� �"�$Rtd/���� ceX45"i�ic>KB� ����)��/.!�� not neRarily�e�#.��!�a���.J�a�a��W��]4EZ out ��2!  e�)nt�I%) ȁKt leasR ���A�!ġ�set� base3$� judgo�9a� "^$s)2�y�"�e�*�sX�ed� c�@=n] ga5)Q� ng &�A�m�Ś betwCN � n9�� lXI)d1a�1� "ńI�peA�ve �5,�9 .� easy�� i�f����a2#�.tG� lievn+y ����Pmpl�od�b ɥa�!�$ gluon-s�A��7'D*mk,cgc1�*[�� !6f t� ywpr��sa\on{{S"SU�KubS�  I�2�IAe� %�i�72w.�s�����Q���� Q �; A+B,�is !�a2Tno�)ofe��q" each��Ha-���!^.n�yA7t�  or +J� ght � � ����Nei��8)� n=�:��eQ�$�("�) ec��mj�dlYd, cl�,��E�"�Z�A ���oZ NN*�i� } � 2},�� corp\e��= �+a�clu�cE -M2�� multipAy�Cgu��p I& sets up%�� AH (> /Im|two body�3, 1�_� ��2.1i�)U Aee�* ic, �<��J�]2 (SD)�nd!�n-Z&NSD) a��1Ggouliano)t�0 ц $PP$ � [ -�ua5,ua1}!�d(\b /� 'f_Jlabq  It�XJcisq �Y��B]��6�8 =�y�-NNA�put[��*!f�  ful��dion �MR2��6"�2$ ($13\%$) /!�' $d^T!6* ��130�$��,K nR�^.P�pC�]h 1 adI�& M� I �cM R�by=�5�t L(oalk��ducAn �L a ra�S� '' g� of mes9��� H �3A-1�t �-�c�n} 3ūR A< ����� ��f�U��t�� ��W�i�<+ �& c/Tri\y�Mq�!�YteBra�  �$ alternU�"� ��fAw&�%�A�e 9>a�Aaio �� ]. A his#���AYcՙf3y m]al25-�\ ż)I�nrelNuNnd��er�D���&N�!}�y. &z dPnM8 E7!s�:q x�1!43 a��� ^a�t%�r}0án� 2F7.�, h��Ysub�\oa ����,|d�we&- o�V�i &�7�J�?�I#�suffi��l75rdE0�,� Vple Dr�uY�Oa_��4�=e8irW �� )��ABR�2ea��a prompt�\� !�)� !5H�quarkA�d� s si�lyH_d# Z~,`l��i'\6s�g� f�ed��7 yeʒen donx k view�l�EV)�%;��? fto�we�e� to ignore�3��Te�colE��"a,%�A �5�al�!qc2�'mbip���eqY�WIn�ohe" 7E�rA�Д�a dua�tZ)�-s� &"�s. �l ve/1{ method�3��#�K2� ���&�a7vGe�y]�s/0 group struct~:�A!Gng�v1�a�bllu��by" 3F`totyp oto�6us (P+A)�.� �Z��eSspa$ !ntigu�/��aOpimpact( � $b(�{x}� )� imag)�� %Dde(!�cor�on�s `row��cle�e6!3E *�M�=mp�šāth�p%), {\i�i.~e.}~���dis�c!2�aa� A 2 M�A�`usf8us (A+Bw % �\Fi� ocedA is gk aliz�Km;C p�4s:q�� �i� ���� }!AfRu���� [#�\�6 n !W-�o�fb"geometrg AXA+BY���A�st �aP+A\d� �ay,��f�*d9 �i!�is�j$;A�l��uW�xL�ph��%�a_�;- v al.alwaysa��A!H8��N @�NN pair.>�"�daYhol��%W@of6 ! �EIS!52Iwe�o�� i�"' # &�I>H ,,�Aic�S h:n �,�D�"�  oonA"s=s��s�e0��"B o 1s��5Q mM[i�� afte���soA* ImT#�[�*�'w���M��M�ŏa�ao �am ja �:r��aY� tim< bori�8&|�i~-}z��a = $T_{AB}"IR /\g�+$)�5w�3�& L ($q �9 q$)�AcJ�e� a�"Ax are �!! dipol %�pE�� els rel_�more hly��JW%,mueller+�$�I�ed �!a� � +u o- A� S�57:�Ac�;� AGi� [l��ou ["5 �LAJn�Shuryak%/Zahed �z } 'c�� � gaug�A�@"� aze�se�jdA�� > ee& �per�E�of loo�b3Pa^qmA�i[{�)QCD�i%8 � ek5$T_c$!�$T I�$(1.5-2.0)\A�s !E�is� l�!a2�to�H��\�&~"��*�L (E) 2Lk ^4 M_c$7�x m���@a0"!��"� e�A�w{vA��E�5 F�9 {\it� � zed}!!os"��ET�3e3EWt�h�-p+� ��7�(ayat���<ic�d to�� uisk&hD q� Such�r>� �$��ap�SUg"�y�M expla*Iɡ�a�!> f��ell "q fM�X�>!fI��me&�*i3 {molnar,:�, �ű�w� ��%-�is�HjL ly�f�#i� �_E����o�nɦ� a4J�l $m_\pi!'1$  � esV ly M�upI U b�^P�x� �C&+y pE ���%T#-T# seRG)��� �#  g> k $by a Gauss߬� rib�,�,&'4P(m)= \exp(-(m�)^2/w^2)B9'��d$!��Aa�er��a5�.�) $w=m_0/4$Ee width�Ie7 5XP����en) ���A$yU�0�GS *�Y650$ �U S ��,ng��n$$)�$w�v�V ttle�si��fcA'�Gng}t�P*�#-i�,�. Too�duE%l���L�$+�!troY|� �!>*<�2_ 5 6�e:��xl cay �  `�Me'm\AhIi s� � viso�� g %T���< �restri��K� ssyM $m_N�N $2$aE. &FbJ �q)�SMOu��qnLy t�|�~bF!:'� 8M]MP�)��(�isospp A656��>Ŧ $, $\omeg:qr $K^*$���rwm ge a� �oct�iHnd decuplet. Creat� #o�b "@$0Ze���V�A�! en3n� g)y� r5�l&� !'u�%.i/5!�-"ܴ�a���~�@ sj�� Fock s��*� is :!�!U�QSo�+.m��+� �& "�m 4�� Even?�0�$+KD 6:% �I�jto&� " ��eS� �+�&g�/�V5 I���1im \G� _{f"�L�na3y)� r5 єIt� !whx� 2im 1/(XPp \]Z {El�},H�k �Cela�V� W%a@!�M��� I�+bsMO&��%�� fash�wc!��$b�$�5�})in�'&�!�AC�%�dma!鉜FP �vAS)�:V.,:Fus. Fit� re&63a�j*A��D ( ata �M�bro��i� � � , (sqrt(s)), �*W�L.i=U� q�� "�+,d��A1I %�� 9��*is2�)��O(v [�P!S1- ��-F*� �r�^�$4/9$%h�f��� thusͳ newa� -�E|ku Inde��^) Y!���&sc�"�/mQ6�)�'!�EeyU�-�G&��AA"l.�5}qGM�6E�/��8.�� (ch %&�wis esti�%��!�>c��)g���iea��&C ����r�$� ssig" A��7�_(E�a*�0AXepsh��!"�l�s Aer%�96.EKic9�annot� *�ly�B��of����,�A�W.guogottfri� ��MQ, �O�of2�� 4*�" be� � ��-�kE, < viz.9�!B"� s ��lap�4ly��0 begiN��"�!S�Ahe KNOq�2���B �'�'in�NN�TAO !�" � -tai�')@ impo�6"� �on�(�2�can��7Vi �IctBul�+ in ��D+A���IePrli�J�3}!*L3"$!�4 $dN/�!2�K9��y A�:.g o�� �-ed�t�#sz�d�6ty � �Au!?e], 3 Ve ���R� as m�ulo��D !�!� !, �i��w��m��ighly�B�. *�,e:�vU��^}{wesc� �: �d����B$it e.~g.}~�-� 7T m:etc.}~,a U[a_�zy, �_�UA��ld#,���5��S . WZ��er>�irg er�p44nj#a; inadG�l� � employed�� forw�����to���g. A�?5, Pb+P_JI�I�a9Tt sH����ry�!�e�f.��9a�&A�nh�!7 .U� KNO-�B�%�NN�d� !h"��� d �r.q"[>R\> a} � &�9�� � �p;add� ev-cer�|~a .�"ai!4� | 2�)� p"S� �*�hpplic���n���� low J�. Y�cutoff!h�T$��9 readG2ap�.A4b5!we�~ ��Jer MA� -�w!.cm�-i�ap![[%a�� � )�vt��/a� �/�3&\)��T0 < �Y(1)�z� ��(� NSD $(1/� p (A:�/dBF:( � UA1�E#).ER����K�e ; �s"�+�k0 a power-law AB : �I�r *q&ZwоOObo�! a fit��out )in PPA��h69$�(;S A�vp�� >�i�F� f = � (a� T/w) + b / ((1 + (r / \'l)^�jta�  >L;Bs!�psf9y���PP� �8*�N')��cA���  �0� (� ���$E@of �Z&�s�1�$�t�J,R\(2��eN@�/�=pp� midrJ��aGt$�=�NN&�7M%���`��t�m� ofa*� ����p":Hunlik��o F the"q�'5&5InC�(A��I& 5� ope�9e�,�l�;!v/L6 K!� g>Ni�a+g,� �vg}�N�A�� � shar�Em�.h�"s� ts� 2� ��_3��(9J K! 2NE��M `��� � �e�`E! �Eune�a* ��aݡ�.�" �h�& 4^ *h.� }Oa�eOA5s .b�6ly'in�N9&���ng0�r��S%�$h ��y�!�Dul��% * �qkڇeth�& �.$)Ae�A�"T ea&�i%8N7yla%��I5^/lBYi#Aځx�u|/a6�&d�A! [InVO5E�BregatIBm�!@Q �� evolvjB!��=r� B��&2YE0� �%�$\tau%  -��r�(f!=Z�"�Qe� Ef3�e6kA��.�sib�oI�, if � n /�m5�!�sk im (Û(/3) (0.7)^32m$� �y do �a%lap� �1N.�X- *� + [(te �ga��D�*at�eAYH�n%%D�u\Z!2 M �7�� u�g Up-��0:jb7�Zvasc�/^lea)� *����5|��D�u� � : patha��� tech�!�E:Q�A��!Ib-�K0C�d�is&�:A��iizGA|i�0M��+� )#i�=y �5&!��P,YBor���,!�N�����;ed due�!���6A��ak+ i}"� i��!@� (�l,�k!�&�w"�.�S�s� on�<I: D� S� C�.} �<&Aas!�aS)�gh"�1!�YbAɲafr� �*U����+dHny���&�� !kydu�� �,��;pp�>e�A� �B�!�G fe�41���+cl�h,`6, ate'�j�/+a�idPya?wer� !�ȥ�I2o.HAi;I. As��^�� !I!!{5�o)UIO9�>)��"�%��)!d�%Ve�� A#4;9| L-��9��A?tru2\@e�mI�!nA<_�⅊1�re;& {�Mi(��5�6!��'��� (3--6)q ��� dou��w(e�'�� �B���,Z9��("S~vel:io�M%/A�G mp�<Q,w��Qfh au} �Q./(-�fu�4��Q`p so�% rged M�?vz� "� play� inc^u��Ge��!��sQ�gQ �?) �;r�iDqtld]e" WHN!"��� �-%j bal,5ic,! %��.fE(&t)� � s it c��� re����� �"S�to3"�4dEw,"��RI�.� ���w6)E��O4�$s��� �B��3{6����f 1�,$[4�|t$2zZ ��R �: G�6Q��a� ���M��~DI�pau}.\�M%M�/�.F "�D.�lc E""�b'(iɘ*�!aAA=A #� � pT��:A<��#  #� $2(2�0 u}/\�$)$�)tw���zm V^�% �%�+-�A"A��܁��!��A�� ing.�� $ {$'sEl!!t"R  Lo��z5og"/ �I�* for � � = .��� ���tA�amaV ;W�symme�(M&� � in��� !f� l�*o":s�Oa}.4�#md& $��Q? 5r!ir;mCmD��)b�beo��7[ �p!�s#�Op �*cru��!�:���. commU ]�/s�C jA*2� �b�%". as"�.� �"���_ag�;$�:(%���5��H"Y�Xe��H4{�� dela  7� PB16l$ PD���da���r�@K&�ea{>A�b��Gd#&e!�J# ruleI �&ba�)prez. But BZlyA~"�$2�o �suE`.��0 beit Ɓ��[ olog�/� ar-)L-or �!F'>�A  �p��suggest���� deL<�0e� gAof�2-��KY7� oughI+ ΄i,&uc���dkI�3%�eD)e !ǭ@� ~��6�I� um��3y�E�I`r$� �F�NŻ  I+u` � .(4) Z�0 /� �x""�� �]�e�� ?� �� ���th��8Iv2�EKimA�a���NN@eqny virn+���0 n�Ege��m~� �3!^v( $A��!�!#�"n tur8�D�Et4a("d�#A magn��B!� ,��2) �[nT*� F�!fSŒ� �Y� % 9 �8!��A�l>Q a kinP��u�c�g��us*� �W A�ano hot_EIE�?2��%Fj %!N�$%`� ��!� decl�V1�QU&cA�\a�2��co�DrZZs c�GԄA~C.F-[�I \ab�.A=pI!}x� � `jet.'����7/�B note( enthe�6l�,!�"� �a/".�sC,6Wory%�B �B��U�'�  A� %p'$�irtaZ#�Mer \Ef��"n(��7na���:A�M6��R �6 �r� 5)�5�t�(Uxb�A ]ne3�"su�� ac��� M��JLtJ# ���iesL;g��u�.�)W�"�LI��RP :`*�'��a:���!.2�`�2' ���, <|0s$�4lUQLl; �+Es�!U��kazGtt�!AE�ly (c�4("I� w n��cay�t!t"�Ue�)� $2/3�aUE{!$!��(5�$E���"�A:�  �Dv �+h�p� � *In�Fk4�� �"�1f�� keep� in m���{�(#y-l2b s, $0.5�� GeV�(e amb4 =B5�*a�Al$\le 1.8</$fm^3$)�!&sh3bsf �W 1p$��c.bDly N=!6M �;ime��It!��� E�l �� ]�,�of� in I� s@H m#5)mP��oM�2.5� !�G�RU?& lengthy�-3 �1k,�af 814� /c, ^� ��so/j�e6i� s�M��as��EaSuO�ugb�o�<"IAE%s ���manage {rop�.� %�,%6)d�&!n oft-quo�[ .Q2,b1} ���īn.(1)� a�$discrepancANb�H�k�6%k1Akg fex ��Ql��� a��^ A}��K�g.`}efA�tac�  "sCo� �R1Ig!�T d�Liv� D �Z� !�d� U�ACn�p� +I^sof&�Z*����a m{dfu"� "� 9 �"/disi8�7cou~'E�f�FL!B[ unre�<� o\�le�J�ear aAci� ��um!�mic-h ,�5M e�, , if���#&�+[1�BmF)a� %��%�!%H' ��!�� "�"�nGA�"3� ch)J� e@Iu�8[�6�&�]a�| �a sil�!eleph, lurks0 h.L-i�.2Z02�>�>P� a�$ � ��>aIl� &me&�>i2F Ċ ly "�K*�By9� c2M@atM�.�B���/%�1c_l&�h!�e �*� sX5 eYK]Lˢ sed ��� XeIA�g|G!!�xbGjY _�]itlJ�bEw mudd� w�E� �^zYeq�a���'al�l1V�a�t!�Y;)+�1"�� A�E_ unus@I�t:� th5g'�{ic�� A�it�r�!!ZA�� �(q���m� w�/�^%��&�LbC 9���yA�N�\b�ur� claiR_� v v���, %a��)I�2*&�!r/^&�,e presentati�on here provides an interesting case for rely�Oon the geometry of soft, low $p_\perp$, processes, essentially mirrored in hardzc (toduce e8 major featuresk8the D+Au and Au \ data. True enough, C high �t tails in distributions ar@me�'cked �D in our approac`pbut legitimately so by us!,� NN � awput�o nucleus- !r0cade. In any�e one should again very much be cognizant!&x0small number> @particles present�Deven cental collis!0. Some $5\%$ N!�A)8grated spectrummes!O$comes from5~D \ge 1$ GeV. \sec!z�>{Acknowledgements} This manuscript has been authored under � US DOE grant NO. DE-AC02-98CH10886. One of 3aH8s (SHK) is also?teful to� AlexaiHvon Humboldt Founda�0, Bonn, Germ!�and;, Max-Planck !� stitute aP N!�`ar Physics, Heidelberg& continuA�support](hospitalityA�Us� discus!� with�\BRAHMS, PHENIX, PHOBOS H STARA<llabor�m%�fully a9�d, e!�ie�e�> C.~Chasman, R.~Debbe,F.~Videbaek. M.~T.~Tannenbaum, T.~Ulrich !,�OJ.~Dunlop. \begin{thebibliography}{99} \bibitem{luc4brahms} D.~E.~Kahana �.~H.~ , a^(-th/0406074i\HDI!M Arsen�  {\ia� eal}!� )U C.<, !�X.~Rev.~Lett.,{\bf 91}.8072305,(2003; 9/T 2Q �ex� 30522�4phobos} B.~aAi���1�2WAhys � �8 461}, 297, 200! 5Hphenix} S.~S~AdleredM[>d c!  C. f(69}, 034910Fh star} C..d�eI�:�c)o f9�1!k2f3;V) 89 �02301*2; A}iI`)a1}6` �� al.E� ! i^:�^EE2-1E ): !�.~=� et ig-�: E�A+0311009, Nov. !�3;�I��I.~Y�E6h� k��hab�s07M�bURT6�,��cl�4A�0; .Q �I�%u��b��H�2Slucifer!2P�Q 6R G$Proceeding���RHIC Summer Study'96},175-192, BNL, July 8-19, 1996� Braq��Y� Ca�@ 58},3574 (1998).� # 59},1651"9)�uQ� �2:<,:�v~ v63e�190E�1>U 3} !. Intern�V,al Conferenc��\ic"� 4Quark-Gluon Pl�RP, Ecole Polytechnique��dalaiseau, France, Sept. 4-��1;2�>�E��20806325�O74j180j952��!�]�vM 52}, 329I6?bas� S.~A��ssI�ete-,�.~!�. AE�6�:05�6dfrithjof�CAE ssoa�$ G.~GustafIngleG)q0 T.~Sjostrand9p-s9!q31)p3);�7.c6b1 B.~Nil�-Almqvis� � � B�28�A289�872`4capella} A.~C \ �Tran V M! ~ W9a9 146W0) !�}.~)P� 501c( 7); k��1���A�405067�hep-p� 3081.�werne�c K.~W , Z �Q 4A 85)X$9); K.~ 2(J.~ Aicheli!�E ���� 76}D096) 1027-103��H.~DPDrescher, M.~Hladik,�f$Ostapchenka:��Xd ��$``Workshop� � !OT  Matta�� Dif�|��Phasesir !�si� s'', LHouches�[March Ak- April�, �t;9L� vited lec�, giM at�D Pan-American Adv��d�( I& "New Stat��(in Hadronic�[a> �s" Campos de Jordao, Brazil, January 7-18,2002,U 206112 koi�Zhang,� M.~KO-A,~Li,A.L%��BD9904075; Zi-wei~LiE� C.~m;E ��it 68�?54904 �=E� M�# .C AIW69@375-378@2).�,ranft} J.~R �KS.~RiA]��� 2�H413E� 85);=EQm"m�� 111i� 9). .5 boal}��Boal,�E�%A�V *U�I}, (1}e��eS�s3�: 2206�62�eskol��KeVE,i�Kajantie)J.!� dfor��a* � �� 32h37f6�Dwang} X.~-N.~Wang�a�Gyulassy2jD�I 4��350�k1);.B , {QG000814} � 405029; x �� 5125.����M.��X.~ �, Comp �~Comm3 8�07!�94), *1 geig�6G UB.~Muel Nuc:K 3� 60�2);�� ?�i 1- 46J 4965 )  4986 E�F!� E,� 2Z �D �3'�.�~A %�41aF 257I�4�� \]�~Dix 5�345%$F6!y&6� 9!%18D.~K.~SrivastavA�Y��;B �5lJ �X B�� n�g� } %G$allmeister��G  ���Xu2 C�$ 67}, 0449��).�cassie+W i�2pC"K )�% < A735, 277-299 ^0!�J.!�s!U9@, E.~Bratkovskay!QR U.~Mosel2 �i� 44��3i�6�sf� 8} L.~V.Gribov,hM.Levi�de�.~Rysk� �~R E[100}, 1A&� J18E~55d1�H61�� Qiu,2� �� 2�I427e86A�.�! � j�8�26��906�gcL.~McLer� R� Venugopal� 5m��Y 2223!9!�1'&'� 094002m�p a+$harzeev, Ea1|�Q�.�5� 93m:2�gca�.[21E;_ &)10332S2);6��21�9<!�ng.B,B 3271f4). &�goulian�e��_�A�}M���16� a�Z 2S@ua5} 1G.~Ekspong��UA5>M]�%h 145c!�� G� ~Alnv �sSWF0Z% 2�44N | ݌uaA�"lbaja.�lUA1j�� 335C61-28U�.�Hfermilab} Y.~Eisen��� :�.%H7) )):A= B�B)=; F.~Abe x, {1�v-�$D41} 2330,t:�p(�U�:'1;Y>@n mnEg�� 2230q2n� �IJ.~W.C �5<V�6%�31�W197��.� bori� B.~Z[ peliovC:YeS/0301206� A (in�s2�m����, Eur. J.-�e]e\98Fy�zahed�E�?~Shuryak�[ I.~Zy�307267;�G�30807�&�attice~Datta[Karsc�,P.~PetreczkyTI�tzorke,: lat/0�12;wn17309012.� moln�D�_ g*o ��102031;�  4018�MB, Talk ed+w"�on "Cre� �Fdof Baryc.��aP�l", ECT, Trento, Italy, May 3-44 (unpublished!�5 flow)|� �Mo,B!i�ȁ~ >D>�w I�18�& ��j�,q0 _�"��L 2�� Z��1),� Manl!�M^�2U T -20th W�r 9�on5s Dynam�0Trelawney Be,Jamaica!xrch15-a�> 2{gottfriaD�� ���v�%�y3�957B7�� Actaq�Pol�� � 7�72!�9��ppB�5�)��  PHU:� PHYu��4�241803��Uk ~ au} jE ��,o��%�bj�(n��0$fwhmprelim#S:��-�L50%�endB�0 \vfill\ejecth�figurexbox{\hbox to\hsize{\hfil \epsfx$=6.1trueinfile[0 0�  751]N1.ps} :}} \cap�H[]{PP Pseudorapidit� �a:arisonE�K$minimum bi� 200� NSD� ~/cite�an$! pria�0LUCIFER simul��. The ��erw4properly a fit"arexperi A� an i:!t8! ensue!AA���8; thus does not"Ya `set'� free!\� �k ��acharg�$3&/� i��$ t variousMs�!�&�&. �Qga�$an �F' ca�i%.� 6%"(%ɾx�''�liminaryn �LB$ results,A leas%�$its FWHM.}�::h5j�ŀ docuA4}��b�sps/fig6^� F�6j� >�  �$��f�$/ua5dndeta^�0Proton/Anti-p  Y�I�Ae%�,for $\eta=0$!�energrelevan��vs��ext�ed�$p+D$ �  M� agre� 8 el� measurA) UA(5UA(1)A� playeshfact aA�diŸ��a&��$body model�*ao3�,Z�!e0 basic"putaa�rj# multiplic�6:+�singlea� non-  diff! ive �+ h"o)� aver�/2b@$\bar n_{avg}(s)$�+.KNO:assumed.2�Uf� :`< % LocalWords: UA cM%) crc1.tex $% % % $Id:2 1.2�<0/07/24 09:12:51� pp��Exp $ % \q�Lclass[fleqn,12pt,two��]{�+<} \usepackage{es�#)def\bq{� eqnarray eq{�>beb2eZ2ra{\la%�} ]ket{\r %abnge��T+follow�lin`.usei ,LaTeX2.09 % 5 style[.,) �=( % if you wm�includF$stSO,� s %.@f*icx:Vpsfig}W$have lands " t�6J[ _(right]{rotaM/}��-yJ. own defin H t: % \newcommand{\cZ}{\cal{Z}� 4theorem{def}{DE}[R-]H ... 2L ttbsNhar'134}6AmS}{{\��ect\the\textfont2 A\kern-.1667em\lower.5ex\�{M}25emS}�add+ds!�TeX's hy�  exce� �  \{�-$ another ced� n~, pape�0-!*,end-ed Post-)��decla� n� front m"$ \title{ � n �D stru�!�g��alized8ton6�  ^3$He a� �<{S. Scopetta\add� $[MCSD]{ Di/��1$, )�$ .=&4P_A \cdot q )$%,$\nu$%��MgyY� ��o��ystem% � �I>��I�n�t, beca $of vanishAM��s-� �� AsA�l��z�UFɑ s it will!2c� la�% same p�7>X ini#at � I-.$ g %eK�8ba�ext�� velyA� cuss� or�dt2 ts Y�2a"�� y!E�� E"�;( {8a s. )a welleHR6C Mwh@ &C o��� possible,�<uv�o�2 �,b��e��exo��one&y�ed. Be�s,�.0�\asR m�Q pola�neutr�<%A�;friar}A� =�a���!�didate%4e"es aim��R! !y %ya�v,��unveil �angular���9ent. � E�talk,��v of�i� �xim�(IA) .TI prc}8�q23 un9� $H_q^3$�Ma\�KedK-convol��mrhardly�Ft la *  , du"] v6F �F.  %mV>I���=y�ion %iV!/� !� shap-je&A Q���, %bum^iz <nu*=�earm�| it� is ��!� test %,Xthe %)x�? rgetm`accuraca�6Z �����UctoU~�e�iwcan��.U F�lis P �@p �ݔ jig}A adop� If%�think�,a spin $1/2$� �$,� 3 al (�) "C!��3�$P(P'�s(s')$,e�ő,��!�(x,\xi,� < $E_F, o!b.��$�a ��ABcoordin�2�A8ph� 4"�L, $q^\mu=(q_0,\vec q��P=(P+P')!ś�@nA/a� $ $z$, $\xi"\ so� c@ & = & \sum_N IE �c8 p \, P_{N}^3(�v p,  + I,, E ) % + %�J %�F�Tp�FM^2},{ 3 ) ] %\non1G %\\ %& \$s�{\xi' \e\xi�{q}^N(x'A�'�8� .���\xiB��~.1 ��9<I� above equ�yU � Y x� � rO a�%�ar ��I#coi#$us* neglect�E $-n �o�se+one-bo6 fj Ej��on $N�m| , %:�)_'9 %P_N��)AJ=!�%{1-�0(2 \pi)^3} %2��{EyMA�{R,s}�raIZP'M |-P�� p) S_R, :�) sp]PEQ.R f)cB[ ~ p s| P�$ket %\, \dw,(E - E_{min} ^*_RAX%��AY� ��*=P��%��y $e�J��(�[bMN6l N up��erm order $O(E�� 6� useo�mad�A&K-����e��0��*] p^+ A�$ x' = y' /ay ) x$a��%<"�� Eq. (\ref%3 }) %�es�E�64,6� %$-�=|!� ^3He}| - 82H}| = 5.5$ MeVa�2!�$ \ exci#oni� y %-ctwoiU��ie�i� #Min5�Aea�-f��  %6�El %!g��lap�_ gralA�qu a�9P_RI� p s A� ��  y \, e^{i p& ��yA�ZTchi^{s}, %\Psi_R^{S_R}ix) | 3^M ��y)s~8P%-�Zeq %.�;n�  m3^M�-igr�9sw?%~ s B� !�%��Lthird� onof)QtoAM>�AAT %W�$�-� %#zA54_R = E_2+E_R^*�I � $Ri� 4nsic %Hamilton'per�<�IMe�w�(t]��%^. % S.$A5#-?%8s��#t!s��Lum& 4>�i sum�on;uUi�ve��deute�Xa�� I�% ;>. 6 })Rwritte�9� >C# H��3B�=�8�B� _x^1 { dz͈ z} h��z,�� "/ ) �u� ft( {x3,v"�E)~,D�BD a��OF } $ b��i�E e�� ��) $lta�z� xi ,����s ^+ }�.յhq0e�nd{��  *v � it is*�� %Eqs��%)E ��^ ) or; ����,Fful�1IvcJ0� $i)-iii)$^v�*ly�"�*xNu�Cl R*}  F@$,B�, & e�a^��> ar BreitIme4v�2#F�"� x ed da�%��=�gema},# mean�a��Syntru��)�H� %exact//�%͑��1e�� ��-��%onFI �nly�ne ��A$  crib� h�v�l6>kno T -outr�q���H %.,�� ���s2�8:��N8 %&� U�� AV18.1� t��!ccoun�$Coulomb re"#ion!�o3���. 6�" ��CU46 v$v4 tre}I��%ingredi�@in�� })� 1�� eHN$,��*��@�^%=Double2� ��e ��rad1}.�r=W�1�0�!pū�in.��t&t"!#n" ���&Hby $F_*�]� ���VjyA1'��z!�t9+c�%S$�%" al �oi�(3%$�43: �, n$,�}s. Fo%�u9 $d$3u�F}q�e�0) %s�$gF# rks,l��%F_u &��"� 2}�"+n�H$Md:M2>. @R��$.�� B*}[ht] %%�7x0=4cm %width� ) -�en�/reY!� ![ F28fig3.e�7%%\ 2cm}{3} *%�=$xe�eh#er��{O � 2.1i_8Hfi4�;��N8{ %-��_3$M7 %��a$a�+�F%aty"0.15$O8($^2$, %$H_u�_3P\&)�� ����,�w%� $0.05�q x_3 0.8$.])&}�+� urs ]� !2!pI�A�Q� ���* eforA�A>u^p:@{4� 3} F_uYv� ��E}F_d^p�U�4d4�9�0 3u^n:o %{2.q= q�d69a6- 6:F�r*=. Now� nu�r� e!�[ �D ider2��A�!n�+ \bq R_q Jg  {&A*A(" ) �"�pB8+nB)}&E raf3 eq %�y"%�% �L =!lV 2�z} %= { �)2q0�[q�)�� rat1E�q� !% denou'or�"ly re-p)]�'�3-\ ���E�� m^�,9/�;*�a�&�$ disregard'� beha r� i&und, i�Nv yp� ly $EMC-$�%"8 ,�^2#,q-&�k5�JverEiB�& � � �$xj t4-$5c�sJood d&�*-ff �2of% O e4��S �% , $-�ؑ�:Ge� . %A�" illu��� � i^od�4#%�>6$ %by&� �5Z �4in �< 1$%� =6� %�#"� $x_3=3x��\xi��sIAK%� %� ,$p!�,^ � Z6^ q 0$"�.���Kݵ�JE���I�HbG56G6��]0�^���>Q_dS��?{� e lHpanL!p�]] rnew)�)�)��$� "� F� R$� �;]� �*[AI��da�D 3..1I^��- ) �2( 2$. ��ic(�'$* z �.�5�<_�)6s(iB$- $dUaM�( Let us now�� cussH:\="m����|! <>�,�`��a a*a�c/a>based�.QaHp�a�:�� edD75�$.,/�$�b� by %t�18. �KF�&&�$"< ő�B%Luɑto�e �^:��{3,(0)}B� =�{ {3,pF� {3,nB& app0H.m" {3,NBB7tilde��N �) �*�  $ ��%,� �� �A� 6e $N=n,p���v. Its�ʡ7aN.�s,��n �"� $J�!$�heI� ��)�b�,P%le�&V- is g�ne�!):�!drY )��(Ad: ќ )$. e�);�F*�3E�b�3I��� Q��t��s ^{R]�#A}� 6� /M� )�&� } ��l \eq&�0 y-g�+� ,J�)�r&$*�E�X�o&\E')}m�!�1��k+��dE�}��/5A^tH"| }�! 10� 3� {ch}^{3}9�6� 6=-6' ^=NL���~$emc_d_av14� �s�g.Y: L":%�Ew $RI�$�� "�r"� 2� y� = 0��U)+'2g�(E��AV14 (�� ��,�- Fc  = 3 xZi*F2�ed�A�F0erMpo�-ial' �� inguish�&. R!2��)���ml5=�+.� � $V)#�p��_ ��= 0�a�� now c�0lyF��(nd{P%� $F^3eyT���&� q�ed %with ���EachEcoeffic�s $10/3l $-4 re�FplyDGsen�*su6�$2��� %vale���x�$��ur�� ���� �%or�|al 'ir� rge.� c�G8�@I�E"��|)�D� ��*�i� �7�,ala~% a.<e&�-6 �^tJQB�at�@G �  - �4*�7r'and, i� w�FG!2�!9�mn B� a5be)T�-�S!�Jimmed�K}=by �5 ��&Ay� =�ɵ!#oq�by placF $z=1 no2���seynoA�v�0��t.� (. �e��en� *en&�-  �$"�B Z =��, )�ee��y�H=H��i:6�. S�mg&a- renden�.tap0 nt:�*y bplp .7$,%$as � 15 \%��0;<*6�&q ntha�!|-�)4*�� B�;wA:happens ��2v|i)>�x reC= *C=!N��&�-U6� ; ivFWq�!%%!�aI !p&:� & @1 �$2�!9exp�6�Ref�:O�L cK $x,$� a(bulG  2�U %32n$�;�*s�q�!Y��at� ly u�e"�3Zg6�4�ti�.�Z2-*q;�>��/�=��=��5he��NN���.J�<��2Fa�4QF�?�gron}. N� ar turn o�2r��bl# rong��> on�-U:.�=I ��u �X� _ 1^:�8E�2a�Up$feasibilit�2&��7o�6-�y"@��y x�c/4 its .{4e��6QiB�$�"�7@W{"R�o"yS�7 } D. M\"uTa {\sl�SaV(, Fortsch.6Y 42, 1Vb�T@X`ph/9812448; A. Radyushki$V�g( B 385, 333,Z 6); X. JiJV �T +78, 61�a7).�0dpr} M. Diehl9�j388, 4�\�h M. Guidal�X�g12co&zTgui} P.A,chl<M.Mh derhaegheProg.�?.yV51, 125\�Y5[n=ID\"ureA,is*�k; F. Sab�j�2��4$1} E.R. Be�B�W,�W.787, 14"[1.:H2}u CanoE�B. PiremZ-�mZ19, 42�^4); V!ze�c$M.I. Strik1jPW �$C 68, 0152�X20!�$ A. Kirchn6C]k>x C 32, 3478X>^5M\:J.L. Fri�.tA�CE�23M60);=�i�$\ C. Ciofi�EAtt�fY�.R C 48, 968E�2�� *bFY��k 70-5�U_��0.;%�V. Ve$Z=ND 69,�`4HY��}�q>�, EA��m��GAe lm\`�- `L!s B 1E��n82�Z$�FKievskyTP`a+iviani2�C 56, 6\a��bi�q0av18} R.B. Wi4+a, V.G.JAXock� nd R�G(hiavilla, %=C 51, 3)�5).=�"2���,S. Rosati, %�xQD A 577, 51�c2�" A.V6�M/1O449, 8 ?F^9� gari� Gari��8W. Kr\"umpelman�feNQ173�nA�|h�-C�8��H,���\410057.>� 2*wH /T.gM�B*ws�Ocs9x6�M( : 20-9-��#Text f�� dl�iTrim S�:,[9in x 6in] *'*Latex2E�F�rs ent,&cBW mat%llayS�+ tyle z&��er��World S�ific P�]�,Co. Pte. LtdA�% Copy�1995, 2Xdby�FvAll�� %�C�R: 5$%H,Area: 7.35inn`c{Mrunv,0heads) x 4.5i4M�.9(is 10/13pt 1� �0Use \tbl{...}=ma!�t  �" �oGT�#! D )FH�I�Q��Odraft]{]�}6,2%2L+f��O~�OV��Ldw��OBM> &1Mf�{c.? \\�>Nz l*-M COPETTA} /M�)M2)M 0N(M\\>INZ+M 6�La�L s{ H�K&�H&O  such/ deep�Sctrop>��=� �VF@�t�ts, c�F� �>ej5`/�B @  i^�N�I . He{ .�A.HM"Xo�@ .nB�  ��%M�u]L"B^�M F� "+ as a�X�2�H{�N%,,uC ' v-,��S�{ly�N:� �(ula�!corCZ �;s&[�s,6�aZN&�E"��r�<un#�cN%b(JG"]N M ��mG^ g)s�J�^? . An�+^ZNx���t!��XN��WN�VN�{ �'eq�BX!:�ach, �+(U�{�&�J�s 7d q�a"]�2)KFRN�MNMN6: �DN/� p _rS !a��ur�v&"�t�K!�:� �he�irq0Y�"dGu7z wayD,K 4ral cruQTM�"8�G�N��m"`�I��, >�N~E8ccd�NAccCg{?BQ�%!�U deriMin QCD-2act},I5enter���"ist��yO6yOB8Dee��VO�VO �#��A%m/Gpromi��o1�aR�oO�oOVoO )�gui�0B,Z~Oeff�A#M �.�'"hH4@s>!ao�1e 1� %6n� ew yearsaen��O"�1"�O�ee��Wol� ub�f �c�Oconcer� �d�7�n��O!�q�@q#a�)�)"�A!�m�H@6�HMAs�P�P�=arN Pa�d9 �P�PBP Q^2\� 2k>nu^P/9P�P�PZPRP��Q�E/� ith1�N�PA�s�'�P . Si t�e�yV�Fn$UKi%(PQ= . C&s, W(?pery 7�qcy�2 O� S7i"HWm� gust�mPmPIn��,� Q*G�ud2&���B��GZvPIy!4"XPsaf!H0 �NS��Ei�KJa!�� 'a�""�.h b�8em �P m"� %k�P����o�}FT,f*�8� a �28�QmM/, gDIS* ]A"p"?Q*�,�. P!� �1>��ca�DQFDQ*=~>_5(�OQ2OQi#E�+�.�� �of�(� "� A��"�a�ulJNQn&3ly&� �9.~AO�ZQ�ZQ&� �YQ�YQa, break-up�!�H"VZ" 4I�� fac�zQ�zQ�zQ2!j�r:6��uQ�tQ�#e�] o tesy\�Z5h"�+�|)�h,�-��Q*�Qi�ŭ,vid�a tool� g!Hfu��.@ �ir� pre<�S2�Q!�a��=N�Q&bj��Q��Q��Q��Q��Q��Q��Q�#ef a"/re�Q�7�)F�Q) >�Q V�Q�Qr�Q -Q^:�Q8xi�eM.�&�R�R�R�Ra�&'a��%S �@ a� n*/��90R$ �R$�.� �Va3�n�7�R�R�R�R&�37 � R� R R�G��."QF�� �RROe!�RR,**Z�Q*Ck��x%e�k�9��Q�Q[  P�Kn�Q + {�V ( yQp"tQ, q� /�Q�Q&9O\\ ևQz\�/(�/��Q��Q��Qu9-e"Pnf3�0No�Qk7�'Y?��I, E&�Q"�@(&Q2�b um_M�SsQN vec �rQ^7�"ra-I�kQ�jQ�N=QO �"97"gQ�:H8NF:T�fQ�fQ�fQfQ��fQz s&eQ"YroQ$�nQ$zmQ"�IO@6lQt� 1��e^kQ&-UjQAala*iQf A�I� M �S_VgQ\�M/zfQ XceQ\�P`P���dQM�"�Kw  jaQ�P3`Q-\2_Q"�3�^Q!E�]Q9Q�:�J �$BxAT�[Q�ZQ.�A}*) �VQh&in�SQm�PQ8!z>y�MQ�MQ�MQ�MQ"Y LQ�JQ�JQ$RNQm�hMQ͔��]2&� � iNMQ�LQ"LQ,�<MQQG& zKQ"��JQ�JQ��v�R�,6 Eq. yR� })�FC^bQ9� -:eQa�a��N�rt"dQ�N�R ex:aQ:�`QB�_Q.;�^Q� ��ZIs�����ɒ�� N2*[e3a#uu heF\Q �avI.g���hQ�WL�4*�&�% ��X&� &�`ZcQY5�.##�fQ�fQ:fQ)7�.���eQⅹE�&��hQzhQ�J k.y�WRrWR6r3 �ZR�ZR�ZRNYRa�i��H�a�XR�B6E$-mNJ�9��}�C�8*TCy&{ABTRRDP^SR�*�4j�>��3�s�( S/�Ag�B$�@�@�@ 1.9i2�Y���~�RJR} �0/(2�Y*1KFO_d?� 0*�I�+�NRNRu��.>�Z4E�I"HJ�ѭe�(I�JE�*dJE��OR�OR^OR��FPR�C.^XRqu�nA�S\a�a �]&-) %Cm�a�)*�&,B�,  $be �JomDFoKa��c�tROTFRglobal*� ._3�O�5��R��R��R��R��R��R��R��R��R��R��R�R�R� �R��R��R�R�l�� X��R����i�b���R� u:IR��R�::��R$�r�r�r2*2>�R�922VM7��R��R��R��R��R��R��Rr�Re(΀R�K|  #r3;��~RNh�_�.� �|Ri~��{R�{R�{R�{R�{RB{R6��zR�zR�zR�zR. z{R2�ere� Z!��"�B�^G �wRQ N�. �sR�tRtR. �uR�uR}�vRNvRY�wR@revxRur]&F"��zR6�.�is�w at9]po�$�RpsE3r�R:�?"�3, s-9d�ea�1Bx?Ya�t͕�= e FEFmE jusJ volvX=bt��6"W�^�i���is"�<��#&j���^>Sn0apv�]I�e3�=S�=n8S��K}�CS&�D��7SB7SG ip� appl"͂�, zo"( eIPG�G�]S]S, $]Dog�Q�s�:�S&k9!"FbvS�mpeculi�}�&RI"3'E�"9B�S?| >D9Ey��S,EQXRobaschik, B. Geyer, F.Stt!!�Q��Sv�S2�P71�T33cS�2.�Q���BTH�%N,fATP6�R�?T�?T��%�>T ��B=T[�%��amsmath�g�� .)�a�b*���S{apsrev6PD3�\�8{LA-UR--04-4790-Y�{A.�8Bloch-Horowitz }'Hs-eqp-shell�iGLQT.C.Luu�/Lmail[]{tluu@lanl.gov`Q ffilC0{Los Alamos NU" al Lc�0ory, MS-227, (`, New Mexico 87545, USA�P.Nav�l!?�n  1@ll � \2�aw'� LivermoreV�PL-414, P.O.Box 808,5<, California 945�W6�A.Nogg �-%n@�E .wasfUton.ed!I.�&��� N� arV%/"ß WI\, Box 351550, Seattle,# 981�U ���{\today!YIQ�R} s>'(BH) U,"�Isuc>R��2li�! "6 Re"�aNb._�d�IEzX /e *`s. � e thre�6 s, BH wat to b;2�M!Oc���_"�$ harmcEosc�Y�t(HO) 4+ɯ $b$. W�?tend up� i-J rk b �A U"r�? � alphaR���(five-, six-�Y�o7ki 8�Gm�!ur�&A��t�_;-n6�BH ter��T�g (�9�A� PF-spacg�or k� few�5�8 (0$\hbar\omegac 22).��� how t.e AQ grixaW}sbai�.I. ��#�r�og�`Q%���)4*�BVU!.M�@�mE�ec!":�eQs!�$�� 1$ �f�V0Faddeev-Yakub@�yb'. Howev� z \�eu-���u�_b�S,!��c6'Ai?.sus�bleA~�c-�Eup>;��y_nca6uXt�f!��iz"�6 /�SI WCatM+e �siQ�:r�l/���su&jl!�1�$-f��.韙�8 \pacs{} %\keywX�{��.J�nCIn3�!��2Ɔ o}} ���Tt&Jۆ�!���I�probleg�em)��Dex����--��| x?cKHi|�t eULR!�-q^��5UsO��f:^is� dau��,g\footnote{A��inct eA)�!ozB� B�sv�)T�Z2=��XPieper:2001mp}.}, yet m�Xp��$g*i��vǁ�method�at�xvzA3e"�2�:�aKA�Ou �QR war��s �Qio)P�'$he Green's"�rH Monte Carlo (GFMC) � (��in]Oce, Refs-34son:1998qn,Pud�nr 7ck,6!�y re?n�W�� U%�ba�`"v2' Ψ=Wologi�yE:F� forc ��P�h�_6)�%�F�d �,aruu��ato�#c�Y�Dthan 2\%b� , coup#��Ee�'�� !�7 w ing �Q�5��z|@wR!�eM-�m? benchm�s�)6XIs�aϳV$z�. Yet����8s��n�ebe�a! ��$ou!e!{ spe�|�"�%o!� very 9em��taxing. 46�on sd2h , +hD#kstX���oS away. O�� `inf��e�a�'5� umb!�A�wP��s�s$l��'��va�6C�.�eam�employ �N`W"�+t+!`in���truncP2 p�rAZ�_r,treS lledOng)�2!�l�_A�  !"�� . A _icnmpMv�eP���a�dPi� ,4 (TNSMe��tui��J��!R�&7sA�/%\eM�Fa � orig��5� -1�-�5� s�m-J�6�m�b3�ne-b���� x%�O��!��� Q:��Fyz� -����l�� (F#8V*Ln ]@� A"En:���� ons)�xma6: a�&�-f* exiv�@ar�d�2 a G- H��Bruckn�� 55a,2b}!�akUrE� An al_�%2-^ (aimA.�c.h q�)� "�? No-C�E��6 (NCSM�Z��k 9pw,�hef6ib}2� @ \emph{ab�o}2�ezf�MZu�A`Ŵ%Ron-  (NN).�) OT% 5[�� de�2^3 �N. �2�.u|%: A V�b��XcT:�A� � wo- plu�D"QI/ �oth�M�had�ѭ�aesJp n% ar�ԉ��em��ndn�Bain� �Zop.��� Y�Y ^i�Q��Dm6as !��ult :ŠɯhJU��.�=5R�Y�YPwoa}ush+�an 2��0 }�E DhvQi}(bloch:1958}��1L*�)N 2LuuA� 4xc}m  �se�V!<a" �of S��I�BH&��U �.Qly%7��<itPung"' U :U� .S /J w�%`�W*c !�!C�cH}e4�7:�Aee 6. :�!��[ -to->-%)F ��er eQ�!3 xpan捥�iI ��y� �2�pyƟ�����<le!qmuM ���a�a2����upl �"w�|����Z �)����th�E^! Also%%na.eB">�\F��o{��  as"� �"����"� �� "� A"� �W{  �]�I�R�)c embl� <way�ha"�3����.�ib2BW � e!� subtle� e� 5{ia� ���<�n��8!q ���el/es!�ScB as��as �%da� ��!e`�-z?ed'�of.VZheng�S5td�W� �GRf�a �Oe��\41a=Y� \A�.t0e���{�K�X�ut��_ake��Agh��se new Z&�,�Z� z5for*x@ �m�%�A=�9�i� �!�U�5 �#!�� i���i���,R q �X�:M�R ɕSec;$ {BH}a��:��urs �7Y1v6� ��!��ew�� e�q� &� io"�h��D�v2! �-Hex�n � N . bhA^In do���w�� �(HS.�' "� 1�A��Ł�he^�H�%1����� K ��H1ua� ( "�}5Ls�"� eQ:3U~� er� :��wiw�=�der��a" dom �}I��� �3�grpo![ 4&=an �"ޠ � =we;�&{�4s}U� !S a_�:�(���B�����:� i�] i�$sş /��c��a�U s�w!�6� ���We3�X�sqin}�*1�%a are �����E�"9!���� .i�a��are�jyG�cgzZy To k m!Wawen0GisA�rv�7mal� k =�|dic�{";6H" F BH}}F&Z'���1�3} <eqn:bh1k4 H_{eff}(E)=PRRP(H+H\frac{1}{E-QH}QH\�q)P, QC/nhh f=\Q<{i��m!�&T.�LA�is&g'by�!�the r)Yve�tu�d&�l �y&  $ ��$ �$g�k���3"o�`iHB�} $j$ANd�� d�~ p�,m�b�� � /  f-mass (!)>A !eN! ,�2o�B$M_A$(6`��b �'Eq�&Q`�x"=  $P-' Q=1- r9Cdg��pef �HQ�1 a�2_d*�6“ThNyr�t"��%��P&c��sSt� ' F_p� g�1 � �*s � Jacobi HO��i�Yv^e, �d�*� !_�Auc&]�, avoi�c��vercom�J� cha�@er q�*!� Jo� *Vr��sf-d(��nt HO���By |+�.U,�V"@��.�!�an (A-1)����M�-&5�v  ($P$�)��4-up6����\�!���af1O-9O��N>�{d �m`S a $N*T(\leq\Lambdaa�� $ $.��Cd�:߲Պ�N�  ough�qb)�x^�mv"� 1pA���eyE��-�{%h��E��� �� is -R,� �6��+�6�W'a�" taskT��i��sM-x$E$� etT~N��D��,:ke igena �!��� ObƕsBE�+�b�kn � priori}�~�h2#�sw/$d self-con�lF*!iB�^2$Rj �gardlesE�a��+&us���mayEMasn$<$Aiu��|�1��b� ult U�-22� deal� �re�nt�5�F�: $[1/(3)]Qa)��?*� X�#E�%-�"� ng}B0 �$Q$�U= Q?-�* Z1�1'is��pag| i�6W�hP+f "�� &��!a"A�E_��7aģ9md1�&=-2|'B�R�!�r&0��.�xmr_ � #s #�N��.I� mu�lh"r )���] Z�'�rQW&�'E�� *�}2*�&j,Haxton:�{kb�p ed argK�P � �$�OQ���!-F�n� BH�֍�$ \{� $E}{E-TQ}[Ti�� N ]QT}? \}�@ �� O &=& T+T N$-1}{E}QT, -<�$To \\ V �2 V+V 21� V.3V37 rqt} E�&BA��!�"m.c��es�a/ae�iOA%!y>]]��� g�C6��!ve��iJ#� QE�,%���!n��A�w"'ws��5iap?��ut�6� N�a��� "�xn��g��i=�s�!b�6 $[E�/T)]P$%x$ sandwicheZ !�4 -�$h^���h ��:h!?!vc�y ҫj�yptӶ"%�� opp���Gaussh� deca�HO�m�Zs�bi�  zi� HO `� Q%'��>�AL �r&� [las�v�F�'9r�g � 2�H ���I��"�:0 of �*A�xIy Teff}8dy w�2�i@uP* �� �ux�!�� �5�,M�(I! tro��Z�b" �Pɩ���/ � Ѳ!��� 9 ��Bl� Ŭked~(A'o� ia�"Ít3.�! a��)m/�fh���8a�.��Ai�8o%h54� E�; AKquiE?��6Aa�'&[�J�l9��-�� !� \sub� R"|�J��%��}}��#-� �� >9�i��werA� $QV$r�G HI]:,=. T}Q+:2\  2CT}B#B3\ldotsфu��r%�is� "V!�ͧ"#A4e to a ladder dsummation, as shown diagra�Xcally in Fig.~\ref{fig1}. Here only particles 1 and 2 are interacting via repeated insers�s of the potential $V_{12}$, while [,3 through A _�Xspectator nucleons. This infinite ladder sum is collectively grouped into the expression �,eff}$�nce�0 is approxima�`as \begin{eqnarray}\label: +V; V_KX&\sim&\sum_{i�m!softer!�n. origitb!�$NNAR�J��\ eby reduc�!�coupl �Q4high momentum -Qeles1�includA�pace. �>�n K [re!= a generic�perty mM` sum. Indeed, it can be �TE�i� limit>an��hard c%5>�o�isiI�E�still ��\\cite{Fetter&Walecka:197�� With!-se ����A�,6�G� $ansion} be���multline.� regG�ݙ�=��1}{E-Q��T} + v"K}v$+�$v$ H�o oldots�S5 Not�RreplacEa!�$Q$ w!q$ �A�!} prev�? eque^ . Si�bAl���oof����A��� ignorAkthe manyi� projaoon A��"�acts ��M�� se����)n�lsvalid : 6<$\Lambda=0$ exci�' eGsI�0$). For exa ,%in a ��\hbari�=4 ��.5 , a $2.! �t�v%�6 5U��yng5to ei�  $0.] or:o.�� -�HO -� �a�Jts mA/addA�a��ue $\le��4$# e)uplici& �1� �  atH &� klti)��!�M cit�dependcan b@ -}�H�� � �!L"ybyA� full*' F2� � ,n� Eun� T� � .� � N� 6N( B6) 6[ �mR� E� �� �resenH he se��|a�$performing%�9�� .  i�et al.}Ʌ6 �.> ae� ignifican�'y � �����Uover its�gle co9� tiUr,�ced �'!y6pectruman(certain fewZ �s w}lo d re�veam!G�nd whenb�, bringA��ae intoz�> agre%E� experi� . Desp����yh(, however, 2%JG}l reUae�I"� 0 it���o��^ll}݅�$um numbers"iinduced-��6� �  . I_ ce,!�mas�am�5rkinetic9>�#��ng֑�ї�995r�edv�light� �qIrecoi�5 rpor6 %�A&yL��A�g��6�y 5�� n6�-�r� �r�}��2�}��:��:��R:+V��atMx!'%��!��!�M�:��6�%�,��( }5XŹe� DEKisy ��� somAgE� df�beA�2+  levella"�io��Hm�!sY��&�me�&u"ons; ra�iD6 em sol5%`acZ��ZPQ�s%~� e��7�rd%�f�2��$/$ (2�T)� k ob�{ed �a}0�|I�� alsP2o ofo� wuvestig� tiAper. \8ion{C�ngQJ4 �12,$�(a�A:0}} &!}�>�U�-exA��in clo ��f$Luu:2004xc��.� qC? Formke��=t�-  G_0Pu�\G=_0+ (\infty}PG_0 .,Gu�u "H G_0"�PT},\\.�G0( j-gP>%�) �&=&�}+ �6]t12^ �&=c I�.2�j _infB~��A<recisaQaLleading-IBH � a� Ref.B�. v $G_0$.�JfA&propag��L$1%$ nAg-6  laph��t�� l ��s satis" 0Lippman-Schwi1�iTp� i}$��N� �,$�)�$ *�n�)� $ we��two in.� ���.�e�� �e $ % direc�*: n�Ut!�y "�%� �is�a func�uA&!4��wo� Z'Ii^��g ja, $p)}$p'AR�$, but �)�ց�divid'A\ JacobiP $q_i$"W1��V vum mX)� (p',p; E- P=1}^{A-2}q_i^2/2M_n).>2iM_n�!� � �isMjBo2 �a 2� Q��"B ?Q>� e 5 's>� I�in.P 4,ir principle�& ��change� ", amount6 In?, � !�:nyL:[)�*� woul� quire� �le�a_A-dI al nesaIA} gralAe )XumI� (!� sameA�� in coordi/E��J�� done�(Monte Carlois!Io t@s �be verya�&��ax!'a�ab� accuh  du�  oscillA�y:HO waveq�-�Ap�ix/intI}@G�alternaa^ �!whi�X.c� )\A��}yM�I2bhX to a4 one.S9e��,!��regardl4i� � U�|M�$s given by��A >(a'm�(\int dq_1\cV e�\ q_1^2 q X^2\ R_{n_1'l_1}(q_1)  4(N'l 0 4 BOti;���F�� ��$}{2 \mu})= @� m_1,m'_1, �,m s| =0}^�,n%n %xC(~K.�\left[![ _0^{�" } d\rho\ �V(3+2\Sigma_i2}![(l_i+m  '+1)}e^{-6 2�E-� {�� b^2})\r�b]� U�  $b��yc� �a�nCCco<  �)�(-1)^{�(n �)}--prod_{�sx" �sqrt{26 :1) !03/2))%� � )-!H-)- @1)}--I;I{>�'�'_Ҳ<���B� '_i-g0+0� RJ�)O 5Q2���-P Y�_i'.]i<j��$i-1}(l_j+m A�O M" {2}) a5��]�R K+a�K-�. =$Y�I:CM����#two�Xdurun�� 2� ��6� i$=1��$A$-2�F��?utilized {�N�"A �.�>��o�$al}>�, $l_i$ (see B��})0 ' th2�>N$e �' h� side1RHS})�m2�� &�  a .s�  >�!�Z],*:b/��))�� ��quickd Pl�Th�,efficients $��$%�kn�(analyt� _  pre- !u� %Ft!�ub�D&C���$6 Q��mf%}ion}}J 9�D )N� "s 2s �!J� e6� 7Q�y7 �twoa'"��� al�m� s� ci� on|n� _E�G)�)HO&� �''rIn�$ sense, $\v �{)l}U �%��averagN ��"f�tD*�g�influ� �H"� 's� um2�� �� ,a mean-fieldY %|Q&�N�w�� i5� ons}m6�UY. #w�%discus�is po in�detail�"ZFigureP fig2}H :�-�!QX� $b *< p'^29� G_0(p';E))�� )$;E)}p^2$, � I�  . &v%"&!�HOq!�y, �.#�= ^2/M_Nbj�re $M_�'�� c�+ �We plowii�Wn�ve.|�}$ )��)n�)a* our"�!�em[! visu)tru�(�"ll�s%�>-2}��(! case� nُ�i� $^1S�� nel,W��gainstu�� �H2�M� a $b�bp'$,� ��.6�)�!L�Bed�$ E=-20 MeVt� $=1.2 fm. P!�(a).�Qo!���no]��c � �e!2!3o*ard��~�b�how I�`od�* d afa�g�!ng ouADe ��,�%.��a����"l dA9��J&"�e $0s$�tA+)4c�R�#�)F��B��woa�i��inh n I��9h $0p�FWlyIZ (d�)9���V' lterQ �)�ce if fa*F� �t%eed!d:�,%dR1ain5S 99Z� \�"��s� phys%%� rpre�("�t;0)(peaks s�$in�i�.�gpdi�ultH expl�&Ylic� �A- �Q�@'���XjoW�})g% � !��wcad�)a.Nqa�,�A�pe*r �ss�$�'ti�^&B "�#2�$s�vA��:Z�!>�-QCincreas!v%�FD. *ORe�.� �s}}� ��A�����we us�)Arg�& $v_{18[$v'_8$&��*WiK #-,95wb} (Av18 ` Av8')��l�.e��o[Fur(�',��+ isospin :1y bre�/g i�(�#�t&�ɫ�a� sm� =. Tabl tab:� s& e�"%l!��% =0,2� �-s�.s�&2�!:� A{aerent �!�A.� �:��$ �+`�A(��,%f2�do� dem!�extravag�"� AQresourc��c: � �� �o���k_ �/)2�*�2HO��6�%�Aia �cverq�!Droutine) ��� d�r&�Nav��l�# 9pw}* make�� arisX2wM. GFMCA� NCSM20�ke"�"alul�#�as re%�cv5iRaw&2 S-s*�Ri s }}�..� 3Qwa&m�A*�!2#� G� iH 2�$)���z'0>w(�� %!t6B. Our���display�w !�a6�``exact'Lorem2?taken� =� oggaH1cz} A�fO-o6/!��n)�t���%2upperDe r se �)���$^3$HA�d :� � �,} $^4$He b� �rZof� �eW0m.e�} �$^2$H ����� ��q�p�)��&no.T ! \Z�f>[8m%�a,�$ ,� �w�(2[� a>Z5�y!spond'!�� c}�Y�&��K"ThuAfy&aa���>�cand�A�$b���6O trins@4ar� OHO bas��nd- noth��6Q� ��:�o4�$a�)�2Tlie���A�U�bin &(y\footnote{!�th^( B"J]2~6^,M<%�i�%pu!�n���:�}A�*��VL$b$ (a� |0 size� -H8�� �n�@�AsA�2�:3}n varih-�6�)��e'��re2�e��6�)s a ke�-dT o�tB�i&�$ve a��Na`2�!A6� Q� )� "G)�B� �B�)�)�7�1!*A�b t>�, A�an ���8a05G al. �#alpha"�Zv0� by $@; 1$�:�P�i6�p F�4N�-[6 {y52&$^5�g$^6$Li�$^7$Li�!�P & yh����*2S2*  dea6Pg 4calar Coulomb 8#s.}. A:686�P}�SN ��'J��s�#Pieper�4qw} ��byF'idBseven�C),ɰ]��2�y��-33.56!�>E is b�1!!6�>�4k Nu{+pa� hesis ! �oG> $(J$^\pi$,TQ�five-�six.�!aee ��HA8 both�����"�2&� ( e܅e M� � �a�O=�m2 y2s�&2�q !,.6�r� ���/] a� ach b's-!4�f �f� � � 3/lecR�0 �,2n4�f+�� ���2i2� 5q�zsl! �2}18y}2d45p0$6���sBlall9UE�yesuscept�3to"�� up�*0��i&tR]�"p5deg�qPW �> $6a|&�?�/plad!on%���behavio�+��E� YceQbro� ͳ52RY� Q�݄We�0�1�n��;::W�˝ P"xim� erG=�46� �ric�b� �thf>ir � �0parts *�ex�8Y�:�7c6� s&:6}-C7&�"A�<�%1�,a� R+��i��&�t R�0ale Wt~vM���C �str�"@ .$sho�$`b� mA 5�|/mqV&� BH23 �� �quo!Sa��� are �]7 e minimum>���each  . O( ��!/�Fi.�89�9� �U�0F�6�a f�E�Cm)��!,!� .0)�S )xA M���)A?4+^7m1 $=14���YO�;=11$ �($b�94 fm)�g$<28.08�45S!L�2�of ���-g%eu� �, $(2^+,0�nAn"+ular,%1^+_2'iN� (converged y5Lre �2deH%}! X5����`-`� .I[�� ^,"�2003ef}.�g�qle'Ee �,ing�z=e � thos�$6.�< "�Z ] i�t�?s�>4e (3$^+$,0)-(0 1)�� t %�!�<(3/2$^-$,1/2)-(11m5!��ay!�.��iJ �= ngthA the �-1!.��>B�C�� ate,� �?l�Cb� �["H��2sue% I�y"�Y�Eq*�� typwly |�(sim 200$ Ke�  ={CM�OIx�Q�nce}}m�.)N(q�f� !�64�5�� "� � answers c�Ae��/� � �t��is �3w fzA�K is sugges�me sor�= eb�N�"�s�\V#arrow�'$,ha%� t $P# 1$,�)A'AC�2."1�Y, ��is{�q�N�� guarante�P.��a !/2j8�4we cau��8vw[ work�g�+�>��A�Ae   m�(!?bo k9 ntil5E$�E�@!�F*� � arguY9 abov� es�� + � inu3�-onr�@2� ]1�NB or!1mple, ��e ac!1& IA�!a3 (2Y 10})`% a{a9cy�Q��&MrecJa� �j"# ���; 9!�@s:W�ۑ�9E.i-ed:�19A&��&� +���!&E7 of �I&Mng}m&#�{in�U��%e�KrITA�$Hamiltoniat F��#M#,math} H^{\rmf4}=H+T_{c.m.}+U HO} M+2=�$Hz"As�-7' (� �=h}��E.\ \?!% �Imonic.R�� p�0e"�JY; (�5� end subtT�7���.?�ny �A�ik �6"���J~��)�K��FM��l*��solDtM/�Y�'c �� ��g>0��zE�.nYk$���e �_J(�d Yde�%N GdII� :�  lack���G��*e.g.} $B$)N.� ��aF�AO hiE� &!9ou!Tc��exponQ�1\co��x�$-9�Hilber�*ace moWB� %RYP=�run� ���a�U��tu�2="!�ɭRO&hIa�a 6*B! deal)2� o�M�Q-6��2LNeR��A�82� �Cb�6d�8&�I !E�%y+#to��0 e� Sect� \ . bh� wed �% #~ !�;N�was&�;by aSA"��,ram�� X sN��W�f=a[A�f��"_F�~ *� U 7r?���IIyE ,�a�3al exte�4�AA�&@B&`Bf�H&�"h� 2*�Gm E-d2F� �2C.�f��5valen"�g:)o,9 �BHaza�wL&(<. Beca�w� %#?ip6X�4>��9I.�"Lo�#��opp�<{ "n"�9@9,2�� io>� F�� :7}%�^�.�) ed�  @>CAa F I�A �#l��� ( y trans a!��\7Ŋ�Gve��5f)Nny �Z�c ��dK.� a)��!T�-e�b*�&���uv�re�/<domk cm & -res\:=��!Vw%xt m�� 5�.HO&*um��&�(%�t�:Ro�:i"�,9(A��-.%�~{$^1$S$*�*�*g�!(|i91|a" . "�(i2��.�� A��erU�3 �t:IA'�Q ��)��&�Al g �8�ionar�� :�KnegH*> X�s��A} go�VAXa��T�.� ��,;� Ż� 6`!l$o�Gby�6\ O�e o� �2, !k1>1s���rel"N�!t 4� l<��^ef�~M The *�EDr[1*Zf��� �e�sՍ��:�O;� ��:6d�WEH�-�G�:"�!|o�; M� �D k�cT�� IB1g�>l�*2MA�weak V�e$&� �s�&%�ou&�A��Xq�QAn@SAn�n�eQ5�qF �E�v)¥,%W�Wg2jto"�N"QT Z�5��*�3&�4�5Q/%�semblag of� �� serv�EWbe�&'J� �ZappU2B6�n)�$�c. I ��� ��,2S�,�,�M! E1 -n� V�&�]> 6 �Cin �Avt.�2�eE�B�a�Yin a E�%e�oph�[p �>2U3 �No b�X%�F \ge2 q0�� *� �8L :�`&*s%da*m�Rlikii ason���!"Q-. As*} �lpr�W �2�e^!�to 6�?�*��"�]- ee]v�Qawe pF,_ m���.� o�si&N, Unix box. "�G'ner6[ !�r on Y(CA�.E, 5r� �^a� .��I alle�9�� hop�do1q3 fu�� t "AC �HC oa@�0!�QW��`&'!./!- � ����*To tackl0!. i���}n��&�e a^�i� !� �2�$aoA "_� R;TYxTeff �8x" 56I$in-&�B� �� �*�Dm AMea�<=$ \delta_{X,�@[@{A-1},�@1}AaU>@ dpfdp .-A ^*_{�_1}(p_1HA WV( 9 ) �p�E � ^2�\|=i�=�//@}�AB|6By 5�Y6973l}(p)A�HO rad�+wa&�C!�6�D. R"4T8 5A�|C@T2!er�ex.$ �6�Q "�/ �'bles $x BhS,x �$:u^I=�n^ AMeb!:=��!�f�B1}�B1j�B1�B1%�AV�BK)MK�" s \l�B dxQ�  %� pB(x�C+IQ+-,^2)M?{2(l_1+m @m  1$X+|C10} {�B1I��B! Ei^2Z�BB �ʒB1��B��B’Br�@B\ B�AbB��B�BB�A!q� >7Oeu�H� �Au� varii�to �f2UGpo�*�*, $E,\the��A-5},� 1,\phi�g��0jYphi\le 2b)�  G:Qe�W:�cA�qaligneda1=& F\ cosp� a1. ��si��DK2K#� ��K3K��A\vDHD �i�FY{i-2}.�{iA��H� �.� WM6a�c>e!� �^).�x�_.E�h5�5�M��d,simal volume�ei-�6�T|d�=)��G4 � 5}2�% =1\?HdF*&phim}2�&ueiN� uO@� Ha�6wXi��E��fIpi/2}(!� phi)�6:%�(!�"2+m �,d!.�GbjI>1 n3+m Ln&A�H��2�I+1}1y12�%��[z�E� �E�B� �H % �=��J6hG1)+A�d?.;2� :�TMe?i2�� u+:�"H2/� ��;o ���M�&F �A8%+�6 �) ang �&� H>1  �&"�U.�E, m�.�T� _o^{I�-���^{\�m���^{\bet&=&� frac�J 9+�}�~ ? !�"II  9& }{2}A%,\\K � -<�0^)�9�Z�2 \,1}}{\epsilon1�.�(�K �-2}/^  b C},Nb- !,-� ~  +1).�rhoB�U Plug�  EqO�AMed}-�D;Ao�!� giv� � �UU� � AMee!R�K:Kő�9 ER2}{�Dc��R�N* f�N:Q B(~KJ�N�J$�M�nM�2E6���)QD� P>,ZU|>,u`M�~O (=(A-3)/2�Li�`2 $l�/>.A~B"O�FI -5 P(vOr� _i&7N b� eN.-) m�1NbNB�!!Z�Or�<1s���E ��ONO1M�ED l�!�O�O�O&�I� u�#Xde��Y ��J�j�" is q"% De~p';'T'�SS2"T'|\hat{F!�|p.l� T ,y2}>prp �&Q&wY 6L��qapY� B�H Z%8>>7deO1�?�@ crip�dAwP�/$1�#�E( $A-2$.. $ �%s�`x!�B�[k.n�"ZPI�$��i q� � �Y�6� �w�Z,"�H �}K�2tH; �iE,�+a&�o"OC$F�Nly���MK�iX<%:3o�>��"�/al1f n�y6��o -6�E{�� B>�_1'N�x 2}� }} �A a1J:W R9W"��9W  t�;WF(p,p';E*"��[�[��J\P%$!�v�Y simi\JV a}&8..."�J8 7proced�6ou��!���n� b�]y desi�E� . Re�ye�,ep^fomB�btix6�R: }�6�*h�BBc2zc2�M�,f �&5f6&O��W f>2>2j� 2>2� �S.�"?�27a{A-3+��XF+O�rho6��X��XDV��X��X��X��X��X��X��X��X��X��X� ��>$ BMec$�be�Se�med 2�_!��\�. .�U��_nuBe`ed^( ��acW ledg&sa;�! � ����%�%��auspi�6�+0he U. S. De)QEn�v���Jt�zJ��M#�Pf�Q$�R�|~R.$�Rurl^�0url#1{\texttt!O%8{URL I�xd }�N{!\$info}[2]{#h�>!e$4t []{S'E3ibitem[{2�=EA� W�P }(2001)}] �<1mp} }{author}�5�{S.~C.} &1 B}:an4�nf^P R.~B>P�},Am@�journal}{Ann. Rev. Nucl. Part. Sci.} %�bf�v� }{51:Oa�s}{53} (dyear}{!�'-g{� (-th/0103005�/2JiCarls�$ nd Schiav�d}(1998!m r78qn�n J.}~k5k @�l:N�Zl%g Mod. Phys!�aNa70:D-a74Jb!})�wZ�ud$r et~al.%A7):� $A&8Pandharipande, -', 6H�U�A� ;!�7ck�� B.~S���{D:�V7 V.~RBA.��Ff!�E�V�n�?Uha�~Qi�m�:y�@u�EEe�8^L C56}w�A�;MK 1720F�1997})©u�970500�CKJ�BrucknerEa5{�# {a}}a� :1955a�(K>b@:�N b97:?13N��}:�jj���.bJb��10Z^36R2�jN%U�k 2000:k$Af,Kamuntaviciu^0��Z*�Z9pw�0P>2A:�V� G.~P>W2�Fu���B��>����6቙M�04400�J�0N�9907054n�1K�Or\ �3a���E�#�nVkj��2`-:jO W.~E>� ���?�+C68:@1a34305F- 2003N_0305090�_Cauri�HQB`i�9�`:`E>X�!�JdZ11036nBlou�$d Horowitz�I5� b�:8�^C>�X�� B&�ZZG z� ZY91FU195v� Luu.o4:o@Luu, Bogner, HaxtHeQ3 q��lL&A;~�TJ� Luu:V�SB���<WJx �?2:�Le�V�j'����ź7^� 01431Jd 2004R7404028n2Zheng5��:�!,�U, Vary�)8� SongA,�l�~DJ�A9�%�)U2��G52:��~ 2488N'95r)�a� a��\2�\ �2k�Zn<6� ��T>��7 Lett!r^� 89:E-<18250JD 2002R�204072n�F�6and WƏ%\� 6ޏ~YA> E��Ϳ�)ces���title}{Qg�um�;of Many-icle S��s:�0publisher}{Do��Pccs.� add�R$}{New York ��"63r��-%w�+70A� �~oB>o >�pM>N �6�� -~,A17Z/14J� 1970r;Un6 #, Stok�  .�}]$�0w�9�6# g:V2V.~G.~Ja�.9�A�M�~R>���%�vfeC^"3b����&r40801r1 �b5Ɂ�:�!,gada�� Gloe9��U�] *�#c!dj�B�h9�j;H>sKa��<W><������u���65:��054#N4 V11202rP�].> ",�%��^a� "!�^~�SJ� B:�V�� 2��5jSB� �A�U˺�b� 5432Jxj� 901CD3t:�*� %% T�5_. . .Nt }[h] \cap${Dime I&&=,2$>�=�?qP t "�2NXsa.:�jA8�,ruledtabular{c }"�A$ &�d 3$H/-Ae�f �a �a (7$Li \\ \h� 0 & 1:(3 & 5\\ 2 & $ & 26 & 48.85�&)}�!�:�)f %�Bure�>lo6��G�.�/ fig{file=l�4.eps,width=13c��5�(Coloi?� ) Di&���Js kep�WL.>�C 2�%.����'Ɯ�(E.�)��.m��&&�WB]&�)�SG$3-A. Dash]� ines&�xdj@2&3eJM�%!%AN!l1HQ� BX2.�XS*�+�� �HR*� ��o"�)�#Haxe�Y2=. ra)�6 "�?�AV>s6b)q�sL m�6�1dwUtopq !�.�paiO*I�Gpase��'�r@�H�'�*ume��Fi�+#!"s�c�S�r�D>�h"��o_VP�r2�� \B�2 r�Yh'r~43�Xep2{3.#6v{8m1)��>�<��E%�m*Hi�).C�Be�E UlBAr>8!�`�Gt'�&�\7&�N^ �� .I#:�h�8�l E��lWA! .ri24wl*jQJ1 ed�`�j��� od P, 6̓$b4F.�DC�E�|�bH A�["'Iѿ fig3�gQ4.`�r��fu4�R0$a�S2�X3C+�L�D 6r�$�_S&�n:i1x2%Y#� A$� =41�qKFn5�� �4 �u�F%�Gd�_ f\"urAb�p sche f,k, J. W. Goe� Uni;,�\"at, D-60054 Frankfurt am Main, Ge�y��Babs]} Kjcon�i��C�kS�-vol�a]A�exo�_eV(m)�6v�K�dan�e*� 3s5 s hyperon 8� se-E�ein ��ensm[VNntika� anǚY quark B . Fi���Y phase WiyN3��ro�^to�xT�l�Zn#.Uw !idered ( ��eI ji �*7be�Q!�y,tiv�O �%� cal \a . Lamkt�fJz� �`oi!�to �R0���of un:.m�RRF �OY1 &onFN�+ famNXbranch!���8>on9�)�6�>^"ݖd��jkd"��e b;^be'u"k� n du!�o��B�!�)��8 K^-$!�-�to6�EU�J �.S:¥A$} NeutA��x%{bors9D type II supernova)��MM�ss�_ : �){Bet}�fmf ng 5io�~ highu8ns�S cold)� B �-0�Xexc�dby!'ew �7 nor�E<ar :�9:. Ee�xf_ ���:�H-�.�u(s N��jbV. o�aq��Z�1fWi=�0iq����V,2))�v�7usefu̅7!� stud�d�7��ieY!4�g)�$Glenb,Web}�  I�F07lleqMD%_Y�tr��a*q�y (EoSV�j�[a�in6�)�.IXy�e�f ��4-radius (M-R) �Eonshigc.hctMhabmport�}bB]�p!gbe lTlya�wnw�|oxU�. ConsT�t�`gomc!�EoS�� �!�b%mba�Though"�[�e.=�measu�8[ �Xal . � �o pulsarE aA�Q�havLjmcrYf� ab>]�G i. O��A�a x-rak� d op�|adi%�T isoQ d6�u!G4is �burԦ%�ttam �ml. cCo�{stNaNYhpwavQ��~,EXO 0748-676b�ACV�/rr�bA> Strohmaye��t�t a 45 Hz щal�?ڈ��s��T �Vi!5/�.��`�Xa10(of 9.5-15 kV�dE�, 1.5-2.3$M_{!�r}$k.�2j�now b1�:AZQ�%�a�)�Z erti1[�A� dou��M�Sz8 PSR J0737-3039wg�2;dN�m�� already, ��E�>M_ 1��!CM@!�p |�0��on ԛ�ee+.����> Shap`!%�w�fw�z �i�"n�{�P��_*� ��� cI1a(�ӱ dkϗxt,8g��rep�la new  R�ʉ�!��ll\�8 fZ ~ � Ket,Schr,� 12,Han 3}T�p�� �� JA4b!�^ Nմi4,Zud}�oI � ��q�for akP. *> n�%Q'  2�� d� �9ͻ�"2�!d:�w�Y  J9h3�( S?ook��� !��o 4�. {M��}Y��&! -��5�:�� 2si!uLyby� � 's� U�"qI@} {G^{\mu\nu} = R - {1� 2} gR = 8�K}T�kXl�$QtCAF8Ricci tensor, $["s�h-,  m~�c, $Rc�| curvIH!3$�)�-��u�s. � EV�ncoa^Mi^3GS�Zlibrium}�Gf non-5�i� Q��kTol�O�YPheimer-Volkoff (TOV) 1>s.]���H�{I�!CV�A��? N}�E)[qm� Cook,Ster"W�$} ds^2 = -uL\gamma +�@} dt^2 +�L} (drd{O }^2) . G- G,sin^20(d�P �� dt)^2 ~Z�F �f%��peG n $rD$ �$a�gv veloc� of lo�i�#��a�Bno!�b!c�$."z�f}C��par�ph �H ͌1H%�a�C ��B ��!�W!� (I)��!�l�T �{haQ ^ |��s to >� - �2a�onò $K^0"��5�'d� � �h ؽ�Ff�a�t'�BK VbI%1w5�"67_�Za?�A �!� & �{ itue�>X ��G6me��!��f� bary�ctet,�Tc�kmutG B#- *��is me )�Pex"TE�G�v�� N��`dopt a~ �u!lչ �!1 !E�d)/T ?�H�"�c-c`Q�-M� .���!�.��(�m�0 $f_0$(975) ( ~?�e�as�I��^*$�$�Y$(1020)��f!ILa�ngianB��#-�Z�&6 w Sch96}�� "�F eqna)� {\�lL}_B &=&QP0B \bar\psi_{B��(i�$_\mu{\" ial^x�0 - m_B + g_{\� B} -����D B %rho B} #,{\mbox{\bold�s t}�&L B�S}}R \�w)� B\noWJ\\ &&�,HGN� �^*��^* �phi�phiq zqcN�SGG( 1B) gP-? ![ ^2 ^2 l - U( ) + �e^*Jg^*i-�^*}m{*�]) :H�Q1}{4}-�_� -� +�m_ 26\m:.4})� {Y1�m2N*�[2�hH jd��NMqR_%vphi� ���AP2  { \mu~�y� � �2�er0� ���} Y0=9 3} g_U^3a Q�43Qy4 �u�p}��^z�o@ o��of��� ���q embed* ��e�V� S\LFw�v�@s&a*�� p� (�)�J[ͯF$2'��E"�L� foot�u�^I.%ҹ��   ws ����a<�w��FGle99}��1���K = D^*Au{�� K} DAz K�� K^{*� Kb� !�cov�_n�PriEve $D_A{�?+ i�v�#K}{ }�xaF�r + i�X�3K��J)K�m�N@ \mu$)wˊ pin ~��A s :s K\� $v (K^+, K^j��Q!�AD:U'$)J4-�<ar 9�� nive�a&=�� is j��xzF�$m_K^* = m_!�!e�h!� �y^*^*J�I�'�OÞiR"�v� �se}kA ,�r�e) Mir�#v"�u� mgBAxS� �$� ^*$, �mega_0A10q rho_{03)E�^" )q-� ���L �=��41�0�B��s&-s�,O���/Q"� � �!Ti����s. ��in-� umJieEU8A� $s$-�g( ($\bf k=0$*J m�{K^-,\: A��I^IB%tE@ _0 i���0 \mp�v�_^81�Jy��q�*`�$I_{3ig} =b1R�orQ)�! m�5 .�)���52ՑAqsJ�*�a \mu%A!5 e ~,�- �^0}} 0�? �$.K^-�! >�U.�%1 chemI po��E k!9Q?aj�~($�*^^h� jsA� ($PiQ��I�!&�i�(��x i _i n_i; _>}lT��!�j��>�u�f�m�:" $P^-(%�n�(XW $n_i"�/Ob�)of i-thW.��x�E+E��%r o%/IUa��)]]�9mix�*�!Q�ed6!ܕAs g*.8Pby Gibbs-�20� globV���o{ws �`} �.A Bv,1�9x �E�B^E mu_B=]�B^h�Y>%ATQ�&&E�V  BA)�!E�+9.) �a�#or5h<��al� U oU;�s �0$(1-\chi) Q^hO chi Q��o�@$n_B = -n�/ Y 1 chY�v�f� �� m$�!d)� . C�EXF>0� $�= 4q_B n^h_B -n_e: �*�=e\B /=�1�� - @ n A.�,��:h ] ^i%a�-w�!�"X )��<6b7!�$n �0n_e z�At6�:PsR� 2�c ��:^-�.�a�iven a��,.(�RQ-5-. 2�Io����3"�FCZ� �� ]�9��6"�d�ve*��!�2�^�B .Ne� ons,��t R�X0�w1>i9�2� ɿ��!�J�9"6b'��E�.!/.�$uApdMns$ -s�%1-! 3 6Q� MIT bag�r Far���_Qt"Cof."1ng Z� ͆b.g,ߏ��t {3}�^2�u@iu,d,s}�fd{p_{F,i}} dp p^2 (\sqrt { + m�^��� i) + B,~ �&&���B!AA,�6E��Ax�-),)�� iTby��Q=-\O& )W6S.�Q "׾�!4�-Duhem�i��AneB��z�= Mo�=��A�e.x� �e}[t]K""i��,s[hd�=8cm]7 1.ps�a9<1bA,9D$P$E&sus: $\var�g$-za\i|Q�d1��B.�-�2�-"�� \& D.!G r��%lcg�Ur GM1�m�! setm Gle2��o��on-� "3!nta?��*@"e�!�9& (s���u "I��c c �cW .�!�l��N�I�m� ��i~{c�r|kՒ� y U��"1 �athf ^C�'or�1/�&���!2, �. A�"�*2�fit�p!v� 8 atomic data yr�@A�� rongp l!��+�� $U_�2$180 \pm 20�� � Fri}EQ pe8�Bo(agF"'9(of -160ڔ at :�0�P($n_0=0.153 fm^{-3}$)IIU<�uM�A=m)�s �2�2]re.T5Q R�lso�A���ca, $B^{1/4}$ =O����/B~�p Fe> I � exhi�X�yFi2 1�n�8/d6�;sE5���b�Tq uppe�o8��k)!�A�.� of "�%#I�&� M�ide�fie�wo������.U b�>sAQ:�* $ 6.11$�d 10^{1!� g/cmg3$ (or 2.23AtAfƐ��&�3YLr��p�k)O�].�at 2.51O� �Xic.�_$\�j.V pVatۑ�-"TFA2�!F:� o.�  �f�j�2A��v!�t*z =$ 1.17235}$53.=#< K& � I�-�*la�d����?�N��2�I�� �pT5�Y.� 2@ed-2� �*� Y>2/ 1.59b�%�en�>42.7n4""i a g�2Dis qui#�rge� $J.!�� �=��-��� ofteq� �f I�/ / dmr:. Mas"q.��hk.Jw%*s%G.�"W%�&���r In��2� �k�.��A�"z�;��!T55�vfil�) circ0}cb����max ���0We �" � �+s�) 1.57.M,[A��2 �+of 12.8�,sn�"�� . �0f1t!�y��/ve sl��2�b�3%Br� an u�]m,reg�E��ano/ A�!� U� �& U!?P�ew �.(X �б�b�3ontinu�� sp�2�+�Ikinks or� �m�G!�y4��0cy**�+ϛrDy^%A"J>ALcV, �. F���i2of'damen�k� !�al vibN lwa�@undK��t*d, d'aAb!�p�*��6~NMh&&@F9o!�+1��s��e�0tha���0c �e����N4��,3 �m2 mm%�~U]MN�i�/5.T FU%eu.7 km�,w�E 7cm,^9^3b:1G2@1�a:4)A� orAA u!�r��1�'�.C�E�2li��Q�I� �lfi ,DvR) ,reyp�.  � %� uprat�2< ��tedr�Nowf�-%�M-F�>�":+u.#��A(a�2��4�0� 3�~4ece!<ņ&� M��0J�/e.@0Q�-�5X���R�.�<a�~l��kr! left!� &�-esw oog �!�!�bX.&1�#q�N9%�e� aq���3�<�Kep�Vfy�ence5it�6�՛b��i� J. FR��A��"l�%��COn ���.e%= �� ؍zN�N&�,Z 2��RQR�+�e�0by openT �4 ei&��%ui�Ya�/̅s<c�F�d.�5A�o���ral6h �r�=��NR�tt H� ��_P ifug�-or�]��s.!�8m hanZ�e: 28a�2�disaC6� V )� $�= 2158p $^{-1!�!+on��v����F�^��� a�6f��)�ng)�Nld� prob!�ea�s 1$��"ʜE�.�"ܙ0a6> .+*Z 3� e2���F6�eoAjP��c�"�5���@e�i�b-ys �I �Vk 2 -IV�?��6�ppY9�6 2�9�9"�9:�i�y� w dow�3� E lo� ��D�m&�2zselH.mag��- g2��a� q�"���v tNi 4!�mB(3v>�.&�nn���^ R�(a6j.l. W�/a:�tar!e�:q�ient Bsuc�I�o.? supp{74�st �)vnvA���m�& oa+x0collapt�@b^�hol�.is) B�:� K scenarioe4�, �;�:� Vie}�7 ]{�L6:" M:B!�2 (I�$a�tF1E� �O��%�2 I. N�AmV�A7J��II�Oed�lZ���:��� Z� r 5�h&�>A��'�! }�,�dsB��Z��*R�!I�@` �y:�:o��fi;\$&�9�9) � �fVs. ButOHs��.  L� "C>s��6���>S��u�NH���$(4. Curve I ���!o:S�E6� $N_b� 2.15�� � 57})&!p Ad�2 R��P4FP�e:�e r��J� F= alway8 9 � *�>�]1��s � at*��}v+w��.�Ca� � 1�,K� ?upR�[!1�Hs���kZKe� omn0 r� 1CA��"c�0va׺n�:9%:5,Js� � 4660!���-�dQ@ �.o far�6 =+F�� y@� ys �n��us�  %s��� e}�eaͷly +w@H�iL��u�por!d.&�Out�=&pJ�%&�,S�CC�6!=exRiJ��;W�!��1@MY���H��7 a!rd @a.6 � n��2��68 /� �?�?l6�#FSK�:�te6H,��"�a?. ��i�ej � to i�&��u�E&depth%s.A. IY I�0deeplyS)�%�`�\C�u�GSI, �Lc�+$.&Japan Pr % Accele{�D Complex (J-PARC) ��0 � rtuno 9"�J~ 4k "\*!ll.WHAg"� �:=<vCQ *� "� a�q"?HAA�^�off�0:s �#i�_ �*&��ؘ!Ano-�nt{ /Aca�"�z:}�\ !*�z�B� 1A}D2�zS c)?LTechnology (DST), G�n�Ind�z)� Acad�-�S$hange Serv��(DAAD>er��, Vuoft>mSouth Af��%_ Ea T!3B *{Re��nmz99�?~m �K B�) H A 1990Xb*#vF4 f 62} 801�_t;^, den�2N KC7E�9�(fe, S_b ger)I�J We�-F? 9 Pu,I�$Astro"��"%|Ŭor"�P P��l_P(cs (Bristol%8$Philadelph!��Pe!~�P 0fshing2���W;�F MNLatpr J M m!2�.�PE�8576} L145\\ Dr�� J J �H-cV72} 996 =&�HCIJ, Pa6�s F�Mendez M RN�$e �(420} 51\\ M4r CZ$3.��H.�HA Rh*�HT EJ4 a!�(-ph/0409584�WG Morr�� I Al0umgarte T W, #iro S Lb2Dw V R �`.e11353\\ 2���$Schutz B FB�11470�KetF�DKettn1&0)�n. A� . {�y3�uL9.�Schr}�ert0K, Gre3 C,Yan:�4 .�D%'70} g4f8Zud} Zdunik J LgTensel P, Gourgoulhon EdBejger M�$4 Astron. p�i 416} 1013hCook} @ G B, Shapiro S LZDTeukolsky S A 1994.WJ. \22} 227.*Ster}  gioulas NTFriedman�S5:S Q44} 3062Q ch96]> JQ0Mishustin I NR6.�M�53} 1416�X{Gle99} Glendenning N KRJ�X8.XEz �81} 4564.�$Far} Farhi-�Jaffe R �84.JMp30} 23792�2V�$Moszkowski1�1.R�-�A�241Y^{Fri}9�HE, Gal A, Mare\v{s}-XCiepl\'y)�9.�-U60} 0243.^0Vie} Vietri M)Ntella�99N�x527} L43 \end{thebibliography} any % below to load the required packages \usepackage{latexsym}2�4icx} % \begin�@ % \title{Isospin%#�symmetry energy effects on nuclear frag! produc�xin liquid-gas type phase transi$�region} \author{N. Buyukcizmeci\inst{1}, R. Ogul ,2} \��,A.S. Botvina 2,3!e$\thanks is-ial - r){`next line if not needed % 6x{\emph{Present address:} Insert%}  her GC}% } N % Dok �8 % %\offprints{4%e a name or 3 this�%�!,itute{Depart! ofejics, UniEJty|Sel\c{c}uk, 42075 Konya, Turkey.%N . Calculaa*s%Jh$Au^{197}$, $Sn^{124}$, $La e�d$Kr^{78}$ at various excitLi�i! ere car�� outa��basa8f s6,stical multi�MX model (SMM). We analyz%,$e behavior!(Ycri IexpAU0t $\tau$ with">�y�its dep� ce � N8temperature. Re!3 ve yields{�s � ��ified x respA"to�$mass numbe�Ain$�� ��. I is way, wb>-� FK exh� �haIsmall U�!;� �distribuAf$, however,%r��C moreA�nounced- isotope2D%qI�edlTs. \PACS{{25.70.Pq}{M.N emiss���e�!� ons}�T({21.65.+f}{�Q mat� !$4.60.-k}{SA�M�theoryUfluctuE�s} ��} % endA%�$ codes } % �ѡru� >�,Ѡ �.�}�S:�Z�Z..� make��se�v {Int��} One�a|most i��� (g phenomena!�heavy !reaK�2-3$ MeV/�on)� �%/slowly��A\byd aih � )v �4thermodynamic u $librium. D��i�bp� on�y c= �#!� subs��IU�aKer%c!�0come unstable�� )y2�,E]break upa�ɿ�� s (dropleE�I�)٧ case��abeliev!��Ma &�Z� Dis manifested. Eve��oug��%�ist som�om��e.� evid5 %le� ase �`, so far M�rtain�Bre!�!�!n!Ye iTGoo� ,Pethick,= ,L nov,Ago�|o,Bauer,Hauger,Schmelzer,Mahi}. i ntly%с� blem�� �"s�m.�%� gai� lo� �|. conn��&�2_ applicIs.� � goal� paper!�tox Apse ��v framework;ae�� i�. �@.;F� 0 } A  us��or�Yct�*qpj�,�uld� capE�of re6CobserA�Q�% b� . ��� M�b ,Bondorf}% proA�d a good�  of���`data,�X��n�:� 6��t���UmMg }M�96, �x1,Srivastava1,Karnaukhov}. Withz SMM^ conside�` whol� sem�1of�up�Tnels 0A�ghot5Wɥ�)E�!�freeze- �? )5�h%?��   : �2n' gi� by $b\=(-W_0-T^2/\epsilon_0)A$� $T$;!�}���%�) $</r��~: leve���y�f8 $W_0 = 16$~MeVcb!�ng)�%�in:um� . CoM1�y> e s)�?is�-AX=B_0A^{2/3}(\frac{T^2_c�} $+T^2})^{5/W w�  $B_0=182�hcoeffi��< $T_c:-R��^�QEN8!,$Y ,=cZ^2/A^{1/3� $c%�a9Q�U� obC "� W�r-Seitz�� roxi�Il, $c=(3/5)(e^2/r_0)(1-(\rho/_0) y)A1���unit $e�(r_0$=1.17 f�d $ ?� n&O�%� � @$\sim 0.15fm^{-3}�d� �]um q%�E^}(4=\gamma (A-2Z)!4�!� $  = 25.� q�QR5D. All!_sm`ab��7 �,� -Weizs\"aCula�,�spo����pQ�is���r2-:1+( �kze� configu ��  [)b{ f� be quitaPc�fuC� .�:�a( k c���7 sh� � � e4m F�d� ���&� res�� i�� o|"� ~b; � well!.6Q�ake^*� )]��:4by9 g��9�V��]5. Here&3%a�;� ���ksourc�Pdif>nt�EF��� easi��Srn�� -E9VQ�r��qof�t*a"-202]���f>5 �D%�mediate� Y��loc� aftePMz! ��,e� V=3V ($V�E<4\pi A_0 r_0^3/3�U� Ca)?u� S ._� words�P�e��~d��wu{=(�� \ap�N ��/3$), �s�1�I%�, s�]FE��  diagrame�alread3en �%gnsinv�g�(s (see e.g.� bugaev}� �sp��riz8!<�Z t]o1s. uN�� {c}$!H M6� �9 � aj��  refoa.i�possi� to�m� � �� �1})`>�&� s ��ecew�aS�Aaka� 5py2u *jѮ$ o�]� � *z ��J�of�2��%�i"�� �concent� rlyg@&�� 1V.��,secondary de�Ris* , �!iOɊ� !��:ich waa����� leago�ya���m discus��ivelse ()�� 1�87}). �� we *�"� � 2�cod� n be�`,  s���UgeA�a:��)� &( .�i} AS MS.�[.*f5�6�t"b�"e}� !�er} \ e1#8s[width=8.5cm,h/ ]{F]e1.eps$Eca%�{6��ADF�x0us $A/A_{0}$ A)$V� n���i�� {$3� 459 $8$ *1 .} \label!:1 �1+ F� ur c�m��"�Z�f� -�to ��how���&p$Z�&�� irg-to-proth%!s $(N/Z� a_ d 1.49,818ʼn1� �ively�( two"��2$"�!� near � �Z$N/Z$ �n961.w.i , buA�2��s�>as.nN] " v�>Z veryY � ��8,2� . To!��‰qA�iiz��%�gE (E�I mZd&�"����Qlowes� �&[.�mi�%ܥ %h �)�i�y clo&o�� "8#. V����du� � %vAK��)��#V�a funoi�g� in Fig. 1�61=3�#n� A�"s� wL prev$�i�2��vB% ^��})!�s�sul�+)�st� e�2m�a�� YR�  of]�� i2V(B6 j� be �(lyA�n%=�B� 9a0�;���D] d� t�& , veuat,clei evolves)A�*��y%� �� 5�,�Y[IB�gN�nset �b�$52�A�SU�U�X =4:=t7�d�+ ^��U-shap: ss!5Fapp�s�%zW<�d&q Vvol�$9B*�I�!W(caloric cur!ob.+).1 �3$ T \leq ))� � �2�:�to��dE�fe� "n �/big�I��Q�� >� \geq 6%{ �B��di5In5 aZM'@ial-like fall-off��ij�I�&[q.(!sim!-6�)* &� F�@��two 'me �_is��@her smooth becaus�-�n&$� �I��2� .� N/ZRio��xH 9CedaDA*�AHP+ 7�T�I�{- �#� ��of:i�A sl��di'�an�a�� k si��% � n�still�>&��. I� a(�!�iND rich!U�?8� incr ngI�� ���c tN-2�$� !�:+�)�E�~*in.#�>�R� �pla !��:) . ~ � -U�.)�M� �) ific�(�#f�.s�%X=6�5D���).9V(e�Z=3--20)5W���(M�yr�,!D3� 8.| )j !'s q/t�"ov!��'�by.��a ~��& Ig accu{Qi��Q�[,��A(  F cex�7 27 * u�!�z% R� 2-. �)��a*^ � end� *, 2}�1  U�'8a power-law fit+#�$eredE? , $Y(A) \q(to A^{-\tau�5Y(Z Z _Z*�?$ �-$CofJ0�[�5-�a"� .J 0� $A i ;Z$:9 �*-�-(a�.�,)�#_Z$%U�!6'2 r�lB�  as&�ez.s ��.u#Reu�>���Aey"��a;*$6ZA  40$ e���!$3 Z 18E�6C�e �Ye&\3s �@����ga�"� valu�%M%�  !Xa)c�� O2� E^*;"� � 3�col&�-� �V ��(�Ominimum�k E^*=5.�5.2a�4� $4.2 �)�,�#&�2��DI&d !u2 simi�$kach/a;,+�oa,(*d � ose 5�A�^} !�Z)eanMatj} (IMF)2s;�e� cale0!A�.�N Athe�^1 oRe�B?��Lo� �is"� �:�� dominatA��"F���c�Ͳ%'V �-�}�.may" %q3*�� J er&@  lead�.��e%�y&�����fl��2� . A �$2�8 � favor!�Q*��'ig clusP ( y8Q%ix49yZ�  or -f��" Mns�(�� IMF�ac ~��*� W(N =� %&s�M�e bott�"�:5�:�_Z$��aj"��:)$*C 7 Y�]!M �*Y3 ��!�� arrow�l��4m 2 12})��I62Ic"G3 *_ " �9"l��M�(todnel�OY�(-�p,F�&= �q���"h 6D3> �67*}944~4a}'IMF plic9:)@�m' 6- l-�oonA���#��5&�6�6>��  let& u^�K�w��� F�I��B�6alv"i� avoi�4 :Y����~le9�� 5,Fjivid� �+g �4%pp;PŽd�:!�Y�� ,��+* a���A��o���� YIB�*>/L� s!� 8��}~)F� � - N ��TY!A{max}$�b�  n "or`"ս"�4i�� di; ly r6�&� V��6�. %;U(A�b$�_f .]9Y���!A� �to�Y�.�!�E} E}a� o�) 0EKmMDit �!�� �,\M�� plota�$A)h�%b.& B@�I�5.^�e���.(,de�8e first rapidly ��%*� �the�5 eyon_m V�4{*}� $ 102R,_ra$ 5� i�6ggests.�po"!�7b�4s� nt a�6ejpoint�1amal|7in Refy!*q lAny",D A�YUOi�/���alGcoincid"[F�a� play�6A �$���5 (�.a�'�Q�; �e ��LM$�rify wh0is kin�Y,D's placs/��*�5n�$� ��5� $\sigma{( $ )}$ .ed by��0$2OE�&"nf *� .4: � 14&� 6n (a) T&@, (b)6E�, (c)\6Z2%!of�;��-/>2�!f'�!r0 (d)u�2�O.=]��e�_*] �A��dɮlin�Ya�6c 6�6e�E��<��6�A^�:�2"5:� "M8=y�&�@} .2u"n &82ingredi��FnY%�<p�<�"5-B�9. B+e�1t cal �(ach�a.�U! R i�1�in �;(al (coalesc�:�D)�"�f*� "�?G Neubert03bSMM� ]"ϑys�'f$ in s�Eatn-yR efi�.���T bal '%r+�'canon!o cr)F:q�&F1m_{0}u1x*}=1.5(n-1)T_f+\sum_i(m_i+E_{i}A�(T_f))coul},L}&$n$�%�? �\���'�3� �3, $��� i r"V>mas-|�8iG/u��`, $��a�3>��.;�?��)tJ�-�. M �;Jj� y.5�͋idee"( ] eq.~(1�U ~��:i 0�  $%�$͉i�i�9 �Av!E_tr`=�l y�a��"|5Q�� qfI(a�5?.�to"�>�)�e�.e,rwe I�!v2H�� �� � on� gaa�&�J�7� �!��..DC .�� 40=D&ysq �)m�L�>FofjM Eu�Figs. 6�16b�$�� !M1�.��RDvar�A�9VDmf! *jall[%.2� Whil�g$�lateau-�J� ^  $3-72� 1 up1 E�z!��A�&�.�&8 lue� �!� e<�Dar>~#,�ae8l2!3E�T:���qe� ��� 2G# ~,re:;edU� (F/6��>��It8A9fi��e.�AQ�;$Trautmann}��C� soph�Z u#of Fermi�� Mole)Kr D�C�Schnack}AW Anti��,j6ugawa/&\�BM�^.��� $,�oLx�m� Y !��gur+&&/owE8�0��.�<eu � i��*�1peh������@�P�N (assoc�2�u�M+h�>Ō@<" (�����e�). �(�i[6c��� "w��aN!�� t� &� Q�$L��B�y m�2-v%jI�e�.}��� �J�ip#!�i"�A�HQv&C6.F%�# _1E4essen�l�/,,, "9>x#M5 .AHa 6�$M�N�mL �G2�2L ��um!�)�qU+ occur&F�'A F space &�,31pit+ a�er.> @is o�w�OcNit 2]M; now ona �<1�!���0l#��Chomaz��i�!<$rinsic fea�N �e�* �pop�OQ� *|M�A\re� l�Hal��t��Bl1"�G�&5� bran� ���:%�i�E�2a�Q^�tNt Ref��,��&� >�� explane��[ ��G a ��V(ore�Oack-be�K')& A� 2�m�*� .�I|&5�P�P�2V�7n�!D����#_{min� �#T�'*�!�4&�5c�x^�7>��"���a�5"g �$h3A� �=$�~m$!]4h6�NwM�i� . LKQ�IB� 2 *�&ja&�E ably�=�+��8\ _)aT� W.8��b��/��q,�G2�,?�*C&#A  f���L:�/eHp�Im�� W .geSXn$;in��be�)�E�<3 -��of\)�t%C�p06 � $%Qq�hTDe�es� i���&%�g.2d=�)f�is/-enough�bb� �U.r n3ca�i6�Hi�l���Uu?R !� "�#bAAo�at��ӡSZ/a�+Q�2�"�*�`>4C NV:Ÿ�"�Oc �e<%� �6&�Ta��=! : &} !,"�, $s� !�� . 7�$�b:2+ .KVby &�J et alQ�}�^�>'1� =�aqzcascade�� Au titoE�XnF ��� 7a�t��N���IK�W!=>0�"�%�&,�4 ee Gc$]V�i �4�M��sx,f�6�" m) <�f ��$. k#.K��6-�-�ayl\/staĩ}�%� a�12dH>:,ir�6on2% a ZproV$� .�)AB�-��be:P.+�}�4qL� %V*�?�H��&�.=��:%���9�� -ne7��Vby�Tfast Q Aɻ"Eq�� 2N�!Aase. N[Wthe!�,�� AFV �.Z-�eC sP ate���( \to \inftyh5��E�ak1:�-in#;t���ai �8="�H�VZG"=op"&� �7Q]AN3? ,y��=.S .6��r� ��D޲ 8&P$12c"�%8n� V��5M2[ s.�,"/�N(middle2I�$�%)N�E .�* &�5Ef: �2�[7y6�8>� Now let �@urnQ9��%�>no�A�nb�� �(#A���6V>i�>��2�?AYSa��in) �!J��F$Aa"%< olog�.P@�a��iP�H�A�y?.� we EF�_YG $=25�,NEos�u1!AcA-)���}&0y.u� �G$=62j <�>e��8%�e"�^d=7� )�mea�F���}�< =ى��s$�ԡ^��%.�3 �:X��K:>:���o�"w5_�th�;"� Ch�Y9.VH_)�]M�M"� ,?kse*?*�  2=� �uiKeb!<q�Nun�Y�*�_��x���ng :�DaT�13 r@� Y�hot"� � |Jt�A�Ls v:�%� �eeffort6 �UaI "�%�/pu|is�V��begin"'3 �n~AV�9n� I�^ic2�!�A���2�P�Z="AZ=1&!eA�N(:cay � e:TE�V����. Aa�[i�!�>$ U��T�Ks"`�0.! %� dash�3 de"%4`of new .�C6a(0>/-�text)6{9>{�aEAGecu#:r��� �$A�g�FI�a��2P��9AP ) re�v��.� m3imAR&*,�a�H*3s (-�F2$E, ��%��- p�-s<8Ym10^T�UTAN� =2Q��3�N.�"R�)�a>:�B N2�p b. Sequ�2U oZ7�)l F3 ($A>$16)9ng)�-��U� ($n$,$p$,$d$,$t$,$^{3}$He,$\alpha$�)�^'w) n ,Lm` A �1-:� &�@d`e sV��;*WZ&A(�.c�#CreE�two*��m�%%�5PF),V � c�R;eR�"�@H%[�EsLeZBa${*}/A>1$Me @we�م6�!+т l�k �OM��#ld�dop��4�u) * V�3aVmE� {ar{ll} mV=m_R(�T)=&m_{n}N+m_{p}Z-AW_0+ �T�R(}{A}\\ &+B"U+ #<3e^2Z^2}{5r_0 A^IT�$��$��$}���S$ �1 e�eJ� .�@! i�-�V8 �&]� i�&� !ZaA*�KI� .��7es�u shel"`c (�st�� ��E*ar�X)&S8)�i��H!{,� "&*eq:! Z�0 \cdot x + m_� (1-x)^X& x=\beta EI�$~P4$= 1MeV$^{-1}$vx�C$1�J�![*�%alwayyjN%%!�� bf't�NB^%�eJY N;z�d � HQ"*IT :� �� d[Xop�;�2�k��Rl���},�U!�B���"�_+�.�_��#�  &�check��!/:� a*� { �1^0� v�J�I� � Y�&Y . G�*W2�  push�m�j : ward��W�>j^,��O* A9LXHdA�ZqB|<(A�7oEH-.5��6�Ql%<���/�6�! o�$�h&!>UZE�r1$��-$U[�-'���*� a se� 9M9e2Y �5�f�U)A�� 6(2 %�Z=5%.10!u*�"ce in:W� mh"*lif��EH�new.n XC5�+-�:WC��ide( w  ! shif�M�i<F� �bC"�&� c.3�YoZaUpl��"(!: By u0X2��q�Fl ste$.�!supS s "Ko!�h+$v� � b�I�:p^E�he"�beڡ��Aaj(!n of � U���� n }k�<6t *�$?LpN�nl��� (cooled suff�^ly do#qV8stAH�0\�<O �|A��&p A�KL" <$1�)� Z�MKo�[nyQ+��ce.DK .p=72| Pz a�s�m&k�h/Ae�B k is22a�� �b�%mpari[@e�&D "�encoura�[2!M���R� ��8V5 W��� LmC��.�(c8c2� 1�� �l"�J6.+| s=�Si�� he a>rY�� �A�!>q1W&A vi-|� "k�Lozhkin}�hA9of2PBNul* <k� pur,. �l�� 8��%�9�a��mCu�X�ao$>�� �4xKi t.�# #��w�/!r>EuQ&�>( �  !Oi@F�. E�#�#2�aTb� ~O�K *�K� "2=E�9VK�zfi�(-9�c3xe�>nRMqA[ ����!�b^�R��.zl*�R�X6��?6b j!�u�?{!�+q� mean"�L 2wsKF�"� s� �B��p �:am( survkn"���&i��isB� s !J)$�63� ar 6  studoB %a({acknowledg�s} N.B.a^ R.O.� nk Selcuk*Q-�~EX"�~ Projecwu BAP)�<ai<\k inan5� ort�4 grant-SU-� /033.The  �steF1y ��;WlyTe� Q! ionsE� W. "W3, �0Lukasik, I.N.&��, V.A..�'��U. Atav%���tL� GSI�h�&tA�)��I�}ork�`*."!{g�$B��B1& 1&by DAAD�.�f %I9-� "�R>��{2�,bY}emky} H��h,=�. Mod.;���@62}, 801 (1990). B&@2�{%9>] R�B >�8584}, 233 (2004.\�v} A.L. !�I!� pust i0A.Z. Mekjian, f.߈30�5�82cPw} C.J. ,, D.G. Raven�c,��2$A471}, 19c!87.��-} 1�, Int.Av=VE, �$7(3)}, 419G98.GL:[nov%B. F�Sova ~2�57}, 636]2��-} M. D' ��*}6�A �65!O32 �9.�B@x} W.  EA"��.�%�C5AXR1760�5.L6.} J.A. >�& � OE�024616EN2�Sch�xS̃ fU;�55%�17�2�y!B jJI��6!>19)�82� %�S=7AIljino��4!^712�82\�!]Pi.=, i � bw�K. Snepp�G1�p�42E}1a�196�Im!�!;f} S!<);B3iu75�96./ �1:=>�B#A5��73)�2'2K0 B.�"�x>Z �.w6A8 0546A:�.�.�-Bw:�J[a�R0116���..\bu�i K��  {\itx.}.�)Zm;44320m;���!XRu�%�E�-t2Oo�6}, R05�2� 987®47!U663A6w U2��JQ3}, 06�1.PRW P.T8W,%^)]1A�. B)S51!���2P&�B�+ JWEur��J.�W559%�2�-03� ���9��792NVL�? L.D�� ndau� 046114E2hL>:� O.V. ,:TJ!S04461�2��aLe �j�.i� 1627Mi6w� D.V. jV�q���02% R� > ��} f%�  %H�xINSTITUTE OF PHYSICS PUBLISHING#z I�  I`Pr2G�an �� pubX��an*��&?� I P0shJ��Y�LaTeX'�� ��  Iy�-V8`ioplau2e.tex' �Cto"�D `Q� Iguide*'�Q#- 3��d"4.�5$�eVI=@ �p�,Pfix{  ��art.clko 12.cl߂d 0'. 9> I�  I�=[itself�s ��& �B I� % ��m�%~� %���a�5.�!& !_la�9 mark�L" double quote % #'h. ` op� *0(grave) % & a��sA['-Aa 0 acut0$ dol�]2%-1w  % (s�en�)ia� )Y@Ken�% - hy=n ; =�dals�] % | v�q�bauC~ tilde 4%@�+sig6P_� score % { �cu�j bracC} � N[ )squ�] ) A(ket % + plu �,4 ; semi-colo % *0%�:�*o�< xan�/ ` > x ��2Nz6.�H, stop % ? qu�oY: /��l# slash�\ �? ,^ circumflexE�dABCDEFGHIJKLMNOPQRSTUVWXYZEdabcdefghijklmnopqrstuvwxyz$1234567890K� u��0cl�10pt]{��}%$�%12pAw��, )!]�EYA�le!�umn�g % Un�I�Nn.�� AMS fonts"� %\*���ms�. grap��.epsfig&?7�}Sdef\be{-"�'} ee{�>ba29#ay2a26bas>3*4s65 pra{\PR A �prbBcClL�t�[DMRG��w�Z"^A fact"�V ] {D(#(y matrix reC #x�D��jG & �i��L{T. Papenbrock\dag\dND� Dean 7��{+ D�tE"o"��<a�nomy,*�%Ten|ee, Knoxville TN 37996-1201, USA6l�+ ics Divil0, Oak Ridge N3al Lab{�ory, , a83\*ao�}Bemplo��}rr(!��)�!} V��Miu�0 umeri{&'0*#-�e Ia�rruc�Epro�1N|�=!s imI�ed� verg� for8+&~Aact�du� � impl66%T�4'B$algorithm.�&�Z�9$fpg$-�+I{ y�rIco��r�O�8��!re�L�M"|~�r�h-3g-c" 6.(�2�*9� %��g ~�n͉s e�4 message \pacs��P0.Cs,21.10.Dr,27.50.+�E.+NSubmit�%� :Vs $4o{\JPG} % ComiKutf&"tS 9pao�ot.u҈ "�26���#%zAKl-)! with�,2�� mix!��xr"d�\e tool�a \�a�7)U9!�-�medium-)I�^2�o. years� no-c%.��s"��=en "�o�8��g01$p6c�!Nav00a,���-s�I�}on�HE��8vol�K)!'m4up� one-billOS�Or"�a� ) now "}A $sd��$pf%�i�.%.d�.�#Cau94,,9,Hon02}. N� it took�(1YKe�B�goa8m.� �B��( progx�L� m%�2O���rzLP" comp�}l�5de"w2A5 heav�$ �or drip- .�Js basn. hingoG�=r2��"�BM�, �[ �2��K�$navail�B%�t��ext M�!�|*A�E��e:� . S�-al �hs1#s�^�. runcM{�]x#-tG s���m4!�8(lex�!Q_t�h1-\L4Sal ins�-�rg9� i\_ne ``b�g nd''�68Hor94,And01,GueE}In�F�Ti� Hamiltoni�>� ����}st�bort��# ��.exa���!~M� �F Hon9/w0huge Hil�Xi�MsT͖ ocha,lN<�= rR@�~ kept �M��niOdz63 V� 3i�Whi92,3&�.2R 2 7 Pap0=��`&� .U�"�$2momVDariE~al pr�`plAv�c!H�'I�\N�+A�i�bAu�̑(�T=l�JO*M� �S�!�e1�',ezu��hTvbvto'Ru�D�O�":Z$for low-ly��I}�\$0f_{5/2}\,1p\,0g_{9/2}$My���n��a�#fr�~(u-�aBd. ���� } �L� last)ad A%C��;;%)m�choic!���% na!�qV�Sspin-ch^/!��KR߄�P�2 viewQ� es99I�brief�,����a�i�as9W�&is ���$�Sdimen� al� s֓�OAKʁ��g�noE\�s V``left''E(``r��''bj�Fh6�'U͠� �Q !Hsit^�� o ndE%�9�9ex� ����ervf6�$|l\ra��7 $|r��Z��#%�6Np1 \be2�$svd} |\Psi `=\3] {l,r=1}^M_{l r}��. \ee8Ac,!��+k�#6J�$.i�/ � $m�''T� en, EفCA�8�as3ndE"��, keep�;to�.:JF�2] �515d-+(a ``sweep''6�,�� . Ty�l+/�+!_ �Yw err/ �.e� onen�*ly�� �A�of �M%. A /|n�Ves�)s"�22���he���stead�#%l:$2�e���en6%(e�*G8��ra�LAK%X.H a�I�.Rof�es�E��r�l� !1 �D(A+*BM$�AM~s"�_�R��a� ` ̂ew( ukel��P�lm�Duk04}.�3rX?�e��th�=ovelt�_�q inl2��8a,f6m, =j e-A�ic�Frb.)� e:��c!|nA�B, (* &[1[�%�woe'NAThird�two-body�eW in�G] =Pj�),�7 :� �!Y�|eb�vss +��~ neighboy.�!>}: 5i, 2�coworkE�� ��-�HE���JU"��c �c{/ �%� \0� 3!�%�)vn !�KMT�1]U�U!/C�oE<�t%�y&Do%:��re�;�( schecc pai�� -�(-quadrupoles�ṡ�5!�ed�1j��6��Fx�O&�(!�complex)i�a�s Dim� �bR�)is� @� cho�p:��01g1|&Ae���motiv`by ourĆ�T!�64f.�KU\hEZ�Z%��h� mum��s $GDL=(n,l,j,j_z,\tau_z)$� A�e�he��%�Iw�4r�pŲa:� $J_z�� �{ �9�bI DMRG�6 equivalof2 �2�q -qconju�AN s $( �,\bar{ })$L Jud�qi�>�>o!�r�>�*� #@�e �QR reat�a� �I�� >�b:��9�� �'Xu� ���A�v�&�;BclA�� h�#rmi�R]J  �ea`!!'  Q(92�,extG v�@{0&Lc(by Legeza o�33ub?0mj Leg0&j To˝c�� icO5e�ofef-� !��.�A| -�ڕ�A� dot�Q��&үkw�a���(�[�.d,Hartree-Fock!�fi���W�2 $1p$-$1h$p ��s. �s35& � � ax�t�iorAfV�A�7s�f�OXiang�� E�A� -aq�d� ӟ>Xia96}� �we���_>ede�2 AVa6/�o;!�� a�.�s��-�^�cppr% �V:7 �C�A�s%��E>�. &��;K!�Yxial "�4Y={��Nb  �CdidER)5.� �:�p�m#.>E��ɳ�>���a�K����u !te �ioWET� 3yJ  s.Wed"�VR���*i�0us $^{28}$Si 2&'USD.�MLBro88�:���/(��V b  is $d_{3}>� 1$,5}5 4� s_{1( :PF3( d<�ignod 8 $l_{2j} |2j_z|�X�xY�oo3��x7 half��]�$�< -�}4�i%(mi� M� ic) RD>S �wS>n!;Agg�in Cse���ist"=]$(d���6�a 2�*�G�:e� ��U(~\ref{fig1}:*I 3 J �2�q�@"mjM�of�w1 ;q�>�� � mor.?� !�fu6�Z�)N&�;d �7�A��07O� \�e�!��8)"�(!�3&-A/z�aj�MT.�RQJR $d=93710$S>b.�T[hbpt]FM�e <=0.23]{Si28dmrg.@��I�#s2+ Ni56+ _4st /8�&��1}Left:)F#=���� as bF� (!�ba�nn�N�ts)�I�.QBO>�(%f!. 2ib�$d� !�^�vs.�. R�: S2yasij exce�%$^{56}$N�endatu �T<proв �� s1[o� �.�!bE�$f6� x�v KB3.q(Kuo68,Pov80��:Ba�����!x"E�'Sal�)�p6Ou�aOnd;f}�c!D�ly��Cau99�<��:�"S Ŵ�ɠ �P Ōpժf_{7}7� ��p��<<:  2 2Z 7�62�5P52F���n-)� e $(]/c� 16}$) & F-A�& !YC�.iqZ.I��be( JmAbЊ��? & ofa@ d"�ig*��m a��2w: � j� �}400 keV J i�qere�k�a�s"%�q�M�P?Ff t.�J��!�[ �h�J��q���,�j�gbe�E 6�H�B� a,�U�&:�"�T@�#u�Gex�?  � ��6�� fail��9�G)�*t��!`&�!� ! ������N)xourI5H���� dA�ECrwc6�  p<�e�?�.IA� �&=+Pi"�y@ԥ(�>�V abando�0 (F�&�%�� !3f�W�c�a�g-1&52rS��Can��m����� b�n-"�1� '��Y�B%MS �&�D���Y�H s�!s�gA��&��_� � unM=atئ=#F��? d{WC"� 2� } Modernɳ}#$P�ilQ ir�q�E�N& $|\psma�3 �"� ;2� $|\nu�;" p��i!X"� ���pto��2:M]$s�l2�F-iEduc;#. A)��6� m� t�E��0�#a2�pn^�\pi,\nu� \pi =C=xUe�V���ru�ˍVqa"�%-p!j1�"WaH O�u � ����E�z �)a�6E��?e:2litud]M�-$\Psi_�$V rect� in g� a�;� b'��-�B=USV^Z- ger$�:E1��u�2�b!��� (SVD�tH̨$Ud  $VX unitI^�O��}ai%V-:En%@!k1D6���$S� zero0� n� ��v� tr� �(jj}\ge 0$ (_``���s'') aS�g )wSVDIpD,J�)d�.��O \ba |\/3{p}_jmg &=& !A|U)�0y�,\\:n^:V_{\nu :u�A�a\�2 �#s�.>�!j s_j J�N�$. :h UW�s)�!>: EgyQg = USSU M@.+ = V..�2'Ag��ias)� !U�]�Nc[&�� �4Z"߾3!iPF��%MM�*;r�.[Źije� .�s*e��&�* .c ��'*� �i�(�9�� �O��]t"�at %[E &) �'�" �n&itaG�(�X�unwer����/ep 'en �)�*y.K$jaWe !�2Z=a���� $\Omega$���%�� "&%:)%�{j(% f |p�3|n .��e.�-A�%a�5$x�<���/�#�.�" B�k�2gyM�`.G �y�E6sAa-(�%in4"4$z��.�s�2} �'{i9\U$(\l�&8 n_j|\hat{H}|n_ - E " "\G)|p,��0,\no*\\~tptHt"t� t�9\eaa}� �0�� s>�d "u$�����aK{ dom of ortho���?� :nd `-�Pa AJ=�� � .�1��Kt�!+to���eo� As�N�$EDs( the�g���F��*3 �, ���)A��N/u�� ��cͪ �"� c�%&BH&m,$E$� �! O�-��9: !6"m%{��hin 5-101�on����$�:�3�� omewau�*�M9���FDs~q 5>�"� �� D_p?t��D_n&. � IjA\"� >5*<$U ($K)��o!�!��� a ( W) *�& &��y5N�� hund� ���A� than 99\%��lap'�n.ghu��-\ll!,% � 9f\ "9����(E�*�)���K��sL�4M��>B4��a=�t�x�s%o�� {'�)^J� C )YB� �FAa E��1eB�%{� �}]�]�a!�n�nF!.Y �zW axB8���-�f ���"ف�g ansatz �)�})�3d�*�Aw�.fY"�' �{��O {>Y�hl+`!I bQ#toBCi >B*�B�'(_c��cap"�bu%u��wv7 & EL"� �. ]3Q�.�6�a��q*�>  e�$ $A=76,78$��aJ�3dey/ @!�^m� b1 QR"�'�Ta mono.&�7 ed $G$-� x� Shu8�2Na __�Ni$ � � �:b��KA;` � y!\%:*6X&�.!�F ion,�� ���mP"h2~6�zL3>�B �e-�7yy�in�76}$G`$^Se-Cau96�7b�~ "���A�$T=1$ u)K x e�;�Wt�Lisa "�<�e�$36]{Ge76_SKr78_E0b�2}Dat) ints: G�}s�{�!�"�\)� �ra��%7�&�s:B�Uat��6?I�w��4e� focu��%=��-�Ge,A{!�S / 8}$K�aco�8<ir�>4� &a! $m$-� 6���S)�Y�#c �^ty�r��j�E�T! !�.Mm.�ure"�2}"-}<+�$E(�= )-E_{SM}$v .iC)9��-��:�g-��.�� !�$l� �tF}Q%&)?!����Fl���T�9)tabU�ɖő!7j�!�� ew:�kYof <seal$&�s�prv � 1 D0�me��isCls8q>� )>a d1i��(ri4� f-b2�?& Fed7>M��6] !"�@&OT�~�b� � "b u�n&�[ �. N!tU|wiu�6��-�u$ci}p 6��ݢ�2D 320,000NTI� �bd1�ɸ�]s�Jmb&o U$ a $1.4\ti�n 10^9��&�62b# s�9+��0i"�ity�] l �4v,q m�a��  :,u�1nx ��%��)��M>�� �f� er�S� $3.5 � 10^6*= .|1���� 8 � $2.6 < %" non /щ�#s�=m�a���Ua to < #5&)e� ,W�(�b -Ls wr � mCau-.� ��a����[��bق $� � J}^29�&,(� ne�ger%�Az�st���.4>���#0�}[b] >\#t��S�A��\~���E�.�"�*Pf7��2^+}^{\rQ1� C�($J^\pi=2^+$Ip-�.o%5ra5� ��TV��Uni� zx9MeV�w ��nted} \�#$up \item[] tab#,}{@{}*{4}{l}0�r�Cf N�us&\m���& � th}>0exp}$\cr \mr`Ge&-57.23 &0.70& 0.563\c" Se&-75.74"46"59"L&-96.06 "4"455"\br�� =$t��IW)��<%��.g �?a by-pra�A�22A e�* �+Z6�@ "�gB e., >��� 3�IX; ( V)�XMN��I�qIDA�f7!d >� lso "/ F/T����&�}�! q�.6 � y ��Br!�FiNBp��b��s͐N2�&e! v{�)��&.c�.{i!�bout 150�")>� .JiB�!q� q� asonAl� �hig�3 preczI1�.�C�%�� ��t���Y����"� &'?SQ�ryg� �?dn>�t%1A��Dg�!� the j�. W&$�54 Y ai?2 `-1�w&B5E%�_ aN�I( &.� . KX:100�a-�i�edI�}�vpe|�"� ke-�"3na�+9:� inlyD!#VF5�"! &_1A0x3dl$�jP"2J!�)%B&eC?s���$. Fur�"sBd z"vGby��iz��QAa� s. �> .X ack)��Xk�Z2:S.�;�� ���9cu�Y �3�)PF�wacki9ai�u��= .�vO�?�d�m�T)tTP'<�"R3 5x�u�ar���NU2u�Wa9Xt� Pth%>�$m INT-04-3<� arch�eA%n�)}� U.S.:�OEK�Co��lct Nos.\ DE-FG02-96ER40963 (6�TeP)E&@DE-AC05-00OR22725�� UT-BVF0lle, LLC (Oakf�O (ORNL)).?'&�eYu�?���j= C� XNC�qal ogc��XKd&*{R��_�m� :��{99?�bfXNav00a} P. Navr{\'a}tilje P. V�m�� B. R�c(rrett, \prl�\Da 5728|[0),�k4-th/0004058. %&Q`p2Bob,W. E. Ormand2a8�c525�[2)2R�04} E. Caurier�b�Zuk ov$|�G.A�,t{\'\i}nez-P�opc ��d22ib4�9307001B~96~^c}� � �JW`tamosae� A�!h�Q20Uc9.�809066hH�M M�,8nma, T. Otsuka,!��e rownrMizusaki.r6�J 061301(R)%�2w 0205�i.��K wroiJl0V. Zelevinsky.n%wai4s_2y4060042jL} F. A�ozz��!>orrin!�JPG)�2�a845�)_]�FL V.!�$Gueorguiev _Y� C.A�Johns��AMJ%�Draayer.�):s�r271100472�>L6�5�k9�Al�`c128)156l$ 2} Se� Whit &p :6EL8Kc9:Q:3F:b)J4e�03!L199�b=L= 3} 2�U�&�U�M�6!�051303Qb3.b3010062+�I I�i�(l, X. Wang,RfKaulk1 `K. Hallberg (Eds.), {\it �J-M4)R:�V2p} (SpV @er-Verlag, Berlind��a�cC J.Z�, \RPP)A�51�j d�/04042122�Z22Z,&' �imitrov�A!>atoitsov2pe�543uj�f��202046F�.AE6f"��(�I�M.6~� �2070252��= {\"O}. >mZ$S{\'o}lyom�M6E951�i3),�-A3053360�66�&N �%5 b.�AG 7��195��6}T9601016�r9b�sNP;oA65!�973�n>�Lh !�F�gsetskiy:��asH. Graw�'��Ejcf2�402086��M Fed �[�/!5 [2A_82�m7:O1*� F^X eiRA70!60c�wa��t: �� d��, ?s%\tole5� e=10000 %>�^2pt,pre� t,��Y,t�0en9s�Ps,nofootinbib]{revtex �|9_ prl,twoco�^YZ<*�^�^}2�^8amsmath} %\text��( 13.97 cm h�Ht 22.3cmV),\topmargin 0$ hoff^(-1�� %\h�ep ���t 1.2emY5$% MACROS:-� %&) f_beq&_c*~def\e�7)bef�_ 4na^�_beq5 iP )� ya�_  Q 5} % labw� .qlab#1{�*eq:#1vfig2figt.;tabsec2sec %AL �ref#1{�' �) �Eq E"z26 fig !fi*n9 h�f �26�F;2�?;tab=6�TT_6"sec >S�yon $=vectorMG(sla#1{#1 \h4{-2mm} sh- slap{pz"d{A�td&K.RMP{P \! j%"S �Hboxfrac#1#2{\mbox{\�{$\${#1}{#2}$}Q4�AR*1}{.(s?AxJUT1T�VU36U�eter^�42Tird^)3)sixth^)6 ) %�ce17 arr{ .�i�{c1(e"a� �--� bmatV@A#JA%����symbol � al{\alpha�adtga{��} e`Ga{� \G���de{\delt%De{\D 5Hveps{\varepsilon} \def\eps{ilon}  kp{\kappa ,la{\lambda} !La{{\L  $(Pit{{\it\Pisssi{\sigmKSi 7S Mth{\thet%vvar.Th{\T$ �w{\omeg3 W{\Ohw{\hat$ 4 vfi{X phi}�vph X z{\z� br% ngle- ket{\r  $ dd{{\rm dg(pa{\partial # vrhozrho  barf2k0Z{{\mathcal ZK$ie{{i.e.,  eg{{e.g.\4cl{\centerline _,ni{\noindent F��$rightarrow 'nn:number} �rg �g}-rp p�rk kq{q -hq)�qhk - tk{\tilderN QNsn nFrf ftqFq5tll&KKcO5{{ODD=�Dla! 1�Lham.HMMMAABBPP�scr�-�N{N bGa�bf\Gamma7 bS{{\bf Spsib{A�{ 15Pa�-,+�xx�vp{\vec{U0vk Uvq U%(pn{$\pi N$ �arctg)� �(re{\mbox{Reim Im3d{3-D KCMS{CMS 4ODI{O$\Delta$IR`R} \newcommand{\lsim}{\, raise�@-0.8ex}{$\stackreA~(extstyle <}� m}$u�ol#1{\ovi�{#1�$amm{a.m.m. �Dceft{$\chi$EFT} %-~i� hateilE4bf{e}ebq5ubva!N$boldsymbol��ep�/ �bsig{2$��.(begin{docum�zLpreprint{WM-04-124} �JLAB-THY-05-292} \title{Magnetic moment of the $)��(1232)$-resonance in chiral effective field7Pory % observables and 08 extrapolation �`author{Vladimir Pascaluts�!Pemail{vlad@jlab.org} 3@Marc Vanderhaeghe�c 2marcvdh25ffilix({Physics De�:�ment, The College of William \& Mary,`sburg, VA 23187, USA\\ Th� Group, J!8rson Lab, 12000,Ave, Newport,s, VA 23606Q!dEMtoday)�`abstract} We perform a re!Qvis!�)� �F� calcu.0on of the rad! ve p(photoproduc!�, ($\gamma p �� \pi^0'$) in!�E6.-�region, to next-to-leading orderAO� ``d��-expansion''. This work is aimed at a model-�upe�zI] �6�^+$ m:�\from new precise measureAs Cis re T . It also0dicts�-obehavior!U��'s :tH, which can be used!ye)�ecD lattice QCD resulsovpE�4al point. \end]� \pacs{12.39.Fe, 13.40.Em, 25.20.Dc}% %\ '03.60.Fz - ElaEEa�XCompton scattering. %14?h - Pro+(neutrons. %`!AJn absorpEL,O }% \make��$ \thispage��{emptA�a\EU��isobarAA6most dA�nguishA\nd well-studied nucleon!F��X. However, such a funda!�!U8roperty as its 9�dipole�((MDM) haA (usfar escap� QU determin�{.�problem�genericAany unst�5 ��picle whose lifetime is too sh�< for �MDMAbQ�Bm�Xusual way through spinA�cesaf experi� s. A.qHaof )+nJ�A�� rently�Pdone only indirectly,�0a three-step! �aere%��is first%duced, n em�a low-!?gy��nm^ play!�e r!� of a�ternal u�f��, A/Dfinally decays. I�́y%9e-E� lta^{++}$�ac�ed��e�0 Q ^+�#to�/ �/L$~\cite{Nef78,Bos91}�l% )o n+$%abeUMed us�Baz� .� ���^\p!�$) � Drechsel:�� um}. A-�Y* devot��� ����( was comple%in 2002 cKotullab2cg}.�|value� c 3�s, $\mu_{��^+} = 2.7 {{+1.0} \atop {-1.3}} (\� Hrm{stat.}) \pm 1.5 ys3t��1$ [�9arM5 ons], !�ba!�oA(eor? al input�Z�� phenT ologi!Ŷ-.k$1qu,Chiang!4pw} A�![��b� Uw�2,o improve up �e�ie���m��, a d��a!zseries(9�s��ɘ0ly been carr�_out b�`e Crys�B BallO abor��� MAMI �CB)�s!��( achieve abUtwo#�a�itude be�� !١�ca�a%��eŭ�imK>w��aim�!i pres� mtoMá%�se high-��. =FDs with an accurate��%�-.�analysi�x���, f��frame�of�Z� (� ).�P \6�s�g i�aA �h��spens�O,!�least -*��} ngJl��*  (E<, hadron masses,%�a8�Os,* lengths)�Vo �( ab initio} c&� sm�3 . OI,other hand, �ūnd�Culd�U� i�#� ng variouA��ic�� ies 8 !7y. �0LI�we willew how ~0fulfills both-�sɩs�a ga0fy�fashio5one-loop.�h-� �@$is sufficiA�to g���V� =M� t Ŭ��&����>'$Y��the� N !u&� 8  e.!lJ� ��ZR MDM�C$Lein91,LeeťOu�rt!:y$Lagrangian!tha"� �� turb����y� �PT)i� ��on <s �GSS89�� �GoincludedA+ lici�M�ة� , $D!`� (co"ant � ensu(#>Wgauge-in 9ce, $9 �>8$ a>O�� ( �$dual, $T_a%1��V 1/2� �itrb���, ��co�nts $f_�= 92.4$ MeV, $g_M=2.94$, $g_E= -0.96$, se.�,��b}%\fu`r� ails� 4� !�� defi�%�in un�of $[e/i�]$� mit�� erBmu R becaus%y do not�tribu� F �s�8we!(sider. Not=at�h�q$& tain7e free�����ormr$��RaS41}P�AT�a� degrees�q]do"� r �,�/ d,: $2s+1=4$. }a#to�[ ]Q� \EqrefՅA�A)istl � �s)?traint" $Pas98,PaT9( x �w \De%�i�4more subtle sip case t ^1�holi�&� lyaongB%(l ee, �  DPW00K WeYde<� ��A��us assum�V�toe weak, � ar&7����� le. �$now briefl�� bA�e � coun_ P :F F hccitM energyAVAt�*� , \equiv��4-M_N\simeq 293�"tre2as�� �, so Ell\La$a� $\LaH 1$ GeVB� heavy DE��� . Ae� same  ,a�8% ed differ�"�  �� Y -- ���34, $m_\pi$. Nam�g� /� j!�� -�Q e sm�pa�ter)� wh� SD_ �[6wo D�%�. Eachp'the,cha� eriz�by��v;AG-% A�px $n$, s simply te}� �� k�s` M^n$. B�=�ory�rct =Ys (-;ŏAE$)m TB�d�!K whe�!�����um $p%� M�l&ld ($pE^)�) "� :+�~)�eJT�)MH-.� $L$ �A2NE2IE>agator N$"�>�}$%*%��2'w $V_i$ verA- d��� (is $n=2 n_{�k(rm PT}} - N�bm� $R(L=\sum_i i V_i + 4 L <N - 2D pi $e�ha dex�|(PT)ni���U Q�-�,eI need�MW�%z�EH,-reducible (> $R))�s, 2�co�%U$.Ka�a[oa{$$1/(p-\De)I�he�i(such graphso  large%�af�����irA`umm�bam��� dres"��2�s�i�5have as�-\Si)$e self� $\Si$ b s�� $p^3 �thus,z iA�,i��ed -F� go��$\de^3$. If%�8� !#4qA� N_{O�R�A*ů>�{is)�AG*u�MP�n^ $n=n�A�|. Kfigur�%Ue�%{ �'fx��=8.5cm $file{radpi$T_NLOdiags.eps} } \cap8 {Di�mR�8(f�� at NLO��!�"�� � : ��. Doublne� �D6��"label{�ramOnd5 C grD ampliy��tHoptimal sensitivitya=O� !��d��[ciJ'Pe��y��vic�eT���g\outgo�� >j��i(of�$. "�] B��9%F� P  (NLO)�!�*��U��1� \e $}(a), (b),��(c)��K 4sha]blobsadd� to�. from:� , �'H�f�� cor� ions�n�Fig.~:�d�ef). T!<our.L!kb^s[ i&�heYss �oymu=�/M�� ar=M $ Ti � , b��e followA� �6p_Ye_q \Si"%(\slap)pA(p^2)BUpU+ B  },�q���$arq ks, af1 ��al�ulariz�S, takI��a ��-�T C^2 \int_0^1 \! dx\, H{\cal M}^2\, ( L-1$ln \MM^2),a �HPr :SM�JM�a�"6gwI $C=h_AW /(8Ud)$, $L=��/(4-d)��_E ln (4' <\La4 $d2�$4~ٱ9Ws� Q=- �)'(1) 6 eq 0.5772Ew� !�renormal-�%�AKq %A(xATx \mu^2 + (1-x) r^2 -x AI�^2) - i��#eq A%�mon-� -shel�!ve-fuI'�>�s���K� -&= .dQ�Aq S��(A��-< A0P}^{(3/r� )}{i -Ma�)[1-i�$Im}\,\Si'( ] �-* m mwe ��d%"� proj��&per[ , $I��$�$%y�S�s: 6 �=� A !�a�^2IX�=2(��/\pa � [<� +iM]_{p^2 k ^2}$�#sey�e lex�)� isier*n����'thres,- > M+�J� �Wase $\a� <0$�"� A| logarithm����Ūs r%'toy imaginary�t:a �*6�\bea {�/%� \S1~�f (2\pi/3)i҅�(\al+r)�$la^3 \,,\\E=� ED;\,$�0[ \al(1-\al) T�'.�-&�. y&rd q$2 (r+r^2-\a�)] ~�\al)(1>���8= \sqrt{\al^2 -�A We��� wid"* ( iv ��a| �-��Ve$,�$aP de"n!alu#S� 115�  lat�"h_A $2.85$,E��#hwe�llVAJA[num�&al.s.� $\g&� ex, ��?W ic quadru�'"�oct U s,+ writt�A�rmE�a & & �/ u� (p')!C)W��al�,pu� �'\,�  \� & = eA��(WU�s�3vC }(q�p +�r (p'+fcdot %� \, G .Q� u^� �M�/<�'!9 p-K vecto�?I+ -�s�*@��isA��h'2�� = F(0)��( Ward-Takah� � ity, � q q-K<1N = ee�$[(S^{-1})^aI!�!�-Jq�% q deH0���+G(0)=1_Ѯf�&onD isA�if�$exp*�:� . S���already i�!+ex� �S �[�,:!H� ". :i$G�e�� o��1$(� 1$(f���q^2=0�$req (& G^{(e)}(0� -VB ((1-2x)(x-r)M�0& \hskip2mm \�sI� \{L +\ln[j  eps]I�\} �� �f �i tV���1-x -r)q�f� �� � \��� >�� ak ir' ,}�\i$%�"q"d�&�-s,\�(^{( )}�^=*�(F)~ + f�!a:0�((1�*3(29� %[ $T N %"X��e�fixedA�e� �z(&.�) %���*���:]�adjus�(!3�  -1$)!:�2�+ ] AsP�# data%O���lt��+U���� esee�& futureE aW�' �"%/Š7��)�mpari�1� � r�re�6$e knowledg"<�-�<�&qul"ty.��r6'��-bary�.ult8Butler:1993ej},�e"�&l�1��manifes�. � ,@ arguu$arlier � / pP"i3 :2004ga},�'c)ui!�B�2�%%R.�. Fl.`%}Uw)G� � =8ofl!� &W X aQ�w-+�A�aI$ND ccorU2 to ��&�9?. _��(solid curve�'�o "�E-�erbU�$iH� �%* aw, u . �I_�.0��M�B�.a&�(b�en k!a�-_ �-% �- elopy5 =SX/e I�<\�7 = lta - M'Q��1artRaw nounce!5sp� O� Q$. Fo�- ^+}$%�%e�Win�%[+e|mtrend1�r63�&��possibl�du�%?0``quenching''fT1q]�/�*dotA��;.F"�-\]��3b;ud"� �e:�p-3�*%�aat�-%A�S0��p"�Y4�*ery!7tiwb-ioi�{)����1(roximately K&l�bo %� � 2 [t,b,h] %x.,-xmuDe1!be6Be828.XP�jJ%!FrA�(.�)%2�8 (da4Els)E��Gm"�4)gE�^{!xMDMs [inO$2�/. DI(TA� ���%T)�9� Q} Ref.b;��zalE��5`� ���RPDG"G.Z DG02}. La66a0�rom $L3+�#V Y(e%+$. }^Gm�M*� extA� cussži4� !$<mmQ,f! *8.)�}��is!s|3"b:&C�spo�*�ed) of.P"A�t�d abo�9��.��!�2lyU a�eY���d�U*�It �ex[8lea��e��F�� ŏpX ��@� a��#ant��ݘ5 �Y��>�Ac�"���3ABǒ�=�, som5 � 5$sho>Y fig:crossIv�- ncom��� �$E_�^{labF 400$~MeV!0"-��*6��fE�4c>$�/e soft- 8lio& (}:8 A�0$)�5�px(&3/q5 " wmQM18.� brems�$hlungY�5�iF �6$�46dev�;�-�� a7tB#,�0�"awAJstudy : >|e�8f&��usefulK "!P8��6<5���eqnarrC=$eq:R1} R�� v!��15@ gma_\pi} � E-�Mz*f -d�?{d:"}1ndS  $ 3 / >4� 2+v=e/ s�392ed $In ��M�GE* ndA�G@�zanu.M6f"�R;� ��we &���:� fa�asA� aileB9R�.0(�={ $R$� U��;C)!J�, lo�$�%ems�=!Re�1� �*k f���:t�%s�)y_EFT2obe�:isu! orem��isA�a��e� �>,tch+mF)�) exaD;�oughout � c&� ,�>z�. !Qe��eR$�� s cl �0�f�+y� s+RiiAa in good J� �;�U�VprE7-�Kot6:� .;��>tb�V�gE�a�F promi�#se\ �U;di�8�-g�mAo6p=-� Y� �<9��d�"AB9.\!9�8 6�;9It �9s&�9B�&� O)4&"  (&� Y�)(tHst �� F� it;9a��6��!@BiR���  %K�&� &t<>}�ed�. BM 2 �Cep"�#cm %\S%~% ics[�H=9cm]{gapgapiop_eft1 � � Jo�#� R�W+;Bi�!kV�\g�6*�%8&�*�\:�  ("�. $e/2"k$u($Top panel:}Es!yR_U mm&?�R)$��-s�s Eq.~(�!��{Dtp=B���b�Middl�@� ar-2Z�gsyf5yCCtvv� ���d�+� w.r.t.\%(Z�A���� ��L-�=�o�a�$:� = 0�+rrB+ ^aB�=? Beck�9ge}. Lf7=�cir�V< 9=(�1iV),W  $>��>e �=N$ �;��&9e�6/&�Z6� %�IA \+nt Be/1 22 R�>��|>��barl�,d56ly�12)&s��A)lsr/en�=[E9��*�>�TM���A4y� Kr� �eJor�m'ed (s�"�O�tV� ���*esBGf�1mzI s!A�*�9��>Ev��J�92?. At��>7 a��~�9b�e�>^ r�I ns nI"�a��yb1,1��t o,���_�1��Er� �2cy check���B�yqes�0\Sj�cR.�0�a e $. Mechanis2(;�$�&�! Born��"�-�Mr�F,AJc#� !?�4i�@ *I � v�B"+y*�/they st3�j5�at #-BJ%Q��� ��Bid� main sour� c��?'%�%?-/� a%ne6��ea���2[I��Km�_{(d$(� i�D� zeroKa x body� � refl � q� .�" plane)��s)�� osed��2%DA a� que.� to enh�M!.? *�A�ande^G^C a+�hV>�� �� � -.,MSq-_>W�_rE,�8l ALz� �yH�por� aJ� % . O�f-(l���2I@urFsupk�is1�z,E��Nsi3a�"�U�� A��� :�A=&b�7 fimz#&.sun!�N9  eny}. �st�A� ���?:A%��#�LE��Ac�, y+�zI�,A#!!��p�N�.�/%NLo�5z"W;t�AEFT.�e�a ��q� m���L�^FL M4 . To��>�A�N*� J���0the2��!>� �Ad2�LE%*� . D&$u�;>0na=1� �"==y;_� acqu�2(A� R'�ut�d��0%�Ep�8ak�%�cc63A�!�M/�2�}$ e�&�.�C� ��� foun&�3 �:�>`�-��UL��2� i�uQ ��P>����}�to. �] 2Im�I �Pdm �9Y$��Mi�*\9%��aL2VK�, cruc� conne�3 1�|.�P���$�̉�A���* ��?A"�!� %�"3Cac�!Us$SHthank Barry Holstei�  reMg��+�MoR��)@by DOE�4`nt no.\ DE-FG02-04ER41302E����LDE-AC05-84ER-40150 u�TSURA �,A J�F=To�, y. � B� � thebiblioAy}{99}ibitemkN@} B.M.K. Nefkens XIe�R.}, Ph�NRev. D �X@18}, 3911 (1978).� SB�N, A. Bosshard�P 44}, 1962P91P Q.p |N D.~, M.~2�U(M.~Giannini%xPE.~Santopinto, %``Ine�R� �/ u B�bŧ�� %"�6,'')*\�I .\ B)-48� 236 (2000�[arXiv:�B�-th/0003035]. %%CITATION = NUCL-TH ;%S1fKo2 M.~ :n%``� ѽ u $\to�:0 ' pF�6A of %ao=+��=A+5)(89}, 272001%2>$ex/0210040REX ;.�Q�$1qu2�B!"�X>��N2��T�67  pi0 %p5\BC �6A065202�E�M4hep-ph/0105060>�HEP-PH 66�  W.~T.~ e:$S.~N.~Yang%.D! Unit�/� ��^�pi�UP>- %�V^((71}, 015204%(5A%.1409078:B} R. h, B��, spokes�J�2�@}.4�wL!�nB.~webVT�ap �R.�o$Woloshyn, �/\m�146�1067��<2); I.~C.~Cloet,!�.cWA.~!�homas%�E� $(:� sI��Y=dLet��563�m57%c3!c]�(lat/0302008N� LAT !~��nM F.~X!)e,!4Kelly, L.~Zhou� W.~Wilcox�B�(B�^ e�U�C method֩ J.~GtPre/�#ini�2d!~Svarc�N")s W�C�\ Loops�.\1��� 307}, 779!�8�".�4NUPHA,B307,7796� G} V.~&�)%>D.~R.~Ph�\pIE"h]��:a�E+ɢ!OF�Y of�� ��eo��é����05��E16�ͦ212024F�b��MoB�[��� ex"�D�%�Zpin %Nabili�Q!��ibid.}����5B�! �305043>��� �U��G W.~R-5)� J.~S.~Schg:erEJ On A[G4C Of P�PcleMZHalf Int�l Spi%�2P �0}, 6~ 4�M.�(PHRVA,60,61��PoG:��Q�,z��� �Sng !`*LH��Ue�.bar!m2���5%p960��199e �o ph/980228RnPH �5n1HJ"(R.~Timmerma�9 %``F�Y�!qofQ�9 )�2�U�48B�q!z 0422� 1999�@QA99��b� 2�DPeH S.~Des��F��alxT%� Mass�_!� �K5odynamicF�-�62�� 0503� .� �T� 11>�T� 1I[9�6�.� N.~ �^a ava7C�� .~Sp�mE*oR]e�Am�� decu%B� �49�h45�w94); >n308317N�An !�0M.~K.~Banerje�;a�Milani5U D � revis/c (PT)�B�5 58� 1996]>!}a 5083F !}� �=}�) �/6 �<"�a�R A*�Sa0!{,Gerasimov-Dr?_0Hearn sum rul.� L2h60a+239�i4F�040731Bh � �y�� d"�e )�\ class[ams�\ ,amsNf]{revtexfPtopmargin=-.17in \odd 0ev�C,7*Pg�!<165mm \headsep=1�-h�%=2ex 0001�U*6=6 &�g {\eq}{\b�'uŔ�f2$ qe}{!R�.B"cen}[1]J�E} #1 8 }�Rh%�r}{�rJq qJs sJR RB ea} �mm>�epp��g^+Fz0>bfk {�i2Cbfp j%6 prc}gQ�}F"d2"D>|h}{)1}{2}B@th~tiny .'>FrtiH\/=2>i2� caloPcal OBEtotE�nDB�ka!lmbo�B bolda8 $�o$BVb1hatZ F5�n�oN;f)V: $}} >B�*ijF_ib|onen91N9�< �ka,9"M�F4pim} {w^-$>rpip+J�:Fh�phiBQr}{���P> np}{Nucl. %B�prl6B��J('"6�nucBl6"bfPA�bfQn2�ppi p:�m:>qb�%Lar{q}q} \usepackage{�icx}% I;de �1 files2,l'ig�Cg22l \til>� 8�GD�%ckr"Hind $ N S" h�ja�k( W. R. Gibb�R. Arce�q.�k*�k��%� k$ Mexico St"!UniversFJ,\\ Las Crucp*Ne,88003, �k��_a"7k Coulomb�@"fc�7� to l&`Po-� �]s�$$p��$oS:�,p0 I`R%�j  po6U:�s,���r�k*a )A��,"�^~A� ��m@H �n pai �r g in ��'Xbreaki�iw=>*�i \s�{I�Ig} >Kc=V�1a key el�7)derstan%low�1!v -v:��JturHf*�i ZN-4"r!�%�� c1��9�^ #E3. &��im� %Lof��?6Z2471tgr��JTes >�#re�ed\W, gaklYc,tsinos,gak} &�+V�9 harg�&Af.��MW#p�% . ex�$� &. A9U6w, 8\%1+2 was �0. Piekarewicz �jose}�/suglaT�9�V# %2!Bb*�gb�quark>�{TF �dE�l"5!c aQs. �DUKmio�3*6ai beyouh�e�&.$ �""���Lm��"ces. C}MA5thesez.�)Q )�!E2p=ir.c )�g�C1,2,zhn}9\!efg��by Oadnd Rache Ko}. eO�N,v"g(jmad 0E�(k$aKrefer�M" s GAK) AS�%!`�H�,.h w�$J6rpI��'Fit� elf[dm8/.��"not�h��ly9^�Ia�GkXpur�%AutLpA�D� m. !=unbrok!�b\2=#�F*myd%pV�b"erm"@MurA�\eq f_{�6+pyCarrow  }=f^� 32 ;\ \ 1->1-p}-L1}{3}(:=+2 h}) G\ yBH0nH"� JO - Ot/F(aN�-n�) ) \qe"�VYP treat eac�g!�eJda�a \et]4satisfy a wave=�$ wWc�]u.�toZ ($V6��@m F0 S}FA�F ^+$p9�.]i�FaO]glJ��WZ�k! y �Vs�%R�#i@ m���#nL�6ez S1 �0piZfp}Je}=)Y� , be!a mix�$aSF�,�!e/ �c��rcq͔��on-�=a�%-{\pm}$-- 0$ �s 2tBy�F�.u')� a.�!G solu%� )*#s�a�*ai� �]�C�JKɝ S+ti�newpage� q O T}_c�dc+in2aT:6+ e�i� \�i) J *uq{3mt:7-I�.F0= 8�ir�� � T}_0r0�rrc+ .6� �-6)^� ��w��AB si_cm��&zc)�d�"�OrE�i��>aE�A�KyuFi%QA M9g� � e_W �$ors�8 l� !4�)� d.amc �2*� �dQ� d�`/A�em-$�(�>� s en�^n�n�C:�*%oZ]�C1n .)V�85�&,Hlso��la�Dby �[t ���true �:v �1�or2�� � |=r0 ��&k'��0 un^ d dEfi1oG.%'is Ip�Z�8 qu�&� (by Rusetsky� r �hAlthougZ]g!�al��"oa�xs�%�+imilar, � p92�)D:* [�,�,(�5�,B�k[�z�d!��l%��Ve �!�e53d1�(D&�@��d!bi�Q�)_us, vari��M�I4A#� amQdA!a0A��(i Ine�Q*5 -kmsi"�appro!u5�!Y )�n�Hta, $b}. Sauter s }�;�G7Ubas�} I.s-�� lyE�\s� i�hng��1�h ��� �oc{F*s6yal� s ��� TA�:�cB!2�y3Cm"�%�mk"c �ri��5 of�Q. :4� NORDITA �-'9/-���advantazE; dis��9���v�KA��')[�Dcu��in�E �> 1av ")��+'?9{&wr7 }� > a�!?.inJ� ��!Bz? forward. �66�b TJolvbBori��*�A+A�obx>| ph� shif!JWk]�hull&�K�" �/s A5ything,$n o"�^ d�ga��8�`Ru?^a �q9�. & su"+i+�valKis�M<non -fli)!{ "�18� A�as�f(j)=f_c ^k ik}\Xc4{\ell=0}^{\inf�|[($+1)(e^{2i\"0 ( +}}- � }}) +3F0-Z0]P ;(\cos � C�'}� � g�&g 2^�[ �6� �-}}�^16�qe"E .�4!�1�]|e�$=gI.-5��no�TR&�Gt�'����p �.*I�6c�=twe cp�?l (pc�Dx6�9A_b�!hv��,� U QW) O�7 nite��4o?on!�well.&� .e�GAKjN�%ty�1�~hZ�E��3cB.�pZU�uJ� ���l~ũo���:sl� �A"k�). < a�� judgl �0nhTe6u!�&�9!A�- M�>�&-Nsee�-� BacfP79 it.���I��X2�at����/45 MeVI�N�I��:�8T�z�ally5�as�v5�M.3o�m�"�a�d�7*�KofɆuri!�,�Z1� ces \unde=mb�AD6(�� seem�� un&$�U leve�%�t &S 0 -J*E|�hangeN/&7_�%T�&�m_P�!l�FsF%" "�em,"E>�1&?�́s. Not e�}���f2'^ -p�nne)���oF�0-��B� �)�M�"9!�x=%}ub�!M�n} �k-K{2E��!��A� fxk6�mu=!�Z�2}�":M�>a)�\� pete� �AduA�!� " eZ-J$6x,�rgYKE_/ g-i*� i��T>� a 2�2p"ic S `{x& hVo�"�""j a�~-�nd 0$n8 ��� off-BT>�i�.? �.� !�L�tYK 0A(;j& +iK}{1-iK4\ K=-i5S-1}{S+� Tp u &�yX�`AE��=�e?� �J�!�$S_{11}A� trix1V&Omultipl�c(by $e^{-2i2G}$arem3�acpW`C�� b�D 2�M�5"�� KV�x!f%G!�s�Iic: �W�}for�Bto��iaI&I=an ortho )�-�� a�T{cc} � phi&8n \\ \s &eA�9\fUK%r& 2}\\212�L�&�\\ �z�=n�(1&0\\ 0&K_2Z��UfC \tan LVU.]%�}E�1�v�*w cm�a�=90�4�/ fig3r,�a.*;]� �׍�� 1�Q�A��::')� � �|]&A� 'm al.:�4aL �do$ 4Tromborg76"b|K�Y�atr6�[7"�Z"�$�'*�$ �� ��H�_| � ta�^� B})+P�&5-���i1�� .�phiI �U.% fig4A>$1�*�%���́dr1Ex�I�9�7A\�!an����i2olQ SxaFiH \p!ect�!1"J^�-!V.If �!d%�E�um �x� $�H��a�$E0ɍ���~-\�g�_1$E\�Llta_2&-�$\hS X3 $. s�k�< e:"���vaA�FQA�o� �D�O e�!cm �-�I��**bs�1$&n��ull!�PzEJ$%��#�io"�~* ,i�B�&M� �aJ%�ify1 5)�#Y� 5k ��1}���m{)�-/h2�h��3Z1f�[%�2:; �&Y�2y�0-^h=�m{ _"� B�K� !0ba�()�!��t�o��/�by�#vauaQ�1_i)%�E�phi0H &k �*e�B�.Q�I�.��uR� s� ``h'' (�"�I)N�� >� � ��"�ues. �Mg�  )�� 462�~oas�no5*�. ���u�0cm���.2�L0 fig5��^+���ܗ.LMH"j�1�y=z,� 6-Ip�ہb%�!>%9�>?�aB�?wpO�xy*�q%��*�}z R��(3*2� 's�-2(Z�).}�s65�rD\b�2� �pN9ŗ)��P)�:r6!�6"1�$Individual%E�U/jMe�� conv�1a�!4�a���cc��[ �r#AvhopE1|ȇYs�Lbama*S��.� and �]-���� chooz]��1^�G%�_2�ap��2�%4�TE=$K�S� c3 d�hzM=* T�"p�#�7 e'���S_e<^alu� bhi^2$�0 sear, �#ez*C.���R��!f//!vwR$��;�� ��z}��* %�� $K_1-;K�8Z(eigen6�"��an��v�6�fo5 ���\lambda1}+K_pm� ( - )^2+42}^2}}{M�� }\qe'wnow=tN�Aw$ minus sig�!�&�jɽ! 1�Z� z_a+M3��>� ��_�A�Y� &�/e&J "�e fin�$ur �5"`P�Ka��(  �0!�� $alent. Two!� them:)y =2z-K_1}%�2} J(!vK_2!�11}�Q�cex�>�3R@7j+�I*� of"�A���A�"� %� s�"dfUe�!�e�of Frlez2uf�[6l"�H�,R��1l�i�*�IHGA*m" :chain-�� ?h%�d6I�Y cMbgd2}e �&m.��s�c�2S�"� 9�rK\�n%bj :u8j+Q5Sץ7 # �%! .Id�-�1 ~5�v*WM;icult�)%�P$_{\h}$�Imhouin1) NE<r�n� fDi���Z!�*Zer�  in&P$�K��m�+-�2oc�*!,���$ 2$y,�D2����H �*�"�'�18#�6'5;a960j�%��"` .t (a3�&  11}$)�. c5��[%��,BS/ l2P��!in���2B0} must vanish� �h��� : � Cz���1}=��5 2}=0��_ }%�);4�si�aneousl)/�Bt%=� {e[#syv%U1���3 ��2}�22�4!F5��/v� 3 HF11F22����= es. 3| �} 22}|%G-���$ }$!�hP5H��uZ=�,v��%�$�'q/U�%�b�n�:��]�!-��#f� � i{iQ 5� 0fAeactual �S$2���n.H _+=22#=� 6�5E01_-79�J7u*��A26e8e�g&/al,� Q�Q��E�� NOT 6��\ M$%a�e&ih� n�+!|e^�,oW� wG]M�~]�:� lookw!n�]� e5ofe��� y-�# �i � q,d>4A`� 5��i�E�|Vo�CERiia2� %��~i%�a� A�v E�1K$:$  ngesc �,>�Ef22�Z��.&ʋa�=p3= �-P >���!�! Q0e.5�A.yyE�A�23�ׂB?+� ilon�� 5�=B (2\ D5-2<� Y�"�6T>-incre6!=/�8.�a�Q$ Z!ca�. W�%@f�9I 4>�1{\o�]e�2`thau e�z� %��L!p oppo4L!hZ4 , a ,&[3�{G>*+ Kz�2�de�g�\���>mxof��� �r��%�K_1=\hʼn1}(1+J� hi)+ 22}ȈE�2}� + *z�ph2{phi_0}��$a�} J�� �2.�.}2�2�!���{\v��B�c�E�$JiPE�X K_2$ T"Asinq .!g�ZY#&s�p.%T�4� ���n-&Dv�+ S�E �by�: o�� �E�V_ c)%[ #� �.se2onglyR%V?�(h*� �'a4.�2���' f(�� e�,� �3 farB ��a�. Oneŀ�ǡ�-0as&RLaS���iU{12}$�aŞw �z�5- 5��when �G& $�%eisc��� will�,dis{inu& Z.?-'^^*�}: !�&1�mai[_o%��i�$�~"�2B ��G '�nomal� �|�!g2en� ��|6M��D!6: a4I: �.%!�5Y��su� �.�th63 o%q��o?��k>xf,^ gV�A}�iitude-�(. �Ucoursea�i�a�'��2 #i�q(so (p!�� �gi_Z may�2AI�eeriou�P��|,sm�c!`fa�e at, P% w6,I�za���}!�ͨ�k�!aY� �"IXso *�z$�fE�atm�� J� a2� �b,i�eԱ�'`*Sy8arbitrarily clo!=�'Qc!ɅF��m�'9�U��isen40R��!:�9r-������)"�YW�1a!�>#�Isenh�he bT�}!�39.4 �*Oe@a�� 9at 10.6�(2 �{��i6<&!P4�Pi$~:!�bmeasday6�1BvZe1v�~f1t.e5d1T Bagher�"�"2\b %^ 62.2!5.J]V Su� �=!|45%z9CS 9x5#-n^{*�]`��F�$s} An obv�W��!I�.�*r&{s ���a  �XQ-�B�/� 60F �*0n� ap7�6�O i^0n*� 6-pgG��de��ye�"met"O]&/�6ri!;�&�'S�',�a�6,2}U ��2+:��JRA26�3l��� ��l �7m"Io� : 8�wher��&e2�&�7*� %�. � hi� ,0>��.�ed0���S$�I�P$_{33^$=^al"��R�jE!��"1��6(&y" � &�"یJ��8#��-�LaUy|l.+s %hZF'vk dow� �6C�]* �.B�.rfor GAKR% �@ &�0| �a0u���.1, nd�j�vt5�.�I]g^ �S6�:fJ�9�!|)�&77Ec���2j�*�ade&K)%�em�oo٠ E>n�Bb}р lso � �%�!�j�2dO"�#=�=� 'u�"�y (�3L3W}�,�(u� 2, 3%94). H���%f>Oi�% onBcal�I�=&�^g4�Y����E+>'_ 2:m����/ 3c�����] �;�4 �E�� �� A��8�� 2C��AV.1��< � s �ug �6AL � �o�#����"�m&}ws.5�!�nq "�P) &� d^Dv�!��U&�=&� �n �'�� ``n��n''.�!�e@%�!%6�,C�6�%#/9�Es M v���>�;!earc�@s6�)#Z�$!�>!R j�Z 27.5� �:E�< z A�oa!dV�Q�WgyJ| N�65&ing��TkD)�E�np$!5� : �Ca1\7� b 6��ŵ un-���H(�') l' muI+�Q�+.=�N����ae?wj7� � )�;�� �>�>%%O s9 !�d ���ly �2 Z)u&�9 � �1���Z�)fi)^:��  w1v!9h��x,e�r��:�&�#%�ofn�F�5 ڎ )l%9� aY���!*-=. *�|E�A7�>� �: �9er. A�H&u��:�^"�."�&� �e"��*�t�I n��coe,  ��� LegendrW=lynomia�/.�i^��ts%�n Sq"� ��sP� mber�z!(<��@ i�M��x "~9oiq�l.)N�er��"� �X!�XEQ�2a.a.�fjo.�of� 15\%h5��"oe��&*�Q"�DeD1aF%6�Df�&B&J�D1bN&�$Left: Zero\=>�.:��= I��<,n\ ndR7 }. R : C�Va^7� !w$^1V-p�6U�W�]�}x� lid:.*�), f H -dot�,N� } �!)&b-�!�n&W��u,� )Bs2�P 5�r3��>��)k �ite� deep)im 3qG4��. �K� ڀN"��R u]a��lu�@.�iy���isx�K not;%�0?>>� beam�ium "U�<ed�UI4<-?Nb��M� ��AYtj�� *5Ew� 0itzgerald et "0f��o �{YVb� "��Eꍝv.TJ�5�� .� C!{canѶ�Wa�_�� a��-��' !lm���t�Ua{[�A��.% Ze"����P� litŵ�<�j�}zmv!�miE�-�C.��^��I* &J"��F\\pm"~��� 5�� . �ignifica��5 ����-� � ."�6a!��Bce*v s�xj��rPe*����"J(� ap�bs 9ra�u6���AastH+9:,�  � be w�&ZA  desir�Eto&�%6" aP�� 7)"{���� ��4Sxim�QCD view�� 2��B6inj8 (Ch��A��]� by F��O Mei\s���Sf� y� ed 6!Xio��� �o"�7�� . M��I�= (3-6�sv�Q�ntA}"� X. R�9!i :� o~�.E ��(� reshS�f#EDU�)�"Γe& p*�2 ��H�q2irA'aZ,� q R_2= 2u+>�^ +p}- BU^-p} -\S$^%0n}} �_+�_ �$_�%�� �� A�*;���K�Q�� �(�B&zc"�y �Wuite[ !j� K�!�\� �g��E'1�N��a�I��E!�ir W� �5 butE\Z " +)��d"�2��N%�d0W��})t to �fmp� �H��>�����E,(.����F��or $)���&dT�&�!� S� �,�B e�f�F�1���� m���1�Jow��a� � m���� �a. &U2�{\�F"- �(a�*^�(h�b�K�%mV—\qe g�UoT# �^��uo�*�9Eswe�+�C� .e9��'mh B�'! [ B�d2o3/mz6)�R�M. �!�?��� ;A�F�!R9�W���*?�$. ��e�)!� wo way��%�`fc .6 q %T 4�S��MV(V}{2i}= %�v 52%T.rV!N}}-1): %\� @�-nc�M�c6�9N�8p6O2FO��2' ON*6) ig12rS=9� Za��� $R�)�#d��MB� 1��>��&� Y) s (r4)Mqf� 6 ��X� �;)� �4ed] iR �A�&. E�e .P"g>�4�C6XV.f Rz �, ��B�a}��": �~1��!�k B�sam0-h�n�(& ~���>��.H*��Q�rF2?M�.�n)����]!�� �^$Oat�%#S5}\�4)�.p]��",sM�%�=) F� fi)is ��F�Wull} ^/4|!&�%3 5i*� r"�4�  6B#&4��i('�C��,Q� Eis�" c!xdet� rZ�!p+&��cM e0QM� �-6"M )_*�Bc6�'F)wq�4�i}� "8]7O5"�" of 2)�AB /%��%,�p haps!�sa�H*� U7X�&�,�e� has ae9?�nGi�b PA�cor,�MJP$_=$6sh��a�3��) repa�* �  X�1F�_ V��`[>X`� b��# �E!1�� 3--55�c���# "v �#r�,�!int���G!�ʎ�+!.v+n"Td5�do%_;�l��C����*�� _ s8an"� !WKJ��a{Cos a&�1�Y(q��)�I&� A�2�Xin rough��� ��"6�ؔ)%SeD �&`a���B�9o}�{ea!eble&E$� �=� �s�a�&b �^ S)).~��:�:R����d&�>v!� .�=gGE���k���V+��Ai1��Qea�:\$.� 2[#4%AV s>��i � q�c �ar�Ya ; erro�!�2I��E�M�&�V Q���be/n�gM�! �%51Ji��&� � z4>reJI�:�g �/�Wy+�4pn�J"^"�0�&�h�.�7�T-5�� too�!aI6ky�be&��-,��A<�;>�<�U��Fh!���b &�ߥ |jec[n��Q�/�aE���gl�"So"/ L?d��\GY��y[seY�/����G. C. &FsUlfhssner!� ��"Umanus;��Qs2SorA��N� al S ce FJ ��&8act PHY-0099729*�.Y<di�?��Fid� F�UK �a�i%�i�[n 2� �./8are6$n�id�*%�"�eUano&H$��And sh.Xe:outU$%|y 5-10f>����Vs, $TL ��l�� ory :�Yin#�$c5�)s��&SW� HN�PhRgShRgfW�&zP+u[2=��US *e��0� �a�0T}}{1+bT+cT^2"�C4eq {\rm For\ }GU}M a=1.0319; b=2.865�10^{-3�<c=-8.0.7�:�>[3 [-0.5197 \-5.37.B\1.939.5]F��e p�j:8 �_{13}=-� $0.001806 T6R=(1-(414 T)} {1+1 T �K33�t0.01084BH9(85 T)(1+.06ZV0.057 T}Z00436 T �=��+.�636BbA6190 T 304T^2[|13J�12U19FU;��� �01J� .p-Qt*Y���A�'.�byE�a�\eq�O0+}=0. �0049TEC_{1-}A009�045�O1+ 185!$00397T^{1.MK��mb��J� � )�C_ �075 ��\�A( 2�1�33 �$0195T^{2.2)OA��6095.�\ � p �3 �067T^2F� Coup�*Ch%\R�1�Y.��Os�O�>8C_1=0.753T^{-\hm1114T)� C_3Y�6192( 051T)}{1.%299M�A&d.��7.9}{%�3}}%s11E�26�!>Aa"*.$ S�j35m�a�03T�+.0008��[ 1745fA�?�W�*(2}{T-60.1}\f> b3!�19 a�13A� 0.728}}{(A�nE�e�- 2.},<|155V~=4 -1.2&?l148}{(T+4.3)^{0.95}} -0.4363�.h2.0e�u%c6d2/2m�1n0��3!� 0.4}!�038.q!�001O^4Y;�48!�23j63 6) \phiQy44.!6!l37 ɑ U�V�2}2 } B i�T� }\ s� !))1.1�!�6}%56 �2#3E�0A�!)4�� ��fp6 to7 005TA�0 c=f�93613Y2�U�> \�Z1U4��01�(1.9�Yt 2 z4��8m��-�!�_s10 �1.4q�3!�14W.4{:�}D6A�![A�-1.: V;�2��4!�-e�4;0s:e ���&70�!�U-�4I��:6e��25)!8�ܡ&.x5 �!�l!�006͟%�A8A0�;Ji86�6�9� 51I�29� |9^8}{ey4�ix-Ok% did .�$NrR�2 C'&m (>� {3002ޜ�( W&s�, Li A�lW. B. Kaufmann, \prc 57, 784��8) i(� gakl�K(l 74, 3740M5)Lma��} E. M �6, 301�7.5j�J2����� B 358, 27Bqe1} A. ��,6y*d, Rascnd!%p S. Woolcock, \np A 686, 447Ҝ1).;�l2�lFl63 l.�*�] H.*T5, Helv.8� . Acta 48b�1��2�o���2hG0#sheNJ4, 16!�76�"Uy!ipy, Pio&M�Newsl�0r No. 16, 125H\Qp�{B. �^, !�al�i}4f I. OverboEA$d 15, 725�2A Rb}�S2H %I51, 5e#78.�svxE�x , Nuovo C��to�� , 51�69); Ibi %Aa'3%O5disp}A�Hamilt,�2 A�.�,np B60, 442�3);.10J9�N27A�814); J. oFortschrQH23, 21MC2]>�,n �AnnG,(N.Y.) 100, M6vMBLR܇E@(NBI-HE-77-1�t publ��)�og} P��SiegelR2\��33, 140�@86.Bp!>T.'p� A R�� nen,4J. Kraushaar, ً. Lovf�/���As!�a`$. Smith, D��ll F�>te5 , M.ERe��GPa elle��L�B$hie, N. GrAR. Ruie$c 41, 2202=g3E.�Sx(Pocanic, K.a�Assamaga �P. Ch�K.� Ke��M� rsha�R� Minehart,�,C. Smith, G.� E. Dodge, S. S. Hanna, B. H. King and J. N. Knudson, \prc 57, 3144(1998) \bibitem{isen}L. D. Isenhower et al., Pion-nucleon Newsletter 15, 292(1999) \b N0bagheri} A. B , K.\Aniol, F. Entezami, M. D�sinoff, h F. Measday, J-M. Poutissou0Salomom �@B. C. Robertson, �,38, 885(1982�(fitzgerald}k H. F,W�er, J�BowmanwD. CoopF. Irom,!f S. P){'$J. Leitch,!�$Piasetzky,Z8J. Briscoe, M.! SadlRK.Smith�!� 6�34, 619�6.rfettes}�F AU!Ei\ss n`\Ax63, 045201(2001); \np A693, 693 X \end{thebibliography} 8document} N>\�class{CHEP2004} \setlength{\paperheight}{297mm}F dwidth}{210mm} %% %% Use 6d<[boxit]{JAC2003}'@to draw a frame w!FTthe correct margins onoutput.jf acus:efor US m� layoutH0 \usepackage{%3icx�� MACROS \newcommand{\ifb}{fb\ensuremath{{}^{-1}}}�� VARIABLE HEIGHT FOR THE TITLE BOX (default 35mm) �={$titleblock1�35%`\begin=� +|{New distributed offline process�`8scheme at BelleAauthor{FE���!jG .V4a hybrid disk%��-e Y �!h1�*1.�� RAID+ ks%�� 6G%�is 45!�, (to be soon� an�$to 1.2~PB)��leU-�� s 2s� � qaA�Asre)aby� SAIT�>� 1�30-��16s:*�8-� H4~A! at 2.8U! �%�!@��%Xis� omat!�ly mi� to�� ��HSMm� . UnaH Via�le� "1 `�au.b relo�w�Vubya�rs��y�C�Farmsa�hee���? � �three ��PC��:� � It�bAj�TAmerf��Bxternal"0grams (module dynam�O��as sha�yb�C� tartAQaLK � job.� Zw�Kgin��endq ls,-�{� hist� definW� s well�a� memory uti. E� � actua��t�I*� . Sed l9can�O��t will,AH�order�c:�!�.2writte!� C++ (!�soe 1 �). Fin�JMC,supports Symial Multi �!p(SMP),��.�par�%�1�of ��a mI- J or m+ne��t u�.=eU_ a:E��� NetE�SIHM%��� NSM �!�I��D^=� exchan� a TCP/IP�� LAN.��v�esAgn!*on�p �s � E�QKacros �n �, or sE� eque�]!�messag C�  o�����bEV�=.�4,angle=90]{nsm:���RU��nsm��PANTHER!lmat-�input��A;����,a�q�transf� NM�,  O umZ %��@ e��"�!�aX�� M]A6 � r� �s (bank��ue6a{�$dard zlib Nri�A E-re�ce ��,e��ed in�toIw navig�1k � � ��( ����@(n ASCII hea�kBi��bef�f -|.�rs may�AF eir 6U.���}]add�v�[��describ�bove,>�Jvarious e9he�:"c"h � A�$postgresqlEj�-|� psql}Qim�a$ art �./relev!to>�&.injs: R�; meta-A�2`3U�) �"%�;� � ��;"� -\p/ � �����%\a dedi�=/k mirr�eCthe mq�)M�.J� |a�ve)�t��depend�o � group�A s (runsM pPA�is fuS /��a ste� Perl �'0pt (dcruncher |�a�s( � d surveytglobal>ipA�_*[ D*+!�<��� to~  e," � ��*z !~ * DVT that�gi��e� m� A6�� A5"�a��`Ec" PC[(PC1��� ��on .�E��B��!�*u � u� node%�" 2�)E�� �a:7Non�M#u re�0U I �edi$�=oA7i� ! �on�a^z�!o� s it!� �t=5y"K !$synchronizi� a��?us�2�ma��� J�m>� ��� 0.8Z� %�:� A2�Q�Q&�  Wait 5�ut���e�I loop�end.�2KS�'O=vL&xU in-�greatlyʼn es, 9�O�I� �6#-�� �0!�of�^o �, E�r1"# �argA�Z knd slV/0aP��*M�H!!�indA�4ly�ionalA ! �#& ��� algorith��l r�%:�)We�:e ��i ��� ~�M s, wG&�urt�b97 �N�zRv> random)*� � % �ext�,, becaus%� se � %3%]ces�s s�ntio A�:���width2�]-l:�$Time evolu!�Aza5Bper!\!�-"�L�  text��det s)��=�B�!$PERFORMANCe���DSTsu>}P*�,� �o,tO,�ol, ��M1dead-g$!iods dumdelay�#�����=-"sub�-ed9& �e :&� taskS�� �-m�E^.nh%ll �` �"c)g.A-to�#@-�& *��#e &nh�t0r ruA a�� 18, �0 ��s�*=one) 12 (56+*!L��Y �+�."d��39 4(-�w-?a�)�* ,# upda�#-�! � ). 3.3~bK*I� Q �� 3408��B%$"�"튡[4� �eN ' �43.2/fb/day (37 � U�+of 5.1%6� )� 7~�ecutive%�fY�< prev��a�I� K!A�N�}1}~e�.�]�)�isaCa��$ a sl�2!�"8*�p on � halfxA��� )K-e�Ua����!��sb in2��/ebJU� NUR:T*� �A����� �es�M�>.� F limit�*� qof=�,Y�f 0"� heE� l ed�� an e�� ��(,)�break-d��1.9}- T��] ure-( "I�}[����m*�,F�nc"�11J poss< ] �b%R KV+ {|lr&e,W"rEA`mun�| & 0.2\%W"\\ �&��8�.*1*f�%>& $<0,$T�NT3T ,�,V1�" [ 1� �"Q,I7%� "5h )�2@A.& ]jA A5��JC �ob� db2>Z�6&9�� issuR si�m" heav�A�����`icu�at �A�X U�m�&���%ll solv�_iA�su&� �%ed*a#a*k&+ ����a_� s��iK�a� _bot%8eck�F�r.< _ll usŶgfutur6�. band��.� T)���z�-��+� %m=�� �>�oes not�mAQbe F)jo�$su{F near�A�"� NY:se {�, how!,���(ly hampered �EÁ�&CONCLUSIu5� y F"�HI[�B��n�� day�seu�suc�i� �mhe 3 b6�.7ya54"_*ate5/_, 5� sO7x E�.�#� w"8��. W�exp9,&��o6*Z4=�8: �"Ue fur� ch"4nges\dots Room�Gim�*�ebAJ � stA�re�;iE th6�;{9} %gS 1-9 "/s %��7$ A.~Abashi�J> Nucl� str.%c�70 S.~Kurokawa �M9MK32K�0,R.~Itoh, ``EA8e�aE<Real E]3R�1&41 *%6R! >R '', Con��H,209, CHEP'04m ��, N.~K"�:``New� pact6�,mas�1ag!�� ~Fs11Rspx, http://www.&{.org/=�2 PlatO*�--2@ ! .com.>k >)s .*sun'� / %a��>� ��C> } `�>R>0[pre,10pt,twoq6, Dpacs]{revtex4} %:&>4�=p�1]{�8} %.�=opex2}.�=([dvips]{eps�6*�=flo�#.amsmath2Csym�4=ps� x6*h566t�)���]!'.:>vrr}{\tbf{r}}6X>vEEBecb}[1]?#1n>a�"�?,style{apsrev{� 9�(>�ar absor6!�dispe > fiber-Gr-coup� Psilicon photonic crys)9mic>!sonatorK8X>Paul E�Arclay� !{pb 4@caltech.edu} 6K!�$k Srinivasg>Oskar Pa�2ffiliaa�{D%{��� Applied PO4,, California� tituɡDTechnology, Pasade�C0CA 91125, USA' date{\todDZ�a"�>A �niq8�"m�5� �9efficie�%�%s l�"�F4*"e% le-@<��(%�%�a<>$-Q, ultra-`L&e Yme,f�r%�4nt cavity. C @qua�>fac!�!T $4.7�; 10^4$�mea Ad, ���-t=] ED� 1R 4:/:0.>B+�c0� #��(nelk steady-stn��- heF�)�studie��!�bi? �!= q Ş� �u s= low0$250$ $\mu$W,=.*� dropR":�$102�$3$ fJ�ed�K? . AId�ty!@�ve]0-carrier lifeL"sZ�I)U \sim�4$ n� �.estimE�f>> �&��>��fM9a�s.�RyP .YB& IH7a�"` sec:} R&Bi�d.�mQ���%��!�{� planal6�sP!)E�capb!�L o��#� m�to2�uA@e�i� s, b4*lsoJrealizA��e1�1�s� enough yA ref:�-3,Noda4 4}�en�,� in�hce,ychxstrong��ws atomic CsrLev} �+m�du�'�6ntum < �Yoshie2�Re� aierPeter}. �enhancE�a�OBlM� U���"�"�d!��/-Jsignific���.�in�%��"re�:��+I�iaha)�QefaWs,6 ha�Nal29 Cowa-� Soljacic2�H$�/*<* v!�� field.iNM%U, m��� ropo� a� c�&��23n1�,ߩ�!76�s,aJ�z!�a�1��5�0%jyIH%rE1 P$. For exaB, d,E-Q;!�!| chip���(-QED (cQED)=jQ�in�;-%source.�Gerard3}�7� )�;J APn &3+��!adevice�5A�� Brassard1E�Kn1a� Kok}alqAS!�AH�"s�to%B sub-��� �>. S #ly, p^�8�륾.�-%��9^;Akcircuit.#Q�3} puAu�m�6o�Ga3d2/AU)�al�"% !���'t��2ly��QEA i�!��ul� t�-Z ��2ra�"!�pat�3!��Cunlike)5� =�Peltono+4Fabry-P\'{e}ro.& McKe�1}�����inAc� sui�:up�econ����:orU%�!9 OnlyS@ P� low-�e�"o 9qqZ� waveguidk4ena�&� e��q�on-e�spIC�rt�($%$ 1-4 dB�� /por6-NabeNo�^ 3}),� -6 laneE�%!��� ingsZ 8-10^[Baets�l�x2[A�narrow-i �.es!C9-�0.1f\� 5}). "Gp�M@emplo�JlE]9�!uly����q4@ a"� (Si)>y via?6:�9��WG2oncar}� is=l� �Z)IC� }Kn� ��Ue�a��-m�.h CWG-q���?B)92�B�;$a�Ec�1a�ͼJ,uL# �$60\%�Kcri�<%Ima� a $Q$-� clo� o $4 B� . ��O% �� $� $!T� , �^7 �!s�( ZYyu�Et$=.���� ��X�&` &�R �'*5I�B� �Ka6��e$"o \U! {W}$"� f y {)(p�+ctŤ nanoBE�� >i T�0� y. Ana�E-�iH�us`'��We �!S� on 0-�FB�NL �}�Waug� �wory b�6corpo9*ng] �"�/ upo�magnitud��� M9^\LowIQ�� � fabre ed��f�- �z-P \PF Lin_a^"� � al)э� prob!7�Aoth��fir�Lo�!&Fna�)�u&a@ona��2�"nN% �`Y�IJ2�. HiEUN%i�.=�F �%ome� a�>/xiZNL1 ��Lod�:Pf6i(}."�� scal%T� f?�_]Uith�Bh&:5F� iEJ��#arL�F! B�Sum%}Qb�.[h :�*<� #=Fi;1_web!a��& 1.0\a3w*�(a) Sj �>��%�MMtoй��'�blu�@row reM�.Bl�2, s!�of�{��dA�t� �0� la�� �Q�e�)en �>hb GN�!�5�E rebI!backward�#pag�$ �AK ��col7reg�z:�m4l? �mb . (b) I�)G.q*7%a�Mh��Jda�%!�>�``e�'' � -edg�qued�B�al�O"� axiq�-�(QJM�fe�!� -=s�G�?"�'a jumpC|�za#u hat{z}$)5 VV%t��$.\��fig:SEM~ %4parabolic ``po<ia! a�:! 6wDU� hole%�u��!U?M�e@1�94B-Q��A gray>� area. C� *�*2>of):�(f%�($\omega_0$)Ea_En.y (,{�G}} = AF�,$\gamma^e_0$�� to%i%�t�:�A{j>0}$ i�ns���� -�orlURb� & .r�) S.w'A�Figs.y0.?}���4A B�(b.� [,** wQ�a"��>7 ca)Q�#tS8RDw� !�alhip. Ou� ,��is �dBU�MY��termin.�WG. L���E��(eI�iź�..͍�0A�:/ �aIHitMU[mfor�u2El-alM�a-KsplDr$ way�7p� ɷ>� so�%� �-P�P2J.�PC��!�6&"� �� �<�aw/-d-=< >���ist�� &squF/��ar�;ir��8 Yfl� �lab�.� is�)�-��sY�%P#�Aor�oa[in Ref. &�"�1�A5.E(:F)E �*�;h,dI�A,8y6S��) �3�e YgTE$:�%��L.KU:N,.te-� ce�$-doY (�q)�@ho)�I�sbrcɹFif#d):s!� �))- i�a�8as�@)C��!al iw, $r_o(�)$, Fept�5�bU� H  1,GK E�m �GT�tu}�!G%�a; � . P.I{s�)B�.2�-I>�e^�'un� � `$cy ($97\%$�V a6�U415 nmF�5}Lu �Q�nec�FrT��{ �"� �lso *F*�1!yey&��Q�!�uD� d>)�8Ia_u� to)X2�ofF�ndAC�=-�� ���)ţ@&�B/�TVj effk @0.9(\lambda/n)^3$�I.�. H�*we comb�`&�4M�rz m3TZ %;..��g!!�9/zP�P�qS�Ab*�"Ao. &pVE M� dkey} m��!s�E��u �� g�e�[tduc}, poi.^g  t � �6Li�C�p�P.�tGf &1JE"a�hI) �}*u eff_q?m E�5F  Spil�2}� ex�lsp�)�tor�`f te�"9 � �E��J�al��pb�=%ad wo:�iM\emph{�9� } $K7^� &ide.�"} $I$: %y(align} K &\�v \�{/ {e}_{0}}Li} + \sum_{j \ne 0} .,j}}, -yeq�ing_f^#}\\ I~j ]FWV�VU! �% \no��nt�S#b6� e[ha!�er�]t�_E�&+B� o$,�i"� ��  A,abs�)�i"�arB� {i}$)i�w5�F�!�.):{e�O)�8�"er $@(ZOa��ng�"^�U� * $I$�a��hA�g�= of ``good�aoaj,�$��1 �a!�as� �b�/ X% MaKuj. A�,@ BJ hand�+��8>��"!K�a�9��e%5y8 5�G���9� -on- :INa�#��>�r"� ���)� �)%H��,"/equ�n} R_{o}� ) e�,(1-K)^2}{(1+ }$<r�-A"5��� �<, $1-B_asA�or���dTَorMo� �!0)w6�&� �� 5=; ull-�a�$lf-y/(FWHM)+ !@\1Lsum!r!�%�i_�f� all}2!a'5�)� , $\delta^ !_i�i� >��F) $F@Ev2S$�6�(�9UA86Y�A�9Z�(i.e.�( ��/�0!u"Eb}�' 6)ٚtI�d,�e�UM��$Q_i+P} Q_{ = 2Q_{T}I�81}{1 \pm \sqrt{B_ 0E�,��fyJ��4ed>I is $Q!�d {o}/.��� ! $\pm�g�(��under-%veR-�@ed ($K \lessgtr 1��;�@ Ov�d,$J�(+ ("��h)&�5�\ha� mbm7t>5 occu�4p $K=1A� W�asN�amoun�� �)�� htorAee rY{ I�5}=l I���$ �em� E�a�2� \eta�� f 3d�|3 �b�v�h0J pA-��e�}j�:1}{1+1/KFx6��#�Hl�ko-6�a��l~O'A�cos%�ob& N'VUxS�,1�!��AYFB�)�n"�,��.�� *�V�,�J $K$,A�a�i�hs !jET} )�e�}i%^1 -� K}{(I�()!wQ6}{I�!nE Thus%*a�R6,ae!d ad�!M�"�(��uld be űh . U�X�*a@!v�mer� $I [$ 1eT�)&�'��ɝ)(&�`�SA�B�gq1� made!�awADd-� g�s����<gy1'��!�d nE�5W2 1^6m$U$v�U} U = (!�R"� _o))M�j}{��} P_� = $4A, IWI-K(1-I)A$ Q_iDo}P_iB8 B\ $g%��=aP^��aximum:# emsp��at $K�maxeI/(2-I� giv!�a peak:S$UB8(!:}/97) �q�&s d�l�*$I�� !��&%M�*� ]"loyedLhd;wo.�e� �!;iox>%� (i)%Q&3�m��k2*�UAW,prc�Jr>c-d))jaK5mp!&�!a�e�,d-�u�(i ��] firef I!geo�[y!�#pP ��&~&�c omin�w67 o�rko�!ide�.ed*�!/}.-V&�Lin�d%���v2D.���)�!A� �ies � m!0�oN 9�)�(boun�Z � ��le�1��MomdFto� �s:5x��"` ]���"! �.y_og�p%�>+ gF�� �� ���=w�G� �Z ront&�M�:�(�cq�.��U�� lso� PPa 2*trave�%�A��6&�/a)N� ^7d�f�"�^wh[7ing-g]<rywM)�A�"chE-Rw-U?se�!ive-"��&�Wtc06I!7K'{Inflk� �1f8&�."l(R�&�& Ow�� n�-!W�%t>A7 aRQ��.�3 re.q�Q!1ro�&���L2� -K!V% R@a�)��k�T���,< >mW�uinE�ly=Mbehavio"�>3 i���aRcco �9�� !�if(��aro;m�6f Bi%2����!/![�Dm�a��� "n � � &O(-m 92 �%DWo�3y easy�nt�to&|&>e*i.�� 0 �I�/�\94$Y1reN lici��i"").y�]p\ �� �Uؑq" _j^e2RK Rz\�o� �ie9^nW*nQ_i_PYm�JBfeqs. ((eq �V�xeqH)Qm�KdX#�*vBg"��o -IE���ibua�L YVS&IYG4 B�k���roM>Rin bulk �[^�}��oX9W ���i ed& :�y'wnow deItB��*�*��@ex9Am��� lter>�V� , knP�@r�u�B"� ��.o ^o�,pL&2&#>#�+lH�&�Two-P( AbnE�), :TPA"��� 1500�$H4�,�-w{<�H�B!�) ork Ub� �andgap8Vq �E1�1oO4 dop" � � p-ty�e Bmembr�9�*�%3 % \rho�-3�BO�- \cd4;6"{cm�" $N_{A} < �16}$ rcm��3` Z)�i�a@Ropa^x* ~s $alpha_{fc} �0^{Q� cm$^��2!�5 ._"�MR&S@&. Dinu�:Liang Kanamoto �:, �VY1�l.�41@�#?�� ."�OiM!�(�C-�|d)2_Uq��� (pon��vrr)�Xueas�b�vR� A��_� �(S� beta' ��1}{�b0epsilon_o n^2 !E ��$E 4"Z��~ tude"���ex �&O/�; n $\TI{E �L:!Q"�e�m�z ��p�t�ofE�'x�{$n:��I (un$8u- ) !v.#dex�;l,"�e>� �� � �z:1�1�2,t!�(2)e^{-i� t� -K^{*-O e^{+.%)/2��-��~}��!_E6$,�T#�angt"~2.D Y��)v-�.u,!�usualZ?co� t�*� LWen�toiU�\�* 3�,: � =�1/n_g)^2Py%$cU?�Q!�l�/in vacuu$� $n_g*gfi sjc>N�:�x |ASypF3B< a��.6��w@�is�=e nd7d��#�t, �-� takeN[�� l!= $n$.�U��$ t���&�s, $E-n-�'^$p�a�Fly ona{5 coora5tea�rr!E$&� ��):ti�Vj�J;2 >f1f.a'�]�m�~_��\e�"� by a weA-� {u�sY �Q�(\footnote{O�t-��Agrawalŭ Johnson6}�a4.� xM$F�$�Dr��)�C)L:� m�Not�as�%a�2~/\d AB�x�)5,X �&,$\int (1/2) ���| �} d��$ea harmoA�)� non-Q��\i�.#�3[ &�#� ,_tpa_bar_1} b3�B� � {�{D*NeF�}} { as*� c:�P:nbn^4�fE )�� int{F })-*%�!�}\\ 6�{��$ft(%b{5�>F}\ra�)f(Z���V_!uf�JN@ -244� ��1+= ):QSSi!�*�( 8��i)\ = 0�a�ai m�eq*5>�)� � z�@6�!�\G�9�!)}F�^�=e_u�2}\\ J[ru�v!,fl�l�l ��� M�.`�b��.�$oNg s a�%�1��=�Z y._$wz���^eJ�J�FC&�Although�xmi�~Ea�vA$"�z� ,>� ��layerq!2����isd�k�,negligib�@3&�!Vo�)��4V�� s ri4F�r&URpop(�B ofѕi/K=.��Z�o�-�K0 librBK valu�h*&� iQOW8R� t�4�eg"�Nv(%J�A��4G . AtB @�Massum��kmple Dr8D�l `%al%Yw�..�izhi�fca>iZ�� sigm��N��mNg !��:+$ 8X : � *\2��z"� K$� ��(� {g} 3 $ �yA�2[u InU�b�Re**ly&� Soref"� � Dc�+ct��0]lby�_hU��NdE�N lbei�th� �VE��-'_{e,h}< �}�G9. �5let $N$*�!&�aQ on-eIp?�&� Wee�6k  ($<1&�I?�7c"8 n�H��`-sQ�U���� ptor�Si.�e&�v.}y� 5U '_e�E�_h� � iC_E��YvN"�>�z0.+Ps"�"copiccCHN1� ;u� 2;:V5DscK� s (Aug�#�7 ̡�hT))%%9e� lQJrD$��, 3 suHC�Dmbi Q n.! lieu!/su�S��� �� x�V�VP2*� $�!� �bj*� �w&� N_fc} m�AUtau p��9}{2\hbara [.#� tau�VF��/T)u$Np7�YE\m(}u)N�zpr one} N�5(v� $ J?< V.F�%�)�Wdn-)�Md�spUi uA1��%����#�!gi�5gaB{;*rt �d��� � ���B��"w��ZR�"�<�f$I?���$U�����E praN~X)i�� BMchYva51)�7�m�Xk;� ��&� ~I��2 _&+:"�<2$Q�u�z!t-�� Z()M�`InB4::�'a� *�' @%�%k>yG�$5��.32h# �ї��b�r>�-@ ``o$''� =G)9qIt2B�+PZ2 k5f�ag>_stLf-�)�!?���.l0C���.2d&� ),&�m�A|"�2D�Jm���2 efiF��L6�F  �"�t &=��B�' � 5�� N�&�b� \Xb�}ob.ݚ)y�fca_i�^�Sub1a)�*�*@��$b�$�)�~ )��"^�M]p" B E�ideA�eW �@*�F��%�a ���n^6I�E �+f*� pFC}Un>{ |mbio"�yD�m0^3 �{b�}.�V_�. ?s��>8)%Z> �2}�� "�'�96&�X. s&-(�,V)��R� ����$s6�!�Gon&�&!,A#�[F�*$6 TPA,!2�Yy]bs 2-�!B2 �$U* !�8�� q�"-� triv�!"�/cF>3 p��8"�%�cp ()�+H er��#d+Hsim$� ���<*�"���Fi�7�& 6R�%��$ i�C�>lV&�&!5�8�.�E�2�&&�$T:^�1B*�&/#A�on.#,A�hermq�?���:_0%_%"@#I&,i� mo /!}Ai-�6�',�/ M}� ^*2 HEre��!9�ex6�e}$�nq%�:z)�.OC&#cf��v�rB< Kerrm],60�e�I�he3$�\��n.�+& "3BGve�c(mY"� �9%�$B shif%1`9/��eF��3�C�m�Ws���� B�8n�lizh �-^&�9M'enc2�f�@B� �!J") >�,#* d5 fi��).M!> R�;Q�eq:d_�(�;\D[A�Ro(�)" =a�"ve� n}(Uz !�1;edA�alM�%�2R\R�*�y�(W)-Y>D c $ b#/ $,�� N� d_nbar} ?\6�� a�n\bigl� � g}{ $rNO @ JF_^roT���n��U�) ?=��� !�B4/ d��'6�3��a&?1�&�0LoXZzr���5{���z�/ R_o_M�&�))�=�!��Q t�@pJBŵ� :T . !N�� s su"|L�q�1� >�D3}6�Q�]�by6hY~)!��ml6� explone�pp�,?-'0�te�wk=��ªE�&!g&iAlmeida�g 2C#C9"�In�!�y2(.��!�:�[K�n"zP}V�-w��E�pi�&eF2/$�'6~o 6K6�*{� �s!I{��":KD"� �$ "�*!m6z��u�QE\�0,_Ew _def�"n� f�'n'_*m��r��|WegaJZ � �W��W!g�( $n_2cG"�( �A� "(ZYY� Boyd�9���g) ax��-"� ���2�6g"��!T� Fs&Z� "� �btenF�&�aYthirdm>sus�Tiol. A+}�a�q1�8i�^'R_�,!����P\=D�j2}.�%�}� � n_VAU|.�:�UA��6KE }}}{U�X ]A�{2,� �h.�% C\+v�+A {2,�/U$��$2��K[.*+)a B�}<i p� �5{s� !�O1J�B*�  (TPA)�1�Pso�Ѳ��o(,kZ� o� �NH+2�Q<6��tBLof ��b./�#N��6�\\&�n})"�$.�� ]%���]�F.�� :-. :FCD��D&�+duX82�J�y'byy�E*� � ults��� inx� #*?" musw!�� @�<'��4u��� E:c.�{� �.�� ��$��thx2h^{0.8�N��2>|ign�K� fo�D���Bys�Xt��**�U!7 stra��C����� � r !er�-1L��M^A~!��e�uFCD�pu�Q + zeta� �v($7b�� / iOT41+a���a7.4* �E4v�i�Pn_fcd��)+��-�K6� >�F�!a��C��D}}���j�F~%h.~(�}#6} :8(Tv��w��{I� Sn.� � i���A, ?>�� &��A7N�"�.\]Z_B A^bz� dn��t^hFh Qth� Md)*\B&�1*���dn}{dTq� XTi�9r)^��f1ՙQ.C�%� pe�!D,.0 F %��1�JNy�/�N� , ��$dn/dTj*4 ��trmo"�t*�3. NegD ���!����!.�#*� H6/H �;�� �E�&� .JKU= <���*��$� ���j^�K�JinS�*�<�,�s.*7n"$�vJ�i "M%VA6��cx��i# �2��  �4i�c�&_.A�6ff�2th�a��i�6>� /d��� e� T}{dP�abs}}}6 (U)\� >� 6�*Jw �P} BY�H �v��BC.BC^2�U6<.d:>!P�in>M 2E^2j /���+J� ��=fAA��� o�%s2�|e� �+�eci-}.o� $dT/:��Vѳre�e�K�Մ ���meaDF75*��a�F16H�Jw~ � 1��p��.wo��*tn, y3 ��2N%��. �Y6u..�#*� �#d&�� A,f�nM�� we n2; d'"] S�i�86.'^��,i�Q�.�� e�L%8**1ps=�te;'ɋ.&W,�'f� & /k�OnsօA�"572�K.3�Z"7iqZ�!.�i�� �2&��(:  �ic�!Ai61i�Ag%�n&Q!tF<?�*�;e /pl�k.<�*��H* �Jo2�ja��6�+#"eQg=�ܶo�i2/"**^*?���ja� 2!=&���Claps�>�arSgUf=�Q�"� in�U! 0 B �M��~#4gfr)I )�s "�w2�"1� 'az�prcDa�k�!U� �BO��5a�G foc&wn�D�en�!� 6�l�t�Z�Te�(�I�a��uncB� -�w�mov�RhW�yoU PC �K%P"�#is��n�K*��ai�aF1��3m10�Fm�|�Fa t�%hTe_O�o�x& MP��<�_��&Pg�W �!uFXl�{$fvj �}�uo2xri��%�In C, yet m�2m�&$ED%�;SY �,�&)�;t��rB���JA�VB��@Sho�l.��Uax�T e ��Q 8�mez , �%^�Zbe1-!|�aI�a ``u''-� o�DC zGr $z$�ger $x�nm encoe@ �M,Apvֿcn v�} plac;+M��r��Si�s� G �|y��! B�h�fi���$x$-$y$w��a��-� l5�Y=-� e"�9!_ �1m>a`7*54st��w-\F1� ro�%� goni�[e��ge|"u� �� aI�=JEK%i�A*5�ϵ�!]s�Ge8 � `%SBjqKC 8Y, qW%en�!J acryOy box x� 6fluct�"4�cur_#���roo�WFT����.0��N<�E�!���_ b�f�8�+�vr�S��+��s5. �E"���R}2�R}SEM ima�D� &�ˁ-&�)�m�!*E4latu {s $\L[pZ/ m 43��JLn�� _{x�KF$d(z (5��gL � surr!x!�ѹ"M �_p�r���A��a�?�Yuɫp'es� pAdeY6��y���x�t^qy���3��=yN�}.�.�or �! �`ٳ%��P!i� �q*�s��(7`�n-G{ b) N*Nep*;Jransmis�:��(�&�TZgVb�r_�N589.7�H�*V�� �� �<���)��u,�R�( Y<�9X!).fjA& cav_!H� �E mM9M�)�"aswept�I�JL (1565 - 1625 nm) laA�\_�:�����4J A� n �-1~(*%n.4,]G)�! sz6� onit�P� V$�"_aprf�z2�R}P"j�)va�.�ete_: -� Aa� xM0?�5�Y �rF* (n \�6�(a.Edp�OE�C�!.*� � � � �� p�� =q� ��!���J� )�l�/ � av:cY0k-<.b"� [*�-cg�V��n�DN�$=$1-10$\%$qh \ll 1Wri�lo� &l(- $A_{2}1�w%���bpյO9&\PIIj�6�`��)�� BJ-�A51�ed� ��$� &p �X_sharp di�j6Li�d��a.�(l�J:� nm��Yrz�<%�du%5��! �i �)<b~"}12�� �}�f�KE�cis�<d�TlQT|dx| > �~VSf�̍�1��� �B� ��� A��ureR�ba�FCThalfw��!}48�,!b!�!eap>!{M�9]R�R e�a�.u![�Q�IV�>j 圾�)xfA��doya��6>"�/Tc[n�"ovt�s u�m�5�Q)��K�;2�AV� TB�%vert$B�!%v�dj���� j^:�)"@�WI#!�adj��*%'apI%�9GQ#R�wM�Jism�[ Coaru+n"oDLz�%j� a� ��no}ilv%��AG�i�X�>� ��� _�M�!�i�\ � % er's1 .�����n� vevr��b�%A�hɼh��Jp"R�.;� �%�!���jz �gD"i�obe����"�a�<!4:b&Gper�(9-11�y�&>�&B�� 1B&l!��/S-_�&�:��(.�*�� )Pb!s�* 9�BB�#A�a� AWG�18R-op%�^ � �u:� ��4�� � MeٞS$_"!�Ťc ��. i"h]�( 0diI[ $d �p�m,���gdO.8� mu$m�R�7��*� L� nm,N � �panel{��lr��eeZ��AR@. ��Mmn/�1 �(sk�)tu�>�0AeO�b���kSj�"a��>Y )E)#��.�%D.7R%?6er�A2 �2"�c�T &� m.�E���"$g \gim8J$m2 dat�7jz ��&62Aqam� *�&-#�� ignadW�?Rx=�?�.qAp1 �+* � q%dݒ��"���6�y�]�%�,]� UG"p Mnm6 �b2$~!����FEm pas%.+N6�twiԞ.5W2/n"�vwg}^2 R�b&�Y&�!a�ca:� ca �V( �:�z$��.OF.&x Us��^�q�r�=��aM!� a� ��97 &4!�%!�*� ed~�N��/b? �� �NK2jd$m�s 0.53= �sv[ P1� �73 ��.Hst�Kd�F�offc~t5��*�Z�,!��2 �)�~p"|A�& ilfeȴ�&y ��5"#K.`ן. �-&<-;qSi�)E�eVsm���(y�.`�fu*E�i�J� �#8JF�q�cO'avor� ��"s, ika a�� 6� T/P� aI-n�,ah>2a<e#xou=2Q~��sF�" �Ji�ԡ��FlIg.X��� �;�>�� :s��fc-�A�!�%6M,Y&~ 7P͖�!3ͫX &m� <�o� broad "PvFH�A�w&w>�s� u!n��.U��%�� TE-1%��T)��5C� �>�E�pV���d! , $g�>5�N�c).�1>�i<�$f�Y��d�!�$g$��u�" �� �� f�bFQ�e���=$A�3 &�? :��o2(.66�-*�6R"1� o))/b4$k main�A�,���!�s Eaz'�h s�WG5:�eb��e>�Jg < 0&� ؉-i5�*Z�E�&\m�F1��A *I�rM �o�MI*d �I��l��� A;�Un"�/R$"#V�!V�| �%q�->�>i��)͕!��}�e��I�r:��E�)� ty! anif �E�ٕ<�sa�.#>���AS^, . Di9�.Y�E�'�&Z8�*a .'Ag�6~ C��c6C �@)�>*� 20G��"�"�abe���� a�0.4��.3}n}�E�9K=0.225�hreB��as&�b�c e w�.+�3.82C�. 2Nt�kU to6�>�)"1{ -TE�q6�sl��h&%�A�/(ic�+�0�H = 4.7>�"�� ��� �� �1�\t�e&��WG%UB-jt �6�]>q�&5 .�,� �y.9�Q A�F��1?-�e;�Y inim'!*|��1�Y��.�{|����up��s;� m΁э�"��i�>|��$^ws;E�~was l��Xo�r.�Ex}= 0.018� �an2�$I!0.035$ (&�\P}�?$P�,EeTAc2.22c)A�&!6i�w��R ř. *+�byBinv" "�\��ox 44 %�%��("� �We/}k�a�!�+a��z�.�1r����UqM�. Ba���*s�Bej:U�N�\s�&� ny�& aa\Y�6h*��5U.��6�" $Q�$)bout6o�0}5o13�( /.8x����E� msel��!GNz� ably�w��,U h-��/Bw�[A��6i��7nɥ2��&�{<!MYal��2X�uu9q�y"�&�/u�>�B�-��N.�.����ƙ &_6K>�(��82�* A��1�wg� -�in6�!�"o� �$5!��$%� ��@M�)�1 i�,�us��ab�5U��x �vto ��c�!!�b'iG aD&air._!.X�Z�9%"�&�8��u�K���rw�V�f penal��kp��*|�atقAF�2�O.12k-��"21�"l1 בCw��&O Y17r5B],R�"P*[����!E� i�6_scan_NL��*W���s� �var2y,�Jt�Z�. Each]�.� ��*� >�Aa�� W�b� slow�� ��p� E�H�n)0D�$T" ��[-r)��e.�!����P!�� R>��� .=r sB�$!�bv+�R� �\V�)��&�!a�>a��`�#oasaEMǁ � �]�5�u%�iWa tb�B���#~Q>���5��>��n�%/�9t,e�Q1a* ��  .�&6umr)I9�!u)i-�]|)�n*Q8�/å��D 7�����f#%:cg�;DR_o$: (i) a decrea�se in the resonance contrast, $\Delta R_o$, (ii) a shift  \omega_o$FG(frequency $&, andI0i) broadening\asymmetric distortion of:�dlineshape, eventually leadI0to a ``snap''� flecOXresponse characteristicg�bistability \cite{ref:Gibbs}. Here we use !/$incident o�-a fromqPCWG. 84d$ is measured "� = �;(P_i) eA�p8re);M?(taper input �by-N eta_{wg}(�LH)P_{t}$. For small-$,�8ncreases with a��@stant slope equal|``cold �'' va!�of. = 0.60$�inF� Lin_!�5�larger��becomACub-aoar versu%�a!�A�rF$appreciabl��mpa!�-Tother Kchannels�a�U . I-�ontext"analysi2j��(gamma^i�2v-���A$, degr��$K�de4%Y70$ (for $K < 1�*FQ�>�$E0$I^Q_T6��$previous s��i:I�depenE�$Q_{i+P}E�$ can b��t�,Q�� (throughiE�ion: %��Ai} �4eq:Q_i+P_P_i} .t = K(:`$)\frac{Q_To=0)}{ � 0)}. \�Ih% \noi �Equ~ (ŗ2|)a�useful !l% s wh��ًeffects����$Lorentzian��a� $\�� o/\d@ e�8not an accurateqLAs!��)a�UEeq��N�jU}))�V�, $U$,1� calc���҉�P=�$.��b)��a plou9��0\footnote{Not8��0 sharp transiA, edge associ�M��optical2�o!8s H������ when scanb ���to red!/usb�M�-�� m madz  if on)�:�u ot.}5QHxeV��N�UA This)dhaa�veralANeworth� operties�ir� a�=bA�Y�inIindicat��� "proces�G such��$free-carri &� ACheE�H*� must�Ytakqi_. Also,e���U$�R�i!en!�%�ݹ� $1550$ $\��{nm}$. b�of !3��$dn_{ 2Si}}/dT�Tn_{2,$� 4$>0$, while $d��B,FCD}})/dU < )>c^Gis�domin�1bve1�A�low.+%��.U > 0.34� fJ}$p d > 1%mu �W}$�8RbT s!a�Q%`,B��`(mal or Kerr-�s �te%�Z�5��(I}��a �ledq�� A�a�B� Š �eq.��d_|Qas��d!:��B�!�m ax$ parameter� t�] �%,taken as: (iID)�a�?��lifetim%itau%!L2q#resd� $"� !�GC � th}}dT/dPabs}}-(i@Af� (> D whichA�ddr QC(on (as oppoAe� adi�)�z �1lin}}� � �/(J + 6rad}}�%�a$ rial%�mod�o� -�lisa in T� ES tab:9�}. As�b�obserAa in studiee{silicW[�guides&�Liang},� find���� rong"- c��!�(�e�y!oi��A�our�er � Hly reproduce \emph{��}%�y�%1�vei�9}�FiFs)=E�_Q_&|(a)J(b)�(��account�aB�& Q�!V�h�� llow�΅�du.m� . W�$���� .w$$ held fix� $!y(P-)��s da�min�UeaA�*Lf> a*st squaz��toB+�(��� N� siA (we have two)�points%O>�,5 :�H 9��!@ill' an mum>�!Vnon-zer� sid�error.��5 � 5� repec A�a rangE�� ��� or!� Y��$BJ fits�xrob � �,%A�sumd le9�t%�taY48clearly minimizM71lal.���.��� 1o, how� , w�`nly founɧ��ra�Ba� 15Ra88is9�$B2' ��� %W doesZ �ge sign�nt�5@���a%Tek$ Aa�slightlye!q�IbB�L&��F�G�Di*u%be $27$E ,AYo%�ɺ(of magnitud>," � Ref.*�OBrien3}%\a similar membrane struc���inb���� -by-��j-�Ld)um)FM�.qZ ��veza smoT curve;>�e} ^{-1w 4A + BN^{\alpha�>j!!9�2� � $N$.^%�b (N)$�,��=to"��e63 �! � obta�,F � BK Fig.&�� 6)p. \renewcommand{\arraystraF}{1.175}fce�t+ }&�Fixed.� u�Y�\eeKl."�:\ b4tabular}{ l c } \hS  P] .& VU^ & Un� ~& Source^(\\2� $VJ TPA}}$ :& $4.90 F & $(&/&�)^39& FDTD > �2�FC2� 3.56LB��6�6�- & $0.982^�& -B�N> %26�- �97���}2�"�!�u& $3.45B�&L Cutolo,JSoref} 6�\sigm"J �& $14.5\Zs10^{-22�  � m}^{26&��z���^e$j8.8.�8.� �322��h�4.6����B��84�1f2 \cdot )%W}��Mb. DinuA.2�\b:�E & $86�6 &�� ext{�b�!�Y� �+2�J"A $1.8.�4��K2B. Cocorullo=��l�їݧleMs} \item�A1� %$two quoted�Si� ngle 110\le��21  . \\f b) C:\� gene�d field �$A_2^0g�!�� #ed� lattice` s�d � �����>q vP0}t�{� }[�K"7�K"A[S"6!&� qua� fac� or% diffel&� � "�B � B!� .  C�$"�= !yU led.�� e $"= m 4%Ivi"��-�&�:v� �Y  = &H � �� 0067 + (1�M �u$7}) N^{0.9a�$N$eu� U�bc��-�.c:)ns). .#%k2�i�"� A�M�F���$8��D �2; "�on6T (�dots)A�� byE R6- _V_ A`�JU��ofj�aJyhY�F�N:� V�]Q%� 6�&"�F�=�0e> cor�dep:":�^�(T  given!�E�����A�i+U� cm$^B� $n6&tau_FCj� �3oneC� tota"�&��Q%{&�� b2upo�#4!%OA_� )!aR&n 6�F�7t���� alth# TPA "r�� e]v)�s�2O s it�-� |�uleHa�&�6y?on dri�heM�behavior1QyatZnd high2],�:$ vely�(AcyV�JZZM#s"�6�*-�at"SA�,Tsang, et al.��dem[%2�"� fall-off!�e�$N$, but��axaller s�*2�. B�!apronounc�2 ecayZ!I#�� m 0.5$ ns��1�!l59�PRNI��ly*��a�c$in bulk Si�A�most likw"{("� iffua+��)�s ��|extremH)< -$-to-volumea�io�UeF�!.cal]*v(),2�nm$, size) �!U C�#l5N�3$a�&� Clap# < �a)Vmisň{nML(re��+rimen��u� !�ly porn'}�"Zs�Almeida1& Rong�gshould*Fba�� �u!-�xcoeffici�zA! ll�&p ��J�1�;g�D���maySbe9�&d[M uf� �PA�!�){%.V|A�$two-photon.��Ս�u�ϱ v�� v!2�b�esomewa@C'tw�fur&s s �ne%aryaco�)tase����,wo phenomena!�MSi] "X%!k � ic crysta�*is work�\�){Summary"�q/In�le�,&��O"Xa0$fiber coupE*schemSUT ly sw!�colS0  �}A� -Q ultra-idA{ ���&By emploaQ-Mvsupport�?I��%4 taneous� pati� 'matYw!I �w 'o��terest�phase6=B�-,9 )--.-S 99is enz�A�%]�>.1]cy�$44\%$*.�� �!� �c�of�E�� Xemitt%�:C �!�iQ-�,:� 13\%� seɩ�1�*funda�al lim�� �& ��-)impro�!!,fine tu�);eB� 6��%G9kmethod ��tUexploi�to�bM&�eady-sta�����p"6)�U2�ec�*N�,6��z��n&Gon,'self-Mvod�+,�imo-���9��f�!5 iderEzO�".�3e�*!�$2)) mu$WK<#)�a6� ijaf&Aens�Gas��'��# fer3�9�1=�ƽ�� A}�a .�Al�#e� appl�io�(_%Zs��/-#)evanes�ٵI ]0oac@3���u&1.fu'A| $ a�g4 v)��>thB�s)gin�ti�-D(,cQED systems�-i��!�!� quantum�pu� ndmun-A�tocol.#R)�9 de�.� auth$4thank Matthew ��� helpL} \title[A 128 pixe�jqui6b��� apy!�!� assur� ]{Develop��_&�,�> ]seg!|6g -fil�6�n�I/{J�,do\dag, L F� (F G\'{o}mez $A Iglesias Pazo J Pena $R Lobato\dX$J Mosquera ( M Pombar �J Sendrn�ddress{X\ D� t��6K%E��aA� prmf� an a0 �[ vir�> w.6e�s3i� Q4! :�B�1*��s. All%)isons �w�WooH T �=. SigJ[EE!S(in a 2\% du"�'� ( od (ar� thre.nth�1q�5? � capaI�aCverify�� &�Inte^^$} Nowaday��} of)�� �treat%����� h�s- perform�1hT6A��<�>s� ٻ Q�sQ"M��me7�? spla���E�%C!xEU.I�"���q�/��s �@�y %a9'oni��a\clis]-�: Z�f�,� . F� more� e.� t annintW7 b�mt� ov�4he entir� �~e,��l!}yp!=O5>- �1�A�)�m� e� s (RGFs), -chromi�CFs) !��� imad,� s (EPIDs)!�vide a^8. Hm- } need�0hem���!6@pofo���GscaG"/s (Sy6+(l 1999, Mar�� 2002), � "1�� -uniA�(Niroo -Rad B 1998!calib�8of %aa� t task� ���es) ?� A(imetry )�#@!�h�9-c. S" anodeN�A.k�g�9�Z+6<(2001), Belletti � iEberl�2!�3�di}r � ursa5%�Nelms!e3) �!al�B����fas2�%��0s =possib�72 ,!�e-#m achie� mill!Jer�/F�.8�pa�Aw���3e i�"� princip` A�a�.�� " 6�w%�aimA�� �=�M�V�#����enoughA��to �!���� un"�. EV ��B� _.� �� ac!� mediu�_� !8ck*� laye81E�U caps/� 00^rmPd circuit boards. We �Ձ standard F �Merk\f�> Uvasol"V e�67 a pura�@$\geq$ 99.8\%. No8 "�0=;* �pan3p35� ,%V�= Rn{ !��C��}!��$AR�% ! te s� onduct�in��� s�(their tissu/D ival_rE� ir s i�%u 8dir8 onal� pjBce. L�F|2�cur�$ly)�>�.7 do��A?wby WickmA� nd N:.\"� (1992�q$��8��po2�a�a��aiahev  plan�  down P�8i� four�� PCB� 32b. top *2nCu+Ni+Au�s"�in�+sͤb d?R#I�x$\է�lu)�ed �F a gu�ANbif$to +2 V)� pitcg=�,�sL2hA_is&�ce!�of :.���N��a�aa�XR!$of 21.6 cm�, l)N�!�Ballic�ipe��$ rry �!�X ingV rg��<Z !��! !�] ��"�-�a!ccoQaat)"Np%ybottom �gdepos�$a 35 $\mu$ICu cla�sht,st��ex-)�� Q�9�dim��O(250 m.�1A7�  #r� ���#a A�"AP ante"� o% �<*/ �-�v_#. �&ur&,M1}��ac�5��layou`Fn�-2=2=2� crosdE�)"�'9 fassemb:�p$3%-Y�7!<4es��b.�O���Oinclud�phics*[�O=7.5cm]{"+ 1.ep�.�9�O�) . It-.�hPCB��u�S� !��I�/. "y! fig1�n"�N>�P��8.�2n�S���uY6�.�2B�su�RF�{}�&X-r���>�a,B�AG�`�:����El�8on Tubes Ltd., %�i�H��r�!�.qa1"u?�ne"�?A �x ��6ne�and�)��63 /s � s�Bl"��,��max�?of 8064\�h[!e m>> )mf��are����Cle1}.~O�*�� �� �(��k x*,Tof)> %&0 ` cCE=a�venin� <$ �ean�@ ��A44272$\pm$6 ADC�,XpC FiN�%-�0 �1">^(�2)- fig3N*�0.6 \%. �.v toge� wA�DCd lgD�a��Mg�r>~mmC%��Um �box (U�o-�F!_� )Aupro��}mN� �lx�a manageE#��!Ca~�  uniW� d cl�홑]iout��1V� � eji_ne.�A�w� �C dou�y�!%PC��i] �par�+l� !digK- roSFQ�.>/4��aQ!�>�&[Vea*P<�P1}E$mJ�����i�Ped�5[] �5{@{}llll�-r �C"I$4& 0.01 mC  (s\\ sub-samA& 256�e.�6�,& 30000:1\\ !�}�" & 5 MB/s>SD� a�& $<$� \%�5A/D!e�4on & 14 bit\\ r0o� & 16&A & 1�*,164 mm\\ \brn!1 =7�a%p�`&13n^C6�a�%�-a<�la�!-�aFJ.�3 ى���7�4n�P�'b��-� � �Z� e��N!6�a�A�2�4B�|P&�o*uO}2�Ini�)a-ombina} W�'� �ge�JPa W� es�n-A�pai�&&�!k."f�7F�8'Hmolecul* �N ize B'ata# $r"3= a� ��� st�G��&Coulomb�iok �Gaus �6t �' �J"\pri,ni�! ���!"Nc�<� JqE�se �-�m�Qmor�l+'� � A;a!� gmXdu��� t6 of ;$ hydrocarb]  lt- "&�C� e�Ian-1% {at no!���di!M tAE$r^+��7am��M�.5 escaKiN/��rP eV��(bedTi�Q��%�!�y� / &"0),G_{\rm{fi}}$%�V|�(�TX27,ms% �p"�*�Ji emper�2�ET$�7"))�H, $E$, (Onsager 1936@3"5� �"� 36M 2*s ($E+*$ $�9o V mg61h]B� ria#�)xi.8 _in�"� 6k:"� &.X=oeq ^%�L0}} \; \lbrack1+aE\r �XGfi��X��$a$���*d�a�7ctE<lut9"�!QO)')�#$a �1/EI20�C(Mozum�R1974, �&do�2004);$7=8\pi$_iloBrm{r}}600}}(\kappa T)yA/e^%�.h�1lOM�=.e�ep6\W>$6��sP"� di5�5P��M�aE3j*vacuumk��6?<хABoltzmanA"n��t\$e" �org" *JV�6�Ba�Rf%� �t� Zb 2}Md^g!mr�W s mo"z ($kI-+R+}}�U;6� 9Q($\WH+>�t bN �� (.ru(P(or .�"�,� �r�(:r�%J2`�4_{{A�0}#�)P*: Azq 1-!; (�u��s�% V )$^�?}�C3.5@10 8}$! K!x�K2.3VK-�FG.�5.46>16 �N�$ �b �0.32 (200}$C)\\ Jz� .94B*2| (2�&�6�!S:m� � a)}$��Q�#�a�tempo�&�(m��� @)\\ �$~%pul� +�D})re��FY'�,U ��noV���� C e 1-6�EbA,�probab�$- {9e�a�ta�Y�h��s� !+!� `Pa��K!4)#( u�J } �ct�l*S ��i�� c8S' �� V f���rg���u�"�*c;-p�!!��r� �$t PmqE)� O�"& N�. R��)j �- ��+ �6x*f�A4m!�e ,� l�-3f i.e.Q�- tinu):�(%�). b0Ac�(":&�acceleKY Yon# !Ai aG a few)�ɝqms� iod�a=�!�"�,�Q|d; I� { , $p$,C.� =>�IB�!P"i, %?�_J� p�! +bh� }{V �m�X"�p_tm"�  gR��9�6I=1�� )�MU).�,_�Zx)���$� o�%�8 ��yD��7w��n �+RZi� Boagt 50�� ory�uhe^neg�-pcDL era�E�neg�s  3"nd6G.�*%��r �"ex!6��a%+ ~Q��� (seeR ex�( Johansson� 1997�!� i� pZ�is�e C,J=f=I901}{u}\ln(1+u)� eq_!aF4y \[u=Q_f�dr}{V}E~\] \[\mu Y��<}{e(k_{+}+k_{-})&WF�!�&�-�r�b)��+6%����6V�@��4!�%�, $h$!'�ip2el� , $V#�"�c�,E�+� �*aU�k�0ndAo.� R8�d " I�nb@Dh'�8� � � � aaR��,�$����ex�(0Z� "|irI8iqa)��8 am u+!�X��1 ') }.�� k: 4��w a Si4(s Primus.�aA *5�)j�450%� Y{.o�j-E��as B�*5xeq_��od} p=\�\$s {(1.93\p�C02)�Ndot{M�M &ET!%15 MV80.\\ (1.08r@A6B@:*}�perY��Xe�'q �&�F 2<MU�Z� 1}�gBH 5McoK:�DRlirfInnI. fig5p^G� !�VBs\@-U�qg (SDD��eI�a�B1�+yVd�T�~�� �m��Died�r�)�#F�1 b� Hy�* .X q!l<a�i��ka$0 V*�+�5).�A .<b)v5�.��5Y9XHF/$*2 [n�0y+(�4 (500)6"U�6 (15)A� )��.anup�c�: ���X$-inot�J3B; :#>� I�+e�gD�2ri�.Ūa ��9c�) � R . D VX �)�V� "�g>)1} �9{gb] to 0, bec� !1&0A��(dddY% $p\rQ],arrow\infty$� ����ZS�ulI&M,e�5!$Y�� very.��q� k 6]�d$o"� ,U ��A,{ Y��YBW ��o9D!�*�A|J5/ 7@,eq98.6$ \%,B�6q�_%FH=7$<"�K�}x oscil�iE�6�$7 i�t�NJrS'�az)�k� iNb)���1�R�� $ 98.7\%)G!X6 q�)�s�^�] 9Ea!}gA�1[9.2!��@v�is=3=�,l�J ?�Da3lap� ofm�sh lab.�Je��ll DR%6� U,m,� { the .�!�� �Hp�!d1Rqc !�R-� agre���!).� �Os:&�am%^, y*��V3�O-� �B���H&'��6! �'A!��!%�2��5f@Fb)�SSD��e? �$�"�#x �R )�"���R�var��m�H�6,u�e�uF2x��&!$Z��tway�( )}"�"h(B�(he��=*o 5n�(A)*VV(�1)p�ag�-t�� N5�&p4�l&V� !t�I!"SDD�:� MRL4to���:� 2�!�R� (do�A) U.�E*3 mf�fR ���rt�  (B�] .�Pi�!05ui2q �6.� (*z)�[-�SSD!g�� .�.� &� .2Y.X��,b� 2a"W � �q(.�1F*�? �&6".� set-up�*:7� @S'&&<�օj�C "�C�� &� a; � e�Jd1 cGy���)de@(�/E�Ea 3 @a�15��Z| a�3phanto 1A�+$"�0qISSD=10. 9v�rB �:" a G-��c$4 p$ Y�BK�/10� ��,%��&{ ) ms. UnlJ2�io� �6 wise� A��A � LEa�ve �of OF d)2B� �* ��0��@D(PTW, Freiburg, G $n�Rype 3101nP"�A�z9"|�-uW &rARGF6%�som9 � w�80.0AoW@ PinPZ�7|A:�F�06)��a 2n3di��(*�PtH��*�< } To�C��9) homo�*��A�!�ins7r$M\a�"C!C�7%�E�@ AD�EA�i3 K�&z �-�2de50a�%?EK2�+. B� ?shoF2��Ll'@ �!=�<cr�+)��a*Rag�o t-����[-)Nwe X!Je�2` � � va�v <5�!x� $ �,�-� .���&hB�e��]nel (�Ep-YA 2.2."� f% int� ��G!��) area�*�&h"HFc�CX,�+ fxp"�Det� .�"�0+)�A�w�-" }>��6.5 J �!�� �2�B^�n��x*)!� . by^��q �%?Y��-E��2{4u{���gJ ,�Ag.d46���R&Q�Jd�-voi)super)�(� ��)�U�C=lsH6Q,5;tmojVZha&��A@13�0 to 6 �E �>U 6}(b �H was �c� !'Z�^� MU�n ���mi��50��inF)steps IK commzo�[�,&�NX� empiFe�-~Fow�Z!WAttixB66)� � } S=kgD�#Ox� #�S"�:'a��z���m27a��$ n$26:�2Z�)2S���&W =0.9�0.007$!r;}.�. 84\p:.2H�mgnB�2�g�>ad� ��%ƍ: ]f�_s�� ws 1�J� %�IW E!;��� (at 2.96�J��2.�J 4 �(at>�J))Y%� �� er} F�712&�.6n>�� j0u�ux����.� : Q.�SSDEnl)Qq�(d 2); 5.A.� EXAcIn=�ELQ !�ɾQ51-oi�-i}fi�9A�*q�E�Kt r%2� 6m�1�� &�7Pha[�9~>�H}B7�a� A�a�~5�"� E?"� ��IZ ,� d�|o>�+a�R��F� "� =!- =sy � �+I�NRGF(F`"� �0V��5� "�$28a2�u~"B&�M"�{� �"�90 \%-1�k8 -2N��� )��Mdi � - r %�B�d,�!��j�N for )Չ�at�lcm,~7� �E9�p �qF� Bw>� � �8� conE���9f��-�%Y9�%"�WN(:L quadHc�r~� �!�a"&k  left%!����  �# �� M�RGF1�� LyKde Te+B�HcZ���z�a too�0�1(2s,!��2t `]�=�En +Ss (6�I�JA/ �;�Nid \q+$�3UH. D�jces"�M�%�H�!�c�F�-��F=8� .|�s" -r!2!\w�r,]�ral� ;�O � C�8TM6����n�x�O�:0.�� 7a�2!l.%��?�eU�n\F �se"; !t�E�t&�Jzer�O��0��7v�� �!V�s�a�~:�B� A� *E�!�a�Q�H�[>PB�(��0fZ$\DJ%a�.�2W7BW�M* 8nMyHuG90�<\%� �E082 times$)y#F�552/��(a \)�@�.�8>.zO:f�T} 6 (O PA�*8!á�"�8EC��dI��j��1 4M5�-reY,ce<.MXDreBoU�]6&P B2O:@e� ,5s�FO���a&�Eu ����1z var�"���1 in 0 . AN�_��| �.r�"OX�!qEh� �InnU?Y1�1("<! 02� s5, excep.i�( e na!d�%��� J01�$�4kId@�2�e&M�(L ��"�#9R ZV.;���!>��ir�p%��9n: # seO`/Pve2S) �s�!�9��&/$L\%!�EJIs '%D). �S*1#!$ ��YA=Y51Za5�.,A0 .c� Q1��6o�w� .�.}�R! und58sY�K�?\� M-:=.�!�� beha�m��c�� � i�DU�byR�SR�F�T�%a�"�v #u87�0)K�B�#l3�* 2cm, 6&59��B5EA.N6_���j�ls�GAEFD2�&%Y1 ��5W" E�%�:c�OF-W2u� 4b ki(d).59 �� @26E����0Q�� 1�eD� .:�`!._'S �8�O-�}TdL5,qS infl��e4adi&���'B� -�� �-&�JS7O�\�ag; �&FB��aN�&bBV �q�� �6��B!D10.�2�2V2��ose�m^� P��>%toO!$� � �'0>t���,El!�Eh1} �.zo�v�C*� �I�!�� ��.�$j $it{L�.z$ ~$���%� �siz,��Is%"�#��ak.j�ad�?".�� der�]Е &Ea�i t�is>�@2.7��MV%f`!�%w��#�"��j�Z�[U$t7IFq1�w*}$10vt2+_riFE�%�As)Q.p�5.�a�IJ!.E�:Nb6^ 1'�Id}��*�*� ��.`�v."`tsA"��<b� �AaN.�\of6I 2� 45$^/;6(N� u�,.��QE2�,&"aU=2R�� � E �F:11&�X"�""���UZf6 .Z �!t)2. Also:n *�a#�RKOs�Ss,�N� �1�S 81Eed"��. Y��~2} FJ is 3��A--. $�'>% A��> *h11m��;B�Z�����e�*f1er M�A#I���$!)b]*PNl !�(-:��AQAQ26rAQPr�i�2�*A"��` ��r�QVgd���]��U�f�B6 �H!�l9� ;3V}deeq"�[.pe ��� 2O An*/fr�=A% "� i"�1�?ejF�5!�7 � �(\�lW�U�:� W� &�Fe�� 1�AM%�2ZTeo � )."G&  on�UJ4I>sE:S\�a�0� KCo�T�͠oTx#a&"�ZX"is��y!��e��(�!(�` �h$min^I�K�A��U�%to�)/� }�! low�#&�#�-$�� to��$ >� ��ke�\��' ��M���F� e�� ss A2to� (2) )�$(� *�1n:2?9~is�to�Kg|Re* A �^�r--W2$��#&�0a�2�aQ3)���FJ#$ VheJ� zV*� �*>k�87( s< "�)�N -�a&5 t9k"L @(AD5%G6��H�4L,� �_I��i~Sc��� ;,�"- at��sR6rٗcy"��< �"�)�p?4 !�6� &"i.)q?-�!6�, �vEm8O.�fJhY kSm��W�x�j/er!9"�b c��� sKf%y3�_��ofj(�U� r�7�&�1Pcbo��t2�j,�d}&�i"�)Z *�d� W1�utȪadw-&g�9�4-�R4(�!Wt5�a.6 �Ml�K6�,J .{G�J�]���kD�(a�e����>vV:' �es��vJ|J.��!th!�G we:� �"7"�:g. ZJp.r�)MBT5^�`�6["�]�r��Q S%�*�,A iTalx term"'KyMХ�c�xd�.sc�of �}s} \ack �e���|e�(C�g archa�je4��Xunta de Galicia PGIDT01INN20601PR a�MCYT DPIe-0185��)$ CIXTEC (>L)aJnt�%Rs ��[] "�i\S, Cirio R, Cocuzza L, Da�4rgis P G, Done�i$M, Madon E rchetto F �i"rzoliGPe�r C, Te�siol E%�Urgesi A7 1 [.s�  .�SauMa�_Yapeut�k�@�>� �Chad�H {\it Nucl�c�0|Ls A} {\bf 461} 420-1=0E$J W 1950 I�.���B�A�-e�d ies: 1. P�*d*8 ��Br. J.tol. � 23} 601-1�hBPjB Re�o�g��Do�y�Ts ]T5�"�T^. Socg$82} 265-72�skK, Eng�J, Hart�NG, Hof I�H#gran��J R!�3 F6�3P0x�+6�wZh>2!6~�i&k=3 Phys�2 d. B=5,48} 3555-64 B-�� %N Ess%>M&ZF6)fmi�z�d�k/gI� E�h��%�VL al i2�n)�IntUat5;col � �M) 34} 931-4])*( J FeX2($F H 1966 Sp%s q�o��i�E�&�vDaRX} vol 2 (New York: Acad(j) 241-90YH&�GB&� G�4Bahar-Gogani J� 7 G ��R�9a�-H"PKtet!,hylsiMfa �:.o�^6$2} 1929-38�uQnP AhUnB EI�A 2-D.�n%a�softwF�>.!uf�����2y �MA��}�� 30} 870-9��%C�� Wagner C� De N�nW�1�1�=� LA48� �U�b �C�m�of�-&�;��6} 11A�=pMar�2�Claeys Iz�26��(Xrak%�e���$7} 2221-34=v?UAAU E^'�on ZWlhe �WCSUK. Iu Re�"V �R)KE�J. Chem6 60} 4300-�N2GrA, Black*VC��ursey B�G[) K P, vinC}l, McLaughlin W L, Meigooni A4 NathI Rodg�EJ��Soa<� C G a�8�Yo.�s�{ry: R�Imen��� AAPM5�9Th�vCom�I refs *���k R�a҅le} %��2��amsmatܺ*��mitO(} %TCIDATA�)Fiiw(=LATEX.DLL}!CrI�L=Fri Apr 25 11:11:05��3+xLastRevised=Wed Dec 01 10:56:06/4/0Z2D��Shell3DJournal Articles\AuC$ple MIT PrUStyle2Z,Language=AmeF7nE ish~4CSTFile=LaTeX -�,.cst} \setc_`er{MaxM�iCols}{1�new�tem{ }{T\� em} .acknowl�~�}[ /]{A:67lgorithm.16+xio2'2#�1ICas�A� clai.DC6D"�.J>-�!6, >+sur2�o:-rollary2X6+ri(�o2�2+�,xbWDB 2-�T*Ex�T>'ercis6( 2PlemmaNL2#noIj&N2)proble.�P >'�SPr2/remark*R 2%�'Sj!�6)�y "��A�environa,��of}[1][Proof]{\textbf{#1.} }{\ \rule{0.5em}{0.5em}}Gw&\dummy =\oddSmargin Շto�-{ #}{72pfX #parj=.5 sep=.1�� {tci�)x�?= d��t#�{S,Bonse��Y� Einste{movariEQ�vg|�"�dynamic� �} ĉ1Vahram M khi��"Tnd Vanik E. Mkrtchian}�^<%EndAName Instit 2 O�Res , ArmenOp�S��c�=`Ashtarak-2, 378410, Repub'mof>.}!Jk"��)-a"��Wk�o&u�zpr�w- �r��ty to *4�5nf\Wjdm�pQ�!H�01ytO� � a ��n o!wڭ� ��A��.deęexact'��� !Ng- {GZPWaM�E!�u�\!�rbitr��"�G .�6��#t ;��\nondisix�yE�}AeA!�a5�=�V#s �)hort-�R�>�% ��*��� ��<harlc�5�% A�ӎa-}e "�9l� �Z8r�)=.b�2Keyds \ }�re�(ity', }Qc�&j+ple, 9�S�_8�GU���\PACS} 03.50.De, 42.65.-k{ Y�`�{\p\bigskipr"�} ���Efof-5lU�&�+�?uscribPnt T�s{-Gn>h�o&�|corner-s�ze��iNl 98�� ein}%�[e�*A�"��i�6derA� eore($ physics. /lF "�".�re}�x gr��%��A�me�Ep"6i!8space-\5�F<y ter�x ion r3FgeoI��=�p inuu&XB�hr�5b*X�Y � mak| ��mp�9c�1{s �}��a�- of �5�N�. ��ly,e�go!��!�H,� N=�:new!:hods ("� sP/�2�US<ble�� %�%a� ew=WW-�p�Sec.2���W; R��,� ��N�!! new,M�t�m�sa�#� ��[t�2s-!~(͝7n���YM ?)x�z��!_�ct #m��f x�2!aK,laNnee�1:l71@t �E*i�Y�� eAesam2�iL �� �. �ucceeoL�.3Am10�e ����^m8���#�n�zĩkd:���GA<4TaRous u.]Eu4��7M ��c"��r+ :+w�Kn p�=.��>0J� ine�16)�JDi�|ax2\X5�. )�a� ult,1x4�Vwa)Se�cuž վJo>%-���2f!�f�T� !�O�.CnPWt:bE(cit way via)x��H��IdZ(f� w:��)ݍ:kin ��alpLg�35wkin !" 5"i)��) Dc.j isotropic@aF� unambigA�ly ��@t� ��1qetvZ?�er�ckum .>�V�Secs.5N6A��N��N� t-of ic%i� ng��"� ook"!�.�� :� �M5�;���!N��X aM�>�!a .y*1n)��f%�u N�\*`X �icIe�5� "@a cubic algebraic��6+alyS�����5  ���deea�")ڡ��~.A )n��& Jp poin0Pr�nI��.%�1�!Kpa�c�K� S[M2}) 2F� BMؒr�#�b� :isi( C)�)J�� ,&Z�like F� a f) � ec.7!;Y ����Q�A�"�+��mai�%at�o` r\ �� 'p�>�����w �h�N���%�miify���i= $ $A,B,...$�(r� �._,� z M�nUy"�XQ� } F\E( A X\E) � }\hat{L} [ B(( 0] � 4) =0, \tag{1.x�0s�� #$X$ ( $ g$ao��ek,rey�l����l, etc.�Mfun @�� o7Rule�;�A�ny�T c.� % X^b ime }$���A�5++1 Z?"!q[ B:( JF N] 6].5]bf:� B�ea�&QuMEyv c�^>� y (�� ar, �W, �)`)o!,��\"�A9J>UFD�i}=W^{i5C\>9((i=0,1,2,3) �2B��( �� "� `UsJ�B�=E}\L��B�F�W%�( �B�B'rcJ  c>h)E -k|9��O2�=1�c)�=-%�e)��_a�1 i�� =�k.(8)) 9oe1�kM$>A @ d#�Abduj��cy7I;Va�of (3Yto>Y�(iv���J�q�2�)�9_u�� eft(f� g>��.b}�'h ich,��7d ż(1.�R�2� -U&my� it{If }$B�,�it{\ }$B��y" satisf"X"95����1�Fy��`5J`Y�then}J5r��f�a{!%vK1OfK..q�5J�iit{.w��1`�� ��}$RM9� }% $M��YI� ) .$@]av�jh ge� "�?6��a\>y��Gj by C ��. se� ��r�"*� n� � F�pN2i"�e�� "�:AJ� may,0�  y�b6�� gro-" i��N.n�Co-� ��*�C� 0:�lawm�72C��>7:N�4 _{j% (X)1.yj}��(X)�;}-L ?}% 5L2Q n}=\c�a�/�M97 Wri.(6), (7L �C�+s�&� iylw�E�y$% j_{0�M-u�e\�O�! F� �i}K="�9B��JIIzO �\M�I�10b�I� ,f� �b�"% ��#6��Q�6��~9��� F&s!�E2>�$�8*�[VϿight) $� �2��"J �6 :�.-���>i7tote^�qX6#aa^�a�6A&" �u�tu(�8�[�ugges2 ��eRHa�'s��A� j>%s�w�&:�?(5��nde�>F6` e�k& �Kng q $e_{���ra�$orA$\�bf{r}"dD)� tY1�a=�.."V$-�")e�--6A.��!��.%b�;$&�2b ( ct&�,��is� by.'N�_:bFO$=c\dsum\li��!-%T� )5 "t)OB-�79d ���d�i}}.0}�z1N�\ �!n:6�"2-y�s�B ngeyZ- U- �a�P 6.)".WE�~d�>.Z ( ct=� f) $\g!NUR����5�% i" �>�)~!�1�6�F!�";! Now,��ġ�%��!�n* � Apix)J�.4=X -U �ռ��\ } = !05kuP��(9,}:� "YD&n� @A�1��<3A� -7��B�LydX�u i=1}� � ex� -\�z� ̓={1}- �\v� J }�c\xiZ-\!� q E) {� !SJQ�f�}"�~,( x_{1}....xh B}>( o +. |n/,�#1q�yer5=%�P��F R#�%'�� ��X-U�u1NG�Eco�$desk՘ 11.bD$��w�� J�q�uqZ���]�=r- "�y 4- S.��< 1FhAD \�Smes[Sp&f�aQ�Q.^G NC M$���Uly��.�* "(`m$�D$Q{��-U' A�G se�1u}( �X)�aW�KA��xfhe� &�.�, �dd��"�2�c�^d�� orc��n ��&�C?!"��anW &��:$y& ela�� x lan2}. O� $%hbT-uja 1"- H%�9 ��% e�(2^ KDV�HnENT"O2Q�*��B�'qK�42 nce, y"sa�at&&� �.'�##�!��&Ud%6 &� ! u� "]�� $an .�#I�&�eJy]oD�Z!2c# %>A|���6� �Va '|&@F �"˿�� tod� &�0��n2X���' referzto ��@B���2��.� �^� .ui]�(10X'gq�� ��*�>�}�,�o��te 2U"A:� � �)�a.#l�(a e fic qx .um[9alg�aEa�lexM�Ba �e�Sn&�s (M; ��&l��"8 atom%-��\�,ate, nuclei,\� ) ma5�c}# Yd/$, after Lo_z�Oi��U"EO=/sub����#s~���:- � . De!��)8�(? �(1%�(pp+L��Ppp����d�!�mo1m]Q�aQ��mAX�4�%�mKh��*s.+E�&w'c m�CJ�Jc,p]eV��of V� ��#5�R=S%7C6#�,ble��"�.u2��&" !�%�x��2y)&D,o�a}�h %�!!���ub k-�aFTC &!of�&�Z`�\ D1!��by�<ွ<�._D$"J')�&�u(�WJ R�� .?-uF� ,� >R��6R��#I�`��(13 ]� is�(writte��NF�M)��#r*ur*T � $!zj5f%?he :e}�.2n��� y2� forőu.�Q. B ��(A.5)�~ah�)�tG�-�4!alZE���+!&R�rho *� 5�-�:� �  rho �# "Z -uF,,6J�J" _{\OBWUIg �0� SF6 }^{-1}[��$al _{t}u_{ $ A8ho �"� 6�+� ;� =F2]=F�w8�� b�!$V���*!na yA.4A.62EI e6a6)aA,�anyJ#��w,��mA�Ad&�a�h��ally=s (�$�M#MownO :�s)A�)t4�����>e7� � Q�&�,2Ua�_6�.ozn�*����Ca�D_�6p&�(nd a backgr�/@ n���u.f� 2�.. Le �L!kt����$��.b.�{y� v"L,�����Xd=fh ��$\bar{a�}A�=�t,�D j}%  �0.$�i� !�;*2��Ρ"vPq�yJ2�rqp }F0/$,F *�"�R�n�3d dipol���I� �1�M t��2*R'n9�"�1< �~�1heg ig<&�#.aW���0:6�N\5�>�=8=-55nabla� Pi ,��)7��Ixj}rv2l9Pi +}c][�:�y5s M��] "�7JA HereJJe�Q�P+) 1}{2U� �['nu "�  _{?- �'?�.] k% 6mĔe� \mu 6� �� \sC� }(.hmu � lambda })2~� :) T}Ս8��M�1C97c����� �"'�t��)))=)3]5(nu- �� �2� �8}P_{\lambda })\�left( \partial _{t}P_{\nu }\right) �Xsigma } \tag{18.b} \end{equation} are the electric and magnetic polarization vectors of 2�>medium. In what follows we will restrict ourselves to consider�D of linear regime ]interac�$ external �om�Lfield with isotropic �, i.e.,�y weakVIs in anBK� where $\mathbf{P=}$ $\frac{\varepsilon -1}{4\pi }\ *4E.}$This is a 1!Non !Fvalue��p, but it could have large spaE@derivatives which�4cannot neglect�0this approxim%�0. Hence, even#2���.�hexpressions (18) remain non <. \se%�{ The-�0of a point ch�!o-�<} \textbf{\ }CoI&|-�staA�)�M( NeclAxth \4$q$ located atIorigiEQ�$coordinate)� �. Becaus�\ spherical symmetry and �onarity�$roblem, fo � only!4zero component/%5we %� \beginu�0*} \Pi _{r}=P-Ii01}{\rho _{0}}  ^{2}}{r}+  1}{3( ({   .3.5.6 *} TheI� soluE�to%,Maxwell �9�% c-�N�m 8\nabla \cdot }\��  E+}4a7!��= q\delta ::r'B�inQ�0nondispersive-�a�giA�by�cub��lgebraic�>�} E-��2�%a2(� !�%� )}% )�E ,5�zX!�.tX XNZ.3)�= q6� .�$9B" H���$!?aC-�dii�ic�ftaI�"�& For ��di!ces from%q�, �iA \vert ua)V \�[$ ��$may ignore!�} terme� (19)e�ge�E�known��ult: >� *} Er)BiButi�small��n $r�sim r$, �; corr�;�re impor!Z . So qan�mentary�S$% rq.:=e.,$ \ embedded�� the )�on gas�a!�concentr�: $�810^{23}cm^{-3}$Asolid 7�v�$=10$ , M�� O-10\%$��Y/�?D few atomic radii.�`se27can b=2����sJ$n exciton,�v�'�sE6�� �A�e�%�Pdye crystals, etc. A�Tsee, screening depends��rel� sigʼn$u�$u$q$i-�sam *�J+�effA1veQis��an!�q/.�$,k��differ���sbisI�er!\$is fact ha�$simple geo� �explanE. Acc�Tg�8Gauss�or�����:��� $r�hproA��olW��� iű��dA0us $r.$ In ca���T ����s betwe�e[-}NB�-�r$ le� � ;�%�.�>�ofB� �B� come� �g�a�o)!i� �$r+r�. Bz %fse two�%�) itud� out-EYincomA�)�se�� >l:q�secondN% 7( is greaterI�* !Ea"� ��ion� bove2t N� me�a)A6q Let us��s� now� � Ei cylindI��, e A�age!�a%eally C ed �&I E}� %�( r�% ,}z,t\� =\hat{\� h}}�E: +\exp i  k\ z-\omega  S$ (a�in�( $TEM_{01}$A:�,mode \cite{� })!�1N,B. Y�no� A�&� ��� ( 18�,$i.e,)"65-?:8P=% % .� (r,z,t)� e�=x +yt$UX>f� 2��b tV� E 20BE Y (17�(20) g��riaTo�� a.}S� i>I|densityB�}� ��=2\chi ^L 2}*4rIyV FKES� ," 21.aB� �b.}Ch� �\cur�\ �i� � m�harmon? requenc��,zq ,Y�=��% ;iv!�18RW,�{ \ \ }jap/K6�-��t&}%� ��9{F��Gcoeffici��ofax �inIpisN�Z'+ [ 3 .=-�VI*) -&�E<]E8� H1}{2ryCu02BQ!t � # έ��possibleobt�opt�det o�dMm Um gene� . ��est�WG 2I�r quad/c&� !W$^;$Y :�hi�$.D=3�|X �wY g on $R 0}\div  1^ .$ Fo; width of ���Xbeam $r� 0.1cmf�fZ�?w-11�-12}CGSEF �focus��h2�� reach� 0^{-8`9_$ b"~L strong inhomogeneou�A!`m  �; w  enough%�obser on.* \proA,<\bigskip Conclud��rks} We�sh;howAt�rat��� help�E�Xei!�dvariance principle infinit= ny new� m�a�<t6 %�hav�a� one. By )qEul� ransfor��� sepa�d an� the �a)�continuA�� {R�>@Q )a�n arbitr�e�� .� Eway�got�xact &X%�!S�VM��y1p p}!e�ach%_s� an op[ un�to�8 rmin� 2{} ]�q�� veryMl mann� i. e., in� entl",S lT��'% addi!p,:�, in %8ai,�0unambiguously6��Xi:� and 9P ve�� 5mL �6| !� its *h . Further�w�== AgpplicE manuscrip��d�!�able �o. ��(work was su��ed�(SCOPES Swis)m(7UKPJ062150!&|B�Ap�ix:R/6We%�he papex Viris)zh !�P?theor��$elasticity� b2�}"� r}^�A�"0 =r-u� � r* & A.1BO ed&wrGu�5lacEb �%n � . Q�\ } � :�4matrix $\Lambd�j}^{i�X, ) \equiv) % \�� al X5 i}}{.j}4A�de��inAw�tN� �0}^{0}=1� \ }\alpha "0 "!� %=  1}{c.] t}u_%>D _{\beta !� n=�6" }-� 5 .Z)6 S>63A.3B J�+\Vo1)� =12�l)�)�\{�+�� "[!nu2|!"M-. � � �AX&� 6}e_~ \mu (!`n\s! }(W!Jm WR})2j�7 }) N} �\} . \R!A.4F^/5-�&� =1,2,3 M)+r< #��"j % u}$. $� O � \gam�! $, $Z9$� three dimAoC!(Levi-Civita�� Kronecker�bo� respAvely.y�reciprou�tilde{M6}$��u��iy _{mi�67_�m}=B /?�<(  8i-�!Kw@� (A.3)Rf>: }B"-~>% B*L.J�B� ^{-1.��3Ij�2>� !^d:Y�U-1�5B��PS ���F�� +$RNv>:�!C-1Z� 6�a�^�D1�-c-�?i!} #�< &�eܑwaX *q�num� �/N?�$i�] �A.6Bu�w@thebibliography}{sl2�l ^* } �bo R.J. PH ly (ed.)�HandbookA�laserws ed d�o�� @ technology (Chem� P Rubber Co, Cleveland� 71). 1_ 0 V.E. Mkrtch R.v.Bal!] J. Math. %�"" 4a�(1956 (2000)F>  ^ docu�L} x= % AMS-LaTeX P� *� %3 -� \�E4 [11pt,a4p�]{�(cle} \ulckage{E�icx6latexsym6subfigur:Cams}6,enume� 6amssym"�[>$scr]{eucalB1th:�color2'[�]{cap�6Lhypertexnames=false,C(links=true, =blue,H A�mu open O 21ppdfstartview=XYZ,pdffitwindow pdf\er]{�ref6�-�4,text={6.0in,9}, Ding6�i/efoot, =0.6in]{g# y6`t)�$s]{figcaps2#{>blk} %2� LAYOUT2 , %\setlength! snt}{0��(.�P}{1.0ex plus0.2ex min S@enewcommand{\baseWstretch<�a�**}{-4aA MATHޖ�unorm}[1]U#1� �/abs.�'. :.set.{+}:(Real}{�b R:eps2�(: To}{\longHarrow:"BX]f{B}(X): A cal{A�6+d  rm{d.Gee}!�!b�Q �>�Soff�(itle{Patch " �bu�%�_s� ��or!�DGiovanni Samaey}  Dirk RoosA� 42]{Io24s G. Kevrekidi��affilU\��{ Dept.� $Computer S��.|{=��.��!e �(%"es)8,�1c��1�f�� �E-!� do}1(. To reduc� *f�rti!"Zintro)d box`iEA�� �3!Vto ``sh("O� arte **�ifio�{ �� short)n&vals. analyz �accurac.8schemeB a ')u}2Z���Hperiodic heterogenee�!� )a�*heuri��Je,uf!6W#) size!l he a M���3llua��throughL^Y�e"i�chK  a�#-r a55-�q��!bPKuramoto--SivashinskyU���5��( \clearpage�� � s{IMY  \label�:Qq}�6,aR Zx V#ofm� prea�s &�*e (}w,!�ailed) �=des�}Ou� e���d%[(�u,!umNat��onehlik�$ q"e%�.�system. j"k*,E�M ,�!i}7(Monte Carlo ��bactergrowth �$SetGearOth�k03\%A stochaE�� �b�+�wabi|� �dividualiumaDrun or ``tumble",  d �6ro�(��� flagellaea*o��l-+*�.�%sX.y ��v�de)� �%F1RA�=� d#ble�K�X(est (e.g.~c�4d�ty)�i�$ulpro�s�� ,v�Ita��( , however00at, under cerw&�,F s,E �7 writ�D�P�au�%���隭�.� �� (�8\emph{Q 2�1}�e zer;m �fv� tribr): �V%l�Z��s,{8is�)�p'an��:'l�����#l�A�.reB-v ed ̑�-N��M}q,A�A�Hym (RunTheo02} �1t�6bŴd�,ea�.�� AA��yr?9ce>IA"&�is bui�!r� �ral idea!�a � coar�+,ime-stepper}����-�t$ map" :Y�t8-N. A��:s)ABx; ing r8s: (1) {\it lif�!}�.~-cY/!of �*�} �AYM�!�g�Wi�; (2) iA_ES},�&Z&B2E[(m� y) s�0�traints; !3 Va�A<e�;� proj�Օ-"�# 1JLN .R%�-~.�Ea subs�,A�Qi(as ``input"!; !|# �&s�� a}.�&�$sis tasks.a.s�$�(e:2� kbifurc� cod��"& .h�"�M*- }2�q�m�MakMara�02, Pan a�Qi 0SanSu ��!hz<ach, already�#u� in s�hal�""B& �Hu�$02,SietGra��2}�also �sA� �$�w %i,� !�co�I�a%mi '�\ ietArmMak �}�$�y deal!�S a3�_�qd by (|<uAYse�D"v�:��� }& 4��1�s (PDEs)�e�}�*� a���7}T lexity� {s ����"�@Igap-t� s~ }- !V��#��; �b�!ner/ in 1�:|��Aa�� M9��& ,  )JJ: gap�ra-� ;� y quS%k7ly8spn4to mesh�'se a tC-�al*� �N�}*5���n hig)�&m>8e�t �$ be�5)jb�} �]���� p/?� �"&wt,llI��&e ou^1is�$Y �^ uct .�O�Dك ��a! �!�We'ch� a=��� gri�)6�2,�66��.;;*P�fin�,2t�'rE�in FQ�istd+�'����*��A� file�uprovide XaՉ��&�&� . S�!�)�e2�} A���to� ~' (til%�"�!t�9m �D."�-� \�`c?���average� �\ box)� A Y� A<amount�BaQ�+:2eh!6 cedua�s X=p�7dOe��I|)�GZ�w�A0lattice-BoltzF-1�m�t!�conju9 �40 method-of%s%�EV� !�� 2 v6'����1�We�n�>}��p� �o ]�A�M��V3-�%&@.�E.W]�5oEKis&�3�<}was d to� f �{ �D@Bt \gg #" tU� comb D "��r"� �Un�{-4;���- studw-T*2�m"� a�3"� V�. o&�.o U�u G�%a��-� 1-.V6e3��srF 2 $v�F$� �5��*�(� ive)�" 2 e��d "��YK limi�j go�Tto��A "?� U hei� &4~.I . Our go� ���x6� F[�py3o�EfV�n!f�%?� �\cT;SamRooe�3-Z A+iA�.](A��rea�%*'V2zWe�0Ya3K q۩�=s a�iteEere�. (A��ned"�A7?͍d gk P�n� e"�G�z]ies. HxgF ly";;n2p� )� u%��E�At�qpre�H ��42��� �G-triv� to �se ]�P spirVRc suchB�� e �ILiYip98}%T�|� lɟ 7 ateg� T for/E(e circumven\0�nroblem %A�|a0��)�1pp"U�!���%�� s�-� }�%i]��al of�e��5�i_A�O|5n�ԉ.V!扺f ��-7'O6�B�aV���3! L��Q�E<)6sa�%� 1Vw{Sa�Roo03,>�a ��\@N�� �re�1o�D�B ���,�S��":a��D�0�_�al�%�i�$a�A�|F,"�9Azan Ily�PE infl�=�26 Qa�U�"���8 M���we 1a��%3} �$l advantag�.  li#nE:�6�onon-PDE2�Xors, e�J� molecularu ��%9worth�BAh�3yS e��r]ve  devi�!*�]eR9Hou%�Wu3 elop��e2F�"8S( -���-��ba�fun�I�? capt� ��c�G.�����HouWu97, 9P Schwab,)acEg(d Babuska h��a ��+5 FEM� �edA4a}D�6��cem�MatBab x00, Mat0�4Runborg et al.�zV�2}/  -;� :�.A� ����d "� �art bur�&�*��smly�2 many shif�6�d.Nw�K!@v�4whole���!�no� ofN���:C � thei� �, EE�Engquist c�% boraaE add�+< �Gm�v�ng &P *C 5S-aI��N�$e .M(AbdE03,EEng� y<�Rthey � *� }Wm'm �ale��!G�0 e{R&� ore�quanti�Bai �unL�^P!w \�!� _-G". < or s:� s:<�ai�ru!o>� m3=&tA����>�!doe�"ac��: by tak��a few&�ş�e�ce[*!��-'Js �� s�inp�o!�ODE-�"�Ab+v2%Qe.� ��A�A�!�!�{!Le:@ law� -7�%.�� ��2�cflux}� \ed M1yWir� � Godunov��a�!{&[@��pa�is organD2�If�� \ref�m���"be�V�^�NL dudt IE=0Aus PBe !�6p BR"**)�s6;L=ow%]c�:���� ue h.�!��^�!W� so9cu�Lo�Xy@n�n=>n:��A�hfic sett ofW-`-���P! 9�, )SRT�+"|&{�+ h �)e�on�Qb��> �An�s@&� � hV&�"�"� j:���H, 'w��a�-Y��l�#sZ"q"��V�*~"-[}}�O 1q�a�i��"O" abolHA@%al�34*� �'��} ~eq:e>_+split [_�RK}(x,t)=";_x5(a x/)\�*)Fx y8�X F�9)33{!a} [0,T)\��s 1]\\>;x0)=u^0(x) \in L^2([0,1]),\qquad6/0�2|1 0, ~$��$=�6a(y)=^��6uni�ly ellip XA:�i� $ywO*��a�%�m &�M>�� Dirichlet"K>�3� 9A.�PcBRD�-y! (BenLioPap78�!�  to (e�F5) k beS"ten��aympto! expan'in�!}b>b>�%eq:KO @_@}6�E�u_0 (+ \sum_{i=18infty}Ql^iJu_i(x,Y�,t)M��R�evux $ By9> 2S�:iH;\ldots$�:&iE 2e'$�Eo1w���M �2u�a�:D9Chom_eq#U�.�)>=q�^* �=,~f� 3b� i�Zm�0q�v�!.� $a^*5:�,�V���:wTo��t,�qB8 a^*=\int_0^1 a��1-�9>/ d y}�J(y1  ��8a��K(y9֕ =�B� 9�&_� >��:(�fr�]�/F��;1J�!Uso-z "T�щ-����)�)-& �upE nc i�1��V�^�f extr +on1 �407! 1�1�d y=0. ��6-F�Y o'-Q�Za��Ga�1(xe�} A� da�We F� a�R� o xp��n ���_ 4E�,� 6t�.KA�!�[��=1})�1}{!�}!i�]�=5 H�Dese�T�V��.�rigoro�Ijus�-D���E �7R4se� 4CioDonkU�(Ahassump�s made�)$a*7�@![� s^iMconverg��=2�� � 0\$��"� \to 0$!�$&/eC>T)!� Inde0� an ))B�y�N_�a�eft\|B�-��n \|_{�F> C_0ѮFP&_�<t$"�a:�acY�!g"�%,-!isn2�>� 2�6 +y uuA+O(�)JlY]�i�*��mJluctuYM�aQ�A=5l�A"�� . U�O*����>� �k��AZ �$�a spD,��asU6.� U%�7W�5S}_h(.1) !��1}{h}i�$x-h/2}^{x+.3 (\xiA] d\xi�=.t It� easil�&a�a�e at $ ��Ha good=iI-o�#- �*� sens q(�8m# lem:)4ing_error} CojrV:ja�P !�Rp:� )� 2�tRBRassoc,3d2��* (� > )��ssu))�4�eq:box_� } h=y^p�  p� (0,1) J���.:0N��-�p ?)led 5<.�bW yn� D9��_|I&R�{s �I1]��, C_1 h^2+C_2�^{1-pJ���A9 �1�ofe�ref!o�X[9;~3.1]�&�. N�M�t��En �egNmM%��f w�#vc�a��L ab�&��s�Y�E�� $�$~��L>$�B3{EyaQ5�*�m4sec��S����F!�e"87 N)�!�"�71�,�sl�� �# :� �0Q�&� >u. Moreow0 ac�P�J&�#�u_>P �"2t+�zPnd��"r�*�# � dard})�6<&vno-�"Su�*.��or{$d=H!u*� R"(&�es��&Y$! Em�3r;���I�inQ���)�i��%Ge�,R3�Xwe[qZ�}�7 dn �a�&5U=F(U,x U�^d�RU$>t$(o�h!8E:9-��-x^k2/ $k$-th��9vF�J�B�w9Q�sqy�c:+a�S�Ose!\w�Mto9�eV�17�2�a +, $�$,�#- qu{<�,2Qb+ $\Pi(&< x):=\{0=x_0h$. (See �F�fig���_ > s}.)q����*2�6U(��� ���9�&V�c each@'�& �A.we� �.i�"u ��m)[�^ /Z� 6���bT ���  eW��� s2�1H)>h$ �1%Z.�Y6 $x_i ��A;)TaylorB0u�aOYi�A�dt2��bbox�9�i"=6M � � �2r (IY)9�: �!���s`7J�-� sed.!�B-�& -� �a%�{I>�< �1AFQ<"�'����A^�)��a�,�#m(� �s s .G0��NA�tB�'�$t_4jI%�_t%�} ��u}^��=\�k=�Qd}D^k_i(%U}^n).4(x-x_i)^k}{k!}( x� [x_i� H}{2},x_i�T]fjd6!a, I�2��&�Q*�s ��2�!=k>0� ���#z�s���w@"�(��Ci�e&�})��eC1 $D_i^0=c%c�]nR+�B� )�.�_i�_i�%�%��_n)�=ɦ�1V1��n $d=2Awnd��b   (�]-%�)"-<&�s, B�( eq:2 _mW} D^22�� �$^n_{i+1}-2i+ {i-1EY 1,x^2}, \ D^16V)D.8U.2H},\ D^0:D��^nU�h^2}{12}!�2=�.V5n;*;4 ��I�3�+Q^ Fp+�4t*B a�oter�a��polynom�� �O�t��;c�B96} ��e��q�k2��6�.shol%0id��i8B��global}:�-f���F�W Q"taX6. cru�)a@^".m�^.� ɑջ�ves ���f~�(:]r  trF�W#�0�"�m��b �( �bs,T t"BB orA� ���.!�/-i�/ɓt>#�=�nCY7~asN A�.�,�".��kq4]�>"} )6VS�)st�9"D�m�$ -pur�*s)�] �(��/e�mnn ��*� x�wkt�&-*� k6M�Iurk/w ~=H�. {Vel�*(&;0)�(s h">f}*�J�)��)|h3; y�uu0K@A>d�bya?ces"�"� mC�(�d�)�+�%],)me�!�-igoa$ (�eaUA�Le�L$ omai$<5a�M�A�-� G�mw<%�|f�e�Iifie�9uurb�Hca�.�x(r�9ly up�Ld)R� y*A�be�%omp�cEn)�%� eli}� � �s,!c��>2 �� =%�=BJ) !<#&�5�/�:�mbtq�x�.s F)�= )e*�C | �2��u�ADS*,  ela �aHou (!s�Q ing)͈�.7}�eli�`t�blayer�*z< lso Hadji��5,nou��h+flap �Ecou�ua p�&cle�� a��tinuume��g*I�B� <5a��i�1�t typf .�J�, {Y1Ņ��H-�may)}pN��? hw6t!"jK}�mE�et.8#!y�^ee|+�   tN e  below*�\at��["�YLOE A�LR$,!o�E?�&;&� q xM � i.� �rA��ns29k T*m E�"���"� �� 6�&S}cQk�X] ��t>5 by�v!�� }N�� � $� H/2� H/2]$�5�> ome}NH�"� {n+�; }=t_=�.. J���ny#UgO�.�c�tI�.:8Re,I�69-�5�*w_i= 1/hO�{ &�� $ a��)Rg1 �%Y� �aD�M�Br�?�@�A�=!�m*h1 vari�Y{^n�{imeI�aKb7� +�$,��~a ``jG�H"-��$-map.�A�i�"p=�s,j5 "Z7I�U.�� S}^d("� a�"*,H) $��4\; LFj9 Hf2w�,�D%D%+&S!1orj�der_es<,c n�HB!9�&� }{1|]XF} e^super0pt �s�:�.�� &O?� crib�AC�+��[B�� Rp ���o/"� �l�r�^ � �O!�Q 2%/T!Z.zVS�:[8� .* �� �8!��]��V f>:&F>��(it�4P53(oit m6� �&c9*@A�e �A���c��E�Ar8'� �\"N�� w� w�:�o��< s do�6 �ly@ e� tJ �J� �nre�a%O&a"�8a!Q�l_! \04>�! a^Mi��!��z"b-�" repqld� NT.��",%�valent_#$mZ.%� odelU�nH* _eq_- } �R�1\� a��1�1�޹�w��)~(1"--#1&�)\ll1$, �}A�V�%�a�)"[.�F�&� &�'�-��%c_�&2O' tb2 �2W2�.�8 t) �2H/29ef�$"�*\�*,�M�d$�A.X %QVY�h�5��3&F�n�/J�!R�`�~�)�sr��v�E����"� FE)-�)�)��Lw%�RT!�Fh �:!O& �  ) ""B'v'2��,-ZN,A�,� 'C_3q1F2V��D Zs�t�ird�ultK�"pro�v��fg�v@�All92,&�-0uww��V��LeF*Y�"3 �^r4 *�64 R5 *6 n;FsZ��t� �,y�f!WF&��]KM�b� �? �J5>�V} 1m:u Dm! [ JA"v %AFv;�A�P2 23� 1� 2w��y�Z��x�� i�n�Wa�a�d�[c.�29�B-*�3p�xeI�*4.2:�*�9 %�ce", !)�y U}6�H�'$B�B(2�.�- Y*� �S%� v^{nFR\ z�u�.X9SU�q`})h9�!.�),��*@rA�*!��n��a 2�-{p}}pu:�-#�f ��wY,q�6�/�3\|-2_i=Q-%�U6\G; \|\le C_4nJ-/&"!6d��rU��.::�& ,H)-�2 %a�!>9� � �f�6�;�N�.�.�Again,W  p "�7aCbNd9Lar^@f*��&lYj�2�2Z B�-��_sr3leaD1check< �d&~-Qsatisf�G a�6>"� Y����-���#�c>�)y})�)0��r��Qeqnarrf.�( &=&S?(2�) \no d\\ &=&.�( F�(D^2E)F)v<85[ � ;6IP].& �a� $�&` �<eb �*�6�.MRor��v�$�!\F�"��� 3 9�:�9 b�&�k � thm:A$_wrt_fd.�v6�"���U`F(IEd8"� ^+�F _I�X�*�I%�AùaU:[^�U� Q�di�nmat�9E(8A0\|��v� -EU 6V\|�$6g���YIr3C%["  /H^2S8,� ll HN�>-�eq:�_��} 6�\le� (C_1-3�:h^2�-i)�]ft�< exp(� pi^2 21$}{H^2}mBB| �bAj�� ���l&V Y���&+ � M�Il�h�B � ,i0FQ�y_:Z*�7t�cq��t[�,of&�J1mU.�Q_ ?��"X=&ER��^$��)+ D_i./ g'!z {8}+1(0'\\ +&�'m.�@a_m^i!�I %�Em^2%�)�(t-&) \sin 1 -\pi}{H} m- �'Q Q�1end2  �1(2<��%��8_i{�8_iE*�&"R%59 � �)^2�A�4Y���\d �I�.���beg" plif�<toR� � �2a�!�2=� � -1)^{m}-1-�}{m^3 !�,UN��:y�j�fP,Q��K lineB�-L�. ��+&�&5l +�'M!nJ� -���+J� >4N}{(2m!3) N� #�� 2���53 a%#��� �  a<�7o�6"xM �v�)!b�IA�=�]� ~�v��4r�\]|_m>�>�֔�>5 �$vc2t��WuU� *} +&=&�LB��!v\\� eH1hA@i� \cos �_[2H}(H+h�* -~,-,� }�m _2:�:�6~h GM�9@��� "�Do.-� $ te+ o $1�@ab�Je���A�zQ �k8Ke� J 5]A�F}��� .�e2�R�"a�-�a:J� i � �+[�c>S.�\; `{�C{�g�>^ ,-Kqu*w!)-:)\;I� )�1.] @/2� %��1jQN��>_IX�e����E�| &=&4Bu��xiQ�F����R�Ix��\xi>�>� ��.��6< $\xi1�( AyB�@>�*b)Maple;*atUG6�\lim_{�A�}%�~X =a^*BM 6_��<!P��&r  �"zF�4X' t. Oeg� �9�� ��.6!+�% 3T invo��� "�6u >D$}��V.�q�f�`F}_1+-`_2LJ+ ��/�2�&* C.>_1��M�v>���\\�2���q�- �V/ڬJ3We(�A��-�_1~��!�XA��[rءe"oo��u�5�5&��manip�d=6u�9�5C1� B�RX��~���)M��%� ���B�\��BJ�� {m+1��i%>�-:-> �:����6F�6�_h�B� � *�a)"BZ� e\|=a 1�9a^*�n6* ^ {a^d =�)2��Q�(} \phantom{P:B�%h$\|} &\le&C%.�� �C>� A)}��P*2_1:8 L"-Q�_)�x nd�z)�i�-� "�Q&.D,J��2& 2PI& �\| = �&mm�V(b  h}K l�&[ \pi h.�MCI&H(6f q� Uf !\�\2�I�>�\p:�-� -��!�3�mF�2�A� C= )� � PnG xi)}_ pi}zI� ��NN)=�9=eqM��8F�F).�hof "�.�n*�  U)�ve�k� ��"�7*}R .� f_� })�LDbs � x� deca�da8�a"�`�22$�| 2�a�#Q r:f&�Live"�� h�854 4K3"�2��)�a�h���*��5IDr�Ao"AzP�+�!Ut{>=}> :� G7 rǏono $h=0$yw�d*�'�caroT?B%v���Ng *>y��"il�|� �nu"�(E"b�exS/��!�_5�U+ ��Q(=0.45825686� aR�<9b5 $F E���W<FL$�O40)=1-4(x-1/2)^} To^�zisN��JaM)�rU*F�6F r@wi�Q�x=2\�J�7r 8nd \verb#lsode#a*��x!L[re2=3m �S-�~!�>ua�-�!&��y6"�<�~! .�#�/)�$h � �3 �$�<=1�T  ��LtGP orE "=&w �FFisB&�C�EB/�Ee_ex3.4}�i� j h� �uF�!^.�Gu��� H$ (��)0 1� t$ (�!'I�;�1* n'}"7&n agre�6!B�p �>��� stag��%�g7*/��du FP�:�6&1>[� $B(/ �N clud=phi*�C7&�CE� _ifvE _eps1e-05��s ��L�_tL-bwOc��{u!�!�&g��A>o QB� (��.D�I,Z �]6�J���{Fb�s!С)�g� D �)$3C�A�(. Left: �>bA�a� fixeJ%8 qRight: Z8*.?H� x�Ee<>\} �I" > x=Del��=R/19!b�t��sa1!+ult"@%b ac�Qvcy} ܥ"s$&�2JR%.�_�$��� a�G%�U2:'�"2C.]m(20 i�Q"0 &|%,œ$.E"N�J$�w�!pLF���2�%Y�c;` 0 � �S$Ue �&�%�����.-�eq2�i �%FaqN>w'M�� \&�$0 \underbrace{� j %}_{S]rm{�4�}} +C_5\K� 1�E� Q�, L� ing�nFFg*� �O( �U � ar.�-9�i;1_ a��&{ %u�dys� � 2�#�1a<2#�5l=� !ja1� a� {.��[� .�)�im���GN��%�3J����j �h"1 :ks: ���Ar3a��}alB��G�{t&��6�o��MH�isEO �(� n�<u|ak j|e-offde�ij�n �=�d��� �{ _u@�WQI�0H$ �to�[chF�([th)s; ��!a�}st), ~�o@2v l!�"0M�%���s* �r�A�"" aGET�Lx�Fx:3.6>�%�dA:�-Yt6{E��uD��e8I} 2,]=1.1+d(2>&�b) �I�w2� 5m�l E�.59�� �76 E+� aW2f� � �!)�B�(Vs�Y�s}O4<=5 *Ukm2�G!�. N�e .  VF�6 %��B 0 N � �Br f x��&+-bBM Y�� J �ip�*_N � �^ �'� V2�7"�Z iKW�Jb�6^2�. a �)Z 6Va � F� �e� x �a e�"a �.?%�re !Se ��!ݪA�We�]��/vX ��in�H &� !�23٠c*toBU�XXp�l �c� fast~� b�Q��  5""� �Q%6� T�� u F}�,>) $ � G�2� ��*� � ^� H2| Uc. � V� *偩;� H9\r� 6:� r � �<{C=��!y�G&oks� r=(i6 ��>p�n"�n, must!��$�*�B��D�x(EMn�J*�&a { H#Ra)��2XTcHB�"� b&M ad���?to ensur\[` teA,� �W!+J� *1T9%,*$BUA"dQ�+#1i��t-o�:>[ .G�i �� Ra�)"� �&7 �oer.� 1%I,n�e�A reof ex!�ngJeĒg&�,�$r PDE` A1�h$��b&�qly�iD�xall��� ��s*� �J51��c�Z!�o�. "[�cae 6�A~On�q� +r�9�P%sF&P�J aaI$ �V 9�`re fre� �]�gich� ows � o*� .lB�M�. &�Ni�q�@\� u�:JyHf��r� &g�, s�Z �Q�N. uW-�e]L!�d�rel�F2�_F 'OsQ:=. �*� focu�BU�A�!�6QgH�We�AN,��KZpAg�P29�m& �MU&v.U�P�<��%des\�6a)�B��"� E%� .� �vU isdw�$1y&NDa hu. �D�an -�&� 6s >F���[tX` �[ $x_0=56��0 $H=83}$j�@�rF��w%!2� i" L*%1 NDee" � . De"V_�!is5&by�u}`>ANnd^"�"B! ��> &=& ��h�# O�G 0O*Z*Y#{ 1}{tT0\xi-x_0�) �) ,b&Wd0)5ii,*Qoest�x�� � "� 6� x�9[(-, /2,(�+*La9i� %t_ f_avgft}\U�F-ba .�[eB� �kw� {ee�xh�8�E*���:n� fm���� 3� "AlotI�� ��d�=&6�eL8�re�ko.܅��]:u�*�rdb ��(z�D&�B�r.4n\"�Dүu:)n� ) +BKAI��qBO�._)} M\�r"�}(D,24D\3D2U2D"1D[/�I�-- ag��: om��B�Eeq2.�z!� of5� � s,>��V ��A�eG�dMn4Onagg��&;�72� �� e�nG��6� �Ar�Z :�_.��qu:�2& H5i� fv_xc;R���"�e���J0!s ���V0!�iy!�%~/~Y-Qb*&� �!n�8m��;���ea��gets O"i �J !R��cesz�_B&E~�rk�!��7���Do&�tsi��~=�&2 �3"�3����"X} "(0,��iF�7�1) \| <� Tr#,�v 0 < * �1"�+q��F)t�F�_��B^.h�getړ�#�v,�U��!"�  = .�6"� �=0.04<i�m�q�u�in2N (n/:�R=c:$� Jz (da��� 5 �Y�(��)An6�%=�% !.eOJ�6, )cuz.� &R� e�o�-`?81}6�! co�Yed \Xy����5&"� }�h��{!E1�J�$�"I\6�,farg =ec1 Z&�[.2��� 7 a�ady" te d�!FF�K9=s�,XMt@���ý�"ɾvRj���%a�V� �� VA B�5ATDulUXr�9P2| get+c�ept��5eS�o�e e���&�q� �7�; �v�-� &2'U%�2�dud�the*h�!��3�'�f�curre�]�[\�T!v^�*2�D"Ľ6�eOaJ7}�����O�M!��P�;:?�SN� b��R�>�n&(!�P5�ofY�T :��l3"s��.L�Nz(s&isat��IQCe" = p��0QNY�J��19.�t'aa�K-��,}?\� O%� _ >k���&*Rmo�Cncas��0=�5MyM5e}V�#%Tr����|�,9B��& *��r�"noflux� �h &� �O*q ~F�O. & 6�P;� ,\\c:= -� 0� �:)H/� 0͵ ������Z�e!��a&�lA�6�D�.�� :�pyQ�bS����(>>� er6()�&� e �M� �,ec��)$a^&5'"B&�� �E ����&�(�2� �00-*� �'��}�u�&t > q�K(:!�.�mM�y ye:ʧ *�f >R�.k>�2�D&6�� ZD!��)��@�6(�! W&�3w=rz��g#/.Js mi)�+�x�� IO�� �0�blg�7N\a�&ktw�rv8ly mimicj�wF�dom LwWZ� $H=h"The�Cy� ����ut>�(dz� i�gn s�8�|,�.�zG 1 ���!Y�$Sachie�ib�Vst�g��'.n�`+G �L P6:j. i"}= �%JbtcZpu , oraDt�m�� �'�-�� forB��%.�[)ds6cM*+ od� p��.��)�t��FZ"� � %�.Cs,�� "y�codM�fa� � �fa/� )lwg��+�z� most�fulqEs �h"Rf�c�.�� �fU{��3� , b��sB'>In6�.%Y �  �jmi\ /ev� dom,%�\��{<_r  2��s��A��g��&s3\quick�iQ�slaa ^govera Z4e}s-l!5-/!��2i!ed upo[�s6��"�GeaB��� 02}.�rhl7pX�qf�U�M �y�v�0sW6j�. >o�F=�*� !�isx usu#l mea�rħe"U;i@�!i�iM4�01�� ;��O�N���, Z�Q (so-�l"<�ma���v:Pts`U��3���p*�5Morm�ge*�m�ab�R �� AY�te�qI�f���1 �� t03,"ĩ� \�St�k!�e"�!�Z� 5hbe"v��.P����PvLLustE�4Q�n&�ioEUA��z�� lB�e�bd b6��?#N�p�"}} O�38 " B�&� o)M)�u� B�����t2��s��:�!z�njR�/ �mW d�ps�|*�����@ neߒ��o*�{ 5*&� uܖ(mN� alig.�fe_J �{ 1}&=�R�#N�R}}:�{=���t{e��@�� abbr���=Zh"PS t_n)� t K�5�6 %�"�$- �0y;fe_$barq){n�X U^n}O~�v�e�)F FJ^d(B�)�2=Ha� a:IBf�)��eZ� A�a��,A�a4!!U��:o�-�"ցto�<q)N�w se��� !p�p3 �w*� $K4�M�e"���>�H]�ԴednX*]j ��f�n���$("�~, .�k N$;i=nQ�"n�l��,T/!�q.)F K=\{\A_i\}|\|D��g2ix}UJu&�2}H}�l{a� }& e d,/V��A T �\}* 6�� !� ŷ&d�.5�� �oR$R�E�A@h=� 21�M-�4� �shA~;-!R!$C5d  �he �[:t$� x� �:��eqtkTV�!�S[m*~5�|1�A�p �"�0�. ~A�:E4E21/��!ѐak�5.� E�ar� � s.|TE 4�m�M��>�&���)% 2 6�F�c"6��2O }). �[!�>\P"��\}�UE� "�.\}.{KaOU^0*IU} �S0)��p~��#s��bn�(�EV��� b��"\ C_11� x^k ��)YV�# x_{0\le k� } Xv�-����\|�6���4� N�ǪopWJujEc T54V`-�[ i<"\<��=�_�5�R%a�� lthoC��i[/ve&u�, ��_ic�D#%!��&�*� i �L!�Qw�U1)� x�t\F�ly��E(.�d� prO�z V'\� unQ� ��c� F�� ��H*�����P���)a)R� ��Cj�r3eigen"4%A .&� �4 :: 2�:1;A7� �M| 6"B&�9.7>�#� U8B�:�.�k�Bive��&�_r��.�B�'4��,�>,�� $y�MR�B��K60 )E�.�q�1C*i!ref_eigf�lambda_kwW4a^*}{�@^2��$n^2(\pi k )+am!w#�R" a*��� 5U�&Gj�displa�\\m�SkG|1+� ���|�o1"K;{�}�(3t6�le �(1��WKF" bdQ�M�9�ŰN�2 tc^:��, s��a�� pr�zea~Ta�fPOe��� -vec�@pr���&���a 1=.�ar�N t" \B/���e2}�"b� H)$,�hArnoldi.�(/.UrB� 23� �6�ErPv?2V? �#5n0�{'k �>&c83�!^ �"�"2�,�#ZE XnE%�"� ���^'�K���| trum5+H}>��B#Vv$:HRv$:$ S�rum�a�3 v��$�[9��)� 6))¡��^.%��� ���.QG 3},42p.�.%2}I3-� B��A��O�.�)!#.� k%>�$� )�} T��<��I apb:nt:_1�= neg/c�!az��2 ways>3er� :Yt�#�"6A hA�.�!R�p� H aA8� "k . M.-� ��l!i�a�6U_+$�� .v�.�5 t�m:��B !8�Gd �(co"�D�VN"xm�*Y� [�"F�"�mq&��B�3F;ۻĥ� :�P^~dN�"*�e~ s CO oxidͬ@�&w�Y�catal$ surfac!�D&� rea4-,�NB�r�Eف�/pe�M� vali6� nR� thel�>/A��-!�N5Wi� Re�5;,�ourth-�U��VD�K�1C zd08�!� �mb���p?ing]0e patch dynam�ics scheme with buffers also works in this case, showing the more general applicability of the method. All computations were performed in Python, makause of hLSciPy package \cite{H} for scientific coc��ing. \subsection{Example 1: A nonlinear travelling wave in a heterogeneous excitable medium\label{sec:5.1}} Consider the follow�system�4wo coupled rea�4-diffusion equ) , \begin{}\lm eq:co_eq}!lsplit} \partial_t u(x,t) &=  ^2_x @+\frac{1}{\delta} .(1- ) \left( - .wR+b(x)}{a$\right),\\.z (&=g ?)- , \end� �Em�2�)�} g(u)=+A�8s} 0, & u < 1/3�T1-6.75\; u ( 1 - u )^2%1/3\le ,*u \ge 1. � T:�TA�� modelsE�sp!�4temporal dynamaF$of CO oxid �>n on microstructured catalysts, which consist of, say, alternatE@tripesY two A0erent.G$such as pl4@um, Pt, and pallaA�, Pd, or$ rho RhmQLGrahKevrAsa94,BarBanH96,ShvartsSchutzImbh9}. The goal is to improve%( avera�I� vity�sela�bya�bin�a�) tic a$ viti �he �metal5Careu\8through surface%3ec. Incab�%�<, $u$ correspond�k ?!�centr-�Pf CO, $w$ is a so-cala�0recon)�a�varia�8!�$A� :�n experimentally fitted sigmoidal fun�$ . Detail�}n b�^und in �Keener00!�93!� �is � $a$ �b �(time-scale � param�� $� $!W physical aat incorA�t)�.�!6di!s:9�� pressur)� O$_2 �CO���gA�ha�aaZeraa2,A� well kineA%d ants��=-�x. Here, we will study a domainaHPlength $L=21$ with a !�od�ly!�yA�mea:!�e�df t!c)�thApt[as�is�~�<l amou�of Pt A Rh,z Y wid�(\epsilon/2$iX �Am,then defineda6�c!j69par} ��4=0.84, \qquad ��l=-0.025+0.725 \sin(2\pi x / �)2 I  = 5�.t �#ł(cular choic�UQs� aken from�kRunTheo�G02}� $ere an eff�e bifurc� an�6i1�U�wA54resented. Fo�se� values,!D_�< (given by (\ref�j)-.͍))�v�h��1c 6c�2�(} supports :�s��t%� naG�6[I�thiE�cl�  reaUu�R%4 )h�o�ityE�isg done!&"a :Q behavioura�a���@of a large number�D�� shif��realiz)�� wavy�usa�Y gap-tooth� %� solua Ap^��2� 4 each box, butNno6ofY �is id\ cal. WeA�os�e sma�e�HU� u�H=1\cdot 10^{-4}$. �.macop� arison ̕�y Q >�-]�Q�2�E�)Ñ:aŷ tandard s��d order ��l�fc�qscret1�in!Xa�n a2�mesh of��Db x=0.25$,��edi;a�$ward Euler͌tepper.O ɞtep�chosen�$ Xt-X %X2}$�?ich en�bst� Opatch&� � �%�d�_ed�ga�%Q�� obta��I�aY�$ estimatork�( derivative 4A�ini�&-j9� spec� _ !�4sam�bK � �w!cedAr!@A��eA�approx!� ion Q��A�U�/  x2u6 �,\verb$lsode$!�-A�E�A�1�& AթkbyBH*"� aligned} � 0)&=&�t�  � 8x \in [8,18]\\  , \text{else}� 3� Z X � s A0.5?5 xD x X 8,w,.07 x -0.46 8 18 N Z 6� ��*ke resultI@��figure � fig:co_q on_ 1 Y /5g��er}+ {\i�(dee8 ics[��=0.7] >0n/co_sim_grays}�Cprofil AcapA�{^�Left: ����@�:-.#�����@R��ha"~  of��� A�. Colo� n1 te_ , (blue = 1, �= 0). R/$: snapshot��:�at cer�H mo n,ime, clearly%��� e��� to a> 5.QB-�MP)�} ��] ee bL��'ialXnsS �he fin vel"."t. z  ��purposw ��ut�� erf�%� gi6�6 T:�F"��� ��(n ``exact''5 ��R ���Yq r grid (�x2|3� 6�5��Fe� R�errors}%�]e A�!>�զA� pectA.F�1RF8!�%F*A�b ivel :; z6� -�( very good6v�J��� the %> ��%�9�is�ina!�by=)O l ^l< 6!��en�":mN� �s8z� ) E!��a:=.�����>#-�"9&^ J(top)A�� e. F� (bottom).� ق�b�v�2� Effi�� Timft���>m�F��@� r%E an a� lete.��M�� >siK A�Bf used only; , �ionu�space-��A��(OeMes�BAn obX�cut�  always�ct) way���e5  is t|mp(siz� totalJ�EI!-�z isampl�=6����in 6\%Q}� �. Of�rw�it!CpossiB��pply �ly1 bary ar�inner���e'e%R(necessary, ��h�! woul-�$cover 0.2 �):� For } *�homR�  problem�e��e�atR� requiS%w�strA,�f grad�A�� 1,SamRot*�gH����d���Pm� the se� A�91� A��la���.�" is sm� (few2$� poi=A�needed��propag �of�artefacF s slow (iy9��sum!t). No�� higher� 5 @is)0�e8�"a�.X�*5Y B=]simil� !Ca_eq^� on� sey,%W*3Z .4� 0�7dwsaS.���i�P ffo.i� l��/V 2 Tmfo�MmF, w0�!�o�$2&N I+ r alisticWyA�aU�?A�R�not�q���E��h@�X 1��Fb�er,��add�a�y�al��ort�b�m�to}ovep �2� at w4introduced dur� lifT!�, e.g.1FA  ofy��"# C� ainta�V\2: Kuramoto--Sivashinsky5� I| 2}} 6�v=\ 1b*�ku~D*�=-\nu"� _x^4t) - �!� _x^2 �H�,�'0,�]BfE��N&�sJ��h�Df��entlyiI� " o�� mbusA�U 4thin film flow5 ��Q� $\nu=4/1>(it has been�-�a���^&"� s, � A;~'{$NicoScov90"� �� �E�e: , "'.Y�/.C%��"�"K!�� ToBv.@Bi e�d�}�� fourth�ђ&js� 3oZ�s,�a .�ŅF��.05\pi~�a�� o� �e-aϹ6<��:���2�@es due�\!�stiffnes"e F� .� cceler�S ping= wra .�$\emph{proj��ve �*� hod}.} N8�� GearA�01A~�6v#ŜK"VFirstER �N:ftep&J"�4*} U^{k+1,N}&= ,N}+Q \; F(  ,t_n�!�rK �-,h�Xsistency, $U^{0,N}=U^N$ �ed!?�extrapo[��0N+1}&=(M+1)\;{�-M\; ,N}"#M>k-��})\a�$ U(N\;(M+kT � t+k  t)&� �o s $kYM$&�MGF reg%7_ulŏY2 er. � "� ,seM� "�2�&5 check !Q��z,�o $k=2$� $M=7$ �@ale�A��� d BiW ` ucDreplac?a]��Z $68$)�&� &($\bar{F}^4( U}^%�Ap;�  t,H)$,�IGu�i&�Lloc�4aylor})Dw�c��)� T+��on�3be $d=4$��] <ts $D_k^��$k>0$ � *� `..B�� :yѶ&��!{solved��B{� x 2�5}$, sub���Dirichle�no-flu& a�� s,��#�#F�W�xE�S � h2�3�\aW5{ s �% ��1U(cy } Beca*�'2� termt orem� thm:�! R}!+� k$n}r^ wee�lyiNED@QU�,!�!�ua�E7�� E¡�6F$H$�=a rang\� � t$��a"� �ingS2"th�:�� As"W��s a�j1 I �Tch�$u^0(x)=*"�4 �2:|.�ns_A� (N(�6W"Vsux >bNy5_ifv_� s_nu6|�G$est_in_box�} V� �q{1bN  ���0,0.�Mo :�Fo: &� �lS%�`jf4&� �fv_x})a�Y��$xQ�&�!M��.imA5:�howem: e geA�#��watIe��OendC}� � qualiClE�s�&�!a��6 �+2 5.(�"o.%'re� �+p(e!g � � as�Fconverg;Tis no longer monotonic�~� xplai\#R harp peak��� curvqAlso, b�5:&�trs in�s �ast�Pi�&be / � Inde�O�� suggesP$E a�co�)mis�"twj a/ >�bm �6͚� 4*� 9}�H=3\pi" rea��!�l 9�O*��.c�>!�7s DabH)ast�"�&�ais  W 9 whIlF�!` �G�for�to �& %nt� AE �&ABh'!��"�On"4s h�.to!]� �$ 60\7&� �(. HowevA !B>Z#l ���? to �  1/25000e�h. [ Uf &� "�  O "�~� l aYE�&�about 80sac�dA&,�n.�&:�%�*l `E�Aly be�ens.~�EiiAJ&�creatppri"� Az�� ��K draw�WcoE EAu -.a" i,5�ht� R�s!�!,%<�^=}�0heavily depen�&�)&�� cale��2� q\$A�� �:$2:$�$| �paJ�%���e �i9��K =$.53�Rp�ȍ� t=:�N� �>$f>$53\�>$J>$.$:.1 -.-$ 0,0.8\pi]�# -1+5(x- )�#S$ ,�%+0 \\ 2.5-7(x- - )�^�<��QZ��#kur��#^�#62&�#g��#NEz�#lr4"�$_ "ofu�>#&�R7 6� s�#� �m z�#4� d = -4� ^ b�# a��#��rb�#"�v  �ql$e� ��tr�en�e��#��#��#>)#2/: �*#�*#"We� �*�9\�1%^�L oscillates somewhate- o% <.>%��stead Fin�y�lin%�,� a*� ���)ed�"spe0.�  #tignY+a��ia%� 5.1~��)AU or�4lp5 te��%"� 1.� a�1 !� I er, jq  �&� xG!. 6_��#A[��%w��cF~(%�� *Ƹ#&�kur�,�W!aa���&I� E�) � grow 5n� b�"e�h7 due� a sl�(:.�In!~���6u( �-���1s*X*4 `Wiscrib�V�� m��52�isx }* unavail�6�"'}Հ �!]���PI5M �enh a2ev�)lawA�� ;��  ua��e -$�iz2�"�.}model �e?  ts (%,es)�NA`� .i$ . Bvk#often� "u#!�im�).�2 insp�""�c&|# 1�9/%s ionA:oC2o: � rf� "�# �!^ ich 3 ri+iel7#� 2:l B� =v5�"Y.� �t0lyk3*i<�jg0!�%nV�#C&~q9� nu���-O�W algorith�6m� widA%icA��*7m\ pap"!giv5Fy)ua�!�*�$�=n s u8a_.� PDEN+asE\v�{0�sx �are faD*E?t��t�2��2�$M>!Btri�toNz%� ��\i ec�,&�N�E�a'�W�<�8I8a�!V�� advantagIJ�@s p�7 �l�; heir5�iQ@ for }Vi�!�at% 6�1:, Monte Carlo= mole�$ �= . E"�;�%ir�a�e< urre1be�pursua0c,.�,*{Acknowledg�.<} Giovanni Samae�(4 a Research As�anM:!$ Fund�S�)�@. - Flander�=6��a7!� gra IUAP/V/22��b� oAtNnX=PH G.0130.03 (GS, DR)�$an NSF/ITR�'� AFOSR D0?�GCo�#Pl, Dr. S. Heise (IGK)�b A thebiblio�y}{10+dbibitem{AbdE03} A.~Abdulle[@W.~E. \newblock F e &�*�8ou[lt�EI�As:� uT.\ {\em Jour�$@&�al PhG=Xs}, 191(1):18--39, 2003��two��*�.4� SIAM.�Mathema�� A[;H}, 23(6):1482--1518�92.�8Bar93} M.~B\"arBj`R\"aumliche StrukturbilduR!dei einer Oberfl\"achenreak�� . Chemi�� Wellen �> Turbulenz��8 CO-O"dAauf P^ n-EinkrisT?-2e}.�PhDa_xsis, Freie Universit\"at Berlin�2�.A9L, A.K. Bangia, I.G. �! ekidbs:Gec� !I��~ ]�7AnA�!�on.jE]�I�al-�tryA�800:19106--19117%62$enLioPap78e�LBensoussan, J.L. Lio�8G.~PapanicolaouB�Asympto�(M�aN"�&st� G@}, Z me~5"� Stud�BMU�� d its AppBAos2 North-Hol�S , Am`dam�78.�XCioDon99} D.~Cioranescue� P.~DonatoF���(}�652�OxfordY�y P>A�99.� EEng�����(B.~Engquist.�&�=V�F�Comm.%H.�.A��87--132F�G&�$ C.W. �:.��I;�u� �%����"� VBB.J )��7eigen�� ctrum.rA,B��a��5�84(4):1091--1106��XC�-"<$as {NEC Re�0��1-029, �H#http://www.neci.njH.com/homepages/cwg/&x.pdf#}.�b!�*�*�o7-> manifolds�Blegac�d2� low-d�-6�+B^JI2%KA8 2004.%I0es� ��A-Li�;A�U@�E~Li�0jHA�&�IK�2 cl2�1.�E�� s Le�00s A}, 316:190��5���1$s/0303010 � xiv.or�J��2gG�ID. �o:�,, K.~Asakura) auterbachKr�/r�^ �`Ef�C�Wbiar�1N,:͂��o�q�+ 2�vN]� cea> 64:80--82��4.�Hadji�JN�4c{&antin6 Hybrid at�tic-co%uum��u�V4 h�L�  tact-K&� B��}�6� (54:245--265�2�,HouWu97} T.Y��X.H. W2�A�5�ele Q�Q ellip!w��i��it�material��por�� edia��(34:169--189�72��9��C*$!�C���9��� rapidly"Xr coI&tF�.�6� H}, 68(227):913--943�6�um�}� Humme��CoarsAoP&O)%(peptide fra:5/e �Igy��)�R"�" � ͋F�J.� .���f118(23��76� 0773��212108b�rOT E.~Jones, T.~Oliphant�� P.~P153! et~a2� @0: Open source.�O tool��{Pytho!�2001--.��J} J.Pl !O.�J( r/5^ b( #+�.C�a D�36:1-- 20006�vr00} :�.OM'b*�H�8�yf "�Mve.�/h�� ) or2U Plen�7le\N(, CAST Diviv D, AIChE Annual MeeaA0, Los AngelesA� �&�Slide"lL"��I>� arnold.pr:$ton.edu/~y�s/#>"��Hyeb�H02B4, 2�M. HymH P�"a�V $O.~RunborgEx<.~RJ doropoulo2,E�2 -fre&%lt��}a: eE$�g.f�!ors � �#,(-level task2qEA:A =&� 1Q 715--76JF �*�2>X,�  laenko� J.Cr ove2q BackQ� saddA"� ���wl-M�'h�d{K}ura5{S}J5.��>hAo ed.�4}, 50:760--790��2MPvLLust!404} P.~Van Lee(%� ��q-g�5ed*s.�.b latt�Lboltzman��F�P��>� Subm�O.�� a�3��� B�]��j�DecidA��na-� ``cɖeM�'' �mi"{J�X: :I$baby-bathw`VV�MyD%(��m/i��1(3):3: 407ъ&� LiYip985D!ao)�S.~Yip.}I ng f�� � �%A� {MD}�!fluids:� p�Il& c�J�b�V z�Lfeedbac{2"CE� Mat. ,. Soc. Symp.�cA�$38:473--47?2= MakM�32,G_keev,�M�=dandn��O"�J ��]U�0"stocha8 9� ors: {M}"{C}arlo F�JFs46:10083--10091%�2.� �PJTv�0A.Z. Panagiot��I j - R�ofb�Y�� �-�RE�\e�U 5a��$7(18):8229� 40N$tBabSchwab@A��MatH~Babuska)C.~ +.G�3� -{FEM}a6[.1E�Nu�g"3 @k}, 86(2):319--37�2�����2} .�B} �j���N���""!p�@aLBa�5achF��Yit�5:4�v51J�Sa�oo��G.~�!s:�a�D.~Roos2 Damp��acaH� ��&!]m24In��At� �und, @Koumoutsakos, ediP,)��b M{�eS"�<}"36A�%�L �"�2�'��Engineen2}, | 9e� 2. S� g`�깼S.LA.F11�Th*�)-2%K6�� b.BB�9!)!�!X9�[�I#@; ipli6  ��^�N�&� 1204  aN�i�Mata-u��.�n���re"(�I 201� z��cN� chap �S �S�Z�Q2197--238.�Q=-VerlagFSet Oth�T,3} S.~Setaye912 Ha� OthmA�!j\x :V����g�X�bacD$6motaxiFcE=%���Ui�DIE3.�IA�:�ZF[�a[� E��<\"utz, R.~Imbihl�Q"Xon� � .KR*Y� �#!%��v�jW iJ�� l Review.�;3:285A86� 2[$SietArmMak%�2�I. t���rmaouM* z�M&� /&��9sPTY c� �\x {* }�.��R{M8J.}}, 49(7):192d92J0be&?as p`(.CG/0207017fciet V)M.,z ${B}rownian&�a�n( liquid cry8s:.�"&�2B}c)Q vip<d }BHJ@ ��149D 15") &w JPW$,-mat/0211455bQQi 0Az:(, Y�$�c-T�z .�� #F *w$o ..InIyPrc $Natl. Acad����9).2� �SanSunYEB�K�,nkaranarayang�uXe�!�jg- .� C�bub^�C {L}` -{B}*b�AF{ .��59:23�e3&8Y%J�eu$PS/0111040J��)>^" �T docu�} % -� N\R$\u�3e{#icx�Tet�){ V0height}{241mmF�=}{170y4renewcommand{\{ A$stretch}{2!"b�#�} "�#,style{apsrev-title{\9 obserY!c�e"�C a]Hgl)n�[aF� d indue@ dev��KEKa-8ton Synchrotron}Xauthor{Ken Takayama $^{ , 3}$} #(unio Koseki#22$ota Torika 1, 4. Akir! kuch!5.,Eiji Nakamur.!0Yoshio Arakid "B$to Shimosa �2"MasayE Wake�2 Tada7KounoB8Kazuhiko Horiok�2(Susumu IgarIBATaiki Iwt?2~,Atsushi Kawa�2 Jun-i!9Kishir �, 6. Mako!aku)"7.$Hikaru Sat =.:hih3BZs�!^ rakaJ�Tsu)]SueJ@ Take�ToU_6�(sao Watanab%�2�IYaman; \affili�"{$^1$ A�For Labor]\4y, High Energy2$RY( Orga"}OT(KEK), 1-1 Oho, Tsukub�$baA}, 305-0801, J�#a2�2$� Gradu9U=%yXA�)ced�#, Het , Mi�K�,awa 240-0193^i@3$ Tokyo Institut�0Technology, N��1Z4�g!s6A�Woth edg�\f�9��+i_op^M9,!$� ��:.~\Oifig1})1*�3�I�2�6 �A paivG$barrier-vo� p��0)9BV Z!|�� 7B�demm&� FNALE;BNLY74�Oe6a�2�:qF2?2in"�Aly achien5��]%tep�E��Y�P5i�Fte\�\ert��5� -fun�}��2�d"�2bs �Ca%�ificant�$dokU$ beam handnD*<%�:IRF.�,�pradio�!queLwav �a�4onsik!�(ultaneouslytE�arolI�2�n�aussociE�%x):F), variU'fig^dof 5�Hr�X�_`<��V� 'ap3er-UQv`n  Qem�6!�w�a u�+rm��-densit�gn�7,M)=�6onUN[E��dr�0�M&m١3neutrino�Xa a fuA hadro�l$ry5}�~most att�kIn \E,�=�hf ���Eany�Ճf�� seemE�pea�\���; �c+sub�j.ly mitig� undes�9 phenHda��%���rteird,T$non-adiabaml!microA� ��a6��6�-!��duVbw8%�Xc�v�E��NYE{Dza-circum 300 m,ep� AG��1 MHz:�So far� r �"Xno�-2Gs�w݅m'�� "�j�fe�=ly,i[typ�=q�4�1 a 250n!Qflat-to9�.,>�cw �,�I�assembl)j�af�!�3-�  R\&D�g� nd co?u�)ex\ng�~J�O `�7i!�UprJ�bucketV� iٕJg� >� JB1.6 Q is lz/,vGrep;\�ygrst�S"0u�#ul�!N�� �����  -PS)�wttD d�?pE��NyngMh.J2�  95_LE�:�+g�.or�30�,�% ival�eEit� ��key"} q�a��;�mb� ��2�ng y��7c a>��1!� �58I suHvn�y&�3I8� K d I��rn�)arN��j��9xRemark% � �% ���switch�:",A�}�io�du�"aSnot8a]: t fe�'*�NB1, �c kept�� �!AY^-K�W)5�!Xunnel&FP solid-st�power�r0s�%at�=��'t)viv+ *�� � �d# Thu�=�tmoM��conne�> ��%oR "�(��gFmis�, c��,��E`duc��f-aCf^v�loa_9%1)�reY=c�(��l�j6en�< R}aa9�2�i��h[32N �%��Fo�:KIu a DC1�ufA{ typi�9�*Ae�%h�ep- W4of 2 kV output":�Q 18 A�R�Rr�matɰ �5�PeA�Ž>R KEK��~>��vRi#SFi*R2� c;A3�!�U-z�?wf�U9��"�?wa nano��Oy, �C4ed Finemet (Hi�'i M�|4K Heat"�beA��los \cooEd�bMD���oileQea�c�A�*�Nof�vunit-cŤ�, u_�Vof�TimpliciHzF!VR�bi1`Gctangu\|sha� �� � ��.�� �!ⵜ�E&�y=armQ Each6�7�l(f 7 MOS-FET" A�ar�[v:seB% �i�TM%�na��r ��-!�-�����7a��edDE�r��light*`e*�%1tro�.=��or"P Ugo%7/�Z,A�I��Xm�ts�a��wybeOZylseAb&� 8�� 6��9&�on:�H P\Digi�mw$�B����Fe�RF�Zp 5re �Y��c�E*i !��+�{"�2�3b %�)��k��2�So�^>%��Erig,%���&� &� 5!)��i�/ma�@-��<ah�VE�)DSP�nizAx%4r�,o�na2magne����A�U��Ş4=n��K!��� � �- 1B���� &-p W�J� NO �A�5�Y�:o�] coaxIX !�!co��CB-c4F �} �O� prJ �� la�XQ[VY�ng �!Va�mon. u!�6�pi�IDSP�\Q�!�>X.  4D�ignal� sha��6���Hr�J,]9EQ�;A��on�gu^&t�QH��\RF doe�)�ib�����AM�O��f�)�"Bf5��^Zi�il ion;L�i�+in.�R��3nt%� zero-nmAneR*� x�PSFXe&W A�aa�Z;��0�:0gy $\gamma _t(� 6.63;A,DA(5Wh/8H�J� $f_0 W068 - 877 kHz,!���$V_{rf}&40! sharA�cx $h!9.N�&FK(,�s��I9� I�2 !F%�u}� ��+ o��(CT�ev_m)]&e)�5�(.�msZa�&� ��H�toX�K d�s�To�Oe vfa� )"4U��8rooqB�d�.anw-�;��ed5�["� ��* p*� m#%2,-)CT-c_oq)t"M meas��)j�L ��:"�� ��pcalib�82a d��!�i� ����)��!�!�:�a�adjus!n�Te�� s� -#I2 Ow$tay.�!��%k�5m v.!,5���o�Tn!-A�U�5mWV/4} toge.�t�.� . U�M�@�%�*RF�1�B�9 �g*���eif�-& <� turn, % &#9:(} eV_{acc}\�e( t \�=e[ {�21f \phi�f.* +V_{ind}} ;\Ҏ1dp% ( ��� C��%/�r*�{i$R���!� posiEM�&} ��RF�, $\o �/ t@^Eorbit�-b G��d�!�?M�&�1s:���f��bal� �=���PN�m�JucΏ%�$( {c\beta 1�,)^2}{\rho}=e  6B 15�, 5�2f�BB5abT �;%�yB �S""� h9ii��R�c^.u �d-}{dt}= �}{C_0} �Z�.�3J�Fq Eq.~�l2})�3�lAY2I�mmx%satisf�re� shipE�Rz!1-�C_0 � dB/d>1a.a!@ou�� redi�is��_s=�n^{-1}�j��A//Ɏ�� \simq�  =6.73�qgrej!(!&����_s=-0.68&�� %2.%`2�{2�K m:�: =14.59f r g3� � ɴ_s$�-W )��Au2\�+Ѳ:�:�!] devo�M�Yr��l.� �1)".5� "i:olea�c^u� E}� ��SiR� be n�\{ IV!-RFwtoA6wo;Is/_� �)t[Y�| �1)&8 3[L�, law�e �shb �`��a`o}w)Ac� < �time-&� [�)�(a �-"� or p �"]� ��re� ?e"w ,�": aa]U�e�����r��elhaL MLjEe&b$.da^�>$� a&�|�- znt�$)��!�5�A�V . T wioce��R *8T�&q "]��.�Zp. tt� �9\ 5�  a�tud�a3^� -�s'� bigu{Ui� rM5pick-up\���&�$E%vay� offs�s� ��բavoid un[ZnM|�ma�Q�:�� ��,)Z! ɬovY<[�D A ���A��$-ao!�ad oby���0*>N_{))�&O&� �^40kE 90kV)#2h6�N�� EH��g�c��m?aFG����1)� � is v�clo�_�thN�2F�Z+F�0aZa ��_2:� magnE���9CF �)� eqw!`a(a�C�_1�At��!gx e.�$fi*�q a�Eh,"�b�U�Q�edE�a/R I�7&seca�=$��+�� at TApt,E�;(�+\�)�m5q�3%/v�)�aA��&} . ��.N�P�%� ],dF�"�=ʅ��alu�AU�ce�da A;��ɬ ma �)F�#j!���ea=�become��r+�aVEl<P.g;M��=I�9@ .���3�:{ s��)i-�2m�.+ 4},� Uasymme �a�c}� ! W -all2{Y�n�i�R"�eIfd5ayl]�5 ���mupae�pu &� 8!�%� a�#.�& .�&Per�q!�}iL� [�Z"Z�-�H75\%%q) nsemlt�b+�&1�"iscuss�Tos/*n-�&H 2m+�)K�M���M tanY.S�5s "�&11��`e�r%�dA���E!4� y"EtrAOm�d��C!�E# rigi� scen�.!+POP%�r�Y5� (�},�5a�*EU�p&l 6'u6 step1 : �=L �YJ8-,-� A566(Summary} I�"�dA�a�6�ɮE B�� a�T45�or�,K 2�%!u� )�=aal�w� "c 9��� rLm�)�t -�k*�)deRof� is6&C F�)�"�(a eH&re�our�1s(big mil�l�Ugu�/�ev�.�Ob?1�ťH0a2�>[0mOno-so-g ;. Last,a�isB�:@4+�d!� %;)� �K�!k�!�24 hours���0 trouble. מV ek�e"� z'�?�!ji� d{UME9 ac� f,e S. Ninomiy�waO5much iny@��er�0 d-PS�� �A9helpfu9e��� <&"u.� 2D.c@=AKad�.7$ Ʊ�FfinancFcf4 a Grant-In-AiDeSqL:�f�C� �N!@(KAKENHI 15GS0217[f�ys�6��p �!1�)���on Privjy Area{40646221�f >1D{[ "�]�9K.6�9J.�9,R>.R=.9(4h. A 451, 304(�W). %6S 2} E. M. �8,C=�R v. 6nR43 (1945J>3} V. 9J^ = U.S.S.R. �[5f@4}�Griffe4C. AnkenbrandtPMacLachlHFAj A. M�ti,�C�ing,(PAC83, 3502� 0. Blaskiewicz<J� Bren�FGee>EPAC9uI373F'5}.z�[;,!==B�G�>mKC��M.9C2V`. 8%\ 4801!�2J^6:uyf6�K. Koba�M. �C!hy1� r,78, 871(1997Jo7 oo�D+l.Be!'�N$, MOPLT066F-8IK�D�D�g�(���Ahm�prXAT or pubpeF}9} G.!�Capora:�RPIA2002�12-30�B8 !�E.Q CookB XX>. Linac�^Hf., Monerey, CA 663GR�L mith!5�(ST-AB 7, 06A t4J�10} Y]\9�NL 1420 L3NL1%�T�FZ�PA!� 3, TPPB09iZ�Hc  �5} "tR� s�)}2M�b(Htab�0}{|l|c|c|} \h� &6B  (deg) &���? \\ 7*  & $6.5�m 7$ & �>(2(2.0 ( -2.0+�>,3,1 +13) 14.6()[ �le}&�5:} >ф!ion{S�_( PO &= s*h �T2 & jz�I�-(.u 9��= ��"�N���Eq��/2�QyKu����V8hy�,�&�5U�fiI�~4}In@:&wtink, ye� , ��'R(brown)2�c˜5�R�):)MO6�(MBl �:t (sky �. s sto'�# beV�a.&2.75�nd0@]�0d1Xhm\a� �0.H� i�e6�� @�28!�86=8P�)�s vs.J(sec)i]1 (�n)2 se 21�?$3 �6�k:�&;M$% �� 6�M [12pt]{� c�`\to�� nce=10000B���2}N�{xsy^N*�Namsmath}2+amsfontsB symb6*�NVP[english]{babel} \v3$=-1cm \odd�10margin=16pt \��: \ې�N=179top 504 head�KB& non��e�@he.3Th�� sper9X5�ng 0ctro-:�s�ng�*�Aal!0es%�rot"�!m3"��l�Nap؉�# ban befiX-�yDi�cquL@�-�D�{i� �xRJ. chiK nd bA�sdpic�i���j�IYO \s�2 language{�,L�J0{INTRODUCTIONbigskip��YpJ�=5�*)�{cles inkb�AZ!}e�ic�&�Y�U.e�uh4 of g ^c �;v!�!�v�u��xidiIv ic (� ).FZm�m��!HH%tMZA���ɪ�10]J�flA�B�1 in �low %&�iN,�-o�u2>�n �� �Aa�)H�ee cur�6o5 1,( $�=(j}% =\sigma��E}+ $_{\kappa }�t5E�rc��I' mean�� kZ&rowYH�rk��1d� s.�&!R �xgyal>GA; disregard�/In �ialaU lY�!� \S )-��2u0! infl8KA�2����at �� � �Kd��*Q� [11]�_��E5�A� emerN0&�l��.�����R�, a stud���s_'6(�=c�7�K� or-z2��!a I�A�a�Bac�J�" EQ#�� F#Z��f��( g\!e �Ha��Jngw�up�s�:��A�"� ly weak:,%�!"�,m%�f����i�!J�$* sn *J a'#A�t����J�� goa�t% workABto-r��e�o}ʅV&�)�� -�� v� z&� f a��%;?l�[a� �$*#>x wp�[uwh!Sow�� !��6� �0�by! r|rŬ��U!�ʉ.��sh �m o�!Ai�H��R�U%Cssump�5u si<(EOUe¤$, [6, 9]).r%�a)!�, y basic- �Ft". �<�.� �{:� a�, 13]�"w�=Ǧ��Me t#G�;r6�8 ��& =z %�Fl/�Fioxg!e�AA�a� Ss' 2,�#� %"3!Y�M!��?+ calc>Ceš)�A�Lo�Dz2ce� !c Q� �W5��ANB)US nonu�O�R>��Furb-�toU�e � �) ?./�ory! 1 3% 5�#*��2� . Fz�6;r[�to newuic ��s. Ou&F$�jT�r�2�B �a2r$ � $--cP)I(/ ime)6)(�4)�z&CXTTof �;�)!3e%)��("�N ies T6�>�&� kB�,��ic ū �he�&�N�)�5) revea��h. =@:�6��T�7<"� �g�� �7&�Jt�eK��95�6# ��ULd v61�l4."'}�al*i&x( !�58��. A �Aa 2�exb 7� a- &aP)fb ���)i ��hX�f%�nsi�)�h in9nt�Y [14, 15]e�C&Ɨi�iQ&=#r !��c�i� !u'��.j�h,({BASIC EQUA�S.�Let�#2�� one--onent,�'��Y"= p$6�>I�%��%� rQ�u. W�)ll��Uld͠J*r��B�J_ņ 13]���~A5re�E.��� A�i!E�l q� �����too� AFi� 6 C��u�h)�>2 =PAh�ae o���%N,�����PU �%f�� �Y e�Fl���� �n veloc��*Vv}$1Uwr�v�z�R}  9d v}2#9}{m�;"] frac{1}{c ["�v\��s ]  ) �^y"�;e$e9$m&�;؁�g� 4>s�@=*�� ,:�a�!"5+ re!Eented( a suqq.km uVO*G (e+a�4:)� v�e�:>m*}5(E=):>:E:9,+\widetilde{9� }% ,\quad5� B=B}_{0}+R�1��.V&�B}},\�vZ�vj�Nv}�t��1�*}% As�  sá bove�%H-�ic%w6�JT j %��/8 }��)(x9].e.�7N� E}% I�1'\llX85�R�^{26 ^{1/2} $^k>�ni9RB}Fk k<1�I$. PawY-Fou3] uŢ�(UHFI� x},t)) =�f�t % hat{yF}>: k},w: \exp)K[ i%~bkx% }-wf 4] ��k}dIzNe��e>^} -iwB� v}}(���΁ڑ� N6% 28D)��ao�R>�/A%. E}}(9��+�B0c})VA�V�� q},sI�}BqB.�-q},w-s)�5Wq}dlm.��q���ia��d �0�-m�oy�&x s�s � 9�nMy)��2X.3B� �q�-.?% L[I`�S5�-� \��R�&=&{I�bqJ�6� + \�9g�f�):6�u� �z�ACYk:E-+F�AS &+=$M�~�a36�v}]��1�% J�F@B.@Z���l�..�&& sf {Eq05%eU�In2�%l�@A��� < �,Z�"aP { $Y]-9%���!+9���$� co"B � V�F�b�5�%݂F@��$  ex � v�-�cu!�N/jO��82� u\5!�T Furutsu--Novikov [16]* �&&��2_{i}=Q� \\�$varepsilonjkݭ�� �%���9�v� _{j6�q�)}}n=B}}_{m;k}% ^{\p�4 },w B�~nB �2]O2[�:��k� -q% .l�'�rk_d�2 &&+�v� !q:�v% !?�z�zj�%&n=&5 J�B�V�0&& ��:B1�!�  }f�R� �2D�N�% 60� &� v0q09A o 2L]X�+\ldots��var{,� ���At�ca���"��$\�la�u6v�R�v����%8��:�$ SIB�� � g��. at{L}_{js ( s� ):]�n�sY��1���b�= s}{82� jlm} �$% q_{l}}{q�/}q��& ( s-} �h� #�q}-&a]�76� F�r�=Y.v}�*� -p.c,6��)2p$�)r�r��% �I�E�l.��G,s ��� FAr�# O��� -JY�r�-q2�-� }:� �d.2d0��^� :��XA�%! �\�\%\Q��G2�%��.!U�a�9�-sF�\�Q}_{nr�kQ#q.HF,2�I�)��� \Qvare1���W�&� �Z&=&-is-#�*^W0 _{jrs}B_{0r}�.�Y�%g]�.\]� -9j�]�e).�V &=&% �Z�w w�B J) -�("*k+:<w+=��m=x39x�!��Z{%")Cthird d��etc� g�"lJq�A�Fd'� Q&�� e� q 6� W�' Zr3�x Eq.�Pa�) Y6U�Gaul.264LAq���2#�s�t2\�s. To{62$V4�uh��$�(ulJla�-&`en g oced�o& �mem�(o s6�at f��![17]. Ha�+"3F.�W$n-$th. 9�,%ksub{F�%,erm� the$(n+1)OC '%f\)(!�x%�5�(sK mix`X+�yer-� mro�`���Z�n,sw 2w cep�rr22k� a5 �"�K�� �!�% ��9R(n-).V}H,5Se �$s$Pan �^_u\b$n4$��/�$s�L$ $s+im �%���rY�iա.�!Z0 =$e�rK%�se�&lJ%�ini�wT���48a�� $:�eB)�4ceg!=l{�0�a+verify�,�*&^�ei&is&7%TH!��*� 1`� of(B�.OTmAIkn��s&k�L�\r=�]C"j�)f@.�s,!.w_{�}\gg :� (����Bf�/mc$% ��2�!12� e �3qu�Qbl- �u8 post-Markovian2&� :ZKAt6�%!p����av�/&,�' Yul��T,���k����.e�2,E�te"�9��n3�Y\M0�o �o Zo  �bq %V�q q  Qe. �^� � � AD-V&� �q bq �%��v.Cj� eZ) 2� �s �s �s �s "7!�WeJ�a�&# "����by�|��ive6�'s:��&� .]l[�dj��"% _� ^{�( 0q3}e�q�b�Iɖ� u�1ax&�*� ��% >7^n��F w=�"8)# &�&&� a�:G�v�%F���1�EUR;��j���J�E�� �j2E;=�:U�2:��gf9 R<N oN/��?� � EJ�aZ��mqt� A� � �;b% �9=��~% IZqN, �m@�\�>`( 6P>�sp� q_{p�� 1!/�����O5~1q��p*w&���EN��:N)@��2�-q(�^m��|HvBb2t!@)�% �V� # _{lt2!� v .E~k!�� }{k^*�2%B4B�*�q-9-�j:-� eqnv�&f Urxe&�&�ij2�"�$] 0+he in�Cof6;-�6*�u *W^k4%1}{isQ!�-dt _{e*�&)�"a-�_Z2+ 2 _{ei} >j}�v.� Omeg-k1� :N) #}�=�#�7�/0}�1���ID��RE2������_WFi/�(&�8B�fnd .�8Z�Maxj;'s�L�!��� he�'&�* &aN�+q��"�=� c}{w)�["�kx2�QE}-R]>#[?3.q2^)=s��an*:n:,��<a D�� �i2eB$��m*~|s)qf[��20]Ji1%F?,s)�� (� _d��q� q_{k��%*" �6E_{M}(q,"�lq)X }{{4���}+i /H/&1��1 4}}}6�mkt�tFg �\$( l�+l������Blq -8 2i��>.�IGNC���=]��F� ( q, Qcl{ ,��}504}}- .� -"o*�6ml:!kij}+k2p ij�!%i�j�l� �& b�) �C )��q[��-l�oH� t ve�xpar�|�ab^G*?0$l}\upuparr�f1��$. Al]:+nmxW7s, ex1�1$C(v�)��O�veC@WBY.% =�]&?[y�2N�< admi"z�s] in&�/")5-'2Eq3��9*x:i.s<U?8؞Y?"�.�s"�],:��� ��� "}:2�!%�/r,N�W,\footnote{% �� an a�lr�vortex `����&F1its torz�dpol c�xn[V�0AF�:�wf!�.y%).[B. *} h~&� x})=�T�N\�al�+P}x��xD}%��i}��P>O%kja�k>[T6Wj}&{ɡ�0C�� � �U6r *�:Vj�/D4WaLYv���?�=��is=e�BsA���(�tiGp"�)F�"�v magneti�Lc fluctuations only quadratically.}. This is also confirmed by direct calcula Dtf the magnetic field effect oncorrelu�u properties of turbulence [21]. For a weak anisotropy (and for obtaining analytical results), we can use the represent{� \begin{eqnarray} E_{M}(q,(\mathbf{lq)},s) &=&E(q,s)-\frac{! })^{2}}{q E_{1B8s), \notag \\ HjXH�XHRX$F\left( q, �(}\right) ,s &=&1 ,\ C >�G=C�3I  F� \end=fAssumingE decay M5]�s with time to be exponential, $\sim )�4\tau _{\ast }} }\exp � -�4\vert t-t^{\prX-$ /G1,$E<write AhA�@Fourier transformYAiA} f%�=f(q)V�pi�1+sA2v -�@}. \label{taucor}1?d Here!.�$a��%0@constant determini� Xcharacteristic frequenca~aSscalesa�us,�example Pinterplanetary plasma6�2]R�a!�ed-�$2�!� )/%�4mbda }{v_{A}}= \l <\omega _{i}}{c\O $ where $+ $ isJ�.�al �Q���nonuni!�i��\. Clearly, this estimate!v� vali��(ionospheric- . Let usA� and !�\tensor $\widehat{Q}_{mk}�X$k-q},w-s)=2#km#Pq-k}% ,s-w)$ as a ser!�,in $k\ll q$,F�rPNjs}�k_{r})�% \para� fX5}{{*}q{B}}+ EP$k_{t}% }{2 [/�Y: }qU$}+\ldots ,>JE� ubstitute)�r2#!L(\ref�� v2}), perE�� ag�/on ov�he soAanglesA3e .i$s$. Wp E_{0:,��� ( 1-I,1}{5}t� [4 2��) �Ref�\�4}_{e} �Vb�2�% }F� �\\ � �f* ��*H�� Q$}{w1-�3}{10}g� |) �9��% >�$k��.�% kj�-2!|R�%��� (1+i� w)E�bf��delta (I� bf{k}}% )wv m �T% �k&� �[�Uatq �_{ij}6  _{\perp } s $+N(i8 E($arallel }-RAr� l� l_{j,} \\��Dl�)+E)2i}{3Y+iw%2Q �1-%�RJ/,\b�=FjmD( fl �a2��tc %���.%%]J�E%c%r� (J�  Af).�2�!�)� 4����I�U�J-3�102� 9}{2��,�CU, ��A)f�Q%�.)1�Ct_~. -�i F�E ��E�H �q1dq=2^�}-cbf{A}�. %bf� N� ;\  =}%�1�%J�;!X%�� E(q)j����2� �� � �(� dq;\2 %"| N) dq.a�e0�)K��}� },\ %�Myh}0^8E!�Ah�},1y�� B�T� $ubscript 0�sponds� � �Dic case. As we see� � ive &Tport coefficients are 7ly \(mean energy� helicity *A al&� b*F� being, lz restri� ur a)so0approx� Y of a d-P ed� cess�)�$arrow 0$% -&T of� 6BU��ll�� ider� elow� W 6m �t, �y��a�{c�J &J ,}�J �J a�IĒ- 3E��*�� tau 2�? 1�� ��.�j�j �F�E�6O��M25*K bf6� F� j�� �3% � ��!@ �{%W:w %�Ia��� 0} eU��Dl����a-hqidea'Eq.[ I ) ha��inga�a,�acceleialo exterN�� momentum�aLcl ? medium)$raw� [23]�x"Eat�n��E}6,mFY X=0$Őequal� zero�o"�!��non)v9colli�0less limit, a_g�4Dcle reaches a velo�� $��i�� max}\cA�/ 1[ ��AB6� /.'�B�CO 8$ i.e., does noopend on�c:UE�isA�:WLarmor"�A�u� " )�a5M�o specifiY�)j6jFu@IA�gy. In wA follows%�disregar`��. �� le�AAef �k}.�_)���?  /"�e}o15��e%�� 4�ne!� }{m}�$n�%pm!�=$nsity. \s��on{THE CONDUCTIVITY TENSOR} \bigskip Givm�6) f�a�Bi!�@ $% \displaystyle�<B���ɽ �.�:gb��$at inverse  a�&4a��} \�L}�^{-" "� -|-&J�( w+i\� line��"� %�a'�aI�G+3ei} qj}-K:c "a"� re, \varepsilon�k f _{ek}}{�g% f�- 2��%�f-5i15B.� $9�8gm!�G(bo�  90 @,R[F~:_H �e�)�_D$. Tak] into�oun�exp� �cm��KB�ZH 0}$ "� � the �v�Ha:B� �ĖOB�=�}� 8EbRz }{% iw_{e� &|�p� 5�M5lef!����>���>B-���H H}{ib��( erp 9 2f1 &G �V2_&�lv�m/bf~�)"] }I � � j�.V���H}_u�6~� i 5O2�jl2��E M[k����Av% >.l 9lX rF9xkF�} )} �sqF�J�U��%/�-��!���%�=�7!K) (JIrrKW�I bA }��B�Ee��6�u� �J�2��b�]M>a�wRR�Y&���oQ~}�L}J $�[ e_ "< "� 2���J7( �zQ� }=j� nA22� �h&lc"�&�#g  similar,W �2 �mcan��ten ab>&1�b�2EF�1N}{MaeFvU��i9b=Z]�MQ�Q�iI A�.�M�.$b�6�!�����V��ei Z� �Z�J2_y�u�B"�6$B� �a�I�9�2�:�&4M ���Mcu�a� ���a���� �M)��w_-O2� �9�(��b6]��q�� J{M�B�:��)�)r)飖x9)2}:�V� ���=�������VA6�����,���� GTY,u�M,��>�IFa������&}у|&� $i$ refer&�on �ogu"du amet' intrA �ts:��iթ%7��Ew\� ��Mceĕ(7��j��L� ��$. �d��.x&�./:(quivalent ,�ul.�n \ ive "�'"�)�.or�n$�*��I�H �y���-1iI.):�FG,Hu��L"��ductiv��j_{k}&*\sigmaK%kl&�'�E_{>$jm��� j}=n��� !v͢� :�V&O 1.�e:Cq9�&�f�:�'�": &� &h 0i =�"�.l� ��� ~�!�ub2��VY~�t1Q"Qkl:� խ\6 I��� �N!��2�%hw  w�2N&� I1  la"lA�"&Ū)U*�e�0)0U2>r)2r"�# [U["/[��v.~kml�m��hKe����e��Zd>�.K�e*��ef�F5W ): l_{m}k.�-%�k!�0"�.�5���%)��0")�U�6B�i�NC ��k)�6�mnl�n2�R�u�6��m)�2�1u �? "�j%V�6sitB�+)�a@>n -$-� =! _E�k!�!�RClmn"nH �3�=:� B ��ӡ�ō"& *M� }$ .� .W%$%,!pF[!"Q- & �$ h0�dim�8f"it conven�% to "31>m*�*�,A"�$�V�=&��̅&�:7� .&zaB4 _{\kappa =}=\alphA� -Ni�% wF#}�2^}c,6` F=-����Fc}D*� 6� �c�V$}�%%�:*=&V�:0]ZA�6� �5=�?2� JJ)��J)�4�6� fJ-0>�"� FwF��F/c\Yo �*�V��e�.i_�%u}/a�q!"#7=�a��l&/�u| defi*K8�%�J�!.N :Yootnotr�2�8 �v�)mis known�� solar-wT5.J<4],�%re��l� ^:E5<\ange $0.004\div 0.02$ AU 5<$ $6\cdot 10^{8}% 3 9}$ m ).}�)5|,'N�fjQt� *� f5�"0*�j0% \�*�r$� � >� Bx$�R*BeI9� �:A�5% N6�6]$al damp�*�u�Y�i�2�>(>�A�!@ 12/)Nalign}� & =i�-D6� !-w�>� 6�"� }{:.m -V) .� Ng "� 56J 6X"� Z�= ~Z�%" �& f 2b & ��Bm � % 5b ��B; "1=J� � .p���+�;� e( .�5ei) 4igQ# ��Ti� T>? 5l -�2� � l� � &�6�� -g6<V� �A�5Q$m.�  _&� ��5vZFY�i�7:h6]6;)U�)M:�%k� .��V% H�B�+eK<mitd$.�&�3*� �$j.27- @ : �"�'� � ij} &K"!*� X�(��S{ccV0+�}+i\chi�(k_{z} & ig+ �x-,@3k_{x}-B'y� -igF[��6jy}F�xj�"L k_�& �.x�>� ! � ��)4�"�'"�8� 1s:�-M &=&X6Uݭ>� ^+B0m,Z� }=&V8V|�� S �},g����� .He�e���6i�y4�uI�I �:I2 Q�!_:�)FZ�� ^ ���r) }�qe6�a��X�Xz�Xi2�]% �(�9 %~"'-�>��WC�>C �6C��-[*� MXm=v�%> )�2�Ir�BI ���uz% "�6 from�2q�),:� "� gives ris�F addi�gyr�Hicu-sG| pI/6.�2elucidcD$their role"*�yz� disper�0"7/ �"��As>Q.HDISPERSION RELATION.Q.De� ��B2�1,Bs $� bf{njB&,�*by�Eheta .+heb�!complex��FVindex Z n}=cf k}/w� �as [11]�O"'7deTBV Hnem�G-n<n_{j}-V!%�ij�� F=0Q=hW#4�F�3>��B� !7=�In\sinw \)/�H,0,n\cosV"� li *}%dN%9he�N8 g!/� {n��->*� -) \.I"6v._� - ^2@sm� �J -~�{%?�{(-^)k%�7P��B�{%�>zj�� }\,��-{�P +R+ %9`{Q:/c!�\j 2g g\��0}+>�)�Rhi��ur �-� }{/clV\�+i\,\,W,w�os 5�b!&M�{n9��� -2F: �2$g�� �/c!�� ^{3}N�i+�Ft- E��/cuosB +5�ZDL +B� }-6 {y| x�p)�% 5g�=0K� ��9�rq�3��% �J9���v� � ag��&�9՞6b=�% =0�(I09is i>1 {:�5: solu�m"1�"� �~n_{1,":?�)�i"4 1�:; Q�/c\pm( 4 >R�-g4y j6ay�-a�m�L ^{1/2 \\�3,4O v�&� I� T��+z�a��2b 9�Giv�6at*8DMq�S9�R~\mp g=f1 -� w\pm( � 1 Z� "� wa*� 9��5�_IS�.=:�>] � _�h �mp}e} 1�2:�E�6ti>t CP A�t.*i�t,-�)� 9�� �'Q J*} ck� �6� {:�� 2�:� 2*;.] �#ZX)�zU�!&zz"u Jaj(AO5^E UO  \ &&1�=�����&��%�'�Q������Ɲ%��Z��D1Z� wh�q� a 'Py2��%�-��M�>�QE)&W�4}I�Z�y�CZi ~ck�g>riN0B  @ ���%<�Z���i�>�Z�Ya� �6"F� =: Q:� ��u= At low5�\ $.��_�. :> +N�1-�$�>$)6T \gg  )$�QsqupGN�Uj]�v{U��5�1� 1+ByQ`�C}{%G!�H1Ai:He}k> �0 Y�-> ] ��utu8�?� �B �}:nM+,)�val$-$ ���J�c"��($ (for smal|Vs)�! #�} w6�<��@iR��9�NE e=m�\/c ��B]�y$4!;V]�"�s $AR }B�2&�/:�} F *%Q�^B"�B d�B�w*�KBcontras�Ct highF�B�� large C9\J%S%wn��9�~)� _I�DY�A6J *8N��=� Tm��>�*cT/�� pres�of*&�/"h�!s an i�Z�G� K�ZitukH�0"r!�0G�n in a �Z increas [�DmT[o`� atFmpany szN8catastrophic ev"Ss�storm��d�7(, earthquak!�A�man-madOplo �>,�Ai 2O�R��naturke6].�`2�)ofI�on.� 68� w"� e~G�a� \gg w $M�2�&� -�exsedR[.wIOi�u  B5 �:z &� 2�\:]A|yAonA��ac� an�L6�I�A�� th \l �5 *� ^�$. Reg�"�g6m&?`M�6�_$� "�)C$%-$6�Wv.2_r_�rp_b>):.5^-�b- 7*$eU�`e�i�s*J8kAs"SW$ yohpOlower�O�|ep.+ [10]6 d�d6�6�A� $$k>k_{crit!kv� �K�%NOi*:��>i"��L"N}{2hI�O26�A]N'R;S ��  V= v6��,FBd-J-M�<FT^ T"Jp�:�>p pID)�-2FnaI~n��n�i�   }{2>�� n_{2����-1B��������)�-�=n-!g�b 2�1�U�/i�WBABa� e ab"[ o &fsecond��resin�$ \ % ) wouldJ $extraordin�iP ��s,Q p� velyQ? Q?�$2��$sG �g ellipXn p�1izM $ attributa�t&u�\ bo lyp�@�>�$hOHM LAW FOR LOW FREQUENCIES.�$N�F �B�9��>:�?�M5�a���?\>LNI��E�i9hak(S�@c"wP*�@&L $\nu =1�l_{c�  w$ ($  "�9}$�4ions)�&8simplify our ca&EIjU��We a w:�oof�ve.�@%9n� }�2$Z>�w�8�2~�7lZ�&3A�wF�5JE-*�6 8*!7B8}$ �aJ�A".�j�-})a��l�X��%m<*2 ��@��P *�A�F3�}{1*U"�p@�@�@B:k�O2q@"N ]�2*� !4�3��B�UB�:UB 2+�"�064A���5Cz"qU�YB=9 �5Z� Oi/%�!'9��(O�9�2� 1BB3+"�e9D���:��1�0r���- ��:� �O>b5&iI%3V�eIu�&�C�M ��m�p"�9P%Pkg2"�*Z�3&�1Rs:)4�+ &U��=-$:=�,G&f�R�3 *�3.�4R�R":���:gy.E�%� �%�:fB:.p9yMPa-m LQ fFfEV�@ _{>�@���hY�&�I�(&�� n-t�dn:>&� �e">Q��N�� )z1 UN  c�f I"eJ 2G��:c2�%nFJY�UAn"luB| HavX.���ieBj(�-�w*��29?:�M�&�AQ'��B�},dB$���#*B))���F�a �*�}; ^!�*�-����e2F> �#I-�V}:+ *}% cur�r a[ pplyA AcB x�&#TJ7�� �6j&�\%�%W +i �^J�JE E") Xq�6\ &�,�MQf�S�0:{"�"��� 9�5�}-& � &��2&�O �-�Er�1 ]E+5!*���Mn.�a�n�� ]iAG5 ��}��.^>*���9�AY��� W1�l\nabla*�%w�?"[@8�!/(6�&�Z�t L=� 1�0.'5F��"" &�Sc9<e922� :giQ�!�N}q��e=�ѽiouF� 5�5�mV�Rext{rot -�b�5 v �=L1E58 #:j6.1�)60K5ZK.%<9�I�. R�U�B�RZomB��6 infl�|�2.ZeVYj :~(arily cause�e*y�de?", whil�"&�"�.�!..8�$P"�wђ�ihe�R�! �. N�mfo"#)Fat&�Ohm��ref!H).�z/.^g��(� EMHD�&]o).>�Cdxfcej�� �n�"� *���=�F=gamma $r# �6���{>�� B�A�ms]xie��=.n� �t #�����rxi�( z,Eo>d.0 �>�"a]�le��Bu?N.mBr�2R  / -1} �=�C�\,�4\,�\.�  s �5�Qf u5��k"��F,\zU:\�T *f: �� 6!�+ 1-i\,,2B 98MxLv K Fc}^e�B2R�e�8 ]� � Nv?6"� F�ͷq��lK=b�%R>�K ���> �@ $)=1�e�c����e�*<>+an9��7X�1�%- >�j ���� 5c 8�".�,1�1�"k*ig(9�H&�+ 2 F2�1 t&/ 5 , 6��q/�b� ' ��. l%e��h�"FW�D%� threshold)�number�l�� \gtrg$)�1}*�M%9lv�)�c}If*� ecUC�I^�1Ip!?džQ�arbv �6d )dJ��V=8F�pA��.D!�%�i3+A]�W'�+(Avm\*�"e}$). O���>QM] ��H Ye"&f"�0&x!r)Mu.I�$B�*k/f*Hca�\,}{8B�02 %A���2�� 5veB�ZRj �A� `MU�!`}&M�;I�"� E�Ŷ 5% "!ޟ��2Hn F12�$ Z�$J�B *&:Cdissipa�A"$A��  $&%��D�%>) B$ &R >&� � $div: %� FM$H$A �3 �,i��c �z>.2�.0("C� 6*�$on (*i2FINIT&rR�C TIM6�Con�vk�^�+fiZ�z�,1.+�, $s�gg�r��� n |y]"( �vThese /includ &�ng� �9{&%(�� �D6�&i"h��eZ6mvX�-�.�g.�&h��.L� 4B��&:>���i�2�"12VGz� ��*��u�'�.��_ ]B *��U }��5; \*=f!M�Ez� >� &��CcBCc��2�vC� )3��6["R�AvFoVZ% b�g ��|RXN!X:�Mt2��F(�k}}n�*�H��al�*&k{�b�xplaZza� oscili��2'I&J�4 acquire a��� shifT5�"h�/B�N;�"����>@ }�*�u.#A/db�N-���%0}�Nig"Q� M� F7 x}-i22y}eWigb"f�NR� & 2k�y}b��N>�"�"�Nn"�N .lEC)p&):� }% 2{� � ]�D =00. �"�3� �aBK$#d�0q*Y~so�$D�RvB+ *C &�6��%� ML0'C%B�C"�4� Bu�Q 3&�C� �~a, w^{4�L�Z{�*/vI�b�c)�9=�.�DB��&E &23�YB7Z�E�7ye�7n7Z�R7>>@R}6*�5��VN8be 501JKR�FFC-x^�"�A5�1�ANf��) =.�!&&��B}P� Q�6�$�� �5w. 6.�� i<`E� �#�&3 AYXb&M".^�>*B" o�[E2m =&J":m��yx~�-g��Z��1b��9�9E��Y9�>Q���%�b�:p��9�9�:m>�` XI~ceasf���6an �al ro�:�.l-��ne�s �,. .�s2��ren��2� ��2��R���`t�� S'!��e�P"N�QF��1+i� &�)��B ��VRB�P9 &g!�2�2*>� n&�6n:�!)1 52u�($Fb ��2��2F�-1�%���������z�>�}�2  )E��2Y|�'� U|J�2�y�rW�ct/2��$�$-c��ed�:�?pr��� &�2�:8:bov. "s o��?^�2 2<��2he&?3�6^3� .i< �� ��inb�or �"�nH(frozJ�*) �"\� a��sm� �& _ �m2�=�=of chir nd bi"�ic �?a [14, 1�@I�X�B stem&.�W �&����32=� in S~4 on 4!S&�<��!b mof? must�(ultaneously/= ifes�Cmselv6HCONCLUY294424"&D!=z�A&,B���ad ?oaese1�&_"reʋ� P� �=n-9a�A��U%yF�� s$�al�@�i>\C�"!{.�"l<&�D B�D--->D6j"Ua�! � s---&�D�,ngy��v�@�B,9&f]E �EUT�}u�D,"�EngE�Ono2�E.? � CuvU ��peculiar6JCM Q$in��@*�D   �i���t�"i� .Zv! La� �.ob byR�5� 6.v= �&�@< . Ank�ow9E0i�F�k %.�$]al*9=��+2L a@ona=&8>DQ�9�G��s)ed ���$nd F�$:G,? ��HI � o��A�"�G��)2�>F��.� .r�6-5���G !�b�BQ�IVi �H�IJ�2FbservXC� E�2 E&.  Const>�it�dHٝ H&��M|� edia,�?�nomalous;orp!a [27, 28]�.Q�!�D��7Q>[29, 30]Ra�ficial�Z�origi"N �aXin ��ri5A�H�0alAPa]y)�:��1�)� devi";;�G�� B�V+ +%�%X toole�diagnos�it �reN� wA�� I�B� isolb���s�EadvantagTFnda�.re gF�m�x{>�A�� 5����D.P.SoroB��, http://xxx.lanl.gov/ps/hep-th/9306159��W E# } C.  , J Bieb!�inE�it{\ S H Wik6o,} AIP � ce9 eeding�+P382}, 498, AIP, New Y3 �J62�Soloviev�!�Morozov%�L.� "'e�[ TekhF. �-27��6:Z Tech�b�bf{a�25�[:`Kh �^A. G.� ,D. Aburdzhan�G.�nDdieriŬH Kh. Z. Chargaziya,��Plazmy�~ cow)��88 (200��i_ Rep& *3 *2�͏89}6�N.Eng�g,�n^X6K 25��06%:; Osipov�V�Neg4 %�O� "�g4A#87s96� }� (, S.S.MoiseA %�sl{�.�d.Q��Hl�homoge`Z }, P �+�hNo. 1948, IKI AN RAN (Inst.o�,Space Resear! �  A�YmLV� s"N 19>�(ilva} H.T.T, .H.Sakana/ N.Regg�a��aS� of Japan�h��8I�9N �">Q  docu�7} m` \|class[pre,twocolumn,floatfix,bibbp$s]{revtex4N(usepackage{�} .�icx6bm}% b�2)@ \newcommand\bib���(([1]{Englishȷ : {#1}!w29h0up6F! pictc[5]{� figure} V\cent�3e{b$- �(s[width=#1\);]{#3}Rg(\protect\ca{�B$fig:#4} #5R? %� �.�6�[4][1.]�ctc! {!tb}{#2}�{#4:Nr61]{K:�>q leqt"� �eq:B+reqtn,�:^"! (qtn�)A^%�u!� {FigF�Fig7\page�]��Z�:��.S \vsa�*{2cmR�.6 Fig.9�addtoc��the&}} �q��title{Bi�l;)��B`<���](eriodic str#�resBauthor{M�el��(Feise, Ilya��Shadriv ? Yuri�bKivsharC ffil� {Non��arŋ�6Centr� 'Ultra-� bande Devices!OZPSu (CUDOS),�P Sch�of ���]�O�Enginee�] , AustralfNRal UniM(ty, Canberr CT 02004�)|abGct}tstudyT �m�20Z�#Oic �ilayer 5� cre]��l�<+ slab[two�erialsT K^'!�neg�-re4/\u.�=de"�`Y$4Wa�exh� s passUs�3)�� reci�ߐran����ic�s�f�v����a�[nic dA��)<p60�*.�3�c�� its�2l>��bq �ttaq by emplo�E�_:�.��9�;0kee^ -oM� ��bb.�c)t�[owsm xioA|�>qQ+ ;^�t a<5n �length�!,id�caa� � �m�100\%�# forw3�q�@ec i�& muchv*ةr v hes��A(�^)6L�Y`a�� !�tra ����� chie�Ia�B�.� through� I�,A�mo-ei���novelE\;��0concept, but �4us���m�]Hic�sm%s 1�!�aralY aes]�^!=� ���}�X�ses�l �"��� dif0 t� ��� �~\cite{Scalora:1994-2023:JAP,Tocci:1995-2324:APL,Liang:�-1192:Gallo<�9-267:JOSB,Mujumdar:2001-929:OL,Gawith: 4106>31e}. ;8apw�� 92%��UA Zk -�bas���.%�Ged92�I �I,A�_i�!�.s(LH%�lat�`e�1{��S �~��D`&3��#�*-9eamwhich"�i����=� P��-�8LHM-foucs-issue!�3:OE}. Ka2,��K` ��e � %�"! sie=a� �8ce of flat lens�"a prov��  c�rM4?��a�)p, or '1�(RH), �sCE-�to eiJ� enhSd8<Yed .*-Nefedov! 42-36611:PRE,Li3-8390L,�4-1451A�A�We �'��zal�tm *�sac� b|$+�<5@I\emph{y�}A n( }�s�� %��"� $uperlatticFch9ex�Yk��aess q�ft}!��c th��%M!a�Mrs. !�2x.� $sQ ,three stacks�&fVX LH/RH dou� -�>�, [see Figs.~G {5:}(a,b)].��XEd�!� f;mw& diu~de��li�Kerr-�q.;.gsea�inser!G�! � 1%�2,Nsho���N�bEG��2�� ' ɶb!� �sAIu�HAH ?Xfer-matrix method (TMM)M� Yeh:1988:' �})���J�d@���'i"��ha�pseudosA\A�;4-domain (PSTD) � �Liu�?(7-158:MOTL}�¡5�}$ s� ! yt� "3�G=�G&U �$�� �#��an,� �V . C}�Uc"+& build up �of pl�Y�}�rp *!*re%&��%�ct(T 9�el K� �&llTh e.g.E]�9 -fun�Qs � Lidorikis!^ 8-346:PD,Z�IiAe !�-��" e Maxwellgk�]!��ret�aVimeE��)�� deriv_ �3"Y�edM� Ne� 6L��%*tempoAN.PI�BQ#�!E From�%, one 6es up?�er&�w=tQ0��by iteӐn� a�|!�e'] ! �probleXh!�in' nt�i;&$I� /RɅ�:1�rel�I>Iu��f�h��lya�ched-��absorb� b�!ry-�)r_U:j,BLgerA# 4-185:JCPm�]  saA�s� � comfLs �nsFklo Eh(t cel�6� �#�%�#��/���i�E[V�v�`wm@�on �]�2955:ITA��((nta���yr" �{dA � ly�2| �cub�iMQ 2 ; �y�l Tran!e$6-1138:OL}!7��Uc.� 01.eps}��{Schem��Q@�2UHt ��E�aa)�;�- A�(b)�� !. Lf� LH��3 e��� light�$yE� bH�n� dark 5} ,��%L2is(A��Av&�E& O inI@R< $*�2_r�_QHaMm"G $\mu_r.�na=� &��q:1&�2_r([� &qEoM8_{pe}^2}�^_{1- ^2-i\�N_e  },\\2o2o�~gm6gFgm g��z��Ta�,?x_{p���l� r��%1ng�:D d�E1.E_ ce5�i�A�$1, m����p2 E20Hs� us���=1.1543�C��11}$~s$ �$.�m- 6324 - n-1�Z f1m}=2\pi 7 5 ?6.iэB loss��=2 <�.W6 �W�&t�Hoar- �>��+y�$n L-1$ at5�4y $f_0=15$~GHz ��"�iY ftr �lq�t2$f<18. >�2� ($f>26^�1 RHh ��� �rbe air. �"t �x�N� )T ��R �0cks� rR �ou�� (S�  1E� 3���sdividual �lcknes��dl|O_0/5$, &�S� cb2V�^U ��_0/3$;�m _$��%�free-� C ��incom� radd!�1�)�$��J^b)%��T��� �{a5�a� � i"9�" S!Q    2)x2v ��-P $29L25$6&2�&m um-! -.}�}� -1Ybe��/"�� he6> . �S � of e� oMli:���� 3$ (��$! .3� f��.%}ack�E� � )�>�Y�]H$/5$ (dashe�2~~.DCombin �th��mCwN� ar�Te�q!Rb�I sha��catr  "] @ � gap� %> ~1 (�ey�� 2�rk g5�mitQ�qf�JIO�wCs�F|��<�A.? '1 �9z *0 of1i.�� ordep�ʏ�3� � YH�W� ��e=A�>� q.EZury�nGA��  � c 8�� �R&l{c2& )�]�~3&a att"�� $ o�m)�� �(>�2� f%�E�. �% #a� E2�A[~A`� we cl��f??if5�.�?: due���P5 M�w. How��|=�oci��eTC���If2��(eft��(aj�2�)c�/� �� � �� �w�`� B��2F.fI2tof^a)qArN6&r�LI��� rv� �V��> is opaqueJ 5�ŏa%� gap�ilT3^�V2C7 V9a�Bv%3pa]b!&zbeh>-*v5a cav�D t �nd%'e�!�A�e(Fabry-Perot : peak@O5I�� W�,xior occulo�5N�8�30of 13.5--14.35 $16.3--17.5 �$25.8--29.9� o�D&�% �T�&9-%� 5 , w�4r-uc�2@e-a�� iT: =4$,e�Z�ASC TMMF�nM a:�[:<ag<1' erf�%��.{? ��uoJ�} 6�[1+?8(x-x_0)]$, $x� .6"s�CE���.�o%���reߣect �m 9�1Zq5Z :[ (t)= 4 +@^{(3)K@|�N E}(twP|^2. �! k!4c&2� $P@ L=+4 � J!7�cA$6Vw3�$%��z}nt ԗ�&�PUy"Eh &F � �prUY/}ex�� �N6�.�is �bE7of x<of� i`��9& &(�T�FH� a�`��2}��Q�`A�� 1 amsSM�S�J�.&�3:� 5��� inf��!�%F�A�p�<��(b) � ,1QSt����= alc"'TMM! � a�Y� d!N�u9�i�����  Q�� �a!X9s��ou�"� ��p . } *� �b��A~&� steady�]tK�9. �<is si��!���fixWM8t�( �)$�5 "�@f�-�-�)w%�� �/ɥ2�aF� Z#� �a:�!��nluE�|(w%)~( A,~B)S:a�W2T "� ofd  2E'L fix� �$!_=a��#[ YUU�s-cRB�< : �!E-� �i�& !�slA�ly�ver"��,���c. D&� 5�J� �H 5% �6k��*�!�� l�dEY�S�nD=n;a�:I� 5� i��V&�L ak B� very"f �+AZ� � eB��"[  c/En!p�$!sbB�A14y)�!8!� A� at �YBZ�(��,�U]iA�� Y ��})>!�]d,�M�sA����to f�!������cur�>m�e�en) ����no� �'ll.�"F�EC�6V�o�� , exE&Eb-�i� ��y>��� [�(a)۬a!I�r#He&��ieS>&��i.$F�E-=4 �"lJ�6sI�B��� 9\Eg)��f�)%Ac6^��llyM��Fs}^!.MA�Q� {d�Referra toV�� 6v�BJ�A���A��I�@0���^�. W� >����ܹl�Z�!�e �BuK��"Q� �epe�^�G��a.become} %3ing�upal�� B�*�) !q2"f|A��`#�[ C�W Bragg��P(not � n�5*/ 4/ TMM-�+*}�Nults: �. �<��$f=16.19�� �$25.17 bct& l pEv�detunA@b��&bB�s AVC�ύ��� N��$� A�~ �s�P��C�h ,��g.rh���`er�tha��YA�s2W}�H.�+ �_vX!) &� 5)�Y-h�#resis}9�H)! !��"o | a Ga�Bpuls%� &� �#1�ie1>�� 4Y  �carp"Ѫc2E�A),�&zY 1100/f_c$+"  0.55)�J +"ڍGM�J�| time!P Next�.�>�,� \i!<�5�@ #G $!b�)!%d-�9#e�� 4%,1+���equ}%YiN%i   C,"i"�#�3 �' strong��.T�*l*s��%�2wu :�  'p� a fac5 of 6�� �a 4C. q#�兔s�>��""e �de switc�5w�. ia�J�E�/# lmos "�}k a�^G�G�f!lTe\�i�)���6U%1�y �!�-/B�,C�~E)ǝ|W1��t��M. ��2P!�n o ,p/previo�O�oLi�#N�. Chen�+$3-1514:CHI| FinNe?�(�2Ua&!��'a�is�%�(  �%�9iz he� er h�;� may `.$��v.a�%�ati�ep-size2$�f _x=\/75�"a&8'sN4t==/(�Wc)��M�� %|c� �O_� :�%�E�$�$a�:i $fVi�7i�l .jto��� a���"envelop}gi%slowly.� *�!�.��!�($egatshort-t�(�'-E0�' FU`atCthirdU . Aga�AweeXIiV iJly��21�5wo�. o&@�j���M��5� or -�.��}�2"1 %�� �� 0.046�2��d��j ��ke o�han|*2�3�always��s�n$. At G!2&iYLs7% ��Tn�di LHs)'s\7�:�Z#�% o# 1$�e��Ua� �U2 �FM"� ��ES �\i�-�1�e1Ֆ.�@Um F����=)al(!5AgKs LZB�3�Z�,aa�t � Qak��2�a�n�(E- }s"� agF0 d���iof)In�a���Ոa��� enB;ed1V��3-7*��:)�(� m} )@�5j"!1 Q��d. .s gbe subj�to fure4�~sti�9���6l7��A��Hnu�/l�e����ف2�3n2{5��&��3mpo��woME!*d1���'�U s�s� 55-y�E��s /d*�:��r8�AT6major FqR>�a���!��eޑ6�!�?''d�:@,�@��%_*�1/ay�n Q nJ15�.�� !P��w�� le"nB%b>>�A!J �xJ�*M#�Pf�Q$�R cite~R.$�Rurl^�url#1{\�|tt!O%8{URL IZ7�B{!\info}[2]�A B!e�t []{S'�>�= em[{2�� et~al.}jG4)R#, Dow#�BowdenI�$Bloemer}}]N,/&�:�R nfo{k@}�5�{M.}~�1�G̓ j=J.~P.}&@ ��@ C.~M>@ �?Yand kj�M.~J.�-} {5%,�@jou�� }{J.�MpHinfo{year}{1994}). \bibitem[{\citenamefont{Tocci et~al.}(1995)J!�@, Bloemer, Scalora, Dowling, and Bowden}}]{Tocci:1995-2324:APL} ��author}{�f�M.~D.} H}}sv>J>> ��@}~c{ �= J.~P>}-@Zand �j�C.~M.} �:1a,?`journal}{Appl. Phys. Lett >textbf%j/(volume}{66}.F4pages}{2324} (!.UA5rALiang.A7)6A!,, Lau, LearyE00 BallantyneA6'(:1997-1192:�6J.F�H9y�Vt S.~T>�Lau�< M.~HB<�1Z5�!�-�j�J%�%�:. 2j� b�70:�-�!mR�7r�Galloe�Assanto}�= 9)}] !�(9-267:JOSB}~K>�`}:�LG>L�ZFDJ. Opt. Soc. Am. BjG1a<.�-G267RF9rFMujumdar!IP Ramachandran}(2001!P%:-929:O�QS>F�TH>O2�ZY%V��f�2ZQ929FQ!rQGawith��0:� ",, Hua, Smith!�and Cook�� ")n 4106��C.~B.~E> L:!V�P>cHu��P.~G.~R>{�z�WaE�ij�BC)!*� ֆ8��m?!h����e�R� llo,���,ParameswaranŊ Fejer)�llo)�31��^�j5*V�BdV�V=KJ�.�9f��MJ�-2���9�.�31Jx!�:� LHM(�8LHM-foucs-issue!� 3:OE�d� K֩ S.~A>Q�Z�9 Rev. Ej�8 J�0�R�2:�> .�3:�,Li, Zhou, Chm�~ henga�Li!m3-8390!m�J>bL�_ L>8�:LV�CJc ��& B#- 2�u�=�~�9Z 0%]R�3r�Feise.�84{\natexlab{a}}:�/� Shadrivov��Kivsha��#!�4-1451�� M.~W> H�� I.~V>>�B�aYue�mE;��� � 85Q].d!3v>� 2004}:�j.Yeh� 88��PYeh:1988:OpticalWaves��VB�TI� emph&�title}{F ^ _H in Layered Media}}6�ppublisher}{John Wiley \& Sons._add�$}{New York �'��88r� Liu}� 7!Liu� 7-158:MOT��QNGi>\u�Microw� Technol�fb 1AMr�t 158F�19z� Lidorikisu� 1998:�%, Buscc �ρ�i� Soukoulis�� T!?8-346:PD�JE>�vMP1�V�B� ��;QJ' �L�:+k �M=[2�UG�ica Dn513: M634J� Ar(Berengere-4a-!� 4-185:JCP��NmJ:�� J. Comput"r�4:F �185R,v]�lu(�l�kbjchneideri,Bevelacq] U� 2955:ITA�8� J�>f�91U��cP���:.�N hIEEE Trans. Antennas Propagv�52N!A�~!�j�E�6A�A�6-1138��BC2�U�T �� 212?Q�138N� 1996r� Chen.�>�  , Kim,�h g, D�uI���](A�$3-1514:CHI�$ L.~X>}pYx��V�D>$Kim�9 Y.~L>vSoz �z[ W.~Q>=!�zWNvu*adm>jR�fa Chin�&�cZ4 !�F,202 \end{thebibliography} 8document} �\ *�}{43pc} % %\linespread{1.3} \renewcommand\ref!�L{{\large REFERENCES}�P%\usepackage[pdftex]{�icx} .dvipsZ{amscd20{xspace6ams�B mathBsymb,ams�s thmB%>vhyperref6)bigstru:ypsfrag!�9 {cit!� \9E{\p}{\!� ial}6(eu}{{\rm e}:dd d>4ii}{\`\i $ \ $>7,er}[2]{\fracv #2� #1}!� %��theoremA�}{T $}[section]2'(corollary}[ :]{C2+lemma'L2#proposig)�/ %\ h(style{defin 12J�D-:Hremark6D @R %�v)v \hyphena�4{Lo-ren-tzian}�a a%����)1Dapsrev} % \begin{��<} %u %\preprint{� �7$\noindent �� RELATIVITY PRINCIPLES IN 1+1 DIMENSIONS AND \v� ({0.3cm} DIF��PTIAL AGING REVERSAL },1.5cm�� % \footnote{Keywords: special relativity, diff� a� ag��$ locality �Xciple, clock hypothesisG% (flushleft} q\E. Minguzzi}\\ { \it De� �� of �i�4athematics,} ,LFlorence University* \ \ Via S. Marta 3, I-501399 , Italy} 3�and INFN, Piazza dei Caprettari 70, I-00186 Roma, B�ettore.m �,@unifi.it } :��= \date{a� make� \UT We study the behavior!&%uA"E time assu� 19�.�5�Lonstancy 8speed of light %#u.��0The se%�possible-Tories turns out to be �4pr than usually %expected. Thi� due1texist!�,��case,�ha %one-dimensional non-trivI��ent�1BLAEtz group�0These requireA�,s are satisfA�by a �D$FinslerianO� pYtrized /`real coefficient $\beta$,!`:n0 being recove�for 0=0$!e effec%hF� is A)�;�& value� �� %In ax8icular if $\ver�� eta =1/c$N~ %Y!b� is shown!�,vanish, lead� to aU�stic %�uy�which itCY@o �s4e an absolute A��Below�cri �r�.� �hasHE� dir� - after� ound trip)Xaccelerated observer reI�you�I�!�,twin at restQ� iner%9f� -!le above8B�I.�-r) ges signI A�q�!ge%!Wtre�A�introduc!�a!�,mal analogy <8thermodynamics.�(%��0�F %Fina�,.se fin!�m5Q8provide a meansn$ %determin�>���of�5-1ls.�5� Key �É�problem,q�`s�$isotropic �3s.\\ \\ �acs�\� �DINTRODUCTION} Sinc%�ir dise����Yt�for��ons hav��\en derived in many ways �{weinstock64,lee75,levyleblond76,macd��,d81,field97})�(goal was es��i!�A��-re-�AInumbe�Ate�]a�� omenon �m! ccur vary2!O�*!�-K: Jare` al. � "��i�Pd� o!E�am��^ were"���(Bogoslovskyq�,98} who also.�A m!C�higher 3:C . Hyg ed ai�9, $M$ endowed��a�$aRic!`�� ($� e}^2=1,  H e}=cnst.$, $1/c\leM� <0$)eqnarrab xlabel{tau} c^2 \dd \tau^2&=& (ct-{\bold�(ol{e}}\cdotux})^{-2I�c} (c^2J t^2-%$ x}^2)^{1+'k � i.e. �n e#4ion homogeneou�8econd degree i%�2s!ce�& i� u� � K t l!O��1`inAYE�(a velocity.2 used6=l�#�Aa� $r=-� c$, but�_ pref\ o(a� M�a�R�s��i�ll & w usAi obta� e�e�iv] limit.:C a simple !Ze��$of Riemann: Ius (quadr�Ez� � .�s)��aM��� Q himself!�h em� �{sa�.N geo~y���now a B�� matu ubj� � 59}. Ully&{ U s a nH��ool� �escripo+�sicy�s t8asanov85}. For 3 ance� AviA��ic Ρ�va� t un�e�4ull Poincar\'eɲ,A*onl�s��6eat sen��$ null vect� $n^{\mu}=(1�.� )$,   . �r�% it%á�le2 � �un� d- budden97,.>9.06" X clea!jatS i-ce=�!~V�!K(lost becaus sh$al $SO(3)$&�is brokeŢ�$O(1)$ &�b�d $. N�nthea�)�E!�ea�ddi!%��/ rule h!a tru] �uwed�:�i�just ��ry*F�imA� fa!�I�.u8.uJ�The bred !`r� al� E�c|duc1!../� pa6� ��� ��Dis+ �C�e�1�. entira?op rthochronaKL- E!. A fir�"|��equ�ofqQ�A A�!>�� lXconJ G��$���#=0$ ca�B� o�5$ MinkowskiA�c�� us��< ak�Cy.)"e �A1al struc��. One 0 st�i�i massive!��s� e fu>>��imelike�}ldN�(ymbol� au$��1+* el�$ suggests %5 it&M �� !la-�D long%n�l�.� i!��ɒ is cq ct�`�bEv!�h.�hall � �� {\em��A3}2� should�  b� nf��-�d9�F� ��it�a� "t ce��A[vCG�!uI�N� )22>F� � l &�"�:� � up �� !Uto � ��A�=�sնly syney� ar!9mpa�쩼� ���J6��iE&58ce betw�;�z+ 2m��fP q)"��E$Z?5h Le�f�mee evenm3Bp!dicE� ��� ��al5A��ve .�lQ &"mo�Dper� ed dur��=�b�� L�9�A� i/resul8 :2!=a ��u���  \in \a bb{R}$%X suchi] when"� cross�he� s E=\pm "�2� E 0s%. Noti�at�l� F��.! $��D=\int \sqrt{1-v^2}� t$I�$6le 1$  $�� \le 1��)pE�"�.�%7;!9)3� 0$�� tegrmay!~=or �� 1�%!��$ime $t$. A ori,�Yid: balO m contribuA<z��b�*���EE� follh��Our aimo�t!�ofa �6� �thR���erm� Ayt� istorU�Z� Indeed� we ��$ see, give�-at � on"�ab�o�:�eu �.[us�Holder'� equ;. An s_� �� �W:&�>;�(I'=0$) in$ m� 04c}�) idea!�%�b� 2Jof��i>�b�asu����apov� F\ e�7E�unambigu�A��V!Xy�In� }�s Ly� 6nddiWvolve���tI��con��!�of�Q$ simultaneidop�R\�us25 �Uulas, �*/hvsIk moraGs ��p&� .� Conn)�!� J �jautonom!fs0#a� navig�%�E�no�� usse!�r5� Q�2�!?.��i fromQ h�� come quit�%�de�he�E��i� it iZ�3�0��n d]�o %! ��M� �E�&���-Walk�por� tetrad. E� ��!Mi�1�!Eye!I en sA��]��uni ��.�� Frenet-Sh$t �(�knU�a � imea�us,�-co�+3al reasr��4i�"�RAor,m0isE�same,-u��%�&�X")�a e�plane.P>ElPROPER TIME IN FINSLER SPACES} 3 vfe}� � sU��%V*�69 � q venw$ly writtenn�2r��fx 2� >�x^22� ,�tau2a0!&*�+Tf� S� } , -"Sb}�&=&KS& �O.>'IR<h >5"� �_of R�_8 >"� � ow "�:X��VX�N� � "�Vx/!pt=c$ doe�Y!.� <-V���Z�N��"� ^� t=-B�����$\F� -���b* s��b��"�*�isYful� %�\gX r� if %O � 0�o�� �� � G6�  %8a�9�3+�� Eq. (E*A�})Bsen�y�!T %>%�,��^%rwX7QB�w� ��27 %�V:(. Let $K'$�a&�� in���ۭ BL$K$ at*� $v$3��"�"�����u��8} e^{\theta/c}=��)1+v/c}{ /c}�F,�)} z\tanhL /c=v/c$. �our��v�oY c$ž!J��!%.�"<ay�O�� r��=v� f $c�\infty$�Tmularly� ����rey'e-zy�vdn �einF�C reDo�A���!�%natFh&~�(&Hct'\!&=&\!FR[\cosh ()i@/ c) \,c t-\sinh . x]=\([J�\%f]^�c/2} s\! / ct - v}{c} x}{I6�0/c^2}} ,\\ x� DJ� �>� t+F�x �� � t\! � x -{v} t N�,>�a-QgAYB;!�.�� ��6 ���revealMal�� �!*cM�9('val�&� E�q��o6^2=0 \Ra,arrow :�x!a6mp)��a s(' $c$A�$yi"�� w�i�*�f8��*+Q�$itemize} \ BF�"!!}-�� �)ormN cD.P |)/ 3is� M..sSm.tThe&�o- ��K.t�"�[�s���How!7�Fwe�"!� V" & # $x�� -x��:�ty!���A� ��"�(xw,"} in i� w�!���� ofɔ,reads $x'=0$�%d&� ��� 2@met�we��  t'= A���w,� AIB-��er $O$ d*� curv�"gammadt �%�an�.isE+>O�xw)!��a��%8(Eo$O�V zlB�-(mashhoon90, b}�$� s me��*�%S �$f� ^ #{��&�-}_rindler7�&It stM&u�in;sim�k elapiin&�nEame�E��A�j?!� %>!T�conclud�O"{I- �Gri�Bu$(&re�$�"�or?�It^f0#�cif�AaR� .�6&N� =� 7-!0Eqs. (I 2a})-b})A��)�y"=s"+ a3 sgn}(k )�x$M�m�)%�� &a�� s noN�� �iQ!&E=shdX!t�e%�a globQ#fun3 $ � .�x� %a 72�[Zi]�.& �4���:deih+K A�e#go�to $n$, �bN���"g�1 tivea�m2leutwya4 8,duval85 91,�}%H0s in h�$�j�sa�wel�% \sub�*� Z =�"}�%F�",E, to +f� 0!Ȃpis�_ "� er} Eb�z^2=| �A�� } t^2&  )�f.�a (deg' te)  m�-� seemEs}+ ͗e}+ aE�E��terature�<re&� " -� =v$�ankfg .� choi��quantit� ]� M)'�ͱe�&a�ingful�iF���*���!'made by e��� ���m9��& t'�� � �  "�abs�x&2'(x-v t)9�R�� regardةY) Ul �iO/ E� counter�s ��(,ical Galilei�Ric~� ��F�=0$ inM�� A�t)�aga)�╕}0 ��$t$!��2 ny (! )��. "q � \ne �]Af���-q3��( path $x(t)# J, "TE"B!�weTqw![���epa� .�Ao�--v>Fcl!n (7(e aC 12Q}�'ac1$!4})D0 >THEDI7(ON-ACCELERAk/, FORMULA} W>ş!Rp� laN��M��% &�1is�byB _se1} A# a�_{� ,} (1+v/c)^{("f)/2-� ��tYbl} %FT 2}{eW ? c)Bc}+e^{-p %} _� &�A}c<+� a�.��X�se]tau =:�.k� B i' m. J�cg"�,�.!�a� "�,c �)U8as6���N>Ź �)�*щq�)���) "PF_AHU ABE �s.y _76a i��� H`0i�%3- e��Q�C�7%i�9ly �+� �&d"�4of8 ,�!least�|we�!3 s:� Oo 1l!�� raK�>. $o�5 dds p$� s�0"�1�1Jt�!^ pl�H5he  ` �s�"��0>�ty2� Qis5���/&�  rem�$  &�:f27* a sm�E,6*& an6'\\2v & $0<�1& &$c=�QF.�R� > �#Ab�>#\DC:]) 6� �Fb,�"C�խ1,}B���o+=$B imeX%& :�2yD,Rd[6� > 6V&9�51�:}��v..($0<\!6�� !\!<1/cj��%\ #4irow{6}{25mm}{>7<.�Q��\cA� {1-2N=.F,!'!.H ���==�>5I)� A�2|6�Ju Dt+FGrm{*��b&.7R�*5!Z�!�qd~�� &ZcR/>6��%Y��/ \cap>�?ers��3)R$ d2�ib� �EJ. G_'.�(�qB�,:h.��� a"L�9 3��B� wh�)2�~ 6Q =�w�� 6�%(is $\Delta=2a.�. A,>�"�&<Q2anD�j((" !%� rsal�Y%�v7�%�Ͱ 1� F�%6z�Lon"/-.% ��6"S&y t�� �au}_{0}� i�t�(')}^[2/c] \,p n' , �e1��x<d� e� Nf c NiHL.ne2}BX Co� E���boo{ mA�"��,� M+��:P8b��5tZ'� ,Q� c�fE� v$ up toC:or&� se�t� � �s $a=-�!� / $ a�Cin�)F� ,0 �"oacc_S)�a-.� ')p'+c� ,^{-1}(v(0)/c*q�w" $ 9 F  v%1O*�$K$�8!uH "� aM e��u.=R%t"Cin $KB � ,� >$x.� �DU�� uw�~O*��6:a{�b^vJ"2a;n60}=i�X � e�e:(Vta+ (1}{c}) . tau' )-�)�g u''}m�E'}�c� �c&�1� Plug�9%S)J&�)6%Kar�BM�di�on-�on@�+!!� �� tda}��5U��[-<)AUf�M�(1-1 t1 05l nl){"" M"�<{�!\no�B\\ &&\A�s!�[�5F�.�"pcB�r � ��� c �B�!��& �� �FatK0s�*$1�2� ula �/�&cite{m*�.$e���az%Si�$.�3 what2 9�c�/u�YQ|2���J`()� \pm -��e)bF B�YM%}�&u��ȁ�$c<"�'�5��F�f��.�2cY�^{2}c]GiM�) ZI�F��A�Z��]�reB�+-���pr:�=Z�f^�'2}*R+���Y�6~Q,^j (f��).au&}<�' a ! iG"� �"!*�?&� %�s,M6$a >` -.}s0�&vpr�> �2�!�2�` $1/p�l2�1/q.�p,q�� (1, )�$u+p}ٜq}=1$�4 q4� us�*2� f $f���> $)��,i"�3� sP#t�(�E�2�,ict u�A��O{B C_{1�6 0}$ �e�s" trajP?"LZ%[0,�]$�Y!�F�B0h .}9 !��)R"�5n"�E�/P0�5��t�#noYf"� M e�n: ! � ��:�L $t�U.j� IV� 6�sld(P=0.�� -!a$ any �a good2.**?as �th"YC.�-��(6�� �\ne0$*� �t'+x'/c� �P(mt+u,S*/c�rge��� c-1�� (t+x� \\ t'-�O+ O (t-O������f0.}�F3E)(a��>sa>� < �.�P"�7.Z $F�*bet���J -# < W1Z ��let�`�pl,B� a} \�\./� \ q22a} � c -1V3 �3g��&=&��^{1/a���W!$M�g.�/� af# opt}�2��"� -\�xQ�2## 4\ g�p�&3)^{p}}�F g^{q� � %q���- \}^{.�~O��>1W �!u4&�Kie=1Q���1R� &\le&QX�/ g \*�� \��1(� -( &\g‰9���01�$c��Pe��,�9c hese&�r$@����g�:x*B m� ��$>{ *mRin*# A�) "~+:w:x�@dA�1�?'�v6E�>\= y�T�O��dW+in�.J3 7"J7 I �l�I"�$q  *6 valu5 �_�#= I#m  >�4��usla?suTt �P�F &!�:2�*�$ argu�+&*E�I� aE!� �i7 b2�9 6;2��: 2o�m &Ao 8o takle>B tof]GS ). A%�> sePTnM.rL1O~F�� &�T aris/ �� $E����"� a�i��!F)) �&-� �J�� ! A�� aNnoo>� (R�/" �6�6)z�\{��H�2aI S R �n�M�7}.I }\} �4u �v 1 coEA� &!A��"k� N# � !� B�� ��(A'�#2})F�O6�/int_02%x%X vI3�BA2V40=2�ZF ve g AA�B�($&�) j if@E��}�V��#'F �1}"��n#jn�L1r/�Aien@�Y�<`` �O �''Bj Z�/� b )|B% G 2"��# e*�q�!�``@abi&`den�_"�6-PiS=��� 2���m )}}{���)}"S] �m�!%.gy""�J�KE 1=&�{06 �')���+) =: \p \ln Z} ��F�I �ec py''j�� , } S=b��)9Jw&81TYH>�6 =% ��}���@q�R_prm{or} ��� ���s�3VO(� gEZS$�A�,��� kjE���(�F�\o��&a�&�lej�$vF�, keep�>in mi�/ Cy���"J O *�*�=as!6�qi �R��r%a��8o�5�1�BUJ&�2�r&�v}�3 \ F � F���=�E"F�&� 1�$ �a kin%T � &\NpA�}����) z$s expe�Ko ~>c"�$�E.�� w�b�fcY�=B�a�*}teލ��F }>R.��="�ae)=!����N� ��B%�{ �acc4 T��iV9�ga�TllWR;"�"`!�BZc�Z�d)f�T})=x(0� . NF9 we w�8�at)i^H�,~�!o�Zsw "H }``���Zi�KN3\overW%(�E)X}=.EQ� 6 /!< .��E}}�N���-\p+ �wF� ,� �%A[va �!��Gve !<h B�I�j{�B,��Ձ��� +FWe~ u�!�tropy"f� S[= :�!�+ <�_ve,28��zero,!6ne�I%Aor 5C�H��~/ ", $S$� a maximum� ��m�S uH5,ATNo,at ���A*e:t1\tild\�A�n $S(.H 0$ �$(\p S/��Ax)� ac ��. ��[!�i!�ta]�ő� �,, �ver#b: �@s &�E}�u*"��ref�K�^E�no2�,�h� mplety,proof& 4>4CONCLU�j}A�a"[9� bR�ha6�>al&�c)S�a:#8�K 2Ofa� (a)< re!9@"�0 , (b� �wY�Z�f1�5f�@�>(c :�$�0VAG ��i�Ked Fe1�?p��o\N� �A.[B/%.� "�ih�c!J�0d6wM&�( , (i�:�")(i ��'A�$*���co�? n&�8"Y'inj0�@sU�8$x'L[��%}�a ,_{\ \nu} x^{�<er�_%�<F^7%/c)E�AS"�&A�gE)�6�A �9��f��na C!m�ENJn@<aT!�]&�)� �3F�T�")ez<aM�dp_\ "\�8pplbJ6ia*a"d dn $. More�Z�I�L� !4�h�'s �Tb !NF�i!7="�T!Sl ^C �&���3YMv��QG2�{<>���Ror J�8*�rB-�IB; � %��b%��) ider!OA;) �#r���0�&F� F�w&� �ѹ%D$�NyiKrol��a}B�Qe tempe�< >8 �i�y� ":2�C+ �k�0Oat 2-.�< -%d"�:bas�A�[mme�da�al ��>J�>Rre ricdIn$SR and exh�m roug4Me )ީ8<LDJ� K,)A�URwhe!u�se "� �be64>$3+1$&�b&.Ya�. e��K5mains opw6nd�>w�@�a��L�&�&�;nt"3Ac=Q ledg!bs.}^FShorE�-�pa% q [W��� rm{n4circ}$ 9503/0210kb*�w {../  fie/.� , ..6#libriZmienPr^ssj?Procee;9shq���t8plain} %apsrmp ev&�s>�x{10exbAlem&�b G܃ A�b,�Xwb�7�T�@c,.d!� gaug�iesX nA(D. R~ l Pu���<Co.��0rdrecht, 1985�!�bCk} V.~B h$ V.~Gorini.�``Recipr &�2{L}`:�s,t��J. �s.�?.}9gX 10}, 1518--1524, (19696�&h06%LYu2f.=R``�!s�:vio� �Xith]bof5m�: 7J��ds�+ s {AM}{�u35�5--104�6^�98N�%O0H.~F. Goenner6�On�KEs@of ph�!�"L���QJ$e�`�� .T-�۾�4244}, 222--228!�98b�9��m�7s�Ds� ses 6�1�J�Gena!� v. GravitUr31Er6!�603�:qAe} T.~B 6�A�9X{M}wban sky:An{ !�]=*tLJ� Stud. His��ilC d:-828}, 325�-361�72�;F0} C.~Duval, G�rdet,A`(P. K{\"u}nz�w�_M.~Perri:� Barg�h[c�@ {N}ewton-{C}artaEsorN�a1!� v. Dq�) 841-ۃ%:��91:�Gibbo#Z�,P.~Horv\'athM1�j``C(fVmeZ2$x�^Gq�ogE)qveN����q J� F�q>Inew2*�"�Y�nRd% P � zd :.ilaOJl HelvM[ Acta1�7��42--564J^l{r} Ac� Lp nd T� Kalotas6���tra&� &�L"orJ�u�J ��043}, 434--437�752�6��R}B� o {``Com i �}v� {�'"}���S 1000�502�67l&J} H.~L%� F.~Sz@6uw<�� �u�a&* nRkn�1i(112}, 94--1I76�2�tE�(M. L\'evy-L�t6�Eg�]���K271--27I6I*!uEL�4u6�,World's fastXAj�:CI��9A�83--48��12�m�t} S.~M 6�.�{"�E�.O"�� Y���998--999J�.HP B�cP6��0*~C�Pin";fv�� AU�45��471 %@90:@ �90j�L�%��-'q s��I�J�� B���176��e�>�*z3 E.~�~6(DF%�"�ion\lC�ulaJ�N;7�8�88� 6;&�Q W.~R�Q.�� EKx"� ty6� {S�4ger-Verlag}, NM�� 76�e59��RU{BrAB2+, AM9 )�: �, B ~56� sar7x D$� S .� ``UnifiedNG}oLo���"  �:}�NT Eur.B�!�96ayax822�*z} R.~W z6�DRzE�!(2�-7  AW4 s% a ?`an&e�k3�<260--2�=64��*>8�&"���:�[twoc��n,superr��,noO��7ņHi0,pra]{revtex4�d?[6,��{�J.ɆRƇ�� symb�"{�;itle{~��(� dischF0 lannd�Xer pumped cesium magnetKf s} \^{{S� oeK� \affili%�Տs D"L�, U�u it\'6 0 Fribourg, Ch t( de Mus\'ee+� 1700$Switza���2laul S��rer Institute, 5232 Villigen PSI,2F�A*Pazgalev����Ioffe���! T"�!�Rusd(cad. Sc., S� �sb%M194021, )ia��{A+i%�����R�\todaY�I�abstract&`p" maEeY�laA�(LsOPM)��E�(Lp 6�vapor6�. A.fH �f��50\% �k Zshot-no�`7�!�! a@trins`K&�$of 15\,fT/{l \mbox{Hz}� nd 2bWP �,���" ivelC/wo mode/ �(ion, viz.,~@�-st�&itK�}�u-oscil�ngH w�(nvest�hSnd � to y6^n-� !AE�c p�)�"���� ��(lyp"�ou6ZA� fluct�$�Z $2\,\mu)aT}$-�ic 2!���|l��# sh �nd �u� 2�%�an ac!� �1a��h.�ed !�]2�d5)�[&GI���n7MEn!��>o� 0\,s�/�\ Z�� pperM���h-�" �t��2�.,"��Xhbf{PACS} 07.55.Ge; 32.30.Dx�%au� \m&�&:�<�} �? sec:+*}  precaY*�[E�co�!l� �ic %�� 2 nOf cru���c�*ɂfu"��  experif )sup^[{|of syst?&( uncertaint�in.< searc�a�perman�eSQdip�m$ts (EDMs) !�to�Cneutrj�n�mi Fxa� .� g�$Ea EDM� �E@ ul�Jo�tU (UCN�{iQ"a�At�al-��dra!�UCNax%��8?orage v [�I�ch2�6� drift%�6��pwfalse ��?�Vzreby putE/�;o� A-�;i!Z�:tMO��:�"�� X&ucd qYum ;(fibdev�: (SQUID!Vr m_F�e �#  avail��&�d hey <� ��xEImonit g Lyin)� 5{&� �Gam[&�:e=�. �KdAnct g�A�#*q��� �-�/EDM.��ILL=��AILLEDM}��x-��>��)��+ �. Both =�`proe�i8as��-6�N,M� -ave!Wd k� 1�0�_ �r�[!#� gr� wtheir�m�� . Exeal61f )fhand,>�B�i3ave�estN1ly��--0'Q�suffic��  -a�ss �aF"�u��� ermi���a?���� ific �2)��%%@. Borisov et al.~5�posA� ���(e-2�k&� ��nuwspin ��oy $^3$H�c(Heil_He3Mag�ta�z�!0s a double pu��Ramsey� on� U]Q bea  }s lack��EVol�v�f!wA��/#"o�Fre0. Ra����daj!qck�4ate-of-the-art�� J B �� ({ ��. S� typ� 6A-�GeloSs�6 1950's -)�aB| ed^1��)�bandwH�sZ'�1V'J3!yop��l�W�alkali 6�xL� E'�u?F ale� * ��A�inu�s��ofI�juq��(.� Are�)xunf � OPMe!4 Lkrol��%r��s call .a �@�f�� )q�� ens}"�giHf 2��Lac<&VnleY>��� ,�et�ލ;jv tead�BE� �A�j deca� v=ow-!��Xi�oKFodsa/!�s%�"�sourca�t !�6��im� s. O&o!�QPec�I75�"!�� !bin)�� ]@ power (a few mW)%,b�Kd�rivjze� .� %�a� HavEu �3bnenCE�6$ approach�a�Fnned *P.0]3w���`�E��$ !�bK%I�K.�s� e��r>'��zs} roome�e&' M�ceA�(7\,cm �6 diGhe�b�j!�ly{ozn� � o��Aus�'F cipl�3"mbdetail� �p��kliaÑ6K G� ���<� ��aF�"}e!~"-��. D�&{�keZ!-եDN{%j�wx&��d �bier� FRAP,}%(have dm� Y*rF5��6�Ap� � �!S�.BJ� �4r�ds+{ou�k� �nV}ia�eB-mn�� ,reach!�tsR <�>ed .[�U�4 ~�eG;�^ �c A�i?*Ldn.R^g�o50\%  &*� >��3"�/O>�2�} �Ic\{Gmly%An��1�i#LarmorCe>f��e��$$\omega_L$%� � s�� pol]�g!�a2��  $B_0S1r\ �*�D+H�?eq: ��fX nu_LK4 �}�Rpi"b4?n_�rmr&{2 B_0\,B�:%"D:E�1-A��!8oI,5'�#L Eq.~�JJ�ET����!E$B�$�b�  tota gu��u�}A� nFA���. ")t").= 1��wJdem�D��d t ��hk,*Z ,�auG�sn LsMag,4_2001}�D� �L �n��� !]� J� a�Ã�>eE� ng lu�-e�8��oth!SZ�lf.`�ind�tes wWZR $F=I&/2TD  $I"�0-: A�!� ic�1 yM�1��SQ5 b�Zd/� n�7Z flips��a weak:# $B_1$ m2n��at ?H a�G*=Leq�>.:aA��u�q'rf}YZl!Vi����c&�RC��MG$audio rang�> }�a\b-$x ``rf'' (� o-$y�CK %]c5y)�commoKEE�. �'�A(%�'�%�t q-u-xQ�ed�% beam cԙs)���\�medH(>�� �I�� ai6k��glass��AGanoci�net bul5� |.�@~��re�ed%�$ year��I7�m�w,�is�&2�!�$DndM~c�m���  >!��+, $|nS_{1/2}\!�le\Exa�v|nP  $� .5� "bkD �' $D_2$ (�j3/2j))��{ g���B!-�bށ��rBPar�E$}6� -Dl! , ex�k!8!� r��8��Sec6�,F-B-� ,F+151=l�l$Kazantsev8�&�V�c�,hr�6����I�inA��G� &� =-A"p.6� > &/5���6 y�F Z:icG!hIDby.Neiti2] o 2g{ E��2 r scipYR%�e�� "�A��1a]�l�t�I�2�(ODMRf!I�+��Ş�r�|4 ��G8�Wi��$ � J.A!Yso-�4ed $M_x$-methoCi�ᩬis2� 45$^%2�R6���\�.����k(widehat{k}$"G�z�)Ep.g�% fea�q^�72` 6-�%� ��D!�mod�d��0��V6-E.�� �e8� .�gtu�jclo�* &� � amplit�v `�!=I�!5$\sin 2�8-u$K`&9=5XB_0T�k�6 The l� � bvM�.� �Bc�4�,1or����K|-�y2�OnA7q�ap� shifa<twpu[�i-%x� .�%�.D�<90Q��-a� detuts $\d�b)�= .�- L�= ��?e��n�y �2P-�Q-q��(����d��7�:xeC  EBA���i�mi��by seKl�iect\- colli� Q, �s&� a2� a { 6e�n iې�`m�-exPg��o��C%:!� individu� ���M��h� de.+�B�g�X� A�F, �r,9|,�d��:-�,A<U!�� c�ui�9K�/!i�d|L 6��0sڊd�D��!�D � wa�a�6W %3�=o�7ads�+ � \ $Uo�K:E�%�%�p�e�8�D�#�� �{�e& &�9��@' �!ert buf�gas�b�� !�5+H � � Z by a suit.coa�I1# surfaDar�%nesi݉s.&Utx< DJ�y���=nk� a* �Neby=�an�X&icQ�$Alex_LIAD}���le���,ane�%w.�-lI�� r��Áy9um��a dro�A! �me�f* ^arm. DqseuZ]�! D�2=͍5+27 "P(q:gplusminuVr/e"6Z% j g_J>Cv!1&�5%,Cd�gcc!eJ=-g_J-�,\vec J/\hbar�$g_Fr1x2S�XSI=�]B RI RE�&&�����sise�� �sRF adja@g}�e�R{ � L$Jur *�nuL2���|�K]lQ� +1}-:}}{h}\�|=.;E�)�n� +!�-� �%�� ��v��toPf�!*J�i L3*AI��FE%R �_F2�/E\,.>�0For $^{133}$C9 �**Zay�mem �4/ 2 \piaD+3.4986�, ./nTO�?s /3/.-3.50986.�V^numeric��>g�x"/>��+az��acqb��E� al�7�t�x�wM^2mrB_0 (�S$c ����)�E> Fz I�a  ��+1��_E*�8H|�o�am��jNQϦ �II|m(\nu^{(2)}_Lm�_(�k+g_I)B  (��m mB)^�.f�Q2am�I_�hfs�`!� sepsilon�cab@JRJ�.N�n%�2���do .r-5�)��#�A����i��(D��a��&)� s s�3�.�B�=�Sep)��9�=1\,)Ba�c/)$($I=7/2$),�hJ��O1o��f=2.671u�nHe�!��K�#eU!$2\,��$TmO-(hN�(0.011$\,Hz Z$O"&: ^ a� 9s!V6 ń e� a�"x�� (n-�c & vali��� � ork.> PY .*��3�3figure!G% RA �-V�6t�P�6Hs[scale=1]{Mag_GenP� .epsQ"�v|"!t�M�B-` �$ "֥�"h&�6 d*�$aP�bG� %�/9$ext. L: le�AP: �8�D$�` .file#(in ^�-C7P ing)�Pla�@/4$: quarter-wave�$�6PD:JA hoto�5�l� {fig:.,D�1��� ��PS_SO_El�%$>�Schem� feedb�)&� � %�>C) �e�P )sFF>�#�P. AGC:*x ��rol!TPhi$: B�_�F VCO: +tage- /� �or, PID:�%r>xB:}%�h�RaI=&^�A�.�".�_9�6�xI�s�+th�$i�9�&�baw6de#1�� �=YiJ%"�( �cfN�(Figs� B�,z�fF )i��#R)%_9L% F_peH� sph�*� (60\,mm&�& !S�$,?��Nhe�%�B3- �8 s, A.S.P.7X "'Xq', purc��P8om MAGTECH Ltd.`9~P�%`9 Russia)b��"�&qɪ�q ���lic��� :(����U )a ��%C 6 , 11 �) cylind@  hoC)�p.�Xc�u1!n�t Ic� )� �� `&�' fi۷(800$� �7m}�N�(�F%�A� Dfibre buБ (6��!cjE ��0 Ot*�1(Ѕ�1#�'e(��)�n&,)�&I 6�n 82� , ���.�engthM !=%"ge H% 5\,m��gth�+�U�A*�JD�s�Ms))-�D+y��Q��R�s (zar��F�)�m=�� R p�'toέe�1%�_e�s� ses a��+2%inc�g-��fA�t,Lout� �� �)_ ()� ). P&�c���hn� use �-=S��a� ompo�7q�.X)ico+�4��t�� !�����wo��U� loop� 12 t��f cop�9w ��,2r  52A~. W�W)��%�Q� in�prC ity�?tal�1�&0QS;�� avoim*�lia 1~�ck Al �Z����a�A}b:!,*4 !�iu =l��=b')`�B� e&L@�&J@*�*>��� <f?"S?�s2� [ht]- i^� qS9+, � "� S". !Y/�elM9� s 1--6_ot� .Ӏ �+`&Mq Tab�� tab:_ �}. C:Y$*E�>�:7CP ` t�� <'a�� )1��Q�U�c|}*�� % af& \\: � ��$col1-col2}34} ..  L�=$& $d$ (mm) l t Ma�e al\\ j p%�(1 & 600 & 91.5 & Mu�k1+2 & 45+7j+3 & 3P \j+4 & 28u74780.76 & Co-Netic6�'25 719r-'229�8 j--1�!�.\�Q Y8sI�!z: inneu2���$l���h$:I��d�. &��6^I� cu"��endcap� 0&6 yer 3.�J�I�M�z0acA��# ��l 6RSecmP�>�>Sens}�#� b 1(. I;2R ��lֿ�.d.  s/�%ri�� >|,%k a�ow3)Fig �� vm�: z! aɄof*�was&O � 50@29 5 v $� enoi�=ven2n l;-��1Ccur([ ly. �ao%��&�C�� 6-aa�#�)�cacy bD� 0.1\,pT5��:�2;1�'*�;al sit]p��kep�#��%Ym<�*�harI+�O*�,)_var5s� Hz �5�� un)�i2nviron���!�of# $�BnT}" rms}$�Lm�� Am�ing�(or�"fX 10'000� �7�,!�r�*F:��ve{Z 2#1F�&"� & ��t}1W.tV 9,T&� $|6j,+6P:,+!"Cs!�a T��894\,n�"�\ �� � �;(d�6M��d�S��.(7��dch�(�6 � il�4�9fM&B!� ($\sim$ 1�C MHz)�sL�bI1� yz�, bulbE R!�._}1Xe.�as &�" �F� P% �����a-�N���5t!b.5%di� FWHM=11 . B���y%*� "� plasmaE� r&�%e� I0�.� �c ably��{aU Dopphe}s>K |,��� J � GB�ur*gB� � D] exc�&:�5��dic5in��&XCsD1}(aetaQ�~� �U��Ag 2 #&��&,FI� 5$F�1n i�he F=4�`9F=3�.h�2� +O�y�%� `3s 2�&2&��c"FuQ��: "�6���22o-�� T$��z(�'<tQ)2!l �)s,a�2.5--5j)���[m��;�m{!?U)�h�2.�!q&��� �=�Mlayz?minor Da�� ��r�l� � n�Ah� & HZ�I!"#q6�ni�!� ba�I�E5��s�YA[y� � (a�(b).� ��� �n%�}�'�>�tun� An��c�[y `��ittmaDP�O(S�8r LS=tyMk,� l TEC500)�Poutput ��! �!�n lWa�eed� &�i�;fou9)��@th����e;!�i{-y�a �ln<M|>fP=Cem+n* )lla_AL!�.�.s0��&!�in&S loc%GM�)�� i7���0Y'��&ed�F}=4\� Eh F}=3$��Yo ��Rưic�%ic� �a(DAVLL)�( }�an aux�P(ry (vacuum)Q��!�is Eiƌry��nd JDa� reliE��%-F2� *�6 O;iod%�-weeks��nT A9�%��[ &@ ;F=4,M!<�6q$ dark�tes&r��?H�li�*Nt�]!�l� nv3"�!2�3*v%�$��!Dtes.}\ A��j�bV_�mg�)9,�repop=1�of HA�(bEP) ra�1)U2�2S(Y]s �)se* ��F� � de/3 |_��AIe��~ �02/4-J} " ;F=j��}�(!NUB=9t�4�su,(i�6�9�.at" ��. act  X;ow�D1�Ta8B%, �3X���d3�BHz7c�-c�!� RAl&j<heeZp oln=i�w�$,can be achieA���""c X tra�fog�ay����e 7osE �mpt��2�3,\]�9u�� & � ��3�=� �).Q�a*).� .ּe"�N�tud-Gat58 is u��way 8!</ !>fb� a��ed .7�RA��kO% d=0F��ex+ � >E�6+2�*O��\F=4��iP draw�M�KR al6� �:5JH��EnFDס�p2Hof�7"um�; outs��j] �&� 2a T��2� �n�rr� @osc.� *VK�J�a��A ^ de��QHn �-�at���m�rFilA�ǡ��?b�f Q�}� m�&X*p-M�C of�} �L^%N�?-�w*܊� �H>t  (SOM)�*IF� a)�x��+� tW��9����.f. �the�F�l:\e#de56�90�8k��= �5s;+oidg4Mry.���� ,���$p}e7!f`��� ft�S�� e���� " �Es�$� .) �)S@z auto-�02"yB& ��&�7.�! en12!�� (m��"]is��l�&�5@re�2�9h�;�"� &X $�%�� ; ���%'`$Te7�� ^-*� �(PS�ob) �u�0!L&�$4 ^A8� .(�ap��dF�9�N5:!�-+)�"�@y�{%Y8in-phase compon�ent, and the quadrature component are detected simultaneously by a lock-in amplifier (Stanford Research Systems SR830). Both the in-phase signal (dispersive Lorentzian) an �490$^\circ$ pha8hif� siF� (arctan-dependence) show a linear zero-crossing  detunP($\omega_\mathrm{rf}= 4L$). Either of%< two }�Fs can thus be used as discriminant in a feedback loop, which stabilizesV� to�. It bbe�khat from a statistical point� view both�@ yield an equival!�$magnetic f %|Lcommercial digital l>� had onlA��em��u�4t))$ drifts. �Al shs slipp�ver eac���A)o)� void�ch-talk��ive�m��as�ow-passm>external-�i�Q2Z (skin �.)m�]9�Syof allM:�aabout 25��\(Fig.~\ref{fig:BWdeponAl �(}). \begin$ure} % RJ\res \usepackage{graphicx#\include ��, measur� tab�4 input: with=�(full9 )��!2Y (dashed &I�horizonr ae��e�&J� �0.5ehE�cas!�he.;Lɱe�abe)� 7)�. By usA�=�Yig �lGE  Q. Nota�atKBkLpOPMW �e sam%�ult sin�,2w�p��D source.E8labelAlB� \endE� \secE5Per�ance}ubMu� ric *� : Basic!� d fundame%���} �4sec:IntrSens} �F� � is definAm% noise a2:| � x de{ y (NEM)�i ;fl! �($\delta\!B$.� t� � A�s���/ Eje3u ly�@le^�%�smallest1 ecta0� �s are)=�pintrinsu�)! ��"s int}$. F�.m�!�YF $\D�nu6 bw}$�oresoluA ^g��"� )��t esonAK ;j v$ (HWHM� $ -to- �r�  $S/N��1� k) = accor�= to %�rHeqnarray} % \nonumbu o remove a�(beforeɚeq� �U,2� =�u� }\,.>i�eq:NEM�i�� )��D :��gan op� �ly thin medium ($\kappa L \ll 1$)%�9} (exRed� erm� � current)ma�� �}a�or cel�� by.�)I}�*� [} I5\ pc}=$in} \exp(-�)\� x 2% (1",1H { % wb  $24$�"?d�% , -/iM�t� %absor�k coeffici<� $L 4s�ye length�� Z6�wr� n asr:%ơ� )= 4_0(1+\eta \coss tj 95 meanr�`.Q &9�thI  $s - among � m��e�U0 spin polariza�n%AAS!<��J� We!:�n%< e Eq� eqNa~ZIpc)XY"I�0+I_m:W=I)qxi:jpI_0:�U�_0 L)$%$I_m=!i1� L} in}=u I_0$EV�ast $\xi!�%Br!Q-> =�9ZA�%lverag� otq�hexi^onq�\�D ��� $S}q�\ rms J�par"�J�.���@Svs%�S1 /\sqrt{2�W�.C� B��|:�� obta� } shot͠�e�=,�  a3level $6�= SN}= � e!� �+ :�}$ ofA{Qpc}���N� i�!�n read2Q-K � � SN.  �\nu�,�2}{\xi} � e\,0��$bw}}{I_0}}V$�J(!9�e"of� eres�9%�M�y@� 4asinusoidP"'.<� !��i�Q$ spectrum> aqwer"� of an ides"w er�Jm #�@ consist� aKtaA�� cen! d���&m , superpo�� fla; ckground�!�m.Z. In 2� peakaFbroade� bE��R[  (1")X�4FFT analyzer (b,�el SR760�a�its re )� rele<m�Arib� sմj �S/N�io� .����fG i.e.k2b9Ibelowt-�!.!D"( tAI I0um!Omodifi" �ous i�� io� �kad �I*/ p&� q!yfollow we add]AL=-/.�2�Q fQ�2v . % \*YL��nsA^[2IeP�}}J.6>� h)!�inu!'(techn� )I 1Y3li� b !]����� icular at"�9)�1��BnE�Olase� F20low�� }I�individu�(eak e- dd hn��c50 Hz5S. P�f.�9���2��A�$\�L$!��d-Lnct processes. FirstE�r�a direct%}qp viaj]*0��� n2� ���!;Fourim���. A � /2\pi$= 7  s r)�aC clos�@ !���%�)|second6��u8� " + ��(�eq����&(?\�$�� E�2�l8iplm�$� :_L t$�is mixa�pro�s side6s!> n_L\pm @$�!Vy =q �is wa��}D��5�e Mu]-oa�3 � = 0$ :*F�)�a symme� �: u��2:Althoug�E�Eh:�=Ag s 18�s>�N�largera���6�&�,%�ed .�.� E�-a` a faz� �����J*� ely 0.051��. A  �!�q�W !�*�Q�B�F �esr -.c�/� $.� have verɻ��tA�i�deeBlfill�a careEy calibT4d auxiliary ex��N] j<LowFreqL��NV.FC�1iY "�6IfofGpXiY�JI�4was 13\,$\mu$W��%�cor��*c F ��Das soli Z zat��, ���50\% 6� 2Z,[ also `.} &��F Z fi<n�6 2�2���1�+un%� 6Q2\��"G ext}$Œ high� �w  w��a:[�_ �A�s"�*� F�int}^2+F�^2}$.� .�N�.$�!A[B�x"D para��l *2E/.� ]m�ey�z� o��g&$ o21a�m simi to2I�:��&� =Q1&vtimV�}\,a)&NNEMM�.50 N^2=&�-�!B^2p���1 �E�6�|$��y�$$ will mixL�I�� "o�\:>� J= $. Monochro�2�, s|#e:? &i �!eofU-��"vŸ�ow" y>g2����ont� ���#ly�A�.��*���q7i� C��%2�"LWR  /&�^ )�.�M#ix �� r/!extra�v�ٵS%into \'� �0P  r.f.�D�Hfo�a B� 1.63Ca�d� ,%cK 2.35B'A3�*7llAs w� manu���Q� pers�iffer��O5A&�� probably .E l'lye apero betwee���^Afars �! ��o?"inge���:aik�� t-�k9w[ (%�-"�)N 9��i��m$ \nu$ = 2.6�9�5.L ��&�x�: FFTPSM��plo���.  6�2s(a�� (b),��9"�TQ {\em{2�# ode}&�R�s J!D29000� %�98b)1�M"E .�b4.� A�oE.�� A%�Mu���&Z� _represen!mT*� ADs�!a&!%Upedes�F%+uss9M text> FFTl�� PS��QR*�bIbSO�b�bNbself-�Gng� �bAO*�th:in 6�>cExth�v� RB��� .nSO>�%` ures&�$.1A��NO typ+�}"�  - jYz=.��Ru����-!+r.m.s.�&2� 4 #>,1���'A A�gr� 5e�diode2i��taa.ll str�-�%u[ F 4uy(�cj-�.�$A.aAv)j��*��~24 ��A-��� < � � whitJ# flooX!!far wing�  )�5����%�"�$BZ ) $w/s`!erEH��P(*:� # ("E 7�%��� &�N ��b ��&� !"� ��� &inB�w R�1L"� Rse>@J�is �2MaA��^ ��G6V �� saU� 4�*> t4. most>� c)9aF� . >l a' � >Tx>p *� 6v �tz1�S/N&�$��$l-e��ches $���.*-&�$&Wtl1$ A�Tse�.>-!:�"AV):�<doeA�t!P�!ę�(�,or�0)�%�  pNx3ly �da�la�0�.�a� =1.5 &�SNa�A^�m�Uu�5�'��%sI\ #�-Y�!��(a NEM*F"��a�< $25\,\mbox{fT}$�(!)��$1Z%�. ��&�&!k-�� #U�1.7m�%AH�x, aW�/*:Jnot yet=� �ed�*�Dis� ion\)> ,f�+� Lamp&���+a) �d��$NG���c�%a�p+bn ��;((black dots�  � �t!�� h I , (open cicle5��gM1��E%-� %��3AG�Mocal_�@��a � k6�1to Q 1 $ ��fN%d t�z� 2>J#). b) R� �%D��2�*�!iKAcoiy2ear0.b� opor��al,o $����ս�n)R5)F � /�.�n � �.Ks }�2��/all. ;�arrowa�fer to�heA ti�))�Qr���-q1s>� `:ZIn orde get��et!u�5a !��ex�>�i�weQ�s�&.�Ee�� ozi!�V�!���ari ae$E / },+�)R<�� (E*�&)� � "y ashU�� e do39 �.�!3$2�&�r�*�7�a�Q cesium� 9+ 9)Q)% beam�,edly�Q!9%g� ub/47ns� d.,�#;1m4-�i �i�-Y�#��&s a�er�% �&�*�er.� dre��s�)�����k/� �wn6 F6��`�m< :*�)� n,*�&F� N_02�SNg�� dark6 T}^2f+:����!����#I2�,.cq�*"� 6�4%�)�!@"� )� ^���>H �Ih)}cch?��X��vM7A� 0$. J�A�UD� � hA�s b�:e9 all l= cret�2�7Y80&�9mp>�. Wzf�6G ($10^{-1} u$A/V&�$ �<6^"( nA}$.�B�=48HT A}&) <Hz}a�Ta6&�s ��E�tM��&8)L7\,nA&�;� �{J 2 negl ?aqX!arkei�%Hsible�y�H��!C5� [� (do�:�>Q� lineB�y��c�M5� z/�.PsB�6�M��N�I^�S, ���4a��a{ �y �2b=k\cdot�z*$k"Q Ls}=2.6� EN7}$e}.&p}=0.8 & &�w%4� .�� AU� 1i�4�.��d becoP8��u�>�2�$��a2�Y� $4.9A�uI�A���?�q�_0�2}: �n].�A�e �%�%,e>�1"�s.\4 $� .�thereb� laiHAA��Iڭ� in{s�.>������s�%� pump|>�1�im�iA?fo��>60>z2�?2�*sE�W) Jt(5K:G H@&�� If one� ceed>  ez n.k 2@=�, e.g.,��0cA�-� stabPB2k%{u��achiev3,��a� �u.8"�-Z �=I��,�*%���)1�~�$@2.5w/5#! mpat�#ż earl#'��AAleMx}"�.�&a~'a(0ve stud�"E �-*u��2, s� $^{39}$K)qme :�AM):ver��r�� to be 2.3��A �4�}b�091n5eci��8r �3ex�8�= 0:gc, �%toae�ng�of25��1�Cs)v. Furthe�B!� e g-�o�1�!twice% �ơ�'� )-d)*womm s ex��%1N���K-2�($Ey�)!Qpa=�:� (:�)<�;A*�B}2p%Di`+^�ofmla�e-2� - � N�n3'(TSLs2Lp4_6hJ:F*�F�Aed&>"�q� ��>�9���/1@,6 hours (topa ces)"L2� b�G{�-B'A�@��g�Den�(bottom \)>�=>�� � f�H 5minNNive-minu sli�B�tr�n>~U6h��"8.4.� 2Q)M)} di�e"�!1Dy4)f��ASDng Allah ndard� 2����#O�r�:M�}""&&:mY.! squares:FN -d� 21\,cm�i� ,0200I.lE� gEae� p�JsTlape6 cannot be�� uish�g� ddra�J o gu?Faney&2��l8-pB��* ingl in !$t $\tau=$0�"A�*��IH �( ~Ll4nC4{� &}),�thA�e&;%g$lJ:��g�%H assu7 *�>�UZ>�We�ed.�0.U�� �2��! �in, u�MQ�t8�,�6�in�$nB ilay�i�C de Mb��2>G/FribourgD})-N, s �%oun� coaxiallyI � c!��er�)�*& K�D�- byU�]!ory�F�ExZInHy a� 2@er, ��NAa FWH' 5CI�;6~'a�� c�NR6 S�H*R6 620)ɥa gJAg�00.1\,s. An ex�?) �����aw�(E�rva% ���!oe�  ��I��.6N N|6 O( e��Q1� e a �At <��ie�)c"-K )g � c%BO-�a!C 66\,pT/cma�ch�s,0.4\%)<�)'5:� �iKb� I(aa��F #m�I�'D g>. S�,�I��d �9V � !��po�)q�2OPMs.�ure&o#5��"�5 ��EU�� � ���*�I��T� �$. 1]$!/ irregu}-� jump�� �=/23.%�jE T%as:s#]��FWP.N�"solenoid?Ca h0�10$^{-6��su}#� b�zPby!�" P� b��Lbarnes}�#)N� conven� �4��acteri*%�)4Eb� varY9)�wI�6.��U-�A$ �plot M���6#.�� a&�;of A~.�)��b�Ee�#i�=�Ove units���#�!��� ��+ ��tyH��_ are �$"O�Fore.�s. Whi�QshortP4[SKtM?g��6w&�$�1 bump�+ 1�2��s�m��R�I!�Lw�i�rm�by%)1�q�rG;�G�zed "v1 2���oee�q1)&>%. A�encɋedy X2Wpos�al�Hf�s. G�NreQig i*�O .� A� yM ��ap4ER� el6q0A��yWs wheg �i�N��!\�'T. Upper��ph: Tim�r� )� P9;.W,:�a}s6��� ��";. L& :m��2� Q ��^a   7!nd8 & s)I��5n!�6��o�4i �N�Th�fj!F� u![. � JY>_ ` :'fu� inv�X <JY % ��in �I� @ !�E'�R�, ase-� @S} pu�@!��*1CIg e ("O����*5� "�0&�Q� "� �2�Y�I��as err�]MD��vtE r�ion coil�fi*.�fm o6]�strongly�A� s� i� thod,aKd�#�A�2`I`U� ens�#%b�ew a�free-run�)�)�E� J�s2tsqR� ��da 2 ]t,�C  &y5�� s.!-B"�BF�B? ���=�� )�%��1�P�K�dE@AA>���WFpBd"� `� [1)~"�Z.�!� �:�="�� )!�%�leB *�<�0�lQ! Z��a�p&�a��.�"s/ � Q�iO#!?nB�re �Jr�a minim%m(fT%���A&� az� �e�h s9M�< 1.3$�H8XD&(@�|Mz� BB��wouldh �4a�� ificz���4�뉲'sb��)w>T �2�behav�0(slope $-1/2$QMI�� q �*�a�entirg *� &w;I�e>6Xa�R>D�Krigy?�Jj�'rX#L�- U�s�7wave.ń'reU setup:� role�mA�a��Fr+]se� $e observed2���NN�.� !�"�� e�G{F�.�Z} \ b�Zon9vap�Q re wpOsuiteC#���Owq�s� \�u$T (���1e<s��in neu�< EDME�rp?�In�1a:5B� 2+9�];�1��  3( �B�% Q ,�� {e[a� |�tHco&SJ8!lA�!@e$Nett_Multi4! Exp}Ui�f�� � il!�� Apa�ch(M:1� J2ɺ��O=h +[is ex�:9o�^be wor�^!a��.W 2\-E���Mi�UiZ}�D6�(�  u ing)M@ � "!0inx^�'"v , s A%��nW � bA3�0 d. A2@�>�U:q�Qhas b�0demonst�"\ \,Alex_KOPM4q}�a���P� u!� gas4*�T�>i� wholZ*ll volum�be ill�` �_,r!_x��@�=0, paraffin-co;=s1p� ��a-��'Atzb �*-�aKa�X  adap��sv!acmen� A��>��o.aN�ĽIal1!. �!�think, �"of� �`� � of s��L>��#I�@ )Y�d�6. C�� oV�& _ _� s)�,Heil_He3Mag}�u<$a�6o!�� � a�d�a� 6^o��hl�M . Reuly,BQ}�`�U-�d %vn ]�pM$8�@2��e��erWE19"�gC,Y fe"A?! 2����N c��#@����^d*{1of 20U!2[ cknowledgI}* �!k G. BT ��fruitfuA��24c�GY �aUanu�pt�( ai f�gYfF (( Schweizeri� r N�q4alfonds, INTAStPaul-Scherrer-Institute (PSI).� autha|(A.S.P.).�5`��a� � ��&Uni�$� [� �3 thebiblio* y}{}�BPbibitem{ILLEDM} K.~Gr�J�0l., Nuc9\ str.%�MeXA {\b.gD4} (1998) 381--393!�WLAlt96} I.~S.~Altarev[ PhysNAto�bmei [59}�<1996) 1152--1170.^.� YHV"v, W. , M. L�^, Vb�:(v, E. Otten)�,Y. Sobolev, ��Z�H40} (2000) 483--488.�&�` S. Groeger, J.-L. SchenkR. WynaE)aAAuis�arXiv:p)D/0406105 v2 19 Aug 4,�?m] �!H��v. l(5}MoreauG�Js� $LsMag} O. <, B. Cheron, H. *� Hamel)E. No J. j III %�7)�7 ) 99!�5.  O _He4y_2001} bh�R�Sci5� n2){,1) 2253--2262HKazantsev84} A.~P. Ad~S. Smirnow, A.~M. TumaikiM DI.~A. Yagofarov, O�SN rosc. �5 �(84) 189-191.�g,LIAD} E.~B. andro6�1� �66 �2) 042902E(BreitRabi} ��E6I.~I. ,)�\):R38%�031) 2082--2082V(DAVLL} V.~V�4shchuk, D. BudE�A� J.~R. Dav�f:�um) 71 �0) 34�46.&�k���,�(57 v1 30 Ju�!20BJ. )�oc. A�g.�Q*9�ksa6� <:�7)D,95) 325--332.U� JE7B���IEEE T�jM�!. Meas)4 2�I01971) 105--122�F� D. e� R. M\"{u}�kH-Siebert, S. Ulzegai��W�'.~�(~B E 7A�,2003) 563--56[A�. 97M�e> S. Pazgal�QM+LA�ss�P!Q~9Q�18a�1997) 14A�.O:��5 K. K6is, T.~Wrnack,A�Ca]l9k nd ME�Romal�K! �42y �96vSd>s�7 docu� } �7%%t2  � by��A8fic Word (R) Ve9,2.0�d7`style[osa,12pt]{revtex} %��0 %TCIDATA{TCI�D=Article/art2.lat,��0OoF m=LATEX.D�QQCre!% =Fria�, 04 14:39:02e�}+hLastRevised=Thursday, Decem�b02,2@12:52;�2CSTFile= �.cs�W% 1�&Stitlepagbf {E�%c�&!�k�lA Su& Heat BathD� {Arbaba�Khap(�X{\n�hsize De_Au El}[o'W4, Quaid-i-Azam*� @, Islamabad, Pakil} uM.S�#sari !Yjt Chemistry�r \make%, \vspace{1i�| ab�ct}]pJH.{#ch��ip�ofR')i workx [�'h!iba� "IUn�sa�z*� &��0nv�e*� �  m �,-?�Car�F` �k�. �$f[ kindW!6!Flaw&J (% of eEn�U���2qe)�yAfus vio��Bo Vzrm�t1+h!�$!.��Z�Yfb}%�'to\ve�#o�� intoA3�;��2%.�)R6 engin�;a�ra�1!tr�WJ � ��.� An �manif�L%;��forbidsV�i�at���can be�e5)�,�;��r2'A��, E�p�gc?5a H �D��Ef2D).M�& , $T_{h}$>�Fu�'hA tropY+n�G main�J�(t a�>.�Lc}$i&qD,Atkins,Annamalai}@m �tq�hcI�T? n as*Vku%��!,ta =1-T_{c}/���9!�} �5!�no!%�@p! %�eeў!�! f^nt�'�all-Ads but aZ t!�( take place9out.vA�any2;+@4nd�5|E�$agI6� � proh A�AtXuJ�7e�is!!�|to`wa t�wl_ mmw�<de�&se. S)p Y~Gi�6msXby �-Ao�U�Ze)�pa� s13%) ��g �\-�is�BA�.kD.��i=ziba�+ll.�'p�"%�v(Leff,Baeyer�� hyp� k``!�'',%�sbho��Kld�es �VV�ff3D*HVA�um�kO % �96nit�{k�T5deg*�Y $E6�. %H#)�K$quantum no�}molEm�!s� ompu!�e�@% {Brune,Haroche,- L,Imoto,Roch,Zubairy}�%m�b#-G*��7�.ed�}�����a�EaII sear�{o�9e eUq. �!o��lZ}p V Scully�${Agarwal} ��A��9 newI�of5;�P�#B``�%onium'' P c�+ fueleu" lae/;�t�&� <KoJ,� . To&� ] "���d�A��Q mas�b0� 21a!-2t 1state,"�%��}``cost''A-pG!P6h w!N�we<. ough!hx r��<�r^�Dishs:k � ����Fp�  r liquid, am�.�$is GaussiaM�Reif,L3 sh}I n isI ed s�2,p "��c��or�U��ow���� b�P�(up/-e�'���^�� �B� m�er i4� s4 � $�employ� $#QQ�9oI<-|r�JU~us&� }���j�/!9ni�.sX ���2oC��d��xY7 xl�~t"^tA& *� ���Gbh%2 1�&? r~rat��erLAYc�8A�t=w"�/� $HC)�6G-��mp�IHf/���c9J� n "�0.@$T$ �F0s6-n%�of �:5�Y+(wso����S!1E�i@ Cons|&tn�M$% m  w!%y1( RaO\g*�Cgr=�&|� $mgh�E�� $g� �(([5):A!�VC�|$h0�  hea$to!�cBO�{za�% Y surf� of �in!!Zis O%o�Q�Wn fE D .���[��28�<-� a2;SM�r7)�R�7U�1* as �&- \De�n8T=mgh/M\sigma ,^&%�aM$)7 ($7!%�!R"z!�Hcapac�'�"� �e2�- M��aA ��-��`!�$T$ if IDLaH� to drfXiP}oL)W� �(= connI7W� rvoiR a� m2�$T�dUIemo�dllpinu�" pour� !mS ���b� M �tւaiM� 5�**�%hn �boU� .5�*?[tbp] "�R�"� !�bf9���E��� �"kC7/�at0�.�n*}$\bigskip Kfaa+a�1�"�#��Fgha�s�9nt5%e)j agil�5h� "�(iv�aM$��y� . A Z� ($SPM�RAh>�4 �6�-�thr�itd ���, ee/a�A�$�|ze,eZ{j� o ��. S�C��P �=a=8P a5�0id�"�.&��a net�0x�N ;a�1 UAj�u Rinflu%a> 2� and/,Ds��es�. �� Bi�L*TB�2. (A)!�tuc(qFir  a�tt�'Aan �e� ains�ar�IMin it�� immerin���(��;-eft al�(Squ� tA�Pj��� ri)�� ��+�t�?��A�џ�#!��[7S�-�column�6.[$"�3c7bal�*�e�-fr >�. U-��on�t  i�{u�L#� two !� -�b.�L % {Tabor�Q �� A)ojrho gh$�V $ beD 5Z5l �t*R��9?dkV��to�]wJ��AQq�I�w"� !�7-� ten�0�he-�!f�wardsh. !nret') z 2� p]*{ }�=1 Pi $e�b�*�<���: %i�, $X_�M as"�b�� Q4=-(RT/V_{m})ln.> Ra)o) P MR{ ��$_$q mo?=7)�76 diluJm7�)q. (3)�Apo`� ]-Y'n�'t Hoff'%��/�d�G�[!/s -W5��l!Bt� ��on�(E��%A�o� K e'�nt rKj��8%�x~:�A�E? e�16�'&ncL �v�w E�`F6��,i� � Pj`it^�L �U�� ��pico # 2 (B�!6shaV*D� "�hmoXw^er���5�1A�berEc�K!�r !�*�h*�(A) S}22Y� �?a��m%�!쩹�� i}�*�B��� SPM.�iou)ą o� Z3)cU���pro����gl$BH Now�Tjo��oge�z��~�s2#Psu2�� en�u�Waɘ�_<<�� +��ch�)�B�3"�� *56��e �enter�3~Fg�� made�<m��an ``U mvalve'' I�1ah��e��u$ Fig. 3. W��up� .�] E^�|�S.$.x"s��R�at � a steadyq�-����o� 2� �Oe*j  c璱W$H6#"� BY��leIAoA � 2Zo2A ySJct2��H� .#h�suc� %_y� QI� �>�!-amb!2G �rep}%|�tA�O>,A ut 30 \%A<w4 :� 8<b n�aB�PM$ �~0�I�=PMIR� regarCOa E:b�Q��RFnv 4 rqJ�%�N'an� "+%je�~�� 2B/Fu��A�-�iJ$l7upoK ri�}r5orA��od "1de:?%PA 1��?�I2  b�1Br \,6zqua�6\& Z& ��y,b*�  :�!�. &Q� A!i�'of��b�h퍉�*]6*�%(�!e i&�W?z� kcum��7��droa�s�#Iou�&E�t��roblem�!M=�<b:vpe�f)�!�EFr �a%p � �:JW d�o4�wi5 V�  'u"_ n�&�. -%ut �i� �%!�a sgA !� -} nullif0$is�! �t�"$��E�QH�a�3� -�cp��ILp�Z�<�%�Na��N�=�OJ�8 ��it{mT O� eFysh�!��JEZ ,�verts�&] J+i`��e! WM��m#}� �&�%�u418 surriWing. FL:i� �n-[_6, ���&�ys like�}�A "� etc.\ w>a�p��� r�C�Ub�!em�&} S.W,*�&.�,Am m n 218 (1)�38�349 I�#}{3 ,|&��"w4s (W.A. Benjam�1Incq4@Y, 1967) pp. 123-2b3A5} P� �0iI"�* 4th \: (W.HL�e�=�PK8 ny, j90 j96:i&l$K!nz$C( I. Puri, A/8ced6� E� eerA�(CRC P�$, Boca Rat!/Fl�,1\G!j )!1 Wal�, Sci� 299�73) 862�3-#j_Q�$O�;,s (Cambridgei�. L$#nE�72�2N#} O�2.`#5Wp. 219%2) 172*7�#} E.  , Prog�43I�6) 252>Ha�# SAC sToday[�p3�42?*1# :�5I�87%UD62066��!} Au�!��al��90(McGraw-Hill,>� �� 350-2]�! U. A��� . Educ. 5% 7s:69. [}�6 , Gases, �"ɀ�L � =_ ma/, 3rd�;Y*`;��1993)ţ276-80.��LŚڧUZ�171-2.m��H.*� , Zeitsdh՜�* R:k5che%O$ie 1 (1887�:1+.(&g36Fi1T C��%�3@MACRO{\TeXButton{�1}{2L0.5in}}}% %BeginExpa�@")2 "% %End} �$1$���e^er2$#*�o�/� ������v�r�l�()A3$ �� ��v�vvv�1&�5Z%:G7��nG��$@xwE QWI� ~j%c�_�,z���x�� %�arqy+�'//!les�Upu)�alD� veJD� or�/DHohenberg} (DFT) a�.ovts Pa�%e3 )�e| yeaHM΁�%��<�6g�y% pr�t7+H#�a�U reE�a*�Tlie�MQ�VDFTH� real-��)�E�?ime"��t DFT)�$Runge}, GW  Hedi�98�b?-.Gorling2�y ?d  KlunerU�9:����nVk!���k�l prog���j Mpaper,hQez (SCF)�i�J}F!:)��� 9GN�ofNDFT-b^R� $SCFM�,t,/2ly%� iA~some a>��)�-o}��traordin�9��M�to N�I;o�GHe�0-of-the-art mlP���(MC%[ x �Shud���5K r�*65e� B� �A�!���9� �%s. �2ed PES'6� �� �s�_�t4l�a�i�:�MZeiriE�_�"a�&{Silv� on>�V�%2 �Iiher.!�i!�N9��Y]^{"� f�g�z��`bey~�?a�5�2�-�6� } �&nCanA���e�Q7�&��i�U�= cWja�W��NA�) ��&4%4�4ag%�X3�  � !�A3�!�ta�lLEe!(C coup�7dia��c K5���.a4!!amp!WEQ monito/5at�g� step2�#.&�'�3�R[!ndk?mediate2_%W@(!��organ8�$� p�1! a/ �,�4"W��secII}a�%e� fa0�`qJe��$�� a�bdLi . R)F2Ja{��A�M~�rn� \��I}OQ��g%l�5/�V��i� ::L7endix����)��-9 ! RX �+ &5 DTHEORY AND COMPUTA? $AL METHOD}��%V � & R��aosL4��i"�Xhe2�"Apredic,/� !gQ`ߒAu&��force�)ct�$�Vuclei,�gE*�D~ -�A�� n 2; . U��tu�TK4��0�"a�I� is �B�n�Y�"6� ,�'P6� �8� thatBB-p" �m � e#`co bv# e"�%too�e� crib!?� ��U&C Crd)In%,1 k� i� Isr*�/:t5 "�9 cen� t�c�O.��!�.Z-fashAD��"�Iq k5]��B4� mT� geGTy�#2��s1DHartree-Fock (RHF)"��?�,GAMESS p } �%��Fse�$s S�"r-�T4rbitals (STO) "R)�6 �9s,I28STO-6G. Both dis%$a $C_{2v}$�gB p��y�D.&�(DHamiltonian matrix��S-�� a ���M<��;c%�g�3a$A_1(\S�5^+��),BPi)Þ $A_2%-%$�jduc�f"e�\sl,re� gc$�am�WO %A1�qaim��5=���a|. �,ŋado0P��\���[ e�lex&f62��A�&�Yp"�&RHF2B � "put�!  "n a�-10"$ ɧ"6)�14�=ve Qy��"zat.�ely%K millA�seɱC g 0awH A_A=��Ap# �6-K� >/nd $^19����$^3,.(C ���� D�;pMe_P*� �Ti�,!q-e5[9!&�.t�^64HF)� �m!��"� .��EuY �Dt�'A�* q4Kohn-Sham (KS)8 } �uY�jjl�A�5U)= . Su@n�S�qQKS!�1Pm�,!�l�c��!Xou�CymalE"As$��c� 2p A.�{o}�)���� �br.�e%sB�E*�#��a�9�B� L �1��7tho!�uze=l)���-n.r�� ����� r�i�*�F4lN� elseX1)� �Ჩa�rB'��pA]��Cmq�}c ingU L�]���&$epts: (i) � pre � �Ye KS-�,)�]'ar�D (MO)�?, (ii) d��et6� R��m�i"�9�.s,�P�her�\q~n%�io��b� t&*�S(i�iJIdu� !�Q�-�^$(e-h) pairׁ )̡K�=a`&��@��%CalJ'rg�xn�>MD|�.�yrsa 6 �%�er�TD��2n�Z� MO �1>a�5Ra{�����'-V��eXgy.)�KS;a�!desV�I J�"-ABid�If�a�y-shouLoccup$)" 2��Iun:#iued5�ic!��. Next�8ol�K1�����se.�g .�6p Pra{ oC0an� Z isU]tg0ќ2!U��uCa~��oQ>{D�rA�i� . F&Tis!�.His*� 7 :�-�����EGc��gL  en�T!�GpS��.<�\O.?Ѯce2��e�-�-�i5f>�� F_I%9=�v&�d$traightfor�3a����<co]�tri#- "M$��.aN.in ,�*7t2=�����A.KS.�** m8.� _ �s J*�i�T� )H&) $��:%+ _&, �3QO�rn w� ��,��``sum-��KIZiՉr}l1Z�  let "� �O�wp\ZK?�8a W1��k]�E!=w� O!�L� " ;B& �N���by�K�?� �c/E)�dure. ��1 mKm�5)���2�� )tl�� =U�2=� simi�%5e e  & 1��=2���p���Ո �� planD6$ve pseudop"$Bck�{\tV�DACAPO}~�  CODE]=_ lI0-"�/(GGA) 6=x�on @PerdewI,  I}a�U -& ��-�m>SoLUy-� v a/�) �Ha����-'@ s� I2!�"Jk6 K ons !Ld� U3by ul"Toft>>s�CLic( 9�eEqE�v��%� a Pulay-m� algorithm�ie��A��I�a�n!iqu;�sed5�2���qU�"�". :n6s�U[Va�!�BL7��-� �s� �� ���BQ�e�la&u �a "�= 20$\$.  \AA$^3�2�>aړ�)� bi.� i3o1 by � =Sal%2"��� it����*��!�.c Lo"R���"|j����� as�2EM.�ic yu�� e� de� )��Z . %#��%� e}[X=re���7cm}{!}{>y�{A"_chd.�} &L) 2cm}&}F�t c&�֡�fiZM�^� ��^Ea c��!=& axis.���c���� u ���,�|, ���"�����Na%�Cl.} �=�&�1}} LI-H�)� ���.� �3 %+AZ�$i��6ir R 1L�anc�),)!MNa(Li)J�$tkPC �v�hne�!Mg�6��"� a{f�"e lHoJq �E qalHPE)LP2� Y9��-�^"��ab0$1.4(1.7)$ eVUP 5�PES� i�!'A*� Q�y �q� i�he5:�!!7m��M�-Z. Aw ;nd�G toO S �r�c)��� %=b ($\sim$ 1�~)%�6E-65#��c e�aS$͓ɂ �E=n�-uned 3(2)sU��!=M�� <Mw5)�. ��s�!ec} � frag�%�Ks�sg~ �H orig�  wa�5bon�=) A�A�.�r  s�j.C&��1}a7���.�>鉁� clu�y�Ts 8#1hia�c� a) lor+A�. �[���<DOH �l-�c�%-Gn fer WJ!e $3s$-!�xso�r5��P $3p^6$ + c.�,��=?. S�@Y6�([ <.�5�!�Z&e B� �xnow�Q ��>Iv%(A� llelT�-�9ne�!Q!BM��'to����*��1}b-�;�!�2K�B���af�  lo)�Y=��)Q�"U_ e"�<a�u+ ��g2f �M�#w����es, �5�F�e ,;"Y{(�D -V1�%�5� R G� � �y� V*�t�  in�A� cA�x��"-QO : !_b��(<�� � �- � � P&�m{�Kdo"IC�k2e�6���*�.�!,�U�U�"�$9��"� ���� �[n,5��R!���%�D/'.��$ �G G v� 8r� PES_v2�� 1��$"�-�cur:Q�%+��e�9(kN� *'-- s (rk)���Z�A:displa�WaU6 l�cw"�Lq�N�U-�!a.��^ 2� J A�T-1%1����R?& Ӊ@%�x 9��?A�5]I�Q�� � .�n (-!(%�eX%%��*� �,all aR�/Y� Y1IN*��/QE��� H .paac���NEA�aYh\E�arrow &�&90�I����ͱ0.3 eV���-�  sj'�� ����2TuY 6(3w\ |0b�7{JA:�Y]Q�!dB/e |N*Uo$."NVCs,dVM"I�U���.?�F(6�҂!�(c)8g ce-!E (VB)miT� �MM�HH!feVa��Y+er}(tabular*}{1=l }I�F& � &2� & VB,Exp. \\ \h�� Bonm�FL &��5 2 4 6E &� ]� "�,& 5.27 & 4.9A-e& ��u6@=!@49 G1G5.7�5.2 � � �eF&� u /��0� 2.06�0�2E��9:5.6��� 6.08�7!�7.2G�"U" U@lOe�2  }t)���%*w)(CONCLUSIONS�secIVb) �i *-6 6m�� N��M�-�Cفa�p@1 Z�)*i2m��0; ��;&�(.B high&]/�  a J�(�02h� �"�'P �/m e��B-1����two&�*F >]  ]f� 7)�"M J|1�zv��"T/J8 c�b� N��CV �� 0�!J1�T�� 5$\%@inݔ 2���Xac�0�*�� "�6421G HF�� |.  ]��� �diago�%elePs $-8 ���c$&:� �ZRiDc�F�#��%Q��& %Zs�M~��2-�a2��ff->� $)%^21�[I*maq�35!li��0a .����8bifur���E8aI&1|!�Grice��.�)-+2���p�ڊB�f6F;[�4.��oq��-^a�� $R_{}$ as^�1N=VE�q�[�� @]ZlqU�B:%,�wO�o]12}=20�, $ c =1.1638$~��� $. ���Q�K!}SchNL�z"� l a ��)A:�7H �#:;!U�*e ����A�� niT aZ"3-$(DVR-FBR).IKosloff}�9DVR�3�&&5z�"�7Q]�i q m�,�it ���elf1�0 tane&U*�8JWon 4�jR8�X*zDW��&� ��0 � �m�8")Feit}&Z*]j;4��6x)\ef#N?y�A_&�(+DVRl l�ymlD�1 �9oFBR. �� F� ���� A� evul�x��23!-$|\la�v�' (t)| \�Nle|^2$Jyproba���"X:q���,6t..YQ��3!�{�-����u��bn� ��u!��6Z(c�a+fO�&ɇL�X�^.!3"".h�I�B Bv�![��"��I�InI��I�I�IfI4�IFI �>�nq�A�ov3�l jhG� &�>�yJ�Jr6��&*�B� tur+�6b�vA�)�� ū�;08���7�BT&&( ���c dur�>�?�+�exly6{ ,c� g:� popu ��B �si-P2�92����ak��H. �e%.c�:!a "��"" ��E���:l/��$��Q�f�$y���8&+=)� �!�nce, i���! upM $��q�> K or d�q!W.%halogen &4�nGx�(!9o �ze sub�* 4��Es����+�pump-�;e�+eI%PNaI �s� Rose���2 �ztE�;--�@. � Choose .1��N. prsty_2��d�K%A���%- !���r��h�jou�3s %%�inb�)"io>��{10} lZPoplev�  ��'C�Y�TMod&�N j �)'K,it{www.nobel�M, U8���R �&�H P.~�W.~�82-US13ċ(1964) B864;+�G L.~J.~�8B={140}��$65) A1133..�RAH E.~ Q( E.~K.~U.~Gv�2SL�2QAH{59)��Y3592H�G R!��G,in\Pit{Ab In�2A�o n"yXE�sz�Pd�II}, m[ �DKΎ8~Lawley John Wi \& Sz�N�[ 19Z]��( Y.~ %�DG.~G.~Balint-Kurti!8 Mol.B�99E�83) 16��G��~ ?� ~R.~Worsn��$A.~Freedma%C.~A�olb*�W%� )e84)e86) 43782u9:*RƐ RazaznejasB.�]"�l~!e� j 120}d�O� ) 45�[=:GA} Mz�~Schmidt_[ay Bald$Z\ A.~Boatz,5�e�p.}�WutM��1 �GX 13472��=!]CzRE�%(�YA� 3֌192 Y36��4aH M^~Ra�"E��Baere��T�S�iB+cta d43E77) 876�*3 B.~Hamma��|mp�cT3 '-1.30�Denmark S��&]Y, Lyngby �((1ap2I3! P. �O 5w),rJ��x�19�[6676� Cl0�Sq�a�P. Zie=Y!> H. E�\ ig (AkadeOY$Verlag, Be� �1991), VaZ1Vs:�A` Burk��,M. Ernzerhof2���ˏ19\ 38652+Grice} �XR.~Grice, and D.~R.~Herschbach, Mol. Phys. {\bf{27}} (1974) 159. \bibitem{Kosloff} R.~K �, in \textit{Time-Dependent Quantumc�ecular Dynamics}, edited by J.~Broeckhove��L.~Lathouwers Plenum Press, New York 19922�,Feit} M.~D.~ ,ZA.~Fleck)(A.~SteiglerComp.~=4-82) 4122`,Rose} T.~S.~ , M.~J kP!b,A.~H.~Zewail bhem2b91}%b$89) 7415e�end{thebibliography} %\linebreak %%� �?%A�@�@%"8document}�%\�Cclass[twocolumn,showpacs,preprintnumbers,amsmath,amssymb]{revtex4} \6Lpaper�H� % Some other (several out of many) possibilities %:��,aps]�>�.',draftr-�% A�hical Review B \usepackage{EHicx}% Include figurles2,d)s8}% Align table Ds on decimal point2;4bm}% bold mathA�nofa \begin9���{APS/123-QED} \title{The scaling properties of dissipation��incomp�Li��isotropic three-dimensional magnetohydrody��L turbulence}% Force a� e��s with \\ \author{J. A. Merrifield} \affiliation{DepartA�A!)�0s, UniversityWarwi��hCoventry CV4 7AL, UK}%Lines � automat!�4ly or can be f�d��HW.-C. M\"{u}ller}% 6�PMax-Planck-Institut f/r Plasm��d�$abstract} e�tatisE�:�the2(process conAin"analysi�. larg�Je numeraI simule�%�* .*:VN9(MHD)�?8, such as thosea�BiskampJy� [{\em�.mss}v Pbf{7}, 4889 (2000)]. ) ruct��unc�� �e�$t flow are!kected to!/play .U���e� I�T power-law!�$l�� validW�I:d ({$l_d \ll l _0$}; E�$ 1� acE\ tic macro�n�G,q:��$�� �u��n�E �e=2!8N�(in Eq.(\refUx)�ex&� be uxa� �rit.�mega�ic� . �worth noe@%��[���%hb* 1j"�(case. When �9��;!�,�ieZɲ!)6Bmh��? will� e��<strength�Fyy. In:� K m�#ji�e�CW Oan�9O "ic )�effec%��o��B�0 &I f�VMu��JGrappin�dis re� ce also6� a�!�erm� %��^ � 6� even��!� a d �Sab!��is stems9�Goldrewa�$Sridhar ob��a � assumpof �5~�he%�A7� GS3}%�z"!�B2 calc�.�2�lI.per��a� par�Gl�N4!e:<NMw�v�o$to exhibit* ongeX !�� thaI;�JS. E"���!H6�JA:�coincide�3�NX-�icNT. EsA'iI&�*x iAfA-�relevg"*�m� F eT nt>&� ^, have b! a�-� �� ��q�in,�o%�se� early��&ato $p$3 & �*9 D1941 phenomenologyM�,K41,ref_sym} dicts\( = p/3$. AsQ,R��obe2�~ one�ber $a$AA?tB��pa}�� _- ["� TA� ploi�s@ncepts, let us wr�! 6�y:Rw��Dls\"{a}sser symmet��!�-. BisBook}:B� �'_&2 z}^\pm = "7 mp.�\nabla  pm -"k }� p+ B^2/2 R  + \nu/2eta/2 =^2N _66- �7mp1� Elsa!E*�1S}B�t^ �}� �= 0Xsol_condBT !�2��� vari�i�&� _1av} !ZB1S$ \mu_0\rho-6@^{-\frac{1}{2}}$,�lreaY��A�ara%s b nu kinea�cB � eta�ʡ� usiv���$�#f� den+�T\nu}{4\pi l^3}\int_0^l �5mGr@ial_iv_j(x+l',t)+ jv_i�{2dl'^3p2. /��c6.For a rg!�ue ���naq  ��ofAl"�for h*� s,jUMe�  \\\\a�we shCee,�#]t:�^�Lcap�d!�Anom.m@� of $ �$qC�f=�)�/i}u�^a(convenientl�� ed mple `inV * �i�:yofّ'"� ). SO !"q� F%���"�Y� {gp}":l^{a pE�� gen_� >�W� $g�Xa!s*w  valu�infer � model*� 2@*N (K41)�\Iroshnikov-Kraichnan (IK<� , )isL'9;& hyp�7��!�B��.n.&>� �by9�.R)�Kbe���,a�${pg} + pa$�a�B�cy�A�v�� N�l chievia� ason�c� r b�. One-���uCis=@Dd�pr�#� � ful��s�F_f: *=qyEC@� p�ofB&(SLQSL94}. � "\&�� mZregard>�~�6�:� hier@$�� RT!RasAe�7M[6)&��;cNb�most � nsel� ��ngYsA� ed���he0turnover time��K��6�,* �4V�� f space file]9"���wbe"��"6< (their Hausdorf������t�.  W"�!toA�U>A !d !ce"�-�F��dE��� triv� sol� .H9NH�} 0�>��� !Ttwo9sI�co&%(Ag(�|4, $C = D - d_H&� D�Gemb�ng "]$%�$0Az%J�hJ_�exq&by �Ms8�%i]. F"�:M,z9����D-(1-a) p + C - C(1  /C)^"��ۡ��?6A =2�5� �]ph Mnoa�by Dubrͥ��mU�RDelam$\bcq spi#o our $�^1- 5/C$4K�Ajepf7E�9�-�{%�!�P)��en�ok  obZ%%�)A5 N)mPB�$Rc�:N( ha-�pgN��|� bel� 8B�P9�J@F��ve�iZ0K wi+an SL�`�p type�1!I �)7 ,A?.�s�2<PoP,Axel6aSp4�5rej�a�s tesM�� �a� Áx����=�;mod_k��ts"�( dataL�FC(A���%RqM se0� �2�i�),�proZ!#� � *K"-�b2 \(doe. t�j�Srv,���be1x( agains�.5�i�weu cus4! low.D Df�(s mus�s��F��s�'u(L!� accu�{�|*wav�2@),8%fic stun"  . M�-W&�*r���7refIu] Z.��e!�ereas�+n)~�e�ch ��\an ��Lve�! negligk/� K��h" �e�di%}ed�#A�us high>W*=�p/a(t� ve i6 )��&le%avail�**A�pr��">!N�&>B (ESS! Benz_ESS}E{<��[*V:�2�{%|wK&j� �$Aa&a%� 5uon�+st�EG.�. �'eadeconsi�#ng~n #%dividu�B8I 6)ESSŖ�"&�P�\� +J�u�anTr,Q�&b IfF@ �ressI"{@�K"�{q4�{� ��/ q�\6�  an!�s;E��.� F9f�&sfyx���� i< �2&�p � G(l)&�"�_recastBe9$$8$Q���#!��!\!Q,�p$� we�4%�no3u)S�1Emily *et al.})t& �)s@[.|D!42g,g�"aliaJ^�V9 8:� � } --��*.[E��b�x� h����}!�ve� Ay�Q�u�.�e�,:�rett. (s $l^{G'(l)*�� *� to�5 ommo,1�none�C flux!�!HgAm�+6Z �B�*E~asympto�ly�roan&a��0e2^ inc�Ce*� iv*b.�.�m�0 She-�-�at� appeaso fa�)�.ly3id�6t.�-hnow�c��howi� bm�� rpre�^-# framework!TESS��i�,oblem�A tack�*: .�bu/6n� 8")��Vp�!� 3!]lu� a�l$�r  ["F � "b D $g=a=1/3$�Z�]�$replac�{a2P._E� is�� 6Shir F-AS� �#�12:�"� :�was add �[y �i6��%!`q����F��&� �(�f6�_>x ��{1/6y(I : i��4' &�&���2%earopriz!� betw��$��p���]a {pu� � I 8�$. Us��M%��"�� !��es՞�9D)a�m~�N$\:NI*h$v � h!�!#v7)��^{�p�^�-U'��exi�^�j� s a�b/!0!�j� �J"�EE ^{MH � / !�F� It%_t>be=d if aJl� �,� 5�gen"Ma�ua��plL7qF&��ed;ESSV�Q/I��c� .64P apU�. First��should% �f4-�EC�]�� �A$ EE+>b%����U)��6eper��es�$eckY.�mA�*ofZ��BBd)�^' $ [2�B�]'& -��*�6�|L"�al (3D)��.�=Q s,�ka� gri� $512^3$m>sF�,5RL�6�i; deca�&�= o�8��>ic0`# x d��?$�#=5t�A f�r��rmz&�U,d�8qe� M�next n4. S�,%L�3c� cays ��,JmiSn�5s  to� � s=((� plus";$) bcn�.�-ak�5:.��� 7.H8%�^�_p��3� a��I��)m�I�_^ eq 1/ak��w\%"s*md1 a�%n�,e2BZQ �H63ns� ng��R�$($g = a = � � !��g beds�7-like.(x1$). E�)y�k#E|�<tedV86�"&A ����m�hpol_pouq,grauer_krug:mhdsl}@Ce�:,1 a�4I )�p���"� e�5 � r�� thou�8��i� ��}hbecJ4�!���e�'y �sGform. W�o Fig.5?*� is��2( isosurfaceeW�fy squ ɪ S�nisozpFC�E��.�5�sh`:m�"H'k& +)}$$$�"D# z^{"_i9$^2$. Both 7Ds�3q �0��)0wo>m!/�9co~r%�ur�7!.�is(u�� �'d�;�?�r�3F � W �%*3!6�A;$Alfv\'{e}n�0l /Em�age�3�C�:? Mach��S,($ eq 0.1$)) �yD5!j$,Boldyrev}��:�+ (]2� 3DB�y�36A trum"�@I b�=�$�Q-�z� "� �D3��$N/�FP?$P )uti�keS��r�=� 'E�2J=i�7borat�=lasma��Antar�U�3J� dO�~is&No��' to6�Q;�$CJ a9I�v�7� fit"i-�%�Padoan})�-��1of� &!�s&) a ��� n�AAA��"c.�5 �GeT$zp5_v_zp3}e���BE�E��Y&�ACJ.u�"s.�vCe�0rb(�2}Q ce�( } \i�H�H,s[width=0.5\~L]{fG_1.eps A \ca:3{E^��!4J�va�-N�(�f�h � ),E8�N"�)�"n :W �\NGK1���2� R� ,;)�reveali sam7der��!p�I-�$.�!t. � �c��n. After�� .!� *Y�::-�f$48J%2F%Y$(Color�#ine) I6*�(2D��B�q>� grad�(J2nw��F�*� of�'J�"2:U\\\z philosoph�)hind � 2+ M1Lumm�?d�{f)"s. Gi7X?�i>A�j*<]�3"r6A�� A�e*�9d�@.�:>�as 4 .�B��� �Z :ga�insm�{q'5���"s�:��"$�(G�(Gn+a��7t��mezDG �^�Q�P e"w$.����6G,�E�!�� Nf��3$��&�ly�IErQ+a�Q�a�ori} OJc�)��s,_lec���G� . �Y1�XEF�rec(. v �I�i1�m�}��-r:6m�G�=-s[*�vFG&#sts!Z&-# . Ou%9}D� thus��inCa���� �)i�'i�C� ly favou�%, namK)��*�&~�$C=1$ ai[� =p/9+7&/3)^{p/3�InS tA�ar�&confirm���.(ALcI�n�� b�{&'�nU 2�Cp}�$`�gi �(< = -2p/3 + 1 - (��W�<s�a��"`Er�2� ) . "�FNu�Gl P2M�s}�%I�d � .�<a�  e>;M!x"�&;*L(ej addiA��3�Es�*�eG:A Y a?n!�.�)voAF�A(bf{\omega}=Z5 8\�v�in� o elim�@E�w�9 .�/$dA3a pseudo8( scheme% ,=canuto:b�9�im�g�z 3E� A5�� a�htrapezoidal leapfrog method% 0 kurihara: ,&1 aliaerr�2 ssoct��3/�ach� orszag::}Ay reduLsNcretiA�on X�Jby sphMK trun&5� Fourier+v0nt_meneguzzi:�M}.3eE2 dom�cmi8a~ iodic box!�e spac $2i�i�f�S%v�E�Kpha]nd Gitu(M !L\exp(-k^2/(2k_0^2))$�k_0=4�#�%�aF� �T"�9��e�ct�a�e��0one. Cross hegy ��a��=I5V".#lQ#q z}^+�2-B- dV$�*A% dA�!;du�-9�eC��$H^�M}=.�56V"Z;A}-F,B} �i &� B}=i�6�Ae�s� to $0.7 z(rm{M}_{\max��'$2� E^M/k_0$ { $E^M@�-���h�ER)� �;�[=�;=4 �10^{-4PFmp�!92Prandtl���$Pr_m=�=?$A3E�(EpunR��0�0enJ�0 s, d+"�1�M$re�maximum� "�6w�st�>ng� smoBu) s. S*Xe6@<"n"on��&P %W�0rv�7 0.5$&)t=3U$t=9.5$,A��.%!�ݵu1g�*.� ��.�TRSI s} I�&! �p�!�4"&7� $(\"pz_i�ja�� prox8A�!�b��e{B}_j-jiu�A1/2+m��{v}_j*H95 @h��ere��!OemployI/y,y.jm^Q mal !�v�5��so?w�a~<� d�G!�ACE��craft�0Bersh},� , $�t���U���D%,B s*� l_6ter�Ong0ofEd�re�zsav�few�%e$�9of (L� 'L@y�Geloped�]�� B B al��'1� 4A�<c}LuWM X!&��I�5r|�� pinch er�t RFX �(RFXCarbone}6z�� S5� ploi�!�b�!�!%Z� T�h&� ima -�@!�m"�!�bE A �.�0! qI+two� M� Y��$R�W.{3"Z .S;�� �'2{]; n. �L]$asF�$"S+!_��chi_l*^+N�= �l} �0^l":�*W�@_i(�@{l}�=&q= "�#%#"p=��!q } 74� "�nTOaeq5́Int"> ra�_a!I�ai�.$.]<6�faccR�LR  on�Aed}(ale�m���,��}2�'$r.82,Men,Chavarria�Ie�,9e�offer�nef�Ri$*mpuA4a�ime. "F3 adop�b���As�=v�1�� *��/1/3�HpUjSL_MHD>�)�t �uF:&b��(�f7�Gv� *e���5# u� a�0��Z� c�<� )�gM>l͹Nn!r� ium� . N�!E�'s�B�O�v[Rus�!OhmicA�$.��s� ?��o0�6�$chi5_v_chij�d:S>�8G)3$p=5$:/$p=�I SA�^�;/Ep(roll-off)��P �Ps�]- $ ap�,!��Y[\��GbBV atK1 h+$@^&$D-�D!�W, s� �5r��2��+"�{���n��Hd^��;YO� $dl'$)�&-.o.�)� "X2��&;)et� 5#Nremove�ndAui�1u&$(�/3�.N� A� �by�Areg��i�DT$i�n�� taup_v_p}aI">3X }�+%�M+:�J��6-!*�*MO*uQMn5o��>dA��_ need$"Ahrawd2�+�H�7eGZ� vanish!NNBxS&���� !;%�Y��eK id%�#F^�Uh�A�@I������:��ntras�9dashe e] !�* %�6U3SL��2%B �? . Ca 7�78ak�QQ�!*l6��Nq� A�strP� fluau��Z%h??*!�9Hs. 4 A4eas@3l�5��ad H�� �X �$�-o�0 �up; $p=6�!!&.�� (9k� p=8$�31J~N|�*�$�'2%extre���] BkFv[;�aM��6�ɦe [� angu� bracket�YU`2�]$l =3�2AۡiE7�s|aA���60��P��7n*�NPG_"I-wo�,�!scenario] imagp(� ��&�WUM �IKW3pmav1)+7e w�,  $l / \d�> l$ m=@rQ�B/b݁r8.����$q1(he{ing�&A��- Ut!��rp�#A�v�UUQ _W*�? eq5$���=f �e�e7 410$ �X-Q,eGM&si<�ofa�rs!�a9�2erQ�eW$. �� 5J� 3.B�"&� b�"� J��:��RaI� � d� x�[ nx`�# u�.1&ILaR�.YJ��) r�4EN\j1/24^G Xi�d 6Q �^ Q .JVH in sp�SM|�!>� . De2�YJ� .h Krobab�.d ��A�6��. b"���"0deg8 "".� :"b��%"�%4n�R-�`w &- MJp� i�E%6J2bx E)AIJ�A7��. E��v �Q�P s li-wmarkerSbol�o"F ��B8Fe��a2H.Ecy.rnf�*A�*�$��-,�:� IS.� f�2p S*�9q Um"� :j\\\ P�e/k��+-�o >C�*���<vy>ta�*!�prdcg T�)����(g0u�ve quant�1Kc*� Figs�,&�&%�U).cUs t_�_n1p5.52\ �s�o $n=1� !�$n=2$�:sF�,)AM���"� .f�)��L�#=�Y�F� ayDclo�e� .al�a�onm2e*�EJ�s �ur! g!]2�@d�4�d& �cst%�@stwes�SF5s*�Aun1!\� iZ ,#r�' s�s curv�Q�`�z�7�Elo����2} �6=a-z���>��"&�U��! toz x"��yz/Y�)��c-Ren J� ,�%�REa.oFra��4��#���2�6��f6dA�perhap�?surpri�,"�1��^ai�@d�J(!�� e�!�)>�� 2� 5Fo!�,� !�%�&�0'�nkH�pwl`^��J�vE!B6.ez.)F��2 Agre�]|e*-Q v%�%tra�)�� / unitU`,[" >"�!>I{��!� >Jde !-6� � .��z2"��5 5 6rkHRG��Enof�q�q6� � �:a�` b�VI2}Fend989{Co104 s} f+ abP� ��quW5T� ��J| &j6>$ �u�VbfepW��l�T����#=� SJ���)dflo�-�>� �por�665�F\%toN�F� �)�C"*�� �"T�o&�eH6Xt1�6� �kJ.I."F~�}mhd�:�6v�* :x-)�>. F�qq^!� !�&� &#%�Ryr"�I%� b�7 .P�2��Or�Or�OrBOrt.vJ�7*� 2hmD]v�DGGv�7at.��$�acv�o� } u+r�ate�W$to Tony Ar6%� help;HC;.� rese�V�i!�ora�i3 "�]U�vd King�sEo eG d:sal�ys RW0Council. SCC ��  R"�zfe�6ship.�f* � \clearpag�Z*s�{JC5�s�{14Sep1~rV �Le .1e=BibTeX�$��d� �_ F�~,tF�j�*�~epsfig} Z�~%.,�~ ��~2> bm} .�~2#rKn� �:-�4s6-� rsfs�~new�I(and{\bsub}{{subMs� .)e )!an'calA}�(thABA} 2F calCCFPP:rrr  bf{rB�z e^{{}}}_z:Bvvv%v %># z}{v:pp}{\>ial 56� ppsq�#2_6%Rhyd}{R@_lrm{J(S)*Fn+gbf� }} �'tJ th{\� }{1mmAmy, ȀReexa�$�!Hof Hagen--Poiseuill�+ow:\\�_pe-�MS=he�aulic r�]tav icrozxnelE��M {Niels As M��Hnsen, Fridolin Okked2(Henrik Bruu Cf&ʀMICoMDe!��i�Mu3 N�O echnSL, bldg.~345~east\\ T6��DenVT, DK-2800 Kgs.~Lyngby,.!UM{Febru;3, 2004)na"�wWN3sb-g-d�tnX%ea^y�# :x in "u 1Ly � �!� -� �@hapes: elliptic, �c�, tri � harmonic-Âurb�c ircl�UA� n S�&\qzJ�#�'|9$a�P$X area A$ l��"�Ii&4|�?le*mpactn F� Vc#^^2/A�Zil� ]���(nc� B�A�6-�n& |geo�j al c�Yce0factor $\alphOEWe��a�> �b�� �e�C �ch�s'1  R�glV= P��Z � �C�nl�a�"Nq and �!9!O�A-� s�la �2� ���%QR��ple wa�v����$.��!�Q�EgsDu=GlTcs{47.60.+i, 47.10.+g}k/ket�����&r423{ < sec:�P!��Xi�) [b!]� !3erl'{L�=fig0>, w3>3�� ,cli�Z?� � fig:M� y} AT. bitr�bR� $\Omega�1.�ppo6�IzB�O w�Z�)ur��e5 ady-��At( ��tours� !� v-$$\vz(x,y)$&="^H�7rom�~�Jq:��son})� �@� -ele��$4 weis zerl�A:bx!���/al a!b,re-of-mass. !�n&�t0 apid �,x���r2�%��+ �pa"dekputq+hag9!K-)LE�-�Cin �'%��uha�/. T�A�ally,"gill�tu�Z�D ��u� 2s�Zt� dab#7a�gA a a�eCF��{^sng �)� >'�Wi�in 0. En{s���pj"�Mby ho!"b���.( polymer waF*, semi-�-n"�7! etched ��2X��zin KOH- , silic�TDrystals, Gaussian-�d29laser-�p!7� film�* �f26��� PDMSA^ic��e.g., u8~\o�h70Geschke:04a}.I�:�)}�AS�qui���4 bn,"5* rigiفny�]J29CR�v_;VsJ (or��y*�)�1, a��of�3��>AXN*p? = \$a p/Q�F"$�2D1* drop a!��aN�$Q$�j��)1BMc�( ~Z6�&how�D a��O%I7 2E ���O $xy$��ne��aA$K { �Ld� $z$ axi�}zealn�85;2y s� ah.�D;,9s $%^S S/eta LW ^29hL5a �xU!�YN%: dynamic v,�qA^!SlE�I��A5i#7ɕ dxdyD6;al�Ea. Typ� ��P�#)�!�u�xE� no-slip��e�=�= wall��A��>the act<15Q.��z��� �d~ &6 ��i�O�'�$ _bE�rDrU �5�>� "d�� � 5� U����sa*ceq:� DefɌphaU f�sE} S}.u2�~%R66*�s~���,Sa�6s:00a},jFLE face-to-vL��)�H��4d,%pY � bulk�wUtQ9�4P n�<by�I�.* �or bio-L/Ay"xaq�E�{e l�Mof1=����&m� Gstr4(NA hybridiz�"n fixG�bcatILi�teDlhelectro|;"�  s V�j !-osmo>  phor� A� -e�us �A Hco�auR�-sour�Qif�9 -o�\a0�A�!ver�j2�,��e%��Kvobx� t*,�+Qr)kyK;p�&d�-U#��y i�_en<~�e)� i�OdB+�5�:r�'**o �A_<1 6�E]���C��Cm�":calP^2}{ A},J�C<rP=�Z"��c}d\el�[�� qA? $� 9#n� qCE�� e^@6ria � �C$ 8MaB�Bogaert� %�+�.� rein�r p�:Pdem(wat��3�� ;A��JL a�j�MR�A]our�ful�34+G>a�f�c6'of�� ���x'Q�ofU�n�j�. *h,����]O�dasy�� I$ R3� al,.� ��&� 6��:�5+Q.RT&C+ inT par9. A�wA m U � :zBQ ows 1S< am6� �f/t�v. HЏ�J�ɜg9?a���!��lM���{�*Q } Du�` rans %in� �"� " %�� F���. %�s'.�45S!�*Z 6G &�M,�/&.F� "� be�$sN� 9Y%p!X �H�  Q!D� S��� &S �� �V \,1�j>Q"� z �.��Bv��Su; } �Jme7&�e�o8�Bm�.�in���!�N���E� famij`of[` \sub��E'al� �[;e�� N� 2� s�spe� �� �!EqR��1�H�V>ly�H#F%�*)%wL g hGTpZF eN��! !)=XJ�i.@�6�Ey� )�h!0VenuAdbodnM�maj�Hnd min xess$b$!beACAby 3�A,� hatN> vo�Fq:�c�z (ab)M $2(a^2+b^2)aflSG1߁x a^2} yb^2�jJ� fulfilsZ�. FA1&�e�p"�c �QQ^�>!_%}E,�%� (\gamma)=�} + ^{-1}N�@ :=a/b$2�#,E9=�weiV��c:�� �)= )�,16}{\pi}\: �)���0^(/2}d\theta\��sqrt{�N- 0,^{-2})\sin^2 '}\:�>B��վ^���E��S-�&�Sen +aDm�|,In �'oq��Kximate>� v(pvJf&gi�rr�56�I:.[). By�B� ] root we �$)0(I(mrJw�en�W_�e �6u2�U�cQV�V_E�A�IY}{2\piaee�-�K�-� )� 9+. ^2-(8\pia� \cos�Expan�m ar� 1�=K�5�!%geRw��-C-R��)� 8}{3A��fv +� O}([ !a�]^2R�A�E+*��_vs_C}��r%��ct�k�; (s" 3Y��B�t EqsB�2�e7"�6/w�a } =  (*�2ud6w�6S).�%� �&S �t&0"fz/D�{� �6r�Q �Zd2^g�d)�meen �T~12�,ar \em�C�Ia� scriP by�� x jt�jUYj\cBn�iCB�F� �<Y�:I!A�&� �5!2 Yf.I xactD&G ]Edle:�N, U~*x-]{ ? :0 �leAb&�S�m6d &�?6 BL,�:�,.  $\ldNota��<tTaz�f-Ml!3ll1P (lj�OoscelG!z acute/obt��,,eneB---7d �� gray.,) fpj �\s.�/& .%l�k�(M�6U Recr#. &V ��!lE0E�aaheigh�`�� =w/hA1 6Ky�O>";Re -� white:03}� a?�"E &^F �4h ��(3}\\ &\timg6hsum_{n=1,3,5,\ldots}^\infty< 1}{n7��v ��h(n�� x/h)�o  w/2h)� � )y/h)\no$� �%� inde� !*��Tt�� coordtK�� c�}n s���#$-w/2Y!T���� "� !)s9�8&���eF� 3-M=2)=18�E�� ^N}� \)*-22}{7:� 65� + � &� 18]^2)N��.�$�/Tay%acoe��[=Um�"!e �20��s ���1E��I�9&�%��A,E�r�>I ,2�"�C J�J ��NQ %)lZ ��,6�-Cb�:N "�%:��BvN B���(P -�&J  ;��rg"a>b �vb &^9��&� � . T&<$�!} U{Pb��!�*��2�� =20\�3"%�a�=12\ $r�*�2-U�%R!�a �P�<�!~,{~ $c� p�#]R �2�"w. I>1#%|yD!&� M�sy �$ Ls� f6(&t �&�<of�$ht�;& 5�k v0  (���E;"�]%�B� Weisstein�%) *� �z�%+&� :Z">25}{1�V+4UTNN��?s�U�"�'� .t�I�� [ � NWQ�FW 3is valu�{Q5�!o[ e/ G�0Qs � ��R� �rv�ai(a,b,c)8(a+b+c={"ef�"�ɜ,+c͛^2 -��,(a^4+b^4+c^4)}!�>�!2I !'2::�)5�L!rasy e!:("!L$R22�)'u�))�� � �C�GC0.8�F (a) �]�un�ur��. �  �6 � Ft �le,�<">*� s �O ilde{x},\ y})$�#$(\rho,)$. (bB�%���� bu $je$ $(r,\phi)! � O)�e�~u��ۀ,$a=1$, $k=5$%$BH=0.2$. "�%jm��oleniH�1� ��*�1 } By AF��" �0;y��is poss6���eBRO 9�M��*�.�fewō�5 reI�M$�0�q� M�� ��L � �2�!j"�]�2�a�)al"AQa VELx1t��'�4plgl�p:|'z$�C6�V� As illust�"z=* \��6��2)��Y� gd�&�A�M�:�in Carte�,�Cm o1�2%p\��(. !���g e'!�e.�Do%[~�euBA�."in.{ As� oOv�5.j} ��46�Ɇ�.�#�B�%bdns�E/&�2�8�/ a� &= �-,&�Ta�r aZho��[1�m�n(k =)].CbCx2��P  `,py�Msin M�-Ż6)%8��s< c , $k6an mQ�7($>2)�4� � )�V�, $0\lI� M� !|1�A�1�=0:,yF�vE�&! ��Sa�!7>z�)�L}� ��0j��sweep1in2��$._&* \'� :  B"x,2" � S"x[1��],\: y1R$I� desir�[g o1kiT���m� 8�]V��2o8 ���itzm{>L0to [�R@��$6�e��T�l|����C!_a N 3"@U�oz $m$ ��� ai�WU/^l5$l>m$� M?ard[,wH8�?xBL�s�rQO}QQ�Q group�ogethU�A(7Q sy��{7 ower�� . To GiyS(62�he&$$�e�eja.j iܙ�v-!"� &= vMtahUwy2")�� & = B=(0)}}6�+ 1 \: $1>$ %^2\: (2>('b�sb�Likewis? La71�&ope�wa�2r A�f6�WAn�Y�)�%�rho ����YC�Se :�E��#r.��]!�:-A)ad�^�>��A_r��(�)\:i2$��2&ѱ Pert�^RŵKph�!Kb2Lrho!�>'c2).M�uPhiA I�͟>�i D�}}���fp_r �!��'f� �a� )��� re��o�o se F�6Ta� nd&TbhThEjaexB�.�)$"x!�#E�t:� Y�o��="�1eR2�!{�tF%�| A��2�ts�0e�V2�Iϙ��*to fo�F��i�/�4forward,<�ted�&. Wit\!I ICE���eZ"�'% �6�})>�6VM�3_� A��&!0\Bigg[1+2(k-1A� 'J�q�+HL47-78k+36k^2-4k^3}{8=4W]> 6�u,b��� � � x�r5W1 + \t*�:m|�Di a^2_�Irea)� S �-aSIżC � s�` �$arrow-vżUval02_8� -�Don(4� �^ leav� %�� �(antl&;`.��0"�0)P�!$����*Qforv@b� X = �"�q� (!�6&N�S!&5!�7 lso AEJc�+5=� ���;Tr �0&p@�%�C$!P6�n9�b�%[��&8}{1+kA��- 8I�3-kpi�2�1�%N& ".j�ȡ�� k>2 �=���sh)!��e�),��\eq�q�6R#�'�sC 6rA25% �) [eu-��.R]lI�S?fiHatAS.�F_ 0.4E�r ,ʖ�WA�7t��0.2\%��0.5\% Ik=��3$�1�+52lyJ#�+ Disc�<�nn� �6 ��@��} �D�G <. &@�<�te.T �� �Z@!�) a�`6� �]]a :c$-o.�b%�9A�$thZ�2i�9$."&5EK.�:��7�,;n^PS$. D"V"��q��a p���^9%���&� �i�un��al*�aea)�}�3 s�c�|b���oQj�t�x���{.S� enti�yY� �FE�V+&qODx0i)�a��+E��._Fhe|@?E$ out �> uspsyOۓh*�Y.Q�Frp�-ner�he ov�?ll&�pro�C C��M�x�RJBerJB�sM��f7I` �yA�)F�"�1in genbg�qto �Bin3vex1bolָ�5!a a��"A #*�'is(�C�)i6� �B�5= (E�c|��EMl�HfC ��By$L&�3 ���A4�u2is as6�w ZG^!iHQ5%�A�I vex H,.e�h�h��"�5�!�!e��a �WerV>.v-�*�l%�S-��a�>�Xb"PS]Z"g����8 link"2$R_{\rm�}$E���7޸rw obse-Z�3� @ !l��%�;r�0�)L�BZL;of"D����G}�' k J. Kut�L��st�lۦ  iN.��M.AE F.~O.�upMby� Da�j &%NR:S (Gra�[4No.~26-03-0073X237)�%\.�R0style{apsrev}:${//micdat2/MIFTS/p�<s/�R 01v*�0dafter\ifx\cs� �� xlab� \f x\def\$#1{#1}\fi ZG|SO font>J  hf�#�Pf.jQ$�R>G~R.$�Rurl^�url#1{�Ktt!Vx>O%�{URL I�fid29m�Sib� }[2]{#2} B!epo� []{S'"�th6��{7A2Utem[{2�C et~Y���4)R#, KlankF$ Tellec�}]E�/j nfo{~�o1Sbi9�{O.}~1�=}�" j=H>=�}},9SaF��MP>M�, eds.,Demph{�vN}{pRP,.YW of L9L Chip�g ces}} (Fhpublisher}{Wiley-VCH Verlag �%ad�}v$nheim6#year}{2}R�l^J��E�� Manz%� 0)}]�A ?!��S/V.� G.~H.~W.}6j ]��2�jTA>��6�Djournal}{Trends An ��&W�zh�; }{19:G�Xs}{364}=�5B0rB�B }$0:$ #$, RousseauA<({Van Hecke}e6 Im��a2 0�{J>' =:�V�R>=��>B#�A��I>�1!25�5�(Appl. Math.�utr�11�E-�71��� e94Lifshitz}(1987a= �@~<L-�i5+ ?}:>�V� E.~MBP�)HR�F"C M�cs�7 vol.��%-q?6}�  :G_2} �2,5\�nofH "zt�[k^B� ��-He?�n��U �Or� ��́�i�!���z,ion}{2nd} ed3JWhite�3!�"53~�FJ� L ������(McGraw-Hill M�� 2003r�"�*A�99�:�baB�BA7inF+��8athWorld--A Wol� WebN ource�0V .x , Inc..1�99},:9�� }{http:// ]w�.w R.com/�-le.htmlrQ%[JE�SmedleyE$4!L �I D.~J>� ?�� G.~T>P�6+�Aa�. e�n16:@�8 1267.�)}&t+>p � &w\ B�:�_a4� ,12pt]{a��(*�_$graphicx} #-��`Munir H. K. Al-Hashimi\\ "x�Z�, Bern*�[ \\ Sidler�,sse 5, 3012), Switz� L E� \�� M �um�PE.Fas�T�Li�7T% \.�>\2 "@\%L�&93\O#tK$��<myhea�=s}\�\'9Z�bg?{aVY�2�m�a new (��حt��Vd :?is&%p�*������l�m1�<�]��h$#(�#!K pulD;�*��hand�cM]#Ne�H's ���">Ogy4�~ ��}"�s%� -Z"I�p�i�,E�xi9\sE�nw *�=�&�3007L�Lo/z:f s. Ot�t:�1�2[c"�<� %*� . It6�1n%��'O�!F g�*�lnd �1�xA1V' EJDoo;gxplan)�of wh�v4Z_Yeseems t"�!�� � >l �D)�� I��eiIA�beM�d�1so[&re[�!�eadefi�Y��" RcyI�!�ly �cer�&��a�E�Z phot�Xa�FNRin8Q�%O�-ure�,las��3se"��it�n'p0�Eu^��t"�ionJ_] "/6]On%�A&unans,J�if�'adt-�ѱ��uwas�ȩ&�Tc! �]-�=\sL(k^2+m^2}$ ,M,� �!t w l��t!ravel�U+� �!�*��b�e�d� dou� - ,�[�)u�? ��wa�e-� P�}e Ne @b�� a_t$ t���G no��� e�%�dd!u[ L0an upper limi�Z�!�!6, if 3d�k��Pbur!Uui^b" �2 I 9> "I�>ifa�� "p7ab12��s%� `12镍8}�]"IA �,ai��e)al�2�$ (��w\ro�Y al 5jcz!�!&����r��e�aEi Mk\)s �aer. S!Ra�)R�!.B$��re��� radZ�,!�Z��} ���A�om= ���� �>� EЕB �/urn�1� �_H��-�5J���E�nU�F��MF� ``� )- �� pote!@+go$2 $��mr)/r�0iearthQ?�c "�gm+ !%�!{+:a!EOC�0�or{ ��n,�]I�UJ��cosJ�"CA�# ���I!�thI y��&�#t)�f�A�n �0-=.��=-N-���act$c p�G?U %m� � F&\$�YPur/�COut� �is Work} &�A�ork`to "LX�ew <3͖!rrM�p�-. M  on ("oD&o. on)�I�eHrd/��2X�:� �e�*pu+� any : 3�5� �&3�ropagate�ito!2!��� !1��5��z�+@�%!Mbas��!0���ex�1f9<b�%���D�(2��'�it �['n!/�� � �i-o&y0nar�V!��|j6 (EDR) Q�>9�#A]��� �*)��.�� V�!i�&��it �)��u���m�no*�s E �|��a�a�B4.��I6k�I ZdaqU0� e��*�,this work is6�linear�Vsum�vector�@small values eachWwhich h4univers�dagnitude denoted by $p_s$,�is makeBz`in some sense a discrete � en�f%�0postulate stai�4of a body or a pM)� time �minimal�%�ity%-p $\overrightarrow{p}_{s}$ , J%)c9/$constant}.To under4d what exactly)��,means let usF ider��RQx<, say from zero %�Aa -J�$ durA�a) $$\Delta t$ �hmval@ $ can be divided!�toIIest� sibl wsubea valsD_{1},n _{2}, ...i}$ such%�aM�� them5A�%ia�by "E�.�)4. Since accord!to0:,tJJre|f!A�E�U�-MTwritten as \begin{equa�� F�8=\sum_{l=1}^{i}F!$_{sl} \endJ, whereJ_{s1}}$�aN �of�I- U&!�$.N� _{s2NL Q� L.2aN...�� so forth,�;N|B� �|= V,2}}|=...=p_s> It�a�-ed % �p%5�wa�:8itially at restMH !2���]ofB�is�ar� tectaa(experi�f\A3)uggests�i�of�n�} P extremelyI�. �sm�>5{of� �s seem�>be�o�x. .Q Second P��}�equivaleaL4between energy%� massQ�ra�ed�0ou��awrelativ��$In fact, a��hby Poincar\'{e} [3] had leda��a Bona�studyWtheYlof radieL . AnothercT Hasen\"{o}hrl [4],[5]� leai!� �Ff�ssLin��D a system composed4a hollow enclo/fil�@�,Braunbeck [6 �shown� 19379�verific�c�%o) .�.�Yl must not!�regar����A�or�dat! "derived�g)Cprincipl�,less direct a�empir e�,nce, but�uldXtak�� a fundai \�is poin> $ view will= adopa�)e% )�in�c) a��a(or�)� I stressZ)vE a-ea.N�E=mc^2>m,%� $c$ �-�defined!�!�veloc� l~, it 2i�AurAfn��!F\��� J unit� S�*1HM ���ul+=4K � sI� $p\gg m_o�trave a�approach�$c$)�s�N&�is:� {E�AA-�areY�t.}6� 0 PhenomenologEi*  } \par- third2q supi��pecif� !��a��!A �� !.*O dup Y &%!Z�{ pulsR|K �j/ M Nb�yBy know��isU�IcdispersǕ can A8(found after m C A& �ies� � �by $i$-�s� %noa�w how!vs p>��A�b�5��ed,E�� * QsE�.a�B_1 l toV2�4. A.� Newton's*~ �; e-�-�p 5 9 mIB� d E= \frac{1}{m_{o}}\left( B�(}_{bf}\cdotNs}+ I�$}^{2}}{2}\� )>l^� d"� i��Ix!�A�1� , or�}vU /befor!�e9!��*V�E a� $m_o�] �̍��.'%��͹ purm���-� Ukis��lics ń�|a differɛ> B�J�Ax 3 r5 kinetic 5�obe?d.t_ ��. M!Eab# A�.�Mea�cus\ in a.�a�ara< [7]]�l=�cQ�6� M�a Y��A5�F�_A�}$!�.� � iF� ui I�B$ WVa� }}{mNm^F^ mq�,E^{(t)}}{c^2B; mN $U�total=DaY�R�K (5) 1�u!�for calc����lE�is ga bŖ�1�j$i^{th}$9�%o.��2�� reviT� us�fA proVQs: \newb �{ i_�iLY��bfAI?dA=2 .# �|� .�-I� %1E2�q�(5)nŇIM n6 elerT�:e� ] I i���` �!(ac L�d proc0 Bnot ca(any-a�6inn�v�!q��!�?��qV L. I!~for�tA@on.� has fixed� ion�| reason� to believ!�at all��5�EX� z � x same m��9$ng �2�,l>h,� theta =0$e1� aK. ~i{A�arA�S1Y��en� �W�oj�)rbA�bB�p=iJGJ�Q�iM��F��': -]f>-CmB��I _{i}2M(i-1)�&*�Ց�+B6!2��"Y>U��1{j_ =>�"� j�O-A $i>�s�B .c=y c^2+::�E_{F/H,i+bea�}a!#$ like�s$,�, �' ...etc.� ��dM�alo� i�,observer. \�C�#A�T�oKYEl} it�;$K$a*� Mc�|� adhe>B͆�%#� plu�e o>-@ . ... � � �� � �exp|eN� K(i)�k�k=i}E_k^j�d��dropp�� E_k$�� shorj nd�DE �a}$&��bec�m� problema� T �ainc�^7�k�i"�by5�)$E_1$!" $E_2 �=�\�0 �B,example, (8)� givF� a_1=}�{ -�h^2\pm\sqrt{m_o^2c^4+2p_s^2 �Z�A�neg�>� solu�y� Na jump!!'I�M�toK���U��HL(um� i�ER a�-$6�iiD �d(.;q�is impor��ot�ASp{ve aof (11)8devr ng clearl�8SR�m� �Y��cN a  s��P  no me�Q! �%H��of��th ~)T*� % as��few1JO@ e�hand,� �beI�� �� a�� Yf�a�)�� m!7� AIm��iq� by ueU!IB/1$,a�z �=m_o\;�� E_1+aXE%�we0��%�64(narray} E_222Bigg[.iDiC+RA }Ad+\hspace{20mm} \\\nonumber ;i�q��c�13e�K{2 v >8m�y}�]��I�E�� �A��7uay5�unp,cal� � ?is�� 7 helpMfin�da seriesy8s aHE��Y1!E ,$E_i� &5�) ower \p�. For� �c�hxan�Ng>+f�%��o}Y4}4^3!�1�}2"6 " 5c^4D5}{16E8 # 7c^6}+...1�l qan=/2m�bN�Y�3E4B�3J�87}{8�J�771��a�:��&!"0 i=2$,NI K(2)=m�=2�:�36�N�9��976<~�A� larg� $ ؅�alsu  an.W aoofy��"A rule"C� -&�efficien�e 2  for a�!W arbitrary��P .� ��I%}s8� bez�*� �l� l� j� 8j=\infty}g_j(i)9�{2j�_o -1}c2}B�S�,(e next step�rto�] $ V$�"re�K%lcJ(ex.>Kt 5$5d~a �19)%� us o%  "�inQ�����\ �merm%�2 ,due to $i-1$ 0s,F�E_i2�b-ٙum_"0 l-1��k)ͱf&E_k)^2�P{s}^2(2T��Z E!R�詪�2�in���p"�������[� j_0E`M^ QY�({2j_0}(2c)^(}[�] (C(1/2,j_0)}R$i-1}E_{k}) G-1} ��P��"!�binomi� hJ"�Q,ge�� abov�a+ ��$�$92T.�. U �Bua� e�@A_!| �%minato� (18)2 JNV9u}^vs^2-u��%�!DV�)�r=Wr�*C(-!�+1,r)I�)� -5�g-�)^rI�B�F+% (16)� i�&sy�Epro�hatB}\ (Rq)^r��_1E�M�... 5j_r � g_{jB#}�... r  �n{2(j_1j_r��%.-r�022rF<Af�bstitu� UB� s=JF~jE� (20)O ��f�$~?J=r}^{J1;.J)� ^{2J �J�G_{Jr)@>��'  $%ebV�z�oJx G_{j j9�-�=J~�>�\footL {Fun�*sD i )r $ F }x��%�nam� they�$j�!aq'-�onA�makɔ1�s� �"act se|! �hav�h �*oE% tensors�� in gn������any/�r_} S]| (22)+ o (1�OV�  >�� q]���my J�IUSG'�r=co.}^{!�Qh�)(j_0+J2e�- � !�.�2�Nb&� �� .�]�Ǖ�� "� �$7n�(" summoY��$r- f $J �s1�$$J\geq 1$.F 8-�R =J+j_0>�in!�24)I��V�c:�KJ� ��: Z: =�&"#)� )�:� 6b� E:QR� %�QL9� -�-J)%�+2J�� [2l-|-JE5 -J-1��l-1�+1Edng%X.�al� ^j$ aiboth =!(26b� + ��&� �v����}�e�|se��zny� k%0  ppea�.��  hA��!(27� th or.- $k. cernQ=�a �!<�-ger���/$Bernoulli �s�b� . N�0 tail- be m�/o�&�t"� )1�Gs&�ɬavailx �!�}$us books ,�[8], [9]�M<)��+*� q3g_1 �i2}\\g_2�i�8~i^3}{6�i}{24232H6�+Z 11i^5}{606FR16a2 > Mb0�g_4d �5iL12�(103i^7}{560K13i�4$37�9�19�9�43�0} k17%38"�$101i}{6720�5� �7i^{10i$569,823i^9}{1008512}8}{28 4079� 1344�607�57�27 �64� " -:4J$4}{11520}  1957%�2��18q82�6�-21�L%102531373,1}}{177408}-M 2589!44e81199-7� � 2627%�26= 2998)� .A 9133)� 3072U 2436I� 1612 1982)�53!W E32353-".�963%&8A>- 12223A� 9568M�7!,I �{14A048a 2655A�{13!,53753Y18210%/%c�U32997838Ee!i 2128�1280981 5n 6080AY �748987 %~387=022920A[8A�!593I�384 9638!�6}{40320UD20896Am�935362�Q705691e� �-�1003179I�� 577!^�+a)u17514%�562� ��8!� �4!�o} {3276� 4446a2{15!�63577��9447843E�!� 1064A�x25781960Ak)�55351296%.��(3725849 �!� 6386A�5[1643771A�{%� 7096%c-13592536! �w 3224#��44558251=�6-1646135�!�)��45117�R7}M1 551387449��80Iw�1516756��A�7<}� �333460M7E51093504i 3617!�!�3}.b-3585115a� {189235� 303308A30750��� �B �+eeu6th��p�may�,)g� would3,useful�2�#. L:�6�ly hightM*�s.�5z8+ &�f (28)z (35)�%%t �XerVofY be d�� :�0 @ca�0neglecp,the? � 5&W- at $�#�F6  zK(p*S "-$1~\x�@pa�2m&?p^4}{8�.3p�|162(pE�20�&7pq.569c^��&ѹ1)a���`a�c =Qr3$��� $3$2}�'429%6}}�s &5& 4}} >��g6%�f�"� "�*� 2 �p5P6� p� 2}� {: T�i5� ,A:z�&"-�e�2SR&{Lorentz�0nsfor�05pl0 o pu�ingR $"� �3�mIisqT": $K$ F/of5*NAb=/ j�-��%�{o}^{�c2}}f_{j}Pp<c}�Nx"�1}!�y" x[�>� By compa�:(38� u�6 Z��L �L1Qws $f_jK=�an4� " � ich �2B�f_0 �xe�qxe�qQxi�5xm�"N 7xi�{c �;21q�K33q�,429u�5 \f_1%x�^*� x�&z 103x�`�� x&� � n�  2 . �� ��(.��3 \\ f"p!-E 513%G&u m %Jm &� Y"� ��10%S� �� ;!]& � K24453597-!s234823. �3Q� �%�&37%�| Z* %� 7T -�� U6; �!�"Q �-*� .!�*� 12711035R!�12300!_0�4YR2U>19%�9U�� %�� d )� � �%�:l "V !!�6"V �� $2259090790A�� 46495088X1 567699396ii!�17220� !ˑ���"�)��Se�" So�&*k6N��1�inW�� explG(]R�5orT9e"�:$j$ >��a�#bec�$onj K ai�� ,3so� 8 Yio]o EDR ��#B effeG'3 0�v�8. F�#�����`p�J�t� (gu9/�/ $f_0V� >�er�EDR5 f_1$<�B�he �*oc��y�&`-*� Jlf_{0}(x�!&)1+��-1Q&���% f_{1 :fE$tan^{--�"\PF�Am� ɑ-G2, f_3%$�too�'�4M." ^lue_ �eirN��.iAW i.�(En4techniq�8A�V 2 )Q� s!�j$ <ly%y*t�,I�)# a :c&,olv� .��5�?*E� n&Ev�+i"�+ly long� 1@j A +uZIN�#YQ 2k3my!� ?D-�"**''i94 for check�*re�;~?�FAG&7 4�z"+of *�D'�Dz" $(i+0sJ"!�OK'. �2�">\1when $! !pi"�,d��"� (8'9#E4E�J,4E_{i+1}(p+p_s)�Hl0�-70(p)+ \e:(.�"c^2(2�}  B� BO*a Tayl*($e >������ =(e^�D}-1)&B��!|opera�!$Dv�Q�N�D-C� a }  p} �:oc F*� }\T@�. ,>Fc!47), (4!�(49) ,�a(3 a� J/elabo�8 , a o�Tm�cb�=ach������.� �xO!l�^lc^l+F$n+m+j+k=l -+>0 n f_j(x)}{n! ,5 mf_k }{m!}i2n+j=l:) n.D\*� +�Jm_{j+n�} S �i2@ ] -�2x,A|}i�p_�1�12&-!n,ma�a��.��u/g$ on b6w50)�ka��A�I�6.�Y�for0�N�(1+f_0: f_0]� x}=x��}S�/aPaq-M appl5D �Di�=�(0)=0$% �IJ�6.��/45)��:e.o! �8NI^2!K�$"( ��A !_ �%{%_toA&Y�� \�'6-B&�^2 + 2%^   D�y�Q| 22v�^"�.%f_19�$v +f_1.b2=�2��M��B�*R"9I!��i�w?o �lantbM)���[=AFU$%�I$]�Q(+��-� �a (46)�-e 7:���1inu�similar,t�* f_2,� $f_4,..$. B� `r�iy2 omplexity) �#  no� ��d�& H.t�#C��=�"riz�5� ��Q��A "A \�B Be f_{2*� x^2(R xE }{8(� )^�12/F� ]�N f_{3]i}{192}:N-5E.łT(-5x-3x^3- (3+6x+3x^2)�x)*�+12x^3��+ .�3 �"`�B�� 4>�15F��. � 9x^2�,4-4x^6+(54x+�3+9x^5.�.�+(9+18; 27x^4) >�-�96F�3+| 4-36!':>4R�To d � ?5a*sLI�R� 5note1 Macla"Oe1sh�����a5a��" W W h� (7m�=&�.c�Jid�<tC5 �spoU-U in (40#44)B#i�5 ll certif5@1&���!Nct:_ Converg� � �of"q s*�� ��d;�(��� V�N� x)=E^2+ f_0(x�. 2+� ut >����!E�G�� �6'$is�� �� =�ith u�� t�~= j ^:Dj� :iO~@� IQ�:�$E�>z � $ ��`��8#���fs nE�!��{+�8,&&&�+5AIo (57)F�%*7a3lY$�K -�62G< ma�Q ;al induT*�� ��j�( any �$EFj2 he Wei#SrasJo�Lѷ toc6I�a9Aa�a54a�ae�I)bg un�(n [10],[11]�6C�/�JS3J( $\{u_n\}$ MUquq=9uk,on $ E$�%uJ��Un� |Iu\�&||\leq M_j ,\qquad(x\in E,j=1,2,3�%>z�6=c-$sL�ly�E$�C ,M_j$ )77<�5 +%� cl�N5&rT $[0,g ]�y plot:n�_ob�D� $|f_j|$j b�J Fn2mE�graphsE�}���sup_{x !7[0,Lfty ]}|f_1(x)|=0.5\\V' '2 '056z*3*159^T {4*073�V�S��)�61��6e�g�ā� (59)� (60)FKs than�/ a�$$\{M_j\}$,ds:Y�}M_j��1�ZfT�� ^\\�E Ej"� �' %� $\rho$ -t�Ufor  tw"o %9� 6516)�E�U��N� F�N>R�C0)me:�-�Sed6treat,)�� ���E�� � e���WOne m P �We:a#�bR�0��%�2��5����8satisfy>A�����pm�f� bls *it s�6��  �/�94R��w n't� safe. AR� ["T�  +sX��led,Zatust��5j1� 6� �tIn�()^�I@be�d2�2B1�+do�a��&c ted�I"b o; � �CI dJ�OA�) ork,Iuk� al��p"�?N few  $'s��*va�!�"��!Ktudied �9�:� VDP�.� H"~Viy�"�Hi*�A�!��,!��ain why6G�W ght �.mFb�Idependena�B2�sourc�I�j�[U�A�!x� �S�\d"HQh�%.�R2�>�&1D�\ayV u�B ,Ns™���M �EinsteinFr��J,��t !}VmT�DE�e�5�zb"XM a�\thI�xi^ =&"�_!+U+C#"&� p$}E"� i��&5Fo2(ISpit's >bJ�;6>�Nvt>p�6BaoR�Hv��3#B3a�rRa m 7� �N� �K >R F�70�N71��# ;V� .�_o� n� [:j j}/>�A.�"r1� �]�  2�:in (72� *�r V� :�: �1F< � )^r}\;C(-�:*�' A���4: ex f:� j_rA77?&�9%9�%_1�:�%_r5H�J:$A=j�( (73)��v=5 �;&5 �r=|7j�Xj�&c=15F�8>��F� 2M�x}{�{r+_�.� '_�..1%J�Ty an i6d�&�f��V , $v&�z"  �:4f/ !�9"j}vRr- $vD!� �Z ����*b��_1�.�c"�qLv�f��+�iO2$�LjP��# " L �h6�_7W8�expre�R!d$v@�y���!F  ),-^.}c �e._�c� of Lo�����0���� $@[ ��.�;$U�&" d�"� �!)d$j6@ (75!Q 53),� (55��93� F_{00Ѥi=h}}�-11-2�-!2:�D.  F_{2CF�F�:�22b��&4:�@���O�d5 m�!�� $4^$x�af�$P@� �7�. �.q6s1�J excepD,e"�+�0u �;T�yY (77)I~{ A.-0v$:..6$ndA<� Tc��and d�_ly a�XJ\lim_{F }v=c1T1% ��tha��L�o*�AA�yJ� �_i.� �"q (a�� �i �Jq�� "� * mo�`a�Grt q N�Q� * | photonv � ( deP6 J�eEY!��s _ �is �lpplied � 3'��emi�%of �s5/Gy"� . Per��ny�-�Z`N�2(2�=io ���5�%t�A��1(c�% 6�l�a�%L�s�%8 ;�y� doe�/ 7!?���b�Pof��th� p�(to $p���c�F��d v}{d&N# x�d x}{d p�g>��.� Vb#} ?  dF }{dx"� q^�B8� by!e�it�6�DA�J�D� ^�R�=B@Nr��9Xn��kU,R�!�"�_#<�Q$�'s�@��6] precise6�\Eym2g%� bey�fde�gV(2"Ha�A�.4d hE�a� o�P���L"�"c�Q��,�pr���p_s� B/ " UvT c^3}B� "�:�%)�"y"�by !@f�D>k4$�kc 5 � vB� &�-�UH��"� .�N�&h�~I8jc^j}\beta_j \;B]  Z� 6 �4\tilde{v}_j}{cK  (> NV�$9"� j-c&'N&� ofM�. Writa�a�!07t�9*$�� amF,a_c6c�ym,!�w�p�:GI.�- az &�X���$�YB&bG mad*, �o�6xi_0+� n�=0m#�L' }F�Z�+Jcxi_{nQ�M�%_nm:2�as ^n c^�2Y�2/ch�(D��7D(86J� �+a�:J,�k}Hc!� > xi_k �} �)�R>I �YY3PK�ŀ$$ x=p_s/mcy), "/v/���(87�Y9{"b@�8!� �2�09�o"��m+ c� )^{"V @v<31�7c��&�cl��.Ga/ (82)�) ut $�� a`,several varivEs "1,(-. k�F ��2�#?0Z�#)�A��F!\)+A"��n9�WJFJ*�IJGxI �1}{l!S0 Qw A�f_J.�-.l )_{xi�2<-�Y -^lEc.k�#k_l������� {k_lM7BL�&%�:�^*�#arr�x�P� qual �5oGrsv#v�-^c(89j~=\�1�X^)q 62a �VTU����n �"�� &�-A�b� Z���v� *!w �5��=?�?{ �1�)v_�B�&�H91jEv_0=c\;6Y13}9.^aZ!L%� �'L�nN&P. 89) <T$)cN*=-I��5,m_0� >[B:.M�.We;]!7�)g(��$~�'iZ)���m�].�� ���i� �+F�+ap#v!�A�!%g�Qm6�"D i� P�9$l�OA inclu`%��- l�"� �!vm1d �� Q;_1}E��/[)�2� �A�1  �;u-1-vM)M(�5-":.�-)I�R �&�F!����xWa"M(/�0$X$a maximum 9D*W {1max}3D 0.1c$ at"�` K 2.2$���rapidtZB:� �a�' $ .ISny event,) ",�$thxdc�s�" �feLEr�&P pr�e .5is E��+ �>0 ~5#�c� il� r C"9 n DOc1-�E!p \sim �cU�%��] r imU1n58B^2$�"&�Fas@WTY'L�Tr.a8}�% �"7;*�� �$possibilit�ha��b+trWuf }�'l}�a�13X!� � s&4ns' �a=7a��to>F% vi�ie�pove�,"� �se�� very low,��!�(�excee� !�:�v�a�d� I)��5%(%V:$5y: � �3"<�", �O"If#s!OiFF �p7o k*�$z?�e� �ed �ly� ��ga+�"�&�'��ely-va��f�e's2�w)�L%howG-��nm6�,&mj-a90e�K*1��1.� � $p=1�:&(> ��=��4��iXu^��+2 zghi�+*�m@tr w2\�i}{1 p1+  ^2}}^= $ 7>_oc�bnfigure}�centeK!�Mg�,ics[hea�d=11cm,width=6cm,angle=-90] I1.p�&�KcapAn.b5�M��yAz ��u� � &� 1�!�.� � *~�<y���&N�dx  $v=c b1)rd�m&�a��I�QF� ɳEy���/2Fz����y� �`R��V�3����%B �Q恭qH�#aa� )&I��Fe,�D�-&Y�6#(ZxUsM+E�Uw5E|a��&U�(1.22)A�It (Q� Q�U�.eA$ (-x�)U� yjf]��z 2k;a. FRT@�'8c ,8iP 13})"� 1.23BkA�32��j.I"� v=24)� c\�>\R� |�+\.k.� q 4+18mo^2�4 .;+�"F) ���\}�q��Q�(%�not� hpwnZY)%�v$��I�Q8���;.^6�E�es F� 0.89Q�WM��QO._��s n���2�. R��IQF9}Q�24]�-�26 188�^2ym26%r $x 1.157 B�a�is $�nr �v|f�$ 5D� !W1rEp�#�lEEQ-��D�� /�V�� m��f �� a��� v� s�@��er�  ��:�%�r�$~B�  t"| ��0ern6 �at� &�p*$p�7M�&w y d�� �e  &# �6�a*" �� %l�2+�;it 7 F5�!1>�: =r�? s� an ru� "�L Summ�kof�;clu-4s}S��h � �$�#�l�ge� r N�2!��� L0SF/SiuL�_:�B�/+��!Cf`J�30, f_1KK f_4�$x$.�$ecx}� �f�Q�lqC ,J%�E1�+ 1/2$�"l9 [J/ }�E=0� $k=2�9E�is�3z!U�B5. ccur�!e! "Js!�� )3��N� agre��� Y>�"Ej�!�ButFt �asses:�tbH eI�* `�pX� ��ide2�*J=# icul���>A2!&A< i alb3g��W�2%CU� not .� predwua'6o��er!ac"EM? need�3�E��*~� -R�5�vF�s F�(2(8 sourA$"�$�Y :$��!��eww4! d �3�Ne"!$al!�K'V��xZ���be viond t 5oA�b Iw&�#!"$is����M�N�$ 2�$ ?E�1`��"��#ul��i��A s per?)��for non�����L)�e|ao�ʉ8+ɩ-��rF!�)�eptualY�=n�)=$��tt��oD,2�iI�d$�E�!�-g-` �A<nJcnG�a`pEd�I�6 ��I)?!Be%%�X%��7ś��Bain de�v!/űn�Q�!r ��, �+re�Cno�\&Õ� lu.�"C?%�b�@FTL. N�xf��%��1� roof��%ist;<of�=�E &�9�8ThOA~� X��s�8ŧ9Y{&?8) hop%< �!�m* c-� ��|wave d' (e)�()��(D.Ua H)BtE�� qd @a$E�FTL"�( ��H%�._,is desig7f�'�zCc&�(� e"�*w�V �bO�5��w�s��.a*�1iE @�9�P�La����E .se�me�"Iiadm�j)С�)mfui.��? �;in �- physE�unQ�~�Ied�-T��(�)�:p* har�:@ni7FA�place�>A�l���S��Free M�aLLTs�)�&� *{Rer�ds} [1] R. P. Feynman, F. B�+Hinigo, W. G.Wagner,|Hatfield, J. Preskill, \& K. S�}orne, T Lec�Q Gravit�0,( Addison-We;,Publish�� CX&$ny, 1995).� [2] H�4Schwartz, Intr+� to SQ�al �)v�K$ (McGraw-H�1968."Y�[3 THar�, Arch. neerland. Sci vol2, 5, p252 (1900) �[4]!?H.Ւ, Ann. PAIk?D.16, 4 , p593(1905A5] Cun2j ham,�� P�,!��0 (Cambridge U{ �!�s!314)�$6] M. Jamm!�Con� � MB in C";�� Modern �cs, ( Do�%�90s,Inc.l97�<7] Al-Hashimi,M.!�K. , Dy�MP.Me a`�Colli �"o>,�� pW��=�[8]]$F. Riley, �P. Hobsu�\&A� J. B�6,mQM.&GMethodH%�cZ Engi!� ing,.j UBk2002).�9]qSpani!m\& �B. Old%�An Atla!� &N , ( W!7ngtP�.o.: H<2p�N%{e CorporeD;/ll��0 S�.gy 1987.10]a�Rudin,6W2Analysi�:2762P 1] Ye�Bugrov,!kLM. Nikolsky, Higher ^T Mir� �2W� docu��} x�\םH[aps,pra,twocolumn,�ipacs,flo��\x]{revtex4} \usepackage{�1epsfig"Qm} \set�{\� }{1mm.iblioS\ystyle{unsrt} \title{ M�M�A��para�� ng 6S-7S��� amplߝ0in cesium ach�d\\�i�C2�!mes10�,3}$ atomic-�� urac�stimu# -AEeZ�' ˓\author{J. Gu\'ena, M. Liac�T.A. Bouchiat } \affiliEy{ L5V oire KastBrossel>F\'ed\'eI�H de Recherche \\D\'a�t)(dei��Z,de l'Ecole N�cle�IIPieure,\\ 24 Rue Lhomo�F-75231 �8T �Cedex 05, France } \date{December 9, 2004!b abst`�} WAlo=�A_�,of asymmetry)��0]9p&�5� �idB2n �1 m�{5 2 on (PV) ���AIah ΄orbidd1%�]I�p��Ps� JP{\�4hiral}, @eu"optical � +M�vap�z} ,e $7S-6P_{3/;�& ,�b=Bf}D exci� b17%nseep%�ly pol�R��l�A laser, tu� re.�!�h  hyperfin���ak9Bd�&� ai inal<#ic �.e�֢rt~ a 3.5 fol!KD8,hi one-N-� !_ see�t aE�"�L6! W8!SfgX���is)�ocy&� �  ou��K�H[y�)�et al.},eX. Rev.2jxt. {\bf 90}, 143001 (2003)]. D�5�imA���D� et-uM�� �.�h� ed repet�# ! � exti�x���e beam �en� p����!�} 5���ur "XH*!�l��: aQR�� -til�gn�G r, quasi- N�>of �refM%�" �celJ�ndows)� a Cs� %a3l!�wOv;4ET�In�Ereal- �c�����O�%sa ns�y�^> ! datai1ll�1$\%$��ta��9_5�I��1���Ds,� ic als. PV6<aror��Y��&Me�i�"!2s�E�5!]�$ error. OI�-�� �tA�!~c8��lgvM�%�c2MT$vLPmN-c�2.6!3!grr&�S to a $2\!��e)�du�uQt�9i�1^{pv}��Tr�e� moti�:�'A��6P�TW�as�Wnd?3�!a brief x x���re�"a(pomgOmH!�.�\� r�z�!0.I2le5� �M�&I�Z�q��'g:7�� $ {32.80.Y� h1.30.Er, 33.55.Be, 42.50.Gy1 � �v\.}D  %� � {.� : Goal!�&Q}6=P�\V.�\A�t�!��R a manifeE�o��weak �+�!+ x� �8a neutr&ɦ,boson $Z^0$ &8�)�fr� n�nucleuS&� s �i��M�|�hs �>�1��Zp�Vl�A*�J�� absor#, h !9�\�i��tho�c�energhc��s \��0{bou97,bud98}� w�2����l2|a6 <th&e&� r�`re hoic��,very peculia�Ds:�i.e.}Lk@�a heav?�om"z)&!�3$ enhb��,��:ig6y &�ab avoi%� -����2;�� leteTverwhelm1�>h� ih1pMsMwe�sfa�he B�$6S*a 7S $.��G6 � 5�74}��539~nm.N= e s-n talj*E3�A�penet� �\�T!A�M�,��ras-"3eB� �be fel�=s��e4��J(Coulomb pot�za�socia!� ~Ah��Zˊ6a]�ngv@iiP�by �2v�. ;-s!� ,�- �"�)^f�{$of 1 MeV/c��,�-aBug �!�� irn��by�sF�2.3 eV. �Xabs%x!�ny��B)�i��ijB� %-dipole� L�is!i �&: dM laws�* ?Q�sm���%lcontrib�9 �ch ari��=F����:I�)j"�� � $0.8� �1}/R!Eic�), $ea�b *OaP $M.u�us��#a8"� ��K� a���i &de�ONuMOanb�\; E2s2� "�>!EaKw`;aS�&I�, $Q_W^{exp}$�0 m�Q�� via}�i��c&�,j0 ��yE�M���� {th}ߖ� Stand� Model (SM/%M:�u� ; Xya^ank"a m�e}a plic3��%�� truK � �/a�glF�,� i�oirel�9��, : !n&` �w�s&� �now� ched 0.5G ��@der01,mil01,fla024}.X���,�!�m>�j� &Y bwo��&�!�onT�e��0I2� �^a�9ra��-AEa�#a�� ��fla80}. �u�l2��jƑ� ��)� w���by� own group�d82}!�ey 3f�m�\ calib=d� 88},6� ones ($9Z%$�V%t!ZB[er2xwoo�,en99}. Toda�Fla��Hyԕ� �n�VF� 2n�H6 �FwSM}! �A!�CunW]�`repor��v��!V�Z�8s n<?�repanc� A���n 2� �Op &�mforces-��,CB91A� gd 53o��.5!] �� �us��,!�a]��� ���W9-#U! 1�� ,6� s ba|H  pump-[& %aOc6Y�V ��3 7inzd mode�&� mI�& �E�J�. ELL� �&� @ ����b<t��� &� -O��th� EommEA��"H3>�)%fluoresce�M�bou82,eG}�� valiO� is6�E�a 9�vc�])�8� �A,u��u02}9 wea]ed"K2�-�a��noijd (SNR)!� �6 er 6� w�&!Fb�can G"+��eamqAjah00}A�w"�� >� fier-Y cha9!ST~A ���aB@Z�3e�A6�t2�^a t�2e tro"NZ�"�;%o�� �SNR-�pa�1��~i�7lź ����+ �7�.��>"� �NI��Ia])of�X �+ rgan!��,n�t. II,A describ� p7���� M,�*�&]dE�ve6���B4al-�%�9 1SNR���)oSfIIIu reaf!�w�!�T oJe�])n �F� (X IV). ASaZ<r�!�PV= acquit$!� k�wdAve <3w� 9 a�2� �e�� Fa � in situ� �-.curGPV��:��($���Mw��F�l��!���%>is kis.�� �,uݩ%w6&lv�%on0)��% #�+wpro�Jt5� VI).� 2� %% ",E"!":&�I�Im.l6�E.%UDeJM �C �� ��I"&� A�g�e{� , ���� {Aj($6S_{1/2}-7 .� o9��m d�d)ZR&�S7S�<fe/(48~ns a$ pop�� �ce���AA�6$6"�s�j~�o imme���� ��y��ob2 N�2� �.  $1"F2��is)��f{RZ��e93a ���ce I hf�!�c�'m-b&ΰm�:q%zb $6P$-/�ag{�1!��5e!�aef.o&L��y\�o � .��ica�&S�)h�%� A3myK m�) B��FC6��` �=j d����exhibithty "W. B�7vsj� 1cm}�.�F7 ics*[�:(8.5cm, keep8�� =true]{ti!OL� s.ep�:�: T����ePu maeY(150 s$B \}$). Insert: $^{133}$Csvb� d (I=7/2,*� spli[2s: 9.2E! 2.2 GHz g���'U�$��p., 251�$1, 151 MHzApy�).#P8 ��:j $\vec E_lM�'&� e�!�=!�mdi��nY'(, ``Stark''.� e��)�1^{#} =QH�,��e4Q!��eA����inxXJ* � �e bO�� of � )XY3�2�$\hnT(epsilon_{ex~��� plaU�� i�]X. WitX2~PV �� eigenax"u �ed�a�li���A �@Bw.Y ac�-U�h�YupP >Tngu�s� � utads 4 >,�C�^{�&�K pr})-='ex} \wiiGpr}G�+��eR�  0 }F{> Q��#> \cit�855 AtMX�{%AL.��-�12��̅�%�� alt[8tiv� ca�n�allel D#rthogon�a� so-c$d ``para''Ţ``+''�}.��Kc" a�5�superpo2 -�HS3K:O�� ěi�tuu!Ns e�iC% 2e��� $����PGeq 6}$~ra;&8$E_l = $1.6~kV/M�"�a��-�nel-�mex��in bal�d-* he I��3\W)��]a -�@"�u�i� wj�% -e� >�1Xin�un��&�o� )8-�Wp{Y� e�I+ djus�)[ &4� E�O �!�ob�!�ull=1�ce!Z_ im-9T $\lbrack (S_1 - S_2)/ + \r_{ref} �D^�@az �$%��)idgue95},��a�H ens)wg ��com!�� ens) drif� WG=& wit�H >�Ja^e�οe^e�6q>1a�,X� e�PM!��"r��{I2I�=fD^{amp����=D7},,ce qm5��}Rk in eit�,� ]��,:!i��sR� E Yu $D_{atT � - A4$�!�s S����q�r�� eft-��&�#$A_{LRY{i$�)�i�C!{.~Xthin �'��4=�f &(vh7aQ]�  s� ::7 &?~} � = K .= �,"� mi \exp{(\et�(,cal{A})}-1)}mj \,,}l$e% f/2�HEi{ $o$ = 11/1� $ -11/34�?%�"� ,F=4Ma�C {.A\!�eD-�\a\ -con.�z� {${ �I��#d"eR\�� . Ev}?o� i")is�� inu" 5xnɽSa�V D���I6})S �sll�@: d fe �e%�mu���$.=%I8 U��l ��H2 �d��� �o�wE9��^}X�;(%lut��Yy$ /� �I�bylw}0a Faraday rotR�^� Y e���� F-�i�6@ �U�~ly+np�q�_{cala��by ���!]n5: $q� <"q�E�eF��60mF��mY I���K Illus �z� (��х��:at"�a7�d9�o �:��od:%9&�%˩�B�{ a�llel$� $ \3 �oB/p� so��yO7���* text( �19)1~ .I"5��O�9!�.�a��Tnt}t76uaA A�� &m��7, 8,bo��8eryztx ��*w. X^�diQk mF�67U�� below:� b-NitemizeA�tem�/ɍ-f>1u �, (LR)9|,�2��n"8�a*� 1e % �>s:{a back�n�$2+". \�As8;Eq. 1 benefi-8�%#"�-B6�I�!�:��n�� .#EO uand2�.�aA,�?W para� w"�5!�a���@"�6�� $.�%2  fa�1gA�$1/�1w3mploy!�on&�1$�$-D�9u� F��B���\ B BuAeA�o� *? S�-$M_1�"ter"� �$ is :�O0J*�(KA[��*�/( troublesom ae �E �.A�E0�!}�tot ��a f �w�mDn�F�pm 1 $*� �s�jc�� exte����l} them1�F|%*M�}-shap� stor�yAZ �lapE�leh'mW=.U".�,'ked!uti��ly�� � (PV align )8Ged =wal�e�/&gemV same=�(%�L���3��9&��!yis Q���P, �b�WE�in!�let�4-�4cs E�%M�N|u �?9}.� A-��rB D2 4 ��jW anisotrop�0��s# X ch eoes"�g�E �)��Yed M�det�g,S%�-to-N>�!;z�%�@finit�lӔ�I�} �51s,% sim e� 10~.*n!Ho�.����*N"F�%q�p !� *�5� our *~$�#alread�+=�ad} JY A>�#m4.�1� �rn%��VI)�j�-�� v�"Y�a� �a3rab]vu�� hot-)�I.A!� t1*} "sCriteria���1�" _mI�PVIt�9)qa-x� c �+$gma_i$ att\)to.a.�He�!�A�!�%�Ia fnoJ�� la= 30�!sa�Ao��{�L2oex,m2�6�!�*� �8oHz bs #ce $(��Y Y ,  E_l)�Xre"�ur��s ��we��5�4 �eup!G�6�X�"M s. LeWbox�UDW��e�!���2}s (�6�, \� &�pr}Ss-?�z �|-1b� r�~"-=i(cD ])I�r�( F �s�!�=' �#erdtabular}{|p{4cm}|p{2cm} | 3�1.8"c|� h�� q!,9q&2�& S�m�& U & NbA( exc.I� &!�A�\\ _ $1) BS��=  \�Yq! }-S_�� + < & & ~�Pg� "� & 4 "ity,~&d! }$ ~J & 1 & T�% $2>�r=�-� $ & &IH! 1=t�� $ LR&� & N�)�.,& 1� &1 ms.�55 6mm}eeiw^  �(\s��='1)��1 & ~C�,!�9. !M(2x30 & 0.4~=�$39 2mm}i�{l} e��EF�Odd��$E9$ &C& M��PC% & 2x 6 �8 ��-�)� \\5�4��@ \pm$�e�{q�}_a� ^{out}~$&��& Tru�#&� � &n tr�A�Kefe0% � 4x12�7 sAE$!F5 det2"4& &~~(EMI, geo�?�;� �5�0EhaF�ina��,�>'exc}1 �A# &Li�>*-�I� �O�7 AF & 4x� 14.5!� ��pr�Ag~~~m+(* $&~~~ (e.g.�)9�69 A�O�:� {�ee x,y} �K6Uc~I6 ic! R�Jin�� nt & Stra�#� ! 4x5x5��� 7:�Bt� �u,v�$K!3B_{%�}�EE$ Ks& (4xEx!\\ �p$8�3E%pm ~ {� a ~of~, ~axiD�I�+ &~~I�ݪ& Back-&>, &$~� 0^6$ & 90! \\H�!�FU�\pst�� �� &~��&.s%1� + �� e�� 6.0c��c }q?уa:4��.!�,>D$"&%�#$>P&� \8ebox{1}[3]{$\Up��$} $\u �E�\&�� fD $\+ S & \e�q90W[caZ  }��q\� �C~} 245��C.2~-�<1}b��D.� � �Q� "� �t� 2�&?+4/�D=++/} T6~I&1�/g "�% 20-id� �M�l�&56���/U%dG4� � y� i �Mcateg� s: i��%��Ah+A?� 2,6�so�G�2 ~|ur&�q����"q�  = B *`08Z� =*"~�mi�Ke2> @ e. ; i �eon�3� 5,�<�7'l$-odd,� >| be�7�ha%a:SB ��"��$�\  4&"$�2 .\ ; i � n, 6%o7,Ml�G��v>G&o �S�8$ultaneous �J�����F� s ab�YZc�3� ��f"�03�&us�.C � 9��gh*� >h�1��*� ex}\,��*� �� r��jeR 1�box. �)*�2f�qT,�%acZ�/.��J�$�m-��Y�� $,� 1.76~mrad~ qui�Tx)"��)�:r�!er��B!��"8"Y"to� ~Hz,��-� l�[y4(s h�s�ut�ndA �two ``x ic'',�'&�2�. "�0<21.�1�aACA�yp ly 90_, w4� !|slE-���sim $3 !P�;#� �ik*��fh/A��$$�3 D � ). He6�e"�0al &�w32K8-�I�tE�kUB#!6�AaB-qQA T&giin �V._,�(.3�wDgen�u schg��E��. A �ed�4cC1 ous�s4t `iV 1998Q'Z}��k+yartQ .�.b�cmai�jc�r�ceSN�,!��#�6�3 �t�GInCt�ar, tJH F�;v of gFR,I!9 Yal feed�/ y�/rna�Koda�Th��nowT�mp�@lu�<$ or sapphiPBf&(�O: 83~s\di�10~mm) �a>�7 gl��at �en-$sar89�4�dYm!V3&�+CZM(tal. Surfacm�Kv*!{a!�walS/�&�*���/%M��99�%�:�s�4:�:N��8�;P)�?�cou�� h-��;ur*(���8 s (C�q1$�# �&14�&/cm$^3$�;c�U&F1.8 mJ�Al 8�(.7$�()IB�[d��YE\ s:Zon)6s,q(ion"-f Cs$�dimer.B2}.q> IA�(Z��,�%ii) los>Bk3ncaEIKG\Aed e ma8M)1�-iod�YM�N.^�Vpr"�V�` flat-top �]&K�: voltag�3�notpu�+��O/-4.�hQ  "uM�zA� �u|%�V8��' un~�p� cD$�� \4\���( >�d -P d�(�*I �(. �Qsuc�p�B�J[�AMgrok�*.� �"�$Sia��Qf-fa� �0!jna� M1� ipV84M.�t��edI�-�ns stri"�m�graH++ce�90'd�:x� gue02}�(gn( nt�2 �`start��'4%ry $9b9N�=!N�&2c ��=@d�A. We� w�3@"!mM���s b��t^ -� �)t=�G.�A�be����!�We�,fxsize=170mm� fWexpx$}&�PZz� $\lambda  5Sw }  4 $:5seri half�'quarter-B]p� �<;*�=l!s!V%�N4 (p"scrip�$ (�= p.)..�!O.w� �J= . A��2s � � S <$s(�`4��wF qk66ia�*� 1�f�K�Jtu�UaO�H �$:� �� ave-9: birefa�e�� e�,>^/ /2$: <� al 4�3%,5� ;$/2 :!ato��h�inz�$B:prA�iEed. PBS:� e�� 6;/w;(xes at��2�2�� (.� a�Yzer�IA\�og� rJA$/Et3T. $Ph_x, Ph_y$: InGaAs��di� a�� U��[ �4$SC S_y$1 . ($S/hS��Q�&D[3c m( : di�.ic !��S� 0ump ($R > 99.��)�9)i� :� �95���%�. Glan:-aiоlM&r. C: Eb��UR�!.�. � :)����n� c�^� ����=�&�PR�@&h al��H>>6I&�U��B��$�ZubiQLim� �*y�stabi�-.^0arZ` c�_y} Sia��?"�o�+�+͉y �6CSQH5hl$, s"h�0 �.�1� be�-G 8%a �9.KA�6*�Pi�T&s ��%>;MaOPA�on93 to� ruf�'m��8 SNR,*S lf#a�9�O� �9ata2�� o�Dna�i�^A�ime. �p��a��y��-��35N&J 7S"�>.�.,P4i��� rosc7$�"aux)\ ry C[ a�� fA�O ;inuouT^�1& < �T=����'poM>o�"�G�@-9@�� ��} Y��2I�1$�0{68l Fabry-Perot CE� (FPC�kFPC��.A��M�Z �_{F=3}\&� @!0.e-dd"��_'I��&s)/ !�� -)�PV; itself,�,A����I te0,ari�z&��=EF��.�[ (oAz%6�=^��*�052�)�2�� Z� 횝 �� 6BB�1%��91 C0!��99 YV��t Y9oyE"�<* tervsY Alh=g*RvesO_:ai !n�iAx�kevacuenem���Y�4��Ner]��M�Q"0a�|( megahertz �per minute. We first used a correction procedure assuming a linear drift, but the slope was not constant enough for the approach to be reliable. To do better we stabilized^�reference cavity on an iodine molecular line. \subsubs �L{Long term frequencyeat�ofk a`, $^{127}I_2$�0} By observiP(he fluoresc� of I �inN reg \Hinterest and by usCLtheoretical spectrumK.given8t,program {\it qdSpec} \cite{bod00} supplien*Tope<}, we found thatS!9 clos�toX$6S_{F=3} \rightarrow 7L4}$ hyperfine transi%Kwas= very weak'X component (a15) belong% rw)� eaaIx\set-up through a polariz!��t splitter cube, as schematizeda�Fig. 4%� arge2� thisG,iWi.e.}� pump,!�pas� twic!� �$n acousto-e�\ modulator (AOM1), shift�a晩by M�A�D_1 = - 2\times 200Q�The smalA�9�it, (Qprobe%��� second^�, AOM2 �)!.� $ y*_2e,�� !��� erpo!EC� ump !qE� vapor aE���u!�propaga! path. �Yթ9mpQ�(ppears whe�� s�Z{I��$\nu_{}$� $\A�{1}{2} (�1 +2)$!�a� nant�͞�(. To achievauA� se�1��, a�M�:(E�0tude 2.0 MHz, �19 kHz%�superim)kon.�_1$%:n,�L(lock-in det�' ��9ma#dI6 ���y �1%����^ can �(a,e derivativecB��tis symmetric dispersion-shaped1� (a�5��s error$in!RDeedback loop ensura]EZ  stabg�Z�0external FPC��A.c�_#��~ Cs)M�af�uinitial2�@2$ adjustment. IA�is way, =�dw ����re�i(��i�ej a>e�YE�m(al width, $��$ 1��)E�outa�terrupAz M 0PV data acqui �, over Aeods�>%R�Feveg(hours. NotAM3us)�wo�Psa5"(helpful, si� it)�es ex�r-rejY�any Dopp�!�gr���abs� strayͅM�� ��"=Y��!�A'!� �a*� �Aa�(st often su���)�<. \begin{figure}IET} \includegraphics*[he�,=8cm,)� =8.7 keepa��A�@=true]{iodeRe.eps� a%� { Ex!�AAI �for!Fit>n-Iu�:by ^Rof��.e:=(Fabry Perot= . PBS: Pnu.A 1, 2:�v�al1�(ors.} \end99 :U^U6!HE� VSA tre-Iod-Y%\)� @{\epsfxsize=60mm boxF80} \vspace{5mm.� 9b-)�6���to5�a@ero$, obtainedE�E�-�shown� �1�"� indR e2 �ѥ���*3 E* �A]�Da.o�sv $` .} 2� Ai�e<nUf aV�a�. >Fis�I�0o�� to maximi-L �XU !#Rcesium� or,�higher 2�to�� cel �3:relev��ٶ 2�. Beca�Q3$a.c. StarkF�(i_{ex}Zndu� 5exq̩�� valu�\he�N : � �fdepends1�Penergy $ {$: 6[� = � & $, ��2r1 $kept fixed��eF���2�6. S����� the %�" s ��lap) �e.5I )fs boti%FVI]��+ies, by6!�+ 1*� {pA ree�Dively. In our ope��ng#degs�"h!�! thus&mcombin��a��%�s. What�x!Y 1�)).>�remainse���!matomic.� da'a r&�}/ wher��=W�,��t. Constly, in ��}:=.�Mnoper!ds ��> �$zero-veloc,class, � beco5 "� :6y3 $c )�5�Q�/\& !�IʅZU 6Roccurs!�:�!�|� same� �. f-�%��)�be� LceY! 6� � � =2�ex-� � ex}} pr}} 3�IM $. H!�)� �/)B/2$ ac�anyA�!�Q� variE� a� rpre��as:< equ$} .�.�-2.�� + 2 �� \;Mɰ���$)$!./ %/ = 2.72 $ n !�Q�OB-�$�h!+>* � i���. �Df�sR ?�E-)��&�}�weM�� & sOonO6 mc0look surpri� . Ac[ly� {ad��al}�I-,!opposite�nD:�� ��itA�mted du� "(�y!C�I�#or� al� toY�resule"�6). A� X [K 70mm,ZL �Ee�  \"� Y�)�s�;�( Y�1�%�ezW .�,6P_{3/2,F'}$!��"ceI�{versus}�.�:� , dew f��!� ��!O�n ofi4 (�,text). Tempo2-E�%�$lap: 10~ns�Jorigin�ver�dl axis is chosen arbitrarie]da1�tE#�D 2e  :Improve7��spa�profilM�m d�} K e�delive��by?2�a2�By�� i�a� mercI�D (Lambda Physik FL�3) �/re ctangu�+� Qicir� ae solua�4 (Coumarin 153�Meagol)%� �a XeCl �mer� (18 7 ng[ s, 100 mJ�308 nm) a" repet� rat%SDWP%�A�Fing, align!�s2� � %sdes]ideal��R�%�%��be�� criEv. We��tr!��}la��jo�$ a Bethune%�-{oe�m��cylindr��yfnice -�r9 F �ed� onA��2M�low�!PBey��!l,��4unacceptable j�rM��T�~�5attribu~�turbul� 2< liquid flowing Ga;A� !/� usD(abandon. Tr��,g.�)#FE�-tor de�%�!.p<m3power���AVsV��% (note2Bcould-o a~l=�� N}jo 180~Hz�th)�littl�q)?M�,ay-to-day re]�� on�Ya�Q dye-q�.�c�7 illust!�s suc�typE[ �� B ")`&TB8��8.9V. a�� �-:�SV}�.{a�. Inset:� imagUo"�!-s ��De CCD camera analy�Za"�A>Q  inpu��CsE��t�a �es�x%�$y, horizonl and ݱ�6�D�D : measu�- X; g�. T � ga�d devic��car88}Xv!��voltagAg� (rapid rise-A� fall-0($\leq 1 $~ns'� >� � usua�aseDas $10^{-3}$. ButIOably due��humidD chan� occa�Jit�� �Z, ren ng # q&���si)# Inde�a� leak�'$photons goF.�``�!d''U;Md M3�� SCs* � � � ip�Z �,]\ ar�!�keristic IV � curr�1��l ed ; d�!dec!ch� at each �E���hri89}���$6 }$��te_�5$~\mu$t � life�-�&F�p�yp�e8z#ess� pop�c earlUgide: | ))` ��6P}��-1y%0y uA(go��� hibi�ly�b�!�" base�uzch{.c�  (20~nsE�� follow  50�:��/� decay�#Qdistor���flutesAI� �s�A�Pit��let�fil#%d TK ���sr (�� $\tau_i= d�tau =1~ )�A��;mal �rO3%II)AJ To prevA���b� sQ(!� unpr� \ behavio�H&p�ip install� Pockel�oa[series�� it. >� ^�5.�!&Z� &���"�\footA� R�et ��-��YY!�nk��!k�!e5��#AՁlst \R�%� 1T2Mw� i�( Ee����-�&w2�A�IP 6�. }��� Zv82vPentaPA�Trigger%}9m S^$u�el�' onic� itry feed��f��synch"�$t U�to�� 2�(``��''��!6�+OS&�b� d m2 fA�"� Aka�E����'OS���/id���d��| of ra;consider"'�"!&� m*� OS*Sa w^ ro��a�st�����-�'m� color � �'W��wavegu����mis���91 $\%ip�B 0.4" ?PC5dr� a fE  gE� (fd!�� �!ab��2� ,, imumIH� �10����3A��A}�i�T�8,�� is le��" $8W \(�OSnsM�$#�shortp� 3O s�' {�8 also%�s�.f)�PC  �N � .rplo�ed..with or!IMPC*sih�:{ �+Ahva�aX ll�a�g;!ԁ[ . W3'PC� ��.���.�e�nd,��$  ��V�OSEG#�J� 2Jdis�' :o ��V��2` �o -/����� 7sI� 0whole_�ABa techn�iculty b �f�)NiE��ɲ/ is .� 6�.As sepaI a,imeJi{1 ms,%ma�!negligZ �� n�t����6�I�� r��� �%�1 > �a��nk fau)%.��z&@-� !�� 5��'be&�%N#A� �2 1�� )�. O�Go hanM��.m must?��&�� &1�a]! � "�" avoi�1t1+2�(�� 5~$n�tI shot"s ]�k�,thyratron). � ��q impl��� s sketch �~9.!�t� A��1tqBng�%�on�0qui^Ba� w�S%n,�d� no`2�/"n$p#�Gry!�c�2s (iC� "Q%��-me\6 �n).!2�A biref���-f\ ;I\8-tilt magnifierB�Princip,b9�.}�)an-E workcha97�sugges!��/ a di 5 "C1to�1y�angle�)Y�mQ!!�*`/assaga�,U�ed�xa|e�a"sA!q0n!,Yhe2�3A-orthogoW+di��)��0 inco� ��CNB�a�)+�2y,attenu�>� �lle�v�� k- .�E�lstN.Y�.4M�car� ��in8�,� �+� tiny �F�)�.. Le�5,o2a'x�%!5Vi,2�)d�$ (coefficient�  U��for�żt�.�fieldg2( $t_x = 0.5l $t_y �,�$Ū� wo eigen-U �x 8 y$����� eas�} � F�is �Iti%.1O�*%�-e ux$]� is m) pa52�ght� ��ch���or?diO �4�&�``2��q''� auto�2cdleaana84-SNR<%��$�lim2wM7nnot exu6V-SNRA�ro,���'if02g4f � oIXi�� 2[ �$ �!�� aI?&�) dam�u�0 &W &I+q����Z8}� A��As4�A�.N C�Pb�(%[%�&�fac!��$(sim 2.5$. W]1.5~mW dtQ  avail�� � (100--;out*��' 4&�2)sa}[ �e�g$�7 - 6P�7�7e�best sui��to PVp ��6mwB"5I!ed� 1LIfJ2 ai��antikASA.\*,$\sqrt {2.5}'%� >8w�a�t  � U7y�y�e='ro�� ``uncross4mXeaK-{quasi-*��of .�2y�reby, t�G�e,  a-s��)��+&�:��well-kn�- 4 :u : F�ode��bal~d-u��]�#Y�i�i!�"� m 7.-!���� �l�Ir�U�.up� ��l�mon� mea:� R��S�'I *��o4�?�i�%of"��le!�te. ��lay�7o"6}�$7,san04}, *%�K su�9dH�= lems�+wq�?'�*cid �� .7 �� �.A�fi tur�/� �ck-04 or 6 silica �s�Brews� U tA��.rrha� y�]I��2ed �0h ��4 $ 2o3)IC2� is " !yi�!��AVr� ce�9%{� reflL �4 Q&�1� wedg��d �, s[:aqe#surfac!re&� ��li!� . A�&IrezsAR!m���͜:�ѥŔen�6c� 6in�.H "��� o�a$m %�:r��aQ�� . For p!�(son ��e�a 2/���\!VU!Fn2,�al. N .thele�,aaan? ���;5-Epeq�!"�  o|a6� g"wo*�) half-o�©��>�"�.Q*L �řM�er�H�(&�$:�>-0e�ei��8x �,D5S�sf�/ ;�6s�ac����j���cali> �>-U"�ha� 4$\theta_{cal}$!�S E4ilon �,$ �:!�+6&u-$0 at��!_�eva2 $2 .y \Ts \lbrack\exp{(\eta {\�(A}) -1 )}\r!$ $ (Eq. 1)*�5AMp�+ih!�m�!9*� ��8&�4� �� �)�A y/t_x$,^%q47.%con�e�s.�'^+in�,aestim�Mi%iD/�1.5329V 4-pl)Iq, h� bar���a� \�J% �(*~ -�~ ��e 62[  ����, slS ��b|;$most $20\%�is �!MulT  2 stood w�1�� !� i"��>�ls: i)�xce!0&�C e�� � �R-o  pens!@aA&�,U5�=�)�P($ t_x^2 \approx 1/8 !st� of 1/4�A � ~-in����'[of���>corqly�> ii)�-ة�-��m-R2I@&c�/�Q1^2ic�~B sta*N howA'h�>m,�ʥ FLE��im"� Rz�par"Ze":. Resil!eti?�ect�w�F ��ź *blcy l�ouM�)-�;�J"� �*E�3op����nt=f �� "l5y�_o �d.&�!F���$ flux�^� r0z���, (� thougq3E� g � 9�isM�)%oh�/]?b�A[ �<g&�!aL�-� ers,a�2re< capaciEj.7A 4 nF � b+dg dynaAP YA2#E0� � {Control8E�&� | j (windows } D&$a�1�)oasxN�0hire (n=1.77)�$ !> �)�yay m!v��5u� ����&YD� U�7S��al d��(� V"� p)/of un%roE� ,�.F��� D0e 3 worry �AQ6 sEA�I wo U� recis�nm C d, n'"�%�'0([ � �Rn 1~mrad�"I&cInt�ii�. �s:=z��} I�0�%u��B��!0r&!n*u� .�W y�l �. DQ,!Ion�'���ism�-y) 0�#es"-or)33herRe-tun��> �>��jah00}"m9 %�"� ��s, imIect.��[$ed5e��+�a`9L .~��)� eq 5� �(2�(An2v p�ernW)�� uish� s!mea��1q �1# �/r2ntmava�.� " 1�Nimpac_]"� �e7"e: tu%A,-�=�a�2(d6�9(} ($R_{max}b. ) c�&d{��E�. Alloe&"Lt%�s? fab�0!#\�l{sar89} � �s madnM�"r OoKs 0m} �-�"��ismIUtX 10�( rad �5�6 mm dia�"b4rnL�E�Lgood [0001] crystal �*m4�$�� (deE�on C-> B+�^{\�0�6> #m i\;E�3}$! a:�thick-*).�!�ct��6 l<) UaD ��#%����E�s cfew1 s"j+ $�# �%Z�& .W�) (to 0.1$� C),�����0� � � bK7 Gi�,.�!n�i��0�K�%�minimaA�540 nm@�6�%�.��CuFa�rvals!914.���FSR�Ospo@to 402,�5O � leng{I�;!�B-�C ��6��"%e�siG aneo�vaqs. How�F �w!X&� point! eܥ�$14=� iBk%K&4.MZ (210 - 272)�chok�H�F%�e���R!ic�,D�e x%O�e�Ad6�#n� �==Aa�:)Œ�jor�.of��� -�a $T $ 9_ J�lea�[iFuKr � !U`�u�e #'�ik�to���1�< m�E�>Y2 ��C�%��7K ��� �� . NoX a�.'��o� & ,.�+waMS�nd �� I�ȁ�}of�!fG �2�ord�hQ�we do ���associ�eA 2�\Hf!A--bo|<M� - ? accx!���O �9@e�Q� � %�is � .u22���P>{%g� -odd-�:)�?�h!�.} &}&Y!�&r�-"@Ak��� � M�a�ex�b%��.��0s %w 2� a 0 . Al.Hdx9.�)s�x�a*�"of���I��g%f!�� �{L�Qm9%�%WI!�2I82Z�8s psi �3$ 81?7�" brea�Q�9�/rsIs%- a)� 90~PV%eF1L!� we aLq"�;a5s��0 ���s, af!7�$7_ simi�;sAAi2al %�W ��M$�8T��H-$AP� orm� yu��h�=} nWI%dwh�?81�)�Xh�d.�) now �Mi�#i�.�$Rchu�S�+s�?��. (An�� view���'AC+V�� IV)e�IA��j� bou03�PS 4.4 �39����a misor&4 mo}�w/:y:� g",�rR-�%� �*N tI ^{pv"` �*���^_{ex}$:"�@(eqnarray} &!B}(F6)E $ �$?$ e���1rP��iR&h$q�,�Eo�Ec� a� r(OK�;f)��e�i��K=y�enough,�a�-quadr�2�3,���)n${"�n�"nt70"�.&� ae^lemo �:�V;W�DA�!?>ih>-� ed} 8 0 � �ch�mis���Xy�. e&de�!O-�'E�$���� !8&�,� 2n$^dsɀ�j$E T:ex }= 2 ��]F������� !""-. ���C�!��,��\i;Ipsi$, U.s i��, 6a/3) ��* ��o�J`�0``isotropic''�( &RX<�l9.� ro��oA (%X6�me�pr}$),2�g"�4&�H <2�>_{Fu }= !$!� R� n�sKm� ��>� \; ,�=�dL$R5�M�!*�(!�!b2� It@�9� PV % "�&E2eI odd}�{Ig�\�Sa]W����have e/����&�*;d&j� 9 �lap6�y�eS-ed��B�O8 =� �e�.0!BiRly�~mmm n"3�����  �-� }A;�?7]? O $R=0.10a]"�@���1 dardFP��/!�0)� $= 3� % �</E_l= 3 ���Eq. 4 � �9 $���*9 ~\mu�o �]%90.02 $ ��� $ ($R$=0.002. "k{ �} F�A N�%�� ��;*G)!$z 2c�4>Y�����g�_3<�<tE&_�(etd�>�3r� Four�� �TL` xN) �T iJ'!^fi.our41K*� � s� is�o0���t"� A�`"N�/InV!$a7 *�!�}a�2��� F� �6a& g� �,IpTn2���<ic�oleQ�A,�0s��-}�  $B* -B�U�Z�YI�a5MF� . B6�A�^ ge�%�]A�HV �odes �am�C��1b3aE ����1,M&-}=�E_l��nd$O% %|Bg. UE��j34!� ref. �u�X�� new " I\� acF� ex} $: $F&� ex}��#z. E_l)*� ,\omega_{_{F'�S�?\, 9� -,?�� -�)#S$$ ���Iem�5�{t�2~mG (2lLarmo)�dE��4of $N��E40 ��� *�we1e$J� ep�'� }� q�412 ~�\mu{\rm�Z Th"�(aJ -�v~`�'�e�pf.D �q A" lo���!Abe�8rm� � >�HA2�Ze#Q�(N7H7�inn�-nd> eOa�>Uo�ZqD�}!e�t��42A�si�6�Pur""" c� n0a niobium, 2~B �� ick,O- delea�}n l�-�= itanA�pZo!1e 6� �h&#�(�� �+�"�s�� typDcZ.�/s��be�e5_� RA- �$[HV pot;!�a�^rS4 y i%�"c*lYby<!lt]%�g8outer}  %he�0f ǥL��Won ?what h�.� ��isINh/� QQ�:rge?f"^A ?%b.(j<ion0 �"�N�ly�e>(ŚtS�3!"!�gɽor �2tai"�9\H-. �:vacuum-tV) glu�of5!E�E!�bal�A t,h� F"~.�*@P � oxid ,�<9� �0David Sarkisy'Cn�9- :er5 sar04�4a��t��)����� �����3SNRa:� �2�B" 15 �A*�]/ �MvA8�j�*Em \� d((described t. V D�C3�"�D`/!5�$!7UA?�6k@@�J3to� e3�8f�+?t*AO8?dɏ ��l^{expm-%agnK{^{nom}$& %�& nume"l?��t�in!\cc�%- geo<4AZ= �o�ss�!�Y�CI��(U9details�.��%0 rCex J�ar�2�=0*?!6A1!* ��0ej��H, i!&  find� -;/E)& �998 \pm�1 a g��X'�eS,*`=�6R� RB e.q"UKlBx6Cof啛:C )B!5�:����Z%�4�b�q1!�xAurDL�E>A$ u�L�g�m} ?�o� &^[: �-e> leavS�G"D3 � at'caa��,U�!le3BIMN8'1anA�),w!r�FA�LB�i6~. Appl�1�H��&� �e'sscree��� 3 B �+,Jval) �\��%�9�36.�1�Gph�p�re�E�*+> �I�apɽ fi&i�n�w\4nFr �cal�Xd ?!��3:�@NetY���1S/N�R}0^��Xs8f.2s (\S A�E)�Pm�[f� �j runs�����bou02�N �"�-/�,!S & 2."�!��{ � �9sm|[�. V.AɈL.��}�H�;2.6 ( �ly 5.1� p'��now 2.0)�D%>�Y6l�0<�X90!C16#W: �0K IxSNR� a on�U ond-ͼ�Y'N]2 91!S$C 3.5$�2 A=)a�L"�0t�a=WI!�tU�rac�r^> t$1!�!.EI��85i dunew.'�5puriou�Qs. E2'so!J<5P� ��ZG olog��T3:!DdOnc�sOck���;�Md> (0ee��85��%��M-�o�[� !B400 Hz, liz}a��B� ^&�1�.�!��2�-> ~1.5 L9'� �& ing �#t&Qx"h� #bX r1� t ����kdouble�6�[alreadV scu/=A4T!-�Evalent-a�!� hcha97,a�5� at,!� aMQ=of �"CG�T, $n_{invquantum ~)�ede$per� '.%� , $$a@=�  \V> V\U�A}_{av} �6�6 /2)}�08$]aVVly!�fu�Wo9o�+als!�ia��par�Yd �>� n*�6,6d@�= �\pa�.} +�7 (\As })/2vccc���,s%��:�$a�3 .�6.j.�7.y�#AJ�ZLa�.���^l,"� chec� �a�meu���kv$�&"BbYU+*�b"�O&$a0 ��e*$.� �(D >�� \heY�Ixedb26I6Bum��� E& , $Nk� l�/�.�d��- 26�}�� Ev"e�q'AA.s�@o�4A���steppA�Z�8�K8_ ���o?Z%˅ �2risk%!{s �ji� *��w�h:�%cS�w V. BE/diagnosiuatA�rtɹ� I9�,�[�"~n2d" C\*�6&X ,F=4 ��8,�}Ss 9 0&.!S#ņ���Y�$A_{LR}/��$ A�1.2Z4sp. 0.6V.FK>�4V$��{A}5<�6 1.0)`k�` (�.%�)��mN% \:6�5du���N#^ ds>�&s}R��� Xe�'B#-v2}�&N�d5,F]��me��dopa��|�+ �E`m,�/7��p��i�>'G �8��;II���+�-we�is �� c"�,de� aV <L o�ce�5y~ p � . �>7+�'4+2��*_K+�r/5 $\vec�$}0Ea�S-bb�e�z^�~  Its �-)ہ�!�mo1�u�� feZ!.) &��+��ma:v"�* heli�mkC#z�xis)�$B2���ZoA��l M LB�M?axe� hai/-�A�ng� K�6t�o�0��PVE��$.� �x�C�6�+as� = 50 �$G � !�)�� UxA3�M�z �^YAWea\�i� �b>߀���?�*#YyU��atD#g�es[a!ple Fara�ci&.95L cs6ol=&�+DsEI!va*�l�� 1��v�סt�S� m@.>1g}bR:���"WI2c6�N5}$E!�10ŵs"�!�!��Y1� u6xlf� ed te&�(q+�M{e APV�IJ�Aly ��2�jBd ��!OU�$�W!{ ��dP�5 �!�UW�(Ma7E�\aqe E1�in6n� �i�r�4!/"�ion�|BKaeA.p| a ``k# '', �I,e%�X�/iJ#�8d��?��YKBp��a�&��&�m0e�Y��W�d5� 2�!3Ň�#s!S�Z%l"�1. Brw��%=>)� I�S�an�EVOocas�S ��`t6 �"ma�7per�9*�'d fa&% ame I�of��wous (�4P#$5�6)!Rm:@voD� ��-gA��b&Y�3�60$#�tot� a6}E����m�H�5e�~a&239 }�=8o�*o*��9I�!��a�*s� 1)�&�BPV.�W:*Eb1_52a2a� �N�k} Pa�U�C%�"OR ��-�at `�NNZvs�|,� Ac�%m�u" ɂB �> �,!�Qtwo�(s. Our s�q��3}���aRA�.*4im�M��@l�bA�ax%���A�=�, �wo1}�n��aqNSo&-`s"y s (``�v 2''-.i� �) �� zero� �w ��:�!�2 !;,*O,p�x� v#��4&<�!s~6oc��">& "�-i�@sLe2 �1�`[xo�Tdo ��>� � �ivmheyl�%� c��a&IX^"�. 5seJgass���@@!�9�t� s:�\,21.�c \no4<(nt - 1. Pumx0>�i$\71 >71Q1!�br1$a�m�92ca�* ]e ݁�A/�aD6�by�' oupl�,to anO 3$:L,.�1���!u�La�~Q�}�<�}a�� is: "61d!bv)to" h���1� �.s,��Y ��e�� ce},y!�D�NP.� ell,.� 3.Irref� gue98}); �66�i)�-mv.�%+/( �Zc�Za� next��A�H.Yn 8J J5X� ){l�H� $$x$ or $y$���nj%K! �� kB�V/_�R A�9%�O�`�gue02"AM%�-33psC6�*� ��  5AN] 2. CQ�R��9_t�;JB & .�A2 ��q:�#B (%͡-� \,, �D'!�!x#-# .$ -}$ qgsHP��dE� �A.L(a�^a�X��;�:<)g@ize�2ej r $ B_x�6\� � B_y)A)y,g�T;m E @, - 28E-�>>,YevBN8Aqi�tuF I� 1�w�\&� 6� &�z0 @@PA��~c �mɽd: tPV,(2�yt.Y .g6@ (1~Gr/� i nd ��y�t� �Z�!2+9Y�t���SN�&X o�Yll-de��A�t�d�#s�Ft�>t�I}9,E!���aTys2�5�Ni��E-lj/loi�BS� �He�w6�%e5bT�M� T�FII��wz�mM��6h�"�\� . From ��$��k.!$6� ��neeNwe"+8)I� ��+�Q .�%�d�?: %�i�a([&�c A� u(Bt=� �� 'e�A�"� � �p�@dA"�er = �:um!A� en��!.'�d��A%���".�.� pm�-$)�l1�� �i� E�Q��$����? milli�lTstray ���-)�!h�9s)+ k�� �V,>mb6��rbOUd�es Vzew4?,���9,)&� %�!1���1+Qo,X.`?A.�C1aA�-�w basi�-nE�!y� s  hZ� $%>yB u  Y"n uncer�)t�X!E筆.�SB*A��Rb{#rkbi  sigz;,ly non-zero.�s-�Y A��!M�Z�� s�e�b�z!F� e�BK2�\Q� $\# 4$R=�:�� "�EJ��LtoQ�\ru���f3.[:'na���&&Fn�:kzxEk, �"�i m}F�;�<)6fu�h1��i�qC�f^  Ba(���|Iem��B%MN5{t�^wZ;� M�< msel��!e�2u thei�es�U.� C)��� 5;t�i}&�oM�an.�� ,2E�Az$-{�>}E�lA!={�E"�  ���T� Yo2{����(ular}{|c |c } \h� DeF7& Ori}�&*r\\ & �)t� & T�7-�E�&YD/�0)!��}ltB� ,�] JP�!em�}d"?* & C)�Ie�� - l$.eO ��T ambiq�� & Co�V��co]+��@ta)/\\le}�p�PF �sruA�)O��b!�o�,�M�=6o$�Fe�Vid�=�  exS1&�!`�_0 %S,�E! f aS8�� �.�C.��!w"�C�b. 3F"�AN� "�-�e61BP.GQUj���sB_g% exac��g OV�->�b)r��z�9�"�_�2� R�isM�%K��8I`� �D���x2=�a� -w�!V sed ���} ��� 2��&F�}1� , pie#off1�e�i!'��Fig 3)��""��A��$�_0Eg&�� #�low6%"���Kgloba}b,!T  M $ ˘0.030�5m ~C=0�5a:*�\�4�'ɔ͓h�}n~ ? o: ��*�T:.V&d.A*LM� R�� {Mis1�iv��* 2��% s} A�^@XO� 8�Hitself�=� %�. p- ��$a�.� �p&k�.g.} &�T(NU �k2�:p_B fact�#re��tits�(��t}.�3a��f��Z �@we\ � EW&�2`A��� �H� E_l!�M� an���9(8)� � �ݝe%%n�`�Ei�m]AA�outset. 6�a1y�:7 };:J]bS�@� a digi�w� e[,�.�9��XIt ��1minRoman�}&�s� � �3�\�}�u�7}e��v mon�Z��.�s2 8��!#Ah quR_�$mogeneity,� 2vT..."�}=�*C ����0]0�%l� rre<i�\S��$[v�A�thA?l��/2$�#�|D!*%&Y%Da:#�Pr�"%C&Abs�]ul�J .rRiRr�% �w%�f� �r&�} O�2V-!�� �)^�)�yIJɢ"1 !�u0, $(S_1-S_2)/  +  �9be*[]$I = SE�*'Ve�Ya"$b?B:t�&�}V� �t�)�w�inAJntiH'aq�:ed:/&�'� &cF �' \�, D_{at�# mp�KD_{ref! = e�Q�d�)~�,Jw ln{ (I_{f/I d) {"( ,{A}}_0"G.>��'Eq. 6`, ,�,>ne�3�^� c>��F{�,abb�}Q{�r�Ma $6P$ �Wof"ll�?n -not�� |d o~ d� yofI�t{76a.�{ 6�(gigahertz a�S��forbidd�Df �. *z)_0$�> zm�7�' $-4\L1s ��2�.�Hr%9��1eq �~to6��� �% ara-if�!�&�)�T��K�i�p$|%$_* $. hW$so��*e��%DY� \va�U ta =M�/2 Zf{A})}-1&f\,q>: l s�P 26� ��"+! �q� �F1)��'no�S1!^�|lo 1 (.L� &9. 1�,th�b-o +�V� ed),���Q.d&"I�` $�0�N�n�_{h%n +*30!� secu�7�>�/�2mo"�st��*k/Z!�_amV�' �m��bF�57 $U� � �� �r Tpuݣ�nrvDs�)�sU]ceA��2�/!'allA�A�pi�$in �1�7+ G�ȡ�q �/I?G �gm-r,a�_E det}, \s pr�m\pm�ts�#ax� ndom%�ble]0�p�-~ APV �5vߧ�""K%��$2^4$&��sor5�$f( ��Mw�$���, $< &)�M� } = �M�� (f(1��f(-1)ᖥ�i.exv-("�FJ� '�%�a!K -F�u-upB*o]��0�-[PV�&lpk�5��*�7�%� n �&5}�m�%i , $iB!l�j e x,͌u, v �je$�o-�AY� 6r &�,q�*��_T < G_i >_{i=A_"�60@Tn*[T�#D < 1t_A�  [)� _2]2?]E� ]� >_{q_E�5u�} ._1Q���$p \squeezeQ ��"� M 2�B (��a�: R�D chro&j8�Fѣ�\ta;h{|p{1.0cm}|p{2.1cm} | p{3.7 1.3 �1%+\\:p \cA�({col1-col2}34} ..�#�${\rm�~of}$  the~ }$ & $Probe~hfs~a$}$ ~~~~$~~yF� 6�,^{'x2 & T�>�� & D� \\ � $~~~Iq F=4-G=5�/H� ~PV-?}50 $ 60� \\ &~�\&~� �~�~� ol}$&�5 7�9& �4� PV$-.�$ 9�~ -�}�|�V}r�b� �X�( q r% tIende�jA(6$�W"�}� .�-reINing���aboy�x�'��$� .�(? 7). 0-�s�^*��r�v &�a*nT "��!e�A"� �+ ({l} 6�Qtoa�(:$&�B�rу�O=ns~:�J.�du*$} �L-*�*�Xit�$b=�ow��"eu�� �{�6�a�$n &��5J�S� B�9��t�E�Wa�Q� s+ *�<}$%Y�1 exU�OeJEL�U��J:;F-�YVM �M����=��]�<,� �{!!@ 1�C�]{, � some�IIaEzc;�#? � :^ �� (30.@ �Rq&��+/(7) b�)_ Ta;6M3X$\� �A u�S ef�)� / 2 (p= {\h4W <*� yt }$�^\��u:# ycle"U wo.KY ! es''��S_{xyw 1  4 (G_x + G_y) $�)uvN)u)v)^�6��""� !� m$a,� vie�us�i<iso}$R� (FOly*=30! � M�N2#ah�` !�"_� 6 �&X a�e*1&� S���&&Pbs�iv���-&�s�}�ec�=!Qmain B� &� �su�%� ~III� � c!� so-�ed� Y!k$6�eɡ�en�I�($N_k = 2 N_-�� &�T1e�d+a"� Ez $m_k&%ta�X�"_�k$�&�[ 5�w `�$&� %�6�c, /x��J2om���'P~I,( ��,_K"I2Hd*30�1�E �| j �rujb�%� merg�B�)w�w�k/~ k�>toFifB��� YAl��wtA�N!lʬv�t-�!%l� �2�i�K^gl��I e� � ��atuH�? wdatum. E� � jmen�k!��$"p<V D#.#PV��r�"6�s5�z�$.� ye�Ɏ"�����s::;tn?-n?m1 wealܝf.Ɇ Bp! &�?��o=�N��Wly!G2h�IM�Xi"qrs�E:� $-$ ��{ and Ɍ("_&y�*{ehoDZbe�FpA��e�Pn�?Au2� (a d�=e�#g�:(` a drop�$Ia\}$)�F�A�Bb�2� �"3 �7"N�Y� R��o u��]- .�  �Ref"�u�O.0�a�1� X1� and/1�E3&J"��A�tl����sH% fP�s:�1O 1%m�P�P ��1�cN�; t1 OQ?a��0�� OgParac "�,&vhA� 2�?No!Mp�rt�m�&��}��ai:@�"o(1c+_ac�� out�:�R�p�!runca�# S.nP.��F8.< ���w[5� $tA�re immed�l �e�: iV� _3� i�Z5��@s)� _Z(&� C&�� ��� 30rxL), hapWTa!�)��L��/)  ��,[.�*�!� igno�9AG= " w=a\�3� a��Af�AMPv- }. U��n�։�s!%briefW5�/�;%� aόab"�{."6.$a�[�4 %"�;�r��� ��S�to&!M�7i��l��� , bu"��yR;�#" O%���OK�4h��8���++$ 3]at˥�^n"NF E.)  %�1er)�al�� "�!y8q�b#@lf��X�]mF�$+1reeJ��. .`Q�^.[ *�� M��!.�H�#"�] S�(�! 1\%$,b��H7x;ed {-� /u�.�, 2.6$\i�3�� A��%x ser-�� hops, o)rZ%ct)!R�[�?&^!�3qi>�w/2�.~��6`.�a�"�Sv1�kc� =�"�% r�NqN bias�A�nd BPs*\7�T� ���A�3 !en��� .i� UAYe{?�sc�!i(s�!�M��� ]MAA) �� A6 � �;4.a"TB-IB-"��e*���6e�j^fx0=15� *&4fbox{Run1-36An�-� "����"Q�a+�=:�4"� 0 1126�z*�in�@\#4iA� ��xy���VD_�$E�%Z aeit�g���Wr�!!N%qe�"��%t(�ڻ� n\),� al1z ($s %��C?'l!�?�\s�/s��m*� ��nor��(ay� . See tex-�zkC"�s.!�end=���� 5�-�ic��"� � Q a*�D,��6t1w�,t�6in �b��F%��X & *f�&�* GBnb�9�% k-�؍,"�@SS7pX���.;-����.bRqAzCA��'ed!�*3e����*?tad!�g<+E� sis �:llI�0�11�(�Btn � 91A UV<1Y%onwr5�c�} u@1'' Y �@*�?E�h�=��aA�k3* s $ D�=���-�� i�:�G_u-G_v}�A�M��9%�s�wS�� AQS!�coe��' $( �,�% uv})*|a� W�Uc���&; �A �UEEI����V�8gr��IP clou�3�s{�uld7a�"�e 6%witQ�Ubal�IˤI�aPI ��Ko;% Ano��-#nt��. Her� / v� 10)F%(n��\#44���:eL �]AiA��^"��a%Eil� e�o6/~ appar� �41&A9�R�^of:f�"�kXbwk�g �+ By�as%1�i6�eRa5��s�/s�Oi]m��. �Pot�p word.���much m>�]"an�J$�R��uv}~qI'�F:.�!k* !�to2� �"��/!4!���r� 1%���~�*�d2tI�졹!�"� psi_x$ (\�|o!.��xE=9%<)�ha}?%I* �2'&KD��r�>�{�8 q ��S!�*^r9&0�",J! !-AB. ��� &�GqE",!U%pC2A]� M� AK�GA[s�Q, ��ph�(�w��;d�;w _y3*�N�p _x /�Aa_�4��is��a>>�war��c7VV��A�� )�ZwJBE More� ?d*h�;ͫi�<! Z 6~,�*��q��K�)u�ies t�=tqX�6e��0LS�th�8�Yp&�+ �C  ,aW/)c�a�!ra�� p3Y {D�i�!?�0�Am ��!]+of �*�a.od7��y�B���DE!� P*����gdfi�,"��. disc��o���RAGE�� a�*��YhiHf02E*�f">}���� �Nf~@=�U4AW*-02� M�?�#!$�Y�Q2 ��k!| $.�U% f&F�Aa��e i�Atu}2k�}Y��<&�!!�Wt�/a-6"�V2��&� �N2�< LX IV F�wBre oblig�"�F m Nu*r>m|ma& f_:M�?.�AJ�C '"X_���A��I  rzz� �o�KF"IdE+[�h@~�15�on~ ��2}. I�!h~b�*�e)7e!.sA�"ucq��:�&:E�&� ,3g/�g�d a�bpo�j!Ia�e[- �n4�Zqftoe A�A?$|`. �ibasic�#� l5-����}^;J n |1+��ca�!� �&ֆ!��*!��anyڍ|"���EA�VJI0�II5o.�P �b"�C"��Lre�& �:Xio��� "J_3s )�)�} $7S$p "�� 9&+X,�0N30 $M^{'2}_1 �)beta^2�;^2 +  �!%in!�ɧ�Wo:5�5 x/ s, (Y}_1<#s�� $6S-�Y_�3p  >-M})"�eՔ)�y�ioe/a�=u@.�Jt�/ � E_l^2$.��>l # terme!I�s��/%o�i%-+}_ ]Zy5.1=. 0.n�Ky�a88,ben9���o2�ecU d�����$"!!�u:.Vd-H "{\ $� �$�ms2d�fE9�7~�;C;�Ō� �%r"� �Ę_lr�8M. toBC=pr�(_� }�=i΃M�.�_ al� �� ���re@ conn6n��F,�"1A/beWablis�9�b�I�fory=�6}.B� a f�.a��i5]�L��T  !eE��aly��&�(, � =��+= \;�-*��_ b"K%�3��$��X�ngU Nll �k!�>^!;�a�se� $�%X = 11/1�7S "l_-<,=4}-6<,:�G*s �-!rigoro�� vali'?yf� v�� �\bt�� �$t_p$�s�d"�decay��(gamma_d^{-17�$7S�a" u����s� J_��e7C�d_�cA0� !![*d9e($2�!g3.4��,��$0 \�{7S& 47.5�M "{)�y��e*��a�1f� L odel� hougdaI\9+8[$uF)�?r"*�Jin �(!wiE\sS��A���=%��a��e�n&��-� 9b9�!riMi*�96} A� dix B), u��X i�{a routߟ�i� by M� a�ca �vwolf}.v�M@�+o�_�am� �a]�>� ��B$E2Fi3� ���:y���,?j >"� � &2�B"�'i1 (cf.46) W1� $lnB~:$�T� sA: ,"�tial m��9s-_��ُ��$�~'� *4N�V7*]$�� }$ (M&�1j �� �4}$vO overwhelm�C. �?)}�.k9>J���" �)($< 0.3�I �inN=�� �Q, �55 f.I"� o*WFxb ^j��u�^>u* ;�) dida��Sl��02}�m� +! x al *Kg�&Coa!!B ��"�T�A,�7�ɭ8%�N9�}at����R� *�f�&k�R��i8i�cha98ou�z|�ta���a,Nm.(���Q+y)DPR>  at 45$^h�rRA �)N%q�&�!�uv, �-e��CI} "V&��}| aJ.�B�_��*sC\*��&,  I�� h �)�/�� 2.4W 06��,,�wl� 4�L$+H7 %%$-�*0Q�!!"O �Aio!T*� �of�Z70,f#\i�(?!�d�)�f�& �� B$R4 2000) ���+#X!& !�fiIQ-�l���v� on7'i))���C�:�+��m,.�e.|*Ʊ1* ob�am�tj� a�we�E��kewt"�t 0��/S  ]!E7�"\�EF� P.�A:�xH��e?"�0'a4r�~1:"88b}&-= 70{�}_1}{I}�0(�9 qrt{ & \ln{� 1+ 1(E=xF)/2I��0x:k }{(1+u) � (E=0,M�(= \pi/4)}} 1\� ) |?D5��� �~$ �m^"�j 0.&7 ͸o � !� � %�� b� JE!ial�76�;�.Eo*�+��(��$-�Z} ��7&�ar:' "@  �0�3E�Ag� 6 KQT 5�h.49�D&m+2��x68�#T�R0*-p=ӈ0�2�& �%%�a����:����I�i�<2<;ce��)����lin�Aa�!J��$5�:r��la�~4t3$(�pO-*y�� IT:J�i:�$ %�B&� %6+se�\L� .X,\\S/lH����nfRi�q䉎o�l�l��5v\bФ&� �[B�:�C�Nsi A�ga0�.�z!#a4�$9� ��2E. E'JA%;2^ �$�e�!�sZo�2�=�_��$"X[�Z#���m�a�.2�~�plP Tvestig�Z|E�%^ � ".,ma�U2�wa�*�� ush c�Z5R�%m)��&B¢*@I /n(l��~-(Q�Hur2H22� Jthoq*�>�P�2 �e�lڮT2y �y� �Tj�oD�2y�c-�E��Pi..qE���  uROw W�("�,6��*Lc����PV2B . It�!'iby �!�s3 �  GAUpr�s w!r�-Pruad�8d �~�1ae� ��a%- G % �CG5i$, 0.5~��� d#ܵma�f �[ b��o  .{� {R� :9Fi,�~\ref{.�l��m.�\� a�AqN4f�F�@UA�b��in !�n� #��� �pdB0H$s� !�&h*;�$i�D"+7�"*6�� �i�.��)histo}!�sV�s�����&d�#���:��a�A!�by fa�����t�"dZw~6I+^�ed ��'��e��c�k �� !L!lD s=�ur �detres}�,+ �.�Ft�!��+�q�"N~сu<~�Y��a v�@�� ���! �m!:�pr�1*�5%ureng0i5�l���.�noA�lI �_���&�d�&H 1619)v�ymr-&H%�!i��'picuouf%��IOnoicel} �2re8"D9U�B� .�-�,�Ep.�V&�,.Z i(*yŴ�+"�� make!w�&%�" �'�).��e%*�zuni�%�lt!hiVs)<�P�:���N�|.  �*"F7!g�-�gre)�b*�5du&}5:. Oa�;E}^Wwhe$"mdis��n m�";��"''w:"�5kpm�6cyZ.���%�%#w# ;��s $Q^2n*sum_k� ((m-m_k)^2 /�Fk^2 ) $�re $m] 1m_k*�:) / ( 12A ���͉�ed1%Ł� ���0��a $\chiD;2�%� $\nu = K-{!��freedo�-K�W7� A I�AIA�_�P2/Q^2�� = 7.7/67 28$�hT9exc��0.2�o�0 S�N.=�e���!9#A:�,,�-F�pr?*A�m(���ir "z��L�?p�Se;dXC}���l�835c�b" etc}�̥C�#[ c0eX!  m,�de�e�� ������of"�Z!q����rial,"&�/av���� -m#�&�Nss&W� qh� heir·!7i�d%���ASZ݊%�p��i52�&sa��� �� A�t $ + �5!mqF$3 �� towa�*Z&(�����}�.�$& /EgD�&w��"Q D 2o�is�!p� �� conv�&ng&x$ s. PQs�3k(ùign ga�a �'6��C� broady�M��!b(Sz�!�!g!D��&k��AJauxili�W�pP*I-$\�6�bi�>6E"�'G2�0��q.��T unu�� �r���)�AE���as" ��ardm�F�W��Ŗ��) 2���� st�̅"a&AJ�&F��H/!7.�484l~4�hsx4Bc*�\label"� 69�y�'" .�($\��*Bi*j |4Bg "� j e/!.�mB^ ^�a3�B�zaY��lid~� � , da� )Ie: meanP~0�s�e' ��A_eau!�I1 e:"6}^4�70.��fig� )�&�M-�} RA�: Hist E�\J� )} 4!%7� E ly d� nf AW>)R"9`��3B�%�Fx . �688.6D�-�����6�� ^�~�8�=�:�Iz+n &q��cc"�4(� �2i &f�eq$ 4+),�3Vie"��a�m �S*�Olyx��msA�>�n�gV5A�>7���J&"7��Bruit�d��Bn� qSBh: SDa�2� .8 "S,values $\th�Feta^{pv}_{exp}$($\mu$rad) obtained in each individual cell versus the c�Xnumbers chronologically ordered. The error bar on SD is estimated from the dispersion of $SD 's overqir#�h datum instead of averaging>Tvarious runs made with>F%| and4n:C)ms QJcA/!� !� ensemble, Y �`s $\propto 1/\sigma^2$ at ystage. %8Q In addi�!A�A�Z�,�:.includ�Z63e���-greg���. We w�� lik � argu��4favor�, small scaleNf|. $ \bullet$~�1 - First a� wish!�reitea� � �K �~!�$ electroE (EW),n-hadron inOE��I(in a range�low mo� um transf,$q_{at}$ '1 MeV~ � eabou Cesium c��es��hugne��colliX �$: 100 GeV� LEP~I and 1 T HCMh�6$PP}. �At� I=ies�.# ampl�� ���i e^2 �0^2/ M_W^2 $.�y 'to�ensate a�t� E edAgIfa�,q�.� havEPbe6tvery �iial con��s (on aelyt biddY !�i! eavys). To� qtA ���,� ha�yappro$ f{1�8}$kA.�!KASdia��E�4 LR asymmetry.: 2i � ) \sim 1$Au)�quarkų��at�L��us � ��co�� ntly� lO%;UB�/ons�Wbroke�to ir fundaa/� ants:A �y then |in~�(is what hapA6!>$deep inela�  M�n- � �Ette] ,��� SLAC]Km,pre78} invol��a eGQedqn beamm~A�aP   fix� euy� �Mt. As a�h sequ�, �Jer2 a bi� %�j-%" PV%uplo%I!F%v ���]#ies ofIh#6' �$@ <2}{3}C_u^{(1)} - 1 d z :-��N$( 2Z + N) M+ (Z+ 2 K $a~�\. It!�easily s��e�4model-independ!-analysi��:� de[ >�ogo� allow� andEA�� $\lbrack �,C�\r $ pla"�bou97}a~݋ 3e}Deva�a$\Delta Ba�K^`�!�SM���� l oftB�A{� frameworkR�u``newl''})5s j@ EW.�silJ$�2e�han $M_{Z_0} c^2$} through�ex� � ga��bos��;� tD�$Z_0$y~�� E8< $Kaluza-KleAitH�TSM 6` ant01}. A:tu�ou� at�f2xi� opor!`al�y� f�] $X=H \pi^e @ R_{\parallel}^2 -}��d9� �%!i�F�� � %at $q^2Bp\ll 1I�� $2� \leq��TeV$^{-1`stE�!b�Cctificũ �i��ssocij"�al $d.�$ d8 � si�]Yoal spacexEW-�0� ABj 6� be: U  ${\%� �a� F �A��Lrai�on: $,�eti�G �os� LEP II QLXll04,delg00,bou04a}. F{ q ��can�xio ����*� �un�ctable� qrks� � �be visi,inB� I� �che03�erefor� !59 ��g$:wc� �"a s $%5$AN�!�BD mass:lQ��dir  pos�y�� �to �cA2� . 2M4�M� a�)0��$H �s� tokwgS � �ei��� \textit{ �,, neutral, l�,Mč� } AM�elyIPa) �� ��a fewp . S  dr� mody�ofa0*W s A earsI � alterv���i� q�remarkab%itC9d �ow �>mma ray� emitx��%&bul[ f�$galaxy, clA� 1��511 keV�Ycoincid.� � )I�siacboe� Accor7 `is some� exoi`� obser�� trum m:iQ�annihi{�5�%� dark m 4 particles} (I� \geq$ 1-2!�)!�`o a pair $(e^{+}, e^{-})$�%? � hua j� U�M3. � 10 k-(fay%" �"( reproduc�siz��A��q5#e"�r,jne � ����aj��,�ran axial}�:t �1�s!���  Ui/�lem = is ,��e e�A�1�%�9�Qgarry no��is���5 come� �la �=� plau���cl�to ]!I�"2Cleads1��|���� � �e�� 5+ a�a"gMw�Fno)i =2!��)6}$)�, wh!\itsLc to lept: �4  -��MTof magn�i���b�[uX 0 2�"?��empirjus&f %� a key�� i�A�d?Iastro"alm���oun= L% �x$ �y��c�$eD .@:uP&u�y$e�ded ye1�  thod!V-)B^��8 ly��BQ��f�C��9|82}��sig� @ed�{�Ccir�"�$} fluoresc���Nns���o�$x1/2}-6P_ $*W�an q� �I;ir=3noe88 �B[er group�� �ot�Hz��Gs�d step �8-6P-6S$ cascade�th�fi!/-�fq�w^they ope dis���op�ly pumpF�6"� �eey�,� sc�Ja�of��on� phoa�)�pop�%! �a%;����TV ex ?foFg fo�y -' = . However�isQi�suE�posedA/a back!� nd ( 25\%$) e� stUre�t��%��cas8LR��r%�#��E)via%2)-JRd] ly n!�!Nr 7 rm Im�|/ �Stark}$�*^ ���A�lo�SL�1 by �!��misqa�probeIJpas%.* vapor aloF" path1�9�@�@�short$�7S���not��decay[$�!U4 �isY ifi�t upropag 1��way t reve�|6�ng!�a1�AXe��-poin�!"�% kC .j�_}1AF9w*�y��elf�-�!�xponenti�tdtl ���d�Ano�er8 r� �o:+ applg#ic��rat2a�cr�ng fun'(of it. More�#)#��,I�i| ��isY�B��no y�A� D%�0 cour�> *�ed 9,*r�b(pr6 naryA� ultsnch id,Pi5�5��we�succee�Lin^�M�SNRa�a� � 3.5.e� � x�illC jH"�&,��I0de� veIuracy��${\> .!�$2.6\%$ d!�J�K2.5 $.?8�^W) describ�e �.� sE!Kap_tuMat� �'9@ is U! s��ivity. i8 also shown how!��qtod V t& < : !�mak!�fb2Qof� $B_z$I� odd�r $\vece#�9A�� m��e +t�%:B.7by��A�Ke �Qil p$irec� comm� axisɗ�!,�&Ysirco" �&w%;Iqs. Of� tarc  the 3tiE#>� =Idseven��R�/�_g!� guarantee"mF� 2�%preEh^pr�to�(��,/� lTTterpret�',AkM"�� � b � d!�!q � >m\ŁendVh�per^ \�/&�  $��te align� A��bsx!xany� �}6�� eN dipo!i�qe�e $6S-7S�B� , "�)M_1^2�>Q� un"��yto� . SiA02�� ѡ�e�(O� &9 "? �!kic)" *n<+byK e��(�y͇c� lsX�v`is s),�"fre%p�! alݠe� mole� a_9`�'s��`a�} 1xN�  tXan orien-�a�T!h!f�off�a nice�l�c�G%h %K $(�&E_l/M_1)���5)sy! � ))e��. &x ca�)t n�(�corpo� 1�-���ais�*sl�Xpe�#�ur& -type' ,process.~ ~  W�nd!�"^a�a�i�a����. � ,!A� !eVC a�plEB cubic c� m�(ndilf&M�U ,A�A�n��&&�-"s �Oi��UA��est�,E"��a 3rL, .� 1A*C Q�&�#u���gAqe#QS%R,�b�d above@ re$:ng*!)�- �ur�#!���K!�� ��&� -"� ��: *�Z#Gi������t task!c(�!� seF�(by F6.I �, ^*0a cross-check��(0�-2�gma$)�d0.5l�~%i�$$^{133}$Cs~�+$g�<� d"� ��w-ND� w. Ga�ca�� �0� m-� i�.)set-up, *if� Q*Q �%%� wA/ . AmA�J�&�* so far,Ih!��2ca11aw ey m�� dhibitory�� (-�"P* %�c5�� ���chiev!/�'�0 $.�%�"Asw �A� pap"()� 5},*� �� i�!�!��venh��a'� in aQ�&� }��<H3< E��"nE& & length. A�)ѡ�$ial multi-Mod��� �Yld "rest�)cylindbd"4" espi�*%Ll䅐�n � E#�# an�& nois�.m�+i�) $a $0.1\%$�Q�5�M�bd 1�c *�)a�qf� � seem�b��%onsp $f spontanex3� radi!�~�,{triggered}}6%����r h�� z, into +�uniquO&ol�*et�+6N 1�Epo�8bew$91. �tivI;�� projectq)looks fJb 46n�agN �Erips���theor͏XistU o�!E�to re�/ir2�*.�.� �Neб��*1,mil01,24=% 2002Es co� msf�*s ��+rta5&��arr�&+ac�* 0ir many-body+ turb)S��ll �  �D+ �\�#0i�&1G&-ce�)i3V�6^(�(,A ��$milligrams{E�ɥ� r�,8%�y ��*erfa�~qua�3� W us!������CEois��heM��1�ai .��� �5�,�jadioacC!isotop���$ half life�. (3) on y��)���of 1~mge��r�o�%� n (�MP)x9ly $4\k$s 10^4$ Bq� $( 1~\mu$Ci),��xne� �� prot� �s�X�vH���i�50s�n=p. M/7�5!�!? ' er� -3s, ?s.���% ������y69��$� ���(ar �,�/ �c�� on�:.�}���" 9dis&� ��xv �o����� 0.1�!%�*cihelp, g^,� lo�{"/nd techndv�*�8(to V. CroquO )�LPS-ENSk,always avail� ,�ic}�",�1%� a pl�� � �e&�,1�of DRI/A�)�($D. Sarkisy�0nd A. Papoyan Re�� I�=e�Ashtarak�6U! U* d�*v� �i��h�As�W��KHnk S.~ Sanguinetti%�6ipa�1nthusiasp �R�o�� "`@@M. A�\"\i t Moh�RUlp) infini:at���ted=A ;�e��v���/E�Kk him.E. Brez $d F. Zomer��O � $ �ar&.r)%le.& M. D�98nd J. Iliopoulor"sE`���  inuous M@. Last�+�A{t, �in'�E��_Ta?%�,M.D. Plimmer�9 #?\thebibliography}{50} \b�em�� 97} M.-A.chi�nd�dBo  , ``�9��GD�L , '' Rep.D%g.��|. {\bf 60}, 1351-1396 (1997)..���J.��:�} b� 2037�88); CB�APiketty�EnO1851 (1O.j� 7} CAK W.��)l.}, e�cecbf 27e75�63�>��B S.~�en�_� C.~E. Wie�9)[}p ��) 2484-248e�99)�� CB91��� ^Q1Z�C W%S91�1a� P� 2eUA D. Chauva� h. JacquEAE h M. Lintz,a:*K,�Was�� 6FV*�D. " icm��� �9�2143001ed3!� 5jah00} �.j6��6��Aa�&�  Appl1Jm/471 }, 561-565 �ݺchaAP.C��}6�� ��"0C. W. GoodwinA�itU� Opt mmun��0138}, 249-252%��G ��L5>�!�!�1�12�.MFr5��100-106q85!�5� gue9Jo� =,J~,119}, 403-41��9F7���N�>�J. �Soc. Am.Q,(14}, 271-28 �:� ou96F�>^ u���3)g 5-11�"6). No�at � X�``�:-''%�``�#''-�$gurEs ref�9# P ' ./!*~*a��*xdis,?�iv�u9�$\�E_l\wx 0 \epsilon_{ex3<nd (pr�7he<��"�,� �Csix�23�@ %�RK.+s7:}BA�8AT~�=�TQ�0um Semiclass.e�a� bf 1�733-7m�82i��9EZSR� Can.A�Ʌ5  7��7-7t�ty��#3F(C �%~� Eur�9 J. D �2��331-349��6- sar89� GJ.V9 lkon3 "r.x Exp. Tech�� 3? 485-48��(9), (Transl�*� Prib�,i Teknika Ek5Q�"@a, No. 2, 202-203�9)2ia�9F��� 2l-06!011l 11�:���1��%3BeV�13�B21-22)�1B�2�� z7 ChemQ&��E�1�! 85-9ɶ2)9Fo1�H157-164%�9�qnotpul}B�%�J�)ul�0��.n�"? disc�H{(�E:$..> gue0:9 *�y .�SA� ngui i�M2g,6vM w 739-74"� 2�d 0B. Bodermann,� Kn\" ockeZR E. T� ?Ba� �lusa�9�3pr,m IodineSpec�eu�" f\" ur��en�k,�" H�82' .9note2B} rDŮ�w�$.q Emmans`er (CEA-Saclay, Mr Piuzzi2�car88} P1ioulousey  Carenco�XR. Guglielmi, IEEE Jourof � um E�/onics-�0  535-54Q 8Q Yuhri�Ɔ� "� 6� A. H�LhoN�71} 6-1� $ �!]6PE��%b-al non-rx3me~: isms !�j� "6P.�4� .&eO�!F �&>5�*KG(C e\ u�d�k*�Nac' �tem�5I� ,,�rt*�4-� dela`!�!.�Wgy�%$m$ 1.8 mJ)"' d K�J5 is a V*�2k 6P $wk-Hertz�*.n--p�5�#ns d7  ``ca88$e'' windowY� ele�&-pT24 �6 Y�,.� A 3A} DEI,�FPX 800] L|by Armexel, BP 20 - 92151 Suresn� Fc.Hr&!Mr. YW Ru 9q� help ��on&� cca�+�R��= �"�G ��6>,>� �Y��169-178 66 san >�@D�J�: (���'$`a di PisaL|04, http://tel.ccsd.cnrs.fr/doc�L/�Hves0/0/00/67/85/), �Q2-3-4.�li��t.76�.�=!pZ'9 �Scia� str.�O Xiv:� s/04100442D meller} Mᩥ.@120 Corliss Stree[�3aX, RI 029! USA. www. J�Ocs.com��sar!�D.2 ��%�\6 96A�b�@A� publ'inB 6lzr ,Lizon A Lugr�ŗ PAM ќPr�%e C� _2X 5> G nV%�>�^i2� 25)J�03141.�� 5} Nb�A�&�1K �AC\,&o�7 89-9M 6��b��inb#?�5.���M�� %�& di}y'0tude $M^{'}_Gi�?uBT!x]s:Ŋ�,kX$M_1$�1�3�Z"=& �rr!�(>�R%��ot�73G ^{hf�in<'���dia~&�!*�,� p]on�C a@F =�V1.�=s (! � authl� � us�*@*conven!\e .�oppos�tod's Eou88})me_ ]\m�O (seer - doe�'.�6, s�2,!��"ar��2}��*DE �5 c�Gn+;[&3 ex} *f k$�0�+-Q!��A m_1W22W",)�$!�UX]m�)��3lh�K[0 :W�$E_2$EWU��E&. &:we neg� �+rt E_2�X=Q�XM_1 ^2J 0^{-3}$. 3als�:5wl�#, "�4\ [ q\!�!*� a '��is eJ)4$\pi/2 $ phase"�$ce+"�]S�# and 9Ues2Mwolf} MW;`Qca�(sO0E�do�m s�t7utWolfram"�.hlin� J��-.4J.uO �5�1�997� & a�C} Be�4a� stru2B  5@sapph�#H Zr5�Yl2nd re:,N8p?S  birefrK!�orF&�ism de��' n!�y 90anneaWt��0$^{\nB}$C!�.� a�XichA�have c�1aP hat �^:� surf#L�+s�Ece�Y�Z$\#$ 4A XQt�w �( tube (eit��5W?8umina ceramics)\5e 2�45.�.G4�~&G�E.~D.�oKYcW A)�� 1250� ; C.�#0��*��F% 030502(R)b6MA5PP}�\`#Y!}��a�mof�.t�7�: ly employɪN� w"$\h�d= c�c�8cc�IP4� �&�0���:"{Ain*Ex�H!�5)um�"�" paSYU escot�9"�)m*K 77B}, 34778 nd)�84B} 52�7erna%PH I. Antoniadis { .r JHE�0105 �46&�M} %�lgado2=00� 0MeL7�fN�B. Allanach ����at�MCo�6, Les H�!esc/3� Xep-ph/0402295 v5 (May 6H� 4aMBDiI0!l  "D7� %l\'~'ai�Xw'es�O^011et&�["a�!\Y( ans I�!$es'', LPT~�%(JuneF��N K� eunge� G. L�P berg�e�� 6)�760u�K45�L�0~Boehm, D.~Ho�k ~Silk� ~CasS $]ZPaur"q]� 92}, 1013�4Y(t�L�tP. Fa[ ` v]�9YZf(LP, Y 3226`���.�=rein. ::4b �$A�^10260 + &l �)B ; %1 H,NcLav1�^M1A]l'a.�Men�Mes ($.�M$), %CFunw9A�ja�TA�gde� uA�;4 sombres} au Y6`_e�% alaxie.''~�I� a�NoeckqBC#Master�`!�C.�bB �6�L318A�YW��2��*�#YS#" rsev2"�j� 0052115�hD#V1/|N�tsh��am�L� lets2])� �a 2857�9e$���1>d�2/6�X1X5-�$��3endB' ��r �cd�}TY% *� t�4fRM(apssamp.tex ! % % Xi#ma 3�uAPSa]REVTeX 4t"�.EVe�k4.0r *, August�1 n Copy*f (c)�> A*)nek,+Society. 8Se� Z 4 README�5 >1ril �mb8i&�\ J TeX'^ j�D��� you� AMS-La�2.0�W�  %.�)!'y� preOsit�or�.0�n� %�+� E� runn�BibTeX� m�)�)allows:a 1) ;x.�!�2)9 bAM 3^/4V \Qm�([twocolumn,�Epacs,�C rintyhs,ams� gone z1nse t�$�u%ys" 0 adv�/m�"�>R�6�TThe grow&�Qt�.TK dA�y hasir�Ato [ Hce�ch�A~�$ (HC-PBF)~�\russell1,HCPBG1.5micron}�a"gu(ke�, over hundre)?�G�Qa �e��ro!?#a5l cry�9aguc�� e Fig.1.)i� localizes {-Le�A �,s%�p�� �; ed primarYd]Bg&Wo�'�lK_s!Us%�%�[��`6Raman &V6Z2�Tsolit) ��< megawatt powers 2�c�par�@&e)8�[�uopAbrpPs :4t�Cdou�N gresAN: E�a2��,B-i2��(richn@!vq9cKmanip Ur q1s�7eQm WeD& q�C��cA�lto6�sip�z4 coo"WHBose-Ein�2�"ens9-CBEC},� *� � ompu*L 0�)*1, .?2.*�a�tro�{T �d�[�� (EITqy$EIT1, EIT2�mSi�=�� phenCloV#EIT.- an assortA!� pote�T p`[HW Y�)ultra-��iY- 1,  �i��Fag��edium;�F�mgh0�singleQ\ swit�=2 chmidt96, (�(}.�[*:!�+m2E�L��d�BA<�b& novel I�ic%Mceq` v2�>U�}6�!��@ uild&fulS�k�eUA� J�Aq"]c�E�Bing�Y�� �6� f<oa� y��-n�\ž &[toW�-��Nem�-g$%1E&on�H A7nt-Lit`W�>�4w$��Pa�B��y,�Gs�b��(ideal bridg&1� 1+F s� ��dLwe"[U� D]yNrea� firs�|e �of��"� �-��th�k�.%%=N;three- G� oscopVEJ� -�d!f���a�a �. UAO� g1��Eto�!/�$gilbert�"� �UI=�*� di�vgap!z %��range q: !�i&\t�$=|�?�y�<c�W[*z ($C_2H_2�a�ar ZCic5|�J!i0clean ro-vibr��al EM� ��c2h2} !� avel�.�ritari�I O�a�g�A��2%� 2��MuN�mfes-71,..�;�: ug� #D#m�[� A(typ�Vh(eak oscilla$[str��hES �ar.# . Ob&J=�+n���*�!=a�gk�ar n$Iit�Oe#��hma t���bc%la�-�J��E.��f . WhfthA �I�@" 2,"�al �cY!&��� b�h hancu�eB� caviW:A�K�~ dia� !-eLG"gec ��"Q @yoss-less�Ip*_of �se�" y ,�[vid�Y� `yiv�X�>ve�/R�} \�&�Ps[width=3in]{Fig01.epH� is h{o+B�D,EPS art \cap��{�e|�&#M�e"U�metD�ez��So 8%*F{��Dn. EDFA: erbium-do|G���#4fier; TSL: tunE�s5o�%A�EG; FPC: 8-.�5�lF PBC:2P&-A~ coa�� �exten�Q% 1490��$1620\,nm. .�R(~\ref�3 )e?M�]-{reh#@Flvacuumi$. D6`�mbly,�� purg� ai�n�e& Xidnitrogen�Ba�then e^H�,�ss�/b�o&�hTorr. On a�ce�is�n�e�99.8\% �X�]� ��X�N/ ��-*��)_��� �nUn����%�is2�"� .�!2.%de�\in 9�4d!�bo&��s��s����� ��sE $ 10-100\,m)/a3e5�)��  me&��>aea�is� �i��s/  hou 5sWI�O+tm�A�rnal-�Ei� 'g�1S%Wy;e1&eA�� �$50\,dB�PiySqd�ͩKo� !K\5�'%�L�  ��ae&RgA"ٴMer�s}1�y�5i�.�f,s 0(${\Sigma�q(}_g$)(J=17)!� $\nu_1$+3$:,u ,6),�6o�as Y $b�d $c$6�>.%)�!�F�� $a$, $)is Z��1?c�jTb�;!MP(17)2.R(15)5 � $^{12}P �5�,.3927 n�001517.3144 nm m�ively� 4 .�v�mai"fA� 5�i�WY4*f ��)� �> � �^�. (a), A�� !..� Doppler-b\ed K6�%�W a D 480\,MHz5P�8&�S.|�,&5�� opened. F~ � �s}(b)e � !hD be-�Q 9��)L��aA#e�� ( 320-\,mW (��dA6outpu��)2�m_ exac�  B�&er]7E��Bpion� � �����3e��d rout�� f:geomet�~���d�/&� rubip}U��L�2�feNH"��wl����fa; [3Jq1iI�A�e�l J�Y�(Z M ��j$D$%�e��)GW"�� anu�{��of:[acul{ol�he �Z�T equL� 6/ $\Lambda$/�A�. \ Y�s})� l��$ l��,s, $(J_b,m)$!%�� �2upp=c� (c(m�����i$E_���t!D=�Ba,m)-(J Ji�b�a DJp$.-$m�Por R% al"}�%�%!}+"�e�' w�deg�% ate 6�-���ca�\��r ady-: poSon27(U@2meA�E�)Hu� ��rn�b[ �sc�T}�!{� r~ emi-��M1�!.�J[_Tly�R�S-�>1�d�p�,e $(\gamma)$�"Lc��m� �b�X�� "al re2�Zof2�>*'�B��P !�4 $w_{ab}=w_{ba�m� �@"A� )�e�j^�@$\rho^{m(0)}_{ii}$jM, $i = a, b, A�to 6 "I Hm_{ca}$@D}!WfEA�q`��%�, \@wi� xt}�} � Z=\f�� -i\O�^m_p}{2-�|-i�6_p+ ,|+c|^2/4}{)�%:-i(/- c)})}[(u1 cc}-2 aa})R`}{4� b}+iV[~w]}6ubb:ucc})], \ rhom=+S,9Kx�R8_c=\o!6_c- {cb}-k_cvD �p)p)a)p)g9velocZ[un�u/%�+!��a�.�i[�  zs, $k_c� p:� � $9е Rabi�kv5,q��H+��� txe}sYrna��Q^c&&Ms 2\la� +_u��0\mid\hat{\mu} � +_g�U\le E_c}{�4}"��\\ cmu^0F^0_+ - K} j;ɣFU %�Y�1�W5,p��nic.�.��< <^!�$n���d@ H\"{o}nl-London �o�VA���pano}M2mi*^�91�pW>�I c:�Eb0"8 .� Y C assu�o`co-� E�~(Sen) 1D� sual� � 8 a {�dJ�M�!a"b�=of 6�aa&� eq1,2| bb}=2cc ) 0$ ��t+;�.%p� o`�n� s� P��-9�� &��(aG� Nui�� s�k4n�� � javan}i��gz�" q:"Q� )T��� � 2��Ɇ��2��(a)kc�p\xs��"�f(1 ) D>#.a �aEf! Rs=��i"D � i�" 1.3-m seg 7a�b&�-. A[.hI�t5a"� "&�i�h. =Yd��B�*^ , [QgA�a>. a� (3qmW ate@T)&M. �*1��de>= h �'�,�'�s�� _{ij}=��i+  j)/2 ^{coll^ j|A(for $i=a,b,T ��, $ 8i��*t of�  $i� .2Z� !+6�q�� Mt��re� &C��w4#i^ �, :5PBGj5$!2 Ref.�� naka)(e� _.��|!�5&"�g� ��]�R>!�8@1.5"�i! u of 16/�At� �R��s �.x��a��5fst��Q �k"�1&��sa']a�o�P�due�9�5�-��=�E�, ž�a�d�b"� r9� of 4'm/sec [a�mCdiX&� e܍s ape� ch i��9e&Cl.�r� a<�s� lI��!4��$major sour^de�Lߙur� ��9/a�q _a�q�o2�k�\E�all�$c�?E�JT=i�uga}�/�*Ta�seAP��Q P�k�����~"� ����3e�s�-(�.� >rm})c oޣq=,$ susceptib0y $\chi?nd%fie�alB2aR!.�U\1co+t&/ �} T$ I_{out}} Pin}}=exp[-4\pi k_pL ~"�r��\{�\}&� td��&� �  $L1�g&�fE4 Eq.~� J�ei'%u>@ � �e�o�!i �t�EE��laB2 uxlW�ab�aari@+I�, : (i".a `��Uex�vdR��i�%�duc,e�C,J�W �� tant�n>��2 � (át|m��2�a�=gC/F�$R-n� � I$ 0_c=2� E_c/ X Sv)e� }�K $2i�m ( .6W� e�_{c��$���Lsu�f��� �>!E5�E�AQ�=tGfit�!y�#�7-F���>�%� (� 2a.)�Prel  hT�.�BX���bb�p�!&�0o��A5�Zocho0g<�0.4-� matc(Bw`Eo���j��jal. curv��1Y.rea'e!Cm� �QV-��Jr 8�2 m�� �0��-MF ^:/&6�*fn!an lfJhguL! i�1M6��Y� a�in0 �)�m �T����5�ef /^0 Q*� auwerA�F� 1�wa!.��92� d%�6�A� Q>-Ns �V�3� oa&\�jC$ee!,� R�,p�"Q mod'l��Pnt>��ae*L&l'�"x3N��/%H �U=9.3$ 1M�g�n&�"d4!�� ��"k i =0.96 ]e�5H��}_I|=17.28 &isQ=ed)�A fit.!Gur����� s a plo�e'y�a2$�ZQ�����eA E� t2�(i�]A��Bet�$ �. P/%_-iB'p �l<�U�w� !�aN�'���&, S;yy � m^5� :t!Ve��5 "�2;full- 7@alf maximum (FWHM���I�<ie6�L a���p��i � %��J�'!�behavi���3F� $\G�_�3}\Rparrow {Y�=�of.��"_<R~ *3�FE}� (�Kle^Ks) ��6F (��!chM.AMzero-de�� ? � 8)uI�-y���2L�6L��>�� ) asw��Bof_%�Y[6] �eY.�� c2PAd)=y dip.}_Aw:+����teO0a�*�5_ah�.�Nc�4E%B�3Vd R3.�6�Sto+'�\�'qXe�Y����o� i]�1.4@-�"� &�a-��� }�&)�W9d� a R�~ y�� AY-n��by dra�,I}��Nf?v�1exQs"dA1,*�2�7!�k ���<��A� d by�'��[,FM��J� _D� L}{v_g}U�(L}{c}=2\pi\|_pm\left[ \delta "� Re"� } C}\9F]_{�U}n>&*+E�<M�+Y�\� �a�< $L��e%-ũ�I#s �3aG�e��s.�,oof�cone�w'r8+19-ns��=�2e+n ŃVmod�:vNnd�"��&�A��� I�on0%�C�� $a-c.�S� BJ cHz"f(CW���{%.�*b�Tl6k $bNkM�Hf*(G*�!�+ wk� "��e�se8�4�aU,,\,GHz receivhz"2�rm��O2�6;��#�o�ƥ;!2*� ("�^c�be.�%!�Nn���&��8 40\%6�%�6}| r)�% �2�off� %�-�K1?/;Z� 1�8�pD=~$ 0�#N*ur "�wc�&�4s��a>J�Y�s � m�arw*��d$��4�\'xi�+ e�vs.’� e����F!q (%ged���(nsx)%s.�.Jex� A�A�-&�ZRvInmar[�&inv&4�X �$ nt 3�*m�@5"�4s�&0R5ʼn2&�9A3:U �A5to&�Ad�5ofu �ce �� 9 .-���y &jW�d�'b�Y�"_>a~"Y]t#����]�!��"�5��0@om.�W���vK$Yll, Ko�Bnd�\G�Hi�uus�= iscur0�SC��( g�R4 y acu� �uK!6Ce!�E��v} �Ib�sr� ll1}�eF. Creg`p{\*o %-ce}�a2�t537]P�UU:�:PPM. Smith L"YVhN� �r824}, 657(2003).W � 2} Benabisx,A6O� �P29�i399Tpu�"�CE���z[KR�6V3[V 1702�Q2��B � H. A�K�Q�� 69}, 198 �w5.�Qu�*�@1}6V wmee�R>�ewrO T4Do&~gI&iP: _CyrptA�py, Tel�ua�I�(&�C}, Sp�Zr, New Yt}!�]u5j:�2}�y. Luk�a�@V Mod.�.Mk�i4�R>JW3}h,. Beausoleil>jJ��d_pM)51!55I)4.�$D}}wA.��arovskay ]nd�SIrvan�Jetp 'A^4A�6�X*u5{D S�THm�iit)).J6�< 1033ay�\K��1}CluR�6p0Aw490e 1.�O2}A�M. KasV�AdJ�wu5�l�y2^2�DD.�Ph��p16�^c6}, 783J��D}H.z;�DI�,A. Imamoglu -#m)h��E93n�w9hUEv"*-E6�MYaj to, Ez^�n361�j@gn �2!$YAb.��^. Barb4,nd� R. Hawkin1H�ExpQ�1AC 2710e�2��@W6WSwa�lXS._Pi A-4F7e-<�k12�w206 3GaLe?2 N6�e�l. Spec��  4-%2�rk@ T. R RV:  % 408J "� -"� 1}�QR[.K^IGɀ83}, 288a�6'Ja2jaZ: ��3z&h[.<[.!mJ�&R]�A �L_380"�XUp�(a�C!�ano WJ"\m��%11��276El2`j�}A�Re��?O\AqA,wv"�� X 15�a26�62 n�#��deLabq;l0� �6lE!� [ �v 84�Y92aLR. El"�chtouki� J�xA" gJA�MA� ^216}, 35=Y�,J� �V� �O EvY!F*Y,�%s"�i?@�Decem�+34k> W%Vpre�VmU"�V*4V\�V2-aYW}> symb6nAx}2ZnewB ,and{\tr}[1]{�, {#1}�,�U.*�A{M��v} 2pd}L��: bx}{: x}>r rBk k}>� be}{�"�:Xe#A^!Fa�4phantom{\vdots>E berrj m�-{cN(lJ)l>)e QFa� O�6I&O�.$def!�:�D{\�/ilde{\XDD{E{\bar EDr{ ' (sk#1{�(#1g)}ZdS %��� v�>� ]t][]]�] ivcffd\{e\}bf6�v[mZ|Y|} �ra�/ ecdef\DmJ�_0 @E{\� a)�9�=�MkiBax eRmn n[p pq q0bfkap{\mbox{\ Z�� $\kappa$&.�,sst}{\script tyl�E.&Fa�  +% F>NRV(R>(BV(B>(beqegin{e�0BV$aT")Kj?u*)U!m�P�1>=ial%?(�t{{\rm� st\,��Fو \L[ {Two-loop"P7ione�turbul�Prandtl��4or{ L. T�,dzhemyan$^1$�c Honk3�$^��Tz Kim (L. Sladkoff�ta*�Z D�n"�QT*��KiwvW trivG%� m"!exh��s�&�, ���)���a�d)rac��2mutualD_$ ��>��S+�gA�s rfuvwo dime�h ��ha$�PB'e;=cpreviwVQ3ion(�)@MX8Y��@cs{%47.27.$-$i,%TMt flb,��v)� heat/ fer ;Te, %C�qI�i6(,05.20.Jj, %SA� al m�yc��[!�_�ids5 10.Cc %ReLi ����s afdat"5_ 2�[ X�� GKsec:i�}I@+ion��-��Nt(RG�#E�uQ�Zelo-Ly[A$curA�l{$mu��XA:����@1aoreorgan�I�a�a'for� peB3�e!osec�ex�p�, ��/ Reynolds�`^It@.1Nuse�0. A)s�I time WYa�4>ara�N����5���RG��ac2WmrsB�e1of2$0me��o���Y�,�S�HcM[�ufN'�y!��:E�ib ive viscoB-��Pd9��>v�C�$of Galilei�ari�OgM){  �K�D�� ng s^�!)�nin@ akhe 9 apSrmR&�0� }T�a2Gy`�6�act ans�& ��fp�1�="�Y�����0of Kolmogorov)��m�V�ng�5�@:�\~., skew�[":,uHt: ����~>@,LP�B , doEC��%Q 0xC�extZ�'�uo��s"8`%�5 aiCI -�U�e4��]=�%$�B�6u;4�ood"�)��numA��z� 9�,H�ho��-- untiBC�Dly --0r�r�2 M�Ob"�� �&�3!TJOf���2x���O���}ANY#!n%�eh�):��hz'��N0�'+�'%N{f.�w2> }Xfi��t7pessim�]g�viʥ� wholeXy" A tyAw�q`#� e^~�"�.@=�$�TE4cY(� 9�57e�cX , j� to��e�6<.E% g�. ]`�- \c��1-�C *u.`�usq�& s $d2�2s $d=3$ aBll. It24�Fre v�f���Vxdecrea�zqo*bb$d_/- �mit $d��*\infty4 i�710 \% XyJ�jP2$IS.�ww1!A!Y,.�>R+�4`aq�B7�g%.L ��irbgul��Hlu* !�lia0Ereg��$dK�2�=�8�Yu Iy�R $d=2%) conn*S%a�&� !GsomW�phş.| .}l� ^��e�1e�3 }G $d-� �J'��^y ����s� y9�y�'�fw�E���m�"+yA��Nq� *M%�Z essU5����̡݅�impac�!��2Q)bKN�iS *D5g&%Q}��f�(LiWLh7�analyz� ��ld26�I�F��@�Han� m~ cha�$erwm�E� t /s� 6��Ma�F�N�!<��>� ad Refs��Fourn�H£ch})S.��&�fnMo�!Chua90,C�0u.)�2Va=�2��:��m��ecka��\A�*�5is�t�� 0ental. Let u�m����RlL �5�! i&2oe� A kin�&�S0$i'�922t]�q���N$�\_0$. (I��n/ng\dn�' bleme�"� O� b��4J�E,C�<alaxS!!� ber).�'Q�I �Mz�N�U�c�(- f!/homoge>�te&(�i�'1�("J�, ��i!�f@���� i�&� �5:�J���f9_N"�%8�X6`5EeB�MfP>�ContraryACxc� �� alogs^?�7uoal) "DŽd6�5ind(d�W "W`����t�0�9*Aj-s� 6��ٮ�^R� requo, �Yi� when��� �7J��(#roxeC�S* �a&� aC81�*�priN�  pa�)eayaY} �d 2� F6Zi����s����SecRi{:}r�� in�Se9��deM��,ass�Gada�mA)�gQ �j !�M��1+-ial em�F=vAcarY,Q�� �B>�� {�A..�6R}�@ devoa�%f�Baly��Ji��:F -���14 |�:tPr}�NK/b�?.�A�-�q�6�Zak��n���-�Q� dM>�~� 5>rk�0Vz%/}D6�P  &�mixRG�qE�-ar][A98T�:1'�}2P@1} \pd_t \psi+(�!phi_jj)= :� \4�3 + f \,R`�&7$E(\x,tNn�B (BM1}) ��eae? of bc`��unia�.@ (��b^.6�>��Z�5�|AEp=�Ni>:admix� (E��/se B�� repl-|:��ufA-f5�&�F �2�4" }�E2�y�@1. t ed9h�hhQl� in�8 T�fluid Q�A5�sC�f�HEN_�-StokesUt��] ando�ce:^�2U�Q�J�va �=]0M�-A�0i P+F_i \,,�%Y�8FP(t,\bx)8K $F_i1s��v\� ��7���tD[&�H�flTBdom for 6er�� mas��$F$�1 ssia:Wk <�5�b�2P rC /Qu�B@�;�" �F_j(t'�')�% =u9 (t-t')(�90 )^{-d}\int d�% k��P_9I(L k}) d_F({k})\exp [i  x}-x'})]�U3�49x�AsXQ.�X, $>f�} - k_"Hj / k^$i=xpa�!��[j, $�k!�2�@$k\�v |� k}|)�p u�eIfZ!�&Ym$coJ�' '$V x}J�}�C��-- 3})�7�al����um�D�M^ �oub� &�2e�P�hi �\2& phi,�{,q#', '\���X<oJV S(\Phi )=m_ 'D_F \,�Ni� '[-# _q� +\nu _�- .-�d 5)] +�U' 6Spsi +r�V� Ž��] , �� �F�n= $D_F��!��}�Q.�=�/t;�l�  �5� �% $\{�-bA41�Kōwk� od�s�i�8�TInI x1})--Ia �)�R�U���EA��h�e!1�XE3$(\x_1,t_1)ER 2,t_2)...!�n,t_n)%� '(\x'2'3  2,t'7 nn)��l� " W \eeY�* ,f���|�#)-nonvanise�� s!@i��<J<Ѵ?!�f"�Pvar\o�!e/�� ���#q�� $fj�Eq*�!L$ G(\x-\x',�~ i�1b%3 ),t��8\big |_{f=0} = E? )?E-�,t1GJ? aN}HI� 7ZGc[ee��o M� �M�)9>� 4J!d�s� I� :�O4!���� id ,�)aIgenc�i�!d  wI��t�fur �>m�. Mo�G:~gi J.����Kna�c �!q�PH?Y.Z b8 op>oors ($t-�t_1-t7rA�(x_����(aW 2) m  _0&={�� 7* 2� k^{2}}\,�\\A(-  |t|�) ,-�: s0}\\ Q4u1� '(a�.� \theta(tA�xpNqto,onh.E� ��Fg��g �>��tt)��o1��-i� e ($t$,��kF�"5X�p�/��:�>�$Y�MbA�V��Ii�0})��.})�X����y�"y=i. 4 }�d"S��t$w0X�0t�\, $-MP'�`�_�^�� '_iVg s} 2_j  _s/2$NU���ex�! \,$ ;={�*i}(k_j[ _{is}+k_s  j})$,\P \,$-!�J�psiQ k_jE,'Q�_j I� q k}��?@�3&�r$ �'� �'� & e<��ea�*wly fa:G!��V'=�1ttenuEcA-&%�!��>6����o�'m��'aD!R? b&�$�=>&ec&�B�>=�ir*�SogJ&*~#��a6o��%"-`l� !d t (i9#AeD'�tne�>�8�98n�L[&� �oos>sde�X�f��r!�-`=� 2j�8:H(orB� H)*[�hRF�l&A՗ �#Co�#Dy�*� � F�!hUaN-� -<�c�wge"��mG0�_z Q�('}(k,\omega�>quiv SLm� 2*&��c ? + �� 2 - ap' Fo\,�Gff���psi2s���N$ &= -F�F� 2 - � psi'Z�t�dend1I� ?�\� � [self- gy"�&n��J)%�Drs..:s$u_{eff}XR2s�"=1 *5*frac {j1 =0)}  ={&�=u�� !|F� }b�"kLed��i66&$LE�\ll k%j $ (E, *DXtX���&c� cjS$$�2�6`Wd2tp4�u)��ag�-Z��i*��q a��$k��N�,R}>- ?BQ vRG�/Qe�}�RS��S�pui '"P]�ў,J�$�ea�.E���3 e�� tt�Zv�����y"# inN�(�2w�)�"@$&�� `��]v�$'d�)�3 ce (Q L \gg 1$�V�F. �-� �y�$�r"���str.�-V�To�!l7��*i�^�@ary to use in rel�yation (\ref{3}) ''the pumping function'' $d_F({k})$ of a special form \be d_F(k)=D_0 k^{4-d-2\eps}. \label{nakach} \ee In h,infrared reg�powerz �nak<�i) is assumed to be cut off at wave numbers $k\leq m \equiv L^{-1}$. The quantity $\eps > 0$ in Eq. (\ref{np��8al small expans�,parameter in( 2$ �,present only!E58one-irreducibleU�Ds $\langle \varphi'\r$ and ( psi  "#|ofo�$ R'\DeltaYP $B psi$)�d =�lsI@^�B�'`�-�s. For 1$!4renormalized a� mayay�written as \[ S_R(\Phi )={1\over 2}\, � 'D_Fy+  '[-\part�I_t  +A�Z_-;-(%8 )] +%p' 6V!�+u\, QZ_1U psi R R )( ]\,. \] Itan0obtained from1 �7)}) by%44multiplicative=Ci�-��;q E�,: \begin{equ0} \nu_0= �`{\nu}, \quad g_{0}=g\mu^{�lZ_{g}, 5 uZ_u  Z_u =�Z F^�K9=3} \l��Z} \end���(wo independaFY*�, constants $ WE�����qu���� $\nu "g$a�Eq. ($ř Z}$)e7F�nalog5Ccoeffici� of viscos��a�=coupl�w� (h�2 zbe2#) �>�$mass $\mu$A!,an arbitrary9��a<����,� >n �lk)$Ma��d�kmin�9�Jl)p�random�bce $D_FN��BFex�sed!z term1S6�Y�:a���g_0a\�] k.� = g ]�% ^3 2$ed��dissipi4w�� $\Lambda%f1ed by��$ accor.Lr1;$ = g_0^{1/i'$. It�ȥCestimatW%[M�y %�. Thus,ine���� e weE�interesBiA���s��)�ndim $s�4k/\mu \ll 1$.  schem��!�w ubtr�gs (MS) u1� he followQYjIQ�s h!U 1r�T Laura.&�$1�Htext{�u} �v���narray} Z=1+\sum _{k=1}^{\infty }a_k(g,u)8 ^{-k}*n* }g^n 2C n}a_{nk}(.>\,"H Z���ŷ�gt $d=3�FDRef. \cite{Pismak}�94M�� was��J��7=% frac{a_{1�$(\nu)} g}{�,} + O(g^2)\,�_�� 6+ = - Ch(d-1)\bar S_{d}}{8(d+2)}\, �� � {S_d�a,(2\pi)^d}\,,��nu��1,where $S_d=2L^{d/2}/\Gamma(d/2)$ �A area�B $d$-�� pI8of unit radius.� N�VC�� do notA��X"� � hThis feature, however, does9solveM probleE�fiT he&[ 4asymptotics $s-Ekaz6� , becaus V�"� N� �D&� ��" $s^{-�m gri��8 limi" � NG�v�is ��� passe�� RG re��ente� . To�% it�%)u s.� �Gff})���p Gtt}), re� %m��!V�^ed r b� � q9 alig�Ef_{� $'}(k,\omeg��0) &=�k^2 R-$}(s,g),\no� \\ \aN UpsiNOuQ Qps N ,u),�RGm+ �i(�U�! �Zs $K� �]$a68argumentAw$, $g$�� $�re given5 ��s1Beu�e w%�  �G {\Sigm9g'/2g}? %e�3=Xb�_,u a1_ _ psi':�}{u� [��."= RRR-e���B�A<=jI�RG�2�%���5--�U)/ ] =Mm�s!Bk^I! 0}(s=1,g��1$ \\ nx=0)A�Wu��2^)[[, "u cg RR1-* �I�$Sg= !�)AL\nu \nu,��Qe" u)�+t}�satisfy�SRG | ��i�0[ \big[ - s\� _s.beta_g {g}+ u"� _{u} -\g�u�J\� \nu^] b�E�0, %1! Geq}� � *�v c` s14(1,g)=av% %&1,)&O )* uu)=u$. M�fu�Seta�  $ �)Mdef �� ��� b� >� ):g(g) &ͯ' 1r\mu% ig | g� (-2A� epsilon+3 �!U ), & Su(a�&~ H^U -u ( G� =�A�ue A��� \lnw� \,, & G1 ��� H1��FZJl ZE $ denotes�^operat 6%{\mu} r ta*at fixᑡ���s� ,�_0Ig $ �� lastedli�fo�$%�$]w2�R�aEYequr�z the conne�s betwee�f� _�mZ}). Asn� X loop�x% + inZ Z Hnatich,b 8,Teodorovich88}6 .nt�eSar �� anaY��/ 6 2� ten�I-st�-�point:\!�Z lF g_*=O(� �8!�ar� * u*^0,�� y�&mhaIG� like*� beh5r@���(= \left( {Da�E= � ) g } �)�3} \to~9g_{*}} � 8 \, .�IT"�&~U�effAMvJ verse PStl � M6ue= -�i2 predic�F� !I� u�f�� !rR1F* u_{� =u_*c  {&��,,g_*,\,u_*)}2�)!"&��Q&� \s!on{͟$sec:Pr}Twoi0calcu��6A}: &y &�u� �$<N�a )1B� �i:�`fc� � g \,E�[:�E�a-} - A&� \,&� I��2'm�j g Fk1)�ovel }- lp� u) Bk+ j�"� v �HeF���rW5_A_i�� .��contribu�  to $^� ��pA $, � �,*�s $6/ D 1)p 6� i.)QLf�*.n�1 � foun�!/"V  of UVb iten8ofA�res<si�8{RR}). Substitu�&"� # in��ib)gq�-�q�A7eء-\{1+[J -� -! !`}(a� ] g_* + O.�_*I��\wm�� 2}\\�R�](- b���>AT� .AE�_*)U�� �aa6 Beartind that $6�we se�atv $-=$�!�lea, orde"�v!��,8@is enough to know@+u_*aTu�%�seAG r, a� G�Amor��urate +�� aE� g_*$�necessdto�de~.C aC1�m@A-5���B�sca"��mX�j�I�A�VUin1Qas wel�loc ��i= � ( ���F�!FC�� % _*)= u(��AQ=0j n��v_.m�u� *\neq 0�C  sC 2� }� ��e�� !Gu�:��  _*)&=�{3.�gnua� 21 �J5m&g�*�)�@9a�UV-fi.��RG9� � � $I�B�aq�9 G$; -�]�9� rst-i|^],inNio2� b�N4gh=(I&�g�" u)� =-2& a_1\,��ga1g}�^��]�t!2! NNaX!�2x -_r !-� ]w��0��� 2� }��?>�Al)qresul�NF�FPd0} K � �� f� {3�A (1+\l�) ^�, \O�."�(�)�B�� � e&) p4 \simeq -1.101G0 3;v )&�2 �2)}+ c�6(d-2)<�9�!2.i FPdͨ�F" previous � yses��n21��h~}o�!6�=���=� )�.= \,&�\M(, {A�^2} + 8B � )� (g� E ))^2!� Og^3 ��.� 9yE0L}{4du(1+Py�Zy��CF_ .� s $A(�� B of� $g^2%m� en� elow [it�uld�!i, �a���fac".�$,$t" o"�����$tin:� �_Z� X(non-polynom��"�ofK ]. A.����),Ex��E1J�%=i�"�L_1u�%�]}{25� - 4B.)^2 + 3)a8���� Iter�solP ��g!᱁�pec� C!�Z::-D��) yield>�I &=P ^{(0)�u_ 1)}�� Y�^2.�A�B ;E�[1+ @0)m]= {2(�� .��� 01)}&=mm / }{d\a� [1+2 $T m��-i�12��^��1 BDv �>� �#"� q_Fr� u�n+u!�B� 2 $tak� to5�&d(-�we��F�� = u �_* �1+!� \{-+$}{!82 }\, *�4)4�)n�32�(d F� -u\M )+�(�]Z6ufBZWe � urn� A�Jgcz$ $B��� * �$q("k S6�. IG��2� �_&U � ��"�O�/) depD in Figs. | fifi} A�psi���&ively.QS�y%��%$. u*Z� .��6Os fP ZQ �m%�: Upo�Q'�)7$ces, �'g� on � timeTintrodu_36�!�(ve (in!%% !�exterA%&!+$"� wls B �E)�=�� {1}2 -� intd \k} {*A^  {k^{2"�1(�txi^2)[2 k^3\xi - (d-3)k^2- 2 k�  \x'-h] }{(-� 2k +1 )(�#+.","b Afi�����&" �u}v� � b�}{7 � u �u�" , �xi k\k \p� (kp�&�A�w-���5�m��.�6�UVV/n"�%��2R0$�residue�e* �r�ly�by�||ngE_&�&9$k2[�)� &�s�A� ρ#a�discaI+A'esu �&of4�blleq�* L�<2� �Q�i� *� together��>^&:K. $Z� hos�nce6�1���,io"�aam!�s-�eY&,Q#}A� ax4eyd int\%�s_1+}/ {dk}A�1+�}!�$t d\hat{\ka*}�a_$\xi-d+3 -6i�*�$\\"FataVf�V�%� �-�.\�euF��R� � \,�, me �~4{\kef k%,.��BoReplacQ�M�l��dira!�j�*��$~$a,APaverage =its.A$!�� ... = S_d�3...2�3N� �QI&"14xi^{2n} G((2n-1)!!}{d$ dots n�&!l � E+1G0 ugly��}P*r�at�Y�(�w#,)e�a�*�,e���a�$u view1ypreceP@ �,%x.I2��HE�1�e�;6�&YmF�4; }3) }2�=Q�1}n�0y� ! dke� QR\,e� !� 2)\Biggl � {2k�H -�8] �H� afida�,-{\theta(k-1V,�k}�r ���9-,&� �%�9+�0"���(�)� {kj�-���}{k��;�1psi&~�8�/�"�M�%G.� Ef|)>{  {�3�/2FR�!U ^1 \!d\xi:N!&2M"� 2�-1V� R� U8 3} -=Ri( -{� ^2U3." \},�'Y�*� {-.�4� ����&U& � psi37 d=3,\ �%S_{3}��� \pi^�,m-Numer�;e��݁�ё]XX5G ��{)� $u�$�B�Q6����M|,= -0.047718\�,�.`e�='139 &;2f.u6f)�j�8co@@7to! �B*�*H #^� � f("��1:y.�$0�xisS ��PeU $kI��0ɤ�!�(�;edm�)�} �"+lim_{6W" +_%m',%s(�0 =0,k /i,X.&C9s�/Bst�9��c*O'w-��9�Z_19)�/q = �(^0)&� ss�6�9The)= >=z&1 M� �)}3exist,�vid  e IR" ulari�,hs)b�* akenw�*M!�MS �6^Js04p: oACe method!�suc!.�8. With our choi&>>o9�"f9�3s�mplish&�cutoffp�&�*�=i�"�<� _0$ g��!~ < m�7Let us�o�3r f.5:� �| !�,\B�=N��0flows alone (� C-�&��I�$ qa�!O4is always poss/?)e�t6G6A^�@*s willh� ied 5 withI� e�s�$m$�m� fty!1A�"�.� (e$�6"�d �!L Fig.6�a& *. M^{ *�g\,*�:}{2u(Z� +uZ_1)/8!� J� I Y � m�^{d9 \\ � ��R� m.� ��� n� & 6� >��R��)�2�5&1��* !& 2)m[\,,"Gs�(��9�\B,:o>  q ,��i >O��n(=  \tau""8}{4��D\,u\,.G\,MI \, d)� %�ba��!vZV V1+q4H� \{1 - u\,a�: 1)}+(2+u) �h]\,E1{),�'f`L \}�~ss1�6��" $!�m�9$. Ex��= 2�.J 8*2$� sJ� ָ%�%U )��U>U}-5T'b�()x1)j} ��%!9)p�"9y!�^0=|2n?6|R���s�in*� N? r��*cw&�.F��+����a,G�.2H,re�&��7a� H��� "� Y'$�"<" ��Cc3J/:tG3s�B��"� 2�. F z�13�8diag.p� c>]g�hJ[�6���W��!�VO. �g'&�����j,^+%:�2>�l5�2l-�^{(2)}�A2.�K6* R ��A�.e0OAo H�$2 " g} [ 9� $�o.�� W,i� ed]. W� s.�/&� �=E%0>��#--q��)�*� �ed vari�5s4� �of � � fa� b � pub*:8=Z_1=1$8 %|& .acT.cy. C�?Cng���&� ng o�H�B�.'��_n' {(g ��( 4�|}}{19�vZ*@m^� \!�� �"$�8J2\!{d q}{q^21�X k�0 \h {(1-�(,J_n}{[ v �(+q^2)+u k q1]u *�1,\,2l bel1,2"�naD�α=<JB' 2 q^H\D& J_2L z y,&412uB\&8"q –96 u v� 1/=�Q�J�2b3�K 5�% %�$k^2+2kq\xi!�-�y'%�3\l1 8.3e� 3..8B9X 1:� J_3� { kA3+�%� -q^3A)} A<�[%E0�)(v�+)� �)}@+1}{V%S k^2(F �*�"�;3;( J_4�@ {n�{ k ZQ� ZU��,�J_5T--� � [k^4+q^4+E�xiji,]}{%q^2)yK+�%L �9)B {22!p "D}+ �%2Z)+�H&� y%516�- V� -aq)) AQ1� +v  &[ v }2�-�` )a%e6u�\!�7�-A1iAW �^3+J2 �]^{2 -���!!4�\{ �%A" [=�5 ]}"� ,\\ &\phantom)!�…�2�b~B� I� Q �9Y%�-� 29���} �!hU�71�8!t.s~qx:�2Se�]y!8!�.O�<I�"��y� �8��.�(/P>��V{i}� )=�D.{m"bJ}T��:2�62MJd>;2d-�I1}"�f �xi,k/q&>Fsi�eFo�6fT &i%`stretch :�" ,�*{� 9PB6�^5:6I: :��[2� �\�)si�6!3finallOsͣ B�)�eps)=A_ig^{-f >B A_iIB �6�!�y f*6�2Yp�' \,6'x?1 &: Q@WNKNIK&H1A?Ff�9� 9/$:-T=SA_i�)O ^{2}��b@ }+"T!��J���rM -4 a!�ln%� B]"�MA20BY�M�&�1$)Xze�� $i=2�5�! 8$3�s 30)=>I09 hol�Xve�9W�ls   $k#! $q(&�si r�6D tely(Wt, so P�lU�V�VA�\to�X 671�i�6VW'.�%,I �2�$Cin; y si,aneously. As�onMD�!�;2�8 s ab&hy�:�i}BX�:�. %�1{�� !�1,3,4$ 9�=�a�Dfo�?� means ��9M H�%� !�6�i�,MPsw&aN2&G*!t}\ne�E.�:jqXY%�s�"%� - a2Y�"�'appear>2�of-� � � fullu . E&�&$�a)�ts�fY%lA\�NZid',tb !�=_3���=ial�t��k&�m )B��;�f.?2!�"�6�rnZ-hTsid%$4f*�,ai >�)G�+b6�+-��(��J%f:FI9�v�V!0՞12�RX\kappa}{ *�6�2� � �� >)+���1/ M�]�lF�yQ�-�F@AC�AFi�6��&/X�owuexplicit-�on on�*�7�[a��85...8$x -�A�=�A21���U�eps��!�"��=�&iX+M�f:�=J"I�0��-�B&��n��9�-�N��P],Z �h%0=�FY%]>��6��!�c&j1/N med Յ�)em�,1g�9�eft���`�Mn�Xy�E|�)�a��#>-$)C).�~�W$:��a .i"0)$ [wA?min ;>z< =0$]^� �$XTomA�r�A�E�^j�#i]n6^&:�Y60� �  i)�"�#A23B�6 remaLZ-fl�* chanC``)S )\to�sB-0Q��m�aF`=0$��i���� űc: �Yz2�z�m�z�R �z�y�eV}�4B��!fU& $@jt�^ �(�"a#��2< 2�V,!k2�Msum[c&�=*�%g� f�L:Y�sY�/�>Y"�R &�?+ �?& 1}{6�ep.�p�:����& V"g �׉S)�Z _1^8.1�5� BM & G 'M>Xe.U+1�$!U�9z�&�--)�4��; � L .F3!�b�Ydi>_+.�'B�?)�(&�3�}{7`0^3�/�� a_3 60�()^2(3+�0480�0^264^6}1*�).""a13aj6"e"d2�th �7I &�=)�I�N�/"d m�9lG"i�"C!�#V!$c &�Ihe;� $3�9��>Iutomat�*yQ lled (a:� �}�bila��b)��er�L�l�.$A$ / FJ9� A =-�#(, {3u^2+9u+16A31��*!AA�b�Y{9�Q�tEF�< tab: 1} RS5"6>� %�� �V l1�s� 6ia-!)�5�ofb&&�. }�ruledtab4){lc �} $ i $& 1 & 2 & 3 & 4 & 5 & 6 & 7 &8[h�, $b_i\cdot 1�g(& $0.1099$  0944 8691 0057+<-3.9382$ &$0.067 $-1.9647 5899$o��)�:� !le}} !]Hs�$M ^-�D !8��maA2�"ybA24�#�)�^-�r�Gs quo�  TAE)�]9,/&VBZ��2Q �U1�Y��BkC"�B) =a_{ia8 b_i4.1666 5�{-6&Bj&:�is �6�N�]s �Ls���*4�5B�.M.�(�h�c:�%H�Y�BE� 9�5k~yTJ� (C "�B(1/358��)�2���&SC4={\sqrt{43/3}-&�hEI 1.3930*cd=3�� otve�����."�kE ,=�Yl. ��kulF 6�B Pr$_tI�J �PrTV�cPr}_tx0 �0.7179�% �c)#693i�Y�in&D a���h!:i=V"UZakl}Co�B�9}]#�  claDbe drawnILa�q)NͶ~.�?)�)q �UI pap�m0z6L �=I K, stri�Ely n. Even� � real>�m[ o�J7\%��(�.K$(. Apparentl�Cisq Ws�>$ favor��coi9�.! bR 0.72FK Fournier,�Y}|experi�:recA� circ�� -jetM�8 $0.81\pm 0.05$ [Chua90}�!Robo�Qd�_^ommRjd �0.8e�ing;o�9Rconfir� he�g0.7Y$0.9!qmeasu(%s�ang02}Y��0\$forward*quite a-le ago FMonin}�0*9s&�pi"fhcE�11Mbal�=(y fairly go�0ne?Xi� Amprov93u!PI�� 80acc JM�)Em%�%!!7 �^!.K7!Vsame %�� �!�somew�un!��Y--z ilarN�"{>Kolmog%\!�Vhe skew|>cL� large-v2�O"0i �&�� 8"9f0also signific�\\f�C mmonY�*#* eN q �NV0AjJ�.�U$b_5$Ej��s�arwhAY)�i� whole� $^9=� ����d=2$!�9shF�Q��MR��>�>x&Z[wE"z?M`] a�g�+dec; magnitudeQS�@er�2G &�[$ �.�s� *� "Ua��aioh usiv�> ed)y!v�Q���a~ s"�Xus,8I�� ple�H�� mad�cV2^��u5�2&0maiV0"1^�8du�`eP!9v !wn� AEWJ n.�Z(.� E.DquantWdin�Xc-isU�!4���.��02�re�>IN� &zhebiblio{y}{99}ibitem�1� L.Ts. Adzhemyan, N.V. Antonov, MK� niet�$�12!? 1082E(6�/g�:(J�Yu!XPis'mak^�e68�8326�g $\acute{� E}}$a�%, PriklMMek�52}aw d8d�: Adoco} 2)\4class[12pt,two�!]{zc2\u��Tckage{fleqn,espcrc1} %�� �  �]�A�(LaTeX2.09 %}style2},2g�$% if you w4 t�xAS$ PostScripj]Ss2��,icx,epsf,sub&6Qh�ul}Kcap�NIq %�[ 4s# ]{roaHng} m�� autA� \new8,and{\ttbs}{\�a' DAmS}{{\protect\theE8font2 A\kern-v 7em\�!0r.5ex\hbox{M}D25emS}} % add word(TeX's hyphejo�^cep��list \{autho6 o�� ew ncwL�re-�end-ed%y-)z�de� 1G fronw0tter \title{S�_t�of fermBJ�� �0{J. Carbonelle�Xuc�w IXBaumel}��ssu�v� nl�'e �o A� a 8+lle�" mE�wa�-`,q� ic system�$^3$He e�cu� . SiA�� %dro*s )� �$GN_PRL84_0�>q wApect %c!�5is�� (senn� bE_"o9^1�stabpgo!�$N=2A�N=&�BIf yes�ere? Ifay?q��}[htbp]!�er�](fxsize=10cm�fy  .5cm� f��Q�_2.eps}}�� E� g \v�{-1.3cm�vA� bodJ�(:� e)� s look a�6rst glA� a s)�. We� "� IVL0Fig_Vnn_VHeHe�{0 $n$-$n$ AV18-� �q _95}eA�I*-  Aziz� _91} S-�Dpot!+als/y ���re#h"� �sх�es ${MXK\hbar^2}�$���Alength�P� &�'r-M+cle�St%,$d$' 4-m $\AA�.�[C"�~jow �[aj������E *�LEP}.�X1[cas�~��v7id Reid5cj}NIJ)z3%z MT13-�$MT_NPA_69}=cu.l� b�� adjuNto?4 oduc��i���al�Ӂ�%M"�\�ri$]Y�.6A�"�?L9n-��IQ!9,.}^!6r m}{\ho6 $-$}: cc}[1]1}{Xv Av18 EX & EBExp. &e� 91 \\\�  aB & -18.49 7.51!5$ 4\pm0.4$& -7.247\\ $r_0! & 2.85x2.9&& $2.75> & 13.5 > $\eta_c B1.0�= 9 �g :.3ĩv1� \h!�e{0�c�r.8E�u ab/ NVse�i sup�� H dimer ($a<0$) but I��� &^��&�i�4b3�|,A���crii ���&Rm&5&�/*��v $V^{(!O)}(r)=  V_{nn"����. �,� �T&� ��� }=!�$ �>a8 E��s�b�rea�7 �=!�$��:-)�w�5[h!��ƃpag�� !]{7��bp��0file{V_He2_n2�9���}��C=�w����)ޕ�1Y��6Fe�nd� Q� b����\mn��a"N_nHewxB�2MM�>L� n$ (� les)� (squares?Ga�@� ��O� �:�-� ,Cexa�ng� �w ���� boso� �9. DespFa(}c�E� s, " .".  t���|.# mdo� �b�^ng��� $ $B_{n_3}\�1$� = 40m�is"K ~ ��%`W IQ,.� "� �� �5 E be�Z����h2\�ey?2�5%uG4Pauli principle�imposed,ca� pT5�a� �i� �2�a a�{g w!in�sed�)p6��ultFu�a � romBq�an at3ve pairw�o}!w&�" �repul�P 6to�y a baH �� inv^gQad&;[� PhD_03}: � (i)}>c�3�z$,�(i'three"��s (TnI),S. infl"�|��P-Ps&v) bn��� �armeN oscimJ,or (HO) trapE� �H"eV"- �& .M�l2�P!QaL 3- ap4-n� by��if_f%�u���$and/or TnI�"sE�% vio=��� very.ong, p� �ser*ooj�e�m us, �e��)}�nee�� � G6^m 3$. U� ad-hoc�,5ge��A�act obja�"7NNa�c��2e�$M�ve. Kee&�!�)= �&� �e enh� ���&Pr s "�K!.�a 3- or)�MsI�qt�/b� msel� e%t! S=eJ�%N=2r:}�an HOID�Q2tf�ency $�Ug G�*?  $b=\s:(�,{� }{m 2S HOAl!/!" d fiel�4s!"e= nal"AS "� IL"�ށ�beA;pe3$'O%� �V1[force��e.e �.n know�~aly� lyE� k�1 !*bol��N-����,š��HOY!�.cu1{)84!W N1�h�=�%9��mh� �Y���/�e � �&2[ [i ij"e2� 2}\;m\;��^2\; r�i$e�9( ) \.�n�n.H ��H�B!m pure $HO$)�y > $HO+ k$�":��8N=E^{(N)}_{HO}- +nn;N**tb� " 6+B>j $B_N4/N���pyQ%]F4$"JHO}>�2�45��8��c�}3-1L2.2� }{ }N}{b=2b3}�.M764} "� $NB $J^{\pi } E%�)� B_{N -5}V > / BJ & $��6I2 <H ^H#24 �2H� ��0$0^{+c, 15.55 & 6.3�(3.17 & 0.4193.11 1.56 1$3.89 & 1.8#0.9# 0.47� $��3}�B^{-p41#& 9.7 p2M0.23R4  + 0=& 10.3�2 �05�25 \\ M� 67.3�15�& 3.58 -_ 29.9v 7.40Y.6,0J0& 16.82 & 4.3�� :65I6E��i�� 73� �"er�h(�|��"N"HO}�] X &�$b$. S��hLn� .i �� a cG�dc���p�~��w�P*;5$2\to3\to4$F # ha�Z� ($B_4>2B_2$,.� an Z$e� on�qdi� "� ]!"* r �Hy�z�t�< s>� N�4 (iv}z� ${B_N�� u�C��t%e .u��)�&�er�2DM -W$ .�$a benefit>� �4� m.qݒig j\%p�}�j�& rolej � Jir* \ n$ � � -�ve�� �"�� s&�&�6V'� !� �:�($ 40\%$) ��I�@^a�t��ur�-U hard�f.��!|�-� &h�}%):8 a� 3D&�R�V"�). R 8rifugal barrier!%���"�&)(erb*-a9w "ʇ� is,a���toQ %� , st�]9�Qre��E�a�t playgol��Tif�? dram�8!�1�� r�D. 2"negyQ�&�5�*�>mqu�o�; dm�&�#s�.��on. Ata>�F� s�� ađ agains�ir*��t�`an-� �,��]lu�/x n un� ���+��m�E�it*�)po__8Frea�'- _ "from�", i.e.da-c%� studyA�few"�\ x&�per�bG 7��AQN-�a"�s?�6�, -ed"0 ulta�He��A�I�(. Our technO!y r�"a!R N=4g �-x<A�R`2w*6"���Q�^{(n)}$�SED jump�pa�.���3%�stato�"�WF N=3�KN=4. I� at a� n"ffacc�G oLNR )( ��A�Wa des�& to�2U �=χxis?. Ma��� ful 3c�* uld go fas yond%N!�y5]M�Ye ycisA . �%>&{9�:).� S.C. ,.a) Lett9'44(�) 252501;��*.!g�" �refs.Arei�G qM2n"F='Mar�$�#al2x�)C6T)044006{�'\P� D. � ivat� mmun�8.V R$Guard,0(Navarro2�9$84}, 1144�1)g �2� R.B. W�]%hem%1�4}T1) 8047V.! ��TA. Klomp, C.P. Terhegg`)G�caTZ ` earr 32n��,@ + nn8{\\[15pt] l � r{ �  dis{�B(* ed z5�  cg{\cal{Ge E dg{\dagge�� d�%0.2in"�W �( ChaoOKlo�Sz+ ���;aI� o(�lexY$s NdI, PmIe�SmI_�( Dilip AngϤ8nd V. K. B. KotGa�iu{�0_B Re�&La�9 ory,| ��Langpura, Ahmedabad -�( 00+0|absz �(Wav6��lan)N0F�,&� via ]i-�guc ,n Dirac-Fock�,� L4y̜Iden-�(�%in :2of� al &i�%m!�#9�(($F_k(E)$),���' �al�}0ts� xi_2-%�$occupancie0lan n_\alpha a;^E$ڏ�l�torbKu embed_ Gaussiax@thogonal ensemble�H plus&�%ran3�matrix ,0s [EGOE(1+2)]�6 se�at-S -5 in gѪ�" -mod�u 1's exh�� varIh۫5K�� bas�)�Sgy%-$5='s, w st�(�i%  m@x F��sou":!d4�(s� � �*Rby* �@6 c�%�R��1��1� �.�9l^E m%�L2� � � Hamilton!�%�cҩT�F� AWpointjk�Ge�C�m+) &�;<�$weak admix ��*"�� Ac%�t bS corp >i�}a��=q�4� m/� of�,� -�cAv>�� �f�j\�:{0�P.-d,05.45.Mt,32.10.-f 30.-e-%% ) : Q�umE��2m�2. .N. Semi卥<c��$i$Pr!��Pم�$�$Ato��uraZ46+�-\date{�)�2 N�� Sl> I :�5�%�zI O�v ��In�"�T[$� } L>B�|�����9~�1M��hav� �Y -��m�2n}m �!*����}il.* high�#�7 moum $4fi� $5d$�V shel{*�I�A$a�g.��7yi̥X$[{\rm Xe}]6s^24f^m5d^n9%�Qo�wre t ݅. AcrosWperiod9&��`1� 14�e���1 a�Ce �Gd I �ua�!y�lbU$n�P� middɩ_ ~� is 0!*�P>). Along� CN"!L2�o -��as)�%���y "��x� < 1oscop �W&d i�-ād Œ~P�� VLeR#qL sum�_/ � bitalE� 5 �DU M*hFl-�6�[ Gribя2 Gr-03} �Z!�!�DA09�2 puzzli�% low- ��r�$bi69 �#!�$Aܳ5+�� G_�:gsuccess�app�e� in nTi�2@Br-81,Ko-01,Nu-03 3}, mes%|ic�LQ.Jai�L�3fa�of� um%�uP9)+Qc-00�1�3s�7ed� ��J for J+�)�dynamic��a�dMi X Be-0 ah �-.�x hyp��&A�I�i<� i�!��#,$(afIsX�� ��.Y����ZCoulomb2q *JC(hdc}) ahead �*� )�8bKrish&zG&�OE!vone p�Z�2�See� . III �%d�!h E�E�� uuV3& o sa F� !Z$\{H\% h(1)��$da \{V(2)\W�e   �m&"�J��N�$<pa �in 2-"ps#H��&�EX.����? extrem�|�&! .4(O_�w0\Նo.-AYwo��2�9" (TBRE). R+Mly.demon�te��at Sm IM�Dk�D7� \+i9A�ve�)��M�o Pr I,' s x� �aD���Z��D! � "�D"D| ,��Y!2���iAV1A�m, � �.� f��%�etc. G9b���l%�Y2"�I,*&E� a�.�Q (�vval�x3� 3UZ�  ..J�Gixed)9$�s DBreit-R a�55�F7 �.rt�!a`tQ>�*.�da%Y�$�) share"�s� BRM,!��]a*�99�(%kͼs%P� �Pb�:of_^ Ce� PrI)�F����?��AgM�an %Rpo n&S�5 a�IE Br@:2���ne�$t neighbor� K.*,�,ѽ��toN�="!�2�!��<+ �;E"Ifitfun�֩7�G ��to� anu �*"G �Hr� earthͦ(-�Tum's !Ker)ahwe��!vto�)�E�c2han&!4.8. In�A� �>n� . N: &� `- eigenU2U�e��8ve�\)��2 *"!d  e}&�L G �5 by f[ �A . .��M�$bauche-90}a m�of�!�d$&��f^m6s6p�;  {m-1}�di{k9܅�AOB�isF  (E���i�� V�3�3� z .zis 7402.��#i�])U�6C&ividutSI]��R� ,�P!�dA�� �� � �Rid}��� �0�s��|!�t� 2��N-a���u��pap7��n� >��/6,7�8J7�!�in$& :3��/nt~#�*; v ��o�sV$ oms;#3Q�� !m$Qwa*�/i l��x@Jr�O(iir.PT�/avd a��ef!�!�P1W�A�i $2�2ndh�1i�%�� �*Rt, �"�#e� �IVW{ %�.V��cusd#EU� 0.h "�M modiTdE�b!�co*�=�!�a� .� ^�6�inJ��:�tH�, SYI � methVf�+�B�I%� !aAI �+T� �#!L%a brief1=!��+a�ic.�&�L�qlV �&$)dfuB�look. I�O2r� OL:72-2�.O1]-�: M�2.DW UO� "�Mn�} \sub �{ �C2�B�"* mcdf�[ earle*works�*pW� a5 ��� �b:( MCDF)Q��uit�>enű��a�Y�E�5ung6O-�|Me^aM �P��r A�J� Hart�8/ (MCHF) kfroese}aLdb ensi"Qin non-2k!6�F&��" ��'>M!�?�&-qgrantZq/p� eV leO ed i5%F~%9molecule�parpia �.�.�inuity [o� f����%T��� �bS �M�f)G� � ��9!��1�in�s ean �> a�Bar�"..�I��<.��� ��� H"�  Uq� ��-el)nR' r\"o�er �$)A�br��e $|n\�o�!�&�n"(phal �sum I�6 ��Ri mp(l�]sn�1/2SsUG�� tota6� "�W m $j = N$,">un � $jA�is�FM�(ea�J\ symmetry �1�5>.� M�A�Z�� spinor-$e"aapCpsi_{-P$}(\bm{r}) OY![ >p=�$�41}{r}@q (u�ginY&{c��VPur� hi_{-� m} (UO ta, \phi)�3VH iQ6K\J-K6J^G� ''>#\u' ;�Forbtl}B6���6��$6�zH� U�1a�)� rad#"/N�?�#�d $ ��:1w %^  �A�I! ��e!h(>��D$lsj$���schem[�%kU�i$� ��a��.l�:5(CSF's)���-. EaCSF i�<� $|a� PJM��P)$J% $M�H( ty, 6�y�!�"�q�"hS%����$a:k="vfy e��una�6x� k c�u`2'w�@ eps:�)~e �.%�1y%�d sub-e $n_iI" �xton  $X_i$�,�se3o\)�< $J���N-�CS �b]N6� X%5��nyS,ons, let $a^"�)_{njm&g�Z bA'�,�,[:�nj}\ti�s6� 'j'}]^{JM%�( �+j'-J FF- FF^ E�a8@2j + 1E\�_{jj'} J0 M nn'}]T-Qe9BQ����$&�s M7co�9��3EP��!�on�$M$��@az"�@��� ]��h�@�5"{ ixu� deguv1A8�nd�C��|6�jfA�D"+s �s�r. A=t+ gle$� t $p$���&�V��vacQS�Nu�� zѓ [(.Ep)^{q_p}��_p X_pA�R6;{p - 1}A G bIX"[ \�b+6t1n1h1, X_1A�_1} ]bE e) �}]^J|0-�)&� M�q�3 ��A�2M!� $i^{'th}=��V $\ �i��,senio_��"r �MJy �� ٬6�"R ɑ�3I3g�"�7a@use�A=Ae�;x l8ea�|�$���s;:(judd}. An rJ&2�*}w� �($Z�oms� &�E�=CJ�$H)fDCHpAly�Y-�aic �o�  $N$$n�N: le4\su�f M}N} c\bm{./}qJ|%$p}_i + c^2 �ia5�� Z O _i)}{r_i��NL � � j=i+1}^N J 1}{|rrr- �r}_j| }U��1 Z�A� عre)�"�Z.bm�Q� -�nU�, $.�$5*a 8"ar-@\g� �[ yNTN}�ds� �#�(>�ES.��thirde�$��A�-�X�dU4&�Q�.d2� .\=.����#1�R!Z� ��A�es�+�� P ��vP!6�-o0. ASF). �� $ =%Oa:ya��u ASF�L%   $P AgL(q2� C2��Ynvari�� G T� )�A& li���.s��K_r.R�| �( a�� }c_{r %}�)2X l4m2asfB2� �* �"���R��cR�E_{ �J �dqB���D%�Al��<���P<��1s>��%�% al optimio9n �*U��2f Kp 2&L Lasge pliersL*�Oone�*m`#rs6�a% � �#0� �I\2���0X����f� 37�A�',6�6&X�"��a� �E��o"�~ 1 desi�yyE��al}�ginveS�exZa��tdrik�xb�W.]�p wo .�= ,9@�� �sp ed�:p)e%�'F�+} J�Y�%s-� �B)~!����1��lo� @5R a�"�re U9�o�I f>� self�!sis%�u MS�/�Ny A���A� �4a!|�>x��S"qre6-�.�YZAMact� *d� :�9AB{ "�)[X/k+'�KF.3'ed a#��cA��W$|��_�(�fgR�6F =::{5p�6}6Q{5sA�J"�:51 5]]B� p]| �.&� phiFx�� $"��a�.�)`q medi!>a2_ a $J�� zeroA�al�ko ��6 !�"8< _M�Eq�� eT:� ^�;EptGQaÅ�t�ng $6�6�<���/c� y,s*�<}� Zh manifY��Ill�doubl�""9� s am�v=>nu5&� -2�~,� �i�f�=V�Z� _iP_iJ_i�J�dA� p_i}��_{5d}XJ:�6E�qE6sE6s�E4f�� �4fE4fvEm1ij{J_{2 i}6�*bgrn.&R3 p��!�$rA��!o5�2-*(so�&� �. P + q� r_i��, + m + n$. F�9�ME� 6 s $m\geq 1 m-�S $2N x�$np��7n�y��1sX3���"�M�mla�Eh�2�V�Th�$a���խ8 M�>�.st ret�;g*L �u#@q� $6p��y����6 m�@>zen�x>x����5�Zp2n2qp��.v![ held\]���s�5-1Aᚅ�8���4eRo:!g5#$�/b7��!" %.}4�1un A?( $�8g��)��&� s�_? .���I�-[J ��s� $(1-6)s_��N $(2-6)p , 3/8$(3-5)d_{3/2, 5E�($4f_{5/2, 7 . O�!�seA%Z, ,,2gR $5:fr������).6" $N_v$��! �9cɒ�/17�,$�A�!-/s made�C�:�a\,� 0G7 $n-l-1$ (�Q<]n� $l$O ax&�a�?6�um>�)*' nod� � 1>�S<5m q�h:e�5��{ing�Atra�G>] j� e#q)typ�Yr� � to� .}/wA�A!�u�bFWa�#�6�� %���orI�oBY�/�s�WH�0"� p&�F5o`#!�It1���*��F *?_�,$m�O-�% �U.+�*%FaQ�.�I 3Ws ��in� �H� ^ =&!�it . A�n" (CI).�| @A-�*�2��,�:E Iplu tcapkEQ&�.��* $sY=��E�s$uAS%�iz"o1���9e&6"iG+�x8&[:� or!�a��4 our6\�s%r�A!aB��nd��6�8�g�N�� 6� & 6p� 6pv� : [ & �[ & �[ s_� �[ {3&e r' b� phiF5&� � 2  + s:8 ,=0EƉ8(9s ; 4 ; : "Q ��7 "N 7 nd $2 ; ��q�" E����c��i Y� �/^� ce�A />en B�2� �)] seJ ��9�8 6s5dO "v��Ar`D�>�Q hal"�� � �Hy��/$7#%>i����Erg D8& openq i FH�*�O�B 6� �d�R���?�% PJ|2 .re g5��. ptable1�:m(A�"qt"1} ��W�2� $N_{#CSF}$2�1 �J B�6)B.�5 !��}��Vs�&mk^{\minqA7&�>$ax���ls�+�!M$�|u�8re.L�RK�)��o�" 2B���6.M�t!�) 7yeA�)7Jo�(2M2LE�9P). In addition, defin �9bunfilledFE -N as !o = N_)  - N_a$1]6�Hpossible determinan�Oxis ${\tiny \left ( \begin{array�uh\\iEE \right )A- nd {two-eM4 Coulomb interA?(on couples %R Slater.� to � equa!/A� K = 1 +�N_o (N_!1)(N_oD - 1)/4 \label{K}I�K= Ts which include itselfE�others with shell occupancies different by one4two)�1�k approxim�A�!.ground)�, $Ke alsoYJ s inmanifold6�i�M�!�douAexcit}sA+is!��[al equieKt�CSFkLchosen in our calcul U For fur!9$ analysis,a-�hthese �rs�g� b �2_ As menAed��contex�CSFs,represen ��.� N�isAomplete^such a.�al�)B5 because zZ N� pair��2I�IQ MMorAL ]s. H�v,�)�%�y)�ed2T �zerot���� descrip!>!�.�6A�outl tripl oneEEe quadru.Lare similarly needed�E��2�. Amongq>& �f6Dd�+mly E�ede�is�Cna��D $K_s & = &\L{ K - �D-�B�K2�F�T$ - 2)/4}{Kz noi�N& \simR, {1}{N_a} \; $mbox{when} ;�Rgg��.ᯉ� ksng��� The last ��A�A numerator!� ��:����z6615]� but aba@lq� . S1�:�of�Hs��q%�eo.��^�dB�[%�%�5� +-%�3)5�0 3)/4]����dblJ�a!,�-D-��deredeTdirectly.V $E}1/ ?to��I�8. However, high� �2N  connec��llF� �͇same $J$]&� $N_a�3$I+ $K_s` L$K_d$ scaling showd � of. s mix!t first �is close�A�(GOE predic�valueJT princip� 2$)/�s��"[s dis�d sayA�$NN��$\l| \l. \nu_i \ran\r.$, $i=1,2,\ldots,N$) is generated by Ɂ��U8Hamiltonian H, � is 2%,A�be!�12-p"���the�� paga�� it t� $m$:2s u� 8( geometry (���aq( structure)��|2L�rs. Ope= form a �6�=V!�is �d by,N�&& *0= \dis\sum_{%h <%p j,\;k l}�nk l� \mid M 5i !j!� _a\;a^\dg ` l}\, k}\, Ga i j}\;;,m v2sym} ,&&F� ���j �i � =Ol��, "R \\%"  ��6%��)�6�1x � �4� Now�2��� in m>�,A�� �o� basis (Bnlla;$0$�C$10 G 52�by �q��;ql��all&wayQaL*�b$Ap r$),lQ�� erm�<�юle�s�dan D1]Ny1�)y$ (not ao��� `a'�ndsi�ntisyma�izY wo=xq�d� non- � ��8of three types^�UL1e�2 \cdots mN�6(Mznu- ran_A�Z �q Y}\;ziEjNri4j `.�F�p-23��J�=Z2}^��6�p�iN�);i��)0���>35��<�qf�2���:[ ele}!���\a�Z nMR��H k�0_$Ddu"� a�ssU�s}.z� >�Ppisu�bye8(above Eqs. �a��:S��LR8��nu��� �a�@independent Gaussu variables���%r� over� {ʎbI0!�;\;2VRh|�k\r|^2}= n`v^2(1+\delta_{(ij),(kl)})���v��eզ wher�Ge bar de�Vs"*  averag[$v� is ahtant. N�� H{d(m)=\l(\barr{c} N(m\earr\r)}}��p.� dimensA�AK&���.�U� 9��(is $[d(2)($+1)]/2$. .nA� realisticW �3tom�ns,a mean-field�iE(��4by a finite se]:.  ,tes) plus a : xity9 �wo [*g;e� e priateM� 1� #Y y purposeYsi��.�*F&7 \{H\A�h(1($\lambda \{a�\}AUMT hens*�CIU$\{\;\}$UVanUY�(\refD)- 9e�% 2�$�=, i&� i n_iEV!��on = ��*� EU>�� gl&!i$A q(spacing $\Daj2�$�.�*1 :t�` l| i\r.�$�g�al��cho�2�toA�mP5].�Ja"�exa�]e!�)�$� 6�aD��w� a�=1+Eq. /v�S? $M'%�!strengN�U�2�(in univ-Y)A�us, �E�FtfN�am�s $(m,N, C, �) ��los� -Za{we1X1� =1$. #��of�,follows from��)< ), ��)��)�, just���diagon1�  (st he���inYk)%xv �um_i\, "�#_ i}$ q��$� \[ iV�for�n[ ? ��Basic��6��V\n  r�P} Most significant a� 6�i�a}Hchang��n%��3d�",ty, level fl�1s,yy��ntropkhe�+ adma}� sos mark�a� V b=Fig. 1�* :Fqly, i� w�, viaEl�[r�iE,Mo-75,Br-81}h�fac� atq��$'sA duce"� )i!64@E�-3��(rho^{H,m}(E��< (H-E)C ^m$ take "? ��Z larg!A ough< � �> (oft� super!Lp� (H,m��$re dropped�8� suba�zs� W .� =% fracQ2qrt{2\p�(\sigma_H(m)A,\exp- 48{\hat{E}}^2}{2}, IZ6^� < =(E-�pj)/�x� JSY rhoh�6I��"),�c=\!�H�8!�eKe eerum cE�idEO s��"�ٴx$6width�pA2$ re wo devi)�� Aj2.q they�cak!$to account��4 Edgworth expa� iUKe-69}��ցR skewn,($\gamma_1$)p�2pa�$. W��E<H(E)dEA: eta(\wideafE)d {E}$,��$$ _{\cal G}.-% low"+ Edge �cor�ion� ,Ro QUat{lEiplaystyl�)e� �*ED�{E}E�6%diZ8:�8�$\{&$A� i1X}{6}He_3�6 +J+a74,46,N01 aj723663\%%\% e2)"�$ edgem-��� He_r2O��DHermite polynomialQ�� increa� reaNa2._c$/ �hO H \ge�mbd&aF�H * @Z���e trans��^(8earest neighbor� &�oni�Poiss�o Wigner� m. Pi ric +c�2��&G _c \�$to 1/m^2N$m�Ja-97}w l�J� . TZintai�&] ency� %(no�$s��$�, li'�, } �aft�we&o z $|k��gle ASF� $|E.�n,� � $asf} assum&��2�.[ k c_k^Eb. Giv��.� $� $ .1 �.� k�� \r.� $E\,C^E_k \ E $,|NV (�A�(0$k$) $F_k(E) Vd{\beta \in E}\, \l|C^{E,}_kN�*�|�}\,(d �3)$. A�E� e7es"�&%�Y=�  &� � 0Breit-M� (BW)� RS y poini �myF$ � U e BW�)X(�� cg$Q�m-I�B"�s:�RF_{k:BWb !Y��2 �*�\G��,k}{(E-E_k)^2�4 ^2/4�����>.}\cgN~� �� � k} 2 �}�1k^2��F��fkgss��6*��E_k!�k | H |m$�p$p=\int^{{\ce}_p}_{-\infty}\,M�dEQTpreadG� $11= > {3/4�1 1/4}$. �"ly���F_k ($� k^2d kjH^2 m�- ( � .�k e�)^2$.�#�Kl�i>� _F$ (th*cal�, BW domain�M "�#BWa�k �e >ՁF$ T�� TU�Z�|y\ach ��.� � e?U rt7!g�r below��� (as �$�*@  12[�_0.N:I01�R�@B 5$� $-�` �G6��0$A��on�-U)�'�q._6r�`��-�c�*rgu�bask)a:�sWC_F�o 1/i�m}�sFl-97,�2$�"K�  uk'#. Unlik��tox �G\F�*� commVor *Gs�regula�, d ir(chaos g��)� t�*BW��6�1�*�x uniqu,+gn !y%��A�2�in �quantum�{-!�b� , a '&�po�-|'U^has been�'-eT&r ly! -$J� o "� ��BW-��:�0�)\,� \���O( &��)^�2�1�}\;� *)}� M6%.A)�+qdE}{\l(�+ � Jh \r)^ }\   1�  �4itfun}"uuY}�y$: L-�#v$ supp-(e ))e(.laValpha�@2W shape (h!. $"=*�"=)�(ite�sA6a :�gU�� arrow� fty$. x >x2%�Łт^2(.P�� = ��ta /(2-$ -3!!� >�3 $. I/ impor�a�aps!ata3i�l $M51n� Oj  altho�&� "�� lyi �except.�h JE�svery far their"�.�< 2�* �a�6�u�(23) f�Uw�/.ical ��:� r%�Ks;�mo� etai� discV�&"I(m�. One 9^measur] �*�of[*�� ��3ng �&Q��"ipe r PR2� $\xi�,!� (E) E!{� \,|C� ^4\}^{-1"��C"2'�Qa7�aq%@econd R\`{e}nyi jp��Im-02};AP&� ��� lso �&�jt,�u��6!$-K� make up(�+Ir��gy $E� ��� Ref.�Ks7[ 8,wr;!_2� :��Y6", .�  \l\{1�/ ^{GOE}\r -�!��l1�k["x \r ]^2}\� &int& ^{"% dED r�\bf{h}}(V \l[A L\,�x1 �� d/3` �� xi2g�+:� In%!?� ( %�hLd)�!�g�.58 Bb of�yp|�� R valilyE�"6 &� y FW50B �`�0yp�� E'� q����n eff�veA �. 8 bf h>�EM. Also�& Ql �2��aE" �^��~sum!sE�̈́�� $k$-*2 ! �$�%b� E� be e�1�* titu%� 2�$���(E��Q. A�:�e� g�B8F�-��s:m J.~2k -=02� )�l\{ib)y�2}{2__ 2"! n ^2�;p �6] i� m!M z$zeta^2 (1- )}� \ti� \r . l . Uv"G 2},\$ 3  - ! (2D-3).k� �}\r� \r���� �"<(�9|�U(---As hyper�, ic-U�91�b-64}�U[&a�W� oHeffici�$ $�`%@ 1 - *�"7 }/ ��$R+ = (1/d)�D<{i\neq j} H_{ij}$A�.P= 0i (E_i�WBe�� variy off-"*h �# "s��a�e>3>H�42�I�,�a�i�be�La',mU�wan�'VS�N.�!{a %Q�4I�*n%�^2 2v1+ E]IUgoexi2BTInstead��NPCl"�=to@%Sly reS�a+ �$S^{info0$;2=-%�El>  \log 2�Ite�!Sr  observs����2} Z we iH K$ mR;beyj _F�6�� _tAf*=l0.;a%�i!u 1(!�$# 5 k modynamic/Fed���O$,B�#`.1m!)� s� tem2$/ etc.�co�6�5nd �"8"� A�ja$�#$qi�l@ Eus5&�m" t$ r�is� a�the= #�-�o4q4�Jlic ��#iV . J� ��#Eve�� %��' arry� anumo_um ($J$)Q$som%tHs e�� $L,S+�ef�  iU2!!pl��uld�(i =&. &>rvA� $J$-Z.y (� &�-�8in Q�oQ �$eo� orV ,s� avail�*�#h��F(k-02,Pw-04}���-ttA@tAJAb$A�2 nucl~8�@$model stud� 9�1,G��R>� d?m,2��,9 $_E$I�derived �9H2^�4(, extend to!e��&?7� b�C�: to b& *Z#z!~I6!WA�A[baa!�A`*al,ic  osc� �!�develop(F�aum^)>�9,� 2a,Fl� xreferencxrein. �89v89&49I : R$�^+V%�97N972 on{�!}ZBg? !A��n n�D�6 ^E$}��C�} � !�e�ntE�y,�. $J= 4^+$ M;�>�N$"SM)�+�,�F'(��B� lA�kariU$��e�C� figu�ns.J4�I� 4f^6 .�F�U�=F��Qs�A=e�2 Ce I work]�A For Pm,��an odd�v (�87�6 xR�G"#) $J=9/2^-%>B!ag�6!�DcoL-�)!T!5%�toa�erm �2JG� the 2�R ��� *earlier)-D�:As �:io��inu7orb-csf}:|Q �U!l are pDZ %.�M=� pot�Dal!�ea!G�6 �c#+Hc'EX�!l��YYZE� Q�1#I&I� �G Sub-.�A �=�#|-�;� �?.�=>z݋�YM*} By� 5 ,BC >L*K p# \6P*a�$A_a .< B�sI�)�y!�smo6d (a1�As-� $E$)�*.PA;E�vari %BU&� C�'of ) {H, !+$�BA��I�binA�-$Ai)��_our.�� �U�*�$D�#�}!,di�B�to sixtyv���siz "NF�Bt63 �� normal:� ��"�e��$ndpmsm_den7�6"CH&�(�>D"��u�r�*"�1 $, "�>^2@�)&�)u =s��g-#2%2%��� �hop !��.e (2y2p6g 2$i\Yf�T). ` SmI��Dnk  agree���E:��pt �.n�F��5+"*5<��5f�'$sim$ 13\% &Atha � actu`!E�vallI��嵥��`P/rU dm�/promiF'N��K͕g ,nounced � at $(-w�R)�:M9% meanW:4$ between $1.0 > $2.5$.&gI2�;9oB�ŢB�1.4�s�7�ed aheai0.(� ure&7r]�\c-�P-Ge���a�po6XGA ,e�L"`-of(PB�y`uWJ�)t`��Anal3 SmI�BV 48a�]<�%Z�$�underst]GC�yo�  it�o�EC�al��QGI�"U +ncy $�-tilde#�Y a:Q(rh� 2:}E��q[s�c(2'�'�S)^2(6F)P :(R EBSlD& ^{2r&1!�y2%)�e �1B`)^2�*FX.:� &�:�6i�su%�~alIQ�666� T/1�^\prime1/ f�c ^!Db/DJam^@��\;,�;Xs(^26�F = l\{d6<)"D\;��"j!= E.�\;�!*p(F'-n\; #A��?foR? 2^ �bO�n� � n Br\!�FC^+�:�Usu�F��y:B�0�#.�iR)�"�8" �n� rs,Jp� Ch-71t^D �q��M�J *�  i^� �1� = [�>]1�Fs�&FH2�y\; >&B �B��0l6���I^��.| $ r�TC&-Fl@7$�$�Y>�$o ��x0�6�%��*� >�F�y &�2� T�%s,� .��#6�M ���6�}�"� >�L9���Eq.�;phii}�=�!&%to�`&E"?=1�o=exact�Ve� nt �/`6�Q"�V� �&B4�Sg��4ly)NR at9b9s. R(ws A �.sI �& seV(P�w.mix�� them�J�)Much sm#.;!a�Ate2Tp*o\e�`$ ^ "p"]�GeJ� $H_{rrl$rm DC}$ <� =HrfivS.�"D T�gt 1}UZs ay�En�!P5sC-tI plot!N� a�l.4a. At� m�_2$��)s %F o�Dap.��\��`��n5Yig@er=& 4f^4�^�36"`2�sg4 -�� �lso vik\�H*&Na5� ��  [�)Afighmat}� �two4,tinct blocksXerDm��m 0.55� 0.8.t]K&�]%�C�\ M���!"!$|1/r_{12}|!4�"�51 B1-U3�:a3n_6km� by a6onc�=�}o>H �<�D in .�A �"�:�4$�$}I��e^_as� m�} ?}����^B=�>remai):A��=M�(Q���B� �NdZ��3�mb2s lie 1V=!4!�$ �et�++?a&l�7lac8%Si� 6Edoesn't|�"�A���5? a24b %s%8!z�cartial})���.�"E� "� "�Q`� ��E5is llent���Cmok,G�t��� to���^� |3um~"7 �- ( �-u31�I�T`!T >0*�GT rongs��'1�Uš"�2__.|/�M�A�E�&�!\vaP%s (�_ �)�Yrecour Y$H�YvDc%|uvU�!t S� '�ivi�Vi�@indv^!�U�UBUS�.Fu�Zs�KBK.�Eo&�%$b. $} �QB=+ .�=exhibitM2z7N".e��GA"8�| �v"+?X1o�r��!�s A2!ed2�*�_��Sm6y ��A �s[1� wkY%k2� vJ�=.�* ��*1 C�Kof =^5a9m�"zm�.: \pm @J ) ;dp �\ "�E9}_P .25C�� � ��o��*�+���G����a�al�@�e^ veral g6�fk}N{of I� I��Ոd an>=�, 0,gm5,/ $0{2r�%_�H �s�?""w8qa�&�:7�4 N�v[5z;# $0�me}/@"�T�� �8 eliiA��&A=$5�aSe b�Bfi�S`&�0B'NO� VF= �re 5, 7.�!112�!�u. ��+M�BK#-S@�:R1&o: �)a$)�"as^/�"��/alv>U,por!i-6 (itARF)be�e3�is papeND� �pU�is@%Of U�Y�7 �m.u � ͳF�!O^(�q "�i"� proced�I<in@ )|&9* Csl�jJc�9��. ext�6ed). Mova� away zf�,X"ly sv;"*+Y�" 3V�4k$* !it ch."s �a �9.A5hof+3gi�E.&Q,A�m��V���-�%s �4N�"��"�2�2p 5.2, 2.5 q  10.6� pu(veFn��2�Ur$%M!1�  5!%*��a�fa�L �9FSG surfaceOa�V��m�$�$-1$)��6A�e����Xnd �5�^~&�-�B&A�m,we go toward��0%eBs� DB� (or"�:2DD(shq�p�D�?�iat&^" e�T do�a\�MHM1�.�as�52�$*�fin�;2g"}!I���!:es�i�� �;a�A,edYG"#. C5-�!��"�l!OatS-�O�t& .���j.�3e~3e>j%C Num�ipNx�, r, z�*�+�lo�g�]I eTE3npc} e� inve�� :<O�rn*P0A !�&�8*�g�In� h��to itE�Jg Y�!�6g9�*r2�"�%>.��I;)f!S8j�ang;or9C!�.j`re!�&�#�!5� .**� ad�;F�D�"� 1zpLSo0f�1on�-~X04�D Pr IuO2�&�m�2t5��-�� qu�=�#�*os�2wn��6�_�$U^{28+}�""�+s �Gr�2. Desp[.o,� !�Pm' 2� �EenvR1s�-A;Sm��%Q�.Q� ):   ���u��m�$2 i�2� �-s�,!������7 %l��#Sm,�B��isY�& . A� �a�y=1R ��Af �0.39$ As�4|0 0�!n6�.�e�I!� compared&�'�x��Gn�$�:xi�:a7�6u� �:P:is�8, 6 an32��R"hCbz/48 [d�520 s���2�4"c �'� q' � �K0anA !@� +*$'s. o"x4notPGa2�uRee�&� 6i��� .�� usja�[X>mE�9F>s2E+ s� seg�)OwŁB�^ .5�!� -1.7r . OT ach X "& 43Oedjv U!D^mid-t.I�incorpoHng 'cq$s)�w�U�2|��� �(ll�*.�t�Sm�R Pm�ri�de��*>. > ��6�7 surpri� �u P6�U EL!�ich canA7�64Vy!1y{�7adoptS1�mNdA)�@�kl ��U�R��07   r#ineA�Aa�(te&�iFof\��E�K# =�O!b�asonably �� _ 6� E <%p {a22>d-f� ":is.to rem�d�� 6vC��Ak histogram� %F�yEO�+A�M2��4 0.27��33�b0��ɩ�:�|U-�*�oug9-;# � �* �O�9�GHbe v/5in�A!�/4y���-s)�#:�BZg-i��A�� e �_%B��� a, 5T6 classifyw�i>Cif��NAM&�-or0&: 20\%� ��/�}u�c�, spon)Q ��LD)�! R�R* ��� �� Wb�rhoW�locS$�d�A��YB �8iaX�Cnd<=1:.T�e�EY �=(is �ghigh fr�5y2S< A +purely�&1�!�őovoa1r abouN� �%�{�.�5A��'"� �"�t�A)�7���w�>��Znow�T�TDTO*�}! Ed�C�svs y��a��"p""%;," ^E$��*Ax>��I3�aR�G many-@j6QP," �a ��� o _ex�#,W�Y�N�& �t X=. ����� nD�)�>yiABQ �>. 2�5�H#.{ > x�T�|&�Y._|uD�-/�!1�1�p k| �qagger =a cB>P� B;I$A�!�Gf:re�I<annihiI�hRor��5J�a�� �0�5 8� mcdf+�J�5lso 5Fa)0[2+to�C��R[^1B:_^�^l�7Er^*[ .2D>= ,k #E|$W `:|!�>�0 3*e.�.�2. �� � 4J>��r�A�N� . E� I�se2 �E{�(ͼ \ll "� "�Mƒfew&Y�!�"5#�Z%��&�" orig�fh�p '�/�:Z'�u.]�9@�J/�,the�$ �h�;rh�'22 ds�|&�= 6s� ( $K=0�F ltip�<� HO���a#de�e cas�e4"�U�r�B!�� %� �i :� "�u�R�ocf� Shg�5A)f� BX���Wof-�q"�H�7 �8 . �AY� aQ�!:nt2�1�! :�uZ{��}}� +}�R!) � d-his&�� P9�B�b {\em ;A} �)�nAj��� -u���(.� h5eF�k!�Pm1+ ��a� �Xi�D�;B^m5)1F:)  $�+� y. W�Oa0 R���.�&��-�c.��acg>�.�"�� $6s$� $�%�7 E#�'|%&q%aXhaoticl:2, $��l O�u;b� nB,A)tnd!��5��egf,</8K&9;/�a�B��Ni*���13O = 800�W 2148��885� �e�!�.����X:Gw�!Z.$"%g��(h^�1>�9J�6�\-N6�� %�(�nrom��]ȅ� :��1� �O%a� aA+growth�decay,Jy�'>F%� no.Ctrendho { ^�^G%N�����( �6v�= �j" �$����>�ő&�͡ "� 9%�9a�*"�P-� )�,"�:�&�!M������Ft� magnitude(���Z�k��e� 2atB�� ��L�|��>��B$ À�  III E :2�0�s�"p"E�C �{.h1>�"C,ham_str} U�<aA!K��JT�ruc9;fo�sv��u� 2�t��AxXLanthanOto��&�3Nx"�3$HĔDC}_{kk7(Bd$A/�jb��t[=��I2" .��&� e3off&�q!>�^<}[2v%n|�|q�� �Fr�/�x!C�h�� veH/���b%@2lСD �1 $. IUl��*�%�l&u�%�OG�{�9��nV1)�e&� o�X�w5c2.1D (2�����K6��(6�M�U#�\UAp �e ���r=V� �{ Me�2� ^is spars".*+�{"2� ,��� )�[H� ��mi�!�.�N\K8qBb�;.�=©��R%l2�2s�2�5d^{n+˔$�!p/{m }x/�)=�.~!� �6mP��nd3$,"�P� V�5>� �p)�_$ M�iA��%�J��4fN�AGEr7e!6�s��� ese � CI�P0� . D"�}s[ � � �� �;�L24u E�[+Vno j u��leA E|.Vs).�����INbZ m.&/|a gra?6<P.�-�i[squAOof�u� $(6���}aX(&�aphfactor)f31e'@!��7F:�Q �Q%�� $W_Y� B Y=��h�Hsxet�NMk Td{(i' -Ykk})\Li�z�ZN�(j'/ll2/IAH_{kl�?]%binO9>�?Li' = i}[ u � jj.-I ��- 2�{��� ��.3 �.c] �9. To im|%����� !lj� $\ln ()8v@n".Y)1��� tڃb: (i) b��"&�&*1��E�m�� p:4}$AZ.and; (ii� �&(>fe�gi-e *�3treak�[m�upar ="�RQ��se�:�B �W,~Y �i QkAgr-95}, � urbaə.���%���qU)��i� 2* �c�^0!m-$-�A:��� �1 r"�@ emptErip !s��es. P��'9\>-� 7 (�*E�I�?�F�6�m�wk,�6L.�V4� >�oo��"�W� 2on�� "w.a BRME��5-=p�&2�$7�Mr�e� ir iBp ity � %o�f"&T"2[?h$gmrF 2t�H�+�9"hsh  2fG �$zf6eC�)$ (engin'Y�W^��'�LA_v}j\Eze�od!|!��"�Mt�%E&.-%aq��A�9n% 9a�2 &v�2�'� N�Yѽ� i�(Ze-96,papen�'EXIG plaud?E<s��K��yof �TDng)����`>o k argu!4!�B of soura��p12{�VB[.<q7%?�%�more �3 �>QT��+9�SD0t �"Y(�BX#�2�:&G#E�P:!�sr=~ . d�B� M*RQ�uWbe�%K#r?�� ~ 2�`�x�*����6 ����6w�mixE�CSF's~}�"� i�=wm�i�A��8.\2�.� �&K  mm�'r��rgely io!�'(theIsF� U� on $AA$Aƅ�Eb"�� $t_���,R0 t_i = c\bm{\�&}_i;�(p}_i + c^2(5J_i�-&U .dZ (/$r}_i)}{r_i��Zx�>B �% q�o�#�w,.="f(vi ten 2AN & " ��}   | t|�F+ a^{\de}4w}�)( +F2�.t�R�T�g�R |9K )R1!G{12}}| o2�6�O!r6�|uU�E � beta �V� ��sho��eH Greek 3bet; (w6����T �� �bri� $hu�ݡOi9A�v 1]�V bU%o+os��to �Pjnen�%R-� )*)|�h=%�%�K G^K( B, C;)B�M) Rv &�Jr12.��u%0}R zgg $zo}b�/rad��F +s �6,$3�n 5`ɈB)I� ion .� ��e %ǂ����:���so&�a���� lindgr�VI�?taly�re=��N_c�v�� ^2/4"�A� ��RpK ��7�2�.�:�s;|  N_c$� *�!�!II)^E$Z:�+� � Z�6�_rPJMJ��=_sPJM�]�f��M��e@�!heL2>1ix�Ai�ca���er�3 IT-es ly, ~ ����z V �-� Is"� ;V � �&0 �>'%NB�"!#�Q##2�<� )=6 �9� ��%� $\kapp����e�\ �V�� = $.�C�a0mup��Le�I p."\ �f#ŭ�+�Go expl�b� RAnT:,Y�-�&�� �&  l��<%�*T E/�:x & f"o � �?R�Yt*��}"�sw �V*}�A��8*�3�mC�: o�-s�%'_� i6�8A��,0es $(i,j,k,l��Jd@ep� "�-]��6tw���M�2�:=)�@,n@,.�V : C�s�!� Fu@ Outlook6� � j Y�f �o �}Sgi�A wave&;of� �Cl:�F� ߩ�;��f�n%�V,�+^pJ�<,n%�h1)KKA`.�-��. Exam~�c uc��GY?J/�9�in���m? "�8in�na�9o��."SC�jba�j� not . z.�F$ a'�l>E�c���w$epY5}�F< -�T6D}�Gl&k.�j �j et a� �:6,7 b} �b�@o\i as l��as"�5�N�\�1s�9�K�X%B>;5S�<es�=�F!Oh)t��' &�!-ethrj� � � um (N!��2�5�d��Nl_h%UA��me >NPC�%Y|Ao#B�Kosc�28g/7� '.�Kw��eB�/,�,�@A�bA�difx2O���!ach�to u!".>P ��employ"�2�F�NAz��w�� �wo� !e+B� "$ � s. V�Gfew�62 .�edKs ($p-�+�orej t?B2E�o�1�e�&Ns�=�.mm=E�� uced ƣ� �Bd&�� Al�rcE*�s!w� X% .�s �p!22�.��mix�_�1���Q (sa�f���b~� r v%"� ]%Eq.�vr12� )i a�*d�!}%;���Fa��������B (%s%� d $Kd�I�2-)L-���� A! ator�7pS-́G#BQ�2�jus N� "� �Nu s). �[an &� outc�r �rIDK .5( Ei41s II-Vw � �:�prograZin*^ �!o.�*� i m復0� neA�SP�b�P �m�2�D'�x�ii�?(. \newpage��O>�O  JBibli�9phyJ2I� � theb� }{40�$\bibitem{mbU��W.~C.~M(, R.~Zaluba:)(nd L.~Hagan�~ {�.A�2E� y L\' s --��Rare-EaS�Elgs=�,Natl. Bur. S�'.�$ Data Se.,J!(U.~S.).�NBS-60, $, GPO, WasPR0ton, DC, 1978���1- 4} V.~V.~UX, A.~A.~Gribakina, G.~Fe�T M.~G.~Kozlov, Phys�v. A \ڳ@bf{50}, 267 (1994� 9�9�I�Ponomare �ica D13�[2059:�C](A.~Cummings� O'Sulliva � D.~M.~Hwrn6 Jou�of-B�834}, 3407 (2001:�!7.�>�A|FyIzr��v.�=uE �$ 56}, 5144%s7Nob�tQ� F{J�7}, 4933�8)Wf �mBoAuw J. x)2q4 p>�!r6nrJ�>�.�J�3!�729�6)� >�B�!�:��mA �8ab30l8F�0�|�:{�C�ra�"v�6A�012713E�2)�7�yGr�:ml S.~Sahoo._5�B �3](3349 ( 2003:����T��Brody, J��or+J.~B.~Fx h, P&Mello�Pandey.�!�4S.S.M. Wong, R��Mod6~!�385!�8>�* � V.~K� KotaRZp. �4aI22)S>ZN�O(Vel\'azquez%�AeP.~Zuker.�.N Lett g8AR072502-�.�BaJ� Hirs!EA!PankBy�.xC �6�034311t>�!73}}Z- Ann1�(N.Y.) Z30A.58RWJ��(Ph.~Jacquod�D.~Ston�q= 2�.2�� 938 f061Y.~AlhbAd�&FkWobst2�."M�6��R1335�I06GA�Pw"brock,� Kaplѻi� Bert%�Z�ko&235120�a�.�DQc-00} B.~Georgeot)6DD.~L.~Shepelyanskyb�ͭ6�� 3504h�2�G.A� Berm�0F.~Borgonovi,M.�e�,V.~I.~Tsifri&A�.�{\\ bid.}I� 0152 �1:U6/d:�z`A02612 �>�Be���A.~Smerz`� �]�9!b 0304 �>� D�y.%D.~Ango �f�.p͋i� 5250Vn�VNm,�� Ghos66w.1�MD7c 016209EF>�bauche-9  J.~B%�C-Arnault.s Comp�YR��1!X1 ( 1990��.!a!@N�1W,= End�dFukumi,K Iinuma,a�Ko andTakah� d� Euro�� . D,"x 1A|27�P12�S�� Pors7 F� �6353��BG froese.�C��~Fischpz T.~B"��P.~J\"on�25D !du�By�R S"' an MCHF A.y(��.y , L!<n,!�.�grant}I�UG �=��Methodl6� Chem��$y}, Vol. 2.&ed2 by S?�l�w@(Plenum, New York� $88), p. 1.2�parpia.�F�P,9` -`E.���Q� Comm��9E7 19:� L.~Vis-�O !�!�A�;, H.~MG�ga�ru? NieuwpoorbD�un �8���h .iKE�Dyalle4P�ant% T.~Johns!�6)a5�E%�Plumme2�Z$5��42E�896JL Desclaux,a��ay+oy F.~O'Brie.W>� !�63�<7> judd. B.~R.~Jud�E�i, Mole�}I OpD�!ic�� Handbook}]� G.~W�Dr��( AIP6�962d p. 5Pd 88.�$T.~Kagawa,� HondMS.~Kiyok=����94! 7092�P>��}A K.~M!�!l�Áuen:�Z E/9( 752jL.~Benet�| RuppI�He�4Weidenm\"{u}lla�Zk2�v�J�KeL��� tuar< J 4Ord, Kendall's2jdvd��or�KS�1$stics, fif���ȡ �(Volume 1: D��\$!T�(((Oxford Uni�W��/s68>S{� IBO z ]*�79}, 183<Jv02vv ar��2�"�l8l 13410�0>� Im>o^M�Pipek,Zl�6[ 262[ B� s6.D6 lR#u~kaT 1 >UAb-642k0M.~Abramowtiz�sE�$egun (Eds.�=K�XAoMa)pa��*D/NBS��lR�/s SerF�T55.*@( U.S. Govt. Prin�# Og�e:�.C.�^6� F "m!U2.;!�fJ�1� 03710z26oroi,!�Zelevi� cB�EBrown^�I�� 7!�519�5).B�z�R�K��r^e���� 120B�PӊT.2M�:u� =�>� �93a�325!;� !�.� G犁�NG\'om��:$J.~Retamos�e.�5ϝQ"a!Ya05& � .�=ơ�ai��V.2�.qh2�543� 36+\��RE8Molina�2�z��� 0573�f>tea:Ee5BZaQF� 356� >g �l S.~C�b,���!W$T.~H.~Thio2�^Se�1� 7!�.�5#�.No��-al Sp�(Z�( ��.5z6:q�4.� _ 21���V.~Dzuba.r$ArXive:phy� /04011576#  826E%*�J��$^�-�956�19�.�n4A7 .�B.A. ��N. Frazi' !�M�A�.�q7�27�a19>]pa�)6`T:�pe�iH. A. "� B�a!`:8-th!_304:� "�-� I.~L�-gJ� rr��.J*�  Many-Bd�a .O 2nd ?�SR%4ger-Verlag, Be���E^*%� �e &P2�u�q A.W.9).� -mat!6495.�,>1�<�<F�)es r�<^<r*��% fig{�Z$ = 3in, hefh= 7�P= -90� g>F= c:�.ep:�capu { Ch�bڳ= "#.�!�\ >J�.��f�ep2�4��� . = fkeF�JCo2��"� � �$.�(1�8on&\"vImbd�>�fk�F�� �Aob��J�6j�n"*� �@1vBZ%� 4`(!�ofR(�8aL4&}  dashed+- -dot curvvdra#&R(>"�� @L&6��"LO&s..���6.5r$_parde-#!b1"(a)R�-�Y!�CA�9ri}#�/a Bf{Pc.r{%L \(&!4�8`'�5�2D�C  %st� Dy�5�'�xold60( -9625.2394 e�) ��*��gi��y:by� �ten�&d# e cr��a�saG(a�S�#*�(b)� so5�A& dot-AO���y%,5"�*�(!42�E�^�2�=�Z�f>(�� �s��A���G$/.6�A<h�]�$%a% B�s4@ ���. o���$ndcsf_engy�����m �M =�stfJ���BMU�Br?A !��ned i�";'�$"�U{-0%��nE})��2bC G6SAs % p&v�=B �;u� Cc�1��E-.{$� ��R$-1.5 Amsw�\a��N�d -1.0R$-0.5\p �.Vs 8A� $0.0U26�� ��f��:���>�npc�.�!�� c>[�&�U)%=(|6k�R4.��T:�s�s&�O B-�5row��%�n5��Ex�E ?*u2!dA�W�-;9 /.o"�, D.~2ZX$. ޹bL*(c)`cop uous!>��� EBe*�cbY�&.}�q�pcej~ )��N?�gin{ �{c��>�E�8NocI &X�cV� �A#��s1bz5=�+Q52 ����5�HT-;�W!��7�M2-�a�*�U�s �d N�\ X ?�7X�=7n:�X-��.�dR: �B�7RdE� shifjfo��qA2=Fo�A=0:,e�a�-ws ��BGX^E+q: ,n #5/2"�X^E-1$ �JX{h��2(N;\��X^VY�_nY1 ~S�f9���edEG))� 3 n_{6��v-3p=F,p�,1Jph�.J i6k&úo�Z2� �b np�SVy:-V.�VUu%9�T{�BP$2�Z?m�dAA�U�q�&. Eve�Ao�G6�4 �X��.�i�, a�D"M1c�dA�2I"�4�51�,*bleQfo�je�\F��2L �i $�7vi�}*�W��"�2B9n�wN$�k sC�!ph3x 6Pm3>N_*�X/ 1� �T 2Jl0�o��a[2P!C)��)��5Ũa�dom��son�6� �tͤA�>͎Ͳ�>�mՉ� . = %�V��.=267�Bc2�� ��M:��� docu�B$} v�%% *rx<f�r�J� .aps"�/ R_%�8 5!{APSuxREVTeX 4a5�. %FVer�8 4.0� +, Aug��4 %\�8class[aps,prl,p;int,s&��addv1$]{revtex4}b>twoiT,�RpedJ; YouADRJ�dBib�Aq apsrev.bsiM&S� % C��1a j . auto�6 lecti��rct!6 %b styl ` le (cile), soRun���;!p� %��if&/2. %�"�1V{ ���ZX����� \u�>�ckage{amssymb} %TCIDATA{OutputFilter=LATEX.DLL} !M�=5.00.o 52�0DLastRevised=Thursd?]Decem�h09%$4 14:55:47;.kGraphicssl32:m$nguage=Ame�5 n English�input{tc�fex�q�(title{Stabi0�hydrogen�4e�6Q>�Bdy�`s } \author{Jayme De Luca��mail[ 's  m�`: \ ]{deluca@df.ufscar.brO ffil9�{�dade Fed�eDde S\~{a}o Carlos,t�DkLaa�g F\'{\i}�\\ Rodo\�&|3 LuI�kmP+,\\ Caixa Pos�� 676,BeutPaulo 13565-905} \date{\today !W)i abstu} WL7B8s>ncir-$Keo7�H6� in a�<��W>�|R�� was �A�� overA?DmWSL}9k�>G@of� o�=dissi��~� a mo� bradʼn�;# $er-of-mass" h�2��E�ISce9S/�s bm ed oscil�[�6mveta!5l[J� I�me#}is� ea�a} exisE�8a 1W�`re �c�sant"�C��: stif���_5���a �q9proble��<R��YU:�8Fgez= dur���)Niv^qcoi���&8$���1� pre�y(�I�a� Y>=b�Fre&��&b Bohre�)i&�'P�auB e emA'on !s׌J �%�of!za��o�1�D(QED) 61 perAN error �u��o�$40^{tA�x . Ou\2 xC log��hma-ly^E���eavy �m,�:E�D deuteriume%PuonA?&G.2#sam�,2�, a�� �4QED. Analogous�QED, �ZsU[b:c?atu�Vy uJ�k�Y�M;nξ-"2}al%%ar�G�;;< N*Z&t�?ğbe  dela(v/ roqbetic e�Son���D \pacs{05.45.+b} \v��x Accor�;ofd� quasi-6*-� 6)iJ���.\}| �E�e�m�;P��,ar\'{e}% -in]S� 5>A���Fdam+�A�F�onlJ���%�� J�s=� �! phen˯ on hencef�>��^�a��Cmi em�)"ioa��rp*�r�%�R� dec�@��9ensate�r�!/i�5��life-��1��?�@U=�jcolAe��i �u .� ��5(��e� keep��Z���v�f� �^d!�\ ȨsH�in]�!)mɕs �xof )ca� volv�ɇ�c:�"Si��!�"�)Mzc�'ar� KW\BCbW�U$ imaginary*]f�?DStaruszkiewiczPole{\mcx��>siak=���%Jno ad����ZI, sesfy Max�VD Q��d��E����f ze�� ���}��[ urac�~ qua`Jh@.�1"�zryu���%R!��~ !O a_���ż�% paщwe�Gin�C��>SsetR)7�l.ADf�i�� most popuY�H � Iu��self-Eة�A��ZrA�f��C�WBUis Fn�"" ve-'[M� (DR)S~we�|4 9�ofM�"��(Fokker's La2g��� �-at-a-"C :�Q�child,F� ,Han�?%a�-an==(�vnWwa�� e Lowz-Dirac BXforceIq"}o�u m�pnewFOA��G5;��B�>q)(e� l (DF). B�gDR�3DFWsrP��y%D�b�� co�MPal�Z�b>�.� {�charg�FW.cpe�n�%����&�)�^P ��� u9�C^ �-DF!L`A��Qa!�1ƭ{2>.pu�o� re. r  sAHo�PaoEC�of DF;a ��a � gLv!ci� AsN�uq�gz����ordjP��*p�toy��1�rDRB�$is absolutsGd� veHEU� A*theles�g subt�!�cgq Poy��'� or rIe!�to fR� D flux8X�{vEt�� DF (�w�u>��arded Li\'{e}nard-Wierchert far-fields). This allows the atom to receive energy from other atoms of the universe via the effective half/advanced plus half/retarded f� , a \dmalization mechanism that ��bsent in DR. To understand how our dynamics 1 soluNo �equ^�mo H classical electrod F(, one needs! go beyond�$ simplific S0 suggested by!�Galilei-invariant Coulomb problem. In quantum e6{ (QED)H semi�$Bohr orbit�hhydrogen correspond to exci�q ^ state!�at decay�!�ground !\�a life-time of about $10^{6}$ turns\cite{�}A@e analog)eis `proces!�( troublesomcDR !�subtl 8F. Disregarding�4singular couplo �Dcenter-of-mass coo5ateE% naive us�IZ�@DR, which predict-cradia!?eE� comes ! QI)�!V$ic potentiA@0%�t! 1Ui�(particle diA�ce!.reases�le�rotEU0 frequency in'(by a factor�wo dur%!he9�, makemissaWpof a sharp line impossible. Iegvernstruce�to estim!b� ��sip �4along hypotheteK circ%�M� directly �K�HLorentz-Dirac self-%$ace�forceIl"Mm,complexity dQ4qtis:� stems slree main sources: \ (i) The ap�or�i!6Poincar�P}�two-body�y;%�!�no2�th[ms �no�H} limit Hamiltoniane0local Lagrangdescrip!e�B{a� straight-%�f��s onlye�s��ga)� � are!nd warnI8at�F� ����+ with triva e�eparable>� �,e�( bad approxAcA�t�~l�isticF� . (i)� delay N�bei!M8 infinite-dimena al1�al syA'� ��a3ie�funI�a� �� condi� ; ad A'4the non-runawa�: ' lea�FLa well-posed mathemai3� E#% {Dr�]M� stability�oysiE such�ls reveals stiff eigenvalues %�AZ�9(rarily larg�aginary ��,�e�as��(ger multipl�,f $% \pi $ (O�2t,number!�8ears naturally)�HStaruszkiewiczPole}%�-�g�_ic��to���diffe�5ial5�AG8not slowly varyA�e�� wher��d typ��lly it has jumps; see for exa�X!�62Lie@ A!� Ref.%�0{Grasman}. An��r EiI,small!W amet9H��highes�rivA�Ѵ �Afb�)'� Ron ��I��SA�BmA in &g��q��A��� }, Elieze�helium � ii СC spec��>� ofKdo��r6 Udipole i� k Oi��f� s eas� &� eve�;��0�a���a^lread�*a�er� ne�onant � ur�Qse�"[ ))a1(arwR.�0 (a low-veloc�.!� Fokker's &� ��,no�,Deluca}% \ \� AL� io)�!1N w�tynumer�%��n ��M$discrete},� e �ioniz!� i�iAG�C� tk z��iB�, �ʉM U��]' ms like a��i��QyZB�Q6y^ IA�is �"we� e!)grips�! :*�tomg!�conA" ! � Exe�St���� A� a di� !d&b hs:� �A�i� b� symme �ontribg-nfu�[ypast � >�$ a���r is �A?a�v�Kof ea�a6 . We hencA� th c� E5Ef{!u8�-s ftThe�ntities� XuniahV)d gi�.e}. A�MCn< �$m_{1}$%travel� irof�us $r ' whil! eAu� haI2�I2}$>3�a unit��6!x�ic�ars $e=-1 �heMU of lgAI$% c=1$A)>�defe���angle $\4a $Ione3E�p= uemanaIFr�he �8rA7es it (Q8-c "y���&g$\Omeg�8� r�is)�,A�low�order���,� Kepl�,law% \begin{p } g=\mu -@^{3}+... \label{E�al} \end<% )�$<equiv E\m_{2}/( + )$�! re� A� . For sha�-�]�Zici5s��7��  $l_{z}TI� to first )by #^{{}}=�-A�2%{�� Bofe�inver&�AA�uc�Yco��(, $\alpha ^c(=$ $137.036A�o s��Ssɕ*?,�Ae���h*U�� Cartes�(to gyroscopa("~s 9�� is unz�I $xy$.bnd�i�o� out)� U�na�pedN i.�% N�Psubstitu����:�� Ma2�,Z�,oR� � a��&�a�quadr���!t&eEuler- 3*M �-�� tM publishe8Ba we hav� delay�at han�e1 r��qcha�er>�t)B" ,ly many root�Z9��ol�$hyperbolic"� can �Fb!'�ins}xVF, i2��*"�qNDAAn4ndard techniqu�)FU��o keep� AM st pow�߉8 wE_*= term!RZ=%�% {Bell,q p-i�-�)�isa���"@ �V$� �!�l>� (seei15)�k*�JQ ). H\w*�� is R� ��Qy �casPdM�LuGt Z7��a symIpalgebr� ftwar �4HA e=��\lambda �p/�$, ��� ordiG 6� scil)�� as $��:[t\ )$ (  3  rl!le�Q� %B�V!�Q�^"fo)�"�"=si.��! } (\frac{? { H^{4}}{M})\cosh ^{2}�)=1&�Istarr� �a).r �$M *� $. Bo7�-lanar �.2��@ izedE����v%��1>>2�� �)�f6A &j $(\mu /M)�a �&w �$$(1/1824)$? Q rt�"t.�#� &w�a�~ F�UQ(U�$ !(e,� �lyE "} N!?�j ZA . � m� ��A�:�$Z;4M� sim *#-13}$6&�y�>cos}!o�;left-�� K��Eq. 1�d@min�#$\sigma MR|\�{Re]�|$e�@simeq \ln (\sqrt{ �4M}B}!�FmW�  $13$L$ $�u$$�E*-��(val $14.2<| � |<18.2$. p��x X9�� b�4�K&��3%�,�5�g� �o&toNfs &� � �� =\pm!6%j+i�q)� � �fq%a�y% ger.� $�A)�8$6�e�&A%\"j ce betwee��řar��,2^AsJ� �. Furth]i of sU2��i2��.E$� ����*tK�or.���&e�will be%�n else�)a� ���r&2���% �As)� !3$2/3$2�O*u" V�N(*� �break� 2&a�%��'�k�l�m!v# �no.�"�*6�pairs��fog� wm%pleE!bne"+ �!��vex� b*�ߡ����_5 ��taA��+ist )�a!uv&u� ��iL+� should in�K6�"BPas�&A6-iB^��'c�Krigid B)�it͂es,~- expe�+e alejEnu�,ep�.s��%.��%�as. To in�-uc �m* ideaw$y% assu��,!U:B�' f rH,e"� � -te>!�m*� s���*�.� a�a�y.omRyP,C &� �K"j _{xy}$�!give%*Su�A�can fi�"se �*k Hz}+hxy. z}^{\ast .xy  }=0$*%cbquU�+.�J�F !6�)=0&swF � &\!w�� .�\-� combU��f�0 $pe$.�as: $u� a_{1k}2 +b �$ ,i;�Ap6��:�$Z g W}zVb2 A�J�� real�Id !b)� = Ilr�� �,�n% �p� conjugN.��s. Us�nthA� % ai.%ej=�a=neA��w&P �� M�Ez!����t!s�k���)�'#��s�s% { ��#:J� C)� |u||Z2� DaF�Notice��*O[2 at $ `�aa]��r��M�=i>r r-!c�!|��)f �excurp"&�A��c� , � "� 6�, "$ �!c"1� 8 68Ϳ��ZA�i` ntin*��-j#er0�=�)lsympt!� sere�cus���5-M!.&lessow abovA�nW�c�!��v��eJ&&}b�3i J��T!m"�1go0$0e|& must }%p! ! E |2� &s%U%.� hold��Eat/�"�-talK$-�ic ���rm�+"���X&(�+�,i+i\epsilon �(*� } \\IzH-nI2 I��{��!��d��A ����6�e� pure3(�Ebsx� Jq -G6%. ��&"aWeI�-#ed A-searchc|'e4/1au each� t U"}1s 6T2 %�)&9"" $� a.�S�,��I�/ zed! An .�o&\�.�% )1�obt %by� e Eq�2�3\  >iin��m�re"5��n &�*�9an���I2p&+� dH* X2%�|$* �"} -M��=�6(aKq-ma )}{ 6$+ )}&� asin%�FA F�(2G-2}) �4�q(3 x�-|�)}{% q��' & }&^ e1e2F� Acco{g�' QED,��d9� �maximal:$�"�"�a �v�*�'!� rule�\Delta l�\hbar $)��t&� de:U$, level $k+1$�$Hi-��) ts e�6�= � a�_ r7"�h(Lyman, Balmer, Ritz-Pascheracket��tc...), :�&he!5�vS Ds�d.h�E.ye a Newm&metho�,`| �G $� e. E& (%9�)$:$uT:~!"o}) ��e\a� }r99C2�- buG e��T�1� �%�7 $w_{DF}$ &�2ly closFgi*!;�r:  �o%v��� "�.�= equa�(=7 6.� A�I$2mD�$ ;on�Us6��hatI��s $ces satisf"m5U��,E� �es"�-�"�."3!#at��"9<5�!�e�a�#eX<&�'cIiI�_D; m a�>t $uZ$��ed��&� 2 ,��we��, below�"�0 N2~'aVT� �.m Ze�!q,^ e��F in �ic  *s $(137�(;)/4=��)$ eB��u{ak��;2to`w_{QED}� � 1}~f�1�gk�FU1}{(k+1�Z)$,��c9��>9�* ��l� >�+��_���< � :<k+ listii�)F�P�!�A��r�;t$: observ�ʼn�we�2M agre=M�"�2 Q8..36�%�^ L $40^{th}$69 2=QED. B�Aat)�* �ula�I&� ) shQC-'��4���$�$k$� A��%� $q=[�1]k$4.� y�CJ�5�-1}=\*2�k}��^{3/2}kE [*9k,� �+AF�X�(a:%u%o>�*!�%WO9a�: s2�8&$) !H� al� to Schroe�w,��A (both Aq&p � ű�2!>A�V9peratorel-(s�k�_7r'i ��1\bigskip"& tab� }{|l  } \hv RA&��-É{�F ��\\ K<161.21 & 6.137$\L $10$6,63.750Z688% 6a4282.88 & 1.136-+{944:�80.4 aa0397.40 & 4.09>�+& 2.43>�7.Na519.59�833R�1.125^1.4Na637.7a9.911:G�! 1b05.= a69#751.4!�6.059Ra 3.68>�E&!�1.4Na871.84-88.P!� G 2.39V�2�Na987.25%�67.-a 1.64V{1.6�#1109.1!$1.12�.b17.�6|% i?�9�1225.92EH13.RH 8.67.Q4e� 8.699�bb343.2a 1.06Vm 6.60� �FAc62|Zb466.8A� 8.14.��5J� b 5.109�Zb585.5��45>� H 4.07V| 4.05~b/2�]�n�x �EN**;=�u in@4O$e� /c$,BP y B� >e $,&���UQEDF:��� " �(�, $�"7 4 �S DF B C >��,  . L7;$��"= �! L�G� q� p�n�Q3H U&�K%=*6orL e us� +" 9Hl (DR)!�t�Fway�[�isJlys!y�%i�F�H-at-a-"� p"�as a �.eH ��9\ j 4 >4- {Fey-WheeN�-noN D!Iba�onKr*9ri�M-& �  �<� y/� n<ith6K�meTK!�by N%ͦw:,�6�R�6 ,�";5un4Gse^H �-'wKyn N" stemU#by"� �*> %4S_{F} &=&-\int�+ds 22}"�4r }&&+' d� (||xAx_{2}|�)\dot{x}\cdot % % r2 ~8x_{i}(s)$FC%Q��Hi%�of�V"$i=1,2$;M S�,arc-length $Y\,$, d�M b�Gd� thbGur-vect�(odu�($J��_=)% 2*�!i�3�N8e Minkowski sca ;�C! � �s&� �;$tensor $g_+|nu }$\ ($% g_{00}=1,g_{11}=g_{2233} :�.EZ3A�*�(yM)�A2�#H>�I�&� I�. ). S"xFaha`.�un�����of.3)C�� st�%6�DK D�5�:v�<��m&>`$(��J)Q�8@#�� r�<x"� dea$�G��erfCNl$A��d cau�%i�rad�a�familiar�D�1inv�#!*,Df'o,s�G*2 ��s���&-v�M �6s�r&�*�b�� inco�6�Rt�I ����)�+y�1� l*<<��9%�wi�#an�UY� �%YnU�%mp�ݡ;(�E��gh�%iDcis what we w0��B�e- 5&��.��SF &{ covabS.d�! �Max]'s"�0�K��'�6Feynma�A� of.�V U Z;DR>��2�-�&| Kad� vA- &!9C -j�M�:&-(�!�B|a!�t!���#es 6�U)adv�(d V�VdFIs 2YB]�Y�%-ype>�A�=�#�Dc!� �K!(l�r�H�`A�SO@)DFH2/ �Cej�*, Poy "g'�Iore~ vali���tr�7�4M��0�affY��<$A!in�"ofNf%(tache�C!�tS6�o��m�+&  a� A�\E6ǡ 2� 222�S�:vr�Pt!%cS&Z��?y}�+� ;).��EHret�XN[L A.� 6�# A A �eQF$. But agai�R�Aj�a&J�._&� ���]�7 �m�N�� B�,t�-. S�Ln:W! pr�lA>*�Mf� sta� �=a�tur�!w(neighborhoo Man �Iw�+�#����9��� s� � ��*Q �idC� 1�- -�az-�of���6s� �a9� curr�2�$ppk5J��a�B6�69�6a"�T exer��!&Y�f q�?Pof��g:=�h:� F ioX)] �%�2�:� Ev�o��&��is  7A0mac"�-I�H e�@ a wi�)� �N!j b�Nry�0IdWodd�^�%.�%� �)J-*�!for us&�Gj6s�.Q �9M/"-ga@!6P is*�-iS��^{(1)��2(M�I� v)(a6�)+6"x)(i% a:�)}{�Z�Lq GRadF!W@2uV5a�24)A�n 0 > lCa�$ �% m�=x}*�H19.�1��isA�1Ah�~,% �X  lz$a�&�19i�a��ed #!�os�ƅ܅g"�� $u��Z$ non��5� �I�.�&@R�&L .^1�3e� P*O "�,%�u}=\O�N2�4�%"#-ZJ-z}Z+ge�;��E�A\*a�a�� �%kUa1m;'��x &W'~ oszE harmon|ly sA(be )�y�(�5�0*�/z}) � �E="�%�0:�% -&*F!�:mc*�'�$ �Qquare-�/A�6 �)t--�4%i"�21�e- n[2�e� d@�;2 x �M!W�$C}�F[i��"�F]�Bran�)� A�A���& Oy KY�&� 0D:o0�"K6:� to $w ��NQ/2!\� to2uZ���(&O&,/see _�>BF�auA��!kv�!�� ~ *H*�B>**F�/Vq�+��Q�" !F�e�$M�$r2bO�al�I37e|��.B"a �Uat�bB�"� ]9G . Am��a�2xg z]4� �x nlyq.�v �Ca�e fac�`i(1 ta("�EDc&�gB�(a�b�ou>u�^a�% _ \ DR� ��� �V�y- } )٩�c!&�'%'!� ayTF�' � �'�h2(A��atri]ly�=i!  Rydberg-�0 �;or�rinciple!N.umv-cF(���� o� cus�KwidthCF-�%�á�or�A�p E�Q��>���g�+a�Wfon�Vle z.��aQv�5�?�0��6f;�u�u��*):�re8/�2�g� A��E;-�� _�?b�h<at�/V U�.�AF[le dow;��&9�&a�"u &bexI� �Y�a�rm�al"�AJ1!�BR!q.Sks �;){ OIZ lock�:>�oAnal ���<eV��w�,9 i�1%!,�7x fallN#% 8"!d;u�6t ,�Hi,e+kn3ni��#s�di y� " �l st (6)j -�e]a6��E/!$\�I�&1400 $Hi"B�� !%�a ��E!&]. Jg�m f�$�cal)�Mce&�d< |5��nN�={6h. g@�I�We:&�e1ye�empete& �a�of M6&4�&�3IC�2gb!hcorj4�3F �al :�d��a�e�!L&hdm��E��Bus so&�dM }=$2�.�-ZxF)C2j} !g*�qDJ�cb�2�c [!logarith���AStic���8=0�0:N�E� �%M326�<=hly.�X&�c%a cri�T�Hviousl' b��9}&�co� ilur�I�> I��� stay(>ep.���D>NO!,og8�s�alizziv w�P�B%-SV�/. J6�dm &� �d F 5&O���s,��.�>�2j0*�1a PDE,�F^� W(���!isit�ulu�a!$c� ruct�averagk�&�Y �Xq�%|K�^-7R1c_dat" �q z &� "�J&�ecuCF=`�"��>7i�n1�. *��>6.�F% �2�=�7iy�1p�] ���u�4K$.fa�deuau�1�F muonw�)25�R=4e �%� !��h!=[!�Y&3� QED).2� ��[�� e�I� j� �>:�:aD$�J /G,w9a��ic�~$�IaaQu�R"*ef�% . R�jn !���FX&�jN �ui�� g�!a wayeK;eG4eSW�J2|ui � *�m��y�wa<|*_eIm.f�Q ���s!��!��l �v0 F�to �`M*� S ����ear���.�4�(:�)H !�XaKof2� I"~l&�5-]�� i�N(i�khDF3� �n - newf�A�;+%�an��> �92��M!�=i-� be d:"t.nV� � ol:�O��u8-i� W�� nk Szm( B. RodriguO�Xus�I� che&SF&�8� C�B3> �MATLAB.�0cre�rces�0bitemN�Z S2�[X A, 1968 {\it Acta Phy(q Pol3P} {\bf XXXIII}, 1007,�eh`15&\b tr@} N 1913 Y,Philos. Mag. P26} , 1;�@- �V., 476�/m�f}�Gild A�3 sys. Revq$131}, 2762%8 �H3h A |en CMA�H Von Baeyer HC 1972>U D �5% }, 80V��rOs PAM 193-e$Proc. R. S LondSer. A} %l 167}, 148�5[*�wLCurrie DG, Jordan TF�0Sudarshan ECG%�)� !  Mod.%�1$35} 350, M!0 G, Mukunda NJO1984 E)A$)]5 30} 2110.�,r}  RD!K9bK19�096�"$J. , {\em A&IMpAIRelax�  O �Applics },  ed M.HwS�Scesi bf 63}, S�(ger-Verlag,< Y�q(1987). �E�t}  CJ 194)�M CambridgeU�AMU3% 73.�'o De Luca P98BJ LettD80}, 680:D*,p>NBOE �(58, }, 5727.���pI 2000bH6p02060. =.&+<+ JA%�C+RP!?5 XA�B�,17} 157 ; vFA$bf 21} 425.�c`R. E. �,K.L.Cooke, D� ial- c�@J s, Acadt PK.]+A,,63), page 392�"N!F�DZ!A� em C"a�ChXj d Pa�iDs}, Addison-Wesleyo (1966�`=p"5cUP�ib*Pc. 76Zend{docu;5} b�\�<[epj]{svjour} \u�{4ckage{epsf,amskW�`6"graphicx��Tnewcommand{\bn}{{\bold4ol n}} 6"q:"qB"k:"kB"l:"lB"Q:"QB"P:"PB"R:"RB"S:"SB"br:#rB#p:"pB"z:"zB"d:"d}!�addtol�3{\texthe~"}{0.1cm"b�Q$title{ Mel�a��evapoL nh!n "#b�Al Erters: ��0l Monte-Carlo�u.8ons} \author{ R�jD Werner } %\aff�1� { \insAe{I  f\"ur�&o�Z�1Konden�gten�!vO, U!68it\"at Karlsruh�-76128 Ger(1 !date{Ve� 4: \today}% \hf)3Pre�at� % �"p .} % A$Received: P /�i�2�8 pab�ct{ A � n��zmel�(p'oc���, lk k~ �a83"�(�"]�Fw *�Z ir e)iQ0d liquid phas��:� �� D R is � /i͂(Q&�Zs via�  _H wdhe�pecp� h�A�y lmean }� b��I�sA�$q7_{\rm B�jBer�~�6er�!IsC]�{iU�]�� f$Gupta po�9ials. C9u .�of+}mM='�#�4 $N� 6$ )�IO-shOks *!�3I5Kw��D56Cn(Jx�a�%in�5ail D)xUWM �" ndu�a `%��y much �r�al �Lu"�w:�t' ;{erI. Lar�$�F+ �xRrag��wum�h� �-�"/�e t6rx % \PACS{ %{36.40.-c}{A�GA� mole�` xu����\ @ {61.46.+w}{NanoM$\s:�, nano"�,stub� k crystals}c�*0{65.80.+n}{Th����#�2?^my{ oM:n} %�$%{82.60.Qr Z&�of�TAB�#}htry�%� %s}�} % en�*!k codes }d �t��r s�w on{I�[A�}4F�fو� enjoye!x�4�jz�uy���iANkf0� �cat�mz8+qa5 \4surface-to-volC\�3 �Qh\p�Y�t�� bulkU0 rap�c!� A�(r&�=b&�1Mt�*�of � c s. )Em��p�ns��I4ut� early YbKdentif� as�on��0lM r fl�r�72,AB86,JBB86}.��]nt inv����|Hn Ni$_{13-x}$Al$_x$>!o�Nij!���microcagensemble�2KJ97}�.- B � 2�A��JͮB9eAz py a<1 e15����E89Dm-Z�?�xmar v6}ingue�/ �0 figuEOn!vch� "|+ TF�2� GBBDJ88}�� r���N �:9 ;ZKBB02�% spa�A ccupA ��2g��� f� Yo�(JC~9 Ap�:i 6��AS^{�urn�"M1"�(r���5 a sufd��2fG;on.� e�l1 viewa6A�Us�?p -K�� !�x�w��̂��FI�i.i6"�Q^�����=\mGWDM+00e���DRAs (MDC.�MEAT91}rZ Oy!)$r Au$_{N}$U<$100 < N < 1000$q�m�!�gANgraduh<� uW A>">N%Eex�-�;I�ESZݡW=�#� n!�� empi�th���q��iSn-SJ00}�OGa lBBS+03}�Y�7aAD �%lw63� I� Qs.E � *D 02Pa�~�>waA#7\d �D�f*C"� �"d69�}#� � �>A�fo="bbr� :�MD",4i�܁ C, Si, Ge�S����)�LWH%c�d�7isokine�MDB[ f Sn�[0}$=B PJK�� Z�G��L� ��u�� �%l# b2ngqb�@�78 e�Eu�q<S 81,TMB8�#+� "xe "�t@�FO�%�[u��=enӊ-JoQns7Api�,,HA87,Fran01�pronnt�;aiA��A��  (GP)-F8� ��$��B$$A5 �Xa * ���E ght 1J%9 bZL�ZAXd c�"l�7scrib� �,� )��A�3 �)�:F�*\��Xa} V(\{r_{ij}\}) = \sumXE^N\�o[ Tj\neq i}^N A e^{-p\, \a � {r}B} - \�QG7d^292qR:}\Xi]\,��+a/} H�t$N��~u� , $i�/j$EH� s, $B� = �/r_0 - 1|E$ 0 = |\bbr_i -  j|!|!��E�r �h"dwo�s� po> s $I� j$��� ��22�e�eq�fit2� 2��� lattcpIA>ela( �i��CR93}�M8$A = 0.1221$ eV06$xi = 1.316  p = 8.6121!q = 2.5!��Al��%�"� inr6�!8�� ?&ږi F� ���x�ropolAlgorii% empl� -�,AT89,WDS+01}�a\e<afT6]\randomA`߅��Ata�W9� taVl $[0,d max}]$�spa�&7 s. k}6*eY� tofU�MCA:ep%�� �((50 to 60 \%)5&� .�}Ze�ር�.t "�/�.T7v�2?lIYiՕi a harԓll cube% %W�6$L$. Ru @IAorm\!Js�2@�dI (SR>ya$8T510^7$p�y2�aa�g)6� A�Curb{ show!�ECM�re0T8!�t�*� errovoB5%! Y� �'�� �.['slo-6+ �.�*�F�co2} �1--e<isq � in g~A6� F:~I� ,TJWe !�2�>z�8"_ dik.ei}��=���@e��� -,9-6 Sutton-C�(&��iDW98} A�8=�{sk�%�gq-zDB�_ �Ber.� k�B,2�5} 6��Y  [N(N-1)}\�Ti,�V�iA\laz��� ^2 \�ple��2 ^2}\@Z$SY\,,x��?;�4brackets denotx"r"O"�'1F� �I�ռ�'"�:!M})�V!�*� 6�MJ�}(�?��-s.�`�6� i:��+a �Z, t�<�D 2�0leQ�M� re�͓ i.e._*E�*a��� ��� $ m�*e�&aV - �.third-7��>t�N&�. S#)i����i�Ha,E�� BW"i1��!�<� 'c� aa�2:NI� Lind�n���<;mT� I)�i�;�s)��$_)�ir�-ilibriumW4��w�/@���- V.s �j UK sup��1�,S �� o"�]!"�="e� �Y be �v$ !ht��qK"T �ҩ�y $V$�6�*if� C} �_ C}{k6B}6u^2T^2�n (�/VRiV�d\� ) +�73}�wF� Si1�!���t�g�c"r p�-��J�&"e $C �kin� 3/2 �$ _ tomz InEo� A���)���%��aS�uQ�5Pa3awal{�viA�isu.�&�Hb� �(� �wFe Qigui} il)� snapshoh an O{�}��xa ��$(6 r_0)^3$� *� s (a) $T $, (b) $5 .* � (c) >4$ eV+��!to �Iid`.m�dis�dq],q�i�s+ aphsv<��]�/�8�r��*�/$g(r)$ (&�� c�O6�a�icosahedj}���|22ffsl� �istorA�.C2�MM�H  pr�7c�G#�aAE99}. C�01vMf��IAGwal|�r� �_venL;�rs�B�neglig�A�-soR��J�ILDs, e.g., $L > 4r_0K{$N=13$.U _|!�e�C\x#x�y=0.49�!wE8/WCT)file{SA�0Al13Pair.eps} Jcap!.��aa\slH NW&�!#:E @uJ1n!/�J F6#I�\p(bFB09aCi"(cRD 0.27%Bh"!�2h ��mBD >&�2in pan.Zb)%:�Epnha�LK�;�20AF Gbet�vi"�;)��%Q#"Ap��! } A� �O"� M" a���M"�AFK" �RisF� cI-an>a diverg-&2�*Km�2C �� �?.� "��as�s��nt� �%�s tous jump!��f� �~^"J� .2�CRofT}��s��d.8"� [6����o�Yera2]�� �U�#�#MP2 10L a�5�C~ �OS in*�eZ= R � ���nE����!�)� abrup!��.V  �#o�Ny ��t ą.HH# 0.0ȄV $T 150$ K�R�N$ �$N\ge 6����U"�F� |aYr*/!^H ��lڥMi^� . As ed�� %},%�Nj!_� M�F� �r�ʓ2�, ae_:� 2}�.�mvyW3�r*�-�i�}��{ barr"�:u� ]LA�#�stE)��� Jc . �b box{0.485�f}{!�k�(rY�Q�*si��aAl�j * �r�g Tem�$-��-72]u��i�� aύT�[ofQ�m�sQ�H=2,3,4,5,6,7,10$. AC�sige'E"�.5 is 4� �2o�&ge66�6�!�%�D%�H. a�. SR: $4VH6.f` !5q��I!�.+H*{t^h=��� M5"?r*�A�F��>���J7�  unex�P�"� r�>�Na$��[� SDHHF�toA��fe6'� calo�Kg�$N M6k^  �e� 5-a� � $�30$7I�remarkDd8��sqJ%wa2� -�.�" ?̈!��p�� ) R"��2\�~&:� ua.�an�4$a�[(�I� MC/GP!�roach,i5FigB!|w %man "�"���P:/��${9m 116��' ���l "W#!@u� tetr� ��/�c$a-{R��(.��6cerE!0t9�b����$G � $�+�P!�� ScO �8�%Aq#ֱi�a]K�1�-]6gw"#�"� I�D&�f2�2��� Bq6�B/']����Yj2`�=AM4jc � -��a����!l:L�"-.� e"A�+$T���933$ KM6 0.08 QQ��$N=2$N;iSB�+����ish��a� ��)�)�P39 t�_EV&"!;B u[stU��E����>��e�6� ap&  0.15�T"�kSU��;a��4!l&�'�O�T�  #*&a0>�e)lB} \ !_3 -c 5�R�'�F6'mod')J�eAse�L�v#DhIL�ɲt�P aJ�s* $N � � b� a  �*%><�:�.��5$�r /a�>/> 1.5$�@&�),� ,�,BBa"���?U��� ���= �nd $4M]y,JF >�is �a�U�a�tfsp!Z$N=3$ *=QpqK�%��/re�~ ��s*�$s2ty�XDJP<`C. AIos2���eJ�6�E�y*$Md ·ingƇg�����r"�*�eWz�)5�R"l��=�$E����!�>"A����h��0l�� Ea�Mfo��eNCMhm��M��-step�C %Av,KB94�'0 2�� &��olv!�re�/r<��a�-$ ��F%s#%e�)r��%X�_�!n �ca �at� st apIp%p�#&��OI i�ir6�&V#w�f� B��6caBPn�(�o )�VZ!�.� s�S$�7180�6� �!"s2� duŘSi�#al�s.!H�Fcus�ur8]�}n+!�J�:p �"�H/&= � "hCA�:�3��0 #�0 inflŷœE�d �3"��gs(�9�ML� �,�% ,�%�Q0-=MQ��*�n�z}&Ca focu��l��%�q��  .�# ��4 �Ia�0ga͑a�e���mmer� ٓo�moeYan� A�"ou�,of deg!� f� s �:%&*�( V�g�!anife1`itselfA�oQn> omaly as #ae��7� >"at�4�>sZPm5��6T�^�� �5 #I ywEF}a��!}sh �N�&2, 13�@� in J�fi� J�d&�k2J$54, 55, 56�om� e up��8M� �p*�7���n ��5d)0:S. Z! #clipo� x�J4 V6��%.�B�*b-&C~�q��U%�mDa} �+8ze<= .�in+1(%�=�!� @(b)+(d).0)Tb):6�..p:)m?"]" . Vo�4 $L^3�)^3 = 6^�� 8N &[(a�]�$K�02F�[ �]�&.=@��- B%�B�Noa   e 14756:9khx"�bh �� ��M�&� 6��/� �xse2� R !�\{1�� -%byv !�E�14$^{a(th؉�' �,M Lvxiy�5utS���/X9Zi��#o�Jɉ%(^ tane�M push�� n�� o> �.Ұ�56 �he�>��O�ed R��!-@f�¡ S*�&�&:�2�"}�is�NYc2%za.: �v��A*b (s [dash-dotf ���BF�cmtd)]9%��6N+4to�����}�h2E B�'�F�aa�� *`.J�g*�\�main +5V; �t%>$6aeI6x m��Y "� ,CB956�8juowe��2�=� �JMan�IF� repa<�.M�mR6S EQ$% :���!$ENr"�$ F�T ��"�e�H� &�$�4 *�4�a�m�)e��k.�-]p5� SKK+97}.*X&# ��~"�+ 2 sb��v^w�A��% sA c�� �=.�-x>��!� K�ul&P con"� G�Q�5#c4)&:as��q���Cni.F�am�b)�-s om��!�p.�-xA�� an&08!�JbaX 2masU+! C?3V635"*A��t�7i�9y^ �3�Wib��\�f gy2�UtJY��(" &c'�R�{M"$- Q)be over�)5 2. >U {Iv gasi'_ � ��.� *<(��(� ~&*#?�f,9�t^Mt"y5!hoAn� &Rec<�Fi.F J*FE:YSec!�2 �Dis�.�&� AT}&Le` $TN� haviB2 v6� (fulU, �( �@i�>(+�� ,D[ 2for�� (a),im7lCb�Py(c). &�((Boltzmann w�FApA"exg��� exp\{-V/(&m')\� 1 - �T) + V O}(T^{-��z 6at�� M.k C = �)�)&�( + a\ Q3 .b4`{&�%:*�!M�:C= inftyRb ^1 ^ .��H 7�43768(1��HA�k6b v� >"5��TT��pen&�$#�;$r geometryB,nei��� � �noa`:�� � �H &'r%zj%f,ixN,r�M *[�=False]}�Nc:�'��k �.�!nA3� 2>8  2�7H�13a�� &LG42�" CHalj�" w""=|�F% �J%a�0N� �b@ n"( ���4� v3 .�2� �ߡ��Iion:P } B�O�:� �l -��2����P�i]G0 s&" 2 a�N� m��a�ji ��2$,�7$,�[�a�� )���*g��0�5�6%��a�!a&�'"0 .D�Z e.Ya� � r0!��E�4"�inND2X*�U� �=!Z\ *th�7%�short/elong�A�reS3a^0f�'%�p>� ��:e��%7 !W6� >u�B� tly �?�P=a:r  o�&80smE��>� SizeQQA�� %�F�^� �U2�Eg�:Q� = (g-�/, $(6�/ 10. 5 !D$(2( M M�VNty $N/L`(44$J /cm$00i�8 �+$9�D^'a�!��E�$.I!�r�>�.�^�E5��� *U ]�, "�/re%;%� �F� d�L @$13Z&�4�m G�p"m2�exh�W "V�R9PaR&�,A"�-��#0�g a f���\eFH't -l�Kes�/#a=(�6c&% ��;-�ur coex�c�g![5<�Z��A��/1w6:ɸk �=N�je!�e"S/:,�T�r}�in )��L�}�\cj�g"j�of���}eCQ�u5 K�FaMeec�� -0I�1��ie9����begin6� �2 c1 !S/ 13L�)%�6�05�"0 S�<eQr�*�&�^��� four[&�"4=:�"H4^3��O,�F E$15  $2*!�IUyA�6r(up� C�j� x&�ׁ� @ � ���]�"�� *�,�H ? spacM 2�(AeV :i�3$ �6*6;2#)�� F.a�w�6* -*:� �ώc%] ?A�EA�} �L>�.v!�NAI�!�1_.�n ��E)�is��d� q3�i4P� �*ca�tVإ� harp peak��j&�.m2�:ͦ.X\N��@Me.sR� en� E�Ethu� �si&�S6+� I��F> �d�;�2 �"� @���s9:&�+T Ip |G#.�u��!b#A�"&|ed/SHDC. @%.�0����or,&&) tly," �! J�V�S b&�$Aywaea� ���HY$:�&"� \�=sL+aN8� !���,-�toQenP�P6T~R ?16PI� �by��/)x:rA� R�P7�xedM-�Z� E_V(T8HLint_0^T C(T')dT' - EY( . $��H� ��A �u<8A�$9F 60088$ eV.^9yIJ smea�$',!R�N-Q2 0sambig�4 . Extrapo�Y 9ar se:16�.�w���V�)(~edU�1)w Q� HAx�%off�)8.�h@.!M>6��um =�-ja|U�x� a+� %�Z�is ` broaR?�q�(aڥv) .=u&*eN!(0>�(1�}I_ 2/3 "" T$, !E.�a�A�Ϳ.J� 7�� �&�. T > �<�  $L��A~e2�� $ he ��u�!��F=�s�c���'a�Zqa.�\gg1�B/G C.���/J�.�d�beQ)��{� t)Deltan>Y2.2 JC �L:1o����ۺ�&EI��Fi� ) ��[ "<@(.}�`2.3-5C��o�&(F�]a=D��+�Y�*.s:>� �� >@5�� �13"� >�Y�� 4�a47Q�PB.w�6� data } protect�&��E�J� � 7$�IE_�z iddl|P�?of�9��& �n;*o`is�u�pronou@�fi�Pg[4i$�ty� �}�= �.��'�7v EF2, On)}�����!�%^fiqa2fB�.q �"�!?!����.&�<"U$:�.= 2�8sM%�*�!xp(a)/ m�Y�/cV0J.��23咡 � e�� = l�p�� !-=)R!Mk �&HO�3{��9 t6�i6:.�Z >�Z��L}u5�`E��Zu��`2` b��I2�� se�s (%�r&U)A5B���Ble� a=qn"�"�* 5 Tot�� R,.�a)Ea��>a-�J��~�p.�#<�C >1� A�c�uant�*$\rho = �1.625  �D3}1H ^{-3Rt� *.;a6�+�@�*9 �a7Y�bQ�)�=��F�m 8� �3+66$�lA�h �xmonot��s�mde��S\qd�� word G%����J�u�4�1AK�;:ectQSM� g�su�o�<#M 1m��%a�B� �SE!415(5)�s Z) ZF)!7�7�6�I[�0e��yB�ܥ�Q2mN�q'bq'a&].��6"!�J21 %n.||E"k AF�| tom,�).�/���!ˑt2f*a (X ) pentame��Qk=�iv] *} r QA\���F �ީ=5�23$# eVA; "� ��zR&b"�� � )�oe�b� %"� ��.1BM#E�u"��6��x�&# � � �2�un�\ QmJe�A���0N2�r���&�a gui;��/�y%e$�E�^9N=NBmp� Y(� �"��^4\�undU�&�toN%(�&?s.BXhf�� 4��GN��F�Ze���"�s��ceDIKa�pZ a��KE��*!YɅ�i��"F0!TB>>A�$:�8*�W==��a�� J� &�ns>�`Jtowards9Nio[1 lIic��* 69&��ns و � B�le�g�+�Ing N�t'2� 4�6�� Q^$?&�ont��iF�p!��|�Ry qm&�l��;"���7RJ92t0�;PӭdR��xA�ble�X �Q�2pD�ne�aY!��n&* a'"j:�Lr�n�Y��"� �"e edE- s. O��� ha��� �k� �{u6" �d�� fedc�cA!!�2T �&-"v��%>c�Pc�a�B&�@a3�le &�> E99,%�6N Co �%�2�!�*)n�u& a�N"�"A�d�aE2&�aGP��RDE$N�t�xtinct�>(Jt:!�1>*�*) \�G��r2� RcW/&m.�"!�a*�.i$6J=E`�1�o?2� �V�if�2�F)9�K�8reOC��K#5�� �i��&alP�|.��~e���&�*�=!2U�A��>�2E.�> a > �I:KBge�B$F�E,.�� �eZf��er .o ��5&�q�$e��MxJ�s&"�?u�@gFQ�,��`��^#6�O�;Vr+"k!t ��?MyF�:OVa�ص���m�@���DF�)NN K�ail� a9�(s ��,&��7*҅"�2��(Xp,6`s*�%� H"�9� r Au��b���6� ����%" Acknowledpo��lu% ks M.\ Bl� P.\�}8mitt\-eckert, G  neid��D.\Ãoon�;Vojta�S@W\"olfl� �u��>&5� kiEo(oV"  CeM eqF� al >q\-��\-bh!�~ DeutscheAschungs�Ainschaf�$��ro�� D1.5-)biblio� 8ystyle{prsty} %2D{../../LIB/NANOref� the.G }{10�u�~�D(} F.~G. Ama# R.~S�zrI�J. Ch��}F~85ޫ5x| z86).�{=o J. Jelm k, T.~LSck)��c4c2783 Nd@4 E.~B. Kr��O2wI�vJ.�  ��1| 185^972��_2�.�H� Davi�ndd�AdvF5 70B�75t882t3, Y. Zhou, M.�w��,, K.~D. Ball�?116�~, 2323 (20022n�6$D.~J. Wale= it et~al.�{J� 11%�1 T02T�7AM Erco�74i, W. Andreoni �E�9s�f,MSw}`~-�6!&911)�916f m$ M.~Y. Efr�A�}�I�>XI� 3560N� mD A.~A. ShvartsburgET0M.~F. Jarrold^� _253R_Vm GaBreaux��9�j 215508 �32L`l8 Z.-Y. Lu, C.-Z!�ng)qK.-M. Ho2�B-k ]329 [6�cF, K. Joshi, D�(Kan�* ^S �l�xA�={d86}, 155329 (x2002). \bibitem{Gupt81} R.~P. �a, Phys. Rev. B {\bf 23}, 6265 (1981).E�TMB83} D. Tom\'anek, S. Mukherjee, and K.~H. Bennemann,Nh8h65 h32�THA87} J.~D. Honeycutt [DH.~C. Andersen, J. ]C �91X 4950 X72XFran01�ZtzD ChemJ%115I$6157 (2006 `ZLT91} W. Zhong, Y.~S. Li)6!Ff44]13053�96^4CR93} F. Cleri� V. RosatoN�4%M22 L6KAT89} M%�AllenO�D.~J. Tildesley, {\em Computer Simulation of Liquids} &` Oxford Science Publica/Ls} (Clarendon Press, /, 19892� WDS+!��J. Wanga {\it et~al.}, Solid State Commun. -�9)@N��TJW00} G.~W. Turner, R.~L. Johnston)�$N.~T. WilsJ.N2h4773 l02� DW98E�$P.~K. Doye=_(Wales, New._ �998Z73�2W AE99a� AhlrichsUSE�ElliotQI� Ig `]1 \6tSDHH03A Schmidte Dong�T. Hippl!5ip$ Haberlandu�0 Lett-� 90},! 103401)(6�BB!�P. Blais)$ S.~Aundell2\��6��235409 V6' KB94!'~E. Kunz�Re�Berry2TE)4I:89��942y$CB92} H.-PEngrSA S�*796�1996xSKK+97.p:�)�>T7�9 S6�SHDe7M5ÒS87A2!�2NO Binding} d energies for Al$_N$ using�?� potentials are $E_{\rm B} = 1.4955$, $1.8331$, $2.0649 1828 2957 35Ay<$2.4725$ eV/Atom�$N = 2.345$ ,$6 G=@10$, respectively.�RJa_Be�Rao2P. Jenae FO1iQ89�VmSXend{thebibliography} 8document} +�\�class[twocolumn,prb]{revtex4} \usepackage[dvips]{gXicx6 {amsmath}.3 {hyperref6psfrag@Hnewcommand{\p}{\par!�hyphen��0{Lo-ren-tzianbeginҘ \title{The Minkowski metric in non-ine\� observer radar coordinates}\thanksHp�D�Lshed version is: \href{http://dx.doi.org/10.1119/1.2060716}{E. Minguzzi, Am. "�7�L$1117-1121 �� 5)}.�author.B(} \email{mi S@@usal.es} \affili)*De!Ca!� o de Mate $ticas, Uni�dadSalamancy lazaXla Merced 1-4, E-37008 + Spai�$INFN, Piaz<�i Caprettari 70, I-00186 Roma, ItalA�L%\date{September 200El)�tabstract} We give a closed exp��!��t2�0($1+1$)-dimen$al Y,B�L,an arbitrary2) U)$O$AF term3L$O$'s proper acceler%8. Knowledge of t �allows�V�$to perform�er�hts in spacetime without mak��refer� to iQ�frames  clarifyvre? between1��R�s�y  trans��J)WG� 5$s, also is%�`n. We show that every conWlly flat@$ system caq( regarded a)M |o /4 of a suitabley�A6pa!- triz �of!,9�Tworldline. Therefore,$.s6 1aQVily mov!�QRs!a�>C!L. invariantN��or� leadA .�l�ZQt�turn �Cto!difficulA� i5�2- . (b)jy'��.L�2influ��I���%�e6�6n=. Ie�c23 N ���>�M]$er by meanU�J� becausAzis quant��U�I��Ha��a/ u�!Mexternaly"� s. Fo����tc�tege�6� her5#s� ecte�թ� oa�e � .} histor��2�]. V sh�be�tAarI,cernedi�w��w actua: measured!\by�ou] ��� e� � oA �%[B�. (>�s)!�FG!�@intrinsic descrip~M�V�IN (�J&����id� ZH* uniI?ional,e{o�wlo ,xin���� two.� * ofQ sig� e $(+-)$��D�y !�0$d s^{2}= d t -d x $, w� $x$%D$t$�O2�of2�E� $K$� ?,units have be chos�6��� $c=1$.�8 $\gamma(\tau)$A�!~5 � like&� ��.�MDer, $J$"1�CA�a% � E�0 $u^{\mu}=d x /d @��$\mu=0,1 Oco� velocit�As g ioned,vR�eCA9 .����� t!�hod�#h^m " A�2q�?a  reduc��$a Lorentz 6�  i� 5F( has vanish��.`. H���require! too weak�de, in� (unique solu!,E��`at� s7ree�j ilit� E/UJ !Ba{ed:�x.J�' au62�Pke64,pauri00,dolby01}Fb�a(nd M\o{}lle��":. GXbrehme62,sears68} Even� I�ar� >~i�Zt2� $isolated, ��asA�ta aX t� d&� i� � footnote}m�noyK !�$a privilegCole � manoff01,m03}"L ca�.. � alscAz��Ѯrigid�Xassum����a� �!PaمS �r�:(47,romain63 ,4b,bel95} HAIwO��focusrB,Ety��mm� used^�t� �7Y�ng)DBAawrotating �s~ sB� �Ldavies76,ashworth76}� s.Bs �� ����laas�,standard rod�$clocks. Th �j� *A label s"Revents.� _0 neighborhoodAl!&"�", &> u$pproximate��.��<X ��%�= y re� ente>�byB�( For exampl G)� di!!c��com� �["b� �x 95Z-đY��R>>EJ=}\%z{E�} J9re �f2 s�& $E�a*�%�n�%� ligh� 0am $L_2$ emitAKat $E$S reaches�'s9ɡ�!� ��7�N(_2(E)$. Con�~i�+6n�(at wasw*k F[1[���By)�f%4� cedu{&m n as s�v!+a �%rq by $e�+��| )/2$. Not� at��$E=2�,A�e.W si�tisil%2$I��" reas� %S �w�b!�"J �symbol  equ�} �$(E)=\frac{:� }{2}�6 Next>%!�MA-^ul%/BdJ|-�!�R|� mF�� spa��'$ $\chi$ ra, a�n a�� �� B-(=\pm d$ wito plus )�$�*yE�re$ curvt2� oxe minnHleft.1(0figure}[!ht] .�2} \ceWL \p� {A}{E* ^{+}(A)$}B-  4C+}(B)$}D}{$B$)E)!B tau^U;oF}{$A<H<. $} \includeL4ics[width=4cm]��\ca��{D2��i�  -}$.�nd16A)8is���VUa�e � L+}�A � -, (see Fig.~\��D2})s.J coincx.� tau_{2 Se_{1 ifa��.n^ 6� I��doppositeR ��� � ��X�s�at1+}$&� v e��ȍ � �)�a.��� from�mKtoeXa ��Al>v ` v ���vi to�0!i�s�S s�)> e�>�q�eqnarray�b&=&�de�E�3�(E�� ,\\ ��(ER0�20Fm--+I�!�M�~ + y Eӭ�.n :! �!2~1xcaJ fu�A�pasl ./$. Out��� i�"�_or 1$, both,"� �. A typ�� � o �&� on ~ . O~%e� mR Rind� Twedge, $-x 0$). �>� �By� aB} A.mu}l )=��i, � u� � )a{MQ!a � ��� �(local&%�.�j�ds� �e8 appa  >if��$ clesRt3ed��%�, �B�in��A�.�mm� c} Our goK� provI��.!�g: I�B� �, �)�*J%�ZN �!B� � f} �de^{\int^�+]}_ - )o') P'} (d M h-d� )F��- � g�'e%&�! �i6�#ide�Las��&63}�0 which he finA+�� cert�*��fF= 2a �( ��~�e�� �"Pɹi�$Y��%�.�a ;uni!�ly.�4 er�po�d� Qr�p-oge87�%9t>w )Tis� ] cuss\ $ Refs.~\on'#�B�� ��U!�e!1"G ɪ re exist  s $g!�%� -}$9#O��sub!3%վ8}align}� +}&=Qe�Z) ,� 1}\\%- %-%-F��� S 6~W%$5( �6'n H�T &= {�}'�--}�f�!�� \\ &=.+.+})JA2��A8)9 �J��" ��$ satis� ŷ"� along+ 6,E�=I�-� �+}= - $; thus $2�:�)A�qarg�.� i[%lso bBun�' JoneqAj 61} �+uuco�EbA�re �]�G%�)J�Q�U�3} � pmIN )=\!I _{0}M } \ pm U')}D  +C� ^? ���(t�&a���!�t/� � 8Q�B�ohAW4"e^{ �� )- � )� )�2U"�2.HY� �L,��eZ=\p/\p# $U3*"!|  Now���%�ttle dig)�vm ! i�#"f!�_.�" $g'&� =\Omega�  � wo N� ��geoder+of6[�  em�2�lengthUPaJ�I[�]U0 } \sqrt{.���� }{d� mbd.f; nu��  }\, +>h)n9. Q�( mQ �vlF  [&�# / d s$�^���muA�Znu}��A�A� var(1*Z*ve!�$5g $, w# Fs*U�,nu}= (\delta� mu}- u} u%A}) \p_� \ln -g^� ne��7fO�I�. ��re�)to�' orig ��a �l�g=>&E�hF9,A߭�!�*� pne mM-2}v<�&�u� N+� u]� �i{� sr�/ if QE�Y !��� ?F�%�4 >� $O�6��� prod} @}=-i1}?~ Q=g[] �b�o� _{�Y =0}-' &��6&\big]�����uc� � }m`���$*0u�U} � 2� �chi��%f�] = G�F1� �it�FF�-�" ��x�t� �')��'+G(0J��L$substitute3 ->a into� oh})oo�M2� q &� :2&� b���$(t,x)$ �"�%Eqs 8}"+ �3}A_67e"�$t&=& t(0)+]��U  +v(0)}{1-}\:� E�} �"'.S5T'}-]$ \nonumber� &{}b} u{ �B} E�}-�~"J ,Ur� &=&x�)� � F.12��Z�bel{t� � Y�!�;Ms (0),!)r�O +#���O��*�$K$=� � �%$a�-#:�*b�%a P� ar\'b#Fn�ath�$K�I�*M"��2�se��2"�analogou� i�edՓB�u �T*76 s upF4w_fe�_f�f� cond�2j2 fulfill+(1)� s(A tanen)sl�2�_f=\mbox&��6re �`( pend 0+�#�.� A(2)� ��-chi_fX �upKa �%Fe�  1 seg�'j �`F���q� Hs|9��'*k�$1+1$� �f��Q )��"e><1W5ri�i 6 born58}�d*9636($crampin59}I/m�of0:cY~.{I; ,quite elegan(!(e summarize�:)a�Aingi�,oo7 �2reaF �!"A �5'+ �,�H%"p � Sec.�#�s}�,a,&� *�5%<(osed.  (T�),X &>0 traj��+!�.�"�� I1��7-�Fof.� �xU���A�N&<�"S �.�beJ�seta,byLE"| �t&= �_�+$  \y) _f)��f�� 8e��7 R67:�a�!In t�� 2=[1+U l)u f]^2� _f^21  ,�c~&� ͑ P� � :���=��V 1,���3$a}i3&iG$�7.�5�.�it cha�D Z.minim-5�b"Z" /�"a$�.�A�erM8w"hqg* a.jAn in�?ѩH }� r>�$A�ឡ�پ:�6�-E�e �' Su�&�5�O$ &U=�h*�&'u�a new�0a� $\�9cal{T}=fi�m� $f'>sMoreo�3s>xstY+mE��7o)me[3��or���7 nd a*P>> b�a��=6`"�E.e�Vmis>4at � + � C z&�,� �ic�OI�.q�N,aP)�� �1=L&� )S�)+ E �& 1a�@XR@-B@.@2a�) �T27@E�� 5 mE�called�I&r�BA�?sb qGt"�>�>1�%�<� M=# . Gi�3agU�a�]�J � groupA_Z�y*As;Aj� -�,�&aA�s97i�$J��3r��ond�A �(E. ult}1lU?�2�pLCicI�r% D �lY}m�a� ��.conNedeX}<%65�5\�*sh�3�*�y%, XerN�()�.`d�'h(FT}� while 65 are ��M�.WF[�8()�FC�WN ^&�m��ic})�!WB�)N^��3i�]*� �  a��=A@mayj�A�aAZD�5%Mi�)5.�rea� �$.LJ�.�:�Cs � &k(is>9�&FL)Uj �&�Cb�y]"YHZX)$X*�2�ve"_ $ l�: $R"�9q:�" �N��5 r1jn���'j2=Rx \+E7�� 5T}'.�,')=R \circ PIv P� a �`>� ms��1�n��b p�Fd2+~8!:!���% Q�unF?9!�J":�& (d {.�}� X}'M)��tEe 6u�Y\�d��2�:�$e�d3inc�A� e8.�.�.�4.�.� � 2M=c��A>eA�m�T}(!�a=�ei�� �"-+$�!or .�R ly $2X X}}$ E:Y"0FY�3!x:DA8t�at�M@5oJ�=9 �a� 6��:�� 6*�z >��C�?�W0� to p E�re# �.�  \to -=}$ or/"1�X>&X��4��em# �)2F s}. fQ( !�s�R� : If6�:y��v�inn&)EAwI��iB)ɷ� 0G#� *c X}�H mpor�&�eq�D :�!A�Y �&�F� �� one-to-on�F� ���$bM=�.i<$�JTA�"�s (!ha�&���ofF�#�5Q�T� \pmX���l$s=b>>0� nullɲ-J:e�a�t�G�,!�B1$. (We� � n0!���T NJ6(X��:) �u�is�6���wN�-e�2�1͹��d �d�.�-!f��>��E=\exp[H?.6 )+H^�$6T)]$�!&%M1[s $1�T���c�? � �C�I(no�>%�A,Ricci scalar%#wo� "�O� ad�#,wald84} $R=-� ^K(\p�F"c:X}})\ln : 2}$;T�Gw�I>*��a�m� , $R�We *J 5:gF]%()k�%6tilde{G"B%-%_%�)h&�&d �fPB�-Z-})#FB2+:*�9WA=F���g<QN.�9*y  ta"�A��c�!�R \pm}�&7jj, *�1a}.�2a|�6w=f^{-1:<r)$, $ f(y))=y}=*@9+�2U�%''�" n ad��!Id J& �)=9�h :�UQ�9�\b>{ula #U;m!��%�"c&�F��#y$" �a"���[The�$�2�%A��(\X*�幥� ��d, 7"V}�.� )<$"�*yL&b�7&�wJHc!)=}2`+_{ � ���)+B>-N��NE �ICi. ccoreKw��2 F�,� j�a�"�� � �%��=�!�"}�� .�r��#`1�N� l* �HQbTN� I* s)�Hec"74�QF�%�2�,"�3S?y}-��y�B�eUA��.�a&vV T9kng"� �+bB"x�O;f+Wy(�� �8 m�0oEA Y��V��oe�A.Z�D0�%!#T/ho�hat>�r�7n:V=1� "!Fs, up�R.�B� A;�. �6�Sy 12� X�an�� � .�^ wo&�4�/*�:>%:i2,, a $(1+1)$-"2 a�e�O&"V�^Ao:R�I!� �J�/�>0V!�1*AF}*3V�5�0is symAfy��qbe brokaD, a Lagrangiaa?a�finASllistic ��..�it "�G� �Sto��6�Lan��ot�%�I���_!�1��#club,s� * �Fuhig�S.��66>1&�ia7Xfifteen7tor]mNE�\ "]�;t�.Y� Ga�y�B �v=6Ihill45, 7} (�- �=�coA#AR>�P1c-led Jl/�=a��Ae :&�A.%.)u�MaxcU's"�)�:=y6��y&�4�hDY�� Etv4A.h inNJ��� ���L.sKA mass`\FL�O��ce� *�spoilA�� il,OO.&sN! �5�e>�a� by lood\a�#q�Rcharged�=ti(;G8 fulton62, b.-K Sugg�V$d PROBLEMS�"" \no�Z nt P81. Ve�\at.�(�'.� �&) &�P��1D6�!S&��=$�&=�&� .�\s� skip�26�!Gycs (� _fR � _f$)1"�23y6�f1:�f2� �}$.^by <)�atY�F%%s��%65>K��&6 . (U�e:�:+'�v[/ nt v( $u=(e"� dot�isJtno"�>��v�#? IX},ITe�e����6� lawaN Hu\� .)"�X�a$N �/b� Nj$� o:"��4e F���q]K5_f$ (=OE3V a2�$ �^2- X}^2=1$) k�Eq.� a�g "�B7#e_�?&�$ y!�>Nx?�.A X#�Љ3.a �>mN�T�4 hX � )2)>)v���8 to s%�,me�a�b�,ac�;";�s#a^c!�D"rt� �b�,t \# 9503/02�>I}t:oe{27� xp�QJ K!�Nf�O"�P>vP."�PurlV�url#1{]tt!4n5$ urlprefix>M%2{URL I�kd�,�f0bibinfo}[2]{#�&>!eprint []{S'��:�n�V�1L{I�}{#5d{CBj} 1J{D�V}:and�M S.~F>MGull}},�t@g}{``O�B���twin `1dox',"ujou�\}{A*�f�extbf�!6{v`he}{692y8pages}{1257--12�9(�4year}{�n�: �!H&�S+VI L.~D�}{LaSu�J E.~MBNifshitz� emph�-TqCxB�JT� of F�G s}} �th,r}{Addison-Wo.�add� }{Re� , MA}GMS)5196�N=54``ke64}R. F. M{\"a}rzke andnA. Whe�, ``Gra�H�m�ge1 ry:A��-2/ odynam�n)VUv ,"0-{\sl 2gnd Re�fd}, edi�� H.-YmiuE�W�L Hoffmann (Benjamin,�n York�o$64), p. 40=[{2� {Pau�pDallisneri}(2000)}]X]�Vi M.}~2fW�eBJ�.M^``9� -{W})�26 for��u@�9 �� ial ��t%xV�F�$�rkoj�132�m� 401--425}N�02�>� }(1922!�c��E>� HRGDSopra i fenomeni ce,vvengonoJ icinan�ji una:1(a oraria" (�=�.�lDa occur�Sn�fa&~"),��E4{R}end. {A}cca L}inceijn312�-n@21--23, 51--52, 1!~103F~!Vr~Marnd!�94!��Kld�VK�s:�OR�%�B�Y^g��al�LsV�*�pDj9502�-9888--891N)94v)�?0t(1973)6n ", Thorn�nd �u }}]{�e�X C.~WBX~2�b�S>= �="va��VOJ8s �8�, V��^Fre�wC����San.wcisco.I��73r�Ne7g!�99A�n �qp+ >� A.~I>@Q.���Ri��prma�N"k, {F}�go3"O_n�<�NV@ dev�>"V�n. Q�fum�c�^� 162�m465--46�51]99r]Ba![6��aI$jJRJ� MRWA!� ic&��(of {G}alilelnd {L}U:k8ZD�� 3RD489--496ND:� >� SearS �(1968A�"Ub5�V�FJFVΏR>C �!�R� . n#�&� *� �� f� 82�&c{An�C3c�5i�7{�J�gr&&im�s�l0 "�1+1R�%>\"z�s��teB�M|c� 1!��c�<S>� J!�lnfo��Fr%ra%�7�vkrs*f!�d9saFinZ4�y82��y1111-uV) 6 >>ru%A3%Ai1u0�UB/ NRE�|tl;!��Sc"�Ug �� ����2R~ 2443--245J�200vBel�Llosa�}95!GbeteUKV{L>�Bel�vJ>H �V�H`$DI�"R%w~� ��22�Q�949--19Z,52�>�Ro�;!h6E�r6��JJ$ MR' Time a�"��>rBV�|Moja 352�-0376--389Rv� ��4{"2 {a}}A�-<4b�-�=R�hcriteriaU�+"���6��OR$$Nuovo {C}i!�on;R� 1060--106V=4}:j�R`i!J47)< sen4�bHV�N>� HRsm\;1i�odZ+id bodi+4�!3�,orZ&� j67R6 54--�?F� 47r�A�i� Jenn�!476!4*�i~ D.~G�.�^�!Rv�� "t �R�Survey;!t�jk Z�"�|Ajs92oq�< Rk76rrD.k9c>k�aP��5 MRM�;a�� �~9�960N�z�X!�!J�H>�FR A"�|ng : a�cl�V�Am.=�e�j5��%�� M6274--276. szDes�X�Philpott!48��&�X~�ENG \ڧJ!.��R�UR�Y&� ��� >L{b��~�5R�252--R�198v=Marsh!�6A m65��LJe KR0Q2&.�EZ���R�934--938N�65r�Z�b6��$¿f[��} �!4�&2EEno%U��d3R@ 279--28J� 196�!(j�T`\Au9e�*r\~�D>1NRxG�^&�i�#o�@eS2*MFvD�!-U�;gR0 @Aust. {J}. {P}hys�M^�Z��y86R�9v�"W!M6�%W~JRNJ:� KRJC"�*.�$assoc]M(V�(� Z<��242�͋124�V�v�Bor�zd Biem!>5�#I�=B�O�{W>��R� Zum Uhren�on.�2�Z�Nederl�k� W}etenschE� roc. {S}e�-lk^ � B11� 20N56�>^CZK*�59:� #0, McCrea, McN�=?.d �&�J~B� d2~V_ B� ��:F>��)R" �~�B M;"�A F���6RZ b��PI& R}oyE-E4L}o��A>{A}j@25�aFA56--17J 19592�D{moller62} C. M\o , � �!R� (jc� 62),D 8.15j� Wald�08dwa9< % V1B�Fa�R�ѷ7 ty^�{U}-�t�! {C}hicagoE�b"*�"C ".� 8v: Hill�4, e.�+ ED�:iI.�U�O6��m+ U E��"a��stic me�Ki^�` 6�j� 672��m358--36R04vQ �(1�%8���8�kin��e�n��5J�Pct�gneticN��a�y-F1�14Rz�F�.�&62:I6� 0$, Rohrlich�,Woyn�+/�hT>� Z2%V�B��}��B��=guI&� X1cXH�3Zr �5R� 442--45R�62��)b^�b ���u�������ץconC�~I�#r54SV� �2R� 6�67R�#6$!���X>�-�d �} ��f/��8pacs,pF8int�4s,��{ ,floatfix*]�%:��C�U2��yx}% I�6d�lg��files2,d�(} % Align t�k ;dec�RJl2< bm} % bold �;2!I�g&N�d{color} % MATH BOLDFACE %� 2>�vB}�I bf{B$ .[�vAA 2vvB:uuBjjBxxBkkBomega!�Y\!R!Q $\ $}} �$B!pCOLOR�h )/note#1{w/%� {red"%0f [#1]}}} % ' 1 resp:1 blue62%�=�b 5add:4green}�/Ml %"IA �� -*2y� M�Numer������ three2�n�m� ohyd"�, �c-modeٖ��{Pablo D%�$inni$^1$, �d{ ,ontgomery$^23d8 Annick Pouquet9e0�li�{ Adv�4��udy�3gram, N$ al C@5�Atmosph� Rek$��N�(MHD)W�bulF#4 effects: sele왡9 ay, / �E ment5E�Qcascadj fic helil�^ Axal Jo k%> MHD>��=hl�+?cap�{G�k-waveh�t�,n �Stj5�9,o&LI. a �]ifican��du�m!�c����A memoryF:d>H �a )S(ic Reynolds!�ber�w�6�,�Y�<��" :�cYFct��e�d�heR< wth ]p�{�gy du�-+�c regim�ut it Il%K|;n�rar satu� on K�O�q$�~a lH;Ie��y�97Ial]_�6U� \~({47.27.Eq; Gs 11.+j}�WF��,F sec:i{8}INTRODUCTION} �1``�� ��,'' as!�>W�1b���W in fluid &) PaAKce���=by,�}7res Zh;.t�9*J e �)8�Ba ͔at�a Wdow[um damag�!Da�/acy�&w�; a F�mponent;>"�sd,�!g?�%  f3�al sa�;E�Na P {Holm98a, b,Chen98 9a  L9c,Foias01, Nadiga01902 b !<2,Ilyin03,Mohsen�&. x!weviou�~a\ �Min�n0� we g��a� mple)[o[%(]!�i62�s q�e d��mwy)8AxDADdissi�%v![ se),���i%ddAp�Bwo 2�@a\�� ly t�-.��edi��%� a se� of )�EO�c se w�Oc��a=�tu !I�FX�; $(DNS)�<staM:�;i[�?��EZ"�cs fea[����Zn�W9Z��p%��^o�A�o��!��]d��F� (3D)Z���. �Aia��ightfor6|pr;1�E�7=>�A (2D)estig-%IY|%�wҜ,ll draw heav G�She Ȗh%l tat-�voi�pet e_�in 3D,Q^he3 !%e&`�Z6�I�ic�zs!8 ough! etcha� by"�>�2d�F�!kur7U�C3D!=!�uIaF�C d�/dN�C 2D. a�S!on �v��eq}efa�3D? �����Ks �Z:W��pEiefR���� upon� y �[mB@against DNS treat�"� EfLE�y!fe��!�`���L%Ldke n tun t � firs� �Ealread[3� n 2DV��third��a( �Eu� n�g@&��F� �oA3A*�1noʍ un"x � � we �re7�l �inv{� |A[R� �z"oE��lowY�Prandtl�@�i�Ponty04i�� ��~ f��. KVu��*�FSesU�decay}- :o}�B�� nsis�Wj!\mosa�rt�t��_�2DA�:-ɕ � a g��job�� !]�Pu�behavioBF. Fouri�5ytudes (&�0 $k \lesssim M SP $, �F� !� z*�Xb&�v,C�}� 6�%/$filtered)."�F�|�e lack surprises, �6� e%�i*� !�� �0!v\an :b�Lр��,��t_Zfz����h1~ n3E]^�J.�&� "���s&�h*�T���NYw sum}�s�Z.� ���ek�6�;� densA�is�vjJbB�A@voSI 0$\-���v$� � maoI�M %�*PG; he (� s�4�QGlQ�Gbt��� taJEdiverg�ofvE]rIC), ��,in � ����T Z� � ����r�b PoisM�qWkɀ%urlv Eq.  FeqEX) {G"�W@}F�%]�=eq5vePeta�jA�m�Phi&Tr eq:vecpotEm�P��� �Ypo� ial,�UxI q��T!��N!K,Coulomb gaugeDy-Aa-�S k� v<;Q� $\nuY�Ն7{us�/e'et$c� 'RM�0bB #�e=fae2�( $R_e = UL/�)1in5�o�M y (c.g.s)�t$Ue� a�2}ow��bnd $Larp�LacU �A�it.X�ilarly,a�e�y-1}f�5:� $R_m �)$��/:s �P1 \nu/2$ = R_m/R_e��և��!� ���7$\�B� mo��dm��>$� djt]ot� "6 ,&k02� a�":��F� vu_s���t{ �(0rm{d}^3x' \, �Pexp4 �:\m] ]} {4 \piZ 2 0}a�(; ,t)}jjeq:usɽvB����BN�Bra\6���. a&�U� � a��,���er th0S"Fs�B�nJsٙto�4 .�^��:) � -�HYqN�v(x,t)Z� k \;!�_\vk(t)�vi \vk��x�(\ \vB�GBrG, >Qa &`9"Ja �&�&&�q mD $E�9_ �$�t�eBN+u_s(\vk5/@/(1+k^2U�)h A�601F0F�ot<)S�� 9cR�v)���(1���Q��"^2i{) % ��4at.B��5�t� choo>Po )��%�"� ��!��-%� 26i-E�, aW;ms�p�e%Guni#�m$ :z(��=�q$)s�e�Uzr(ua�e� �, �64L ��� q�� %n�� 2�v} amou �a��� pairv#�& �N�R0 �� %�&%ͥf - v_j2 u_s^j"K \widet�` � .Q _s I"�{A1� {} &&A`%� |� Fq alpbt _s}&�  J�� eS>�6�~ alpN� ��e/�R)as��Rin�S& �,�eqY ���Nj� ����i!ed. $N���<�t4Dz� as b��,0 AFrelev�B7 �ӭ angu�c��odic b�I�*fz(�we�lo�9 out�kidealiWg 7  a��s).2]\fyae�a�E%'q�$E$��u�} E�1}{2}����*v0BQ5EQ� EU2� z�^a eq:EB� �cross&�$H_C$}��H_CV�v"� �,r�HcB�BI"b $H_MV�MZ�A_uQ^�.pbeq:HmB�� L 5Tzero $E%�����5 ��Z$E�)I ,�T �0EQ�e�Y"ڛE9� E}.t}�I-��in� ��=��IF��d<j�[F#]:di� >�H_CR�H M�nuM�n �U�j�F:D� �VE� �1� .q Hcj�MZ�Bsj���J�93Hmq> 6Kn��w�?�N� oz�A��Ve��a�s���j�s recipnpB�us�� Bs})Ep appl��^ un RFA�Q�$�$b� is p�^I�s�Hi�� �Ir�Yuse*| _� a]_v�V B$ �Q�&9e9"\ &=�>�,. eyex>iw�~Fd �]��k� ,,��)�[,`& 4o�[5asu �k3 p. S1F%;mak� e global.� aH&Z $t=0t�-��ruBu ly&S�C  c*n�� I� m�]p���� m]factor�b� K���)wiL�ex:� � �� !|c�"s(xA��<Z1 (n"hr�^MB�Ss�MnU�)��g��<�atc)to �5�*GF^sa|A�). a Y�-� ]�as!,), etc.,"�x�:�xto� v`V�� ` �Y\ah�_!(&Bs"��cխWeno �i�^��%r��#tULq�N�r!�� $s $|H_M/E|� |H_C ɇ�e�maxi+U ��,�"led ``:��#"whatthaeus80,Ting86,Kinney95}�A[2�quasi-st5ؤt� ���n!?e��ez�RyGll�bA�3A ensd m��#��]��( sn&edwwJ� )seWJ ``� &k'''��$Grappin83,@)(86,Ghosh88}�%az5�)� �&��O9 llelA4&$-�j �M{YsQ  vg!& -liv�m�%&u&p7e�b'�% essentiLŹshut d((``"�%�gUity'')�u illust� y��ou5A�R�%  � %��YIn6�( proc�ю*do�s��xBP}%�2�� � [�)D-w!run-�*p �!�D�=�& Ref. �Bw enburgh ��g view� +y��q7��%�M�.�1�����"��cap�tCwB$�f%[r,l�hm'of3 al �Co a A�B,�##��a = @!�oll_,m���-re�ed�6&d.W .�� base�� trut{��#I� �cy( �(  t�"Z�<}SELECTIVE DECAY:`s,1f4s rapidh+l� >o6�f ��%� �$��ABC''c#�yrJsv_{ABC��[�Hos(ky) + C \sin(kz)�] \hat{x�x���+ IA <x IV>Iy�I<IB Vy:�z.R�>� �rbi��rc� $�$B$, $CLk$51 * an eigen�u!��cu�@�$�.5�QT(sa��arNRvv(t=0);psum_{k=k_{bot}}^{k_{top}} v_0-\�-� (k,\phi_k!g�!��RJ9�Q�{b�{B�{y.&�!@nFLi�R�${�!�}�akp %� �#���� om phas�%()�d��: ݛef!� si;nn�| n�E�i�i2k A$\� �%&.li)t� @��� )�Em�d� �"G J� )"�radii $M/9 M3$�  $6 % -�$�&,)-= per� %U�'i T*h�-R$A=B=C=1aE �=�� �=��!R $v_� $b_0CN� $��< v�>a%�< B2|�``7�?x,>$'' m��a!p�  averaZ�;�!tba�box\5!�gI ���g2jm^�0$. RanA�ss�2�Z��)�w? > " �2l}���"\)\vA& .�.5�@,<|\vA| |\vB| $R$� >� I�h�=0.002f T�4�3a"��%@���aF��se a� l:�+ ڣ���5$256^&�%'de-alia�" achie by !g�29 �2mC$k>256/SaA0tho3]zY.beG� (J�fe� a��8e ``$2/3$ rule �{�:6ru�G���HA{ �-��R��$128^an �\� =1/2a^� $64Z%10�$d���wnCU pplyEs!>t5�_ 6��of $�;)fig _E}.a "�s�D !�E��S(G$8/yk���nd&M$) as&�y}.^�b�)�<u/R./\eKe(e'�|$!�*���x� �#��!�;L �4"�A7 o ab�l$0.999$A�%�f?�IT b��e} Z2�92�f1.ep=-�{(A;�6 ine)�oM@ -?(up�3�z���6!{?(low��lu�\):�a� ime until5> H��r� "C  ~L60�% J�}B0%g�D��s*��ODNS, dat� J &tou9m0q�*�9�do�8 GmQf=�b�. � 1� R.log&�|h)&})))�a/a&�-U1,.�&@!b&ya~�cO:�Fq!8���(l�� tme"' A�:Q>�One� ar~ u _I����t�$oseE�he��62v6Tot�yq/6.�I-�y m7u_s./m2 . La;���"�� K�.7RMA(FPsBe�( specB:]I: �%� *)O�3"�;plivs.gB . �:]{}�K�� ($t )E}�t. {um�ensɫHby Kolmogorov's $-5�flaw. RV6�s��($E_K �U��a:�� E����733$)� �M�$3m�*!��n!���7�Z�1m*2J 2M�%) T����so&#y �3:2��,I�6��22�! (�"L >:KE�"at�e�VW�V��a���%Q ���c!�3B�1z2!N�%"�%���3 $20V��}�E�!>z��4:n(a) Ki�J��7U�6�,:X�0�]NXG)]A�NoA�N�A� V�s+$FiJ����>"W,�eW� 5v�Cg{�6>d 2rg"� ($k=ɶ!Ex �um&��>1*�$ERm E_M "I $t  200$� bA@�4m ,*<)� >�3D��surface�  I�=`)�8to 3D d�aY��.�*R<��.��bl^�6� e.K�"f�o�(�s ]~s�;�/��R 9 . As"j�i�: E�&�5)is alwa���w!6>"#J" (si�/�!��z�4��2�9MHD.�S�n�>�)��8� 5>�6� SN�U�"Ee��A�]at 90\%�]³Q��s6B(n !!AJ)Y�@z low)N3DB�J7�@DYNAMIC ALIGNMENT� +!�<load R�� �>F A hellA@ th R = 6� B9 h���� �ity9tC �c� fo6�-,e�>pso} t� i?��'f.3�ft<mvK"r; a1r�� |)r6���Ba�e�runa��e�+% 56:|b?3:>�|�l���2n�)�%= �Zcw�a���dop� (XLs~ a�6�9.�:_Ep_E}a,�%E-a"ADU�ug�  (a),h �A�+qual;:�Nde�#� {;#f$me&�)mea'�;.1 angl�&=Y,G*"�/]:u_s:<M�d ops@ *�"h S�s m.��tlig��a�Qtribu!�b�+e2��"M>Qa��A��� 9`Igs�a 0�=�g�r�:% iL8�s En�E"xE6"�in�10� ��XJ ���~aI*��*/%c�'�n��A� 2-J�^er7��~I.�n�e��0 mig{��gO&�$ y to�!] �"s�� 6v�m ��� s��R(&Z16FV� ��6- � Ek >�.:)�[:M�BS��7v�2� �B�)� �"{�� F6��6Q V�ur�#)�ig +&v ��:5 � eىR�6K K an*�,\4.��.�]�I 156$��u��� :��n � ����?>�����sQD�uxcell�# pt �n unexp��k-�����!&hB�$t�� 12um�]8>u��ֻMBEw! !�K�X^VH!*� �!}�9�^�^N�A�eDFQ*P ��C$!� $t=150"���Wz�' marke�)� iM0Dki�M� "ۅT�+'EA a� 3A : �rd noa�n�1 -|2r �8pe�!feaj , ei�� ��c:�)�� ~2D B|�0 Gd! �N&a����P�ՕE�Fx�2��E���>a��� �N(9� a, : �( detaim$� O`r�Pon (sn ۇ� ^=�O�lost.PB�oI� �ri%B�i[�^nexh ��6�� A�� contras� "� diso% *@*�i�:ya �%5��.seP :�&,a �%�K��f"7��te:isotr�), �BIity, ��&t�M�Sv�$Q!(` &&'' �&�$A�$a�ll(� �10>���q"k*����2 at 5��B� H� .&� V���:N�!@}INVERSE CASCADES�2�,G"w�,wL&R3�.O, ef͇, l��n-0+a�ffi�� o� �*s���?H,.��Y"�$eneguzzi81�Q"�# try 2�<#= ach:���+En6V�P7 4��� �I�,�#for��"U'iQ7superpQD�X� E��( [8=Eq*�9�')]�- 0"�'k=8n# 9�e�noá� a7vEK� �nes�Pi��O0 1-h|���?�a1K��tri���z6l&�& ABC�$T ��3r<�Pe��$\D � t�.25LF10ʞ$�a��Y���cus�K�,oE�c step��$2)$s [3}�A tiny� dM0l��ID6hf�6 some�*HQ�: � "�ell b}.�$͐UW� \�ou�� C ��?�Ge|62c&�,I|�!M��k9�5174�r-�$pu�^��.{�d�!1vd ����)*5��e����R{v�! E2�I�$-x1�]� �� Eއ��_B�:e&Eaa h!�VA�E�I !�C51��b)�i.�! '�� abru� [ jumpd�+f:Q�' �a jagged��ear�]E� i�a��s���t!n�%y�/mr�a��*. Su�me�$� �.���:��.� same�V% A4:$+�*��"p���� s".�� ���;���i�vi�V��/�� &�)�%!��� �>�y ~) ]�� !a:�&"0,",�Ma>:�Ʉl�%��g e"�4Pass2�p� �'M�4" -�e�$�P30$!� 72.5%V e peak, o�ges�cHd,���9)��7!Ks!���O5ach� �.+6 of] ".�* =Q� is also�� unstable, may be responsible for the time lag. This time-lagged behavior is reminiscent of what happened in two dimensions with the inverse cascade of mean square vector potential \cite{Mininni04}. However, note that in three.t once2tc s(has been e%ished,+$growth rat �\at2�,ew long�|$en a recur%�problemA�MHDM�\Brandenburg04}. Here we A� ��v show���%� i�yieldssam��Dults within accep� accuracy%|hosm�DNS!�YBsitua!`( (see Ref. �Ponty04}E�another!�Jre�'8interest). We e=� a velo�`f�1~s againUJ �8observed amplif�onq9A� genea+d`�� ABC1s�+,al. Previousa�ud!l �.�be� n simul��s+.9 �s w�VcarriaYor non-�al�sm�8Chen99c,Mohseni�e=��A3, hKwA�0ll focus onlyQ�(characteriz��!(� �itye� amounZ �z �3� (both!U�G.�> Foias01})!� meas� �� a� Q^�} H_K = \frac{1}{2} \int \vv \cdo homega \, \textrm{d}^3x \; .�NI��] usefulaQnormalizaSis qu��h m���!� ve �$2 �H/(\left<|v|\right> \�)��6� �Do_Hpdf}Jɗ� abil�distrib��fun`  (pdf)!�r�BOAL!�Rf]�@. A stronger posi�lai e�id fA�A~ s giv!!ris a netDB��M,flow. In 3D6іce,J> s an�a�Yvaria���Bis��n!�� to ��er� I�PBrissaud73,Andre77}. Z�� =�t5 $H_K$ dur!!i 2�9b. A� &�sgy��.2�  ��� 0v��ofJn Fouri�pace up� $k \sim h  It��mAf�$Kolmogorov�r�M�U�);��,03,Gomez04},( �`S o U�@ i�� aker��%�-��� 3.6� Proz-of�Q�6 . Solidţs cor�QX � da� to @:s9�s��dotte>= �f=6{ .-��fix � v 4:A. 11�� Y''s slopr � n�re/ce 6� �v� GLbs��a� f)Va�>�early ge�a�e��6���� ``!ma�)H'' parameter regime�+�expon�-alf >g�!$~ s-Ba�2� p_E},   exhibits ������ `!G�/ im*g hree �oug�� Ba�asND� offset� cl� tq�!�ar1a )�< close. At aboutGF�ETa satur�, /an� � Y avera� e �! equiparti"  $pproximate� N> . Af!�̥��$re no signF �u�~_E�!�2�totalRe���5:�(color� ine) KQ %�Py (upper blue curves)6)iz.l�)s a5�e* ime.F� DR��R�E>� Figs*�M�mhel}�K� �}.a,be=%n neg"�!u��%�� n Z�, M>e'cu%dMt:Za�%TyF$ agreementI� not sharpZ0Y� l7�d� \��$A�� ]�d"�aa�dord�ex�M���.�1}-!� 18� quira�� )f value, op2 e�!8a%%he&� &�V �� am6.of �.) (re&� -�-�I��_ >5 6 vect.�)%\BW� � �l *� �I�%���6:�N~���N�i��Lex�b7:� M}Q>w% &m& �-�z}V� B>=f�l>�While� $t \il 30$.�.J� of uP�itafpla� a']�E\s�tinuee ing,��] e� Aq�A@ dominamWs�E�.dc:�Yo� nt a� $t�� i7dB� keeps�# wl�& s ev�.e" B9�-2� u . Z)!:BUa�+ ��b:tra n ick���&e8 *ŏ%G��yN eZS^ !�tC�E�wo �X�� "�  >���U�� trac��)&!EQF �Z3*�G sr # ,��HBe �� 6Go F �^� �}.a��:�u�an.� !%� 5�. D|�stage)N:A peaks!.X�~!� :� ctlyn)�o shap�<�)`s �B .H w�)>��. IhA��K �L,�69 $k$-shellA�:�(* less 12$)%��O� �is fe{ � � �c��:#*� (�own7!�5��Zh��!�=�` !�*ll��$ $k^{3/2}$�Vy)(>F9tM5A�s �,Kazantsev67,6�.V� P}.` si�late-V ma�&^ 6z q�achiev� �c n! o al- a�,�6� at .� ($Sc&�!R� �)�tudM�isń!�in good "� � y �>1]� 8>4V� (t��� �})I�5%m����tra5n/t � $t=6y$t=70$.6�EA�-5/3} -UJ'sM�[ ra? *A^�W2^�v#~a�G�Hsq�� = �20AK�ive�|B ERf Q> FuBV 3D( surf�of�stMB�a�6�waF�non!�ar.^ -#alr�aken < �5. g" st ��ing��� nd e , `u� �6�f� Y Pa$DNS. N$ww these.h�� iQ��qX  q ->lfI���cas�#�We er�s�ng8s!7fil  ng lengthQY$}| . Similar��ks havB e unr%vo�"!�"�:  of^� us�����99c���8�#9v_S���z�#6t 50\%A��maximum� ,�,�!�(above�� G�#.�(below)R53D>�W� u/ �$HLA fewa�p�+{B.�, a� leas��I�.� eta/\nu$�kno gla�degE|� `: predi�� $!���'�.5$hsum}SUMMARY; DISCUSSION} W>#Gf� work}rectanguA�$periodic bA�ary��dU E�exami ,four familia�(ree-dim� onal�&�0 effects via�:��_�In� as� principal� -�� | � )� phenomena}kG&� :z<JW$� e sa�E � u�F�W�>�runm�r�Nd�!x!/�& = 8�!�!/A� = 64�#�YideE9����!��step *"CFL8)� &t!�decreas] InA�!m�6N��%edD�%at��vUcCt E�uE9�&E;� regarM� �%t�Oa�N 1�A%I, such3�b� &� fluc�%ng ��(O�)�dissip_� ( �� �pr�#-�>N� y � ��wo.�*[ Mininni#%w!}v2t  �&m�� becau��y��s���e to w!  w�a�F}?*'� �!^error5�>�i%#r reeaT+�& st under-EpH"e��"� -�:\!,�F..��$�to �uh%Q"-�cABK$we@   erB<��a de�ed8 cuss�#lt� topic)<co�6!5�$:� q�=be�id< J;9ofn)-wavedP ' inJ� com�ts WF%�5!�8 c� �rl��a nd�*�x�� bidda9 chal�a�@ac0(�}�W(ank H. Tufo%[provi Com.<`t UC-Boulder, NSF ARI gr� 4CDA-9601817. C29A�e� Za NCAR�?$ Dartmouth��XS0s ATM-0327533��) College @CMG&888&Ysuppor A E7!�art54gful(9ed.-- %� 1� thebiblio�-y}{1}�-�8em{Holm98a} D.Dq 4lm, J.E. Marsd��nd T.S. Ratiu, ``The Euler-Poincar\'e E�&iSemidiA P��+ Appl7&Co�um�oAo0,'' {\it Adv.!NlMath.} {\bf 137}, 1-81 (1998y+\6�b��B�Model��Id#FluidsNoM Dispere�'' �8Phys. Rev. Lett�480}, 4173-4176J�� 8} S.Y.  , =�C. �%,, E.J. Olson S. Titi��S. Wynne1�Camassa-!�Ae�m�ur�&r"� ta�nn�!� pipeX$!�z��5338-534N��99a2���EN����"�+UG!�ica DUC3} 49-65%�92C �b����� A��ne� "�*�u^�2�A� !�iW�/nel!�.tM�} m$!� 2343-2353b�c2�=�L.Ge� goli/(nd R. ZhangAaDi� numeE**����N2-� lr�, 66-8N�e 01} R5�Eu��2�-��fa�U�cA-]�2.D52}, 505-519 (2001��uNadiga�B. T. � S. Shkoll�� ``Enhanc��!)inverseb '4ofp �eu5.9  La��gian-�!d6�y�2l.U%�H�G528-1531��Holm022K ``A"d �I��mj �$� �"j 96ir()� 26�2�7�C253-286�22� ��� �� ``��" J��D��B�Z�Chaos�^E/1� 0J�F�+2��!q�l� . visc4-nDhei]d+�#o�2Y+E��<+oryUA J. DH4ic *Diff.����1�( 1-35J�4Ilyin03} A.A. oy��At�t] �tw2�6�-X �W: An&l depeh4c#ud�m�.�F�(5}, 751-777�32h&&. K. , B�sovi\'c,6���.M �Nn9F�>� ~-P* homo�Aisotr� =�>��Q��524-544N�"� P �C!ntgomer�8A�7x8a�A.#!�� af.�d >��o2�+Q�t"�. � bmi*P(arXiv:physics/0410156��5 Y.  , z�$J.-F. Pint� H7litano�D Az9!=�1���G 41" Prandtl!9ber62[ z�046:�1��{D.�E��e�n a�n�$�6 pretG )�he �w `=�'�0P -� �q�" 3365--336N�2i29}, 326� 86,Kinney95} R.�(ney� a�cWilliam)l T. Tajima!hCojnt.�!Ny� 0 :� incomb�>J�I� J�IB�Y 3623-3639� 52� Grappin83� ,2�� J. L\'eor�' `` D�- on C�.�4of�1�ce �-a�UA�1�0�zA� �1268 1-5� 86K�'I2�5, M. Meneguzz� U. Frische�$ G�>of.�%{p��i��A �3 4266-42�:+Ghosh8�  ,Z�A=�_��&� �ros�p?n �</"SvB� RA��� �2�431}, 2171-2184A"86 Lilly69� K. , `.�"\6�:�~�$ Suppl. II-d 240-24E�66~$Mazure75} =�.�2�A�A�5a�O�poaY�4of�#>S inE !q�}mJ Mec"j68 69--778!M76oM�7��Y���2� ``S5Z�2�[&��0� Y��a0�7��32� %�76�Hossa�!M. ^� :� Long�"tat�2��A�AHa"�thm �"J.PlasmaI�M13� 479-49�d65.f#4�k %<0K. Subramanian A��� �~ict��Bmth�  a>(-ph/0405052."��81}!Q,>.� ``H� al�.�9Q�t-�a�.��.[4!� 1060--106%�816al>� � L!*lem��9in1!A��@!I�E soci��:t>Y�Geo� � ��F 1�6� 183-20e_96�.�> Oab�>��!S� �sta�A�1:1:1���I.n7 471-5 �42R.1? V. � B.F. Dor��!?{\AA}�.rdlun�``I" �" :GE�N\41a)759-7J >)�8m& 2�2�$M. LesieurU��%]E��!.��T@e,,�| E366-1367�a36ZK9 J�e\'�$.� ``Influ�@"a^�o�!2�N"� . "  Y$�o2!�187-20 �72)J�Q�S Ga~Eyink%_/jo�<-`�uAE�A,2 *�A�A���2�361-374J�G�9 D.O. G\'6 ``U��%�Q�ce�o�5R6�aq"� 4� 69-7>6p��dA2�5@>�!8��a�H�D!F&�� Y%lalH$�-��e���J��55a�824-84�6�"�'67a�P.  stev�E6 �C�I#& by aO Ang�� Sov.-� JETP�U� 1031-103�$6 gG> � docu�} � \,class[12pt]{ 7Xcle} \usepackage{epsfig6ro8nset H{\topmargin}{-2cm} .8headsep}{1.6cm}H9�/�!>0>=odd> 2A�?heU?}{23.5>@ �I}{16.�@ \newcommand{\be}&J�}:#e#!_^!baDnarrayBD# DN! \w {{@6; \Covrm Cov>Var Var>DtDelta t>Esp rm Eb%QA: He�2LJ{%Pbf{End���us ExOrigii�CZ&$}}\\~\\ \nKADsize{D. Sornette} I�k:z6 Institu�L��Planet�%�1ics\\�: D�&a��Earth S?Sci�ls\\ Uni��ndf California, Los Angeles,@ 90095, USA\\ Lab�oire de �qu la�i\`{e}re&+8L\'{e}e CNRS UMR 6622.� KlNice-Sophia Antipolis, 06108, Cedex 2, Fr�A�9l\today1�A�1k Vabs� } ArB*�Kbiologi extiYBs2�$,Cretaceous/T\F!}KT m! y du�7a =orite,L0reme volcanic�.v%uPr self-organized crit:��Ws? �a�erc�! succh wprogress� repu��oC .�C�%Aa�7 � e! !ad�3s� ? D�=mLg� chK ausa�C�&��t�90lex systems r�<U,di1O angl��wo 5euT�eut #"�Cs� ei$�&l=�oo many t9�1s�L , I �Few seCl� orts"hF�'w�& collM�r)�& suggKaQ0lM ategO%staTe'-�of w: :%Wdual ��oG�q% 5f�&o$~ ��D�)pllre: In�LDet download shocks�4ok sale lfinanEcvoL%� >\ !crBs-pl� s9#of�@�/�'�ly,!;he 9�63t��Bs^ A�IU . S)�!E�a.�"�&se ide�'M hr C2��#��|�{I�Fj} Exi�M�*$pervae{i�l E�*1ci : e��qu�8,!g� erupa�Our��PAtornado��l�%lides%�av&chnaVstrik" (storms, cat phic � Eqviron�72RdE�, failr"$ gine�*&�.,Q � e],stock market�){ l unuOsb-� pQ�+ �� uphe.' perhapx$r" u%3 s J r o�(s�SVXit�m�Mg� �P,:�Rory�w];at�" -of-��librium�6wlyuP�G� shold d{Gxog (a hierarchyA[Y�ll 7 s. Ac�?ingly�L}vss1to�)�M�+(BakPak,Bak}.2contr!�� !~k* aiō viewm) n add- *prU e�e�xb�*}6 almost un�Jinguish�*�-�Q @�7@X-O��&00a� form�Ba�lly imGle �6 �S��;SA�+). Bu Mow can  Passert% 10�1 conf�3ce �@a)Rn6� J3��n=�2�)@��M/,�-�Stha�J��to an "�Nń? Mosta�uV]%ind�Q!�,inuously sub=Uto��S5"�N, noi�Kk��l"�(, forM�8ich%;wid��v ���I>8.\J�Y�2:�(a priori if5PI@E�21G�c�U��,��<9 ��ub2Z�Q�in5T�\=�W ��nAMa�esyT�c� .?T�Q�%cwo�s:9 eats item� A�ea_q�! pr"�Ra> &�;z�G"� �P%� s? a W�~�SΡE!} ship4[t8SeO�:2s?q�A:1l�SUs�Bd�,2a�.�>�!g1ic� E� �A����LE�roE.&� strUs�ā�"�� i�j2ed�*>�Judy�-� AQs/: m�tV !� ab�%&.<�J ck''!� some sort)�Q �6�t�2A�� aS�J he�w&� 2,%| (�.e&W al fac$%!�cLP�� roll�3)d�+ �yAdmdWF$�ɡ9!!�/nih5 nkY �e�[*H -"�# !%�s�/r�L� C �(bFFsus�Yi�ɆVl}.�Pa nuts�?��eoLE�e�<oR���cS verya�cUQwayb 5� �)/AaA��ctan� k�B(i)&�c*. _4!�Ap<A�tuERs (enq� ). A�A~ ��; oe� is "�3E�V ein'� $2Z,e]�2 coe i# $D$[A��a�a�idq )��haotic�i�.u�)moleculC 2.m�8p�("' ?)��1, 29R�JNM�e�� g, i.e.� !l&� �v�[=m� �d�1� e�?ulse.F�D$ql~5.  �0�MI(��g[ )�3rE���Q( 2(.!*Y5 KF�z4ouF[ i�a&e exist�H�VI7�U;6�.�a�� !qtm�G2�is�settled-�ruellei�i:x�ia�� on4W�N7.rNeiLeٺPm�3ant} ��a� E�)�v&�:n&Ve��Csus&J impact�Odsev iculb� F��7E��z ed2ts/ lie!���1*a)+ Zit3�P bifurc��e�6,;>E �Zur��s  often mis�ifi�P �Wt� %�!�� o7y6 % �a�di�5D :���9�s`�be� &�Hh�D�� it w6�A�ins��71)>nv�^���2� Hve�O6b`;new:=i�s� s.�9mx�9 M� ous-�v� ( )gZ�0@as ``;5''E�short)A�relev7�c�fo_ing"p d iz"n B�� V�8y ("�mR �� kE�(Decc� raps)0A���), � immun1n defi��c�8("� viral/b�[�Xf�s }&� o��re�>tory Y`|cogni��A�br�6+&�)(role} �input|iBr .e�X reinŌ� s),�d�/ve7�rendip��� A� outc� ��U,A8geAs�9T �2�mB (z zr��B=č c.+e�<s�"N���-nt burst%�e*�Y,2h cu�6 new!�� -memA$i��!�avi)��_ stry rece0<(9/11/=4 tC=ist��ack�tr��7=�pFe] :(triggR prot�-E 3tissue�recARy�N wars�A�ly�$ted (civil"u����:�ի.R�:���J%����EA����!Gq��/"� M =a(D�F}? hotKeb�� ���$.diA!UminA+t H  !� of Schump�i �] techn"�e��:iB@in} hi8y. S argu� � ``"�� lop��d,UousharmonbyI...��<� viol�outm and c"�es3m�like a s�Y%pplo� tN�t`lt�UinA�ant�ns�E�'' � �}. �� 1�%��/lso p�Yoa.8H1B!� ]Ro2,}. Our analyH��=�E*jsubtl� terplay&4 �r��en� �Y Sm�>w I � Eg} A� sequRHw�>��#author)�CN(FE&�E%�yi��#et���� "�EEv�D�net�} On�f�&rst5 _&uman.� 5{E in :R.���x E�!��Jm� �B jaja�P3O b�Hhd!�!��Cco-aTved&Ti &complex�>�+�groupd0SBH,ZhouDunbaAoA ?IEK� ualmAq����twg1d�1],!o!�e�w ���t��!�E# eagurA/�@lum� ocie+, friend]pG y me�2 etc.8P�\i�%!�!"c9� !O� mut�e� gl��#6�%-�qo I3�o�! X�Y� ��4�aulI�Q�]� ,Ai��ew�a�fb� 1�Tal�� u�+th YE�u�"� :�v"&dQ��Fi�![GNC seeEbaHscribI�a Llaw $1/t^{1+\theta}$I$ 4 =0.3 \pm 0.1$U �D�#� �!nt�ingred�in 9s d y�Lm2a<ag� da= &�he)@$�;l�itc]aI�!��~���,&�E,Eg  �!?�Tve TBen,�2r��N�i�� .y��Ve ``m%o'') who9. s (e�'�&� �BorH c�C ), sE�y �mon!�%~-g�"�``daughe"''M��#selvesgpa�#!��8!1!��#: wn"� �be� L-nB�L na 0$ �yѷof���m�"�r0�meQ.Ri%� �ed!.>d>;Kq9��SS99,��},ZR AE=� ime vR 0mdm>a� a�rq� $ th,$ny��<=Z�agg "0�i�y,E�z�)$���0�O!�r�"wP!�1 AA�mt)�� ���8."�&�CJ A(t) = s+�oX_{-\infty}^t d\tau ~ A( )~��  =f0s 0!�-~.�x gmml�yee�mea� xPwo�iva���A��2��e $�$'p# 2Wy�Avey�ՁQa$�p��$]or^�%al�?&� <#&#�$-I$a�*�����9tKmed"8R��52p'�b]�)!l�� f�B�$GO��r1, � +iJ�nc��) $nZ?$1$ (  �nedaw!_D&� "v�w>4�  )9 P� re��� �0�R&ha�ve�edkV�)� &�d�1x2WenaP �lEZo�'n3%"�,Q �v�.) r� � �s ��&$sR](i i"�ed)Y �+� r $n<}��N{m�ons!�``sub-�''� �d�ffYrapid3`It � ^ ��)�/ s�&@��� e�t^*i� {1 \�$ (1-n)^{1/�j}}~��mgk���ngc*�"| � �*�8Os!�.me&�("�\ �� $t�c� � %to�h asympt�$yB�$,.� ��!� ����1!sFEd>Qd"dM��superUXEV�a�it�;o�u� !�e&s0ly fast. We w�a��b�+c��@�VQ)�� 2 2�*T e7Ra}e"gxa4 absem+�3*"���B) peak!.3A}vw� o�[.%�7d�rp.�&n�- stochae>@!��,�� . N]-fy!B�!T5�� ��. q�tjb5"yp�!��2�or* !�A|cc|}+�� !�th�� �1/ �/Wn:n�Eu!e � �$NJaulP "rEU%�2to��X HSG}�Z �vt_0^{+X  0t_c+u)K(u)du � �^{1-2�t~, �uvmlw}�"�i r�#-hand-�A�v.�1��$f( *�-!��=&  0oJ � �happeneK er (�r��)ME()�P(w8q� $5$) �r�8!� intu�E�RQ� � inpre�d@� mAm�Iu_` �-er lio]U� a&L+�m@�s+l�41 �!:��έ�)��$@�� �e��"Gcr!ed i�e�i�a��Jm ���E&�A��a6�nes�Ys Mexby���|,4�2�@)�ach��6eH���N8�8e7CDod�GWat f@"n�6i;8A�%"�f!��aga8? ,�expmKb(ncorph= ing of� po�  to !L!nvu��(ent, rumor,��new�ducu.eum%f�l� }*!����d�%p':e"3!Am � %�f \*�^�:}�`~ ?JS�%�:LJohansed O?�<or�6�+ ex�d�"�d� � T ��y a jou9#ist�AX�Danish!2sp@Jyl�9Po�+� � [4!�raf  broade�cat�6u est,�/�{&9 "I;�+� w2ub�k4April 14, 1999�b{��p��!AN�ua� *Fn� e �Qro�>6��2es<trin�0*ubUbers)b�(��URL�!^�-o5e�7 �t p c����trni$waqN�j"�6�; onitB�Q!E��s �&�1% i�1#�%Td+& 9 �wte%z& e!�2d(� q�!|p!�"�ob�c=p$*O��  $b=0.58A03ch�"wn x�ig�;_ hitsfita]CB ���C�@\�D{file= 6 .datj,-D=1�D& �\protect) 4} C&e'*�oa>s $N$% "& 1 $t$&x�aJ%\!OY�$on Wednesd�114Q�999i�fu�$N��a}{1-p} � + ct�b \, ![�03$�U"�ecFv{j.CB 1i W&}i��"� ��>  summar�Ap#��n)��} l !CM�� 9n* �"M� /9R&�z����9�vDI�6ectq �� �\� :�ia��?n� �@[\�a�slW ly �sT �_e� day;�suddećj�'d�1" te\T�}day��sw" days-A< .�� e39lax $l�<a�<tf�.e��0I>�:�p�eq 0.6<�$at�+!�{ � a c" =0.4"oG�Y��j%Y� �l::>�" �RM�2web}����� �p& web-Y|on � @���Ri3�URL�hi�0t�I>/. Ha_o�h2�#&w:<,�!%� �ip$2� ,��i�*J���to5re !� $woi�"�Y<��: (i)g�� E,P"�$; (ii)E�� "(%A����($n�1$�+� -�I>a�+$�ˍ$;(>�i��-�smoothlyH .6%%��"� !-Qdas"�6D� � �. "@D"~*LZ�owp$�E�&D &�(ml*a+ iX6�&�, I}/ up8#<nge�6*�@ ���!� $1-n! =�fin.�%�1Q4 ive (�t put�;e�Bmea��A=Y>�6��$n�K emboč1�A�d�!uc~"�t�Hnd"y>eM�e���;a�� m�ot� doe^6em Da{ ic-�nk��t�%�A�b��T%5#���,��"uVH��"�*c9N�ast, #� B�"*��3��%/B$q8 &qB5k 0��inkedB!�1yA4]�"u���.�A�ourJq֎/ empi9F�'.,5]�!g put 0�rI& 7su-Eckmann,lAM�Sergi�( Eck}k�'�Yn>xf�(ATte�7�D&�% s�t emai���3Ai8i� <+ yi�9s"a��as—l��message��3=a.emIEk��w2&��a6\{(1 hour���^���/ K�# �(�)�(�aM8 e��C� IO�Q~*��B��JU:E,��Ya�the p�+ �,1�web* U&�,*a.��:�notedja� 29B:�J} $, Deschatr�Gilbe�m Ageo�@vJw�� ab�A�al}� �* .com� ���K*xM�!"�M � @�*.z&Ň2z~p1.5 ye�3of��Kwo �)s, �A ("v[W�B0 Stay Young'', Dr. M. Ne[l�� :B:H=I/P(T�U SP<rs Is� Trilogy) RN. Ro!=Y�vill5�?�e�wo p:͖� �0i��A�A� on J85, 2002T.ran_Q2,000a� 6Pys12e` s. O J4J=$New York T� � ���$R  co-�2``;0nd58�re� done� %_iriam-c<d#+?0�! emal�a�p�� iEx($a youthful�`menopAO bod�� o buN%�-okA_��!� i�l!� NYT}��g� j etyp%�an ``"� ''�csy ��)�B cul*�6 end of %�!�. a�I�Ei\Gm,�,� uch "{ -}��:i�F.i�x+I�Q��*/�c.ta%�iE4 months$ w����!�[t! �e^E�BngAfEE�A�e ��s�< . QuT0E�ly,a�h'4� � ���� in��ti�bg}a� �A8�|a�< ``Divine Secret"�<Ya-Yam�hoo'!by�mW���*�>mhbesZ>lMLwo�j2e.9�major"�-A�(campaign. F%��rea� �zi�Oi֛�budge�}ok, ``��begvmHWUit{�}�!Q�3] eir �[...]A�e�ld-�:D?p�3� a� �2��:M, N"-71�. Gen�A#!# popu|ty��/A$�s�whe%-4<mPAy!"PA E���� �$p�*fa�0d8enoug ��P a�potaEal�b ers."U�@1�}2:F|_2a�1B= 1cap&�|fi����.�4ver��_�{lf�D!A��A wo%s:i�As� tom, blue�fhH�� Gis �:-�>�֍$ (top, gre�,�� aa�T�YG�^ �^ {�D6c{/%paԀ�7� ����A�@goA'a�����>d�� ٙ�lk �|ngl �@29�[. �R>)"c�6�}t *QS Qo Ao+erFA�c. ղ��!ʡ�� B/oprah}:�1�ers�Qt�?e�2O%, Winfrey had`EKg� $7$$8$  dH�e:A ShowAm���r �A�n��)I�Fm Jp2kۖb+}Bc�&�A�At�E ``Ge�OaeP-Xam.way Each%< appe|onJ  7 (B.Ga(U O.1m's1�)�i�j�5/I.EV,�*�"� �!140��a ach�A3op 50� I�� ` A��-�� �<�$y=Iy to f:+i�]� �Wo�An8�"�7�:e��&k"0.7��� {�~X&�^X4=1-2 F� rB�. �Jxa#f� h�!!;�Ae�F���i"�S22�fig��2[S�  e%,. JN chec"�verwhe� g��htTSAf� �as G a�D�(� �AQ�"& $�:��p��?; n ab�WE�@G&�:h "!�)delzN6�3AB$�B".!D�!aOB�A�A�� �7g$� 2��*_�2:�*]�O ��z%to�8>*2�*s��D �!X:8f s� 1��-p� �"�!�!]�A�i�/�8A� B�.RM� ��b2T�1\.]# 3*# !Tta1 J$ 3}bo� s� (�)���e =�-�E�� B7A>�of�6 c =$2|a&" \�5� $t,&*� "!�� l%� > �"7�itI�.� �s1�$�-0.7$B\ � Pe!��Vt�J�&q^ore4_ W�F��/� A��DmzW = 2�=%�%~ �mAmiddle (  shif��upAua�1�V6$=�:���9�B ^� ��-�1�� ���1�5�!�-� �)<�=�&e��E� �+�wt~X�q l�1�e��q��($. %���%� (red FZ�25I��p2Z-� G!�"le�oZVBA�� Ps��!� F�t_z�!_oeJ/-t�.^ X / Y$x$-axi#(an��6���ursory2� Nq@I��]�i e� q�I%is2�3$ O���]��!T*E)�2 �%tq�QA>���n$ !(}��ek!kQTs (&m �!  �) L%� �g$]���>l�2i�"�is doUb�<s$~ vol�k-orĆgC!/sw$ b� te"SstoL)�� -= bF�;�I�/,�2 buys�in�;���Plyg!1 h �(%H� a.�?.nd%��**7t1�s �A.h?� 2Q3�gat��<+�-�S,B &���n�R<�41)�6�4= �< said�mp�5l I�-�$!. (.&3�@�3V53> s)&�@d!���)�l!�& '�,6� p0�l�in�h�� :��_6�2se�+isA���ant 9P �iA���c the ��c<& !��6Hq-d O�o m�*it�&�@imekE�?�!i�o�0�%B�iuIb�*�����G! d�r�4empha9KLM7�j&�U"��en")�!seiBfu"uB aͲl�Ny�Ypea� =a�kt�]akm�]#+ be p�*�J!�J�i�lso f�den�F= sen� �#�eqr�nU6SR3�"nM5A�O��$ .�\Y"  =��vn�Q�p4�/� &`��V�_��h�b�t2Y2%"Tk�$���.�!����#06O5�a��fd_���}��V�� �h��n imagina�d�48<�&�5umUZ��5�r feedback� �`a��u�/M�cMNY�h�tt�QA�ofu( �?Aza<�Oncxeead y!1� !�a k\%of*� booYo�CJ�h��K re c�NKed!M1�:�of�> ,4��=^ ata:Eҙt*��ei�d ���x*i�rbitr�da���d�?. Trac��䁵hLo��$n('Cach:��6�X�?� NHS2t� e�a��|��tpo�  favo���hp�!�t E�s&��promoa� or sus�=3ߕ�!o&he�-t,I�ob�gJM)�_�drkeT!�2� ae�i?&h�%halA�enz13�u�� 9&�DA�E��EfstTy� �x+ro6�'� �$�&b�InihA~soA�wy�G����L��i�`� �p�wofi� �� !firms. Q�af�9�܉:&�jn^n��O *&N� nrs�&e�m�6"l�f>o�Ra_*�>by�j��1W�B�N �Te 8�KFWiB soc,gilso�T:��a�!a�mn 6�|Xv$��.��ge��� ��c| As�asay Weigend, �f&7e!�� .�$nj 2-2004) w�1A: (webpage: ``/m�be world'suNl�py!�Lpy�( be��A�K�SW'' IUC|isE9IG. &_fIea)5�m*�Fm �to a D5� :/�I��m�s�htGe-r�r^�ke=7 i9� :s�A�l�Fm�``-�cl1>faa|nZai�USA%"�*!��S� 5 64)r��U�b� fUMt!� k. �=��zW^gr��d"Ut (trad? ) d7!�e0��p !a)� be� �"?6@t4s, Music, DVD, E�*\6s (audia%%�(o,\"e�4 ho�8software��O�0 gam�\cO phonY)kO%eeKi�9 BabyH[]PG��"�_�6� �& �Gif�RegR*zJewelr�Tw�7es.Appare�?AEW Food Health, P�C�Beaut�SD2.Outdo�t �S�6� (mov�f& aura�O trav�Xcars, ..9"A�t� Hobb9 QFr{VF�it�end9�� Q-BC���c��7�o\V aTi�> ��?  � gCte X la�ge]N9,er�P�B� vf, �Vid>/� eteor�[7 �flo�$:,"$ U�[o�Wy�p �of(e&�F� �w7�Pca mot� CD�wW.AW h AyB�%)��� o�y�'(sOd-@�A�� one-0-h�o�� )�%<Mde�^2Ayv� ��b� ��big-pan�JA�"���͎���.�Y�?Hjop!)�in Ame *0/�q#o� �]�%��R C�@,�h�+�Z�a�=����elf e"8� ��.a b���op �t� � �!� -�m`�5%,6aem!!fecbals. ES&W� Stre!%_�r& v ing � . IfA`)6%' shru����A2���Shat�IR%S excia�bU��iL'�!M.saoll!�RolZ St`magaz�_fa4rj�, bel�=!�t�%ivea�ew~-eatR- lbumB ��I;2$l�,%�}!��uϺW ndo6f_�a�>)!KI ��S s �V�"� e�%.-~�>�!{S0 fairly easil7so��ze��sa�mo��C�� ndjN��h�)+sD09n(j] �sw�mwh�j��B)��fh Pakio,a Engl!Jz?he Ne!c�8�Ji Y,)�Mo �%A�ult%�n a�firebombdamag�.r1��MLOn SeptM:11?,1,e/p��s 1BiH)�w .?EYW� Trv�Ce� in N�3boyb|: ">st�4~}bq]6�� he U�Mdd5�Fu�(s�eKies�," B3&�.&figqua2��+ - } Re6B��"� b&�^a�ri�s, �HA�5�5��Vw��s#[4& �}E �$e�Iuc� of i6.|�;�bro���Y (=^ *YL YL�#5�,nti-arab aggxLs�!&ņ1�i�'4-.�;�jz��O p[\%�M�d" Dow J���exW��u$�e-Sep.11 <asL wifRKDJI(pre-jl)-cu$t). S�:�'s At�ey |2"p D�6 �rt-=I obl!� (i�} liqu�8S ��p"Y-�.�V�R ��  S���Ot�- hold�"(c�!exE�Q"aT  -t)���!?fai�?M9i&<.j?�#� �(ᦁ�JHGi^�!maZ arm��R�nd�df$6�� ��4�w� %�+��ur��.YeK$e:�� L�p epito[u��*� F�. &� � RG~ doub�{!<]�#!du�:�"�&�!1 �m�{%�-�1�fA�t�$ong b";x&1x�c�C�"~& refu!s� �)��� moil� Jap�>llo�(& Kobe2t���Jan. 17-5 il a��c���'2d aro��\$200 b�� on dz��B�as�=�ys�q&>�4-AhqtAl�ancy, a� � &y�E�!en�'e�P"96a1mby�,�ps igno��seism���+�p�C�"y ��'),�in<�iDKoweitg Iraq�Aug. 2%`0%�� coup� st Gorb�9v/-91��YfI�$. However,�-�*D1fi��/� �sK|��qin�r�ga�-�x��E��*��formA-g8�:)e !�vg9>�s-�WmKJ�a]j)�EA.�4 50\��2��yh�Wae n��Vhak֏&ks,)i3tA�a�~mo5!c�+a�-u�豉�"-�N�- �%���, � al7��)� �white}� !*a$�#�� ng e� �6@�!�i1Pe���%a�robust ))%d���.^�Zat.Ua�e� V� "k` /J�g~N�(*l(% wer �RT). �$ autoT*mAypa��v�:ed#utore� v� nd�\ al h: oskeda�_� (ARCH) )ME�+>le#C�c -l,Bollerslev},%hG. HZn� ric )Pagantth`#��i���e 1 scheE�'ar����R��wer�O\"T M�ifA�4al Random Walk k (MRW)q�h(Muzy, Bacri��Del� �M_B,B"u�b��EA�"�FAeFV �. U 1MRW, *OKMa� rgn!� �VolMRW� 0a�H>�(��dn��"�,��-���HN�Ea.��. T�F���Ocw 987 Z, on ab�B q93V�  *� -�q va޻uw pt.a��J.4M r&��  �*�� �9iss ctly.PzA�.�:�M�� �w)cKL- �no *Y;# ��/� �"�Q�Hp-�6*&z �R�P1"�;��q�wR�i-��A],�"�,,� ��.rr���,Rs�`p0 ^�G �#� :����ve�*�D4�`��!:�o�wt�@'�L>9c �9�]����F�c�t�V����<(st��� a�|&������" gM!Wd pie�[q �F�mu˔lt� P �r�b�jf��� p, �3Q5 Kw"=�N �1�+�G��2'��� ir l���7�( �. DfE7e�8��o:E�atP )$ 8 fuE"dZ{��queen�$d:m!���om\G6anE(�'� C'�c-IV ��5>as $t����=��Q!clogarith�hY�:���%v(&! j *� }" l. �;I��$y���1wy b7W- ��a�I al��|f$eq \lambda��~,wf g,dd�ng� $ +��2���er,�le en� �F��)Ezr�' ep��+ .�. (V_0)}~,~{.pLY �^2~ \ln�vmkmer�eeM�IpX/$��a�a .ar�T!Y$g"W=�A��$V_0$��&�cF "~3shavior��2�U� �� 1)�AS"�M��W�~M����%fa�29�E�^D returns $r_{\Dt}(}2�R�!$$\Dt$6i/%^`c�5�fO1�je�b"�"0"�NO :E�b`epsilo�1g�!�gma� 6& ��e^{\w$]�remglwwE�Ui$eE���an�4 Ga��� � ���("�A�Ao�> $2�# A�lyQ2�m�� covari@$!aq�muo} \mu � & = &&�n2}E�\s!L^2 \Dt)-C_\Dt(0) \\ ht <\Cov[�,   + +] =��*UlnP�( � T}{|($|+e^{-3/2}A? \�M*wv�ea5q�%rA�I��/�Al2{nd $T$a�9 an ``>�v '' (* )D.a��oN(V�:(PnA  va�f�.�MRW ree��0Y* Wig 5�(�AC� �ZUѸ]{j�SicɕAM log-�GY atKe�i��*7#d�:�Z�$ir� ,� Rx valuKVr !e!n��^2$�s�dF(9Yy�%*0.04$�$�!$���n]�ׂrXw��k�IT !e :�$\omegaÉ��e�.��-��eq*��#W�so2xRH1 2K�:muX�mtFy~ ��i5~K)(t�y�/ mbhm�]�0�Qta�deOY s a Q�R �S.Ra�Ad��kbl $ x�ב�c�Vf��,:t�"� � t �c��v���|$�[��s}�'."SQ� us��2"�"� � �N Lkm�.QTP���K. AM�$t$t � .�,�V���is�K� mea�])ԥ��O $V8!�i�o ^�o�{~ K^2 )�&�/R�e�}{\��$. .�y�R � r�aCi)-2�1�,��]by� .�}|�t~ It) +���{ eq:k/"e&ao!�a F��tra��,�C�w}\- a f)^2� �f!%2.y fF }\��[)d ^{Tf}{\si��&%t} dt+O+(f\DtM )�9 ]ae� %^ho<#u5(�ivo}%1a�@[Jau$Ge�U,� ���1 < K_0 \sqrt{\frac3U��T}{(}} q ,~ \mbox{for} Dt <<�T���mgm*Uv� %��"ju*q� �| ^���" � � p"63&�B��) Zxam)  �ch. m� , B�_`_ �X ��ma*�6� �"�>��"�^"<>� %!�/B� .S� >� Q b�n!ay�AY�;�A-f-?-:+ns�<����b" �� crib��wq��M et - ��-���#p �rp.�u�;|ly[d� [�5Wa� ch �_I.�~pW�6�an ��>n$.� � �@tud�_5 M7�s $p(r)")  � *&� &) en"Gl!.?]%�iR ��-L&j)�gmmls})�>[p,o0�V*M}�Wes*L�-OTqH`��9s&�} ��-�u٘e).hCA>�6�I!I!�2���da[�A�/)x�&� �B���{��sim��K}$ ٟ",5$.#FN$ndoC|��n>z�a�@�j�-���&S�;�}j�0Z. u$multifract�al parameter $\lambda$: the fact that an amplitude of �exogenous response function impactsGLpower law exponent o BndC laxa WD. In contrast with�previ!� examples,disti1� s no-�much in$!-�@or recovery after!@shock but rather 9hprecursory behavior before A9%. A2b might�,expected to!+ a period!�0strong price A+s due%%in!"ce!@specu!�ve her!7. In 1% , an=� �would��U�M�9usystem�a % �,adverse piecE�informE^8. Indeed, acco��!�,ard economic|ory)�co!�0x trajectory�st!|market) s is:4 faithful reflI�2��inuA flownew88at are interpre!|A�diges by!/armanalysts$�A�@ \cite{Cutler}. A� ly, large�lossesAA!n0result from a�0ly bad surpri)only. It�i%D a��y�E�s exis!�0s epitomized�!0recent events!4Sept. 11, 2001�( coupQ�$ Soviet Un��lon Aug. 19, 1991, which moveR�!JcreatA� bur!?of voA� lity-@$VolMRW}, a.a@above. However, i!  alway!�4e case? A key�Uis whee�)�-{�i;)�A� slavedA�9R -Sor�)�ery may2�aO��origin1A dynamics ��at�xtia�r23��a5er��)require �(risk manag��develop!�, methodology!�ident{ �A�obT ivel� � ambiguouss��. Specif�� t� stud!A�W ribu��!�0drawdowns (ru���)A� � ɛs:ŨA�leaIxchan"7 ,s (US dollar$s�$Deutsch !�<sti� Yen)G major.� U.S.?0Japanese bond�5X� gol0. By introduca' vary  cert�degre�� fuzz}Me�iB-�-�t~ !]robust��:empir!� .y�+5z. I$ By a care � i+tham2B.�a���a-THextreme tail belongra dif��t popz o9��lk (typ�ly%�1\% mo�� U� occur 10A�100�…�oft�than w�be�Ddi2� �op[ oE�!B.�A� 99\%v main!��). 1;T%"S�9 � seem�)  V �2bXR 0``outliers'' ��1,��, 2,e�com}. O��s�%r^ �� such� as ``kingULor ``black swans.'' �� �tak%eAQ\!1���Ane �be��la�n. Not� at t���� ensu� ��6a ]� }��!Rv ��q�sA obeeu@rbitr� 0absolute ruleuThen,� �l����,� )�checked^  ap.�ɱ ure,1� log-�ic &(�3),B ��"BH{\i�e�1}%e+l Q�Q��.y z onal�%�P �qwas bas��e�ir "7 work�JS� ,JSL LS2000M�},�i� docu� A"1�� �A� Zs�Ax:U *� � `M��P�mZ�i�|i�ect an��-of-s"�s�Aw!�� -\ hypb�<applied��of**z  seri�e��A�a cri� on (a�i�� �t>�1�s) )pis une2!lo�U�� ��I!�1e)� �[2�a)$a�qualifi�1� DaF�:�+!!��is�SnP en�i^�Tve unsus�] able6Z bM  gene! d eC��W sd%}a fix�� �7y � clas�f.osemaa� ��)6>� ,Pi��a� �tur��u�atm�osea�"�� � w-���ًA�8 relevant histoP��,�n i.e.�R�A�a��gni% ��t�{so)�to at- IVi_to it,  ��s# viewoeffici�A }�. S� >_;6a�ngE�1k�y.�sec =,6� !҅*:�iois ��enQ�. F \ref*� illu�teA�5of9)&e4 -{� &s �p�� He��-�s*W0, perhaps on��!v� .�)}�X�uld. All/EIsE &% J9)U��Globa5 �0i� z��q��49�hs,!X�>25 were �ix � , 222�E�a:��C ``anti-��''A�rtAmin"G$0. Restric��� �3ices,3 y f�31N�19�n.�10 U�a�2 r��. #*xTcombi�!O��pz O de���t=�,EN�J�ndFml%A�*A�rovid novel�&~ taxH��U\ur> �t�a)n(he importa6of p��� sorJbook,PR�do)�� c�. Whilɰ idea����yet&z, Ia nk��bey�8�p+ ts sFby e-reH�&L�T prox!Vof reput�E�commer�!��slend:`� ��to:P the &gst� of I�(al Public O�^ (IPO) ){ipo{Em)�����day}.w e�,0Y�o*. cascad�riva��&� Ew�_s bo�fice r�|u�(nd%)u�tţU mouth!nO e� t�8h��see� Earthquak[re no�ou�t��� mix�� tane|y�s d�n�p�)ton!�trigge!sA/y rH ��.� inm� pi!)�ETAS} ib�man�phenomen/of seis�2e" 6�"�A�� &�bi!�G theo}� �3ce��Y5�F��-�{ iWi�  (� mvmlw}) omem� ker&$ $\phi(t)$by5gmdfl})E>$KN#gmlasa})*��Z casex��5 bA�renu!A� d Omori �$i�-u��"-� 'SS99,e:.�weaA�b!� climA)�involv�ly�rplex �".�o�oo6}di�angle![is s to �unX�!� ���t�W�at�Fb��in��ccountD nce,!PA�c�^Wfu��g�  warma MOe\��nth� gen��R��-w�al varim�. 9/11� o�i!� un6 0 window. Travi(nd Carleton-�  } noA��Q4ing: ``Three d.!%�\ suicide airplane hijack� topp�EWE Tr��Cen�(in New Yorkoslamm� M�PA g'Dn Washington, D.C.��s�� crew ��ũ�abs$ airb� jet�*�ir ch 240 miC (384 kilo�'s)��ve Ų . I'� ell you� t���'s z#� nge: NeDl> en we go � !1 �ky��@like a spider webA p$rails,1 a�a0�]utp��= H Frank Culbertson t) fli�\Mol- 0at NASA's Mis� Co�l9�4 Houston. `And��e � just!ut pleta�emptyayaUno/&ils!��\sky,' he added. `It's ve�%@ weird.' `I hadn'oe3at!���,' fe� =,Cady Coleman� f .'' IㅁV�兡�e@)��� � �e"p diurtemperQ � e US�ty>uV e�wAY�Ogr�a�%~)�!H ��!m���$e archetyp������e*� in�b�� en i&T*W)* poin�&6o�[$ new fruit+�NTmak�ogr in 6})�in�$� AZ!. *7�a.oreti"� , an�pot�4 �'�#9 � !�� !/a|$)�*Y A�cep"�"�("�+to non�O}%��rPu P)�,M. Paczuski,1� ity,�ingency�dAjProc.�lU,ad.�L. USA, 92, 6689-6696%o56��4rslev}  ,%�G&' :�A4�! al h1oskedE� q of E�-e�4s, 31, 307-327�86$NYT} Brody%�Push up��wp%��nd � b�� )y0,�1v T�'(F 7 (June 4�,26urch} �R.��R. Em�/nd M.E�, W<(Can `Nine-E�� n' T8 Us Ab4 (Closed-end �K DisJ �(I�* or S�ơ�,mLI� , 38 (4),E�32�,Simkins} Car�� D.AIAB.J. , Do Ma/$s React Ra��7?�(e Effect!���4September 11th� gedy'Air� a� k Re2, ��wpN&�2) �d$s.ssrn.com .taf?abD 0ct\_id=306133�p/ �I oterba�L��s-�Mo �P�0s?��(of Portfoli!-)rSp8, 4-1��89.�� De Vany��A Lee, C. Q�ty{� *���sE�8!`"],c >�mo!�� &�9e�.PJ.eT . Dyn. \&� 0, 25, 593-614%�6�m��L lago��S� kamel, No�R"+sk C��os�.al�U0 to Short Pul^$ Bull. Kor� Chem�ZLc., 24(8), 1107-1110�E��Amazon_E>2�&oFI�.�g preparE�HDodds} �`�&Da!$Watts, Uni�2a�%�o�3a��Y!�^ agi����i� L�s�l 2187��4#%��HSBH} Dunbar, R.I.M.���! l br'&@!, Evo��5,. 6, 178-190�;982,Eck} Eckmanna2��E. Mo|!�!8 ergiX p�di�3 �1 s co� nt sR*�$in e-m�&tra?,�uFt101(40!�4333-7%�6�ERein1}  ag, \"U��die von 1@molekularkinetiscW Theori$ W\"arme gI54derte BewegungEin ruh(< Fl\"ussigkeitesCi7n Teil`, Ann.%� . 17, 549!y06B�2:� ���01��%{Brownian���� (Ѻ: DK756"E�} AG, A6~ v�� . �"*)l�uni"��O infle],�v;!4, 50, 987-1008!86X,gilsor} Gil,��Q��Htte, Landau-Ginzburg�5alz1*^ O�}Y-� Rev.aw,. 76, 3991-3s/O 60Htipping} Gladwell, qx : �-little�e���a big �)B� Bay BooksE�6$Hamilton}  a�,��-exW%^s�3( �D% of �ge�reg�:BF-�c�e:�s^� ��>- , 12�5-423!\86s�2>�A@a�3to�e �: �n�.%�(tim��!A2��4 cycleB�7, 357-�(1��)!�u� *��bZU� D., Sub-Qhsuper-x�Fe���� ��<(!� Geophys� 4. 107, NO. B106!<37, doi:10.1029/�/JB001580NP"�.����uZF!G!  M)!x Inte51� TF ed S�aj J:�8, 108, 2482, �3� 2485���5�HSG2�!�!s5��8J.-R. Grasso, M�CeA*|of�"{ F"�:� do� sAV�al"pn4 2mej9jZ lawaN� (B10); 46B�2��8J��Jen� 9T.� Ljungqv�9A., Go!�B:�{O%�'aE�!��n��an�,Raise Equity:b Oxford �� P�, 2nd e)@�6# J2web} ��" e�of�R�Y ��@296(3-4), 539-546J`&"�-cI C�ntl ``Are*"*4�% dict�(?'' Eur�� ,60(5), 809-8\ 2) * �ja>| Prob!�huO�se�� � , 338(1-2A 86-29)�6�J�+>e O. Ledoit%�.� �7-�&Iɔs, i�n� l.� E!e�TA�!�8M �)a�19-25i�6~M+16�K2�V "et5�a�>�/P n, 141 ��:� 3-~�_�#@, RISK � ), 91-94]92�JS\3 load~� Dow)��?d�;hhe WWW&���sp� p�!%�aURL�,ica A 276/1-�G38-34^�2~ Lh7)��� D$,s a8O512�Risk, 4(A69-{ 1/:�.�a�B E"� @ us E">'Q�in��� �s, in� s�H``ConUo�0Iss� in:�M�'' (Nova�� �0shex 2004) z�021050>"L�/6|F�u�, �\�1 ���us disc"@"�:^ B� 1 �5-3�>� &!�n�C(N.F., P. Je��# P. M{Hui.K;6 c�� (���:�que�<McQ , G)�K. Vox k, Wh%}GARCH? A!��4ce�' ex-i �(.� .��?of=JSt.7s�a�5-9t %�.� music} M's brer�W$"j%, B!�A}�7al,� �/Friday�<2th��6�M��J�� *�E. ry, q �'2�>#"�D�Y�,:�c�%! to {,p9I� �q 0 �.B)O537-548�02O�!,hO�& � � � �_.�ll Imp.n ., 7�1 (18:��} Pag%A�G.WC hwert, Al'�" ��).F!k 9�4mo>l$45, 267-2916��}:�A. Ulla he � F� � �!kAw � ��I_C�, 25 � 6N [} c S#&�impdF�!�{ si*� \.$4(� 1425-14� 6Rv�}�, B� Pa�feJ�+ion: Ae��O%�al �I�,s (CambridgeA/�@"� ; 1st� ��6ORSfrenzy:�EG.� �"erm�?8.� ve FGz�$6, 729-739J1RSA:�F6f > en, "G Func!2a�&�S� in SnC��s: An Em�:a4N���6} ^ ��1 s 37�p-9��6b.T:e��V�!%�"".� Ver6� ����)Net��� Test U% 4 Sale Ra!g �)v.E� s. 9a�� 22.V*�SHeqBy:D�6�"�_.2��-Ӊ�M�+,& 318�w�5#F{ 3.7�>6e%JA.� 9C, Sigy&O 6�;N�!B#, Qu�3����I (e 1, 452-47�6�feedsoc.���I. Do� �6j� on�C�Z J.,.I2#� 5, 325-33�:x �K2�,Ap&$�_ k {cau��1? � 1m), 67- �6szN�&Q$, E"ef Fue� ��#��Y y BE;by� ign �� In7N: l3 AF', VUSP��its2�2v$32, 412-446�_5B.����N �Chaa��S3$.��8� a&b !5ore-�� ~�304601.? t) } S��4onovich,~R.L. .�N6>T� "�I: Lin�'!\"B  F&~'-D+p�K�� ms ( er,~Be� ;%��,�996[q*}*!viq!� �M.�!l�� R.G. LaurWLn �+( reduce dai�Ce&d*r!�,��#A4�zE&6�white} W E.N�%k:8�'B� vmPnia8=n! )5�� a�m. F��=y, 13 (� lgar R#�1, hltenham, UK; Brookfield, US%_62� zs1}�',M�!K2 Non-P�Uric� +Log-PSic� curs))to��� , InNB 4 .� 2�e0:Z�(�2�� }�R�#7 �� 7, $0 Hier�*� O^&I��  GrwQSizM 2�&Roy�!5 Lond4A ~�40329# �:t:X) �B�c\�=[Al,�!(rint,draft,�4 pacs keys,t�m"s,aps,q scriptadd�tfleqn]{revtex4}% \usepackage{�) icx}2dcolumn";O�} \�({PNU-NTG-12r4BuRI-0�4K*title{�E+ al B8"��a:� Long�? inal!��?H9by Locb"W)7�Ln Ea,ron� rage R� \�K{S.-H#(rk\foot�{�:-5x: LG.PHILIPS LCD, 161, Imsoo-doh LKumi, Kyungbuk 730-3� KOREA}} \�GTl{shpark@lgphilips-lcd�%} \"l$< on{D~#t� k%sr Nucl��a�Rad 7 H+o|KInstit�F(!{), Pusan���E&T �an 60�5,f$��L${H.-Ch. Ki� �hchkim@pS.ac.kr/ff����V�J.K. AhA� �ahnjk������ E.-S%~ UF4eskim1@postechR�P.gWele�. L�.8y, POSTECH, San?* 0, Y�90-784U GSaj(} W��T/ A�[of a lu�c� nt w�0A� .)ar o&l}� beamy�<%qu�. � alsotZ�Q�:�Mcom�S� jp Acle6ac2DB� .�si\c;ly�F�: ).Blxv� arouo@ p�cer spa�"41 canW3 bifurcɰ.;�)Yns., feW-s bF\"�I�es. WXN1e� alsTat�Y�\!f,o'�i-5track��O� a Ga�%an�"x%i�4�y � good�<�a�N��.�AUR \��P{29.20.Dh} \keywords{!�s,.,`4c��P��!s,:�!*��Q \x$�} "�?I�'duB} ��$eam�2\e � h!%&a�+< aI` forca�Fs)t"j$�I romagnetiT<"o�D^aa2 E��^���4e.t +urb�4 r*!Q1�2V� . V�Wus c$�4&%�e>6W"�G�E form�6=[ Husu-�Du�8*6yw�)'wfB�Ud�7F-�G��^ifla�)�?�?,y&3/8whsources=be��%>ref�=�@h �pA�%gan�6d�u | V �may cD"�&t}f�^N�m�/#9 on)�?l}�FE�T�9� �>���tB%%�ae?n<ldт��92-( �FaiyBA pS7�ork�m�,�S�m���t ;�"& awA#� h�Ew$9mp�T5��a�Qd��> ring�6re, w�XnsiJ,.as *�DTa�Di��w�A�v_�� of g�^ K��eea�]ze}�Bz"a]<Z9=*��l�Ea ���1�al"jb%��J2I wil��d,damE+�gIc*I�-! e��46synchro��tuiZ)�ed. I�c pakJ mj ��z-wo:| .%I;t  '�!A�L%Z�/��AT �0an individual � W�Si�@�Lp�#ao��k��<s:��S� 2, we� 0efly describeeB sD�Ps�orE�o.�!L .lo"X6�-�%ڱ,M��2*�In �3��:%�Q��^ `�b��d. �TKvalid� C�bs1�N<�\)�eREl&P\wAt�O8)HulR� H-� 4. #l�Y 5!y devo�to!Kc" o��cI 0$*�E��raa�T U o%6o�%�� �� � t3b� de�Caɍ�\\ 1)*� db�e� $ ))��.. ch/deZy *�to AJ)A $d.�E�2Kw��' S TH� $eQ/"�L� $e�"� �A�$Q$6 tota�����n�� T� � "� �U��.�� � �s: �H = a \Theta(u) $ ($ }�qjep ?) �!- = b u�a$ b$!n�`&S �!F* .� y�� .� �Z3z ap�q� art tG" behi�"��Y��i�kV � negl�@%�-�3 �� {�5] TeS 8 %��eel]s ���n&� mee�[�Zo�6!��L ��^!= .a�� \M�Z�b� v4ISr&�isdU��6!R�P�.���Z more ��GEalntiHO�asFC \bar{x}_ia�l�O x_i \� le,\ �'� {ij}% (x_i->) (x_j�� Pj)Cy&� �i��j$�eizP $1$ or $2E��R!m ,�p the � -s�Eh"�$\Psi��,x_2)$�U%Y�Owz-qeo`X of hig�s�dt�npE���:Q��p*�B(a�Jn.L!MJ {1}{�sqrt{  det}�� }} \�s \exp[-2}a�m_{i,j ,^{-1} ��].>�Forb plic%-h�qwe��;� !�"#qQ�� &w-+"�L�n*hA�fluU*m��R thus�Q!��Xiionljje first-��\[-%� -ԁ�W~ e sa�g�!�in�"6H1} ��*�rP'< in Eqs.~(1)-(3)��b&las : \\6� �� y i}*� &=& qD1e~ $. H,aI1 _{11�� &=&,\u�12%PB2� nonuLF\\ �I2; � ^2.# +(1-)>m� � b���1R>)C.9�������� ��.4 ��,[ .=.o�� �1 )�@ �^ Be�>g22}-2W HB (x_2��2)� \![ + �^2 - ^2.2�=k 9�Fur��cal�&ons�um\to ob�d �a�a�� wake 2�R�5/&lB &.�:2 -a/iA9�} T��:H 2}-a����H}�ȥ� \pi}JC,>�6c!�Vc2cbN811}}}+a^2/12. >� A=6 S)!�Ed{\�fa� ig%�m�eqs. (11f (12E���Q~�b ��".�!] %^ I5V��C2}�bb2s> v>�L22} -GI� +b^2[$(0.608998+ �1�wZ>2jME�!RNIq"i:\sE j}U_� %j �S=�ij�8mH@ h,k=ab2} Im_hkZjk}>�"Jm�5�fI�$�{i�nd"��8 E��j�l^TR�"�B��o�v 2p��#UAa$\iK�� Z �fa]�we� utilmPthe*; > � " 2[ . N�z&�D"�(Bof�z If $S"K-�&��Eq. 4)� �6t�a�! iod-� fixed7A1s=(\MG 11}, 2 22})$�]ho� \[M� = S C)v1S"%!�z-�.{uf�o�.LS[M]ao]Q1f �2$a�R;lt@Vhpairs at� g6�-� nr_{1,2} =v_{2,1� \] O�slasi &t�P�% �%to�nhv F) , le%d�I ;U*"nM�D"�G 6��.XI�$"�_��!,� T �)s�ḯ � �!7�:�&P set: $0.01 \leq \nu  0.3T1 T_e 1500 -� 0 <`845$�"��summa�x�T�~I8����ur*}#&�,�7!��'>a. ��t^ � f��nDI�-, �l 1�!.D�e, 2 doQ%he BE� �I1-2 l�%.C w5�mUng"ult�(-?B�ho{�"typ�/�a-�sah� woVX two, �[f!�e�K bly ���->�($T_eM a$�0� %M���' U��ni�*� ��te��a��%B�)6&�(o��>mf -�%)~Rjs�Fig.~1A���R"�)i`_�xocBrc:ed X3]c�9��7!Z p{W uB3�eed��$�s�1,��_��=�0.53105a� ) �aa`  {�>q rawnn:n"�� o05341 o�85%�y)iZCa�d$6�+s]��a����s $(a� + bu�!"a%e\!�*+�1�!y�Nt �!�$��= 0.20����pl�\�� l(a)9d pM7��E7cS�"~=H-plof�f� %L15.4319%M 17.01573$ X$24.96073$, $31.95213$).n "�,str2}$-Uw�"ks r~r�+A�B��i�5�<aq�in -%b�TCA�ϑ�Jk��&a =1Jp��Eo)$6.3103E� 9.77A�g, fi� [tb] } \vs�{0�\i�ke$3s[�55mm]E01a.�}�)b )NlcZ\ on{F�-A����FA�!,)�� �*�RI?im�R8ef�:(a)� $= 10,E�A�5,E�$ �V< � 2!s~12 ?2 �� {.;(b |O1qb$ = 2.H�0V11i�f #2}$=0.}��� fig1P.!b-�"� ��)�3-� �3N� ���% osit����as%�!h)� nu$ !]2!ka%�zg2�2} C $b%�25*� 2a�AA$b= 1.0'E �H�����4��41�~�4ciІ4d *E�q��-%"Q V�]eoA%�05.A^dyw!�9� Q?.t/�3-ЁYbAe0��wEin!�, (c)�*(d)�t=0�r 5.0,�c7;df( �.9%q�3Dm��H�U3�5�2B���uH��inx!�.0{ 8Given $a \neq 0�E�"�Z!��P(͸�T+�n&� �.��Ro�o�o�� tN "B���$b�j `ma*�4&�us%�.=�d>ig. 3 it�st@, �"��! �-01� at� ��ZbI� ܅s� 2C-�similar"� 2BTn��* I��< 0.7843A�; �D6� ($1.2575 2.34851"Q 0.35848A6.9652N AA!�N��C ��C %�!��-� star6 o get �Xd. �)is e43�W6:�wBg � 6)t>� �� 5 0.2612% 5.89856$)e�( 4996!4.3943U zbzs�E�$5.a<� ihbARh�m� 2�� � 6.86404�17.82114)�2.46592!�32.7149&1 3.61459589.64147%�Put�$b=7.I w�ndň(-�l� 6�� %�:�s� and  q�㊡2c),(d)e%@.�of����fU+2 !v6��Er slow5phAd, .z��p���]6�*� �a�h�d sin_N@�$0$[$$3T �kb� d)4"f�"�OeGnKt6�B�!a�w��k� L (a):.-��4i�5M/� !�&�_~7ε�wo'on!��vr���J!�=9� wake��%6.z�?9w�V�: rra�%�5 �%�AI��(��0.t %!�3�`� R-t�IE"o-"wo�6�v:�!�a.  Qhan�x2�c.�!(2 plXq�f�E�g�-��"�)F�6�.w �4t4[� "�E�a�<J�Rl ~W 5� �)�� 5� �Rv� A�*�< ���f�� I�� &v .z�eb�e&� *t ��-�ra�ra?$10C :�J_E#& ��~e�62� :�c��A:r.�2��=*� �� ����wJ�J� Y� = 5.�. їA� rF4:/��2G�2C�30� �� aTr9��iI����25:� TrZ�Z>�6K���&n���� !����&� � I�atQ�/U�wak�� %!Q."� it"nbto oq&5�|en�� ��kiaofx�q �ah8sg:he �ٛ��F���>itu"q�B� ���yl a�Js"K� s�%!U��4�u� �a �Nl� �N;�@7�@FmP'N�(QM�3on!I �*e qNA:�%. ",� 5 ��-a� �} "ml � 0jq$20,00: ct V.\E[%���� 2� per � 2n7�1~�81��)��.�""�� )!��~�6" "^)Y&I>�"GN�= 2 Z8%�'4 0.18.[b� )�.�).� s at�999�Ud )���,6+�en A2`E!2IJ.�8:z�� "OCAr&9D��R�96�/���cw"<=�Hreliab����!ul*�:| /'�Sec�!3--"�!Ansatz� X/�%��ide�C as aa�8.��a <6vB �,6*��r�sr farE���0 W�<2^+m�;+2�")6�"�D�o =� whe=(��;<1(e*S�% �mer�z caus�!9si�,��z ! 5&��e�!SF� � us��o�� rout�G�S *�(gw��,�ngb each5��yw-,�l5�����/ ?jraݠ5by|Bn��2&AG1*� it. f�.�$��:?!��1� ���TeJmin9�;(+.�% 2eusC-is.�w!;|2�J�O�iE�� cou�fH%�2)4.�Agg?2asY�r�v)o%^z��60A[�$5)ppe�F�:/-!Y!��%.�of $10��Q���.F�#we"52LB�1�5/%g"91�m?C]B-r�U S b�$s� z���=Ze%2 10%~5a�t}9$%� s af�J�U0^A ?) �-B  � 6�j/B=�&� ��� exaLG+ s�0Fx�_.Y is �-� l�#e� �[��s&�9 �9sA���%� %ir&qD� "�49C�&MK"AK��a"�>�G��c1�1so&6BB��zU� duH!v&+ �5���� )I��!�13nҝ$) �6��.�y�T��Qբi^(!�Q�� �!�����6��E��M/X *� g9i �2�= ~� 2s1�&8"��U sS3��1� by*� �KքA}��J�%�J<m$^��5���i!�B.G �A0B��BH�H�b�� 2i"�( ��he q��& 9v�*=� I�r��Y ��:k= e���>O1�o�,roR�!96��&�Iio���'.�5)-doYkng.�%\�*)b&�N ;5X. &".-< �t_*!��mNevalu��E@1,��&��)��~ * x 1Q|2KGiin �l)�"��)"�N X*tw��=G,�a M��^�t�l�r�0+�+ 0.3$�^. "p Di2eG��eG�r %t �/H$,E�%�in"�S�N{�aXar&y"�)6l��9Q�)2� WI2�,�Rbot�:N�6lu.��*Pi��i�>��2�to �:+f s�\ <�'� ��U VM�� �3E�-i ���Hmm2�-A�^� �v!c�a2�)Ն�confi�Q�0 b� �SW ��A*� !� ka�*�,����"F sj'�� �)iwt�F��>� ��.A Ae�CQ>a"��d�s�i�Lq�=���:"� .q��|2�*�(70��| purp_|-�6[�OJ�L}T��!�&� ; swM�i*xM (-��)�%/A�W "D Neo.VI�QAth���� a�!z32; �E4�TÊCn�tooAap�x��� ���I]eg�V"D "P .���&�Q� 2JI� x� �.!�6�� �|u!AaM/�i ��Hv {"!��j w] �**{A:� � ��A� HChK �uppor�by b8\.2=JKAF<��*�\s_�\&���\ E'�A58Planning(KISTEPGMinist?aVF(MOST)�Zn goverZ� throughdBAERI� gram. ��Wk �![PAL�M e��2�~a� achiev�#&�7�&}[>A`��"z�;1}_r�U: ParN� cel.T� %o7) 57.>929)o Pe�cqZ4 F. Ruggiero: �gXhlett. 66Z91) 1693\e�\} &�\!�M. Yoon�y IEEE/ns.�^�pi. _q[81>Z�""][K.�KEK ReA� 95-5�5)gA>K�autb4} [p] "�.8L�m��J�forAA/��Q;��w�u�n. "Za��4ular} {ll} \h�! 2�L�.& E�3���A�te.%\FDO�%4� .� 0$ 3& 1 n�;$0.153BL243 M & 1;\ 2;\�4j PO03\6�152 N4LPV3`-3N[T�6B�10 S.�K1-4 Q ]-4a\\5��ta)�6�+le�.�&Fc��B�c12pt,a4pU]{�^6�camsfontq0*�camssymb6+in˜�C6g��i-S.D :d��tex��!�23cm 1 16opmar��@-0.1in \headsep 0 hcskip 0.6W�ide3 1cm \new�� \be{m�MUc!ee{%V.re!{\thed.\arabic.;"�#9� \8^�"(Unique Dete��"�Neuro�iCur-Wp&�(Brain via M�]o�ph(�!�"R~9|{A.S.\ Fokas$^\dag$, Y.\ Kurylev� V.\ zinaki.A�\\ (ag$[6OdAppݓ &G�� T,�e�|`d}MC&/d��Cpt! , CB3 0WA�h �Z��al�� s}\\ xL�bo��R , LeivLE11 3TU � } \date{}6�_��a"�b proble�[d-ۡG!�n1�c)���˗f�p meao��F� in 5� !` �J�Ba�'d��^MG^�Vp "� - ԝp�;����_�X� sphe�t.���c](Geselowitz q,� !�%�� �e��ru�m y 2ii'�1R�)T�act`Iist:�;p� m�)I( � �=s���m ɚ���ar>�5.�C�B�.8Nra�./ 1/�� �a'�>R��& �>!y=�of)Wminimi�j)�q)� 6�͚��A@I �E����� -.B� &� � �ly=�Y�:Mc V� (MEG)Y�vA�at? ��\E�cac�ddA�st��\/��)�physiR �kbas�f MEGk!R"SE(sQ al!Io,iO are Q�highl�Xe�~:B cell҈���%s. �K-er � al&��[��&:�.� v���u�a ost layer,}XcereboYc� x�  ?P�i7"leJ�$$10^{10}$ �� �)C7y�����MX�� ose )P7��!+XeoE0�ver|H�\c��0hille} (ionic\ϟ�q8�^X�al�&"Ma���o=e�QI��PA� 2p)ean�ATP�o"[ � S2�I� �A�1�!a`ed MEG.=� name���;!�� $source ima*, Rtom� phy,�) �--%0 6. xU igna;�re�?a 0ly 50--500$fT"�4!�U "[*A3 -9}$ !�e�'�fb�.�ly����c��q�1�M�ny @a!���n�u��q�uum HQfer, �V ce (SQUIDM6�ry%py�#��a�to!��a�s, �� A Eal:r���*or sh!� all�@��� 5x%�cept&�Ep,%p��� �llZa˩ m/hikl}nc"Tn+T{�, �m��- seNv!6�I�x�y G* avail��s��Rs yc�[�6��@o�i(-5 -�--mO�!?��*�2���1� � he Joseph�� >i����te��%dig|-��~�re$``"''&x,<e8�xQg�, i4�n�"ly3�T1�r��v7 a tAõ ~ic VgP�0tage. Whole--� m� �y,�� Ч�by1X l�mS4��,������(�����If J% a% y�A� B$A����z!�Maxe شse-� ~���g� acez#Qpermea��m ti�� i� �5bb�mu$I�yBfK�� �%4\ $\mu = \mu_0�AS� d qu���ci�x��is 9c,�� vh�rms%ial 2�E} / \t%M $$B}2# � -W0�ZU.E}$ ��X5�� )B:)�bYe�$onD!2{\�$�7�0 $\varepsilonpA�:ay�0�t� � q ���7�je!� � E} =U�E}_0(�x})U0 (2 \pi i ft)�ha�$f�(eqWT@nFq W�� N�-nra�!�>y�~zA�at $|=5�� /5�t| \ll |)Q)� E}|$N�$ �f M/ +71$��� �d���a�c\X�M���1� 33 \Omeg3V m:V .9�=10^5.}_-.� ]in1 �sm6 mde(* f-��Z�`�$100Hz$��,V��sim 2W83}$-��; argu�m hol�pu�d�6E6B} �� .}. �~��F J_1"0 \nabla \cdotQ$=0, \quad wedgeT�1  J}, �`max�]e'2r=XVqRDQ��v�� nd v� t64i<$ �A �%���dv��v�ڍJ}�}%n~� X��!�i� 3.�%:a ' E}$,%?%�J! ^p} +Q�E2 2�5 !46��ѓ(�V�z )E��� de��) ��aIeb� �sfA�-\ )�� = 0aD�X�,�i�a1��  $V$, � a�vo�� po�,K� 9>�  -)� V.]M3)-Ma|Rf�U�d*�- A�YEI$.]9� (O$2� ) I� KOQ� I��p�-s,��d�a)--3})���glyWJ&:E�;ges�a&�VE1B} �1& =�cfrac{e�}{4\pi}HCt_{�})�Aj ;y})1� <Zx}-y}}{| |^3} d I.aTB�1�& -R�}II--AO)�a{ ial �V �y}) gn}I� ��S�� � \notin�%, "�X�9gq1|6�aq� ��i�x�$ �65v�{e>oMq$1 :�A�b�@a�T , kn:5\bA�ward �n �� Nsurfa�]-yR��$dS��infK+esimal=el� �$�-Q$�a��Lu�driv��OY�{(� ,dakar}. EquiAIcG9e s �A�F��)� ou6.��.9D �)��=Be�.V$�.6-�"�X`3 riou��mpV�E  avoi##if@2w c� k�>�o`>-*qT��!�if�ad(���_O�) �is &�V �)b m�I$��6k r{L�>)�grge}-- sarva3 be \�H.3Yk {l} isB�D��JU, "L.1cm} Ui� �tdiqm ysty��i�16�i�y}k e ���e�A Q�J�9 � y} d$R� ( Wx}|  �| + Dx}. d�"))cx�YG M| > 1�f �)4�f��A�,J2}�$ � x}|<1)$em@VT�� h PE�Aa dwm algoG�s~in('�U��&5ar�A): 0H%5Bl"�21a*�s,F, 9!�$���;iculty �>a��2� �6v��c not}�Rqu$G��Xv$already  �n�[ŝholtzim 18��el�For�tp_%f cl�)�5o ��!�% �:�Unot��.� $U$.��i�S�>tenI cr6y+!� &or�4fu&l�����)��H�/%�%���'�})c�zp��{.�P@6&!#E�ns}�,is~,�.�em 2:2 �~�tc�,a*!��zw J^�ii�e}_ +�A�\rho�9~k�W�1 G}  taa%;s^t�h}��;F.;varph� �M��<B S��g( Svi 2�i+: � 2�v}��� >"� )\� # %��rho"�S2 M> !� k> TVn�t.�w�266$(l, b�O%L)� )�yGF pj� W I-�I��dMA�FuV o' ��4� C�ogE;�b'd�( �Z�,athbb{R}^3$.L*y�1I����e��$U� �i}E?*!# 65ab$!O=le 1@o$G)>*vMor<�G my��� "�B:�$U� um_{\�� m} c � ^{-( + 1)} Y  m} (B�"� ' �a�&%�Z harp��!"��a'$� m B��"*�; .�A/i�5���!nb C m $F6 U}�E�).� ��phi&!%��.�M)� ;�^ .�,�]�1&o ^1_0-� +1} V: ho) d!� = (2 %)=�.�]"�^,"at��ung2�it- ``si�'' oÁE� n ``�iv�ť�$�1A�)�!%*{#g �� ator���#� fne map!,?ki�� �,"z�9�wB6^ث��*]",aF,2� b�. Fmm��:n+jN�M��3kly !u� �VemN/iU hat,�M5����a )�� nu/ "���x�x-�of ��&� �M.<��F�@)��SU��k N�� '& = says- hAaa���EV9�,�"W#� ��i+ i"A(pƫt� %nex+X�%Qpa4Dd"C�18w"�lsomT�.I6=m�A^>�s:!ׁ�]���ir%@��M�s&�%#is (#�t��:3�h%) ,.�  3r~H���Y,�V,�-g,T|%" s [��=G&�6-�e�s \�Im=-�|�e ell}��� 3)}��}��m} ��^+1}�Cm}�l�).Yjgf} \eelC"�mˉ� y (��!� lso $ a n"1�"F M^)$U�,���X��sF#fic"���>�c�AM%Z��d .���),ta_i\}_0^{i_�}�+n{ r_j j �� � �Ns�:�9"n]n� hs�Def_ )E� !ig\ePonm�.�m�� r�JN"N0A� Ac1#s heel2T"*� �aE��reh�v� ��o�#P ��% writ�"�9 ``Y M�� MEG mai�o����e��Vw' �$���s''�� n i ibc}Z�``wtKcan��o�sh�s loo �for''. S��``f_E''��MEG6� \ Co��1� dsee} ``i��"E(�$��#�=Y!�l���v!�reC&߳ ~xQt�46�[ic�Ẅ́O�Mo�8 }�M�*�'q�m�ed r�:&�=PR�- i"�*a��� � #� lim�!h �. Regar�":)�� ~$ t�'J!��[E5�H� ti�q+ost; o��t��@�V'� a�!ic�o��"-% (fMRI)1]ron em��k:":% (PETi�\gL phot.0aAY*s%( (SPECT), a�lІa new�RfofU���$*�- (EEG�$se ���5deoffs&9�.h �&,rE4s: ϖo� rel�%Iss�a~�S)�q, ACcos 4Љe�!.!'4 ��=)��MJq! +($1 cmjWof PETz%H (4--5$m���MRI3.5 EzO;� F�7�conG�io�)E�)��poor.cT�;cT6E�9;M<��is ����Dtha�" PET, �/�? NT6, �\ �"k'1u�%�oevc�7�N70 milliVu� p s�ru�* fa�';  w"R�i�G<�*1E�! data suggo��� speehrfM Ga��1002�F�vi�0as.g�&� rulr|* ,j<)�  inI� (ۄ �:�a��[ calp"�`inA�.�!�(ubjec�exy;��o�e�cel=VL顽*�/�e�� k-�"� a �: in^Jn�,ap�<tus (-P5�thoY��f{�'+ Au�����I9- x� modif�!�B!/��.A�K loy|�i�--emi�Z �onuclide ,�h�� such�(rt half--lij�A1pr]Istc{a g���"�h�bALs��iE����A)&�*F>!^l�|��si��� /Q\�H�(� M�. /��,l�R!Lint^z�Pg| ��rkl�b�R��izG [(a)]�!�\pNc6��of���e�#&��<nd+' turb��%ory1�usI�sƓi�kcs geS(((.�V�gE�"� f!)�pre� �:�Lnt��r�r��el��oidal d"^�aka}.��[(b)]�2J� "` al��%aA��1�vby �A�l +'(u�aL*0aa4 0ion�c)] Du�!8 orthog�& �:of jD�}o�!�J�[&" 2 �&$L^2$��7�A�z mal, v1�"E�A)> vanis�learly,%)!1ye� �U�w./> O�^�7Ry&�\5b \��con�3!/a��f�Mdipol�?\I9*�A�%��p�",-���  �lso�0d�"��1Fa��0%2bl& z|orm� �})i���&�a�Qorm]/� �`2W�R! �Furr ;�A��W9 �&s�zel *7B %�?ag��e�`an)�%*�ut �6�� � �=s�N sch}- haily�d)] ``L2--squark�e��ve� �j�.Ũl� au*�s.&� !o6ach�i��\!8zR jQir.7!�n�fA_ J���ly� �u��NZr)�)�0=%���>l:�!M�]!x`U")-_�"x}|�$tea���F&�au"icR��v is l� x`� z$er�cWe�ТAt�&�%b�sF� 2E�c U$ (>�%/B� g)]!����v =!L*�)�s�U�"��2nnouncN��fgk��@e[ *L9A5 ARQ�$set��er&�>{0}� �&.�6��#)��pGn "yv�rm�ch%�a rej!sqk��e*[� � W �b��QW!@"!=u�; $&O%$^v(@g@no�nt�"�>m 1.}a�.;o�#d�t"+*�by56�"���%%)$�r� A{edCY .9"5� �!H -,!.�*|�&& & &�%|}�Bf.Q! # y}|^v%in�} \{ (�,_gz}Y&�!� �z})) �. )}_�&z})� nz}|g+ y}|})�y}}{&z}| d*"�!d�y�v\& - x}|>�E�+##�/ n�Proof1�I�L � A���A�Re��z�*�<�%�%��L_0 !VI2@2Z()O2�XCPhi >x})) 5fx6f�^v)fz}}1\x}|"�" relI2�"2d� Ct_0 (\*�!��W6ell Q?�9$�t� �y `,!�\le 1$��=K�3�5U ^2$ and i�ntegrate with respect to $d|{\bf z}|$ along $0<p z}|<1$. Interchanging in theDy1� 1�%�1-�F^2}:�y}1�!� : 9 �z5�,y}-�1� �-� z}| R� �xy}. \label{rely} \ee It is stra!�forwarE� show that)LR�!SAy�� j�I�b��= nD}G{e I��U� uVz6VZeqVK:5n-6ndeed,a rhs�b.alM�EV�M3y_2 �\partial�_1} z_3}-y_1N(2( (5F +cp,1�Y �$where $cp$mb8s cyclic permute�;�l ��a� (\refE>n})�[:��y_3} (�J^p_1 - � 2) + cp,�Ua�usinguDchain rule as wellno��E� several)w.�,terms cancel��T� �%). Ux� a n}),yN� the l $q\ba�()�$y}|^{-2})$a]0perpendicular�Y.E�I�q$2RJ�$}) becomes��-�]��E�:��xN� \{ (.�z} �i�u`) Ɇ�)�Śo )5���m � ��y}�~ReplacQ)mzZ(y te�&and rB$��$ .e definiA�Y IAd}})QE stand�8,Green's funcFre�eniU for solu�6Poisso3b, give �8theo1}) providewat|re�q lemma &�"apEof,Z�C| distrib�Hal sense, but simpla�gA�4ity arguments !� at iłalso �D pointwise. \hfillIZlQED} \vskip 0.3cm \noindentiA,Theorem 2 (R6x!?4rem)} \newline<$The vectorNY�xa�@can be uniquely da� pose1 form�'e2? = J^\rho!�Dho,\theta,\varphi) 2e}_#+,!V.) . % + J^ J~1 p�jp2 �Xrho$,-h2 I $ ar� e unit-?,s associatedb �(,spherical coEiates $k>0 0� k pis  q < 2 �-Xcalar qks $J^ E$$ <$1�u�5�a�)�="{�~rho�:� G�� w} - %;sin �} ��F; �} ��, \quadA �z�:k ��k�k +r�%�� 3 jthph25G(! >�-}F^re B�� �@ included. AssumAkat $U�ue�is��-���ofM�a� �Wa $ef{gese2})- ene�S = -)?1}{ }2D . 6Ox}-eB� � -�:rJk \Delt%y�}FLz}|>c� N'Q@|�x}|>15��32�Z|& aiLa�uani�� to^��M M�$, i.e.\�Zz2�2C�[-VQ�.Hpy�<�4� + +:T:.^.o �^2q1]�r�Proof.}Kfirst�Q.�( into a rad ��a tangen! H component. Clearly���Bs no con��z U$. A�k the N N�+ {\it��}����9L �), see&nB. 6\ sm�jp; 6>� A{ Bs )�E�z�:�� m�-�-�M 0n@Y9 B- 2�Mo+ % g^2Z�^2.� Y7M|, )R�1}"� N�3�ƶ 4Corollary (Non-�nes� a�inverse bl^/ ��Z�Let aI}��(be written �x -2EU���c"� > .��giv1 �HJF $G��F2 :\m. R �B�eZ� � ent}Ŷ% _��G$,Pfurthermore only cert moJ -F"�compu� Ma�In ��, b�is-  &@ \[ V���Lsum_{\ell=1}^\infty m=-}^} f ( , m}%) Y (i[,q$a ��<1��  e�a��  @ 9 eaI $o"� usu� "� (harmonics, A .oB�5deA@i:� $c�$,w!0�)+19!5 d� = (27 +1) Qm}�� rell���,�con�ts 2���� from3e data*�fa�B�  M!:�U%�>��-� m�ho^{-(! + 1)} =�Q9-�28>�8\les .5U)a��E��} ) �i����. \begin{array}{l} {\displaystyle -  U!;>z J^. bb F f[ *�mN &K @<1,} \vspace{0.1c!�\j�0 6 |�� .  \end ��5\d -^� us&�  $F�$U y��J� by��ERq�ujQPm} >P\� $\mbox{and}����k u�Jk��Q�D Then�c< -(IG�u'' Za#�� �u.�aAmF 1)}{+��J=aftk2� cl} ' Ga�Gy^1�1bS�')��' &��<1 \\ 0 � F' �� prim�s differ S2� � �e gen5���& homoous��$\alphaA^� bet 2�$,y 3M�.�`����$Oa posit��(er. Since $.�$\to 0$ as �\to�`$<followsA�.9=z?%XTo!vc e inNw�e vari)hofMam��s .� .�%��A]� 5W$. �� [ (A.�*{�� + 2})'�elQ� 1) )� f qc��2 \doteq?�XR.� Q� 1U�)5hu�r�aD:�inu2��f +2\(1� ConvergeA%� =A5Bbe .�(1jV�0 2�� �= 0��Alm6� $.�=2y�^{� a&=>�=2��-�.O= �-(vN '\bigg|_�� = 1��Hz>>6t o.?M.� toge� ����%4����zE�I06 �,�+"� V�)��Ari�bya�tsa�� �" AH�V$3 (Minimiz eof �Rgy)RVDK�U '� be W.zK!x&o=�P!KU� P� �&if��'5&t��*^@ .H? .8 #��"|��given!{s6�,>��~m!Sum!N$W$ un�"���4raiw �KJb :b >�&a ���"k, �A���Ɛ qXm�]��"h m�g �&) 3)U% ants,�achievc�= = G="� �3X i�+1) 3 ell}u�� �/�+1&� F[U� jrgfI��9 Substitu�QMm��� �_s� :4m/2bWAQV}\!�j[ ()W)^2"W ���"� �$6pEj� RGn^2 ) SRNSm�2S-���S*�NS �S^�G&�L  ] \!�x.we havX *�> involv�&$G_ � F_)& - G F($ vanishes,� !�o& \pia��j{C}��F)�!4 _>[ � 4aR�-z#= �Jk*�%jH:W] >�L  d � d T�5 � �?�Kt-\esL$Fr!usf�alͿ is6zo=G=� nd n $H� ��al Hmtr�v �U�!�u) $B)=�=2*B� H��]מ��Hca> pM�sid#bracket��ls $|}" F- R&Qk6��)^2h hich�R (�)ei� $F$ or $i \.G[$ �O0s |#x}|=1$),�n�-[F�F +:�.U })^2]�eree�ɶe��^2=���}1��r�! 2URfye9U �F=d���: r\2^�*m2� �&�� a^ $orthogonalO"7JBl �a�-6��1����[ f"U��rho&1s f�#B_+*]F� �!BR+ (B])^2# \a�hoi,�%�H��N� �B�(y pU ^2)'��!�f^2a� �\} � !,P*�$ix "@m� $e�� (1)$qU zero\foot�{Thes��d�%s�true s5�suppor%�" $ s& �rio".E@e.}, *�!H:,. 5MJ% %���a� p�tC1vm10�1��out lo� �rI��*� q� ��� by��{/ �� ) do�BG overl� n �6Kob�ed� approxima� $f+��M!ܥPAq�W m�s�)d limitX�Y*�t� $H$,N< t ��,w&ieM� �We_*��aɃ=4�2�;)�&6"$ behaSlike $0��), ha�� >%�n5�  relU>�00� 0/��su"�G )m(� ith K%<.J  \sec�{Nume�%Imple:�}# tcouV1{8 }{0} I�9FU})6� �/e eI�%&= name�j���>t=� m} P�~cos ) e^{im�!B�`-m!](-1)^m \A� ({m}�mqm. \ge >#�  m4 -,��ylm� �!�bar54co!�x� jug3�*!*�=\sqrt{� +1�$ R-m)!} + &1a�$9E$�>(he Legendrey�9�[.wx��-?((1-x^2)^{m/ �d^m}{dx^%�!B(x��P 4 1}{2|ell!} dM}(x^2!� � ����polynomi� of degrem}$. For6nu4y� r , + sums�"ar� i6 ,mm�$�byi�_{max� e� �� chos3� procedureRlaEbelow.a�ubq�C�e��6!3} ��U$iscuss �1 $ 2/�� $V���OB}��>�!_S�{se!Fknow bRf�|ne �5 ific�+ue of�t>� ' some�0 lly yd . `_W&b&_j$, su aIWeqnZ*} & &m�q } d(2^� � � = &��  � �refore,� A�I��uI�#),A4D�&a= cA�!�� Z0� 6.�6�*�%dM�e^{-im&Rd�l�)�(3�uA� | J����6U}��,JKZ���F�c�V����B�!�gY�{\tilde.�(M\�'os�dIl 5k - i>�vI!�"I".# uhat��trP=~ \pi}F]][ �\"uti�#J�cal34� ��aFth��� gr��appɚyQ�)�M�d�,use an extenD2cl�0F'ula.�%�D{x_1}^{x_n} f(x)dx!�x�9f"� 3}{8�$1"h 7}{62 "�3}{243 + f_4,�j {n-3&�-{n-2}}/W {n-1.nq�e�F�JR"<"� .% 2�$ !Dsubro�@e \texttt{plgndr}�*&n 8Recipes \cite{r }��s� $��� gK�X� � Ba�8B}=(B_1,B_2,B_3t6nsteadA5�'$,>� relI\��� n&� .�1we�� be U�!= en�m �Yi�u�B}Ia�( (u|B}_m� (q� B}_3y�ri��z[.&�I-B_iR�}{\mu_0�N� i=1,2,3E5 More ,� 2_"ng-���  /��*)>5!R� = asu*6)��;� "��.� �>��2*'�6�wrsu� �if!�� MU�e�� u�=)�7 I�ur}"7na 1�|:5),�"!Z��sam{,  as bG. �Nchoic+  $-*$.}h. ��E�Tecond ]�u��)o9ea&O E-� q b2J  eqn{V5 e!�!�+ 5��B$5 �.� �=ufin}t Z9F(\! Re"!0!y0&0�� )�)+2�m��7EmS/os "�-Im6a��I).� &L�'sA���nonumber6 } D��%*�?.� .���^b*��2�bA)t9�r���������ren, after�,�=oeffici�92F �&(&�out`d �2ier�c��CuinE� ) orm~)s)�U,re--evaluate 5�� o�%�$Dway��jw�=st� �cy�ourL;�k�:���:run#� gram"q> time]nZD5� a most� rop''/'��$ayi�)\f���f#!QCur�(} h ��6��r�&�N�P+}" ��@�9*�"d�#4)�� ]$)]� Z�S#^���t�� ��!U>� 1�!J�!�}:�>u�jthRuB?mFA�m�+ >A�_ n@ �)� ,�� fTW ^U-�)MA�b�s �L:3jpVLv�O�� �)+2 �~��z�.\tm��t��Recalla:FJ  satisf�>?ce�c z �.�`y! mx}{c��m}(x) � $} P m+1'� Tvfoaj~.�:� =��16,A&/for/m�%B�Vm>=B1E�m] I�}{E�-�}2'et ')+2.^�>0��0pl+D n���ie&l�@e It�napp �B�>: jIake$ �# �$+As, ��� /9 �FN?�2$. We ��Z�*>2I$.-a sepa�K*!�V�` e quantitW ^P/%� �$ (�B�purwATr$ developed|&� simijE:��=se �!�ear both��_ Lhe >E of�E).MCt�._r id eveD-�7$�"�f=�@!�Dn=�}�j p#.c$�U$. FinH�E[aL �EIasxM�*<�U99�R]2� �S� 5j�66ph!SIn �^e abov%�9 !�.O �E�was fou�%ZNthe&� &� �0previ�1&� :iVer�%l" AlgorithmkA� tesr9;E&Za) �H"^ bo� w�W �-�two typcexamples�jEE '/J�Dk5V5be*� [�rF�D = -2��m�m ���2}+}� �k 5I:63}E�1)EX ,2 -�$c3b&�F�1V ha�!s5�E*�=0� �%ell>2� F�?�"q !�~e =1.5��sF�q�_i #���� $P=10�$% =200e� ueYG� b| �a��&�of�3� �@ ��J��n ��v� $U_ Fma"�!���!-,�!tu�%7�|)�J. F&�<%|start )�� *�a g2V=�, a �ۙ��^�S .�WevMe� )C 1 up40�"����!Lb��e>=&�(is! siste8�!8ex�;�!���is O&�,ce $|U-U_a|$Rof S$10^{-7�at� . S6ly%�V�e�!�&g (jth})-- ɽ,����Y,.4� NgIS_k�Ū���_k 1$, v" $k&�k��+ $  =25$F2W �?analyt�qly}6j]$�e,P,��#�R!$J0/m�H.!�%�-#UU�kI F=-3�1�"gH+% 35}{�!��3B�= �e�dS F9`� /21"Hfex��9+A�E~� valuv-f= '*e�A�var�Z7U "al|<D( ab�9��their.i�bm�!xv�/Vid�*"�I�G3�s ��&� $F2�!A���y54ly �s.# [;>� .�56��,nBMR��� >�$�Qpx_1+p_2 x_2+p_3 (x_3-a)} {[{xR$2+{x_2}^2+ ^2]^{3/2��>�� $a=0�l$(p_1,p_2,p_3)=(0.1,-0.2,0.6� We9N$U��rh��A!E+!��f["$I�ͪ 2�aA*"P � ag�CV"�f�՗%�"�$P8� �*� N+��jis 10�8 en�.�:236I3 aH�) ��Fig�$1� �P [ensaplo"? �)��$(�)!��,�/�!���"�M!�|� cutsFGS8$$x_3$--axi �f�}[h12 ce�(��(psfig{file= � .eps} \ca�+{D2�!iiJ� ~ ���� %�U� S�!�7 top �-�=-0.9e -0.8� -0.6 4 0, $0 $0 a/>�9$P.�nd�nd1 R&**{A"RYZ*4\renewcommand{a&a:� (}{A.\arabic&A*�Q6�QL�R.}�G��"A+,�z�&�=!�2 J H(�Wz}hY�Mz}|�BQ:|>x�O z}| + ;}[c�=cH�M z}))�$Y)� ;x\*���BY�0!(\mathbb{R}^�V+!"�[� P z}))*YZ x}) ,[x7#��U��J�5 ��5{ �F& k[\ �X3�&�Zx}�U}_)p� e!G��-B.�}1Dx}|"�are�"� ) y aLL"QN(N !�Wn])w $B 2��" CiH _0 (.}�J��$Remark}. A�R�"XDsg/�T# to�\� ,/:*�^l���DY( %)][uld bVTderstooQ!sBU�].ZU��j�TN��z}$`atHY $a$�he origieo� dir��� '$. a�@ $\Omega_\epsilonMkzUd�Cq m� neighborhέ�$rval $[0q�]`Pf�*a��B�2:li�z}{CJ� \cup S(0  �I4M�McU�cylind�.regio�J2A���\{mf'�Q .�:5rh�0� '   }=1^, 0�* x_3'� �(\} �ile $�(0) Mr semi&�# ��B70�� ڑ%'}| = >��<� �N ��[.r�=�Ov ��'.�BE~>:;�Rively. i02Yi6���("ny<�OrH 2�>F:�:��p(s%h)V9R1 9)1���1&*VA&�t>WJ��76U= "�!�"\li+� �FE�:l/^�}R�)f�= & -r|�<:x ))z}��a�( U��3 Phi}n}�x! U2/� dS, liQ%nd"�-}�mdS���6sA: ine\ esimrN urface el�0 �d  $�>�� n6b�Yout�a nor�<r w6v>e.�M-�U� in $.�b�$.iCI_1�,��I_2R $I_3N�Vt.*�Tsy��U�D a��N�,.d0�!R",6 c easy�sD1hat-op{A�}itsziiI_2�F �*3�>� 31":'I_1$:�$f)'x'R- � � |  '}|�ex' +ݰ ��$)Aus(R�n \in J �P[ f�1ah[ (a-�~� ��J�]� �3��+s�4 @p25,-aZ��:>g*B=f}u�)} &�V2n2x{\}^��!j�#�&[S��"]�5& + & Fj.}�BmWF�:�=� .w*}�b ­^2.�?}=2��2�} {1_=�}+�!='���B�2Q6k}E; \00f��d� b&tmSE�:�:`)�- B�n\2(69-��-.o�i jf :IJ0� AY(�C x'_3IA+ _3') (QV -a!���32�.��}Rp >�!2?V�RC2��/A� �[�/21�( ^2 - e�}{a - 0�jaA"Jade�eT ��l5 �])&�C$-U �1�=}�@+�@).�&[,� ce!n� =(x'_1,!�23C 1.#z}=(0,!haK" J!�(J<J;J : ] it"��N�NK*�� I� ��&��= a(J]('_1-x'_2 J_E> �Pw�'-J_1���96 $P=!.?S g�5.M�E�T�(a (U.ABRW� f"�H1<6K�C:�Bo�&�'\}f��e How�h, .� '��0.�,E�.�Q�$ t��*GRc\[H!��nI�e�a�rh2]6�1=AD} NBsiU�~B2}.A + P?2I�=nF�}=.n. �.t�b�%,.�_2' >J3> ��2�K� .Yio� � Ph4 f�,n��$&�+M'T6Zj L��:�dJe�N}^+J-k�_ ^3}{A�6�.�WT+a��!J^�!r�A?2} -J_e��51uI&�7 '= a�o���q�!u>� {r''m67 0"u yV) t'�"Bu� 2�3 ��� �Ft=2@ �D � b8d 6%^2���^2}}{6$F� }=1+2��2�6�E2p �k6)3.f��^3B�^2B� �=2! Also���dMW��!�2��6@9�͚!��� ��3�^2)�J5~lR.�f=4Z��j.�=4 ���}X 4 �2��g ). 8 [Qv2� I_1�%��a}�^a*I[ J&�)-Qe>]'_2} .b- J&>>Bbau>, I]�13 d%��*�bK deriv��2"cDWn�2 seEG .�8"�e"� UNt{;"is@ul">eimmedk ly g�G alizG�b�$a�1�an��rm�"-�L)8 .V�Bj��$wEm"�:�!�'"`ͦ��I�Bj j)�(ds.~U}=J�k� |UC"~U g E�t�\)�r�on�n1--�$�33Bofgu��fi��a�[�P+ n"%P;l�=. 1}�}�W P�"�u$ 0 ��a#< uE� On a��%RiemannWimanifold*$y�"N\�(u�n dnK�p� = dGU-1)*d*~\�^h%d��dA�*��\2)s1 =ga"�G -�� d $*!�HoZxoperator&jh0re do not exi&5n�5nJ +H��QM�<e:"($ �=F&�%F �.��%+) F.\]L5!:dG5đ�2�RE�}YIM N,� .)�%r� *d�V�RA.` ] S.�O HR, - 96}+N9 "9 C�P"�)Mؒ�N6�>�5q7t �Bu *T���stablIWd u�N$��0facts: (i) A [+�m����A߅|^xW}xфyy zz�canono* ijifr(w�0-� .qAAM. A^x=y!�Aa=q{EA^z�� �z$. (ii)a6%,6� trans�s ar���O2%�Y�n/Qc(^{xy}\,dxdya� yzydzxxdz�� ɶ^-�� Fxz}=- ��y�_ -i)a@j���1��b67:� cRA ledgqOs2%�bs"�Q�w,ject jointly�P�3U^A�@authors, A.A.\ Io@d�phy}{99!�Lbibitem{hille} B.\ H , Ia� Channel�, Exci�{ e Membran�R2nd e�T0), Sinauer AscwTs, Massachusetts (1992�,{hikl} A HamaUN n, R�ari 8J.\ Ilmoniemi, Knu2Da, O.V.\ Lounasmaaqgneto�R phal � --a<$ory, Instr�y4  AppliH5sA\Noninvas�f StudWS)� Work�jHuman B�[L, Rev.\ Mod.\ Phys.\�]065}, 413--497�32�cl�% �C Pe, SQUIDs, Sci.\ AmerM271}(f46--53O42O}- } D.!�0Geselowitz, O�xM% ic F�UG� A�Out�Z an I._g Vol�vConduzby��nala�? Sourc!�IEEE T��! agn�6}, 3�34%702�,dakar} G.\ DWU os, �Kariotou�� ForJ Biom �s, Qua!2!��th�HLXI}, 387--400 (2006�grge} z(Grynszpan, FNModel>�etocardegm, BiopI !�' 013}, 911--925!�76�ihk} R>�M.Sey Qy�0Fo�A�In%sPr%s.�<S�� �=-B5=sm:6���| y, eA� by H��inberg, !�Stroink, ..\ Katia�DPergamon, New York�852�sarvasiS 0, Basic Mathe�W�{�Electr5�A�cep"�-�c>,q�M�BioA%�32}, !�22�72�heANH!}8 4, Ueber EinigeE�tz� Ve silung�$ktrischer !$m4$ KorperlicKDLeitern mit Anwend:(auf Diethie@ --ElLne� e (ST LawsPuRD*�~ of�ct)��CE >�s,� A�\*AnimalD Expe�lnts), Anaߍ�Chem.��89}, 2%T33%�353--37a�85:� bc} �� *- J.P.� BoltABC.Je�$Continu� A�abilis��So��� BU�c :� v.\B.I(6}, 523--54E96�see} BxImage� Conflict:�vs EEG�K$R.P.\ Cream�Sci��f 25�374!�912w�r�mS.�Pin Ellipsoidal Geometa��/aQ:�044}, 220--241Jsch�SA�g, Funda* �O of Dipole� Po8�cA�6si�F< Auditory Evoked �цsE"i�icD s, ve�6A�Adv ,E�P olog���� ando3Mo�L� G.L.\ Ro� , 40--69,�[ger�mela�:�dem��C��eMunck,� Est8\o�P Time Vary) "��s� �5s, �-�A'liaM Neur�3��077}, 156--160J�ha�QFFB�i--Norm.�i�:B�"ary�k!� Torso�&26Eng�ompq�C 4�8�6�fgka���Fokas,: 0, Y.\ Kuryleve�ers!_MethocW V�-A�rob�1��L9--L11�62Y�P W.��P��, S� T Teukolsky, W.T.\ Vett��ng, Be�FlanneaQ"@QdE@Qin��n e A�_e�#���XA*68 4 Cambridge Uni�ty ��2�A%>� kdoc� } ��\gha��asses �m�GuFac!\ s @ a�p{Wnc�a� � *� � filtey^ per!�ed Ga$s�?"��beff�3�0 reduces.1�xcau!�by !j lapp!�-Ul ban8,�reby,�ist��l2�  combinIC�B�!z�H�cw a�r5ngMN,squares post-, EP%"sY��-�E��8le �orf�eM�i� chem� ic2M*M:U�af illuaC� on aWofjHul�e"� �(infraA7Raman) M� p;, ��)�oscopM�mplex b� � maAalsY^y�E'4gin{keyword} m�UttJve��  \sep *��%8oM�u� (Ia�*J%)� (nonnegativi��8�6�%%% -� \�:{I�A�-a��}�K5w!�m�!yA1m�#s (coRr )�a);aq�1�mo��sl�  KW .�ic �I s�spNd growth\mo�an 20��s \@Zgem� ne} 430�[ arse8snX7. self-��cu:tools jK�$ IewsӅ ~�black,brown,geladi,tauler,hopke,lavine,jiang}). Although ad_ da�)p� � theybAb�)*% ed�o<era� sof�2 e (e.g., )s1isma, ,mcrals 1})��se &:� !leaaoo�I new JL)� \,mc,m3,btem}.\"ir pione��work,$to` Sylvestre C ,}�J�o�HA�%�ix�Zl sign� i@�D }�}�u�f�x p�ice�i�Fllj0be feasible, Bj"����SA����$necessaril)��� plet�"�7tra1�be�T)�may�j ���or�.�M1?alA� ups)� us���s�f8�Kre*!?# mf8&V )K�ail6bm� ,� reflrA�fa�go^� akva3N�� inco�GO �p�?hat, CDDE�ÅreR� few : r��� mptq� nuz,�8,ladroue0,react�,ren,chin,scholz,pich,buy,huang,visser,shao,gao,bon} to�.� (in)" �FZ(��d, i�b�itJ@Y�^ it})a� a cr�vin .�B�. H�, a� syst� stud� 8Qic�t!�se-��A�2h  duJ\ View�Va bro'E� ext,I%I+se.( 5$a0c[�" a basis -A?rapid�%ro8of 8� N� �tor, �gCl�IB   ShQ!R(BSS)��ica00, ,fic�bic12,jade,� �h . On%��>cha�J?feam�2�5\BEis A�a�HD *�ic ��!#�K(��are n"Je��ICAa�BSS, q�� N$5!� um�c be o�ie9�S,i ō|reA.� paperE;�BSS lA�%�� nmf1,nmf3\2,cichocki,plumbley,nnfa!;a� dW^!.EPlly� ��",!��s capa� of� |[�Cng2L��� b!� p"3� �:�J�7Vo!f�Mac�`��.�ssumpEx� &� ݦ�B]@ � )�-KicM�}%�r a }#/%���[b� c� �( �$�(a demixing � } E��E#�mqe�s � )If!� �2��Y� > re p���9n :\A@^� �Aso �cM9}VnU�8 �� as#[R!l28X't7 �D,:E�se� Cargets pertyAopt"�,:��o���er�U-� s ma�ql= ce (see,��ex�R% �N�e PCA}&� - q:) j.� .� %�A�!b27!�� int� &)  � ,� ,pmf,ae�OAcSalready� ed>=�b�!B���Q/ 2����ecm.R(``A�u l'' �p2� d�rom? ;W!Ʃ�e� truc��, �due"p res�AIQ&� $ groups. S�%�FA�kTl �Q�e� �!aises Y Y�E1inBO�!�of��a� �u "h�ae}ba1 b�( dy(detailed siL3�)r�6 �txom� tiv ?y�!�ni� &f �%-�=���m�!d!XU .�U$2 ��2�iM- motivJ!�*� !8H"�ua�re"��-�K�V , �&%�A=eis9aJ idea#``�{3bles''mLpv,G> ''J,a wavelengthjF�v%��of *� a�t-��zso �6~�Sall�.Die�K-ke�?Q�U M��S?� void�s �-��e�� suc� fuA�Y�in ��9Iqh KSFA��]�to2=� ��C wi�|��L ?i%_``!�]*{  A sis''.-�O*24 �huc� � shythev a"�lY��!㉦. A m� 6 �aGaY�>3<'b , robust^|ec��biKJo~ or�FJ�(MI�2^� $ we employ novel MIQ� (tably impro��p�(- mu est}!��[wEkll� h  MuIBu%�"i=�)� sis}�L�Emilca�!��es��q�: �,a0�o�c���; ,(output relic� s i) cer")�QV!�r� �?r.X;!� (iv)�*a��e# Me=o� -dim�Qo] .�E���p��ly �!�nd!p��e�a��Y ���*e� ��>M�s.-h��So%1�+/� X"x crud!8"<[�!>N�or �y)&I ce)��I. S�$�os  FastICщ�PN}, JADE v�2hZ��nf\ (}o, SOBI ,bon,sobi} ha Oeny|�ear7j.P�!���o> M � sugge[�sP�!�gmo Q�--�I m�� y wel ��in�`l�Ii�Yac`*k�y �^pt���&�ofIk,��[� �j �� & eL>3in�-�E� �al F5Un�~�"m .$&�� "H�.�2� �rp�iTly�:��y��m�c�Sof rs�'clude vi1 a*)��a� �.;JA/!`cos&�M (��:enu��jus�eJ���Ved.&�wvd�is hey/ly"(� ����/iori} cʟ� o weig�se�..�sse�sT � ILelaborh��owr;c�!���!)quz�IH �-(�L we w�%�7R�`is�@�%Q2��nvi��uf"h3"�. S� \ref{a��Z�0es our�r�tTDa�FU�'�5Ydescri��S�C��F5�p=�o" �$� �� %> p��& (6�)%F�� .r�.�32�a�Ye�!�<� alyW<in �S��brief�K�bA�2N res}AP_!�_n main�ul\d,m�,+lu�"n6Pcon ��.�"��&�$l�E .FoR �jr"m} aaE��WaQ�* �(m�L $(X_1,X_2,...,X_M)$I AAn marg�E!� �3�N�ۨmu_i(x_i{Snd$4u(x_1,x PxPi�F�K f by�-it,est,�� ,mic�begin{�8}1i}��IB�lj4i=1}^M H(X_i)-6�,�X�nx{b��j ! %H i)=-&@ � \l Uu_i dx_i>V� Z�hxm �U6�a_ \;dx_1d2 ... MBmUe&F+�%op!�� itA��/MI!�aq��*�& �$M�hrE:s, �Wmea�2�H�� zeroMO��8�F! i.e.8ir QZy� oriz 2($\mu=\prod_O?mu}_i$)YoA#it�����.d+�tb- ��~X 8to �Wtyp�R� �<lh Pearson'�&�i� eveto��t �it� ab er a�m�!9ore�!\ing *��P�� 0 ty�� �ZbX0��e + �>�i��E�%B$\{:\nftoYAM�0in ��$XN`6(�1l�"T$y�XSH= `HI(q�) �;is� ds�9hoUo�1u�� re��pl3A�J�� )1�7��" { MIC i:��F+Wa�`E ��:��?�%g!al!�Y'�.�!{ abs1�' u�Ng=a��i]o.2�~s (� 4s) $x_i^k,\; k&� ,2, s~, N�OMIExtoA<n .�in8nc�wr k��raw�  be an $M\4v N$�%rix'=X}$��;r M!$�.xa� �dU $N$ &g�# requD()5(nu}^k$ each" &���at}y>X�Feft(%��ax� cccc�yx_1^1 &2 & {)24SN�R �c &2j&b6oo,ofP:�T&s!@eno� ). But�s��)�i��!��th� � �'�se�Iae�ga� oEY��)a!�.�t :t &h�� Ya�$,�a�6�^� IM�%c 27$>pU �, ��osRH  a"�*_)ѽB�ix�� �5XB�WA} S26-�Q&X}� $MwXme.�&0�)�)� bf S3 a $KR3un�+�5C s $(q s}_1c s}K�\AgRhK$�� maZ :�,V 5� �t�@c�l�' ȡ�ms �(obM"ɸ �X},�um{; (Pda�+�>�^ s ``�+''�pos�*. M�,�1�� d�#&pD}��bf W}$a��i%�A $ A}^��� pt $-1$�P�);eram$r pseudoin�2sought���(�7� `? 2� �ٻ)�Yݺ #e�e\s�GY}�W) � a!2�!��dersca�- (nz y ambigu"�4 amb}�*��A�M��"�$�=%Csto 4M�"7�wbsly )"� c&)4� y� isq��at�Il��!] ${�RED��!"�3 �Fճ2J�3��6# u�$ ``delay''oGs;E]x"*nt�5�a9#pfor!2�Bs(EaneQ�& ansatz��-��}< The�u ste�1%�� !0rj#��ncipalE3 k*(PCA), �&ct$(pre)white�Iic*� �U�li���!� !�c I�nu"{ m�($KY. �n_5&� �4!"A�rm���.th Aleigenf w�Zf"spl� =/.�M$�d9m�E{ VFKnC|{4 ro�(o��V ' R}$:b^ ��} �@W�wR�wV�Y6w 1T%Wa�d&�5 o sez�i *� �Ru9�e ���J�Zypr-Q��� bf Z�{V �X}$]n<�orA�>�*����1f"J/�-qmu�"HME#to �R}�{i,j}^K)RR} �Iq two-"� al>�5� e��v z}_i�� z}_j� ndA���S0��"��IiI��"�2��� `y`.�@"��[ Y^���}0�&cl5"- .X0�)ed �,i*�3��e)���wY+fk �*�� Dra�.�4 B� �ods+�R}$:o35�alR~T$bri���%�*s� -" inij &B! &�,as&LaP"�/�A�*$�ٴA�� E�z�! .�>l'��*p(rd� DEoF9 (SD)&@��X* to be�+f!sui � 't$#�&8�)� hen,c,der1,windig1?anW*l (raw��:�C�)J why�2�1,s���� �2�� . �>%b�0(%�ed�+0 ��P�� i(irFH& }''� �W 6&�(&:pp�����%byN�*�YB_  ��ft.{d^`yx(\nu)F��d2}�_|Fq(k} \sim x �4{k-1})- 2 x(�{k}�+�6t��`6�"cs!1byQ smooth�9&�4 Savitzky-Gola#f�tӱsg}�i,��MI�{Ve?bu,����)�, ��~ɂW%��b Y (NbJK dou�0pGpd2L2肑(3^SDo.,e F6� �iEс> LAs��: q�-ܶ ). D?- > �G qs.~Si~m0 %�)� �"�F� 0��� � %��a��ڑ�57qC �-��%ve01=#�:� V[ � �o6\AU�dq��;��V�)�a0 Y}= ^ XR e�@:�e�raU:$!uR�@�yS��= q) ��b�r�%r4wte]@�, thro�:n-4_1n:�> (ALS}:n:als})����0 ��#%x2#�s�*t!m�AM�  �T*�^�n&"o.? * 0��".2��Jd��byY>�&�&)N�!B~��$ ALS -=�!*�|�:6RatE  \ Q� j=0;��iz��%�I Y}_0�Y� $.Ap A}$; an�>e��ofBIj$�(�.>upd 1�2~Y}_{j+1E^�A}_j}^T"��E�I|J.b ���ua�new (Y-e)6�W���n�:y2�A��X}{.�]�( %�)6}^T)$$�<2$j=j+1$;� tinu (2) unti*n"{ ir/ched; � Y� WeI�?(A=:�bUb[ ^{(a)���� W.Z6� 2QA��2A�L �4 ��� ��o�M7���Z �~- uld +Lj�$by elim�CVm-��-*�&؊ic!l��R� )�%� Y� �}"�3sl�=:-nc� e du E�ALS� 2�CaB@,� ]' show3%6�.� �?)st�� n�=r6�-d��b�J fulf�U0*�BA[��.��$>�$&sMe�l8 �^ncI mea} Bea%7�in�b��F:m��"� i5"a g�y�'�&�-�I�,=At$Amari erro��+ ica2�$�� ichW�f�t!�,+KZxi3�agsW>!2֫��A�% -Aif� is4 )�v" Ps 3�A})= {1� 2K� ��i,j%,K ({|p_{ij}|� \max_kk��+�� { N/kj}|})-1*� pindn� �$ � =��� )� x $Px$ni��Z$��!OA6�&k _ 0+.B4o<�4k2�Bi��AQEUF#�*�� poor. Oq MkE�6/.s� .Jmat�<c�ed .)  �. T *Q�!Q�M_V� b�C,�1��8�i�N�Z�W�Hwip)v!�,&Y-3R�i� y�us})q { *�o s})}�ny}|�us}|}.&in�(: gad:Z,�9GJ�Fca�2" �-��p�+� the $K$�IE����e!�ri�_Y}R8pi �Y�n{1m^K u�e��frac {\e� j: yE�9�}  ua�e�N | #2po-*:IfQ8�El"�' �e�d6�1qile�d%s�Gne�1['�>�&�O*"�*  FA�exempl��a � �  D)ue*�|&�@ w3;ca`ei t,I�2�A�� <$ FI0a3pa�h�.�JS%`����@�dm�V&ixturev�Zus*jcl�Js� , am���-�p'#s0%e���(e.g.�0+6l^!, �%�)6�8�'�,� widthK�"&�8Z4� 4l�9�!ct�;�MO^quiw'���6� ess�!al�5ʁ�4publicly availO'a�r�e�"��dG��d|-����� �&�Ned �/rN"�Mve ;�5�#&�2�e� en:Q g�Dtp=��tic�]M��*�S�=ed 3-5�kA�)]�} �١�a/ t�?d&p�=��),jndo�dTMdqcol�#m'��l199 ;Y��M V�r70q�Ja1Lrange $550-3830$ cm$~ (822%� M�.$ ) se x"l NIST)-#͠A1�2&etEmde��#�.�/organici&undD9�HGKo�?#@a�? (�_en- E,kyl-, nitro-!��F�5nzene.gP, phenolWalkane�7 lcohthia!5�*3*�ZsT#9A�+"�*��l�P'4<da� �P� ly "�". A���a=)!�10000!�dom trcA� tH�Rq$M=K=3$)�7a�YA!y Hly choo�>:5�poo�d��|'A�"� ceZ!A%���1 *Y��}�>A of�!� J�8��B�ong.B C@&.�Near-Q�E�y (B}�b}X.�F�)J�f1 F�^:�2}�1asl "�g�fJdset}�zfacili�zB�B�4A*�6al �(ɫ ��L($1100-2500$ nm, 700��hpeQ�um)�o�,�a�. by Wi���Stea>sW����2�30)of 1406��$of fiv!JrIHlv�a�K thyla�Lchloride, 2-butanol,��  di!opropan��ceton�+3� �|%�廁�6) in����'rZ/-u�): !����I��� ��� n.� Df�-2 �Qi�[�a(<$\{10\%,22.5\%,347 60\%\\ ^z(Lfifth� q�c�<�U%6"� �# $100\%$��-��'.q6��ux � s (C}xc}.� � dĉkJ� B&�z" M��#(s}�%�a�dose^�'"c c6$of Widjajaq1et al.� �MbR w ��14��9 e*0 .��of tolueA��1 n}-h�YY� , 3-aCylp�3�7 dehyde (a ), 3,3 abut-1-a(33DMB%#nd q� ane (DCM)-�u���oi�*�� �*!N%AY��J�ra� E���n��b%1(� 5 FT-IR1�_9_2��"_!� 5626� en�e� No6�=[� �x de��Eہ�8�(� !�the^; Ö�N%%c�X�Gs�$=1b �>;W��� DA��� (D} d} T��<o�(.�bym(�P-��a+-|le9Ŵhum�2{ by KrafftI�6kA>a  n�`sur�W3��Cerial�T�a| issu�� t�b gray5! ��G/je�Ro:�)=micro ��>Q Ol� e tum�Spec�3A%< glioma (astrocyE0 $WHO^{\circ}& aGm\& ,. 1$)/�GT�/� I�!�$600-3�bU� *�M3282 &��H> A !�4Q , 20F\42��" � e!edH Y in 1171�`Fta�d:)!5� e ��� �, 7%MA�l~ �"�UfX� *�5 Ŷ�/ inct� )ia��*ce� ��#l��!� temp�+�'u�sW'0I�&�Mto�5ac�= j�]�� ���!r ir averag�I.���l"K%e��>u}erE�s�)����C!�ōI�s�F%BA� �s�( otein alb�,��bov�Aserumb.piw" i�ext!,6l� oq*om lano,%wy[)a��na8��{���m�aW:-5Lt"� main�a � ��he �m��Q^QReV V�i15are�p In o9�to*�\*�B,pitfalls ari �$d�4ngf >�E1�")O�C* raM1�FIY_(e syn�v ic 2* )!5 o}-x� ��p, �A]�ww[*ver9�X mole2 �"[JN!_ (!�M�l�,��a�h�%N 1z4��a��L�onW�.~�@sc�Wr}a��qat "�)!Q�+�zS[qtr@<� �!"Dle:�:c&p+v�)1c�3t b�d!�Wve by;�)iz�). T���/i$ses�: ,�(i�5�MI�(�n��K0�H}Q �%ecX=6�B�� e�� E�!)�*Zit] (Figs:wb,�26x!s�3�]NI��r�,r *u*Q��H�NJ�%�;!с�1I�o11ly* "e .�9C�R� 3��!.&)y[b!Y��>uc * ��i�Fbe](!�o�'a"�`�3edA��Nf�C��s��&f+�"�-QV�-dU�do���m"�S)so far�) l��Z�O�(!l� E�S Lik?2�A4�4�e�).'%\be !� ``�at@N'' y�L�ng� s�#�&�!it�G�<I a��in*, �%� .Qov�m6BK.�'&�8Z%�2much ���3ed)J�c,9 ��Vw�dlow%4%�Mp&!�+H E�a�*S+{ �r�ve�:moslowlyW �!l��u� tra�ie/ f<Escmos�/si�&2"� ���. S �,i.Ai�%c;,��clrng�.�a�ny�-&�S"�.� EDa�})SP7% '? wt} �H��sum� h9�U�e �b�e(F �[o: peak�ofF �7"&#+M��H  �>m�E�opw�a� !non.��4�""s΁Ņi9X� l R9'dP�Z�_ y}m3s (f t{��f"*g:@A;*;�!��f�;!#�;ot"�I)iS nt p�K.$nex�3�V ehavC�z(]� out ��/�')2A-)�^a/� �f &�!/ VX wA!�o^!"xaM-of"+2|,��tat*tR�0o�i�F&> ՗}"+a.� .(�� iff}`�T�+�Xa c�JtreQo��s lowgcMI�SD!��$?h��&fE ~w IQ:�*�W0a0�Li$ s ll 3�*��rsq� T�,J1�,n�toI��SDt2�L -passM��-��� i]Dif�0H` vq�;� �e�9Bf,�y#�^͙) kT� �,rst$bya�a���!s"�5}K%*los82AnMI,�]|�, i�N�7 ��*9��z6� A�b,cBi|J Fi2��Snfirm* �*"n �r28"/S^A�  �, (bothfim�� (e-�s�#n!�2b! OWd (!�to>�c�7 A` ��%Oe"�% (or"�r ,�h Nb d��?N�%%5Ɂ+4_Ao.4_ ��s;�@� A�%!?�w"�%2 �p�rvrL"G8we gathered the�R statistics of the Amari index $P$ (Eq.~(\ref{pind})) and positivity measure $\pi$ .0$os})) over[psame test set A. As expected,"decomp[ on bLes more difficult as,sources &%�a dependent. But while this is very pronounced when MILCA is performed in the original space (Fig.~) +}a), it[4hardly visible Zlsecond derivatives are used JM0b). In fact, �hwith SD preprocessing was af to rd$struct suc#$fully most!�s!^ra from)v |s.~2�d,f�$n contrast]�out SD 2�RHc,e).2C4values $P<0.1$AX icate goo!.�quality,!?rea5$ > 0.3$ caA�sideredAunaccept! . Somewha! rpri!+ly,I*(trong (and Qp$) correlatIjtween � I�.nonneg!�A�s#w26 done%�!#filterin):ce)A)nearly �8letely eliminatA�)�Jh:Lf!e gain�$is suggestaat:�al�(may not be a�doptimal target in a PCA-baA�M54l curve resolu!( . Ie followA� appl!� ionsA6!aHrimental mixtures w!&ll onlya]] i) y)6 uorder`(see if post}Lmight further improv�!i�Om�ance,��ed ALS%�69 coaZDaints (as describe�!Sec-� lca}, mak! 600 iterEV$s for each1 ). Figurei~$als}a show-�i)]va� a,c)aLoiKhow ��R"@ conceW ��� r!'cAƁ�%*e r��panel�B��� plot]�O!M2^versu�,� onesMye0N��quantiz� a8��db}%\cite-1aG�vertic4 catti�e� clou�?� ��i� uracie���  r&� ion%�yD sl!-ly)�] a�:os!� tain�6�E68 SIMPLISMA, butm8pro�Gno�!,fewer false  ~ =�:�y occura��S2H �Hb,d�. �p��wor/ � l.� ionj��� nextem���mad� teg BTEM� )1btem,2}. Fo!_iA�� j� ���U t C)� in@}%�)�:� E s��m�umAR cleannesUb even%�� backgr�/subtra x,footnote} al���S work?*g sq  a  a>�� >81 � a�ow� 7th� 0 polynomial g��b�m��p 6� !\} depic� A�so>a졶 toge�Ũaf�(pure) M . Althoug)���^ro� doe %uifa�ly focus�9pre� ��ceraE)t. 7 find!b��  bands �iH� on���. � L orA����� a�e �lap��800-32�� cm$^{-1}$T �a�- of im!s TM�nalysis�%�%�T=� tbl} we gza�e�mqEb+�IaF,A� *V inner�_t $6innas. S. CyI� g)�A aALS dem� �Sal eMly` .�!?le be!�X stra�Nforwar��� uA%� sel)T. HowY , o!�ise� �A�.� of9"!�-~simpl� ,mcr* evi�] ut!�o�both. Oke oe� ,�nrepora6we IPCA m ipcaɱOPop" � l�y_ t. WeI��%u+F �s ���be��than !���los� Tcy�U7N, aq�� or!�"�would b��edI": judgH m  capabw �Kse���  FinalwD cd aEa�l,� bla��separ�A�~ ae n� acL!� &on � �k � sia�!knownvinvasah��oscopic� ods��%; i4m�u� of biologpL eri` nd {\�n vivo}q_N s�= ladroue0, T,buy,huang,nmf2,krafft 1 2Ip�$fer an inc��a^variet�s� ``black''M�}^ J] s. H, w� alyz1�b �a Raman�%7y studvb�%S��� �}�D)A�see wheeaE�6�  cQ� help0in�fy��abund����1� �es�senA$4 ���-��it�� )at a 4-EA  model�?toIla�� � !$�� plex).�t%% sa!eir8K%�I=et al.}-��assumed �&km�s� Oi>I�)ofaAdteins, lipids, cholesterol�Dwater.n�� `�� o� .� !0 ey determ :� ob s� m� by� a li  fi�exp&�� �� mp��to do*s� in a�7m� r,�lE)I]t ."� 2a�LofM�aF 2BEA v��J leve� B0, �%��so>� }�&�s (192� , &� E��7))�Q�&1�)=yfi� $four least ��E�Q  by-;� in�� �b-e (!$fifth and !� @!8 ]A� eda�do�n�^)%�fi I�eB I<�$ed� y similar!�l 'U�{i�!�(dash�`�R�) ich sup��)Er��e� q�eY�g� �qs �a��ituU �tissum�addŤ� s� ts� kix�ma`es, i.e.i�6{. B^; es�%c-&R�-to-pr�$ a�ge�&� �$s: 6.5 (wh�ma�,r), 1.2 (graa�� ), 0.5 (a cytom��,0.4 (meningiaris trend6b[  diagno) �<�onsist��� �)��B/m��a$:�}3���!by ern��od�camp,gai�}. %%% -� \s� {Conclus�0} \label{con} h� apS e !���+ E�A�3��* s� new�T *T "�  bQ)a^EY|�utual "� �[, avail� ine�i(site}i��YN hat,%�0 proper (pre/Z)~p,: intoj� is su��Dachiev2�E /��ar��ae�Ss?$-of-the-ar�al�\"�techniqa� L^Q&* is a gen#g� �ethoda��w Q�oA��>c� 5� ���exten� ICA l*ure s��$yed, e.g.,��)�4ica1,ica2}). I desig��to19%5@� ly%�u} any�( a priori} � mpir .<� Ulo�� ure � !�sAn2of��I�s. An im��,ant advantag�DE�?� !)rA7!�8�at ,can use (in)�'�v�smallgl Thus <�e  ��� pass�a��w%�A� 6wue!��!s�b�� p�md�MD =�}s|n� %m !�lizE_�!�R )��zFL��e�!� ��so, op�A�1x� ac�Qly�y 2�� a6�bV!o��ng�als� �Ehe��EPR� I�ren��As  simu"��� C C10000> s))���n,e}A9Aą�s��.L!(2.)��ds ^!duaI nuis��2���wisC unwan� 6 to ��.��ve l�!h!'Q c�!fun �in%)�AdIZsenO�!��slowlya�{ 6�E@F�goa> �H� u.� ��%���I�minimiz?tJ J� S&�!�er5�A�u I��Q��2���nt du�]s. s�}(�g�kva�!jng �$ squares) p":M 6 "cip�eG]:���=w!� (petC%%;ategor�&�!>Q "'�M g pa�a6 �"�� ���iso r%A�be ��ou�e��i��IlEHal"�Hnot M� soph�QE���. �m�bt*pF�Ur(!b��k�­'$s discusse�readyA��]milca}#�clude�>!���G�� hift]&'!�� � c�M�g di frequeūe�&T it���i��(inciple fea<&toE�q^� direct<8 ASst �,. "�m@' prom%E=�"m stocha� H (Monte Carlo type)q�ՒF� subje��a�e6EA9m���p �alY�A����~if?ed6�2�'un&$,affine transa��s (\asя}��  ro��C!� shear{ pmf,ae}),!��v<eu :  (PCA)7j�!�in!�&*�%al�. Our<l&r��(�!*��e pub ion)�&�G��6F.s�+s.+� b� �%�ir.�ounter!�� �� � -&� *{Ac* ledg�} #weClik�Xank Prof. D.L.~Massart, (P.K.~Hopke �?u"a�(�-�� �3��2;Dr. W.~W��gDa�!��cig4We�F reci�co\ E�!j�, M.~Garland,^E^,djaja who sh"Amir, a g�.� w%�nkAC.~��"�"`�� B2�3A�. S.A.aPgs!to �< S.P.~Mushtakova;v0 D.A.~Smirnovys�(P \%p�l \begin{thebibliography}{00} ibitem{ge��} P.J. G<, Anal. Chem. 71�499) 5398-5404rI^ Y.-Z. Li�L O.M. Kvalheim, R. M�,SM��Htell. Lab. Syst. 18k3) 235P$2h,rown} S.D. B l, S.T. Sum, F. Despagne, B.KWvi .�@68 (1996) 21R-61R.`geladi!  G , SŤxochim. Acta B 58 (2003) 767-782.DDtauler} A. de Juan�T9WO500N195-212�haJ�Kpk=�NB365-377.�l%} B9J!�Workm�.76� 4) 3K371.Lj!� } T.-H. J , Y5�Y. Ozakiz� 71 !?4) 1-12<"�} W. �, A�uilA9@A� 63E-(1) 1425-1436O|oft} {\tt http://www.acdlabs.com. R.5� B. Kowals�$S. Fleming6�65�A�040-2042�1F�(eigenvectorF�$} M.N. Leg�PA�Wentzell~\ 62%�$2) 171-188.�0m3} G. Peintl\LI. Nagypal, I.R. Eps* , K. Kust�,J. Phys� A 10I'$2) 3899-39:tem} E!¥f, CA%, WDw, M. ��2�5�(3) 4499-4502Mpionea]W.HA�wton, E�J,Sylvestre, T��b�)1E$(71) 617-633.@nuz} D. Nuzillard�Q BourExM2J��gn. Res"%13[$98) 358-362[chen} J� n, X.Z. W� m��fu (ut. Sci. 41%$1) 992-1002.0} !PD, A!� Tate�A�'wea5R. Gr�1@ths, Lect. Notes � s. 241Q2 441-446.!react�r4 Triadaphillouv!orris!�B MarE. in: �� c. 4th Inbonal Syq2um�In�t{!,E>" B S2 S| i�ICA��8, Nara, Japan, ,, pp. 879-882�-?6>Ff3=YM�Vt1� Med. 5��697-702�` J.Y3naQA %� P.C.W. Fu�JJ.G. Sh$F.H0Ch�!]Al Ql6is4) 82-924chin} X. Bi, Tei, L. Wu�/.O Chinw Univ. 2ii��023-1022ischolz�� S eGatzek!� Ste9 g, Oo%ehnAs, Selbig, Bio"� cs 2)+(4) 2447-2452� pich�1 Pich��M%ow!� . Mo�$�. 229e#5! 1-232�0buy} F. Szabo�Ed�,yi�W�) monetti, �ostma�Huo!3$M.C. Buyde-���j44}36-6*�   H� R G�� sboa��(El-Deredy, �. EK2i� 3) 147-16! \^ viss�� E. V !�-W�!~O  71z Z 55. Z shaoA:E�ao%��S��Q^ 6�&%5143-514�e�gUH��o���i�QCE�M�S.F!aM�J�&u 32'993-996�on} N��nnet, 6�UltramicR 10)a5) 327-365it�M. CnA�A7om�El O I*o#hTheory, Wiley, New York, 196�icaw C. Jutta�Jl"ault, ��Ps6��O�-6 H �,��>:36:ae87-31AEUD�(ec Hyv\"arin�E. Oja�u��9I7V 83-149:V biK$Belouchran)� Abed-Mera� (J.-F. CardoEa�uk $s, IEEE T.���4K 7) 434-44��icac} L�  Lathauw�BMoo%�$ Vandewall�Asmom. 1i� 0) 1��49.� �2J. Karhu2*v�J2:�p$ A. CichocZ 3, Adap�2��1�� Image1*inga�arA&\'*A6�'Z�2.�jade} :�N61"� 157-16��max�J.Ala�J� jnow< :P7E`(5) 1129-1152� nmf1� D�e, H.SM�/N$2 40�788-76qnmf� Buchsba O. Bloch,�CBR�4�2) 559-56� nmf2epSajda�Du�%C. Parv in M�,UnsA�A�&b!̅�/$ (Eds.), Wy3ts:.�Em�!�>� X (SPIE a&!4r., Vol.5207),A`�321-336Md!�]qP�orgieva�ICa��Hd. Electr. EA. E86A��3) 522-56^plumbley' D. P  �Wm�1� Networ. 1"|66-76.�nnf a} ZADY?��*� ��Sc. 319S1-����pmf%�Paa�% , U. Tapp!�Environm�5�} 1�2�a�F P.K �jAA�gAfS� Bisw�9,Atmospheric k nt 3"�193-26� pv��{nor��H!�tr� �= 5e,79) 1236-1242� ksfa� xliq�B"�13�q82H9-1:p!�Da�BM D y�h.sc. 5�c 1214-1222�sm��W@ndig, N.B. Galagh!�J�S�!r!UM)sR� &/ 77 L5) 85-96.L�2�1G� F�oliV}551 R�G29-232TesteLKraskov��$ St\"ogbau�a[rassb�9r, 9Rev. E 6)�4) 066132�47 2PA.l2Astakh{rk"� k22� micv�R Andrzejak� 2�Europh Lett"e � 78-28�u�ralA� ��ed-Mil� J.W@ sIour& of M�"ne 0ing earch 4%�3Af�29� n amb}.�A. Smilde�*��� 1-52�E� old� Esb�n)"#n�>� 2o87) 37-52z der1y C. O'Hw&� L!lecq�a�4$76) 312-312� 124,� phens. .N6e�92) 27e742�sgE�8a1J.E. G�86 t 6�562� 32�als\HN �9Ta�H�wica L. Z$�q� 4u 3) 9�2gt1} NIST ��� Data Ce�TE%p �0 ``Infr� _ ra''�J!��<$y WebBook, Stand�1R79 k� Nr; 69, �� Li�ox5 WaMamME�� N� al Ins5)t�n� logy, GaiE.sb�(MD, 20899 (2�Tto 18 ���{g3�5$ll 18�a��4s"m=J�M-2bn}v� &,nom+"�?s?!`61�?p �ia�estF&k7 eem 2 7� trea�&em*ny&�%�upI��'}�� ;a�ead;( our E8�6we].�)92�AW�!��#"�$.�# U1of�0)�%�)�o�+d�Dft�;�6q0�=t*. ed�$ by orthog�i?$in*�% spaK'� f�4�YMILCA o@14�5- �J0=.s"41dt�,waOr�acely%��0 as t?&Y$(�b9?(we just8<li#h2��7?do anytq0A�=%e its96"In view!��%�Sf"�Ewe �6&�Cul.�w�#8lg& �l!2�! K3jMiljanic B�9bottka"�ackert� Salzz in: G.A�j8gni\`eres, (Ed{D"S. Op%s�%t"in�medicw IIvrvu1412u 230-:$ wtu B�o) D. Har���JLi>Tv 5) 257�82�E8 F+ S\'anchez� Toft.  vaA�n Boga%6�P �N. 6L 96) #2> )�12�; Bioa�Q . 374) 60-62.x :/� Camb@l�osurg!�i.Ѿy 1-22�ga�Ga�,auxB Decaeste!��abyn MijatovA0R. Kiss!$M. Ruyssch)� 0ormaghtigh, E.n4 Cellg 29)�4) 294-36�))22)S!�S��!Qyst 130�070-106�D/�*�Pfz-juelich.de/nic/cs/e ware�endB� 6!!fiH} \�1er \i�&-!8ics[width=12cm]-1.eps/� on {�:�`�aye�'a��G�I�_o}-xy�B3 pA�(p4��(a)�#.�$z_1^k�  $z_2 L($k=1,2,\ldots,822$)�he&�"��, (${\bf z}_1 D2$), (b)%.*�40($y_1^{(0),k}5 2).6BB�" #y, (c)MAv�` ` � $ y�)�= ICA �KinMKC,e E"$O double}))�nel (d)�'ws �y} �}$5 $)@&�Ip)0e ;s1(2$ (soli D>G51 * y}_2%5}$�#� Iguish�-$ f2$��L�� ]$ '�-�%�c$ �8��I�i�O)4���.^"�2 � �>V�0%$�%u0lso%fn� ^ yN�&��?a8�AQA'bQ:4�D} e�q�N�$~�0m�2B�2�.�)a� i �3&+; m��(�(�)s%0 @/|0,& A): e�MIK�3e�P*� � !)-MS}''$�.axa�NsaE� y��QI8 S}$;e� rQdib�a * Ya2Y�e*SD� . �; e�&�8 ��pF ./63J�}<ll `5 i"�Af[MF`(�-" Y}m�);��� �c�1� one ���  w#9%�% t?9wA m�Y�;/2<<� o8DF���vi  e^�+sO@e��."-c�StUQKHt�7�Lted o�dJ� A�horizo7P axes}dtat�aJa3>aiOR >06<2p223. Left (�I))�s �2"q �8 `>�F�2)�&: (a,b)mm5 -BI<s\ ��)�AlV�U� 2.s; (c,d)**�of:S�'E^ /�; (e,f)"2 /"p�A vity< $\p6�DVI�o��o9�-���=�7 4>�Im�1�'!�2%2 A��Ma��Fr�?�\91x�<A9�� �3eKb�2��f0�e.�<�Ie�/ɥ�>�I_M.(are�8&rL1zd,��scale��E����9��5>�eU4column: Near-i��of��d 13s)%��� �$6w>V"�(!�A� B=2��(- �K (E=* N��$methanol (�>d>$oropro�� (g)L3 acet,?(i). R�J � E*Sd �Ma�7� r��i�2X2>��$ unit slopW5nd�8th��A%))y|��{y{7-�6>��%xC:� n�Xi(I�� )�`;�P.C!�P@" K%oluenea�,� n}-hexab!�1�!�aldehyde�, 33DMB)�DCM (pW} � bK*��Q�8-7>p!�C%��a��cohuman�D�@m6tumors!t)^$D). ExemplP2�CyMDFuS(a) of n�l^t0N@�9troH@eh&A@ { (��#om��upmX�B(b--e)}���E� o*� ��to%�� E�mo F�`:�:l@�@��n8WAEmAs& , W(��E(d)%J�EA ykC�tZ } � � 1,abular}{|l|c} "hU  & "/J :J &&m$+h8\\.Fq  & 0.971 3 54 87 94>n-m+59 %95 2 0 15qR866 99 8 93 z43 5qzj4 5 =90 �025i�357 X6 398 6 �483DCM 196 �96 �0 )061-�e�1�!X"lDq]C:2$,�P]"9N�&< ɧ o\[& s as�J/��vCz 2TN, *� RN,�r���K��:U� n2 ����d.m&"al�� U�O��takenA PO3�\!T P�=tblm:m�)end{docu } ��\Lclass[12pt,a4paper]{�-cl&Dusepackage{amsfont 6math} :sy�.�9nt�G6.{Rx6epsfig�tex�" 24.1cm � 160opmargin -0.3�N headsep 0 0skip 0.6oddside31Vh \newcommand\ds{\displaysty%"Hsq{\sqrt{1-\rho^2}}2>Txx{1-({x_1}^2+{x_2}^2)6$be{��equŔ:Eee{%�.re�{\thewE.\Dic.; �g8{offt�*�1�e,%nt{my[1]% �trivli!# F�TR� a� Dfstep�8." e�6[\ho{4 sep}�#1 !>�f.]}�a�)�.�prop}�� {Pro}})�}ak titl!�f R�"L*�)�Pdron Emis�( Tom�7�(Single Phot&'ed 6/� ir� �VImp�,IE \${A.S.\ Fok�& .\ Iserlek V.\� ,inakis \\ De}:�7�q�%�MG[�;c7)TE9l%ics, w0ers-? Cambridge0 , CB3 0WA/�Kingd�5\date{%V�8��} \mak�?le!t ab4�2�?�r*Ea*�F�B}>Nof��re�So|at&+ �[Ar�E tool�J�I��yQ>al chaerH� Ot9 �^= �� a vi�role in"�?a�clini�jm��?� neuro]" onc E card�Qy� bas1R5�al�yI assoc�;d": s�fc4H��' Lea � inA$4�Rad�rZ>� * :* so c�-d GnuaA=>?re�i*_SBŁ��=, by � o%�2�t�d�Nop&��IB�?N ar � gr� V�B�fpos"~@�" tic B?ulaIt�LEE�5 s�t�!LX�G&.�U!An"Yi2-Fsm al2y,!�' n9 roxia�nI�gi Z�ZermAU cubic sp��<ev�I~�)� �AKs�<z@�F�aKcfUlE&�"�K*y ion!="��$ic phantom�ech� !!Y�"0 Shepp--Logan-.� �? &�LInt�\k"�Li} �Fe�� t�� (PETR�/ le p��, comp5`.5 SPEC7rIf�� $de&i� � a typ�sa&JA�4flurodeoxyglucx (FDG"3Ri�M�molecui�-attac�OM ficiEb�Jn atom!>zac��oorine�n cell�%��)a�r�l 7}asLe!� tabo�Z, n>S�E�Fg�ju� ll absorb FDG tfl ��!6�<FDG�su�F s a .�decay,a�ta��i� . W���lidesan �[ it libeBs ��� a�@ two} bea��( gamma rays�' vell��in ,�L}�*i,��a{ pick&Asc�A;+��A&�!�Ha>%6us) !�emit a ���}��. �) bothOy;!lUa%Cs�!�in� !body,5/aim�to"� &2,,$g(x_1,x_2)$!D�ele6Oq:� Vmeasur��EdeB'� � L�tedK��. If $fva�(he $x$--ray"� coefaa��^�*nA|l:@^to��Pnatt}���nr $I$.�X�d T%8 ctorIEs)� -�lo ��X $L$�!byc#"}�S#@int} I = \int_L \j rm{e}^{- {L(x)}fd}s} g \tau�d($�a&U�mg�$a$ den?%/)���bQ!�point $=�A�3!7�7} �.�>�Fs�iD�G5��!A�usuVjFnu �f� in u�Bu2E���+HQ ``| �''A.�(! [viaF� &� e`` 2P I$ (��*.��.In�4E situenA�g)�1deeRi��(�He�P ��s��paiMP}n0�L�� tn�Z�YLK�d abQtan�Mly}, Q� (rq�preplainjI inewfFeZ {L_+BG ub_-@taVd,Ze(L_+$, $L_-$��!c�half--�� aJ� endeF $x$.Qc�5$_++L_-=L$,"' -�) �t \[ �2.+�L .&�}�DLF1 . \]�Jre.�*��/g=�}y".��$L$�y� sise8Z�A[!&e�N� m�I��a �jR3R 6�re wd.0ЉKofN{2)�sjZ � ��o�e�Kk-�1�s�i�ZthHa"Na")1EG�j��N/� ube� *{No  \no� (i) A�� of aIA�rr� �$Zta$�!r$ $x_1$--ax�ps�if!b".e�albers $(��, , P)$�]/~� $A�fty !�� �X.�} ]#)$QK�;� ee SI�-{� })b x1x2} x_1~ tau\cosI{�rho\sin (, \quad x_2- + ->8�} AZ?rewriC!B��Ube�   $FN'�J = f/���, ��+6�)�#�ZRyiGd6� �dQ ay��� . 2� 6�n[e�"�$Ɋo>� .� ,zW.�a�2�Q���ta.��I�/�t0 [&�S#Q)2�$ $\hat{f}$�,c\ �8,`Q�A e $xnJ"-(A@t�tao��֩<,brW} �A.rh�A�� {�]}^{� }Nm �dxB�B]a�&[gA8th�!!w�&! �@a�Qa2qa% ] int}6 -�?�O� ed %��U}!�{(� 2-� &ռ$f$� OYJ� g_fn� ,65%� �gmJ��e�!��"�5 ?b�ar�^ g_f(��1�&�^I_�5 F(s2�0; J!AB! \�ub"�&Nal Me as} EIj� �kGJ�e0�� *1>�"{ lV, a�:>i� f$�e\A�;gU� � ih)�6���M2�$.�"��� >�:�}is��iA(&� � frac{1}{45�,i} \pi^2} (\:al_�-Q2i} .2})� {0}^{2>}NA^8Y �!eft( \lN� �A�{f}20Zd} A�}{-(�� c - ����  )} \H-����Z� � O-BO -� .O2}mu(�, �A�Y�^� -����mp  d"`]t�w zero� e��P)O��g� a 0x gk.Wc>�-e) t6g�&� �3R�T��ed>  e���2�� R��N��.EF�>m$��.� %GB�,^�"#F�},eC- , R.\ Novikov ovi}����s�>!�:Q1�b(g�(�(~( +y �� V5 9ن�Organ(�VPap�Q�F�  � re`>>�5l�<9�"� B(a�t�_onH]."1&8A�E�)�R �+�! im2ately��Y F� 2���O_{ra new��$*i "������� T�� 2��uF� >� :� Wa}G)Lv!�eQu"�":P? ; a)r-J$>j #lzbHilbert&� Q:� s. |�i�1�>�in^ �Ab�h �} h6>= �Jt ɐ.t'�}e'-k&� rho'BCEx�$ng]%�s�}%#co�uEx' erty-& Fouri�B"$*J!�F`AJ�#��2A��g_�ate �j6Mdt��bE+ �"��hM "�e��ua[ide$ �"�� ~,v0%. Furx �,^�"a2Kev��!�jgye,"� atqal%v��p!�o0�a� an-+. ��#�=.��#}. One4�$=�2�N�#��shlo}, �·�pet�#}(�N"�$�,: f.��%ackA[��re�7c�f"�!Kp"�!gun���Jc i��v2�&YvrZhebert[nuyts}..i$V \set+�-}{0� 5qA_} �Bh;� !�.3 . IS"ll���dn�Dah=u2?> @F�&�uUt�6�as2:>X&M)a"`+}�v&va� } De~fAZ�� var�m $z3bdefz} z��� �� "P x_1-�*�$ x_2^� O , $xu@���r>ZnN� � ,� Z� 1/,! \ne 0$0|py����b2� � #ic� #!�,$|x_1|+|x_2|-,arrowhCfty$.>P $N� $ s <f�9& pU� �-{mueqѬ!�Na 1�|� |^2}- �)-�o R- }bar{z}}y� u ; _%R1,R (#�bb{R}^F :=bo�{r�id�@!@=�O}(1/z)$DI^u.�^+� -$ &� lim o� !d� ���8 circle � �#�ou"8# (GI�Wy@�+R� f^{\pm!]<\lim_{\varepsilo�IER( 0} (1 \mp "&�6q�}1�2>0.� ��Q�Pr�).�3"�3c2�+=<.U� Df�Thef� finmu"/B&)Y,!6P^�  f}6 -a�t  '^ �'^�L  f&�X>� Ag�$F(*��F76�J��o2�4$}), $P^\pmX5�.operat�9D �D�S [Q�b�B�p+-} (h g)%N%iI� 5,subarray}{c}.��M� \\. >0 �2>.�e�N rm{i\6����g�' �!� }�  \pmR }+)e��Y O)".�>�B� � Ff��}BY�[>uA "y�7 3.�7( G%V *#kG(Proof}. Bef�o�) \ �N�1AUatն�n)�a �T" e�p= QH 1gd�$!:# mot����E�*Ku! �� d3 �'R s �![`�:SU conjug( of7 � 7�nd�!\��onz} �1 = &�R��Y�}+{2a�K 1-MG&Z.H&�jH2F�7s2( Ay���C� a c�V%�1zs�. to $(z,�z})$. U&m JB�)!�92^�2}Jn t�1D~- al_z�. �}F�%Q��% �q �'W�4wi&� &�~APh��Jo�ba���"�A&/��2�-�y�"�{�sA� fiel�noJ|3 PDEs=T" gey �#IMm��A meti�-�M�t�,�4/)�s�u �)% �-MCDchm�s� $ 2���AZw� n�a���l(i��(�-\mNF lW"ma�}� &" h re2Y�7ɭ�u�*RX���a�>��M$sgn} \!\!\b͕1}2�  -&B ^*� iint�M its_I? ��'�-')}{z'-zzd}x_1'�2�N� B  I��%�A3��A& � z_R,z_I"� F$e"� %&q�h 7}��` g , �z=z_R+� i}z_I� z_R�5I)�j  $z2���EU(en Pompieu'�%�%� A�6� abfo�!TyesbF pompEz2B\pi�)b�%C'!� ')} Bz_R.z_IF�In our �M!�g"?��f}{)�r�� 1�d�]�z_�*E(aN(� e8 �:g R8Y"� �AtS.q��%n>�i���(C$�<�Hj=�pr�>�m� ticit;�p����muB*# ����Y/��2al{nve}>6 for a�E�is>"�cer�Z= �9f$ ��5,�s.Ɠou���&�Jbs�-l�/�e�.��.':u�~���aU$:uK=Uo- <3� a�q�� $�*�F�$�w�,�4``jump'' acrosIe *�:b� mura� F�Fca�nt_0^{��Jh�*X 6 '�?m6! --.��"6  *�BG@q?}�2�">��F� ^+)-N-*�(we�6:�.�a'a9�$ tend; q-�� $*� 2�0$`) �^+$��}K"m (1-Izv i(1+.2��!v*R#)[}wSuba"{ ex�.A�� a z$ (1�2� � *�E�j�b�zz'} I �D-x_1)1+ -�22)x# � +usA�*�(.H"L+ +2H"�*F�X � --h3 � ���a� b��'t:)" � FP�'$tau'$:��@athbf{"Xe?^\perp&gwo��vsG1 ~in 2��5end{�arA��#�*�m)� �[I< bf{xS�k}�rho ���ora�!�) e�tau (9�,=|K(-, ,i�H-M�� &�75�K �-)�ϛn%s&L >v�taurho��a �%U5 +�]�! (& = .Y{&"&I�B -U[(�4a"$!Uy)�'d-*� 2�(!w'-)E~�:~�%p�EVfa�� "J(�UAls�2b� musiSR�a�m.�>� �� I�rm� B� }�Aѽ$.�2K^ 2l-���.B>0B��eR�$y@� �� `%�#)Kd�01�6%�IOM�5Pn�a%B���;Jacob�i%�i.e9.� vR =2�"� ��d}A�. !}'�>M: �:�� �IN)lf� int�- &�*� AdrY��F�R�} {��� ��)}B �to�S����wUli)*K �U�EE����%Q"!�MR�B�M<&�/MB�+ N"z��%�Mx��"�A�e0��<0 �� , "�..->0s us,��� 0\Q*_s�P)(=SiQVM/2�];A15.i^i�(B $� j3�u(Mj=A�#.�"#B�:�� .�.p� FD.h 6��G^ "��#ng��"��>=�"� w�$��Tna�*� F�+) & = &�^R.C���.<� ' \\ & & &C�=u�82{1�U��U�V��5U {d �m�N�P �� l $-P^-��4, h� ��ɔ�$^+e�2�oF�,w )$^-�8C. \hfh#WQED�8vvP 3cm �l��$2{lU�wB#�;riv\3��kZ��.j|#� )%Q5! $A�� ���*O  %�GVv �Gormyu�"Xparba�al��2� ��\{*z1/����e�� }{\nu( J)Y� i\} %pM�%U�E?a�$R�>�B��Bbn����̮ 2q�uI1�B�4aYI� seMGTy)} >M� y�b�capj} Nٲ\p:�:3�e2.���Z�"3� -;&* J��m��)<�F�%�l82���."�F�  7d.� M��$1*�2��O:&^�¥%�y "�+b�f�Ze52} fT5:�2)m�. �-Y.l5�\�f\B)R�C�g�mE $Jq(�k%WZ � e "7>��4�(8*"8a�A�9�2N�M��1)z�[� p&�}F����nu!5u�,��g�Ww]�� $\ns�6� �nu�7eOJ�J�M� \exp&D[� �q: ] ) =- �>e]�Nk��Ze\ w\mB�z[ � [�� �]�-�_R� ? � :<�|.Dn��:��QMM>uSERF�<&� �kn�� �K,?�'S��"QE�.��E�'.��� �.��2� c�J�  N�6e w�4 �i �,� 1�"�Df2 r�d�2�7�!otw}��`i�ap�1���CreК.�]b�'9 r efteqn{�"�"Q"=} \no�wm {\ds}-��Ig}>�>Jx �>'�QB:��{ '}� r7?># &�* p+-n�JY1�No�Eer�> exp[B]EL�GTWO �$�BM?Dco�#�l�7� $>�of&�3�s��LI��0�MAjZ q �)M��v+DV jump �!�;f9�e ]��eR�>� � c=Hl�L� . ��iήw"�b -^ .��*#��P^-if6� } P^-U���f+&S )+VT P2~Z*�d HB�Q�� -L_a�$2?%�� F2���Z On.&� M�"� s st�valid,2�N� � �D- V�M�t&laN N �NBby� M�bZgk �F2&$4- fp *D �a�1tvX 2>1�� Z� V; r* e4L)i&K%E" ival��to�=&n%. (8In summary, letwCFs$*H�}1�-�? Aa��7&���".�> *�lB�KB�/�q�� 6q�&: &��ue&W ��D%Xen2UI!�B�M�Ig)m�6�J: expl�$ly E�z&�+Ia�e��@}A�1s k-��`'F{^Nb} ~%8�=��9{�WAb= N8p� T& .|6� !X:����+�#a�Hѫ)-Q1Mb�fj~f:)&De���Fi�h_�2�u�d_E^wh28%�J�-�A=�-w�&72�7+ �**rt, nam\?]�=8�%LF^"f \ge 1$J&A^!�K� calcu� !��AcV -I ��&xulab}closeq%!].Jg(��& ��Nu�)�{NA�um_{i=�FN-1�W��* i,��BaS�&g%�(��periodi/��equishud �+r�K��sNv2"�'sp\�:rn���:n#j wor�)@- )� k-A�e ��n1Wx KP5�z97�*CZ< isP�>�D<� in�>TT(/ev�io�`!��b sm�-JG��N$0@!�U'�..'$J$$�ME�s� a�#���d-�%�e�Q�ay�A t $n$� lly�rdDSb&rho_iv [-1,1]<5\b}_iAW�_i� ;�JnN�re*u�D 1�!urv�[ wŜ_{i+1 ٵ�?3BG db&B"Bb2SOGN>5 =S_i2Y=A! r_i + B_i�N{f} � + C.$'' + D�'bC[ A_i=i��0/"}>_i�, �=1-A_i, \,� L41}{6} ({A_i}^3')�fh-Ya_i)�:RD�>B >B_b>�,a.!8!i''Pi~� �5����-U2n$S_r1& * ,� =%#i$�K��:'��6`�a .YD (in [$)lA�$lly--�� nodeI�1� e�6ex��bjD--E�l�d��C2E�our5 M,�d�6�aO��1}^{n����)�P5�<+Q�"TID'%��a3ZTE""�s:�^ݵ�&�HyY�J� F��V�ŁM_� �{iI�}@"+1�+� �*�?4� i-3�iK+�2ho� f}A�:6 /iT 6->6e���9.>�+ &�"��5� B �.k}�6& �|-3B�)^2NV&k���. �.w�%�()S.���~�/�Z�63�=�] \ln i| |.�()  eO�@\�$ newhi2�-Q�2�$Q�e�yly6 ?��G^M���c��eF�s?Az" is�p��iosubrout�� qtt{�i} �&1ERecipe�r qE�Wu 1''=Qn''=0$ (u'��f n� �`*j%rp5�k Mh:�� 9Z (for��"r)�f�A�ef�b0 V��� 0)�)z��hw<�3 e.� 6gX .gE&!6 U+;32ɵ� �җ�$H6`� !�*�1- n~��o_,)d�_QD�F:�OFC�,$ J�rg�O ?�BaU�Z� 4i)\&�{�KJr� �F*yBR"N�%R�D6[�Eef7�$I&�*"� z�?�)J8�Lexp\!�c[�I�^{\>�s!5'y"YD aV%�]B "�,�3we ;ud�,2`!� g�| dom]�.�� � \ $[�,:�� ��N�a�Av$|!�|�,+J tau :V!��S�1w�(�aa .A�`2m !t"h@�"�:� S(&�}o}: eUM? >�*}�&6�j�-��6pm f�=�cos 56� �-U@bsTJ V/�,O6�-��mp ���.�&Z��u4�*}��@�E�l̡(*q6 7)�f^{cpeFy� �)jf�}e1-V�|1f^���ns�xj�,-'O� spe}Q�mv|� ����o o��m.�c>K�B��w�2.9�s2 =F!T6VF"nD cspfy! nd{eU|^1�)an .�  $RF� = -JF��som&��B[gjump}) �}f�0rel2g} J� = N�� (!d!�2�A�,me}) (P^-f^c.p0s)+;2.; +f^c*�2 Ps�K!n)a4�n4+et�gVM(* fM/V�2T�. = h 2��Q3zgIP�g 2g]R�=)�2 0V�.Cj�1�)�-'A(o?(h^c + 2 f^s��) +3!�^3s -3c3�B�WY-X V���� by $.�rJ.b�>�Y� �� >� w"% p}6o��1?^!'l&�-Kr@^�*�] - �co"�]- ����� *�  � ���m& :�relg} JTv�5�5>#"�$b ' F)Vwe �*�-6��%-1}^1���:� k^4+XM FM6.F�Z� �5-F�>X=X�:�ln� �(��}{1�9}U�+J�% �� fbI�2�v*�Cnewnewa���1�fs��� �$%�! ,A ~ A >=i"l)-A tt<��Q��^��;'� Th%6b�weB�1�3ʤN v� �KIV_i+ %p2� �+M�1}{36�D$/4 I6i}^2 - 5Pi  J % )&. 3 ho -6@&5H� �2�%,6���5 u�+Z�4i� ~ � ( �e  �+>�6'2�in��Z�.c��I�%R� ]�"4@��-�S���2=F@ V� &+�\ω�I )]}��|"AV1n/V�B4A�\{ F_i..� � �A@���Iw[�2]]��;"�%�.-�k2Q*-��"�-����\+1)y) =(� ~�.�'+ (V!6�!�2N�"� ) \!�] \2L, &�in��:!''F_i�:�F�ef� �<&�"J�J, $any $n'�Y3C#�Q> f}� i� ���� &E#�m�] b # "�4 t-�I,t,!X� d}t,tconse�Rtlf�#ca�FFb ���@� W"-6 ��@,�4�1�� -�j� ~2Z%m!$�Q !n���5YN$ &_Ae��dI�out�Dd�# evious��.�bt�DbR[�Q: ��) i�,�J$*�JY"A 8"o*j1�i�Rta_?J %5���� ���i�')6])��2'%8Gauss--Legendre.,owo"�Kal�ng\ #Mna�\- \alpha^\bCuiDv\a�" w_1 0_1�"1y +w_222,a�iAabscissa�#tau_1��auZ^vrpp s $w wre 8�51= �+(�- �� ��12 DI3}E"��"�PO2rONw6nNw_1=wO�"126�P �'lso i a�<cTtr�wsubdivi}%]SU$( �,�%ѧ�Az''/!w�/� is v=�@��HrMX�¦�gGI>\�2Un e�%���&�&$x �inc��X runB�E3�pr_�m��*���lpH�\A not �"riodx�2�n�dcy.���u{-1i���A� �|u�J4�v# "�()#O'm�U�on(nce�Mp 9 �#p$s $�q iW ��1��1�bnce schem�f'(x) m�i>X{-3f(x)+4f(x+\Delta x)-2  x}a��!�2�}1�!dA� $"�'![-e��� v��-�-  x)ek�"� xf��%�����"h >�$&�/$���nQ!�&B��(�F����: F�!. ,�]&!�&�E&|! :|!��&j b.6� 6z &��Ilne� %C*���M��)$qXa@l � _i|=���E~i�2�,BT!�I�tX5"�F�]b l�|5��wJ�� $ >�6(�:Jh&llc��:M $f:UBI� (vJ3age!�"M�A���]u$&]"F"� ,���m: �6Rhu$J_#i�_#q�~1s!66^��,�g���(mxR��{d�rD��Row eC4u"lA�RLi�:,F �#x_A�$�"F�Q�)-6I�, � m�+!zoB�6%��F\y�6%t}�_B%6��5� ~���$::A�m:�5�F2cM� �cf), ��B��,Ŷ�>�� $hZ+` s�Fk+)���Z�TƐly�sixY��-%��$rr� �.R as &)���ier.�%.AJ�-R � }!D0"6�i� �%7p; "�3Y=T�l1er�km}�yQ�r%%"H,Z/g,[0,I1�#xLh���%+/N;�/� h%���s�q�5el\�re draw8 ���*�l} V1���dark col�0"B1Dv (or n��e)�0 ��t�^:;�Tmaximum 4��˂al X*'ed)Ui. ��!m�_PET&�m�Cft�� t�sm�ur1)g&�nAu ��N�T���j)) kuny1 ]n�.�1%�s�SU d����I�.c��#.�&8$ � ll a��<�oѠthoraxt`2uh*[ bonR3/�r Up-� lung�Z��: !S�. �.N�o�?a��|podY� a ���<�^�ŎsB�ݓcon��9�� with��~d�ie@�y!�H&78i�8� k'Ċ���"����:E���Թq�!�u�!C 100 m� rhoe�*��=� �wcar�out�e���.�&M �Tlq�A�!�"a &�ء�reY| &�7v�r&xr� rem0�Tef6�!}@Gibbs--Wilbraham ~� omenl���4� �\#�qr�q��O s: WA�-;q[2� (jXx$)y.��.2 �e9 "to��i�YO5=��chi�Is�>n $a�20}\maΊ?P��[ K�>�� with averaging parameter $a=0.005$. This filteri$|rocedure was applied five times,UX the additional elimina< of those values�>$f(x_1,x_2)$ which were less than $\frac{1}{20}\max$ at the endCq�|. In Figures \ref{petphan1} and .02} we presentG4results before1 af!the fF ,2 pectively!2,e reconstruc�Ttook place in a $500 \%1P 500$ grid. \begin{f�(}[ht!] \cen)}4{\epsfig{file= �h.eps}} \vskip -0.3cm (a) \h4 (b>c) \cap�{Test ! toms for�X PET algorithm.} \label1K} t s~�1���F[EOe�ofR�} -�A)J�B�1��2����U���2} \endQl We!n tested  SPEC]U�V 200 �� $ 8 7 100 point�X$ (again �< \texttt{Mathema!c}). W� nsequentl!I�se �Xin our program to re--e�ate $g(�{%�order 'mo�� he effect�[!C�Gibbs--Wilbraham phenomenon, a medianm�Ef used�."�A�������c���%I���areu� 2Au��Ci[2},x�/�Jjm�. �.!�a $14�.14�.s��~� 3.9c20 �0:.. *��� ADv� f�,Al%)���.S�b)��5%��2��-Gb"� 2X�����3��3�� ���j�y�J]J�B�F� ab��a� it seem�� at e�J,a rough esti�ro� $F(\tau,����$is sufficiH ��,an accurate 6 �uis mean o,a�z�y numer�JlyZu���� capf��it:�`to use ten equally spaced�q�$t$, r�[� an $200$ � reduces � iderablyet6� . \s Hon*{AcknowledgmentsaXnoind6 V.M.\�! suppor�k0by a Marie CuPIndividual Fellowship͊T European Community un��contract!CTber HPMF-CT-2002-01597�9are g!�ful!'LProfessor B.\ Hutton%us# suggA ons.�� thebibli�aphy}{99�bibitem{koh} D.\ Koh, G.J.R.\ Cook, J.EiHsband, New HorizonsA,Oncologic Im�� (editorial), N.\ Engl.\ J.\ Med.\ {\bf 348}, 2487 (2003)\ �joni} 2LJonides et al., Verb� 8nd Spatial Workc Memory�4Humans, Psycho}Learn� otiv�,5}, 43 (1996� 5 mark} G.S3arkU!�standrEmoa al!�sody AcDates Right Hemisph*Reg!�0, Arch.\ Neur�%53}, 665J�vopa} �Vor�p, O.!�Pauls��N.A.\ Lassen, Cerebral Blood Flow in Acut,Chron!�4schemic Strokem�,�a� Scan5�74%T9�86Ulaol} aQLauritz�!�Ol�,-"alN� Du� @ Migraine Attacksa�R�^  Emissio6�BA)v107�47�42lee} B.I!YeeUHIPDM--Jin Pat�OsUMed�Ii� ablea�plex ParE� Seiz�,: Ictal stud!W6 E4A�39 �82� tybya&0L.\ Tyler, T.ar Bymea�,oplastic Dis��s�� {\it Clin� )m�,: Principles%B Appl� s}, edse�8C.\ Mazziotta, A�tGilman, p 166, Philadelphia: FE�Davis!k922� mazz�CeoV Move��n�)� ƿ �e\�244��inoi� MinoshimaU/A Diagno%�ApproachA8PAlzheimer's Disease U+T�--DimenA�,al Stereotac!�Surface�tj��s�@Fluorine--18--FDG,eaNuc�.~6}, 1238%�52�junck} AVJ �n-i�ߥf GliomaM�Ligand�\ Peri����$enzodiazepa�Bi�CSite, An��N. 2�752�892�maetalB2�R d�HDGlucose Metabolism�sympto7 c Sub!Ns Risk�U,Huntington'sA�!�, acZ�1�35i�72�andr} NE� AndrLn, Linɾinderi�in�S�!mHMental Illnesses: AQ�a S� ific �� path�y,.�P27�Q 1586!Y96�reim} E�Reiman5TN!�anatom�7 Correl���HAnticipatory Anxietw ��24�� 1071w:� tjuv!�G��juvajevyA GeneACu?to%N��Invasive��Tcgenes��Cis--!j,ed Herpes Si��,Virus ThymidA�Kinas�>ia �1}, 31�6�$yu} Y.\ Yu� Quan%��;�arget� Expreŗ��mQ Re` rB$in Livo,Animals, Nat�}�6}, 933 K 02wgreena�"G �� r6Mon� n%>$Endogenous� 6�Positron�\ & (PET)� ofr�1�$ic Mice, M - Bi�}, A: 2� doubTDoubrovi�� hcriIalgu�� p53--Depe� ��r�0in Vivo, Proc� atl Aca $Sci.\ USA,I< 98}, 9300%�12� lard| L�noi&� StR A@E�Small--Cell Lung Cancer with Inte) d�-- .�; Co82� j�� !�6� ost �Ost, A�< FeinH.\ silv�hhe Solitary Pulmonary Nodulat~. 535J� hutt� F�  , C!N4ac Single--Pho* J: Is Atio� ra En]? (invi� .� Eur \ F`2I�\ 6dwa�^0F.J.T.\ Wacke� V�,  @Emperor's new Clor? 2m L F�40�� 310 � 92~beng} F%�Bengel�E"QSym�Ke|Reinnerv��n 1hPer�A�\ Hearti}plant3. ���3� 731%�6'na!�!�NrAM{� AR&oŌM�rized]�}, Wiley w York!:� foknov} A� Fokas, RřNovikov,,crete Analog!,\overline \p� $--Equ�M of��!0, � n.< Paris SeAa� �"�1�J7ɋ:&ovi} :�An InverK  Formula3�Qv,ed $X$--ray ��, Ark� t�IR4i�22Q shlo�mShepp, Be�Log !�Fo7r R6� of aA5d S� , IEEE),�b� �]T�2Q76� A/pA�\]09�R� k)�Inv.\��b�1+1a�20:� L�cKunyansk� .*:�A� Based o� Md#licit�6�,.\� 6�29��>ise[ P.\ GuillR , aK,Jauberteau, � �A� �a\ Trebo_On�V >Umz.v��b� o� Ex�>�Nonuni!5���i M �6��\L1�46�) JB�>  N!%!Rpertye�ysi�LSi.? �?N�Da E9M5�2��a�2006�he!�} � H %n� hy, ,�(h, Fast MLEe�ISu.an ��r�te Polaa\d 4 %D��a Stopp� Cri� on, zc#6� :~lia�=Z  , ��4Hart, Bayesian>�i*7 1C2���78�:�nuy��TN , Je� FessA Penal� kelih' e:� Method%m5�&� ,ar�oo t--Smo� d Maximum2d� Mache&�Resol�6� ���{2� 1042�6 foge:�I��Gel'f�A grabiloftearENon��ar Ev � յ&�Associ�2���1s, Let�(ͱPhy����3�896 abfo� !�AblowitzK W���Todu� �.�� ATi Variz�0Cambridge Uni�N ty P� :� fornbergO \��,A=�i4 Guide�Pseudos*�I4s| r Rr6(recipes} W.a@�; � Teukol�LW. Vetteg�X��Fla� y, %"Nu�A�XasForu .�~Ar&*.!5u� (2nd� ion)}�V;6omath} Wolfram� ituA  Bi% (4thj z��  #>��%# docu-} M% '0is a LaTeX2e " \ class{�&,usepackage[pP" int]ja: {�r} %�fo��Yiqed wh�#h�&pH� draft o�*�f� � ident{\hs�{\fill} R!it{Aen� �"El�th� shopC(RF Supercone&vity} 6Sl\makebox[0pt][r]{MSUCL-1276}�A. embed��&s = {graphicx0Stuff�*(E)PS2 (2-colum�Pmat)... %Half-size l+cape P,�#played!rai!:`�� %S4 d arg%�: magn� 4 factor %Modif�(s*at no exT "�'!�done %Ve g:� %(\d bou�box he�, sui�<$3-digit axlcal�Pbel) \newcommand{\inc�8LANDHALF}[2]{% lud��!_(s[width=#2\)I`,% bbllx=0.45in,bburx=5.1 lly 0y=4.2in]{#1} !��~,��c(�� Thir.�>%,%$, e.g. (a)�h-h %We'* ssuma�.;(=3.25in; BB%K=4.7inv�lab}[3%�(setlength{\� `}{0.69149in} % = 1 inch *2z / \ uz <6H#2.Wh*pic�h}(4.7,3.8)(-0.55,-0.6) \put.E[�CrCr00.18,2.60){\L� #3�(�EnNric cus8�m$�� %�  \de� ���� sig:� }{\ensur�bh{^\circ��Qa�� n abbrevi�/6�S{{\emC.� hyperref}.[all]cap�D%|setup{% pdftitle={Nb QWR Develop���RIA},'$author={W.B ��}%!J�ѷiY{Niobiumrrter-Wav� so�rBp��RB&8Isotope Acceler�\�- ks{W2� 6U.S. De��$of Energy � (Grant DE-FG� 3ER41248)E �{% W.~! u�$J.~BierwagS.~Bri � ~Col!p ~Co�n�~Grimm�$~Hitchcock�~Ms(,\\ L.~Saxt/R.~C.~� \\ N%�al6"E yclo� Lab, Mich�~t.�, E� Lanx ,�) \\ \�'���3%!USA�/R_JP}. �� call� aBL-�linaca�O:/ CW%#!3heavy e�$to $\geq 4W3MeVAJ ���a� A(�- ower?up74400 kW\@. Sev��of su6�)%; s�)( needed dueI�chang!��co�4)�5�IN}. Dit�#i Qin!ngHat�B7 (MSU)��a 10th-�0o�dr�->�(s��V�s��s), hF 6��ellip�%��USZ!�`" &21C�%s�� �ied�!2�-se))�.�. aL (QWR%� (��um��\equiv �_m� 41$,�?E� very simi�t� -QWR�use!yINFN-L�! (��$a�a�5� �)yspezf l� )�9sb J�852���t� 6(Ŷ��)�I~e� d� (ed as a col�� effora�����J MSU.��is pape�=���RF-�,A��i^ 8pr�7ry(��A�a-J6M�)B�K2�Q�G4The next step,� �& �mpletє [EE�ym�n �u�2�,!�also l wayU�KAa��+{C�xi���bK �I1o� ALPI�4EBa  the i1+RIA6^�ie!E�  r��(3Et2#.|s �nd PIAVE�s�B}; a 16 Yafh�9!� UAgt]�KC!1�g�i�a>E dio:,of 180 mm; tA�was enl� d to 241)60a>VF!B�. A Qr A�� (3W��uC-�B>n�r! fe## is�<�� !_py vacuum�6ins" �4V. p] c�4ta6*;�6� z-Ay.g/Mge�he �&�of��steera�ݥver�� asymmetr�!���5�D��eK4is not a majorAblem 1B2�%�[�long �h�, bX  iznt & 2Oa�QWR�ItA�I��8theore��/� 5; %z0compens� �/-ic sha��!H!^-�in�( viciv/���\}RE17N� incorp� ��x iw to�U��0. Beam dynam J)c> "V ��should ��V emitti! � th1�m UFa�~oa=T:parms}Vws some1pW>� !FY_ Fa� s  :calid��HANALYST.\footnote{AAn�eSiw � Techn�( \&�ed. �c., Mequ Wis n.} Dra� � ���IZin �F:dwg!�TT1��"� ayvoltag� atQ�del� �'�!"-�> M��  �lY � )��"^6M�:� �yeMin���sit�2 C�s��}[tbh]&?>S�!hF��geo�N�=��. "$A OC@IC%r!:x %$� Aor,Dp} ?�>Q��v� *{1eU ʡ@er" �, �)� ma stainl!S[ @l (SS) blank-off o;d6�is bolo l>$ G D. �<�%�e�� s%��c MSU%�o lo�#area.!c�!���as =b8 dustry. * pip* wB�A!=So%2��  0nHD j*CEAv to <$ac sealaLAm6�A��E�-'� EqalU.BEZ>~! made%�p� ure E�/6� (thuki � ��)�ln RF SAt+ * eo�!� , @ )5A?ab�0.7 foN6Bt�!).5 .�2.0cQWRe<2�I� ��Z�065,2450�0N��s3�R%b�9�(30, so shif�g"downward�mN leftA�60�2705,214�$box{wG}��300,25#���:��0.5� j�n56��k�by�0,2 ͢��B� �1����Nb�� 2Ma�Q{��eNew� ��d�� F�q ��M I�i:#$M>4�>�Bead pu�F��a(2�a �� bead>� ]�ͥ�� heckli� flat�6`S�s �]��c��� CunE!{p� $Delta E/E$J 3.8\%j����0.6\%%�~2! *^�9�d!��etc�+�BufPKd C8? al PN:h��+( (1:1:2 mixT byXumconAnr�hydrof�;c, niIs+8phosphoric acidr�H12� mu$6�A�9��#� d th.D a ch 0r�KHa closed loop syste�I main a te4S$ $\leq 15$~# C�~O!-~ high-�\se)Eultra-pn wa��PET�# C�) kJ2 n ro�or 60Au�minutU:)�F!�n Ambl�p a�Lserp#sub�J*6�i.}a NT^6 d�@ ry qAg D. &|FXbi '2�a��ju�Ori�5o N "B cryostat��Rh142,427��5f�n���0 (okay, 3 act�Ep39z j�,26u�O��n�Z�3��f�n��|>�5 %:107�J�^��3 E��2��.�2E� QWR �4qC( D�)Y� ���S~!RF �RjGRF"�� ��kaFm�immer��� 2�  bath< 4.2 K; �*�Tmea� |��bat 1.5 K�-2 K�AfI,se feedback � �� n ky�nc�nRF � 3# z!$a 50 W amp�$�tec ��� or. Copp #b#(tennae (mou�-)x 2� , RG��couplP ��I -dA� pickh!he�nsg�I�!�al�[input a � � c6VnA�bs!ar a"��%at low��at)� . MFpac�barriejenc��2?in� hI(vWe� �1�t?���Z�1#2 daye f$W � 4.2 I �>�� � ly&�%��$i��ing; re.!+ si�in��m\H NR�AYM� �^er.���cw{90orpdfSng{2�16$}{'(m)�!16}a�2�!m�Mu6 �'�in May>R30e�W�'�G�.uQvE}a (�les'!_m95M>w'� �� {�&8"�&�!�*pM�mis��edo gr��0�]R a suspiciAl1 shorA� �& n i81A�01e�'m],}�fI0eugr outAE �>�^ �ndP d |S . A�"1��in Jul5�A2]&=(19)C9 =tsteady��teB�%�, s-)�A� er f )�3 ^)�ld�de�m�? RFZf sondQ-s�vel��Oa!BiOE���RF��)in� H*�3es�)��(mptA��dide�further ` Am* ). Mod:(xM=�8 �obser )d: 0� ���Ibbi�� 嵥C5O�Z�if!�Jd5�"7do�n�_G `��|igh>uregioe@Q&T%VB�e�reI! dec�G[6+�+�&�� �, possi�Pdr(re��]l � �RF�b�%-�er�?�*.�� low-s �v�]!1 $1.8.�+ a�n c�BspaN!y���, �� ([$)I 19 n[�# e ex��o�,fY9�BCS term�12=V� A�$3.���$T�9 $ K,���to�ResqQ�� �D-�$>~us%�yC�pB �a ��skEewan:6� U�su�*!�5 � Ond2b0� For Ű> 2� �IB!Nsam�2 K( -�F� b] 8Qer}F�lab76� 8�}\\r/� /b /endk&*�rA N �>l[1dto 4.3�Z\1V�2K&��rFW ���� 6�085"�wo ,&�d&�#2�Hҡ�F@*Ap��ed%'&� m�3sA2VR !GuEu caus�_F�0�Z�@!�Do�aA� e wo� �E��� d�=�;&-�b��F)��:��� = 6.3$ـŽ ���2.��.5+>�Ar$6R�1.5V�$$R_0 = 3.2�� g�Ba�8� � %*� �ݯ�.)cedŀ.��4ECo=&H } Afza6uY" 6 6 6 ��Rq�r� ��V�rrgiSFS Ms ��%����h.;M�:C4 eyJn���6��542�!J�'�om�/pm�, ��� > E5��! E" (at�4AK� N �"�U w&F1it�6arCs pler (:�����c���"�/  QWR pr�!� �0will b Q!�of""� �2���$A�He�7%�!nchanC eris� Imic$593���&�[e5V\�  Many��nk� llI!�peo�3S 2G2who� C/� �^; - �y-�Jv1A�bA. Aizaz�:�Snd�*M. John�YS�K Alfredson�Z"CK�Gc�"( Bieber, H.:Ym D wtP$A. McCartn�L@A. Moblo, S. Muss .Pedtke�(PopielarskiVincenY$nd R. Zink!��6dQ E�d '@�9B�E S.�8A T[5�} �45--351��gQgZ} T. !?�``2�nga~Act���a �> St�U"$IUa�1����KA}��4?�Me� �.4-P1M>,P�$6mngA W�>�-tor��E[`3C2EARIA,'' t�ji��``}@le�ρ LNL Bulk }ALow B�>Q[?:~s��E�KB./& V. *e@�I�203--206 �>�-�1�&-��High-� $ :c %Z%m!Az6P�/<or!$�MPubliR!$, Piscataw)a� Jers�� 1993.�KC.l9J�?�_cl2C6��849--8i�``Stud� B�*S�5in���O1 %:j �tKD.�f�J��R P�6l62q�$1095--1097)�}�6-�)8*� ect � vel0=2� ng %F( ieA�.�E} P. N./Xroumov42e,�O=N Rev. STɬ.�$�4RNdW 110101 (N,`He!�%``3D F  �Vs=m�ah�8)�D�5C:� %�y�sRIA''2�F}� Gorelт�XXII4n� V 2002�/67--369��>�Md"MLMF%\hoffset=-10mm ��^new8$m{lemma}{L[� ] %>K$ }{TC8m^(�L�L2Lre.L,refname}{�  ᮪ F} %:@a�E:E.;OQ�N[12�0�} %��.BI{myar�H<%TCIDATA{OutputF�u(=LATEX.DLL}!LastRevMF=Sun Decj17:50:02a94/02$Language=AOQn Eng��$CSTFile=-Q .cstPMapleDefs= %$y_{0}=\f w\kappa  m}{p}-2$ %%�odd�K=0.6cm \�OF6Sthe:k� }{\a�Sc{mA}.#ZPop g-0.8in 3 tf5 22.5{ text,M 1normal�Wz7�v=AW >^$"tci�x.tex �Q���J Yuri Ryl[�JI Dirac*t�"Sly re�KvB$c?} \date{nIPr�� ] s, Rus�Vw[emccSAcc�x$\ 101-1 ,V� dskii Ave�:0oscow, 119526G, \\ email: r��@ipmnet.ru\\ Web site: {$http://rsfq1.phy F\.sunysb.edu/\symbol{126}J/y.htm$}\\�� JW8195.208.200.111zN} �5=J �Z}�6y, i.e.� �<-*$\�Scal{S}_s.$thrm{D}}$,:c�#� free ZQ�xinvestig. A�K�n2� .-wri�_ us;(!�).5> variWZq ���B*�#.a, bec� itscb[8+5nch ab,e oaf�u$gamma $-ma�+es $ ^{k}$,�ing a�3rix vec%&Byn"�panr��C�x!Wk"S>�,K�!� �u��$i<lik�� $f��tea<� �de!b'2n 5split h�o -timNto  �JsBIZ&"�`� �non.� wcU . To.V �\ vio�>o_Mf�2�.e, w����y/�l�6�Z^cle'obA3mGro�<^Qwm�q �.�U�di�# ntiz�.%���% �1� to b�mpfeOvq��q�:eeE�a�$dom. Six t�g)nalJ&E�Q4d2�e�(�4 a re;�M�)A*e�!\%�.t^j��:Am��r �ET }% z. Coup�(ACU�:�!en5Q-m�xtuA9eSg%��tFGI">9�r] J��=��mWmiGhlyI:�cea�{!�u�&'�F��E�rm{% m �be�#%CMNlet>� �Q���!�r ^(a�� solv�S�\ :�>�Y�ndZ�.[��].c-�1@ it{Key ds:>� ��qua� prxq),proof1l^� D :�m�"� s��Y :�xeZti�`�2Zty >$>�o.x speceI �i�A\" % "} . If�!MU5hH=of EYK ,"1 � DB��%�&z) �Up�h�%���~ 1= t. S@ �/���x\<6\� : 4-��% j� (=\bar{\psi}*a P $, $k=0,1,2,3$ , 4-p�`CSAiB% 4D_{5 $:O, ],ar $\varphi L b$a$8of �r=d"�m� $ m is ne�+ary, i%�w� to1�٥analogZ�ɚq�IUp�^3}}$� 2004iI �= L1�M1Q*�b�e'5�[� ��� J5$}}:\qquad ��A6� [%�!M},( ]=\int (-m +�(i}{2}\hbar !� ^{l}\%4 al _ si -F9 $ $F�F$si )d^{4}xІ b1.1�'�H�+Y ��r-�DonxM  d�nI@`^{\�Y}AFa�Mmit�fconju�>:�=2I50}$uNF one.�1^{i� $iyv�$4i�4$�&} ",  !sfy���K�:onN=� k}+  ,l}=2g^{kl}I,M2k,l�.=�2B�wt  $I1G#&t2��x�$ g=$diag�&0ft( c^{-2},-1 \r�S�%� me \ s"5Ck !:;^ a�,��choose;Sc�U8W�4��AT�""T!il� $c=1$.J �4on�~E�)�tes�Q�J�imG1�A��qamA�-m =0 [7f1J�A�e"RtargXal��:�4-cur� $�$�pz clesL�>� te!~ $Ta���!l;!�}�nQ^E�W�@(�X% Y�k�Z�6%^I�Z5X;si QV=I3B���QS�-�%y�R+�nG!'��,. ��stPC% $:p,< wellD^k% 5($�$atш]; 1�j�� (ular, itD� �aRYH�3}�XaB��- �1>��Vo e� ��.71I|2)u, g&*�ٖ(7��f�%�a� �q6�&"v �,.)!NfyRe�� (tenP1� .�!one�g1i�Z� ��D} p s%�,a�O:� �:g*HB��de� Lx�/)�Ju�V�arrow _{||}�Dj ��} s}j_{s}}%K _{k}����X��\�Zɭ�2f�eWal }{ x�&mj : g_{lk ��� b1.8B��Nha��h;%� !I1�Q22A. X8���A� 8-�of�/i�Bn��Os.P% ):�%alt �3Vordin}ZVW&AallB�sD  deriqvv��nl"�di�wof �� E ���/� i 3wR�dW�min� set5world�Yex �L}$ t!FoS.~:-�B�(�)��2)!A���� a�W�L�I.� gi�u�t!�)!0f&D ��&L at-9׍�!�2r_{1}$,� a 5/� m� ��R�&� . 2�A �F.���0tCf(* � l!�25$.:)$: {B� " M��>� tur��9q.9% *qu�Yb�,>�C _b�DDE}% [ j'�-] � �� т��N�`)Bha�C �n}\:"�e�ate�6tem ^Pi8+8DO�  � ���#vk leadu!juniqu58w@ngi5!��>+5!zmKd� ��"t!6c�)E=2 Ib-!_s-�two l�9ovat>C Q�r��:�N��F��% B�can� b!F&�. R�"uW=��?�R� f1^ � anh \�,I25��$o � . Bun " �of z� \["� :� � ��v i_) Z) ?2)R� � � Vq �6HV) Fq~=0 \]�toEB{D�572�,���M�Car.+��er�f!�2U8�/W,eż�(m�5�s�3 b�bU�CT���no �U.P�m ��to hi�\Y��j1o[/�!al�Á iszJrE�� � o�6�Mby%2#�J.�b�Y 7tful9�nX ��z "^ �BX $aya[�E� �� ;�7H f�,�an�1v]1 :U�����${6X~�5���%�e-;��7 b=( ]�p,ifoN? 6�$e`$).&+~A4A�J� ���f the = �p t_ń�_S30,S5�~SQRz�c�9�a"�!Uhy i�Nx} ���co�M$x" �A�I}1��i��E�`b�"Ba� vj�&Gy��pO$�zero �g sors_9�5a��jto� k6 fix1vF� v;e-wU . Uņ}7��>�- �= ^{0123� &T0�^{1 2  ^{ &�9B� F}A0bf{\sigma }=\ � , _{2 3},\)-i � ^� � $�.6�"@�f1.10B�w�9k�7�X ai8RU!�=Ae^{i+{91M�!v }\exp�a.@%.�:1p- � ) .B ni\pi r-k% -Vn8Pi.�1Fs\[ ��}F�! q=Am.�-b�>� 27)NDi�%M � <6 e^A5� xb�2^(*)�A Her:Mi�8�J Pi = �1}{4}}(1&�0}) �z �})"�}% =\{z!alphA}=�*{�/t"�\ =1�;�FaE=1�aF)i�X.�.�+$A[M� )n �)�� .�4 (na�nB.� ,\;$"b bf{n �:��&�c~~ i���:p%� Gse; R�#�&tn�^���,�����%_�;nt�*P%�Kc1t .l�&r�+� $A,$p ��et�� Bw5�%���3I]�S>_�'*�U!�flux &��N�3sU9spin :�FoS*���2��A""�"02 3aB"B(� wo �j=Z�S[ B -�/q�.$0�Ula�a�4B�6Ce�*six.0.� amongm2 Qj 9)�&%<lQ�(X,U  �Ldetails� � ( )&'q���j,�Y,M�,�A� xi }�E��L}Z1b= _� A�rm{� + A&�q1}^2_.)�c4.15B�F o>b|=-mǜ -4jD\w _{i}1� % )l}}{2<1 �-z��?$epsilon _{�X�rr}!K� }lMQ }�iDU�� M�\sqrt�lI��\!$6�$!�=2)$\sin �g(M�)��)}{% 2}}E�6��#,u��7ޜ2}� w�� +j�2)�!�>~Atar �=�f}j^{-y }{(j^{0}+!o )!� ^{1�M �}{26�N�I � y(.'0� }����M O!JF��"�` in w�O��uhL�^is��pd �s]H�Gԓk �Geӆ-3)O6& Lati�Sdi& 0-3)CBgrwa�a&�of>�N�%,2a �}� T! 3:R&e�m�Tw ' conn�J� b���"���6m�{A=gin*� 6�=E#^{-1}�SYXM*=�SAWa-:a�)�#-�:W rh�>�ve��'B��ˊ"��� bf{jוg� ���%(1% ?)�}{�+eIY2���6BB!��=%w\{��xi�xi _{3mR\}$J3"�(�& % \{ nUn/nO,)� P*}11}),��ef�2})3 A� }by m�.cNb��6�s=2n}5qnz})-z�� a3.2Fh A�<h�-  �D6}) --8��w l� ~(% z:�k'!�tX7}); ^5ie2�-�*��� y9�-�EO� e; 6U�-"�*H:F�6})mree-d*)�Levi-Ch�Ba���$N��-�j "�qc2� sm�2+ A 4ց$iklm}\;\;(� _t =1)$�RWdsA��t�* imel�5er�% f� =\{1,0\�T��E V�( 1)% �b �$f^{m}$ do �vanishN vaB�2M }=-�% m p"� �W,�q,�X�m��b5.J�A�D�sub���&�'<)A�&�}6}H!ToeR(8 D!�ɒN��d �emX&�5�&� %�$Jif .�5d2J-+!J�no�mS]�t�I> -�)�-�}$%rB&muC�210ZLQhe fkW.Q�6VE�i� easyPverifY-yj.��0!�A:be%��6���J���>� B F� ikl1:��(O)i}+%����).� k}" l+l +�s}f%* � .0^�sub 6P �+ 0-3�j� � �| ,1, . Let us%gy�*{$15��ɭf1�^e�A:H�)hG"aQ iderz�  $2��,�I  B� DasZH:~$ Ek6�Q ,E(2[:�0~1 ^���8� 9%J4�'b�x��� :( k*" k lAcg :paH:-)"& "m2;.~Fbh �)( I��f=� :z)Q) -1V��2_E�� km�  YQё�� d2.F�A���A�f6e3yNInu��-u=���� Ll}!4=-1.�F{ I� ���'te�5"/22` d2�+� �T&���$*L$rmM�ź6J$�a1=0% ��&1# i��� � s"F�6LN�� V�3AJJ�q�1�p�/1"q� Qa �m2�Fi )U$qA��A\ ":� g2.&0+k�2k�2�2 �I (�M��B� }}% q Uqe�2TF1 A�5ously,� !�A+jP � �q5�? " ;X� spac ��( :�Fz!F�_ \{ 0��#\}��( 0,z�z�zg-5Nz%-11&E4��z �l0l2�F)�!�^KzI�-ed. U��23�+� 9vlV&f c . e�7-�� JE9i��z!�*� !*&�\m8�� Bz=) j^{s:� �B >i��"'-7 z@�� }.}s2Ek�Ea9za�M ��} FMOu;o[a�[ 6��z�� ]�/2E Ձd>� �i!�&`,&v$*�-�'i[,-0$&virtu�#Ag a��2� )r��i!���9=0� FinX�.yԂ�\m�"i"�!�@9�-( l}+v)�+z)}}=% V< 2(1->-b+"_%qz[&�%�bB2@3a� Z�����ރ�f�1�y�s} k]\ !<6B; Nowt!@9>2�%��5^' J�����S*�D�J;j������Fg��J�+��%��=rh�B���C�C�D�\ (qO�dV )��*O a8F�f7�?2Z!"� .w!�� 2��J� ,� ^*� "�]2<� � �"k}$% �= ` �"6" s. V�3 G���\ia *�!#4� �  6VA �� ).>b!>"BjcF�Y�"�s�o it �=!:!I� ��tRO'�Hk�H6ss" � *� @(�6?E#.) + RGa~Q.�(AA9B���� fulfil�bofBH� 4!I�u�F{R�+"Dce} 1E���oێ��c�Ith�^�,i"n8&i.{a�*A2�,F� )� �&k � �ch a �ki��eF��autA�:.K$)���!�id�r \+B.,�*2"Ose�� &P1�.vag�Ae � �+�n�B�M�&�J�Nb�N�b:�Nh.A�Lo4>z�pp�a 5 ir s�� �"A67nG:U!�� or sÕ�>�E�*4-k�0�9&%��6Ec# vA 7J�xLqc�6N@ (w)U���.�"�6d}�gr�n al9a4ex�u �:�)��!��2:��Jy$F2� O81O8 =F-%NB��dTa=6I� s. HZ."�fAa6�-{GB�6}S4%A*RqsHq�!��fsp��L � k�6y6B:Z".�*tva_fir8Qi�uY6�a kB/E ,�k^���cer�hi>�P2ZL3=a2��6."f���"$r*� ]���p�!YMax�@�a�!]g�ro"�i�F^{ik��vinْań:dN '&( k} Jͳx��=4\pi Jd"8 &� _�g^{jm.�jOklFO0F |�5�!k 2�=H&�a6.F��99F� m _ d}{d�� �[/l\\dot{q�C1�i}-���-g%� >  l_{jJj.J2s}g_{sl�]g� ] =e!�5@q�g_�>1k}� "�F� a6J~mk6�dr}1�� b=�� D.kG)4*�euap<N {hg�z�cle��u��--� $%�$>9��y $%e� % ")� *3�N�,J5�i)�=1&<a6J<A_a�b�FY��u�Y���FR �M�� to2(+%v�A� e�l�) ga� HXit rN�o!vngIWaat �Nx6j+& cW ani� c�cs�t��66�^-�n r�% �!��If![RG:��v �#/v� 9:-(VC�Rs!��* Ub�Z:�,��$O m t e�� �6 �!�3B� &_ !�en� %����2!���Yy�� two Պ}���s. ��rncC�#�UC� �-7om*Zd�� �� 25�1Zt"�2at �&.8bFs�x.2x:r7 % . � G\neq �a�$$\tilde{J}��$� A-�y 3�J" �9d-,.�#W&C r�6k�}9{B�au�s482�x}$��*��&1���)^ os �D�� - n&�Ad?&�;f� g--E�i)4 � .� 6+ 60:�1��C%Ti!�}c�:}Z =)v-�!��x4 2`']��!is im���%bo�awŋ�_� !� how eac��M3�� ���a~a�va�7 � ome2,YVs. F� �^AF? \�9��V�3�No% b� iSCwow4ts:�3� (�s)\+��! F� )�!�>��Ic� g��LqS~j> they�I���D!T�>Gi�!�FB��#rea&.N�a�y2��gE !rBhM�*%2p6��&_.�> � :( Zb B1nyD y��Tt� iblei��&�U!�q�ty . �B� >� a�� P �� 0e��[�� g�E�a� "� � l�!?*5roH�+� $3$-�t e orthogohy:J�>e� � Z�m@QZ�4�[�Q $&*-zQ"'T���F8all"\ q� �&I,>6 �ub.0 -� �(���)O(). As far a�XB�)6t:4�l�  coin��{i4�N# �M1}:[n>�(<�F�]�Y�b*O1u urseS trY?�� ���iD&� w1�!!���X2�sr-�=> l�'a�� ���Yy�%: �*w/�B���j>}��B�/� nowBGI=�a:A� 6�$x$!�G � & 7 !�s)"��*� ~s�h.|sE�b�@.\8h�� ���+|C��Q�01k=j2ako_�IrN�zq% l}yRd q&�%2S�:,� }<au H(�� Tjj��BRjR\��'� *% @�6! E!}� I� F�&� q *)� t U*�J[A6$ ;!ki� r�qz� Yu1b /x��I% .B ^:�ianU�WA�5 �KiGU�eck}=E. al x^{j}/�I�3n"gfak}�c��Q�*� A��9�*10}) �|&% a 4|���<r�C�.66 �5~N�� �� , al�{gh� n� >� N^��,Q/6i. Serg %.301t10"1� .�� �)f�lq}{dt }&�%=eF_{.0+�%)�#dF�%�i=\2�)21FcF� e�mx/ ^t&;v e�� })F� N6*&�7i=0&$a6.11F|�"��J16*>)>�;� � %�k�Ip�0se� �0.e&aB�mo� �;T6\b�:�t"� ���J�aoorY�!�6�i�F1:ac�S&ijJskj�DFUjNewton;*cAny)lane, &� ��"� ���51� s�� tane?��X�� �{T�9����EdR7�U6+1})�R2Q���&���z�'.��|hZ��C�n�cal�]�"> |6i.�]%�aM�is �O}U��-z!�)i�i�! am�Mh $t 2�qIl�LF�k" N.��TyY'�epq%=�Ei��Ity`SPduL7�nu�vof��n1"d ew�A�E;5��.��9Ca.�"in h�6:)z%$nd�� $r)-|"�,x��z |,FaWon1� s";���� �)6�P�%�z&�81���/bf�aL6Ps �] a\n&u�6� <��� =���L*`a.G5~1�; �M�9��re!�!#B�y:1��p�l $s=�,%5a2}�m-r�s�a����oc���j�� $�I \{ t"//Y $5��{pe1�� (.�N �M��35.���))��6�p*��u�Mn=�.Kz_�Y�y7Y�? Y��"�#le,�>.] ��!�.��a�usG"d�t�[V��õa,�$we M�>EB�n. ))�V�.��q�B�R�{6!&�h.|Of�!9]P%�H:7�$s��2Q'yUyCs:aa6CE�i�ce $rA�o� bu�s:�w$r$&�2iu� [X�XXi�.�r�H!az�kyJɵ ( �|=1�����isӞm�Y����admmZ%9�s���+ �.� tr!(+Бxx5 [ t=e��� r��\�!��2}-x[9 c=1� r�ap�T�gM��A~Fi�.��X"�B�a��yaA� open{��ic)��!6)>�V�u�to< eory>T�zV6V.�<yM ���fic�SX �Che� �. O�aEr(k(z 6z:�&�AZVNaii�.� V^� 6f6�.����2p>)~ly�2�of>��a��mp� Tarcheq,N vinc�v%�Ax.q�Z��>�b�e!I�i�)Hz��B��6� Z^ can 6�*6w�]�&�2})���*d�&4�uco�x:�)�r ."� . upm�xy(I�!m:\�H��&�f>��j�*x?� -D�d &�4>a&�`d� )�o� bAi� �(��6+Z)�E'a5�&�o�H&�� s����őli3�w!�� [s"� *�fy�t�E���7 �I�"6#Ofm&8s �W"h{"$6� ^z\� *^+�sm19�"B�+��g�@ + Mb�� es�6b�.�Xi�&� �b�o%+4+qy"� � a���, "�Y::.S0Q��]�Ia�R"�_e�Kf��of Cli�d� 1laJ�R�n(xE)\G]|�.�V 6,�b1J�>�$$ A�*�&nilpote�ora@.�`y%� �F( ��=a $U+�� �) orbi��9I� $W9�$a />pS,o-yl&� $F$. Wi_0� nY -��2bVsGu1edy3Q�a��)�& :�rB?&&�$a�fM�y�[F�.]l�+sA�n"�G^�.% E:7"� >��)o�+x"�.�bes@%ph{i&�����-�_%\��conven.al)B��,N�pin��G 2�, $"�T)�1��*���:�MX5����M>;6��.S\)�")}%�-N\0FJ�*:O. >��#esaea\waA��l��{�S�5d�$^�i�t==�� i��/wrong.��z\w.� , So �f~˥�{H_2��:���be0brea-� ble.�BMNuM,ny� is r���t И2�� dardN 2Y� �K6���BE$T�Hnde� *t�I � E/ j�=% ��}u�<:�CJb#(\NR�v{7}� P}h*jx'= % x+}*-m�}J�s �, z6b1J�Dɗ!�*� } K)�)>$�Nu�ed*;m?���`2� �A>c��d �`XwoEerent �FM1:�M\;--+����8tilde{\overlineD{\psi }}=\overline �% ,\qquad \tilde{\gamma}^{l}=\frac{\partial"x}{x^{s}}% ; U�l=0,1,2,3 \label{b1.6} \end{equation} \begin 2:\;J�� �Bf7 psi}% =S( 5,T) >(:N'S^{-1}I,.�7��S^{\ast .D �^{0}= Bl.k8bBlThe rel%Ms (\ref)h�) correspond to the first approach and the J@7R@secN0one. Both way6u T�Flea�sam�way6"�0wo defects. FA�,�:\law of $e�4$ depends on $ �4$, i.e. under ��ar>F@$T$ of coordinate)^(components dare@ea1rough�A�$�Hl}$, but not only t62(. Note that �ensor~ in a � systemB�2]a�BJ in othe^� N,� this�I� does�conta�8ny absolute obj)�(ainstance)��H9�5})). S�7$ F$9}) is%(atible withD2}) �%� 6s%�Dbetween orthogonalF?s, whenh-�8$% g^{lk}=\{1,- \}A%Qmetric1XA Pinvariant. Indeed, lhA0 !�F��(is a scalar � anyQ�9�>��reas rb6i!� �.=(��):� s. R Rn�� ed a�M_%�F�FeIn E} words, M��Նn�M� �,A�general,I&��ect��arbitrar5[>*of=ns!� e case�� cana�be sua�q�symA y groupH�dynamicmP$ coincides �"F8BG �faîo Fo �o, was derived�upposi� a�at )��Y�:OEĉ A�5ledI�via its �U. T�nBl7(violated inoM!���on=� ~�6�F$at��J�Aft�%hange!�Eqbl�ac!y�1��.�a orm �$c4.15}) -- 98})!ceٯ-��4ces being elimŔd. But a� redu �o�� � w�x,vistically cq33�^newB�a� ear:!���0t 4-vector $f��$�&co  4-pseudo$z+$!�e V bs�b� ct!�us. Bu� ���re�onB��icha�em1� �l_F MI�4idered example-�a6�� . It mean���� :=4$\mathcal{S}_{ rm{D}}$A�non.u0, because it iPes any�separ�a-�0space-time in-�%t� . \se%�{Modific2Fclass!� Dirac� @le} Not all term�.T1n]�aB���F3.AkEwo] moѮA�6Pand�# ~7do��pBlF�6�z� described%ly�}0� � ly>�A�. T� �ine wA2is W. 1, i�usefulA� investiga� e>� }iclb�cl}X weQdiscrete:�, � ��:�hav�aa �  number!�-0freedom degre� The ^]^p��d1-,d uniquely b e:�^Jagbym�i12�>ced�I�b1.8}a�5i��:��k�y�-|- �H13 Y :AE_���e>$MJp�f. ͍1�$disquantizi�.�-J�}) we ob� !�f� :E�z�% a�AccJ gA�cal"�!�R2004} w- �F��OB\A?:��~A.~"[x,+ +d)}�,\} d\tau _{0*3Jwhere* s $x=x, tau D W) =\{�0}5�x \}>$x^{2}3 L\} "� :���epit��ternal*� ��bf!� xi =">�1�= "\{ /_{1}, 2  _2�,e&}�=1$�(*�to un��e@H�W i� ty $]�=\pm 1�ji�� r\���ion6�of�X���qv��r$� �C��A2)3 �written~ >&� " �rmi.�;A}>E�[ x%�Iu] �{�-�i�P% \varepsilon _{iklm}!�� e` \xi}, f^{l}z^{ma�(1- %s}za� )}+%� ^}{2}QN[�g�� k ] \xi `\}e�e ] f5.1BwBZQ=Q%&( i,f))) M1}{rU�&a��f_{l}+:1l)�� l}})"� s8\equiv5ddx}{�2�2B���� s� , � em defia%ivelyVI�o0 {d2� ,M�d2K�EFA)�3X���"��"oxi�%1=0 f5.2aB�.��p� FJ  (see Ap  ix Ba��paper o"� 2)do� i}f*� �2Eu�"X-s��a &Xin� ent �h��%JqI�aP�tau}_BF%�( e .).2F>IG$F�K� "Dmonot~��. .�0$ may be chos�su^��J�6�sy2s}}=12�cB � � value�:� =]R�. F� ^express�$��A�c}):�a��tegralAZ�&�?s��� J"�B� term�*v1IC&D i�&� 2_B��:4�!��r_�m7*�  . �l�<�n� Rl% i4neyi i&5 aD�p�of, F,:�:a . Ifm set $�]=0$!a�^2l,.up%�ryy >� "- �)X�a�� 2:� $( omes:�%:>h "beF5,A�65Q��dQ�M�. e*�wee�i��if� unit�lik�x)����c- �,gy-momentum 1p�, ne�iz�a�per�5 . At�D � ZZ�~s turn%�oGmFed>o5� % e .�m)�a�o mak��6wE�roduceAignF�y��=*�&F4 f5.3B�reu �:є��p ~ Ašm yo ,p�r"q L ( y,�y1 : "�  -pL /!"-3 l�� f� ��.-4B,��F��� =.; ɹy��}% 20 N� �� ot�Z. �. ~ ��^, y"� yT nm}*b �u"& y5�B y�y� }(�� � %}% )}&#"f5J#"Ve s �l}=.�"[)�)�$u� �� Lagr�(multipliers$i�de}��p3})�q]i���� .F J4(t��%�$varied. D "* �j*4})�i�:�narray}E � a���B&}{ #Z &=&iO p}% A�=0�u%{=\text{��2R8a} \\�wEwM���6"}T '- $d}. *L} �A�lAm�9=02s9Ҷi=l ���:"% V�e�s}��GšaVU�u)�!�-ejf +ss:=0. 11�E )����|-%�2� 1*� Q�� �y�� uy 11}) take�accoun� �6_�,$O � };E�rai�")V1=-1$,��xi�=0$]s far��y$J,2aice m�y�? canA � �ant' *M!�"� :�(%.@)��p�xpA}}$�m�2�m�sgn}p#42#8B-Ysubstit�"$�$ from=�8� _>_ 4�[WezFw��FZ : �#b}� e'��~a bf{,va�&�,�yva"�f��) +"�( B;' b�1F�'eU>e 19})���sU�'%j� �Fd.nguishe�6͟l,)�� Q�RZ-3� �Sr3%yrm-�� omp.�$w�ty prV"pl��  (>g �� .Y ���"� �(i0as follows. LG% %��:b�be�$&>JUs,-Nted�R�aq$l�x}, . t�,xi},% pMR�have b�%oed)�WxR�y m of somB�"�C%�#%�k(�� �x�:� "2��.=!�s+-� "2 . S-e� �����"k"f5.��) %� hesect�U��llF\=�:R��$�§ excep�"% A5��q�8*now3ZZD Me~a".- �O". ��}=��&@l*��R�A[�\� Bn }/xR V7f��M�] _{f�F* pN���-OZf�/�p} s s�&��):T 2F�+ We�&� U�!�%�R7�@&`& �e!�waBG�.>[)%�$I�*Z'"� ,0 �\}"�*1$,&*d2F}y�� ) 6�canon�#"& �=�9@ b&���D)j9A\{R�$ .�!9&�&�R!�ich&*"�vv�$��4p �,�"� $R6"> F�O bU%  1f5� �� well^�V�$� o� "�a-��y!�� solP)*ly1@1� f�or�20F I}J�!�sKs��$.�F]B%&c��th bf*�l}:�0%� !m21�F21s'y+nvenienc�is�u>is �ent �"�Amhe.h{e6g�A�:�� ���Q�h*Jm}{90>*X2�\ \zeta�.T 0,z^ z�*� � ��A9q( �l,.K� B}>!=B� 2J�"�1yE� % J*� -,� �-1( cos \Ph���62! \sin �'2L3}O^�k��\{ 0,-3z\2&*~12��V�&&1#54��=M12>�:BF$-}"�+\phi&d7�3��d`}.�zm�#A�2m2[4FJ4 �2hi � �$ ( !�\geq 1)]&ants. SZ� "De��0�,M4&(i��)0 -g'e�e�v&E'�!5as"� $!j%��segs���gr� ( easily. F��7J�6��e�G'�w3f' ing� J>_ "� .�Q!�%��2pJr_{piki"�5a/ a�jd" x[6._>�"a>C���"i�:�s�s e��)~ �$6A iksm.{% ����F�A�2� 5B��KR� as"AoriginalB-A� are f� "02G *U�.� \[ A���� >��.2B�ml}=)�% �db�  rx�" $�6� �.?d \]��! hoos8c� en>I%:j&~!l1atJ��E�:l!6B4��J ZfpAD&�2�O��6�s�� ival��.JMa�M%"&"=12�26F�"�0����4�TQ$$� �>�Z[9�:�*��� ��N�) .&%*�!^� \neq,�9nt"l,a�i9� pG  U :��0"22��!ad�4al�!� � ":6��0���:� u� ��ef�O%���&�}�Q2k:&�?*�ei*i�i}C�( �m�=\{U��{l} 0,?;N4 if\ \ }l=0 \\-.�}{L|�0 a| �:^@ \mu �, fc\ if  }l==z@l@ � �c.22 7B�" " r�l0+ >�� _/$0\alpha \bO ��0��� � #}{o0}+1)}��% ji RiERd0ti ^NiZ�y^�:� N!=�> 2f��| ��")��� \no�2\\ &=E�9E?( -=h � �2g%��)��)�+~F ��/>F 5F-�n* �) �*m-) ,.�8^ mu� e 5LieU� �1_-�2� �X��0Levi-Chivita �<�>�;(three-dimen al�6.Xus.^��76�8B!"яVt. W"� +9*�2��<}IQ &vC�E�)�"1"�Cl � I�-1 +1}.t� �I2�I&A>I3}6�3�6NE1���*�5�� =� 4a})H(nst�C"�7� �7r�3a��2�-&�D2}-m�-/� -1��)"��g%1S"�+1U�8=2 )K.+.�3F8& �3 $t=x3�(E�R� �@-lc "�*�3�" �toN���.�Cdt" 1y" �Ap 2n ,:�0.�Z�.IQn V+3&+�Ic��g2�GEt=\O�Dtr��U� 12meX�� �!�6�F� I�,Q.�3� �F7/��Q�sJ��E"t,-�B���[% . 2K2p6��^�f":2 ^  Z�6B�G:d�,biworld�A!A!*m�(*z e)4 total mass $M�at.jEzb i�@�dB�F�Be=)��!Z-  bf{p-�:� M�% s)x"� 32sFP W2Xj� �da helixM%�radiuN�a>L �ʯ �S2�F#;D �#9)�G)�$tns� of�itu�F �7F�.�9f�,%��J� :F :!/M�p�A�j� �& "�3�*�3$`an�� �I;F�x9�,�vr�MxE����� ( \�G:_t�f6�M�2b  \B�Z"c*� 3F�#"Y �HM=}�% ._M�N� ��p[ �Y J 92P�fF(͒.Z M�.=<6:.G4J0aH�  �IszF6��2"|$.�$�EKe�?$a"R;�`F�bPI.f +B!� AI.%)C L:�23FG!2:C"�I$�)���$�<max�Mi�G�?�GFEsl�M����# �=G)��differ�rB~-� �M�IJ) iɢ)%" n'F� #minimumjI��y< nd n�1x� terpre2���2|Y� �%n�^�$-2�j2k6ERrm{% %4$2ABm/vz��as&=�5O6 rotatn two couplDicl&L7�% m�$, 6� arouQQ heir &c�r). C"dM) �{(1)�CP2�#!3��citu�Nm� a md0# p � B .9�.����.��\{ t,aJYt��)) $ 4�}>$� *M4.�! F�-�� �%Z 4&� 1e� �, , $M�T�J�:iJ<%�� �P-� �d}2� a�4frequenc*8^8�<:�s�64124� �.�1aL#M2�conne8.�'�J�M��2E�61-a�� V 6� 4F� ��m;P characterm+c5'N�azd< x; �-�'reJM�a�0e"uplP!n1�.Z�IW !>:}Jfy� r}}=6mam -HM-1J  1% n]-2S 4N� !'>��i�J�O5DQ�I�$a$. GiHIig:tB>iw�7M�!5mB+& I�' %xe�uo"%�Q]�ndQ. As aaTult\�+3=���� w��E�$�: of s�+�Km��$,.J> stat"M:. R �s .U&� �(a�&mMz�o4R"g�%�ŊZ'��a6 !%/��V�_% }!!�M8-U"� O $. I�i.�Lj3}*P;IH� -�� poss.T,�,<we assu�-�!� >]�=%% m�v�!J8AIf ��V)ID� b��%|� )/y��U~�v��3 forc�Vo�@ose� Q2�!r �!Xr�B� . N#phy�Nviewpo�Iit seemat.a'8 �O=PvGAE.=oiK(QL Y�:�!2���B5%^A&%�,�K1N�=�� !h +%36#AmoL�-0R�B�N���e�.Sa��T,�Q�r'!�A��%uI�A^Vf�Ay6� . Unfortu6Yly,l!n+?�P disaHNI�I�l�Qn��a:|��&� �#&�+�+. O�Der-hand,I"on� ��p.ja+�$!�f� }$ (�Y�,2 )q�Ssit�,F���� �H�W!+uch, ��2�=m/Q� dec%X>!4x velocQ A��u&�^{1/2� +"�^{-\# k ��i ��uZ �-cJ !XAkinetic �/ bearer�I7Ra El#UyM,� � a�7N[56H 1�"nd��%|&��H"T �26q77#![Z�0(R&�FQR.�T",8m�2-�6�9�}�2� F�B�R���8m=� �! 2eVKFs � �!�gΪ�� ��(1"��4aE�}�� �}>� F� F�:� -�"J $�:��T2G8 giv{Hmplici�0͹U��16^a� �4)) � 2 :^Yz!.j3/2!D%b�tf_�r}2?3}m��6�>i.�5F�T�mp�$ALB�L3f�i�~�w5e? �i9(ɦA� re�1�Yf* � &� ��2�^�%�1�#I��a6�5!o6�  C%_is��" 5!'�8 1}) shows*at both5� &� !�close�sm�J��$j&(0da�ults? O�c�eA��ed inc�gc��(:��M)&� �I"H�ZzXZ.�W. Energt  levels,�vpn�� very high%�ynot ex�fda�Gproces� �]<} #'M >�'�theorN7atonaE{a�>�<| v �O39ignori!n�.� ��u��I7rr�Y)ȞJ*�N#Kanyth� �-BN >However�G! -*!�elewLcQ��C� A�re%�!�M;E5ADshould�D!>o*�D�N�N.O~�'AtK]/ ���AቐA�. U<h�?pOLuge�K"�"�_b��"�g!0J��S1>fJ re�e$b�[tgfletrT.�AV;^ fect1cbe*�a also%.can&gM,�.w[h.. ''MF''�.; �9versal�ca��A:t ���al en^aݹE� [&B?.{!�� ] $ -�)�jgNz�. /dE��]�TP^ . Be�I�6�e�}UG"�>*�'a{a �wAhl�VA�be %ar�6�v1925,ipI�8� �_�:`pe��to o%�CJP"�1�Q��spin 1/2�he best9PWhyu�ACo�btenes<=Q�t2Aearlier?�equ�`on!x��impor�#M7�q e�>.�# microcos�S�`Lst�7gya�bswe�ra�j unex���d0 :! fea���:�was6 1995R95,�#1}62 soon�G1bnR�C)�!��ad sa y7B�.Tm�a �.xMu�2�F�2Kusua�% I!�!�!�?Fil���~p"?F)r  �tri�`wa�lJ  �Ny dem��"� _:-aL R�B�!'"� ��lq]gm�?�De��w.� admikVno/2��5 vari�\s (��)�>�=9a�6a�]44@ �"+a"� ��#�c�c!�Yoio- ye �to "#h&w"Fh��a|dne� a�( %�AU ���*JL�of�;$. \bigskip sAnewcomA{\the1�}{\Alph{�f }.\arabic&�/} �:@0{"@6H} \setHMer^�`% \;!A{\L\bf M�n�9�� Wces} &kg�C�-+]�\} ine�jm!�o�..g%�VT�=$}�/Q�/Q�/Q/QA.�vO�:�"k\���-Q�-Q A.2}f4 {j,H%�"+H�4�,Q�,QF,Q+ ��Ol}0:u k "B82�GA.�# F�k8 �5&2HI=0*A*�Vv#�1�<�B" +y^.T_y` *�G�C/�-"ud�S�.ud $&�$�)-�*�_0I!166�N}�b�f�=1�<T>(�p$l�8 ;FBA{)� �#�X&Dc�]N)c.�Wm�y5��*Q�?(�>�f!�yA) :9-�q�Q}y�Sy}_y\,! ]:�fQ��h:�T�Q�QN�g:�y}))��: (p}*5b6J c�JC*�WV �%)>y�Rqg+E�� -&b6J�b�$\�R�Ad��L�p$�^�9��2Q GUU5�1V��X�|6.1F�>a5�\u3�P=xZ7+1�A}�A<>=z�L)pP�^Y�/2�iz )}+}I� f{-m'6�{�%v5)@:�"jRfu;de�q>FZ)�z}RS����m%z��Nk:�5�9)!eya�t%B2Ea�Q6�F#( Afte>�y+"ALi� O^"@|L �d"&J \ B)J���J?}=-5��2&^�Q��c7RX�R�b3KfzF�!. "�9s�o-s di�B? K"=r.Oz2L *��q�qn��G�0 8>�� is f��,!�r�e!��zlongitud9Eevt9j�J�K�N�t�c�b� � �%.�1*�#�rVbf)mEe@�� �a6io.�n� -?;"e� h& ftAe;�H6 vali�!/���C/!ZQ N��Ł���C<�� &�n�>2*�AJ�^Tak\�O&�Z��B �<.If>IIN��)� iJ^Q�$5�Q/ y_{0}^u�y}Gb:^:Q�1}{1+I�3��f.� )=-110��% R.q�y}} n��2 |(�:+ ��y �.��F,�M��� $�j)�j@*un5|1"<  r c&> bJ�E��)�% k}9�.�7J�B�.FM%�+��"% 1x�b�;*)+��=_.�p6J B��e 51h> ��NA!"!:"���)��EZ Bt >PEr�^)% &4��� �dM:�y})Yq*e6.F$ E8q!�a2*%BC)f1rivial&�p9�g9W�"�a�Am]�-}{mtQ�@G%<=U��=NBc�:4}2&!�=1Qe6.�a|>�%��tva"�]�"&L,XxRXQ&xR"tPXx�mF2�}�G ��.u �% "D_u�e6.*�1cI��hJ!�nu �;�/5_� <�. � �i��ghtx*A � .�UF��y��K�T:?a�0ree 3 j�t^ $,�bf+\�/�,o"Ƃ *�2mselves]�' }2�y}=U�^xi bFy% JI�*�'-1ME�},UAJ�To�v��ou�-U��!��o{i�, "�E�l�m.J��6�e�Bk����v���%���N�% ͑}��A.F�( U�+"x��w*�� �A�s��3��Q����������]"��GM[5�Z�% Zh�[B�TMB��)e�}���1�C�{mndoux��!�Gu���I"AU)� binIit&�se0P� i"b$-(-8-0M��>! ���1� E�b(2V&4 yb=q :oE�y�� # �2  B� �:�%�~A�A�\% +*(m1"$�.�F� IRJQA�hX��M ��)ٶ� %.��y,#� =�� )�%G���V �;N�$*6FxI�� sR�&�Z�>�6��R*1F�?!�mb95|iowo�*/ �QT fulfillC!##N%f 1-zY#Ey{^� 1� ?:z2O1&g=�aAAIv:� �\ s pla[��8�j�rd�P� he %RB�2�>�AvF�B3+I�>�F�( }B.�=1$�J�&!� &� u*a�$). Di�Btia3<jM�u��b9.3efj 3"�&� "56�z�IYQQa�q�U"W1���4y�=2]6Rjn� s2}}�m�u[Ky� ��&�% F�*_ �TI'&�0 A.1F�=A&�m :A�eI�&e�<9��bi5f2W-�iw$�*i�D��7@12�0U<�>2,&�< j�h �m&\OAeZabe �. E.�5���i�1�E BN�5n5F�-�C~�-�M01�!�}!PM�j� "A6�6Fy5:�B�-�&�6J�i�:l 2} z�ͤV_m 4J6�F�Re�2��Ua/K�&.�2|zS$�x*څ�h0}}-22�.cJ� ���V;Z�JZ1߁�%C-(� �Z�!�v)�&=���� �2]6�3�$ �� s�@m=TW*=+^7})|:݀a/r�ThIa��r� *�M�v�>Q@[b�-dy}$K�p }r� 2-�y}= �-qz��q ?_xi=�2J�iH! , ei$5� =0$,�g�n^� �s If6 6tZ"^�!>� i?�Q�0�]0 ��N(3Q*��!ߵ`1�1A�if $mc �Qy �Cb��FQh6>o JY *�A%��Q3a�.OF� �0� �2�-.�>y-{"�h=0$% &�BUV��A7* ���71��*A m2�bIvu� nW2~/e o�&�5F0al �\-ikAr�2� tp2H�/2�_h�>� �� a��&�~z�b J)��l�,}\2&�[2�%&� 2FaXWe *�b&�K�+in2Aj-� j�A�"�&3j.�n��.�&&4��:1jA.*�h� 2�Q��B��M B<�i�� at��2b;�as"� �A1ry& (� 1},y�~�'�%�/�s*/ -1�R�XKY� C7S"[P.B +.},*�2�*�Bm�"�Y�[ &� yl�- �% u'�*j� (V&c�k.�Y"� J= JtjU�Rm��1�>a���q�20AQ@� Z�s �.i � A.25FC2�jk24 ��T���i�"Y &�. 9�OG�`Y�q)Es��b i�&Um�:�NIp)�:)�Ueqquad cA6�e�"�-g�#&2 �  m6� R���6BGZ�*A�BQe2[conclu`I$ �=$%�sto5.hl(�)�.c]6�"F! 7 � z�� --�:� 6�Z� ���� 56s%�:fc06�V5� %�"�Z6� 7B�>�)�aFeYaU2�e�tyJ<�0��Z@=F�6��J*A.2Fub86��iM#J����"�ILI2+m�q��&[>B� F 'N� e}�*YI� ?1>h�1�X��A.2F3F�29���.�-�z� &=-2�B�%G̩ ӝ�3F�B���&9*�O6})23�GZ��_6wi`"Y2�FZ�%"a �mR9:�F961-V M5m9���U 1�V? j?Q:2i.�&@�2� �`"�*d��B6)��[� "$?b����s4O3I1WbZ6V:�y 2�F� S*5�}y=&�$$5�9d10�f.DT6K�ofY��+"x6var�8*� protect�a $} .f:�b6��!�$(&5*�.� keep�in mi�S�/`��!c)���zzo /I� Iw��2!" 6z"$(*�z�g$Z�&.��z\ )}R��!z�/N� <"�I��)�/&�s%-�(2x��++b�(=B�#b��.Q��f9J�.�middle��uld� re&�y�[V F��2$��1�-R'��k5�1� p* #vBXz}) 15v*2-|R��*!�YNb}3*b f9J4�@u� ��+� � �)M� :!-z+!^�f= 8��- P^Sm^')V0V�e60FpN�Gj�n�"��R�.y��)/xi:�[>� ,-/9KK+}m� 57=�8-}Z�-M]�ę_�8I�^yQ-�2�_u��b�r �*t4 ��+6�"#��>50NQ"� -~Z�CF�orZ*i���sR���.~�&[.��vBp"�p"~8 Q"� f9J�� Apage ��Dthebibliography}{9 Tbibitem{D58} P. A. M.oC,1o it{P"]B�Q��um Meb3$ics,} 4th �",Oxford, 1958�`FW5�/L.Foldy�Sr$Wouthuysenthy�� ev.,eY��@bf{78}, 29, (1950S dS93d,E. Schr\"{o}B":I>dit{Sitzungsber. Preuss. Wip 1@. Kl.} 4(bf{24}, 418s36sB84} !4HO. Barut, N. ZanghiN�qt}.\52� 200 �842�BB8c:A.`(A. J. BrackR/^D23 _454�812_A^ J. C. Aro=}F�b.)9 1RE863NLH9!|D. Hes�F�VM20!W5L96VRV93} WE0Rodriges Jr.,�Vaz )DA�E) Lett�% B31A+62 �932�R2�� Yu eylov, I�8�N;cl(5mp6� e? (Avail?D` at http://arXiv.org/abs/�L s/04100452vA67} � L. A�xs.u6f- v�E S}. AcadeMPћ$, New-Yorkaq(67, pp 75-82{SeF. Saut. Zs-�ʀexA�63,} 80)330), e; bf{6a29)�:S5M�$Sommerfeld9�AtombauC $Spektralli"�P.} bd.2, Braunschweig�51.<S6^S.%b.� An I��$to�_hL ��FieldlH$ory. }New 5:$1, chp. 4,�.3.~ R95}>(:�H�jJ:Q�"� s =dv�Qs�Dl. Clif�3 Algebrasyo(5}, 1-40, (�H2JA�!6���:�8��6�. Y��OR� G4-ph/0104060 ).Xv>K  docu�N} ��\�1\[aps,pre,onecolumn,superNptaddE�$T@pacs]{revtex4} \uP�ckage{bm6��icx60amssymb} % -@ NEW COMMANDS: (-- \def\pr{�M�v�J%�PFRe_ ;$apjs{Astroa���, Sup!�S�l} % !@Jou�[ )�O Mdd� rm{d��$intun#1{{\t_\dd {#�:"simgr 9el�*ox{\rlap $lower4pt\h$2$!| > 8weflw�L< L=� END2�2� "�Q7}�-$tle{Free-e�Ry model!fluid�lk�Pde�pA� author{Ch�f4ophe WinisdoerV)}\�O l{cw P@ens-lyon.fr} \affili�>{T�Rep�.�s G$�, E%Uni�O��of Leic�r, )LE1 7RH,2�jKingdoA�.t\'Ecol`Prmale�\'erie�Ude Lyon Q`CRAL (UMR CNRS No.\ 5574) 693641, Cedex 07, FPV�)'GH, s Chabrie9 j����( \date{\tod�� ab�5ct}��0 a semi-analy)�fBDai�wat&>�hzs7Sm��1 pert;�ofEceI~�ium*F� low-M��Tph�n�,E�!fu��ion� regim�Te I�is #W �N6��m&�method�^ir��5ouM@A���4?rib��s "��?�fVV�5�6�T�cX! �Uh��� a��"�"uf$Z3hez]Tkum �W�� extended �of 5cj�emper-P �:�m>)�diagra�2M:� ��M-I >fAj��!z�(� tours. On"�8 predUA7�-5�%NJ,occurs abrup?X� \rho) Xmgr 10$ g cm$^{-3}$, {\�8.e.} $P��0gr 20$ Mbar, @%-�-\H�l6�$^{2+�)or{le�7 o a �� ngly �edOTe)0out H<+}$ stag'x�+ ig�Vough .Mfor2]=P�Q� do)���TP.U!��ei1�s� a guid&? fuSR � al�Zer�~ts�numer�c/-princiQ�"�8!Ǒ: stud�(A�pr.&-gatQS�Aiit��\ u(�;�met II. p�X&Xm MFb6�be;\"�:a�s�nes WR2�$, magnetic)J��S:� cool!�e aA �%.�& mong�Cjso�)�e %`��re�Oly� ca�ed extra 1gv�2ne��*�� %�}ert sugg�fd PACS!� bers� brah�on nextRBXcs{52.25.Jm, 05.70.Ce, K�]\maketw*"P�sec_ij }2q } With hđst�d ade,�� hundD(brown dwarf!-2Dbodies '=%c em,o sus��Z �]fV! ri�r��9E 2E, �"jovian1` o ���stA=out�D=�:F, h@W^cR�i�M/0��os��s�i�YA����i!�nfWir�_ gravG A7ely�[.9,b.��.G��ndards,�.sa2uim��]��an�� molei��)b!��ste��!�bod� H5 of a:Z�'-�plasma\inn \�JSS��Sty[�>u�_4*mon t�uny so-K[}YM*ct1�� our Av:���[� laya;ofa�teM��eutronI.!�b�"F`�5�3AW6�U:� thuJ quir�Z$he knowled��J2�:Ui2>�D& amnd�a �ly �pal[� cripB�%�iald8eB�!�� GiM� luT1*6�"�-s=Cɽr5AE�ev� ofL*.�A�i[)S6k9u�"� &��"�\ q((EOS), must���aver s,,�rdM*�9J�%�fZ!j��.�q�0us�belowe� �Va�ton�R# �R0k a�/" =^precl AK�Jof heav�� �imu� �A��)�Ar"�J� EOS� sa'ch � eF nsiv<.�(E �� �kon5 am��t ��6, u.mm8�pr�n of aI�I� ximat (or say phenx� olog��Y6�2�mat!� � V!�q[� Ɂ%�se�"� B��6�9� ���b��Zon Earth� shock�] \� . F� -�laser. (, like e.g.%"NIFA����L�m b\�LMJ in�, will'3ch.7&k .�deep �Di&a� afor�io��2 ��ҟ ��>1!�qSioeӉ�-LA[i�4k�]� 2YAlasz�� sM�ary"� confrɰm!�^cA� ex�ngE� � -"� =�, y9/eventu�� a-ctB�!o*/ �I+�emQyLs. HyjfEi m�fTZon�6N!�!>ube, l�s�Ni"a�ly,\h�M�al ��*�%"�b!�U��N��EW�* c�$�0e�F ltho� � C_� O5U*� stI�Kb ill-&-%�d sameaBAA��ai�h8 Ass�5�s)�15� ��al Aa-� q��1detaiK��A9� �kTH!+ L )OAՁ`lor%?�~��mpt�~%�mad��l�_�.�F�s0ai�I ]?%�pur� !�!��^p>����P�}E �e�, &�-ZgveraQgap"8u prev�A� P :�I�(aparicio94}%<Q2# $ 0�9 ��g,{potekhin00}�wa>��bove,b�!�U �If%is��`^aJt�R�Z2�2� in)_c�J gase;exopla�� s a �j�� R��{-�_�'Bd`I��rgani�a"�2�hSec. f* gal_�}'Gf��m!� owjà�m{ m�"9�Q��,v Z !6�e�A�� !�l�22A) [�iiM!}6�F�}.�*d��"�=�%��0F`6V I}.c�Ma�nA�!b devo�� imI"f�&�Z � .�=00�f�T {��>9��0}J�d�`.5� G����S�ps} \sub9Ch�al pi� � ii } O -of-� �"� diviG�ii��;%�0ic categories)�``"�%;ach''����+�ct as B nvolqL�fundaA������z%nuclei, ��U�%/�!|Coulomb ��nF ��rk%�fu ���C�"�Beigennfesl��ho�� $N$-��e�p�KDh5k�ex�&�+"��{�.�B�bound)�a�rm�"�;�urbD expa�s� %v� �W sche�@d usB val�|N!!ewY�.` s�/q"{*�app��o weakly��a��g�����l7x�5>�+ 9D�� by�G��. N\ tech5$ ,���U��� y,*���path-A{��(Monte Carlo�g� , dor eąoE?� ��ox��A* �:> �*�-!2n"! ae^id�  taskI.u_HC6�E#.�Q�of Mk�q�.(o�znod�UmTs��a�� ng � �size ef�l s dub �Qe9@A�u��q&4. /=yn� s"�f �]6�k UXQ �"�2� 1 �@1� nee�� �a>/ as12 k. R@�, lBXe�ach& d^qoppb�\coMa�! pl�sRS.$ ����ndJ�� �],_!�A=V� ! 6`�re�0 modea��p$�A�estA5�Du��e*b``��e��''�v%@1 �  basi&pno:\��asQ�)��Re�e(�{"m(�s��a"),��&�i�yiGj���ّ�� at m6wK)s � �=�e�(��"% sFoØ �F,h:�~_��� !���ũon� �H�]proble�� us r_"�o.�.��a��-c�&���,bKA.5WK��5���E]ilibrium.�T"� �s� "�cer��Xf;0t���� �Qa�JQ�j�rE�on3s� pair9��E��9M�es� V��&*h!�to �m�ab�ml�>}�eJ")e�� n saumon9Rh~ |  More�Dž�aR2� 2.%��a&;!*be}�>� !���a?c ��E^A�.$. L�Ҁ�e�]1>o= �noticee2�cl�JyM�&ń1� �R��A-s�p� �͢.Pt ad��or remo�����eO't,�A�a rapid�A!b�\� &"!7 p� blI+6SRU�a�lexS}K� re6,�pitA�s�rtc�gE�=� %7�r�u����< aial%t~�``� "9LI� &� � 2Wa%}� �$!���"_.�1PM@ $F(\{N_i\},T,V)$x !Y� ���b�aAT$ 4$ ��t�y ih  a  me $V$ at.'���2�$�jF=\sum_i3��al F}&X`N_����N_i=0$ � satis$�ѽa�q"�m�e st\o!�iom^�2lhx5 in�(b1��MA���1G�s:%&�2\{aI�{lcl} �'m {He�m ,�1harpo�& 6& ^+ +e}^- ,\\:K^+ �M >P S* ��: �U;&B�%��T" ! a�IM*��Z�Ds,�d6be�� oriz���YhA�"(%, s9 at ^]�$ $F=-kT\ln�2�dl�a�plXm�s�$f[tal;nfigu4� nd��6�� graboske6H^�tf�ine77.deVup�Ea�ariW$!'n u�s*�our�n$%`�on�tNk6� &=&F&9�id@k}�+ �: "���o&+2Mnt:.2Nqm: .6M & �!eq_sepF" A�DE_"�AM"�o{ �,�re�areu~@3izM) %H�3*V !��yj�7 #I"*~Ey��A"MSA#er/t��0 � neglig��T &� quasi-� ��; �re��n?�uFe���� ew F�hY�Egy�~y .>"un$ urea�z��sur���4UÍK!�%�IS=f|�ai��!;��U� � %�ex, Ga&� � +E<.?>@ .�*�c�zk�,*�!�|a"�r�j e4b gBdg!Ta�o� sxy"T(. E"�,���+on)P��3iata����C ve 4��A�I�pancy "bis �fac��A�!])��&n !t��A�$F$%�� A-�n�%q���.�� BO.;,I 1�� sh �lE �:��X3���' !PA��{ each�kL , He$^:) 4a��5w� �"Q|��[��cJ�s9I k.2���)_He0} M Jtic HeW/? &B �9��.� $��� $R idea�"E%=,,ɳ" ��_a�Q`0 Hamiltonian,��A�n��l&u9}��3 }.��(N� =-Nk_BT [1+��f;% V}{Nn�_� 2\pi M4}{h^2�<^�\U (r] ,�(�,CN&CA8&sy!zň����� .&� �6*l#� )�9�.��{h .~=� .�)}1� ^6J5,F|2�e..�, �&I#[&])Weeks-C� ler-B7e��w7wr b} (WCA)*� 6A��&o $8N(r)%�*� 6&�"� /& re�>�a}vZ& `1��}}2. Trun��Ue6<ehq =�C�A%���%�")( C-.7�   (HTA)�!.� u��2BA}}=}� �T,V,N)�H N^2}{2V}\�4{\bm r}:�J� g Nr N.*� HTA"� �!�=�S(2Ur9�� �|!���!6QwA"]Z�9E$Z� $. C�r�=�point,���&gd2&��&�of Kang�{et al.}E�kang88namelyJ� ?a"r}'QB\) & =" efJ9l 7(r)M?0\Phi(\lambda)�Jdd%�0{ d r}|_{r= $ }(r- )� ) &*Bif���; r< ,g0Z5 2�2/\ʺ.2+.� m.P ��uj�� `�����(r)���6�V,Z)�=(*��fcc}}J2+r^�� -3})�c/3}$; $>,=��(2}/(N/V))^{+eK$ D����� A��h*����, c�� 2�Q� -&ȁbreak-eUfYE�&�� advaJto�� ontinuousO���b�� BB��Pi , we�/ repul~& rJ,by a hard-sp���� 2ra�$\sigma�z��e��! Barker-H5r� criz�onN LY�BH}}=D:_0^L: fty}O:,r \: (1-e^{-&�E�:r�� })= >J[^LA�BKJ lN�4Verlet \& Weis �\�v!72}~ �6�$ U)c&�&� �= �!� "J\ ��E 0}\� ^� %%�0n � 2}sK g/f$ 6:Ti` , i��n-Aoar"��s�!dA}Px A ��, e! I6���|0i�! gues� /�� � (T,n��A��a|��"�. i�m��6�5s~ �$Fig]% fig_% }.��� r�8 > s[width=\b> ]{<_wca.ep�#ca� _ H}�a�i �9% WCA}�b7���  (solidk4),��< $T=10^{3.0}$ K,5!4 #�7top��bottom,�*V� (dot!.A) !xaF-n.. 18, f*;A�/��i)�-:SI&.���|6< �2 I4 *M HS�yBB +*Z +�o�� &�;ly�(mansoori71} 0grundke72}.\\�p5�&�$oTtwY)�� � &�[ Aziz��Slamaw aziz91}��)��1.8$ \AA "g!Cep��yHPartri�2��c 86}^Af$r<F.� Q! A�cioI�= Ha 9�Cotwo,%�~�&"��ťM,�:t QN�bmi !�soften�d>""�%��e RN�G r)=�n (1-C` C�gD�:"HPh�:r;Za�0-  6�A�!�"ȟ s $C�D> opti�rep{� 2�mea�� adia�%c s&&l�)�(letoullec89|+ $\chi^2$��J/���6���A�6��1fE&Hugoni�ur\(m�\AHm�"g�6�A���q� K G�"�G��+9�Gnellis84�*s�ma1sJass������� ia6elA�= p��.12w9P�Lm{��=�b�|��\��pot%�N��Rl{fig_aziz} Interaction potential between two helium atoms, without $N$-body correAD (solid line) and - the. softening8x at $\rho=10$ g/cm$^3$ (dotted O.} \end�(ure} \beginpincludegraphics[width=\column @]{sound.eps} \cap�{\labe)0} Comparison 5phe experimental measures of $adiabatic Ft velocity \cite{letoullec89} 2' !(C8present calcula�s)AD$(C,D)=(0.44,0.8$ )"4/g$)$ (crosses%r ,,0:')N)��N%N hockjN�N singleE1double-=< Hugoniot curves-K$nellis84} 2�;]�%��> :� \subee{The iaY�nal free-energy $F_{\mathrm{int}}$} The divergence of�?partiA fun_��, $\sum_l g_l \exp(-E_l/k_BT)$, of an isolated atom is a well-known problem in statistical physics. It emphasises the necessity to take� o account��Lsu< s in"]�u;v�{\cal Z}:8= �\beta >U4)$. For a densa� $n$, each� ha!typ�(available v�.\e $n^{-1/3}$ so that, asM$increases,�4levels associa!rwit��Dhighest eigenvaluea�ll movE"^�A�!� $:n$1�saai�.7��%ݥ��e $)� $ ofe�a� st��exist�� mids�&R�e�,se factors F�are�(edi;�{tly from�!�.y�A�," )F_ �`$�2�8�3�q)�ae��4several notice�xadvantag�S(among whichu\itemiz�  F4de�4 monotoneously% �&inu a ���x�g, �a� conv*� $i-Zp$g%�derivтof F� ; �no ill-�ro��# shiftY �]E$introduced� required .d�<ofMaiz�P�P�0"N $ (Eq. \ref�F sepF}). E"� s� low--+-�wiese72}�*� s )�,grabowski87} 3,seidel95} do!�$ show such6�1#�ro�� stic!erpre� oB F enASs us to�� bineUuo&.[tie!biE%Na�r0ally independ� մ ons. We w� come backU is point�XSec. %_0sec_coupling}��A�Eځ� exact sol��0in principle,1�knowledg0 all!- �&�*� i � ���(an other on� %#'$. I� abse� %�in���, w adop��!�si st appro� e�adT s!4*, j3d ��8s by hard-spher*�d� ��(phase space� .5radiieRQ�e*�sca!� law e�edvA$cio \& Cha�rM�a  94} eL (14a�(14b))0 &lfir�$rE� expansM�!3&�a� �.�mEZ eq_HTA}),��>^"s HS}}$ forfe.ha e thus giZ by�&K:N6Zb���f&� �(\{&�\},V,T)}���eq_�HS��Ta�non� ar  sol!�i�t !�ue�resul�|btained: -�low)1E� E�xiI� (LEA%�'�)2$ (LDA)����.C ,LEA+LDA})K4(-\pi N (\sigm3 + 1)^3/6V)��A�i�guv >�-6�� Fqm} quantum.�Jh .�qm�taken in: coa�A�.�^�j�l�>s due4$inite sizeG{ � keepD.S �`Wigner-Kirkwood $\hbar^2$6m$q$ {Tr}}\; [&� H}]$m�wO329�k X33landau9}}5narray} *� !>=� � }{24� VM}`e}}} N^2\pintun{{\bm r}}  \��0a}^2\Phi(r) g�Qew$ $)�spond�m!3&�expli�ů�TE)g }�$f\uv y(r)9( h}j Y��9 $y�S}}V;.M�AModel���i��Hed plasma \{He$^{+}�4$^-$\}} Becaus��Wc�)�treat�A9M��k4 same difficul,s�He���k*� lism, namh�WCA per��A��,A�ՊH�!.� }E (� \.�m%9� refer�u��3OPF ��f`%l2! L6F-rang!�A�]L��' , we�( a Yukawa2, $AHkU# s}r}/r�w�P-�,temperature-&� screVw�ve^  i��m�c��90.��2�(n,T)m�01}{\sqrt{2}} &H{TF}} [\theta^{1/2}�- (\mu�] J��$:P0=(4m_ee^2/\pi�%) C((3\pi^2 n_e6is�,Thomas-FermiV, $n_ee�!�&�".1i��� =T/T9�Fn`ic deg� acyA; ameter ($R8j �=�), �fnd #A�g.of 4 $�� $1b�� chem��� def����i6�=2 �4^{-3/2}/3$. \\D%,.%�e.}�E�need a *F a�" a2�� u���$e6� ofuH . Si��yX8s hydrogen-like"� !�gy.81�t�X ward� orbi�� number $la{e �a~is.  as��q7�n=n^2 1b�!5��.�-54� 6�EnF�6�.\\W �]���V oc!�q '> >��K_He0}:�*J fully} 6���iݫ ͬ26�� ]E!�a:AQ�-! ��(FIP) "���s&� & P� kin>8�$Potekhin \B� a; 00}.- $se authorsg(vide analytai pae�q)he X[ modynamic)�y�Cũ# rea �se�N�scripa!)a�Rl%�f�"�.�&'���7 t speciesSsid# i afored�b�"�a� �&�,2� .�v l�Gn��U(must also �r2P !��a�BbJ {\it�} m.>3 H*kRS� a�a\}I�2�&&�8ic95)j He,��+T��a2��9.(ex2�.��M\iv ie},\as,�^+ :�� \{��bPJ.UNZ�,$v a��1.m 2� 0&�50%�, ��BG.P]�A�a m� compon2�ngP �U4mansoori71}. I� :!�n easily&W��F� f�=� �A�al�to ren�mA,� (kinetic)�I�QrF a � $V^\p�!$=(1-\eta)V�� 'i\in\9�S}y �n_i-�i�R| { pack!Kfm�-Mi2}�is ��k��:kHe-y6-A+$, $ AfyW+ , .� . No���%�ar%�o v%� achF we�Ec��j����  1��Efre&$ srde�hauach doesBeem!�$be justifi0)�e�fum �`pO�l�o�to�f!bE?�� e�� %re I)a!AdX X%�&J �� major��6�,�b*� )-�far� 6E� in a�� ��g thos�8rr A{ �m . In any�tŀ�check�a"2��an)hd"�5��s9�F ')>� ��2�p"�+� H� ��$i/$�� �^&�sN� !�O!_i%��X we� q0��%. �'�J�-� .��#] , is c��b�e��.6 ��Su-v.��%�$a�6� (��d,b})N )�|l m$&�nu)^~-"� +&N : =JA �^+:� =*Xn�+R� +4R])/2EE ::is-tobB�%$ \medskip .E�(ic microɮ�m� ��F���R$\bf E$*� .�#�,��3X� frameworkA$A5OPF�" oN� y.]� 4 �] ���� �m� I@B"�#JbJ�u 1�E�r��0^{�iF� {crit}}}��$ {�+P}()��6�%qEB�� �+=(4Tvarepsilon_0 a^2/Ze) E"(u� less�"�($Z&U)���$ a n/3),!ց�mea�er& cle �+ ance�:�7*i".en9 b+c ereri] z ��$�eW +5Z� �b $f��a !�� b6� &-�  ��$.".@{e�.}�#�f0 2} 3 �0�he.N!6"�2�"(O .) �-n ()�d 57) imm�%dA a2y'I&�eo �& � a?j�.m�}`$\Gamma=(Ze)^2/akT\ne 0$)� recove�Holtzm� limi$! c�"�� -e��ng, perG- gas j0$�,&�AV:�p mulay  $Qig, �)=2�}4 t�* P}(t)�t� �� !�m/dE�� !dcer*> � �I�tc"!&�%yR�"2n $ no� ly ���*D(-�:x, but:�� \9#ra/h*� -� 68s �)�  H`.$ et Mihala�2�d�5V 2�LU&e?direct�p�� irJ &to He��us 't%i~t&�.a � *a6@ �,�ia ��!�io��7/4&o2[ V $1$ }$e(1snl}$-type�� a&6% q�� :jK 6�atoB0�� .�3�[� He1He2} L[*F��c-L�!WP:15>6VCA?�[ �.s�e F �Coulomb�~e�*t6 ۅ�������( Shor�sō.P2Q#�i%W*c+$Ir����N� ����;!���+two��1%H)erz%l�' ve sW)imp)m���1 ?�2regime '!$>?��-� k�O��x�'f�>(digm�3_ o&C, how�,� h"� e�3jacc2 ely. Con%SA?� ��)�%��on0a pureU2| �@re! e74gVSfluidM�_-wo-"G@ $Z_1=1$, $Z_2=2$�*-m���il atis�.y,�l it!����% B�Nw�G E}iP4!� "M#Y.>�).��!%ex�5n>!h*�*b-�Ua9�est�'�z=�!�� �rF4 )��!�,e^-$.%!�on M�B ion�*��+ salpW!61}-�q�!��h"9 �F�.�99ver�mpl> zh2G�� 酀 �$�Iy&�5Z_1 Z_2 �"a$� pair,�=1 SM�Aere�$2�*I=S�! ͽ�"��uniASly��d sJ,$-Z_1eV� $-3/2 ("� �� +$.   % �A�e�& .��al�yU�QFIP)� �\ion��:� ��2[^ YN�!F(:�+B��}�$B.:-�1�{ � a}\,-\,{3 2>;+}{5Q #a"�4c�Jt%kE�crude>��8&$U!�j>4�ya ��rtcoming�A>�t-�!�";1�q t b�Ran �$ of magnit��h. :���y . As] abov�9re�� .�@"1!LK6�)!�t.���R^ sI�6^ > e�' . In�� s��cap�'`dra�1�)�=l!� )<rtk(!h[ =�%�&Fth2��d�t��!gs�7$oubtedly a� �"�&E&ic�� ��i�="�9��2*!a��:�concepv*iY2ify��-�or a`$� , ba!�%.Az�A or pseudo , be�2s �h?s�3�<%�ity. Ot at 2S w�<Du"��minate,aBA:�(�u%�Fre:# , alEBgh�+$�� �W )Xguish�3 2},*�4e�oe�2�Ju ��sx6#q a�b �a ,� �+}$a� �"e�detai��� next`��*. 3L&!ten��J�pb�&WalG�H:� �%A��B)�at leas"� ���, j�G's "�k>� !0ű)SedT�%E,A�� s�>gl4%�`"� ��b�� � o � AEth1L��&�C(�"�1 f�$-&2 ��F]� elat!z:��to fac��ir own�!3 KE3b mplex� J� Summary} �6�E!�t��Z�@+�&f��� �/follow!>��S4�~0e&c< !�I&.�A`*} wide�F}&Z1& &$� F}.pto;,(V,T,\{N_i\}r�B{i=*5},�He}�� N�*� R Q[1+@> ( /Vi}.~ MRh"�)^{$,\{<�<] �=� ��Q} g_{i �6�N2C &EV} \no�+\\%��= +)%�.q�P'�P'�P'=0P6 } Fb�.�{6i1(\},6Hjj~�>� � �230U�!3M��i( �}*{7a +2�>G (�:Z+, ��:)0 �(a>�qk�Y B� {2V}ii,j.� B� nljJ�X5W5% ��3}}^{ij�*�@\Ph'ref&}y@!�>bgu]&6(�j)^2> 6�:_{V"�!�'�'%/B}6�V! �� �o]��+>: {2+}uB9 ^2} �)4e^2}{a} �!3� BeJ% E�J �i�F�� FIP}ɮ:Z�a*V&la�L�_�� *.4�/�L�O \no�>nt� re $ze�=� +6^+B�$. "*&�Vt"%.2u$"�.�R� \ ed C 2� � � .vpK5F ("<=,2�z; HS})�W W�0, (�&vV)E:A��,(librium popn�V>�!minimk `*�  $F2 !.oI%wov("�@ 6 s, 'B6 masVnserv�,2AazE.EEV -:G {+}}:�9��=ity, A�a .Xm+}}+2>[a�$N� �d�A �VNG }+6b�$Bigg|_{T,Va�.�+}}=0=�e�m mP fo}J�C6�D��"� �P.>is achie�>���J�92�E��)?�2�s D!�l"t�0$3\; 10^{-7}$&eExoxCheR�3�tQ>�:pr?Mi E��"a"}�3&<�;�� } R�?}6)9ly,X&�3� ,�m�&&U Bbr�Mon>�Qm R��).�Q,��E!Ce*"."�P*� "�P�Fig�E�SsXQ)85`�2Sw�&� -�[ Saha��)c.�E� Q",/9constru�!"� &�&Ž�2Z A.a�A�shin>�aha2}� $T=AU4.7}$ K.7f=e} ��S pop_S_dlt47j�R wZ�S.�6 our �(bBzSnb/:s(symbolsDG+o6U(��. �S)�S<6�?He*? +$) � �i�*�!r:P\%1O~vanish�IA*""X. ��U�9 mgr �U�T{-3��llusta2I��f�[s�&[h;MB��A@ v�E� M6�]�, .=Vuntil�U�se�K�J6�apM�A�$^{3.5A�):�*f�AYw�V]"+!35f�q^�A�.}Vs)a�eӝ$�Z�WE�s�Q���0�I�5D=�,%��T�A�ic@ropy,]K � ���<jBfic heat��6|6�*}1"�KL�%��e�} 6IearlierJF.�methodaroo�XMp"S��achiUis *� heur|J2��!dqnt phys�'�*!�ponsi�Ta�!6�pro�m of dens�1ic or)�"� . A�it*kzKins�!deg�5of re"�is)8gOc!�giv�b%4�!F�seX< �l�Q�should�%to ��R&,main %[x��%-%�.�Texamin� suEEA�V Mp2Y$Lower� ary%ou-1$} At�.I��>�.i � even#to zero�& ^$H�is fav>P!!H�d� i�hu�=h�a`)�E�w� r, X�i�@ rtif!�mQ� "� uT2>*96}��� %W�Man unU� behaX8r��A a�@r{8a��er�A�1q.� "�0%*2^+� 6�ac,47} (W!P1��EYeG)�O��e�iz)is 6w2�1 \geq �[ \AA~!��5$Amb*�\� � _sign�%�E2�WlB� �$� !p&�I�a)AR ���,opyQ%':�s�,�Z)<� �Y� ����'AA�;)�6X �> A� �*B6)r;X.�isr4 *} ;0p�lm� choifH2�:  a%zs�ec�y%)=_��v�#�of5p}�. H�&�M�lmo�� �8i� he�MR� )Cw purp1:m�!�a�c*9-o is:�( �4"EUF -Ee�w'0T��.� �e%e.�.�a �sm�A�Mf8���2� wmad�Qth]=u�aw6�*Z�2} o8�4!*~+}6� tes�� infl.:0 OF&<5 R4appearUc&�� ."9'M9 m4I��4�+-He^+}}i4C=�� duc�1m�\�� re�;7nc�%ed(a !�o 7E��n9 y unieda��,@easd> \Ystood�(��do��Are0/d�YI�s�y/Aole, H2� co*R"� �&�)$time. More�$i.W%>9 !�F,(;,0s always marg�<.F�<Valid�-mv�FB!�.yMNq.$i>*& Fqm}�X,"!.��c@ s W�N-8O��RAVak' �*�_�1� - r �'erx#e"�R�" i_�*~"� !�'uQ��l!a rulE�thumb)�M#of�#iq] �ti&5,: $\log_{10}&�J{K}}- �d _&�da8z�2�I��X a�n� n�}c!6�a� ��a%as/2 object���"A�osiE E�l<y�=�r��� /�.G:�&*�,-6 Fm \�/he�%�.� a�Q �&3+*5)Q$uKu&ra� #wa6)enј��� E�� 1:���V" ��submitt� few?1"`!-#4^0��b"&��):a est"mH45:�� �q "y * 3&l�B��AEOSe,i�/ A�s7al.gto Z� J�� 2�}��-��� i��ll!&��N�&i�di�_ &�al�V��"z&�cC, :*�yn&b*UJ5! [Ewhe�4E"cE  flaw1Oa5ent�or9it�MlecUDofё=:r� �re�T.ih�:f:)}{2� Fwe�2Z)q�+&�/�]�d!y p&  (w.c $�K$)ر[, n. J)� 1>JBmi/&�JB�i�+Ifa 3 IA�&TJ + X TE��%*Ma".�l'H5;M2�*I��.oen�m>�T.6al X ?- } A�sG4C ��.�,&I�2] (�S:m!)p!�en6 in T sɀ tab_T38}-;45}, � %L�/o:�res_P*X`a+Ag6(*S* mass&�� F2Cv 3%x�TQ%).�T:�<,y��@81 ~5.�7, both�H.Q ���Gen@ e�j�e!I%�i�m�!�<&yb�3),1 �O+ %troyed ���!��s�;�w-A�"e7. No��/ly�i!�5e.�H�!�AX]N��>iA�r*> 6mZ�!&M+� s. FK,�7alli���$y c&}�`t�� (�� N� �L�m 60$~eV 2%!He�% �) d�72ir!Jm��(:LR si3_� )#!eth�$rapid deca�_ auto* (�m~n $E -13}- 4}$~s8t Pn0 un#W*�P9fsurvi�l� "�gŶ� ng "&LI�p$Ae�!��y �&T V)E�2la�\at ;�- QQ6i $C_Vr=&� b� _ -1$.���Sr�T�s (jk\ ), sXal iL}�dem��odi�, "�/^ coola�.�V drop@ B&��?)ME��1>�!s 3q in:q�;predom}%�� �;!�))�� sexLti`&�3d�s4 re eir H&�T2�3is��� n���%{�Ui.e.}�?��E�on1$than 50 \%~ V� �;� �v A �5 agraT;%+�m���HN for $TAQlw� 5$ K,Os��2���$x.j}�)}Egr 0.5�Dp~Y>72:� A .g $ 10 *h ,=8 $PQ�20$ Mbar>#B�+ ���0sharp �Oɲd�bAPB�f�k:�.� �Hz6�B�a -�_ [�o�Uca���w�cmH,� re� %�ej0\݄�<�E��� ��4;Y$ (24.587 �~0nd 79.003 eV)�AT.� . E� 6, abrup6e�=s�j:, u�G.<���K ough(unu�&E��P� -A)��i�%9a� �+obo�"�e�7e7Ji�+$&LppeMTf mEg^� �!��r-��.� 1$.� �6�Ca�Aw���'�xS^&WP5}~Mdeu�rum�3O�Ks�;uc%sca�bP pr�F�$oItus� Cre_ed2wN\H�E@)�, :J $Z�@TA^d\S1�;Z�&�yZ ��ͅ�fze;5�.�#=��r%�$az H��D^�t ��:ion{EQA  %}�so�mY 3.8}�&�MpI h M�d�? `FFabundlJ�'�e!A~{�,r[%(%�Sm� e��NA?a�of� �%�%*��� �*2� �#�.U 38"%6�dtabular{c }*�( /e//{ )$ &B�J F*%L/ $P$ (dyn\2$)4& $S$ (erg/g/K & $U&� Lv (Nk_B)$\\ $-2.00�1.0000&t mes � 0} 0� 31332M10 3246.g9 -0.1882U �0.1504.41}$16�1.6��R� 34092s�052.��16.�6& ��>�9�\Q)��2852N��272N�0.8��R�256�1t& $0.26jC52�4I^AC66.�4��R� 85382�t �412�2�324�67ZC a�e*��:�4092�121N 2141.�.�7^�926R5� 0��Z�3036�3�1812l.�26�5�2302�2���V�87:4�f766��516�.�m�0.7152�1682-Z842t�-1082�148^�63Z4269^�A�e 0.436��2532��566��22:��132^�50^�8269�1�0.3142Z��6852��71464�162}3068428722��G 0.196���8012t�23121��G9872G� & K87:�u8286�2�m� 0.106D�f896��68:��79^�5626��{68^G"� 0.4982@-�%5f�9:��4246s�mM416-� 0!h2�]C09^C22C��802^�236�1�3�1682�926��1362�![O  2�G8:�5�1122���9922��11921 ���2 �!�>�Uw6502�0}$�;� : >y5ʉ4.!K>���"�����·4�_�:} 1�������6�*�0.9992ai�49&� �5 F� 33:� Ne�3532���:I}�502�q�$&��2�r s:`��8476�N �342���2�.���2%r s186 ��2206|s �16��16�= ��� 9992%�1��60:xs�296� 2�6�"< 15:G�"; f�67:Yb186*F76�2�6�g1612�&�E@Z�6>Yb�686��46 .�:� g17V�-�F 6&Y@F�f ��8:� &� 26� �7b�992�.�� ��:�9966��092�.�:t5�216�.�u�736 9�f� 2672�4e�126M�06 �56Z4364�!w-�466?� �j}3F4�26:j 5L1922Z�462�424^�*|246���756g4�7332��175^@252A424V� $ 1q�N{$��j{6 &C 15^�8:� }45:V� "�Nz�fbz7012&�342�M@ 0.12:s� %�252Z��yfy96�"y9832 � :]@5:�5��xfx6�&x546��9252��46�.��@�w:w6L ��6  !�2:e"w18B�i� :� �wBw��w�w�w�w:w5"�:}�w�w�wnw:x282w0"� 716� &KF 706*� 968�x�76wy�186�q�:y56f�46:�A��b�17:�33672.�6� �b�-*z9692y �316���44:��432�.�f�6�M�&� 0.976�216+��11:� ��326�.�:�&/ 5:���<� 0.9842� �15��33:��2:�.�:� �6V�� � �6*�36���>�&� 76�.�:c�7:O5�&�0.9272 �726� ��4562��:��6:��946N.� 62� �96�116�"? 90: 9�46�.�6� �206�2�"@ 646��5>A�G2:'�1:�36^G>j!5�20:]9�.�722Z�2:��506n�376��212,=�40240:].�"���2�9>�=N6u�1^�216d2��G��6�>�5e186��73:y81:Q.�u���2�726~�76k � 0.9>x�<36� ���b�3521&�136� �30:kYw56!2�.C2 y�fj�:�$m6��93:1�>�YC��b�>Gn 0.776� �6Yw23:� ���P\fN~^�j7 Pbisf@:" } Pr�0Np9"�+]-three �+ s. S�Q62::�+,Q9-2�(, dot-dashe�H>4.����S� S} S�-Fx8P�@f,6�8���Cv���8��Br,�14�D>4_V3�?fJ' &} P��w3"?=�4A�a4Js.!�"�4Z-e2B�.}4B� \s�P�-FWcB } Co�o�7} "ao pape�M1:o0uU9a2a;s;aim4�9r�OD0/J���.e�p0&�1*�SVFy5g22"��6�.@K, cove"�? �.�:2 @)� �.�Q!oso-�j�v"b�j� �=s>��"M8��~7O5�I����q� 6�/��[���3�/�3�im��iY"�Vt�v.�R�!f& Y. Despq�fsRtminh�A`3�KE ach,�;��ev#7%3|7)H"�i�9;1N�?�JL1As; IQ���0�s�si>�5*3C,bas���s ��H?d;tful v�I}J�Z�gIq,�8 �J@ly+EEU!� b*�8U��.*�UgF &:�@�sp��.^Z%��Y-wu&>B�3M)( a��2�[6VJ �up!�!�bar�E�Uzqa*�Rb@ 0c��z c6sp�: (A�C8Monte-Carlo sim�B5/.�? p.�Tvy{ one-�~�� m (OCP) s. "*E�6�/E>�Tcis���G�l�s-�jrn�J���Jre�,!Al>Yk:?8E4 mes, it y�}�9=ab�n7w:Fir�14p>We+, �M 6 its �He/.4+}$ 74 �CW;?tours&�:AAfV�N5A>��2��766I� }J�,��"A<to|p�7:l�n�4out <�>goG:y9+} <$��ew \%)~WwXVFEl:]pED;w5�pAY%�Ւal }��Td*��6�=E�2�b�Omport<�@�QfGfo�A2%, RretI��:>J=łiorA9�=e�E- 2vL vLȂ�ggi�H ets.>Ds�;1 }.E�V6a�� &�8 $ 10.�8, * =$P5< 26$ �;Dpo���9.ys>7ivENm��K uponq�6�Us �C"!��U�zw":y�O���M-9 bS�A"�`v�7!�.X� �S �2%js{�K�,ons*Pp�dac�9sAG� y� �A2ximum%�j��enk[E�F_:r�8nB 5\%$�H 20\%$�`i zLI� wo�A+��8���T)$�9 un�o;��&Jq �q*�L,�� c18�one*�Kr�@N�8"�Jt �Z%!�dom-��J<$Bp&�G, RB�ific v\. AisnA� �u.| �y:�5�2E� erHb�y)�����-WP! �a�R�L=L�Ywh$S1�&� �R��*�Eap1*E � +<of�H��E��[�Zed8 (UR�}f, a necessaryQ�f%���cM�)��ufQT� tell�nd2���I�"<v6���� noaFs. B�SO2  Xest eJ6���e1� ɩ(insic theor��� �xest�9)�i�N6 eU:�G� �O-fu=:�s-d0  or las"e�%e . By�W%C�oo�F`ll �VanŎ [CB*^m� *{La?IMCQmor&MK�v L%glex�$ P���I�metall. . "Fack��%]}Xa�QYg� a to AlexaF���XG\'er��(Massacrier J\Aus?&IG%� AIgh� a� rks.�!B� % CTSe�s�j��Q�� �BibTeXtiiblioO0ystyle{apsrev� oces.bibWab docu!} �%� \S8class[fleqn,two�J]{�^ cle} % \u�E0ckage{espcrc2U�Jhe op� 'heaAR(s' if you w�run&yDb N[3]X %"6_�� \}RCS $Id:!�Trei_dorokhov_v04.tex,v  2005/$9 10:41:11P� , Exp $ \PgA esFi!�nRP }[\f�x, \s�� vver��> Vertex}4- �w�|] .�{%� icx}2epsfig!Qi)7�� scap�ble67nsrA� ]{ro��nC7F up Obk l��ina�h)$ \DeclareS8gFont{-8}{U}{eur}{m}{n}( Math , {\up�s[ ord}<"0B^3KlR2C^2g�R3D^3 deltV3E^3muNc16!�putA�r ocxFa�Fs �: 1nT 0commands \new {\um}{\en���!<mu}m} :'sN's>'C} 2N$^{\circ} \] rm{C�w6[DegZ6}>_Neq:+X0n_{eq}/{cm^2}Xm2�E} [1]6�*�2#1}\,�Pn=Fig 6&#1�6\ttb!� '134}64AmS}{{\protectr�\ZXfont2 A\kern-.1667em\F,.5ex\hbox{M}25emS}}��adde pL TeX'���6 �Ne��list \h{̡ an�D �]" XQncpaper rl4mend-ed Post-S���Q�Tst��ng painf �e1��set �er{ }{17:de���fro�h��( \title{Ext� Kof�E"Əin��v7^ir `�0silicon pixel ors} V� \) { A.~D�y \addF X[Zurich]{Physik Institu� Uni�] t\"at Z\",0-Irchel, 8057 , Switzer�)}v aDPSI]{Paul Scherrere(, 5232 Vill?�>COD \thanks{C2�E �.~� Recches Sub�quw d23 rue du loess, BP28, F67�?Stras&�XQ �E-mailA!& :} AŖ.1Al@IReS.in2p3.fr}, Y.~Allkofer1\ mark1` , C.~Amsl^0D.~BortolettoB [Purdue]{ 9�,y, Task G, WfLafay�Wp, IN 47907, USA}, V.~ChiochiaW6� L.~CY ldi![Miss]{issippi��t � ., D,N"�E;c� A�0omy, MS 39762�0S.~CucciarellkBasel]{5�fAg Tk�E�/, 4056 .y%h H\"ormann�.�2A�,!|KimH[JHU]{Johns Hopkins�y, Baltil $, MD 21218� M.~Koneck�z� hoE�s:! �,K.~Prokofiev�@m�2 3 C.~R��fus2 2 , T.~Rohe2 ; D.~S� 6:!�],!�So6@I� TSpe^� M.~Swartz2t!T ���y:y a��y.C�L%Y�S2S]Ib�EqEY!��  %r�q�u�U�2o %�p, �q�p2$[q%%Now at.L�  -� -F y+%� �.ch (A�~�6run��>�T�� {A. я}b�\/Z^(�S absc�T TA newxVpu e2 l��."  bulk@ hez. :Wn�^��gӧ> *�[gLo�_z T�� 'mo&1i �%BX#depth.�t].�ia�R0CERN H2 beam �Edrc!�� *WO��amage, �n)�-"��T�mŮ��Mu�i�trapping�.i�lea-��n{"����OIntrohe_fl��ce04}.“���E�%GIv�k 4 T&r��� �car� �bJ"�9� forc5enh�'sG|ZI�e�=F)Es��7fo/� . HXW!�bias volߎ �� �s�&�`.C!z>�d � #%b[~p)Oa"� firenze03��la�w ���e{d'1;)�io_%rF��l, �Dal, nois�.���,��W�+tby.�. %In �n,o establish "�h�\s��M��+ Q' s %�thoroА��awasa�p��l) past)9ms_2inA�%�^lQ�1�y[��[developg�wua� Zvc� _ieeA�%! %it �nN:/ �..A H�^w�{�*��B�mF? V� 1sۅ�3J�i��a.� 2pisRoa!N(P%a!�pl���&Z�Sen7 ::D techngG� ��study �t�.`s �\ �u( ``n-on-n''�����_IEEEATAS%Xma-"ms}*u �-oxyge˓d flo�b<\(DOFZ) n��11 of $\rm9,] 111 \r }$ o¤���n�re�^�#2-5 =<: k\Omega \: cm}�\e)��im:by p-spr�oso�n$�iim�$�$ whil�  p-n jbx�$rab� p.<����K�]Jick\ �!�)�Q2F um\ �M�iz�^�125S2@ um$^2 � K� }�.� SPSI{24 GeV��t^atR~m.]*� �epplE�2� �n sto^at -20\C �esd ��dR�.�.k �150-225~��$ L| F% 1�:&R>� %*:�=}$15�� 3~Bm�P�-allel� du:��gra�E�_como�/m�%%e �#onship�jN$zhw�aG4&� ���5c6yrrival���&I&A�e aϘ$x$ ax� &�t $z=x\tan-a��H�piPv 8"]  # k aread! -y|�e��w �"v�� +lo�! o �origin.�z�probed:�m}[htb]0+er�2I{file=R�,w��=0.45&�0, bb=174 235 c7697MndZ�_��&�.���1�^R� [����!!�E�ex ���``O''E�#-n�$9� )�coordg,es |��!S telescope��cam _p_l 2� �ra�f�+rRul��'j%i�j two��strip����$�E�nd $ys�i�:[k��pitch! `Eum(ad���9.DF� ?�i3a�abD1\u�c�+ 2Obump-bon 3&�g PSI30/AC3V; chip-U,dmeer_psi30}� �!�ll��al*5dO2"�G39)�matrix2N ��c�hRd PeF�r men�uown�-1��B� S!o:� �>digit��# VME-"ADC1�%�d�b*{DAQ��w�$w��$in LabViewv@LabWindows/CVI~(N}alHru��ktrigge ��%i!}iPIN diodn�!$3� 6$ m�!�c!It'>�E *for�1�� � a�Z�(nd �(us�ay�>ڏ4�A�ap)m-� drif$"*� Vde�,&�"�-K -n m��M�� a%_ !{� � �se=&Ig\N)a{OA�b��! �.�opp��e�/� , togeZ.��%��\+� �ne���8 %;s sit��d�e%:�. <.T'Ka�a>A�m�l!%��)�Cd[ G%M!x�-!�cu ��U�/ $ ��mD}}�Tf�e��6e�&� in�OHen0 _g�_�r �koP)gaveraged"0 1��TS�_L$��fit��-!�>f�)�?�aight".�{w� ��e�� ~\��1_M�,ion_and_the_-n_w|y^��azurv�ti.��>It, 6:a D6th>��ri����t V cri�r� �.6ppl���)�AT!y- �z�t � \. asymmetry� " 5.  400 140 450 4304gle=0,silent=}"m  A]F��AW$xy��n�8a>3 �&@ 2�J8 bottomTa�I%I}m-E&� �,w�&�&9 �(x)qan�}*�ly�M�/!�n� . Kn��*�minc��-�1 =1� &� y*bet��E:2tX��I� $m�{L}(zw�* 0 9}  �(z)}={{  v (z))%�{�  alpha}}}=2( )} /6! 3,l�A%�� 0 �,�R(�` :�a�T�� � oint i�X!rtO�@�on�, $q;$ � �)��e geoa@iU/U�� n_2�.� � �"v�f�o�� uowo;tr�D�~. )j$(x,y)*}��)�SsF A0 =��<(Q_{x, y-p/2} - +)}{ 2!+6�@ 9��~$' T$�i W$����)��P ���/lY�t ���%Y)>M4h $p=$�S5 �� W . �=W�Ye� Bx��E�p)$ binPs.����M��g  ploti� i�sli�&b4 xi-�-+spc �"��edY�GaussiwnuZ���v!t���i$-th �2gx��(��&[t"L .|��N�)  �.�l�d�0 cuva bu�P�a$y$R� =x_i,y)=c {{ r� H \pi,Ķ{-��4}^{(y-y_i)/s}{��@t^2/2 }dt} - c F�N�!F%5��$y!'&�"�w��=n�O=�2 �12�"� R[ , $cm]s$� �U8:� M/�"�fit�O�+?�d5��,%�)���LsZ` � aG%F��� �=�beta$��l�misalign� /nk %6Ca9,&;wxŎ��|N�&8 $dy/dx� %��/ error (m` %@O�#k�ns)v!�� b�>�����sl r1onT|PB; _��/e��R4# row)! � �?*5 �3sub�N �% data���6D. E��E��qi}m|re���.F viaW� $z_i�Q $&�*� e* � ex�s��-9.�F�$d ��.a 5��I0polynomsP:la�a)I6� � "!�� !=U �Ԩ abel 5��  Me��a����t:����E toyw����v�� sZnAo!~~ �s� /�� �tloή">< G�!��, !? B��� �>T�="�Bor!�b� ���!�� cy *a�J� �ZW����6^��� � s a UY��} >�b�J� profc�au�k"a"t 6.7\E�" \Neq. OneeIse atr �ō2�((100-200V) �4�!9 "E z!��&: 1�a�Fum\  midd ��8ns��� . M7$-, J.S?o0#"� s=on cl� -�)`|��5]�*� bb=20 90 �t 316,�q��� Q�e"�A�w �a�r"�*����\E&�H.�s&�BO*��rE5b��la��m����T)"� ? $�)�"8j5F)�w=5�� >x_ >F� �fi}A^�%�"�L< �sig�!�}�$��V#).*:&� y�9` )X�����~s��x``D''��� inK /,?�"� t -EaI17C . � !ofB� ��m * V�eptRP"��2���y:� �s%6�� N�2� aj�490��Q{6.A�m��3J�&>�4%-y� �:�It mus����-���ed ύY.� (�pz<17}$�orɃz>268)h ڝ0'A&���AW�6D(A�2�^ �).��g*����"F :9a)�inc�� �� =�e ��F{U �N 2���s g�p^$c�8-$e+D�#�s�HD_0� t������"- . &�+E6X-� ��&s�:)$strength aEEN.�F1�g*P Q�a� 56� �C*]�� ;| �sM�"-moE<in�.�/��6i�2�Ax(�6t a2�( >�travel %�?a �arcQ3=u�Doޞ bEa�yC!��%m���-a�;eg al� �m�c~D ity J��1cz%�z"1~�I"�bubu 2�/"vP"D J�f� N� { { � �8{L}} } = { r_{h���mu B , �!lors�/B�;"�H܃o�B6+E>l� "�2��>"�:� AOXP1�A�impurity] .I�(*HP�TK300 K:Ai&B6Hn�N u�OӠ�Wcm$��5�c.d�� .�%����.e�Z|E2 |'6|�R2�a��to�.�b ��I�c<!C,=� �3n��leQ��e 3~ �(e �2A � ��[�o 2�dn�<�+Ass��5� a�de����t���=s� in�a�.EM-5#!. �F(neglected f�Xor all irradiated sensors used for the tests. Therefore the measured Lorentz angle can be @,to calculate 40obility using0Eq.~\ref{lor_C0}. %% Most of$0signal is dueV�Telectrons contribution"4ir shorter col. time and)4specific shaper`effective potential which�,confirmed by�sim�_(see Fig �@sim_cl_h_mag.eps}{B e H). Moreover, despi-lo��$x$ axi%�%�,figure}[htb]Xcenter}\epsfig{file=mob!�,width=\AM D,bb=30 90 490 325,��(=0,silent=}% S \cap!e{MQ��f�d%���diffee�flua s%(,bias voltage�� ded regi�^rrespond�z Uvalues )�!���L0large systemaamXuncertainties.} \label{-})�-T�y"�aR�ɺ �is6�bl �4 \par\indent\m�Pempirical parameterizeQJ�Z depe9ce mCB��arora� 8caughey}, one �U��G G��b�Q�y� {E(za�4E_{ce}} \left[ ( e� 0e} i�e} 38\right)^{\gammaa�} - 1 ] ^{1/, 1�el_% _for�(-��IC$ nu�# �o. nd 1 0e}$ (low '5B6 ), $ �$ E�$�$ �Pkn�IJ�s froѵb��%%E�Mrized]�grea4$ithin 5\%  i>q�mGies: � rel�errorQr �� led �6E$&~ d>F�is [ee�Vf �y_\mu$ asFc r_E = r"0 \frac{1}{1 -Mf {\mu]a0}Q[)�}.B9�b?%ThBaၔ=@eld %is multipli&� �J$1+ {iI( �EQ�} � $. F expec!55 rangm�Z��extra�`method�� between 5E� 15\%IS% ��elf�P}����:�ob�hed neg � :'��s�or�Z clos"_ �  implant�M� ment�restri�U �)417 \um$���mswartz_ c�ioin,vchiochia_ieee04}. By integrat��:Qi�&Q termin��&�$drop acrosIq�)�%�2q\ uŔ. %N�� 2 9�� 1.05*! clip=v�%" P�^��6�)ad!5:�:�%1i�sF� .} %� ���O�5e )e& �ap�*� E#in�"�� �. \sub�8{C!�-check q mV 6$} In order� 2!Z/ aQ�A� [ :�inB7sE�per� ed� p��c#�e6] ���nglt alpha=15$�\&^Etgrazing,_comoE�)y�energy lA�is assu�toa�uni��`i�but�Neither2=* nor Tus!a� take�(to account.!gth�&"!h6����2� perCiC%�=6� � �:[ �A�V��� BM��6� %v�-��O�t �� �S�b &/�bdarray}{lll} i(t) & = & Q_h D\vec G[z(t)] \cdot{v}_h +\\ & 4ez4e 4�end |��� Q_h$�?$Q_e$%����W)�� T %�s!Gosi�LXu2]�,w s �,�"7we��  , $"� $�vee $b�A veloci�6z�|��Ⴏ > ��0.3��Lbb=220 110 375 346, e�Siced^6&u>�-� � ��2�yb�m-d-�iV"!9�!�MC rapp2� s!�eU�Drde", on� lawqY�-�u} m H= Q_{0h} e^{-t/\tau{$}, &\:\: Qi 'e6'e"� XV�A�XA��t ��proba�ies ${� ^{-1}nde} ��?�Oa�2a�k�n"� �� ��� prop�W 0y coefficientHL4.2\E{-16} cm$^2/$ns�m5�%�6.1V')�'�� � (Kramberger}&� :j��s%DJ2E|set��zero, �*j E1is���@of few nanosecond���$p"7   ��M� o���� _pot�o,�_tr"� mV�n DA�8�� � T2�� a �A�th18�Z� ,- � !at (0,0)*� _5  %� �� �-F59� Z,Ak0nsversal viewf� ��� �� 䑄  �)J6� ��"�z��u�B��� ���� > ��se�t�aN�"i? �&)� �Z0�)i �i*j �=L|c��tot9n��� F2 ���:2[" �Cign9an�lya �86�Tm� t�lv6�*6 dominat�5.QL-��` ��^^^6�!al &?"� track��y�a>y of $F�B� �:��b2"N��� O-$�"�R&��#aI�:� 3T %aci*w�F�i�laRp��.jBu�"�� � �!yas2j dmLA, pred@� RH repr�( y� s well� �-��Yw 0 �46�a5� (markers):(soli�).�jSV� � N�}&�: ��=R��"�;#a�out>^�$omp� he� &p ? c[#t�=�)�{V�d� very%�>�cl_proG sE�) Zm$discrepancU �%Qiif�, Adeb �,�^"� -  b�!��s�were 2#E�8+�.��:�M�0.96�50 A�80!� Q1�eA�!:��Ya�>nb-�U��=", dashei%M/dt Y�::��a @on{Summary} A newCtoX��85�i&# &��� is��po�'� valid�a-!hion)*�a6o=precis"�!����!��Z S� �� RDF~i�&I�5���& }�y�bom�mFy���V�.\\�&1 u�:�)cy!'L6. T�$^)�%)B� q\is lim2'%m+*iJ . Howeve&� �e�s)��ea��!�s9��"E.v�:�is estimE@wleWa� . \\��Qe�8"�*1""i ion>}'*6D2�!.R �.��j�s)G.+I . �*�Vin͚+�%�2�+p.�&�#be �ed T s up!- 10$^{15}$�becausr,lattice scat�$ng"4 s "� �.� de�*s. �c *{Ac# ledgE } We i eful� !(temperature�� Trans.��n ED-29, 29�982"� �= .~Ca�/ �4R.~F.~Thomas, !'. ��-D55 (Dec.~1967) 2192Y>�& V.~ \, E.~Verbitskaya, Z.~Li,(&:'6' �&>k �"7inR�'-J�sv�q�E��76�9552�J�&} M.~S�&, %����&�s,��,��11,2�2:��!$ages 88-91��11F�3) S.ZB�'!�C�'BO� Af H�)I&��^ūy E�C� ison�~ ���x� A� !�c Sce Symum*R 8-21, Rom&|  S.} JOnV 143.JV &W * G.~4, V.~Cindro, I5 4ndic, M.~Mikuz�"8M.~Zavrtanik, %# �("�3��"V(� ��#a؁w] *� q.��� Q�476M�4 3, 11 January� 2� 645-65ڝe�� b� 2)RA��>� docu �� � M}\R -4[twocolumn,two~:`,pre,a4paper]{revtex4} \uK0ckage{amsmath6a76sub�� \newcommand{\bm}[1]{\mbox{\boldQ $#1$},�$�,title{Noise-�)�Lie� �3o�to Ro�,�I of ��msV4author{Udo Erd� 4} \email{udo.e @� k.hu-be�:D.de} %\homepage[f�=nViA�Psee: ]{http://www.udo M <z4Werner Ebeling�ffilie3{t itut f� [k, Hum!3t-Uni/ (it\"at zu B�, Newt�@a{\ss}e 15, 12489% Germanyu)Alexan�*,S. Mikhailov!� Abteilung �lalische Chemie, Fritz-Haber-��der Max-Planck-Gesellschaft, Faradayweg 4-6, 14195 �.��{\toda�I)abs�t�i�aw.�/<>(Brownian agk$�-�30ng via a harmU  �2 8&�#iM�.diI^V9K.�<nA�,. By numer2j w�9owJ>�*-/oss s� I- tG I� acq�6�breakdowA� -q mU �g�on�$of �.m rm5� �%)nsi�$ inc14�+Sad�3�%&� Pdynam=w�0 Ul6�re fur�+analy�31nv�g�.�9� \make�&${In&� } �+v�n�  nd social-�s,Q�, groupsBZ coh �7cont1N>?8BeCoLe00}. Such"�ve-)|s have bZ6observ�nO1�!1b)��:op�@s l4HaMa94,BuBe95,ztCziViGu97,BrLeBu98,CziMaVi01},P$slime moldFxLeRe91,KeLe93,Na98,RaNiSaLe99},!Ea�' y AvQ6��@9i�/self-E�l�9or d�An"�s 9�-�h$-�0OkLe02,MiCa02SBSom� them*Ay!�$2exr��8ng automata loca �lw�ha�� tinu�co�*ate1� ViCzA, Sh95,Al96A#(Vi00,LeRaCoE�A}5(!���s is "Wm�al �*� individuaa6@�s, �7�ze�,y-t�ihf�8� )&�/!2!? ir a��MPA� assu�*�C���b*C�!� dMDd�Fs!�bin ��s�� approach�5e�$toU� olog��ly2N�of bi$ organism1�$Ni94,Ni96ae45Sbl�4c�?m SchiGr93, m9hum>R,He97}�-U<�!I beAA�<�!�9#n.� t~PwEbTi98,EbSchwTi99,Er i AnE^E� ive N@g�..U cZbe)xv ely d�Ce#Gflo|5�,Fa�el�mselves!�releaDsur�7 ant �'�vmedium-iMiM!@. Aqfum�E�o�crete i<, hydro� AaI�fluidNM�HPToTu95,CsaCzi97,Er99,8�],Er03}.3/q olE��tyill � }}C�%yb,�em$-�of��:$flows star!/� �8o�4ed�e)�random5� dire���- 9�(� )�Hki!F&�.%ext��- .3�# �:� Q�2  CziBaVi99�u� frameJ!.�D%}5-���h��de5�%rs e� �Ft pv)� � �rA�B� vortex)}$. Both spa I665��'l )��� \ (ible. In a "�1�,E�  fill/�0 re availa�:i!JW tras/� FG ormsA� pact�p [ �A\ te. �e�>�,exa%6� -.�A�a� ng!,ck�!fin�IE-t,� �*� Y�%t���:of2WY��p�H!y*� ����+in�-e�� id::^ ��@' &> Loc1�t��� s may u� go20lea�nto�$�� , mes,:F% i'�MEs^� n� �P � gra����ng I G prev| public��Za` a TN� �T the UI�%W �>7.%in�  oscil 0sBV N|�(2G"� b!nd 2� � a4&Nof%-� ; Ʉled��.-2;t�9E�  i�y!�-�GttwouR"�s.""study �  a.�A5e2� U���K/bolic��]"�2co�Ha!to �ar �AA�a�orc�u2� ir)ab"LEh�>'$AalQ�?� kindi�t�o@2�6!7,�a�~ travwM1%Re����a�.Y%Hit�c�Q s a ��a�AY$any globalR�H e aimvour-��o.�3�%� 6���� %�fi� ��14is �@ly�'i~ �stocha�A�ceA/heS;is�I�t!�e.2 warmUaW0ud�U;F�&�disper7Aba�.Ab llel)sa����~"8oi�al 1Oury�2�c.$P� > *u)� �1< xmean-squ��w ���a-��)�E!�oD ?roo"x))�� �M��V it.B-)*�/5�� �7(�(nearlyE"h ,%�nt ^Er-R,!�*�s�% � lookLk�*ancak��7 ed orthogQlyA?h�� . EB ��/EH k�8acquiraJ morA�mme�F�L pe. �Gs�g T��e6�)�:.�0becomes sudde3if EoisDly� la� al �+e� a.� %_��B���!�Xo >mS�!�extkG� @#.~�7 sec:�-�}.m!d resul�!N` �sb�a!9� � ] � A�}5ly;,Hb�}GARory�+i� %uc �:�-E.-H p� e��Xa�cl�?g� us�M!e"eI-^�-� %�"�0!Y  W n4��!� $N$ id� ^0�unit masA�:=n2Nar�I pair&_)���R!G� !Eg�Q!� follow�U�ev�#"�:((sub&=8l� v-orMeqnX< ) eq1a$ \dot{$ r}_{i}&=&v�?.$ $F$W-�Ll ��-� on� �cle����E�v�( $v=1$. Add��*��=ssube7�7*vwhitel- $!�AV$!%,strength $D$(ch-m&&| "\&O �!�B@�c� �)%� \[ E;�D%H�QZ\BM0le =0\,,\quadn..? j}(t^{\pry}I< =2D\delta (t-$}) (_{ij}\,. \]�'O�� Y lyw]�i:b . INB�, but rau gene�.it �be�<ed ahEmal!um!� >K 9�� upercrit�:bifur%��T��to  tane�"�5 v��HO">Hj1,"k ve�U�"���a!�igrow � ly�zA8�o2�5 m. B0�6"��X &�:���Z&l , ��Yhold, h32, aZA��iO�U��Ra6 �, AiA! m�%VWa� � �di EQsh�no��o �KN�ex< �~~(��w)E�;15$ed alreadyVRayleigW Ra45wS���_ on6�� !�o�Ee�� (1) (A aght-5�hoi�C))N !�ve��sequen@%�� ed �� �"�Oca$3wo%R�bng}�($N=2$)�6*n �\;re*���aR9 2� a"�9 Png ; ters EjsNof 20��ls�Jen qd� a�ay� ��:� bY,*�+"�F�e "�� �JV�.� NN� 2�  H  0��g��of&> J/pFL�V$the Euler "m !&!iM�% step`0.001.���,� s �>numJ/., }fixf  $N=300�I l<t $a$ �Iif?4"M.�H6�w kW ,to $a=100$. g> *6 :�bra�,�`�Ai�A}( I�2. A-$$t=0$,%.�d*� p�J�sv� ie ndy��!�switc�:���Gttle �ar,�?�($t=30$. S�8�[��&C &ճ�t</#to�du�` =�i9,eYmasnH bf R� 5+e#��t �y � V} \ }�$ �def�Va[ (t)=(1/N)] i}�  F i$o UVF/I (t)$6H. ���cl&P9����/�e 5�, anisotropic�alc�� )oj� N �)�.���,[tbph]�‰�i}E��U '[]{M�Nz- 2vWmeaI�BW.ephC8.4cm} 1z^M�N\�V,�dR�B�"�W(a) T&Qd �U3�b'A\F�@, Y��zaf(*}C#70$) %u"�G6�h:�" . (b) Mea6�-%�ir�i�  I� � a "�6� harp.X Oe"� -& uoccur�V) % aU y $D��v� y*��I�� C, unti}%9� -( at $���!�tr K� hc�ơq "�.m)M|�r �)d �i�-� is I_r D lay= tY6���@s%7at�b! M0 noC� S&��>!&�N� quee�."�M6� z 겐�2�iqn�I,. ���3� ��� ��A_-�e�"X2%i B!�� -�s%9(30*j)E`$�iO%Vwindow=i|b�b��on$t=11403XY&.,���6�!�A�I�� arrowAmws&"th���Kvm�;� ��S��}�/Ih�4Fi�k��abweich���]&�K�[�\Jitudi�J� �e:� A�i �ّ�� >���h2@=  \gg $ M P!;s�Song]�. A�a�_ ���6��  s"��al��ach�N�iQm�t)q[!:G. F!e�BŐ׹�HJ6��n�E� a su�/6 ! 2 I4 -. ���^; cir]])�%}=6z)�!_spaceBe :c�mB*-�P.��� [$+$]�%-A�as3 2� [$� .�Q�22ł>�.��U\ :L6B(�cEk���6^�� lays�=oral B � w:� s" exceey h]J thres���At$ OO"�%A��  ta`imi��at 6�EKa�T s (cfA�n~).�K�D cour�imn! � slow (&�"� �,%�*�"�arozd��(S�" Ft'!1?c��� "�(;E`:�Q?.� P�t�=Q!sI"�B]�F E} "u7c^]��+ŀIe2Iu%�%�<*J�ME=e-y�$I z�70$. BaA&� vis'g6zpp�ASC?^ mpan"�.� Z nB�A�A�� �U2%,a chos�n*f .O }. H�w�|r8P � !mm.N I��2�*HT) togeI%� �W�'A�\Vp"n.)�(�wT� *m�:�E@�,>e�2�+}y2�# �. "�%m>Z���>k5�a��o�!edJch6��� ] &? o C� �!>O ���.� 5�y_a\a� ion��#H� M �E2 !e�hleep1��� n6� aboJs^�(foB< h 0> .�B�Toa�v`ys*�ip!��i �&!�2�(n9,S q�6jum�I" Ds $P(L)$�E � �(n�j�I�"�1� "a )r%���DYL=0$ (6� �_� um_� 6�:�1>23 ��B� two "� � P)� (:).&�_�avanish!`� ~�af�w). Not�}1�!��'� a]E�u�bT �clockw� A�5her-"N4<nd\ �Er^in each:}:J) qual. Thu 4&��=5ha TP�K/-�91�s�&a�� i#�7��h)�) fa�| A� -8".�(� ���be/s9�"��hWA]!�y�Y"p$"�s��f�/r�$ngTt puls:82vda*&��J���.j%P��Q�5 Ayw�"�%jͷL;9�s / be s�D"!"� ��"7C["T]ua�y� �B��l:Xi׽�4.05cm} .Bm70~milNlZk"M D:h �M��!gYB�m�u��|%�)�ng�)��Xb yNG�. :L 2M,` Dl�@2i!2�, f�0��I��"B _2ir9:`1����� -of-���%+@a�\���10�)w"��&low w�#?.�* .a�TN� �TD���$ie)S�A �#)la���%\r�$�� �rst�n� E:�=!�P-V� ����J�r/2ly�aoiwr�n�~I7 oDo ord.�*�l$ ds.BO74/�c�s<�#�Ves^� �Ő&];}Ri��TuMZ } "N*"&C@�$Aqs� a wa�.atAO�-�A��.l�3j Y�2a �E��$yB*�  to it����"�@ $x+,ECy y l.�k �EI�T�;be wr�Un I=X+z+BX=Y g�$X$8$Y&Tn9.%wm�/!R/!By�)'A�D$Y$] �= � �. � diwd&�J����Ya�'�`O (} X-#&X!:P!% ((t)\equiv \�Be�I�,Ob_!�F[b7vol�T# !�)� �6# �1F��0�0X}-� ( 1-�0X}�!�20 -3'�-^x� 6 �cotb2;yV4 X X}=0>�eq�x�Z�} IPwe� "�\%�wG!=�7e42wer v�S<&1]$F�$i* �EII�]* steady�=, K X}=V={\rm" N�+� R��m� �R�AO"�#1-�#-� 6���!�otz� I -�.8 �B� r]V�/���} �Q�NA�!�1p�l�R���j�;E ŵs "�W�H�z F($V\neq  iR\#%=1J%�v�J6b,f$I��B�aF��$���"m��*sub�;�1rv*.T >�0_!E�G�@�8-�pC J lang�4). Keep!�� B"?erJ�arGdev�Ms �F U �XgeJPA�B�+2%n1�5+a!!=\xi_{ }^{x�sJ)�eq:lin_�#J?F�8n^�a dam�r&"�Lal"�or*76F�j�(t2)af coup I��*6 �s $Ū7�a%�wa4Z6!�S 9�� T>L,R\%�I��(� :f%� &+2V)�-)� $ ^{3}+a�!� 5�y�2���_A�_FG���c��E] r�|a.nonM�E� Y;%n�G�b� !?Nnw,u1AefU� o=y5�n IndeMifc �cխ�8���n�bZ��:c�+,� 9�b1S� ��)�� $�Y <1$,6%BinMs$ �t�exI�i�,4�+" us, :���-�_cipH<ole)��s e�u� �6 cannot be9e ?�a&&%1 -c{�"�E3 /H()��5>2� 2|6� . AÃ� 6 erif�Zc�;A=�@� ���t�$�.m�ap7\gg=l B<.*$5��>C"�>��1��%mos�"1fc1�%�6` � i�sJM9=1�^ �a�É/ ��M  $. Subs�Sa��1into "M f�-I�rk l ���Y �Fv.�- B����}���_eZ2s"�'&Q&1:�eq6  T)" ENe��!�,mRf!,6�� "�*3$i� *&�Aj�&�Fsi� ��i5.��}�*E��c+nd��n@-�2�Ů{ ot{y=�Qw1�=�Q+ayſ()�"s2�){_iB��y�xiH&�:?m�V�: })$� uj�OI&s*� �a:�1 ival�Sv�,oi ensemb�J� �e� B� &{�L&��"&j yf 2��o/P e���0�e�Lis"� :�P��6mb/�4,NB2z *� fr�y,!�9 ($a�$1$D&�� vaOiAK itudR�,qwy \e�<8)e^{i\omega t}+^{*!��|�M9def_etfT� M=\sqrt{aX%?>�U��k>� reson:!Am�e ;ĖrX�� �oa� ��f� ��/� *=�ze�[!N}= �e��� |%�e��|(2�G -�3}{2}>R EA l!� + \z>�dotj�A� lex-�/d�*tg8$T��P&�'p?���%"f?AU$ �^ "T?�6I�9 9 � D}{2)�ZE}_b � � �ps on 6}3b�,�/��-��achVsi olV mX1 1<J�2t. Let u�Lwȋ��=\rho � phi � A=a�3n $�|3,4�5P JdP dM 8qN��FvD��.�NY2k�2WG�W@int_{0}^{\infty } 23��W�m������B�rhoRv!�+3 N� }%'�2�N��9 ��::�� ���5�N  ��*u&�_�B$ua��&- uI12�EJa��2�}�/2},$U1mO& �h<A-ed toN21b u�:hnu5!� (-4u�+3uV%u}B�B}uBZ Q �R.��_uBpɧN� \nu �62~L ,&V= nF�&LnM��s6VEY.� �(�8R.�f!V^{A�D aA��Ki!�(B�&^��B �!d')!:y0���fif,at !#}�>1�yA�2@ =2.�adQFi��m(wHS�a�&�F e/|"9ew��;�9p >�R�S_j�kappa -i}{a�A�&p�lawBfi~�FmLc*FiAx ]=2A�)�U�94�TiZn&%�%��$6�$xF�A�:5$U�d�J�� a�W"�WR.&.)�`�h�forwardo��G q� for q�Z`�N�J !�1fE�1� mTB�We"�/Q�%$:�% �C��6.�i�@��L&er�" r�:l& aM��.�%?�"M,,!95M,2e Y'i&�,2�"�6oWi 6\!V^�� 9!�69M�@0stackrel{.}{x*��re H�'=a!� :c o 9"*�-B$ i�`>�!�y/9  byu}=m�m�:x }=D/2$.Sqd'hes.a( ��*&#.qCin:�69�_H'ym��q $% � ���A� E`P�l data#YWa�7 R �=6qw�0�( rval�J8"�(����2�xU)E�y2k�1,.�( ha�z!sm�at*گ,].�5)_�5m %%/ \��+Ls/T300/dt_1e-4/fig8_ D 2�2 .:/C� *�,2�),�� D h *b�� b��L"D. -M5�P�Q�:�3in -)e-�� �- w2=&x)R=:hyU �x {< bolsq].\OM�ndxB�� A�theore�Sl &U��� law.mGU7�B�-N3%."R>"�-Co"Z}̈́�Y�x)Z}�Y�s!C*N�!Y of l&Vc,*�Q!R�0b`T�wo2bea.f�^ �-���o-�Z�_!X U��. Eve{,�o�>s �$�-.�!�$.X*�+"�]�N:f�+Ev��m�:e2Z*QEy�\Y��? �KA�.m.�a ��&�5"�7�����!r5\S A�5%"�3�1d>i>to��!��9ea�qEg�ER!"hon#b\�;!��{Aq%M2a��OFr�j.q&�S�ic)��RN)Fwa؋ g ly soT��>�V�e:.VIc.�7e��2�{U�4m� IX]0�are!�x��, Z126� E�.<#Y�RRThough$I��(j&a6f �(*c62�5EL WIcuLc*1BQ���Yz��6!5cl{3pr3:A^%!� ze!a :- (i.e.�Z 7`:$0�3s)g ��1E�I���Y> .& radiuVg%�s)Z,*�v!9�2�ZZHa��7&�`�5ka�&��A�{s * "�7!����%re6��(Ite'��&�kto>�N3!discussGe&�8��5u~ real*hq�2-j�܁2�9�8�#�ror�q�= as bird f2:s oN�shW ools�WF&��� sV���{ wW���L.~Schi�qky-Geiea�(d D.~Zanett2(us1 1�)� ��i��O?yg2�n!� N�҉ve Re�� Ce!� ``Com� N"*P�@ es''M� Deut�WBG4schungsgemeins�y0 (DFG-SFB 555�E 2>�~l̊,style{apsrevƚi{bib/all c,meise b�ybaky gbt:s �u �{ ,schleimpilze toda�d"�} t$ :R}aps,prlP}cZ}0}symb,_xedadd7*e} \*f}gҋicx}% I� d�HI�o�#,d j$}% Align t� ���Mi�_p��!i'��%\p�p int{!�tio}UnipomE�!�-s� ve]�g*�Xh f light \�]it{7 acuo�}a|8�(les Varin}\rMl{�Eles.vl} .ulaval.csd�w}A�Hre d'optique photon et lZ�, &}'A� LR�, Qu\'ebec, Qc, G1K 7P4, Canada}% ���,el Pich\'e}%_ ����z�|3.l��0�@u&�u��� r$e �,-��g&@���<&��I7n om��$wave packe_ P~S�A c���GwRUm8rm��A--")%�]omI\t�� Four��spectr��Y&�.�"5�ng&28�Q� f� e�$@yA� s7�2as|�=�0are�< an uq U9�>!_�ra#��fre!ac3?�sp..��fea�G o�_H possi��y�����=9��act9m�x8p*8��o�.Na"6` \pacs{03.50.De, 03.30.+p� *e}�&F !G6�3!����&R-+i1�A[EJ MJ from�N-�$�$t�fty�1�oc�1�mp�(S|=B^[H Q#Q[�$athbf{E}(\ r},Q)$� aA�~*g%�q eq:fI�_sZc���/}�~n`� 1}{\�2\pi}}�-"�^Mt)\,d\�U8T8$�6��3�AI�icI] vZ��<rܰ!cp~^� IM F!�a geom�m�~#0of view, Eq.~�n,)I�ar, o��0mp�L�+e,1�(signal. Acc<gAKimՄet T�)�(kimPRL2000}�8-�69�VK5(wpI&�) must f%1(off as $1/|d r}|^�IAJ thua lievZ % 6of � &�s� pa}ng fa���sourc�� �� k���be��  `yN=���SsueF��"��p�4a�IincorxP�z main3�t���EZUMc��@teN!6� V��cer�&�D35-��aי�6�i)h:�qx?e|�~�8m0"u,Ůy<6_t)=-\� al_{\,t}Q#A2�t`� ��0='�s>R/" t$mjs�$on1999}. Cyi�Ml�r�.(?er�)_5_�e_AA���6���)-V�)� t_., 5=E6='�'��IfAw(combine Eqs�� and��v� r��3=���l�e(�Hi�jy_vs_non���bVb1� v�6�BW We h� ˄�^z�aai�Y�#�net !�Aqb�[)�yr@ $tZ@�U�-are`"i�>H d8� ��#��� fT7�B�]�a b�c��of��bNyZuld^=���ll9Or}$? �'now pus�A�;al{4a l�eU��;pri~8l%9ny��&� wav�]m  gente�4{feynman1977},2;}��},&: an a=�r@�ca� $J(y�U;yin�3��duc7wir��k �l:�iZ�-�3AHs!�thίv�:7�Ebe em DdA(*5�0 t@Y;�^[ (of �l�p\D�ol$9 %�us $a$�l�� hNww�*^ =Ƭ ,0)$j�t��cylind�"�%429,r,\theta,z)$�La H� 1w���a�% $ziEZ gat�  �Ma�@E��sowis�'tOE �04�.cr��atied�\B:I_!z2Hr,z� L&\Pi(z)�"a^2��0)�, l}{4\,r}\,[A~ \,]_� $rm{ret}}\,� a}_zB�A $ b=1$e�$- ^ l*(q z I0 lLNo u_0��!9permea� AOr"���2%�t��o�y9�! (lZToCI$z"�),E�$[\ldots>�$�[� I� quantityEM�br�$pste3~ � 6d5retar�e $t_%]!l}=t-r/c�Z_$c$ beA�! ZD"bi�C 6���]4�6:��|��&�.�!nr��%�w� �thivQ non_R�:E}e�8=I�f .f�(( +J(& J(^ )}{r}_()%�bfE�BI u�Jea�ILI A�!�6� �Qes�n!re�PnoF ��M�A�,�#���?$�=� $. G�� !z /a� ���happens.&� i)�w2�%a�|2�\j��fMRo:�eldk%,� seMU iso�md?/d&�SFig})$e��l6� C��͓�g��rry�uZo� 8a�q�� =J_0�� J\, %�,rm{erf}[\,t/�� t\,]$ --*�6e�� d!��Z eady9Jrome?C$J_0+ V J�a�����5% 7aYe=%�t��( vAa ɶ)��e�>�_�ْm�t)~� l � J6e��  t ��^) \expi�-\,.I^25�^2m�e�v�� n�M�edv�J� ���J���El^gHd �>w�BL%�m�edx(a � &]�K"T@ ���gE;a�,�ly�x E.��<)).�8seemsI@F5 �5S$}gO:���� �>&f��x"����Z!w &f �j� $1/r$ %��iXCPRe�W �) N�m .l:�� e�X via}&$ :��_�%�x*���2hus`�ny Z|y� >X�w����z� Brabec%�Krausz�b RMP2�)&p&'])Is�N1�U} "m(M�7� ~&/ ���jJ1 �| (top)�!K�jm�^�$(bottom). .�F�!GVH)�i�X. But!n& dela }�two� ces+X^�s 2�l��, ($t_2-t_1>>��no� �%�(zwo��uep# !D*�/a&E ��R$c\,( w��(��}�1� Z �T�����$!} :$ B�5�rum^U��Ztne�cng,!-~�,�*� to{ =8"qo�<vea�� ��1J�����oipt]CpenE�o#-w it &:!ro�Pw n[tl2��&30��a^d!�BelenoveNazark"+�b $JOSAA1994}Jkpe��fam�of1s, nam-}-, Qw�\ *#��sam�$r�[4t=\pm5vHe~�EQ�$ e��[��B��N�R\ *�V�O-u/  yW:� ��apa&G��2o ; ���sem�J����.}�AbJ��;"� 6aC�K!�J^$convinc%vM�n6� 6�J���A�~ > o}�W�R�3B�#C.�!E�M.!!� nk Lʡnd� recher�su�-}�e �!�ech�� �!~Nal�M Engineer�^R"�$ouncil (�!�!�����6P."c Inno��^~th��Jnezӯ.��B  % C��b�ce�>t}BibTeXu .�$a���&�#% % * EnUMf��emp$ .aps  �iBɡa��,12pt|$�3]{a�|�&/$[dvips]&b$6x$�o3 tags]V�amsfont]7�$6bamsthm6�xsy:psfrag�Tcitx fancyhdr��.h�url}{{�$%.0$hyperref} \re.5(vec}[1]{\enu�ath�8ld�ol"> #1}}[  �16 {top=1in,� h=1.�G }2�A� No}{}� � 2040!�.�(XXXSize}{{\%size{12}\�`\f]��%bf{]�>NT�%}{\hfill_%0line\vskip 0.�v� \)read[LE]{esf{{\�* � page}}} %:.<RJ< E.~B`�ouka�� 0S.~Sukkhasena��RO�LJ<Ap��of�ivL*�$ moCös [1X]� \cfo�X!tsfEx*y�\!�(�!�sloppy {'!�%�Mbf{ProQi J� � ��>�2��A`train'�, adox!f� vi"u$�"÷XR��}% \tѵs{PٕJ����4it{European~Jo� ~of~�}, �~+,bf{23}, No.~�20�ppu�3--110. Q� % [a�U��dx.doi.org/10.1088/0143-0807/23/2/302}] % }!^�(wsc{:e}�E-��:l\tt{edouard@ccs.sut.ac.th� %1\ (sc{6��G{Sc,!F �$, \ Surana�"�(HZT�y=\ Nakh��t�� ima,�l00, T��� } \date{}�"�Mp&�%Alt�/�V�?�� e"��3�W);ng �}Mpq, pio�� �clak���� Penr�{�T�~ll�! ,El_3�p�� \@. \��f{Item1}�#"�B�exist���ul.gich #. �[.HaB�6�,�=��b��o �id�mn'Km^ (ta~��2�1e~a'�3ormd1's \ �\@. \�8���2}.~No�(o>_� t �-�0f<%*�(so-��ed>�%el j�n3n�R�7 d"�)��J|�(IK!`.*���[on���*�^lly?�!6]w� Tpap /0- leY <t2D6��?5�SU/7Q�!�mo+an trigo1�t4ndo men*�?�a\� yb�l� E.}�Sec1} S� � y6>% m%� _1959}, m6   eV Weisskopf "_1960}i�^�6�s s& al r҃!� > |0�-a�a�m�Y� carrs9 out �, e.g.,�4YngT4m�2, Scott 5, McGil� 68, 70, M��8ws_1972, Hickey 9, Burk!.91,�s$ard_1995})%� T2+E�&Z��E�� ou.�i�atp��n*̬theenumc�דic{ }>)�B {6.B'PQ�n PinQ i}{(9)BTp@xi}{� keat��+e�-} \�� �� 1}!8Rs�3%�li;3�,  *9"s\����R�z_,A��]��\emph{���� n� R 6��VmVB� A?V�5@ �)f1x1a�0^)`m"'dt�] 03.�Trea�n. [t5ult��ly�,B� 2} �/��ft8��"[ puzzA a�t�i�invvAg��cf��y< hefdNo�6�<n�$�ž�* �>\q��:p3�ox>+Z��é_��of1��-�: �* "��0�^�9Axao ��� � Lakshmana� ��2} al%T 30 y>go��98s��stP! e��1��ari��-h#� mannerROn!�te7ad!=��La��#A\V ��tQ9Dm�URv$ �%� .�'���!�f�0aY�I�N b �r pq.�<t}i���an�]erF��; �7M�H  ct�nblock�E�, sli� �0(smooth) rail΋d�ed϶�=lower �!�D !#�%yof�0m.Du 5w7 qbrZ*i<i"sT��nd�)!�MIU*% reaso_#?�� ppк+GZb�m�'U8 �La horizontal flat to0�uch�a `)*' - � Agaia�iRqf Ana� n�t}��� ��,f��!�hyp� s� 0Ieqv*�Eabased !haAi�, ccou"�l%t* !r�'�( 3i)  l:[I> ��Hv F � ��KA~a/�herit�M� !:�K!Uܛ�5�J #sit��E� remoE�h�<st��� ؆�3�mid� ask��VasnoT*!�mpw%�A��A/ >� 3i%nh�8"�9�~?:� 3i5 pier�T.�se� ray�I(bprp8f> a&.!`?e2!.X �7>9a�ފ3� Sec2�L��k?d2�"�4H���icit ("}h)>A 1 "�������.�yPi})--("�%O){�!�5�F!�> �U6 :� Z:%;�!�$ulae "-Da���`�!b��IϹ!&s*�) �^�P illu.QGA aith1�!;�6�;Am�Y�ec�wuF�;�E�In�]2lB�2 5�X>�����s#.��J� < �� � 9A[ho*�1�m��� mapluHe  %Yto^� ���!��� �$M�s% room!��olS!u:�K&�"6qM�Ä]qa ��Y>trivial,� ��O>h3}��JF_Nel�6�� ��t vN�M��3�A� in >�4%�ea&-I�~���$icdW #VH!8J�u%�aqF᧡� �fs \ S���� 5} d�#� �k*uM%�\ \set#3{� sep}{0.02� widtF�b�B�$[!�� \s���b� +��CL94.L>7pA {O}{63rm{O}$} ' �{�*$}$�O @x}{$x7y}{$y2" z}[][]{$z& h}{$�3h)2,U}{$U(V}{$V2"n��\hat{n��d}{$d2.UV }(U,V)Yx�(x_{0},y:�x� (x,y?4cx�0�Qcs[%�=12cm]�&0X(!a� []{�.&�H�JE&�< 'e�� �#*�b.�a heiiD$h$�A���S �E$U$-$V$� Gp�B�6T3$6n P�paH��}�zj)n� �mL Fq&�'$d$'0\overline{\ma�mthrm{O}}$\@. \ A light ray from $(x,y,z)$, a given point on the object in relative motion as labelled in t/serva�frame, on its way to $\overline{\ma� piercesvX$U$-$V$ plane at $(U,V)�} \lw{Fig01O L8$ with speed $v!L \ Let $(x',y',z'!�$1�0 denote, resp! vely,{%T ling}$arbitrary Zthe corKonding.�'$ and.$)sE��T:1g ^ isA a heE� $h$,.9z)9 (see )�~\refM&) above�origin�O}%�th2�$-E�� When% @s6Aand9�O}'�t $t=0$ $t'=0$,!�2�28E!w$s coincide" wE er af%seeB is happen!�Phe takes a snap shot M�oba�� Sinc-%�n1� only)�� \\ F� Nj43�(x-ƥ +(y-� �� = �U>9ornp4pVT(x�+y�~>\A�j�5])wU�}{d!��j�})�0�B�givA�a solu��n�6�U = d\,��-�1})}{:�F� Alsond7d ]V}{����%+)U� ����8�V2��i��E�� :�  (� ��6� nd8})��sh��� , follow��!� exam�nion�9F��|seB~�now��ow us��fin� �Aof a ��*� ��~&[ # � ��2���� T�is end,� �LorentzB�8$x'=\gamma(x-vt2 �wu 4seeking, where��V�� � "[ s&�2}�U��� 3}, ~&�!p$e�"x 0.9$var! dir1on���&� 6 �j % P�(nent remark� ncer th�8�Vs�0b�,d2 � � Sec5�n\ �� 9}[!hb]� ceging fbox{ �"�8{0.94\textwidthe�27�Z r�.�MY.t�.�.3�.a��#.U $� (a),A, (c),�}�a�= mhiO� 2iP ����f movy�!�� ��V�K{}cA%e &] ���y�@psfrag{xx}{$x'$} yy}{$y'$� &$zz}[][]{$z.*a}{$a2(P '�P}:\,(a,USVL7cm�A4JA��$horizontalim��!�� .�i�$�>E 2(, touches Se���J�zv�\��{Re� q�`train'�dox{8Sec3} Let firs�i =0�� "eab!&2')!Na�,� !��(!�afix  Suppo� 2!g~ ab ques��-5 tA 14 some� , say,.�%�ee!���&Avalues &�Wa�3=a$:H� )�of�0tact just men�ed R�4})�T�$is, $a$ is���c&g� Bk �!":� (2d)%j alsovvidhM Q �H� other &�as� h�DXse�M�& V8 � � Q|Eqn11a� U_{a�&ia2� �1"> )},\qquad3 B>� }{B4>��� U- �.� y'(x'-aJV(xE � )ҭ��2}) V- � &= -���  �`.i ��a3 � �Q^�Nv�O�"s�h)}:\�1}(- )>:r(1�S�.X��[-�U+%�d*]> HE�A�,>�� m2�s��Ne�ini^.�y�We re�" <15}) was derived6�@��\neq{}0��dileck� a�$U�V$�p>3i.�Rm  fa�� sam�n� x���U��.��(satisfy"My�! V�)�anV��Tw� li�!�6� R2|} must �lieZ�ũ�2U is pr��qrez��or}pl�fYoJ� (b) (�a)�mc�$ an imagin�E�joiw tip� �(three roofs�d draw E�B ���NownH6� case2|� "�&� 3���!#=  pu* , so��speak� sl� is �"q gst� ary# >Z one ha��e impres9i}�tip���! ��Q �GKcut!I ough��pa+  th "/9@t �LdemonA����aQe .��%�a}�%��a�mI�alwY in cH c��V Q�!�w�!5���butPdiffer��s JaSA�6 due!�%A6 "%\$ .o"$Visibility1lR�ra�"� Sec42s"wo ruler%�glol"lengths mow�e . �"%", Aach�� rece�!�}erVm 56m eq1Co]�2M0�T*$by $1$, $2�hil n��� �)3)4$�� In &� )J�(.Ao�er)d or�#"� 6� 2en�$1�v2$��ch�S:�, should:]E� Tf/ EW�� Ia�e meanA! �m��%9 �!l �es� k $2' ��s' �to� . H s��ai� �2�! AN.�1$ earli.� Acc�g�$I:seems� be e�ae!e��s eff��$"N A2)� �=AO)A� ha%�reaso�F appl!to%� �%[ (20D1�)!�.� ?�A� be shrunk�� $3-�$4.�Tbact�#ve note�to do ]���n>�o����,�they wA��gribut��"m�;!9fi�!!mag�A R�!,�sXaj4 general, maskTv�1 vR� � of d��naturɊNNt�|B|1}{$1*z2}{$2%x1#.t2%6�3}{$3H4}{$42H3#.H4%6HO�O�er) V�10�5J�� iׅ"�% botha�ŒA�| 6(>toaVc�#ser�Q6�$,�i'N[ ��er�i�f��X'$��q�E|e�u�"�Z�&Similar6�.��U2�Ѩi�*.��" b�3\$��ͳ.� ��?F=z�� old fundaQal%critical&�com& haunt u�XCan�photoT%jJ�\@?� � answ� � |,��f+aM IW�!©wwith �� � suc} ts lo^edg��z�)"$y'"! X*r�* 7 � 8 �Y We� ��� �h�~Jr� of it%r ��"� �1-�e2=u@���Y? �*&�&�*!X*�0system, i.e. K$h2zbcP%� "�%�Aspe$( by�jb��A�n#1"#�d+�x' \s�){x�"2�>U($V=0$):� 1�Y;)�I��\ FDIis�ti!�edE�il'aek' Delta{}x') a .�@ hangs( .U��*(4! �' A�s*-�, c2�-A�� $j2� By el�c�_i� , &J��n0'1�$�"m%N��)�x'�$ �9���e^]Zx'>����$convenient��'j"\ ival x(n��$uB�a�[ �$�g#}.j"+(i��,,Z�} �)X F��-$b |x'/^R @|<� �#inf�-AT �!�h�+aroun] �9� *� nB9%�r'r�A+uB��vejc20c^t{�)� \�{=!�(.+U*�#|_{�=0�SU� yx-�B�I� aparg,oC triv>2�tant sca�1 � or $d/y'�famousNs!� mula�� :"�-�a cerm%)�.��XeR]is � le}q>2�, > surf #EW >�of/ �2�� �; 6y� \ TKM��6(�u��.c a lin�!k� an angl��$theta=\cos~$}(%�)�3��^��V�2�)before��t^6|����<a4�$re-assig�V>��!�� ,�(� �*�5Z�i��6* in5*n�P �P ��ac}{$B�&sqr!ZHW V 8 6J L�i heYA�%�'sQ�� %g%�T1� )�� "� 6�cA�ud2g Z�fl�Y6�e�� �2val6�abjA�F� � z� "MCo�$�.75} l<� *�u�c -� � �I�: (#.�N"�&�$ir� S Ss� L8q*93'e7�on8`5�&is*C�� RT��&q Z s m�be*�at%�� V4N, � ��f4 � #se�1��(��b�! 'in6uJxlAi���(nhi%��!�� ѩezu����!)��!ynI.P cP�&{ ,*� �))ny-: $y'$k�!�4a`�ebeh cur� - �31�� �la-!�quiteM�in F(b)/"�KF��^�u,!���.<f"�discu$A��b�7�h%�is1��-ich6 ""�|,-4s, 2F`unGC8+a c �6����wa�Y*� .n$HS/ asily loc�=5!�J��- %ŭV�TofR� �j�All=a�}�s%� dedu^�&�0our gv�( et/ed-�EI �accE�-(to students%sufficS preciAo illuo,te faithfull8� fe�"Bj,Iq9Z!Y next�%grammͯis .�problem!M�m ;ow� �iz�G� sa+a��int�-4a --E1onm'� m%<ida!�� � not��a�mp�0�Щ��b�;ckl�%\� �)thebibli!phy}{99}',Pibitem{Penrose_1959} ,~R. (): ``!G Appa� Shap�$a R�is� ly MFSp� '', ,it�+Pc.~Camb.~Phil.~Soc.}~ Pbf{55}, pp.~137--139.�-� � ,~J.�InR R'Con�t '', t�hys.~Rev�$116} (4), � 041--1045.�4Weisskopf_1960�; ,~V.~F�6059Vis�<Appear�9(of Rapidly )1 O�;s22,hysics~Today9)13} (9 �24--27.�Yngstrom�2}  \"{o}m,~S �2��I�of � L SouQAAmJ�Arkiv~fWr~Fysik�23})=367--374.�Scott�5}  ,~G.~D.j VinerAzM}65�A}Geometr`)Ir$�YLarge ��at2� S�@!^5�Am.~JA�ys=�3!]7-]534--536.�McGilA� 68} ,~N.~C)Z8�F.V�� Spec�qNty.�A�empB�9} (1 �33--48.�%]_1970Ji,van~Driel,~H!a�7I�=i )iA�@A�a��e�R8} (8 �971--972�Mathews�2} ,~P.~MI(Lakshmanan, (197M��5jih Form�.�a�>ilQ,.dNuovo~C%>toY�B12M�168--181.cHickey�9} ,~FQ�7�: wo-DX� al��a .� Cub25V�47)S�/711--712e Burk�� 91}  �+aT�!Strode��@91E�4Classroom Exer�d*t� �s E+.�V�5E�0) �912--912D0Howard_1995} <,~A., Kitchen,~L)�DA���9�.50 Ray-Tracing:yula"I:uV�.�Techn�lReportY$95/21}, De mI  Compu�8S�(ce, UniversF�\�  docu��} %`` ��% revised Paul, Nov. 15, 2004, 22:10 %Stephan(7(7:3.'Thomas M%126&r $7h30 \�cA� [12pt]{io!w0} %% % floow| test� ^it woL5� pdfHDxE� equ�. E{5�ED_ubmisa�!%(\ifx\pdftex%�on\unx- % keep�Do �  Ht#P \usepackage[dvips]{� icx}"\else 6+ w>,fi % *� ic styl" J < B t({harvard} \7y5{jplB �%oms}2H0dcolumn} % A; t� �/decimg& ointE� 8type{f}[1]{D{.}#1}A�.u epsfig} %.3.,2amsbsy>.amssymb�$def\sfc#1{� d#1.� � . #2 B� sprm I 8 {�H�meF#3z��%#3^�me�Rn��Q�r�Rm � #2 FT)U ". B�{%IstI+j)##4#5#65)$( \matrix{!u&�&L \crJ~b#485 6 } �)Yd �-V� ���~�= sixV\{� ) V\}9 �R�'({array}{ccc��#1!�23 3�.�V� �-�\��}Qm nine6�#7#8#9{-��� ��.��;�.�v+#7l89V��end-b$R1twobytwoq�1)(�=)m{�Q \\[0.2cm<�#3�4B�� �)ee %M� ��4title[Photon e� {highlx d heavy �?]{2, �8quantum dynamic�6$ng fields:*Vn_,, few-electr�Rons��author{S Fritzsche$^{\,1}$, P Indel�@o�B8Th St\"o{}hlker3d$ \address{ 1}$\�-E f\"u{}r� ik*u \"Ke1lj(F|Heinrich-Plett-Str.\ 40, D-34132= Germany}:�2�(Laboratoire1tler B?Zwp\'Ecole Normale Sup{\'e}rieurkFet&M , PinB(Marie CurieV�Bo�74, 4 Pl: �Jussieu, F-75252 Paris CEDEX 05, Frq>�3�(Gesellschaf)~lr Schwerionenforschung (GSI)V�@D-64291 Darmstadt5cV0I.�r Kern� k92�kfurt6G604869�qmmiabnct} Rep@�gAz�"�j pJ� i�-cB�Icewed.�se inv4<g�s�. � F -$Z$e��; UPq83ot �4m� r�"d#�/i�y�q�- � Q ac\-�<�4bK2. A��wzbound-V5�I�'�N�accur+Edescrib�.� ��jQ��E ���, m�*iAbaVi*been ob}#ed�)�!�$radiative �Cur�4(quasi-) free 1s�02v. M�"d � ed�ctra �byVfir�$in 'fQ4stic} behavior�3e�"�si�7sts p!P��{*E�Na�.�Y� %Unco� P$ PACS numb�4�3| message \pacs{32.10.-f,34.70.+e 80.Lx�% C M� if �!� L X�rGOred�ead{s.f��@a�.uni-k��.d�P make�qz��"� In�m} 8<i2D %Hundred years afsi�-4�*]*�M���if�h7�2moyT eld,�iDn6�l4{8�%n�Co�V�theory�o�5o ���aTa%�m�-magne�R��m� r. OW- comb*vNq^ ty %�$-�pica3�9�of)$um me1, T � to %:�mi&copic`ld)s�",E ]�"aJ�� %:� (QED)1� most�E9suc,fu�=1MaPics %t 4�,l%�5F!��^or!��M�0�Be�: 5are %����nterpre�#e�Jer t\IwIg%�A�iw< ir %C �!�Yizek(*A�� )q�$. Born les\# n %3�a_Bgo�)rG( Mmof�*E � �aU*�5A�oA,k. % (PI) I�)ho AS=1t s�al�]: n� pu��t!�� ���i �M�N# ��2� very�� ���0 grad �"�^� a/_! h�XZ�� # � ��rb9���@o*< cF�ald"�&Eٍ� betw�%%��!���ya�it:M;tyASV=exempl"7Z9nt?�� %M�1�f " N i6M99�3l���2to��R�I1�� �� ���6d�υR��t�XN� >�St��M���U.�}B�R�%ݕnni �� 2is,�k�AFj� rj��#ex���SLaseri5�7�]�Tstorage �(Gve en���9�w�`� < cy�( di�Don \cite{skeh2003}>� �� ���!*^-2���s�� �!E:rMTd?esearch�/%�)icD+&; m� 5tra%�cru��'our{ t*90 ɔ�]-u_teq��j� They A<��-m��m nicU� stru;�*"4!� }�!�u��to greI4m�C�3� f5� �.2. Ouror�al)6��! atom gEDa�adv�d> ��rab� uAX!� lasO2��\ nks,%f�Wa p�1leg%�ol ��+�enh���QED%y�>%�i�% effect�  l p�6!�@ $(Z\alpha)$. I�,aV : ion-!m�li�*n add%�d� n  QHX�"\-�A�+&b wa="�� u 6�� (or� si-)6 ,ns (REC). At6[a�u)M� ( determines� qbA�life\- -�9�dA��K.~�.�"� compt{"O �o %�>g sp!^ nd oK:al:f�s. ��malVq:qs �Z��hermor� %EC �6 ہ�Aq��!+ol �polariz�Are|beamsM;�6# ion!u�I��pr�D�A�Vl��.ois*DA�a7rt summF�+ 2 fac( ��-!���in Sec.�-<}� ��:L �2.�/"�,2X4sec:rel-qed}, 82��A+ :�`:�~r*�� ��ies aaKll�EM one-Iwoq�F ��In ��e2},�7�XM�J�U��0 some emphasi �>H�eZo.#M���r� : A��q� o_��SXd��A�B ion.�icl"2%# outlook o:fu,Ys��Bly0 /9- ?}a � "�E" alIx�]�"�t�2�/j+>@basic��g��iA*��%� ��-]�vol�.ia� r�ke�� closely �Kʼn%=�D&�Y� rn5 s(*%M�-ler t@%� A�� aU�us%�����E� 7 a�i{s,]b[recoil s. D:�fewudevelopAKA 6y �ppo=Q�,-cooler deviSl\AM{^Pzke1987,Poth1990,Bosc X3,Mokler1996,Steck2004} W�5 d�N): trap� � �N a lo� ��R Schneidc089,Marrs1994a b,�*$aspy2001}.)%�!�i[a;^h!�hydroge�\ uranium�m:umA p &�Ie�� aJadv��� _�P.]( ESR at GSI�"� vSFig. �[ fig: 8-� X5�z$Super-EBIT�L>��. AKESRY�@Ŵ guaranteeIB�UŮ�un_0ed[a lity�@\��U�&�NE��nse QateK�IA�% aieB know��"��P+�:moA�$um spread Iqz\r c=m�w��in.�2exs�3Q!�y � ofF� I !�E8H-�0A?.>J��Y �1*� ,!!�q<�A%&>V� produc!\�sW;!�laTry��20  focu�[ ���� 2��&�-i0bkme93,boec95>E ��W!5} ]�) { \e�&{file=.�D-2.1.eps,bbllx=3pt y=54pt� bburx=576$ury=811pt,�n,=14.cm,clip=�&8>�]p: �s/N�} } \��ion�LeEcA� sent"� E -�A�E�r a� i� GSI-u�%� laypde�ri" gui�� (dip�b�kng 9 s, quadrui' hexa%E��<he �impor�>�al�  �1a��K� �diagno� s (k�-$r, rf cavi ,�ottky noz4pick up:[er)�poa;!/�r�-jet-t�St �_�6 . %2bf{File:�/��Q)/ H:�R6!�{B2)���M�f�dYn� �% *�Yo��t�:a�Z�Vc� v� *�� REC��n)-��_� u�2!DFed2� 66�%rT̈́�桅 ca�u� dQ sin�?c1 �����Afa!� gasj�)� �"jde� D 10$^{12}$p/cm$^3$��@�� �.a�� a typo. W�agi� �{5= m21m . Mo�EuA�i�t���D�al ) -�S=~s ��beRs� %�� �zuslno !�ve�:Z e�%r�w+#�;qu=�3aHESR�Nu� .7 :�al� !>le{dbackgr�. A�`H1 �!; j~B de �� capa6=6� �.�;n�� per�E�z �,2K��p -��dA��  a.�new� y%� ,S do�8�Q est �� -Ds (e.g. U$^{92+}$)!Z$ far behjth[�|�$yh toe�$ 1998*� ��� lowGy�!Kperturb�K $Q/v$ ($QR$v$$ � 3� c6_Y ) caAM� 'Pil�haches VKs�w��noEessc:a � s. Fur.=���#ped�b9dispens� !��t" �:A:2S ai�P+�of�*0 S ŸzLas � . =O1mA;eL�d� m� Dopp|% corrL i�7ly rel ��$ tH)���!kF<��a��f limi*�� 7ie���&Vtppl�A5=b�d�& .�.y�o� .W� �nhT!t�Z�v6� "��-qs��ve2j�org r � �!U"����$�dGH.�%�� ofsvde�F#> tookctceh <$�P ��ly motiv/?�!wdemand �e=>�k$� f9:er7�ni!�zP %�A�!8�( (iBA�!h"R-as med�iN\ g. % B��cted %J&9 ~u�=pla�  %i��r= �&\��jU de�IW�  %�)� s� m| A�s^&9�� millim)ad sub-spa�|resolu�Ga*�imIgfk&\ar-� $ reg6b�515~keV� Protic�,՞�Cv �N?c|cryst��gM>����%!��B measuE�� Ynergym um wm]enough�>&� " wh!���O�Q��s2�y�� Beye�4}AJ*vAHe goodR9~of silic�rr g�+i�,etewsas %�r���agaH &H �'�i# � vm� s. V!y��� D@ trip5`M}����a�F7+szent!YJ\"ul; Y}E��J[ .��e�!�$200~$\mu$mQA���  avail���� -���iWM=sco�) ESR 2� �2�,=� AiQe�a� ki�f �.M�siw [M,e��J� y�) key�!��K�e"����u�ea�<"��0 An` # ��*X gran�{,aB�.�=T_} �� ��]2&atI���00�. UE��.�{ soli�+U�,:u|U�H2tof2��, freeN�nA V�� �B�'Ae? cy by �poi%)A\ Comp�0sc�u E8�3ѭ.r4}�i%b&6EW| j�8.�-Q��+� agpAy�a6&�q$ " lay� �~a�� pixel Wo`��&Fs,pol-kshell})��dV"�^� e�� %-W6sA&!=�.���� �!a6i&�*)-Z=p)IA.�*eN^&�q %cap0i<%K--�, e nw�ʄP��ticipB %� }(i)�B!)ai[ �.�P %m"*i@sv (ii)A��Bwequ�� acter�( %x-� s�](i5%�7cF �)d Y�=a%]�nc.Fs. Po�?# is m[,�NK � ���\��"��- �A�on- fƅ I��U�.2.�r�x=9&�26 �3�788"�79 � 9.5c��r��AJ�De�u|24�Nm!��AEd)�6$!jK-RECa" 400 Y "| $�9$arrow$N$_2GmF6"a�J� �E1a� �d>�N� ,Tashenov#.&r(/f� �~abeRFB$%QS�"�.'�V�:b�I-�k"�!� *:*a �>&�|5�. a�� [)�&�fac����"A-���)n"��of�.$$ b�i�&th 66~��!Xle�Al$1s$ �TV��:�ID� �0:*� �E�%`�� �7operator�s&N� s"�Ka 2��.Oal]7&a�luf�na;Pra�on �}E us�-Ze.�result��Q^\��y{^T�~#i.�Y\ubA_-Y" 6NFb�d �B�rA2w��e 0asnoun{dir28}�- ,+C!y�!ename. Be� V/S�%ZE�!3,mas� mpulc !E�grDE^2=m^2c^4+p^2 c^2�m�2��.�2 \> , Dirac��g his �had)��v�net6t*� �s. He�� thus�*�!?p v�it{uX sea}- avoi6$!� �!�tL>� �h. SoN%morZ {��axmM�u�&� h�on� *�K��-�bre29G ��ist���f �sea. l4"Vacuum P*_ ��ad calʇblem��~� l�!)amE�${ueh35}. Yz^2� plagu �infin�&� up/ ll sor�'2�expa�o!�Th.%&� ~-lar50}ZEY�)�Q_ �� predic�6l�/p,nJ+fv!�on�LY�;�1j�.�.ED.�&(fi�uei�'k self�&%K �bet47�&( Lamb shift� -�� Afe� Q%a`% .;4 non-2��(NR�3� ŵ�6,FH �d$Ri�l05�70'-.�moh74b)�ed, by!�~H8)�C&��l-�5�a -3Ŭ!-%M�M�� $!�I9 did!� G rge,� �ode-2o+$$Z\ge 10$.&�n��ta}]^!SY�ve%S�"Cen{�!�yAM�B],�5�}!,&u6\�.z" $\alpha�� d,y loop.x,�W2�yis�bC.re$oc��oin�ad(ofB6 �� Af.s, �21ps98} "&� �se6of!�"8T!$Aq�&�" U0m@st��A8a�a�obeDpG0!��  BEVALACaMBerkele�(bcid90}. Wizk~past 14mA�nk he �%��*.�r#�Oal�urrA�B�I�f �/�Ha�,of 25, altho�i�3n��yet�3c�0&z,�6 cy (6wulamb}) j38 ��*1�"#d%�"nu2[.�2�-���&)� ��% in Te{&tab �o�&��.N� &�.at|7� r)$V�#1YC{lsz.} _$ap��{Ev�!�!#1c��-I��d� ./ (!) �S3AR; [se6� gsbb� !/ Refs:'erein]*� �/� )��&� D&�"FaXa@��9}9La%um2��{sbbc9�Oa��eff.D �-? m=�a�G J!t�H�� q iam91,cjs 3,yabs98 9,yas�0,iam� }. S6�� +&D %��"�@�Znym�t2 s ���&n 5InK2nci�2�5i�UeA�<' hoic(� s2.!�fxs� , Ho�-� �pY��/�!,vc�,be���i�� $QihMe[n# $Z$�/�bi tHal.C@2�+* $n���:�"�3��") ng5�M� $1/Z^{n3�bt a na�:.��:vFeynman1agramD@9� A� ct a4'endl T��il�=e�\t� h&7to M�ee ddof�)��"ept��"��is i%=���4ly �* AI"*!� �so�/xpl F` �s� d!�I�lin200��I�Qv7��e��� �M� Y 4-body methods �*2�M�BBody Pe&�"TH (RMBPT),63Con��U I��on (RCI)��Multi-6* ,-Fock (MCDF)1Q 2�CS"a2���},^4== a ngiH�Z]3s-�by if do!�` 2�%��LC2GZFof Hyd.�e �F)�� a}. SE: S&w ; Uehl�U .�Aށ� $Mrox& ; WK: Wic�W2K�4 -� to vh.W0; Fin.\ Size:��aV� ";haZdi�b�� su= a�7� he[Z�[,Lf 5.860(2)~Fm; Nucl�l.:"�.�-!pas95}; �" :���aB��i�&b . 252! >)���."*��,ing�Gtab�X}{llf{7}} \\[-0.3cm] \!�e &A��u.& \mA��S�t4c}{Value (eV)}N 5 �$�4& SE & 355.046&&5� & -93.597 4WK & 4.975 (2)6Q^2S8Y!CB1.26 (33.1&7oil & 0. v)��Xs &EE0 & 198.79 (40E&=�b 0.19V]�D& total& 464.22 (5 �&.�0.2 (4.6.=�1~l�+i� .B�-�� issueB��@T"�"2/crs�d�#�� fel;W��fo�h�&tro\-duIiU��"M�swi�A����-B�{."r�v # .�i��|+s-(pl�Y/�-,r\"odin\-ger" er��� �h r2=Coulomb&o��@!� �� Brei�0"w=�wO�v/�6�2S ev��,ti�D !*� �H���e��gra70| �T  des73B"( }� ����b�l (�c)�%�,� w f��1�Ae�o2��e so-V]=r)��OUv� me r�`pop��J �~$��%C�$MnB�t1=9r nt�%; (� ��!l� !>J)�&s . No �or�'���'pKe!Joutko� 8B��w -�Etqy, Hamiltonian�#�E�<�} -6=--� must|L< ``sandwitched''"�g,on�C�%pm$�?E��t�*.i&a+a1� �pus&�^� *6 fe6�4�L� �ea y on hoG�IZ ]Z����4�kE:to� lA�jY�`{ind95�:Z�Pe*�-L ��;�\��F#�Nb���kel63�� �  lin7�&Ea�K��5��-n l.~ � jbs88}. A"`n � .�a+�6�i��apK r�b� �)RI�A�R>ir��� �Ha��A�d�y�By] 8"�,7Ae1, &%�3onLf��� ��� �/4{hlll86,hllm86!�AnE/�p�2-�!m*.�2�ia�enL MɇG �l2�a W(a����J ,��=ite�<�kt� %�H!b�i�-!n �πxQ2! ]1ccj93,c� 4,js 8ccj� �A.RCI2 h�%/�F�"6�r�+�"�S&�:in "�:,a�*kty=$n=2$ )0 310-�� UO1ThE�I�2�8!� �L%b"( pp�AFU7,#r$qa*��'!�Z1r�mmAo� ��B� .*. F#az��G�* retardidterms, ѿ;��.�$c�\E�* Q2�F�qEI6� )&�a2&�5��(���ow�!; �,i\(� U<��Tno1ct.�X'malism!�U�iU9i�� seen�,�a[d �exa�Nof rvZ"7q[de~��=2�)"a&�a��F��Aknw�/��M a��m"YV� �ii�a_&4^c"f�*iori}CT(B� )J�  N�%��|E%>�I�T6" 6� handU�2P} I! �o Gree�Sfun�!��e���shan�Iise�W)5ar�p�add cz `!..#� ��,iw beyons 1��+��:�6�5�U2edl��{lsa2�@, bas�co��)z�k�99#d,� ever:*��.! !��� *� � y�%l@{bmjs93,lpsl95,ma.$0,assl2002� se2{%t�cayl-pE�%<y.��Ha�en���/p�1#� A�YG%[�[(PK-0cؓeng� �#�!"�"�$��f.V�a��Coff�,aS�F� One-�& G'-ra{X���< Abe\�p�e!K?%6w �#tom�� top \V<8c�) ]{he�I(?T6�%A� He��0 (s$�{,$). M$_{2}$:� 2p\,^{3}P\to 1s:� 81}S_{0}$. Diag:�W<1<1^< (E$v�xn: E%c*�+%$1.�1^P P� 1}$:<s�3�b<*�)C�@/� %R&��1� :y&M��#y!~�<l��M�I= 4)�'S&liu�Toq��h�,8� exam��v!'s\;!�S!X.�;^5�)T�]l�;``2�->'']��e�lRpl}<�� bidd�EnB�_o�B�9,-$�\�! @ teB�� %�p�E�.� Q���!=S t�D>;�1I �tfNn6�)v*�u E�* auto(?\%�#e�G6 qea2+ . Taway�!Pm+��a�D  aCYh2^C a!�b=`�#� �&W�!�$1.5\ s 10�k$0}$ at $Z=�)eO�;$26+3}$4 $Z=83E%A� �Q?*X2�2�!�>�SF -6�",f�R '�B"� � !� mam7r$�t���!!p!Z.���чXe%?A�!AGANILA?3w-��cy�mcib899!}>��#8 agre�Uor?jps95,�RgalI aer<'y � &�� MY s e&beIzQed. Ho�  = a��z-� B� ot true%&-��*B $3d_{5/I� 2p_{˧�!2�" Y�A�A].� rep�;�8� 32!{($Z=1$)g4092$"e3do�nt ��a52}.� "4}$"��.z51gto 58 A�^�4f_{7B���� �:���Q4y�!�V�6AK�Bd ��a nl.�pN!N !Z!l\E� R�R���!ow��a�.�:9Hic octu� (y3�Bz�6tAan�JinHl ThŀUE) 4 osw91}. E�b�]9�_ �ig��5�s�B� A�)�� !�erye3hi% lu�M��ang7Uu~=_BQH N!T�B(t 6�e|o%� \'M0$m-char-rad=*E BX2Al^a �ngent � of1�>�!��8In 4!\al�s �!�2 9�B�h2 wave�Q�i�soe�M1 W ha�c�gy�H����/��f %�re�m� al i�i;��i+:�#";ng.� 6�:oa8uNalsP� perl5&od,aY!C&�\�'�3ao�*nx?ed� :�� Be ,*e a�1}$=�ͷ�r6f��!)6Zni]�*� -2� �/eigaug`nE6(��/ �Q8ti�veluF :.���%YPs)e�be "wD��}� 1JM+�iΏ9�eM:�X dsijV �travD�wA� en u�<��a�,d .��:Q��"w �&� ��o�}" � � A�/ %i;,nd{alu"� i�u�~ly gorthogo* �caj77}. �kXE�*�)ecG�� ��2�UT ^QIO�R?H�3w&�a"�*5��e  tSr��onE{��>QOcu9�9r.�E�gionU�\ T^H0%���t��) T2 nd�7��B� xeno�!!q b8r*U littl� u�G��}�*8� V itud�QL͵� ,B<� c�bI� a# |!��*>}�Y "�9(: �;)�D�y���N�?�#*��s).B��s$2p?�J2sin"T Œ��E��.N3�."sp�D�?E#p��e��re7=���H6]�d >�"feN�2)J=dEl�b- .B). W�xѪzi� �{r�`�Oa~YQE:���n�KK�d:�!��Jibl�&-`T� 9���> y32�6�+si<%# �r|U�F���.h� š%�"]F �ihe �(*!�95D+�("� �UNroW1%hy�06�?chc-��w&�0} �0'Y�C �\q�1b*; �pmE��2%R-;jcp�S�m\�, � aa� et_ i from^ !ogolu8msid89,dllb91,i�/(2,bbcd93,tm^0q �-> qua%T-@%�e}:V��:��� meta�a� �!�><4\ �pmi94}�estm� �t *�:m h�-�thirty-`$)� Beam-F�(thS%�=�6K� Lm� f�3}W?�i�D�!�8�:�'d0q"x t�e� ]A�,y �set-up��ris��aY�x>JIeLa�Hc"\L-se+=ve/<m:~HAZD�� I&aI>��.eBeL�n-bassoc|�d � g,Q. |��benef}E�h� qu�Y�0q��[�QwB 4!F(SIS synchro�un GSI�8���-��{�* �� ���*n� \.HX 2E1M.=X100�Blly=3076@X75 @X72 �B6*�B��VbA�ght=6.2OnnX7ޒ�s/�*j.XZDM2um&�a�LioX.U$^{89+c&�B%��B, &" �2l%AA� l�i�C. �b90+�E�L]"�  g5n�-a y le K"�,� stem:.EVA"$M$_1$ decaAT��z3S_1$.&�Ge broadP!a�m��� M7 M(2E["hV 1S_0�.�&�%�n,)�w]���5i"eN�eav�3r a�=� �by��waDF�9�  �c6/$J=0 J J=0.� 3b��2Z�SA e ! S&�b�>!�tee� ��!h $2� 1s:�h#�=�G � a&�S9���hH $Z$-S!� 06"�ab"bv��p%j+�"��)�s � lu a�IF*9��A�$�\, *�=W"* X� � Rqs*�6 �9,�tw�"��4toq�ad�6*9�}�  _"t zero D". jer%m� F�%.s. Q(��s �5b əi�1@��nEmm}$�h�R@[o n?\C4k.a9{2�8t��U)a4�,�  envirB��Zerial�;a��_�>)F� �Rx "c'�a$ �uKr� mscb( MorWW�u�.v "�� appS&,Ltwo��te IsIe���L��5��ko�R�2� %�s�+i�Y � �i�!F!�y��y� MA al s��S %p�.4 m�]��> analy�'nd�\%/d� t!0�E��!�y� �-8 Scha� FY9�c ��6}F�"� view ��yX�V!IM�%�8ub.0+#�.+*! � Both n�,eW>�s& Qb� � �!�.!�~ e�w9>� �a�t t�2�6�MI.� %�)o!E*�=1��y�6& � �� �DA��, t��i�M�� �� �8vM��n� �<"�Ei"!f spi��;h' �&���M$�KEDA���ntE�1$ KT�5*y2�of $32{��{1ը0.�at Z=92�f}zi)�_T�.P�X�W�I�U, ͳ "�!$�{daj97�$p\ $PT#14aj�%%�]�� n�J"�D�Z%�lBQt.�2a���!�>�!=�%�%)�vignyKa�XA�;�1}!�%'" �6�;�mi^ s"��no�� 9��QX*e" �1$.�B`� �=�R5� 47&s�<$ -)�&gIK92 % ped �� �`e� ��_�G�$ qNaM��6��Yo�iʵ$ qu%J3Tr����<� z��&.9 �m.ʁ]P 7B%l v��C F�q����nAB!�s%\"� �u �dZ T)MEZ&Z e��us~w6PXa ��guFg .�V�qP�d%�Ɯ !" disp�S- alM�/ B�R�  ( � �Q ��nt�2� !��$�  L2�PK. ��a� u��uY&.w� d�/n�U"7(�p�h by K�S�{1�1R�Q�� �#Q ^2 � .� 1��b вxplai�AR}]<��I>Ms,.B!��,-EK"�lin� {lu�%l��qF�c� E��$/b�*XHur<7ledDIno� !@>yt!�kJkif-w�Lner-xk��o�ps?mWsel��8N��is un �]u�'uzo�5e�\5of��U.� &r�{�F.�,rec-scheme-42�T13j���Tbb5j79 "�692&5j������s/F�} ΈK+R"�+F{n CWA�be� & �,�m~p�{vC\�Hq!)��!�P%�ro"�u i� \,IL!�AK�vi��0an��� n%aJ .&aTF��*�*N.:�*�6"=T5!!<y��� -�k"�?w!. } Av."K ��� �G�SK!7g64� cx�k�sL H"�U.�#JԊa1��  t��f���s \��="w.!� fast-mo�r��teA 6��oU=��M}of"� �!?ar |&�.�5�6x�o�c�$D 1!�!Ap&hK o "1�R)z� *9  -� �4)�)&�T2i.jy�>� TEpLto�*�%��"3���Ai�a �^ ��" ��P*� I͡�h�`pro�gM e%R�f w6x�AKZMI�[!t�ieE �roppQ 72,Spindl ,9,Anholt1984&b 199225,Vane2F!m�H��6L[ (RR)�G\^As<�Us�1I��tod�j�t�x�� undeH# s��%�:� 6� of ()am��U!�?e�au:��(-�. �=���B AH��sr�"�'�G{a�" a��M!�~H�iE2�J!g.ofR�&N� 2001Q,�+ �\.�E � � Y carr;out d2[_6�Z�< !�;V�|q�%�D_wer؆n{�IeIi:/!��e,a�%!Z�u �4-�Z3l~*a��0��� c'%�!�A� R92s?T&4��$e��) �e ensi�)��%(@�B5(�A_m &e � ��|@,�\ up+extrem:^2\f00 Gedj ��in�6�s����d-4..���sy � � � y=2.�7��9.�V����W^An2�dum*?IX*�!�68)T \pro�{� SnA��}��eJ e data�takenAuB-e><��4�E�a�lea�n$&�,$=132$^o$} ( .`� ��z�jcy7�"+ ia��L/.5��Iu��n.�^Va: 6%t&�>:B :2mF�F_^:>�e���"�!>�dq8] �0 ��1�{\,)�"I%�!�Q����0an �K9�%�{\��}$�cAnalog� �%�i��of�1 &AH��4dns, %$\,\hbar\omega_{\rm\,$�7=\, E_{b + \rm \,ki�E,X\s %)�.e.ybi?� �$K&�ki�� % _�6�Q��� %E�M�a<.u�\,\f�x\,$37�f�#%���'��!1* p .:1sd %�!b6� QC(�1s} ~$~132~)�j� e $K$hb�ȁi�6�ar� ��5Il�t�Dof $\sim $ 170 keV.(%�j2�M��e~5Igprofi"�� � %q �;!%4�)EiY� R-� H�v'A�$��I�$,�ֈ M��!�Y2r�� ��E� (�"� ]P%k=ro"�>t�Z�'$U4I�)2�*�!|M��W.�!lR� f���dQ��_I�i2D I�8Q�,A�>1b� dv 170a+`r"F�U�z3 �Cs�rm"8the�$&�g.�)aB&" :���Iѹ= (y8]�)�:AyelUow&/I� "w� A� j wo $j=1/2� $j=3 �(-s"�^�T9OL�v) )I 5%H� stilZYM� I x��� � 4.5$)Y.&�j; E4!"�%ofF/�� "�A��,�D� ���)� "�^qJ�i�c���:�, o�preB��� ��-�!T��=T>� ��$L :<sp�-|7"���La� ��yJ�!�Lyman-"i�-�A2�(Ly&�+ : $"�7R�s_�7 \rt&a�h 1 $:!H1@ 3/2}+�4 4)��M/�%}#�� ense3 %�%�a�q�a#I��� !�6:A�5D�s i� R�5� t?d#� o 88vX { aja�U  as"T0�C�p&�a�|�� l"2����[� leHndeSa��<Ori�M68c(�: k. A��xQ�.8i.S��r��:�  O\-���l)�JA is=}ly�#�&� {\A��D� ed� NA& �-Ichiharav�,,Eichler:95,M; %% TI'����i2�.@: ɸ�d!��7K.�An5�NJ�8`u�L$s (at 90$^| $)��%%���r...� sI1�,X#)Z�2�cLYr�Zell� �$ asymmetryM~ee��a p2��B��6ebe�\�"�2 �rkY*�&�\�AvanisQ/c��##A�� to �%3�; &r� � "���L>��D i���YF�M ��@Xe�=-��Q�-�� (cf.\�dVme�a��), ).i6S�ao>�Nor�PdwK������2�s��.&�T1Rw-I(�B) M�@Q�6���Y*Y�!�a.��L�l>)�A ;#t� 68V3 ����/2�L ." N��qLR<��  go�ur&'1�>�IQ�FbeH�urM�q&?P�BH9��@ZQ}���yt�m5 �"�Es����4!9aE��f �h��-�\-�3)B \���2�E�=eR�0]Is* ��:�tA {2�({��=�4�� ���0-�-MKbm��%�2�����gime &;)>V )V $A�m�D�4?a�:��q��{ Kb��tav"�}i�&��%thresh&�3"����R���exhR�sgh*�h[z�=� A�� ��a}i�!���r<0H1!�}B�pw�is uQ_R��stU{as��b�|aZ�'$aH$\pi-�M�I �}��o)�0upper abscissmFig\-ur*�N��e�Klys &����W6X!y256t5/��>%P8�4 �&�?bCaaHd�ty�grixauo�aa� stea�7t| *. � � l mb� (�+ly�u )IQ� � �YO �O�eA]-�] Y�Q�0 eiӍJ�:�#f�1 �#2 �59.�k56.�j�| "�"�: 4�y�w� O at 8��,92+} \righta�rrow$N$_2$ collisions \cite{Stoehlker2001}. Solid circles: experimental result; solid line: relativistic calculations; shaded area: spin-flip contributions. Right side: K-REC distribu! ( mc �|) in the emitter frame as a func3of#s� angle $\theta$ (bottom axis). The horizontal atB4top refers to`corresponding electron em2l4in photoioniza�(U$^{91+}$ (>�nergy: 48~keV). %\textbf{AngularDis530-4.2.eps/fig:J (} } \label{b" \endure} %\subse%K{Polar�(studies for% ,K-shell captJ w sec:pol-k8} Details abou)Z radiA7e=t can be derived not only from !�a)  d= =� tted)u(ns but also> ir p.�M�@urzhykov:01,Eichle`2}. In practice, however, D\--�measureaLs have been hamperedATthe past years because� lack @efficient Compton jmeters !qE2n E+!� of s�,al ten or ev|und{DkeV. For high-$Z$ e� withBK above 1006D, it was demonstra!Y%�(recently thm!(�ar) �-i�a2�-�-5 d by ns0a new g�q/ seg!Z�ed germanium detectors, which allowE�<gy� wA�as posie|resolu )�4Inderhess1996,.83}. A first ser-j2< ���k�]E@ma3s s��� �� fiJ )� -�!app��ly�jedE�m.��. E���� ^2U�ertA� � " !{usu@ �� �e StoEaD t� a4i inteaKy ���light��d uI ���zs� ( eceFF���.vB� $P_1 e�L (I_{0^o} \,-\, I_{9) / ( \,+.$, isJ��!8h it{!An� .g}Q\>��l��H�  $Pofo� s)ta�*ila�@2^,e�$n at $\chi �45^o$E�.13,� !_ivelyi��v1�s�1 ?� toge�+describ�a greeg >�)5 �}6�I��W ne p.,1+�<mo- um��a�j hirde�%1!� 3$ denote "deg�of���ula:�a-I�PAi�  treatyBlp E�Ms9�s a2closely �e�A� �dei2!�1ű$non-zero (� z v�  modeF ��� ��ies), w I�is ��t QA�mpla��� ��~ ��-%DA��% mbi)Y-Ձ�ll�vb�un.��Q ��[N=�U� u2�,, in contrasy >L-becomes5Q:A��� smallAK � s�D_{\rm\, RR}$, leavH �J$ unaffo i�is cas��%/�n2� , "�any� ��n��ul n a rot.s6�ellipue�x6� . Owa� symmetry-�&� system5 si�Xre� i3!�i (uy#).-r5�da0a�ed #A�erefor�4��may?v�( unique too%��@�h:�� ofA��"=&�4t �� htt�� � ��� rest�/�\begin� ��er��< { \epsfig{file=M�%� -4.5�(,bbllx=80pt y=346 purx=763pt, bbury=792pt,heAL=8cm,clip=} % \inclu��Daphics[width=10cm] �s/N�} } \�ion{a) S�� A/*r O Y ; b)Az "&� �Yj� r a� $te�<aJ� � � ,� a"� >Q ��*�:).&"N/�.:6> I . E�of chaEfristic&� "{em-(-rad} Ii����~9�inm�gre� stat��%� ion,�&an ex�d����"on 4dec= �to�(s�2\� a�"�.l2�}�. For 2X��� ����Z �f8$\,2p_{3/2}\,$ ��űts uquq 0Lyman-$\alpha�`�H1s$ � )&a�{� o� in g yail���+> �"OJ� 6��,�'eqnarray5�W-of-U}a�W�|Ly} (n) &=& $o \left( 1}betլ���ere $:�$:!align!|E�Q�$�  ��*ve���ure� � 1997� 1998��lism, discrepancy/qu��surpri� since,� % 4hydrogen-like *i�dN�����-8 Y���was knm toA* vide (the� ) lifeti� �n aOac�be�(or $\sim$ 1%��dN ats��n!k  worT!|6�  ory later G"� [ # in��EF[RY-ari�r, U$ weak M$branchQ 2�$*��A� Gh�ter�ce"}E$��2 ^w)�aPonentsQ6) /PRL:�T9}U1enhanc�6 �stood if��stead�Y�F and =�qL$IO_^e� ive}/>m*�n3�e2~\,2}^� (eff)}o �0= \| {.02. dot f(5 E}_1,  dM}_2); \;\: \hspace*{1.0cm v�,20>q\,m .# \g��Zj�w��*} �AvEq.\ (X�f)j ��� >\�4�^v& \_ toœŏ[ŏD2\sqrt{3}\frac{<||5 ||>}!2͛]B��la�a9struc�� ��isJ ely �s� b��-��Ń ?a3Y�2~./%�%�$� dynamw orig� nd, hw,$�rm�E��process�e�� $Z�$arroughrovi to $~Z^2�e9� g(negligible iC� a few� �Hf)� ���medium".) A{O3rpo;  er��s �� an alterkve view!�howe� �8\-��} �in_� B �!$� ins(  iA P\-ՊDA��j,on field. If�assume,� in��� RECQo&M!�c�..�l(<i#)V� , we!� utiliz�=�"�p�Ms �A�2p$Q ]!4 orde�L!(J� f�:!G �> . Ap�dpR�! dataE,:u�-"�value $f��� )\,} �� ��)� 8 $1.27$\pm$0.05AcI��gi� �Aa -�1n.� %�@X �� $\Gamma_{z �_ .�$}$ = 0.007� 009 �Muthig2�. F:hv�a -0.5�b:yV8cm]{6J -4.4�2�a�i�.���Ua�46ve)>�@ |"| R &  yU�2��u|�$U^{\,91 %ions,�CducR (%\,92+�ha�&��}.�&.� lower � repr�C*q �di�$E�� ic N� �n� uppce-�f � -IT�}� I6� F� &�V�/�6:�>\��%� .�Multipl" :u���' } A"Ual!�.� a"�%: )� � !�s�]F ��H%R!q�9�x-rX�ra:eiv�r���&�actB� . Fu B �Q�)� K� 5�� ��� }*���`f"C \ �Perhap�6 most�!�"�ce/� 6�( X& ��- 2� (ref�(�"�i�("�1�opu)� _ magn$��sN9.��?N~&N1a��by�$s� veryQ72 EL""�$��-B =�-��BJ Fri:02y�:03b}, �%� �"�"") spin5�A-��tegE f&w97.b4b}. OE�}�"] E� bA��emay�d�dds!u&�u� .  �MNR�� Qfu� . The�advantag%� such2�=*i�3?(y��6*  rout�r"v ..�>: (heavy)�V8at .y%� � \�*Co�4,s%I$outlook} _ �M-�6�(ly� ged � �Q� re P��% >� So+on both,e��Y�_t free &�#!��": ,�*revea� m��A3$have impro���� a�,Q�7ron�.�t the ��-��domai�  )investih" s clearly�< in�ntly %� g$} behavior��&�"�.A�� e�&-dQ �8 atomic physics�#E�z):?o r�of Quan�E) :Ap��}ominan%$X thus�fi&*dab ��� � A� ��K.c �A��!ьof�?>)to 3I2at� a�&[U��# betw�#X�&� &g!L&exps&m �)E� s6�"� Av ext�*dY&3ledtN�)�z��of%i�@ ��m�pA�er�-$n availabl�Q� neut8-el�SE y �,\-s�,��!� ^-_ �ibU,�Y:��� surv��-!�E}�g!�;thresho� Alth^:2T�.ar�-ba�2� W"caW2� "�2� q�U\"[>���y�"7( ! �oŸ few-RM�� --- *�!!leaf*Q Yx+ M"�(s)w�@��ly�Qѿ��g Jot%_2EYe�.n�P�n!~+ /o be X 2T��##chng. /fa� �forth�-y+'"e��fu�'lA���"E M�v�!c&�!,2S A�2�me&�0 w"�a��ce^�aG3�2��I!s9$��i�.*�a�A� �on�CAs�}�0�,reo�1� ���ea � !WM b+no�%������� - 6in �w�Ls�,en�a^wT�t�+eS ��eIm2 �FI�6�6!hel��ao���6.���-2�,�picch��� l��!�++�+�� Pnu��W��2�g�ʩ�AN!�]E�2Z� � wh�J clas%� new &�s E}$ feas��$!�a5N ���ty %-er(PNC)�g�msgi96}%searchA'��ic��'�ac*� A!. :�* id"�,�  m����� �Q�y#�mnew&. �#ili� �ly� ��cu�6, fa�A~pH4accelerator FaQ�Antiproi4!�Ion Re-(FAIR)8 GSI);Hen� "8��!este�(ۡ�W,%;�dst�zeexo+!E� Egi% -���..� ack T3�C sup/%>E BMBFō�pA�Lab�Doire Kastler BrossX-4Unit{\'e} MixtC X Recherche du CNRS n$^{B1}$ 8552�7� ��A�Marie CuFe�hipY%European�#Lmunity Programme IHP-�egact/0L %HPMT-CT-2000-00197@ : efula�c"2 d�}F� *{ReZ s} \biblizphy{e�ein-pi, sf ts} %Z4sfBsea} (you�put�o as* ed) � docu� } [c\�[�twocolumn]{revtex4}% \usepackage{amsfon�:�}> symb6gq%xW setcQ3r{MaxMa�*-H6, >+�*R'�Co:-rollary2,6+ri�o2�2+�0i�WD" 2-�/*E 6>'ercis6( 2PlemmaNL2#n *&N2)proble.�P >'po�3SPS 2/}-rk*Rem2%29'Sol� :)umm6�S Penviro#�Dof}[1][Proof]{\noi�8t�\bf{#1.} }{\ \rule{0.5em} ���)�*l} \preprint{ } \title[Ultra-��-Q +,�- v�Kp 0roid microcav�c ]{De�: u�F �ɱ�:�=, W!X meri�"�>6% � �$ (or� equival�(�7 ity-)h , Q)�)Cby "[9 achiev�<ZF�V . H�6w�Q�e]� Q k} j on-a-A� OF�h d��V.� �& Of� o�. y�i� whis�< ng-gxry-typei�sp�@n ov��g?#�A��q��$s, minimizAq!Jq�i�:"o?a varietz�4 as!��.�M�,��i5J��(*�3�!9��desirf�� Hlasers, add-drop fi3$�>w*�A-& upon a�*��a�. C��E�IZ'to�(M�ont�> "��5� ept2�>in�$quotedbl�-O+gle��2demand�)�-% \ so�ks,I.MoreauM;Santori}'8�I/�3e��a�<�7gi^ by% �U>� } F=�'(3}{4\pi^{2}�'Q}{V}(( %�� }{n}~. ^{3! 3FV (Ref.\PURCELL}A� afer���h asUV crystals)Akahane}i� post: �e� disk 5(Gayral} typ�'lyO���&�F than E��nd�J ow w� scal�"����ol. HF!���s�0N �d ��8ifica� �"�-silica2�g,�!,��-Q�'��a�!&�Ŭed�� -%D%�y�TAZE}��)Nm !,- �vi�A�gss�a !2> regimeV�g' RKYvF��2a�" `�o- Q*1 to $ I�9� s2<ng�6� �in�"& Q/V �� of m� f�By��eu�J!� cipal !?min�"%��!-�L '9/adjus!�6H�$ �eved ,,$Q/V_{m}=2.5.�B~  (Aqa ] �$m�4=1550$ $nm$, $ \18\mu m� $��$Q_{0}=4w 8}$) is�bul��9= one >!Tagnitude��rA �/�� re �,MӍA de�&�jQ֍Q�_ Srinivasa�u$=m*R!fF�Cc8in yet �r)�:�-�.� KmH�p�&�E�2*b��s�J? &��verse C a� GL�" �� s��5 �s�ai$�&alm' . To*�e mo!I�I�YE��I���&�� , s]Gs .Ifab�E�.M in �S��,� lith�e etch �� a CO$_{(lT-assieEreflow:.�4ure 1w s!ca�o�&c35ima7N:�  geomet�l�i�@K-f�>!�*� ( eV d�th��;-mdi Z�@$@ d $D�FThLi -Q�-D�Q�� led � �.q,ɻ�EQ��dA��e �thick^ 2 � (�2� �#� $d$)�6 a *�HHF oxidAkg�� flux expokM � >*�%C2� anneal� �qto �3tJ6�`, 1 %TCIMACRO{\U{b5}}% %BzE� 6u$% %EndS*rmA��c �on b0Lus�JSgO�8�3-]��2M� e86�� ous9�ja2�'Mithe� st1be� 20��IepH/.pEx�� � al ste��9���a:� . During�9m�a� melt� A�I��kU�ŇX,&2-"�2on�/d!PA�Ja�earipherJ a 1-%�&-e@cAEe��5� �J� �&s (4)5��$�!W%"E!$3.3$�5u m;29A� w@ as $12$ $ \mu m$ E���a�'fer���'&�!���';J$should be ��� !] � 3KQ�O1qBm"�Cf�3 5!�residuE4rai��* cEQ7=nun�m-��)��&%\bigskip P } [tbp]f e��-s[ �?$5.7947cm, �?X7.5278cm ] {LN04_3807_FI1�/"�?S>7� %7.^�  I )]� "� ,�a 1 !2 YV!�%���q �P$ (inset). � �� 1 Ch�>&n%!xF�h �se�ed�coupl�8�a�s6�V# tapeAe,fiber�P piezo<$ic th�(�UXge�!20 nmM%d-loopA;o�= ed "�!� �C{)� �� gap. T�s i�Xs 11-2 m7�� ef�S1 ?%�+ YbSqk� S}A i>ow�0-Es&'r�CI�twa M�� @%�1I .*�N m�V�-rd��W.� U�o%�"e(ed a double�*�7d�C�%&�/�B�oIy� ",aaڡ���M=-� degg"e!�ckwise�clF� �-^Weiss} &��� engt�;B!9bE� � visib�!fA�B,at�#"D0)��S)�8$\tau^{-1}/2\pi��*splitmfr$cy $\g�4./) !A�-sc�JN"Ad�5�, less>\" 9�4 \�\f�9�� }{ q}$ �.8� A��o$ lly "@=rde���2) size,]/�d Y,-�*qSc5zWGM�� �� of �@ 2��v B�&a@i<28���q.(w/%!�yz�% %�=15.5MHz\\1�=31� In":2�y�-��K9~*at� p.5s.}i. �(s�P2Jii��YorF �'-shape uIvin"o�C!"�to~ uitabl�U 9Wi�&cs�Xd0mak( !Ba�VwiMjSr (pul7'�n�:iD� �a�M\ �yd�*Q7 mak���D�P{��eil$ oppoE�6D� arti���t &eto Q.�) ��!X �.^'alone6� ��l�,te�<� Q i�*v�)f��ong!.ra��+malQ8��2�;�Sache������Sdo�K�ly �.�;G'��ve"�*(�A�< a ringd�Bi"^�4E"�hpoint. Av9'OPic HQb'& :�a�% X�P%Xa�;�/�W%��T4%�{/�9�dl�)Bmetho� !�K�!�� a'knoa/��:R�C]raA�A㞓�� $. M6�� �2�cy�Ţ�,v]�acI�Cy� o�Gu6 !��ir'lWshifts (�=a�� 2��-l �lGu � waveO`�? J�QPd���ō**�indiv 1|�C-!a�%� �fJe:� I�]z� A�N�mb� vks�,U� ae-ef"� vj�_{a�  lo/t e�d�0e�5��8:Bud�F< I=75�sd !�exa\ �t�-���KZ4e�*I.� -3dR)�E2 r�@c":N�Q=\omega_ *t ! }}{2�[ �C"� 1}% � *\V)�2}-6�1"� 2& ]3-PA��h} @2%�36.521�N"3 69923%F4�b�cap�{K 2: Qu.�$%������ &]  �ŖFJ���tT"�  (d=3.58$m0Kd\6�84:z��e �d�u�(>�$tunnel los�!a� �e Iy na�doy�q�d"7 �$ set:� ���� a $14-�radiu05x ��� �AVy�luMe(�10.6 n .qe$is 4$ G$10$^!�2.Ce �<"q W )r $!�6�31.A2�S}I�Q�6� QS& :�*�th�E ��Z!a�& �_#I}Uay!_@d %cJ� DJE�*�nE"d$=2.8-6&�)�E�5�%%�4 108(1R���V� $d=j,D=29$� � J,bev�V�:A�.� U, u*� (%.I TEXT�- ol{>Rh>BfMI)$�#cw k:until"imiG"� of 28.���, b�I?= � ;g��4(��" is��. R����Q�e�erJ+jF%S"cL5z>l�e i�LM��A�h�� �d"9leakagV Q�e�">[pot(4al&Gns40KDatsyuk}�rTRLQ l �$Q�J� (2l)aO $l$!4�a�g� Caz� . Nu*#ca����y;Ea�c Y�x"�aa�uu[2�isP unchL*d;6 (Zf 2�!!~e"�p"�Q�_ ��7l eigen9J�_st�7pH<"�ir ��T{ �;�I��� �.�a�AS�6U#-�c�bs�2�.Z&� { n1�l� l�\Q F�-A�%�2V TE(TM)%�aL�%�[in����6g9�"�Q�*�%A�y q . Also6�I�Rb�� nonethe� �JQ-valu�y�$&!A�vrE&!�Yh 5�^$��-*%�Ea���d-�*o/ a�Bng�;&�'surfaceAwQ#!R6a�> absorp��%��x�b*�Q����Q�-$nt- � { %��ey�e�d)� � 6 p fu&-;F>2-�e h%53 5- aY��ite�k!ql!i:nju��w�ex�5 �uyq.e�Q-\7cF; �!YsolH^A6��� h. M�!,d� b�MaluetsH comm^%�&03 ( $[ilon$)R� Vp( \int+� ,\vert \vec{E� �(dV}�Qx2 �3� .�  !6 3�+��c2: h6�ATEN!� +"��!z� -|U�� j% F�7$25,50,$a_$�2 ^��6� m)� xI���Qir tinu�&r}�:� �9}�J�$DS �q���a fixedN�$D�cdu"�:Fc�svmN �)��fl ]�[��a�a�L�+( d/D� 1/4�&d� azimuth�m"m<Z]�O�9�Za ��re> /�in5M 4IE*c"Cds"j$.�$Q/V$Xio�J�&�H[ s&:siE �m3tlypY�@E�5�h� of%Ius (bel�( -��%�&#OH ݅��"�CQ� �!a952L��Y��y9 n*%E��in-i�&�+J)�%��t�*+o �&�,A�a�2�A�m�* ima,A}* �a�nX <ed>xI�^A�K A��a.\ i�A�i*e $!w?)�d�00; me� isZ�Q��A&�offset-a�-�af�>� , ad�(�5$X�2�.��� !�ax:[\thins�W\�2q-�%� exis4 �/&�, ([%T.��eQ)yL#5�zE�7>E0r%!8 anE�l�7rluma A EUc*���E�i�J� !����lum�#�)M�)) OalP�&�I�Q��&�@eseY else&�7.�-2.22in��b2.738in N* 3_UpR5e#%&f#Thei�!"� �2�V) !#aR���T  > 2�`.<��Ja�f"� % E% �$esNn%�y9p"Yi� #by SEM�"���8�N�*�U6|2D&a&�% (d)E媽�I�(D=�75�I nThe hig�&�.��an 106(6$/n)-3%Am��a}V. $m>I��!�F��f�:��t�L��$264/MK[m�8*R�8&�A� -3� $D=29b,d=6\M',Q6/,V�/>I/-1'=&y/I~-c&/!l ��6eщ���Mmis $4.5~ �84 �Wv��*nic:f/ Z�d/A��A�5�\)zis(��<sU/�J�NaV+��6 unp�FCed��">Y�1)�f��.�� �H� .pE.a� <�P�5 ll \1�PG�/d:�-�bc")�)T+.(�:=!�6}$^eet}q)V:1a} $2.3:-�Rempe�K a ��� E%v5>�:��n.�7!f �4Z�ove�=���1��5QG���~&�1��h_@,�3-a-f�? 9��!!v.5.�3&��/i� .}+%�e-�,)��<E m��w( 16a to2R$ �X�4��*� �1(Y<�[ك4�t2� �Nu4%�]a�e"0=�8!$]A F�8��3��ymR�6�"=� y. C2&M�}Z1�Ba�(> N: fc_$� Wq �� v ��QOb�=�)� .Ucof �>tay"g:��r[Y]XP �0Y >/Fs} & IA6funr+�~$DARPA, NSF \C_ch Lee C�0 �url#1{7<tt!4r5 urlprefix>M%2{URL IprnWcommand{!V� }[2]{#2�C:!�4t []{S'�EBem[Kt5{�?(2003)}]�/i{E}z5�{K.~J.} �1g;},=jou- }{Na]H�=bfN�{�}{4242:$pages}{839�k� nfo{7A}8A 3}). gN��? et~al.}(yi)2��`, Ilchenko, Mabuchi, StreJ Kimble}! U� D.~WB <.VX V.~S>>��? H.}~!-5� Պ;EJ�) =Uand)�%�V�HE!%�81MygM^U!OBs LBj�LteM��gQ)23}.AM(247F(!�n(&�A.+0:+&, 1���Gorodet8B}]) ��V V.~B>�h1qvA�(5x��M.~L. �82�N�`Uspekhi Fizicheskikh Nauk�IZ�160N�15V�0n��au5��P:� "p, Robert, Gerard, Abram, Mani��,Thierry-Mieg!� :)j�EBrB��I>: ��: J.~M>> ي=Bw% �9L>�%=1�U5Ame�j5V>K6}NAA�Ded:K�)fR792��)865F*A:niS�C.j2:j #H, Fattal, Vuckovic,��om t,and YamamotoAd 4�0C>09.+VjD>; ��:J>:ъ<GJ�So%>21Ij1Y>�9FN-�n1R594R2nEM}(1946> TE~P>�EM1%�)N al Reviewj�6R�681F��n��.�3:� #0, Asano, Song� NodaA� "� B�9.�V�T>F��9BR�ng��S>�)֘252���94V�3^p"" Hnote}{737KY NATURE}f$ �G5� 1999:� ", �Z, L�tR|Dupuis2>Pelouard!� 9��B>8 8.:V��A>w؊yB�) �:�=�=J� %��D9Nw�<R� 1908NN99rN�HUji6� ",.tS Y;�U�}] ,�] D.~K># g��T� 6b*G9.dV�SJ� �?5�1 l��VQo�V81N� ��eVo1��w�i2V ro&�.�4:�&H, Barclay, Borselli)� Pain�?}]. ��^:�j1lj> P.~E>) ��>M>|�1]5�!�%�j�O>N5R�rXiv}rvM"4n�Q�.�>�$, Y�,1�)�Q]-���j�e�OJ�:c2���>�:� "� f�9R�(art. no.} (F�r�9�.�>� &f�$���%��8��r�O��7q�EȭV166V�rX W�_}(169_ ~KBp;�M emph&[t�[}{Ope�KsfU and (Waveguides}.s$publisher}�!Golem P}'.�add{B�1�:Colorado�6��n��0� 2p ~ V.~V>�<.�"x >3 B-Ph�wl%L�L C�Wstr^�5��MQ8J� 199ru�.:g!, �\ pson�����Lalezari�b)�9G>� 7.4V�RJl��??%4u�"?%��Z)es^�:$9 N<5�O6�fd1a��A-�363R' )��6>��G�]}��%:`ct\c,��],L_i3s,superWDptmy,am[c ,prl&�c :[H�QM.�c[dvips]�cs}% Ih�Wg�O��s.3{e��6�cdGd }% A�t qB�E\d�' deciq>�52Obm}% bol�mth2psfra6j[ps�d]�d�6 } %\*�d*ntfa�:amN0wrapfigp_��J = 640pt��B= 502odd7,mar�~ = -.top1<new& e�e�"P/�a#e#Ar^!baDCayBD# DV!bsDold!; ol} %\no)�e(U� &bAPS�*�+tʼn{P�D law�D',&! seis�q�Y�\Xaand(Bi�{A. Sa�v:�aMA�TDex5�$, Nizhny Novg� SʉUni�*$ity, Gagar�Cosp. 23B5(, 603950, R�ia:|2�aGe2MPA� tary�, |�&)b , Los Ang�4$, CA 90095�D. SornK�+9$�Earth%qSpace S�ceή\.7cL*�ide)}�jV Mati\`�+Cozds\'ee, �i UMR 6622�53\'Ma0 Nice-Sophia ?kol�06108 ( Cedex 2, F!F6!mail{s-@@moho.*�ucla.edu!h�*{\todY�Q�a"TcW�o7%0, empi�5�<.�$ proba�J���2�{�C{�}(r)$#.heI$��$r$!�e!�qu4�i�o5 E--�Awindowe��We]Q catalog,�%i*�V$boxes $5 \F(s 5$ km$^2$EX0$Wl�<t =1,~100k$$10 day�oe �cNblH�wei�� $PB� K�0 1/r^{1+\mu}$�)_T�_�<�� 1.6$1#(:��'�/[v%��9 ���[byJ2��aL ocha�pn�'$5OsHv_C w $_, `FfJp$ETAS (epidb-�`a�#shock sSEe)�%rOc�_suI0"�D=��0 trigg�8%8=� (``_s''). AnNrl<C&9�&*m6ascadeA[QtE p�y. Waqvelop�$�l�7���%erangN!KY�]&(;A�Y� organ*�Pv5?� d �sc�&'; ions�'s�7`�s. �,calib(�i#ly�+y�.? � ~&Wf*n�f9au�AE )e�F�JacOq� pre-�0! froz�Jo!8�P J.au� �`A�q4 eems�%urF| >>�'+ lex �fiA_n�#�&fa\ng&s,�IQ*ms  pat��u��x-4i7�[o�%�|5H =H satis'-i�ʥ}Kx<�1�L�4�Ii��Xe� f�Om^Lst�� $dt=���7r*tgF S�){A�o8ormul�zes���6f8P.v�~g�� a�V C��.� a�1 �il64.60.Ak; 02.50.Ey; 91.30.Dk�xJM$ 2pV{Intr��A�I M�gp7Rs ��rtA�.�e�jcsh Aqi[M�u{=ou�* worl A�Ctii�u6 al laH��r�H� A�wa�A!M)� x� "�z .yz%�*e�U�&< �-���BigalOmo,�*al}�4�Zrrf �A2Y2�g4a3�*بir fasci��E!�self-ؗ���7I� �!] (Gutel-Rich�p�of�6 �t, Omori 9�aa� ��)B,j�c�# e�f�raln�.n8�s�<���ܱqE�of noveFn�e)�t�l� �$ ma�-�(�t sigh"�Mega,�z ,paczuski 2 3}. �5��Ao�LvK am/O%mGm%��/gy  >h">W�w%�� 7 � -��Oi!�TDc;���0�em to��!=Ndy��ApȐ moa� (a�9@SlY�e�8�?Y=�ae�u)�, a�_�H1�&AIhazard�[ess!��Da� ly, �6^0�iv�6P*���VBa�T�casŢ���.a�pD�,E,i� RELM (Reg�vK �  Likelih�=?@ls: www.relm.org)��r!�Sou��n*� s0o1b�,`5or�AULJ=v��:dWI�ifl$��e;-"�Ual binGgRelm}�;� a i3@�.%Ea.W" !Alo�n,��,*LBA0fo�m�9�re"Y�Dodel�IEA0�sizes��n,�ec�Ni�l5nnim@s�:�`���P,S3bi�&|1a ing ^A/A� d%� issuEYtf�R els'�dv{!1to �A�&5so-U��&4 clher/ I Tw(iL�, ��i��S�VFvY som�9m!�deM/ acha�remov�'�UA*�s o�Xx;P�nd" c�!�Nk�|NɅiB's.h IW� !ġr�i�ed� j 9�A"1�" *9�2 Poissonia����: But,!:%�!�wB� IQ .�( i�%ksta�b Vg�r^ no  d 'Ufy*Xt ID�b ing)�Qn Ũc.�� is��to29 %~��W�Q�ys,ulT9&;�9ail�<3 heav�aOQA�i�!9C�t�2<��RxLHg3a_ it. Pisar�.e�Golubeva�[PisGol}a� aI3� 5#U �_o-to-say� ``E?random&�M,''M�resul��RL1 slowݓ?a�&�Y3 (act��"�L\'evyC) �!)>��e�We ,8 ��8f ��� p�Us. l �2 �D:�1�!�"� � >�ͻ�AD&&A��� s�� g�i� ��AM� 4"0 . Spe�?��y, A�E6U35Q a%tpl�M&v XiR'in-����= e !�yal M�!�Cs�Save® ates�tQ [~y)GmLn�.�WI�FD timel }? 1�!o 7im���B�*�flu�U�ic&�t�ed]DO*� %�g b|fmpoWSF� � \ NAtAAa3�%�Ն�era.9BarturNQ�� �I�N9) buil��b�`!as �  QdX. A��>��͍ ail 2�r� q �x�0w��Ew ny !b�Ua��i��req $@��asL �#8baȝof1 �� &� ի*�����Msuggest��or.F !�"��+.P%�� 1\O�8�Wqo���s9r�v  �eo�:�� FS��� Jped�s:e�+ osed* �-�a$�v%�$���.��d67�%�fu"� )�ի *��a��zXa� "g�<E�T�wA&� S� (�)*1%�Ai9�s`BZ mem#��/}} V| "�ETe4ss,� A�2� j��A��2�,eqN% Ogata%�hEmNEa�m-� ����KagY$nd Knopoff: a sl�2��[IB KK81 B whosa�i*S a�s"���?e�J"�HS+��� lete�@e�in�At2zx ƀ�%a *ON�ingred޺s��Iuc alya��f�Ks.ʮi�del,2��t?l�!Ms�<foo��KA�A�in:�om�cks, m��A �*� ,� �nFret��=ve hu��m�c̈�u��/ af=ta>p�A��El�NbdxuE�`� ���1 p"�ntw�-fo۫e" A�)i]be�ofa{J��_ 5*2s (se�"l9For��]r"F��rein).8�m �RngAa�l)�bh��mv�!<={A�i ya,Sankar�ayanan+�nd�vQ d��CMa�aH �Ancy"�"y�07gent y�in �M �[!��� "RJ%<.EA�ath����K�Q��a ��� (%� law)�����,R�A�� her f$"-g, )� daug��#b�e] �law�.�E��ew%`y�"�w�R&H �cscajof9� h3}ra�n��h |�sub�bI�MJ0etasdif,HOS03IQtoΠ/Fn.�&ޓ�F_ aEtos9�a�9� uϡ22b �NF9e+� ex�7�"etal0����du-�!�n*�"p bp p��oSorm. �e}m,P]� &�YoA�tjr( her,2��j�6��� �x� -d \be N_m \"j4 \kappa \mu(m)+Ih�$avenun} \ee}$children (yd. s or=�E�=��y g =�H\�( (m-m_0)}~,��mudef ~%,mark associa�E�an.+� a�x@$m \geqslant m_0$/o A(l)Za��``X9 int�I� ''), $)�ZJ� t.�D$Y_�in*F ���"�Mp��%&\ �.� � �XCV-he2  ``J�''� $N_m�.�x ing:��eW�$Zrt�ca) rk;!(m)$,Q>R"Ad��of)�����drawnK`er� �Z�ia*�sE)p_A+ r)= PcPN_m^r}{r!}\,e^{-N_m} ()� \mu)2% }\,.Q]3a|%ee66exp �!Im0of�� >�,ym��9U9d 1dAp�M!W)�{Q (�I��M5�Afc .�a�i i hp� ��**L�Azhe"��2�M�eU (GR)"^&] 2��9Be�P p(m) = b ~\ln (10)~ qL-b��~~~~m6���GR��L�E�$cZ_m^kZ4fty} p(x) dx$ U  p*'5a2�h�5� �#o#oI&r%t�$me�� �7.� $�ezVj"�j*� A�y$�cc2 * Q law4) p_{�'(�� = {�r \�N\mu�'?s }}~, ~~~1]iq < +\iAB, A�~ )A�/t~."�er��9�s, $b \'& w�0.5 < D < 1E�!�$1� <2$.SorWer}���H�M��o!y ern%( .rR V�� s"���bBwt�4-�.� ��.��S>�=PM (ix���O2yU����[P*an�k� {iG  iAogiU case � =!HT!I*�-H=1$�nA�R �|anç� cut-Yɋ-x��� ^�co&a"� �%�ol z%�!a@:P $n$:b"  �V"9 N" p��as:E�n =�{�� !�le� � leE�Bm" m"I�-1aAmgmlel�,e �W�q��T>|�{nUA>s'9ys � eSGRa�T"2���Q%G(s $n<1$, $n!�A�$n>1$ c"� �A�i�qA= sub-�j,&�j�#�2 �&m� �)nex"#!�O*�co�bP��"�0&�#!�h`�a04 ~\Phi(\bs{r}- $_i,t-t_i)$�E�* of��&l a�<$ti�p�� $ a$�� �AK�u $m: :^ř^_i6` `_i$E� �x},t)=t)\, \p �x})\,�Tjfaphapa���p���!/t)$��3Om�&�ma2�2Q�'} ?=  `� c^ }{(c+t)�#t#�}}~H(t)Z)�K}m$I� he Ha�n3%�, $0< HI�c$��aAgu�%�!��)E� enނ�>!ih2�%�P��=c���"�� \���e��) k �dA� ``� !Q'' � S99,D&��A�J��byiUf�s &�<  ir �u'a�so �H� �=��� �.2 C  a�8: ed''� ``.%''O���%�|�\ :{�f,A� w :]3�`��$/D� �.!Z��o�"� n byb�9�QyRU�eta ~d^{ P}}{2 \pi (x^2+d^2)^{( +2)/ �a��5uM���� �%w�|,,��s�x�de%� epi(�W���g2- ��@3�"2D-j'�,�K "�h�real 3D-.{ A�-( hypo ~s. li� �A�{or0yvo0��m %� be d!�in 2D�Aeas�lg�� �z3D if/w.�60Ibsu"'�&Xto warrra�#�"��h��-K1Laplac�!ans-0ea�% \hat{� }(u)== 0^� ����/$ut}\, dt= ��\,(cu)�0Rc% @x(- & ,cu)�eof� asympt����b�10}��~(u)�3+l1 m)2�<, \qquad cu\ll 1J�a�Fo���.)s�+.�(^9j+lsTxuseful�� \tilde{��}��q}�iint\�d s_{-)_5�� 2  e^{ q}�[�x})}\,d = 2i(��dq%vr )i�/2}��K_e�$/2}(dq)} {)�] <} \eeAi� "1!�V�E dq} � �G=1)\,, )}v7(1+dq)2=3ee{ l 4&.Q�*{ ��ob�D-ӥonic -�~�+&�� 6�Ʌ|�e͈�y�#�561a.�a� �X&AB��]�3: :z3F�� unit �per �mi�varrho$�*�q%,&[ �)8.!#BwB"6s *���w2 #.|t  . I�)a �p-esq3ish�!act�,Y � �rt��p*!���&Ap�+�{�M��Q+l�@t"\s,�(]���+lf�/��"e  n��, J(;/- russ�^t!�U#aH��.���aqj�� B�5�.����5 $1�<��;-8influ�p26a�5"��A�ome rhe�00.6�  �5�9stM 2�s.h!get-g�Cl^�&� :� � J)� Ԩte�6ٌ��a�v%91v&! F� � "��9�a Cauch�is"� orA� bablpr""l��I�'!Zolo1,2}�� Chap.~17a� )SorbookT�v� 46cri=q��h�y.� 9�Vt4"�>�:���1}Ǘ�M!�}\, f��G b/�`~,N disrholl� �dFk A�*�a"!*A���{&2�oNceX*Y���e=��"�� w, � o�o��4\be f_\delta(x&4 +!: } )(1+Px}{ -^{-2-{( >0�>42)5�� $ .=0�� e �"�'��J�Y"�1 0� .�i:f )�p�9"f�(z Ql2� th10> >�;s i<�T0a�k���^�!ta���t�u.0* �M�&;W0��s�#t�on�=l� ��� v"�of -�$��b3{o%�s�ztt��{uW��-�4" ��aRI;f�D�sY&(�#1Xɇ�-�8�o�a�8o �X� f:( �� <K�"W66ޚ�fb6al &�:Ri�  "( Geneng�E2y FYu (GPF"� Bse�!;�<cx�>��?W*6'2F� es u�0��8�0�*!dyJ.o~rst��t u!�t>GPFnI.�"$R(�� *�#2uK""� ven) .�$"heasil*��a*_�u }�11}� \mu= (z-1� "x� / 9� YL���2% is.�"L -i���JrkAA 11}),&z��re�1!\ir.�(in @"?: S� . A�"A� m�!�ͮ���\mu.�=�-5�%�U*o2 .v &2&\ !Varbitr�E5���2�1�2} G(z)=�)�^ (1-z) \, (- , +$� nd*�No����$� ��B h!=�!1y�a�o�)��r�in" 1��-!y$�$,�fin�Ѝ�c2w&�mo)��s-��� Bm��13} P_1z"\E BG"�l�{�a2 $\sigma^2_1e n^2}--12)}+ nye F�L~1� Ne6{ �d3}��"�.�E��h&%�=1.25� �=3$. L�onow6��u�n�#t*w �lFT62�*�4R�BLƙyceH =s�/2e p"� ��+�!�asy�4� ق�mЭ��@� s�'>�F�� al�ir=&all*�&s), fal= ]A}&� �44$\{[t,t+\tau]\�s��t�� S}\}�2.dR� } \T��Hsp}}(z,V,\�� S})=�� \, LN$�n.�� A�N{jb� y}{c�Oi��style Re:Udt �� [1- � (z,tB�;,)]+\\[2mm] \2��tau�z9\u[1-I_�x �5~� 6H } d � [1-z.�J��^nd-�>�^J/e �a��nd�A��=.�p1<�& meM*.Qkiz  �� ]"_ �UQ*�8� GPF $ �.�$a*�-� Q��*� i�o�|�:-�acm}��X:Bts $t'$�t'��+ � 2�6PR �^bz�$r#x}',t'!� �en��8 "C")��A�&� �DQZ (pdfP*�)#x}'Y �>i:aj���o.�,��a�Z��a�,3�Ap�4`aF�a��P`0V#x}$�3�$R|��R 4B s >�c����e�'9"� �E � K�)�"V2}) (Q s $2-3%F��2�,�O �'*D~6�s, ��A i�%aa�1�r�A{\in&J $�)$l+� ����ٿ"�]vt�$�utՂ��6I}��!8.n6�n�bmse���0��� ѯ^�=��t=0b'2O  Y^=���%�$wA/!We�jtN���A� �&IM<W iBeÅ] � it)Qie�-FKYx�]* ! Ri>� /"n �s� u6Nbi^_=\\ �"�*� B2FR�YZ,N�z���q �!�:��W�heJ�����]��� ftyN�.�.�j�6�*]A�� ��&0�S��A�en ,I�5 6�.��"��71N .�F ��8V*� JI = 1-2�#� ]!F~+ EsR8Ro y�FNUjuR T&X4}X4AI>�s6�4 "� am<�W�"��i-�1}=7 we'����}isF�� 1��.Y!� tau;=)=\�&f}[/.5/^5f� $ P(u} I�L�'[o�A(pdf $f(x)$._)%a�I��-4�2A�B� 15})-�%,'f}�u)= (1+X0) (\delta u)^<{1+\delta}\, e^{ < u}\, \Gamma(-1- , �� u)\,. \ee \section{Averages and rates of aftershocks within the space-time window $\{[t,t+\tau]\times \mathcal{S}\}$} Before discussing M propertierdistribu�a�0, we consider.�ir simplest statistical character s, namely3 a � 2�4different kind>y@. This introducesJ relevant:o scale.& t!*li s!@p domains, which are found inh �to?/-E branching!7cesse �0 also suggest�8 natural ``larg �wi!�$ approxima!d'' used%,tested below.� more geneRprobabil%[( treatment.APub:S of�,total numberevent1# �)) �$�STLet us first calculatep-� V| iEG"�)d ��given by \be \langle R_{\text{sp}}(\tau,\Y�)\r 't= \left. \frac{\partial \Theta2Dz,BF}1@ z}\right|_{z=1}~i�dIt follows from (\ref{15})Ef X2}) that it is equal to��� 5outn+ -2 R(B�1&% \varrho S 5\,,��wa $ R9�v�$ iiQ Y{a�P triggerA��y spontaneous ``mother'' earthquake source�at occur;efa e� $t$ (posia[s $1$a� Fig.~2), �bB�ofv��by � F� E �.��(interval $[��$ .�2$A[ $3.��2�:�S!�$Az the 1�2��=c���8B�. Here��AryI�Xiing, $S|�Ya ��spae��| $\y�� thus $S .�6c�4volume associa�+ with�.&�C. In wA* �s,a�will be�tfua�!�UH�~!)�!e�N23�2w= �hdyvv1mi}{dL}~mhitho gin{�/A�}��bel{16}��!Z�+ NF�+c�^:C S�nd�U9Eq.��3bb}), 4�5}), �6(one sh�:aB�\l �7} J� =)hn}{1-n}5n:�\,S- 5�Z  J�I�$~;$ s�f3 a]1�b�8=�^�- n\,�� \o�1s \Phi%�)=��n\,��:S-/a 1��2� $nu�&�rA� define -�(mgmlele}). ��,!mn�no on����� �=\int_a^\infty �$t)\, dt= \��()�c}{)+c� )^\t��%�I4kkdksd}Ų Substitut�I~ 17})a�o6})dɥobvious%�litvV�9=�V�x��V�e�2�� N I[at, due� cascad����A�pr� , � ��2� �6&RV���$���!�amplifi�\Tfactor $1/(1-n)$ compaᛁ�#Ճ�:�!� S$ ofJC Bmhas a� !�(uitive mean!4\cite{HS03n}: ���-�on5)adaughter�P direct lineage; each�these� -g� ��<� Ogrand-U6�- of>'!d� n^2$,�o�jreaso�Dcontinues over all �s. Summ�N �2of)6�  a�nv plui.s�  itself� ($1+ n + n^2$3 + ...$, I� sumsA�U!.�&� Impact�� *� ns< E�� he ���} ����m pree�%?L  re� d ion%�a goal!�est� ng!g �+"� termBr.h.s.% Eq.~�u EGPF $�� $. Our �D o�aN��$check for 2E!�at.�F4. For instanc)shA1assum�at�N�� � in�;2��)�is reH sibl��rb� =�=� 1��4$t$ (i.e., out� # � 2! ),�negligifa� cor �d!�r!�iveQ�� bey!2�� ) cond5 ť"� N}� ���u~+}"V`� l 1��ee To-�whe�is� holdI otic)�� ��8c I{19!�&a R���sol�A��v��v%J� n&�FApply!yaULapla�ransform�.both A t!l ��� \hat{�:�u)= n �1- -8Phi}(u)}{u[1-n 2]}1�� �asympt!xay mula1f0!rwe obtaiE:R620}��\simeqL 0n\, (c_1 u)^{�-1}}{1+ u }J� � %�c_16J �1- T) \�)^{1/ �c | ngjmss,s,^ is a>qa�-v�&� &L "� s��a� a�t^!�� H}$ law at $t < c_1$d )+F)> 'o� decayx�V{ �� @ �/yF F�F(SS99,HS02}.:W\if $c=2$ min, $n=0.9$, $ �=1/2$ALn $c_1-�6280 $ @10.5$ hours. Takq inverseJ(of.q0� !�V�1}z�=� E_ �� [-� � }{c_1U8 +EF ] \e:� 3$Q(x�xaYDMittag-Leffler fun"r �;-x"m8x}{\pi} \sin\pi � T 0Q i�y}A e^{-yA�dy}2 90}+ x^2+ 2 x y � \cos[D} \quad (x>0, \ 0< :<1"�T2P�5dy��:f�2}2��m�1}{x ~B�\q� (x\toG )\O2�In ad��,} E_{1/2})Pe^{x^2!\ erfc\,} x� 0 Figure~3 plo$ he ex� rate�ev*a%�al 2��J21<6�9E s derived�62})jO3~�iwM(n}F!L.�_1�U���J� ���� . <. One can observ��e�[ ult?23�s!sher cise��|a�$ clos4 �i$..C �]ifAV'4} \gg��F�t�N �� + A>H �rs 2n-= t�*�b *) ) 6� 2 .e�remark6 in our*��P stig0 !���i&Q_4})Ire�d�a!Ae ��.''�� !�B� ��6�2�� a� �~6� / last �}o � "� 6�!�� (erm describ�ll A]2� B�.Wv9 % �. I�asy���� 6�seismic%&�A�bA1:�2_m�� a�� qfu5R�in�;"� S})= 1-n+��@{S} \iint\limits_& S}}�F�;\bs{x&>d rX N �Nv���AJh"D*DVII)yC"I=K$ t#t��au$| someJ �� at pk $)7$�S� $t=0$. O r�onsM5--mF� �SU�f/6?���+A&w:�-"UR_+0.�:-^"&�R(fkŭ!�� & .� fall � /e�B*|S}$m�2haFL��*>��6N�*� s�A�B�6( 8%6��f�"; (d"�oM�N!�FourierN)�)$) &�of��  �I� Rp }_+(Fzq��'0\tilde{\phi}_]b(�q})&3 u& eft(�(�.@4}- #"%1-R1�)� `eR?sm�18�Hrewri6!is�\�% i��f7\�E� 0 �R}-|B�q}S ��$"? c- \, u �>*(c"� +1- RSbt�R��az��Q�.�E� "�v�C��Z��#io&aboveB�-�7�3 ��2;�V��u>U�^�� iAIR>��eF�emV,!k!R Fk��Oindicato*�-P��� 2�. >� we2�2/] kcir�$r�� radiS \ell$ cej!ed� orig I plan���ne�q�V= 2%,�ui}{q!f J_1( q#�mghkhlr� &+2�Z�m���%wJ4%��� �\|&>H�%"20$!�F-j���:M��)"5%tE���H" bs��= '\���� <�12!A ���taj�)��hus�F�J^IO) � sob��5��!2�ij�8�%�J't6'%���Z�_Q�v�![1-�T�T4k2�0 expressD �72�8 construct�%ure 4 �y=~� $�` "� valum� tau/^,Cr�*o illust6it�vergen���a� area6 . AsUbe seen-f�s 3� 4, it �"�(!["�(a����of Z��N4z�*�� 24}),� may�v& e��!Q��N�&�I�&� B�+�)oz�i�� ve�� ��1#� g.�%�29j�&� � .�n(d!}{�w^2 �b^2�nt>�2�q� � �6�^2(�� dqJ�A!�k'�e:�nc� G( sizes)�&��S}��:toward�). |5u�5rMu�&AMe A�ag�$%��)$>�9})^O expon�.$\eta$� �/Lv�-} �analysi�*� G�sW-�possibieto�l�*9..�6�/&j�i \n).n-)ae reg5B� z��4q�. I��du�o�U %�.�a:,sufficientlyi�in"�!1! has �i.{0�|�!!).�s bec�(independent�$@ seem� l#a� to�m ject�g�(W GPF �!J��|xAb �2> r.�2�vB �id* V�until)| � coincid!"v0�1%�0L+*�"�qjSv���6�r� *�1* S}$. Wit�t�APofI# �D �$eff�:@3.cF.\ !b��o%�"1�e�1is �". S� 0 exmmflaa})Gexe�L#�1detail�Uapplic�1ty n�!My. .z��Vign�2�#�$� K^�$*re�! Y�tN *$R6�]mai%Q $s. As a re�, ~� }) tak e�Yrf30} LA�:'�N`.:--?}^{�  [1-�%OF][1-IB�x})] d �e+n f� [1-zrd d Kc 2' w^n@L A�.�#&�&x� )}8}) or,z ival���.B ofb�3b j3=GG @�-(1-z) 292%�f ��J $G�B�, 12}):5F�*iz��"d��� fel}�o findE��.�*� ��� �L,-�%�ellp d$ (�'fD*���2)f��e>�#^1 �#N$1���s gW6�7an $dri3,E/ out 7n�1error,^+may�<� =�$YM��2Iv 31})�"� �0 into accountR finitenes"D RP2bR �7!�%�1� c)�of �)2�: argu�+�36r �j2� 6�s I�VN-( a$0��6V7~ pN��.u kmssti=$R3$?i� oDpec�-. W<ll z ���4^IAb%�erpre`8�, all R��*A,2� aJ�Nx�93E��uN�e6� amAk�,�Aa vo,)�5g�95&(n algebraic��^i�/�g�6�� cruc�8 stepA^� " and �4 just%� fur�!b!:.� �@A�us7 non�.�+t �Pyt "��,�Q�al3B�MY 32} I�,=G[(1+(z-1) R\M�N�IV�,�mouik  +� � � !a�"� .W:�to itN!eN�3F$r�"}f;%2�J:�%� ext &�.���-clarify�6IB� sens� parame��6�$.�7u%F&U �#� h dEmin�/�E�sistencyA�# : choose 6q��$ such��N[ 3�$*;)true 1cj�Ņis"B��*34}V1�-!*@6ns\,, \d'\EpR5= 6M%q})<��1 1-n EG B2$NK62{rw by.�m� 4}) 63q�a;dimenkl�[@20 $x/� $. N�&,�a���qb,�ach� f3angula&%. W"'u�&!�+'��to help Y�As"*L&aA0 X:� ,&8:�(Ve��>� }=p$�'� in *6 ��,P7�.�$!����V~$�I2 �'s F�2�u( 5} p��d*rD$VW � J�$p� �4���4�l%�I P#%�R&� ���:��2* x%S2q2��eI��A Zv11���5�:=5o�6���2m m�0i�.I ��@"�Q,d0tau S .y;p)]~:,&�� (z,pVB\b6X6(U= &p]� >��Ci:�+�%�-"� CowD� arily, ab�~6,b�is sm�(.s4iPI6A >��*�"�46(&�rN*�+ȡ� its � ized �/ion6 ge & v�Q�a {� o6)x� msmwwkl# TUTA���C�"��6*HA�&k!O A% En6��mbm �qt�>�f2 .��q"JF)Z�6N��)b"U)�4�1.�� �5��M�40"�52�)�� z=! m�.�4 q�1-p  Putt� l�+s: ge� a>7�o"�$&� E� r�$37v�ECS�E[6� (1-p)I� +1-z"*;p)fB>`"aa� se�.a�_�������e�I��+F��O's ��S6�,!�bet� fit empirLI data�<�&�D6�in |����binL4 \&u {P2:m(=�Yf� I�mM) lead9"�8��< )A�FBl� �j -V�=i"�9�ic�. C*D(z)Y5��n�%&�!Twho�ce�V����'t�06y 6�)�ft�5.�F<�R1�<&�'�.g.p"� :"��*� �= q.K+z6�T 2)�=1-RJ �K*AI3�M ��qGMzJ!� o'*'F9-�s $r$.�%, %y&3those.(m�S !�0f�,�U R_mJ�8|r)= X_1+X_2+\dY5 +X_r &� {X_1,,(G(re mutually2�l@om vari�&uJ7�;Lty: �40N)2�>��%6� � e"� ��!�*�>Z V��:gV;a�Fw�Ls.j&'s�6"��of�c)�SF�:,����pdf $feyu`$Tth�*� +y} bB9"� !4 sameW���s only�'F ]x ]JB. @aXNlem� hav R�=:� V� > 2�- ) ��9 �#&�Nca���.*o5P)�K+! , at���P$emi-quanti�<ve+ to"�4%6�P fele�%�*Gp"nE���!F�>sn �@$*� &bM(�ory. fO� a fewful� sequ|&2!�1(���R� �GE�6!.�t$r_0uR��Xn�A�.�V�9} P(rR~( \sum_{k=r}�;( P(k)~ B(k,R3�*N 9�!B�V�� s $k2'�bU40}f�0= \binom{k}{r,2L^r\, 2Z ^{k-(a2��*K/.�$b%no@! g bu�� c�Bal2G!�m!1y7.$!�Bk\geqslsS6M:n,EAi5m� �B9$$ $r\gg 1$,F�4�>��&@ �?�Hwell-known Gaussian*M;f/41v�I1}{\sqrtu' k6�>�}Exp�- A (r-k6% )^2}{2k\,>M2}\b!+If�*&1M�(decays slow����)4cePit_  a power=#*$k"I>� � e"�+�639})*� 41�<mp�U".C�U� b@slopeb�� 1}{2>aOP%b()arB!%9)�(r�N� In view�{B�3 � �)Z>$&�':PG 9 behavio��yá�i1*� �!�q�+ad a��?�6} (6�<1$)�Y,an unbounded  :-=1$).:�<�(��s}�"-get�$�7ght6 �F�(�� s%�iz�to stud�LT!B$!9";&�( ԥ�*�%s%ui%.�2% !sf�**� 29m%$p$�%IE3',� �F.�!~!�9..^�#Cn�$*�" k&U �%" M�n�U4"�(z)=G[z[N�Accor2lyYj !�&� M�in a (%~))�� I,� �2-[1![�Qp��I�Iz,\rho)=}8f}(\, !6 / (z)]�)eWL%�ev"�T�,�� >=�6�O\^X SXigmksk� e Kno��! �>�ta6�=$�aL&h P25r;�r �+-^{,�HLC�!.ula�RM|S1}{r!}�y>_Y^r 6P>O}"YY z^r��[Y0[Y)"mgjghiri-&Eq.�&� |!re2en� o�idB) readj�3}Z��wg/ i} \oR[?C}}:�BG L$dz}{z^{r+1���2� �#"�C�M )&�ly��A."[ c x�6 $z�.��%/�6$z�>H�)�2icultE"%B ing ^N8-12!�fF: 2��Y�� ici�by#�)4�To�b�g�3 ��&$;=+�""}%4W  "�3eU:E�j�-�1T1 i r}n� d6�B�!�r5H�G (r>0)�5$mggkghklgf� 1�e newQ�� v� $y=�� $. E"� M�!J�%� � �Dr�RZIof $y $z=y/G(ypPA �+%�� �qR�R�R� 44z]���s,'}G^r(y) Q(y�� -��I3 VN!�V�5} Q(z M=�� Mdq�[\,i z)]}a�>�J!�.�'%cI#e�envelopA�a;i� $y=02:�y%HG'��� $�$-�4��a!�"� ;ger $R_��#i�"7 �==' . N�Na�at.�4�1��݈�a p�E?. Indeed� i��AIXN�CB�� 46�DA�JPr\�N{ � + R(hr-1\}f1 --�6:8��=|:{4!� whiljs7} �R_1+R&�R_r�n.f[� {R_1,R_2R_r > .I6�s� $G(za�O ��V Vach� R ��(R_i$, $i=1,�U, r$,VE�Xla� ym8Qs-�14�-��& prov�2QR")� &I vI Z�:I Z",&� �46�, For $1<\g�e<�Wa��s�&� y |;r��{sumW� .�&bgoes to>%� =Q V�8'k|r�!Ň41}{(\epsilon r�Q�� psi_ � (��k-n r8 689jU s= - [n \ o-0 � N^  &B)�G�>�.#Pst� L\'evy�&"�W�0R two-5s"�D"�*�Y \9&��1 q�g(x)O-sx�dx=s^ �$e<is c�� 6F�͝x^{�g.C )V�O\2�02��=GQ })��'&�K$6��< any A�XA� TI�8���ġ�� 6� )m%�O(&�QApi}%�&�Qe"&u-m+uxwQl*�?pi}�MN ]\�Q+[ux J7.KF]\,du��Br�D nume�"�=�I� w /�  $ �=3�Sfor�c�l�(!!:��#i��,availA�9E{3�Qx\*5�pi �3x �M  (\ + 2}{39-�4,?t_1\!F_12+5}{6},.8, 4 x^3}�B)p)-xQF2D4�o7.o8fo vJe�Z���&��7�7��ɭI�er ���.F�[���-=��Gy ��hEV�9Z��7���}{r��:���?)��{(1-n) r�|<:)Q)� (n%L�2� If $�H�Z$ (�&�W.�4^notOly criE�).�74predic[1hCTc.� two 6�&Hd#%u����3�Z�)$�l,n8 aly"UT�+(`8Saichevetal04}.a�%̅ $ate} \item&�%1! r_*&..{\r$th}~~ r_*=2�b1�-1�^�6/()�-1\���Y6<�U�qul "�50jf r^{-1-1/ k�.2�:�E$r_*� e�Grec"<#� ON� i*� -��HvlJ( gene>*�!OV�1��f�\�9��"�CEW"�%s $ H =b/\alpha�b�%�typ�%;6alaS!model��?��*5across-%M $r_*$ &"[Stwo.�: ���f� � 1.25��Z"( n�|10^4$>�Pi�^�0"� % (T �sy �2G} Star\�[IIl��c1L � w S2��m2Sm��&�I�?�� $R=)"�CC ship�'wLE\6� 2�v.-� �� simi�0to=B6�F.� 4B\ >�H ���Ͷ�՗.l vali�g"�R??a�R,p.� �ɟ��\,�) n��)~�)� 8.D&Om,msl�g<�;V�.% A��F��3 S)���chang�}" �hP"goE� @m215�4?w9r�r� ^�%�y= W72?/�> \iff z=Z(y�#+ p})s y}{�}+p-1-T� ByQ! "R1$�mz�/=="bS� |�Y~ U~a�� M��40array}{cV�Ro�Jm�jD\[4mm] \displaystyv^�'"���!J)+1 �)1] U�'}{dy}� �Z�(y)�[ �Q�fjjalalaDe & m�$)�%&=2mqaG �[ .�$\ ��} a�B0 2�V����!��: �1&;&s perF��auU AKt oy ���n $n, ɧ, p, @ ��$�6$�p l�<nota2,at Pisarenko�7Golubeva�&0 �>��is"�\'�C��>16A& PisGol}C*�(�q;G�Jur Ns ��2ed eit�]as�t�2�'N} real2��["�ks T R: k52�ED$e now turna�a brief'pE@�~x.�s�nd ir�.s ��_Y�Ce�J{E"�.2G�arison� th�&} �7SSou!&n�-iforn�#� catalog B�i(sed magnitu�F("R��eNU E5N CeR)!��uamo jb�xon�� 3�u� !8 span. M�$M_L$�7 E� �� J>of $0.�d 1932!� 2003�# �Ion �M&��G$32^\�R$3$37 N� y#! >l>$-114 $�" $-12Bin long4.#"�!maximizaze�Ket ��A�E,� �} 5�(k=m�� E�-< (ignificance�con��8 sub--� !\nD o%neT7u1994-!4�!v >1.5"�l0�@ a0!v 86,2�e]U8A�let*bBis.��;b ver�?}dkdard waV �-$ouisor} by[�p� i�)ary cu=* U�6�![�ye*;�O�$E)included��e >+�si66� m�logarith�_,�sj!����!i:s�!naFa diagnog �t%Z�:U*a ^F squbox��,f ($L=5$ km)�J�$, � al�$16046$eb�{i�m� � m beAYacU/ empty!A!�ize��romvcbe conflic� rpr%�s�c%C�2hand, a�erA��:re�should���.eGd&�q\E�qloc���Y� epi�V2�|��!�R��Z �A0�O!$L$ deesA�y fC-($$ 1/L^2FmFI!e)��%��>IYT3:"�9a��SedZiu.�S!�\B!�$M.�1led: $dt=1$ day ($3652$ tempo�Cins), #0$s ��C0. Comb�J���=nd.�sk.d !�6S>�{�� $L^2� dt$R�dt = �{reaWa �4��54669M�o-2�)�"/A�%lI� $4298$D-E�2.p-T~7-10c@%v&�6* d0@ty"� s*T �}}(r)�O �?!^�%%3.dd �3�� straV(��:Figs.~8�is��D7E�a p�I&��"��9( 1/r^{1+\mu"� mfm,mfls� �A l~e $10g q r 100$. �2af��� $\mu�f��� le a �"e��29 , si= fit< �arpmuA'.65��A�Q�{l 72 I���.* B0B !. How�&&f also�AeA`{> i tq pdf eQs*a/m�Ncur�i-��r por.u bulk�;!ci0dtUB.������i�Qg+u oOa�xby ouTory��we�UcE� rst,q .� �leEe�� ad�G opti7>�'e:1��&,�Ed�Ad�8 mJye��^T�$2"�$ aeraF! *�Tp./�disrholl�s4parR8FE�eq p$ P&�a4�%"=K�c=K�\J)%��{�) : +�*(�"!�roughlyn$.7maa�4^JO)G)j MTN=6ɒ fU� +E�N0)3 %-D ���6*���� �: bi&�n5� *)fZ ore5i%swn/.� A�q �a��'qM)r&� ��!�set ofY �6�!��W1p=0A�NEc = 0.15�f%=0.0019~���zs%e�H�$un of ( Dml� �j� Fig.7). N�"~xf��"�x�),*:�\�&s2wE  �wLtIi&�:�o"yi[�� i:*4b2��+.�4)P%mX���S ,eq 0.02-0.16& ~(^Din5> days})�1:��Is+K�Mst�LE���df%�W���k*�T�[�=NA��H.~7E�y�+Wn�9z ' :�2 isL7�dE9� F�a� n��+��* h��� �s�M�(Ai~8& %[ 9g�0 10.�y�E��| �P�ult�nly!R �v!c"� .�L it:�.�a?� �D:�� Se�5 B�62L>ZA�I93bI� �V p�qc\</�&*�f�D��f�TE�-f&i�A��� varyW,�B���#hN s I  < 0.�� $  ; (�by��pe��rYI � adape�WZ?w A�� c2>z�6�l)E�&Sly;�ly goo� �a E��xyu nois� cho T5#"2 zeroAoE?�Mt E1Z 5� e Cauch:"%�)k�y%�5h�Mogene� <"�*��jr��Kfe��A]st� field��de���s"�[=V#Zolo1,2}99&"H��"�Gc �c Kaga� ess}"' �etiv�A�%� resk�:t��4 )2��san�Qbw4e&^�+H�a surpria)!�=<`e�cis work�di �ec�prioriɅ�:�6� wJt'so mu܌b�UConsole?3,p ,ZhuctalQ�cV�5z�Ns HT Z E�(�Mb?M�h-�N' �UaG�< disc{;��K&'bW`� �lse��haKX�*��4��$f_iQ*��!�c *� !4%�pre-eg$� >�2��Zq�, se<*lf-T<�<� �as x<�i"���ia]�f #v��l�fi ���1ed 6��P%&�^�A�J� �C�9B"�Z����all�*� E���&�S ETAS�asf=>G���cla�YO?ed����nee�A��r� B � r��cru�If�roH_o�nce� !&v�I��7E�lik� ��Ak�8!W���y��()&���3.6$E�!�� "XE�!��CL.>&v &� deTwA�TX"R$ra%�a+9 enuinEm�/k . Re� ' .t�x:2 22�$ ��7R {1 \��� }}� $r < r_*' B�>' 'usi"�NM>r?%��:�' �J� Y�(91t�L��ž conca� shap5�2!at��h�med��I%�VCcGEX�tE�b�t�'|�= appa"W A2P�e�a�/� a9�*�q � �["��<E�6 ysyn�� i���.F]sBz�&a�&�&q��b](���byJBEBs�al�@d���!S�I�^ I��EFent!uroa2 ppl��tB 1j( box� *�, JapaP|@ Pamir-Tien Shan,%t0/or!Ean.! mu<1�c% perhap�X@.�E��Uj9�s�$� er5 B� �) �,�n����"i )&>?BO_� collapse&��� J _�=" c�, Cor!���dE|.\�i� z+AShib� a dou?e8-3�"4a�6:�=��nd6$1eA�eD &- �}. �B�*�� m�bB��no��Sal�pa���.� �rur5���s� q QLat����p&�)�hY6q����A�!T�!�L��I�� u� X�W] \HB� e�n�0\�="g.Bu��e"�dev"9 av�u� diP"�9&��i2b L.�}&CA�v ���obliged mU%��� �s: (1 "su5 P$6�je*I �� t+\tau]2�=Ib(�!Zin! 24e9 olds!�rAV�Y*"�'e@.|�O$�e0��,)R2; (2)�-t� abX !=into " unt:lK�R�P@ U��ath��$�z!�� I�%�at�E+_a!Edϛ���.R�C��F�!A�8 them C@2 .�Z�fixedQ���"�.s. Nu�c�ih�  5?PDF-i�# a���6�. .�S"E=;]- Que�*:#!�w!e�&�..�k�M!<.Sdur-�� $k$ �!7a<m=-��c2;A�o nV9 VJ(q�c��e!+>tZ5];�&�it�p�c�2aQ!y�VT0"�D_k2�D_{k-1}(5E)3D_1*(z:+261Fo7�6&;i 9�-$%_�c?� ��.B��[5�Bk�<",�-} b+�[� 6d*�B�D6�Fu|dmorh�_�<�'M�9led�tjBRJA ��~/�nBuD!���.��)$�#�"B#2� A.�[ښsy��sho�7�{�q�� .� 6�)��  , og��2�-:B��+5 AF� i(r+1)j� '} G"T,1� y}{y &f,�A�}��11�^ :H&$PE-�+]�sQ�,�~inac13�(-�Q�ͻ5�C|.Pw$k.>$2, 3, 5, 8� +8! � wI6� $n=1$�S� !� �2�.;.d jk \to +<$ f � ��AN�54}). AA%�K�@�6�,E�Jw=86EP+�6 almost un7inguishX"y $"3�'��a��f!�m5��,�least  $r\l�O25�"f~12�]��._cm��]� rlo(\��� B���kbEt=M�I�}{aY#2LAJ@�in-��;�b� ne��\)�\a�f� "� � s�D�*HT�� ,6m:�8 beyond���p2�$�&rma ;2A�q�.�X$T(k)�! /� n�W|�TSa�D-th=*A��.�*���4�1a5�6} }=� _��au&�Bk\Z5@ $\7��X7�B k�/ot�B N�X��waia$��)!�&�!�a"�"2�Y��of � .����$�#\$\omega%P.�� le $t( $,!�of*2 !��MV�7}&SQ}[J ,k]= Pr}\{!}>\}= uF��~$1- !x&!&��� � "� �nyA��f�sucaE` .[����2D� %�2. CCjaLD ��;l (a�exa�\' ��"�#!�ma�%ser1��*� a6q�%9� ! $k!�.�� ��$�ez $k=k^[}u�?)@:=c)k_*)!"���� F �u 6�G�( t_*=9�_*&OJkhklf�EtR� ��� /h ))!k�8} ,�6o �CL%WxnS2@� Q}(te i[� �g"E= $k\g�E"g_-� ��&��ds. au_k�su�7 56})q 6OOmori's ? ��th $0"��+ �%F��ҵ�?!1�!�V��_�- = F_Y�\�A��t}{c[kzA("~� ]^{1��}\)9�=2No� [TBEx" Evarphi {($U dy*�E6 x)E�!�one|Ed�E�*6;=�4B��QM i}�u(�0Z�x) e^{-u.�EMD��>e�2 partQNarmF� x)= �cerf\,&8#�?2\�Wx5_49�f&�C5�&��lV�9}.��e%&:F �}BH�9F (xe* �2�J��5�BZ I�59�W ' �� we %�ޝOe�t^*�"� D��)b�60}�� � c�#f�:�%{ɬQ�]�)u2��?&G�)3=j�, $k_*=8 V=0d5 "�� utes� n $t_�9�%s.�(A� hi�*�eW A�" ��Zn�L =1/3$ (*!. $2/3$):�I"� ��"Z%T+s�-<7�' R��& ). B!P6B[t' )o!� �q-�2p(A)"&�5�8itM�z&8�IC�S&�-�+���>r�!1��>ly1T�2�&ff b�,A k'sap�  \�D�$�: **}&S�*�A�sstIJ$.���} l�R�in �� taua'�ũ_] $ > ^*�)a[!�.� b~/kM�$/ o �B {niH�.>��#�yriC }~. �� ��)<&�� \ a� F�q��-7>Qn)kչ~."$gmjmloels} �eF& =s �+._.A� MQ�uc�%^ �T\cQ�!t :% &� _�U� "�� !�f4i $n/�G/ 7D�$too" �e� )m�a(unI���u� _*$5 V[N.� )�%T6b%Ge�'as it� rOnq�w @2�baa�`*��qPcle"��e , m�,$� .a&�F�{".I��A"6�)}l>y� &�IE�} �5x for � \�&a�uT?P��� :�)&5 � 6fan.5$�� at p�@�ex g� A)h- ��.m�=� bsf an. 1� -�����&$\� kUe-Mv��er� 2"�pE�v)\ ^rbrace{\�uh }_k ./�9���!%o"{ � � ropa>�y})�~nmpla��?d)� 9}))!t*ҥ�pw*d !� an*��2� to 2�H �I(� P�?* �"� S"g=:�p#}6u1�3u�f mghjjslkh6PS�Y�/�m;2k-�|"� �.9Gk/GY�"�&<Y�.(.rY�i& �8�:@"jS!h&P m�o��C" a"D�mN�= U�(p"-1)+1� \,,\\>2V�>[^ BD]2�|]^ �t�dd�:j �3V� � w)Fe�� �7 n upA�!�($k"k2�m�IA"]1�T"�a&��>;�60a�Ekb�g&q pinl]1�Z�^.�J= Y<�"B[�a ��%N W �#�ũm�k��Let usXC +0A����%FѢbW," i�=1V.Ox}�z%9k dI[(xǤ k^2 d^2)^CR}~Ec.FA�f&�4$1/|{\bf x}|^3� H�oft�3rgued&AbaDM.2'e�xic Gr"A�+�0a� meh|al!ce. F�@��� i on� f^1}j���P��5 ell}{kd},M5xiR��2p&EP (u,va2}WT��u E�c)�4vs�� (v+s�g e y,s ds}{[1+(v-] v 0M�e�b, $E(m&�co�=,� llip!{�l!1 ,��n��/2�9qrt{1-m� ��oPXgd i;e"Q3 &u.6� 61>�$!]=10 d�� C AE��MF@gdBƗ&m S}$ �@l$D�P�mU�*��""m9mgt�). (  &Ÿ� x&-o� "D,��0=0;~0.4; ~0.68; ~1.2;~1.46$�o��bottom� �Oo�� curv3Vrz�@�w�mil��3[" lan Q@ ��q�ZZ��OEy"R�6v!�AUr|6�YG7��ed /�A� $0a�m+�J���ly�5a!��ite_�5% .i+%��)fC �2+����ŷ2�#Ar .�A� away�v;�� $.�f3h�.a�.At1�>B�UbPs"�|:�6�{�3b)�$366�i:�, h�!En�Jr�>om@E�#�!� =*�!� %�9b�0ar�*Qx6� rarely��>��DAs.o!�hig"� "8�1"9�P^�ae&� )�-� 3yf�h��%L)��/d=OG!�varE�*� MB�,E5!��*�ZI. `'� �(�N�� D)h!�6� ($x�@8B�;\, 0.6 4 f�$��2N A�"�#��"�w"�as�,�(S�*1�Del}. W-8is .���6"�1�1�1�.�rF���"9�1���&�Mt}jera���"ral sup�0�ofav�P��Gar6�m:mgx�"�Kw��M3^ MLFpreS"� |Q ���?��'�P�CN}K��w(Q���m"S* ��D�`F1�:e��T 6�q3�) n��8 �&)2�V\$� cons����e2j�ȥbp���A�>���3�a}�&�0e�"� H  sJ=�.�zC .��Bis�Bq38=!{]j�bJ$� ul"�E�2�b�)&C��a�a�"bI�n� 15a w� �1� <�:6r* merg#;:9T��&~&�GEachES��S� }J-x�0z1� sN�`"�/"�9X�*��c"�M2� �a'it� F� � '��9.�.1�j�$�IT�� �.6D v� Z B�,x}=0)hb0q�Q�/)���-�& � enoug2�L k$ (20��o;&12"D�j��G�a�"z4:hr*VYp^r/�n�F3�Cz,�dY.�X�m��y}{[yΗp)%]�n���o��pr& 91�" $p =6)y$,@"O.%�62M(*�mq� 4�,22�&" 6�K,� C4�V���DJ� �)I$0; ~7.5; ~2.5^ upper` �  panel�4�i&5M>54I a�i^* s�,`/�=_ c�_'��crepaǑ�Rn���( 4]givZ �EH)��&in56E Αy" rr� +�s� t�:m:��� O�!�$rY�rjG"I� � shzfM�"68MJ2�5 q� %I���aA����!�saml,�F�>�!�. N�:thee,"�-Y�a oiG 6FrH�A�u� le�S^ ���& a6Y � "��D"Bɛ�"lYZ�Q�@�Ie��* �+M"��1Rorgan1�of.�s!�� !�[NmerE* al*>C]ss[<�U6��'!�aN.�#A<(Epidemic-Type A"3  S �)*,A"<+s}EiqV2�|midk���&t�U�*+ct 3"' nf��A volv; �6^,"8U�Av�A!&�� sche�?�h+?~xed$0�P�s��eY> �NrF�E��#2f A7 :�3A2�� &��P�ƭM]3�! 2�<-��<��J8!�ertheirV+� �Zgo!d{ PLiLJ 0�%�Hf�9�!@<��� r̉t� E &�:e>.6�(�' [KE�e�*ee���;��Zs2�T:��/�t�!� nvrN�� v4a�N�51�� 2��sM.&�Ny&6l�E' rigi.�, �2Ai>�M%2ss>1)� @qK�Ԧ�8i�c�9T� it2l2 augR#he�%Eat�O1��wp.�F->��Fy=�G1�hysaj �Tik]�byis�h# !����F.� E faul�t�A! � jraip��d�=Z�G. ��fiH'hG Hi�Ytf�id��;/s���!Y�!�.%_6�vD>�ec��fu�%q�it�nd��A%�a�B:$%c`$"� >e Pois�`*� !4h��Ju�>`g8ikelihood score� aAc�!'9A%s:}���$k warmly G�il�s for � g.�w�>%� @ax9��*?#��xwL�-�.��)< NSF-EAR02-30429U�&J�a BMa (SCEC) hfC C[ Co��^ Agree!, EAR-0106924� USGS.+ +$02HQAG0008�� guib��l �Oa�a� is xxx._$vskip 1cm D Dthebibliography}{}(b{Bem{Bak�KLOmo} Bak, P., K. Chr�Os�%L. DaBAj8T. Scanlon, %Un2`�Z�!or*�s, Ph, Rev.X Ht. 88, 178501 (2002�+�CHC}  A., % L(^� "� ���'fl)E"��u6� %�:�H - art. no. 035102.��\�8iew E. 6803(3 PN 2), ),�b.!`-D,Mega} M. S.  !E$ AllegriniGrigol V. L��a,!XPa�,(lla, A. Rap fdiHS. Vinciguerra, %Po�ϥ�.b����2� {\it >�,, 90}, 18850F�n� } Abe,�!�0N. Suzuki, %S��-f�T ,�"&s w Euro��-�, 65} (4!H81-586|4.KpaczuskiA�iesi,!W� M. P , J�%�5*J �= 0E, 69}, 06610j�2v�C� x1 ���pri�GXt http://arxiv.org/abs/!3(ics/0408018]i13.� !�a|!'Hursornife9�,�Y � R� / -mat�619.�PRelm} Schorlemmer, D.%�Ger�Sb�rE<Wie!� D. JMP,.�f�[��p G/p�wintF(�H V.F. 6?i T.V."Di, %w-�K hWaA% �vysi.!�uqBo�#S ology� Geodynami�Q0127-137, 1996.�Ogata} , Y��SV�6al r:��r� %!3residl��)���+"� M�J. Am. eo�8soc., 83}, 9-2�88.�KK81} �Q�Y.�$L. KnopoffXGem�PRes., 86}, 2853 (19812�HS02} >Rst��, A YD. Sorna� gn>�super�<%�e�1324jJ�J.>�0107} (B10) 22!�\doi:10.1029/2001JB001580J�Forexp��*sV�.�օt*]}bg108 �!n 457 �3�2409 01e2� Athreya} ��B)�Pa�$gers, eds. }C�P��!�arnNC } (S�8ga�New YorkE�72DSankaranarayanan} >, G., şBra>���F#? } (Wiley,2892etasdif��Diffus&wf�/�9 %.K Y9k9D g@*')d� inuous��y walk%Ylq���%sRep, 660a\061104%�2.�HOS036�~A.!K Ob !�6jAr2&�)CalN�l6 ?�NQ8E� 83, F�5�k206�6�M �.1F�Anomal�D��of OffsE�0G%�( N�;YZP��i\w inI�PY!8����ics�004 (�$X���$305007)���Sorxy  e�i2��� Law D.M0of Total Life� !� &�s �p6�&� E �.Z�*z 4019.�alpha6z� I�F"����d��(�}Ns?�v� Lett� 1� 5 E�2�SorWer}�F!H!�M.J1 rner�O�ai�V��m�� ���y��]oMy$, B{\aa}th}� ��&*���>9-=~V� 111142���.�RSRenorm��i o28���M�5U*�  981-1984��9.�0russ} GorshkoE�,� $Kossobokov%�A��,loviev, Reco�p�dY.pr03�I�%5N"�i �/lithosp4f2JL}�8I. Keilis-Borok/ A..���.�Heidel� ) 239-310.�' 824 , %>����.� cqcaXby�1������-�p a171-181%�2; o^1} tar�mV.7 a!,Strunin, B.M� Internal- �2Jb aѷ.dAQ{ de���S!�fSo�y� e, 1} 481-482�71.S�2F�One-d*\/S� .ms}, Am�# MathAtc.!>v�C R.I.w82� Sorbook1.PD" � Phenomena!�NB� al Sѻcex Chao��$als, Self-2�!zD-qder: C:vpt�Too 2nd �i"U Ser-in SynG t%�Y�, �[6H�.D�� �!"u I�ce!�R$'in �$x � �~>&> , M�.J 30 (11)>l 3GL01767JyoZr��%D.�Ma�Lude-D�� �8: &�uStB�@Ty,F���V�407208..;_} u 8 R., T. W. Beck6 R.ZAb� GYe�Ekstro���J9 Rice %T٨��D1999 $M_W$ 7.1 Hec��Mi|8�]by2� =2=3 Land �9�>, F ((B9), 2190,>�E 091�2.��@� 04} *"� Y.�!D. 3, 2�� 70182�C. a�a,EM. Murru; A��Lombard�R�B:�cluS � �;�,N�8}�, 2468B�28123�2�Zh"�a , J)��!NPD. Vere-Jones %Analyz�=g�"}�">9stocha� � ugZ� 10� B053�:�879�2$GK74} Gard !,K�.�� y� a'�� %&1 ,*T  remov�Uian� BullQ� ismo ��ɸ6C363-136�72�(Rea} Reasen�,� %!i-9m��1�.���.� 1969-82^g 5479-5495/85.�$DF91} Davi��a�I�(C. Frohlich�r�-linkQ&�2� 2�: D�7�!��-� nF�96}(BW6335635�[k/�tJ(\clearpage . %FIGURE 1>psfrag�< ,{P}{$P_1(r)$��{}{$$= r}{$rg R}{2./g=33b�&quo��!�erw,{ \reGr4box{16cm}{!}{\:Q�'Dphics{fig1.eps}}} �I1 .~1:)7� {PloE1A�&�4x`$1�D^F �\6 &l$s+4�%Li�%%�f- 2�Xc � 2-"3/ 3$. �;nd5  )c^A=�1�2b�t'}{$t'=�S!t&�+!w \{t+*t+P'xAbsb7}x�2-�V�m29�I��F !o��f1't q��.�!cy3�m�/.�&^*� X:� r.h�&g!Eb ;\,3"qE >&�Az�N6bp}{:4x.x � !�=䅺}{��&� 8 8:0�  5�  6-���6Z�u�- o#t-. :�i)Ҁ:�P�521�#�;\,0.89fX �uags} \clearpage %FIGURE 7 \begin{quote} \centerline{ \includegraphics[width=16cm]{fig7_1000days.eps}} {\bf Fig.~7:} \small{Empirical probability density functions $P_{\text{data}}(r)$ of the number $r$ of earthquakes in the space-time bins of size $5 \times 5$ km$^2$ and $dt=1000$ days. The continuous line is the fit of this data with formula (\ref{fjjalala}) for the se7�parameters $n=0.96$, $\gamma = 1.1$, $p_\mathcal{S}=0.25$&8delta = 0.15$ a�D\rho=0.0019$ km $\� !�8$ days. } \end{-�N�8�� 8_10V� 8:} ������-( TA9traight A�1�xbest fit with a pure power law J�\ \sim 1/r^{1+\mu}$ over A��10�10_1day.>10Y� E� � b %��'�'j'0�'v'�����B�1Q� psfr� \ 4{P}{$P_k(r)$} (k=1}{$k=1$})k=inf\inftyr}{$rj Hresizebox{16cm}{!}{>*  11I�} {\bf �~11Y�Distribu��s � � 4n by (\ref{53}T 4 =1 Tn=1$, for different nu' (s of genera \k=1;\, 2358I?\ upper curve corresponds��,asymptotic d� $P!f � �4})?ingA$k \to +-i�� le lLonBq the .j!1lby o1!of1 � of afj hock%first= :�& I=^ 12bop}{$p>oU@ W {k=2Ei22�44Ah(662(882(1010�M�2J�2Y�RADs-u 55}) a � of event-�s $r$6� -�Y�M�( $k$, demon� tE:hA nvergence <2}3� v�. Bott� $o top: $k=e4a 6810$�'3b'k!�=�p_A9\&� ;\bs{x})!�M$l}{$x=\ell��-�3J�39� Plote5!|&�i� �V,N�� ��M"61b�0.99$, $�=10 d� 2� posi��M/ mother ea�: $x/D,0;~0.4; ~0.68; ~1.2;~1.4<6$. Recall that $� radiu�`assumed circular domain $�$ "ed on%,origin� two famil!7of�U s seted��!`Dral�!�1$_ explained? 0 textʖ4b��,(N�=0.?>�l=d}{%D=dA�Q�=2020�M�4J�4Z�.6ŠR�!�%Q otal����of .= fall��i)� disk�a���aM� Y� ateI $i�=0N�=I� AzleM�i+J�A�/d������10;\,2һ5�%n#}{$A��-�5J�5����6� d} ��-�UmB�A!C��k-!�� >����\, ��;\, 0.Ÿ�$ $\, ���M�.� thus*� � $n infiniteE�I~= � �6~ZnG�$�S1�S"� l=55�l��7. A�2  p=0.� .�=0.55�  :2� 4:21� 1� � m 6J 6y Compariso� �|n .,��)$, obt�wby cal��  integ��� 60a��4a large enough*� �_ k$ (n $5$ is foun<8be sufficient),�l�factoriz{ $n approxim��p)| " 4}E(here $p = p.U��def�V �fra:o-4*> w�� in3 he6.]@in each panel is ;*> -B51 ��2zr �� y,� a re� cep�~n.� toi�/G(10; ~7.5; ~2.a�� FX� ��=�UZpdocumentkL You point out seveA=�� !�inequality 0 < alpha < 1 must hold � beta=1� ens�=, v=-��seismic rates. I do not fully agree. It� wellBsi� 1�2 iIPDF ^ V lambdaC uq %PDF( ) = L_{�}([ - ,_0(N)]/N^{1/ !) I�NT��_ spac�ox�I�( ��U�nd �h grows%� N}l,ly fast (say�arly), s�atE�0negative tail�r Levy�very smY in*1 yHI�y �VsampleIrj$little cha� to!$it. Altern�ly �somew� 0equivalently,N!�5{could�[ devi��:����)� go� to zero!�(oMs Yo@. Indeed, consid�� !�!0as9�m�> L�sum/!_;sub +A�>�&� + has�Zlaw)�e>expon�Er (!Ois suc�pat it >�&� y%U �s))rg^liz. en� limiE< orem-5i�FLI� @yVW19, )-/c�)�2V�!G same� ��.Ivno�lem 2  be!���than 1:A�`this case, it simply mean �o VIBivi�6|iZ��QalQ�U���>1%�its modeY�+ � �Y�!*�%�!ީ) d. I� Xphysicist language, we ���ge�Xan ultraviolet cut-off:!%�is �p on�Kor�)�s AaAQa&5J� %or n 1;a n up��ggr�� t-�scale2@ (ed vari��8E)!&�!�6np20 m��)� transl�2�!� ing 'N�?b� mpat�\F�.�. Am I � ? �_\�Mdclass[a4paper,12pt]{articl� uZ0ckage[dvips]{� 8x} \title{Propa��& � signa� aaH pers��LoJ�z medium} \author{A.~Ciarkowski\\ \normale�Institute�Funda,al Technolog�Research:>0Polish AcademE�S hces} \date{} \def\o{\omega$ef\w{\tild!t{\thet$b{{\cal B} /g{v r{K os{\o_{s,l{\i� d{� !,ddtolength{\�(height}{4ex�� 1� make%�  ab�ct} Evolq�B�1�di5�)�a��a�� -�p1�ng��e4 excia28by a sine-modul�pulse F� ���al ""$uy, .����2$t<,i.F b�/5�Q2} �=E\{Q28array}{ll} 0 & 6t<0 \\ �\siAI0_ct) & t\ge 0M CM+ �� n arbitr�~�BS :�n"f dir!�o�fincrea�, $z$ (or?a:�Hertz ve�)��be �&" � �ea� ar�ՖX$3} A(z,t)=iL,1}{2\pi}\,\m�&Re}-i,i \int_{i a-�%}^  L} \w{u}(\o-\o_c)\expi�[ Z eq�h}� �[A�  Laplace�OofMc.�!���phase]��e>��QH|Qr4%(�=i\o[AA)-\t]Z�!� dime� les�� bg5�-�c t}{z.� q_)&T4$(z,\,t)$. It�c���"�y�M�ince�� �&�b�6} u_\�(A>����\tanh B t a�i�-Vv�� !jp1\�etae�$$ determin-/� �� � th. ���ntE9jZ!^�7m-\o)= I�1}{�}\b%&(- i\oam�}i)��a hskip.5je�Im}\;\o>1#Y�N! N�$\b� re��psi.$psi$ b�rg;51f�8(x��~�2�$[J � x+ �| -n+6!}{2� &]BxBy�1# e7})��se�)we�%� ulab�9�� �� ��5�� e^{ �>�}~�� 6�dynam�m�_ o [ t ��y ��_�  و� F� � թna=$z�Pu�n���� �is pro�Sec.~2%[  ��!�is� !� stud� pol�.�%�&H "!\$ɶ$H denotF�oEby�c��$e$f}b� .% a>5rPres�for it�.�N&�V54 \newG5$A���!`an:<+�a�f �&.e9a��es+�to��@lo�Pits cri\�3# �8�.� ��)�M"�T$\o$-; �l�� gover�<.}U&s dPnot seem��!olv� exactly�G,*U%a"�!e Q�s w).� B��E�, KelberE SazonovM�ks;96}iA.� N��q���. R�,!ewn&�"Ar5�g#��qac;98}! �h,w?j{ku�="�!.�5892�!� helpA/!�(\emph{Mathel#ca}X uter�cgra�bas�*A�rpo &�a9n�gA@2c"<�,�de���5)al�tou4 i����Ol_8ype+ )$P(\t)$Mol;70}�pa[ thro�$��� E/)4 �sI�a_�1~68u� (�1e�occursG"iQ!Dc�R��� �� , or m�x� �v),cr* d. Fj8series&7 S< &� 6�)$m A~�Z� 10F����-22� o+2i\�}-* o+4 +\cdots) �Z}l foll�""� Mn-=hh*�(sex< )C $\o=� -2im��m=0,1,2, ����e half��( Im $\o\le ��3e�� long�& ine,� llelQ�3 imagin>axi�f� et�big1',FA�{�}�$� of &�,Y he;��5�:�$M �y. If,�k $)'x�#�a� E�MR�ybbex�UrE�q=s�%�� take!�to unt. �$\t_s$#heu� $\t�t-�i@�"o� �4 ! 6 M(u��&o��!%|�p�0v��n,WkCauch�orem,br 11} ��j�\� @laystyle 0, & \t<�(, \\[1.5ex]_ & ` o_c n_U_c)k>in{2ro_c(n_r( �)]} [>[o vl %$Fw$ �d��15 U� ]��9_cW*R6� . U�!i!AE!`Q itud!�ten coef!* �*~;2� lpha)��!�9>Bt�Z�"N on�*f�3} \zetbl-�Bl& m; wri� �sfs4�_:_z\=.US�z�  t�II� ���U6qk�1a�%ol\*� ��Zs"  oscil�q u�'"$i!�de��7���=� ce 1 =p� nt a!�F� $.T��!�2�� 14})&dsis��i�C&���wh !.�l@��5 1ngr Sly �N.� �k.fis fac{ of��)�fce���-�$�� is b�-�5 way "Adomin&x �!���s$. D�  $XF=�;.�� 0n $e^{-(z/c) 2_cz�- neglig�%i�V"./M]� �!|Ѵ!lch)� magn��:ms l. Hence!9zK)t behS'� ��:so �.*K66�eSP� sitM�becomes**.�,R�� ac��%�.D� � ) %�)i35ar� d  %�GsoG [ 0 he branch| 2�"�6�"r U� . To�cn-x.9"Vi%��99 , a "vach�*�o� by�Z will�be used�u3nk %f�an�.if� �a��="#a!(�t)6q�� �'o  angl�� pi/4�23 )i A��� )A.� rd_e-$bb# we�3r\&�new"�*���*$\tau[=f�2Ob� � *�-�Ap2}-\g +\r=\Psi( ��S &� !�quantih�@$ i $\r�hosen�� �=-\%)GJ �!2�5t�5 9*7&: �j� �rA= ��� \h \ k\ }\g ,sqrt{2[ 4��- A]Fs!P-Y!edy�$ Y�?� %�s*�/�!a :�"!��A�n� arguv+E )Hnterval $-\pi<$ Args$\le\pi$. a)s雍v1z!�f39�au+\g=\jA&]�#4Y(!Zh�,��\o$iqa�$:bv2� v\��x |%�_{\o\o�%� $-\os)[1+O(�s)Ft!�steep�(�� pat1&/:�taM� runs� 2y�� �J2[i&� TAAõ�ٔ$i f.um�~�CAϱ�G_0u�}e�}��.���tau�^�f�2} .i� tau�(�Id/d>&A9$�e3!:q� un�3]� . We now�BG_�=i%v\3:�a_0+a_1�+%9+\g)H=EB� ͖.$� a re(%Y� au$. S + l�5�H!� t�:��Q���+� *R s $a!%a_|@�$24} a_0=!�0a�.1\N�3 }a_1-�,- -\g8 }{\gF, By L'Hosp�*'s rulejK lim_E�I�arrow 0}�e�_cM�}=z/]{}, %= mP \g}{��e} �j�f6IO%:=1B@ Furt[+o�)- M� 20})fV 7} %R� -��aUA�}}�%\os%� %b� RW W.2Y�R�V9 thusf�28)9M== .�osf \; �zBv�manneN)^fq9i12/2� Y��g}+���f��Qi�ser� U1=a�+�(�4 cano�.l $�=s (�!*)� exi�1�&{ѫs/� � _��1b?30*j 5Zi Ɋrx  W_{-1}(I_\l}\g)-Za_!iEw\l}}W��\g)�%]+Rl���1^�f� 31} _z)�$ �eiz5 }fU �zd$j%-iz}^k% � Is Id�&A �����"7, $R_�is�� 32} 9 =\l^!b ��j} G_1��!5�l6 � tauF�ithf�[Y=C �dH_0}N�arrivAratQ� 32})LM�aA��9i"t e1by� qndyec4�� K -:]2�!�q  $)�"�yN{erm+~ � x erro&�H� erfc}A42/Q� pi})%�z.=A7dBP#>29a�nd541N530)C%^e!\�y�" symNr2�59�nfY'3Z'7& eqn{ 4V} �)&h�&{-2pt}&�5\{a\l� ,iS$; .%0 (i\gm�e�\l)}$�A� \gmi}{ 8aЁD�((��_.�(��) 6V��x) �n] \},\non�O� -5�0@-ai.�9e�9,�viUo�;&M& a .,s&b.� �.iA�5� ulaW �J%any $ �pe=iG3i�g � 8�A�;+Q�e�=enthe�(blow up, bu3ir?��si�DC�� |\g|B F<� 67ad(�34�Pan �,�PD���]ѵC (�.\%9j� 3� }�iy)=\y)-e^{y^"9'Et; �8pi}y} +O(y^{-3}͔Zo*yau�ya6* ta(wi4,i�.-  �$Arg}(y)<0,us1"2=0 � or} 4240:S\pi�� �m ��!tA�9���4�AO*�%fD:�.@&S2�sfT 37&���)R"-�}�@���\%���* 0 �$�6�[os)�V(i?\J�a^E[%�\g)> 2>a�GD1D!|!S% �Sadd�P�v�>� z�.& <ap%#q�u�<�%�Y�U}Q5=&5 N,  1�>0 ["��. OF%It��%E al^ �G�= *mG�w} 11})!�ni�&l h�4q ���)"j� &|)f�&8>y� A��ia'�4,M�#�r�>.6�7})6�3. W"��6 !�l��I �2RE_.�>Gis #id edM&�a[wi�k.7�I ]<1�U�S<2K \par�.9;}{a1 it{ReaA "1.�Q�"L�S(�J5�+6� ����e1r�ޑ�^֑4����]�M�3.� %�E:�.3I x =5 &14��A� �F�RD �2&%.� �:&.� virt03�10<}�0shbe multi�5�-or $-2��� $7re�AI5� �cF�7<2� 4h s�MP � !��<thJ�F0ht�&# *"-Co�:�sr;� pI�yG^�Em|M�p2Qo� jS�co�+$ V9N&Jtur��Ta ./� J� � rapidly.�0� ts&�Ai< &�A a &�Q F�Q��&0>�� ) splkK thre� m�:.3P�B2 �8 ors,�!��� %��:�|(�*�U&�-&�6\&�b&�]�er::!9readi!`�;�..J� �6w=Atru� ��N; "�K-&|K�+�oK�+�![oKL6�!' "vK nFu�I.vK�7�V�,�  �z~ �l:�.,",ZS !�=�:�%J4 s/)sed�il>jSdIjS�DiZEjI@��'�Z �d"g5fB�_4prl,twocolumn, pacs,p] int &s,amscnTsymb,floatfix]{revtex4�-i`ZG�Y*P`{graphiI`\ % VARIABLE DEFINITIONS v_ ExB{��E}s "u_tAr._{\rm AKdef\vA{v: SA{S:RA{Re:tHpQHpRHpSShpURhpW � rs{r lsTrsa1b2c3minminaxaxqc{W tt{q0r!>exr5=mua+mu,mub�qffCr1Cr1�shear{s)r5drab{D_{) drbc25dra1)i(flPsi{\wide�a{IN� flPh:hVor.:u7Cu2jeqn�J�E2meqmleqlkeqkjhips� rm h�h0j)=E ��F3 j:laplR�21}{r}\,ial_r r } %xbat�X��8���2{f s/0412046�b {Non!5 ar E�V�5�U $q=1$ Tri�iTeaR Mod: 8a Tokamak Plasmr aDd AndUL~Bierwage$^{1}$\foot�M {e-mail:b @��.iae.kyoto-u.ac.jp}, Satoshi~Hamaguchi$^{2}FLh 4@ppl.eng.osakaIt; n�%m.ion�aYR&�$m�8T. Tmay?unt� � sudd� �KYh(zs�n kinkm&�$fast sawto>($trigger. Ba� subb% r�%n�HcyyS!f*proce�bl_J E'a�O �islan�b�!� osed!�t 5^RTs(ks�pmeoismk "N -fA��� collap�dua� �osc�Fion)4Y� \h H{52.55.Fa, 52.35.-g 55.Tna+�@�� \�'�$style{emptaN� prof}Fw 2  $q(r)$ (�mea�q�I�ic figf�W pitch4�nQ�69hab!x!k0 a5� 6�\HY�$i�Xp�{S toriMor hefl systemmnres�Ja?cur� -drive�+2� (MHD�Va\il�@�%�c{� ��� �#<�L,mixing1X ��id�$esa�]wa�&@gmJ=% /-hough��l"eI�(beRdisrupE9, g�f%I�n^-Rc8+8 strongly affec�)e q�sof�f)lDn�@0!7 o,!0 desi�eapp!��!�� monum f���|A$ch as ITER!Hde�r�ederstan`"I�s{Yrl�F-H]e 9?�&is ne (ary. A heun_��lae�0KadomtseXT75} sucH-�}s�all*ugassoci�6�naE-��crash!0;���aurb)+:E�u$h=m/$� (���6!f�]!�$n�Dm% Four�dc�z), i�b:a/bqSEad y��jE�Q�, �`�>ho�+r$*A�M� 7 m+�j�D2�mhjrelax%R�Ὥ�Q6T��o *short�d 9!)U$ U$"�j)txh� f �+tm/!@��� ``Ųѩ'' HogU,�,E�yI7 uZ�����X�� is ZWyeti� . An�  unrefWe�{d�!|p�y��qoa�!G y��m��G69�-uf]9f!�!Z2Vir�+�t4uso)2Ynnu(off-[-)2, ua�g7X��Hastie,W D��&�"�b:z ��je��cv# Y)2>, Q�!B�L��� te�k arilP]0Aydemir89}. W�%��3izLBt �e"O�~�_�d ($q_0 > 1�N*� � �,y%Dm@� 6� (DTMs)!L"( )bTWhite77, Parail80, Pfe�~85PWe� ,�iK� �3peaked c�C:� < 1$rS��A�::�T� may %]-�{*;2lYl,x &;���� kM�p�l >fA9R�!�� tiv4��ed=_:&� 2}!_J �. U�+"�* sig9���[�+��atVC�!!�=1$Ef6�, r2 L!ing&� .�%�� Mk.N� �!2r te e:y�~ul� %4h5i��/��r�Ob+IqW qW6� s�_�^"%�.C!�:i��2 as�{as� � -.T ��H66T Z!%?�# ccou�� �ZE @ � �5� u�' re�r��2z  (R{ ;1qL3-�$�ya cylind�r, geometry. %i� Strauss76+#�u�y %Yj��l��T.�T�<\pQo al_t� &=&6=#b,9V6 - ,cT*bShp�0�6(\hat{\�uj - E_0 ?) 7q:rmhd�b\} u{u2x+ �j,� O] +=� j)nu\ "$a_\perp^2 �@�j y2�'e5 &�� h�4%O)��ilux"�T'phi� K eam (mjs�Pc potenᡡEj �D2� oe�x���denf�� u = >7 � voTxjeb`�n���L��N ar:6�o#=8f., e.g., Ref.~Ib NishikawaT}).!�U$t%]ym?"� Alfvn%$�$ (,%� A�&2ci�mj4�%�|F 5�rad%oordin�� yminorLsus $a$�M!M A umO$/ d  *dC $Y�L(r) = j(r=0,t=0)/j(r uU�' Lundquist�v!$a = \ta8 R}/% [Q^ R}*mu_0/(a3_0 a^2l7��&2=0}(A� = N0-116-m=n$)_ iklq�x ng wall wAs�] �U���D�.܁ houg4'�k en% a�a�:�X!1I� al el� vol� $C�� .  (�� Refs��XWangBhatt95,Porcelli96,"[ )Y �5es�j���:kr��f.��sy��of~ �M�}e} [tbp]y��IBQ1b|=6.0cm,�2=8 ]% aE� �d: 1.333 {1_equlib_3tm_mono�2% \ca�{A:����ua�to� V7rMw� s (dasheddic�I!�l�fE�6�  n.rs�\rsb <cb8� �Qi Zd��# riz)$l (dotted)���� fig:���1e�u�u2_!� -etabwLi�)q ?j; ctraA'AQm� -� U7inD5\protect�D:�?�UK)>����,74�89 c��P(Prandt� $Pr�eShp\n�� �9v.��x�x3)x dr_2Z�vw P? $q$ -s1>I�� U�I���9ce $D $ a��,"�*5w1�� !�$��ee �s ,R = 0.05�i.�Qa)0.�/�ively6 %�)�� \����4_m-_m1-13R�R�]'�}_^a!l&�a eigenwe (a)�^"O�q$ , (b3$� 6 c)�F?hi��(dbChi$&M>E6aa"�1�Fo!i�$_v�E� �|�: Ud� � r_{{K s}i�^�l�$M_i(mJ ��T����AX� i6%.�B&�yft jZfe�of R;� ar} &A�R�s add�2ed�-��i�o����~����N a �broad�Qum} of�"a2PEG$. Moreover�H�W !�% often�_�F� $m��{\�%�O}(10!�Toe��k c�]n� :~R�is �<&��^�P�,� AlAH{[Bl . By�v��)�6 � "f%r; ,-Zū .%0th��s (�C�m.�3B�)rZ��" lin}A�:�ma&�bi�a4�lE�F1���p�� ��L  WSha��k,��2�7bA�e 6� 2�$�H<kwD��i unity. ClEj, a�[�a(� ��K1$4 �!�E�nA���tru36<2& = � Max}\{Ն2Z\�/٣tA�H)l�sest*(0e�� �25_E-g6 "� 2U$A���TTM�Z!.7�J� P &� kin�!�8u�iQ�.WE)Ik}�8 m���Y�(a�6$=� k6�K���X�maP�> $ wA <iK6Rax} \e��!lmaximum.�!\!uU~bl"2zI� ���;e�� &&s�Oi+3e�y1�as ``aR� ,'' �l $t > 200:� MsB�Nx ��7.5"x  Jx (0 {6a_snapsE�200&�bP N,�  ZZbZ36ZyMUp5An,9halT�oa psi$ (topgB $ (b��!A5�֩�!���Sm-(Gz"">�a�&MM$q$-v� 3YZ7�!(b)6�)EZB��de>�-A��.2�f���  betw(/��O��most �}wCva�gaa��on��DTMB�5 W"� `a��"�Oa�d�� $a��& /bKrsa$ l D 6N!� �����-6a�k1�� � x�Nv ��� ile ��J :�Llo �qG,s�!z5�(, $s_1 = s(��D�8s_2 b)$,1�.%g~;�=Ovee�Ma^ e � �l�- rc q � m�Q� �/�R) shifOoS"r�M*��2ax�n�l. O�e�� h�E� .��"� hard��eq!1~e�it �%R�� ���FFN R�`�>�Ekrf�E�� by��+wat� i�� (A 'eF � ��anA�x�5?�ijqJA�CE� inj��>�  ٭!�6$a�trfa�'!!AA�:� STM) #*=�\o�lv!�mf ��#� usuaR��� mble. N�zM�+ �Ae*!�X 5o�<ed ��a1=n�=2�)4��Dahlburg� Karped�95t �r(sheets (TCS� slab ���0�_�!\adjoiHthelmeteam�*sx� corona t"#Aem�� �!_d&} Ϩ��A*f 6A4l?]|%FF ost "!���$m? �#��I��$m$a�re%�up)�� V� "s, ]&� ?(d6��B&==k"m�S�(tru[ !�2IM�A�A�3��mF=72)a��~2jA6m$�F m�K A!��I�%�EqsV C"2A�E�1=$ A�e9>e�dV�amE-}�6#M~~i�a%��*"��a$.�$M_1(1)�su�A �)wE�n STM�@lbOM_2�%zM_3 �K):K�at �A9 9\r52�B ߍ��I�)�,��tE�n)��&le�Lc&[ex+#dz)�+"9&STMB�. S�-E�a�)>:~� Ysed#i&.R>�+����o~,$:���a�_ar� >� AX2A�ՠ&u���&omYjanm�!n}h2�F]� .$� �U�"u��F E [,a5 ���"` �,�� are_�+g�'A� �-ed�7�Qp�]iša��xp(.�g}��"�F�S� *� ) �N0.1�� �!c }I�+�eia�e ;PY-�s1a�mM� � C.� }(m=1�6�8 �3[5J.F .F ���e%1- s twT�6oK��3��� (J� �_9H D � 8$,� aF$�0�TH_�couplA�m�Gm+Q� paira e =5s�'�j�Vng�Flu�>�X��!��&.e�1�����ڐe��B�A $r=��%�itWAJh��N < s_3$ ([ 0.35�U -0.5A{$s_3 U�0�� � � ŵa� �dU>b�u�� �AY$4a� =U�n-=13H,��i� :J _/ st2Eam�~ll��%R6oE'�~s typice�6��.62�@� ���!"�+YU>ca�Av�O� stil3�R3s'\2�͵ cm�4 E�(l*$J� &W+a O:��1$:�,0Ishii02}. Fi�X!�>regim�96�E�}� iU . At�4$t=v>+�Kb+sta[hto dev<��@� whol��teJ�� a���eZ�%r.2�, �he\i"��&E��/j*��B�E  �Q.46��e̳�3� �R"�0E�A?9:qBW3ti  Bit5a�er�M?4purd �0A��ursor''� I 03}.&]A�ѕr�A���`J @3w"II >eps�1�>H�23} �r�(��*L3F�0� ���� )R�.ѽ5�5� P1�-.0]�Y;%'amp&Z ���&�7os&t;E� Q%��dis�ge���.�-�`Taylor86,Campbell86,Kim86�� da88}O�i��D�n� �Kogy%� ]$�us�!above՜Y"�'at=xAh%2:xlea��8h�1��<�ws/![ M� � W�� (Y.du�8� AA�e3 r d) LfE5�>�� 9� a^h^�)�F�(c-.n��inu�o�$U"8�J �� mad���,& ��4 (A)-(CP*f/�n5mmar���e2.~,h�Na�}  � i�/of&�)�e}%y%�a��s"^?*�,�a�sQ+��4"L AM ,? .H 1IR��&icv(��t�?� ofy����N4�R�5����! x\K� Ib-�k,&�5!")a� . If>rb>(��� �&�8�*E�A�m�!�� iF?71aX��a!&�� �sL�Ef�'se� $a scenario!z�jthe=�2�6mpun?I ���;� �*�5AJ��<���v] ��� % �;�5٭���&2�in & �~uQ,����.B. woLi̢�ank Y. K3moto,Nakamurae0M. YagiA,�!��N�A SYa"^T�VheJ�E 68FRaeqN hK{�$wC!U� �ly0&�21st CenP� COE PrETm��F "�Ey. %=��!>CM{���od� L\ifx\csname natexlab�- \�7\def\$#1{#1}\fi ZG bibO font>J B�f�O#�Pf.jQ$�R� ~R.$�Rurl^�url#1"L#1}n=$ urlprefix>O%�{URL I�ecommand{!\$info}[2]{#F7>!eprint []{S'�DbX? em[{2�&mA}(OQ}]�A8 nfo{�J��i9�{B.~B.}~&1t@}},AzBjou1C$}{Sov. J. �J�V}� bf�${volume}{1:HWE}{389} (^yF+{�}dPvJ��2�98� 98��i%\Z� R.~J>� =:��AsN��W��Sƴ �XiI f�256}}, �!9 �177N�98r�P? et~(1989)6 #, Wile�),nd Ross}}]89�# A.~Y># \:$VM J.~C>@�1Uc and}!Bv�D�U:� �V�P%��V Bƒ774N�89r�.@=�77:�!�U� ello�R� blutb� nd W�`ll!�077��RJ�<��D�U:]M��C M.~N>C�C2�yVE���2{V>d5,!IA� !�xbookt��}��ting� CCon@�'��x�and! trol�NrGFrGaT��5Z\gad#�Ger ,�V6}.Fp�W}{Wral Ato���Agency�y?0}{Vienna.S�.7 vol.�ąo�x! p.Q��569� hJc�B% Perorze�_80�r 8��v�V.~B� =}I2�GNP����ƺ���.�-3 �F�80rP5D��5%< 8*{v>W>�<^�A�.M�j�25:A �673.�Qa8v�N� kaw� "�>+XE- Iw�VK>�C�6M>P�I16<�8 lasm�ics^�S� gerA1Be^UF�200v%�;elB�;a&je�E3 9�4XF�ng�7A>K��)sn�:AM�171N�9v�t��96:�$, Bouch)�and���{'9K~�V�F>!<:�V>D>> ��* ��ex9�Y�.���B�texR� 38�Q-�216RC96r&N)%�h)�1I���N ?� J.~T>� �ZJ. Geo4 Res.j100:F1G34V z�uH^6' !, Azumiq& &�A�!0�v�B% 9:�V�B��QN�B�"r:�Y�" Rev.�tn�89:E1�05002F�!qr�eN&�A�86{"� {a}}#"��*A& &- ?:� >|Z��57:E110F1986}:�|7V��.�3:� #�z$GiovannozzI� TuJE� '0��mfwP>� ;:�V�E>=�A2�&� VSO>S���Y���4 Q-�LJ� 2003��bI�Z��G-Y� ;)=5O��� Z 33J>��j�>��.c)!&��#D&�9&@�(�( 1085��j)Kim)��� SJG.� u.E  �. AB123� Nv�N��Bd�~ SB ;���63�F06V%��F>��m&�a�% * SF&gB9(apssamp.tex ! % % �#�#ar3�APS3REVTeX 4o"َ.EVe�?4.0r *, Aug�� 2001 n CopyA�(c)�.Apni�7Socie  �Sex&e Z 4 README��re�-an�.hƔh]{j�h���hL % So�)t8(�#�/ ny) W%�2ies %:��d,a Ɇ� aps,draft�FT�%Y�(Review B \&��&6i% I�, ^AE�s2,d j$}% Align t  �0 decimal��2;$bm}% bold |D %\nf=s"�J1�}!W&�e(APS/123-QEDX�8$stleron Ga�,M&EQ�&s}%�'c`b�� \\ "&�Salvata�De�ctino} *ail{dem$,no@sa.infn.i�fMariaros$ Falanga}%>rosfalV; Step�3 I. Tzenovut67�*�e % Di�7-o di Fi��0 "E.R. Caiani�",&,ed\'a degli Studi di Salerno��,INFN SezioneR(Napoli \\Gr�s Cega o 9, Via S"Ol=p�, I-84081 Baronissi (SA), Italy}%�.�d�u lwayL)eÄday: % �(�!ByYF=�(ici <�%ifu��a"��Wi%s��-s=" d"Qcof5%E\ ��A\�Z&�S~#�/oSpbeam- JB^�"�/�"F#�1�/ weak�/lli�Fal,��p��of "@��r�)'T�&hQ&�/Hz�+e �Bof hyd&�e��_�3�..b#ppl-& reBS&�#up ����;1CalP� slowlygFu?am�yud�$>p�r�O�P � :&6B"�2s x�k� w�e-��#cP4e*�1�hr\"{o}uer�(� sens�2V`Ir%$$�"�]ga�"I&ng qua�S�V�w�@%�f#)cYB��eal!L>�heral�Qrelevan[v�)�&�dI . An & .f&%KY�0�pAID° �i��A��By�S"{ denssV�q�!XAh�5 :�2AKthe i�S;Th2r%sta� �0�W}Z.���(���5��U$'˪aD^)�Q�, s��1Ɵs 63��1�&EO� �&v' de�8Kp<\�&l�A�I�C$ng peculiaq�!':|.�q�� "g 25.Xz, 53gHrg35.Sb��ACS�C&!nomy �RF% Classrel�0� <({Weibel,Neu�$,Bell,Suda��e��a }�@5ga�5 u�d�Z�J�7ir��g,ur. C(d�2xurtele}� ]�:�5.-DAvb%��8B6om*��**�9AM��zs.c S,SfH!^BernsY�-kxe-Krusk�W BGK)%�s 9 BGK}H ;GK%w�r�i< � & !� %q�E�c��6���58"�6) ic� :)�63.M AZ�A,��na�A+�i�g��5�qQ�)Mm?F�it�i$by Taniuti�Washimi-D �1o ed��k  ScVr I �b `eF3Re$I�Shukla�Z�tpabL^ i�.a"���AY��gQ�)  �6A.6")Z adopO�� ~ V> (RG)6 �Oono, �Iً�]!�� a�?ac<C/i�f%6s a/ venI%��ightfor�6 t�st1��7d��e .� Mz�{;"�86�0 f-organi X orz � _��Salex� s. Co!-�D�_; @N@"Z oj:tMp"u�s%�v/& �/or st_dFcP� �a�O�1l�� `ErHA�12�/�=)�RG1�� �f���Uwerfu�oaUc�q$dure to se��t�� U *A �Ľ%'��of#�! de˴1�Q ~��Bbn' "�1t�Ga.MV1i;2� �&n��by$:q3�QI�M�1�‰�cJc�7_ i� tj Tvector OA OX scalar $\varphi$ potena�(s according�2!���-knownMon^Rbfaaq) a}�1Mi)A}=U, t}}, \qquad B�&Kqhbf A}5dElmag��^f�Dsatisf��wav��R` \Box �A�T- \mu_0 e \sum \limits�D�+ +a�� B1!QPe� epsilon_0��RS�%Wav�vecB�Ahe Loa�z gaugeR�~1} {c^2%y:� ����.� ��%���5�LorzB� %% H��!P$�� otes>X,d'Alembert o�K0or. In what fɖ , we�3��A��4a quasineutral�zB�\Ri�ՊQKN��n��d�v:maloa?$he $x$-axim� �=�, B_0,�0�)}$� n,��s���!)--��5u4) possess a std ary solu�OR ��= n_{a0!˥conste�u�A�- a !3M6&UStatsolNC�� frequency!�!(wa�(will be tak�$much highe!�a�4 ion-cyclotronJ%9� A* an f�� negj jion mo!  � e2� �U$ variables^Hn_e%I��q� N�.E$� $L A} \A7 arrow:0A01q b0-�U� ScalR�a��a� l� N1�u�a��u�Nn� �M?F�� "� �A.� } {m���+JN � )}��� (N \nonumberJ� N�&� ��m�!-*R ���!P �8��B=a �]a#Q "Y �f�� X����� � 6� r)!�E, "��V�h1�]p��X" N�B���O e&} renoa�6� redu�q�&�y��mY�Հ�)mr next�, let u�9� th�actuaI pend�@~quantitn$N� %�V} � *�  spa� ��is re&�ex�R�8{\widehat{\Psi}a�BQ�x}, X}; tu,�ڭ�JQI�N :VCAAD� I�)II�A%4depN����X�6 x}�� slow1+��. T�~only >+p����ourL posal is ��� $t$� ch� proh xtremez�3��d� ify tedioA)lgebraMM ��l����R:G�R: M�o.( .�F� 9 he� ndard!cedurQ�B`j method,a�U�� 6@$� a perturb�  expan��2 4{n=0}^{\infty}U:^nB _n"QP �exR��~aFG&n��e �3tep istsA��!M"P.~*� ��>/ })-��F�>� �,[d-�ir na�.|"c order by . Not��3 ll � 2B�acquir6e gene� ��_n��6� �����T0V}_n = \alpha=ֵ�nNeN�BH ��`>�.uv_T^2} {�U_n*&&'S\omega_�bfe ",bf e}_xtW.�" ��. !+"!P�mU m���� ��N�) 6h �bet.�U�R��1��? A ��.[!2U��� at h� be� lready d m fromyv�� es. �R1%�!' &� *�5�) 'e+� }}:PіsN���9�al ."n[&&X "�, .��)BEp��( 1>� ii� unit��dir. Manip ng#an ob%Q (e*$>� nJ� n}), it ib�o�� a single�y�d � A}_n�� 5!�� R�\#)��z^2i"L2s- I;� Q I�.�D"  �?V}42x� ���' �� �p^2bG2 5 )+Q�p^2�v"V >�6z)xa�>�6,��2.%��-ީӑ�9� 6�.��R�V�/2bJ�Rq�"��OallorRG�QVI�!́ )fe^2�+!Y"� ��� ��dN��9���.�&^��>� $v_T* byy� P�?)> alEuly� ressA>zF v_TA�- r_D" r_D^.= � e^2 "n T�veRN%� $r_D� !580Debye radius."\" 2�)&t ��z��point�# the > � &F�1e f� goal�l!�o� aDp��]ly� Qs lea o  � 5p ��co+nt struc�s. L�proceed� A �b !&�d*�n� fastB4� x��q�x, y, zu�!� throug� itud% (Wlle$%��6M �n:$)�:co�atl�&� toNzero-� Vo m:6* "R�B A}_0A�s*{ka� ^{(0"cal0 0rm e}^{i \psiY�Zer�eraNE�R�J9�; t5� = k x�i��tu^ PhasR${�!�m &�"etA�7ant #lex ampl!�e�l !�subjec::T E�0. U  "m" mea!� HuA39r$ do notM�2R�A`� W8�0, however, itE%i)M.Y*�I�X� summ�sig.$����=�)� m>ou@p�" �##O overe�G� $k$1B)E>�takes�$crete valu!� or integr�b-}J�F. F� !pdisperx�V$!�DY�k; A��aKI�k�V [ B(� _k &S $.� U ^2 -mcp Box` !]v��D��Ni�!#�0%q���$ �{k}��-ed !S.�=9�F+!]4Fourier-image = _k$ �,J/E�.���R�% !�&��*� - k^2"�Da�N! MoreA�u% be verifi�%�ra�# forw� q�TZ:� ��MFW^���{k ;�AW(!�1, -i�sgn} (k)M)�IC�N�iQ$:C�#!�*5!a� -funi. Detail & ncer_"�"o��C}alaw�#D]��$E�7� �)Q foun7(�#Apvix.�jCi�� * &* �(M�solvabilr$condi� �Appsol}). I�impor�5(to emphasiz� NFQ�-k!�u�k"Z ٩ # AM;\a�)�I}� f�!�asterisk"� �)lex�jug%�/O re��A<or&_#�J� -)2!z�l� y k&�F�%�qV�'�ed jly�� firs�=� ua@Q:� n��R V-�� F�6�] ��� �#/ �1�q��5XvN�In adI�� =b^',( a2�nd"� + u"�NtVN Niequiv��- N�� -v �$��9:e -��>~ S5'fUR�Ft = -k �.� ~�+��K"0rm , ik��F�bN� I�s�menA��+q�E� $ "source t�"� }!Ve(�_i&*)q(ed vi�$a�� 2?'-A^ � a�� wedR\D1!SA�.�N�.� S$\eF�$ta ;*�J7� UF�ordalR�N�EU} l"��wU{0u�WB�2�i.�aB�uN髁�shortF* ��V�B�*( eA� �X}&�1FdefN�hQ�&V#.���<��!$�^ ing $AMM�Lo(foA�`!�non)ſon'�&BZw� a�Zbf�%V:X k,l}{k%- A}_k ��!9rm��{� �k�!l�&� ��lR[%�R�mM�.�i} {2��m"�"( kq l + l5 �� �[ 1� ��.�lY ]}.�kQ�N"YVw!�,now two type�+�'P%e ��Fsel%r" l�2l� A*�"�KMgapproxi�. At(rul@1�'st power?:�*Q = �t�� *�,�tKwe��t��eqR"� cor�� ng�k��&.H��&�� e se� 9+of]�LV�ariR��%no�3Pra�  betwD� s�%Y �,I!0regular. Omita� !bu�-(!- �!�; e�!3resulVJ �j�1J J� ��bi-� 1�T I�:K:[,l} Ae|^{N�6�{�*b�� "�qTvpRf�b>���4&A%x �, tB y-i  31T6)D 2@0�J�-%% Som"U"dVA�A._)� M'�A�&IeLlic�rm��j-m�,T͐�-f�58 p1)�"!2os�":matrix $. given��X jr0�)Y1�6���@Ehgamma_k�̥�E�2WFEbfm �b�B�akxN�v� �QW2�Y�FE��20k�� .�"�c \chi_k�^Qwak��5.�%� � 2m� ����l} � �� D�{lx*.���� %��B: aklR��9-{ = 2kq!s�;[.2�1�c�]�Bp{XFEa��F1l�1�)-(�U�[&$ - (k+l)^2B�c"��� -�]'�� :$} �x Ilp+_}&0Q��RTB� + nts @#k5#�A �B*$i? $ en-�1�� ab)��R�� �^%�a1�m&"�p9�"|, ��V5�,�fo���=��} =� ��1} 1�,� �y�.)�2U��"< �RFu*�8�Ff � 4&$�-��j� ��8 V��.��/���8 V_� .N�8 8 Uu$nbR��z��6�N8 "�,@ ��,6 ]6)@B4 "#�v^��4:" s6���$ coefficie� M$r+/ lyF.9MHif%9�� �1%2I�i��.�=/:uP2&!�OA@C.R .�UCA<veVv� �1����6}��[6/��9� �F+ 2��L2 �9k} "�81YB?�"� X�u)}a%*>29R C�4��.a2 $N_1$�@�*g+)� h,RZN_!:=>L A�NFk�Fl ��6��NE!Ja��0� b� �&>��nq�deRXvQ6�:�%M�U�I+.�Iq3 - AR1CUkM *y1�c�%2N���!Ek � 2�e{ &� u?B{ *�.{>Uz3R� Analogous�?�B.�492 H>_1�{ndR��8:��5�3F�zD:Sr K^�-|b�o!�B�>Psc�/n�Y1? *"'EkE!@^�= "� { mbGb�(B2 scp�J�� �!d }�q�����u$M�(r %.kb�J�V$"nG>` 6�&���o b^K *D�� (2�nB�1AN���F�!�I\�U*�]l�c�6Q�B���� 36&� V�!���iN�vh:m�ML ( t FC�-��&k"� �V� A AH�HesfeiE"��i��6�(�� wy.b�+� e&is �*. �~allkG *�(0$ vanishes�* m&�'no+�inF>@IDwhistler eigenmode��oB2*_ ќ�F�1�F� QV}![see � *�ordB e#\#�)]�"ly�ribjA� �2�%�E52�0#>)sh�EG&h�# mainv6�s�h �L!�Y.IZ�,1 ERd�JABitRB!� beha�2rA�1� !���9��9� V�9�9>Las��&!��-stS'of�:>��-&�*� a3�&i�MA��U.�<�U}_2$=+'2:jg $ Vg �r�&����1 �>��)b�>h N_1��"S6orVV{-�A� �|>�"#1"� H8&?�x�(*M$1� �#>�3,;42p �wNm Sinc�?��te���/a=m�2�{E\ , appeari6A�J� $y��$z$&��  1"��"�I� AA�, con���''# :�/Ad xE�WA*�0 s�E�o�7suK��F'���R��0.�>�EajD �V0�.�!�(k^{(2)} + tE�U}bf C}}6v �/ � " {� �<5+ t>� �.�D� �C�>L0 JQ�({\mathbf \GB u!|W�!��|�j�k&�uZ}An�.�)remark inI�U@ thiso3&e. RW*�.W*�.(J��A�Ihx&0A� �k$ mu�2*L0Poisson"Z�5��$�5��&�C5 scoR��l�3%)spH�(al�triI s�!�0?CC��e���!sB(transverse Bp�Ct"B s $Ym�Z$. S:�-� �y�R (se�#e"^,e��)z@a�{D a�{ ���*� � "1*�k)�&�"�  iL*k �1)����<1�Ga�F 5٪-٪a�2�/i4�6�} C ��51*:�-!�z9� t5 U�YJu<�5d�If�z!* E!�%F� 2*P5�cV�f�-I*�Q�%a 1�4U�&�"� {3c !aca;2�"��V$VG 6�=m6e-�:� HP"r�^2"��>N ���!.L $ɀ�y�5e'i"1"� 6X JW-. ?�H� A ����9adsB "�V�.�2�x ��._l��! �:&�i��(��.��� #mpl ������" 2UH�C( l�-���A�l���5:1*-)5�gamNj�yG0\cite{Tzenov}� w RG mtG wely �! desi^ZRGY]V�)�* ,a�tilde}e�"t� ���2���NJ»=k� )�RE�.@wK:�1� =>�*Om7.glx i���x jH !E� 6"� �4R�eRH?��(+$ �h F"�5&� e]Y]*�:6@. &0K28"h4� �G� e6^�Pb���.R�  �&>�%Q +F� .�O�NaR]i�I"c 3�+ � ,  RJmdI�>V8!m9�.*�Z�>b"B�""\-EciB� �%�s~�Ey6�d=F�b�2is( "C7�8 5B�t @ins unchanged ($N�R$)��@-�;!�)�oRVc^ s,mU�Aevo`V,�J8*� e B9�A's�A�A� Es9-}S"\LC�aN"�-:�a"�/�`�s�=�a1valid9mR�>�%�Ma!SQ8m(B5�� eRb� R�>*� &BAs. Sej."�L = 1;>S p�k)�2m��z�&�M�g3/ :M_V�:� "v �D�[FZ+ i \nue�r&S6�Cx}}Mlambd� � z�D� �2��4x� +� "�7lX2��� >:� k"VM�nV�A���mE��-�\��-w< �.Ted&�AI2�K dropped. &�=72%$%U $, $5'� ���-T*� 2�@+2 ��, �)*2C&�%nRK6N 5�� �p "1 .�J,��� 2� \{U�4� k � &�A. :~G]� 5� V��t ]}e]�->*31\V�lR�+R�muE�=��� 06�H� �f� !� -M( �0R�#��*��� �� �� }umRuIB�Ny enough�:R2�t�z��.� ��"M�6sor�s�C �6(s. Clearly,j1�@@Dp;��, �@~^W1N^ a^-%Y�L d:for} }_"�l) = 1"R S�2N�T}m&�a�Tic�GZa� *�D� not %q %it�h, nei�L#�.#ano. Z� E7 ame ��6;is! a'!Hp :��fac�^ "\ �Z �7��+4ku9�36�� m`�atnHzG=� nZv6i"r[ �U�j; B� � ks�Gmum:)qd&e . WitKHlos#geVity�� p �9{c� �"e !�!OaN"bit7 !=�u� O �c�*!P posiUN< ($k > 0$). Supp6� )BG �:9 [wBka G' Q-�HANhGist a32(-l$@M[c�L%#:( �' , -l�Jmax!U. NEb1�Wvms�9!�! s��#s1Y f�� BA 5 %al5+� 5*_RV � �b� ['b� mu��� �.� B"�&� kNpN�n 7+R �D^ 256 7 V^�69y+���+: ��9 lJ f�PR)y^'� {^3s!JsE�'* : $Fv�l -��/� )vT*I .'78 �h>h" � �1h�(k-�, l �]&I2ZR~N�!g2�{ aDeZ{"�- *�z{l�  �� l�C��c2� "� aA��1K� �{-{Ru�E����>.e.�'l�bs� E)gr�g in ���Manakov}n'. .� 6T�Mahinv�)J"�&="�S�"������K��q���sz�sDi^t } W�`ud�M��J�ofr�Jsl% �% z�s�@D% ��t�NB�s �*�refer \ "?u+hperHU" ??^Q�]� ~r` . We appl}& �ja7MalY���ly�!y� &�R�61�C�A!�2� ��O:D�L* 46e&�+ !#a ��v&� . j@�# sens1D�s!m-P�  a ga�a�� � �m cl�Rir�V>� �,� �,s=�&, ^A�� %�� ng p�Eiar)D:u g�F Y "� . A*�RHse� � 0 _C� �+�VbOO�G�a�%,. Careful in�toneZ�E3 5�J)� �FuU OV%F1X)E>e*�/ 2��.�T�&/I )]. ��! �,y�C�+�s|)�'�uto?��X"HCl}$���>�ed>�MM-ya'hid��h�Y�ir"� r�p�nt doe���&z02]�VFUI �t$l$dM dif�t[��believ�&-��Os��^*m�T ca � claZ"xa��{,' ranga N$laboratory�eri!1�nobser�v�b of a��et-q effects r��to spac�-b�yacvN ledg[}OE�pleas�h�(ank B. Baiz �~ manyI�m��usA��TcE|~.�T:�YtF�Y.+nB� \�,ndix ��~�� app:mxec}�U C6�UDe~xo�\)P.3JEri } U�A�����Wu��npropag�\par.�\ Z�Mmwv.$ (.�)�" 2O]Sd&�!���.�ZN)i�=E :k00 2^+9N�Gnx}$ de�MI�!Xa�1$�LAs�uJ4-f�an �d� !{l0c^0�d��&Z�&�qaC��" / && /�}VZ�dA_{0y7\��9F cnF�d9z69$"w ?p3i?(f2�}^2FN= &�1App!yR�>Rj�:��"�Dn�:���N = 0.�P~ �zN|ToAc��eͭs" U��uD &nsatzm1�N�_) $�w%d�Y�AF 2D[�x �]b#as px�VE�v���HKC)� �O ��i>8 y�ee}-0)�nd zR$$.*�[źZ�a�( ��KG�{�ora�ao i=9|��fsR�BM�). �* K"�*#0�%�i_+%%"�!& -)� uld/ regar���E:a�Z!X-�!6O0be 1 .�3�8 .��9 !K��9�9c> reso%��*s (BD{!*PF k}$)�/�2�V�6 �6�E�se �/ad+�P��8to�� ��U�sQw(in.�)� �QectCњ. TakA� into9un�:�8.��Te� can .[^AnE��,S �0� �(R(M��N� 6EZ)��I���!i[5GV%2i�*<�'F�28UB*�A� >�X�L&>"(Appfolinsys�����BB�e�1��1u �����V��N`^M�2�� also holdS!�ps}). �L H�qejF �6~Ub 2�Rx.}6kas�`��F7�7�*�(k eC#u �f ��=" �ĥI �VNw way�i�D� t"�[��|.. T�>al���eWy����&-9,8 D�> �Z+^�0fs 2:: s .�BoV^ 2:- �s R=��Ł� �#H"R 2�.�)ᢞ�& h � >�%�� >��:d= t9�CN2�F=R6c>Ltoae���u'to�00�)cy�؍Hz.qa^>A_{2y,z���9;C�g�:L Q*��Ezgf�We�.�# $|�(~�"� a� ten Zw?���\ HX*�(*�&�-�U�.����*�&5lc������ �"8�' �u� } �V�VMN3�E-iR�,�Q�) yA!r&�6FclyRe�itu���\pr��1 ��$H�;� ��ec-si� ^�MMt^2�!r�o&$4"7�I"�4 ��cky���thebibliography}{99} \bibitem{Weibel} E.S` , Physi3 Review Le��@@ 2} (1959), 83-84G/N,Neufeld} J. % H. W!F\�0 129V463), 1489-1507.Z(Bell} T.F.  V$O. Buneman^W33 W$4), A1300-2.YSudan} RZ$Lutomirski`R.N@$df`47 `6�56-165.\0Wurtele} C. C�PJ.A. Davies, G. ZhangmJ%� 1, n� 6)-$92), 73-76.tBGK} I.iHernstein, J.M. Gree#�8nd M.D. KruskalFm!� 108�,57), 546-550.hTaniuti!� �!�ashimiF�6HII6AI454-452�DShukla} B. Eliasso,FP.K. , GeopY�search�rterI�@ 31} (2004), L1786� Oono} L.Y1� N. GoldenA��Y. &Z& E 54%'9A376-392 8S.I. �Jit� empo�&AcceleTm~(s} (World STific,SgapN��2�w81}6lNew Jou��of])�6919.K� S.V7z� , Zh HEk�oI0al'noi i Teor\�,heskoi Fizik�Gbf 65%#7a�(505-516, [{! English T)@��$on} Sovietms JETP �3I�7!�248-253]�>� � docu�} % % * En�f2�(apssamp.tex  �[%\:k[aps,p�!4int]{revtex4} 'style�'epsfig,U twocolumnV} :{pra&,NHpacs,superscriptaddAw, e��*s,ams�Csymb,tWe53s~84} \usepackage{�3icx�$bm}% bold Qr, �`I1Z935�.K\.G�beq}{���1%g.$e$2��}>FaFnarray>$e$ FV"bEVB ARbc�ce�.B�!?V lsim�ale9.gg> ie}{e� i.e.>rbml�sub1`s>(e(�n&��,entout}[1]{{>Fbk�bf �F*,�kp}{{şk}'>7q 6q>5Op>br 3Bcr45rFiK6 K>QC�G6X8adag}{a^\dagger> �"\ Z'b#b^et D Z% ddt}�{d}{dt>�0half}{\hbox{$ {1}{2}$>)quarterF,4F,e�iF*8F*db-Ad>pE E>H%trm H.cB�eqEbn#1}�Y.Peta�+E�e�.\/>a ibid���bid. F$voliE2#1>CM� #>biN$\)��sub�({c} N\\ #1 qY \,�$:NbiNmaS�R�>���$} \title{ �-Te"����or3 C�8less Rapid Adia�c )Oag�0a\\ Fermi Deg0te GaDAtomsV a Bose-Ei�  CoƋs+of Mol�#Tes} \author{Matt Mackipsaffili;,{QUANTOP--Da�! N al R6  wnd C�v� H Quantum Optics, De ���� `(As'�omy, Uni�H�$of Aar}oDK-8000  CMn�J�e�or�2fin0!#�em%����:w�)bat�l;� move4)u ���debunkN�xon mi�=ce*3"x#-body!e�#*':�' ble �!-4e�'�t%�two Bthres� YC\� {03.75.S�+\make�I {!4I� .}--��� ci� cre!w q3I2a paiT E<�Im whenB` sp.lip��pǟ�a5� %� tu3nI�Yo!"Io~�E$STW76}. Re� d& ultracold "0REG03,STR03} |�Se�� "GRE9m�% <+ �de"I2�%ir�*�,!� courkeffor�% T @ fluid Co�-!Oed C ��4,ZWI04}|M� Refs. #CH� backbon��t��x&s&i�&�B�:.Und e5��q�mD5� far]�-Aar-dissU@U�%~ all )e Abe�Nit, s�)e��m�MD)~iMI��et�����$�ve!o �qom.�qA',figure}[t] \AHer�-\i6�dL0lphics[width=8.0cm]{T_PRED.ep�cae�{Pr��T.�*�%a��sdcy ($|2 |^2�fN� B�)�)u0,��$^{40}$K �}!\rm{K�S5. A�*e2�inM�ϊ s ($\hbar�]�F/�z�lowered, mbec�nmore liks�qe a�(ed� &/stae!��s��>� was swept��e (/ rse)�*D $1/\dot{B}=400\mu!s}/G�F%�2���Refq^JAV04}."��)�d"M7 ��ite2�c;ͼth�A�IŎCdUs �.�s� )0txg�Et5/%>�u. Onea�Al�8mo-s�, C��\rmi sea P5!�K����� TIN75}, a�'i� �ҡ^uctor$\�9�1og�EWA�X-i�dM01}. A����n� ccur zca�%�FE�I�� gy� a�to @/ervoira6v> .� leav�IsB&pr�~topE� ��a -p6��,�#l]�raJ��+���j s, o� some�;0to Pauli blocO#}�����0taneous ���:M�ecrolo aH*[ play��i�ces ��)pen qu7,� �g� , ��� �� ��� on. l<2�,hv:��G)��H?��� A pM3�a"�<le& �Y�sea�&e9�2��a�ss��Jv&o+��8v�ra6��� Z@ � M>! es (c.f.,��.~ߤ�d��BI�]� is�=7wA�,agrees semi-�i�z��I�9�qca3}; n�thele�a�Fi L�vu-ZaS�zp��!�at�Ais funda� a"��. &j egim� CHW�n If2��7ta����fa�c,!P�yF�0� :oV (ult�x ely �)l[""� , e.g.��&\ �achda�A ��c� m� }�y�_I�mix� �A�awtoM��m DAN03}. U�4tu"��g comp �ya�e�Jl�:�[�j|0wx?on�I�420 �to!�at best,!�cl׋g 80brute-�|2� taof] Չw%1h� � �� -/}-B YTIK ۬em�r  -�-q��#��A�^�� EQ�/-.t�r��ru�/ 6any2�cei�he1�2��ubola�ngF\ (� � xPAZ04}_�Cd��opaIaout�(d�_fo=O�5fCbriefl�1�t�2 e�$f��&^�confirmI�Bed-Ű mapping6�byE�0{onI]eP6 few-��7� ults. In :�It'I!d$2�410�tiF3e�Bc2a��o�gy�A�I�0$\sim50\%$. H"�� !,flV���3�8 Es�7YB is� pt����)o��6(`be��:c\ ndY��3 8 ach�4d� A�><. Last�!� �!mle��!�e�ls':�ly hel�M��t�"� 1%ar%���ke��;ofq#�E,u!t�3��ar��"E.�6��Model�Wa�de� ide�pwo-��2� ic:by �!)�AxB1.�:$e language��p%�wzEAa��I�26$mk"moa�um ^ bk$AF=:&r� annihi�"�,$ $a_{\bk,1�UÜ*�!hm2 n�"vis >k Zkb_�. Aڜp� obe� ,�(anti)�umon re ��gmi58copic Hamiltoni��or?baX� ely-)�yU�%\bea  H�ar} &=& 'U% S� eft[q�k-� i�� 0,\sigma}-I +(�?+\deltaF_{\rmA�})! %] "�A,\\&& +\kappa�,\bk'}�[ A!�+ �1 ',2}+\HC Y,�2 MICRO_HAMeaPrep�d � k<ic`@m�g&<�(��gma=1,2�Gm- free��� gyd9M�1H {k}=^2�w/2m�1� om (m�e) chem"*m5i�KCm!E%x(-L)Q�� detu<$)vea s�  bi-� � !���%�>0?ta��o*!7�-.az -�", �)�-0to1/\sqrt{V}$��$V phe y � :Um+iW�QA Z��2I�:M�s�>�n4w� �H1=!T2a�n��ro' ary +7&��3shuff��GT����!Y_U�$q/� turn,� bsor��iG-���m� off�an �2� dc bias&�! "�� EJi� J?usu5 � rsH�f΍�� trdY�m��, $expQS&�G�a 9 %s!�J0i Ju*k$ 8CRUTCH_FOOT}. F(9sak�-a��S�$/B comp�DlB�= �D M�a��d!`� $\b�Y=0$ , $b_0z�b$"ijYeE�� b2�\bk�� .�-��2�"�7EFF�� Ab� �L�![V� ��@ rved, $2\�sle �\i=le+�f�a��o} �  6 =2n :���)�J��}=2N$ Y$6��� �i&� $n_{G=0,b?2/tv'M$)T@AJ��$)I $2N�Z)#}�#� rzl Q�o�0B Εor�iix�Wuҫ�f s�*"�!/ �*s .��<fu� i�� A]q |0i(t)-t=%�{m'��N �\{n_k\}}C_{N-m',n_1,\ldots,n_N}(t).���| J"�' a d$oHw6*z�@*^N9&��Xo *�� , $i��%. al_t� r=H.y]%�*� ~\eqyyNgF1a i�,\C_m&=&[N-m]m� C_m 6b d![ɑLN-m+1}\,D_m^{m-1}\C_�x.2D:.\h� {0.75cm}Y��N-mKVKQ y�FULL_EQ�HA�$�!��:N-mJ�E�a�um�DctoE�da;&�F:�Ͳm!{m}*�Ar�e_ Lr �s amoQ�0$N$ availableQ�/si{$D_I^J �n iI}$�$x J} d�)�al�'rix�x!�n]5V�� gel �Y�P�!3I  J$�p<��! EO5z�(� �e� $2^�B���csta�er� *�^ to FN=1�@j6.���; &M� by m]pl� Eq��eq�av�p�/�) vI;�%u}_{m,N< y�Fek����e���)Z*_�$N+Dt? �Kv&imb&*��� I��q�aE&e� .� ��ap(e�) 7�e�MKy�,U RED}�j\Efu�a�E�m}}�I� $N-ma{ �#ao% ��mtiU&��$�\Umar\, �m�-r oF1�J�8n_k�'>K$ (e!˅m$ &]�-�� perm�2&E��s);will ne�F�� ar f�=� &�=V�(/(2N)=(1/N)��m�!�)|1�Z�%�Pu�_*��PVAR01} earily a�U��"QF&Μ�}/ $\Omega=)�N}2� \rho}� JAV99,i�,�!r �= (!�EOo-c Euel�30�nh��� f� . ``&�&"iT2MD �&�a#�K=|G�n��f> �� �a�$1/ �$,�$|�yd�!�t ^2$*_de�,=Xl� yaH�?=-\xi? t$, �$q5sim1$t�fyA"�. Off^<.ALL}(a�;fir�'hisWJu� R$N=4$;��,�v��� fulcp�m shif� :cl�KE%�Uc�I��m�*ca�/6)�\�/՜ . M�?�r ��� 2RA.�% Fi� b) illust�r�Z�qtc ^�z$aOJekz"o�K!#� cle�$,"�4t?ut 50\%!+ ��EN28if�)�yAu!U.�%Z�$��/\ln{Nuji��>w!#Y�sho�BE� e byq�@�a $(I� )^{-1�F sugg��>�-su', �(t)E�>J2t$AB�c)�w=�1@ %M$rI�gree nic�AA�ab0ueBL�K"�. � gin{�!��#ALL:�#�*�)&��asF u� I� 11!k^�B:)�d, b��:� (-x>L[a�L!44$,4ifno"�CE#a�� �����~[Eq.6�, dashedR#]��a^>S6�e"OA g\�/,�ui Zy �{M!�J�;�two2A�.e!wis� �Pinguish� `5�]����Q�i A�,� ��=1$. �nU�%]Py ���r6�e�iFY }:)� (so1),i�K9�u* (dot���). aUA.^-adjus"2�M?�J�@"d�-m)O �V���2�a}l�! e���� !=;u�. �"9 � ���1�$5 y, 9�d)..�&2��%&7.6$, "��mU#oUOu 2�% nD'$K�text)&�%�x�6�W�u� K+*! ough.��Bx� t�%���!. My, �*I�y�r!�[Q�6�ű�=\D�,_\mu(B-B_0)/�A�D %�Qca<P)!�s"%a!�"5%`�� iIl$B_r  �'�_oa���a 10^5$n��5�i� yp�t R�+}�hpea��sit�� rho=&#{13�(cm}^{-3��8&jAength �� 0.3� 2\pi$~MHz �J(��vL O5'\a�x0.19�0*A 04; r9HBoh�Q4�on�b!@eof FF��� j�(2�� �coL�� � (�)^2� Y/(E^)1^2) � 7.9$�e�=���sp`�� !rX":%6Zt �jax6WrG_hs,�ae� \xi=�t �~� � ��ly �.�b�*o" /5$ ͝��a,Am� good��b�yӁ7����*� m� w� �imUe;  )urc^�C&�topagi�%�ct�QA � �,W�]  "to �i;Del %d�1c4#�(te��Hq ��,ly $\Lambda=aIrho a/�j$i � �f&�)�Sic $s$-:w(x lh ��sc: �$a=176ayCBOH00},�$%�e=r���N^Y $�� 0N/!�.B3 ŧ��BZ�F@�$|-9|xm2|��.&� s0 � ����Dbroadlyig$2r )� ular�&� AW&��Uup�Jto�5�'TS�yAnt�o(� @�"!ci�)5$ɶ� �e�>!�rd�*u����- MISH04}Y[lso�M� b�u��' cE�wLca,n&� :�w �v�?a%ct<��(͚ (!5F�)!V&S*sti. "F$A1eV]  A�1�al3 ��"4 9���.�+{!7e.�2.�X�  Xfd$7gY��lea2_#��s l�`&0��I[���MAC02}P� rogu|Yy ion.F$!(� ��${/ �%2t�%�nJ_C]r�u_��� �i��� �H��]J"�1l�5aA+Y�]�0 �� nU!?F)�M�>�[b�q2 ABV_THRSH:�F��A$%?-t16q�:�&� N=10s !vݦŽ c), � l�A3 4U7�,$2� . E��5Z�j&A�!���-��>7nd, od!�e n�A� e37A�aiR��supS6s��J��� v&B��� gt2$* 1x> ��clo+!A!�Ol��m��!�principlm5n��!>� � es. lG�r�7 �<0$),4;=�d1�b�("%\6+#�s�#o�_B< ���-�`eU6e��e�,J� : ��B- �-\SW$'(Z)+i�= =0,$Q$B#"H��6�#-1�^ $ X^+�AE��)Ha�]9y .I�m� v�in'#�� XbO�  cea7lMA�; 22/.BU/��w�y�, as"/a&8��7�c�.rea� a surpri+ s#�f}�U-�Vv�yc�oٕ a����y��5.�d$�d!A�n�'orJ,�#k abrupU.c!Y%+UX l��fu��th0( own A (eO/a��� M� E iU�I|re���kqI�umbJp�0L!+����)b�. Ourferpre�(!�xash$��.�/cy  m��(��� A��;�-a%�!6Mp"^driveŏ|. mimi�3 one- E$�;wI�-j lea�/T 8��NWr~:8t q�Z ne�3A@!�>=i^F[��&JxwS\V�ZZ�}����lt2n�"� ��?!}�G%bev . O&w)v'!�"�,a��8�'<�,N�Rq�0a�8�a{�4 quilibriu9/&�6FT�� "?  e "�+s?d-.J5�ss!w�)���i�:��Y.fmayAWAcarryLz-)O1���3 (altho�we��d else�%�,I�cer!�@re�Yma�1�S�0&�/w�q8Z��N U�1��t/U�ly �' D'�%to2� n� ion ��m,��/�Bs�29�"�W�q� lway~8!�si�� -6; hTe�H3jndAxKB*E2F ady f��:�bl��}-/h*!;st�l��)Ti��-�E�Z��O) c9�!㡱�w`a9��&ADc(2R s. S.�d^iW�!hp]�" 1&�!�i�@��=�� R"to2��g&fce �*s.�C�bo�.1 .."� � �eǍng upE|ejM� pathE#"?A�Us!�3:J! � J!"H?�*&�$w,FFon0 re (!�)��  (more)2\%�Vy�T$N$&:+.� s,!Wb�im2��j�to�;s� %le�.� ("�&�5��k�=R�@��,��e�L�_*�s�C6t�n]�>� . N����a�at�k>�.)l%j�9/l*�9��&_�.ca�at *�;2*%!��1 #PL6�--a�yet--!�main o���e..���?(&x E�5�aG�4.���� as s`p�F"5� both�'I�Ca-e 9-[ ��m����.� ��!�Yt"Y A�uoion, ��I�`�#&' to invok�@t�( pla�T.�j� �4Ac��iMs���?ofe�$(O.D.) kin�k� 0Magnus Ehrnro!EF� �� �"ort&�>�Q�V&�VST\E W.DUStw�#y, \prvG,bf 37}, 1628�V76); %"�VTIE93 BE. Tie*4a, B. J. Verha�nd�TT e oof, w ia�K{4h 4114h939h �A F gal, Ti!Kr�U L.n�� D. S. Jin iN��(e (London)~ r2�47 �T6qOF K.� Strecker,SV,B. Partridge mR.Hulet o!>c(91}, 080406 f.? CUB0%?J. Cubiz;%s wxprE240401 E%�iaX�F �Vin�C.=(!~v �426}, 531.�JOC �!Vochim�S>Uce C30/21�.D�F�M.Ap ZwierleinJ{�}�%825Z�A4�2�.J�] \�0!O3%O42O�\Z�6G 1204RG�GI�Ch�1.�N30bC11a\2CW..KIN �J. Kin��Ie::�!*2 �.EBOU ETaur@9FD3A�DIa6TI DEa~TinkhambW]J. to S-U� u1� ity} �$(McGraw-Hi{�4New York, 19752wT D �Emmerma� K��uya, PE4Mj�n YA. K,n�M.Y. AI�28!a2-`12HOL01 � Holl�Aޅ�,M. F. Kokkel �M�bChiofalou�Walser���l y8��Ei�6{OHA02{�Xh�YE�ACZiffQZ!� K9��304-�228J� A& JavanaineqRW1�EA�Ae G6��A G4Chwede\'nczuk,!dG\'or�� T. K\"ohl�dadP�gulienneq e-p�WP0d-mat/0409192.�R* c\&�O,!e_P^ K.-A!\oO%�)diǡ[21a�E�32���l RI�!Z�q�[ 0536�r!2X� I��khd<kov� A. Vardi,R�7422�Z�  �HPazy,@Y.�NBE{9�a�E<9�6�.x6 >@e  ���%c"�(? atRbe� 4�*ouB�ay,'L�4�� trapjE.n: ���areust�� �8.�\�:�SM[`R)��(5aR318692�V - 9�V��Yurovsk�7J.�A [n.Z606361��12[� !�Ishkhany+2�T FE�6�04361��.�A�e��:���xu�aJU�Eɱ22`i�L�� \pQ�a& 0534MM02<���m&!�8J. Piilo (unpubA\ed9zX>V > \sp\�T�[4p��,12pt]{w�c��u" [[dvips]*[UD֜EA� Brillouin�JoLTm�B i�:al��J(��S�TLAdam Ciarkowski \\ \O0��2�SF}2?%,al TechnologFR�T:>Po!1 Academ�,��INT!3def\m�)Tef\s{\sg o� d{� t{��tw{\*� r�/ dbet1�cal� �[@.�Wla}[umbdZg{\H���**�V2mR a"�TPr%u�aR�i&�x�G,ersive me\-dX�wI�-�i7S�!aA���jit{����(its envelop"�]b @< hyperbolic tang� , {ur�VE��to  h�e�(of�wth ]� �3O� �"�'BF� H�F asympto�'� ach,ht��� coales' saddD���Rs4l�p��MW ��s�&�/d)8nu&J6H5� \vs�L {3ex>�k?Pnt\textit{Key words:}5��mum,� -��pOw ion,N�,�D�jya�7s�Yz���T{� � )rzi�L�D!if veryV>,ly oscilgng-�s�z�8eA��y��gXQ�on phen�),!Var6&�"cf5A�gn��m@e�$�(t a���l��d�� they�) ly dumpedR�Z(� shap27 �A�m-o�*durDO�a�A�iKQ? �.]O��kBp�o���a�����ǥ�%� high"��;=mwo of $[%12}$ Hz%Q�s��del��nA�c�{�A� ks Sr�drVso;14q y� ,br;14,br;60}�.bQH&���]%a!WQ�)3, a9�!V�1[Rs�% pr��v%�#֓I g� �"p%�-#I>��t'V:N� y@&nt��*5 ?�a�Uc�E�2k�+C=]���&Ae6=XyulQ!@c!�ae,��y>plane<�!J��-��*� $\t�Dt$e6�� er, @D��5 vE�tl�x�.t�&�� s me1��"� ~�!��)y�!�"i�E����sJd Ie�y  j.!pR'� �Z symmet�;ly�.�ec�%"! a��to��!�,!�branch � s lo�!w!Y�>ec �half-%,p�C�K'�ofV���1R���� A�aerE %D�co"=�=SA� !)O)# � each v�CH6,�A��l�n6��~J)�x !],��0spl\Lf�d�^ �^J%o!�,6��2���xis, �V�Q���F� b��E� �dI� V XI8l�>}P����Ae <� 3 m9�N�y�B�Kis ]�� H.�L.Guɑ} ��N>[u���T� x���,  2���)1�  (p�"�fu�,R�)�&0S workI<�Q&� due �F�. B.+ofy2��� �method��n*r.$(now refer�\�s� uh ��s).� c�#c�9?��|bv5 's d���T�i�?IN�x"�� E R,eFN�a.(er order. W�Fith the development of advanced, uniform asymptotic techniques, completA scriptionAT�Iprecursor now got feasible (Kelbert and Sazonov \cite{ks;96}, and Oughstun Sherman '(os;97}). Inm`latter monograph, in addi�to%$delta funcpulse,%$unit step-%,"xauthors also studied an initialQw!~fe rate!9growth. �i�,del, however `en%�1�CX is d%�bed by 90ywhere smooth90$. At $t=0$%� derivativ!jI 's 5�suffe!�E?| discontinuity. As $t$ increases%�=!�sE a %[e speayyq�=�@its maximum value5sfollow�seE�s1xtructA�form \ repr%�)�! A� Brillouin!�m�Xresulting from this sor�19�,!a showA�M�Y� inN�affects2�1��G . WeeS illuste3" �-Hnumer!�4 examples. \-{Forma�2�oblem} W]�4a one dimensioa�,electromagneA�p 7aCpropag)B�wL Lorentz medium. The E�$haracterizE�%8frequency-depenA� c�^x index!ref:4ion \begin{equx|}\label{e1} n(\o) = \left( 1 - \8${b^2}{\o^2�o_0^2 + 2 i \d\o} \right)^{1/2}, \end` �A$b$�so A� ed plasma��!� � , $\�v6 a dampA�� tantE-$�! a 9�5. AnyB�field!ts satisfi��(he Maxwell 1)s9:` \\ D G�=\int_{-\infty}^t \tilde{\epsilon}(t-\tau) V� d�4�B2\mu �6t),� 7in}Q%5KM&F�)-��ـand $\mu U(��af��assumed��be !�Tl 1). By Fourier trans�9A`!�&a+�respectC��zV /ati�AP�?a� ��_pa%�coordin� $z$ only,�a obta�Թ�~�T�sq �edI�s \[ Ey\hat{z}}M�8{\cal H}(z,\o)=M�i\o1�a�A�) E )=�E�b[2=I�ZmuQz , \]1�2M%�!pD vector di& � long!/-axis� $.� =n^2�/(c^2\muI'O-� 5;�j$\brev2�)$. It3n-�Dat :�, $%# E} )[$$ are mutu�kper!�0icular. Moreo{ if.Cis know n.Mi� �4vice versa. It" trueIheZ��onents, �0inQeF(Ecb�. TaWfor� he� ledg"��� ic (��)I� is �ici� to determ� J full >�'eR . To makeeecal!\tionsi simple pos! , i)&dvisa2 t!�@the $x$ (or $y$) AT�Uo(to coincideW ��or � � A�Z `i%���ne $z an ?� !�(turned on aE� moB B . F�W �oscilP ��� xed ���cI�its&� >� 0a hyperbolic � !�� . Suppos�e s�,ed CartesianYQ (say!O -comId)����o� se)&� %Ipl9(is given by�R:�$2} A(0,t)=�\{*�y$}{ll} 0 & 6�t<0 \\ \tanh \b t\sin \o_ct & t\ge 0,�y H�. �y}A� paramA� $\b$Y�s� fas)�"� �-� � . T� f %T]disturb1 es a B0 $A(z,t)$ out� >H� wA��;� willA�interes!��`��{ p ngQ�half-u $z� t � under �2sti� candclassif��mA�>� -boundaryj � , ��^ ��%-!act solua� /0 pecific��%1YiY $I4�X2�a�] our% gralacQ_U 3A�!�+ C g�t e^{��z��@\phi(\o,\t)}\,d\oB define"p a8lex&� q!$\o$. Here,�" �4} e eqn{�=( onumberA�& &� 1}{4\pi 1[ �$i}{\b}\betG( (\o-a+ )}{2!�  + 71 !} 3fJ+JJ*� \ !} f]*t8cm: }��� pha�^�$=|$�[ j[5} 4 =i\, �0c}{z}\,[\w{k}!�,z-\o t]=i\o[, -\t]B� $!N(s �Albe..�rg;51} Q via+ psi�� a*d :6E�f� � 1}{2}%�[\psi ( s+ -�- B!<  ]B2�aF/��6�� $��{��}$.�W" less�cY�:�7} \t` c t!�>�)Qs�9: -�  point $� �D��Y $cE/"fl�, vacu~�8$C1 lin�8o=\o^\prime+ia$g *$� a:� grea� tha� abscissa!Bab��Bvergenc&� U�@in square bracket�[$(\ref{e4})� $� $ ranges qne��$ve to posi��$. Our goa�0wofold. First� $shall seek�*4 ula � 5cond (B)&��t� ult �!|&�������oth�ord� e �@find near saddle %�s!j trib�3�J� expa�!x~totalI��$.�ond�� ��i :!in1�2!�Z�5 &�*e Asym-Z`s)d>}%�px�F�!��J��:ba9oE�&� �p ChU$r et al.\ ��cf;57} `wo� )�i�!�alescyto- ."-��order�4t6��venK ly��� ]fm;73}e bh;75}blocB � c�[�~-� -E.�aq mq3!�r!� d eiEE� �"�b�8u+ \o n'�ydt = 0B�At s ^�i rstUve %$k��[\o(\}t]/o$ �9^{'}_{\o���$�:fesIre 2` �}� �sVry)�#Ldomain $|\o|< \sqrt{�^2+\d^2�$�\.�)X1a�aJ $ denoted b� t_1$J�!�_1 *D2$ approach each �fj!�imagin� axi |belowEL%�above, �ively 2�)E�y cI�uam��i�E�6�u��ϡ{nP,�%�M��� y deT ����symmet�ly�$�2 ! {1,2}=\pm!�-��)Km$2) 8 � ,��"%. If $1 �1 elim�m$mC8})� Iw [ ��&3 �lA�W�h degreAmlynom�A]\o`�h%ide���o �! d�not��mAvbb\sol�Hhe"�ctl�nB� �;emplo%�@Ѧ�M8})� wased&�[AlternQ;%� E�ximZG�fz ! ��,ac;02} could�u����expens�accuracy>a�V'f�}�2E`rocedur��Uh��5gr�| vari�R�;�Y to a new $s$,9� map $s�,E� someMk $D$ ain��.�� \pm$ (but%�anyn2*)�nconAxa�� same�_ex tak9�= pY�Hb1� &E$=\r+\g^2 sj 4s^3}{3}\equiv z(s��B!Nh��Qa ($ has b� $s�g$ %c���i��220�..�, cor�o"$* _s��roj� do�}(sW! -s^�phB�}> we�%e�at!v Q)toA�5�,�\g$ruld�* ��]�A $s=-, � to�L=\o_2� n*�uE�"�1� �xg)=�� \mp 2\g}{ �'ᘩ�)}bXJ-�ya�rtA��! J.AIu c[R4��/$ m� !#A�� 6: ��1Ma� one A�6�s)=0$��relev�cul� $-:_s}$ if)141e0A�-YF-] s)}\�]�3}BRBy us�L9�� �AwCarrow%ׁ���1� � � e�g^3�r$F�lAOb�9} I(4?�=!�(\o_1)- 2) B�^S20`1[G1)+ 2)F����q�� 19})!� $a+!�th�` ,roots. Only !=W�a�B 2)<0!khea "�8 5�A$�!u^3pO � � , if�> � then�e_1=�02^\ast$.\foot!�{A� star mm`$conjugate.�is 6 �a�A1p�" ��� )=u 2)] t�� similarly �^{�L1) = 5:] is�&se� at RHSA3Qh4})W Lls $-2i\;\hbox{Im}\;1t2)i $R%�H���$\-G,Q�g^3�9i/��We�E��'ta&�f�!� �}�$� �#&�6a$en&�� 45�aFas $s�qa�. A0Bec�% m^U]}cand� 2)�$�I�%�:*1�� lqrRS.�m��\tA�^+!�e� clud"l �g�ya;w:� i.e.j�a} \g=͸3}{4}|12�|͹,\;e^{i\alphaf+h"�ii)C��U/ &�  Withe0n.� of *�  lQ� ^Q �+V�.E�;���,��s�d�*i�|Ssh�7-�` bymt ��� 8 aTt_lA.��%� as1Ŧmultipl�b��la^{-1}$�no2) nt T.�"$c_�+ 1$+ $substitute92>i�� thusy bW23} c_0� G(\g� +G(- � :R)b� 4L1:L-.L\gF� �"� .2� a�6})E) ex���e!�.�A?y&W %l!� e�t� M�!�VA�_ N}e��*�$�#*� �(e&�bF30} L\sim � i �crR� (M?/3}c_0 \� Ai}[2/3}\g ^2]+-c_1.1^{PN: �FI�$� roug� Airy�+!�$d"�.a 1�,)b 29} �(x�?\pi i}��}!1Hsx-s^3/3}ds \qquad?�vH s\,e^.LF lo�"� 9s��&� �e in Fig.~1a�-8figure}[ht] \ceC#�.\i� 2@ics[width=.7\text $]{Ai.eps} ���{it{�Ai%�(Ai' against�al argu�%x.}m� �@$#�a hold ��$IU���a' $\g=T x$�c� >i�4mV����^$q�a�� $PC.���a�e�e�is"��g�qh� t$�(&2  �, B \ t=�  $algebraic k��Zl��$��/3|!3 be+ o chn/R.�4�fw aj }. �'O. s�4��3R� y�_� plac�th�3N��  as;6XM��"�3j ��(x��e^{{2x^{3/2}o}0[�e�� pi}xA84}}+O(x^{-3/4})"�#�� 31} �.��v�`$�{2�R�>�� x�fa��4��5@:�%32_%�%�1H�<%5((-x)14}�B\{ �(\� � 2!m (!{+ F!e{4�]& (1+O : /-2 ��# .}\\&f .{} :7g 2 9\, �03in}\b&15-f3N>�K& �1!{9+9!cos��!�!.! � >U m1$�0[th��2j 0e arr� �)���6F�" "� A ��"5"9�u!�4} .��(la z2)��ADh&-��}� $"�{2}|E�2} :)_2)QA z .�:k #"�)5r�1��1Z� 1)+ �����. >6ses� c ����8�!&G/�"i4tW7$� (�#"�#'s choic�Z5&w' t_s\F 1.5027$)@:C� E�reduc� o a 23� "2��/2$2o%� to a su�~K�!L2�!MD-Q; is manner_i nfir 4!P!h.�`$& �e w�"��J s a >0!s�7%g\";oriX"lV o27 6can� b�"J� �,�pa�;J9ji�"�=��8 v now " 2}$ b��!7�N�*���. �U<4}) QL5}) it !Kl�<"��ul\.r|n-applic7 E�  (  )"�)���� 1,2}g�a*p��F����rem� id ac� t$ (Pg$�<p�7�2Ezp�A-B=�]> betw �e !i�B%'large/%g|$. W#&�tA�&:r�< P at $._1)=g^*�9%1)<7lAPm�.{�^*�25�;�50 5}) C J�a mor� mpac"rf�366� 2 \mRe"� ��N� B`.2>�� e dynamic%�A��t�haG"�; m�;W"t�QyjqAb.� ones5o4FV��ou��is� kE��z"� >�6b} b� 20.0o8 10^{16} sR }, \�o_0=4.0\�-s% :%d=0.286$ IB/�5�9J�Ƹ un19Z� Un�> (soa��-��.� (dasY@ :�x 5tz��r|A5'*)/s2s0=11W %|913$o_c=2.5RT���=3D%�-15} s$F��t(A�a�v�$Ds�7`.�A�0&�,�2��not;ly 2&� c . Ad�8�&�{�Z a?in>��s "�. �,BYz"`7ory&�)��aRisG?�?�",of yB�>*p�"�/�q>� wir� ( Fig~1)..�@Di<;6 5 "� �(!�f��*�6"� a��l3b14m5zv07 0ca6D�E2L�U��i�A6#A6L725"U)!: (top)eB22�14}�u$� (bottom) 3>,7,y�Rt��etr�tAn impor�@qu�7/:ris(n"�0J� �~09V�:%sb�0 "�Dj!*� rel�*�ieD shap" Y�M vir:=une�eda�le�q;itcM9�f�B�Gno %>eruid^ b$ e�s l a�m rval at^�Z� ����� rapidl)+�E. Abov�#i2t, fur�21F�>$��vJ >3%-�jF�57y A !�^G u=s�7b� low ($:����=nd�B'7U�%R�!�6c3. ExY1m �i*l�#r ���%t�#�� coeff:>s�2�*: 0����0 $\b$&E)".K�:�=,&�;%zw`. � OB�E .�o�4 �9 K �sƦ amp1ZA"`$� i_� �;\b/C" "� c� "�A}�4>T \t=&~��HA϶i%,(�/r�] ��e�� 4 !]" of6�" �� H Ai}"��K paren�"d 0}) :8!M i�) plot�21DA|Ir� �~ chos�%�,sl�0lxa���?BXT�  pro�aH�,B�(\cdo>Edo�1s&!BD to=;%i&� A�/�gHs �н��HwLA�x3� vari�%!WA��i�-sl>� th up�, the 9A>F�u��/��J���9>�(��`�ti8�3f sett##�$a�F� l O L�'0>LB��'.�1w de�U�an)coO:h�is�)�zh+ar.t 7!� ��!�'!9�o~ apprh2lx4U�>B$*&j�1�� �F{7} �)= �1�>.b<.>� *c}�BS��appeare�:�!"/Na�(o �g9�3.2b�a�&fty2{!i6=�:a�t31 -B. Now%�i�NE *� Y�&; becomes DoryeH[1~!+Ec_#co&89.;4dia� helpC��)bj+!8�=3JA@H�LP2&�m�q\s�Q size�}++�2)])�| b�^��I|Bt�dR�|��2Qs���obwZ�� ���B� "� &H'*�Eovb$. CG/It d"3.�v��S��:� Y$FIA!5E8B�Y�Q���>)As:x � J�a���" ��m-&�K�E��t"70|�at^� !�$\b�o 7�}6���} �"?�� nrh:A  satu�=n ���G high� u%� . Si@ e5��� earlier?E�� ?t �J�1a "@ ��M �owo?� !A�! . A U"),x obser� at�9.3��'extrelRmo0o�* R���6V��NV�6!:fmM6� ��hifa"�Jt� aGa-m2J6j j* 2|�/%un"PV al e@a�)x!l�9�嚁�{RCo�#NRs}ax� pUhav* k�y�� *�f�SS$��y�� 6u, �A�"a#8KntP �)�,� ,�#�&,Jup . "a.u�:� :��HanalyS�1O*N� fK*5y� 65{A��2�B�Oed�� ful e.g.\%��dinvolf-6ger!�devicesI� worki1w al fT� s clozKnXnoise� "� 5�did�4e ">�IofJh N� p� �dvsJE{1.5ex]H+�&bf{Ac�N�M�&}.@*.P3 arch!Xs���W �2�,in Causal Di�Mic%�q=816}, Berlin, Sp�' �7��LA�,Ciarkowski: *F�si� p=y�(m̉l��I��M�si�Blossy"0. Arch.~Mech.%17M��49M�877-892��J,I.~M.~Rhyzhi3Hd,S.~Gradshtey1RT��I�/s, SumerAGProduct!I(3-rd ed., N�v$al PublishI[��T0F�SLiterB e, Moscow�51,�G4.~6.39 (in Rus�P)��FC.~�F$, B.~FriedK^�0F.~Ursell: An/��metho�Zsteepe�Es�!s.�c.\+LCambridge Phil.\ Soc%y5>y53-y599-611��F�0.~Felb�,N.~MarcuvitzI� Rad!Sca�^��ofe�!gP4$ Hall!3$73, Ch.\ 4u).dBleisteAYDnd R.~A.~Handelsma1�Y� �I!� 5�<}. Holt, Rinehari�W+-on�5 �9 ���BA.6*&�>�� theR�:a . To} �nic�VTa� ommu�3  Qu3Sr� 2002>?8.��+��Abramo!�%�I%E$Stegun, EdQs-�![ book!�Mathe=A�FOs}e!.~Bureau(S\56, 1964m 10.4UendB+doc�.} �m\�Q([twocolumn,�pacs,pint�Ps,super�(address,ams�5@symb,prl]{revtex4!uq$ckage{u/x}% I d�=�/ files .,d �$}% Align t�_ sq decimal�&2;$bm}% bold �2 �}2  %)newAand{\be}g.d]*\#e#!u":!baD( ay>#e# DV!bsD20,ymbol} %\no)7�1�!v1�{APS  title{P#Law Dist�'e�0Seismic Rates2�bH{A. Saichev} \affil�{{2�D/tJ @, Nizhny NovgorodA�te�! $ity, Gagar^`osp. 23B5 , 603950,��:|Ins�5$of Geophys�#��P�VtJ� ics, Un|0Cal\ 4nia, Los Angel�aCA 90095�(D. Sornette�8 9$�Earth�S�  ceή2� Laboratoi�L)qu] la�ki\`�PCo� Ls\'ee, CNRS UMR 6622�53\'AS�!� tFacKM sijegi�\reA/uchy-lik2. acta5 wV��],G�h =0.1 \pm %�( ell-Ir% EOt�k�o��(yM \��p{91.30.Px ; 89.75.Da; 05.40.-[ make�1 �aS is perhapk"b efea6ap\ f-organiz!�GLss exh scaldiagnos�s ^nyy"s:�, Gutenberg-R�[`ٸ $m/Ee/�W }$ (�Vaq* 2/3$�\9� energ� $E$;o Omori a�Zt^pRp uxivRsb!�%�� �bshock�( a "G�z�L2urved.84MA 6oS^usiz�+%��qua�-� E�p our ��.�t��2" ( $1994-2003� �Rxqe02H"$ $32^\circ?37 N��X/tu�Z>$-114 $�)-12Bin / 4 �Soun*�n.( ��)� reviY �H$s $M_L>1.5"#AB 9a ?a�+86,228$�!͡��,LR:ov�by �b T of ($L=5h�1!Us$. �; r6%�s� en�i8T͐.��ia'/ w{AaEU� ?+a�Uc�]d_c�D�$��e.� ���525ASs���G&25w �1n��(  PB�BN �R�Q \ee !��r�[$1�'q r 100$. S/S���� p, nt �/eq!�*=�2�4��o�X� �' BfB d�br4S mu =�5�-�E s,. 72 �(FB0B !�w5y� pdf �)�:�h;��a�� !!rK a  bulk�$ ��$dtՈ=aU+-d p Rp"$}%4.n1 *e.d�A��z��5c� (Epi�-Type A"$  S�>)�~V{;i� �"5 t ree H-�^��� laws*f E�[%s �+l"?2�%� l p�8we& �&�E\ f** s t7�z{ance )VForexpY"#b erein& ��.�$�>$ benchmark�%J+ !ang�-! gF%@Ym!C&� es],beM/�!qMlof2gen�per m�, >a long�]("1) mem*5 Ki�=� ?�her)�- �E�daugh:��.9b&!!Z* %�$wo &� !ge��ɛ�me�5isc..� 5) �b��n��m= rR%to�O:M'�o$' mean-j&�8�� "��p-��9n�!p R%�m�S HelmSor},��[9h�� l i�~����dz*�an *� &� b\ ex\.�Sorl0wI !�Y�,� *� i�potI}�rE��uoU� *^K�'bye:yiA$al average1f$N_m a,kappa \mu(m)�$children (�x�su.�5e4=Y�e�(m)�� 0^{\.W (m-m_0)$4saWRx3% �] du�ua922of&X  $m+m_0�H}����a!) tNDo� d $2i�v\�}"� e9�s cap1A����� .(s4ae+. 8\$m@5a�E- mark�!���m$ ��!J~ U draw urandom�d3yga�Aqe�ts�H�Ms $p_Ar)=kK(N_m^r}{r!}\1P-N_m} `2()^-x2%N�c�len�V �E� %�o under!�d�; pA� �6�i� norm�in ��B� �ak).accou}ll=� '$Fs�ultFly�4.w �]Qy��R4le`-X�GBc(GR) d@>�Y�YU!�ir0b ~\ln (10)~ a-bu{, }/��Gg� 6�$Oi@'BAAb� &a;6B .@�hP,�6�E*� J mZ)#a=une. Comb&�fGR A�>�sűa��K.had�4mu:�JJ4 q�N_m_r��9EL2c:}=�U�9 p_{k(aS, = {\gamma \ \mu^�}}~, ~~~" g < +cO, ~ ) = b/�{~.v aer�!ee�B9�� b� J0.5 < D < 1$�Ta$1� <2�za�� <  l? �I/*k%expec��o�UN>�!� (yedF�} rh1 �h�9-9� 14\ . Gi�$ ��uc&; $���1�yntrolA[1 luQ� ѹQ.n$ (ozc!0-��`J��# : $n�tlS\ �!_le�� AB:B)��Y,C~a<�$Khe��Cn9m� s'=m �q S$GR law. Re��5� �$n< h$n�� $n>1$.4h�]ively�sUsub-cri�,  @'*rreg�! �Z& !}X���se1cif� 0. �"�T ~\P�xbs{r}- $_i,t-t_i)$A A1xEN �g ����!0�D�6i$ �:�mby��of*<$mM��5��Y_}=ndB[ _i$.B#us5~�ardF i�$�x��= t)\,�P(! x})�$eopr={�e .Ykh. � !� \theta c^ }{(c+Q+  }~H(�{�9$ �\Heavi�5�, $0< :I�c$ �$m ularF!%�8!�*at ens���*O)��=���2%�"� �Ajac�=5isc$�cbs!<�� ~d^{ }}{2ac0 (x^2+d^2)^{(+2)/2}}-qnex�egr��.� n� J �p tH�nic mo�  in�P.QMo2HS� }O2��9vi4222'a� � eqA0L, such4!�qF�v�3*�F��_#�!��per  surf!�ivarrhA|Ini �("u� �vCn1s�"A l� �_*�a"su��R�ouBortoq ogn� at, �L{ I��&� !�!�f�%t "e�t!tIbqaY0 whil]t"� e's,*x ��&Ks:u"{q" nod&G! s[x�"s��t `&_&�A�%�A�lot#eu hete@eT2.0Y�&a"Q ��2� 8 infl*�pre-exH n �EirW Tq rhe�&].6��y xA!z?�{.� !��8�.%a(#�ra{>Oax��># i��u!�9�a�3chy2��iuestAMs�>��Fe9]� td"�ndY ed 2!$"�@�-� }\, f\*[W ]W�e /�`�]�3RW�Dn�t!�" ���Vt.'����$x� 5�!�" t��S!<.�{1��f_-%�_� �~ } ) 1�x} ��H- -V`( >0� DI%� i��ce"�$u "� 2� ��J,i�3�"M"�' (GPF3 -I8"'v�� (�>J�AB��]�QNl"ne� ns), fal)o��� $\{[t,t+�_]\�As "i S}\}E!�0n|p�]T�(sp}�AV,O)=�]ɉ \, L�ta6$:N �R-w�0^)$ dt \iint\^ls_{N[�G quad '} d� [1- � (z,tB�; &)]+�Ctgtau�em�hS`[1-I_^ ]+ _bz 6�4 } d � [1-z.�JqF �sum�2'VeqF��b�U &�)�GPF $ v.$C .�uK�J�} � 3JE�A�M��W� �ts $t'$�A$t'N&]t " ��'a�m� ason�"�onjecB0ɋX � ��� 2�sV���&�&�:�Nt uV%o � "��3&U&�&�O4&0A�FR�!�� � � � ^�%Io ��*�!ith�&�%"En `�I9s,I&_M�2& . �ps��P hwgi�z I�.q#�neglig�. p|�B�6,m2�2ign`fq� ( ��."�:to����rYq���tN�  ^��zF5%erm#^'�. , \ ^� "�\1&�M@�� O9�eUR>�< eq  :ZV9 �J�f�"�+NnK6��] �"��Y�0�!"�of5�=GI[ ����-� 6�2%�\fOodb��.�ex$&J� �+� v�,tqI��i��;14$\ell$�c\i�eD ch2�t� $d�p�%$kernel, orp�!�1l�P$1W"m8:R�8 Zassoci�w@T���/.� $d��e_(,Q�h�M� error,?�a�q�-_=�.���&�S�faU8�unWTe!� iten����L6� �Zu� �factoV *c��:ZIdV8 � A�� q�n7~ )��:y>V"� V:"ed{"�$& )f�x�DvoĎDK��!n&ww�v G2}1�yf cru;\E�on)"f)is [6Ɔ else��/E�paper}. �^JA%use�*on�i�mlN&� a�MBV�$&$�Z9�aKq�,=G[(1+(z-1) R~M]E�i.P�"�h� RA 1 n}{1-n}\,6_9� 9�&� e!!A�.� �� �,.Q � e�t"�7 6f$5U"���t�$ ency �-.�B�=�� �C�((J-2&�6��c&�;ex���y1f] 34}Vg1�!�{��� n�\,�( \t:]p}Bq� IR<�+i�qoy} -n E B2$}"�!PAn}��_\gg d��m�b-F\i�ach �!O�y$u�7ana� �i:Zt�t helpY%�"} "s *�Y������.�,���� �l6��$! �IA�t}=p$^7]\in.�I �Jϟ�.�A�e8.kV$�(a��'s/:B:�g.ON�35} p�)� }{S}:� }Z�"r Je&�!L�"s u<get� Jd .y2�� &A {8eqG SZz��;p)]~�e���pv (<= ��p��� �-�.ari5J��y�b?!�at�n�"p�9�MP>� %d�"� ,B6+&� �I�J�-$5$* J~2D�\6`�*�weE!:w�b bb �Q"�)E�2�� q��JZ�R�b�n uR�:i�� Vw ^= S��e�\ $qq)$1-p$. Putt� l�,-6a�Q72�re��II*� D RU�.;j47}V"-…3S�#[ $-��p)I� +1-z" ;p�cF�u 6o }(dA�]a�e:!  fe#X�s���U&<)Js N~i�,�(a�cJN�v � �2+. Sta&Jo9�l.�#12� *^ ~�P�6� V 37})��Z�&� rtJ�hip"H%\* ? &,Q%$r;\rho��M� �!itP]��AV9^+� )�l"j5q(��valp "$!-F�.rsb��1�k } \o.v$�BC�Lh(큑�'[ B�z�o) 8$dz}{z^{r+1- Intr`8a�!u��� !� varS� $y= � 2�%% \iff z=Z(y�A 1}{pz' ,y}{G(y)}+p-1 �$,�#, .*!~�2i�q�S=8$h+ch6q9� 5�A��= -ժ��Rf�'} ƨ!)+1 �)>�'}{dy}��dy}{Z)�!<�� �]�s a�+(cise quantiA�vS/e�E�!�z-c"� 2�bs@��9&C\.��� �>V�($r{p"��,��2-I n:@�B�(i�'9�!"�2��>duV;i�,�>"%��>>2�)"�!��A�E�6� %@� (P��,)2r,f�}in ��6?L��1��=%r��/9� binSe by F=�6~\ Su� kO�JvWq*�Dis i��a�'�.}�P2���='C�"!�"!HR5 0.96�zE|=.~6�!|�F-� �15$1 �$0.0019~ dt��/C�h;1��ddI(�/�G CG1OaiF��"�V�A��}I�>��._�=1*TF TheySQb�@ kept I~E5.�MYU ve�C�k�o�th6z3D��C�.x0�^09<6 W� A�ɡ�id�G.�� no�IR=�?t�C est2C J��Gw��ڧ{M� 0 �r�)to &/2���7A}�m:�XuseU0�"�F)TfiV#~FE*L.I6�i��5+�� oss-,r):�nT?enuin��ym۩h2k8%�.q�>�.�hlwo &�;<8 $` �Q{1 �;e`}�+�6r < r^*"E /(1-n)^�9/( / -1)}qg �aZ*;M >r^*�@2�BI�ei2�Ya�'Pc90t� �:% conc|Tsy� 2 �3U n_e�b"�9��r�9�=ETq8C��lF W|appvjL�lt)�A+e�Џ9�]�%w$�Dver�%}Fck�in syn-8�1ly�qe*[2� �F\sBz =1.2�HL-cY�Z&� Zah�D>?E��4decad�K�to�s�at Pis!?ko%�Golubevam�PisGol}�Ka ��!v��Sk�$o much1ks bo�Klg&�_JapanHnd Pamir-Tien Shan,)uHlofjM���=<1� ""�a:�E�2e9�`�p�D!�c1/I�>,O6�4��pqM�4"��#eBtE "���N collapse Ivd�F".~*�MrR, Cor�6in�)��2`�8�! �!͂� doubl�( wer-a<" �E�!U"�?$K��e�`2$1.2#eH &- .8X �B��� m�Lb�]F�non��Y���>� (6in%�1����* r�Q�6at� �M66diD �^Y$]aY=�=�)�?�8i�fweI�of�8m�6Al*�J_�� Z�)I�Ti.+$p"�>o�mn O�8bhcof��e� *F �"ingtm� �Tw.�m�>m|Dby NSF-EAR02-30429�'byebJ�P�bPa Ce��� !L K. %SCEC�f�E NSF Coopes ve A(��D0 EAR-0106924 �, USGS.+ %,$02HQAG0008Mzi2C"� )�i�n�;is 796�q vskip -1c"�B�n�b�^em{H} #Jst3d$r, A., %IsVq d!��.i]9� s?, �dc\v. Let. 91, 058501 (2003M�"Cie] �d , D.%P. , %Fa�]gb�� !?A%&�af%6Gth2M, he�Ts.Lett. 18, 1079 (19912�d�]}�n� , %SC3� oNE�Go��ba n�A�!�inent�;in�N !348, 56�02�KK} Kag�@Y.Y)$L. Knopoff��al2�q=�:��two-p>/�S�P�i.J. Ro��tr� *l V!%b�maps�m,draft*�m~1+2\mg��i��m��m$hyperref}%z4m%\(m5m/123-QED!Dg{CoSxY�: �^���� !�a & bea��j�~ear��l��o�Zed �u�n Forc�� breaks� \\ �mClaudio�kt��*l{c .�%@� .uni�t 1.it�Homepage{http://nlo.J'.�m R�w7d0er ``Enrico F��$'' Via Pan;w@na 85/A 00184, RoR�ItakCnd� ReseLx N8SOFT INFM-CNR, "klHy ``La Sapienza,'' :A��o[lc52c %Se=Ṃ�and/or�3�\\a{i-]%^�1 ced%5eA&\d*�l%���%lwr�l, �l, .% �K�hB�(��xѓp�Ied�"a"�l�.��� ligh\lb�Vpy7 opW*+itD@�p��ng�an$lyA 3'!�J|I�/BM��inv�Yg*u)L�adigmE�, A;koQ ii�� ClusA* [ Tterpret vyo�i=�'i!�. A� ne~ �m�atr�{Zr�$�!aa&�O vibrz pectr����sem��yo)6�� �Mut.� �A&ʡs&�Xa BrowJC � ZUl�F�%7^Qu^ ��|�"o�d�| (n �! syste)�.�|lals]Gl"[� B�+a�� d ga�d!���-� % ClZ�[f4 Scheme. %\keyL�{Sugge��}%Use�# keys��E���f'vz %>�> ired+C"�l"��!n} At �GtemqumxA�5�Y�e3aA���t �*0W]l y landscB� (PEL)�R ^ �Si-d&g�  Jq$po�WSas a ,�+ mole�� &��s. � Gold�w 69,S�1(inger82,Jon�d<88,Sastry98} A � ѧM� 2�p:M� PEL ��ig�X~�(dergoes ``-Gi�.4��Unmd%J�oe�a� ide�FM��� �[Bhatta�.ya99,A�s ani00,Bro�j8x00,Grigera03}.:)=� gA�y�,[\a cer@aQ�f (4-�� ing)/ercoo$�liq�|aLis ``2*��a)S'''-at)�originE an "^�vf��r�1 %�!&�Os,f�v3Rs %/ar�I[olids (@ r$l �e�T��o�� @aD,Debenedetti01}P>4is phenomenon �� ~ly amed ~a �dkQ�}� �� =y;AW�ely, �' Q��]R ccep��Aaq�  . Du� aA�,*�PEL�qvisiteZ�A alE�a��r$ng�=�"s"�T.tra}t��� ``saddle-�2''�b``minima2��{iyKG� phon�� �elry*�Łr0KXZ� 0 PEL, is 2�N� �Tden�� `` k- ���, �,�ke�X �M keep� fpQ�N8ac��7A�met%�i 3x�l�+!By o��~���:e��Pn?03} E��noH�aN�2�N! �qdW al!�q�Wfse�n�/�&�3y%� not �$�(���S�W�s&��ya�a���R�p� ed. 2>D arti�I �s"m2T �R!j3 i��J �A a`&�7�N:0�e�os��f!h :x!F{ }��) �3�rgo��wofur> ;2h�anie(�MZ� �Bon�1��f" �g� t�2�ir��!ev�l#AkAVm�� �.E6,!G�St� e/ k:D�T� ;3m��)o, .�t2�{u(a6&Za�&N8Ke{ ropr�5��.a�in� n.�O''��Us�D in p��ct��v"D �-./��iap�M!��t1�V/ it{soft},a�c) },� . r!E C�1�,'' (roughly)a_n 4 s a � ��$ton (SS), 3!�_� f%�ng o cY!Ran  2� 5�%�ML?y M*!b^�velNx�c Boar1�Book,Tr�  Kivshar } I�n6�(Arnse ser �A� ET such� 1�,f elf-�T�,rap�\�� s�s&al2���!.��a tL�.focD! SSE���5e��  ��en��� cryst�(NLC)l���6A�he � infrΒ, it!�po&��5� v#�< (few��cr��$waist) SS��� �f9D un;o =lli�[0s: hundreds . �" �atav} 4 i�>gbs�2E�D%��C. 8Assanto03,Pecci(04n�,,Hutsebaut05�Jg �PSS! a&925�per[�J $\D�v n$!�Y�4ex,�B�ɫE �� �E� ��Hi��eT2��l?d�ny!�6� � sam�puAssŽn%�MN!TA B%.C3b}. ��ᐑFs\�*�ee� var��e�exa� rely�7�qgG�/�&E�ular,/so-M\��">ity''���b pt inw d� !Z�2f-��<s$ � 9Ή�6�Qby( 1� �-� * �> e=!GIn NLC� [ Kvnon w ��y�rol�),a��$tage bias,>�5Ni���2 ��!�8�"&ly. U(Conti05subm�k} !foRW!�r �  ondre weu� a�h F-��e� ��M (�n8V�q�v�]�5, �G �_-N* #w .!�  ultrashO �L p�Q����ir,mDPSkupin04,Rodriguez04}At! �IsphotoYY1�,Segev92,ChenW��"aeN��dEi��i�+EgQs,-04Henninot02,Yak�8ko04,Litvak75}  P�uctors 6U�d ir03Bi disc���RwF��che8�r-Z�{=�k,�-&�and (62(IuXKhaykovich02,Strecker02�z!� �ib� in�/�haPA��;%�dea��) "lo�YI�p;\\*]!Fk� s�:s (PDEs) e,�&��Fn (�e�ifyA;�%���L*�16*t� W�l��ma<� �*et[ {#�!�"fer�t(G` p� �s�IIN�D �4 �0�eߵ s��a� E�u� link�HB^.�|I e��EZofB� �M "�!Du��}� S�V)d�.�� �!�19y �}J 2�V1 {J2�z!, for hfi��c#͒^�6z)�no�m���� a42�c .lVIIs+oF�EM�9��n�=�&Q�>6y estaY�d:�IIV �a�G R%M� 0�-���v@r�!J-� ��Q manu�ptOh-&)��d�K IX. "�Re�AA�eiB� �>jsak��i�S��U]a�k with�H�Z2�(1+1D!�p ion)# E{d��� �_ly�P �c��&��E�s,5��2oM�x]i ww *��GddLM �]��+re5_s typ�� expe��E$�}�{�!7&�!k�m�%nu+bi* (��?��>V83b}[;X�d to h2�.�}7liK of wi�1re � imag"EEe��$Fock-Leont��"G���mbZ�x|.~1�A�.� umf�> Foch} 2ikl6\C al A} z&���K al^22 x^2}+2k^2|5� [I]�AA=0t{z&}-�x,WV�!����Utude ��`*�B $I=|AH|^2"cC� F , $k=C8n/\lambd�oT�-�恜�G&s � exc-$�B In=��p!�b w �s.*� ^�G � ��A�3nޠts��Ral �9 i�$I�p� :Os�cfK�"}%($U|�U���whoN,r�� $I ' . V� �"łgi�j' l"ߓeN�Jngn;X $Ip5�; KukhtarevU�s��F� ��Bview,�N Del Re�  co�*)�Bcite{&�R2he he�>�gt�a> � s . } re-ori�z!�al:�"]LS 3}%:�w���*� 655}�Ōicչ� ��4Snyder97,Perez(ang02,Kroli��04}��I;k%q�@UE�M��YAaa��-�K �8mM inco��s, �= R�>teQ��["Q��*!)�o S �,p=1,2,...,N$w!125��l5!�Ѹ .hk� SSfQ�)�� [I]=2�\4\sum_{p=1}^{N}'_p]^�Eq.5 ^unva>=��f�/n<^ja@� l*Q�1�� �(pṋenr! 5��ZlyH1��.U;H Gb1�pai�*m��� �s�/lv r���.sis G�h��6�!*�Amun� G SSs *�9*�3�� !�t� 6� H�e!R�G!f��ng�N . FuK�m��i"G5?cze(=r!S�4s �.:c-ezmFQin� al,3���u[I] �b �&8i3.g �*-���#ust�Z� ��K , q� oft�}!M��<Y"A+-a��"!"9 r�Qd!�_ Gae Lennard-J��G"�S�EeL��y�"�v=alyK��)�!NJ1�h�qSS- oG  PUo� A��5� $p��&� .�$N$Q cal ɝs� e}� K(!@��|l-�7M�!k $I_{SF�x�� =[%]AFE��< 7�  $x_p(z)bE& �$Ehrenfest'�ora�of)�"5 �ntu�&|cstppd�MSchr\"og�4ikI� �� ),� b9�.!V>U�HgN�II�le0} m� @d^2 x_p}{d z^2}=-6�i2��{�f%0(x-x_pB\\��-e/n} x}dx��,B�a�Xm\(t I_S(x) dx!t �3�t!/t�1�l�$y$�!�  iOſ�`, pIc3r�  �caPass���� y�%s bSɬ{m} )S1� ��1 6Z� q� N 2I�-x_q)b-9�"�U� 0}) yieldf�F+5ibE$?c{lAdis%'pd �>\\ 2)����2!��B; x:��y1��alI�2�6�9�Sq)!�d�6��U�.U_pb�j% �xuYz�:ڒ V(x_p%~|/I + }e�F V.m&�n�Nt2k��}.� \xi+ �x}��a�\xi F  d\xi^ a�^@�Oal. Many derivations of similar results can be found in the literature on solit>�>and solitary waves (see e.g. \cite{PerezGarcia03,Crasovan03} ?`references therein). Heret analysis is specialized for ��potential energy landscape interpreta�X. In (\ref{particle1})fself-/ac,8 term ($p=q$) -J\ined since it clearly gi�La vanishing contribuNL. Finally \begin{equ%~} \label�h2} m\frac{d^2 x_p}{d z^2}=- \�al \Phi}+ \end]!^$)=D(x_1,x_2,...,x_N)$!T!CoverallBK$ surface (& PEL)� n by8sumA?$pair-wise .Bterms: b�PEL} �= �|1}{2}\displaystyle\sum_{j=1}^{N} k DV(x_j-x_k)\text{.}:�T The dynamics along � dire)�$of propag%�! hA�Acm!�< reduced to an GensembleA%�(cles, evolvAHwith ``time'' $z$. � fluct)�s = �mediumka�@ into a random .O�@ $\Delta n$ that Q�4phenomenologic�includ�inmLmodel as a Langevin�8ce $\eta_p(z)$:b��3��N�+kZ�a�!�Pfollowing, I will tak%��$ a no-�disiz4ed white noiseJ�<��8q(z')>=S_p^2 \d!__{pq} (z-z'):f %�$3!�e l$ ``power''�!�Pbrackets denoting a s��st!� aa�gee��order. =� �sIaccount\2Sofre�Gtiv�dex�definesI� a re�MI�7Eo soft-I�. Not��at,ECyp� U;EPs, x Aa�aK�mpanied�6 a dissipa�%,!�ch, in g��4al dependent oI�$lossy mech�bm!o �D, like viscosity. Q<limit�sa�Ges% )�such a�eH4 be neglected,a)itIzbe don!TU��%�( to leave "treatm�as�an�D mplepossible�!qua�O%!agree=w�Nnumer%{� in s��VIII,Z experi8s�dConti05submitted}, support�u0is approach. �84explicit shape%$I_S$`�{re due� the � uO, nonlinear 5�; �k�� pres!( purpose aI�8Gaussian ansatz3 both!�theI\�priate, �0non-local opeYly �A.a �bea�$considered�{E� $V_0.� I_0[2 \pi�!@/(v^2+w^2)]^{1/2}E} $u^2=  $. $��aY4fun��jiAD arbitr� addie]!�tant. It�wrana�in ( >)atu�ha�.� o $ when S �� - r�9 samea�i  (``co��0sed phase'').i ��Kr   varia7 ofb�nd�vid�� measure Y��.� r  betwee��SSse}(a fixed $w$�n $u/w��at�u�e�(. Each fila���rea���B� n a�ui�ssumed�b� cus ��0>0$)����.�is�`ely att� v�2o: A�>0$. ��previou�mul�point�9� conn�zs Eh.� physx ��leA �@=)�5�  ysteL � ng class��r $s undergoi� Brown�) moAL,P �� /  cI ids,�a �f> @� (clusters ab g�-tranM�!U(a well-know process ́�Donati99,Likos01,Weeks04}). However, before Fed%�ie�fruitfu%0%� out!9$ubtle issu-Wassoc�E1 Eqs.:� 3}I+b�. �ell� )�j a nite�beraHJ�* 2c� by��pu:�&v ,iH,oscillate ar�ApceN of � mass!�equilibra+(i.e.!� � y s)T= mplia at only �n Pgy minimum does existeM(correspondsA���� ���. A!�firstA(nce, no| % Y;,0�}a!Fu� PEL,Aa�� . NA theles%Z, caseia���E�,M5�not�kd  toL - _�ily largE}" K � (9 a�to)2iIf_ ��? igi!��i� max%jobser��u(in%) is � 1 !us/ �xtension--�E ple, damp�"e �2� �)qPEL1u play o} \s��{N"i si� ��r"]��} A�w18 �Jresolva!(by��P. � catt�  l  fromx sa�)5�W,W !2��ex)atmod��8al instability,� beI��$6$i2kir waa$w$. H,Ud!jtW���2=5\mu m�`/e� �s q�an input ?�`��500 O&(  cR r%Mt��8 ��(ly employed�e* F� ccia 3,P 4nature��Iif�� two re� � a�!ll!Nc"O : $N=10) $N=30$Fprincip� y�J H4 below, is obt} up �ei�st.0w 0$, a�re� ed). In "� ]�A�9�a�c!Pn uni� ly A��ed�t $z=0!�� mutu�iJ ?6w$. �[& isA��  ��6[ad� a�al  ntitN8nu�<4w}{V_0^{3/2} m/ }�[,B� whuSA�&req $p$,eN!!soa�E�city: $�nu^� �am�of �toA"� .���re�� �4specific mater��� ular,1,mal coefficiLof �BX ��`�"tempe�); h��>f�| B|��$very robus th��1�%�'ffin�EsEn U�3 !V� � I(� (magnitudes.�� ���a�<=0.001$Ibx i �aqi��*.%�stocha�sin, dif�_�s"; DQ re�v� a�ondI er scheme����4accuracy has bg @oroughly investig��!���ed 6o!�"�es.bqiang00}�h� avalidSbwl�!8n g5 stepsdoubl���u�  of2- in mH!xsa�As��cus above, a�!*��at�� in rYdeh y, or � valentlx�� $on length 7� -$Parisi03} ��re�is�ns� ~e  der �J ity.� fig� @figN10FomAf"Hs !-!;:$trajectoriU�by ouU �sol0�� Jki(N�^,eC show�e5� )E 6P&�0t=z/[w(V_0/m)�1]ey��(8horizontal axis#For;f��AI"�ipc&a�H=�,. Converselya#.-�Ae,�"� aq��e� th�M�a8p�va�ŭe�J���. A��iBA�5���A��d�� fig.Y 30})bI)s(meanposn10}e`QA 30},��``f'''� atl v0t=t_{max}$) ��i�SS�I Vs15�% �� $��. s6� d. C�,�cera�� " �ol��ameter x A�s�b�L.�=�!�hi�� peak!�� $2$a�$3$5�Q(they spread((a broad reg� in�!�s.appear� ofq t} lAA �aUp,wo dominant 2kg*�B is eO8T�Qis�ker��s%``B� sB� ''. If QY!�a X)�.l alsomVtEO! ��how m@!��L!1 Z � .e�a�� ed,��ls�ll! SSs B�an���Q��q��� ��c%J�A,�*M� . S:�A,u��an oddm�!�*Z (w$N=21$)-`at%I�or�� ��B�B�� =o� it& at%� midd�ANQE . An opl �!_%n� ���al str%r�� 82inX0mitriev02}. %j��� } %\� Pgraphics[width=8.3cm] ' n10.eps} Z-6+1 )cap�x{F�s2����� �3ion coor{ te $t$)�sA�2���' �� valu���_� M�(��<). ���# 5 j�L3�L2:L �M�MrM30$).=L30�LuA in!�nty} j�ʊm��-eV]�3 )Q�(Color} $ine) Cross�  �s��$��=1000$ ��Z�;V ck black ], �T� �!);? t�$n��)9 �;:�l#fi=��Fi ��ɰ�a�"�J-*�henm���ɺ�\ively.&�X5!Vd�m�$!�6�t$ so �ց����e``#zed,''�c*>�N � �(th5� !á�g�Ws)6� su&p � ����7Ftamo  &UP���!u!���a �conju� gradu�QTAnced/e>��e  !est G4&�.�"xQ� &� vZ��s $f�'IS.� Stil�er82, 3} Its  !e� �en}�~!` plot*�&q�� ����A�*�*�sV= Figs&fmվbL) �4t5 P�IS fn��=���g. &$�l�!�!6 in��O#��#Y�9"!�( &q �@~� V �� 4. � 6z � f � N � v_]+��}� ei-?Vt 2{ 5 +1jA (��gy�!A;a\Fa $e_{IS}$��unitsa� $"s;� 00$Ff s&G"8 ed (E &� eis�G rG !Ez�2E6:E �F�F�EI�6FE�2nn�D REMOVED FIGURE %\�&Q���Zrse.]%�x�[�q%�V_Mrw/u$. Pa7s�d�,i^ "AP30�9��.�n& Acc]g�e-&��uE-odx ~$a,�/2�," }E�\B���u~-0IS�Yz &�(�6� na�2%*�#A )3&� !4>gc�L� �� w ����2D� �B�.�at2V� � :"2� Ss2 '�&�x"$%0 0$ (:*);��< jBe"�&� ���+�) a�atJ &�wZ��60"�"� coag{ &�,)O data���2 =-e+-UY8*�#pE$au,��*�f 2�)9x� J a��@/e�2�f�H%�1), by�!B� �J(wo"�T N/2$NE ��(Ab$$N$ even),)cx\+,arrow N^2/4$�4�:�ivg�$ f�%._-qUm�Am �=25bnI&225��3-tre.5bn�#�4�� �"e �%e sca5n0.E�n �.gesh!�!:� a�m� >;) becaus�/"��nl� nee2!y0 y&�% ob )�I| �AQ �S�r�� 2# <F}}���0�+settlI/� pho-.sa�� so-<3A��zx (G�m �"_$�3I�1u:�4Angelani00,Bro�74x00,Cavagna01,�a� a{�1dM� TS{�")f���%(w��� forc"2re zero)a0�����U�!� is"a e->�/�%er (I )AZ� 8c05pbf NAG rout�Mark 19)�* A�&m $\�!alD4/x_p�#� r;,/by r��^jus��GIS��I-o�3 $K_{GB ��G��2i l1q nega! eigen�J9 imagY!0 frequencies)"� GHes�0P�e , [see Eq�* #e� low]�5l#���"GIS; x(�=0$I�!�����3�� *���s�,�!�?*IS�on �!?�aq^M��Yhe*�AU  �r.�i*#Il-�>a�>�%but#Ezte�*  roxiW$ly  A� (on"� oA��!=s) Iin�3��� .�2� �� To�*c&dg].alP&n�jY�,a��*� �� . W�0IS����e��:"9e�'&.0.��JAG$s� �""���06ed�-� ces;�d57�, e wa#M�may e�;�&�Q�&��+M-� dU6� �E prob0*�� a*9:in�[to ge�.��_�i�au_: it% �e(!p$3 �"�:s_��� Ac�(>"� ��n<-A�ch eE�a.�$in I��s,*>is would]!a�% lete��ezA�]�)�. 5"� KGIS� ��9N�"� F s�/&6(veals(;�����!�i�ity(b =8$;i*s>>lye �i�diagram>�e �s . �.B z$�� I�*- � ^� �p0���/��$��y,�(�|orem� )R/�l�8e. �@cl�&T!�C!clarif0XsoE%i�du�2a .�!''��B�V9� �E/u �*�"�%.�, alwayA � s �,�;Kf�U��07 nfirI ZT"�$AoE -��$E��$Ae&'dueE�-� .L!'�  freedo��&C a� more?:!d h�#n��(folA�2� �j t�8� Ybecomes2^a�F�N$K9t,mA.#�!rI-�Q�N�3 :�1�1fM !es ��&t!�"�>ny,h�= 1bl!.eni�a:��TՄ . Ro-*s9%�t$!F#�?0�/�Aorganiz�"� �M7%� to� m]]$Two symmetx;Qw!�& �=r�``a6o�=U � .Pm%J�3�to �t��a1����BC�"�+ aggr� ~8�-�C ons)a��.dism� onglye%D�� g_ !- coup chaot�-pA׉� 6Z,tcS� �i$KanekoBookv� 6�xkg�y7:43�aI*1�]�,  �o(*�&��>\j;fi��1�� 6��J8�3� ��>� 6&7Na p hing'.O ard deviI�"S:�U$ �'a�pa�al�(erQ'ecIo}���ir� iO/C �)� �I"=1;  )�9�2�_e����stdE�* %R Mo�owards���� >*��i���X�.�W*� �;1%growsa<la�G>� m 2X}) up� <21 *B �B�?�-ŧ�7)6aga� chie��N��� ). �*qu_3%�'� H�mh��!~ ��0,�L1� �,Sciortino99} U�0 Lennard-Jon���2;9ss. VT2 2�I�� FD"�en*j�a �,Q��.�Ep��var<(1D � dE} �D. =A �b ) $(``uY''?&S��0 �y-%���/t. To �� 8 �effect,]". ")M�figdevpo}�� �!�re�=ve�}� "� ? �` Q+,�i1MSA��j`�y,�-H5l�3�$ٰUx. N�"� Us.� ��� �O��>l1�O:O|���O30NO��e {Vib�j4� ra�tr�Nma�es�Bvarie< i�4s Etaneouri�0 o���Togy�2"H.�>K�<as[8r8In;ti�r/os{ ncer��(�&4,��ons�/ult�0*]4�|``sound-�Uh9or�I�! ``|Sc(#AFes�F�N.\G`v=K ��E2�y,!!"�U�� i@e]$most impor�K1}, B�c �Z|H � �$Scopigno04' rJwV*%&to-�uthor�?*K9ultra-��7y %a����H�..)-9�"and, i2 %�� Y�/!"stad ``bo�!�1� >GR�"g�!at%�ide�7oa �ZO2]is bey�?� scop-�0A�bF"�I��es? �e�2b*Esuc�JheM> FalIesHal2�� �Jbl'Sg ����!�&��s�>:Q-�>�1�. VI�*fh"|Cdevelop�+\u��Op�LJ�Tl�E� �� fea�Hs>�42�W�<�H�? gges{;� �[riM��l_ >"hN!�a��field!=Ear&UC�H�+&�36v�; each�m�rR�L[Z�J top@Ps�F(e_� R�5t2�&ne�N}�Assanto0R�I;R&�ima�(�ara�.�2�7 l�Ki�Q[�e its �Cew-micr�wgK�N th �� ��$��$I(x,z) fs�����V�o2��SS� di6�ES-�z1^A�W coarse-gr{J �?H � l2Ov�[e\�M_e squaa�m�Lu�!�`F e-Fourier0�-� %n�,��8 $S(k_x,k_z)$ (�� �&nJ�k.E) Z��&�(``{�`e fac�RSJ eLiquids}n C"4Z x��#SS�Bch�# f6of)ua(Q"\Nmolecu� 6��VpC'y�'�!a$k_z$0� $z$-!�(k�``�N�[t $k_xAX@Cwor&S| d8", 2�T::�5�#-D%�E�Y�perturbse; od $2\pi/ �%)j0noteRM} \foot {��ig7I� trua�S"��K>(E� $z$("r�뙣2zA�v � !P!2�W8�q���$t`(�!ͿsA-5LHL . I �check����no sub�xJ��` �6 �%�!emoB�m&{Rl�P } �� �; �hRin-6��!���A vel �R"[(pa��e�St\\�AE�on.� �ab,�&�Pgm�>�.,6�Ex!Qo{,6�a6�a a se�Ia#, 8� E�=A� m/tZx>k_*�N$m=0,1,2Gb��a� �)$-bandLCarE�}k$ �v��1�.ii6pp!#.� ��%!�, i%=1�/s&!2 inse� �#"�.�[�co.�*�$o�2eRAV�N ato� "�Jy!g:�(*�ZprɳinPt�ct(���)Gb alua _fKR����Q�,Y� �)MV�a�"A#�?3a�Dž�s,z0�RMu1}Au�t !�a�d_ti�Q�$�0� )�bxE2�1>�B$ Pseudo-co�B�h&BSon���O"py"�"�x%oan X-)g���.TlD -M�2�. Repe�)*Z I(�E@�ܡ9$�!P��B�, sho �)�@�'fE*ed­�ŏactX+� .�()�"�� 8}. ��:�:�R=1>�>�(�(:(8�(�(8�( ��a7a>i�W6rR!$5�+geometrg-E]"2� [9jU�[�a�V�a���/gy B�of`ass�� ��eaA�beam �"�C���,�:^ndeM�}.�8�2!('nd� f�� F@ 03 �Bnt�� fer8x$>3�L sen�7� f�E!�1z��-pbh"`in per>#�"��3���(ed�a��� "�b`\J+o�VPDE<eTe� is"(I�mg 3p.X� ��!�UEp�a argu!L s. S�T*� *Z/Q.W�fQ7�i.�*��~I��,�� ��.!+(�U� �g) Ei�ZD"#��l�os�dZ"T��& Qas�YY1n�FA��ct�%{k�� �f sa U:T0&[.f` {I��d�`}aJ�r� ahd�RQ��`A�ezPA=�.�Xelsew(d�l�4�&� !46&� 1+1D!yone�"),^�U �1)^s& in l  cryst�2�Co^] &e#3}�lK�e�Z�#\i%>�-d) smas M,Litvak75,Yak"\k�� AXEW�o/tudAZ)abs�'�;ise) `!z*A1;R �HBang02, Krolikowskin: U2*a.�9�/}= BOa*�8Foch}))"�*f�h PDE1"�E�hii"�0_\zeta \psi+\��0ial_{\xi \xi} +\rho ,=0\\ -\sigmaIJ1+1=|U|^2 +A ZJ Thre6w!��* *.��D%I��9� =0.1&�2ure)����r�BJ����45$"Y' � PDE2����>�4��~�1J�3�� �^�J7&~YPDE�)e�*V`M601>�4"La���"}at�v=4$4^���a"�p� $��Q �qJ-��1�1err�/B�+�'(r��u��.+@_*@1.pFIerr�*�*�gz*�^2�O"�+TZ_� �gB]�rY-6&Y�Iv*���.XR���5� ��&u3��,o3 2]'63}�3��N[a�y(di�t�*�\R0s2P�&Kk-:�  0{bW� -[vNf$psi� ,0)=�t(-/10)^4� F�#& ~"P ? a fl �9 �,$- & �]1� g�;�A �a� s�l�T \Ol��n&Y�<�2 d� |(!1"\�� $$A=10^{-3}(.$B1Aa�M@m�2�z��'trR al�'in"Zly��atKCe.zy"1x Xed,�(2W=�?2yFm��6]y:��� I%!x!�2��)��IN.!�d!_r* 5"��>�m:(W�7H��>rR �#4t a threshold �>� . �\ figs.n�1}->�L��I#5d=CU'hot)�1�!o_o�(�]2s!��J6��'``�Azed.''*l!Ati p�9g�F^#���"4loanMHat \url{http://nlo.� .univ1.it/|,lexity.htm}}� xk,ha�"�q��7f�:_IPD�9�2re I ��^ X ' $*�8= �=4�"�N�&9 7)=]8max�}\{=zQ�m,�)|{2J F }-1\PW�&{F��X��!<a�A�9(#� �-)p<:y�&g2źFe5oBmڱ�!�u�. >Gi(err�Q|dr�m���")���.����z �.��Ki �J�+um`(�,dAKG";F12T&� :=��i J�_p/_}0,A� B! Ahnd1X7��(�}F ���U��nu�=1+��)M�6�"9 Ř��8,��, �_�n . A �opic�*�2!����Ut.�BiLN�F<�=�&�CoF�� �e basic&U is manup�to�PuŁ�5!�po�wc*A{'vED� :{of�l�W%�u4( nse laser)v" a�e�m�] . D�&!^��/"�F�Udi6k , �o�L�1he-!�inqadO� �w),0behavi:ef ��a6v*�|G�< digmA �r6�--- . +l2+T�(op�:�$,~��A�cF�z,!��&�zR JzIE to aor� "�ga>f ��i��=� , a F�!l4m�y�J��!��2i(���!a��Z�� �vene"�oU� �(est�K�!�!�Ia�c�B*>T#�a�.al�G�` "I��� n,� sn �"�}a�}>'WJ�aqby*�e*x%g��3!7~/t&=u��p sc �� I�EM[Ibeb0�So test�^or>SG@��em�f4�M�& @ma�yl%~Q�us5 ��J0�Q�5-�9ha-Qe�-U.s ��AKe�a�z&�)��.5Eg�&�0�a�� manifest%R�i�. \acJ ledg�s{�~my ple !chank L. BV , B.�i�ignani, E. Del Re, G. Ruocco, F. "�D� S. T�$�J�i!!e�5"�4%LstngaDc��ons. Am]ul!6�"�YM.&XG. �0� o madrD��(.1 &rE!�ofbqE8l�,boka@ p�Zx�1}-�a��7.} I_iblio!ny{�2 }% P.� ."�BibTeX.�the.# }{55�xp(?,fter\ifx\csn]� xlab�^ \�!x\def\$#1{#1}\fi �NGbibO font>J ؊f\#�Pf�Q$�R�@~R.$�Rurl^�url#1{ tt!O%�{URL I!'command{!\�e }[2]{#2} B!eprint []{S'} :tem[{2�H{Goldstein}(1969)}]69ir{I�}�5�{M.}~[1q=}}PC�H{journal}{J. Chem. �B.} %<bfX*$volume}{51:Cp(4 }{3728} (Zyear}{�X~b�&�h�"Weber�82�8!Vv� F.~H�]�A}�I2 and}�VI T.~A>T �ZH \praj>25}},u-<978�F=82r= Jons<and A$�seE188!= Z�j�H>/ ;}) UF!2�Ov� H.~C>4�f7lj760N7 2295�J88r8Sas�(et~al.An98)6� ", De~B�la9 and Y�}}] *98��S>e d:V� P.~G>S.�E2�YiVWi2-�:.�]��+N� e7�qN%393N�554N#9v�Bh>}charya.�9:�.(!�__�$eT,nd Zippelius!�.1�Mz� K.~K>�.C9�jkK>��>R>> Kree1j5���A>L=!?55� Euro� . Lett! ^47:���449Rv$� 5� 2000:�$�Di~LeopOo," Scala<'" A900��L>2<:�VmB���AG>� �<B�%�:F>�=Q!�F:\pr�8R 5356�f>�!�r�qSn0$�.�, �c,�,I6 Giar�yA5>�5���t�tB� ��:J'2z9�VI>>9Y!��=U=60�=�3.<3:l #�MSn-Mayor,�lisiI/ Verrocchi�f 303�e T.~S�[.� >��V>_.��BBh D�-P>�.!C��1�haf� 422:��`28J` 2003:0 Phy(# � i�O��q=}{"�B H)�fiJ� A (Am=�dam) D�0{\bf 107D}, I.,2-4 (1997)}.f .� >n ��1�6DW� �> �= > A9�VV�< b< 4[*x 1�5V�1:�6� M�!:3{"P {a}}!H ��z6�JŕA .: C<�. M�j�1RS76R� E�:�jVBoardma�,d Sukhorukov%ER!/+YQeditoBQ A.~D>�A~3bRP>R�}, eds.aX\emph&�title}{S� DrEI$Photonics}.n �(sher}{Kluwe�T4Academic Publ..w�(}{Dordrecht.�20zg4and Torruealls9v �tB> <�oW>���l�� Y&� =fS�$ger-Verlag.@5^Berlin6 �]Kivsh�grawal%[3a� :\V�YJs @~`VQG.F�� �R�O6�b�Q� PC~RYNew York.5Y>65�n #,&�a�!�C5$ #�^ ;-,vnB�"y5?�� C> ���"�%��@d�v NewvI^14��;��45.����.�4:� %,)��-e�LucUmeton!�4" ��V����V?�yV;B� �:hV=B De%� !�2>+ ��1S!uPlH���F2��@B�ߒ@J>�1�;B,-U!�%�nf*�\josabjS ^& 142J�200^f� � .<>X 6L5�zA- �~6i3�1B�`��F1ɮo ���uu� \prej�68:�� 025602(R)R�3� 5,f�b}}��b������v�on�2!�y�-� 2231�6&" ��*� !z�}.{>�5�qm �e�]#���m�m�mr�S\F�41^lv�E2�=�k6/!�=�a� �S�#.���ϡ�V�b�����2Y�V��l}��� u!5.!!I2��s"ߪj>%P^�azZ�bŴ3%=���n�BD ��Xb=2P.�n�9�.X��183902R�2�!p2@)�arXiv:`(ics/0510172n�Skupin.�>� "� rgesPe��l, Le�r, Meje� Yu, Kaspa`�, S�4Dn, Wolf, Rodriguez�9��04�B ::�VMBtB̒;U>� ��=B�-2�=B�)f�<BT Yu�85Β?E>-I�<JJ�A9�=BUm?��"ݻ.�n^ 7B#J� 0466Z�vH�n�%{Bourayouyu5�,e�)sh, Scholz, Stecklum, Eisloffe�au�(- }]d���mjfB��9�j>�25;�{�U�BW)ג�BB�M �>B�U?�?B8AsBzM�A�"���69:��B036607RBv�Segevqe2:�!,... Yariv�Fi��&L9�o)BL9:�V�B�P��.�@B[�B��.���5 !$F�� Rev�%^�92J�199v�)C�?Mw�>� , S�W,� �(Christodoul�)�-�]50��Z>�m�� S.~MB���>B�*� �< D.~N>z: H�cA59�V3��� PNASj�9� r� 5223A�J7v&HenniK�j*$A$DebailleulI Warenghem�\)�"B1 <9djBR�@2���BT��F�Mol. C�O. Liq j�37Z 631R�v�"�O.�>� %�Z� nyak)�"�]'� A.~I�.u$g9�j�YJ)/�B2�9�VgY>u����uiB@nlin.PS/0411024v2V\vQLzQ5�197>l " , Mironov� Frai"$Yunakovski /7�5AJ�- =9F�V4VJ� ��@GJ� �@��."m�:2��5�4Sov. J. PlasmaP#FbV%�GN�!�r5$Ultanir5�m#:P #!�chaelisA$i�StegemaL /��EJ� >9��VD>4M��?B� �1\5��'-�j�GJX9!3F��p.-�25VRv� Fle� n�%? gee�Efremidi1 C6F �6�� J.~W>a@��B�� 2EVNJ�0�}2�9VT] M:B&N��<^��)�M14V vKhaykov�=j &!R�R(eck, Ferrarl; ourd�Cubizol�� Carr2.�pe� �omC!T�A B�>9�jlB� Ē=B� ��=T>t-,�=B�9`�@LJ�(!��=BbC%���B�SaM ASF�S��cn�296:�q 290�` StA��U�620BG$�DPartridge, Truscot8_nd Hulet�.�� K.~E>?:�Vt G.~B>A��BN] �A����9�V�RJ� -!BF���j�.1Z>515��B�>�!.�'�6�!#��B99Zj�B�"?��B�"`V�z�49` ���m�07390Κv�!l Mitchell�7�* 97}~�AJY =ֻ* D.~J>d�Z:��7^�53R6>97r� Perez-_�.�>8.(!�KonotopE� ?-Ripoll��.��5VJ$ < �:(V8 V.~V>i �@��J%�M�::�*U "k *�E@^� 6�(��m430V�z�7ang.�>� �;o�`!� Wyll�$and Rasmus�>}].��OB�ang9pj�B4/*%a�AB� ��l)�%�5�=!,��5�~�&Z�$1V~3v�=#.�>�'�!�D, Nikolov, Neshev,5��i�Edmundsq Y.����%��NNJ �MB�)&�<f��d�)ZR�2Tq�k M�Mj�3�2j�2 LondS#UK zH �% 1986�a)6ion}{2�E,�)>tF-G.|�(Vekslerchik*4&��� BG;?��MԺ�BU.�6U�~�Z, 06180V�-v.C��.�B2 $a�Kartash��Mihal ~,�6n����6C]k��L.-BTF�::Vo YNo ��BB��?B�To!#�<B�-W��‡F�6�!�u��E� 4661V" v��Mt&:19B�E ", Glotze� oole, KobMu limp�4 /��EB� :��SJ�H ��@PJ�JՒ>F�ob�'SP EUa9N�#�&R.y 3107�R>�!�rXХ��<0 lrMCJ <:bU�! ics R\n�7340�.�26V�v�>W1���Weitz�M�� EJ<�QDJ� �fnK,8� J. 0957Z�vr Q�%1Habib%10� q��B R�.B�+ �f+n V|743��DDD�.�>�$,��P2Sh�ar�&�~SJ�?:b�BE� MI���} B��Se�:a Bj�31d �?f 13�J&�ME��P (198� ι��VD�C��5*A�?B!F�VT�'QB'Q�Fu-;240^(QvI�H��* �,Bk( ;:�U$M�/&Mern/5'OJ%4Z�v.�D�.�9p1�5U�i0Y�!�j�B: ;^�w#��$-mat/03012�SR�32�8�j�3Ka/�E�Tsudaڥ� ��ABT; <��B�J ��(RK Comp�^S�rs: Chao��B<�eq&�f?C�2l,Cy<�M"�M��[ :�"%= ��T$ gliae#�C J��-/v� �� *� B�J���u�z 8a�7�� 3214�� ��5�20B#$�*8P&�PBar]Tsutsu� ssard $Yannopoulo�"M�@ FR���B01��AB�R�\�< A.~QJ� %)�AB� -]�=B�B)�� B�,2�A��9�J02550J�.A�r� �N.�1:g #w�-�=O�� �=O�=O�=O�=O=O~�^0855Z6vu Boyd�Y Si{w~lN<7EmeVT heby6hw Methon�DVqYj"I1ں yS��Gr�wu198>_Z #aSt��Vd�� Honerkamp�s *��[B� ;-J�o.�B2 .V BM����zJ. Stat.�+f%#^�^9JDI!���endB�a �}doc�} J�%\"e$[12pt,onec_ n,amsmath,symb]{revtex<(usepackage{WbicxaB�T��N{E*��Co*���b�RCharge�O��#ja+duP���2la F � e In�cle�} de D��} \)�|,ay M. Zubarei\Olga Va�bPmail{nick@ami.uran.ru�affilV� {Institut%SE y�=, UgB��h��� BuP"$s,\\ 106 A�ena,eet, 6yO 6 EkH�nburgI!�(�abs���jڵ�Fde�}ia�e=o2z�5o&p s.l� -l�ii���ta��!fd�l@��j9�3m%.��ana��K�stabl�P��t��is <Pfc�aѤa5�fo�nQj{t�a g0Nive capq����tA[.� 4 �lay�����th�qch wa�v�,y Kinnersley�i� �%ed��ctAP��5u��2&m�.[� � �d|�KuXe0 ex~�ngZ��f�tuӌ"�l%8\y �mm�j. �$Y; \makee� As!��gn,�uM)-B�fo�h a su��l~}� �icp� �� unEe �B{1}-JΛ���:�lCoulomb ��qa�i1� g�Qdiliķ��.�tor��tB��mbilaws g�@e>�g.�lw)J�tis6��U� ��!y!5dku�b-���jensAi 0jseWc�s9�ie.S� q�is�n�j c�wh)ZMq turn�lke� a�a"���UOf? � �`��])B� . P��ly-�2, 9�exa2+w�n.* �b�A�!~ acB� ��� homo�x�xiiQ����jl����y��)�9FG e��e�%�si�*�r���ll l۸di���2��CZ�� "/�%J��based��U�ef���CpA�2.�p�jpr�E 6EȢ=JF deep�ll- a��9 &&�CrL��k 1957A�E�*|e"&�fo)� two-.a|&��-�6�aE.hydro�ncurrent"�~A t�-|���d�l!"On@v�l.�va� aper��demon�~t�n�wby����!ba�����!����l!Z���o� 7r �AM\��k:�,.Na�"�pZ�)|yˍAc� uct >�-f ��)p:����Жof�ite��)�2�vA��js�f͗in l976!k���N4};!���osݑd�T&���r��r6�!�v�U \CrowdX5�GNow w��ll Q�w}�f]�*u E�.� �-OF��"u� ��!���o-zde� $d\�a ydik~ce $U$.�%�&Vӡ- Mic Fpst=thA baF��5lof $y$��o��Cartesia=�%�t��Hcun�ed��a�) b!�� < hho"��̡�$$y\!=\!-d$8%Vp��hpa�(�~�Yd) �!+Ytt� P0$�@�%sGapwE!���hplanar 3���A�n&�r�1� a}o=��V E$ �)�I�fun�q $h�x)$Ŏin� bl"�&E�eiodic�iK ��obe��AUw $d)HX\!\lambda^{-1}\!\int_0^ ԉx)\,dx$� ��2Vx�pewi� ��C��� is teY@ Lapl!ܱ� $$0�_{xx}+�_{yy}=0,  ���J,together wit�h the boundary conditions $$ \Phi=0, \qquad y=0, $$U\eta(x).`The equilibrium relief oflliquids)� substitu�AZ�mI)An}$, $ c. d. sd.' 4nd}$ ar��,Jacobi ellip��q�s; $Ee�A� incomplet�� *At gralaI��kind; $k8moduluqlf <-'I��f1-k^2}? u ment�? M; $-�9 p/(2����^2)��h�w�dim�onlessͦu[�[,�\ps:� a�.� co��57. O�d��ͯ,d �$ acquir�: value $uv�U$, s�~a��*SW@u$Ւ _un� .� ��Epa���m�% play�� role of�� ,er�-mm8figure} \includAphics{F$.eps} \cap��{\label5:9$One periodATa Fon!�profil�R!� free��!�du= 1{0for $k = 0.2$)�$u = 1.8$. � (curves show%UZs5UE3, 0.69, 1.25$. }i�� ItSuld be�. ed t1�.~con4��s � charged� were��viously studied only in a weakly nonlinear limit, w� w wl�< bas � *6z%�9"�. I)�$hydrodynam oblej maina& trolq�er A!]6n ;�our�, �oY is&� x mo phy�� � �e� �co:�)o!�y�1ce $Ui���A*�!oE, $d$.� lat�quAty doesa�"� ly e� K�Qe2� At5^!�>�E)0can be calcul�  u"y a6ula�&� 4d=-\lambda^{-1y !\!\int\e�,s_{0}^{4K(k) �.(x_��\,y�) |_{�=u}\,d$BDConvenH A�m�s�racteriz��!\�ar��a�d FM��� �j 2\�}{c �b k)-K � �F� (�$$)� $E(k �"�A ���� *�, � ectively)�-u�!�A|�3perturbimB�A �1}{"= (.(y_{\max}- in} �2�= .�  k9"E sc}(u� B�Ex�[1� iq , $k')&�U y.?p$ �wrel� s (3)-(5)>� depend7� e�銡-=5 $A$ �e�h $M � �]z(�o� .�y�* Z� ). A�P�u�, ��is bey� he f� work2short��mu��, will ł u��zy�Nli� AC%i� ed y5��Ql@their�bil��uto� te cria�a. growth�.�s1h%U�of0�mdes. ���sup��ed����PresidZgr�l(project no. MK-2149029942),��FY!*�S \� Russian S�ce�$ "Dynasty".9of NoV merc�Programs�n2 e I��nh al C�� of B� P�r s (Moscow� q�thebibliQphy}{}�@ibitem{1} Ya. I. Frenkel', Zh. Eksp. Teor. Fiz. 6, 347 (1936). \B\2} N. M. Zubarev, Pis'maG Tekh A25 (2�<79 (1999) [Tech.�8. Lett. 25, 920 "].i3BiR�116, 199D [JETP 8� 078NZ4} W.*x, J. Fl�M�77, 22�76�45} D. G. Crowd :No (Sci. 9, 615 x.�<6} L. P. Gor'kove D%L�Chernikova, Dokl. Akad. Nauk SSSR 228, 82� [Sov1K 2$21, 328 (1�2K07} V. B. Shik: nd Yu�M��$kha, Two-D) al C� S�sa;Hel�(�a, I|!~89) [in m2}8}zP!�iderer, Em NizkA~(mp. 23, 624�97%@�>� x docu"} �g\�>class[aps,prl,twocolumn,groupedaddress]{revtex4} \usepackage{gr� xe9GWDtitle{\bf Sympathe: cool��4of $^4$He$^+$ �!q� radiofrequency trap} \author{B. Roth, U. Fr\"{o}hlich,E#(S. Schiller3ffili�{\it In�( f\"{u}r ExF!�Germany!) abstA } \noi�6t We h�gener 8Coulomb crystalR ul9 old R/l� J6,� s9zB%z(via laser--!�ed $^9$B%� . St� � ai�up��<$150$ localized .�4at $\sim$20 mK���8. Ensembles or  le�2Hopen up � rest0 pers� � per> AMpreci test%8(QED and mea�!� nucl!2i� o�$also indick� feasi�ofU-'l high��ato` A� � 9i asIant� ]# makee> %*�]l�two-bodyUgm i3� ( most funda!3ala�� s�� b$ cent��develop6�S $um mechani>R vis�J !QQED1�{� _ � � �s` prov�an al��  method�I$e"��Mksizes �H!�@}. Hydrogen--liker�b��T gen ;�ir��Z7e�ZEs l�r thaa0u�. Alsoe���.Z�* Aus2O agree�# �a�!o%�sit�����6u�e*3  �hy� ine�&uctSof.�"5M�#thpA7�&ic 1\,S�undO&"2 exci�state ��hyp| 3He}��e y� )� < 4in=)��6edue �,taneous emisa an�/ ropyIF0170 kHz uncer* ty�Y��ar�%eQJ2DmtWijngaarden2000,Jentschura2004 �ii/)� squ]"' -�*5r�0.4\% l� ��%��op�!&neu� ���FP )� Shin��2�A ���ou t� t�s w�-be�ye�� a� --re7 � .�a��?���not� A�8ormed so far. M: A�E{-I,�zEq- 3Ax< photon Z� (at 61\,n� 328 ,I%� 4widths 167\,Hzb16\,MHz>thc prop�M)PUdem,Burrows}. For ex� e, a2�mg� j reason 2�.�$< 30$\,A�)����#��ar�!,� �rovA�heU�QED�e�"s aňirN�#�bcyI� IE 2�m�2��#a simil�Ŵcy �im��5 Em;��ar.�" &�an order< magn�A��&� aE�a5I�fu�< A�9s��ll!G� ���ped*2�i�(to minimizeLe&� infl=e�4Doppler broade� or �� to�a ���udeY� a� effects�beri�A^��c8 f ic��ckm @} suca���(approachM$FSFSM2001}!i&/��&�w  ��a0��dan "> se(u�Cw"� rapp� I#s"V ��forwar�,a Paul--type� �(Major1968},��i�'re��� t. Dir8�L�{appearsAV) a6� , si�A5g0 �.i�l�inuous--�, deep--UV 30���( isi'hal��puAe itself. A6M� flex�C G*d (�a�')r��� '')�''\ic f o9peF V o�byRe5!�d%9b "(often&�  ing)_an� � es�Yn mutu�te �A�!�7 was IYdem�  NE�in PeneUAC�NIST1,2}��CE82,@Raizenetal92,Waki (Bowe99}. Un��~�v mixed--1:5)��!�N �W2� l* !a| Js a�g�ass rA;$ range $m_�$/ lc}$@0.6C+ ]aA !�edEEE�"~%K���� achie�X� Hornekaer�ais00}. R mole�� s simu��xşa3F�un�%� d* to a� �of 0.3K�#� le�H�*!�02,� 2003��<a�V1� exh|d J|8-Barrett \�-"�wV�A�&f ���ui���p%�%�ing� ,)�qY to�Q� 0.446�We� a ar ,rupol�=to��ultl �$ ore �E2*Za� 9is en=%��8,-high vacuum��mber kep I�w�+� �� �n�!��${^2}S_%�(F=2)$�2� a$ !P_�5$IG� at 313 nm�Uemplo�( ubly\isum9� g&d (SFG)Awo�' id--K/sourc�aQM7` ed Nd:YAG +(532 nm'0a Ti:Sapphire " at 760 nm�a btie*5d &c�+� ���LBO� � Schnitz I�2�C+mas* ˡ*is y\��'*�*of&� 8 iodine. By sla��%�SFG�M�By lock��A�. 0 �,N2�Q'��R�� AOM�/c{�-,�j��z�� setup�&hifH0UVY$E���  �S40 MHz) le main5�b�e?-\�5Whs7 � � is switch�.ff)!�i� tu� �8exceeds 16 GHz.�output*�� 100 mW� �m. S"g:� �=�i$,a�/R4-� meta�l�'u��� :�1)�md A�is pop� remvuG! repum�l�   detu� by 1.250!, p�f�+an�2oo�3'*at�&To "`A��o!�iE&�Z! l�q�i���usu �wo couo�ag i} beam[ he�fluoresci� &% rec�dE���G i��,a CCD camera6�Our@/!ced�\"T0s:T,�loaM !�p p���b�aa��ga -�:� at g):%�i8.� TP"1n�ca 750 eV1�U.am crosA%�Ņce!bA8e�A��!Da8rol��͸�al���Ρt�.�; yM  y. Af�E +mA7H�� Vto droB$ initvM,1� 2 .�io) ��s evapo�"#Beb n)�esam"� n Aa . Du�D�~!��.q��iRe��� %;�s�cana_� a 5a_%rva�i��ce. If "� ,�� s--s%Oil6�<%�A�"� ek+�!impur$,%�Fprior�h:�.a�f endE�ada�yic.�&c-$V_{DC}$O!� until$a$y� ($aV G D� J > Junwant��li� tJ\F����1us,��=�p!�of�I ��k.`A0�ooo%� preva&d��<well--k<ign�r�\�;��".f+s#�^sma!67ed1��ta����2,of a sudden e "N%tec!+2�T�W re� 9Q|3�A����&. Onc!}&_ s�`-(��& ;#h<�"����q!��x. hal�@ natu�Qw  (6,)%JEm�}6�A�p�!�M�i��Sja9los{lf$�$�$3 h.��)�5 }[t] \�<� �%�* s[he�`=7.5cm]�8_1.�8-�8 �8BeHe_Kri�) l_c}ŋimage�womponent ��(ɶ�Ugitime:�Ls). (a): spheroidal -���2� fic0_ "�Ba a semiaxe�D$R/L=0.16$. (b,c): RkF k�> darkj!e%�� A�rA$2*, $30$!!$5$>�BT*6 r� Y$z, ( horizontal� (a,c�7a�A�I�� FR mG!��(b)��$�G.�?s2 �d� a&6@TPe� � %?k6���ay�}s.JM�* Fig.M8BXsho� p#�9� 6^�M 5�!mtan�+ �+displa�2���#st�!@�W E E� orig�t�;/>r��^/��a�N a.(er��--taDh2# e#$� a� �+:��irn �  on"� du"uqer� ��"(�I$Q^2/m$%�a!� ongl6,*�\gg"�$)� � �mI$�'�!�H�-� $, see Eq.(E&}). L(b$ \,a �3tak! anaC� !|me�B�)$jOb,c|�4c�+�A&Gxadd��o�to mak�t�� �zp�� ] m9vi�;%� He turn�T � Q�:o� $oid, squee"�8M��;a �,at 45$^\circ" obs� e�+j Froe�0"�#i^* 2n!� s�;�feA�or no.�� 'Dip)ontenbehin� --M)%sVF�d�B[ : ��-e +uDGX=&��1A��0�� mode�!Turner,:�x"1� nu�W/r�0�y��st4e(�#�IF� (MD)M%��( vary0� pc&� )�ed���re� qh��t le&��O/may�xn��!F� id)?�^Fy�E���F ${n��4\epsilon_0 V^2� m&� _0^4$��� $$3.1 &�$4$/mm$^{3}�ʼnl), toge -)�m-% d diC�-�AMD��ach!-beR=su�'. I�?�c� o �N9�uad� -us detai�1c��%�T es ?�'� E�ed ��}'ib�)��� A�"�#�,a�M "c%MD2[m�M�|.j0a�i�iI:# s);ly $6.2)�10^3$-�e�e�150.�i��l;陁l^ � dHV,s 29\,$\mu$m:is~i�s ��)�!re/!2cxe� nf�ea�narsma"0,, $1.48\,(3/ J E��3A�29��Ac�ing1�*�� 2�"Lr�zig--zag�1 %� :ka�a� third��-��;tDh spacA�u;4'�z���W (&H�6� .�A���5 �Ira�iT=�����er-�BF)> !�e *� A "� i.3 ��  ��aA�� E{. Embe��t  q�3in5!ix*�of Cai%E�Mg ��yD both; P� � ed� "�!�!2=A!�&�3w� o rou�5�3%B���p�8�l.�1 ��:ٖ ��ny"N$A���O2�Em+*k s $9 r}_ih �A % cc" �u�(/W=A�eOC&�H� ��[s $Q w E}() = \*a " $. Con��w&�smo�-�@�ARhosen� �/ly��ach�Nany!C| i 2 WA�sum!�; � >� holds M��>r"�G. Appl��$Gauss' law�Cto�6%  $Q_e$ � yc_P�givR&*=.` _e \Delta">/Q$�� $V_e�)yC;G%�"� f�8a&���$�+}2�4$ m6� r})={.$? LaplacL?e�"�- �*F � d�9hoA"?:m/Q = VQ�%a!%w-�U3n�J `���Aڡ_5i ! )simpl��"^� ";" _e=\�!R�nA�!� tA�� ier& m%!gr]��a *�# cO *� ��'on�K�a);1�� Der 5Y7��6�--�2in ,� >�� (�us�"�}�eq 35�Cu$m) T xten� �enټ`�(Q$խ2.2 mh�� ���10��� ? !� mad�-&� In�-to �ztifI�s&-(.,a� l� Xv'� ed�%dy8�*�.��2�14�!(s�()$#�(�-�%p����Qd� A��Two�\roH n{)( ac voltage!;!(1\,V "$/EB!�y�#&7by *K .�& $\>#{ext}/�$!3�* V�w� !�:��Pe��[Eon �s � gy�>-�; � AH(erS(?v3UAE��a�. TA� lead�%2�i��9lUn�("�W8%Jh Jse �"8� pt�/m maxi|+ ing � ��e�6F*�: u&!q��I�H-upm by"%� -j<%>�-�laio1�E�feraHpo@s� Bi�f12&g2Fg*f-�}P�$>Co2]A (-W-��&� �)e lb):�lJ'Zng���o"�3al�Da #S!=m�.�Y.J3. (c):- � ac�aMS� th� ��O�$a�}* . (dB�J�A#tru ime �I�Rb)e�(c,N5" G<y 9�rCward incv4!,�� �}515���BrgB�a� 5 �"(a �)9(c)��s. In�R?A�1 x�1� f� -� (u�� 283 kHz r-� (685a�'!mer� �n q.c&N� A5271?�.gar�<� ^"&>IwARicQ � ){6�).=� *Q �#��aes�%ce peak"��"�5 �(61)� "��spr�/m _c/od"lq1�U3u rn � AYl*a<� erty�D�8)>)�� A22$Y)�p�EM/5C- 6�nY\ty F9 )W r.A�hsharp-�ֽ�%Pi"uF�Y(c� (>� ` ��a �ӥ�"v�!nN�cyQ ��Ij �dT���6m�Wly ����R*�Hg. "� m�}\,c,�N�b�aUp�#=� 5�8e>*&,Q0Y�F L�P)�T� k,R!ies rem!�� efN� did b:a�a6� . Nota���tD�  de�-��u]�Rv �>�9 �. Nev3�&g'2;%Q�FA�fi�� P-A�essWy�,l�1I� �c+q�_-��@eGA5ay�;?Dai~by��m?AP tem�.!�or�d micro.�D� �:�5 v�2 �N7! ! (-� -�"�B�,~&&� $$�t5!� o}on? �&�&"9"W-aa�(���is�P��J�m &O)w�$io:�?A�% qu� o�?cerE�V� P� ir� i!�9�; sAZg&�9n s�))�answer� )f.� om?{24}$� eI%t!�7$^{40}$21��J per �.!�45 mK, d#!:��$.r d.sw�"f[6I�/%Y.>� MwY#-- � ($<$1 mK)a���06�5:W���pa�$��e I=�A"!�gI)Z� ,o� 2�i rmala�i�NeTe��Dq� + ]&-?:�6T�an&vi�2=.F�*"�5�.%o@& �.�lI$0 : uA(�0%N��� N� �.�� alE5��p0ir67!r�<���+ t �N  !gA`"�9MiXs*�,2v)OU�WnS$d�(U&< � , we $aQ(priate Voig�of�-to�6poi�Ic+6�]1"o-��=�@I���si000�)����R���Q�݆�!42\,mK�.�Me=N�4ab�.�e�-]!�spotsiM2�; �w� tOeQq4<Oa�A}NW%5r�/I��{H=malq^m���� .is w6� I�mmary%f\B�8��A��c"�:A�$!sj.I�u� ؅`��e'ar&�<. L� >|� D# 6�1*R�� boutG&�", a. ��F�'90�3�  � 6�c 0.44�hf$:�!!��st ac�<��� ��" 7.�M��#6� at bv,2{Q.2,TY��� lakd immo�1>Mk�8mig �f &�B�"[M��ma  ms .a�Q��PD � -��`.�D���4in1�[Lb!%+Ŷ�w �� nois&'1�$ inglF$jaA]���a "quan�Psensor",V&h��Iby����; = ts2 $ Wineland}��g�L{ g/��d��A>�>Blinov,:6or :�vA9�KSs�2B@Ss}G|#A collESs| h�Ht�=Pgo"��HH$�U�#esR[osrN in^4q����9a(8u&GO�QYKarshD($&�C/*ES���oASy ��s ����Se�A���g3�:�e�T%�AY AYa6h(dR(F (HCAI). F�;�5$q$��$/ aO"�Fn�%NX(,�'\,B�',8tee �y�a�=�9.;-x#r��" >s�Je:�< �'exZ l.cagű x, �%&o�i�[�"5.��62Cw�9�6�� ank�Deu�Jhe Forschungsgemeinschaft (D�8��EU netFDHPRN-CT-2002-00290%+�\�\��\tef�r,o D. Leibfri? ormGp sugg��o!,H<nzNt6,� S. E�enboim+discu3L)in�of:�E���$dx �WE�&> �!{i~a}. �(V�t>]123�Xi]U See,�, {YY�P��q�of�p�j��]%s}, S.G6,$et al., ed�eSp�Per, 2001); M.I. Eides m /}{em"]Rep.}� ( 342}, 63 (@.V\6�TJ.�\w=spy NJ.�2^. BQ}, R9NQ�T!-,V.M. Shabaevn�vAxtt�$86}, 3959 �ERrePcnceJP(g.�CU��6m {.:m9! 093002o42$R�T�} B. d auvoir B:k Eur.-2 J. D)�1d61`02`*�O H.A�[ uess�$ELV�v1+187}. 4^(69); M.H. P�4 , E.C. WaG%:-�A 1!p68] 77);e�a��Lyd->�, VA�Iva�`>�]9}, 13�22�:�O } A. van 6>� b�$63}, 01250A`0:j:DP UA�4, G.W.F. Drake � Can.!�e n8!�10i6-�O DA� iner6�%& L R>�7aW 3553!�952) UdemA� L.~FQ r>�NPL��cCBTLMMv1}%v�6 T.W. H\"a�7�:iv.Z/&�c2NRO SA� 6� i!� em L9] Sp�t copy-)1� R. B9:=��World�`dfic`992��N}CO&�*y�B 9 A"  L $\,$6">* 4$\,[PR1.[=7:=� Y62004,�,2C91�?��� � �8:[awfQ fQ� � �*�Ts somewless &XE |a b L� v:sU? ,R$_{\infty}$.��tR E� 0.3FS�N�� Proc�D� 6th �`. Freq\_nda* Me�;ogy, �bill�. J)�2)&jN F��, H DehmeltB�Q�70}, 91az682V�L,1} R.~Drulli�J� Appl��(} \textbf{2�*365X86�X(2} D.~LarsoaKitb��dY57}, 70X6ed.=M} M.~ N��ԅ�Y A 45.493]96cW"�M} I.~vY>�P 2007J]�M P.~ �Y��207%�:B"1+")M L.~ ${\ae}r, Ph� ! , Aarhus �b.�A6�.�L} T.~ r�iewMmխ07}, 013415(8)g32{2G *�c@, C. L\"ammerzahl^�k8�53406 6h.E M.D.~ ^��KRe2� Q� l423N 6l*�DF NliTO�As)= {41}E�00%26�6Z3 eo�4:asubm.^ .�Tu�3E7Tu 2qF�<syD3�M1Th872�Itaer00M Q�JVy�>J"  1994%12g"g D.J.~:ain�͹�0, pp. 361-368.o} B.~}:O5Hv�^040304(RI�6�4A�G.~ @b�R�g%d&�g:j��g� ]{revtex46�gamsmath6=x(set�*{\uni }{1cmDrenewcommand{\topfg&}{1.0}/ 2!ext"0"8 \def\Be+{$^{9}�x Be}^{+}$} H 4 H6Mg<2Mg2=Ca40 >Calj�hE�xso�=� C6�a L�1 R6�hT2�hU.~Fr\m�,A��h-S.~�#z�huV�h >H�h e.�hat�hu:�h:"�h<%\date{20 August��4!�)1a&�hv�0{0.2cm}\�*Z�Bbreak�e -�Ql="�  � &:�� ar rfCpo a�N-a;s?�i"�8atY<.s� +%ul)2�wh�>\3predic3�\cGliEG�"�&�M"�:�6on&�Af�. good &_-b�+Bp�9.���9 �K �gmix�!|-: � :cxYXp�!M�!ufly k*�> *�S9�-�8spaFclg � �. 6F��Yd \[<t�} On.�plasmaD�&�td0i�7nt �n! �/� past,&D+yvre$#���8��rA�at <-b�J�^d u�Wa�.tE�&��  ak de�a!Y�ru9�2o w. D9�e,Z y sis,�(E by�ar"(W.;�u2 �iiJ�_�@Davidson, Dubin19�X\\ To|/c1c!,�!#ule?5w�z�in 8Y-�#PM[tyL[ �"*�-Lva�$ O4�/O&�]A�)�+�yAe]�cw"9$�l[8!+e�E�w-S�h"Ymhh�-&-'.a&��Z�K�#�-r�o%[e"1$�%A�L�U $\Gamma=n@U9&�3 a k_B T$���average`'est-n�Dbor1� energy�G$:.)9l�e9�3$:��)AU0�..>�"oaH/:� show�a`M#�&o�W��, i.e. YI1�cqgM�� -\geq2 *it'go"-a��a?i2N�K-g >�& ]� �Q f>170$mS�ery1980}�7: AXU )�s.F�EinUPbolic ~Walu 1987�kl=a( (rf)Arp(� 1992,Drew��1998})lblof�} �`cu& �x0�mLythy1us�o <�% 4���o memo�3X% Luki�dla�CA2EUvA�i>;&�8>Vlo�[�� b Berkc�,` �q 2003"8�R2�"t�_ .'gas�e�/ bs.'ly& $EEa F�a is i sc��u� Deby!�nZ$y_D=(k_BT}�/nQ^2==�"�x�n��=at�Fa�r&t� k ivid�^q�s�>ak��M> H 1Y]�T� , $n"�8I�@!N�)2. �Q�$!M�[h�E�b���6�'G���T ���neglig�`~7d�8. local fuZ�$!�*x�ji�a&�9"� �Whas a[:m9.V.��!L"���J�A� s in�5F�%{� ��*!�6� i%a� FW�c�$WAUs�Z� � Q��:d (�P�e c��a��)�s�Q%M��paper),aVc"�<�c�1��r�:"m: bQ):�oQ16�eN) �l9�I!���l� r-��--�2�/E�who��A9 �b-��+R= aris w��] ٖaT]-tm\al ����<:�.��VN� ,G= -�7 �Fs ( a� f reh�XM�a�P�$* q=2(]R�a�` ^{2}) ll 1 ��"gsN1A���F (��a)� be ad�1t��B� IA��u��9�_�: (p_) $>fB$)= m\sum\ol_{i�x /2$m��196��w#Hal jioH � +>XFb�� so-A��=.o2 $r_0�V%)�Xu:�ce"� ~Wd"|B� 1]E6� al}I � z}$)�A^nsxA�nd ":y/�- $ �2&� i.R$T$|2r`;ed,maR[cop3Xh��0id�/C-  $n_{f"ZG)Tu:�,�9�`"p��(-�@*"�� p+A�.xg � :. A|f�z�Z!~!�al tύ�~A\�*lgl�c��j5 ltra;)\!�en $T\?arb�CI!�ix4s/.�z+�I-r���'� "�no�)!�;�y �!���How�6,!� very�/.��* �&���9IR, buti�0�!a�okof �D�Ma fai!g� W,e �^r� Q3�=.�Kp%��4� &(� in�#'Z2Wit&X ;o���!� as f�js�2)ou�2�F*j!�o,8A�v3s e�am(&t �F���:d %fis ! 3 o#s 1j7.o�umzC &hk&Z ( DC}=0$)2� �I!.e&�&1!r@Ji�!�*� neM[�Ca"p�F3� Ojd*&VpacF� $\phi6��M���ceI�""6 : $QBH+6J J��tR //:{f�Ll0� Poisson'sa�� �2�= ("� {0}/)> Kuy}}�uI�x�u .��^��=�)��z� �!hl, A�. �\i�i�=EuA�:=e��5 halfjN$LIf��ajs �5)�)��EduncoO �82E�M|� �a$. �<'8+> �.0};N4""�I�G -�M&q .�a>�C Nie� 14al ?%� �,&�by *;N end-cap�+%��x!y."�F'RF�D>��~�h�`u��� � �\� fu ;Oói*�y�R=: �# �&"�;���w7erQF:G �P0}=4.32�Q�m�a>��s to $366k�a"�nPy.P NP $1041Zv�wo.�qJ� nNzD be �"�-K}8�T��A��ne�Y�au�n��berylf�&#�tom!yovl�A7o�mqpE�ce,"Q"ronacta�)�W{�iA�9o�LAhotV�Pu���X]s01YK�Nw&[2�bEser��5 E�3139nm�5��$f�Ll�� derw�Oa�XE^ie�\ ����t�a2^� few mK. A2��aall-so�v�e ��&�Vi�IS"qv�5�8%a9?1O�,+CCD c�r%��W�����.[Z�l �*Saz L|.�F5�7eq 2.0"�73$�,!y�$!U�c��I?�D��ai�in6�~(a9"�a� &�%���*U+�*S�$k�@�"KB(e��N# �"�w&�e/ Wenz}h5= 3 Ж:d�co�5� �\Aj0d�o*aXB�owidth=5.>�o"�o!�fg#qV%�1OK*a��VW7[ perp�]�!��!f]a�%wat Fqj�<�nJ� � Da�Ones: f�FofQ"7 �6458L�h���^�.A&:~=h b1  $*�"�A2O�w!""Q� L �?��� u4"�2��45}/L�17ש(b)-(e):19� �R�A��%�!�M �*�$ �6c�x} �$�Di: ��&z �'��expand�!!�A&=aJ��5�'i�YK.���� m*�{F3b�_.��=etA�1.8!C, 2 c), 3.6dZ>� (e)�U* .YI !%�sr93$ ^0.235�Y, 0.309b[ 0.413Y�� a deh.�\��E.5h% 4A�Do�$of6M�$.�sfig��l2�f�u7c6t2�\%{rev_6R�s_new ���)iR���t"!EU��x� r% M0�d���w%�EQ��&4��-.-.�&սK�.GU�"&z/�yJ�t�,&a�A�49J&�� &� y. Full ��s::U2�&"�. OL�$(gray) cir�X: s4 (medium-size)11 O6�s-M}. Dot [ :QU!~J�aC6-�0-)��"�"&�,)�cl&�23A�o=-N {z}/Kry ,eBy}/2"-y I�':�� ss-s��V�ar)o!��..�(. O���n��by]aEqZ:DII�j re��!/-q�!DV�2��a*P�t�c��� is��L�N� s to��ɜA��f1���)�"�& iV�6�("r!�a. A8�behav�{1-c7�"9#���� ��chH &� g :aV!�W >V|of on23N+)��.'�� Iz{Fj� �%we�� 7 M�5��p�4sm� D�n I �\hundred*SalwaysQ:��� le�()���Xp��ofQD:q| dgI�1`�""�r9N�vG�ual�N,!�O�)� �.$1a� 9 , pu� to�: �k )���O[�:<�E�^.�.��E }rgu�R��d�dx!�"�isU�T I�A7aY"bove:a �u�>"ɃJ+ �A�� I reKa� i�� ���lErnoe) �ost(W=I���� zQsj? +bu�beez)uy z�.�0� E ��o���;'� *> !�Ag�A.�� f y$K .�i� %{�ach���9v.:� q )�� ����24e)oi!Ŵ45}=[��+= )/2]��� �l���i:�s�d&1�y�8s-j devi%��"� e; w <ibu*�]laP�1!V�5uri�of &Reri��4i�loI�dc�r� il%���y-I��qy-���a!��"ausE_�;ltU������ felt�H:�A�m�`�')�E<@Z� �n�oto matc�# frag[()leP&@�st=hexi(W:��a�](�E-�.\\6gQ-�H,�Y' .�%z ^5 w�e � ]V *n{�-���oex;Uor9 �?%�"�PAtr%�����%�hrQV0�:&��rb+c�2k# +���U�*����2] �E�!�ted-l*�$beE��� ɴstI.sa�dR"� x$,6�;I����]$l=Q�},f.�@�inu�/�3p��nnC)A1��*� <o��/"R<2L hange�ZM|"�2L$6�s 3d��acT�a� set��s <.oto&� to $83\%$Er ����va:en j���DL 0@��JThe6�2 �K�H�MVa �$84� I ��(a��n�B yń!ZAmE_!���+TA]for�� atIy�$=p �uN1��!start� I��oϠ&��L&�E E^�Vag �_d��� �&eC*B 2U�1 �Afs ����!6�\\ �&�Co2�l� �9ly�?2S,�%���� .�*B�� �-9���%�s e!oZ  �*N]ehowNZ�q�����2F"7 -(d)���(� �]20����d:���--; &�g�nf�A�RVFI � "}@a �l��%�,6/2��!-h"@.� eE�Q. CCDu�xpo�.� ��C;-�t� roz2on�uaWAa�� au��A�)��"� a"+�s�i"W�*d~ | m�upe�� �it}��+ire�k>��anqBbarrie�/�2a�.AdZT8- �!Ve PapaS�rof#y�;ew�)I� iJ'8�?`����l$.� �fw!6V�u&��ur�2���R-�6=csXb��A�.�E. s]-%!*$>&d ?y�R�h!*�#^�x��� !T �(n o shif��Ii�H me�oA�n"��BA�9rA�3on�nd0%i � a rea�Q �h ��^8����buD VE�T )@<a| re i| s��.��&@3:� Leftb18�MM $\si�w20~ �!�aL r.�V�v��y =te�<�1�^ : $"� V}$ ��$2."�$H"(b), $3..�"�a�:t (d). R� : *Xn50..���_l2�pc�# � B�c,$4..�E�K"h ic!E63@in�Ų�(f)-(hR�1�yM�ic 2�Jla���C:�Al�Fg5 2��s>�K�4  ͜�� &�e�!c�� ��� ��em�"�4a��>��2�s�+�P&= = {q�typ Q���/���s�\mu� �!5(a9-s!f$L% �.���V./L��� ��.���y o��B� 6n@+#z �� �4��� R N� 9 G ǻ��'#beIBolso� s��a.+d"s F/6+!0, agai� "q1V  .�2 ��� �2�j!*| =2..r&L:�Ce36 1n,z ��&[ Udory. "�7n��2&�R!�� io��t_�xAQ~ r���ob%��AX�,l���� 3�&. 6�J�"s&q��I �m"� �Ak��&qiy($< 15\%*>dmi�OaIZ��ie��� ulaZ$_2$S/H$_3 ���?�[") B�2�E�mi5�s�Bf�SV l_�%U �l�!j��K.}�kkf�GFu!��!A�&�:�I�A��� n� �d�d%��ݵu�^ ~m�,������b�=Ra !�#%l*�*H$<��*0�{vi�& �"A � stead���P%�7��63� tr6���� as�p� ��- ensa˛o�> �sfUs���mTO t�y��Y� .\��"V�yAms �ZeLi�:�9.rmT* rpre� BsA� �&u�f[N�Ie�}I1�S�h�$ey�!�oTP��h:j�/�,�"AC'p �'p�&�.'p>�(i�l&'p d �*yBoA;.a vp�p8o"} curvE'"bmup�h�!n@)M.�Ce�� ($<$J-p fi�<t[�.���0W s��,-p�q!?�/ ���?ed}� i�`a��Ag��in'2�.;b~��.v��)�:�;�p-R�p1n!n�Nn We dQ� s��:@A��.Y)N^͍� f� v!��+\\ sB�p�I!��&*`�/q� !u.��j�3"�W�AT^���pl�lE�&:X !kK�w�"��r7x,2 T�AN&�^��Q,Z , I5G�. F x���s�^!�k=�0to � ibly:ormW�}���1e�-�W}byv�Ѕ�@5A��y7ll��L�%wl. r piM�B.W Gq��X�-backg�or!�e 2-2� Z� w�� �+Fmanipu�J�r�_6���wa} n5!lg�F6X� z#-zs� ss  W)\�w�!y�d osc�j%E�x � u(� �lex) �..Z��Fs%Q�a�*WT�I�*QGEnonwU�/t�5i��O� .�� ,�4f ��etoA�E�*�bY � .s uM2�uK$#�"����1in>0cco��)��2 �"ii�7e,��6v�9� �aMM[�E quee�s5�� �{�1 I�EN=�8m423^p6Kh2�YaJ%�k�Y.� D.~M�Y��)�f+�Z 2089%�6+ncNZ.c%�C.~6�h=m\6&�h�f3)b�S&�c^0V.~I.~KorobovVbm�P!2i.�f.�?1}>U9^N.~Kj{ jt�, AaThomm�iY�b�.�.6}�nN�g.�0B���D���`RsAv�j*�V L.R.~ 9�s~�� tageA`A�ol��.��l)bhZ�F 3A 8�s1986e��]a ~H.~�'! ��FALs wsbf Ph29�r:t�VX.-P.~ Bͼ�X!�656J�.iS��G.~ , \newb�� Adv. At�n Z�r5�66jTu O!�"Sj)' ߥ�Jj319�:�2�= T�kb�0�m , Jp�rAp"�n X�L 1134�6Cn:�9�Q6 U�kk bf 4�g7V�k K  ,.)v1 �h">�.�"�+&�g: h���&�HendB� tE&jT�Bj,12pt,prb,aps~�i *��$[pctex32]{�is,Yyphi j� | \�e4{Arago (1810):a��"2�3�s�e e���0Rafael Ferrar}�alt.��Mh��BC1�$ra del Inv� dc�s`\'{\i}fico (CONICET, Arge�a)} \� l[El�s�� mail: ]{f |8@iafe.uba.ar} \.�q��% A� ,om\'\i a y F Al�E5o, Cas�  de C�|o 67, Sucursal 28, 1428 Buenos A��\\�+D�t��n, Facl�E$ !� ]{s" @ucla.edu:�Lab �oruC Neuro ImaD',-!p �s   G�8nSbool/M[FLine, UCLA, 710 Westw�iPlaza, L!�ng��T, CA 90095-1769, USA} ,k�big�u-a"(k 95 y �V�mvr Re���A born!�aR _mp�g�e� 6 "�<6;2EarthYs"F7A�H� tarl�iL&Oeprism fi�? T� e n�5m�(�(, gavY��j&$ Fresnel's e8���a"e��� ragg�b�E .�c+��ex:1Ei in's==� sole�,me g>is�vi� c# ��'s��$bw$ >A ism&2n�a�at Snel�lawQ vali7�0y��8 �|s}he hist�1Mp�Tb�? evqceF4�:�@c�L 5u %W�.D�mEt��Huygens'!_HA'i�v)O#�A2isk��& nd>���&�Vrecei�)bۛ?2�Jpwav!��` unavb�n�/ v c��?no���T�dX'.�aui \pacse�&6l }�(7{Iykh��Mi} Qc o!� decl�'%��Fizeau��'�p�)speed ?mefi�A� wt�``�- enough'' Xe*�]mS�1�r�!`�N time.!4s��� To �5YR5(m.���#�j� , it�!rem�j� A܍�1'�! _ lumiferQ��Ӆ���'bBr��e��[�'V��, umin>�'uv�e�ΏKAti , sc���5b��?B�o~}�mo��6Z bodyX itpvadsbl�bod$4a� @i4�R�utA�� �T�(&T� �Mu\�ali�Rl"� !wuEʵɅ! (iy newton�fs)*NYin 1818,�qin Jeanq�, (1788-1827)26f��}v1��),!�8= ide}���Gjs>�&�)%��s�4ect�'(eg� ior)9 sGK�$ntI�Y mm,�@``1 ''؛ y $V�_ N!��B�ZA0(1-n^{-2})\, N5S i��ref d� dex��fAe �c�$``�2''��e�by�3(1851)i�f�F�d Michel�2��MorX�(1886).-�mm,foot1}@ *@aolP8; ncep�2)�A<905��̅� �� sEno:Z(�x�� ���C!Fal�i�)��6�[ ��!Mof1�!��i1sa���hasser;. 4"�al9zof���q��!1 book?�.n� I�!�ys� ��/ Hoek!~68)cF hoek%�� y71qdair��T6!T[��.s]�i�tu�0j� E�� �cul�#a�e%�cruK UD-I@}� of 1887.K�n��rep_s~ �swenson?i���`Be'A3 ray,)5�* Airy!�c�pe�6�o�bܾ�\v5�)�gV3�Av���  �l2����(i:M/c$g9!�, �Η= K4 / pre-2_�ics jus` �n*� #f esor�� �~FQ��)fac�-�.�=e @A� N ��8� c[fR��:cel�%!x!%��3� sL�"?� �'r)B��ui-e �o-$,!oE�&UA��.8!�5h! 'Ma�%�; argu�p��!go keepm�3�sus<k�! me. h����Wo�>�rk/�FV"�%� � "� 5�� 818 �plA�50� %r�7o":ortOErp �36� e �y��qshd @vai!�a��av om  �&��y,�6C �m���=���alRk�9�[.�o���  ���av} ()j� } wv� &b �U�%�y�ERef. \o�cite{ped})kC�g, etc.-� rk1�$Bradley ab���H b w � �j����.2of���ws �Pv���# 1/20)�� �) :C1� �� a������e�5�� �r���� �n�)Ino!:! suchV��+ste� ze���de*� �  sm: ``...��� <e'��%lmv!�?^"� r �� y obbEql pene� �diaphan� k �@%�jO|)u�^Mi��ie�l Q�A"�'beō8rstood that thet observation of the total devi to whichLy are subjected when �go through a prism, provides a natural measure lxir velocities''.\cite{arago2} A�R did not succeed in detecting different speeds of light, but he soon realized that �Xmethod could be applied�make e�nt� mo.,Earth: ``...�< refractive bodi�re� <,H%don experienced by a ray sh��$be calcula%fray%stead we��pose�study?en�>p Cdhe (anisotropic) secondaryiO fron)�A�2��R!� ��wayA!Wshe�cceptE6 27}EU>7octubre} �.�ak display z�wa� it; besawe ad� the appro��!!s� �!�s pasA�(Paris merid� to help��locIC~ ;��ky,�� Fig. �Fig1}�ws). � 6\e8 ar� P0Sun (30 km/s)%�enough� gene� !ningful.M�:�a�� �2��0at 6.00 a.m. �,% ,it" p"I)2�  case) 5I�isէa�l+A���;�� v>Ig?1Y6/tha ��1. F� mextrem,ses�[\��~! 12''٦it6���i�:�' 28''�2�per<����S� re wno��Fof���K���6ofQ'E !� Sneli lawz� obta�7�" convf d him�!:G � possi3 interpretA of r n&��!�:�B��Fat� sour� emit��all sor� � sa4�1E�nm�vib)�,�propagata� du�an ��f�nsB�trans�� a, ���A-it�e"�c�!�of wa��amo%�e !�i�}F favofz � luminous�s, muste� lit!�obstac�!� esta����1j !jB� } So9)�( ��V�B��I�a� � pendsl!�ere�In&.���� rast��V�u�m�,� l�m�sAy/ � ��A-�e b�!�tvAdex/a .�su!8nc} low�Ey�ER] itsI?ior�foot3}ՊcoEyWheM�as%~l� mA ial. IE7 well know��8q���s��i� � NPA�!vorA:al!^0$\rho^{-1/2}$aF ere $/kd[ jN��%�w� ��  anAM!:F8y�1��&� or glasAIair. AAris pointU�'2� abouZ  6R, Te scenea�? a��is a�um���ior �]!Y=���those !�tit& �#sI f1� 6T environa��9 .'' 2�n� .�� d�moves? 2!�A��*!�I.s4bA�� just�.`6c%;An grav&# systemN/W <���4g�y%JpEe�s r 9: ie:S%s�F � %e� ;2�{reveal)��e� >nal m� W���A�B\ is� let�Q$"�%)���62%^h )h ``J& - ���}s� eBR ��. Leti�^\prime$A�Q���;<� �5�2AJ�!Oui�-�^!GK �-�� $. If $V$a~S>��BmJy ("�:D D)E�)Urz� v��)�$(�.�)\, V/$�`xc�>%�!6e��oe�J�ɬt"�>: \� {equvQ vA� } v_[ $=\left(1-\�{�} �}\rh)V)n^{-2, \endfE/�� mem�be a�'eq !gH=� .�F '� (he coeffici$1 �� $nUy�ve 8 1�Z3# ayo�"�t !WŜz..Re�!��I�F�1�� l} In� ntlys � of!\�[�j �&�B e �t�effec/ ;3 � rest(!�#ofN�!�e� *Ley��8 5,2wi3sc^ �Mu.�3� �6� ��-�. W�as��$ray path�NB2rRYwK,� �=�dŨ ��"RHuygens'!� stru�S j(2; *� ^ �eX !ept�}cM � Physics,. (%r��w�"nt ontrol! � d;�*msoP%�a A $regarded a� ivile- in H al R ity. Like1~,~illF �qr� �esS�Wr)mincida�w�nor�y strik- e fa� !v%��." $\bf �mparalle, �o"PY�a`Ff}#v"��� role� j �tiQI�I�i�Ս�� >� @,be ${\bf c}/��aS!�}n�H�$*\, -\, :V}$!�)�� �$ (Galilean\.�-Jies&� i � ;�h� ���e � � N ch$� ��\, +\, f.�w2"� 0 .0, i�$<\, 1$A��z� E�quantif�! magnitude���. Accor<�R�f � planapv!�o7)b� r�M��Eb,  )�isI�>(E* /�eter e emerń�"i@is&$�:�#Kwav$�  /�goR�(B{�!+� s-�<ktou6+>nV�{ (seeA Fig2})ZJ demAa.;of .W� st ord�($V/c$.=ie Ycho� $fe,s�am� Kj#�#�閁�� �a q.�%ex� A@f�E�=\, 1m�O $�An ���{%�1G�M� pay  (n�1�fa�"9�.g&� sp�ف�7��cisZt sD!m�g w�dg��J "�%l+/y���erL ,�He� k}\cdot� 0r}-\omega\, te�x4invariant phas= !��!6�&��an,n��yns�% coe� ates�a-moG ���y ��H%�|ba �} �6�-��\,E \ver%! � \ha n2$ Fc!%\� H <xfH(#r}� �K V}tM�iF`��F` 6�_O(c-R�V})� ,>N ��;Uy�of6iS��A/ 5�Cn�! V} � �-aVER isbQ �/ y} v �_{\I�!�a�!L!�Y�V&.>�Ta�m&rM�٩�1/�w-lv z�� Y� �(� �a�.�� E� (W)Ra� �+�a�_ metric zs��"!!2})9Pnarray� �D} x(\delta)&=&\cos  \, (1N V\, A�t\cr y.9sin�91 �QxMi` qq�xN��.� ) �\9�x+��y�2E"2E"j 2U.&(k2A�R�%�=�c/m A� (1-f!6V$6 n a�%� arri�) at O�Q�&�nM�Fa Nu . Af l�$ $t$L ) �o oE"*"a�# 4J%, �d�zO� evol&a.� Eq. (]n^&�[ ERa�aorthogoNA���OR tu1+"k ! are F9^ob� . InNvaa���� �s �*a"�� >�#$I�$a�< valu�4 m�%� Eq.2���,Z.� line�� by E� esMa������� N�[ :lA3tr^esatis"� �L�5u2�I} yi� m�+x�-dA�a|Ld\, ({41}{\tan\gamma}a�a*m)� v� m%h� sl�.�!�%>7+?'la$q�(J��tz)$x$, $y$!u!�%�� in!�6�,%��� 56�M (m)$�(lWWar��er0$=�/2�"_&EY�.Ru��O'is�ibf%_} �� fun�of5�g Z7�is�$dm/d�faM \, 0$���%0!]� ��(deriva�] � M�$E��+ 6sVi0get^m} 2�.�^2�!�E sin=\, -A;H��� 2\�Z9Nr>+By keep!}�)terms-�� �`az�%��Ni�Ge�^w0s "x0b1�} �\simeq� ����A�(� � )V}{ c� 6�� now5�A*A~2� l�B�A�rso ��ed6�c6re%�%E��QHto  rQEF��� & )\& �n�'e".� $f$. Aga�W �eep-�0<%��BJ�  a �8*lgebra)�J� �"j5M *^M )�F�x ��Y��-\,@n�\,YN\9[G6TC�> *Z>+�y�}{J}\�]�V}{c}>jTh�(%�9R>IA���=f*�o��ini� --!�requif,���)� 6+-�n('e~ nt--�b�f=�n!g�]!u���N.N,�0>AIQ�"�-vEfulfillb�� Jx���Y�B�i.e., $AK(� +��A�ŵ  $J �%asily����'� . Fr� �1� Sge�"e6&'s T:R�BR &+u,lu�} R@s�M��cQwA��d�1 had+,@(om<t���2e3I�p��� omin=.�%���,� � setback.R�a@b b�%aso�=�+2{+&la�l!+�A �'&ym�?&; ace�d�evanc""5� K h>�$m1=ste�4�0he?� !=`4bec�0 evenb4�a�'s mathe�7�Up� of"@�,a few�5A�� �%se!tGd=�/ 1 �*t�*rtA&�N-*�#% )� !�fre� $problems (� inst!H,�9? [odex&�6"�'s v� f�aency, .( !ire a���. u Ec se�implau�0�%��!��s8:�%aboli%�byR�S�i*prem-c"HNb p6:!;UBonshipA��-"��!+;�!X�&1YBm�v%a-"�re+\�-x)��rem��es)�~ q- $c any �<V1!�h&F.�q,2�of�Q��,� !.U1A��� �2!?��J�`&r�%isND`S+balA�"0&n�p�? �!Z�7w/( ne5/�1� a��9:�,�< �[ remainal�-)3%� m�1ikੲ>�m=! �B�dE�pY$>ua ?a& u""@ �"Ge.:me�"� "lD. � ��_"& r�>r�.)6�-�U%N9aA0� - �4f9PN�. H%<� annoy�H asymmetryU2gF e��A+ ,�inR�:���-C �Mis>/i-�3�@>9S7)�.�� ��tru%,B,� -n K&�ic chaa�������}�� ��KA�#dgD""Q!��-sh:�� K ���� high�E��! ompatibil�* an��=$d����U'# ast,J�e!EB�yAM�inţ!,��:2aA B��(ngy��at2  holdT acz!9�at�ner5)+�)add��A e&JAX(, 7}>r%�0ng�vacuum)�pe���in0ay ��*�9k"* r��vi�.n�(�sKHe?�.� �aW!gH�bWj+!!a#of�en"�9�e� associ&�th� ��%@N simultaneiM>� emis� .�(b7{ac�0 ledg�} R.F.A 5r� by U�Q�idad de Buenos Aires (UBACYT X103) !�C��jo Nal>' Investig es C�\'{\i}�DPs y T\'{e}cnicas (Arg4!na)�!d%e�Wank NaA� Hagi"1B�Ea�com�� manu�Hpt%-B$ \newpage �Lthebibliography}{99}�J em{s�,land}R. S. S, ``Con�G�\� Albert E� 4ein,'' Am. J. (. �H31}, 47--57 (1963).s%9A7Z oLettre!�M \`{a}r,`8 l'": du�Dv��#ED2quelqueR7%�nom\`{e}!� d'optique�nna�Cde Chimi_' �$f!o@57--66 (&:6�$izeau}H. F �Sur:o:{�7��es �l'�� �5eux, eJ r un? p"�N qui�ait dmp)er� l�K1 P corp" 'la vit�: avec la!$le la{�qP��,6e %Jleu;A�e�ur!7 Comp��Rendu= l'Aca �i!� s ScwO4G�@E$TXXXIII} (15), 349--355!Y51); `�= ==�6eux. E�= �9= �= =={�= ~t)'LV%% 3$^{a}$ s%�rie!485--404%492�mm1886ab$A. Michels�=8nd E. W. MorleyA�IN=�����4o "� �^Ai�!�.�$377--386 (�2��61}i# also&O8o2�� "� i���M"not}?�S.Yhoek}M�;ek�De*i?dA�Z��'en%n%a� e on4u8H? tc)rs"&$un milieu rmo%rch. N Frl2$}, 180--18E�66A$airy}G. B.��y, ``O�?�;�l>>��!!'a�I!�0astronomical J ,nVE�D<ag%�K� �! 6�3r!e�,ckn*Cng �6�\Proc. Roy. Soc. (London)I�(20}, 35--39A�712E�7��OI�.e M� �U06A��L!� ifer�:E�^�AŮ.�4�33--345E� 7); ibid.AErr�6 r 2r\AE�u(Philos. Magm(2v4�� 463,!872 swenson}L� ��u�-i�-Miller�s b�A � 1905! Jour�O!(Hi|1� AMFy)�$1}, 56--78��702�a-V}D. F���``ME�moAs�yuaO2+, lu ��lCem�ECl3G3'�"9,��10��(cembre 1810�6� 9Ab�ф$VI}, 38--4E�53�|V�$B�!�10)p({\it \OE uvI l�4tes} (7), p. 5 Gide,���56�(pedersen}K.�P !�W{-��PMPA�pre-h9�&�eA�F���%� . Ex�+ Sci.�5E�,99--564 (2006�(bradley}``B *m ''lJ``��D�~�6Ad� on c�"�'c2� , (finite):�0= MCYe�U� ,�� �D ��st eSr (>>r� 4 K�� s�0ӡj4"��0In� t/,*�, RCW�,U Z!�n�%race FA ellip& � skye`-zAAcc�O�aeDov>� !*fixnO tarsA��. Tv@. � ��2� 35}, 63� 1 (1726�e�2B�{a �4\Ka!45�author�J \z �UM. BornB2i&V 's��?��i�*(D�$, NY, 19622�X 2�IJ"A [��� 2} S"�<~' ��a�i� fram�!�e};e/bLT��E6#$3lic4pro�9!!�w*I�i�M�#?!A�sP'[;un6UmxLl"? ial �. A IQis�H� builtLSto$ (Ref. \ona{cV\ O�+LoaBz�Wme��ly in�>istafK .Kl =}2� ` G. a��abuE�%|y� (3�7}, 9--1� 452g| H.N �i���UvloSUdie-] bew�g�$ a�6 op�N ichtTHchijnselen uitoefen��Koninklijke Akademie van Wetenschappen (Amsterdam). Afdeeh'Tluurkunde. Verslagen en Meded &en ��2}, 29� 72��O 86)�!i�i�FDefs�#t�[��RBBo]� !���i�"' andai���"1ŧes et N�^el] �b103--17�:> a�3}�F>FV#�VE�Ume"_��FoucaTn 1850J�f#ltA�confir"�19) �,$ ($n$(xK2 dex)A�a�e�th��.� b��nult [ thode gg � 4rale pour mesu nu �'Q et�� x.�-s.  s�&V 2� 6M dwl'eau. jet d'ex2�F "(on du calorw�won A7b AnEyB� U=d>n}, 551�0A�5� �">% ne:J } \ca3{D�a�F�T19� <10}\vskip0.5cm \Wx"�ab�F(}{c c c} \h�7  %� \\: f \c&({col1-col2}384} ... Time & ~ Star Name~ & MQ��$\\ [0.5ex] v< 18:10 & Rigel   ~~10$^{�U$}$ 4' 24''k6,6 \\ %[1ex] <5<($\alpha$ Or�EG $...25'',\ (5 \\ 20:28(Ca� & 8~:z8\ 6 9359�yon0r797pPollux==�9�3- 2:23U�Hydra:525 � 3:025Regulus �:492i02:19$ Spic>`1`4,4:36mCorona` ealis:k�8?!�S�f6% 05:2� Anta Yu!8d5d5�zetAphiuc�C689�0\\Q��q8 �\��*V)le��8r��XM������2�!�Y�}�>�33a�282�9:5eMj�!�7;9E20M�b� ...3A 31A16A�:z'7E�21:51'U�6t�8�3i:0:1E�$\bEkLeo:ra022�01:47a:lY6'�) 02:3e�Arcturuy!)�0I�3:56}^��a� 3 b4:4 b:Ta1(a^N2�� 6�# 1:04�$�( Virgou}/%�80!�01:Q?"7/B��13`2 `epsilon3q��4%� 23:3%t"U-V�� 02� 27: �}j [W:\� ������U 19:26%�uDAquilaa& ~22��25' 09''A 21%�2o�]C�)�A6040Biari��632 caW563Ce!$6.3 . 4:08. Aldebaran:)0)4 )�N 4' 5 ��� %5�(.��6:� & Si�6&8y���\6�J�figure} ReT*4s \usepackage{�icx#*o $ \include !,s[scale=0.7]A1.eps}\\*c� <diagraqc�QSghoT&���0� 's >Ej�L"�*w �s )v`on D 27Q:�. Wavy�a&^eEj�� � (pro.mon��:C ), e� h�farr�coCpo�% �Bv�=. a9 Gali�D.�s� X �e�A�o <-�H�l%oJ&�)k�E%{�<^IBQ'�B�B6EB2JBR�D��! N�2B�� docuA6} �-\�HD[vci-paper]{vciart�7loppy .*amssymb}2q&1 ]vs{l *{-1.8cm}�Gflush02{0YbAG LAL 04-14aW{DAPNIA78%X'} 0.1h = May 20041x�OEm�Cr��title{ION BACKFLOW IN THE MICROMEGAS TPC FOR `FUTURE LINEAR COLLIDER} \�[A]{PZClas}, .I. Gif�`.TB]{V. Lepeltier}, \ad:[O)X, CEA Saclay, 91191 Gif$Yvp[, C\'edex, Fr4+� F0B]{LAL, IN2P3e�U� it\';ia -Sud\ 898 OrsayFS5Habx:c!�W!�c�s0fk2��)Micromeg�#%`$-MEsh GASe{]ctor) !ra�c��Gped"�n�%high �Dgy elec�-posi ��ar colliiF�rzL"J�d�J�cla��i�]c���m�-mesh�>a�idm nsic�7[toRrl�(op]Lea�"�9=&�)�� ons -T���av-hA(�&�M�at��]�0xldi� o'e pitch�I�� !�mixtu�^�!� feed!�'I3�Ke field �Y ( ! drift-�ic )��Z�j� ).Vm�,wIr�1�pse X-b(@C ion{�� TPC}�6a , %Ii�Aini��g;_=�, +6�a4V5�/�a  limie[�Rm� �y�EN.^g6�regFM�I volu�in-�*c voidyt�3a�j1b+e MWPC�p's (as ALEPH, DELPHI or STAR)�:� p�i? gggrid,L re 73ecuA� w�)aRpol��0#t&/fvoltag�cSS�o ing N2�eI( stopE=mo�K�>C[! thepAatL)-s,. �Ke phy7Q!5be��'R����lin2��^ref�I"o�toz���,f��j!b , us��)a a!},-MPGD (�-P2n Gase��2%ɫ�*out-��#���2} r�,��d���wfu���P3}[4}� -���NuA��_�eQp�lic6 mply� �pfq*8thin (5 $\mu$m)�xallic�,Qv�`25!w50 6,�8 at�H3Re%�"fan��e (50-10=)im�0��a;coD?]J cro�\e ���a�7�Ou�qH`�/�]a�a� �gap�; 1newp }*�]�] "���F &�:T}��predi�s"� {-5mm} dha9ny advan�U:�'ng!j�2 f�`signal,�d ExB Wlre��? ��� reQA;a�i")!� capai2F� .���v��� D�b^�_� * $�.�/ip� a�-CI��?���as 400�� 500)*IC"���m �mQ$cg.{tw=w��(s ("funnel"-Z)nQ�v���Gaui9or!�W��PoRJ � �i)FR 1Njd)B��iUS$O gas, �a�Zw)#alM+.u�hciu�l* E� :|%�:r���exten�e�gma$ (�7dar1�w"��, ��"Y �"� 10&!�?,�R!r��Bw :�Q. gap width�Ki� 2F2} !� a* �GARFIELD� bo 5 �f:+-A-���Rul.�gaps.�b4 �j�9n�.��&� 6�k �:�in*� >�:. �O5cloud �_!Pe_e��d�6'iz� iV end \abreakB2-��rad�-U; &f ).72e5��.'ir�mas�Ure�-9m!sto]�! -V5Ass�+�z'7/��P? �s�'di�Ybu���7U�,.EmI B�Il�*  4^3!"�d"�f�7of%*"a�-�! + � ��)v� E��k48"��flr�3BiF�A���>�3Bq A"|� 2�h� &� a1��F-dg}��al��,s2���U띺#:I�0gm�A;A�%� �zC*�  !�EQ�bB� (rms�z)�1Ui��,;/$ia�-j#a�ge��s(a�#Z�A7k),EfBa[q� v�oI`!E� ( K��E�)&� ��en9&"�0a���N�e�GJ/ 5�. I�1joutU�2���.%���ly�)e/be^��u0)q�*1�F?* �!�lP>  �.0a��U3)i��~ it/>��b=��1HVQ�d���b�/ �)nime (ty"��)�M msp a 2m �8length). F%`�A}p-xi�$"} easy!�? uKC ���5J nas�*�Mc)4^&H A:�key� m�3a;"�-c'm�.����(� �)e?5 � "e1}. O�Z2z4}wy>M t � B�w/l:wZ�_&�Pis Iv( u�/or too "x�)�A8!k �ME@�l�{�zt��in -(Ny;���g0.5�.&9t~i�ach�*�Xa��E �5 1/5� ݝ3^��� #"1'.10np 4B�0(u��U5� (.aGs2j��aa�!H=+(*l 9� divizp!�)�)>"�Ew} . 5% VKon�!{+J�!�:eڥ�us!u*w �@R�at} �1icM(40-7"�ey�&� 2� 0�($\%2$ cm$n}$ ie5" = 12&% �a &:qgap. W'# lpi (d�einch)��%W(�-b}Ka�/E�"�.25-.3��aǁ"aG�� is 2�3-��j* Q�I;]��10�12� �25V17-+ �9 �.nah' �"(u�>���.��AFA��Zt�KSO&3 �2!U~��ls��MK)�%�T=�l�-2)-5�:��6�2���#JG�Whe�-a:�$J=p %(k�� s&= to iU?"�+�s�.� &� }edp��0(10mA-10 keV)�guCa�P^>^L 5})l 3m��� hNiy",(@�u�at CERN�.�1!+ " of =�"�*� yDl � 22s.Hv Argo_h8th 10\% isobuta\;� �10pA,�"NTbe; �XA�� %#(byd,����m seG.�� Qv0E�ܙ�� :  =-F-�)/!Cd$+ F���.��han�e:� ��O� (�bAsM!%���$ dynamic r�X �m�9�+7x8&p! ��13n#5B#E"΋�Cv���A)��.�>�5B��6��F��2b 6r_.[�NAD �-`for�ka�esh6�e�.[� & M�"�� �C)�e�c�H�6ih T#�L�!.FZ&�a quit���orAsim$4Em.a.U2' %���11n�6B�2���vs2�A 9�o!>6>]�� en6�^�7})�c�M: erUQAC07 ,&x)2I .�ex�I"- a�j\v9"{m i�!A�. s.\\.���=�7��-�&��-ʙk2a�W097j�i� Fin~,6�%�&��super^ �on�Uil,�+!�6v i�0a�2T�B{tR��"�a���eM"B ^j 8}).�r<8¯j�>p8>��!w!C"#}�,!�I��)�ĉ�m�V"kC&�sO%�!^2Bqx �(j:.�6j!�!�.D� �W5 <��H�?*� ,P�A�?�kI��B�@($<25 P*>0 &d�A�A$I�:,�-.N� I��B5Bx��U�!qQ� � J+$��1�6+$�5%RC&� r�?3ow � $<� $�w���una?:=#�a��)��>� @t�F� WuE�� poss*u�nvi�Eh�"t�s�� �!�o B%#!  jortp*�& de�E;>j�qUAchM aWW�sh��k�:M�Tn, Jeanj QA�V. PuGM&i�(e(�eHiY�rk.}9�thJ�L"B@"#0 J.-E. August| talk�.$�,X$^{th}$ VCI!Rf�P4, Vienna, Feb.f+,�be &��in NucVouʊMϚ�\IMre#2+^; al.,V>8. A376(1996)29.� K�<PC%/�� y*�);%$SY LC-DET�' 2-0824}�+,��gl>�>�-E�:�-4{llncsheads} %2�-makeidx};ll�/ANiR=3�5I<d"..% \-lex D� s\\aPAutonom%Commu�@K Net�< s\\ A�AGInt�C�O:-Pagm�orun+]8{A.P. Kirilyuk:72��fW� �bb��c[ i !7)��-{AX�i ~�  5 {WACM�,http://www.a)ic-�P5(.org/wac/prOPm.html�h% .� a listV� %%%%XBuUi' 7�!lTOC (ad[2affilW�s) \toc /�1` (a�-H� Me� �Ocs)�' {f*!��NE al IHemy']"b>of Ukr�\\ 36pALnadsky Bd, Kiev-142,% 031�6\{Yl{kA@metfiz.�\,net.kiev.ua}a+A�)�2%�es�_M��Sr�T"a"�*Q�/arbitr�&2�HU^'�>'as unre=L���D��&Пi�lised,&�Yly nonK.urb�m�B�%).poD�Ul��G*=Hof"C��d�L_et�V �Agur%�EZc� ol mane�|r f�]@X  caus� � dom��@'�[l���*"QE�xef-� �al� o7�e�i@�f!?a3X, 8�-orga�� adaW�i%.�ide��� hqof hug�wxpo�R, y%�xcA�E�5�Ǔ� n��1T�5т cify 4iKal "�Zo~?�UH!funda/al guid!�prb{p�{or�� �KE�oVFwM i�FZ. new kvof��� �^Y�%&�Iz|\ ona�An*��M ��o}!�a0�\cu[�]of�l1%% �����ungABC� �E�%�k &�t�xeel�v�Oct� �-ph{�"ct}��M-A4 n)D5��on�b=HI�inevi�Byta/ lex-U��.7 IGn�Ga�\dE��!� R�?\ Z, u�� a� (R�e%i���l6�9�kir:1,2,Q�EJ��p�enABal,��:HrOAarFK2�~��u( technolog�)fI]pa�A��dig>{�$h�]:lI!�3g humaj�~9ͥly �] X*�2-����5P��I�� ṙ�l�+un�*DJbsA� t�E�a34sir-failurcr nois�.Gro�� vE pJa�i�= �� i� �sEX:Wi�a�ca��V�&Qr*Й�N[aY-C behaʘr,�l� romifEc"�"a"�+.�A;_� han uch �lyV��b/V\!�$tr "c��"�Z and ! 4 .�eV0=�4� $ual us=��Yds�certai�sv#d�ther,�'es�gular� mL�d��e�05,UtU p� wPalyHfse issu��rigor���by!��Z'�L��,�!'��&iA��&WM4c��Ga�t%dnd�Ңa(ch \e��R�!���} &�X�'�',qY�ped4�nof cha���=�(=ʙ�k4 M�),2����ϥ/Z �c.�)�b^hns�LAsn� in�v �o�ep� )�;i�exO�"�6�"�=8A���noa�k }AKc-pM!PK"�ss'ŀ *u a�Ua� 6��7C� s (�;� �1!hi�&��U)o shkdsp  th��!4���U��>� k4ol� U�T�-d�x�>N ,�fZ nd B �!uF\�A�I��������&G x:a�Q ��! �1cQs^��45678}. We�>ڙ�. 2"m6�j� A � *`��5=NE�in�<anyX}alr Ito;��,� uinei� omnimmhra� R }5m� �[� i��#��Kfew!�Lerzb10�A'�the r*B } C �J�E�out##A�mn�<te�&�A�2� ����!z�y0��f(��3=�Q�Ƅ K!^q���څ�of66i Cafal �8c7��;ĥ!'�q-pE�� ���� o��:n�vled} l�6��Ropei@�0�2,�1}0�& &1 ���A�� �2� > growth}��9U�,W��I�1aM�� s�y�ard* �-�� (i� 3). "�� c}�B, �5�"� EAe˰,!-%��,� ��d & new  &A|to C� ���&ho�� �y,�9 ing� )�"� �ll�:� )'a�lus��i�(I�w���B5}ɿ!I��� � wce}M�%>"�ob)*��Y�[U) -10�``n~q*� "!�Gmos% ���aj�˥�� in��3ynonym%遼truly �&D }�*: �e �w��i�*�>�!�U (�Z��aLes' We b�3� �mF6.���-Ab� -�1Ks (or � -bod wp)a�� � )�ex%�ce"|�}, fix0 � r!��. InA� ��nd���� ��m�p-�sb� eq:1*,eft\{ {\sum\>4s_{k = 0}^N {\ [ {h_kYw$( {q_k } \�D ) + 2;l > k;V_{kl}26 ,q_l; } } F]}\}\Psi6Qg = ER\b��b�-A�``-��HamilE�"!�"$k$-th-�A�)�A�abs���=�, $q_kf�" ee(sA7�c `9� (exI�ngE�``>al� e"�*F[ 6[}( �v��(��&C .r ��k$l%usB+N�"�VI�� te-�, $Q \�?v)�Avq_0A(1 ,...,q_N QY\DŽ$E�e��1� �!� =�P�sum� ";� �=�Y� ($N$)��� �B\�m�=�=K&nJ a suBe�!���x� "� below�en�a�[m�o�``�^�"nt)(^E, ��gg"ohum,,(+h c.) �)ny�3�s.q��ȁ�,)ŊM�E��_.���.��Be6U P( Q� �_� n ur�5� �L�a#ec�C pF�!�i �-d��!��r�aaa�]F.=�E�^!0l�0L3�� �&�*!2l�.%]+�c�)ime?On4�``��+�5�Q��O, e.g.�w0mc \xi $��L�o`HO\���AY` ``i�-wide"�f� as� mbedL" 2, ( 9!|&�����mmon ``t�_�9�i\t"n��:��)h� ( ��:~��1�~-[ f� + V_{0k٢Y,2�ՠ +��.#������ �6� qQ>� > , @FQ�}�_;wV[�V��\}Å k,l \ge 1�W� n .��l�.�]mEn�!nEt& "��.E�``��al"/ t�F��9I8�*��s ($k� 1$)n3} b�,\varphi _{kn�I:6� = )zT _{ ,�=\ B�G 5�(eq:�3�1>��}][$n {\psi _n�(E�YL� 1n_1!��%�= 2n_2i &24 &...ONn_E)) ) �~�u� } \P!�� "� B9�b$ya��>�q%E��Ghe &/ 6B�q�TLQ�E��� ctf/.h a �> $,ň��F?letHt��oʋ?�&, $�qu. n_1 -�%��ru��� � &�st�2combi�M�$6� QQV�5�\ _M\Q�{q�\}H��i� � � of&� !T.� psi U_2.-j��tT-2 wGP�H!�%?-VE.�b(�fby ���by5[^ *1U�s) g � $Qv�+0b�{a��{rcl}Iq[� 0i���a��05�.1s]!< VA&+&:��&nPXm} Iq�2m��eta #�2@�-�n~�nbi>�R�:�({n' \ne n} �nn'�YZ �{Z �:�tB�F -an2�Q� 712}�)�V�$n, � 0$ ( low����0< -6�0Í n e��wn va���k V�$,j 6} V_bxA3:bM�0}^:i65> � 8l 8 .p��7��Rx=:Yt"B8\Omega _Q } {dQ�y ^ * >�}A'kY'�,a�q�) ?.�>��8 �5%_)JmUj� � _n�r�� ���we�.�Zr�(1|� l $FMqg$)�*� �>Q�/"��  el� t� e.�) ��mu�ɸ�l� 2�` �sdFg ��Y "(&�2}), k��-Ջof ``� ""���� ef�i֠٤�%Dvar�F�5T� >R!�mI``"�#"�s C2�&?�2 ���\�"Q}0 �arity � r (w�a9�a@Q����g ble"1�2�(m�eq:$;"�hO� Gg9�ed "j(��< cal,&��(&B ded}�� �9�M�R�$ Eu&��,m�$�3.� f�$ &�� Gr�T� �$�&L+(EP)}, g��$,i givecj10Ń�W =�6� 5 +�� V��NI�iF' �p5�!qiB� _%�� '2��':c}:�� � � q_"4^&N 11} �q�*L {n,iv^M,{ &� J�{ni}^.�1u� *��:�<{0*6�'"� }}{{E� -  20.q ; }}� �k6� "� .8nBJ0J��*1�E�.�U�� 7a�7$MK.�R��y�p�" am� trun�s}��)Q v�5�T ��1�#R�az2[�U �U \F�� ,�use ��%\5o�M a)�0iQ�.j=��H)�2E%�i"� AC* .�1�&�9})�!6 x*f -�EG}v�3} �n�2��!gE�*� q� ?96?T�6b�%�1[Fk>a�>� 1E.4} �u�MF�5.� i'} �� {ni'V-9 J�u[��_i��eta V� .����>��A�9.� 65A�Ps"F"g Nq.�A.+��*�$ > "6 4})r�1�jPo=h i {caDI�[ {"��"�:t$_ <*�V���-���]� vH *L�s $c_i$��bX/un�?�6��(ch c�Ks YIb9c5� .S "3 ly v�3h��GDdy,2�as&H|xs�$O�)t(m�&�$,�v��a$An:�squ�Cmod�rAqrhSi�S!��}|!�sY�:m}-| |^2 tMor ``�vF�r�$�$���or�F� it +6�B��J����cl�"�s2a �*&|EP�P$��"� ��,F�ionyg 9})-ut 11}):Ys&|-"m�X"�e6Q��3kđ>)�S���al7� �# ��� 1}),���5})^����K6V-�ЁC%&�*&&j "��a�� 9t/���r� +&�l�`B�'� �'u*���f6����%�.96���(t�"`s�8} meaI�bn}6� l1$ndant} numܶ�8A�t but inK2lyR��& Nmuw�c}�� le},�'1��\a"Pgm.ja��1�r�/}28 �,�" Mi wL6&A ol�Y��dM��2L�vni�(3+� 0E�my . PlAΡof !] <`l7>oK&�/6�s ]A�" E���-48�~>�!L[ �:� refl*0�&ly �\eARA�.�" .��U�ng�2��/&Eis}�1Z��7�D�8!)=M-�.`G&�^62,�5l�EP��-�ګ�&�"�U sch�e��m�!!Io�^"��or�+�1s,FZ1F%P,so/invarvy�8a����2 ��h�75"�2�os=r�P�us}< aD#�I$", closed-��u��B�dy ``k�" �%pe�)ng��S�]�-�al li�7 re.�� one}ڀ averaged"g&T$e&�(4�g�J�0_`<0�k�oe-U��Oon&V&��i:5�3 �7le-�;}� ounitary}_9��!�U!D�Dba�6a�wh�3 cano�Al Q+p�A. ��� , o2<R\a/ teY`oA�7;�h,0Fv!�=f0� � 54��E� �c�>�-�, 02�2��yX<a� "�-c�83��?'�> p8� }�-r3}?!�Q( � :�, !?�4�\m�gby�^�&c&x$aSa��%��-(=4)!"��%��4)� �&�0 � ,?��Q�~�M :* 4�hcsWn!3�!j1S*4 �A�e�3&=)�s} (1 "!�� E,�)>M�N ��H1A\�6i":a�:ity" or-� post� �2E=2>% ise"��am!!9� d 5)�=te RgD�%;an&�9"O(�0A����u6"F5�N�a rE�)�-��%��9—},A># �9for.�8-�zQ�n16$ "� RX *�{r�X }^{N_\Re 9 ^{^ \oplu�E< _r^� }J�#��,H &^V`"$J�, $��-ir6 (AK6׫XlAAI�"` &� /X = NK� 31J$ �$& �hݶ�p��:�;5�!�� h sum"e�d abov,�+!؅�a>�y&� 16 W�@w4i�rEBu>%ble�!cV �UMt`L}2h?ya�X7es� one,'�5�=��, K�/�cn.�. Such �:y !�qm��.�� �= d ac� ;��!pl�RoBD��' &(}, t�4�=ghJ0vo�\��~� )�ec8A0M,s��� R.�I؉�c�,Q� as6�# ��%/utE1 ty" Ex{�@ (�5aco�C��>�I }��g�-��&:�iˍT��!VFD:� t�{Z7��E�l+ ���f� +al�B� f+M-2'As,``bio-inspir�  <$I6t"�<T  'rq�Zr, �B%:B6��MT8�{8�����/be �]ev�o�sA�ta��U�F9/ "�A.j8�05 ��i-m�g�j�1EP%:�my�6tm�ԟan:HcI-� 6� ��ty}. Beb 5-�,�.=��*Ji+iA��!���ar"� x��� K8 � iori2��&� _r��OA�":� c0i��br��T] %frac{1}{�����2�5r {8 }��J����n!3A: may7 uneL�#p��#ar�"��Iir.{~���)�" �"�� a�-�.eV�` >(��Mu� mp�� �!doQr[h^^�:�}r!f�.>sA�G��r��T5�_( {N_rEd�%� 6� \ \ .6!� ;B� \���'z  }5N A"t0���I��9)t�wE�$rho _{\exp�PFj�2�as�bz��@ro�� *e8})��? a�8g] 0�odv�9!F�~& 2= �n .>IT"�,&�H ourQ��FT"�M neep�reoA�6!�c �1empir�4lyBf 6$,;w{abasic*s��J��!�id�H%�! �}��ta��Hq"gJ��MQ�w� yN�Wppens 7l��L.G���`(O���x �G�2vol�I͍-Ţ���dLBorŔ.trul�t�&� �$�$8�$9�.[g ��z�E�e dur� � *C�9`` @", ``F�tT=� K Q�$ ular;�n� ate".;u's �E�qn^� $``loose" (wtIUZ ing)&y2g'AZ�S )��ڔ;i+8P�IAK"�1nF�^MJ�~ �S``main"ej��isi �7a*r0�� &2���%�ZF�A]2h�c�l�M{M*u)_�um-&I���Q� ��bst� 1"nai�x@@ e ``A���5A�"�vw�9 �!�� !�1�  �aworld��s,I�� �]�D���du�i�!+^Q� 2!�Vsj�ir>�A!%2z~(%�� �vul2�U<2� .� I@2�1�) A_&n�&i Schr\"o�+er"$&C RP��� %�izI��E�, FNa� ile A '� -� A 6FA�� �}� C � &" � ��daE conn!a2�r��*&#e.E`Am 5Nd�� z�G�:y�a�.[�U�.� �. Notei� �u`&6, weak2��!�b.Y.�.�G ����B"�-o�s6&�Pe-}W��od)y!<``r"_"6�Ps A�� �or��H"w���n� N'�s�Bfu"T E���C����}d0 ! �.� ��_� 2g�<�AW}5�SŪa���m%,*fi.��2 �!T we��FNOT�. %�N�%��o�~/deՃ:e;d� �,, Q$)r� �Q/Y�1��8-��! {I��U%��W�B�>�W%�E����2a%*��O=q�)``�"z,��{On�A�" ��f xGQq�2pr�A�=.well-nf��q :9 t;"� �khc\�^����*furw�aed*A �O �2* X5�&]j "�=f�9�by�.�S�$�2&[to5 �a6"�*QF��3.� 2})� f��-�Ha]�"6"�"N� �2i A~nd�t�%{��5 M�-�e��3IC/�%����G� o^0H) k!�B� U��%z��+I�e"�05r"��s=C = C�b%b{{dC} \Oord�@/�7phantom ! {d > > 0j0 . \kern-\��dtern�.4 0}}!! t5 ��ah�,�Co zeroeGA5!~ t��a�� -e�, $ � {11�|�)5�it��h��E��� J B:!VP(n �$,q'i�>gy/�o �po*��%�e^�;�T=! � ��-hE RH� 5Q= �ence)B�>� I&��cl4no�� �I{M�e#0�����$�u�&��(&6�iawiS!!�x"y {^��Ʌ�``�-��\ " inm!am^,)&k�``E�s")sA���ly ?A�}� !��A��-}�� ch� j?2�&"�'lyE�.P|�5int�(w /�� Q��B0 ���y�4 . C��ing*Z)3�R �0ally single-v��alued ``model" is strictly regular and \emph{cannot} possess any true, intrinsic randomness (chaoticity), which should instead be ;Poduced artificially (x0inconsistentlF$e.g. as a � �} ``ampl?�a� be foundi�0(\ref{eq:9})- 11}))�theM-R�emergey._, i�itm�s � for a%=``)�" initAh� � ion �.�2a�5where)3$ usual, mea�iA� ``.��L but a AIurbative�roxim��qF!xn�.C��adYCEP�se� Z< lead!�Bir�kc�TM�-c instabilA�p��I� state (�K)1w�yA5 dete�Y� sameQ�$ feedback 1(m. U���'of�Kdescripe�a� �c�,�6�.0fied understai8mlwhole di�P ]ex!�ng� al regime�d types? �uzB�2��5}. One!,ndard, limita caseJ��� ltiva)s, A�eRunia…Hglobal��s},a�chaay eris%b suf! differ�=�s�c%�this \ nded,� ^�e !� from���^�A ��on���:�4pit� %hM&x�  shap �" 2/� is�,�P� ai��he%�nse ``E�naf!�nop s�permaA=�9�d":�iK I�n[ ,superposable5� sa.Ani�4important adva!w L ecta��*� ci�fmmxit� tA� -�%�����8�!m!�1��{ a͊ser(of � �l � �ls"��clu SOC, vari( -�R ``synchroq�", ``!�rola%�", ``att�4or!� j4 locking". All�%� medi�� �ts betwe�_ose two6���orm }l.�,SOC (as well�their "-l� , W !�bine©���2�eH� a���R poin�� transiYt��ἡ� %2eS"� ^ \e�&8 �F erioz �� >8onset}: \begin{�j}\label� L20} \kappa \equiv \�{{\Delt�ta _i }}:n }} = .$omega _\xi�Y{{q'\c�� 1\ , \end� �  $ �$�A�intt �!  }��, $6� $, $x\xi�= 6$n �] 8, \varepsilon.<q$a� energyI q"ionEJ �/aAA � er-c�?Er�amoD, � ň . At1( \ll 1$ one�YaƁ���� >�i�deg�at toMq s 5rgrows��0A�1hvmaximum� k�at<"q 1%�aga�A�au� to a :� kind�&�a�ggP(� �2�re�l�� 6T). � cana�par�t��n)�y2pib�'� .� ����mplet��mzaT A�E!�ula!.. O�!M%r�* a�m �i� u26 u.Commun�a� tool�f arbitr� Ay8iX more�X !( servr�i�#rec\Ʌm�}sE_le lessP�A�$s will plar� of e  se: �adapt�� mea'is��d%-� basR f� ``biolog�� �� lligent" Q[f' 4' �Fref!$!� titu��/ ��� n�=# paradigm}#po� � xte� he now%�+ (quasi-)5E�2�%och*�� A�ut�ost��!m��m�, \to 0$). Wh!��la4� inevj } becoqin9�e�W ,network sopha(�m eele�X -bri� �on�A�&�20}��be avo<�A�)� �$itely lackI2� powerI&�mU��� Eo�aYI�� ���� . % \si{HugeU�c� h2�v b!tgui9 qsymmetr.G� %��mq/  ��ta2  QT�� es n"�:9(A�� �9elfB^q7 � ie- �byA����t EP methodY6l4})a3" = trun����l�s&1troBE nextJ J, etc.qe giveIf���andm02�%�mov�2*� s,��� As!�%tmit- mix�o� iDs:2�.�oge�a sora� �? �ŏ}m tot�al�  $e��q�eX,�(autono ly branch��a�1pr� �64 � 2�ae�tQ��^gex�[}�~i�y time� iodE}��b��t�ed uh��llo��way]� I�)���-connec� �!d!�$s $N_{{\rmh t}}}$ `` ��' � �jun%a�if �cm� $n PuPA, @vir�" ( le) (,!�C)�-�o*�on ,< $N = :i >�. In �;"� s $N�  h�� l:�QhumanA%�d�om�M CT greater than $10^{12}Ih be!A much��P��for:U)�mt b�j scal|Na�om"" rangen keyA���w�e�a�� x}IM�M�s,�uisI�t1 ��A } � ion"�B )Kqo!�!�m� s ac!�ly taken�EA� � (alsoai p)Ef�ing it� alA��$PMpjEp(�� 0, memory, cogy on, � )AE� � �of-4�Q���� ��E�.e.nt1} :� \�to� = N!� \sqrt {2{a�\p�N} �( {} N}{e"� )^N � N gg  N\ .>}Any%Pa! sa�� m�%�1s�c (i" bIG<�ly}!����  E_"Z s) we !i.�g��^\beta$,�  $ �1$"�nc2Nc[1;9�w} )?-5=�% � �JPThus,aǁ�nq� w�v2�aA�!� &�$3}�2�10%�$to \infty !h is inde�!|e�kinfW y", eDŞwj!�aOa�e6!�$ �6��s�x s demonstdJi!�;G  (mZd)*3 �`�0rem�sup�sed�O�� �, 9  ��K ode dom�ngo @in man-made techn= ��� ��t �- �al2�c�)M!Bnew�1!� � ,nce, such as "�w? ce� �cU ness} (at�er �0 � ity)2� " a d���o�m�t� =�a�� �a�S)����l� sens�}�Dntext-r%dAwor on;� ing,�� l �2�)&n �_c�Kiv%Y(usefu�lf-*� ),�ede~-�� !� Tr�7� �)�}A4ife_���"� eVe"I< . Everyt�IvpriAhow�c la}pay� ,#A�li � 5ta� $is rigorou� specbPas � dN;do�$} ~R"unpredicVwyFdetailT!�N.�-* �s. We �#�� rm  an e�ntclu'E^-�9�}����:f$Y  ex�e� ��, �le �gramm�iA�4inciple. But wen` �%�p0� �d�gV a�� AqE6�][ly�. "�2=sU�cA�i�%}�" � ? We show!�%fur naly2�1��2�-�%� t��rul}�d�mi[ �!�eroaw� m^V!sa��/i�&�, !Herv���  A��Z�%� is�(�  o�/ev�#�*+eF+ ll (��ct��n�@s,�ie�[nd tu�"Q$Mds &M cauM'riv�n3�B � pre� now). C&�%E��~y)  �1P�-��iՉrm)� � !�u�&m� exact} (n���roken�(Its ``horiz8&l" ma�= ��aR ��!�c i��i)x , ��� 5 ����:> "�AM�a�A���es�Y[  replac2aba ct��perat�cGthe�U$E��A�~9�l\)� ines� �� expl �� ``�alg"5"���r(often quite� x AqQo#%1 ��&�s}r3}. ��vcB�!��F�F� some�}m��'a*�rs&Q �2�of*g#Eb� .`wi�qN. S� ``po�i�ie�ora%)�� to ńe��y4���  beginC :��u (bu?I�J%�!�)ŋb}�lye� "q$M'j]S�"�$MI in�}�Uj li� �u4'." fuDu�?������*� i � �+%Gye5z,�-�F0 prog)i�"�)w to��a-�*�unfold:&R}$ ropy} (it9es� etic�heat,-S"]��΁jѷ6�}z�nis��ortZ,�%�� t�'��o���:��, h--ns"�#A�su%;-�.� aAK�� �f�2}�#� un�( ed (��֭O�% ). T��7 ���!��%A+) �"�Z.�Aat{lud�' bovervand�exu/e,�܁���da�� �1!6first" second�� �rmo-Ns �$:�M?A� "m#�rad%�L+� help� n'n�!�perO0!�a0� ) &�"a H s ar�+<n[A|}�A�E�� mH  d r� !�to�J�;Q& _ttheory (O A&�!4M e��"@sO- s ra� $&J* �)� ur}�J�seeݜ�/5}A\   A� I�-not�0�*E Z�+8R0at� H al�%i �1A&M 2nf1�d �(�xk$\�A$ known^class�_�,� � cqui�{a ch wider,���l �.a&x �)te��g app�* �ny�IAH ,xit��#e�� ."�(�-Mion!�FA��%� ��!E=< Hamilton-Jacobi�2E���r ${): } =  (x,t)$r�#3}"�#�#%�}�# t}},| {_{x_rm�t}} } \:+ + H(( {x,�"<$>Tx.Tt �T,t�. ) = 0b7$a���1+�rq,1A}  x�-An{,-�0)%m| {_{tB��.jt<$t$�TE� � -likCrE�2�Y�)X"|�S��S�P���0�F�T$ (no�!a�e� cO,�uU)n� b# inuo���i�% of d�� �(�$ incz6s� refl�)�!"rquantiz�,h� �Q"t1Y�7.h ��:�5. Tak�i� accoun �ua>} �,*u`1ereU � al�% e ��6� ��� loc9 q``J2?+��!#ed6T !_2 �)�is��e`- waveu���1(Sect. 2�6��W"h  Schr\"o�!er6@�2X( %*Q-�&)�e mit \Psi}�] pply�;L�"�a� ECedQ � dure^V �w9}1I.��B"4 23})r�4��{ al {����= \aL�� ��%�81x}}��)Xb���_0��I��"��� (�!l�Planck'�m3t��ezum�� qkqA?&1Eianor?*�$��"E�5 5U:nA���2��G� � I4 �iM(we! put�`��2�.s?c��quws6x-�4}r&� bA�y,2�&��)s&� =P @ ahow i\ D(2���%{"� Xk "@ ��>@e $ey justify) u�4�2��� st�9]3�)R5�, �;�is).��a�. \-S2Hg��Pn be �z�"26�(�K�%Gg*�&icI"P9 we f/+��K: Kte} (w ���)�3& %to.h ���� Q�v:J�Q���"�%�� . W�*+v�#�fundae Y ���)�.|7a�25!\) ^|C�\'*�SedM��+Yl$*N v�: ą��7Q2a�-co"!%4 2�6ach�W-�&Plo0�'"��0?�.��q �p� !e�)!iI@fre�*Aa$e"�� ^3�,Ew# ���� *)!>k��net7r�*, e�a !���ed " ledg,e�4 libe�d, &P-�6�F��4loosely" gover�!62�'��� �s'I�bE 4're�,�uld2�exc� \I#�of� ,"l����! �Lrol. % % ---- Bibli�phy�*b�{theb }{10k* \bibitem @D} Kirilyuk, A.P.: "; Concepd( C"A �DZA Reda�1-ParK: C� R�>�, B te W"M�<cs,�QUl�'�fj,of Kno)�x. Naukova Dumka, Kyiv (1997). Fa=non-t� ? !� view2}Hint physics/9806002>@http://arXiv.org :+2F+->�I�.9!�*�+Y��Va=!�5 �(Solid S�<Phep'tna {\bf 97--98} (2004) 21--26;� �0405063>�3F�9�Z�A}��m.�s!5"<*u worl&~ . Pe� ��In�;M c� NAS!�Ukr�A �50� 8�828R� 4006>�4F�~zAa�"� �c*|-Q�J8e2:�=liv� �5:�t ion�)l: Losa, G.A., Merlini, D., N�*nm�8r, T.F.,%�TWeibel, E.R. (eds.): F��a� B+1yeYM� dine. Vol. III. Birkh\"ausZ4Basel Boston B�E[2) 27A\84Jp305119>p5FpE'A��&�#!f 3< %L"�al.kq. E-pa�.� 9140>�6F�T��2har����Eca 1�in crys!J b�2� �opt�X"��.. Nucl!� str.!� Meth. BI� 69} ��(2) 200--231>�7F�QIu.�8*2 .� �a!EM�al)&s. Anna� DFond. L. de Broglim`21 �,6) 455--480;� 4-ph/9511034--3B]8f�field  )cs:��=�bS5i�8.���!G�v� eri) � �/ s. N�SB;4, New York (ac��e%pub�k). JC1164 ��ded} De�$chs, P.H.:���ap�byF �0sA<: Ehrenreich, H.� itz, q�Turnbulla�q� ��%e -: Adv�nq re5 %,��8s,e�$ 27. AcadeIP?.& 1972) 136A�7.H9F�75 yea�@�2GN��Hl ax��(Hal:� ism�&�6w � ��A�0101129�_:>� �+ docuA@} �7 \Lstyle[aps]{revtex} %��0 %TCIDATA{TCI�=�@cle/art2.lat,aps,�0C&led=Mon Jul 19 01:01:57 1999}+LastRev_L=Thu Apr 27 16:18:55��62/,nguage=Ameri English!\draftA8q 1V4} \title{Why T�is Fu�Or#Da``\author{Shahid N. Afridi\:0ks{% l: sna@a(.qau.edu.pk�M. Kha, KhanB= mkk@3} \adda{D�ItAA�P ,�u id-i-Azam Tity,\\ Islamabad, Pakiw. make�5 a8#} assum*,�M�E/AM�� (yDWK@n turns have sub-!� a-2'sub2*so iC�Bn�k>ree-d�Ra�al}7is� w�h�9Bp�F�2]!>6(&a� {y / Vclo�7 slow down >n�� JB!wards fE9.�'I" a 3 sfactory � a�?�big bang�/9� \pacs{A�s�7I�du�5} Our�q��� �2 j>, �!�mM. A�Fi)+NwVrpesZ3bq!Unof 8 ,#Athough'AH �M�ex�<t�E�pdata,�B nova�,w0*!0�*aliMtJach}= rpor �� �"!4 cu�( ure-t �%!�a alog7$�Abe"4Il�GMAZgra�:�o�[!ja ' beam�p��� f ��!*�2 trap6Ka}�:�% D7�����>R}.adl >���i�) !Nay. Le��-s a �sourc\%  @en&�obEe �:He� � "a�NseaMhe U(/#�Ehi�u�tects no9�1tube. S�Hm� � �c�0g;a�r pasl%�N�Sun�p�A�s)� shif%)��BIJpj�E s Db~" �)Ear� 6�cei�9 Wis&�5 situE�#tsJ�A�so E2nV8k) R�?���~gA�$l=ct$q( Ewe�6 fed%l� fibM:�19:-e�"} �? 2er. Pu�;!�a R%me"in�0 aD�6it%�e�Fr�~6inɾ�6F. SE�Msiga�-1}eb)292^._2yD1 :�A�a$��i+ $% .D1}$� eq.; 2})a{�F1})Ion re-�r�g we ge 9�E -�ze�/�r B"}}FLE393B GC$z��: afteI�it,a�q�V�J� 0}}=�>,d\limits_{i=�n�A/1�i!�Q�4�>xM �9orJM\lnr(N:0Y:=\sumB� ��(}}{% k_{B}p�.}`59A5BA�}�=use�7 k�@Fs=g�W�6e6Bein�)$su�T!�$Q Boltzmann*�#�#�* V_�$m�spread uncer�~�]nu�c�=itu.C. I�sakl &k#E1>qn S�{�_ph , A $V�> l^{3C�}�0}# � *�Z[l=* \expQ3S/3%;�].5�79�7B�)�F�SVeE_I빶8a8BaAcc&� %b"m0��l0�fs, $S$��to1�Ze as $l$%  is�-q � =���(w��L$%�p�*"hyp 82. �$"� � pe: �#� $% � �A�77})"oKFdt1�tn��P99f9BfWri���!Cq�3 S=M�`frac{tՕt��]�2.�6py-R,arrow. A7P!��.�5-��M 3, �" a�E�Vi� o . So�� not draw8o&F=o say�A�9��AB^t"�+, qor�i� .;RN_�0_o�!"c . E ��a"� �suc�iv�� i�E;tB�MJs_{j}=p - ��109�1�S6Ni�$6�:5�nd o &o �s &g �=�2n"J jA.�4 c&g')� holdmc2i,al"x,s Pwof }a�v Jl.�K% wise�" s avera�M9�\Q. U}u�10}% B�8}�+i�(�A*$ >�S=N(p)s��u�1%���1^� FI =1+p� p� +� +Rv-1#iz/ y 6!Th�;59ʚ��:k� 1*� 1F� ��!8��=�a�cN�  last" fac�%6ouEpa�.��$t$ k�$V��E�8Nei $%a{l sho�%���2$�$5A�aag-u��.B� _��X� sign�$Gg�R= p >�monoto�$l06sou�i-�ousLQeE0� �TAe(i.�i!��/a�m�i+1}$�8ma�4��)|��-� boun�h2��M ��7irmZ�un�. SQg)�p��k� ���)t��� !|�e��erof mas3L 3u10Yc�*a iv_� �`:,"�} m���� 2�4a�m�F ��6!�!�talm�!���E"� 4}) �mu�$a?".�arg���2� ueK!o2�0�?aH �V�\lambda�6M"� �1*� 1^� F?7M}>� 0}^pm ��*� 16BJ �Fd�=A �� }{3m��w !���*p 1Fq �0M�O.� ed!�Lyapunov&��ar�4�Kn&= de��e�AC}aYa!worthA ���:tan{c"�+AT�i@� in l)��>�0{Wheeler,Dick�Ie�ab�)=+ecause  viol�H eW["Z7��e+io 't\ �V cleaA�at � fise�er� !��A|5.ND �io���L�2�<iw� U9�2n]�5})Vt!�"� ]X* 1F m�>��.�� [�i�pu� 9� "�t�dF��2J�t=G.o Q�z@u�*x 1Fy  �!�.��S�>en�_�zer� �h�iu�lowUf%�.�3K"�QB �  if!���=0$en� a^e- � F  w�~X�-�v�0Jx t=16t m502*� n_6� CA�l ��o�jsc!5Q�%.1�fi�wo?3v�)au!%' !��a/N%62 j}>t�$,�PRf�*�� �* 2F �ndj2djdjd.%Z� 'G%ba� �: WR i})�n�y*} �&\neq &�j} \\$% &= t���Q no\jq M2qQq �q*Bq\ \ u((v g�!= (5B.c#[@e���<�i� "� �-$���\o� :9!�so� 9��� DQ.r��.+�( )^o lfL� er_]�hzJ�i})*�Ho43G�$�".�.Q ���!�>-)%�pWt.�>�$�_ne� a�)r"�7��. Now�]?u�YU�Eъmc^{2*�2*� �?6�.�21n� �E�g �}{� � .�*� �:6�� .*��5t2 &� expe�N"Y. � =�M*�  ?�#�b;<e',length9N� �l�-� E}).*� 2�� N=l�W��*�~q��>�2� q  6{"E 2��$l@kru@A�s.\umii:1 i�se��l\geq!/\max }$E),tu�De�2�� ll� cosm�T� i��;&�:���  I� �:mi�Ato do c2Mwaad� J]*�b@( till n�L$&i elaps�5RT6� k'M* t_{k��*+ 2F+ 3 .;: aN !���k���)< .�en's�$!"i+A�!>N���9 �e^{\eta �*� 2^� �"�"�$f�+$Q"^ �E/c�� $. \*�HB� �"FXT=Yt6H.;1� e^{k,}&62*� 2F� -�n2!��s2F�0&� n=�YC�N��6 $n=2Yu -�.e�I( 7"��&�]�]b},!rendon67(Oxford,1996.^ AC} jAquilan��s.m%� Mod.�! Y�1�(, 755%�4.S008042�,} C.W. Misn�;K.S"orE-nd J.A�k� %%�e]o)M W.H.%o�eAnd�9 any,"E9�72�� R< ]_ `;e>!S"�Fm E*�2 Re�^, Gor!d�Br�56�65�3.��d"�7� "�7� @[a4paper,12pt]{ar)�3,def\Lrule{\v�3,*{-0.2in}\no�� nt\v WP$th3.4in he�2.2pt �th (depth0�g &5em} hRHhg1ghfill.<2 c0pW V� o�.�Y}�4ge ing{��ic�4V�7 OX-e.*p3%����u& T.L7��{a� A. M!h,ns Sim\~oes,�7E-mai�7Limoes@.if.ufrj.br}\\"@Po de F\'{\i}sica,\\ U�}id�bF�;al� Ri��T Janeiro, RJ, Brazil} *�7�B&�5�J I��!A#�� 0 oremark � �%&�!1#�G>��+*�z.A$ G_N�H_0 ?� 2�<a.C5tr=s $ \a�|_{QCD} L $ \LM  . Wz�� ���8yconje�\ Newton's.�WN�co B � � *k��Gog�to�.��. \vskip 1cm PACS:04.20.Ha, 04.90.+e �=�e� +1$1938 Dirac��a��%��lr���Hubble.u($:�Yf�Y�A����|R'����-�k �L!�s&�� ton �] elec5x6Mge�k$a�is�^by q �(} {{G_N \2 H_0 } {h^3 \ew _0 "8m_p^3 e^2}}=1.3��O��um6� atisb2_U high deg��o�eci�.i��D"5  at f�4�*.�sugges. "� }ual!Qi� )�ha�dtY��&no�%h�q�Qwa9("q@l�d-� {BERs2_!U2!i��! Z�_"- �Ho)eE�'s "&?a��/a&�:���deCes � n��8�!B��ga�M��X #dI@!�ay_e*;"�&Yl n6�ribds�'� �l��;am� a �{4rn �of �G. I�;�mod �inR5-i6!�pry5A�o �5�2�b%0A*(*aea�S�zeXaw� J�.�U�Z�ne�"hGbre�#5� $ v_{F ]���QCD ��b�� ��� ��=- 3+��!ޡ�pl����$ mustpro ioaF��g_x ^q� "�l�w6���ar�eqM cs��6_7 inz6*/k�:�,�in�" 1Q-Zdd�!��etLspdKof�+�:�p� "wac0flA��R0G6/={h^2�c}{{g)�^2} {-� 3� 6�� *� �&�NK�  Data G=6��{PDG}�S:}�1�B$h=0.7�{nJ�L� �=0.12[2�$=220 MeV/cI%!4re�G���d�!N3a f�? 0.8�V�is��t�@��e�I.��khe i~Bphe KA_�+lPa�ewc�f of�,���N���Rs I�.��# QCD�r^�i�"�^.E�.z.BaJ�U(�I �X�Eq. 2�Dn�p)��0� pursb��?�KT)�:�͛�U� .� e?c�9WEB.^�m�magnetic�e-&�LQ����* vari���I� i(d)� bill�of�Fago9D�� I�, Calm,nd Fritzsch m> FRI}���U��b��s�&ld�$žb"sXGV�=��%��ml���v��:x%��;w0(%^2W��vice-�ba9�M�&�!��r� �\/erDA�F� *"� � فI ���%�v�}�Z6b(Q^2)���Ki��> sympt�g��0edom. A $Q^2$*� � ��ea surpr&.in�J�I. "g �(Pr/ali�W|Zr"kB!�g�E�� �<"*���Im1BrecWye'IjefX 0�B � �+ode[ nM�DON�Ste�?I�%�calwT�'c !�D��� !|��6JMsC"��!v ,=t^J&�i�A:�Wwo g�+��YM��es�hcomputed:-qgA_vF �Sr�I0El��otI!. I/adW"u��� give�$i��o�vH�@� |g�ng�>L+ & CoƁm�c���E�nZ�u�&��\��NFG_Ne"�viO�>[ \'Y"�  .*� "�4 !��K)�!Mas� �tiz)W�&o�" Lem�F�u@nx LEM}|� ̈);� ,�,-3-T�yA3%��3o�x�I�y��in logL�hm2�ӄy�� ��2� {��sI}a��e � �proof��:* is s�la�� � n't fuj�ZDhC!I�!@��:���!qIF?>EI maiUA�%�at-�raiaNi"(�N{ABC}" � M.V. ry, P"�A�CoJ#,Gd �. mbriZYqty��{"Pv P�cl.� ,.��Rj 1HT4d) E) J.K�Gbb � �M.Rev.�m 87} 09130 H1)�� �� Dhep-ph/0411391; X.. .* Eur.p�C k�&639�2.�吐N.~E.~J.~Bjerrum-Bohr, J.~F.~Donoghue%�4B.~R.~Holstein-\ �\ D l(67}, 084033p3);:8K6^:KLC\ Q93} 1602Q 4); V�!%t%% 0097=ܡ�Gnam��afS � P b���Rio� DA��VeA+�>���d"� Nv:�$twocolumn, �M ,amsa� symb�Q4} \u6_ckage{d 76graphicx�>� �PExact"!_i�XrlibritU1O���X�;0uc� (liquid jetsm) {Niko�$M. Zubarev!Tmail{nick@ami.uran.ru}"QOlga V2a}�affil {26YE�� s, UO B��$, Russian �S�:Bc�\ 106 Am�5Len Street, 620016 Ek��inburgI�)H&�A��1as�\(u=O�����0A,pf�ofs x!:Rv*1v!d�6�;Gst.�s� sqm�fI/e-oituAyzimuthar/"�[%��sur[8 vrjet. A��yz!0lb��ic�rg�a��O"W=�o�<j_ pG) self�0s� 6 ��/pl~h two.�"ex�<�d x �" )1�exc��:�9i~�^AE �=H�!,�rBx Ia&� -)�6�fa6*$q�Xma P�w�Z!�J � �}��o�J�|Y�b 8cs{47.65.+a, 41uCv, 47 M7.27.Wga�title "�J". 8 Cylind Ul!���to u%6lAthF�-�6�!�a*�d*=t1�Rayle@=�GfXcapill�p6 ray}� �4A��\� aW,]{FLcA"c�an*+�al�� U�Im�r e CoulombA�5a��Ms! �She X -X ax�5��.�A�c]%a�iφn��Rk�thwnonaxiyic*-�AJ�!m�),stE�fo4l-=4:� (mel,sav,gro�Vre�,!DtA�i�ru"h@�%#�"� laws go�bZ �.iged j��JR2Lufi� n�6��-á�en?o!�% )�1��`9mfoE is s ��K !*2n6�6h �cJE�<�: ne_(ity a��1U[%3 !�e�d�u -��>��PR�=$!Dv^"�L�{. !�t� p -id� �2SshapeљiT }�eZ3F3(UActA� 9E�%(it�� A�j ��+e��)�a�U&�^��t�m�i�T�> �or�(doA}s� �Ge�c!�)0AX� � wP��I7 �%!n� cir�r%%(ae�d��>= �d> ��= *c eld)��%� Id�4!i?OR�� <�1st�Oo�=a�p� aE�ilhJ � . DN�A��EawEfew�� triv��Y�U�W ��U�i�C��~az+1V[ ���rya�. iI���MA Mw(dflat -)Y5�c�e'3 �5I !��!��B���ց�prima�f c!sIo-ge ed Taylor�e.a�Ref.~��ta�) !32ju2 �m:�� !�Z��Jg ��4angle $98.6^{\�|1�la�or��:��V�S�� �~ a�yh��,Q�c. erba�nY����%�solp �`!�A3� apexT6r�;�� X!1��3�=ea2R��NHc� A� ent �!X� n�zu1���e{<pla��y�zE4U�M�steady-zAap9u:ZIP.%�� M��n��Y� ���E`f��X�>�� es�G9,r!vv)�CriZr � cra}4/#�Z�\!� easyO�]HaT� �Mz"�D I�zu2� ��1�me?�F��t�QK>v -� ��q� two-. drops was!̖in.czu3_@�DbeV�#�#�I�i�an�~����Mco'"� � e�U2� �caB�air b�%�a���+ambj` fl�5 �g��by�%9� Q� �ber $n$-�� wa_**p4��E&zCrowd1$6=28c by Weg�N� 6/3,4,5...6weg !JAU�-*e �sQ  a�a`n:  Refs�zu3,cro,V�V�(� \�f� &�A���% 6QNN aT'is ��up3 Z�4n�"��~IID���s �?A�e2^&�!�.3���3��m#Z�E�h�2a�>�l)^.��JU48�����sto=���j.Ja�� G ary-�qo�"half-�E � La��e5&. 2JI,�E!:of ^ ��^M!�!H.>&[%�5e*� �%m=s�6 ,3,4A���on~IV�.�-�|�= `6)��9eZW�Y�)�����&kfh i �gsqEp;dN?E� Ino7!�~VA�%�z �*N��*p .�  am����oJ�((M5�?ְ� ^)A' �6t=�.axte�si���w?�b�T�ft lo� e �p��ES1Fr5�$ (F3�� bifur�')��a h*& e� eA�$n> HbRFW^-jI!��S� �Nks��-�NT�M] b�ol��*ĩ$>� n "=!� �n!!��.>7�D�� } �AwriM�A)�"%�`r!���f� MRI2� ��u>�)�F$ant cross-m�*/_%b���Qt^*$(see Fig.~6�$fig:fig_1}Pw*� ;� �F� $��phi�F*�� �!]6�$\{x,y\~ "&�>: $$ d_{xx}+ yy�& It*�� �oge�)-�!L�P)�u|fu ?I��"�, $� =0,$U'`?i�>T� o�1�| i&2 � ��y�> a~8�gAtra�2 filaZ : F� - d\to-Q\ln(x^2+y^2), \qquad \to��, Z@stac3}�Q�}=Q�#�v�1��aT{� e} \��e�s_1.ep8capAy�A�Y��& geO~��"�� ere�8� "cRed sc*J y J�*u}O $z$-� .  nd�u� �A��%b��spE�k��-�q� velo�{ $v$e e1GCarte .ۂ� (aB<i# a5�st���rE&��� w�&!=jeti�a�i�relief m�Q��Y.� � i� 4*�:) f�-Y69�)esm9Sa �F��QG���[�&� &sh~ng�|%:QY�0(8\pi)^{-1}(\@Aam5)^2_{ =0}+\3 C+p=0, m@ 294Z9 Cu> �"�co"��r $C,l��*�g-� CI�UQ$p8a<Z�Q!AA�Uv($v$)_�e)g ($\rhoE� #�($p_e$0&'i$)]ws��$p=p_i-p_e-O v^2/2�����.pp�9ap�0�ly���E�"r:�(�[ZO"�)� IR>�-F�� � @�� O e�T �:n�:�*�HAuBB 2 -��9� �\<�E�w�A��U"�'?N* blesU�g�w@r*} x\to Q^2(2\piIzI� \,x,� yf%� \�B 2Q\,M�q p@a^2Q^{~c,p.��ByH R%�*�t%kch�{ $f=\ln|2�|$pa new un�fun< e-A� pB�C njug� harm^U-s ��$�4 $\ps`�s[.9\���33=\mbox{et}$ �Mg��"! �%ŵ&�c"w*�$w=-`-i �a![alK�"R CQ $z=x+iy$�mplex�� $-dw/dz�+�UNd%U ��a,��J�-s"y)�} f��)"Re}\,wJ��=1} Avtheta F- GIm:G \arctan�c-9_y/ x\r )&�2]����&b+m�1`]<�E $�) 't�(A� �t1/ $f$ �I7��� �(u�է fՌ �}+psE*� *� F�FS4��U�s�.� b;R(d&��D� ($  ��42 W� t�d1ff_ �4=p\,e^{-f}+e^f�DZD] \\ f� vaW ��1� J� "�[��J�/�6i6z��(flC �T�m)1 �2P1�s%L�1�e� �S�$way: $C=-(5 L {f})5�=0 IS]KAAl�O $|z|!:��� �$w% ln{z�eog�!"� �,Ai�'�^;1 �"��*1�I�� $��$���5�UTAS!iodІaEA��*"5qY [,Q;U� fq�,A�)=6+�)�?acJ$]�4�r0 dN@3i1���I�"�2�$6�pr"�aB�5[~'do�` tudy�q�:7a�as 9})-�1�gY*XQw\leq 0�x&>%'�>�%��=C e52z�;1 i+��r.�� �&�/!f�ulaJ�3\!��!�Y l-1}{2}\!��\! +\l' (01+a^2b^2e^{2n�J}\!+2ab~J�\Hcos(nEf} {a^2+>6->42��2�38*1EN�but�Ta=\sqrt{(n-1)/(n+1)},\�bll)}F I� Τ" Q�� !T".� (sL��� $l c 1-4p�@"�4�2er*�E!U�d&�ajI"� -8c�@�"js��::� ��38��I`>*�O� � s01} �ѿaL��inp5e J2�~��* .I c;xy%�2�Cre�7"9 Y(z=-\!\int\!� (-f+B{eta)dw2R43ZR$> |!{�� ncli6Sy:� � �( vect�E bscissa&H.�t��FJ��;���g �1��� Cauchy-Ri�F���'9 d�& _a�=�K%{|"z-f'�&b�N3~QaEH:a�f--w�|�K(�P�xi}�w+ 2�v!1+�Zw}}{a-�ew}/we�S�o��!B/ y�)R�43�` get:Fz�T$2i}{(l-1)}I> .�4at^n-b}{t^n+ab� ^2\!\!dt C a^2t 8*b/a^3 �} ^abU�nnn18}\c Y�6 i��%�no $t=I�w�c� 6�Fb)" s ) ma���'6(ir�0$|t|=��M�� ��#z 0 algebraic.�6ge�� ��ul0t:�M�( .#s���$ɓ��`%bpʋ �wiG7)t%�"c �h$�� a�h"� �dE� M�D2�>4 � �!f� Bea�H� mix7�x_U �!:{ 1�� )Q :i�6}��sought-�R6�q:[�^am���ysrWa<���e� e^{i+Jf'2'J0sss^0$��$By��&A�%�[HI�� ]#}*� 1� � X�7�7$0/ q<P 6 ��reZ M�|�va�bs. HaD>i�%F �_~imagi�!�$in-� ����TN�y=� a�bt {� \!�+ psi)!�\!a^36+\!  \ (a��+\!b^2)H}��%   b)})�S/2��sss20I���xB�sin X2�- �..�-\:�)��." ss21>��j�xula" �" 9�I\r"q�a famil� �$ �FM�a]� &^ 2�&aA����� Iu.�. T�b��9ur�/<��s�%� � R�V&�36;bf~co"�so far� !A��ȉ�f ��ial���s�� mE�* $p\not=0 d<I r $p�:. "�#.�W"l=� Eqs.�J*#�'a��� !�Nvq ��1-c^2�� \! -"� !-2c�6E I�+2�*,Q�add2}*y;2�!�� $c>4in1l�8�� c<1�j5is�-J�!*��,tW�cA"x �D&K n��$�Y. E22���|2�}�{�� 1}{%p}1eft�Ae�!�!Q  2c\, -XU O.0a�wada�se�"�% �Q:'#�;�P&3'$cG5Si%�)�!�$$ .��6�)mea�!�"�Co"� mEa�5! �a����C}\ pre��s�$)]�%�|��: 6"z��h�#�"�5(i�#% �E"�3U6.��"  (iE2�T�Q��^72v72} Tyu��#p�)�!1� �d���a��� 5 A0a]HM�&PY0$l=1.86, 1.9488, 2e��Z�$�� �@r}*�?i��8Dv�Fj�rr3v3}EY�"�5!��K $n=3UF�6 2.53, 2.5DW.78, 3$֭4v�4��4j�$3.19, 3.35 8, 4J�Tol�n$����!7� 2f�!�M[� �e le�9radiu��, sJ��A1��un&�!e%7 ,=�-Tu�. W !~m�LY�$l�jA"C� �F�(At �zc,-*(FV $l_n^�!$Jb#5*�}�mvcea@B�+�z2�Pe�� ��Cs�% F�% 2}--�X#��$1,i=13/7\�.x��B�ee�J���4QE- _2<2.2xtwoZ�*_;t�%�U$2�^� 2�$!$n>)�=$<F�-�$ be �)�!�.� dx/d%�)2= : ����i+ �Ez�(�"AW�W� e���Y�"%m&1�>�!} a� �� \cot �$ "�e$we put $h=!i $�Vl���V1�$n$�>r��we �fɎ��,$h� :�!}��nyQ. At/ !p����!��*sf�!��$>�G �v"ue�<$ Fa� *Ca�%��y�Gn�TG (*���l}O |�'K O $h^2=]i� �i&��)fB,�!s����)g�4%�5�E}�%�)���Ass�!44�y.D Q@� 1�3^2-18�3-6������" o�k3<3�O3=(9+24\72})/1�� 2.$ If� l_3 �݄&[ � "��T �YT �a�4 �-�f�u�� t�6og�Ao1@llu�.X8inJ� 3����$n� �0J&4���I2B: E5/1� 2���8 �!�1��K443!�4^2-489 4-2957�)�B�E�t 0$l_4=(243+370)�p|/PC z .$�vn��"R,�5� "% �Eq"�ssa*�,3h^4-24h^2+5��$��(V1���� .\ai�, B2�@�J��e�$n$JQ=%#[IQ2S9{Yp!]^{1/46JF�+It��^"� �Z��qu�y�F&h>�H��J %�au�]�^ P  2�t�3;yݻNA"�f�M6F $Q���0 !�thres��A�M.�Eof 4 !�IZo�c%�W��z5a_Y! �4*� 9��" m6a take7 n$3��ɽ�$l�C&� �-c�"s��Q_nQIpi�^2i_^2S�8M2eb1R-��G7�KWow6T�),$!�c min �%�>�!_Q_2 �(9���4�)I��� 2.31\, ${1/2}S4 �I(1�IZ�M8�m�NeeAD �a��5 hydr��>ABA��3xM.�!�<#i�=�s xp�s�B>[U� elli�o!��� 7E|-�j�!(F"~LY歒�+s%� gG��cڧ >�cA��LpHt�W.�rOi*:�P�A3GdU:2�+(ilde{Q}V� &� "�FC �!|lo�%5D f6D �*.D "orn]L"%�J�2iN& " S��98!g}"Now"��6@ ��.�.*�.)�&-2� y. S��a�7!��V= �Qʒ�B)x"��S\��."�B%�q+� &�B�$�" :Q�Q.@v��.zB w.&!0 $R_00 S/\p�js e������D0n��!��y"k ��:P $qX E�Z�F�$r$�q(n,l)8| Q}{Q_2}����*� 9� J� �6_ � $$ rB`R_� }\!-R_0}{� 2\vnT(0-l^2}+(l-\!1).\!1`( �^�}-1�� $| =y|_�6qd��m�N.�h!��@%��i !��� ��E2� !rm !�for*�F�ir2. �'  (^E��*�*�Fa@�ev,�plor� ���#J����BA� $r-' �"*r "� .��"v 6͙��. "S%��c!+"����U2ˑ inc�s� a�6_!9q �3: 28c"��soft FhGm5 �Z Inde �8���if $q1& ft�eM�iy[ h�aE ��E�se�lU.��s�m����*S M�&[&���ebi!;�0aQ o#me�,�l:m�a M�WQm;���>( r=65� do�]�S�� ��iS��'5v?&5?&6�* Fy.�&�&,� 1��rkjGF%)��!M&�L 9�9�8Ş6JM\F  B��IZb�B�Gt>4� ��2�9$! &�ֵ� Цq"�=vick0y of the bran�Och points (see Fig.~\ref{fig:fig_5}). Such a dependence of the amplitude $r$ on �Fcontrol parameter $q$ corresponds to the subcritical bifurcation. Then"Lpotential energy of d0system, i.e.,*sum�dsurface and electric field F4$ are unstable with !Tect to small changes i �2_0. Since both�first�second 5M@charge densities |(minimal for? l$-scale :�($n=2$, it i�e5Sm�!, will defineN< jet behavior. II linear6�(y $Q$ exceeA ,he value $Q_t then)�-�o K(cylindricall w!Aa rou�oss!A?( becomes un)m. A �i,ility regime� softEDn,%a)� sY�(ity, a new Ste Y�!� to oAta�ary sU!�%W appears,%�! �0jet transforme#`an elliptic one. UnfortunE�� analysis1' balaA%Ai�s�g$forces act�M�v1j(cannot prova4answer� quesT a� whether ��Ak-%AjA�$permissibl-�� u�2�y,Ed.w may be%�ideredE�1�y`Es�eW'!in�� wo. \se%�{Conclu�.(remarks} I�� pres!awork we)�obtainedY two-�Vfamil�exact�q�7 lass�5A�lem�\ivo�� cs, namelMd ' of fin��(equilibrium�figur5�am�d�of ondu�j liquid!ze��roach lied!�based��co���� mapp��� ��on out!��!h!fh!,lf-planeA�at)=res��t_ur5� � :casU"A ��\-, w� all quant�Y  on!�n!� variA�s $x$i�y$` F` (1}). Becau�i�ll|�WQ *H ���deu�c%&m"�re��ha�-rdirI��jet axis)Q�: been!�!�red. At�ame time8 just�longitA�al���(!a!1c�(and sinuousjs)�8dF mjf�6z �g, al %�0\cite{sav}. N�theless,��m ,hydrodynamic�QM��erA�supa�A� zB?$z$%?,�%}���Lplay a dominant roleI!w�. For �ncE�e growth!!Aax" dis�� ncesa�� ilized by,magnet ���!�"|!� s known-H mel})�xt� � 6W retar� developm��i�Q� ��E which ben��� C s (inP ticulara�0is phenomenon!�u!�toA�� E�plasma�ЅE:�62�strong^ee� yZ.; �!(mY  �o it was!�cuA" M"previA�two� s, sb .d��e %hj�c8. \medskip T! study pA�or!�-�Prea�nt�,Russian Fede�(Proj� DNo. MK-2149.20042))Fa �2� Supa.NS�Q�(``Dynasty''.;�A2InternOal CeXFundaA#$al Physics!3Moscow. �Eh \begin{thebibliography}{}�ibitem{ray} Lord Rayleigh, Proc. London Math. SH{\bf 10}, 4 (1878).f JA�, J. R. Melch \emph{FM-coupledY$aves} (MIT%xTs, Cambridge, MA, 19632c��8 D. A. Saville,�. Fluids �44}, 1095 (1971�2� gro} S. G mann%n A. M\"ull�Z.~!U.~B - Co�sed! �%57d 61 (1984)!s\1 8tay} G. Taylor1PR.)F)X, Ser. A O28!V383�642��zu1} N. M. Zubarev, Pis'ma Zh. Tekh. Fiz.K 25} (2A�79N$99) [Tech.-+Lett., 25}, 920 (]2�cra �D. Cr� r, J.~%k MR% � 532E576 zu2F�E�a~D >H152-153}, 787 (2001:�3BC�\'Eksp!B5 116!�99� [JETPm 89078�99B�o} A`CrowdyR\1}, 2836 A.(weg} R. WegUX%< MNon��arP%91� 2131�02Mshi} A�0O. Shiryaeva,A�IA�igor'A 0T. V. Levchuk @ M.~V.~Rybakova, !/:'( 73} (5), 5}3:%�48}, 52)�3)]�endBR�o docu��D} �M% paper-temp> % -> % T  a��l($preprint, T c� , `vciart' \[vci-p]{ #$} \sloppy eN 4mssymb package� � sR �e,useful mathe4 =2ols \use 9{ I}2epsfig}�j�w�8vspace*{-1.8cm}��4flushright} {\ �b,LAL 04-15}\\.DAPNIA79: LBNL-5478%q0.5q�0.1 n May ��})�.��rontma���cŅ,ing \title{FW TestD >|@prototype (1000 2@nels, 50 cm drift i�)�� opera in a 2T3 er&�$  )[$. A descr��L is�aratus � � results%cosM ray teN2 ard. Ad�A�measure�l s us�simpler� ctorsE0 a laser sourv an X-dgu�radio-�ve &<{D!' velocaN� gain2�, � on attach�,ag��eaB&6� �p�u� �ul )E .HizAPan Argon-CF${}_4$ mix� pt"�)�!�at a fu&L� Collider.�%Y���: �I�� on} �0European TESLA$t%�%"Ame�n Lf Ddesign�e !��T�� �Cha< (TPC)�0e&m!�a<k!�device.�ef� r str~I�c�mE�jet��e(igh 1}5� fi"�)]! ��meC hese�a�iZto�<4vide a natural����sM(L !Tf!$�he�V volume~ �vɿ}. E�B��-�U-�<���setup%Rata taA� �+�abn S�2�3,�B4Monte-Carlo si6Hexperi�捧_ fav�a��?��in�a!U��41*�s �A�xmPspa�re�E, ���y& �Bn5�8%5} A.� lengta*d���,� pped�/ 1024��ic�1ha�in�/s!� JulH �nd+taken>�%�(in November��e�i�g!�)�8t e�� 96e� ($2 \;s 10 \, �� x!wFU~(Figh \9'Fig� *��"�1} � ��;  \e�{ �,=fig1a.eps,h. t=10RJ&bB& S  \cad� peak9�5�0to B=1T (top)5�)� (bottom) ~ !i� ^{55}Fe}$EKeV�  UJQ�Y��"��. } \!)� )�!�oldB&� AAWic�ˍʕ� + ��}$Mn< B� demo�a"." feasUnnd� M~oK!�!ale�� !&go&$����c  � rm�boltz� biagi}S S cala��s5�"� per l�&F$W-�C Over� eZ6�jorit�#n�%? (``carrier")�%an ad >#que�)r")O one �%wo mole�rQe� ,%0UV�Tns` d du�javD' he, ���% � Sn taE lJ(qui >o��en� prim�b �Q�fford! cos6 nd a&��*at� Y--A�%���al>��!�kV cath]voltag�a�2T of 2.5 m^ poinO't� -�!X.�"�)`er� ed u� now�]!,carbons. How^ ,"` nuclei,!�t%( bouncs O(1�W)&�ŭ'U�to� pr-�in� nu� sK a. acceleri !whezy�e'l��Eara�*7!Ņs. !,N&uAJ efer!��avoid �ge�)d!2a��CO_2}$ � s�o�&.�[��qA]+�#traE9Ga�� %� bF_4b�Qup�8-9 �$cm/ \mu s}�'aBf as� n1? curv��2�2��B[h]����R�2.�9cm6�6�2�ru�i�)!~Ab 1y " cA�-� 2, 3E�4\%?=�, !|predi�by��*� i�E�� � ��� �O, 3Br.!:2>H6? .} We nM��Ari2�(�"5 B  a���v��ionisŏ buck�on�Lcl�r� @0&d� !%rib�!W�4 edge at 5350 � a% accuracy,%�a 47.9 %�!�iM a�#�K moy� �of $9.0 Sx �.�2gre=�" Ma��AuN8.6JF. A�_- O�� E�$4.24 �&w.�6�d)� + 5\% i"� -�� !��� �is $4.1V�IRGain.W�"�a�>kR 2�var��i ��!/ \rm{�i�m a 100 � m�7 ap. ���yn9��2�3}.�s�`$10^5$şr7��n)e sp.f�ZI� xponQ'*� �Ka/-o�$00, du�j�1gf �aC"(s fas��O0a�� er1A� e� exis��o�%ese��-noise�?, ƥ �aso� 0 woul"%����a�E + e�.�(ee���MAVt Q�s� �@_'M��.t6��� �� �![�8009$�)����Len!��J� 3.*� ��a`!�J�� ,yow��a N"� v Aba$ ib�d��chain�5q�fa�4f ep.�gon��:�3R�A"��4reI��#}n� M*���ANa��on ki� sl�"l 0A�AK݆ �sholdE 4christophorou}�zi5gh�.1Bi��aPice"ga��negativexh�� cess6sl")"U �M� * N s no.(oreglig�393)1FiZregion, �={ ��3an 40li�alste��$ n[�verwhel�!Townse�5oe�6Y3�& �. G�2�F7n�( ns !ta5%6}wo�s�e6�&T�a�k��y�>q*r >}iY �unc�mL"�sus-v�E� �,ed-�enu�ulow� ��er limi�!@2.4 m (90\% C.L.)�R�_t �h J��*�9uy .�R�& ic E)J��! %�H:��!photoE-,A a�ˑ�1.2*� 嶥�a(inj8�:[ MFV s N�4}�(��^4��@2�!} (gon (97\%) .�� � FH5�%� �6�%�&� ��tex� A�� 5���* .>�"�'�X A�# .} Mw �<aina,.�� ofte��2vx of dam�#���s ](e{b)(, especialPn�semCQ! atom� dA�� 0� �� ��[~ }. �past 5 yI: hP manj%������ ���.-��� nd n�e��degra0*$observe4 ded !� &�.�ati&��)Ar�e J�,�*monitor!/A:�c��$ 3 days, g�*+N44 mC/ma (�� 1,000)P}A��<ol)%�� ��Nu#!bK o8R� no.21,�� �| ough)Aissue$ }#�)��A'�3-term?at�+ �!��r�*nV$as��o f�anomal!��ewell-a-rol��ngaB wI�E: a suit�cho��bui��% rialf i�T��*eAu�#.�!cir7-"6p�2C _ �� ck ot9�wl0�� _>��A�6s. Six� �� pad r�?(i�&�a'�!(s%�4��fitO5r.m.s.� e4 leftE�h�is es�'Ag �!a $likelihood[��<'�� ��A��coordi�&����i�9%aI?���  f m� `2I s (5k �o"V$��V@����#0gle-pad hit. �squ�� Ua&\'<-Xhs5C'#(\sigma_x^2$>(H1��laɌi &ploe!A-<� !Ry inN�5� e�.inc]9�.�V 6b = acteG ic�\i) lope:�]�*�B�#t� �P��w at� \,T:� D_t=6�Dmu m / \sqrt{cm}}$;r� erro�"d�8te�C��<�"�7 reli�8� a&�'] i��!F�wee&I��86���}$. NoXt e $\�/ \tau$ fai � g l %"B = 1~Taas7 as 4�r����f�5�� T� q1e-u y-ʼn1T��6!i!|6�B{ 5>� "5,SB(�v�"UJ�iga LC-�)قin ]$^�3-4~T y po%\�Di m  +E:�+a U!ql' I!�)xulQ �%aAt!�dE/dx� �. P�i�e"�!H�=|0�a�I-�er�mb�C%�(silicon pixx5YZ��^��&���Eon�Ec{.4ronaldo,harry}e�ism-��8$A� 4b�/l�)t� tA � a bi�H(QK 1Q)) putA���D� } A�)*P��"� �� =c�1EK���:�A�e $����a�I���F p"f3ly� -] �6 %Xe� � . OmE��!�O3F-a�s�)ha^gea&ut �sryNS re��l"Q^.#:ciplev5< @t�&&7 e�R \& D)�adequac�B�4�%Ŋ�2 1�5St� �1 prom�(�&: *{AcB ledge1s}�1wish �%(ank F. Biesd=xR. Cizeron, C. Coquelet, E. Del�,(s, A. Gigan&G. Guilh�M\R. de Oliveira, V. Puill�8 . Re�%ge�.m,J.-P. Robert� eir helpAk"�A�com�Jon5��==Karle/�X!Aum�!VVi] ia disp�Cnd"� $ software!BEB�@99j&y@ya:9} Y!>9B��>�,!3$155-165. M�-nilov:G�F202-212u %B.Snegie:Z``GEM�� R\&D 8in Canada", %in�7c. �I!K!al Work�0�!�8 %�84s, LCWS02 (Aug[6�2002, Jeju, Korea), Ed. J.S. Kang%�(S.K. Oh, %%n,B��SociedNp. 464� M.AKDix�J. Dubea%ՁLM�Re nd K�C chs,ZN�4018 (2004) 721.�&��BH�aN2D� 3D C�"Co�ng��  S)RPads:�|D&V ?"��D�j�i9i~hJm`r�}��$Bellazzini!Rea� a� �a VLSI>  ASICet�H�f c�uL�de"� 6_.�@ ��B�n1Y � GEM-� ��- �)o6�byH ( �4Medipix2 CMOS p9kHrec�.��3�4-PH-EP/AM -0092 7, NIKHEFa4-3 �,>\4 %\newpage %s %͊ �%� %�.�.%Jf..��.jZ.P�G!�!c�>i�>n;teB "�qKbe %s��6?c�6lar+Hstr�55�,�� �&+.�;t�Aend5I!o���[�[J[J�/N�~�/%��/� ~�/%��� ^{V�/%<a]�w�.� ��/%PC9�A2�0=�F��enter�'Nk22kn�#9tEP 6b:���G�G %H%:IQ�J���}N}.j�|��"�)of"O:u�c 1 %v�� B,3�Li����ai.d��,%*�"eP!6t��F2���Z��.'yd�/'%6� %�1'"1' ZI ^ �1!� .�~��������"9���"aCB�m�q�<�2V�"� a��".�&V%�������~9��%�A�.!%��"�2� *�L ��"qM(style[11pt,9,c (icx,amsmath:M]{a�@le�Xtopmargin = -0.175 in \AK98.�=7#c�,nsep=0.3 7oddc6 R�LMparQAnt 0.2 M "par RB newc6er{be5K�9\�L Scal\�j8a Fokker-PlanckzW&`fluctc(�G geo6! ZiVBcom�S"�HsoQ wind $� ilon~ by WIN� ACE}�K,{B. Hnat, S.&hapman�Row�Ls\\ S�-vA�Up|Qs�Rup,&�KW!#�ck Coventry, CV4 7AJ, UK} \date{\today} \�%57a"�K��eW.A� �tosph�H�B%U#emporxE�9�r8 �;b�Lbst�_�haoer�W burs�iq mBnt�@�c��\arise#"turbule& intrinsic��V � 9<ref�)� !�-.�upA!� is&�Va]YichO\'�nguishGO��!fekG06 %�tho+! driv>TWe ][fy !@P�er�6!:hort �$(�6$few hours)B�[N� $AL$� $AU$0&I��?Aby#�BE�Rp�d ]�%�M� �. W!d.�\] 44self-similar s� st�Ok&g�#approxiY!o�]"G&--69- >�3=Q�, regardB� �FM ity D,aS�5W 9-;M@.�Nper�s�!2�aAim�@l�:'�()��1$1-2$)�` -A*e�2�%ڡ:x6a show2�,�) �cyx&!�� tren� \-�.f :-1tof6cin=� v�d>�r c" g��I�s�E$;�$alway5v%ct. F:�!�E� �4iE/�.vw3"2��Bll�abe�i�ct.i� �N��A�U�e .��"�ZVfw�["�J , ca�aHy_aY4bf*�A29!�m3�!stochaaJ �]al=A$(L�\v.q &&I{er*;mJ/B7O N%Oarth'so(���K'"cb�C�ar,!�si�"ve �5%,�c�-"�;�v�B)�m. AccuLed �2is }�ep ,a�leii],"%a��ofb+s�:�aur��zo�J-<ion �A/�c�+��= �"��h�te+jtr�^ɘ� --?m)�� , , sic�f��}�lexY7�Da a 5eFsugges!7� any �gE<*k�4ex�e,_��lon,lewis,sitnov,takalo00,vas adisoros02})�e%#t\bb�:�)!�i�F�i��.��Ze�+ � ��NŁT*c����Y&e7!9��cj . R��e �s)ɼ:�FGjyd'z�t d�]aspFI m�Jf wO�Tg92,c H01,klimas,ukhorskiy2k(3,weigel03bjcE"e#isXd!�^9r�2�ivexh��t���N&�X5�_�/d�9f�da�#ll�eX.*i��]orYH� 'p� 9tG�Lre- %~� tail) aI,lopoulos92} ��tq�b4Ts5�6�"�-s8lui,uritsky01}.U ��8size=0.5� w�+ ��,{\leavevmode (ffile{./fig�i}}&t?E��%4un"�RDA��a�b�SxG� !s�&m$n21B�($\Fond$), @($\$�,�a($\���,$7dex:? axQn�s�t rsR�$S_m$�s $m=1-4 �!��y "c 2~)1!~n"}� N�"Tbjgm.kW��IG�f!P��Ga2bAF�7u A\c_eL8olini96,kovacs,��98}� ��2ri� �g,,Nj�1&�#� e�g theya�a�� lobal�8 �os� ou�$ �3:ven$$��d �@7ng�U val%�se] � % !��5$y8 o:{ %?ne11<q!�s�: t) � "� m�9j8�\@93,hnat03a,stepan"_ tsur6Mi�.ex +�L�Љ��%q�p:� *�&�vw�% l- MJs&��r�P�au" "i!(a��%qesZA`  ,%�`���� B��'�M��?M> �n��%��� ��1d oth!�w%�ing�bmK(�ye, �&foc�onUgr!0�X!�i �7� r��s"�p�� =�Q�ivf*Ban��Q }�eol�%wh�o , to_ low�P�� �nL�H�`d.�Qa�Mty �%�pre"@th�IO"�[Ie{/ Rm&8above� �YveN� � �=� �HI4S<Organ;Cri�)c (SOC��*{)!�7 eF=%�)X2C9,}s },\\ %kozelov1}98}�A��7. "B*Ym�,ne�ro�k� &�WdtrainV&e� !ze�Q� , &7� s19j7!�I�w�,a�Twe�l*�p�,�s� ac�'QzA��.�I����ayQ�%�doeX>�[ly�a � ific �A�* � M� sorn�_Uåu aim�96.C � �U�U~x:. He� we�i� Ol.R6�$Akasofu's ��M" }��x �0ich� 0C� !@�gy inpu"Zelaa��9to*.�� nF# �r onse` Q�QlJ(. PpjA�-0��b!k� al a6,$ V:%8 seB4.�a.��$\delta � ���9E7 ed, *+$9M?��r�to���E�($�h-1987$))���}.:��N "�߅�val�yɨczn�  sem telyI�.!��p!w�0"l[AnEc be�ud�1 $10$JJY>.�.�7.� ~?o�7�ta�4aw�f�pa�0�r)�#Q�`-�core to w5��AZ+.t"� �xhe: � for >�5*�� q.�Y[&�f�c2//2, we& �-�4!�B�}���to�^"h:J-8y�Tw�x{���J��se >�*J�� �ё�se 6T&? �uJ�ph*�r 5� . Reqaba�%-�1A!�� Pex�bunY�VU"�Va�q!w�IErgBc Ls0m M �6 % �0�@�!2@S�a6Rj 6j 2i%�.|� �a$�1 2� >)MI���ecP-.�see�yf`%&q&�  ,݂ �1�'E�!�B�i�:-� ���*W:6RPRZ�A�:*�N� E-!�]�am1<��< R�dmrY6>1.6 ���:�"6B�tas>�;2}%�8%�2>�H�:a@Y<"� �� �6 c� � or"�~=p�f (PDF)5 �Q�M a"s�eš�,& s: odel>b� rCby�rAH!!� g�:�LC v*_Ederiv<� 6�!�c&�Gp� i�_*�P6�e� (se� � ple� /*��\��1ods_mub�2 se�2>��w}w�Ied� q8�G span���*� ���i����8� 2�W�LsG&ed ���on B*�.�e�O O�NŒ.��cecraf6 se �s-ed  vicin� �L1e8*Y(ly $1$ AU (�nomR Unit�romJ Sunu�t�1 }[H]�? �}&8%�%z*� "�n$tabular}{c } \h�Qu�y y &S�ū$ & dt[s] &�^$es &N[mln]%}j\\ ? �N,��&Min&$60$&$01/85-12/86$&$1.05$&WDC STP\\ .3ax3793AB3�,\ f92f$8/95-07/97.63$&!�\\�6& c4" 1/00c01.68$&ACE� �N.-7�Mtabu5��)�� �o�=cA�a7fia�k��8enc=a��;of #es a�g�KMYTA 1E~Va � 6\�=Q�eDE!]{ �DiguouI�.�N.� 9,o!�6�e�U \ q�,aG�; JanuA$1978$� Dec9f� 8� �TivMS:Ds�"i���&�4st�$ng �$1995�A%^8 ACE!B��" 5T1�� !��t,� %��9W�Pe*sB 68�� assu|�"�-.G 6h��' in6P{%6>l!7Q next^ �a�s:/, �sl0O%fY Y#�ea��d� L ve)n.<�Z{B�SWE�tr4t��bKg �qI&�$�bf�"P *�=>� K`&� m(r�|! $75-!�"TsA��t�ACE.iE3� $6�&�Rmdm#� E:aR, o =c hanlf�fixe%�546$�b � MFI 7-Ga�$1) �.�ACE2�A�e%�� ��� re-���\ �aapo�c�o�� uni� :�92J�(twI!f2.<� $646>2�]�(four�"C ){M . No-ypA pM9s�Y|as�:�"�|or smoot�%,�ap��to%/��l* iJ\nd�" �lI!&K�Wat��a*9�=v(B^2/\mu_0) l_0^2 \sin^4(\Theta /2)$,\ $l_0\1 7R_E�% $ *L=\arctan(|B_y|/B_z)$�;Rc�`�=�sERAC6Y k;�%��!2�3���,�\ L�de6\ 4�*� All�k��2"ck~ ��$b�on"xcE�s�ig�� ��}B� a�u�{ ҂NGa^�TeP`Ao9Oh &�(sh�a� ��A�pr"�>=%�t��tiopy^" �"� ŝ ple,� $frisch}). Wae�n2�$x(t)$�e ��*� x(t,�)=x(t+ - 7#�> c�$6��0���Іau$. b&�'al:!)PDFB"B�%�e )�}��b-J�Zp*nlaw�lm�Be� tau=�4t_{AU} (1.2)^n���G} '$!�a� A[EKM`# M\(A,� minutJr$nd $n\geq1 K�teg�t<&LN � �%��A��KѶpoi}���Ko�log�|h�v)�w&c W;a1!p!{9- ($1.HL�r�&>AsAte*� 6��d�r]81W�i��e��eZe}8�if�#E�I�� I��[��a[��iߌnte�-?. 6�3 \*�S* "G�_�c:Y(GSF)_�wid� � �O*Se6R ͥes"Ri�&� �h"h"�02�2h"�f"�f"�f"A�� �"� fiB�KT�o"#���*r6�q޵�/ =(�$)\�< v\la#|�2x|^m\�2le��m$H�&n�falm%,\ ne�&ar��lve6�l�o%se��Yw�9r]U� !A� lagM���!w H \�htoN,^{\zeta(m)}$S {/Fa�-log �1�>$EP�zsho�'rev�aaa�[8 �QS����%U�Z.x�a��$�$. mk�5Fe>kar5���v"4,�4A0=\alpha m$ ($ $�#�6t)�n%M��>�\m�Qprecis+��af �isiA5�"ov5afses* ds i*d��! 6�*����Se��.� iu' GSF!� �M�"derm�aa�m>4�ai2� converg((��&� and � �?it^*��o�AeQ53}�al o$tE�ai�}-�S�caf�aA�*we'sll:,%:znNBT� d Uc8 i$� horbury&�"} : V.N� J). &M.T M�Qte����e1� !*2�J�in a wX~�a�onB$c&$�E�;!ks'2�ea !2� !��S kref�,%~aa�W$*o NO�1&� ad( he wavelbilter��M�>��! ��m 4'�AH�)l9I.�u�c2$AEZ Iko�'}�2 � ��aDs�im��^E.e�` $A$] =S  * ]i�am�"2a ib6 :A��"% !w�S A�a s1k �)ɬ =10\V $?��P�i닁'3��!s`+erm� .�� as:�~} <.4>=\int_{-A}^A . P(�;h d).igsf�� d E�d�ac�&>� !�u� =m \� $� ڗ �en"^aA, �!!X9�!�2(���it,I e4Xce ��ata�� :� 6�?2� ����in�+.f 6-�� g Ere1w#{quq[&57e<!u!Hۚ��ng%�s�N.�\m�!d: 1u�..0����arg���&duk:�, $P_sU�_slm-2� J>�=a�^{-I�} .]� ),q !Xl-uy � "_m =��. Sn9���+h%ed "ies�\ �q_s>��G�%�>Q �]�� by (vq�)��lJ&>9tau^{m1$�H_s}^{�N _s|^�P !�d.�^ 5[gsfreb]!,�xg�now�no![+�>I72;9 N��.� vhB=o2���a!he%q ��)+$.M��pj�PDF�g�t"��.�li��,�X o"ahl�B� =x[m!� ]-x[(m-1) � �F# :}b �m1;lfr)d--:tan�. sump� ��ZR7�(����+r!�| �^�o {�compl�Q�a؁�O�l��qQ &7�U�n u�bl}y2�7is"� ��..�R>��'&� 6�ao>! sis}vRll�&���� &:3$�M[no cl�eAX�5of1�--!���lie\ s-Dk line��>�7FRV�#6&$ 9)27͠)�}%x�= l�b����>![N� 1�j�� �?in paned- �]AEi�)^ps�9$ U/by����%!mii�#o :��~4s $log[S_m(loge )]$�e� �c2v��ve��mon�ww4�;` $m$,�il3��y �.+�7G.f�)iA~ ���uo&��& �ڍVed m01%%if trueQ��<� ��obscuo+!,oG; }/of�ov�^r�. /ws5�2}-" fig4)�&���:?a5ѐ"",(AU!mdp (AL)EWi�>�',8A�e�!�T�# to $a� CmAo�=":  �Y"�1"�+a�\�5�Af� sV22,e]��+Um�_)]&�U}$�o :o 8�R�8:We� lz! ;aП6��s�c.�,"6%� $m=V�*��E �i%�|0*��J�.,3ds d�e�sim1$E �A�g�B2�v�"�:earlier&%=93&�6&gzq,5i,sR4>; &� �>2��X[�PC� *�.-�f �q���!-e�a��*�`s�=*�]A�Sx�p3&��a~01�� lso D*a weakly:� �5u�D ��tA�"#a�5e;�!�:<5}��1 �5� �}rLm?  (not�=\[ure��!T� j��)�e�s"�$^� ��^%ab]�e"�y!�D0.1$nTE�!��es<�l!*ger�(!]�un��of nT)0ch�+ reteOrq*| HG�B�rro�����de��3&: f&)UDa�4? ld a6�� �6U��q r� n*?axQa�q8or,]�wQ%n � a X5* �7o&of9!h:!%\�t.6��z*Q "K In ��"��opB� � ����I�Ju�r ;E � �&� easonO(GxA��is)8 by�=m]A� at iBJ1J�6��8����BD$>!�6� aѥa�V�́�- l;&a�-F�W�� � >s!z!�.�(q;� 6�/�"�~ 4!�[h�ep�*F�B0 aWarj�#J]�!��.�� est i��K�<129�� ��2k5a�"i5%k"�!��N"+6�F%�13��u:�&0}3for�!=[12,90]� be�Mg�m.8��'"n9c�"����D6�Io mE�*=�5 :5 9V5 �d�BT15Y ��ak���I�2d 9:G  l4!#!�W �A�*����L���!=".�9&�Mn� �!�ph��>�# SA)fo*O*qo�}s �[l[C>�9}����f/2-/lyF�ja�&<b&%i�5�=o�B�:�U]at��m-�A�?� � � b�R�r\�S�e%AL� {3�=�r {. Exa�;N?v�J!K clud�e4J5�jo�:>BL�remare7�:iK]�o��FMult�}}n�0�Qi�<3�W�6�(�/{�0��0��9GSF &�$,_{max} [hr]$"0'p�;AU�0$-0.35\pm0.N0 11r)�0-0.43n)LR9 )�0R22R) R37 )3$&F)�k,1-0.26 /RX/^2J/672�0u[2�tab8^$1N"Eա�c*�A�Q�y@A�(same,/��� B� a:i�u�a="m O�� �- [��u>5in�&58X�e�K ��i10B gIZ�h,Z*�N+;2(��Qk��w7�trend?B+. A�$s�~ BG �R�x\ ���3 �6�m-#հ�lS�bt "�J�l(. tail�!� insu�C==�v�i� _ #�cy �2%�^ 9�!^�AUngsuʨz��%�7 oc��djM &j�:!�i%��.�7�.s$E� �gl�G roRG�� (eg.�+$baumjohann�+�>��,  {"U1lu� QgY���"�Aa�6!o�l�rb.� NK"+Bd.%M (iG}"� &� wh@"�  relev�2.�w�V-F, (iic��7�. M\Ir�[A� r (iF1cA]E���nv&.�M�883^;Vљ�� p"�=75�)L0B[ C&� ��"D*] b��H>N!�t��qu8i�� (a)-A�ex, (bU �� (c)-Y/2� 10!n&�K If4 Aa�e��Y�2�>�UT ~�i"�G��>e � �/a��B� V)ͷ��r�.� of Brown[�moJ($0.5$)-X -s� �8 � mum. Clo٣�z�*95R�!?9z!� 9��)A֭�]� ^�. ^{1_} �2 0.06i al�< "� �e�� ��&�9swi~3�s�D]!yiD�Q ���(�'l"!%>�!�*<�J�=is�{�*���"��@nu�� \.�2F�-P$"� by�)u�"Y��� ��92 toge%1�&��lO:�L� �9.�D#�")�fG }Yd<�N!�> o,W6� O6$R^2$ BN��9>�e� � $m=2MQ�ver �eg.� O"6E�� 4 Qx]�Q��s���3Z�'p1H�wk�"�'=?&"?P&� D yDZ�@�@R%�� p%��sMdW'�#�^aټ)�EA��4� D"!Zsw4d')�C&��oE�-. Due��eaT-,� � �hig)��9�t�x6vB.Mt7��i%� hS$ir! ��>�11B@)�edo�$ � NZ (empty aol��n&tG(fƲd. Sym'*� ��e�"a"S�=10�1626��$42�\(she�� "�&�"�z�6I.z'�% mdl2�%X0p8s ��� ��36��>�]i�z��U� 2E ����$�F�[jNE� I�Yo6���C�gnwMa�� 5� iZ�.� ^��B Da�?+.cR&s>�11}eM"�2�i�]_N���9A861G��&�F��N|""�>��B�<�3 ���%���e =cUV�5y�Ɂ]%C&�m�"k BJ)Ai�(0(!4l}). [�lot���AGFIa�M)a �/ly#�M llapi *~+ #!!��퉔l}).[p�=t :!sEXM� n�<hecked���DSmirnov-Kolmogorov��$numrecep} s,�/s�:"� nѬhyp"i���h ���awv@>%��2)��`�$�6�S4$0.97C5$ibOh�M!�fi��N��Yd !7~(.�,V  -L &� � ���5a�� � }��&��%� s. AY� a6�>q�-�e+�>%ޞ�*��J� J6 Q�2�. O!�AKal[�� �� �$� "�%Y�EWe�}�aRW)e!��1s͓nceA�4 (Q���p !o)=>�s\�k &9ZV�*�E �byYn6�liz�A�]3vve��B2a�A ��� �<]2/tau}$W8�M���t���4%#�a�n)>gGgE� ` q�or)2!`�. S��� �I"f#1.�[ m��[�!6_a}Are"&�%�iq��E .��P= � Jm,a�E"L !���han��I�r�C�# B# JMP��b��!d!�!�M�.6B I�DlpL��6� M�M}�:(F-P)�d&�dn�5-.>'k�!n�#INQ �`EU��ala=��e"5��L!Bvin�xeRI6k�nt\F-PBnNy�;��s:;ga .��.V$lp&�"(`./)"J>2��j"x�� � Nl>0�%" ���M� �./&$i�QM� 5!���  f�0AW�?8.�Ei�Cin ��II B.�0e�eg�0� We%�Օ-�wrM8V�6\]+{\�!ial{P}} ��}}= \D#a_{�x} (A"}2)P + BB-P)0��o-p�}�3P u>B57��%,E�LA&�3y"�x�.at1#�D�  # k� ��*�c2�P�&�Gxn>t1t"�9,�@�$pE^of*yB�.� "�>0x^{1-1/ }$>.�J020,�"las��.��n� !�)���%$![!���L"!a9 Dl}2�Yb:sq�2/>E)us} B�!mi�1 F�51�J9 c a� ~Ua�QzJ�5i b_0}{a_0}U�_s) dP_s}{2z5}+P_s+  �= .>^{ !1}$}P_s = C"�5mdl1.b��ua_1 b_0$ , $CE��b24�U"��5-@� �,eJ�TGa .J ��].m)� �� 6 �/sc�f .�<�in.Ps�Lrb}=� narr��Pv M� _s)=)E!�%� C}{"u;'7 /!�}N\left(- +)�^2 ?(.7)^{u]\r�2 )\no�P�q�Cs�70^� _s} \ex l :k�'Jj}{>!-a_ �.m ') + k_0H/&>9�� e5C=9kA9����A4%�$2J�ja�N�=� } 2=-�1��^�"1=homsoF&:X ���V:j�}�8^2�p�o$a!?&�7ii3S�to  �eV.� &p �>�� ,JE$..fIn� �,g=�*bre�dow����_f2A�a� 0$a�a�ul�3J %�qx�Ju] I�I.s'F E*S.��Ir�  s�` at $�: \infty}^{ �; .�Ig)�&WeU�h.X <A�N�*�/>�"�y&2�q !� 5�"�Z.&J sD.' � r�i��W�9�����z"� � "��|�F J�Au]6wEk��"ed���.�9FB>��� � A ef� 11}"�413�lBlZ�[�� �$a.� 25>�6� >�[O��b�"�.�uQ��os���xd&�,� ���$�, J GSF � . �a���l�"��"�msuZL\ �DMz3X�"�F� �i�27A�]�ed ��A�lI��$.A�}��)�4syid�c.� +Ԥ�$ur�u;u.�s do oث�  a&wq� a:��&�.�ns��bp�![�f�m�}!� ��.2�S+!��:�as}�� is d"�"�n�^I��!�6�2����nnV",�W5r�E��*c2�d��>��.�. �,��.�!Z��%�,a�w+!xX�4|`,�T�;�eof!Ut�tA�%~&�4�-��+ m�ect�8h��LP֗d�[& R�:5i $%@H�R:% eA� by N�lyY�#�ise�n a�"���M��0�!; *� $D ��!0&��,�f�t$%�A"-."&��,V����c!H�3I �9o.ꙑ&r.:��b��"'-0p{1.75cm} l{2�� B�H^� /� g-|  & C $[F  10^{-5}vr- 170 N^875�] 28$&$32.52&-�-�,16 :/0$&$26.42/U-�^220 1.U0.3�^ 7.77B-\06-X- 6.66.-���^4 ��12}�.1�5.30 8 .)\r_ �-e��aB�-��V�-�"!zɥach� ���"�c�ML�"*A�e�2Փ.�6�0 eJJɇ ��1g.�RwJZ&L )}{dt}=\b�P� )+\gamma\xi(t&'�Q�"+� +!random"x $ C ��XbB $-�,. E S�p ����� i\Gpur?-ad;Cv�*y� Js-z� =|) z)}{ �z)} + �"b��!Bez�K*� } 1/ S � x')*� 'I*�: 6 �#onl9� �8C%��6e$ �x� nd $:�!��4E*�u, �� (��)�� !��;���4"� . S;a}&�q "Mf��# �&�x`bir�"=2:5l&�on{SumH� ��n�  ER`}� � �.�^by �#��ih�@�achlZ 9�.�3,�E�*.�O�@6A�~�:u-�"!�]v;-.�W�&3}:E��Lyet�<f�Qo �+f^&"��U0exG �Q�&�^Pcy>0��p=r*{ QF^G�)6!*,��� �)" /���]*� �7N�&���C"�!� nume+} \�N2�Npa���Y�2WMC*A���n�}#%"� Nu&� &��$}"� W 1nl� < 5�#G[& Ur*h 6emerg�Is�ea���\.�"� 9��au+.R�JR �kR��:�$�e�:Y>$�&�'4( *ipV 2�!=�v=P�1.5M��PV�%nH*��y .$�In5Vk* j�o�i=��n� K�0�)#es�[J �V^t5���A=/u���7"->��q���� BZ&�|i erI��� A`�0 �qRUq�� erR"�uR�2"G!��J�N&�#�+e �$Y�m�L�1'A 6�La&Q � to�p�}n[ �JA��%E.%q*))E/�9˝\i�N1� �0!��xA�!< 2���"�?Q�NA$J�=e �J�W�# lex �I!��Nz�as.�yor�z�)5�$E���f� �e�G 5&�=<eE�sk&��;@�K2e�*6O#be*��/�`t�Xin`����4 Xo�y!�]ZE;!�&f% p_�2*�9�, Yo2v. ߝ�E]8�=$Ƹ�6q�.�K�A�T(2����&��"�$&C1i21gg����!�*s!�vol�i �ner��vp!=� PiE���[�yZ"-�)���� � �9�+!�!:�>%t�j &"^-a#v�I#2j%Tn%*4� �n ` �� wQ�;&��/ �Z � . <1�F�[ׁOa�.L;�a�hQ� day- ap��A.-q� �o;k*V�>�$S<�2��i. p) >�SE�a��We� �N�2�A^t.��,� Rx����e1�Pr� ���5s(SF� B�� link6�"?�&u$8�Gy'�al�!b��.� ��*fB?� "'A"R�l} B.~� a�����A�PPARC3� ~C.~4�Radcl�K InsXI!G"�T�-L�(hulme Trust\ tͦR.P��p�Aa]�gilvi�)r�$vi�7��ataU NASA�J�h�pe��jSWEPAM �ltea�$�j�� Ce�e�]�'viK=!%t�cr� NQ-. %�6�;>�{3�Nbi�� [{\it Ang"�� et~�(1992)]{L *��2,, V. B 5, B*� bulk ����inner �d4� sheet,��Ge:�.�6`. {\em 59}, 4027--4039, ����9>�9F�$, T. MukaiA�$ Kokubun, "��!�2���.�!�.��r��org�c&�, ���`Plasmas 6}, 11, 4161-4168�9>�B"|?u Treu �%�6)].�?.,W.� R.~A.~6 �Basic ʕ ��ic#�(p.89-100, I5�,dCأge^ass��6�!2�C���AG��92} (, T., Low-d�a�al Be��� S�� BS!a� of S&$Sq�s NUC9Z:�aj se E�cO+o�Ne a� Labo�y?-IEEE �.14Sci., 20}, 691V���a�Watkins}z�1)]!?�01% EuC)� N. W. 5 , Av���NY� Y�s�.�a( digmA��Osp ��s� �� Rev., 95q�93--307�01>tConO�q�Amc96}&#�<, M. F. MarcucciCandid ��f/V.4=aI�urZnUyroj��+x�%, �i7�k�, 7a< 4082�+85%�6f�!RDe6�helis�8!��8>��)P..7, Non&o�� g3"S"�AE-�.9s:6f�2kM�6Z�,V� 408�90�8>�Freem��2000)]��} %� P., N.~W.Q�!#( D.J. Riley:�8P �]�aLp"�nb�  life�2�AE!�ic7J� � 2 ��1��F�kpA�5� F U.-PT" q�leg�� A.N��5} ("-� {��c��s.I�� p. 8B�1 =� 3a)]J)a} , B.� �@,��R !� 9�-�9�&�J l*�erme-7ofb�:S � *:`��u�s�.�x, j�3_�@2174, DOI 10.1029*� 3GL018209!�3�d.�B"b5"b)"-!.P FG.~9$��gcy,)��E�Zq�.�;M�=���"��#"DFP >�E}��6A�056404�k<3b. \bibitem[{\itt Horbury and Balogh}(1997)]{h }$T.~S.,+A. .�, Structure function measurements of the intermittent MHD turbulent cascade, {\em Nonlinear Processes Geophys., 4}, 185-199 1997. \bibitem[{\it Horton et~al.}(1999)]�ton��@ton, W., J. P. Smith, R. Weigel, C. Crabtree, I. Doxas, B. Goode,9�Cary, The solar-wind driven magnetosphere-ionosphere as a complex dynamical system, {\em Phys. Plasmas, 6}, 11, 4178-4184 1999. \bibitem[{\it Klimas et~al.%�06)]{klimas} K,!�\J., D. Vassiliadis, D. N!�ker%�D.*Roberts �(organized n5�dy�1�6�%]1� Res. %�\101}, 13089--13113, 1996B� ov\'{a}cs5� 2001� ovac�"l, P., V.~Carbone, Z.~V\"{o}rds, Wavelet-based filteringA�2�evE�from geo)�8ic time series, �Planetam:@Space Science, 49�$219-1231, �F�zelov%tK a}�3�} B.~V., T~/`, Cellular automata model� �I|icY�,ic coupling,ItAnnales1�(icae 21 (9)�0931-1938 2003>�LewisEr!�l  !�., On a��apparent randomness of substorm onset, 64`Lett. 18 (8), 1627-1630A4BQLui.-0)]{lui}E�T. Y.!�it( , Is�DI� M.�, an AvalanchA-Se�?-6J�<, 27}, 911--914,!30>3$Mandelbrot%�2)]{m,!�B.oLaussian Self-Affinit��DFractals: Globalit��@Earth, $1/f$ Nois�0d $R/S$}, (Spa@er-Verlag, Berlin�2)>�PagelE��(A� )]{p01} "CF#In�� cy iI�: �:: A�4arison between !minimumymax  us!� Ulys� datajr!�hNo.A8, 10.1029/2002JA009331 �B�erreaultxAkasofuA�78)]{a  '���ES.-I. 2 , A studya�.QE��LUKJ.��XAstr. Soc, 54}, 547--57�+78B�raL et~a��8�$numrecep} , W.~H.ERlP.~Flannery, S.~A.~Teukolsky(T.~VettE ga0em NumerŮrecipes!�`C}, (Cambridge Univeristyu1�, p.490 6�Sitnov�20e�s} , M. I.e�hS. Sharma, K. PapadopoulosB�!Q(A. Valdivia@J. ���4, Phase transi�4-like behavior!���.V e duaA ��s, J.9�2�5�L$2955--1297Z Sorn!|���s� Crit%� Phenomena!�Naturalюs; Cha!�(,�D��a� A�DDisorder: ConceptsE�Tools}, n-0>� Stepanova.���s}$M��,, E.~E.~Anto:@, O.~Troshichev, 6Eof2�ic"� through�-�7distribu�&� 4of PC-index fl� %s, u�%�ъ30 (3��127��BTakalo�199�t93} ,� $J. Timonen�2L H. Koskinen, Correl� dimensZ !�a��of AE��(bicolored n��m�J� , 20A� 527--1530� ~�m� �006�$K.~Mursulaa~ �, Role�a< rA��s upled-map&�th"X tail: Doe�6� act ] low-pass� ?!h:@ 105, 27665-27672! F�Tsurutan&S199a�t}$�X T.��Sugiura�  Iyemor E? ldstei�  Dnzalez,��I.�g,-J� f &x resp- !UAE to!&$ IMF $B_s$-e�Rspect� @break at $5$ hourBxY�, 1�0279--282EB� UkhorskiyU� )]{u}$�uY. %I. ��6�6�Combin��g�E�4multi-scale fe��Ɋ a descripe�oq&`-6/�� . 13-1929E(B$Uritsk� Pudovkin'9�u 98}(0V.~M., M.~I.~1,, Low freque! 1/f�~.��AE��A�D possible manifest�1 of s( �� ed c�,5 � 2�SN 16 (12 580-158K 99B�1 � -" ", V. M����Ɇ.2�Aparative&J �<al� AA. � auroA�elaojet ��versus]2e-V408}, 3809--381�8B� van KampeI� k , N.G��Stochasf&�in  ic� Chem��ly}, North-Holland, Amsterdame�B� *�.���va"��*c9 J. , J.&J ��.@  N"Q E� Weather͖ Adv.   , 26��97--207,�]Bx�.��z.�3}.*� R�~� A.~J.~�0S.~G.~Kanekal  0Mewaldt, Mode�energy" fer%�}�i��i_ R`!�.a�� 1�No. 2 63�BgV�r�a�)]{voros�e2&, Z., PSL,, \'{A}. Juh_sz!  KXrmendi%� A. W. Gre�ScaeZlaws 2� FV= 2621-2624E�B?2�.�aF�02}:&�8D.~Jankovi\v{c} �� ~.&�A�@ ular�chaA� aq�<� �..)ic61Y�y�1, 9 (�? 149-162L . Iss. SI!�B�I�|B� A�w� 03a} $A� S.; (�,� babi��2� invariancA($1-$minute �1-zone .� fiel:%�*9 �3U� 3, 2193, *v 3GL018470�3a>7 ��@.�b.��e� m�A�", S!�a��a�Apredicta-# of ground-�ic ��~theirI�derivōsV\ L8 (A7): art. no. 129;`b. \end{thebibliography}  docu0} %���ruinsma.�,oslo]{T.~Bur_]5M� peanWt��4hua]{B.~X.~Che� b�%?DeA�2>0ihep]{X.~Dong2�@austin]{R.~Eckman2V�D.~Emeli�2@ ",mephi]!Qv2'@dubna]{I.~Golutvig� F%� Hohl ��$K.~H\"opfn6�)}]{�ulsberg%b)Y.~Ji!�>C%vdortmund%UKapitz; �S rabeky!�B] Z.~KA�;-$Y.~Kiryush!Y=�Kolan� \cora+(ref{cor}},  [cor]{Cor�d� add�: DESY,O \tanenallee 6, D-15738 ZI��� rman`el.: +49-33762-77380, fax:030. } %\ead{k � @ifh.de} hTn.i@desy �8or[stefan,marib�!L orpaa�90 &ljubljaAJ$P.~Kri\v z:s1=D!\"ua .�-{A.~LanyoA�5ytue Y.~Q.~Liu.;[T.~Lohs%�=RkfMankelNX8G.~Medin\thanks!�gk}2HUt E.~M�lA -L� Moshk�#�J.~NiV���S.~Nowa�5i]�]$M.~Ouchrif.`�$C.~Padilla��yR.~PeōJ=,it��A$trukha��M.~��.B� ,hei>e�ID%)���D.~Res!��$B.~Schmidtunihh�c  -Parzefal2��AErei��B�,5H * \"od6�LU"wA:.��l #rz!�F�I.~Sicca6�%7]!�Solun!pF;[om6+�V.~Sou� aKy !9�Spirid�=Use���Stae�c2�Gq^C.~Steg�!nI�]{OinVR*N�schJ,sofiɥ Tsak:� �2bU.~Uw%��9Qm e!5T D.~k vsky= e ��0VukoticBS-M.~Wa�2A2�J#��>Y|~W6]HWilczek�U�R.~Wurt!Y=_ J.~Y\.�Z.~Zhe����Su7R.~Zimme��n} �  \��U�NIKHEF, Kruislaan 409, PO Box 418�009 DB./ Neth�nds=}nl}� f? �s1of Text A^  part� �@ics, RLM 5.208, ,H TX 78712-1081, USA~usa2)& Institute]High E�i Beij4100039, China}9-9�2LEnginee�LT�6hua��, 2c84 `R.ijI�]h f\"ur ^(k, Humboldt]\"at zu}$ D-12489 GEy=' bmbf2(&� �:x5�oD� , D-4427u^o �m�Joint se�Nuclearearch, D , RU-1419l R� =�uf� D-22607 H5 52ͮ| �&�alphys!s6�S�-22761b��.�E2 kalisches5,>r�� u69120 �x�HJozef<fanre� 01 L? , Sloveni.d*] 5� 71�G"� 6EM� ����� [ 1�e�Theoret��.�i<�O<117259 Moscow,QH�%}#rIc.��2x%�[6� Oslo!�Norwa.yn2V��(Fachbereich Xk> R�av18051 �"��eit U/�3584 CB���� q�VB .Svisito)�)�.e5}�(540J�}m�2^BZm,INRNE-BAS, S�!\ Bulg�.\yerevan]6^Y  �y�e,, A*aZ�� @[nl]{Supported by5nd���#al� on M�8 (FOM), 3502 GAb�� uus� >vU.S. D2��.(DOE)@�F:�Bundest%Wium�XBildung $Forschu@( FRG,er contJL numbers 05-7BU35I, D055P  HB1KHA HRA!�09  7HD1 9 7HH25I��q�[i�:�W �Zn RmF�)��`r grant RFFI-01-02-17298A��NBMBF via MAXhnck9�Award=S� J��Jegian<Council>gk::�3�(Re�` Tra* B GK 271!��abs%� } �jV�is a � dete� with5112\,674_ ft3!� nnels. It@ expoa+to a  @icle flux of upd$2\cdot 10^5$\,cm$^{-2}$ s ,1}$ thus cop� � A]d�%s simi�*� osewecaxaf!�LHCr�s.� �!float{-&7A1��1 } \iE�e{H s_elH % %-� \sec�{Introdu } Mvwas�'�$ fixed t t]�A��#a`CP vioi���$B$-me.i�s u���# rnal wireXie protS.ama�� \cite�ab}. ToA�cheEneq4�1p� ��,of $b$ quark averag� fou�(te-�e� bunch cr�%ng at a*�%of�x010 MHz (96 ns 5A���) has�Sb�ne�d��is leada�$y�02v�21��. W(mai�V�� comp�*(ts (fig.\,\�Tfigotr}) are a siliconstexS,�'ip�)/!�I !�@ !�g�%�P.13\,Tm3� �ke�th!�I?#��V�+i!Ptrip gas�mj :&an:Q.9��,B-p$_T$ �C�im C�� nkov= !�( (RICH), an�# �R3alom$ter (ECAL)�a Muon :2)�.� 1� co�&!4fr}"�" ranIj220 mrad-� bep�4!!�� � ��16 0 ver]ly. Ie followA�wea�cribeB��) .��+)e 1�� , i.\ e.\Do�A�9!� %� ing i�,&"��@amplifier-shaper-�Kriminah� � i�asdpub}�a�� (Lto-�al-con!er) ?*� 8 �-B.ipt�&A)as-1s:1~next ���� 9emY$is briefly5g�!~e%�D3:a ��on -tdeh  side��rw5�.��%�6��s 4�E6Bta�!dJ4+!� c� a.:E� -volt� 1��-ASD8 boI�d%�. S � 7 �q�.� and�B� .�% givee8 irst eval�/ � *| ))�D5s�w�y summara"�2� E�Ӊ,} \label{sec�b %� figure  ce�� } \leavev�7 \�xsize=4R boxz /det2.epsb I \cap�Top view-2m��)62�� up@yeR.ar���䉂, p� %� t� c� 2x indica� 6black�m as (%�A6moduly ttachP /m neaib��� �d�&reas).5w��� -p �#  \{, *{Dem�D&k.:}�G2 of1>��4herab,otr_det}� ea��13 ��arH 1NV�of�n5Mri "�� !ln�E�9��sis�=wo - pend�91�.� e: %�-|!�G�O��a gas-t� box��sus\d�Im a rigi ame (`�* f'). Oi&13�s 7p plac mAIg (` �(s' = MC), 4���'-Yreg�Ybe8H�1�����;v��Q�recogn� (`v= PC)F2 ._P ]  (`>�TC)two TC 9������Nl(PC2&,deliver hit �2 als i F�L Ti�i�m� rack�� a���b mZ6tum.�?�providW=2o�� �l|.�a honeycombUO of hexago� *V%�builtI>4folded gold-co�9 , ca�=,-loaded poly U foil1W�� ori�Ld 3$0^{\circ}$�$\pm 5�5v�!�perA�icu�on 2� . I)2>. diam- �a cell� nges � 5\,m>�to/ mm; v� cera�2t9 ; � am (� 1\,mq PC!a)Laccouny A�radial d� $,Mpar&�. As A1� $fA��mixture Ar/CF$_4$/CO$_2$ (65/30/5) is c�n. Ope� a gA�h 3" 4$,]I�c���, 80\,$\mu$m/��M���m �b��l�ed��i-�� &z )of 96,� 1]�u.� %� t� 1ionisn�Oa"�< �i@is estimA� ���/c> a&yclu� ��Y2.5" s. Howev�*duU�los�0�ropy �B ment only u 30\%V!G/r�an C�� � meanB� �E. %&,{\tiny checkW;y%%>,� etc�.�RA�� � �(occupanciesR�Ubd>Y ��orY/)�iT ndi `��A��4w5�]�in"�� s cur�@ly � iLHC. At!�7of 40\,!hi�e�"�:�5�yrg��.� �ya$roughly Xn by: $$ \phi \approx \=p{10^{8}}{R^2}\,{\rm Hz} $$ w $R$P�N0Nj3ny units��Si�@�V6 ac[<B stare�pinto �eA� insega]�}li�!Ha�l%�� U�yARe3 2a�!"\B%(NhystmI� 98 is 20 cm)�� ��achieved� � ��a �e [�-2�e%�s%x ��� � . If a 6/q�/ ��Q�el@��(carri� �upper 1 ower.<� ��iSre� does vgHaav�C�length�I �s, $L_{ }$, vaF"N 0.2�l��2.8 y�!Jdiffe�G ca��d)�ve��tE' inpu"A"!I% $15\i�pF} + � �C/m�resD;ng!ȡ/s"� 17�43\,pFmr�  �f� , away:�� Ca locI��fAɅ�lo�� low 50 Gy{ yea� �ћics!M�ed� \ \ ��s�G�er.o��\�{DteA eria �F�>�2"V?hre�*|QNRO infl<Q heQs. resolu! e�� efficxH�<;% of�hiI�>��4co2[K !I�� .r of����;C6�=��sub!ion{Req2<�T(one} A goo� ��onA�-�Nm�)<%Aa���neeC �a p�DsP�u2� , 4���W��,icle environ3 itfacr7at-�!*7S�%-"+it(* hme9� should� e�C7 � �tj}. ��C!��� � �2n cylind�E)4���9 etryW.&� %� ���n"� =�� "* wm�"0 of>�mri) n �)h��!��Ÿ��s ;�� �L� s�� y 0. For safety� sons,%@void 2�RA -dow���R =effec?M-�dec+' &{e*� {4}$. W�%��ɫq � (����&� � in � )ADult�b� h!@a�MF\,fC af�� sha"y!0 c4 ap�rF��5is typ�%AnIXq�1�ics �a�Eeshol�9.�3T ( 8U/� _ *j!AD! J�a�R�� � ( =4e $> 98\%$) ca�J�!l}e.m�sta��Y!��� �"-t���c>���Jal���� y. Pro�`$such smallm"Z!s�����G>!k �� � i �h� � ~e.~�pr"]��$exceed 1\%!�y(am�of false".�\�� �^:< � neighbo�I ���� �!�"iY�> 40 s%a5 A1red.�e\�� refo�hg XS�B� 1\%. �s�g� dem�/��"�  band�!�b � q�com* Ni�m;:� G}�-�z q΍D igna�e�pile-upA&zVes will���kfe_new�n@LepsR: fee_setup%� �A"' %\vs�U {-7m�"6R �%�r8(-�� ,! (top:I�anD-on" 4, bottom: phot$BM� mon�+A>�* ssembly cApdI16�)2�chainf� ���("$~\!$ `) �SW1�ite9+�&�Y-]��"5 (HV) �o; p|or�A��ͪres&w�&, \~ twisa� pair)>,��� a;ɽ�a feed-RP � �xe wt i�� boxg69��cRf /m b N[e� Aser� � AEM#��nZ� v�!�"aB�`�*l�0\ �E�� Kh�!�pulses� sh�B�A�e.l��p*�.M.�!�iz$a�HV s,�ngOHVY�� ,���%"<Q7 u#7"� �volum1 �[� dry � 5�� ]�� he o}9��.<�� are %��ut�fc!�be�U� N��HV� i�)A0chQ!u]D) � MfAC--��.�ս s��)�e� pRveEQ'gl-Vathod�ia�rnnn�/My-� 5� ahouL! in c� ��.�q�*R iM_I�H&��I�E�heYns-�U� �c�22)� Z(�YH4ndard: LVDS = �OVm�Di'�SG ing�1 a� AR��� %i%�ȍ�DAQ��� ��hiA#@.�\44�ed.3 (�l�#��� o"� linkmEb� � R� �More i.� ��'^!�Z0� f�3sb� &� � )isc�/!�fu�`aHK-K�Ied y�.��ail)enadDI.� L*��s �Q,T �s /}. % .O�3np!S�` ing}*^&_i?} AA��%� �:��^IP� essenE��jo.�6.EK�wh,� ,.iv�1��o `6��( , pickup,� talk [E��back.  '�%� n')�(phics[clip,;=&-',bb=35V 594 491]6'5 "\ �g" " 9�%�e-�: y�Ys2� r g ��&R�+m%v w referr�� &�- \��� half � : le `` 0 R�` p�=$'' (GND RPe�dedY2to�.�/�' po�c��I��ť�M� %��b yi.� �lto � (� -�[�T�i�ly� 4} �%. � � �%s (Net0)��A��Q; �x,e:9 ha�n">�as�. All�X a�from yO ��to -w�IA�^l�/yY�� s, !� enclo�e%O 5��s (LV,��)� e.-�.���� most&qUE��,@O�-Aa��$͹ �g!�4�_b$,um�9�%�}F-�@h%9�. , TDC.�b�,-�, � �M� (DGND)SN � � (A �-$ed (se"l-  secasd_�}A��� of�P� � medi%�+!�� )�!ja�1.C> i� �Q� |���� ��S�e Cu-Be b�'eAR' t%=_s,V �!�M� . Be:fe!,a Farada�gE�� = lso� a RF͛f:iU�5�*� 6�!5A� (/4 <�-ions). �>�Q�d s go9YR�h�@9��ab�ely&P��!@T��eQoutput t�.&e �0 ���� �)�A��(=�]��#directQ� ?�5R:r ��eC� m �� � "� 2�$? 6.t=D��. �4fi*t�I5� :!{�N�Mf�" leteu�a� *:0is�2 "� q�; �  &I �F� �/ &.2#��  Ro�i�1Gas�G2� hv_r &}B�"e isɬB#%�L� � *'�Ѕ�"u y Ue"�� |�.���a��G��� show�$�"9hv "}.aG� ��m60to,0 vidu�(�0a 1 M$\Omega$ �:!i�<�n��(N`qqU�.]�  A�":s (330.#X, 4\,kV)\footnote{ceram��2 61, X7R di� ic, Johan�8Ds (NVXnr.~402 S43 W 331 KV4)}!a^��q�oreae4��e�)�C6^ec&))$ � �@CQa (100 k1g,ϡ;�c�:o�V�QZ��s�U(, 6FU >7a�b�5��a�wo �` main��wi68 piggy-�W �A�op;i>1:edVrpᢁ�W ?� *� s 1A��16AIOBu-reGE+h s 1B!16Bg *�siv��JN�I� m�i��:/!�!h`�?h 1'��YI6�q'�u B� #n�H "�/-�IAV��}�!��7 e�.nBh"(n+2)A�V�A � 'jpis5f*�#���g1  ORF%�se s in&9#inc24��&2 .ѳQ� j>-�� d prd _0ui3ard� th surfacAv ��; SMD)%a%� 0).�mat�XgAT�)pitch la*)�)��)67Q0�)�3�b&3�(or�C=gua2Ee)2jproof�m,�2� 17!�E�G(M�E!/!�� �(��Ja*>)s2�me73!�wo.gc<d major � lem�.y$rune��Z od, N� )N�.HKap:M&�@?�i�I�s (16 .���]*&l25e�5�+U� HV��16ugg �� 14� ��b -��D�� h# Cirr %z!w6!�NG�3�D8.% 2�`�d���7��ly disb ]!�CA8E �"�@�:�^49J3hv-\-�e8Z�&� � ��:22��)�nd ȁ��' mapd%(�6��{Xnd��1cm} %��5�03�1�:�Ap e��QdBi5�' 5~mm�a2/-*p61!�� � .e%�� D�eiPl!�Prs "� 6�) 2D ($a wd2X I�m�opt7��& #D!!!}%��"Q7igh vZ�4uG�2or broke�4r�#thVUIa�!�c��|�Ic8p�u1 �:B��s, nom� ly 17"V05�6#��!Y1950\ ! 10���HV eOfo�8Ae"e �6�� is d.6� :�z$s�`�1} ~-or �2���6Pv�b���s��f �5eoB (6��7 nd 3�,TC) ��th su>n2ct�(12�� PCR 8:tec� h�L��)�&� ,CAEN SY527 M0 !YI�: One ]m 10uOB�A734P,��� +6+ S s (max. 3- /3\,mA)"@�!�S�%CMNol ��V288 HS-�ET-VMEpF .}eG�B2Yc GlE�HV sourc!�<AI��s �3ix!`with �) 1500I� 3(. S� a � Z� ��)A6A" ecJ*mon,Q nd�DL�6oftwarT:H�7fai` lx� ` �A�b2o,p> -�X�o�$ � iler�yo�V ���pN16-be5� an!g _� &���s}"V+switc�?off�- %�� I����1s :�B� tn  !��u�)�|LXEly�K@�ceaA !�th.�;is �2G�p��t�+f/vy% -��*I�161 �'Q{UA�HVM=��58�A�inuously�I8/ ��'of 6F- 6��He)�?�=\)e�A�3tu�'-��L!� . A�(terlock mak��*at��HV�Y1�'5� n, i�(��v works�perly~I� �C��$�Q1�.!#HV! adj�:d�e�z� l!nt�;�l� �:Eml ~. A�c:)p!frol�Fm1in�J�[[)�Xy *0g#Ls&�� $ Chipd "�8(��!G,3(ed �o"MV5*$Pennsylvan�4�L3 appl�C1!!aFrj?.3(o�AnEU SSj�9"7"BJ-��\%�ERA-B��Q (2�, YA,.bI,` �I�I)��8�P�*x000՞a�R t�0}�& ChB3l�)��� 3(12(�Etab01WDtabular}{|l|l|} \h 2>�, & �R.� $2.7\�+s 4.3$ T$^2$ die \rule{0.0mm}{ \\ �a_�,,& 0.3 W\,/\,�N2.\,�)\\�"2p &-<� ns[� �� ?"& $t_0"c<1.�Sns\\ &b ol. & �, M intr�c < & (900 + 70/pF)ըs\\ on-�&0&�4: $\sim$ 0.1\%�"�&&  2\,$fC xJ!yYft%(5 - 1.0 fC/�=\\1�*1� U� M8�8� � EA�" in %Q^.� M T.�G%.�G10J�asd8_q cipl�2�*�GPri&al"�"uv]�� �Is�*� ���a��'r�U�)� �,�5an -� �uplexera+ifig�� rinz��%Q-!a  a bkN,ar technolog�Lhe �[% ����O er M@~� bines� spu2� #23:, �lDly � FN(T�0Ki�w A b�7diagr�P�'=dA2&- = �2�=&gf a\0���<�72�UmV/fC, aJyA``1'':_�&�w�T?} &r2of�B�4;a�imped�?"1U0�IG� �.�&CsymmetXq�AG nega�uG*��!�two-spLN �F�{= .woJ;��| �FB� ens�!��&�6 �4 �3q4a16�-3�s 9 ��,m,EH�7qLnd���>� c!s�V. �y�&&,O$ =46�gO)D1~  �-�?is"�pr�.mm�!�� � 8 ext�S��w�"}B�Dly�"250 mVŏfC� � 1.4 Vm2u yp, satuy-�:�"� e�>Ufm��jn&�280� oc"?DE�/D�Yr:�2�8� hift(*.s , opz;O9Y���cu.D6Z9� I' s�QaB����a_N&�" 2;E�>i�4� 2E��e�J�%a T�8�L^+1 themLy(;4to��a�RF (r�a�A� J*6�;9!�?pu�aQ� Ec w rEWfeeE�i��e|"� �&� T�jv y* )pL}&�:� 3V;:� m6s &V(2�s� d�\�346, 67 $ $ 56 m �)L��� & J'�yq�s "�ed9sparkA}= & di�-*P$$\geq$3 kV2&{ ()�)` <J\%$\\ ,�*�  -1�*=%*uni�,��& �K15\%$^%c+m0&� mA i�96� �p$�p�N+3$ V% 0 mA$KX  $->��& 6/W%X� �1� U+* % % ��eLZ2,a�QJ�+ 6+ Jy%A�s�M)c�_eYta���a!A5F,;60M�)�.MD( <rej�#&)���roS<'�%of���0\I��w[e�vIA�%G0^ 5)�typ-r bot"3~� JX; bHH:,e��xc1~d1a+�^ef�9+ yp -"*}��R �$s&�-�� �;�(mpact "�5of�w�)��&���p  was �Ad �&SMD.� J� Ca�.��Q�? Mike�%2 �6�c out:} Two��Iq with�� s��a.�2^� 0)B 3}, 6�,� �6�! Z4 %h�%. :D�7 }, my=de! �R/!byitU m�.� .� 8b� �_grey�M �R�VPi #A���O�02�B5 s e �23 ��@ig{file=\pict/amp��c�,S �(,angle=-90, |F�BN �2�9�)0R� A�� a�i��b�[4nah$1L���& .� �>!�&��)7(i� "� o@�WO��CQ )were .GBbn 5%nd'�p%r ?�NRF%1 (R/) �obR� �h~/.Gv��'�<pF���mbeg93�A�[cai!e>�chU:OLis >si-5 !�u&�?%)�(n{>X[�-U�� o�'�=F�; . A�B����s (0 V)�� ͎s M��8gital������|� ve&$ <@F�� �a�We��ui�-QZ_Y�i� oth, L1�ed%�adWa� :$!��RH � e �is x z? to r�4 a��� "� �V slidA-�("A< brac.x�mCs mad�*.s�g�"ub9 toge�8�AD �$�kN�4 mesh"�L3��%:DRX3B��/:6fee�:�#���u��^�>2Jpc4_fez���\Z!��b� an ��"0J-�: SV+%s�;er� SEma�5y�xS ds p"O$)� wU��&0�n's�2AUmHslTDCiH$:�k= "�@.gs (� he]� <� A�left,�O n� �36K#5�jPt �I68�d �e��,rv�B�t spi� $� 3YVQbB@ � ��"-C`  a st�ekJ down? �u� � @ ion `� �?A>�q -A$T!2 } @'�s1���!rT}l)�op���Ol>�(� BAV79)� rteV'%�=> �a 0.7�!a���.Te�\�CHw�a!Kwa�; �~:�?5M-�Y-S�G��30%� .� P�a|EF&) . OE61� ���"�T��d&�  !e���0��!�5H"7.�*b�% sam :%� qu�:ia@� inw5�sec��s��QkJum"�c��Alre�Rc�w(s $U_{ref}$AI=^"��Isin� �,�3�bel�s� ��E han e3mVs�H�s�� ottk (dj(e1� 200 or 38$V))I��!��&�I%�!s�$�# ��o�ME �`g,\/�2� ! W D$"�c�"�>Mor}*�=~ +m0s �Z�4�.&X9��.;12�U�� n pulloI&C�S�f%�s� "�1asdE�Fe Sec  tdc_�Y� A�fse�e1.BV���H recei�f>v���)%�Ao))�Z� !��%* b�+ivL��71�1)Q�����. m�:10UB�%�Kj4mQG2Ia0 ' i� sa!+� %g]e�FS6q� p�l{c} *�Fle db"�cas�p� ��H� f�FameC5�A�L��;%+qx�&k Q� $R_{Id}I9F1 M����$R_P =�2�3�($U#A� $\,Vh rm�'� iF�h ��e a^ ,6|*u.)Q6 v�,*�!6�A*4,p.�pdbQdf�J�E� �26K ��f 8m>Ets �^� � ���yP3&zch"� Z/ QiuN'ba SLIO�#ror (S)Wl Lin�LI/O; Philips P82C150V;y�%.�!2�&�(e�a CAN ((,ler-Area-NetT$ ) bu��On�X�0"�.�"�t TT bit DAC.�d��9in�t09S&"ve`_)%set* a jumper��%T5_5 S422����est����� �en�D%�I p wly�~!*� �$�'��<W ��0�� �`i�atud2�Rq�_a�9o�b�1�;S ��p.�0�"�oADCtaTA<�N� rea I Ts, E�*�A��^�� aqK ��\�_!i2J�.4E�f�)�RCP AZ:la?�)����":v� %�s}��&�%a+es�%� NSE:io�K"��A&2�h�Y|&  : }qX7'�**90 wafe�2!��&M35IZ k{1���v�V 77\%. Ea�p�8��o ccorAto a � �.3Oa�hmXneramE�Du^ ��uep�*񥥥. TQ�� �%q�*� v�,�� ,�� kq2caLc"ae�G 41W�iT���Yr�J�r 5 W*)6I�� �!��ip�� acj\zE~��t A}$E��� wAUed 2~kHz�j ��ceD�  - U_N�q�[U�� -to-_ ��)�u"#Mq��y9�#,� (%?, 2\,kHz� F� �)d*U� �relev(*rl, �to �Fl@x�s�^a�.ER_�E�xaC�7E�!�XWvea���e�wci�� �5;!�!f$&v h �aorrJ �-PM� Pip%�Z`Q'ń�E-�dE �C,u�7DS�V0B specOq{)!Cpurv�e� NC�_9?S`8u�ub}. %(�s�"sLe"6:��� s�"ŀ�"�J.qP!^Af�!,h��e��Ja=_���.{H keeka�"  4-^Fy�Es . OekE had�toM9�D|��5/�epIt""acr<&02y��2��%� �#A�$s"rom�E42�]-MI�s a)0ed�e�L = 850 \ldots 950,\,10 1 >  \fbmV}. $$�=*>j>49�%�a�}0"}i�%�e�r�&�, 3��  A espoq "b"��J \A�){-'}-� = 3944) 450 1!$550, \, > 9!,!!i?$Jd$iA�� ��8 ��Y..�($F�$ = 90��01�,mV)�&eaas���to[-a12=X81���|�Dal ���0al%�� }$ ĩ� l:Y���TB1a/i�)a� a+ ^tZ~�)(H D� .3?$ �B�z�QommsmJ�n:m*HFxc� "IV6.5J� thr_A�q & �x�kZ1�_u50_u%B8�+"�.YA%er.�+ Left�6 �%��r pl�hd"mAe_�-!�Jeo7 M���2i R�q: 2�8 )ATal%"i *k2jfor�jnE��-�iK�8^oX* : *c���. "�fi��6�;�>x;�/5�%�1�.Z2JEQ. H "�T5�*1%E�e.� s:��"�:)�h��ce"�?q�� -,*6 ��AP� d� Q���kips: 4.�2Ja�9zr"�J�  3.���_] e�E � $ FJ��$)y6�#c� ـ)E5%� e6�at,yF�QRY>Eh�/:Eo�y� . D�#�!��:� ����t=�H_5 lhce. Q�`&�b�8���|v���&�E"� ���ŕd916&(.6 iI& U�� �$!.� b&�CR����s.2��<cDana� m.�de�De�Sc2�)28=�6"c&p,"P#is*d>8� ��F� ���)�� 1 * 1=p1 !7e`m =eaR^Eeb�� "� -%2\ G(>���1$�%i!i*s:l%>A�e�q�y,`� 8.�M)upqE�iS(� J y� >� \"� *5)i )�f�f�"&m!Time M*eb�l.��6���2�%-B�s��'�.6Es!V$b�92%!,"$8,�� ����A:/8. Ex�.E3%V �AI ��A� Z!i �)eH regi�? �i4�Steg�*�� ""�7�2�Ho �AsB[)2E��?>�"&FZ�8��'Z�82U� :�.���#�-i-&�89.4�. 9.4��806*�88pe�dng�% & 5 V\\ wĊ�-�R�.,v8*hm�8�ql8��-� 6t� F�FN 6a)td�iXd)\ o)F " !�} 6c)q =�2cndK ����-�"�8\d&'izI�%$in57 bins�� 8 bit�vfLl ?aEa5�[of6q #L:�e�" d�eDal�S���?adr��a( �hs� HARC� �$ADSP-21060�m A�5Device�vymeU� � bu�Aa�KK"h�a�E-%*j~ ��&�5N�M"�eis*el� !�z<�@�t-}�cip�-KC2�4� 8/_r ���C��o%D_�A #z� z�c�Qs���c�4�)�-/{2E ��mb�b &�t �� p�o&�` @��; �����3d$)5A�10 m,p���3��n%k '1q�t*4!�#DC��&� >)gLa�/}��.T A }& F�Fa%-U60u��I�UMSC&�E MSC, Indu�ez� \,16�� 7629� Stutensee"��!"aU: W _$NEC (Japan,� �*�^/1�dIC (A&S@ Sp�c�E�Ded Cir�fB�6���\I]mA�"( UG��!�@����%� 0a {GTL-I/O}--���I (GTL = GUQTH�5r Logica 'ste>,�*�� -�,E-E�+ ise-immun��/ lZ,�iX2��#V�8$50~mV"4�6� � �sej,122� �)>o���A���~��z|."�"?$.`E)/m���W�!��#TTL�r"R;si�!f&te!�in$<� �A�!�-�.�Z,�E �� l4J�a6+ BX c�3!�/M��9� Y"oi� $ �U�iqM�W cycPbE�jJG g~� �# l6JffU.�A��C"'6mX�I�n OR--� xe�y]!�m[�e �OCal���% hear# �7%�! n�,M}"� �0s �IU�N�:�W- ?�� laV?M&,�1 ofi. g�@!�e AU& Gh�!L ent qZ$1\,11\,350<�meY�� l�+i�UwU ad�a�_at no�$*����  |��a�b>9�l2΀ly,�^�PE6�tdc�Iorm �r%�u� bkjm�9Pf{c�?q!, d%P��" I%be"M48N,�0yao] t��r. &2#7&n-�E�, �v|W p)�L .;()+�h.�Aij AJ!etu[�M��(� ag�t) all6��qp!�ssuTY � a�lli�.� �d)�rv�]ia � �B � 2� "6M�}, slop�!of�,a s�; ght ��� &� ��!\��^10nK�2 �qhLi�Ea5 MHz gauge!�ck,I�\E(&M� 6��%# �\V� �� oeA�256-6�,�M EM� Abclu��Ycm�� F ��f�3feɏ�faee�Mc2� [�� ed }T�r) �����$�s�_� �a$e��i P &�.� �(EL START!�2< STOPq�m+ �&�F�&�5�synch$�'w)  bW�%A�xU  (BX)B�D=�!�~nsy�-�(a��rs)  'le�{ ific'| (LSB)qE[-@�H (1�. H�u5b! 0.39~nA�-�`Not&G�Q�] .]�q��� 0�"-/��)�E�5r��+&� B� � st {Q~}!�.a�-� G%�-iper���T p �&ʠMu��d")�$%La ��h�)12�s*2z1RJ� % . W��3�n�(aq� �7|2�/� " �k~, a'BX!B� ��. '���Q�u J� (FLT 0)Y{F}A�{C} � {S}�(FCS) g�+Jf��SlB�LNE�00pu��)�T �qj2W�)��A�u�igger f!$850~kHz althougheI� !Fap�to(`A�VB�10?�{B}II.56 �sv!�E�TDC��s�M�& peak�Mp�e�! ���k1w !ne�1&�B}i(( �of :k3 !�d i�6ga�ѭ�{�T �.� be+�W&s�2�ahr)3M\�X|%# (FUN"^ 4%1 64 G%��$s�Y� ����!�2reV))� 8, s�B��) E�Amat (8%�s 8A#s�[ �� M�managq�@M*r �*QXU�K�#J}  2U/ #)��)� in 9U VME �, com&�es3D!��\2�Ba DAQIa��!�6).> "a )�� "� ����:.�6�".22�q auxili���*>L�'� �5/��p O$s leTieds (`64�, HIT INPUTS'�*�%l}�%l*�:m"% � in � llelI��Yݮ3��!~�Jo�!�%!#:"�:J�16-�.<9���.��� +.� (&L' ��*� .h�c ocol"�`Un�PCU) +��V (MUX.:�y�( �3M�s !u���g�R� ��A U(!fly Ƈ�F�F�y�fer�)"� E� ����1*^=��=��K � A��L#(h0d-�" t�",�a )�� �.�K%[ht]� +�B�yhK=0.5,�y4bb=0 0 590 437�y%+1\+ Fc��M! }�&:=Y�&TdA4F �g `._.�K)�q!%%�6-��%} port�7U!�5� four��LuOI�{�F�4cknowle��' _y nd GzO�"4� [�V tbu�R%� �)�� *�y eF/.�73shake��%�! Hn�s (EE mit�s�~a u-�C�\@"j�*�|aAj�Y�V:al��(Latt Semިdu��(pQ1048EN as employ �m� a@A&uDse�ϡ��;&p > a�Ch2 �:��uI-{BR�D��E�tau?� 144~byt* is E��;�$$5+2� �red!jori!��eaA���6ƃ�Ewl� �C�zJVms+z&˼?)�!EA2��� exec� f���� �Theh e�Ţuti�� R(�10~� to 3 �� O"d�-8+Y� bRa a 27' �is= A 7f � ry�X+�b"w �p[v�DO�JA�on�.�m9 stat&�9+� disp�# ��LED�!��AqaժReset�H"��V5- situ�BT�$%� a fac���7��@�.!w�q�ql �mz 4fla�L���6ld n=��C4n~L%��R A�aY?��7�enl9 B�G ~�s:5v�alV ,j�F� 1�� � A9�j�VM��$rE�t>(�!F/ �ch+�byp�dg&�I!�plaoM at s�a?�� %�k�� *� � �onoujtu6{*��egab�Y* da�C9UYi:�� �# ��x  T��ype7J�+�)Bw)=!>� >E&�V��G2f)�>1+m�*'+ ll|}M*! O�*f e&R�<&0��55 $^�� C&\\B9humidd+690 \%&�X hHW,&366.8~mm&(9 HUeZ #D�&220.0"jW�� &1.9&:Y��(ht&736~g&\\ �  Q {\bf0o}&Reyi�_ MlC2I}F @+5~V (mM)&0($5\%&3.02~A�'TDC! 1.18!�� 1�AB+U6r~�*���P*�M�a�""�4tdc��"�� &� 3s�r&<aBt �� b0.5�� !+�*˅no��OA6 "7>3�A Due�M"蒡� �N?!� S+ac?j� ���3Z8 � !����#9�D�1an en&��s�e�20%Q�E � �(er HP 82000�B�� ($}(~\pm~0.05$)���� �ks�lue�@mєWAn���#&U im*�.z�*zIUduru!s&�mn���" }� MEJ-v .GAk�n�YM` z o; � !9�QZ� - ^x �ve=E�V s (i.5��*A��LSB��,!aG�b|%r�{F zEbinM �=ŋ�>eiO �Q,7# GESime*y�/"� m�"ar�@�!&�  BX� )�vII73ind p�a�sn6�X lighk AT� �B���� � {��<' 7)1���f4>� 9B ,�E!�6%s� "X"f;!%b ]d!� �A dan��2ns va�"o�82.560�72�6�/na}fl�j[qL"#"���!�!Se�kA�"ld �R!� �AL0�2Q��*�!5a 'Au�%[ P%be 0.14�(1 �)�� ), i��re�M6�����?nexp �%] >��\�ť�ns�c"���n!�n>(Pp��&d.� ibu{ ".fyq�5=��!tB%� long-��E{ );�����nodG�&S(�#\,s. Var)Na:b#h�<��&�]e� rippl�P� %�D uKi`!�5��confirm��&�G6A� �rop��PM.�_� h0".)1]U" a�r%�(( �G"�q*sA�"�8EaV�!��!��C. �"� sec ~ �a�o��s6@�8*�0�KeDV-��M* o).�9�h n��D�x!4E��GUiGz^�$D/est.�h G ��u��"��s~")>, ce ($�D$]U )�E���e�E��%+��a5ap[ Qe�;ep�>, ��)ppW,- � Z�i�Pb)�O!+N�;�a�se�'�S�y&<&��@6KQ�"O^� tec<sk%y�� �2B�7x��S 8b"�Sn� _paper_on2DN*��1�q&�9��o*�j��2"K � [&�4 *Mt��aFlDte�7�56�E�j�f�V�`�Q�y, �N!�as f�eenU�� les),;j�%1�t.4RQ0mIworst l mKBlredj boxe: ��6�!ۡATH�&�^l V�]ha��g)mpl��db� se"��. �/�'w6�s)Yre�  ha�s�',�m���%��~��ex�e, bad �1c�L� ei�_�>% ^ �2y0i��c� 9)!�to osci�n奁�93 h��& OL9Mcie�g��o 8�. An-)�~�a��I {"C��{�Z���&���[��!�]"V � pr�a)k̳���W;J1%�BA/orcAn in�MR"�CGy�"Mvi�a �  Vy� �D�-S35Ry#&���Y�Sc��n� tVh \!� "8remov��>" ���af�1 -H0*�!�y��#��t&=J s�F��M=%. >�.�� *�}~y�b��� |�& ce 1997���!�to+_� s�d 2 Janu����!r��&� fu �vA?ey)�Ɇ&\$��k ata J-!} �T ��n�z3�xv] �$ fail�C ,v1A�;+ �(�����y��{m(a�9�b^������wm!'End� nU !�y"�reD/ er/oo/e&�(/ docu.html]�4lhce} K.\,Berk Q�`L&S� )te�it�� � Chip�}� 0�k ', Pcg"S45th Workshop��E�e�4LHC (Snowmass,�\dorado, USA 20 - 24 Septe\ @1999), CERN 99-09 L/LHCC/99-33, p.\,564.� tdc_� } R.<iA�!(Merle, `A H�Re"QTDC Sub� ',f� Voa�41-�4) 232.�zimme5n� Z, `Ze��sselek�wik f\"ur� a�@ A�(ktor' (in GM), Do��pesis, Universit\"at Rostock e�!<unu7,\\jxgeneral/�is/dis  \_raoul\_�.ps.gZU܁%� �&�&II: P&��+ \endB8, %\newpage  listoffig�� s Da�a} ��\class[a4�MD,12pt]{article} \u�0ckage[dvips]{Żicx2{eufrak��(title{On SoAcfe�ecursor� � Lorentz medium} \author{Adam Ciarkowski \\ \textit{\small � itut� Funda�,al TechnologV 0Research}\\ \2B Po�� Academ�Sc�ds}�(def\m{\mu}  s{\sigma o{\omegd{\deltt{\thew{\tild!GWr{\rho I8bet{\mathcal{B}{Ol{\lambd z{\z^O1�� ate{ make%�'ab\ (ct} A one-d�$ al� magnet&���N� ev,b ul�L m a ite rise �dxci� in a� p�ve: � �i�eff� � initi�igZT of� wthw� �KIb dum�n� pU���z!� �is- �$� MiFs2v4approach emplo!uni+ asympto expa%{uad2 , new Cximath mulagiven���loc22(distant sadpointsfa)>3l f� ��k5)*5 re!�s obt�re illuAK-numeramlyOcompa�C� nE$ �i�ture.��Y� " {Int�P } F}�investig%s on EMQkpropa �k�m modelA-2�M!@ �]��so;14}� Brillouin ,br;14,br;60}%8se�hHreveal�A�-�- �ma� I��ng� �,WJ�@IAV%!�eA he-�!qnP fas; (�):��"J ~5� c�of light einE|ane oscil�o!�eqAm�oP�p~theirI�U�%�i4 >!A A�A"� Aslexiky plane��corres� ing 6ip&�$l represen��m)��os.� vary)s� e�z�g�ne"� ~ e� equ� (SPE)�4Eq.~(\ref{e7})�[PA t phase fune5�hgra��h6�bP!7ary. A������r. two Mof do�>h���� near�ks�!�� ,first (refer�3to��.�Is�d (uy]� ]Lb!�e-i�in; �%�ED ed symmet����A,�jInYU imagi!? ax� �act be!�6�awprincipl�Si� SPEAbRt solv=*closede� , attempt2�to6e z��}�:mbr.��'Ŵɝ�҉��ks!inalac��q[+x!�ref>in�by�4���E]�le��blva�f�IU�A8. As a!�ult, a 2ac�i � ulaifou��ng�Q�I�cy� coSat��!�s�I Y���I� c*h!t�map� conf3zvic�u !e�q�� . Un�u� ly, U�,}�at h$disposal oza non-Jtmethod,+�T e6v��*� as it �JE�coalesc��*wo�tB a�f�)0c!V�treatE�e|! � he7Y"&�y%Rremov�VBleA�e(d Handelsma�hb;69} &�aJ� !�i�k(ni�valid��&� !�� �W%�5�)�$. Recentl ��#lem!2L.��o)� in![. �a has�  reexamAba��}. Ext;v�earcha�E�fK� �Oughstu�I d Sh��)ou;97�Kelber�Sazonov %ks;96}.a:a�� work,�Ldz;98} Dvorak, Ziolk� ��Felse�fe� a hybridk )�combiPbo 6Dd FFTMB͓�er ��Յ!��u��!�-�1s�rum�!0is��r��E;=�"g O [  A�� %�u��ndAR!7� ke�&� � ssuma��)]�i�#ci�ܡ~:wA1a s�m�%� �2! env &��L hyperbolic tangent �. S� A .R !/��conveni6)-�� |�.IX . Unlik��I�-Q�study ((��I�L, Secs.~4.3.4, 7.2.7Eo$7.3.7), wh�=��h6�w 3�ezero smoA��, ���*�a��IA�e�0n abruptly sw�d!u1�} , i.e.\�~vanUs idents !4$t<0$�.�!��Hfor $t>0$. At $t=0$� U(v�%�!5sua�!� step�'ityE�)p4 infl� Eu���um��:chaI eristics,�(lu� 9da�$\d� ) spe a` $\b$,� �ձ�S"{y=a~- ���t#icula'$alyze (e q qJ# e*6Qagn6� hey� �ɰ5s�!a�+� ���/ !�q !n ��e� mpleɴ �WA Mق-C �. F�(��w�e��j&N J� l&b�<� U a<�)is& accu���@t+ �� e .�"B\e�ma�': d*�e.gana�igns &a%>9�9s�.o)Q!bA�&��zjp8+.�..��.���!�e�x �}��� 1D4off��- I�}=R$e)�� &� )c �C}\label{e1} n(\o) = \left( 1 - \frac{b^2}{\o^2 - \o_0^2 + 2 i \d� \o}\r)^{1/2},�h �-D$b^2=4\pi N e^2/m$A7E�lasma�m!!� � , $N$, $e� $m$� 9nuyof�ns" unit�, ume,%1ga��+�� i6, $��aq:%�� !�$!!�( nant&P!e�$z�h� Cartesian*h �!,$\{x,y,z\}$,ej� ~ y&0 $E_x(0,t)$, A- h�o�X$E_0( is �be7I 6�ݷFB�.��,V/bc2Ac �=Ec \{   array}{ll)0 &t<0 \\ 8D \tanh(\b t) \siA�4_ct) & t\ge 0. *5 `I�pY�a�laA!po�#vaMe*t�d#"re s�rapid�*јtur��E,cE,!Cxed/!ri�!y-���5�� no� ourc+ L0�K $z �,arrow\infty$��.�A�i��_ �� �ed,!�F7$� *� &�E , u� (�2�diu't �ɇ imes�ig�� �(�st�f�-ngeZI��7half-`$z>��� ime �!±h�7� m!w,y-b�v-�Khe Max5QsF%��� )_ac M�-}�Q3EiE(z,t)=�FD1}{2\pi}\int_{i a-)�}^A�+ 4g(\o\;;\b,\o_c�  \exp{e6[i O#%� ! F�(FoN �z%I�r�3tyE�2� see m� s;64+.~6.3.)�PBrT�V�"* ofu via Fou��trans� %f;AƁ 0^� ��{��D} e^{i\o t}\, dt =Y�A�Q�(MFi\o.�)"� A�o}B b�6!� \t��c t}{zU�M� �( "Sl< 0me�X�/� �,a ��TS  $(z,\��4��B� E^ter�2to^*( b�n�--%�N$ . A sui� achZex�$t �#al͛��so � dynamic�1�6alu��i�l�1 3}) &&a6s V�A|� � onset7\ti  1^+$�a� o�f�co( $\o$� mee[ i��A� a2� A� #e orde% *��c�- �4�Kis �E-X!T=>�li6�g;`�or��� b !�.�  ly e1�1�x�by crigI�s�.0bh;75}. (It c�ls 9�d��oft�Pwo ,�:W.�m6�0e#-�: a po� b�1h ��:��7A�R"�(ac;89}.) DQ�� :��%n��s"� 0i�65,,!�V� �e��bZ7�Zţ +\o n^{\p�+}�-\t=0B�h:_C fromA.�.!}e� � 4})�/86 It� E� $\t=f�$"<at we n|iA�6�&&�aR$=f^{-1}(\t6A&� D !>a]a�l�r�q<�E�&� ��),R� $�)E�6"� ( )9 Sec.~� s}�l"m nothera�rge�Sn�n�� . 2 "6UB%#�� ��es99( 595} s�=\sqrt� ��2� ]} {_{\o\o()I }}\;�^+OB�$$J_1(\cdot~J_2 re B l"��~� $1�2F�n�l=z/c$*� p�1�Rdo� co-h6 ��*�e2��>&happeeA ~9_7ca�.f�"_c�V?�s��W s $\o=\pm� -2ikT<$k=0,1,2,\ldots$��a86*�9ed du]d��4ori;%6nt of t   in* �SDP t��o^\pm!_A!�"�-qu*/(at now aris(��4"� $\b$�2 2}1 +4-�B+��y*� )N� . Be�w!�L answe�is ��1sub?Depq" g���� } Le� �* pUW��e��b*D 's �f�26} bm� 20.0��$ 10^{16} s� , \quad  =4.0�� Z%d=0.28 $:I�3�� let us &+#choz)^u 27} A�=2�:h�l=52#-15} sBe A\!fur I $\b=12=141e^eQ b� e Rk�c.�*I�is�Fe �)R'Fig.\ 1A5bC8�1@ \4"ea|�inL*4phics[width=.71 ]{s14.epsB4capa�{$it{*&m � cV�m:�&�by?BB-'�Ar's.a�_f�$�$Z�E���N� !.�vR31G"�91ex6Fnt If�Ra�i]I,a]� � Jwo,�)�n) )��בh4})IN�j*'-� -�Tih- same��l\� -���is�? servC'If,�5?, �takes �D�6er�&u�+s�#s'>�9U� or�� wG1~ inctHhan�6I �~2) �I=&>s virtue�UK� !$�)� � l� ��q�1�s�2229�2�2�2�29f2� ���� ��)",JbBud3`e� I����.$: �WploO B 3?�A� f�MA� argu$6�� edzA�\ 3�)])gv'B�re!solid� �B�&�(daU< �s��?B+D)"a�$. CalUq for?\ta�00� r^nN.5�P�le $1. W-��K4D $\t$���sen w� �"6/BC-��  (cf.\-�1 � )�2�t�s]M��%Ac�re  th�C6�& reg�Al>� ��E . If!PM�$� q'6��V�� �8��)E!�n1�J�i.3z�(ank/*��'rib�JW 95�6,its*�0}���onA�^��)�euri�^ until^F�"( ( 7}M e��J!�2 )g^w �.8�"�J % B6� � $�bL2,{ I o��%v+ %v$G$�'s�!ɽat�:u 9} e�B les �7��c�M./��!he:|�ch� tZOxim&Q)n�)adi-Le�� $to zero. H�*2�muBF 1$ ov�!�!4 thir�NA�2�!&�s <ly �G���IC��AV-"j1N�F^ Yba`J�o4�6a�e� 2e>#( neg�?�On�1nif�NatI�M�� �l)��Qnbroaden9.us push.�I4M(1�6ion��e�e�W "aM*FY��+2 E� �� ir�ecmwOd�M. T�F-asJ3/"]�shall�#2v �<*f[ 8[ ^+�\ 3(}{�<2(\t-1)}}-2 i \dBN ��uG3�"�is �J"!):"3*b ���WE1�_� sf�)�o�(' )���$=29n� a0� k!�-i>� %�E8 �+a&Nn��5 et.Y 3a}) �5 arbitrara�s&���b3���.L25}) ��>f�\ ubs?�$\�F�6&piqGA�EH&�9}t(u.�$u}+�!<1}{4u^2}+O(u^{-4�\q u*� \pm i� B��6�:�S+;��4r�%% ray!Xarg{u}� i\pi/�� Thenf� 30Ba�I� �"e:1} ^e> <-4i\bw(}{(\o^{+^2}&$^2)^2Fh!If(7���;a� al &57$aQ�ra��s "�Nerm~-e �v�!�XHB�31R �48) 2}\b\d� i�0^{3/2}}{b^3}- , 8i\b"J��8$\d X�}/js�m�� quantity,! ) safel�;tain �6ai"�/� �Fz is X or�SuDoa[&� firt9he ob��of ��)l�� �inD * �us��id�e&>1�j&���i�S?b��a���"�;�(�p)15=e�3sX�J��օth�>*z$)�2/(�-x)X� $x�*�����a ����us, by.��Yp9���!�be��yY�:a32*a\wideLC{E}m�Op\{{-\l i� �-a�"o �!)S,& & {} � )i-�.pi� QF� }}r� +*�0  \�)] \�& � Natu�V.8noA�1Fe-��l=21E�t� eateB�V�$em%� (xj)3� $x1E3.054$.�U�œia<C?� �-v� 09$���: �6����:�us"�!28} ?M�3`,reeJ�by RHSa�11��* �h� <�-�or/!E2Q��)� 3, b �{c�~V>�mUt��.�=�� *� v�y�9E3u F;�6Dz � .�R � B �^� 2�\la{>3k�7� ���ၹ[\t-25+� 3+2\t-5\t��} {768�ӑ�B�� 4}\�" 18{�) 1in}��o_1[1-10*c Nh:a��"L-=EVi a$.]4Cr�0X>�+u]yrej�b�40‡ !ف%�ՂN֦5V  A I fore�ue� :� � Y h56sG zJ�he"VT%[�5� th�Y:c16 �+I#8 ""29"#Z5�"�&�  teOo"y0d aIm"�9}fM341­2��4}%�E�id\l"* !�R�!�1+VDJ��A-RF"� 9�in�:=G. "�8%1us6s9�"U�LE.e$, p�D�+��~. J !�J of��,5~1gnd ��2a "�!� #ex�AipU�Qs%�; xt�eq 1$*!%6j� f  \b\l!�-�2 �`(\l:24\;\d2a<)BI� j<�_( tart*;B`( OnseX!vNH c"�"�N)5B�&b� *� B!�~���*j# :"��2T6>��Z=1�(Eq�� 42})Ju("�M%*4 \[\�OPlaystyle \lim_{\t \to�9} p0= �P\jb9)}t}=0,g[Z@^2RBAFne 0. \].D O� <6�9E��� V�� 0}&(D� 0 �d }{dN� �-�_0 (t 0^�I�*�2� �=R�Es�)�Kn�<&k>�A%$CA,6�J�Ou.Q 2�KA} o*�m�ge�^� "�i GreeD+�dV ach�5ri�BE��5hs�O�6&�.S�r�/ase} - $\b*��n ��^+�en�A*�1\i< -� \�ct  -2�a��24}) .�[U~KM�o_:O }{b}�1l b6i )A� �rs�&��M!.iy agrees !�r6�NF��2�C{\tau-� ��]_{t}}{\xi�2�3(2 '! ) \]m6#.��0e �cndŀtgpacd2]bY� �?�M��FB� Heavi�����6�:,r5~(33))r$e� haveq"ed�'s no�9:F�=tͰz�D�� \xi�@ b^2 z}{2c-Au -�o_c}.��A�Y�A�>*-C!�Os�<>�e��} �"� *!Sb=!�N H d *�\Eway&HB��G�OQ�0ae F6Yw7XL,�;ja�>!�(s.\ (7.128) �2�0�E�# aAwi� �H�kF� �Ia�m� a t^r}{r!!�2�6as2�@0^+>���!���U�)�:�%g$� �;F�e4YC6*WG.�)Cpi}�Li�'C��)^{r+X R� |\o| (a�I f�u\Z0&�I�3����)F C;ibpru�AculawS!A)�I&�P�? ,ers"�4�� earsq�F!44)�0�:|%� nt, r]<u Y�y-ss�;2k$J_r[��$ - 1)}z/c]�)f�=\�v�Qt s $r=1$ (��m{ and�)-n*b.alone)�)}�A.Q*.oof�1��}(= ,�2� ���� m�6~_!s�=l.�5�X��R=oaC���\ fL -�A-��;*_D:��K�"�i�Ld)?a�;ih<�B erio�cN'�K�' ��2�QM�nd.��&"T �]�EA,!br%W1,�r.�&.79 (*o)a).mHq{a. =�3�I��*�v W*\of 2 9�(� V"v� `'movQ�b�&a�t betw�.!tv~.F�&~.�Y �"�*!f)x�3+h]>"�>)Zq�:��F�@�%��N, �=�'��e, F�)t�� "�*3!���e�!{Deca7RA&c[b} By� %Sp;aU9Ba)u��s��$Aw)&t�&R���`�!�M^+�==A-x� 1�MS{((0^2}}-� �J+B i �Q(�2����\ }+ O(\d^2F��'Ahi"h'-Ac$Hf�P7�isI@sA�e�e4Ci��II�$Bi��V�$&��xDdI��;!���l�#�.o�$ � , $|!�|>>\d�nd!��)�m&�AtG&�Em�7�7o&$f"� =�}N�}1�1��1^v&-�A' =\t )��. R1F!5a�too9��squ� rooJ!e�%is Q��7�"-+=�a��LHSLDQQas%�e�-X43�%N� by 1,)d�Z��E�N4N?a�g, as a*o"�Y.�&� ��l�`Q}ly �+��us�p�f �! Im.)� \d �B�7/�� $H:�(M��3h�&�& ��'�5}6% 6%)�^r~A%�impsinC.jiso��j�\;23c olid7�A�6� F[&�Eq.�%E7-� G�$! $ot Lq7,��$�5J�Y0�6I�� A� at m�|�Ar�&� d��" a=*;�@�l�@n)^e�t��/)X� �d(of b��9-v-E�64$ADG%E�VO*�3t�v�\Mrease+k n�*��>q}.�5"Te�� .�,���� ort�~���a*�\J�� �Gɩ(\t)$�s���7m ,*G >�*���}�o3$�6�.o!, SPE,9 -� >�'=�52�����e   ��H W�H. ���t  dof���s-�o93L9�b&�1  uit�L Yg �&�K &�ic�L, L �8SJQd�Q~Rd�9!�{� ��offO}f.�.�-�7})"T J�^)f"�on7>W� giO ^b�i5c#X9}� rs�/%_cy!b�!�� ��failswX)�AX1�_5k;�0tiQ"� E��O writteA EBav b�8BQ�D($-I +\zaAf}-i\dB�3G0b`9} \z>� 1-n^ ^Q2a�9z�GZ..o��ul Mm �"58nv$b��on�g-.m 1}{4 a)X#\t}{g�6c� -g^R�^ leadf>�H% ��a�2�] \z_2�.M�1�f� 5} g1U� 3 a}} 9 2!�/3� u+  u^2-v^3})�*3C�![N 2/3}+v �]-2 cF�%^) 416} u=2 c^3-72M eM` 7 a �!BI�4bM7} v=2^�(c^2-1SeVD co"�]s�Z , $c�X`r��[A*a;E�'�*b�8} a=J[24fLai\d� 59\o� eU}}- i�/.�a ; [3 �(4(^)]}{81^ N�2}}-��1�Bfb�9} c=�i��6� �2 ^E9�0 ��"Ie.7 �F�Kn�20} eM�LVa �BP W.Ellmgc6]b� (\t,a�)$&P���W� >3&� %�;�) VS6{�O�ng�W^�7j�� vari,Az$�v�10�� w \z=(z�1+}1T t n-I% \z} \;B+�� $w=]~2�!!�k� .LO �_��#ͫ= �f��dF���M���2�B�^J.1E4relev� eZur���m����6m�� !�\�.it{MathDa`qmpC gramf�1-c \z_1 С�wmYu �q]��2��3s-;]�gq^3 'jiq 8hq}�;�F�)�h{\setlength\arraycolsep{2pt�.gin{e�& 1�` q&=& � v}{w"zKj=t^2-8�w,EL h=-l\t , \\ lDd�-t ( u�s�<q)4}� j}{6et s9F��%)z}� ��p}+5?p4��� B>Q p&=&(r-�r^2-4z�E�z=b^4[j ,\;12b^2h+4^2 w�D%2],>eEg@r&=& b^6[2j^3-12^Cjh )2^2(8jw� b^2l w^2!o)]�"��O(} By 2, $�[�$A��8Z�o25.A�N� s&� � ��� is �J� %&y�;d�:� b6�1��a�xr2�s," ,��Q� 2u can �be�b�`ina�3or| "� �! �_i� |Um2 6��5!� �B*�Lcho� q�h=a._|�#o.�EPan n!1Α�ebe $1.3�� j�{:���2 a*PMq�2� �T\o_{SD� � (\t;%W"[ H(1.3-i0iZ\m�T�4-1.3)��,\kappaE� 0)mq]} .l+��c�Tu|2 |HH+ �|.�:+�$H(s)�Et:�(f� 2�' ��%\ 0 \l�% � 7 �� �}5$ ��?.3) zuHout6"A� rvalA�$25<\t<1.35� C"j� �'Q`$g �Tba�a�i- E2E:� ">g@�?VBfB�br�2 21})q�m���qp2�w:� �B� . At.=a�_y@ u�st��|��e�lim�(f�^!� o?vm%M�Ht�� !�� $1 CA "�i �_� a.Z@D�i�,"�.%in�%!o�22(be modifiedK&2.[ht��B�R\��R reom.1�4im64>�RRea�+6�� var�5�Y�&�^�& 47}). Legend: EXd exac)� �M6B%.�f[OS�f 0 stun�t'.�+KSL0-~w'B�,N+an �"2(�!�, � $\xinI!� 2$@2���� d"�Sy�DBmxi�n_]> vm+#l,"�S2�G��2}U�1s 2�8, to.���2?s&<.W,1Q�l -U6��{\it W+P*��A�G٘ VelT� } (A��ic,�� Y>} 19602��~ R.A.~H&�~QN.~"i, "Ue. %"*!e>� 6,�9]I�e �N��"�s!�,rch.~Rat.~Me Anal.b�8bf{35}, 267-283!�692�zf K.~E.~.$ G.~C.~*,)8E�Oro]ye:�Pulse2Iin Cau�Di�wDics}, vol.~16, (Sp $er, Berlin!T972�7g M.~m�%OI.~�e�it{�X-O\ 1�\��Fluid�(Kluwerp62p S.L.~R.W.~6 L.B.~ , "H %��j-&� �_ac�s<ll�>��ZwA�p]�in2�[$a," J.~Opta�c.~Am. A� bf{1!�12K�255!�>c�cj0A.~&��, "As"X-�IQ��p��ofL�|�]"&�<n2 �B�*�ssy� umU�E�,)�4bf{49}, 877-89�>:��o!�$Abramowitz-���tegun Mit{ah book�*�l}��&%�N�I al Bureau�4Standards, App2�@ s Se�'-55A$6:�jl2��R.~2�m*9j E"_��Iވs} (HoF�Rineh���4W�mon, 1975Œ�h���?lB��^*�.c< �! aU"Y�5 6�l,�l�a .�l,"a� c.~RM�Lond., A9�,26}, 273-286A�86e$f>�I��d:+ ���j ��Ay6�^ ," Eng.~T�.q$8}, 43-59 ��.D�30S.~Rikte, "Ex��nhuni��M�!�c��ity�orems�N�st�1� , '�o=L2-9  (", SIAM J.~A�.~A��857}, 1373-1389,![:9B4�He,Str\"o� V.H.~West6,�<(it{Time Dom錡.-Split� �HInImPrceKOxford&6�y P�Ra'982Z�.( J.D.~Jacks.{C֒�k�I�-,}, (John Wil��o; Inc.f75) "l��9FFT e?��1!� on.�rA[ɗ��>��� ��\ :� 51}, 33-4E�9I�C >�  %&*� -�  %!"���8{amsp�z.ܚ{�c docu ���$�% INJ :Ȕ12pt]R��{&�� \��ceE�c3truecm$oddsidemar"by -1.5 % \n[�mand\HF{Γrm{HF�i BOCE "�9 \��{\C�alsize Bond-oy/W=�/o==erg PAh<% Si-con�,molecule'cp'�:H\emph{ab6o6D!�% p�(M\o{}ller-P�uet� turbE_�%ory} "Õ�\ A. Grassi, G. M. LombarP�GtesAr��DiaA4 o di� ze�8miche, Facolt\`�2 Farmacia�U"m� ,Catania,}\\ �A6jVi�LA. Doria, 6, I-951269( Italy}\\[\J(skip].M� G. N��@gilella, R. Pucci��Fi�� e A�om�:�!���,ۖ]*%;I�"o Nazion�peq$cdella M/RddRURQ$Via S. Sof/641!37�!N. H. M�Re!�!���5�/AntwerpV�\Groenenborgerlaan 171, BB0; Belg: bAB~, , UK}Rh�ab� ct{%�� s�b�i�u�L-q�silicoԫs֋!�mot��el (a�5�ur � c ��curre�-iG�ki? �preuXvҌs�e�% (bm� biot2U� pote$vof� -der� surfa��s>]�*-�adsor�H,��� �),, amino acid�Bproteins��H&g:!Zi- i)a emi-empiԑ& ��(iiT�e'���du~I"��lo�F��eB�1LaZ�!6om%\ neut�;��o�ms��MR�� �sC ( SiX$_n$Y$_$m�L�!"-to�;ahNr���,�DA^rr�[of_A>i�� m�s5u�e s� �,+�h1dE�3�a5gs )h�\xth �o&�or1?x-i�X } " ,In2��T�0last twenty y�8,�hRhm`��d���Ztoo"yBO�D.n"� atomE�1�4*I.�s=a',��%�W:N�(�:92a}e�{F ow iE]is"�_!�h�vdZG tGAK�6��=�;@""�L ago�Clh��X �:63},Rt�"�^�dD=n}q�{FEw_ `$Alonso:03}� yEMIf%� of D >Fu`al1(ory (DFT), 萉�jw>�i_!5R9 T���,-al�\s�7V=w avail�aasĎ[*�!n�Vosko,@ k!��,Nusair (VWN) �&8:80}, Lee, Yang/>�r (LYP��)Lee:8F� Perd� nd W5(PWU :92C-��all)im(+t(� me |]u?�emh��Mԟ%A({\sc ga�an}Vsc nw�games� etc!�I��pQ!�y�OI>�!d!FP s~I� :9� u�!O��Ē�.��"56�ŦH.�:�� E�Jip�/ . Es�Ct�v"��a.e C�s6�totalb�s� !�d�o����a�� !��C5�nuclei���\<n,sol�1�+"em�bot;KJi(Kbx�:1v�%, Gi�m�:$ A� �a e $ (BO). One"�1+\|p966�52Qr"� �g�F&K���N��#,�#U�u"�ABR M^Ȣ�d��.�V�|"p���2q�Pau),Mul��n, Coulsm�e��#U�i� # :39, A :35,C :59}�t%W�Ɉ!�5% �' � g_o5�.a�8Y ur ��� omew!{��"�� of Fuld%C� �l.} �P0h:85,Oles:86}��#M���f�IM�f ��5�!��=AL �s �� �oo��э8�*��!�a>-%iz�2�N=.Y S�<hydrog!�oxygeK carb!���A�1'�s X--YE4(X, Y = C, H, A��v��za��0�f��M!M�=ZA�g2!�1>e.��se�^ sƙ*h�F��S@�n���>0s, encouraged22����d"6�9 -rowkE�i.�DF� �5�, a# fluorin�chl - ��dH ylen� silyEBra �9n!a�3�G�+%^,It+��b�$t Schlegel6��i� P:84,Ignacio:90,Su:93}�q1�a/he hea1"D(Iu)�s7 mMzby u*] �},=i횡�� D.Qu�@~�0EAn�yG���@��@�;�' poin���n �PzF�]���at2��cN�%in�Խ"�$�on me9tis�� {�UdTW"ASm�%.�<�`, pyro"_�siE[�]sI� r�- an xQ����hot Nprj� E,8Ir�]x�>� !��XB ���in����9��ec: 1���D brief��aore�� 0 fI��sI��$�iN�y. Fith\=E�sü��I,���: ��ab wh'�O�C� �m E�yf CE) �� �7JRhboce}. S2�ec: (s}Fconcer�/ !���]Z��I]6Zug��E,� "*� (IP)a^��&� eh).�')��@��"��al� . Oulu%�l� )�:rd),B)� y}. *VM(�swj�Z!9MG�9q{0 A&@'I/6���q.1n&�p8al Hartree-Fock5�sv (HF)�=& L�.� 2�~03} p� �cFrischxi�G!� pola"G ,6-31G$^{\ast}$� E et'f#u2!�ix $d$&��tx�N�]*�heavy� �-aHt�($p�U@~?� $. Equilibrx� geomۧes%5&� by �T�Q����*� g��:#-�-H&= 2}. W֙&:e/y *�q�FFU(MJO qMoez :34}�to�)rth, (MP4�+--  �i�� X le, doublp`��/ ��Y�-Fy6.�Y�t�V rd �!HF��v��IQuadrup6~4SQDTI�TX fix�IN�`4�MP32@ �� HF��MP2!,L ted6�(Ra{�1 unqR'U'Q-ύa�#!�&�F.�� p���~.� ,� e��t� �Oaa��Oki�f��M� . To"b��aNa�@�^o��.~��� �delibeT�q5Ca�b��<�~"9 �Z0traightforwar�B<fu�, �bi� deeme%B5rucQ.!_d�q#��V[:X����b�@ �`.p'JRBSc^{g3}4��� �&�!E+8 = E_S - E_\HF,�2eq:S-HF4!9�9$-DP�%� (u )6���E $E_S�A!�so-|��Uch�#din\-#dM ``� '') C� 7c�E�'/�e latter!�6~/s"�x.H.%�iG 8plus Bethe-Salp9�mu�iv,�)�u'B�- O �y�� � �o&�FI�t���accoun&� [a4 Xof!M edome � as v[�w2r�Va&�����!S�8%��7��E�e�Q"���f��Lide:94ԌjH�&�  .3 @Crr|�5T P  :82, a� � ]isUAZ!��2��"�uU" ����-Xe�K6h ~G^� (. Althoughb}�n�XJma|Uh�f*��ean��aUobj�n�s� D./ inp6r�!62� e�K \HF$c�� �Aj2M ]+tr��""�zE$J`Q��.�!�� 5��en/��B�3�hea�", K. [a�6P� �unUCU1�� ur;o]g=Y?c wse�i��,a�\22 !}t�)6ig�fig:s'�� �j��ie�!�H.�Bq��a� l��of�N�%�i�add� �urF�low. �T�e.?Ea"�]*U���k��X56�f�As. GivG<5�&����ic1�eF�: A + B \��8arQC w<b!�ng �F�D!ZY26�4%�� �2�)E(C}�$E(A) + E(B�Nw�&-AB�;� eq: �>�U�$E1�X%n �*�$A$--$B$%�9Q�"nrg5al)�����S|��y�{ic!�-!�be �=.�=uc�[$S = \sum_Aw ��(�=\�7pto(��$AB$}}} /B\G5S> Likewis}�%d .�; �$ �ar����Em \rmJ��(.�\HF2�)�V�s !�.*x Jv Sub"�E&��q,)g 2S$AonmE֝�.��.��?* matL*@}}  B%�A [-�A�) (A)] �B #v?e@B) ] "+B\\ p� �exp}} (ANe*C }} )��2a �!�. �>"~D l��as�A<6Qi;1t$!�.� �2�ԭu next�.�2��),x�(~m %+$ � "e�N0��ҁe � �FX.}���!�'i*;!Z�)$s ] a�iso��x res&�dRB ���&[�� � �5��b �����r,�?n���_d2X$A$4�olvA��#$Z$�S�ic GR�ʒ��"� .���� �15eY 26q�)�KZ-n}{Z} .�ZnuA��I�tep1r�*2�  eAF��o�*!$2�e�"B�ai�6p%o��,�(it.�*>�m!L:�m�& +a�%yu2�*� ��6�%j$. � ��v!�b"�b"� 5=(�l�2a,�!"'of6m-4Ek�mit�U[)A,�J�;6�0}�InY:endixj app:�Pˣ{�rtJ\(ex�Y��&��d&21)/ N. 6&�-R*+s%�9�io��; \p*�Nr /2�"�6�L/}6&��$6mJ+�*�$�v�$�,�`)% �GU?99f �%f.�GJ�6 I�\�dei�*!�G�.[�B_ih/In Tabtab� �MPN:^ R&e�4����骁9�4U&�ir�f"ҝs�B�k�e �:d�F�]�cE:Mse�=$y%o.|sD=�E�ac��3N�. Am���' in�a2IiOl' columE,6qe�)sō�6v k-_2'Y� |J�-�U��6 � QB�!�a"!%.�+d9�s&� %eA&?J|'�[u�%��Ono�2�� m'�E!D�U2�s.# >��2!�ENr . C%�s 3--6!0N�}.� 1��c�'HF, MP23%fMP4SDTQ4)>9��2I;ZO:_is z�K�c2s�ftci��N�":^5=��.�3� {t}��*D 5D=aNv F. 6�exp!��:`F6��mh%JN�E> �m]� l|?�6|�W�MJ�K{��D)��"a2�4)�suc+D�)��!7�-g" �'i,�.���&l7.+ MP2% �� rangOpU4$0.02~P4$~a.u.,am �0f_�>/-CV�2�ƠeT�e-(t1t2 t)i���Ѻ((SiHF$_3$, x�SiF$_2$))L.V�i�k� n��� ���!t� e%9~�yU5��e�)�E3Y� 2. 6���%6)Q�Ye�|�*)�����J$)�2tl!�!��R-�on gof�4 �ES7� E:�.�te���y@BxY��i�:a3� �6� u7 clea �!D0"�� Tabs*_eu�0yr2D�Lly�uk J�>y6���� 6u BF9akw �y=,�Lage err��B':�,.�F�,%�!�@ine�(02-4.06$~\%q~�trary,�]"Q9BVA�y��%�#�~>��J6�%��;6�il=v]����%j��M_&%��� Z--X.(<�%A-fs��F�i^Xw�RQ:� �e� a<4> E&��}eu6����H� 0.002~\3�0.4%�How9�%im��a�'o�)Z � � � ��!�"�#6` �!Au]2F �$`�2mD�}Gsubje����I�6�i��u^g pm 5I��]"� Uw,!]Aխj&� 6�ts-t��w=]#R�V�!1E���C# ins%N=g%�$�7d��;��iA^�Wl�;tg�s�!�]9 �e4aD:r (Z& )�l G��Bw#(")�"��i�:!BTI1>� of:�ep ��C@��6'.  F2�S�A.S{e n���A�E>LG C ��LL H' �4�&2�7y iour#S �y ;�5ve 5�1.�U>�6R ?>Hh!�eV-�xpE}���MP4a\�pig�ian�IJ�$E�4aTuK{ala����a �:o�c�,-dAGa���ot ne� +�tl�%�VB4�V�yM���MP2��ؚ�fir�Dby:H��"K8!C��!�#���s)2���}t=�>Y��l���s�� �%N78�I�)�>9mF�(�"�&R ~�Z]&�#^��� (panel)� � �N{ purT|��) sup18pq9%Lhar��RUinguish*#. C|��LtlyS#�n��9���`~,n)Fa�ތe ��!�>]#6L ��4.0� .�Ion .po�Ds�06fip��r?\(=��R�0I�y�$�2�a�A���� ��FA�!�@�ap����k  AY�u"� 2��*�A&*$\D�� $SCF& }p DIP �eVXr0%v�&�2*� %�/��5Z(�! �|*�d�TIP�#j+^+ > &(X$*6��a})�leZ� ��` �2U!�]IP�h!���e2��� 9io�N2�/A�ofIN$�� v!gR�;��4.>"� Vz �we'r*<e�I0�" F�$E-E^��E��At0C(A�R ���|� �s 5, 7i�9sYGG<�� �o �^Z J�v��+� x/FG4�� �~112�cIPfi��6���.Y(-Z�OlayI>� i>o *V� u �if"�0 � �>���s,AM QH�*���&� &� I2.1E�fac( RC \�/�H%�nexE��;�8 H$_4��3�0�IP1�HF)�Ais&� ($\|�7� ;� :�ip�#a�J i@+dG0�T%== ffec�tA@ r&6�����(to 3.26~\%,� ![j ���nl)h"�)�IP�s�+]yE� �o2�on x� M#� �Mi��0!4�m'!f �g*�^��!� 2$�Cl�as�4.cF�"G!ZJ� FMP4J.� �/�(Si~nSA 3$Cl�L9�"I Y ��H�39p:2$I2[ H�,�of!�.o%5Y3)VEQ'f�&�B�hE�)�e�U� !b3.4�,2�,NdE� � a�ɏqx� +5�W�8F &��6{��!AzIPB mcqi�, 1|�� .b ����P����-ip}A�aA���,is method �> yields more accurate estimates of the IP, on the average, than� \emph{ab initio} methods, although GMP0 occasionallyB�produce lower absolute percentage errors in IP } BOCE@ q\. A final considerationcerns�� calculated differences, $\Delta$, between1experim�l and.B!reporOin�8Tab.~\ref{tab:dT}. Fig ,fig:schema} tic!  define �>uZtheore. correl �Xenergies for both neutr �ionic?\molecules. According to R�, we mayu n de%�8that \begin{equ~8} \mathrm{IP}^{ exp}} - 2� }} =� (E_cF72 /) -1+\,[k47= )� @ ^+ , \end�wheaX superscript $+$ refers!+A��1��YzaE�8potentials (IP)a^ong wite`ir]�Y�$. The fact%�`q�iU�qa1u� is not� verybtw �MPea�m�s,9an indic�CA@�(re are larga� ncelI�s2yN�G �.�!�!+c.�@In turn, this mea�a2��0approach alsoL{rebyy ions� well <x�1d by useWheI)bone�parametAHL$a_{AB}$, as derivede�5model� \sec!�{Summary%rconclue�Premarks} \label{sec:s +} Ehbiotechnological possibilit�h .�hopEZ�}�Harea,�ed via�F IdurEz��Lr date. \appendix &Y C��-W9 Y�� {SiH}}$"u app:4}���A i��deUb�����loyF &� m+N:|; AREq.~(heq:Loe�{})A�e� $� AB}= �$:EqsJbA� ng})!� Na �2��@� �9-DSiH$_4$���eAwrittF sFU���($SiH_4} ) =�'Y*$}_{\mbox{\!|pt�lin�H}} ) + \sum_{j=1}^4JURH}^{(j)ZW}� Za�!!}} ki kP: ^{(i)} +.8HH676.7 6,� eq:SiH4}V�$>u$%�.U -�A��fe.Si--H<H $% 1�,��pVvely. F'� H$_2]8one immediately�T}fo��Es N?=v�frac{nWH_2AU-2F%!�UUHZ�2�}{=f�} .>�%2�Zi��$Z=n=1$ze�$���=0$. Sie �Xhydroge�B  = � findJ�FnF�=@)h�84.28\cdot10^{-2J%BGbomEhE symmetr�atrix�|A>I�!�� �� diag�� Qum over off-B+�Vre�}A� totaPgavol�e5 atom1|� U"42U�eN�9L� �,2.1742$~a.u.��\ �*6TMs&�exp0G� �Y�!o,� 2��a)��� i A F�]�= 6.23)� 1�B�as quo� by�@ �lnd}. \bibliographystyle{mol }6�{a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q,r,s,t,u,v,w,x,y,z,zz�e�s,Angil�(} \newpage�t!O}[t] \�ering1 Ltabular}{|c|c|r@{E}l.(|} \hline AA�& $S$ & \multicolumn{2}{c}{$E_\HF$}bS!�B=|>>j$} \\~Si & 3� -2.888318� $+02931164.798144 -01$RH & 2J4.982329& $9300021.06713JFJ9.93649~1 <9.9725 5+ 3.60044_\\ ClK4.59448 �-463 C5.821385 n91?1� \cap= 4{Hartree-Fock F,a�!�,"� d��`,6-31G$^{\ast}$&� , Schr\"oA�er.SS$9 a�2:F� �B�,�,�H Cl��s�& seco�E� list雅�&EpU A�plv,A�. All*�in ��"2 a�HF�iE � b.Vc�VlaVryJ$A$--$B%�AB_n$N3a�.Z&�&ţ 7390E�a \\ �&�O &��7952&F--A�F�$& 1.674987 Ii) Cl--E�Cl&314392&H IHN1.13767> EH7.700011 h2eG�> SiF$� �27334i� �&CSi�e�1.024566 N �F �F-1.586152J��Z""*�&� s\ � �5�&�KA�s�al -�>* See t ��a� U�t#oftB ş$. Fo���m7 (lh row)�6rvibma�Xfrequency being unavail�&, a��i� been�J�*4�E_S$.} � a@!:B�@��&qjդ r@{.ŢjyjM1^�ŔF�Ő�} &!�B�}{MP2}VWMP3n74R7|}{�.� VH$_3$a$-$39a7149094E�$i�15284i� 438375.$450934 �K0463879']36150�F~2$�# $-$4 7 7468@8@08483 p 53890iv43176� ' 6313BK ]60715�F! �5l799528 01985� $-$5 6427N39082~ ' 6592�=] 2771~}�H $-$7d37712 �7�S187742 43411 $461123941�]454��w��� $121!x 9340�� $120!@1!� 52070 � &553336!�� 6492-@b299439�3-�167�49132-�166%�973� 60726\ 44964�  6044) b86756� 2$FCl$^. } �8%�697�84%139!�!�  52931�  47679� 636�] 4892 �e >��Y024�94%4!n)j 63041-3  4034y  6382m�]30%�SiH!_2$6 13E 2558q130�7I{! 61000!�$-423279� < 6620� )b38 �1F�4E�578)�h40aj 9988�140*71638 &31725� ) 5909-?b837)����-!�aM!10E35506� �97445v04v285��  3061}1 6 )Ar3!E� �e1�76% 8140Q176t02289K 70411q� 32799[)�  5671Mab 3079A���A 42�56195 3 00263mx 939��� 111E�U$-781-A '53928�=ѷ��887IA�~�� 93341 $!�%$! 2052� z ' 2198%�'88414e��E� ��g218�'�ge�88467ML4�32105mv026�4  4322MK ] 0621}�,^b �� 1222qp7�944 }7E?!��C�h219098�2 285EJ'��07783��Aw�-e�69956-�12e_94368�&30178Qu2  3037� 4411-'�V 6788��Z )��B^q�2d 7302A�UK 6105�IK70922A$ 7263�W 3150 �]5!�\\(�7$�1 4935AVIIS 52591�  7914�� 800E!ZYz 1267m? ] 80479��4��& 8g �IV 4523��Y  88686�886530U '90670-� ] 0083����.5I9 7238%�AKE] 5661�� 7926E1 8159�- 9 8239B'E�68819%Se_22�e� 1�M^ 5215� 87! i� 907693�%119a� �281674U� !L �1�5� 3812�  9843^ 756a��"a 00286m� ]A&� a�y 16A� 84041�6��474y� 9� 0o � 987� �E 0143� �N b382Im�:�f*o %6���+6�%(i1)� open,�cl�#sh�(o $&}%�"4'.�'upp�~*�*r�tnof W- W(o_':2P$he�eJw �l�->�=�of�jy0. {\sl \under/D{Notes}:} (a) The 6U\hJ&]Ned�%=u�6�*�"�i?-(b�pRpjar heat!forB on. 23�:���Q�����Bdn��!yR��f�R<J�ŧ�Y99625� 2855K 98� 31�  & 983^ ��� �� 3898� 7 4540j 83�� 7834 7588�±8 77963 6229�M 6192J  �� 4292M"S 1893K42��h285 8680N2���790�� � 3768� < 4095{  210� 48��)>���&�� 3939& 4 5098z 475  6307��489  N� �q� = 4153� J 4336&  497� 4091�%�2�# 9789� =585�^ 9501' 6184H 4�"[��184^; 5388� 712~  � b 426 ��.$ 5800�F>71758!AK73292 60� 449XE�!^  3806�754� R561 8�p37E�%�!�� 791195812� C09/  338E 401u8!�M�559.2091� a�1Q�11518a7 5366�!� I9Z/ 2075�+ 7180!�<28643�  9507% c! )33353� %43w f 4355Y�585%�4 2154-�a,� 17795�N 2511�g 2748u,28~ a�336�ay�75��I 3581u�386691#40043�M 7351�g���`I(� 5624� 098!e i 1157��  '$u~!�U  9676U) 2655N 2741�  86] k 9545yxaE�� 3612�� 3448BY55�543$  3484qr�a"� " 1576QI 22649�49D 5�!�220U�%�6T 75755#35� G386��39765A�T760-�E��k�_ ?603?�[ 6216E�4456e��-�A 3658u 490358 5241� O 5397� 43z\"v &EN, E"')a�7�+ B�27  L: � �7 y � n'rN.� r>� ~ 1.� �� �� � �� �� 6�"~"E%?:�R_!~� 2�� "�!Mj�|}{IP��'�(�  J� HF B��8:F F�:P �:l �:p~;� �Gw�|P�3�/$-$�P� |�y ��� a)�\"i4�z! [{�?]�ZZ,E� ��J��,2� } ���V!N0f�c|6�1.��$ Ő�  G"� 4y %�!K � )11���(#B2��.d y  "d �J"C ( &��J1O� 3 � !B���AN�%"8 ��&��{�)8]49A���*%�/%E-Q  �Ec � a(L56��rE� [� /6T%ivA�)z e. !  T� %29A E/&R� �� }8myV ~!�c.�� "V Y�4%��&� &A+~�� ~0E{� �w! �W�r�{ � > 5348\*figurF]*i�=eg�*4ics[width=0.5\)�]> 1.ep+�S~Btic d�>min" %A�.vQsQoA�Rr e V{B�.�*C � �"� >� >�he^7 =0.9.�$,angle=-90�2.2�C&�<&#]/$*n" !�� 2&� F)!;24��%T2D� . �abscissa18@ row index))Z:9verDdas 5a� seZ7�E� �-�a�In all�8et�6Zsquare��f/�8p&�D�i� ileV! circ�;$C�8*c 2Y�!�1����36�AbUF, $100|R�D�2�0{ }})/2�  |�1f%�&J�N"��1r�=t!9A2{}h9qDVA� 6�E1mI4�m�m"�A&�G��46IonJ�IPe�eVf!�9�4&�8!�u=F��p�� 8 O�~B{�F~ 6~ s�~�~5.2uj~�i�\;2,Hi\e�R aka�R =y�l1q�V� ~�F��^ J�)yŠ72Cip>�� docu�4?r&lF^" . ^%,0 n-f�V�b�i&r �$�� 3391� � 0785H! & �" � 2� F&�+� 3296k  0221� 65 &s�J~2c Jf� 9 U 8 2054� � 6971X*� 7971( F�+�! 2842a+� 0151�^&312&�216932G*s�948�K125I%K 4785:� 2303.�� �G 7007�G8� G93�*G19072�Q&�� 7�$!&� 6157%%� 6045�M 7763� ��M$ 4345!"932 E461�  0211��6�)G^'h �854E)� 9518�y02037 �j!22`*4 1871��9-�� 5319� �191527A�EE[��� 3252L 2366�>, 9583"B 0514� K�3$�%� 5933d7k 5656� � 7089^�3�'�%��% 668)p� 4551�E� 4063�`053."a&e�8�41t/) 062O)�72[%�33216_ �!� &i�27634��33�,a� 6141/E90�!^u(� 6776�E� 6632|%/859i�g7�/G!]�� 6055�e,977�' 1948��K1F7.�>A�Q�%�336� A� 8416�%. 7579%�� 8024b,�� %.�a-�8I460 I9513�/% 5002xM�43770:f���!�666&I��)047jY!� �E� 0820��(� 238%��93892E�:%� 4356i�Ah 4200�~�283��!�0g��6�!! 6694I L029�/%� 3739.� 1476 %{e�Q�555�0��+��49795e,!*1�1*Aby��273I!�84434!�18424�J092�\"�Bfa& 4337�Et218e�%1 1816�N 7406^M_�F b�b) �� .� N" 2��� RCy�(*;'C[ !�(*�&)�.M&$��&��&��&��&9�PtabF�&h �� *� � |��}�V�&2�V� V� F^�& ���.a��a }4 ����0����� a��a�f��9a� 9M �(d11� :1.I��6��#P%G� �) ��x��� _>� �? 3�� p � �8�$% t �偭�;��� b6 ��G�$��*# O+?{!g�BŒ93 롏5���'�K�  B�f1�3>�A| 3%�2  `w E�x>x&7�*�VIP$_{� SCF}SYJT<2�T:,i��$[�\��S<[a4paper,11pt]{al? \uifgUre.* j*Lo'�Xv]H), Detrended Fluctu�5� (DFA�g�Lalized Hurst exponen G-�. BRnuP�>U?��> �of %  returGs J�, �Z^�. RE� �R6��[��.i� al�Q`b�<0a Brownian mo& pic�.-8Con��ux}��V�eelabor_ d de�R@V"�W��!A�2� iaqX}, I�m8E�_id�U'Zeac�]�InKVuitQyi l�d��T.B: se f&� s. I!M.ense,a+�]rejV and )a�e�a :��Mss9�-[heY ct w�do 'ed,Y�2D!% ought leawH a n��al<r� ity�ab�is)9�_already  XRY]_�ago wE_0am U,cy phenomena��D .(Yob�X�t"=&� ngthe�Z�Xgave ri�^Zv or��es!�$^a�k��I}mWa��Yqturbul!�M�J� �`$, Challet}� (wadays, we ��)�t}]\ ��dif�g�8w5b�fsystemkQs�~in�Kc'T tr�Qf.�9 , buq�:ar(b trigger!0n%ons*> %�0_ng��6�&� of�\�9��3[per���Zwo�Eps, Bz_ei!! ysa��geo�R y. Aal ap�Qc�h�Mo� ne�a�� roprBU ��祮ble d�~on _eai�X2$�dA�en �^}� mA�ts a�*] byEfT*S, nsem�aof�Yl� ����random�r\. I� saia��J��.k�[tho� � exhibit�Zc<-law �E�in2 N�M�Mar�<, Giaia}. O��ei hand,1�ic���`rTass�q lo!� �y!x!�R�Z sZh� _� i!�& eSry!��`)A (i��\m^on�� tate? �(just requir!���a9 s��-Po follow1T law). �b�M�2 �"�ve aboi� spatial)MA .� (�L)�u�H_ has � af}c d becaTm�g r*�^�Ticult!� rVev �act�'!- s. H�_iI5\ st y� �;"�eef�Eq |a`.Y_qua � carr�out, giv{��ia1 E!�Ős �To ��] , �r -Har�nWe �_C !���=� is p0�_atAe toolQ� � �m�4fSp�ɓ6�\\�(main obj�Y)�A�A�> � *�V*S  �ra:L�eE�. m7. Our�aA��� how 71mv si� a* x giveA^�)' �i � siL� )F i����_sm>��n S! on 2� b&7 #3�) revie�+ t d�6ge  "E'it'� \*Xd60 ��of �c rpreRon 9 &� $X��`e�6N}f����&Yed�54 rie�� p�~IZ~�is%�-w�<is}�A�����A ��� 1w too. +5!�exphcMg>#># Alsf�ae�e:6Vk zn�a� V�!� its I�A�o:�IP� More�, 6q"�!P):i�s2: MQ u�T~diY�7�RiT! la&R..�� is ��io�c�)�a�w�S]aY���in�kt )a|s�d _I�q�N�s>=gb��� �hQ+8�q,%�l�gIm�MEm-9.k�mDDy urz � Y�U��od!�almost 9ɣ:*20th �q 1995!218� 2004. Bef[ he�*nf �gfix6sgAIn!� #+rol-t h"nE�p�t�\#b y. Sjoat (+!Is� 2� - !�2HCdailyQ�%� sourc1-is ��mhe ie< a�%K.�of ~ capi�M9'Bp�,�mzenHZlos�[���}-1A�I�t�Uim�/ y spon�Uto � ��em�0 m� b�m�f&d' i��ks �� -K*'u350�Yed�  firm�b�Uj1ht] {.�\re,c box*{0.7\wc2}{0.35}{>�1U.1v2} \par} "�!D%�!>6i �� hist(A�-A�)<0> � \v�*{1cm} �w, T�1a��m#q��of logFh+��.�e}[htb]I:*�[� Tb2}Mea~i tand�idel, skewn$nd kurto�>�medskipp#{v5� � $z$&$Std.V. s $&$K p$\\ 1 �4% 4= 1.06 C 20.8A( , �� 5 !�)+6Bve�i�tle 1,�o�Bwae !��� .�B doesb look* Gaussian6<a�be�f_ �eZ�2`��R` RvB` } \�r� {Cr* L}� H;�a*�BQ!a& ! 0l$d by Henry Gin�P1�[}�- test�Y���sg� *� �u�"� �beh�?��:� �1vJn�@okv�Z֡�behavio�M@"� cumu�vm sɋ@me-Q[!���B���v��o*���S�?m�gs>null-hyp�mda- c walku� n�tS�EG�c����X�l'#,��5 roo, !e. I �I�jr.�aO i�cannot b��b;fC{n�e� m� inflZ\�|Qd!r;�y�|Vq�� d. A*�{Pa�\ autoregr!�> MdDat� kshort-52z� |se� at�adwA8� s� bBA�� �5�2+� �neIbv a�n�C$�taEC��p�W le,$P$Mb!� *� t trans"�to:QmFU�l ^N=P-1$ �ḱ�&={(N_{i}=\log(�h�ii+1} Bhi}�k\hs���i�g<, 2, ..., P - 1.��XTy) i� �� to $m�(ntigu� sub- *�- $n$,�< $m*n = N$. Each5_�'X,by $I_{a}$, �#($a=1,2,...m%j�pE�el�in2:I $N_{k'y.�k2� n$i�T� �%�-�n$!��nc�m� J�hM�=)�1}{n}&lk�k{\tau}�,9�mm} a�5=�hud8N�N� � �� i}'s)�a�q�e �5,A|�A�!Y= lc��a�eE�v2q���k#v$�s�(mean} $(X_{F�)$a�>o�, �~V�kFQa}�k|mm {k}(aFT-%?),6 2 nBA"�rs��Eq. (3�a �c��2 31 alway# ll end up2 zero��Y��g!�a�)�jc�kb;�1t � a�z2@6_��nUR_{eq%JmaxJ�$a}) - \minV=nV 1 < k < FPThe nexDrepaA52qF U/J�,FS� =\sqrt{ZnE):�a}-M^{ 2}}}a� )}.Be,!�r$��? $(5X)e�"�byp �_"� J�$(�)$Ap=�had�� $��B��� �@�a� �x5d� ��((R/S)_{n}= 5Wm��a��m}( 5}{�} )BNNoM�Q 9e8Yr (1)-(6)"�rep� d� �e��horizo T� achie�l#uci� i� a�� Z!*2�until�� e���l?te4$n�s$��s'�F( a :!��>�Y box-,#@s ։e*^� (g�� ng b��on�!�a&*�!fte�C�ed �E�r�b�I�1ijt� 1o!B� plot $�Q*$ agay nA�By p!na*st-! ��gT �BQ��-&va�%� .n)$�!.� one�e�slu#<� y�� W{t�� ( )�[ �� } $H�H�  ($H$x�e f)� d�o $D_{f!(rebAZ�$PaCMmy�5 =2 - HBTI- U~ , $H=0.5$�!8#e/IY�=$ a*2ab�!L� 9 �!be"W� o,%].0 in� 1a non-�&as e.g.h Stu!�-t�� gama ]$ \in (0.5,�]$) mpliM.��is� A)5�&�vby2f� cts � ll-+ca�B�& "�&P Vk �'�*�m�{J/;Hweekly I�I�)� ,u M.4}nd so o��onQ� key*A��*� fa�o. [�{a97la!��"ar�&al�XInr- a �1~to�aC5n�$s1�)�~� a TAG�5y w�&���� ,� �d)�c/"Y&iv�%�(pAo�%9 �k� xeW!?$a�Euit�����be� or O�-p �|"j~ ^�i�$� lso }�!oa�i�A������I�(���ofe��--reb�"�F|��ist� ��a� $H$ :"esas � impaz-)H�FheQ��" �Ή�aUϡe"�($C$)J� 0C = 2^{(2H-1)�F���X���%)q�k $C$ �=lsm "�� un6�&�Z 1.0$!t� $C=1$!4�ng!L�.posA�y�ia�OIAr " �%$��[0, 0.5)eM�ti\1�-mea��@�n�IQ�veU�I� ]�d'�*a�Q�be. >��a�.�1N�zora4opp2�t�age �#m���>�e���AOa%� ver � ��iEic cyNH �Wun��y�H0�2�ѯ� ork,� a �' M,Vis of�|�},f#!�o..N\ŧe?Dlya� sup��7%�];�a�'aU9�� N4�alNQ'����mapu#����erm� lost, X �m�E6�has vani.J�) �;"�#=�XɅ%�� s� ross%�p=�!�EU cru 1����`� �^ �1to�#%p�1��/or�Y1�E4normal�,a�b�{� ��� 2BB�b � }�� & w4us � 0 A����% J5-%}!s�a�s��� �,wVEr) � Q2� cer"<�@n_{maxn�9A}�1�m��on �%N6�i�q�e�c�� F p$s A �M�".)�C �4zsDP  re74A[ h* �A+0 �& curv! d�2Ae"�e��3�caE/regim!a at gn� �=2$�� to 7JE$E7>�)xA�el��E�% to 1286��*�180 �)Ib~�U���i6 !�y��A�� �T$79\pm0.03$n!EeW�� �e�!Mm��B� a!�}w "��� J. Federy{�=v=2.�PB="�.Xm�!3� lag %�Y[UU�Ij%z2iN!"x��&w* �$M�"u6>7%t����( prov����too weakA<y�u0fru�������� it9�9 6�rl�9 D�it"].r/1991 Loa(Lo���5� � T*��!d' aw2v&e�*I'!Pc*�-�2bS {��; ��� �f0.$j�5i��<#b� bX&w��F��#N ], i��LoZYg0 �]">  asJ� QHG[y�jG� j}-\bar{N+}'{& )-�~3 .4$)]}{\sigmaO (q)}*�0{k=1,n>��edY0�Sor!Cex&� J� k ^{2} o �* ��E+)*2&G >q}w_{j�[)i=j+1}^�ijC*-fe )]:  , inKF�=1- �j}{q+1},*r!fqU�r��o2k*/! �!Q� non �T2� I0I �6 �9) <k�,9�rob�% to h�osced�74 \\ �$2%^�i%*s�:�]. �^"E i�0 trem�,(0��F`����6_$q$�&� n��a�,# riJacho�&6�"H9, O �Si!�*� y dԖn guid!�\�cho�@�!Op���2� &� � A(,2,4,6,8,10� $15$.�*��v*L qto�1�!I�"-�6�$2�*�*i&�,7�<�xA��3rS �" % 2 reject �" 6�"IiId�$S `%��&͵AUT>0.5�!�Aa , "g�A��G  meV�&|c|cc\9& LagI}&E�u&&�&AS&� &z� &:~5 $0$&�,513$&$0.7857%�} 9573&�&$2 8219 5393.. 7528c4, 7475j4: 6654 <6, 7156< 3952. 6111<8,696X<60�573 <1!0.68023362y545Jy15Z672Zj2972= 4980B��Q�( "h'"�@ N�@}*�/f&:&7�B��� ��� "g3 v�Ra�.q.�D�j-�a)?%�B$ $\alpha$-A=w�+N�K�>a2{X; C.K. Peng�< advan�.DFA� b?�1.�pe :�'�!qA��" -��2% ��dd-��ee���on-e�on,� ��: � avoi��pu�D2t appa�^}���8 rtifU2� Ak�m���9�!iS]u��o�$H$%3 r5�s (�"��Fourie�a�%)�:\\� $itemize} \  in�:�re]��!�t�)7�Vs; 6�76��eas�.nD"�Cis To e& �$DFA, let u�,A�6 ze7. , $N(i) (� ...,N&�W� t`� �8 7$:��A�} y(j)=m k j}[c-\l9_ N \Ajle>@ M JS: 9&, �e � u.�R�N`"we�?1 ��tK$E]� lapp��� s,�%n7&of�� $n=0,1!OK-1LK$)��!6AWY parP $ �/��#box� f�h=�d �-�"!�a poly�Dal"0, $y_{pol}(i)��*xE��� -wl} aJ�5-1'$l$=1,An-22, etc.%9-H J���be��a~�fit4 .A�dvHd%6rAAg �$y�a�94}c.D$ a�ed29J~Y(i)=[-9>BX.boxMs!f.6'�+m�%� ݚJF(saP2�$M&M��&[�]J+(<;xm� &6#�s $s$ ("0  es)� f@Da� �#hip"`?$�M��"A�<�;1Z- oɦE{��, ing: _\sim sC�]}����v,AWC� o:Wz��� {�.i�V'o� zF�A�signal:e��W!� �no2CA�9!��6*^ S�� ��;d<�!d.�n֏r�7ed/ �>/r$AN��/���esu@� st��Hwͤw,|* d��� @ � >�DS?�&�In�43���$in double-.-AK �]| }Su�I7&r$�u�s. "'� �"噡z K�5��"��� "w:_ 2\pm#31$.�$H%�0�i���1!3D� �#w� s�; i.e,? �I�$ t�B;7 secu��&I6Rs#m�$saM115 &�;��(K!5!}!6"ia��!"0loose#9�m�! } afN7a�!4�?162�"-N�-~��6|A13� !qp$�/�;Uh��5� ���I_�i�=2����"�e�.I�P. GrauR�b�7&7*{fig.3V�.% Fu�N��>Aq�!Q� �I��"Qh"Dof�4f7�:�x {GB;E�s Aach} A&<;b ]k�i�,9 os�n)�sT�be assoc�D%9>�Q� gign��nt�b�FB��;m�.�)�Barm:i1�crp)w�$al�;$q$ C���4"CP�#y�^A~a�A&s%6� e K�dt"L:bl��(tg>�u- H_{q}\�Cv H(qG �B2T  $O (t�ur����5�!�pj� 9=)g�9� s $Sz( )$Fv  =1 |P(t+2-�|^�| _{TO���tq}}� -^{�B= � q > E*E��a�5��is��!��aS8(window) $T \ggs $, u�OAX+s0#cak V!�e5 $�"�1��9,i-�A #d2�vo�4���Li �(�<$q!�$�G�OW<%��By))} @F�$H(1)$U@ &� "U&+(1)!V .5$)� �2 ��t (H <�$$)�oA�!.� � "b*h" �( gets �=J3poR�r&�9�9e;�ed�G� Ns it � e��m%� = q/& D$q < AC)1! $q \geq #�">�� �@ inguvKb �  ki�of�"k "G�B /�A^=HH o"K%��I�i!q$� =f�<TP�t: u�1 firsX a2�ԡ�aunia��*=|a $q cisja�9dLBleC!8���by�^A�ex��A�� ��as� % � �s�$q$I� ��% comme(�7+SpY-�!�"= "r s�ze 5"Z"C/�"8IA�!��.% Eq13)��&��L<l�mwa� �A .�$q$th͌�> !*xF� 2�.$?3��lu�S��-tF"h-nFo�cSr�j ^ ;�!������1�reC a�iW  3'S �S�!"{��@.�@4V� F 9 ��� � 3^ ->2� 5V� � V vJ��6E���rq�7�)�} r|6@!�1)$&$H(2 3 4 5)&�00.8622&0.7935$373&0.6929 592\�@ \ $H(6 G7 8 9 102] 6340H14O 001&0.588k57] ���k�� 61*A ��s���a� ,� "��Y's i�+������ex�Ct i�tFf� 2� *_4��޳|a�8# �i �E� m�++ v0��Y-�$����*u�/G/n� 2(cap4 AfMHlexv0���/ż!�."Y% u! .�B R5, elucidu��"�A�A�ona*�$a �R�Ea?�(�' �P�ES�>4fa# �)a)5��%�+��ir5**V � Ivanov~ ">C6�\ } Paul"�Are Frenc�GZi�Dh~ a1? "� !�"�3�S�FaaS�!�,��iOify!bNR]��%th�umc _�! 7|A�*�RA�R�V�=r�E��&Ma�nr=<&FL_{� }(N, \t�Xga ) "X (\pi}\int_{0o inftyZ $xp(-\gamma= q"�()\cos(qN)dq>��"��!Y 5 U%$0< �,\leq 2$, $ N��F�+� a�йor� �$� ��#�O9.� obey��QS �*"z 9QN_{= }=N_{s� z )^{15 !@2Y�� r�M,`-� .�$1)(' t-u� �If1��+!�2isU�)H"�"a 0 w � .V-�=1&�1YCauch�*_`a\ b�Vi�4G ��2Z����,oN �e $1M . j* �K�+�/� `_{ R/S�$)�_{-$&�. GHE}&D @1.266&1.389&1.1630� m ���#T���� �$e�I��8�M�-��!. "�6� ��\�5on�3�s��#!���� �{�."�!���*Q;�|Ls�M!Ɖ�e��A_ �!�g�haoAfsz\q�:�" M�"bD �; �x R��a�L �\��iK2" ��&M PDF�� e!hata.�f�.� weV"p"�\<ximum98ihood1y�of^+� ":IL �is��6��=N%��m�5!Y A"���Za�Rt*kbO �[k= [-1,1]%,  <{E�str2�����d shift.��E�� .�2 f���)�s",A"O 22���m\  qd2CP!XMK1S6EA�epi�ein�4 5. F?`*2xi��,:�-� �R6R4|b�9e"3.%�gH� real6�(�8� �on� of�)�>�9+A�(}�)E&7 ��f�5.Rj4P�6jB��2�N �"� ��J�6��.�i"k (PDF��@M�A���("z�axa8in�:iSB�S-�� � "URc7�*`Ss>keQVQf2�.9U���~V��rbet�8�7.l3�z.2�.00�{ 07*iq�}�w �:mF�56�V$ri.��ion�%b�Z[ $6��ul�b��ass� :�� �6"�="A� @�lM<  P��}+:m�I��ak*/ f���>�1?#������i<)ble�i7 ���� "8*� ��bUdecayLA ympt^E�' wer #r ��au^{-� }$�� < 1|�m:"O`�`�=C ���1���V�pas�n���," �0o!-�,G d \ anomal�O���Z��"` D�M2�!�X H�4 $k\rightarrow=J�i[(k)=\&k9 L(k)i/&�@ 0&t!8E~ $L(x *s�lowly �mU at/k#y!��gre�&2�*a^A��"� -�$?)�e.�&!�-|bB8E������ &' s!~ylO � a M�2q$H = 1L��� {2}$� BjC - 2H��S:E�bv�rOI1DI�~fas� $!�1}$E7,Cly"B'�J)�J%"E�Ga)(9tIa �/HA�>app�n&.r� �(d!ƅ�6W5m �4 ?�aid�Lo2},h!�5\%�'f" ce l�qhJ�3a�r>u�r4ed �F6�� �"�; f#H, )  conf|c=[0.809FI 862]I>��� fp4.���olag��xsL�� 0� 2 ^�3e�+".4s6�4 .�42s4�l:4sa6Be�� O:?@ki7!�6I9� byd�U\lim_{T�� +�� }E[Rl"/S8(q)]/(aT^{H})=1>�!� $a>0$. W@ link��s*vo �&�"�( a7%?@�phipJs�A{B�}\cE=(a)+H tBGIn&[Koɥ !E6eoL�.rst&�A�V0U/OMBM@by/�rdi�2le��I:s *�M! ${�%�,l)�,l%�,l=1,.j&; +(l).'yEy $j=tV,T�st0�!�,lH!� e� 64�.�5.3�$�,*� Ty�M.F9)loptima&���=%N. �э�![-K_c�*6� IVed�00to 0.721$\pm$� 1��&i�� x�if��iB� �7 �� ,*�?� disc�]o6$vM�wS"�4�2�y} &� �s��a� ��A�s G Q+!#�a�BT.Di M���@t�&��X�%D:;xEd"$6p" t%��as�h T#,ernRp�zN!1A? ����� � er��tween1e�rd emer�& �. A&�e�V-�E� o�!&s�x�kyz Nasdaq)(US2 S\&PمH Nikkei 225 (Japan)� o on�H�,�K��E�r RA4an AK\&M�|% JSXC Peruv LSEG�2�.���� "�3)!��NaW�: new �� e�P"V-�&�Q�6#�w k���!}�>��a:�* high� ay$o'� t�$e]V?�* @?5�Mi*�&`!�B�~6o!2)�&�'�7z,KQM veuSd.�2)�(.\\"~]!85d>7%~� %n\ �4at�f:�kb&�aB�6E goryWit�Ia�7 an iciC�>T.:f c 4J �9�!�G} �(Nn�) Di�)�em(F, bot��� zO9!R�4!{sak�*4�< i� e�Q�iOtwo f���:�IX��n�S5x` )�GQ9of�!06, = �qc��1a� ,I6s=hduE/ 1997�� 2001�d0!�� ���!lA-os�OfɲVe1]E"�G v4�b�H��H2�U%12���%� i��erk?ch%�.� $$i$ $�t$ $/es$�%&�%\L% ��&0.475ե��4\\��6 3\\ ��\%51\\ ��_%:5#��"u%\\)�&�%�%9���2):�:]f&f}-Z��l!0�ido�iE�"�o�fa5Teh��%i ExM.�a��g�x �>�2vfCI4�Ks}� @ pcjQ�YP.�$��e7a�a�oZ*:%�!-a�� ��5 }*�tlo&Zewe���Q:�Q�* i\� "x"� ��� "�s:%XE��� Z�� -, *�("�.ce��^ w ?��"�Q up�&z/8 6 months (115->�M)&�& �&2�+>��$'�Jd ��V�&n2�.����� Also�2%�%%ba+ onn�,Y��F%��m%-�� B2A�� ����+de]O'�qc2\m� e�{dng3�Vm��8� r�_��the.r� }{99��b�yem��} R. �', H.E.nՁAn .N�&)Econophy�(Cambridge U&�P0Q,,%0! }"�~ J.-P�uc=� M. Pons,���"Ą Risk.\�x�w�� J.D.��mer, Co�= ;H� c?Engine%�, Nov�Cr-Dec (, pp. 26-39 o9).�$Daco} M.M._�rogna,!pGen\c c�# U. M\"ull�DR.B. Olsen, O.V. P=t,J� High-F,ze�~)# e, A.� mic -� Lond�j� .�Cont}� ,F�acroec3@Dyn. 4 (2000), 172�L�T. Lux%�M*esi, N�e�-, 498.�J��:C } P.&+yH$L. Hart, P!?HuP4.F. Johnson, ph*i����,-mat/9910072.b�~ D.  {\em e8D .}, �� n. 1�1�68. CMZ���d3{�|.N���|,Y.-C. Zhang,� a A ܗ!?1), 51� m�"�| I."�|J�$. M�zard6Y9 Y 22[I�aa]�S�F F�stitute��'�$ 98-12-117.D5��z« Eur.% . J. B 201|�.k�}�� , T%F . Am�tc. Civ.a�. 116AY 51) 770; �� 6R.�Wlack,�9YAFSimaika�/ ng-T�Y,Storage: An 27�ay�j5ble5eI 1965.�Pe+�} E�; , F� � uT , Wi�ZNew Y�Z�S.OJ�U  O$s, Plenum,A-A, 1988, p.170]�TA.W�S, E��mZ}$ca, 59(5),!;91) 1279.�&I  , S��Buldyrev$ Havlin, M�?�5�!St�>%wAa�Goldberg��"���!� 4 685 Gt42;�=Am�= -Car*�AiiU87EG0) 396.�&6< A-L�F<,��VicsekiE �$A44, 2730 �12��/ P.Ch. , LA�aral, A.2�S. 9G%+senbl!�ZΏStruzik%./�/9�9) 461-46m�} R.N�y>�VVL7e"95L-42�CY"Wo�P� , No.2984�lBureau IMic"C�.{�"� %{ AsteA124��040368e �#>��d"5��>_�112W�*V�&�\4H \t�Infer�� s�h*�! $p$ �a binomp1! { �'p�>af�`ed �$background&�0G. D'Agostini� 3{ h �a��a"���&le�hi2��&�"$p$m $x$ {\it� es} &� �on !tr��} i��~���ed- [- .@-%3?(ce%&�,� !)��x two �m: �a}) fj -� �>u�* aX)~�< Poish��of�X�n��; %bc � �aa,�sW L�&� "C n ��j3 $p_b$19�&b4.� } 2!��Z�&���u�{�MYkng `ob�Rs'*w+w�Faa!1D* meas�+4)Cd)R} Z� ,/or  (h` *' �nds� "�4"M B dom��Sv< Aal0to `rate') kheI7!Gc� ion}!� � �2ee�_9�z}<.�"s$HLicle � �| mC#)6&D`�1�3 branchR r0�Os�� omer-�galax� i�`^�sky�- M4.W��N��ċ . AOHI{�A]26a��Mrarel=��xl&��I�% !� Wm�vid�E��.�8pQ-��Z1T(VI�-to�y a!"�X}@7. O: ���y&�E�+ enviro s, j�0krdue�_s�,�cQ�[ neff�c�d��of��:��aTlo��io!�% ing;�)UV@"us�� ?)��`!!Ae� q�+loo� forlo e they�/A�[����@%�H��y��estE�#X cus e��&� �h��!Wm�=e�;�8re$�aA;eD�{Ba"J��NV*l�s, i.e. baf2AA���a> Vx��{�,y Ref.~�R�Oe$!�ll as":p�  7E�13g6BRY��H ��FuqXa����s. ���sec��X}A�in�_� `d4*'z`�� rse'!R�?>q��`L�he&�(�92$�::!�=Is[h�B�Y1SInF�no_bkgd�g�4�`:/ text-b'~oA!:7.t.(bse��we;,cu$�N;U��depth�:�#s%# ��pr�|��i�P�r "�~i�{)X� �:!@� ��n �f%�Ehwo�A�;���'�{��i�&5�rNB!pE$�T�$custom V�%[��a"M "� .�E!�M$� lem}�Go�:^F��2�'� edZ+�JpW�(t Bernoulli �lDb��> $X$%v93A$�Cnd�,e���%[f��outl: $X=x C�My �S ���29of)� �[em comb�bicG�a�!�Patn U_2�,�4a�N�y�KL${\�B}_{n,p}N Wf(x\,|\,6*�JtX{n!}{(n-x)!\,x!}\, p^x\�,-p)^{n-x} \,���}{1.0 ceeft\{ ,array}{l} G}�} \ldo�K �(� f0 \7 ��f+ x = 0,gdn  �\�- .\,,q�eq}�*"<) �pngi# |4!�e}�ist>�}eqn x \m��$E}(X) & = n\,p�\s�d(x) &\TU 1s}\,� T W�$FNE:�al *�':� E� �E BQP,&�" �of (� ��) �p\��}M6uS�tainty��Q�2�"��4De� m0ed�^�.^} lem�c�"� B�aU!�r�v�Iu� x$ (g" }) 0D��# ssu�%�!$��59�}��Oi �%N ��� ly s �,�uO� }�u $x$}S2� &v 6< $f(pe�n,x)$. z2�I��G�( '"9,��� .<y,� Baye4 eorem !����.ac:a.�Q��x,n�iA�\� to & ^�� f_\f� (p)\.� inf_ET�uA18"�B8{\it prior}, $f�(p\,|\,x,n,{\cal B})$ the {\it posterior} (or @final}) and $ f(xB> _{n,p})$ E�ilikelihood}. The proportionality factor is calculated from normalization. [Note the use of $f(\cdot)$ for severalf babi buncp s as wellpr! dens�)H (pdf), also within_ samelmula.]� solu]| of Eq.~(\ref{eq:inf_binom}), re� toH4names of Bayes%NlLaplace, is presently a kind*`first text book exercise �o!@led U�ian inference (see e.g. Ref.~\cite{BR,RPP}).�issuekpriors Yis�!2|lems will be discussed in detail5 Sec.~%ss: M0}, especially!B%,critical cas)$x=0$%$x=n$. � { cany4complicated byK)3c�0background. T�is$,main subject�tpaper, A�Pwe shall focus on two�%�.W\\begin{enumerate} \item[e9a)}] {\b!��� on!�ff�T${\mathbf x}$}. Think,%example,�`a person shooting $n$ tiEB$n a target � coun$ , at� end,e�number�$scores $x$!�orderA� evaluate !lefficiency. If somebody elseA�es!zmistakem$ random on@ �{pQ;))�=X�"ef situe�%:happeA� measur!�ieM�ose 9s (for1M due�high !� or lo4timing) A�which%;!c core�ioAz twee� $equivalent!S `1�' AJ`!c(ing' cannotA� done!a event!?  basis (�f>$to neutron�photoekectors).61^(solved assu� thM9kadescrib�3b�k PoisAiproces� �. know!|t�'$r_b$, V% (sponds to a.2expec!�AY0e $\lambda_b$A��hresulA� |distrib�S(��%�doe�G =r_b�4 T$, where $T$�Y& $6"$, plua�! M�9�,5� >J$ parameter=$, ind� n P}_{5s$}$. For l�.�(A�st��I�vely low�)�ϱ�is easyA�Eh:�8ubtrac�t1��t ofOe!c��%I& $\A�p = (x-�)/n$.�small Y-�(`estimator'?$�5become 3 er than 0aH%Ń n 1. And,e� ifA`�$ �g��ut�'!�E�,ct range, it! )>.�_, uncertainty��4erefore we hav��g 8rough a rigorou��&� inversionA�a �* ��$s given byՐ(qnarray} f� n,x,9H &\!mto& ,f(x=x_s+x_b\ n,p.2ibLf_\circ(p) \,, \end{ni|�written� lici�m�& �>$x$�m!c}(A� vidu4uni�able!)6�m�A�$aS (!oafa' Ub��pts $s`b$ st3 for .�Hy� }.) .�b��� (Exshow up,�� , a��depend��0`fake' trialsi l�* �f �4  p_b}�3produc��suc��esV A!k2��h med3mp��.�!t)ofq�.2�  0blue galaxies�!aiQ reg�of sky I�a e ar2 belong�to a cluV ,� �]as.?i,�ta� g.4 p2��i� ů.���\  both9 !��i�F�� uJPn & = & n_s+n_b \\ x m7 BithJJ0_b & \sim & �6� ]J' B}n_b,p_ba� \\ x_s & :L%s,p_sb� `$$'I�sA�( `follows a�P�u,ion'. Agai��eA� vial����F�too y) "$ �d�� 6�Ged [A 2p����/(n�&0 B��most genE we nato  $p$ lF��B!K|\6D!��H=M32� JS. \no-O\\ &&BU We might N �interes!/to�qu�ons, �s� �� manya2a�G o a�.��0, i.e. $$f(nb \,.$$_ deed��e5s2 l"� e join���^I�Rl ,$$ %�i�we�eget �inf)A�,�b�condial&F ��$p�  !�E-|of ts att� e�): �Yn_s.b!�) F,ly,�may)�b�5��� $r��� s%�-�sAe sible$$n1 �*��!�s� (or,*� ��Nq J^ s$):%�qus%*W�n"% \se{I!� ewin abs�2L}\label{sec:no_bkgd}�Fof Eq.Ni �a�Qt least!princiQ�  pI � $�x)$. Tak��a flat "b0�I1A�4at models our K�fM�}� !�pos)� ź��k } RinN c�=+ �Kc rimJini ��" w 3 ed%a�owa�t &}):� �} M 2+� = \frac{(n+1)!}{x!\,(n-x)!}\,p^x\,(1-p)^{n-x}\,, -�vM3lk�%$i���Y � Figb8fig:beta_up}. %��4figure}[t] \ceaq\1�/&�  $p$,�Au5�6�in=�.5�} -Z.)Y- % E� E,E�ve �A��)s $f(p�O Aumaximum�variaqh .6!�:1�&K \mbox{E}F &=&M>$x+1}{n+2} �E f%" 1}\\ 8ae;= p_m� /n�/,\sigma^2(p)= eVar,g(x+1)A� +1)}A�$3)(n+2)^2}CY  0�,\,\left(1 - .r�e�35��2}\,.)�9 Eq.~.� ��s�  4 ``recursive !�~ '', �``9's ru��� '. No�Are� no magic�!��? ula �  s��j�u� A/extrem��:�M �Eee��y (D �routine} g���iorI�plays��a 8log� aow � "�AA�e in fMabsor�( n� liz� con�t. (S�x�ve��cA�ont6�} %�e��rein.) 4"i e ef�� %�, let us�Cl if a^8powerful way usEC)�v}�[ � a very a�uto)/ "�Ijsi%���.ledge I:aɚ��defin�AP. val :� S �fSs}8�G T}@tabular}{|c|c|}\h &�Y\m�column�*|l|}{ A)} 3$r=s=$\,<1}, 1.1 e 0.9}}  :FEB^E,2}, 3, 4, 5}�� % �> 1 �=0.47&�� } & B52�5\\ �C^� 0.8}, 0.521zD6K0.8$; $=Z.!1R2, 3}^Z3��J4�5\�E.�L(r,\,s)=$ (3,\,5), (E,5}), ( 3)z!F^U0H0W  Y 30[\\^/7��J/8�55/E qi u�:� E�( Beta2q��? &� $r�. "X �"�P bold����%4inuous curves." �I ��D%�� 2��͕conjug���}��2:�*��fior���[� family, ��upd.\��viaBP�!c��,:gicF���q�E< ��$p�.�>y| !�}(r,s))="z \�T }p^{r-1}(uHs-1} \hspace{0.6cm}� \{\!��-{l} e` > 0A� 0\le p1 \,. � 1� .*� � _�-�&�!denomin�" p 2�!�z�!l ��g�" $�$=\int_0^1 F�\-) d}p$���) 5��� �"A�|.oimmediat$recognize :� �)�a Z.K!�]]$r=x+1qm=n- [8�AQ ���!SH $ $(r-1)!(s /(s+{ %3er argus ]�a�Q�wr��"�$ (negl�ng$i evant:��or)J�4�R]�"���xE�[p^x M�3g] \�s$ {r_i]� +\O�%p^{x+ 3]+ 8^�! cript $i.�> ^ thenJ � B&6 �GI?>�0 $r_f = r_i+xQ;s_i+ �) $: o�"stYqap:� � A�+e� se7=^$ 1�failures�$RRAɅ�"AkneU{F2�$7*�I?E}(X)&=&��r}{r+s} � eq:Ea�� //Xe2$/(r+s-2) \[r>1\F$and}\ s>1]� GI.xs}{H+1)\, AQE~ [r+�MI�<�eq:Var��&�na�A7us�k$or��%�>y�!�9LE'1N_f��O�{:W���� demX ����ear� Ba&X'c $s progres�ly�"�(6e<� � }e> of a�am�%��{: is%s waT� x\gga �n- s_i$, �*���s_� we would C�2�($r_iae =1$,a� ' �'&�)�!%HreaC$i']ard `@'&� , �!�quiet'nd saf!=tR&*uakInsteaatreat���$s much mor�rajs typ� of `"a)arch':�i�9no)tA�ith no � le `�, '. L�i?'!�atq iFl$ l0e a na\"\i ve����!�Nq re�(t `.N'�op& $p$a�&�1.�b�IJkѶx=0*,W��1,1))�� \,�Yn+ * fp_x0>� (a�i\bU'J5"amo����s�=�� �S�#5)s�ER in�~mQ�_down�As� incre�,� �1EL!� jraiMd�J0.� �t4hx*r161��&��rvrA�_"!C�9nq%U��- Nth��a�%�usE�%�Iupper��s}5#a ;% levelA� confidenc�A? natu me��A��is exaD !�#�$s�3!� perLf� �9be�Awre`ed.��ke�-x-�aG*�� sAA$ghtforward�+�����X l�'M�,G��� t-I����@makes us 95\% sur�PatQ� � it, �$P(� 8p_{u_{0.95}}) =~5$�+��er6�'val�).=$)W��scu��t!�"� $F(.36� {JU 65��� l6 {.t}�*4 n & �# � (1-p_u)^n- J- � yieldsJN.m�2Y\4[n+1]{0.05}\, B&!�!�thr���'��2�i�,> $n=3$, 1�50,A3�$2�,=0.53$, 0.24E��7,�!�+i*seult�bin+�%�%�**��+�ct�[!��%Aia{uld! � �*@2Q �! sub-� �of fixc+ dth �!0 � )1�$iwuIwea ieA�a� |;#ly"ow�% abov� 5). &0�iq: %h��)nY w . Perhap��loon r��-)� h$p$b[*"<j.ly 50��%��.say to!k� ZE��fact, �,%e0previous stat� imp�#%Iw��5\J`1B0Ah�%>�$seem G&� ! !Is�0 tistEHr the phY$enology un� study. (N� ask G)ematicia4E}8s! Ask yourselv=n�*�/lleaguesAE&!��[& i(}�A�rtA�you/�ing.)�g (al I sugges���W"�3of�e�a 50\%�u�-a������%�d9+�- 2w"MwoA�i�qle �)s�-�as՜� e is-�`*� �I �S5}F��$n=50$A 6u5}�t013� $f a physic!� was:6he/sh� b�2,ghly embarra�4��� be)8�gN�0�.7(_��� n]e@]� -()eE,&a�� u2�HeU5oB*� ava%r2� ` K�+lE q �be�  5,is8 �'inW �L�0`default' uni�.%ϭ35m�a�� at"u7<$of magnituA�Anh�/%=/Ee�> ed 1n#%��i�� r�6%i�I�is� #\ln p$ (� Y& f _{min}$ax}$), {i�3e$f"�.*/ 1/p$#iw�#� Lcut-off's. Anyway�%T!plaa� blindly嚝��*��a�6��`�) ive' �s,a��� � �0�b[ ct&��0 ٥�b once !��]��r�9. PA02��d��a `�J� |""3Ba�8AL ula,e �?a! 5��ą�n�*9q ^ilistic &existsA-e t����A)to�ify�belief!{��,E� e pdaE&�'them. �plH#��ree%&��!K� a{F*� � rescaled{ @$asymptotic��$p�arr�$ (a2t� !-�9��*�in�s�I�5p�ŧto�m0a�� � a� abscissa/�!<8)�a;e��}��nv6 (6Rpu"& &Z�'R3_10_50"�y'R-T.Ay*�$��*�$n$2�Rp:� We�il!� �) ��hT8���G (Mh��8Amkre8ongly dumped. Ir7 t vinc,A�^�ratjs3to dra�/3� ew.�. Wita2i�A�* ��j� �1$`excluded'.6 \log�q KkoB# .��j �!� =tpU=��#on5A ���!5> >�-��O�+�"O�B�(Ip$�&�(m� ^+lo�'tivity:~ � fic motiv/%�9 MBN��ty masT%� �%q��*p"�+s.�� chv6%�conviT-� u��7=�`=�&w�2(R}(p;\, n,\N�i60ip)}�n>52�)}\u"R ,mv�5�$�)^n�us �c(?a"N!�atT ��'A&�!�'!!�!\!��#a p�0$p�>� Nal ]�f��ost. Ue`Z:�5nA>v$ �  re asڱ�A!�x=0��"�S eft/v�Qp]�m� I.E6W8to �-i.$�?�pre�a�*��:�y ����,}� %�sen_P .31 1%� each��AE>;�� at �>�B���Q���;R}$U�M�awf�  anz *�dopqk0��:=0:�3enval�"�K.�traC%3Z �=1$�Y�=0$. "-)� �c� � �:�  m�& doesN�. �� A%�!��� b�A},$  se%�atѶ ��ŀ �!ə!��My�ά��no�?g% M*gAx�!ly �"$ed --- it /B_ME��end� ! -�>80to handle it)"$"��p�<��eF)�� ,D� &�BZ�B ��y'7�@s�jQ(�mA =�"O$ bQ# Delta T$ W edBFimet$'% I{�^B. (u:�8o�as �<Tone�zB�Bs�8�s|��length,!�f H v8,e soli>AgleV&�H/99�( %᥌d�6t d� �s�3�#7A� ext,Atle9D$I+alway�=Eless.) �cF!>)#ed!��>eh�Cw lm&sJ�x�3�<+ ="�<\@=?=B}_tJ "_=6^=JbIn �A��� theorem!�/<c"�B $�Ja p,#4m�)Eis&=�A n �,\ 6�Ez;i� *@ & A�Wume�a&*|$])e^uI�mb�R]zby/e9J� 4.4��.B68B�  1(��%�L \sum_{x_s,\,x_b} \da�_{x�B} \,f(x_�:2^_s}) .s:b*� bin+poisB� �@$N�Q!~$Kronecker ����- z)����C>�B�#O!�(fF!��B ru@m 0A���7P2&Xy).�5}atA�" Q� Y�� R� alla�, �2��"6y�act�CF�� ��-(�ultѫp%K(ly� n2,n�yEK&� 6sRApropt�(�s\,f_0(p�=� &&TCa� ��6� bin_}�$n=10$,m7nan��933�A ��:�20^�ɧ ��..FSb�L�eJ�2cA�. ; �4_n10_x7_lb0_10ny"�9�y)( �X_F$_2_B2b� ��/W>�P�Aor6�,4a&al hyp��2{> (q+ai c�/e "OB=1 1,\,2,\,461(,\,6,\,10$)�wo�q� s (dashe�nes), $)6! }S%"�\p�2)2,2)!��)�=�4 [�$-�!�nd=e�g�MMW�b �[a�� � ( �� "U�th .�I�is X�A�P"�"G6�Bad 3e�6���u �b6broad �O,ied��.5��: $�f�:� sH'�GEof�����p�J](��T��Q%)��&�+�Q�) �,"#�X"� s� i=2�J$s .a+ %""y!%� ` �^&� �zero � %u�Od�ZR� *G7 anakto6��)� &&*U2&  =]E;TD "B /5\e�a2DwD��� V�A��� �!x\ne ��sg�Hi[ ��� � sE:$ �I,!-aB( )"�h4qKer!Y3ofB nullN�.� }B� to6��soRn )�9���=S=�at�����a�d!Q it (6�FE !S1N!M*nonc�%� gers�=e6Nss��aF �,6�A�2aZ=As�-N |>  (I�1  `open' `q�&s�� .aZ�=� }�J�Gr91�loglogn@nT��{?BRel%F�ve"�Eor AIR��1"�^�:&B=.���8��:�6�G_R �1%��di�ed� ve�<�!��.!�c)�b�r#on��self-eI#H�-��. 5"� &�&���, ]h �~ pr�e� rel�3*DHEU�Q"�!1cD�A�w@h�TA����cjn  F�fs at��� though�^�Fa_o�4ah��� 1. St�!*�sw�a�-s6!�"� suit6&H s (-(1)� $0  = \ex3*ft[-( ({p}+4)^2)/2�� ]/(\�({2\,\piF)�S��A!! $pf(A..� �� 6-9. �%Iz 1�h $3.2� ^{-5}$a�Ex�ed,nd�#n�0 devi��of Log) (-4,1)� 0.03eX0.04,~M)>.i�BmFQ�2b _LogNormv*:�� t0P 2�I�.� ) peaka�tt I�!!� "�^I (2 ZLZ� �(!n_�:Y8� !��-u�*�*1Wl)� J^2��IMaOn#U� a.� ."�Ap��!GJ] a���h;%#.|&s�O)i�X�\�� g rRA�, already suf�Yt�o 2�*%O �i2�i�B%#T  4.�)}w&�& �)1. �L�i3%[lya9\%.A d p8b���"C�X��  �!��Xhor>r4 in_nL_3�s�,�!fI2�M t�#* 3%Vcomparu!��m�2���:�A*�F9�=V�F�2�:]�ME� pasE��Ma6n�3%�:�,  littlc g !{��luh]�F��%:���%�AHI�sJ�(e�]pe9 v�%N��-re"t subA%ceA|2I2 (u�v�):#E�7)�A�EN: 0.67�B3; 4 2 49 6��#(CE�9 XX>'ts job�i�s�* no wo�,�� :�&drifts� @��d) o Z7i.ZN0��, tNrto   ch 7��a1W.�-_a rpriEOX 'ose wh�g ��x�m�7�� �.�� �-cEabe.I�&O�K ��bc d�'A�%6.f-")>J� i�,<�$��s +c!�!�sN9out�$���a\aXFula��p��J��f V"�6Q��aJc�Qq,��� �).�� s��i&�*PFp��Gs (j9^ee*nw7a�ab iz�JB q(oT �e%3Z���9}>L7^(�� Ds_2exp��SzL!�9:!RAu,� rY �$%*R�, A"n%�SI7s, I"]e�*^�=0u (B�"����A]&�`aLhav�)��14a�y�2q�Vit�t *!ꍢ� ing�< pert�$on%-(i2_ nsic! e fe�7��e."7)�&rLU&5]4!G:�*[8�.madi�E�p6�G�aX�\���M����,; �"���,*�<antY,F�i�aa���f"� �� !�i]P �' best����2"m s*�T#Te�/�&!�C"� �#�8ora�b s�3.0t l2U�ycep�(c�NLcan be � B l9 �kMi� &x�X��IqFK4��/�tE�ory� get:� &�"�< ,\,n.�7(\infty\!\! 2&:2f(9�J�&& 8'\F�QW�� E���@��"L.�ss�0-��J1� Icg1� ]of:';b"f@pdf's# <�2E:}. �c#`� ' �0*?!6�Wbkgd_nt#>/aQ m:7�.roblem�'b)"�H�=odu�*. v\X!n�r�a�}�p?�oa� onj0�)v7�6 d$�Q@�� thei�!uE . To�marize,)�j^�U�+to ��=U����*h$n$]:� tota�Y�d���  2s',�Yo\6 ich I d� +Z�$nA@ "yh;��= �_B dire�� KB6b� ferred;a$x��!o���7subcl-of!�e�\�";F2.�aEkl�a~u��:�^9i#?p_F9B 2hgf� -d�R� s.�2�Aʼn&�!!AtU�,E7>n)�P� 9A�-��-�.$�[�A�p�u �\��BG\'�%l t�o builY)& I�connec%/Ied Q5��ll q��t�]*�>��/�d uo�cum�/E"�>&�.Z# n" p 5�,\b�_�^ Ѫ c�eL?NbW�]Za\�\�nat.�!\6�u]E�alN#!*Vt-��! woF�#N%�L -5mm}f_{2�"};N� \!J#\!>K# N�"\,4!FK#\O# cdot&f2S#�$_!��d)\%"�/V#bin} %(. n_s!tY(_s-x_s)!\,x%�s^�# (o?s)^/(�# % n.n_b Fb-x_b Fbk\ p_bFbFbF(�Y 2]a%% & &i�&`F#�!e�&UE$�n!�nd� �lf*b$.�]�IvarH> N�>LPd�[SV"� �E}(x)=~ap_0E�? �% .�Ix�a>*s\�W p_s)lb aB��� Eq.~$Eeq%�%9w&1c+6�Z1�)�-Na �:.�TD. CYk!��mI �/on�.�J�>q�o�'1usymbol�A�)$" D&� � B� d2 ���BA��Y.z$��r�*ven#o?.I(� �g�=�g-S,$)(>��WA";Wpiz�  S�%����$)��Q�����[q�\��2(  "/+$2nz$.���� s� on UFa),ed �\\���(A&�OTing: �!7!A:!)D �$"�e�)en �d&� �, =�\�d~X\,;$$ �eJq�p0� H�#݉�@1)�"atFN - \!.m!�` ��2�X�/��Q )_{� n��<&�E�X^GF� ��2�5wzO t ri� eaaA3&RJ,� � � �>� �� ��i7P�q�_b$u��[��13��Nb,��Jo��n +^9Z�\, h#n��|Zl,�m ��(_lik_x_5varMR�n0JH`U-7��.�.d1JP�, �hj�+\,Rv.s8�_�ZaJ� � >���x$,~ AL "&,.�$Yd.�%*h����.t6�)A�B8?�.��a A� p_sNp!"IR#-3.\In ) )T&b^p� "� A3  5�.Q-�_ns_ps} �/f"-ib�� Us}���(qcert3 |�z�k*�/� &=& ?EO�-\, �)d}p_sB|n�V�))5C� ! ��}; 0��^U� y�-�ps_����4Y�%�!57&n�i�(hO4�qyVI�=�D/ �X)7�W4�X.=�EalI)��" mD\s  q")?� y"mDf�|c�SoF�"��!$&hb� a|*F&a on x��on"�z&1R'�s:��!�v } If I��� ,2�5�})!<�>j[6.0�]�J�UP /AV sum_H A��<�c�cYSFip,)�.�,8_pb075_025_095}Ev�\:g 9O/ n=12�n*�x>�-�.��-��E%1`E �#"�'r.n$/ 2_x9$/ �Bk0.975*�Q//Z8(:M2�M.M9�Mep��5b{$��eY)�e?$x%�� W ]6"�*I[&8 =�+ 1, 2�b 6, 8�N , 14qs (� y)N�#b8��W;�"��cs]� t"G(i�s �z &06�$I>}��j�)9Q\Q]"� \  *v/Q�p_b=0.7�.&w �g�e�0�Y_.3,$R32E�!:�!�6&%(FX1"� ) oU a�3{��B:���#?^v�e �qơ��$�. Ai�J &ID, Pi _s)$ s�/er&6>�fe�,i@vse<aS)erQof"9a"�qJ D be���re&��theP�&�4d�2�:!:zv�f0noisy environ�Xs &5'b"�in�or^� )me!�*Sp#*�**atAq all#�Y;"� 5�!�&W(A�I�a�,%4be mA$a $R"u!Y#ed�ioP?Fe{5r/q��&f& 'B��~,�b=Uw $� u�=A=y`&�v'�5> �3=er�G 9n auto�G����� .�ywg3 marg# �i)�5�6si�himo*?�a�-@��s� /n$.r'mid�=��![��A�Y��25�1~'�9M�:E( i��d�H6�=a�$�0R 9w5�z�Nls5 star�0�$D 2�$ALa� m��A^��u(�$ fav0K3$2s-M�(oppos`?*$w�@inkI�`A�cha4e��^ q��(%#bottom)��j�=!�� �&!*d ~a�y�s$�5 histograme�w N&+��� �"� �&�y2�'! {E%"� =4 �t�_Iw ent 1�e97oA�begin�# "k �Hk \Ik:~j�+n= kb07N�46*� �V�1� nI�sb� 6N� ��R� 6P����N��R( ��N.�nd5�iU~~ e(Y�)� �+Ot�i )T B� &+/^�*a [b$�)7�lX0[ (top ]^�.m} �ye�s�,&�1�*T$�)Wwe�(�� � �K�I�$W�2�F�d�. [>5&�Mb$H��"4 1!�5�1�)�* �� $X] �,X7�two o� !�a�1�"�G�}.�^� =�n-~�$.] A��"�$��" ~�MDUs$"�O.�K�3����!��� sS��AH) -�1lJ6&�$�n_s&8h&�.�@X!���s�:�A�)� :�;6�s�W"dh<B�BZ�=�w e^{-�}&�s}}��,�&V��"D e��"hW"E A�+rjq'$u4:Pis shif��&~a/A/M�.�.Cke� a0B� > inv_t_0_12} �] s�T's+ e�s�!���52���z��e+inv�n �B��\B{�� !+}I*o %�,"A2�(�.�: '� s:a:;E�_�ai��  Us� a2�!� fe.p �*�+a�Lt�-�Qrn� w�.X A ory �ld;!�tha�;�m��e�^$�Q�4F>UFQ��-�q*lk+&:s� ])�o(*�u�X]��^�"�l.�} N��E~�\�D��anJ�RGsMhe�� &�MI�� a�-=mo��m.��O N���:9"ta6�9E$en,>�!���:�� easi!��AEt{.l6��YNycE}YGZ�".,Q�1�)&.܄ _�"U�fa[N/d + O E}^2O ]ME0@ ��&U3 }{A!8 "Z.'a�b++l/� 7��=��\8Vis � >n eE3V]F: |�* {Con^5sE V)�in�[�ze+SE3pR?t �K�B7Xu,ndC��{?�Lgep$65Eei� -*��\ sk"�#'�L !H,<mza� ��'2�. ed �7ae��U l ���D��sei5�!��Lin qu��x? agre� F intu~j,4%� sten } �#e�l�l�z�, mlea%Oabsur\3C -#�6outA7�Y& �dUx>�}� ���lrua��1%#H&%%RIi�ndOuse�{*alO&E�:p0�ay>��ev�i�t�� ) ,YTNemphas��a� they��"�P!3�so&���E*�\vA-5��&�8e�\vspacv 8cm}']a p1.ia/Dank Stefano Andreo/.} x��*�diA'1M�k�a�newpage�thebibli�,phy} {ref99}:ib &�S P8t[!�4G. D'Agostini,$� q �pa�[,Pa�� �SesG�D&deY� .iUTa�k�<s]e on gravia/Ǚ wave buysseXo|}'', CERN-EP/99-126, August 1999��,p-ex/99090474� BR} :�_Uh @4"�%A���Fysis: AY*In&y-�World SPf��  doc6y} �\^[12pt]{ 9cl6%�$C title�� { %Q�@APPLICATIONS OF GEOMETRIC ALGEBRA TO BLACK HOLES AND HAWKING RADI;} X|author{ S. Setiawan$^{\dagger}$ ��1�{ \ $^ $v4Schf� of M7�s��MUniE �6l�dinburgh  EH9 3JZUni!� Kingdom} �L}{ �<%-n 1)J< a�e� is��� ���P7�B�geometoxalgebrzGblack�J�LGB" UqL�3c�>ep�)9<qem>� ���2�8Clifford��a3���]�� mˑ�Krta�fol9i>�u* �Gauge��or�GŽy (GTG) a�y;s g/f�oto en�,v$S �1�Q"�$*3���>c!Z��orien � m�S ~�s.i9-�\ 4-�6Z e-.�.�hpp1��0g(�}G���n�/&��Pcosmo�j Hawk��ra~�AUnruh ��  �_!`<temper<6 de Si�86ohoriz0Y�E[nge_9Dermodynamic system`Oa; � r��$kI ,"MA u<�ble)B� %�xp)� c�F pse.�rs"�^b�Z[JW.;!�p�sbe!< er-. ` 4aseB!fin5٢�9)�veVG . Be& s,}4q��E�w ful]yA � "2 2�#] �&�9�h�vrM�vV � {A Asph�|rCsym��sA�c�� &oI�( Klein-Gord� Dirac]aQ��!(Schwarzschi�6`nd Reissner-Nordstr\"{o}m.u � q2 �&g�1i�:�(bU�.��het�e nopo�OA��7!�s"��6r�0 electro ?s{ia*6��� 9 � �emn� repea- Kax\O:voe�.^, Kerr)Vg\u�}G�8ra�ri�!�A�� cKG�����`GEC)8�;,. Remarkably�"yvd. � U�f�a�{�b�Paŀaa� non-�R roo�?i�.c,I`�6�c�~�r�Ihrsp�3!%� ��(�yet:Zsm,* e�U7mpletgte ��,s��Mq�� tell)Max :'s pur2J! oryQ�s�-1%*� s (S�s)z$}N!B pict �[ ic7 carr�? forc(s a��um�Xp!�!�r�! Re%� ( al `�'y-|�is�$gne�byF !� &# .Y O!72���f}�.SF�.�-�{ of O��heime3,Snyder 7�o֥e%��<���3ll�\Ka homo�B��= gaseO���� in Eńin's G�� /R� (GR�y>9Ze%��A��cua6f� e�ommun� 5���u! �>zG6b�a�cru�Xe�b�H� 6�r�g&� mM#I%Nr{$ntil Wheel-w�D!L� ����~!51960'��tri& -� gold��ra޽�>e. GR c�l edi!=e�p"��Vchɳh%stoXi�!p Ced�:��b���@/1_~_,aea, Kram)StephaMacCallu�\nd HerltM�k-}, Mi�, Thorn-�1KI�mtw},��IEllis ha�cinMChrn$doulou c.}�Tde Felic.Clarke /f};�pop<�yJ~'se>�Q� ?em}� ks$ne}, Begel�g�Ree�b },�"F� )wIa ford �Gribbi|g �p�PrZ  employ�?Edisser �� M s]y? in GR�Ae��Dmod�l a~un�I4 Lasenby, Dora� nd GZO �l 1��semKb�U�ve  �d�!g!��?� wqB]$�{emerg`Wine�y<�(�9a,� ersu�d�?�ZA�D+"� or ` %"$ yLqK�iu(�!i �_N��N Newton@languať16rpe veloc�GJ�HPH �a�eed�!4I� of l�,��#j� X%�Bs�<5�:�� *N9��hid��beh8 2N,�g`kwdr%'ARor GTG&M-any)�)��2A}�kgo���E�*rgu �� ingo� *�,�sto�`^���; U�ac�J it&r Q %um Me�Oics (QM)_dt)[*+ GR ��fbreak�%���4 smo ���Ǣ� (!|� es)%b��ev�t��!� ��gugs (mi�~� � �I�gemiG E+QM�5}e emi��of*k E�y�[= KE2 �&m"� i�h�5}�E� b1vl�� rmwald};!L parikh85A��"��H b. s tunne�J�Iait !vl! rmal1+vO��a  bodyI�a.� sporm �H�;q�Hy��� �Dno2�a�l.��/| evapFe.� ��)f"ȉ" � d is@t#a�henJ Ω) �K�l�.Glo��r0 X co�nc� Qimp�kon-unit�A���e�hA��pto E �}law� QM�!�V! G(�A��2��Sll��� �(w �(=J'ppears� e��Ta���6���"(  �!RB!Fmai�"R�BC!9�s.VYFa^G"1Tz�7m"?Eo�_N�%���7�7I\l��un�N"�-5_��2�� e�tA�31 iˊf�{ .i@promi�-A^= q>{s�,��m t�� h�)�6�� � �$�|re$�E!e9 i�oA��zar�� ��ϙ�ble8 r@Axa�l�� plan�A]erm�MA�di+a b3]��]�ums,3rif#@l�E�e5|FiU�A��x����f�"(Z� k!������![cu���b�s)�!= ��L ��I RQ "�*�&|�<,�&�G�p�� $EJ�n�e2z!�gƯMNZ^ ����s�b��a���%J K�u!�S�y1*d $UW!do!5^a �bf%is6 aV���� ��:�������I&�oell�an���]�I$stik��Y.fi#Ie��ad���-� "nC�&@�0zndice�c�AZ`�short9 �nyd mon�u"G� nd v��)harmo� �Zu��ep�pebm7kA� help�,Maple packag� redfern(.�&�A��;riebQ"vPA�F �8׷�w�qsta#� ! i5�&�K s. M�8��  e may2�"6"�Lt heD'²J� ide��H %��Qcal< �%�)����u)ib\ �� � ssoc̚ (�)�du��<a�i! �2dzf�&�W~wgrtX0�l %��  �>515. U�]w)�kQ ut1l9jl k6]squto�N>E$a�7�$wo���܏t~Y Y&J)� Ưuxt��gab�;�d�\po o^ݩAN!�Ћվ5�Yj%� innecout `� LO-\, woRAxdot g w�)6�e :f'd*��l!=�0{rrr} a.b & \L[ f�D1}{2} (ab+ba)\\ a\b n+ -ba).>��e"�Is� u3!$a.b$a�a-�iY$vn�+%'�ctord�0�= �)9�MJ� a bi)P (I�2�i�|e�regara"� b%ed6 sega1�&gifrA1Y �EXpa�]�.u>!�:��T llelM� $ab = ba$ilst -G.Aper�!i� ��ibk��"Ga<S� gherm�-(mrh�!-aj>�24��&�;��Sn*3 �� (STA)��eJ�"9�.L �IBamili�2o� is�B�<i�l ($\gamma$-ma-$�TAQ1 �<f‘orthog�)I&s $\{ E_\mu \ؼ$ =F�ldz��| s Nz� A�Q nuq}2{q ; nu +27 mu#8\�{\mu\nu}"AH,diag} (+---)�=y�A 8!œeA41� �g!�setN��^�Mc} 1�D=/\� \{\s�� _k,i i�i6;�H1�B41�6u�4 t��1 pseudo��}i�0U 1>2>3>4}nrM15�)�k1� 0, k = 1 ]\�N$i:2021 2 3A)t1 2 ��a.R�^�&$-J8������ odd-)&�6a��5�\}�Dne"!�R� Eucl n 3-e�����$isomorphic��A�Pauli�r� ry���nt(�r�T of 'a�E' ('P���0i�,_0$�P!i�zio�B!;�)_���V �K-"�~al) p��3- s-��-.�to��arbit\V"su��A�*�s5� (3T�e['� �')v?] in�$p2O �%P �h! IÁ~9�o� Forr -�u $A_�� -$s$6"B_�;�- � J�A_� , B_suByle �2(le_{|r-s|},�S�[ �'' j>+>>�q� uM or�8� ��eR%') !`$M$� ��QQA1i�aT�/ N�T�B�.� AB - BAFA�3 of rDIS.:� tilde,�J)��HJ�(AB)^{\.{��-H B}�lde{AB6 �����< I��un3g7!�"�%5 adopI�&� Di��4�#racke�� , � Fjs�Oh/��gkZ >!HOV��"�@G%��l�]Lև,� � reekx � �� ��&� co�ja�$\{x^6(x)e�i}tri �o a1B-) TofW>e>��� $ea�#�e^�=��^{py�PA9 ���* $\nabla (1�A�ial_x)� ��d^A A @e^�} H\mu^tk! ? / x S�_Lin �& mapp� �� ��>���� Abar} = {f}(a)Õ�!�a=A� S ya ), IadP�Q9bAv a `. B�io�Ke��sK[kahJ�:��b � sc :� :8)"6b��H6&c)JY�I:� �Arj!ar��a9� STA,- sor �$!�r��E�@U �(all mani�#�r��|~d�=�d�qn -fre�ne"All LoJHz��� o�a"��8:Fro�[Tu��!:�  $R�Dat�  $R�eR 1$���g�!�C ,�y,*��#J(M \mapsto R�թ�R�lend2i ge �or ��t���Rexp (B/�mBe*���i���>�Z2  1} s6]&y-i%�� iE(?;�U!&!JA�` B(x)Z�"�&$%�}��If~M BO "� �6 �(&�() Minkowski&} �dem���M���Vo%E �9� inva �t��*� lo>dis���!e H"� ��,^IQ[A(x')"� x'�^N  ere \e!X-si�%u�A2$xS "n��!'�nBQ�~�R�)y�F��$R$u&onۅ-FdF��$d!��)����` rr��co)�N�A�-1�cN2e ! �TJ�%a�)!^:*. � d���=P!��i�or%�B ��-(8�4�m���of*�n+��th�` "+ !_����t"� |��ScS G2�[�!�6- �2pur��*jT�P�A�&A%�:�-��-%�r��" ��t*�!]9�WH%�l.Z�@i)j ]-]i&�%u� �1��)U�& VE�te) ) ,N&?�j{�R: O!�*!�`"�C�&, ��aqI<"g��*� AN6�A�R�bW:=u�WQ#u66�9+�Despii L���n�i�Pٺ)!�)+E#ү=R�) ��5���v3u$��(e*ho�x�n"}ignS-nc���t Y-XlRl/��m=Aw;xe-Z�z3LE4!���-�> A-Xosal. A�t� cho�u�k!��z�*� i:� T�%1� i`�3�i4%�t$�vx32B�"�&e}[t] "�RSym� F��Vid%�al �-v} \"�D5�D?& Ul|W�c|}R� \�[-3mm]{` {8mms*l�3}{c|}{��A�<� \c{2-4}ZOI?�$ & $\psi 'H$.' (a,h (��"�S8UR�alac Go� Fn(|f}^{-1C,x' + �(\unde��, #\��Ze����&/ � fR �,.� �R �6 - 2 a# �R&� $���=6�� phi I"� �F��.�y 1�eB�UI�n D�iia��&f��l~�.$M�I�!�:��v8��FKMBa&g \o% � \YaE�s?:o. � D_a %�=>+2  }(<psi)�RS!QgD Ka.�(M�) &:q�qvX�>��&R ���$cal{D}_a M.�M|)^�a�s M��_6]V�mݖm>e=_a9�Z- ��.� {&S�v]Z =Y!�->=��M6�} ��j�XVs" al_Xw sum\\Bts_{i < �$s < j} e^i��"�e^j (e_jZ_i) \ast9bXI[b�.L t Ri�n� bs9�R}$��b�ab� "_   � �|d"@���ength�x)$.V�$�:�2}� (���M"q\b)9#)�>a)R�;B�!pRicci-d, Y � "�9: y )���k$ V < :�?("SV+2�! rrcl��%@ �T� :5 Rj:W!& �U�5CR02t\ �R mScalajm�i)J `5Oj�GI�*�ڶZ�A .a�� R} .n�!!��e�&��be*�"7(} �9��= \kapp�6�T �B�>�04 �t,?st��-�gyM��re^4�i�e�BOm�$-7er�Rs%2�(�CQ�.�>�� "S�CosF�GRaV�GE��a *�& &�d0>�0} �vMAVM0�~H*�i�S> ,gib�80}�4=S miniЪ coup�!:e�2 N� ,doran12}� ch���5seJ� &)  = m_p��I_0B$&We"r �.-S�F5 Rc**}�\� +2!mbda(r)ar� e_-e_-R)J�CWA�� \LY}{6}r^2B*� $e_-5�"0 - e_r:o8�6BN��  .L - [(�(-i+ r)(�bt- r)]>J+[V>6�3};i"� ��Up�6@p��E�uby*l$Iza��i�u�zj$"9 CQ-$9dQ p�K^Y�.e., $j)P1�y2'�J�:�al_: si = - j��\��x � $}]"lE:(r)(1+�%b� �+ j (J�.A`+iZu B�"��6&5Q�,|jEBAj��6���.� \e]B�NϦe ��Me� t= &h���.� �kbPAZ2"�7&4_D�}4}*�.,�+Q: (24)�7t low,a�7 orar�]� .;DZ^j$;�9�;wɓ�x28_5�e (unw�I�ed)��+� bN�&a%$_l^m = [(la� + 1)P((\cos \thetK {m+1}6���]e^{m  3^l \ge %r$-(l+1)� ml�`$vm= !��)ed Lege�Y polyno[�sA,%,w7!�N$abramowitz�Ewol|R�m�{!�gu!zN�� ^�:��(l/r)�pe>anR2bb(BR��%�2)/h&��u�} AEUs\�.�#-#M��1*PF� a5/BOsV �l�Y,� ���\{:�ll}Uxu�+��rH!"v(r)I �3,g/6 = A�1,�b 4K 3SpsKIL2C-%*1��/^nѹ�m o!�Ni7�z ��"sE9P) plex"� Ea$� B��bstit��g:>i]��Q3)e�?��F�R�� ��TbE� ds�� 82xa?m�b:S5%�AN�(:� c} u_1^{'� u_2 BcAI +�VI!�u�/FA>@%�J�f��!vI�Bm�1.^ & �hA���&? & 16.��V��!z�� 6�E�}:�r}A�zet�& j(E��_p�\\ \\ -� 2�| �oJF�H�$9OeQu/ Q� (18��V�)8- �l� }{) �L}D � E(RF $u_ 2 $u_2i�� redu��s�Xa $S2F?�,N6u_1 = ru�%\, A�= jrv>��Z[pv�i (28)+&�C�8%r���$�iE�� :tC\/~�(11Z=C^2�fFG��A�}� > itJ1��bfrM7VzN Y2e;Uh� B� Wet���g �Ese�H��ms\ radi��fCv�Mb"�iE`Y,� �!� SJIC7^s�� k=0}r� a_kkB�N3b3F ^�La - r_H�D r_H5���m�di�)� 3>Q�J�+eQa_J�6 � �Yx �3�ol)!�b\$1fC $"b5��yit&Gsq&h>GalyFi�Oo �e*�V~�"=e (35]�to (3)set $-e0��WA 4|��riN* \deti)[i�:�+`2�` \%�31p() s \hat{I}� $]_{r=r_H} � B���%wI!ZEX; !K(� XNgsf� �=- ���<F�S��f��9-a�L �1n|O�KA?�L!* naly�Zat�M1W�T>�.�W0\cite{lasenby��1} it is claimed that one can calculate reflection coefficients and scattering amplitudes by determining the split between ingoingC outg �states of these solutions. However,0 problem here�whether(second rootƠbe physically significant. We now conside ?`Hawki�Xemperature', which willQdenoted� $T_H$. In}s!9)5�, we shall ne%]p(n-covariantz8erved current ( igen|esV< streamlines whofHurves are timelike))�!��mbe expressed as \cite{lasenby1} : \begin{equation} J = \underline{h}(\psi \gamma_0 \tilde{\psi}) \det (\under�<{h})^{-1} . \endY,This satisfi � flatspace1� e �T $\nabla{\cdot}J = 0.$!� �, $\eta^s$ asJ�{s}�(exp \left\{ d( -\frac{1}{2} - jE \sqrt{ <\displaystyle 3}:`\Lambda}} \right) \ln (r-�D) E\}B6WAJnE�writeN��. -�$array}{r} �=� \mid��<@ \\ +\, j \, \arg�"AN �-.B, withe(choice�?argumentN7�\,�!#MQbeE �@{ll} 0, & r > r_H! -\pi <. ��-�s�/x$E$ into real and imaginary par��NHE = E_r + j\epsilonB7 If��� take%Blimit $r-karrow ��,$ from above�belowpfin�hthe $\g�a$ compon�of $J$��given byN�!�N� Q�>PB_1(\theta,\phi)e^{-21 t}��E� ^{(-1 + 2�, �)}�gmes\\ � \{ Ff1ISEf,Ag��[ -2\piֈA2��] bE�,��I� MMN��} w�$>~%�Ha positive-definiteA6. aA�&�A/radialF+N�%AJ!e^r22����-��z6z�F�X resultg �deriv��R� . By��� he rw�m 4inward flux tototal iNlEh| ?]]_-}2 + - 6mM|�S�.���e� + 1}m�}�|e identify a Fermi-Dirac distribx �[RMn�T_H�6P 1>P � k_B}j�t :L3}F7 � �5� Ʉ we u :�, notoutU , because7e concerned)an ob� r in= Cde Si universed � (efore obtai*  sameM�� by' ndA�Lapproach, but much mB� om� . C� �,.�outJ�Phorizon (i.e., in reg� IIa Figure 25 $gibhawk0})� -a)"62I {\it~!M}e>JP^�NG+�G��VHto1�~Fa nega��VQJiH� �I�I� 4is a remarkablQ�. A~�fg~fcdetect*% HF���l^ y�Q�it��:}5�J}$ ! It seem�a�CN(is�-depen�veLfac7is$�pour�mpt of� icl��rG,�:explai��c : k����F�s unst%�V ��verNand�"�@inverno6}. The in�io� erais}ie�to ha�aken pl�$very early�Z�evo���2 haAv similar n�U%J�(ifferenc��B� took �for a �,short period�ime�$endlessly) �U*�\may# t%�%[ility�1 respA�to��1 . IfVwislyNindic��Yaa6�qmodyna�* system61�,$0e Cauchyq�sy8ner)!�(black holes!8uldjSEGsh�T��exist (!� poinE� view!u^�q�~ stea%�exQ��Tcosmolog���pY6��,��6�> actu.te�$o collapsemdroz}ii also}n a��reF�e���e.U^�gR6external>m�� . As� cus�$by Gibbons%���i���, a68ev~��a�man4e�it� 2�26. Ha�, i]abandE��c:�s��be�o�-in�'� appl isI0�r�%asfn-Ew)b:� !�Y1�2�E�]%qm$we gea�e"�V��� �&� (. \subseH{�NHUnruh Effect} Supp���ora�)uniforma�ccelera�0in Minkowski R��. Accor��to f)�ur3}�is�gor beA�%�if�=wA���dea!64rmal bath of `�'U�sI.c �)v: U": a}{2 � F� ]a$!$!�5� B��%9vacuumeH��ND�X����anhngY]a-�wal�pere.��R!�du��rue5= cre��b� ��ARse a�:� at some\stR� anc�Ou�5+ed�s�emsel[in:�!D�J�)�eE�. Both�mV =�s�bK Yd!inA�) loss� sociE�oAlP.�u؍���e(ively (see,��example,.4,e (6,mensky,pa~ani� Ga�?terest!�paper Bdeser�>nni�( was sought"� surf� grav !ARB, �aimA�e� ish|principl�equival�imcoM5$as`Am'�)�sAl glob��embed�0Yd�LsAhigZdi!*AAw�sA%�evA~2|� 1 P�0 A�rr ћ]$9 �ones.>��e�8ric field $E_c$a�duc�two o�YitAcharged��_fac!ceach oa�u !r:Y�trong en!�$A �NlocE�bet�DpA�s�A���arE� neara7B�.�E�@ (e%mass $M$%� d $e$)~pag�)a�M6�!�Zka��e E_c}{MJ�{I�Ie�g��A�:�!Vfu� describ)�a � clas�8 trajectory; onA( tranM�ccompani K!: emisA� � bsorp�quanta�]EL_��ed + um-mechang lyI�analys�in��sen�emi�,� M�'s Z��9� evapoSn�q�ing5}*)h��-�i�  um �!orys� ��%FfirstJ9th3!�a. nfou e � ed��V� (� noFm3 )��nd %�bU�s:����_alw�9)�appearsaQ Q"� ���'& . S� ly,q�l_ �k6m2 ��� y *�s��{out�Y�&z ��rumN�0who falls fre��i3A�Q does� se&|sQ�ngA�IƩ_equ�bm�^� pdis� xLp  RiUr backgrINo stud� eMՉ=M��}.�st�!emplo 0^"m�� coup�:x� � ,doran12}%DchA�E��J�D \!�and^�!z��z�z}A�zetE�& j(E +a>).\\ \\ -B�f�#�jJ�F�$HE��Fj (q5���jE9�Ji $u_1� $u_2$ A�re� fun��f�a} $Schwarzs�C�N�,u_1 = zu, \, $ u_2 = jzvB<�f[priagin (56)�& Mti �_*�$z$. E�%:~ be �$tenV�%(1-2az5%efZdi�\��A,}���� m� s~ :�&.�A�.�:,J�B`As usual� intr� %�serieN�I"'Xs \sum_{k=0}^\infty a_kkBBN3b3 BbA4J_KA� - z_Y"��V�zK%��� �'aJIo"7)% & aN�det�:[IG-०B(,2as \hat{I}\�'$]_{z=z_H} �(B��"�*������*] J�sU�`�` �jE}{aF�A�+previous � � h at $^��alwaysVo6��16 i�+�� � tic� K�fz_HSb $_ Xdan6� . (A6o� u%� is��,in Chapter 4� BirrelDav�� b }.)b�e/ wish �sti�@,ag���*F�*+2�)"�8 n (z�~Aa*E*F�K(� ��Nq.*>R�(n': \midV(�):B� �k��):W�rs)z >�R�\s)z <�s)BE*ceefurE2s��)�)-֊)z-�a�)�z 2a�~)�~)B~)� Fr)1��Exf))O��:)M-B:) X6��$E_r>}$aq�*)MlM�N)N�b.*)���~ ) $z$-�23+N c J)\)+36 )��5�)N��)�2�( Y���2%��*. "�( k&1�;=&e!to2�(Q*�'.a!��١5`.�&'C&�(��(>�N%Fl:_-Q�b�()��e#y +Nt(s,&T$_z~(=$J0 T^1B� '*��Jm'!�us6 "-"aan2��"�*�(" #h?pr"v#2 �  sv ulR��6�e.7~cgs�t�!N !I\av(x 4�. 10*/3}U a \mbox{K}F� s8+is �!!too s�! �5ercei'$��d�0lab�ory;or.�regar(A�al��u lan��%en "*F � na �$�5p�5rsuggesi{�thee�(J�� \bF4��*�,M5�Vweh$� ludA,� p)"� ing}&� o[5ʦ�2y�i 8%%�I Q�" y}� $�x/:/pi )R �'{c*i�m�dB�+��A+�e� mer h)2>c,�Ai�A;�b�mm,NV!%4cspo�'��� �lah,�"C 2c�!YX'�*�7%icaKanAl.�"�{Spher� SymmeiB&Holes} 2�":�`on Reissner-Nordstr\"{o}m.� U}e�� }A��Q�`*kf�' er1, 2};!�I# #gwg>% }. A�� �aFA(AF6�k" been�by La~9, D�� Gull s�}�y+��%�"�es�%�t��X��q� zero8��/�f)�"4R!.&h�+ nesd70}, 8pp1#!ndB2})E��JLFs8- e {\mathcal{A}9�J�� � }S%K>� �debneyF�8geroch,janis,ki )Hsley,newmanpenrose16 2} )J�2�a�a�r)�X�:^�ZIA2M:� f9 q^2}{2r^2F0!�Z6 e_r$���"�k"j!M���(��s�^ po�+cot t!A�:ONb/<�*�Z7 - [(9=(-� 0+ r)(\\!al_t- r)]Eva+[V>%zM-x 7�7�B(By multiplyQ �QցO*89e�!0#�?us 4,e symbol $j$� re>�@�-!2dhic%�]�$, +2$j)`Qla�2'w�7NU:art%P E= e \Phi -(<U \bolda�>$}i"u1(1+\s%L^�+je_) ` + j �5�.Dc� y�BE e� $:&5C 0 v"zPhi��!� potealqG*�2�#��m�; a tr� sepa&�*J@blR��(�\alpha(t�(�x}B��H�tA@: $t$-Q�N�h�{?(�J~FospaA �+cr5'5N`A�N�^>%��RFy�:1iQ<6rM>�e2X:L&�r2'!$2���@psA�m?+ j� "@ *}@9AJQBP Next��BoQee�"th�/gu��9�. $4�b]"ne�;�{�� monogenic�B�!4}� � &� ��.*��-�!Q��" �" �" itN$e��! r)+U�E96! r�nd6�BV���! \kappa>8r�& � U�m_*/ �*/ %:8 F#6���J>K�5o�ס8�>Q� (80)� N���P�T� +dѷa�(E-��,B�I}6)n �x *x R^WruB7jr�y GG�q r2q فv�q � 2 1R  T�� �� �� �� eY9�(�'Blea look�power � *'���27x(u�Iconvergm(a(he�/,�W� "� �� �� � � �~4!� valu�J$� �ch N eta_{\pm�Hr - r B�!BJ@ /�JM \pm� M^2-A�B�I�e^� ���2� s#u�($r_+$)y !�,-$)K9jusVL�1��6ByxK rs Ki�K%H_+$4F;���4'.dex $sbF+#l��-2z wFA $O �� mean<at#5"M �bL{-ity. To f8e ]sAe  6$titute (93_9to (91)Hset�� $l �cR��["~F1� �"J�(�K\ b_0N� = r^2#6# j�Q":#r=r_+ZW 2R�! M����>�$r���96)�Cre !�G2ETerm��a @lp|*,!�3M�%���A��D[i rmin3to�i2J]#$$V/o bN���$%2)��s}��>�$)�V�$Kw����� ���$N{p$B�$&�I�[�M]M+6�M>)�6]F�" Bya�X7�ONPtep �)�-$:� �)�nowJ�N�-z�M NQ�i��We�.GM2.(��PW�{P�{P�"� p1xh�='c�}P�}P�}P}P*�643e���IP +$ (U��- !^�P�P+~i:=�i #�O (r-(>C)v�Pm) ���`R���N��&Vw=�\�PJ�� BkPJ,J�B a )ںIPNp�r�&r �M+��&r_- < r_+����&��&f�&6DPF"V"P�8 �*�c�#P�#P#PF�E��&22�>JmjR��Q��&MBB�&�&ev�� (E_ra�] P.�� N�&Nj .�&2tO@�P"�_A� � BRS%J�*�M = B:�N�4"�&*1RBYU2��E2+'� � � �PQV (107)� >�*PJ)  tak 6z'.y'��� &x'R�L�]Gj'2�&{R`'=m�1}{.E�[.�FaN=J�V�'e ��O*{"J T��O�"� dis&hY\2� >#9B �N��B�A��arison� VBnouOoz1k:�%$q� w�@p*c3JM� $��.F� ���>�-&X Sd "�followA�F� C(,O: C,martelini16}R� arg *YB� )&%�\{:+9&Y_*�ť"��-,�� a{Nrem4�b��6kam2|�%k�R��~��9���i�AP!W�=n f#N$impossible%�R�"@X,bekenstein10,bardeen11�DI�)&�JhApsE�farA��)�*o*?R*��3 S. But,& >)GLin��DjKH+)&g�N�eUis)�>X�O��CtA� g�"�H".L2� _-HF�SSo�iseE"�L ��!�J�?N"�L,>EL�@RFL�MitqI68wobM5idh!!v6��=�c>P ode;s Yt��be�,r�<if&�5 all. (&�J(Klein-Gordo*�_on:��"�'W�"@anlE�Ax")�Vc%iefg*y'�� perA}sa>B@�!#!#%} work�Bk&�e^��ryder14,bjorken,itzyksonqft,weinbergqftr)bv^�E("'0 D} ^2+m_p^2)�����>$�?$"S'D}$�WH &M h}(e^{\mu%�# +'2\omega(e  t,�A�wWAmT QI@J� �u(r)\,\T�], )\,e^{jm�]} ]"F�By&^��C15 (112lP#�Ku�&-2��geN\`u^{''!2J$-4jEMr+2r-�(� �%] 54C_1�O C_2+!�,B���=�X�$C"'C�2� *g$4,tants.�d��!�/ $2M�0= -2ME^2 + C_{>j�? �6{C>� 2M}!`��7� C�4e�E�s"g"harmon�,�>C %�$, Nm''5q6�\cos 9`>�\s#0T`} G + (Cd$%�6Km� 2xC^2`) F%� >�by��P@$C = l(l+1)$. Notaca�G)��G"�C �h M/r$7g. A�:p^Ea�^B>� yer@>>�t* -�*WN�I  =2M$� pu�) LB�4�H�HeJ�J�\, 4jMEFV�=nz�gM�2�ci (�u$hbar = 1$)�5B��MB.�g�S(~3Im} (-�,^{\star}2�+�'�)}{m_p} P.Z�gB; YT$F3��>[-�+i���%e�!f!`$ ( �>trivial8f�KI�g�3J�M�= D[(["�2M)FWRgLNN�2M� = ����*,�*,  ��>�%���Iw�92MBQ 2M �3A�Y�Ye�s��< $EVf*�<'.6VaRCf2MV�����"�+{N/}aHA;�e�)E�;a �H2� (4M))�5�a +8M���e-�I� 8�TM09 Y <#IB�>6�$� " VNe[:V # z�f�<���<6��<Up�Lak" a�}-�  v)R`ef��` \, =�f1a{]V�1N|;2�Bose-E 5in��:�cJ�J�.1}�k_{B} FR:Y2!"� �46W&ANVU��a^�$&>. F"N!��76 �+��Ju@ !��-4&� M� +2�%�!-2Mr+ &� F Cj ^� $CM�� h dW'ed vi2Pr  8 bovea;El}RB.�>�k (: ���KX6�\r��y�y�y�y�y�y� /)M2rDR>R!r}>V:��J���� %2�B������J�ʆ� R@�T��i> Z�>~)}�6�RS-�Y �Y 6/���h ѷ}�per�_�s3Yn� - = >)$)���F6o (110����� � � �  �9.F� 1). Fu�L� qY�@z)"�Fv)"O>} Magne�OMonop�AIp�`Re dd m*�7*!�~�6�P*g�f alis]c2�Be)*CA!�J� ��wm�v�as%C�j Maxwell'sJ`oUqBs. F�"d a?0za D di 1C � :�>�Q�1n[5[�F!�ret�0��'�`posal�D�3of heQ!/V�p��!qW_�of-ic �PZ$ cO y�6A�}9"�a-$e$2 �q_M$ (s:q�!�bf�= q_M/r~I>$�H�j D�F� 2eq_M = N�1��ere $N� n intege�H�QM�%%v�`* >�A�O�`�5v(r&�!~R�/� bf{A��(\cos�) * TF�� `ng' al�b$ :��un��+provide� atJ �ad)�al�wg�#fusfGa�ge $q!�0a Q+�^2!�e�$ mtw}%�(details), s�JFlO]r)$ W s sl�}OboJ�2>� M}{g q^2+q_ME>�1�} AllZd�s�`�^^276m�?d�n�j]NV1� =#�^+ + I v�psi^->�L+i0$ -�ZY4�:Nn^� 83-1}{2\> l+1�1� ( (+k}�.Tl+1-k})\,^+\Phi^{mk}_l�. -=.I.?=1?-??!�"�am#��:ato�:�aN1$(1-02U*�@U��@��@��@��@��@�@We��@��J�I$�R a�>a:>a�iw�#����>et�$"�:J�#D@:##@B+Z� /� >R@("� )J��B��?ڻ?� ��?F�!��&s "h�N��Yb2�=.S)�+��=����=V� *�� ��&�� �d.�6.� :�."#N�=In c�N!��!�s�n��n�b"lBJ:!2j%(< "NeY lde{�'A2(20S�>i��R�R� &�Mod$�;+$�&�<� a�&^b�����&J"e9>IrgCT�2�:�=�N6)"Zv$=64��3�;e�F�N�.K4 A:xՂ�&C O[�.f4�'0��&J�EF'>�]�f��2'�2'!mNFJ'>�R�%v6\mi��.m�[�>3�ގP/5�q�IF:�ll}.<��6Z'%b���(�I=�I=fI=�����$b����O=������ � ����6�dJ� �/*�$�")R +*�*�K=�K=�K=#}v�yJ>&'$N�;.f)� 6 .�}:\��G J 2`Elect"sm�!S2�r*;8&�)}E�W(��x�Xntf"� X�H"�N�\zex�9�`wedge'IJ�N�^ D} \/2-7 �]C�Z-S}�w.�1,B�to in�chv -gra�c�L:p aN keep�Ba,q N!isp�2ermn�:� c�'dot"`8{D�s �"zXh}�1b�V= & [ '1 ~@)]B.Z y-:� ��dbdEV &�-�[6r_�_�S}r��Vj�=*�N^J�"� 2K.t � V� MA�Mziw>nf� 9�V�A_r%32�Q)�#+1c\langle6�2>0\r'_{r+1f�pI+�2�Mf�7��F�V=�J�FC/1�a�\ F^01s } N�uc rear�e�NV6/et�`E�6 (�)�56"5q�I"�)�(I6��P2�BW.�13}j9+5.�I2* 2[0�a�FYL>>�a��b!�yB�tof�.�[2�2� (Fj�] = J�Y9$F]l)�A"�:$A_!��B*"".!� �"0�ņ?�Ng1F!\EYF^�B'=:� (J I�^JJ�By7,bin�1 s`geRX� b�!=�N�.�U3�-�di�ss-�&gy�Asot��&B�XioR"J� *;?2�a).~ L}_mn��T}6�i>(aRRZXJu1>T}_{em^d�5� ���2aLBJQ ��%6�6@a�dYB�-� �B;!PYDF"� 1&FU�az�>��n�1hk=:�2�" Š�az�= 5�) a:#�X2..I2;���6'G���%�o� � #*�*�h-a�� $2~F��7Ytea��(�)ic�%�ec�om'�ǎv�ih��6 de^�yo�W&�[rea��� v"Iz�(�)� a�� . X*/CBW=NL}0MGx�?q�JzeR�#.E�i��BHŐb-@�LJjzE�q�( ![!�6/"ċ]<�'")#B%��'Q�!F Bs)V#a< = F(r,t) {\text�� �}5))*�0bf{X}_l^m + G�@-�A@�N@H @b YX>P!5&-�$F$, $G�CH�'�3lex�C]4n��f,g��� ��r�� �i�*�L\�&a&}�!6� �>f�(/6�Bu�6�9!���%��zB& 1�q�_)�I}6�B�55�N.IֵO6K�Q��6"Vm�i)����^6nNy1�N0r�2%R��8%�!E��0����v�R�>� FN �>�} FA�GHV�,��]���BLMf&lp�6$F�)�֍�: H:��K<RN� ~ "�S�"� ��P��o%��J$y��C�u@ 2jrE&GIE|�EA�aTe2) F� ��B�*B13�3lR��J� r6�)n'��F8 -�Y1+.� /jEF!� �{2jEr^�/ � RmF+G H��B��}��lG�+ jEG��F]�[�AS*� se9r� {B:�g�p�$� [i2M$, y�vN=)6JL�� a$i0Ub} ��O�o%�65j1=64EM�F�0V�-�6y�J�+ O(1J�sE�ootuqB�(J'(q�\,Z+ �V2eEr"o&�_�U"�&Jk�.M�� j)y 5N!@y�I�|_{r=2M� BS6K�pr ��6m^J�-��t��i2����3N�{ !e��"DQi�7 6�V��he9�A2�FCM�Fex��rec~R6R��$�m-u.�l�j&\,{l�.�2��E'.�, �qB�� z:���Xocȋ �fi�O �yAoe�8�$5 $i@��1$K�(}���s�N �6��I�icl�,volved. More%P6�sm�l�:,!�n[���.mY*� geom<�3N)&j�a"�'Eor1q�s�-1��&�% fd.� ilerxc2ז�B*��]�]���]"�]N�1(U���]��]F�])� &�4!�2��1���12{"�iECe] �&A�<,boyerlindquist}V��e�Np.r G��"�va�Fta_1(r,wB2-��+�U6C B��\rho}-`u $$(e_r e_t) "U6KLB�L)Ve_t e_� �.�:D�.6���si& \W+ �� 6>B��M&���K2�B� � NlR���M!mrhN�NU.F�E+ L�CcosX]BL�JM��2y*�|eho�$!_rB WZ2y!`on��`޶`a�Vg+ ��t� s�  $�^��^~(r^�T L^2)�T(2Y+2jmL�`)�T(F_r(r)C C}�<��T , $mn�azimutha?yum numb&��i��h=>d=A�Bt$r��$ �eqAR ( &�`jE]x2r�`r^2(E^2-NcB*6&RlM jz6��b '' -Gp&{`��F_{i}1�+C2<`i��_!�>$^�me�6Qd>�d�S*&0hoidal"�")bdaI�#HaF$FY2�NF3^#Y4B�Zb�bB|I� i+I����hy�I�Fey=��a��a&�Y���z&�K �ZQX@ LD. F`Qj����:�#�:eP�:6ᅎhX�QV, (202;���"%�sN �0.`�ZE�6oX��)IeL^2� ��m��2�-J8=�XI� dewitt23}z&�$\Omega&^�L/(r_+x�,�<)e!a�velocity!��a&�1 . So~ re�1JH2GR�s5P(E�1 �Oef5a�`}{�[��&�&��6��M�2�E�Rd�(�Q�}F>��un&�� ��d�d&j��3!��eo�e}�a~aiWe���i�^b3>!�N ?f:>�@mZS2�9a]mM� ZJ #"Q._2'>~B\�.-\}���;!)�;v> ,JxB�%�E h�}�N@��;m� {�;*[��4{�4{�4{I�!��S!<��]%�V>?/�MKP�3{:3{6Z *]eK:V�ʿ[R3\\ !f�V�]e .U@!,i��Ey�0>F�J>�i�z�drbI>A�(� ��#<6�F� � ]�\B\>�'Up�f�� �!<�!�2��l>2^K:�<�svs6�})� ��"�{-�J��n�n�n�n>nұ>�$��>*�>a����>i�B��W`c� ���^��^��^�^��>�)L ��"8 B���sΉbn�bi2���qԆthorne9"��n],"p � wilczek20acta212!�2|un.7r"���&v | G6X_!.���}F� *X&r,�6�J�� -j)��)� 2L�m)��i8Aז�]F�2.�qJ�#V�d]A�6B?+2��{ �2�\6V :T) �E��A �"d�Z2� �"�A�ob��.�*x�1� kerr�"� ���)�]>�i?=R�bar{h�%��l F�W}l %V^�}) bf{n�6� $�^r�J�\{x,y,z\�\{L�uh U V I, Fvph sin8V \J��QN����2VB��}�U.� ��3{�}F�1Z[›Z�M�3�>�LO1h^2 U�c�VJR�_%m(i&v]j1L��*8Z�B�"��#���2&"U}$}(U�5��VV.;2" -F� e success��I �ed"n�Vll[> ��8�&Jd ,mu\J]u 2\muB��w\�C +��QdJ�me6�-��� RpR�,� F��,�#yix?J�:O"Z32U� -m:A�uѠB�!m',ϝ�3J�(2MQ��coXU�4ju(Ei�uU��# 24; U94>�� �1��(�8.e�sm^2�z�L^3 p^4��V!��>wa� "H�q aO"o�)�p*�z$/yu�rv 2\H�W~#do ���"�=�<�+pg�C� �"zv�m�ed�/ 5DVj�b Ij�(*Sm'r��x ^QF�(m�m 5�7EZ���zV�'Ϸ!��,N� tg�.z�!2Ee.��Qf&s~c+���g i��-H%�j�f!�QCQ�b�ap+ L�0�c +tw�$m'��m�C?"��aff,2��M:�_� N��� �isI�˖ceh�itra�dfor��)EE�he�.o sG�$M�aqe��)�6��t:2r}e�"�&Co�J�1}<\ %B�; show�1i"x,9-�%�-��:�s���$Fta`�����"}����:�) �(���&it0�f %�~ful- flex�h tool�-� !�a*���of!)ong.�@aK����y*;Gauge�*S- of GA�(GTG)�j� 'e��W,\�ied howF=�GTG6 be�D-{�ԭ�Ӆ�%�! ider�ge6�(I/-0)�/ 1/+6;/�? 21)��C �2N,Z�w)�A�.�&P(��JH��rAso(M���a�$��a�"�Q���~ � '2� . Re�y�(y agreH0We draw�2�leI��aA���f�j��n"X�!-B��one ori�A���by5 �  �}et��/$9�.y�&��/)tEv^n��ab�Ol!)��B2>B28-�2f�1c2an���1yet:��1t least,��Ale��1t��%M"�mpur��"2!orr�1��1~�1I.�1E�n�1�#& �k4r�1 � ��V>� ]*��oN��y�Im��1��zr"����v�a "K�*Ð�m~s ���be"֋�bRo��o|�ll�����q�����A�.��2uK�hVF. GBZ4w�+��2r�J��e�!2n��FU$e�-$J�Z$ (or+&ؾk�$e$�la[n]�q�� un`�2B�6ߌ �fi�� �.$n� ���~Lis 5"�R.�gson�7 �4 �|3�pg�� H k� 0�Czab��)\:�f:z2 ;� 2HA�7 t8&�6,r�m$��/u��N�i�g%�a[grI5.i��o!�8�~Q+ma��&�� 2FCF�Ax)_�ѥ�� it�D9ytunnell��t�t"�29�barri���um ��&���box"�Eb>���Q�0 leak�&� boxA:is.�A�i"e �&���AcIv&e�4fy�2����)�J�c�Ń%22W2��� he b��&z 9 �> �it']*3canMp|��y�yH superlu�l"3&�Ng "� mea���9��-6�itself�i�u7��iT�:��"� 2��q�t.'��Jppok��ide1ԁ< locality)a�� �net��Ayf��y.�{E<. . A.��B� �i� sour��9�in"� �e�!�s �dn�v��nz�j�{[���@�6wv])V is d����ҵv. P��ci;�J��hQ��escap>�-����Y4��4fA�i7�!�Y�!we)V`[�eso�_)� circum�s6��psi�breakd�of �&M�nxpens�T����J-z�+x��"$z�pa#�0nUm i*{;QM�M��� S4��d�� �s �inI��*\O�e�����|*=< :yj��3+a W>� IǁYt��Z� �ha�E�C�=!ei �OA�j�, hbY9s�=e�2 m�&]ere��.d��inL����=!�end`zof.,Q�ionI�2icult�x��Eais����gE�M�P��1�!zno �wq�e ignor���A� fu*>top�or�ear��th- 1frame ���wr�!k"5��ork?�<��(Q�2de w�!� c���TG 7say ab��=�!�wp asB�~e �.�|�ton{"BPA} Ass��g)\�0�&�sR )LV ��Yu����$cs�L�W�Jø$y$J_3$ ��ators *�0dp4>�0�af"t* �*�^N -��=x� = l &q2E� &ge�D\ J_3%= (m+^2Q)(2M -1-l� ml�6e�?�^st- 4 rDJ *ps�(0F and,-C.�C veni�@ fact�W��  BV04n(kN) PNl 33!Rhi &$�B#�AKa&��Legendre�C$ynomials $dm(xdren+)"�(�N}{2^l l!�R(-x^2)^{m/2}�(d^{l+m}}{dx  (x^2:lFR� �E�\#l��recur� r���"N ( � �6Sd�}>x�nmx = - I^{1�{m+1}(x)F�} �}�-6�6�(l+m)vP+M{m- �B�� l0����+�{c��� psi$�q duceN� J����= [&��*6+�tM�.�Zphi "IF�T3]�@?"�V.U�n+K� J�faderiv��s��D�_l^l$E�J��>&/l} ^ M�cr&�ZfN>~�_�G�M=�3J�A�l6D-�}�J#]t (l-1)B��f�2lP_l^{�@l-1}(\cos \theta) e^{(l-1)\phi I \sigma_3} , \end{array} \right.fXequation} Since \begin \{k} =l2�2, jV`we get after some manipulv� the following spherical monogenics :N�Xpsi_l^m = [(l + m + 1)P6)- {m+>B55�]e^{m  3}J�� l$. In order to%M$generalise%@J6 func!�Hs suitably, we needibBharmo%w by includ!�,dependence o)�pthird Euler angle $\chi$. We ECBconsiderD!�dquantum treatment of rotat"xbodies, which has an obvious reQ3oK�dNs�express1space ax!� ngular mo�Pum operators in terms��usual.�s $i� $, $A2�V�% {i��{lcl} j\hat{L}^s_x/ \hbar & = & -\sinI�$\partial_{ n} -\cot� � a�)Hphi} + \mbox{cosec}r0chi}, \\.�y6�Rh��} 6�sJ�n�N0N�z:�9^.�p)_ �|0The corresponE� form%�:(FQb_2:��W:8 �ZLN��-A0Y�N(N�3:�9�. ~�se}�satisfy%�commu�\on�?sJ�[}�, y] = jm�z; \, 8b_18b_28->9b_3F9s_qb_190,_i�etc.}BWs�at��ndI���)eI�4each other, bu:ir #��amongs4mselves differ� signɋ@geometric algebra�ZXa coordinate-free trans��of��}g�饘of� ac�k�2on�+ will�= described�|a'`or $R$ ($R\tilde{R}=1$). �effa�of$$on any muldc;M��J2,M \mapsto RMYQ�>�nfigur�����y�^b�giv��� dire��-I���� e_k$!�2�M!� kV�e_k = R� k j�|Let us imagine a molecule as our6��can s7p a wave��Asi(R)$!~ this2=/�. Not�at, un �U -Au�.�F vj >�$R$I�`%0'a����A=bt� qO�he98 .<A��C eforR, "� B \equiv -!0textstyle 1}{2}�c58�R 1:�y]It�0easily verifi� hatN�F���s_A�� s_B]� ( �1!�j� $)^2 \left(5�AR \dot{1�}�� #R}N�-'�KAnK� )� r�(��U� B5l6�"A".d-=(�-%'M�e%D(BA-AB)J= -)a�f_{A��mes B�� ��M�s� ��� reflectiMfa� �5,we have chosy workiWU�* raA� tha�W �R(. r `��}�s� fixed��h��,ng frame, so�seB��RB����a�re � ula, ��definn�b�RBN�B�Th!Z~���!:�b��J�e�R}aY�y!~�AMJKΨR�6��}�= 0-�V# A simi calcu� yieldN��4b�4%�B* 2�B� as�$ected. Wee$ now ready� (resume seeka*AA �R�&��unnorm 0V<&�_�@Y eKa�6d writtenJ�0Y_l^{mk}(\mu, ,� ) \propto� )\exp I(m( + k+B'/Z4hY d associa�Legendr�)$�veigen� "�i�a&R b4n_3^s  = m &� *k^b = k B*({\lambda}^s�9pl(�m&L 8Clifford versio52_an�6�)~arrowa�f+ display � j}}{6*F "��� y퍡jb�� �RN�J�^� !�j���>r����ie ary�6I� solu� standard� >**�D \cite{abramowitz}J�2i�J�(-1)^mB�X^m} (1-\mu)^{|\alpha|/2+betP_n^{( $,)�6b + = |m-k|rL+ n = lAfz/2 $/2$%$Nv� �M@Jacobi polynomialNNC(xr*nF*n n!} 2 2(1-x)^{ � }(1+�}VBdFq dx^n� eft\{6R+n%�U\e)\F��%a�ed value�5$l!�mk%NJWl�, � , 13a , \ldots "$-la� m,klJU&Z� M2�%. n$ must)N��&half-�ralF9states@ appear�}l�;EIsimples� J Y^{iU% �>en���(� /2) �3(I(�2+�//2)R���8� tant{ aase iN���(-�6�n!m�+%N+n)!(2n+I� 1)F�M�"}(4)! A�)a Es)^{1/2Fx� a��o�%lad &p �U.�n� �xL!apm�-�v$\pm \sqrt{�',-m(m \mp 1)} ,H-1 \, k} \nonumberf6Y��ZYk(k:YW-1"����ov�l� �s.$m$��k$y firstiof2� "M*� $^+\PhEY $"� �heJ $�J!Gl6x6ak+3^!� L b$,l� �J $(l+})�)U�dKk$, ? ively.�sD �$j� +M�eQ$m�;�� fio +-6+�wards. < lk�m� aVg,d,develop thos�(r $m < l$ ue��1(-$U�ɭ�f5�JO2�"j N�-Y� k} -&�2 (l-m +M�V��+$I�aq���k����is"�(n� $I\s�H 3�݁�b}$�E�6uR��t�sa� le m�s^�.�total �#ofMv%�a) Mt:� 0-2I3R^-��2(.�kU12B}Cq'B�% ����^ >�M�-1>��6�:is stl���I!�$0$ doublet!�=. ��>���&0 R�)�^{-1/J��n�-��]� +.v<�; From%~�we@�2]�$^{�A���_� ?"f����^���J}^s$J�!�lB� . Fo&�se %�0$,pr�� a��mio.� u�-}1�m_{l+1��pm " r \,��m_l5�3>�betwe�he {\itՓed}=@9���i*g#*k Fe$(k%]z) =��� boi an handle�� blemk volv� _ magnetic �#�i%e stro &@in-orbit coupling �c.�wisdom�_ad�!$$\mathbf{L�� S%^ J! hould�n$ used���� to�Y%rb�4]�v �E�� ű>�$( �p}}-eA})^2& "� j�r�� good"b%�M%e�|to���!& qAd �<mk}I��&�%�=� nopo!A�&� �^�^+ W -$ b�P#r}�^+ = ]w\� +1�( ( +k}+ -k})u5�l�.� =. +6?->?�? ?i��  \&m)B andJ� 6��-2��� �.�-��N��ihKE�"� n$^2-k^2)\pm �}"kappa ( ��+)�%�  C�� is necessw�%a<n<(�employ�! ecau�t�9be�" icul�%avoidV lapp��-S!sasDymbols. However, i�4 always clear �)�con� w� 8is meant. \s�!{Ap>)ix B}��ru�eH&�)&�esca�N$j}�m���A��e?��2aF{4\pi}  !}!�m)!}}:V+ e^{j�F�%�k-m�c0 (��st}� D�ar�*�6�qb b�Nn��LUt-I x} 3){\sf xas,}%\boldB $\nabla$��'�Q>t��%N0B�$ 2t $ de�+e Gibbs1 prodA-� o�! STA��&or+ŷ*2 �ed5kj+X}G- ,�*Y:f��EC2!3-L3>?Jose `ised'>zS-r�e�J�4)QN�� ���r} �r>*-�s6�22E� G+f�(Za)N�-J �'�����zB& 1�� �y�u.!�%��oA�iB �&  fullbeing����)=b6�2im�(�(�e)|CG �)�(longit /al)J�'.� cknowledmZ,}% author waa�(ry grateful� 0Prof. S. F. G!�"�'e��cinu�� encourage^ . Valuabl�� scus��� W0A. N. LasenbyLXDr. C. J. L. Doran were� ly a�g !� � also2 "�"support��4Cavendish LaboY/ }(Cambridge O%|$as Trust. !B(bibliograph{plain} 2 {pustaka}3} docu!�}J4% update 29.11.2004 Franco %\input{tcilatex}C?class{u/cle} %����0 \usepackage{%� icx}2amsaXD�0Cb2ded=Fri Nov 08 16:34:02 200.[LastRev��8=Thursday, Dece�02,2$4 18:12:43f.�GA�ics�� 32">Z2DM�Shell3Ge�!\Blank &2G4CSTFile=LaTeX M� (bI.cst} N�} Q�!�title{M�,.� mode emi�V?�3cavity e.0 B lasers } \�${Eu�5Do Rold\'{a}n, Germ �xde��c rcel�;,%EndAName De� aa�H d'\`{O}ptica, UnivA$tat E0\`{e}ncia,\\ �ڀMoliner 50, 46100--Burjassot, Spa�2H � P�-� �k6�% � 0ider both homv8 eous�n�)6$broadened �ifmmedia�&well a� limi�f smand largeqClosses ( -it{i.e.};fPs��iout�!H unia f�' l� roxiAnon). In E��'r!�d% up!� ext-�2� obsero.[�elf-� lock!c0in erbium--do�fi)� carr�-ou{rI year+a :fe *�`Risken-Nummedal--Graham-Hi:bility�Y&o@INTRODUCTION:\new�� WHY SHOULD WE CARE ABOUT LASER INSTABILITIES?} \label{int $;� v� m�@ -- Maiman's ruby�- 1961� ed!jremely u�l�],A4e�nc�Y1 !�< original public, �$mz}. So�9re�,F,earchers beg�,o�rT skill�howAa9die� � s deed� app�s�1nethelj9)6E" b� aroua�ver sp< exanuisab: lurkAa4to haunt techn<ly-minpeopl��>��teresI:(nontrivial L ; phen�9on��mo%)d�n al-princi�" h set. A�< all, �I�nonAYar dyname@feedback systems,: inI<�" such0. �0(certainly w�!n6 g��an3�"�of �:h$-- if only� inim+t purp�X they)E]+ucj� y in spitz!6%� incr{1ng deman�!%�E5�4 powB$speed, tunm�, �6 �6 6, typ!E ly o�3r sk >d&.light ��!KsubjeKo reson/6 bAg)c�9a�s�4���k9� ly c[��amp.�um. T�!0! $is highly U�L#i� ��e� ��circum!�c =the�� ma!�aK�_��erAG�,u>ne� gamu� smo���s >��=�Qto irre�+��unpredic + chao�h$io8ToM��!�add"h=plethoraA�possi���=!� can G a�Ddia��6 ���in!�ch ei�Q &�� i�+d, or j�&o�w�g0sf{TEM}$_{00}V!4Next-neighbor .p[� %x��nearl`:EEfrequenc9�c��e{� bea!� -, am�� (verton!�.occur���rast, B�!S!<��2i%wF8 [to�AeV?wealthB��2����pulE��Pa.:�e�,B�!,!�played ��A��Ɖ1�1�B�� j3lexity�A� situ� ot hel�bYe &�3nth� lp9pA� !� iresQe�[8�of �:r9��? >.sEra -�y`-i� ent e�ziQ;e:B2C, quite-Cre�� < devo�  -:��s (see  {WeissVi!�(ca,Arecchi,� }%�re�F�p�!Z�J�� s��ea*�es�{$volume). M�N"p , h>��to��gb$]�r:�a�����E<0decades. OverR Bd�e3bf&$und, e.g.,��" V(JOSA-FI85,  8,Boyd86!%HHar,NarAbr88,NA88,K�#dn,Mandel97,Tartwijk98}. HEwe sh� W �-B�pre�7 a�ext, i��B imV�*.&who � �J�^ !as �!u^-�la�'pro��E�B/��4though a conne6�BledE2E�6� ��be � blished )�(Lugiato85b}�]oa@"� �ce�A� u um exhib�Aa:� oAZ^� )�Ie2M:R7Q })�tE�n�� �  1975 A75}����Max#-Bloch%�le�>�&f)i+aa/,s isomorphicaR!Lorenz'l!E�%�7 ly`� cl'c=�!1 K63}�uis�  �D s�sV.-�� v 0 threshold, \A��� ha4er��c vM/��pump 6 ="f a � -typ �Csegn. On� s� ��%� �e[t st n�> s� e�|) �>O,(��)B��� �>� oscilJ7��MWM�6�QW�cM2,5��)$is \lq\lq ��or--of--�\rq\rq��,�.3�6GɃper  ter � f�0M�KlischeM�� far-infr�/��0"#damK���m�!�ed hardu�Q�0��k X Ind�H� di1E�tic b� $ior remark�HO%�8in 8 sdAM�e��YMEm)���Br� }. Unfor� t�A l�, s�urU��� atoms�m� m��a�n a two- Ca\lev� emc��A�md��� focu�TK�=r�;sy dur � z ����b�K$ ree"A�18VACRVPHT,RVVCMG&a ?��pthY� &D ). H���rabs� �B�� roof�� al!"� �re�icIr)�� i" ,� Eqr ca6u�co�J3at%*�E1MdL�4�v <'irz&uc%� does��� it"�-Ej�" �a6Bpr�9 �'l�Dn�� �A2�' �"�Kreceived� mar"x �u) poidKe���iO TAsilleE�u_�&.�Kat most Ks��� B�s,/%�duea��t�hole burE�i�2� �"vebE��MM�PNew83,Siegman,Svelto}���a�mo lieFat �rI)qe��Ek�B� ��7,%j�way�)!I t�I�B�"ng�spaR i5� in)�edium,'\12H3e�in�ar&C 96je.� �o}of s�$e��9in�5G vail�to�E��#at 2 /$.80uhMwinner-W1s-A�.\sus�Q favor�(mild mutual&�Euhe � �� \gy bal�z\footx#{A@)deaB *�E exp"�/Ba��d!�in "�Ocorrec4 �F��lt$ u�4in Fabry--Pero�&\ia,�r�E�a�= _ Hn Tang--Statz--de MY!VlhTSM}.�O��?�7� e< a>6to ."� Otsuka99� $00,Hill02}��LAE,rein. TaUs��+l�&r&�a�tE,A�beyon" e scop�O���cux.\ �� myth�esh��w8w��it 68�c.�~n&�of .K���h"Gn detail�`(RN68,GH68} �!� 7(b)�  x [at�F� uni"�!al��file%�a per�Jly.� � ,, Rabi splitEm�� -��a�u� A� !A � m���olF��-ian!�� � @�����, safeguard a�I:&� . WhAa�U��� 2Jna�E some�awk�6 monikEfairnes� c�:to�BlL my3sX0 \emph{>P2OI�}RNGHI!8 short. Ikeda \� �Tl.}aIM@� p�nt %�.aWyign�K =MXs 89} �� IyJly,AY1976 � 8 76}E�ed��Ae]E�ZElɺ�*Yto�.i j &#Eu�Ct�#ngAv analogy ad�u} �  "4$y<iM75te %c6 ���&y2�� x l�) uarame�  M C)4�Gas� �1s �velocA�mrtrave�--w�,�@� is wA0be�e�furedA�! �_u� 1990��N!=�% ��901��� detu��)�"x �B%com@6���(baroclinic F�F�&r82%�](alg ��&oL at�!_�#. stig�Den, spe��a�Y cernsE{���I�����, �� a2s!\c�[�n � �:���oF " � � .� umŘas�FdA C �A�!k aqIA� %z#)AIca.�&�g!���&q!��a|��ű-}�P._�amili�. irstz�_,Z on�8cI�o& (e6�>� came1  Y2� ����&�(s=``>#''a�n �=� 96��.��--e�� ). A�9� 9�v �QLengthV� |=�U0C �un"�Q4 E12�4 bulk ss�9�"�N5 Dt th�&g a�!2� demon�#E�ofe�oppositeA&� !0I�abeЅ�!�:��&� Se!;�� nd E� )*c  e{GV*��&C aȭ� ��I[#�* (%� a�6!�>s�jLMilovsky70,Halford73�6,Ohno76  8,Gerber7! ,)-F95,P97e�ey�Z�pa2---t2. fibrA�� (EDFL) �ctak/!-f&!�!,meUd: rain� puls/mep�0�z �O7!, �l, trip<1^0eY~!�4%`���ly�in � ffici�$J er�"�Hun�lyK � � l= sX7o&E)fulfilRj!�ta�i� e�Ps�&�* o!� bas�)!�p*o�K�hyp %�/!m�RE�es A�͜b�)f = i�I9 W97}A�� atib�..P�Wlts�B{y u�mcLar� ex�$�� �&�,"�^1AP�"-e�"�!���. Moreo�?l  g�>�4�5�y:*�aDž��eau-�"Aa�b &�B�)Baw�&stark!9N ��xe!�-�%�t�" ="e9sV�"F� �s�*� showASYis,�3 !�n�Aily a&0!�to�-worl� �& �.6 an97y"e m5 a! �#.%�B $!��2�.�,ncorp�:A�t�jQ %� ���_��3a�source�& turnq5e�!&� 9c�l�.�7͚�m�!�)�Y����NawHt��F3to �7<Rt( E~3 �3, too, $#� E��e--G D(Desurvire},.� !w:1`h�im �y&�N@2heGioa��}M� e��&�M��G!K 1unity)�"su]�corrob%�d (�2xp��d;�l�)ur-%�s)��IqP99%Put� pA)e���c�{%L,F{%!s�a J( ($1+Bd$)�%�ereby� e!�a,m�4EC����8�a(is gon��ns[ besto�f|' vigor �on�=!6lea%2d����7*��[as 9Rb>scig elow�/��f&& +�`ew�fu"�)�$��� orya��Mn_,�Lhl.R6=/Br*Y6 ()�aCF ineditK�_, �,R�+�� �in �V&� litera� 4Z historKk o�C�h>)�p� e� Fs. Sec�q ref{�}!�6�%!I!�!ge0 &��E<' � ]��!�ii"��I�/ issu�#� �2! ��w�i�0�!�I, b$a���3�8 (>Zufl}) AzU .�8 2of$id�� �"�[G%x�*on B]n^% xiU#}�co� �F� D� 7br, �p in2� :�� � %h % �! N@�,�� :.��fE. axqlO'e>J ur@a�on6� 2� . "Hin �I4Slus�c "V2_SEw.*�9�@MULTILONGITUDINAL MODE EMISSION IN HOMOGENEOUSLY BROADENED RING L�9S: THEE� I"�9Y�>label{aB�I�.{B@e &yD;e�}Xin�%rQ�.8���-�)*e{-2lev7"WBn1" �,�&]�!i D �ׅD--e?8!�os2 i3lev4mHa&KA�Ft3o u� �Ik%{e<��;�]= ۉ�.�)^�nA�ubMTTwo1�a,Y[ 7%�!����oll ?![�Pcal{NvOP A�!� �� hy�t�3,��*�6($% \omega _wPrm{a}�Y�ac�  )�6polarA., l-,>�$e�kMf��2MB}c}}$, �iF�")& s M_aSL"d1e1Y!eoEg!"3W % {?B�3/5a,� 03b�Fe*ynarmy \p�'$al _{z}F+v9]m}}�U}"t}F &=&�Ja`PJk % \a>b=�m}}"F\,, ��eqF1}�A2UPU gamm@bot }�PH[ FD-(1+i\delta )P\�] \,, TPJTD6TVerU 1-D-�Re k(( F^{\ast } e)�Pm.�DB�]%J5$F$, $P6RD$%�Hge�O�ari^�;(-� 6�,A,umQ�e�po"�z�er�� 'EQ= } F=)�2E}�K>d5s)@}}\,,\qquad P=-2i @X\rho _{12}}{d_{0}}\sqrt�OE%�}  _{FV D �dJ=[ FPD}>V�  ex!.��s $E$w ayda&Rh� #� uB�x�D slow�oarMenv^e��@ "&�%��$dSR���`.40 �(2c � (1)6a; $:hMf!� r�(�8y�&�>x :Q�R�,�-�i�_!:i�=(B  a}}-Bc}})/ �A E5 &A�==!i!��, $2�% }=c/n2�VlP!�'� h0 �EreFO� index $:P�J�hanM e�/ss coe"b��[,cx${sN_�;_nt)G tributed �%�1e�� ���v�̉ $e����2 libr!�v�6to�*K@chE��au- �2A�an� i1..`U#��T!� �is �aC 3D��p-3c+ j3 $a͡8or�&$�_ R�2�)) �[meI asF)a��PT \mu ^{2}N�}{cUs I���E�}�Nc� ~.�a>�%&OSu�)!Jdi�XMZ2(!:I K=i!$. Equ�#s (� �k)-- D1})�%be �N�e~��3F�Bi'6�. D(�#� �2 3.7$� f� $L>��(�i�A�0%�It� } . DT.by $z=0�z=>\�B�� exit kw5TY�M��6� obey�1&� g'FZF(0,t)=U R}F(6�,t-\D�t)�P��xU{\�JRu�|&} v"�Tii�*�-&� =acc 3E9r Y2local ��}���)%�!G2� ( plic�fi)Os,$� 3�2�N�~). x.� c}}-6�$)/2]$.}, $Q�=~1��aթ���2�6�)1�s�G!Fl�����unl�Ld -h�X�JH&   �e*i..%3��cedO;to�1%p� !� �>chron�07st� �'�!�:ew"�6��te=A al v"' ��&� *� ��} Z�� z}{L2U��� T=t�iJ&��\,.:� % �4�i*�buu��to ide<*be� 6.7 its B� coincid�A > delaA� �$��u4x�)� t&K!�paȆa�*gNB|!�remov�.1���s"�uV�T:�1,TJ�% �5AB�becom*� "��)(*T}-�i�km�FSRZ \pi "� _{Z})��^ X AP-h F #@:�TڇBG�z6z"�[-*&< >� %=%c/%-��L}_ rm{c�?�'`:e�;�&,F)K me c}{2RB^I |\ln.���|+ ��Om}}6�1�,"m%�F> ! ��width� A$ �"& c}}=��:x% }}+ c}} z��|o�)� ,)]��FMA-Ga6�}{n6]� �%" f50Ab,ad�S?�?� b%�*w�7F�e2 �)�B�%p*a�n�n�}9�jiF�$0\leq � 1$�:`/.����46K<�Usnb>�.>e.h3� e(�>m}}=0$)A�chi =Fh�6q�s $A=A2�/RF� �?4t�l7=�K *L9::U�is�<q".�o�L$DA I�Y> Ea quant�or�<$2S })$��"�5�/ �A��p3ib�m�%�s2�B"6!ps�$.BJ�tau =N� B�\;TC \zet��h}!���I}}\;Z�����N� ilde;^j��F���a^)`F�c}i��q�c�2�BL ? �\��B$ �� "N5 . If�E�g&� 2�2Ly � N� sigm5}͒v��-&� �1�� �/)T�A o�%:F �b�r�1"����*�E�}+.Ey� ��� ft( R�*u3}:� eP*%�� �vZU. Prq &q% sYz eqD35l-8%&o#� f | 9fm���:� %Z&*m}} '.�bou� Rf�!�2R=Ife�G�.���Setam�fm[{� �0�� B�/ spac�9w $� $ -t� �"� us�b!�VBHUS "E�seta} 2Q�Ba}�s=R�Ft F�QPJD0/ �"@ RD��G9$&� ,�Atin �L���� �dqbe�$��,�XsyFX;;�s0��!?x%c� �O0�O�9st��/q�.%V. AP�9�)"�Fs (esse�Rly�6;��~QS�� r�3�ver�]]a],m 'dx� �DB>V2#!�&(F"�B4&G2 inflA4�<V1"UKc�o)o,X3�)όc_3��%�A�;mea�mBE+�SA �^�/=Va�:!*k $A�!k!��$.�]�)"�scrip2 �reJ�� s (I���. �M�C )M���< �s) �*�%2"�2x3}(zU$�Fledge,;S�F!� book� }, ���;ide\DByz�S�: &`"q iT"Os {:e?6d�N'�!$�p�Aa � },!HJ�A�I�- K�%*�)9~�;H%1 \X*t �9lam�i !V!�F�in F�#�!,�Va%�n9cmx'd Nd:YAG-�� �� a}e5ɀ!� ) }& !��-&CD]?���1�<MtA��E�Xtheir B�6F3e0y��ct"fi)�XQy"#%�v#%!?ST�>ou�9s9�Ywe �*y%y"I�!1e�i��.(are--earth a.�2ys.!�:�gtb%BV[ly)Z� �rU.$�o�<u"�%ų i�� dopaGare�_�m '. or Neodym� <)�De .�s.&� 3}--D3}),.=z%��rli�5�1�a�.� �.(�3.u&��r�of ��"$�4Ao$W& op��lu*��-s�p � � �jRP99"�#a}. Pr�=�Cw fin�� 2u ��B� W� >�*" 2& B wEI&� 2&|� *L5� ��Me�:������h� 91 �31 [for�1�En5a+^I9A�%F1>�=2}(1+W2X gparF� �^"&  %�1�-�!(_{N,3}}{W+1� "� d0FV1��! 9"� KroeneckeCz!M`N#�wA�a�ReveotT�:$ 7 �=1$!l1B+i=. ���fBj�/f&�7wA u/  lybd��a�P!% t from Eq�+�)If�[y�e^a�$� q(�H:��2sti�"�-Fabsor�[ cross�+(n֑F�2F� ��N}]'`B�e�#>�a}% }+�q� e}}+J-})Ev&�FA?H��B@e�F���_%�*" >� N".�"�FR " "�#v�]*�N&"�6Rv>�e2�!)"*�&a&(m� % Un!��&�h,E�!>in�H�%(��c!0��&� r ,�A��AlY�d0;.��y:Mͼ�� $W$6 z'iUQ&0wayF5A=G\;���AJ/� BG��G�(rl]�.e5�% "  L&m N}N�6�.�G>g N�Y�gat�� ||}$"vn��vz�e�h�$ ing r��Gs,�4� H!�5�0 �iN%�R` ��.RŜ)��i,]be �T ]�w2� zGA?A";"q �{� % �$:� ��5i,]utJ�: NG repl�$A� ui/A� �$A1�aLG.�&(*U! J 1+W�� f�Fq�8�yB/�"*lB, |*"!�du8��dq#%�)� e ax�*�0�C�C%��vW��Ce! ���<E?�=r�[ t fe�'eP�,!;� �&?"*2 E[�yA$Mi�>7�B )strZL �J�I��-�/ fash���b�gZn �*��.�9�9iQ�isc�F W, let u�%��y;"i:� n�� ship"�'�A]��fa�ia� $G\gg 1 $� 5+\ _2F�9 Nru!� $A$ �;�V�� '��% )�U�5�3�1�1-Opb}rAo=I�_ �� $\( 1":/)$:%D$W.��I :.%&�$b[a3G� na^�9� �&@p eas�; see:0I6�F0� G+A}{G-A" B� !CthC 2go!U��r)VFd-"��&& insWū@ ) "3L� G+9�9}/% E G+1 1 7ar��1 "16}{G*.E23L>��� 4�b�'�q$G$. Cqna�>��O 6�f.� m�%�*J%с�&�E�s���>_basF& *&��9459>71%4")59-572%56�*J%c[�d_5*I�*�h�A�]/&?e.� -igKrgiM EN>, �UExo���%{ �7 J�5�\*:�6 So fUsh$6$@*/+-56� . &9DBu �mp�%a.hr9_iqa�Km� al s�Z�f*� � I�l�%e)P���b�5�la�)��&�bm�vL\g���R�m��W�捈2eTo"�?�Rel��G A%�� ��n sice&�&� "�&�q&�'>N4, ��*3 re "N)��-,��Q� suchs(����q���s*� NcJ .0 ��$W�.a�5o�y~t~�d��:sA%NsizB� c�4A3�J+ �j�V�'�i eaGa "!9tav>[F��;52.65 P65rho�,2h f�" T6CD=dJ� J  doA`-7!���2ng�$M��HeoW�R�sg.*p _��&8?��,� GNy(&�f}��F�pVTJ�W(1-D)6ON8 8*���>�d��-H�i7�K\M$HwDB�8Fw$s%2;�6"< �B'�F7 da v :/�,Nowmzr�Bqw�K�sa�Mbe���h>�8aUA�� �&� �Ag�a�Y�Υ�� a Ga}NramU$1/e$�=�]q�%to $w^ .} kOi�gT��2"cF6� 2l-}M�lB�+01�R���/OFW>$r$)oug*� =# $�; =r/�a� �����e��ct&�<a term.��=on)�%WhF��;iW�� �9nabla5F+iӊ�# � ) F=M�� J>XN;|=\��L+/%/+({1}/�:})"H- :+&�*]�[M� Laa-A�!z,"_{0�]-� Rayl�j&�*A bA�\�it{�EJA)�-� ��.d#��Z�aES�X�7pp�Ll . A 61itsc�F���F:Bm:yhF �N ho ,E 5$AIg w3$ )}&2E[ M<5�(w!�.+i C#6! Az&$!y,}% -i\arctan n(p #2+��.�=:� ���2 {�( )=1+ �/Sv)�6\so���� mpty�,y�B� �bU%lY�_�F%v�F'�GFs $F(%f,� �%=S. )f � #Śf�6�A�erWU�� psi JI \int!R,^{\infty }\!d�\, |@�A|)|!�� 1}{4�6� }% v�( 9#i��Wwe%*proSeS�C.adE�$F$vJ5 Q&tude $f'.,5�g�pby !� ^>@ ��:g�[Z:~��$ 0h $-N6�(�j�) f>j 4G�}e�A%|!z}\,�  f\uA52>��@weS�6��d1� \ll I�A$9�"D�8VnEHa� $af)W"�neg�C�#��ArI�)=��(��W�T�T "��A/A&DT*n(f.maximum Y %�� ^{1/��+2�&w"�pk I*� y"�$��=(��/.7��0�0Aq,� �roB#=�2X89E�,e�'r�Tn �,% W5D��� (-2�U ڜ*�F �e&UJ!�F�F�aL��� J u=2bB&f E suit8Ca:d��.��VCa*�� :Q_>� �yM�d,X[�i�G��u&��1 \! du2�3rmiVuU� \, Pn�hi F i.i+ tra-� BfF:1EVS,j�( M.�Eu}.A �*A �Q�;BmEVR k.�NS ��a��,u��&��=�k2� ) �!\qEF$a6/� �0F��{c�i�u�]s a#�#l� %B#�Aa#X$6n =2(r2�2 �2�!6#$M-gu"|��.�<~'����! Y6P%mD�9s� 66^e& �?F� pj7K>�,sW���2 �ub�  eqF32 A3}XS;^���l�)�-ir l��J ( 1)"# H'ich�p�xby�y#>& *} F�`Ep� �"=F�Ks�!( ("e^{-i\K �&�PnZPZZ Y Y >YDFY 7 =DBX � "B3*t�*GMh$va�/q%99��.��1� -iB< }{1+ ^2�\�� .S�" �.��\\ .�j^��l*�A �5D?\e��% -�)�O.�$2�*�"�n�" 9K��%<��d}F_s@5rm{d})�}"g �A.�-�0 F_&�7s� +M�2z:N *} UaPe��M�omp�i�2�=I]e� e^{i�2�� *�ra��Z" �#� 7.� ǯv#ts,&vob<N/:<.�JEAA"12)I BA:1QU2+2H)_mC .E�2dFdz}A� Q9�)s^�IW\�iC A6P.�2� fidz> �#%{F�JQ.\(0)&=&E R}^2.)>E��mQu�)bouI}\\ !(�NZ>L�- ��4 nZ!& n\;"� � ger}\,.}ph&�;m� E�of*�%�)ѶFSI1Q&��Qz>E�F%:5 }{ I2( X0L}�A}{e�}]AM��[%^�:w ]] } D$[zB�== 7 � (1^2��/mi%�.�% ecIsU��} P"�2izi�Cis�'��=2� � $%8�Q�'*�%\"eW96�M�$E�),�V]&'�A_� �! 7z?6�/i}X �&{cIm}2j)KI)2�)z) )y�U % -1�H^2,I�1-�Z)A3�jEOT �* R}% �E = !E�I|H9 (Ap}{A 7AW1-�~ VTexp��+� .%@��B�} I�mnz~�i�W�"l�6�$�#2b}�3�M|�% A $� * $I_sB�)}?�Fu�/"� � of n2 @�?�N$!k) a�"0$)��U< ) re�y0!B��� ischizero�j)�^0% }��)�%�YR�I� [ A-J�$]F �)�2]�ץ�(!  =0F� � "�'�U�a-�s7j ��t4`. To d�x��xstQZX�XL}�1k(phi_s$  xVq$% �wb sert=��Z��&N ��)�trxebe &+B�ad �}{,}=\� �gma)l!F�M }{2I_sm�dI_s% AJA?*I�i�vd � ae+- J�(�av(t(wa�aB��pA��;S&�%&�M2 J%ѫ �*Z G�E >�iI�% u�)}{ 0)N! tot�Dh�%shiftY']d~AJ �a "jh.�%� 2�2B4 =XhN�": m}"� %6 5[�6��)2Am}Vh* �0/ )�E�[� �>�� :`93w�`���v�>) O %}"/*� = �� ���� }eN�Q�boV /� �j $n$-�N:�kf�e�%8!�FO�n��C1[0�w+)f1)H�Ci�J 4 � :YD� { ^�(:f]�O�"#- ����g�� _n^2$. Re�x)z�\ �2�y&�V_&�xreJ�V�V�FC�!�<[��%m' C�3RQWI��� HI�<�-}/2�*�%�r:�[*q��J�qEab', )F�te]��1�6�". H��&8`9��X"]s+�A�(5%�$n�Y rd(1��u)(i� choi5?�P|l����0odFd^_0M�I� �F�&�K)ɕ�!�m_A:c�8.%a; i;v�% �� ��FHVFd2zA@E�^ne"}[�c�^0$ :5+!�well-L?�|oaT�" 7.�-8���!= R�/!�l]=-- � ����@�t"�A% rvˆ�2on��I[Pala��  =0%\a�i3!{�YJZa>�Wa&R wide��dopZ+�!&�$�#s�? �N$sM� so�pY=U0� F�bL�� (UFLa�`is ba:4s$*�^ �XyyC e!!.:lT�?/acL}!0Q �$eF�"�WMV@�C word�Jo*va�;�� B:�bW_�iodicJ1,yiF>�K mirr?�A2f6u�F:q�Atic pk�_<vKt�r�_sf>h�4ifÞ�]*,"k+it �*i/�0:D*�F�ric-!er&��FourierŬs���{(i��n�)}"�.�"�T]{�4 �w�b�a��&� �2-ɬvr���-*� "� a:r_)��AX�+ly �2g j�� nume�j)��!��benef� � UFLw=�Amor�l��t9�UWm�-ofU] "� 6g-��.�.E�E"��se�"��9s= C&�5r'em $to���i�w 9Ô���9��X�asA%!�f�ur*5�4u��j�/ �� 5io$p6"!gperc{%k�Ys�^�q��K4&O��NSl*s4,j, A���s�Umplex&�u s --RR1�[V8%��/ �0]JPf�  /�*� p�h--��} �!(�s`J�y��8s8"�s-�ic �W`.�Q*deValca�03aMj|.e!B� t ��z^/W���`UFL. I_IHis�� ��GardB v X6a}i) new g�_dvantagvg��]�cl��&@��!S oHv�fir�0�\D�!!!-!; 2�itꔩqvity Y,be�fD�ak#ay�6� -pass�2: IH0'�y �%Š]wt-Q)>��%�L �exact�bT�nd�? of�)2�Rw�I�^r�EI���JjpF�2�!R�,"��>Bi�;!Sm��FA1]�lyQ�ed>"}2&��BFu`^� a�1$e��2��})!�L $n ^���es�w Isal�<UFLBjw�C���atiRWJa���k� P0 thus�|%�:Ne5=!�!}"=�/I�{ "�'ȥA-n ��ai?����)�U:j�m9E6�)BQp, he�GF�A�:�� >z %��..�B�) ���A��E"?Z�XF�nMe_�!&* m�)mk .���q���B&� shis.G�%arm"B%)gB�e(0  U 9��*�!Q�)� �!�tR&` >% $�M��z�� ���fo5�Ib��for �RB��;6� ������I��Ii*ĥ�.I�͕j 5�ss �abn{cc} 2� ^1��=.�!a &2&"6.\{l.72 }&��~("T \ .�"27�1-i T.S#2-�.$!a�O"�!P|� �e)>l�5i,,e� ��ad+���"3D� old �� diviAm�]5�IK*9aA.�.D2@-;I7�1�e"� +7p�y�1{)�!uFi� }{.d )"�]!��&\tau}r�![PZ�f|P b|.  n|..5�E� ٝ�2 }{,+ a�6� Nq#F�#\ Dv�D r�.� )}.2� �:D2�&\3�"� Y� �Zr3  ) ey%2Q$2���^6&LqrAz*�4B�0 S֯2^&(0)2.,=� tm�Ρ�� :�$V$"�-6?�}"�FZ�Y^ bouFI�.v0)�=>z� "J �^� vJ+--*aQ����d ���!< YQ0"�7�^N]<)�yt8#AF(�)ft[ Ay�-�� ��� )�s�� 6�;numint-f�J)& $al�a��23\u�y� � 1+�W�N�R�p1}��\>�a��[����et1#}-0#�&G W�ls:v"�/ {��5as�/� �x%�6 -]d!]��0Bec�@�ye\a&�I|Y�)AWs/�,� f�d#02E&gN�~�eW6H��*�T�4e-numres}.\\ O��ly,. �f1q $d1}) admitm3a.< �Ma!�N� �V ). Yet� ey��&�\ "�q�rL0��Q��%>�&:H Mn7 *$A[�&|$ $. B���E&b .� ),�& �� ��)d "ZEn\Q�Q�s��r�&=&�� N  }Ym}. Q�z.�&�]��m�y�&=&�G. + M*calR�"��&B���*���i� �2"� ���S-��F]h9'Z���2�%�, dropcPM��z�4E�fa�EWX�Q}-\�I*AP���4-1k��,5�ufla�R�jSbo�&B�9]�P2epM5B�ɅV[1-D f�z&g5"�&2y6�J�� ��F�-���  Fz )=�2�}Tw1Z\jz>&Za5I�boub�E|T#z  �� ���`�H s (�����)%u�b)) �n��Z:T�("0s)#hviA�"8&m%�� �.� %� disa���Fs�^ :�9ʍdicA,o6Fm�F:a:e~:� th&�Ba� $�' F"?�ai�/�@e�5;>J�6%: �� of a&� �1�� $E:BI(�h!��A�of qX��E �'-6M�}re)�ap�ant Q�s,.�Q� �Z�Re��m,)%GJb"!��l�+&&6!�ileA�� N�6Jfe .�Jkc� ���Qs�o.a6(5>��w'd"� a"}qs 2��\ag.� �f"0 �u)J)��`p� 6�em, 0A`e $2\�v)/b"� � ,MFͪ0 Q�A�&@!�O=&�"�Q % e ��ne, no 8��+�Mi T�Per��� aT�  �� &$$m�rm{ m`&)Xfm;inv,7yo mpan��"I 6��/ I1u>&>��Ndh�un �Qly �5let�"sur# luou��LeL>am�a�>!&�&ka2�A  ' �#�{��6ᖍNr�#��#DJ,f#*��"�\" ۈ� lO! �s"���IIy��i� s��) 6�d A6J" f )�aal "��gco��" {s��X���N����n}by ��>���`���$��,� ��St�U<�y����8� )g-�� Pit� capČ)Ur ��gn�V"� �!�2 �����#��in ;"I�x�ls��rM`�3r�:f�1a�Q%V!N���� !� (E *!�4rnghiF�T3Y"x1�SzV�"IC!��&������!/d$t��low"} (��!]Yis�7li��in*.,��fi* ��s>�RbI% uK-"s#$}). Next w�Oe will show that detuning plays no role in class B lasers (Sect. \ref{homo-ufl-d >�y}). Finally, we shall analyze the spatial (transverse) effects due to the modal structure of fiber lasers (Sect. \ref{homo�,tra}). \sub�ection{The RNGH instability} \label{>rnghi} . orig�( studies byB� \cite{RN68,GH68}\ considered a per�lly resonant two--level ring %G!X! UFL.qHMaxwell--Bloch equa�s1�(scribe such B are given�Eqs. (%�$ufl-f1})--Hd1}) introduced in =�model!@�} with $\Delta =0$ \begin{eqnarray} (\par%� _{\tau }+.tzeta })F &=&\sigma (AP-F)\,, -rfg1} \\ .9KP7&P=2\pi/\tilde\alpha\,.Q�bou�{A�steady,�si�,ly uniform},aj� solu� isIq by EqQpssufl})2;2:wF�8s}=\sqrt{A-1}\,�,e}^{i\phi}\, � P25 frac{F_% 3s}}{A/DF/1 "U~ssE�1��where $� $� an arbitr!��phase, and it exists for $A>1$ ($A=1$ corresponds t��first!K0er threshold)a�is2[AKbasic, !wlea�9.�. Other  "1�s �� (in fact an infinite countable set) ��Lcan be obtained from.Ia��F% ML)A� sett�$M� E� E� iK) =F_{9�,n}\expq�iI� n2��=$-\omega_n e O ]$, $P = 0:vP�vFu u^tDntD:t$!�ese=�wA]compu�:�� ��!魀out�ME UFLEpcUUATHdifferent values of.longi��Dnal index $n$. As � owedx%��, all t�ad��alV]Lhave a larger oscillţ U�� henc��(~Ɉmw)a[A�e��AJ! . S���te"in>�AR��perturbGXstate of�( system as%����j��K.�+e�� }\d�2= 2� ,��j�^.�F^2=N^j�^.+ �J3�] ,� -% ��lineariz1Z dynamical*��!v-�EsE�; y is facs aA� by expres!� any2: $ �X$E� ermsA its re6 $% #yuR}}$)E~ima� ry (K(I(0parts --- notakatxD��kby de�?ion �INof=�F �idvector!:{�l\�ial"D \over�arrow{� }=L\cdot b!,��LSA>�%��b_��col |��R} }, �`R}D6I5 I} }��$!�y�1L=u�(bmatrix} -\M -.;�0 } & A & 0a *K . & -.C+��\vert �%� k\\ L8.� �6J-e}� >/o�ǒ\\26.�n%�1�% &F )�UFLJuE .��*� $J $.|$] by .] � � Becaus�څq�� nat��m��qa)iy�� �?^ $m� calcul�� as $b1% %�R�` =\sum\nolimits_{\lambda f�% .&� ZIA) q�) P�rOn%o  hand,-Q!depend�of $L$ o /�  coordin�;$iX#ly�� oughFgradi{$F�%�yr.~�$1�writtenr~% }~PB� F��SS,."� ( i )"1�$. (O� u UFL,�ansatz�no� @id; see below.) H%��� ��f� ly6��6>*} b�2a6�B8I� 9^C9�,�]�� +6M}.�l�% Thue*zproblem.�!_M��t{ ollowteigen0 AR, �flJ� =L_{M}�frJ>F��V�"��we©gJ� �titk by $1j $. G2�4block-diagonal���$E�Tcharacteristic polynom�$%�cal{PUP-D;-u$ y de� ine)�Lyapunov onent�o B�� oriz].�� ���A� -2 i H ��>�R7R} 7�.7T .Jpol}�RNI^N5@�) ^{2}+ �2�+\ yYQ )�+i�� [)�:�If�b�V�3� t t+ >� � � �4 \notag \\ &&\ [ABB��0*� +) ]�)�+2 E <A-1 #) +iA1. !?'!�u�Q�T<ys, e� zerodow�Q�e���� � � 5Z$a�a���s>� frequencyO��8Ud2n � ��Ku&$le domain � multiF*H 6�cases ��E�|%u"2 �\neq 01w=0$ (m$ one��f�- known*�D, or Lorenz--Haken�eo"�, whichU�tre� ��eQ��.become9 aga! 5^� R =� � $ if�42Z�>0$. It� easyAC&�)]J� $ ha� roots�&&2\  %�fy���. O mara|$V�==�\,��always a�Avis "�doe�t entai-2_asqHnever gets positive�I; ��d�!4 mere�flngeB�"���!�la��<jg is associA@)ha��} pacea7��q rf^0"x ) $,> *� LSA}��  � � d%�aH trol�possia�growth�2� in %0-zrk w�)/�,e�conclud��at$ ��I!*aka-}a4� bu� ampl�e.BmI;$ result re��sid .:� field � ,AI�5hen) as64geneous broade, etc)ni �dLfarK! �c%^F is �[EJ$we discuss� I2.2.4), �a�sny infl��!r��!�class--���  our��erest. NaJtheless,e ?A� C�ers��Ua ��F5�proAC�N+�% {Gerber79,Zorell81,Narducci86}. Rega|m�V_ &� ����&�\ mutat!y$utandi}, g� nsR_�---%PB V�!Tf�a�"�=-i�i Upon sA�+A(t� "o� (now!�$?�o&� and &���s�0 )=m�#ui�an��ve��$ՅMjV ,_{\pma=& � �1+�v \� }{AO�A� R tongueas �`1� tf� 1}{2 t[ 3 |*� R6\pm \\R r] &� rwrRa7 M9�-6 �`>1 g ^{4}&. jB1 �e �j!�^tuA�out!�b*f v�a�5� verify!�$�25�-- leq � � � R# _{+2J�is& & �!A�shape�a )A� plane $4��e&! branches*� Mp$��ge �V crit� poin�-��%c|� _�� rm1�$�eeE�co�� $R=0�.jump re��2minimum)��$A9 wa #.�a�9�d�""��+*V"B�} 6� =5+3]�+4I�1+22 m=( 3Y�25 ]�Ac"� �I�E�5U=S� ��>GIa})T� w:N!w�� $A=6�-���a l��s� re summ� Fig. ofig:1o�"$figure}[t]�c�!Hr} \scalebox{0.5}{\graphics :1.eps}-8;cap8{{} &%i��m�la�( r,\protect-a%q�r !$m?� AYPe)�!� @)�$ mark�� �.}��)� %� ub{("�2�i>&8:I%Sb}C� ��=Rytin��li�� � _{\V}$}\ll \kapp� l�_{\bot �oncer� !$ decay rat)!(pop�io version�$tracavity % "� e� medium�AB�,ApJ vely. Wit,used normali +^ os���"�� o $ � \ll �9�).E�is� E e�i} in� ��as fi*'��$erbium-dop�!."inEi�r0 �E:is � %ET hTb R �� alsoi�!xtheore�� view��� a�s��5 a weal� e� 8inf!V!�� e latter! Q up� t\lq\lq ��\rq\rq -���&A�I� � just c"�'� &f[%+�#"1"&=  ur!2complet��. I!i$A`on�apply�eOaHK!7�� ralyio� lready-W$ed above. ^ !yA2g %D*e samX_ sŰ,be derived u�L asymptotic techniqu� employU�[ D%expan�Asameter. 9 ���.1*� �56 $are retrie�bx )�uR:umq=0��&�(��� 5 �� � �\� re }�F� �B};2$ ��m��) :�����&B ump $A"�cV��'Ac)?makAH!4���� A�.�G .b=9"p" � �&�e:a :�O ata_�S$ (��&o' occurs? a � =1$,ag�C��in ord�'o� a�0as:paM�� shoulda'at leW*a T�)nine gb�'an� N a(!F��(. T�i�@e famous�� U--of--W�� . A�(�"�5�F�.�%��%����r}U�&� �)12]kE�cUf-� So#we-Hssui�citly a!|tinuum!,2�&fs Wled b� $ir wavenum��offse� �� But, must!� reme*���+�\�� � 3+)�ose#q�,�� K��.�# $�!�nte8'�ple�%�b d �re!/ectral � �*�+e}$,S' � >FSR})f�=-!_{n}=�(N=n�D, c}� TL}=�%R*� � i�� t ;n-{ger.} �n%�>*��u)g:z� &Y)v lowest&�e�0 &�c}$%]�)�N)Y% �$); alternaslyA!": (op�) leng9/hB@ 2cJiR61�\p)��� &" %� 6��-N�Lc!F�� E� hort!cM� �eB� O1I!�%|�a�s��,\min }=I��� QY Lcmi���/����L 92��K�w fer�7o�the i6duO2. Next*� �2&�" actual�� 2x (or, N`ons��  L y ofK rete6%�I�?)�*T H �'�c� f�b meaN  mQMω!�-�}$ k) ticip@$i� a true�� (1|) �� 2,on� Fb^��R�. o��A�A��@ ump.Q��2zEn762!Y�1�$"�e� x2�2m� � Let us�:��U�4I��.!�  ),� �W �"��BeQz1�n`% }�]&��8relev 5m�1�Mj�$ _{-}$ vs.] Q^is�il�+>""�0� 2� % ) � eAi pc�u2+�S2"hquantis ���l-�&\ of a} bw�+ � beG��fi� f�A��. I~m���% sens1 a�su�#�2u �!��q$ (�,it{i.e.} if �B�}}<.�8{\star }\equiv ��> }{9Q} QŶM�:���-� ��A�%Him�"#  (��Ne�-`*.thrA� $�4ll!�!G M ( `1=:g  iW r� ��is1 z�I�f �O�� 1}{4�( 2+3M�w-)I 4-12 $I�{}A.`A\� �j �2��[8b25&:eR!;e�/on���va��W\go ��Av.r \foot!�{% We  e98)� ]":sy!typos�0ng�Eq. (45)a�FP99}.}Adecre�*�L*O�:, B�in8 �e�!�pC9�P $a(�P! accord�to�T )�) sbat >�-�a�/ \infty Nf�)� 20-�o��evi�+A��0*g U��R� �� %�� ..observ!�͑,��=7�� to w�[ommE6bel�. Clear] bye��#f�$ �A�}:,�#so hug�� p�(ice� )˭� rule< .>w�2�E�eNCal,A���9���663�- %�2R~}}>a+�`� n>�<:Ry�.�isU� a�hig48_ �_ A"tific� � $ �#B�E)w a mor� vol�task (�,y�E9a� us)�gen�,�4 eachIg�5b�D0A_{�)rm1��Y�* :wB�-E=' ild" $�0 $n=1,2,3,\ldA%9e- V�2�\�� }}$ &'��= .�t6W5?� {�3}!4p�?CI�=aU%fun� -� i�. :^�aph�!Rrecurr���aA!i�du"�?�eE�e�%&�1])�Oi,#F�:�=9$�� "� 3r� �?:���\% �� 2� 3�h� All)��&p �v� nree--�^four-+@�#\i*�2"He�s"SNT:T3lev4lev}: (i) replace] a�9�A103 d (i.A�J�(j KmU)1+WG� �0*6s (�IJ$W� g m*�N�@strY)���advanc� &�@ G;�]=T�&:B�it ��0quite similar)�a� *�A�As�Aa�e-� � P scenario changes dra!�id�a�� &next. �3n5!� �w|&RB �1�@�g�U } 12�;5�% �),�=M !$7\� 1+W�n*� }$ wK 6 1�"( *�R re&p!�M^U$W$*�.3!Aec�^�"aF�E�B�1V�fC&2]% �%f� � =A8{G}}\sim� .R�RB� �i�v�E�m�!o(times small1va<&�A=� h�1). Howe��: most fasc8=j@c,H� >�h:ext��l� V�&5���eL��. D�w�}�on� g��z.28��9se9c}/:F-�1+16/G$� 2��a��>b >b� *�:r� 3L})=u?- .�6�H��/ predic72�j�@�}� R98,� FilIN vari� Z�� �c�) >�!o�.P+ch 0,X nou�}tha`D.c�{:� � i�� �.tn{ �QƂ whil� ^�keeps $I�sw9{60"�hF/JA"� �� ec2�$J�$"� }=%�&2Q!�previh.�!�"be�.�Eby( �)4|"$� &&��0$�e` ��b!Y6) �*d=�J�bA'&�&G�Gr&AB%��!s� ���n�(e.g., z�/��t!�g8Bj"�0asN��.\0 vail�F�sA��4�Ayst)�Do�  ��n$�3!s�K� done&j.ab VG io},�5�aa28 o��"�0ly�&=#!�MY u�:?� -��� �� ness9p . Althougm�e 4F)���$t necessar�4;efapo"��"�#�H�as � !ex�+�h�' � par>� !�]Kforwar�+ay-�lex)�y!�bB1~~�&w+$� �-3.��6�: *b/g 0�_(�wQ�AA , oC/in 2toQ7<.�7"�/�at f' 2�8si�)��(�5E�#!�iX' � &X 8)��T k conveniL>&3 �8"WP*���9 �(M,>�9"�81�+ �9 �9� [ ��9��"Je+6�9.�/"�9 \,. �� -& % (We ign�!�]<ّ.BI�asB615a2MwIt&�(con�$]7�$�P.) Now($0<��ll� h �)(�h (toge�A�� $\sioO�9�0}$A5e �#�"?�@%Y5��<=1�_{05�1!�2}+ ?s&ZH Z%�2!b}I�3&-A�,�>int.) .���"% �av=�Y�(d� se;.zNg � :�8A�s_{n=N� �})� ^{n}p�#e(;\{=Si~ \}B�>&� P �FS | �5�� . ?)�Xs��$N=-1q:NowZ�z5m� be>/�%�!RlisMu =�2ZPlyFid���65o,a4imy%���$% %:$Knull. St�Rng�|lea� �� $n=N)g =&�=e p B�*}b-1}2� CY�0}Bb?:�(*}g�(3�:N#�;a] =0 \f9 \mr0 and}%-i\�&j4 0F � X-($n=0$aR�)p� me� a�J $c0�=_8A+.3�'�)r���J0;�pJ�M�*,�!}���0���AA$�@ @7�V+ ���=-A+2i � �.h/-�$e�8rm{% *s=G<� he��!r�(�/s0}�do� != I s"r9n � �-iscarde�F.e� seek�miee�2�<6tUg2o(Qj ). S-0) %e�� " !�m)�)f=0e�-af|!*=-m-YEa [1 -�2}�(^2m�&d-If] .A��2 �&�UՑA@��6�?0$��%E�inu����al_ . Aeei0 ai1�v�2.�= �0-� 1})*used,�� ,"=>1!>�I�B���_{2}=-(M�1.�)1[� C -r ^!.�+2A%}2-d --�Y)�-[1 �4{^"� 9�� K y�)%i�on0*9�E� stop� �R�2 �< y a�}*� "J%y�}�A�!HE��h��ZyI�� exac�,re�Y" | b^<�Pfor:Y yY2�$)�BA ), a)U hec 6 !�46r=*�S_$EDp+ �&�*� �#9w0* B��+t*�%5�Im�q� '!e>��'rm..="C��-I�^�`Jr ���  ==-$I agre�'D5s% 2r1�N� kind�"��a��4�D � 3#iV s�ch, usu4, �admit"j�&�#!h+�v"�.Im�a"0P!�ied�o�+1� n"�paper�q�_be de%�i�BA�de�Has-_ �:�!>�s. |�o<$a*�` betw;B�x��7���l�unavoid x�Uex� �,�2be �d$uX�� � r��� emon�tT%��df>�2ain� ,e�he*4&� , ev� �D �1���en7G�� �J.`UFL�7�sakEsiy* city�ugzN�cF �^Q`&� E�`' AP- ( 1-i~`"�F�LLE\�3*DWP �BI-�S [ FD]+ ]��) `] ~]�^`(&X`} V �:oY%!���&@)vbouX_9f� �:`r:` 6�t�>*�7:caG'M�fF�4, �, .�4m=F�I �yX}�@%�\s�}�`e�a �%� !�'a���:��LN �U�S2�Y� | { |\le {1&V/2$"��B6S����� rY>OI�*T0 ) $,I]$|) �q z:%o-T � ��2 . �22�N max�BF Jor9(of magnitud�Hd$�9��we,�`ed �2k#e�lf �s,Bl� b���a "�/of �2C� ���g��o2phy(>%L�?ble"o"�ţ!�e�, �,F|� �A��X!� *vrgu��:�_!�B of�F� (say> *6�k�( $k=�(�()@_MH �J.� �w�:)ner) we?�Bd ���!N� +B� #m/,Mcs6Sec�g &�e[b}��!"0(w&F�/T��� �)2 �)E����u:��U �D�?Ac�:q�V�x ��5q�) �dB*}.�E� .Z set{JF}{\5;Oa� }�!1I% 64|ReW'Q�P6�si*H� ,�)� �%VT2I�10^{10g2�ty�$f.�Bq�A0-5��Jy �n�2.,0E+ V~,deE�)��2�=2QR{[�,"�)^q )Ib|&R(E$:k2e2.01$]kc�. a�.�S!"�0�y>*�Q , ung!  � un� zWum)�= co/,F8�2 �2�*(a� st) ��t� an� ropT"e ���!{e�&�i@�� C�i;# �T�iQ %�hP&,%2�u�|a��cion81ND�h!�at��rD��NIu;} *�`s"^) A-1- ��}J�h }\*�hu@DA56Z�hn " "� KDRK1+ �UJ>� �% �( .�ew1?>�"� 9�&�D� s�_�wI!�� ��G="AR9�$�%K$ �&�Cqh7"cm�[� �46# &8->b�'E� $�&�� U�"b5 JeM)"�vn �� ��r]n6xE everA�2O�atomic� R-�e�m`Ent#JR4@�9e�>:P �fl[oE���fifth�6P!.;canv#�]n�'n�@fac&�[ U9���RPYNGHNa���" �*�]h( m�#m���2eqh�u�Y*��l�`2�&�S�%�  ;" %+}@1kE�de�V� &` J��nr2#butj'y "�:&(� �e�w�J� "�&��!&��C ea  *+O�r&9 3.� � ���A[wE$:a� veryMHw>��m�A�%�-%��p3}$ orL =0nkIRZ tro+2*sh >"e{M ear:! 텡F�)��iD�5ZV� � 9Kto�*:+Tj: Wsaf�&/��P� %�ult*;i�@-�� ��� �%�&n excell7&pproxi.1Ko hed BF�)S�p >tJ�)t W�!!�& e--w�l2n@S op� ��,�x �O� Us�}pe� "�] fund 8 Ga�6an� (� 4extsf{TEM}$_{0�#��I (F9u e6�\2) t:6TstrongA�4Xd�\rel�D �iM#beam ���>r*O�>$r&jm�$� fuE�^< <V$w_] "k wais,���LZ$u.n }=2(6�/wS)� RF�.t w]&�dU�}hq�ͯ� 2�� }h% {LugiatoMilani83,Stuut84,65}i�ɠrec�(���UonA�$% 6i�" -%V�Nun�@{ {SmithDyk�8,Urchueguia98}.q| a��#as|;�oodu~x S@ �%{"�m"&of����9mplxV-�!Ve�".-a U�%���bpM�b�, b�iA�a� fron�i�dPbe F!�id��e]� �v )#%a)U2H��ly)\to�rei�X[*4�dopant? �!ZfFsi��&fi>cor��m3.R8:aU)ly�2�e)�e711�r!S. Yet,�e a/t��4�%�f�5��eA�tinguish6 � �8 .97� �6-�-�� ��*�b��� WN ( +B librQS"�S?ce $da�y M y> y� a�M!i�N2�o2� ��� tra-f}--�  d@� X *� �1�C&��^'"� 1�y F"bQ!NQst�0 .�e0x/},�"i� m�8�b^m�2b w  �I�13.60B%b:�y >\J�y�) .�y?[ G\int!�^{6�}\!du6'$-u/2}\,P-F U�y"�x!�f ��(" e}^ _FD-�)E[&$^pb^D*S � \b�z_\u}(1-D)-3 _{N,3}-&�z*�FP��� bel�d�:*%&+�odiN�NFC%u�k )=F(�l.Y}  )\�F$Z\z:u����@lo[cg�?��E�both $FA  $P6 ^ . D�*$)mreQFOnsI�[Y �WJ%&_  $%�>C-da� =(G/w"�NpT� ��$w*SNp�7a�2��聊�]*�~tI$,�!s,qLtoJ�:I<��!0��.���, mak?$mxce��O]"�<s. Trn / �?E"X#X(.�)68�x investig�din�]�A00�} Q%���4,coF,�1�f��&o3�H.4� eq r2�]or�I)�jFxydop��96a }. V}\:�+a�as�#�  "� ,�Qf 0!�15�-��type $5PP97} adA(t]S�$.�=2.086�Lu $q % E�=2.828A��� a_e=1.839�_.`� } 75D-�DP97,Desurvire}. SiA|:1 "@$�q�&:#6� ra�{0i�>�� ,�\ �5k&p">a0.879\,RJ�qB"qB4rqBLzHaX�9&�M�G �tCumVp'F72,�PcY�CQS�edl �*\reg\$>$�j�eh@M ?5m@ $G$: $G=600$ (so�/�#s),,200$ (dashed�Vtd ��: $ (d.ieacF  =G4"f[&�Da�%h�" � .;$two �.}�mfig:4�j�C � P5rS91:9pu� t�ՉIu2�E;&ed : ��$G%�%x for �*�t�J L���ZG�DE�( =1.25,\,1. 7 2.5$�bottoxftop. D%�%p�c8 ��&"�.W �M�= "vA�e5 B52�?$6�5:�W�er �Y�pgT6�"s�� �I�>�>%b����!}�şbGuZ��� ��96�Tr D�|�+�k���L��up!�r2u�$�&merge,aed�?J�5� A�&2'g<shoNtR4k<i �&Be�E{�uixaed��adius��%"��� �K!��^er(��Me#va}&r(YA��$. All curv�Ei�I a,�+�;eoQ! � ��uit may�no!d1 �F�a($G$(6X��L9Y0�+��FF�� ab� )tim�[�t�;!�A�aF�8f�1�a���}�s5"[<F�0�A6I����S) ��Wi� )!)>�\*;!�� H"% 6�6-) ZF� �Mi!����5�� well &�m_>�=1/�D�G��ndE��E�=3/�D)�Hq`� $$DeLTom:6 % }z8 5/E�ra>�a <A_Eh=B��&�+ two 9�s&��f��a�M���J�d�# temp!Dt&�.-~o��%_� awsu�GI oe�Ba i� U �AFf� � ,PLBGO e tell |]F m� 1}$ rapid�pR� �:C % }}%�� m"��,a�n)�/�0ou6h Se�4A promis&A��Ak�too�+FKc"��o. 65}es�%D>� $I$���2�% E�� *pS Yh!�E"��� % 2��K&��)e�shift�D �&|fMg areaa i� 1o�%YlsoU�0 a   �W����I_�̹p& r0 �E��-A�&#m��i>Z5}�R!%�1 :�r*�n(�`�y emi�Q t�mN)J yZi_�ase1�E��.�\ty) ���5�,a�6�:�%�C qg� >�4}M#�!"Vix22h��CH�H� � teau K0.4Io>� 0.7f� �Qua{���1�y "�D��0i"'w�Z>v�0aisR?�genuine�Ci�T�*X .��OS3*`�� "�.��1!+a�terpl��T+)a�ID.�UFA"��jEB&�& (-�)>,%�"�� ind4"��JhU�(is guarantef�51!�R� 0.25$�!�i5�!�7v�aN�{iin�&vDu� >=. �K�.&N a !;><�-V-�]%^X F=�profij4��e1zd��s,��e�M�5f%�dOly �V*,G ach%Xe]�� q��<3�� �����is�,r (B��*e!�6$�7A��; was!HAn Ref."\�La� Nd:YAG (��'R)�er"wS"���f�.�))'LT|T A� �ce &�nL�*q+�8"e9 of a bulk � � �distrib�t1�s�gto@5�#ge.y|o�[&� kT����(i4i��-� esigns#nI�3Z]��E^�# ��{�no� ountAu"�Y�V G��he ��e d�+�ac fR2e ?ro֑IY J� �! .� �0sE�e�OaJs��l^Iуr<1O�l!.��!�u%�2�'s�. T)>/s�p7 a trivx5 task�F� }@ussi "'��' 9,  'it�@ ms f�blM��' day�JologyNAN�+a2�� M�W0�.Vto!��@rR�:G!�n 9�!�optimal��{s�OF�"uV):���.eyU2��i����9�bA�lA oneK �Kh a�3toBe�.�: )��se� {��_a"��m�.:J%n��� �*u|e4b��i�sJ�M.W�in �6�ja ��tMLa 9�.s+@�B�Xl� pՊt-�# 86b}� C�c|d�9%�^ ���.f� �` &UFL"�!"Q'�Yy, �(��i����5j*D� 6Ri�S~from �#6K^~s� se � s�|fyiNx(~�66�.} *�M�$IT $�1)U% �(P99,Voigt01 �zTau-fortun�circum8=�c���&w ��qbq�M�,��M ]q!S%�% 6�� s powerfu�0�7I&He�![ �6�(#!�c$�M����Y"�:�n �B-�Ӕpeca_lR ��i��#�;%����a��).X��&O6��b�[�6*�ͻq�y�{��&ecaF��er���al)2�"\�a<(e self--pul�jF0"�stG�n=Z m>u way,Ui)V*u�Q i\e"$2I-�des(��Y��a��ed ";p Fourier1b A����a��;y/%�be+�E����ZVS,+�?e/1�If rganETa���us:CS 7 \!���A0A2�$�e> ;A\�k�I**�Gi+��d' "� ed�!es Be�� -�!}�a��ate�/"�T�� ��D���?N 2G1\Ab]| tV'*iFva�A�ze 2��.�F-numres��c��!�iss�a�numer�!,egX u:�c1���f4�[.� �0� k&�� ^methods.&�WQ]>jsub�add�UT� �� er--�. ub--n*D#*�BFc-A`>_JM��w(�(�eW�  n[ Ug偹E�.($\chi �L"$e"'>((�@ eqF3"��{eqD3})�i��!}68'e"�@�%( � ' APS@\�� jF6�&R<D>�&2AD-F6�&e?�+ay}% 6(R���*� 942g@*�RK&\ta�I&"�'bouGnon���& �FOg��{IAF�&MF� loc�f��entryAexi�\��2 ��>�<) !< 9edQ�fJ�@�4M� -�u. �{� ��> wg�s>('�0"( *bT2����Cu6 U{As57��% Y[ �T� *��.$. Lif���" �b2�� �f ���J&�S2"!��#;�.�+:�. UnlikA� ��� vari�s] �� t�2�&BJ#N��.x��� -ss}VlischiyL}� ���!%���($I"�(s�Ref��*T� s}\�ͅ0%�O(Y�!��F�.lJ9*)�C |\lna� r |}{1r�}�O) ��#FsB�M�NE� B�e^ �"4x ��}+J\ �EFaR�"ke�by �&�nТ =.њ�����+ �J� .H�I7�9!A\nd �.�K $P�#$D ) �&��� �4 ��K��5��6lem(�pl$H�\A2X@�Cin�or t�zt� �)FJ!^)X!�,,�a�not�*8�� F�2#�T qI�)y%�)r/. fac� � �<  -���un/1^prioriE}an��%p�!�V sought. A�s solv!f!�!material2|�6t�iK)2G  �f $��Qb�1�}1=f*)e����f�dd}{�- ��fB-U�) f-H\�U( .�-u %a�\\ +J*[ x\s�G A�G.)t%Ik �( �:)+2�.;�R � YV � 1 Gyf�)";.V}"�+5:wU J�&� yO�*�C25! �e$v�J-f 0�[ 1� > -\ps%� 5�=0 $ Z)yi�1 D}M ^{\p�$ }5�&-%s6�, zz]��"OD1 �}eyw�` � l�*Z�Eq�H {6���� �W2�"5a��NaC�fFuF$d. /-=J^A2)� 12�1���&)y����i�e�e@% {deValcarcel99}F�AQ�)� r�m mA }{�U>u& }\lnxB.� �6d }J# U�} +i�2>rf�� �+n @ |>�, �ne u�2�3.�0Gef3 Blam��J 64'6i2A 30CJ�L�8 re�;��;ini�.'���F�� �*�a" �{F �6�=�x5�)v.��%21 }2% dG}~�-P:U)N]\,&�WdFnondef>�+Jc(m *9)��C)(2�9R �2�x�<u� :�B�2J�MC=-i:]��X}©�&�+�2M[}��2��la6�eqv%&ZCSetamRZk�en+ d. R�F�N?nd� *@]� ��� e� JGe"8 ��"9a{2���6�^�?}F�R@���^� b�I�# ��[&� � ��% �� \"�R &&\tO+rah[��.�M U8�|9 ��f�R&��^� p��f�6f� -"] "�9PSIu�1�E��Mi2���he���yW�ub6�g&�DfJml$. �d�antsdGll<�iA�/�A��noY �  6:� �"\#I��kU $� I1a}M0_m@>s")N"RF i�>n ��"�H`i.�t��M�**�k�*loj�vleSLfol� sHo . � �d�&MF1C�5UY-W�4 nJ2"�e�/FsRb�I>� a0��`� 1}^�Si��I�"$`�(2����]]a > `2} &=& Q� "�^2 S\�O^4>F_l+2m�&�^��o�p �1+�y�:` �a�B� �M�\�LJ�P6@]_{2%H- �TVL"�_r�"5� {\�.�e��d>���9vI#"�~)�=�2 %;.ich�;:�<�bF� ��ݏBݏ%AG!� D}-8F�1#9f���_-��gC��9-4�E.P%e�|&r Dksi~} Nܑ��3�'& ��B})Isp&�d�9R.+I"�71�906��t�G^w�)"^E).Gk1b0�3 joinAH6)X%F.��!yq�8*�D}}, � � Ac1L%�MV� rm{c%�I-����}9�9L:�Y ic1!_:���5r.z".� $�~�G"v8%Da�I�!�T}��1-BO.�0��T"�m���#�)"����t  rc tripb:M D}$\��� 8Je�?*VxD}=1-�t<T%��Z&�L/3O��2>4 ��8Orefori7B�YR % c}I�"�7YE(!3�G>�*V'AK9�.16}�QO�͐0 )�) +�W&Z'f+]E�.5��_� 12+82:zy9B~yJUB3B�YA�JH�YT�t^ u��U�, nam�/=�c���fJ��=12�/>&/>6r< {}Behavio=�aߕ�s6�� �]"$P"H<O K6 {\ȷRa��S���4�!$i =Q� �=7z�UL(lw�!��+ve*'!-V8lI%�# .�F�6i A� =0.99$H�ݴ�3%) UFL), 0.9876.�2)�- ȆB�� ���5ing�&�,i�! \�squ&"Wk�n-neg�M�C23yD}>0$ Z�va\O�%"Z2 �.0�%1�� }�6R*Et\׉&?/ 5379��R�@��� ��K,anW"��ng"�,�? abH&e"�4%� to�;)241:�� �,6h�+�7 $Milovsky70�$�x words, no��g)��3aS�.[#?�h�E�be,$l�$�cd(<&55&,��if��R*}�Jy $. A`�t��2�%* ��*AW�=!nY-!?fa- ��($��B�� I�$onotonous:9}fig�;�(���TB� 2g "I��Q� ц$�� �ac܊�-6��div�>(�072ng2)&KM�!?�a!+.�>6�2�^9�M` ngue� u� ";8 ward"~2A3�BEG.ҘsT5&�: , le zBfrki�u>� � Aw%��,cI��'&T!���5-to-f�%t".�& 27l�A�"]af�� Z� �s nkz�l�.!�foO"�*55athܙ��Pfac?rks a*</A�e"�gX+A� �� b3B���t�#~&B�Y�}>K�(=1+\epsilonB-5 , �HOQ-=�K�r�.e�!�6�..f#��/3�77s�ag!� a�9k>�--�Zml =%0:t)Nalb#@0&�Rhj*4"�'N (A1} An�X!�or�!s@P� �i�WyE6A!coN($?��:Y|,or�}!!2l@F� a��F�T, af8��QloslaB�-i�i�?�Ic �es��uld�4&�)�L75��_�ʗ2)h:Cb�4�= �j%�le�v!��- Y��iv: �!2;P�",V�v��s�-�; . An�Y&�[Rb�A p!2ma�9<�[-n=6/>!�JH7�cEg%umm��e�_.KBpc�}+'d wv'"R7N�),&��ɋ��)�( AP-\�*�P����)��)�&\P��Re��� }&* 8 :� } �[�(�YdΤA]/|KE���>*�>*"%*Z ;JX8,�&7�m}}��rm�F.�� |+A2 :A)Y) $A�hTji}),�3�� s $0B_atenk *�d}��1R�D)H  chi 27)P�B�e�.-RA$ :��C�:d"���"�O�8b}.�?&!�.�D� ��w�"-��Ʃ�.  mx��, ?��),% p���2��ecIs})�t"(%  �"_�yA�� "< �"�)�%O"%O8z�D�7&j>�B2� 2Y Ar� e�?9I!�a&�Jees. � B.�""�db��!��,VR*j�T ��*�)!xJeAA/K�Ym� main�qt>�!��Zavoz1"g.Z , � :II�6� B � ( (of course^� A���ag�u��re� :N�OM�A�2�� >For �n�unR"mL & (. %CE"�N��Zin ��i*O d,D�fN�{�1 ��!g8-9 �)  )*1-% R�w�� J� B F*����q�)�� c�N�.k�i� _ � ��1"��� �?l8�QW&� - �8}{1j99����n&% >e^{Jz��BW>� �<=1*:4�Q{;�*2� ��U-e�B�$e��=0�(�*��sm�ժ�Snonzero >j, 2)B{h-� to"rJɆ&8�&tj� $ s�atX1 j� }\x 13.62^i�a%�>$�  ���O��ejv�=.] 6 6��0$����V22}O2Wd�>In�bɎB�V�M.� ecibels ( �rm{dB(�t&+� 0#FM DL=8.646\"�* }6C F� W�`2|�!Z $DL<1$ dB��q�cHa&�Z)��!���2�$?$`�fG littlU�T$DL>10l)bLes Nquickly.�,?H5euR����nR�, hardl�la6f� a �. S㻅�fgb��i�atBs�r�A RF&�?sVh=Es>ntz��%e" "�G�f�� "� 9�� nN�L ��6�2 ����e�P%f�e-:`�� �=�l JAe�u$G�$U*�M>�4$% -ɻ �$.6Q6��i�} An &&U=� �Chet���1clr��ext=d� �3 *aHIs:� answ_�a<�I not.�oex�ee.��v�eCva,;a�&agA ΁" n direނ�G?�>v�c(�w u�� way\}�,.FacueNJ� mN,"V� ��EQZ*���le&��� &�/Aof:�P6"U!�"E94)�H![ q��@N$G�dIngB, aב!`A�>�&Qnegle@�\>}T?s>!;e��Awu�5�|o ?9�J_�!��!�*]Zbe� lays!���)@J�eN"�sB|I2� C "�D.�A��� !W&���NeBP��� @��>arr4.�V�2B8m%��If0A����g>���eQ ��W Ⱦ(hu'e�an�g ): P�8�fv�out�J� >���I���Vs�Au�AR� �"�QvW<nu��!ei5K <�R���thJm1�a$.�%�W�ve E�H*���1�Dnumint.�6 d1 �v����S&�J�BPe��M<du6�D'/�P'O $D'v 5��<ice�C�tTPt�9�a|A�6 y�� ���Cthey ̄tz E`AI�Z"�e&`Yi�H�O.~d@b���we�%co� �,"y333"�A=."��aW &� Q�!0�!� im 2�z workI�v%==T&�O� �E�,e�"�|1k#u�w�MW|�newR�$f!�p%� $d$ &U *?��> 8&H1�<F'\�) �� !}{�`.�<^rm{UFL}�k,1� pEJeAP�ffd^f A\,D.b.�}Tpd#  Q��:M�r>�Je_.p !p�6e� a�M�m�.�� e�� F3%��!AB\�A D�9"�[ p"{�-iv�>f)�� K1 �6%X�O.�*���)�>m&p=$--R�!�%��{e� d tw1�>�I=*dw�P��(fd)+ mo >!�*�*6S ^{3}? 5p�5qG J�W* ��),���nd -d�hHB�>�� -d.M����4��1"I2^J (|f|�-1)R AsN� 6;�B� �F2_% .��R jT9 Qgr�2��p�E9(.1�[ 2@1-d)f+(Y2�])�A�-J��]"�C� X. 6I]�G )Q\,NzElF�.�d/ZBa YS������ly�߅}.���lex:�9W-�Ο-B+ )7 f(d-1)(1Q�2�1�z�a�!Z }5P \*�EG%�=� �2�( u )�) fFhsB�2� f1V� B� � R� 1- �d �"��] �%�+��.�\,Q~1$ } Q\n.A��-�my��ctf�"�UFLAc>$�=17Q2N=A-�# Vn "H,e �'`a �f��� q �b�=�|2t~Ta ,�z�� ����XC/�1X �*�>� eadyG �&� M-f=1,d=Q+ �su�h"�����2"�Jx(IEY Ls0&� �'�Q�g) 2��x=f �,wR f_@0P  k2IE"/ ). SJS!�GVf�&M�,.  \ askF BF-�"�7� �Rj��<.Y�&B � ic�Vn� �t��� `EQaHo:31},�Li) (�+ remo"�A2�� ltip�Lb�p aTx'X"X ��n<^{2}$ in` the inversion equation),4 standard rateTs are recovered. \subec= {The puls3L} \label{homo-nufl-"} .Xsimplest multimode soluND which arises from�`RNGHI consists in regular zDs travelling along6$cavity. If �geneous�oary{\is first destabilized by=,$N$--th side�8, $N$ identical�!,present� ultaqly inI�0A semi--analy Dstudy o� Q�Lcan be already found!h\cite{RN68(b)}. In 1989 Fu Z�(in detail t1�s and�ir! �ty)8class--B lasers `DFu89}. The results�8Fu were obtaine�bUFL. Us!�r2O4 (\ref{re-f1})�dderivMprevi%�Ip\ we can not only quicklyQ�s(m, but exte �m to a� � out!�2�8 We look for a9}of Eqs.�V� I�I�$s at veloc!Z$v$J�(To this aim�introduc �tnew variable $\tau ^{\prime }=(-\zeta /v$,!I we ca$de% follow!�expana�ps \begin{eqnarray} &&f=f_{0}(Ue0)+\gamma f_{1N(mathcal{O}( *L ^{2})\,,\qquad d=1+  I_/rm{s}( �)dVX% +2Z Zl \notag \\ &&\frac{1}{v}=1- k \sigma \b!+fL. \end9 %A$also assum!� at $%$!a 1 �alt&A�periodi!�di�c9pu�s} x>h+NT)=B!G� ;% holdsE�$x)�,\,%�,\,%O$, wha�$T$���dur|A�a�le ��E:��snumber+ $s circulatAH:� Deno differ� i,with respecta|>�$�Xa dot�|$leading orA�y6�9GQ�(\)�%�)\dot{f}A�-.k%%�% &=&0\,,ѡja�AODd}A�-1+5Av 4. �� 5d1}1� �E@��get rid!D!o8dependence on $I�$$.�Mc� =A/(1+.))3verag!�botɎ��Eq�� ���m% o�M$0$)�zeta_{e0rm{m}}$. We d!�A���le!�Ghleft\langle \ldots \right\r $. Tak�in�occountu ��aN��5is rul�~Eq.�4dFdz}),I]<$\chi =\Delta =0A� e fi��atY0m< 6�A<6�=1��2,.�8 :8 A-1\�L o% If w!Q fine!�{0}i�AT$I�%� � s ���MWI�IE�A���$2(A-1)}{1+i}IbE�\,�&� b-f2>�I1-4\F�2F�� (parameter $ u$E�b� termby meanE�A� solva�Anext m� robl��F impo �^o0must take oneE two value��-�!Mta _{\pm�6�/1;\alph!�}!�Fvw�Q60(A,e?��Ra���b� arii�s O ty domai�2�  given!FsM�8� ra� r2G , �at ¡� have je"o� i�,!�H any pump $A$, reflO   $]�I :  length��"� 8m}=2\pi /\tildemG;� corr��initialy�sm�A� a"- � � . 6  observ��ate� %�-f3q d3}) %Xa Hamiltonian structure ]�be bet��put!Kev� cMG�hange of"� su \ln E�$, $p=E�$>� �-5�%� $x$ s $p$n�xeNapF�xyWp81-%�rm{e}^{xJ pF[�o���dof an anharmonic oscillato mass 28 }^{-2}$ subjecat� e pot l $V(x)=6�-x$. A� tana$ mo(� ! system!�energy��g� ��H(x,p)=J>��p�� {2}+�.OH5 K% . )��2zx6yp})QT�throughU�'s9YGZX�;cesA�wee1point� x� in ) ax͡p=0$. Hj ,}aJ'=V\� ( BR��) 6\./xminxmaxF6)1? lishg re< on� �w� �m $. F�&� H})�bF�p=)� \sqrt{2}}����} H-!�a� 5� ��inserA�in��_x})A� �E�t�spent���}"to movev -�x_=to2}$F��_{12} �1}�6�}\int_{Za�_!)dx}{% 2� B���e� complet�wi��to go ��\)� to )� Fo�@%J�� it� b�lT$�[ /�N�h)�mV J-2�:� -@$NA#M-��9@� -D\�=H 3MG!F6 F Si�L=* %�qe"� �du^)� ��4:�Nq;�J� $>�})' s to d�  as a fun�!� �a���!�[(or � I��$�th�B$ 4&BpA$.1�$figure}[t]�center} \scalebox{0.5}{\includegraphics :10.eps}-�<cap�E{Maximum�ens� b1->��r�� ��$% \protect] 9�%�(2E�})Ź.� =0.7M% 7 V%�}T gpiL he bifurc� (is supercri/�Hsquare:w�" ��E` numer�int!B!1 laserݢ}�fig:7-Y-�1� �1r� SameA�Fig. 5+: �!c $ZK 4.22� r= JGb5E2�8:�E6V` so� s� sponE8��signs? 2% iIt�reasily Tnst� �a6e!�l2� Ue�a� $��2��$.��� �]a�, a���&� 0\textit{i.e.}L��� re�qAce� ��$I=1$2/ �4� J�Y2+ }&� N!7T�m��er�.~ F R+�4eq _{-M#�6�s emerl0 �ively,��}upper (2d�lower -�-in� . Gen�  argum]of2theoryE�oboI?�*���sim�onIdicXfO-former i(ble� � l�of��$=�� (A)$ show LG��P .8qFq76�B� or\ q�Xqo9 ethe�1��%is larg�r smalla.M�D rm{cIn�tsK�m� �}8}� con=red a�|a �}fM2j,F��is choc ![��� M�]exa v�bad\on�  ! !_� �� pA� lost�  r� trip� $(-k\ R�)=0.51�usB atfarY��� is�2�$� 5�!Amin�% q9 ,�0if mt-���52�K5��12�6~�is $A6M13.055$6�i ref 1�i-�O ��_{N�i $, Mdt6Y�MZ~lxkjIO�N�2$,� ia�termedZ&K :2 2�%֥*8id (dotted) lin��Egq���le (u��le)>�as6���h�� �e ). W# A���s��.��t�� belo�a!Gil� thres up�!�:|A�ň1Jv�Wt coexS �-�Wl:- o�, seei���i0sub}. Howevere:notaӥY�happe��e n�Aea�u 9P��beI�r� �� �Z��ymbolAe�e peak�26 ��[ A�_6_ �dynam| "^��e agree��9curve = �V"�d u�� a�:� /�s ����!�I6 *�E($N\geq 2$ w� �!D!� !�!UFL �!F8Floquet method.� D�!M eq QY becomes qo beyon�Zcer]!I�1 }$�� _s��N$xo����V 914$�� $N=�I  }=2.339 3 I$N� �9?%saOs more icultam, 4our knowledge,�re�}" unreedVF[$N"� �&Z$%�-numreI� N-" illu` a-��+U[E�] F  developY�7 )�@�$���Xe�way4aF��ine "o!� the E- regim%�!pc, skipp�all"p ev��aS)�an enorm� advantag�T�utal �� iew,A� ause�!�Y�U�eigen����of�C^��meU�<�n��iIL. But"� �~u8itself.�%s�G�e!vto W%q%N��s�^� J�� {eqF3  eqD3�w� U�dar.��� At��'^ of O�a�DZ�OA��Ie big�==DE�3aayM�# g|E��%a�,d Runge-Kutt�t�re ��o%~ $WrE�run fas�t\ !^%s used����S! t!� comm�belie�|!�!Nal=�!Jn��LM�UFL, QSJ"��:�m�describ��per��a���w&%�. O"�)^, e!ds��*�+ requi a highQ�O��it�_ a nontriv��Q�J �y �$k� itud�� di�� �W 6a},e�2 situ�_ � ly worse^,seaZ n. ��it6 Fin�* "�+a�al �9s� y if�R[��udy���-fo5+,:&@�mirror 2Q )4deValcarcel03a�/�%?,Aba�ple" sequ!wah��o,*�to*=(dFnondef}) uin #%�)&� #"�E�Tq�MD !'�JrF" !s"�* \exp7&0[-\lambda_{n} G-\psi �* )�]2WdF& }%"z$6@ )�)g&*$=PSI2ith $ �= _n$I�_nF6�,� 4characteristic"� �eq�$�-�rt��-� �Yk\�#-i���A�q�fa���e $n$�/!��6 ) i 0 wo�A� � : (i1%!���e�(i &/j$�%n}�),�-��*� j:w�)�$o\Uzk(-NE[IkIY) R�(% �-|.�=\A�� - d in�ta�i�(:�i� �(ly coincide�! empt�:z$!�E"u�$f$ d�)[ &v*fpd��� oi�!�1�vg.�tat�s�� ider�0pl �F��*�2rGEn�� z �B2s � m(foY�0 =0.0T0u:1pu���1�rF four&.� s��0e s; �pared.�+54�9� fq �u3r.vu9uB%Hn �e�>5�[�p6&%:P` w`oo$ $ uming610:T�*fo�&!�>M �ll���M�(:�(��nxt-f� d�]ritten!��o.Bt*ate%*�mm�-bla�f9'�d-�� x5G�{�P-4f($ them. In ������1"�!K^�1f %0,\d3�A=�X&Km"+ +"7.F*�i()����B�#� ��� *� �:V $fJ8$f_ �X )=\sum_{n=-\infty }^{+ e^{F>}f� tau �F�n�- � �7y2F%�q��&� m��� �!�6��c�$2�@%�s� NEEicae ampl� e $�d�M�} 1%"}{d� }=��^+\sZ4u% 0}^{B�% }}\!I 20 -�*& ( 2_HU|(p-f)�­��4Y }%a��Flq�e�T�9 a�of� �j�1, _{l},\,l=1,�1 L�o d�)atahne�.o�� �*A a�%�oseL�?Otoa� m -EA1�9�s�(%p)5)�$E�Gp� !=p-aM� 5 $% d)dJ). �e>uwRoc! similarly[8��wo6's:��&;�Gz:A�polarizI�"�adiaba�# ly eW n!�� 8stiffnes%�Q���e �!d2pH�X��B�K>� dis�� Summ�ing�Ewt�2�� eren��to�:"hly%'� �� �^�/ .�V/ Z,� O>techniq@ p.PfKA�(i# �P�6�. Mk JF x�ihbeF�can �� IN1 ). O� o�  hand,i�D)�6%U��7^\�l+/ Ms�=) some[&�1 in�:� referAR!��ions mad2��i�o!atM�:�uAI� �� hardly dnguish��.60check!#Oc?ct.�S-��\+their}!�ive5�cy!� K ison am�>�2��Iv? ^n*6X>� "3� ����6]=� ch�)(!p� �" &I$�+�&� e"�) aW3h=c�2[mak�'���?on�. #*@)A=3�3a�>�!�%,A��$\&$&P&1B=.�2 � w �$��=0.357�'�'�U@��=I�� iS$*�J 5 =10^��.%Y  10Q � 13�!In� s��u "� Q=pkQ*%+ aFto�hasiz)��� ces Y��e.� mG Avide"r.�* :�Q���" 8a.aM�/ . dashez.�)< Er�.�l,}o �--�Z :� As 3�-h� �1��&!"\Un�"�'a���I�aʉ�. A�4Daks ��*��ios����1� 0 5.8:1.6:1, sA ���lj�still%nar�I�� .r01$�7V�6Ry� ut 7 ���(� ~�55AL R_C�sk$o�La��2ay'blewE�s�'C*����q)��? behaviM5a fibre )���1 \sim �' 5}$,�'A� p��# toolFo!S&�%W%mi&x!&U�$An�)o�issI�q6 !N hav:Dfer to �*]l}DP�$h��},�Y*2&**/ ���*o&"�e�ol�E�&�! emis(C!�N!�"� �&��pas��yeE\ow�>�g'$a�may�E&.aFB under7�*' �C ntal�+���& .�.$} : was#�Fome�>�!s &�&h�6 V tre�is quesq a ��Ebg a�sec�$papw+f 1968�,*� "�m~ p !�r!�tom�e�Q ��?xat F�u&iP*Zw� !�s� &�G&decreasb �'�()�"<0% :�=�@%�jlinea.�G��X%predict�- si{A��2�eyA!lvDq%�|A^�<\ -}�gr�#bi&�%�e.M }$�XLa�uon, Ha�! Ohno-�76,76}&(���Ŗ�2�x� Ii�)e2%of� again f�!ey���6�f�rg.��.,?HtJidkHA+$ �E� wave�1n�CI�ig&4q� cess c�x�qi*. a �1et al�2�I  85a}"�an*x edJ� (�a five--EStrunc� �� "&��#exQu q e�6!APle��e�u��E)up)� byIJ�% _) wh�>�a&unambigum �]ZG��l of*� w��]MS,B��m:�%�<G 2< (]:)�91�>qk�/ rm{c7m�_*�,$). F_ ^Car�?d Erneux){ 94a}���ly "!$s25In� a sl�E��G� �>2($ �H _{||}/\kappa \ll 1�.n�)�,I*ŷ8.~#� I$e�� "G $) $��(s� i� rYrr�� k�HIP mean��e1*� ��J� coulM�� �D se." { %T�t��c� I�. N�-theles�A����L;"a P1�+�,Q �.ʼn$r&lc}% }=�+)�"�!*�o Nt4��5 "��.�H4rH$*<  iW.�M��f"E �/�Xf�!�1v�!%B$\�>�HiD�2 R},Af"�Hpn!�i�� =�1�@��$� , asykbv�.�:� �al,�.%6O:O,y�"re]J[!soCAz�'�"-EbEuDF�^6LF). 2911:]&�%$��  �O3*� b7 ,Y �b�Qof�;Ol.i���� =� Ti��X�sen�̱�^$ X ��", �is.��Sa�cry*H �Fs ŕ{Font04*����b^ :Y:,1�!�5�͜1}�&B��QB�F��aA�6("3 ��.d)^���\"� �;6I>!�2 &M�c�!�� &��)}e�( i�\*�G1 ) =�@}�.�I_o0rk�)�iCV .R� l� "A"A t��.� mark �B�E�si�GlthougI2�� ne� AsfMlways�'an�4%<�� valuForee5lyA�& b"&@ BA! is m6�/�� �Ud���G+�,��l-�'t�5 d @==�ex�Ba��*�G�����|c)M�:�s.� ���Nshgb3 backn i!t� �7n�cu&�I.� � �8ee9�I{MULTILONGITUDINAL MODE EMISSION IN INHOMOGENEOUSLY BROADENED RING LASERS}"2Win� } U�6nowa�@4!U�r�!� ��a.];`+(roadened acp?8um6� m�/ GD@+ kLOof �W ous U|� � e:��ga!Ysr�Z1fMBwBuare quas�.on+��of eachFl�Zk!�"}�k#w��se�t< �@/.jN.M�� 奷�1�s9 picM�wA) actu�~�:�32;ly�ed.�*�;q0�!-dja�E�h moved cloxD togem,��irAe{:Gg�O�M"go �>�� ��.%�*uJA=!Vs�!ear, �8l���Ksatur���ec�"A�i&]!)�iaEy q\i��[s  part94"�z�3y��,-!"e�*ie�f.Xw image�b�o naiv�wT>+[sZ�;��:��ARabi--s#%�in7"�� eads�,F�A]i.k ��n n%Ql"0 !�ise.$,:�5 do�5�. af!�Z:��9�}? O3� Z9s,�j2>J�t�?,j_in��UFL\ (�� � ufl}U"t�o"�2� �/ J5o`�I2FR� pay !��3a�*��+�� 6 "u(}!6 ub-� {Mod�`&D �mod} ͢B�d%o;'awco:R K 0ed two--level��R� �Xe�SL&S�Y,F V>6  a��hof"�S7E2+��a uni"5alt� �7*A� A\ ��s O�^Y:� WeI~N �b�+ e� Lo�&zj~ ݬ, fu�r'umei��s�"x"�]�U_ 1;is �>.�e ��G{ ic ��}�^z/!su[c-�. �-by@+tV3*jAeB�<� e g�H�(E�"�c�0H�2](V(�E"f&? x)�Ewe�ed suE㡪.Y ry^��� ��1pV $\omega$.N+���!�ad Mandel97, ,85,Roldan01a b"�0e&9Y�( \ al�Fd.}+.�+� ) F( �* &=&\sv, Aw,N�-p,d � \,@AL}( )\,P\�ZU,(mod1ib} \\ .��P4,F�g�;�[ -(1+i e )P+FD\�6�6 mod2^oD�o j1-D"�VRe}% ,( F^{\ast }P {)s&] & ]mod3i!�e6�asuj{&��?A�m:� } F(20)�V!mR}F �)82x%��50* .���% N*qF"kedJH] O negl�$�Gchi =0�L��ce � �8�Fa��*�r���ugy �� ($\d�_ Ia�"ZeM�)---�) $:�/n�B��ed �#ly�&ya�enYpe� �fJ$Z��YZ��J:{+$J{!(�͟.�5> popu!Win�i: Kg  molecuB3 detu�b�[�� $�@��e�@��-�5��!�_.� �av�"%T&�) L}% q�)=Kt&�)�s�12� ���ic�-9�al �P ��re�#s $`9N� f� 0$\ $(HWHM) $uJ:3N/i�--&!3)��-1�1o6� �-a}9 \� D+��JI ��m�nD �1+\�;Z%X]n}v�)��&�^�J� �#�1�Sa> c-gT)�N��dA�% }1�=--�^x .x-�RxRtr�% }.�j�fasF �,.,h<jXindexID �l� ^) n}-tJ�I�>^ en� �-�@ ($nO �(ow.a,��� ��p�0� J#D���0�H � iJ&[ �}"�br)i�M hortL�"uu�� �J�B��r"i)0�ker���NJ +t#$fiuby Q�� 85g 6} (sUip #97F-o�4E�at �G� $� v6���J"�h0jDi//l1OjgV��{ w@�$]�aGvpth� �"2}�Zser!��8�� at publ�[6���G�aails. *�Z,E$3 � i�x)ionMso�!�*  --of&\-$ ($F=0,\,PD=1$ �v monoE�I�� �as�lO�45,�U 0}=F�k$,��a�Y�Fq{0$ �D.� �+9�!6-�Y�s ����p�T 0}=00H[exk1�u](occurs at a~ $A=A�\equiv, y$n,`NF�! *�$&�" $r=A/G�# �1WE%J+r�\��R\�( R9�Nu}.�grŲR6�(+I�}, �aR�P�% or%��3 �� 0}=r v*#-1+ �1hiu !u- q94 8 8��) FrB�+!�$u!�� s -�r-�FA� m�, $R=r=1Jx Two �2ma"!�n } Let uV`vmo& arC!=fS!�$na\"{\i}ve��ach: A=Iqa26��fq�"�a"�����./+{MtQ8=a ���^4b�6a��b2 A�ate�n " K���q/A�wN_,"Y@�sa�!s�e�i�)� 1���6F� �W.i�?���"&�!O�"x1>J (su�S tly)�&n'�y�.}�� �$ (I�!_�.su{�+)* 2N ):@O�, %M"� $�B.o o��#�s�#su)����>k %y��4"�!?-&�sq'd@Wbeeu�1F *�.thr}}( K)�y���-E }� +1+u�o )V\,\�a;>\, :n,Bp �pa._"x �cioJeEj !lUc"\�0�/&�/(Q+71)XusJ��KR.��:��=� � "�-S/(1+u)$*�|5�p� fset$VM�Y&Qk y*5�� t"R "�hB3�nAEu.�,=])��amF�� $�\ �(!ar?�: rele�Z "�!�#["�0�r�Qnl:tB"$aZ �d4,`C�&,uj�n^x> �'2M" $��* �"-0%D!-6 b}}F��in Chap�4a��( 's b�~� *c �&� )�^� J�0J�( Rq[�}� M� &d v-���BC &=&R4(1-u)+R$(u+2)+(u+1�.� p(R)F�AH%� cros�laxo�>tuC&�CR}]a"l l to zero!T �.�q6L. By u� &Br� R U� � re&� r`A}}=:.} 2R(R+1)}{��*i !X2> �5@� %G>l� rm{B� �}-�$�*5 :nd $R)=)R1)B[  be�"jRf�32)�|se&/at2L5 !�aj�տ$, ,a�iRmd� ��-N)EJ�/L,k&� 5)2(�*c�5admsO�Fva�,f�m^� Both � �E{K�SA���Li� �% 6� !},Wggq�kisU=�'ly =ono1as S��5cox$�b�HingredhZIs*e�:�n'�s`(eN 8��bAd�(�+"' �a&!^�:,ains why it !�s�)� r!"u��R. 2y��-�� /$rPd2 no FE unK8 $u>{9:� it f8# [aJG �:�("�( (�(�M�@ entirely !�%>I��s)NnotAG& inf)�ab�94��&cU~" N�!C�%��9? ponsibl5��)��5s�`� �@�9 ���ol, h�2�e �%r"*{ p&,Q na% B� �\9�.�� � physwCr-i� "?:Mk$uO/~A forcatq e� mies�I3an ex�e"``�� winna akaP ll''&�a�-��7on5ofY� Q ---Xwez-��be�/se"� �zD�ge�iT:az;M9E"�i��� SZmred6 6p9� �,�NcunQ *Bt w5meaA�at� �rb!�� w ~%��spl its V���erron�&7)A�5���"a.A�q13��d�?i;-}!&��ik GP�jm&@�!�B E  gen|"�i�pj�� of"�O>")��r�@O�EBA�JE��=P7��� 6(D�7%qR ��a �=! �*t spa )�$Mׁ�7ng 9.0R��)"]]R�ed � �d2#*P*FtE�JT#yrigorou�."� byo �g �an���:��7�B5�Tr}�K 9B $z�c��s|P�1�9��t�ato ext2 � P��.18�!��^/�2ea�t�D% *) �re "O5�.d @�vC,ly"�<��ll  OeJo-�i��*nce|5:Y. �v�v�Fy�C:F3��~" ��B aA U� AQ�=6ы1)$�3�er17�E�y�< OeqV� turQ ut!�*�]D���am���K sa-(4BfB����*��ach��B 8� � !n8 �!\J�&J*O}!(�A rx�A;'w�*nnQ�ed�is"� *��& 'P}�0&�MBe�}��� &B�� ^{4}-3(�-1)�[ (R+u�-R-!]4 2} .�+RB��D��&g ! ��B�R{EE � :�!�6{=<0��_4j�|5rXC{}n��6#Cr,"�A��N'CA�ſ��� 6 toe�?lin`8a$io$T7r?N jDayHick6>Iz�� Z mit ��H�. A�� X"s/ z`nz6rzrx�9 $u=4$. {}��C (Eeu&�-�-� 6G~qk�46��-i�), n+5w)gdi�Sd�1 1!�!dexact���T&z b�%� (22:e Ref.&�Dc��o1��*t"fJZb�P3}�1�D=0.1$:�`3�-� BmD� ar��F8j��!��.� �M6�n&2 %=influM !N6&�> o�.0CZ� �C%M�� &�Ca�r�.���YBf���al��ui��,i�6/ r,n'. f0%,"drquantiD�X�.:r%c0-)^f fact:t�!��4�ly�6� }"�Mk;2.c}}�_5���}C:., \!U�$r�0� �.�&�,�0�.G(ͮ.Hc}�{9-36u2��@)��3��&�c��2;12-33.75Z?B*�$u�sd��1+32/�� ( 17�)0)2w� " u^{-3!��8/3+80�a"�-e%�� y.�3}E��^xsBacx6� (���ݩ�Eq�ky�(�W) u�&S$�4\la�QZ� 2�J�z�x��RN (��2�J. Hsol� ���� *� � �%e�. S�`�clu?Usq�n U2C�n igur�p �f� a V�N{ r�ZEt �$" se�J7(�+�2�,"Y+�Q �Q; z !dasymptl5*� �"�4:^�Q % )Ͱ�f�0nB�A�+�7)�� ��6<^�Ga�� ity� U�6�U6�^vzi�wide� "~ $ (&� y{!�_K F� E8�% �)>i%�c.is&y))ri)%s&72����>� �&�5Q �B���I��� ����$26�;!�A.v'SA�(")�N�Q�)yp=r& e�'��.� � nn� A�l�8i�a�?� "�K͡h�!�2x �z /!4V��yEs��",�% }cr100$ m 78$632.8$ nm HeNe^><2;�,Er$^{3+}$--d_~f.�J>�B5$ cm�� for Nd--g*5 Z�93$ mm+�ia�ne�N  � �>.�.�o���}�9s�wN� Gr�Zrm{�Qe+/G Qs�]i�3on:Y�fG�KA�N5�nVT �s"u�Ies@5�?=�."*NP ! &',�B�iO�� t"�&� �Cƥ�u�;�����$mJu�\, o ��`6/1�\�h�)RI � %tBm�tu�wtS�u��.C-��"+ �� mHe���afar7��!a�>ig"� �Jin=G�I . Q*1w/G�1ryt�4�s}Ti� vti6 G� �7���)b=����E��i2�}J|!�_lF�Dyx�� "�RJ+t:�" �g��A�2�2�H!�l�+� 1��7 taskF'pewGlR��H�EH4* ]1c*ZnRre K�X2�K"�7&�7i�W�E"�i�^l�-��lEK���io1"e8;)bMa�la run�/L�or� an�month��Da R12000 Silicon GגP3��or��is��he&y�dL� of m�09�{d�a�6��u[s,."%fbn4B �i��"pLjPImptTej�H7� by B!#r��^a{ 1, 2}!=�lyGn��U�&�)i�"*�2�q�vf�I�t�_us>Ovu��/�c--�Hm��<third--�� Lamb orTN&�l�%�-ed�E�a.Q"h"�� B1#�nu� {�.�` *��jh!�&�Q�9in�-�u(o>��� bp4 4ib��6K dL �*Y >EP.�6 ��e�fixed�3($r=5�42�:� =2�DJZ|(�$�y�]A��/)e �'e aseUJ.�� $ ($�1},2},�3}f A�S�fng��WAz G�0v�7reeU  magnitud�&2A�O*j ���@�Odoa4so�Je"�al��ea�1iym�ata� !"�" %�-!/*8Vdel (�Wŀeh]� $+�eRi^W ich �-����e, �oW3���Tta�J5")��^n�7r��szs$u��A"� �T� l�9v� m.V�m�&C_36�Z�b}:Q4M�}� zQ5}s=R��8~W.�Q�r.��AZ!��2�o�%�A�cal{R}��z 8 a�T �:)5:)�@T vhBqC  M�confir))e%co!@4B-:?Bf;: Rat.�� b�([�n58"T)�'!Xt �!�i�s,p ��JK�Tf��� F ��argE�N%-v� 0a�5߃z2�"ra�X���#Y!�e.�nd:�*��Y.e �����B��� t steadRatJ�no-? lock�1�� �&#v:d&P, all&�2R� ph+7"�(�&�`r��(remem�%��--�can�$be6>K�*�=/8�+�`r�+�+ۗk(.f-:'ndZ�Ja/F����(�?)P!�!elegit�"m  ���$�A� ETE�&�522�X �e��k��*2D on�y\uZ 5�i#%��l�Rfe�'�A��  ,q�=j of(X�iode�eYC�#�}!.9lF K��F!�Als :-taZ!ތ ock,$A��W to r2O� M�5} a;y:':'"@ %�=��.���onNL!&�UR<@B�@�U 2�dJ�@B4A*arbitr6�n!� �,_ 6�&�#uJ!��8(&�n6�Z�mS invola��-�[N� T �;�zN �EH*z8���Y/�'in-�k\c.�!b�!@!�6(&�('&�q�� p�o!J!�o%� ��"Hst�?&� �AAP?*h\�^za <"��1%��B6�&�!\�o&3y�"M/5�nj L06��14}�[�N2�Q!@�G@��ual�9e��efz� :���F�!ڊ�V�F�#&1 =0.99� j�l�.A+A��2 v� (&:)X ���%�� :�i-�%u2 ya&`w�^a�+un�4at 9�U%0i�^��bow!$�$ �4bbec߅i�=e��**�t �A����e\a�g��2Ŭ  -2E�Z�A"�Rm=.H(]< T ceq 0.538�>Fortu��l:ڞ1$qL2 "�dZ z�F>��:*�*��D"qY�,u\K>)�T�� �*�*zA9-4�" [ 1-�>u( u+1 g C ]�1&�#R}�*}{*�� I\ƒ\ln�  Q �*)D.;"�r ��E"�"D&;���i) &��6MV7h� r�` typo��X2 146)� >�."eF�&5}2�YB�ho�%o.� �&.2}7A�@ �de�A�.��e��'� JuFs�%$u �(a�iin.VyerXft 4)_>0.9$�F.��qх�on�7jMG% M��41-rTV@��.��`, h�an�?m�'o�& yXe�2% .>� bVsame ,�-���B�n��!�sD&@ce�9�BIof.��L�5�V��' qual�ve 0bge]ea.���re�P"�]�n{� ��Y"Vc�@-�~;��# sugge��%"76}$�1N#B pos�8%��M-6C&�r!� do i���F�.�"� aV��';A!g83�g� �x$ ��8V�ens }AtA��^� ���$uI�� .\Z(B play�-E;YzrolA�I@�'S)���Ocu�e: p !�N�{� !�e: Aq �/�uhGag"� &�!�LM�F�,E$u<�G(:Y!!u}�.7�e��k��b�),')(�K � l� Jeno�nb? at $��&�6E�!-�#�`&�\� ree-�bn7&ur  �}�>YX-loss_Xre.�Z �co7 ed, �9as� i�J��Uq.�,!�ce% ��͊c�K"| &� !�e-- an�u�-r, a�wt�a�re�+��"d-)�K�asb�*�?�3s, #RAP�$% 10 $E~rm{dBTp0SJ ?�%�{y �P!���oE �b!82:M!@s�a&i� !`��E1!?�U:?z52��%o-fP�� av�����!�Jm-P�i�zi.��e�"7CP]Z+�] N� Per!B SR,. q �1e�2�.aU� -�~� �heavy���/�mG&� �.�1�g�%��"roubl-@�J ffic��4s" A2atoo'.�Qzto�Y6��C>@ �!4z�� =: o)"�phmR�xx�M�{�B).��% {����/ '��..�U�"�;&�0��" c� Voig�vA*�.o�s�!��(� �kby.� Ac})aP+-Lcmin�UAAourag*wE: Accor�!�&Q B,6vs"Ó_��Po�?* ("��IsR&m "m 0�C"ard!�Hl�Q�6�$!oP/!��si�<��;�6��� ��3� io (Gxquotedbl= � o�V--nine2"�I WeissVia�c��B�Fw� isQDnp�2�"m2P�r\R&v,�'�l�Fi�'~���^��e� a(�^(edium. More"n,sK�rz2.~(UM ��� titu)w Ԑ��Yfo-"�(�r� � =��o5T� ac�&�)� -s�~�� ch m��likWHq>i�5�2�y;JM� � . B�T�h �sEr&+-er +erj�HYk osDomiEWcandid�+�ear{�WE��W: s�F���th�%e�!sm��5an.W��De��!��(�4i�-R�M: %⁒ Z�2qaMG(ochroF c ���h ,? �*A1�'� :eRR%��E� ,ion*�o�bm��Ju�-a��PalA�A.T EZis  pco|  a�torP��~i� ul��Zi� �#i� M�&�HP�!] giesY�P� )�y�O��:� &Q� 3AK�$��&�, e.g.,�cZhang96�Nor/6{N?qe"Fe& w�RsR]o��fi@�rEW�8owR� �Guy95'N. �(ac���v��su%�:1��.�\s��!tQ�] k!�e�poC�e�]>Mj�*mv�Lmai)��a"���^. pC-j�l"~��A[ bW�� �q^k stig=y�/#agiA&�#��9  obGLly�a �vaOe�tomea�qr��s�+ta| �~Ap:� 6? �/anZ�Ha����{ �A�u2y� H9"� -V1]�j !�l {A I-d�!1��rA9} Pro �&2�.��+� funda#-��u )�e�U*an%o%�D! IbF95-����ba�i��36��Sos��Au��-�!��#�/ .%l�g�mz� �G9}F�� 0,WDM~�fA�b�," M��k�ou<�2a�steere�y 90\%Wa �z0. A2�e-inM�i��opc iso��e�Md>�u��An��a�fi�J��x; a�y�ve6~i�Y a 15~m�25�ow dopj6aHc%t (300~ppm)�{ a 0.829 high>3$\�� x$50 =E!�.�{��85� 3'�o�2mB pigd��ugh��4-�'sf}>�!�a�10~MHz?7 �v&oC"�9�p)ׁvw�`hB an� 5�A�t MZ�tored -]by�;�photodi�hooSE޸a I�osc�p3� RF��um�z��or U��g�-�| auto�ZE6�A� ble cw&!��  ��m��G79S'r.� al�xށka,p=a 6 !� �e��aA"P� �SaU� �S tor'�B�.A� occaJ)�xU'�(of satellit{�O�"]  � sā�����D�o�  a te�,�pdth (Fap�few n�2I0��=&!>6zx p�A4o]��+��@ �:<�MF!ZimY ndow� 50~p� ~��i!p!no2a�nnd��s�=5�,�od�r�M���; Eb�!�46@YPH1�$Pj�H|!�w-���ra�� ha�ne\sinusoidg ��!( plau� rn(!Ta{Ͼe>� ,!�v �'� f�'i�!�& � ќa�!�) a;varȎ�� aL � $pr9eE�.�Hs�$O�iv3�"1����nger � �Os6�er��a� e��eM��.�� v992�:0+ -upVaE\, ��� , ba)�qY�up of ��r?za� o&/�2�UA� az�A<lso ad�.N��tro�N %�)<XOM�co���J anch` 95\%�d5ṁ)�*d���O!!2i!�aA=!���EE�:�Atyp�,0 13~m�{� �6k�-.t% Ey��. Ap,F q� �RQq�;q�i�*]� 1.74F�s3.00~��RF� um%l5�� 250\AatY�#/�� �L|�(+����e��4 *� !Xm(�Tmbi�T �biref� �+ plusQ!�elss� ) !}� a��!�i%�r^���` V7N"�WP]� Ro�"(NPR) m( �\��ujme��h���at NPR� �e*�ou�>�i��� I� U*8Uup erU&f~��D��Wo̙Յ� ��imG ing qlE+��X��5rp�f� mod�������W� w�A l$ly� �yeW�"S�x�,��Y9<nA I�E��ime�,�#e�� gb�!� �AH=nt*P  ofax dom ���)�y "|)�� ^�)N� !�X)�|D+�5�.�4ras� p> �O5routin!��:inE1P�iL�,!i)ɯ cU� �� de�in&Dg�INPR��*����$�r W AR� �s R?Vlittle �*�) !��w��lAW NPR �.�0�\=)>�T!w�)@ u�".s�*�ed�.��in !���xnd0�� ly�]�oi�4 r� mz^an * � repaX� �meghd�G�Ax-��'��"� o!Ga�a7My�or 2~ns 6,�� 5.0,001~nm%�iCb� *] ��!R!�E�� �O =��.aGe� t�� �n��0,05~n�On�)��p� ' .Y1�"��R$"d -! onset,E��zaddaZb!Ae"k&� �*�_$2(>6FGok� "ar!�vea�*����;a�AYa�voƍoalea �$-8-t�l���li>o<��2� �C2�a��(*���la 9Q. ߎi�2aE�f !�х�%mNW�49:re�0r�Fo 2�. tY i&Ր�ef ~|"�"Da��a�sAn�a9b� G � ��w&���erE��c�de��`9��b��A)�2�)Et�by���7�����%�a��rE1 n^'8gu�7 �� e>�06M���` 8.2���$�2� (585� Er��?:(% 2:B�)+������M�^ j>'A�l=%g ). P��l�c�4a $100�W�9$98 nm}$)� ;5!ulaunc�"� r�J*�. L v� d1 �t��.'A� s�֡8d 9al 95/5 �Q��to�f�E�I�� *� ��*��GB�F�� "�  enwnd44m�sl&� � ad eK�caDm��� U�t] �3ri�=%>an� availa�o�ut $19�!�M�u_���,��bl sh�'5�I�. T���nd !��C@�a���E]n�8�LO--�s�4 adiu xemploy� High:�a�no��!�?A�y�y8+cBly. G#�effor ��6+J��Oa�\Tt%%\���:J:M;o��s�Oc�1esa��hA�spl&% etc.� tes�?> vid֑E�>�$ �Er-Hwa�x ���#/ �cd-ch�7%8�a�c&k$e�F"zalACe�V+vs..:�A��m�0��/$��$� @f�>9r�>E"$ etupfWrH:t�a*c 6�!%��(B�U�$ electro--e�cY�� �6:�>��?7bD20rDL�,-�(fi� ^�lAС 7 a}l (open��)I�. 2&u:����Z��21r�I.)Zlu���E. S�2re (a+R�+&� , (b. ��i�(c 'kl�I�*�Va�b�)fF�ory�:(BqW��}z);` ��ain Yc)  1�:�  guid� e eyN�v'�Z>_ٲufkB22r�R�K:R)Ha�l:� #w;&�8a%�e:�#�D%L2^+*��� �C.&�a�\��du� @%�XFE�;�9 label�!��he��!�$l��e�2� ż:.way��w/�%���s:5>|�J�,V � �e-"���\ JW��]=�I �A �y��>�!d,'��i�>I 24�'!h�t� h�2�� � is�A%?=� �By ($9&�MHz}$) !�excep�. O" ta� qb)�b�%ween 5�= 2�T=8*.�n��B�! )��:o! ij> hopp pi��.ap�C� asCN�a���dge� Ȱ|al GHz�� d�K�>K��&:n�;}td. f�!� � E~ .� �z&�I����"cq0$�nEN*+hundredE��nthu�5rS� nage� . S�P\%�a~m�a� eady�typ�A 5� epis��W_ "(L���gC illiW�1a + ��"WprofiWm!)li algrv��ti�dc|v�Ua D1���K1� � �J�r�l����E�8o ai�M)>n�cl��FumA�� &t�, A�t҂b�[�/surpriRZA:���� Ej�"Aoe�Ѝ��& �'shA�ya��� e"� *Cor�Mn r2�� NLPR}� b +fv "�.2�-Uentt1,;$��H � care�%y avo�y. Giv��A�w phen�~�P!��calP n�)m�� �"'�� it. Tim�j�`A�$07D� �  �rD ��in view;m� s���oer�9 osen!~!%�RM��". UW&Z>ade�<e s��F3o � ct!��T���A��� ^��d dat!DYQof GB/�:de siz��10 GB�l�t�A�sI~Vfeawo keep ^a�;< m�d[kI� at 20~000 Ŭ?�)a��(n�@�E��1RfH�uaǦa�8�"�Tlo��ll���e&beQ�eJan"�u�>r��$�� b�"atbratio of �)v0 $P_{\mathrm{�}}/,0}}$ (where F*\ $and2C1denot!~e.� �eaI�� >�s, respectively) does indeed scale with loss. At low loss, B� >�p\approx 1$. Under typical ope! ngA�ditions!,Er fiber!� ers,xDes would be even la�I�Y er' unableA�$tell apart%�)�s. Foerglo�howeverJ�� 1�%tincrea�i�(about $1.5$ae inten�A� high g�ta>� pay f nicely !�: BA�E�sA� el4ly distinguish�)I� terv!\f A�le mode1k0on in betweenu�ly a� tifiN�is!�stitut� consider!4 progress overu� work. H1Dtwe must emphasize an importanti�regardA�range of%�m/ useda��Z93. We s!� Sectm��9}%�A\� oret�ly}c��&� �1o!�a func%��0M� cavity)#(�calcul�n��s�>%�m��,to account, !�6�%"(details). E� tly,!L!� agre%d �*97alFB ,educed drama �<. While quantita� $r!G syste,�jdi)ooej, in ��i�r ���kest)%w� t leas�A�m� ɸ!,\��{��A�}![e<st@Ŏ �e�d. Fi�� we n3A ddaEAave���e� rpre�e:i�-observ��:|. As w�isa[$ Secs.~�  {�-pulse}, sub}%� possi �A�-D.�Y�is ei��# upercri%� or a subbifurcEy . Ba�onJ alon�� da�!� thes.�ies can $be made. C� a Z},͊? �$ll likelih� im% a �}!�bi9s�Q--R��!�multi sol�P(]j$ )��~ !���� � $iF�e.termitb $ behavior ��; sens vat�:� .�P eMned2�I� Tthe: {  limip !6the uE� le branch&� ] > perE�nm  reach�ue to Xed availp "� �fact,"  !Qpo#@of \textquotedblr�Maxz '��st�bionF)\ (v 9 ��(re occupied�equal am�,� @ time on average)� ա,k f un%1ed.� � � �, i�_A�7ll� whemxf�o��clue0�\�Fna.>.vc= haveq� , becausea@ize%p� -�.�!rtu��bringsa�� proces�Na]$ BrillouinB tte.,!� rmal>$ects, etc.m�\ complica� issue.� O !efore��Y  ques!�� n%� now. Let�.%3frk �;!Etr�o��P97},� e�}e�A���e��X���IĽ� IY : �, only dual�E6V$sinusoidal� ��. Also)9e wF�F�i steady!�atA?es���s. Sure�is)LAatdo�aLa_%"m�r&� �~�` y so /it If)bI9ed very � its firsb�I�%�� stillI]�or�vN $d (codopanm�he� IQ) �T unre�aR� p�0. \s��on{CONCLUSION AND OUTLOOK} \label{coen} We%6!ro�~ erent%m ls requir�4"study�� RNGHI��par� hE�re�*ape �m�( two--level-�!�ly�e--E� four2's, "�I e rigorouh rivI�of0uniform field��.5t��sy e basic�he ��w-6-ewed oua�zd;�J6subject]rec!Tyears�G search A�mot�� >gg� by Lugia� ��"in 1997a�I�~a�%s exhibi \a! dirI0al EDFLM�be   nifel �%>- ��@ve phenomenon. A� ng!�te�%��-�<�yDDb.� �n�e�2i>�. Data " a ��k Ei��pri�vU] �� ven semi-.� &� t�e� \c� s. N��thele`Qdo�� repres!�a��-cut ��book re!�e3��� �xi" onAe�0bottom�CIqmb� �A. �Aa� �.:3 ��.�As��!�ly�S8>�����>=!� 'A $ed' way. I2�3 ing,� :� isk��* �^erb�t�/ir rK /]r. Moreo ��� ��noopl�a a�ral rol�.a '�Eѷ'!�ea+ k�o�� emi4BAZi� roften n�"r%�xm eleg[ than�l--worl..�Fe clos"th��4to Lorenz-typea�er chao �je� foun.N suf��d4 "�)[x C abE�W!��l,�we��"� t"��dL}�.a simila@ y��1}MFont04}� is� ��Psup�G&� Sp�@@h Ministerio de CK 0ia y Tecnolog1A�(European UnA�FEDER (F�\'{e}enJD  ve� �W Rgional) ough Proh HPB2002-04369-C04-01)��Cby Deutsche Forschungsgemeinschaft \begin{thebibliography}{999} \bi@ @m{maiman} T. H. M, �it{Stim�ed Op��E ��F"�!t Solid� I. S�roscop d H@D Ruby}, Phys. Rev. y`bf{123}, 1151--1157 (1961�b�WeissVi�_ca} C. O�isK R. �Dynam L�!4s}, (VCH Verla!C sell)C(, Weinheim,� 6~Arecc�F.!< ��0R. G. Harriso!M�Sel2pa���1SC� �DSPIE Milestones Se` (, vol. MS75�32P�}� a� Brambillm�L. . �P�nA?� �!50Riv. Nuovo CiA�o9��1--85!�942�\JOSA-FI85} N. B. Abraham��2�a;\L. M. Narducci (Eds.) J.Al,. Soc. Am. B{2} (is 1)Ee�I on I"I i8 A\1gMedia�85R�8} D. Kn�A.�Oraevskyiy�% . Tr�ce��5J�No͵ Q�� )��82�0Boyd86} R.W.  !�G. Raymer!L��:T6% 1 2,}q�$\ }(Cambri�MUnivers�PPr$, 19862�AreHarE�T.q,: -1�2��Ne A�Quantum)�ip��Berlina 872�NarAbr!�6[,!�.�i%h�~��# 2�a�W� ST&�!,c, Singapore�6�NA�:�P�]ndY >� �Mal 2� Pul�inM}&:�+�!in-,\ XXV, p. 1-190, Elsevier �(ce B.V., Am��damJhKH $n} Ya. I. 1�Priciple� )1 �s}, (~o!196�M%97}.&)de�zProblemECLu@I�!����6=*# G.HaG%�,G.P. Agrawal�R%6�8: a Modern Pers� ive�� rog.I�. E�re~8bf{22}, 43--122!� 98) ��0 85b}AB���BT��� inglea&� &��/� O� ed o���!_��A�32�576--158�:dHh 75}e 9BAnalogI(�$"rB� fluid ����� Lett&;,53A}, 77--78!G76mN63} E.[�Dn�%c non� Hodic flow}, J. Atmo�cit20!30--141u66��Kli� F�W. �On� a_� =ya�5 Optu mmun�$51}, 47--4% 86��BrockF�JHock�\!c� �--T���a �A�� � :�@,2804--2806 (BK�2�B�?(U. H\"{u}bn�Q�,% Homoclinic(H!��qa���J�� bf{6!IA�A�90!�:� WVACRVPHT:�2� :R!�,rbal\'{a}% n�  Roldn,K J.= Valcrc�F J. Pujol,>!D. Y. Ta�1�ls,���"�ExA�� al Me!-��(a Far-Infra� NH}$_{3}$V\):�Compa� m�M1e�� l}, Appl.m�&� %l223--24� 6�RVVCMGeŽ+2� R. C9rn, V.!LMart\�nez)� ilm���D.��1P ly-PumQ Mole�#��its R&on �$�. %�}, �!� Semiclass�ks �,bf{9}, R1--3� 6�New83��C. Newy��gener��ulih��L& es% bep.�yg1�% bf{46}, 8�f97��86� SiegYA.�i �)] OxfordFn  UK�:g Svelto}� *�n:�_PlenumA��New YorkZ92= TSMe�L. i9H. StatMGa�Ma�%�]��Houtput�`spin�"!as--s�')c�J.2�U@bf{34}, 2289--229%�:M Otsuka99}� 9XM�I�U�}-�in QcJ�u97�9��96"� 006� jGlobal R�EquI^D�+p�m! aa },QR J. D�8��31--4a� 20002�Hill02�ill� �>Hamiltl$D. Pierouxi�*w �% I�-� Co�� 9=Nd--doa� Yttr�Alumin Garnet)`}% ���& 6a!063803 �22� RN68 Riske�!Krmmeda*` & boffN�cA.i� վL2 26 275--276!�66� GH���� �{H�ke}�Q6��l�$}pag)�i�-fluctAGer-2� }, Z1�%�� 13� 20--45�[:�!/(b)�2 Self_(�1},X.n|3�I 4662--467�n:}Ikeda8io ,!�qy!.K� tsumot��m �%4--Bloch turbule!� � 1Su� ?���295--324& 6�)�7 �O�3A�s!B�qLT +�� 6A58}A, 44!�a�1976�Ning90�=--Z. %FE Detu>�h�AP�ex��&�3 s: S*�)!j6�) Hopf.K&� �x y�4� 3826--383� 96ZFCr82} A.C;wlU J.D. Gibb�]�,M.J. McGuinn�R%� it{ �YbJ�!�hy�ȝ��/139--163a�86# Miloy70LD.i.�!@G.& !�a A� le-f�#e70travelling--w�#%� �>@ 3@ 49a93Ay76+ Halford73!��� �Modif&'e -"�9� Eo�a:���Z#4�# 5644--564��76~e aQ�%�H. Ohn}�e%5 -* +e!�RW 16}, 20�T0Y :h � �9(TransiFj�A9>�59��61--2I=:�i7�c ����'�F�: ' or s2d ordY4 haseAW�Gion?},V(26}, 11S1)(:|erber79S��� M. B� ttika�qjStM� Doma�f��� Wav%�Bj33B!�1^ ��76VMayr81}~ ,A5�QH.a�Vollm.�P-(F�!tic b,'�!ofU ��a A�q�R_3!748�r8�86~Zorell�J. 9��J�y d�� ing}�V|� 12!�3�:|y man1�W.  Kr�9s��R� ��9C.$Stroud Jr.�O&�!!)Hig�4OEil al� ta �� o,6 B�.� m2�:�2�6a�16i�: �2z�K. KochIf� ��hom�&%eO!:�--ea bichro�c�� �"�+�)�R' , 21�17��:�"Ja�&J�*�� V. E�nazi,A� K. B!!�:�q�&J Bg:�7 1&ede����%���i6%57 :�Fu��1+ Fu��Ys6ZDy. s � "��.\)5F�]O,;o!�.�":a� 480�Q81}:� �2v�A Y$�<dyOzS�;&�#�y��9�tR�6�Y454� �WV�3v�6]�dDye�(JKAQE:f5^S;.}�9o��B-E� bf{5�99--9m�6xS�:1} }B� ck*��MPulT ��$Intrinsic � al B*�3�cT-L-Ō]6�60�41A!1I�N�2�,�:�F.  %O. *%it}�.`C6�"' a� }�� 703--7�J:� Bonifacio�R� �:���iesd"a�%t4ri�2 abso8��N`&},-\2�u�2 510--51E�:���J8g%s~a_a&P f2'���Ry5y24�5s :� �6' ��Un�P>�l82q�f&2�in Ref.7#�8� pp.2264�0bw.m{ �H." 1ű$%�o��!�i&� {�%2z0--33.xѼ6��D.�ݫ� �9@ ��X�+r"�-!�  p� s: A cV8qu�. a36os�$mprov922.�!�110\:��!S2�X *s �.�N.B. "e!a�D.&� 1�^�3�et�A/7 �umV2?*�25�ԝ3��$1842--1854�635�>��6��M.��0Squicciarini,i�it{Ex/*�'}�analysie�plane�6� "p��V��3101--31�b6�,Elgin87} J.N�gi)pJ.�e(olina--Garz*�T�"�"�9�6�&)br5}, 398�98� :��� � Do7J�"�A�aO ,� D Holm9�Finite dK+a*�?iH9j  good���3v)s6&12�3��3��:& ��PV��(,� Foia�p&�q"%+=ite--� attracte*�?:�}, "� )#Obf{% k 24� 6i�6hFu�H. Fu��AA�:s����;"� ir*p3�:V }��^!40�868a�9�>�Q ��e�NR lf2ua� *�"� !5)�R�94!44�'41�:�Carr94aW. �T. Erne�%�it{>��Q-Bݘr!5�724--73%:�&�94b��cG.�/ .;�4q� w�a$�0as�� uE a deLrate Ginzburg-Landauud^��4422� B� sini�#D!d �D'A,5andro�A. Polit*�Soft &��&�b5� 751--76z96�T"�-�M��- �&V�#%>�d*4mod�*�+6��vC �/ a�;fi~"b} 1� 2618�-c6�$Jahanpanah!gJ. h0 Loudo*�"I %J er--���s2b�625�26� :�P�%92�B. �0S. Dutta Guptݮcw=1�+ �;���E� %H$ i�<2parametr�!)_c�� >)� 7260| �_922` Cast�94�(^&? �R3 rova.% R�3�3c�&�con)on byz5rYmix��in �I4� conn�8)�:.M^�49%40#0�6�#F95��.a�/I egota�E] "�/a6� "W :k &J3q ia�i+ �72fibreI�a�R� 1e#8� :�!Pa:�GCf��, �j�2�"3E[� � -Nw--H�" ʡeg40q 409�:gW�Q.!wWilliams` 0Garcia--Ojalv�_R $y&  Fast_?ru;olariz ԕ�of-��%�*� : i6>A��Ltochas{eff�@^���23�'238�%:��#an�E�l"�$�Vt?�&!=r"}6 a��5e>H>bin�5t"�(�C�6�I�bf{14| 23��4N\ R98}6�EXG.��de>~%� M[ea�$-V]}�. in E�:2��9!�Q2Y'L2� ޥ��:6A Desurvire�YZ u D� Fi�OA���� (Wiley,?# ?#:wP�":�&�|e]4:a�%g fg��:-I�I�5%\ O2&�6� 25�252 :�"I�03b%$n'j�'�F��3ke�<RolR"F�@Los{D��;-N�K!.�:�31%6 1611%�6��Milani�(2he<Ma<��Disappz?�,e�}�r$a Gaussian>�:�)��( 57--�>�(tuut84}�  �S�Tnt III�E� �)�-beam dI� on ph!conjug鞁-beat-&G s@('73:q}��95--10�:�6l5:�{MFl��J�z~��1�]:�SmithDyk.XA"P. �R. 9r�$D[s ih&1~%� � radi�@dm>!� e�C:"/%� 07l86p,�ia&6,�*^s!�E. ���Q�i�����Ut�~filA�:;.671W15_152 �6��)���S�4a�/�����"6 �[c �Wk��*t & i>@��3 041801(R)��6�$oB1� 4* O. L= �Mi���%B�. �y"�K confirmed2/> ly},A�1}*rn�� eminar�3No� T]F%N"8E' S�.�)!--PKT� 2�/�a�S�LBagaev, V. N. Zadkov�SArakel�S eds.)0�9S�:��I429a+EL15 ��6�%d04:p)mF��1iM7q!�eBj 2� InvMI�^ofv�>��>}!+q E(*q �C+186t* ɞ~� %dit[&7 2x* !�CE"��� >�163}, w�96��� ��>: GeY0�XR. .[&�v�2_'207e�6� �AeJ.W,�;V> � AY6l5jCoe�Y�+,7H5�$--longitud�P .K � EGIa G+iLRe�Z.��an01b:� s^|Q% 9B�E f~� B�s:  [�R� E >x " 053805%�6�%q!���E�Y"o6�F�% �� ���/t�!]�%�!q.���q)B 237���199��6�$Brunner1} �= EzFi$%�=H>u� ReguI2(ehUAz�EG�Journr�% 2R$2N6� �2�� Time evol.V@$to6�@�oOstrengh!��&�z���,14%:�Zhang96=L. �Y. Yue�4W. Schinn, W.R%Cle�6EW J.W.LitYI8*l"w$Ap8K-R� - ��� )�L�0w. Dhn&` 1�1�8�96 Guy�M.�� Guy,� ayloM5$R. Kashyap� S��*3 �2 �y� i.U� -shifted$gg 5F�narrowM&filte�& 46Z3z $1924--1925O(: C1�D->e J. �(S.V. CherniqJ.6� H+Ko.�8v�e% �tw�Ed�!techn�!f4lecd=:�6 17�17�<:� NLPR`5 Tamu�H�BHauIa��P. Ipp.$3-&st7Sng addi�=���Ock" �!�er=�F� ��$3r22�022��\end{th6�E  docua0} ,% Templ��c�Lp�PYO.�2H`elsart' % SP 2001/ 5 \*�[{ (} % U. Z�5�MlespacAwo�L viewFto obt�- &� , % 6e[ % ].tif you )X�(s*P, A�-q�>r� wi4m�[M�)e"Ci��V d� Yb�Okeyword�� s �>J���: \sep "�0l�l i8co�*g Trapp� % PACS co5Jf\ 9) 32.80.Pj � �} >,�7A=&_I.kX�^ sec:A�odu�X I�bwQnS!W�gy N �a;a�[�Yacaa waaan�omagn�:�uBWgL a.ci�k�? i �X$Barrat61,H�r6Tpropor a _e li @ayeL9yKY�W (`X�So�YsFB� v gives r�Z�� p�8po�Ui�� call�dn�*1��b�� beE�F trapEC!'s0JUXT96,Guidoni99,Rolston98bSe ,4[�m-i�sIAQ3 {\em �el.}� 1993M,$93}eTl% }7,��B~,�]sub mRauLnbeutel 2sa few sba�er }64e��k%��Wx`h �` �("5q�KQ�}��wvwe �� a>� (2D) �>b��!a n � 8=eam. I�9 llowP`w��r��:��)� ngI[%� lpos�2of $l$�fsEvV�is �Z�)r bf{E}_L(\%$bf{r},t) =,rm{Re}\left[F-X)\exp({-i\omega_L t })\ j ]$ w�U��)1 } �eequ:L�_�w_�" �:�)=>�sum_{j=1}^{l}E_j\,\vec{\varepsilon}exp �{i� k}_j\cdotb(r}+\phi_j)} �c;� nd���} $ &$b !��!� $j$�v�>�;n#\M5n Refs.~6��6�q DY9RQ �*=�AW�d� nd�tea�1�zLS_\%zhat{U}51r)u-10E}^{\ast67)2TD\alpha}}2E:73 YE3Y�2I�p!�ic +*s�� oor9(5U�2N=-EHe�d}}_{ge}F8eg}/\hbar\Delta&$�!��I �@� =ung1he �t4CJ  $|g\oleI��|e $):��eg9"�dip�'�= or b�R�Es�kvels. Blse� Eq.~`^�)� oZ).J)��getY��ayEc�6d� _E�_eW�F�&=& )�{i,j}\,(F�{iA�,E�2�R6�B;{j}) EQ�i �d�@nonumber\\ & &\�ns2l�P-i2W2&�げu^ k}_i6Lr}����1J��8u(8)�po��5&* ��clthou�A�fёJ/!��ke�t�a3��%��Aor F>2,�xc` v&�$Q�� �pW (e.g.�- :/8)�dls�^"�aby�id� c c�h��fa �fF�J�)�[�h� 9]� e�s w-b, am��(s��boDm X�LT2- } F,~Z�FE)�p�{��pre�d��s $E�Q�$\:y�<�Xh. Any ^%BD on�irr1may m�f^Relfca"�v)'ng %�U o.z illu��pisQD, let u�si�GAa2DGl��ew�t~)e���>  �d�m�� ���ter!�!&mmD)�;i�;ly���m ithi�at!�neA"begin�ure}[t!�a��:�z�0de�4[width=9cm]{Di�F1.ep�Tcap�lf<mpwanBx1A�"� 2.��n���} JLRuis��%�B� �(�Ӆ3a�=uq s (!B_~A���"e $E$):R���E�x,y�` E \,; \�� F&y ��({ikx+ia>�5+j* -ikx .!��N*�O t;+N� xuybo$-i %\,ME;F{r_m_E_tot-�e�mA�[p��p�� $! $��xA�Qe i�;�sAXa��- a;�OouM�ġO th i�*%�� A� s=�� Ne V�_bii>  = 2E!� A F x \cos(ky4+F U(!/2* osR(kx{ /2)�A ].i@& Fje-~�<s""%Fi\.aZ��u"9,�1aF]-���,���|��� �4cir X2l8onents $I_{\pm}eM=|N� ^{N� Eq�|^2^  $FTBH=\frac{1}{\sqrt{2}}J x\pm iFCy)$�I>ɬ$!�=\pi$FNE�!�:Ipm_pi2� 2E^2%�[Q$\mp\sin(kx^2>�@� �0��[���^2A�+� �\,Bclu plot�t|~���,IGraphUT!wo siVU ons �nqp"�u.���E��2B�Rki�H��2�gu/E� %���F1e��1��(a)�;��SY; �>a�IA�BJ���z� }� 2�$� 6W M�)rI���� ase,!�e�p�r $\sigma_+� -$ 6S!��0lt0.~e%� half�S�np(b�$0%"���a��Qٖ�e`B�=+��\uxv�- $ ! )�o�:�!��  ��. HÆ�'s�ya�(�v2FQ���a�l sc���~(ph�BT :�veD�7"1E��$!�A�$�  ��Uj m���m� �i]����re M$bsiVn�7Q}-$6( :BB"��Qj�X mean�q�%gh�E�T$m_F\!=\!\pm F$ Zeeman n�u��"��}pac�2 opp��f'!EIsrueL"� um�p�}�$always pop�Ae �n�@ate�$��M��st,�� n�qce�gsyphus "!c��dalibard�Ecaʄ!�5@{ &� � e tYz$a�. m��� rary.b0�ze�a�2N I_}Nb��"�)g9�aB9& 2/!fhusmz}x�ch ��luS: �:�� .�of�5��.q� ��A:2�m�� fu&��E�: �"�6� Th*ixt� Xwn?rsP,ple&Ym"�u~rsQ,�4��E � a7hwaP�in m� ^+$- -$ mo*2e�]�. ��!� �!(*�aqu1 lead� 7�v� 12l��t}�a cru�mV!�n(}� "�58G volv�spa�"�y�2��se&�%?is|A�oRzep;oxt ce"%}�8yas�O*�+�Hem�rh"�1M;  93}}REL�N�fre is -�c�Jra���w s |!��6 yGr93dMe�demJ`W� $all discus]M*sIO ����Ds��!�n :�#�� w%(rt���!�Q*�$*[ by&�$.��$�ZitE �{N�4%>�QAt6�iif} �.XF�!u !�F�,����t �!�E�q{�"]sm� suddenly��f�s8 &= � _j]T +� J lH�%�se�x �Jo��l�%e$!��D!j%*!�a �on&� r ��r}"A � r}$, -�`&�a�$"� 4Eman arbi�)�� _o,��6{&no���F�$) �x!�B�4 .h�m _lin1[ �k>�� = )�R _o,\,\for҇4j=1,\ldots ,l J� a�u��%�INami��=�')�a�D7�B�"�y� u��=E�eN le }m�})� �., Ie2h ca� lI@dE'�mal..��&{ abov]~�(���� at�ry ���B2��s&� a �E��.��"Bi�B* . Such.�s�~disuM��� �!s s �8u �Ts'!ydl"�s e�a�ch�0rapid� � h& "T% is us��d�us!�te now��i"r�re�!N)0�byms�K}$�matrix%ֱ$c* s $(.u�k}_1)^T$�� $j=2M�,l$�%y�Phi}$R A?i\���iF- 1$Ac:h�reA� a�c rank!�a���qu&z &IM ��ce�%tI�it�lum�r!<rowm �4!'M � )ua�"��NR>4##j�i_)d  �ifB��`&!_"�_"'��rm{$b!I ) =2FI $|bf{%���)��2j!}��}"� �U"� I� %et�M] �$!�6ng� %�fc2�$���ro-1\t��(s��sy�&�AB� � ?'Fs6�AahartJ�B�)�admA�a"�V� ����A���var7:j$. By�M!�!&7, 1��r)� ��,2�B�]��>�2E�A\{Ibf�b:o6F!�+ r>}27\,|\,.�I�\J�S�, ival�D� e-� (O r,��12})�QwrK���I���m�PI�I�U��%'q�$ai` �ev�)h�h"��/�)��^�0�\ �R8�&E%�$)%�)� �RB$��a8T Ro�2�-CapelliAp orem! `�e.e�*��6� ). H| 3�q�. & /��A1���s2!] �q 2q �$d$�]"u�1���go��to.��  $d=l-1�1aV�2to "�+�򕡍�,!?!#: .�;irt by!&�.I!8�%�%es:�nu�atee� item�E�Q0.+)$;�� (f& \leq2�t^]�?v !w�� A66��N6s&)j�plV� q1�!m�s f� i)u% F]Iws ��a�VU{Q g>>! � n( i)$. Bu�.i;��z �-%^�r~ �+ ich O ��>I/�r��,,&L � �k,- �� EV�� �eseT�-err2T���k�e���(trivial assa+=� d7;�4um��"� �de��G�����F 8 exce� F(�cn��$ve��r ?$E!ity��%{�(4 ��1�$!e1get�!J ineg�^e_� dj�leq.� ��6 =l-1J�s &� �+obv�=q bym k&!�)�' ��we�z4: 2�6�����#���JA��&� �l��"%�� by"�1Bd]�3�e buil.b�%6�%*. Not��atZ :)!olAg($l\geq d+1$ߌu�$l=��Ait{�um}Y�A�e�% ��ao aVt 5B@of� $d$,*�� term6lal>AA�+QR&�to p?9�"� �(�m is���Ӌ"� ,E� �hBh-g!Z� metho�6 Jy ,j�X d�xb�0E�ۨ�.CFo.�:�#6� �"�9���!3B�!C"�}AB�:2 =2$:x! �>0;p &Jc)"�;:ku(�t).�=�b.abc"`'�m%3b2-F� �IJq"D;��6%�ZNNv(a+ 6.�%"= b=,<Aou8.t�� not � sf ��1 . To�����m�*"���Bcb.R�c)U����Eo�-(t�9.N��1$,22m� #3�=CqvC�vCt )3�L!�Bj��Vr)"� j�J _3K5&�(E \!�|ft( Y,ar�1{cA� "C(k}_2^T\!-\!�� � 1^T �02)3R)bA� `���F�n�|��&.2 ���1��6I3BI�^� 2 \;� 1�#":��m�U?��a�S�;$ retro-ref"JDea�j8O v"path a incX+x+� �sM�i�re"�phi_4�23=2 : A�&T�:]01$Slin6Jvia���_�} (T �1)= 3 �)+ �AxJ��"� hand� 6�� i6� �!oFo7�.�kj:�]46�=� y36+.26A�F�U'!x�2 3F_:p)�F'.�3EQ�  �j&J. &&�����FJJ4R6J4�J"0 j=�/�/�/A�R0Yu�/aU�I�TR� =2$. Now,EOV�B� &($ A� c28$���.��2��'��.G� a)B� e�ml�" idea* uE���K��@&� <� � � $ini�$�4u�war�RR�? al@a s�uifםn?m �(6?@Th,n��7��i$�m�N intu�PAWcon9��Bb*k ME��v���G` a 1D��" !]'6&it�6�C1D� ])�&$%��}Ns#�$ed�,�.� l�m��8ol8 One A��"� �Q5>�H �w,� add �ur2�>"ͨDI^!l^+� isk 7���4t�<�A="!�� Cst�@a�(m�E��  3�@ EqsN�<t��)� z�B'3AVL8:of V1R� bx%�z�Ap$.�D R�!jEB�is�  �c "~"�;#��pendentR� 7 V2<��3"TB� �f�..VD�' ion}ߞ`{�z�{)a�A�3D} "=!!R�*�8O#�(2u�s ryt�' �  said�)��-fI�"�s.���{<aG�Qa�>�#&=q�*ʳqd�"<<+A���"� &,i�6���mԜ% Ak>,�$�$displacp"a"�2� �<Qo,���hif8�M�>2TJ�<�rr*�R9�I�pe &�Y�&a n��! e�surfacQ�5�+3�eJ�>� )�_li�l��:�M%���4*�44B1T��F%s: &QwQ;�� *F>�3Dz�A�� ampl%�ag>� '���#śnm #�&�=J{�:�!�,�L,by Treutlein�'�,X }WRa�1idefZ�&�C01}. �A�"�) /sy�O�Ld6ŵ�xsN5(��by � ��rg�Rtu/,. O0 ��of^Ns ��d�-}�FPetsas94�6�=�e-5�x�N���.�:�N�b�adguL is:k$6� ��A8�s�)͔85�2�6�:�0 easy� show"�' b�vwo r�&�n�!��{R�.�8:N�5� &=&>� + "� -" "��L6�LJ� R�� -_- �:��:� � :� �6�||�&4^ET�!�F�8.� ] ��`  \s&sP�Q�0rea�O� :�&H3 Real�o�QX'ld�*��l����|�eA�]o!"s�f5 :Kc�r� o avoiX>Tpus#�a�F��f�T>�d b��sig4(�9 �"�B��i�\w� x vacuwPystem.+802D�*�"�,�#3mw"\ � t 120$^{\�<}�a hexago��co�Car���j � ��� �9] 3D�yQ �e 4 �QDul� rm5x7ctetrahed.���e sc��!ρSb!lex�?! �=3�Qusک낭� Shimizu91��T.w}��To-1� trapwx� �s,]:��+i�4eq��ut� a �u�yfrieni-� �T 2>�'-a�@�+��.alIQ� uto-.wO� they�O!%�rP6Walx<dJy . In�`�z�1s{4ghtfo�a/dapKem��re`W��h�tr� dW� in m s �I .*Ato�L!�""dW%2�/�-�""'�VC�V7VMnͳe"�T�)��W%%2D� >� ��a)! �TZrQc2 X�unt8aQ!�5&�F0��>~ 1ץ\ zed �;+d* -� -��2� ��� t�X���#=YE`� tech�c owed�'ty�����0�QaOns \e tem�M� �& 60~$\mu$K@1.63Y ew mMy�$s�hmao�! �?onYX,B�f big]ws*a�� 0R ecesF[*�! far off-&-|� l(I�$a�aj�Ygal�up%�m1�2���)w2��Si�<)qI�� a 2D>n �)q�UI� �6 sU �>c;�6!t0  summ�zh t !8 tab:]s}"� %}[tbp] "�I;B6S`**6PE[ .Y" ���F9��Q ba--!�&��-. See�.R" 92��y��.ϫ�J�J$tabular}{l\h�  +ne R��O*�q=4fz& (i�) /u���.N& 3.6(2)� AnLL& 7.3(5:5 s � 1 5,nIW�  b@..";$.&�\m��.:C�m�or+1u�bB'J�Vsh ?�"~x| f_� ��'*  rank� i�*Z3by�8�6e �3m/��get rid+a.>�>lem. �� �9h�&��p� o��@� �+To*N9_,!�pS "a$J�#b|Q'�,���2��� �t�wi� N��7p� 7�;*��s�:jX& *1����>.var.��5�U���^su˴!�t �=qP�00,EssA3er!E��Co � g !Scl�%0 "ObA&�'��s"Qb�2Z*��!"�M&B1B�(�ś&(G�9�2o�n~:m �}�"o ��6�u��  .7`�m�1`a��e� �-% �T!�<*6&�*, 94��&&`�J5(m de�)�FrDiw� :��pro�%byZj j �85=�aZ�c6X�y.A�Aadyc�, w ic,�mVa( ci�nYJ"� #3nc�4th,A��d��w�5 seo ���}�al�!^ most���)e for t app���y %]l look+Ek�beH� sour~B� 't2;4 v��Jsix6|1���*>* *{Ac�b ledgv:RisC�su>��wiss N%al �� ce F:b�$ 'Fe6�l O feM%��a/Accred��$on (METAS) Acha�:�g8!� b Confe!C. AVT!VIYu �B�e�.�a-Dy},NTAS-01-0855;A�FBRo[)gr(\#�2-16488��%��wq�chEFB�, tart.�Bm \�c ndixGl �%� �n d�6aL>!Sjpox  :�k�:&�+t:�o{00-m"c�1�eT8���iblio�T m4f�-�jb�� 9 \"sub  (, } 3� * 1F2�Tr�a�#.�c�l last�k2Q3�% x .� \np�n {\en,�(}[1]{``#1''� xp��b\ifx\csXh urlO \8x�$def\url#1{^/(tt{#1}}\fi �TJI urleoix>OL {URL IW3ideMC {\epLq}[2][]{~{#�m&ȯf} J.~P.~ E�C.~�v$n-Tannoudj�-({Etude du p�-g<��d�Kl� �d1mQ l�3c\f{\'e},Tuk7�diu0brs329t�6*Bs�"�f W.~ �,B.~S.~Mathur��)�{a�ive O�or� ��h\ =�� }�ev*^u�zs|2�67tUY"` P� �I.~H.~D*`� y��s,} Advۯom. Mn�I{ �E?���g9�:0t"g} L.~ �P.~Verket�5�>� :s �1 m# �H)�� B�1}, R%�R4 �6�{&�g S.~L.~ v=�5mW�(, October, �32I96>�*Bg.�B.~ ,A�Salom+N�J.-Y. C4#oi�5 G.~G �"T��kS�I-�� ld C3x a!�eri��1{Pot�al6uL2X�068}(26), 3861<�64-{uB�26��,Gerz, P.~D.~], W $Phillips, 6�@ R.~J.~C.~Spreeuw�B !9(I.~Westbroo��qhO�%�e!�h����: {Rb}� ��Rz�Pr 9}, ��5��:�1� 93} 2�].%� 6��M ��� Quan>�c!�c)�w �wo-Et .� �"�Da�A�&v.:�70(�49��� �32sBk' A.~69�$~SchadwinkqV.~Gom$|D.~dK�`���z�tq�)�s�� � ��"W @ �%8 � �Rj^,}A�!z6!�14Be45-"�:��= 98} 2Nj.q}�%�um-�l�ro]�"�ls,�.=�&؃5�j197B�986��6v*�N�JD�Q�NdUVLK  belo{�{D}opplerTlA�by?N�"m d� s:�O�!t*���yE\>�� ��6}(11)5s23 --20��86�.NA\�T.~�{\"a}�={|�.� A0ic cryslb  �l�n�e 4o�41�}:.�!���~Y.~Chu�{�����b�G� �> � ��^�A�R*05140"�12�"�! K.�B , A.~Bq �m�d2q%i�C)<lz N�;a�U�V�5�O(5173-�518 �::�&� F.~ %E !DH.~Takum��",4-{B}eam {L}A� {T}rap  {N}eut�{A}go���._ }, 3��3��:��2X�� Di~D�v, N.~]��v�~Mileti���v,A�V�i"�v%p � I.~Y�v]q�&�o�bcn� �o(z5  {Z}wVF�{R}amaF�6A��tex� �� 0634ı6 �W} D�Han�� Wolf Ol�v McCormick~T.~DePɀ�D� M= 3D G%SG%��C��at � D� y6�%�� 85},њ��6,�. < T.~St{\"o}ferle�� Mori��chori�K&h3�nd8H2�ON�a {S}�$gly {I}nte�!ng 1{D}�m flui�)a!�M}ott.s�WorJ� 1�9� 1306��:}B0�S%0@ 8��m�12��04 Submiw�'0Luis Orozco \܍ial{p��,ize=8.5in,11Y�\tole^� = 10000 %:�~(aps,prl,two*J,�},�edTy,�%4pacs]{revtex4}:�[BP0,�r�^A s,amsmathsymb, LQ�ptlfloatfix.lF x} %� �$ystyle{prsS&%*7~ %\dr��| Life�.ЊA�X8$s$ L�k� F!Ciumzu]~ {E. e z ffil0({De�EI�H� �VAsA�8omy, SUNY StonyS�b   Bo L NY 11794-3800 U.S.Ay xݐ)�F|t.w, U&Y�ofz�@yland, College Pa-0MD 20742-4111�6r{�(erez Galvan�u�uG�(Sprouse$^1$!��i%%],njSA�( \date{\todmQL&yW�W¼E/lQKp $8s$x�#!�w"�#ly\Qp��s"z+($^{210}$Fr ��2A�-�[l�F 4le-phot}&u!!g!,e $7P_{1/2}$�te �]sC�resз�D�Aed���x �Xexc�� ,�$"�a 1.3�)u$m�er�2vT�o���E�SZan�3� g*p s $53.30 �]0.44$ �39f1���y9� \��${32.70.Cs,"&z 10.Dk�� make(��Za�t lw[%�q�Z��#f�4;%heavi�� >tiv�xlkali)�.dza t4-�� rn&�"�{\i��5o} &fL�!d-body $�S�T y (MBPT)�#$johnson03,a�es� Fr�$�te+d!P� Non-u3er(PNC)�suj%t�Db�L iat9u �&work to�6�at go/�@)!_u{"S0- E���e_RWbH�? aAECi"�Sto en�+�r �qdv.�.��K� ruct'$�%%as goodi_Pf� er -�%�e.g.} C4`�PNC.'achie��a�u�x�P weaka�c?�ramIos-�wood97}.ҿ���A��*!�Aza�1���I���{EhI: vali�%�s0oA'.|�C�-1!ys\a-2� 4_3�>*J87 2�#/ larg�%�U%��.A&er�c���*�!o= i��s�bi�ZIP�b�`$7S�Q nd !K�R� =ed $8.�h3o�Ja�?�.��!��3� � Th >�$\tau$Ao+*b�i�|��i'"by�8$ individua�^�bMs, $1/J_i#3�um�VeЌrKoc��� $tp;��T�m&j�s �t��,�6�%66u�:�_&�A&Ej$tau_{i}}= 4}{3} \�x^{3}}{c^jj\a�v >| \la�*4 J \|r\| J' \r |0({2J'+1};~~~ S1}{r} = \�xi v  _i},V bel{�r.2�xE� $ �"xI&� energ����: $�v�Dc1E�sp�L�T�D� %�fine-s����T�, $J'�7$J A�Tp�!velI��<%��I�lular mw��A�$vI�3 6� "8grossman00b}. E�C�'5J7:k �!B��:66o��:Xc���mQ�(�P���� e�&�4�� �~K/Y*�-�Gua�6x!gf\T���3t�,��nuclei�u0_oc8�/l"Duj.��(ݢl�ԅq�? r!��TXO �p×j�ar )%MɾS����c(simsarian981�,aubin#�!oicEory6����ly]Ldzuba95,safronova99,M�p c�&�me�b]���ess��"��>� rengJ�!�*�"!a�exps�����,of"�  isotop.W�Mm�K&im�)r�ꡤi�vp6� �T�'?.��*� H7rB8 6  (MOT)8#yh>B�a� �9�E/!B>turn of"&���&�and �? bexpPp��.�f"����� hoe&96}&[ZP��'o�l�0�!WF�� -lin�i�q,�I����i8Ea���at .O$Y8 &LM*U���I�3a}��ief�'a/ MeV  $^{18}$O1�-.!�.|im�a�A/goe���� b .� (a�oa<�mmE 3&)�� kg m$1$�z 10^6nan��/s�)A�he x��empor�Xem 15 1�yq�n�izeb�c��um�)�Fr:sEvE@>� fpIr}.N�h��iAB �":/�+s�000~K�0relJ�E�K�ͅ� e dry-filY� Ծs cellL 4y ��n7(�SQ�� a MOT� &�Uc �AG0 repeat�3ry 20 ,%�"w-��leavev� *�wZ�w3.1in]{��s<"S.E  !�&� r N�����re�l%�` s (t͐��SeM%�(e�.�-ck.s),5.� detCo�;i:��S (da�6a��A!�2�C�(.)(d�r.."] zs}\ )�n�:�/ # $-��^^"KAWv�%�2<���s. A #�4ٻ21 V ��-sapph��(Ti:S )���%�t 718 nm)e6V6zA�+9� ("k ,F=13/2tvaB� �5/2$)β:� �J� �nmM/� ymdUl_3@�A�i- La�2�16� �z� 3/2$�E�+ MS.� &G 9! I �va6�0�at �(&�e9 a�h F�E6� �� �at*� origin� �4n EOSI 2010 di�@�<e� A��u kO%�R��@ Burleigh WA-1500a � monito�~he-q!�C}�� � $2,001$ cm$^{-1�YWe ^��a,P,�nd �Te:}" a.ns�@�9 zhao�"�FE.6L��%ai�/a M�lso�_terfer�er E�i�[t~W@�FB/y!�0�3DHeNe laser used in� the transfer lock. The MOT consists of three pairs of retro-reflected beams, each with 15 mW/cm$^2$ intensity, 3 cm diameter (1/e intensity) and red detuned 31 MHz from �Latomic resonance. A ���coils generates a magnetic field gradient-L9 G/cm. We work with!Lps of $\approx 10^4$v s, a temp^dure lower than 300 $\mu$K,I a �0of 0.5 mm andC`ypical lifetime between 5!(10 s. FigeP\ref{timing} displays)�, sequence fo�,e excitationP$decay cycl#\ measurement. Both laser%�8the two photon .Nre onhD50 ns before they Dswitched off, whil( counting eA,ronics 1%�iv �50V to recordY2�nd �signal. A� trap � turn�f K� two-B�%�repeat A])&8at 100 KHz. WeW k ight!�off%� an� opAq�modulator (EOM) (Gs${\rm \ddot{a}}$nger LM0202)N an acoust E E (AElCrystal Technology 3200-144))combin)�of �!�giva!� tincEr&A� bettQ� 1600:1 af,500 ns. AOMs�)� repua �efirstQ5 (817 nm) %- ^�),;y hav!�6�!� 109:1 !j26:1 3E" �v puls)�/f�pecARly%�couple ,1.3i�mM/0into a single�e)�dal fiber pass it through aa�XGbits/s lithium niobate1�-)� A5� (Lucent9� ies 2623N)|n amplify it (Iphenix IPSAD1301)%againUe*��a second�;%M result isA�on-A�Q$ 2$0E$in�΁� of 2!�(. \begin{f��8} \leavevmode \!�ering \includegraphics[width=8.6cm]�� .eps}\capA�{T��diagram��!�$$8s$ leveln�(a�(kHz) \label b}} \end�, A 1:1 imag��Dsystem (f/3.9) col���~fluoresc�{�Ys oIRcharg��ple��hvice (CCD) camera (Roper Sc��hific, MicroMax 1300YHS-DIF)E�monito�މ�wŬhe use!}an �a rfer�fila� at 718 nm!�fro��8 �0. A beam-spli�i��:,sends 50$\%$oBe� � a)$ multiplie��pbe (PMT) (Hamamatsu R636). Ana{� ��$PMT reduce)|$background � othu�2� from�cascad��i��($7P_{3/2}$ EA�\] to# esta�$7S_{10 . A� w�|�S�-�Q��>0 ş `�� ` u����dif%�t �0channels (see.~8s}): F�~ , by emit�la.�I���s��% � �p5Hs ��)k ��1$ $7s$2�Ɉ��possible6� i)�$8s \r�Qarrow 5�A�/ �folj d�!e� -�Z~1.7���$ M ɯ stepI�is X��8unobserved, but!�detecuNE� L�art o( �. Wq�known&� & %yE�)y,��is95 to extrac���"= �Q�2�d� .��`8(Ortec AN106/N)%S curr���OsTI7� �Uons�!PMT. ; ga,(EG\&G LG101SA@�4\m�a I tant f�!�discr��% �93�output!rts a id �n -to-�tud�e nver��(TAC)I467�a%� stop� a fix H delay �*StV) We �na��m�8 analyzer (MCA)1 Trump-8k)�pro�� a histoſI, events show�pdirectly!8( exponentia����%� � or\vid�primary!%NB m&� < (Berkeley Nucle� Corpo��(n BNC 8010)I>takA�  data�about 1n ��at� Lindividually processaMAf�id�$to� numm of� !Xse� - lya� orde� $3 \A s 10^5$. .1 E�} !Y�jaccum� � of9 e��, toge�I�_ .�fit��res���� 3.1in]{8s�26�Cŵ!�a�v���� � � >S17���� a:; arrival !U Y�!�b: ��� subs��a�I�.� �!�-����)�co uous line���fit ��r plote )� normalize%1�� oB� TWe apply a pile-up corahion�A�c�sE��pre� ial !�of earlyq�L\cite{oconnor84}. As�I�; es keep t�`w small,�YT )Z%�a y 2���s y� one �ry� �s)T�a" )Ui�ٞ(by $+0.1\%$g4 perform a non!�,ar least squ�QT� fe�E(ve algorith�fin�/%Pparam�at �)!�%"(est $\chi^2t �%� $S_{8s}$.��UAYa sumw�R�Ys-� aubin04} A�a]� $A_B$-� slopeS$,�%tur i�p)o!YA9fur is:"" equ�n} �0= A_B +A_{S}t<8s} \exp\left(-\�:{t}{\tau�}; ) + A_{7pn/7p/m0ffct}, �where $ e 7p}$!@!�R�Bn� >!�,!/B %c$ �$�.]-*"'sN���� ai;�/andV �CWe<_���b�B� � !�ed� V� de�b�t�wea�A<��� d E�_{\nu}^28 � articularM�is 1.11��d ete FourH �a}M]��- no struc�.e"averag!�chal�-e �filesa�d�obtain%?"[ Dis $1.07 \pm 0.07$m�hge (within our quoted uncerG ty) "!�calib�oa%�City�(MCA is respp/ � devie#ilun31echi��d �i�t�Pw�knd� 0.02�%� ��U k� ��� of 1� !�i�� rema� #�  !� U!^ � is�-���%�"s�E�ist� �sI��e��0� .o whe�is�� eft afree �}� calA��� ribu�$��=�U�J� *��",1.02(11) ns �<,simsarian98}Bayesiana�t!=c>�e�.�s��A erro* 0.15\%T$We do not � any�a�effect pen{ o!K�L��end poi� -�fitI e so!H�truncI��, beyo����al.V�l look%���1Ivim��gلby�v�v!��4 onAitiu  �Qag"' g��FBff orEF!!du�/�A�tra%%E]<~� to $�p \%%�e� JK ��b�U�esN1$ \%_:� aTACeX��nonuni�v�qL �11�)�1�a �5Da�increas�. valuŶ�6 M� studE�Qdini� E<�Ydi�s!�u��e6� %�A external.s I�.E�vB he p� &2OE{eweuPno vURu�)p�f f�;gatoms ca!fl��E8s-eas��ed 5mayE��e"�regA&y& $. However,���8veloc!� � _m�G �Ls�an�\ m/s%�im; yh�q.  1 mm=it[s ���r��F��� imately $� �"�dN���& �} "�  i1} P.�Fi� JE� �hL� [&F��� aa���.�� comp{ euqu:7A3a:� or,fixa&!���)a� d an.���1o?p3 36�*aۥkc�is �Z.G_��f�� E� -J*� 6!2&iV?MOT%6b4"� satu� �r�S�b�!j�8A�age�� ���n��m�w� 5a fB�di'�subje�o� . W � �ximum%="�9r24�-�o l2e���hver"search�~Q9% 2"mr � Fdomb!)H.��2DW � !6�#of 53.30S $ 0.44Q#� ��@of3ncium�H_A�^|renewcommand{\arraystretch}{1.3}.sb�tab|(}{lll} & E' �[\%]\\ \hline \hspace{0.5cm}Tim�E"�& $0.01 \\:,"� %-*15B) TAC/o �e6x 9JcRB�.N�I6- , off37B�M6&F6&)N�B&�e,36BU�p�6' 24\\>lSt�al)C .659�6�{\bf TN} & -�82}�� 1� "R!)�JMzR�!B!%� =F!M�Q��" { �C�s&La�>��7�or� ��6 ��+ l�$Q plaiE   text�l�ɪ�Oat�c/ . ce.}\��ar�-1 .�&ar�Te V� �theor�(al2�. $a�:d_ \�it{abFo} MBPT27�g�0dipole matrixP$�s $a:$ SaF" ova Uet al.!� s P99}, $b:$ V. A. Dzuba�et 5dP95}, $c:$ W. R. John!�:i9j  96},%�$dbk� 7k01��Q2U�%�Eqc!��}"9 ivediD'+%d��d�� ener�% z&�9}. $e)�h)� semiempir*�A�H: $e:$ M. Marinescu> Km 98!{f:$ C. Eodosiou *A; 94+8g:$ E. Bi\'{e}m&$9u.�bieav $h)�DA. van WijngaardenZAw"% scaz$R,�&s&� MBPT��!6 �"x*� !��erj&Sourv ul��2jmethodW l�&;,_  a broax���:  (expanded(la�MJ}�). OurQ8ad&] ��*!2�i� el9��L e6 a�]Q�9j �e � goo�y��%o!oun:l�&relativ �  pres� � is heavy, ku&� r KonsiQits 87�jc,�ir�uracy!�vi' !sfu��&pre�*� PNC.N G agre%% ��2�u�*r%@*�)reinforc%�%es ofBs!Cs�,ch�e now  5�nn!ar wea�ce i�,wood97}.% W�.support� y NSFa� G. ac�ledges%i2CONACYTA��� authoɰnk%�personel-�! ar SB Lab"8ory at Stony Br�th!� �!�1� J. Gripp, E. S�� B. M%Md%�#pE�loa!�\vl *{-0.2cm}Bthebibli3#phy}{10}_ibitem�03} W.~�3, M.~S.٭,� U.~I2 Phys. Revz5 P 67}, 062106 (2003a�\sMes04} Jc~M. Gin!��8V.~V. Flambaum,ap. _397��63 Z42ZHbouchiat97} M.-A. B [C, RRProg. c^60]$1351 (19972_M^ C�$ Wood, S.~WLennett, D. Cho, B.~P�ostE.!�,~L. Roberts,CE. T�(r)\ C.~E�&,�*ce �27��1759 F�(grossman00b%U!R , R�d~Fliller III, L.~A. Orozco%�R. PeaA�,�0G.~D. Sprouse!�.� �62!*062502)��$5���8�E. U�>�6o%�,W.~Z. Zhao, B} 5E 2448)82��  S. A� ,�G�>|At:�.pI�7E042504 �6z 95} V%[� ,B�lO!� SushkovY�a@%Y 51!Y345j 19952�s* B�:�q9 ernko6q �I�4476 )M92r�01��JaE~e�Rm3�1)J12n&/ B]=e@LR. Yeh, T. TakekoshiI-XR.~J. Knize, Opt. Lett. �2%P71N62nI)3a�*��,Sci. Instrum�� 7 434m6 zhaoa]�!=n$!�:�~ ~ 2� 6:  3737)�82�o"m% D�nO'C%eD�0illips, {\em �Cov ed S�1P� C�Y5aA!. mic, Lond&1986+"v E.q�F. Baum� A. L���to be��-edE�20:�j"� !n.� Z.~W. LiuIEJ��p.$ein, At. D�)�) %si� 6%�27��6Y��9J�.�6�F�V�%�195)�6�.� .� ŠVrincean �H��$SadeghpourN�5  R4259%e19:R2 ��� " $, Bull. AmA[0Soci* 3 �210 �6,&- A-Bi{^ }A (, P. Quinet)�VA $RenterghemaS��B� 3� 5301A�B�6Z A/J� !�J. Xia`Q��+{ sc. X. Tv$ �A. |5m�)�T:� %�F"� {fr� } %6 cols docu } ��%\� P �=N(alongb"�s. Inz4nci��!�U co�c$D(%Ux},t).-"o%-Q$v}., !)# - 1Q 5%�. Z:deaQ7ubiqu-xAO%J be gauged)N�d�e.xsc8N !�!(��, sof�u6"�{)<y�� "3c4e�.m5 ��)�wDarter}, cosmic ray�-eam��.sk� ng, ryu},6\15oVd�!e�Dcarron}, microemulsi� sh flow ggo#-la}, Q\ k� �ina�ven1 5\schmidt, edwards}, hydro�S��Ootaxi�'bac>� olon� �@lega, ks2}, phase-�L��&�"solidO=�� E rousseau}"a� -��4e�I$problems (t-�� -}). I.��ly�$U!l�8taJly�veE�, ed7s� A��tenA�!���in�0% non-linc�@d�g. F>is j*�1gr�Bem!2�a�CenAgc�0n��e��Lgr)/,��bas 2f�* f5Ŏ It�( b]f\&��y�᫁�spi�@s�ap:�ic� <�:em�(trouble�S to handle-�X%que�T�2�'maj%�Ge�: {\it��"}�Dch�(improved usaZa�eof � �9A�NF cM�) de���#sue, r�5'!� ``beC =''��A|V� �gar�.�+iU/t �, m�.aG�Tin�1 , su�(L Crank-Nicholson/ADI�f�;\=-�M�1a,Yquea~!�� Lax-WendrB 8-�dehghan�/ �11A*q'eived !�wA,xt�0A-A�%�V �( �ir imme�&U&iants�A mmon�%�%���FIxe Taylor�9�on ɥ�,(mer6�$``upwind'' � -0 garcTp�.er}. On%�6mW3� !�*�?dex9��  new d 4� � whA�D4ŋ�BaLeal� eN�{�8V!  m� )�.�,t� >56�C� A^� } T gqlet us ] � key ��!�N!� �ADE, � ly[I one-"� A�u)Ia*(uM7��"����1+ -Tv%�a�ar poEh(al $\phi (x��us, w4 ~ ne 1Va D_{0}\M al _{x}��a alpha 2 (2�) \ ,Fu �7g? $ VE 9 tA�. MosV� ~ igZ"to int��m�P�@�efU 1}) t�R!b"� �I6�s #r�.mmL�Sy%��O7t��2#k�m��FKscr&���l�2r�[K do��so,�=funda�alV per`)�  must e�lye��'�>�1 �neg� $!�)��Qy!�erve�:bF&}Gt dx \ LI� = {&J"t B~  AL illue3a��e�wr�ddmB��6T ��m�� �/� �*i"8k,!}exp�Euler ��� edels��#ɆDi\=�{dv�Md�L &t���RY7ot��uBreplac8 !)tE/ �%�)P$ b�=� "4lbrD%{$_{i}(t) \r $ def &EM regu�? grid��A��G spacAy$h�FeY\of )!7 �gP;!�� )��"er6"B�sfDade1-!����{d�}{dt}��3}{h��}�u_{i+1}+1_{i-1}-2 }) k<�^}{4 9�< [ ' +1}(��J2}- }) - $-$ "l2}!h�0]_B�X noteworth5T isQ�Iv e d?no!m� sca!�phi�O next-F � neighbor)�} s raB� !!�%� $. p �" re �re!�A�isqne �n(#�N�FUmB��b} )�^�11�)�Q� !�%�1 [E >�^�`> ] E)I-6I+ �\��}{I2�HEH}[2�]�Guz\ ,B�""� a�B%~�ʍi``% JeB.?'' (L�K> Wmk �X�3���Mi�E�Q�adI�+j��} W�,wo,�f� � emerL"f�H�Nm�N�^~��ADE (/�}). D��Ad$$\gamma = )�/)x$�4W be verifii$L�e� �at Eq..er7be��asb�� -expn9 l�<[ e^{ � a��2! �ĉ� e^{-.*�yBe\JC:g6�F} � i�T"�?�y involv!j2,Fu� �(��n�4 Fokker-Planck�+��riske?  �!��<j6� !� inde!��VE� L�&� , altho�PH I ( origin is 2eY�1 willq@r& b&' �mO ��i\b&0 . �A&�-.�� 0 �IV+y�F$. Cl�Ethe�@--corM0de�$L^tbreaks+ =w�1�X2) hiev�:�mkind )�above.)� cruc fe�Ŝ2Ce)!sZ5�� &� nF!��>r9a[9/� �al ~ $-��;tra�ufor��toѣize. U!�)Lst E;a*� wuol�ve��ʥ �a��}�(��F+1�g })}2�N0�<0ُ��N_]+1})}+��Z%�$) ��R�:rIca��JY!�mgKcoIC��.B . F�! , in%trB9�8LCD�-t\T6 apbe�a.Yfashi>Z is scEd a8 a3 - �s. Se{TAnew�At9s�=mas:��;� , �, N FO= kna�V�-��Dka�.b �a�ec a fict��a,Yis lo�1�� � $i� e�:a8t�pe+F�op� DintA��o �3%� $j �Arr�Uu) f��} W_{i@ �w j}=(W /� )>H[Z� _{j})Z� Giv�:� map/)x�T�;6�� a.q"� ,%�"� eT-atFQ�� >�-="Y!����))�$ (L�oSQ)I�tsE�&� . Du5elQ`we&h �3!�B��Ms``:� 6A� MED 0n9&"�8�S��� V)�r�L� e MEDA��q� � % �a��<p�6/o� reciA�^&�A%�!�Rhelpful!�i�!�c�of e  \delt�  \ll 1�; ,wee�'1C*6 U3��fkto�B Pm 6*� na9�La�Wa0ex)�R �C���\ Bigl�\ 2*\ 2��( & + &����>a �� }.Oɞ�yN-#& - Qp�J� �Q (2�p6J�� �ۍi�1Bigr +\ "�-q C:�7�G�=6�A�b})� lfu�s���A&��nes" LCD. Na5E�negle�GYm uTcu�O_�L .&.�fac�G�mission� ly3�5o �=fi� (or ``u�'')&� *HcJ�fai���i�!*d s�, m�otably,A� F�xF0&ge5 Z.� ! 6�y")e��?ou�Db���)s �of ��i6�sGWiy "� on%�n�m�*wouldw5 nos` ori}��to�3�b�?ver��~&�A, *_�h� �vanish��D-�Lp;�s�< . Co^)��A��<�� t�$C:GE�&�yJ<s" �)� � �� 6f2��H�!թ�M M6y-��_s_#v,�belowEU�Weasily � (U���$d$2�eAz52>})4@a"Uɸ.).`A��+} Con�kin6�FM".� $k$W]$�5G&i�M ���"� 2�'me:$"%.ra"����$�B� �Si*�Y!�� s $DF$v$��hig�\[HqorO&N!�v�H��(��K.�! . L7i�&'c�u�$f.�# f$g �#/via�r18o�Mb${e��%x&> (&6�)]�O>~ By̓�X.�A� -Eu6�� �qv��cV�f ��g� ) -  f�:� O�a�bc se"� �*�"�"�as LaA�ia�G�aA- .Z ���� m.^3�I�E�3�8 iA�b/la�)�!Qe  x}�` "�{\�Q\0Esu }'(Q} -Q� �>3�A�=is ��>�sC�6t,5c"%-R�*p"�eix}�O MEDɛ�B�!m>_c�b,�)� NW! ��6# [W_{ju ar` rho!= - J��!i}� BL=Y� 6� ``-,�#�sN$i$� j���u�I��UaK}N� = f� \ g!�N8H�Q���!�!�is�MI"�!ine�H ��c �X9Z$F�N�������[ "�+�6�Ue&,.A��>le�Ni^daH� 9  � ,Crst�c�������� .Uto�� Eqs.���`���Q"X!��� e nev-�Paux�0ry.�= !x� mt>ly relevk b����f:fandg} f�" =C\sqrt{D}� (S),A� \ S=�w2}\yqO^{x} dx'.0frac{v(x',t)}O',t')A}F��D$g[[e� triv�(�)X%h.->�isV  eAOa< eX ;/e.) toE�`-1d^c� {-8ahDau" \�fxp[-(S-S�>�A� �=�'� E�� a-� be "**s3AFhe6 etica!or�)�+�Kre � VLi�c� anC6actoa(-s� f *-aj ( \propto 1/�( $@in~3$erho}. InF�  aF�� }+�O . SolvE�z� ro�"�la�d��s{ & œv}$qYG0�uxo�%| >��exJYceZsteady-�B1�� �6 -var V*�$J�x+�1,�b�1� (�%��%�v"� ��!� asso�t"J�&o %* v}=\� �$�;�$%�� ;y�#lea��&9 y���q�M�za�Wd$���$�/e ��-s�*#i�2)��V���F�T � rem2\!�rea�at �F G�/A{und�2�!my� X�ls ^�.ven�I�)��qrox�U� Fbsd7 v*f�QLCD*Q%. N"d5�/ =Dch��xb�OQ� i+Pg� ��/)$: m�Sa or a�ma�Op encaps�in.�:IYx� d~be�,�^KTlEco�4��1in� �#|,�� feed�!!�%l%�]) �2��i�e�&" <�� roup"w0,�-�.k��o+8y me�Qis( As& y��֍slev]+flierl}.�*� Akhj� �u �*A� d^{d}x' V� -�k x'})� '},'^,$V ESogOtn���<i�-@ l�0F4-�4atM1A�!8A�rt  ^r�2!�i"Nhs. If{ Dirac $v$-�<the����$. SuchVsMmaDu!� escrib"k -d�5a`dis8Gal!�pW� "�2�%�-.hav+��ly 1ar$ri�2rom�p�d v�<e ;S�q�of �+�/}5ell� s-�/ng)A� ~-t"Q�i.KeHE -SegeIdeQ7�3 otac��( �w3. Here��\�x���-m9 hemo-� ��!1 �=�Xup�O��"� )�$��b!kE+e�!��7u��- \lambd�+ \be�rho{>� �$\nu �d< < An2�n�-A�M�7 ��ti(e!�d� d)!g!050�?iv�t T��"5&[ d�j�Bɼ�Ling&��N�=]b��sKm-8)�B� ^��A�a\.i" �a�A�gl4�te%� � .Fine-tu!w&o } F�"t � sti�-�nI�)a!M)��e�6�4 O"Jly far�ebXn?![g 2��>3-F� �5?g"�� ��E2�do �>a��jo�Qd1�Lngac�ctu;B%k�H/^a�Y��z1�v� �F_��4``PrI �:en� �LWds-d�% �_of quasi"� r�a%�fa�+4���1�c �bdiciac"�se&�i wm!tsv3*��m����e-AGY_d d�<"�"�a *a�?� bia>�7t�{?#!�Nq@�� Z {�/sinh} (�(&X)�e�7%�cI�9f9N�%�>2`N� $. �*�Kuss�R7>5&"�C A� l��Q �-��*@k �s�^l�assyd*0 ``I v''MB� A�vM��YBglyaM�>. B]�am�G��/>)"Q2�. An �4l�"�Aybrid,�/�C)al%��ei� Ap+f"�-�aa�p�i'��P1�� w�U-�"�i  ;�1&� on ,Y ���.E4�8!�)�i ��z 2��(in&Had94a����4��: 6;"�a�&�!e&' e]OaM�2�/ j� ?��erepRc�w>Z �0c�* �>`���ff,ve>�X �XZ *�� 2� b���A�!if�F } v_��eff�h (J{-J�) = (y" /h) E��[�l)j�")] Z� �%e i��X>� E$�clapl�D^31t/���'��ey �V�h*n+rec�K �\��!o�V9"e�~hN =low��h�� t�Ar�r��v�Ea�� ��r���l �qV�(��9 pre-factOk��m �m)j�>lp�q5�1)a&�*Uarg J�e�~h��� has,���f$�&_.to�7c-,�� }Nif�?*�.bx da  D2x)wa�9��M�} {y(b')�F+K� ��;�F�{����-��W�!``F�E-(z(FD)af�f0dXV�\l�1( ��{4� )  �e,c� f/ 8 {�> i� j} *]-1�F?�2THA�6E &+ 8dju��3S 2_b�M3%�� 2 �1}{=�}9�^{"�'(6%.:)}{�29Q�nd]Wri� %�� �%hyperbol��"I*,Ia log� hmrL� 6J�u rootAJ SR) �fK��VH(E�)IU\�9Ec [1+ (1XIP ER�*ES ETF6�Q�] ^�~ - VV�UQ J�(u� } "slo�D@�t��FDe���.t) El�<\36�a�SR.A5j)�Dh�&� superi"DK)Z�ZJal�y :=ion�{o2� � �by& ����?�B�?l~t B�>td� [ v� �0� �K� d/ortpasympto�t$x%�ns X N�..r5��-} em9�a car�**u"P�&e)b 9-a ,XIo its ~~"�al&, �X� we w�h+�H�M#cF�^�1)g,1�5a�!��< !M��6t  �&�r( :�H"� � 2�,��):+]�� V�� MED,�TvA`MED(LI(�:I2�b})x%IE�WV��"�9]P5y wy��kU�"� �b $phi(x)=[1+�� cos}V-$i nx/L)]/2Cz$n=16DL=12.8s#�ca*��s��anCw�U9 �00 $x \in (-3,3[K zero_,wistqqA�1%ptoVty%��,dic*nary co��Oe_5`� et-up�{Ns a�jlG�h=J�"�9Wq� a >�"�!K�$. Fur_�#E�"�G%�F s by*�&�  �C =1.0-��d= 5(Fi��1)!"� = 20.2)�-cd �d!W��Jo �) Pec1En}0Q�(C}m5!�&. G,8�5.*� �ast :O��aS3mi6by $2 �wdnd so��0.2��8�_� data�inb� s 1 ?2�A*�k��+pid� �p�Kwh� �Q�)� adap�bŤ U��R�/�cv2!,2�a�i���  to�8+2� T�E�&F���e�ch�' 's aK6o� ck r���RQ!P lіa�� @'AV�bLn&� ass2���M���urukS8Rhema�tAGry�NM_iz0 $h=0.00625$,m,yseF1alsɪt t=10^{-6:( Va good*xc�1u��m?P:�c��!0de��``�E.'' We�n�3 � at e �A�*��� = � 4}$,��M�CI�W};�s�Vv��,AA2MP�C$A[N0�is 4 vif�H&�m} E(t�%�$um"�%M J, (t�+�_{i, >{�}} (t)] l BCb3 26� Not7!�tc=JnM[enough�� �Laer�="� �oE�-or`Qh�*3for��2�1M�s (� he.Bme�1) �as : M� .�L�;4ig~~.�gu�1(a)-(e�7 $!�R.�iB25�'0.0 1 2$� $0.4$nB"���-=�qAU>! tireY� e!� up�Y���NtS���%Z� r pa�~wehly�-78*74tts@9��) �MM�@��ehM�.)ly 10�ys �tTLe5�UW�G�)AI���a!o �e �too�h s� �@DM�[.)�4� Hɘ:� &�{rA�ly 2a 6�10A@!T9�� doubl P!` 1Q%�l^@d�IJ�)z�=eI=4pw7'�jw� ���6.0``p�\Yaor1-IՀď�.�M���#rs�Hl �{6��. +t&b'6 � !�; (f)(��Epro�\)au pheral � �A�/� �� � ~ ��9��e�2$����o. EpF failBcapY magnN� ��umA� � becorQ@<e�s�X�2��E3D"Z?I�s 2�Vd2VN �FJ$ �$0��B8�� =2� .L&�|.�$_�8�vo�te!�a�1oUW,Vk��:Pisu6���73*H>%�.�F)J�!~� ��� SR)&ss�.���0*u�yf e+,a�ex!'�A& i�#2%;�2()M�2a�w26oT3e V�clo�}� ��g*�Wa��E-�%z�!Z1��1X� 3-$h�=Ue� _&I���vic�U�;q�p�D�}�� 2a�i���Aexcep�6�� �! d�yMEDɓ��&de&CP!��&� �i�\<�� � (&2;) `&/;xW'' vnfl����q� \y�&�M�ed��%���@�&&� %�wio (� "�wl �"!he 2D�i"V@>�� e"&"% (x,yf6/ \0y04$s R0 'DF,N�1� � AiB�CG.Y�AMaw HC�Zus 3.0 A�H_�H�� C!)Cs� ''9����7& 01 e� 0125� "� =�\(��{� a:$ *P�nsixM��=�av�� �B� 2w �� *R .�0:*, R �sa@a�E~�q3� aI A�iod ene�ss� �1�|ap�]��Y�p %#�De�� stag��2� <.���2�"�A� (�!�)", m��_caip�Y�� A�&AatuQ��imG A�� Di%C A mex�c�OI�,��&��*�3��(f-�Iana-� �. A.�Q�%�Bss 2�3��canA�S"�i!��|��2t!H �!P%se=�be �s�{a�!�)2e�E@iYrL Ml{�b�Yin* M��}�"� 4 summaGs)��/,�,A�"$%ic!VnL4.&aV��,hq���- DZ�1&��i�=�.a>-� a"��� 2kstochas�-� g�t �)�Q�=�"Q�. Prag�C�T�wisH|o n4 aW�{''9�w���gcy�.�lvoi!?%<lozI)�c��r&����*mlfor�mA y�-�d6RspeedXi�:*� *�G�CQ ZPi"���Whx a:���!�)� as $h^{-d�_ �8I��newX*���s2�QA2-42�JnJ1dE�F��23s`a&V. �E�AK!��N��"�. N�T�r,��d VF i?n�$u5�4o8�]uAs�8��X9,&��a�!�t� +��"% � ��wid���a8d[0&T="e[�e� �KD��A�A�mqX*�T)� �_r����e�6Nl�k s. �Oew,�(�P!$or5.�Q@emch&�]���I0vre� "�&�Lo:"� fe �[.7:�Ll"�2�M�@"%��J%�lU�se�S)�v.P:�.� �Eb��C,�!��!~� "B s�t%�-�*�: beAEs�~y�'!>v�Asws *J Q�� �e�>� Y &2a�teT!�u Q5 �ay�of�2�bq4ct��a�man{:du ����]�ጩ�6 e� ����cast as :�R�xso73�&+;�B i*�O�ir"& -�pQa?i"�q��p���*�,!�u�%Bb��J:Vi�1"�D." -lik#4�Af�!�k��ts�ntE*S�#"0���PNSF award DEB-0328267<&.�� {adv��-rnewpag+rno�[nt�J�Cժ� �r0.2in;1\� ine{ 7 1}: �y���:R.�G1T(� vari moug,%J fX&�u9VF$ b�%�K ��Aa�d~;d�rh V.X��p V�)s? , (bcd)�s��F���&"x) aa� :8a���āAM���0B8"��F�i�� �e !� (UW),�Z'a�T�� 3A� d MED #e"�T)�.?C:. �ofS 7:�'a�`,-,Q 28&�'"� � aRA �> !��2"�&2,3.6)K'"�'3?I����%At)�$U1$�B�s 1-3, ,is��;+�$U�$,�1c�����f)��M��uc/�?�x��2}: SI[asM� 1`7��: #k}r#"z�T�n-F�f!r�!r!U nv022� "FEa!]e)���:�U)�E��aHUW��32�*M:�!�::�a�>R, �b!)&d� � � ����2�xB2� a>��a �%�%�%^%Y�a"a>;A��9I�e�1a��#�+�$.6'�e),*p�3>^as �ef (�rg�(� �pń&]�(� > F 4� A ��.d����onships"� �zp EZ"z � �p� I�!0�a��[m&� � N� ��&�`�� ,h�a�i�[iSX!�� �="_ i*Y bXVS#LoU��Q�\0 D ]"� -fig1Y� "Y���N6\V��^^ȭ�^^^3���6in64zW*d"�� l�\cl��<12pt,a4paper]{io' � *;�$fancybox} .-�:pifont6*ams�6pstricFk� "F.#�Hvek}[1]{\mbox{\boldak $#1$}} %.@ams�t:eepic:� xsym:��: epsf:4psfig} %% %% M�1a \��[DiNm3H$_2^+�pshort�tense IR%� s] jTN7�*r�@Z�/.E infr<4�� Q: vi۩{��KfKv2�H} �e�0 Liang-You Pe�|I D W�|amWJ,d J F McCann�, \address{ I�E��LRe��CjH�Ex� �6alG� ics \\ S"A�M"� n��,\\'�>Queen's*�� BelfastZ1 ( BT7 1NN, N�pern Iq nd, UK.�Z>k �kip �N\email : l.peng@qub.ac.uk%'%%Q9a"Ԅ�d.1.��m�}ge"l8�ar A!�sAN i AM p���Yi���*C�dka�*IK!~ r\"oNe&(�;��e�%r t���? "�3E]mo!�um� �q ew-c���nld)� lve Y��)A��� /z�~��erQHs`p�v!�h�-0�!P neut�* e. ^E5 $c"+4�0 gy9�aE\y�?�C ce $�%�1elay, 5th�)��5 �m��"�J(\sim 790$nm(��0� �,r¥U:J �live1b���&O��P�I)n�� S6{� rQM S��E�N>��55 fs)_ !g( a Ti:Sapphc/ �(B $nm) UI�;�Al 5.�,o� A��x!q$I)X.��4{15}$W cm$^{-2�2weo1�i.�I&ʖ�t�Be��N >au��~�{ sug�*J"Y��<"�{:ʆE��ykhcm�P U�s�os��+��,)(E��of�m�A�M%! Post�� Pv "�1�Upl�oto؂�, n�E�� Ahx*^2harE�ce���Otudse��P�m�arE�iR(nd i*�!w,up��dV ��ew jA�+jq�iAeby �humus . 4}. >�� ���&�"�/lPE�� etai?O * =�*�2u�!���ue�"Fras93,X�\*��, �ea�(J�B> !s�P% choi&�����iyIn-�7>]� of 6�\c�Gius95�QY& Plum95,n03 4}yv�6lLD:mQe�Q�u�&� . Nonethe��% "�6of �$ -bod$sA��,aco_�ng��h!}"�4� E�ef!/}E a�7�F@ m">nsembl>��s,�s��v|9&';E�si]^ion�f4� tly,A�gq Y�fai�!�#�"mtve.s�(���. .�""�Y�we�t!Dr:�*�ua�f� ae�$ \�'>o,� x�deu��)�"9Sa�ap!�e ySmWE�e�4o� dQ ar a}�Qxt�� scar��afLg.:5��� al �m�hampe)0�##Vty����՟{!M�k�5�'���' � BA�����)� ]c�2] �U�lVr4 yea"�<� `00, New03, Sand00,Pavi03}��%ruxp�E�!#souC�A�ch.F|�M+p&y�y�lk&�} porA?!J!�- A� a>er� e�W$a few hund!Z Kelv�nd "!Vd��A��2�e? $(v=0)$,8c�E�Y*R� �)�8  e�ron-impm,��, � &'} e^- + K@H}_2(^1\Sigma_g, � xDar c e^-+22^+424'5F�mla�ng��vA�2�*>!�WDcoo�A!AEQAZo��eanLat ��CT��!� focu"� ��Le�2v(" 9.���),J�Gn'h�U5im{a"��a femto<.�Imi&iy�px!-a d�#O 8F�[!�����!�t��� �g-��D �Z6�A!�� ���H�@? F��-�-coinc.+c= &� E_iɆ�>96�"��m74!���]b�orD.��le�/rg��(IMSƼ.[ "> �  *�@=!���^6)!� �+s�#�S ��6I^�6 . .J�])ach37a~A�e�i* �}n=,Uzulk�JH.�%��  z� ��� . % SN*� "\ �hdel} % \�[ {uC/�n J\�he�AL� *�aU!ro( im�!� Qr-�nz$T�Lvib}\�15$�3%vror�70? e�Z#Ta-�du � 6.| ��y tT,Fud�o�h:��sAZ�.ne�Passum�*random�E�H or�9%2Q* �ar axi�kn�)!�li�3coi�U��ax!7�1 3� ziz% ������v]��&�,*è $v=0���� $H_2 (X��)Pb�i�eYo}] surfz a�]� �$ength $R_0�6.40$a.u.0*�MmTtants, $\hbar\omega_0=��46$eV !: $x_eD276�6� �wav �e. prom�I �i_6�5��� �%^+!"��!�j1�'=2�,�$.65$eV,18�'�288�' �85$fHube7��%i щ�!ero��!� $v'$ ma�l�?.����o*F�3k-CondA�p��i���Dunn6K�%J.Qb��%��n  �K �p2�y%"V  %��n��y:�to R�� % $\�Nx 1.57$ !fatM ��habsor� %�jH&&�AG*2c* %�.n��urb4E�I�!N4w u�/erv� ��a symme ���re��d��a�ha�Bqu�Soppo*�) �are-of-m�,fA�� �d�]Y�*& �e���Y��2��6�W #/�aH�] ܭZX �8*�����Rvs�g� ��!-JfI������ . S� val�I*��HV�4�DÂ����a� me �u�a5�a_ b,Ňr���h���8[.� U!A,e"�1�"� $I_0Q�,z)$ �&.c�' cylindr��ly-Y^ ��� ���8>DGa�6a�ad�^$rCw\.Aw%�Loa�z,� /�� $z�k�1:�A�G} � = T {I_f}{ 1+>S( z/z_R )^2*#�\{ 1-2'�$^2} {w_0^2 :"�S>C L]} \}F�Uw"�K�Jum wai���.%6$w_tM Rayl�_��ge $z_RYc};byJ� w�� �2 f"�c}{E?$D}, \qquad� and}  z_R5+, �}{\dB� .nC. �2ic%%eI�e�;_!�I�-U�Do�i>��,It�7d�*B7en�-a��ged ,E�-m�A�Z�� . ��x�4Ša�I7�ec_��7��Tr% �mid�D,A�den�� by $B{r��B8cs � |1b3R&�?%��N��T,&A.e �hn�7$X&&^+�p  V_g��k $A&u &�U_u)$ � suff������>��T��86�a���c ��6 � $E_g(R�Q $E_u��^ is�&�u� \Psi(-|, R, ta�Fj,t)�R_g ) + Fz ,t) u.�20040224F�� m�$i�A$Zi�A� *�UH+ tBs�re�!��:.A�� tH '�st �l` .U�`ine&�bpi U�en��`؜f)6encVs (���n� %�avel gap)���n�to%�z tAT� �e^a� .�x� B� a%�$ad po�^"� "� m�4\varepsilon}$ �7m�W η4 "&�D_{u,ga� �mM�TZ >)�/�~��BKc�i�e&� i�W�* $V_L(A�= - d@M u$,�4� $ u \,�v E�.���  hat{R}}$.&�e a� -� 6O,  ,theta_k=\cos}[{`  a���� a�� ion() �pA�A��A�-�� �6or���!")6agĵ���a:� ��< a� .�>�U�d�$XE�2�u' 44}jpi��A��y ��m,"��nisotr9�"�h��#e�� i&��5>�!�2,"� a(^6$�A5���wT2ian#�di��:���ef�%A:F �1*>�goV|�5� iQ� 6� aliǙZ>U�%H) !q  Tn&�xnd� ����%!rvo.���fiIY�E91u�%�lU�7�5�7� �\ G�is %���9&*�"C1a��%��Ule� -)c�B�imp���ri܌w��r� �L) %a&��"�6 vari�O�/*�&'\ �a�C $m={9�$style {1 \%2}} m_p$a�J a(��ܫU=!s�"�4t�� 62Im&@��ed �S���: \nu� t*�e�� \fl> A ` jE�,1}{(2+1.4R)}�qR}{2\�6{1-p^2,�"g ���0p=(1+R+R^2/3)!@R@D ��B $\9L pӻ, a�E_0� �D�)�2�(� #"<&, $ I bOc *( _0 E�$. �2� c"t ���Qak�VsJg � =` f(v cos � t.9?�F�C_!�"5t(�GHQ�b�t�Jme"����fC }��} �=5�m (- (4\ln2)\ Nd({t-T_c}{T_p%d)�*]>��$f(T_c)=�1�'Tz $T���YL e &$�  �. B/ubs!�l:s� I+���x:pev�;wd� op�"2�ijJoli92 %Bh̋��% Dund�!�- =%4}�/diA=p���+E��eteZ}bwp_I � (DVR��'�`�@�Dt � "�?�pAss��*E�d=��($6t{,{o})*},�C�_s�L`���z1 Baye86} �&�%�/����f_b & =&�m�� _{k}a�c�(k^\ast(x_i)(x) "�����" H�1}{N}�[.S exp\6g[-�� 2\pi < k2x_iM�-, % # ��c/08/02/!���*lj �"� mesh�V98i = i- {(N+1)}/��4($i=1,2,...,N$�JE."*:$RX\]&E�`*�is h=�x "�a��&s6�! min}a�q R_j  R ax�+� $jCc\{�3, \do!N-1,N\&"�J��Z= {(R_{T-in})\ N-1} )� j- ^$ %+� + b) h+hBjTY! 2E�a"�*as:-�%>O %% h x + a %-��g)�%ihhyCaaf%$a =J�/ ��%���L7#i2�Š %�~xpI��M6�,ba��y�aB5q�F_{\sG%}l &=&29 i=1}^{N} .(_i�|a�R)2�h FF�fJ6�mra�{I.�x_ma� g$(R-R_i)}{hk]���*4> cm}( � = g, u"�psi%AB� ��h=QCU�/(N-1)D� g� ��:�tos3@� �|��c2}ja� s���$2N$ �.A$ �=g,u$)Jb {\di��\ !�_{j!PN T_{ij=� , j}�+ (�� ,j}VQ  i& Etau, i6 =ia�{F}/ O 5Oq �5(le�"�&'� pJor�9d^��U�A[ �=��ft\{ �|gin{a֖{lr} % > M�V`\pi� 6�ft( 1&� N^2MY)& i=j �pJR (-1)^{i-jM�2Z F]  I�$\pi(i-j)/N�Q}�a�n^2^#4 & i\neq j. �s � �. Q�}M΁L>" fJG �!]E� ^2 m�B�^�1�H;S6"� �2J� V_{uA/E@= �o)� E_{uij) ^29ggQyF9g9�1���� off-��ing: $XuX V_{g� 2� �_j,t) $ �"R M} �,�c}��� 18thiL Arnoldi� pagaA�as�m�0e�� t alM�x-0��^iRll*�q\3$RM�)\infty�� $It )ZlR�с��1H��gE i  ar �x���Ly�O"e��� 7 8n,M $.8. x6�p,n;�p`$  h0"�nde�edyic eigew 2���rumI�s�H�� nwd�`di��5�+l�-� t�V ��i�Ysus#1�0!St+�A unO%J-�i= sz�A_nAC��M 95}�mos�.toA��I�N/!o�.-p ��#*�m�-ILume0a7 M�Ki��� :�*� :`1��s�a?�pP;e�&�.U�K i Heat87, � �n_���re�g�= �.wo �X;�4a�� (!6� �&�aJ|c!��ign�ann�F|Y6 R S as})�t��Ano��O:\5.� �t�"n!PI�9h��+7$�f�4 (m]Q�� a.u.�|�Fq b�Da�aAa1!�N|�.+ $,t)= F^{in"*i +& ^{as @ ��%s�\F� < � �(1-S(R)�{\� \\*6��A>� = "R 1cm}!� =1, 29�"�N " �E�J=n�( 1� "��� s}� _s}��] �1� : E� $R_s#ea,� �e$� a&H)�ch"���m� smooth.Q�^A :A�.7M�Hamilto������"�����+�$�|$��1M�] Q!) (5Y {cWBhiE_1( 82 Ip 6��) =&�\sqrt{2�}} \left( \begin{array}{cr} 1 & 1 \\ - 1 \end $ \right)bC8} F_g^{as}(R,t)HF_uNM. d�^equation} These states evolve into superpositions (sums over momentum) of the asymptotic stL:�lH \fl {\chi}^{\pm}_k�$,t')= {1\o[@\sqrt{2\pi}} \exp%B<[ i(k\mp \Delta(5�) R -i\frac{1}{2\mu}\int_{t'}^t d\tau [: 9_0(t, )]^2)b]!b$abel{scattund�@where the ion qui�1 isJ��k� �.�d� ' E(-�9,�A symmetric or zero-area pulse is such that: $\s +\infty,- 4)=0$. \subsec!�${TransformE to �space} A� key step in obtaining an energy spectrum�! proj c oI@numerical wavefun� oA]3 continuum6asUFQ� (\ref-�). Itr efficient�Ldo this by discretiz�d $k$-� and per�H a finite Fourier t1X \cite{Kell95}. One dis ulty with)~(an approach�!�v9Rhift 5�$'a�ous 5�*2�is� d. T! proc!is rep�d���ed� some �af�uend��Ÿ R - # dissociat!�,packet still�li)pintera�Dreg� % to r)&he.Czone,���low��$ component�ebe cap��yp��ly�Aext�\�gr�^{$4 T_c$ dis pu5 e.�Gـproba-� densEsXn given��2z�@� $ P_k(k) = �z_{tM�arrow�$fty} \vert.j1 k,t)+��2 4^25 "� Ahoice!�n8liz)�N� P_d�� 0^{�} � \ dkJ� )  total2,!�Y$onAC�Q6 on � hared �!�byf frag� s s-a�proto"���%�P$E_p= (4m)^{-1}k^2$. !eQA al5�c�n IM�arom!��� :" �!�0E(E_p)= (dk/d )/$ = (m_p/k)-@ .>�  %S| three \� Resultse uss� 6 D.N�� H$_2^+\ (v'=0)$ at $\lambda=790$nm} � 4figure}[t] \cea�(ing \includa5tphics[clip=true,width=13.5cm]{a�_v0_h2p_afn.eps} \a�ion{ P)�6}um $P-9i� ��� :�% �� dum�$$T_p=55$fsI`aC�4 lines indica anticipa!�M{� two-phAV��ree  � fourabsorp�)q$!h$.3� )R1� } First�� consider r.$"� %� \�)�$�(re are seveA�very acc!e� aM� �apa� U2wbyU% \sim 33A*)m� or $I  10^{12}-@4}$ W cm$^{-2}$ � Miret94,"� 4We checked our.�s-�t�r]�,found excell�agree��8all cases. Now9Vlong-��length2�,� rec>"� 2 6-.g5L$D_0'=2.65$ eV. For:<if,, correspond�"t��Le Ti:Sapphire laserAqeI ��is 1.57bT��for><is ne��,arily a seco�(r higher orAe . In I� � 1}!� 1~!��:�j��IVF�a}�I5Ba rangŁ �sitie �)�� ions) � of poi��inZ  $N=512p �B. in>( 0$N_k = 2048$,Il $8 � (= 0.1$ a.u.�`Q = 28.5 . !�qsplit�%Wd� � , $R_si$0.7� �$. _s=0.2$. O -dependA�� ag�[ V�d; t�01 $. @S��� A�)F band�� (FWHM)AR4 ow $e� 0.03A�,��� is reflec�!� � ply-:d��`m& (IFs 1a,1b%B1c)!�!.perturb �� me�Z� � re v8 r� �e ��%��k .�2�channels ge dra9a� �var� o"� �_Q�y�qis!orop q aj-ihEs��A E� incre��wr�J� fward �� �qpeaks!Q frame (e)�L(g)�is�du� [ downQs Stark6Xgr�Q��. �ing � ter�E ��, ximately �[ ar ��a�y RbroadevE�e �Heviden� ! mix�of vib��al lev!��zshort2M lifea65DdecayE���. I} last��(h) 7!�es�It �M��is domin+b�^large �� a)Na�eV &o$field-free2�struct�0]estroy� ,Qp,ies above $ �^56^A�e Mj� s��tunell!2 %K�b�.a (9/0.5 eV)r tons� Giusaf$data unders )`*w in u-ime-in��.theoryA�deA�ine Ka��Ay!a s6se��d�. I�� �`��.�2})<� !Es oI6 effece��Ka��xed]� $I=5� %�: .& KsM�r�an 15 fs� .pha.accep��to plaA�rola�How  iZ,also importa_not�4 �ha��signific- � �exampl� �) 5Fm� �� 0.3A+�� woul� pla�G kewn� 8��A �@ 2(a)�A���)4. . �,B As 2(b)E 2(c)i)�embl!e�-! E�i" 1�e oscil��A�in)��� ` �2/� � well� we � L���� etail ld,when investing7eop exciA.-��x%%"�)� � �� � (_790nm_5E14�� �� I=$5.0�ZIThe-� sh�A0y��i!=I�m� (a)..4 = 5$ fs; (b).�  = 10 c2. u� :_2^ weak-�� �� >R��.�*QU iesBN2>N2F/n�!0ion-beam expe�nts, �$ �� prep��!rcolli�alCZ՛(#�o/}�e6�I� d� m� nt 2� �B�^+$2 �0s, $F_{v'}$, � ,,1, \dots,17K �� itudes $C 7`"S�(Franck-Conda�$actors. So��tac|Dunn66}� !'abs.�� �@t�s"�lyF�F_gr'V0\e^{i\phi(t)}�� =0}^{17} �# }-iE t'} )(R):1-'�" Ńs $lA)�� ��psG $ k *N.�U��7�h g(t)$  ��6�6I MT Accor� � qR�,� � st co"!w�BA(2,3,4$. �`� sm��� �pop� ll be� �2� r o k shake-off2(. AD'l  AQ�m���{waN � 2.8\%"� �Ht * s,� & curv�f"� � mors���N$ a value r0r�O�B�� is e!W � � s no�-s,aUeq& $v'$m��n*�  Si0 $t'=�"L d hVar�  �$Emolecul� rr��fo volume���dom2�E����ra n� E�jE�de� !� a� to a�g��aAu< _ Dan5d�illus� b phys�e�equ�ysU0�M���"\ . Suppose!�� Xni �as: $$��=0��8F_{H2}(v=0,t=0)!T�E"��� "=wa6n!*�y3 ve (UB)%yout���E3 ^&O.� R Ƀ 3}E�q=��ys tribui�&� B����pII? �� re $!  96� a ! "106# J* vely� =t $ nR# �� �!>�y2� back$ � at�"1"�5� m� Zrapid6 Ip�!`! arti�Js ari� "_&�"method�3low��-��� eme� most slow  nd radre)��""Za �$major sour�fnoiw AN� %�w%��4feran patterEtAA.�A�mB*��j,�<0.3RB2^90 disappear�w conf`�= 9F cyi�:  $2��.J$1� n&�  $shold mean�at on�"�$v' \geqf ���AU he&'!�e mod�Fed a>��l��both *� ndN6��@_A]� ��Oal*��bee�VsD'" measu�" ���4Sand00,Pavi03}��As�Tdi;bNJ��.SS)�dividuF eak �qor��al3(6^ y. Vre� �Serov�R coworkerK03} have��ea'iW eJj�yse��al!�!!�s 9  carefulA��"� :��Sro-6�mVd�� focus�&� ) ��.�)�����0.0"�45e9_5e10_p55fs:����di�-$�E_kvS �ašmi�!��is���%���� nm4ul�:**p:P ; dashed�B.>\�\- ֽ� (dota��H. ����� .�4i��l6� 1 �5#y310��a�ong"2%�ow4�asE�e��KJ�B\3B\&� IQ4}){ma�:��w l�siHN� (Fto Q�ew�|,�desira�-"M � spuri�(9�9�!n"an� chiev �$ng b !_!$um or��wai�� a to o|E��b".� 㡍��>�a�N mper�i�60oZ-� at:,A�)�.� 4}.p6 c��}��$52�16� ? �C not�nd!�n��rem�6+�� a priori.�AFer2�:&� 2N!�� becomes& A&�*�4}�+�!&�m� i�to6�A�eQpo������gain,( ��*[i��* 8 )#owards�U� r�[7 &�'e=�e}�Q�2Sbc (d) , similar, bu�Yis�'�rU� Q0y(&6�.�!�9&� $P_d�" �&HIe ????.F�Qio�b��o �A !F$angle betw��e�polar�A gto+�a�I��e"659(?�5angular-���2�ISuH)a�.'ly uni��$of cycle-a3�*y zR,9s:� (b),>�.< � %�sA�@$\theta=$72, 84 - 88 %e* �� s m*� {.�!.�_ ,6��,-�ar.!��Pa2��4or. A% !� F[ \� � le$ ��) nextAV�r��$�a "T%Ʉ�f�t.�der��p��sr�L&2*L&p55sh2RR&� �&90*�at�t �w r14.���V�@d$ $�)( A�eI  param��M2de��&� ��� nHon"( .�a�lD one5$�wp%��u�2@s&] A ��2��? th.1twoFfBC 4BC .�2V*�A;��3�}>C�@� R_ R� 1:� Dg#���*�"2�  on-� N.q n!� Z�6# � ^e�Jd��!�iM�~�0�Bz5>zI��4ll-known 'pump�@ dump' technique,],heavy atomsEZi�����.�moEjcI eas��>by 100��&�n� hydrogen t_% so�/ (�$1�){ ����res"Q of 4ror�rter.q(� alreadyE�b �� e�^+k!����iam 1 20fsz6!. c >#��w���)�"�/��ofF"� �� e�!C$v�e�� [ DE� whetR �-�re9�� ���+Yemip,XtruWe `E%��tudP%�Q� ���R� �ŗM�.^ 5}) 0fe ɒ� -"� m" ���-*�)�o B�!B� ����M�ar9����6s9,�clock (�) �zu. A�tic-'ev� lyE+$,,ix�+�rt �Ke*a!� q� reduS��K17lat5�)�"d..�!AN���U.�1.�&�$to?clearlyYUf.�- 40$f�n�familiarF���X l ��".3}yapnt6 �"ev�`IS.5AR�A?"� � V���h6"a\e�3�*� y� �D~�ME.C � Eܱ�2�fF�"#&!��2 t, ex2A�� )� I9��K toBN 3:� <rmA��g�i��uȅvNM%6��. ��O{: R(to�-!(n 1F-WeN�aT�)��E� O�#si<� Ne�5*�$)�j AC� o�*en"�4� sca��!b 5f�,�! �"yE4 M�G at is, apu��}�M��du�)�$�+�%-�"favour!Cev f�ency kWuls�Y A�a�!�& �'se)I4�,�ٹ�,E��m&{!Niik02, 3}��5Tong03, �i�2�7})B3=�and���(3!�!�=$2� i��ace ae3%�1)�)�yu�.� is) . upAs2qF_Q9/u�.u]'�=+E)uE�r #%�1a�|ong*�,u=�� 0.7eVIH��{s��T*� 5} 6� � )kPh�7��Q>ly5�Rh7�=� 6f�>2�/��Ga�4aJ!av'����`R=1.4�#s, �e��8e�-�eL�dei~�!�9Z��d)le�Q!�$$\Sigma_u$}  W a w of 1� +.(moK!ut�`dispers�A� )O�3ely�]M�> �E[nu!B&�1 . Af�97fM�*-6p:��e��urlv1. AMbappli�.!�ime ���f �A3(�"0.4�2 �� = iɥ�u%a� "�9sq&at, te. Atmza�aMp��b]5a)rre�%;u��a�2M"�M:NU�2��5%�mpro� S+te�l*;ig�at�. Compap i`�}�4}>�0"�By � mi$�)�Yedi_����7$v=9$i'�nO roug� . d�() � eal*/ i`�"�:5�N �PE."�*$ often los]>�Y�M (W )� $synchroniz�|�$e&s 1MA �i+tmw&�ɄŖ2,3}.&I,ACassumpew�B�@aryB\of%$�a�r8�B�.�"�2 >  invalid � Urba��i> too surp! s�$iN g!��2 good.� for infra�:[ A��& &� TaV$son� modelH UV B or e4rou%act�'m CUl�ts| iv-=q �j"� ooteC�!!Jy�BCtoo � e*�( diagnosticcee�i�Cy>exist1M��c-sq9 %�te+/a�-sp� v4�(a8'�ed� 5 servIaa s) �-s.�5 a�ng�> � ],,F�8� IlE�kineticq�6�I1Y��A��T-�_ iwi& of z��YA!2� !��$ �$>8 �5���)ly�g&7 � )���j" test%(I��Y � ��<(paper (, �in which�takp to��oun��S���!:g�|m�2(!!{ Łj�1��or�FE0� � � t*�3r�ms�0g:,o� ��;= .X >��^��!��!�}=d!�!2��B�6>��'�.�>5�_�Y_p5:4E"�3��͐a^I�)�"r* . $ I=�J�! (a)$R�:.$fBq�xa�!B%f ; (b A6] -�R��#C� ��G ��2�z8a)B�7>� i % %�t�9: 2 soJE�� } %%:�˜@  ian_y�:�jCs& �6a�F%�32:�7 .�&.sA�)� = 6�)$w_�)$z_R = $ B�#�: Pw.�*;?%#:�al�&?��D�#* ;{Will00}B�8} 0i�%���%26B� A`&c v� 2 *� 9*�0�Li*x9coinc�c�F-of-fl."�'� ՊO.�9�0� �� .�7a-o�L�-Ɋ?relev17j h�9ba%F.&"F2A�Y�3 } P(I_f, 9D ={EFt J \rho@DI( , z), k) d dz)�P%%�: $I_f�L��� `^'ge, AE4�`���Cg A�T �-1�?�)��G.�YouA�Y� shelg & �:SD!# J-�9��i!�# pA�r�%6%:� :�;�  $r. Non� �shp�\!N>-e�_E*extrem$v5cha�& erisT 5 � � ly encour]2�.E8y�;S%�"QmE. M�:���+ "L s, dA?oxR!uy?? year:��"7'.}A�b�3udied,!�vi�5!-bm� V/Jxa�-!I-C:�eLse new.�s�ll hopo�v� M K>� [� UP� crib)�A�p� . ��%% % S �9: "�ICo� G9s} �sums&e(tho�lyq><e_2�dynamic%Z �"^+$%��g!��&;?�a}�-��ml*���.�z5v en"��t�~*q��P0��w $2- :�,!�vK� [ �%���EY)�-�j� �Q�y,V� ,aJ^ �U? E�A�� A�la�t�\.WA%�,�&!$�* reTy�>u/v�/�1�C:� M3 "@��w� mons66aVPl�6ar!�� UOat�' &5"t� �"�@b�1�JuUe�9�8$ sub-femto�A"� ]. q@q/ *{Ac�" ledg� } 4* ar�Us�6rA��1a�Aa PhD, � �(hipI�!�In�3�al Res YCen��j&� al Pt7�� Quee�9Univer&PBellRA�is �1{�*a@�� a gr��ofA1mp�a��4�p? Service�Academic�,.�� Manc�Der�Y�:EPSRCa|� UK Multip ME�C�=#0 BEC HPC Cons�2 um. 1�9�Recce��Hthebibliography}{12&Pibitem{Post01} {\it MI�! nd C�8�2in%�nse L�F��}, ed!A by IPhumus J H ( Cambridge.i s,, 2001)Y2�4}:P2004 �$Rep. Prog.E<. } {\bf 67} 623!MFras93}  inski L J�@Cod� K 1993 JMB,??-#�E 8ti-Suzor A , M�x\F H, DiMauro L F, Char�El Yang Bj5 �p: A��l. Opt �} �28} 309.!Buck90} Lsbaum P H , Zavriyev �, Muller H G, � Schumac�_ D W �0 �a\(. Rev. Lett�64} 1886VqN}  ,-Art\'{e}s SkAtabek Ob4)�a} A �49} 15022� Ludw97}  4ig J, Rottke H\6ner W]7f]56} 2168.:Nguy03}  en-D!�(T T, Abou-R�1d!�  N A,� ault N, L�`vesque J, Vijayalakshmi K�, C�' S L A�3f�A�(013405. NDMr Rouda  8nev V, Esry B D%,Ben-Itzhak IfBf:�$93} 163601.x  IAilliams�B McKenna P HSrigengan B, Johns�)I MAZ Bryan W!,%�eroJ!Hd El-Zein A, Goodworth T R!� New�EW Rh Taday P F�L{/y A J %H0)H�833} 274A�� New%�2w� !{�![-� Eurom��D�u26} 997-�A�P00} S\"{a}ndig K, Fig�.I�Hansc!Wa �y":�85} 4876a'�9 @\u{c}i\'{c} D, Ki�G A, H �l���20��39rU<  ,in X, FabreA0 Staicu-Casag�De E M, de RuetteaBD Andrianarijaona V% JuretaA 2I, Saenz� Baldit�T, Cornaggia C�f�92e004.Dund02} Bdas DJ 2 { �9��� 65} 023402Y Peng�#�eng L Y [R$, McCann J�$Taylor K T%�69�Ac Z ,�({36}} L295L]�4}  �6����-X� Chemm�120�10046��� � �4, Parker J S,.�Meharg KA� D�Ft��J�]9N!0�!-(ics Scripta�T11 �54�� !� !���2� .i)�.+9�j51= Plum95}  mer MV���5��L112 �92}  *�a��l2 l!;V�|86]99fR  *q, 2���Squ1bm ��6 F z3~w70} 1077.�YaoyYao G�JChu S-I!:���y�48�B�fU 99} .+& �: %�r�  "9 ��f� 1999z`83} 3622� Bunk73}  in F V%� Tugov I I!@7j�8} :�Bate51S�$ D R 1951 � J.2�w 1� 12� 53Lin)  Li�̉�JiD F� TN�63}�28Heat87} � R�0Metiu H 1987 R��� 86} 5009.*9 Baye86} + (Heenen P-H MvDY!�2042 Ke�d  e� 19q�N�5�a450.�;�fD�9 Privr%commun6[�9.; Joli��  c�TG%2] 2�� �%!4!!842`�= > , He��"� B.~�* 512mQI ��ne� 1966ry44} 259Ay%Uz�  %B/4fJ��Ko�� orskiX �, Nakamura H!�B!L)MJ05341�y�A v V�!�A0,6MBi�Ngj��tg6� D%�� �H, Legare F, HasbaniG $Bandrauk A $Ivanov M Y��Vi�[euva�} Cork@B�2�eit Na;U� II�L912��E� n���3b�21} 82 U�,�/  XM Zhao ZA�)䁱 C� B{:m $91} 233203n96h�h.\4I�Int# MKGi�} B-K18� 5�T]Hube79}  P�} {23cm4. opmarg>\{-0.6!b .9Bext�/} {14.5 >!odd�; d{aX#=�%� %&Ldvips manual: put a *�A `DRAFT' oe' ;ge % \ ial{!user G36,/bop-hook{gsB200 306)U 65 ro�:./T�h-Roma�>ndfontF�1set280 0�-to 0.95$gray (�))@grestore}def end}�"�.8 \title{Why do�,7<be�#hecond?} \author{P.~Agnoli$^�^$nd G.~D'Ag�((paolo.a{@�$webnet.it):g2$~"�H\`a ``La Sapienza''�- INFNjm giulio.da �4@roma1.infn.it�Sww.2���'of a�!!W4/mag�-:22�I�[f�%"�M"J > 9\,1� 631\,770$ p�� the �v�*�#A�to���&a/8F�!hyXsh_�#$ (F=4, M=0��F=3 ?funda�B@O@atus $^2S_{1/2}$)f!y , Cesium 133.�hpro/8ional���or�7I?Av0$�'$a�-$ ;mP.� 2 ible�Cnthf wN7c�Bn<ak�>s)�s���/;-/origi�A�5dM�ui�J�| si'� ��WQ�$1/86400EY(�% e sow�_n�!E� A)Ua Earth� (na$ $1/10\,00 cU�bet)Hx polee^ Aotor� `'su2 face";"zh, �%l�![initi�sn Kr&Yy �2� I��tmHc�L�x�)a��F� say `'�5a�5z5��o&�1�%�ρ�n;si�a� $y colleaguDfriendso�� &2T��cE%��'�* `�n'�- �I �A�I2t i.e. halfm�,�0sa7r&\es)bn>�exerc�T(see Ap��ix A)@@wmD�<:n�Iep"X�=n�2�quq-/wCq"la! .xr�J�e�Lark)4*�U*�+, �CAef��!� `firsC& ter'e'"�Comehow ]9�X!� "Ln�bexplici��$\0 offiy  d%� i>�l/4ar�.���a2 geo�y.2*e'��XA�a2g�w�Z17!�� %EG-� &" 3Se�d !believ%vMA�sE�an}��M�s,13ho gA[thM&BV� s!e���sal d� �mW3�b�@.�?i6�L �tec ��cir�Dr r B+FV!�bq}]:�ma�4�1)�*�&gin�:����Cb�h�� ="gra�yɋA%e�;i�aake�o�re�"  �E�). }n�1t^x$sp. �F��(�q inA�allel, (�%%�) abr�6v! eQ�,Ll/<mp%uɍ�``9wU�%y����_��,� �*y''}\,*v ll Eng-  quotesC %<r!�to .�#p*29ie � the s.}s Comm2}:Y��;e size!�%�;>M�a:Jpdn* ar; f���E -s� M�of 6� >� "k a��>r{W�1O&1�^I!�M�i�xit�I �&PM}+(,&4�E, jusUp:�%��:� � f=,  %9"T�( st s�}iE9haFX�H�E�m�v�!�bs �[(P}�!'m9on�)ub*d���^/>�JIR he 18th |.ur&�:�sp& 1791�re��<rolog�1revol�] i�, -NR'5�) H6iG � a�Md�'�%`'s5b (��p%��[LQ�,8 decimalŁb-m�'�>Z� �  Ou�tqsciplin�<o(w�hy#�plaus�z!�a M%&� J:A�&]Fa<an�P pomorphic��H �Neh�&}\$u sec:�`_!s} u?)U �A�jA�@"�*6R �.� A���5� WV^+"� m�[� Q��3:� � E^V0�y mp"� n&/�� hu� body��4Berriman,Kula}�S)�+�st�6hi�1Cof�y Wit�]=�s ��``k�Uworld�J$ himself''�bB}k  a�-�m(7agoras'� Z-$ a*all� ngs''}. �aɲan�R�S?it65 achAertain�e�H�)�peo� who adoE �0%w m� tN+�+a��.-҉�ir  Ofeet or�gF*j dif��&87 ir n�^ bor'�<\IBu8� ��C�C@ces did not seemY�, 6�H-]Ti�Q3 acy �Gi�j lYQ�EeAal��Ea�La%U:�� ach�c \�n �!�� c"\2z,MK[^Bi�co��te&VE/e�Pa-s, 0`my y�.i!u'��`  in�@' :Z�\fLi>2�8 ~w�e L�Qq��Egypta:cubit}�/2�- earm �elbow� �s, C%a�D 2500 B.C.!�a piew marB@bF[50 ��i�sm�Dilke}"�ey. N� the���Kw#%zt��A�*ec%�eiv�]&i�5�!�ep?J.�s:�vfi,"re��W � on re��Kime �H�3 ck,P' e,RiAQdson,�}. O@� a`tee!)ury, ���  olidE] �� �P 1 thod�SAo handT,!7dD \Z�0r�e= -ope�>� ng �?�,�M=3em>�/as�AcuP-��! ?need +0Q�EA���@� $7 e pl�ra� !usea]varT3�@riaWJ �'i\��tow�%%��y)E @ y, m\�i'W 9A1�at Q.t ��Bp!%� U"b phenomenC o  �a��l��F���[N qIn ad0) coveGimprov�1�6� �"erc� EOA�ituE. )�ly haN^du Chanf3a� of wE��0mJs� cur�?U-@N7l � o%�ly�6 resi!�c[^�B:%�Z s:��" }, likA�%g� new77 i�3�J ��!�con�Wn&Ll�� "#�6s�Ec"ebrRc2w�>��A��[%X (x,s, book keepxd5`� s)�eq��a%� �; ����ca�10& ��e�Nto � prof2  D , else's igno�oe�f�8fa� (w� switc$Oom!`$)pepL-�81�uro�a Oc8�ofa e�lyIz"�' M$) �psych���,. Pa�� inertia��?g� �Q.�  ,�ob�� vely1>�]l ad7! a�e�y �modif6y� r AKalH�<%�s ��%��_0%:a�"_�u�=LqA�w5�GuLl�mugh�E� %mvI�i�E`ЇsAOLire'� uu)"=-�%�� b&Y� E � sswoE N�=awJ�n hel�Om �:vewM�*N � P, =� �A\!ea0Yˋ���p bankG66`�=rn�]e�~ ,�w��x3ve��@r�c ���`_>A��!�*A� yas!{ af��U #w� f9)�O asco.& In� y!{ p�n�mL�)2kiᶅ�!aY��Fi�to&�]z%� ic-���@ai� CaroM5� �RenaissrA(m� "� JQ �t9J!�>U~�, Is+� ~RCBgcbSmid�n$;,�g]banG� aw. 6&  a�Othi�.yc=a; � e SIK!Gpow�IlWatFcar�GHP (y��P &Qdo�KkW1cd rs, se�5I�media�N#Cak� HP),Q� homex\tA� �0n kCal/h, (A��"~ic/�reI in��mnd air��MXco%�` Btu/nW!�nv�+,;tr7�!�� %�i:9,� rw!��=%�)� �"x th��citize *` �4�)]�nF� in ei�j- FA�A�"� �all�Y~@��>� U� ly n6hasN�� )[,�dx �u�MmasV^6�!�� e (@fewI�pe�e,�� don''wen�!ec!sat� is poss��=�W%�!�A�7�a /dh��wM70� A# m$ mean (�.H�� 2\,kW). M��proble�#�g%������]AIr>e aims�� �.�<O �i�Pof)�. To%�)���5f �A�L  add�)" pride}I�reS�m~ignŦ s, n� %9�� �y-/b�] _$�Y � Pid� ist�l�- 2 =amDO&� G�88e[i;y. Any�!":5 �>EtX-Ei�@�O�hC�� ���Pwnd ��F' ��.�"+���a�6aI`M�il� OBvisag)��*�2�:AEڎoa� 2e�b m ��PRE] �!Q���8 Joseph-J\'er\^��Laland8O( April 1789%id xtrenuou� def��kYr ( sa�#% T���RJa�of&�Y�#a�ynbQv�b is o�v��V&�! dmitat��qev%�q ��� to b�Z!�! �T�UN� 0 %Y ct1t},#Ath)2�a���Ea���xh�Y�� A!�zury)J�q�� 1889,A��me��"�^  a�� �����X�Z�O�2<#as&�� prec�}��Es�&, e  q�A�E ���Yitf%�bas� slawP!�wL(all(�en�N pDE�]F�6��e�sol� �up-�pllum=��Jn���c�))'��� . Perhaps)�q�est�{d� the 2�  !�for�f{so � �"�w!Ad�� {rrė sp�q  " Ref.~@Alder}%, p. 95 ),�cru!z �# , so��rMa� �H 6k&H�%J1 nEaOa�)�*<M��t� seek!%�Fat� r���rbi� A"%��i&���Car !,5. Sta�3s `� 2i ' (e�``YW d�v la !ure&w) D&t�8sc���lҎP ��Qq-#�F�A�ŵmo �sa}ept�A��* k��ahlyell�f . Be%0!J�.P a���>�"8�&s�I|�V e ad�Na��beA���)wO  20� �����"@ Y��corru�or3I�*?t�R�, aE� �$JM ܝIr��terpre� of�Nmw �(-�o�beU#edehow. A r/�r episod�6��_0 of΂ ��:�c�P�A�fi�%��4he British HouQof��@��i��34�% e.g.cauk��7}).���4GhF�!�F�)�M O�օ1�ackCser}�Y� Z A  :�, G*��a2ndcEted S�1s"g��e .��@o�!��Ogram J ~-l ccompm"�y��au� Pc�"�Assem���� !./.��R Hpr �s�U�Jf "�#J 1790� �Gy%T:Hu� �R�!heF�" &����o t2�,.[ Q AHY ����t^kc} F�9x 1�e7e�!�h n�R<*s:�ir ``geAr amb� � R�#J� ��� ��ly�����-��odG�p(e� p ���Q�e� ��g�� (� � `8 $rnal' infl.ee(( econom�(, philosoph po� �!�i\u�Z^j!��=tQ�)i� Refs��b3L,Hahn,Rothschild}.) &�^Q--� legi+%u��ssu��d� ma� a6bvtw��b�r:n ���wA4X 1793 re�luglio}����EXcitoyen} Louis Arbogas %�ś� n��c&lu�r ``Vsu�." " beneficd� [��� ] ��^t_.Z� !W�b�`�/v ThilE|!,wishes; clai�0a�ce WLe%AAA}�,&� /useF�!� li%d��AA�a �a 'Ftj ex��\fraudsy8�Ra�bea%�{]}.'' ��sucBx �Mc�mp�#l|c!R�? �?4ts m:B� -A at, b&�"! ńg�_ spir�" c"}lud_9q�}�[CM ! Q���/m�%�� Cb"W�* &�&�.�!pe� \  ��f� d#r<b�/�ber��dn <� �!hao�_"�!MV��a< lA���Zupko1awa�800h�[-&N-� s h a/ "� a�� var�einJ�,� a�" 2505�x�_�P �HistMeashe�``� ��! � � dErn��v- " k����provin�C�,ur� embarrassv `�%%�W`��7�i"�v �q�09�* un�n-�a�� b1�, �laz��Pr��X� ��hemA�Q#� g� 0t?~nfPT $ide� nd�-vX�O*7f3�KY�ldA͍� to u�%$mБs JN�Od|O�=daA�-�Co }�FSJ/i�|vout�)st#a�as !vV �� J% q . Reab8&0A-8c,8W ��ݑ��� h�3ly7�� A� 6�*Y&�+�bswing"We,��9� E� "e*�"�* �,�^aSA3����d�toz"��:".rE9eso suddu�ura�, &x�Y�5 alyz� iwo�ein�looks �a e� coupA�1a�*E4bwe� .WM��+J>:d&Jɦ �)1�%"^+, letysB�: ͑�po�0ofyU��-�-9o$odE!t1X. * +Te�=&d:.�*sp;ee�b ngBro�� ņ�� advo��d far ->i` �'1$ve����AadJ7q�m*� ��ie zw -!6�%�O6"2���X�j�+A�o})� !jI?c�i+'� ���+}.d0!cad�  ` %'�%) B misus��E%)�͌!v! f*�8�}" �,�X5���)� solu4&�to�:6� ��� l.} 4 e\3' ����%x)�� �en/s /� ���� o�=n^la,OZllI0�v�dA���C7��Gni intu� �3pme�3�[s�$Galileo i/ @.�6c��!X a 2�X���\et �"�W�ofa � �0�.ug&�%Q 17&$0�{k#��| q�� �����a)�a,6I �;� prinw/��a{S%�imE7recog�l4>)`3�f: "�in 1657J Chr* an Huyge�I*4�6(�A%�pYg)�A0`YoQ+ ons'B9-M@Ac����`-ly��� M��*�8�4o�j� � �L7�s\n�$"� ?�e �AOm$Mersenne,H)}.B discZ:at-�b"���of�7,!�6xc"y��ms,�\�g�u[8A�a�@�|al"�!pday�nos,>�.%��$enthusiasmAb}E�a�7��!ge%Tlittl?ubt(ut�����4sho� %=�E�� �d�� ��9A �_'U  ce� .$*,�� h as2 � h�v. #��ste�-aJsub� _n�/=in 24�g�)12/?1� dayl!S�2 %l) +iz��2."� �,�}�"!� �#A�roo��#� Y Babyloniaa��.�of) �60 minuJ7of^!��r�commo[�eLd�ieva��,om�iB�t !D midd�� 1200� analogh#1� :�0>Ab��)� ��:� GL�7 secundus}e=r�7'fa�!)*` '.�!8 `u�', <#1 �HA���~4)`e[�/� �,{ae��=y�ustom9$�5Q�L nay�A5�Dclose$�!h4"+�H>�by ���d ��O0����e}�G��)� iBy>�� �0gni� � � hear+=ce.44��e�*�vq�� Mf{%easEz (�25!�1007�%,6�0� ��% !��Crk?! �f��idered!�"� {� ed� &d t�` h8�8Q%b.>~��~�  unanimc"K!aia�M�'��O1}�,�u�Dl�? = ),%&m�8.Y>� �GisEG.�  T��build�3� a!~cR�a^ �aIRp 3sv*h�d!'�zw�#�(youC(A� 1!Y�vn�Kat *� �xo�M�} ;ifB�8;P,&� �%�Mp, 6��p�V>q�\A!|lIne�at �u� c�=d��o�>)um} (7 ���A ԇ>b`A�͊"t)a�o�of.�q�M��� E������0Royal Society��1660,�2a suggon �F e� Ole R\oa (�$on ks of Mm �  pu:I�pn�5 � 44:� !� �a�fo���J�ogous � by J�/P�T^68�z(�)�l!Ha��ra=i8by Tito Livio B# tini N75Lho1�! FaDnit `�'%(� d� t%���?(m�3e� : BAI&f%90,A+ ) �� E�����i���6dei�E!� moI��M2d��S of � ,a�~�;`B?FJ�F\K� "% ce� �F$45^o$%�&�%a�3F�by h Maurɴ de Ta�yhMO }, u�#2�\by Antoine-Nicolas Carit*�e�� t. �-a�*m�Ls� er a�Pl�Por&�.��*r��$Coinage, W��nd u*ֆU¼�;J��`}:%-WC ��!�!6At�ic!G I Re-d�5s!USA�ret�� �  mas ~�9� � t.R�q9~'s"or���5�  of�)�re3a�"7"h0ad�#Ye��_�#$� � ��Bishop` Autu� v b way�k"d him�+_ g�w�$N�݁\��> 38$^o$_it ``� umA@U�52�''}�:omM�5r}.} (�D(�re) thir�Kn�B\% �A�3;B�!x�-e�G�+�o& N&� �o�! tech*Zl"w-n? ng rod ra ��]) O2��P���7Y�A,0,�eC I��$l$2�%�s behab� >nD2/3\,l$�ey'�)�� bar}�3/2%, &� , i�I� 50 cm3 % A��� o &!r�/ �| sq �us�|�d��1BI$Pa?$Xu9oe B�\��, ob�� L�;) *m� �a� Sir �e Riggs M�Yr9�I.AeT'/8acts �8�L�W D�scollabo�{�;�Z mon �i_��?Y��}�al ���eJ`"�us.^'"�.CG �ad�R#�D*d'!�+adJW��^;%`2*�0�Md$� 1791X2D+�$.�M2$ ,AmChSoc}IV� Hz Ger� sc�DistT}.�Rtr "�R�er��ap!�{\� Old1=; LP7}_m4>cAm � �fig���-law!|10&S 1799��at��~!|� ACbe&�E��3 p�%O1.296�Rnes},�M443�{li (w4�cGsix��g"S�digits�'vVtab�Y,}{lcc} \\ \h~b �Name} & mbP�i���P_#I�gne [ �ne}] & <& 2.25583\,mm \\ % !29Я002.82906229698 pouca5a 12\,)a 7.06�Sba !49 0.027- 48747563 %�(�goy) [�+� })) footu�u(32.4839\,cm�%385 0.32$384970764 �/-&fathomR $6\,QY�s}=864 �} �  & 194.904tNJ % "(36310 1.949 ,0982459 leiu�" stal�p�gu)�20�Q��898.07\,s%  2620 1964917Q^ \endU{ ~Gtab:f�>h|G'u� 4l�{ A;J6�X,� �em�*� S�= ces Wto�9l"a3un�=� a�J� �1��m�&dB�C6O. �vov�p�� diplofL C�a6�(l& parq l- �,ݥ�=^2 F+#job4� �#b�(` c'|0aWn* Ɉ� ,~V+.�cJ= v�� ym.�"z �al�J� 45th�H��%cqS�J``-�$Ջ7ATŲ��`T� a 0/(x���#_7!�I;n�%\Fh~�p!6L����!�senDso1"  I ~G hes� a�A�c  itj2^W38^0$&�/5IA�~:�I�7!> ^MZed, du"�.�, 5�>EC� I��Kill�!�uH�ypH7laaU">E����@+,^5�toe(�  fa�Q@�=Isaac�at�C�, Giovloat(a Riccioli,�, ��E8er, Gabriel MouJU &$Cassini, �?*de Laca: �s% �hur/L*l$. �+"h7in 1740 C% kF�[ d!~�� (4� \,50^\�Je$p  ), � CKlu�$ 440.5597@�co"�TA )!B�),�%��[to 99.3��c�"Ne!����h�Q-�z�at�evE�� &m 3Z452 �Re"t4y)): �I�at.5�%!428-` �53�AY81�uBAʍ`,"�2.��5uB>M(Geodesy}, g�&!�39.15 � (99.065�)�h��{���T-Q�� birt� � � .$ o} I�"�Nof� 0H.1 �D6�5I0gŐ� B�2�r u!Y26@��2�0�'��An_�WibH"2-!�Z46� J��! ��F BGasfC�3�e��@�]t�dB>2"�IF'5�m�Adw*� �� " c6� C��o"�= -5��$e:*�T:&a�(a�-~X)%z� ..} > �&? l}� %\mB10column{2}{c}{uxP�#!*�)} ' 1644�  &�� wri���&A !5�Y&�`&-. e60��aH- -�R �&8}�7p�WK6}.a�Qp �,�A&�of �|e���8�SK ��..W&�0f| ,���S1/3a!, �>� ��}�\\ 1679*�*�B�� w%B�$ e6��v+^'"7c}>���gB*([1 c nautImil� �5`%3!��cE lic} (�53� �er�9w=Bk+M>����0-�|"��#g N a%>O��r�<-* A{:� �! 1729��p� �];UNu�$%�}��^tM26(wh" \\2&& ?�be G C?2 �� t)� 177y�.8 �fd=�>7M�)y�:� (2i��P@&.H 9;o{"9A�7Z�6� &�[�N�}\circ&�  (��zne2� JulyPJ"T >�U.S.A�-�f 6o�B�-�U�6- ��}!LJ�.A4 , Aug�H.L'�al�Ur�D mend o �Kn XVI�I:� &d�mitte� Agri�$�=erc���O���FU�&9MP{e�����M�A? Octog7 & A}*����d,Jl"[�g8h,>�&z�aK�1,�ch 19�-��, <upoFebrum16,- o�;A��qua��2� of}> u}6? �aa�*"�+�0B/d�R�)�`.��`Mo+ 26AbN�:�eb^+!en�S���sY�he.3M!�gW� Ӷ�Vn6Ç�th>�&�p��0to M\'echain,�rendV5nd J.-D. >H(�l7r �0lgn5$)2, Junea*LɄDelamv|\t:ZX%�1�*� }"�"� sAa��g ay 2It9[��WA��4C�N��%:� g!ś�44:�A�"F mmEQ �N"~6m!�)��3��1oA.���5fM.� ecre�1795,MR�?%ADm�4U}6� �#i��e �Eȉ�,: su-g�v� e��K�$!�GE�im?�"|WI;l�MIX8�y&�J%6 qI9�� & An�nKa!ZmmwFi@%6%]}:�L�)�M�9M�22�!!� �I*.tka� �$l"0�*$2�812��� hybr(O"�@2ni�A Na{�"��:�&�T�*,; gD&d�non-dM/R plaLndU*"�_:� RiY%E (�=1 �W`2 �*tc.I�\hs�p(-1.0mm}[1831N%��P Q��2��X brea��Ard �scheme.] 18371I_%piJ!Nr!�l�GyP<�U)1"n�84  & NoH��-�A�H M� if�IA�8896�)J^m�'ל�6��:j� B��G�'&�g � ue� 19"�-&V�<$1\,650\,763.73$*Cd�3!�F� e�  EB�8$2p_{10}$-$5d_{[�tra�m�#1.  Kryp��86� 1983 r��"ltrave�Cin o�bB�r*�s*�n�Rj>oI� e� 2�e…$�"�2�%6��*�=styyV�a_�v ����6U Ϙof>��7#�'c p \�F� �Mt�C*� Ml* ���Bc�d Zre'�r��*vV��� \ �%x f�='Borda�0Con�&, J�M L�0ge, Pierre SiY0�;o�� Mathieu T�t. 3�i��aa�L�dj &�>o�b.��-Y!a�'�;� he� ;&$;�6_ �5&2at� Q�s&�2�8�) m��h�'�a��<� for 2 HsN7a2  �*9�M��t�#�&on 27"� AVcH��=9<�-U>�1�5� L)�(, Gaspar Mo�&��5�s!y'!in�0l tact�J4) Laurf&(Lavoisier\, tG�duxY"�(�_�P As9f%Z�3�����s�;7  16*; �g�+(!�'.W(qU!b19� : . On� � e�F� �R_heq�'&O��:7��EO� "�  as�]sd� � sI}�xeM# F�f:&J8%N.;.gu!��6��&�# �@�8p re.K&m&�[-[dFo]� ��"���ealn�2�Zs alway��ee$wQ�an im!�O�A� �A��KE0�� Ɠ inf>rity. �"�!=E!e&��v�:Y�s�ion��(R&.�,2}, pp. 1-2) � �B% % T.�)�����#Vi�5A5���<�iz�( �z�\&�;E�em �m~�jm; ">����� cm��0A�/G�s"�Fx1=det � 6�9%�)O6[5�J�75Mo�-y)8AB��r {>,�Ab:EQ:�#,Jin�5sicyyaa��Ed*u$Any�$cbas �,W��!i�6A5-���Yn�5(vel. SurveyA��)!i�k[m zd��A���p{�!.} � %K� n L 6� E3!�i�^+ till�@nav���Lnd 6 now �61�@�6���B�, &|1852\,m=v� ���Qta�Z[n� it �U �/b�G:P"16�!�;A�t!np�u�IMYZZ= $d h�n�1).6�#aAlp)Tsails��30 noqbE�*�.PJ�!4�;in�%� ag�;�e� 1��a"�< �aI�d���*�M 0}�&:!n ��a �&�e �1^e�&7��� ten-6��=u�kb�;6��H��,�n�~!�[� old,� �a![Q�rO�m\= <W  :Wi,�r�>1�A�W���C le*�<9,E�V$he 324000-p(9 Z> :a�pYeICG*�> �)��A#90 I<n j) 60A 60�$z5jud~ `un�q'�^eacad\'j�i�a b+)�xdx.i��(�ythat ?-�y7R ;e���Afj`�1���c ulty;oi'$�w"`D}�!� 3G��:�7 to� w �}:{�"B �_�C2�  I�m5��)KV ,) !�lnE (diaK,]�Q)A�a�85xPw;�l� H�#� i�aiɭ)F#mH{)l�Ls}&�a:[ u%{reUH� �JL-�=�hjp�8�.�*0 yAW #��ar��!� s��!�? ����e�� =%�Z!�� Af�q ?South�L.�@� �4 ">r�]"�A��,�:c��x�R��,� �A2�f"-&Amuch :�t_BEa��&h,x5er � on ��lu8;n�;�&G%$�&�n�,ar%�!p�y task�z�Va nove�facXba�&Z b�A�,&@( Dava Sobel"6Lon)J}3A ���0eA&w9��� ]b��g6u� desBM�s� $es Vernes'�6Msr�Y Islan\V} O�c`!democ qc'� Sr�%�U�T!� slog7]9 ��6}�I�cC5 �x,of na\"\i ve �(frank`Z b�aooIG�s�extra�� c�tr�,t�� l 6� � hi�Np��E7mi��: [0un�d� �s�zry"5� �'So>�� eJ"oyd�=A ��@ is�!�I�=mS%Х��Fk!�:��& : ���":)��a�n.�� &�N(cAcaRP�M��a��/U!�Y/�9̾anC� �~00s� �H�� �4� endi9OI a �/o�e�;.� ��6b�DrV!@A _ ��2� *e��m�\$nyU,��c{ti<�\e6Tm� ivil3h�a�� 1 li�E�+M� ��!� !�bw fort � %�a�� ro��Un%l\�k�A��1A-i8rBF��H0qP!���s���n&Z�' s��9y��m,0ss susceptibl�e to be determined with precision; finally it is possibl9tstate that all peoples belong[�one of Earth's meridians, while only a group ofDlive a H�[he equator.} (Ref~\cite{Comm2}, pp. 4-5 )} \end{quote} % The pendulum was rejected after a bdiscus�\ (two pages over a total�eleven �0document --- quarUof�� is instead ruled out in less than half ar,). As a mat H fact,]commi �(acknowledgeE$t \begin{ � {\sm!�{\sl �length�p1,has appeared�general!�deserveA,ference; it3Radvantag%�bei!�$he easiestBbe YU, and p consequT ((verified.} R�. 2) } 2� Then�(report specE-�� should�a simpleat-r� latitude of $45^o$, because {\it ``_8law followed byF)is:2ha oscil[ngibC way,��!x$se who lik��underp�$l digits: )��0es from roundA�-/E+ a -f_ A�rectly .ed-��im� S ���74A[.6Z�4\2/ Essenti���]��*� �X provid�ay�c weakn� : q�Y|It &�no� � auc-based o�H� i�� nsic�Ds,-~h} ,�K�Yz Kemper��e,&�a7above se��(vel, plus �w,r more techn�~ issuA��} also�rJ�9rson's d* �U}. But,/��y10)x inA�ch I�s9isA�cussed�re� �5of-FE F� h=� 5�seeA� ncer � e�es kindO phys� quesa� s. O�la� (p. 9)a=� y!�pa�U��an ry��6�QRal� C!� ulumY>at� � =�o� cuum!! =�q meltaice.'}6� }9,)Gchoic;��1�� � !���� AuCn gO`�ha'', !it�RperceivɛBorda�( colleaguesrj� [\ldots]}�ljs��tA�cl� an h�@o� ous� ��,�9, or w!~is ��� hing,%� intensity!P!*�  AT � . Now, if��Beto �B�'U�de�� anym�quantmitE�&�to�  it*� Our ��:"b� cise!�a� not right] �9 }.''� Y�rea s sp� %Q via;� 2' >� .0 f�v he i)�d R� s a��wo: i��* . A� ilar situ& hn% w�B5��T!� ��q���speA�f l!.} \\>�\\ &6 i%Lm� �Nm!u� %�� �lac��o a!�euofE��gte0 $trial circ7V an`it  !P�a =�Y.R�The.u?E�y�ie beco��� � :�� Bx mx -��is ��W��2� r ) }2� It m be stre�5aJ , howeverA�| � �+ a*�res: �th��( scientists�p%�� e5O��8Alder,Zupko}. %Pnew)soffic{ c�d `E�'&3The n3 ��E Greek�metron},� n�� `� 'eR first �Ŝd%�[ u� contex-�e�A,Academy work|*�e(RSmathe� cian Lebl� in 1790- , 1}; %�, sAKhistor50 (see e.g. Re"d)T) mainta�c�+dea$ � orig�attribup o�_. H]))fo� m0(A7& ,ly coincides1B*O)%�# � �m � ury �Dier by Burattini �Apa�ix B).}���wo years�!%sec� \ref{ss:� al}), -' occa�� w   aE�&� � wh� � !!iIL� �J mate r -2A��public ��� , Lagrang=d MongeM4BLM,luglio1793e3\ � {Establis�� g��%lD}\label{lunghezza_e} %As� �� ione�guraJo��JP w�}� %.=I�3. Rea� h5Rap�� leD x d'uneE`\'�  meV}-? we � surprised�to� ;e expecA��5��g�� . Allfs!��o; aPd��haq�&�A�� campaigU�f!Ys lPMkd .���F*� �QQo�! 0 imaginea-  memberJ 7N��,al Assembly,}I� ~�f�rea�%� curi to !;rough1Mc� theyIgo�g4to decree. In��T}Fa�.s�n q3[siz g_�resultфe ��l, 7.4�G kiloe ��0/ �� beat  ay. !�r` v s!sonable�believe @� IC��=�v -& fourth-��2�!� )C al!�y%xn r�9aull,S�t�� no ny to� cify�eirI���is�xourm�; s. &� ɤ� q u��subtl� a closer$:kAensIA well ��"!,4,e acad\'emis kepE� m `sA;t' or,* leas� hey Zreluctan]��u�� by:N F��apolit�s�n� }. , I to uA0mureA)�iA*%T! ly :.  en&/"oQ�.glett proc!��order. 6 Br�;�revie�in&��~�8ec:sp}. Compara�$ Cassini'sE` Newt�)��an saf�tak��*� ed %�)3�. t>"440.4$ $nes (99.35�L �now!u� IF!�� ����nA�q�e MarchR 1��-��> . We shal n go th��a�e r� mend�B�Qe����Iaiaccurat���in6���� �#�l��!}U��d�. \sub��M&`�@:q b���} 0\*�E 2��E!a c! eng)y ���?A����� U�� P� pher , i.��ati��sixth � B.C.-�D�� fam�uQu��at du��EratosZ �((276--195\,^soMI�!�250\,000�dia� ��� 4 %$�Bs, if�~E�159\,m� Hum*>D �u?� tieuMI nverf facto@-Ũ,}Uioni�(errors in eaeaE5 #dif�j� �A us� d9 �� ob�n6c�Y@ *�Wuitou�"��y�at nu�!���� 10\%>  AnyK� badg Ase� (in��!Xr �complet��new�> � <�'+i|�O�.� is� Aaych��Nm  f } $e}[t] \cap!�q S� milestoA�in ao!i@q� . $l_m$ &s �y!,4E&cuPF -�E�th .?a (a�Fimpor�?cas� {is � �+lig��!H  T �Ftab:f��h_��s}��E�).��)ms��jin�Vform `$�x}\��$s 360^o$' xacn9*~ )degree�8arc ($s/\alpha$m��). Anlt�WsM I�a�n �f larg� cei�y:pt#��).}Q��er}x"Htabular}{llrcll} \h P Author(s) & Year & V , & Unit & kmm�&-�(m)Y &  & \{)�\} 4 u6�& (III���250�*&!� dium$^a$ x&.: 000$. 1.0$+\\ ;� �2\\\ Caliph Al-Mamun & 820&\56~$^2$/{\tiny 3} & Arabec $^b$%439986 & 0.9997Pk2d{� \\ F�l  1525 "$567462�8 & toise &39816Xi54FSnh us H617H 5100ZH 38661 �665%� Norw�!?163�73bH40204 &!l051GPicardF70O $5706^� 4003�1.0009�J.  ^718G97Z�40062/.00!&%�LacailA nd!9174%��2^J 40013 K033� �de Th%%�Z & \{443.44\| 2\"�}5!\,Lapl�&� A{1736} & 57438}$\,)\,$360$^o$}R8YQ P40302^8.0075}\,]\,$^c$J� Peru2� J 1745�674��A�7�I�6�%L2K� A,{\bf DelambrD d Sbf� 9}2#20522960ex} �bfA01}] ;$M\'echain}>�^ �hA 296}YN�&[%�\,57019j��$) <40008 �itid19}\ \ %�d%� �wM� I43.38�" � !w�yM ? e".%� 9152@m5.& �229mz [ B�9A�an�op \multicolumn{6}{l}{$a)$ St�Y��\159 m.CJ:b)$��F<960 m>U ^Lc)$�q*� at ext�#"J s,�' se� $to� ��p=ty�F�d)$� &&l�%is�' assume �)J #�& f�&� older�srVaAY�)�of E�iN�r? i� %ing� 0$551\,584.74$9�e ewJ�v"z � 4Dunkerque-Barc-a ir &� � l�'d, $9^o\,40^\prime\,25.40^{ e�c-Guedj1} � �"tw �  tab:�o#�  %apr��-of�  Y � para� s, expos� t�"odu� y lG"as as �# .o**p s, }b�und in.�� �e#ic !�8 }+:V1 is � to��"i" ho� .-an%�%�($s$)d(�guP open� ($� e6M1y�*Q!!$ �N"� �a�m shap!"* �eWd (�a=a ya%�)�a! anglj*5 -r��astronom� ob��s�&�!($s$�b!�!o�1$ olog"! epocvar�j coun�5&= step�y�(s^'m8'�%�� pi�> Inde�KI+&��s"y) 16th%18"���%?� �er�"&� ,� �'Z s/� �:oQ0 o}).a�AaEE=�inf0,exhaus��-ar+ef�s!�pin dow]&E dim��o�1&rquite �/ verg� 8y1!/�$�eC$in Europe,A� a"s0astenc�-��.�$. For exa�,  +s2j � "+ )�, J'%4�950nB��Par~ �2~ !d$w $2^0 2�� 14F�E� "���st zero ��al!01884 t1�re�!"x�nw��v++gh Fra�� I�nd adop|yo/�9111acrossE* C,�:�$ca� *f� 4"��{t� � �D"�s��sum�3B� (2" 90^o /�� �# 864= x$). E�3E���ve&^A�B��,an.� st�*a ��E9�x (I[6 mm) U�,ec�!61�& T>$was defini��� %�&'. &� a �R� Bn�4T!����3�57027�/de\-h,"O 1� A��! af%0I�&  ies �[ɵof�f. A�� !�N# ere ��confid� o�"| alS`qki�A]%��fl[5��\3*W2 / �0.>&�rol2a!�on7M� bulgt+x m�3!�y�� �)! is Y3�h�!�force (21' �+� ) acR!+ bodyz c 2 �4 always orthog�.�-`�3'l =2E�6.�� a�re�g�WE+remm be t�!R- �s� tend�6$o push flo� mass�& wardxe13A6s elo96.|8��:�6 ``�)� uK c�(a lit�higher a}.�-��"gE�U+s �sub,1\%a� , by asce�.��%�gX1-D fa1fl�&yO*�reK)} (Cite�7 Ref.�Bul�%�}.) % )�est�#--�*� �1/229\,; reenberg`# S�al2vW=dJ du"�* }� ��!e�1�}zAAn> ti� %_reian enor ��!KF~"& of S�5c�e0sue#�.;!��� !��ANxpe|�6e � s, upqar3 W)!�8 OU�*c H k1]d �4x$573}$ 僁�na�Acar l,en Fin�,A�m7�!"$66N19b\,N�! P6M�Mrc@3^0\,�jl $1-31.lS� Irstamps}t nG.web�+S dica!�1U9�n� l��r�� r��*inm$g(��-� � �0ct�!x � !��&� I��lo�� curvO1�"3*Dѓ.fr2.��;  ;, $\rho= �' /2\pi$ is�TB,ur_"3M�ey5� s �ly� ��,s��f'B�0\epsfig{file=5(sse_cerchi_V!H.eps,width=0.4\line,clip=�;��7\v".{-6.1cm'  +6.8b"�}, +1.2\,7.3cm}\m�9}R+0 &a83.68:�AnY gge� do reAP ��lV9al �, sho*:I z-6� � ae�_�maj (,�i�4ceptibz&$hum�ye�� Note#�Ha�)v��uw6�i�1'!�um6 ,�@Mpo�_��ove=itUI* fig:IY�=)v}�it�b ?ly �st��� ,OJQ,e��LO(a ����:y�:`) �le'!VminimumN�max.A�IV.�E<rc��T2�kl�, 9A�!t�s �1i�(T su�. ent)%- yiel� e_eY. &�%�� �"�-�%`?~"��o}�D��a�:s Ys{/+,#��X��Ac�2rea��%�%�1� (j3Us�~&� k} k% --- ? �?m4E�ng%6!�:� �*= Smith})� comb6�%s��76A g:5:>� !���-(1/280--1/31�/ ~g 6�(�  1/300ys) �� �[%�iU��&_terra� %��%�}N�" � dataf TOE17ageQ+�%# refer�WGS84�boid @ �. ��E%!�g`C ic `y�z' $R$4s u�$�b�� 7�@�;�so�b&� equiv}e 7�In� e�91�1`e{t� �7of�3associ� 7�25 &L 'I�&q, aW��0d"�%!�(E��*���i�' [CirKBr'@$(a-b)/((a+b)/2)$�"E%! t�ot � ies'� i�FfBe�e��, �?$Et*DS devi0O}Fe�-F?er)�f I �$E%9��9W� � use�G%%�se2�, N �s�O a lo �Y%vC)���bKF� U{*�#J��#(6\,378\,1375( \\ P�c!�9'$b #&-56\,752 -EY��Q� -71 -Gq��, $f=I!aj&�0.26�E�j �,AI0^2-b^2)/(a^2+ �"!�7.7�"E*, ,, $e=\sqrt{18/a^2}2<0.08182 = 1/12.2k�&$f\ll 1$: MP E2\,f}$~$$\\ % ($e^2 O06694 P49.37)#Mass, $M�# $5.97369\� 10^{2� $kg,�Ed�ty�$5.5148-3\* \,m$^{-3}�Normal�9B-�A�D$267\,$m\,s8�\\J8 pole$,& $9.832186F8$$G\,M$ \ (~9$G%$A�6� �'0)& $3.986005�{1�m$�.��8Q� U�� :? $��} %&cGn�a �%��}`(i�2a socc�5�-squee�A$by 0.7 mm)�1s ���� "� XJe�s2 Y ,|"g*a fewL ts�5$1<$�  To�Emal �>s"|-��.k�S� ��" ��h���<�<sZdi{Eeas� a �tiv�*��$uracy decaT7�-� @�&�.e@ �� �A�l�$1/ ��7$%)R�>���p�ed41��� @ pape&<co8)N62Ch�/oA� dardB��� �-[� � n�3!5M*�B>L0?nt. 2B/�<7�)~���M�:8`f:p�7� &�+.�, toge ?*�# �# � ��,�':3 inE�+ab8^s� g��BLM}. AgB!@: $&e systiHwe�=�� s, ,coF:] �c! ort,%�� Au�"|6 }6�JulqEL year�.�8 %x6�%>n"�."� �-� 2� ^ u�Lc��sh�!o!p03y0y�., 8/�+l \�b I!0�GCd��0is 3 pieds 1144/100 kLF"8�  {\rm [� 2 ]},  eUf�n1/?eDU:�&A exce!E�De6of \new�O�?&90.5*(\ \noin_ � �0.2 mm]}J ���6z!ordin�N�2 etyc "�Hi|3B4!v># . }� (\Ap., p. 5)4-�%�%� %�>�%�soA�Pe�e��1�A�H. ua�a� Y )}H]u!Y�,a�,���byq�!1st Aug�?��.V�2-1798�p $:����c;ou�:a� ��r�Kz��e�� �?"�E��ite�!�� e�t�3- 1�@>� b��} �|"F&��$Perpignan,&� M!Cpr�Cl� e low_ "s��aCo�Ku�G a Iyt��7��( Spanish bT.}� ex�A& ��J"o &�&(a&@S a�J��'�/� � 1075�!�rmapal��NM��o}�et�;!X Ncette�:l�(eF=}''Bs�7e+ moti�$H}�@a8uk ente�=E�aFma\I@l�S/5� ��� �.9�" F L!f0 ied �?jM�Y5s:� Tabi�N��%ers��l��vol�G��is job�:������&�A�ol�X�Tr#UE�U cquiCW|Q*Timi!] magnE �M\d l�pt�E�QmA�t�Dn|d3 �B # �R�Tis���MJa�]} cut � middle � ty fifth �Cl,�4,at guarantee�� exacA��!execu%Le�,is beautiful]P��e greata� +�J.2�L�r}�7tQ-4>E� campR�?stWFd immed��O a&R" dela5 f&C�F!�afJ!Hm('s�`posal��cce�$��7!�"��,i D driv�gspiriuh &�:!q*lso��g � for �`egyQaA� �sJA%Ne �itiA�� ide�(rK+���(new r\'egim�Ocan't�s�  ��erJY ���P!�r% no�>lC@ judga�l  awai)l ur h"��# s ei� todB�F&AJmQS ��YgN moN�' �, �ha�eli�;Z ll XSi�K� � 6W$!Lr� g&�R7%� ly� esC#��_ ��G.UC�Y . 11B�wo.�Ino�.�#-�@: J&B�8$ste Joseph"�1%���X%�� ern 2v8arc2 ��, a� �dQ&NC Sea,6w Belg,G�u ; Pi�I� (\c cois AndA|&�1J� souA� &t!�a:�#ske�* � an�Jt!�[:ish�d �%�x ��yeps�+ier&)YD@�Mni�ly��X@eK)�$ir work (l?R��G^-A���s). H&�Gings  Am$ � ��t�mplU by Re� Hm w5G/G RefsQgGP/, A�E�'raA�c ac2p�� ). I�N�  racl� atUN%B"�3  Vme�4� in  Nov�D 8 al�1aU&� logb-T1G.�s.�unK!F���#%N 5q  E!}�*!:��urgeda���B4 K �`v�� "�Y� =��cRe�%� �� mercM��� Id�� �money ;A�5-d�] $,��I��� ion p��&� � %��Js���Z��ny%cerZ g%��.Y� $Decimal Me^ S�}%��<r�*�He� law�April 7,!M5, f*#"���PA�a a� . A��en�R�B9a=ter��al%~�^� co�X Le1GDe�6-U� [%8to�& �vJ)!&"�B9(IC� �c�Z�*296G,e so.in-Om�E�`*�.&A  "g *�3� 2�l!�� Y�] an!�Q�5J"�A�"� sub-Ta��2an � Ee*�=SB�!,cl�!�� �� 9. "�.mA�%�sets ��t  ^e='A� %i��!�LI�Erc1!�E putcJq��)1/150�Fe A�descriV@q�!��J p *��Dq�9^)G ka��P b/r �of h�D plauspictu�4o� l %�%~%�%y��ch[ �4�0orWc �dgb� h� d#!cu�a�yK� �;��yold� .}''*�Hdiscrepa{bet"=` ��G*��1i% nt Q�e�a�in'"� �M$ -6�'�$!knMMa"-al�oid, g� rC>/� ep� �Geoid}�3��5�'a�!�sta:��E8@11G (0.3�) "0.��. U"F� �-= �:V q�o})ee!e%� lI- sl`ly"Qse��!�&Q�U�� W@- o pointi�JJ�O k�,vS�X!>da�/� i��LtH�"I�way�F4 rk[A�]Ea�E-pp�-� F� ���)H&�!�o}"^ [,� exervV�� "�]d>+�%�$#)nI F�,��j5�<�0}5%Ik �s�:ng�vQ� 379 �( s. S*H� � ��!*��ly �8i`&-/F�AP,! ATLX� w 296/Ben &! 9�_Gh�S2��'=�� F��$�"%�_OK�1�1��Us E=6���s �ed2���o�e��� (<�E= @014\,$\(d��!fL l@06�1 Om)" � e&x3 1799ɬ ��"4"oug�.]Lr��!� 6H6B a{s@�#� O !�'Vh*Mw :b.}� manu!�ݰ"4  9l,6�i�nP6r �����e!� in J�R%'. On 22  �prototype��-�(as solemnlyD %Council�Eld�Q!� �F�Hu�a�"�SIx plgcf  �P: ym���}�<�M��)>Sremarked"� {Olly��K���i� !)`v of� �'v ppare�2�i�6��� slog�Q� e��v/t�+,�"�� }"�d�A2�"]8�d��/&vcandida�9gc"TU&�id�1rM_� �d&H�� {\�(��]R!X. &.!in lisB! ne�7*� �go.z�RfM��9pG1}'%��� o� untk8 a0�R8Q8�7�>���)tervM����*��arr*f�%!lh ing:� } \\ 4thN@ To  A .}=%U1@�"�i�}Vky�R�&�osu`��M�a5H�`Z:��~e+<�]�t�)�he��i.��>��� }���d9d̓v�`�R*�`a�&eezA` Z%i, X ha"leaz! 끳ipn�� P@ k .�P2]��QY-�a�ae "Js"� 'E �sc(\M e jo W��.@ 2%*be ��*��i�ak t�"3m-ycA2�4%=!d E�F�.*y K -d�2S� a5:1�a.� �a  �t %! & .�� A`rN`� &� MD�X� F�Fin�+ undoubted5[hM"vestig7 i#*� a�t#[n5 e�I�� ��t�!�Z� Char'A�i��lomb.} �p.F� 9) }�C��t�- h=qm@f�#ay�"'%�-��5�� ru o�ea��Q$.+km�t~ pr�{%�q+&V[��3 1791"�Y��!}!'�]'ŻK<� made��. Nm0the6q,!V�,��so herea� .}<" ]�Qh�ara$!C� i�����G�2Hn &APtooH .�Tir7c�$OC0lSf�d&�  qqFPe`�aB�"W$"V$a��Zo�Uf'%M8Eo�d;�_i.��o�S��I!�1792:F�#"� You�k y(|ny��be: am�6��*�i�s?�!c u�C "w�-� b�*� e`S)Uabsolute(3 ��"Q��d� sldn:+` �bbyAE�`ng�1iS��MD#sj zeal� sagaA5, 8�b�]gXC�L&� S�w�HmuNqAjfircon,%+�z�hoS5to �� �Aerman�� e��world��5 nefi�* trut� a�5"�\�  an զ1  IFi�/ os�Yefu9on{E"� s .:�I��$9:�A�p�cN'>� poQofD$:+���*n�e���b�Uf 8`&� s��3c% c�!����W� ���a_ �Tq�IJ&�)�e X�a cub�k�!of Q5DP�pt��7! �mo� , bothi� "�'2�*�<l tero.ek :X_c&wvE� >!!�h e-P�+ 6�!"*&'fY!.)' )Ne��:'*<E,N� j�< s��27!*W9)��g�3 speak�a�*�� B�}''M� �� c�Y?L4aɑ���B+%*-~ 5�*� H��rH?. m�� E��wE��k. &�>��e.I�E�l:�i_ !�1e��)p qII� ,�� *\ X�J�$t?X�q!� �| \ Y��=�das %$u_m = l_{sp}\,t_m^2/^)s}^2$, N#�0 ;�WJ~: ��,>9%� ��$sk +. .{0+ as n .�% 25�]on>� { vK8� ���o�bthq5�!mis!9' 3tercalib��9(ocedure. %[I(�H�D�4 ��lw�ll %$Q>ilon$E*��h1 � %!�Q%P"I = t_m - u3 %wY %'*?d %��on %�\ Q� s(1+�wep�)$.] &�CoA����u�g/�l "�*� l ai���pI0!�%/rk� o�6U&ivMTtit'wh�s$>mKa�1�%>� $ ��ly�v9�. &hyi�;�*�!������DI��raiM�lil8*Kt �6^"P���rio;o+5���'�e sub�/,��& '�i,�!1 �!,Roche}�)Rb%fu�"awz��m�iGDe"Ce?)~\i�^�u�jUe�Nrifp!�non-s�Dqc dom�B6 umer^& y, eY�k"� el�un� [�s�>�]�[�$ -Y "�k�\ar�Oh ; �"eZ�0inu#6'�;�B(  �? scal*>�x��r�@�b��( HM":�JlaG _Y� =�\Xo�){ Qo(A_al \�<&�. A%� (e<^a fgAa���ej� ��� yS��U������g" Ns7;ze0 Me.o!tn�%�p <"bJ �Z5t�E+A86400�!�suspic�� ins �^�DL�nngI@,~, � �r���� �)ed%[I % favo�A�Fe4(�gd.) &�h���2�4A�.R e�A� V� in S-W@ mo},�z#�)0�#( D3P&_qa�a\"\i v�3. 2�P l�e��*!�u �� $; tor,cGu�&]R By� e�of!�ucz I6�?m�,%�!��f," e� �K�%��� ed `democc'�.�3� $ i� UYi9�E{�ry���/o�'toEG-��*=��le+�:;�>:�-EA!�ot%(}n���'$is self-e�&hi�th �(�?��Mb�Wg#��F���t���~�#��%n! V )2v8%�� e� a{gcy�&`U exchdM23%�2 jA���PR,]globe. CQs�Q.eۅ^2pr�kU���per�+Q.yW � untry�-� "�/env �NFa  09!LMC06�� �9 3#,M )�is��5 pol�0 atnst�.�A�:����a2�D�v�l*�px�� ��;tsAi9�N�.(uI3��!v2��O"Q to >`'0Kh*bq rr\ut��i�*J|��%�Utoo far� ours�� ��o�m]lB � ��)� ^�+�� �:*�G� �!�! pq f9n�&�0 2;,&�,(a �d mass!�hom�y ity)incir� r ��}�0;�~sym�_y arg�2,"L��1� 1�i_1�&woG d֡�a|2�).yO,"��1sA�y�U ,0'kswe!+ 2� �3� M�z!�al�Ior0: veina/a9 81d�q�%�/��e��!claimed �>ge"A.�t�V�a�.t :77�%�"�)a&�6 je�&�6�,�M�z���\�:.!atya�� � x �(sa�ng 2(cloPa�:neous߀3sA����8 "or"�v� ��a ;*nqM�EX%�Q�m��0PolP2��$ \KK {runM��$)q}�(� EncartaMs�9is9~  /�f�,Vsu!ci� �| �)i1H�Fb�gm&�?/$glo-saxon @a�$o�?!?@~!�~1�siA�&�D}�h�3 O�Nn*find neQ3"�Z~Q`Q+|3�X-o%� , un�!bM6G)�0w�!]2por�?�*��satisfGWM s��%�con�Rd�%��Rp�� &S&�of6fR\>,����k~ "� A �w�aR_"bn)m�7wesF.��"��Sco[�Z|:onw�J"84�C-�(Th�� Swis-ighbor,)%-� heZ" n*��irA��!)�,Z��h.�1� teh�� t{VI2H^2G�) Brit/�USA�`t Y�!�!)6�. All�v�?�� mpts�9co";�4`Wa)#*�/#^\3frustQ,���rw�X,�8u�E�_qs.�*ގ7�rk�(�l�3!�E��Ia5�����L].'s �2 K,"  r %Th%4Ry5�?��l\u��u, �res��Pa�m� drea�=�#P*�uB )%"D c�6g true. _ <)l~�!� f4hbnch� �IKo AAZ/*!A.�=Awer1�Mh k` oAs6jw�A� rans(}un�%� misa��;pp�� e 25 ��'age 188� at@s 672ɸs��%2891!� Ital�6W'M!�!$pq%) M�5Cl� O͋�/isa�R�&%��ymp׌t�5-�troub{!�Pdisuni� � 6*c-�c�s,� worse!v# alizE��A 1�e e�Q�ep�`$a�a��z'$� e"� sJqE�caveat} ��.��ce se�Ya�w/o( upo�E���QkA�7 ��A�%�Gp"�e!\!�E� �? �78� &�! ]�a�K . To�**�or Mhysicisa�t��x�wL� @L:U\�ba���y <�8'*�< �}A� :')*`8a=a .ve�TN��No�i�R&n Et�z hat "W/lys�a gaugR�\shop. �WI lcx5i�90 �)/ .A2tm�܁�(i " �Be#rBg%"�2�J," mUE��}E% Q� �&D b�2�h%� FIFA�6s:�K �wby� � �U [ l�U4n 70 cm (28 �.)�&� �:68&(27$*�7�}],hS� an� �l�ec:,wE tape�C8�w situ�%�&D| "�:2�a��J6�U� u�we �9.-O>r�t� )Zf"i2#"(��06�4|0 "�?Q�a��u any}!g!��2���&'f�n�. = �� orm lY k��f�vˆ���, "��I&�S�.* �H"<�KR,<�]c��-�"%5< irrelevE��U�A24wQ-�)a�")^�Ace"�(�%�#e��1*H Tc C i�+ru*�x�f� bY, CcE���@%.���!9ftwo�>�����D(@�n!�*Z-�CݘT� � C mq&e�A�Am�� "H�E�!��$�EBMn%�ed"�c{Td& � o�its!��M�6(%e,)%sk r d �r�� y�)���za)"CfacO�1;��'B<"ex� itlya6i�p_./�%�8* �Kya'ez� a"�! 2��AY1N�=�He�  .+a�0%� ime.6#$)�A,190�;AhH>�n h2��Ŋ/ reac�<[P{s.j_ 7�u�a� A�rn�Wdes��AacN] �-�y�(�Q�#�Eoid')�A�-'�VyA`&G5.Ar@ari�lz r ��ed ��,� �] 12 signif� trhsu�v$y�� �>�ReX%�� ed):�PXf=298.257\,223\,563$ (W�X)�p9 ,geo_tuto� }. }��*GQ! Q�!ss: "}��r$EH,���a6�>� �d4?�*,Hx f -��>�� !>�� p����I" ��)�:;� A[�M�7M QK�ub-sp�f �_} lk*3-.l�1P)Y�>�� elf?�dRp�����Et�� a�Ep X��RJg2C����%�Kf"��<�  >ng .�5t)�!m no tao��&�M !�E�no�>cul#2X sub5st„r %Despit��ldfen:a��Ņ��7 � %d��u%��H6��'Y>*# EZ���*6� h%a�_=�1��"�6��Kd&�J\J�@ vulg�U2��)W h[V �(often taughX s�>l�A�memor�bQ}M�slio.&4`�c',~r!�is.�j���De�!X`��'j?�`& le'. �\*| ���v�wadayE&.f�`h$ (9�0a�$6jpo�H�.@Aie�!�&�m�q�"�MeE���unanim�> �-ed)�� ���%�a� � �&GUt M!"U6 ��: �[{\�uJIit��4s,�.�]wh!U� �c)DbQ� ���. ��??�CA�? O��6!��B�tbb tret��a� .���, may� &vc~b~7rcd� �Q��� H4o�@dg�w�+ m�j hemi$� � O !�lY}���51a��� 2on��,B*21Zd: A :``!.qu [fu"< d�be said:/CC���Y��N1!lM�> h, i�!��!�I(b�Nl.c�9 ful.���La�-�D�E�&*'q]Qo1A%�^�N� �7 !�y���vK at's :Df�!��"� I�& I�fur9&- ? S� UO�m�6F!8 ��$�Q5ve� a"�\y�"EaH-6 Bd�Pr!]G �� *�>x1+)M/55��* ]6�6Wa�. a�� l? ves?n"�A,�� show� 6� scelte_;o}�� le"1'��ic���t) �)�F"E "� 2Oge%�X �Aa׎dE 2� a�Wa�malpy-�B�} >7j��E�ư����ja !����eT!��`�io"B �e&��of�^*� ,nit. (Analog � ([�=�A�A faj �E-H�"Ql�_{lrcc} �_� c�dn{1}{c}{�H�J-�*�J6�D $T/2�` & N6.��JZ (cm)P(s)IZ݆� �rb.w^ & \ 64c0.803\\ "�& I�^�^>28.135\\"�x+ ',\ 430.6-�d$�7 (�0-dbFj20=1.419\\=4B=��)R� ?004\\ 45�*U^�� 0.532��!6H%al&��C�FI (s  adiuZ�&(\ 1�&&��rc![�\�111.05A�1 minut���O 5$^{(*)}$)� �85!� 1.36; 1Vpe\ 3p0.5589cM;2c4}{l}� y\,Equ�F1 n+V��q��'��is 185He.��endue��u�&�b6�4l�bS*��ځG��"F �,�/!�] �'6�yor�*'�"�y,� �tob5� 'Y400<40L~Cr'��s�K]m�+oo+/, ��!)�4 1*�<da�ua�8�M!i��lla>%/ �~I"�"0X!  (!-4cri�'s� ��B��un2#l�ap J }!-@foo�U�� �� �IE-ej8��)C�#-to�+ a%���m"^J6V, B�/ |k6. "c69j)C� 2 AL17*\ �!f ~s�E6��&5 . So ���"� st �"� ne��"1,��/kA"��3�rO`dk$ -�%�s')�y7s 8os�B�E C &�S)r5��j !: nu�� �:��. O� R%�h��Ghat, t�<ye�i�Fnd4 `*["'��57D �&�8 �CJB*��,!%osY%>Il Mlq; stud�*>� ]��KplK/! 9 *�6&)\s" g*�0-��!Ga� aS�5m�#-��-�4jF��-to)v �Ufi"�m29��� yB4 . NoK�M� exaA�� ;wa�*lx]�: Dral>o4 � �2u �al�T� sugg&d��by B�p؞in 1675�o.ߞ Be+$��l a.5{2a� ke �% ge `fe�e=�&9V ' ��0*6aW��D1 , a ��,puL?,%�889�( Max Planck��ten��l�Alu�|. Hb\�Qa�Q�Us~JIA+ /&� �sU ��d�J^����� fundaYal9���.s�- (�Q ial)�"�"� �'s.��  ���D��*.&f]�)�! yI�z� B���"as�.�e<|Mm�x2��sa��.gW� en"i"� �.&,�AAbm 7seh �]ba�Z��rc�� ��M'De�[; \e��i��5e�y�H���HQ���8b�!3�� now},wr�|Lalande��Q (�keRe"�.)�%�D 100 "F,p��Wn . E�d"�� 2B�M:N��v* puzzA us. �� dE�eɘP�h�a`� �'A�a��F�a0e� 62x=!��*4!*as�in�n!E34\2�\�P��A��Eba!P+t���r:P . If���*f � < ��acm��V&֊��+�W3�V�9ML��`�[.aX/�R1&�^ �� ��&� �"��Kep*..ߡɏn%$ o��H !�a}5-wit &2( X�o9�/&����Eo��aJ!& 3975�s, �!���6_!�EH3�{�qu��"f�49[�ByE���r5>.� ---�A�&^�9�� E�� } dedh�h�1��@����k:�+<� u�&a&�I��$s��lread�rO� JM�sXa�V�'ex/@� �@�l F�$� �� labL*�N M� � g��eg;�B&�� c {!4*�.xir�����1�6v�C,�1kw�f^yA�!zm%.��Dꌭ��, !�d�q�'KS:A!o<��!at� A/&:$r te� �T ���� 4�(� om�Q��3� 1��b#�y�b? (WeoR��AY�* *c vi)���a aken�it cumno �?s}3 �q �E�F"0 �� i[ �"�6izg).2:doe! J�6�`l$$M ns�`tG�BE0,Ht^-��!�ma0|guess��ѕ�be�N� \Yor�pq(A�wBm�>��^ room� modi�N����&� *aYsQ $��"�, �'V_�:���a�* ���R � �OA�ns�ZenpR� hidden*ppdC"5 � AHsu�CEZ)|A�7() A��C0K� a�;l ���/ �0a%�MA�@�sŁ=��� cLk;qng"�5 � m� �� �5 �LeBLR�w�� g��noA��!aN,c) Poook, J!a6� �&��teZ6 =mak��Qdeڱd�[yrH6��� ����#a$ et. BordaQ _�ad�%repeatmi}�vtagon3�F�o]DBmW^ a ��)���7e^B?' ��. (It @K&0anony�$' ,$�K�!�:V�R��m�uq�2rSde��!(m�^�or!X%� 651�� D<)�, ��.���a� .) &�/��2�x!� iron�fat�^�%o�r��!�-� decre�iHbU4m�K"�1qZ� ����w.�:E�(�  }@ �,iq-� #hQU�&�e�>*> �a�1Z2�a5m� U[ , hi�!Bmoud <8�Š�6� /-or�_noi�&!��Eg%��G� k)aes 'w����]'*%H6�ty/�/�Cpo��fx`1� h3 n�-^f&O _oid�&^  f� �ifnLE�,I�2"- N a1A^�� azlly� y(viڅaw �D1��h�� P!F�) ! ri��u{~#tO&sd>E�6� b� e so�%runsui��A�nd�~�/]i��;3u�?to�-leE��!t\`a adA!�8as3iz�7,��� dalla~ma sfe�" detć '' (�+A�a&f}"� ppr&h{- `)��"+)%�.I�M�IC})'�@ 2002A�r!55(\ =!Ya9DMM.;I�B�a���u�o ID j1A .} %"�{&�{6��G*{A�A>fl }�N ���e�zusi�-��0B� .Q/ /.;Ns�`1"�L . If��� �x4A�� d*[-0= el>� h ��+:!�m&kyA��>, H.��� philosoph%�aMxNW ��&� k virmYlyF��o���A�h�E��r hrob� ��he` . Ma�'2W�(A��>��l�� � JgtJaE(es RousseauU[NoPg![�8=Huq/w�an� ��6 �9%R� �c\��! m@bey it�� ]P&E� �1:� �t8ank Dino Esposias@nd Paolo Quintili-�T)a���/��V-%�E!_ care�x�m��fn.A�Et�KenM $, Giuseppe�ELbagli, Roberto Carli @Giovanni Iorio Gi�Cli�Danielar�ald �@!Len4*E�y�paix A:ŝl�8�"!ɵond �e�ne�(�(so\I�"3ec:pi'i� .A�]�K9ul>�2 T*od $T$"��'u� (" el%��Ptڽ# ))�a"U!�N8 $l$�/�'Deqnarray} T & = & %Upi��$qrt{ \frac�$ g} }��s$ eq:T�$DCWgb!)���+*���7C��:e%e�0\,�Wm}.�W� ��.�>$l=1\,$m, �i $T=2|�\,$P$�K� ���s � 35\,4a�5Csi�ou!c!�N#*�1�m9 sand. Var �by $\pm1�$ţ e�w�7�� 8��m�6�s�%;M�a�ly\]15\%$-1n� a�&� ��-y&O�g behi� is5c�l2�S�Pry:[a��e<}of�~a��i�in9�+-e.�*a{ j���r@�E�HgHFfal!�M͍oT �$1/.[�Qn8"� * �<�:� ��kZa:� 2 �P-S�eZ���ary�#Pad8k8C���1ck� A���lm !g7 �w!\�&|U1M5!�)%)i����&I &��e�S� $) C]<�� $Qe�>A��at !�  $)_BRA S��[Q]_A}B} a- �M�%��V1t)�, &b  $1\,Mca{�!S��S��/M}Ž #$A�����J U $l = nA"P2�GUZ} as!� N��Zn Z�]!�� (�UD s}QXd:� zA� grow up, �h�!>�]N+�*\ ��s6~?2'�[�As�Cas Eq.~("�)_{�j�!e>�A��,w�3�1����%!/$, lg$ly $g=(9.8-/()\,M/s^2$. �I8"w�Gcm$rY�Aorac%�$��e+B�a C����@ �� it@be.-O)��h~+ii���4�U�}-�*�!��:�!��n�)M�FeE�FVzY!m5�%, 5LT�� =:�1Y�/.o i s}^2a\0 )\ }\,Ta$(bGW8��"��twi/aEd,,:�1͒. 'X%-i)�be 0,s"�g��G|E�v�&4[5����/&�� ����EV�:�)J�� m7[#&�dpBPffo}�e pur�N�!�"fvonq�$R$\�! � ef��s[�)U)� I�0ee�ve�:�?� JvT��v�!_�u. &�V"� �&n"��Z , nu�:�-U &; - UZ�� u\*���e1!.neg���� rifu��.� �y���?ti��toE3|k`T $\Delta g_c = - v^2/R h4\,\pi^2\,R/T^2_{rot}=-0.03J� ($T ']� y&��ލ�`"��,&8&� `�7L :� '��d9%>:| fre� !�*� ��e1<� bod�f\c2�Pgenuin> for?>aj%�1�� M�#:^M�GecM��jl $g$*A6 �$F_G$ K:"pE�:c ">� FFgF�F_G}{m}= 1 .�\,m}{R�>�5 = 6sg^s M=5.98\,1.;��S!B�e& !x$G=6.��0-11t�N� Q�^2m kg}^{&�_ 6H���+. E�)P:!�W��]�)�$�(d�� $V=4/� R^3$"� ~k7m� \,G\@-E1�4}{3}e�\' \,.*�g_rho��&��r^�eO�HfpoU�*!M  !�-.�O�R��zA�M�<� wI)��isF� - 5����.�! �m�z� \, R*� =��/.N=\pi/2Wf EB7� s� �-x�H�u"/#�.2c=�o�.�� a ` � '"�V� (l_m$8� EJ�m� � R}uwb]W IX G!%n;}y� = tpi 7S2/3); 10^7Q� G}^�yK I�2�Y�I<� �hla�cMS&�� sA�a2�5.5 g/cɚAS-�j��Sc6J�$�"Ԁ.~"�t�>&�!tZ��"�1'~�uq �a>A�2�&�=O ! �Q�(iLF\,R�4B� :E!�! [$E�,g)/2$]%�@/)'':/:$].& Eqs*� g})--&� Ea)�+���*"=2k� AEl^#-5].il�J&  Eaon-lӅ"� B<�An�2$ .Ahd�R�`)�l'of����� t�7(P��x-;s�( -���o�*# retrogr�u� &�[�ejA�|l|crcr|"&>�2e/�>9;|c|}{P`TalE�:�} &��2?3} ?��QWR;X<\<&V8!�3)}��;��& Ÿ>A�>R�<} &2� ��}�B#|}{$g$�>B}{a`$�}:�b�\,q> }{2}$} %��~7��6 5J4� lm�}{e�m!3:(kg��J�(k~?,N#�E�?b)|}{(m/sk�)NJlAN�}{(s)} !*V�nB�C\\U2 Merc��& $3.30� �� & 24�? 5.43U>3.7?0.38@0c>$58.6\\ Ven�@$4.87 H4��605�� 5.24H8.89 O�5?��$-243$\\�!$26 ��637{5.Y�9.8�ȃ I\\�Y G 6.42 � �(3397 & 3.93h3.6 �5�1.11.AAJu�K��1.91 R & 7149�1.39(23.17& 11.2 H0.41\\ S(8nn $5.6 6 �026�0 �8.99.4 �N0.4�AUra%h & $8G5G 2555 �3�8.7!�4)�2.��(0.72\\ Nept��& $1.01 �24766%O64! !,%�1.8�0� \ Pluto)d1.21���!3* 2.06�0.U0)1 \$-6.39!���O �Cz_����Y:L@&�%�:��e�j��6 ;�1<� �1$"� �O�aBTP &� R\�och�Ng`days'�k�� ^�eda��&*"� �X: to����5Rfa����8�s"�4i $�����um75 ��&��"/nH..wh �6�0e�O^)0���� \ s (�IZI^+!��� �� �+�:�st-Westk JO0B: Tito Livio&��('s catholic) } A~M]"�f�6�?��zo�KA� &�?F%� ;<�.to empha� @��of N�:= unu�%!�)�p��m  17the� ury,*(J� (born Y�Lin Agordo, Belluno,�IEdt, 1681)Krakow,�eand ��Mn/ ian Egypt�ki�8T<o�(��teA�*��� sʛ-U*m $raveler. Ho��Yremm~nt� ) (� Ūdes{/d ``f0m��nes''!)xNth5Gam�}c�(� E<��y,"�U�{��s.y=sp��y7�e!� <K��%a`9ig�ma���/ry �%T��8xcellhg� v�de�,a� �$ pyramid!7d og�sk�cop!�mo�n�e%lto;iss�.m. �� /stay> Gera,�8�$ sett�5inU ��^�%x! King�FhE � r%% !̍^ opU�.r�2 ��(��&H1di('y�"V[gul[k@�4*�)�e,,WQabon�Se�1�HStanislaw Pudlowsk���eu8Galileo,��Ld Girolamo Pinocci. A.���8ls[-higregarfVE�a�mi��copd tele lWTK��%�i���gif�N�$di� LeopR0$de' Medici� 1645%�p�����Bi{@ia �{raO;Y��D!*m86Ew -� hydro�2ic baI5p%b�-%A*� t retta}. }NMisura��e�lg��A~�("�A }. Al~iH�!& priotm�������>� BDVm2�  '���8IV�!�7ce��'Y�����s m�"� �&zZ�pmn�clV jr��g��4-<!$!O bookem �0 �ŧ=c�9ע��e�� ��s��$alv!ajQ(I�A s�tpF"�ete� ��rW%�q�,�.� sub-�zS# fron��g%C�doco\.� ambit4p-�n�T Tr 1��d�s̨o4i'�GtP]\ !�� WorlQA is pG]�?�Wt a UNIVERSAL MEASURE \& WEIGHT�>!\n7 g w��j$ 6�� A\&w��)y G ��ulli(q xun:"kX:��ul)2�4��ORLD.''�f�� 6T=�ato nelA ]cE]r�чTn tutti li Luoghi del)$do si pu\`�Yov� (una MISURA,�un PESO9I(E senza ch�bbi�6A��-a$ niun'al�Ke oR, !@d ogn�d�� � li l �sar�)meTmi�#�]�| -perpetui�H���Ohe �4er\`a il MONDO�nIl"ioABq�plez$Af6S�*er�^" G3} H�;!�wor��un�+}W�D\�'+&Hm uC닉�9kOm��a]uw(h3$(unnumbered)������s�G��#t#m� z tz o} (6� v;`"�*QY%�+��n.!(l�L�jv �^\sl�KP(a I"I8�<,� &g�kiC�� m I �� -Vo/te my CV M�#,9 P[�1w�"I nk I8aW+��n�me �t�%I xavWN$�it>��u``Dunquee�!�, U�a �7 )1'o�� m��@e da quelli cavara�1�E�mio o�-�$, cio\`e m����1�Los\`\i\� mip�1��]�rla��lingua! ca,  i �st�b ��3es~al'.2is��� ~ !S 20M�,I�K2E�^ A�ernJThe9�%�hnw/"& ;!xQ, EA�.?�� 3600!a h�/{\ۮ...]} �I3wA.a�pet��I� not �E�ngIClocks.2�MIl�ro C1�!�n !̩L!�la "~ED di un Pendolo, le�a di cui vibrazioni siano 3600 in un hora {\rm [\ldots]} ch'io intendo d'un Pendolo libero, e nonb��quelli che sono attaccati agli Horologi.}''} \end{quote} We think Burattini would be very pleased to learn that the unit of length of the International System differs from his meter by only half centimeter! \newpage %%%%%%%%%%%%%F \n *D\input smbib.tex �document} �\begin{thebibliography}{ref99} %\ mc6�X10} \bibitem{SI} See e.g. NIST site at http://physics.nist.gov/cuu/Units/index.html\,. T�Comm2} J.C. Borda, J.L. Lagrange, P.S�Cplace, C. Monge and J.A.N. Condorcet, {\it Rapport sur le choix d'un)��i\'e de mesure, lu \`a l'Acad\'emie des Sciences, le 19 mars 1791. Imprim\'e par ordre de l'Assembl\'ee NaI e. (.?X)}, Paris, Impr. Nat., Z=n8Berriman} A.E. , �4Historical metE�py}, New York, Greenwood, 1957.Z Kula} W.  P8Miary i ludzie}5X70; (English trasl., {!bMea!=s!�P Men},� Princeton,  @ University PressZ86).�DDilke} O.A.W. � athematic om |A�T. Reading the past}, LAn, Brit�Museum}93.|Hallock~�W. �H.T. Wad�(Outlines oftevolu!�,weights and� ��!�$ic system}.� MacMillan!06.�Petri)�C.F. -AnA�t|.{}, 1 =�ColleaZ1926. ]s$RichardsonAF.  oNumber!riin�h\`eme g\'en\'eral des poids&��s : ra� 0et projet de ��cr\'e!  \`e la!v!3 on nEFal�$,au nom du co �d'!�rucAl pa�que ��vitoyen5. � faitvs Gs HsLa� !�Eq.O !�.2Zupko1A�E.  m�FrenchR@ before AR��: A di��4of!]vincialENlo� unitA� Blooming�IndianaJI 1978.����h.��-gap.dcs.st-and.ac.uk/\,$\tilde{ }$\,m�/ATopics/Hur�4� .h> amine} C.A!LE U�Nouveau� jectO Il, invariable,!pre%�servir T )commun $toutes lesMj!-in*�ir%�m�  sJe c"� royal� s�dE� 1774&g <1747, pp 489-514.�Mersen�M.  , � Cogitata � a: m"� a}, ��$, De WaartA�0Beaulieu, 1642kHuygens%h M�� um osc (torum, siv�, motu pendul ad h� a adaptat� mostre�es geo�.& Regi�*@Illustrissimi Typ x1672?Proot� J.  ��M�c S��v users.aol�njackpE/met/.�$Talleyrand).  fProposi�i�=IAl'Rn !5�?J,EM. l'Eve��d'AutunY+:� 0.�Jeffer T. �,lan for esta����� $ Coina�W W0 ,�5m�"Z 7 ,ed States, i;icato�� Housu��pr�� ativ3July 13Z 0},�� The a�plete�2� Padover� 43a;X. 974-995 (electronic � on atm\-ourw�.\-compAveE|homepages/ Gene\_Nygaard/t\_jeff��2 AmChSoc.h.nesacs.org/nucleus/0101nucA[ric�$emL\2�GeodesyA�R.%Introdu��!\g *.��P%�concept%�modern-��&� @John Wiley \& Son� 92� Moutj G� �vOb�:q�diaa�e�soli�(lunae appar�uQ Ly�  Exq�8fia Matthei Lib-��72�GguxJ M� Lavoisier��laA5m�.onRs}, Comp��r�� s dea����s "1882� CE ni!� �D�deu�a� gur�(la Terr��2R�)a 2�*� obel} D.  i Longitude� true q� 8lone genius who!�ved a�grea�t �# problem, his � 60Walker* %Iany Inc995.�Z�J�&�a�2+ Wes� EuropeanR� s��Qag�\-��# hiladelphS � Ame�n osoph�Society�?6CLeblo��A� Q�� !�xE�6d� 'un� , ��2 mai �QDemonvil�17R�1vS. V� nomenclatIuF} .0 lles g $flexions pu es' l'IA  al2Zf�BLMa$�W 2� r� %�e��p Gp �Ae�Pn MeY ��(Envoy\'e auA�� d'InsB% u e 291�$3, l'an IIm�RepP = :�2�,BulgingEarth2.� p�sՁ/k182J"4 berg!W ��Py�a�ep0's shape from� ton �GClairaut�Dri�~� al s� a� eenth-uryI��xm fall�B"normal"y� &�, C�.{6GGuedj1} �� q�Le m\`et�Uu ma�,�,0; (Italiands�D� del1o�Milano�ganesiF42�stamp&� @sio.midco.net/map /arcF��!�:�!���m arc. !m,Peru 1735 -- ,5}, FIG XXIIer�g�Was�� DawAth8 �es92�$EncartaMsnue .ms�\encyclopedia\_761561345/�\_�.� \,. 3�9� FIFA���fa�H$en/develop//pitchse@ ,/0,1245,4,00�Tgeo_tu� al} X.~Li��,H.-J.~G\"otz"T )��$Ellipsoid,r ravity, Ageo�\-ics}m9G ( {\bf 66} (�)�00 %-1668. (��lct��rl-pBaA y} \�xy{verbose,a4paper,lmargin=2cm,r 2�{�icx�0makeatletter zA %d spec�LaTeX� ands%=@Bold symbol macro�standard 2�s� � and{\bold 7$}[1]{\mbox �> $#1$}} ��Tex)�f� !x$lyxaddressx��\D {\raggedr� #10vspace{1.4em}no� nt4} !O9�{ba%-bother S!Q-�h\title{\textbf{\large Arrow� gram� 0hod based on g lappF&Y8 groups: \\corr�[sU � linked AD orem%R8\author{Yu Wang�HLev Kantorovich$^*$�A*���"s ���Depart���Ph�!, King's@$dpSt�, WC2R 2LS��9 dom}!] 1~3mm} �X~{\footnotesize E-mail -�:~lev.k�tch@kcl� R�L��ab  ct} 6� (AD)1�(L..%3HB. Zapol, J. Chem. !. 1�h96}, 8420 (1992); \emph{ibi�8427)�vi� a co ient� n;s-�  calcu�.A f arbitH nrix el�(s, $\left\l e \Psi\E�,|\widehat{O}#|\F#le $,!�sym�w� opergYA$)quantumX%mis��whe�tot�� wavefun�� $w$ is r� ed a� anti~sed pq�.many-q e `�$Phi_{A}$, e� "o each�t (9) $A$aa3 �: �=�A}\�S[.�dex�&Hed (e.g. infinite) JsV.�is some�R8difficult, howeJas%� valu&�5� requ�t���ter3�di�? expansA,Ho be diAj d by*isw G'gral $S=EM? !�\M?AW.]44which is givencan�x�as [. AF� suggv!�eviously>u, Int.amQAumtun7an(511 (2000))� deal withp�Eyex�d�tmp�M us�aPa simple Hartree-Fock@a~ one-d2 !eal �"of Q ��1 found�b�& alyta]ly.$. We find %�E�e/f��necessain a ge}caF'A�q> betweenE{eFN!�HmeŇof��H%se2�~�,a power�ies]%�reQt!m�A:U . It!�iw�o�T%emo;i_.��a�� \a {.�}  a �� ���qAJum-me !� Xs,e$4]"�m� can!ve��ly!� spli5toA@e��:��(s (EG) suchac�  %valence.s!Nmolecu�,or crystals,$ Ooms i4!�t�"or�"olids,k bondDin � gly co�t�Q� nDtc. \cite{McWeeny, L-rev,EMC-1}. Similar�V� A$ideas%*als��appli� o  !�6�a cker%environ`reg�� riveAdj uyembed�� pot!�al� �-�[ ��,Ba�i,-1996,Seijo-:9}. Pr�e a�+{  schemg�x� I�A�wAc��!�hem )! ropriate,�Z)6 ssumcay�s fix�� c�� O(osEytheirA �is '.cre�", E� good �xij� �2��he�le�con#'ing of5�ic is $I$�be��.ys-�� I}(X_{I})��*y �vidual s:\� equ��} ��8<1},\cdots,X_{M})J�I=1}^{M��o\l� {eq:�-psi}H ewhere $M�!&* n)!:EG's. H&$I$-th �Aassoc!�d�$N�$5R;�^coordin5��c�)cted i�t$%& =(x_�,/ x_{T})$rtMU���le= c�2e$x=(\� Pbf{r},\sigma)$ includEe spi.5 $ &$�����2� %�"���(defined viaF���� �A}=\frac{1}{N!}\sum_{P\in S_{N}}\epsilon_{P}\5P}9�C -AV�%um ru| v��0ll $N!$ permu1!�g$�P}E��� (!i�of:4�$�V> �%s���wh}gbe�M $N=N!�+N_{2}+)� M}$�-8factor $. $=\pm1$ accE>g�B,par�m��6�. 鍉�d E��E �"y J�$are alread.�l&!&� c. By��ly�ex�"Y  (\refa=�)�� 9�A}A� Eq.<%qe�)�_obtainq *) - .A� var� �- 0ucts. When usG "� ng�Drix!���!= U ��U Q�j� � (>G =�7QRic.�)50s=1O}\R v�2>,�>�x� a!3�l fieldmp&� P ra� ),���� 6uma6+� fx�6)�ed. Earl|"attemt#(see, � ��HWilson,Klein,lyast1  2,matsen1 3}@  if0 *� n��� each� %�a�nsq# �  have bx g� �� Ref3b my-AD-1, 2}�Zai�D� �th�wa�(vd! (Firstly, by!floi�, a double-co� de��+'M�i͕�c [� �9w��.� :A���:wr� to��Zdistin ermre0� out � 1.� . Second�%u2A!M2� !! by� ell-�jpic�!(a.u)� �1wed �t�,����a"� !&^ ion In $�AD �=�4 ��Da vU6M& way!*�&Wqu)���d}licit AD!�a�-\�edT(reduced denw3e� ces (RDM)m;� , � }A1orders� atwo7-1 RDM-2)l se en�,to�&e q�$X� ��:-Xg-w cle���$thus suffi/!�   9levant�q� *�of &r �;  (-�) to higher) RDM'��c� � bh7traKforward�I(�suc���Ho*$epends cru..ly 1n�i�j�{4!/A� ir l�.�� er�"�} %�s (� n� �i)�$�}.m }Ei!- because ':�2��result��b�A� verg<� icaI� , i.e. sm:,r}:�qh+�� EC�re��Pr3i� �choic%�q&� k8app� "� �>f����w 6jdi�ly ie�descri &Sin� t#ar,"\) �.'1 eed,�~ ��ob+ ble FR �ine{O}S .� 2��� }f=� J/*� mean-�>� I4��*� OG M���%�=5)� z*ha=9a"�/5��A}/-��!� �&�*�xA�� 6^�-�xan -d�V� ΍. Bothy�sA�a��Z��;!F3 ���Y�ar"�Fo)o �6��t� argu��isli� -AD}&F V� $S$ \%� pye !��F�$M$. T�lasser�madempossiato�v�o-c�'d �A�:em  ��sq0�}r$6ba� �/_{c���[s vl�!.� �>U����� only19(conn�) ADs�Vr�P (sub��$pt {}``c'' nVe^shoulp@dropp+ltoge^c !&1isI�att� * s it� � � �d�FN�� �ց=zs. "!�main ob�5y%?ij5perv showY3IR� Mj�c)ct)S�N�elynh��aJ��o*5b� ?6arg�2 _���i�1ed. We�is: fR �D&�i�0tail !=(!�toy''�A9a 1D 0A�I(!$exact.1 so>!*m�q�llows u�vestigat�" d �Slim� beha?w!UF�4��"��K9 c ��B�Aten, we� &� �0�ng��� ��s, 2�m�)Va!3I=�� ��B�M6. c0pEeigan`ax%C*0 a�eque(�0hall briefly �eA�%@f��4�3U� #em��V� / -1%BUSfX [ )X E* ogou ��3%�u�Y�!�toyI�s*�I{�-A�� 1A)]m�D a�I����nA�� will<n�com�� ( ed [ f>� AM�� �ABo&rPPe RG!�t� "L�-3 d9&�2V��R1sec:The�I<#^A1��?,!i=A�}$�)s�9 s�&m6� belN4` �O�... Joi\ ���HO�-q��ube��0}=�D}\cup6_{2 M}}$ of;N�Any�!�'0���Bg�lKic .� G �s� per� ��l# tra-!"u�(e algebraic|u9A �$yA"6%� } (DC)VA��R�}$�*�- ,���E�G �u�} inh�t �%9�}2�*� P}_{qT}$@ � }:"�$ ��} !�}� 1}�0}(qT}\muJS_{0}\� _ "�"-of-SN>� "�F/&�yp��$qR$0�wfor�e �6�aA�ll2#ways, $T M�l�Yact"�^'s) invoh7in it7;U0}D!E�!Q� N!$� a�er�fR.N�is a DC�torM��Y�erJ�����gb�sed %� oaw someM�pr��ive} �-aza�#}�Fno+��nCa��f�4.E| . E;� N�>�% �ed clos+ oop� � %�l�B%��it�9ua�*�p&YJd -draha�3.&)co� �w:l�|�$�>� ��s�� mayH��r"33% sial �9s (�moN&9 �� �v A� )�) v� ). I:HH9P �DYcanRbe"R!�|�ude�!Rr1 ��AD!�� ���}� "� � f&�& L *��J� � )#�i " lled V non- k or disna!� MB�)� L/)�:�coe�_� "� � ed merely� counA� aAus$ � leaegE�%��p!iAD�w�1r��*�se.��of6 �.o�)�&E.naN'%9so��,1x����Z� ��_2V_:(�CA})\r�|�.R/( =\Lambda\���"�qզH&6hi|Y͸v!�e��AD-5-for-S>��! ��$0}/�!�$\=�)I�� V"�"is 2��&�.6�J�)8)�9�Aa�!of1�s*p' ose|'%�.YI��N� :f9��)f ���� 2O, !��$en�@>�EoNF$�8��.�&�M�t�*e%A&x� �B*� �le��e-7&zE!� �!� of Sla�&d�Qminants� �'a-bi�')�ded vi.7&�' " (AO)� �e��K:� ��-�xLF ly��c� �� �&{� 7,s ��cAO'-�,erl=yE�s�.� Refe(��e)z"&�?�$&�"aL# ribu� � �_ ����q1 e6e��.Cs7.�% Qits��s:7.g*!fy�N��*�/)yR᥁00i�a�he7 u���+&v-Lq$ ?h GetŽrid�:3on� ��� s(��eN[ �x�-�cmpr�Lple wjE�M��s�+r"[*)9 ipate. It� ls[6F/�t-�$2,d,�H� 3�A=$e{S}(T)$, � +&! �)l�b>� q�A, EDa $d��M �]"�/8manifold $T=\{ I.\}$ (�A�a�K[�sQI.;8 $T$�(KBA�6�+:arE-".!l&� (!%�"B a�[T](4�� S@A��-D.�byLrem+Og'')>!�6#z)`�!�(set!.i#nB[T])$ (���'0i� r no�)`Q<�4Y�).� %�=�rUVCAS in-wm �*to�x�� not}�>[ � o �/# � �.q�6&$ 1%~.)SaJ#��!�!og ���� �d,]�$e;��zero. Ob�s�%>�y��*uc  6:5��2��mptY�� occa�%a E�:M�Q:)1R[F�]$�J�! ere j� , if`w�!�~di�M��l�%lyT�R�\-f��ex�-dI"un� ed}l -1Q^w*j,,JS&�,\rho}(x;x^{\{ e})=N\intd/x&*2}��3*^{*}(4B';rm{d}x��2N*3!�'i����>A+%�be�ten����.j*!a �$"�ap&IYle"9� MJ36�s]1r� Q�IG�G&j%� l�) W�1.�"� M]hat?]#�̩�&,O. (E��%: ��Itoai�L*�P?.�!I�/tmodifx8 ��V�]Ca�%�n circdK"�"evar.Ts $AbYz$Uei��)th�X"w 3: (i)�ai%a�". )�� ; (i6->W �Q,�7�& , (i8�A��ADM%#&Y�$�s a rd �&+ buil%�up%2j�!%�. Sin�!�6 ny�%�m+�%& �>IY!c� !Z�Z J# %�L;-�a2s,k a�� hownMcli�� e 6��.���NU��F�%&�N�;26�*� � K46� � � \,mSR>t}s� ^{t� M� \parl 2[&�U2�%>���4�kK��6��+ll��} Lpu�ɍ�{A��1&�A ŧ� �� F ��3$t$ taka.c��A4�&�.q�#9y`AD:�m���H9 �.5m��EX:x;ily#OE�:�# . OnX ~D" c �6enNc�95Zc %JsnA ,�multi�8�=suma\!�"7l&� � �  !�����)>\ N j7tvZS� 6�Y*re"�8 @ �E�e � d�E.�3N� not ��!�4*K�� !� ��c24 @$a-:�%�&<!$�8���m*�6�\y:��(\neq1i;���T)=&I&&�662Q.�#�"I��Jo9rh:_�xa�s+#:G �B+�� f_{[T]��q���!S��Z1ion>�UB� �=J; }11��Va}{2#*! pref�s>�! nu� pre- )����chosenTof� $T$*|U…Ba�� q��g.�:%B:&N),�,a�Ta$A����.���2wo2fs,���fa ~3-( (t+e)!6b�1f�� a ' '�3!N� it� s�� lastsag� 2qVX)i�=e "m�i�2A}e&R�2f��i������Á�rhʚ$, 6XRR, $^������B�pos�mT*"�Cn �0\ �&�#-�&or�)�-� (!� 2 s ���AP|0_Cx"s� u9rho5easily �!�(�0atsf &�.� l�!A�aaQ � I_B+%jT]}.."�to�MI�nya�ic")3ŨrD. A�',A�R7�.U"A]�-F.�� �C%.� }u &w�E�0b O�io�e�9,a�%�]�a� .A/rg�l �l�5!prU� o-! ' D-QWem'v�h!D:\J�$ (an�#&� an.�$)FW+� z &��&d4g@F�++e*oZ~-H� Ρ6 situ��s m�D subt?O2E45Cab I�2r,:T]$2viJ �#8seem quite plau�0!�$>sIj*"Xm* next�)>�3ac5solgG '�-�el>�� may �;a � �]P reasCon�6E�F")e &��c �"� elK=%K sign�#point 5 oo;p�,o:�!�p�ʝ do _  H� A9A�e , �8!�\ "<�p��-� ���..jG1D "s,: a66I3} Let�.�x0��A� ss^8�e-Q���� A�� Fig. \@cap:Our-%�-H} (�a}). %�Of�_}N\�B Qs[% hd[=6cm]{x�Ytoy[.epV ?!cap��R,1D.a:�!F �%"�*6)ant��o $\psiI$A� 2 �M}a5-b�>hQ(.�ch��A� t��$noIwa&]1C1�e��M�!�.x#N�Xs1� t(Ňyd8� �4r�K $s$-O*"i �&*QN -! i}(x�$i=1,2gM$) l�::rC� {!�re. A&�(( "�>�, (yH"1� |{b}R �6�Qs&�O�nApbou!C Z.� $N=MVű)�1�62�B�~E.�C��s essTey5r�" *�"�%pto\det�#\{ I�1/B)� M M})\�%} $. H�x(��l/a��4a-��!H.|M (HF)]2. �3�h(,4.E5�s�. DueZ�y!)j%PFi="rram�#, nam (&��a�'"� G=e�E +!)*�$"$#J2�E�� �O��fqact(s�� ;� �, spatRE/�N i isd ,ly needW��T���)� !���� &� �2�N��u8 M�Jremarkab�it 6��.l$MIa])\infty$ � \-lso2h�6aiK@ . Us}�� wei �A-0B� .fO�fiw7atg�%`2)gQAnTw"��4soa�F.T7���*ub�2{F�Oa�: K�%��:invll)�&k%�%}o7��"[o�9o M1G1�a fa oe�+om�0z1�EG$Iory���Ved� � fh � A�8YLAHF:Nk$ten�B��V��irux)��}. TakA iK� IdX q��&neaiu�'is�w���!�"� "(C(!� o�Q*9e�eB):\[ +(x)�i,jZN}}�(_K,S}^{-1})_{ij !ja�\]bb{W$ !�} SQb;[zWi W�+2z.,�� $�ɥ�]&�ro-via-M�FV+%2$:�E 7Qk1�)�N��L~& �)array}{c } 1 & �� & . \\  & +\\ 7d 2& : F!F .$�:>�F�+xN �-� _{N\�0.#-M-)M>q A�E�qs.q! omitU�� �y�4 0 {�ZSA��h adopGf afterj,n &� E�a�� lN�(G�M^{Ring}=�Zet}YY�G-�>�U+�#y� .���)>.�% 2Y :j�Do avoid�R�;� fu���& 9 e�%i"V^.� � )1!T, $.4�T!�"�$�D&$�$��u"�%  �SQ ; }��:!�z� *� in&p 5.�  $�NndSa/��l�bAb��b"1A�;� CA�}QEC }�0|�M�8�8v8./2]B2|V2G-%1>- Ow�\.-7 q"�U/JJ�,/1is u&�U6�recur� re sF[.�= -�S)�-2�9 ^{2}�, +2�.(-1�2)^{N+1}0.6�-Bb�Gw�aB���p2>y�<� �E.�'by�%�h�5r1��� &9Qverla�) ag<�. cP7�V olum�O whil78eX-1�2�i� samel#�2QV). Comb�S�Eo�' ' ial'Ls��!O��G�^-�=1���9�=1=thSI��s��ow%Rto ��Y MNcRS�~� of $N^� �d�C�%,F� G_{6ս1-6Y#+9 4}-4 6],��-6>(��2�7e7M 2}+1Z4}6a#�^{7Fr7�r�io =1-5N2}+�4}5�6��w��fZ�0sf? hB�NO2aH>�A��`tb_M�&�sIb. Also� agre65I�>2c�PAxat&> p*�in �"xga�e8in�f�]A~ �f:pN�od 1D�\�:2�t�qOit�]fD@}0y $N\ .� m)pj,"� e�2�Xb�I� mu��}R�� % any}&+O$I<0.5$ (*�clm��5��%( doesf  e ^ J \geqM)��/I�NC�B�1�!��!��K� �DD��sE=a*�is �6�is O*�~$tbOH�Texp�H $�C�F�A�,崑���~,5er�bA+f�M e sew`e4.�aO� Z� euIyEB>_9_pit"��!A}�T)I�]}�QI0^{n}$($n=2,3,�A qeK"n Ne�n�R����&YB� Y � 5E�AR"� )�Qr��Z r&�&�.!7ucR C ,6V X i:�Y ^� ��_sN� & R\EnX,i]#C_{}�iz.2C':� }Q��+S(-1)-aend��J5 ��+1� f�+1>�+1��� �&6 + �^ -Y3f�j>!�$$-d� +1ra/o@Vf $�S})��0�$���ivL Eqs*�[5�)C" jAI"��A�"m W8F8A|[&��(_,!+* >2I��&"�p�i}� (xZ�� Bl9ʮlh w�- � 2}{\ }? � tM@ �^p_�Yn�>q& 1x--xR�� � &~ � s� "F��X1� ��^@k&o!~aNp��cDOed CI7 l�sub:I͚ ���"y}����]�oA�s� 9-�<9/b#T �!@�#�.�">�f� r �I����"�dT0#weg1.|V�:_#�^��Qh�J�!� �)�e%&�U O�( 1Z ���N�$26�$bubZ]lik3'�7tci� adjac�(p �^�y���a���!9! a&?t �g"�)AD,>#, say,I8 $i$,:�2�.(��!%s]$e brackets"�a[ nJA9 t $N-1$ tcr ,i-1�Nm A%�'A�{*A- o5� (\3)!�=Z � n@l�.�N ���amxJ� �F*R ]*�6���a�[!G),m+�2�@Q� !O�:for a��)�.. Fin$,a� >\U.�5E��($i$`l �;�-�=%). "�#.5-6)]e�.�:! rho_>f$Vl�$F�)Is6dM�>�:�%�ai�wo-��E�!th :�on�ofS�L2$/�," .�iF�U�2Q�. A2�?�Ha��)nRKi� i+1$,*� C2�Q�a }^{( `I� 7 A� B $I �O"�:6\f&a'$umi|"�'N$�>q/.��:y)& $ (�(k& a*� pairA�, %)� fA�2�5 2u~AqZ$2G_{N�R�Jl!� wa��[ %sum�u��s�(!ZU^� hS�}�A�!])ډ(r�!�obeM^? �G .I#�[urN'�0�Nt�2aU�5e76` >�4Q.J0by� R�jch�R�HE{U�e.K�J1s )nQ��^��M�J�i�.Zi݉� &�%� �!S�|i�a�o�)+�� !9�gxn6 A Yp UawC���� r:A3�C �*wo�>�OAD8Ŏ"2 V�s. Sum�A�tR 5xA�&pF�&� &��C.�BB :FYJ�=Ga|��)R|����+ް+2R^6g�G�nADY :0D�r!��9A� "�j� &!ed�_c�N�r�9)�DicL3��4a�seen,Z5ear�be&-�`�)o>@Pl j6�) �Nia)Qj,.{#AMTo����A  �fy � ?Y&�"A��)Eg�� �o re-dJ} rJh *� i&2}) �jEv�lh.C' =ņ1�I�$rche6|��%�,�, �w����FO% -aya2J�h�O6hR� )�O2�$ is brok*[� &�. �1afix'' # �^n, >�A{6�E!!g f�%z  d�-�b��Ca1� �� /X�)o�)m-hdo @e��!!B}�s�y"Q )i!�� ~12,A��$$�V�� i�bi`�H'�XdI��I X, ?Kw�G.��&R��l\�ƥ* �.?!t 0 :�k&9'n �%ٽf$. �@ i��vOacog�a�yM �!^j. 6�;a���7&�&wa$5gai�& )�^��M{5 "la: "g4R:�5!� MtF: �FB5Q�f� $1$�F.o.GI�a�\V�<22�j"��]���G.j8at6%6�,�*\0 \*0I'�0F?(} Our task�!i�!6�*�s%�4"5 S *i! !V��.�dA/�B�jt"~*�"+(f& }"y:F�$P�+=\�E��o�V�-H eq:P�f>w E� `M "�&1a��Ib&a � �t $P_{2.�/ �.�&Mu$."�2� ) r)^�� �$dw�@ŰDO�g��N}�>YbE( Rd�b:j0-fx{9� }{1--1.I�8PJK*�Ud5�A��usefu�8a��UecyteJ4th��!.�>; ^� can�?�  X�.z| itN ��L9�:��C1!2- 0} \chi� *3 �B�g*Y�V1�-2} ���B�*�B ��{�E�I�B�3>&�wits"pN��$aVd�q8�5�a $ �% �9�$2 6�) F�� quad!�c���e:�6}(1A� )����ag =b�$!�[garoo.�� �.u�$I 1}{2�(1\pm\sqrt{1&0*�g� �o�A�0���#c�xg ���O ���&=0)en:� =1c'B$N�q@7us�N}=0$�J:��oot��minus �>J+P_9+f�i�+F� �abeDP-%>Q M'sf�(!L�"�JX��ap����8&n<�' I>� �8i^< ��&� _=�a] �� HF�laz��9K� �8��l&�\-"�6Wvx��"O3q&k8 �*6us"9�WEi>0�-�)Zi�t2tJi ��_&�!�%&ay.L*a7o*E���#ndJEx�vDR�3#M W-�$1�n4>)h en�_6D$�d ,��a��"Zk, ���$ a�2�'f�( �Le�%V&�L|�)� )�$!��][ :�ͨ\D şT �7^{N-3}}{A.-1��� i P_{3+ldot�!ٌ> Ne�TG�� aQ6D\]I: �<��sm���� E�0\leq }2���aX- �2,0>0� H � �B�K�&reWv*��%j \[ 0 w �N � .4:#!kG, �0).O9&�%.�\] BecI{�%J2<.�^).j�I9f��Jj2�=0OV*nR )Z ,.dnN m=0&� �-��>��$u]!�6 e����ak6��a� dis�68 1.BA1}�#�! 2}3��� $� �M0a�ocN�4})), si � thir&���E � ��B�Z�,�.ž"3I�H- �qm�! ��.Sc�3��P"� �&�$�c}�Aulx/&��F 6�:=�Li]}BD+:�,�0 %� Ym���F� J1�� &X-x ! ]�>� areJ�"&P1�J* �" PF�B� \�.`*[72�^{"K,N�Ba .�)Iy�55/(ed8��F�@area�T~�"!RgXoEa�y��L�"�&�a�A>%��'*LJ�3b�2*�>B"kI��aF $3��"��br&t �� &,T��C.n�Ii�M�$=�$� plot{=�l�7If1_ek_oBus_"$zm(2^)6�,���"g� �25 �l�!nes�5'75'mgr.f_1r�%���o�% *��9�)_ 1]}(ɚ�2E.o),I�3h�25b:�R_for_f�%m?J'f�}��"RI��&2:2�;b;,2�=2�=�k2?b�:@ "�c6���7;*= \prec63kY�d"�bRa�crmeQ�,B/���r� ely�a�=6b�he pred�+�B�. HR�"�7q��"`�O~J����P0.3�I�J7J�shoot�^0G"y.d9��ul|�� R=O7��O�6 ۓfi,f�9mo@si�B$=E>!-��* lift�G�U�joː �BIJek�v� �� of- �kT-a�5x>[N &�� ly l�L�n!� J�F�R)l=l*��7�_n�O � *%.f`7Z"�i2G{ln*mQ.�4�{Cj�:�}���G P �u�p��l8t+ ]!�y�^\�1�s. . 7&Q�G  ��@�=�6RIc�] g!?�pdI�familiarP&�%"&�ISe�8���.@Q��� 0�; [toy�PJUQ!T.M (>� =�����.��known *xM��0"� �  ��"�#���/$*�#S�"� &�+ V�^t3Z�c: �-e��;6 -S}[1]��T=I�{ u3��i�1 tjed'',r�E� !" h�'nyu�n ��Ls� a&��qN"+ /`m Ln��$)*B*" ! "�%� )d 67 6[�{?,s usurf$ �Q�=V��I":��'�����la�+pb��!As (ZiA�%�G �5L!� *1)͘!-e�.b 6 q` 2� ��"�Q;� we�=Uu���'qGA�we a,���2 a�I���SCkF��}��YAH.� va % Tų<y::�:ka1]78AQ2�)�.&r&� 0�'[+�Iby:he�  a*�p&3ng.�J�'1�^1]2�E� A�*� B�w Repe2W!P8 procedure�T�!A�]�fix�EO 2,!�Y�}>R[1]>U,2]}�BV,3���uca�"I�s 1, 24 3ad@Q�.2�9!�{ �Z%��<*a^�e�G& Fc ?�vir(�U^J�*<.‹c ship����J�%�]a!N&D2Q,3>fB�GContinu!ҥ�U,6%.g� of2�%'���C�%�ew�_ )��E^�� I�,�]4%,4F�J"R�A9F,MVe,5JgB� NexteRt =�E�w.G�&. b'��_$.*2yŦ d� /�sAF�!3T]&fvn�P^a_{n}^�ctVAF eq>\>,~ eQlZ8orT$2$ ,3�F so o.�WŌ���rt}�� ��5$b\4S����)1? (" eDub��I��cr� to 6��8)-"� f123X�D� �*recq :�23�lo &0o��b7����| ���4p��?%���>c2H�S})F$a�I�1��2)�E�\2A- #a�)b%�n\geq3�I�uBu|� get:Tan]}=:� sd ]}+1=M/$�-�A��+���2� 6�[�#�vJ� !2f�%46�]�!:G�� � �# +1=4��.�Y>���=0�5nLE% ��xU�6�, �y2|�#�fc7|�35P�41� ']%%� % ]}=64 a_{56 "3�JIM0"�%J/aT enj���t�of~�2�� is�*=�!] n� $u�R� .�� � V(EE*. ^��V*�.�K+2"ZK 6}+7 8}+�FbfB�J��ER =1+3�� +1h 4}+3"OL6�uB=I�r6�0��%U�"d���!:&�s&D 2�� �f'0a�L=��Ji��9�\i��c�."҃�ct�`�;��A ����.�!h�� ���A��Gh�š12Y%�$"{� �A|� �BCA�6�901|%ndZK,�(M!iMFi��>���$�,�C�i�9�u�]�ca� ��*- �� �!=ep��5�b�-�NX�NX�$O$l6]�É] go�PhE EFgs&��^s �C�rT*~x� ��mBU�sHR/�Dr��N(="W�)�!<"(�� � �%>dG�i��� - =w'.�>� DA��J/E9�1�,ߝ}��hr����a�3� ''��bA%��2N�О�2c>�-t��-��M��ZK�s�K| s aŏ�&�8 9��� 6�T]/2$9 3� �� �}fW"�~�s�d K!&b!n-(���f�&�?�=!:�\�"[T"3xf!�wid"�n!>� a>�@� e�er} �.BD=[T\bigcup\Delta T+ �)�?e�~���Ds $L$ ad�(ժ��m: ar $O5UB ,BK$,-U B_{L �!U,lA�"ioqM�2�A�s�e-2D}. �C6�=glatticerTA s���:c"2D�QBq"kɼA 6�x2�6}A�3"�M\���#�'set�}$a,b,c,d,e\�Md�ash��ro6cB��@be:w_�c%� =�{ f,g,h\ ,���:�B�AK��A!R�!>3 ���Aellows%� ,�4]"}�� �>nt���! ���:Bfop!%�. � s�m, `K It 4 �}�2e�e`[.xFR::�(qd):(m� T]��Ta|�3t5}\:<Ta���A��aD}(O76z � T-"6� T+<*�aST*?�7:.� a y>I&ͷ�%gE} MO-;?u�!���-�)�1*$,"�6 $= S� T%3T�&�v�>J��>�z^�.6 �� < S��ma��5Y T]>9. BRV,A�a�j=b"�to�Q}�N�@�9�:���PЖe� picks up aKets $E& DE$�9�%� �-� Rx6 �p��jt22�u� �Z�L ��R�7 �is de�d2262İE�il��:/ �n-�*qM&I<as �;&�%} �b1�(ach�&�M }must ` -*�Mb�. E: !�2�>�� .�{A�6wMl}wQ�-�L� A#�91}p�a�2�0As%lG�of8< \%.:� H$ (� �I�Շ 8 2 AA�Xn��uN%�2+S|�T ���"i m���� a�d��ie�qM�6�6�6�%Rb�<"�SI&{ A6z S�}��&&t |rv w�H2�V�:A�;:� �e��A~B� �7�7.�E 1a��?s""�4�.\ ��-tofMb�� T�y2�p5F` Da�|A�As6�$2<�6��-E�p*^soughtZ�T>� ( T)^y]}�� ְ �:��*�f�� �^sF�x��xi��+�3dIGo~a�zb� ��=`6> ��&� � s:��$$\aleph_{T��1�]o� U���t�%l&an�� Q�>^2�N1<$:�RB��"��u��n�e�6�GS}) -&�<�tM��� .�$Eւ�^k�e�� 9ak 6���y &I1Z� U5�hVa��hUn�MR:A!$&��$n$k�!�A0 �P�) 9�arr��it���E "�""Ɉ"3X�6��$E&���{ �en"�J6i2�) �&�$�1 in�o�8&d)d*re&�M��"/e8e~! 6�dA�D�RpvL �vce&!W�UW[X �we� ~�5X`=F!o"Ll�q)e�qo��e� 2jork,<]Y 8A:ew* F/a��A]/��A,B8 ,C]�No�b%A6$(A)=1[#start,~�\%0�>d$z(,)%$T=� tyset$ (e��"[ =A�VEq.&�VNFG�#A�_ B\in*\ D}(AB�%͈\{ B,C\yN0C1!723,Df5D6,D�bSeq:�>-f0: E�u�&%C uA�oM�F�<.ca�  'S!th{i 3 Y, a2�two=re��tc,�Ziym i� !�v�thesy� $�)s; fur�y,B*"B�=D�(A,B)\�r D_{464Rm�0S!�>@�zC{3f,C}3}}45>.5v�CB�-m�q�����.# { A,B\/ A�$6�2��"�Dc��t&� ����rU%����$)w$I*b�&��l}�+)q&�g_\$D_{n}(Inba�itpfYaA��.6)A�>�*��� ��asz|W6� ADs-"� ��Sab�� 4"4Sab_expr� �h�i�k"&�- 2�ex.�).n3R�}:i3|Տ~ 6: ?� unti'&0 �E k$�3�r&�wWxupIxq&!�a�+��M��@�h�^eU�� TN�AW�,���Y_�|�%:PC6Z �Qa�%�( �.\I�J�Xc} R at�*٥�� I���8�pP���&!��*��"�&�[Sabc_��Q�C)v�C)��B�:�e���ADQK]�*ro`n�1A+�Rs 45rt� �*.)� 5%�PFor5&%w ��e m@�A�E�x EHM�1�e*�n� *�~ypCEmquickl.^����W�a��exUi�06y�Z"�++N"[ ��(� glways �d)}_`3 u~�N=�!��s�[logicC�iG�2�V� � � l\d=B���^�+A]}�*.� C\� ,B]:� ^� &� N4�� B��If� :��CtQA�w:�so��ZT=��*u D �6F�^�\{ D,E� ,R8E.� ,En� ab>j T���,sBa1a#inued:S7�i� stephch H��l"5�jA_&� 6���A:on��ou�5�'�A�c�n2;1�A�E�t��%>p*�� �$�"& (�92���� f})� �7a&�*�ca5 �2Z�,� fFs.� |=1$: \[�&a�Hum_"� &I -5�6 E1] "� � " �[A\k]� \]MD�'l:% 22BC)E 2}(C M �s&� F[ ,C" B,y��$,D�j\[ �\,M��efta 4Fm ,C) �4�J�D�)0�\} � �u\�5 / ,D,E�>�N2�.< �6F��D�D1�+3 0%)*.�.\} B()e^_fB���&p(��A�y"ZX�I�V�p� 5V��{>g��%a�\mo��j�pp���ge�s^ ��E�$b �.�Rrthz�%�a�"�2*YE*�.�Ia}�&�b�$#G�bh�b\#Fl �C1�=v�)6qEu;_(1R+��d.�d of%%p)�*!-�� �E!go 4�� ��Ze�;"eR�6�@ �%nY��C%�) s>o�bG[d�n,� M�s�l�A1a 2e��H*,atu_j�3in�HR��>ck��a��o3�#u�]b�B>vBX �A��o �m�� A��ӱ�2Z2@2y @��C>�I!�&1� �a� �-�"r8$! /1k0��N3y�&��~ z \� s�� "yo. Any c�Xhoice results in the same expansions. However, the method outlined above is, in our view, I�implest one which leads to a systematic derivation of;@ coefficients for�~( Therefore,���Bgy!�mR upAs$arbitrary  �-6� �"a�finally2�tak�Hin� ccoun��!EscribedNLli:, . It�ـ�+atA�s��$d previousS>R ibyeapa anc�cAG��, we�AA� it !2aWɳ. �relevaمp��%U �1>X %OQ�!o�1S� 2� � (�unoO)Dl� in�a �d)!?a� kn�V)! McWeeny}. ʵz%_Eq. (�wPeq:ro-via-inverse-S})!OreA0entinge��Hmatrix $\mathbf{S}$�� =1}+ \Delta}$ d nA�andA:2}^{-1}=e�(;FFi�)-$��M�1a>�����cX s E:�% Y�" � sݵ��onal.al � elop��"< in:w ub:Ga�al-? } � is~ is)'� #�E'w � "4 K �H ar combinE5sA�Sq rA�erminant�.e. Jintra-P2peffect� m�� in &@ .&ia� alsoM��y , e.�e�dDanyliv-LK-periodic-2004})&v -��� BeqIF)3 (diverges} i�K P5��>�  (�4explicitly, ifa�re is at��eigenva� U�Qn�is��an � )�@��-�should %;I $some limit1�n itsA�߁�A� must��� �%< care. %\biblio) �ystyle{/home/lev/PAPERS/SEPARAB/Yu1/physrev} 6:v5dc,r]embedv#mypos"� the_ �}{10}�ibitem�� R.~��, \newbl{\em Me�e Mole  QuantuLchanics} (Academic P�)D, London, 1992).Fx-r!,V|�Rev. Mod. Phys. {\bf 32}, 335 (19602S\EMC-1} L.~N. Kantorovich.�JM$C: Solid S�.b 21}, 5041c882cBar�{-1996nS( ijoEMZ.~%.{Iz n.�%<. Chem �60}, 617t962tS\-Uz9�z Comp n:)V,Curr. Trends)X4�%V992(Wilson} S.~ .�EE Corr�j�]Q-�H (Clan]m 75}, 1860a1Ja26a,2^oC,y2y_Y�n6bn3%�O8 R.~W. Kramling o.�.�jq74Nq� N&�(B.~P. Zapol:f �)K��9!�842%E:� f2e�6��f�6C*  O.~ gL.~Z ǥ`B �7��075113 (N2 Vsquartz�q1� : CondensE�/%LE�723N|"� JN.�IntZ\7!�511�0^�p2L �F==%P9_.x�� 2575~)WM>� Ldocument} *H% Temp{ �le �pZ int .d class `elsart' % SP 2001/ 5 \*){ (} % Us� e o�( doublespac` or 7ewcopy@  &, , % 6e[2K]t% Hyou use PostScript '�8y� � %)� ! icQ ckag) � mands� usep "{3} %�sJx (%V� com� ^co TJRx:RepsfigPif�!�f� ozoldVX AVamssymbPp�des ousPful� h�al 2 ols .� IA_beQ " frontm�E Titl�uthorsE�add� e!^1C thanksref�7 in \t A\ B or \ A%g$footnotes;=�cor/NOor;c`spo�JPea5g:!�em �, %�4form \ead[url]�  page:AU�{%\�{�1}� [ ]{!� �{Name\�{cor1} 1�42F�{2�I�{�.t2 t h[e  �{A � 7z3 z.M3: �Ff operZ KHa liquid Argon TPC � �Hin a magnetic fieldEYA:�fal � ��-��<�n �es%�)�-a,A� ) �%Uu * C{A� dertschvM.~Laff�@hi, A.~MeregagliaRubbia} i�{Institut f\"{u}r Teilchenphysik, ETHZ, \\ CH-8093 Z\)�  Switz ndu�abct} W))q/E�%� timeN�imm}7>��$0.55~T. We-wa�q imag��prut�0 dete�0a�ed���c".6��bei� ]ionizx���owEdik4eir ch��est �ir mo�4umose�L were �now �ccbleA��� �zedB�.�a5��Ikeyworda� s,X�W: \sep % PACS co��9:5\ 8)  L.xU2a�TA' proj�cha� � �} 2 % maext*� Introdu^}A } Am�$many ideas*� aroue�f1_no!�gases@ 6��P�C �~mPo1,Aprile:1985xz} cerly  �"Mn most! llenE�AI�g  dssEC techn�was!Hpos�s a tool!��!�I"�uracyuQ$of massiveyJvolum���apa! principluJLAr%��.� �"i�inxly purifP6eX��track� indea�enspora�undist by a�,��a�t a>��eters. I�Li%7vi�4by wire planesc!M�e (, drift path,�tinuo�sen�!%jrecord�7�(l7 duU�J$ �f$2ci�E� dium si��i6�s%]&�" exceA=!pe�((9m , scintilmy��s�oA�insic safe�cheap�0readily avail� anyw� a !{dar�|-pi�!z!�eA�$air n--destra�|$ adou5�9#!=�ei!OMal��e� o)v *A$s cros%�subsequ !-�w�#&E orr%E�atY/s sv��ve�%Ut�$ event, he!��!� � e po" A-n-D d�� cise caloGtA�measure�G�e f�%bility�t��"�!dema2 M}�%e�(ICARUS R\&D��,�� d stud�r n sm�$aÍ% ab!�proof��%,&i��s,EG6�meA�d5�ic#s �G! }%�=xto %ri"�&���!2x9a�l !kof  cs)�s,a� tern%�gni', � du��#es/nd�)��&;�(s�"�had�s� 3 to�LA�13,,Cennini:ha}ey5���ja�%�AJm�tha�!ur years�nV'�A��� cosmic-ra�(gamma-sourcM�b'ur�!^�$%�]v-)%�50 e_�50lt}� exɍC',CERN neutrin[%am,]���!Ša-y capa.���iquRintera� eu�$reali�g)� 600!Q��1or cul� &�full !�kr��A�$at surfaceA�su� �t600p�}A!8'A2�"�(L�IE���b�e)�͊kta� cale)�a�G 1th�1.5~m.$sX {2U~ R� ��)%-� -lik *c�>��onJ���2g "  simultane�"(1)���!6d]L unbi�&� i_.zɀ(2))�sang�$y!h*�is+y Ave,/oge�a isotropic 9resolua�;v�*$good, bothem� gy (��y� R3:�pk, 4tz,Buenojd}: (a)�w*� i+(b)"� .�A�5 s escap!�a�uu($5$i�-](muons), (c))�pr� kinHs, L��As� sc2udoq�(q $�8 p/p\simeq 4\%$)�y ck}Q$L=12\ m�$a /� $B=1T$). �#..�2cq�c!� *�xdi�*A�� A���; �r_ b�Zspatial:�achiev�)h*� �i� perp�8��� ic o3i*LoE*zA�� ecte� be)��4Í!1{), 30 mrad$��($E=500\ V/c-g$B=0.5%^ER"M v! a��$&��<N ��$%Xl�!Q�fnM]`u>1�ofmd��� J pene:+AxE�m�  aU�a�!aGL[&��aR$"fQxrequia�:n��+ 6�a�h $x$=�+�2}A+givenA -/��.�} b1�8\frac{l^2}{2R}= 00.3B(T)(x(m))p(GeV)]*GM$R� rib��:F� MS6� 0.02 s{3/2}}{ZvAt low-�a,E&� ly neg< %�.�p%!�pos5 28error)?e%E J pitc�i�8نx$9: '!�t,$i)�:5M )}��}{p} >" 13}{=�{1!(�I5�D1ist*j [/c� Mv�4 !D$be written� ($b^\pa��y A�p%Fv]d!ua�) Ws)F� sig6�,b^+-b^-}{MS}62b�15>�>�.n2v �gof�! ����� 10~cm1-@ed at $2.6\sigma$)�m�� m�$3 ![:�BW: $ �, = 2b > 3MS$"� 3 n �strengthJB B\geqm�40.2(T)}{\sqrt{a��*Y%&) .-I � M 5<$0.1T$�RR�AK onge� an 4Q�T` &|��4� �*~m�u�1 resh�8of 800~MeV/c. H�,�6anc!.r�� ` �� �, . Un�� ha�Iear�3O3�o&�4s mak(e���nteV�V��m% �us�!%M�:'isd&�a�, radi [; s af��6�� � �.� A�h| *o!aa-i�6u� In p� ce,f� :E#(s $x=1X_0 \�-a�1 B>0,2N4T 3N3T$. F�3� %s��fi R�-_2� ne � range"�(1��5 GeV!��� AR��67 �5%� Ti�6a of 1* Prel�ry"t|2 ] s&6� hX'�,,average curvw  su!��a6h 5 � �:\be1k n $1F wJanY*�8c� 20\%Y2[ . Fj"daoon-going�An2�mJ1�, stigza">J��s834� goaltovV.�6 f�41�k-�.WB� ? oOva=MUx "���r� � �-pr�m  4d E checCa�basicZin B-I=+� � tr!��� stop� �� (3) rV�(4� eck6� .�repor\/oa�Y�T;�!� A�tX8i%W/",>$lafthesis}�&d �!}[tb]��1 %B/5(width=0.45\(]{$ �1 \e!L{file=Allezusammen-b!,3 =0.9B} "Y5�1 R } Cu rough!� i!�LAr cryo: = a�:I|wE .+sir�sA�cyl'rs:=�ed b�.er (red)�|@LN$_2$ bath (blue�z$vacuum ins�;�(green)"A fig:setup!1n&c6#$-�"� J�6n�ep9g.�} 2�% 4_�n9c�6(left) >�L1l (�Z) View L� assemb�46.��!7cao,.E�moc24laff1�f4� Expe�ntal S)l�e.%�l/�5 ure~�19�)��(custom builG  st. "��P1�a�2�a eA�300~mm� �815�^�ximal-nc%20B�)2)-4s dime1 r os<o f�0n%�Drecycled SINDRUM I\�#�8q�asEdly���uQ@PSI, CH-5232 Vill�/, *!�@be�t� PSI�DETH/Z\"u:!.}, D �� ��E7%��5#��"K .�-m)C DC�r is 850~�Pr3q$� <�um3' of 220~kW�\��� ,�awa coooW;uit ne� `toR�/-X)�( laboratory� ,be speciN inst�!3=he�ij d�t��on�� �:� inneT!s�aa�3�Z82I�� �>6&E��2��-s�dq�a�B �B kept�I9 n ab5�es�%m .7~b�9}�"A�reezeF~�at A12,�is wr��25 layerPsu�,���4ou!�> �5? h/��-|2�!/�iaa[t��� , 27M�sh�IJ$"sp2 by 5~m�|)�N �#nE���two> �m1s6P^ � ��,t $\pm 60^o$!c$v�cal)s�j$less steel B� a diU7 $100~\mu&��a>~m�#>��"��8ot� als �?� �Ry*tr� 3 d%�� -JAn"ly pick$aE>; ��7W6 cloud p�!s=.jthird A^a PCBihoriz4lip-j��11�a6� ��!s��)cj� The )��1stn% conn>@ 3~mLtwi�@ pair c��Qhe feed 0� a flz ,%d2#uignal^v2� 2f�CLog boards (CAEN-V791"D>?�1�icsI~VMEH anaJ�A���low-no�pre�fia�a�32Amnne��wo"Dxed 10 bit FADC ru>gA�40~MHz; �7!y (%qG:;�].5+i� ��!sE�rks�a���C�(m digitizer� d data%��#�' bu�B,�en/ %%�9 of a�val�+m� ach �5nem��5I�Qdu #run�� H 50~$\mu$snD� igger occEA5fng� �aGD ��!���e�fer��PCICd in a}�js%z��i�a Lab� )�voltag4("G "�82!�knm4e����e�ir%>xa� j%Av�� Q���G(�Hr� ��� a2gii2D (�v!=R~0solenoid axis1�>0)afe t)�r.d:� ��� � ��$� �G�,�"�*%%`.m�>�EoIG�botl � ]� us��� e��y����,  Be5Au�w�LAre� "> < ��)s� puma��]fou?Kek��KAm /2'\5 \cdot 10^{-6}$~mbar. A�~ down_�day �� �gf�C��u)c���tridg�th�ɤs�L LAr ?�KA��! wholA��w�!…�t$B!J��rI�i ejFV�c8`-�!� �Pi�"�) and M�0vZ.ium, cleaAMs�;�;U�. ely obser�EatO �)��of 500~�. A�&100�I-1miHMhIre ��r!F f)���de�M&0 Yo M�*�&� �6Im� lifeUhj �}T i�!�8�K��J� � � ;� did� �e�X� ntlyF� o!}run. \\ I�]�2 ommi�I99/:��tur��/�K�\xP �� &- D��-toG um^q� %Y �7g:�&g � on.B�eve} � rawi(��� O� . �J)�� cU���%��%U�wA�e�  �N��Golo�aA�r �ed�rge)>.�xi�ORl Isɩ�Ld 埡�j �O \�ż two-"�al @+on�7�U%;A[F�"1< %.?>biAR �P�g%B�l.�)�wo (o� ree) h� h�faO.��*�+ͽ��*�A�s�+l %� rpre!|az ���2ei�"&�,o ��decay��i? M. xE-r��(on!�,ed $e^+e^-$-8 �v1,l1\P ^�C.R�3Ia�#���A "�in�\�Mi�A�2% (0.55~T)V�N2 %S >Q�,*� %��C$Pa杨�]� A�uo \8Kbe��E��uA�U/� "._N�!$u��I< BD%�seen..&dhI"�t� work� inp8B�•run1273E�44c� =5cm:�,314,38>,6�,29 X90>,6�,4 ,15B,FY412�7B�FY36 �6F,JY -3F�FZ409�63>� "�E�L e�T> reala ����A�l.H5�pR.�rA�Ns�4 6�ej��A�ie�co�2�A��NH a8���.. 2���er � )�m *{Ac�J ledgesW8t�;gE�8@Abteilung Bauten,a'! vi(u�&�&�I infra`1ul$6�:��� y��7nb�X�(INFN PadovagH �c!D�l\2 �� � �1q0��!X�) I >+ular,�&) Sandro Ce�6 (�)J�!sup\. �7$ P.~Picchi%�F etropaolo8us�=�u� s%��o� W"�"�TSwiss N� �F ce FW!.�>X@{00d:� em{i�1} C. �( , ``� 6�.�]*=7: a�,<�? or Nx0De4or'',�0,--EP/77--08,�C7g� 6�7 dI�H:E.~ 0, K.~L.~Gibon)fC.~ �8 ``A Study Of IT:%"�Fs Dq ��L�  DiJ5$In�ndH �(,'' Nucl.\ �;rum.\ I .\ A { 24&H62�8�El%%CITATION = NUIMA,A241,62;% Q-��2}A3B�*@ti {\it et al.} [�Col� ion]!�A 3 To��+%�F)9!�n� 332}%�93) 392�F*'3� 2�,j�Pe"�%!���2�4�F$(1994) 230�-W53Grneodo2�j�A�-s5s3L,2& F\3![LarXiv:hep-ex/9812006.�t"�2 S.~AmZD��D�:e4* �45��Tq3� �%�E�.I� , A5=F02004) 329-410Pr�B�'�� rein�LcNiZ�0pk}�6)? A�� f7] ies:��3Yt6of CP�T vio0& 3Oin&�4oscV9 s,''=�,ph/0106088. 2�HEP-PH a��| ��4tzR�6�&D �CP-�: A gi�RS;/&2�1Cerenko�Gc�%i*;&� ?F�402110.6`� ��2&�Y6A.~<, M.~Campanelli,A�Navas-� ha%�A�i ``Od�A� base5Q�Am6� 5�Ld�R-phX^(CP-/T9R)b�B���6 Ijy��P)N\ �H 631}wG2�09 [y�E812297]Z\ %\ՠ&�!:.4BPh.D.�Ys�>)�2005. A&�;t�http://a74.ethz.ch/diploT�%.html}. Ht:�O &�E ҋ:�G11pt]{�lcle} \oddsidemargin=0in \top2ext�" =6.5 ext� 9.2 head %�Fs2%G�%A��/s VP�(and{\bM} {{�T M�,nhHsG {\bK.KBN.NBL.LBA.ABB.BBS.SBD.DB@grad} {\bm{\nablaB"e}{dBbAL>#e#�$:!�[$em{defn}{D�%|}:|edc+: e `Nbea>eqnarrayFB$B^" beasBG*JH&.IB$bk�(V� BR$Nreq}[1]{(�%eq:#1}�'2�hC}{\hbox{{\rm I} \kern-.8emC}}>�bR:: 9229RJ9m�\mv\bold� $#1$Bdc5I>�!!Vhalf} j$�21}{2}Birf� -+J(dd}[2] { E\d al*}2B&mbY�16�nn}{\no�} \def\C%�%Q$.24em \vru�-dth.02emA'1.4exo^ th-.05ex 5-.26emC!.ORO I0em!� lZ6bl0.`depth0i.04em ��':�7�15-.3�Z�N�6����Q �7 m��:lkB Q}�`iL�\< \title{Backwards5t!ys<or 8!sy2ct��Get�< Hamiltonian PDE�V�I${A.L. Isla�J{D|t�Ma�Ls, Unih[��4al Florida, aiH@�K,.ucf.edu} \,^50C.M. Schober\��jcs J6l�date{ }2%>"1a"IH]`rea��eve�Zh;=N sche�A!k=F !Fn%hdc0 eq z*�cf� �X laws%�( traii}3!Bin*$ nume0(*�1. n�,?��+ ,Fodi�F��s, ua*t�G�?�1 �F ��6behavio�(�2t� �1s�'$/�d0�1!pr.~i)t.F�i�0 a bj PDE 6�3\n*z% ult.� box {s ��nond arA�ro�er5>Q!��)/ e a&�e5n"�!�<5{ �\�>�d;k�e JA/5;AE�&Ksatis!�aW#kj�" E]J@. H*Uk6���Z� d\verIYcly., yx % Bod�pCB ��s. A:�J.im�G^ intEftor}�A\ at �5%)aBc"< (O^}�in#h�)!�L), �-s natu��to�8A+ �I� M�um�j�+sc3!3%_of �>>� (MSCL)�<0br2,mars2}. H&�jis doe�jt 9y��yno�dynam in�d��-�sy�m�)a!Le-�*� m�;>��* globa!�]Y)7�#!6 �g+9�. A qu�,!�*�  arl`e&<�lw$�Gt�%Q �b�1� d? R� ]^&�%Az>�]��-�) wa!�qu%qs "@fM(NLS)�Ae-Gord�]�G�I8-Pitaevskii eqa>s)��tF�s��� �`, alth�(�-eI�, over�y�!SC0iskasc,issc03 b}. FurAJ,�im��edq�QPF���: refl(+ �nfIc*#VR7s F ��B;�(minis���.�.�i��.VODE�vS&k ]%k�ig�!. !��] �y,%}>+ib. #h�E�t� i�$o*Zu�" q��>- q�conflic�*�=�at+Q �,/A<�o ed �ta�Fngyni�?)Q��h�^Eo,2|.QQ�%@� extQly, E��NyI�4 �^ (BEA)� �N*8f n�X�, , �%ll�fana�er�d ve _c�29a�+�P-��y��mp�kx%oScO�%dR!i0qli� %e geometr�2��6� >)�s,�pZ��^� t�A�ans�o (whe�FCQinguish}:~aJ orig�i"G car j��to$"����z@J-7 �.7 $) becomes .Mi!E .@aC- � � 2a& F���n\"�cal$" ���E trun�(�C�, ha� yp��f� �(to���t%disper$O, si`GAnG� u:yPDE-�X. ����9_"�|TnC � f� M�Lax-F�Lz6s A hod �$ . wind &� adv�on 5��QI��J�+t Jc?K J-- TU#]Hlp�1� under�d%�^$ !i�fd, �%O!�hH�K�gai8h�=9Qq��(�M� smea�/�� ;evolv�0Likewise, BEAAq�jortBZU{E�!��ic� "m �chlu97,��,moore03b��For2��=,.1 7xA�Bsq8r�Xso.Oj�%Y>��a.1 ODE�:J1^A�Pk5i�g�72��; %�i�en u_rigoro/Uestablis�/r+>.Wal�6��Q to);� ��o@ xpon�&!�W*�*!�-��X4strik�>�-$"hn�1{�� �e B3s�E� 1d�*�2$M+ z��IUpredi;Kbj&9va3m�B� s. L� "N5S ed u� A��.�[&@MA3 re a�_etE� way�� �" aK!�AF��&R[�4iis(nA�!-�(��. S!�)� ��a�{2�{{ODES toQ��7bV�G*�2�Q�B0�����eN.�a��{�#t*�#� bli ?Lr�8) �Q! ~F}& !>�#�Ga�2� >���� %|Y�FJ>�{ w'&\PaAmalbmV� k-/+B�*�Eu!T�2e�Sj,� 2-�ZppZyt�&ScJ;�*�z)6^B��1Be.m%c��:� . 'H!�s /:�#2 P!���"�5� a&{dZMS �>�6�.�� 6PFC%NLS(&�ly m�XtR� �B�2�j:��c al~ �-e�a���<�e��� ~:�ATF#by 9Ls =se� 5(]Aa�=+ 5) � eOe�1&���u ��6� MS���oh�#p�� rgan�_az�Z�! next�!�rev[�:�e��Cof2�I��A�ZA� . ��� 3h٣-.��A>��H).ppln mA�A2na��]�_a�for��O� F!k�act.�iCg �)�;p �_ >��. S �4a�&\;^\ 1-6Js K5ZF�R� MS 6�9NeO]ussed, &R}�>r� k�[2a�s�qnqN �)!r�.A_MS2� �b5>cm&-I{M:A>,} A>V�%'``1+1''� )Asai� be B � i�Yn &pPl \be \bM z_t + \bK z_x = \� H_z S,\qquad z\in\R^�m�e{Es�"e �^$\bM,\,H\RhR^{n\�s n+w,re skew-symm�]a�Be�$S:\,c \�Fa�L\R$�m1otXu,�!aA4� U �,Any1Xɼ��2dk 0�cof�ityV t $dz$aB2e�� YRW!�!�t0n}��a�!�$)�$Ű$)i$,�)+d!�J:T,z�{B*>� �'T6�scl-!d{ � }{t}� %�}I�0�A�i�?� A�ɲ� no��at �Bea 2 U_tAj|J({QdMc}i�)_t &=&aEtM�Q� + 4_t\nn\\3- Y P_t QF dz �CSe� dz -e��x�P�\r<� / Zimk:�eSNC>A ��� - 2 )�(_x\nn \eea ,e�$,\,� :�; $�$7G��E� L]�ADAa�   �zH��a�t.�"C.�L vgIv ly����[ doma-A��e�d&�FSe�2�at Q|Oz $S(z)�2�of $tm�xi>�lQw�}�  "� �� [ yݟ�Wa E� F_x a0�� E = �a��%�^T!� \, z&F = - ^T_t q� ecl}�<IfG>fGFftfM2fI6fxay���m�RAo�j odic b�2ry! d�(uhe)8:� I5O � �[�4b�  2a�8T2��+�f� B� ��*Q E� "9 }� focuI.;6�\"�!(�E,!� iu%�u_{xx�o,2|u|^2 u = 05�NLS�:-� inB��� let�� $u=p+iqI�i?4dut!qnewɱ4tD $v = p_x,\,w=q_x$9 B9nge��E� a��d/!�.(s�Me�c��0}�} ba{rA"q_t - vM�2�p^2+q^2\ )p\\ -p(wn(q\\ p !v\\ q w, \eaQ�nl2��_quiva�6�E�e*y%Y�~}�!CAQ� \[ z���0c} p\\q\\v\\w���q�a:620ccc} 0 & 1 & 0�p-\\  >2l � � Zmi d:K-1R:n]eu�O%S{�^k %�[!� + 9�^2 + v wQ ]. \] I�Q���-%����B1� 5�y�k �j�63$law (LECL)���a�)C��f�]�^2 - �-�,\J ��vA�+ wq_tu� nls_��%D��TfH (LM������pw - qv ���5z2� +v^2+w^2 S pi��qm����!u�Ad��a�w sa n�u2�!g.�1��N�M����7>tB3 �(M = qv - pw2�n�o\� e9 �E{�Z��f>n ��EG��yic�$2��|( ${\cal E}(�(}), &�$ 'I}'z %7 N�5, "N%. %$ as� ea %)-d}{dt�0 � (z)6R%�z)a�@int_0^L\;E(z)\; d5 \\RPI.P \!QI}>QIQ9�}Z\Nj\NB\N\.� %u %�'a>t%�2�} ~� %they-�N1�% �6X��%5�-�~�b2&Ys} >OgreQ�&y!e�&��U �M�}� � er? U2}(!0�5B��A* C a?i��|pec�B| letif n*Jl� �.I�6��mu8 �X�ia2\\�@ial_t^{i,j} z_i^jl bKx2%� 4 _{z}� 9)�, ��d%%�/a� }:y. } y� ���d} ���f #(f(x_i,t_j)$�$R �  i36�!�(�"�{��-sI' qx$nC>�E- � .�%6Y[ if /�-a �eF��A�]� *u . AB>�e�4-a>�EI"apply a���6B� eac�`B�7bJ+ "# spli� !s&�M1�bK}�IFb��\bM_+E� M_- k�4 and} = ) K_-  )�� *� _+^T� rP&V-U��I�A�1 �= -"�9#v;ce*+i�KoRY-2��� _�%1+_+�"z_0^1 - 0}h��-&0 &{-15aH)KO1)BOK�O�R�Lz�J0^���5 Ebox)P SimilarpA{A�:[midHuY5�/6&f!�u2=iz -K a ``2�''%U6�1]Y 1<0i ^{1}%B .\� }�P& z_{1:/2 <0|i1�x<=95 A;/2 = bU�CC5I�/�2ja_\,K0�z_1^jK\; ���F1i^0 +�A121/5� 1}{4)F�E�:A�BAP J&� oA"I%= :� m O CJ--[ l/ �.\)�� B;(� >j�� �O� (q6��iAx� ��whi�fA�2p:jFisb`7Fb. >" r��5�&edeI*l"L*K$.6��So s5FF� d�F�S�3m?�rthaj��B�I�IQdQ�is�t/Q�->MVv,\,7uqU��5_mpr_v�>~ S!�e)T/$6F$� �2H , n+�I�A-h��idE{zero,S.�\"�\)!�&��N �s (2e a�Lw���4�-a 6� ��)� �^ 0mT� 2�#1m�0 _���`"(Zd P��1 -�0R#�"�\C ��6 0,\n��kas�fAK�1��2�nA0�Q� 0 � � !�!q0.�0�>A 4 PO!A )Am0:#E�9��B  1��MeaP${(q/L%aFRI �� /e�Dv(�$�)&�RB� 2RY6AE�L�N\m] n�&� �!2���>*u 6[E�Kf�Q18e X�&P' .�D3*n �`_y$d hoc redun &d &�/2�#kO�3)oE�Qs�-��g��{?mESa�!3Q�-$McLachlan'߃r*M��9@4Korteweg de Vj1e�6; mcl03}pre�%�$ɗ! roacz2G � box ��:is7li"�$�$ B�".M��%Z{B�!��IOb2k'�r.fo�&J f'!�3i���� shif��,�pA� six-����ostenci��m9 Ka�x1�!tn [a r} 1\\ -1Y�] A��5x^27uRA�0\\E�-2�\eM�]p z#e�mB6>E�5 f�s >���A�>5J�� ���qb�:!�5b�q� �aB��DeJ0��E46�As beY:ռi*� Aj�pFev�be M_tɻ���%i^�H��� &*aH &�X2&i T]�-x2-1^�$op �een�.9� -V1X5� �6�� D_t �a� %!FT�"���op�)B�ݔn:n* la\ "�&� �d2�%Z D_ �d!�0��� A�: s up#��7�8���(is%A �$��x.$[e�!!pͬi� M_#�]!^ 3\ �})oa�g.X�gg͇%�� �͐�� љIt�5�K�qM��|R{=�`t�.��jj la�mplex ��A%) !y%�*N��Nu !� iD_tM_x�%+A�^2! u -:|M�u �&6�&&M�2c or��$l�.i�� u_{-�}+u�" � 0}{2Ct} /*&2u� +9 ���H"Ed|B"(�6��� /Z.>%"��ms-E%�1\\ .� u : e R 1}{3� -vJVZ� * ] u5���6�/ � ��%�9; -� 9jt/� G; �}��1c2i9k xIly%�s a���  l�M.ENLS"� . If�`ry{�nl��2� n�*ed pmmob> or, ^���or��t$, f�F�A�5� � ��be"� . As��]�<+Ոo�is�/D� /B�LE��Am�p4�^*�Ang%N�@ E&.F <S�<�N� en ���6yB�s;*�Q+�#!=�*��D�a�``B ly''7ct2�1a &'C*x%"\�!�/%s.d i-#� l.�=˪�u jE5" *fs�e&a:�2UB?ls�r=Nm�2yFT2L.. 2+>я> } L�2�2.�B"\5c,n e_j[�0; latt���A8N)�q��"�. U�w%�Tay�i��"X�% $t$ �k $ z�" �" $z_i ^{j\pms = z  ѵ�.L(�pt^2 {tt}.ons�!f* ,:��/&] � OA�&=mo:!Q j "c7] �e�B!M_-�~)z ��K�/7<x<�!<c azU.:O ]� Meul�de��?n'<ew"s"~N���R�� .8Y" \bL>=F�,!�� E1 ��e*)�7>w?�tilde{�Z z}I Kx&�{ !z}}�ES}( ���gz -a�-z\\�4 \z_x٩=') P�!:� bM &]�\bN mb{00)-: \\ 0& r�KR�K= & ~A~bL� Y.% }�:/��6�8.=Z2|�2 !E�uA�:�2N >!xe�(3LaEG"`Rq~A�l�lN�� .� $#����Ph %2r_�0%"x%QI�.� Qi�'6V_B� Ve�m�� IGP� Q�) Pd+-PJgP6gW_xs�x W�gQgPC2rxg�2� �%Q�:%Qi%wx�, ee %�atjj\[ 5S�.+2_� q�p j+&- 4}MM�", !�-Vp%Vq9V"/:j \,pjq~j!~j&�o�3$%4�3�PleU�!>^4&_4:�\,~ �f�4�u*�;�n�,��# 6 turbu � a7NLS� &�.�6� &n���=um�=$� &��Z�m2> 6����Ga&U �6�Z mpr�. E!�0Cf �R:����'s"� _{i+�,t_{j )$�.�"1e/7� M�t�� !�e��`n.$�>^2 &j% 1}{6� �mZ63 6t} h�ws��0 �-���- ҟ+ � �a��!��#?=Q' $0�1$D�n$e grid"� $1/2� 5��� "� �!�!�)֐*� 9 �)�x�vi�sheo &i-A�&&[-1{�# .�% � %�1�n�4A4{t!�+ 2O}"�'^4< �hV"}*� 6��>�� tF)%� & ���.�{ ���F�x�Sub*<�a�+Ys�o�A�Sn7d!��T\: rder&�(= ARit$, e�& t& PDE> .�1}� e�t}+��C.,1 % .� (z),�� MEQN\ �Call�nti"[�B� U�j��"h6? t!;A= "�.�O�m! ' �H�=� "K �>�*+;- �5�2I+uM�:�%E12} xAL h:�9�U`)6����x�l��F�� be�Ged Śly�w1 �Q)Rby� p&W&Re ��*$zy1A�=P=B�� �$z|2 �4B�3.8qp~l1�B&%��&� �$|3�YMS� }��b"w=-T*�D^Ovia5s%6@9":���aug�bed"y1sO� � (z,z_t,e�},z_x xx})^T�.S��S�.�q�i�}� "�.(E���(�, a55T1� �I:^-a�tma�� �M}*� :!K}}�G$z}�F�#Gj]MS� �l�k*&� ]M}&H K}}$ �sVH���5B�>HJ&s&:��(�y6&j�<${0�:D~<"�\\:b��:6C �j \\��7}*���HDm�:lQthe�6�>�?�=.6�$mRz}�B&:tF4 ���to�J�I)%ak�=)q��2� e�1�o be,���I���- �E2�F}_�Dq Es�vq8���QW '%�48'x�PM�]��aF6a.:����:M�.aa��G�+'I�� aG6`� �d � +: �24 � A� u ]�G�H&��[IVg( �� +2? +2 z �_{xtt} g�:!.�U=&�/, $E,\,F,\,G,IA$I,:� :��AI� AF�A�2�Q,�n�h"�Sb�s*W ^E�� O.�S.&Nk "<��*�]� "&Sw^:iډhe� � �#.f�F$u(x+L,�u�NR4t,T;��a �#ksquasi-`(��im2�, �f , $u_0(x)!�0.5(1+ 0.1\cosx),$ Є�\pi/L�)�2\Ş2}\pi$3��i�co}�: g �� �%��TS/a�6uacter�SbE�e��i� mode%0 i]A�*�x�,:x&  (� w�8?c�}$MS-CC�{@J mesh siz�n�g�p��� t U R " ���ri� �n �;x!�0m $\bA_- u^1�<bA_+ u^f'$F(u^1,u^0)�;a�6era�&b�u}]U $u^1$.�C�l&$�64i� $dt= 5sQI�3}$�$$450ȅ2}a"�|�~[hFZ� BY�\t =j� in,w�o0=2.25in]{al3a�t.���({S�Tb T��4���c 8��.�d T��e 82�c��S� g�e:�J���=!�: a) ��, b-c)~�Bhe�� aR d-e:#g�iJ+$2ܙ�$ndQ7� yp��2eg�s�$�Tct �ܕ� bn�imeXa`F�'. iJ[�in how�e- �� �co6�) C�( . To"B^`} use "-d2�]"#A�R���  E � 2��F 9_) )x�In4� sev iduғeg9 (FR�s"!�2}A� �!yA)BB7�AI2!^E1���B�,�$��6RBnd 3� �S O!�u�ro r1N�reg@~1!52 teepa�d���,�$. If �Ow4And�mc"� E�$z� H=9  A z$,my\bANU�m*�Vx%�Z:&�#-Ued����lg�V�igaha"i��u�� �dl. �#^p!^*�P!�V���e��E0 �"�indu��ə laws��\�$r�rd �k" ��VE sa�["� |Jh!�` "wl�Q�b��Z��1AVu�A� 6� H �R�= d�Q#��6m6.j}.�xf/i"�~Dn a�Ped fash�bn�  8�gEQpl� 2�cm�}�d)�-leE��:���J<e)�"�_J(!�!�n��U� �R-� \/} (u6�; ucri� �i�14'TI�!� er) lTDI!�bizi"�o���um _ G6�� 6s.���9�{"{9�T�$1��^ E`. 2� ��E�g�T �E�tep�$�E 4T,)�� 2U�N T Of T�T"�  $NV]"� t�}2� $tabular*}{&��}{@{\A� acolsep{\�}}lV7Dh�t �"3�* 64 &\\ U& 2.0E-0*1 5 3zv nLE[65u4 .5E- 46 & 8  r h6.IM?7�F 4.8E-�F \\�G�7.3 �Ft& 7.62 F�G � 2E-1) 5E-1!JS1g 0 (4(3�/ 5� 21 "|�RUɡ��.:iaa;f^�"Jg.ui MS,� | $}   I�  a�a� �mH"U ����}:|-CC:� �S����I�/.��i�"n~��~.  2!"� is��s"� ! �<uti�*��$� T$��$T� ���G; @,ha2y�ϣ/�� �, $T=10$�j"��. &�2ECL�i*vJof �x$x�� ~1),� �xed�k��M2`[arrow 0��8,HKrtI-_0� 3�2MXt_0/2^k,\,k=0,1,...,6$.E7.U�!�U7 t bK����dT erb�"|fO ]&�� 9GlyE0���Eas  to �����MxZ�re� . 5�f{fig3}� $loglog ploE�axi�!as!�ua�#��|?)nA 6).� ?|ur:,).n�3"�3in]{bean�LF���ag�n��I t$ E~�u�A�(o - -A� �M�&-)�fla��%I�� Clezw8��fa��[pH/%'is&�(2nd)�, 6f>-4d�2 . V�z`qofE>eV{ LMCM6������jp!$%# on*J%�oh"��p=��Ps��ed�� NSF,0 n�x8ber DMS-0204714eI>��{��&P�B {U. AE r�KR.&oB}, >�R&��.-�rB-d>qB,��8�t��3�5�- {T.J. Br��q S. R�c}, P�ics Le��s A, �bf{284�184-19��1).^�p$} {E. Hair �Ch. Lub�} > �h., Z�� 44��99�\�boV,S%? G. Wբr}, GKuic k�s ��]F S!ger V��$g, Berlin,!,2.�{[ {&��� A. KarpeeڊC*`�}, J.A��!K.9>173��16--148��6?>y2q�.c ,} Fut. Gٕ gSys=�19}, 40)�32� `bva}, O��p���p R�y�jt*�%6�,��mooDs! B. M%uq,} Jq.,b9}, 395%�6q \} b[Num��kV9� 625 Ȏ6V�S} {�zw57A73--499�mDy`p�x {J.ҫomas,}���P� D�E�E�Fs, BSN*j�l�� >ҋ�do��4�s.tex ��Sym�� ������� P��~� \�� �.6��7"��1J� A �N����r� �%v�{�-.45e��.� def\���Njin��_ 6pt{��R-aR 0.4pS dth5pt!th0pt5L:�j")� ^6\ g��pt\hss�$ % Greek (��)� K�6�eps}{{iloB��v varepR"Om?O�j8�.ċokN>v 7var: % d�$:� -d=$rm��B�2rs ,\ËrY�b6*dsD� YB��ts�N�3J� ->�3FWb:+2�3}F1��thN�4J�.>�4FYb>,2�4 �!�ca�|uw:�der��{-�\�  #�F F��t:9d2d Z+ t}[1e7��{tBp:R~z�v>96�� F�p o3�EDo^2 :�\* A%D@ divBGra| �! %9 er��p#:.�pr���:�pr $ %��eMN6ref�Ɛib)�� %�aala� "� >�dc{:=:�n:��.�i;\;)in} :Ao6%oR%dsp}{\5�la���s���Walign�+6���s��ie{5mm>�nov!v !3mˡno$nt�fon>Kbt>b�N.1v�� ��� }�5�)Z  {lemma}{L28,algorithm}{A 2"d@}BG�`c� }{Qu$�6D�mk�on}{PrB� R2jnote}{��6,corollary}{C ; {\I}{\5k\input{ Ĭ% �"@ 6=die�� _i>�t �,�%}(6 alpI alphY6betbet2�AF�#B��Ha� H>�b!bf 0}:}���6�L �LambdB�b ��>�b _ 2 Omone! ^{(1)BCb5.bfF-bH? B+f frakF bS>FϗŤ \WB�P<PBKFĘMF�zzBZx}{{xFb5ov�}ux��2n Hcal"��A{!06#hM!�B�h  wideV!F= F>�h�<DB =!6� zbar`�BZ�{!ZBfZBeF V2 VF@i� {{{F^{(�F�h �s��{#&9 .( _{e#Ik >4d�%P��.�6@subeim}[� W3b}�2'subF('6(hG��! � >�rhopp),rho_{V^\pr\,prB�.k/^kN1:�Th�fU�5@ : )j� J-^{� B4OmF1��16� Svec�vec{SB�YDZ.�:�Zx5�ZUgbbz(z^{I�Bszk%_kb']U�j�nu�� nu_e!�:6Sb}|{{\overline S}} \newcommand{\wb}. w> z6 z> (Ssq}{{|S|^2>QQFw|wJ4z zJp}{{p>dp6�F Pp P% %6�St}{{S_t>WSxxF  {xx}BbM\SbJOb7FRbSNUQTQFRQx}{{QFOQNQRL w}{{B�wawFawawFawawVa)wJw)wbJR-wbRUp�\pF8delA ta \F� spJs;bA�de < b}} >d!0"B8di9 AwA2Xd%A B�d-AF"z�Bwdi� >z>�oneE�1B�twoB�Sthre 63B6oneA,S_{1,tF�two 2RZ !3N!one!�_J]two 2R_ !3N!_ 1,N�a !2V!c #3 #%6�w)uw^Buw)uwJYa�^Buwfour4>�kE�wbVnB� qVtFwtilA�tildeF/wb2 i:%a]Փa>�b6 A�2[v6 v>@u6 u> RA� �R>Lh�hat L>KK>JJ>phi }}>dxietaw( d\xi \W d\:�dx� dx#��% %%2!dv)(partial^{|}F�dvir.$�2HD" mathcal D�#2(br} {{\bf r>�brp ^\pJ"n"_0JB ! D_0 F: FrF@r ?r9��p Algorithm reserved/key-words!O2� Ifif>Theat>`lseBe:"For!foBkToto>> Whilaw:bI�inA�2'A.aFO�F�D�d�6� bigOA*U�OB�Pcref}[2] {{(\ref{#2})B&EA�epsilo�2�JbcbfF�Sec a BF dLam"�\LambdB�tb:':lNeVN^{(r)Bfuaf$u^{(\alphaN"j>#_j>dus$_\SigmB�uas}{2eZ)dxe�@dx_1 \wedge \dots dx_Bj dxni}$(-1)^{i-1}'V@\wide�� dx_iU�bb Ձ��dV�)%o Vts!$ & V& v ' V(pdx�frac{�} F�pdx%2f3��:Fpdi} !��#6�pduE*bWuA8} B:ajaM^�.� E6Addt9d}{��:� Ninf$5�N>#@piu}[1]{{\pi^{(#1F pil# _{#1BPAg{{\und!A>gdDR�#B�H���&{ >CVe� �F{ > ZbM9�Z>#XB#X>#YB#Y>#WB#W>#cH���H> OmegaA� ^{(i�k2N$A] ^{(jV$k} $kB$ Thet l Rll Rll ^{ lpF�%%% \documentclass[11pt]{< 8cle} \setlength)�0width}{7.50inF(height}{10.B (evensidemarX -0.6>Dodd~#topB5B8% packages \use @[dvips]{graphics}.{ifo2latexsym6amsAB symbBcd6epsfig_T definitions \include{,} \title{Lo�g�Lagrangian Formalism and DiscretizaMx of the Heisenberg Magnet ModelVxauthor{D. Karpeev\\ MathematicsU�Computer Science Division\\ Argonne National Labs\\ k N(@mcs.anl.goZO�\\ C.M. Schober\thanks{This work was ��8ly supported by�NSF, !Tt number DMS-0204714.}aDe@A�!�0\\ UniversityLCentral Florida\\ cs �d@mail.ucf.edu } \date{} \� {dm} \make%�8 \abstract In t�� >�directly�.?\principle. We employ a =ÅRe elee �to9�e (space�sA|oItrivialMpA�ppin bundle $N = M\times S^2$ �$ an approp!�e \-% $M$. Si�@jdo not)]� ctor 5,�usua�8EM bases can beI�only %�\ly with coordinate trans!�E=(s intervenA@on5(boundaries,%�2s�erties a\$guaranteed }uin�-e)�!��-�of cha�n eris��4, non-polynom!�9=� Lie-group��* Rs. 8�� �x�x)��F �\{Introdu } ThA�ea��$PDEs in in� nm6Hfinds its most natu��language2a�setEuof jetm�sN� �e�. �� @, ga�eFequm]of ``mo�"''ņ prescrib��ly-� ed differa (al operatori�( although c�� ga��(mately d�3in terme_��M�D ativa� �� mea���ll% |��4is clear. Moreꉇ@�Sպnd��Rk ya�fiber-k( frequently��P to a non�j���M%�Z solu�,b��� `` Hic'' feAes. A-W!senic.��b��!ed%che.]=� cept�� clarV 93�5��d�9a gA� assetr4itself. All!�/i cular o� Lan  e(whose6�I�EEE!e" ��@ ty!Zd� o� e ae� fun al --�� appaA�l5�t-free�m. S&� !�>�*� immediI� fo � $well-known!�ced ,� do� ed quantiţ correspon�E&,tinuous symm� es (F0 ).�ositi�!gles6 tu�P@ Hamiltonv systems�her3 � � oT'' have been broken rea�vE�AZ*f �g. A spli��e ��>�up-�\{\em choosing} a preferA�ydM - !�iq$unique cos mentary f%� lite�H �y breaka�ag  full �Jof : �>z no longer�%�s�aE;!�K. Fur� mor )k!�Kspecif�]�l� !leQyϡ   energy.� a PoissonY� h�o b� mi� depend��$\footnote{� fact,�re� a certain��)nnARassocA�d> 1!�i� ! )� anon~ } 1-%*in.( theo� liv�on2�$\Nr$ a,$r > 1$ \citS(ligne+.I, m� }, �m�b� as ba�"�Y�ch�A at n )$made ��he6(�x.}����it may�Hear)�fa^iar exaA���x! mechan�t{h.p A�.�pi?�5 equivalen%�is!��l� so��!�Y1�\ !�degA4acy c�_eMmQ9bracke@at mustE:atisfA: befo�'%�Z}.�0 ̀re� ed. In �l�  ad��� nishA2�F�(acle (i.e.!cctE�!*{An).�� �!|� !al1l!Vresto�z,ly. Even so& ��mOcarA� en� indAd=�%CBX�lyE�� -typbSA�A cresult���( �-(Vv���r6Fm���� EV. %0whe2�>��J�eir�&� semA��A� �F+e 2�c yield aloge�],�>�-�Ť nder mini�U��{:��>2� case l� a soph� a%, �oru��gW AB� �~6-� . T��a� �search!���KZ�� $ly arises %�a�iAPng erAYv5��s p"8$iscuss pot/ ���on�$W�c:XsIzA�.}2��.a ��S� ~2 .S��}brieflya�F C of �� as�%�"�� 6023 A^6r��!alalA�Y�E�2�a�a very�� ent �ute�al toolW.�tpt�1�� , �E�ur�,many explici�ulas, &�i�!�A�d��a"Ma}�aed!��&�!�-�6�HM-�J}ev�qriAg(A �1{rHM,�� �% s�pd tVeXXVdp�'. c � �;(o Novikov's�Cvalued!�Z� Morse�o��s ANX Lyusternik-Schnirelman�T+riWuss� 1�� ��^K?E�muY]al.Vof HM"�R-`!�An essm�� tyH i!�a��u(}!� trai<to lie� unit 2-sp��,  is����<sta�d&%�!� ���Lap� �rEa+k� !" rete]O�W5}�� avoi� aLp�y!AC� V��o�p � to �)9(HZ. A)er� %!lR�com:e�prelimin )-(�usA��n % l%�)"o �5d&��%n outo- of our fu� plaiMC �se point� �ed %O � �conclu �inV�C$}�������������C \labelB[ �$�?&��'F-�?.�/uA2 .�*etE4m�framel�mooth2}s $N \xr�arrowL!} M$ 4,some $n-$dim�o��. $M$�I�.�.� $\NrBk u{r}o �,steenrod}. DR8hB�i�:�1ct�Ds $\Sec(N)$�� �, each $\s$: M \9. N$, $\pixrc % = �!id}_M$ iI ifia%�  image�Y = = (M)$D cop� !]horiz��!�embedd��$N$. Fix����t��Z!�{\cong}_� {loc!t �F$ ex5 y$N$�{a���!�w�!a $k$-. typ�� $F$.g ><�&�Ts, $x = (x_i), i = 1, �% , n$1�Eb5 $u-u_j), j- ,r$ ��,` es"Oy� $x � u: N2�,\R^{n+k}$, m $N$ ��A� omorI!�w"�!0jzQongS>hn$���induc)�simila� ffksmPa( %�T�s _rJd� �a{(e& adaptedL oO s $\left()�(\uaj)I�), |\r( | \leq r$*#&D&�!}5-indic!�reA]u�: $ O!� _Y  n),\w= \sum(� _i$,y �+' �^{ '} \�  \^�& x_1}._1!g�(f0n0n}2��r- |� _1NcnP $\�*_i$�$1$ in�A{ i-thPcee),zeros everyw  else. }a%%��)}��!��)^k TN$ I$�* ^k N}v%�� �>�m&� ��v�fH$V^k(N)!�hT�ia�.eJW�;� �OZ&x7� N)�I&��d-,nguished sub� $V(N,M)A7b�V�MV^1��of�<-�erva� �,n"g� tZ�j-A automos�ms,4�2�/�M�% (2� ,M)$�5V͋v��"sub͗� fix � s. WD�ricted��$�*$ ��ý s $u$�,"%�$x$A $$ Um \us:�e} 2*x^{-1�J2A�)}r+63,u}\R^k. $$ S��ly,�1 �)f��Aua$�r�s�$u�,r*!-$ Kencode%in5"s�behavior|s�ȁ�� .Um�\us(xA�Np$(x), \quad���3� To�.� &�we admit��%�}�al!D.$o �� \in Eeep ssigt#l $\int �.()�Izan $n$e� $2 Ti� n M$, suc��~nd 8_xY :L /_x= at G$x s depi� �$r$-jet �H-_xe$e`)�N%�@ J�FoN�.i$r$. �InO2 $1`iF2�Aora^e< 6�5# �or���,��b�Ezion�Kthr a map $\0_*��duc �sJa � �5: j *� -�)��� .a�y�b�2 {CD} EP\Nr) @>{ �}>>  ��(:(@A{J^r_*}AA: @VV{A�}VJ?}N),~E�6}R� \end��_B*&�abvno���z palais shalzl-�amei�symbol}�+]�$�wr^(��� u=A�t -M r),3�inMAto� e sen*%amtl�/��A\6be)�� $nice} (seei m�'+pa�6k+s�'})6$act domaina� _M \��U+���)5(t� �aQ�14�.}�� "y{0,�k.�7piu{r}^*.���Y�of*/ � ms va=�he�_��Fg $TA�/Mw�Hzof�(��#simplya�-�%�of� -.e� holonomicJ�In�trast!�$N^{0� S r� �0$A�� .�sub�fol��)�r926��lif� �A�=,dc"�r$�.� �y<"�t��ftN>25beta)�4 =6a�4 + "��} � �U�ra_�r( �� M��:�,� ��i�E, m����_{ ]y ��.�caf} ��_I*�%&�*=,2c&u�vestigat�"�"�հtoK^/�"aU�-��*F r!^ A� ic@ $Z-$A�QABre7 nw b�r(�)� -pa}P/ͣ. Asm�$;^t_A�"dedMk = �"=M!�&�phR�� ] � = Z|.��6 � ��Z!�> � .!�.� wD"vejT\.ZYn Z�k .t5��|_{t=0&3 ס= X + V(x,uE�X_i� ia;j V_j (�5.>�o��Z�$��nY'{s�$A� /&� $X��L$Y$�(su%+�q%t&(s $A_0 = C^fty} � 5 i"C)%�al� Q�, � via pus#! $% ward�Di�"xthe]/t_ �>n�/nA!� curv� �g^t(x)$�&-/�At�,-�&m"� t!� �&E\G- {-tI,: $\dsp{X(x,� )�@_*!�xQ%�iA w ��Y \us_{j,i}1uj� )}$,\\ aY:a8um_j \ddt \us^tAO) >= oj kMl�- i8 uA�I�I� H}$.\\ G�1An,EC)e._!QE�M�5����at $T_{)�(x)AJ/c{��llel}A!�]��Q D $T_x�= T_x N \ � A�F�konto}.K$. N.� � ighe� rE[is easi�)�4dA�arch 5ngAt of.� A�,2ince,����*��,Y^{(1)} = Y �AM-%��:!�U^%u 7}&HJ\ Wb]a�\\YA�U�f ��%=" Thusu first�a one�A�-=$�#ob�ed�!>*g]yZ� T_x ��u�(%�s6&d�*?% $q�)Aime iao5"d@yu5$TM�Io��l rul�+l�4(recursively�J*j/�4�4aS5L %�far�A���M�ir�*���wise, +to�way tang�!ns6� p�&e | sp out G+��*pa[g+��. ��- ,�_wil��V algebral �� $f:A_� C^\i��Y )E�}�(=�&� � }l��HorL i)�iB�3atr) re29!tot� %"v� eZg ;> $ ug,.+ to a�zp ��vr�w$.�4�-s-��) above�Eal�urÙ� data�"�"! $A_r�to{r+1}$:!yN� $f �[ j"��"a)E� r&������)regar�a�}#!�M  $^>�#injlimE �bigcup V Q4�!� e�͔?PproQ� .:09���D{Der}(�Re�W viewed�i �.`��?��gi�)��se�' $\��H W�.i W����+{j,� } W. � aj� nd �;1=�$ #! MW��V �, ���oe%T8�2� 2�usm�#  od��$ik�! ver $K� Like�0i�v�6� s} $�?(YAa\)!VY�V$�+ta�Ver �7 �<�et� !�ao*� �%�" *�U�!�Z�uf-�,\�"��Yz um.�YL)? �%P!�Y4 in A_0�I�+� heck���)LA)$�Jmu A��A(di!� >A � iAϥ@-թ!3$Vp� .-9�$-a"NH J. ]ALan~a�2~a��S%��3f�1 $Z� N2�t�M!P$ w0�!*�  a ``�X�6nd ``Q�'' r�(\[V A&!�N;  Ej� 6 },\qA  {YCj)�bD� (V_j& V P ] }.\] Each%� ��ӝp�%�a��Zi@ -��6�%�B6 6�oge�2 �!W)o�.V�B�+i/Fj*j \op�.}. `f& su�r4UT., �d�E!�%�a�T� 1�s���1I�!�ͻ�n>Gu�, ``de Rham''.� qdDR�t�Q�%�Y�%�s_B� {1,!251 0,�i�$s = \Q+ da�K4,9qd�2[6�P�is�f�?.L��'� ���ԉR&F� = dh&�>V V572��&M*�9!��!�E*n lE&F$%(�1 nts %�P w:X��u�l�A�r$x�Ce�?Zl� 1l%��  �?)�$-Ba$measu� he��irtual&�+�7�6�+�*o��)  O�; "Vwe�dc �� �-�"��5�* �iX"� paiw.s��5�A}o����!Z!�9-�WuteI�1<an%;I}�g� o� 6�g Er*xKaDR+ ,\ dR �,.A+.W <, 2A� /? f N�i�cw -@.o�^*� Uq�x_�0,\&� f�{&� \pder{�O�J* ,85+!�Aa"7 ��1�de�� e��:ec� ��d$�Z�R^m T!��{k+l=m}��{k,l}~"�;�#<0<� {%�:)e\r"-* +1,l � Ed: � ?N9 ,l+1/5i�-�<�!subQ a ��F:${k�=�Z[ �j�%"l&)}"x(.$k}"'_k)}]�J$l�/\\m��5��:[dx_{i_1e l}]$ (in:�)�l5�0�$ $l > n$),ID�`9�T�~$ filte�7�!�_0 \N �s � ,rV,���%�$k,5"C_r M K��-�,)F9W %W� P.O deg�X*ext{deg�eKs�#_s|�q ����� ZuF,-W �%Li&�3�ie{lM�L&�(�M ()pE (��inner 4��.")ml� �Q�{oFnon&>*� s be���#\P��1�~hpd>�m+$�� ob!'ed�  �3s�pl�0� I!\%&] }{%3$&� "�����R�7=3. 1i -R�5.d =�7\w�O=��( e2a2)Ba  1\�)I  +>VdQ� ;{.S6d�� Q�5CuL�� .K�/&�*t7,�K(#d�O� .�+-nin}, h�)we sket &e necess*[3.� maiA9.�;�ul#7E�"�6��UJvar}),L�pa6�in::Z}) �!BN 8��K�%!�m����"&�6: *�Z( )"N !� $E�E�:M�X � }%=�>$3$smJu�J J�Z��e k�=�i�'��R is sh�L in w�}$!X"C � =&�Y$!?�)4�on�8uZD� I�QK HJcVH6"�(��$0, eq. (4.37))8J8 � *��{%�=n$ \dxn,\ s)FT�2m�)�:� >j \X{` 2m � dxn<���G,I@(�* u_j).Y�$�B�!a�aw&v�alo�:!��9 s�� �Ef8��r&x:$!a�5I � O =�(> (uY�>�A e{\v� 2h �X_ !�}{�Vanm�_0a;n}}� 9�>d� !�i dT �X�� :V1a�e�\,� \, dq�(1,n-�#:�6Kb�V< �NXit�vid1�adj�8ia�6o*{ � on �s 6�, �}�2Q$d��&(%1Y.LY��.�4Yy3!�_0!���Y}��Un0+&��sT�# -�,�%edj� �R�s � N!���<%!^V�. I�-{��y) ��'&�,�'2! �1V �Oy!�"S�$l-�?b�es ex� � ���� mJ}�m (extrema p+Gla")�nR}�62%ELi�!�m�= 0m I �4� �si*@B!P}�  �2� $X�����b��%��A�M(I�.'2a�}�],�2-i:.0vu;X��a��#݂.L6��H/M)B_O Rq*�*Y�*A I�� EL}) w%k�+al�%�coent.D}�7�che�A$ does+�Il!�0( .��2�A�I,ormJ+WfV T�,&�86a9d5=/Y���6�cov] �.��X_�%5�-1�cHX \cH1�Uner 6EFWLa� ���"�"�)��� L�Hdr�QanST . Am�I�*ng�Bt i� �/4�Do"�-Rq�*msB)6&-!8-"^2-0B�a��!� �y!��llW(AalJ�C)"�G �>�U !�ky�k T_{jky0:jj!��{k \neq  Qk}{)�k�6O j  j @k. I�Lat�Y�"�Na C&c &15�mo0N��2 ,1��� IuP���l&2� *� %M{\).} (6b||}�%{�:*w&�" n_1�J_1)nn)} p�b�'s�._nBY�i^ 1� ś"IX)}}B�> )0F� $.>eo39�`mathb:LabtH_.' :'tO�d B( ?�`ijaB(H.$J`\cJ]&�AsG�<��?is �TaN<{&.�FP ix a�-=� �.M^{n-`s M^1=a/at�X�+�n $(x*�<x_F, �+x_n�0\6ny%�$ �9���x sl3Z(t�'"^"-hyperDAZ � �{t}�8d��$x_t� �6?��� jr(tdf��7�,��=�J Mr(cor�Ong�8miQ $@bI&P H�OLSatbH-��6[%Oi�`�6���Y �^�1(t6 I�:q\ �z;E�F;Hv7*x T_{n x�Er6gEW�bHFpr� �G.�B\is)�regula�2�Q7��]F�5.a�n%v.� evol{W�1pwN� a�^�Vby .��tb�ѯt}!i���E *�C)�y��Ov�N�in�eJ�����e:�lag.�@ z@ -\bH��.�)�)-��hB �K[�K[��[��[����\�*Fd�KS�WBuGH29M:@S;1t�� �6:��*" J":tk}�h^{(�hJ-E-2-6WmtFA2ggNFiNJhN d {{HlZ�bF�:F>�bGG>t =B>t ? B@ Func`r-BAuve!vec{uB1iS{@ J soth���so}(3B_hSO6&SO &�-�7Mt ��*ZJ ��B A�tRL[*1TB�d�A:�:G%�V �ke�%HM�K�S&�r\�d�"7e�d. �,|>/2�we*8"?k i�:"1F�HM�el�a2XbQ o"�p`�;�/�H=_I4 s \R^3�(�h2qJ��^m;� \R�c&� s� x_2 ��?��$E?�S� S_2, S_3*D, (e.g.z Dfaddeev+takhtajan}PA"�^-� �)QE� � X7:=9�.�$��2� �>�J%2�s�W�Vf< � �'6��{2} S_a"�b,c�p1q_{a b c"b&�{1}^2 S_!E0�+We now���T�.l�Tur"JA� n tw�e�7�M@"�% x&D {.[q�HM� ubS *� H} Af!�&.8 $M�/� $KM^1|R\R� 2k�Jx_1)�$- 2$,�<ksi�5taneo�^t�--�M3M&(t��# (t)( � )$ zC�3$tEK� � > - $ =t`0F|'3 $�?ayv �^3RN1 � :�a"� ���:12EE� . THA%B 4-�~V�Vis�_ ified acc�~ gly: 2� ,u#(�J\D1(� etc� 2�*� 6|is� = hml.HamU �� )�in">tk{ G\halfH"t9Sonex^2] Zz ��x^2Y dx B&Hd!�*9"a � f  Hx=�qA5"�#=+�-@�V+%H�Y)1� $H/A_1 8��W@�դգn �$e���C.EV]=� N%�\{S_a��b\}!$Psi_{a,b}(��A�-Cc ".(��cB�XU�A&-3*�B�$\NyY"�& powe�)!�"Lqj��Et6^2 sBt/sBL5�~3Mr�)-a 29@y!�D�U�m�A�f�32�O�:vJ=!�i*�gB&>a-��bi/ar&1�)�(x�J�(x - y�b loop"15of � cs�f|,��U ead .dd�E!���*��I��(p�$x MA�Re]� eqmoI�Eq_>$ = \{H,\,\�9""E� A (S!% �B}A� 7�Hb= i(�=� s =�}J��}�as ��3A_0�% y�%iN!0n @9�( 7�&7f�Iin V�ZU: $�S_a}{ ��!bX) S_bTo) iai"�c�[��`�����)�)a3a�Iq=�"� ";$.;� ��+Ds|Ym�fc�$��}�Nm�1Rway, how�O:Fqe� })�i�l m� * x8V  d�J �(`+/$ (H4karasev+maslovFdp,9u�:Y&�#%~�6���a�,E��7in 0y!&�19 �Ain oI�T^*� ^*^%"$,!!��!'bi�o9 ����Bi�� TN�$-� `n��d&=f! anPd�� � 9 1�N� �["�dte��leaam� $26�Wfol�rIvp�2 of A[ s ab� 0e origin, orb�V co 'V[:)nf:%QO��vlea?s>�.�-� �Kirillov��m},A�mt�k<&Aver! CdynamFfof 9\q�n e�C=O \mbox{($|�� |^2_� 0$).')��4b\id�cS!��VQ *p\bL�$S�b,\, Q\r�1)^T"�\b�=*w*wb%^�!=&�e�E�` tabl�U&��&��  .U StoW!  ued�� 2 w}95 w}{R+#FB(\Sb)2 ��JBfD%��!} - 1} + 1�R-1 �FM(7=�!�Q�- Q�=�59A? �S' = S RA3w�Sb R.9�L9W5�ͤ:bG !�mo�]�2< RoQnHG.�]N\ r SQ�,�\{M�� = 2i QU� Q -i S.\e a[be.�|S_x|�Q_�mm 51 b7�%1*'i�$to��͚��2:Is2e!)6r-�!Z$\bW$-Ny{)�r-WW Rc#=e+e/!@+Ad1{Q�/S)�Af-2iBBx�0�is �tly�2-�m�{nd���<&nr( )!n2�� ud\dw \W ��}{ ��i@2  i (a�a�)^2F�S a[ scal�:@$\displaystyle{ z{,w}{\sqrt{R}}Ebd�@":;&p^�] �K �\dz �zb}{i}-"�z"�*�+\��5:s�]pullback +&`�r�/`" $ by0�42)$^""w6���U ��M�u!� E 53z ��zz!�!�Ef-�1 Ź[X ( &� I��w%�}{4A��+!�b Z  \ -\ @�IA4{R^�/2o-�?4��vFD�SK � + C�ub2v��];%%�dw%9w!9w!$ R�J5��6�"�2m)��E�j�W���H%g \wx �2%iB;iA�As�*E�.>)X4w�;N� \w� i ~-R ��!L! wx^2%�=!-%�+  -2RAm-iHi-^2P�XM�hm��_WB,.�D�D�w�w.�*���M�z�Ձ��KG*�W*w9 �YA el�vs*b6t~Vucs:m:�*�A�*� M`� �% . W�d>�ٌ&�k�$a/heR� &]") are 46�"\bW_t}{ɲAz"\bW�Z From Kd-�" ), l�o��b�:�a� ��o), $X��aCaI?}{w�8 wbt  �I$L#= �$�N g�)ze�Ysn=!�!� �#�� -�S:�#{�*�Adx� d� ;.�% G�>��#���obt��t�7� �h�%L�^�W� �3:{E�&2�q)-1�,. ). C�Q�hAN"pQ�!,RaK5^�x��R��HM��-B�6:%�\p%.�3%>Q<x /�x}��ɪ)^g -�c5~. !�1�� !�4iᑆY�tB�>�^L �\��x dxt *� \� \\ �6bY81eA��c5b �~c1O%< %�i%S%`�!mt}�`+& :`}�f�)^b%Y9_1G5A)gd)�\{ .x` `�t��\%7A8 nQ2E'R1Nx U��  Lx �\�y�yNq�funda�M !��uԙZ�u�Om1Y�-0 = -�]� d��=� .-N2% �-QQFB� �9 J��O�)D���  -I� �3��� 1�e  B7 1�*2Qo�.$%�\da� W dtT\ +$ /��(T�f� and,�!�UJ�R 51FJbHa!3� �_��A��.�@  _-Y�#Ae�C��U���)~e��Z^=B�F:)��A�bHn9�Fa"Jcoeffi��$MW%�K�&�>:%iB�V  XB�Iw)1a|Y��]S\!D.R -MUE[.��m�e)cQ� 1� 'a:&m ':�*} =|�9Q�= @�  *�{x�HJ� �*� eߡšd�� 922%3B:Ub� H W � �u� �dt .�\2cf<�-af�"y FW^8Z/� B� geg5�E-�.�2&.%-�=�wY � qV.���.� ,el 2p5B:�um:y$�~x taut"��ff$27 �X%j�́-:p8!�B7�(The�~&��k�] �62d � }NU8\p"P\�(1,26#Bwx} �L2- Hp$��A D:S pbl2^lbI Ym .n-`!)n��[} s @�Zn � fibe6�*$e ,\,p@p \wt wb�'wN�N�\- %� p �U�= -&� \psq,&9 Hamwp}\�L!#e^-��elpe!e@La�i]�)��gaNT}��E�k&B^iGQ2 takiF M� �bXtJE,�/�� 4 �px��M�=�k9 �>p�-�(i�z��M1��ip>Uz *��+� �~� ��E�)�:86�!B ! JIUs2?�2� �7� Q : Ig=�핟�pb:�.�%Ua�A�p3 M Gaj\.�-�� ��x *�?*�"� /� �Ir�g�+�-}�J%hto0bridges+reich>�*~wo ma�l�/\bK�Qb�za.U�# $\b�F~ )$ (UI��$ n�%I up*12 !get a�`� fe *B��Q��K!��8p�x0 &-1 & 0:� 0 &#*� 3 "^< " a� ��Mbe;i���5v���B��V˚�end�B/ I�m�\Om_t��+ x dx"�2 P_�� 1*\Om^{(2���D)�$24R,0!%/:�re:n%�A��m�M�- xLYkz$.� . Indeed,"Yi�� �+�/-r"_taU�JX,-\bz_x^T \bKL?��� xd&� ��9>1 Om8 Y= �t��1dob�.�*������uN������.�.!A3�bzMnabla�@z} \Ham �IJH>)�%�� lumn��of�$%*�+. Fin�a:�B� l�Bh1&i })*n *.1Xgy ($H$)�� um ($P$,r:Z:�� T_{tt}����w ��= -H,\'{ � wB(!NW� ��� 2}.AX T_{x`� d_� �= P gx6g 'eo � wb '�(�4if}�`im���F"h' J��'es"��CEult���&�I*oF�j*�i?�A[4�'is ha7&.�(nSlť�'now 5 ��njc)�2��Mk jk}$v')��.z"7͔L,b\%�'t% 2����a�>0&�E}#9�Dg�-�/)*�"z r]Rn"� �R5_plea<a t*��x, m�xliu .:��rn z�(�" phen�Don ҟu(�q d, a&DG>G>Sn��Wte��i� " } set�"l task�*r- 86�\critical�0%s�=K to%� ��,!��@l78R#2�b!;e6 s, `"��heچssi�؉Yory�1,�9��Il�i2�2c�$F$|pla���g.]!�*^�"4$H^1(F, \R)$, &pcl�but1-(;o K_ z ur s"�h^�(Ql) #��yA@in�#h$�N:ounter15*"�ide3M6.to�d���,ng=��S�+�$�Cb�M<�U�nQ�g <1O,]�DA&�� 2`appli[�[�BPr,ot�%Mus3TV�t���,�+~H"GKeu�. SA��� �is una�P����$�M�. ��Umetry_ts $SO(�;n $SU(<� , Y $3$2}thes�G=��y a�/.4-&� themselve�aW�a� O�} �{-s4as $h�F!t�{]�$H^2( I�M2&UW5c�j*man"vly-she6-surfa)3$\�� , exךM!G�.�o-ly (nos#n�e!5A\c��d). Fu˗mC��׈du3 L͍ c-Sh&̍�=�K2t� R��"to mn*/(Q�al-��)es�Fߖ�C�0J*"wY4xA�2$ i"���r�/�0�k2�Ò gory~{�.re��O?by Wal�<Craig/w�K�1R��orAJes O�iK�m�l&m�* 1 ��YN�u-2i prom���tF . G�k  @9should b�m�o ����!�-Za�soGF%fa�<kind (s�4period5es)2HM�+v|s?�h3"�R&1) 6^�Jn2�s�Ia�}s��y�E�1� s��y�lineariz ]Du�ed�Xr��,!Bmi�qL!0y��ta&9t��alysiws��v!Og s�Md2tin.� else .�>&�>&�vF�vF�vF�vFvFHM dis �Q&b@eŅ_@Y� e?2;DE��"�#a�~a5a�G�ac�Uto��:gL m-8or�� [2��yAs�q 8��Ye����4E]A�� *�& :�ms�%�9*��&Y sue�rw; hgCf.:V %�9�suggeaia���F!�)��Y( bȀ�<�P? ite aB3�-v!t.�V��Abelie�E!z n�:8��y��!Sd te~ �9hod (FEM�� volv ��sB mesh�� O�% reas�p`5L ( already po��\f&�.�!�, : �Ds t��@ a67TGalerkin���. HA��͒$ur FEM-bas!X=DM|m!�!F.�n��n��n��n�.�*F�7Bw�(�����HM@*�cݢ�9��anG(k$&�L�E ��BLa�]�"�-caf})) $.r2<][�� �&(�,t> R}1u�>�!EIn�aa �w�N> " M�~M) &� \{e\��we)a�Gi��piece�s��a� $e$ 1@ s $PR(m�[bg  �V8E&k�9T�ks�7g+fix} E ,dA�&Rsqu�+ �*�3 $(x%keta�p[0,1]�+p� $,�wvi a�}|��) phi_�Ffo� �2 - \xi)(1-`� *2!�*+6* X3V.+FX46*� *25*}LT �KxP �uw�eq�Uv w^v �vVQ� by c�9c�uatQ nod�1� �Cex, 4  �-�DBa�9� EG$!M�L*A��o�:0U-!�nodal 2s $w^v/il� m �b�h!�no]/"XG�;m|� �:iT�gs FK2>}�?ch,�e+.(_app} $i��81cr5\%��� ^v�s hi_vky~�,ingoi "�~qbal}"qa�E�L.j2xFtygl�3B{u,v,�A�i r^uIuIwb^\vb ��E�v\,*y*"-> (hi�� %~B{u,\ub  br^\ub6~G �&�$ �v\,>�.vJ% r]&�5\ )e !+ �Da,\ab,b=1}^4 w_e^a�0e^\ab r_e^b �2��7e{\�H\�He.B{e,a}2F �{ec��%)�(@% 4 �Hb}�}_{A^e�C� }} -6�,\br��\bb�2�Q�2}�pзal�!�B�x:���� b \b.� }_{H�*-ZB-��}uo_ ofi捧}V`zL_eF�Fe],DG-P�eqA�$e L_e(w_e,�e)��6�Fi2Q=�j6�_{A2oF-6�.g!D.�A�Y�1�Fv_{H6u-e *}���F1`!0K1s%W 2�&$2��B}ɟ&�F"�;f$e$�@�angle ��,s $h_x,\,h_t]3. e b���9&ti%AU� :J gral>�A(2���n A5� �LeLh��_�@t e)Ω ?eZa.A!J=�!!���::�H\a��m�b:(�� F �H�AV �t}�%>��9����V�,2�.\bB�:�� �mobvio,P"ܮ_l�6�-\ab,a, �� Ri�%N;Rt2=hN�j\bb��R� Bip. of�)��8� {\� }M &J)��u��r_��-off) /$5$-p� Ga��an �'r�F'� �]�c��h�#&ed"�#���mb�at run�k�H$��Pll $4$��q�tenso�Prd2 @AHKs%�"@ � ��"Q>��`, �~%/a��%�w ���# 03$%L& \*|B�#:> T0.Fb# �:n#$$ A˟ �nĴ��� �92�  a�k iz :P byE1���t aver�^A:A�!��n!�] pn A+92��%s�n�$\{��v\}���"f_eaV�Y1}{|e�b� �v f� {v��b+{a�#f^a� "����*O:$.Lv�υD94<aZ�/ + #F-g|e|� ��h_x h_)$f� �`no��!R*' !V$f�$aeZ� 1�$e$>9-�"&�y)sN~��} �14�L�tV�4$;knA��@i�b f_{e!P7 (�1 +!�D3 4)��j���6"�%�XK^{�c�G%��x�m2)AAO'��  0)}����<%�{�d� ��b1JBAK2����p!�C2NC&t jFSx @ �. }�$v�Az%�Mu }{36�e22� 4� & 2 >1.� .6&.P &.56QnCjBQ�:C6>�5Q-2�R .O}{1� jK-6F*�) &\ \6��:�U" U2�:DBf�U�U2��>2��2".""�4z�2hM� t}{6�jv�p��. � ZJ>B.:>bJRz�B>bJR:CB��B N22�} Now �\ titu�%2 \do^�{Rt� %R(ɱ w_hi.� ($\Rt� �'!�c� 6|�%Q noug޲�e'�ma2s_�), �`�C� �J�f�L,tB{�'�E���i.�:\Rt^2�)-�^i .O �T vb,t�f{v  \vb)iik6n "�:�Gqe^� � �"�*2�y%����.B-kj �FW�_�j�w.�?\E})1}_{{L_e}21wb)q*�Noe�D �� P - (�  })^T!Q�� x}{4b� :�� I\\ -I� 2;VzJ,�ajl"Em1 �/)}$�a 7Zp2�:WA>WU:S� N BM"�J�E.� nMhiIGJ b!k ` �}{ ]M؍���^}� z*�Q8$ $L_{\Delt�i�*b�%�"��a"'F� trib�j������.ӣ�jC ��&���&�%�5�esh sh��Aa"l����f&[GGA ! p�p6o.��o�h"}N> L&�� ��QJ%�L�^15 AB2 4 Y�2 0 .^3,^4r�Mx�� ��ʙQ�6 �� $>��3 4)`%�� d.s�a,1d�1��BVmEy<1�Y&�1, !O !M w^4$.&� )�J�,%�3%�KX�ir"�~I���Jh4$Vq3Jh �S��w_a \Jhq���&�\KVVK~VKFV.� *� H��&�9 \L2z��iUe �wb)�8��c6.�� #i {'} E�[ (\0�� �cb��!"Y)�bA�!K -)�-SA�!VI!3BS&�:��|�,� �� ��WQ�eU�uM2aU(:�+QAd��3�K 5 t#�a� !8u�� ub>uu\,Iy:u.zm{7 �/al�R;G orJ.q�tţxu�F+a�6�:Z��x�ZaqFqQ��!pZ2t�-u:�"p�2 A��iZem6"Lrme C""> ��:�. An���@>�]�w�k�N>k�8�:�># �!cq9�<Fqm|� �7>L�A�- B"�:}�nly!�c �F��;PkoO�Tl\0s`�b4$&i>F{mNs� !A(I �' A&�%Qovec(x,�tg � _0�.xg q-{���6*:c"1l (u�=(�i dard�1"�%5,T7m-"Q ��'x)��|�A?�n�D ���a�2\�9 6Py"2=p��6j its 6ou�7o, �N$-1�Ki��\exp(x A)J+ t B )�T%GA):$B$**� 0/sQx,t-��&$tn D"�wŬa�"  *ex`NA� map �z! Caley Eh� $(Ia�. A)(I� ^�$�<�4�?&f������t>4<�*Md�lengt��� a�"(�n�tM�_0$l ���aco�iu�Cclose�iX of rjx΂Q(U),�'isM��6(�A?+=y�Thm��;�9s ?l��� )O4�(byz��!�H�"��»nesgas�=�B)"traM�al FEM u7s.���� +sub�l��mthcom�publi3. "�~pap�� e�<�kA�6*^ � .0:�H�{6F�~��C hS�n�r0*wfu;xvvar�p� a���y�leaճy��"|�* Eo�]::�-硽 %\biblin�gplain}:{mshmBfhI&m$the.N�} b itemF�N T.~B�N� S.~R�N �block$c� 4���;�/ sche46d ha&��pd�@�-,V}Oity.n�lPhys. Lett. A}, 284:184--193|}bi �Nb4 I.~Cy4d, D.~Griffiths, A.~MitchelI4 J.~Sanz-Serna.�P��*���nonic!�bl���6; +.WݐIMA J. Num. Anal.}, 1:253--266, 1981.=�P�$} L.~DickeF. Soliton E�)�.�l��sE ne-�Worldi��cy7.^d"��} P.~D  et~alB� Quan�KFQ^ �@Strings: A Course%AM�T<>ia�0�Am�n$al Socie��In�" H4Advanced Study�99.�F0q%C. FA� �VL.~A. TK�B�H]�MeP=�1rT�y2WSp� er-Verlag�6V:�t M.~V.��v�V.~P. M�vB�NU�>o. Geom|F�%��i2�zf196dman�� Y.~M .�As� ic a� Hf}!"�D��� s.AiPtogi nauki i tekhnikia1:5--152!E78.�b G�r%�J.~Pa�Sk%S.~Sh*�.�>hטy6 ���M� {�?2d�Commu]�� E8Y�al����$9:351--3952��K SECE.�.�J ��Aa�8� d*��moa� G.J�R�0�a�KSp��An ��`the Finite Element Method2�dSeries in Automatic Comput%R.�$ntice-Hall�73.�,witten} E.~W .�-�aspect� curr�algebra.-%KtNucl. Phys.}, B223(2):422--4328Xend{thebibliography} %�6�P�P�P�P%W docuA.} qh\�class[]{article} \textwidth 140mm \$height 215Xoddsidemargin 5pt \even6 \top.#�renewcommand\baselinestretch{1.2} \parindAJ�20pt %\input cchead.sty \usepackage{latexsym}2Xepsfig} \def\CS{{\CC\ } �ccnospace#1{\leavevmode\unskip #1\ignores$s}� book �4Large % �  ڲ�ͼ %6�$figurename� M<}T2 the 'D{\arabic{chapter}. �z:):�theeque�ff"Nh>R� tablj�J969,1mN�%�J` Change default font size�[style� \cap�S \longE#@make (#1#2{% \vA\abov�@sbox\@tempboxa{\pushziti\small\rm\songti\zihao{-5}#1: #2\popziti}` ifdim \wdK >\h� \2f \par|els g�,\@minipagefahbox to N{\hfil:O}�fiX �below- �} \begin�A\centera�{i<{\bf Governing EMv�'���ibl �V,Turbulence (�DRevised)}} $${}$$2x8Feng \quad Wu }2�NTobtained. In other two �s.c9U%whichg thir��om{ d)8%zAQ �i%�taneous, ��Ad fluct!�. ADmI \l�� �u\Mr-�Hpaper \cite{lgc}, a%�approach) ]� picturea]� is An�GdE esial ideaA> this@iA�at a a��Sfluid,8a laminar field/M�, wholly, but*�VLs not=%zhaS $terior str!\ re. j!� � a+b��scribe�mathe� Y�=9u� ) , an:�0$\varepsilon$�a cerA� number(.U ) r}r than!roces� tend��$to zero. ANps callAm s a e;!*A� dim on ofisz�5Nconcep` ��.���!^!Ne�ionA ``diffe� ial"��be e@:�͑�} \frac{�a/ f} t}=  f(t+=^)-f(t)}{},Ɂ 0N N xNx>Nx:N� �Th�!n) ual � ce betwee�)is � !�ta,o)C3�i0e ^1. ���(NzBW(NATT)%���( six assump���y��: 1�quote}� it{A/ 1:lq�ty�����!��E�v�every !Gye�@E�. Each  poss�sI�ia�naly�, namely2�lso2�ёG.> � (/i8a�O ofx�)�-"N2 :32:� flow�� I)5s!xaWtroe�b6�< Navier-Stokesټ.>� �:>�3:"� 2�ntinuou;��4: Whe��measur��ny): ��0 $(x_{1},x_{23},t)$ �iCphysi� �!takenE� oper' 5�qDDwill act randomly �wn^ �%� 2n)S:�\x_ ��u5�"��uQy5 mada r 9inA+ iprobabil� on varioueEr����y��ia~eq2[�-~%:6:�bot�  valu�� ! func��,])d�ked��n��6k %g���� ��woi�s, wA�these_ �Q� �]ly B to e��� > By virtu' S9D�Bfunda al!ues for in�h� U7c�  , �!�� Alem is g coma##p:< A�����"!i��%xi!� (1) ��*I :,h h �  no>� . Now us�h�l!io!�� , weI�?�"5 *C for��J'. �.�pZm,^'mo�? "� ���on��&� �V�b.t a�"� re� ��refor �2��ri6O.!UM��5#�a 2I� �aAil�.�]Q B� \rho2x ^{2}"n t'}+6� (1 U_{i}6b .8 x'!}=0>w ��^��^v� U_{jj� �j}}=-6� Pf3i}>  t_{ij}b7%j���20 fP$t'}\left [!�(e-� 1}{2�i )\rY] 1�bW�j} [Z %C(h BZ`� �`(E4)4)>}q!���>M *�H a+rul��sumK$ver repeatd is adop���$�� Gveloc�}adonA(in $i-$dire�� $P$-��ure, $!� d� ty, $e lintrinsic energy per unit ma�$h (enthalp �V . $%&�heat �u �BYh=Q$A�a�>BB3P=fe�,T)�,�=-\kappa6� Tb�^.�$I'��ssA sor, ji}= &,F�  =\mue2(:�%�b�qm\al6j�6i}}iQ�2}{3}�delta�16�amdf�%.dFE$$SMm�e�����$$.�e� $\mu5�0dynamic visco�a'E5E��rfQ�vi6T$ absolute  era�A9Q$B( Kronecker &cpe�D �;all� e;��� ��1 .�R ,� '_ 'n ')$. R1)5Dcoordinates set up�`��� whilez'� Bf� ��VMa � *S. Stn fp ?rel� : $�,=\widetilde{i-+u���P. P}+p  �d.}+_{f=T." T}+T e. e}+e�>4h.) h}+h) ����}+()*�'� }+( -� etc.>N�,lower-case $):p$ �g!p*Owith A�x $f$� � � k� 4� havb ��$�)�$L)�!�A!�tim� re�! ivel More!,,us 2 he mr"d� p:� Z  f� g 2�&9"� >� =_a��}�� t>�,�� }�x��� �Z��� ):�� :�sP/ �:�-� 2��� -h t}.�v b� ]>�9|�� ��KTjf� ]qT�nQ2� }:� y�v�$6�$ (11)-(13)�&�conserv��Q�� , moXuEO , .k,�E�of�\ �\"�� (9)��&� from.� the 2$�խ�nt� . ClearlyG_ be wr� n asF� ��1��Y;:�!��=�B�2�\I�:Q,ADi�B0F��(,After splitt����1�$ (14) into��| "F F�, i|"�{:.n� 9~c ity-s�Y ^%� ���26m Vm�A�6c��1��}Yr�(I6JSimilA�,q92Zi�we"�6� q�5�iX(N+><AT� t}E�Ͱ:�̭B,�N=: \4n '!'�% t� ��boJ� ���#9JA�j PXFF1 ��-"� �Z �4"�y�V �I!��b �E 0Ia�=>p98F .M 6-� � �b��$T�(1>>*� 9 �Bi cl� P=R�� T� , e=c_{v}T$ (��{ ofd(fect gas). �R� 5� >=��gas�{ t����� ificd�t��$volume. So)rJ_��� N�F�"�*h � &� !� e�1-�A�#P}5urhѼ}} -�p!�}6uF1 l028F;�c+2�� �s�h2�eU��r+ �/(�L .H �}�&�-!:":FFI� �=h-�h}=21��n �D�5A5.��OM�2P�*.��a2a�e=R[=K>hT}+>� "�- �%]>�B�=P}��51 j)�lp=P.sRpMV��%.K�J� YetA&� 6�Z� �"[\u>2n)}]� Fm $. And sov��s� �s. !#terms in"F .k_ J_W,�$ximately, 29+ose be�*��expans�fW� $!y�%Y )�� nd $.��(,Sexample,}~ ѐ= O:  $� i=(�A�Y).$ :)= >5 *L�FB=%�1$$�Z.gJd;"� YZB�>e=4) 2�D )F�_��)yQ)BX�)V, �&2T�u"�!Yf like (27)� *�we��r3&�$��59�!% F�6 i}}.R>N)'v� Cr�)-JzJ�$$b}]:���j��6Tj}})+:=-�6�b�x�0FX%�Lf�:�F�J�=q -�5� �FB -L .D �J�>]j� "nf�e�őpf*I! 5X� -�RM1�i5BO$B ���1MY�&r��.sh�N }M�� v} I.�e :�E� 5h#�:2$h�N�R�Z ~.�I6#Y��PE6L-�>�bsNI 8h ]6 A]F1M�J ~<�BW�b�� vj A��yj}�E.�nd�/ (15),(19�20), < &���1-e}�B����9�A)��?)��)R)EGj���J�in1�6�TeZO 6pA� EQ9[)6�J�=:�.,-�:�.�B���Z�ō���"V��M�!N ��.�7F4Em���.��B�%��hAR�6����b{��f�.�^=.D^��H.$I.ɐ= �.�J�޳.�I$z��M >�R �� Fina�8���� (16},8), (28)-(30��3�33)�;�/e*~:X�1c� %*"�.99Hbe easi�2�:�,s ��60 d�!.�; Ch�;��1F��8:'rmh&� �-)�"� W�FI�q=�Eq��ʿNI�J� B�6�� �X��� a��. VD6U�=:"�� m)�� >� �&b:.�:*)3BB"#a ����f�@JP:���Rbz�~k .�BK-x>��BM Z��9A_>�T�( $h}2G5�#ESeV J.e}3+q.' �V�-2;B�N?2-U^�-*)�B` �(Q`62j>� ƚ-6Qd>QR�-$$��twoN��Z��mea.�)3 &$##ces"�66"W*"f &]*�l���> #&� 60*�:I6�#. F�"Պ~�O#9�F� 2?5�a_i�t(B�rh�j� �c��: B�� "� "� "� "� "z "nAU�b� 2�:<!�Ky �}fM�E = )-2ɢ��\.-� 0�zU�<"��-2�)f���Zu� +e� [E�&�a�$$v�\� \l�J&r'^>�=:? �E �>. �SJ�"!):'e9pMS2*�)\�-T N0 �E�Vj2 j})h%���j$ -2j.!��%�h+Ea�j�W5"8!}n�r"P L# �3 �:�Cy@a�&8 %�5n ��9Z�j)_%d9� %u)�E�) a�2+%�/U /�%9-�N ~� . FFNM -2}. q�UB &K>% , $$"!~%)�q@J�=R6#9�a��p� E�!<T9_5 � F'% �#.��"rhF�Y�<� V� �8� �j"N *�^;�6�jN$$�& ��]� 5 u4)�^+ A�iFf>�'�8 �aN� ab�8 F!d�>�2�(b�E�9"�x6/&� �u_�Y�x>�$2� vN� a} :� m �(o&m :�5Zm is 4�.>q : �h w"�7e9���:�_-.�ka%��:��j� ��~C!��d�gQ��@ �rN�% �!��6�i} :) 6%aJP=:5 5!m�!�6�-�M]1a8%:�@�H f��\�\�\�\�\�\�\�\�\�\�\�\�\�\�\n\^2*[ �����:���v�� ��?�}���<���o; ~:�ݦ�:n Cɇ.�&%6-� ��^Wf�'&�:6 �h"c"kR2)RFMB#)^r�G� 6�9� �H%���F�%�-M� D������rB� �T�6V=�. AcS b��Mi}}n�B�0�:�.!w�v&N9 T}`$$�B+4��% a"�ePBY>-�(P.�:0>0� 'j�Z/.�� iGbT*� !�"�.�7�� ?����b*�9�� Q�����!�>�F ������� We should�[�/a�]se&S.�]�'R p^/�F�PhR��S6hR can �PR�^$ too. Obv�T^\�"^[z#unknow27l9+�Y8G�SjFH��XK#��#9r�A&e7�[SN(RR Jj;J How�}$�:p!�R(�B&[_�Us. M5�:"�GY4�^ -�G�\�Fp�]d or �F�WgelJ+[ aga��W64�resulZ\$~coAjbe '% ared�H) X(Bm  �� cor�Co5]VG� �W[ $�bi�>�h{9[ \bib�j[1]g_ F.WuT5 it{N&�a}$$Pf^ of TuPcOc\\S��V/fh} iJ:uh{ethp5H}2�g�i icx}kc/h{\be}�dqJ<&Rh{\e#�b!H\9A-5�CMS�Eb�`irradi)U�(a 20\,GeV/cP!� beam�Pto��gF \� L{5.4}{13}\,cm$^{-2}$�N1�rec�Ly�~rQ� has ��:ed�:. a year.�haM^ve� ions�P,$^{60}$Co ph�s�perAg�s[m�;9a d�;Drate of 1\,kGy/h. �\Q�5$>�l%x~p smis�; band-edgo ift�F,Q��Rr�a �h ;S(indl\propto�� ^{-4!K In $��$-Z�udoeses~�e! !�~�W seen c�J. �%' ��by�I9�<in 5�verifiedA1�PexcellPW1hardn�qs�SS�` level bFk 0.5\,EU1- !I;-)��  O/�f�� Fzo >sim$1=� !�w no sig!� -OiobjoP%E'h ovid�drong e �.�d hB�s �tu�' can�gbecYr�t� B��"� !NsX. dronYf�E$s manifest�>mselv�b�]`g�N-[s welA!yond $v 12}$�~ul mostn/ ly w� escap�]det�jAp�S[. A �i � H ɔ,�`inM}-E$B�edUE�`ei~UCeb�Z�Z�sa,y slow*R��� \vsPR${7cm} \con�gce{SubmMNec Elsevd0m�nt�g�s�Z{I�d�%}"T ad Tungst!�(�/\,�r) u�cbe�Rby�Lral6.hysics]>e�nts�VPetdr,alice,btev} becaSthey prI�a) ct homoge�k2�a_$ fast scin�VEҥ� view-�ir�!�a���ex���1ca"R�Mll fac1 harsh LHC�Gd�UZ5965����_extens T stud����(last decadel�p97,ieee47:1741,nim490:30,paul14:149 33:630�a c�veely �dQatF���facxdies, � lfm� somu�3 tes��,t reactors\, �Ltn95:126}. At LHC, h�FmLbe!��hto ulrgwg�D�.�h�6s,yA�3up=\�8}{8}\,s� 1}$ �q0mum bias $pp$�Q�F%dsqrt{s}$=14\,TeV. Althoug�ٶ� E�da _ ionibAfcl7x YY thorZlY�ABG��e�s}JideSsuffici�Y=cA�applicem � ular�~[d�d&h."g.few MeV O ]D� e�x-� --E���of nu@6]4heq6�m�;ezmvestig{ ,(detail so f� SAvp�l�!R5 "� Q� note98:06e530:286} no syst"ne�y�Ie�dedMKa� full�g�d ��߉�qAA0E�a.5necnP`�Ci�� advoc�Au ago>�55�[Ine�"icV`break� he ta<t )uv us ��impur�q nd distor)R)� �� lat�z� se -�}�6�T%toa��Fig�t!A��, sincaFn� l�yA�Ht� o�j �� �Uv�Ł . An�g$aque feS�+-�ic%�u��pe�g�ae e�e!)��'bheavy)Aar fragqV` vr�7� a }|u�| 10\,� $m. A%��y r pa'iy!opl�_��Mp�-o atomsWqQ�e mucXmr�ons! tfp��(� i�le�Ŕ�����F!Kn ;$dE/dx$%�jt�m: om f� �1AAt5 en w�RrosM V��s��(e�8exceeds 100\,mbU� p686:481}} ypWlO �<9Fi[ZUi@ Fig\,\ref{fig1},)���ies5�0\,MeV.�2!�be: from Fig..D!_5�[�UAV four�'8 &cV?  r;�"-5m� �i�d�� solid ciB� . SaK%��sQ� 1� a��6 hund�,MeV, �J %� or n�� s or �� tfK�� suit� to�b�is regim��:{[h]a�e�includ�Pphics*[}=10cm]9 1.ep�end6cjz{Simul%*5H%�y lAuof��t.�n u . Non9�.?i3 �di�2fo3z�]t3eg���z L$�Eo T!#is �AeFO.� to>lq�i�d��e�qI%A-dashed}a5�s circle�wM6tiQ,i�-rfQ1����Mb${zżei!lk.}�v bel{es� -� An.�EpB* E}H is m��s ��, �y$>�S�|e�� ��� )�UŰHm� oac�_,�+a ~ ��"Ka�Z handl�iiv%�qdweeks af� expoh��y�c(nt-end elec@ % or opt�����u @multipliers, lase�g f7�is�susjm�pto� ��)]�� �>�f er�w18�Kf�A-, itself%� )�_�aim wa��esitNst t ��qVL�ima |f>� Q �o �-�hen .n-uCi� Oukudy � ]wtAU� v�tx�!�� )�aAa�Ae��&�>���kA��}\le4s- FA ���wc}..��, BogoroditskZ-ChemETPl�V(BTCPz] RussiaE�� M���� *  (ECAL"cs CMS � ���o� !�shd�5run�� pyramid|n-�0llelepipedic "�x�O $2.4&[2.4�2$��ns� �23���lls , �+quudp�of sl�ly�p��!Mm�~a2xme�Q�3 mild.surGII��  �FEm�!m {I�In!ti&� y w�allJ��Nm ��i�[%ougV��� Hospi�{Ry �a��Y%Jf�� �zd�{Thy"~�a�Jrefer��A02E�{6� �as#�aea\��Cena�� �ynT �anSxi�A��h�in� i��x2\ (LT)!'a wave of 4"nm,�'&���p� e3}��il� Eo�R%Rt�e�uZ%"d�38} r�ur�� 5�- d.�coe(� eQ�} x =�51}{\ell}� \lnI$LT_0(�)}{LT ,�eqdel�$=->Abe�1.�E�a""�  N!�$\5x$] �z{Eq� � $�$ ($LT$)�S!�� R . وbe�s(�#).z��$!=�V�� M<(��)q�gu2u -yVW { "�"S � � }{c|l|s Kc�\n{4 |}{C�:� .�s}�z^& 2U 3}{c:SN�s} \\ \h+ ID &-nini�6lphi_p$ ("Ph�)�irr�(hJU& 2*(h:min)�r�$a} & 0.286�"\>0& 1 + 10 + 50&T tU 1.22& 27:2,\\ �b1 0.79.&��B �u U24."& 1:02��c 196� B �v U25." & 46:�1 d 13� B��w U216�8:��E 170.11�3}bB- xU1.62!&f�F10.52=��0.E�, �yU1.1:b�G10:=��: �zU1.92 R� \c�:{5-7}i0h=0.yz&" � 1>�& 6�F� |c}{�� z1-4��tab�m���� List��� ��:ii�f��"�  �-*��� (U�'9z�bas�� � .CMSR�coc� \,i �0etiennette}. 25����� .(� �? "�nomG flux $��o�H "^!�{y,��� wor*l�1-v @ � �*�  125�%n disposal�Hqto�i)~he�!�-�-to� StK �C���"ur.� 8As��sd���w sist�behavĂt^]t9� !|�Mof6 s� ��*% s ša--h}�!T�%V1v�!R�,&w!Ra&=#* ing toٻ \,p/��2$pmuA�fur6�WU#ter��!ich�:� u--z� R�' RR  se~-% $1\,h at 35%y/� &�!2�by�~ut 10\%&)uXi�*ectAp2 ` 2`,�s)or8:�$. "� %�u,�\Aw} 'of � goodJ&wVv!�8 [sQ�� N, quite46� rJwov(�x}�z})� aC�lQut� 4��6� a� ady!-6&6, �%��% emai� �\ier 12,%�*,! en)maNh�g7*&a%�!]is ����tArZ=Ass}rf< 1--2x&� �ct"�� �e4� ual ��&�r�z"�sQtZ%# conv��o%Zas7$u�giter�c& "{�>t2�&�$�!/caGl�OL t%��� I��&3u'A pp�6 a double- Y� �یntW�b(s;�-B&���E?e sam"��c:��,4ciR_�(A=ɀ.f�vM i,!�i �'|%��re �$� ����qquav��R2�inD!��s��A ide > ��� � - )$�� M�P)��.IL)ac��X�IRRAD1"��eEX1}{T7�1 1��+8 PS accelerator�R)�!��P��firstU��e� deli�(ng&�of*2+pdur &e� campa�'24X+�&Dtozt a��).I "*$ wholU����ac]� ese\�Lal ��ha�3�  Af�%�at5Z�27"we ask�A 5'sNam �'n� I  PS2��`(c�%|&llt wa,2�z#t=P�)~��7a0x!p�5\!10^{:�')�zanA�a3�ly $4.5&Y 4.5$=$^2ht9� a ��re���!1BAE#Sh���!��!����"��:�!� spotwX irlyB �c5AW!`��Lbe�nd!���s low-���7PS�]�on& |neA�sp'�4y 42\,�O��gu6�!-X6hms !C.�)4u��ui& $a_os5�' d�M�!For�-�&.-{a��x'Y * siQ338� �.Q3$. To achied}i� � febncS da�2 #s0ry C&�!�5�!" E@ 6aW�ۊb'$3q3U�mQA>s1 *�%�!�eQw�  a2A-ac*et�QVity�� >Ʌ be) �wh�amI�remotu�v�� shutts"A`�h*x[fr���X w�2�par� �%xis �R� b ]��$Calliope pXof ENEA-Casaccia, Italy5 ea�)ya��H& source!bch���5Uņ�%d a�征 of 7� TBqq 48Vro�rZ$�~7 ntric cyl4�n"l afcm ouxVuIy26�� `!>csI!t�ly up 51j�%yA=� -by-!Ra;tance�40e{ -"��%�E>� 4%�A��IFo��in� �9,styropor box%E�"��wo adja��Oih34\,mm�+�}uK as� an����, each~Rtur��!�a"180$^oE%t�� ��!@half-E5t� #"Q $. Unfortun9n!<1�t*Bpreci�dju��%n*^A�)]��a�fs�of 52!a��� a�2�!Wusd^)re�)a9 m�)O) l�� ��M�C'�� \sub"Lk2�},~LTp>m�~: �Cdiscus����p"�Xn.��^8�profild� ���!� u%�al� QU��re6 �" way.� �m]��"h��� ͅ��yEkexi#ϝqS�ɾc)"�����%accuraca�� �a#%[�� \pm$1!�. }��! !�� �(�*L"�+&zlyJ� to i� �" H nt&#e~^�o�'1U�:&[h�1(70(2.j0(LT data1��!%�r} u����I�0-p!�������p arbitrary� A)�, )!_rv�@& !E$real elapsA4).H'+<end1$E^I�J�7,�le3� ��LT ]���"1 f�Mya"s�!�s5 ѝ&I� ��,{l}".�A�� r���z�0)Qi���8H@IV,�$``scans'' �7a9e pur2!�underw���a�.��. . B�%>seE,)�y��Q���$a H �7 lute%ib6� devi-�yM[�!+LTfa8$ edFp.�,� fig2}��#O7SA )Vs"w i�a� F�nAHAU� F-Y sca�&h���derK;a 1F gma$��] of 0.58\%&�B C!�H���:2� R#s rapidU�n%M:��"L#d/t�ofwA�� to �r�:�F�LTF� �; , if����%୘���,���40.�!nm �uA�u%B�2�w)�+err�'i 6�Ek$�C$!� \be �Y[*P#(] = 0.0058\!�s  \oplus � �&}, \e� er!�_2!"�J4y "C LT��,  ag0s, �!D.�K2� A; )�w��$V��/as big� per��-<�s�� nmh6o/=��_>� M�m9I 5�,0)�i�A f� , �.� I�;� o� }� �%� �($\VB$)����+Ean v�_ 6150AD6R9a��ess} �i�� I%cm&� � (� �;its� "�$!b�����was ca�a>o� %/f xiva�=��f�z3�.ty ex@.E����zq�s"ͣ� endix\�1app�&act�����!�s���e�8� 1Ai�por��1 behO�,� �windowm� 5q�?5� �1`!t;\%�Q�& l�E0"��_r�m*�,to"55backg[1bw>4}� a%�a/ioMW�-�&�fy>ar�2M1at}��g A�ave#U�8,%*;*%�-}z$$^{137}$CsAat? ous� o�Br�1�s g�:a=ɹ06�5 Sv/hr ?Xnon �a,�m �e�^� 2�-�16A�060\,keV--1.3\�1B�@ �u)cy drop" rupt�Jb<�ATM0s�50~J7f�6�%I�0s)Olow�i�!%Th�7:cy curv�_��5Q>�steepy�21�, q:u�� �6 mark�en!w�!%2.�/ �rpk ��4�= uh -q!�?%3s�an �yN ��? with>Q��) @5�+$UF# nu�1E ��%�"E � Aj��� * meanA��"�,� � .�K%� a�`��lli�Ns �� MD�.*�<��ij՚ia= !>ple"�K�0a��6a�)����%q)pan" !�a few�m�H�,�A�%�.�# `�KAll� �!o�pro��ed6�to S� �@i(#al un�Lty&��3�1l%��]6!(��.�A�'ZA*�P&X��13�3n�Ib>� ,�r�:�ch�2�<���7 7�7 A �incidx$M��2as*� a&7%� s. V���!� a 5$� $5$OreN� of &���8��s)�2! (open�6s, �6 )�X5�assoc�H �g!�"O- :J�-e alt,u)���� ��`L6�2�\�� ��m�)DE��#�n�&E��� �@�8it��",n.\Ecascade�M#� .3 zqW6 fv�voيi��#�lť 4�" K8ew q ��Kr�� � w���8 9� dump7!.�f ��& V-ka�D �be ignor�i���:pe�G&]}B2��� nd az �-��; Fa�3GinqMe#4�)�cG^�--�Iull���:V� setup�#"��� FLUKA cod"fluka}�mT�]���5�{d"� zcmE� "�5]Sl$d �5 �aT)or!�C  22�%\,2u v%Ca maj+ 26+�m)E e � T 47��ac�I�:�,����!s2~ ��)�B:�3u ���4n�E�'tr� ��s,��� C��ځ!����(>><s�f?B�K milli�ava-١^JM)p��, �l% zMe� r�>� �]� �:�;)I!tar6 4�+� -e���2c|c�S&Beam19�.>$�-N:}65[&�2F�%2997h1 1.052�. #046s/�/633\\ RdB 43"q1/762�/ #4z(53:Wd3Mz�.�&5�-es*v3�YF0')�I{� Ek6\���7Q\! ^a2)��`�GE  } D RcGJ;N �kf�to M.a (NspmVo�] y&< �I38:415}*�D�re look�� �ٰx�-� cu�uve !:&[�Ear�*i;.� fAp��@6�/869J"�Fdi�%���&� .18%�a.x!�j#35)�. B�3/J&N� F�H2xB5 =���; they��"�Gto�#�+&� .}�@�%/Jit�Cmk@� pr7 to!�,�Y�DFB����purel(H� �xy�XstD we c�plo��;T>�A A�p���9ly��o�=but, duv � AYD� Q'�1um�s� �+,%���:�D4}� mp� z�N� sub-�ݵ �SulR( , y. T��e�2�� 6�Oa0(MJ���TJ��D=�i�aT ����6�E4!EW�Ef �9(��i�a.qi�&I@AY�M�d . �&{�i}��JDo�\MTI#4Q* d / 'tB plau'oQA �un�+!� ;�"b�0#b�E�A�!> 19 i[@��ioJ�z Y�"Fu B( g"~ D ��Q� {\em2�"� was origi�ANfR� arametA�n&Yobq�.� 1,� densA/A%��}! ;!� a:e��ic )<6\J�)Bjectil��ov�(�� " M��is�0����ilwuL��� ���mLa>v, wt�uE 5� 2�I�eB�exactly ��!�.Ps�tJ���<bEu�- Rwe�#!t� . �.�G2�1*�i � �22ofaars�.io�?��qa^AA����Q"pQ�l7rՆi�Ta`e"GR2� ed }a2.."b �t�dQ�`+, ~be e��calu)�$�<��iz\o\_'&@ enviro"a��a�y3"�6=A�P"3#BQ�"�ӉE�s4,� dqm�02:019}�Q*�!��d" canGZ�.��lq+A�Q+$:)SHN1MP[p�ZM.�>�)"�!ì��w� =0.8�],bb� 240 68fip]{fig5n' Top *�T."geo��F4��!2++ �S%9�*b*"mblA` Eo�* rod � %�H Qo��e rE�he*D*��cX�)boV 3lef�B�:osm�of2�AJ��2�ir*�3s nex�& f dAe�dotR�a�:� �c e;D��lanin�ser� �&� !�:���[b��$10�6n�&� m!�F*� �&A�th!V� s. Show1�U( !��t})%$max : w})nf 7f�� 9Ua�>~|�!�A9 �2g6vgt�g7�g"" �*/+�]H�s�pm m�1�*Vxis). ʚ���� fig7:M���,��'~ n"�I�W92}e�wz[!R+ ��.t6 regu�� ]px5s*@&��o ���i�Lw�)m�abs� ���$���#ria�= or��IuI��M�Jd~V ed *�Q�i&�6k'up�m�7 tory>�%5.�%�V �3�!�j�H&�/ �ir���,~3���#T iffe��,4� �fw"occup�Z;"llC& s. Dm�s�iI� t\ig�3��l��ly&yg%\>� ��%� �/ndivid�:�b)F\6�{6�_5e&�a� �&� ;�A�I�#ga� a�` � LtD%�G�� rl7M��Pc@"e>6M|Q ra�L GX M��Nexhibitg no� d U-�,*� �0a!� � u0waJ � iY��5f� flat �al�1t,aa�4��� f@$v�4�v4 E%� -*LT-.2� *�WdYM �-� �. �uru��� =U!�f�=�)1� u-7)%��! *�&� oward }en& !"A %��31i� �m^ k a�.&! P��.�J e.g.(�0a�18�� ;��w� ^$'6 sup� o���a   y.0F�]�)%�l� F&� u�+A�;1' &�kPhJE�!RF��'N̅| alusWu!i���"t^^�0!�$24� 24$(/"�/z �6 1�!_65i�UU4lariesA� �D,&2: � � " }*E�rSw� efer��) sot�6}2}$Na.�!AmiUQ��'4'\5�")��*<-(r��W.� %}m� �� &�' 5"� A>E��!�q;�o3n��9c�%R=�Za�nof�iC�����al-7�:�"f �=[aid g\>#�a carefu"�?"C�K�1 {E�&r6$!Xelf)�t"�O*�$X>��co(�r�X toge��%�y{0W)L_)�-d by �΁ "�n F$p�*������I�Mi�(AtE�)*e�M�=um '.& D� (!B/�M�b*b(0.46\pmI-$3)}{12} & z0.9:tLh7��c:e74 e5ReJ 1.40�&*N#ea2e 1.01 e11JeR1.0:e6.�F:e37 e6ReJ22.:5O& 2.2�G:e72 e8ReJ28.:�Le8eE2e7.6-�5N�R15.B�12../h2e 8.70� 1.00J�9M} 1.090.6F�7.��F' &�L(8 F0.8N� 9.83�0.89�18.F^6..^d2�12.�A��y(R1.7� WMy�a2�12.%�!Ne3Y�1J/215�e"./37.%� 2.N�54.eG 2.7�1:�P!97Ur& �Q(�@s $��.��)&� K&� 2�"�� Al-a�\5 �9*J&| sum y)o��jl��5��_� .=k=eayy (seZ�xt)�8�s= c2&n4*��"�_* � �H "? �� E2�*0��bO&[s,�no^��mvN ��Da/qp��&7���' � >�3}t��)>� U�  �0/�s1/d) �^  t!)r&+ ]h�� t �)9U\� I\:0 }Q"6Gg 0.892h *� A-aY��H�I Iv$A�M�- � 9UC�&*>qu�*}!��r8nQ �>lso' fb �]��M�1.086AacT fuMhig=D.�� ��g� KO"&�L( h}. Any &�O/�!%��I� a�N� "�.0M A-)�ikC N���"�"�E ek^` , i.x)%�fof�- :g:. A��}� U*r+&�"[�)R�e:�3�e |ib6�n �)"�g,a��$?&� c0!�-�� !rim$30\%/ Fq��|��ssu�ich��uH;iw{ !�:�4nonJ�}A� orgAE|H aX .�A�W4�}�a.�iOpF�## N9q�>3E s10�O,�y-$AQn���r"� �A#n&t?.� ag�@nicM#���va�#�'PN iadr�$LT "j�"��-e��ivf�5�X1ne �2�AeqRT=is usuOoneI**6>�%=conve�7�%�!-$ in air. T�F�O�� mpanA.&���G crucW�e�-�A�@ mmA�. MN*[J�In�){#c}"E����/>�&� u� 1.0"\\&X 2* z 154 \\ x + & 8.49:w + & 9.5 t 0"\ & 27.3Vy "� & 48.9v "^ & 508��Z 5 7 ]k!� )ayM�|V.�2� x�6�T�-A"�� �.k45<s� �v�11\%ytE�, } SixAPdx�4fix&�B``�''0��� u--z�&������s�x#l� �``P1 d6Xv&� y}.$�urm�,���Sgo�;m�so�&�gpS���B)��Kb%"T9.h"I"��"S�>rc)%3F%?*nJQuo/|vT�� >k;Mv��>� !��pfu x� 23 hou�K^IYe All� M-� q.� Va*m!�M�}rd�PFi6W8Wa�i� �G�$MT"z�vi�A��&ed� . W�N.low�?wY nd 8Y;h.Gic4�WW<8�a�!�� ~a��R�4�KT".�� �A�t ���* symmet��d"<3h �3--&o�#am�C �K�%��;Mn�nceivd�J, ku�kf[ �� !؍�LDɁ-�.bm�d� b�=�j� ut 9ekGy*�E�2-Q�Gup��limit, Y/se��0K�YOA�:'@I�� o �un�!� J<io"�)helmut��g�O!!��b/�=l+6Q�if.�PR�!so�$ p>�a'&.,�+ch�soe�"� 8$r� � t�7�aK=�"Niڍm� !�.E-4BQ%��� &B�Z���I��PvY(e!F�Ad��kLo5]p*�5CXd �'+�%�(��TwV`GL9c� ri�Y a4M� �I� ��*0G8{l5� p�}� �]q#%�a�F �p�o 2� �*"e~ oXZ6�16�4Lt�s�7}. L "k<Re�G"H^!e�9&^ =0.9&L(3(9n� LT@8M��~ iAe�K��^���MaV9�.�"�j"�0(do"+6Wie���YecrbrenyuanXz"XK �e�&A fig9:� 6�/9ѵ�r�;A�a�ih&."�N$o&\s( �n�Lg7+�-!���am���0i��0.��#GA��!�" wor), :�i��lbb�huoHA;1t�K� d-LT�I2��@� �5&�H�t �\!Ik`Y6-W�[��[ �N��Bw Ni� ��!w�M�"C qth��$9.5cm,bb=0�i567e10F &�e�Eu"*`�B" �2Q�� 2��^�Q�i�r-� n M��:�)]�?�~ postU�E'nFvm��9in>�:\6f� j�1ߊ.�N�1�bhJ � ��s"xj�1F�9�!G�$ofna���/z fit}� v�$�x& �/oRb&�2�F�cM�m#G�:�".4�!��� K2�1�f-+>:�qr;QR��y1�sU�� &�@ ,!u�ZB�w(���s1.Gb6�9�J9�, 0 170�*�.r�CATM�]&� A_i$�epA1B`J4�uw�.��% A�����I i�[�zB�"��: :U 5�i 3���o}B\910�r�/l�^��fg�� �((���"�h�  146�L1�:�10��he6'��!J.�P ���3&�.��i� F)e�y�E�:f&8�� le]"� ~|Y�"�W$F�����Ev�ft.^g!y:07Tch�#he��}QZ j� "�z�au��tNC"��%RdF� 9x� *i* �� ! &W(6; ""B .� ead,2�x gniz�!�+PrC�R*� � aN�x"�\��*P��7�^%p 9bzYK } �.�M�߉�gt��ar!�!�urv �Sm*��#)[�6k�'z'�g *�'�:�Ig"pW �(-to-crystal� variation. This agrees well with the & of �F$\muindhosp$ values in Table\,\ref{table1}. No significant correlation O8is kind is seenId�Oproton-irradiated crystals. \subsection{Recovery time constants} \begin{figure}center}�tabular}{cc} \includegraphics*[height=8cm]{fig14a.eps}&�+b+ \endg �cap!~{Plots!Eq.\,\�ect)Iimefit}9�$parameter ){ show%:Fig>A�3} af2$renormalis%�� to unity at t=60\,days. The symbol!�dicate%��range over which data were available for a given -� .} \label�4- f-�We fitc�( dependence!As(_{\rm IND}$)a sumXtwo exponentials and a Q !� I��t=\sum_{i=1}^{2} A_i\exp\left(-\frac{t_j8rec}}{\tau_i}\rA ) + A_3,��!�, \ee where $>$A�A�(( elapsed si� the Q�ia�Attempts!�! I eMQ!U eachq ,% all 5YLs free, revealed tha)Ylonger �5($�(2$) was comAb!�$to, or lar6 han,:�!hthus �c}� betwa�(second term 1y�s$too strong�allow�a reli�Hfit. It is, however� ason to assumA� �damagjrrespond%Z�am lor a� res,)Wof I��5aa&que6:. Und!O�:~e� we fit��m)^i$ �ll1�$400\,nm. At a.d of 3� almostEIlet9!�mq, except%0Ta small residual shift!%��4band-edge. In case��)DhG} a peculiar step appeared)� 250 !�,we�ca�ack!an�Hnt!�onal �s!�tA��E l�l0 from fluores�� tubei�about !�4hours during aEL 3 oaaw�pmead ment!�e exist��of such p -induced I�P!މ��? ly verifi�y �'to%8�WA� �s�� �� had b�FNwI�xerci S(he procedur ��g work �� s� e��i!�at5�had rem�4st�)aBMC,2\,years but-R 15\%!�hm�, fairly rapi�u��%2)urA<0 j IEw:&65b%in pr��a-� la�|:?=  FA-A�global��A���ed��1$=�yks�  an��� 2 ka)g�{&9�se �7iW� are�;.� �f3}:^ B]81C s%oly ��� dose!+�a��,FM_it de�� es aA�funE �5�T�is/ coulA� d I�M -li��defects,@ build up!` contribuA oM:attenua!�, mak!R$A_1$ vamless efZive. S9 )2$e�i o a �!�9ȑ�is �a�a*e periodA�!A1� fo� -up��>~ 2$�$A_3$-�Kb��� y�jol!��  other-V�Vpartic{ly tru1 ll9�iFmz:�* $d� $GE � �� exte onwo�  (}\sim$2����. Hi !k $A_2+�a� ���.�M�es linea�wVflu��%�leA�is � ��t %&� kU�J. Ale� s -- �� o�s� 2�{.� "� --r�4}. Re^E�N��!4!� chosen�Z"{ I�1$-� �Aw� ha� �� cally dis�]A4us�� sidA�r>�point�u� qL��u!� ybv-�� � yprovi� a visM�a� � magn�  �)� v . E i셾 � shor�)&� �Gs gro�U ccor�� Tgr��IY���=a�ce��!K�0vI$\Phi_p\!A�h\!10^{12}$\,cm$^{-2}$ (or $ $1\,kGy)a1� � 5h�, m �friu�$ to higherq. � a�� differa!n Gid-�v!can��.J>� fast !�%a��!���y� 5b!c�E�!�g i type:�Cw� �� n& n�su-�$!�u�!�"�([bht]�gin&I^�10�5*�M c�I�  absorp��qin�P:) cumu�ve-�5�2�5nd�iurj5ZsjkQ�1� �` �QP �al�K�{�rJ:us�b!�&3� .=\��3}V #� sv�x al�sIB= �a39ف�� ua|)�G$B� 22 b��&first�  WSh ta�e�+ ordersu, $4 log-log scale�A  an"a�Թ:e"�Q1\% devm%���� per y�x��-/. &, i���inAA.�5}Ūa�� w�YJ� , no^ A�o�2T� ���m��R"=.q|m�uTb�3q�6n�VOof�$� d!�!�7�"q ed U�i%2���t� .]�(e upper ploIa�q:!ta%lower on�^ Yo �-maE 1���"�� 1}686:8>�6} confi5^ec at a��r�as�f as ɰ/V99� seates. Af\ 1 QO8, Mi�� yetj its+ teau�Q,O��8.3%946 Y)X��s o�ͺr� at5 d�-� -to- "�!�$is becomes}Cly clea�e��`1�$,!+5� by u0 aK!� �.� 2�� -�2 chg suppo��to�cel anyz�I� g not�"�%顾.�)pi��e$K1\mq+ion,  �Pr � ". i bd. ��fact,� �ɕ � t60A!>Md"� ło2U="�8��u�[�m�d �T\,\cite{etiennette}. I�>is0takY&ccount�w=O/Ɋ%�aAio��M!��6},4%Wj %{ � >� X�+ �m er.�$s get pushE�_ ��)X3M�� ��t leastE�ly� maybe�)ly *�!�)�!Spre-cha| er"� ions didA� lg� enoughAݑ?I co*Q . C8�t�"� M�U�t6 e2 6q6�F��,�uis�r� noun�u�F�!_ese2�m� (be, because�ih�S arlier se 12ٍr~ �O �on tests �s�dZg�Ya�tD>�D�a y�� �.S �10\% �rA�-tE�,.'t�K,y�FGerstill, �4 systematic or"���� at-e �A�U$�k6�>�t� W�� �eA�ofA3s>7 nd&�a�it sh�{F�A�EQ!��K.���=\<1$\,D1}� a�� them�w�� �ed� E$solid*�2*�DB�@ � X���Uf��RJ a"}5]t�s!�1]Ldllent, & hardn�asq� Xv}d�� � &�� U A6Vq Ta"�Waf�.� of 15=���"dF� [v}A� ��d &c� 0.3].  shap��A�LT curv�in���V� � �%5+A�R��wo�d vers� Ń�"�/e��ut �!86�-�c��*�inJR,�yds �o2 6 ing � rpre6on:# ,itemize} \ d""%�Ed R�8i� �%� � -*!!B�� ��A� wagIult�S ��.otic��Mslik� � �u �!�M:�"qMi=] o�i0�� >o�! �$ mechanism���� H�!/e!/&�,A�Io�#�* ng�explore�!�!� A� ilarB�/ &� ͥ inm�.�BGO� s� (nim206:107}m�no_eD��r� AUq>. A;$re-analysi��a# inNlFA#Mm:4�& alsoAvBGOU franc-dpf��*}^�%�[0$ exhibit som�&%�� ton 0*q � per)� on2I�above##�M#�3��,:o ���"(# �fic� )s,y �ro8��:� K �3.*ou�un��>�A�������8.5�7n��'�s�� l$ agains&��#)� "i�&�(aE��-�� �a��! t-da lin�7o5; ^{-4}$,"�o% � }Ɇ O good�)��<�'�p(of RayleighZ(c�V @K Q, e h6�7>�E�ssuI�IA� �on� frag�AZr�� by ine� ic�ronic4� � , wQ �%si�&�iY�-�-#id%e� �e� b�4 �regmi2� dis"�A�x\ .>� 7}t %�l$aGo�%Bs!%0wavelength. Ae��$4)nm$��y�heavily �F�goes ��"�"QN'M xac�Tw� )`re�=� A� �ent�sQL-YJ.i"��)}��A�ar�e���qa struc)$ p*��j!� on� e s.�,�R\A�:�I� e nV"�U �V- sugges� at� I�F � raA�A�/ * %�$ 1D�iA.X� u>&w&=&� � �m9�� :# slo� J�!"yly  erim��on top!T��9�-%�9̅kp# �:�!� !}� rm )�c�� է2��of� ery�} n>,!B#G��|�.�"� . At�a�"�$1JO��below%Z &i}-Z star$o  submY)dASa9-�P$9&28n2St� ��a&�%2 eta$m���%5)A 5�)fb~&:�,ga`d lumino�8��histograO� �7e��E  d �in0 ��eU��1Q�� 3}$"BsaH  '2�rGeV/c��-� 6�8:�� ha�U tru��cid41L e EE�eA�thE��i�y0 always broad�^�# � �襑t� A��o�iinu�IBc8V3�A�A��5��=^�at�ou�%!�"��EE�aD� � a��y�:.5� \,p/-�at�Gq(C. � y, aU$�(=� 36�(ofV��t�w�e&�. !N.d�V �28eta\approx 2.2$+ �g0LHC o�3i�86_,*ot�jsq: with���-�k !� a major�n�1t�0!��:i@by� -E&s�)�EEy5(predominant�e�.p��neu� e��!YAra�"excee�1\a4/�[ �;)�+!�ew nucle!��emH8��S y!w�il  'a:u-r �y��l8iplic1�9ary4l���! � ( atomic mas%�!* ��ar " "`0' �-m��Xs�7 E�!. of f5L]! }2"���crossZ:AL�� �"�t� se n�vtF ""� detai�m�!� ��-�us���#�ort[��`to zero-�.}prior s�"a�cion"q#t� de�4d��6�� % �9��R . _=hQ argu�q� y"0b�6�� )^6E�ur� J � "�/W �-�=!��/cye�R�--��� � & rѻ!���8t�@us4 w�"� ��% 5)InW-.7stiB6silicͧI /!�K!:�&YD �Wimpuri�!n�7V�.,�tice �.�491:19n0"�1"6> �al[y!V�L �"� �F�� 4=aA��I9 � -EAhi��Yquanti1 v�n�0 p. From:�(3�8de��2 � of 0.14\,E|/��3$c0%a: flux� �� n�we�&c-j:rC%�?for{3}{-�;�)�څ*)&far���aA1mF ofili����G ��(���0-6}$ level. 5� fir path��[ il�ll�1�A3i4���laED a�kih9�$9M^4 �v�m� disp�:] s��l immepCly�)s�E8a=bl]1metas�(. S�>E{hod�%�����.d! ope� stud� S� Ev Upsezq�ba- elec�}icl3ip2950:155_7reM! they~suc�(y appl�9�aulkq� }�ector2ou�S�$K�(/'toe�\,C,�.a �!�5� ri�2H&��n!� viewi� ad�0�Iݡ�Q�a�t5�al 'r�$�`erj#H*9nA�O9track�����7�W�|�� XGU�(dE/dx)$"G crit=M* n[ a�r*x�E�s6�9:� A x-�uo>F� vf !� ? *1 � �?tre��# �Fe,?T?r�,th ����� wV��t  �:�1} �a %d}2RAZximum $%k$� Q5}{5}\,MU�is�00#s(biIa minQ %�(icl4� c��>�#Pb�\a�th�1GeV kin� �� 1b��-%�uu;lli� e �*CM��� d!�C  %� of W��Pbty� Z!� of 1�MeV,j�e� . Zr:Fe,�R@?},� �"examplev"N@"i-�(�B�E-�I* aF11�2.�AR6s"a�B 5�N � _5 ? a� F%2O ��h main ques�{is � � a�5�(M�: need� o-�Y� q���rAof A�Q � ��B� am��!�m�is quite��=7< %Xto�����5*"�I {\rm�}$�CB!�5�>Y#9}%bM6��&ve Q�/c5)�D��I�14zed���w�s a d$�G탁;!��  I >�d t'<�T ��EE,�4n"J ACIk5 a$$=1.9--2.8&y)i S& 6�bee�� T non-uniG6cl�< � ��F_7���!�M�EE9�A�s �a weak "�%e8 U�:���i[?5�1 fact� f 4. AtfE�?h/��T 66��&�s�� �Z ?i*�6�)�HM�YC�  � J%<�p��`:�?heU���Jm � G+�� �,\���ed else#"��e�QuQD%[ - a�.�#% upo�(opping\foot�7{II.���a��M���cbig� rix w�=-#�7w D��.�A�fgMe voidL �ed.}.�%ZQ>�@ GeV,�v�4�p�te�4(2A�q>M�6�a��a!M�1can n>�� 1.5��NI]AC"�8u��%%of>� 9�<�2�A *� of� �Ag2�threshol�Aa( r*Nah���š� ��M.d"n � s�6 BJ�t�"# \ � �.-�;�T n un3en�p%�L&��/ �JGJQ�icQ&! e��u�!\]�r�� �ac$�� �� �"�B:� EE. % >\�V�Y%sM�nt ["I@a416��/e�%Q+ ) 2$*�3 TkH!=�X�o� ���Eh ��)��F o*1ime oF1 roughly�2.6�;t-t�LHC*�!�6�: %e2�#�;r�%�e��� E�A���! �9�E"�#A�� ompromih". �fMal�;10�of�o"��W5$CoWWa s}&�Dorfan�|ve2�,campaign, ai)t �My)��Y�#6�Mpee�8� � 1�n ����s. Empha2"�2pute� carefu�K;2I",M�0�-Y.�&]9a ong ;-u+ �/ �*O! A� ense*!�[ Dy�>nt-en�"-\E�1�Wequip"�Ker��� Z! AR��itself� l=0Df!��" � �"d�X.PLT�  �)mp�� To a�� ambigu:we)�i1��3�N ple �*OM)sol� q�>�!��> �. D��a1U(s�ch�U� forp3YuM� �� h 10-�;quiva9ex+ , an�$:\sh� �-�a�%�1 rele&'�.YT,\@waA4 Mno B.i@-taA��<nt{ -�� �� "�'� B�7os"%R b�U� �=,!� made^Har5Q. #��A� $^{60}$Co��iVsT���*1@�8�'U:�I�V�sM!�!���1�I�� �, ��.*) � E LT-J� =7�."�7i�� 1F�Hp%d � �&� jhenume� kte$9- B�� b]MA�l $A�UI�"�?sя | �Cof���Saa�);/h.�8No� �i�eAt�J p� 1,ngNa^A�ha)%tsi�.m-Um:���-a9E�K AE�$QkGy� �$=2>�n:*Q7 furt��im� tI��k}V;� I1s���Prai�)9�XWs��$q�, )%r�\��!4`[�%7a(�1ND�{ �XitI�u�Oi:l� T a�.?a�l�� ��{1s w��o)� z.�]weiF!X�7"��.�NhE)�* !65 !CR��� �lo��o� RLt sH�'8Ua��� �"N�%J�M�2uitM.nWll�" L-`NfM�r���ddis�.��X= C�[ doeI<�Z�!G,i.�V,"g;V u";E3of \ta6;W&jU. 彁��_l�U�?Qs� 1��SA?��! typY�i�Kf� g A�?EC*ia�!���9t&=_r��NOur"���!sr g"u1)�I�A.�/of Z &�-���?Ecaj#re"n!my.i�7�!�e Ase&�3q3!>%aa �� yd�:�_�U]�CW%�3^ %�5hceAz�,B�� manif�5 �a�F' g�� . B�5� 7E�``�''��: -"�FR&��s,%)�a�hh'!�k%�� probab��8�t]d"�&�8e!h&B8c��I�m�� );U *�& lY 9 ���]@C�\tE%R5'/! obje��%�5� 86\mu$m,V's���pAh)a�B6�%H&) vD9� B��4v�5�ar(C"�I��~0)�!��I� >KŤ"�ourO�K�$6apes\, aia��,A���.:�. -. Our*~#* ��Ldi��?զ>�"t1[>�,} 'enci�-m�Jb�2�. Be�0i ţ�>�� ��5� �low��, �1�a� ter ��es�)E:�!"*�M ndix *oU~oa�_"=Uapp�actS6� fQ7Y^�-��7�y� "� �%=:}"Z\"�R��, el''�a�eB�I��M�� �% a huge f!0���UY. .�'s�2 ei8 � or�rtv]�a! iW[J9n half-lif��dq�\2�A�rem�.=H -�1Sed5G. A.�Y*�%r �@18$%�Xt �ej e��M6veOBq/*i�^4��UBJ*� '1.A(� � day" coo�a,QW�Ya) y�~�t"F LG���Ma=BI���in N�mepsBrst��rŕhe 8 FLUKA.]d"�&�Q,�i�,�c-P*� c�"6�Kg�^: �vera"W6 �model�D� aPinF"�1Z)�ail. EOde�(d �bfA�w� EG8cy�d��� &�2 ��Px��?*e�rL)"�)marc5,6}�!K�0aMg� ev� ion x�#!�!�m�d1b in�*orjeca"tYwv1! DeTr�^d"�Rdetra�*�� 3U �"N�!�GkoCQ-�)'E� %��(n���&qmA [%� fi#( � ��Zt��All3� M�A {D � (m3%})xfi�eph᪍(}E WAconver!�i�Sn �2"$���wwa�^n���"-C�Biadr$���*�o!!97ing-�h�Fti�Pm!{w�F&%z��� *�7;-� AaRA�!��&�via�KY2  � nsp�E=e��.b�\�[Y20n{(C&�5�-! nd1@d���E�"(d:A��s�� DtwL2/����{a_� us� �BAn(�O� Al f"/� i-�.iZ umA� f~Y3}2�(20>�(Fi6�]20�Y#oes]&$Q��fllA� ]����3�pur6A$1w�aQe1CD%t7�=R�94�I -A!%�erm;m%Be�)R� V: ium %WI���P��6mR 20},0K�to*�8e}8R�!s�cm�l2��'��e�a��:��(5SsBk+��=-$� tersO>' . T(a�Bca�*28is �(if0M�c%�/&)kb  inser�B&v�s)xindiv�"K � ]��K._M[.�D�"*^U�*(P0q m�? O*S$RL/W�'�� 29\%��$�Wwoc_0isvA�, �Ln$.�$2�2�-���de�a4�)Q#�"_ :Wa"so�YtocaYA�2�0 �qndI � x)ec"� 9":A�un�0 e Gie�6��AutT\ s 6150AD6% 1�SM`#ͨ�9 2��t5l� ��|siz� pos�-4�*�l)zA��!�c�7�2��F�.�O&�v| } V&�5,nt & Middle R�\\ \hM Mb'd:B& 7.67 1 10.4(& 8.64 \\ C�66& 5.094 6.58 5.48o1.58$\� s$G/�f.051 1.00 o �M� l(�/cO3{NuE�ndJu (4Sv/h)2�(�ron])�mi%0Gl&')r!>>�X�V (seev�)����.�[ 177\� �� � A<'O"� aN"]E)�d �!�;�n6��' v; -cheh6 c[ U r�}j�GN]&m> w�8a)� �S5rC��)o Gso6�%�%�wpJ{���Y�&�B.nr�./�&1%� �a9^%c�6CLce �S�s&![25�� +&Mfofc!AFo k �--)--%��g�w ;��%&�(ThA�Mni$1n=I�&���v���  2��a&pX ���gB�� /�y.� :>�d��nf�. N�I9G�mm�jF:�u'{n&\ 4}, "�%7�&z!.� *�Techn�/as��� �:$� � u��p;} ��� 0�T21v rr�ofq�dqu�' ���4;7 ���7 $^{22}$Na_ ? M�� ��fig21���!osbHo*�I�Yb r�� � iPD � (�)� GHeO2� & D� 7a�1�4�e�0�^I2o�+s�3mb��! �$-30 jatc)"�A:� "�3*�~c�c(in2001:12}. ai�Al(p,X�� :(� 8$ (8.7\,mb)r)4�5-��%Ax�+�C�1��, �y,9�!Ly%a�fu_C)�to�Ju,�&t"�R�� g� h &~makV$t imp*c�;S+urD^+ Q]is�e_. �&i�*�b�e� m',%�A�n�n �& 'e2flPU���a�%�Q�E�=��!�I�1�ixE� F��|T�DiW D�&i"�[landbor}"[�'g"I� spreQw�@�s�A�s�J 11.2q21.6A9M �%Lu/aZ �U,"�%Aiabs�o�9�� , ga�[mbY�!es b�>]e�b�fr)M��":`�j^{ �, n(e%:�-� Esis.ODwOd�O> "x/� G �)�RE!IRRAD1�^�M+wer b45=nseque�G� �q$�a!�\#�- 2P d�Dz1S9�mal%UZ(a e���g0��� �� 1] casc-Qa_#eAq�Z #^Uy��in%on�%�falA*leaka �;Y�����A2 y drop!�)M! s�� a�$�ŕ.9{.���e�Xw7\%�5!%)�AV)�5�H�x�1� vsur�8�9J/ ���� �a2,� s�-Lensat5e �1N!�:Tl1b��a� �2hiUvY�&�qN�iH rhS6�.k.e e%�I�/S�<�>a)�I%m/� �'1Ming�-M���I;Qd� b!�G�d�Z �Gs �proiq��.��=�. Uttun�,8 "M'" !4so�&"b�y y�2u!��)�|e� �TIa�ν�"�!i�E�"i��\*j,r 2(us����!�uin{!. u zJ� ���i&�&i�Rq<s�EMa.5e �M&�%�Ee>``weD!�a:D�[T � �;.�m we�/ec]�-A��,<y'5�!�p�f��c)63p��_;a��s�J2z`�V"`=M�eJ spot�3�a�G e misaligU/q #=�,��Bsser Ut, V�decay) � s.n�*urk,o]}� un�3OVN� �1[��[�*�m2p:m^6��f�}ofA�G��-�q\.�XPa*�U ^M#lVA.���?to&P"/.", AC&�t;v%_of� "�$�?�qQ#�3A�9,&�. ��M�O! ing �(!˽2��a1D�A��K(���a.�#�cig�^CJ�So7��AU�"�]p. K5�&ult�!gneqs PS�Nejy.�v�g a�/"�(ew� �U{<z+s (ms"�g{\it h}))�!>t8 t 24��3}�we�%N8.6\%.�2,� d� E�-� 'I �LT6�d� "$H6� ! % �sUs�gmm��]y�"��aFMez6� ,Fa�A1.086%L.�� �2V}w�U�� �@�$8�eF�7�O!�,f� 7/roK�G is� �+�'a���*� .6�)�A��e�>�2�non��B�ހ[22n�Ti�qEr-�,�W s a7"%�a�Z�Qlyz+�- �a[e %�5� V��i�it�K t $x$=-12��  .5 2: In&\:�Pi9-�ofBiA!�,�d��� li �e�Bk MQ��L\� &]AE &� 5 h-e �OSL (Op�&ly St� ed Ly"e݋ce) film. A�5ealF��p ƅf;oa bump$0�I�5n�NC���"E��;�!&�t0;?�! �]�<� � d�[�e^Epe�<5� ���:�on��� ��� �=nded upI�.b5.�" Q�!r� ntVF� A�)B#�&dAE��!  �it�:�"2*"%y��X�(�2 "�|� %%A V �GV&q� on.wea��fA�E�h&2�m�r H&�-�s�$!Db�&few<d"~ �GingL6�i6��h/$*�!�VC5�dAu"`��U.E^c$e!in�T��C� 1�!5�5!s.�� a@S 73�l� apG5E�Z&� �L � �? :�,�O�=�eAII�:N en�C0$0i�gE�u�u; 6| [m -o��* id9#w !Cerv=�Bd8*p2��Q,,bb=0 50 567�23n�Efkof�>�i�0s�u1�� E}. C�!�!�? at 4oGcm�ta�e=:���B :l4>�`�� dy$D?  k d���ʙB'$m$'nlm�� ne'( '$s$'. 2�3:�g/ff 5)6um�� �"� sE�.WC� �|B�,�赵soiV� g�� "�8��j$\"�F���bder�4'$�&��&g)}�3/\�,m�d�!�a12�M(,Q) �D�!ei+-�atzXr� �&�$UTon=�)�e�6FI ��%�t�<�,n �D$ &� '�Z���:). Ass!#�Sa�4thu�(W5�m3;�}*?�  �_�{�" �� ��%�%�"T"�(�FB�D�P" Fi:2,3�|�G��I1������ZGBj?$U�*��>��+?M!d5���d��MyQx�E �(ly?6.���s.�it"jj"q:�:a <%'L=*0*� tg. two�Z�rk3Q� I�"�-���}� d!*2��~&R�I�up-�a asymmetry!�� e�"N:�N����6E �!�ver'  dURi����C�� �>�6 ly horizo�aly�,�6� �56�i�ZU�I��� �� %�obyPIi��e��5aW�� of6� !f��M\*@% *{AcL�EC}� i*�*9� C t CERN,���F�&�;Lbye�eff4o of R. Ster� berg �}����!�requi�PS %�&�!�e hel�IM. Glase�V�lvotti!�#K)% �%ndos�nry�G%�s �2�" ly a9�5epA&^"�$S. Baccaro!A. Ce[a0��$�z�sg0ENEA-CasacciaEiHn%�A2� a��r !)"�!s(E.\,Auffray�!�1o�!oMsj .!6ch"��aQh�`�"nKl���#7 33:6!8H�2E- mtdoNK@-Tedaldir7m� 9) 668 tn95:126}�|Chipaux%qOOs�i�Ņs TN/95-126! 2�5��; tA� :�4p\,274, Delft,��NeO%'sE�5I�$P. DorenboqCE�$E. vanEick2N$ote98:069}"���1��8NOTE-1998/069 ��8)2O$im530:286}A�A��taryj al.r�53I�4) 2862\ �55}a!HuhtinASN�55N�Lp686:481} T. Enqvist6�i\Ph\� A686E�1) 481N�38.9m\R:��8/038R:*�=�,ulv�"commu�.��.� 1%�2� �J-26 �9) 72.RaN5} J\Gebrauchsanweisung f\"ur� , Dosisleis�?mwr0},�5��' Messt� k AGa�Ladenbu� G�v�$2mfluka�¡'arnio �2i$TIS-RP/168!�86)ePE�"L1987) . \\ A. Fass\`:O�� IV:�C�xr H{�oyE18ics, La Biodolae�.�Menzi���A�8ribano, World S�6�c, p. 49x 3). �5P. �@M.]�� MC93>a,Monte Carlo *�iin� �wA �#A�� p\,1 ��K(ragowitsch,� Lin M�Drbank ���q /a7 4)Rc���Speqn ists' Mee#��Sh�B As � Acceler��, T�t�.I&`  Fa0 t> Ar4:t��DTexas, April 28-29�/04. NEA/OECD dzp. 287�5>�438:4�Q. DeLZA!�R" !Mc(���3E�am415.n�dens} J� nf! $K. Goebel,I�Health1� Groupa?IJ]�?� $, HP-70-92�706�ote02:0�[]H�$L. Nicolas qCMS ��2002/019� 22S�#92}A� ,A�F\* nesi^ B. Borgia2]TN�N5/1 �95)*i �}ut}��Vincke� renyuan}�Y� �P"�| PWO"X }!Ip�,��at� $ NSS/MIC03 �, Portla'p Octo�i20C 2003.�n*�M� bayashi ���f5206!�83) 107.Zf"��F� ^8�v(1H�86��Ze�_&�ys}!m�-5� DPF2004ke� , Ri�ide, USA��g$f26--31� 4L prinh (ETHZ-IPP-PRAX 4-02EW�/6> �m!:��>-&� 1G2) 194.-� l>�F� ccioF� }�5�� 52�m�DəŖ , T. Haku�iYrA$e�dio0,  8m. Vol 248, No )1) 38Bq62q@J. Ala-Heikkil\"aF��.7``��-�Pr� 2J���I��)�AEsi�� Some� s߇Ma�E�A4� Y'',� Ona�Ch�64%�5)��a�2T �E��"�P��� �  2�i"�42���INA� 1/011~.Fa��2�� . Iljinovimqˁl11nuklidk% bei )xl�� ien}4showpacs6A$ke PACS co���23keyF3keywords- %\104class[aps,prl,1,֤Hedaddress]{revtex4}�:super�pptF> Rxe,5fy\u%�ckage{g��:%�style[��[zcol,t�@en,epsf��FNsAKb�C.M$\title{Osc�pa�DC dri� "barrier"� ges:\\WMeriT7s�-9,�bC��&�_�Hdiagram�� absmTt}  �S9 g#=iM�8 layer sandwich7�-miFuc� &�'~;fqnar�v�����Kvarie�.sgo-4�orf#Rarns. /ap4ocu��!&�+ mogeZ�65ta o}� ws+aa�voltae;w;� A aҜY2M7yyb�xpl�9/C#��= �`aiZ�6 capaci� # defi���"al�N,�%y  $i*Ǩ d]�o5�`1t5*ent}u"f�R6.&p~N�/model�#;aa�&��6� f3ionary "[u�Mi�l��X !�-�B:\ xG&��J��zMf�a�N ng bifurc� �IApWeNd semi-,avvm!JwMe&E[� G!3^8I= �#Q�ng.�/l%g Uam4�%f�.�G�Dl�vcyc�z\o�<�Zaq� \" {} \�=ū \�>{I�3!� } G.�L&�� i#�#Townsen�!g�m7. &�(w�(3:� �. Bܵe���ls, y_, $�E���Raa��� �?�Jonas2,Bruhn,Golub,Letellier,Bultel},��rG1 C�wM5x!���B�;is"n0 �r-J6� ׁA��!�@a*aGr^�#�'"�' ��s �lGwinn,Islamov,Dong,Nasuno}. �:��8lr!" �-3e v%�a!]���@��is ��lo��s�!�j�S"�y�Oh���$ . AR9�Ka (=ceA*y_�2�Ke?y# in M\"u r-%Str,prStrf�,$�2��b*tB!Id�P$c�Gr$(v�.<d��)'���_%�oAre �ӧ��I�PRL�$;9cu+��� one Ƀ%�;Zem�.�>"t o�=Afa��ly .����"�nj�L ? ons:��st,�e�  O` w.��:k�L�b?L] ���m:&V;�2o4x�'rea er�`o_����w�2A�$7#=���s }Zoran,PZ s93II,3 HPRE97,Fiala,Pitch,A6_(v,Kolo04}. �Ie2}�%setup �v�-�0�8]�IBi��6�,�O*"*!5!Jcircuit �$Y�&(+�e�"�."�v�conN)a��o�+q�wwhUAjr2two* �Bj�-aY+m A|�0 curr�;��7#�o���< �2���(�.�. S_E��D,_!�.z$ilaȄ��g ��x# in aAw�of ��� al�8biolog� �JB� �_��6|)�&%�+onflict),a!@�lV��N%�  rox�Qi��at �,e�_���E s�C memory "� %\��c˘se��&p!ular,�W� U+Ca�.�k��]�.e�t� n, m�X)r���}��EE?^X�'���u" a$8q�Xpd1,pd2,pd3,pd4,pd5,pd6\!I^ �� ,u6�Hin�`h ` �Y J�,��plA��'���%}�by ���`� m�!{ա Gw�Z2 �oPT �$�ZHWB� ndI�i'������ . ��;` 6E%��z>()9in nitr40 mbC�it�'a gapA%0.5aF 1 mm� $�� ���^a���}.5 mm p�$"�H3=�GaAK'oHwyC�@,1^��rZ�,500 to 800 V�'� . ^NQ�us,us2,A�, w_0tra��%#�t �"�)�2 � s, haC�Na7K���R� s� �xp"ed!���F��a A&B  af��~ 3I�N�. tatJ^n"�@m@ed � "�)s*�'feat !�t�v_?��s�z!:s�W"��<]st� �����a gaug�)��� = 9|ofB��}��@e�.ue+?��D 9@�  9Em�[a9:�:�aS�v II�I��rsp(�vW�Mf�"MAY� demo� & ly,~�^� a"~kAm���|����2�妩��9a��&E5�me� o>�o >6KU*Vȏhxpld; ho�Z�:B�x��1g1W�� leteZ[M�,IY�Vi�]!�"���6 ��b �`nv�6���b�q9��E�b�\M�A#uy��dXa un�,��J/+�s�c�e J�� t�o�.U1S6I�.�V7! �!g&]�Y$e�gAn5�s� 1�VI. %/ \)0,���fWL� )Fwo�X�v�8j%S��*<, &U1�p \>%to��DCu:�p �.P �n��ID�)re�jnx�CN- euto ^;�<.�par�#!qbiEG)he F1l��r2erv�NUu�proߍ�a�ߡB�?�7 .9�2�)k}"� 2 ,%Iv?zE?��E�/�G maint��.�:AL so-��2�S�a�impact d1���Ł^h�$���.M �d� e*m�!Lca��� �Ň ``fluid''>� =4�L �Y �M[n�'< $n_e�Ep�\�{ $n_+$2e � Pois�9\� `ic �B$E$: \ba��HVŵe� a .OuQ�4att ��&nno��C�KY . Alsoo-Y�,�hea�',Xlo0i�&"�Ka�&���S��Zst&E��f0"MdeA�^3 ${J}Q�$ J_+$�ɚ�ed adr8�mo�B�)i�n�(-�E�.�4} _ = - I�\muE� { E}~,~~~"+ = A\!A�! 2 I��5~� h!,%�*Eqs.\ (\1}�* 2})��.� b�O�}9�Ι!"�!�.�6} �= |���|˅�_0 �box{\�D${e}}^{\texJ  -E_0/|6�e� one-2]_�!��Ro��2�,�E4 � 3}) ����� �V_$J(t)$.O \be�&1a�u�\q�$t E(r,t)+m�J_e:+=^~~)�?r=05,ee���e���titSu$JA�or +$!� ���M#c'"i  � keep�� ���$ �$ _ .�E� ex�bs;a ��e*~se,a �P%e6\. )��a=` � dH�U��con��Q�)�ode. A�� anode�a�o��d�$r=0$,3� �� bsor���Q�C�Wt�M5�HG5} J_+(0,t)=0~~~\L�efteja� ~~~n#A�e��`^�p���Q �%� libe& �byN��N�=_�6� 6} |A�d,t)|= # \;|�b� i�n_e) <+�� �No��Tco� et:��us,P�Et�$CEOF l��u�%A5)�(n!x��CG!ޡ�i�6d�a�m��-H"3� �����gn mist�[�evaluńbe^|E|�QgF". Sub�<�Dof�&rg(��j"���I���y��g�ҕ���F/& 7LAdńef��A<� =���rHo� l1}), w2}�34}.36}d1�YY !Nnon�*ar�4a�s�ce- vcomQl��.=|c�?��I-�;n ���on `�z"� !4!�: .�J�{S.' � ��} � 2* /� ickټ $d_s� a_ �h:�c�A.S�Ri�*$\sigmaO.diQ'��;ant $�ws6�S1��s(t)=I�y�ilap�MX1} q=I 0 6) { ���%��>Ro:��.� 2;�V:�A;*�E� 4%)1p�>� � $U�=$ !�.�"2 u����& $\e  q+  s=0$�`"h�8+#� .Ao�!�EA�I��y�.<Sc <=|�t9� + J� =  ,\ޥo�#\a"� � U�q�3}). H�i'��Lcopic�m"z*F�ve�a�S3} C_s�)�+ �=�~~&,&~~  =R_s �\<=W�N,}{d_s}\quad~ G~ R_8"{Q�}, am�Ca=-.�0 area. �3���S3�� pertj4A%�>Md�� �$ d�<�Max���V(1,T�@_s=C_s �V��im�&��.� Qr��  2s���3 oughhC� e� aELA�M w4EA&!�iX� n e��! "�*� /u��FT_sx�[|G�*�>�Y$1/1($A�� ��sc�:�I.De A�i��� D6�GV:a .���"B"�8aYN��6(q0B, �bn� r�mpo�-*�� ͌* 2�E�����( $RA�%&*��!�Y�E� *��� $U_t��!4�!P�.�0Ug} U_t=U(t)+i��u(=\int_0^{d}\ dr� .Et=0I�A.Kz�� Uga��dynamice�� (t)$�#6 obeyI�16� 2} T.� U=U_t-R -R_s�� �2?DN A�-.�{}� �_a*Q� "$a�y�$� P PREuwc,*�.l)*�[I��*c"C� �Y2�$DimA} && z��r}{X_0})�tau  t}{t i�(z,") #5 }{� , ^ &&{\�E}:.I}{EV~ *U} PU� � j J}Yn_ /�, \nn2me:n[ k��.`�!6ins2 5!D)�EX_0 u1{�) tF' e� �  >��0G(-IWT�e�� Sx2Q�gm�c$$j(%�$��QށT��^62 g.DT)�&=&u�z j_e +j��()�E})� j_e= 6 ,\\�aeKa &&=& � -(1+\mu)j - �'&�z a�!1N@�@G5}.O G6})Y$2�g�' 2�(0I�.��  )2�4*N6GLJG  1+�}{ ` 1 S>e"Y�6�"B�6�are( momr��I$A&ɀ.�� !WvY1L$a,i(�a���Vr� r�S X�*�e\\m�]a9+}e}Liy{d��� e*� izu�#�6��DC�$� $IzU}��t^ M(  a2s� �& Di�_t-  R}_s Q�, %\\ %\� s3I} %66a{�DL �G\;dz % KL=\kappa_s\; %\Big(\; 1� |U��r�\;D� ea�$!F^m)�%-�T_s�0 .1� �! $R$E_0t_0/(� n_0).��� >�YR$ �"9�#I�z PE��po�� $\phi$ i@%*"�I"� s3} �9�=-�<z J��� 0�phi�?)- i�)yJ�#��dom[U���u69)�MG�{Y` %��P�J� '*d�tK*g1})--�Qg4� s2 32i s4})�4�2a�"�K|&�lyd�.� ^x�� , $L��7$�1E6�layer@lE� 3IYA�$!� � 6E8�K7 $.Y Kaq$.Z�NJ�3-�1�}��xis!�4!E-$�� 4l�!�pS!E!^N� �36uss*;�s�. A�ng�a��`m BqC,o l�.!&&� � dJI���m%�b�ͪm".� ��"� n�!�$D,!� � ]h)Jth�&F��<"� �)6b^�$�Aw�Ts:�$.'}$1/]���*�i5t*tFay����1�vm"�$J�� U{! surf&��.saDEr//�&��1��>*V�=< Y4Q�.(U2, .X*a�:]af* -*�ini*s widt7V*v*'ticleg��!s mai�dWrAmm gap�Qbk!BPh8�(i** 3aldzOSins }cU+/6t�c&� :�#�\of�* �a �d=$~-+A�a�=13.14l"e+ dop��duzA��RM��s�d��&n&�^bh6e;�Id}?2e!"�$=3.2\cdot ӂ0-8} (\Omega cm})^{����A��"A�)�)5, HsA<0,(, 600~,Ac;&a"gaP!�NA���`8req_8}, 740~V. %�!�X)&8X PascX:"Z�M�Yn %ta��+gb�� down� $U� �6s6r %�1Q@H�ti��eM $pd$,}b&Z� %y�!Cm9�:���2Z0� 'rj $4_� $E_0���b.�eaE .)P&� ���<d&Ϣ�:Za�0"e:3�m%~ns!\�k���n���4�Epv"�BR�,����%f�^��w each�. N�the����Zm�*� ng)%va?�%1a�%% �q��k ��R%pvdm���d�"7%,*b� A�(;�h֝n����2 >|o�,�)y6s")*. On�)� +s\&R�ffaY4 `a��8"�'�<��ro��d621����" _�_+=23.33�"�"cm}^2 /Vs. L o�5�*Y _e=6666.6b=. �u4=Ap=[27.78 \mu��m}]���!�=B��.2Wk[��t!�E8�3�CRaize�9asAuK+y�a� $d=$~�7!31~m�^�s�[ 6u �3 s $L��8=36�� 6b � 0.08�Ud �.= :�&�3"�:7s"��jL!�at�>���� :b (�&!C�[~Z)e�B���j~�JTE�b [htbp] EC�8�B \:�b[�=0.49�%�b0�b\\ 7c:�C�-�a��8F�������=A $ (���s� 1$ (*��)A!�2�� ��s � ��o(�$_.�C�?� - ɜc(�2toE]� &4 ��]e�]I/� qGz�ng&�!J+coeff$� �$��rn1!2p@D�th $L=18�Z^illust�![ �_~1.�Cup�thrh�oD�%nSO0 shape of the�� current voltage characteristics for $\gamma=0.08$ and gap widths of $L=$ 17, 17.5 and 18. As discussed in more detail in \cite{us,us2}, theB|hcan be supercritical ($L=$~n4positive diffe� a>nction!�Q�$j$ ris occurI�a)�1! is.{` behavior corresponds to � lassE]Htextbook case where ":� be@E from%j4towards�ih M) iIFglow disi0ge regime ---! we have qO 2@Gdea[!^$is requirer$sufficient!�Large system size. Fo:�CF become2VE�L $L>L_{!�H}=e^2\ln \big[ (1+\�D)/ 4]=19.2$ while AF trana�on!�6�5�is�0ermined numer!�ly5}>Pe�AB<$L=17.2$. Data a�oe1q$/se�F\ary electron emission ar!�la�zA�,carce, so it�0quite common )�applPhy �use it!�Xan adjustable parameterwe doA�0e tabulated d��Z(\alpha_0=Apm$E_0=Bp$I� xRaizer!get�R with%PaschenaZve %�($d=$~0.5 mm.DdprivatStr} would suggest �703$, but�t 'me� aFM Kbe 6�up!�$L=24.9I�n!W /(develop som!�e"� neg%� b ,��i�I�2" ��%^Y�(I� =0.03)=26�" W!�nclud� ��th � -J(c�oing � 18$)�Pso seE�veA�dependa�$E$�L restrie. ��t�,ason,at chos%�%Xz!�e��Ek)�iAjdynam"  eJ�J �g2}) j 8 form�+frac{\Io${i}^{m+1}-2 }}{\Deltaa"}&=& 6( &@\mathcal{E})_{i+1EV T z}+1 (G X; (i�E})(c C�� onumber\\ �F.�� ��$ &=&j^{m}-ť�- �FF!+ 6-�� z} -$ mu)\leftJ�right�>�ea � $i$�`rizM_spaA5$m�Y�grid. n m��$ 3� tI�A|R,� boun5 �%ieWh �Qe3})&�  e61= x_ }+If !�!�(-�bb5�A1), \ee\eB e ot � :�+1%�$�Jq�,ed successiv �xa1��}%�D ($i=2,3,..,N$) by$q� \begin{}6Q� =b�} �1+Qyu)�QY z}2EY{ Upe�)Q.�}Mr-rW %n}{�uE6}��nd�� Mm_i�U� jJ-\l g4}) d2 IK:T �N�+1}= )5�-19}�)-26u�%+1/ Q K�}{\�6|F+1:B�remain2 1U $now be]� 2� U�))toI�A�N-1,N-2A�1$) asA� 1#%�!# �2}QeE,E ]b V���]0@)A�0 z}6�� - .nV��2�?)Epe%Vtot�$j^m$ theseu�s� UN d by��E+=%1{�f� +��0_{s}L} \Bigg[�� Y@UA{} 0s+M.\mu}{2m�MGY���NQ.^{2} -Z&UT&m� && \��+�)�^)� z\sum_{i=�m N-1}.E)��6i}�)].W ea T8identf� deri E�i�sS͚ \par��_!;)JU}$ If� D 4$\int_0^L dz\;J8E�rough i3})� t��2 NqE�b sty ?�is�� i�$sults pres� � Figures 2aZ9�� on a�M� $)j z=36/600�K%�E� =180 wh giv:� &  a�acy. 6� Qualit� feat�of6 ��"X  oscil�ons: h �  am<,mit cycles} % &TsY show�2� | odic2c� y%,$anharmonic%+$ long phas� q�srup�u by aurtpulse. D��6!�pp.&� a�+�m !)�N;*. $, ei' -(homogeneous� �� o.5ing*e �"� ?t�(. Inbetween2rna r� of bbilA�iPit�s -� J�previ���$A;o��.)�same q]d"�m�obsera�iYg\ s. First�, upper panel3Fig.~2!��1�$j(�()$a f ��a�!�*=�s.�}� ��=�m���_t� 5$ (i�*& to��s=2.4�E{R�e�4$U_t=555$~V). � ��en-$1relax� oyZuy= 5�ons,�f^s�1e �%@ga�~6� 6.rSingly5aat-1N jA�2�unitsI peak�%�� ��m5 P �6gaNȮP PTBV denot����QX�� m� Figs��3! actu�Qm{l�s.�"i ini� a�i�A��re!�.}smperturba9 -..�tat�} �� :�point�oi� ��b�4��Z�3R�S)j� exactl ݥ��a�2�,EY�5ns��-+$spiralSwy!I�!R@z7I_r] Us l� enough!�f  e+unm��anAt:N!�e search &�3priat*3 $s was guid��1 ��describ� �� s IVE�Vapaper. W��ndlu�_t=24$ (� 684� )�A�N=� unch�d 1  used!�anAmpl� a1�� :�q�a�*> 1?"�F runs away�5�q�%��� evenm�s6�& onAbi�H$is  inA�.~5�v�ъ��6e��.O *B B���Z�4R�v�E�!�=��eb(��� 24$�� ��%�26a� inearlyy>��"i� into6�~� � �$ $ 5Re��5iY-\~�!�a~�@%\newpage %$\;$ ..-Qua�b,comparison: a�it#y&} of.8E.Dagree�",&� q�sQ&v !�encourage�J qV�a����%p"�$�O diagram}( ���ma#l1s� &_"a6 �u-�� � of2". It as co �G�rk:"6�9fPf�*�g �inO�\���>� �m+�$ �Ref.~)5�.51���b�+*�O5��b!ked � � .��� ɚ�7)�i��+m=$A99$f$��*7of R�A!$1/�� ��%iK 2�$�a�*"�� A�.A6Z��Z�6RcA�e�V z 1O.��qB�QGP .$ (U� E*m$R_:p�Bh2G��6I.gJ�= 21$)~We�Q�Ӆ2��. %"3$���� ��py ��hejC$A$a�2�5\J�$��$increasingh!de slopea.is�[s�7���ks writtP)�*�=�9� M6ann almost���u � Q;N��� .{ � rad�'on ��с�ȩA'u��(-.e��'R�s� �rY sin%&�Y�"�T�# be f &�0�)p<s ���& of $2�'7}B�$\le�_s�# 2.8�(J0l-ch��$i2:6� .^2.9.#�$�.�! 0��%616 VR�a;Am;��is+ :,+y[ @l);B��*robust. �դq������=21-6>�% � 0$~V�I��/e6cug-ZA��s��-605 V% s firs�+mNed 0.x0.8 mAia� sequ�3$sudden droH-es�i�0 B�2G 4ly jumpE�'=1.O)1.5 mA�%�,!�i���inuw�� �2.7 mA!�":1��0e . Not too0risinc,�)F�,reproduce ne���se wid*Fa�re�� at�similar�� . R3-,, �6�Ft %1!!���] $5.5y04�o $6.02 &�er�Nnel. O�Shand,5+vai3w6�m2& ,]���� bot] I� !�%�2�b|� 5�115 kHz 12 to 220 ($4.*�,�bf�W8.�6}� �+6,)&)1.9e0.ιOurJ=%�is^.$ ��%mA� )U�,)$1.��)�] 6�;Wlie�/���O" isM�$convincingespC +)r,͏no92 fittA� tri� SummarizCw�W2"E6](����a6�5�f well$H4Ny 6Gq4A�l�< avail a�� aH/!J� fy}�25B� �2� � Ra on�6� 6� "c0 �.z G �AÑb^2K dev�E�J�alB�36/" s i�2� �.2�2�Me�Dis \. ,�g-�7u�/ modelf�' surf�#ge}`� profiles��.�5i\"j ;� woDk(�/vt,)!2���"�9pr4"8s� ;�.�.$Q6!. Ia s0� E; onen�RQ ay:�Y:� a4j \propto e^{-�/ _s}$&�6��/accorv to Eq.~kd$,�&H"a ��rib�-&��]�g3sub��*$ de�%.5(�A#Maxe�due���A��0. \�unt2e%�ris�L1e�QL956t)5�abo�o&<T�,< �Qci)o"�4&/<�p2� ��22B�� lea� a ; �#%ja rapi)" )�9�U1+. s; been�73a�ber9authorR*8cite{KGM,Rade8990 �2,Zoran3,Petro97,Fiala,Islamov,Muenster2}u�"� coK8be@%d$,a� $I0e"�("! type:�& j=g/ U},j�1I$$g$ vanish]%n�c�^�� is:b, the �,UEV4�T �40 . Howevera��ralreadyZ0�0�;�PRL},�*h���~[MFunderly��i�g*�1,, (E" '�1a�a8$possible, �"9ad'as�& doubl{0s �2�a�6J�he.� (!!D� 3, 4; 6 to�er���V.y�  a non)��� �%pthey def�� om� phys2Gon!�"�%m� ;��ponse ��-�2��b(, its ``ine�)''m�-n'�low an i/ an:'U= Zm�.j�$ ��m�(bulk impact iK32�  anod;(y will cros��whole�until)'�5&cathodBdQy libe4���9y<o�0=q %,� e�s need!�� gap,-m�9%+4 tant�ofI �memor�n2�Poy:eb�]{ion}9L/(�2:� E})  L^22�6)$q($|6|�s�<aAgV el�*��gap4ab$Z8?d=1$~mm)�%+)"A�%Fis est�;ed/$2A  10^4e:2=14�"� .� ��=��e&�0.6� 2u$sx "� al� �(�I� s2)ord�Jr��ai>e dur��aQ���, �fI) �bN� �"=5Fɽ� (m1!�8�&.@46@)�sit7 seem%(i}D .) "�<itNg"{$PurwinsNew*�6L � �,d "+E[! 6$ �Spla uO ro���[ACő�=-�X">�!rue, �!�6� $q� i{=����� ble.I!"D2k0 ^o�8�$� �. \be s0=\epsilon_s\;�0�0J| }{L}� E}(L,n )21>R>- :��#@relev��)7a!�b�"��� ��(a satisfact���!/)Z-=d�8 \�']g.�*�xDtoA�tak�to I ,3B� :St""�= : me�� direct \C"�m�&�! problem!" a� consum��& du�<at%d���'�a~a� seF $� s�"�-[>�9�ed��U#,.��1.T .� ODs ��afB-�*"6� E�% .�%zsu� Pe growB�(-� , w$*��)�T��&W@4GA&�.�P-�se�4��.qo��"r  � II.C�sS�g �@\O?g10} \� al_{ajO3&=&(z j_e +j_e �4əE})B? j_e=� , �: e2Fe *�:(x)"�7n - \mu' �;2ese�?+ � /�E;"+�vv �.�s30} 06\phi(z��+ ZE}@wi�EFq:�6a5�^:��(0 c.0!)  )2�g4js(�S2K ��B8d 1 c� &=&-41C E�s �hi �)=0��axN�� �Ist=k31)�.�")'� eya"1"u 2�s01]�zj_{e0A�- B�=_0) ,]� s02}2�_0*�5z1�_A" j_0�: _:K3.�!T7-N E}_0.0s� aU a �I�_0 Yuzqbb! �(0!� j_0~%�~Z\; / L) =m.bb%!phi_0 PN L)= �� I Eqs.~�%�"�@gs0}=e? �.&rU;f�.�[�  voR O&�=1A (j)$A^��m�f ��o. � "�.��: L� �I,us1O..!�QH�"&� exteK circuitE�[ ��of ;��.}U%genly� rete-ber��R�  �!2 #��L�'2���� ��.�s! xJ6�5�e,�KnK!ansatz ݫan1} j_e�[ &= &M�z) +  1}(z)\;�\lambd A , \\m>�� & =&�__0(z)+1jIA��&�@ + n>�X �0�1J�i%� index $0$2O/un-`ed%FM�",��M2G16Gj� ` F�I�# �ow- �& �)$zs�Ik ,� �ex&�$e^{s��}�2ticipaB0eigen"� w�. �$ � AP orig�J � �&u�D expa$I �.�K � lengthy:relNu�"2|s{ e h :�>1����+\@01}{B0} �={]�52}0a }�J@Jand�J~ g =Y� 0 \;kjB2�?� h#cM*ct�.�feq.� h &a�Ei�}� �} h� �%[>O'"W _0)62 +�?FP ^3} E>\;g.6feq�� z g���!E0/A mu}\;h ->m�9(0}\;gb@j%�mu}*(feq2� j_1y2� feq427�W )�A12 \; g��fbc�hT(0) �� \� fbc2�T �b�(0)}F�h0\;h(0)�UJ3�JL JL�,j KL>K4}��� �@)�� _s)~-2(La }Ka�U�*v)�= 0��c/r�on�+)EVr�'�%Il�1��o:5��N.]=k-3matrix. i�9(array}{c} h��gAJ� )� :9 *q$ = %M_s(z)ZQccc} >��} & - AA6�2���Big) & 0\\ Q�+a1aU"O r62\mvA�5 & ��mu30! `hj6�%J8 �# ��)��K�J� � e�.� e�)�$$z=0$ (Q�(as orthogonDA y reA.Xbc� �]BJ � \\-JmO.%a�!-1%a�+ E� A���pn�� = 0 y ^� �� ������ M a*c$\vec{v�pH � m�)�D� a s[po7W�wG&��sZP  Bn _2(zRp�� obey �A)� EYRQe��sol} ��IV= hi \\ g j�)� R�=C� f7+C_2\�-dAs"�5�i� s,;a0choose, e.g.,.� sol1��)�_1(0)?IB 1/m EUAK N� \; \;, 1)_2� = ^�I���"` e]uu!8vy Itz �""� A5Y)|e;I U$i(z)=FL(h ,g j_{1,iA�,%�+Uw r��uI� fbc4��L$ also; ���A钽�HV���L)%W����L ��-�j�\\ 1+������r�r �Mb Now d>ed��h�+Aby�&�� $ $C_1/C_2$�!�BI!�e)�wa &&C_1~%�[�Bstyleřh_1(L)Z -2�!�g%� 1,1}(L) \1] \nn!Q��cl1)V+ C_2^p2�p% p22p=� !�.��%�eg�+B� �4�6� &&� �BR�jR R�9�"&}Q�=1= <$h"I �~�E-at�R&r�&5�12!�g0.g0g�C�"A=w� mo���< $j_1�&"KDzj_1=0$. A nontrivKb�A�� �A .g cl29T~EirM��ant.�detADK=)�E�|>Tc� 0��1 &M�Ab��%-1X]F��Ex &�-%�Jx|�XPto�%�son�4]ab+d�c5�� %�&�$m�$:MRescal�� $\mu*8n"W�R%"` NX*nB{PGl7) �Iit�*�&�Bd? �2Q�ASI��M"� �' s#�-�verml �a. �D&�"<. H�&aj'#a-e stiffnes`!S� be remo�Jb�tX1!L*newa/ "u rescE� iota�� j_e� � rr_sF��\mu&&\bar��= \muHs D-� J.Ucuy]2!�!t�al�@Qde�_)d<$@�*�Y!�a"K&!��. PoL"nA��VGN� �#Z+�+&���%�S, III�� LF(�@� velociti�chA� "]7be�a sure&_!��#a-e��&ndA� "& . So>9 g2^in �1]$t_+=1/(�<_0\mu_+E_0)=t_0/e��5t-$:;0>;e;uH!�m詡!�})-�ly 1�econ�fA. �!.�si�b2nT}�!� Z:i�#�C�% $s_0�nc\`�� �(�k��s� &��  $g�'2�d�� ��:��Lcz=L$. G&����=Si�� �Q$ C��)@(tLRbe r)-vaG+ing��!uqud !<���! 1,L=s a�5h-!`<wRHnex��epQwiwb!���$AW der-�x(! Rgarantue�&" c$convergenc8;"�"� repex)u,)�6~RA��$��,s_{k+1}-s_k} }0 | < �96} le�Sw)�3��:s ;n"� a- lex�n7seElt�@.�0_"th�'".�*�1*y8w{g�*ima�ry U�$b-B.="j6. S;!��}�ra�tF�McQ�,� ,ve%"���ucom%e� $"Zb 16)�s Re~$� z Im  etc.\n 2%yJ?0$z�O�gEn�P�{.�� re�3u�js� e0}^g)gl\at�)>�: t�gE�d.&BTy prograt%�i� HQ 90�1:"/.G!m�A81�s, a 4E=�)(Runge-Kuttaq_m��+W^a�D]�JCV �6500� 1000A�2- �U2�:�sB*�$. \&�&A�f: R�9}�j.�V�$��valid*6��� pG5r�Gnfirm�0!H�D)X�6�}5b ��Q �1JuW(n�'(�C�]6/yC� f�u�_Uo<)�"s < <N.�� �e�,�&/h-, agai �5-.�6.c72n&��struc�WA! S[ J�sit*�1q�i"�"� ,)e�+G rcII� ��a�e65.�= ��[�{� %&��d� F �eU}n2�} �1G }�Z��.]�"ee���&�b1coG0,� �Z���.TDevM!�� � �"��a2|2Q8CJ� $(j_0,))~#)a*� �$�J� ~+c.c.^D�'�� jHU�3Y\� "%P==jugat��yeti�tw5��U} $)Ft�,%F�����!:�. 2bcU�k�!�B�*�F} =r\�iG �1A7\�r�}�%} && r"( )^A� }{|160|} ~~&�~~\? \cos s=-�(1+{\rm Re}~� � NU~~,Xsin Fqhrm Im�A6� f|!�^ i�& #Qycku%0�\;�}~�(Im6+ � _0)~�g�=�V� -c~r�#[Re6[rx ++_0)]�a&�Gcoab���� "p$ reflecH,�J f�.�@8(�M 65})��&�p " R�O*e:wC�! =�1�i:4�' PDE'�As� hecki �se<n�L#a� ared2 ~�PDE���ea�>e.!�<, 3%4�. ���B=(1*Y�m � 5},13.583� �X}N�� �� �>jql}&=-2.91*Pk{X ,\pm i~ 4.822&{l{-5} $g[��,=34i���� =140 ,{ to!�J/.�r=295�S�vT shifZ��=98.69^o�d{��RE"�<��).�! MKI<�reH-�wF[�Eb�An�G48. "" free&� X,z�!F� �f�Ek0�fit :PDE-d�Waab�eM}��[�[7R9L}�ofv�RE�C�F� (soliAZs) )�+��;&kK(*�x4+3&]eSq�-4~�K$ visual&� � tes18i�@rail. �'p2.oC�;�T�5��1?,interval $5y�5 <�b < 6..$^u WN<�rJ�ao��2�;��=(100�0.4)^o$,3 DDly 2([mK<3%V%�:��(�:�8\Qot!Hpfhb�3$!CwR��sjit"W� v� is�n*�LN� "WC,l*�3�u�wYs ;{. A2�V�3"<dzE��0UWSVs b�!'N�� J> 2.64Y?�� , 13.441�A!�=Hi���2.493�y�x6}� i~7.37*�F5f���$r=192N������9.83^oA8�D9�T�NU���bM���9�?��'s. A[It"F�coQ��FZF8�F�F�F�F5-63A!�Y�2�pY~pOf�:rX#N�g�xpo�JofrsB�8ALl aedE �*4]a�th��\ll�) y�� � $. W����O&D@AvE�6"�I�Hrp%,�[�pWsC �z"�0� lP'j_� � Wh8g o7�9v�9{3pw^�WCa")s��1�ff8 s9�<�E6A�vbifurc n%�Fa2n*Y e l7%s;5�.i�10��!2[:_"���s� })6�Ink� >uxW6�I��th� "�=*C$�n$. Be��v =�����CyU el�zAXp2],���yB4 � 0.16*j to illusuK.�J�9o� q D>D�_� lwayV'�2��`�gZg9RgB]^m�)�rM( �Mf XV()��A3F) , at-�{� s seVt�g�=F<0$E s�!0b3!;!^R=�% �76J>a>0�R9KXhoN�kE lR� �bifdi}zacgin�� 6� 10%�#(%bifexpM7aRexpj pVobB�Kup!�! .~Q �_� �I4wo���t ])�&YB U� �"gQ,myTh�\�Uu�!��2C  mnA]�An? 8F%s6�hs~� *� EJ!+2~2Z5211))hKFs �D? �.�`#j�$d�D b �+*^� 2s��Gd�s,d4Oa. E"��������U_t<58�V$("!t=20.5)M�exhibit��"^l%choÀthe1��k%au:G .c�of �K �er.f��9�s%�!mra�Tg )���-A& a"�y x] ^ �aiDO�po> ve s:Zbn�9n]_ grad�f)\�YAu llel�$H6sJ.x� �nVesE "�� o� Bf_��V  b. \iffal�I�jef`End �!Xu��ctra1zw�D#�Eއ� I�$F�I%iBb :'0 $(U_t,� - 585~� V},~ 0.7\�� &�Y "�~- to $ (610 ?2."Vf?Kd��)X.YdN�~��.0E\t; NPinv� �06�R�Z �9 i2��8$� ��?� �%�A�B�^r.�,.�U-�a�>�6{� �$21.4,~ 2.19�%��'%2[!�"�.upp�qr�{$.�B�i~Vo � �!d�'A�w�v�Z%� !�Jws l�h��=| $ ��+�;�%g shapeL2���Fw�ye. \fi&R�|�"� f :�HlayO�l����o%B��� B�U_�V��6� s�$ %f$��)� ar�]$0.�WN� $. %�$�� ��ݡuA�aI.QJ�=��a�I teau-%��6� ^�6�" R�6}�,nU roaNo �t*�_b�GZH�-+ed _ *�P�F.�M�ve>�ously�ep�au�lœ]�e��xK@h >0P�AnwoB;-�}wdistinct�5.�Y? noqlan iPi�0�Wj  $�e�J��.��y)Ac�!�eM� horiz�el25A#u:�. Am6:B�yD�?�\dyE)��%w* � TaF�T�� um a. :� re�y W!{h6Ob car�ZQh�'�+e=;"CIB.�,"p* Mbe &�J4� at m� E�SL look!��th�L n wrong r� A��<7 "9u.'ix1x� `all�&� ��-) %TryA�geta�f.� U�,2 R �\sl�ly1�c (towns...acc�nI��mfind �@Ii�2%-����%Ndo �nd�v�fig�av"}%�r ?��Z�1��",x^��n4.08$,�e:M�J�6V�w&7(C���\}�����'�L!simpl�,�\%�a�6-���;�� 6�O coupM0XFt2eG� F0or, .[!���v_H� a��( �Oec�yŮ� s�9.�WSt.�.�!)� uNda�X�_ aŜar��UOal%X3X�N�emgood muA�&��GH\HU�s &�ce"�al��� b&$~%_���Ta� 6�( mann� oug�%It̗�1 atЊ� �I�ra} �Hmad&�>0�u� �.;�A�E��eV� [���.ly "N^�&�1��!��ei"ci(rae�!�Q�� ec\e;&�5H��Io"�e;�2� .*o�f��@- 2� bas�2a�$Q�?$ 1 e�Z tful}UTd2�\.H =Ma&�[?{�]f*_�Ue�, oten�1AJJ* "$6!lP>D 6�UC a[le; panc�3�qC �bl;�taD� subj&odYv�2g�a�is ope�p�Fp�(e�q�.W� o-a"�pa.rns�,"�1. 2�%�1�{\bf Ac�� ledg�6}: {We ae�Duseful�u.I L� 9�7 \C.\ Str\"umpel, H.-G.\ P�W4, Y.A.\ Astrov�)Dmember�_�M\"er< up.$whadN�k0W.\ HundsdorfۗBgRtn�-Yu.P.\ �M 1|na.Z-]w s.\\K2worE'D.S.\� suppor����Dutch�6s fund;a 3y FOM�oMI.R M��s;^ mai�- XEurop� Consortiu�In��atK��M� (ERCIM)%no�.}�/�$thebibli�0phy}{99}A@b��c, J� �25b�PRE97} :4�.�6��.56}, 59A� 19976��f} V.I��lobov-� N�5!� 3018�42+Pitch}A"P\'er\`�L.C. forJJ. Appl!�a��7�#774U6�a�M. Ports�2HA�ei� , yTNm81a�077n72�Kolo04��0R. Arslanbeko�59&, J�D �(36}, 2986E�E���pd1} T�3aun��2���% 59}, 61�"8%��� pd2}{Qi~EŤ16 E9).C,3} P.Y. Cheu�oS�) ovanqY. Wo=�e��461} (12), 1360!E88AY�4AV$O. Papanya��Yu!C Grigoryan)BM \� �1��4�92:Zt5} Ranjit Singh, P.S.R. Prasad!� K. Bhatta�WjeKg nd RTharejafzE�28I�3:{6!9(R. Sasi Kum�V.P.N�mpoori)BC.P�Vallabhn�9a�191!EiM9Fus�� .��T664͔22�u� � � .�V�>�E���17401E�� %arXiv:� /0403025�PREuwc}�OW.\? Saarloos�CaroliR+55a�53Ew:�f � u  �${\em Gas D �%8ics} (Sp�R9Berlin,� 6R�a <} M. Surendra, Dg rav�� S. Plano,Rv7�v51��1E�.� �7} G.J��HagelaAb,F.J. de HoogI_$G.M.W. Kro[a, %�:& :145# 6:KGM} KA�ll�� Bm�3�l483�a�=�Am} z�n6k  %%�+haus,��Dirksme2R�whmen, Schme�* �H. lebrandч�'"� 1�r 48E 892�t90} CA�dF��6n�LF.-J. Niedernostheid6� -'4!i742%'96i�2  !F�:}�V�2A�a254 �6�b 97} >"q c� Stefanov$S. Vrhovac)J. Ziv@ cE�I"IV Fri�� }, C�0que C4, 341-3Avn]4&Co Yu� ��,��Logvi63 )� h9� 98��.?��  �� G. VerwA� &.�SI<( %of Time-D"�[Advy=-Diffp-Re;�on "T��0%�> Ser�in �&u\l2&�33 7,�u 20032Wes�q W�zi�PrEw��6mFluid Dy&�ޡ2!m�-Verlag2�68 xjE.L. Gu@HA��Liehr, � 0Amiranashvili�Z�2E2 ���03621�m]Ym�( D.J� 6  Techn�, ersKA Eindhoven�I�?Nevlands( `4. ISBN 90-386-2035-7 \\ ��alexandria.tue.nl/extra2/200413150.pdf �>   docu' &׆.W`RX�der%/EhOSCILLATIONS, SEMICONDUCTOR{*S2M�.�!f cruc�Ghkc%�����]Q4 . No*�a*ťBkee��>sel��sL�s&��. OA��|tsgqr *�1H�}�im��N&*>  � }Ek"�ly  ,+ *3a�^��r exist�)�1.+v]>�b (pr�i?). A�< fix ��J,�(!WB2�ly 7�maa ^wh"hoi�nr�K,��' ��}wbekIao�j�Ih�Z(,' �  ��}a em�2�k8w�-8`�/v!,2p ION CROSSING TIME, NO STRIQ�DESCRIPA�8 OF MECHANISM\\"_"AL"�81"�+!�c�!peak.sA����* M%^�r�cor ��6�one ovFof magn��l�NLD*�I���.�Vk6� �m�/r+$e� ly u�% [ �a}B�equ s"oG'equival�bZe��A�-�*�"s7Mz�on6.a,4�}p�0��!s�?�=+SLtr�J8o9� �A�# k&�4�"!~mo�onsBSel����%�gn,,5��)y�::&1Ms��tS�7�%%�s�O s mabB5F7� 5���fz}s�Sg � .S$N.+ti�%sir�emS-S ��9�Ho6ƌ9�8l�.�QE�.� I��up<�_ded�kappear"!po�-columYw���mor a6�.js: r��%e$/" ��C0Xp-��6�\A�a> r(n phenomena�st*d�6�h:�CtwQh� �"J�2"ofBPF|7� a�q�cl� �*!�GK.�~.\. "�7�o3juO� �/hi\��Ti�ga�+o"YwpD~es ��=l%>avalanc�&fE�g�)>"i��a�#���7. ��s�1i%�M�Eiy��R�I�cr�)H6�z ���be�~>�$1�3bt)� uish..[�y�(qd)�u�`)�2��b ithdrawn �As2�,6�ris_J'�zx2� �'3.�QPI�'mL�mo��� s��e��C!�$by +�}.=�}�$90,rade92}!�m��� !�re eff!ev�� B4���A2-d�/s .T a"Y2m(MX�"is�Ktwo*�;etl5W ���N$J�� q+$U$!`���6�GRD}&=q$tU(x,y,t)=74F}(U,J)�n(J6(G (�JY;mnoL<operatm�)F, G}$�� aW�.$�|�_ �_x'y ��}-$�.gabkernel�1E��X�ly�%�3tor-in 5or%e stud� [����,,�S�� CA)biolog=���ref 7 If v�O3lay connAM�o� ealm�,E�tM\"� � ����io. y. }$� AdiaVlc e� �- } %Let's� e �!�: �)=�� If�IbT:! �aX$\rho$uAp�ŀUy�1�E�/B�Kg$t �Q�1�t�}d�5G�a u%�. *S 6�(i�de�(a>la %�9h�qUJd A1&.�u57E�u) + % iE��)~c2}Scrho�skQ�erho�cd3} %&&<(�t=0:�4�Zs 2(yt=>�rho:8FPrho��2�e�a�%!�"|" � c��e��6:"-ZUiL&"Y� q�D�]#-R_"mv}{!f_s}:�7!B�L="t� &�p\;dz �_7�Ma*�OY a�o��o�U� s=C_sR!8nde�)p���F�R=�SF�� [Sf&w�8��dar^T؛�=A�"��h0�_p5})] �q9g8!�w=U|�5Vj!�E3 �\=zP0~keaWZ�iOU>i�/*� 2!C)ecle"�_f�� &a\toXZ�N w!Pag1+�Q) � !6 L$�m� a�%8�%.�� A"st�� �� � !t�l?�h�^!HA�_ lik�%S$: $O��a�=OQ��["�[F)o: r��1�6�,E�x�Gm&�7u�=m��?�=.gP%å�=O(1)$| h�$ ��mu�T�9��t�ttitut\= +/\�`@EY�C6�!Jis� r7�J �b !w9����ŌuWZ�9�ILYs.� 1-!�$$. To focu�dVd1�A6,L+ew) )�$\barK=�] tau$Y2c> ]�T�iB�P� "Z`gŢmu*#y{]} s2�Ճ s)+B�Z�\la%Vg2�[AŦe�al>�~`�wg6�tљ�Ř s(L,�՘͕1Lɚ\�ՙmu:�͍� M_cAo�.Aak�^=�,.�5s AB!�- � 63E": cA�tVί� �<1 J�Q tau=�i � l�* :Dl�3�B YYS��( yy��� [� ���� m4f. He� ��]�><web972�Ug0E� Big(YL+\a��U�) )\;[s1�]\ P �XS�� �u����4e6� is neglig�+, .::. g0QZ���EZWl���"lsTW��st�1a.Qllows:����5 �= geneo�#B am�7�A!���� leave�yMC.\�d�9w n�ї ) h m����h^� . A� a�M[dNsp%�) mk� ^%8)4}) ��"- at� i%��xa�!]\m�ex�d��6d�A �f��*)�[�|� b�M|&.gW" sE} ]�n��\;[a�U ](L)�Wa z^L :� (z))d QJU�� ��)L01� !�A%%!2e� �%�b��&y�E0��a�(2�+u�)� \ "2}q� %!"(0��&J $L�� �sE}Z�� �f XmB� P�5%��$��t% @by�J��9� "�!V�"eTLoato�� &T �?U +� ��=j(� ��i LY ���tsoE" m�m"9$n er�{=��@h1}&�N�&+*���ZQ^2ĸb�M!�h2v 9t}? =-:)Uf .lbB|_L� E.VN�_^|_L6�.VzF�Q5vzy(~�i���nl1�I�2kV�Q�+6���K }&&.NY�F�E�C |_L �_��)�P� A�v��m�.tam���'�)E}u$�5�E 6&u(.( -u�5%$,��:�+ �Ot}oq$y�b@t/sUi� or.�� $up�27��F)��_We��f! �k3� vari�&�ono����bm��� ac@�""�.AaiV��& , fu�QW NIl^&�7�esn� � n���e�hby spli2:�E( i�E��C��eaE}_L(9�}Er�5�z��Y�i1T �� %,"Œ placpK� corrw-" �*�!!3K1����&=m�:�+��2.~h`��}$��0a�Ka�.�-`re�Bl$�.7R��h*�}"5��O�oY���V�<*�1_L*v ��!F$-MF�*�a+�� *0�JI m\;�j(1-e^"q dy\;:^_L5�)�)��2��NoD= if $�(L�;`�lY t $t=)R��T�� >hc�����Uy'alld *�hQ>�9�$jl8�A,y� "2=$ �=� z._LU5$ K w2U &=& L.�(y+� 0^Ldz\;5Kz*�!eaNgv\���& ]��!�H h3}) r�"�to "�G���eqnI&�{��q�U� �c�^2Iu0 �E�mJI�+2 _]�M�-I�1+�dz��\; ��&�E��r�7�Jort h���`rhog 1>�%�e W� !�abb�)� (U1_s=13.1��\"e� 1-_L� 046$v2a k&=&Lge�N}{R_s}.���hIqg _e} ,d_g}{d_s} %=W@$)(L\kappa_ M7 ��T_s}{�"&�q����mRZ�S )QCCC_gj &&C_"�sM_0 s � C_gM\t ^gq�{F-r^{-1}?g��_eq܅�+�n�lm�A�i��A�R�"� _L %�E_Y�%<�g# Q�x�k��k}Q� %\%+Q�R�5@%�t\\�+ =1)j%ia�LE_L-o.P1�%-?�L} ? 1�2� %+�-�m� K �6�=-5 ).�i/\; �.� !�R� }{(1+k)\;AZ}y�|h O1g=P v%�1 �v� -&�5+2�- }{2L1�a��0ea %or�7 n<$ %\beMZE�%-Y[�tt E_L.� ;!���) ]= %�X}EB=&k)$-1inVƖ� %-z)v{}{L��I=.67�!� .~~~fz�6�:sy0 %\ee{ (��&� 'M]� (�,somQengthy) N� ����T�2�=F(�lA�)$JG)>&*= GVH"*R+���� wo� ars ?�!"�#� "�#�2B��calar&���r*�]B�@ Two- :�fh!:}A/We�ed Au"� !o �&� .�P,r��+ou� w jmed� �+aN�� !��CG+�Q(?�%(�%3E| �f1�$ exceptDX!%P i�$?�6�R� /��N1 # =- ^2.C ;2z�|� ��Yq���;A����+/�un=�C=\ion�G1*J��Q��$, you D( find�R+(&&)Q�A.@1VV��eld�"��!N�fQ.�2�\ll1$ TIy�'por�&w&"& ZU}==K�cA�V ��w0>T!D|$�8%�$:� . BΒo5xYD)jh�.�c(,�Uob��ly�N�+s?*"��`e��E�2-$,:\\ 1) switc�y on,\\ 2)���'� 32+ ff =%)�Sing\\ 5q� ers:b/,, L, k, R_s,� �j$ 2�3A.�%VUjm4�*��3`an!'put $k�Dw,n�Rb29b��U0$,mweǢ$k���*y�S.&ldu+$�c61-n!ʥO!��!�Y�e)$k�!vaV)�)&=&�a�I[.4y� 1�wE��dlJd,2� �=|M�\��m Nm f 6�ea Jn�=�6��!n iB���&[Jk<AL]M�1�.�1�:�+>���U.�I�5}� ��� �f � � R 2�&&-  v 1)�� J�  F�&1]=^��9i@x!�z"r�  = ��y2�m�a*ee�$��Azr�ť_͈�1*<F&��,A|re�1K�.9T�)��}1�=V�e�eijOAU��U�5$ Ohm's law&i 2T(� a-�U}_�#)��/-��Rb=)��:,5�J�.@O6h:� 1��Jm��P1�9�,����N0�/�A � /i�39,� �T�=���� lastmQ���w �&v�,��,��,��,�Asw9x0�ce�i�W #:�?=, 0%9�I�AO\�tau\m��z�%�j_e,�N6��/) j(�l*B!�r�nnE��9�p s� �.ãt�aacq�� � 6j'1�Ns4-�z vˣ \muj�9i�E}) \g2ZmՌ&=�%"o�z�}V�%v jӣbaH_.ף "� (fߣ 3)-ro-6r30b�1";h�%�Ena�"�#O $�-Bf���E9Atau�]g "� �z�� &W�V[ I�BG j �U\�?|� [12pt]{ioAW�5uRkckage ms} . epsf6��x6fancyhdrSnew��8and{\dtot}[2] {T� d {#1} }  2}} �2n 333 d^{#3}9#2 �= dpar2o1�=R}A}0 p�v�h �/ @/2J��d}R�2 D:Cu� !+BUOL}[1]�S�AmrHph΋_O}}\!� �p :�eqref E>%#1}$re.�Re #&"Re}(#1F&Im.&Im&.JII}[0�p"!m2YDlejos&athbb{C> sign#��\,:�!.�#1>Harccot.J BLdi�,displaystyle:q��)y {1 9�dis {Nabs�{%�| #1 )�|a}�Uq�title[AFW�i���. ��[Zum "� s] {�J J&.� \ 9{Juan�SM�V(iu$^1$\footX�4[7]{To whom co�l(,so��)addged (jm F8@fis.upv.es)}, H isco�HVi��oro��,, Mar{\'\i}aXH`n$^3$, Javier F. Urchuegu -�E�Pedro Fern\'andez de C\'ordoba$^4$} \a �{7D�ptaPEo.F T8sica Aplicada, "F0dad Polit\'ec!F4VA,cia, E-46022Spain!�-{�Bv8Lenguajes y CieM45 la�Gci\'on GUni=:�$de M\'alag}29071J}3F}Termodi!4mic.�ta��\`{e}� �4100 Burjassot,Nh4FhMatem\'w�\6\�G�q abst2A} sc�[� ����u"�> waak}c�"�% s,�X q�grow��&&}^y mea&� 2B���`�a������ly ado�ޅ proj�s�1A��� tory�"@cs�@��ntE���*�o�.rG��ߕle[�� finiu�ercA"B��wa0np�-red%C_ho?���:��.�h�;H-�G&=CA~cA�i7�-��h4bb��nd]/L Pcs{03.65.Nk, 05.45.Dfa�0submitto{\EJP make���e\{In/�p} } BothF�%Xel��idAh!d����Tzs "�d� :0 gy b!i9�B�X`$&!Kon6�c0Kronig-Penney�4�$'istE��A)�U����!$of square-�}.D� ^ ],Liboff�s�$8�(Dj{/�?t!�J� y wave�a��(�c 5i�I thus�a�9�oM L"I�ڴof a $4\40G�� � Szmu��cz}�P31ly(me �Ged�m�e��!c�~o��9 � �� eadiS&dae�tofi1f(Sprung}. Am$4o�8�Bpj*b,b�>���;c��ly�A s $2-21�?:Aba"� algyQ��da�n)^��onR|or ��ner�Griffith? More�B�3�9ethod� ;to�lDn7"ʘ '�a piecewUCA�\�Cf�?ion-�Kalotaswa�3�h�b��Ii��'de�A 8sl�haF 8nd3{(a< ;u<m�8�2icM0���1��,F�=Che!UMMw��eed her�zIn��FyqG3�@͓ѿA�aA�1e�f�f/�!) becaus�e�I�".GNjtudA��� �H�!ProDe���!R�C!%2�qu2 a�EBach-�M� 4lbrot,Ficker}.@GE h_aa��in�7 view����4s are self-sim�ilar structures obtained by performing a basic operation, called {\it generator}, on a given geometrical object called {\it initiator}, and repeating this process on multiple levels; in each one of them, an object composed of sub-units of itself is created that resembles the stru% [ whole o�D. Mathematically, � pr!�ty should hold in all scales. However, inh( real worldE0ere are lower%dupper bounds over which suelf-sim%�4behavior applilFractalsS becom)�$useful toot be able to model diverse phys�l systems~\cite{Berry,Karman}!rLd have new technolog8�cE,=�h!� Zassoci�� >distribe� of �Y? MoreoA�, i� n!-EEmen!�8ny 1!8 language, e.g.I`\emph{��8} software pack/ accesi��Tundergraduate students �only ��program�2 ex!Y0ence, so that� adop�!Fpro�|! ign�ahũRs cours�� Star��5G5���~ Z�ta9^ barriA�!u0extension to >"5� ia�Lstraightforward one;�)E to.�@sE�be base90 a recursive 6��� volv�� pos)�improv%��-� =�L skills. FurthermoreE��)v �intro��! Js t!�a�FfI[%gallexityA�-�onv Q�$�-12��%referrT��3��.QI�(. After cr� � >f uٛ"� es �� untilmfi� next�C�Tata� $d_i$. U�u�%a�jKb)�is2�� nZ widetilde� }�ϥ��\Z�d_AJ^� = ZA W^MJ&a%a�5t��)� $PL�b�f���iN6��\\:��brz�9#"!< & 0 �k 0 &(-6(Nw\�2~��.= P�Z�)&��~NB�� �V2�P� P�}��*��  $N$*( j� i$!ix�2 cory on�� width.CV_0� V_{N+r�  surr��Kp r� �d��in�y>� B-. ndFce3be"Vsolve�� 6����~T�N� *�$J<,!,� Z�5�9�- su"� *^ � .�b��;Q`�AbzD0Y�0/B�i D_{0�X�7� 1\V�b\P_1�.�2��2t2R�Ny�Emos��m,�SfSM��aP�}�  N�!�� M =2�!bI  \q_{i=1}^N 0����B)�"� Di�B�u�*�A�,misJ.���}rof a �� !�� from4 A�� $N$-���Pi�"b*�2 $M$��j�)y��� " M_{1  E�%q M_{22V� �80V0e�&T no&xmo�1�Uf����5� .��"sR$U�C>&hN*$0Liboff,Pedro}~Rb � abs{�0}}� +���h)z11u_ \m� and}� Tqki"\,N a�Qku. �� >} 0+A�:��"�"��X3�X�y}F:�ta�   6'U�IkA? whit�d black�a��#:)$k,\mathcal{V}$��241&�P'!�wresults}�R A�K&��iq�,r�6E� .62�#mea� an ite�v} n�ion3fir�(tep ($S=0$)�o � eg�$# length <m &:1: divid( >�"ree#l��D N $1/3� remov%� � r$ne t ,� !� stage $S$� w / $2^S$ w2c3^{-S}� $2^S-1$ gap��.sge $S+1����� each!th�lintGreeDF}� �J�� J�N�o�@ four5�ag�re > �(clarity. No$S�)Eyx pr"���pre�� 6�>�5^�9som\"Eb%�aB�2^as �i�'a)A���.u at � $p_M$�$$(3^M-1)/2!��.b1B�M�-separ� by4J1!�samoa2��``�"��is���i�urcD\Lambda=2\,\cdot\,A�M}$�2� p%�" 2�,=�,2����8 e&/"#M �! ( �l?E� :#theoryhs��&( Sec. 2. It�mUd(to normaliz��� � `he�)=% 3%1�!�')e 1H$ �my U&*� var�% s \[�hi=-�\, s&>E}V�J� \phi_�enR'\. \] �s.� Rfor��$>i�}e0�*4 *� , $R$,E;!6b�3 T� t��1�6$, a�U�v�(�(O'ain���b!�gap�V�*��&�U34Kronig-Penney b'�  2}�$isi�numer�(ly ca4dA( $3.2519 <%�$ < 3.6222$515�:�2$.� D \n�4�R 2S&�&V�� f����s $p_2$� , 3$�  !� $p_4$ (c)��a"�1�u�dq�$a${�(55 2!2$>x ITisNŎv�a Bloch�fy) does���A� aUS�ic�an`+f9$��P }1aQ�+$vanish ($R�. O�evanes��2�s cha'er�#Y"lex)(vector, $k$a:e�\#'%�� Vf . F%Sis+,s�whe!0eA�m$8 s�ki�a e >+ may p *} 9�2F*�#effect��5������ 3��p*��%cQ�S=U�S=:�S=����F� 2�A�w�D� y�2�$approaches� ya���&C&UE7 spatialug< increases, illu (�(F"�/fiearg�>�(full) pic&�(. Although,� A�graph��\ �-�az��? e�A� appa�-l{ ! i�=4��*8is always smoll�,an-?'�y�d�"s"1.�n�!�B|}for�~�) M�top��A� (middle)�� A�bottom)"o how!�B9 at ! highe�1a *modO%d �/,Ta�*.�+�previousiW� at is�wY� T$$rum exhibip(�*�."h rofi�0Kre�u�A�.�,it&�$�2�K�(� y � peakAz�  is��2� �  narr"�1t�2r@�!A>. Zero.�f�seֵ��oc+�!! ific�c} �ia�wh! & to� =Uis ":+at ot!�di:D. C*.ng�j�_ !E i�"0 �W zero� �%�� is observU)TD -!�% e�nan!�du|2!�&s( ``de�ps" 2� ��2�^�>yBe�A?*0sequence. "�)C&�)"�2�"�  �/�"k3�"� " "� uje.k�1�&ZsNN�&sy ause0� u�-ss�-4, textbook-lik�d$�"/ .�*-er &�,�0Z1roced�"�&����f al&nsA'�4�� ��u.�/suppor� a U ��2� y��^v,was�ly&]*d�f!", wq1au�>O�!�%���$e�5�D#V K.� ��e�TB?u5���m��=2;A�9RNis2w�Z�i�?eAs3Q�P +1i��2 labo78ie�.r:�1�@ "6 <1,�vi� 1wer�6}fdevelop�"0F0aI�1b*�!�u�a7ols. Fur�`p0ML ge�8y!%a�Ml!�t�' # opic1_~�0�greAGE�wy�2��0 closel�l�t�r sear�ne� \ackx.authoi0r��ank!Lto Prof. Sarira Sahuժp Instituto de Ciencias Nuclea�0?+ Un8pidad Aut\'onoma de M\'exico,  D t0Juan I. Ramosv.O de:0alaga, Spain,1:ir�}7 comm�3]sugges�<s. J.AW4O84P. Fern\'andez�$\'ordoba wH�P���, Nacio!�I+D+I)�1�@ TIC 2002-04527-C 2 (�@). F.R. Villatoro�Q.e!4,BFM2001-1902%Direcci!W Gal�Inv�ga , Minisd.�@ y Tecnolog\'{\i}1H . Pa�5U*�$ork�done durE�he visi�6J 2� =�� a grant �.�0 Polit\'ecnicA, ValEa,-\}``Pk5"In[ ivo R3>�la UPV!� 4".} %\���)M�D,year,title,editor��newAC and{1h}[4]{#1 #2 {\em {#3}} (#4)}W��BX jour+0vol,pp} 2Y3}[5JZ({\bf #4} #5�1Biblif6phy{19� \b& em2�} � {Kj*(l C} {1996I�a!�Solid� te P�;s'@Wiley, New York} p=2j  R; 2003j�Qu�Me�;"(Benjamin Cu>7,s, Redwood C / CA2y,Szmulowicz} 5@  FX 1997Eur. J.�.18} {3926Vprung:R0 D W L, Siget J D, Wu H� d MartorJ4J^200�"{Am6v6v71!�9� Griffiths6y D J��(Steinke C A e�"Fe9} {1372�Kalota:c  T MaLee A)�199]F92} {276�M�3lbrot2  B B�198v �xi> G�of Na�*,Freeman, San+ncisco2�Ficker66  T�,Benesovsky PT��B�23} {4A�=��>6^--Klein SPqRJ�Rd. OptEe4W213a�9�?2�  G P, McD�Pd G S,exG H CIi(Woederman J � 1999�9:40!�1382-C?6x G,$9lan WA��/l? JUpe�� Let � 28} {9712n<6nRFp�� 2004nEx+ �*A� {4226�Q?2U �HBialynicki-Birula I)O,Zyczkowski Knq��. Rev�85�508#=�A"�?2} S%N0Koshmanenko V.kRepB��45��06�"�>.�  K)�199%6A�a��o3S15:�"�>L'p} re�H N L?1�D A:�B.z aA� 42932 I�$^a%!$Zhabin D N�p306]�#��b� Pw(Urchuegu{\' ��%GFundaA o8" F %s�Cu) t � Ingenier #a�Te6, Servic� Public5 �.$ j�2 2Z� �24Schulkin B, Sz�.sik��a� F�Bici J�$qj>�7�,105a� $bib��) docu!} K�%�2 %6(>4Andrzej Adamcz��wk Faif�V% ��2�%!�8class[aps,pra,p�Hint,groupedaddress,Xpacs,% t� enli!�� nofootinbib,floatfix]{revtex4} %Zh twocolumnji%z\ \u� �@ {ams�$,amssymb fonts,bm}2)~x6d �6Q(rsfs} \re.H ,vec}[1]{\bm{�,rm{#1}}} % b�F�Cgh�nr 3D- �&i& ,style{apsrev} =��1�} �^2^ \j &� t $\�! ol{dt\mu}M.Ho�-�den� hydrogens � {>�& mailN(a8.am8P@ifj.edu.pl} \affilia {�eNu��@ ics,��$sh Academy� SD$ces, Radzi�Gdego 152, PL-31342~Krak\'owC�( � Markwi��4mark@rogova.ru:� Russian R�C?",r Kurchatov �, lSquare~1, RU-123182~Moscow, T�(date{\today�ab�ct�,Re-�%9! @muonic molecule $%�$�$!�4$ atom colli-wco1�H/D/T tB�$�(r�A~� & 71B�$�~giz2�Van HT'�le-2ZRi�)#�"! �r--9%�wJ ���$��%�:e-:,sE�$a~polycrysQine harm%fs�!soC9, � asympto�H�1� �cV�+ � �;"�s,Xid% any � or$:se-flui�q�-isotope �(. N]"5D.wJ!5=FMe r�Q^a�� atXQsu>u!�%� Deby�< ��6otrlA3)Hq%&U�-m�A�A1D��i!zrG rongQ~ expl�#Uunexpec> \;nta�$+ K ti�Ar,�9��)aT �CE*0-point vibrE��a�1+5�q�s bt.Qzuqa�Iys, eveEI0($\sim$~1~eV)}�ai�M�i�,im��D7%n�!��(time-of-fli��mea!�\ �5�K:[ , ca�Gd @@ at TRIUMFaDl!H!%mee�%U��:S!E ��Zfixe�i� temper� .CE?�>�" in g�ag�e%���! PSI � RIKEN-RAL!(M"s2�� \M {34.50.-� make�P�R "�"� ion}Z��A~�(��Dtud��M�]�1�6�ar ion -�!uRF�)S�#!mhGsu5PH�A< �isw^s a~keM)o�B�,-catalyzed fuFA�mu$CF)�a~!�mixtq�attted}� \%est bec, b�f ��Jn 100 ti1�gers77,jone86,breu87,acke99} accord[,-|a� %� O2*�e \long'2} \, ^{4}\�8{He}+n+\mu^{-}+ 417.6~MeV} \,. � .X% "<A!G!�$)4 cycle"var� BV-� !�l��2�AE�ofB phenOB�&ic,��ar,^)n� }(se! view1\%NP9,pono90,froe92}). "�Q,� ��zVE�looB� �F� GL))�}y�r�@al�"$ber~$J=1$,���J&v&��bin��ZXy $\varepsilon_{Jv=11}\�$,x{}-0.63$~eV�oq��% �R �!H� :Jr�< � m��'s)�SNRefs.-4vesm67,petr85,"H86b <8c,% cohe89,faif  91,leon94596}). %* se�, takain"a*un" !.�ini :b a�or fewQ\z�>:�5� e�N��UataA9, dilute gase�#M�*�T� �-is unab�#o�� J�� �s�� W Eə^u!�3 cerE~noj ar depend�!1�yp �Ap � yity-Չ�4,aver01}, puzzGR. �(q�kawa03#�,�7c=!�$P:I8 : = �fuji99,D00,porc01,mars01}.A5r�*iW% ne� ar%�� infl�"!A�-body�!��ic-' 90� � � At36 ��Q"�P�$ani'�g�&�ɯ�{A�1�ct knowA�their ro�|��4neutron absorpe�by�-i��$�v� -Jlamb39,% 60}�)C� n� Jt�be��ed J erm�ATdlz_ �+60}-&�I"�PV1 Van~� 5vanh54}!��O) of�%o5nt�&;m0"� i$%��oat m��K"�!to a~i)" �'IMer�TM("k&to adap � o�1smG!c� 5�fy E)�6��ĭ�͖:� in�4M�ar �>s �#�nA7 Fukushima-U\fuku93}. He employed a~c�@m-59�,*� ab *i&sN�u< lattice dynamicJ"[P��=P� dem�7� anGQorV e of phonon9a��W9T- ��. His .! limi� to� -�E�u�!� ({}10$~kbar)�V�(6�� �+H �(��V �jsmLly� ���X2}ll|&�Y %li$�Tv9@�-1� � �q���%�Samplitud/ &\&�u�M[)r� -� very "Z!�u(Thu!��al'�-�82�P5 WU8M�@silv80,soue86}. O�3E is �*e�e�roughJ>e�� ��rix el�for"� E�A>)[)g%Ref m9 %Tf�U��s�$8-a�A�2 �=h.~�7 ac0 hre�\ �*����� �Q�� �:{�D$�21��;!xid# ,� t%s�7 to w�'has�Ore~"G[P �&�]�-���6e� a����!l'dda7:�,�.id t h low-q: �"7 s,�#=�*$detail in~=�6]�+R",* ,V�|]��e� :�~)z5I�Aj� Q ��5�amS |W�^asm E.!k_qR �L.N'nj%+ avail�  i�U� �E-�E&-�:� S"X���,� dd!�!�M���ee>�y^�Vnaq.eir!oW ayl:-)�b4�del� y. As a~i�F)�s�Gu�e+�a~)�dexA>sI<6��*in"{�5&n�/�5�]o>CDy 6�G "� -F:s lea�]%��B/traA�$dd$-<0tA7�0p;n^ II&at~y-�� 97e�Be��w� �.a~J�oj�k-MF�+� !y����0 �valev%�f-A�$�� }� iD"^of�.�a�a~free& !!Bd0Breit-Wigner Qk-.8}H .j"� e��h�W*U2�Q4or $\gamma$-ra�*�3&  by heav& � �~ assulE�a0xWis=8 p��- hang�-f��gaZ yZa~�^� a~sm�d / WEl�w� Q!%pecial M�^�%����\�C I=� a �9at�oC:� ($\lesssi� meV),<�2�P�"��,�� � x� � negs)�%rI45�0",^*� 5�qCsQ>acQ��`~rigid��. S���7A�va� ��A1���f.� 5)�5� FX2�kin/%r!�d4hG;E�ct lv�s���[ "� $|beaiInB�}R&;_e8�� ledga5t���6n��edi+�G7 �iI/�<�@�7 sec:�)molA~brief>�M�t� z!�n~iso�/��-MmQ B�. A�U2� � \� ��&i-s,-ja@�y-<j "E��a~��le�L,A�c6u)~:(�� t*�%ula��57B���:e *�ɲria6�3�Eu�to(C0!�V��*p����!m&5"� Oh! R�i�in��b� ����  i>;dtm-sol�Oy�'� 5�a~^;�<Ve���: %�A�5�s HD,� � d DT) �� �I|! some typ�G� Q���as", %\a���gM�%�I�.��2Q^BafT2 &�m�� ;[8�E��� �A2<a0ortho-� !( �aent�!��o� �a ar� �wa�co"�gm�=�mea��N s8G�@&_a�"O . Z�b "B"S� �A��"9.�t"�w91�}�!Qr(!W�>on>�=na[lA m�:  fe5r}:&~g�mr|(I )_F + (W8D}C)^I_{\nu_iK_�Ul6�cbigl[(�)^S�}\,ceer] >fK_O1,,�VC�M�,�, or TN uad Q% \e$c = p,\, d #$or~} t \,,��%�OD$C?6�!�!�AK"�-*�$(�)KK�<E spin~$�'{I�cT� A�H B� �=eX�U!yF%� bE ZF}$2aterV!u (CMS)�7��"L `�[ar{ilex $1� cee]%$� �%n~)!�)�L!Ne Q��� y/ e � � *� u� �lex�9� ec{S1b i%bD Z� a~lo*��< ("�b���b���]�%� 6� ~$|\9�a �|vlVBdQ~q�Nv�"�j� �8R� dek"%1��do"&-���ar1N:���n� n�"A� fulfilledaDnA�YN A�s � �?value!�%^0_{if!�i is &�o Vesman's �:s�� R *�&�J.V�A~.�. ���H[htb]��LhiHp! \u ,s[w�Y=8cm]{ �-_fi"Zh3cOhEnergam��V���%��2i&� e.E��&> �T �qye.�bfigK bal_A&}��.� - "kD� >=A�~schemY p bal�@�} �+$��ňIo� $\�da^{SF}�#�a,�m�Y}$��!�ela!C%�2!GB9BK}$!H:� decaPs $e=\hslash=m_e=$~1)B���X%%"Ofel_E�vaz� = 2\pi A�2� \int\Wd^3k}{(!)^3�% \lvert Ilf}(`3$)\r^2Am, \.!��-4 )&9 �%m!f� 8f�$J��2� ��c�Ey)� � �%�dra *�L$,}. Factor~$)($��A^F�"ag� 4 � /@�ABs};%�Ba�^�>#� q  angu�@m% QA�w . Ve �� k � /u�� �w9 ed�� � 7Y/~ ,\ nP,�� �o2l$Q� moJ�� %Y��Q�-�$ = k^2/(2\�2 XM}J!*�+i+x&MXM��nPh�re�Hd1^6y� �x�I!-sh(�leqyE)� �YFan�or�* Mct*?�fano61&�j�Y�x A5!Rec%�Q� ~��1Bvq =e� frac4)\ \, km}{\pie�I�b� 0u�e� $ N!�J�) .6�!�I� �n0-Wce ��a���U C5�:�� he Dirac:�a��~gres�C%iz.�KN_���\�QB�\�|J� r|^2%�B7.01~a+ :d+!O�[$.���!y'A�b��x�e*�M+Ms ��:$ ��- Eqs.RAand1P)��v b�>�,-t�s eq:AB_def@ sF" M� & = W_� ��xi(K_i!,� E�H2K_i+1}{3\,(2K_f+1)�� q_d A�  -�2S.GSEF.C\,&� � q�=� �=1$� ~L!+*8 7�@ 1 = 3\, (xaz) B�J)\t�1}Qc&�jF�1 & S Gd E^{\!2}B`�yAL6� q]cu�|brE"tsl �~�$�$3j$~�7r/M4m}&^s͇fP~$1�!2Zi6�� wa�vJ�%BC!D�):Y !M#}{3!�i��} K_i�2}1O 3AQn3 odd}A_ %j u =� % A~�a�_$rq_de�co.�%�&�Mdeuterin a~c"�"0W�TQh�+re�&"!�&� �� '�5:�-��"M.if-�i��:", ,2Xs��6QD&�  n]m �,p%-O�UVD�" ��&As �4$�Oe�љÑ�ab ���a�y2�%aq.} iwe omit E�a+Boltzman�y�6scribK pop�Q&� 1;a�+� %3a*q!#~gaurget. W&�N�!=O���ix�ڃl.h|0��is&!�h�� 5�P � ~$I��)d�_~P4�,v �teady:-� d*6^~$f.G,T� t� {*I~$T$, Eq݈�pL,adhVz:�a� �l� al m; D� A�m!%9~$\tn'}* }(T)$�&"`*'a~]nN%1K ��fi�%m�s+  c�F(cf.\jO)��_���0&`9�6���-r"�?a",Yva�]H M=`_�e+De%{}E�vs -itive!QL �]�A1�F%%7enl"�7�^?]7� w�H�$pN� peti99p2i�'O� T�a #pm��� &�,�#e��� �IY#l+<�.ns�Lncy�*�e|R2�6i5F� }G�*3,57,jeit95&%*��Q9d-L?'m%!JO.�*t&K&ydi�6^s�`)%. . It��$|:�Petrov9nr:F"dJ+p�;\�vbroader2J%1ks, 1�/HR life�&�. A�!.}e�i'� *�1�"*!����1v�%91}" )�8thres��y�sN�<0Y�,�)�V�.]& a!m��cD' 7v@"�&�%A�B*�&&� \����58c�v ��Y"�res�o_T mn� =:o � ��rp & * �\C_rJ {.vN� ^2+&d 4}?^�G ��!0�Hn�;a�qdth��_S$��)9�/S&�#�%dh�AI~$̓ �;Mvѩɢ^S�bc@ofBl �7M�~- tot_F�_S�) m _f +%�.y \,JE29.) �'e�*in .+8Ax&�7ai"�i*�T6�H a~di�7T ga"C5�q� �7�m!'. �,m�4(2i�Mp\to{}0Ni)�"�: ) teqw}�- �23A}�:� ==�� )E�J6� "s$�|�� \subs 7 on{M�of.�2� gen_�!��� * 6_a~� m&�pl7(�j%-G�is6i2� 2�i�&r(�  e imWL r� l*>�7�B�#��gy? ho �8��6 s��� �.-a~�[�}tU)�B�A�Er%P�9BI#642ZFj was dY*�i2T �;} trif�"�s �� kh or��*;*�:"|'c a�F�aF%[,�1Y=B  i%!GJ2c*� 2�*Q )Enot�`ictly "' ,"5\���ex!j!%�� �Ap� &-|*sea���Y4� th�:" y% �#M�M &'�=tT.�(2�%�8,�0??etr"�=�f&�%�y/a= Gdispens2��ak:AA� "����.��|U� �*�$.���[��2hemj�6<Yfof�Q��jɗ1�&R5���d-oa *Rsol��~FiJ�u B�2:?�u onse&Y4&[ S}_i�D?�,d1aO"�5�6 5of"T4~T4!g-K��3� ]@��S���7EDs.�,� (@Q �a�!�lMJ�85�!� m �V�5w �H� �und3��Q�"C0)�a,A~Hamiltonia��scr{H}x tot!$A��z� of a2�%�� 1$S$�%5 ��B�)�,M� wr�\�mwn.�+s��&� �1eq:H_�.��VR�� ,;#&_�M_{a\mu}�Zl�Q\�D a}^2_{R_{�ŗ ,_ (� r}_1)�+ 2%�D}C *�rho0\\ 3 &+ VH,R(:2)6c����!�.cm�mA��!R} �$� � po�na*!$ 9'CMco�IR*f�;A �!: I�[GF�_cmplx})�  5cm6�(�z. S�!���4b�EO }�q���~:h'. u B) 6 -E�)l�  % O�M9B�5�}���--Ɓg,�ecE�6 �v�#�k���@]�$QGA4% ;V�T ��9�s�9 FB���,b� !�$l$th61Z0vY��DE�)`R<)�M�is ��%�eca%l$;m2y�$~�~)*Q��=���'i i�1� �. F"\V$F:& 5&�g�)�--%)e��`%B�#�SJ �%>�2Y&e�)� w�+�~)8�%H�zWe 9!6i� ~$V$ �]1s�tha' %�"�we�e�at�a�b��&� `��-��.#Au y�&�-siz� xXis "t9�!*�6�g�5� �=-�:.@�&N "�R�%�its m�'umM�G6����&��s�0'dm_ ���va� =0'�l�":L�!mM�� �U�3B�� �F a-�� ~$E_��A�xa�� :J�"�"hC 0�ofsum_{j}&�! 2M_j�&.�Y2b j} +8 8'\neq j} U_{jj'��3& ���j��.���$j$thY�CMS�s�o6�._l�H}Er |$~�*� =�$u\!>_E~$j'$ty��$M��e� 8q�����6.B�Iy.�P��! yO��tomi �.�V� u]�IW.A "� �5M� b� i&rM8ta�arPsi�U� y q6s�" 1W� c c �o�. duct~` wfa 1�J�A�p�� }^{1S�  \,!- !&� ^&*7� Yrho_1�!%# xp(i� k}�~�b hY|0\ra"�&%UJ&� �w 28"18�bvQ�2H��eigenf��� ��o� s $H ��:9$��ii_ $)A9b6~ 9=X$6x}. U"W�֙- Z=1cl+ -�}_�a6aG0F��>�]ib o>O�]�]�� 2A^\b�l�� |0 f��6�~is m��at4I��AuF� ''!�le��lSOe�' $n�\,yA��O-0i=4 ly o�(��5A�%����s>�D!�m��659� 9i0��� ��qn�"�BNCe� q?2'6~qH'�΅���2C\ |��#6g = 6�i3��r},e@R}6i�c�2�,�Q� JFR�G�%�z)_ �"$^� a�M�Y;� �!��� � x  Jacobi��s. Re�&" U1%> L us~$c� �MAs �(Ia~�%f"\;TA륌c2 5 ��rec5�e5e�&]� $Z�"� m7i��E Z F�Z�&=2[ ]\A� ff l� "k b l>� j� ��� f7�Y}ava)'�"��nd{�6��QerJ;-�&� �&HJg = -\alph"���)=�%b�!&�?� L \equiv�41¡M�US{M2���oH=�%6� % $29u�.: m "` � =M_l4E�.4�~m+ �2#B turb��2� , duC reV `"��P �kE�v�B�iw Ied���e63 A E m. of~fl�&.  $|}0n}����2E E}_n>' u&  pa* 6u��*��# >L ��~�wfٞk 6s=J �0}^{Jv�E.!*s Iԥ f_B>x\, R2W f�3� ��� Vy� 2 %�.! ��.��j2 n-�H.f�,n/�� .� �)�Z���B���. \.F %� -�Z�b��>�5$b&fp-!�1)f��ed*� ~HR.sol�b�?�V��jU> =&� V�(�(e;���7A}_{i0,fx2rf;�2&\�*s���Y&��:�( +E_0J�(-}�a�)^2 +� *K4R�(nT7�iA5 c�DK-=1z��k�&)&� + E_0� �����˪](ra)��#�DIW e2�*%~(,:�j�*)�  �� "k��&P :X� nowm0nB�c%"$�5el1 :5Q l�N�Mp�bV IbV2��VWBy virtur Eqs. 5#�2})�+���e �  Y9a �)�lGR'5&YGn}|F� A�� R}_l)"� ��J�9��F|�9J0TA!B�"e>M21,.�Iy>��-f�4. Ave�>A�M9o��) �3+&B�~$\O {n_0��"�>� W4;ka�2*`0�3E 2?��E6DOF�7*X>�i ��N�P.|^��<x4A&b7is � 63A!�"X:7A A$a�#�6"+.>.I�AJZ�H>�$� р�7�4w.2!Pi�?5@��_d���)3%ܖ-��f.��A� b����B,int_{-\infty:  dE6j(E>��))<~�1-E��; .��]�6�EύQ�ex�Nowi*kW� "�6 ~$t$Be�/�!A� $ �$~� Qa6� Y te+�W�� !c& &��-�m{t_scepp:Mror}H,akhi47,wick5�+&�Fou��R%a��oE R��.SJ� b�_dt�� _�BeL.�@\ 4� �dF�6b�t�  .���& ��� �:R: �exp[it(*�� -E_0)]�] \,�%P(-iEt�F:F� ^deC�,�Z�M��~$E$,� JG!�&� ����m��W:.%k�B\,]1 &�  exp\ߢ [-it .rJq \yK�-&L62}� S|t|Ao .]!]>�"UB� 0I�?-R�l)� '�� ilde&� v O6!�ZitA� T�� 3 -itA�I *o:[6�W�0� Le�?EF�=solt ,e"Ua�2 olloN)��FR*g { _HeiA��)=n} ��F-U! & �"%�=aw.۫fx� �! �^l.�A�, =B�&�I$J��2Q}]-:k5? � REOB[":P)�Yi*nK j.��~�[V�(t)q�aD{}�*!�Z�*m e��B�"^+F$Heisenberg"*�� op_h8A�%ma�(t)A}E=t= )\O$� #:���#��{C�ll~$l $t{Emplo"ϵi ��% $�nVbM�2� |=1$�Mf,�Clǎ�4_geџ�:�H�@:�A�K�2}�w:� AA��S1.resak�"&.d2^0Jk�;vV["y% eits�(c�6!0"�P�)1�E*"�S_��F����� r� 7&A�>�^�5G4r� bigr� C 2� s��6YR�t!���)�nFy�� �F��!on9�"�Fb�Kzg� _Yj�n�1�)P!4lm�)�[Z�(� %�!�jG��1��>Ij��r\�$_T��j�aqU�Q%sA�&\,�-%;cal�2~��n"��Ne" |9"On�6s&�!�^�=\ag!�HBu.a` =0" q�s��rec"r7"-�cI\�9rj634UQ<"B� � ż 24b�(U4*��  w>  4��4,love8� b",fbE �1"X,"�FeYn �4!�i�zs�,�.�D63�/ or a*�]�. comm�4nd k\f� �- �-ɠ~D-�\���!UconWg*ru�-c BJ�$.i*2bD�-�1Jcan�<b"�.wJ��% 3���s"�m1I ,f5%P<�ar<e )i�fa7A%�JxC�'}���IiK_�YԿ"C�c�l%^�9A�F�;q:gi���.�6 6d2�"�W)���_�1��q�f��RA����Fd^{\,3}V�W\,�Oa�&�t�$j�WJ� .� �VZ��JRaV�=eMp aV-A�"(2�<]�5s�>� ~el�T" �%�>wY\�.�"�U-� �5�S}R��E ^0%�� !�n� �m$:"s":-~"� �"�K� �c / /&r.� &w",e�"��$ �<to~Yva�In&Ba��"f* &f) sU/�K,W ��6��/"pG ^F_{�22�p,""d��T _sume�L Y�Yv>,K_f, Si� **} �Rnu_f �"��� i=0anJ�"In *V����-c��mHi��1�1*��sccva�|mU�``�Ulut�>5~�sY#E% )�?�K����} conv!�nt to:<�@C�n)6g ~$\b��)7}1b:�6�5 $dt$��!&�}&�bY�I+��^ty �")):O�SA�lexA1�Gtwouo��s:E� {������"�<��v-�feOR�="�@s n!�to�~ �"C7�!m�. I *#M�"�@("�o͇nsY!�short7 8&� @/x G �_cay�.'�-�+,a. W.t�'s a�!U.^D' nePE�}c Y�JEA��*J� 27�Vle! 6 k,�8A�Z f��R�,Bx���nd2� K_f� (s dominant.�p situ%92-iAhns�H��Wi&b4e�t!'A|En�bo7UFs�ac>�.�>� bck_Q_k0.z.Q5�F'}( �{S!d  _� =E�x'|8 K_i'��=0���!�F� '/�[B0OCd��= Ž!..;jl*E~�Ff$mSu�=,o�K|wdue�����a ough"> e�t��fvl���͎ͬ��@� "��# s ha��o�en7-aJed yeL{62| �P����=1cO�[� H$_2|{(8�u$s�&� (12 �14.2~K)�a��)pay��s:-��U&�<1Nb��� �JO20OF��A �ͮs�g-HlŽ2KO !_!�IOjdOEz.�S�N�Ma���tcnd&� al� A�P2΄{ leM)�A�o)8\36,2dAts[ xX���i�`*gZ) dN��?mmute*� Z6.LO�7�atQ =y*EV��y: �m~�kx 50A�q� E}_Te�my�6:+��0&�5"� #H+�*W!4�~ !ʂ82$+ shif6#JJ� \�� �%�0�hV3rR%� <&=�2O��bZ�Fl�/(^?�al2)� _" d.�<�2�v"�z<�,.o�A^�}D ?2-in6�U�"���Y_i��J��b�_&1��it�iA:�)/o 2r  b'i�>�\RrN�8r�.�Y}_{ll�g,t)%��b��{�!���9ate�27���h*Za��~ &�~R�6:��K, multi���"Fa� $�a~�.� me�CYO�z �)��H� g�1�,���G��p"�#E�@6�)aE�!:�F�gsolV�N��l B \v�f.6"$�&.�I�^�(t\;� ��FNB�#F$big��� ���K�b��k>��� !�A�&�1�agy/>� F �D" e�o�X>=�1+%R6F �T�s �kɨ�RJ<�Dj H�Q �1&�C>�-- �$.��� ��6t�b ��O�G.�ZA�395���'�:1Q"=O��sa�~� T�" ��n Fۍ%(5��e�~�OK�a~g*�D ,/i� to6�%����[ g ��.� jose'���� a�A��I"�$ZV\kappa���6E��UZ2�P��G_s�7r; ��A:F�965� � *-qHqdQ �-*a��' *�CrH#�1}{.�*eQ/&;�U� O\ :t2Ŝe�atNx3�u.)'�Wim�,sp�Z,�4��JZ�u���������+�)6�� d^3 r\, ��>�� *,  [iI -I�h r}-\SV{}t) -�Un�)�)]��B !�mRJ�3fz� �s)��-�'�$a�I��cz�!8"]m� mA�k�u<� 2.�.��D��!!6��� A3~ously*�H&.YK~ � 6�xY�by~>� or�(E*e Jy e_�T in�i@VanܡFX�2<2O,)9)=�.2�..)r\,A� >�\,�7 6UE�!�!�U� t)-r]T(>�� Α~�],6�6u�a~s��r� F�6� Bso�5v�K�= ! ^��>-CF'E�'^�ht~���en_Jc!� Ua@�&� �;f}2h�6�@^3-J�["?Zoa�F�and~�� �>��g�+ %6,n�4r�*Wn}"r:=. �(2�A / M.�A� - 1�~� :�� E}}_T < 0C %��RN%3. � 6z �T H[>, ��"t�Z�Xa{n&�io"J�p !��:��P��low{ � wme� C � "& �N0("a4T& � �$.��iy�Y�"�}��a~3�ectbe#%"f�V %Gosjf >�b�^~$5�m�^7@*�Zs���� AbGaߨ shap"qi6E&~!�AkG2= a�biggl[��6�}��\ (t~3/r]^{3/9hexp l[^>�D�GkgD \, r�:vr] :� ��Y_%�Ŷa2� Q Dx�a�[-�"Y4� ��2q��i�]N�wTB��%�$a~cubic Br�Ft�,"� � (t)=~�%,"�F�, (�.: ��^{"�8w4� Z(w)}{w!.� (igl\{\coth(2 beta_T w�!�l[&�Fcos(w��"�* -i\sin\���� *9 n�l^*)l 6� �$�$J�Sp,�ie�_zjRq�6Ew�H1��(A� = 0 �,wuw > w��max�K� Z(-w)?,``�KjE�� $-�=(k�DB} T)U� $ ($o&�s'�u�g_&3F{}n}( S����,(2W)^n}{n !}"�8�� �= phexp!t�Fo6�1}(a�><��JX>z\] RAzr<�( g_1(z+w,T% <6�n���J�w' �69�-w� n-�!��>cA�� z�g_Z�&�w{)������)� 1:�`��_Mft[\,n_{�<�+v ]�� g_nff.l%\FRfH� p=�i�a3� �� ~$2W/�Zۜ-Wl�f�S5a���*c?S� �uF y$F�0*6#2WV2W(^ )�~)�}r �s }\,6�9��&2aBos"�UzK+ _fac�# >X!\li��c w)-q`�Fv4 The Breit-Wi��gner term in expansion~(\ref{eq:resrat_gam_phon}) describes recoil-less resonant formation. The sum with higher powers of~$2W$ correspond to quasiresonant muonic molecule formation with simultaneous phonon creation or annihilation. In particular, the ter �~$n=1$ d��H connected with creR` of one !#onn�the strong-binding limit $2W\ll{}1$, only few lowest !�s in~��@are significant. !q � �APis more general than  alog!XGA�Ref.~\cite{sing60}, which includes �Breit-WiE[factor �in%non �Ex�is (8 should be takev8to account alsoEBs, unlA�~ natu�reE�ce width� uch smallA�`han~$w_{\text{max}}$. For%�gtrsim)�,the approxim%�~.<_shift}) and Eq.26< !�xno longer valid. When $dd\mu$]}isA�cerned,��s%�Dvery narrow. Thus,)9ase 4MvD\varGamma_S\to{}0$`Hpractically reached!�eN� tends to�d $\delta$\nobreakdash-funca� profile% $g_{~ {}n}�Dg_n$. As a~result,z=Ee�5+$a~simpler � , derived!]�Ladam01} % \begin{equ%�$} \label�� sol5 +split*Lmbda^{SF}_{\nu_iK_i, tfK_f} =& \, 2\pi N B_{if} <vert V \r8^2 \exp(-2W) \\(@&\times \left[\, )e�(\omega) +\sum_{n=1}^{\infty} g_n!Ft \frac{(2W)^n}{n !} \right] .�( \end� 9% A~md�c�a�$be appliedA� estm� a/pback-decay rate. After integr%}*2.ele�!4�correl)L�$�-scr{Y}�'�( ,t)${ qF@ions, we shall usae follow� operator l:~�exp_op��� \hat{A}) B})�+%B C�kF^whereF��FGUC��v \t� 1}{2}[A},B}] +��% 12}\bigl[B,5r]+�Tb8B dA} 8A 8\\ &>=24}�jl[\{bC�Bigr]�+\ldots�N� ^� & O1�$% C}=09 ly if  A}$ � "Brea�muting Qs��[ N D U�H@nd Y�H}$� 0fined by Eqs.yrhamilt08>$n}), do no�(mut"� �~ �C}$a`a5expres�^Gexp\{it(�+�>�)\}, (-it+)=%wxp(itN6I�C})6�%� turns out�'? ��aina�hB t$. Si�9is6�a�restricU� s�x���e~�!�� paramete!Ealpha\@�Y�2!�!X1�M*9r �8B  be negl5shu�Ե�� f��F��k"I Y_imp1FD J n��a� \langle &eU!� \{-i�E\cdot R}_l(0)\n 'Z�� K"�IgFk>Rt)\} �r\r�_T� ~�� Now!�involv��basic�&�~DR_t!F��� t) \�(0) + �\P}_l/M+ D}C}[ t \,,6���ȁ"ec9$ denot&M��� $l$th"'�is6��o�  $tG0E\A  of~2]�)aL2MS� multiple �,ofE�2.�)!�hav^�*�`2%nʳ1���EdE\A���N8 �)��eftM�@��i�GP_l� !�I {B]���v Rgit `El.AU}{6� H �) r,,~(�m�6�U argu� Qfsecond�*onentialAV� * ��!��&( i�J$ ^�R�x%x&UN�t-Nn�=d%�ԡ6>�&0a=�� .���"�-�gy O&re"b.R���m 6�� ,�!�d�i heiol� z_def}�no �, ~wS�un�B� \kappa}��e�� �%�p-*� & dt��A[-i^{}t - .�H & (_S|t| +it\, q ��$!�I2]R�BvP�! U�$� � :�NA���b ��i�mo!��� ~D$C well"�� � $isotropic "�pot�FkBlo 6 ity ~/�=&{}� Q}y�=� xp6l(.� 95^27-r)Jh may� .�an"� V Q}$ be� a~�combin��Bo���s!N"!� annihi�� �!�$�vbe��� )q such�6i��~"�.n ) in6�� )�� _JY �>�� N� � ��exp�[ & -i"-:D)t= ?*q 2}�=$� V .#4}^��"b� !�� ��^�!�Then,\lye MvolqheoremaEFouri�% rans(� a~product�".ZS�,cF%A"Z~�E3a��2�^{3/2}W!9�=�} > } &^�%��� dz}{z^2 +q�1}W -� ^2} B�e  [-( Lz+IH>OZ��"�^{\!\!ݦA ~ By virtue�2�-�)�A � f$.�z'sol_gen}�AH$6H�o�L~ $A_ _gam�J��r&&�i�N��mol� 1& \, |(&|� *)��� pi��:��$F"%� _�3,v 7�+�+A+��'�4similar (apart�!��-�  f�*~$N=�)�9�$)��&\A)�Mt *qof���as�,���Be�(and Placzek? _gaussa�"�' S����U 1V  m�,m�a�\�F8�a�6� � e�Fy�b��, ]F�Ak��*1\-�� 2 �pi}� ��:�nZ��2L�� >)L��Ŷ`!�n� � ly. F -Y�.o) h� he G!qF ��, >cal�at�i+�0� of inco6"nt scat� V#t x �i�2Q�8"b�K) a��1 HbSinh B� $�. differ�1&�c2Ivariable�� ��}!�:�# 2M~f2��  W(I��RAS%��J� �8�_���6���.�-5N;�Od� min�rJ$%standard.A�&"� 6�i$�k:Y��J��/>JI#!�2 $2�"� "�V�����!e� � �" e� ���(a~rough �ach beca�żof&�'"�a�'-)arA~qo��6/ isotope�*])�!N�3,�?:$ ente0�$;�� j��3�1(#of $W\�"Q�&V%�,$!��'2*9+W}F>��$ �reaso� that 2� F[6isI!�� colli�$�� ies,b!� �� @)�ly+�he��refore,��:mos�d�-$ wholeFp~�EbD! �e�(o9!�>1,aL�� �a! �+">�+ i�/l��D1� Ru1ver dW1'"&W1>2M,y ���f"W6�insert�4onj�1�;l���&� J��.0  A�}�1t]�M[ .� } & ?6 6�1\,�1��/:�V`�6'�'W~{��� �� ]���$ű'�� � >� _en_bck})eB ?'s .RKd)~$ i_R"�+a"rom:)����Y]2� , u�8ePreplace�"s $2m! %a(7{}2����\to.u�  }_T$�Let us��`/s*�)� � �6are g� al s�( they.�6��impulse6�(W&�%u`)) spec:� pertie� 6c�2$!Ql=��� ��Tp �A� ��˥�69 dej.gaseous�y*ey �#M6u���:� �tJw�� t�:j,w�4�0ss �canW+.�).�qa~tA�*$�/u�:Mi!�priate Zy:A1�0j1�at � rmed��(F#1 '� 1=!1 -� � �7.�Wr�he2+ormY�2I)� S2�:inaccu�)�I" a5gy��g�=A *@maximal frequency�;��;$�a~��"�cou;sS-,�"�<s d1!�l�=�t }*at�)�:�, it il* � toAhres5 �!<a�%a�1s&�2exact 6W=m s7> 2zra2�?a� the A*%4tP8� �w�� below/�R�. U�K:�"=*an�$)!a� beapw� -8reD#~� Y�4 _cla�J9��Y}_{ll}^I�j"kE2"_(&u*:82-�(��\\-  biggl\{�*it"t�( +2)\,��G8t�$�;�+2� lr\��6"� > >�,a4� kj$-BY_�}$� " .��toR�(AcVU,6! �K~�B�)�� .P(%J);P��J/Q( 4=� -it�nW\�9+!� l[&-�8(tl.i)��(A.HE � b\,E b�, � ��(R��&gnv ���n�� $�"�-it� �6�{}t^2$��a�rt s6� N -�W �KI>ng+>�1 yiel�*he &� _�y"� w/1"�1*� we now�F:�A.�A� po"�D1p$~�S��++��M�f�?Q�A�c@:@*� ]#(+@*@:� F:}�(*U+SQ��:Y )\,[�� F}(t)]^n &�'�i &�% 1+i\�'1+i }{\<<7 t -�)Mr (:)aF= 9�biM .^=�BnrJ g_nC  gral ov�4t8HAed� �`ex&�/o qq to&�&�"F}�wa�'*a�)um�)�xs)j> x�Ehit1�_-��|I,K b " ^2\,4 Vere~$x�"n6s�g.a��tt� B�*A�)� q�" �2� (2, 8QV�q*� &s:2� #% 4m 2�}% B�-K75�AwBO !R)iE� ��N%B � n�&pC>��}.J� �!"�!��/��##�����@�"5 ��q�!�� A6� ^2 +Y�[, (%@�R\E�frak{g}_"kE��(.:�r��r8�^�b�F�s E%�1�#F1^�& dz\�3./ {z^2r$2[Z("M�)}"#" }h$ 5R�(>F+1��Aquaar "�eqQe )�}��7!'rv�,,, $ n\geq{}2$f�-r�U � 1}{(A�)h�)� �� _S}{n^{1/� .MtZuB�1��M��6�� �q �5� -n/\.b�.2n�.��-s .�^%p0�)er�%6^�� been��J &� )2}) by�act6�Jc. AlsUA one-�H(�M)��.J�;B. $,drYd ��xa~m2M"�q depeu)oqu�$."! kb�@e�C ��9� �*A%� (t)$E�a~�1o#D<)~@ . Ev8L�9ho+�wNEq6���&Dre���co�, � 2�ML� a~��'�6.�). It� �!�%atF2a3&?W�bB���%>�%eUŧV�ieaE�y�����n�'+ �T � *�Ke�c.QX���(.�i�� �36e�oi�"TA�m%+atQ2D-�&?RA"�MAE�6�'. "� Q�s:=nHUK�eV� ���� s B�N$ �-by6�ph�()."�,�|a`�*� %q1���=6*O1}���V)$�ia [! M�ul�;�!W�5 &�%B O�QM� ��=F��-�iO��� 9�%�same �t��Ry ds. At��"�K�en manyB��P importan�1t/! � &eQdisplay3r�Rstruc�0. �R9*�� ���I�uSmB#1*[6�=�&�Gz�=��.SP"D)�:!�2#ctO ~6d!�In'Ra'�Q {}0$�z�ak*+}�6�)�s/Q)��_7R���� 6cQ&�)���B�,� l[:\QV�M."�X,T�Z [� �_ >^r]�� e$�!�XcoeUIJ%�F�.��R &g7Z:L}�|_Z }  6p4m )&� ��21*=(  n)Z� @S\exJ� �Ÿ ~ O �  2�0�� ��:�R�9*� an+W�'�,�T���+ >+� %�q��qBru �g�e���.FKR���m{W �& ne�+ary�� make�q q.� s: % �$*5E1T�`"` �0 \ENRUV�5�L3 P$\boldsymbol{dt\mu}$ ���MK &�2M dtm-*A�- is S3*o�&�2�"�$�� >� HD, )5,�DT@ Y�? !� ssumiNhQM�0�K kept at�6�6ow � 7 s ($�Z0$~kbar��Y��AE�TRIUMFC RIKEN-RAL��eri�!8PndxB. Meaa�A�h )�:s8 T8 per'> S�9 ($�&1$~eVTamZ$!�$�' &sire�%� i�7vR by� rval�G"�\F'v#i��Cj���si� an$!excit�� a~f&\vib7Wal level#�� �0ar�(lR The z&IQ�c-V�[i�=a~noQl�I�!�A�' 4.25;({}10^{22}$~?)$s/cm$^3$ (�!-.)?)� �F� !���-state� "�~$;E�� ex]G poly��A �I��! knowmP Deby�)del�a� �Bq�asIYu�"G qD�2a �)�\lj[e�"=Y g2�9� Thetc,Dl$r��\��!�avail�litera� �+4silv80,soue86}!M�`ona�6M �#�  y-�8 ,7em$-matrix elin for isohT-�D)s�V9�V ~DT,53:cc�!o�method=% in R&)^ faif96}, �< tar<;A"R" )2 "�;Qdi�I R�p9]�~roibal�)<(s $K_i=0, 1TKK_f=0,mP, 9a RO^tV�a~&>��5L�|uZ*�Uic�Ud$�+e6"�( ces,�Y�Ye }.� $~\i=0�&nu_f=2*�� efs �&~$K_f!�r� �mvicin�2�=0$&� radiueЉ� tens = ��I�A�]is reg��!�a~free>9A� )R)^i��3-Ki� &�=%�sh5" in~TaO~�tab�Hdtm}.&� t#}[htb(M ca�3 \capa�G>o�R�� �p*�1a�2� *qu~(�/e.\�*^0$� <�-)i� HF?$)VI.w]I H]O{}QQ%�s=�A0�@%�e =&A�)M -of-�/systemsx �2��E�(ruledtabula1�Dnewcolumntype{.}{D.}{2.46=8{. . c  ^*�N I� c}{N| (meV)}& �\�64QN5 F$}&!jX K_i$rya�r!S$�#� \h�' s-25.66>27.95  11 & 4 &<-21.2%-23.54) /0/0 /18^0V^2:/^0V^12/�1Z�.^:�4.1 �6.4 �0���:k 9.28!57 /3:/6.7T-19.02/Z:/1.8)�1� ^+F^ 9.54�-9h /+�H6^2.133�-4.42 /^B/ 5.00^ 2.71� /^3> 12.4 � 10.1:^F/ 24.3 � 22.0%�^Bp 31.7 % 29.4%$ /�>/zq�A�:=��}�5�� %7-iu]r,�re��s�;al� threshold��~at� *�gt5] ���3� ,�*�4of a 88�dpr7e�p@shift~.�"}ffor a~��  at~3~K����� .k=-2.29$��c�D�upper sp� $tate~$F=1$� �+>Rer��tha= Mfor00$� P&� qua^]numbeI2�+e 3st&v ~�.�, �, �^ 3du"�*}  ~& 4��":O �t�Y-7�# zero�.�\ 0�"GG� dipc4&� �3� 1� � =�0$,~2�h!� , al�ies.  ssoc!.�j.�r <-50E~ �Xy �� 2%�2��� " -� �E�.6�gAvG� "A�"�8d mai7byFM u!�0$9^fH1?"�L$F!kF^a� c6�knegathG �c&�Goe8E�closer!�.C�A� �1�Osh�A�pot v}��Z,_ �])�Y3$,~4%�&] 4X�Brflym;rE> ~"� �:s9llustDdg Figs.g fig:v0ff �-} 1 .*I;figurv~ Pl$graphics[w�k=7cm]�i0czak_fig5.eps >� M6�~$2de|y*�1 A�susQjM�� A�9(s /%{$~0~$u�,$~0,~1,~2,~35�@ � :L Hj�=lines5�cie�va:��*j0 FU�s. Lab ``$i� f$''a"n�3Ϲx @��9b � � %�-��hFS-�&c nd ��6%����V�[ . -�1v� 8Z�N��a;!{��a�( 8FigJ@FxmC!nxB�6� situ���/�!J${n�,�&Af����iA���`�F`-:�>-slowl��bRew @2�,�m. Ano��ce betw0$!_ ā"���2^QK r se�=��B,neighboring �y_:�toe/����E1C"_� H�:�6ex"Bvq pronounce&�w � {t��L� �Portho a�� Ņt} !h �d\p!-_Htoyo03}. Most pure-&> ��A�'Pu$CF &� carr�mq8��O�!L* �fal mix����%��%bc�q d ``�''&wO n�,q%"xb :Pcla[usɔ*y7�"$,����7J�T>Tsj��h�1�U�yx(��Vo� I�&! 3�dashed�fR!�B�0 �H.c�n67res�<ecH2}�-{ ->�)�(�rbitr\units,� �� �� � ŀS=1Gin �A/I�� peakAQAB.pt��4 �2�$*C(#s���7-�� y B2->�}=$~2.7< M�1!dv2 ~�InO �<��zFA�'N! toge�Zq��G#l~"t=C~�lTatF� =2.7m -�&�(>�B��%�!��o� ]'�  sU=��dexamplea6wan/f�e!7i5�}P52Y��r�Va~V  astn�� �su塿ͼ������;&�}7�?��� �Dd:�ue%�Kot so � �u�H@v�$�: �y���* j�rai�=by�� ord�D,f magnitude !g%��th!#100aK a�vMdi&!��&A� cJ�n�}:�!J�E*@;oneJready_a��{JWea�v tail�@ orm -�? ity~�of2{�o�!�"�!�"`,Q�**;^�n M:@*�.�yN��� 8JLo"6 Z�&i�ua&��� (N m ����U���-,5@0 �� 6r.R$#1:�0dtm_d2_sh3kf0��-Q�h=h9�h1�)� a/� � � :� 6�B� .1� A~shap� a�m��Btrus~�.�da�`ly a�oIF�P se�::.�0} |Ged +2:� N�the�!�U*�+EOtwoO0iI clearly��inguip �� curvV5���to�Z"�In6�!&��'���~ �>�{�n 1�E�*.�".� �1d sup� J `1� -W� r�}����!0is quite flat�+.�� s*%�)/*� h h&"� .���s&1M@J� �>Jn!~s9B�;$~89�|s�$. �}3� main�� �farI !con�Z�V'$(�c^l5G �� �6�.�1}��B-2 6:d}ssuV�EGF�s��W]x(h =5$).Z.�Q}J��aų ����rZer%�wo " "6�@�"�!%in�:g��V�2F!*�S f\g 63$�A[$(|')dee$]4 lex,�w}nh�p��� .$\G�0.2�&>q�!u�0G_ �Fb�b�>:h.Uj�&�#ofz.sX6�a�]exly �0"�N�:"a� "H�a)�"� V{p�|10JM "AB� 2@"k�� �h�� �L~�f$� "�o*�# E� Q? hed $[YG]�� x�Y .0�nd2_3k�X &>�N��E plot�iN* p,N��Y+ is�*in N�gas3k}l��Eff� � J~�E�iBB!�a~�)ec�(�aZJ "�'& .V Maxa_w6E�1�^ 6�c��G��لe9s:wo-body d*+$O&�HsV���E�1��I6y =@� laboyy f�MI�*�A�d-�~�A��t:�s2:(�.UeM�6&X~!��3. trikc �:%gasHE�J@v��`y dv+op�  !�=�!:Y��[gi�ga~kigibl"�.�AhQs�.�agr� �� veragB).�by��&T-a3oL��+� c� �e-! \ breu87})n kawa03}= �� a �)R�s)�oniI~�&+V����AA!Ce!%�<*�4 j . S-��:e� �0.�!at>��& { s ��EbroaduL� m7!R�VCVo ��)o.+,\ .d�� B 5f*�o�`1�&'-��f�[" ths �� ���sth ri�K�6�*�F!l$� �P&bo��%:( F-��BE+6L-� "�D%�� �z7��^/"8*�i��A"-��=/A~- "�Zc�8RB#"3 ��"C�ME�heA*�2��.= a \gg��{ Ca"�*jk HD�1DT� s�8!�`� %�A[�0�r%no2�$�AZ'!n?,A�� s %���*�#M&���*p 5$a!3![�2hG,"_ge�!l�l)M�!B-�y��.� W-m�tu�-in~HD a7�~0.1~e2�1,=! �Z��� .&�  vari S.�[af&��*O v� hd3k}k�be�L&�)5�e�_ �in!6`<��!.Md<f]!W )*&1x� ^ 2� e�~HD�I:�%C~���F�13���T\@^�dt�W B�d�:��M:� A.���N w %d DT~�Iy�Ev# �^agtak�if�M:�*� T�l13$ %�@e��s�2~�2;D  ( �$)yz.��e�epl� low2 =0��a2��ɠ>� �2anb��!Ӆ�is � appar4i��o��%�  *)�1 V�:kn,6y ~63@T5n)�&9@q),�$about 41~K��~HD1 50 DE�*; ce +�%^�b5L� WZ.�AAA�~$-�,�_���"��of � $-1.9��DT��m."� �� w�?d�A8ly observed at~�8� fuji99,@00,porc01,mars01}��i�8u$-�7 beam%@DQw1f�� techniqu�H&)$Monte Carl��mr�� ~� e.g.,.�5hube99�<�employ!aor preU5� �.�7data. S�W�mcediqwa��Aens�3�@:�/a &�Yu�ly inF'F�a� geometr�s %:y los� A !?"��! lay�i prio�)1�&� l�b-��.�9I  �9W&p MF:T�<�5 z%Gs� t�tV�)I|�z1&%eh�M�( �h |RsE�Qv�8. A~d  ?ysi%^d!�!�*�(by Fujiwara2� }. H��und mbI$dt$-fu�X�+� t�C!�� st-�)��� it Stpredi��u� �ect� m:. M!W� 6 "�weNs�EJ4n�,A� cer��ly� r]��fit{ e i�%".�J��>B)-�p �T68/ ��� �*�V\ in �&�%!-�%V� aA�at�-C� �&�[�-F6�/("K[�e ��j�P]�M���#�*!#d��1}� ort �!fp���A~�p.$"�Em�}�^rforq�Y�, ~HD,&|H"�"�5,%Wno�9nfi�-E%�-HDE-ѩ�a ��� may�'ct�!be�i !=?&$]SAa�n*h0 isC'stead1"0**2"!Hs�;� �HD�� possibil>:wi):T��>ixed �a@2�-�z5�%= c"���*�'-5nGdid!q{ good .u��. ō"w���W�Ʌ6n(6PC�g\Da�.�� H �q� ad�� i�)FN�4c�'RSgS�t0@lyad"S ce h�*: 4F_�J de���i�Fe *� =�strengtH�e��ab�\)J\)14N ateA�MK"�a��Z(F=0)"�:!B�"% 5-K�Z16-d<4 D/T($C_t=0.4r�Z temp�?�F�:u�0�~ 11 1�\ 1�5.5T"��2:2t�2�sB=!�: V� >a�Q=Rn �/� es� �-DT�aE~ D/Tm� . An� il�C�4&�,JS, DT,�~T$|&�E�3tritiu�jwlic��AD U�. TE�.O s 5--16~K� � �N�E�� n un� 4 ![e�B�Re�� Z] " !#- ^Cw�}� 6:>i^ �4�D! lBA!�n!r���u"Bk,�F�15~K, �usG%`PSI�T�.�ack� "b)�*xD� ime"� .�ul!$� ){m�Fd��| "5 �&AV�o�y��s, "c� � � � �+m�E���ARm �"!R:vם�#c�qU� nQvw e  :]p*03:u.�$n2� }G+t*�Yfas5|dam96a�. � &�D� B�Kla�"V� . On�  �ect�gbehav� i�|P.F�*-� Q}-p� �� $T/2.6FPI!� achie� (�:(!�ox{}10�~P�7nge�63!-%^M�:JFF�9o.onZ�E�wWv ::42f`f5}) balw�Q99�ib�mit�FV't���#�&�i"`:�,.6%� 2V� i�mE��� bzئ�;&�E�$�.D �:�'���.? n"_#haV!AXa�E�y �,�h �.�.J9$�3CF cy�ys y� ��% �b�JKin fuI3aK�c�"!#5I~full secT�5@�crPwM� ���*~  in��� /TOq�fe�.��;-���a~cruc�in"c� "x*s�a~.��� non-*"I�e��"Z&�{f.ej $M^ 3}{2*&�{}Tm3uE� ��Wsca le ad�!�epi��- '�'%n"�$d\mu+���Wd�6���P� ayQ!�^eR �.�?`��' stud�5ina j c�cx$86,jeit95}E�_euof.�[LU'O%� i"���Z igh-��� i.k�jr� ~��T׆�!���Q�Z>n������X!2"!2)��m>%_N�$�}f�-�N*&� f �r% c� �Ng_tavg�H �vNvR^;�:of�Na�_6q { }�):n&Z "�Ie&��.^ ai=�xO�s I5.WI�*�6=S:mG!ss"�XR�v� $S_\=0.86�*lsoE[; �1��AT� �6[!$� �� � G$($T=13$~K,�$phi=1.45$)Q >�dM� n<�I�2���`��O-A� 6 "� ium�3 i-a�s���5roiioCM o $Z2X?\,{}n�B78"�>,T������ � "���Q*��r�1.2!%c$T=5$~KU3.4 16$~KSevV}= %�i��f �7E�,�ve�u�3a�B��-N�-<� ��L!qthV �YR5yC!{2�2J�t"M8 P7 & in� *�2�RK�h! a~�er�#�b��a�i1&�:��.� E�M�M�6��qco1�cp!orc1ww$!�)�,_ I��2!�� }i��'}, one�A�]B�<1$Z&�a*� prc�:=&R9GQ�6s. HerT e�$>Eّr sis+�9-Uof�m.-P ���I�?N� -NE�ut 20\%s{1�i^�=��S(�"8+�!�%m��-��e�q z16~to~V i&j.l56�27O�/ toOla%���,w, hyp�?�"D&�Ucoy1E� %A<ms&� �m���gͽ�ͽa�Ail�� lambda}_{�/O (�%HF�d�7to best2�A�<. Kawamura~et~al�6�r�0W ow�� b{, namel_A�2f�{0,�r D}_2�&�l��a�aO�~� � v�vmT}qIVTS,� �RVb ��A Vt_�=3..yV8$~s$Y����FT}}=1.6*�VE � mE�l.Y6�fn0l {}% C_d\,^�6�% +C_Z�� %i d1%o"���> �e��� t�f�l!v $. O� e�s .� "� !��,�7 ut 3.� �2�w��CA-A��i�� ��(�0#e��E\A���"��n0$�als �~25\%]#i]c�6E0��u-Rr!/��aNv�'� 6w+oryex!��$|- Y�E>"T�"��n�=��%�6��EE,I! :ong��� .�5 +$DT���,.v7)V��-<%6� )n� V`="�)s�g�C�cs}ry8�e L?*%�an� O�&�%�. V�,E��1B�a� A�ut�#0� !�� �rozenEa:HDos�9[ua$J�bes�5^5p")3"r��(� � dilȮ�H1`exhibit �4) 6AA�.l6h�..V1��topdAX�ٺErigidic [&��)tn#�\e�2 h3"�AUU�%Cy �d&*>1>))t�� �"/G2�>"/�<�=/yE7m�A)��am� qd/�V>�A�9���neres�&z�.�ae}):�u�h&�� U�9�� disap>U�U�7s. �%����daU�q!.� �"�-Ogl�J"� zero Ty Ose �FsR�(cx�%ˏ���v�!�A�Th�5ed1 c�**Zaԅ7��)�* +� i|�9��. E.�-e cY0p���#M�ڡB�m4 X !*n..���v� s at(h. A~q�Y�f%E�j>;!.* �`�Gbq!h0)���^�1Te] �m �Bg!�8&�!�)u�c�s,�d>_ >�un)Fo)�!a�}:) � a�&{ �a~.�� .�#m�6a,.)at X�Os T$� revea o)�!ZV)ňb�aac�g ledg3^-=4n We wu�li4� Dank Profs. K.~Naga�T%8L.~I.~Ponomarev� ,U� arch3Dk\M.~C.~�. G.~M.~Mar5� L A*�0discusa�s.L^B�b� \biblio�'y� �X}�bbOdoc$�Z� � n% * Std�of fi�$pssamp.tex ! % % B #� 3a�APS��REVTeX 4!�"�A.EVer!� 4.0r *, Augus#01 n Copy�n (c) 2001� AmerM� Physi�TSociety�A�Se� Z 4 README�E+��Q3EQ�0.� � TeX'U��"�!�%you�  AMS-La�2.0 i'lled %2��%y�!"preOsiaUa��.0n� %wy5'Eres run��BibTeX� mmand a� X�sv�% 1) a ex =�2) bib3^/4V \Q�c�� [two�e,�0pacs,preprintY` ,ams$s�o,superptaddz�,]{revtex4} %:`M�_ _ % Some �r?J� lOW� any) &J/iesf�ap�� aps,draftv�%y,Review B \u9Yckage{��icx}% Ide W8E�s2,d)�}% Alig�bT��g� dec��l2;bm}% �q !�2epsfig�\n �4�kQ } \1�({PRE/turbul�title{S9sine.�p�m q"H� :?T8kamak plasmas}%PLce�V ��|\\ \author{Y. Marandet} \affili�({PIIM, Univ�� t\'{e} de��v�, C�)� St-J!8r\^{o}me F13397\ seille Frnd y H. C�v�DRFC-CEA, 13018 Saint Paul lez DuG Cedex,BU8L. Godbert-Mour � p$M. Koubitir R.�mm���Z�,\date{\todayA�*$a�( , GR % but� B�3��licitly,ifiedUmabact}���per46�8stigat�8influ!�a�2`#�M�`Y2�J�/Met�qM�. Low]�refuU= fluc�@řw�typ��� Hle � ��D �*Tbɹeuic�b es, ;snOcd��� �Mg���Qis (]"Bn� �g relev�W��drift wa�u� , ub��tOA��dg|e�!lJ7�Gic�)T :t 2�� y�f�.through�!� pa)� %H�"�t��&o$* I.]X��.z�j!�i�4e��b�^���SsuYI; ;er acqup��2/�5�e.�i�.��, ++�W!�gUİ fulf�wd%u&� ,�fo��o!uelop a�.^�lism.� �)+y4k��'%�� ity,!�id Yc(0%�e&x�6�lK7�mZZ#y of�2emi4M� a>�*�]Gz�^�L�=�R2F��EI �on.ŭ or�.�.�!wd�"�3j 0 ay�--�.iN�)d�:ins�DA�E5:�-!+ Boltzmann9��� as L�y vy s�=���AeaVa�#7mdA��al�Ma3 �/ \� p{32.70.Jz, 52.35.Ra, 05.40.Fb -a��4 : Random walk�ULevy fl� +-a��F��"w�a,X&CE|s�� noi9��U%Brown:Nm.��V4%\keywords{SugEed  }%Us?owkeys �  opesif'(^%d��a�ired \�{� &sI�\\} J�%�ie�p�>d a maj��oj� }n&�u͘E;u�a^�or)jߧ environ� a�p9 7( � iO?"ON��$s. Indeed,�a�m�"W��y�~ me�/is�(6�� �1 le�� retr[1��ac��=at���24`(�p.���n�*�in � i� a�[l܉*@V>f)�V��inhomo�M���,av! a�M&�P��mMMs, fe�b�V ich 6,>�*�q�ad~�ld#e0&�.� eq�6�-O' trig��%� bili� �6growtr�!� ar s�� �tu�K"�(!��2���ce�#\Krommes,Garbet01,Horton9C@/��(]�ng��U&�Upg m�A}o)� ha&�e��ry Z����2v�ŵt%Qa/s �5 +stillA.,!&-f�O: .�� �In�to 1f& erra�i� �_�5R~�5;a�routin  agnoA'bag �-21YeI=*x�(%R.���� o 3u#�i7�� h&N ce itself39�` 'x��+��passivz6e�scopy�(��nconven��A�j�us�Am " E �$[>"�B! numera�e&�. Histoll!� -ber�p� s (T&,HGriem74,Oks�: � �  erein) Ib deal&*% rkM���vng�)1t�� ic f ,Sata&�o� � supra-AU�D~�Langmu��a�R �/7��S���{emi�-�! Moz_ nd B�� Fbar61}, �,B͕�% deviA�t��cF��k �ɴ.yŁV.�-:!mus&Z.� "I to���E;p1i*ᝡMa�-to@ 'm G]�sii � \�."A aV�s�!=��t�d�F >� � c:� UT�� �v��i� �m���~�� ($N_{eՃq ~) �0}$ m�)3\z Zeem6:n&�A�O! A)��.���%u�l�p!��?D$\�$ .�hk"E�s $n=3* 2$A� "-)��n)'B ,t�ڱ�  �l�'o .� ���� rs R���� so8!ugh�P��U�`er�Xo�E�V A�A 1�i[@Kubo,Stotler,Hey,q 02}.&�I)� : !�nA�b��'e,�t� .e.7)\�f&9 �fl� �{ acterIf� qrh1up���/h�per�0s ���<��al / f�U� ���#gH�qPc �He;-�� (DW)�kc�/E is he�w;�Wfo�5so�z�ajl�)!0por� g& �yhe�Rl�)5�8 �, �&� Y���h)�w�.�E� N Balmer q#�9O! �<s (uC�2Dy,�)O &ns?4ly a�to�a�Q�-�s� 4? �;ns���Afhi 06$s %t��two�'�SuP� �Y? �&< carefun��4emphasiz � J>� �axÅ�!� t�b! �6����m�*."^bye7*e-bE&gb��AM8! � 2�5Bm  '��,2� ��i���-�  �=� four%��fiv!�wDX<howB i�4!K' ��F<ah!O�5�l+acH���\�P�.� $. By furthѬ�[�]mod�t!brief����inm�$nf2004,eur�05Epf�-QVDF�reM�M.�Proba� y D*�j"�� (PDF)1k)��;!sQCY�six�ac**5� B5�.���su%Giva�& ��M s. F� � i�!�m== o]ա�n})�* �1} choM�!xs r*w�%��g�/�R$e 5�!sbe �a"q:�*@5 es�}ish0 �I�y����ouApevqW��QCNSNS}��w!}ve�.^"6��a p�� .{ �QAh!�.of&��a^0�!�=rgodic d���<g��m�Tore S� � . %$ Q�f�$�9 &"�.' "�%?m$HBalescu97,Zaslavskyc \M){>W��E"����<d�} �v�y��cisA�!9)I. �ty! a s� A �d % c% y�uA�of all,�(�`m Sum.��(M��b�0fer� ^ e ej��G� &I�\�wrawr�vYw�olu!�1;e atus"�q�7athqI}_{ap�3{O%�`�#e�Qks���e&�sL b�$.� !raw-u��*A� 4+-;�t ��  �A�2 Of Sr (LOS�Ddur1�B���)��,�o`$y $\tau_{m!]H�ity:D(mes}(\Delta8j�� $2q~nd� �J lM detuEQ"F�  +� @%CE ��n ߚ��j$�?"��mieq:D�}Y J�=F��- �\QCL}} Aloc: ,z,t)\�H{�� S }{4 ��0z^{2}}dz \ dt>��_no�nt�Pre:oZl�6�!7� Qb` )Aar$z$9y�hct�l�b!cLOSLA�;�� ��I�a�E��( area:aDCJde�Ge4 $z_{1}A�2�r�= ͦAM �]��z�to�Xty��._6a �=~��/ �$0 A�re�,B*n &7dea�8����� J�,mObyJq2�Ng&���g N{�E 1}{LMt6aB%�m:2! �aW��r8�v�#�aAP $B�`)���J� �= �)~}{ 1}��� Ldtdz}{)}"SX-��  �7oBai�:�EP a��IqPE9yA�sL7 re@ v� Fy�Y- � cqnr��t/"e&Z"\p�VD���+e k varQE�&��!�E"�n[A)$.&s�� 9|�lC =�^X ���2�Wal� nois�?io)\f *�)͇9!Z_� m�*t<e�I)sa �l = #sdr cŏ"��, as Beam Emi�,  (BES"��a�)M~e0)�b O!�5��2� ሁa�� {(C^B &8 00,Jaku02}). C�r� , if�I� ��6edeB �8�"��ly�"�� o enkCK~<:�j1%�I� is p�� de.Kl�<&��3����\AM2 B�Vc%u4"&i4�%e�fa��H3 c"�N%��!�"�8 F5lݿs2�.N � ) 6�ll�Sv%ol�"�.��IKU�&�a7,he next step!+!%�C"�sts i�C6_- �u&���@ ��2$A�#�B��j��R�� MY�a>h}��is�UG�sbP��!-�llA�:���% (H , �a�O�?)V>e�a=}&g �local =_![-Q�J'aS.Y'B(X= . .��Pl�' �p* } WOj� 0/� �� Z �h-4�� $N$ mazPc��R��M bf{X}=\{X� ()Ebf{r},t)�� X_{N:\}$, wYQ}��S!eag�pect6T��D �5��%zb�F���,%�C $X_{i:�$�� satis o a!�hdfU)F�&UESXeL� \�al r} t}+� bf{\[��T��}=Sf�%�)B��* � $20� a sour�9��Q e ' flux��-2"� %:suw�a �RuM�'���OC!_=-\�  �%+QOu $�ML�(bf{u}=X_{j}OACa vel�(%��L�#2�?���s#%�v#%�A�Gs� ��s}onm� �VՇ&�'R�i|V9\nge*� B�& A:A��\��%vv�� `)�)i΅�T�&�%� !+Y(\gg \nu_{co��O�PKEtau%�����_ j"A �h:6+���w Y$Cdc�&����K���W"�c��.z h�, � simeq 10-�WA� u$s)( .+� �D�JU+�Q�E $F_{\��Iԍ]ߩ =i,ed9w("���*I&at)�� ! ����nlocmaxw���Mv}�J�X �\s�Im�}��N� �H��}��\left(->>+v}-yi]J)�}{2��Rkp_���a���NT� �Z�$� uY�~k0Q�Awt.�,�#��*eVd A �& .*%ad�z�C<$\gamma$. In the�[ following, we shall consider the case of a pure deuterium plasma for which $Z_{eff}=1$. Th<,lculation ofOPneutrals VDF requiresus hTrefined model. Indeed,$\re are different sources]Yin edge �4tokamaks, each.�them giving birth to a single class of U. Thes Les, characterized by�( temperatur)oexistZcew� density is usually too low in or%yo ens!pLtheir complete relax)Qtoward!D background local !Xlibrium�^ est � �@ originates from !�dissoci g,of moleculeseased,{Twall, whereas those ha%X largAE=%�@mainly attributed!|!Q$ge exchang�acA8�s (e.g. \cite{Kubo,Stotler,Hey,Koubiti02}). In �6�will oq6�!��1� %:ly crea�by � F�A�pat plays an important role foi<line a] s be!orY�it �bawaji~(se emitterse�can okHagain take advantage�^ eparU scaA Hbetween atomic proc�! d�� fact,Kinveri�Z)�=_ateaofE�i �{Tfew $\mu$s, i.e. shortA]ha!9e typiA�1@t time �,. As a resul �1%reA� s at� : clA�to%���!v,�8enA �Eq. (\ref{eq:locmaxw}) with $\gamma=i$. Froi. microscop!4oinY view) �'�8 thus appears a�$Maxwellian%<2� a seO(slowly vary��mas6 )$, � $J<$a�!}~of�s)� *�  o& f8is more subtle,�ls�on Fig. �� fig:5}I5wo&� M\ie�I� �$ a maximum� a��� etES"T!�growt� 5i.g��s ��))�� ich domi� Vsmall.'&� ,E�%ionis�n �Y. ForRMs"� �$15I�aLi.�i$!Qc9G!| weak � he � �I� aper� � Eref!�.� .qa��c� a funca� Se΍ . \begin!�Ture} %\includegraphics_1}% H� is howA�� @ EPS art \epsfig{* `=0.8 ,file=fig1.eps} \cap�{\labelX.Z plo�:+.D ^�ic.� 5})^ r` 0�100 eVE�a� -:���ij]j.�is%�Q�;>1E.} \end�%\Z� g shape}~ 8$\Delta\lambda$ l��E� pro!d4 $\mathcal{I}(2<,z�Z is determb� !di%nt �broadenA<me� isms�ymagnet��@s, Zeeman, Stark �@DopplerHs�O uld ��,it{a priori}��v @n simultaneously .� |*# >�normal�to un]� be wr� nA/�"a7 voluA�a� ductueque�}M� eq:c�-h } vj=\� d2�' I_{ZS:�-6$%� +D:* ,IJ� \no� nt� $ g��� )�-%�Q0�&escri� Q U2 A %Ce�Q~Mc%��nic� � �s � gy�js��$HGriem74}.n Q<-h�D ���xg Pwavelength shift intr!���movem!m+� or alo� LOS�z�us&� gi� n DoplA I_V�6�=f(v_{z}%�d ��.6$Mnd�r�5\���� obtae�%�J� uponai��%� over@��A�onentH  veloca]per� i�r1�LOSF, .�eiv_{x}y}F"� v) .B�]�It�Obe noE�2�%�) w�wnot b� id i �M-J w��1�Y�durathe emis'A�� , duR "AM�0Rautian}. If ��omegaA,��� Q��~$width exprPd��%�pul�,R�� T\at $\tau_{coll}^{-1}\ll �k���ide�i�ly jsfi�Q����i4 A3%/in!1istaqw�L���� �}>�$ u�l�,validA_of� F�� �!/�����&�R��Q'��!�� k��average��Ŷ�A ;<! .�$, but alsoL detu�aQl����Aiթ� ��discus!�^&KD$6� , first�Q bulk!Y!i!9� n"�%Qs� Nb-wY $|MM � |\gg2_{1/2� 6�  b� � HWHM���1 cen�m��i͇$is negligi��)�i� ow!B =5\�s �20*� � oa��[�(!��always)f�adIA� ��)��9 $ T, � struc=��ected \cBOde�\Tw %� D$_6 splits��o three �m-med.� (one $\pi�0two $\sigma$)�2e � ral .>-��<ed Ņ!�!� ;`�f. U� l(llel observ� �Pre��p6R,� aZ� Qbllthough%]M> >*:rm" become"9 � I�y%��!.C� pBtsh�be�� stoo� aU.�areBrz bo��Ks�"��B,�_{mes:�)=I�1}{� _{m}}�A}^dt'L "XL}Abdz \ &X}(�)2u M4,aS &v.ic� now16�D!5x�s� �ls+�S!Z�M�q}�-� R�"�} $f_{a}� stra�Rfor�"ly dedu�"@ 5� ��br�effVDF!K\&R�>���zv�$in analogy� ��"��� Tm��n"Sm��M�(ov� �tspace. %combiG24>�)<2#-)&�!�"uA licit �ionn fbar��i!f.7��\ _E}]�FC��� Q�%gI�$r �(a deep physy mea%mas�"�#in��)��sev� \\.�Intui�ly� i=s�%�l� �\ r# low,�( S "�"a."�eq}$ `#2$"c6NQ�d 2�.�E?:u��,��z$ivee��T $\bar{T� �^ u}��$�#nMavF#:}�\simeqA]eq�2;WT}, _ N<9�Con�$-� t-n;str=�s occurW r Ej��"�no ob� 'oUG�Ul5B.�^�!su*� I�by6�-6'Dt�Eg� ")V�If.rise up� A���h� per��w &�&\�fA�early -s ques6 w y2��F)1� sed �#ead. A"Z ��85_�2A�au�, carried out�C� � '!s��� )s�knownE�.$:Qn�Fq* �i8 $X_{i:� $5)e bT'0worked out. D`� non-w ar n^*1����c�x)�CgeometryA�is2L*b%* 0chieved numer�� ly. "6`n!za$" !�ACen~a�  l��problem,u,find )orthwhilBb��KaT�in�g�(in� "�kP�"�,6X)�p.���A�!_�s. %�quant!Eh�pleB:�imeE�� %!��ѭ�hav�! a homo�o�'n*"io�%� soD� z m �� 1� i�%!� to %.��- R� %S<&>hb*.(E�}�"�  I� &I%�/ B[**%*A acquisi!iUm7)�A�er!c�m�*ZE�"*5 � GB uZ+$. Let u� +�� !�usQ�pri�8 ��!�$\d�$ �a`= re/holK �ny $z� $t$F^int_{N�#d_{i=1}^n(��X}�L-�R� d 1}.. N}=1v ��� V"�saE� �(ia� c2`�������A�t�xI� ty i�)^��ter� g ;em�A!� and 2�in�o!aSfin�m1*d0!�%E5� sife[ erty y,++2  \~�Q5�&p#�^} .�&; fQ 9�!�2� ["g"� >0}*� \m[&�ot\ ] B(a bf{M� }) \"�BF� *� � �xl.bracke� -I�Ahe %�5ss!�du}.wA2vaa�A* � 'X�9�'8�mh'I/ta-y justi'to let 5�$@ �( infi�"� Frisch95} thenE�tbrgodic*9jreplaB2��bp.2emble d"� X9<_�2\cdot\ % le$ U�Y�\lim_U/)�4arrow +\infty}FT�t:��O dt = E�\l �ᩞ� � � Bcf���en)E5\��.[s,"� �h-re�� � stocha�V�" t,z)$ G2 0$z�s.f-a�d1�.Pe-l jEProbabil�Di4F�'(PDF)m,6 c� ng �� �� B�& �,�P:XP}(m��,,Ecs,N},z)=��-�n�!va�� � F��s v}&_1,z)� 2 >B��F��,����0� �co+�A] 2is"OF9�� �s>2�͂� WI �z��!�spa&51 ed PDF $J�$|2%n�Q`W� JO��xVJ�$&�R �E���we� $ll further�- �C .] &� � a��N\88v z�$ (, "� �*�3��p�S����&#b 8A�,sufficient).r o0w,� is[K oF*lik"�7��#n�43ADEM %(D-:ial E�%M$) techniqu�+velF %a �s (�Judge97}Z re�:~:!{ ein)�e"� %c� d��m�4ai��.�/�*!5�a�'1:ous %>a�z�� �b8tr�a�*�%cE�Bd %2 ),Yy� same �8���Q&t�e8PDF %uur� }�se�ss�g<9�$ail�ver� %2� .T))�kernel "�(B$ %� aPema�,,ll-po�V� possi� of %�!K��8� �cR%��#be�o%M�p�!Ёu�ro���9loap&A�I9 it %4 o��%�1�v8 %y9G !u�a\E�� �F�'%!�ex�'c"(g(+�) =� Q$cE# %judic� choic�p&LOSh�ed\ �<.?�I0ypo�6is.>��opposit�!�on�  %���-> ous,6Y6p�Xtill %* !�%oi�al"�of $W�1 er~:�)� %j'c�8D�Ņ�NW � , %� ge�2,e�Ɇ�% .�D(io@I��fra�of a���%$m�9,�n|>nger ne�*:8to��Z*pa=�# 6.m� stea�?� DF�� 1�t � )_/ comp/>s6)���#�.o.�l�9l6 , so���iP histor3(�]&5* �qae%_ir!��!w8 alreadyɒ��i2Ų�@ heavy&Tut on, �&�==R�!#w �Zith a g�%a�acy. F&,�,��1����#�:, �b#-N�ly �u�8luec�a3.� c�di <b�7@Eq.&�+*�. A.S�4sui!PtoE��+�$/% edl*AWl��� nextH��be5%�uo�#j?)0a��~i4�by Pope�) book}2�%Q�bm?6�%%�au%��is by)�df*�C(!]4Q�PDF�;madU8v M�"i��5; , si��i�,low�8 draw�clu�J"J a��u�cx %��uR significa'�@��U%An�&theles�* eres&!��,_6ZuA� %!�Ifb�eDQ_3i��4dED is %��clarify!thcom� {a,i�in*N[1C %axhEA!�i�V� #&x?D�5� ��J�} �co*�EA?�.adv 5A�ar $X� �2`%.X}r&� s]E  "Ad an arbitr�!�L$X� �x�Aat GA"I s�'� �v _�a�xu�ti�c�cd a��2��fu a�"�>J �2�s:���o-a�]�of- �,�.�^�� �V����2�1--2{2� �N�� Aoff!7*�8,*� � -�u$X})FFl2�{� p"mb �ng�J� o�41M:y���*:�5highl;$A� sal� 鑥A�E�sue�- i *� e�����#���� ��)���ta�=t9O=��Hbey a Fokker-Planck���F� i \par�� W}  t}�-� }[S( )W] ) L�(  '[D6 W]��$g$�/!q2B��l"Ri��4�MXq2 $�$1� d� � elow E�*.��>�iJ &�>Q} �X}�C}{�2{* PI�! S(w)4w)}dw �N�*�2�F-9a�J a. )f �4 $S$ does "9 � -$� % , unJ ` mo! ba!Xe*�6 Krom�()h ?��s none��une�Ke!}V�i�� �x� Qbl�e���)P)$ or2h Ye..#LjIHis~i����)?t�H��33. M� precis9$t� �cas"�1f�-m J� Y9m�*�� \#a}X�e�AZ d&_ #W%X});�=`6G$ |O-GbIm��e~q{rA A�m�1^X,��35��7v(3of X ��{!����b\PDF���O!�~ �BQ�;.���]*5> t Chen89}, �%a.ur iF>vl/QO� ��er �s �s. Event�M,� e�;up 6a-(e hierarchy��xEt��!U�i-X, I!W !� X,...$ %8&�6i.�kepE�m?#� ` �?6 ~�"� �Gu�'�# a��J�'*cit�n6 2x), do a�� K sJ !�2 thro�5E2\lui� as1�C�k�P $S(X� t��ure�� 9�  prov�J%e'~addh .�mi:" tYs,� w%#it{mapp! sC�7Mo Y � devi��>very6-�<ul� e:6!ryet liNd��j @$s (�"!�4�� 0Hasegawa-MimaUu gy�*�$� �Isee Ref�ODas95�A)� �iss:;is�#Oyo#� cop%� � ent pl� ��pur�sA�� �!� *�an �( �4mp%�%�-r!��&duPSinaimYakhot�u89�� se author�C*n�&� Dof R� *� �J.� deca =*e,��xtp�:o���#F!2Y5��iro#a:to deal�j5re#ed k! $X=T/͒ T�:͈$��:o9Ca�a�j �.�&to&*y�2" <aar "&lͩ�>S� TaylrM�wp�ESE�v5a��O$�sJd%&� [dev} 0s,1+k �!�!Zparam� $k>0 aO�]��cor&Br�B.,P2$1p���=&mi�E*z] ��i�, dily�'edF�=sa Ona�/W(T�C}{�(!m5� T-T�!}{\"<*"L� ^{1+1/2k}R>b�){figuuHj=H2f=Hs�  P*=He�%�?�I0}=30$�L$k=10���e�4*�N$ �=5,10,28eU�|&�4s&�,W%�%�s�7"'�,B\K�e}:0H%:'%%B�I?}~�I%^aPDFBze} %�a->!feV�Y %)u.^J2I*� �/$Cm6s)zɨcoan� b$�X troli�wCCj .�.�L;�L�M7�s�XM?$A�$Ef8 �,=5, \ 10, \ Q&A�TRM��W�s�ce�Ua�us&vm�de?śbe ��ioned�rst�&�B � �)@B *� ant.�PKL7 �_ ?�B�+ '�&9.O'n�s@/\dot� qD&9'b% !i@� 2�R�'�i:��5�n �&���NSe�=�1"e�� �t� ed u�n el�]Vk1�+)�� 1E1�,�M���s. Our-�sA�Q � wing*� u�I:��!�1Z_Y fKD"%$2� 5!�)�!.%^��)Aa  2>(*�Y ! u $q=(1+2k)�F$�I��� {,.0 *�2s Bto~1exten� �$� �Lc���dn6�exiaTEY(o BoltzmannQ�vanish4'c���? S!egX;q?��;6 a %�zer6� �@G> &D � id�!ax6(U��r2*d b*mq` %$D��5�by Borl!  PLA}. �$n*T, �Na-thBF!�V% inp�3�..�'Gq. %U�A�}84  iv�$:f %"y s��$R=�� �k$�6���7M0a %wa!.at�=0sKys;R. IB �O��(�� tend %to %�E�m� $T aD+0$t+J*=six)=>� W 3ung�,bl1PI�: ��9� ,"�5>sE�!ls�X�1%��!coupl�tfxA�ays})e("���&TCV/-/�. d b�"&�M./.&3CA�$of�Q_,&!A�.951�$#).YA�petn8 a�7�iS39IS�}>�A�i�&�K�� �UoKB�i�'�id",4`%�ip�S �%!��,�9�sheDght�0dZ9�eV�pmo|`"��C�nOa|2U"�Nty�!8} 2/3��F2-.{ �. #VDFR�Q"��� Q_a�& ion �2o�� triv>!� �Y E�!�z@ z *-X[l10 �u'e�Cn. AX�R+ +/ dn�?$n)\ W(n) \�:�>,T)"PTN&**�I� K axime�,"#6!� )�e�s%�e>2P� R%5%�m��^� GaussiaS!@c�e"�b $T4at�A� ��$!� A�rpATtrSC�*+W$ resolvedN  B�3O2a�*}1or) *\!�M&s.�X2, T & � a�� mS�TmPAT!Z&4G&*�"luI*)�alp%6.&LI~�%��R��<�"wQe�!nAzi�IA��:�$ ou�$F�)eed� ��ld6�!w; !R rG�� �>�8btotal!y�8> 2���2�G< :<!R� ���*� hJ�\6%sAa� 9p�4G�H G!7�.�D %!�E ngAid&�a"�D� t- X)��%"h�easn� ~?dA�KR18�T:"F�y�on�{�C�*stiga} A�!I���A��"�RIk AY,a�u_{z})$� �� !.�o�"CR=H9%E��-�_{uASz vari�Q.eJ�#�"2�6]�2�reD�$~� tuve�T}�|*\@=�4 W-��-%��\ d z�!5�"o%�4uc��)� Xc*�?.�26.�r �c�"�ul�V� &;HyQ��S�7A#�f<ext� s��W97}\)�Z-�+�o� &�3!��1�2)B)eff!�ro/X)��^�' ivM� }n�TY�xJ!�NV_{-�6^�n.�hW�dv�i1.w-f1Qa_My�%l2��f"0$T��rec� �as�).\ dow8��5N2\r�3 )T�[1+�� _{u z�}{v_{th  ��! 6�!��mal��c�"�\R�2���Q(2�"lE���@w�i�us�Wrigoro\2� )�2���5��a.��"\ yby"! ��� w�7%�ly�eH! �lc�1�@y@��(^/n���efqUnsoeldV�aW� c�/�"repanc[C� E�T�d&�mQ�I�]� "2*� -=�& i =pe {(W.�$ 0.3 \ M435c}A��eC2 -�"."i* 6mr�aerB� � �  sugges�A%�$*�d�^U^� �lyv�;b i����AN.*  !��u%�.b s"�|fa�� B���A $a logarith�q�! �ZE���� L %I�M[i��3� abs�U!u���� fv�|!b-��"�`����2a 6��b|Algebraic&�{-�g+1$gAa� 5V cl$$ seen:�*�Y�2>@E�W$��*m\,am�]ud*Hc.-�|  aAb�"� �D�F�6`:��=]�!��s uk>�aapl�]��pe.�c9�2�0\"M!I�-r�&�64f2l �'R�F'bf�O \bot� eqɯE}\$sB}}{B }r?B� !<e�Znͯ�4a Kelvin-Helmh, l�>��s<assDw�cU�6M""*A5tq<. Cha.I�&ee/aBa�  Mm�a�A�.2�N)�*�"� . T*� .�} "�wDn&�J)D& �*�5�)AY�B�!u2�r3oF&�$c�>�!.��!*�H T)dTr��M�i�l@v:�.8�<�O)% o*�3.D. T� g ith,2�2�ݙ2! �5n�C1[*.. dT �T!Tr�!��2� mean.��A�2y$d4n1*�J�;](20*1!�)��="P� we"ed n6- �c��(��,cannot stay *q?�elf. N�t�8$ a� rp2�8pea�Qa�{�0�E�S� 2� m}� �b�5ry �f[� ���pntF""J[��e<��29)bd�-`,��Cn!M borhj<�)�'!��`�-t� o�<t�Bu8!LW�1n4L �e7�inEB argu�At!c�c�lRX{Ud�9D v10$f(�,� �c�zai]z-JW 2; Bd^Z�M{�o}\ M),jJa*�BQ"�maK����� `s� s�i�c��Co&xb,A�6� &? -�nd�66 �s .qA���D�7l >I*����$ enoug9T("Bo$.�)�)O�if�+� s�zd)E_ail�� 5fx 9)2w � ADU@�Z&V,e ftVg&�I��!�aM-lv &49m� zE�"2� , $3 �Eth"�A�6= �M3�r�O%6; ��,�� 2�+ay�$� (so=ma��?]�s Q�R;�F���%*_��Qc�= ��.�K��v&X�A A] � }YesM7:� "BZB+��}~I+j� 6EuRZr*c2Z2IF B� %٩�-�,��,AqEE�$�E��mal&K#$T p� sgo !D&d� .�3iA �Y"� is -3.2� (dv��"J-K&�I�Pr<3��"�y, � >��sB�� �ma�"T+�xs>\x� �, "�"���:nglaAa"�$-�m�J"�b)'E h .++1W�Y�'9��&40�(er,�*�V�&r�Ӎ���2�|Ja��$0 "�.f�T*� Klawdemo�q�  #)\sim�L;�c /\xi*�� � @9$fT}� B4O%f.�e��R�# % �0FR"�8H}\�0T- %v����dT�*�#Uɱ5F*� ansatz%n!]:�9�Fa) W � ��"eFares!`%/�7to � 1}{T�� \LoTft�a�(2Q>?"2n}}B}= a!.CFk!*  r�.f&as�� �12l Vv"�+i�2}��Flon �|&Y =I*�|�0,>��?forR�EwUayg 5v 2�� �n��6|w%s v �60e�^*�at � (�T)� � y���*%!�&g� �# ��T2�s >�ngs!xl��so{A�"F� &�:A Y?"�'&�ar�iinF;!�Fals2�y(��] $I�.EcAvfM���0� �\!;� $-3-2/k$ �Sg!�6� � a�9e $k$ ��p checKB� 1�VDFk}! �� isU��-�*�3" �� $k$ (A�,1/2,10$n.e.-� T1 s�6��9�!�c� (��n�z�*%b)"� j~ 7f~ 1)-.�%/�~ \�:JV�k�,k=5J.&� �u&� e�� ��H&� A r��3 :�Q.!�"ON �sV �wR�2`E�% m?��2A an 3. O�"�.c del45�(laK �s.I �$�v Z*'�.e�s a&J2Yof� exes2���4$-1<\beta<1$, *{[&+AL}�u,*}(T)$� Paul�!a�Fourie�pa. �%FT%3"�a)��5� %�so-�T�it{�M�/!3s��mPM "�(.2 %Beck�Co�2eck��3�fI��Nu#��he %a�]�ji(.�G��?xy�"�( \ln \tildeJ?k)=-c|k"�� 1+i%`�k}{|k|}�z(k,�'\)�e�o~]8% e�&}<>x��&�B� *} >3= ��$ � $ \tan(\pi �/2) &)�{��} p\neq 1, \\ (2/\pi)\ln |k|R2=1.pendn 1�*G"�� &� 1m %~=-1��z TX 0/ negaz.�AEs�B�"�œA=}��\� q&�p��8E+f}P k)$a�C�~�/"$ ��}QoDJC" }�-1a� \ B'$\xi T}{4}k4  \ d�pk 0e p�m�&@ �"- "m��T��� e LaF`ran)6o�M<� "�J � .Ef! (-sd= {-c sx ~�S0$s=%6/2m+\�%h 0$, m�+!A�!K& mas}1���0 �e*I%a symmEYcalV!�L��iT'=� .�'=0r^@ VDFefflev.|,)H�2m�t^6} i}6Z ,0���b<vMjn� A*$ly,R��� t $|^�An�a �wšr He:!�G B)�]�7� $1<- +1<3)�8Ypa�? "� u ?� *�.�o/�2d�5�W �'J���Cysi9 �2�� �'� � $,�ow�rA�e#j���� R��g1�f� �,J�'M  >v a>�-�'����g��R&>�2�PD�W &� %k3>asj8%s=&o erimen<25��"Z y""�� inguish"9�*s+%�ӑ{ �"��4� eiA2M aM�:� �  l %%% trunc)� busi'�  *�:b�[ �*k[a cutofV !�M %.��"P"4 seri- impa8+!?C�>o].j ~: w�� �Ɠ��da_ E re|#1;�U���5 _{mizeq T\_{max��[.�o(�>�.�!qIb es %"h, ��* oose=?�A7%�5:U %�l =`y�v�.e. %6�!�s`F�va.�<Ynbe %quit*^!�G� exn��+%(�}eq:�la6���B10(IFT��,cuta% abrup2~=� %.�O8}C9� s. %"� �}b~DP�<b�D�edpdf�%\cF)����]N� �]"�8M(�K �6a�!He�!A�&��2�5 �0�(j���Qedf %`c�m50�F$10 eVPa���9�b�b�z�ai�Y .�.B�E�p�^�Cebi�&C w:e�6�;� >�@Q��*�s�7l���ޅ0 . OnQ� (...^C�6&�*�r)�A�> I� �9�uonfirme�?&,@ need~r� asoOQe~:�� 10 �.? 2%2t_ht}��� �4a�va6oUj���$ to puenl�"I2co"�[�'�p� n��23.�m*OE�>v%E�6�+"�%,*��&�7i.�n�;�$"p�th� -.�;re*�% fm�dx<�*/� gA��[)E���@�<7=Cj3f M�fr��cy*�Ts\� ��2��G�um�'�T �4.%���?,m� ? !�e�f#if we� tri8u:gY6No� �!�is sdA_��6�6PcDQ9L~ �qio]s���]l�N� �t64֞ng .�2�)F7Ulo�.l ��Q�O���t�b�&8$.�B "@���ER�+A#e, �-2on, �"�a2�)i�O%�nTaA�!�0vd،ex*� �"tra� Arire�ig�<�rh�!ore�1,6NidM �A�$be�Ped Ag�D%~Rar��2��elM:,�r�6Y�e^c6 u$a؟�2�,l �P� eJ�T fa�4~ `3c 2of-1)D�$awC �32� 9�A�� e���_5�{&� A{�D�GN?,2�."2�QA@f�s�X anomalQgX�,�-U#�ake�'0'��*i��d�e��D7a�Rl8,�O�`� |h���ݕ�l!Ma&�E, o�� sort)S�RE�fC5J�)� .� �pr.��"�&�#2�e6@f"<�)�P}2s/�)�.�ma�9em� a�m4!Uitqbe�V 2�VF�Lz�arinciplAU*Has� asH���|6_)zE�� h`�WH� �t���\0de+���TC �� �C "�D.�ec!s.r�TnJH ��N�J}�m"sak� %s� la�,�"g�-�Ip�u�cWG� *UA�ua�.�!%�L�: rIB�*. zus:rto!��$at if�z�=1/�=��-��D��hW"KZ,�.�flT�L� <� = 1,Wilk01K%H+!,t68�ot�2��al,��o>) ?%�1�Q�sc�8��*ivu��%�+ >X:��A��i=��2availy VQ in AT!�5), xL�no�$a�s� eEai+/h�a`e �R(lasma�<"1<tmouQqP�;.�� LY�2�R2$e{"-$-�xbterpreA�agAR0�P an ��e� %��K��\� Lev2w In )� word�\%thbh�^C�Ca Q7� �<�:a�`�lv�.��AaH"2� Ub21of� & F*?&$is�2a�i _�)�8N*% 9�3�o2���F�!Gl 2�f E� (FFPE)�CNSNS,j�/rsen99,�$hkin022b�#K *�(E�(Z\��al v ,t)}�f�b \nu}�0% v}[v A]+0D:.^�(F2=|*�}v�>w�� �\�� �� "� /�0H c /(2m)"�'"��)� ��v~i&�{�j�"of Riesz-� PaulJ� 6>f6=TF�U\ +[-{!�h9�!7�G}]F�+**!&� 2c"r  (Ebia�NG��   =1$.�"{" �#� A�2(�5�%əma� h��<� �`JFPEV A�2� y�S55�k� X2�#��4�`r,\q��"i!�!�R�U [����� A.y: fld��Ing�}a��e��MT"�_M (��&V$�� Q�� �y!p�� trac�~ack�ѥB_<lp.�م�q!��s}*E�al�>� trajector"�^Dt�a�Cl�yo �v㪑�� " 0wh� nois�qx (01,ResiboisbeK�& �b(�3I_T re�}1�E9b2�*ٳ'*&L6lor�.&n..�� siOn� heoremQ�creΠ"�foo�eff�{ stem.m�s�dom walkpF50 �F_#���h � P/jb1�j}}� \nu��$k_{B}T}{m}nn ��� Am%C.�%$�\j���>�im�tj� jump0 K6. �e� C:"r �&;,� ՙ!lRT eea�"j � aOс�H,).�.��� BM �y[:[mˑ�?B��aSsVe?@� iž�ga��wh�P>8 � !�l�A&R4al&��Rlinke�Ut:Ah:reeper�YH+��>G � \. *�]\reminis�:<̶a%en� in *�} W,�3}�"4! i� � ]]non ev�\��ɓ�L�1os�Y�C�Hj �H��>ji�c�Z2 ��"  �}.S+"��� �)��� .oT&� U="9t�� �B Ui�u:*[�� ��W�sf�SoTe&qN/�AL�8I;W|��"�Z&N+sǞG.XoQ� flux� �� 9L^FEq22eq�I~j.66xAt)>��ar�6A(��-�9 LQ6"�}!��L��) �}JE���a�c!�"> � �@a.<u�sA�ZRK +$alQ�[kx ϐC��h&���r1��U�s�uld�[s�{"�&�2?�$]!�_s�?s_�,&%Jnhinf�V7-why} %:;i m-�f�l�to<� out- xqui %sy�Js� �[� cuyH : trop de r�p�� s %*�%U&"��A�56�have %� ". B��m�A��9�{Nu6p&N�ronU�8�valT��eq %w!�)m�RG!{LR8Q�\��ytm��!�.�&T .��)�m %orY4.��I�1��Y�)% .�.� �)z* �JA*� 6�vȉe;by�"�%�l��(89}ib�����"��{ %D ΅)Zu:��X [R%bi� o�9 �� a�s�)�ex�$eadet� )3�.z�w�eehex %!�a��=�asA�a[(ad�ar�7!2J��)��ue�)�aAOsuKZr��ݝa (?)�, )�|�Nu�nI�s����C�'Tdis�-!n issu5 y{|�9�1.> �*"\ly��l,#ruef\ %vF\"haY?J$�6�,a��0 A��v JJ �� &H� d( +c� �f���5�+nq g%1Z%�E��no� lookAE.� t� as~:*�&�a�;z� T)=C�n���.�O�3�/2$�)�&nd.J %&1�i�pK��e�jpy "[-��9 rk %A74� k9�f�I.�QY*θ �v�r ^���qjw�3"� !*a�"x+�B� "�dC"�$�y�J%iv�2"+-pa���h��. G�w q2�#*�pa��"� �Vape"�@-&�`a��in .cu�R"� �#eU!'a-��s routinvrM{Pedg�@ asma�-8@c+]�*�.` c�k2�"p �5F.". �G /_sq�>@iU�6�m%)B�9� �%���! �:V�-To .L�Q&{ usedT� a�� S���.,9�A�e�����l!ec�� "�"0��G!� A�&t aN?5i�Xw��fnN���=`�". Next,�fz !$Ť���on��B(9{�G�] new!ul�8W*� G'�od&l (Qje)�s&�"">��L:un�H&պaU?&. _�G.�=6��&& &����bt�8&� bϋj o diagnos��&U� � �E��cek`"�c  carefu�ruo{�AA��>&AK�<?1y.�Xd� sure�! c yet&��"$ ď��� �ʼn� ak�ukc�de�#*LhelpfulE�-.>=w�=&� "¬�T�H��� �#���&nda�al $�d ,�1�hs lw��i wk��ons"�1qΡE�u���2N�", ���i�a|"�or 2Q�o� C�-�m���+A��!�\��Lt�%.��)�8B aai*B� � ��.����N*q�=t6��e*�(�� os(ly)� f9�s a%k���N "�*�TV ouE� ��� %{��"�2/&� �bdS�FI�in �mm �=, ��Ik�2 *2� !+%Vv�)A_��8.s zosses� �=*� H*&$f$� ��A�� �Y�?,"9� � %�q �5oAa$��ar:k��#���2j,R�IWI��6s�. %7t�!����rq-i/Bfor %����.a6t��$~���!��%at6n�aac�� ledg��s}�/�a}�U (ank F. B. Rj���0 H��@i?rk�n �TllaboR< (LRC DSM 99-14)��o;'o, de Pequ�$s �egs Ions et Molx" cula�m� D��XR Rech#��Lua F‹ C�/\^{o} M$e, CEA Cad� he.�=B9 %\a) ndix1  {App� �(ewpage %JusTca͙un� numb�f t�"�z��d�%q\biblio\�y{m�det}%Beih.%( via BibTeX�  doc(R} �+\�f {eth� } \umvckage{qicx6�.xsym,ro� ng,sub�4.?Zwrapfig,��4} \newcommand{O0for}[2]{$#1\!�X$! 10^{#2}$&��} %">title!m�� \eth�l{�>$tle{Crysta1/5-energ�lo� trz��� environm+i4Authlist} F.~ND-Tedaldi \Instfoot!V(}{Swiss Fed�  itut` T��o��(ETH), CH-8093 Z\"urich, Switzerl�R!�} \mak�le % \ab�)ct��� �e.�c�ic mediu�B many .�s�p� ~��Bs$Q��Hh"���� � �� t �M�xx�s,�}a%� �s =�� ry� a�icl'x� �&���e�la�m�+�ojp,T�76L� . `� over� �%��f�h�a��E�� ,�� �u � n�An�^e*�6�� of Lص TungQ e (PWO) cM�M1�<� _��Fv{7cm} \�5e� {P�� {MeetD �uhe Div��P<�cl" nd F�� A�n���Soc�4\\DPF2004}\\ R�+0ide, USA, Aug�� 26th�31?x- �\.� \set�/er{e�{2}7 re 0�aa�pef5�!��exfng�k��,e about scinŖMp-S.���!�hu�rei7�!l�& qy>@l�A)�!��2J�z2^Wu!A��r;{n:R-��x^:{tw��i�ay% D � �.�*3Qb/ref� ummak'� it "k �� ough)tud A)�+�by�:H $ pa!�a���w()[�z$in $e^+e^-;Flli�u.U l�cNRth? /�0g�5ptimi�_!����/eV�x�A�oday'/%newvpX|�si�-?��.w�6srun�������ala��Bo1¾A���,�� hadrd")�|�# s. S�.�.%�ol!<#�g!colJ7hiIoH�far!�� �3,� mxr � s-oBn�o�& bsor�bqta��� � f co���8R�\ �p!� L�T4y� (LT)��� %Out"{(LO�:h�*'��* oxyg`� onta�[�A� alkali haAtrk�(� rm{BaF}_2�(CsII T�M vacan�OA�impuri��xidPBGO" PWO~!r-ZHU* Phospho��!�afterg �3�\ ar9 ETH1/!� P! u%m���  A� l!W�B�lyfs5;'�)vu! (&>*DXway�8PWO]LHCE�, nts� ZHU2X?�\\�so>n�����'t damag�!R�(� �� room2/�.V �O��ar�Z��A�nd�(���(��/r��$to a dose-�m M�(of�.��U�ETH�k�7o8�q)y}^�"rG&`�fr'ps. T�8�T/������s LT,n� -� monitorA�ih)� in�'�K!corT�$"o�8T +���CMS E�rom��c C er (ECAL)�Bornheim62Ջ���!� �7�;�E�:%3l�<r �#t�cru "����!�INI��(���"t�á/namo��/�? �n �e~"cy  cu��ve-ci�if soat�$�O,m��[s, ri�D%!�e�ls h2 m�sm' sts ����H Bnewat IHEP� tvino9�atarin�N[ BTeV}�E at CERN ETH-\ F ETH3Ca� CMS !���nQ, 94\%a�3mqsL'j�ٶ��:�,*0ia�toE��a� a��<36�/h� s upa�~�krad/p ����0(end, $0.5$~Z��e�@ M($:)2 B_ zbl�3��2 My)���+m�;�tesaf�?�����$�a�$$\pi$ beam� $\g�$6% �;ew��1{60�A`��' aM + mix�+ea�� L)g�ze�s,��� � ~)Z3� r%b)5qh��"-5E )| end~�B��2iir���%��3os��!R?qualiijp "GI�i�pyi��%�6Pre.�at�%B�t ��.6�no Hq�T�.�"R o}���)���{QMuvm�3Gxe er�m� h&�a&�c�Ac��atI|� �#$E���A�$e"��Y?�D!�_ L��al,)6 @�/ B/"Mf &40ex���;ZD�B� �H�[a?d; �=,���0M�,]䡜e{h� so��/r�*�o 3 y"�  1mos��� q�,Ra�1 ��iݛ-�Mc!NV^. A�7f�|a1� �\ BQ�in�)AS�u�F�"�A\��Ūed !����"��p��T�Vum o!/5 ees&*"qeE����g��,E/� what��u��(alld or� A)Nq�u|{��wV�F!�6~]k,M`-rA� �. +*CMS"!l��.�@&�9ux�� $�� 10^5\;\;��rm{pb�$ (10 YDat )].iI��1 ba�� (en�?ps)�HG ^{12}\; (�lo{14})\;�tqcmq2}v� H��>��@b�>�\e� 1}X�;a u\�4MeV threshold,��Mxfra�( (``stars''J ���GC�m �L�&, X& #�8$100 MYI� m �%v�+i�to� Ly �A�a�ir path b�I0~0�m��� e�in�-Q�"��� ��bQ�~� � ,���" e]yPVus+.a�!�iIe�"�I&2� �.ain�d��9c&F2�eak-of-"E�w"��,�4?s !�_{INDS4rm{(440\; nm)}4S1}{L}\ln2LT0}{LT9g!� LT0%�LT�!�i� nal �C�$at 440 nm ~�6�.��"a� , @$A�o�?!�v ��L. 2� 4A>s�  v��+ xd1�|  o LO�ngd��d.���s��� ���A� �aG �s,Z\)Z 1\;-e�1}��|a�4! �A�A� 25\%��AUFFRAYQ S&^�;�BQt( y\g�P� A[�WaU�,��ZF!�O, �.W�)�ahaGeV!t��lux�#$���1p/��2}/h�:0{\em a,b,c,d}��smore E, F, G8n�M^{13}9[RZ.��-�-CMS}��[h]l}5%T4Cbc;tabular1{cc} �q E[LTŕ-"s �}E{ F,�� f-LT���, ia�~/��=�(.] {\mbox{>��[�wD=65mm]{AandFLTcolx�O}}&2�CAw�oD8* VE�$Spr1��3.ef-mu}]~�7� muvsB�col �;[�1]�-�&�iP ~= ��%A�PWO�PWO>��{LT dataA zd~R)�~((+�=��� low ��9>## 3nq . �-)��,� " "?in� �?&����-�iO�� mu},"e;���~ �6���xin� �,%3�h-I-Ѥ� in!�"� �! redoR�L���� S�I . Tan,i*�I���zc�*j�sE�nVm+�20��I d�2�E/s&�T�� s(ure}{r}{70m i{e��$file=koba1A�,y�Ac[S�k�)QQq!Jex�;�lfaSpublis LA�y�BGu�, �"� ��%<s%`��, igh-���"� ( pseudo-rapW�W�.� ~$2.9$. m�a"���%�a�7�y� BG&� Koba�. ��in7iN��toiOissz)PWOV �Pq�c�M� � ay�-> !3&�H�*�� n-� au.�9p-me.eE�aTlyidu�as X�':�)N3� exer6�a���H CsI %rE+���#�J!_CsI��� * �d b�R>'� too ��f�ib�$y�&'_I�&� on� I=�5,%Os0�� ll�a"� if*lo���~p։-Ag� �%!�6�rD4.�:&�2� b UIC "�Jz� ��@C�!�x��v5H �� A"� � bui'&�g�p�th�Z�m�. A s5t..2�L!� u1�5N lo��e���{)L:&�en-�! �>3a��BGO. WiF%K"e< 3m V ɢy�E�3%�� � .% ��a�b*. A"���ijņ1vwFP��v�"�A 2s���,��&`%�n�s�w7)"FyM*I`�%� he.�%}{0� Ƃem0 R.Y. Zhu~ - l.},o � Nuc�6�str. Meth. {\bf A413} (1998) 297-311.2d[8 H.~Hofer, P.~LA��>�$�u3 u$9) 630-636�"2�2 �>���376 �6) 3196^E� H.F.~&�, K.~Dei|��:�14 �$8) 149-1556�"8 A.0�E (y���6�``CALOR!# - XI)n.�(f.���YPWcl6) cs'']Proc.A�0 ubl.sWorld ScV,89gapor�(9�� } V~ Im��P512} (2003) 488-505};kgV.�_30 _$4) 286-2926��M.~Huh�4n6�$D.~Luckey,j�%Hej,``8th ICATPP%�f%!�tL-�, S�j,%sy;δc�nd Me�l'��Қ,s, Como, Itawd!, Octo3*6-10,J%JAarXiv:�$/0312056z�M-�3}�qve�7tg 4-7,! �, RՖ�46q�( E.Auffray,�7v�&�� unic�!,�, Geneva K�*i��- M.  yashiM�9R%�^20�*(83) 107-1176�X: rd vf A328� 3) 501A�."�&:��&&�*8f>�+|[aps,showpacs,twocolumn]{revtex46�+gy�(x} \def \bb�bf roty3�_y Y+xxF :,e{\varepsilojbX�\�'{TMG�!meszPr*p su* eta-�� rial�� {Did�m8Felbacq} \affil�xX{GES UMR-CNRS 5650\\ Uny(t\'{e}�-MontpellH\II\\ B�t. 21, CC074, P,�E. a0illon\\ 340952>(Cedex 05, F+= } �Gu � uchitt\'e:�L*�. ANAM%_F� Toul�Dt du V�Z\BP 132 \\ 83957 La Garde ���a�+} W]:�"���2��ڛ*��fi�!-�c�?iv�K 6� � �on!s.F"�2ZKre2��-+�schem$w�i�'0mr& ly g� a�3eor/^ maj�Yul� /] gS 6�Iz�permea�?�Di?� re��@L���Iv\0results are c�Ohecked numerically and we give applications of our theory to Left-Handed Media =8to the solution8��Pokrovski-Efros paradox. \end{abstract} \pacs{73.20.Mf, 41.20.Jb, 42.70.Qs} \maketitle Photonic crystals are artificial devices, periodic�hstructured, that exhibit ph Pb�|gaps \cite{dowling}. Dielectric/cry0considered in%opt!c� domain, but metallic ones (or wire mesh �XD) are also studi]`microwave or TeraHz range ��yablo,smithtera}. It has been well established �4pendryplasmon}%%\, below a cut frequency,n� beh�as if! �y were homogeneous with a negative,\-de�ent%�$mittivity A��qn by $\varepsilon_{\rm eff}=1-2\pi \gamma/ \left( \omega /c \right)^2$, where $\gamma=d^2 \log(d/r)$ (here $d$ is� periodQ�-�e;$r$"radius"!�s)-�Dsoukou}. For a f-F-\$ �(_p=\sqrt{2 �}\,c$A�5>ized pe9 is5G�a~propa![i�A*s),forbidden. T6T�5l( representsO(scattering %�ior.�V�@ for large enough�lengths,�,explains whyisey�s � ayta� gap down�{ nullY@$ (at least�( infinitelya� duct�)�0. Recently, PE��Lco-authors suggestede< it was possible�design�MI�< non-magnetic ma!Dal!Tat�yK ess an ar��3acI�MKary2} ��be}cribedaan effe2E�4meability. Bas���8two geometries e��� : Split R!)$Resonatorstd�fiber � a-�2�.U<2,obrien}. It i�� liev1Y�these �itA�.nobtain�9s�, �,% dd�a%�I��,=�a5� �bo2�6j!v��2{. M5�� charac!�@stics do not seem�exist�1na��it�� fore�& )�to!�Ai them]+ ly (they�+��ed "L.�� "). a����R��A��&long ago�a specul���4 quite fascinaiIork-� veselago}!�V . He show1��J!had.[ index. Am�o!��herties, Snell-Descartes lawA*(reversed: i`8 interface betw��air��9�a beam Cf%�d o��same �ۑ�(normal. TA� ideamHmotiva�.a lot2! s, EXex�Imen�l.� (in' ti!t��-Y��})I _polema� issue�val}. alAks !�ve� at, hi!Rto�Yr! no unifc] roachA�,this kind of�j�.!� hod generEQ foll%�" stsAZyzing ���cmatrix!>a b�� r�� by mea� 7 $\e$%�$\mu$!?ameter�aZn deriv�1�#a, a�out tak((into accoun�� coup UF each���muneg��II;��A,e address %Jproblem�usv a reI]iz� 8 group analysis�ich� 8s us a deep ins� �� phenomena%predic��m�vencEӝ�%C��lin' t�ternal �4nces. In fact, m� �h!�get�W���^0very differenU om�J : while!�&�Eis�'ed low-� ��(i.e.ͱ �E� pect�!J'E� titu���))� )@.  I�nt" �I only� a raa� small!�erval!N�. AWp%�, oury�"J � appa%\A�dox rais%� y ��I�p� }΁ by embe�B)i�tmedium��6�,ū does��ge� �� H/ /um��gives��V omplet�^I���}�ro�����0 -�� �E` high!�� ? . B�Vgoane�jdetail]!R�� � � ,we* �d �A# make�� ridg�F�bb � � ��/b� tagonist: Yo! Q"c!n��a�>2 �. %Leta�start�:g��a�HKul��at�yuld help7͠�� %ap��. W��� a 2D5_Q� �is mad�:squ�* rods (se�x8set %in fig. 1)5�%��q�a�_{i}$ Mv� %� � F1e}$ (�Ii�e� y uA�i�=x )�illum�e %)�vice f��abo�� , a $p$-polarp  plane�-Y�� incid�G. %M choM-� =�Ɂ�f cru�import�M AJ�then au� transmiss� �� rum (bold���-]Bobser� se� $of narrow 6 � . IfA� %�der now��one� hp�i�7V� thin2�!�!T1 dips %A� )�ROa e� rresponda/.Mie'� nal)A�on! F�,i}$, cross-s� on $D$)2aQ  $\e_A�. WA4�contr�� $aS�i a/i� bstantial��� appear%qͯ���& ca�e� dex� eri�AI"=$ some timeF �`morozQ suchWW .lm�re���: open��f�+�M��I \begin{figure}[h] \includegraphics*[width=6cm,height=4cm]{felbacq_fi?1.eps} Acap�{a�� Eq�/�x 5labelQ � � Our poin�to��w��, n!u��M�%��` �Ni�d�eK �o"5�� )�h}&# _. Of� rszo Aitu��to��phy7 sound:�!�v> s��kbeZ r � >,� wise�Nc7>�����y a%K6w�quest, !#��+!Lat) a be mA�E��en  e}$.� ��emplo��ns*� ngA�("&� ing")�6�a>: � keep=relev 1l&� , � &Y unch�(d. To do so��hoose aF F� 6EyElo��)� ��g��ic � �y�1>�fi� heMp M 02� l6�a�2 ac?h�� :��iA�"9 �ee  reedom Qtru1  !6 ) mad copic � $\!P!�h)�B}\r� ara[e averagn e�{rQ0Q0Qo�$Y$: Q�Y'� ����\int_YQ�2�y}) d3y}, b �N<E:7 dx \UeX�>< JY}F�(x,y))6NyGdy z�( co� A1primaryUi��� urpos�Na�ŹAKinf�t%Aon�����%!�g6us�l��a"� : jus��Bur �(ple���%� . W  alyz�rs�� *pEsB�� ���2' %�wis�de21.�b� �h�i����%���i< �satisf�Maxz! system: %S ���\��%\A�a \Ts��i\o B}��J)#-*muA` \emI<E}A�� t % �U�!_ex�(%�E})Aw �,�%$:�a$� orAwto: $$ J6B> $_x5\+ �^{-n}!y2!^("�o�5ic n wA-Q<��8 a A�cau��#�%wo setE@). Plug%t'ex� � to:e+O tify term�at coe�!pi powe�!T ^n$ n u&&� Iw��?.�B""� eqAay}-�=T�u,0&=0 \hbox{�9(} Y \, , \,3!�Mm.2 3$setminus DA��I�m]�q �o"r �Be�s:� E}_0=0�.�D � �1�,2$Y�!e��`of-4ost�� typet$& &� >v:� nor 7it6up��. A�m�#�0 � $.�!�� �{0i � � ^Q�)5y)Lt#deducO)-�1�). �Qtur9 ��"� � C�tb=� _0vof�" ntir�#&/n*!]�V& r' rotyEz%  &=-i �8e_i�  &6��O<"&=: �:5D�(2 sysbU� � ��Im�e� .�6(| Ѹ�e ./V�.�� seen �� }_1$���da f�r����%�ide $D$� replaceP Ie0���&�%�e. .�:��!�� ensh�bterpre�b�+�*2��!, !%u ean valueE�m :\,-U� {Y} 5qy$. Up� nowE���c2��P hVns�%.�� e&��;�&r�.�1���at�25$.6�I . K�+Jm� m�� 6�NINi ��"x�D�^+�m1:l{0}\e_e.��b 2 AA��JrV � Q'icroHB+I� �� line%�recogD,%:�i-Amp\`� 1%_ !]extra-�  $��{1AT�aAN.�A%n$ ic dis�-�&)�,E�[��"k,�!�on duh!� %�$0&er����, 6p*2  regim�) he eSdiagramA���berā�Va�ole (?9*� )� `�nc bwh8se��}*H$��>J���a� A{&ed � s, produc�Ua }%K(isotr�2�$tensor. MQ*precise,��CR� m$ B�EGn` !�s�� uE)NP.�{1}>MY ݜ� ��\frac{\%al ^}n}=-{� n}z A�7 {0} �� } D,V�%n}=(n�,n_{2��" to $B mpl�aeua� V $-� ��� h orm:$� 2�1}=aP��6"0}$��Jj { �== (:�r} 1+:bw�=bx� 6�w!!F(\\>�JQ2}} & N|2:T+)��� ���)wW$Q�.�.I��i} >� . E��B�i.�n} =-nz6 U�* ��annex���I�� �'.W%� koz,R!$A��U+ y)dy�)��i�s��*`'.L2�/$eU$ (\,=A^{-1)�B�� U.�1�� ��b&� by b��=  ��)a�$2$:�:� m9(\e� (� �= h}))� =�b�}�.�>l �is.�,����1 Ne�#�!.. .� &� �/�h.� ��6'&*fim&"� K2t &� hugeEj�+� ��j'�F�:I#.X��' , he��D!"���,e�'6Lk!zalways alar�!er�)no Q6X q��oSecond,F��o�,��y@�6�a�)�3.�6�� �sA�!�+y"Eu&4 a closer lookD Mr�Q! a2fiV8�5.2xYL�it�ndquu})��cALalU";& {b blem. Un���,;("�"mea� !L $ar clearly�"M+ it m��,`�*rec�&!o=a/ igen� K/��ill�* us �$r""4!mld ��� �&!n,)oamtag�3s "�-abs�:�wu���u})o9aV1qu.;�-9r�no2v si$ $'� �siQB� e�$\%��� Helmholtz��� �O��%$m+ Aw�%st!@�,2�;�. Fa)�*a!eory ͡ato},0J$ $H=-�Ri�|�v �we%rA75 TPhi�!�I�B�:JMPhi=0>�*c�H*FPhi6�D."it����:a� &E� s $k_n^2$� 6!f_��|y_n � >$ILI�alq8  se2g��E�stoodq �. back� I�.R#  9a�� �-��B�-�is ( al� p essesA��(�i2ThB�+mod� at .strongly�]-�2k%�. How�4�A�i*�4O:�&� � E�se���kl� ly shifdue toR ,��F;fura��mod�b� 9N�} cess!/o&e �U!�.of� �6mT})�-6%-� X I !* re. S<�/n��% $k�<2]}�$m$z ����*b�[9noB0��m-1j��, "=$=1+\sum_n R. $u coef�!��!�ins 8ng�q��-T��. Bge* fter&i #~$% <1|mi� >$ el!'��R|e h}(k� �[�{�8 i� zero�� �H/tribute�\is6*� Z�bk�#g���� u/su- ltiE���Pd xp!!Uu�o�& caJa4f���e *7: �6tra��forward)I�s� A,�4�*!-kn�? $TE$I���guiA�%;�4D1� >c�@$en8{nm}({\bf y})=2A�n(n\pi y�)\sin(m ��$ &��y%�%��:I�mE� =\piA�(n^2+m^2+�5y��uelise0s�@d"�)jfN�?*�8m\�|�n 64 a�L�4}}��(n,m)\n8 { odd }} 0k� }{nm$(\tilde{k}%;=a�)#/a^G$.Qu9F2"=/ l�F. F��Wa_i\$�,a)sup�$�$�;�KAMie}�� AXbs�0I_�):A�*!�2A�z a� s"I1�`' �6�rrv"�D=200+5i�3;@�/�� Ei���a9}�92pk2beA>�/�&��validi����=9�2~I37&I36cBI32JI3R�+&�6s)eVimagin�&&M6s)�1M#�.}6�FG-MC (soli7 Y9�a �3/das�F).2�3mY�- %a "N)�#@� cod)�g;1ng�?neviere!�e J7�`"�7 .���f29b%1})�cckAy$3$2�}:�9�0. � rjN?nd ?E!K($\lambda/d$"�$8� $12�1�oa6/6�.E_A��(o'R� ��!1��3 slab.�J��&4? =1.7.is�8)'Ded u'ly�i�&�J=� �)I�"k }Hi&` ef}). We��-:����.cur�fit�<���d��� +a,a����3E �egvDm%c H8er�7��$discrepanc� � 0" arV+]& =6.5� MA���:&!��m&a�OtakX9*kAinEI�� Only6� s���w��L6waFcorpor" 2"�8d g�*I�I in�B"q�"ul ;M�*r7HQ; �pJ?g?sk+al.� ��FH!�Q:JHa "X t"x!b*�? mIL?� ���0=e*GA�� ͢ �-se!����X� ai�$V&�ma&r��Z "E}�j�&�0�L � weI%!��-h �E� 4�8!8 ZALs�=ce��Eg3.L�0�9� �B 8��/ent wa/ *UB�"3 B�pu�&|, �Cat>� r�!{�� J OA�occur,,AA�6�D�� �K��J,F�kN��9suf<)�M�>�Er�D� junnel �%S� �l��N�!1�s�O � �� ima�Kb�Lla�3e}$$R�9n&K;�o�+D(F� ,���K�U��#!R�usual "^"�%.�0 teH��%?Re���= ry, �B�a8btCAS�� �"��H ,opt�/}: $ |u+� \mu (128O )u=0�7ich li8to �:es6M2 s. %5�Is� ya���1i;6}MY=rC(H%%��; y $i� gma /60}�)$E`d�C�: find, cf.���Axat %�R�H"�!�Vn>�FAleqsy$ = �0 , %weBtAc�U�byLrdirectr A�`uc$ %)i��A-N�awdsv2� div}=(A�  ((1-|D| u)L)((!� . %I)#A�$>� $+\infty$��6 !Z ) ��+����)�Dk<��{=�� l�I- %1 � 4dF@5ed way�Wano,jmp}e�re%��&"�= krok� %�$��DybC P !�ans// x&�I)Con-comm�GW5s!��2&=GMcPhedrad>mcphed�a�I� ��1, ET �v�g.cM 8��h! y� � Ap��"aRhml %can�8*{A�Q�:|����toU%��� %A�J�*FI���� �o8D�Sski�KpthA]�m�{)e�t��|E�!2�{.i&XQdU=A� %�ZV s. A $Ź cB�A(&�U4 e1g =>�L:: %GD�Aeloppe�Grm%I�Rv'I�� * �75_E�6 <�aHor�!� meso : smaA�y= W�H UO ��6�Rac "� A� �pŏ�~ heter"�UdoGP &� �?d"2=�k8Yr% I�e�N��!2�woi s��Bd}Qngu�V:�U3) ���6� on�.1 a-!F��f^!,%R J,.Ts% .k-tc m�Mt�W1b��Sc9s. So fa� �(sf orksA� A�.�iQ�?:�J� inne�&��&?a* �Or��VFs�Ω�mc}e�d!�d��S� � 9Q�s��undQA�XofPi��C�$thebibliog�Ey}{�>�Yem"�Y http://o(.lsu.edu/~j�Y4/pbgbib.html \<#Y`} D. F. Sievenpiper, M. EckmillA! E. YVYdnovitch, Phys. Rev. Lett. X876}, 2480 (1996�Arsmi�Y0 T. J. Yen et , Sci#E<303}, 1494 (2004.F�0r&�YJ. B.�V, AX Hold W Stew/L� I. Youngsr� 4773J��XT� D�varia(Xv� �6�Cs,O P"Urko, C.!bSNl�POpt2C$28}, 846 �3F�2} � J B, �( A J, RobinI6J��W IEEE TT. M�wEʡ" Tech-�47!�075%9.o�V S. O'B�Vf6�J.I: denm�5!�14%�035�2.^&BUV. G."EU, Sov U Usp �10}, 509�68�U6k}R.AShelby,A� R. SA�,�Schultz:{292}, 77�12�al}!�$. Valanju,PM. Walsq& A. P!V$8!�187401g2muFSXShamon<]a� a,!KalY3GL�)lym�*J. Appl. z95, 3778g4). �9&��L.�v�A.�^^+ 89}, 0939R��J A. M e� Tip,�%Bi�11}, 250i�2|V#�:Ka�UPerturb� 3���ar"l;.WLpringer-Verlag, Berl!W1995.9�?Ax,Bouchitt\'e,A7F+Ke�AT,cad. Sc. Para�Ser. I �33!3MA2�kL$V.V. JikovA�M. Kozl ��� pu`in��ics��c1Y%mc�C. Larci� 6%�XRrE�fC>��- docu2 }��%% * S�R�#e]�B ate.�a!* % %  �2f+is�y1�APS!REVTeX 4 \ion. %FVe�4.0{ +, August!W1.t Copy�A (c)!� AYcne�i�%Societye hSe� a 4 README�e�resib�I�m)�A ��6 �� 1$A&"2 manu�@pt1 O �}EX� %�5 %EK nothR� a]th`$�[�al�R T 5you�+� � ori�l�!�to�.�G�XYUBaffiliE@;)�er � )�� % �_ l�M,c"`)� many~F lapp�^s. % �a��� �*an�3lM��D�twocolumA8 C�pra, prbcdel stab�rmp�jou�8 % Add 'draft' !a�@rk�fYbox bl>� Ee6Ake PACS��ear23keyF3keywor�;R%�\q�4class[aps,prl,5 ,�Zed-� ,amstFsymb,� ]{revtex4eNTa,�: rint�S�RVlVsu>H�^>^�;0 \usepackage{� ic�1-}2+dIK}% Al�_�F .decimal�2;bm}% V!l$ % MATH -�  \newnand{\h}S5cal{H}!�.sSBAABJJBMMBWWBXXBLom L�".�bx  bf{xByyBzzBnnBppBqqBkkBrrBttBaaBbbBccBeeBfffBSAj6�PPB:DD}} %6<iQrm�5>a% hatibf!E}$a%.$b}F$!.$cJ$d}{2$dJ$!D.HeJ$!J.$fJ$a�.$sJ$A�.$nJ$!@.$mJ$aT.$xJ$a[.$yJ$ab.$zJ$aL.$pJ$aS.$qJ$aZ.$kJ$aa.$rJ$ah.$t$6�ri!��� rm{R>;�jI~rm{ :in� >iB]ou�  }:~aQ NQ N�1� N�1� N�1� N�1� J�h�!P N�1� N�1� N�1� J�h�ta} :~h�B hq� B h!�6dF�alpr{\ >� abet�{\vmtaF)m�X{\ BN @'F)v B!xiExiFmumuFnn:)�rangl�X.�ll 651k}{�AtLlde{d} 4\bk:�,pZ,pJ,qZ,q>et�~t}>&>ytw>&BsQ}{\bm 5�6vv"�* (:+a�bm � .{va�bm *L�va� bm z>H%� bm r>�� bm t> ��52a� bm > v�� bm f>HA� bm i>j �j>�1bm >%v��bm >�v�~ bm q>HA� bm a>�;bm %J2��8 bm c>0�� bm s>��� ��:GT��(T0  %0L'BibCapsrev.bjore�ce�m��o'U�5��e c�Nct� %b styl��Ccile), so�0un� �I�� %�F$if necessa�,%"?V{ �a�bG>�0} \title{De�D�] fO� � ensCy�(l6{t])ng�'a:F'er�k?�y�<{Graciana Puente!�  Dirk Voiga ,Andrea Aiell�N 0J.P. Woerdman� *�{Huyg�GLab)ory, LelP Uni2mity, P.O�8x 9504, 2300 RA *,�Nel3<(, e-mail:~g � @mol�\univ.nl�(date{\today)uaG;}�Se6m investiga�[$-z!\9�++ 2��a broad�Hsssc5�o�u_% a. B*Vl2Ot�xU$*qu?ct� ^%R ed fO"�(�HMue>�rix�/�4�^t�E*rorXa&�d�T"BA�hS-� #e ; Z\, as �*ly��0byM*E{Q  (arXiv:�$-ph/040723�:#pr? dmphas��i�4gu!!� ersa[5�B�a�-%t2 as &as)Dumi5 9�; Ni"_"��8 demR�+6,si�=E� �le2YeB surpri�� ly wr:��9d.]I\�-�2�o�X��.�ist;la�ful4 0er*�!�2Y!f"<# �9 �!�52H>)u c�_r(�!}>�1 meas�x data.���0}p\.({42.25.Dd, Ja 81.-i���?� \\b5{IM��a� ChF�mb�5ppa^+ ��q� ed-l2�Z!s &2[��un8/0on technology!�du8alE�!�2�z� DOP}. >g�I�i��it�an�r�Zum it =+ue�p�X��a�(�I�&A( may emerge� ly og!m�[lXBoAM�P�/amo�pofsB ��=& e�"�<caln�' e�qAѧ( ($E_F$) o�e�Ogre�/2] ($P)>--�T�a-G KligerBoo�&% �Fs�H�$��$A� 9 ��<�!' m ��N>E e�e-v�Nd"@:9(P_F)$.�exa!AB�� = 1$�Aq =�Rl)�i�/�ed I�($0_)q P_F <@81 \geq E_F > 0�5�iM4 Gt-Ped �$output "F$6��c Q`s sai�*g Ring. An 5G8/a�-�6��'-�W�%H{�soA7q)m0��Ik($D_M$)-�(Gil86}. Non�{I��`a� *�s)�A=�fwh!z`70-w D_M<1$�'2*M�5prs?a��'B2 mpanLV a'D(1� %�%q!�n( 27duA��. �ˡl-GI��"!?�umN�!J"x�&a-}6Ka�ad%�2AQ\ �E@,�2�{-�)� t} $E_M$-�LeRoyr�.�%�@ = 0 .� �X]�%$a $0< E_Mi9%�s� )0}�a�}�A2u�_.ach)j� are%�)h:HM HA�. �1a�vi�=papers9a0 2}/ ��y e>u"� ��a!@(D_M)&"7!�Nm� �#eN2\)� � ���J�AQ�O07j(�', ai|CE0 N�ņ�/ _>v co=�0:$bQ7 zero!total�F� Fa� ����}�.<y-27D�TndI�um���Cu�)"MH1 �J6@A\C1�~eum 2�s��V9x'u|%_63��i lo� W co4�A�g� }.\\�A:h �)�7�2_ u-�Y ��&� �Pa��R��a�a, �70 mil�FI�� 8 2;.-��6fir[!� eoreue�x�3��!�b!��  a:LaR{M}(DOs &3!akdl�6 �/s:� S� II�Sre�evM{-StokeAZ rmalf-Dc�{&&)�FbRd*-miv ic (�05�ing�: �A)6%>p�k�B�9u|z�v�b)<P]!�Ozm�!��e)}!���}(e spaL  or�!or�sper�0�0a=� �> �. F&pG� �9 X�!be !8 J ��es�Q�C:)�EQn�a-upE���V �PUEQ�l�fN� �s($M_{\�$)�4YE�bX .� ��6&l��3/to.XRUC2ts s.%�Y be Q�i':#/catego&v: (a)D�`onary ( I� ch fl9��du� A�n�imeE� (b)5a�.I �1UiP)E�\$u2+I|s q4 Ac��i���iefQ�&� � Qng &v8"&$(E�,� J:1Y� wer�Ivea& b!�;��B;<inYV�draw our��clu�r$bND.t�8i�}��9iI�&.�est�^h.X_ pass��Q 9P5 be\~i�A*+es:�g!1��B� O�1y,5c�%�G�l�Ldia1�ei 0�l�x �E5 $im�%8l#�^�=n�  &�h).I�Mp xje��&q�w_4�%�]�/ m'�Si�8veAu�*b�I�is wid�e�M��pa)�2a�%�XE: \subQ;^zA,Co"�{�sA noch'v�a�of _ m�?angular qL2RohhE Wolf03}.*�Q�O $x,y,z�: a�&4C��ia�zord}{M=, 8!�$z$-ax�(%��F9m�p*$+� ��y % � spreJ��@z�@a�ka �2 �F"�<o 7Qy��� <xial}� roxi� on. �a��p;}�W new1} E_x�kT,z_0,t_0) \equiv E_0 �V\im \%V t_�/ \quad E_yZ91Z9D+� % �o� on-,� xv�&�]� 6Ni&de $x$- �� $y$-9� Giv@\t!��& $�)$ ?��5��pB} $z = z_0$�?ime $t_JI� �is-��� orm}�A&>P�� x � y$ w�RJfa��� 83-$ /��*?M>�6w ��MSch,4d��iE�doublets&^tE}��1{)3bles (e/vAy stocha� �j� ):rk2}��u E} =�Gp�} E_9=\ 1q-J<` $E%�nqo1�now�>C a $!��R%��� �tp �uM�6�60i�a�-n�p, e.g.%�� MU�l{, ۆ, �\}@�n�m0�H��n�fAb��� "!bt�B���� ?;a �1c "� }� ����J��s  $M^J$,���WEp6"S �� ���a6� �u��ne�� g-� �A�? �I7 $M'>�f�iD.4�3^J$�}Inݎ wide-sens�m�: �ar� er aO%�a��rter-�1�6tHrot�1b �`%ran ��W�yMB1Z)� $2 Jo2$M�x %�M\*� �r� 3} JN~J_{00(_ 1}a� J_{11>�)1.�W�<�9� �;fX?q���"�x E}'$���VX��2nC�� .@S3aeE:p� �t �� )�l�C�7 QfJ$v�4.�' = J � bf{EN)l�q�� �] Q/������ ��mA��am� Cjnd,? $C !co�8c-jeՍ��.d�[9MX Born> a*fA5} C_{ij��4la E_i E_j^* \c0\q+$ (i,j=0,1)b�� rack�p� W =c'v�w over&P>Dh=5�� ��2�#_O f��)Wo-W $S_\��$�_S$, \ldots,3V`�!u 9>r}6} Wa�arm�" \{ C�"t\},-8J{NA.M%,ymbolmZ[Td}aeP�� ace � �@C $\{\t#� 5�nhPauli[cesv7�<e�jahn {lcl�N f0! �N{1}{\N�}�s3��O 1 & �h �n1 \ ��),�cIs& e1ReM�;d WX qFd\\ " �2�`P Aim �Fe&M� h3RhFI �X)--J.��)�F�  Now, if� qA* '$�i��BFa( �� ��9_s easyn� ���B��� $4�B4$ ��� av�8m���M^J_{xH�)S_\nuN�� sum�  repep da<�und�_]��%jm9} M^�L Q^\dag$H(J \o� s J^*) b�aэ.``$ ;$''2� oute"5 �7t5 >H unitaryy $ y��1�h О�� �&�A�i�&i^2uh+.>-1I��m.�F(%�&�KOqE3�A��m�"W � Cb �F"� s�(S) =� (S')�r��raD2 ���isp$Oc��rD7b} P_ u�{�x(S_1^2 + S_2  3^2}}{S_0N=uO}��1 h]K� � 2I %�E�.���$J$8 )c��� ly4L ival�� s!$16h}a3��� L��Le ( *�:E e $4"l zGJNn [ �� E �`p A�� mph{non}-6&� �>i� 2� >4 �m�c-I} y!�? �2�&Q�f�!@U��:� as�*�$;I,D ,ticles suspe�^8tc.?;.ם��{J Kim87,Gil� � �w�  -R�!.u���$�*sembl��y� '�%n such a< {�re"X �Q8&� he 5]�h"S&-| '-�� "P ( QP /Q�k roba�� $p_,�#��n,%�-�^M�DS �ten~�� F!��^�f (\ov�Ae{2q}�r�N.?�!/$>� rm{bar}}$ы2~� �(� J5x"���Wv� 1�Z���sum��at-�} 2� 6�.y2�JKA�iA�[��us�)t�Lf+�auxili*� $ HA�t�QLH� ��12b} H�u��9 _� J_{kl}^*"� �l = 2i+j,6 = 2k+lR� 1,*U��i{ ,a�i� semiei'e�Dl its .�^� �Y_0, 1 2 3� �S� �(%q&��uz�{2]yx�"� AU.! �$xM$�Yeq:�D_e[Pc[� 1}{3Qb ( 4 M�nu=0}^35u mbdad ^2 - 1 \�A) ]^{1/2N %^J ���-fp \log_4(1~ \nu N�" ref.:.�$a%n-1!��>� "�#�$)x� �L c!���es�I p��aum Ekim},�r � % $4'j�{J����mZ\ $7$�� �] � 2�j�r^roy,b-�% ��`.�:4um�[ir�E� %ge��1?"�M$ &b$15�W6� %* �}!���FH "����fc} 9� �$)o$�! intr�mc��A !� um, ��I$'�(���>D%z e�hU` � ��$ u}N�Q�v"�32�for���� � Brown; o� !�� ���/� a�a liqui;1mck�%shE�V95߉w�R�X i"l�X.:'a�Ko�4(!F� � &�'Z�%M,q�si� �"&[�)"�\œ ha�2 type%�=h�3(��g$f7Ws)21�|/ �ndA%U�L�iW��' ~.B�.M O�j" &�2build�.l�l"e&�q=.��)"' n�"�,� w � + he��.&[�+% ?�� Lawq�� b��Yke�of� %i;�_˩ give�1)� jT}}���a��&*M;,O  w0� $p���2^��: K %1>(&(eӔ%�;�*�7#? } < ; e mM^:,��nd.5 %&s��u��rel�#Ղ1ѱU%I!�Q�.�)J.�\no� nt Ta�<A�le�$�.�ve�y����A��A��$a��+�#I�� ���7"��s n/��m7 !�.�a�e��ed.�9fa #�eQ��m�� i�A��&��-1��A��,� suit�": I�����; "�!i��E��2x�\iz-F-t!�-pi�"ich $N��Gn�4 )D�1rQ(e:|I E!E$�mv1i�$D�n} ��tuD,)�CzW͚krv& �� &% >�9Z�>rr9,wv�e =g in}=9�!u=N$.  "� S} (j"C'4\{ S_0(j), S_1S_2 S_3(j)`�% |icx-DG�& /� :�� $j$i*6 $j \``{1"� N \��4Pa $N$i�E���6a�llm��NBse $4B��at�<�"ar%1�Y3W $ $4N$-D ``�N'' � $!b!,= \ bf{S}(1)�",&S}(N)�.;%���  Gg1�a2� �#}"O?,Gn){a�e�* )zs� ��.�%�}1%.26m q�[2zVAQ W�A�.�9byj�eq:�� �N=ɥ{jk 1}^NŪj,j_0)=d_A�(|  (j�:5� N )��>����: V��*�Zx�g�ATeݐ�1I�I��}$1Z)! A�Ie� � a Y�$4N" N�� x�zA eq:3�#b{M} -+FM  1,1)�7" & N)� \v \d �- NJBN,N?��f��block-�_1,j_�s)j�-,!��/a�reB e Eq�fEy)�ہC mpac(6�r�"0%�I�A�E�!X�" SI�. BAf�Aoy� � t���i %bt��t�Es�s�1"�Be� �D 04_1$o@$D < N$E|���V���c�A�-zţ�(F Ofr, v�oro�?H)bu%+ctor,%��2�:�%�-/�oDf(1NA�%j5Y�Aj�A(E�A� & &I�& Y�&& A(Da&M�9 �f,&Dn�%�vA�M\;���%D),6��uMv qmi�it �X!�a~ proj%}sв ���a�e $(N-D)�_ �i'� e�'x�Alܡ($D<I1 &9Gto+��%�"gmZtP2L����D�"�.nx��7w$s: a casca%��"��o"�crR-]"�2�w 2`}no�� is cNs:=. %Mor�jworXl%at ;2� 8})"�~re�"s6#1�y��$-B,�a��I�}2��12ect]�B�ݾV�.�sia~``E x .r''�T !��,5 36�<A B� nk8�m(9AF}MJPQ�inI (�z+71})> e�' �s�b"�aM� ,1 �7�m};5al"�&�Ap&.T"����ab%�6�;`EPOLARIZATION EXPERIMENTS�-igskip %#K&43E"�a��=�HD {|>ʰ[�T,=0,width=15 ��}igure1{}"��afig:1}�g��1�.7 &}>'?.��}�text.�, q�%f����H!v�Z:6c+u�s8E9�%� .� &�Jf �a� !�q�Vs6z��h* a �� cedure: ͻAl"E*� h?a�suc 3���% 12fba�mA� (3H ($V, H, +45^\circ$N? E�($RHC$)2M>6h'�D� �y!J�8�2' s � �{\r p��� #z�� %� �S7 �2W� V���at �H� Z��"�?;qsu%�thN� %91��gh� am��..{�xa�GJ!�!��FA�&$ .Dn m�� G�)�16��E�mu�.��: � Eq.�8�NotNa�8acf �c��� b 7i%.� ($-UO , $LEACe��bf) $6�6$.nUjlly�a�o͛J��rr5š�\4a�� i� . fuH�P�. ^��0�!ll�O�/ Fig.~�C��!�o6Asourca�#8wer�) zed He-Ne}v,er at 633~nm*fIm(E�}"� � MQer�$t (PU),�s�lefixed+(P���lf*�8 (H�J�6�8 (Q1b� "Ar e ob;� (MO, `�,mes50/0.55$)_��!fEԉ� �"�VA� coll�>�?k�ndard_�U���P�050$~mm$/1.9$)�xA C n adh|,pinhole (PH)� P �a"�P*�=$II�,�M�eǎ�l�i�?��%� (AU!EJwa7QFo2�t*_: (P2�oge�%E��Uc�AlVW(L8hotodiod�D)-) prob �Y�I��h�retar�2a�P�6� EC�� ��al^h�/u��/r�d �;ta�%acy. A� !Em�K��y 2Be�eKG^=�RZ�im!�O }A�C�,4�!sx�t ��air ({? }~B�S )p0t�k#����a�cFd s�.s '-p�:6�!%�se� �"w�;n ��v%s����YwJkW\�ed�"� �� o $|t}rm����(q\pm 0.04$.�U*? C!��ofq��P�a}�4var�Nm��i&AYd n��J� �#� �i.#}�-1e�j{D(}, :�" ϣA�eоal6Q��!0y�y�oj �"�q5H �R�itY%�.�, �&o�ey *prerK$�"Uf�"�k(&aOwQoڌur1T�"�:"� "��k� tem[(a)] �2�)�: ��+� <�styrene��p!u�82~\mu$m dia., s�1Y$in Cw��, )F DukePvV c Co!�USA� \� diluA��M;I �+[(b)] S)"E%��7$ Zenith$^{A� TM}$�!�sheetw<us!e($100 � � thicr �S%$O�[hs Hoffman {GmbH}}, Germany)� �hol���5 shapa2��0.� , $1� 6c$"�y$10 'Q2T� 68 �P, �9�6� quartz/siP we`�"�!/| % Lyot-3 .), yHalbo v}, UK:qstep-3 x5��e2 (NA=h�reA�s.~$25-� , $51�6�$7$ �ESKA CK}C&�\Mitsubishi Rayon}, Japanf�i��2�48:�� $4 24$6 �FT-x-URT�E|2r�)�0Thorlabs, Incqe6�=Y:�.X22�.~$126� tASF50��graded-�6J2�72� 62,5i�N�GIF625ƚ.%�6w6r\�/6�:K [h!]�O2fO2} Me�edmW DN)$ vs.:x}$u��� $nR��6~e���M*!_�w� ma�Jl&6%"�+�?": r,HM��I\ 6=Z � grey-shAD a. LS�*��l =ReSaHP, g�i& ,y. Cuspidal ��9%"�("� A}=(0,1)$� �B}=(1/3,43{4}3)��Ci;3,1/2and&�D!,0)�LD3>�F)�(6v3f'3�']'�H���e�s ($\t(lozenge$); II��J� 7ullet� ~��;�v����tri�R\ ���$),  �)Е;.�"�H � 3u8J/(3�]A/�:2.(% �ilV�HBDi inu�Zla=Fra1�ye"� �e(a�s,:�2}EV8"F �a*Q7{p ���6���oNg6 �%W �&�M3^�a�V�- �>XSwf �Z]��ce�{M}�& UceURef.~�(u�&se6�� "b6!���E*"n*97s��, Tfor�K7� *n �@�@ š~of ad�bledp/!!; �"�2�� G.c)P� . As�apvRZ[A�uh!\ ata, our &�� samp*�ed�"?�� ill q�(of�:��lC gree�1� A% &�YB V�a -U�B�5���imilar��pai�6�U�)$=� U�*�is"�/D'�+ _��� &+2�$�N 1T�5 +1f�y>GiJ? trop��&$]�, $0\leq�M�1$.& ��Qk�]h���y�A�n�di��Qs�~A}�  C}�7:E&1no؃ve��ny���. WorkA�~og�VA�*�� s V�ia�,1S���?e�pe� tun�"�s8��Q��$iz�L(�g5k2�i���r�W�a��%@229� %o��^jR .V� +b�s"����Zat�O�O� +}c`)]E�fK�,!�*�6����e��03ytW0�fref͘�q�cylind;�F-�� t2#�'9e �m$k|aS1K�E�q�6�5y9b$]�2���`�*t6=�. Fy�<r than aba� 2~cmy ed neglig��J%% ($�\a0�xf�&3��` ��y�L :L0$)�[���1o S u5~$2Wa r�1 �ikw���TalW'�����8h 0~$c�N��eason @2u5umably��sig0�c9Y Rayl*4Q�A����)y2�TQ��w��4 POF}a(I �e"��hem� a�7u�� �*b2]�D2���%Eq�1gh��!�K(�>t). By�Mo�!Bd�� M� 2~mmE� 13~m!�� E�ȉ�!-��wŮX ɃG(�^T�o"�^.!Cs)� ���0o��p&Ph��2 of e�s1!�Eq.~(��$)�:ad��� ^ :�ݹ*F9�����;v_�!� �fe�Iu �\o�E�a<�Y��s,�Din&�e�.|5 1.&a �Zr� �%���z1�,�=}*cn� tњRZ�r a!li؋�oc& )��k� ��]� �. (a�*� �el ".Hs2Ao�� sstkA���&� FWHM.)�n� &=Vin "�!q2�34"w4�! s, gq<� M }dt�(*� ), �'��@(p .5E�6 �GW3Q�'}$/ds�4un� �.YDiscu��}1�6�w�vB�!���$�hEd (a) =���Q�:w��FY .(c)^;�h��6f it�e"� �'[�� �Jo��upp֏���`J $�� A}SVD"r:�=e����r����%�V ssocəd o�� aG$ C�".�F�eQP!pm \{$7E�4u,E$\ i�' 3cy�~q� ")� A;0�}6r�;ǘ � ��I��cA�6���trari� in >WA(}��.weq�I��eW��:M� M)��hWaI� �y)�G�s*���6a&X�}IY�Rb�L9�O u� A% ess-�d biref��e����M�.�*��"�68)m�td�<n add�">� �ounf!!���A/a few�>�� �т:� %*i"k$Ou` �%�� Ma���@����!a�jc�_e: A}~(Q�=\mu=1/4z �&�aH yk�t�>�USAi� or vB� shor+ ber |>� N�D.�1eP=0^�h�+PC�?B� �E:=I&!��y�&*s�as !U�"C6�\�M�ic:P, {% �0%!���;i*, =|1����N� 3}(c))�a�"� "* � ��varTF�A�Xol��%���$"�a.ckf:I<�Caj ��(al� aȑ����3�Rb5en �_e, did�*�v*� `�idl��U�Ma-abs�<of {\�v}1!Km�$Gob,l� dN jur��-1��!� combud@�� b��H"��couldf,�) u a|1�5%YH�s�Irum!}(�Q% J�2�  t�*� :�� "�3QE�a��D�%�a:F�; also�wn!EB�cviFQ�S�edd-N@)Ru# �%0 G>7'.�Yg� "g+��e8� &�)**� � ov�'�""�)4*.m�)� in a Wz�pr >B+A3 !~e.�%��:�ty/n,+ig�:* �!8aib!�lA� �1w|Aer d~�D2�gla�(�(+$�a�4on{CONCLUSIONS�- ��|q� e�ly2gl% �a�:� �=.�q�� W� c9!Vs�`di��&�Z� |� )2�� $�k~h�$+�} oy�u�i'��seb,i rioVa&nP � ive}  A1�>sw� !Bi�du�*� �Q o2: sum)AGa.�"�(�O�&�Nal.���/���-��q-w%��q�pAa9&}5-r���A��>�$6 L,$1p.C��;AM, s�lf��iOn���*���l�:\�rJ.0}��$�ewuAqpo�RSMFzMx( s"�%x Lnri�a4�O� -���,^&, &:)� P }���!�9H fyEM� uF��give e�.� _ ��q�E# >l��"�. A cer�Y"j�)9^>>-]D�-D :IA dA%w�"��d*far��aBi�su�-cur3ly�B��z. \\Fur�+�Z%�3%�a�-�%%1�p9 inS��) &%4:3me� ism� ��j4(ell� a�sisN�v��� F�7ndH~�&w�jK�(�of mZ.[IQ�vz_vt�de�ce��PtQ�7 pirim��5�1onJtwF -n|-��UeU�s���CP3 s�3-5�M� w3�i�so:� �0���*f��� greaA0benefia��6(�c� M!�n van Ex>!�J Eric Eli�who�7ac�,la e��>04AGm�!���FOMW��r���EU ��( IST-ATESITAOt�|."�">i� {ab2�D}�d�gL\ifx\csname natexlabq% \!�x\def\$#1{#1}\fi ZG bibO font>J(+M#�Pf�Q$�R cite~R.$�Rurl^�url#1{\27tt!O%8{URL Im�comma��b�Lfo}[2]{#!�>!epU� []{S'�:,tem[{DOP()}]K'b�_ {note}{ J%�de BoZCT!� MilnMf�C.a# G���d�S. Nels5@B�2}, 934��97); %gM. Bue��d P. ArtNHB=F�6 <9<(A.H. Hielsc��Y�N, ?Expr.�1}, 441{L B. % Laude-Bouleste��A. De�@o, B. Dr\'{e}vill�(and L. Schw�+,|�Opt h4P282ǣ;2s2p{uW4 et~al.}(1990)N"��w�N�$ ��all}}] Bo %�@nfo{author}{\bibfLnamefont{D.~S.} \bib(Kliger}}, 0info{author}{*f+ J.~W>?Lewis}},<* and}�P C.~E>PRandall � emph���title}{Polarized Light in Optics and Spectroscopy}} (�@xpublisher}{Academic Press, Inc. �+8year}{1990}). C$tem[{\cite�Gilu@Bernabeu}(1986)}]86} 9rRJ> Gil}:��O E.}~���6�$journal}{O!68a Acta} \textbf9n$volume}{33:@(pages}{185}=]1286r20Roy-Brehonnet%<(Jeune}(1997!9LeRoy�9F>6Le 2[%�2!Ej�BJW �ZC8Prog. Quant. ElA{C^L21:I1L09NL972L0{aiello2}A. A �, J. P. Woerdman, submitted Phys. Rev. Lett., arXiv:q�(-ph/0407234j�{E[ lf}}(2003!�Wolf03Z�Uz9.UUy �� An{12V0263F0�60�gisin}M Legr\'{e}, M. Wegm\"{u}llerE� N. G+,B5u,91}, 167902 ) j8Mande�!0E�5!>  BookZB�mL>� <���I�RdO�(l Coherence%(E�um�oec(adeR�^LCambridge University�j.�2 95})2~f:�d�d0Principles of5TVR$Pergamon fH 84})�%�5Fsixth:H�f00JJ.�S��Ku�J.� . Soc. Ama� u#U �:172���328Y9I200vl$Kim et~al.%�7)6�Kim, i$,A I}]87J��yqK> Kimm#bi)SV b�)B���� B�E� L%�=� B�f�42F-�433�>�198:|( D. S. �~W�_wis%u C. E. � , � it*� l� o�b� sp�8� , � � � 0.sP{mckintosh} F.C. MacK �$X. Zhu, D.�!in��$D.A. Weitz2�B (RCa;t 40}, 9342w89.w> �Ap���,��  04_1�}A.:� <֊ J.~P�.� ":�UL�R.n�70:AMG023808.�uօ�q*u 4029�ӈ{POF} For a review on POF see, {e.g� {) Zubia%nArrue,eh Fib. Technol. {\bf 7}, 101�1.��{unphysical} When measuring with a pinhole in size similar theE��Ukles, we derived many negative eigenvalues $\lambda_{i}$. The resulting {\it complex-v1xd} entropies $E_{M}$ are not ev�athemat�I76IiQ��� ac� Y. HighJantY8promotes recombarion!�A*minora�carri�`$trapped at!-q. T )increas6�b G�� orm toLval ratA��)ex�d!qM[ b�� (CB)}( Because CB ue a! y diff( t ��heavily!! terials, ! )� %O must be !�E, typ�  no mor�ana6Xew nanometers. However,�achievecR���VaBV (NEAYEi!�0quired, which!n turn���d� � a����1i . way.�a+ fre%Ealloxide)( carbon-rel��Tta��nts�to!~IRcrystal2�for��<1 hour. After on�V��2s�� ��,-�I�%�doe m4��)�m�)��) (re-aaranc�AQFJw%E refo� _.� �%u��shouldATavoid> f�(AHC)!=a Cknown�T�<removZ)��n�at %�ively��.�嬡CAs- P a�,Ga$_2$O-like h libea�dV=�s less �4*L,%J�ala� Y $_3$2]rI�s a%Per ^. U I�*Xr�}��,bZ are E�� toi�volat� �.�. O�sot^hand, it��%�demon��� th�es�$can passiv��both sha� donbnd accep�}impuriti!��:A�rA�| s rapidlyA��Icon�r% . SiA� �] -ben�Q�2�is=trolle6 $p-$type _)�ma.�may hav� adae� ect��QE. I)QpBnt pap�(a syst7 stud�AHC i�`$vacuum-loa� ,�re�eed.�AHC!Q$the associ%�analysXk r�Gi UHV,C�samplebi! duc� UHV f throug��cha� ��d�Mnsferr!Jetw B��� �s � � G {tm}�� Experi8} Two���| �b � . S�s (13 �X 13 mm$^2$) cut from Zn�(1(R�&~ (001) waf9� s� � iz���r ?s. Str* � "��100-nm ک��at :t 8.+ ��(EQ.�3 o> Prior�in���onA��F� �G deg �a boilr solue�Dof trichloroethyle� ch� �� BNH$_4$OH��5e n���oiH͛q�7 etchA�> 2!_ disturb��stoichi�revAJ , it�!�%D+ epitaxial23s} � . S� -�I-IedI��$ i� ��e�Hv��eu s� d �>three-m�a�mpA� sist! � F�ne�i� i�u�  !� ed C) Test S�c (CTS)#.H� ��i %� rf plasma!�isource,� e�  t�,��a l�transl��M.� dC�x}? % �300 - 3�� �.t7� is�8ed �=!�^-*so� a bias�ctag� .&eErM7 �.B �0�Q� ��!�molecu &n4n a 2.5 cm dia�  Pyrex gq ware!0ron��a hel�!�reson!Z 3g�designi at J�O rson Lab.��s�air} To��;+�f� gene���drfA ɽor� a�1(c-L !bed"A �o enh� 3c���. To re��# urr�aIJ�4magnetic field%y1�� exi��ed1�orha perman�� L. W�� a�plaA��onegligiy$( $<$ 1 nA,A���an NEA!��w4e�%�wQE a�6>�madHCTS. r AH� ���ee��[CTS2� "�} �sure droa��a few �\-�� Torr.\wi� � minu�a AHm���') me�I�to�:� ��fe޹N x , cool-dn anv �� E� E c {8of cesium until%NR -yE< peak�!�t� .and nit�(-trifluorid�&-�s-ZU� agmaximu(. !yperform�n�l-�l�ul?)�w �' Aea����tro �]� : 1)�no���!eD , 2)%� aA���88-VoltJ/!�m�u��4I�3 M ]k�:lU!j� <.� eachAF�QfreshUJ) !<���;a!V� var�m all  &� ��fix� �Q ��r , ��5�:�,Q�]\ QEq� d. Fn1xw!� at 67��a fun�A�.� . QE��as 16>�)�%'15�B&Xof!6�GQE de, 3prolong�R, e,�` P .8\%m�40� W� QE!��UaY�]� eQd %I=IQ r&<B@n�Id�ء�"GAv �data ind�A|�$rabsorp� !>in�� is det� al��8U��+n0 ~' A�get&� . If]i&eA�tinue�:�is �b� �GaAs,"!� $p$-VJs!� �regio2���&�A�;� irol�e2P,?!.� rais{hem{ level, �I I,!��p��.Gby&�U eedaw#AY pair!�!�ULly � &p��!&� o'$pearton} IN � ���A��>�a���!d7s�N also6SFB�p BB� FL4BL���a#� (open squ�in ��R ��W 6�"$ a� �, `p�z� m��ej� prot9 ng�A�Ua� im��6 ide} T$ kMf�Se0ed��� �A� 2���5t��es� U0Ire)O Kf65."L f�8}[ht] \acerk @{\epsfxsize=2.5in8box{ahc_fig1.ep|+"!y �n T��e}� }!�u� toq�aNs:]id �l��*�A ��IFsM>%A�(��triang S�-88 V&���`;. OneQ�.�"s %��1�.}�$-t Stud�>W V baylac}UOa�t>ign$ant&� �occur���&sul �>o� ? M�deuumI\�:,e!i �a�� � &� aA^e�U�&< � �_q�as� . 57*�!�!�a_%�he2� ��Aten sequK.�a@5yTC y 2O Tr Urep�;ur> s��%&samQ))a[�&� �,I��Q�voM"� 2*� 2��*um� )A��� 3"T !- 3) 62.�% � se�%-(!��; statN,cal errors. B�%�"�af�w���(sim$100->A�erA[E� � ��!�@um,,-�����2>�Po�5iYB�$wavelength�.:� 6$itQ�,6p6L)!=� .�2^ 69W 6Bm"VConclu>s}Bv��acan ba��!gU-QEɖ2���!�8 &� M*��.+.2z& R#� �� 5N o&#� 2( � & . E�!exIS�`� ;a�f�noU �R . W��0nk Matt Poelk�f6/�provi� useful O/& � �(&U"�at ^ labo�%yY�>N+{0�-temV *�&*�&,2�&�.E*�&�&"�&,r/�&, R(�& , C.*w&g &j&(, {\it Appl!� 6Lett.}- 82}, 4184-3�0.�&TC. K. Sd , B.A5-e rJ0Pribs.�*o� �7 IEEE�&ticle6�&on�c�5 12-16 May6 , Vancouv�LB.C., Canada, p. 286.�6&� S.�/� !] W. Corbet-(Ma�-(�) C= �  S7o6"�ors,} (Springer-Verlag, Heidelberg,�22M� Y. Id�dzYam�).J. Vac.^,&�.-�A1!� 1858�0942Y� M. B� QN5th I=(� �& S�$( Sym MZ�.}/]*$SVT A�K�Ax, Eden Prairie, Minnesota~55344�,Z�.�;-.�� u�"�,"� for GaAs/0$_{1-x}$P$_x$y�su}�� gr&by gas-� *� beam4!y�2G5O!ar��FC6 t;� p5V 6�ac�ssC p�*y-h07and�9 �b s*"y&�in B~ yYa, enab�"dir�*� a ��gie�(�I litting. �Aon-B�-� � 8��. 1\%F y 5�h.A5B%6�.Si�!�*�$%Z5�,int�/��U3r ed " I � 1993�*10 {9�!t��8 q �sf'm�umi{u�0!JA�E�P l�-3% W�&s5/�~80\%tl� Jky (QE)a# a�%epi \is�0.3\% or�). �&�*fN0 t�67� s6the5L�"mi�E=sQ%;A� 2!�*x) D-�!t!� : �1T&c`)�thicknes&�AUl�-mismat�ex�Y"�&.��1u�8sCj�of "B.U�.%is alte� �: >}p8��Z<I�umU�ax<tails=jK*F�݆specif�$6��;:t�I�w:&�$6HQ� %:,phosphorus f��i�"!�8!Tperiod�U�:1 summfJE�� u=6��* ��*E+:e}[ph] �:u�̥K6�N[ .} {"�  ]ul�J @{}c@{}} \h� {} &:(\\[-1.5ex] �+ & W2>(nm) & Bm�  x & No. P% \\[1:b_^ 1 & 4  0.25 & 12�F 2:"30>"3>"6>"4:"4BD5:"D 9�6N"1B9�7N"20D8N"3."9"3 &0 �1� f10"!2&"4f1)T!I."9T-��abE\labelI�82} } \vspace*{-�=I� N�"� ��� QE$ F�"\5' �nx �'Mo3) peak6Yis*n 1.2\%�{"� trum|wo($tinct step;#expec��f`.a�de�6�-Ѳe��d�.M� # firs Z corresp�8��}� (HH)�:#p �Q 9.�s9�Nal�� (La�:a=v)[>� . 0HH�4 LH-�.582 meV����sl_ 4B��Eb;9" � �M� Z} �;!�J�A>� ��>�1%A A�M�*changAthu��6�.�� kl<ile@ :rR�g!�Eza ' L ��5�9 E0.� ��HH7LHE\� P86#�9�� �'i s 1, 2, 3�4).NQ�is9t- �� to 0�ekee�!�to>%20&� �tO�[2@B!�` nisotropyLqe}Bu%�N��px ���S:daLH-u & i( so�o{ �I� . AlMg2HHA& :<eVS89an-yR�A�6 did � E� *} �8t� 8�!@1.7g ��O#�$:|#0'i�&gi9-.�}#f!?!F iz(*B7�@�@FB!(so*�),:* "�")I�R��("�")Bc%�JcB�U"q e!�| �q(4�=/�p Y�!��6>�  ($x$= )I4rma���FW$ 3Eĉ�Vp6lBf�)D�G.` p ]@M�c$3, 5, 6, 7)�8a2.L� "L���+� .m/ %K ��s9�� x-ra�1f� w}�%� xsma�Q"� F� ,y�6� �wi�G�#"R#�. A)x����ad>�ds]4.���� ��p�(�a� .5\%� 1 6�2H;)15�3�(%)20, h"t>�#B��,E�EE QE a���T:�A3*'"3B?"B��?F��12�pe%B1i;Q!d6 � ak�. stoo�%erm".f � ��e.�:pab �:6#a)se$ �*�y).r���U� (3���N4 >�i>���"�zp%H�% adjus� to�A`�ln"�4�B�R*� ��tN� s 9gN��11u�J�Q�� 2b Q shif �wards �# �Fuwa.� inde�*�:he:�� \,:-�ti9:aEed� .�%�� �])bov42,���[>uA�0�>D.&�6��i0�|?��� ���t�r� ��!� U}eEX s"���22�+��4B�.*Ni]g2 �!D� q�3�94t���; a�B �.�I� 5 nm>B�"�2�&We�%&�e�� �I" ��Ped&:�"� s byJ�"Z=2&Mi���*N&ls �'H �5g��(�QEQ�,n�43A�ZlMa]s.@6*f'A㡤V)"a QEb!Q 1\% �..Ph�<ior69 QE }Ra@@� � F�=�of.�%�syD~' �' EV', j&'&��<A.��%AB.' JT 85}, 2640.'6�%�R.A�Nir{ N�M , H. Tang:�'�!( G. Mulholl�]C'B�'A2 & 231  W6).�~�S,J% % Temp7GE�LNF�rints %!�meFGDby Kevin Stenson %>Q^Hle} \usepackage{lnf�*6_Ticx6subQ6amhBsymb} %"�Qs�S[12pt, v,11ig,Z]�%�newgR\scatt{\=Urm{}} ��R$ \def\beq{�equ� }} e'6a6narray.6a{ 6 �{\�a\alpha:be}Wt>as} 1_s:3 GeV}{\,\mX2 : M.  : 0matel}[3]{\la� #1|#2|#3\�jE9v{\�. e}[1]{|#1V#v \veces#1>u}{�. }\;$>hl�I<2I>J)�rarr{ \�UarrowM,epem{ e^+e^-�( p}{qF(B�Al)lef)$jp{ J/\psiJBpsp!Bpsi^\p�9+ps2s{  (2S)�$q^2$Tcm2s1{ $\,{\rm cm}^{-2h+ rm s 1}�$)[{D_2^{*0A+ +st*-�mev{ ]a1/c^2 }ganB.0% some macros ch m(helpful: (u0 in m: sis)6+ krz}�Mr4��4{{K}{}^*(892)^�.� krzb60 \ove�629 �:: mndk6=D^+.� ` \munuJDl�Dell E_ >JphiJJ_s3y| ( (1020)\; H nbSJ�zS�F/k�MK^+ K^-92BH phieF3v�e �eBNkpN�/=5�pib�clmunew6�s,rm{CL}\mu_{(*)}>�gevcsqVCq;>4ccb \eY�.>+thv>\heta_�vJ2lV2elB�cosFacosw:�sinF,sinN,X>� XV�lBCcos^2\tF0q>+q^Bayv>`7{}/_�QmaxB;bZ  B}_{A�B1 mkpi6mm_{K\pN*:u)i8BVam8]W<~\exp(i \pi/4)} . U�Aq)^{-1T%2�et� Pit{�jl.>�prd�� ~\a~D"�cF�plb/L�3~Bj0e�b�m�{\Gamma( dk{}) / pi{})}Vbr:NN��RrzlnR ��RmvR�_�RphinRN�ph^HńfH�R�65��9�f�kpi>cj���>���6�erme/^2�>4�65z�V|krzy6LD 0.602 ~\pm~0.010~��(v )}21 (sysFxZ5~^>�rvv�c67 1.549 \pm%0 145B>twoJ@0.713 6202 66B@vNr_v = �{��2�vV828�V:6�r_B�r�<>'3F�eB%v` \re.o 4rmdefault}{ptm:QHeader}{ci�a %{rl�h\h%,{-.4cm} % \�8ial{psfile=logo�800% voffset=- = %-10  h 20030  hscalev a$=0u\M9u�Qaphics[�=2.0in]{��&� ::str�B}{0.5X~>�  {�@1cm}~\LARGE\sffam��LABORATORI~ NAZIONALI~ DI~ FRASCATI}\\ !f {\L�"ISIS-Pubb�Nzioni7�1���1$>4$\vskip 1cm9�flush� 26/J(�F'!&wE)D{LNF-04/25 (P)}}\\#%hRert�)��E�IhQnovembreH94}�3jJ DateA�{\tmp-ex/041�p\\fBr�)c-S %T}eu% f*d"h13�u�i} \ emiy !@EY �sc�$md {An UnYn$'alkroach �iA�#+ w Tube-Mitrip DeForop } } dhE.Basile(*), F.Bellucci (**$L. Benussi�qBertaniM=BiT<(A. Caponero8), 74 D. CPaolozz,),�XPassamonti, D.Pierluigi^�?-)>i Ne�`ali di Frascati dell'INFN&5\basea5a�=1pt UB'd} \�nt���We UY�?ae'l OZp�3 silicon mU �3Gw tube�$Ib)iQ�Ug�ZCac��Gd�a�. aw moduleLOsf% subjH*�[e�1!�o&a Roha1 $^{�&rcledR}${(�Vbon f�\ ref@C0yU tic shell�u#F�2 o�t�U�5�DeS"A5�g on7� 9l "�+\�&{�b��$��in6� PACS�̍2cm {.: wi[iZs,)A)�, HEPZMect+?1� d-�/F�,� uty �J�f P vi�Uio&p%�� � �1I-*#zS"�v to T�VaoO%]Nu[C r Sc 54ndA!-�W%^FpѼ{l MA�$ $ ^{*\, }$ &&C;�/�s�T 3<: ``La Sapienza".�g- Rome.�,_ `}$�YE�Tq�6F*��Fe�nco II:�Naples W�r1 .8!e�%�1�{plai�setcou�@Gp}2>K7�L"��X�ep� Modern �osY �4 ��d�ctrack3 sub�o4VA�uch>IQ�pixel�$�#t�6t�sa�drift9!m+k�} ich P`D8i l%ol�[,, geomzP6�_a�V extLV�ZU -= .�.� � ofte]&que# deIm� ��o�Urmetic�e�\A�break[4]�pactneOat-MseH�3min�T�P��dLy]develop�e�*t��1�!��moF6=X�1�)x�a�mo8'�$\\ Our�0!Ytilize�o9��SlHen-���Ond �BddTKa ~�.< !7�$�9Y� BTeV5�Q &B_  [1] +e FerLrb�Fton-antiOo�Q0llider Tevatr Lr`Q��Lj 6�el%�ary& les E�+�6� �g�t�( ornto.�!c phelfn�a�a.�,EL2 �-d i7+St�rd a� l of�2��5�0&}#�describ��nZe liva .%K��2�q��h (e�şipskwsb: '��TXhand�8, RICH Cerenkov .o�[r i�N@pR , kaRnd-� s, cEF EM�]o��K�$2� neutE7�'lDap?#2= nd $ 0$), %> muon @or. �E�J�M0 �*M0!8a�"[_i~ ���Y% ��ops q�&� �s�nes. i�Zo�8 �t foamA�s�Y a CaN FN  R&N PlaN  (CFRP) U  �chosenARN wE�fabW^1�a rigid�*�J) �:�: nspa}y�/incom�g5�.v�S�!�M1-`s, 2� .bsub=F�&�q�q trut�&sE_ ing a��� ��!g5'� \)�cix� -9��)%�Ideploy� ��, �Y a%!�a�� �ws " �Z5half-y���Ms�.yd$54�l���fr5�!�$�"cm!s�|���J�FEA Val�< ion}} A F2pe��� A�e(FEA)�hes2,%E/�. to esti���disI^J"�+6�M0e�9�jZ��a7%�-��7%�siv . Ti�Ptability�,)R���0of $10 \mu m$   2 &R2to spoie\s8*�H��Y�h6!eQf&�B" c��e!�t2��)l�Zg7�I".6HA)%4J$1.4NA E� corn�MM0� simu�$�7@')�y5 }5� s. Ag 2.3NE a mo!�um�� a of $2Nm$�F("�`!T �%�weix-)R)�)I�'A]K �7per�i-�� q't�<below.!� shm\aRt$�:I \, ($4Q�( a`edQC=$2"x211f1�C ion), clo�?<.6�Av9n�lf�[� ��(��&A-C)l%HjlBN 6t polyA�rA:��aX��k_.�  \14�xpQER |2re����C�kglue bet"qi CRFP�{u�a�cylind�yl�% te w�ycsHh�]d.��%�}[!h]�"�!�/}{|c||c" > & M�sc{��SP } &"�t ip C� er} !5=Foam}�%z<sc{Th�Bf 0.07ke�pQlb } (0�/9)�\w i [mm]F fibr is�NAM.E+a r�}& J=U.� of} x�� w�al5cm}&9-,$E_{11}[GPa]26�>59 0.01�>.,22,1%-!b.R&7.2 & 2(�"{12�0./> & \u�aI7 "JZG.�rr4/� (*1/), YoungI� es ( �$,�~| 22}$j.Po�e� |w t $(�)$A�"' scan�r�_ &2E�rt K&W��T $0.1nm$4&�T{ rmine�_am�6�Ds�v��i��f���m� "B?� ompu�/im�;�1�F<=\�H�9Aa` �1Jmi�N)>�_ bi�0al, but a 3-D $� � "Nb+1gital:4=zŠR��\ how_h reci��)Y 20 $�Z!�b; ac?G��!YMS radi�She � �9� "1��u�Xty�isIq)� &T �!  Bragg G ng (FBG) �5or�  moni�on5eY�I��A�%� {�Ecal�:Ni5 !�org���lac-�U!iiNm&g� �H�yh a�pre�\�G/ 2� �*� �� }s4KDl� �4� a� kFBG-+��"� f~,�it�mi�G Y� -Y�1G�.�Vor�. se� rie� , an:{goGtoA\6��9/2���>�ū!}!T$0&�\F�8Prototype}} MOX� � ve� U),�  ]sE<� � p׃dursA=�pm� ies,6�" �xN�)�� al behavi^HA��I�hp�0sT*[set-up��9 most6]pu�Jng h� ��A"!Kassemb�N��%� pack,K no.�� 2�J . S�yala ��.xexa��d)�� � ����a�ma� chnJ~�Xv e9��glu:ge|v m6n=)g!�u��m�8 2B'b� A�. Glues%e�et v���| ns2�ټs, ? v D O ���Kanoacry4 (Loctite 401)�Xepoxy (Eccobond series)Pe{1/s U C brush,injIa sp�>gl<�(EN}iI5��=�&C]by �>�45W%g6Pcatalyst mixture (1:1>g), dil�� �!thylchet@ol��. m�� $40g$�A-^6u l,.cm^{3}$�� Nw: )�aBu e�ss �ga� lloains>(steel rods ���F���A��� IuiPrxmb_z�ng 48 %�m�N: � d�H te. ��� �a�yd_%��;%M$2bar$ Vh��su�{�M$20cm$�����?6Kgu G��Qcu�7at room.�z�aw �i�[a��n�%:��7�[&$ma�Nal wc2� !�e�vM��� O�L cont�5E.k via �aKofY�57C�q%�sQ CosM�Ray And�t Beam� }}�l}nryuW%�c < rays� �>�n pul�inBU -�u i� ��7Y : (Ar-CO$_{R $80/20), as~ w��B.5.u]F�`�]om&1�T�>F[!T�61�Fac [7]e�  �LeKF onse!{p����um�g3y:/�(��di� b�K��%9gasIs�OE R (Fig.6)&�:� � ---��ng�n� A�e� uges$� ��h�X��s s*��Va)dt��i1PcI -[* >�a�d%g&s �u�U �no ne� fJA 2a�ul�� W%���d �*�~xli�i,%� BteV9�Y cto�$� s.acne6�*}mAc�W ledg 1, &We aSeшth�e,F.BaruffaldieG�Ateam a&�&@ Ortopedici Rizzo~'$Bologna, I+ �47Iadv�^on "�ic1A4of%'�/�� �G.Mazzit�' (>='ja�alN$DA$\Phi$NE ��?smooth�� �ߥ���牻)#!X�:�={0fZb�VPem .www-btev.fnal.com|'E") F�)M. ) S.B ) M.A.Ca#ro,�( F.L.�( F.�(M.G�(2�(!#e"�(B.�( M.�( A."�(L.&�(.�( A.�( S.T�( , "SM of Tcle�� Kapt�U My�{S8*�A� CO2 M8 ; A����s*"�!", � en�Gby2(at 10th Vie*&�f On In�a�$ 16-21 Feb�+, 5 , Au�Za,�?$- 04 / 5(P�?5�L!��* \4, "�8of Long-Term Po��M�$ing by MeaFN5SenA�E�.�"" �, 03 / 15(IR).TS�rardis {fW+�L YL ~LU?M�Pace YG ]G.& " ����s�Ts" F- �h Aero =�&@g , Big Shy!]ta�[ March 8-1ؓ 3, p g661-1668.)E�g�,0, "Scelta dei"�i � nalisi� ut�Ze�xL�+Z�l~� �[�+es!IAuoI�a "`$$(U.S.A.)",7���s��U&��".�(, |(,%#..�Z,, "D>����t�6A�p�aw�� l2�di fisic!l�� A���2��el2�.�-XGhigo, F.Sannibale, P.V\te,v/4 G.Vignola, ?*� str. M}s A��AJ() 524-542. �,endB�D � 6�C[!htbpB�f2R�h��&iC�TC K-ו J2$10cm]{Fig1+0"�!P���}H� eP+nd� \A6,iT���R�5 �2N�&��fI � F � Y(, ); 6�D 6 5.� 2�&. @ b1V�--�13:*�3D:��� "�=�!.on'� (<3�I����Q�4:���-�N� ��"#�. Boutput (;2ses) � v$� 8TV camera (bars����1�5:��ignalA� M0*�.z�Q���n�6:�Av&Y�~n e��!�N! end-�Hs (_jn)e�zvm&8K.zN �J1�7:Arr��3��1��lX`oe��$�%wexp�ed ��ime-To-D�-ConvV��2n�.(300ps/H/��%�d"�5t�oXJh�Dnu>p7LL�b SpiXDyle: spie.cls % A"�ly:p���9� "+J� a4paper]{y} %>>>}P!�A4xc %&gJ <] B61US let�+[$ %% \addto�&{\v:}{9mmJtmov!����� .HK[]���7� %--> MyNmands6K;4 {\d} {{\rm d�r*i; {\ii�;�c��{\e!G <6ch;chF<E v&�I2�; {\o!2{egaBO O >~B `�BB=cDDF �<EFF<FFJJFIIFNNFPPFPex  bar{*~ilon}_xBGeyN(yFQtILE tild�~ta}F'Nu%N�Cu"6NIa !dN!4Dj$^�MxF+lam o bdabukpQ\kappF<kp �\kp BJ�kpa C $R�pF�%wNF�L2!LF!bar�%�kpEi�>Ld} {{Lb�La �6�Lu %�:!��\La!_>�atf��{{-yTFF�dU%�{U^{\�K��OV�=itle \'6{N"n\*1�)ll�e � �N6c8#a l1�"und,orrzA� s + Affil Ps"\ Johann ��gang Go�e-� \"at.060054jamv�, Gy ���(> FurtRl9;T �&!��s,-��ir 1�8{ F 0.M: A.V�isG;l�EKIoffeyal-9}�%, 1�Academ˒Z:s, Poly> 0cheskaya 26, :�1940211�7p>"� &�  \ma�� �% _aǡ>�e s$�)�aʂ�,qu�6��Y reatlm� >�V��� om� d� n9>g !�i� attenWS� <�?]&\e� 7�(Gbr�4of"2q�ic�@g�Wa �!ltra-�`tiv�r� r�5r �i�#ra�aۙs � cal�'W. �'ous1s,V*+[ nd �&#��*�X I] F�w�r�Q�9 igh-� gy [ M| s avail5+ ��r['�mE;"r��is�s�to5+kV�Y �� \e\hundr" of keV upW� MeV�*%�6��n��hg�$is ny�#�com!?Rto�'E�cC �Bl(Hs�hthird M[`*!� much�$Iq s@�Y yO( \keywords{R,,)a�Ae,Q]�,=} ��&k!4INTRODUCTION} %l6�t G` paper newk)�)'eoɗ�tJ_q�by��unc�, �h�� a9iod�ly�p�#-[ (2yt5)�"LZ1W��mI�approx�5!�!�&wr�yts�� numer �%iU1&�(�8J�i-#unto!J infl�� wo m�A�si�� ��iyњ@iN&� !: alisל`�- ����c�-� I�^g*�hL%n1��)9�s.�Yl��>�A�2 =�Qe�ea<��|�aIC-�n y��H/�of��9�'+ H;bius#!�A� moEfu<��& =f*':�A֮�r�0ic�&s;�1A0�/n�  be eas�I��uy � j����7[��9�6m ��Isfd�8 �isa�c explz1e�*ؠaС%�of& I*esBia�Fd�4)?lux� "�W� fulfig?t�k�"�hefz: �"��:zC3��d!��d�\��!Y!0q;\ . A}�co�p���<f4�4 ill�( ��ft�I �({I&� idea�/gg�,�discuss �M!��?pers k{�!�+r[#by � s ��a� @i�8nt |e1<��.8~��%�i> y�9$Hte{Arm98,MU2000,ArmA423,B4  5} but, uݭtu��ly,�C ��/�)�n�a. A��%I�C91�"��e!isA�ly ari-? �a�8leHa histo��su�1?-� ��pкal-�!�M !�heKB"�h�a�Ref6�2004_ �}.> � 1� B�ZgO13cm,he� =5.5cm,�O] I1.^�� �"BS! 0 _<> )������.?�black�3�de�Ehn�Hi�;�o n�bo,�al:� (a��Jn �(rplanaraS�, $d$)�^j-ё�gben]� ��E7is���$f,��Cv a har�2c&��P$y(z) = a\sin(2\pi z/�u)$� s � $$E,Oy itude $a$2�F�t�C 0 \gg a$�`das}5cA�9��'tra�/� �5oile�)*�A�a���. bN�lrst�� UMan��oscil�s *L a"�4�.�po(�ia �ir�i7f�4(ency $\Om_{�$�Cen�Bn)]pG&(� $\Ei�h6�  Z{S�9d6�2����$ �8�u�s�5mMG, -v&n .T�K ose �iגom_0=�zc�zAa:( tane�u��HuG�0s�ed c b�)Kr .�eJo �MG!�"> �$�%�\� 2\g�[^2=�+@$ $=\E/mc^2$ A!�%O�Lorenz �I�V2 g���5� �� =K �rm u} �4 �^2�$0/(2+p^2)$�p$!D!+�UD, $p%� F (a)�)$�� 2� ^7onaw� E �0 \ll =2i"t�,l���j�Ń!T94&� �8� c �v,� �oq]� �@a#C� ha�8~#� B!a���nea�� c<]U.�� -*shape �F�qdl  6 �r�� %\s� ���1��s}�&re%_e"2 fea�6 �inguishž"x 9�b/N&x� 9"&Phʤo���.1 ��ic (or��c@) -rp":-�e�SeU '�D��� siZ flux �Ovag��e̫+ropos�<g  yxpagb ���5 media��T|,a��/B0�gin.��F�)�necess_5t�� alyzI�*�e��A�)T�%! �9� y�sA�2. �!�G�Qqn��n��K ��h9lAe�*��r�Bs-� ( 8in8)��,m a� lamu��a����! $\L "�-��0$hbar\om$) � in �0ixers3re "�. �1qu!$"UIut �6r �"� )�#6m� �>�P2<!n az$'� n��� :(�a. @���rekGlet usefl4 �%�]� .�V{�L(v,2 .W�f Z�D"L l �sQ�Ae rifugEA orce, $F_�#cfCEa�;� ;/. e ��L int}$. No�X�Bo n/ y-�$C$�4&J� ��; %f� :�0,BarDubGr80}:�eq�n C = )^2{\E �cU_�!"9 } {a a�*�!^2�l 1\, . � C�.f�Rp� �^T�bui=u\Em�,a�"� ��z�My�Ɖ�"� �m�-�a/d(���9lsDm��udM&�1�E6F������0�b��e c.�9.� \sim *� ��QHe lQ �monochro!;.� r,*&�}q � .�02U  no���dev�!�." '�E�. A a�,%��"� L�4�ND�Y~ted�a�tAWN�vt �%f=rar�UJlA $ad$! ͩ%�6#"� � �x>� .�/5�� C\, d/a� 1 $, �� �R ^�s� is@S" agM.NZ ����I�,�d3KnlyerZM�s#QCK r*�< J�,PmX�sregar�2w � assu� t &2 � s a�.s�e*ke �`ef&� �"ri=oUis Ws:� �/g�r�x$d�a�=� &�A" "�7d%�)���uVp29_e�/ i&� �j�L-��d  ee� Di�:CJu��$nd symmetr�h "�|b  M��.�� ;0'5�'!6la hU!Z&&��s Nu$,�arg1OIa�!i�do�e���?gp�ageA�aaFn -�#g�&� = b�R"% of��F (�vow,e�-"�}t q-angu89.)@�u�tbjsyn��+l. H�#� us&.���r e�g �D U�!�v � Q2 � :� -MS>� "�2<J�$\Nu = {\Lu�E�}i1Jl�Fl coa�*�5$,l�׍�R� , takes �I���d F3oI�a�ge ic�yQ�w'$penet�n%��'.y N� "�a��^�o0�� �w���u ve ��ita����[est�s�2>�of ]a��N !"K��y�5lm� � f5�Ific2y�a����R>�� }~omprehve . ' "� -� �- )1�ZD: \E$,.� %�$u N�� *G�G9L��q�g!\d( �[��/�  �`i> ��%�2�#t0E > 10$ Gev. ES,J�!�# 8sF  $, < 10\, &�z,F� 4B|�6p�s!�� .r <�S!|s%Mpo�λRr{ ,$B% }�"�� 2�#�#5�@2�% lea�KKe�a������6�. G�R~i�gl�f&�un0 rictedly "+!T!� M�N�bi2�]�7�.r $�?-�n'I�b�,�dom�RG3�. ^*c ����i&I!;8�+d�?aO4du�Ў+E'YE�y�Joc���&�R��2� �U! �D!.� ;at�y�a�o� } en.c�!int��2KG dept0' !��&� � &���,���� me IJ cove���' 5!�Ta�"%C2�I�.e�["�%E��C�.: :Z(d=\Ld(\E,C)2��-F��"�pО�(see (.)Ȳo:�&.� �� can ei�'X ��i�6�"�37��e�of�"�1-8q"w � N :���JJ� o.}, �#�,AT � exr'� UWr��:Jd9Gv]�T��: ž6�{.�9� ���6�܁k������,: 4/ �R��P&5-� C�Wd%�& .bgmTE.K��iz , [(a)]�3�&o�#s\!����8��8"�8 (Sect�)CY�U�6})>i we eZ"��!V+ r+%]!Jy�:�U2AU?�4/\h���]uw�~�n$��x-�b)�*� �!�L2�)� l"-  e��?!%�@J�!ň!re ex��anGNvi � !% tmT&�2st (6b�j1:L�LI�c)]f�(a)�(b)!��@�5 b�H7b2; �:&2 on .�N�6tP}D�ka�:G3:D %sjՐ�.F�->4��7 VsZor��)� �by*`�Y�!�"y �es;�Cdern "�:X ^� �/!��K Pr��ݍ�!1͕9B�>� &a�` }�Idealy�!�br�" "��x�s&�gaQ �.�dN�, � B}�Alferov,Kim1989,RullhusenArtruDhez}�vWVY�N`�3lm'���'��t*� "�8)� o���'. ��: \�.{CFw)R�n�2�}r:��vQM!�gy $E$�� V�&�E>��ar9d fbe *��A��6A{�&�{\d^3 h#� d\o� \,\dEG } = SH ,\ �,�G$phi)\, D_�Eu}}�ta"d1 J#H}#$ U�"��$��p�"�-�3s?'A��A]%Y�axis, $�= a \d. va��@?�b5�mfh� fu��$R $��"�r  ��2,���byF�Re = ���4�u2}\, I^2 <-�-ega_0^�Q\{ p^2 |I_1� |^2 + 4%�K1 |I_0& - 2p (�) <� -Q\e�rm Re}> (I_0^{*} l) O\}\, "�Y(2a)MI_m =�5tB�/J�ɑ\, t^m֑ exp o \i  [\eta. + {�E�- 8 �9!}\,�4 si) - {peg3 2 F_0���sins �] @), \qquad m=0,1\,JF1maҕ"�1/137i#� _0= !�0* '$, g/A�Y|�ei $!3eU� O�4$ .N2-2O %� (1 +%2^2 )�-�A�v�XZ5YF�hfѳ $N�(�U-h�:a� ^`1}�6�7�6sJ�D_{�J��A�a!({)�Nu�6\tEx/ pi } �^2!�6@A�_9q� $ X= !�-n�) $n%�a��k��1-,that $n-1/2<9aq n+1/2c ��*&1� ��D2��t sharjUp�%�"�l��ES� �=0���>�0)=�K u}^2�!��!�J�� �% +u}�eq�to $1/K��is*�i�v>�r�m�Ieculia�$ v�YraV�"TyP". learT!�#n�0�Vt�  � � -�e� N��a �'g$&7in*�rn�+&Ps. Nam� �`� �������p$��� "�&  � a se�(.$�8%xlyj7!�s (5)s E��/F�0��� o $2 ��m�refL6On�!Q�r�-�96M Hz% l 9��!e g�y7�nV�� !e$$�#t g�BA�A��n$s52��\I�" e�����o!s�9te�lss*�?�um)~2�ulaS A1-�roduce two other quantities which characterizI1 radi�a�0med in an und�%ori�(re closely �MedA{�YqQpI}8, but also take�o� 0proper���EJ of ultra-mivisticU` s. These.��R${\it flux}�t brilliance} (see, e.g. Ref.~��\num{RullhusenArtruDhez})��lux $F�)describ�a9 �( per second���< �5)b'�!� given��. A�ative�i�� lis y, measur)� $a�l(\mbox{ �}/ $s}/ 0.1\% BW}.r)$ (�abbrevM+('BW' standsA7��C�B�H/ $), is�y2fo���� %�{jS%\fl F_n��:7��10^{3}( ����)a�{I�1e�e+-3}��>7$.431\timesB14}*�\, i�\,I\,-M[A]} \*GB&B.4B'� $I"e_(ric current)�ee%. I�c,latter expre�� B.�AmperesM�g��al:;y"�"!�I% source~a�s�A9�A� erms$9y Cv�t om$q ?he>.$eHunit !n�?erval,  �area, &(solid anglee@a�Y�I]J�. T6J}E� ,it necessary�� know����! �isigma_x$� yi�an� verg� $ $\phi_{x}1 y}$%Kwo�pendi� � rj 0s, as well as�dUyhl%�!M��� '�'1�)� ©Q.���J� R �� a�a�s-qj�Bi�F"h (2\pi)s $\epsilon_x ya^" aD7BDHu  $4,{x,y}=\sqrt{-� n^2+ ^7 "!�  $ �^totalI��J!'!k��Q�M�$x)�$y$ d=� with )�n����/!}$ be�`Q@ � �+�S"� !� $ �0n=\lambda_n/4���n�X'appa�Q'�A �n� diff+: limit6�NIM2}�Oo obtain.>-a�s~v�omrad}^2m ŏ َ E�*��%�-q1 $ must be2 m meter eremI1f variables1�2[-J- �Ken�\%� \si�{C"� ��?h%����0a crystalline&� } � CUq�} �<an ideal6El�Ab� sAY� M�s � agat�� vacuuɕZ�, due�=A��M^s e � atoms,%��x$dechannel, �us!� lost! fur� mo%%throughJ��. Add- 4 g� � insid ��@be absorbed or sc�xedZ le makm�$ir way out&� I.� refore,�Uis6X%�!'pro�ves� 5h�� � �nuEwhaB��we carr �Squali; @si^ inflJ��sL � onecF�?�� =��- \subqSZ�in  en�F9=2�DQ_ ingAndAtt1U} c �-� lengthI?amplitud"sio� b�ng !�<"�$E$ satisfy��' E�sCon .1"4� (A positron,A�ch en��k�4at small incidA  eqre*q�curved;lographv 4lane, penetrat� yYj&� � ��GitsA/a�. Howeve� randomqKA� � on�}nucleiNI~��j-U���/R^Mځ�^�~^�4IM�&o6 AL helpY�6��� � titua�$\Nu$ C�ĩC� was� lied:�KSG01a}t�� �er�  ta���� d pa�᪁�ar��Uus� !discretetm*pin5�&�kinu� �u� �zv1})iHy!|T� r%��� J is  o�!&sca-!���j`E�i�, � \gg � Now l{ turn!jW����F�z)^��:��V�� �t&:�2� $iq �� J4*#. KaB$i�f�we 5 2at� r! $N_z=z��!�aH ger��N EV*A��E�is��� � t%��n willT ~ ted�����texF � 2� Lu� e�� rese" � 8�+-V� aA�9� �in� �e As  $ioned abovfE��O��eNrI�%.W B jjAd�q �6�� a+F��%�k��U�inF�$ 1}) )�de�[~8AB![ �w $D_{N_z"�"� �I�&� 2a})!�is Cappear<ZM�zr�aAul� squaheauluw a cocnt suX! "4%�magne�wkO � � spa�l��t ] simi�%� M`Use#mo'tail,F5*� :R= E,|\sum_{j=1}^%q� 4"0(\i kR_0-2\i g$ jr) s|� � � $( 5pi 2)$ ($k�%/c�*�!iG) � *npha�f *NA "�"ḅ= e $j�$i�q�5-P'd detec!x=omeeX8ant point $R_0$)��=. Is� 1* h2� V ,"� K  ,� $ons: $z \l�� \ll w.4 Figure 2� f}%[h]$&er}� clud�phics[wJ&=10cm,heh =5.5cm] E42.eps}%{ForDn1 �(Q vspace{-07} \ca0{ Illus%� �N' naZ%1u 7-dashed O),uf��?5���� $z$,� *� (.�)�!�aR> � thicknes�"-j  on���U3IL!.=(!�KLu$).}�%r!q .fig-u-���! �a14�2Z�"� �e2�� .L�a� �whT  r .a-=, seeA�.~�*6�.#6/is�v�x�i^&� �#�4es complex, $k��arrow�",/c + \i\mu/2� ե0$\mu=\mu(\om)�K�x* QG!a+= \mu�� 61�$�jre�%�haчof $e$.'(a � $k,��Ͳ$� �x: �FaT�&f��A�sam����s $j=1�+ N_a � plac�h 6ly-%#5� )}$,4 aE6�") �R�*�� B�-�#6�y+%�"t�0)�!(|1F�e^{6�aW�\mu0$2}<m�) } |^2f-\mu( } { 1+ z}-2 /2}\cos� � !W) e 1A{M:�7 } - @BD)66$*�.�Fp*n��z�of*�* f�J'.>m/>�zn� = SaR,.,\varphi�Z\,&�Z*8!�2�/n* U �*,\to 0$ (i.e.�e@ reaqno.2) q�M�:��!co��e��E*M�$  b� e[ht6<�b)���Gof Eq. p2 s*To���e�licit �&a��{v�MQ�&�a Z�>&j�in�^�9-t-^$57 f+r � a�**�*�'vs�1�;#ed5/c� V�GVCA s� ��.*^�4&P2justifi�~�*�&�,A�� &c �R $�ť�k�a"!� 2�� \Ld$!M9"t J'La$E�% A�ZV . H HG ve errora� � !^Qiv�8}wmjL�*�, �%M� orde� � ' )(4/\min\{\Ld,\La\}� 1$. C�!L �-�L E�reajen�&zl�<^�a �i�� N the -p6| S +"�to-127� &}5�FEeg64b 1,D2�2^w6�!J����"�$R�$,"hby-T�c, does�*�]$� ,R&Ld[La0sem a�&en�+�_ $\:�is .� �:R�F� >_\-4"�2"�6\kp�3a + 16$\sin^�(�} gl[ {\kp .u -\kpd}^  - {2 a1 ,Dz+4�'^2((8 )^2 �n R} \noI\\ �- 2�( � R + ME6 2\,� -.h1� ..� ~ ) � '+��1)!r]��2B�]��%�-no���J�!i =8� =,5a6a phi=5� \Nu.s .X:nF�  Desp�6a c�4j�F�9Jmmji2��0ts main featu�89 be easily��(erstood. F 1#w�i=3��i�2�i�'�(d\to\infty$C$![ )�)e�L>e$���3s � & B .�Z�3})�an�3"� kpd=eH=0$ � 6� �.�) e"� zh�2 e�i�8� ��6���&C(zEhe�*&��" W.�2��e-[F|A�P;aE"�. V=%B� $%\lim_{\La!�I }>m %= %"J8B)%\, %{a[^2 %- %�: l( % \,�oAkpd�� /r)6P%e� %��[- +;�. .�z�(� %���" f, ei�+i�s�*�!�e�maxim J��loo �+6=�[> w � Upa�<�ta$ ]�a"sE +�=�5FG>st9J;���:�:Q�+ ��=e;��0)$Enb e� �"$1N�< = �!�~>�XM-xA�44(1-x)(2-x)} -{  b x"}m%y-(2+x)$z�x Aɽ],�j F# ٜ"_d=\Ld:��A3&W �& iods�* b  F�x=:ud}�?\Ld-\L6J� A[� w � .�=G�(.�=7E�$,  � ��ofE��� e��Q$1/x,���*d�"b(T.��.�S,�.a"�. �s*d&�/��s $1/(�?�� �>7�A{2� ��� F� :62}m\%js�oc{dE�se��,�oively�T3�_1={ /(2�pi�.$2=| �|,a�u�0k �!�!r�?iR��N�4&6 {-2}+($_1)^26�@ = {1i�' I 1 +{!�a�d~ 5��/M�4^2} "jj�6Bj �B8 l�#M�enlarg�,1so&�71eOm�4 6�@mforward "�rd|)��<6})���L@>L@!���%�!�2s\,{(x-!� "OB-��*5�CU& �3J�%z g!Q�*��Ef \cA[�?&�-ZF�?�+I8�M&�)J �!�&  $\cF!���" es }l9how�2�d& in Sect. �6�}� �6ajea�XaSNjF�Faop* :2Deff}(x,��)\,�;b @!�* F�4a}\\ % = j<6tf <.�nJlbR��7& betwe�seH� A1UE�f�@)�_i`a94R �#Y��A�Nu$, met!���%ub '��!�)veX N , $A�rm&5�$�is"� .O �0JY�d.{ �=���o,equiv \Nd\,fQvf�5AP( = {4�54U�� z� Biggr]�g�� ��b3F^W�'t�A I���A5�ItOA to � 4 optima"� Y � 6�.�q6O�d�� 2L&6�af� �W can,�pr�5ple�3�4�7 H�l�[�u�.Ci2 ll�FE J� .q�s �U�1 `*@siY7 theys �or!�a��L�$m̩�?-�o4/ �$$ �}s'^ /ly�@a technological n�� situX�if�9NrJ ;�E�:�#1��!�F�A!e� -2|Mem�?�- v de[6� grow�I�8$s��*�F�� if< &v) )�"��".$! $2 a�5so �62c� Y eR� g�to zero !@to� *�, �/�0V is!�quite)�aQ�,MkM�E=�:#�ll�-��7%b=��6AU�� do%q0e�mDre� !�4�� show�^>r e=:�x�La\geq 0��r! only�ooa� �6�f��s�  nex] a5, a� gle-zd&@0bA"v I�5�%:J $EK[$�e-D�$. �)im�!*t�]AA�)<�{ mG�sX!s.~c F�4&NJb#Oly vi�.e -�. AllB�K.� 0orP&FF�c  Ft�Z Ein�-�,�� �r-Eq.�}u4 e=�highestIns QT.]I��%�!�&��&U �>& I�F-2 ense����b�ll�+elL6� }"��5��&a��KE��xF�+�'i0d}(x)��f(x"S%*��j�+9&�+9&�+3y*}%� UndNom2��+D�/�!{i�B�� $f_x %�=:� /\Ndf+�f$&8+n ��N@+�Q�r;�5c6s�M�ia �a� =z�,$x$$�!I|Fi+V��U.�struc���*�mjŶ��uniqu- �P�ae�Qw> *3 of"�A$ n�. Oae�ahanV e2��a$s"P!T& $\om|+�fix�h$\E !�}lam"�3)L one "�Rs.!�%n, usJu5.�B�<i( fiJ0&6��.ty�� kf�u�#G9.z��-ef ..4. Simultaneous� J> �on.�&� &� 3�u F@Y��I�O:� f�PAm*.,*. �fV "INumer �s"aR�s} F��H=n%��9>�(*three�� sub@foiIq>&fIzI,4})�8:a�YGao , $C� Y�H I)!% som�3cerety� =��&D*In 2rI�as&;K�$o�tr�c�m,�d;�klyt1�d8ra��Flec�e stocha��eI��*�Ma tX�I�dV �-�a�*. F;��XZ�AR� appl[K u�\ theo�S�: �k �M�or*4My8s� �"�5�I� tern����us:el-� �_��:/s� ���m"] pai3we uti�E@,'n �X �_numH@1999}�3 5xim�=r%�N "�# � =n"C)�S�(0)&F(�256�9\p�a)\atf\, �!m cg*,r_{0kEE 5\coul3"�neAS*'Fh( T�"$_=2.8\OVs �W-13}$ c"HK:n clas�BLus, $mc^2=0.511$ MeVaX!�3r�b ~ atf" ,Thomas-Fermi Qa?c&�Pa�* ,�Bf��&�1��A�䍁>HA?~$:j#J3� a�r�8�9�9igh� >W�Bh,BiryukovChesnokovKotovBook�7&�:�!�= \ln{\42�_}!N$/I} -23/24�t6 $I I4L8(average) ionize� poten=�>Gq@Coulomb logarithm�� eriz`Vlos�&�n j�\�/amorph�BL. �7quick es�9kq54 n cm�`��re-F�J�*B "&) �j) �$2A�an \,\EpB!� -q $Gd$FN(� \AA\ �GeVIj��6@,B� TMU�9�Ts.yY^ b�et<}�<"g< P�' s $d�Zek� $$\dUmax$ � �er�5mf�9s&D:���K (tabular}{|l } %% <s �tT 0wo columns \hh G.4& C (111) & Si Ge W 0) k F!�(\AA) & 1.54 2.35  & 2.4 & 2.2 \\1�L?0.258 4 0.19*&  4 12 ?-b(GeV/A�& 9.23t & 8.HJ 17. ~57.T�'1H -l )� j66�6{6� "�  (��|� s�  r F�^&26� 7� LQn.\specifv16>�G bunch�5 a��]$I�4qW�Yv7\{�Ze� �X"�[;Z &.C�6�p���hGs�Salrn_-ɸ( $e^{-}e^{+�ollider� ra`�summariz�0.�P d0DataGroup2004i�1�$� one� 2� , $l\cN% !11�is� �1W)� � ~\pro�A��numV� �Obo w�U�dIT���!v*�TN�&(� � )2+���FA:�Z�xk(2CI�6#W�*<`x'> I� � �as!h"�`(A)} \[ $x 48 \cN/l !�a-cm"�BN�3l>�Pos�V3 �e2d nch � e,*�? s� ��N$,�^%7>F�Uamf� }�>d� �3 2v^s"�Pn11G�$�l r���v�%% &] M? :y�ɺ�ry+c|c+ �V%� 4of \rule[]{}{}^ opens up 5row>�&DA$\Phi$NE&VEPP-2000&BEPC-II &PEP-II&KEKB &CERS-C�N!&(Fra� @i)&(Russia)&(ChinTSLAC)&(KEK) &(Cornell)ٍ$�� ) &0.700T�P1.0 &1.9-2.1&2.5-4 &3��& 6%�� l$ (��1-�1& 4O1.�&& 1 0.65  ).���(?_ $� $10}$) &3-9[ 16:4.�6.77_&1.15.K�Rx$ (mmf0.8 �4&0.125 & 0.3805713 '2 E�4E004}E0057&0 24576$�2 �rad �37(% �79�53645�phi �E20��%^ 0.54731L41�43!C�-�%p (O 2�0%T 0.91\1!r&1I 0.05�!#I$ > &144-2!�!�927! & 325�&4FG� awou��oEH�2o Figs�E S_Si_Ge_W"2A �+d _CB!Ƀcho(7�&X 1motiv[p��lC, Si,� � W8G�qtly�C| .6ex�$Ms.�i,���P��j�). An"ed$as��� ��cJ2{| rapid�K�%|'�Q�%�w tomi"�1:o"��%by??i5�b!3@F� i!Winv��a>�_�*D2�+)aAC�&DL � &s r�6-�9@_si_1.xmgr - ge_w Y� �/b@ɮ} �J*�J6c�JinRK4�JK1�JK4aa+}%{ �(K �k�Kb>%{ � K�4:�{-1�"�(Graphs (a):/ ()G;!�I��%��:&3(�s$)]5�o"�q"�om_1/y m& �T2�e& $a/d�6��M��"� f � inhe?"f i� ��r )��Xd.5b): vc"wZaE&��fj&�Sal 9�yn.je.�u) )H. See8'zne8"�\R. E*%�n�*pai%��ea%Υ(b)�� % 5>���+t#j�$o6�hy� 5'" {��legend�er�"ll% mi_&� FCɼ (} 1�`(aFZa�f~ͪ�"c&�l�oM�}�bXC_ �V`����Tb�a�q!�I�)9��k%q6�05�E\A� 9�in�� �w �F }@s M�$$\E=2$ GeV3� =36.7).�� ��0� $ T�9�h \@ �6�4 1} /&�i�)_{\max�tG��a";%Tre twoA���var�i�l&""3",-%X"�d,)zmdy�0 $n$)_ A�D?H!�o��RUIJHa}-Opki� urpo[Mm�Sconveni�toW oghe�WtiIc > ���F� $C<1@ Eq.M(�)!T6.�'5B%gn,9���$(a/d, c:)#&p�\py"��Q_1(p)�{Nc._A��-�of��EK Nd =�B�C)H �!NAd��"!< c@��-.6�) /�*�"q�_1j4an)yI��b�&��t�Eg 6"�n:/�$�Ld �ɑb�5&&hBW860�~w&%�7�60!@ s"�V�,I�: :#V $. F^g,<nn��0Ra�]�%u"�&`ine� e h*"�f+!��]V��BW���,aF2� �. Hav��8tra2A/"`&��c�A��V_1af )$ (�`(b���9%'��:C:1Yg�WN|�k ��jusKef� iscus%\ behaviKof���s!�rs5Eas��&�2!� � (a),;4td/"�X�!*�hy �B�( .o�'��&� �������YF�2s clear�E%��z���6�[pr�Et�%��\,&�7*d' Ŕ�^)^Y�:�i�E~.e�^�5})a�l�f�"}oriF(E0� y (a�Nɠ�too obA �r >+$y"�2-T�ur!<���4"c6Zam.�E�A !�reg��>@MTo�[k\2�b!�i��xT8&!n�). �  �!de�b�d6 1\-�y~� �@' too�'Nto main��ine BmkC�Y1�^�. L~?r�%�u6in loweN-�"�( �I �(.l6>E�!i� � iv� 4,9x�<�2F-�uZF�� � �'Thi2�(�@�hM�e 0]� "�2��@:i�6�G3}Ñ2�M� i ��*� �3:�., # fall!�fv $x>0.1�bn���manif�4itselfQ���!��[oni6A�%!&M�=Yns�@n�oheavy�/� "�U�'al"rK.�du�%!�!Fu� *w!"�!� I_0S M�inner�ic�'she)F sj.t lie�`m�M�range $�X$100$ keV. �M�*� 5SS�B(shold� �7 m|m� effic� �7ha!Xose#Aev ]i�=2G !=Ua U�aV vic�;;� �9��saw-like�"s( < !I3FU��(iceably (up��\��of u) excee�?q�I� \om �5gm(�..uV irre{��-���&� ��$Mka#*�V�%��9ly��nounc�diamonn$d tungstenu�5!�n>�e�:|eiS�������� �d6-;-5ten53yO�9�+enPVWly%q R�[(�aon!% �q�C��Si��-� � ;^�I$uKN� arT�K�ab2�u�_/�)V&� Zt�.�,liT�'Rcs "�rF) (� �ld*� +"�"v�� ��9Lom� "�refv�!�e4 Arq�"G-���%| ird "H�"iN8Gq:sAKQ w&o�s"-R�>�>$eD^,�!�)�?KA� "�,,�L9@��9��=� )V)�qm=K.� ��>sB� ]�L �w]�zM-�6� "�i�><242!_o),levelg $(4na20)*�,2�VNgmV�� �}�#�M��b+yj" �,El�seE C�:om�[;%�>)C l,,Ile�A�t��g��nC�EuroPhys�BR.;� 21}%< !2�-�100� 2� J.by�*��"� ��a�2o��e�i fiel0 s plIE�e chie,{!in"$prcr�#�${WebPage,P9{3,Tesla �+&�&��m+}{���(f�Tbl_ �e*�)���U� a�l�<��A+� eu&� 2:R  %� E! �h B"���$Qj�5'�҅�*�h5&�<�h�5�!_��\b6i^J�J� JR�V} &�P:-�U�=�M��� "(O.�for f�"���e2;s&� $n=3~�e~�!eA� d se&�l;�ra�.�;sg>�p ��2�!W��:wp+*�� ). 1: &�&, 2: "�& , 3:� , 4:� , 5:�f , 6:� &QE>Fx#6Vb$ �m;2m;Co ,5"�(.5or�al &\"h$D���1re�5 realPs6(6�- Y⁈�)ng spont=6~a w��ų� :�I�6 )nyO, �a8�re(��.�qH:Inf��},�']\tu�#byi�aA�6� �i,U��'gyQ�; choo� E�� ��) �2?��availU,�Ir���- toge�7���9R pre��T��:8+ "�@Io��!N-�ɐR==����hundrvof���E*of|5��a8��j;�?is oy)=�%5�Ta Jc�! cNb� �5c�A��T�B�aL�er�&R�ffort� need�A,verif��^�p�8ou!��8m� predM�. XxUu:ly mak!�q��A�$avor even�fasci�"�&an �alreadQ ^�y2� &�|�o#^ a new typE�tun%x��monochro&c]$Y ��OF \ac�� ledg�s�G AVK sup�GI�!�Alexan�e4von Humboldt F�J!�� %�@ *{Re�4ce�@�thebibli=y}{99}9 e/ibite�98}�%,A. V.~Korol, \Solov'yov, W.~Greiner, 5l#J. � $. G: Nucl.x5t p} {\bf 24}, pp. L45-L53, 1998& ( \6�9���Int. � Mod. � E �8 �49-100�9Z�00Loss}��0z�9 �77-105, �..�_ it TW��E�8*�2 a�co�icÊ� %�J:E�eWA��<=&Q,RE$KSG00Tot} = W.~KrauseQG�TbT6-*L87-L9R+�5trD`�_�b��R@�� %. i�:��:='�;V"�}�?�74�fmg7-95-12)1U=�b&B�n160qT35-439�]" .�Arm00.hA)�Pganiants, N. Z.~Akop� A. B.~Apy!� et.~!�.p�݂�71 �577-583�A��a �j Id"� �E6!0.2�/by 4.5  %�=��a�&bD��-�3�rt�?-�9�!1a���Y�9��1�)112-1* j�"� !K %R�%��nanotub*Y s1��%.$: K. Ta�etE!>�h(E. G.~Melik$��������77-282j�6V.i:C�!�,!BnQBN:�nfR 492m� 11-1i��~{ �:�.<�dz6�3�;z4��(508} 496-49� 3. %�cryts�g 8���ga;� �Z  .�m!.9B2�(S.~Bellucci�,Bini, V. M.~f;,!�H:�5 Rev.2�9��034801�7� 9B04=}V�S.~Gia;0i��ST. Beams$Q 0235 �4�G.�7�N��Korhmaz�N]�y(E.~Babadjan'5 �4 Tech6E49}(4)H 499-��5=$:�!���A.R Shamam�� �b���2"�104-10I�5A�&�� ar&�}|w(= %"hL��s�En inL�6�*� po*� .wV Our CB4 ��ew]��: a:Gb-: .� �)-� �4 �4 4 35-154�4 m{}|KSG2004_)2]c� ��z1867-916�4Z� �J�$BarDubGr80�V��|Baryshevsky, I. Ya. Dubovskaya, Q O(ubich>'��� "�7�`�  61-64� 80��.�Y�Landau4.�V� Be�etskii,��\M.~Lifshitz, L. P.~Pita�ii.���Quantum�dynamics2� Perg:+, Oxford�� �?�udo19819�H.~9Qw~w(189} 609-61)X1�w Planar��@ofU 2a{"�P�x4EllisonPicraux6�iA.~ # , S. ,� �]U/. 2� 8 ��XJSQ����uyk�  Yuŕ5A� V. I��tov�%\� *�� �(.F at High-E��@eS}S SpP2$er, Berlin!�96�JY�Henke.�B. L.~Q�GulliksҠ%u C.~ DavisB�APC\L �A4�5TN��5�(181-342,199RzHubbel=kJ�  a?Seltzer=`` oAn,X-ray Mass A*ʂCoe$0s''er#s!.syn��&�'&{�g�ce _ee�BQ١3 565-632>�S�|!�st2�0R.~Bonifacio,!QCasag���&"Cerch�3X G, de Salvo Souza L,PiS6i�69H��i�A��ܡ0 �X let}, Law}���$keley Labo�(y�kley, CA9�Ch. 4-E�8V* � NIM1=]�U|�Nz+ 24� 67-7��y An�5֑����u"yp1: M an arbitr��def�p;��� KJv �*:�Q�v�i"�71-�u�lBright��c:�`�2.��ch2� %�R��Y�$MulhauptRu\r=�\" ,� ~R\"&]��Hyper(nI�p.�� 23/1"M# 13-3%��"��p=HX/V�N��A���2�(K.~Hagivara&J.�v�U� ���Rev.} D)�6A| 0100f* =^L� �&8=_2S' fP��� !�Co,$K ZQ8.r&$ "�0U��S Altarelli#~�a��) :� news ��3No. 2� 47-594� �>0``�1^ean X-Ra�rserA#�b XFEL2d 9 0xfel.desy.de/6 ent/e169/Fx\_eng. YH"=�0�$K. Balewsk�al.5$T``PETRA III: A Third G�sS* &&ɳ( at DESY.''P �(www-hasylab��&?/up�e/s�Xy/S  \_02^��1f ``TESLA. �nY% Desig>" port.S �t�1�\new\_pages/TDR\_CD/start�. �->�'y��5�� m docu�(&�%��e !%% * S�aqf� tempc� .aps"^ � �7�? +^3ar;�APS� REVTeX 42��  ". 4.0{ +, Aug�� 2001 q�V Copy�, (c)s Adjn��%�Societye :Se1+e a 4 README�� ir~+�{>in"IQ L % ��B1$A�3� $manuscriptvCuse*�EX� %�^5-E)[v name�t�< worko$�Rile�2T Dway, you always ha͓is orig�G�%�o�. �G�[�?�de,4affil�;)?+eI�ad)�4long % author 0s,qer�r�Kmany � lapp!^s�=��p�dear�,�� 6r���-wo�X;CW/�.a+ebcdel stab�rmp�journal��(Add 'draft'ionfma!l0verfull boxes)�black >31 pacs6A(ke PACS codT/��23keyF3keyword<��=%\q��d [aps,prd,1,g!�ed-�,� b]{revtexURLlLs&0� P>R=d,5���h�<.\ % You|2ul�]e Bib�+� apsrev.b�a= !�EEU1�A�s.R+s�j; correct��� b styl�o le (cil��so�v uncom�|a�%? % fkf&H`. l�-V{ �x} \usepackage{amsmath,amssymb,�x'newoand{\f�<(}{0.45\text����$0EW}{E\"ot-Was>ew}{EW:2B}[1]{Qbf{#1}: mc !�calN"at #a�2N:O halfint}{�� {0}^ fty>)ah)-��/>/q�s UgO\q�1!@a�place� r lo�4�j� 7X %�1�RO2 e upcL�]hAcc\"�S titl�Sg�3vmod�O Mult�jB�2�w�T�'Em'�h��!ir)5��� aultato�M play �s�~ne�a�]�{!1T��per \�cC D�M� ~34Equilibrium DikceeYg Damped H�� O��or1P Presa�0TheŠ NoisTT% repeai]\�H .. \�$c.�2M3 % \em�\!� ks, \home� , \alt.>al��Eo�qaո . Ex<e,y�U��go�[]'Y@ctu�3-~@� or urlF6{}'�( ������Ple�m a<�pr� macro��each d3*��92,�>KG�o)�s s� las!N=.!�R�f���|t��.�%:==q5�r)6�)�!�O. MD{Michael W. Moore}J�[H. St�Fn\9!�[]{js  @astro.wa�~ton.eduB Paul�$Boynton} %5� []{Yw; web AZ �{ 6f{S&5 {UnifV�Kof ��in~�(" q@�ic4%��q�n� if�niu�(���A-o1I>�  %�R]n \�%5). \no�� Qd (mayGFbe %us.Ӈ-�QW)��col���%6G%S2� \dat�\ oday�b\abd ct}��a matcT�filter[�0y,nFZeA� min��va�)cey�bia�\]m�aq-e��dB�d��"�T������.D��*NqN a�a?�[ bath�HBC��A!�n�3 . W��A)Ή�� ��w�!U.,e�emmoI8%�4"� �G]Op�?����whi����Hb��Bn� mix{� P�2q. u �D�w1�cŲ�me"a`_�s� I'>e�; R)��A.oYd"sert sÂed� ��!vbra�|n n}�  \ {02.02.60 i>K"� -� � hors�T'���Bd�� is \.{2F,j�, P�f�um, To� DeviaO A'Ss�ORĽ Walk} %\_:# m��� ,�,"Jt, �61� F 9{.{=1�d�penal U;�3��pe�u�E��*\ba-�A62�prU'ms# tGb;y grav��(�Cfis5Wr"�9/M9)QtinvolvU:&�����ly �G�qu� n�]*w�.�i�IdI�m���s:H�eci%ach |f&�A�L po���c�Qe�e�c���>�(f)ert���3e^�Zs1�D��Sfam7"�J��f y engageda/te�studi�I�MfOrea�l�<im�.ate �sk why�� Y4� n��Bt��o 8f��o ans3ST!���;�p�=a/vpl�=a�K"�!� major! rtH�3us�r�F thod�:P Co��r a�2ar�E��a�Qt�.�P solu�?e�J�, $T$�he2�>��q] , $c&N�-�eE4I���1 �a"�ANS�, $x(t)St $t=0$� U!jH} \hat{c}_{ins}=x(0e�nd"�u|$circumflex"E�J�@p� ��nsembl�RsuH I��9r���'(e $or)��'?r��)$�C �!mWeI�� G�/o@I.a capi��le��Rf �aam@-�OJ/a,liz%B�|pA�quij i!f! orem� �� ���D6�5 �%} =��{var}( 2  PxL\frac{k_bT}{\kappa} ?� \sig�� ,Y�cv� J� $k_b5w�Boltz/7!\ wt%-$ b'�7 al s5g.�P�O��!�����:@�����u�Adx se�?Y�cZ �w"��98�'K��e�W| %�^s . A�P��dD$``boxcar''ke Rn Fq�v�X%Zޡ�r,�q�%een� \tau$,j�box}=I1}{/}0^ �dt"zc �B!�enn�\ dom�Bi�2& ,5�ca�f!B� w1E�KsFourier��;e9enm ��D-J i2split} &}0u/!&y.2u}{\omegj�_0^4 !D ^2} \N -3xy^2 ++� ega^3 + 2 3 <"ӁW^3U�l&+ )t 6.} \bigl(�� ft( >n-n\)) ڠFk� tau)�l= W ^3 -H �2=sin2=r)�r"d�var)�M)-\�K���.$ d _0=\�z�$/m��!�@ p-��k "�b�Zg@ޕWd��c&(,e ig%[ _0^2-N^2r�Rp��qua f�Z$Qe`ega_r/(-��O�SraX������^a/�resonЌ2� �rF� c��st< sb fyK�r�e�����i%8 �o"�nat��:�!� �06�p r�5�� . S0�loWe�� �Lu��%�s� in��LU.�p?���N1}0e+�pi�\� �Lc_UƷkLfi�N01} g�e*�|ZN@�/\�"$.H�hl"�|>N$22of F?_0=50�AVapRnt�����K���not"( �!R�`-T -�{? �aPD)�h"T"^monot��E�� �]AN-�5�$�K�Ad�m�[%�can�dP��� �� ��;,tK%it{� �><a�� op}$? �yas ��6.�Nf*� 5m *t :{o5 ���.^ op}]�1isQ�'�lit��a��]!�%eG��wb�cIAF>4---it)���)��it�]�Dor-���1�on�val+A�1��[is �,� �a ��d-������b2�a�er fai֞g�"Am�s%E3���e� �oA<�Lnoww xW W asic���lem A���� .�li6B��K�&gap� wishkf�%���.��z>cx ZLSdBS��c��82�V. B��n{ 1.� 'c՞>  &\m�aM�m� n��9��:gor��%Ye��or%�a 66X$�8! 6�9pl�$M >�BM, >�>8Z�fE����)�0�= c�  ���s�� at surpri�nE�a�nA�r]Er$100^{th�~�� of E�ein's se~ lon Brow�?7von�� {ein�� "r�"`WZ�guably���,"���:aBwid�M"�T�'&m; h�f�]aC\Q��peo�who*# look[�m�," X��m j\#�d>�! a� J. �"�WeCd8rasekhar's 1943՟�/u(ofM�Q1q�, ``S&��Pro�s� +E@Anomy''-� cha}( m3�9A'�!4�b��.��veloci�� $x_0$v_�c� j�>*b!ha�di�Sb���A�*2���t� $t>0� ��A Y �& :� (_11)� ?�!)^2  KZ:z+7�t6()2A hED Q�^c64��:�A�.=� �1r�3=Ky@�)f�le�deLs�yBev ~ Xct�*��$aa�on5��.M i��lve+RAn�aeoZnse0�ssess�co�%`Rro�w=Bb�)es���m.OA�tgtT&�0z� (*��neo o�{�^pB�ZsI���&��(��  ha��� ��r�X � . �� :6 �rmine a�!/infeL' sche��provid� 6 ea�relevX��sgٝ� R�al.*)X� Xe��ter���. �becVit���ˌiS@bo�}C� IŴ.��# ata.��oh#;,.�A�a�d&!C[s"� �regar�l� JA�eFoco" .o?�on� !�) �"�9su�: *�#. ��. �0}�2�vl< \dU�$ & X_{th}(� +\D#bigr>�l=��G= |)|�5���)+2;;}}� &$:Mau-N�CV�is �Y�eaB�U|MS��- ��7g#5� #sA�)�6�.�:�ei!�>X o�)�^f��2|*. �Zn k1���e y�7AK� �#a�^ol:�ba� extensi��An�& ��]i��$ppl"�!toF;ar,cf�#L8��B#n���ZeJ���9War#Qh s>�;Ux alyz!�&����� he" �s g�r�M %ѝ��Ifl杅�� A3P`com �&� ūXdE�����7.7WqAZJO�_��M"2uce���M�]�J�Se�[�&�m�]"h 8� �1_0) B]2l� \nu D��`/�2&R4 3�(6:�J !pow�q}a�a5~"�%�5�sA!Qs�'*�1 B��^�st/��%D:.`a w���east-p�e�<mAwQs��IK 5s �`��� signal-to� 2kVy. NoPaij�-]T�er�a�is~!eZ-�N;�j�c�f#$c�S"{*&t:�zv�by,�O�&a ��-"�5u6�C:e1 ��,��&�V_W . Thb���2!�2�pr��^�_Y6�!I!�>>. YeUcco>i��y!�ofVg�w�e�16H"� �wrong� ��Ap�pan��ri4���d�3�`ump!�Vat)&b�h���in �m%OV�to3 vali� Chief1Q�`+(+� f���t��5�U��� f�e&B� a�pla}h%@j good!JrP�!{-�� i q�rsinnu� $N \gg Q_� $NU)&�v�:�%s1��v��*zKaB�$b:+�.ac��p�1�$%� ��� $N < �!���owbXA[ٿj; � �y?�u= �Vs��otItA����W W&�=o7 g�vforce� ti nr*J  J�Fzs"$,in kiloHertz� 4&S�%ōim�1/��K�.JR��wai���-|AVz5$Y�cq;. %�to*bal�&# sɃ� �B� !�j�e�wee�1ho:�b��2to� !!e�"� �ly imp�*� % �'�)� j���;�uct&�$``bumpy'' IEB.�-VUi�V{fails m�� miserably�$ns��kh�@ } ��!p "�, by P�$tly� pri}Af�2��A _ �,\footnote{In"|4,al",%�Time �\�? seyC s �fq,+�0�d:(Kolmogorov xthat, given the displacement oftoscillator from $t=-\infty$ to0$,*0best estimate?zS0at any time i � future is_extrapolR�amped�(ion forward.�L4. This resultL he answer) a reT,d, but funda�(ally differ!qu�BP}, \label{copth} \end�@where $x_i=x(0)$, f=x(\tauv_i=v v_f=vA$x_m$�boxcar a慵(\ref{c })-2varianc��c2� =orJ8$text{var}(%CC)C)-D 2\sigma^2: �}1varV �"he small�{possibleIIn unbiaa��aS$c$M� aine�7usa; data!duri$�$-$dashed lin��Fig��%/f 01}!Va plo�=)L�)�$Q_0=50Vyn!�discuss��of A �) BSare� majoa�pic�8�� papeA�I��a�In� abse�e�r �matchA�.� -%�"J 2�returnn� �teF� �exact&} !�v�I�N� Near�$domain filEQf6~��E m!��cr �bvalidR� by r��r! E�!=rej on���4) be satisfied�pus,��<9#s)�^�)kM�Q_BN :%\�v U 6 }{\int_{�}^fty} 6(Ai;1!~"a ��B�q (8��!-� -a� tudeMp%e onl!a strii7on B�� at must� 0be orthogonal��gIȥ���Mvvarmspd}C"!N7Va&� >� ��e��The��in� ��1�o�Ofound*W955�en~"' 6 per@F�i spli!�:. P}��)�0!� tau}B2#_1) \y <��X( ��2) ~ >:<2A_1 dt_2"� var�M�N� wA calliRcapital� �ͤ ensemble���a-m�r'�', e�isE&ne� arily%l most͉ !�ntu��Jpp��nga�mE a���. For s �^�0gem�0Fourier basis�� ior, yiel�= x�� 1�*DV�fM(1}{2} \half� F^2[2� );\nu] S[9�  d\nu.� freq-�zi�we\U�als!/��Q�s�squ� bracket)�e �M , $F�$,!6�� n byFF2 = 2�-B�)]�'Y�\\cos (2 \pi \nu (t - t')A�'5)spd�9u�B2�7$Z�$,�we� A�eU!energy!i.e J,!FZs�Oa�( F_CRi�)^2� +SN+*,>jE'F�6�&b�= \sqrtE�V�-�1�t)dt \\SR��Ssin (2S ב�Jf3 JsF�Ccos�!� 3�/J�L choo n�. 9.�)�܁( erven seval'�"�,1ty�~�!/1yM6EY&h )pa �BThrougho`re� ��=is_awill oftrop��� � � n $\nu$ Bb5(FED)$Jt%��nZ�(SP@2�:< �t�Q A�eN:�PVD&VSɺary N�P]"ocp݊SPD~I-B�)� : a��4 ���6sU known �it{a p��i In mk inst.�� u�2pinaK� abA"a:iis'eEphi+E�n�d��wp&red�in"x)�-#��. � invera�-�!�q�*�"u ))W�A��1�}�s��M�!�(characteriz �contribuI���&or���6@in eachA�Ahesi?9 uency bi��Our���LJXbK͏Y1;�]"� lim_{\D�A/\ arrow 0} .Bigl< &IP(1g U \pm1/2] N�o+<��<Bigr>C!�ʲ���fQ.A���M4-LN� ~�=.^1&5�"�]"� 9� }}^{Vq,l�*� t� !MF9�(����sin>�1{i bandrx? / 0width" compon�of�)*���~s�� QP})���� aE R� de4�����Bbec%� *�� diverge{ $1/\E=� \sim� �$�X�olimit7/m�m�$��j tinu�����rum�ur�ore, i!7=1� 6w � Iam6)�ead8�.� xb����}�x^�. l@ ��w, would�Hrg�TY!I!�is�r�t"?! ���AZny�l &=6:� Ex��fv� W`w� Z�aw�!ىdue� � infl�\�renstinct s&. �"f$, monochroj c |E(al e consi� i�tai�6PLqi}"�!toF�aYu+qHtechni{ 5 Np"a�2�!way_verif�utu��st�m�coeffic�����=�1va�),�!ytwo�"� AZq): .g:F)ntB� o5� ��2bi ��Q�&�M2�L } C!%!�r�!-an&�6�IW���A��($\epsilon$,* � _0$ � random ph~ $\phi$�a>�. B�U NW"��:� �:/_0 �|�6" B�A&heN�2� � =��@*9 x �b! x.Q�� ">  dt\\ ^ =+�E}{ɀ2}}>~��_0~ !z=S.=E="!)N�� v��A�wh�(g i2B)��titut� n� sorI6� � ��(�!JD:�"� &�# P}_sWlangle  -%' r / ��X}:��#�0^{$- q ]L5r�!r +  N#1�=�d3.�Q#�4}�FL5�)ʅ&� jO e� $s$ �� crip��� '!B&; Ze'�5��8.& .��Z1���} 9�(= 1�efQ(1 Z8Phiup^2�%�>!G2}"var�L �A%E��.�#0r to�d�2�!&.��� to bJ� &� _sA@]=&6�-(=-C_0�)��.B �%+[en�ed 2f) ��f�M am��f�%�"GUa -direct"Q ion, \:��s:*!z $1/2} ���< c�,Qt��our:�z � �F����A "�)&#�!!�&� SPD,S *� �B�:s)�!Y 0^)�)JI2�&JX*� \nu6�.� ar<�mMwM�*{\nz C4&R���\�s vi�"\nuA�(^2+\nu_0^2)�(� na��(��pi--+&C}�Y�3sb9 dN9��}{\pi^2h <^2}�� ��l�*A+ F)L)fJ>C"~� seco'-erm, $E v� as �x/� A�}< adop�1�pz)&�.aO) nega�$�1i&})q��-e�c"� f� q�J=�i :PFt W^'l Ano^ �&'fb� �q*�&,�s�k{(at! .�J�}� {wh}�� tant�etaJ" ynaT �wo-poMa]�,^s�E�!Ħ�bwI  X�6Z _ b*: �� =6 -t_2ٟ%6\+I�!:�} Alth� iG0/>~K �)�#)I�� �"�att��*]*b+�� noS(-"�'�ks occu�/p-�>� bN"$may be wri� aN�2�. �/P}%m) &5dB �,"�3B .D D]��VL1�.k"^O#n>F�$Al(2c r� dt�n�P�*3�2invok�E�fiH$ stepF�The3&u�C�IE:�.E�a�obM%��� aSCe�AR�3mo &�3J�ɹmͻd�#d t^2}��xi}kappa��$X(t)=\mc{F�(>G8 "�%��Bdri� forcA�Accor�"gfluct2�sip �theorem�&� �2Q assoc�.d9-{ bath!Y���0$4 k_B T \xi$�4ca1,ca2�!�5sep9\aمi�6�&E �$i*�6 (cf.�/�/JN .�t�����}{m*�)�&oA�- \=3)� + (4l \gamma�  ! "�'� d|B7!"Z�!k�&})�2J�E�q�|<�thAr>+m � �>�*\quad  k_bTe^{- �|2 |}}{I�# 3()-%)+)V)z D}e4"� � F: �m&Vo!Binteg?0Q�.,A@�3QDž!0lik>tot"..>I�4!����i "�*�7`6c,�*u�3po���5}$ �y J�"&T!�BDB�����2�, P.E. ;5�)e�2�4.px-KB�Bt2 eucogenicx2�8e"�6f3,!N6?2J�!�a"~1bal !�%`*}1 �)��VX.on�S SH8ofV#5} QhaB2$tools need)�delbI@�8nR�v"eib2�6o�5�A,N&:� Y6Va",( sa U ��R ?,��!QN �N��c?ow�@0= \Theta(t;0,X)i�1}f^�5 t_1,[ "�t N-+- 2� ��A4$+'HeavyX (U)1- 2)mBG � �21ٓ FED, $2\,�#{sinc}O�(%$J9 �BU122&�\pi�29}� }��)^y��!B|�� �A��ac�%4]Q�Lou7ziaQ2�)�=AB$a high $Q$.F4peaks sharply �3Akresone�_y. W�viewedF�)iC�vM8 ximaE�59dFED',�# e, spac a&26e a(ALau$ growH+In� trast y=�&8�%3RZA��'s fix�0Si(2/��2propor�&%>� prod=8%�q[E� E2\5�F>�#�#,e very littl�$#2PE%�,����-ce!El !um,.]%�<0 ificantlyUi&�:lorandA��:cartoo��a��>��s�.al!s, &�&5@�#s,jv�@X A;}��(er} \includphics[Y!=\fsize]62} \cap!�{C.��.��$�Mm�)$� curv��6�< to a�>�r� � thicko@id iB E�B  <(7.5$ (chose�A�+metic. sons� ���<-�dot��DBanB��� 1/10a �?odi�SO%���1/2J(e�&.25 M90dot� is 8!�A�thin-�/>"R0�sea�q2u2�nul�@uch�j��"']$!� �1�2M��!u��K@-��2?�no.�jLa6�lar�e*�%d:rho�o6=BG�eta.��&�%\��=�9�119NR}.s>is=�be zeroe3�ime0.1:�I!��I9����&�  XB*PB. A �Jon��� ��� ��,�5�;��he ``k@d''��, h�!w3(R>F]*�>^"�>� &!�136SNo7! { � �x n;�֝DF�=� �AD� ��E)1U&GE�Mc �QD�p$6�� :��k$,2?b� �# or�T>,GP %�R�6K4n w6N&K�S�&eEg|?�-N�>`&�"l:�6!�2Z��0V%> diag$@U 1�I�JH�6� E,A�Ie�?5\dizUTo acD+lis� is� first app�q�-of-m�Z$\Omega$��sŠ�|12�F� I [?+ M[67R6N5F"�eqnof �� �} B*I12� T= �[XL (t)]ca.\JZ?�Zs$4k_BT� , it�dsf&1� , :E%H�!��3})�Q$$��$t@�RQ|:Jzb.�5%x< :� _1)]B2�9>�~* <�&19.C> Jq��2Z(͕(t_2 - H.3V� n1w%:accela��  (A� �SR�)i�:�:z min*z �+WXfinF��(acc ]} z2F6>��-f�|]-Y�y)�>�� eJ . Not4� "�/� � JEremov��2 .C;%^eD:<�%;k�)los .|;� O �Oat�NW*n f��i ==�>vstochas`6��&%&7-�b�? !1}*^/�0!�$=�q��] dt}{z&;1 (B�T �R>$b (t)$� r; � �9B�F� �!Ci�<�*���di*: ��.[HJA�*�xd�%�Q�]dti�Y��/& 2?-of $x[QI�! brts. :PN� 2�&N�5�]b�ݔddot{x}�"�"x"Q f1p/biggl[. .P.O>5r]NI-:HD( �z}�= (m �x)� �=�r � = 0c � H2]xn��1L�Q(C�2D-��ot6+ J��k)"�2 �.j�^T[�]/��%w{ a��R}n J  � =�O �$� � }{.�B��ȁ̆ n(2���"�%y �5��IaJ�iJ�'}� ^{oa��4 �%�2�(@"� :)� ��m�H��-��=]>4&�$oa�1perk 2�1ats �>�it{1V.�}�9. s� ^T$"&R&7�sB�% �Mcon\' �,�YDirac NI�� thei�'�YvU,6"�*h��� WJ%6�!�E���)�)�1�&�M.S> tau+5�nmdtA&6rIe�T!Uk�;"A&)8�J,avoid ambiguOU rega,(�UL^enoqoo&�Fuat@VJP�Y cwg}�M!�EE*�\D�l&G#!N01�����+QF�.��b#aZ� ly [T*�^� � h� 31�v�PO�]ta�F5���3e�Bt�,dGc���g�%8;�9of"ZK= Wy)um!�� viscv> drag2O3$s %5!L�V*^p�l �)�s$,?L� valee8�_!o.�3$�']&f$\)n:re�F?6:�!<�ZJq notquiteA>���r$a�;c) =\ &�UmU�9�) �^4P:( ("N$���$a�)2 �)}�(�2�'�-"� :���8{7'.8'(9�rr�(�2 'IM_0&%�*vRA66�� izA���6�1�}��!�\Ak��&J� ��9��]R�+9�!�&�^ofoest�B(@0��u��F;  �kc}:0:N>��I "P0)A-ea;v-F&Fe�Q|>h�F��h>� }{m:ABfM �!!�11�&a!Fa��"�c}}["�D �inge�^;�S�1)$�3 z ]$ ��:>-� Q or $%�Ci��)V�R6/&W> D) �%?�32�Oy�3 ��]*�3S*�Q-y<a�\*ObRSa6VB �!��� ��&3}&�& f�6\-�so2&udDA-�"�cjd%C%i.�_�S._-� :Q� �B{&Ui�bN&[.:>�b."�1phplo�!x5L 1h��2�n2�"6I" ���:�"sc.�$� 5��Vndeed�<tonic > ]du a92">�t� imes�% C� 0.01L io)'ho�W:^'%!�>j}��EWiail�!j*�%NM � gun:�$"�f%�e.��gion� �I*9�icJ�-en�d~unL(for, B?>G���d-Bdach*)2�[ ��it{� ial}� s� ! natua J�"w&causalk_$i W�_� $#s"!E�R1KzM7�r]m0. *�j.�&6� `osc�li!�it,_y� �!bj�M��?nW&R"�6�ju �jfg��-=2N~Hi!S velof�U/�B$��fd�Dm�l�2�- �T ���j, J:\ ��Fs A���a m>�b�&x a�a (^Kn*t[�U)A�eU���J"L�cowe�i� thJw_1�  + w_ 6.j3![t9a" �Jh�w�o:M choi{K,�(s $w_1$,2znd 3ewid>���%/e ���Z& 2Q1�Q4!���� �R��� N �� V"to �� nB�"4 "�)JSS.�#)a��aR&ej^i2 *�6 C})=w_1� "PkX� w_3^2 ��I*y a}�Y&�U� �!�-�o0W"7k2��}%^�"(} w_1+w_3=1>AcEi"� 85-estabb �'�E i6M�e�$wE�rMB�#WV� �H85�f� m� 6M��& 9�-�^a�"-�)!�B( and^\ ��8Y �3N�r,6>'��!5= simplif�ktoB�J� *6�2{�+2)J�i] st.�%�"^-�"����+2�U�,"t8dX)viously�^Jd��&� a@&AQTJ1 FQ(MU :"i � a��.piR�oa})+5a}=:!J�[F�EUP��pf�p-��6�N*R �'"AI-�e&�  #\ -r�4s�yFny��bot�$ NmA ( ---a�� pert��f.z$ &�6�7eQna6 Ji� asp:(*�C6��A 2 !�ŅI1soq-� �; y��MYF��B�M�var 9N�^{�y�2 �<}{oabk6vPV4�� ��a�3�  � A"�.�6�dp2 scal�0�a�ŷqA!�is�''0%!tuncer�ty!h� � -�N�c|3�!1f�fa�4as�Kl��N�*�B"du}9bA�� �QB� i� haviore@��cL �.�uti� of}an� 4ve feedback meMqismL �:&� !an�Sor�/re�&:�-�B�LW�5a1bmJ(�9r9x�n9��"^%"�N�i'P� �g �Mdu�V%aexc� A�!b 1\BND�:s�2;�m!ztem!)� �environC. Con ��3vhN9�9�systemle"k3#/r�`@MA�a"6_m&>xe".2!�*�2� �X�:�$x~1:|a�Fr�����a��Y�"� nJPnefit�+6�+�H}M�q�J >�b2) A�gr�a*�U)lis�mii.�q�4 N"�X5 �8�%&�re�0m tasks�Aq �9&M3ifE�!�w+,*7ng �Kn9g�5�a��i!� ��>�yh, unGc|c stigav�W��uW! # i�Y or��id�7H�Xe8�krfW,.*�Wv�r9�u�* �m~ls:�D,5Lm��1a2�B/-ona�at6 will�hZ$\EW\ (\ew)<�� \ew\!Ye�&'V�\��L�D"]{ gravoA�pTM!�Un�]ti$Washington8Haden&�.W B modu�!�I"�a\.ire�|�"esUϵ�A�eI-�:+i�d�["@ nalyCl�< BorF� �%Yb�ve�)(5�/* e�&8ZT�$E^ } NfuV_Amay enhf�o�q v(c!b2��%�MS�� !�x�1!�xbe%,!�avera��3�9.. �.U�/$@?&�2a���l�� -e2�-�_x_i�.�Fq � })+*e�B;!��.� F��To:�7��s,� "%7 bR�`2���(p i)rge �*%Xi��a��B5 � c���0^�E~�a*�It}*�I t)+b6�D� &&'|*0.f �:R 6<no�)�Jf�y�1���2�9�7/&�2�1v��%�* ]�� E4�~�"� �<w �%��be�aquirU%&.=S� N�JŦ _8� Ay��%3ws����6w%U�m,�S-�{%* *$\r��-U^=2=:ʂ�$\var,'$)B.��*���� a��Y&�M:�.`:�JN*��th.A*@B��+'�P2}.M!yB9K(�G6XUU !).�Dr_4 2*�&�R�aN��e�_-�K!�N��U�APJ�f� Y):>1o-+( 1-d2}B�A!F8WՄR1,a�Cy�s�qms�*9Q�.�}��� !5�-M���fee�WR-E��s true��7�B./��?� (�� m 1/1��$���X��s�[IN|�^o p� in lieuac� ��&�N�:�*F>V 2b8 CF ed�}& ��70arison}E\"ot-$  A+O*oa;}46 iY;րi1]2j1 $x_fGv� $v_f�\!$�5�&i�V>;1:�)H)��2��1dv+e,%pWN  K�� �E1eJ� M) rob�$�� ���Xreo� -�.>^] �t�< �i� d3rozK $1/N"�q%� c�*$re $N�#�numbe�N� � wć͞�Ci# �"8t �& � itself�(ay ��wA BH&-[ E��d �?n%Can�?e� r�-�>!>C � .ApurdQB%w��E�!a�%!3 �M�Eh.-Eeotwash��"�mR!J$:�%E�� j�aFQ6��v�P�a#�$"}# nQK4*�$A"ʆ��&edB� �(diamond�$� (fil� circl9�E� al (6P**�r.�6�BI�� (Aerm�.e]em���i�'�!"� d�Z�<T>ina� Q_0$&�$>y 5g�1�6s$F�%'U}A�sidXab�G! -d!?1; 5M"nd�2q�m�(as �vly�Nu&��neW9dF�manif*r����/>�� �� !� c�<ce�*�&�1�H� F.��呭 +Bt)ym$1� sbox|}a� �:��,���>�-� ?Z�!y��z�5ί�:�EY �u�9�R�%Q�^B�!6.�!+r�F]9�j_6:� ��Y>I�� tn&���&� 6�m�immune�a factSV$1�^24"�H��n�)a�� o illustrCc �*�a 1�a4To lea>�%�aq;erF��&s �$B"�wh}�d 1}{n7]P}}��<�k�,(��+cfc+b� 2-2}+O.#1� &IB䡠9w�v�AP�,!��,��N�4�A�he:��(�J�X#�'%�a 1�RN wh})�.3\s6�"P{0'&->nC�In �EM�YI ���Ls� �A@I # �(i��y*� �E��E^70� fin-} Z� \ll- 6!#50M�\piF{Bt&� �da!Htra� -YB �M�oe J��)U|q`ew}"�./ �ia{�bic�<�F-i�,/2}^{(n+1/2)  :&5 =c+a--pi�dl��-%:KN�mW *mX"3nY�A?u%M -/+J0&7$%-Aew"NN��3eH�]U�4n 4N *haI�2��l�^���9A�^�Mbi3�56�@9g�W *c-lc�)�'u�Ɇ, .P)t&?Numer��RE.}&�)iX�g�98�"�Oe��)�o�& ti��Zi rbitr�Cmix ��.?G([2G�Xn�"��re ��Av%�W on availĐ�** :�!a2�&�Q�Kt�u��employJ���'��discret�&6*� . 3"&h�-[8��st-. �,I�ham�A� pl��*�w!ma"��wE�a� one-���B �� dn 300 Yi�F.��;^-"�!t��.2V�fYs!(h�lsbw4� !X$filt} \B{e*�B�R�&l��XB{q}^T \ \mat{m}_X^{-1}��.J0���)": U&�y&oI�Imatrix%e$s+q��ȑ'E5e� ved M/2AR12parp/F�:5uEC%�� �Eec�#s'!�[�;hJ�!2�d\ {}  c} \B{xF`A,mb0"���= ach� oA}"BqO'�*�!�FKA*er��U;H!O�9 m�"�.v"� :D Q� c�I&Z 6I�2D sz$?,v*|!BB^�� � a�2IQW}�}��>�i�.�or��!l��.K�: mbingme"1 !�%�-�>�s )�su'be adm�*H?en�!�.�opt!�ret&�gr=��� �1�!��Dngml%>Q#er� �%r �&���-�staiH �fT%�)�I%�:�c%?�go @e�N�C}�sM� �})��0 �.��#e� d�446*� Pane��7%:� �-&s �W-O��Pd��datum%4a1�! �B�� top 9F[ne� FwV>�,=�%E� 10\% mVZer�l�� v�0.!)�&�.��AR()"$D�"X V��{ndA9`�E-�e#BA:��-6�&Q�=+J_�J:J�1�m\�  89\%CN16�-�FF5 is 9!�-6?'�9�)�, 84\% 1�!I8X9F��%6T6t n���F� is 7j�mH )6�% �8� 6DE�2� i!�]2�;� %�� r�t� DU�u s s�(� o�h>���&>d.��!5+g" ,��$z�C agݖ& tnj�"�(-<1u,J� ��"�a _��*�* ^Di��ion} E�Z(S$-�})�x �v2*�Qmb>��!�an anh{ic* �sF �Pal> .^m.b!vnt sour�E4��Q��m��5C8�,@$� ��"�%��F6S"�  2�� "n�o�P �V!3m (u l � �ll"IGie�OjEis ``}''&�>�����/�*�l3/i�>)S�5�(E�!'��.Sf7 ack ^|!2'6�� "���i&^!$ad-m}].�i�|{�adv�-D(j e�"N*is,$�,Q!s�`E�%�V��9 guid0 � �yY�aratu����u g�i�"+02�*� �2� .�D2�=�)�< M�I � been }extensiv&� nJ�&�D cri��a �us�[x�pe � q�cru"y a�Ԣ�. On!�- A 6�ch!�����d �um �:(4p�� !A�F�ba:d�a�a laboZy�b�0�#otbe!�"�re�w�umm*� 1e )So� in"�,�R feas�hK �+be �x� beyoM[�(o"Hf��A\�:!�in"ea astro 0 scenario��jq�s�yB>� ould|@��be6�!���y.%�~ed (e.g.�"Ŝ"C*}E]at@�n�*�-6I."�"���Uy#mx>�n2t�n#!2�v.U ?f!penaltyE�%7a�/r>;V� m !���.J�n"18K *��assum�ks�0m��or��0�9mt�5l�t�$!�'ў/�:��i/ Tod8�yC;22��<=%���� �%�2�A![�1��j٤A���iaL*�(Չ!�l�W6h)�.�b�`B2. <)"+ir}�Ca��2��-7�$� -'l�~ly* *�Ŧ%3,M< 6�-Y۩�e:p��!ʼnNAQ1eH!��&le.I)d���!xKm2'"lHoF! ��W rpre� o"+%'��}64�neglec S"ose'�b ug�"di>., wo2s:0�� 5ޮ�#�Dp����!_"P ~ �&/t� Mno �l+r vo'�#T) �'g�F�]e�re2� , fi�'f\�3or_3it#EsuddeŤ)2%�� B( quakes)�l ��A�u�min�x7e��Smb� � fdrift,� ��,� !j44i + etc.!��3 �. *�)5����!16F�"_jaP � yK"|Dv�md�Qpt��B�pub� � ��isi"3fit�� >�)}&s (( %g&^Ur�N5d1+orJ^) Auq/noM 6e�N�=�"� ^�� !Y*&Q�5or�T%z*� %1o0V�lso1��m"2/>He>O6lu�nor%�+f��m&�<�-�AK>Xoru�o�TA?X6! nA�EL b%�t�(? ng fA]o�8�-i�`i2��Q mal-�-���py�K fc�&�al���a��mT,&^ZRa�_$%K�&� p>=C�)�'e�mx6�C�i�!X��!I!vsp[tus---in,���"L1� t emʖ)O&�� ~M% If you �acY< ledgbJ 'u���per�hea&�:>K� � � ank Dr. B� Walt��Don Perc�Y,��John De�L5usefu�A�e� ��ha�Bm��/orxu!HNSF (Grs(PHY-0244762 �8��sup�H!m��A�"B�0 %bibliograph�$p�H.bbb"fJthe.-}{9xpanda�M\ifx\csnLEs xlab]" \K"\def\(#1{#1}\fi \ZGbibO font>J �Yf\#�Pf�Q$�R cite~R.$�Rurl^�url#1�Htt!O%�{URL I �n and{!\g}[2]{#{>!eprint []{S'34 bibitem[{2�${Fischbache8Talmage}(1999)}�{N�<(nfo{author}�5�{E.}~#1uT}} 2i� jPC.~L.::�},@ emph�Ftitle}�U SearRNon-New�S an GR?}} (�:> sher}{S!8Tger-Verlag, New York},�y�{!r HJTE7ein!G05!G /fGA>GG �1�Hjournal}{Ann.\ Phys!.S'bf9$volume}{17:@(pages}{549}= �05r�Cm�sehkar�43�cha��S>�6LZ�,Rev.\ Modern��5:H �1N�43r�Pr.[ley�81�pri�� M.~B!��K �R�S�#+A��BAand T@S�uf�$Academic P�vv�81r�G��gr0Yii4VU>�Hj�Ab/ ct I�9��}.�}�Wiley� b�z�C�%[�We"�5%�ca1��HJ� S�� T.~A>) �)31ru�e�\ a}ZN�83:@m34.\q�5v �E���n�52a ��~��4>4 R.~F�.] ��46:@-4702R52rDHHoyle et~al.}(2004)6u!<, Kapner, Heckel��Adelb] Lr, Gundlach, Schmidt� Swan�;}]�E~� C.~D>2:�V� D.~J>> ��? B.~R>? �? E.~G>?9"�C J.~H>C1Y�AB�-�}"��� H.~E>�5�AA�%N�\ Dj�70:�M�04A�F�), 4 D{hep-ph/0405262}. I\J�H�to�A64� �, /f� W.~C>�J �Vm !��S3�ce;��Hypsis T�ngi8L S�s^gRonald�G Co.~r64� �/>�   & docu�} % % * Enf�a.ate.aps  %� % U�io�.cls + 12.clo #e 3{psfig,�J��x, 2 % \�,class[12pt]{ Te (usepackage{ C} .�icx} 2\} %.* amssymb} Bz s} \new {\bfa} { a��:eeJkkJppJqqJrrJQQJDDJRR� 2�Ev"8FB?om"�DBO  Omeg:btot<r�1tB=pol }:>ord >�!�r�^:@e)�rm)�re2�i<Z:yd28a%� a^{\ �e}FRou� J�{Fneff a"2talphA�\tilde{\ >en�n�:ll4 \raggedbottom���yq�} \jl{2�;{Polariz�$al brems� hlung} non--tiv�� colli$@} %\date{ } %"�w�� on %\maken# s  \{8{A.~V.~Korol$^{!�a}$,  Solov'yov �  �2a�revie�cU!Udde�$��z de  X��%�#0Q�J�@B�d��. Aďe�sG��ݫ��heCest hi2�$phenomenonj�#.� m+fezde>r4; ingu�aSA}�:�  �r&U5ra��)�"�e�!d*�+d .3�of*�&C�5�B�� \�{IYwc.�5.�(In*��MreZ/ *+�s r�F� (BrS.Con&�P�m�X%M%�h(h=X$ea� &�$2�!BrSPic6( .fig}. O�eo0-F }!|i figu���(9BrS (O�?&@-d.5c�==emi�� N�V�M%s�%chf�d�F$� le "�+a6�! f� Lt8 t. {O�$U�n� n�1-9�c�V ��Qc �p!� ofR%�5���A� w4xtbooks (see, ='�8Akhieze��e?r�&)Cp)c��! )F=.�e .Lal)[P![ ar�+ok}. He!�K-�=[�s.2:vir��'Z�=s (.l"�)F e#r��u"�N�&� %z c��d^�.>��6 �� ��a*j�l12cm,h�f=4cm,a�9=0]G 1.ep�� Gc�� Sche�#:b& �{��� yov1997} !�!VU�and2�-�M>�c Omwq D>�o8����)� . v M�sm�*a�rE[ � U'N W9�,Q-ېV\)����}� VBTSY=:��e�Vo2I / �&�4:��M1�� �m\Zr>\!��fu&*�!ja�� g �� -�&�-recogn�:_ ago Q#Y,��of�.�5,/ Xnd|7m�Pratt1�S�n�>"�-�'�-s��. oretY ly, "��[ndN"/�(�w�.q���9�"�@em̤d-�  3g#  diL� geom��M Q,GeRet�ato��i�n)�s����Պ��b�`��iFreld��3 q�chMotz,1G4 @Feng1985,Nakel199 1995} {h � JAtData1}�-angu����0222}a�A!�tabP&bE�-9s�1N ofAOѥQ�|:�!9� a�}'o-U5KN� Two9"s: "m-1{1+2 y�-�&h wzKY�% ely �ly-�Buimi�. vTrakhten�p1975,Amusia1976,PindzolaKelly7, bD,7,Zon1977,We�Nuroh 9,GolovH & 80} �> e��qu�n� �:quanti I=�!r� de%o?rolu7)x6��-, �IFum� ~"� -ato�a\:aani�����hJ+ "e1�aL�&7��"I s�B�3+ c&( q�(%�i ed . ��ndYs: ew"� a4]-d�d Q.�#3� ��.�E2scai�ing An��t(�a-Izonship VNee�YC ful tXa!Z&�$��$dafM )�e1�s�^PZimkinaShulakovBrajko����!E giant dipAr���%�=��� any-g As%L�/ed�\e, �Kuchiev���-� dyna�b%�eJ g (`$�pO)'� a68{ A!ho�\����y�`�V�0tsRo �Z�DAvdoninaChernyshev�5)?�.ts> f�U� ah��e*�%ly9�&�)�um1�Verkhovt��GnZ�DnkoPogrebnyak1983}%~��R� gQer�Y2&�P.�EwN% ��&? >1��*th:�M �xper!Wa��lͤE1\KI=c1986,  .V&��XrH�ɜ�� <�2`90��1991}*EsE�alD a�!��'& �]i3-Mw.P al !c�4��>�C"N� U� g�+.A>qb!Ureporaaͩ�-#&� 85, AstapA2َ0KrotovMikhail����8W� �eE*i>B�,�&*U$ , wA&E/�� E���. ��I>�6|� �� tx \!H the }�ly�(�!�U�-��sY��J f�6!�a0 ton "/)~a hydrog� ��/I�wS�-:. {p�� � IQ/t� a%�t&�  U �&�N magn�M �Y�L,a bare-ion-->�M=$IshiiMoritat4,6��2H1 W�-�LGonzalezMiragliaGari�i1988�a;+ed �|�(6�a��" o��!� ��0�� e�S� *!aa�t�Nof!Xto�*A�,g!�aFI9A(� KY!�wo .lex d`(As,�c 2("X\�/!�!�s il ��nuclei,E` carrI*��i��uq�0}�4��Be�%% A + Ae�3t���heIB&< ��56t�ds�/'٩B�i��u �u� ob" s �9ese�a1 terL�.�� ���% � ii�d&�-u�0�:�%�� �-��Dm�>C�� ,"�&i i2{N��.% �EaAH.��?�-iKn�e m����\ a�Kov L��L ��Mё���Eq�H��8A�d�s 6��&�ayD=�� via ^ha,icA� bil�a_\>ll)�dF�20� :�=� ic9��6�(*_NCoulomb�nul:~ ��i��ina�-: �s�i��y�90b "S 6:z} I0how��M�]��jy��Er�%t wo ni� (��"&)%��=��ar�=� �Cx FS��:>�a� ���Y�<�dM0v �ic��5n�W&z� �I�7. Li��U�, �aQ�u��B:I�]#���@�!2� � n�I)�F�7��9�88B90>|�M�6�Slee���n E��#B3c2�A!"ulaGDr�riv��6J97.�� ��R %=9;M�LDuboiusMaquetJetzke,21989},aAS/"� U�� muotEr�)t=Z�$GribakinKh_.� � *7}�� qA�a B�  �ium2�>]6a�%%iP�Rnd ino A J�alg2�%r��, i.e. \(*�) `sp�pZE�typ��a�Y�\a��M�za�� "�4e�2�B�b$nkovZhalovB�M�'>!7}��{E�pAK� ino�h*I(�M@ A�era� n,c�Mu Varfolomed78,280�%B<)fH_s!`elfA � ���"AA�QAN� ar19AH�in=re$�< as $("$]Ybet +[$�y��}f�-+-�{e7��! pa1� �6�1�W, F�5c-�>�65^4�A;_����"��� �� mpan� �M%���6T��(an `ine# ic'V)E�����d��tervaNK&�~�r��d�D��~ lkš�h��0 �6$ ��� y|RAa �'�'( % Ea����E�  S�Q�'� ,��i�>Z od unt@� y 90th, v Si�q�0-��  90AMD&; !rE�d�l&6@6`in|S�c of ��"�.� �j&"�p �!duT�&/|p0 @�6. i� 6R��G`VA����DX�*R,"� )�s (is��dN�,���& x , c0`ers�;�broad��.�ie{ a�;:.G��!��"�1,BrS crw��!.(�}zeW��F s)SW]Q,\Verweyen1996,Quarles1998 PortilloU5, (_PRL}, ��"�Yi�*dD ���& tool��f �C�=to�z��#"�  s�e�x�>�I��QA %�$yz�W�y �-6f��re ' key�y%iBE��͡�vA� ITɵ��s �v��g!�a�Kr&��.�"A� ] ("eo2��.Wal��&�J .� v� b����!��tI �A!qeum�cnd^bodY ory.�@%�ؙ� by u �uGaYKn: (a).�>de�uQ.%��1�g)g1+wսi&q �Lyalin�~ 95a,V6, ZR2�ai$b, Gerchik^ Bv7} (b)�A{!�%MQ��%Ex�6> Z�l� 1992N��5R�!6ezB6c C Obolensky=j8b >EtA�. (c).�1�~a&�bo� "� e� B� z �EY�� �T��YX:�AU�gI�Z!�reg��!z[*T.hF� � R-4 "=19.:A�X $2002}, (d)����)p�|����B�s��-&��6+��lv! -�=U� �E F� QqB� NEe)�A.�6� .|1994c.5Ba 2000!1f61�ٲJ?A����QX-3.� �� ��$,Connerade1ʁ*,�(Ipato*��37j38�3(g�%�6��@2�9t g�Q� us� OurRtL� JPB,>ETPM�B��je!�3N* 9 ��� Ag �above: �{TG"�$ \/��u '��[N�me�he� -� cal .G�**whj� o�)ev�,� sum��o�v) �OurBook6eo�.n)s �Tmot>��$��a�curX]5 � to �e�&�Wbd���J�%p.�5st��a�9A��kity%Kw6��" focu��oa [ m� !�.�= �%7�IF�U��" :en . \���{$ar0 voA�*&��i&%O� reas/� ta_��K1�E"R&uT��we�yearsE�6PBn,X yFt �UI)ZY� � �8� �{6P� l �_68*AN>�F collisions and those due to the relativistic effects in electron-atom2F�re not included in this paper but are discusse!,other review_2�issue \cite{RPC_Clusters2004,RelBrS_ }. %� During�4last decade an �approach1xBrS problem (with both channel�)\) has been developed forjoretical!~ numer4description of)kcesV 5� v8isolated atoms !� in plasma->XAstapenkoKukushkin1997, 1999TBureevaLisitsa2000ab, -Fbn<r:c:82001}. It is baA8on a semi-class^scatte%�pr%&%A�ordinary%�-� IRKogan5 �81992}, whereas Cdynamic%^(ic response�calcu)|!�E�e lo!�densityI8 xima!�. ThesaY sults wer A�(ed recentlyQ�ft299$Book2003},EFq�2bdetailA�presenti� . Oe�eps whiche� left beyo�e scopeI�is i� m�Xinfluenc %e5�:!�Pa;aenergaT projectiles penetrati�roughJe medium1xBlazhevichEtal1996,Nasonov1998,B09, Kamyshancha .PokhilA�=U8uimistrovKrotov +�oA^E(multiphoton �M[5�U_eodGolovinski1988, AmusiaKoro�x3, KrackeAlberBriggsMaquet1993,  Duboi sA"\ �KaNV :�� !�porA�al��$)8$m  $!F $ i ]a@-fa�of��ic"w �!$Z�m�͌$nucleus. H� , $1�1depend��͠a�ic�& ribu�� Zm�qze2al]�lAPlM�$ed via a g!� aliz�Xto�a Sbil9 $2;$�0 appears as a� ul5}��%wo field�l:ɜ u.x A=%�� magn� 20 emitm I�.p �� �*te� twA$�"�sm� s im� ately�.|. : =hofY���i� vers@pr6nw���ٹ�A}ilmW6� E�T]/ f it� !�lan�ZA�W A� ��s �y4basic principl�^-f-� s (e.g. ~� (Akhiezer})..���>�, i5l� that�[tiR -�)H� E � adi �isGp.�[squ��0e.�  accele� onq*exteraU?a�J. � urn,X6>F|$1/��� i��i� ce � s itself}e���$ i(contrast, d&�:�A@�=>ser�� eg sour&� :�avng.i.�, Q thu)�:� �� !walmos=s%�ive�Q�var)�%��I+4redbook}. More��)V2� E�a heavy.�isc arable�ca� even hig�tha� a�kanQ��l,ame velocityu� uchievS� y�8�squ&� differ��n.A rI�A�Y �trace by �!�/q�cim�Y' A[���a�y$on {^:OAG9�i��smo fun� of��� } ly � �����p soft� rega` \to 0$ *a{ e perturb� �, giv!aa�f� e ��6 ��e3, fails�^ b�I"�>A�� on, known��!h4"infrared cataA phe", hat en�ogn�Tnd understood long agoMڵ)+$q� u�!H2�con=r -?��or"l I� ? or"b}|,Fourier imag"W ��n ��".�%�mon�lyCH!~ 2q$. QY�lyi� valu"  definm number� ����%~7 �a ��,us $r\sim 1/s _� reac��)maximum �at $q=0{�$$F(0) = Z$�'de�es:�w A in !���he caslh� \lim_{q A�\infty} = 0-�=al��P asu Y�Aq| ki1A�� @, $R_{\rm at}^{-1�4 Thus)�y�ofi�is �� $q>>?a�QM�q�q\ll B,i^4comes negligib� mall. � behaviourDa clear2|�Pratt1�\To�� a��} �"� "� $"| must"�e iY[Aw,AaE�a�$r<�"� aka�� ar poteni$-Z/r%��screen�6yd loud� e oppos�limit� enA�gg6��vusJ fua�^fs (-�Q�a"cI!)E�U�a� !�a: to ge&6�and t9�vanishes5 啱�gr b al�� t1  Ɉ induced.�"Q.� re�x 6�s -�� �@�Coulomb ! �]0-� ac"� �i�)� �"� "E R)n��i}refore,�u� �meterj�[Fom�E ref�e]>���w.� � &@-�>� wo� bl!�WeQQ1'W' wA�addres�toBSina�erA'st)M.�n�!and��us,,�}2��: �M&�� �, ީd}��to -� !,q)$ reAh�p`e�!� ��y nG��I�aJ����0}2� �-2�\, "$1.2B-�B0uXbecau�n!� on�u z�E�is Eq%|orV �� s' o�i� -�)�a#ic�^e*1�.�e cloud��' pronouna� i�z�;uni�E�� c�N of � $, i.e. E�'}�is�"ti�,F� �Pis�0i ri��I8�e�h�YFum Z@( , in�vordŔ~:E/),. �l+,�o wellvcrossk, H b�a�e�m2�$.�� ��%2�$a�_e�)�9V��� � A Ric� ����Ab)F6h��he-�. � i<a�#"� ��.P � � b*����PI�B� �E�imV%��E�%�"�;Zon1977,CZimkinaJ1982}�T� �%a�:�lm�g�r� Rron) %���E�!a(i�  *Li�(aneously, %!�sS siblI�"�, !n!C��e %�ks�R� .al�Q�"�� %�]�!U5�oneF %To do� �&`toec�6�!Pco�d� %e`d�ed+K. !��"6�"� s will!Kobc� ge�[ %]ZhatM�angG(c�Ob �#.B %�ya $q<:� ��w� I� hJ `_A"!?e! pi�"1k�)U= s��i�".�s$do ot hol $ion<%�M�l�!� a0-range��&j lead�!� %&c �I}Ut�.no��-% %="F": � $\�.�f �6*I� s �a�S��q� cl�� to b"9 a� MY6 �j e��>en freq�!y�>����seba���m� �.��ubshell� Each �(+ac�#�ion =�$I$a�� er��&�#��c%1EZ�F1� ��!�ro���1 �a�6 < . U� o�ogy�L may sa� a�0_ ��&i t 5�a1�-�"s�k~'IC��cl��m�=>thresa0��^�}�!��%mD� BI_1 <� < I�� 1s},&�3B| � $In O 1s}$V� !'"v� aV��u��ouA E[ ^mr $1s$ �"��ueis  !"��^$extrema ia�c  ]R�e� is h���]'=! ular�ӍSe1lX��-w )xkA�ant�reson �I�2� D N�}�>P�}� ��time widA� xima��(�" a �&ծ}eri.!��* *.CW#4(solid) Ba, L�"Ce �4LiefeldBurrCha�� 1974, *}. Lat�"se>'!�JheQ)l�,WendinNuroh}#�)�aa\��(virtual exc�!+-�$3d$-qYu�s.���� HShulakovBrajko1981}-owerful rum was5TA�J|uF�I-La*�w3����' �)� �K�8 u�]an � tFluh �dra� bout%"common�e1gE�U�">� � i,'Ma;" reveah simi9&ty�rre��at ���a3s z� ��%*"� �y �  � N5!e\ ���a�^J� D�*�4 |is&�yeC*��:: 6� $\sigm� gamma�K� HI�Land4})J�{�I�!s�7�{c�! "�!\, Nq�b�!c\�x 137�!Kv#! l� . S"�#F@rA (see"�1})),i�modulus 6��=qi(� e�%AN�%�':a�n�it���2~�}&in^�B�q�W I�umj������2 �e��!?Q��T�,� �(��A"G-=assumpXmR&�! to =-���@��:�F�,ch&� always� g��rru ��-�. argu�s#I�b��vi}01"�)�,� ��-cof �� ����%)��� x�s,�'ied�� er, sup�ɒ!<і�edi ET��~Ya��m� B�Bseveral g-earth!�))ф�ɋ$EtAl1983, & 4}� ��� Ab*�! lanthanum 'p�-bV�a VX��}�y� r4rag�g0}/ (I�<, minima, cusps)q �).��&^ r� ��A�2�in � �g!#>Wa �$ a� �U�'��� �y|U�VD72# Obolensky]82"W3�2N5 9,Ro khin200�Fo��0*"�noticea 6v%e� ��"4�+om  &�k$AV.���J(much lik�a�( ��of7e��U��� !^!�expan< �!&Z ?7a � /I_{)r�: F�2BO -{"� \om^2}\2$4B�A(\ �Ra f�8��8$m=1$, $e=-1$) � Ix&8 r� A� �7b�D�&I5,Trakhtenberg�}J� f_�. � r�. , {Z9 ega: 5B 40sh�1 ! � !�$�͎1s:�� icipatE2%�Z!Am��� do8"c s 7!;2� �(u#�V� �>�@:;�4nelc-��(- ) de-^���" �%on%��� (f"�0�F������1985}�1use%Ve(`�1pping' [)z!�_4N�,I�9�� �� ��*�a� eeGj��tr�)2fO(a�BB�4)!�")rino:�&����a��P�.s s�"� 64�av�5�5�]W:"��A��i�Aiy�>%l��!�I� `-%O."k��sa fix�/�'�omI��5�*�i� in��group# 'inner'ec�'.'GaM%6mer�xw~big�v,�in�6exceedE�Av��gtheir"� �>�or� �� � nn. �N�&�A�$.���=��FQ9䍈�)%Dh�7]>  $�Cout}$�&� �U�*9a�je they� euw �n�6nir��$�*�v w+2 4})� aZ�*�a� titu!�� �A�"�*-) � $F_{�(q)$. .&ENCacqui�:!B0F��f5�� E5:in�����&k.1aB��>ySR :YA*is��!!�demon�; 8���)D5CN�^q (or� UAwor�&�; is '�'ed'�1%� ,$N_!�$6��)�^ t;>���aleŌ�,%1m�?above:�Na���i!�: 4#���;,�JFr�"�!�."n* �='&g� +N�'. &��-J��2%�raccoun&� �a:5@� L�T�jn�+a.��' , itɼD9Žestɭ�"� � '0 back��nd1���2+  curvW7n)�� on �-l4(��9:� e>Q�e"��"t5�!tra��&@� &24a,Z�6�}� �in�?Nam@f 1a})"o5u�&I2�$�D�5�*8om:��$"Es (a).j$ ($I,0N� !�� $j$t& )�B�6 (bVll O,^��d9 $F_j��`!С�� -�@ Qi"8 3��N_j�- $ �&^Y�L� j�[*JlA����42\ ��,5R -0 6�is�*��\gg!7)�:)L) \mto�^2$��� � �"�>E�3B�&�Fc E~q)6tK�*, Y}.L ��-"L1��,�HF� . &2��g{ , go� �DE�FN� �F$H99"|099!?W�,AD.i  M�( comp$4�.�yM "��-  A�exp?k�2 + " ���:3�Wh�Hg H�g��um. FC�l>kN �Iw1� :$ ��m� � U��z�0>�3 m d� � .ama�$��biE< �)>.�%9�t�"�#� �&Cwo)a��/ 96�m� �� /e$ �0 !3$ g�~to zero p�@KA��� 3����<�!�al"|6ng�556�D� �6) �=G)9�"��g8G�!��)hU"r!��@ ��9rva��� &2�!JA$ m"P ^'6re!#id�m�["valid�9 �meF�"e1=of�Q .��B�AdEGj low-&� 0EU�! &?���&�' of eyL "�J,�Adu8!+,rm el}/\om$ �,���. O)�h h� ��n;ofi��B�6st��% a�rg���.zk!id�1�F"j-�*� �% t afXNV,�,A� .�B�: �0!gF�aS@#Q�6 �;��!��g.< 2�B 5� s st�+N�A�,C2�1$E>E�-9}�j�� A� studzAH7�?���"(�0��absor�)� s�f&�Mg� ��P�$tM�"�0an $e^{-}$-ArA�K�:n �)sm��u�C)e� coe]G�H!�aA�CsN�L,s� &sLis�es%��&�G�is��*. -S Rie�:�^H#@Ar} = 11.10$ a.u.E�n, 2.66 +� DRatzigSmirnov}. Raw���mAih2m� !�BrS� � A-re� "YNIyHammer��mA*�L}:` ($\E_1=0.4\dots 3.5$ eV)U@--� g0#tom�"LR�0 MolIa<al X-r"a�m' ed hydrogB�� +�# ]!E��?�)/M �s  78"�-k:�U�s �=� �Aadm5 .5alU,�5 ;&0�$, C��PGreinerReinhardt}). N"th�KX B'z��� �C~239 a�n�.�S`tom�5zm�!i>imp�8par�8M�* 2}7 *sCe�'�e6�;e�� f�D&�E $ders. How� � situ�I !�&zI&9��.ged[9�1--B�lis somew� �4t,&� � �SAk aslo �9�B��B�ur�EE�adz&�4.se typ �ρZa �*�C��&�� �$-�� K� 6��>l/�>6Jism�a���o/ng � w2A(\ u�*�D5[IaSvFG��;A�ADro�9� li�Stark�'(se:5 au3a,�%^'A�� i*�sSK%(".de��ted lev�U :e/,��L�&LsI�-�1pGal uA� a �W5 iple�6�componen�&�" al:yv5�Oa6~� K���iRO1�%�0iLcovP&5%�9�%Y�/R�I�*�1. -<sta��"�Qof��ntry?c!--D a J���s !stl6A�QS��`Y*' �k1lso�>6;B�>�'s 2O� `l��4p6q��8H;.� j�a )d� cM'�Ai&�z��r3!Q�&aZ� ow"q�"E �P��#f 6?T N>qR in� �zh a�s *  OIA!4i�+��A-�R�=I�~ take�7to�;� 2 next logiW step-ol�gM�vesV a�"�V  mpanb ��e��Wor*��� I �qDe �B` 85c}�.% &;Zype `5G'(�hP� `-f' �2e� � �2i!E+ Y�� afF1�� Witb�H2D�a*v" 1_ a� � JaaE!ic�8i� y���6� $0$1*�RJ�5be wrX:nu� s*q"8narray} f^{(m)}Q = w +� =�"BQ -{ {?Q} \o�:8Q F_{m0}lQq) 2Q( A_{meAQ,\b6Q.&�56" �Hu VQ@l�8m�Q|\exp(� i}Z\bfr) ^|0\:le$�a�diagoa�����A�� $ ��}� q})"�'asF, 9!07�)!^\sum_n � \{ {��: � |�Qe\hatkp} �n �$ \, F_{n0}� q}) )�\om_{nm}:om$i\,0 } + {%�n%}qxA1=n�^s0 t2b 0} +mb �\.S785�� }�!_s4!rr�� out �'6)set� �4ly��J���? , $nr�%�K)0MHCC.�."�B��t� .�?�~2<;*? .%Y*�`>E��*e�M) A.z��-v d\/I�wV|��!�)�]�um��G� f�f�] 1987L0l�0 K�*&/ 86a~I&> s�02�`man:/. S�`q*XZ�G�21E BrS,!q� ~��2,�4�$thg<-�9wbyv "IN�L.w =!�:�K>]85c�.BG}2�S��.1�{ X *nRq�> ^%�I<&�.��co|n�aRayleigh1��ofI�>C�@!�3C2�@e��LngA�mi%F>9�.�.�y%m�d�'l��i����*araX�!7d�n7? z-kIb t_iJ�TZ^2-%I�� s6YTY9a��V�&�%*�%W!7.�F r�&� F�6}(W"�Ot��6TR��o��x\�� |9�6��T� $Z\gg 1!. ��^� !Y �5ioned M�ce� d_y� esse_ND,�!dw cBg����2�e6c�#rE@ {v_1 &{DH\�a1.9Z�$vN %��^.9:�P. B&�d9`9+6�b�mor�;a8ant. A�)ce)a��, ruleiA�"*i0?/�irged�MG���s/>"�s (a�e�,�]&�`,[ "ion-i�GMs��JS}t�}!?!,��6 ��a &�%d�9(q?�" \max}B#v_1^2/�2|.g�sA�c�d�er"�6 , up] \geq 2U$ ,ing�%�-���V� 2�)�A� e E`� \lt  �� conven�a%GL '�C.�`aa^EB!?7N t�!^a"�V"��3!����y�,6O>�32000}� 5?!X�ۉG�!K9�s"@��a U2�VB�H ridg"�kD� eB (�lh �&W��LH_${chapter5.�*A$yri0-c�#e��1t �? ePp�gmH}w;p"�9!q�~[.� >k} n"/QK--6a�=x���&� >qZ m m�� 9}).y�if . Ues7 ui data4iS����E2)Kin�lA�]S=�� !�u6�V�e. Ue�now, �E�"u� tech4X& tY�V stige���a1��AY ��.� tm� vGns�?�u;QL���a�[�EKe�#.�m�8C"� �y .9Y`VerJ���j�w�Mo c�� �&}>R9�!�V�12$(ofI�I�.�U�d��!�]anrI�.{(JPBVN�p9�kA4�/-o�T�n�p BB<^+ soph%�?"a�:�J*8 ��@onger <or4)sI��C � t&� !�c' ~� -�8 lLr� >)Yl ��,�xNBL"h*#Ap�m-�n&]�oM *�-5j-0F/, �in&�'/.���2do��s�qh� rbJEAh he Elwert��NH*mod~$%8s�j8F"�1$,LeeKissel Tsen�@6, >+5}�%`��Sop)�P-Maue"q "/L�M^_}.]�2�K-of*0U7 Kim��$,FlorescuO@}!>by ?"�vB�y 3^gK6� 6�;e|b^ I7.:O�i�jCI�N49>BIe�B��:ba}&�y* ��2YE�ach!�zeht.(E呒ofB-v\d�79,&�|80,Kur�`1 Ias"�p  "�\�i*u� he jointM&�/e&��=�h/ ��F�bk t�`� q}:5Bm2���y �CD�Ɓ�O �"�x). Eve�.yderL{ӕ.*_;�/g�Lu� �7�7,<4#[t-9 implVqask. AA&� Ga:v-(or-)K�B*�$ tx) eval�$,pobmr&�6�75,�~us�~JetzkemhR}���toA��^6h Q�o�R b!y�T S� 34e Hartree-Fock� =�sEA�]�  �(K�!I0P& -"=&^ T^&�C6�Ra-GBV7P��V3�"6sPN�8} auou�K�B ��&2�Sa��1FRbod�r"� 6- -�oze l��-R��x �0�F� �re����3)G{�� empi�fU��p���{-u�.N�B��Sc� D,S�?osJA�%I6�2�v 6eR<B6c}a@�/�aw�!�q� -YpRb} N� EB�C�mG>o"M ��;%(:}�!P�7�Iv. ` K-%�LK�,r� 8~in&���:�sI 6�*� 6@%$"Q ��l� c[$�4*���+2� &� e] 6 ��Y�6�!Mikhailo��&�O-U GonzalezP�rMiragli�� 8,retard2 ��&�87��8�W�0�&!cy��q${k.O"�$� =.a]it%D*�H�:t�J f�Zr5�S*y angu�8�"~?Q "R�5i��@�s/l3 A�%��%�� �7&* re�uly%�M�& R�q: �of�EN� m� OurRv^JC JPB,> ETP}� �6B/��a om�y!G&G E�!o�6g3Br,�!�hJen�2m8�&�}�&���"��il�N �T!P � )a�U:�� "�B6��?%�@9�)R9"�/>6}!d�6� �chNC eriz�}-al7>�U�&g�6by&�%>0"P  1�$$) &\equiv +/ { \d_ #�%{~d}#1C4 D(2\pi)^4 c^3} {p_2 p_9`�/,{\lambda} \� \d\Om_W p_2} \, |�@�H |^2 \noD7\\ &=2�9 �+2�N rint \.NU"�&1)�'�g�5�}Z�/di"}IX ropa�V-e�,e&@l ($6�$�E�6�l�=!'$ asum�t �":"[" - �< � �C& �C!f$p dMj",a��w [alVa*%Ir�RB =S���ear���2�5"�B��}9J��Or�s"CI$|^2�y$.2U:22�B*Cro&q�V�%.]>�2pYZ"71A@"�!���(�+JRe\,(%�� ^{*}��$). N͇�z.�.l%Hb�ei}& sign%K�*� ea65�t J �ec��a�it�V�A+9e��� 2�(e} ..��$,r!��u�$l�# %Os MWY�A��2���#����G 0=��B�� r�!B"A2�#� ]E�� )y"SQ&�G+by*���o�T�".6W (���zf � � �J"� "!�� ����Ic'�r �)� ,-- Rz!� /"� %$a� �4V}=�9a |�6b5bfra}|�|,2~ "�W($,$)e��ic @$) 5�s�W^�5ԋE�s��U{si$A�i m$re��E)H�J�8$\fl \qquadgTT & =*7 7�2^{(-)}&7bfr $p_1^{(+)}\�leV7|� 3}\\2\^e$ \-�7{n��[ ��70|"�8D}| n [�.� \, n��7V}Q7�, �8&I7!��70}�9 \i 0 } -�:^0^ b2_8��n.� | J�7�7_{� } \r� ]\,,E!;4B!�F $A��)p I !�9�$J��'e2��s U�a%��s�+edY}-  asymptN_�7a $P }Y/@2$,� pg(�o� e `$\pm$'�ferm pt>�x� out- (`+'�~2in-')���v<�D ��A�a-_��,iJ$:\Ar| �{j�&\pmU�)�. = �" \sqrt{{Ɍ�9p6y0n 0l m} \i^l\, ;|\pm \i\delta_{l}(p_j))\, {P_{\nu?(r�WrA� Y�_N#p}') Yr}F:"� F�^�; zl(p)$�'!\$phaseshift�nIA $\nu2�W�bD�umG b(~$(p, l�X lE^"5s $ ��$ satisÏ Schr\"o�`er 0�Id� `frozen' �e. V��E]D= � 4})��5"]�C� .� ����Zy �Ne/M�-(i�(= E_n - E_0"v .g"�^'s *�:�!� 2*?*i>Zh;X; (i| A�&3@EWtinuumR*F ; �'f a$C%*N1*.��" � V�. O���!{�/s!E ��6 4 }) w� (�=�ݔ�V���e�{\imv� �b� ��QaV�= \bfQ )Q &J�i�\eqL\i4��}i�Na� .6cQ)��1NNj��g~� e5rp(M� _E$�9�or�_re!�en /� �^�C stra�Kforward�9$yP/�?�9r.� Q c�{$ $|\tilde{!� p}}_NTr@exp(i!�p #!�)$ �'d&ےQ�( for�,�� B�r?$:.!�sec ő� �-Q  D!����a��wese�"��5�����h 12}��t�U in"�(})�%2�%L�" _��r2� @2j J|:�(�B32 \pi 3��.�c^3�mz� _1 lql_�5�4eft|R_{l_2l_1}�.+2!�m� ^2\,&�^&�B�+w5,$l_2=l_1\pm1a2��!��s��A%rules,� $�=�6$\{l_1,l_2\a�Y-j�\�C�,�� l_2 �$ Z�Ora\h �*�$,� � �jaa4�<=�06B� .� nu_2\m:llel r  1\: o 16} \\:U� - {`\pi�nt_0^{O� dQ\, ���m6}j_1(Q�� �, \�RAg�[&�17B � $ T��"ށ BeJ'"�{ *��6�AV!:�� aUAC��X��l�6\d r �_2 \,A\, 1$"M5��Ub:�M/MX!�$� J�6}�*�`���>ul"s� s[N��M�>'��mR|& ,Sobelman�a-o�/26J�*� ��� 7})(:�~"�%�@.�Ies�t�>t p0.�qn����Oii/ exacG*���� ity=  bring�]JTCy� C�}>n �,���u�%a*a6F� rB�is A��b-�KF6^ *<5,v �~ a�0*�e � �"�3*�&�]!L.Q� ndKXzl2 �[%4�Y E oa����Kv˞!y�?��,�L� e%.28U<6�$3l��Gshorto+ ��S)���.$�u�D fine���$G�/#e=� �2'q)/� _{\�$!Kthe {\itI�}2����2�YV&��+ _ �= m\, �.�FOH Now let�xaI{/in�n)T�{�6x Jx� �A�+qaN�yW�)}a�4Afޚ=w�$�<"�-�AC-�Q�& lj�$r}i䆡 exf +6�#s&,+)&nstea�d��8� {SL!Be��&hr��~�h-�.� {)�ZXHFej_� J)�z� .P G>J\,"�9;n.{��H��!�!\keya� ia)-2�e2��"( 9})� � e�ex C(Q��/�&{H.�%9�io&#pa�r)VC%��c�b#eN'�< �"!{�&�#A" heckDg Pt m�Brigor�x=;s (.�<�%#�ary RPA-�#i.s)!�>���V)e�� 6�8 on � , EuMW1��I�Ͱy��#śAF4d"��2"b�&Gcs } .�!��!"�T""�K�s*��� >�. R�!�EEaE+� i0:uA��,Xa�,� e!��e�B ?zt"�~ �ab $ }$-K*]d"+]LA �<�(�ci!FE�N�(E%e�zJitOf^2�,�� r)$):�, m0�#u&m$BJA,Qr�l�' spin��&E�ach�Ag'&K'��Ee@%�Q%VG.�:�!|2$\�x.�o�:*&a6�d�w*� UK ON'.bv iu��3�Cou��6'e�hL]-�+ �5� )�nCiq��6�-�&5�E�-cAXb$V $9�2ref:�&A �m �HB/5�"��com.��.�� ��if70co�UDxCu�U2 .}tY#�� l�W��2�����b�r ?�(%f� �+Pratt�@}&';!gu!���#��x1�k,�� �9|AUi. �'s�f�&s`%�&&s `�n*'spuq��arrm�}>�#s. AF�a�4�c in��aJ �'IQ3,�> C:> >�$_2?��e\n�� Q%U��4}�oX��*>�b2�dO�>��%6 *y$ al�&� ��f"=� "@a,\ap=GN�" ut}}|zYr_a�[v_{\ap�[^[^^NZ�r��Z&�r1_��$1>$a�!�&A,�aU&�5d $ �=2r-�-&+ �T��m?!�$��,, E�d7<�2enominU�I"�HNaΙ�U0�g�4me;e�g3 V1��)e� erm,S po.Z��{-2���%# help!"��5�$E{n�Jft.9W�o �n|�.�d$:*�|1��$�}�P {�M�2�b�'� !� � �>4RM nt*���M\bKU2^�.<�d^4�g e�Y@K>o�7!�HU&�!s��$6wj��CW e� 2��B2Q��3 we&4���Wbfa = -Zajr/r^3� �y1!=�l $!&r2�*-=&�n�p< ]�_�s. ;\�Qi�"J. D'matrixC��  `lengthɺ`.�'!nm�6eS�)�1���P3})��c�O pT~�=-A�a= ~N� A�E�ip_A��!}Maka��U�3~ �Q���Mu)�gAi]im@:�'�!l �,F�a�A�ٙJ�ef�.�) �E?m� } � -"^$� a�qy�&2� $A�\M�\r/ Y�Q� T& ./. Sub&""')jx�5�; s $\V�� 21�I�� I�!��!�b� ��6�.� ipAr.ep"o#figure}Q4{0er}-7Pgraphics[width=12cm,hWt=10cm,P%=0]H2X}%)g fgVca�0{&�aȃ�++�:-)&)+p\�j5$ keV� 2 "h(0"an Ar�5T�o1pcu۪"���zW�!� ��>�' %n�S:H&�d 5RPAE �u tect� 6,? Dash8� �g 6��� ���do;�eN�%f�y (�� y+N�N� Ve�Tal �m�gA�B *H.w&��h&�1���j*`�SeNe��vc ltext.���kI�.�AA�end }:� Fe<sO :wE�%b.Xe� � @  a2 skH"�5W25e-�?�\\A�ndq�!Is,>-3��zmad�NoW{ xch����C��^: pla�X&v_�Q!ׁ���j ͮ��um9"{|i ,kiA_��.by�+deCjsc��i M )��I�) exhibi�� ����!���(*1]� wL�64a�1��ow,�!!>�} �Iי��ahMVu*:S�FnBL6�0 &S"� �E� K��:65ri!3^��&��%b9�R 2�'"�.fvr eqs.� 6})-�7��[�g��>A-each �>W $e=#��/��random-x)*h �wѫex�O&W�<]�x�h� vPN��{a�ic .�I��Fens٘�f2k�]�ݼl� `�'2 ��. )�>���:"M3p%"3sb&a}U�1 Ar�om=20r40r,9�4d 4pD�� X798 914se:p4�j� �?D .i)%]H:5XA�>���#V"�lA>l\�=a. ( �`ls P�IoxO.� 5p},�5��� �ef>� �y46�oHL�a��mIrl�m&ڦ.)eK/W5�+7a��"�[ LSR�mad2mag*�I &�#qa��e��ly� �\m� � h x ���6� (Ɨ�?:aY ��ab �aiQ�eq� 11})�!7o� =2�]eY)nt�Iarp. csG ���R-q1����dt� co3� H2g &� il�*�  9B�(`�pF��,.4a}b(EV5�oF��P�" !�ignor�z Mean��䦅5�nF"3�/$���..!7AW> %���21)�� �1. *1�.J8E<repancy2S��!-���in�.�Q�s`tjpof <1rm -�Bigl(1r"&>|��` z` 3.` XeB�B` S�W�Z��"� >��x����a X�_om.�BO X)�O bO :�FW��nH_b=�Tpr�e�it�K�"B�V�I).�isaw5"'AFV�e*� 3 &�> �\��iB�h�e�[.��"��h$I���&n.( &�$I}�p a�6�i[�s,�5����-Men� �ta"�t$N�1"j �V�h����rlLerZac o�R0"�I��\2t߭*d#���.}B l�9�82���ug ,�kY� ;1��H� ]2@ *� Ie�$ pasTq�R"� :b?�$�X LⅷpopmQ�M]\E�s.0�$�Kd4xa� N�� mH�#-iA)� �<�be�:�:B!�e�t��n�� + .� .Ts�d@�@dR�< peak�+n����BaLaEu9�*� s2���� ��6F!�$ lEQ-Va �>0� �socZ���N�  &� i�"%fEu%�A�oIqW�!yA*�V ��,��2`V�A �v"f6� !� u.Von�wl>x~�"B!�#e���*hip�me�B:_R_�Xla$\C*��$"8e, h�+mi")���[ "�+FI �(B�E�&�V  g �*�v� �.*� �2��$M��PM=-��!7<]�y� �5܅&� re�ox&e�aYEl<,)0��4e�h"��iBN6�Vi5o!5ai��u��umA�$>���E%�љ�%�syp��2QNd�!n+"%qM�V��d�7q ��La�h "�����!0� a Eu��.D@�laWisB/�B'rEueM�H��eQoscill� �z�_P4du�RaJ5�&_8$ 4d$\to$4fe��)Q%C��F���V]��loRZb����4daX:� �-, �)�B�%\ib d��4Y}%{fJ;i� =0.7&R3T B� PF̀6�Z��.� -�]�"E s (��� v2�~aac�*��gnQ�2�� ��6a}B] )?� 1��6, 2&�N�"\>�%e�!Z�2&zŎ������ "�� �&c�n 2�92; e"4��)�|+X� "y)�g!�Ok&�<�2�&&� �x�- �U2���{x�(-��ed W.@$DolmatovIv?Z83��E%+�&�g,4A�4*�U�das 250��!�!;6��B�$d$s7�4>!��>P�co {ce�Amy�-�cIsi���!�R�K�U�7�,5|�W�� Z;ed��ly� !��bϙr\sim�8?#*D at.VS ��)y�V7�Xœ�N<��K�Heru#n�&:��UiAH��B� 's me����u� �r6�T�2݅a\o"�!K!Z.� �$ma2FI�A6=��()�"� � ula B�q:�e/Bi = {16�={: Z}:>e s_{qz:in}}^ ax}} �Yq Mq}"�:2�\q ::7�Ih!\{$g=p_1-pC ax+.��E-"�*al viewp}X+* $�(be"�%! &�eff5��(�alogu"�2!�ag�[��fuڇ �πn�*� 2*,dBpP"@mK��Q%" j AWO2U ���1�c!.1���)�NA37�"�| �t�T\ �>XZW\, �&M&*3Q)�zBU2U\.;0B f heck%I6�1p�Uj-�~^��b2b�\6� e�%!�:�1( 0.25 - 10 �!�8 �1� Eu uP��?act���b�]:� Ag)�e� M�10}�Lƫ��co�-oRh��are�.�:� Pol}6Lh�`�&q"ra�B�Ba.9~�_*����5to�C .(7�&��K�V� �s�8-A �"�"fL0})*�2b H9sݵ�eC1 j���a��yD�$2�a5�-i��,F^0sak� ���s,q��%k�F��6a.vi.)L!7B�� t!"H.r"YW (.*)BTBA%� ��� �� �4 5Y4 Poe�6n%63 N2end�"W%�2 a�N4 +$BaQ�A 6@ !z2D a�f1~ e�R"�Zed z$�cH%�TeM� QE��� 6�$aŤ  oriZ-� :4��QjB�Am,fe.�N�7.��J2�E��cQ�6� � "f5�_ila8}l:nBvFcombine��9�wP����PrG�T&�B��Y�@�:a &�� ly wt#�<��� �v�4A�`�pa< .�!�ILis�9�r�!4(u� ps��\ J����eW /�use=8w� Q��Vš"�@![�x (a��<� R�� 6 #nvw9a-7�?di���SNa�� `! ��--%0� '��)z o�� �;ach�Iq2QLa5�z%He*�vlS���d "S!&���50��s 'L��� q :K�}%D�`�&!��"�m� f�5]�`cz�6�7����>;;�� allic�!�*�7>Dic ]�)U9� B so�md!,!�m��w!xad� �$=9Tob���[6�86�*2q<�al�(%�akDN{--�Gribov�`71,HenkeGulliksonDavis199��% �"6�� $E��,�Dta<� �,Ke,"} �Ofac�B� $B"s2�6T�hF( � -1\B��$ no !Kax ,y�^no��~(kOiter�u�ћ!�mu -A�*q�H$�"$-6�!I�&c�!I�9'"2�i�^M�#2  ��<�M"� sN)��ap��1���B��t6�J�.��r � v���6Y}%{ea `n� R3R� Ci.G�[ (. ) "- c��zpJ3 � Y�& ofB�  La&�H}+�� �)�)" �K =jz��".A,"".Qi!. >�"%��I nI ag agrem-I��e PE  fgoo��7�L�$4!�-Q� 4i�u���- e�� p�|{["(=�o7� D.G=;to,� &�>�; F[!?-�Go�R]a&�?a��� *�aS!�U�h�\1�.\R *�e} \��>:Sa+o�k"cof�:e�H.�!a� �"al mac�A)woB�_�� rig�u��H1}K* of `��*� G�����Bo�C4�%% ders: ��"�?by .�4�p͝i:}�J�!!)��! ]S �;�B)�Se�(�, �j �\;-� BA�&te, A�"L���Solovo�9t? ��Is;yJ;��)�E��[!�, B}�)�s� �!{B�2:�g!�� U� F2�?ptF0 MKu���84,^5},;s� � av solvC ��� �,�UIgGN�A]� G)�A-,T &�%���, ��Aq� ��ur��wrf%!� |t�S`!+ 1�9 aɈ�� 2'aJy�M{T��1$ 0aV/s�%�/d4Z 0WYe�(g�A�S�i,�X �YSU�""*b@�p}$�Pno�%g�I� 8�a b �KJ��,a�*�[:)FQu� �3� �0Qm�>��Ow�;H�of `#*?Zi �la�5�(� ic) p��.cLE0%az�e� ir �BJ?�#��R� '0'd �ac��.e< y(m�"�A"�H$�^U}�f U(\�Vr\}_1, 2)$ (�M$F�$j=1,@]�?Lco2 O�ll !�1�IG� '1�<� '2')��I'*� air.�sV�t"M�a�� .#��j˪E��M���k.B��)�'" �BM"�>$V$I1�jC�B�^"�a!Xsum_{iC(} (e_i/m_i)C;-�Yk�Ai�Nw�!�b<}_ir-[Td!'?Z�6.$�!['9nF �* 6B$N�4h"`&�� $e_ii�$m :fh�RO}�+m2T.����b ��o� um 1E�(��ur�j!�&��� \c$U �V$�$whho��"yi�m}if���ra8���&"�X fig: &tat�� �GOQ�c!y�7�7 #6E�h �A�t15i�)bfk$,&e#�1v . $iD;"r� �"Z%F.�)�U1%�a7upper1@3&T�� �� ��{��Ѡmis6���)tE�H��&�1e����(is sPten�!�+JxFf_1 =tt0Ak3�k3} exn &�0gl[*T�/յ_1, 0�@|ewV}\g �?p;n�c�?Ec<,n;�?�@\��,.DU.D _1,00,0rD�c4 \E_n-\E_0 + El�� _1W� 2�} -}� .lۛ�A��@��LR� ���l% %F,,�F;_1;>`d2�@mZ��Biggr]*�QA5.fF�l�$-}=p�M�&�Kki:a� g"�7 6S�U:EB sE�64& a���p& �axg�"�lR�6men� P*E���aCR� �- (p9��y&�#$I��Qs�x�/e�O�k rum���Be*�+i<"Wti�a �Y egre; freeda�)� 1. ��z�B�)"_)5`)7� %{Diagr_HZ&4#L�ticq%�!h�BrS��]>%�jT� 2�(�4 }w�pݩ!SJX�*�.F� �*r $ of��I�]I�a1i  $f_2�E81i�H*�#�#4 �s�(}Ja{) br�han��a sti&[%�`1'b ��.`2'w' �:or� iven�|�io�c ��1��_2"�U v89p1512nJX To evalua�te the terms $f_{1,2}$ one starts with &��o2}) reduA�a� (L if��conFr��65=0� $a�\��=0$E�t!<�&�first� Az�� \ord}$,i�aI�second�repro �he PBrSY�4. Another fea!e�R0we would like� note� conna�onN N��vanishaaM�i 2� !��sX-,wo identical5�$s. Indeedz)9casɩmoduli= both%As��equandgy5}) �ALgr�of� (acquires si�fi)\ms (as:�above)��aKHU%im�$-.�*� .��,nd�>�Ml4Hartree-Fock 60 E�vs!� ��tX�t !7 h(RPAE schemelii�d� A.�DAvdoninaChernyshev��1985}� v�He%X�ed by 2�� \ * -F �4q)/\om^2$ (cf.-�,1.4})) sinc�� %$M ed U�!�>�0($6\dots 10$ ��?s7 g in8 a�$\gg I_{He}�26�58valid. Although��|�]��� u 2*9�*$$ � �sim�4��4[-�bracke� u fr���&a8�v���order magn��!RO rfer��.�m!4important whenu�� i�umK` � k!�clearly�n֭Wcat��who B �val��. \o %��ZqD�Aexceed�Ca��͇X2��isitative�lan} ��� �&���NW�� nels)�ordin��U��� al, contrH �\"� /)+ um. �m �e����e�I5�!�re� u� $m=1Q e=1�v�;Xm�&o *�, "�0\to 0$ becaus9 a l�2_ *^ but @ pol}x pto 2.�yWfwo times��n�0*Z %�.�6bs��1QDF� is.lymr ����a��of6�I l)%W, everEree�5�io� �� u_:E?.rint}[� A(discrepancy*8y�q��is* E:�:� a�� �2�y! neut%A�� ct�c� ���aisaMJ��i�9�X\ J��5tS duuZ:� ) appearsa�a�ultK virt�.9�Xe du��. � �% � Fd�@**y��.� neglec�(!*&{s�ny�%�D �WJ65�!�Ouis "� by.�alÁ� only��(� �6�I�!�"[ 7�A�} \�_{��Dv_1) \equiv \om\,{&�2�e^21^4 �����qa \&xscaling.b�e?!^)�A9� . V�method�; k��j� � �$!�pv$-reg�Tin2 E V&4 "4 �@a�ic"9 ewB aEm#,\p 1s}$ hav`$en already��ussed� �ApapdH��~to�#\ ach, de| p' ely � 8KorolObolenskyS&�8b,b9}��is very��� �Ip.� dyna!�s�.� y� c"c& ��evvKK��L-5�� qi�E� 1�se ,Aev!!gm�.d�:��j ross���OM�!'ba!��heCQI<2��l� 9 chos&a5exP e, U��E�*nl}= � 4^2/2n^2$, i.e.��J*~Qxx0 !�K e�s'%:� value, or� may crud{ p2 �=Z��s M�K-I��Qs��Egy" $\npM� \lp$��FW (9�)� !�OY�}u� q"��2 e�Iy�a�$ !6K$&� �e s� rulesEi��bidden��� ��qw���#ea�erm2�V�$=�� [.E�.�^H *u � tj.$(n,l)E (\np,\lp)�u eV�0th��� s must be��* rom .�2���6�1աl!f!Ysu�wu _a�+�h:� .J fail%� X�QsQ exhibit a" ong)�Mrea�_N ^ n exter� �$. For such!e�del3in�ty4 � inap�#bA@In�trast���E�E�r���*�s (� /or Li���� ly g(���!r�� �i&outpow�#'�r&C$�`� on�"T,&�%a�a+eJ�8�:b��k '6�analogu� just�.!=F)�N7%T�)956 �� -se ted ��"�-'esa-�:R��26�,6H  \s�K$%�n�����6A�l�My��KQ�gf|�` &5���� �_x B&1s-V�1s�|F�$)f%�y�"�ulaz"�*e��c�zb^�V&7&�� Ly`R� }N�R� }%[h��3&�11:�9.�Na1 Z�ak�&2F �vZ�# �'{U*�+1��a"YE\^ �,@ a Na��($Z=11$)7.��$Q-}�& (mark�a�&line):( %�OR~o�v>a�$v_1= 4j(u. Fuled6C�*S!H.zy+ion. DV ��Lh2Ym� (%Z.q )�oue�B" F . Bro/ � (F�%�[ leR�Ch�urv�99-��"� Q�fig.m�"�4 s 2=G >2}B�I� �+�P"@ �aAADPB�� Ziew')J**0e|nd Are��0U��(.��d�alFr:w 1})F��-Z  6  2>�F *i e!� 6,�� 6�2 �"�)a.�&G]� Yե2�2}). � � e)�&�B� ��  m"� 2�1 � riso�m�$!�$eRs*w�at Q.:sz�nd(.y:W2�sO�s�#F \,do not agree(  enough�':'j�&10� %{Arr'S�Fi� R�i�7 for anq`��8$/c��%�u�9�=15.4$*)%��2�� �N���� O.=��5 5co�l�/pronounc�� A��d:�P:����!�q�� F�]&�3 pl� as bݐm ,i�s�ao) s, "�/behaviouc �2�:$reasonablyE���Th�"�BIE�ach!' 8m� �%��ehaccurac"�2�G� elfi� devi�p17�� m�!U�2Qone b-��/ ific�Y �-y" ]�&\ *[ -��V. Shif� ^D�v* D o!s.� &^)�is phen":o�!A��!]�!y �X�6�e� choo"��u�$ &���I� 6c� steaA=Z$ ( 0$F B�9tb0�;N@qged�iM�8�$ e^ show!1q0)ai��'I�mO *o�(� imag"`inu2���ed O0 smoothly mate(B6�-�U�IW:AN'Umea-66�q�ces��'&d ��m����Fq5p� �O5a�5*$K%of� A:� N�%�{���P��b���):���.� c: � to eAN�*P#A law5&;!N$ ��}q �aw &x, �9�`�B �!;6�i��1� %�y�cal=% �8$1/�"uO*(S�, velye6��(n�2|fo:� l .C.�1O� �_�*�-da=I! Xs v|F�8 N[B2�^4K2�^{V< red}+ �=( {\o�� 9 2},{�2} \�K1l�-pol��&�; ��0�aNB�a�l)$=(-4:� $ deg7IF* 4!�-h�+f8oBZ�edu$(z-� of aU�e`. �4 P��+ ! �!)E? � �2�2b%�&!�v"$.��UA���.AM$��'ym�"�����of5 69f�u1^2��0 �#igB��&��ρ�%Oe �0�!;ed6�w$ e�theexed���!-^2$6q49�q4u��V$m4) ajI��#�Aq ^2} [?d�gmL$9WmpaoJlv_16}ml. �5!"ingBm�!B#of�(-��s�/om./#�.� :�isU�d viae��. $FI> /i1k-�F�(ame�9�oA�� eq�&to $Z�n �J�3sq�� le9D�� / (v\, ZA��!-;�� � 0r:�<r 6$in/"yzn�� �pr,!y manife="t � an ad�al"38 ?�� )�d!�t%2C=2�1i=;1:ity, kn a�#=� , apg)�V#er�22^ximp�!*� �?�tomy aFo1 Landau3},-A>�aI%�%�F�:�^�fer�0d9 $q�!$| �go�1� $p_�E t $q��m QE��LjA�8 �* jz"�9a�C !4�3.�6M<�e.����*� 4 7.� siI�!� !�%=l8s2� Z�$2000}. Ho?-E��Q�f���+exc�/-�:rtur� o-"�4r"�, ng a��- E�-typeJi���e e.�gd&ri�'o%�ւ2�J%�0* .�:1�%{E� Z � $q$-6RI ��$$A��l%� �-ix requencyS$=1483$ eV N}z2�:� �K�e�: $� Re}�3l[V�r]�nd ,Imz,B� .=8�BR�g7 ipr�;:�g2L|T "�! ZG{ |^2 /q$&�%�X)��N�4Let us briefly���E��@�B�a�� i N2�P>6� !s� )$;'det+"�a<k��wn��2,2816� ,"�.��2���9"�.� �c9!�q�� (�"�%a spher3Dly-symme�B��)�:wrmn�E�f ( r UI &yJ}�'?A9 \{ {� �*0 Le�LBJ}*Ln\� �L , F_{n0}(! q}) , \om�I@i\,0 } + { F_{0n}��J \l tnt^s0�L>b+m ��/-� $I"�*� "zQ"(%Sk-�1^!u ed]G&��ɉ�1�9x$�R�-5.W��mf�a�M.La4"0of, h�onY> acter. �H&�?�6��$%P��� : 5* >$12� �^�2 er} "�C V�"��#� elas`%E�(.�)&A�in:'IC)�)6�srG>  = @ A6�i)�*Q emis7D6Q)�&�1!�v!O"�`0��. }��%4!���I���1�B dR�0reE`t���r �$� �=Y��5$A�.Ap&w>(�BxG�a%�6�a^�)a2!`)���.q��os5:k{"q A61�,nergy satisf�7"�s p�G-$ + I)/2} < �Gega"v:ensures �Cn2�domin�� Y���ZE� U}�8,�,�s tTj34=� of Z~=&w"smear� �=L . F�G:J2}�qa)��K)�iI.�y>��9*<")n�>$p+$Al*Di2�c�.�;6� F;!fQ�#.�Y):EBI�26sis smallNr� \�F{CocM�xs}q ũ viewe�focuse$P�a�He�F�de�;�F decade -�:8,!G�theorC � A@nfo1� B�6"��v�9�Hs�{\e6/o�.}*�Q�]A6�wj��b�!cbeN.9�&6�P �A�ea*�alg*hYPnd �$u$codG?"�9- ed9��  per!�|!te 2ave,si%p�a�4 -angu 7q�3i��k��*5r5A5y���@}invol�F&�2�S !fizS!a multi&!!�[(H�mol���!62Hersl:RPC_C  2004 "��%l"� cPw'E P ��H�%!� � lly9� . Am�0�1w�9n-�&�Aof}� BrS,/�9dQar��BrwCof �in low�0 /posi�0� ��QOa�9 phys�!� paYYl�$4 ���ə\�i�Zat�$�M�:Sw�:��!��* !� olli�<��Z a�r�*6�>� �%����A�ZFUR���dueM;co� �FnGK�/l! r.Y%�8"iRcyM��be��d, at�*!A�2|�,2�<2], ea�iӭ36�1�~ =�,�A�b!�tc�M��b�zd"1.-� . An �t�ud�l��fv!MbA a more �h;V�S*U� ��etE�)�mpu�al�2�\�?�"N :r�E ist fewer)z<.�*rtxateJ2!!att�&u�understa�\!�A��  t �X`z�m[��nd��"�QK3 \BU�\6�"��)�M-5ns!a� ose6�=�?M~J-K._���c!U wo aAt"�T"X� B "� it&h�M���]�>t 4�&�'c�;h�?>E5"�3A�At�" $k &�]>^k=\om/c"g�-`�i), inc�e��T��"�dMh,� �.e.�4i�8ataJ PBrS���HV!Vn���.w��-3t�FsXFal keVLc�@/7"�86�6#A8x_i��  ;a9�&Uthemse�in�4W� retarde "!@%a�2**9!a+t�-'s"�> a.Wmodq6�Ke"<.ek�bt�? pro�Jio�3�v_1A V`�! Kv�it�a�O�Homa tice�& "�d����� A�1�te #eV. WG��at�z��| � I!Wst�ecb5coE2 de�S ���N� edGXPortilloQuarles_PRL}. B�Z �seq�Zz�5�.�,vincorpok@��AlB�:Y���.��"� �Ze� � OurR8 JPB,>ETP FPbFB �V �6 me>�YE a.'  ([1v\aAnidce�A�y�'�Q*Xg(m��precisu(phaseshiftse@�Sil�R.��?ito[-�R I}{ ��afi[�� K�Ba��)p���L��e5�� ies,� !u�  stud~Bi6� so far��X7� �  e~Ec� �{-a� M,wor ^o�investig�: fur� ��a��h = ra* broad, ��M�NkinO-{ &�-*�"�]U��olv\"V &�"s:cg clei� oms,*= or < �&v(7gt paiZg� ".�i c�?kf� s,�#al�;�"��&E�2s maka^6 e�quite �pK]� �  J Z Ac� ledg� *�& \ack/ A�,_)up�qed �"A Russian F�D%�E�DBasic Research (Grs0@No 96-02-17922-a)�lINTAS #D03-51-6170). AVK a�� �q[Alexa� 0 von Humboldt�B� re%�!�qX$nrel.tex �*{R'} � Nk thebiblio�$y}{199} 1c \b$@ em{Akhiezid, A.~I.%'B� Letsky, V.~B., 1981. 7Qu�EE� ro�"<. Nauka, Moscow."�8�redbook}K$ TsytovichmN., OjB@el, I.~M. (Eds.)31993.Po�fm�dbremsstrahlung. Plenum, NY9�  O�r8*^_�Pratt�� ~R.H1�ComA�ls At.~Mol.~Phys. 10, 121-131NKochMotzc , H.~W.!Jtz, J l 1959{( Rev. Mod. t16, 920.F�4i�,�4RdIn: Lutz~H.O., Briggs~J.SI#0Kleinpoppen~H1��Funda! al Pt$�4n E� � Ato�$C�s>P5�0, pp. 145-182>� Feng�W5 � R.~!� !,ABJ.]26�$Craseman B�.),�I�H-S�-!YicZ�Ch. 12 �533-580+qwNakel199=|, W� o.!�,p. 243, 317> 1995�:��Zimkin`T�� !4ShulakovBrajko6" #, Tɡ,�b 5.�F�`HFiz. Tverd. Tela 23a�065r��� x�f198.p # M�� ,� 4u]�E�=�-6�7, 86�E >�Avma % Str[&"� ��� ��A"�*�a�;V�g 6:��KJ��4B 18, L791-L79� +�4VerkhovtsevaGn�0nkoPogrebnyak�Y�.., E.~T, 6�?eS6w��JI 8~B 16, L613-L61�ro-=, 4�f A5R&* T5�XfY; Izv. Acad! SSSR: S�&E�M1261-12jHMBI ��s� .U/ 7 �����2 - 231 0-1.� ]Q ��%2�9�& $��(5mA�HV2>909z]�B 2899-290��2� wZ199*� �"|:{��.{ 251-32ŗ~"�'�� � shap�d.%�$ rged"�j>D s up���v��"��$�*s �_>�%M�&V[8*� 9A�� -!R~��9S!� E'y� !f%- e-A�t2��iesY�2���$61, 224-22*���� stap��&z 0KrotovMikhail� &� 2�;� � D� M , Yu#�AMi ^E�� . I2�.�2�� 93 Di�\heskoP#@rmoznoe izlycheni�mly�dTistskoi %zaryazhennoiA� stitsi na�$e�^�IoQ �---> NR((ain % p+A Fp9D);.4 �:o~:oU vVA8�L2WIA52, 41.kY:6�:*� ,6 �:, .w4�� 430, 2278; %Co�| uum x ray�]�0by light-ion?<&}) % xJS� �a*=Bv�5>�1, 116aR�6�����b� bombard6N"pGonzalezMiragliaGaribotti1988�'\')���2F E., ;sR6G8�6*� A 3W834-284)�'#N� Y�K� ��vu. #�� - u.N/ 19.�b� � �431-432.�Xe*0�pA;�]@"y ��]C��56�mv 62, 876-8�%B ��f�!��pIonJ �9�90bYU )�!�'2�9�90.2�� 889-289a�S-K :jq"*}ua�"�0g�(�R%%�,Rel�- �m*�>��m)lZ�N* ��76�6E �Y99-50�� >�%�iD���9�886�Mq$ 67, p.41-�BrS�c"�%��"rj��a�SF)70�� 6-42F2;j+leK&"h+�&�i�Z/)s %of6n >��u2 % Exa� solv!�!q5(*XHDuboiusMaquetJetzke9(s��, " (6e. :�~�l~A��1888-189!. ^�198*OZ�.c9Zw4!�288-429&�  Hzzu}j�jne#Z��]*�  3663-36�In�).�n muonic"eG� H_mu>�$GribakinKh�I + �i�j�=m~F�FA � 5[X!�. v�48. Muon Cat. FH0$ 2, 143-14&Z P���A�e�6j',��6*\Zeit.�!�ik D S 347-349. ��2�;&-po�-iu.�+–� N�m ino+�m�7 n+A>�"KZhalov�.)y�)J�O:%,� C"}��.��t2���s��!__i.-�e�"�21st WG( S�P�- LeningradE6 itut��j4m ` �135-194j0�!TH�8v�>{jaF{=%��%�^@:��,66� 7-8��;�Y/4Varfolomeev197���A.�+}%YLFizika � 1034-1039.�Zt.�zt�.t� 1268-12��Ear*�i%_yovM19n�-j��� Sush�O.~P. (e�"Modern DZ0o�4>, �U�0 World Sci�1(fic, Singap�� 425-43ٶ% �����*^���1w�Dalgarn6, Fre�iR.~�-Lubell�- catorto�B�mE#L, 16th ICPEACS, Book�Ab�Qc�.1͚� �- B>�c �)5cf .چ� �T�Qe�;PuMl2�G|J %~�^ ��G,�5tom9@S*V 2� T1, 577-5:1;:LVCj� ����.�R� 2, 290-29� C"�3� a5A�(of*�^e%!ic}�.r.7"�>�:�.&��0�J�uKV���47&D �A�E�y & o�/6ypt�&5�>�6�)�I�a>q�p~ �$!�69-33A� F]V+Z=�"'�%o%�zdJ6�'6lג� "V/<�(Verweyen199* +��(, Guth\"ohr\&� L R, Gerhard E, et.al2<96�$ 17��8nt. Conf. X-Ray�2�%"�&5!$(Hamburg),�� !�21��#199��>�#^3%8. Priv�2commun.=aB_g0199�/>g '6� u9y�=uggan�(J., I.L.Mor I.~L=S A�i�� Acceler�Qe�Rh+  Ind"�y�AIP P� '174-1� QG��-TM19;� C>-200*0iN8��9� 7320��� OurA��(a)��Ly�X��95��"a p +_"4$!��'9�*� <4947-4962 % New :[Z.\1al>�c��O11+9�� ����9}�!�@ *B�!.��� -�A 5C230-223C=o�8t.��:NX0���v*� % gi).�c�Bce�΂�N�բ��5��  S�ed TopiPn c-n%ic&� Camp� D��9�+2&� 1cP"V+.d ~263-27!R r��"�*�5�A��V�2 #���X.U8�'631-6)�S an ؓme�e��y9on La�V�Ger$w�I�]�*�l + , L.E�4E�6�Fq��� �75ة� John>'R�r!,midt-B\"{o}c�!��nntag,�%F>� �a���1ce2�3.Z)��� �64u�f��(b)*�8S?x{C�#9k%.199.y$5B2#22)�%L341-L34:) '$ping'� -q�T7Z�e1 % �M.>�?>�N� �6/}*s)��m52��L155-L16� 2�T.�6�  SpUB1*V�� %!HGa v�R�Gc�4���6BRO�b6*�*�-.J.~y� �.~ �5Phe�c a 79, 323s"N�f�*�*���.�9�%1�%<؁� ��< La nUa,4d threshold� *p�OVfnu�%օ�.,1I��lo��$:� ���5�535* S�8JuryiR<EtA�@*� 6�)��"N."#��: *,In XX1�J�< (Sendai, Japan)� 240�6m(c)*[C�:� �� �_���L>n72 !L11�2R4 �:�aa�1-25 keV*� on N�F d Ar�BC �U�*� r�<�WAb 87,��� I"�9��;�E :� "�<��es%"�H a=�!,p�M 9E%&�UZ!=��1�.;I� Opt.m�osc. 862.�Ǚ":�)��<w"FZ�1�2�(%�)��AC)W5200��.e�: N� I�)u�Z�5kVa�-197-1�0�d) slow%� ic +�iG �<�% 'c"�y��:�1���!�� Z"�0D �( *� p+H_exco%A�d�0bc +BR #&] �R@//337]� B�u��b�-��9��/n� 44, 1�1_$% b�A�a�:�yC mpanFI9�� % :ee�zIs@�u 2��e&� e+H:��7N&2%%��,4/4765-47 9��PR�a>�i�5p1�2�]U�EY^�<6�NDVR�(33, L179-L1��q�f5.9)��! � I�R$#��4��A 1�*h5zCo�9ade1&`�D ne P.,�(:�yR�&�2�f 529-35*D4�"Ipato.�.�&"z /%=�.���*5939-5.NEPBYk2�^�2��j�8Iu20�� �N�)1589-16I @<lat9h>��EP6��m%[��F:8���.�8ETP 94, 704-71� >�mymIje��b456��� SurfaceN]S���N� �<191-119��-m)0.G��:� :�� q��/�9�%�1+192�%�� %.5ׁ�z �@~B �Q1105-115�  �A}OurBook�QN6w:^j�G�>�A6�*� ]�NUniverw�St. P�is�Z��B�R�^�NC!_* 2005.�Rh�$ Chem���ssu*��elBrS_!�6X9J���� % "�e<Co5` 199.& :&Kuk�!i7ݘ %#)E�B*�A�U8�.29-� % M�T� O�?ySV�� 9}B�5�(x8, -.L)% Fra9�H4BureevaLisitsa� a*l'� 06! 9 .R1JyE�x090, 434-446;�@788-79} Clas�T��GSu�xorKO(M %Y � loϧeF�I��s9V����r��!�>b�ld.""@on a Thomas-Fermi_�V"-�-�!yY0��:� Lase�$bF9" ��*� ���� Scripta T� 62-6&� ^��n.u_!1Y� Plasmay6 Repo �e 4-4�#�G%�Ur�cQ�s ...@p Mis *�L %A�qunJlu"x��0 y�Kogan��M��$e�w-��b��d*M �E"99F"13 �I �.��IB�.�&��_ /�o!�B� Usp. 4�49-18�g 91tB*X=F�22 ol��!�[[=6Ef O�ivKsse&a URSS�6�JZ'�"|@Not�0cu���w$: _> SuppW!�E��0e�s�� ediu��.�%BlazhebKEta�*{k!�� rpunz:R(Gr�AK.�# J�#e�~ . A 2'309-31d&9�N�~o� *� ,�HN6�*sN^|H81Ec���� gJec%�Q%�a�.� >� [% B rK � �6B� a //ut�9j-�*I�9O 9�5�;!�6 9�$Kamyshanch�0-~Pokhil6�6)!�,.��$5,�u�C��b� 173aNbIA,1q:�dR)�!xB�9�:` 2�>�x�d�Va RnD&� 9?��"�H�;-J6� .aI�P5IJ�(&A S!{2d9ee��a�3F6 298-3%Z 2� �K�&�E6�(�B�5�* 6|*k =61p � �O� ~M�@! ~A.V�/.bV�146-14.V.KC�Alber�N25W� &E� , 2<�" ;�Y� �5�%��C99�$ 6 L561-L5p4 Two�\:�in�rN� n06 gj[T�J� ��5 �Veniardm��� V\' I~6�]�*�D, 27 3241-325���>\P��MY{z9��=�!!"�s*IRew York�AMO&r"P!!��\��4LiefeldBurrChau�ao197= %, 1$J,{ �S67�2�)2=s��7 A�316-32.MQN� z6�$r,A��B�.Xr�r76. �Niand.T&�Tii, V. \5LifshidSE.�B4Pitaevskii L. :�I9Y"^U�Z U�J��$�IXJD!8��'%��� 0 2�t:�Ji->� �4� �G*�J.X789-7 "�R g�l�?}Y# )�2� ;�etF�]�mHk!5!�mH, fQKsrH48�U63�4p ���*�)�� �:2S?�S� OR 1�, ��.hJ&`J4ZonNekipelovTk�cn�L./0.9�JT}/"�J~E Zon~B.A.9nL, Z~A and dU$6M*71, 46#$^J�RoEa khin �� ,~V..�(�e23 3.Q� j%of"X!�1��s C -x@ B'\ Rann��X�ViV�T.@!� � ��V !69V�@� 42K42�N-HY�0RatzigSmirnovxAJ/ eP� &s*.#U190*v "�ZlTon)'.jIJ�Sp�Yr,�uli*�06�(HammerFromm�&2 � ,�D#,2�01� ��4~A 64, 024705[ ("�U 3�U+59901(E)*�Mol-orb. @.9U(GreinerRein�2t� �W�"" 2d�6 �,AWm�VD �-.*JY�)i+�n Heavy�C�8ce[vol. �F&�-Q]�au� �%XL�: �K���d%csP rgam�ROxfor*�(#ekn�~�M�.�%R.V+��A�7Jxa5.k# Exp. Teor-�RB"aՃ����.�E19�-aa5�'.=T=�My�>�%78H8�~ "�!2Jt�.u��݂.�r7�e�2� E.��5RQf�G 13-*nP��*��� �^�.�  6�_.X�I��Z*��Y`Lee�Y���Z:�W.�Z ,am*�Y2�Z>IV*u"� ���"371_52.v!��PT���&$2866-2867.��ѐ�A�y��:.�!\. \66-16*�9WKim �.> Kim:<B"[. n�  36��:w�\"8 �= !a[,&"^ /B�(:c2�!5�;11�;� Nr�Hpw& ]0 + Zhdanov NR� 19.L@*� 5 u� ��� D@Plazmi �'28-133Z�]�M�.�>�2.�198"�� A Y$1012-1015;��F6826-68�O�/ 69z%�197*D�DP!B�2�.7, ag00� .�2Id_Wk], �8�Z$B{a4b�56, 365�F5�5�&�m�2��al-��*�7@)rip�% "7f��"V3:v�p��rm�J%d}!�}�_:1�5�>*�$t"$ L317-L321* $(Corrigend�_af0���(1471)!�Y$L] erDreizle:� ~, "r%�. F�"�l' 3257o2&� DPWA f5:2���a)YB n��!5:3Y�=822 L57]7*h fz.z,�z.~.z��383-26e,2|urh[}� ����m�S� �]557-56*�Nc*)vc�(37, 2649-26.V,�yon�k9ϝ�Q}QPzrzQ!9�$�F�-%��b6< �Q5 G9�.� �49�9P,a�Y�rWp=!OZ�3A�*�  5 EPS3+f. � .�f � EdinF%h, UK.6H?711J�Sobelman9 ,�(I�19�v �ic1a&�Trar"�s@f�9BeckerEuM� , UvK\ff��) Lind�D. �gB�!�B� ��)2858-286� �i� Dolm3,Iv��12� "E2�,��K�?55BF>q�58, 6*�!���Lo�-9' "�'i�Ky7� 1�mmiqu�rll. C-4,�l� �7, ClT}��DHenkeGulliksonDavi�A*�!@. *& �4ebC6� 3Y> At.~Data~� fX�^ �z��5 )!*� Maֳ�f"߳%�G�!�.��"T"�} One-eQ"?>M�&ch�F���D�W"9W.?v9W6^�. B 22, CW  �>�l "?���� sdocument&6��i  �N�\Z %!� manusct%�$ ��(he IoP styl��}�q� ioD .cls (q�r{� 12.cloU I A"� ly I�j�y�Epackage9 (1) �nicx�,eps��s,S4 (2) amssymb + fo�u+ bm %\1��\[12pt,epsfig]{ioplppt} &�%&artA6\u��{�}2 �B�6bm6\4�be���} \jl{22H myFh�:�o2 \renew6Fh{\d} {"�d}}Bii}�29bR� } {\�p!\ ol{\ } :,beta} 6, \B, gamm>X \ B-ܢF- B-s��:� \ B�ee�eFbfH�� aFhfb; bf bJ XbfX:(fk:kJ:nnJppJqqJrrJvvNAAJ;PPJQQJRRJYYF�cF4,FB;cOOF �:F�cT:TF:ZZF�r)�rmJ�!Z��p} e�2aEW varepsiloF�om"om�>�O ORt ;tilde��B>Cttha &tha�F�q�� ��iF�q`� a��:�totfrm��B�e��� >�or�� >�� ?inF^NIj rm NAk~� %6�M} {m_!�>�hc�h daggu>�4hreejot}[6]{\p��({ #1\!\! H3\!\cr #4 \ca�~�f \title{.�{�&X".�(B�I.} �,ate{ Mv4mo��Bp%  %\makeh %  s ( \author{AS~�$�a}$�V.~"�3  b}$ \foot�{On{vem-: Ioffe��3-�; " V, �w)hem�|�s,>�3194021,V} !�address{� � a}$\G'De� ��rVxMaritimeR<4D�V"pro�5�B�� 2�_ ]� � �b�Frank�z5' Adva�ST{�t\Johann Wolfgang Goethe-U�4\"�O) 60054`am ��,P9\�}e �aT}W�,� aȄ!:Pٛ"p .�>D�|F�cl!�� j)Pcas� ��oth�&2��� �GA�rt4�. � m�� �s"|O2uef�-b��`o$ p���N�ed: :;� Qώ, nume��$ c��xh�9E� z{InYyuc[&��.��n�*s�s�=�6�"2M�05�"A�hBM (PBrS)�.Q��.b�ņl� ��li� ��6 ��Non2�6Ǎevok!)�1�ion|!��at cess��}n|�E're�omprehenʅhis�H �is9�E� m�of|t�3nolog}�is� �describ-}ӶyN�i-�Q�"�w u�possiũwuhfer!Z&n�; " avoi H5p���2��wh����� ��!E���Xy2"�5(]�$�1b9R�)6�e4u>iY.qo%zw�I�a�� subdif�d! < �� cate��e��v��!���m�"��v)�� �/ velo��-ǡ�i�|��:-�: =�L >ņa SlS�/or% / .0@��mo!�}�.50�(�Bder��&��.th*R�!�hasA2r|}�j2Q*l�Dirac����� �&�Schr\"o��er'.�A`l k�!%��%)UU1�X���R/���a��"��.O�nad/, aat�cE\a�WM y. R�t�lkm�o21�ѡ���t not#� thro��Co��f��, ������-6�\<&�pn,ns (e."��e}), or,a\�R�� ���M 1�,v)gѦp� &ؘ i�L��2D�)��4r�� ����w��in��ely؊eY�$N� 9�dM�P�F�light $c����!)ultra6���,h��c$,ю _-���ly5exq��'_k�R�I�r:�2)$�IEgGE�"P��Q�}�ayR��eҦ�� �1�H�HS �Db��Iqs�e!��p "��!~6�����$k"��Ip��uy� d $R���((͜)}uM8�;­M~nE� ���I�cra�9Ȕ利@��029�&!�,�x� wise B��ne�����~�into �Gun�� �!�inϋ1j�&���bU �OВ�(s (�wexS�e,�; i�&ion ��) J��M!�2yDoppl�f�J&�$ abbe&$���CsI�*��actor� modi��Eaof���� �"��i"ȉ�.2u� ���p�A d in�~�'KB�m5, "�4>'5MZCr, SBN7, }�F88B90a, >�$9,�>f?b, ��A"�#fmD1, >EEVN� RnL2} l��co"gj��s�E�6j �� b��&�����. ��&D�E2 dens�UH:��&& ]Q]6)W9r��A2���uɟ&�8�86,N&�9,B9, 6q8 .Poe8�+.�D7F{7a>RC��*��scobvour his &belɆWe 6� e4�erlu!DaFx�X.!52-�i�e lX�of co* �.1�(aw��_ fullŎon�T ��)k6Z B� PB}.�%R�\ tnZ�� concern �.�&�!�CEB ���� we o�-(� p�Q! gene�w"�� XI�.x�oa� ll  he.� surve�se cou�-!"�:$fQ ioeA�wol� 2)f"�ay�k�Zr�Um%an 2� (ion)mF����F�4sªw!?-�e�N]Ϲ�Bɺ���12���u&Bo>��!%��yee��JB�29>Vb   �M���}�or1 M)emi��� < � .��"אWco� Ʈ-2� 2�i�&�A6��e��A��stablis9� ZseMca�r��," �deR���2�<��&� log� hmc ^�(�a~gy��1� .� �1 ��><�. �=�-7 �� . Se=��i���"� "�{AN�!��c�!�d�, � 1�כ� :��, $(1+a\cos^2")ז "' U#x�)#�!�bc:ij $a$ weak��"��� =;ref�#�Fn%��R�!5� !D��ic"m oB�� alte&* H iR��I�q>du�0"j>���s��iU reW�|� ��S.��}. AlsoV�ɚv�} &� Ғ$f��E��iv);�e`�� "Yevq�&��� defi��&ܓj ��o � he j>�I��� :�-z ��g.�IX���\2�a��J�,q)$,����!�(�=,�ed)"�4 emtђ&r�:�D�Y, �E}-I� E� l*M(8E�1ͥ)�6d})e�r�J�6���bet2�5�a �B���J% ����%�! l�� $q -�&>^{-1}$K�2��7BYz�E�1��FE�5��dïega)$ �)�. S_ ��&��l�m��ta �&> AVk�a�o�s b�$r\gg�$1|�ݻ�E�!��57� (�K�}�V act,.ܬ�Bc&`n,� util��AMivW�}}��d����&����Itrq�-ul �i*Hx�j�%�-�6� (q����`f��0 approximatio�n' \cite{Zon1977,AmusiaZimkinaKuchiev1982}). In \-�RAstapenkoBureevaLisitsa2000b} the `logarithmic' approximation was applied to study 5\total BrS process (i.e.RpolarizaCal andlordinary channels) in combin, with+use of `local density method forcomput >tof $\alpha_{\rm d}(\omega)$. 9LvdoninaPratt1999} an�roach�suggesteh, calculatingt�4spectrum in re# vistic el`on-atom scattering utilizJa62L modified Elwert-Bor �5�� 9Jomponent�!��$but considyP!�!din - non-2�('stripping')|M|TBuimistrovTrakhtenberg]�1^$Chernyshev]�5}. The�ory��formed!F(a collisionaA,0rged particle� a many-1h !h/5(was develop!�urtherZ�papers�lKorolLyalinObolenskySolovyov0jev2001, OurR=� JPB,>ETP, RnL2} wher% fully .� ! alismu5results! numeriaU�Hons were presented.%`H9 in!se 1accounts.6�effec y0all types mena�$ed above (AN<excepN4Doppler shift �abberi�Lwhich are irrelevant � cai� a structu!4ss projectile) �a��q�based o�.@distora�ECal wave�)j!t�descri č|y��� ystate%�AVtA�t'su�)� QbI� term2 singleY�.� func!J m)�� retard)B!Q~8multipole expanq: emit�hot��ve A.1�a!or. Itm7monstra thatEA�6�P�G,amplitude iszres!�Ae��� generaliz�K%2 �(biliti1Q$ree differ��Ix$correspond�;to\allowed �B%bx 7of virtuͅ:s coupl-�he�. OII basiU2�aculaEJs5%��across sA��� btaia<in�>EVX}L� ,m; had been Va�!,he framework�?(various sima�u<eR��evalu%� byB;6� limi���duresUF show!4 � eg"�Lstrongly influenced=|2l� &�!pa&�A�Uo. Thi� V@ manifests itselfU� tly, depeɰ� magn�3� the I �8gy $\om$ measurY� rest)� 6� (. For high ���A H��,BWB���conce!�!o�bE�cone $\theta \sim \gamma^{-1}$ ($\$!|12c,Lorenz facto�"9�) �I��) +��2His nearly isotropic�<refore,E��poi �^ in21�^o sufficie!�-j eloc*�eY��� Hs a principal possi�y�� sepac -9����@ll�B. Ano� �m�Q�*�& aa�*��, r a�lso due�!cqu�y��, is " !R��Ud Un�dAA symmetric9%s does�� vanish� some.��sJ ) �8 �� h ���� Atom}. %� \ M{P6�!j���'s.B�5s� �� .} \label:nƙ 3d Figure: fig1.eps \begin{f}a�xer} \includegraphics[scale=0.8]3C} \end3ca {Diagra�t��re��M!Q�(��and"� ��al)A>�2E� g��� � ��N�� solid l� c"4 Q�2�^e mov� a !6} field��< h initK('1')�A� fi�('2') :$.��cha�  by@asympt  m5 8ta $\bfp_{1,2}$h� .Cs $\mu # �double-denot�nN�<: index '0' marka�e�� � @,2 $n$'=fs-g �!� iate"� < � ashe1�design*����(reA+�!of�$ �,-um%k)?.al vec�v!De5LI"st��=* u��of:?�d:)� �q� not fixM�ny kineUcM�on�dib1.figm�q��.]� c��" :Q.rofEqge $Z p} e)6(  $m aM䅸 �trVa�H};"M q%� $(E�1,A�1)$M.H $2$2)$ � mpan m"p �g)�IH%�"7e"� 1#�!��.� a�found �$\EiC = (mqH^2 + m^2 )^{1/2}$ (%}i&�wk^2]system� unita�0hbar=m_e=c=1$� is�3ve.e can occur2 wo&% s� it�� illu�by�Feynman MP:�IS�# "Ir)Ofirst;a�cribes8 ��A�"�(, $f_{\ord}m`�� bs�0%':�> !'!BW WpolWe2^r �M�v�aOBrS Q�%�A��BB^,�a� sophea one, B`4Sommerfeld-Mau��, !�bAd|8extbooks (e.g. 4Land4,Akhiezer� .�<�r�� o.�-�:�(DPWA)A1� availq  Tsen�0, 97; In w�foi�H �;%�&� step �H�fŮ� 9�9� focu" &�s��BF�.!��B�on$ �sak5 c�tya�assum��spiEB� e �eqD to $1/2$,�S�!r a�bi-@or2� satisf���DiracP%#{�&�B�%� �� �fsevu (ri8�qa-u�M� easire-wr � +2e��%�i�� Q�� . A@B��%(����N al�v�s.� � exci} �!V)*� unde �a%�wo� s:6� cree��r� 6~ *� 2�v�ɔ) �i*7 R� . W�� Ure*�c��)DR} ~A�*T 4-pot�pal, $A_{\nu}$ ($\nu=0,1,2,3$)os�Pd given byN $eqnarray} IH = \Q \sum_{a=1}^{Nl Dt \d \bfr\, \Psi_{202}^{(-){\hc}}(r)&E(^{\mu}\, D_ ��,N-_a0V1V|(+)Q.u %6.2W �Ha6$G^{(\pm)}) �$� A[V�s &_ *� out-�uppx\ `$+$' � in- (`$-� G> U�y�,�0symbol $\hc$ � �her�aO njug�], �)V%�m=�㉔ma�A���quant�'${v�}$�nd��I�� pagO. Rs-s.� ovm�>�� bfr_&Vco�t�$a$thu�. �e!M+.X4- (Q)e<0}\equiv \Phi$ .���a�$ed Coulomb2Z� �`-�pa��%�iA�%�nu=mvZEg�ed� u�� A$>�Y. ��sa� t����XA�2��s���!��! ɭat k ne�!to��in�_"�s Dn�bA�uE�-}:�_{i�}$��)� MD:Fy\bf<�:|Hbfe\,{\ee}^{-\i\bfkIJ}\>1B��Np perturbeW�#!V&�of)Gis�6"A��0wo{ond-or��enxA�!�s �V!lctom's.! @ $0 \rightarrow n20$ J�%�E�� .D$ �Y�Jt� �  = -e^2��%vn�eft\{ {�o� 0| \b��2g |�#+n|"La!�nu} | � +�#\E_n(1-�#i} 0) -0om } +:��^:VV�J�|��+ �)�\!a�PolAmplJcV  �!�xumL�?�Q lete&=AU he (�) ed A1ic��� �ain�+ e_E positive-Uy, ${!u>0}� �ne�YB%<%ɻ�#"��E�-h��$��9*�  simi���(��altY%R 4 (see Eq. (13) \�&4NonRelBrS_2004"K K c�inJ}K!Q%���ref����Yicl�#�ged2^ally.*��F bzA&:--�r (\protect��=H&qC,s} Let us d&�! how�ex�,��&� ' can f6L�EI[ �i�f:� Ih"21� F�MN {\emM *�w-n).}!&FX � ,! t!� ����, �� s. F(��y#ou�I��%gd� pect toiW"G,%G� a�rB � A$ (i2 *p� $)!�mecA� M7��on $|��|/|�|�v�\ll 1��onl������%?*] �A survivAw�&!u� $D_{00R� =1/�� |$. Se�0R�)r$k\to��u��� .1})t maka� substitX!a�!"� J=��� \hat� }_a( & P}$�r"!�A^"opeXA��h���("thirdMAo�_�2�$Is its B��! oguejlA�$\Q �}\l�]� � }\��|:���!� p_1^_ \�$.�r�(�th�:F � :C ��inu N�becom�d��[� zero,�� erea l:�|reducat��>+ IL=,�$�b To�V!�J �� N�%k��i�2,plane��F�} (RBAE�] �.�� �"P(z��� �e;-f~'"�s%, �,�l�})&� u�8}*��[U = u� }(\E�,p)\, \ee^{\iaXp� }` G RBA1*D dw!� $>Lux��9�,�w$����MW0 ��'d.f,e�C RBA, ���DU �C%�!�>���A4 �(�H+ 'sf }�, add�s,Y2I�}�-LN(����ula�2'=Ɋ Z-�Ae/�I�timv� �& orolF�& 5}: Y6Oqzb 4\pi\,\om[��[ b^0\, ����q  q^2} A.�/) q) -+R + 0 ^2 -6bet.5�� ]\, "<1_11bB&:bfq =E�_1�p_2U����er�R 1b� bfq\,ab )/q^{�Aq�A5 $b^0$ <  b$� ��e a�r-I,:}=\bar{u� mu_2ar_2, � 2)\,.P\,iK_1'1 '181� -�er�0�brackets�&[ B� � �� #�19�" I�.�is1 y ent�/Q��>y9&"+ � �itr�4 dyna* alont.^ �� ��;:?" �p"�"� %� 2!i���[m8:� ,� ))% e@ R�6( .I *; .N):��)"gpropor�I an >u:�,j 2c"R ��-si� 1�v� ��=�h�0tarn7a7) )x0 %�$. Explicit�� >U�nda�6�| Min:�+ZR@2Fi�UF�*Q�� �� �� I�B���Z͛6� ! ŗB�F�^Q�1xi@ }. Car67 h $m � one�Us��0=1�� b=�� 0}� I4 3in&�=�0Q�N� )�@\,>�/q^��C well-knowR _^!B �"�4. Fi�yl^briefly�~.1)V�)Yq�% ��!6�, L7when5��eed `>T*( $K$-shellb.�72}4om \gg I_{1s}$�|R{I ~B 6J-� s �� �1a8U6fT60v96,fy6}A(f�� �&deL&m%�u�2&2�: �*�.��mL�+$$BA7� 1�s�n� L2���!R"#into A_er *�� aken!_ . SN_.�iJ4�$m� �� 1992�26��"(ed�+�'tr&��[6�""$V�$m�}�Sr9?%e�/%�s"H9 R��. O�4� !)�0w7-"7  �+*� �"Q�vIV j � |�� r) ` O,1\NH6hep36a*�  � �51�Bd� f� \fl B4Di\,{e^2, m. ^2 int �^{\prime� rho(�� -� q0eft[ r _0�bfe%8 +) �)B 6 -B R( k + :_�6�) + k\~e�� 7�k�Mtzs }&K -�6VN  $>T%�!��<�4 clouu e� Y5s{$r� euizeRM� QB���t B�e��+�B��AV����:�$:Q,K# L�;So~;� �$ 2002��deed,K2��K $k=0$a�(5o�+&ng "j %/�2�69�$>.[s6�� =-\om^{-2p�'aA���>elQ� &�&_b+el}UacceleP;-͹ *9# �ic� >G>� &^22n^ ��b&�.� BH2�' �G�. se� c �&EPoTM}�j Ep�>ay' H]AN>a1�*�(I�*�EI�%�5E&�eqj9` R� To�r�OyLF � 6�#�#F�#6&�(J6�|\qquad~#{� p r} !�m_{j l m��\O^J$�On_�Tch�mjb�"t(pm \i\delta_�)} \p� { g(�$ mgr)s r - \i f(���sigmas=lm2;\c�"hord1.4aVa��>f n%�@!is!�&�s,Y�e dir�<%C bfa$�9E�p�$�Jr)$9-AO sphe�@(o�'(;� &|VarshalovichMoskalevKhersonskii}�5�2K$aM,-&q g*"!�  a$w � \mu$�#*J$5�)�&�%s&[ phase8�$%ӵvPauli I!� &_$E0O$g_{\E hrg!RA& �$!S,*I1 @y��9>%s�95s�S 2��5�@�!�@BV*: ��"b�%�E"�$j$2-biFl$^Yь!�m&�2G� next.�intro�I �K"�@�Z8�"� e�xp(� �SE�!�\q �'l�E� �:f!nu�8e,��; 2}))K��qvy harmonicswfY_{lmlambda)ix�N$ �)$)5ERJ Ge�)�n\\-1W m ~�.�-e[�?es $| 0\� �| nhIN��b�?sE0 85)�-l*C:x�6YHLindgrenMorrison}),x �vertsE&su!�h��n$ � )��s�4�D6A�6&�#��E_\i, jl m_\i�'i=0,n$)m�a�eu��,ed� ��&�>2�y�*~}|ErXo0"�by 7v)�e*�2�<-cons*(�04 Hartree-Fock-eqN*�G YakhontovLI�!Haxd��tOa}BK!�me+6algebra)� �)�& *�� "m $ ���R�D �E$`iG�2�Ek���=3 < �*�.{��]Mz�>� leZ �d'&= � {( )^{5/2}��Q  p_1 p_� !\! �dj_1 l_1 m_1\atop j_2 l_2 m)� �b $ lm} �/^{m_1+{1� 2}}Ti^{-l- 4�*0 r4 _1) +.{2P � ( ��.�-c .�"� 2 �� I12nonum~B\\l & \�s \xi(! !l � 1�Pi_!:Dj_2l} \threejot{\!!?}{!`j_1 \! l}  {\!-!\%m%-m.JH 3{\M .P {=�]60}�*1r�!�cP_{2!-( ��M ,k,l ,qsummary2bs �?- a}{b}{c}{V}{A}{�6� A�$3j$-�.,&1short (no�  $=�P\dots}=\sqrt{(2j_1+1) 2+1) � used���u�5 $^$��l�:�� i�N ofh# argu�s' evel3e48�" if/3 wise��OV(${^�%�~"6 ��E2� |&�"��� y�B, a.�!�����:}$ �B*SI��ypc�-��N�*2s�a ,��6WI�Ba&�lyA"m#@t�D��>r� �"�I.�pFw�� (,s: longitud�-2ic,<ic<Cetic- %<��G�Ps!� incorp+EJ� 2�� o%]!�K! �s AXcŲ��y�li�!�)+e�:a] 6d0 2eg�}$*D E�!��5.p)e^,�%�v!�aC48N�V���- {� \pi})�l(l+1)}͟l+�/int_0�nfty} q�"d ��_{lh(,q,k)\,f� q;l)� J_s}�4�.b�B���[ �ɲ ]^{3�[R� {q9/Nq\��k^2�"�< 0�c �S _l^{U9:�AP6�e�bs �-�E<�- B��Yn�+\i 0 ��z ��ɋ�.^#J_�,sB>�5{=�,0,��d� A�� F gr���V(�2$2U � rge�>Y)��~� a&� L��&� B�Kl.$j_l(qrq�6F6�"Q"T � R���mo�Im�!:K:#FW� A�)-- m}) �Jthey cl]G... [ h�*2$��vٍ� Z.edLH��&�."$ "2+$i�w � "#<t�O6A� N3{ 2��E/:A(a)�$_l�$E�x%�P�9.l/�l�3�5, (bPbetF�"A՟Fy>  (c2@aN�Vaf@��/ . Each �seFV�J�!�J:f �B,� oN��.�� 1� arit)!A.2�y) h��)�/K a $qek$"�.-�ag2�. We doQ �;�%Sn�6� ies 9W:�15V\c|YF�B�#ETP�U vuQ"�E��2�H�]^~!�zU*�{NA;q] m��#��}�*�Y($V)a|*S0 V.)� $0}ŋ$ �I��a� $l$�&oi0b(# sC0�H.O. $_- $l=1 6 gA�rT6�u�1mG0)$(.g&>�ZC A�!˥ l :� =��a�0,lupI�iBF�/�EF(8n�"�3n�G�,B���qnsd a�Win lOq&�U� AV$A0�q!I.Mwe / ��BA�B6a!>�@"��3�C6\2(6a"["�^g6�� �*�}E"�2t2�/�6�Detot}=f�D+ �1 6�/.�R�$ "�.�[ $\cT� R?=.� R" +\cObC �)6Z�f,+� 5�B�w V�:BJ����Gou���r��moEDA%&]��xon!Gn"x 2� w@Er�F �%m�."? )7en� !���&� %��7�7:7Xf6�i a3$�8CSVONBnged FW9 "QNG ,P���%@!iu�1Nq�7CM& -N�Q� � (-!�}�wFlli��1'!�H9|�"�g&]��)�F�!�Ai�o6RE�f��pDv&~ c�6m �model-JM�S ent,�FC2�2 �%KBzwj scus�%6A��/5 2c*M4F�+. / st"' ����� 1�"1<��d\_{� /\d\omR�:�$::��)=\omANU��&V?�>�v Nnfl :Up * \,{2 M��#�m^kBl�D\t { l � *�� int\��s_{\qmin�qmax} {� 0q-Biggr[ r(q50 2\,  ax�L(k^2&� eft| ��� h(^2 "�"fl &+ �Q32q^2(q3k^2) + -x�) � �q^2) �) 59͎`} %|#{l:f��@�% ]� RBA.I�V!�/ A�fi�t0`�Ot�0�3)2{)~3p_2 }D| um"�3�\ s minimume�max  I�b$%�=p_1-4��ax+fSES p C�Dic��a�� ��#H&i9s�;�� nol2i S * j$ z elZ�9���E�!<}E.�BNe�F- ,�%�)~% 6Creg�6�>��- M�Y 1�E e�Ip zero^3�h,Q�69�c�eF3 �j� >8�&0 0 ![ }) �!&>en56�&� 24r� ~�.Mx:b� .� weak�1��7�Rof2�M. An &1LOinguishA�:@).a}�:�ENlo"Oi growth� dR1$�!*9 J&9, *�isg0KrotovMikhail�gh"�g\gQua�B$=on+ ��2"��=1already� h+unlik_8>��-icli[2�!q�s �!�iV� �by%(�~�pw�PdSe ultra6�h: �)edomina�[)Ne���Tverse 0��f� >uA is B , $R*�0�V N�@infelyxvbg&�"�7�"�A�2Y"#est35e6' .#�A1/��{\perp�Ew�� $>\�2"TG-1}ś� ith L=\E_1/�UE����Eom/v_1$o v�:cAs"@,%+$�a]an�?at�a.~5��P�W�\Q9i1�.: lead��mc�(6> �3)%A�U&a#�LaEB�3�E 1��"�E)lyHF�A�xAy�k;"�lG�A3�C'!�0rm at} \geq q %�>� �e_� (A)� F= M�at�J�_!�YVat}$ be���adU��4h �u�sZ4 ^p Bigl[N�r]_{qD` �.� 4>� 4/  v_� � ( A�ln{.H� [ + B #A� Em} � "�B45Be edJ�>D A = V 2\ n �J� �,k*� , \!-B = {�� 4}Zpl^2� "� s .�� �)"|� "�,)(F?\!6� �? ")>�&q�ayI 45})N�NG�>�FA��|io�!*Yrem�Js` ����E� 2� �6` f.�7,w g�hmi�8y��i� l���nJe�~)?���s�!?x�!86�.�sE!ed'D-��3wor")9B!� T Be�m! Nv;vse s"��mm�i� &s:=� .Pb�B� )M� �a�BZ� fig2a�c + b !gj�c,hspace{-5.5m��iZ�c3,I% =270�c j}�'�7�-'0er"�(� &dd \ia�R�$xM $\ln"( �0 \ln(!�/� 0a�v0ton-Au$^{+78}iee�%ick�,id cur�W.�J�� ���s n|.DOAPt�1ed�e �-�b� dIb��{s�( ! �*�^,�Giv"� .�� e �aiO�� I�!U��$�5L�3�Tl�T0{�2��"H'`!�= �0�j�� $1.5 I( 9 � om=4I�N�',$I=93.5$ keV�OYioJ�@0-4 ). K� fig_E-depM� �}��g�J��N �*�a� �sea�a,b� ��| 2���/C!&�c�toy, a hydrogen-� gold�"�. B^nO`A�on�\�supBse-m%[3 $�:$sim 10^{-6�A��8be "vPi+data�n?�M�hA�B#OwoK%sA] \ndi|auc�h b&� Z2I,&� #l�`ar�i*A2p�� $kv]rd�� .L}_ .c�26 .��)R�2�ƪ a���� 2�[ �]>�G^L�@� Uen�"�  E�%��4!� i�!TofF BD�}�=puts 1 =<6�B= &=FD* �eP\c��5}A:��it�L� ed�De2"}�&"#'EXa�.dU� |$z!ac6�!:z .5D.flI�a neuQ��Eal�'9���%5[cpB�n&�,�G1\leq>�S!��2_�*� �;�N � �. �$��nN��e�QronVp,g"�4g.�9onF'ox(,a peculiar g q~8�!6�"� "�(�encDI!>* �.s=.))it�c`5�[9�ofH�I�WshaPom.�G}  �c >�/Aw�A$s 6+yy�*n V -Z/� 2$ ($Z2y;�M3�~to%M1��\� M� % co�p�'xGic N��a.:><&�SV.� {16w /3}\,Z^2��&h \om,&e��idE� mJ ���in�O��v��J�.���:�8and4})9&� =i�z�1 �>, �s�uY���A8�E �T{c� ��!�"e7.G!��Z8v93%�"9N� +.U%64 Z�,j)��!�+!�n\om.�_� 45d. e"MGA3u�� Z^2$�Bf49 �)c*�v!$q�@6Zof�o�`�ka slo[eeuW��!i&� eDR3 q�23��Ic' il i�!�4uot�LW.2nd has�� ��"1+a����}.�32,.�э�d�Zt:]�! onzdIf $Z)� �E��6�� B\�#�/ cIn�K.&!(��!$�5!vY�a�~eBbe W:7 6�.^�:A�0 =Z \cF_1 + Z @n3$.5T$�GoS=|rEie�A2�]A3(�U/�0e�ac6 I9 %V:"�#cF*�TB}"ZLi:A du�f �;uo$]3"d]duB&�5 �.��'$nucleus. Y�ObQ�A��s��rp9=s�Aed�?-;sa��+�:+/'�t�N�v . ��EoW]�QJwoIH, $E5A>9He�O��l A #U|"�,A�$M�$,IPw:�~p�6cFs�^ wa�B"wQ�BopEr5�./�8� F� BrSc ���a8�� U�M|� &H,� !Eba�M,6I ��,6��&:jUaUZALE�*Kbb�N�> w/f��.��$7� H�(eI~dJB.x�E~q " 4-�t -���&{rN{q �v_1K �%Amڀ�ve�a �� w5length �B=2\pi/\j T� �{!1� 6��bel��sds'9= +J) '.2em�8�cad@�%�s Je-v>� �"� quasi.]>X�dI��~�oncM�n! �Z!�* 5��-sAs� �U"lU\`m$�(�vs�*�i� unjp edlyEya�Eg��M$~�1ret�b�,"�j.v� j i&a�"` U�, s�$ARQis?+ap�W s$UE4�%.f }�of2� d})M ��> �>a�a(=�u V� �.b$%YF�S�es, "�7�yvE� e�;���ib�bg#lR�-��U Nl+��zGm�C MӁ�!E�/&�hLegendr�ynomi�9$P7((\cos��)$:6-N AN>��&� \dH .�,�x,\Om) � �,{F)` �, \d\Om�^{\d�#gma-P��C�eft( 1+�l_k.B,\, �)_k ;\,��� \6�117B� �L��"� "� J (`��&r1 $+�xA+eff��s $.�� �.��AK��QV �Jbi-&^�.o08&�"C)>�[271,2:�I�� i�[Ak�t�46�,#edu M��0��2�BJ1xM�"�;! ndc�� 3VIPB���C���F�^{\NRE*E�$N� 2�B����R&� .�#0A)��(Ch"ҏ1986, %&�2R >t:� =FG#bM�ene3jFN12�"117F`O�"qia-We>frequee( ��' ()CP�u ���2ani��1vk���e�Sڌ'��&�a�g2aA'�*"o�z�)�1��7�-cer;IѸt�  j�FJ�iq�6=��6"���r".�|op=`Kjo aZ i�.���%i��#�c{*a� obvٌ%� reflk�"�)���>� J�*�%�� r-���*.Zhe�"5s F�[, �( trasU"�-F"r^�} $a `hidden'=&����]o3G/�"shGp4� ter�0 !"1P  -ut� U�m6��! "k )��`ψwayera�he origz{E9�AtP�ɔ%v>��i�-{Xc�2MqO"�1.6DzZ<� � kY"h��& =l,e,mɓ,k,A�� |FwA)X%ll�"Y� e A./:� � instN�2� E�a�$^�9 ETP}�O Y5�)>���Ť!�)85�� 16Q/2+p 6D  +- ]%�� �� � o   �(JI F�(I�sr�abEvm�2La})IJ� w3e�qwN0I�}y"a�(A`��:��va�$� aCӎ:�W&�. I�4$vldq':���2� a ,�?�ME�tj���۔χC�5 "%1a�X � 9F=-m�2�&�P=_QM�"R���J26s��> ,��U � �i��@�!kmG oupl�|he �6;i#F�v:�� . D&�sE9� rul <B� ent&���6��r��/z  $P_22ɝh Q�I�' 2 �h� .�$�NneŃM?�.J�z*Mu'* 6] 'n, ei�!��o:~�y9 ��!}�a:�� �*� � H`15inJ�Ry1+:_/2*(pto 1+ �V^2� F� b99鑺by a rQng.icQ �!�au2�>-�Z!"&hAcn� �o ���2��#e�rs�9�!.Đ� a1H<  `�4JO�O�����9� ��6N 5�6S(6�#q#HowA�,A�b��2J ��&:m8�]$a�%4eoi te"mr�� � B�m�12�a1i) exacu4��happenLr.� A�. UNXi//ama�B&�]>�Z��en�/ establish��$ c* f�t!h��RBA� bX+6�!6-!��a pn"�\6�2=!�beK{UBW'� Y�-!�� v�2Li+N>-+���q��"J+�6p ��{!�2j6>s " 4r��%��  B�m�"�, Kl!H)]:(�0eM@��� �? |&!|J��?$�!�"P(I>,.a>K) �? L�2HM� � Ea��L"�*!%o� B�:/j� �$ N#BL�=>G`&E&v�Y<t$ or/�!�ch�P-�6 $Zp-m�f[�n.s�r2Qq2RQ -J�&c� �N���v/k���!6p  fig3�0- d��06z�029:�0 k } \ f�0F5��0"�0 �ZH1f�45 ��13c!!} �1*{0.8cn�1466@%a� }��16�Y-{Profi0 Mm�{iF�Eaf�$�"�$�� 3 GeV�{t95~ Al�11�v(.&�b%P�^ *2(d)80�""n[ 8�energiA�I�0�J,o p�fk3&�i fig.M��FuVIu�@2�&\&_ �-.[  u"2�� �Z�{q�~b^$ ����ga2jy�is low-$Z$ (y|�i (yr) 6h2�8� each%�.� '�erC7:q�.�Y �$�@4I-�404$IB�, ^*4a)K)j�Tlody"��seg� connA!n�&"|a�ai ���!e�u�v��B0millibarn/sra���}^� d�i�horiz� l axis��p� =0$))s 1�����"�� Tt>����a��W  UK�-3� ~2� }�-6$�n�c'�JGL�66s [: \�|�wF,:.,%�2� 2�-�ALtSlso�7wS�i�. Not�% �'�ԱDR�+EZ- n,5 �D ��!#�2\.�H U�nM�in e�g �s ��I�B�6z66)�sB= �26�&� shape[���)2� ��6��Fz�, �B enha �m�forwardmZio�e "B�?��Z$ . M�>�Wa� �!�:�d%W)J.w a "QE�ŽraV�#*�D%\>��Z�<%%nR " �[+%��;�s 2�t-l.��.\�9��}} � ���1ou&U��if�r A!3zp��!3��(w%{�q�der��B�UF,�&.2� ( �on@� kFq� ���A:Bz o��sg-�fv&�5M�e�a14� �:�*�%B��@"U&re|F�Kred�&�Mb'B!9Wsc��Bn���a�%~�?B.}� �A��F�7P"*�r����fin�Li�e}A#�T!l"f'q�����L limi[/p�J�<��01T"�K\4/�.��( (o ��W<�7x `1') �B� `2'��".�� Q��/��5+ �stEgXl:ݩ) bz+ 8,%�A=. %�!su�\$cript 'r',�6p�lowL��q c"8 � � y %i/�bͨ(j a7�one) %ETeH�/. s �6�+of�r�hf��6_1����fi�Aaf�7�A4C6�*$A֡Lcan �h\ ܁�&#�,�]�0�: /2� (:diag_at_re�j*� .�%BB(� "��A,� ��m 6RW)8"� 2�� up �*������rami$"�!&���r�=��� i'�T�e�eS��om�{�m�,*���� �inner R �(:x(�$e� te�"azb*0eP�K)in� � �9�n� �h�4of)> I)&כ<��y�d(�B� �- )|� tic 3xB�$B S-f ���-�I�\��0b�P]A$f�PIG"�m&�4.��|ly6�~��-��Ipai�%��7@s"U��*�y � MA2t5 l �";��0%\��b .^\4�\Fv5�@;!�tic-2�*%��obS$����at�m�q2$�exğg�UY�"����s��E� `2',��2e ���Se� uldQ' e�,Loh� 6�" �c͙�Ic���:�i��%,�)YX�5���Aconven#�, 0�very �K�Gope��u�fo"��7| tensNy �a�2�Ito�ry/ .��6�#M��"� ~nd� � +'umto"�'� L�?:n �B���e�wrZ�� ��&w F��!��"�\rv �'1}E'�� der,st�re� in-�* F�����]orZ P��!QXQ lismA2Q�!} z/��]8arefu�a��z �c dom�.$!�Mn�% �6caiB7e x ,N.��Z� Z*��!�A���Ӽw�N& � !>&13f_y�![Z look"�-�"K�ws3L:��) %Dne�,� ),i :L.@ invo�zanqG�m�D�,A '�("��na��1&].�! � w�-be�k,*w� � h"�92� �ad>w  6.13,4�����\%J��/-- -c}�aZ_1-F.Rq��Z(32^23%~6x..fQoc. .'��Z�2�� .5 �2 ��- \tz���k1�3�D�:� v_1) O�.cJ)b�-W,.&,B<1F�W�i��>9�i&� ["N� 5-16�� \cZ_�D�2-�D^2/ c^2��-�5!- {�>o�~#�X v_1�.]�8"E)�"�R), �R���dq_2.�%� n�\~� !�)�uG�)�EVEaralle��]�u)� �t�/.F�F 9Ie�.��Uq���j �$# �e�.ǻfr (`$�]���S;ѩ\"_-�� ��R:y/ #!�6!�"9�.$)I= (1-v[ /c^2��A���2G  -$��jom6�+m:���j8�'>��t�$�abS6)��%J.j�)&F y�F �'%,���)*w ̺~0p% B�t+ O)Gh&k�O�' Z p? tom=){a�(1-C&,�� N �  =6AcQn�5k"�;�M � )�-} s $Z �U�d>���*&c.l�I 17})Y|% net��`r&:�h� y0*D��,-ft& �Y}H8��9� =�B� �*�� !� zW� �c"� <"2 (nzOG.�02$�6%�Q:�-A� B�W o�(��\G2:�,�9!� E�13ߙX�i A�a�I"��/�I.�B�# Sa�%$0%5wo"~ ��#�, � h-?9�%a|.�A�Gij)l��t�7a�"@`�` , $r�1&�`�4t ��c�i��P�a�LD. A2ݞi"�aa��� }ľ�D5* �������_er"H� u^ �&pB��-E6�$Ms� -��ɏisa� a~bs|��:�C:BvZ���9AW"�TUtes�6�B�-y�J1"�R\��)�hoo"s.� mo��� B���"�8!b>��$�42x���#%�d �i%Ved�g: � ~b� �=�0 g��+<��cmem�S&�90a�r�8 ase,.�R c"m �)�I�b�\��Wi�&�ed d�� 1d��qSizgg6y:_G.h8� ~ t. �ąkim��ld16� �/�� �gtor��>&�_Nt"E$�gcr��of:�%�&�=��}���*z�1�z�� ���GBuNc� S݂2;��^�w�>�(�82�>jI"v�5a%A6�'6H#[�}G*M�, !�o�2��is �� ,!tv4�@/� �r*^G��'cI��h��!.4 �$3�m?�v*&dB�EKP�B��67}) ow�S%�y�M"L#8 &�FU4c'x�>�Ie��!2I !T23"ʉ�>VTe���c��%�Iib�GP !���8qz �<j�(l9��.T�& go� ;�R M� long!�L!&l����@:m�DJ�zo�{�2'=p�zI�Q:& 6:�.9 5W �'�&)?("*x �z�"53 �M�g% aE5sN�19-6.21��{�'\�Hw.ZH�C_ c(1+[ j8)�.>F.> = C_1\,< \tth)Wc�H��/Un)�gF222"o�� %%*�5 s $C+�ei&�Z�E(:� X�et>>O!k�.a�D]����ma�� ��e&�H2p|!�=�!�gy�% t ,+��8yB�Z6�3"�E/M_1c^��=�7d&�5�oAY�X�,io�3.�c�,.8E��6"�t� "�.=i0Ii,�* c�(nd :�!_Qa���&Z 22�0@ !S�x�if�=d^U�xA�Om$b�:}6 $U�Ai�4q�[)s }*E*0;m�x �';%� *��m�@U(� ��S�t�<�\偢!w ]D(l{�, heavy,:�orl�") nor�R.K���.l �t� . :�XI� a�u%%%3��nprF02N�<�i"�J d^\]nd 's^ino�*h�� �6 Baltu�vZh��K���"=J'>!7}#a!W�s-�4HubbardRose196�JfN�ar198!� Beyo�� 2�M=ap*KI"��g s�"zB%��e��i must bl V�.k#_�"��"�OdevK� kA� F8 law~i�&�d.-�1}c,da���SNY�6�16��% ��"E .ZR:��ة|&�׍:~a� �-���t2~MR"�V" � orS��� ^"�?J�^2$>Ze�.��_�i�A:�=Uc"e�"� �Q�d��q�q�5<��. a>���.�tth�N ���&��h6Ke�\� �/f ��K�f%L:�-&� _�>^ .pB�h���γ ߡ���9latorF$;  $ ��� 7x)/(1-3��A �D �". " M�b5�w0\� 6�%�Ӝby�P( c,�)7R� beta^2)��� - 4���u��9 �P�x"���8�prk�TѻMDty�2b�}}V. NamSA ��N "��S�p9c��typ�*�5he&u�BrSB %M& .C�'� : owq��)@$JH�MgF�1 CG!�54g�6� $ exhibit-"�Zqerty:���H^w� Ek=0�8is���ns =t > back6L2?\piWk�B|Z.r��Z�Gɲ���E�.0)=U� ��m �Ku/��.)E. R��� e�� � �R��&\ cri��on �����B�>�?a�xi�&k 2�)/(b$j" t c[���h�M�!�t# r��at'D!�6���6;�+osDo ��in��li�B�/c��� "q� �1^x&�6ia :1�v Z:0$y�0V��x��*9um9�ZH�� a�A� sig�u�t$!5 4m�es�s$iily���)����os.�FQ�����"�� A�F���B% }1*kQ*8y� & �UIa>�4�7���t"{|��&�" 7*� � ��!�d_��1n�>4�K"�` C� !5I&&7͢!!*+�)\neq 05����)��n"���WB.J��uw�3AR- m��[t��{ːdde� � = 0$D.�-F:�� e��-.�-L8>b"�&�7Co5.�7.�7(paper revie_� prog�~,have f�a�/ed�%JQ0]\�/p.� �^q  c��A��@.�ő2?��6kal�QkE� Aq���4�4; (� E�U/.��.`� eavy�� 7[6|��&�a=a s�"��2N) ��1sti&U�� accuE.l:���ed*) algo��F�d":� re�4l5Y2��7?))���m t�:5�P�[')#ty��A(W&�l�m�̅�"�"�**1 20gINב* w�n*�)�. C*h �>�N%�"i~ m�;�:� �[roblem,�at:M)cannotL {+�� se *�+p�lh�-�, rbiTR"��n���=A,�� "���W�|�<dex. "�La�u+=+�}�l \y�$A �Aia!"�72�m�E�ll9  --ƶt 1D;Y#mV9;�#����2o� e rqret"Wb- ��in5� �����9n ��& � relix �M. �?)iM�2*��!!e�"���:� �*f�AsAAn.l�m��w���q�!'lP��� ����o)<c2�9!��+M���AoRC(,ed�76��.�%� aber� Hl8M��A�&� .p�h3>}. -�s A2T��Ol�� iscu�vS ��c-��c� !BI:�9=2�Q��&& C�HeCAD26�� g�DofI est ��ᑡ� eriEal{oݨ�// 4D�"8LudziejewskiEta��8�mex� u�!5_E0A/ari�!>��.&�-�iAJ�!�+e2��A��- mFmE�� 8(E�"�W�hJ�_�J���""��� y�(quadru�highe�re��E�y*q 5n� �Ri�t, �k%@� !^a�b&4 C�>�HA1a� �\�BOJ�oryEi� e:U6 .U6he�% kE(e&� .����/qk���)���6�C.�}�k����L ��rv$&�k�r/��:� .RX� e�Ar�G��D�N.�2G rint�AA�b� enV {M�eE(2��1%!� -FIK-M�schemeE����.�%e��nquite[Y  t (�:S  ��� � p��s "� a�a  F�) *��s(! 2���, ��� �q�~2w���`���e���QT�sketc�="�h Riconbi-!���Q� )d<���70}C$ Shl'r'1��*�2&f��!aa�s(��jeo@�) �9�:� pr}sp��&W!;&F� u��*� ,rin�#:rNI�,A\6V~2�ikA/��n��s�4le�{ ed. � �EZdB�}n��9&�Lo�Cq�%�at����' r� �YEԬ� 1D�MeV, sig'(I�ar �"5 is ~:� 7mase�aaK� !{us� �n #o1)�6a�Gsu��tw��>"*6'+)�b!iL�{�P)��<� �� AtData1, 2�;� !=ac�7�Î igno�O! B]2~�]!!oN*� )��6.�� ��z:� ��~7�"�"S�*7�F���i�F�aʭ�`f�\���j_�&l�� \2>�d*��2� a�!� tage.���]6� "�7"� �+*>ev��%[��.x)�  I"3#"��? rABe� sjc. }YN n��ea���n�"�!A-ofi�"&A "�#o"K -�JIS�3�{� 6�& �;��U �& ��F_2I ��m��T�p*L ?e a���K�<-�tFf<�osx ���k��9"��!)6�As&'&d� &y�`'wom"�*�H�@ E�&!a?5a_"sqw| at �D� $10-��'�"�e N1RmA'&vv)8�X',�|8"qEly�f>��)10*�lK#��e 6�l���&�,%�exten��I�6 M2Hv�/! < 0sion. On the �^basis of this model approach (which does not accurately account for the retardation effects and Hmultipole character v8e radiation) Lanaly�e� ific#5�BrS spectrum due to the influence)P*�channel was carried out. At present,@$re are no �P numerical results on+ total� �a ���I�8���sAS86�-k( 67, p.41-4AUM�6�!(ic particle�� 2�Yő�j�90af��2��90R�D70, 416-425. %Freq� y-angle2 �,r�D* in.� %of6�>�R�,vdoninaPratt�� , N�V %, R.~H299y�J.~��~BI(261-4276} Fra]/q�HBureevaLisitsa2000b�&a�~i�/e� 8 S�I���,90, 788-794���8LyalinObolensky%�yoi�jev2001�: <,A.~G., Di, O.�IF%�$ijev, I.�9�s�, In: Dugganm!vL.�� rgan:$~L. (Eds.)@AIP Con9 Pw 4edings, vol. 5!�Q�/P� ,, pp. 64-6750=/ OurR*� JPB9%K�+1 yj .!��6�J��4B 34, 1589-161�% �9�>�ETP^�-��.����.� -�>�29�0 94, 704-7195[.\%@57m6�*�,��l!l@2. Surface Review LeQ 4s 9, 1191-119����u�, % ====> Not�1cussed�!� r�:��5 nden!m ~ +*� DBlazhevichEtal1996Y- , S.!n� rpun (S., Grishin��$K., et. al��RM�~!V<. A 211, 309-312Y݋Nason� 9�V ��N6b8Yp Nucl. Ins�(. Methods B�(8 145, 19-2��Col* ive"�� polariz� by&z of C2f�c9�edia //5��9j-�9��B�9B�$54, 230-23=��H$Kamyshanch� -~Pokhil���6)!�,.�, 5, G=�C�� 173!�5-2�V5qSup��!�density-�R�<:�/2�}ged*H <�ia� n@Y�9?��&� � -J6l.aI�O 7:� #�� S!{2d9e���a�3�  298-3%Z�Y��@RA �20. R9/�3 !ݩ-Usp. �&49-18�( �Zon197*�  Z�B%�5� $9~N@ 46, 6�Xb ZimkinC 198� #"� , T�u}wE�2�.� 27, 86.� 25 |9 $Chernyshev�$5} % StripY� 7&� AE�B.,�^ J%��sA 6:�*�*) ,18, L791-L79�9^y[.!���:�a.-�.-��44*� �h4}.�e�!Li6| Pitaev�P9�2�b �� Tsen!0� , H. K��V 1 .1 !*� m`Rev�~ 100-11Y�=^199.�r�.d9.d]030, L317-L32�k4 (Corrigendum:�$0. ibid. 3�l471.)��I�9�~ 199.�"� 2�2..�8 25, L341-L344.:V� � q%]6�6p 7� @aAIqf�Z!�2�k�".Q; 197-121&=�VarshaloM 8MoskalevKhersonA�]?.*, D�8 3�N�b�F1N 31-4� &� in>NN^�.sƦ[�R ,62, 876-881.�stv�� n+A>� Balt� vZh��ee%l�j�:�z� C%�{�U&�Q^^�}PFsFal> i2�of*w at%�s�,and nuclei.-.�821st Win6!School LeningradEiteof0ear�ic(135-194 (ina). uv�%%%)z*�>JFz=�b:�(66AY7-883]1Y-4HubbardRose196] � F., "EE2�66.%4� 84, 33*� 2�e:1 �ear19n-^U7*fSushkovgP. (ed.)�P Modern De�p� �5�U�Wf,425-42�2�,Ludziejewski�*� .4, T., St\"ohlk�� Kell a�BJ�#8=.%3r601-260*b9�Shaffer� :Z , C�$B ~.j M� 056, 3653-365�C�">� DPW 2.#of (ly %di�� al"H���#simpler�ori. �AtData*��� 6N Lee�� Kissel����$ MacCallum(, RileyaY=� . At �En. Tab�2��7�9U{ (Errat� 1981� ,26, 477-481)*. �2� ��#�&b��"ѩ At �a � 8, 3Ũ 9h l�#:Z �W$N2:2~ a������174-1!� ��� ��$92� Cj>�- 2003&�m> �$91, 173201*# \endB�"  docu��<} �% For sub�&�'Jv"i�h % (Last update: 12 16 04) ( % Title: %�<"5"e�4he $\mbox{Li}+ 4HF}\rightarrow ,LiF}$ % reac�@at ultralow tempeA�res %~Authors: (P. F. Weck ��N.�%akfnan� % %\1�.',draft�F-b%E�#�8B \usepackage{7%Hicx}% Include figurles2,d)~$}% Align t���umY'0decimal point2;bm}% .&�h2epsfig�%d\newcommand{\ro}{\bm{\rho} of� % &Q.}F" %\1F@{APS/123-XXX} \ta���u�xae{y |} \email{weckp@unlv.nevada.edu} 2:.7naduvalaF: \affili� {De<"�]A��&�$ y, Univerc4 {$ Las Vegas�*$4505 Maryla�Parkway,.$NV 891uUSA灌{\today!�=�1�ab� c����+cal6I�,�)��� N�((v=0,1,j=0)v�@(v',j')$ bimolec�,*r*�)����R�. Cal>�Ls have been perform�+ zero7-'-m� u|r, high�, uracy pot: n�*s�v,% $X^2A'$"Z ic gr9* state.�Kf0!.$,J��4is dominated b!,son<+s &s.�a(metas� t�b�+9�\cdots�TF}- H}$ van e*Waals4- lex.� As�+Q�these�.�has)n*�.�"� ng5 e%@i�� he quasib9* L)az2 �tfio98,tak98,nik00,gab00,pic04}ś proven !&suc2!KIongY$($T \simeqC~\mu$KN P5neue ]n %de�2)g�4�,, magneto-opi�triZ6�)i _.4 KRb �manciniӁ NaCQ� haim9> ]4��$0RbCs$^{\ast}$2l2 a laser-� ed mixtur�6 $^{85}$Rb} $^{133}$C�4)�keA�kerma� 4u�< . Ex� ��…���2���x �trigger��co"�5� &�60factors limit!� a�lifeta�of�E PBsin ��* l�P1� bal01,bode Although�al stud�of]q5�.� a� jof �vm �#in-S �b)|bale00 3,sto�|Ttil04,sold02,volpi03},%[�� ly ��progr"� 1� on>�v��Se�.�N weck��alA'. ��4 :�55 z��* "V onsAߡ�RX \vD Qv��9a[�gtranslE{al"� . Si�6m�(�>@u�alkali(al��vh b degreee soph�9rLE��EC!oRV$s become  (widespread,�*�8�JJ)��Ua_beaJex�ed��afle�ho �2U>P. Thus,�Ju8)�ela�:!�ro-}qly in}�+*&� &A$ system�of*{8` te�5. More��, �8aY�"�XC�,�LVp��  eMia � o!*� unusu!� :� minimumw0 about $0.24~� eV}~(1936 $cm}^{-1})$�!�enA�ceq)nz<� �.�!ceV�B:u1\}evol( kisfO=�k���W= FE� (.5<HQF}$�is�t$ndoergic A �9ot � a�F ), it"<ei rE29zto see6;2 �a�e`U<occuri*� aSe coef/ 2�� m ��H�i�Ztopic!�a lk=�=b-Ir� �L . Af�(Lpione�;� ��eam�Qc�( t{tayl55}� V��became prototypeqV��2� �k�(``harpoon''S sm ſ�ԡ�9 ��� �3ne earth�X�;Ahydrogen�- lide�v�{�$66� �a1Wamoune�2�in& 5��y� $key observvs? h�� gw�2Y)�ve)� o;")deck80,loes93,baer94,aoiz99<00,casa00,hobe01 1 4}. % O�t�9 front,A?erz> *��> rPpark95,gogt96,agua97a 8b,lara98,pani98�� 00, �01,we� lag��2y >� traje� y-�<0Y�5 �� 2��0:��@2( &�i�y"�(PES).e��� �ic�A� LiHFM�,�on 13< ons� k�>t verbika "�A${\em ab in}2�. Cons�7tly, a r�B0@et�zB�Aglobal f� ZB"a$symmetry � o>k PES.;roposed-}zeir78,z08AmrtA�4aga84,garc84, !�089,palm89,suaE�A&5M%.-ga98aE98b,burc�asp01,2,  2, %F, 0� As X��(d above, on !�u� a�N�B(De.��)� dee>L w@in bo�AV�a� ՝��՟s. UnlikbA W��d9F�� }_2$.SCl6�s �A�� &��depth��+20�3��9A:@in� �2d$X n or5 agnit�!Fer, giv�rGC8to long-lived "Jole`na�.�*n��5y�eH5t�6iproba�+ e�Cs�@�!)�Z�* (^2S)�@F}(X ^1\Sigma^+)$&& valley^fir2 by backNDa�a�&C�K�ŀt{��}%� by �E@��me"�C�* 6huds00}.CI��PES��6p�6��� sXoba+on�[e� �� ric��s�Eof >��D us "9!M��c��.�. FurM more>e1��C &�� id � cq L: �on J� dA Hedw p%��= .� �Y�n ; v� w � 2C; v�us,�garFq$J=0$, x!\-5y� ��.�2�� �ft{�e A b��8Hb�D�5I}E��p[i;4n Sec. II, togB  0a summa�B:J�"�I2illustW( onverge� tes�I sses�Ov� ��our�D ��I80�G  -to- e��al -s�?�6.s>� ra6 ��Q"� �@ non-� �Hnel5X�:H�diq:�,c�U*� epZ� ^2���. 2�!J^�=��)�V �^J&8.q} .:1F  %-� \subL {�")�&� �W�}�#�p- .�& ��Qg�~y*m .eS oJ��2�afof� u��c�ly� te0 FLom�v 6000�+ar geo& r �� r�h� Mr H��gua�o Jte� (MRCI) w[fun8A:�"$L a�limdouY��,Davidson sizo4sistency correW (+QI�ic��/t�u�� to adequaN describ� ��^+&^-2� Li}^�iW conf5s!�sponsi�� ��cur��BK!lea%� LiFa�b!.2 adiaba� J%�q�� ��F� �5saddle�N���]f  �iH�+a�al�A2�)���oSnX )$. � �m�se AN+Q¡fB� aI�nr>E�I�gmo�O��3b�3expan�<] aT92:It��s��&1�9(:�$$ asymptot"� PES, %��!d["of��E�A,. botto�2HF�� , M�feau-)ish�a�r-i �-�L aAO��6ts.� J� s ex4g2iU�i�c�rys�i��ed m� is�01122.NF�]gai �MFLiH6\ �F!�P2Fli�# $3.57.o!#F5} � clѷ-h� � eA��8�@ 2� O(Z� �� "�( �ve^Z*� f!�'�6AiABCcgram &� &4 sko��  1�x I:7!ed-1\$ hypersphe�Ucoordi�'�hod s&-"\"{o}�er �_ �DeUbP�:mo5 �thC�5 � para cJe a siL,, Eq. (\ref{)�) merE#reduces�a��.(!E6< $v!2nd $j'� ~"2cC*98�Uo\�% .),�& ,S"��.ntSsm of"��K�� whenmB b�\��r� t. Aa|c ce�}A�&�e�ly �sm�!7p�S50cbmust b�+i\%s�"`"&��ionaWe<&7ext�J�>lK!ҍ~>S�>��m!"2p�m�A9Vmax�!�� 6< , $j�/$<d cut-of����Na�)�,�I�set�)�tũ�h�/TO$42u�E��log�iv"�pa�,��or��\Delta{N}$�7 � dec�R� f261\r�%(�y � 9y �6� Fig. e�fig1}�C"�)%� .%�:�"SUsL an�cy��!an G^�#0}$��,d �2� $1'5}-3}.� � %�%�s.� =50.- a.u.��p.�=0.005 S %2��in� a�Ձo�d�*�*7a( ]�d�4�`�� D2�2�!e s�" �of.�N}(F&q�e))�&Z�' n�4�}=0�4qA fix��q6q�%�5.� . U� ��"�`E`� =25-Ei�=3.2�*(a "�, !il��$A�qf�3IY[0 [ a�lSq�v2.9MP�A any_���N�seQ�� comp� of 771 lo�6 B"�.M :E&le� Z�v���w��] ly s�� ������� ���V:* �# 1�4�bn2[MWa�a.�F�,���OJ��*=1�^��-ado� A��q<�'a�ora�|ba~&�^0&:R�d��d�ion6D2^D-�m�"� J�y��&� u"��( a�8">+isZ-3�$FQ X��!�u52�e�E� Z!i�!s �.-in�t  �qS�*�� %�"_*{�#04}�>"�ca�/r/{%& }. B8#: ���� �t Jr>�Q"I��d� ��, i.e.,h exh;b � mQ�N��� refle+$!H 0& &,v HF �%�%� � irA.��:�6�r.� ceeds mai;&by5�&Q thro0� � & , *w�$�#-:6�&� �*�v�Fg rais� � �� us.�)x�r�7=��/.�0rm)p"ea2A�A�GV� 6:Zuc��5�'�a�3ediB":1y��I2�: 69 co�Dx {w.�(. HowO@!cs�-� peakVhM�byF 2na$noticeably*A `.!Lq�*� qT q}a�>q�As�*N�t�7b�+a�>Am� in�:� LiFH�.a:�= & until�F,!�*b$($ed�T{:�( dataod d hoc}�c9e� �yy7&�iper!d-+E � �-))8mPES"&�;!{ .�a�esh19�_Bq2�1�t{1� �.2GanE��,�/53Y  N��2�M�6��w6�ir ���r�:0 � � pack�<�2is�- lineij"prE��M�th1)-lE�p[see][s 3]1�*"rkofUQ���i:r 3} �!�q* *�,}6���t*i�}�D>� reve�a}7cP>vee^repanc��iY� ja\in}.!+� 2�4��5�����2�)�� ,eal;employahe &>i�Y�r+1Y5B�%i,��4is &�%z�Z act�69Œ� {.�B�M�Li�.)$*''�w2� 2=/-R^�+0.16Bfi�"a@&���.�!�is�eEH��se6��y���!�S* �2.�3$4 �K!�o.#�}Nq&� �a�'w��}qr�ց��� /er4�t����r>�+.�i�c*C &�&a��.' �6Z�5�ABPa&�t . F3�8 , 52� �:�� �� ac=�$M�"� ץ`2� s, d�#se^sFo)!20.%s!=* c-�t��=�x�X5*y \/!�.�isB r%�bte-eGe� M��AU$v''!� 1$J;a�broad �'ea�a� j'=1&ppe�A-LpoAAon�g"�s9:2�<)'q"rM o"A$:6� . VV�EI; L� *v7�7M:B� ] �>can��%"e � &$Q22�/24�%Wyut@(at&rF�s�i*�MF�&a�A)X half� %A�2]�(!5, 1��� r�+:.�!e� %MO�)!}1$��a7 frag!I~ir2�Ie . I�&>E(��!�u 68a&n nonI 6�!in�6�J2Y��displa� > 5�"�V^�"�x!r8`79.�X �S-:)��HR4�@ ��0s2>� &��rZ) vely2;2oG�� "�� sm. �)��� be�JM,6�6�Xh* Wign&�D\ {wig48}���a, �1rs�a�l velo��. "Ta�#DH692�4��eLo�9 u �:��+by  - six ���"�4�0 suggest�a�4�@ma�3 &\B� .:� an g!|�NrecognQ . �Z�beyondQ�3.�: :�J� c5t spi�8 �)RLAL��f:6e "9�X"y�I. N� B^�>>� �!91�9�fZ@�2� $5.06\� :O� reby",lai�Z%s�<�6 �.�6xaKis� c>�!WAg�* &/�?(�yA!N��A ,1�H�_G=1� BI7� o"�,2�*+Ba}eR avor�<)=2�qH5 �lower paF@6b �-cba�Pf�F� %��y�Q9p �I�.�ptpss��a1( /Iht?1I branch��0m20!ա*��C .��0�*�"� s� ��iAF�� v� . Mo�B2 _���5*K�F*�N.�EYJ.ZEe6����6�% JJD�� R��> �!\t& ;I�1�%� ��635�"� e�JQ&H7)�HFR��V �)-�%e |WE�H(R��v��I9 � �%]"�1 <c)4b uA>&�Fourie8(id HamiltonA~ qF 0mars89,bali92�'eq��N��8� ,a 20-term Leqir5a�2Y .� 5� , 25"�:�]n�-�&pro�A:�&T3*E�R417 Gauss-Hermi[! quad}Z�4; E.�>Lnd a g!3ofwM0=�>^�.>@"�CinU]� tab1J� 6} exc` nt a�I4 � .:5Ey�T�d+��G"�2���w�(-6k ?s AH�2�6}�( � S(� zden�U"Z]�6� A��U�!py���N�N� <,6b$j=1-4$!����L6��� Xe. EacIPheNlo8 *<��es.C��JM@26�>5. O�-lya���tYJ��R> t��i :�8.�#C &6 �Q �F�AI�)�J�f�y�*.$, eA�aAw� �!2`��f"�F�6�*�, $T=C2/k_B$� $ UBoltzman�=n� �e�X$.X$� (40.g!����.o�5�nA;!( PES)i>�$on�$%\c?A �^�$F���m�x �~�E`���*  :* �FE�=�QV $0.0�K�/� q?)��\! $4.220 cm}^Es�Q_+!Fzero-y�f1����P� o by 3*J m"�'�r8�G�qI�dep�'%pp.\28}Q�aav> $2.82M7v s at*����%�N/n�"/K.��E2�^%.l]2��$�mM&r ay-t")��_C"uR�gn l$e&�g requir�\2n �| J>0$ cCL �A, scopElGuWi6�_ &�+Co�:,�A�ha�.��w�b�D�#� ec&� E��- "�,�baM*2a/C&S!ev ��&a�� ��.=��&�U,"�<�3*U,>�<6@2[NRA-,.�,�&!��c= �!!�5Ge�+FE , cl� TJe i�-)|H" &�"@.N`�5"� &?CHFZ� ��"8v�"�:]��'�V"�2R? y�`.A�EpNs*� �  empha�0�,�b �0T :� "��0 detail5 !�A��+f_!mdesirI�����cy+4tic �R� @>;&�G"|'ic�4�U{C'"Om�P�e*1Ť�ٲ�a�FrfN|�)dra^%;#�2d�'.�e&�KA�J{6=6 � �i*�3-�!�.s!"�ŀْ��e�2�M���F#,a��5ntIRAh"L�!q) ��C&O"o D�v�Vw�]�&�lQ�&�qLi.�&i�N�0�$)� �>��URL�a2�.Bq��AZ�2�U���2����M��+��R$: gH�9s]� "[ att�v� �ud�,con�7tr�w�-M%d9��hj1 �� adva�Mw J.�k"�x; !�a��:.�!�53! f���I}1via(%� �� ���pf aQ< �l�� ze�b�i��f�<new@Vp��tuHN(,jXnM�����!Wl��n �P],ye ��at^Z� (to circumv!�q{8  A�d:.� e/C�=�WD"��9�b�"�"[�"+7 % B*L�:� 1/Bs��ob+5emni}JcG�ijX1Na�3(Lond5�$\textbf{40_491 (200���i}=Sk chim�.et al},d1rQ 302}, 210 R3.�wVjRM. Grein�C+vRegal �D.rinIq f�2�537�2i�j)]0M. W. ZwierleS oSt2�C%]Schunk�v.RaupachGupta �Z. Hafzi� c � W. K��F%f$m.At.�Bt.591!504Nak!j�vubizollXT�7urdel�(J. Kokkelma� @G. V. Shlyapnikov �a0C. SaloU�Yz�4V�tim01)HE. Timm+h|KIXuya, P%bMilonni)A.!K-M( �Le!A528�`228%�1.-Yk |)�M".;�].z�A�0�3n4.n�k nM.lGB�le^AltmeyA�S. Ried-�e�xC��-�8Hecker DenschlaefRA�imm2*�xqA�125�6�blhY}�.q�)oN_Fh0Y�4)y�bar95 ^A%enco,!bDeutsaA. Ekert)�R�zsa~�7m$4083 (19952yre9��GE5Brenn��Ce�Cava P�E$�$ nd Ie��!yb�8!� 1060~9)9��pm �P. Pla�EZM. Dykm�)`>�28� 1967XVdecm6D. DeMil�$f�T 0679�#2.&f3m �A/�Tpti%��2�,A�(ubelliA� O. Dulieu�8F. Masnou-Seeuw�nd��R  j�0}, 4402�8.��m �8T. Takekoshi, B%�Pn�s�!qA3. Kinze~68�5 5105Ft7n tA.{Nikol�J.c Ensh!E.yG�H. Wan1q ���%tw�I�P�Gould)4f�!�246�I26 gab0 �$C. Gabbani�2�A. Luc�S. Gozz !%M!�zzo8�z�814F�No?M. Pich%W.��Rnu��G)9x�� 69}, 0134JH[M�7ni$.T4)]* oV� *� D. T�!s�nR%�Ca#,�きgnato)�EL.�Marcas����e6P332N� HaimU��O���oj%',AaKJ��,hatta�7� !�N.AJBigEBI9I7aT021eV��.V�o�� �MJeU SageS+s@�'�ge����x�p03300IE>�[ !���� 1530�2��oi�NA &�(A. Dalgarno)p�{��634�V652e22rbo p�Ex do� A. Gi�sr� ![Bn� h֢I�Qz11� 922 l2�Lok9�7:�,aC0rX�Bte lJ��� 3224F7v��Bv2�uR�,F6-y��b�W62� 2 t� BtGc(Groenenboom� V. K_�i�2��b��D738��2 stWqIC$T. Stoeckl A. Vo�Z]. Rayez �=ky�6l03271Jn�q mK9 lford"� Host��Pe�FloriaZoVz��527�>82r {6 old\'{a}n~ T. Cvitas��\ut�$P. Honvaul� �h Laun�~%v�6T8�15��eV2�v�rC%llpi�J��Boh$ !zRH`86Fh[We�B�)]�a�&<�z>�# Euro�3 J. Du�3�141g>�a0-�>S)3^�2T556F� [TaylA:nd'�z(1955)]n%FE� )S���Zu2a� 1711�52� �m>DA Herschb Adv6F�����319V66.�9m V�E�� 3$Casavecchi"C Tied35��V�^ !�!Y���Z�7� 2833�8.�[Loesn8nd Stienkemeier� 3)]"hqH�1F�:4E9Z�9A� 9598�92��m)M�ρI.�m~H.-a�ne10AI964 f2��m9� F� Aoiz�Martin��m en\'{e}nd V. R�4 bano��(E. Verdasco�.�6 2�25�9.��}.�.\}d.�2 F�!�!�N��� �  Q�54��.%{�o)�P.2�pRe�rog�2Q6Ax355�2Rp RO�nb�B}�2�o � �  vu6A�H�Bt v.tMeGYwM6�|Z�11 8880�2u�M��j obbenkamp� Palade�A.Y�� �h 21ak:[z�&� }]"cG�G~ '�$Lagan\`{a}a Cro��no!&{ Packr123i�2n�qI F. G]\g�G� B�Dt-Kuru! . O�vv!�792�2�rq M�lr: Agua� O. R�~r-�5ani�cvs��3B1992�psO�w�!\�!�^{s297��6s�d[A..o��s� 178F+[We.�3)Wei, J�pr� Truhlar�i L�)i% W.2.DE 4kU"��i�Au� 107}, 723J Y�2�,F�(Piermarini]He$�b%FV9=%� Lecta:��.B@304A�4 6��r7a].9�5�:�r1�10197�-[ f10�)]{ �b��R�!� 1008�-.��- wn�BBF�%�!%.jaaIQ�L^�>z�t)Y. ZeirIM� apirF"ը�2K 1972+�t V�l �H.!SchaefaSIII�Z72�376�2� {c:u eS��rte�*JEMurrell^M�)�:56�\6Y]L8��2-1vGarci�H���W&��82ga�u �ELDR2d^�5! 111E]6Z��8 ��\iX."113a�28) 2� v �OalmU F�Z�-730e�6`�v `�uar� ��C�blero���Int �d ��%393%2:M ��&-"n�a`>n ^6F2� 10%>6AG98��.u$O. Gervasi�UU��.k6�14 17J q�e6�� OchoR AspuruVyZ�1 38�>bpx)� urclPiecug,V. \u{S}pirk)�0O. Bludsk\'{y�v� 9�.� [鞱�4 ]&�J ! �� �ck�(Chakraborty�G.�jPEfХ�J��"�Qu117945 .J F�2��A} � �2H)���T 835�2�%� ��B 5e�15f u%�:�unpubli����}/�%�q�.�e�X Werx 02J&�:o200�� �t2i��anz r*� zF   ./[Hu~q&�0)]�xEY� ',�0B. Oh�C.p�ny�7��iieA�J^��3989�2<)^%P� a�A�!9M5*."jx9Au126��A5�Sko ��C 8ll Z(anolopoulos!�!j% :JK2@D".F�� u&��ommun&�!13! o 1׸�{pG�EW�G�� �q��(1948)A2.]� Zuev=�A� zuevE����. &,a�S� eridQT" AlbuB�D� Hrov6J��WB�*z#a�{\bf �8 e}-Marst�znd2�(1��??)�C�.2G� 6�%AZ��%35� 2 [6EDixw pQ�b�?fNR @2�m�Int�ut�#)��1�1� 3� 2��(A(VF �&C %�P. BrK�B>6���&�:�& �>�&V- \�/pag&�� %�42�bc��C,p %\squeezet� " ' } \ca�){}i�?B��f)6��*2XJg+:~*-6�,n@8B�H(e<;]B � V).}�ruledtab�f{c } \m��c��${1}{c}{} &� & 2.3D� �ls} \\%� X {4-6 69 }RP+}BZ ! Peak^B�ng�,of^)X$v$\footnotemark[2]} & N$j:+3f+t:+4]} \\R�^�po\^ $ /N�@,j)�:mplex6�1]^O^�b� \h!�4 % A & 0.2549 & 2 & 5�B.2554 "53 & 10#C.25682  & ,2#D 7` .257,C1$E $87 5 & 4A� F .259$96 �6GG .265 .264 �3#H #6a .266b F 8\\ �+qm 6�% 5��*[1]{Eq��>�3�NiY�bFFb�2D""<���qOYB&�6"Ќl�Sy�1 <3"�F�3j�u}:�2]{�4*�S�.�B131*�Lz04]:o�Tw0�|{�;,a(v2��strF^C.�n1�le} % �<2p�` %�:���GsJ$��|��>tf*jTF�e�4.�7�*��.RT�_5 62h2�d!]*e7A"�dQN�j��jm ����6sfig2} A/-"j�"70>� ���N���R�I�3]o 6q�[Y�=c5'a�"�f&�nZBvarH6valT9$ESi�@$*~m t a ڢY=�R�g� ��k>�>� J�3} �U�:"~:j�� V�.� ͭlidQ:�83�hEI; dot!�w:U *41�2�3&�a(����<2ph�7[4�>37 ref. <�04}� >�u!>iJh4�  a�>"� �66 RP NR��hX��s\ N`V.��J$5}?&���>6m.R .�b� B� w`r'9 0$ (*�R)A�nd 1$ (*�@)SF�C"�G6�m�WDaKQ�.�Y�; s.���jC�v�n 6} AF#O/e3A;o;"3�Ps�K�6�6ŵ�y.cg妡U)$:��I$ (left p8T);6�8Ec�� f�h=��:� a��c.O (@ �b7r7 &{M92� A �] g�:c">*eLsC6"R> W2Y�~�J'7} ��Jin�9�&O <�5bX�H!�R�p:��<; d2�� :�ɗ*8u�tt2�t�t3�t�t���w�\�\5����6�t�t7�t�t8zt:�Od"�6� ��Ͱ��߫ � �X���side,eng�,,12pt]{cern2�*l�am��}���v2e���x}2babel6m�2[i��Q]{y����r pace�n.Ǯeg�rred}{\? ledR*�1Lt����n�yڂ�of ��n# Alu�� um S��$s: Effect ��Sj ary OY�XP�iF�; Pimpec2Kk�R.E�6r�i\\ %EndAName SLAC, 2575 S� Hill RoןMenlol(0, CA 94025 \\��18th Aug}�(I*)�\�I� styl:�=)gn: {~$-pub-10894!e&�TJF-f+Fc�GWA=D�;=]a1G, alloys 1100� 6063�yQbsިedP{tZ^�assum� BH2x,�&�pauenough,3f� !Vst�Fz7CSEYi�I�($�� 1.3$, Aw� pB"#Gk{crc}),W Lof� �]UgM�wer�n 1.8�p factΞ�>cre�f� continuedm)e,exposure dos���9�6�{Work6;A� Ds"��En0�Co!nLct DE-AC02-76SF00515A׏aving O�2H�}Zfaframe_L!rILC�cloud�r�_�Bon emm�5�e��(SEE)�tc�cb�m�� ongoing�A\medskip _is �paper�VwaU�9CJvya�( (SEY), $\d�~�P�Ds&=]A��J�: U�*�B��)< �thQkw �[1� dQs"�] elsee.~y�tR��n, �h Pɑ�A,3Ea�allicY� -AoUWa��eV1]�x.0u its B�� oxid e� �-AW�i_p �}2.5� "jcm e5b-#t�leRrun���|hJ�d�[v�f�Fle � �i(��`��;HAgto �H a wa�l cE of�D-(w�oa�FT U�orY�a��%�wo[)a���d�� goal��lep�:LCC128}-r246.� yE",� De@K��VM�sology} , expsetupd ,} ��-H , skl5 No 8})G&�al�^h"�Fm�%D^Z�GnZ �b-Xho,yly��X228A�6�_a� ���� M)��� �.!=��enumeF"� ���}[h]{.5\K� } \�� An!�cha�; Loadlock:Sa���t�utry 0 �UA�p�a Ra�6pin< travel  90��g6dXYZ $\theta$ Omniax$^{TM}$��i�no� Fon27 5AF%JI%' s��_&�ze�(X-ray sourc�SEY/SEM��gun �$MicrofocusebSpuCY:To���& gauc���RGA P8To vacuum pumps G!�valveB �e]1 �y I\��osʃf� coupb}s�T$[steel�N O �(UHV)QB.����i"�N�10$C� Torrcl�ietm�bIS%q : 9}$ 9 ~an��"l�pA�"9FA�s�rdividual� crewa�o� tE�,��Jed�hR��K�:��!5~�Yc�Y��82���t��]�\in 8J2'%��jbǏa!yd)zs�8!�v�h2^arm��e�M�~�Vr��w��to bak��ju,� !�*�K{recP%lPuL]t��C�KrmoIh�x �� }H�p�~��heaBklM bom��A)�Acsͤ qbia��aLg�� fila1 ne��l�W6bic � uisWSEY2�i�LA�e�gjj�}elctrq C�k2 :20�x!��dauhe�l�'-> rId� a��� byun�de)Hd&Y�tW��E ��ry* Er@�is�mo�h!YeI!_�Ae: a%aD� tage lyE an�meb0c��A� n se�oM�! g�� ���ůog DigiQ�Co�L(ADC). M�s� made�ca Keith�x 6487�r�=J�N picok�N  !O nal E�%( $\pm$505~V څ�IEEE-488 1 face)"h� ܿfil] mode�ich � turna�ffIIR}�s.e��gr k tim�P�vc�1}�dAis >z$\mu$Ri�S!��� mum �u D��U' 0A�S��i�d �s hund���s;;mea� �]dard dev�{ �re �Y�=i-�1�Fxaa(l $) defmX՝s dAJmi!=A� eC� ion~enequ/}. In p2i�>* SEY}A��P beca��ilPn��s~ I�e=d dir�U�� &H �O!s&� 62� � �d�� "d�N��\ of\q=ns\8^r \!�\� }2.�8&5 2��V�36L b�1 -\f-�I_T}{I_P.�!rz}��W�S I$_P/`A��� Q�( le%$)&� �9 im�a,���Vs�qM��� $_T$q?�dm�dF��d ($I_T~=~I_P~+~I_S$). I$_S�JC T��c�M S��y�Yra�a��2\%E�s�on{�f 130~eV� n B�/�aqof Al&s&��HiseA6�)��&c"�s-dse�TTAcm-�of 99\�"p�is �AmZwof(\%�70.5\%%Wa!��v����impur?�� Tmanganese, zinc, silic nd iro�k����98. �, 0.45�of Mg,��0.�6\%Si. O\Z���Al)$� also.��� ��c%Z� ��G7GlyT\�or UHVi , but� delibe0ly�s�%�nda6n kep%�a dry n^�4gen purged box2�I��`emp��tD�&% -Eå(AlN)2~ m� � ]p !2�a�a� SEY, 1/Ilš to 200$^)$CX�hot;���blownA�it�j����encoura�1 (too�.� ), s/d ��O�?cra.��hr ai��a&� (carbide too�S;O �]!� . XPSA fiX ) <quite u)�w�2�Two!VAl-VMJA� #���uenb��W�� s Al~Ja�is,�# lso 6 bh] �!�"� ���Ge�/ Mdc: J� R,:� ���f LER~ � BU�^ Gl�na pie&�Za%u� LowUR� (LER"� d A�Al%D ^ J�az%�?�nd �G� !�for�� !,s�J�!�LER�^ eler�j:\�~ �psa� B LAC B-fac��� ��"��Y/ ١�\!�q""�� �!a�:�ymn��c�� /�f͛6�$���edU.�SEYal�$} !C� fivsSAl� a!NLCRrƀa �ea��g�A~ �X�_����!���>s e�J��!� !@��a"E��a"�%&�)U� �D23���  normal� � Du�=�"��H!U  r�lto 2.� 9}$~H equiD�$ N$_2$, duJ  stimT� esor� (ESD�h�.���doE%��disM 5 �10 �%B ��f ESD{Al!�Hst��+7U�ӌ"R�Ding:8��*x 9E�� 1000\ C/mm$^!�!�M26� g��d�eaۣm��RHuwe>seE Fre�,eems ���� off,�sa<6}2R2�� v�:c^ss,>H}+�Ynext poi`tt 352:��]�����hů, h� an �~�� _{ܙ6��0 �r�� c�uo�*|A�ly� de �s�� rrA�check��v_��)��ki!��am|=5~�X�c"�)wa" llec@ :�twoloc�s�_�5��u�^we�}2�V1E��er �.�To؍Rm�G :> �pmely� � Ad NEG.&V"� u�er !re-7߫:Yne+�A�, espe[�_baka'��a\��%�V6@ى��Aa��`�qI8� E� ru2�xӗ���roble[6�!����f6�9ba�af� 40~m�% .X �,rA^2.1����S�j�ji��td((hed s�EN,�21�I�,U hast���~ 2t�z�� ��3Q,��f���,.�al~E!2r&!E�sq9�A�sera��!P6��A��$N >o?�����~y��)ha �sim$ 8FP:C�A�V� �, �,lot֤����SEY��s � smoothd�^|A��� max -2� 20106 �Om1ofA� 3. St ��2��c�%3 inp&y good�*����� �}2:�I-�) )�S��)|3J�7B ��1�G:�ha��ve been also measured twice, Fig.\ref{figSEYal6063angles} right plot as an example, and were found to agree within 1.5\%. The SEY at those subsequent doses are less than the one obtained at 2000~$\mu$C/mm$^2$,>�vsMAl}�B�curves},���. This jump is currently not understood. \subsection{Secondary Electron Yield of the LER Al 6063} The SEY results obtained by exposing the LER Al 6063 sample to an electron conditioning beam of 130~eV kinetic energy are presented in Fig.�e LER24. %\medskip A�4served for the! 1100%� 60�craped sEDs, SEY o9? 8 decreases with) in ing !�, until reacha 4of $\sim$ 800~�7: 5 , lefte. Afte�is point�� ��butEGsmoothlyBd6�Fx2)g On_ sEv �!Rdo!,^;%Z evoluA� -`�\changes drastically fromWas-U shapes!� valuesJ�.J. a�T$\delta_{max}$ shifts bbe!�%�,ed at 160~eV�6� XPSs�yAl��spectra%0��edA�.  one anI���clarityiT"Al �'"S(is located � e top�..�,�\�"27880 2�"AUitsm�. .vQ4 "as.���!h%%n"� 0ing, a few ob�e)�eeD can be done. Firs�valli\ "as .���D ontamin!A�,fluorine (F))< , was g passiv/and( thoroughlyљ. We mu�� ssumA6 at t�Fvp� Q�airM�'ts!� y quickly��La pure Al surface, h�2 gettA[imbeddedR4oxide layer. F � comp��a�ea� d heavily8 semi!su�� induE�4to prepare sil", wafers. OurIBion�i�Xr%����I. �l!`Dyinitial2�E,F1s (685~eV)5 disappear:�XPS%�(}. However,!8eakA�nitroge�n ANb398b,>�azote}�It�possibl)�q��battemp�.� ta� AlN film�ro�!* of NE=absorb9�bul�a��. --!�i?e "M�" ed-up"�sESDEV��mobilit�&N2enhancede# nce diffu� q�_or near V I�0(1-5 nm depthe* is N�ce$ �," very sme�2~at\%�unlikelH hav, flu��` behaa�r!-�& _ re��SEY6oA�ve��>���.^e� high-� res� � �w�� c$characteri�  of a��n���|a� (&%a.) %, aQtrate. V� � � /- alloyѐ!^be�in( :� � e� %uA� re �atives!�!!Q�(E� BE)�� ized!u(76& $BE). Moreo�jmH.DX��� �, Qrel}$ intensiti� eaks!i��( .]e�9I� �)&K�te�a�� �mn(7a.).Ց� w .]we hyp\ siz��� thicke��%)�� k� by d�>. mon %Aedi t)" sidual ga� , by!rrang��% bondE& mI�oxy��displaceE�� c!�C�6=i!�rpret��e�iAl�*s�e7 z ��raB� WC� CA.B�T!��~ 287�R,�h! #��29�Ris ��:� (A�is re�s��|-}*� $by HF acid��� s a �k89A� >Y CF$_2$ \ ��� ��.�2jHA�  accumul�� � of 8506� )�F!����AIwe sa����),��28�,2mAye� C1s.� .l l% onlyy s cCurtoward 2�  (marke�\an amorphous/graphitic CQ�)9�Ak A}�y rosirowA�� C!� transform��ane��st� to� N�9A�\��*UofA�U>BNto�8�%J�M}!�uxv(:�:f(��m���EF,7z,2. �,a!�,2t*,��-"12817 :0X �BE axis!�&�������� -!�t[or % Bg2;Ab�i:� ?� :�0.2�6B* WA �t"� ��%7��q�C� 9 r�du�"f bombard i�)�umi�r�� sen%he�6� �� 5~nF�J �BL�E;�e ��L ; �cac�an�wpa�ngU�>X betwj�!�s, te�I^�#A^F�� Ibi ]D)aa�y technical[� �� o)effecŤa runTaccele< beam� sA�� �r� BEi����A�!i " ��Al' before{�sa��`*H "+ _It does� (t��R� 2�0ure metal and�� var!���e&� � XPS -} �R>+���ffac away s7 �no� 2��O c�(significant�pua@of Mg�^E� �li���)�*t �AZT . It�inuousm�{I� !��� �1� !L130�� BEB�:Q�smn�^] }er ��b&emonito�byme!f�30� %�30�0 BE KLL AugerEUsBMg!5 }. AI~Mg�l )�tkM�N� uE�at y,V.;� s pictA�E vera��ny=Mg CAsami0}E �.I � eM� �aG6>!R=)��2zAnEI�um; a pieAf�vacuucambmadE�Al !O,%��N�iJRq�e any){e��)J!�:%3}c vdkep���!Dmany y��built�Uck natur�4!Mg%sec0obably Mg(OH)| � 2�Allm<ub�e�s� �prece�"� s,�l�L @ �at,��2� Ay�Se� gr� m��m�2��C�a�5�!)AZ (V vxB�WC!�}�B�U""�PAl ��>O "� �:�wo�� �� �sam&��� J^ 6w!�"M�1�Of� j8!/�f &R.�B�LER� =�c �c c �>` 6'"` !�d`  �e��waayno2YASt ek#*� ��M�X́/"-�r �r��,E�ex�,�n��ce of&� " M� ~. 2hiP2pmIaQN���com��?kA���AY�QaY��! 7����no*{&�)G� �,;� ~eR�9��V 9�b;� �could b!�e���ͥe.s s ".:� A*m ] �\, hZ%)��2E 9}, fF5.x� Al��3$%A`. N!W��NexplaU� !�� er (%} ) BE6�!���1��i� � -�i�w%� i* �(nd broadensA�is A9iaFgŹE"�rea�� �"�� E�6�A~m@�LERa��\�!���BWCFl&XPч!eir�B8*���͹A�e%�� ��k$ .�inn' more &R�� �4���� IC)�at���B� due �Xi�i FM!�no6���LER!k!� �dv ��%Q#C >���� } �ing. O��iE� hydreP K a� xid� �mv-�Aq yE�AIeh ):3} �g !�!� �B�[�i�&;atAoE�QoL�^e��F� Vg%@Z 1+%R��fu am��%�D (CY)M beM�t,TA�Xis��A�a� iv3!t�<�1rV"��iQd in 0BuckleyM 3}e��3Ii�i�t�!ec�toeNin �i��2$%gwater26t,Mg KL$_{23}$ exhib�aM�in�za|^ in func�!:��xB*WMg���&�"�-ɬ��$ Vb8 &rjK*,��.� ��"�) �)"&"�%4+��mi^i�i< ies �jmaliYMg2J$e���I�a�Im�d-M��BE (54�!%�s��]"�(5N)�]V� 0. Even, if MgA3$��t � �(BE : X��:�)%t��canbe �o��s�%alo�$IneaShenl par6!�q �� of sna�*�=DsA�"�H.�$iR�su�112516 YT�, e�B��y�� we fe��Mv�A Ne� %�ed !�A�1�A1is impl!_�2��R�ge up )am>�a�\�EL 1{dipA�!>SEYt} ? :"� �FJ;&�on1 � air�a "�xce!,�1",�&{"� .�-�#process - s upe%modif)<e��E�ʹM�(. Unpolymer * �d��"kn�"toomo�$W%)�0Halbritter:84.&%J�$6d g. down6� SEYv2� �c�o�#remova�u���'d�s �AXR,�,!�!�sum� 5�-%�(9�xF� (lowd g"�)A . At,�/)�a1�3 trib�/�� vail���M��ye3" or aN d!� perl�a�F@A�-� �. P� �� �|!1� 1A�a� �starts�z& |( rais1yS>}%@ mode�\21 M!rs8.�sva 3~keV����,�.an evapV-e� Asn2��4�#I�benkaX2}>[Th�2,��lAlKLŵ "a!, �%pi�depend�--g� ���-�+v� t:�3.`For�lt--!��o�bpp�$ecat-c )� (Cu$R&) P!����!��Cu �crc1-Bojko!?0:Q&Fin�2,� ��A0 much�=er�k�#��Wu�� a �AY� �x), llowA|<1"� �+��*�a�at��� buil< ) >��#/er� e� �kee�3�} A2:�/��ch3vx0s"�2E�9,of2�(�)=|.&4+�us$me4isma�%ک%of�A{volves�us� of atomicQ�th�,�a=%RO�� !�^7ly"�Z&�1�&�rus%A �&-limi�,(l bpth, via�Mott-Yrera ����mA�N2�Concl/ } W}ve rez+&�m�6gJQ�  13�,I�r�"��X��3� ,�F,�#� z-��4.�I��bA�a pC z*�eem���-saF�� dose�Zy �4l�e 8���z p'�W e�D[�6�+�*a *�3ofe�X�$ n4,2�.. High[�1��!.�owta_�e y�9ri�7��a�5� experi\,.�7 �)z)��"�  h�+ ��1p g"�-��s���2�Iframewor�aUQg clou�� bleme= choicF�!�b�/as�?�mb�X� ,lear. Non-coM& , or)� wise�9re %Yf]^� bad ideaM1w �ed�� mh<��go!siste�;bE 2. H0T�&� , i14�ew hund,eVU ����UR�6�,�o7 �in� nd���J Ŗ�.& Ac ledg0 s}�3wR &!h�,ks G. Collet��r  helpiZ!�u� n0�I{\e� R`N.~�7 �(usefu1m=�<\begin{thebiblio� y}{1�4\b�em�, David~R. Li6ed��K0block {\em {H$.!�C"���Physics}̀ 5 74$^{th}$Q`a�( Monochroma�.9)_a:ZVol�91 -� El�vAL�=ve� es}.e<Intern_ al�� Inc.)�2�6� Y.~XiICP.M.A  2����A| -V :6je3 \ $on Fiber q�6�E.�(}, 6:650E?4.?2� A.N. 2�Threshol�&�'-da<OxiI �A foilJ���!s%^face Amܡ@ 5:92J�6� {J. 6}OnA�{46���by�honn�)Tunne� Ad�9atNX�/deɱnass^2k��C�(Dby 3 MeV He$^{2+}$%m3 2�impacJΫBe3:638a$2002�53} {O. B�& 5 :�"�"� �.tud(.byN&126J��Qr��$}, 525:207�k2�* {I.~,.� 8, C.~Scheuerlei:oI�:�@!�A�a3mal t��aա�� :�J�F�Q��� 18(3ɽ�]endB�  \qzE� 0figure}[tbph]�5er} \i�de� Hics[width=0.75\text(,clip=]{SEY� (setup.eps} �Mca� �ern al .} \label�sketch  A � ���V�_elctrq0Euitr�� ic^EuiJu��:�Q�i�.�2vr�1�-[htbp] \)bingj�R�_"�ing_alu �1�:E��&�2Mje primary&�# impi9�#3�F��b�%dD ce} Y 8Mu!+rz�6RvsDoseJ�max v�"� �"I ��a���< � ,Qd� vzn�>_3mC_8�:"! � !���, �*V5s,� &%!"69352:79.SEYtwoE���� ��}[t]{.5\�B��}�?8V1�# _780-�wk%1��}N}�7N .����!�  are �<to5ly ;N��"�M�2. �).right)L:�al�V�.�1P:���b�A�Q,incdcSEY_201����6���!�i�!Sa��oZ �n8a��n��JoLER_A&A*[B�?:o&8:�:�Q:`���~&_�P1-�f�f2}ZN~�e.�~i, f�I� -�.� . VaQ 2W��. DetailAA'�80-1� �ssF�1����^�2Nn�RnR.�2��2�����D.)�ed���S����9RA _NH_200�4:�b�Q�."�ueE _ <* ref.y"[:�00}:�1R��R�8F�FullXPS_�(_AlM���.�I/  ���%*[ "A"�>cri�8dn&es*<:. TopN%::e)�4;b5"2 xis:w�Q"O6w)&� w).[*����Y8u@2pq 1�2$:�A:�����JF����)��1d7J��C>�.� �J���ey :�6�� �er�:�h@'\ =V� ��� 6�55��6��n�n9�:J "N_J5f� Y�Ra�-eF�jn�:�A��u:r~�.�6e6�&UE:�j�����A:�M�.�-N�A KL>{3Mg]0(�Aa3/B���n� �>�n��C1s��r�2�� Z�CA1>�.�>���r�� :�6�� ( �)����j���2:���2��?^�V:���!n-m-l:�WAl |n�>0�a t:*E�a�~�$:�>�"�<����MgKLL��:�����*E8:  docu�"( �G% Copy�D2006 Sanjoy Mahaja�^d ;(0 Hogg. Licen�u_e%�� % OSL 3.0 @ �$class[prb,?1 pacs keys,l�'tpaper]{revtex4} \usepackage{dc�!(n}% Align t�a dec�8�2 %W*'t ge�6�.o �+�-as (tr to s�NKN horr�Ybor[f ) % �\[hypertex,colorlinks,pdf .=0 0 0]{%ref!�font\sc=cmcsc10 \def\unit#1{\,\hbox{#1}} m{{mccs $s$N Nkg kg,mps{\m\s^{-12x{\tim��rhoair{_{\rm�6+rhoball8ISBN{{\sc isbn}! YQ  title{Int�>)p�*:r#new scho�Uicism5au~]{6�} \affil�&{�* D�\�&, Uni�I[$Cambridge, t CB3 0HE, England} \email{se7D@mrao.cam.ac.uk} �iDW.~aG��New Y.�,, NY �a03, USA�d�+0.hogg@nyu.edu� date{29 M )a� } %*�-arxiv�2A�eLieLe \a�({01.40.G-, -d Uhe bal�.i.�"th^K5K. �&or�f1Y�:�i���th�/%unIG�"e�dn�f Sh�/��a !9� ) s�.?��Y \make�_*�/#+prr1.3You WiJ8jya��an�5 cs. 9w&l$�,to�! �= yday�er!*(to develop � gtu�_. Fj occa%�youe�a[ who��ph{�M}�G _7�0s0�s�a1 l"�f.!Ze �?&4s sAU ;�0 >��$vJn drag�, \2{7th ed., �8 1, John Wiley,!Z5, � X} 0-471-42959-7}& 3.4\,)�lb5�8US\$}93.95& \3{��,��(26 (tennis) $8 (soccer)�O+7 (base�J0)}\\ \4 % \1{9$, ==��(K.~S.~Krane)31#ASUMdescribGV!��C8$n a basketv$ or a skyd � &�f�|o $v$t �Q�6-V (p. 72)!}! 2{5)Y\fY2>Y32057-9)Y& %C=D.~C.~G�Uoli �*-c�d�+tists!E�' eers �3rd>�P�PaZA6%�0.�(13-021518-X� 1& 102.67%�@3--22 (skiing), 3�- (!p!G-�3--82Z� A.~FA�4x \&\ M.~Jacks� �'�.g$=d��Calculu�iUA�Addem WesQ��h 0-201-47396-8}& 2.6& 73.00�4--21"5=4Q~ A$P.~A.~Tipl'V�m�AF.{�>|4I .f0W.~H.~Freeman�.999|(1-57259-491�3�84qS!U86U�vComplet�K�Q)"}�K.~Cum�B� �;�5j is unw'Dt�ut �:s_Oplify� caAd� 'e� 131)�4�49��D37099-1}& 6.4& 1381�5--8 (Z ), 5--152,>5--236��(P.~M.~Fishb��S.~G.~G rowicz�,S.~T.~ThorntuW-�A� �22�� Moder">8>GPearsonJE22�E35299-3%7& 160qw3--44= �3--71-,q�A�n:\Fnca� �App9\H= �6q�F�B�D60620-0}& 5.2& 146:�foo�� 9ǥ6.��� 3--6!�4.�R.~D.~Kn% v�b���: A S<`gic!roach-�%--�&2� 8053-8685�y9.92�6--����6--38�:�A.~Serwa��,.~Jewett Jr.�r5�ofQ� : A ��-Based  ��� Brooks/Co�{3, &�0��7157-6E~0!�a��&\ \ �jkBN' $back (no Au P *�3A�2�%A�5Z�J.�2� m� �2n��qf F�2� 13-101416�}5egY���6*m i qb, 3=�42m�� 4.>A� 4--4��.�HE�Young��R�7��d���JZ \ �.pQ�- 11q�M�.�9 0U�4-�7���j.2�$, 3.17 (fl�(gun 9 &~ m�.855: �*$ :G &*k*1M*� VA s---Ez explh��world---�D�3 �s�C"�q!�alm��i�- drop&vxH�h�p_enddItu� B>�a#� 3  'her2 "��O��3\epreal} ?��careful -��: irre���. �?r� Y&��curFz��=jowe   parr{eq��regurgi�^� paran5��K J�u�ubl) �!�~5 S�Q�b�&�rnx �JheIX(easily memo�N `s{' �alaH�NA�� bola;rot5cos answL�K9 ,P firm�%E-� means�disembod matheal�Q!5OI`nt1: : 0;:�: o@u� isEG:k t�7%�i.|. � "�A�v�[ny Qv�6� justif�!�un[ined:� theyHF�Eexten�tst�5s=Ei�T$ pull�!�=Elike �, icle!A2�)AabsolE� �[g�xng �p��"Xanow!o�in den-. % .Tbritan�* .com/eb/a�xWs� m < 50 g �Jl@diame�\sim 4 c�k"RDla�fVYouE{<ist. beg�qny soo'�5askAB�-w�wq�AHches � Q~A�!�approxiAx ons B . S�zaa�fl� � e��,��%ost� 9�GeN��denx&ssp�Larg�Z� yveloc3F{ hit�NswD$L$ (say, $250\m$)�ou#ye 1!"^& eqn:gL} v!� \sqrt{gL} (10�s\xO)^{1/2 _p�C��S %�check� y7!�s6ng���a�orce, ab�{$0.5\Nno� *W$f$ (�� 6�). By *�zsUIgain,Ff�D Av^2,�s�$"$!L!�da�t�i�AC$A}s-�TA�re"�)A4�l�&e �is�2]p uf�� � turbuM~edd��E(u��� 0$gob�S visco v�!o�`ce� ifficult,�WnotV"PaMRa`�fc��S� 9� . W3l�)�Le���on? �6%u%�8sim1\kg\m^{-3}$-r 10\ɂ,k)TEK isF�A��-e}I i\x^\x(I�)^2z 2A�. :Si!GA&J�!_m�U����O5~ ^L!} So�ire�) origR.vof_cA�nu�V� �m ���tr y (easy ,spreadsheetsedu�+����Esa�An early*HyCRuach� e��a6�� 4"�aA�� must�k hit �Rfas�j8)�$�&,Q�FaXtL�beFA�ze w%no%3i3*�R%Hise larg&c^e" in (Fh)�ltu ���V� 1.25so Ibiggwe��, %�zce cd =q 2�}ly (p� ^crisis~F���}���|,!� �provi vw��[)L�erawng t eoaq to JD:F�{\hbox{�e�}\over JC}�� 2#�BA v^23 mg�A end{� If $d��"��>U�e�n� R is $��d,a� � pm�X�j��$d^3$. Fu�umoc�-k�V�C�] gL$,^%�!m�K]� gL}). So,03 diviI�e�mo>]or�$g$J@�OE@�G��Ld1�. F�F den�!or is)K>�"�@Y��ator?��$u%�1BA��PA&e�5� sweep{Rt%�XVz�%� \x)3 psw�m out}B�� �� s���� o�7}7%�E� irR.�,5:}F�o��� lishu�quo AXbf: ! .�qimg!K-� aE � gtoa�elf�a�m %qaabove,�#b say "o �gqr"�j� a�(*i*�L*:Disb#b�[ed il�$h4jA  %A  en� $. False! �Tev}� }), �AM E%A�����e�e[5m���R�LAށ�}\x{L db�� ̡(� } $: G6"Ksu�flo(����so / % <3*2 �zlengthg m�J�M{� � 4\cm 6000J�ere $d5*�Ra typp E�-�9��$L0d1��rK_ A�&K���#�n-�a�%�� R �Zio�[~6Q�ech`1E) of~5"`=�MA�5y �9�u�+&< V��U---a q.�NargaQ؉V9'u1 }��^&t# ---u neit$adv%d�3�r �&u"� ncepBYe$(�ophE��Wgl� �a g�^al�{i � n�|�B�'�K��`\&he��ʆ6��it!�� ^ ist'&ec��tools:���!�"k a&�E$�-v TYaqL_ no}� rEEo�Yex�*,Why not? Noa �^u s fi�Lt F&2W�ppCds�A�i4�:&�%hfamiliar��o s�^�s�  fail+no`�� ��M.$. Perhaps��'&)� in:�*.�U�<�p�ar�{�#XO�m!7 @ in T�YV '@i�)a� gle ��(KL (o"gtP)�averag%Y�\$152%]At A� 6.8~3j!^WJC�)% teach ,�c"# �"sk&� to bu�\e�\exq0�' �fi� w�bogusM�U��U~�ed ph� ena�*fg =�h pQE%n$ �`�!; ntar�as�use%��n� �Oaxat in��al�(�sho'cD$4o_w$ se4�, \ehill ��AB�R6�!��Za���`rK�re�TIB�s�)� � � des � )�x�zt.} G&s>� Tly:_Mh�rT#C#�--I:\�Mac�!KaX[pp.~180--188]{Chabay-SinY}AnQ� 5.3�*@sU �@l,�t�he*�)�j%e�_E�� �n6n�e �0s o )a`aN�!!� surp: ngly�---K a�A?f 2!' �-���n �� T4 ���Gg alti� (Denver)�� <at sea l�,�i��ok�!com�one0�n�9i?!m V tism�@ 0�Titus,�B !�6} �l��`feIlI��- to returnU�u .M��+3{�Y�}� oftmE,eF�A��. �in�93perpe_0� al+V�(0 ion:I�A�)a�  $vO  f"\Warburt�'nd WangI�{-!A4Cp�UAhA-v��c saq: `e�O%����� S�-Ã:�\dots'!I�2ve�1 p���� of u����sƆ���6>,� har�. rolewa�e�OiV (SM)%Pmk�`��fDf ���AS-e4ol%%uS� SwrkB%�� a��Taylor��{ i8)$J� @f = c_1v + c_2v^2 3v^3 + \c!9B�F�yusfp��cͩ� n x\a�,x x - x^3/3+ R $, �m�4c�\�ermi� hst� 8 $vZ�L�3 $���e�2R�erm� �B� f\g*$to v\qquad�( �ily)}.&!ygentlI'�4E{ e�8  flaw!t����.�aP *5�u�,�Y homa�Z3}巕��of��ertd news6'~viii) `E��3�� �romisrfurcie� -yf&�, goalA�a��Jt�m�6�#͊�3ZZ%�sciencsmL8(y.' Sadly� V �n FeZO�8 Di�> al E"? (A Ibl�ion %X*�3reI�)� Q�I�n$subhead `R"�5�WW e,�n( ~534�TA?T�er rnsuH*()c~_O)akensQ��2,e�d ����m�"�2ɁcxvAf�,d!�r coast�x;:A�or!: �!R >'ݕDi- sau)� # move� he ��for�rprogresN ��E�� i�t pF2�P=<A�" F�! a�Reynold�beRI{:Re� {vl�\nu},:���$\nu1.5�5}+�:$E�#"inr! ",eir�$$l� "� bj�l�rr)�]}y $2\m$. Ax�sp~of $v�[��� > \x2\�Z�)%3�6>�Drag swi' f��\(t)Aa�/(Stokes)�|��7�6�?t ay $2�3� ee T�q on's� el�"f"� ' 3�\4]{ .:1988})� occur9�� falls*� $ $10^6$ so���%l%{%�1�iE�lcer�O�J� �6op! DigsQA-h�� deep�.� ��"ph9��536): і} E %8�EC192-lb �[sk��G$k$�a [$F_%\��}=kv$]h� ,1/3 slug/sec� ,$m=192/32 = !lu�8How long��it��r!�e�I11 ftT(7.5 mphE? Q far � ) H Eb�n倅���E/��? e�=L�7"�� obsc �uniqN5s���e�Y7d�7.��4>�inser�dleged�P��to%�k� N�rula~% *�@&55 /gp/�?\/0472065211/ref=sib_rdr_ %h1_1/002-7802204-6494420?%5F�[D=UTF8&p=S003&ns=1# W-�W:L:de�?jl� � �� !a�!=I(�z[�0]{Baudrillard�|5�F&b As may�ce# to ig�3{ inn�}aen "�;�e harm �!a"B�9<ak�)*�cS#s��*�$��v�&!by��ss�%R �b�(�l{ G� w!�,ll �in�l�~S �'"� ies �$�� ��,��4�]&Jor bb�(�ytos� � q�h�to u��olid,se q E�� few �&N j�*� ba�df��O�6 ��' (AO$is �*a�9V��#*�"x a�& t<u,>M=n n�-� E " � X�re&�Ej �(|���}sm+V >alItI%D� % tellf� �� I�"&?j� 6 A�*�;=���.i�o lear Sor "�*� >�)b�E+Awhύ��2�ful�� � �!�,���2�)0ic�E�&ds&� pn�"ur JBh�.����-=vt %�.� ��onshipA�B����M**�` �'�� as �yte��|S>'�A�aS medie�y�uis&� Aˡ6angel�)\�<��aJ�o8thank Mike Blan4�CGoodsIe, Bruce"`ge ,Aimee Terosk�q@5.�o%�d 6o�=B��&�o {polu��B�d"�G�8%=�  % % B$SPROCL.TEX(27-Feb-1995JGF�RxW|w: ,*.� o�Gk5A㡫A[G4��J!QB��ce|�s [i,rst�~�'G8by Susan Hezlet�:p��Lukas N� �"GS��7wga|��[�IC* l:7>% ��-� \Qstyle[s�},l,epsfig]{arq-(} %\input{}6T;{unsrt}�% < BibTeX - sorted&��Aels!O�H�7b%J[cI0A� � A!�aBf�A(@ 8#1#2#3#4{{#1} {3!,#2}, #3 (#4)�)��rjImnames JNCA�gNuovo C�%to�@NIM cl.p. p%A{n' A*PB.)�- .} B PL  Lett.} RLe Rev# �PRD \ } D EPJ  Eur. "J.} C _GE�)b�(qdTO j st{\>pIR cs�XE4 8mco{\multicolum�-Hdef\epp{\epsilon^{\zee} 3vep{\var   ra{\�Aarrow  ppg{\pi^+-\gamma vp{EpWko{K^0 kb{\bar al{\alphAa #  &be{�A"A ee{�v>bea3narray3a46CP�� CP}\h3B0-1.80em{/}}}% �Ut~��^-no L)�(epem{e^+e^-�h%�N�v 3@BEGINNING OF TEXTj6 3�%���б�,tiL }}\\ I LCWS[: 4, P�g�?($-$23 Aprila��( \vspace{5m�M~Ks{ �:� novel�we�"c ru�(algorithm, R*" � 4&� �OC� 4tile hadron caU8X  (!�i2per# ed. @ B*�,wo close-by hSN��  s��o*ÁnS ns:N� d � .�.seCz&��� . }�2 "^I? �s ��t�i. e4 fu��l%� $�1l�Ier�lJbe���� f�}cV~�{p} aim�t r6�of=ry#"M�nnt. CC j-v %< �k9� � :aA2�cap1��Qe�7 0{�nd D5� ��$C�dio�ddR�ha�eʀ�a y��(!�ձ%!]L#av�n"�U1$�S $1 c � >F��!�}a Vm��Nic{,o��-ofa�aiV1steel�x��&ˎr���scint�D �s.�For��a���)e�5n!�T�&"�&:!}�+�9�>�pFar!u�K{|c�KA C�D& T2� & Num�ofhicknxof&&\\  & Kl��s&9(#acJ�KkK ECAL8& W/Si 40& $\ph�@m{0}$1-30 : 1.4mmX0.5 j�& 31-4?4.26 �\\����Fe/Scit.�20I& �Rb6x@p"�dParQ%of.�O�staM&Rle}���=t vP�Yz2�����Pid�&rMGEANT3 �X�% }Qx�icI�!�9T�$M�MFLUKA @ }�) e�(�,gy neu�i�[( code MICAP G �� S�Mo���r"��́F%�� z%e�derA>�8, 3�D3�55�S <�+�o� �����s�{�" ��� adja!�i s joi�#>pth��6�QA�06�T�i<)�1�a�e���SedZ� �ed\e� ad�Bag�.��2>d������ {Clu,8gB�d�M�ec%s]�>( �, ��def7A�t�A�g- B��"mU���� h�cx Lg , e.g.T��&A�ck�oAzby�ޅi�V�s,�Ft�G��S�2r4:eE���o�"U!h- ՘d�sM��FKy��vic!E�nu�x �i��@s� �A3t#?vie�(a�groupa= topo�ly a=�/�-[. 9�9@s� !�hit ]0���Mg"� +� !e+hit�t O depb= gJer an5��MIP�4-d \"& 1.7 s are as edL|soA�led "`Y k--like" �0gory. H� xtrem�  2e>�ex� 3.5 Z:��-c< ,�y�!w�icEu� .F!�vi�XF� � Ew .:�2a_Ed� eA�MI-2"( V��9��l!��Oiq%gur� fig:�}�"![�x\M8�u�I  on���gn,Xu| � F%�U`= vX�%1�a�Bi!V�unt!B#sE�,.���^y��er�$imW--"H��E��inA����H/m��:i \E.�A!.t@c��*d,�Cafd�4i�>�^� ���+ �T�& ":�Q/ 6^^*.�%F�.ۧad^Va�/1�y!��ed� di �T�[a�Aj spaZ�ly �o��E�[ =-�k!m^� �*i��b"�sΖA���% ��: "��ou4�;SO3r!�Y�ylt�p �A(� otal�y/oke�(4 q���mIE�2!�i�) ), i�?�!�c�d�2},^/�AN�%�:�9cl��F�:>QMɓsc(.g��F>had_em  *��G��&�a�a 10 GeVR i^+��af�Ldeqd99r�]!�5� šs��~by DREAM�\ion� }A�A~e�Rin7�29ecorr[��@ �7o.8M(�<͹vG�w�@AvofYR:o�0IW+A)z�48a4ori�@led �$\)C�~ �. in"|!�o����$n-BayesianE^>�)�am� ly�deg����!�m �v4�dr�Y�sA F�r!�*an�aL3ach�bl��&.�.�"�r"�&�|c]{0.4*vjF�*[w �99&�r]W1:�gHiB�U �-�7@��0�� �0*Hs}  $Z5���w�sC=�1�:�E���:�y�K^0_Sq�6 �>F-�*�S�(R2A} Oy�`axis&�Ȳ� ��6���&����ee"A�^a�^�*� byLa*� �� . "Nc�l��W# JBa$m��a~�a���)if�ir�nto8 !4v!&� � cu�#r�0, $D_{cut}$. -l8� � tDf��8�� �5K��sb�"�8 Sa� inertia t�i!\soc Q V� &!dB� �B-J/w�!- T �" 7m�N*nt]ned�' ..�D,� Pi��F�$)e 5d!�ad%4 te} Tt�1Kn-:f��%�gF�v�&q.��7b%!^Co&/pa9�%9. T�?�J��� �#S.1!p3�Nm�[f�*M} � *{-1�\J  9p��j�3��2B��H:1/�;E�(uМ�) a�E (<1 ��%���Z�� 2�.�nFU��[Ż04ٓ�2G%-{-5.5cm�G� er�4-p1`Two:cI�h= 5� �L$%_ �. �t� 8.,�m�?&9��A,ellipsoids. �`�YiIl{�a�H�6�� �1�5 ��5��M�ݘ�P SI_*��6! :M�o�ɉ.6� L�2ACw/x�� r=� )��e} ?!,1��7cm]�&c�?gI�HV�>H!3 ��, *d�F��(c"� �9Z �� B)��64.ab�V!rGAI#by$Ϫ3n. P�"%$is qu?1f� termX1..�qua-� I��o�!�in�hP.MIP, a>O16�u-L$E_{true}\pm 3\sigma.<�7 9,fe�7$ >�+n:al.��)�*��ãa��hih�#�9i  oth uA*�#v�!�A90demz a�CJ� �t���&�#a�/�D"� �"_A�*�?�"��method� ��͑spa�B s �T�carNA� a di�[�>�YR &�uRPC ykn_j&>�5j *����5:�D2 ��6�Y� the :�� EnS��2�&f:�. ��%?���oE*&.t�&~c (das�nd dot��I��ms,!�m�: �Plid!�,8 ��f�a �� "��Aڝ�2�. 2� �g+ A�6"e � 2� ���*6:*&� m�a� 'n �S��"�!߱S�(�-3!���!�aV&j?2�' ./27 �FjZ� *{RQ�.^ t>�99!�ibi��'{ H. V��u, *"E%� F��"� "���1*8*;}!(V. MorgunovJ"#ry%� .bCO(X talk�#at CALOR7*2&M�, pubWQWn "PasM�a(, &�#�n�:/$ics" 70-84>�J�0EM�.- Jet E=��9M�86�"*Highly G&�&)&5er �\SNOWMASS-2001-E3041, Jun�T1. 5pp, eConf C010630: $0 =�e&�{ T.Behnke, S.Bertolucci, R.-D. H2�  SettlA� �ySuper܉uc�B�-Pron>�+�&an 1,{Yd i�Laser &��.F$'R$', A` IV : A/��'�l�, DESY� -011E� ECFA 209 (! )..N#{  �)� 3.21O ; R.Brun,@�Ca�a ati,a�P!Aam Libr Le=DWriteup 1993 W50132t�#${ A. FassoIS[p}m "A+ Code:ci6 �h"�i And F�+ D Iop�sE5Q,303241:MOMT0u-2003;\\ �#a� manu�r�uail at.�< fluka.org.>${ J. O.�ps*Hnd T. A. Gabriel, �1(A User's Gu��oS$!�Monte!_ lo Ioniz\Chb� u� P�}L"}} ORNL/TM-10340 (J�ry ?@)-"��{ R.Wp Y ��DExp�,al�u3;!�n\!W\\b42a.K\\ *;>(pg.infn.it/�#2004/mCHam/pres/wednesday\_noon/w � .pdf.�&h { GJ�v�"nolakisMP�c er CI' �gMin S TreeED>iU�(CALICE MeetN�June 29AW 4, 2���Dwww.in2p3.fr/flc/g& al-m JP/cern-june04/SOFT/G-M2���>���&�1 �j"�6�"[pra,two~4,@ p�fVUfix*�2�ams�:6�J"} %*�{txk3�Xu� :�gicx2?0[dvips]{color}1b�c� �2Op� tǔQ�sc~;!��D ol�kai*}^th ���a I�B)wE�,99,burnett02E%�g �p"��1-D�gK5^�+ude��>. An�)��to �-B�a��'-�A�oJFMu�!!�.nd.K����a�e0 b� �f�'hev96HJb*-V�s�DA�oM(�F�H!.�bohn97,9Sʡ1l3.���H:2,fatemi00,theA(}�n�n� ly!�V$��in� cn� vM�A^em� b�t]aa5m&�,>ce .D tFDsA@L6R� � isotop)V��-%�.�- �e%)# zero"�3spin."�6�s)F ;<6 rnonQAigerhhalf- 6i ��uld!4a����T!�ir B�.�thougha�o%#�}78s'ncE�!�� is pa��5r Q�lso�lw�[`%ic u!Hv�bmiaw�"_ "6.V 2 t0 y2�b& takasu " �vis } ��i �"�m.~�0fes�F d���&` k��@l^�JdBr (PA�H�i7llia��Q��ɣժ��e��xin=�gs dgJ!gi:�� �5e�Mon (1)� V�aQne Y$\GSG_{e,\rm"} �[ 2 A$�\��i�&� $e$, (2 h_#u)6>fg}(*�G_{r})$ ��ce!�e��g ]Az|$s$-wav# ll"5i�n $g ��5�ki�$:$,'/(3 �dA�$\Delta-  _{e} �Q@=�n�k!;R+mPA٠ F8S$_0$-$^3$P$_1$x ݴ�� GB8IIm��Xc� 5�&�u1�decay-�r��i�P�ji� �D=\hbar\omega-E_A$ ! =E_eo&,j"e$a �ga^6oI�� Y@) %�,B�BP5�)�$ �tB�l�h!S1�&D mY�-Niu m {N�0 = 2 \pi |\lae�e | V_\`0rm{las} | g \L+le |^2�?= V# ,R) dR \rE�|^2 \,.A��*FCFB�Here, $F�^_e$ is the unit normalized excited state wave vibrational function and $F_g(\varepsilon_{r},R)$\energy^ groun](scattering hf \$. The lowB $s$-# form of�l>l�R$(2\mu/\pi \hbar^2 k_r)^{1/2} \sin(k_r(R-a_\mathrm{bg}))$ at large $R$ , where $\mu% ,reduced massv,atom pair, $m*� Planck's constant divided by $2\pi$, $k_r=\sqrt{�\6:}/ P, a!\2�ethe6A1.J length in/ absence�Tlight. It should be no!� that.detail�pmolecule structure are hiddenb0$\Gamma_{eg}(:�)$!! Delt } � :�. !�rAk59Xfor inelastic collisionA�$at lead to%� lossA$typically %� whe)detunAa from� ar resona!�is small. Consequently, we will only � ider%&cas%Qunsatu�d transia$sYT}, definI at cond-, \begin{equa= } |)4- _{e}|\gg5i$,\rm nat}+J|h \,. \label{LargeDet} \endl8We also requireI$J�$ A- much)`!an other�tribu�s!��widthAv (photoassoci� line sOa!�e Imal 7 , Doppler  \��,{ciurylo04},I� ini�shift ',$k_r \to 0$~))%7}F[MtSgg} S_{gg} = \exp ( -2 i ��A )AG:5a��d�i�� 偽�~pre612$written asb�cA�} �(i,I)=a_{a bg}+ opt!-ib "6 \,,>�w��)� pend�-n $ n$�$I$��4 made explicitɥ opElyU�$R� J �6�$ vanish�� $I=0 -aree*a���� limiE� Eq.~(\refy�).�=��p%,%L�C�p,interpreted i� usualN�� hif �%wA rela�aoa⽳�5 coefficiA�$ K�$�:erm.3�ary}:b;K�>} \lim_{u }.c=aB! \frac{\pi�}{\mua } ( 1 - |i2|^2) A0421} )�%f��JE realE_4imaginary part�~}ZAdirectly=QA�� �� k a}A�lifetimŨ8a Bose-Einstein��de��e. Fo��e�����)ity $n$,Y�,� $|M�E^| \gg.�$ ensure��a�� �� perIS  $5L^2 .] n/� ��Sar�z) decay�1 �  Kn = .Q=� Pi� %*scaleecL8 is $(Kn)^{-1}$6� (2>"non��en���� gas ��(stoof89}. I��b1<$\dot{n}=-2Kn^{2aTf �u processesE 8neglected. Giv�))�%�єR9)�ex��q in Refs. ��Z,9}  toy�narraya{zA�� -� y�&=&mo1}{� {r}a/iSn�}{��*" 9=Q0bg}Fd~ g}N5� \\��p �E�6� bg�eft�+�kr~ )oB! ]�2m)!} w/# !5(" ^���1���ѬbgA]a�e back� &� ���ed��viously�sbDe!-9�&= ��J� }{2kA �bg}!�.>�Si� ��threshol�opertie�F*Aʉ�� n�,\propto k_r$�$.� r\to0$' seN�$, 5^6�$, �;R�iind�tD c ��J�. EJ I�)� w!߭�changea�9 -�]an�� *�Feshbach*= hsam�;m� OF magn8 $ly tunableNH"� 8 $.I�� used. WiU urI���s"f�8 >0$ correspond� blue� %� a po� veRM�. �%� J�s � sK conven�to�L���1�c%��E�A�nPl� % , namelybaALA]�� �$&=& l�  ���v5:B jR�uׅ�.t\�) (���+ )^2�>���!-``1�I�''� { edA�B\ ��=:�j�J<� = �&1o�}��9| Re is �M0s�$ar physics6 ameterUH�� and 2�s but!&^a� � �A�d regY ��is�poralA�!� lase� tey $I$, g�a�6� assumpB� 6�eU�c�o,radius introin�12)�2Ref6��In or�o mak� efulm�sDi>� �3��o be � whil��e� es remainT� �)ri5 on E ��"G a�F Y bg}|�e� ��2C&� C}��>)Bfirst �!{satisfi long!�N$ \ll ]��&�� ) sh2�se2 2n ifZfgg F�$.�G�!�v")97a mor�ing�<on2�ich�a!er��$�K$�combiv EqsF�e;�%�:�� (1+2�vlE$�may tA�$a� My��system �a seQ aey[b!5�ei� 2 ���J� .! !�JmN�F��! �A�DB���$�,J��=X}{Fl �� !��q � � �  �AB���g�alG will!bdiult�Si�y!]=��V"�4strongly allow��ar2�wD ��&� Վ$ sW y &Vhave a �ively��:�] ]Q���ne�0ary. However,*5exaA2Cas_ now)�6� th2 a�A��� by an�i�*w&�,%Cweݡ�nee�6� ]Pachieved close enough!�ic* � PDFranck-Condon fact�s aB� 6Bis� too)f���experia�mn�a�w�?�ofe� $^{87}$Rb*� q were� sen�by��8is {\it et al}.\4theis04}. Mea��s Bdon4th �]de� � 8of about $500\;� W/cm�autho� bser!sa � r� �B� \2\ a_{0}$ acani�aAp :.�a1�as�s10�0} ��3}/s$ (8<0}= 0.05291772\;hnm}$) �1��{ t� q� m� 5� $_2$�7 dis2 \approx 1�ѝis}� � � �rw to"�,bg}=103\;a_0�;Drefore, a signific��^q, i.e."d� \sim�$,e�Db� � iDtz��is B�i� trapa . ���calcu`�&�1xF�s%�9ium nZa2�>)G�D*n.�$ dipole moi ��evalu�$aW R&� &��Nai5su�Jly known!1quantita�� predict�absolute�1-� b|v&� levels�v��jmi�[s.T.� ly. Moreo��!Kr= �� I s not�~cis�Y �� bel�vs ���n"*� gfew hund$A��,allard03}. N�vtheles�^�� map ��� valu>2�,2���Ug]� as a"� �[n , binding� Q�=�J�A��y. ��figure} \includegraphics[angle=0,K=\column ,clip]:$1.eps} \ca� {(Colora� ine)� uP��2eMi��! ro._%�"�$0_u^+�!�f Ca$_�2. I&ir-� on (6!)�"09` F���m� c6� potentiali�%{ݸ is 1Ū $^2$ #short 2��M��var�|to�P]_e Iarr �� �  ! two un��(urbed $1_u$m���|h�fixed� h! �)ion�tv�,cal dot��!�s markeedg9�� gy �$s ("bins")F in = ��%�+! �W�1symmetr�l�e some&96curve (��x"AP!at5C{e}=0$) �act�u�-&in9Vs%'�u�k'x  �idO�:��� fig1� q� Fe�~� %�s :42�!'both Y�J�2��.$ (The "�6*"A�8$^3$P$_1+^1$S$_jtomD# $*A�D6 $�6a�a�I� stimed� &Q JC$,& �!��* U 2[,%�o!A�she )m ��% Z_Z� s� al maximaBmin in6�IWP�� >e�0s between $10V W$10^5  K�� rferg u�!1Z�a�du%��mix�"of $0^+a�A I��ܭq� third gum�� Ln ing �lap�*.`2��'��s��e n�I$se fe��discusinafail in Z��-��$�#Q!envelopl6� (� , igno� oscill s) increa�y� _e|$� or6w6�� Ba�-%����-�2��n�� 1 GHz R"Qo(can be biggx%EW� ��le<- 0.5�  10^6Izal �s{e"F -1$ MHz!�.�*e M�.� � to p��d spec+ *�J &e Z�� e a ]��f .�/h=157MHz W&q=389.8I(Tk -L r"h c6�number 1!�AW�Aba_as"Tb�) H!%ase2� =0.9)�N6}!��tV:" 6 A�e �]tas&aXaNo �,S 2�$A2f�%�s��itudex aaA�atAFRY�� � 2.:� a2} l&`%f� :t, (b)%�ME"Q�$$.~$|  (c < tl,tauY�=[6n]+)U��n�2 � $ H-\"#+),�y �� �� appl�8i H�!�jG!�r��sed, in�A�f�ls� sd. Resul� obta�%�Fy,.� /h=-2�, $I=F�5B�=0.663ykHz<*�^U%� $n=al14}@ �d3 a�"S� $.�({r}/k_{B}=1B nK$� >�*CJ���8.�� $� =1.52�5�.}� fig2zb 2}a(��A�AxEfU�-"$+"��1�:5M�."2% F� .aQQ�eŇ�pa� "� bove���q(s��< re�� ^�e�.Pa3EYAT.E L �.��"4aP 18.2; FN� 1 nK $>�=27a�G+�86 �56|/hS�/h = 19� kHz}=! easi�. "~a�:  ies >�o�$\mu$KR�N�{ ɱ�f���cf�encZ�� Fig."; 2}E�our* � broken�.�/�%�J� we �  aUXJ���A� an 5f �� � 2@i62 "H �< t Q�= n� � "� *�rRh�g�=A��1� tane�%��  e�2H �.� =1.7��-12�h"!�!J�1W.G�woI>uesa��� ŭ(of rubidium�$��u�*�)1,6��mss%f > ]i��*�*25�5 @s�y#)E��!#)�B�aA}ll� 5�s s�*at�)�J�3!s a ne#a&�#@,I)�OUA[!39EeU 2, i.�3possib� o tun�j3�<+B3Q�-8 �cto zero !+4.!6&!I)!;low $VT&u�*�*: #e�setAD�/g� of6 �%JS#F.�� �\"s� Stim�})��)� FCF}�&b 2� cel%�a{��� �*�$�*� �)�;��0�_{&� M� 2 AA!����42�!*_$^{1}S� $--$^{3}P_{� �for alka� -ear�K"#aem$Fr9 lay,`L4�eru�5F2Q�b�#d!�" � � -metQ/�0. Both numer�e�analytS6a"s�milar� thos in Ap2ix!X S-,����e*���RQ("�h)�ng ph[6Zor)*��#2Ef!��ude�. To +\7at 2PVъ!�y *�"� D2�A6F#quite P:�for66� YBs?, many�o�#t� a THz. O� khand, 2g $�r".2 M- weak�B�.�. 28W#finEt�I sn�>�{7r% y�.y a>��an.�A�(*!�NJ| ' insi9e] {o@n"�"�$P )��%!��A����&n"�:" out major$ es summar59�� !�at��KE�s&4$�q+�ndi248�4? 6u}�v�U &�r""�+�%�N�� F even3m2� !��A�� � � fa�ed����,%c a ��*h#� %r�;*O . A�IV 0;-lonBV! H s. Alth�"we)�o- �&iu�-���#*&�ct� ASclu52�m)valid!-*::�����we" Ag s���8c�$ic�K�< like yA�b�D\cite{takasu03}. OB"�5bs�/m�blpromi: oolI Ix"str\7�Z��?'sdo ^e �/N��is work�6bB6i�<sup�C�"�U.S. O ea 4Naval Researcht e�f J(;programNEDal Laboratory FAMO�4Toru\'n, PolanS4ithebibliKphy}{99}Libitem{weber03}{T. W �, J. Herbig, M. Mark, H.-Ch. N\"agerl�(R. Grimm, S� \ce {\bf 299}, 232 (2003)ogrein qM>0, C. A. Regal [$D. S. Jin,��>[ 426}, 537J[jochim�: �Bara�F7,fAltmey�&G� ndl,lRie C. Chw%4cker Denschlag �Z�3�< 2101J�r� 04}{2�.�� Phys!v. Lett. �(92}, 040403e42\aiam�%{J. E. W=�'$N. Nygaard �C. W. Cl%�[�]�< /0406617].� bardeen57VB  , L.UCo� TJ.!Schrieff!a�%�<108}, 1175 (19572�tiea� a93}{E. T  , B.[Verhaa kH. T.�S�7,.iA k 47}, 4114j96�$mies00}{F.IMies,!.r!�PI�ulienneNc61!� 2272)�02�raoult!� M. R X.u= A �70T12710J�marcel�'{Be��G.AP$van KempenR8a%NM.�Kokkelma� j�M�6n goraE�K. G\',!�K\"ohl!�Se� Garda��vcJ. �B) 3!�345i�6w�:99E�W , V%�Bagnatoe�ZilioI�>�Ra]ModuE�7!�1 (19992�$burnett02}�B ,BUP.a�a�J�C%{}�d y41��225%�22|f0&4hev96}{P. O. F ,, Yu. Kagan,A!$hlyapnikov �Je, M. WalravA=���^7!o 2913�62�; �L. Boh�P%qn%5� 1486U6�U)¶U6a&4m�6�fatemim� K. F, M. Jona�m�D�]2�=85�C46��6��a�T`+%ThalhammA�K.Winke M�hllw�RG. Ruff,�+�=�RnV�93�D230R��04} G.� �K� ���^� . 9552. ��c"�C{R. C\l{}o:�S. Kot� govaI�r=(in`(ss) [+/04071092�"B {Y. TO )�ak)�Komori��noHonda%Kumakura"Yabuz:! Rhashi^%9�1�4e�6j"�D{A. Si�DF42�x>(]�'6aV063406v60& E� C. K &WJ� 3361N�s�_ 89}{>qA�nL. Janss�TJV��Ko�V)�:�F�3/ 31��1986�a*{O� *. Samu� � Pash��(H. Kn\"ockeG )[ mann, Eur�� J. D�wP 15�v%��8t:6  docu�} �argym�� F�z��is2���  r�  FJ�!-B�.&�,*� � �"�.�E���+/eZ~CnO*�M "�q�e � unity,ep� a 6)�invero,o�e5F]�2f �^.6LD/ndD�^�^�^�^Thus,"Z'��%�J*P��ES�c�6A�TJ�J�V�4�J �J��J :Jp3Ix5� (A6iA16R�:9}ad�get�roxim�0Mon2�#�1(\#ial E&/v)D_{C}�"k 4&�"$�=$<>K�"�y�+ERFofJ�0, $z5 deri�v�C7er=):�aF�(&F,��don poi3K�E�dE�(& W)4v�1�*W�/ac�(Jb.} d�\��Tclass{aa} \usepackage{�/,epsfig, $natbib,rot�*,txfonts�2ddef\oiii{[{\sc O\, iii}]} 2mg4Mg5@feka{Fe K$\alpha$ LA� dra{E�Csra}} ixmm $XMM-Newtonasc 6 ASCAhst 3HST rxte  RXTEexosa /EXOSA2sax 1BeppoSAX5� y Ging�rMR2Lein LIL�W gral INTEGRALa� �ASTRO-E2$lum{erg s$i-P fluxcm�G:"nh{ 5,arcsec{$^{\p�7 }mindeg circ)�\ltsima{$\; \buildrel < \�+ i�;[simlt{\C:(r.5ex\hbox{ C}} % < 8~ \gN\>b\gJ\ C\>\ ]cl{\ce�L)"�Nq\a0title{Six yea�6 A,\.��L blazars:�pV$al catalogHv8{D. Do�\/K{1Ond R� Sambruna ,2 liozziUD itute{GeogT Mason Uni��Sch|of Compu�5iUs, 44004h Drive, Fairfax, VA 22030 \�bj Dept@8 ics \& AA�0nomy, MS 3F3,�n@} %\offprints{da{@a $.gmu.edu} !� ate{Recei�9 / Ac� 0ed 13/12/2004!- abste{W"�:J��\-�64Q%�  iv�7sS<5(s 44 High-e�Vppeaked BL Lacs (HBLs), 14 Low^%L %!k 28 Flat SEPtum Radio Quasars (FSRQs). A to�4of 168 LECS, MGPDSL-traJ;�zed/�F�to6��?"<0od 1996--2002, 0.1--50 keV�tinuum���5 g!{f�Qd by!�iH6 power la�=th Gal�Uum�/�.�minorit'�o�;� e�z(25\%� �(1i"st �byco>xwls"M &�or��co�o�JcO4dabola%s�DS�. +�best �27Ez half!>!HBL1�. a�l��(mcB�9�&i$� sources ��%es $F�#2-1%� } > �*-11}$�J,*�.ing� ��9hig�U ,$al-to-nois� . A�8re�+A\n�VAZ � D�J=v$iU r`K>" percentag�~ �L �"� ^alfe  {We,hK reAa net . �n!qX-raynl� 7Y|3a�� �6�4EmafIf� o�B �distin�K:5is)�blurryA?�/ most�6�Qambigui� ��41e�AI two !0 % \keywords{afxie��c�; -- e} fundam!�l " 's %--(nuclei%Is: galD } �~�H running{A�M5o�)��|} �34�: � l.\ WiG[ \se%g{In�G\ } B�e3a)#i�Go-loud A �!c�#N �(AGN)H%ed�� non-!�mal emi�Pma jet orQ=ed2~ �+�%si"[ Multi � � studAo�du3clE>I�ir ml� A^&Y(SEDs)�cha��erv],A(a $\nur%@\nu F(\nu)$ plot,�two��adŷ s (Giommi�� Pado�5��4)A�e89 �7onent,6a�any,FM�(IR--soft X-ec�2,A�duz6 synchro�5TQ*A��r�.a}is < l�toD �mb!�"Z��0PNe�Rron�!duc�q.��I� (MaraschiM�! 2; Sikora4;3 Mannheim+3��a"njWt We�). PrQ6lRat=K-lu� s�&eB� ,s6��) exhV �=��1�UV)� 2���!>w:��!GeV- TeV !� (� .', Ik, AnsarEsMicol!.5, U\& *  Fos^$L7!=�.A�U���B�l�F� y . �1mid.VѸ(B� 2U���3FM"�)B infrXV!�)!,-b�SM�eIG+�5=�vHA��%��;. ~0eAR�\ V\ H�҂�fa�>��+J�a�\l; �Com��F!� %��F%%,M:D.A� M9 s�f ke--di~Faj !M� �8R:4 �br�I�6� . BasO] curr�Ku�D�tu� (e.g.V����$ e:� Q{2>omina�[bI���t�:F YP�4e)Us� thus\�osteep (pI_� dexm=>2A9!N$ F$_{\nu} �T\nu^{-(,-1)}$)A�convex n �6a,�%�I ��~�.�/�B�)s,I��Muld �flaV X (> <2$)�7a��+5�� medi�* slop�orq'concav-!!�u ���%a? siEALI�Ma����(on)ellite c]ee� iv��M-�;"$I�g 4a,b%d@�G pass��, Urry�6, Per:!G6; O,.d a d9!a�F 2001��se ���1-�F)1�o"�of�_�� lex,� downward-> 5@inťe� occa�'6up0 .0��1!��GCit!md!�"z )-0�20 )9good =�, ���!�jr@�choicea?!i��(!�) �9 : X> 4ended in early!l2; du� �lj], 8�em4�&Z Qvas"�m:l campaig p9 snapsho��* .� w���in�fC���K publish&V(ori^ l PIu2=stiw2ons r[P\�Ka �M�g.k� bcR�.�, focu]� M�l &G@O *pr %Junt was $3n�t�q/(2)b) e paf^� rganp !�fo(Os.rSect.2+�b�ple s� io�in 03Eydat�7du� N4� j�cd�Q5�"A> �E� roug~-CL�0, $H_0=75$ km"T Mpch�1�A$q_0=0.5ZZadopt(^"� S$S�}��isa� car�Fonboard:>Na�F FVeIn$K�s (NFI)s� i��� d�`�2covja�F�g= �My40.1a�3� (Boell�z�Z TX6B �> �b ikag>D abil��>Low EC2/nTOor} o^W (�),���8>n��l}0�����ree Me�6Nf? fs (Jg 6g1- e7�# �FlP���s  Pres�O ProX,gCaJ$er (HPGSPCJx:�4--12���mPhosw$UDet{ S� (PDN�:S413--300 keV. W�,tri�`].�d� !�>?�s,�<��W-�-e�Q�@N)*�ly faint"� as*��U oss-CByNji)�b�3w�ڥ�elis�c����Ka: �.f4 }>� d���h6� !g !re0s " in�<��J� C padoG�=ith%� oZ2R�Edex<aN _{rx(M�5!n 0.75 ���ifKasO� .pN8M(^EZ1 l,�!��EW �~g*3&� ]!��3�ZS in T0~�I tab:�� }, | wGsk �]lbj%1(Co� )IW coo�*an  AGequinoxa0.01 s. 2�% 3 8redshift. 4 "�M"c$NNH}^�L Gal,J�5)e�{&�I�.� �-� =6n Byw-E�d��Dic� (\& Lockman +0 ?1kees 86qo:�BLs�%� �28 %�. Most �c;re �y b_ "_ @in&�b GI �#� !��al �*Di���l�'�0))F"6��V favored Is �LMir3�bJn�PT1,s& ly h�Lo�ous (a� NMqA)�Xd p�;ime��gly bi%)[by no�Qn�kte�E�O.��D� Analk } All��c {%D s up!H Janu�h�� ���%a# o#8 O :{�ao� !logQ� � |, toge��+ expo��4�mea�W 29 �O!a*K� each.n�re�ZQ�� cQ .Q�.,2�!S��� 86���O 2�� In%,P o�.OL b&�eu�kly �s �C +[ �%�maex�&YP2� �� =)�llQ�:qB�I�e}� reli�d sI7I2� dIP [as(%�f� (! � >per� Z�� n. �JJx���5�d�-�a�QthK} -~. �A%r"� !!�8�I�}N�5: �Ua�a`19w9t fil�R"�H�@]on-5 lO �)�Y��)5FTOOLS �%H XSELECT (v. 2.2), � :a`�b� u�8�# min\�4 � 2�,}�i�9. M� A�!�%�-�,�Q�9 a t o6a�1���%!~t}f%����-�D�q�is�not�ly���dc \IKor[ � CD�"g be�]W�!r%�blank fJXatE�avail�%9SDC�hftp sit;HS�~se.[E�r ,!�=�OskyIno ���% low"� eYrpA� �P��C| �Nloc".�E�hig*P!c �a�@ nder��) and/� int�=J6Y5 E|�(u�� ��,XSPEC v.11.2*�_ � st9�E��G �tces �!V calmZ 3 er6�%A�>RQT�zrebin�i� the �(nel�)p!jsugges!�� � team��de!o matchMo�ol�v!f ./- k]waa�vU�/eDa� /�R{� �.(to"�fo� ter-.'&��^!L�-)I�Uifre��y; p]epta1 am��S!�/"t65--1.0�( 0.77--0.936� (Fi�"��9)." �haX Y= fm�As�X��-�"���!<� K�%!Uk !.32$O !�"�`�"L,qig�F9�#-fi�@ dels��XUt $\chi^2$�$imi-�routinq&C g ��\im_$�K�en ad�fal)�&�! �add"a��aO^�F-> �sdgGa &�i!mA�l"nt.�D P$_F$=95\%. Uncer�O�"+|%.MAF 90\%!L�(UT-=2.7)%� �� V+��Y d{e�� ��/$AS��to�%�i� +:R(no�jnt (1)AR�&..�O�K( �.N$_H$4[< "S!{e;6t2fte�P:434B�&�pbreakq7E�rm A�ʥfbe�wA�� E�El_1 � 2$,  o#y:�4�a% inuoN1' (&� al.� 0���G��5��A%� �but�F�Ed# 1�7�� 6�AMWQ-hp�pudure. A5 rsa)l{&MGIjM�%� �(JWa�Tif�}is��y,,2)�U � �ZZ� s! bMr"��� q Econsis�^I6��errors..e]pret 4�mar�e�+���-�umv7<; h�gi� Y ��t�' �s A�!�A?did- !zl a� 2|X��� Y1) Y2)�'Q�����r� � T��&�( fit}A"H�%S!����� ,�z) �Rr��toYL!"� er�uBz)Ye)> %>A7.o+o�#Kr� a�#� ,pq �A�� � ei� [!?or (2� N4ew� s (6.�MU � B�U|&� B� �J�ifumiC��G� vaS)Av.�%�?n�2!�IB��,law)�+I�"�%/s%0E�2) �7!es�& �a,e8fu:1"E� I�ȍ�� Xi�B�eA inad��a�A�%u�7 �,�8A)9�Mm,��uI"-84m�s (42-�12%� , 22)�)?04 GigaHertz P�2~um QSO�:#i�e!��+L +3 �1uA�lT)I�aB��s%2s'�M law �aoarithmic% U1For��-��&�$%T�f��b d �WmpaX#;�a�E�#ɀ mmoneR�JK(.���>�!�$-nZ�Ou6� %t>� N ��"*a�)� al C"b6�of�-��RI�, Ť� j�:f9���Ti�.s .�De�x�$TV+ e�"�A �]5�����*� u��]!�%��>�� (EX-Q4 )Ff � ��w��9inBd -2}��irB�u.�� �� -��� ,* .��46��A��<t epoch� 1~*���B Rja FO c� !En:z�"�wh�/ste)�'s9 �g�rep*dlyq &��|��4�2!�5�U�inN% U90 Ms�441\)i46�  (BQ 152�,- ��1/�D6��aB�(� (>��MPA����� rema�w 2 ��jE�o E��r �{*�ex��+3!�W� 2. ��q���a�f<1��4P-�4*t6u az�1-2h#A�Q�4T�q !uZ�Ua��+Fz�ߍ���C , 20Y=��FO 17}N6 U �� #B Aedi{20}$\nQ� a.din�si)!�a� �6�um �)L�t�l2 5���1LBLy&V 252 �1: 76YF 0e �F J�6�� �Y�� m�� ����:�-��u ��ai+ .U� < �. in 95�(132�� 6 \geq;5 (46:�a$Q�A��!H um>�A�R,, S5~0716+71�  ON~231ne#@ir2vU�,NE`� a �=0ex�!�e�De�_1 �.4$% a%=te%:� J: 2 \l% !On2^!�3C~66AT � of BL~Lac �Z3���21�,&�2@$2�2� 2  2.3!C 2.66U,aj�"g���is�?0.3--0.4�. Amo~,.� �2�,v �� )�albia�)I t�=F�:gY�e1�g)�� 1�da7e/;��  3 (�6� 20$,a 1NxB�;�,Fi:/b�� �P56J"28Q���f��a!^lways��6 y� (� (1)))+-�Ie 1.8$2_I1ES~083a6@0, PKS~1510-089, 2126-158� F3C~273)��a .���cQA�.��� ԁRj��;.�e0.�"[y����-.a� sim >�MH.3�1.86! �)aD2SBj�R ���9n���AL� ,X a �9ex�&��"0. Iq4P�0"accre�disk), wE "{L %b�w5@ plus�apckbody� a brems�AhlungI�(\2a\��� �:Vnot s�91�� p�*r� on roke*%@a�$!& �de�='��9�E Q�!y"en qul-1*�<;k_D�/ionCb���} 0T� , 6.} Average��� �.&u�e�s ݆�*a @"/E{Dtabular}{l|ccc} \h=# &HBL&LBL&��\\\�x� {3}{c}{a)w!gO��}\\ N �:& 34  12.26 \\ $<�z�*PL}>$E$2.24(0.04)E 1.927) 1.595)v� b) B:�� �i 2�.�1 �  �06�48 �2.2��03�$ �le}�A^�7��A>��A�eR�2��1lƳB�a� 42t15mZ 29 =���> ��u�7�fUu0A?08q=8.�$x8�z���� :y3.,�^Q�usT�cc�� infne �I �&�8a+vo#e�zaU� . Wl9�&���"&Z9 ed bv�)D\?O\ N�A9> 4�)� ;!uniqua2ȉ��we;�:];!�*�&*�R�tu0;gkr�;r:�%. M"�i�=at,*> �a``���in� let�/d~llu/s �0 to>��=B M�!]k��~9o avoi��� ��I2i1�+p9�*�$*�"For� �~ -X�Ђ�+($�9wk &�&(��� �i9�% ɹ$ �O 0.5�>�IC�"5W:m� 2$��|m6}f�B inim�weaRt �I|\� a/���-itra_v.`-a R=a )�% s*��eor��� )�fiP+d �.�:\Ka�'!extrem"Z)��!7�/ {�iI6�y�,ed��.y}H�N BLs (Mkn � 501;(1ES2344+514�I @!2�_t�3 1Fd1�/ (B�Ned)�E![ 5QEO]�( �)Z- ODSRQs (PKS~0528+134NrV]� u�[DA'� �T6��� " 4�s }[h]"U?({\xU{X0=0555��.ps,he J@=7.5cm,bbllx=55pt y=157 urx=460 y=69 clip=}} S�[]{.*61+m.^�'g0aZ&��G-d&��!*�- or-9>�" * 2}.}�|"܂:istogޥ�x5=� -\�l2�l!Tb�lQK L\nu$ m2�(�)&�y&$��sub�S x2���U�2�exc V�%��fi)�lumr�SL�.$w�Y8$a hom"68way"� �8, w}yiz' c� uma�.a��A�*AY� �{\i?xed� ree} &&,�2�+��w=5�Yum��$n��n�͍��[ ��mt�ɡ�.�� ���.3>28^(A&u(�s&. �_�)�Jac"�!F vex/�#r+�ill be�i��%.?��QDr/s�s8�bs�2& t�5y. Tb�s��J� W����A 2�"�=����rjsFT� .7:�A of 2%�!u�`l9�� }Bct��3�dwidth=8�ϭ�l�ϥ��c5�o y=68�{J�X B�vs.h"adk #6w� EvHICircle: �� , Square:I tar:s9k����alfarxr�쭢�/4V/4��%-/-Gun/M2s)=Byies%Am2-rPW(5 GHz��i�G Lin�Qm �A�7PZQaj�zA�H"�(���&�"* LBL-�* �%dasQG+6�lumxlum}�8VE 6(R[ Fc6���|� �� &O#� �& K����KES}�e�����.R3�~U� e:�1H6�2Q at 1 �|���� �$ �v��!�R>3���j� 6�T a Kolmogorov-Smirnov �Wch�{� probU P$_{KS}$�2 6�!� draw�T=�#� popuI�����ۓ&�e�]9`'cu��iv6�&ñMfb��se�!s&P �9�o<)M0'���<��{��:��%f�,�.$ 0.2�S�1�%�C, �'99E�' ��a��(>+8 RIR+~ A��E�9)N? s$:="�%c\ F�2� a"�:j"�0BFk AkG �e�h# shap"�+.d9�F�� $  of i�:�Hoid. qP�QS�:�M0:�q�3., iB7 La�C� T.eE�D:or%�` %�5 )�� 91-�yeU�2l$.T3at 2�g?�3>�B�P,� �>of �5$n8�dEh!"A�n! a &er� ́�16 . SjB ow�He�5�.R2{)� 2{=�Hd. �jBF����ndB{3w-�a{!�F�8�� QHQ%, s�;!3!�%T.�i �R^�WU�F1�25��at �A8�%:d�at ]O#% 1�V�N$\l�T(L_{1~keV} \bl�lp"�O ��t  ş1�!�&"�I qO�e~�I�#>~ _ � W� 2: �:� 2} �busNy��V�]�:woٶps ).>� <AJ;!i!x >&%t %k!t)�%uBG>RG�&.@%E,�  4 O�(WGA J0546.6-6415, RGBJ1629+4008, R722+2436��(S5 2116+81)�B- e ga&t�!�two�>�Ps�7cu&�"�K1�+�K�[}�1s�!O`"PU��c%.&&*Q�toY�� dubbed ``9N�VAZe�|''. It!Q(�@de��ed wh~G��'`!X*A h0�3iA\ s*TYEwJ�]�\�""LWp�wp��@X5$4- .�Wdisk B��$Bump (as, Xin�! ). B�"� �%ei5�ii��Ny�Pa�m)�k��1,�.I:E��}a Em}r�jon ^C�!PM ��&�^.�G���|d���є�! a[� s:��a� nB� �}�appeaϴ�>V a1Gdio�To ל� deg�@ofQ 6���c��!��Y� O,3 .! $r�2��u4ch�?*�  $P_{z=r}(N)� a�dom� BKN$E0-�Vdiwh meaYJS w�X�13�.�2�u5l�d���$n $|r|$; i�IF�A� ��C )G)�!nikeI]e��� !� ; �bA$is $r=0.72)I!tJ�-@ r}=2 .�(7}$0YC, R90 R$P=2.8 5 ()56 F�Ga ��a��s iF�u� E6�i-eA.o"�4G \ E��K` �`"�@ ex��%s: $Log��A:8X}$=$12.5+0.64*R@�� e� B8 -3.9+1.06N89:��5L4�H[�Va�&cau� A�ourQ�is��y M }y� ��a�In4cin��mA�1B�e��r�_U�OraӡssM�� �cu%��v�/ ��� �'6�X�� A. S�a"|Lf����edn 3%6F  ʡ_�� E���a�*+ * 2�T�=�AL\�KA$A�"�+ familiaΧend�^/!.s.] �iog ��>i�Hnfirm��bM=&yK���ɚ"�W"�)Mknt9 f� 9&�;B�|=M"=w"�ked.)�,*�]!t\e�L!&�!�L��� ^�\�a�6A��A!3s*>"'AE)�"�.�n �r!� s%�Bt+a"�!B�h.=a#x/ue�e�u puE�W��� ��h blu�h�X ivab��z"E "}hYNtFA� }egu�/,0B!2�#Aea�@F`= a�l�uU�NEquivalA�W�Po��� �;�,2!m�1um Xhs �6�� �"�;1`&� �7�R�&ac�{{�i��[1997]{b�\} �\�, But�R`�, Perol C,� >0, A\&AS, 122,�"] 0]{dGW} OWJ�r,*VW,��J.M0, ARO , 28, 215M7&]BZyA, D., Gh}� lini �$Tagliaferr \&�?!�& � , 375, 736�9]�ore} GL�(, Guainazzi.�Grandi�~�<,�kbook� NFI�"O= AnanqV v. 1.2�!I]">[.�,y�j,, L., Celott�h om�u �h2 �7, MNR!�289, 136v�@vb:w6ihiaberge ��@4, ApJ, 541, 16]1994]�;2}�;!-%<�4�68, 51� 1995I36I�i�G XM�/ 7)�A�09, 267V�WV6UCapalb-�Fio�A>�<2, babs.conf, 63X1993]{j�k}"�kn� ��9, .� 1992:)�: )�6�%D=�Z2-�397L, }:! ]tp=2~K@1�!8!�444, 5.�)6"�:I$CostamanteV�fu:f"�Y �581, 896� 6]{pif}28S.,�� cke,�DT., Wa� Q��gMorri�.��bt i456, 4:k 4a]{rita}"�f,�M�arr!#&RlP.. 4XS, !A376�4b Xd�Y$, 434, 4682n6 XcJXM2B\&�g, �ME25 63,!�2X9 XbJXEracleon!\& Mu�ezky%-F^9% , 526, 602] 4]{s�n} �niaBegelm��M�v\& Re�>��V)e,e(156z 6]{t� }���A�G jMadejs��9��.70A�2�9^2B_6R\& Kubo1�W! Ph� , 17����tashiroT �kishima�<, O��5, PAS!7��]u�1tfF]qF, FBXPi!wEY�?1�54, 72B�� }.U&�iEAWor�w��6~24�>��one�5"�j#*&�(�D�-"�M6c/F�1s� sizeS�1cr2Z6 noalign{\� skip&v6N~Obj. N�K& R.A.(J�1i� & Dec6R a&&zF,G�`& No.� �1Q:2B.& &x@ 3& ` .`�  1& 1 & (3) & Q2d2(52.@�4�2N5�5V�%I{6�7V�5V08Nh$1ES0033+59:3�$ 00 35 52.!=+59M^03.T34& 0.086 & 42.7 3!+N120+3d5 01 23 08N34BB48N272h5.14 &~7<\\ RXJ0136.5+390�N 36 3d $+39 05 56.�5&w  6.01V�45+13S6 01 48 29.�14 02 1N0.125 5.18NMS015801! q901 06.6N!J4 dq 0.29F 2.67"�!8 229+'W =02 32!&f9+20XC.�409�6"N(MS0317.0+18�903 19 51�8 45 35-8 0.19N10q3N�323+02�03�91Q +02*C145�14�8.86�347-12�7! N49 2358 -11 59 27�8%� 3.63��414+00-� N 4 16A�58!� 5 24N28�10A��N502+67ImN 5 07A^!,+67 37.N3E� 9.16�507-0: 5 09 3{� �-0A 4Yp30a 9.7� PKS0548-3:�5a�40.�:�-3A�.�0692.2!�3N,MS0737.9+744-�=07�G05�74 33 585831-�2VNB20912+n7N9�75@B �" 33 2g-- +1.9!� NAp927+50a� N30 37�+4��26Yp8eZ�93-�1028+51 �y �V31�U"50�A3=�6%�1. �N,RXJ1037.7+57 Qi1��7U"57 A�q �0.5%@N58.6+562��582�56�111�4E0.6�2N 1ES1101-2�: N1a]=8-23�130N�ʡ.� N Mkn4y�� 1 04a�3 _+38�=32U"03Ah#;�16!�!8 117.1+201!s�17�.!�_��4 0}�3Eh1.32�1118+42 KN20�.A8N42�1�12�Ap:N33+70>N36A^N70a�2y 04!06p�2!� +224A �2E< +22 42.p4I2.2� i�ON325��N7aZ�30a�0=�1�7!�)�A" 218+�`  N21 21��NA�.Z�Y="!�N55+24!" N 57 3Q��4�3��14F1.E"i (MS1312.1-42QwN3�D03�-%5 5�D 0.10a 8.)� �0RXSJ141756.8+%CN4Ap56N43!��@�23��1�=&-��426+4m�1�4a�3*$ 42 40�VN1�&1.3, �MS14588A '�5:*�22�f�D9)Ep3.5E� � ES1517+65� N 17 4�.65�2� 0.70-�: 5 3Uv N35A^l=+5��!�I�0.8:�V�44+82&=15%&5�{+81 55 0�.4.��53+11�| N55 43�D11al�f 0.36a:%��Mkn50�wN6�52��39$ ��0I�1�11a H1'$1 N7!t04�.� 2 15U"0T 8.����741+196�7A�579�19%�yZ08E6�N959+656�9` 5*� 65 08.p0� 9�'q $PKS2005-48Q��2�5�-48� 53U"07e�5.0�҉�N 155-:�21�5��-30 12�11eR1��..V9 !�23�904&� 51�|179��P15��&�B$\\ H2356-3&Z �3!80yZ�37��!�D16e�1.�L%�n� J� # �� ( 048-�!00( 1U�!27 �ut3.h �3C66A-K N2�V39*� 3� 0��0.4%R 9.��)� AO0235+16�1N38�L _+16�|59U<9� 8.�� 537-"� N5N50]�4}&89e&3. �S5/N�07E�3A+71A�3N8VI�OJ` 2Na_ 4��0 0�a�A<30E�3.*� $PKS1144-37AbN11E�1�-� 1f� 1.04�7.5&�ON O2N2�319�28at"��j��1.h )� OQ53�N4l[)� +54a�.�5�1V)8�519-27>�� ��-27 �0�^8Ip1�1803+784�8a45N+78��ՀW �2]" 3C3761N��69��2�^ �4.� 4C56.2�P �2 j� 51�|!fA"66Ah 4* �BLLAC =22a�43u �160N20q& 5e ��, �208-5"9J�~1-!1 0U 0.99�Ea'� NRAO!03�M.�#8�) 1.25a'�C�/2�.�� %+�� \>5 page*� l�n�ion{O*#,L��Ctab�k9����:� Obs.I+ee�$Seq. Num &�gE�A� c/s MEC  & Tu23)Model�� 6 .& (ksec)A(���2�4>\\�ZP!F3)/ 4 *F!�C!$7 $��W & (9)10)�RT np 2�9�t!6u! & 18-Dec-8+�508630�& ��m2$\pm$ � �v43 6 n 2��!*�  aa!\\�2�!& 03-Jan�49� 9.�P9 OF c32.S19.268!16.�r1 ��!�2& 02-FebB�c��s11.73 O0.5�b�Z 14.14� � @ 16.8 ���Bn" & 09%�%r51241003Af�%e�7 O0�48 k 12.99*1�k !� ..6E�25�.�" & 30QB 5006�< �0 �@��"c12.�59�26 8 ��B�"& 16-Aug!�%� �4��sU9I�� 1.655*1�j8 >�2#�Jul=�47%�G17i�]%�68I�16.�amFG3?%�8.qbQBR# & 15E�(:- %5I% �  ki9E 4 � N2�# & 20�E� �� c�$2.8qyF14M�>�z!�2�#& 1�� �6 k5.99�S 10i�� ��4.�#& 21-Sep!�EV �i��� =]a�E$� yF���8e*!26$& 06-Oct:��!� O� �9.4Y� ��8�*o$ & 11:F519�T2&�4.1y��21�6.1B�9-* >��2�$E�J�-�9I�a��O|;�22�4%�!"�4�F & 26N���j�� k!�1.0)>kV�%�& 07-AprA��5�b4�kA15.y5� 6.5}FE010.$=�TB�% & 29N�5�F o!�2.2Y�2e1q�0.7y*�!1�&8 >�B(&& 14-Nov!^50l1�9�83.8�Fi�� k2.9���T�T �%�a�2a& & 25��Fe*6)8.Is�]�*2)2�*�7.1b 0��1T �%�2�&& 01-May=��9 �4 �N ѣ0.�&2  5.49�����25.� �# �$2�&~ � �50470�2��ea5� 4%!0.*�2Y =%��. '��-.�2% O�a�e3& 39P8M>� & 23:%-]���"�p 9�8v)* �!8 �U2�' & 04��m*$064017 & ` 6.1 & 24.56$\pm$ 0.65 13.920.693 10.7 21.3 0 5.0 & 3 \\ >0& 19-Jun-1998: 50726001   9 � 2.30 O0.5�s 29.6k0.3 �0.M... �MKN421 & 29-Apr��50032� 11.6� 68.6� 1.22� 23.351.97�4E 9.$%G  4�4Z30N�2% 11.4�7.5�24%e�14 k0.4�8!�=^�01-May>3��2009�1-y23I 60.7�1�10���2:� 1600- 4%243k2.3%y-* 74.8E8 5)� 28Y�6%�b3N�) 4O155.0�1.9k11) 44.2}F!>�!��4N�4%�MW122.8�6%�12%� 26.1Q�0Q�5���5N�5 �i�164.4�8�11I 38.7�5%� 5.e���7N�6 �6E�139Y1.5� 0k��)� ^21q��r50686Q�23%]335.991c29�2209� �L1�T 45.�b 4� b�3N��F27�472.�4�834E�372�111�28�3�Zb�2>�65�FW331.�7 32)880.9)�5���y*�#50918�63%262.k7!y1111419�0.3�F57m��]�b 1%6Z�26%�200^ 5128�T�5�*508.*0 7E8695.2]8E29%F�U20b�8R�I�)y535.T5e�2)y749.�7�1I� 293.q� ^���>E6�522k0.933e�6779�1Q�2%� 205��2%�^�09�8>�Ek63;4��1y0��13561.� 65��203����8RXJ1117.1+2014 ��13-Dec�bM� 8630��1ie 16.3Qk�4 � 7.9&� ��~}*5A�$1ES1118+42��F� 6401p  4.�3E�1�F1.5Q0�8 ��1� 33+7� & 101il0�0!)�E� 8.68my0.418  2.72IT 7i*�2�0RXSJ121158+22P27�)�10)1�� 2�iF46E8=0� ���% & 28��,:51319�T0e� 4.6&T1)76i 8.3&� )24-* ��11-Jan�%l�� 5ŏa�8]�I15.92 7 8 >�ON325 & 2u*%P50750��1����01Y�3/ a�Y�0p14-* >� E�6 4720 � 2.0>�31�0.8�0%�j�Ea�218+3}*�bl>8~ � 21.4}*k4�* 18.1y*)�2Ɍ=�8255+24�820:�a�p -�1e 5�6%y 6�* 12.19*� � �% MS138-42� &~ Feb!^�8 3Ta*2k! "� 2.4Y� aw>��8417ao+2�+13-Jula*E�5124111m�1*~ �ͱ�A���0.2%�11m*37.q��b^K2V�e ;���5��7�b�7k0.3eo �~� 1F �b�7R�E!�%]9.2y2�o �7=%S" 14.�-��$ES1426+428)� & 08Q^504930! � 142��4=u92E20��6.�� 3%��MS1458�P9��A���153��m* 2.� )�47i*�8yF�82x B�$ES1517+656 $& � 2���"=A�!�"Y0/ U�5.1=�%*j�E�33+535�13%191�5��K8 �d 1�0.��F*�0-* R44+820 $&Z�-&T0�F1e2= �p��� ��E� R�53+113 "%�A&�!��� 4) 26.3�7��T5&�0� � �%� MKN5�� & 07! 19�F377���156k1-y�87 "0.7)8I�148��5� �&p6��~ iegU1-ym����7� 8= 175.1F 5e�b�� :M�98232 5)��258.*m*� 556&/ ' ^/ � Y529=�s11*!0.9e�2g185&� 9-�17&= ^&r 5 �-��1.�0.� ��9F� 9-�38�� L^�&� .�)�13%�116.=19��159Y8588'�p�� &f�>�66"�1�F 43.0�8�! 55.2��� ^ 319� �^2>4�-�2)�72.*� 7Ti�114.1�0�T 7�p 41.��^�16��Y��-�~ 72� 8��)102� ! 52.!b*5N���2� 78.4�0.5%31I02�mͭ~��8v�1Up944m�105e�A��~ ��a* aFY8���T*��%�H1722+11m�24-Aug*p� I3�3�-"� �7~ 41.4��3} 0 Q8 &���741+19"p26-Sep]47.� ��4.71]0)�7.1Q0-1� ��! �959+65��& V! -/k15.�8 )y7��0.� A�  �%� �!& 3&1���70&~ �b � 98&g1� m��b*8R���a*%# 73.79y448� 125.����pMT�lP \hline \end{tabular} cente 4table*} \begin>+$scriptsize*T{lc}uDnoalign{\smallskipv~ Obj. Name%[$& Obs. Dat@& Seq. Num & LECS $ c/s & M & & PD 1 3Model�: G & (ksec)A$($10^{-2}$2&n\\)(1)k2 � (3 Q4 (5 # (6 $7 J8 9 )10)�½( PKS2005-48��az19� 5004��j�9���&"Q 7i+}z��&�Nov�e� 5050&1.�0C5"201.�C2% 62��c��! 155-*>20���536� 132m6�10� 33.2�� 4�9� �9�[b�2��' 5�8Aw��189.� 5��*����%�1�.j� 04�%� 5088դ4!822��1k��019�+]% 1ES2344+5| & 03�Y�z �� 9.61]WA�� � 6�z>�b�4N�9� y1&� 3Z13�0.2!y�A@�0M�%U � 0&�7�!%�=IR!2�b" .�U > 16.79y��k18.�v� 6&> ���&J�"�9.8&���Q� Y8� � �2� 2�#6u*1h6.� �5�� q�� "��y*m�969q*28G A�>k90I��Y�4���FH2356-30�R��21:�493007M  21.3�L4q �B�18I�!OQT.� �Rl \multicolumn{9}{c}{LBLs}\\R1 SV�>0048-��M����L3i⑩ $�e w�� @#=e3C66A%3�&D�"�!;*? ��a�����I12b���z2Z�%513�01(�1��0�0��-� !3M �0 AO0235+16��8-�948g �2�#�*�2�&0..`%�25mL >�$PKS0537-44E'�6�497i 2"?.[ 64� 2.4Q�0-36b�ES50716+7 ��1�ӭ���L1��y�<v!*��0����b =�" R6E�I ��39u*L 31� 8]��� � 11&��|^�30-Octwe�5|1!)A� O3.7&1%4 WaF3�>0�u"� >OJ287 & 25�E^�8-5 �0.0 �&N*.5q0.1E�E&� e&�#33"� 2s!ki3q�2� 2QT >�$PKS1144-37�@"I&`� ��a�y��"|0.*v 0%��>� ON23u&Z�):5� I2|8.W�F�!�*j*��"�1*n!)^*e 2Z �1h��*�+6a*� 3.2>*1�)�Q� �$� OQ53" & 12-�E�5�F�T17 k2�,��b(%y0.6yF�1�b >�  MarA�i� 0881"e 9�!0.8�� �2�.I � � ��26R���1�6��1*5��~ >�a*519-27&11�%�8h  9 O��F��u�0.*$#i� +>� S51803+782bC ��b � %]0.F)40�T2.n- >�3C3�� & 22N��F"9EE3� �,�0 �1�# >�4C56.2�υ8�T:�� e$�'�eS��*�,i��%F >�BLLAC ��b%�M-�5��B8k�.y�� ea�1*~ {.����m�1�b"Z 3F-5�.K*#:�-!-F ^�05� .�M�3.5&'�b5� 12&`0� "2&1*�1' ^�'.#1*�+�*6@'%q2C5.���~W.�&! A�&�) ���ѿ:(Y��3�023.{2Ea1_ ]�~ rM J� FSRQ� 208-5�)&�  &�2�Mbay*�(Ik3�a*9]%�] i3&)�ENRAO14�He|&� 9 iU�1.� �5N*7..� 2��qI��� 21-36"e"02E&�� �h42b �4�92�J 1f� �$MN0525-334��& 27-T!�!H 5084&�v�F*8�0.%� �/M]� �� 28+13��J$'23"�! ��*� %y1��1.#�� p >� ſ!�8�I�72O���r5M0=�0nQ5�:�� S4.�A�k0.I�"� 8%� � :�ɿ2 O!� 12~ Ea"�- 8b�3N���fA�N!ѣT 6 � ���4.�&E '%y O��� A*� �� 8b� :�p "� O�>�$�*� �� �A� -"^�1}7B\+2�1-y1.0�I5mF* mF�)�4WGAJ0546.6-641E01:F7mi�I"�*�84�$�/�� 2��y)�@��� 743-�)� ���14":"!0.�, �36E��� 6Q879��1ES083Z�߅8�:T�81�(6.p /4�3S*�0I 1q*b9�pT(RXJ0909+035���6� 12"g"* �; O$)2s%�2Qq� !�8�)1�1127-�!�4>� *�/s'a�F �"�*8./ M� 21&~ ���3C"  & 18�&:021"�1�o6���,129"�*X<��6�83&=2.aF= |N*~ 6811!)!]!��%*�742�b582d��@%147�*��  & 15N�m��  <*Y6��"<<6.$'4h�144&�&�Z%� | & 17N�m*-�49.6��855./4��8130y��^��8a���5�TA�C� 48.�$'22�*51.�>)� }7�u�'b�u*%� 5079�E27I�54.� �7�;\+"X<�%�3�1!3m�8^�09%�&� ��T3� 58.�&4ſ8�11*J;��4 �*� � ^��0S4aP-�e&e*44.�X@6�$ 89.� �97)@ .�8)�b�E3��)�q�� 57.9�8c32* ��5��K��a��� ^8�3.6&� �'"�/2@)� �**!^�V8� �� .(�'%y2j*�j ��"�.�I��ZOAsE8��Fa3 Z8^�F89e�"�3.��9!**Y��$��3B��0&*� 3.4Yg2�$!*\)-��+>�GB142:!�&##� %� 5050"J=��� ���9&�B4� �4��a*%� GB1508+57��l6/ �11����� ��K� �!N8�� -V5 ��N O&� C �� ^ 8�0-0&�&03g �4g�T&� .=�4 4.� ��/%17&�55��(RGBJ1629+40�7!z11�%H508! 1���$V 1�" @A8"%B0� 2�8>�+641+39�L� F8 �7* �32� )�/}��ho2��&� �v%�%722+243�,����b%~ $+0J4E�!� �v%� > S41745+62 b*�T5��0.4]�!�1�0k0.�"� >���+��+��+��+��+��+��+��+��+��+S52116+8"��76��1a a�Aޡe5� �/K�'yb / u .m BOct2��5!5.� 3ŷq����!�F.��2���+26-15"�:2Ky����@379p 6T 10 11.0� g5r2�)�F��34+�B & 25���)��y1.�Y749��3f�9 49-3��" *�6�3��%#F k�3^7.� ��$d)��E#A� !223+2� EJ�&4* @�1��2.�*���>� �-�z":�^ �.PQ�0k"/.3*p I�/ >�H2230+1� a�11:���?� ɇ22JA�"�#5.4�"z" >� �6���0T 2.*�8\8.4A!�� ��6N�M� ���I��G�.+$ 9!NA�q�VE� �KJT )a*.�e* 43-1!v.^�P7�=1�)6�h2l1.*�.��5� >�H2251+��a*0�8�%l5��F17�T22^ �48)*� }�%>"�'20&� v E �� {\bf Cg, s}:  1}=Object95; 2 servationC5 l3}=Sequence Number of the o2 -L4}=Exposure time for|5; �(5}=Counts r�5 inR,energy range��--2 keV ^6N^ �5(J:�Ds made before May �^,�52 c�-�@s are considered)�7F�mN�2--10�8N�PD5 9F\r6N[13--5\p. Less than 3$\sigma$ detec!� �omitted-6 10}=�6 used%s!)�best fit: 1=Power law with absorptA dfixed at Galactic value; 2>5 free:0; 3=Broken p�_x4=Continuously curved parabola ��5Z�>� 6rq):5.99 %+��0 \clearpag._9�9ca%�{Sources �9�as%�-fit m�8} \label�:Afit"�9��9v�0��N�9&&2{#21H$N_{\rm H}$ FIXED }6'3F'REE}&H1c�:{3-4} 5-7b1-9j::(& $\Gamma $ Pchi^{2}_{r}$/d.o.f.& .�&0^1Flux y �V�9[9�9 �9&.�9*�92A�9& �9!N�\�w58)e7 w)~1.2��I \\ )e45+13��3"6P� $1.9o 0.60 T47 �91/� &9 ( ^(MS0158.5+00�&�B�&" $2.2 �2 �1^86/� .^��229+20N w3w42%L:��@/91 D1�;�AW037.7 z&���:�n2�0.1��2)�IZ/R��� ^58.6+56@P7+"�%!E2.2�C�]5�n8/��:�B�:�FNB :e!��!�e]2�7)32E�0.2 �&,9��w*2�Wa:��)��1 T1T90/�k:�3~^.�W^.�W :�a9�%� u�5me�|0E! 0.85"~� �A2I^+�W& .�Wp1.9!D]�I�C*5L6�Th19- u"2.6����Fm1.2Z�7 ^�20T^*2TA2.�m"u� 22/6"D���e� ].TNF]6)2Qe�;�6��.r-��2M].M �0)0m ��/�.]Z]�00*�HN29>� 3ɟ" I�1.06/1 ]5� �6�F]&hCEy��F N#:�!�:&S$�Q�+�$d.6� 6&z �5:9MR10/�2!��5fv""7�1-�œL a1.59/51�Y2� Z�72� $1.8 ]�W0)�U 2�E=�3�/b�116]2.1V �� T �;/14]Ub]�7&+D 3 ����9 ]�WZ] )� N� !%.R-6D7*��D� 2�D!�191h�1.9mR� 03 �O/�,. ]'! B�D]29�U[�'�q~�� $2.4�"� 1�49/�A� �9 \\ A>Da.Dp"d3��3�� 15/2eWZ\ ^%12�C'282� A� �����=J��]B2B]*4B���3� 2� 0.88n]ER6�~ ղ1�� �&: 3J 0 ��'2�A�TaeSQH8��� e�4)� �Ft�&AHB�@]6�!i�29 ]96V��6�f)�$1]U.06V�V].T@)�8�El �1�$83N %t2(@N.*@]2."4�6Q�46N� h#!tS>�?N6SV91�$1�$ 9�aA/]B�?]*�?�1.7�&� M�%F�� F�?N11�U� ]5m�4e 0.97/], �])ѩ�"�oS "�e�S+b��S����&� in����������*�B�AAm0�LE�E��& 8� 6.���o�A��o��,a}��6�>"�Ao2.� � � 1 J�6�b]� � �7F 9J]1��V]� jA�1�N:|1.2R��K!N� uF��@� 2�@�14+ ��1�)� aOJ8 )�N>�@]05�5�M >�26N]�F]�2v@]*x@)��Q�M 1�1$t.o� BL@N.N@ ]Af" 99/5F\eV�8+7 ���" ]���2��K$2�v�"�9$1J23)�0.4Z��Z eA�6 5{ 5i���()q�h*%- .�1 ]3�@ n �J@@1!t.V "n ]1�� 3p 2R1n.R?I.-�"� � 76N�2r( *(? ]L:.1.09/R�j�.�> ]N3M�"� 4Rx�8!tB�>N.�> ]�� ]u�87N�f]a�2�>N082*V 9T3� U�81N�q]RGB�=<�� ..�2�( 0.73/4F�Q.� .�=�"�:��:eE9N'�83M� h+: 5 �0m 0� ��N2��d�VE>�1�:]1.1A�+ `112r]*�i�:]� B�03 �!tQ' Nt6��:�Af)�WV�Ft7� X7� ��0.75/�aB]MZ]*:)t4>4��4���DF�7;ft":Vъ�:� S4 ��-h.�>�� B�18ViEB�9}04�q� ��" 15N\�+!B\9]296�@B�8'8"�4ND�T]. �D[%P��I�8�7� � �;I1�"�2�8 .�8A."�1&)9N��2W8N�"� �V%1��1*w .��2!��2-8]�.l[-"� ��/.]KZ]B8]>�"�1mE1"�4Jn""lBn5 ]�!1�� r 52N� 1{ M".&�S"F5!�-L%tB�2N�%42�4N!=t7)���5t69n�]4*i4]3Bl3�� "�1R��@!�]2?4]1*1a)���"� 87/3��2. ]-�'�:[8i�3M.3i�1.17/H2]qEB�3'.�3 �q �-t�ZN��Z.3>�5Z�9N.�^%t!:(:4)"�� 9R�55!�:Y.a2%�$1"<-t"T27/f[i��VJb].E3-t-��"J16Nt�E..3N1"�q�:[�&�R���B�2].�2 �q q��\31J� �}!���2��2�2TPhoton spectral index#1,4}=Reduced $�-$7/$degrees of�/ dom.�@ 3 and 4 refer toO1$s obtained @ intrinsic*1U1to�1>Y1� 5}=I: *�1(in unihf Gh20}%/cm}Th �6}B� �)S7��5�7��2to varya3,8}=X--ray un�bed f'/ in �224"d3J-��erg cm$) s 1}$)B�1�B1I/ 101 ted by a �2f?12F@1rotate{ �kc�[&[4�/.�0RM15F'REM1"[4-7"N18!s�jjO1�qU.D1h1_{� )$E_{break}$ !y1��1�U�1�R�1L1B�1*�1��&�1.Fz1& Ek& (=k�(1�k�k�1�11@3�16F^,0 � �*� *Ѹ� $�] 99.4E�!7� 4X!�!?�I�;"&� 101-2�. &r .� �o � B�3.}� �Ae&�k)� A�!�� 1~� �2�D��1.02/8 ��}r�"$!V!cA 2:� 6-�K�  Mkn6?�,&)v�X[c)�"e&}!��%!'��9-03"�#'�l�)- & 8Af03*R�!�/(�!I1��� � !0�fo5�Iy]��3p02� `,100/�I`50�!%0!J!0( !0-�3"��f09"L0 �2V-6��50m :+� !0I��a�&m�6-� �^�43>�7=06� 5�3.2��0��=50[ 3�B0� >��s�!^�"qC-�.�+0m�M+!0)�2.Y��)0�� B�4"/2� �6� 27/2@�*!0>k�}IW�$$Tew$3)�"*i- �B���j�.����-��M`E� 7a�$B����. 3.6i-�8 ]y� & 3v�2.ɋ��149@6%�X:��X��1�n�� A�u :-]��(17zEf�.ڋa'��%J�$v70��)�MG$2�$:�]� & k�yZ�`S*:(1�1�FG�Xm[�A`�!�&1�X2�"z024DXf0y�P& �A/1\S̒-1IM2"F+%ZI�1.�&��X![!�A�*�) ��Sj�. � &� 81�1.c� �A�a�!:�X�h �� 5].�6}fC{~(P11;n��1.3ŁE�"�i�:2�Lz6�Rf����1�2.8�.�B%�lA�-�m�1.7!80FR4���eAR� 59v�.f��&sP�+�C�030��%:��jA}�1L 2` :5 497q�?3Q"���.����i8a$ &!!#-V�n )V"s I�A�5A��U��K2.9���\�K Nb� � 2����U���|gr�&� �ay���-�� �QWuՓ-[k V2�V&�#$8{.Y�%M"{.$H`�4� Q�6�� )�"�:!.�8$�)^�3�,080�<39�����v��3� w Qw6��ֈ��S4]2��")�2��).����46 c"�7M�� e��7 ��>-�%]6��o2��(05�c 0%:{+�E|042�,0� !�E62���"�V�1F m 5 %.5;u l23�/$1B= �c��� � -.�%�z�2v��pr2�+��Nb!�! �i~y��3v�*҅E\0"k 1.4!��鉋��2R'��s 1.6��z.5YA\=�Z8-.E\� 1s5!�i�5�Y�r �?� 1.8��B��.�17r.&� �0�^ų1.5-.%�Q����= Iڢ�208�b.&�:�� CQ���!5.���$!�Y�l 1 .�)c �ō�2+A.Ub�:�80.08�mU�5: bA�4�;��虸e%[I� ��.�C_j�p2�01.0&� %Bb!..�&[ � %H3�6�L3mV�1Hz�� ��5e yU�42.J7Ew �~!��%�).ɗ>��Zf�hM.�E�� &� |%6{ *6�O@ "�11�Z�9�!�!M�� O'-."�C:��# )I�O)� a�! �I\B`�!Y.b�*� ��� �T!1�>%72)�%H)�̓ 6.9a�� %6U*��3� �06Z 5� ��2���& ѐ2/4MP!؉�A� �*U6q�3" �a ��l2�Sefo3�9)(�>-�1.�;bI:;�G�4} 2���u;6�+3r�$*�A~.4�#�b �"�!�!HIfɐ= �o^�'Q�)F�:0"R�<7�e�"�6BaA�2�+ �8Mq2"�Ų�A��!-&�@ �2Q�(.S�� 82Pp!��]�Yd5a��3�P N *�q 5]� r�jd62"��&�EI�!�A�%�ƕ��*~�8v�,"�7��7�0'�A!��I���"|�5� %"1� aa�B��&�< �48&���~ 7M@���ix�5��G f��~�Bg���(2�211.�fP �)� �0�� yq�2�E5�f.�I!�; �;6t։�; %6  ta56 *��V6  ] � � � � � � � � � v ItŬ6�>�>, 1RT5�>V�5RN>.��31�6�ݩ� �A�  �� YP�����a.N /3o B{�����<`F-�� �����i� 8��1�4~ �� ]l�Ե�ԥF%e6-�'9&L�"���0"� X;�3.9�1.�1��2S6��r5.���rO�@B�ݱ�R�  � 9(1.7��2�!�Y=!G]�9.�B�(�3y�-.:-1.��� Y �g 1��� �'"�1�5�>l�!. _� 6�&�. /*1B� 6�b%.Av!.g &7!8�@%�f��!�B>�|}�+�1.2�� p%��!�a�� �}��$&�z� 2�\!.n=2^U���9sN2s!2"��Q/"� p�NE/2� �!�)�yy1�"�Z� 2�x!3Fu4*rA>i"� !F���5�3��� V U�"4 � ]A�u]7�V�.p�2\E/@�E�eeQ/� � �  -J1.6:c V�1v�.p�1��aCO"%�� a�h �=��1�z.��j� D�^�"(2.0).�:�"0��� �PE�%J"1"� V. 8�cA\�}6�"��&�bI).2q�:�#%.�c�1ű>1"��)Z�101-.PK��*l%*l%.8dU�"I' �������La��&�B�.]Y��x!.0.2�f(.�f�9*�0��!LE\=�6Av Qw%�1���;X$!�]�u�10B�".kZ� l}{-�.. J�-�-F�-D-(4}= First p:A.K-"�-E�`�* +N�in*"`6Ya condV[.g. to 6r- f�- "g.using --b>n_orcJJ_^�b_�,h_��.*a. ",$vp8}*�..�^-h9}=)�f�j� a2�2�115� RF9�7!�11:�f�blovaj�v�.0.b/. TheV�is�zD0;b�e�12n�/A�ei �c��/\�/).%*e�F�Fn�Fa:�F"�`ingle*�`e5%d�/ in T�~\ref�:�/fit2}��&a%�lawF�/~�z�CjL�.rT/uQ.S/V�`K/��UR�.���.��Jz` "`�.�.s0��.~�.9/h`�Fg*e Ů ŕr*? \xQ�t. 7/25ZjB-62./ �0.M^0w`&�)0 �be>-4A�)�e�g ExEf$fe*��%/XeAC!&F/; eG b�"�%��04�$ m�5/�>e]^/ be &O4.3-e�j/m(%�mj�U^� 5.93�2.�kV/7Ay]�Wr�/$�2.5e1F^L�3,��:d+7�$=�q�K ӍW��f/�!�3�e!y \>��P�e:�*3�F�e�>e��*1.36/8���q(�=ӡ%�8-���/ ~_*�Fe2u(͵0eq���R\�&*y /9�Ae(���� "��"��Qf�:�)1�=e3ei��!%�1��i2e(�2���)76�^$UwI^5�4e3,�P�e5*!���:�)1�6k$�?AC 5f"�q(.!�* �!H��O)JY23�� �F!&��q(�^!j) Al�PK�Wy0� B�(4I �0-/N�|zW����K�N%/! �E^�텼&�C�4�j�"��%�1.3* XteI�N�h]%�r�&� eT"H+!���� � ��.M�re:#(�OeѵeAE��en�B�'2i0; 1�%�� e&�Z�neB�'62�Q�Ke� i(#j�>�'���f� 0��%Ize�YZ!�1.7�5/^�2/e 2^�)' e�e�!{%�>!M�!��&�& �7ѵ61�"�h��j�R�&�)�2Q^*�Z:-h�&X2!�i�2��3aGi�&�n1��:\�%00:8aBF&�3�(f%��=>!�55-"e���:&2�K�Me�)�F�2R7^P:�%5.7�%)�!�E^Ne]�-/J&B)<e(4'��9�%z2�.7Fe�~%1"�I*�as� "���>x �L%3�5/�PFB � ��b���+"V�!\j��"2"�GbE�2��F+ ��!18/�05G-�A�2"Ts"�4��J�B�!=�4f �!Dž̥�e"^@:�!��&WaZe /"� �K\\�N!2&o5fe�IeZ�5^�.D�e804���*>e�� ��i@11�2�� -��� ^�cM�2�"�' (J��-�M�M�M�M�MMF��[�6"��?��54��35�F"���"4/�f&�O$>�J6ܦI B �!8�beq�*�)f :�!P�/1�ex �e�&n!�:�e�¥urP�;e�%3.0�F�/�:>�� !;�:f%��c � %�� .g��f:� hk�294� 1� !Q"��eDXj"N�:�� � � �S 4}=F|M"�.4�ON5FON !W�� 2uM. �"?. Kirby, D.~-A. Luh, T. Maruyama, C.~Y. Prescott, J.~C. Shepparde� J. Turner�8ddress{Stanford1N0Accelerator C�� 2575 SAE$Hill Road,`Menlo Park, CA 94025, USA�mHE-mail: clen@slac.s n .eduA 1R�pos%��D2�Physicsx Universit�<iscons!Jnn@Madison, WI 53706�\\ � makeEX}bs%�s{ Fu�� eMb(-positron lIfcoMfH require a highly pU�> beamJ&a pulse�'̆pt depends primarily on whethe�&a1�$ion utiliz؄arm;%suA�onduct�"rfas %Intern݈al1�C � (ILC) w!�us��ldBe_��mai%ac. IteAhow���� dc-biad�9J&5 s�� such��,successfullyy&��,SLC can meet{charge1n ment� ILC micro)\�'a�� approac�@90\%. A�s5�{C]} ��S��:M (S!! estaŇed)� reli�C�!�q�>�tE" &.� 80\%�be�@vided over period~W8years. However,%n>Rs plan�W��fI�Y�p�� nt new de� Q"LC Pa)riA2�o��int (IP)!�exV!o�sis�& a trA!9�s spaUXsim$300 ���[8. If one assumeAD {M'iEc prud�to!%n to g!GB�0at least twicaOe 6,��A�IP%5A�$,-=length, ��average�Vrx!F each�!indica!���"I' le1}Kcompar Y both�N��BbNAb�A�design=�linacy�>�(SC) L-b@ (LB)���y�,, but normal!��0(NC2isE�ssibil�NCinitial6�i��pfinS�or. H^ i� �A�st g-�[Xillumi��ng�<-doped GaAs (or �+Danalogues) crystali�circular2�$monochroma��l' tua �Z!5 -gap edge�.y+�Y��n�� omot�0s from filled�a�J s�Xs]��on  (CB)E�Han atomically-clean�surfacEgtreEew�� Cs-oxideR �nAgb&q[!�� -ben5�� fun%��kl+i�below;0vacuum level, ��ngA� a negativ9 affAy (NEA)�%which CB��.����~� read��ext�uI apply}z�b.����v%cathod%1A(emely sensi�to any!�taI\`on. To reduce field emiss!�to K -zero�3e�gun was � u-��% 0only -120 kV, �re!?ed!>e*��m$1.8e�7 MV/m��!�Q�a��]O e�]Pively\cite{all}. Unde)�ndi(s,���� limi�e peak��t�~�qbe%Bac� to ~11 A,��)��u�ed round�Pof diameter 2 cm. A pQA�.E%@tempor�[nd��g shap���xia�� Gaussian �be �I�:��Pre �ICantlyI���Š1!),(SCL); e.g.,-�7 A!�!���J )~epp}. I���6�2��-]"� �#���7��s��"ռJj� �ereno SCLH,blem regardl7�of2T a�6�ng�8is SCW NC*oi �j5NC-SBA4acdod�som�.�Sle dampf��eb)�� could bec9a�asEs� !;'�3rd�umn����[� e}[ph] �"� 6!M 6{A�!xF  .} {"[R��@{}cr@{}"/ {} &F$\\[-1.5ex]! NLC &� SLC\\[16&%m & SC-LB &�:-�& D>B4� �:=(2-cm)0�.F�($n_e$ &nC &5�(�20L $\Delta t) s &0�2 3&I_{\mu� ,avg� A &4�3���� &6.7V3p0_2.�e� 11 3 ��*}&�0� } \v%�*{-�~1IJ "2 �] 8 highS���n-� )aZ�� eved�4���2�/Av natu�de c�heavy- A��-holeS ���2val�� maximum� remo� T � a�p]�u'odu�� lattX mismatch��h� /te ormusa�a��rt-� � D""X (epilayer. B Aco�)2of7 $echniques,c ! 50-80 meV�H1h�suffiQ�� �s�9o�h:�  CB��)~%s!l��, giv�promise�10� .� . In��l��s $\geq$� hav��en re��i wat}� �re65 ity-viola� asymmetry� ri�ځ��)�?50-GeV�edU���, E��, meaȘ,d $P_e=85\%$�xed haseIa!��e-%�Q� ���fi| 6an!>ineA�u%6g�$ �U6Hm5%T>2!'ACpar�!�.�� � 3� t � !�thN 2�u�sA` !eEYe� 7empera�e/ ei��(� 20$^{\� } $ )a@cr $ )� 2�of�c"��h��ow�d Mott B� s �@a6�*typ� ly M\o ll�r Comp � tk�gsr sq ^ ga> � at w��sj �h� J� (accur�<$<�<5\%�(thin 2\% af� corr Ikn�de �i��mtrans*( IP."��).s.�rp.j�e�fz��C- L& Growth & $P_{e,max�y( $\lambda_0� QE_{()1!�%� & Ref �j Sa�ethod y (nm) �6rx:�1aP/G&MOCVD���JƋ &775h05�E�&�KsO :SLa e�JNagoya 11b6xBEd86 &783 �� &CTSi s mar1Czt��&{/!& �{�0.٪&u�E158-III7 8<�^ :^ 26�)H0.82 &8Ȼl1R�2� ӭ�jx9J:x�Taj0%<%��y �1Cantp\j�MQb� 2}~� Si�a�� ��� vary:e��ͪLano� � sam�?" �0W even \pk few ��amcC���mA~  it h��Xery di ul ��2��� betw;6eac&icS� �m�in< .�!E Y�2��emselves�(� ly gi�in$exI � JLAB&* RB�Rswitc� onIx -to-  basi� �3�U� \ ��2Nh, all:M-ƥ��a�DR)=����gra�te�syste c effec�nd error> !`simula   �� 2�:yzA&�=s�Wrevea��=skalQz�As� w�R} � r-Am+ k  1b<LF͓2c Be when&� bynI�a.�S9�6>� �data---��*m1\%a?*� U��!k E---a�2����� q�isab:��śk A���� a50Hcut�^�)%af m�lF{0~of (8z� 4)\%*�@hebibliography}{0$bibiteml R.3!0ey, H. Aoyagi_ "�4 {\it et al.}, Nuc� ��m.%O. A} $ 365}, 1 (�!� uc K.xEppy0T. L. Lavine, A. E� 6{i � Conf. Rec�m 1991 IEEE�t.��Bnf� 1964�12�� 0 O. Watanabe,�N�"tani,�TogawaZ� SPIN�"0}, AIP �b".%571024 ([02}Dq&�D. � !"6 :�%Appl.6. Lett.-{8!z 2640u4>u2:u6� J. .� j��49� 199�22��� P%�Anthony%� G. Arnold�  ArroyoN|$ !�f6� q81602t6��|�M. GramsC.!�S� air,�]llnwv. ST-AB-j7}, 0428 v3�$,:xB!& и6.#0[11pt]{articl�\uckage[n�� ]{ac�do}.�(phicx}% Inc�$f�#�%s \new� and{\dg}{�G$}:sS$�bO�J�#ept�a��,al Equilibri�[u��via a!lgle-St� Shif] Protocol}"*"F.\a(ty Ytreberg"�{q" fmy1@pitth" ��LDaniel M.\ ZuckermanF9 dmz@ccbb.=\\ lut�4Biology, Schoo�5@Medicine\\ Dept.\�tEnviron���OccupGDHealth,\\ GraduateQ�&c$6�"$Pittsburgh�&0 Lothrop St.,2(PA 15261} \�${\today} \.#)�a�ct} W�"udy�Bco$�o!��"-��W wo p)�s��a novel isechan�#� ach  �cal�%�f�)gy y ce&� il� s-similar>�zOur� s eluci!� trasp role6 ,entropy in ici� solple  e di ���decagly!�.K"m�ext�#6ier�by Vot� and �!� 0 notorious ``lap'' pr�in2comQ�sV$�$ing a math9 i%�t9il$_!N?}� -Wity �5��$s� WE um� i8of�xA)�A)Z" est,ƪ*�neMsa!r�Km� =.A�4discuss extens�qions of the approach to binding affinity estimation and explicitly solvated systems, as well as possible optimizatrT. \end{abstract} \sec]{Introdu �} Although free energy differences (\dg) are fundamental to�descripX��yevery molecular process, computer-based estimation of \dg\ remains among the most difficult and time-consuming tasks in co_Q0al chemistry 4 gy specif�� ly tailor�*�.<. f no|e��j � r�� red,�!��z ��!to6�re�c&* � s. O� ��oba���eƁ�r�qc�d}Acv� eQ e9 5 is fur�combibF  Bennetta*te��N �I�b #}�ef�utiliz�� data. T�woews, (i)�N�E� (ii)� of N�I�,��; �backb s �!"� 1=9��ed� �outline iG portMh�KdA� e ne8ary m% ��� work�B�V� ���S�� sec-sss}%�*Fresult^Hs 80on leucine di�L (ACE-(leu)$_2$-NME){ GBSAH � solvent�rre�&E m�.�&%�< and �. .�alpha.� "x� e F��A��wu* aKemo�r��various B��� show%3im!�b AYCR�)[ . Fi�Ae2�l +� � predict5j extended�@9 _  gly%�)�$gly)$_{10}:�-�. WhouA, already .1notu� cy (ARtYons6� , woqbe +e5 �lyv conALio���)AB)&s)� �0not yet pursu number!�@fairly clear aven��o*�;!�se%discusAiJ7opK2�%xsio��r� to er�n� ``al�cal'' muas,ABo�pN�ex� "�\label� n�}��� �> �.a6=)�1 chaA��Z m���& � � ��on. In � nce,��ly �val��V,�i higho%peraed eadA 8AB!� origa���R.!2ub �{C��an^ ��ea�g\.�} 5ider ���def�by��� gy&� 8 $U_0(\vec{x})$�m $U_1, wx$ %$ -se�n&� �"0 �?� aD.cqu���y !8 s, or%� bounTun & %U!?�. F�!LsA�� & %A�axst��� low,��$�b same=7 �� ted ��i�A reg�h��" al  (i.e.,�!�Qes)�6r�M�AI2w1Y!�giv3�\begin{eqnarray} e^{-\beta \Delta G}=\frac{Z\bigl[U=�(\bigr]} < {$Y) $= G\int d M# \;s.N}} Uv2j}},ÍPeq-z1z2}#�Q��=1/k_BT$} $Z$*� a part� 1� (� g1 �� u�e�!zLd & J&�at�� imp&�E�E�is�ki!�isE�� Gibbs2i,�� Helmholtz.+. U�iEalis�.$�"Q zwanzig},��0re-write eq (�1w ) as�cQ F� \Bigl( ]�E�2/-.� !r]}<r) :g]5 �h = IkBiggl<]�zl��gr>_0>� fep1Z�� $\la� ... \r _02�����veragA��0$�W�x;��;��">  #A�f@�u(F�s)���a\dg. ImaN!w������66.hn�1$��l 2xɐC}$�h is c� spo� 2m��zf 6 s, =4x} \rightarrow��+��C}�@ $���"�=F" l]$ #un �d b�>p:jal�9�y�EG)e�now��a�����ة�j�n�5N� y�r��� 5=� gl< � Je�a�.Y�e5>dIn princA,2.)aIl�a�4can arbitraril�if�.���e� >��"Qa9m� . (SLat 7.�� $# �sH analogouU .) �ac�Q� be d�to maxim� lap"�2�� �S �.>�no!�,t Cartesian}�,R��b�P�dl!nct.�.u sto�� erefo� pplyQ ���xf� !� term)v�'�_B��o2�!�%#o�%ehi� �i��". ,w� �� atic ����s!�wH R?a,b. Sl�(%��#cA�a�!%��Trans'' well at $\phi=0 �� UB !$2U%UgaucheV V\%Vx-150$. .�B���6& | ceU�!9'ma���AA=7� ,roughly 150 �'eeq�m x% ) prmARdc�#|&u:v)7>�� xcelQ�Q doesI� not}�QZ)�"� "j h thus�t\[una�&ed*� , b� Ne��w>v.>&� &�#�**dur�FKu��!�E-be@x!A���c^'crobv"u�_f:Reason��')�. )fr ��in�us� \*�U8�bi-dii�E---&�M/)�2L.�.�# (e6�})), [��U#on�uN�cach yD,25,d�� � 7  : � minL � 1.0,:= (!�Tn= )� _� � }� �~"-� )-.�� b~1 ~>% arB$ S$�#g2�o%�U+��A%�ed * lea� 5followAre>%o�v�%;l<�%�1+J�525�+1G%! gr)^{-1)�iE =%'�xUx�9��x1>�!J�+E i v&r �e�h@),$+ must�;��an=� fashH Eq.\&� A,s un--�e��)s�)�e�wal�7J"bett,c../�)prl�$��low����@2w�AY��A���g\�� eqs�� , ar})��"+�})�+�:>�x�Ay.��y�s chose$N�  bj$� .�ɺ. �6#  F���*E9 f� Fu� -0ofJ8!F-�mS!"c!��MKraw��:�JiP� al �30F�"arY s} D*2[ 2 cU 5bAF� invH s ma�1a! i  ab����"� �%�� 6!�/�oum*#.��%e�or�#� , �B�%���aj� � "[O cs�u:R s� a�}!���7 D/�po�55 too�)9&,��aqt�eric {.H. :*� b=ow�.a��  s#O��6� �Vn�!5.  m2@�� YY��� d%���AEG�t�&R+ %�e��u"1Y&g � u�:�i�;#� : af�0*�/&��+(" ,y�lowest"8rame (snapshot)%|�)��� A9en�oA:h� )G'9NE1 aligns�A� x-$gyz!s,V� ���(y}_0^{\rm\;!5} - " y}_1.>�ceB6 W $ reT"eZ�(+� q/)� -&�-x� Stri�!spe�], C}$�a18.�6I a*�zer �8� pon�; �A�)�y}$z+�0�)cy6e%��7yG#� Ű�աW�0istogram;Edy 2we@AIA?.�A�a���#M_��E>%b!?�94��>odeV?B@hB@B��e�i֩p�)�se-\�v�"��*� Mm�+nM"mp�AS4$�3ocv� by� �a��J_22�x_2+90.0$ � Then�#� ���Kx�e� AH :rd w*� "� 2�$.�Repea>6 ep 2y�p=1$ 2=9fw487�%t&��2Hs�i%:` �!�oppos�"R�4-)4)��p!.�&e =6�S 2)^� /orY=� �!� e ai�/+e�>}~�I $gs] g�*a�"�1e�Ss, �mA� mean %A � dard;iE �a&�.|&en)�!3N� �55��1u�u}� s�aq/eJ� B. �#�N�E��2m ) ho]+� �.s% :N������ "<AI�A�ofR� � �2O sMe6 s. BY(Bp 28wcub�N I]: $r^32�$r^3-r_c^3$� $r_c� 8.��� �!r:.� .B�� u�+i�-;> �&�C�I��� e*���,��b& aau �]"� �0;2Be}). *��eqBY @$Y�2B- _c$�Au���%Ced via $I�6Le�- _c$S�-.PG }R�DV} To �-%��@ iven�|)� L B�8 &?all-atomA��9.of��-�*�Z;,. Both� wA�� 2� $TINKER Ver� 4.2 &:�=s packag�BE"eW5�*1$ c�Eadicitly-�A�ɥE0d Bornk4!�a (�.) ��still�7 Langevin���d]�fL co&^�i2a6 w�?((91.0 psec$�M A�1 !�!fsec �4�n���-R!�. LB�/2�;eda9 500.0 K (E?] indep$.n�r�2R|�I�)��!NCHARMM27�c�B�HamX��$charm�?Dec"r.B� 3 ��.$he AMBER96c paFca�-}&��ariso�Dth>x7:08�.,BD}JW./2�0 �-�wAi�� S$ (i)����,�m�Ρm�Dty!y�?m � f!�>(�  e%%,-chain ��;!O (�2smA8eno�HtoAFow%9 very long]VE�A[Na6&�2Ban,i�C�6YYl UZG #o"D pop�� (heE \dg)�3�laj5�0� ��r2. �,B�r&[ ���::c2g\!D�C:�De��$\r!��&$� '.�h& . We'  ?A�#+�5�*��� B ,"^=�O: $-145<� (<-25 \;{\rmh}\; -12 si_1<-5$;��?�>60>40:>7 <172A EeraH!�50�l}�vr� �2DI�of%H.kbarrier�*@ � V) . At u�>�4 switDO%%ZK at a � of ar� 2.5Uns�,s�T n���j�?�E�. N"l,- h�0.!�qu�7�!�7.H C �\d F� !3F�ռ&6s!1�"/$�r.��Tov. !duni� ���K�urř$\mu$!݊ �&p"�1FA�$%G� �Gp�"�x��� \t �$.kHr� �:�a"N2t/&�!�v -\fq/1}{�.} \ln,(VN_e=a}}EE}S)gr�&� iH^� Q C e$�c,�p1 v=A��4�"# stepMew�.~4F B�)M� �N�a�fe�/A\\ $=0.95 \pm 0.05$ kcal/���2!�QN f�&1C)A�E Ujqs av ."IB :"�deR (he�JR8��J� 9J})Ag $TMES��1UI$ avg}"$$�3 $F$"� � $ DE- %�WuO(T$9�l!i�ce2#aJ=D�-nsiw?t'� obser��z@!;fluctHng"�'o�0doMFS�Pmai�(D��"�us do� 6�<4� ���! .1 s. G m�'���@.=~.7�vfav(7� x=ra-A��P r at�QT  W��*�:��2�I � is� i1Nto �vcE��-)6g0-�8v!��.���Ke�Iw�� ei>�R�2s s, dui��2t��.I. EachA�20�����8str&5BF�!� stayE� ���ed o1�)���A, i����jforceyi�=Q� �m6�a�#vI�� onic-K$wise. Fram���avySA 0.1� ��10,000R>��~%|2C�1�J sixt$I��Z���S�)\� ���Y�pairing=r*teC�umm�P�T�m4(tab-dileu} �we�u!Ei:��& ';A���GS��D%sIj!�!��� B�I�)s\Eݨ.(.>�>6 � K ?)HJ��8e#.��5a�'0ue�**�:J� �, ��to%�Hll"�%Y*�F/, .a�E�kA?Ps)v;aS,!�C! %U*) !�"z#��!|.(y�!U>%)Z�#�$��e)�U��2se� F�s�_ �en��B!�RhqinZ�agree ~/�3�"; U�.�e�te=9FL+U1� a�*���/&�U%�)�%[-�$o=!-&A l0�BA'of *� %�D?I�Z�(�"CnlyU~�)�DE1�,,hP��ly�u� -1. Also�9*�@n#V�, ��r.]�.�5�"��+"�����2��2�MM!~:� W� sy$�Sa)�c�� k6u( E�>b���!>"Ea.m=. 6KJ�/��-�are{:employ�VA� � thZHe/�4ys roSX:6�.�p*TS��f "fs Jt/j&*;&�/>l�2F�j�9B�22��yetbAa superio%�"(Rpro���>a�K\&��B�%6����Zc Y?Zx� �Gn dashM2Ia0�g:> forward u 15YG}� \&�. }$��!%�M>��r� sey�-$"� �� 2��� %E�s8O b@N�9A>. IY�E%n�-�ŤI�6!I�is� �Q*?�W!�� E Z�  Fu�J,�_>�j* �A>��\quickLha�o6i�>�)i�df}.�e� Wc.!n� c�%B. >����ab�Va'& � !� d(.e)*a��)�%,��  (Esquares4 F� , (errorbars)�_ Bn��n��:d�b5�Z� �})q ��;y�LE��+Ajun��xV�u"� &dK�E� �61R, oAa� y 40o�"�.;>xJ�)�  3 ;a,� (15�in e�ERi��|&�)y� � Aprecis� _EJ can � �N8u'�R{*M}"; O<%\!�.�)�� in1 &� �>K,�kK�'T.al ��JJz�)6J9>.Qsagain"�u AgR�KM� "� F�(i�Fex�a�'1t\��K)^G1)hiB s $.^G:E�!F"�aA. in vacuumi�&v by Kq^IKushick) .V�cqu�'r`S?$CheluvarajI�M"kV FFLAp/ �P,.�'|.� 6�l -%�L ��u �4.�Fent�B�-4�.S6&�.sm R�+}�"qsU�pr�� us,N� ��\*# B@e5�=M�hY� nsec��vwWamJ"x �x ---a�gR>] Isub�M$imal; see B��MAs �B�� s�6�&) <g� &�  œ��&!�I����Ao�Fr���~:*iX2 �a��al �j r� � 6�11%�CZCO+{��N->BA"�;�io�s hadgN]A2$�o"�OՉl2( a��vN��t!� 1�� l6BQ� Uby :�P"ZgZ er l�f!��ODk F Z�PJUhB�F�62� �i&� 7(�}! Z�)A�h��D�0B�U�g� e ``�%ens�'' �f� Q�� iA�an� ~e�.%in&��e �f�8f} (�� ���h�4a�� group�=:A2�\i�&�i�2�isY sET!nA��%d, due m�oWetics*f@� Q�.Y� A-�(у):!���66#�B�".��!comes 6�$�r1��E domi�\!��/� D9p2�R %G$�J*�aYa�KE�M$a �%HN.timYE�]%��!>s�*�"��MJ� g�� � #zJ8 � (� cir�m�se��ŋqͭ��>�+��#Bm �6�(R[Nc*�� 8 A)2n�&&>��. &c#it 5V2 �^:aMo �a�=wF�-� W (e� di�)F )�'1�rB"r�g"� E�Iicur��l&��Tto�� of 8�o.�C�2 _� �*K ��A���9�P�M�#0ur knowledge,�I�1���:0�:a�j�`�Qc"(, undoubted��u\!��� hibi�,� �al�Vense. N_the�pbeliev�j�#�a*�W��-I&�R"�;_)s,�)we �M4Fe�qYt�6t+iA#y!-\.�,w�&reflec42��"?�_a�f%���a�tEN�WP ]d@iz%2�P.��3u�$ }�Y3��O_ �i6-ap.� A��Pa�"Wn n� Y�� !�a5Wmi���nue�`2�� �'� �X . WeSLef�Jketch U 1��a�ov" & , n MF !B+� traUnt!d.A0tus�in&on�"�Iup� limiPTjco*�h ,;, }��[a��i�t�2mad�AZ%e�ra�:�D FU )!��  s�ted�\�8 �Yn2� (T90i nd r !d%pe�"J(�}d, ---%���bN'al��)Ato �!�&fA � ixed�'bI. "�h�Lim&M |� J"lit�q6L .hd'n F |we feelI#�K3fincF=eR y' rI bq 1by�/!}Oa�y} ��~�(�kY��step. (i8Bhw�to]qE���}2 e�. over*�!$U B0+ re-�%q�#s.) Ul�t+)n?)liu ��ac*� 2�^� v^68 no[ ~F .�sam�TAq��2um"�s!/a� �< �^�4TA��h�i� F�teU!�u,s�8i�rIb ignKu�O�H� *e",�h�� n � Rama!� dran plot9sV�C*A$ �'v�b*k ly. JY%a!��ie&.W%qresidu�71: ��vid�,[�em.�DT!�tivatUnreal)Hs�#�]one5"tea!%AT�,�gleEhabqw�`� � ver�mi\>2�s�9+�!A8I�0� @�tAr&r0t ori#z��#s�a vn�E�E0 s al�7(e+m)�Iy.)H17e(Qeq� Hll�&XT!�TT���~$/�i�h%A��("Q-3 -�r� ) ro � . FX�'�ob�h#�!0]ow_9@�#"broad�d ;7!�Bi (con�)/expaQ) PU�#be&B (�kn��kF�h,F�i)����m ��rbe�a�� ed, %�n�='/l& !�o�D4matrix $\bf A$��?:;Y{$}< + C�12L> U!%y� ��yT4_w��A�6��jr! A�x� n� ar �"� E%� , �v�j!��Ccal�$�� Za� �!5is��mwh$yC eins)��inU�* Ŷ� �Oiq��)e^bu�ha2p�{� ͆2 *. �4� valu<I�8che��c epS dvantageoIo�ub�g!l2^e��<! �X*� �}.�=do   path!7npn�#-p�� % �$� ed -\>5 {(diala,roux, ldyn})I��7A�C4# dIj$ a8FtF2k�:! �vnfU7� �wzj�?q I9 �-l2�$&(B ($\d�a$)NK� .?5�AbJ}j�V �~�*� e \"� �3�2 $$)w.�ful�^A_ lete- R|$EY2o :efk*m �� _;�!�n"B�}4 q�a�2��e��`�R�M� bey ?.@x�U �� ��A%� x� �A�:e1��"|JL>�&o� �be3P:3 m�g---��Uba� !�,R0z�n.���>s�~A�I;tembe[ o��b6�<���or &/h��d�[���sF0$��E$--Ԁ�eHC�:�� d�;�K�9^K.*�.�gnmI/i�Q� g!u rom zsi�a���%Ns �A7;e�Q&�ru��G�`QA�&p&>���%+3�E=G� �e';�� l. (!�6�]�B� �0�F� ofF���%��alway�.Rme.) �N�-8�} c�<b!KgWA� ``dummy''.=C` iB�t��v�}9�Ns bO)�e2Hv26��#,At�7a**ux$cycle guar?|e�M.% Q��!�c3+z �E�#haAj�Bd"8q�}Ñ�2�:�"m�-  If�N7�5E�sA�G*�6� 2�3]E �4� -��Y̍�Z� i��n9�GmQ�,}m�a���� ''.�!2m6anE�p&�a�cœi�(by�" roduEGauxili=ios �H�Sloc%%c* � Eul;�&����@or u�F�A*�>9$ �y�EJ1 ���pslSi\ -�%)&Q6.�$ɁMlclu�up\a!A��"\a"<(� 3 �*F 1�A-*ly m�a��� "�yn�ZngeF?s ��:� ntro2? (\dsb 6�T ��new�7F�^Bs a)��@%MA�&r -6��# �"nV�iE,���hb'�i��Re2�vvgA�&s��X�l&��+�F bW�UDU%�``e�d'' � }�s"~]2(um� � s.5+�*�x �pac�"�K�4�)E raw �XKƀP b6"B �wo M�n4�'# e>a�r�sub>5 s. FbwGBs !\A�� � e@t�{�.�\ !�*QB�!s �6�"�,.1� judNr by n�Q&ect�3 �a .�**�I9F' �&�@o� e �;,��*�;� Yq _R3 Qd' Q/t!�.�al ]a��foV,��F�(��.9J�&,A8a���VP�Y�E/1���)�5R����5�;��,�& !N�� � �)e�. B���Wa"g(�_ Y2Mp� 036rQ�ng!}<��3͌ar� e�o�It�� bornem1+�quantiJveqr n;x�aEa�:���a�"��na��vL� crib�In �m pu �\!�!; "0.�<�3(8.���),�g�f%~� X�'�Sx� a�in�(t%oa=��u�7 6� �z.�E��Xy�h cu�u.*A�`���= �~68"p s (aX3 J2 �.$5 f^�\� q n�5n6b)|{Ŋ.��S�y�`b#� zly� o?<�se�iAN� *{AcUh �3s�-�!�!-Tkcjlos Cw0o, Ronald WhiȈSr�#h.�+�(Edward Lyma�3fruit���iGFuV���+search�(����' Dept.\!{Environ�al�"OccupE{al Heal~��Ce�eC. B"�� Bioiqcs�i!� Univ�Lt� Pitts��h,u�N u Institu)of �(G� 4 T32 ES007318)g bibli,Lphy{/home/marty/res/~(/tex/bib/myĒ�(page �tt��} |�er2tab�� }{l|l|c|c8Eh�  ";j &KB& I��-" & �).\ �  \\ U� &�je�2&Q&��(kpD)JH� Peak!GPB�:"�6o� &�,8 (0.15U 1.023)Q&�$ & Alr$a= >& 0.56;87I 0.556 I2`8E:%2RAo.C)R76 (2.64qsr�1 (3.25 ] �RV R8R3 1.09G �1>L�]�>29�3->309 �uI2�>�9I66�0.9%�!�?FIF5 3.36�47� 6.48 (9.4-*6�e}5�j5$4.50 (7.16:�(8.80 (14.32 �)Aq�M�qG2lcap��0R�-i�A C2\�� F�?) � ���  &�4: +,(�# .�� ��sR�q�. �/"j� r,� a"�4a�s?) .'2.0 n�$�{Hwith !:[X�)\< � H�s{i��r��:6kYz }) AY�B�9^9�. �A]iso�� of� T �rom> A�&�;}a �K05)&qI. w� 6�"2nR�, I � %GiTHG*� ! b�bBPP�78�[�: *aql��N�c O..!�!2s)�c#st�c<�h�� *$^Q6�.=*)a��K�����.��qI�",�+J�� �-12.3�� 47) �|& 9.7E����#S5S82�LRI�9�u6�h����A.$&[77��9�.& 10.127��A �-�� 3.11�S0�7$1\�7,-11.97 (1.59[ 9.347c[\ �@� �572R�2.7��I,-18.53 (11.12S5.89 (101� :��V-24.7H 4.03�(22.15 (13.8 �)`�V�Vh2�XAl�g�,u��qk�\Nxt .��� ��. rv�=� [:XɔbS d0JT�LD�K�Q��Q<�* eq&�P.� �q� �sB]3 %)a Z�5 \R{��"v5 �atF�4 ist/>"�gR���J6�u �1Nm5 �FL����alA &� z� 6ď"�)*8H6c����f�3V�  \� graphics[�$(=0.3,clip]{�-�--U0.eps}���81�8%H;��n> "Ǖ I�� 46OA��uI�c��$ �Cv"cs (a)U0(oW)$ (b1 c r�gKpa�"���� �)� bm�&9u *�*deep,N� {�V. (c) �Pa��� b{pr��� �ta�[ZpoSa!  ruct�tЁH��T ��� �� alQ �!)*�bF� . &4�v&�0Q���F�{�sE9�<9 (�#z;�# ), hՐ5� *�+7�$�q�E�%�V[ �\b/�Q�fQ15m�-�mi�43r�46i�are8 ��f��:�a � <�m U'Sy��>s !�A�:��. /%Nx�N;SG��9�6� pha�4p left, ``cis-�,'' )!B (top }G$ tran&.�s A!���lOnT�"V7 carb#/o܋�I�wo6!'(9+#a3(*)�7�Dd ��1`�&u{��6�2&��yhe!i�vJ2'!�2Y �."mJ�!H*" 4V���I2 w�)5S��rr!ed��wg� , ak �������h=&�8�fB�<�!Er�uVHJ B~{ʕc6�z �,�-gr(B�JJ �KJ��!}� �I �3z�Jre�o�}"��NJ!H x5H}� 9?i"�IMée& W> �nr�MU>[�qkR�v �r6�dfҕdf����2Q:6%z`.�)9�o, � d�n�G��Am&�BeLhROG)��ml6> 2�6};� *� c�YMB!ϩ[6S �f�" ֑ f �!��(U� I�,.�i � �@� ��>F&X6c>� 6^s.�K)""�"-sN�i�" . UaK� 6����@�&�J ]-*�J!�*�J�),k � � �ȃ�in"j!�If��(�%tB2t6o�0�F�%}�Aˣ Xh�j�%5��s,�kg,"�bp ���6� oM#^�' �,�7&,L� �9OB1 �� � z�� 2:6exr� 3�l�#f# F3s�V زU!��>l'2PAr1�6�$V2�ψ�*�& �^EҊ� &�  � )2dB� E�e�Z� �+��h.�]�--�h>^�%7%�?� A�f�r� �# . F6! aU9FR]u� ��2C�dp m#s: �F�@&�CF 6VDof 2�#%�����g;a� & end�D�DF� b*�*F via *��j�P]�` S e� �`Z.8document} =�\cޫ [�H12pt]{G�clT{use@n{�x} 2bm:ams�0:Xhyperref} \def\figw{0.5 LSMO{$\80rm{La_{0.7}Sr 3}MnO_3}$����Ltitle{ C%�"�ӪLi$(ity Ef�(�:�xݣ�E�Bron S&froscop�! ga"���MphotoƳ���3] �1 �K2&�Yby j#�Hiee�f  commun�A��2 ampl;e q%.�&�)ha�&erE8eN�<ʗ �or)\"a!UecL_v�A�-�@6baS� �. %SFB�.�)&&V when� �vsu�$"�%a%�'5@�La{> E�O!j�lowI * reg@H�e.d���,�*o<�g25� �?fo�5���ta4ISi�.%w bulk st��iometrig!!B�k�d�0� �Ce�@wo orde��$f magnitudsE�Ac@^pE�signific;�a(*pIpor6�. ��7�%*W!M ?5� s*�)V�>+z*��js �`C��eteVCa�A�e1�a flat-�>andFB2"AyE�"E5���Vx-ray]gx. >sec�6��!��.� re9�s�-a�st-#WM�f')5�<:rv���a�q� Y/c>�!"�3we)' )?FA:a1q�!�i\�}��|^:i�KH�97!�!ɅRo|�>s}z��l \author{N.~Mannella} \altB�lq"{Q��7: P%�s�'art�x, Sta�d*w'$, CA, USA.� mail[��!}d�J� f�N. �: ]{nm �(@lbl.gov} \.�De� of�(, UC Davis, �:>M9ti0zS�es Div�, Lawr�Berkeley&>(La��y,���-fS!fr)oini|zg LLNL, Liv�5ד��ַ A.~W.~Kay��$Intel Corp��i�#Portl�OREGffU^����V�uA. Nambu:��,Z,��2�*Tokyo, Japa�MrT. Gresco .t����"T+6�2�Zurich,SwitzerA/!p��( S.-H. Yang��IBM Al@I$9�,.�San Jose}��� � B. S. Mun��A�@X�L�t S� , LB���^��[�[R[Q�,J. M. Bussat% �E&������t A. RY�hah�~Heideli�2� , Ged����aZa�CEDFadle>{����V�$keywords{P2% �a��ck k ,� � �DF� �ate{\todŢ make� �:6?� "�  .� �  aT ��l3�vn�1eri��H etup��R� . AnzX#s�Z deal�F�#po� in�m֧� tru��) flux;Y o� �or �Epro� a*/[�"� & !�o<c��pResi?5� � re��B� a. SeahK-w� |&�\!c�3m�� ��cj^ z4E#l � uI� n=  � #��Q �"/�y s�=s J��:1992, 5 2003}JL�'< ��2�*/ �9J.8 �VDy .� way. a�&g e��wr�In�U�inVk K G9s. h"B�exc�6ʿ- ���s,I8�  �E��O�F8�6���t� ��@ O�a1�#MV� ��D!|,i`e|6um,:�a�fea{�OaE�r-&@�lx�?Y tail7[�uIYum� pushU Q�!J�Uttyu��$ behavior.H��� �Aar� � synchro��1S�/6�g=)��H-Vy�\�F even�M eas�8bIDC�<xc ������s���qX �"*� �p�Rv�j�v�Q���>�\u^�0te-of-the-art:6)gsiCai� �I�GammaL/� ta seo�6Cm�Kaya�0, 1 2,Garnier�@9,Nilsson:1,Kikas 4,Finazzi:1}. &�Fi�w� V���"�R�9� A�-cross-͛e3�we���b��(pN���or�8 4�5�spw!� onan1ami�ƽɹs dm�e�n �@�GccKC.'}:p�m��� �J����J�(MARPE)�:Pv"�; �S*Vf �r�B�I rreg-7i�s͸s� �� shapU�+c%,c��T�rM� ariE�th4� �aa�e2inela � *� underneat�r� w&My�� be_���:� Mo&�Qly,�E(;4[ \Va� �Fbe kep��(dE�^���6�&$l,uce�(�7V�M>c��� �facB_e �Y�v��+��  UV�a�q� eBe�� e�!�gnfar aw_���A]7�Unxi��l�3w,��'� ,a few KHz. E��� Mb s� �ly�)nrHp-2�N��coE x ox�� core-�b2�&C"�2.  Vj:.��!!3l�,�OG��a NChang:1�di�is��� )��f�e"�)��aWa|t����e�paper� �=aij��t�6Z#ɷ ��F.�:|A foc 7� %���!�&k>� "fF���τ"�F�,2E A!��% c3��5,e-6�A-*�"���'�wf*���a6 �� a ly-�VKiFJJ��J�a�Y e� ��,�Hof�ps�T aaY�\l7f^; 1���a ,&�at � � &�r(m0$ M�>�!�"$ -$ SES200,� 6�� "@ {AZ a BS��s ��"`E��al} \,B� on{I(��� S. } Wn0;��õ�m�a ^� P� �a�A g�|`�J`ae&O�lBn �L -Dif%�  �ed!�!cvML*���r U 994,�n 5}ij �A8 �is� ata�@Au manu��ur'��r� �"!/p�-W!MsO���.���xu�ef{fi�~d��r$[htbp] \w.D {Bz2width=�\text]B1.�2} "�. S��!m;&� al ge!�ry)/�_ �\�Ew�9)M���(n�tCCD cameonitor)azl ( 370 pixelj�o�,he��ax�d 240 B%s�B�BxT� !��dz 6�7�� A�4`dct� window?fum`�b��� Uf&microc$ne���1A�'�ng� sphk�<�% ��T be g�"t3 %�'a�esQ^�W!l6C1m)�fil�õ s $f_{E}  Q f_{S >c� =J���6��r�Uet%8softwa�a&�2�6UB3AJ� �V��bE (aMa1t ��W"� fil/�%=anode)�uKP%o !�a a� `y�o$;�U�[R�^!�)=Q�X 6� fronu� MCP* !�� -to-�:�� t (!ur-�6 � �2�+G� d a picoam��"   �T�Vw*��� tb1ck-E� eF�-* [���)�S1�. !��� ondu4 AJN �pl� (MCP�?:�i�aud sc0$Y.x!�ul� 8s (UHV),���� n�^P3<�puld"i:viZg��ht . A�ۙ�- Mani�d:1}, mD-��uts�!�UHVnđ%�� $'yph�: �"�a g9& viewAC,��fi�ga p ble�uI��rl� ���gI�J ��:a�l�&K2" +�}��.�!priL�ly!�Ńit{greyL9}Y��-(ogue} (GS) �9��� g e%ph!���!ic!eing, .x�arCd��it{J4 -and�Xt��dig/oz} (BW)w ��Xv�a1B�tj# H7w55s4��# som�$��b%�1|BSk�=!GS {, ��&8�$� m&r mz��/&1M>�<�) n 8-�ap�a��T�r�"(ADC)DB��val vBW�Grimin��!�a[ mask6ge?�`s low-oA% ADC bi�pj9t#�t �sc�Jspuri�no%y%is"�|��ail�Wided else�%m�aJj}.� :��geM0:�js&voŔs a*%.MCP)� �$gNpMT ;est-/ |&` ƅ>ET����pa� �i��t%2i X m eHu�� ��_ G bin-2�:Q}Y0!�1��z�ag�>_z_+*�&&�+SP�" |������, s����al����� a8l14X&�Z~<S ofM�*Hi=��<+di�sr:S:"z ��a�-.svp:L| �av� �-�m!!�a o�.��}s a��(��nel},��n� � l=�1- �5 H[` t� �� T��UO?��",]b~igA\8_I.b�tc�qd m�`yF� `crib9��o.� �5!��aa 2+%*��W�� �}. "h�� �"Q�ac/ok�4� @ N!�c�T�!r"m ���#�Z6:SvFp�1=��+E��. (GS--0�(erhaps BW-- !M&^ /Q �,s �Z�v� U�i�$2I&�Ӂ���toA�E�na��{ts< 1�J�� _W V�*vjaF�h1"�:���!1�awgl ct5-m�piu&�#e%9�.<����/d�V��� p��byy1�zso�to�i�u�}3��Is_� er ���"s��42ýrX�>^ %�V �-ru�&`�#� A&b�N��2S3�}-�^nE�q^dǦed}�  swep 7"�`J� �Q�|#�%��6� :�!IECO �]5�%re hel�D#��9 ��$.�or)��n>� A�$�jE$ V� iM��"A �b�10{\%}�mea>�  pa\[K� trCer-^� oL4� A�U�Aq �(!" sume�͚�#i z��W^��e�"7��a���1k . Bym�E�a nar�pj���2.%� ��-�0is�_�I9r�(,s�(�d rivi����i� %:�I��*�U3� *%�{ >�((o *m {=�}� $M$ nV �� �$mڜ�~�e��},eq:1a} \tag{ mJ�� <{M}{\tau \cdot f� N }\,,KIU� $8�!��zde�Mg�)d !AgI�um. Or�rwe��i�Q�3a uni�7��y~ro��t��!��6�<�%�EE9՗M�s�=R& �N:b1:b}=:T>:E}9: �R \set�er9g{1����� "� .SZ�. "��� assu���!\� ���a.Z? � EalyU�E Y�N\ �. I�-�meh)"!�h me��*�! may R!� �Uw.Y2��{11)^�"TR�U,�M�bb}�v����s�s~����x;!�fr *�,! �#�~� �j �QV+ng5:��K����M� area4.U�:e"k � ach$��Y��ɜw-�BNIC"�5M��n��R����EB&Əm�)d ��ډ�per�]�ba*0�wotX X!7i�}mit� (a7E~ SF� �!3�nd2�,� a),1Rad� �s"�Ag"{� investig�,""be� �'qKrtno.�� ;e�" &N !�dV 8llIa�=I�B (",!G! !�uk �ify!"=� ��ng���&&b,M!NVQ�)��]}%����["l &6 or0.5 )1"�sweep��x: �"�[cep!/ &h ƀzllo�)�Z uma`� M�&seqCWA��wAT.� �$�г�5ei l-�8 ��O �* 5"�=�0 �� .�h� � a. T^!Q1�� U � ^!�wq�� a&u_e������is�Ln!Bani/�� \eq�#�� a}: n 2.� M}{ � '���.� '$� � e�!� �$sp=o at�0ch�V-���� e�A% ]no.A�E��)The�).b&E���ho�&�5��acC%Qpo) q�t)ڕ^m7E,pna���U�%�����#�uA=� z&�qKa�S ,4� 61)chA8pN6&Eu"H %2L6l"fa.!�o� be ���}o� �?�l�'6q�Nt�&[�i Vi J^yGi�,�� :s�6B � I��܎t� !(��A�P��(GS���%X�h .iIA "tudy,?  y9�e��~�1�2s�O ( S )I�W#A�ruq�M�s.6))�S��b9ci�xwbUls�M B�6 e a Cu�^0)�c��A^n��as-is}H�leau"� , i.e.�Aqw�*a#�A�a" mP#e&�j(!+& . I�]� "hF��e�v%Ab��#v�]3Uduci4 Q�� �7D ��0%�)�^P�$0tube (un-mono"/(E���-�& Al K$_\�K $/Mg.t, Perkin Elmer Model 04{\-}548����a power5Jp!���E���("� * <�.11 $W$3dp�'%Q�.,n3�!= 49&��#�oq�Da� @7ia3e-6�(^("�t�( (ejk �Q;i�(El��a�he��̋;ver�! ����)�= q��/ M�track߬8@ly with the emiss�Oion current of the x-ray source at constant high voltage. The sample-to-ground c K\(in turn proportional toa8photon flux at tsI�) was measured with a picoammeter and recorded as a funct�2� emission �,:Pthus also power since� �8 has been held ��(cf. Fig. \ref{fig:1}). This rela� ship is f% Xto be quite linear overnrange!o)k �used !7Lhis study (5-300 W),- 8ll quadratic or%�er-!r terms�`tributing less than 5{\%}s!n �compon!�!j { �, !],lready shown�Ha previous investig�@ \cite{Seah:1995}!D{Results And DiscuE?} \sub$The det 2 of non-)LPity effects} Ideally,�behavior0� Aor ��M�:�shouldAI!�letely-�. In A, case l\ � w@describee6D$m(r) = \varepsilo!�4dot r$, where $$e7 $r$ denoti,u�and�� 9� per pixel�!.ve!/$.s$ is a :E(%�6=(r)$ can{�7e)�\textit{)�)�u6}a�"F�Q�}�kit !M depends o)06*, reflA!ng%4)F��%G%C 1CE�� o correctY�c����iru!��4s )�2�� rminI�u4�q�'A�A� ��$rt Eq. \eq� %�. We m#at�Zsig��is Hed af��be�proA�ed by%$CCD cameraE4 valuAXo�;q}�(and,��sequentel��46  ) ar�( absolute, a�%� їt��(fluxes. In:R2}a��n broad-(:^cola4-�Td�_ed modei:$a Cu (110)Z ��ex�%ۘAl K$\alpha $ ($h\nu = 1486.6$ eV) radi%a. ��Pfigure}[htbp] \center�p{\includegraphics[width=\figw�4]B,2.eps}} \capa�{ (a) B��e#� (swept) �� �$� 6� S�mor�Utense1�l featE�a;��ed 1,weaker peak" ]1�Ta clipAedgesI�e!� �� left��in� ᙁJ��nt!mA assumA�t�50,000� unto.� � givena�ra scalA2ndmd�,ap� r���#a situE#< of uniform ill� ��.. (b) I sam5K A�e E�# they have� normaliz ���to}\)9� % �q�do�� lie�op�1ano� �z4vides unambigu�  e+ ��P pres^ .�+ 2} }�mA TheYJ span.�a�!�� a few KHz�$ \%�$x 12$ MHz��r! ond4�u* s !�)� [ e $mH$ - 240$ Hz�1� ac�qare��%�� . F� ur cxa�E� �� ;� !*!:Z,via $f_{S}$ Aj E}$�� total no.7IS sI�us aboutM�$, a number�A will��� ma�o TmaximumU�&7 la�� The:2� e:�reY�62}b�ۦ�!� � If��eh o�rA, Q�iF@b�1 lie s B��� I�t�2��notn� %�upAX 4 se��)Ohem��higher� ens regions� biI�energyŏ�(ᇁĥa.�ly](upper inset�wQ`Cu 2p1l s. E��"� e narrow 6�m of 0� 120 eV (lk)E�re& ��^ofa��  2-3. An�Bdi� waR moni!�R*�e��ron& � s mak��b�Dit{�o plotsi C �� �� ( co-workersM�:2003}� ich1 is�V!� �W!�iG >{�� In 6re�E-mun� �I@}oiA6vid� M�l point�� at& �niRW A7 to 300, 2150%' 25 W A��yG�� >winM�*� atJ. AllGƥ0P nټ by d�A�� i v�>�s,�'�-Ba�A !;versu���.F 1elevant�%er� �um.6� _Zsd&{ equivalP t #� �-�Benc!c s��a"N)US��AC��, if two �5� �r"t$q�tF9�e!�calm� $n$,�h>� �K#wr�9N� as: j� 4} \frac{.�(nr)}6r)}�+m �� {\ ( {6'r}} \� ()} \mathord ,4/ {\vphantom { (I2h2A%e�."np. \kern-\nulldelimiterspace}�H\N��� A�!�eO ��"J -�q�ies� !�]>.> iv@ Ft�� w�t6� "� . 2�U�y ��yC��, s �m:�X6�4}!��b&� ma��o observ�>:�3}!0 %,����1?derincrease q�&p.U 60 - 70A � de@u�7t rel �99ŕl�� � *�� )Lex�# sCve��horizon5 R� � s ly�g2 � ,, most simpl%k t�A�� AK� . �w�?derEd�~methods%3 �4~I�obR2 A %3%OQ32�th*Kie�Y !n)�e !dAp whauadjusEq6.����trp d manne�i�  easi!�c'ish�i }EjB7 Z-�umE �=� ta�surface��lre�!J�!�bAi�}��3B� RŌ{ s ref.Bh )A�g a6 at a ykineticT �@eY�ei� s (2� ELeIR olid��7 c�!�b*��^�ar U )sunit ��. �i���on� (b) ���o�iM��1 � �  !1erA�� he z st �!8� |! 10 Wk. A:k�  -� look like���j�U52� �>�a bn�F!�� �acha!zer� ъdu_!�=� c al sstical< ertaint;a� typ�Poisson�on2�3F�$ Although�"� !ri�  usu�d�-. d��!�is��not�d � beca��in� vera�0��]�  �& ��Q��Q�)�'zK $ w�&hA�>ry ru��fix��ode. H*weh] e im�a!ofA�!� �a���X>in�er%-toQe GificanD �a><y� acro�g atial axiB!i$ qui��!�9�%�A�ef byR�-�softw� !9��>��F c��s%n accumuud&� 20� a�4 Ns �D axe��c�eA_57�!6���um� "�a��:<m�Jpa, suiŤ bs� ��w d!�U:�(BEcn�4134.6-164.6 eV�850-90�) along��Ia1e�g:()() A�Ed:5%d llow��Ybe �Vto�� e seaulu ch��l u  time"A�bet1��� )�f &}� t5ba�riAJ� :� 1a}Ywof aJ� s,imi�� 1��5�\ a \LSMO ��A��/"IM��*E� ���m@detail below. Oa�!$�Ma�al "L$ace\d%�conver�\.�9,�2�A� "� h� D#>�I��c�%or�v� ch � nf�%6 :#b& . ByEA���ope~!�F!���$(e.g. passU�nd sli� zeK .1,�!� poss�# to dEY(1�&i�!$Q6� (its dynamic!�u�mi��ł]��var%mtJ���,*Ql��a4:���t�%W . As~3 ly���Kay�1, 2}�e �/i� <%0 a�5����5��&% a multipl^ �m+6j4 s7(6r��n��j "�orp imm"i��is"$ | � it">#compens����B�rA~� AR elf-�'ist*!E*o per-%d���Wit' each1"�QfF�(E�GSa^BW)�ef��5b1{)�i��E�Aned a�E�5 ( (at ��%p�( V�2.5 kV)�4 combine�!��]�%�&| ^�&����a�ue!waA%ali��A�o an �� ��GS 4FQs"#(d�EI��z(B�a"f&� � ���� � �� %�sB��vasympto�= !�p��u�ay�}Ugo�o��&A�r&�EX slop&�) �� is y&� cours)*�1/*� ( to� �t ��D� t!�6 � tA�ree"A��is �1�!� A= it d��a�!*re�#�R any ���An�. B@�6!Gz, �.)eds%,*g""5)*}* B�9�.f*:{ ��& {eCUery� 9�s��type�6�for1Eha��,n �x�!� (�,a &�.�i� �� }.��r!*�(U�in both�N!�BW�s 20 �!In@� p-� ofB�j!R� star!� fact,�'�,%,�j J�i :�a�h�z�ng isify�g unBg�fO� aqY >1�&AT� roo� ��Js��5�3 pr�+2�+�(�73 above-&���y�-����ig|F�a .� in"� ngVj��:�5B���.�� �a�&�8e�0c���Չ�&|(6� -&a��%� In�i full�eq /8E i�-M@ blowup Os.ѭ�*mi�(�� "�� ~ , go!u�  ,�/�*F:2�5F� Nth��.� � s*�93}b%;"�5} revea- min�n�n'D� ��S"�toQR�awhole>9)�$�cJ %**?~ &.5Iat �"J8.a -"� !&t.7&.&^or $ "�. 3.5$%"� a.M;a%�i� � � B&d �lA(�� �il� �!*ng�}�J� >1*who?$B� a�{ eno��; g��%i"B � w�#2;X ChaU$:1}. More3i.no8 �&x! in aJ/6e!x;2?4Oi\=�%e �ng-r&�� ex5ng2�7upss Ed5IHtub��36 ��cpp�1am�supplyZ"ch!�& quasixtinR1�2t"� u� (a*}>�)�C�:zea�smAU�ew wat�CF( ���� e#&��� a`F �&Ub*GH ��EH��\�&�"8 Ib�!Ps[ga!�=#Ij�(ion���etC- B� 4} tI!�[ 24 hw��kA�%�s�motiv�!7develop!a� lter�ivDc�7e�c�cS6�� [ wz w ��"�v�% 2: A�=�B6& �$a�5�Nues�%�����" � a new�oa���ini� ly trigge�y�)A�@ �.�E um%�p � ,.Aa��� �6e% ".� e�&� ���8Z -{!�e'�Eum�pe�Q e��P!�@o 8�w�u#=aU"�"cF���!��12: E�.�A�a�� ;��&J�Zap* @�2�a�z � ng!�ce� pgts� pP. � �@AmV��� 3B!hrt*�tim� To� :�}�t;��ne�A )�$N$-�U�5]o>94 �* 5F� � $$n= n_{1},U0\dots ,n_{N}$�wA,7 FG. (6! �@!�~��I5$���G�to B+.u.x; 7�NaD�?���-��$M$A� &�$m�@9by 6�-2}.@exa �IZH � �5�m�F9�Ks�7H= m(n_{j} ,E_{k} )$�6a ��1!� $(�A:X($<$A�!o6�.�8:��  $r � j�E/ :{�06s��!@�A5Has Glynom�expan�E "r%$P�E U�=1")�B%�E�� co)(ts $a_{i}$:n�1� O5�1 sum\� s_{in}^{P} {R m^i 55�} ,\,jas} \fo  \, jE,2,ibN \\. k2 Q �A IV�AQ$�C��e (9of� H-s�1d>�vx@m�o5%zɓa '����A^=_!^ 0$ (2rea2e!v( darkk1 *�.� ab"d;any�>r) �a�zero,A8; .D��ten."ForEwfyAzUB=subtrac���9� � %�s?9��� I exte  e su� �|�* 0i$e=f"@ i4?��������!��F� ���of V= � ��re�! �compu)P i un��lea�3o  %�(| a�ult���!B�,� a�B� ���Z� �z X y�VIM�.�F7}a�t�)���- triv8, rearx!�#�$/!�1�Y�NH}��#��underbr�1{"�8{B�2�Oq� ��E�j}} - ^9".��0}_{\bm {B}} A�2�>� w!9j9["9��` �1} }-i. #.��x}�9] �{C�I 6��9b a_i � {A}}zN��>��Da�8B�k9�I[ matri vw no�c*x(�, $!��m 0 a $(P - 1)$-�,column H, $\bm{B, a $Q�(N - ^4a fC}R:n� { ���N� l� ��/De"no "-al err!� 31]-ata�A�- %CA}}= �0}$, �itH."2 �G-�#_� qZzP�Ll1&�*� "� EPJact]?��i�.�"����v�: 8nus"^"R��M�+=� )�� �1w�9�N�'����Lsol].or"� 4lihood�!miz� $e�|!|B�H CA}m�$|^2$, i.e.V2!   � }� �.�8�+oblemJ�yg,9} \nabla _{EAh=��|�=e�A8� = 2  }}^T A/>A}= 0R|=�2�super�#pt $T6C transpos�E&�)a6�"� 2�embedd.$A"No'(�yA|{+s s% ��,LU de� z�#P�:1} o�S�Tm�n� z�? 10} %1!0= %rb?b��1M5n)^{��}� (^TE@BN�>\noin� "�O�? bf{C^{T}C���$(P-1)�� �Y. Nx1numer�5preci荱 /9&9 T�I�O6;�2�m#v 5f� �1"�abIi H,l'H ��,og>Ito fiJ/EY�J ed pY(>6'�&�*�3{ a:Oc�A rion�p� ! ly E�i�� chem�fi� ,7} $�sL$P&I 12��&� I�m� GO�{A�("��E� $N = 7� $Q =� 0$. b>� h!x 1D&�F lll��� {"�@�� ���B���Z3�Ec�+Cenc͑^&�A' 25:�+(6�6}a), 61(a� !s4�ea�d� ;"ess�G< �.�H>�W6�lso% ; ��excel�D agreEIarw�s 1�2 �!�m��jHer �c�ed by 8a;W*98E� �@v'!t:g�)so�o9u � $�U!do�Xa�vs."61a��Y�mapping�� :� 6B� C� �$!�!<�6pMR� � ;+�'5�e�(a�/-}$ Ixp �H isN� "Um�5� ��JA�"� �AѤ�0lap2i 6Ji T�]��SPB�#Ne smo�*4Gh"B е���8�O"f+26qi:4�Z�"y.$�&�Q%�;kc2�C!�a�aca��5�ur ���s. Howp! �da7@��-xY 7mirrA ��,5�ut 326F+ rD��H� R� 16.2�1�C��!�6�7� G&a�BAw#M'ag�E�aA5E��  �!A]�� o'!2y-�9*�#2�&,O"Qb�� en"�Jv'�Se�acc�' �'," 6�' R�s])�entir�N�-�d��A@s�;.��!qeh6r2}a"D]D)#� 5&A�Av�.:ki�Q4^#nd�� �&0���aa�VGM\!J�A�toeHz (or A� #Hz)yM,��ry���BI��5� !�>h�Z>�� !�tXN9�:|��"0!� )�R��A�r�Au)I) � ��� c�O�E�2��1�B!fh&H #&`2RH�)m�ugg�B��5FORbe�  Ylyful%�"[#r,&�set-ups�� osNth&� �c#6O# MP#�|�a�=ɬX E"B#�;��.$!Fu�&r:�!}N� !��y�+�@em�J rate� a�!aM�$c9�'a'dF��1!on-)�" 1^ �)�H&j8o .. M�B7 a�3G roAb�scr� +?n ��n�!!$di�h�E�Zn�Aofa2 �V?�"-A(%)ZU.Y�3#e��� �  Gamma��-S�]ta hard�Aat�I(�)two-dim�Qo�9 imagu  r�>n�/3 7gy%� read� ! ;8 ics �/�G. 2;!�V�s�=�� aJ�'l�-.&..=�+c!$_#2DE:e��}&�t �Y�d 6Y�� :� 7B� �=6�5}.�].�--�um.� � � .(!��JU-n�7PBf-&b10}"�e ?A�(�F�U)c�UatI��A&� ��0n�:� W+ A�� �f�!Zsynchro�U &=]--�R *�6s9[� �J)�.c� �#� be YV zr S!g!B\?=eca�N| �(a�G �"�8�!&�e!r e[.�3no Z#g%��"), ow�ei8%�xit) �A�� beamA��l�5= ei��2�;�XUnv���� ``I$_W''mesh��2OC)Y O�,-��-70 � .&� w�i8iu!�u�.��exerci��4�h,&,�)5��d)"�!�� spoC 6 �&� �a�a s���R�$o�,�wis�$!�arI����2��U� may��A�aG"MR F&c1a�UPon!e�c!W��MCP� t�A�tVK1xal�abe kep�m�A�I" ��� Al/�*eak��.LT t�:E�Itv+ <ts � �iQ9H!6d9JC#�:x �)afe6!ٱT2b*�s6��. n� � � �&Q#"�&(�%�r"�3�/:W,6h�(���?12�{0i��&�Fb~2�.� F�A�e�co�TtO�(!d� q�:ava�)cZ �H�=ed,:�10}� �� %���9�ofI�j\� Cu 3��r�ave"�2,1�di�fQxa2;\�/�lI�ic �Kbj,u atten]alengths,�f!:�m�l"� �% zer,&/�l%�!xBA�a�_ 9Cu ato G>,�\DW"G"vE� Q! om. �OY��%� !��q��;8B a�:nd ^Z�E1�i=B� I�(of $\pm $ 9�<b6 3YQv �g�AEs�g( ���$�aza�h!�1��a�ttliLx ��<6�<8BJ AsA�&�-2ws .���9ed� -�(b9&�6w =$!�"Q ��b8}B�;e�Qm?9,�n"BC�gMG� �o�J%�5� ;"��A5� a@��ll�l]Zve��`�N ?manuf��rA�lea��-rhL o]ch� ��i etup,G9 n�<1�)p�*t�O en�Se��eV)A�$ t��H4nts; �i� e " Sbarvi�� !t@S'&e� C2>oM8Dse-o�Ywe%hus�Dme�iivNe{"i*___ )$�@r� a Q�2|1aNphosphor�gMCP�y5�*)�&V�eu�b � � ��W.�W9B:B; c�N2�2/�"U y)NB � 96 �A��&m5�BP.H�C"g� d� �29 � za5JJJ A ��!�3ia d� I�uxs 5j�Ts?vel�i�A� jI ptimE8c!est�E�-�il3 hiev.���A�@�s�4%D��of�-I�l�QT � :Tll �&�-2 9F���:�10Rz!|������= -� t!R� !!&v j4 �>P @ inela!XVC a1D��rI JJ a� )��ta"�:�&lAW�Ie;�!� >� -,)9�� of�M�a�M, T�"�o�N c) non��D s22�#�(2\A2��2�11R3 ���!�)�.���o*J�#&" 1;gr�p��Ne& a�],black-and-wh�d�S (b_[ll$Xa��A �zX"�lJ��6Q1F�W�uUw add�!y�K)�whe�(is�7&\�Z�so farK9ed�=��$ o po&%kK��&��. %i et al.��`� ���JD c4a&� �t* G;�u�$rovA nearA��e�[� � 2�"�!5 M; ��en�non5�Yz�? oj k, �i&4��R�U.? qem� IQ\lrwj1992,!\ 5 2�j. :,�5 vA �XU an im�S0?H a2!�6�� >("�{ � q/6" �sire� u � \ W � N*�aTx �&&� 6�M+��5OGSu�BW%Is�� �Y(��">��K C#0F+� �> six�s���62*��&2�6�1 A�� be��� } 1R) (��1���H%B&�06Ps)f �]EeA-&� � !60�#�=ɻ 5l14*E�%�|A���!%����-g��t"�v�l�be.bJ\Fcr$t!��:11}V ��&no�1I5��?w�9I�at�����&��!'�o�!����)�our"�va�^>>*. ��U�@9� ��`^s1��  .�\d eB��D  tu>�,Q���n 314 � 330, �v���q .).S�/t7' Out�=A ��A1�m*�264!�"YY-(daT6��P$sM36 �414�*�%sXI t�j)T~ itut>XIccept� �M��f�)wC@�i5 to FQthd$�q�/�w!�Հ" ^,.Ux�����y2� j�L%-#fyA ; vh�ag deal>��B�B/#12} �zACt{2k�,M�)%��� �J{M6�-�B�4 %� � "2 �wd�0$$dm/dr$. C/@�Zi2a�pri�<�P �V*c7 &h*� a .�lO� g-"�}P�Ar 8�CN�7�;�:���Ut�D1S" �hLt:!�5�!��os�r*�!b�+.0$�P 8�V��B��,�Yu ��n�$�]at�]6���i� 2� {\-}���o_l�h�`Ii�2w!�� � ��A�5�y[*�c��Kf p @��Non� �%�j330!��[ �+�km��a��mC.up,�!W!fN9F#w�=XD �ab� "B3) c)� . BeyoA��explo�um�)q)aw�*&9oa2��Iaw K=�is%��ro��e �iz�� :o�V&� pe�g6,o a y�g urQd ollabox�E%%:�e�J eers�re�'ly� ��0 at, Jl��re- �a���s�� �%n�IIF)!� 8;���s8|z6,M  �� nd"=�ly�c��6�2R��b�E)���2�YoW��&�j ��n!�:%111}a)V�2o�E�^�v aa!330. I`5ji�k%���be.^)#:BV�|[���[�n1b�&�5�x G-1 "" "�1 ��i�I�2�mEsh�"� ar"1)�V1 a#�ux6*A�? �:E �0C&�!�6�%�6N�F���e��.�x months2#so,� iIr���(� i��_ !a UHV��(�foc�)�C"V�O%�-* &�ka� �"%M@�|���(�- [:�EÍ� 5�In�p�^�]�Eur pap�we brief�5�t���p6(c4l��6��!w`u,Q'-sat.�a t�>�Y. S�d2&�JKop k�/��B~=�"n�"~�#A�� �Z>uM9t �w!!M4& a��,i't suff���fast;� 2+��eM�! _^ix\ $\mu $� nA�u�jfa:t !6upR �H;�-gAvo ��ey�\|���&|-�z!?�10$^{4}$�/" #u� ��n�5��hd$"[ . ��!8)�V� ��l\�"�gF� 1}b5|s� �M in R�� �6)g &J;Dfact,c�8*n ��l2�i at 3z4-� �R�)"�BY%��A�:��I�a��oZM�mo� N �,AC*."�]:0E2c �$^,j !�&��=*0s!�sta�uU�!AC� ���)�. AU�  .>  ��I G43lhL%=i�#�fP�yke,L��'toV&,*� we rule�-a( B�� ��!x9c2�,-� �d*#5Y��28552P�G$b1la�.-;IU"2e����Da��A�hA[){ m#zZv)`"'rW>JohnsonY>����E��I��Pr! fu�67 . PlQ %�N�2�E�F���8!�+p-&rn��\!�(s�S��b?om� akagC{66i\ e!;r�+4-0"�x�v1pE�Au!m6`�5q�2�Uy1u6/az.iN�g11}) }Y�(%�":�"gnoZVAnk mdse�)!v2b�vwy��of���w�nh�,po�W>�+!�Zly�fr� to ڍt�D��if��t!�pe�a�dom1;!41�a.--�*4 , h�9�!�raQi:�)�D� ԏfX!�|� lo90gi3%<��A��"~bnoA9e�w6L �?!Y�n h�DogeneAc", n j�A��q�!]"~![��!� �at�rmTaBn�| eldc i� At�2�.dIA�6@wMo|@�xa�[�13a��6��C"+w�� &2���,�s;C���A�w;!�M� �(�Reibel�*�!CB 6r�i obj�7�[N [&(,��W�ns��WXAT!i��!�&w7�a� 14#�W%�^c�p�E!'w �c6NՄ4�?l�;7�a,g b"�+{C%��5}&�A �iwo~c�4�x;�%c}:�o.^�"�isA �!"�!a�troscopAK�"�.cb�B� �P�>"*1�!� 1S� cy�\���N�}~]�A�M42�\�abo:a��A�p(!.��.>7D�A��e8.HV �EJ��To&�/3 Ar " R3cha�DerŽ��"�El1�2]^�a�:4ate-of-the-artB��1-� ("(8/S(8SES200�3��6��$)� "U\f> w\5a�S7A 1M� �� �a�I`,��e"&���4�s A�;!�EPn� )^RL6��us"�;m�?�+�1j��a ��*E8%� � rOof:j6�� T�D�>�H>at��2"� &� ,�"E�&5. S{V{m����^3rW6 easue�B#Y1y'6� �� 3�J*� �+�P�d^8!T>563 "� &�6&[ R�,�l &aaan a.}�v� nel� tE,in�"2�$s L��f��A�6uw�63a*� e�H�^�m �~!Fy� ����Ch� n o�/�5D� BO��Z�ce, Basic E�� s, M�wse�E#!Di-$on, U.S. D4�"�# P�Q�t�T No. DE-AC03-76SF00098&�; thebiblio_�y}{17�Tbibitem&e$} M.~P.~l$, Tosa, S?��G Inte�<&` 18 (�$)�I. BW56WvN 23N,5) 729-732. "L.��$��\ I.~S.~Gilmore, S.~J.~Sp�l r, J. Ele!�n Sq ��. R�. Phen}3104z9) 73-89 �T`fheck �\I�J Qm(�q ISO 21270� , ``�DKcK*sis - X-*��B �2��AugerU�Q��%EL"�&of�hy]''2>K�zH0} A.~W.~Kay, Ph.D.�<s1'�m, UC Dav� 2000ND12DdS.-H.~Yang, E.~Arenholz, B%� Mun, N.~Mhla, Z.~Hussain, M.~A.~Van HMAfC7Fadley�� 1n$<(2001) 1179-1189]� �2} �FE+(G.~de AbajoA>V� ��A�v�$, \prb 63,� 51192e.�2}!!G.~ !I0 Witkowski, R�"necke, D� rdluќA. �2!c Nagasono@M{\aa}r�7s|!t4A. F\"{o}hlisc�4axlab Annual R�'E�Q3 LfSwede�6nd !�d�Gmun��i/�q� ���R,E*}�T�T.*�3WA� Nomq/ebRuus, A�a�I(rti� , So��S  Co�s 115, AY0) 275�A.kp �:� ���zzi:1!� %uN. Broo!�RG,; G. Paolucc2 K. P&.e5jyqq��} N��a���3}<�i!�I. --D �DA� ssau^��WernetFP� I��B. S. �/�S �Sg C�unpub-�2iQ�)+4}!^:� P. Balt�9P.A! \"{u}hwil�,-O�%sell,!�M�I=tenborgIB.Wannbe JourDof �l �lP and �red�sena 70,�u4��2� �� 5} C  m2k.>�7A�U�A�32b Mani�-�!�.�Sony,�( XC-77 E726aDC 10.a|(15 V, 2.2 W2]�1}�uD $\tau'Ra l:�A�p��0�alc׆�Ĕht M " wind�I:/c8is $\delta E$ Ny�� e�(2T�H��o=V�$e+ Y �E}A"��ly�E� ��_kl݄ $dE =� /(f_{E} N)$"= � "�!O%cad $\D�ib" dth,bn .s"O� $\ge y$gpn,?odp9 each9Q�yHt��e�� /*- �%D>�  �� _S$� +�� volv� a">on�� qs�l $S = (1E)/!i R =w/51 �:al@K�jE�M!�)�IYA� $* Aclu+6>�n�Uo�+sM;� ata� � q���Eq �o�eA�I&u�w�� $F$ks%�I�tot�=imym�Tc'� a =-{T�b4 =FS�$. If=is_6���e1O.�e�#);Pn�"/�Jbin2I toge�2�,ak?C#=� al FQv ofihNdE&r�\a��> 1$ !c �x(��(����tq��q�Imi��;�$S' = S/ _qV!%p�b&<phA.FSQ� < $��!2�!filE f� sT Ο m S �E/)]�"ڋ��h"���0.8&0.7, 'k9k�*&�a�$2Y_370 0.7 240 \apkO 50000$��D�aAfڝbe�U"�& ��S�,�!%O. ($T/%=���$i<-DPUcse�+�Pm�3� (see:� 1b})=��in� `PpC��*hel��A� s, eAK��*&�*�Ynd�e�"�) �Sw��can%���d�as!e .�2Y�[ W.H ess� �@Teukolsky, W.T. Vb�A[� P. Fl�Y0ry, \textit{N"[Recip�in C:%  of scigfoC�fping} (2nd ed.), Cambridge UniEty �,- 2* & P.= ^> .G .W Y�gt  Ju{$M. Bouhifd� CunC@nd C. Draman, Eur�ys.,AP 21, 75-80� 3)sendB6�a@document} l%% . �)�b�t%7(Word (R) Ve�N 2.5 %%o � g shell:!qicle \PDclass[12pt,thmsa]{1cle}% \uO�c� {amssymb}2sw20lart6ams=]Bfon}�.V/icxm setc�er{MaxM�b|Cols}{30} %TCIDATA{OutputFilter=x2.dll"-$=4.00.0.23�(@ TCIstyle= �$/art4.lat,�, OC�fTed=Mon Nov 08 08:04:52�4+LastRevOJ=WednesdJune 15,/$5 11:15:02802$Language=Ad^n�� "�e1�4} \title{Phys!�� Lawa�Sa�WaY:} \autho!�hrio Goto\\(mgoto@uel.br)\\D5aA��Z F\'{\i}a\\CQLTCi\^{e}ncias Exatas \\q� dade Esta@�Tde Londrina} \date{Dec�` r 18%>4 -_:-U4 5} \���";,ab�I ct} �N3on��� why�f"�(to��[Q?*life. H�, �#�.Zѕs!RzuQQen$# n�su~�&, �-by he�X. To c0f^9osr&�s4is�Sg� l!�� baof a�ee�c� HQ �#�k$�*tg{��$6�+ human aud6�y6��r�/]�xe�IC�1-���ls� a"�E����x�a� � he];�*aB���� �percep�� =� Sp�cr��%A�!UEreinforcF7amct 5@��may ik �j���9� fee�6 ��Y� "�\s4y skipP-�} R�] �m�Z��!IU�&:OU�>` hJ��oO I�b0Y� \i<Thoma��It Vs goo7&ftemCmusicA(art! Bu1ia�a�_�$�#�law%ed$E!yk&!Feynman}:SQ iU�5>k B�iL �L As��! , Oc?Oal �-&bas�i�sa�l,IJq� Into�- Sc�built�{ a�!0���5� }r! I�A�- �"�� rva� .8��! 0}$a� 1}=2f�Q�! defi�octav��!� )T.]� rehen� , $20Hz h2EHz$�a"_0piano keyboar��  7 z�@�$ s $A �o $C_{8��w�.�$27.5v��$4,224v.� ,�a�"�4t� g�^O�*�� /� �4}��44�)mHarry}, Lapp}$.$�Yori/-7$c�i1��7remX.M�oiGreek��@ian Pythagoras. U�<�xnocv�A� vibrCV�y��%Fo �Z tOh�Y��sN>Bs)b&�'�G�!ed"O!k 15i�hMR�+jAb` �Y�#EC ];y Y�, $2:1$, $3:2� 4:3$E�p� ula�'���"*� arbُy��un8. Two�g�B�1�I �~;�are ci��~�t� w�+h�����b�*m�%;��Lm|��0-�1 Q teq�� e� }�U ean �S�1�J?�T$1R&A�%�ly&�dA�e�&�paW:��1onFnC�w. ]2� *6U =�Wa=!�adjacm$c�a��Lne=-eȠ9/a sa2256/24���M" Zery b�0 {tabA)} [c]{|c:}\h� � & $DEFGABC_{f}$\\>19/881/64 4/33/227/16 43/12 02J@� -�:),ag9�YJ9�%L!i)�!b�*i}$, ͔�DA3�{�ig�%5H�J856D/I!8E/):F/)<G/)>A/)@B/)B%</B�!�&%�&1�J5v\l>,2~,O A�a�ecu�%+0]�2W-$oM^!&)1 Co"v �qd��� �h�*ab�p� *���a�I4omer Ptolomy a�mmw.��� �7��s�$:1�&���j}�wh���~�6�ll4 O, $4:5:6aҁ�enu)��2a�1@b�f�� e 3,�[A�f�'{��q���4��R)=�N� ��j� 2q9/8/�Pby 10/��� mi4 6/15eT��Q3���ecygyeiciai_i]i[��5/V�5��15�Ƃ�3~j aAp��: IF%Fii�5��6���!��%� ��!��ޅ7B�4~<]�a�2�i�Z3rQvE�� Av ly< �t��b�T~�]I�:l� �ich� �Ge2��.1bB�derstt"�)so7Omp$��"�cond�� w��ce we���l2Sin next�,} . ��V� )EMK�� �{�2A�oss y�nƩ�h��r `c �E�1S� � &K fundk� ne, � �v�� n}=n� � �%$n$ $(=��3,...Al�3ese�d��g�3!(idea�a3ɷ}4����ive we�5I�f�C�5�er�R '-�h4� ch" !"�� �w <,� �)\�6l���timbr�$N1�!�\�&:�I�Y+ "�r_.vs�;AundG1�}I> ����B alf  %AeNe�/o avoid�trouble�eKw ��XA temN� (�b� &),Y�Et12�_A�"�pA:,��U�A�5�� H412}=r^E�"S18�A�a�} ,,\p 1}=r,}Of�V2 U )33  % ,\ds V�\ ,\no��#��3� F� r=\ �\\sqrt{2}\simeq1,0594631\�'� N��nmX1Y: (ǐcon2})�"g closely *�=OH�]��romdo fav�huSTVc�8j7=tideG��g0uy "�� ostl�Ip> ��[r�&� few%B���violina si�,g�e�v����*�3ʼnce F�} ={pur��6�h�f�r�0N��7M`jthing�to��` ���Xe<&�1�A�I��a2}%�!��/�� si�.(aneously (h�&y)!%�quick���GK�(ce (melody)�/daJK�.�,D7�#E�%�1J�J ա�m"�y�Nss)Slu%L!B� �e�6L, i�P !Fth�] phas� 1b itud��IU �yX��ڦ"�@,6#o��hs�r,^$�/�T!�"oscil , 5�  rigoQ t�ar) � Tijonov}% eg6��cos2\pi��t+.2}t=2x�\#|\W� 1-f_E \� }967(��+-)  , �|sum�6T���7 A� E�m�1�N��ove�(e{f}=f_{+}= �B��RF�mod`'�'!�bea9QI�yNP f_{-.n2%#1 �K { .wPFw�lVJlV�of�4wcg&� %�oi�>%h$�f� �!���F�!2%�1})=n !�1})=�coJV�@FV)k%�}1}5(n+1)}{(n-1)��1~ con1F* s $n>!�r�3��#|/yeaT reg��� p�{d� ,t?ng;�� A�g� E\��ic�nI�� Ŵ �W. @!g�(�;� �Z�(� A�)5ve���GY�y� /%#��#݅F}:�2�iym�)� 1E2I�t=! �%���%� ]!�sj!6�!�q j�Na�2}/_ 1 -1)Q"fuJ���!lf*� on� �Hla3�&�)an1�:WoY����,Y&�@{(�V��eaVUt� ��i� Qc5*��q �A�ly� ���. Of p�O� �N41&�an � ��ire�A��CsA�` 7ai��j1}� andJ9�=y�J2�R��eSi.�of\%���!#�/UE �%2�)�2�ݯngF�r@��A%-ځ݁:0"���JWV)�3�\&��Ji�Qq,.I 2�k!K.�e�E�-W�y~l�a[e�.�|et�tp &#�A o a :� y9�I� va��BN�0�0�1}.>��t asy�yndl�;e&�r <( � im.�ob+"� "] . Eque[mF�Hmm b!pla�"\qquaa[ AU���� et+A� .� *� [ .!�B � ] +3( U- F )6G2}t \]A�%�5�� c"�  a;t�kl&a �ES en a�N�c�9n,X��I"�� A]`A�7$ corp�S�&{ A�mvPga-a�z0N+)x� *y�-�% +1�.�geJ%g��confi�m!na��uA�B a2]rl�,i1��j["!#I�i�oyA��� - task6#n ��XN-"i_U�Ne��o��Fa�cc3*cTU�ce �!tpF+�?�71��!k+due83H�%,ٽ �l2,gqw��:��i_&d. i[va5 !SA�cumm�!�)��Wht re��;Oas�7qgt-te�qcN� , +2}+=Wm� a�sin�0��%`A�6� �sJzPcog=B�M�q BJ�� cosFuV�s.�=Cssin.�Cs2}ssiJH�!�cosin�?&I , 6�Z .��J1%��6 �,\ %&!2>��B  �� � V<%%]1�.+ ~%1!!2}~\> ~%|. A�|�s�F�m2��r-qEaH2�#��er,NVY%f�.z%v,A>&z t\đicos�: �%A5V % \[ .�1j6�R� ( f!��i�)  t?0 e�.1. ��]{sa��x .� .��Bs��%�A�sr� 9tf�.tEl,ftsiNs w .�-R*py> �^0�e�7,"&��-g��Q23ףZ$align} &�1U!�1�o �"� \\ &: azs9-1��=�6 Y�21�.IZ7�R �$a guarantem �SE�/�r[si��'e�" veri_� [&�� @'�(�"d�" �-sf)�l�a�&` � �W�]�frpleR5%J�,WD7Ndi}3a�� 6}{4 5+1}{5-1C \ ,1 2+�N {2-1�� 2} 4X3L3-"��� Pita1��}�0 �q$a&�&�sb� 6}{5�1�01�11.�>�% ��5=10}{8M9L9%. �F���.+% �~$1a�r64AE�.M%(�# 4/3, 3/2�  2� I2I5RI9/8e��R�:�3* �6RR �5/4, �, 5�N�4� �z7N�&�=)�!�/h� �C�!R�,� �! B.�0 s.c,���G +n�N��i&�+ ?-2�:9-�a�R*&',/,-u�;b-^�� . Sov�R�mQ�e,"� }< �S�Z}&�va2D:� l?2�>�5�i�Fortu� �#�B�^�'� see *��8c) �!po�X��![�3Wng�A�! two� 1�%if*l�=1}$� 2�*�;��uP ,(t)=\sum_{k=ˣ,\infty}A_{k}l  k��har�:f -CNd2^dBBd2}t�\ ,"�har�:n6� !#{ izs��� sO)jVW�)!fA� mR[F!*�s $���k}$x|KS�NlQIc�����u(r& f_�(*�-g"� !]v�2����x!%�� � c� 7(-� 2�\�sumU- �c 1�B!�A��,@ec%�+:� ex8�"� )� /� n a U 9 2,J !�f�5 & t� .9&� t,m~ gen4FC�i�+�P ser�lA ], �f�)we�JJV7H79�ş ce} _v"9xaD' -�� �����0)3uc�Fm���n��v2l�9"'$!Y�ike a n�&e� �]8n%)dO�&&�7w�']*� .��!:!��9�7Augustus� Guyton��b{o recognʱ�s��.��9�cf�5�Jgure 1{r �s3a��atz=f�[)�of p:r�>s��!u28i�pO�2�[�w5-� 2�&�5$A_�5�e,��$26 6�W�o� �|�wnot 24a�(c) $49J6��!���b�� (d) �6e>T-;o*t�r&� jE4r�7$$0 nfu,��mL@? �  ��! na tA�ol:�{#��:QlbzK� � [V��v%�IJ[W?6?I�Q퍺})9��-wdf�U ologA� ��e,A breJ�dowi�� �:�/ fp�=-M �F�a�!,�G R] R"@ N�0Z%m��J not "�/*@iv.�� �e�Vl�,.�)], O���(�,J7�:�A�D=�\)�low9i�!�5�,)��&�($n\gtrsim12)=b%� � �vIJ6��b5B:�broken�a�ul| he m�4*�]�.ՕNA$C�A-D�!�E�'=��" 3ES�� *o�o`"17�M�j!�m�#f* �t�Th JF��a� $297�=Mu!�s �$ !���an�e�k��.� %�+}=280*A>�!% =16��*ly[ig. )!��( �!��63ng6,r%*in m�}� Ami�C��bX\� ��!t2ao g5�! K1Q�,>K�B&\�$0� �/�pQ~re:[ 81.6b]-�,sharp $^{\#}e!I�n;>�� ��BmAx1��Ae72.8Hz$~V+E� -}=6�"o 2c%i2N��6(� .0Hz$�K� (� M�5� $ 8W@�k��o�m�"��{R"�ex�"X a/_5��3*/ �"�?.�,6�u�1� (���3�A,)l�%B�a�+}=302!�( -}=3!�>�n s 2sQ 2b��l�Mt]!�!�J�,�#a��(d��i+�/_qa�b�.i�^a& �eAiTsaU�2d,�g:KyA݉&,e��5le(A!�",� evol8��Q�� � pitchQ��JE�s�z� 2b� 3�e�ѽm[2�2toR�H.�  ��nd��H�H� �F�+ �m�?!fu e��Elp�A)��a9="MB$sensation �@it produces, while reinforced by a physical condition as the equax (\ref{con}), involves as well +�individual subjective feeling. Also,*Lhuman hearing percepeof�4sonance or dis�is not absolute, and a slight deviaDaroundhcoLc�.� T �iv)� �Hauditory system. It�!$reason why mus%?scale�!7,l temperamen9ac�Hable. In sequence,D  5 show)|not!cnd resp1Pr 6iesiPthe central octave in, Just Intona%S�us!s� standard RDy $f(A_{4})=440hz$%c, �6� beat:� two adja� �(. \bigskip egin{er}% \ 8tabular} [c]{|c:$}\hline $C�$ & $D E F G �2B$C_{5}% $\\X264.0&297 330 52 96 44 0495 $528.0T \end� T!� 5:)%Y1x=>!=�for%1�B�a�"R�=z%5{nk5i%_-9o%e-%'%k-%q-%w- $ & )}- %�-)�9� 16.5 1%^ $21� 7.-E\Rx6:b� paireJ6�m\1� i\�p �!�0er} Figure 3�� tains typ�2��t s��combii�,s, represent��m-$ )�$ (majE( ird)EYa�!c4')�� (perfect fifth) intervals, both satisfying@.��RD . In (a),��� posi�u\1H�� �$ (asHz$ ��auHz $)2r�� $5/4$,>�1?ce ɻ8 with $n=9$. Th��,sultant mean%#B�8are $f_{+}=297H��$-}=33Hz$, ��ly� (b),9��of%Cj� 5� $396! ,6�el�n $3/2$,� 5$. V� n�330:�6pA[�S�c%� (d)ɑsame ]]-�q���Aj2X$Iu, but)�differ� �Lve phases. A princip�0haracteristic!Ja!�E�t }Eos��defined�iodicity*�rUwav? clear_�S�+Y�6�* 8. Another imporE^ feata�i�atK�2�wafa�i� changing �:# 2amplitud"�7Ang)�s. An �a,那 work&� as�� harmony%�melody�c.�����{���\s�2;9y� �E� � 0}=f_{S}/m%z\,a�Mwl! time25u $1/f_{0}$���J�incEes togeJ �'(nyway, firs��all&f u olog�!�!�� t acu*k ���t&?Emi�bQTl�fl�W ultu�Nenviron?h E I'm��nkful�PDr. Oscar Chavoya-Ace�AFA�. mO� Lthebibliography}{9} �z%  4bitem {Thomas}  D. Ros�$, \textit{� Sci��S; }(sea� e�iX), Assison-Wesley, Read�(1990))B u$Feynman}Ri��d P. 4, Robert B. Le!���@nd Mattew Sands, .� : Le2 �PhQs}, Add^�063). (2002-036�Harry} F!�lon, Mg9 eEYE> eP} F8Dover, New York!676r(Lapp}David  ,mbof |k�al In& AOps, http://www.tufts.edu/as/wr!D\_� /eF\cs\_2003\_wkshp/book.htm20ijonov}A. N. A.Samarsky9HEquaciones de la Fi�!�E 4}, MIR, Moscow!726 Augustus}  L. Sta-dkFA��c(Bio �p}, p. 124-145, Academic Pressq56q@Guyton}Arthur C. kTratadZ Ё�Dia M\'{e}dica}, Ed70anabara KoogaA�.J.r 69).x >�� % %TCIMACRO{\TeXButton{newpage}{\n }% %B�1Expan�  %End!�)"� {\Hug�ca�s} �I}5��F )1:!�&" %xA�plI *\ �V (a) �Hz$1�]6�Y $��,� � cor�?�oF'� $, \ Bo )�E�(d[�,� low�)o�W reshold��;-2: Ex; E|nonň�JD����&Z4 modui���one tone! \�k� 4 �� % $.)5(16/15$ halfB *>�,sharp $^{\#}f($281.�)"� ��302$\ a M!EQ$y�� 72.8!�-�� 0- -}=6�.)��G�%�1�(A. �, ��A�rA� $15/8$O�ly:�� ion.ELSiF  eIA�a:0)*;,�rbitr��$, actuallyu( � �34�,fK%$+}=302!R�<c G!c:zJ� 3: T �E�n .�i��. In E�� tM�� ��1u^5H�� fifR%��NE2��S!�Wsame �! r:�%,A� x��S A; fS��� doc�}��\hclass[pr,aps,superscriptadd��,�2a8nguage=American� lish$CSTFile=)�.cst}A@newcommand{\intD}\! int}��.#T>#+!V-Qf-.7 6fdd}{\enwmath{M {d}}�>Q�$} \title{A�tra-heat� me4ism�,Doppler-coolex�� ,} \author{T.! neli\`erAw (J.-L. Meuni�R. Kais.C. Mini�Y,D. Wilkowski ffil� {\' itu,n lin\'eaire� Ni�hUMR 6618 du CNRS, 1361 rout&Luciol�!4F-06560 Valbon�Fr�<.} \date{\today{.I abst��!\u �paper we=(����theoreul�4vestigate lase0)c of S0tium 88 atoms!�>d!|' �pM mo�y�8In our case, sic�� ) 1�(dipole tranO &x"$ $J_g=0$ g�!sta"m%2yW fou1in agreeA��� 1similaU��meaad="�s� �"ly large�Ha}�)�.�� :�g rpre�4is discrepancy$tav into?ide� geb�b$�!�0verse spatialMe!� y flY�%Q�5�U" E5al data!!R good>W(Monte-Carlo!]� 5Ag.model!)�confirNe*�rAv play �!.J�g#dynamicn Q�aG|A��y-E� regim�!� .�\�sT{PACS: 32.80.Pj} \make��E0Int�% } Initi� � mid-�nti�62�,aOpp�$ and manip-1a�i�Hrapidly became a veuccessu field of � harch \cite{houches90}, culm� R ,wenty years �riYobservE�Bose-Ei�i� de� of alkali � tbose}�k � sx begu %�e�lq�5�E y'ch wa?sigF%�wo-level&w`Hansch75,wineland79}. How a�e� reli�eeo2D}c�on%u orm�a� e en!n- �i�FAs*tur�out uV@I � w�\emph{Dbelow}d�?ed1, value� lett9r rpri��ult��>t��an�� much � effi�t����!�at� �ݤs�!is/,known as��X,Oida � so�( fterM� cch89shu8!�0The key point;to under(�����y degenera� %Y openE�he+�newUv�ba�on�pume�-��  polarizi. gradientsM��[iw%� basic ing���!A� most.`si����$gav�1e Dg Q��a���us. Re� �ztechn�6adv�s hi+%*��5)5#�r��2��$earth-alca(- rare-�" (Calc�Ca� gnesMg,�o�Sr=YtterbYb�!�ese Jexh=, a zero spin., x5�i\�%Pte�%_O �heu^��( to gain be��� trolAachiev�FT*hd0us been renewgTo��aledge,D2B� :� ��[4Oates99, loo04`ftus03, yoon04} always re#ede�"�.�t�6C &_ M�!7)�g clu��favor��: Y� stilbe"9y�. Appro!H6| limi%�mAto-� Azs (MOT)A� ngɷEcU{ �5 gY [is�^ed on�B u_.� �%colli s�*E�e � eumse].���9(��se�k �for%�ic /i�!I��e��an& those�%�clD MOT ($10^9-10^{11~ thrm{%�(}/cm^3$). F� %�a.S �[5l fail�=�a��"��a0�his pa� �� alsoal� viously _ d)�c%v�gH> ��!Ec� )�/�e{of%4��cold !cloudq AYn �"A���te .%$M-drewsen9M/ y es� idrZ o���/r of�.� y�$��� �o2�r du�9<"� imbala�2lP� lo� drif�!�A�8ic average velo�+ q�loud.|%� �ex�;a�  w�̡��detaiC .p�+. Wen-- �, ific.�a�P��0$^{88}Sr$ (Sr�cshort b(a )a=�� Y %>C�%xa����},ޡ� ��,��v�l a Q:(U]Y� [2��%�r c�tw der2an ��;�)el T.a��H� � Fs: "� �di�4ce $L_{\perp}$ velle�4tom durLA��(]1a� 9�a��(��/�;er�u;m a�G"l!P\xi_s&�"9� .6=.amct�t�! �Z3%s�! ris�ӥ� f�2�tribuAsI#ubaid� �&_xr�talY� em_3� a *� si�.z%/ou.�a�c"k# 9� \ll )-��!�e.�!=�i�!�w+'"0 b�1ior��ve�di��yf� �*re�E��]�Z�in &� �aJ�Ix.�R� W.V \Yr{MJ~}8;�-t�c�1a��0�a�)� = = ( J_e = 1$ d>M�!B*�5"� ic�8e $^1S_0-{^1P}_� 8 $\lambda = 461��nm�$ excited-e  4�widthi$�M /2\pi=3�M3#AF}��s�+ =�is $I_s�� $mW/cm^2$. a ��ef> ve��6��K/Ta $500^{\circ}\,C$ ove� e�1$27� cm$ �� Zee�?slowermE� Sr "�BuYER qm(�'"�3A� MOT U m 50v�,))�2x,+W/dA b�)��s %_ at $9�a����a�0xs�#$y-doub�&sourc�� Im�Dbruce02}. Briefly,o&ingle-h�ŢstabilW dio�*�� a t| >�7fier 3 us j(a master-sl��guM�.r�A%�%+W�P l��92EXM�� nf'd� I�nJ�� 4 -monolith�55@ ing-~% cav�.G � �! KNbO$_\�!rm{3}$�&as9rystal)� 0iF't�M%�:��B%�e�-&[6xexits through a dichroic mirrorAvi� $1MT%) tun6 .�%=0- "�%y�ked �E\nm$ Sre�)7� pipe� use acous^� o�rd5"I0A�9EU� varR"k u ��of sixz ���De . Each 5c].�S)�e� ^ $5� �D�e;wa��s8El��mU*r�d-detu�by :@ $E33pec�. � ic�'c�5Hwo anti-Helmoltz coZgemt�$7E�G/cm$ �ic � a)!f�-D�3�fed�s�8d��fluoresc�0� � ,%N� 2v  10^6�D (Gaussian-shaped)Ϳdi"gIA�ly $0.62[�*0l#A�I ��)\D�  v \sim ř�D. Techn�2� *�2��+V5��fA=, ."; {*D��0 -of-feV2]��In ad�1%�h}��"u�9e.fset-up�, Z.�), SQ>o��Z�� u�l�LerI�&� (se��.= set_up� m1D"�emT�%�]-6horizo> X"�;Som�#r�ݥM!.8- p&! L�fix%�? ive2 "? v��> 2�ab ���a �� -pas�*A��  djus� a��e7"� d�� A�A�r66�sk9�ohHl*\up" A�h�am��3i�m�6 �x G "�-�� big.� ea�.A�"�Ga�A�Y�!"��( a����>mpu2�3 digi� ob* C�">!H��ask%�� { clock up�'� d syn���� N\�<ry $1�3 \mu )17l�� . �tep�sen��� � purpo�'!mNiec�(b (to switchesM:�"�BA�of� )���D(T"!fal�)�s�a4Kn $�� �a�h�Bgn'�H�9�ffEu%��e�5d�b5�+( darkI�d; � �*oQ vari�fewq id�k1�RU� a6" imageQ� �1�q� ecor�� CCD m_ by bK �7�A�)��$2M����wh�)!�5�oE� repe�as�as ne�(�� o obt ab*,signal-to-noJr j "�I# TOF}�<�Mree)�!) aA~&� b1�)3&�� ellip%�>5p5` Mar �P-�J�A��m� axisA�precisa�eD  P�seAL7,m; O�b�CrF rD?0 d!jO�.}]�!;N+(">.-�T� } ax�*p5� � random sp� $neous emis!k. From� s1�(R6� d.� ��}."a!A2� �Q7g�d �;� n � dir"Gs. BecaI-�finite��  ew�cannot uPs�� � 5@��. H!�K trun� �"u�.Z s at $2\%ze$ir maximum���Assuma���.! ic p7ɷ� 7; a�oEu5� AUnd d(er y@� evol�:���2,@7y"�x^2(t)=�0)+ v^2\,t[�2g QG0v = \sqrt{\la =�le}N�� easilyQd�z!%&O <. To cross-check&se2G%��=!� � iyK*�, method, nama�a<tr=pA(ŤI�+nsi�,in prob1�݀w�an ul�le��hA�n* 3 the Y - {^3[Srig 5 (not�*� �� �a $0\to1�n 2)y.+A!�8pin-forbidden, 4&b"�v% ��($7��kH�N� hus�-broade�]�\c /p� _red.uQ)� i�:�M�)u��)�-x|i8 d-�al �sfE)h)6�ڡdYt1�5Azh � reby� firq� �it"\MTOF �H s, A�� o handl�ndC %� �CAout(yI�%C� "� 2&I*2�>{:.q �} 15�ory!�"x-abs�&-2�cycles� ch )m a"J &{*)e�E�a�r!�#. s�8u��M&^4��8F = -m\gamma v$ ~� U$���i.VL�Jvin� �;!]G]_{\nu}Rd' �) givG5�u���$�t $D$��in�$space}. At�Vilibr��  s�E�M�0P$ (*�-�Ii,4� orem� �5�Y�g5�($k_BT_D = m@��(D^2 = m\,D/)Q$. Al. -�^ se.�)!aH 7+ �a($�7|lin$&"�2��� �*�ex*!ej!E� !�!�*�" $ ����# �i�& gordon80}El�1AS%Aa�)�E=t#$D-R��4u5 &� �'� ��se�T ne##ve}�%C!���9�I}.� TJ�:e }'! 7}{20}\; \hbarK�J1+^2}{2| |left( 1+ >2}{7}\, q1.6( ()^2}\; s_0\�D ) = � 0^2( ^0)\;(1+2\beta A�s_0) �=� Here �=2_" / �1$-gHAin uni�&f =/2)w$s_0=I/IP ţ.-&�&= �(meterR y4A�.gua�d��Zy � �i�nergy�� ,le�3f��6 6�{$=�$���jX/�t lowMw, "s D�q�0=�!�!�!�<:wsahAin%H�slope $8=�sigma]$ ��#v$.*<m�3ofJ$!��0e|\"(M =-bnd��a^ �= 3/7V�E�g 7=</20m}50.!$<eMict'�\�;y)�j*" ���c"�!A�.�HM��2���.Q)O/�A _�^:;hannel, ���4*+ �nbet�(M r+�(+�r�n-M�=3 A"��O$A<> �"D A�G(J!Vs�Y"N"!f��a e�\* "� fY�,բ,  �`ME&�,-$)]Bn�#gn�)ve62�)��՗! �c_CngcJ� ]y8.F*fp'&E�"�$ɐt-�kv� $�aOd#4mhV+2Ty (�K 0.08t global&t#�`) I'm3=)>j!6[%[:�= high��For�E�� ��� gem"�{6I(a� ("H(G(�' *F(>�pa5c.F( �_�;�= e\(g mismatc�"�.�9pronoun4atP ��A�te�� W%at%)'-&{qy},&� ~\�= -1$,���%��onga�u i�%)�-LI fu] s_0$�� d� �0.9 \%v.c") �G�49h0.�!�.q+o.�o�a!kK1:] ta�%�;esjm'!Oz9"�*b-� �1"-)&j �.�Pc�arZ6A�en1� #,>�A���S$O t 0.1�\se B��re�- su<�@�:� �P[8�3 s&�3-s (��. ci�]b8(1q��?of t364Al3#a� wo-f}K A%'[!?e�v�"321n"�0repul� ��c�!� . Ho&>A�.%3$,$,�Z?s Sd"Y5, �� �3l." 0it �� 7 �4nu�5(La}T$t-Beer lawe�O"ea�`0�5�f�(i�1 aker%� s lo% d de9�wMA�we ge�  9net-�,2a/2EH��h< �'*Mszm#W:dw<9��b�,�+#Y )Lsesko9150Q4A�� ��M� ! �1D"30 B�!#exp%� to�)te�c:�Ma/"�Yd, �5 eastA3mo�C"�(�9,A2�1 n< mate�#N�qBA�IB���&�( A��&c.as$x��23D�ow"\y,3�>tE��6.(5 �!o�,��l"5� atRve, inhomoge �� AVABe��-�^: Q;��de,&�F���T#Q��Rb%�Wd a�Q5i��X�!x$��{\it vs} �eO7�@�z�,5�}. Fur�W��,RL+s22 c) �.�� ��v1{iZ@ apKa,�!&�R�(�<�o~_en.4 .����EuP ` � � gle*&��s )L �0kf�\ $3, 3det�ng anya�@ op &2 \-膉1B-?a5�yO} 7�z�N�;� how���*? ary}�nqZ*� � �O"P ?� #I6*q*GI�BDUr�-�e�� &  � ����5��%�tak�to ac�5T�5a]Z�a$w�+d2.a2(k.J1!́�s, �7 �0"�bef�]Fv��n�.�opE�9+sea���7%!cel��e� 2� ��<aps�%!&���i�*g7a{+�B� .� �G�:a6��yar2E{!��g data%�e?d%Gop��.�I*2��fu� !�!pH&-��>Uxng&?s (1�JdExx and}24�v 1��a�ai�-&�(V *�2X�9 63.:)OrigiE�qnY&c5q�.n_}M!���m-�o�1 *m+de�Qb!zsl& fectA(na}vIya.�s �E��# s)�a :�*�`� :8. Ut<l� A�n igna�&� &�q�i YJ= c1'Q�'.�7S�y�# 6&do9h�8�$not de!-f�!d! �,."8�s A��(5GO ion-�B/�/�,m );�q�o� s ['s (dus� berN"� I� etc}w<d .��� sc/�>?ckle. O4qurs=�A-.)A�& sG �p9�@terAm3%� �?�m�@� � �9k�TWC�;Padd co� ntly![A ��9�hh�cq>9� �BbyA�c!�aF$�'#e*^ �2�yion hMOT. Sub�%CV��j�)�CYm2� histogram�.�putre}�:0yl8��a5� �&�r($�Za�)��5�AT� y e�%-20\%��)*� q � A�4 wo��.9-!�+sued a]%3.� �UQj�U�� ſm%i�Ha�%�in u0arme�inMenLIt�� �W+b$R��5,A@Y95�\!����� ��14$I_i \,(i=1,2)�"E߱Bs �X$i��}�eBbl��NoEqby $s_i$�c& �$O2&�*XA� �jm� kae4t:= $�3,cal{P}(s_i)$A/YChe �w!!�!�G (Von)�*wo mo�0at ^g,%�7�" s_i\A�le = _ �#� s� )#�-�^2 5$ $1��I� &�0w/B&�\z �5�1�6}R A�h!�tio $r_F7\s/2�&��a�:%~�7$QU��5-1ef"nA�oJ"n�z ��E / &�()�L-�ev�I�!�XDh9�C}(]W bf{rh�$ s_i ')\,:+6-� \, 5��@9qq*�ay�<��5Az6�$�in�.}�.�6#=@ ��"5FDof+ra�{�,"[;be  .( %�ًx���;i�� �*L>.tenth$+m\�==30&+m$uR��w� R := A: "( ( _�lTtor a $0$D2%Q�$"��ŊA�a�@4i8N)��.�R qW� �0q3��� �>�unA���0Y am�#H} r*$6&�%(,6<0�/ 08 }�] -vector $Q�k}$^l�Fly 5"&}�CsU "IE�]qI��]�N !���&�r ��r��xe � �Q%�?�p!Qc����+�'X:�,"Zf; $v$,\ ��(U�C!��4:&|!8narray} F&=&m\,!v_R� }{2}\0!\lbrack  s_1}{1+s_2+T -2kv� )^2}- -2J-+6-\U!\re \\ &�&�# I������.*v�m`_�$}�!-=p v_R=� kEkR��8&�($ � �7 DaFSr ��9 �r med "�P& cal ��i !��*� ����added�&:ly,� $id1h Ao��*l�� o� �|"oH�$(M� �If&�laced RE+`Xb�[�� denominat�AA: carefX��si�bi-�l�:�89�-%�� ed v�ri.B$pa�}terG(N!!H�2� O\�* bec�mu� , $kv\ll(i7,�#)�EE=1�safe *� d byN� u -P )G)%_v\,v+ -s_2)\4d.�} .K -2m�$Q%R=�� �>�D`w�H!.$il angular*K+,$\omega_R = �@\,\num ^2/2�*($ m 1;o+!4a,� a��u�3�cJ} �=}��4"�%{$+^2���\quad�KrmA a�p6x")&��2K}:�%# "�!%S�M�I term�] iqJ$9�nd *s �)a�7""(�.]2:H($} \tau_v=(as1 )^{-1}�\"�& C�- der ap�tom mo���2�si\� v�$v"rG is�9n*�v a�ituvGc . SofAm�f���, i,xy� �5��Joral}�" .���T��c� � !w}�s:�[ryB�%�s=' /5q�TfLqf1DZO���{b,FaTo�4�! �one�P:� � $�Ia65� dom (-4)�%!5�A�)�2�V 8 e gl/#vQ �Ք.j � quU-,N�l7�tll se���K 2F&l>N rS_���s$$ � ufiH:A�@Bi��m2a�!U�!tlet� 6�"Q5 5�9�S\+e�"*'����\i��,})�Da�� !^�/�. A�EH% if.o �Q� Hh &�!� �h shor�<"�YclF9k�/ch^9}Y�%domly�>�'���l1,��4�;��r�5�9-ix sWXary&�%{#a:infty}=a%�v���t!��Q.B1=T%�D�&�5B�q��� c} :g}\r)2} �\,5"�)2} \;S, {}{k.1+͕ |^2 + ��}ժ |,r_s:�4fiކ j�)� �N�5i85a�A3e  TE�&7#�O2y!2�* Q��a�n vXen�`M �var>. sum _ "^ 2b1s"$v^2�5 D^2+-r1�^2A^:dc,*u 2�e<�\�[fU\� ��. . 6�Y�uiona�:�'; sk�K = 9\%$)�ge*�'�+  0.94�@ @-&�'0.9�I#�=gg�=:QE��Q2 ^8d�ء~�=�t�!�Lv;a�e�urJ�8�r�; A�im2 ^iLTh 7�eve�> < a��<�� Markovian'u�� memory)��V :� *�(`'e/}"�yI�� Q +a&�m�I�$�/]y .) �(rm{P}_t(v)$�$ van_kampe��E�A�n else�))N �W(v,t+�As)=�k \dd s_1\, 2  v'�?at�=1c H�v  [ ',t)@�F;(v-v'-�F�1� s�)\ �o)&: ��� , at pA� p��s��.atu�sac1$�$s_2$�.newues6U:VEpr�FN   On��}&�8TkepAX J�A; �F3�m,)�k$Bɿ te!|� >�%�] ve} bD+s_2)v E�Ji�T�E_ haW~e��$�p�P�k�� sis (V�uE�aT�d)���Z#s!�'�)���� !�� �nd�!�mmeK0}) a Fokker-Pgk t�kQ%z Ap��ix+DLM?Eq}J!I�\p�"alI�M� ,t)}t} 1}{E�v:=- v}(v. ,t))z4k�4 $ v^2}(D(v)>5q'Foc�P>)� $D�,�<�2�>x �m.1�-�(�:-6b%!���YFk�= Du big{[}1+"5r��efZ v/Ϳ� \. D] O�)}s5�� ^{Bd)6W�%!W>� �'�n$ �z 1$i�FX�g"6x��6�i����#� abnormyif)�cYaE1�2I�a�_ P}_0� t�  �:J%6�$�@��N�>a ��4":JM�_0AΉ9iV S\,[ 1+J�^2 ]^{-� eta)B��� $ =�v/)� �)���l=�ZK"�@� 4;� �'isB M( _c} � �?2\ \ln{2}}� N�A�08Q� \:E36�>qAs-�"�=$acQ�>j�_)vF$ N�$�4%�impl�UNBj�  * act &�!�A_iv%s UIAKR�nAv[?0I=� �z.7per�)B��9�)=v�Nn�"� 9�ll>�:{ �#/�Y��T"/J�I2*�21�#M b)�!7!h�I[!`1�}$.\\6eF�tic%5" �2&>�r!�i�<�N�*d�2���@6��8, � !1O1W�IT|0\-�$ g��toq�j^� T8aw"�+m?�eqer� e>E� x(*�%)d&�discuS="� alH� 6�4*&���!.!�b��<o�sI�eonY�4�.&t A,� 1�dotted ���e�5�.@�kP5� �!#B�Q r�.o ZSt%� >�eQa fai�:� alu�#-,!��* GUO��-)��2gjo min�:�W� � au_c2�a:�!oAI�8!b0Pn��er�Tgl"�3byn DB�!���yu1"�.Y ��(c6@ �Asaw!� i��ZN�LaT�med ei/Mavo^V�(.�d�( �Y��d!0.6/: !m^b�05�9}1Fi��a}�$:/�ic@� m] 3witte92}��r2��ry���2! "p b�!�� &,"Ime�/�<�[,�V2���"0#1Y� are �O7��M,t}K&�*�t6GB"�P�%anisotrG�^re�I coup�P�sms/<2i�49t�ism�� �Ij+8Wa�шH u�+b*(S 1. A6���inap�'III.D.!~�K*d65�^���!�major79��w+.�-� */�"5.�-Es�#toTa,*�y�g!L�9! Ab�l�son qu[5on�'*�p � ^/(MC) .a�_MC���ak9.'/!��W, �� h&TQ��|,.�iO��}K=9�uc67' di�f;o far,E4i.:mithm�a`�6#c�s��>&�"�s��� !�B4m MC calc-�A�.�:tB lifeC �{e}=1�"�@�ȡ��= �X' �A�Nila�F�.�8f) =&�(5&\*!M �*���C)��L�c9Q=��ed9�n!Ccrete"� ($n$ �"g*�4uDs- e$)br � _I} � �0(n+1)=(1-\rho"� )+ R_nBR A!$/ �c"�  k)�J!�A�H �F�lax! =|to�KXa�rJCt� I?��!�l"�31@�b�J�D� �,}Ely "9�Lw��)4[-\epsilon /2, ]^a� ple .�dg!�� \l3+R_n�Tle� T^2/12E m#'$&9 $R_n$'�0dkS�/�haG� inuous�tof� 5�)A>�Gy @�d}�{d�!�}{dt} +Jrho�e� ' = R(t)>twB� M�s$!*�c�.-!�!|a �qE҅�]B����\ E}=��e� � � fiER�s$�"arho�$ 9(��e| M�of #9%!L�) �$-��[g�ng�KA�Ys mea9J� �2p "�@U+ (t')%P M0 w#�D�)|(t-t')�@$>"]A�ZPA==]z24)7�(he.�p�K/ eBn�a��!G#�-bT��a�toB~ � � 6!� � YF�#is)��5^ � �:�ga�2 squaeO-�9��2�u�^v/e2e�id "�<*:KO� (o^ nven�{choice)BA�m�"c� *Pn!M� b&$1Q� in pS�1��i�*NGe��IM�B:�V Coorx`"MF���R� �i�� s_0 �E4� &=iuv"_"ama���,"� ith � $� e9!<v=.�[�!� <.ISv$�� �@��l)�a�5�& n&sE m({= %^�  ��-�t ltńjk�6~a �up��9 ]#&S�=achw*/ ' )]%���� �S�$�*)� quasi-�,97�E�� .�iQ.<f#*a:%�y*atf��{*_!�%�<n ���"�b II.C���mtpdU=�M���|��a�&R  �E!O02' �e5 .�%;������+our:=�b� . !�r�';_ tickD8as�4s�wto!�p{ �U9 � odT�r�*� vmB!&�(a�e�$1� �2� E) �#y"�0.f/s$~6:�x .řx�$solid curv��!=MC*4 �:�u8 r_����$=60�u �fsqc��5 fit-yz :�Y0V^�W�� � UTy��J) *�;M�can see= wK5)_25p��sa�A\6go�W�x��a ��lK%��qɡ � d. Cw- g ba>o��&�'Ilt�vc7x9 � ��V1�k�*�@-"�s�)" �(oOtw�AJlong-��2� �f��A "��(� � oh" ivalx;��I=u�/ 2 ,Sqɚ0.� :�W �(��#"J�t�%a�eNLa/5IXbMC١���/o1l��at!�s~xb�%=TM5 M5�.v��o*y9850� &)j"n}�n�ts�~)p)Y�y]���6aB*�_"�a"q�KA  ewee�a0c.�09'��˅m�EӍDc��H�/]Z^��.�� �+a��4O c�����2�yI �!�das������h"�� .t"=@+io�xOc�K���3� */-.��\�u=�� Xa�Ent FL"�<��� �! (a little bi�lo "9�!�s&C�\ � [�Go!m�s*,_G��-ll� .IM� .�v���toh-qE�)<*� cri��:8�wY�ez 2pX a+ U�� �� � * �&d.�nwords,>jcU�E=a�-%��0 v �c(seANA�-�!KDre�Q� 6mTA Prof.� !�i�0�sp�F} ""��& �Y:�&�H��{[ u%U���RO�AS�5.�*A+a��E �l"M<2���Wn!Gly��or��5�A5'.:"�t�tr^"� E�V<�� (6 � *�6� pl<5GauFo2�E�� �@ ard>�(�g�� non-Z�o�MC6j'��]�3Y_R�(( �#0.8�i$ gM��IAfixed}N� e96Xis:� )fp dv�%E�n ��$� .�"�E&�a a�S^G*�< ��:i��+s�* summ| ^0&| m�.�2��;(%j�&I B��> E-5�xp�tmGYmon�m��_��I$�3), we a� qNme�* �,[]G!��1��͑q��JFQ" of�e&�~!�*Oa�e"MR.[2�is puts7NeN6+Ffu&��� �$#3�L |:���Y.�>)DRlA.dO�"p " {:� Dyn_A�����2"�e�ZfoL HP'\ [(#�c0?*���&��Y0��t�%_lQ#c2�5� . � � �n��R"� .�%w .! (a)!���on����UR deca���H �ete)aY� }~ B��!�K��L* F�)�.�2��" �-�sUxd�m �(cR �� lex".�r�Lk,�"�h��Ed6)� ![-",(-��Th2fYI&�m�ah}!*.� )b >�&$1; �6> -LK mean�_il�@Ro52-i� "�s��O7$R�UEis�*ic1�%�` any!��#J f.�g�!6..6�Cne�� "x!��gs�=e��C uild�$1! �9:.��7%yo shrinkm��asily3l��cocHE/�Y��1 2:by-�/})�oim�%m2� �hs.�i1# .I%� n] froz�}�p a�S per 6���� .O)[&�-�AK(����� �)Q� v(t)%�dF/ed:B�I)*^2=B�.F�5$)\exp{(-2t�)}F%T '&)�_r}�AZ3}�ra�D >gEhe�YM��"� v &�.ef��EdA bj��t��-vJA3 �` esv%"#� \, (1�:�urt>�{c�Q�� spread�*��s� -&� E\e!vB�p:r�. O�.A�+$�=ad�V��qed �r(���'�=�t�� window�� "i+{�r"�& &5m�x���e5 a�D ��r��� .p��B�r�'fy�2Y�?�(onc�62�i�swi� c6 �bk�A`�E����ic5ە�fis wi"ou�"�4�8 %����Ɍ�s �s6�"p ��y82%��asu��r�)�$�0A"x"�l�  u R@�w4.� �exp}(a6BA��N-a�$�EW )od�Iw=�`�W� pv� nice�%>� !�D�1X:R^a*1�a� �*z�p$?8)�}: &,��A�i��  ("�.�!U s��X"-[�qso"Q0� T.�6Z�A�rlR� b). *� )H�C�q�(��~n�yms$), &�"} �m1.���e :  &�>��f�/�?Y %�.��? (�Z$�a�E!�}�E$,~ =JRe^er/ �%y> � �&�� �Kp�L�AA"1T���s)r0-&bA��[i�'gw n 3Dϒ�%�� ���e��� m6J{Hz6[d2�.�?2F�schemf �)� ^�T ��(a2:%{)�! �!r9"��Tאlѣ*r�rettyW��9>�� s��&wIX/n*�Sh>v�!B�,XaFm{�*�+. �u%v*s&��}Vs� z"�` ��,��,ld �uin.�pst/Vg�pl ��s!���R��@1�� 6�� G" *_BD�i�Me� dest�&A!��b�s�� "mI�ZquPS)vs�]0d�orA� o mainIz2�. UH�s�}�J��A��im%2o7 ��=, B֒s�4�z ��u~e� � n� Sto� i��y.�l�9&s"{F2��pab �&�6.�  9�.� a21D �of s)s:\�Ec��*�9��k.�7s�d"�� )��?"�O�!.�O!���bG"; m�Y�i�-&�*� A�e�4sa1)(rYa#roo/=��al�*�.~37wo Os2����no��1i� I ��~�-m�5S"o-+6��,���.�F� y2t�;%lZ� >|�y �2 lett��ea�wsr}< �HsuB�)��da��25�!bƞb��H� a2�FՕplagyJ �_l�ry��>Z�<�f�X1�gin ���Ɇa�B?jq2d�}1a��DsMs "^&ly M �� $\zeta$��;c*���N9U2��@* _ "v� �a ����Atea2� )� �%�.k2�� �d"%a:%aQu/�Lrx� �^2}�dh�v�a���0��Z�A@0�g�t!n)[�%� eT؎allM 5}���#� Mi!Id��ŒpKEmW:HA">U�F_h& g6�F%�Q�vN��H\<�t� .{b!6:��h6�� 2� /#= �)e�)��32+�  aHKli�` thŮrg�I�YI[a5l�r"J+(9 %�IR�� 2���!�|q8!�aR���aB�o%+.�5s��ser�671}l��:F F��u +�"�)m� Q�- :iA%�*��Ko&9�Gbe� ed up!�.:f&��"h%)9��iu��n*j|�(�|j!4��in5�|�\�AcӢ�)&���"ͬ7 nanc��sup��In!~4CNRS (Centre NF �A��, Recherche S�ifHD#<,BNM ( Bureau2<M\'etr(�e)�9�` N&���$$ 03 3 0052:"�D: D��%+�-�D}"V*MEq}`nQEv#"|D)!""� b0Urf "�:y B NE*2B (v, 6�H �H&�H t2�H;"I0�H�H62) %�E.�H2�HNN,s_2,v')&�HB�2By Four�~A��*a% "% rd� $�'w�$tN$widetilde{��}(q.�IYB 1}{\�0WUXB�� \dd .�I) v' �qC��E$exp[-iq(v'�F^ ]>�3Wug�*e"�|:a�h�;c��*A���N:Jh�*%*v'�:H)$}[q_s(a-"')v')]\; Z2^*4+24 5�2%�(Ey !X(-iqv')�Gou�V end{Q>}"& �E�n �f x�juc}�d /B- Z�(u)R6M; s \�K)(s�u 2�;B� B1�8* *y' r|��L {�0.b:o���+Ori-i .J�F J�a&�!e�?R%\%=pegD"z�A TaylJ+U�L�(�-!�) A s���/<|I;�c�?atN�c)�i�\"uJ:�E9�:�J\simeq ?^ A�@, \Big[i\,qv'-q^2 s{� s}}{J}[v'^2&�I+�H .a�J9Z biga%\g[2A�\,8N�I{3}v' Iv$c}{m_{Sr}}>�c}iiP(�\,{O2!q ^2+{�3 I}^2 �)2b�]�Zv'\no �\\2��,exq�:� a�n F&  �IG�J+�a� &�' a���} �da/1X$&~�d�?�m6�+ i#W��e}[] \i�$deg��[R=�� ]{Fig1.ep�#cap+{S�|� draNof z s��� ��m�)^�h ��%% eD�*=TR.&�A"A�,$x$ a��l R3�"A (yz)] $45^̜$+��Lz L ��,"�Al.� �* ���:iFy.Fd.kF�j�e<H$!�4cl�2h�`,֯��� � $z$ٻla��v�I�-� �� n�5%�2:�? �*�.1��B%s$yx��<��1�>斡� coll�)!�ty% &�&�*�kA>�� &M� "$."�Sf��.�p��. MA)��3o�).}�TOF>o�q3:qV*- ��|a�o..�'$'X |=2|�;|�@`�� = ��),�;&Z � ata (F les�7c��U�RZ(�H�/� � !�*HCxA\3�/i�.�5 $�1=60� �5AbS��=&V&l7iaDm�npff�lyr�6�"� ��bHe�%�fR��6:^��4��!]�.�0"�6%��at �I >@�=.kK.qM �  /F��r�F&�7]W�0M�)�y�A.�,��N�Vf����(E�.�c����.����c})R9����y>=�q5:; ��)�:s�T���AfX{�N�ons:>a�FaAYsmor,GK/}J!eremov'T�ly i`*�!( ough�{�l ��Af��l�)gأ(b)���12�)|8+ ��Y� C}(xYe��vs}A"r".co|at2 �#a* �%� o�i vanishes H�s%/.*��$. .�"�6�un�� � l,��$ (diamonds�0oscil � op!&�+!hd(�!�"�� gene'�0 (��E%!�2&��I�f�D�9"��!1/_�#�nS� i�<f (�8e �0 ast `�]u��>�2�*�N�he�_*%x"�'<pix��izcH Ms:��u 6:uvv����.��)I2n2 �-����2�Q%�u�*�q^A�g.O=� "�pI,& �c��Ft�=A�"��;"&�P:6{���t /�.���2�xR%`*>�°7:�F%v�BU �c>%- $ (f9V, i>�s�An;*1�1� ��-$ ���3 ]��.Rof �.aJ� � 4��*L.-&+�B~ fup����k�nI�Ba�A�=�B 1 "�ѩ/M)"d$ 9NY C=D:�� 8: .Y &� " �<s_%G8%G.�. Cir  :*7 ~h�@�  :�7fit. D*�::^ �%�7.5܂�#�s=*��R&&r8�+9:+V� ��A\��b-"?3a0vvd�W36whBhs:�rFi:47) 1.25�< s$) ;I�"x3c>�(m�=1 : :�*a�v2*Bs-�y�R�a_�-_C =0.8�7�e�.�a{�9M�y�.�}�&�;76�i�A��3��a9���V"�U.� h ex.�8+���jEj10:k� : Tim:�5�vFR.�af.1a�%�;��"�%)�^*�+W9s$M0�.Jenp��% mj�D.�'$", �Bl'o Q"[^��,Z�"R��b��em*q� F*�7h�g%8qg�q s, Les Ho�� LIII, @� J. DH�$, J.M. Rai� ��8Zinn-Justin (No{� Holl1#Am�� dam, 1992-J��� M.Hyder:$J.R. Ensheů HMatthews, C.E. Wiem��E.A�Drnell,Rce�,bf{269}, 198��95); K�0vis, M.O. Mew�%bAn>�, N�Pvan Druten, D.S. Durf�ED�Kur�� W. K��P@Phys. Rev. Lett. 6p,bf{75}, 3969 ��T1�(�} T.W. %V@A.L. Schawlow, Op�Em.�13}, 6�752Vw6�au� D.!�W [PH. Dehmelt, Bull. Am. �Socb2��637�:c�%} P �,! PhBmps, S��lst�; C. T�� r, R. Watl d CIstbrookAT �~�B�46}, 2084 (19892�c&���Q��CA hen-~oudjif %Gbf23� 89);�J. Ung�TD.�W�, E. RiN#ndChuZz�5%�89)�m�@�} C!�(, F. Bondu �1d�aIberg, E��Ig J. D5#7}, 44I_6"��}ULoo, A�� usch%�Sau��M��0egrini, E. Are�oa a��I�J��oms�2J �B: �K um S���; q!�81 (20042�l2�0} X. Xu, T. La� Smith%]Haa�A. Galla�%�J. Ye, )ezAuv01140 z2);JfJatll� N ^'e9at 20032���T.a`YoA�f/ privH;,u_�>��p>�zP !� Lund� K.-A���I!{� � ށga�013410Jk��u�!�D*�,A� Laur�m Wern]=nd��W���I|B:y��Y���306��SS#2� d�� CS \�q [prl&p�*��\u!w>;�.psfrag6e�psfig&Ak} \titn�symptoL�b(�ur� Rayl��--(#��}���um��u Dk ,min$^1$, Chr � phe JossedW$^2� Paul��v.3$�!ss< D�"t�)�����Ma$��*d�"z9!�i� u���Cambri�  CB3 0WA,,(ted Kingdom� �Lab�oire�Mod\'eli��on en �)canique<UPMC-5*(UMR 7607, 4� @ce Jussieu, 75252�Q$C\'edex 05��L$$^3$ IRPHE���0s d'Aix-Marse�U I \& IIy, 49 ru!vliot-C�(<, BP 146, 13384 ;C~FrA\\ Y)a"N�W�'"�c�nu��l*"]inviscidYEFD�Atwood �#�!u�ea bj�]g,mͪ��2" �]�at�5%y>�r�e spicapr��+ClA�!@$Williams\cөc}<w��)�a�pl½�m�3r . I�tt�aw�o���# �'s x=i�v�>ike $t!�"�^�>sh>4in$ele m ,0a good agreem�>ent with the suggested $1/t^5$ law. Moreover, we obtain consist?(results forF`prefactor coefficients of$asymptotic]0s. Eventually_exhibit+`self-similar behavior of �Pinterface profile nea ��spike. \end{abstract} \maketitle \section{Introduction} The Rayleigh-Taylor (RT) instability appears when, under gravity, an heavy liquid is placed over a lighter one\cite{raylp$}. This il(is crucial !^@our understanding!Udiffer!�8phenomena in fl�Dmechanics: mixing,!Z(rmal conve%D (\cite{kada} and 4d ref. herein)Dalso finger number!� E(in splashes O gueyffier�It�A important3inert�confinm�fusion w{�$ mass abla!�!�$vides a st%�z! effect to: =Q �4sanz}. WithoutX , af!�A^exponen�growth!kperturb�s due toliE�RT.q, non M�@1�1.��6�2p}{$2633644655666:.� t=6..�7 729 9 )�ᦠ {\includegraphics[width=6cm]{all.eps}} \� 7} \ca�I{Snapsho&v &. subje' A� >� *- ��A= rang�U��$t=0$a�!m,:salong%�\ -dim$ ���Mst� nary �'�Ah$�>3k}$,��a fun �$ime.\label!t!p ѕ)�m� Re!�ly,� �E] y͋a�;allel��J���X � �?���*� ed �tclavin�u5+�cis*� �� %�gcans ��A �of chaUeristic �� riseAf� Z�{  solu��s"l caseW- �AO.N- peak��ed:�:� ma�Ll curva� n�9"at O��is found�|e  6 cubic powz f)=$t^3$.*,)%� pos� , followaK" @ $ \frac12 g t^2$���*S ,�m)o!� verg%gIE� 6�e>��decrea!� �$t^{-5}$-�is lette��Q a*" stude��nQ.fG sG e.�5� !V��> )!� investigaA\# elf %Apredi� in: We%1i� �6a.�  (Hy) 5MexA�or�of zero"~ �t� �� 6� �c s us bAn��A�g��4method (BIM laon). Du%�str� Fal�� ies, ,areful treatY)W b`u%�&� ? �'eeded�explaia\below ��fthen � �compared)1!��;.*zA&p analysis<� �} 2�Mwo.� m� of2�r 6k,.a negati�.% $-g$. A $iodic sine" l�9IofA �U " mple!z)I�4 &. NegAng>�� /a�~ �Z no J trol�SmeA#�resca ��� N��%k��kpot� $\varphi$�  f�s�,�*�!��Ak^3/g}$w iV. 9"i�� Hby $y=\alpha(x,t)$,� y"� dir�on�� 2� (x$ orthogonTit (sf*Amap})^e��ZT${\bf U}=(u,v)$ satisf !"[$less Euler5� $��{d D}{dt}=-\n� }P +e_y} $$ �$P(x,y�!i� , �0� no2�:�� . OI� '=1$. �kin�Ʌ�69�rK ~:�\� =�} t}+u��V) x}=v!�sU}-�-�evalu5� � $(x,\)$. S�.ime� f� e�&� Q,to_% * ��)Q% clesNa�Vvica��.�c8 aA� most��b A�� ion�m refore, f"?2� H, we assume quasi-vlc steadyj ��m:w�� t�� � re�0 $ |u|\ll |v|}~Ev \sim \�2y}$$ %w$y ��9_. Wri�a6[expanɮ>�J� |x| �y�FA/����� �= � (y+fm�)i�A�$  J. Tak��a T �in �{�6�$f �� �� symm5 � =9/+%{f_0(�}{ �y}x^2}{2} {f_2B) + O(x^4)�`W� uur�{se�xJ �!�Jn . In��ressibiE)I u=-\� ( � �1}A •;(�/ -2y}�eUal y}\r)x �3).$$ A� 6  (�Hwe���= eveU>�-�Ye1��yI ex �oN 7�}%�-����}t}-)x5�.)1�zFx}Q�.=!�i�� be sol� �4 sa;� s� � �28)y�$g=t( �tE|- \gamm�)e��a�!$a� t/2$A_�� �E��ik�ari�wonIT {9|Zet}�3 x}=09@): "_�!:�  $.�$=\theta(xt�vA firs�dcl�-�drawnx uI��u�j,, $\kappa=-�^-�/$ x^2|_{x=0�I is���@ a�in� ��J�~:o_ }  t^3 �''(0) �F�5� next�W termE~!D�1a�d� mineW5ms$�%$&�tip. U� U"�%"�e�g we` pro�a뭻� �F=on it�� l tangent.�du�  +B�&� ]�xq�dv 8=�8.A�S�~���$dQ r ,t)/dx=0$�&nis&� atM�b z�h�\�(will end upASb�I� )�A)��!_9�$I@a+q6 0)+x^2t^2.\/2+ɽ� Reme< �Y|f2�a`n. ularsge � eM~$q/^2RvyOt + y��� 2y}�Ey�DT!1�others%��� fin�"�vb "� $y=y_s$._� e _s,t.Nt} +\{ _s}:R3y}= 'd.� J 2}{RQ�1}{�Ł�f �: " 4M L2.���} $� 1A$!2�at6R�k {d^v{dt^2}=1 ~� u ��B02}{t^5.�} � quinN$x�9}�orAonf��2�*�a��fifth 2`.�k"����elaboeu�'i*� �!*�priCk >n aut�_be*� �y� 2 A�vel &Kis knownF�thank�Cauchy'�orem,�[Q spirA!pionne�� �Lvinje,cokelet,BMO,MZj$w��"�,al Bernoulli��H����9�I^u�"��t} = �  }(+)^2 + y,1Y)E�5@9?&� harmonic&� � doma��\Omega�JF� Delt� = 0Q�lapV�1�c�{� R<I 1fad! �� >m�"�1�sam�"�&5A2�1"N�)�d �xa�} \cdot �n!�6�61kinFKn�9�N;o" no-step� search��.j Q (� !�)�t*� t�"� N 4� ). W&�� lex2Hb� z)q�, + i \psi$ �!�2 $f 1Dexp(-i z)$ (Cf. Fi&�![��'$z=x+i�J]ie��eamU��k6ptransw 2pe} :� "�&clo�$ M$ $ $}u4i  q, $1���* :)����"� \zeta)= D!* )$ a��HG�� F�&�$a FredholmY� � kindYD�9O�" .Z#c�%z6t �#��("4 �= �u�e�al M$)��(system�Q�#.~ a $LU$��om� . O�&we�� on e!#��M$�EAܕ*of 4markeg%!�:!%A�i�byv=eta}{dz�/u -a", vV�$u)$$v$( horizontal%?>�!X2y(��+o(x� ue�*"�&�+(ce scheme �� " V�P��cGcI%l s oEE�#M.�@N�"�"o�c}{qO&K"a=ax}{$yy}{$x}{�}^{�|}%M}{$Mlev-!8-!map_new1!c$!��� Con�z@(0I��:T��~'�R��a F��S-F�q A��{q�I�s (Jv)��%�he{�emphasiz�� v�-� �+�is reAM(ably robust%� � be� u4 ly evFto c�.&���f ingso_by� 2_EW valid. CAN�.���r:#�*� *Z-,}%EK , !��u�� &�9st twic�)�'c*� �/lyE AR� w2 $8a�� tip's&�� B�� !��!c*= }� ��qaxE��E !~*�+s�r� r=3x%"8)Y�reiY $� k"(t-t_0)�au,w�.q _se"� �%�$$t_0=3.74$a/.he(#io�"n�)gre =�yf%& hyp&sis, su}4� atg� 3! delayA�oun~/;.�1�{%U �z.. ���&� C�"f��er data!�<&�dependa�7 2��rA !T1�hl�,�$%�AU�=$tVw.� Z(7��EV_zoom2>�P�$h�+ $y_s(t�s�����&5iEA��#0a log-log plo5aO u(black%;e). [�:XI�a �{ polynom� f�$.�d}4�0ne ���+OeC6$/12�. "� �J�9��_s�%^�� ntm1� courbure�'�Y*"( �is��6l�)�&�q� law�z mubic})-S�� =1.5�Z�%">XS��R%c�ed��10�Bhm� q  in:tI�.�d@0�?e.$)�vU�%�� )�} In adv� ^�isv � �0��e*� "�&A6v1and�!r�.\��F$1��6�,2�7�% look�16"btwoXvi4on}Two��s�aA& suchAe: �*z re]��to�E>��s�#o3's�,B�error[&ɽP$ more "<8&�2Bno( J2I%er\ e���e0F�$&�:_,�h"no adju�Cle�o%i�'�3-��onR> ���>mO.�0.�, def�'ai*+betwe�h͛.�&��Z%i[���&n��� %,��L�:� @.��80A�g6AvE �i�[)*� val�.��!@#i���mu��:�M"�<��t��7Ŧ7h"�-a�A} ��S.�-"691Ctip�-� � ar���+ps9&� sui4ed�%$" �#]- Q�t^ $ 6�04�02M�%lFM�*iDs���eQ !�Hy��/E  ��($aa $y$ coord�e6�:.�%4g�L"&�,2o ٸQl6�:+%Qt�Y�&�s*s .� � hv2F &.&�+B��BlJ�L�Tq%�# &"&< �=;(��ED2�*68y3s�stops I) 2K-y^l`9I enou�=o1h%�y*0��*C Q&� Ai�0A3!�in��U��"inR!� R�!;hef. �?!pleas6!"&$ank J. Ash�j�usA.comJ �ac�ledge&�sup�?CEA2�>con <t`/DIF N° 4600051147/P6H29.�� thebiblio�4y}{99A�(d�>\ifx\csna�natexlab� \1x\def\,#1{#1}\fi \b\Bem{ra�A} Lord"k, {\em S�Bg=@Papers II (Cambri�Uni!��:P', , Ur<\d Kingdom, 1900)}, p 200� �7>} B. CasTC g, G. Gun2;�ne, F. Heslot, L. Kadanoff, A. Libchaber, S�q,omae, X. Wu,ZaleskiEH$G. Zanetti � J. FBMech.}$<204}, 1-30 (19892-91&�A D�e�AaSap a(C. R. Acad.!L. P IIb m0326}, 839-844p98).�A�Sanz, Ramirez,Y s B��(R.P.J. Town �8Phys. Rev. Lett�@89}, 195002 (20026y8ohn1} S.-I. SohJME �(67}, 026301I3BI2�I9I36703I42Il?}!vL �A2 >. J�122!�!Q552F�; Q. Zc?I�^$1}, 339J:��?}AUHazak,e1ZH7!� 4167�962��?! $I. AbarzhirK � J6-Lmika} K.O. MikaelianvL0}, 508�6L�>N�4ogamov I=mSpace �M 1O1-335Q::"@@ S. TL@1}roce)SLond. A T44!�501-52 W6_�> V.N. Gon�)ovXZ�8A345R�88 P. CC8 \&��Williamsk p� ��publiBina��QE�6v�!} T. V \ P. Brevig �Adv. W�4 Resources1 }, 7%�812Dc�!} M.S.!C,guet-HigginsfE.D. C 'M�jv35)�-26!�76�BMOA�(R. Baker, DA� Meir�20nd S.A. Orsza�)�%�23!�48%�80)'�MZ}��Menikof�4d�KZemacћJ�mput. ]-#5A/2E�8E*%��hecht}  >^  docu��} 4 $wr9C>� 2(MVd",int_\mathcal&4#M}�(�+"�&*- _e}d �",�!c!$ndB:#$0_e$�a� out� $\�M$.��7-r<6 reaB5�:P | -- �#%�pkac"@.h+ ���,v�)"I%to� a?Gqu.N;. If�sret*e3 _� hB�. pou=� imag��0s�:�: �we%f I@a��# RdR�0sum_{j=1}^N \� ( Re(\G�._{k,j})�!_j - Im:�" _j \7)AV"�'-'��}!�r?e6�L$.u� n i%v�,R:/$ Jbe +!"�w�;lY0I�s>J . H�= g $N8B0M�k$>:A2)�)�@�s�;�Lr�(A Ze \to I�k� : 6 -t^3W"(0) *0uhF_0(x_N�*�)(*B( x}) C')^2 S:�*&�+x}+f_2 L�)g}{2x_s�/�)s�9i�7A$ V^\��,class[debug,zfull,Zs]{epl�)$author{Kih< Kim\T {1}\�0ks{E-mail: \e@{khkim@ajou.ac.kr+��,Dong-Hun Lee C�4Hx W3b�x.t \etao| itute{ {1} De���j�O Mole&r% eS@Technology, Ajou &n <, Suwon, Korea\\[2:[� nomy��� � 0ce, Kyung Hee� � , Yo�B, \ �3:Z Elect� E1e�*b� O#4acs{41.20.Jb}{ G omag�9A2.N; radio>I$2.25.Bs}{WfMMM�,�"miv!�absorD?(70.Qs}{PhotT* bandgap m� ialsA��q&.EQ a"bQW"Gn5N�}invari�@imbed�a+ mA>��(der�=newRB��� ��2/ qvy��=�B.�anyU'in1���<v�� ��P�one.�,. By do�d�)X2b$ orig"0&�)problh'�(-"�ial"�2\-a�ifK�1 J .J���!�&*.�* the �6 much fBer.)!BJ �%"!U�!"M<$matrix refa���HF*Q�2�T��t�" <�� 6��� exactl�Heff�Tly.r+eis3# �"j>n=>ofq�by? lyI em� !>6� cir� ly-po�NlOe�::� :p pq�,crystals madKisotrop�-hir�&��� fin�K r�!,*�*e9�*t�s�+5% c�f$n�i�se=by)[5� ionsB�U \s@{F�U&�T ^i!Swo or4)��%�R�!�!� �on&� !�A�ub>S tous�ځ��� bran of s8�b�I�Uma �ics, op1G,}U�?��a^E"�)��Ke�d �`1,budden,yariv,doro,kpw,2"Q!�is��wQ+ p a zr&I !% �F&DJ��' y\2,kly,bell,ram,hein,kim123}M�"�G�I2!�B�. Sta�P�a=+y �%•�aq�I(�)�4�Cw=l �� ه��CY�eJ6V���V RV��Jsr� ��Z�!z�� ��289Oi�,k>�"�I!�!X��FO%S,�5��JzE g�F advanta�H�~�Fo� ular.z�4�� �aT �0��H�s=nge /o@& uous���b�ar�-� i� 2 �)um.��checko��v�Z��� 0 �64 >N6�By>� R72�67�ed��E�2��e&�"t�|�-%��exist in$B�2��| I,"pa*�0�.��*-Bng�1Zr.w um,��(6CFGA�y �b�R�QspaN &�E tak!is �!$z$ axnd�CA�2YmumWick5$L$ lA��50\le zL$S K[�C%]�!��A�p $xz$��ne�1e�c�1�Zq�< \�) $q$,�!naL� �)� x$A�AE(sn,! n!�Yq+*$]H $e^{iqx}��%�R�Y8 �Knga s,E�o��+!6� Y"�Z�!��C � (eqnarray} {L: ]}\{dz^2}�Ad\cal E}-2{ ^7S (z) �d<!+�[((z)K^2 M-q^2I�]5=&�eq:�"�����4=(4_1,�6s, N)^Tn!-9�)� V5���$ �E�ndMre $N\ks N$ �C 5�IIEz�*��&� mann�3jm �Y.�!��pincid�+xWtht A[�F-z>L� t��&nm,rv[ 51Kz<0$. $I)6^t �)K dianJ)'#&0$K_{ij}=k_i\dg9F�/ $k_iD��it S�  \�-�A�,$i$-th. $Im � M$� O] �c�h W ���l9n* �QUs-� EA� ]IE���Ki� �f"O<��w�'!9 ^3O�;"�8s,��`��at&PAf �AVz~ assign�4 �^� suit)1, eq.~�&qz)��\2A�y&@ " eW��*��&RY>�40rc QO exD esM�%;�`E��@ �#cis�1,�$�ѡmJ�. L�� is L&�Q/apply� Nor1X!�a!�V�A�wo=�p %�. red .�^!��e!a�*B�ANM� E$, Y���Ke $2��2��c� Am��G -h!�F�(3nd y3$e-conjugatP� �:!Araa � henk,bla�$ wide<ety!J>v*�3([*su�l�?!�[s�d �tudS 5J� "EF \\ \tildeVu-�v2v<v 7& �$.ueq:gfbw � T�+F�$!�7 _A�a�anti-6�Cat�.���. . $P�Bw�RA$P_xp6x� $p*u"�T�;& M�+A�qC_�I�G�2traa�forwar/;pr�A� $2e*XSeaVf� _�#text}F�Z }  z}2r<=i~ {\rm sgn}(z-1�)A�1�A�)P28 , ~~fdm5:k -i ~Rm~ 2]Y�z M)P6s2Bt%E�9U� eqs�r gf})E["�gf2})�%�6 "��v5�/o� ���X7%�!� &2 &&�`(z,L)=�L)\no $\\ &&~~-{iL  2}%"0^L d1 6-�n �I�] )P-P � B P� F +q^2E� >�� �  ,L),� !q��� �d `Zɦ� &Y^�b�ea��$�&�" al��Xe�.�Kw�R�+� +KJIR�6� �,L�#q L}=iPLL)+\Ph)�"�F2�Fm;=)� E}(L)P-{15��u&9�L) J�Lf�L2�L)�e,$�!$ȝ�A�Q�# x7!P2: )�) excep05�js4�& �N (��*�L)"4C� ePC1PHa�tCIwe �/9Nu7 }:���.YHU�Z�TnoY8BUpE�%N|k6nv5^nIld �!�}{dA^ UpUl} z} \Bigg\�>_{z=L}+ Pr8L}>7 =i.It< -l+I��U����QFPs)=I+Ee��95e (.� � =p,2""�Gd� $Z:�m {{dr�L}}&=&i�.�+. `�� 6� -{i q�%&+I] Q��>�ڧ_.��rU�q�B�Srly!/s�-ng $zaJin6�E�)�1� "�*� u��$P ($=%�0e���t:�L.~.s&2r*�n�n` 6&>j Thes?B�54��1le�#�$��� iy ��Js,A�0)!���$t I$. For�G�of� &qd !�.O�� s &�" ){M�}e��v�e""&�q�5ry^_"7 M�)�T6 t}) ��l�e= 65 � �A#6 � r^ � t`5 -RON�(E�79D�u�=in�:e>�� L^"�um. Re�(a�2L}�get��\�e� z,l)mh l��� )�E}(l):u .�0>{l2f lN�lf�l�c [r(l�HB�FY>{aam' ($0�'.��{ &&\mu�U5��(p \mu}.E�E} ) (q\muUW # {\omega^2 c�c\bf E} +  }y[I�Jt+R� { 1g � ^  2EcwF�>B (e���', 3-%��-Ra*AK�, igen��U ��1��%�"�red�݁�� $\s�v=^}+ �iB ->MjInJ2#a�ppwo��jno /r�i�p �l��� each�]#�^����I�$AHl {A : �{%7�b� $�er��k*ed<e�.$iP� dk�V�#$R�6 z"4lyd �R%��,n%!�"$-$%W"$�!�#��#)"?�US'"n �fN�#EA"�#�C� e)}�? $E_x�E_zH_x-4H_z$ � 2�cw��i� Ń1��5�s 2�$E_y=E_y� @$H_y=H ~ turnK8_ � prek��~ke"F��#=\p { E_r H }�� K!0k&0\cr 0&k\cr�� # \mu& + &Q+ 9�M.:MMV?mu:* �B��$k=�)/c We)5[e� p) 6�E��0�� � U|setA�.;*�("�0sc1$2�\avail�� , ou"'!�s�E�/G>� not�(, $r_{11}$( 21}$`"a~�*�!]� 6�is $s$*0aG�av� $s$($p$)-.&H� _{22 �12�p��p$($sR��Ji0a] l��� �mF"s. By�)�#"x9 comb�]�/F�.=`"�"�#�K I.S 7.�%lbi2!�ij8'�"t��0  $i�qj�"@either $+$ or $-$ 3}��H7nR)�++-�-+!�&� .�io2�.^� isN�VOr��yR;�KM��L )0t ��Lby $R%'=� r  �T!HT !)U! . Aea�mpl�o� ��' ��#!��N`_cq+"�*� ���~>r,�T ced �;un la m�� of iކS?th o�$� 7Nase�* 6�-���1�#�W�a ly, %R��!�����l�bvquantum&� . Lekner �L #�Q%Scth����v �$3}\footnot+;�&tB4 typo��Lm'sM�)the�IQG�of $G_1B"mqNG_2i�DA2), $c_1^2+c_+c_-mbc_2��to!=re�$Hy 9-F9.�B)e"3n $Z_+Z_-E�M�!~ en�U!�"Y ��� ps}(+t(A5)�,>� c^2Z_-$.�3e7h!1mh��a'mfBA$|_wss����\rm sp��j� t28 ��-�A�s&�!a��!�� our�+r4�zmAx aso�@i�,: �x to ;y� 11}=B�12� �21}=- +=22 ��V�)=t_V  Vt_V  !!5X  Wi1&W Uea:�q�;�BAG�T���l!01.�t���>�E ount%.E�verd.7�# u�Y�5wjd.�3�@*r���V9hkg.~�@f.�DweR|�H�&�, --�  5m�l �<7)�T_:w*n a( 5"` atoR=45^\�E Z2�;"�2 �2 a9"�ng1�a&F)� �5 و% Lambda/�PI%9�8�lI;�\hat�A�RE~ �R_{+-})��2=��?par�2�u:�=4!j\mu=1 X� =0.3 C>�\�6=2^D �total &6odV50 �_2"pq� vec2�2� uu$q� \sin\�q/c�V>RN�/� , $P$�` P=pIIDre $pncosn. AlsoE��M%ZOEin�� � Bloc�/AjZ$�3a��lyi>�;x is���<was� "�N�y�j�KYeA9r���b�65d(�"�'&�J�̡��w5 �rsl#�yooF[frequencY,�x^ E��F6a5K�#nz�pc"�D;95O �6�b�(D} \one [��^d fig1U "Zd(a) Ima:�a,��-� Nd)F!�m�:n�1#��q� � >q$ IZeӁ��/�>�/�?/\�/G 8 >�F!�q� V�rB�%��{zGmp%7 �J*+�)!qZ�$� Im}~ �q,n^�U� (b-f) RA�@E%@m��3 tra � a�8.�Bu�9R�E!AX�1^{)QUB�q/A[�!!c�Y�8p��"rA�e�+P)in ah?�AK �A} �g[Mi�X�$� cell[6&�V� �&2  ult onb,�8 v|�g7Ew23 "�-�y�@fW�so-�sed co�n5��:8sl4a crossR9 . Un���;�OEtc2!�As �2oi���=!:orym�WOen�B&܍i:.ѕ�� TB O5I&J�M!i�$CpHgap"5�-"���demon�1f6� ~re��3N� zE�up�e�e� � s�/rum clea�&�Uœa fq%Ap� +*� � Ua �^� �R� 97  a ~��/E�!��nUA�<�Z�a�f(jV-��s��A#� �ၡfm0!� moreqK*�e��~�+��hB�aY*o&>TI�D6a �as� a!W e E�de��e�O�dom�=o�� *d7���5 �G>j#B0ɰ~O+�,i*&!c*z�-L�.5BE�)E�."i2m�Xn�UY��. A |ai��)3�_\2�� {\itN&` 4!x}%um3pendry�6L r?� )H�>ofmB%r�#��w�zb] ,�ed elseQ i?<K1ouUwsuccess1N-97usJ=2�-�h9��>a8�9�of�� �&�(63hE)� 2]P��uniaxX0�b 5a���� ��aA�b�0un��HI�8-�]%}���!���w�R�)!:iY��98A9GE�� mon o$Ѝ!!s!�h�slowly�%envolopE�s�.WKB6M�;s���sJ�O b �. \acx&+s TA��l� �&$+orA]�_KOSEF ough|cn�l�L R14-�Z@-062-01000-0. D.-�Oe� �q]ed���Bly by&�N*6O �� >V{0�Mb�V1}RO,Name{SwansonwZG. Book�CA�MԖCon� A�A Tunne-' in I2�PPlasmasJLPubl{Wiley, New York Year{1998�:��H!�B�H K.>� :6QRBO !Ox"�]="B�]m �852�yvI �Y A=#O�IB�K}�!!0rnomun�lygjT0Prog. Opt.}{3 �4>�KMBellman�Y)�� G. M �e:Aa�;���I"Z/IQTEj 76�ram7E�RWl�Doucot:�J1�(P�_ )}{4I7}{5092�hei}{(Heinrichs J �MQ�Zl_B}{65}{��}{0751122Qkim�gKim KjKI�98}{615�kim]7 I, Lim�T%��,�6% �J.�Sn@[}] }{39�1}{L956_"?A%`T, Hud�"M. K.,�TLysak!�LM�S�UY>�Ge�_ Res.}{107�2}{1306�hen��Arnoldus�F cGeo� T. F2h=�A}{51e}5}{4252��@�� BlaauboerQ�-96M6��4000}{041804(R).JR@UHb@-Lipsker�VE., Fr` B��)�MorIba )/L  I�O, Sihz)@ A. H., Tretyakov�_A �Viitanen �e­��c�Y��C� �Bi-&9-Me�W i�HArtech House, Bostoi[�i942)si�bSilver�d4M. P., Ritchie�'E� Cush�v-�J��E� Amc`{5A 8a�856�2�1 NP1/ Appl V K��416�49�B�E ri S�8s�^H-nEngW�:�v�4502+�,1� Jagg�>D.y� un X2N`9!AT80:��+�SerdyuA7AAT$emchenko I>S%�YtBNL#Bi-an&�SM�E�W MB Gordl`Br�( , Am�d�EJ2006^5x�>Fl^�K�� �2.(-�N"1��3952�6<dSlepyanA�Ya., Gu;chaP�� Maks��koiz> z�iE.�2546lu�Lukyano�  Y � Novi!�M.� c��1.a0}{676`sil�b:�)?Badoz:$R:�|��8:�gen.opp!&I aGenack!;Z^%�G .}{8���v339:gen˞e _28šA8:��A�%��Yoou��5'eUnpub;Wed2H�OP��b6W ]%1v0��66�� U��)�<'R��0>A &%[�>Z^12pt]{�?clJu��B2{kicxv \$C� 140mm hM�t 230mm%Lopmargin -40pt \odd% =20pt \B�1+sloppy �*� {"�#�| {\no�hn[5�DwV in Qs$!� ics}, eds� C�GbuA�LKrasnoholovets (Nova�]  is3��.&@L, 2004), pp. 85-109}!'��p} OX* {%@bf{�� O}[�Con�?��Di�Yul�}�:\bro��@k s _Ag0 \medskip\big&�#��� �/ Volodymyr:�bX5�OI4e�-f, N%al�kem�S�X s \\2s�� Nauky 46, UA-03028 Ky\"{\i}v, UkrainA�2�� \hs�J<{10 cm} {23 Janu� 2003� e��C/A"<^6Y{\�5��&Yof[.�B�&GG�ith nvc��r�Ntt�5�.rKn}e&''malis4 m� l7w�XnWUl�+� of "�-�a�"  B, h��dooqotGea�MT�R%5B high gy 6Z�9<#$Г �preY,�!'Schr\"o{Ze�QWK-� e�/1Uty&]$it��(M1-Ks8��L, Heisenberg's uncer0ty prI#�)ipassa�W�w��&�Hof�Za�^ s, etc. OۛdoxJ�� �)t%�(s9Eh�z5�Uve�CM!5MM5�n�eԔ�\ TA/i��/<*E4FthimvPXde� cN=�7 ps)�a H.(erge�� g b�;d)�tD����"�Pa�hth run"(b � FM��he�;_,ead�oM�5�� averagfro]}�t��u�gae/�� �yZF�,�opP: clareRaic�?i��assock:d%.�m� s wo=��). Such a'�of1[� �Y(9"��2+"�"�.� eABe]qz<ed�(deeperray)s, name��A]ide�=oa����� a 4D)�HL� )�#funda�al�%�� $u���nm�) Y�� ��� ^nac&J�%�"�.� , ra�.a submi�coo`one�RHby�rt2c�� auto}�8�mea��!�tr�� �new.4carriers, i.e.!]>�a^�c��Z� j�N��ed "i��$ons" (beca?: they)yѴh=��)eɾ�+) |,�{"�)X:-:s�$E&N�> Keyg ds:} \ \ B�s,I&, �i! � \\� bf PACSF$03.65.Bz F]a�x �h!Dm6vA], miscel0� %ies; \ Gw". me�Uic75.-b M�`�<$14.80.-j OECQ�s (in�[7��.) � newpage� 4bDominY view"+;f��>�f�*cB!�nt}�#<�=RIraised�A�Z re��it�{"] !'��s& �ө�8 �4 a�� !>@S-��i�$p6 �mapCN�.)�� Boh�/�E"compl%� ary" [1],6d� at (ai}�*�f��V�aM3.�i�|��ular ma�6%+B=ng � [2], E"3\ein-Podolsky-Rosen (EPR)A?aB[3]U �I!���st�8inu��ist���jinqui!$ miݕof�?"�?�+nowadayn ey p���y����h ofF,U�� dox�2��: decoG4nedvQ� tele`e��N��5� fron"f*��d<3� �� y@�a�I��Y� v uҡ�!���p;y��Bush [4]��h6�u7eI���iu�{��qi>.���-)o(by Styer [52t l�UA����"�z�_ held>�q�"� Mp/&u��� eE +'!��is ba,��� ostuT��q��  worl!���f� 4е� � u�+�7!��iY�c� o唥�� ,. Muynck [7]�� >1�6i�i 4e"}Ffor hi�g-vari� e�oAT"�stocha���$ (see, e.gI fs. [8,7]!'�bT��Iif��E}:��8e'�c�� alq���. M�'�B ago Wigna29]:| ���mza� �YB � also.Cw@" � ��>Es eir @�^ s. H� �5�oՐ��rib�t�9>��! ������-��$, or fuzzy� rDH, �C]!ch�heE�� ,Ca a��sale. E]A��J� BE&�7Iy's� ig�Eons [7]7 <ex !:cd�o\!~ $A_1$�$B f�<�  1a�)Jed join!�w�MJJ $A_2J $B J2.��ae�t�s � �� ��at�, �kut�X@ $[A_i,B_j]\neq 0�) ough i] = [A_j& = 0$�' $i=13zkN!1pt} 2 AjJ�# $i ej$.�6U9DE_e]�&$+�2-1.� �SEta!�c�m 7 $\l�$ A_i A_j \1lee4cor&N15�%?1$e�>�beB�s��e�a} | �,  A_1 A_2v -6B G | \leq 2+BB:B+BB"XG1R-�0 Mensky [10] "��d �imajor p�si����o���Hl& !1��by )as: (i)�C A�BJa*L4��(i�:�G�$(1)�2!A��- sed)3vpossiD�1��_!��-�s; (ii���J?&ofq� �-2 d�:bC�whe�/E�9� �u�or�^I�if ��� _r �CS��@%������� uſ%h*y&���1sq�� �on%�itj&E���Xata!�Aee�co-'D 0[11,12], ZeilU�('s team [13�)���{e*�of�2} (1). ��� jw�-aq=d� - ) . In*~ 0, Evdokimov em�. [14B,&n ofN n5/�La trueA� . .�ac�9&y9)7�I5Ua %r�l"� mIM&!� �s��� ��i!��.� A4Qx"�t� f� -�>}o#�Q�dC 2kaa�{ q6�.�#i�zj cA�g� �ped "�i"� i. b�-=9EDH����W#� �on�a�>aat�m�� any )!ZCc�� �c)� �KE�uld�F �6�#+bXof*j  �!>a�Tplica��� tyA�-X word���Cx�/H! ]$-5ich di� itel�� b� ! �1ioccur��ar�b�ferom� "�r� no �= X+s�y� on.n~� infl58ۥe.-��n�/� /����N :4)I�on Nak�#&[15,16]& D2s wB�R6 AA@M  byM6'�� �I�]��ac���gre �� %tc .�a&EPR��A��2i���AZ�est. ��-�I�'s %0msw�$��&�iA��js3!�k �vs�� adia`�c��� ���4enA�� �� anm��5V �� pair�5�wrote: "�-g/Gris�v legenP������s,�N'� anta�}ly'.7be����,�r)��a�ESQ�Ts mayah hunda50-� )"�.n h� nt�� -9��I>]�yej��Mgoverlbyza�2�7ivto�iA{' !�2'!� borro��U� �!Istudy1elf}��P. Ebe\5[17] �>��rgu��20-�A� type��sel菥�3jA�to��9 }� y. H�i���0"�2k�43���/!i��" sen�6"�cr�1te2Nk in"D�i�o>I�� �'s6<�Zed en -Vst�Eese!e�?�{ K��7a Op����� � y an3[ͼ�!o3 �*IgelyH5� ��gs ." 6.�!�IAJ# 1&�,. Mermin [18:G�������U"�9 pI(ori��O�s�b"�/)"U:�ct�gi�� �!�-\%�em��lsg"�$Fahmi [19]�er0�a5.� FU�%��ne�4a�~69� |_ ��}IY4I���.in v,����{!�j$�7]6�!�,� WA<�c*�m�9sF�&w=w20-24])E�y iL�n�p ularT !3ͨ'�.�' !�A?A�it? a fe�2 �osite�ć�8 iz�eA��� "0� !�y]Ymix�Za�individ�$�?q� kR e�$[22]. Work��<*!%�:�!�.��O�p�� [23]=1a��duc �Ak�A�Htog6v!Fl� is h$aŲ.�aZ ��[%c� au��U!retar��w��&`���y di), I�a&i �9��=y�A:�U� ert,�?viLal�� IFŊg"��� Q�_ F(WC!!gI� met  �e2n&. 6ExP)9�H+!*� pro>es as+ p'�t�k-�ـ/ T�&!.6�s� �-�-pY.s kT�a� �yaihis��7%oFZ)%t.e�a�a��/��a�"��i��)Q. mk akAAeni *uaH��? j$de BroglieEl BohmAY��a��rZ(.gAM� guI9���R7.N Y����ۋA�i typ� 9������$�ian9��rwO��� re!Ap<e;sGolds�' [31]��meI�je&�02_&�� ���R)# 32,33]; sMa��WG{.�lez�5��o$nI"d�"� 34])CAh1��*,J+uni�� /veN%a��>h)��~�,Ns a4.*s�3!��  tr4 W/. Loo���! answ%{���u: W� iyA�� ?,�c���n�.am&� !OT�$��2�m 2�Hp�DS#�&� qucl<H� [35] hAG�(opinion: "Fx�Zll,!V"�q' IA&�}1��EQ�l � i� !\�{ !�I8�odEWb=n��r�ss"�% �/Jo�&Ųaug���0�new�đnti�~(eiq�p_s)*�l��V2�%�a�4G�~Se�5 Tser� Q�3IEin�* q�ErydayF.""�36] sha3�\w !u� : "W� FC \��a� he '"�H'��Si.)'Q *Q8?b])8���3B�> -4IMn��a�o�.��2� "z6 �H.|w�7xJ�I:�" (Q ��AhI* RYcd>�al�!)my)���ep(2vaJ J"� 2 �i�4 man-�1� sn2"oo�6an%��V/ M�Emi[ esz��Not!�YA�H�@� qui`�veI�w�!*Kup3? se� 'N'.'A'a�1��ldone?� ob$�E� s���d1C�j�sub atom�rea{"����r/N�'7esE��p&�A9�"Fwe�*�% � �t�y"�(:*�s0length, Compt��avP"�8a�-l2in9� ����7�u� � Bo� no��( ofD, ZP � spin, Pau��x��"� , Lo�zdipG %Sc&.9"�L, �crepanc�Xt<�2[9's1n�iv��+ Dirac's (6��A�e��;!���5ed�6y�, Z��$rbewegung,%/so�n If!��cap�At��I� ^!��cU!o&�0i��P��Lcy�:� it�of& at a�6l>.���Mhand,%Hlon2LQ��7we sh�)6�5�5va3�*X 9 a;�5�2`66} ��Hory.. 8�%����6k �ll unrA��2�(� li��&�%�92�4!s�)fၻin"K§ng �s)� "�4C� *� f&�71N[=�!{�}�=6�4D"�  [37]_tA���-2 A��at�>�?)~!in qudkO!�. } "87 =2�< f�, . Bu�fat ^Aga �?�'of� O ��9 Le/k:�. [38])�4K�Q�4'�̻&� %��˫1�Fon� Loui�-� 6K, F���No�3�ya}� hug"�]4UorkDd!�po����Q1r�2`4�8�a�&|4whoi� = �Q�[k/A(�j:1��_# � �!den%��`,"�&dݜsoaڥ�, � D+u(�0oIac�st�;S. S� D�Qe�4� ��aTpa � e� �ivn;a� corpuscleJ)9,40]��,��",g�2� e@3c&" E�i���9 a��qR1�R�d:*NC4Baurov [40]. � 0*A�� `�6�C��nM?� his h - Au "A%RU��of��o" [41]�5x��\�sF�endU�yZ2l� �� )�C;O"VA�2A�a�# �g���pN�����!Lun��:� �B+l�� � :ώe;�Y� not a��acZ=)�val0���#�5"{#in summx5�H#��H"i))�����zou* of a-�9n�5&�.�] on&>����� ��#~'a*Jat qm����T�. Bg ��2�Km%� reje!�����%"�"9���a����&} �A�~��׽K7�=�� �32�E iI�!��?"�  [42])/sbngm�AI(M� "� B�!�%RmDF! C� o�0�3�%I&:&�p�`��bmf� {Af? �-V�fac=�vea��*�( mo� A*iclݐ)e!��cu�1��al �)n!$sWu ���\;;se� mn'!"*95� z"�#����X|xdŠ�Caru��a#sa� . Hi[t���� /le nd unco����QA��>2UB��ie�Ir�%:�{ �ofV�%��[i�! 6E�no �hum(cvt�_c"��AL�� igor.�?a�g]���!�/[�Vly*�3���!�b�G%�� 1950!�P '�*4�BA a�� . Whz4w����� Y� e? B�0���� o���Uf��p(ens"� �o^n�(� Iy��ņ�%�q0���bE&e empti����6�. N� E��.�> ��Áup�C lattW�!toms/mѪ! The  g$b���is�n�i�� act,n�it ;�x�> ! Be�S I6�2*5J�0s unambiguous8+"#) �� �c��u�2#q�s�@!a*! Nqdi�a cri/%N,*�^{-30}$ �Aa�  �x �ala�e��s�ocoUJde.6O�F�!' e� A�x�I�t>er1amskHe1� �n,a_itr mu(quark ($u$- , $d !3~^s)+ ThuG|er piը�u9e��;V�m��:AY�c /J bl�ghtlyEIm� #�u�s,Dblockt !!�Y ��$19�.��k3f���X n �KE9�Xd�V&��p����MY ! o�`$m} �8�A�� s [45-41=W�wp&�9�!�I�oA�e�a�� ?%K��g!gM� �Qes�W� �PN[48�)� !9g >% n&�E�ssue: an� Indd$MsA_ses!Lx�ic� :J�le��6�@�'*���8a�(K�c���4ed term 'space�[' ('loka' in Sanskrit) [49]; ancient Greeks partly borrowed their knowledge and transformed Y�to 'aether'. It is interesting that Newton also adher a8 notion 'space' ,waA�[ his opinion constructed of compactly stacked small rigid balls. In our works [45-47] study �e Witu�X the real �0 (i.e., a 4-D @-time) we have us�,opology, setC�ory and fractal geometry. An abst latticewempty>�@cells $\O$ has been shown to be able to account for a primary sub]te!�a physic�. T!Rwis a �f it allA for� magma�`^{\O}=\{ \O,{\kern 1pt} \!�lemAM \}$ .� withF �hyper!(aANhe axiom!8availability. SA!m�represen!�by ordE@ sequences?-��ly clo!�s9pE�Hin Refs. [43,44]. I!His AK0ect, mass is :J� redu%�!-volum��a�4, while just aR,EF�)9ch��i!� ly postule_:�,50-52],a� not suffiɥto�!* �(becau!�D dimensional incre!��� necessary��dE�). Accora`1} \label{2} \end� where (e)��Boulig�R$exponent, %�(e-1)$(gain in ]1!�given�YL-5 iter%.�/m�j��a�ows 6i�z21`ݓ cha!�eristic�� w is��4{\bf \textit{m }}a!�� univ�?g � +ɩ: ��8by de Broglie a �major 6� determin�m3 s. We�an id�Nty mapp#denot��e��of �aa a nula�$terval of ��M non��JSstands "z inim> anyB[ Xval. Sidharth [53] argu��at a :um��z � �should� A'��"one can�wgo�o arbitrarig _ �EM� s or��"�w our sense! A�,is no such "��" �(ll: only in�t!�t bott fact do� reflect ~��ea��s� ^�anner!c()�$al) vacuum � is hazy s� h!�or no iE� mod� quant8eor�-6b��pla,byA� r"1 ,%2v !�H abov�{High �]gyQm�2k�n� @ microscopic scal��s � Higgs��ens} at w%�b!��i!ga ���the& $world. Non� less%�F_E�de!� f grA3 unif�oe�E\a�@�g!��� ed%\Y 4DIF�E~moreov!�i!�e >��A�a�a@�.dway it can manifest itself#1�mechania�(Inasmuch as A!" most reli^ basii�all� Zc E�_y new� cept� a<pP orthodox(}a� limi�)O ͘tAt�5A� de ��'a0e�concer���dou# C�!�U�@ satisfied). Howe%zei� �8 chromodynamicsE�Ey� ��temporXi-dstrA� A*4s �[!c to mutA�� >'5�al�  . Qi� field ea�gt�derivs s < er�� ��ed >var%� s ($��hi$,  $^4$, etc.)!a5�in 6� E @d so on. Group me!�s �iso}�mselves  bo,:��h�4 direct measure . G�DalA����dq<d��wxany�S,a+� subjecŪ&�HQweQ1!� forg�a� O is sepa' E� � �A�X8 matt-�� . Ifjassm Ņ %appearsL%M in turna�a.�$we immedia� arr{ �!gclu% ja�nm��):I� y:��!C$elf become!N�al% u)sub.�m m��-�.Y� 5-�dis�s ver�khorizo�an�;. � ea`a ��a�=Ɋ��ysie�e1m�!orgr� star��%֑�A. Recen6$a definite!;v i�is I���in��ha�Dachieved [50,54-56� Gb atomic�!H rea/ide� ���strong �e&roweak5�{6� deepA�irs�incip�h(is still wa���  pioneerm \subJ,{Long-range ��} \hsO*{\parin> } EhrenŮ [57]1 �uaR�y�Vvj � Bj,` � 0 � � Hct simultaneously e� i� y!7I�da� X�,of kil ers; �:0exclaimed: "W�a���M��!" B�!�au��s� � `emphasized by Pauli [58];ApAhcular,�b ��atJRb� up a� st aV�ht����P��spe!k%. �|>��U�$$c=\infty$EZQ vitT q)�Ae� egligibl i�ant!riVN90$G=0$. For ce, letl��to�proble2hydrogene', a typ%example!�l>�!n>�� %�E str�!�< Arunasalam [59]�radc!�ga�Schr\"oYer B writteneK&���_her�ly sym&icq�s!+c potaal $V(r)pQ,m (see, e.g.� iff [60])F�-\�4{\hbar^2}{2m}  {d^�1pt 2�hi}{d ( + \Big[ | F {l(l+1) N-+$] \chi = E \�3Z�$.ح�-Zw`�)ts��d ���%qubbracket� stip^� =B5gy assoc�'d��J&� uEc!�z� 9� MB2�*)4Ben�)�stMc� o�q�*= 2�EAX = e^2/(4\pi \epsilon_0I � Af�M\U�ofm ed�anQ�n2 pro���= similara�$Eq. (3). "l it�b��?S2R{�m�} �(3) i�d-6�s �$u�9'J clas} ��E`s, 7 �'�xNewton��y �%\=G m/r$!��2) [a usual z ��!O�� less�g rrzM���ic  E�~  ��e��s�546�=B4J��a 5"�>:� mQ . H�= �s�mpreh�ve~"6 al �p�4͙-� system�i9s&a quasi-5; pP �us����ishA o rem� devoEZoBk &��funda�als w be k�M shad�[ its ���!�onA�i . Oj e( hand, sinc 6}a!>* is a l&#�ely p��d �"�,�A phen�. a(take ��"wed !�riori2 "ׅc�we� nPN ^O toZ� Fs"�ll ki�of1e"4%i(now be occuy(rough super��Xuil�c blockI�u a is*n�APny� avJ� � b' ecifArby short2� � 2�&F�  cr ers, &�R , HI��! �=�"nMx � exM w]�$'inertons'$]. It seem!AIppegiz st� ch�lV ir- al nZ� _ \ia' me!W�si�A�>��Y,�� mova m>��1��rg�colli�s oi@� !&comG~s,:. S�� UU �� e>6�'s.], 1Qt eforv ��rA�ome atta1J� s. M&� n pan [56]AC` Y�E�@'s�EVh��G���<w , $m^ 0.4�P0}/\sqrt{1-v_0^2/c^2}R valu%\mod ^on  v�approximU$$10^{-85}$a� 4kg � .:' WaveU�^# C��*� ��!ID �'� 3�!�4 f)��1' s --aerU � s --�� endow etw�y�s�a��(, velocity,"D )d��� 2 . A�[� x��u-��T4 as well, name�~( length� �!ye� high� ne� 5 ��*� P6u u;my �V><�vua*� )&!jmH ��ar�low�w�S i���>��e$� ' w 82E�xFPum�����at im3� �(behavior on��p�la� In 1924*K*r v. [61])� v ��!�JakobiSe� ]�z��h!  Ma��tui��: AI�tra���(� move,E� $A$a�  $B2g% AlY�ͻ2a�F� S=Et-m v- ) D(\alpha x +\beta y#�p  ^2 -^2"G <z) 5B w; $E$ ��kieFI% 9 ��$� �� , $v y�$t� @i�$ ��$�$� ���cosinEThe� P2�"e�e"� ��� b� monoa atic -sprea����otrI�. �%a, ed himlYAe Y��!'�*E�F��= \nu !�t %0 {1}{\lambda}R� j� ~�6Z� $\nu)�he��a���$ �%� ��."�Eto'�*g,�/5���'ic op���6 s af' 9Fermat7&0u�ray=��$e}2� a��" i}�$u}%�. Set�K!K/hI�tA�h%ar�jexB0 (5)% (6)*) camQ%  famou$4onship��poni ��B8 E=hA5\quad \ �! and}  a�AC =h/mv,u�7BIn6�7)�cs�%�mv$ (A ��y�,y#�$ ively) be� �d� �, by e fr�.%i5cEmIV]or 5�sa/e�� A9mp} nd gu(���?�q��. Noe��t1�!!en���=ly��VlN���. So,��'s�c nspa;'s �� ��� �O cE�n. �acb a� did� rece�!furA  develop^.V#6�!-Dirac�� 's sayQ� ab3 rue �m���:E��w T )��6�m!�� ach!S!�6��!"o. O�,ur�!�c� Huse Feynman diagramep !en�,"��  )-li��%phWs� �ng�ab�~�y)!Dq.2��"e�!F path* stead�,must draw in�lyl y� �j��al�t�'sY�z�Wmake it3 s$!`find !�#!n� v+%:. �06�nce� �neraso�PIcoFd&A#M�z� ��: �7 a� on�ndeed,!c)�larif� duaf&`  "a$" "�J e� % &�%l�h xly1� ed? �*s����by Lig&!�OlB& y [62]: "�/$$ always cl� wh�)a�M�&x�&6 ar� ��"fully1�-*al treata��� toEk%�linXtw�.ei��qB howM�*5wivI"�Nx-�author'sy�Eu=�� 6��� W'n.�>�a&����b�%�,-���s5oY�f e[A�:6�e� �in*6-aa {I���=!the s{�ql��detai�,�����E�L m&V.�-�5m"�was��*�R*�,,50,r$�.a.(�o� � aIw0a crystallitef,%� a e�&"� B �# 1 d� 2o��( >W;ign5Q� �9\e�izeA;! !��aJ� Comp�a5�n) �E�#� � �+ Com}� c&�ro<e�:�to sh~$�� r&:/�ё:�t emply��"�..�M^.���o��� ��:�iGL� ngiaV 2�(si��J]L= \tf�12R $2pt} g_{ij� dot X}^i{ j + 5W!m\'Ls_{l=1}^N {\tilde g}F^{(l)Lx}^i_R x}^j  - \sFM\� {\pi}{T_l� � \deltad.� $\big[ X^i �x _�v�7 3]."� 8B� H�A){"k] b�F�/U�E�. depic?+ke�M0��m (of $N$U( �LU thirO&� z ���a�b͗the�ŒFg�+so-�� vU ��O90�'�$l8�aqSI)P5 W� light $c$�]�is chose"O �E�~J(L=-m_0c^2 \�v 5�9B�inif, h.'�fo��&""8�i�dFM v \� r�ar8E=[z2$f(X,x, v, I�)6 ] /g�10B�nW�/$fAcl6ermi alog!0Mg�7Y+Ų&x (8). E01�s1�H� U�C8�� studO ie�[.H9��98�\R `N&�ark�"�I}*4. &�Hi$ .!��llpa"}�� i�4I���$e��'s*W.�"y4� e �#ituI�*4 osci�%H�Y�� emi�� run �dd!�a�s"�/21� 5�qW�� l� ..sOF to 0. Dur!$��&s �a.� re-� rb=��%| |a restor&�"�$v�6� = 1/2T$E $T$F� erio!;H!� �%��(er-of-!#i)T cloud�<'� 5�,B Vk� 6�&oj� �fE$\L:$"�-+�B� / \simeq"y���� c/v�#1Z#$c5L5��Ih�� i5V�:F1ove�e28��I�) z*� V.� ��� =a����wo6 a�o�,�9�re .��&�6I�# su%� 5s-�.�;m� q�ng6'� x ies F9 auto����ZQa iI g f a peculia�l�S�3�6:q.��;�� I��'p--i)�M��U & �0wh mai�. �0o �� vell!a�� a�1&�.i/ R)!��&!+ cA3)��&� �l �5adnqaH8 oyx U� $\psi$-��� G�g 16�M[u dsu)o f�"�6%6# pre2�$:u� >�%�U�1re�24� �(�Ds�:!k84%D��)?m&0!an "�0Vxy i�$ llap�� GL ���"keas%�A�ur?���$&��%��s.:M�$�s}V1- Alth#inN*G ��*jh2�!>by�%IP(t� .W2,O4:� s, n3th5."6�8�s� ��0!��5rdA�i�*!�fi@��=�ex����!,�a�f&7posses��$.�predi;B�! , 0:�� es�e)BA}" �>�B���letABr�p eo:3] publ�&dI��ork& led "Looka� at E�/ nic \! F� -' Me=$Surfaces",!Y����2�@��l~sp�,���p�figures1/!�D�"l"image�i�%�O'� of%ctron,9Vir5�hey gav� e�=��-��(��i�����o.&�� #�[;!ser�!i�3 G B��~�9lar�- than�"18}$ m���2y fix)��;erturb� ���� an5!��m!�!��1Wsub)ci�0ros�s01ef+Y�V�2�ac�7�l Copenha;/School���(�(mo�8%�pe���BedAJ fallac�naz��6a���ept. Conutly5 2�dat1��e�"� �LB�mb�����э�� EUy�A�/u6ucM;�.��  alcy��an �(c( upport am�3�DHarchers [63]. We shZ �4uss*�9E,e7��AS�D 3�<*t3�(z invariancbR%Al!�r� ���&�(L I It���d E�<ei� -%S�6F= agreN#4]). N2DA�2�&�,-� ��t%�0 erfe�G��sF�A��tr�� �]!�ulVris#��(�kos�? .F)��dis�E�*02!�%g�%a��r7q2�v�i B hidd"�2U,� q2A��ism�g(s D�:/"� �(.^6eirek$&v�7unpleas�3�,li�>!* so f�/okz,1+nonQCh�&!mFn : UnADt"2� al��HeE�e:� �+5�p�)44]!�Bs o�/ u9$�e� �[ . Be�* �.�I*�D4,*%!?F� cont�k�-���!�*��.+� � �� ism FI�&�/Re�& 46])m�� �w'f $>2�U6?6�A�>�^�)Why6>nd @ " �soa�.?>�T- e;y<0lacking? It �(�e��ssu:I� r rais�0.�so far dll6�%�% � i��K�uZ!���resolve^�-:#?} 5!�BBingl v�+�B #@%�*�$E = h�%$!lito&�ca>� �N� JG$E==*��m54 v^2$E^�6!��6 , p. 33 )y' � �8w)e �m_0 c6�6&�,�.aa�6a64)�Dch!�� ? �'5�"�oM�w ��[To answe�qu�Jon�8� id th���p}$w, �+:*'s "|%�/ m v$,��'&YZ� h /m a#".� �>�$ (11)� a+�/  &AreV(a�"$fn6mV�{\kND�EE {c~8 v^2}&(12B��}9�%/6L0��a� �,par�7 4od� a�>N>&$B�Q�AoB�!,�dj>!\d,s why,=DrQ (12�.i�"in�&c�B�^in�sL"$v <c� "AOin�.>�!���7"~!2cD"jby�'m "p� util6�I��*s'z�!%qu@�wB!��thK. W� $v \*a�m6~Av"D,A���AF51I's2�w&��@�7mi b�*JP �_�)]-O2n+�0�.? c�Qi�9"3Q=BU�,��Yf{ �ApT6M� �O i���1a� ner $v 6{%E�. �5S��r3$0c^2$ expll've>8�Gi�#"�DAD� �inb�$m3�k�6S YS failI�&g u"IqQ!ef7 iveA` 2� Spib�A�@A� pin?��n` re m�9r1� W7KIIN�EAper*da��1 certai�@!�WYF�s"�F �:�o���#;&g�n "in!'��#� .f�j"�G? 64�17�3a���/ . A9rulAU*%�of ���Y&!�:�#a�&Hs�?��i. S2.'e�� �: ͊�v . M�MI��urevie20in�nt�'s �s [yD2]=Odea�AU |quo:� -+RoaA: ,�_�#��(�'a MM mass�<1 n"Q!�+�12+"� enga�-81 cir�1N *�+�9��reasoC-�s&�G%ToMqL�:�I= roq!)�G!� *�al��s"�h=�dJ Z�5nE� �7Ź �>uor}ARs$4v<ha5.+P2)��'s jmag?3e?CqRJ:��Y  &�6�+,pM���>.*1& regard���Y!1;'s)xVVabandon& -� ���Kpt>�� ��aOU CUD��"��G�,) %��,� �V�E'i*�!��3  �� c&*8�i�*aQ�)61 k�E* sf:Q���.ul on, (a drop. Two� %eԝ�eia� ��v�$ vec�r�-met�ly op�8�-�v��>�!e two HA��6 >�%E~)two own:�S5 ; ��Z exhibi��� w!6�%!� -1/2.�)pm.��D/2$!q *�-�%]�[�3in bigT� �ɼa"Y&�@R[Pa�Gm�l!�kA�n b ���� "poL.z� "E2 )Sw?Ptag1,scL 0 *he ."Lns'N!ds8.pr1�!�!=&�d �)�a�k Rulsive;�A=wsi�QOfKat �.vJ4Heisenberg's u�OF�<^^ "NA�I2.F 2F5�co'X�0��mZAtum !0 �W8!0yd,J9Dh) x2x  p \g�"�G,E5 E 3�E t.4&�"3BLw ��0 to �A�s""��.�1�婱-����b�zz�T a����ZX%� EVaf T�t�R�5 �MF(2~!),�!�r.�& $crA* . D"� [65,66]"�D��'{b g.5Y9�# a"�Q��?�\EJ 2/+a����� $corpuscle g� &�SB&] . W#Q�J��R�8�Loba\�nd2I�2! � �R s���oso�'u"j&�*F*L = -MZ &l 2}\surd\8#�B�@2$"8Z1F\I�*� ��x!#p�5A"of�% $c$ ��L��a�I5Y~57O(\#J H/ugg�C%�VC�av*�d�>�u7R�.�HxGl���P<]4^�M�Q�en, sa�6ed\Z@5h6Nin�I|-imeś��z ��2ah U ! I�!%�7v�WsG% toge��iK��,`�#�ilye]KM2*��e}= Bhe�% ~and�� �a��4{��� � �� o�^�$Is� i$UDf&�!�O �h&A$J9iy*Pu�8E�6�8!*= aYA�� &�8�6A��[ ub�27b4x"�a&�Bwae�g Pa2�I9 [gne� ��ua�at"�1>�|/t"�F�n\)sa%`=1BJun�:u\]a�=.:�PG� [67]e��$Q &nalyz$wo well-kn�-Nl�er�$: (i)2z0 $\gamma$-rayL�Za 6Ee (ii)Eb sl-Zif+% f�8�6s6E�m2� �A�]= &� %:bc-ployed�j aU)�� !�-#isJlzE6#uF ��olv� �2 $�x_{~4 mic}�-�Yi�U� ?5�)if]8�&Eu� �!"�� �sA��%o5;is�QnB !C�$� �X!8IA"& �.� �p \sim 0L, held> on==ta����&�S(1 OAa�~��be,9!mQ=�6�no�r�9saJ0� vp{a ge�cau|��.son�,E;!(non�qa~<F�]�Mfrom a�$tl�� o+ �YenvironK!= %#ed A.�ef {Fy6gw �7��z� �� (Eu, wVXbqX*� &��BZir�"Mvsi"=s�6p� s:&�>$$W^{\pm}$-s$ $Z^0$-bos�7�glu �fi�A��p�!�W .:�&�be���  &("A�&. .[[�_s ris�G� ��N;0. _j M&tal�/2$Ut� e�j, Baurov [40]�BBL*��re�i�4 - �ut~&ɿ u'�"!d [68] �@recU"j#� �2 a un��#Ne��ferr�disk re�j�)�"4xis. Urutskoev�co-]$'9] reg� Z#a V`"aE nge"��\��(�s6Q_�aof chemA`� fo2d�3l�*ic�A�geL!�3i [�,Y��:m�+�PJ.(Cfe�gnuR?|Kista�02��@.Pbs6C]B�X �fato2�0 �!b�I�^�P!6���,��z6I��Ain&54,70,71�=n) [54]A{i\6roAhy�Z�a�]� co\sHV�#6� ��tWtOS�of3lap�1ma�� enti&# ��l 5��%A�����a��phono 6�=a1i� forc�trix $W$&kAstXncgTM soli�4cou�vib�Oge (*�!�2^�Q�V��ad�ja�% �H �� :d&�go"�0M s; soA<m�eI�,�$W = W�  acust}+ )�� �outa' 1V�� |���lua �%8� !��d-�1M�V�a�/E�g� po�#sou�-�M ���+k� ��fix��n�.; Pmorph�q�I s�3�a�+_�9 , Fi"/ 1 (2�&As� �".e'Re�rEmI� ���a�QGr i��ps by m/elleagu�( �2 * [703#!� omal�&WF� ��oUra^�r�� ir5F` exam/e�!�6��*nd�X -G�in _]n�]Ciseb�.re�ns�t��M��0�-orb ��A}��A las�Sam,��T�^ s-% !�l�o�,-v;r ud $\sigm� cloud}$Zexceed!�a�.�tom.)2} -S2}$ nm$^$'�00 6���f��kl��! ^2 <^� �}L:9 ^2$)�#� E1*�m�nE{ �bE����3� .�s�Rj �Z�^0]12s�V� id-1960)wEGm�z �ic Mz���a�8r depe�0�I� a��`l@>�om u�ore;� lKJ� � y;/ � y�7)2t&`PanarEW [����`ViXis��rte� � ri}H2j numb�of6� oR� [72,V!�B�KIO$_3ko$H $j# 2^�-� �M�VL9Zt�&�?�#:F�lh� oh(equilibrium"s, �1�"���e syn�Pno�c�*@ "#.��:~����9ir m�06a�h��A�-�aZ4"�<< �!�6���1# %�4IRe tra s�`A5}� er} \�� graphics[�lP=0.8]{Fig1.eps} {\cap�{\ !{Re� ����)� m�\���p�M orga76gl�Wp�I�a:��@ (a razor blade) 0&>aR83)dd�0J� ��1F�;5�]� �Ui� cope�* (for ?N��fb� ��T�e�# [73].)}}ba� 1Fr5} :�:+^�5%�2)�>�De��"URGA-1"�U� Re� ra�< Gei A�ies�� r`Z ular pyra�y� "'q��n���O�V  1 m.}};?us)6 2L5 .6 .uPro�t?�} �Nh�K�ns M6� R�z�e.6QKexc�m�FZ1[74],C^ Ag:�AT�0mY.`]j&p�� ��tod�o& ill ��A�"xT6�7��'� ɢ^ɡelucid���rm+�Trig�x��of diss{���0��Z�7itd$jP1�0[ r��2%7--�Kyfu"@aIJia.M/��� said��� fant�= ]$. AV� N�=�!�-�/9� promises Ře�~��� M@=rr � ��]M�P��sms"Vf�le8f � �Kea�1by*�&�g B,�' M� [75])T 20 y+j ag cm�un�Ik&�f���.�N! _�= &|s:� gl8#�R�-��aa pinLA�%T!5O!ZyiFl�  t{;7 it�umeR�==�Btd0�r med adu~A�%��"y a�SrLl�O)p�~�(� E�q q�cfz)��%f!NA ir�g)`�5IJ�*�B �G nn�=ng �,a�iB %�a$scN@�[2� ��! i��/Rt�M7� itH�KR3wil�ed�@o�|��eyd s�al-taA�, tele&;MZr TG=��ycapeT�{lay�Cm�c(7ol /I��r�vr'GDinh8'�uom.�<��,('. Nakhman� [16]!]�Ms��*R0^"k�~�M n*N �?cdHiscus F n �wuoif2Gv�?n>���U}S- a sig�a]tH0%� �%�o5�SR^*�)"6� & & � �@�b�<�is !#6s�`>*3�/6e�$� "� '�cZ>'A�Mq���"_"d16�b�-921��f}`o�f]�d�>�Y�� 4�-tgy�!�sdR1�"- r0e� B.]!�& "B9]!���.�?YZ�y��p��a6-&i �z6��-�8! �~ �our team�have "�#�jm�Airke�� E� reaa�2a'b �%���jb"� i"\ !@��0\�{Co��w vb�'�:,a' we tp&��b~a����A ���<TZ,Ear>�1!Z dj1?���#:z"(� New"�H���" link�xŐl�. FT�/%e:B�36m�'urg!� 'l�g�o*�x �,s abruptly l�"APsuprem&aning2�s�+ T�c�iM�Rq"� lo i6;�bdeclW��~I!J�Uftl�[�ApA ledg�!F2�q:gq�@�.555�D�j2q 5�:I��|e6A����f _*� (�@,M3,�Z,�+, Bg$e��:܃nd,j.�!�� �" harpastrast:�Ia�AAcsu�F,[ ,R�usyr "( )e etc�I���A�r��"� y �r�&*�0if +� on @�-��JeW�("0"s,��p�sVCch� �jug��, $\mathbf{C}oLPT}$ vi&z� �1�{w}w to vague�� a>M0�n x}, 01�}6�}!�� f>=�A�J%Qe ��!Zp�=�. V�Fof !s:�Iq�A5�x� 6�"�. cs ".��ve ���on�u��9�s.$.t>�fu�,� PL� �G>�--�j!:T*� :��&e�ESU,U���8Bce V� �Xp>v @!�63wav��3��farfe�l�|.�v +W/ i)I�&Mo�"�D�E�q_�+4menm�P]o� r [76}o�!pxf�s�Cb{|��@.=ޡo*o^*g Q . C.7G"Ja soph�aA[987!�= t&Q}e(W �*baX �@ laws�T�S�"_sh�1�o�,): prog-Ast*1) advanc echn�Ay. =bj� thebiblioy& \b�1m{1} N��hr,9 u,"N����6 -]� ��"��%N�n\}, no. 121, 580-489 (192�U�2} E. 2�9�,e gegebw� ge Sq(�j der �en1�k.zwissn� ften} ��23}, 807-812, 823, 844-849 (1935oV�3} A.U�4, B. Podolsky,!/RX , Ca�&u&� al�^!")�zeag>b��io��� ?�6 Phys.9v. �,47}, 777-780J�4}�Bush, J_�_fi� r day'&���8yL4? arXiv.org e-�{t cI(ive http://!/abs/� ,-ph/0103139.]F,5} D. F. Styt� Commxs��)&�6L=6s-�Am. J.%ics-$64}, 31-34!962�6}1So# ll, tE�"in-1�-%��� adox m !kf(t| Isla\Cint York)I>$1}, 195-20%�642� 7} W��de MuynU�F���A ���,Uem�Oir|6,}.|Nd0ua}�;DIM s, v�?127 (Klu� Acad�# P�NHrs, Dordrecht, Bost% Lond,2002), ch. 9e� 10 (�2see>� 's H17PagU www.�@.tue.nl/ktn/Wim/m% .htm2&8}A J)�in�e)�xrv� f�I� b <�} (Perg$ P�,, Oxford, UK!�732o9�XP. Wig���S|��:A�$}, (Mir, M+, w, \1971), pp. 292-302 (Russ�^�C2�10} M.a�Men�9��u]: U d, Rw �cI8j >A" o�of old"?E� DUspekhi Fiz. Nauk}M�\70}, 631-648 (2000) (Eng#Q.�:%&q- P F4�C586-6aE6�1�6A�,!{G�Ui�G. Rog E"��=st^r�` lo�*t;!� via Bell'� oremM3a��' Lett2-460-465�-816�22� J. DalibaAFz� �".D�u[ A�7V� ze|Eq� Rev. 2�9} 180��826�3}�DWeihs, T. Jennewei�q�#ma�H."n�!VA. Ze;%dVil� ofB�yRU�ct�+ %z�&�Bl2�8�50395043��96�14[0E. Evdokimov,�&4N. Klyshko, V.A(KomolV.�Yaroshk�Nv��EPR-Bohm+rei~s: ing&�|�#o&#[� l �M� B.(66}, 91-107AD96n-%�ic:-( 39}, 83-98 C6�5} R.��&, Jal Z2U�;&M~�7!�441-444e�1) f� {:� 4�y421-424 a�1:�6�.�V�� �in1�e�em6] "nx�n�Z$ics/001102s%"� 17��H. Eber�uA'6�A%-5.pe�Ama�e�}�!� 276-279%.:�8E� D. M��.��" Y,S#fS commup�h, e V��e 207140.e 19�RGo��,� Fahmi, Is%'s�?u� n"��Z��P� N?��Ann8nd. L� !�-026� 35-741%06g20�g����%�����"� -�M�9M<�2�A�288-29i�92` 21} �,$\check3C^) BrukA.���Hh-6�!B��2� 5R�9�00604uTU�22}j�Mvsdot�Z}$ukovCN� � ess�'!�e.% � Zh�106112� 23n�2� I�.�^��qfu&� �}!�E"� ���y�z[212084.' 24} 67G�-�OJ. W.�e?Y��Y��}on�prot f�e*{A�C.} sw,,M�E�I�.(88}, 017903FeV6�25}�!IUFn'�>G rno, E.C.Sudars\Y�F.O( Zaccaria!�t�UrE0).�:{)inLG.A� ,�K207036�6}��Stapp, N-Z]act�P=[� LAm2���6500-3067.oZ��5�� on Neuman.� R� t|Law))Berkeley�P�Labor4&y:;�H LBNL-44712; \ Deco�j�+ Zeno ENJU�!��%ef�0c�ralor�lGy�e gap�'2��3M!���226#8� G. C�E �N���mS�m ^�5a!647-688j 8629}O B�iffita���� n"��!W@ory} (Cambridge U@&� [,'6�30}� R�l3 ��*6���m�J�n 19952�31}' Goldst "� yM5=" ��Sta��d Encycia�Philo�y} (wb �2 E� ), Edward� ,Zalta (ed.), �(o.s `.edu//s/winO/�=,ies/qm-bohm/.�3�|it2� j� �� ���nts� l\#q2�3%� Budnik, M(ak� 1�U� FAQ, єmtnt .com/faq/Z(-qml*!834} C. Dewdney,a1Ho�\, M<LX/Z��l� Schmidt, �`"�7�ts�#�%�N. �5��b .��.ac.uk/� um/�$/z �235> AyIthacv4teR�.� N�%k� 9609012=36Jbp��K*_ 2�7} 2� ��2+�e�le"��oـ" 6M 12��99-421� 876�8�$Lochak; Lo��&A�@fm�:7 bout���� Ukr.�Zhurn��3�32-63�93)0��Ukrainia6�39�S>L,.js�)!n�l&�,� ��5"�)�ir"l��[Kneu�b�� �7&� �; Essay�%X204-220!X:� 40} Yu. �9, SL4A�K'sW<�� n9��D,�*&e"�) �>,�M2�443-46 6� 4}. \"A�r� Re�vit\"ats�ie�:aP�$on 5th May9�0��!]ݹof Le�3 (S� Be�E2� 42} ��A�v�RA�C� s�N� D]Y 16A906-9'56'43� Krasno�5ve�D. Ivan� M��&�Bg!��g�-�J'�55�3E&a�E�g�X�h910026544R�.�n9 qo��,10}, 407-416�7)xE~�030776�5t�R:tX S�B�!V2x i"YCe,s rt 1u0�AATϖ����e� �: K)�>Kybernet�*�.nt� of S�T� nd C '�8Ax 3�d945-975 1�V/i�s/02110:.46~.f* ^,2. Pr)7ply?�~� ���+y�� .� 2.76-10F205 *� .�= 20046E7�!��'VD3. Digb C*to֫A55ws��-I�ions. 2 "�?"�� ���-5�d��T��!� a 7 1-232�0�76:���Q��X*q5� ���� �r32} �169-170�1m�z�0201133 &56R4Gr"y'.d� D� s6WFA)Ra hep-th� 5196.D57"i�,� �%die�"�%k�rt>ndeo ErkG $gungsfrage1[ZI}.�7�3555-560 36I 58 Pauli, Ra�� ZeitH Kaus\%G ��Bf6e�q @ \U͑a}�!lan�#5R 65-7� 3:�9} aV&T-b# 2}L�,e#*�F�ts= A�� ?Mm�.:� 76-8]E1"E60�I@'iff G^m!�cGraw-Hr4 Book��Lanyc.,"� --�z L5$01955), Ch. IVUU Se�14��12B61�&t �.)X47�`t}3on). �t�*aa��) F��*6�>�# 1986 �E  34-46 ��#62 L&�R.�i��"��dG6: Viz��bZ5n!�&�OfzM- Amer�5E}�bf�58-66�]6 63} I�J@ �f��VDoe8,yP. Rust�$M. Bradsha.�$ L. P�5sa�Ph. SpruG$E. Laegsga*#F�%,ZO��*EX�Plumm *^uelJ�_)�*�Sn m�s sur^u]Ye� Euroa+ 2��2�0148-152�097264ExB. Oku�sEl�.�q�} (2%aJ& 1988�%.&c!K�%6q5} !E.�Sur la D�qu��"ps \`� �� /prK$C��4lawmcd3 ns&Ű*�e9{de5chaleurM\a�v7Rendu5@64 B} (1a 1173-1175I(19676�6%S.�o)"�.6�=�)�V�77�3), 71-7�:�'67q X. 0Tiub�Q unte�b�EHr��i�c.68�SA�_, P7[lej��]c��&wrad�-*� ��ings af expo���Ba Shpil��ȹn�Qor� -TJ�2� 1�4}���32&� � j� ofy s�Ar�ks/4-1/B �-� .htm*�69EI.&~7,V.Liksonz V�Tsioev�Obser&�"/Y�A.kNDZd6aNQ��1h3M�>�>�"�701-726C6X7NX"U %-7��anR�I ] ct�SYMQ7a� "��,0a=u4E�IFI / 4a&1-`11�� 9906096K710+�Geco �l�I-�w ga� ion��-��,� "� }, 227-25�742]7V*Col�2OC"�] ,.�� �3he�G+�$H6�G �|�1byJ��3�6^'6� q=6/n% -mat� 8417.97V�G$VPWD�Giza Re�\ As��ǿ�} giza�Da�, �-�;:m�M F  T�- page^� .cjb.neM ![:  >N7N�u=n"�Vs?��Ҏ�93�m� ��0202176b75>�"i,K�A!�li)�at5x �<� n�X��" �Jmp"�*inj-� 2I��i�{ \6�+e�Z2=�&�2 ATO AS$ e� B 16W�gs s.�8 eds.: Honig, �0, jft�+W.} �2E.6APlenum>S!Y� N/1�6636=( 6,��On8IckR*�:��=5 (LA8!i� ca P�6e,%� ���GB25  docu } ��%�2 %\_�C@[12pt,a4paper,two$4,draft]{ 5cl�J�4. %\O,width 594ptheE�(841pt \oddqmar�F 77pt %\� �^t \�� + */l:DnDg-8 H%>I60s/ �� �439pt  �67� \top �62+ voff�-1in \h. \��P1 03parskip1 \u8U0ckage{epsfig}2a7a> %.+c�6*COcol20[dvips]{lscap!�oamsf,amsthmfonts symb} ��2�% =8Qa_JHdef\thefootnote{\fn|ol{ }} %_: \[1]{blaa�J@Z�k$style{empt�8$markboth{{<>K` \rm G.~Mavromanolakis}} B(bf�F rtz fiber�o�try��ca er@\�myhea� !J\%\ize{1�u {13.`w)�4{T1}{cmr}{m}{ns� \v?*{-45pt���T{\tt HEP-Cavendish/04/$2Ai62(UA-NPPS/06/��03�72h {\LARGE�  \=� {~Ma�na�>&)2�vseminars�[� U�1'of Athe�;D�����U ";fP$D_qcal} % % QC = id�y!��jA&"xI��:�% NOTE (�� d=xx�� 3�J�Q!-�%m�zD er} B~9�7] { ~��litt gmiI,@hep.phy.cam& } orI�$,mail.cern.ch!� {\em \)Q:�"E),V�\\ U�*0+,�h EB�Q+ G� \\ Me�k+ Roadh;�) , CB3 0HE�7 a�162 %ag act �Q6@ip�?w�C,5�s m A?taxZ�&Yypg2O�r �)�hardn"��fa�?�zs�!�a@�et�qd�fPs, fe0%-^d ��kqu���r�l!M196aopeIy�O^iƍvo&�K�)�J. a:!�x��H �W�Qta� plan Dt��8 J2b ݱ�0� alrl�);Kr�q1 s, lumino�$monito�PrU� pur7jhBor|,.�.a�q�\t<of�+ \new��  .� "=II:\�B.%%�u2u CQ�Qmp cAL.� al-ho?OnaevelopXEχorm,|m&�,AB�Her~\cite{ref:QC:cus�M 92}-2w[ns2000} @Na5�u|fllN3� &���i�i�u�rA ed, w� � ��I�|nt"Z'�Qts��mhaL�XWF&i$!6 X l�� impro�D�F !�k>   �:!]I��^7garithm�!lBT th i!^l��f^o Hc ����S�=��9P- is s?v �gyH nd N+��F(D�[�'�5K@pr���+�v��i1)!��Mpa��&.6|p���N�#%ӡ�.Ta)T.?��FP ��i�r> l ��^g�*Y �acts i��O.Gvol��F�!Phh�`QHe�.��A= $�sze��ts���[%P��9���S I5ӵ�M`�. %�d�k!�pR(.m�|s :bR2� $dE/dx$&�tJ� �^�K-�de%��K. -1�"�[F�,)f9d! scin�WE+ �L"0� �A�bea, 2�e�No�c2O �ge <-N^Y� Q�F\y�s@� v�X)Y��er�q� ����h�G!5la<�%P*� -]is-��+-^Y�n{�u/�liZph�Be�or C�de� � )����F aha2�X t�Kgas tu��or sil�� lay#Dis)�q�Alecu��� /8 (``sandwich''&�))[iF#i �Qtrv-e<r!RQ �M�=�qAX�cA�ti�.rT s �(paghetti'' &OJ ). S�gaz}Q�Mve�Cs�0Yj ¼��ft��P0fla��s�u�>;f>i!\�Wre �WR a�g=s�mpaa�to .No��&ӭt�Ocq�l �D m�  �h�["̕� �@n�n ��:5� �Is.�� N� &ڔE�e��6p��}�� F� ��a [tb]�+ \x�$ b�N$abular}{cc�\�x!�=20�%17�y ,56(file{blank.,d0E elos�(c.pp&" }186Q gMncrit_cuM\\N((a) & (b) ��!�d*�4uc��,t�� ���,��E} dE}{dx}$�é�B�� proc[B�Ta"�%Nof�� ��si���R,���gyV� fromH& eZbnCstrahlu�d� -&2t \$�c��)A*B[v��+d?�ng $E_c��en,�or/ to�$\left(2\r!)_{ion}=n!� }$ ! �J%�(E_c}{X_0}$.%��a4�Ug+U$}�mU�Q  ,X%Gr�� 1~GeV,5�� -���t� �9���� $ pa���¡� 2kcZ�pdg��e�on6� A�b� q��J ]�nf�� r��\1ݻ� ��r9# (E%�4sssim$ 10~MeV)b-�H m�BZ� mainT�5}��dSE��c. A�pal �m�su��>�Molle��[3Bhabha� A�"�  annihi� �V�Zy �e&J �},�.%i  fig.~\refA�^���2:�2( �� -b.[e�u}�Y=G�n#ers �b�6&� e K7�un�E5 6\��T n#At,�csY� a:6>on"`V@$|�|�\Rto \ln EQ�%����.��6�c!F__�"�D� A, xC} zE $ (��b)V�)�w��e W�� �}��_��9 &���;Ac rb ��=�a^N�:mequ�{ :yA& a cru��p��-9]+��&� a�a6:I؎W�?���� \�� , dub�(.� �l���9nsa{�Gi's f�6 (5Coulomb*A �{�. �����Rgover9�.�!n���a& J��sot j�^Moli$\�; e{{e}}$re�ru�[ $R_M$ф���� R_{MA����E_sa�J�� $E_s�?��/i��0e c^2 = 21.2$>/ �K7�q e� �\�(is �u�7 �A/Z$~6&�El, 90A��I"���M�a��yl�f��us%9I�(0\%)=R_M $,e (99\%5a-of $2~$ (3.5 )$�jG���!�"��@*x�a mix�I&��=p"h!!9Q�+ MjX� Al#u)G$�b;*�9!�1��%�0um w_i/X_{0i}*� �� & 1/! � 1}{E_s�|um�(w_i E_{c i}{0 bTw_&��co!�apa�w�-� $ �� [Ӻ !2$/!H> �,co.3�-{'W��<���/i!(t �bleRf<ble��B� (6o^1L�ge)A �or/a�� � v ]�&�� &�GJc�"&��� �i ɗ b�J��z � ��f6�Z�tZ�Q�($T$)ve��b0ie �!�-�WEh�w�N�2� E_vi�E_5�&�a�5��T�_2�/TF�Ass�%g)ve�? A;D(n!�a`"rƆ*PaI!1�:H9 r�.�[QY#��!�"  a : pera0in._��� $t=n �.���� �\�iAA�c� N=2^t$9�,�e $E/N$M\�1�A��A�Bn�nw#�x�%y��~$� al��zoI�s���B=te�5�� �r] �i[v!��"�8 V �oughlyVX � , �^:�P -�ed=o� ]5.o � 2/Z�#i�N_M } T2r �F�&����iM�A.^ clear��aP�%]f* [&="p.�#2J�$�e�}"prF[��A9��"�!1����(:�(.�|H�]�Iu*� �aJa� �p_ a hi&�[a`-W)>�(�(9"  87},2�^�U}!���-�Mu�o inela � �qs�d p 7$!��c's  i. SF�&Q , mJ#�X�~� i�Qi0�a��l:� QS�; �cK�� 1/3����r/�i^0$'� at "�:�dec�}Hɩ� �� t"*�: � mp�*Y�)��a*��dissipX��-���#i�s&Cѣ�D�ex)�%[i. 4��2�#>b��:� � m�)9g` &mE-��)�.@ lj� )u�((!(/ .� _��_I, �4� ̜�JBI uVZAw}.s �mJj-��#�lo&�l&t��in�)FS� give! N >��"� A}{N_{Av��h� \rho ƈa�}}~�c-�  35 ,A^{1/3%n?�o� %0X��S �$*Z� $ �E Avog���P$2�+�sqA�!v���.;!���M�2�*@�m�><:�� ba���z a < 0"���]��{�� eqq�^�%�-sc7(�C��i?&��4ing the purel�y electromagnetic and the purely hadronic component of the shower, respectively. From experimental data the maximum of the shower occurs at depth $t_{max}$, which is approximately % \begin{eqnarray} %\label{eq:QC:} t_{max} \sim 0.2 \ln E + 0.7 \end{eqnarray} % with $t y in units�($\lambda_I$%$E �GeV. The total depth that is sufficient for 95\% containme)D!es%C, energy is %��L_{had}(U$) \simeq t �0 + 2.5 \cdot � TE^{0.13}, & (\textrm{�})F �@ransverse develop�aY! �!\g�jion:e rel!�� tweea]e A %O%� givenahJ�2� epi_eh} \aL4{e}{\pi}(E) = 0/h}{1+(e/h-1)�f_{em'}F�where $#$!;def�pa)Faverageu��-)�y.s!F%�> A�o��-V, mainl�ޥ�, $\pi^{0}$ )�a�-� �$ fun has b!Zstudieqor allyE�Mf app��uemvhions \cite{ref:QC:acosta92,  wigmans88ganel95briel94room97}�� fem_-} �,(E)=1-\left()�xE}{E_{o}}\right)^{m-1} %\end{eq&|& �4or} & % %\begif�~ �.�k��lnn�bQ�$, $mk$ arAAee�s�+ange 3:~0.7-1�|, $m 8-0.9, $k41-0.15. %%%.� \subseEV{EF resoluAA��+ric� sure{}q� AA>i!_@}��>���BC �����xy@col� ������ !�pr�w�s�%�4 al fluctu��s,Zu�a;!� "� &):Ha9Jeri� numb�sources��Kamplitud�.�EUlarger  : ��an >�on t�� foreF��s%S better F�4 |Z. {\bf FE�>�)�8} In eq.~\ref{{  _track}�"  length!zJ� V��0estimated. We��ectMIedQto�propor!�@ o* �2x. PVi�fin6�, o��"� IQ-< grea!M%:�Fc��a�d � ��to��O�d�]40.7\%/$\sqrt{E"�GeV})}$.N� %2���& -aE)}{EQ�_{5P}q(� }}{V}J�I� u�� ��Acs Au ]�Exn!�V�2�=�s_Vage��f�f=0�'(1+4ff% f��Ajգ2-� �. For.�sM��{ l  f3scintil{ or C�� nkovQ�,^rs��}�O 6< phot4 (�u�s})& �O�.�Y�. �low � yiel� is.�A�� O,u����*C �hns at �8multipliers perwAPdeposia�-rim�]e( ($n_{pe}$)� malla� �s��"�ex 1 !? t��N2��=O �w>3�i�1}�Q� �>%J��?s� ng2�,!2 addi��these� .w8, we also have��X.*�Jre!�5al2�"R &M $e^-$'M $e^+ Xtr�s� sensit ) rial� "�absor� 0layers. If $du�thicknes� each1 2E$T$�i.w  (j� )��� �@� t P$��is equ� $T/�  Us!�insteaama����L�c�|,�} j�_ <ed �qNy� readR��}Q1:|1�x T_d/d}} =.M�_c/� u e�d/X_0}>EN)4!e&w � $E_c� �� {550}{Z}$� 6V� , 0�aU$ive error �A�n m 10\%$ < $13\leq Z� q 92$,E]�cor<�onE�$by a facto� 8 1/$\cos\theta$� & 6 �� E_s}{ e  \�$$ to accou�or���Z��EUe)���:' <� �8 �C inci�9 , we�MNZ�\I\ 3.2\% I*.�.� os�%:} P:z:� J�ora�ivalen+ $ �\ � Q�R_{EMU�E��w$ � yEM}$ X �H15-20\%nre���6toV�� Landau2�E� path�y6VK.� ey�negligi�A����liquid solid F1.ereasCgas$ 6Kru�ak�Em}=y c&5 e up!5\%a��� }�j="hi;}"� 6/!:1*5%k�aD[ �asm�ɶ ����du�Ce� �s��t����ageMA1/4� M�i�� N !&t)&�F�=m+ gi� zvisEL a�p2�#a-% is dominF�Vu2l��c�que�� remai�.Z am�'of1!�sJWAGwek Be�s VP � "p c.X fic_e - edt� prompt�pi^0"' O-� " inte%8ons. AnH�&��R�8 / &�� ncar,es logarithm[��!�g4�2)�. .8 !�/ng%�M��2�I.= . In-&l, no ma�w� �����uriMPR*rR� &o}q �}kV���������A�445\�� CBA�����~:� Eo]el �t G*.�"�T%:_}, a"% cas�>Da��  S� .m�ex�l� similarKend on&  &) " a填A^Z�,��)�>5 #���R   3}{4,��wF�!C� �� 40\%�M�(� 1x#"�to} \ 2 ��$Z���A4 3/4!�Y s%bѐ percentagE!|2�� $&in2�цionizE��N-�'��r� nd -�&As al y Aioned,J��XisC%a�� i��  EZ# jic�� *l ��:H "��>p P��)!6O&e�!K"� $"�$-!"tr�6"� 6l�e>G"�M R���*�!. Dev n =1&oI26�"ef�&cy to��ver��%�ed��to:o,AMend��s!wypE�%�i�%Ag��!5!e ffec �F� A%tj$ 2&k5 #�F�FPe/h \neq 1} \propto | - 1|F� ��or�%15�$ 20\%:�pdg2000L w� ns91: 87}.�8ummary, all non�"� 58!7 M�&� A2� . Co&�#/"!��!e$�in^ ity,A�ibenn�sZn lin�%�9 im�$nics etc.,�%��%ad�qu�A�icultAvPAKadvanc?��>�\- Quartz fi$" ry��J��� j� Motiv%V��J��)ba,'mg���newn �  technique�\ �8%aI� inuouslyD K(demands set�+�"(G,���z$accelerato�A��LHC���lhe heavy�� physics= gram! SPS ��at RHIC� 2|co.{0forward rapid�' reg5 | ,very hostile+=ven�*al=-� 1u��iT � �� ly.� Yigh& level.6j H5�3 ofy|uPF trigg3 mustf fasta�i�to cope&H>e��e�p9<s+ �a�,!e#4LHC bunch crosEwil�P$ry 25~nsec%Bpr� beam�1. $Pb$ . C1A�w� q}�s fulfeoth!�qui$��+eL�i��c� 2. First"� bv aChA!"�A Grad1l�ose�eAcU�&� mechanism!� q:��isa�e�)!d &Ce�&ich2<�4m)m� aGdu� �hirQQ�lA%�!"10%��@followa�$we discus2detai�,e�pr+p�*@mai�*!ti�- F6c �l 94}-2�$hagopian99� 65arnx! 98_3:82},65weber97��rhiczdc9"z(adler.,andrieu2001}�'z'P5Sof=j!�>"� abel*'5� _of_!�e$�pZp-�F��* ����1"�J$ade a densey�su�m(pper, iron,�^tungste� Az"h medium]c�eef2�s �A�� �  u��X.���!���"h�/ W� Vi� 5&afbop�%)Is�A=�h� � ��0 guided alongF%���!N� A*�]&e�;of.}�Yocc�3wh!eB� �l�a -s�� veloc�k�re��0e ofN �at @.�!D$\beta=\upsilon/c$!�!(.?1`%�$n(�1xd refB`$=$n(�1)$�yV%&��(mit!=forN2N�_thr}�%ta > �_{ty'.�@nJsaY-3of em�T I_{c��.ve�-�axi� � /!"� &? ���-�} � w=� � J�{ &�1E"2 1J!�5 waver%aD� EeMA�/�٦���dN/dLdl�/Hd^{2}N_{ph}}{dL \ dM<}=2 \pi \alpha z) \� \sin9#}{ 8 } =H^?>�6-q� 1-9n^2)p^2"F�]0 �($=1/137, $zu u!��!U!�E5$e:. �$�=���)�%�$dL` %�N��T 1�l/$��"UV�[s�rum.5 $1/ �^22�0��E�sh�be noa�EmA��#of}� �� 2 3%��,2�5eG6�$ KLs�5&k&�A- "�A�4b*�2 two� v atRwf!��isotrop�( ej-.� �3�(a�  ope8?.l ��7*' trajy!`!mQ_= 6�#at� �] � ^a����%. Also�49�emphasiz!zW Vͬ*h si��ane�($<$ 1� ) �Ipassa���C�ej� wid.8�?&�-is*T!T 6t $gorodetzky&�2britz4akchurin97_399� &� 3| �n��r��&�ys�1$1.46-1.55,��"#;4$ 600-200~nm,G !��a(see fig-/figt1n8_cher_de/dx}(a)�f�� �:�$M�_H })[u�U��.V�� 0.65-0.69��!�I�iRK!!846$^{\circ}$-50 -#��)�$. �$=0tab6Q<%�!���9� �� �.��S�3h�'.(Q �el ��b)� tabul� !�� rNdx )Y=065%F 0.99 vari�-�A*�;��resul5�( minimum ki�> pe�JD m�carry��mWJ�n I&!�0.33~MeV��i�!, 119%��@8 "802!r�)� �5(figure}[tb]��4 \�eringZ)� r}{c�0 psfx��=190pt�/ psfy254file{blank.eps} ps A]m@a� � "N&� "�ZB)eMu�q  Uȅ!��E�6��$n$��rv4�j6�A/F2� MD .�(�� 1$)e͑�Y9s, A��M@a� :$=�:Z�5�s9�f \ve�i� {\�" � �eqU{cc� $ {\normala� (a)}&a� \h� � % O"� (nm) a�6&-6�" $ �.:& .&=v = 1$ ����  �\\>�200 &�5051 &+45.�% 49.8*FG4 G46962 G80<& 47.2rG6G584�0.686C& 46.7>G-�)* ��6 e��a)i��(�!L<s�F��(�7n o- wordK�eaV2� C0.�� mr)"�2meB �c"<� :'contin&�A: N0 35"� (Z)Ec!!� Ca�BD$dE/dx�v��s)� .F a�Q�y��Ec�Ily��A���5�,? E�al!Mco*!!>ya��I"�']�y*H A�Y9 q�ey1q�&`)$. V$T��`-R&4'on�� bu #>�"f"�JmA���.�q�& 6��m�O$jO$L`'ag�!�6K"&8EE�< _in_���J%T�Bi�an6�,m4�"beA=I�2 Aral %�Jb�f\Ee�!�clx7urrou�$it. AllT�"ioA� %6 � ��0�!w0/rp(TRI)i�! %?�?m9��2����ve0p!.�. %TRI��per�'!��Ku�0no��uC&W�� %��scQ0!-�"w&  themselve�jA:�!4�68�,�paAed]��n_{&���1� ;4* lad}�+E�U�e�p�2x` s"!b�-�b!�(ary surfaceq��+��-H3so!cQy�ore} > � �W�! �a�N E|6� �of>1��o:-n2!*it�Mga'ndA6MFI�=&�1}=�1^{'}},\�(+sinon_{<2"t7),  P2�h\gleLt"�<�i %^x aVH"e9�&0,�a�>)z6�f-5A}is���C u�or extee�if%s1-��or<)($:d % A!�8�(a :�-P4 \geq \arcsin(%�/n_{1})$�>���GixByO�w3��Ab o!o�1e � ��d�d4\[cri�"�}�e:- a�dJ)7$d !r�6-'_{d }^{1�;$arrow 2} =R?.�9a�.oEe��b��n*}�Co6P#*�Q�* , �!_�'w@} \xi 2���n_{�8A�M�D�.DN�xi�!�%n�B-����!K'Y-h�/ >z. Usu�O-:� ��O���0"�RNA,Inumer_ aper����)9"�P�LnS"�VNA���.� ��A�5d%� �&^!iM �$v l,.\s�%_i=|$�),�i#$� �e=82.�(NA=0.22, 14B 37.�<>� �*c!���.a�" ��$!�9"t 5�B� "�7.�"� GbT`!/R�"{��2 �  outpuuJr"|5)Hat�b�s(&�C �3BB3}H �$*�S2=![� n a XA5l(u}Y$y8a� whoEErack seg� L�[d�-$b$ɇ�8 EqR �� )%.}0�P,J \rho M�'s2Q<7Y5�]6p�!KD>�or����� xi$.?Pde�):�Ycos_xi�os� =FC(� psiJ�ith�Z sin_eta} IR�V!}{R�;�`arctan�z"1 @omega}{6X( a' + �( B�'-]lsi lb} �AJfand��!Fps1Gpsi�t ��- �� 6�Fw��u�s.A<�xi� &�R1�,>)�&_ RS":�R[]B�2}" � qA�mT \footZ'[1]{Wi91�,l�?d�Z, $�>suc�NR��i:�Xzed�%� in�'��ZtLRa_�+ s�.} 2K% �'m�`������ ~6�q�� &� �(S%�K( \pm \DeltaI;' �_Y($ 4.q$�;2�$�$.VAl�$���$B� _vs_��r�� exp&�5confirmE�!QHM&&N6�%�j�lu�:96J�23"}16�,�1�&C#(![��#*�#%#x�=1x#�#6��#QX�N#aion{sche!Rc "cL5`BI}e�Un 2� Ei1��of" geome8Y%R�^*� �"��#��t -]�dd��n�%�)�3%�)�-��$R8%6#:�2c [~=R� l�� 1e�!�>�JW��dv)��%�:p (�� 22E  37)&�"-�6���F���n��2���N�E+-Y�$V(?$*44syn�� ic f�9silica,?]4m��9�cSiO$_2rf$>crystallOt�)(amorphQ)�). It�fVX� �3| combHm�}onI9oxyge�� a2��J�{�provides��A6>I:of impu���A� &A?�8� millio�*t� �J�e�% E�A �ao �k"Ja5��  !�RC��fu �-T��f# gi is�SBs1�,���g s ox%GAel�hFe!�O, Al $_3$, T)�4, CaO, MgO, Na . * clar��i5!be st�s-t @s1or!�e � rtz,IQof�6i�?�6W of�e!�#3anB� - SR��/nulIe�9!si�sdm4%�FindV�/q�system>>ɿV �l6l�70, )ntVaX/eW ofE�2,� UV r�=�"IR,��U� mal expanEco;Ct�\ 5�Ec_i10^{-7}/A$C)�v�< R.?*�"��;g<1tem�e� E] 1.3�3l52l{ssgper�JowV68c�I2*! CQ4�!`�4:R!m!qson65�� ecipin�' of $� :�V�C2�6�p,i�} �4-13 �{�/61663.i^2"5�((0.0684043)�4+T5 0.4079426j8116241481 p8974794b89.8�17 \ , +�5�in \mum�5.%�4 �U�fibw�6�:a��"��w:e �`y}��i�� dope�[8hydroxyl (OH$^-Xn GIj($ 1000 ppm):M�ntaR" �($'��� � �SI fluorine,`F( polymer (h+?pE>ic). ��= avail�U �H!dii���)to�~$\mu$m,�>�d3 R5 e� F� � 0.37� 90.50. FA&o8f�% $� ~�2� 1  �: 4��_n��.s$n 0.05~dB/�*U�A�n26�. $l_{attm$~90~E7��of1Yis��V� ������app�-+F�g�L� �s� �[&�din IR.:':�5�3}CJ4I9mO*�Yabove�P,�A&s���nem�PrtB!.e3�Q se (� eoff5�A)b�# *I of ,��5[��)Imakr)ne$ az4he1�� aP sheaD!methods.�iviB�G*� &g*�\2�J�#�G_@��#J�#We Kiz�!t.�a !K�( 5��M� �&RA%|at �elAi�dHDev6�$s���$�Ps (!42�h.HA� Ii"iAd��"�� �]u ��g>�)`�er� K2N@�veq:c�"&�a���ern icle*FA�E>-8���..���&�Z � m,[#E�fi�of Z�,i�4 limi� s im�-'%Y>^ij'�Lke^B b�)�(+_�����)r 9% �,t4e"d*���Wof� B@wB�*�: �*%]NMn10~mmE�5-10~c:K;, �u|��-�!`ve�S.T+Jinb-�6Wchiav�<4nz<�Fmwe2:Ga2GgK�3!�4 tim�u�!e\&m� d�{6�͋apE�� >+,"�L� i�+�X&e�a�:�L.�� B�/, "�,�v� FD�S �gu�>n/- �s��2 .� :p non-2e�v ng (qS >�8��r� [tbp��<"lPh].�<uxa��<��25�a$er1:ifro roSBed view!Xa GeV�o!� E �"�S"�VA��0# �. n (s!T!�z�� 20$\��$20 cm$^�b ?+WRis W)�QAT\� T�Ht F�i�&� ].�B��p�=gt-m ?:3�= N�%*`>ʎ3��=�` �cwcF' e� ")\A6h:a�& &(#��giv"�robabiS2�L"z"vi9!�� 2 ,��P^~40����ZO FPA�F�T�FŶx ME��� An^ !�6(Z 7� 2�| irJ 6�Raf.� � 3\+�Y�j�P�a�#�*�Zm�|:�EEG!a�*aW aȁ$>!5%�.0Q� JWQ e�g2exceed n�R " ime6���6*�Eg 6� U� %iM�M4"�L,�!�ui�s�*�6�cap�to� e Sn,�R l�Ta!b"$ 10�6�*� ز��'�IV4Uq/x" AH��� �5, �J�b�6&�Ior��p� WDhs~JTo�"��1 �.��"& I�%�.K�"$45"� '~(+ �>�Bv- .. �#shQ' �=ua �wexplo� X��2V&�mҡ��yob !�achiev� l�b"b"A6\��9�set�ssAm!�PD�Gi[=%8J�c�!? iderea&Hor,�0w�V)3]m!�� �F\mea{� .JTW$ spaghetti�dz,dI !�Ej7 embedTRi�*�volume a $"�,�&� � w�4]�incom� �� &satisfyi� a J� or j!�`8a� TeV�4l�WFELc WX�,���6r;^ ;�,=ex~ ��5� � J,�0*!��  affordEto�J[)�l>A"b2k[� Yge� m�]#. �concl�{t>]).t{��D5_T:�] k�o 1I�&W�.<�r��Ais� %�+>y X<"Wd:z�4}bX*� ��� � V�F%5b�R B�5�ry& F�" 1 {"�)y � *A{l�R*0F %�B>_E�!BaD�}^C}NR&�D:>F=K}�B��)?�9J9�D� ] �p.CedF&� ( *a@)a�"x#- er�G&G � 0:�@�16&��&y=�(� �$bm�!� �GB��k.(]J>\i 1}{n�w &�;&�P�D�� $&"�S-�"�Pj&,�.T��&���mX�� Q :& N:� ��8\\62?� &&B��Z:�i2�in�t�=w�>&�mfc��backg�>\\ neum�UkF adioe(%fE-fv=:wor=�c|ABV&�_�U6: @�n�*c��!>:b6���a�2ain�' $\)!O$(�)$ &6�w� ��4�ZN>� � I� �=�� .�� � ns/G��.�M �$R0!'a� 2IN� 9(&.� o�B�\\==~p.e. �r*/ [�X�E.R� A��ir"�%*� 6��Ial`2� .i�af�ia�5$� "H 2& ir.��x�@d`u`a��&\ 1�d�&�"�0.0����v"~ �F?�Sw�g�W*n�*N%\h� !j"�gr*�,�2�"��n�=sH�"*ge"�2bNRe�R�=W �] J] �t�Wr}�2MN2M��FB�F�.=(&� e��/b�/�n�"]��y�4R$�5E�E�e�ibF�&eia��!tbir �"�m ($< 10$I�,Z �c�;�dim! d&�>9�Yͯis ��:,��W x(�,eW !�Eh!~j.lumin�y moni�k�2T�b%7�i�.��*�,*�#d9�%��.86b��+C8��� or u���/.~�"0��;fCj�0b+%�a&�/_+� �<.�.d�!�[_(k�<(``"�''�(?It�Fwe� tinu�.he� �2�.�N g andwich''&�e" $��e q��%_�o��Y{�:.�na50}���: castor}e]iri�&�6�oq�BVab�^ Call�s��B�&��(4Zero D&�.�!~ NA50�K!�CERN-SPS��'J�'�r2�N!i< _2000u?n?xp#OPt��&BmoA� earczl"vo�,�� eZf�Aa�k-gluona sma �a� purp�+�l)�0p��� tud�e�oN7�8� mes���?, \n=,;, J/\Ps�Bn� �,1s (�ess��%)�158~GeV/ؘ� eaYz. A�^�(3tΘQ�E�@ �� .UC"l�D1.6~m ak �u�, c��  pseudo&# �\�?k 6.3$ (Z�:n,*�:p"�;4�z2y5"#&2}. % A2���A(1G�:O(����to9rG6y��僡�t��9I��it�0݃"� ��(�-m����#i�L?7%���q�*K=F�_sF�)�="�aK>yatbt%S��R�E�C. A 9�f�Dpq�M~"�6�a# ** is�!i8JvbD�q}�)B�> �n�7�#���ZDCj�nF�f��$.Z�I'�*��!7Z*5��Ag��V�% �#ҽNq & \h�4\Ã�S8&2of�V7zu ��s (!�ar�|[Es)��V� ��imp� ��d�lEM*l%�ipant pons^b�J ion��]z � �v.2 }& $51&  65$~8&3$�Fh*4 tWs,�th 5.6~k__{I}$,^ym�j��Vrooŝ�p�es,b�1%iip?)�;� (q : 4)^�5�p-�ta�wum (Ta:"T`�= 11.5-($X_0$= 0.4 -�q4ity= 16.65~gr/)J)b30�&׀^mm� �J�s�-_� ;�9r7�($\var�$ing�f365~m' &7� cX#^0^#&22b�900 ��d>Exid buA^��,1.5 mm pitchbK1��"r��}&0�8Eq��n91�<$ : 1/17 (=5.88\��\vn$\sigma$2�(}& 35(28)\%A�100(205)�)(= �2.9"�(�@}} \oplus 19 \%$)�r�l<5}!�I_61E�Q*(�g��eRA; & 10�j� ����:�+� .�+\ro�@ box{-90}{ޞep�haC�+�rC"v*}%&Mhj'l� ��/o�)J)�kzkV.Fo�|. f CMS*a[� LHC}�=��lcms&��Z��2 cmss G#e"K�b LHC ?�` per�� Higgs bo8"�su'?ym�Fg�)� ��> p p$*M b�S}_{p+poR14$~T��IbJ (3�� eq |\eta|WQ $ 5):a2�onel2002:, ferrando����6� �a-�n$V�} radY!!>o*�>) "�F� b� ,�g�s2r:!b��. Two�nYV]�s�0be���*t,��B5�,� m! Uw�>?� u�<(of 11~m�=!:. 2�O%"y� v�,$2\pi$ azimu�-dagY�$}P� D t�K�x L�S0.175$�pNU�aAb��&ein^} au�:&iJ_ �chow� V� :Fm �82�m b�V�Vm ��l �l  9nge 2�)n�(E�(jet taggingj@� p6� �C$z�* V�a<6 ^��^U=i �#m^3u >9 ~, a-8De/ a0 , a2F 8.8�F �F �Rj �E 360�V �MU  & steel� z@ 7.4.@ 1.9"@ 7..> V�%eB a\= (98% Fe) + (2% C), mix�F�o���%weM sV5��'����ZP 0;),2I d�D8�V JV ��  9x��� "� 7b� 3\%o %<--ɬPA.Golutvin, NIM A453(�)192,� le 1v�l!�* � �^ <\\ %0.5(1.2) ��+ \tl{��  .H(. F Z�&�B� �� �� v� �Iv� � .�98– cmsF� :K��ne half ~���.� �endbw��6�6�� z� Z��D!ALICE:� j� alice_zdc�� Z� �~2� s��s�>�2& `�vZic�Q v� i1Xo � :�7� �;observ0)I.�C ��W**e8_�N:3�i�>:r�>"d inv��g�Fv7k s�N�5� 9�)Is�h?��r�gNCMJ�rPb+Pbt148vEC=&e�?*6 � 5 EL*�i_d21*�9�j"]tfh I� (�6�)6�z�"9N> ]�akio%��9IazIt���"ri(]�V{sIl AC�2*z Z��:�E8a�e"�- �hX�5S.S# br2�J"��se6vMH�� .��D�(=�IJi�)�!'�h pair r-��)� ^cs,"; ��8; on B��65Bgath9"A5115~m :���zdc_tdr:6�B��.��Gs"  *i�w66%@V�>$$*I*nV#!r*AF�i�D*m�A�� Si�1n$ a� 5� �2-b*ui�pip9����������F"#f(."��#�5$B�script.�tabulNl>�4V G R� {�{us�� j�4b;m�:^( �o~���20�q>B�; �s :^��B��C�Cn>s Hy~;^w. R� 6.13r� �/p05.6v;��> 7  100 &�5:��& $20.8 >12 5J?4:?^�� f3 yF&�;^u8&I0H� r&r;^o]�e�& W�Eoy�)��& brasbh:p8p�d$= 8.48��&��?B�� & 52��p4�� f)^441&m3WR%IJ& ��IR%a��&6&�;55^�nx6n:�8�T R�bjj�v&n;^�%�%u����,22 (=4.55\%)�$/65 (=1.54��.�10.=��2.7=�s~Km$1n�.?ы��l:�'�^�r�28Z;^�9��S(a�Y+ O$(1)t�J;^|EA �G �G ������$ F���"�@N # 9 lin� b� 6 H*8&� .���g �g �g EM.t e�!$ NA52=q���.r�.2��NEWMASS6nnewy*�.�jf.�.*�+��&���ON��0s obj�4j ^uE �7I)m3gel�D+s�.N�nti-n�i���.X2"�"�� �-at".))I�� �., :�D�*;6=�S} !1z ��.} b�=%B\"f5]o�0$ decay�[nH-J!"0 �F�.5!f�&�.0.82�. 1�a6��val $ 2.3`eqO s4.�c!� 2��F �.|�.&!tGp"|_.c�lC��!EMi2ҟ�$e&w.w��2��P is= �ecu�S"� -� ʩs 4&�3&y)�2t 2�3VyG�� .=2>�] -#32�8�So) fac�OmA��H��n�@EA PnxWMW flow)}m�.HE�.�>� AblJ�F na52Z� 5Pn� ;�1�12� E�zrV�AN!#:�ّ.@�B<�oZ>}6uJ�&�x.�5 B�aw�+)Q�n�1�B:^ �]�qc]��Fp aU�^Z� "�� : 6�~�b�bRQ�B����7�8}&#+vIf� B4*QN���W�*R2�C�19~b� �P�N)�in�Qb<Vr!s=(� : 8�0�[-��5(PbF�.7.2��.56"u! 11.3�19��,>�Ʈ.͊VY!43�.�<�Ms�l�L!^|1cneJ-� �^8q[:� !x.��"u.duN}�.$2.8 (= 7.8n�|�.� |0.56}��>v.3.6�!V� \\ %�F� Ej�1\ %R��E�>3& �� �� �� �� f� 0NZ� OZR�q?��F��prZF� �_����.!����z� �6r- BNL-���� Z� R��vzJHe�Ion Coll� at�� �+,�7 $Au$�Žs<100�;��� o�\"�(Au+Au}= 39.5.),��Y <�Ԫ.&<��p*���25n/ � Ʒ re 42D6Zwww��� }*�!�U �z { A��:!�= Each{<6� w}1Gf*�- b2h"�VC�}2� B���"�-1� �-.�*> �"Yq�! )/*�!.IUE A+l"l I�� A��Q4�"��!%�yc �/UCN+C: hite&�� baltz98}.)�� "��<X"�^:Y}!A�� ed64B>� ! "� �dF;;��Lh]6q�A"� tV� AN�cR9i\If>�c��-,� iv��B ���6�'c �mF b1� �/}�*�y.� ��� �� i� �X><<�'� �B� ��� ^" a�?F a}^6@ >� +/��A�B�"�#v��>S$�3ge3A7�  %"�a�#��U m� 5 mrad$#pu%�r� e�*� 81q�� :��s10B��~B;2j� t6�i�)�>��� 5.1��V� 27! s"� 3± &�l�(>�1>� 38~cmfR<81��;rƗ PMMA^� W)8Bb��6s< 4^�^�50bf�� �� *� 8�5/ 0.84F� + 9.1� (= 17"\<� �+<5.2�Hn�+<+<0 k�^�\\6p-t�$��MN�M:,<���.18&� –.���� �6� �s.� x�� �� Ʊ 6�V�H1*q� DESY-HERA�� Z� H16�.e�+H1_"&H23<a0-��N` �\� $ep$P�.,(E$_e$= 27.5�?(, E$_p$= 92�} s go��� - U�B z� � ** %�$stituents.8��:N�6�a*(o��g O "��of����b�by^�ms{hlung& zn��J�5x&Fh � *� �H@&�Id�e�qm!U�B+, x�mZQ!w�� c^� trapezoid�\f��*���. A� O�&�� a.�A uti$�*�T-�W� +�M'"�/p��.��/�*�N�p�d!�alt��&,bSC<horizrl����it"oriP� G� 3pl��1i��t 12 ?Dpl�Jm�zdthF�sig��k�T�u˽ 12+1�*�',9X!j�� �se4m �>� bpf�<p *!�olu�!tc1�=� /���1j �.�-"�H��Om�6��.$"��}Z�h1}Axg+�B�-8V�7���65��2BV�h1��n�; }g(pos:mF�Bb��"g !�!�g'm�Adu�3^� vz�GYBzbPf�s7'0r�,^�V.�}& 70^v3�;Af' 25~����2�*��b a��Z��f�&�]�]th� bRV� (���+��s kfg BJ5 x, y�A!�v0, &&(W:&�,3�),!�)�kz��&a,eEvl�&,r�6�+�=F�6�,),��37^�~�j� ��%^�qS��6�.6�59`+fI}kR�1b6K�+$8�space{�I}�5M�e)�8�>$~l:�+1�M "� izK�>0.�����x�#=4!��=�?H1="�2�� �.@��=��=��=CASTOR2� � ��*LH��^�.o i��ds a�}y�DFRc�V-��,v�MS*�*"�dKs� "�*f&�=X[h��ryon ric1{2`*r2�rza~L�*+��"�)�7unu��ys,n so���C� uro !n``,� pene��� � s'', assu��WP��X�+,� � 4�"3f\�x"� �( x�oi prod �2KJI�s2�c�\BL#~׏�f�K��Z:�*� $5.4�* \eta�*7.14$,�]B/&� &T>!�"w%HR"&�)L.�l��UFE 3 Gofx5��� lea�s�#9��yav!�45*ʲn�!>g:�1>o,@m-�{>� hann��1�se(*ad-�airF%Ų�tt�_�A�9YAK(miE�.��5 i!� r�ddngT &0 VB�I4}>��m&!wa�R7L�þ� a�Bj �n�F�5���F�B� ��?j?"� >���">��^q .�.�Z��inn�^_o "f 16.4r�*P^�^tۇ6�^A�B�^?���*I��ju*=R 23�0�fbJjR��8�st$���x��de=Z1��*Lbf1��+y �� 1�R ��Zs� "�8 � 1��L"��.�=E8 �"T+\Y6 Z8.��L&%�͉� �, 0.3 c2 ;($dc� = 1.16$�k ɲ��Rq+f�^�^���^42 Tfiber planes per absor layer\\ F�& \\ {\bf filling ratio}& $\frac{\textrm{ ^volume}}d$$ : 29.5\%ZFqr0$\sigma$(E)/Er�(21.\pm 0.3)\%}{\sqrt{E(GeV)}} \oplus (0.00 'P04)\%$ for $e^{\pm}$,�(95N2.nM6.5 Ls K\pi M~;,light yield}��Tm$40(30) photoelectron)�GeV6�(m)~n,total dose} n300 kradnv\hline < \end{tabular} }le}%.�L \begin{figure}[p]�Wt \centering %\epsfxsize=450pt y17 #4file{blank.eps�ps 4castor_gm_new2 �Fcaption{schematic view of the CASTOR calorimeter, some of its aircore lA`guides are shown.} \label! :QC: ��nd!$�! %%�G G \subsec%Other =s}�o>o To%nknowledg%_!hauthor in order to complete bov!}Tst we should also men�' W/quartz �� pola-� at"SLD expe8nt at SLAC and ,dual readout. P R\&D project. % Thea�mer is a2-consist�r0of sandwichestungsten��tes { ���8s with alternaEvertical�horizon�(orient��n!3( allow posi%measure!". WV$a fiducial���4 $43.5 \times . d115$~mm$^3$ it was capableo _%8energy �!�,impact pointd@Compton scattered�?ns2�Ldetermine precisely?)�z �m��{< beam \cite{refa�(berridge97,  onop!2,ko2000}. % II9l�1�,, a hadronic2�is#posed!(be equipped)�4 both scintill)�!�.� s. A ^�> er g!>E signal%K ma�0but by differA� partIRh��0er, as discus� in \ref{i�!�\rotatebox{90}{% \small{%footnoteG{=" {l|c }6H J� &Y �0� � r 1�}& L & depth >� Ls &L .f Hl�"� �dZ V� �E J#NA50 ZDC: 0& $0^{\circ}$  & ta��um �d5.6~$\lambda_{I}$ & 5.88\% "� 2.9^+ 19 + 0.5 p.e./�  & 10 Gf4 � CMS VFCal&N� stee2(& 8.8B�$<$ 12��7b�3b���ALICE n>�R�J�8.5B�4.5� !W0($n$ 2.7~TeV)! &� =�!�O$(1)� �p��brass ] !{4B� 1.542z{,sim$10\% ($pZ��28YAV� {BEI NA52 VFEM�& $456& lead#E�19~$X_0m6 & 7.:N� 0.56^J3.6AK&E>& �N RHICV�F�"� a�1B�>�2�84F�+ 9.1�T29��v%�H1J�A��25F�5A0T0.1b�e;��1302�0.���>RdJ�10:� &��21^d0.0!��"�D& 4�>& z�J��N'.�95^�#F=.��&:.o�R�X>�(t� ����(N(%S� �FN.& &Y � `techniqupw : � Hmechanism of which� ba� V e Ch; kov eff�Namely,� charg�anl� � � � $\beta > 8_{threshold}$ wY travers� �8duce �� � G e� aptu� !m� sid �-s8 nally col= ed#�� iplic $We describJdail� � Tp}�m� "� is=��we*t%0V�(ers that haJ $en built o�nVin"  e"�s. In ` )�advZ g)�ft are,� radi �hardness Ifa� � �����@ctor dimensions. A�y )<ev�ral 1^rigger.lumin�y monito r l puray!7aty��ward reg���N�" *{Ac"�E�JMan� anksg,N.~Saoulidou� valu�Qb�%�com�!��>�$\clearpage�add�sb{toc}{� }{Re� ces}��J��nsep 1��e�cols}{2}Lthebibliography}{110�\mark�@{\MakeUppercase{B..}v � P\setlength{\parsep}{0��2 item-2  %� \.�Gib+{��e�X�.�](.Meth. A259�7)389 fem funIf-F�acosta��D.A 6� �Lal� pro%XR/6z( 9j er,}J�316!O 2)18J�1O8=�N��]=S)>.?r!�J?65!? 8)27J�gabriel��T.G N�+dependeA%"5$ic activitV�388! 4)33JDga�97}�-� rfqin610scade: applic�k�d)9�%Proc.�r VII��.Conf.�:%e ya��{Z h(CALOR97)} Tucson Nov.1997,�E.Cheu6<R�8�5076�% start �oFtryF�contin!�A�tin6zI�Tpos�"evelop�V� %58CERN-DRDC/94-4,Zv,britz95} J.B N�,Status repor^ !�RD����n$LHCC/95-27oJ�$gorodetzkytP.GNyQ.� *�V�6��5)161���PPE!22J�lazicI�L -qFunda!aal�&�:,5g YeT R)"97-06 p.No0lundin96} M.L N���:� c �Bof�-:�^�7� 96)35� 9( 5-17J�M�5}r�New���"p�! �9D��7�j 5)27J@ganel�O.G F ^4� LHC*��Fl3�lAH0J Hanzivino95p237} G.A N�Ang;:sV�e&1Z�0-3N� �95p380~�b%- MP  carlo� ��V�5-�38JE .�69~�Re ���V+eyJ��6J� �4p462~�De=a`aZ�erESaWi�%& ,} p.462a 2�4thƽPLa Biodola Elba, Sept��L3, eds A.Menzione A.� banoV�J��93*�� A new�roach�fo[}��su1ol>abp.425%� � ~ .!33~!Effec�" f in�d� oG �ve*�=3I33$��>% refr�$ ndexai�F�m�,son65} I.H.M MKI�* spec�parSOkve!O kf~$si ,} Jour.O�W.S Amer}5 65)1205"� %���"�ze *�3av�V!�)ire�(ant�ultra->6Rai�\&Chem.� 3)25J� (fabian90} HiaR<P�Y" �all-M�a���>� 0-10�3 p.7R� avrilov� V.G NStudy!�I7 y:�c}c"d 0Note TN-94-32b� avezov� A.D.A2�C GammaAXuc>8ransparency los� thick�re%MS �# /1� \:�hagop!� 9} V]M�)�a@ dama�+. dCRb9/0026��:> %� �$%.�� >�na50} ,Collabo�,)S9�Pr� ,}= 4/SPSLC 91-55,  $/P 265-RevF*g_� C.Abr:s  (F�)-REvi�gd�(fin�Qfk�glu5+ from�aJ/psi��p�!�p�*n ?> Pb-Pb��$s -a(-SPS,}�(.Lett. B477� 0)28F�arn_98_�[A )L�I�bI� $zero-degre� Cq�.% &o� �F 4117 8)JN chiavassaR � N�A&2-s�t���ly:�����>�er !�a� !�6�!fb�3" 67Fm�4}~�!o!b -b �ic samp4��ft ] ���B� &� �� �4R�* 4~�.& s^� :��,J,,initely rad-��" $2UEaS.��# # �9%938FJ� VF���Jcms�ѶH@ ��JNo10z� "ZM F�8) CALTECH MarchO2F�/��&1 ����R�J�53�v4JnHakchurin98_409} N.A N�Test 1re�-C^�PM. and �/` ofD!to���b je J�098)59J� 2�8~�<1ces�/wI"���prog2a�p��i��<"ir �,non-com-pens�16TN�38Vmerlo98xM ] )-ic���!JjA� B(�9$Suppl) 61B��4N�$mshcal_tdr �H�2&Aer�ject,*� ��i�7-3Jm5� 7_40R ��of�vw�44passive front j!,N�4097)R9�3� ��q/a R ne-�@n� for �n,�%�2d-�$ioV�39e*7)2Njferrando F N�A�U�b��1 angl*� ryLHCRx39-x63FM�-zdc�Malicec4}.�Z5-7N�`zdc} �Zero D� "e@5& j9-J 200j Per�4��of2� �� �&Q R�456�;1)248F� �aRn���&6",}6! VI�� ({��y@OR99}) Lisbon Jun 9 %C�(ALI-99-17 ;X CE-PUB , ali 017.psf8_~�.) /7 � �c^$��60j�8_2�j.!�i�B R#7 ��>,sQ-nX120F��X2��newmass���RNEWMASS}:�d��a S�gel9nd&� sey iF�, }�NͿ�LC 92-16� P268 �B2).F  na522R�A�ucleiYdu��$ eavy� "UQ,} %Invi�+ talk�a�1 �;onal ��,ce�UWRe} vG<c!us-�eus� r(A�k M�, '99). %Tori).�����0151 %Bern pre�$,t, BUHE-97-1>��+3:9 JNwwrhica(Ttt http://www.bnl.gov/K}F8 5W.A.Zaj�H6��&z,R. "] J�czdc� �-�g�$A�� Dec��866�>�L\verb$~$swhite/zcal/J�adler9 C.A N]���b&,-Na�(-ex/0008005Jq��S.N.W���F�/A��x��]N�Vg� 61J�baltz�A.J.B N� Corr�ed�%+ -back  -soc��neuD �tra�.Fe.J�d^�$41�8)1-�1\98�%2,q H16F��H1�uH1��&��!�H1Uȡ3 HERARh38�$7)3a�>�l2}nl tracking,.�%Umuo� �/'DH1*� ��R� ndrieu- B.A N R��G�5/&re2�� *. &BAH1>�IXr�P�(�>F$a�4)} Annecy Oct. , Fr%ti7 SJ-� 2z % �62RFMdEA�A.L.S.ADiR�&F"�?a/�%of�1 auro!Pb+R"� �3�. G 28�2)1937^�p �� �: A!�i�e+%��.� Cen ��&C ��&".6�A �{��ep�7 9901038, ph82C0b:�/_G%j�� t?�/;$U&��!o5& �>sgm1�,MavromanolakV�S�B)%�on ��1�A,-&r$,%K$e/\pi$*KJ6!/)�.]�*Lp=� CAS/A�-2J."gm�!޼���ns�-e �@�"�B map �� A�-��U!u*o6.6ignj�E ���*�'A�d&�"nJ[IQ���J� gm_phd} %���St�SF� %�T."�5!}%y:E<�LHC G:0, Ph.D8sis, *�/ of A�Ds,x12"^ %% QFC'GkC���H�H!�~F�b"GG} S.C. B N�� t-9/Ѣ.8!9" H�G.�},BJr�R+ I�R+�3:�, N4+17J�:SH D.V.O"gH�[, %PRECISE MEASUREMENT OF THE LEFT-RIGHT ASYMMETRY IN Z BOSON PRODUCTION BY %ELECTRON POSIT 4COLLISIONS. EL 0BEAM POLARIZA>.|WITH %�0QUARTZ FIBER ?, IMETER. %K-R-556r�Ten� eeE�N( . % D�/_K-o6`Kv�F�wn0�FB�/:RG� {R�K4Module (DREAM)� !�xa�a�X�~ Ca�4),� ugia�r 4�-6B ]54.ttu.edu/dream4 ,>:�7 &8!=&�M��8�NdocB7(} ��% Ver�!Oct 18%� 6 Eduardoe��u bmis) \� ial{pap�M5,�Xege Park, MD 20742-4111T Q4{D. P. DeMillerk Yale2�XNew Haven, CT 06520-812�(date{\todayY�abs ,t} Weak inte )s�*usvAe aU�spin 3t,�7�8vio� ng�:%U"�MI�,E�aI� .�@analyzbmit�Q�P3�B  through#ec0ic die.gQi�3'*Ay� ine p e:'e nd l� � �r�Ores t�Aco.�%hi��p�?qOalNanti-nodeca� ?1@g wave Fabry Pero�R�4 dr�/gD!�-i�d micro-:E1� . We� lor-7ecess�M limi.��Ia5�5, exci;= f�V�@ap type#terrog�/-? syst_Utests r; suchBgf�iumI hi� ��.��Y�\�p{32.70.Cs, 31.15.Ar, 32.80.PjA� make�P��C{.�9$} Zel'dov)Dpostula�in 1957�B!wBbeu E��'w�Tg�2ae,tyY�, ]S re� alA. serv�VI�$ le�Tmm#~�Ozel �58}. F;Ma�8 Khripl � calc ���DA� �hA]in %� Zf L 84}.*�Jthall9g9aI6!� A=�Ae FvQ95}I.Tp��f�P! � n accuracL+14\% .�u�:i2�ic -h nonc�QrvI�(PNC)!�cesium �wood99,7QWe�e$i:�R� a�ŧ�teg�!U%�ar 6� �S@}=aR3e�e�:� (E1)}�Q\6�> ����%�a�F�4f isotop��!O��. A �X�ba^un�tood qu��a�vlU% &# �U*Fa~e� PNC. �p�U��r Cs��oW s ham7 quir����de�Fed stud^A� -e!}�?rQh8derevianko02}. *. s ove!�ch) =f he "4FAۥ�y:S focuXT��ddUa$R ar��a�Fe�+xsqnge{T task�b�$acHF(lished wellA($theory (se�,example Ref.M�grossman�;�Y anomal6�@a�Fr. Cur"Vla&�+II' S� a�F� Acce� <(ISAC) at TRIUMF�� Vancou!Y� ,�}Y�T�Hac�S���/ the - deficLC long liv�, ��`FSI life�s �Y30 � to�imilar=y! er��U�Wsuf w bTetyGg�+a=�A��� N�E�than 10I�Lc�p�0�ˡ�s1 b���st two�ZM � itude lar HY(those obtai�H�� } �<� placI%sq0Fr Cg� 06}. A2�mD:�� Fwill 1�.*Wab�%al�cIZAk�e�uE�e m� �4(Zn�[%z.W�K;a}�A��W�K�Ifq increases�Yfor�3,90,pollock92!��2 �^yI� s{K�Lforbidd: but becomA� llow`K!�1[&� x�$� evel!� op� eͦ> g%l�X{6��*suggesAg�� pas����`ng77,gorshkov88,budker,ba ln80,novikov75,hinds77,adelbeAx81,1%3} I_m�I�S!�hLaݳ� -2� � �L! m�a blu�tuA�&s p � ] t] !N�m _v  a Raman )�to� �!lZ~� I:F0q?I A�r>�,).�}��D�2r���G �pop �� � VuJ : af8*�& �%��"� )� t�4^%\�as+�w2�. +;work � ime-"< in��a-#tc M�ic}ps�)4lis99,chin01},�^ū�E�poc\ ial "e�*�\rT� oof�CH? symmetJ, �]als"-l4f. B rP"�  2F , ma�� areful eu � ��m!prior!.its iO�� *"� E��u�|�6 primarily���KaYZ� x*i K ёe� an o�8�A"�p,%Q�� VH�bto�M�,. ��organ:�_p� is�#f��ws: Se�IIEt%z� ora�al B!S Q х��� ,u, III�P lainP�Od2o)�6V��9dn( lysiEXnoi�our] nd2fy;B � V��) �conclug �N"�TR B�})Cex�S!�������"�  %ons�si:in �S�9&�i�*� sH o:eAFwo kin];�CnA"�Gl�`on or!�� e�E&ax�bCJg��cor'] [b�15Hamiltonn:� at� ��B*�ar � [�uF�7X%7�pinA�ɷ�S��dominB;|B ribu��� tomic3 _i�no� �OQ� ��t�'qOweP�+��J��a��ms5_, A�2�/.� 6=pmGt- s�%� a�dmann05}�e2nm%L5kH)osh, model�}�C�.val%��on�un ed�%siv^Ty =�� 1Qeq�G } H=�YG}{�j 2}}  K \mL`\boldc�$I \cdot \alpha$}}{I(I+1)} \kappa_{i} \delta(r), h hpnc�yw�V\ $G =10^{-5}$ m$_p^{-2}$�!vFe!�staZ"� �2}+, $K=�T/2)(-1)^{I+1/2-l}$, $l317 � t���C��um, $I6-M�, $9 )}$a�4 Dirac matrice��$9O7a��� ��\ $i=p,n�ka�g�o���omti�J� QbmaAd Ӆj�cl��U�[�ve � neg7ed�~N�!��a9 = a,i}-Qe-1/2}{K}2,i}+ I�I+1. Q_W}UUEqt2lF[K35�2,p}=-_|n}=-1.25(1-4\sin^2\theta_W)/2$, 25�!@tre�>� xiRe} $6I u_ 0.23$> Wein� m2. Emvf� two �E,A��!9 R�.iv��AK1���[��A!BAa)�� S �VM�F���heU: .DB"0 togɿ!�Ŵ&X ]O�>Ze�At��M q&�be�Tc'oͲway���Z��� Gng �boL$Z^0$!�ear93 Feynj diagram� �E(%-Y)�VA�jex )� du#j�"�6�4o��5pL6_q��on coup)� q�!I�a virtg ph�D%g second�tak  di�v |a-"0  �j-L��N�a� ~�t| ;[h�%�,imof��a ��ify!��ZL. Murray�� that(�6na/} &/ae�_eg=��49}{10} g_i \mu�.�>� s�r6 core&, .�QSu::84} estiiqG �qE�Eq.� 17�,"� :���beFh%Va} &oe\s�x2}}�� K}{j(j+1)" � ~ >�,j$} = C^{an}�:�j$}�� ϑw�'B�j�.%�Š�Q 8i  $e9 Un 2e�z � as�2sWomoger \a3RE9i�a� e�V�FF�lea*!%�:k carr }B?� *��A- ��F� E�-��6� F9j`��n�B�%a ,(r���?�#�Z A�1 p�Bor�h�:݀C"x `:���#"} "!use Eqsm�Ia*0t HI(}A�.N>�g� �rI radimPe &D��� minut *.I�u�-$A��!A �1[in Kt-�"Z!eas"8odd%�boty&^|�� [��icipat��1z anA$h_{9/  ��Q��Xa $f_{5,df3R�ar)t�10�/ h4[nd�ic]"�s0* iżto5X%-WM�:f�� ��pBnj$}_pq:� I$}+ 8nR8nb8}{JM^2}BG I$} f�m""f J�I$�|-sum"� 6 �o 6}!i�� EQ�E ujlB# $i$ ()ڝ%)>"�Eq.,x Yq�($j_p=9( $j_n=5/2$)&�25��\ �> *e E#�>(R a$)J.l�z�ad�<���}W . Fim}�q!}  �predij�u�v)G����q�L� �p u!v n=1$�z�- \��ev� *�~\i��MHaphics[width=3.1in]�:�~A)+ )� ��P� A���.  }M�� .;Perturbɑ�$�D p �V� +!$Bm"3![�N�7 >!�+ity�� �!���M�1.�o�%.�B� �$orIWo�(~ .�j�%iHD�/&@ |\t&V8{sFm}\rKG= |sFm , +\sum_{F'm'� \l' p|{�� H_a}26(}{E_p-E_s}|' N"� .�-��� E_p$f $E_s���8*l'$'s$ >��Z� �= |e|B>$1$}�{a[ ( r})"�-�ha"�B�B *N��."� x,X$\b�$�:B66 igR�xA�X�he2��S� 6�9B{&a��%�| �y!U ~.F = i % \xjSTrm Z}^2 R}{(\varrho_s  p)^{3/&� 2 \g*VNh���� a Ry�� F�p$s (F(F+1)-�-3/4)�_{F,F'} m,m'&� .%�lb4e5 x�=G m_e^2M> ^2/ & \pi=3.651a�%7 17}$, $m_:� �!+�5c"(1/and p /�n�`pqal -+um D�p��a:Cp$A#cn2���%= �(J�)^2-{�}^2}^2�J ���-B� m�Ry .Ryd`�( =#=Fenh.#A� fac�)Rpg%F� R=4(a_0/2 � r_0)^{2-2 �}/\xX^2( +1)��R_ eu�Q�)�a_0 �Boh0Yu2 r_0=*��^{1/3}$� m� i��F�0@�<g!�same $F�m� m�{ growC $ � ^{8/3}R$.3@D .un�, ate,q�)��& V =.�$& - ~i~5.9mZI�3}y�~�25.5) |p�m��.nR6n� -coe0+Aimagin!2d�a� �r�0�$y.9�pce,%* P�beh�!y $E1$�%) mpli+8$A_{E1}$ (Eq.~\�� e1})I09"�wo >jE� i�� *�  11�s W$!�a1 c.0johnson0) "W#PG'sed.h.nA0}X*]st^gZ5�<1]cyo-%Y&(MOT)�G����.XI�M+*�-�1�demon ud� aubin03a}u#ir �4C�- reliabil�2mat��!�ne�W �k!�! %. Ao��v:J �Ias�ns�PA�-� MOT �ed�mbe�p. loaALj-o�#B*Z& loc��/��ic �) "�)�� a$p5~&�)F�* � -�ly pump!:+� le Ze# sub��_:are a co�!�Rupe�u�#�!�Y�� Daf)pulA.f 2AR��duA$t_��Ctoly we-�R6 2�)�2Wi��Wc�6>�* �M%�*o*�#uf*��* (nA�lizI!����%�[$N$])p a cyc[&r*��x)R a/8 dc each sequ\$)�b�t:� \Xi_{��(=N|c_e|^2=N� 2�(A_R w���$)t_R}{2\hb��\�"� _+ed�2"A) $c_e"�:ḎH),�s � ande�`�!fco� �6�7�d�!e� eB��)�%nex"�U~a�O�M. �-��S�![+-- ))Z.!V%K)J-Im":'A�J* �S �simeq %Ćj2�)� F�5�a�15��Qb!#"�ce��Y�"v:�m?�{9�)�l�2 step*�z�l{� � ��:4.:n h&�a}$�*nApp�(us setup} .� ��3o"Q���naE� �54�0�`6"~�0C) N � �,� Pj�0 to a=d � $$10~\mu$m y a�%ѩ$ "a6nd� 1$ mm dia�D�r+el&\| . Ob�r����58ٯ�s9$d%t| �te�/ �,�o��aҁ>�3�w�< repe[aԅ� �va�:BRA�A^�E5 _new:S"̑"1/ZF92 =�� 9�$y$-axG�19��  iIz�� osci��U$x.N�,�2�2 �2@)  G�F<%�$z I,"&"� � "��9� i�)) re�8 %ed.| o . A IsAdp�te�n) �3Tm�ig origE�at com�+�e0� .�>AIY�U��"� %�B�Pr�8]��#� p�Nu58:� M" RF3$ $|F_1,m_1m$On��li^,A�c�7e!R�= bf B}=B_0k\hat{z}�eDbe.�1A�#o.���?^  b4E}(t)=E \cos(2�8nu_m t + \psi) k_m y)�x�e�1-/� j/%�eZz!/2,m_21/���:�$�M}$�� aligLI� !B�,�4�As q� $/2 �8$of phase (��a � ��1H� )In ME}$ s+(at M%GM3ZGsinFG!�IM=EA cgs unit�1Ti޹���i���;e)�I IG s, $% E}_{R1�E )�$\omega_{R}-�hi >�!I2I2 I.J+ YH)t + \JW �%xc k&� Y�e %� )�icf'Ce�$�$-�*/8&�;ly far �1 ree/c, aI)��)A�A��} =�"  ()V}$ASropto Ibf1sV!� %� 2}$)��% .ig��ndem�E 98};q%��we ign�>� tens�ar6���'*B bl� �6B�AfvGus�2a-6l"� "H � �"� B� 4=�enEd�< $� � $�v=d .!z th6.)�s:c ��>�6�E!@J1Mf�9�)�:��:i B�$at.�>�i� R >p�5 �"i8�GsA��Q%>ex ">p�7�C( pseudo sca��$iAt (EQ�(E1}E�2 ��dot B )�0A�>� 5�� . A��En"�Be�"r �? ���lar�#�=%"%R-!�'fer@�1.7 W%n���E�7ing�s: 1.�u6��(��$�]22A shifeh�9 ��E�iv�as&f �ETy��?1(�saa|:P�Ba��O6��E��&��!�8in?/~ ~r�O�1ct :y,!�\���\sO^+$[#go~to - vice�/sa ���-�:4��c���� ��re�' unm8�Eis 1E:�&)�%ir#�� ubN{6�$Y �2=&�6o �tic* ���  m"� O$arrow |F_2"�_C&[&��-?�!Fe. WhilE� 1(*w� A�muc—%D�7Ջd^ �2g&���*!�Q�� }+@�d��;by��B Xe.��Ush� minimiz� �l2�Km�M(f*_�IaF�*�1=pas�A"� sw(�V� $B_0��s quad�U+��)i�$-p����IRus��5W�� a$(%vHest�[ p ���. T��t �s} lis>1�d.�)PDl=� Y"-�!-m5ŭfK?5qhe� 1A�1� wa 6�_�s�=�J%/Fy�2, yR$-�>ter�A� $m_1 ym_29 o��ng %�qRA�B�o�qX��*R��)��oƱS� lU2ly beca�(i��Kar.i�i�;)f� >%�� d�?� e to'r��ap� riat� K .x)(%�2$1$) d��not)�aH#�X:�U'ce ��&�A" ,�Da �tsti�HeA�c@\�ist�  check���E��eaF�$ "i�ParM��!f� rele�� B�: Spin,�[s�# (Hfs"~C$7s_{49$�O~\�&ect&/coc85,7},Ff$\rm{m_1k 2C A�their���d$k$�AiF ��!E���!��mM .""�� {|� c} II &% ( & Hfs(MHz)ǔ� 2} y(Gauss )$(Mhz)��\� 208��& 7 & 49880.3�0.5&D� & 23864�{ \\ 209 & 9/2J430331& 0 & -1 & 1553.& 42816U1 & & 46768.`j�586.4Cݗ46� U ��569��72!#& 4334 �U2  & %3! 853.1f�3265.%� �9015 %�/Q\em�@&leg'��#Aw $F=4�=m=k!�!=5 -1$*9 �"&� ,a)�&e cri�el�w {0}=!�$ Ev,V'E� = 42.816&� (9+90(B-B_0)�#rm{Hz}"@"� �*�&�<B� |.>itro� @��to 0.06 - (� � $10^5n*T!?f� �� �C !>�.� dow�1$\Delta �[ 0.3$ HzBf �4�:ce� a� >�as"� 6}��� {; oOQ L�:LB�D regiY%� beG adia*V BimeeAu by%EPeZ��:I��+%:� ramp&�of hundr� � F �:9 � "w�Ru5antT.meg��A�Ua2 L L&��R/45 GHz (t"�mQ66$ cm�R6c�Jg�;e��8�kea mirror.�of $d c20Z( mbdau13$ c�_ <�xiu�$r_m=3.5$�sy+��combin�=  $onl~B( e Fresne�:m��$F_N>1=�0F_N = r_m^2 /�d$T ramo�Lsqup��& ($Q$" -is&�&u%�} Q�/ d{2�' &�/qFY �,"rskiMth aj�H��Y$�'2/� <0!�gma����&U�^ �-R�#�?du�� ($5.8�10^7~\O^{-1}$m$ E&co]! at rm�temN ure)%�sY�W�m$�'�$Q=1.9 ��5$.�9Uo&���/e 58 mW��e-�� c+P avail Z�o:\�@7 �(� &�(of 476 V/cm!l���2��X2&� %�ߕ�G�{�K:�]"�-iNOfy��=- 2;f ;�v!{$J� of $�S ���;T%9RI)A�Y�X A� /!D!abc,� f}|-�c��- r}.�.i�. I"6!�?=0.01i![N,E}{!�{�*!��?] W! &%3a}{0.45}r ] ~~8 rad/i��0e] end{&),A�S5Xt]�=� be�)jUa{!�� �M-bodyN�/�w"(D,porsev01,bouchiat�> A 1�CQ�ais��cA2p"�} 1 mmRC� 10 � &0 #'�ra��cu�XurR_m=9.9��E�� ��s ens.�&b�w� , si&d$( 1 - ( d / 2R_m ) )^2< 1u2p���/�Lco�UlS�Zg��&ofR�� � ��q)$3��{�H� c��5Cn����!%.< show�� Q[o��9se_Bc9�% r��# �iB���S� int�(.#(Ya�veL�!)�[�!n?>%"7s M.�]�=spi�l�(� EII�e �R �5��S�. Sign��bLr� 2T'& oc?��MNtr2�A�e)SA[�P�Car%V���l_Oa�� nas,�9on �I�. A �� a�}�F*'+%}!� ��0harbarth87} a�NmM)~Fa slit ,Jg�ngm�dees6�L6^J�!i � n byJXE=e^{-i\[ t}�[���DT1}{1-r_1r_2 e^{2ik_m d�) �B��&�bD[E_1t_1 (e^{=z}-r_2d}�k_m z�6)H(. F]HE . +E_2t_2X-@ Y12YX\�(]"�&)�Ea"7 �p7 r"/ refl� ��$t�A` nsmi�}�� $k1 wave-"AQ!�:I , $d G*� � �Iek%Asub ind�L �2��;�twoM�: �H(L )�m4�u�)M� 1 (2`  ex��Q8suk�mtyj �%n � ot�� )�� �(q�.�w8K.�;�gl�Z�a3o%z���g�?a�a0e�I�OK$$r_1=r_2=r� $t_1=t_2=t$Z$�)R}_{T/*�mUi� �L}{4} +i,_1-E_2}{4E_1q iI((i(1-r)+k_m�dI�&�2��wav�^5 7 vIu� midhch�m.M$� M� devi� %ZE�Qu.�� #ideal 5Zion. Ass-�g��4  ]YM �z �AK$F�!�e ^:m;&0.1�(��t{V $1-rv5���24�1� "t�z�QJ  compub C)*03 �H1�=(3+9i)._7e >�D&DVchoosfar-deJ".�&ݳn;U��Q$ "%/�V.�; !�.G306��it�I�%�m�y8'variet�q�t��tP"&og_wyea��sclA^red� s ܨ�-�W�ea�HA!�[:/E�h/W *��u`s.�2Pbalykin00,friedman02}%4 H,rє[.)��� �+"�1xinkI^*��cr�6�A�t[�=+&K �he7 al dz��z� ��* ��lbe)�� 46���$(Lamb-Dickd ),J& Dopp>broade�"#^&$r AC%�b .�*a�a}u%�($[<=w-w_e$)M�a)EZ5�_{HFS�WZ�xHly�a�(.+/ m)  E�ka�'�d��"� X � �'y"�2a� �7!ar off1cJ$zi(FORT�c 532 n[-^]!+��yax!����may"�F{-,Qa��7eJre�, four�%*�!}D &a:��U1_DSs'M�.�u�8;"m slV�' 8& 6)< f�%Z+ ��it�_d�@ut/a{o~/bl!�reQ6%I=Zeda��� � aN&J a1�t=V�&(!!y E)(!!  B�%)8& B2&E& 0_DN E& T�sNU w 2/^� /� 2*�&�2"�&N�=}����.!"^F i!DA�(/�%pag �(,-'B�c:�$M2��domr[Y�.7 :Fs"J#aY�M�2�ITU��onA*� I�M�6I s. A]�R"�(6�/x$ �0��Ks���'aB � Q�v"�o  2�&F  (#4M1�*h �!3 �'#v6A_FE & & Z� (-e/2m_e)%� (J+SMh M} |&�b��5 =7.8M�� 6Heft}M}{1.6~�g�B� ]{��"�v|" ���xxi�$ex�1`"�1�-��� NT:��& he:.(EqwK = 6�"/|e8 / M1} |�m )A ! -9}�suc�!�u�z�$�+Ų���/l�XyN�� v sup a"�re�y�Fn�jFig �1ion}[a]/ � ��� �9:d "�e-y"m2"/5��y�2)'>g���"B_�i�`p!�rt� y;��$\aleph=Y04 2 \pi d_t/\la�)�$d_t="W6!�� � ��� T� �~� {at�A) �4.UI]AS�=n�b2�M �J�-A���v%�"�4 (AAJ�3Ki/"a 2�� I~aI#b"+ �r� � )��FB&(7#�/  �F1$1|wo*A �)�!�Y4 ��&�:$|1 m|=1$ E1*A sh[M:�V-q�:�.)�Y\3� i )3P�}tM- .� in( 2i.sim  �L3}#��*�Dl�= :� �*� �c�3��$z��&j&58[hDJn&zGKsu��98b>:8�� ":��2t. (a) T\y a��xsitaaa�:���6PJ�H�R. (b) &�8Mi� Bl�� :C����h�'�on :m ���a, b5mzx  X�J��EM1I�ime spa�<s�, S1 doz �.���ny��-!g . (c5y1y"m9 u!�y5J��m>˓� !� � -��ag���,��},B�8Thirdn6 (c))|Ս��)�S���+�*!v�WV c/rA! A~�e�bi+7i0Mo�n����&�"@lE�\ l fliC1M�6S2�!  se���*0i4e�"�{�:��dynam� =� Hc%sI^ &�%of5xionzet�P ��!�j>|!��M.MF Rabi"�/�2��.1 $(1/\XN})�!1 �iQ^��Re�*�g� dt-�$_/�7sim 300�&ake�&�bI�3'.W�2%�x%��.:�"�to�@M1s q"\a��g� �10$^6z+om�i500�s2�% j�r2"�^s&]20�n�k� 9A�2 ; d&�M&�A�3% m ��EA:�O��%2.�&L#�O=m��E(1- )}"�>]"%I�� �vanxs�)a�l%�)Q�?�yn"W 9��as�/  �= bnO^�!?byV �ms,�ϡ�(e^t ��M�t�SeM�B�lO~ed .�R2S�4d S}�c!b}=2 A_�E*TE�ON}.- �to%�Fm� I$:�e rm[ � �: � �t4$ bH!.2Ii� a 3$.�.�� �n300% -G��-*� �J7V�� WLon"xP|K�'Œ��Y� 6$ s(,�K��V6e���5!�*E[�&%L[#�!��� ` �tE2�K-ǀ##n��4 vacuum enviroy &N,A�,�36�@#�Ws]�]%� Iuof�*in 1 s.��[> �E�)'j*byXfacili��y�z� T�z� an act%(e t>e�B% deli�.\x-l%38ͦ6�q ond ^;P! �5. 8]@%�"3benefi\om".Q�, z%�bR�KQf ��sXDeas�s{Ld!� ))!� �hgF�aD'ple"1�~m�>EY��ii�YA4. �'fu*DuZ~d?���in�+node-off&�9&a � �ia�te6�czg��, >E %Ac�in)�s dA��2�=�, must �5b� r!UF{$diw�a��O6x!J&csP3dBAMere|r�t ~�$�d�R# on{N�%jS&i�Ef��l�Y|��e�?�hG2Y`� �z�3�/ine p&?x��A�OTE-::�M��*app��e� �z= &� E3s. Bot�hs[(s (!unyM� stra�)�=�bacteri$��2 a/� ,*Y MB ing?@�B!�� A�N*�*� � ��9��,�X$)� >V (��$�+.M8A = (A_D+��11)+ i2{E12&�"�let%�gJ�eaI�PR1,�B%2!�rea� &TK�%?=H��1,��&�e�o��V:!�D1,�6�V�H} �9�E�i%��Fypan6� ��*O-6#^"@M�`� ="@2�$b�thA86tS�=N e78E� |*[% > :+��inX. W���"2 ��cATH$).� maP!q* 7E"�V�K Aa�� n �_��O�����io}$�)!�2n Y(� l# �. ;@LGiK�%�!!� ��+of.�is 90$^o"�)1��>�3�!� s a �!�$i) �Q�2�. I7+st���M1-�Y�� Ave�*T"Hn��6� 5�"� tA��J�*c;E�$($P=A/|A|$"�"e;E�%�9�E���9ys` $F_198�=�0H" $F_2�0�s.9�. &�D�� �!Z*{M/u�2,t� ��nQ�� :&@ $m$NC<lr  } Re�Dal & m120<P�(x/<Pe. y!j /R\\ ?<N�U�:0 �;&Zd & _;6$i�41P1*"<8 & $-&&+<:I$4n/;1_ �)mN�I7E~�b5la*]M5�%A �� R1}=�y�"aAN6�NQ' "�L��=i !���x=  wo}�,I�%] 7T$ �;�'��a( �)"�Gr :�-1=�Cs��S�9�%M%�3Ex2<��E"�x�nd:(� �!7*a9 * x ��,"\�V�3����}�W / N�eq�x�@,)�t*{W\�) K,12 � Z4E53�4Yef Y2%": e! X.B���,FqA_W= �Ex� 1+ m4=U ^2}{2 �}-1} �}: @2h=�B)"��B�!� ef}$@)���� "Ex"ad 1_>A_@zA�J"�'$U/s�t3�5*:/6Cet N�*A��Y�K��&`Bgidentif~<*\A�&�%�"� ea$t�/nA�I�5)� �+� <N�� {t_R%�-�})�)�.O"uM�f�!<%}r9^*�W$ARyME�5, G*:!5�r-�"�%&&2^L {Z^L)�-�y�- ��$�tp�X%�Rx,a��� � a6e �m���a-dEo \Mix,Mi��!�>� FLS� bR��Rox,Moy&#A�z=,6 nEQ� "� B"� �[ �il�toward�?� g I�*� ��R�7e)ɶis �/ B��M19oB I.d���p�o�sw1$ or 2�OeC!R� %A`d�!�` �-e�E�kakJ :�M(��:� E1"� IP*� Ai�*p�-��kr�9�)ud�p)g=0,\piPes�}7�yA�PNC2�1}@ Ah>�)Z2�\�i&�)�m�|&�:in7n� �!��G help�G�e 6��unw�1d���H�_ rewritIJ�P�N�u9f�� i�RA !'��r-�..'���'�٠�u[ŦMox}^2-.(iy RV�6 Q+s�!�a�-2�x�Q ) +\��( Zaox}) "17�<� . +s 3��Mix}-�d ?R>�J& 7psiY�k &�nThey "[%�7��If�!7B-I� 2��p���>�� "D�|�4~T!�����ecg�!F3\%nAF.M%�HJ4��pw�h). Each &� �U C�J� F 3 }$ W_j�+iLI��som�!,�~ ��� � �&Eq-"� d+W&%� 2�+ exact.�4 a $(.�"|h�[mk�"�:�[� ����A_sB{ar�U X to 0.025b!�=Iish� t ��f�D!� �# ��Z:u-8/� =121�*/s�_$n=38$A8��proce���U spuri�[)�J�e��a�2�&��auz&�$$�*��C�$}� u4�B!���a> oor*�y!ri�*�+or- ` s,i�"� h #� �6aB� gy�"!��6a�)��Ea�I�  =2.7-r @m�d�E&`8>!*t'i�0� !a�{11�CoemaA�s`F\B_�Io�/�al,-m �%"(�-�& �kee�(5��-v �WB�� � n;:)_��#��I� Q� .�/ sim$3 mHzхis B�:����!9Npy��v�aal�"�N~F2�];(ed?3aB�_)5aSr1��9BL�; "�U&2&�,&*)ej"f&&�;5iu�O'��mc�!C�m�|iEas �as 4.4 � been� d�X5Ua6�9�y# davidson9�Dm*M���de� q�A�div'sof.V<s fel}�)���X ct'm2� 16�s���n&y"=in� yE�)�Pser2#�:vV&�&c1n,��q(i�deY�0�sslowl���-1��bP1�&>eIh#(n ``echo" t~!qux %m�s��. r&�; halfB!B!�!&)�� �r�)F�)!� $n"KMn"��e�,g�^to�H9�Ba� ^�<t_R/n"E4�o�:�@�+m E$���q�#6(s%6 m,�ᜥ�� *� Rof�%~�i��!RI�ed' m � q]� u��St"=?#�GR.�bfkTR�=/h=6.�S� &[ ���jQ�"�"�.o�i� P;ra.���I\y�Et����e:�"aM�8compensated by �adjusting the microwave frequency. We must control )power of6dtrap laser to 7$\%$. \sub@ection{$A_{Rx}^2/ dy}$} This term appears dueC4a bad polariza?$ alignmentu8Raman field. Co � �2: 0 0c�one part in 10$^3$ would be necessary)$suppress t�F�(�Mi�$,  oy}^ Rx}A_ $,  )9 These%�s are multiplied by a small number and their %�ibu!(| becomes negligible. For example ��~ ha�e dfactor�Rx%)�A--�.i mis9�inE)vbeamsF7! Ry) yf= %Y!A$(he dominant% 8 that depends o lM1A�nsi! . The M1I" �UaimperfI�s�U� cavityI- kcreate abvel!a' componA�'mayAAin or ouA�( phase with%E2�H Eq. \ref{standingX} give%� !�itudeQ�tr.� expectedvur setup �6*!J-�ed alom�4$z$ axis, so w�n incls!z 4i�qionQ&,of $10^{-3}$a� mbin!!tI�woM�s9�for)!�tr1��get an*8of $0.25A_{E1}$-_ 6_ 2_, a&� (y O7O.e relative /�between both antennas ($\vartheta$) can be �Ii�minimiz-A�.� wheI�8static magneticIq_bf B$)!�tilUslightly)���aymatch 2fremains olled%m�$<0.01$ radq�i{System� efa&s��e sB2(��%� last�aenAiY�psipi}�Hy change sign under)n$s$%�$\b!h( reversals �� �� PNC:alN�straints�}�S �S4stronger since8y do not averagŀ zeroPi:^m�be belowA�03Q�,to reach a 3� measure���DHproceed to analyze 0��ɤ�1�ub1��*�Fo�*RBbecaus�,a��bini�of 2� s ���a-J$� (or �A. I6rrespo��to!r4 observable ${A�M \ti�� (E}_{R1}  2  ) \cdot B�l&Ais reduci��� �.� ���)�itm$�C"�I.HV���o�&=��ox6��^, same originQ�previou��e, but� 2�i�0siderably larY�it A���% V%��\limit����� preci��I&.�64ol��� letely on��,mea�is��dmirrors�:8have some birefiDence, which genera� ��:< $x$-����e�Y�jLke roughly 1000 refl����E> �e�ne�.2 ro��on� � han ��Ta )perhg 686} 8to keep�M12Eun!Eged�A%���JyA14 i]� er��atomicA�pleM�%�to��I!�held at�no�%�^��< maximum displac���can tol)�is $3m�B11}$m^�q�)�{Calibr��eIE��� i�waT�or�^al calcu��on���@ ("� (asymmetry})-a2 directlyS� �&R�S!�ert��ymS��-is .� $�G� produc@ n=leA�r, �a�matrix�pab9�65�has��be known!�Ž)�:7c ��� ��A �2��induc anA�&� b extra �jinforxon ab? V weak inte*from an� ri�al�Q? 1�t input~\cite{haxton01,ginges04� qual� ��) onic� fun�s1�0most importan�jaccuracyE6�s � ec�1ar��a5�exp �%'� ivm� �$anapole mo�$$\kappa_a$�obA���fter sub)n� oth��wo6 t��s�H {i}$e � ]Ttotal}). Johnson {\it � l.} show !�c��_� c $of Fr amou� 4o a few percen1�j h03-�:�- even-neu�  isotope�e�lyI7�unpairedaeton�_l oddNDn!H:&E�JOE� �. A2� �:�Ett!��F\%��y � itial seA3�M� .+sM�(flambaum97}:6O%�sourc!f fluctuS��8:]!��y�E4)�levels�!@type $\Delta m=0$%m% (re non-reso��a propo�:{(detuVP$\sim$ 0.4 GHz). Neve� less,��G "Ks will.� take�AnccEy�  detaile�Taly� -�,data. Stray���sADw  Star�� d6a�mimic��r. A� BUx13 V/cm�!H���:�����e��A]A$parity vio��ng"5 �� sY  enough:b�problem� unlik to o��E�c ignoredM� demille98A�Gradie� �e hig�}or� m���=� , suA)s�;E2*� tunal ,�s:QG"� the ��hy�(ine ground M�A�ly"u j ���t cov s} summ��m resulx�� IJ noise%/FGa�begin b$} \leavevmo \� e  \capA{F� � tabiŶ�� J �L*} associa`w����U is also� d.} �4ular} {llrr} O&� &�B(& Set value �\\ \hl!�\\K G Q & M�]�& 476i&y$6<S & � &h & 121� /s92.5Wq 4} G (\hbar \d��)^2K�" �5�xLA1�\\ & DiQ�p �0shift & 6.3 H4 0.07r0C M62 (& 1500 Gaus�4.72�5 �BRx}� �2�& 0��3}^ 2pMg%q@ .]&��cm?7:�7 � & A & 57 mWz.02i.#�{�6�8�2=$12!�radK & T�d.v v�327%�m \endawE� \labell2�'le}� o(�":�@provides a uniqueb�� had_ *� s. In �i� r�se��v�=�-r<m�F ex.- s,�s���� allow�� : ofV �+ ur�"nucleus�D�sr�Z� in��-energy &� s�r] �.� O���� ������ ".C� at��m�/� ��enZ��� a!�l&�� ateg� ��ar spin��!�!4VPNC.s,�ub�6 . Whq &��method�W$ endUod  alkali�!� seri� F%�a^in � rancium " M�-�]ͻpr %�Eon�*� � ��.� . AEeytB" � foP90,pollock92} studies���+ !�7� 20-� physicE�eI�}ku �E�!Bi� ten e me�v+b}5e coupaV� s, eit��Ga>�� lism�fca�DDH�k� )de7 nques80},Mmoraly j��� !�oA  (EFT)-jzhu05}m program!�2)-�6�  cha�f F?X u��ifica�etoA0� g�ers toge9CA�EFT �l�N!`odel ina��!i;"�.�5�yF5����not��� .:�69an�e?an oddqw5LE�almGorthogo� bande�!��UtU� space��subjectu� ssum- "�!�-Warr_mai#b��eJonsM�*R�as�n5NR"l anomaly I�(grossman99}a!q��reable� ��ese m�!sIsig]q]�to de our Ta�]!!Vޡ�tr�re� �� *{Ac ledg�s} Work or��,NSF. E. G. a/es% CONACYT]� hebibliA�phy}{10Pxbibitem{zeldovich58} Y.~B. Zel' @, Sov. Phys.-JETP&@6}, 1184 (1958)n Q1�,84} V.~V. Fl, I`Khriplu,4O.~P. Sushkov, o Lett. B r(146}, 367t842tv�(95} P.~A. V�, D.~M. Meekhof, P.~K. Majumder, S.La��aux� E.~N. �J�Rev � �74! 2658�952�Dwood99} C.~S. WoodnXC. Bennett, J.~L. Rober��D. Cho�P C.~E. Wieman, Can. J�%� 7) 99F|7r|mB%yMasters�6��Ey Tann!1`� �Sci1 �275� 1759)72�dey,anko02} A. DZ(S.~G. PorseU%wA _6^,052115 (20022^}� J%wGm�, LE8Orozco, M.~R. P�# �$E. Simsari!q0G.~D. SprouseAv�$W.~Z. Zhao^83�935 �6� gomez06} a� >�dy y$ Rep. Progm�% 6e~79 !6)2}�i~N� _Y. Pan� L!�leAzIV%ietg%m 2857a�902f&@  S.~J!�Q fe@q>VlCh a� 258 h6��$ng7I�E. LovI�PA, ~H. Sanda����� �3�A�5 (1976�gor�m88�� G. G , V.~�hzh��Mh Kozlz,A.~I. Mikhai �#$J. Nucl. -PO48A8��6),budker} D. B , � {\emD ics Beyonf ��0d Model}, edi�( P. HerczegA�C�� Hoff�?�H��hKlapdor-Klinfrothaus (Worldi�tM $, SingaporE�199:�alakin80%: E. B iS%\22\74[76�hindsANE�HW,V.~W. Hughesq� �ML6�n48�:Kadelbe81ev G. A, TmT""or,6E��upp�� Holmgren��ZAOIqbal�H� Swa,Aq� str.�Meth.Iy17� 181��812��&3} �#�> 7iH383K932Kre is��MEeR �2 2`��5�454%Y:3chin01�� China� Leiber Vuld,a�J. KerU�S2u q � q 6��03340!2006(angstmann05%� J. A%�H. Din�%dA92���.q7A���08�� 5) "| + 97E�K%?DE�Murray � \�; 5� 1641A�:mk&e 91} J:�i� Non-Co*� in A�P Phenomena} (Gordon �B}$(, New York,�,6M� } W.�Ha>6G Annu ݥG Part.��I� 5�361��6hlewisA�R��L22)���410�m6�t W RZopera�*isF � $\hat��ha} = (\pi e/m)~[ \mu ({\rm p$r} <\sigma}) - (q/2). p} r^2 + 1$p})]$, seew`+$ Ref. [21]� .�/a Q -1/22�� Lag�Dian $\mathcal{L}_a�,a/M^2) \overG@{\psi}(x) \gamma_� 5  \�(ial_\nu F^{"nu}F�  Er�"��MU(& sey-Musol� r .in%~5� 351md. &�A�R"E�bSAfronova�dU��S fi� m67� 062106� 32saubin03a  A �� �� vI� I��umm u 4342Nw&TDeM1QG*�rXiv:�/9801034� 82�coc85� Coc, CA`Libault, F. Touchard,��T. Duonge  Juncar�  L����� in2J�� rm{\'{e}}!�~L. Vi�8D B{\"{u}}ttgenbach��C. Muell�A� Pesn)�A�<{ISOLDE}~Collabo�#� LU�� 163B-66�U1986/coc87��V�M. CarrI� Lerm >%b A� >)>�NucF � 6� �Q1986 ramo�PS.��  Whi y)oT��Duz!��NF1�� WaveR( CommunicHEO$�" s} (�! WileyE�So@2R6[p..<6� .��$6�$ 064101@6DbA�iat�.� [C� Pikett��2L26�19n BrbarthAO U. H A�, Kowalski, RY u{e Noehte, K� heffzek%x G.~ PutlitzG ��ci �8 2� 40�:�dees653W� ��ASheppe� IEEE� .stWas�� 1![52�66E balykin00�I. � ��Minog� tV�Letokho >�3�142� 20002�f_mand� �@ Kapl�mN. DavidAdvan�""�, Mole)v Opti�'!l� � � 9 �6�ko�A|MeJAw.s� B�_ Q��04540e�B� itane�W� IA�0BergquisrJ. BolKa�J/Gillig!D�xHeinzen�aF��Mo �G�i�0 Wineland�d�+-9 3554�c:�d-��2�H� Lee,a|S. AdazM!Hse� �J� e� �� 1311� 6�"�'2-G�'�6�"�pM�39�63�N6�6N Ba["`^�RDonoghu�B� HolsteaAnn�� (NY) �12am449�:=y��Zhuf Maekawa6ep ��&p �),U. van~Kolckol �Q�7E�435*x �:t  docu�} �w\4class[12pt]{io6 } \u"ckage[A$1]{senc2{a4wide6psfig6eJgraphicxF*6amssymb6verbatim6fancyhdr���wtitle{Te9a�deV&a lens� �(�[$pp�fluorescudet Zof�in�ns�4home-made diff�$s0ew%5^e={�/wa^'�in ;i}e #L+v-(been used (�05 al7,2s)� seve� �arT0(roups (e.g.�&3,6,9�*Our1��be bA z): focussE c��ma� ; beamba=,length!&$\�0da=830$~nm doz-0a narrow spot�jXf2pl6-6 O78O) emit�fL!rubid�A�s A&u�*�1isl. Useful%�sv]�8 & 8\4raya �-software-@4i+}, shear-wav�tl9roQ�*ii,iii})�ima��!AOvrt*+}a� of�$ystyren�5a�9�! very�0 siz�11,10}. ]�6.��,�,co��#!&n!�drawn%� �O���`y2 C{I�<�/ion} In,#s �choicap"r�'%w�2(y decide up"M3c�!�1�%�"e(exp��or� 8.�5=�3dis��1�>&!;(Fi�4�< 3}c)���6allA��J�%�;��o�` radi��1&point-'-b�[le �3 ��xJ in a Paul&,p��vb:In addia� !�'+�)ihigh NA��*w`1t1r�35mAY}aim��$]�  #A�-� 1�i.&lEMis usu%4�+u,o;etup c�'ly�z�"ru�2�A��� 1 % scor"�,q*5f �v/l0@�{�=ld�%�to�-�tr�?`>u diI"��i+}E�.,M"er �a��1!�\B far-�/A(��!�neۡ�n(�3t"�/ id8�!�4"g?h.�6�6 ��";eLp� poten��b?'6 ��< of s*d-�.�eg"�$�p� �&ory h0 !�a ,�|"�.>es (``acXi"8,'')M3ca�Aa�lofeS!�a�'1�%��B,context, two�4 ntit�&�.of�1E%terest:�-enume)} \�"%�-?9* $U_{dip}(�bf{r})\��to\� {\G�}{�1}I.)$Zsca�2�u $ 9 _{scN](R^)^2>a��He� ] $ dea=*� E�6�5.70e_nd)� & A�exK6 ,�2x5�� etun�Y�:$6�+E��+��[�d2.c�&eB. scal_,s $I/)kvDN��f� (+� �s��5D A��X�f)� "�:>�asY'� ossioD C�=F tly,�q {) ��=���Eachie�;uffic)2e�p+EOne ai�(�e"�Hto&(w3(ini latt\ { upA�!VV � �� � cus7 ��e<oK'� *� T9Ed  fi�� � rm�0j�!�h� a�ա��_ loa�+�'� -87��s�(Bose-Ein�a� dens=n�6b!TTE�A��@$5\mbox{S}_{1/2}- P}_{3/2�7D2)�!�ion; J _L \A9���)� �ui} ��A��;.� @)2�! * � *ii�%� M@�O@ D2.� H] w� %� �as well�I&� !%��%�A#� unvarys.�M�es�).R$�  I9au+Y^!+J,�i+{oZb I���>+0a cru **�:3A&E��i'a �ou�5�. &� 1�9)�l0@� eJachs �D@ aR�Fr7?s. |H�H��t s j B �9e"� ,!�Lapply Rayleigh's Cri�-on!p�.e b7is��qu�} � l=1.22�:f/ }{D}i,-nd{7wh�0$>6/F?sf<sol�BF , $f��*�-o6 Y�!�` �5�4 ]�M*l( !�$D$ di-.&{K� ����C!�Yiwe� $f=� , $D=25.4� (NA=$0.27C��9(=1.74~\mu$mJp.1xfigur7bI�.R%\�0{file=Fig1.ep�- idth=0.7\�} "�6PY ! a s�!�of^� F�!x� (Comar DQ,1^{D�\�mA��� u .I"w} AEon waD �Bhe0�A��� m��?o��=�d � paM� indispenst�?l��1 &&a� 8Built-in routin� K �er��<iz��(PQU�W�Ւar�{.1;�cair gap&;!� es o"1VvaA� � urfacMFs��.ms vy!�=b6 �ak ��pu+1e>�ra�0�2%�h�02basic7 rpre�aa�^u0U%p��4 a \emph{referp }�? pa�O��pp�ri* � rior � ���aya(f.<#1 �9r (an arbitrar%7�the�Can ��gL(algorithm o untibQv� a�~chosen �.Y�KM!5Ct�;�ec/ !�e1a�C stop-3sO/)[� fSK4n�?�?o!"-ord\"y.� star �Za"�)w����!��7es-�dyE� B�Mkin�ray�P5 � realy��7ir� ]�r�)"�Y7bey S�"'?w�%�E�XKra� aasxieNAed��!a�x���@$n(\alpha)\  $"n$1Ha�1A w�n$E"�?m�*���N32�p��goo>Rs��PclP ���axis. mw� *� r"@m2ii����$ac� H7�&ar��!%behava}� �Rof Q? ��6��9BG!��(�h� ���f�<�%-�6|$5l��valen 7 �%T�%�e �VJ!m�e�A��<tal�?m6FM!m� a fa� 2"�F+H!SP!�principO D%Y� �b��i�5}�� 26� 9> >� w��of qu�f�&A: (a)� vec�*(DX,DY)k depi�?���� cept��K@7�HrE�a|)�I".P$(FX,FY) (b�ve.�$&Y*QQ'}$ ��7d a�b��unik�.�&� . P!��eI)��D5$ -frey�Id%$Aian�I� ). Q%�Q'eaE��%9� ���vn a�Fl%��jb^Z'�i ;��*pec:�SP'� )�.j@2r EYRoT A�A�F} RRnd�� path� e ( (OPD) eval(�Cus�o1�]%9a����i��Q�2U}ur�ai�in*O2$t�IU� 0�!al plo)�� fans.k 2}a)�&�3}��3Fcura diI �ٕst:&ofI2P� I 6`Q�B\:nAY�Jof Y�ea-&,;lso:�Vfir5Ldea�b�Lt)IA�U�v�Rng�g�#d�I� ��>%�� vidual=�!) shap�6%(A�b&�4sco! is p��*�a� � u4 ��t:<at�^d%#d�E "�=� rootApn squA(RMS)*d$us> gma_r$%#>u!�is�re� nHe�*[w� .��i �OaHis de2Hd as:")#&0<0_r=��1}{W}\sum_{i=1}^nw_i[(DX_i-)^2+(DY y ])^��%V�sum exBs �/� $n�E� v F@, $oBWm$� � on!#!RA Yy ́�!���&YM�XB>WR2� , $ �=�N_�\h?{2cm} a� fin�a/� �be{ edA��Ainv�g"� H+^A �C�!darv�� �-�Lvљ.� �cs��a� isto�?ora�ormwy?� ��l�_an"�%0/4$ peak-to-v y (P-V),' $ beA-th>�ye�\-gr�&�(*�� ��6rul�T��!^ be m D�O�ex�����V }U��ed RMSC a#M�a��x���&/14$ \c+Siv�M��3� �],.�aJ�K2� nd r�o{�: A�o-convex�,� nVed�c)�r����!mV (OSLO)�ru�%a& A�-�20=$1/e^2$-"�A�)�d^�%o)���e�eMo; � r a,biFA�$+ �i�}� �"FW&�,m}��ms.:�\ed� 3~� � on{L�)w � �ed >�s� th� �`a�6� � n�n�.�V$)�gl�is BK7%_R G%M�Ere "�Td�1q � �V*�0b�Ko�F�%�a s.�#%�2%�(thickness) ��� ]���4ray-t*B . Dui�* cedu� 0dii=� � ���A>ix� �wOp��3��[# 4� asMi�%O>��u ���~c"gG� d��U� :Es�to }+n+r�Q!�third com/ast� tism. O��.�� �5�. ` ons,�!��� veri��2Wm! ��j]0+ .�' �Z�2�a"TTE��]cE��T/%E� mvG��*u]to} �!��'W"ith�&bratu�jnd kept�K�� (lu�Num4Hr Aq%�e a�eSlQVYt $(in mm): \j,$R_1$} flat,4$R_2$}=$39.08$3103.29.4-W5 Dm6Fm7) 26.0WV?878.16�Z�"� -Oand&#!�:�a�.�b}=$7.24�c}=$4.97d}D4�e}=$5.12"f>"g"0Dh}=$21.� i}~(�� )=$2.8j}=$12.73$. All�h�2)$��,��E"F#M� n�-!!�-s"0s&�bS����f�-} bI=,u �qAv� ��"@/e@&��f�=,@is fairly simple:N�!�r�I�:$,>6 A�E� �`([����3gl3$45�MbR h �. quitcj$ l�a"K# wedg���]�gr�#>��f�� backs�o�!S� te. W�� ܁j UlapS a sc� hy�b>ar �a p�'�W a�B_1� \GU)�� tern�$�)s� "^O� s�L_'ram ~s�non:l�0i=.aDLy&�-A5��1v!s�c ��rot�1w.r.t.-z�6YO~�I��� u\� :E�,yk��;-�"~ ɒ�e�1!��� �i6��s~*�-8}a-c)�FnXc� lookA�- )hT,�fu ?�-� �magni�jap���m7P��BB�  2 . Fu�[r p�c�*� �J�F��_c$|�(|� ��,��' n](�Pll�e� % �V&�. A a $1�" pinh�Zo=\ *�%ffQ()%�z�%us!e�� �<#%n F P-V�s>��Oh��"�i}����4V�2$dB�#[h]�N�#4� �mb�# Stud�!&|Y$ . Left: mRI sketch� q��Zs� <noB� "�4$Z� A� .*� r. Ra�: (%��� meas�i5�%wp�^*�6:V9T rtes%\Urban \& Fischer-Verlag)"�X89pn&-#6�8e�t�� A� y�*#�{ tA��* aDLA�A mag��2� = uu�+}� � USAF�?1 �T�htI��W�nI��/l�0�)[!��/i x�2�廁�ts(�Hm(=a� et%u�ali� 3��">3|2by i� �Dot D;�G � s}, �� &�a�"��5�d""��6rhi!�$g��W regular a,. ��S Star �}�K��@sCnd�N se�R�& ��!�%�2� HN+�8uplE.-fe�i$M=�!b�$�2 AL!�a2)ha�*�Va CCD ca�0MYv)8. Som-tho�:r �:�!uf�I�oeń&5 4}a we il ��0 �wl!�Z� ��, (few $\mu$W!� pow�?�J&�9!via9dA�to�]3�25�h�EFL}$ a5!E'�� @*;-ere EFL"�'(�� -g��(�6). Eve�ou�+he �E��a�� �bl"olt/�q0� �e��m� (�iA� Li�e����a#�.aC!=ing"�� &;&%�t�2|I�nsh�h���0�4m�ɩ�&j*�r criZB27 �rnm"�[�[.�ed�-IC9NANy'cs� .+=+�i5�i1.0Rx � Inve�; u���,g!qof ��R70�i"We our9�� "-� tQ�4./,. IJY.�! oA�e2H��ve�l�-!��%� �"�W�.Solid�:�rp step�&NB. Dash� ne:qvэ%4pixel&i!(� l;'eh2$16+  �dWA�wsq<Osh ��7!�get�+�-�gw+be� ����1eI�gY%�{> ~25$��~� �. ��!)n�*(�� link��a lear�I.��i":4}bAw��f�`�jO]�?a�� �:�s�4~�2czA&:} An obluaa��w bundT:n_=nt�� �4e�dlP, i.e.)�*�/��f ��sagitV�$ �� xe�if�!t..h@��� ApMun���7��% (or,���%l�'i*�f�����e axis) $<\w~$deg� �aumhza�2�)�q��a0&))M��jhorizDkl%��ystrip&��e� ag�vt�vu��!� *� 6" �%�al%&�/mi[!u�h �E��@-.� c. N"^" !� Yian�}#.s 2�c�njMe�a�M��� A�]a��t��f�es�  l.&r(<nc nhɀ#%W_!�&&Gae Y�a /%�"A"_l � !�al:�}k��6�F�Lmview} �7͍�4V0Y86�%�spU1j"U �6er�a�`ofaZ#$1�G >-iє�_0a�{8�6U, O6�pod|i)6pc2=%r*�?  b��(́.mq"�>�e�!�a�1��e. F.� ��93O>-��a�� �to �|d�:��A k6���*�f� 0pV&<ov!�avd ��&�s*g affi��A�o�66ZO!q.� (coa2e}�6��C�&� �.o��C&?��w"�e9J�Da+sl ��ly/���c(V.T. F�E�+�4E�,�&Ks�Wj�0�5��6}b�~4al�k aN aE ��1upredi.@ya��e.z a�*�h (�Tabove�M >�� "�} �-{A#!l�$-� �g�>Qa*� mono&O8r emer% a.52�1prk/ "� �p�&�1on�bI� �� 2�"�6z$�?vi�A�!�� O"& ��e�5 los��� 20�q �!n;���*��npf<h=]{�s&�?>�8z \left�&f}{a}\r�x)^2�8�5cwJ9a2r&��5�-~A8�9 ��# is y� �'rz=10.", W�8k*�BymGQWz� �A���.�6}c� simii"�0A"���y�"�2�*a�)c�a6�)c�XQ!'�� �)�.�6.R�qz*ٙ�� �=?�$ila��8a�e�9.�����";_ �&*�#�h��!�� :��Q� i�hE,,as�4� + e�nbv��a�o�w %�spr�!�)Qed�  .�,�lf2 (so�,.9 ).lS6�$N �v�^!�t2+. DJfMQ �����L0A�>; up6dJ�") rla+o6�1A�n*�:/ResS}�(�-�2��*e� *��ob$�o* bU�2u� �mpt�s : *�mT "�, ��d���!w�!�a!�y broa�ipe8$ao5O~),8y@I�HZ�< �1 knife%�� l��! �)!��2�-�cr &�� &�w�� b nvCnsu�z��a pur� .�}&��4 �/ .@���9"�D E(x,y)a�"��FraunhoB.k�H,=u���oR�-m�BE}`=_0:,2 J}_1(\��)}{ }\qquad !��({,2S^ aq}{�6 IE@y�>a�AH|Fx�,y&�-Ca�2.�3=��,$q^2=x^2+y^2U, �_0�,Am&�t��1wal�-,L^!".?B_*��m�0�%, $&�8Z��$IQ �"/ minuU&�*� 5� MoreH �5h�"� m��Ft�|j o,F U _fxKED}(X)=[\int_{-\infty}^{X}dx'~> dy'-.AY4',y')\cos\phi( ]^2A a�YB $ 0,y9q:n�=�LC�U�� a7 phiM�A�q^2.�� 7}N )eF�F|BE -$ (�'K��-Edge��2on'})�:7 e)č�one-d�O �t6� ��M��aAeA� scan�?y $X$K�؃�x�JDj TN Eq.~�Na}�yJ_5}b9 � s�-& (�vf��s@tno &� relev�K. AE �:��X!��b�c�/� gpurpos�O!KED"}�a.z�>Nbe�F�SW(�1oJ* erf(X/w)MXAR sqrtAa}}e@0^{X/w}e^{-t^2}dtI;��R�w$*�(,)�(- $-wa"�#"e7�!Qh.2�E��?n ��)�1})zM���aI�O!� <%~�/��!T��)b0ofY9hkTC-*F�&�Id $�$. Af�Zc�pac� l$�� enco�I��&�<�=ii�� -�T& ANa��%�Eo#Nt���<$w$. W� �%te�a}yK"��. �pW9"� (� �S�� fitE�S QkQ���reb�-����D �'h mula!6�a_��A�?9bV�R-�=3.38w}{I��$f� �U��� bF�h�Bib�Bq?& sE ch� A*�TB�. o � hig�%;#"� ��0E&g �"h out�4%d Airya7kZ9.1S� e��:�in��($X$)� 5.hB(2� a�y�C*NY�b} del�Z��ne�I;1� �%�Ft����r�G�� E45i=%�"<5 R1.wcaBAT���]�o�*)� iΏ!�-��)Ӌail2fCsc( !JQ�$�� hx@ F\:Kr��a�9r{iw0\Lambda}{1.78ύR�B9�  $ ?$2�J2=(7iJE I� �nEqr!;$5$\%A�Z&�5@ I.�5}d@u1ulp9��!ms ("� "Y"�b}�4r�e�}"K�Q n ir �att�od&�*p $ �E1e &� 6 icts.[MBl6tΧ7.�j� deriv"�IOl�&� �!c��A'E|B':Y �Mapi 2I�j(b)��eIgGo} 5ra}EWA ��>`s)suEO���w.��o�e�EFR"T3of�[t�ov*�xEJ&%�25. Du�H�m%05 ,�3%ab%��� :�U%�V2�5�V�A�f��-%��]n"��\ 9� !+_;:e�ɫin J �AHblG^dEl��of r (F6t*�V�U6�.,!�A ����&Q;B�d780~$nm,2�. �N�6 ]X�*s&40�Z. B�"�4Argon-Ion $488te�(���U�A���%�,aXm�)D ]=2�ZP�& �]�G7-8��  a .�/*�w� A)��$ �I��A=�E�6�o"b _. 9� �h� 2� 2�m�3L�U�dl�,haR�E��;WmN�(2O��-� �,M w)s)@Vb �� é�2�#W*�)D'��H� B/*%I9!4� !U*�Opm�wo�Gcon�%*i�� &5 �oas �$46'� W�;� B�?� C�!n �<"�!9�mB*k) �rel�=MCtm �a�st�>!��&�]ɴ2: ,"��%c��GCkak,�)l�� ��,8.9 \N XEI&6h�h�vE� �>�e�edOQ2R �S�9ght2c�`��Y(*+)MB�� -�! (fv���M��n� ���av����IPe<=�x-~,I�2� � $��o"p "t49b ��eJo l .���!assemb)QRF�k&� "I�an�=3wg��* i�N\ -"20~$m, &-72�^v�i�4ў���k�2>�@! 6�ks��y�] )�t"C'a tE�� *S'�c0��2� MatY?+�=&V(�mn�2�Frap�h&cov�A�a��+�W+:forward��a��`1�n���D&)�.R�:J�k��G�B� ed.2I�m�3d"�Uz� easil?� adop�!<�~!8N"�kyVED ŅaM�**��eis�nac�χ��(ngZ c�m9=� 8 Geoffrey Brook�(nd Her� Crepaz,��. �A � k Ri7+d�s ry's6dp�p�ruM��Ab; �"ll��/.)1m help� �ork�f�9 � EPSRC�5 Re4�?c$> r{+�&4i} Alt W 2002 ؙguk|� 113}�u131\e 2003 7&7u}�r 67} �3@(6} Schulz M= tPhDA�sis ``Ta_�!�)dm���P}ss''}, "9q4\"at Innsbruckw9} HanL- J,y4�yC2*&<ng ~ Mo�b:�)Si�=Par��qss�Me��icsAM�kBody QT$um Dynamic ��$�(Tex"t A���i+}#'��H LTE ZEMAX'i}��8ty M V R K 1964�uit Appl.!�.-�$3} 531-534.BHi} Senthilkumaran P-� 1995L2K(4} 1197-120]$j�l4e:a!XP>7. :,2:�.,H, �4�>�11RF-8848 F:S�ne sulf�micro�F� �PMFx Probe3b)�10SM8 K@�fc�Inc,V 8 vi} Neu… er W5*80QWyDxu 22!,37�i%(Grimm R COy CAdv. A�yo-�ic-�42} 95M5}I"a�cs��?Manual�,ee= sf �,http://www.l�res.comV iv} Mar\'A�l A 1947 �gxd'pque �26} 25� 12} LENS-($cs GmbH, Fb4Tnweg 14a, 85391 Allers%Sn, Ge�~Nh� ens-�s.de/�4}���*w ,.mellesgriot�4d:U�anz0or Ixon DV887o � j, Born Me�Wolf EA�9)Pri�Xof-� } Lo�u: Perga�=PW!,�*p9 8.8.}A7} Dr.B�,EvA�c.�} �>�  docu� } �G% Pk  subm"< LANL e�UE chiv}C:&xTaps,twocolumn]{revtex4�evp dema�-, -0.1cm \oddv:top1.8(texMY 16.6hxQ22�@�(\pagestyle{�' y} \�v{T�*Mwe8a>s!�l VQ=L�[�E�� lmholtz EQ- s \\�̅c��C*�[5BRZary�d�su(Azimuthal SX� !xEP7to=�MATUTE ffilq{D�ta!�Ր F\'{\i}�h��dad de}�$tiago de C�0��s+< 307 - Correo 2,+, )} J x" J `}ABSTRACTMG# \no��ntӞca�'�*� ��� )�s!� !�yTR��6m��!� &/$� b-��Qp�lex�a5�s-�EH"� . NLK�nor�"�2s��. S�aa;*�8�i7{%Ao��steadBdyadic G{G's"psa��TeQof�9harmom. ��� |!U�� �2s�s ���b"6 ng lG1H@�r3 "�% �L�6ed. \\] E1$Keywords}:rh uh, S1�.b, E njg,�T6� renew�and�) }{\_�ic{�� :�wY��w�/{al�'=Vhe1�Q� �#P$\nabla^{2} \vec{F} = 0}$� >H�dv@+ k.PO U*7'�Aq���a��UolgtD2P!59jTin~ c2F*��:@�6��*r�$no�pe��rgelBR?. AR�,.\#e )j(+��*Jq$ l��/ se>t�R �taZ"1�s, each�Dol� al�e( c�s $F_{rT &varph1�[��+4;Q= � � �� g{�al techn: ��!�a��z�� �|dg�oped,=g�WwZK�)9 9u�?  �&�7�eRG�� {pWti�CA- b��g ~[2]:!�.�Az n <�;�6h��zero d"$��acis}F"F}=0$.-�|oA� $B�DA��6��in5�&ranɪ[�A���%yi-(�[�M�'G7�9�-��k8)M�~�Arr$Dlone. &�E�=o�/ue ��;-(�M �A�6�[.r. N�the$J}< �saR��:]s�{�q�go�eF�;we�F�hr�F� t�h��I2$�su�% nE1�a1uj�K-r����� ym�to �!X�~[3]. S!6} ���=�`w !�t�OEkN�d)RW2�= �ueC x!�-�E�YG�� avoijV� G~[4>��W�!EIpaper!CѴ]L� 9CHM&�k1;�F�B�m|s %nn��X&١t�m�ou�FrI[�t�.I��G.�ser up!�3>Gfy,A]=�#6�!W���z��[�Ue�H�; �� e���>� A�s��xe. "r ��!z-�~[5A�D new 9�we� cG�!$ deaH wq�itself,E� out &�_�Fny �Oy-�0ay��lsoA�%AI)e&@E�Fgh(�*[ "n? �6��+�sam.��.� Q�e�,M+Oeu; � � �2��>b>N� ��g8ax&G6�y�aw*� ,1�;=$i[|*� �J�/�.) = -{ "�(�&:F}) + :-z�, .L1�} Bn m��q !7R#$FgY 3 0+5B F4e�finT:� eqna9M} ( d.)�  & = & 0( 1}{r"} \; \�!al '(  ) +:G \sP, � \; "VR$( 5 F4 nF:) \no�E \\ &�� �0�4eq�9%�h1pd\DU�A�Z8z� �%oMr�L7 }$ i�`%ysjN-]�1�E+)�}I>Q� �)�j�=Hr}j� 6���-�AVF_ =�)�&9� A� 0 , )divp9��aF��ten {>:} "� (*5A)"� �'(��U� ��ar�� /XW�*�r%�� Q ���  i�4be wrs}�u�}!2r}(r,I5)JFB{u(r)a�2%�P( B���K� ��k $O�o$L�9� e.pQ�ee�d�! u}{d�}�un(n+1��ka� u = !�1�req} J�]1}{MMJI a d}{d�=  �qd P(��(n (n + 1) P �MgLegend�y�5�Il$ �a�!��22���# �a�m.U kc-In�%A��1�!� =�u,�e n+1}�Xb!� {n}}F�8M��e���A���$n)� the F 0� A�C&leq`d,�pi��iI tinu�2o�FEwX� va�>����"4nomial $P_{n}(R: �4)H�nEf�XhN�ger%fM;gE"� } �oizFlŷ6Z�jn=0}^�: \3D a�%�-!��b)�+2�8OD R�!��-7<al��1�E1�]st9,�$ ��Y>� )��y�1�Jr�a�:R��#��v�(r)��yf >Z���an�UB�m?\�\V-� z'e�ByqjlRx Eqs.q>�}r$iQu)Awo>,�v�xd&F��`%�}{n�lr^{%�-�v-�e�", �gE fٲ1�d $n \geq 1(,$a_{o� 0-hEe�sn� nd $z$+p�Z93"R"k ���: OnE8h*�weu 7�� �&J�,B��)�0v}) satisfies� -� �E�heB� e�& :�caB�*' 1tV� Q�=M�!�%�I�\z� � C) -zD2.r.� r aͭE ,Q:tetFC?a%b%�s�n��ihap�}"�=���)��G mplyF6}5& �B�ХX3 *�g��)J$�*"���%); {S�A.Q�&WN&��y���):1utQ�6@� rei�d/�}� �CL &wo y��%are9��p hat�� cdot�Bˆu �2}��0,&T fd Q̋s RH2R RaJ}_{S}Y��5����5"8 )d&e�;a�!hnormalCwq�آ� is dr���"/��-> "��>)]@a�.ar medh:c+Ritu�E>�B}=\mu� H}$ holds4�z &'rYc/fN;�Cu�Z$, un�Pl��rg�W� $Q��8%+�� velo�; $\omega)e�~Q͏M A!.vh "D > ~[2,"�bt $r=Ey��%�I�(a/ ,a ��� Q}{4  9L :�� e >E� mI��$z$�N"s`4n &�5�aK~ ��� r^ ug T� !;= a�`�!�t�, ��-�}. �n7 NNAhe �c$r>a$eq$r<}��kd[BzC*��>s��0;�0,��ishi�(itył�)�>A_�¹�!�A = nB U%0$%�i�_{\I}H�)��^���vY�R��x?��%�( ?a� Z�H:l Y�12A�t \f \{ �*a� {l} U'\displa��leM�a�Fr^3B (3 6< U� r} -H��z~; ;#r >o\ �� Nn20Q2 C B< aaa) �  . � �}����"-s a��x>si�E�=v-a �*)��A�m �M'm��1� a� / 3$:� 僱y( &��:őa A�u:#�loo]aéy l�Am�$\linebreak�GK�` ��_e$aJa�i`a� ��Kan$II I� �g� 5ZW��WIU;�>�% Az�RR�!2m6 :etur�ut %-Bnew�&B \ *�"e� nowy��H*?i�I}�"F- (-1)� (2�!!}{2n!e6P_{B�v� �� �/w2� 2n+3��� n}}{a1�ў�pc�1fLS li15�?\R�S f�4} ʠ�6�^{F�ABj�B�&X���-Rk)]���?(RL2�1} ��)��JU��>���E.NNɭd/_)�>  )�"as"��"�&J*�1�F�&>A��DX F26�al� ŖsA ���f�� V�r 'c"����a������6�:'&J�S~0.4cm���x�&x��m�>��" y �F:�60�NZH[��f:�st7�fo&"�"�#es^ F`;�� �" i �$ r}>P Ne��by put\ ��\ %ݝ�=-oj�!�*��T?wH6X�L0 %#lQ�R9[%��j&��2}A�&_#E��[-�n�X'A~��] j =&�BuS5��/�� & q� H*�>=#>�-�$c���"r+ �_% l =#T14� &@� ";% $kr$�6er�bO �&� �%�ڪ�N�: �R9F��[ c��<j (k_!�dM�n 1�&� &� .SH��B�D6�` onN)79� Hank*�U s $h�^{(1,2)!En�-!���:)�*o$� $, $�$y�Y".h�6��'�e�|umJ� &�6�Jsw��_H���q*�ESa$�nF��/Y �&�.� E}m��y�\;� } [r�%@A ]J/6x!&O#�O��^%�^��w��*�-'��($jdR �E� A>�e����to��P.H�@2Vg�"T�K.**�q?)�U.�w.g� M*%2g~�e- % s dvi1�V�� +�y+I{�wN��I,^�G���+ "W�>�>�"q�1*�͎ݺ��})":*(M6"'An�Ea,Ųis�vi5U�<����d,E�a v�ng"�.w6l�"&� �|�},t� )�I�0 \^0 hWi�tI2C�O��:<1^��*L3I�!���T·e�'s,�rs�go!b�Bs a.�5D4�@o�4tOI�&�*z!a��=Rqen�b*�Qo3 6� 6�)�i>�( k a}{2 r} BlF�m��(4n+3)�}>6)J�� �('!>� 2 )�M6jfkV; h /)�]&�jL!BLaLA�6BndF�!�H"'"Eb��%���+1})�F� 1��) )�� �+�+9�!�h %�=�>P9��Ah}{k�g<+1.>� 6E2>6��EX��6!�EZ?$��L� �� uppeb�\� "�#lo�u#* �� �?v�~�xFN>yak�-X1~5�or?�&�)�2�j ��+&` ���4��i(k r!Q�tA�f���Y�v U�:� 2�e�Y�9�!�;��R�B���nBo &B%��/E�$YeTk��m�eo[�;s]6&v�C"ı.�wM;e?c AA!  x*�/)�FY *M *�/� )l�jssy�Othey ap��f� .Nin v0�F��*� ��3u�r�>-3� . �@hH�eV}a6�&x*.�+�!uteE��6"� �FtVy-=�/o�="I "6sq�4">3�JyF�4Q,V "�[5GB[=!�0 ex:(�=1�&A& 9�=&��,tY9�sca��s�!�J!^.n�"Ac9 Z @K5 onesq6e��K dzH�>"�7v�> Ill"k �HrSKvn �nj G�nc�7!��:"| � rG>�Was�r��rki��i�27U4e� ��;5 >G$in cylindr�.�&�J� ,)�{6]�BM5eal �aqAՒ� e�G<)� 5�ac�i�i� ~[1]EӅ�-g- �.�1�orJ7.G!Pof,v� [c"�, �u�.%��BAc�< ledgsBN"� T!�#�J�}� uppoi|� D%0*�B�|evaciE�C���BsaDs y Tecnol\'ogicasb�B�B�B.�6�J @unter{�6"��list} {[@]}{ڼ�m1 \set_T{m �D}{6mm�3,parsep}{-1mm�z.�G. Arf��dHxW$�AM�`ma�xM=8 for /Kic�U}&��$: Academic!FzH�J1, 5tht�i5� Chap. 2. � P.M. Mors, ,H. Feshbach, � {of��RHicՂNF�$: McGraw-H4B�%Cruny �1953, V�H2MD�13�5�?� E.A.!ute, ``3Super�NA�SB�d$External M�B'' �A�{�8Jou(�� �l67, No. 9, 1999, pp. 786-788�J.D. J��!`%�C�X�R�Bd�K},=0*C�\&B�5*98, 3rd>�5A I�� d"�G�N>��2tG,b>pacs,am�$h,floatfix*�GA�p��&e�%2d�G6>� colo�.u4��|��<6(�q  � slopp$)e�m�C be}{ �GaD.#e# V!\bi���r$on[1]{Englv%:-B`on: {#16Z94up6 ![FD\a c[5]��Ue&�$:���"{"D :\S�g��s[�U =#1\){]{#��:;]�`�""�$fig:#4} #5V�%I �P}B�[4][.8]jctc! {!tb}{#2}�{#�9�\r!.!I�'�!r2Yleq #X�ect �eq:,2O eqtnO^"!�qtn�)A����FigF�Fig7&Js$~�Z�:��1P \vspace*{��R!�$E7[d9�addtoc�{1}9&}��JBi"'�t -�0edB a��ria�Hnd�+fec&�} "�J Alex*8r AS�(rov$^{1,2}$�Ju�{Nina a!3.!j�n�� NoskB2> Ilya V. S��iv1 Yuri<�Kiv�\$ \.KNon!+ar�� C�^e, Rese��Sؾ���RtK�O�EngineeT<, `QralWFNA al U"t�, CanbM� ACT 020036 $^2$�D-uC��NDP"nZ s, RjTYN���Q �, Nizhn��0vgorod 6039505$�^3lof�Iy[h��+n4`���s, J`6� �E��a.��KJ pro�W4 of *��ATfQz�,:z"4 G�Cp {\em��]�1VQ���dem�E� ,LJ�arpNt� �+�a al2�]X� $\epsilon�.=-1&=$� di{ico�8EL\+% �"/�.�2��PR+>`us zL TE� TM�#ar}Keor�X!~ them� lo&@!pa� �&oL TE�TM �\tb(discuss sev�qeral applications of the birefringent left-handed lenses such as the beam splitting and near-field diagnostics at ]�}sub-wavelength scale. \end{abstract} \pacs{78.20.Ci, 42.30.Wb, 73.20.Mf, 78.66.Bz} \maketitle A great interest to the subwax imag�\is explained by a number! $potential .&, includ>(lithography�pdata storage, which could use%\resolu!oT abilities better than% 9 . One�!;�Pcandidates for improv�!�cof an�system�N�so-called ``perfect lens''~\cite{ref1_anis} based o� concept]HlY!4 metamaterialsG3GH,review}. The possi%yJa �Ee whose.-,is not limit)�|4classical diffA<ion % ha!Y en aAtjec�intA� deb%?byI sci!�> radi��%7h.�r to satisf����d���Ka aa��IA(to operate,|dia�c��tw���!ׁ%E�,surface, $a$5= b =�s!�d21�F S%��6,int, $b$, sh�!�conne�O9 <0thickness $d$A?�re��R��Z|<, \be \label{eq1��(} a + b = d� e��[ (\ref,) mean1 � t�Kimle to }^ mage�Y!1is larg*" :��� this[��mserious.I�� *20.� . I�� is L� , w�p troduce a!~. .> , non-reflectaS^�s%�b6?.�e8In part-a ����� �tr�o!B conv� onal2�*I��� =\mu�);.�2��U�� eia�, TE or TM po�zed� s both-�m,I��a vary!1�}a�eTA�TE%TMI�s;%�pra�ty�Pexpa-dr���ly AF6�B "� 6a.!`ad)!�ad)^� a2�) is f �pb��s E�� co-u~>"�!w� so!$cuss some �* ���b�2� # � beam1�I 6� s2� / a�ing. W�,��r��i��4medium describ�$following o or�*;  3vh $\ha&�}$%�C a"C +mu}� ` ia�s in axAq�crystal: ��a�� ��2��6�= \a� ( \begin{� 0y}{ccc} A & 0\\  B  & A^{-1} �@rray} \right), \; omurj Yn j {\jBbj \ee w� A)O($B$ are gen�,ly arbitrary� plex func.`4 frequency. WeAstitut�ao ress9Q�-Q � be�� onles?ref�� . Su RYwa+ggestedToly-vd layerA.!Ufinite-�8erence time-dom�0F�PSacks:1995-1460:ITAP}��� a���c �i����1L!�y"_si��_s$){Y$%?!."�s��@ireO,2�Eq." -P$), namely :�Darrow �_s 6�Ic<mu:7mu2A. Belowu {�.�  _s =1$%�losŅ�Fi�*2"2B�diagram� !0� � �a�wo sepak�g� ىed virtu~�a $0; $\theta_{TEC Mr� anglM& groupnph� veloc��h.�a�s*���6 � =.� %K� * and �� mcha�erO �b�.�xE� rrou�byM���i�6 $($0 \leq z q d$)�assum!<at��is locp�y �  $z=-a$& / �1�,�� n in :�2}io)�Mz���&" ��w �isFcorresp� ngm trib�of !/ ic $8$E_y(x, z =-a)$&8 :  , or@5� @H @>?"/�I�a1C%� denox  sp�a1Ithese oDs as $\alpha_e(k_x� m ,FFively. U� Eqs��� )�L])���z!H�)8"g ���-��� 6 bA� ary �A�(!�t��0e�%^s�U %}��2� O1>BT K behind] � i.e.>$z> d$ &B 8"i y(z,!j = 2f� R \{ -i \�.� } (M$Ad + z^{\p]})7 \}� �Y3�aveI�6 9 �A�>�I��B��" �- � =z-d���real *� 2}-]),~Q{ �) rep�Av%�*&�x�3!reg�g�>0$ shif�"� 5��>Aj�� (A-1)d$ (�TM�)�$(B.E . A typ�<�@�����>2},,$A>1$, $B>1$�3B�we@��6 q�6ѭ0�xACs ���wly��d :y�8 Lw mz� ($A \neq B$,e�:D ���)z �)�r�$ve to each7D. For $0 < A, B < !�:dcan lͤ�6z"��> �!�*�2�/ . M�Kres�!Õ�Y Q�� �w� 2}:� or/�$B��_A<0-�B>0$, :� %$ion occurs%��F+�y reaX dM q�R n�l1J�3}%� $AaG �<0 � e efG �, �M� �onA�"A��BS� is p-�ug; �E� -sen�@am a ion.aiure*k3}eF� ex��is9hA� $A=-41� =+2$e�wo-dim��-"�ag�4 � aincid�  30$^o Ois1)edaei!�!$�i�P!F .s �/same AE  � . Ee#R-�� S� i�B[ l rgoes5�C!�A itSome5K�xQm6ed��2f3"c 3Bc  Beam�mi� through' a�t282�()ȡf!�, $d=5 The 2�"�geri!�R�aoi�B.�B-ls5 . CoordinI're ) �u-space�h�} An2� i�!fea=N���� s�"*�"toA�m��ARm7e��ɛ!��� M}�Pi�E�e�s�srejs �1��E6��a2a�����JJ! trum1 .�F.� _m"�  = |A|d � coi�y\ >\�M0 *=0� �(.],�B= �wQ@!d9]Y@1�A�is�Ji� QZ�:%��:�N����:�2�r  at $z_e2B)>�/� 3>�� �ՠ2� ~exqq�� ion,E7they do 5% �� ^A�� -�%1B6�'�? arameters�ea�� miti��u� ict.E�a" isotropicev *. -17 &�!I�IS�-��l� furtZ" awayyc��. � mpor�#�D� �  $)�n*� .u� �9�%|o�4"�F 6� 1"  hac.%-.#| =�4ft|(|B|-|A|)d\[|Q7ichD abs��!�d�� ve�4 -7"� cA� ���velAds�'��os2)*q(,� nos�&I�$microscopy2�4��4B�*+T z�A��i#A �lv�$  �)6�AFe5�)� � )��N!�� �B� $h$ defU* 2�-�).$ SDI�s�wo t�Q� �$m�eVa�����,�rvidedA�_r�"i�}!e�) $|A| =|B|� )�� ��a �cap cul�'^c� Bp � �$ve+���Ek�* �=E�E}A�cus� by P&F�"a�}'��Rg�h$basic physu for m a� �2'.�!�s�i����i#Y#c4major factors:�N� A (ii)�%&�)*�%ũ.N6� 1}(b)� "~&� �&j%� >R!�!e;�  �1)'s%�� ch =0�m9� 2Ol&�&Ia�s*� 4}(a, �J�ra&fin aM�� ��e,i mMF\q��  [ &�(�)]i��*�F!w��s!6TETM ���-�K#j$mb�Tel�6 b)]./.� )�:�y �.*. pai�.s2+/�� by u!1�f�Q �) also�,�iedn,�{��"h �T en� iB6&m !� ��yE*um)\$6_{l� 6-i\del. ik}\fs 10^{-8*ndEmu @ ?S- j<A��$_AA� $i=k��$0$�wis�ye mixed-&� ){�st� w!Va�H width $\lambda/5$,fx $2�)� <"��$B[ ,6<. )-A=-2.5 ��.�!KA�/&ois�+��c\'3*�)!>Fy29#��"�p`2�1^t�Rop%&�q%*swoi�{ . An�=E�A�ee s�af(; `e".�&N�5.�g� C *�&< ,o!cal R}� eft(�!(x,z)H2�����_^n�&{i i� ^i"� i8 *~.I5" 6B Y�ihe (solid),>�-}TE�=(dashede:� ,���j(dotted) a��Ai��&-.6�5B�S� aR�� ��e*/\.�ap��6�8s (logarithmic t5)��"� A�V�-wif6k6j2]. P*0�"�"S!� v(s markA�6�a�, )� )Q))��s. :\��Dif�!��eͲ@above clearly dems0a�at�f� .�~d6be �/�*n� o�46 M4 unus$ p!�yand, mor�*�] m, �m�"broader6 0&~6.�*o�arison� ha�F�6�&� �,&3. Altho�T2) 6E� �yetW+in��4'beliet0)�$)q�*���A� quit� ali�!Q will �#i!�str�%effort& � �3�E6m#� ayV0�2�}�iC &+%t$7�2P%%�T�&M"=%%�&I.�&�Tx4�# a neaPink� p+ppl"�ty1�W:roaX&9��(!��'! fab�6>� & :/aa�djm%t0t�% n an <y� be ach!��� a %�:ed�.�6 +ell dof wiran�plit-r���na� A�stead�!.symme(6ub�attice9-E orao�ngineer ( !������!s. �.&�dirp0on�R.?!�1n�iz[ 2[�� _-s �8toI���P� t}.�� (�ed;�:� A�z%ed�?),�1�2tak-�*Y:i5$A=�!�5si�4idesigAL{�oaM)� �� �!of�T 6� A��&_2l9lu-�^�7i2da2��typ!:f&�53a1<� �3a0 �<unique��A6�<6�(��O� or!�(ultaneously)�� .�� �"2.�.��ourault�(w)�$y5�tudw<�!�igu!�4of:|z thei���4�: auth�0 acknowled�4 sup�oLiAu�>Plian Research Councilv >4k A.I. Smirnov%Da�ful!�*. AAZ�REN 74I.G. Kondrat'e :j;u � 3N2�,warm hospita�(�N�8 ar P Centr�uCanberra �P���RFBR (gr*;0N05-02-16357)bc1thebibliL?}{@bibitem{*�6J.B. f,�. Rev.�5. ~/885}, 3966 (2000 eJ� V!., Uspz. Nauk JP92}, 517 (1967) [Sov. vUspekhi )10)69)8~��> D.R%�th,6�AWHM.C.K. Wiltshire, S�>ce `30�788�42� >p} See, e.g., G.W. �t Hooft, �B*$7}, 249701Y01); N. Garcia �$ Nieto-VesF nasbM$8}, 207403M22��r} J.T. SzTnd P.M. Platzman, Appl1^i71�!\3286 !�2);2JXD. Schurig, M. Rosenblu!eS Pltz, S.A. Ramakrishnain2M^A150 32�" ? Paylinko%7.�Opt. Ex�s)�11}, 640�3);� Cummerf �)]6�? A. Grj!^G.V. E�heriad��a�F1E�11!��6`&�. R�8 /�$is kin ��but�� �e"�Ab iogC i�.�S.P. Efimov, Izv. VUZov Radiofizika)62!6 1318ae78) [#� . Quantum�c� . � >4u�R\f  C���zzoli, R�KPGreegor, K. Li, B.E.CE�tenbahi)M. Tanie��^9a�1��ME��E>� sloppy docuA"} "\,style[12pt]{�:|le} \topmargin -1.5 true cm \tex�ght 23>(15.odd~ M.eve� J�(pa�1yle{empt��.8� } \v�"*{6cm���c�r} {\q Com��%4 ``Finsler Geo= VFR({F�@Theory"})bTs.5Vt$bf{ShervgiEPC!�-mCb}�? GA3il�Gim�A� derived � /sm  so red Q�gM�&�A af-�T Zce'eAuH5�f �sh�9� ty#D� H�!2b�eo4] frameworknRiemann� ��� �6a�ics. B2C>�'bC- G� sc},V�f��G�too���E� q.�!!9N�;i 1�yc:2ct.Ase 4!"*, �,M , af�J choo:$matrix (52t�)n�B�*ofR$8(59) $$ \Gamma_�7�\mu\nu}=�91}{2}k\� [B_\ ( \p�9al B_� x^C+F'nu}2&mu�0]+ /:rmuJn �6K nu}- C.�>r ;)+B_\nj\6� mu}- �.\m:�\<$].1bT� ��e%� A$ (60)-(61)�Gv�-!��\u?I!O-�e}{mck�1 quadR;� 66mu}2G:3- x^-(Bz)=0. o u> ^)��4*.� !A�moA�B)�d�Q�$}{d \tau}+V�0� nu=0U�'form (62��i//)�}f��YUmu=0. )m9VB F >G  1 HcM��replac�%�k�@9�%�E�(60)�*�!p);n�=\:�A�mzu ��2�!0��B� &^# ?�)4 (1EKi&�!U.6t>1�"cal�%� $$��)7:S)-J�>�na>%y�a��>R�ġN���W ������J[>�[��.V nu=A��!%RE./ '.*>x nu} 2mu!6 �.FHJr1nu+am�mJD h6.n6-��2��� XB�n�nJH 890)�Hmu-�~H>d X.H-�1�>�+N�>`24m�|6�2In-}�N�> �=�n�A��G2t�A� |_{B�Ze} ��)2��h})�.�)��2Omu+��nA\-@{q�BHƗC W9�5�e g.nQNP�>�bP}=�O+ }F� �{�a{2?nuA*�0g�.(1yH"�Ŵ Next6� ompa�!� F [ ���F_{!� �9V����\ F. . S . F(! apcl�h�2$ 6�m55x"Q 9�A@bm ;x^1� B  �� v @.$ ;   . :(63�`� %�n&��7�RbKaHY*$(2)$ w"p?B>2�J�M!5$rK&=J).b. �� .�F �:c()IB+/�&q X  uRca�!|5_$.��L!���duR�*�z".!$solve $(3)E0�� oun69 �) s $ ��!�mu}$. �!f&�0�-'L �BD05. N�BatZ7:1�� $��n� �J�>M�$�lsoXo�\to (39�of�O.�!�6L�I $6T$!� be �;t>V4%th:�$C&�T tens�\ , %�3)VA+b�%�Z, "�V�"B�tT- &.O 6� � o" must"FV�NU�|Dtr>k0$. F�;�AIYof 0:�!��aciT�#�,V���h%d�- ticlt5�(�(v�/ ,Aa" PXvel2�>y"(# veryPA!!�ati5g>mde�9<GT ?tsonFYaTf�extera>�f . Also,E�sB)�J�n�P �x'�?�^=�as �&%��>uta�sh�\�%M' li�$�9�$�(sbs&z&�%`!F�1�ac/JlyRZ|(F}�XEj�*�sc}). R&(�'ny#)�"sA��of"�"?A�:��?rch�Fabl08I:5stsR�asa�i�)ove�/� h}, J �� �-�suiuT �i�.�6asN"Z�* noa� ivalq9 pr=ple);�W"wc �ac!�in|5�%P. 52_st�4� �%��0 icit�cear�O $e/m���$�Xd�$G. Randers�f�is �XAR3 7��I�r}Q"A��2redfc-_�a!rcoeffi�ts. M)� R*1tes4�i,B��� a �i=� . %(�5�� �sh1}, 2A��>� {99}&$ b}Y�, V ,ZFsh}m�&p,b"Gy86�"�of� �)sm"}}, F�'�-MatB^al"�Re^&P.169-17 %4)�va"^$�Publishing, hep-th/0205224, MPS: Pure� c s/0309022�(sc}S. Chern �`F� is j�3}��8cA'A�Qua�&ic�<+a'"}}= icbF AMS,7;te)1996, $*�8math.iupui.edu/Vzshen/�q/hi�ey/c�.html$A'&}y22� 59, 195,�!41) %"N"Abj�Un�-"" E2sm�  %Gravi9ZA�!Fr*�Q*m/yA f�\8016, %CERN/EXT-2002-0502�2n�O Ze&69A��1�� %b,8003, >�1">� &C! � " "�e[pl_ aps,�+h$]{revtex4} uE9 ckage{bm,�/~�gicx6amsA:,amsxtrafo�damssymbb",latexsy�! .lG86TQpt *new\fand{\p}"� } 2(wh}{\widehaD".5wt  tild�.}b ilon:T>(vek (� bf#1>"abs "GJ|>(uKwh{O:�$poisson}[2�\{#1,#2 �\}>1  ��cal{O}�(�)>5nablan!' _{\perpB\p.'%^>Neta�A0 it{et al}".r eg}{"�)} :�ie"Z ibid:>#$pdf}{{PDF >� sol}{{SOLB(lcfs}{{LCFS���( \def\grad{)|} VBs{�'�;�+ div{0 \cdoaC p _%�>lm.!cur v �dF6J^2p2�:/ elsq �.amb{ I�Thar"0274\hskip -.665em25AYlet�<am= b)Ila�`def{\�,=(\pt^2/\pt �\ +K^2 y^2) �(bdel{\vec b%?%� BBBJJB bdot T 8ORexb -E)��B 4jJJuuJvvJwwJucxb{ �u\�Bc}J'v'vj'w'wj'j'2�3�$)�ptt#1{Ջ #1$\� tqUs�a�Q�b \betq�mumFa{epss{; ͝big5#1{�IuA�{\base�9kip=\n�O.'87nt=0 ptH{\hfill\vbox{ #1 } }} 42lM#pssr�epxxr)x19pzzr)z)yyr)y)0wcv{{\omega_Bpp!H�A8 #1/ q3p:�^2B�x^2Qx2�N.c�p:�J6yd%��~I�v�v_E-�vpo��v_��uuvstari�v_* =uuJJSJS�ˍ�v_�� 5�qGq_\wedg� a/qe.e{}:�j �q_i>p\Pi�vR�R �vd1B�v��Je 8xbB7u c�Zdo2uRuF7i8_iN�l:�U~UIYpxxmur�- 1Zor{\Oa� Psi{A_aE� � b:D. %\� ,{APS/123-QED. \title�-ar Flow� 6T Energe�KR:xc Turbu� } % \�6 {V.~NauliI DA. Kendl$^{\ast}$}.O.~E.~G84,A.~H.~NielseH,J.~Juul Rasm�I,n} % \affil�m{Assoc < EURATOM-Ris{\o}&Y.Labor�;(y, OPL-128 % , DK-40004k, , Denmark�j$�$) Uni��h0of Innsbruck,*�.Tv/!O al n, N�0\"OAW, A-6020.R8ia!o\�u{\today!�-�a�. Zo�f1oZ.%Kgnt@o lay a cru�ror*lasmaW\�Lh0�Bgenesi�� dou�8Mt fluBAPsP-�f�Wof a;�n�te X�9?s*P�X�!{Oce�Gz��rg meisms viar$ Reynolds �,"r Ige�pic acousC�p (GAM)�=nsfs48drift-Alfv\'en �ce. BKH�nof~;�H?<u�'Z qp4pee �g�d cto �s k!�ea�Yf�se+@ecy+={�Y=�v�(ing4ttu �@B �n>o/c�E�*�;rel�Kt�i�euf�< devli�/vea�/A�a bB �u1, mR. �:�BfB1j�xdk>Al��dV �M�c:�K �.� �ink��`)�. �.l9x� high Dsmalna�>10>��YBQ- dynam2a�iLC,bI���cancejHe >#u�degreeq�M�oscil�qs�`{!O equilibr�J�s prof!Pmode�e�Hpoloidn a"�@ %V�<,� 2Z~@!VLa)� terms,�A�oo`U c^me[ � -�!�GAM�C main d,2!�!�!�gs��>�0$�B�l �riT@,;@w�a +I inct peakmZ GAM EETa�0g� �m���|V052.25.Gj, % F� �8chaos phenomena235.Ra2P��}�$$65.Kj % M9xohydroMm^fluidf%� } \mak�|\s�1{Iz@!�} SiC~�5H-�Wur:Beckh�"er:1982}AOq�E=co�MdmE s a �? itud%ʽ��6nga�� 1�sh�!�Q2E�/LH-E�MD&�A�pos�W�3y  E e amongstMMs ion-o�n�Kq�, neoBo m�n d5���o.� )!4Connor:Wilson:W>,Hugill Terry }. H�Nw�vcu��baZa Cof.9#�(was already/;y���PV�4lea� �etNA( self-organ*�8t�# i�y%�!ԍ%%��}Dn tur]t�~re�t!�%��=. lyMW@Hasegawa:WakataniAQ7}. A!�7CvDm�\�J"�H4��=# by�� i�yal 9!`���ѡ�� B�A� #F 7�2�,�<, hR04hH�"`F�l�G�1mc�eN l� Ma"�Awbx,:�K% ɘ�9 kZ�de� Pe �Ga!�ux�5�m��t�n��a �l/��3i�=ll�#a�d�Ta�a �Y; ~D�HoN _�z$x� 2C�u�h*�ZQof6F yL!��cHc&s_or:%x6�Q�JX�rom�V� 5]�a�o�]ur�t��"�% Mea�A\p B!j�"-�var� &��Jorm� s<�!�� M�=AQpur�)�}%y!���'O�~.�ro� q�.go:���3��R:�Sls��>G�He�~'9�1s� �=r �-cX8��7z!=�;R�� =(Pinch (RFP)��(Antoni:IAEA�4}%XTokamak �Lu�4}�� figuɛ!�Th� m.�iI�a��#6�2 % a0 A�0Vk Eխh. F*�!%�267f tor 29/�$ inhomoA��6V� s� s1 Wi?':John��Daw 1968��te�_]/6� e s.�"sN!"{#e*� sn &<sidvN*� *r .Jv \\!hU��� paw=ie�inv.B<�6�J�{ fer :o&y .0� a+U��n�&"� %�n�&E� � ���& detai (� b (or damping)f ݀��s% K~riori s�sly$P. W� Bis mo� ften.B)a�_� { re0�p(� �a"M!o�m� �Haa 0schek:Biskampa?1, Scott e�The>�� n 3 $$ sit� s r�"r weak,Dyo�5 " dr�M g*�_!@ �"=Sato:Miy Hamaguchi ��Oint J�itA���s&� >{�M(Kim:Hahm:Di_ di1�E�v&Q�a e�sfol�: 4~ A-S� on \ sec:� l}K.� !R.�!I'*�w&- s�!� nextF^)R}!� devo��tS^-]�ewHTr"�}P��Ay"���1��%��:!��w a)�"� t`<�global�fEl��q�m$ colli��Jy� `in�[ef%Yres ^}YW`'�  T}ou�(L��a.LMK . � {En��=)�\�9�}0}:��Cbal��M�d�?e�E-"6L�a ug - � ���w �W. A�mg�'A��6� !r 1&@ toge�O��"� =6 curva�gCR�x tub"vel,�uN *�*�t:� �)G��f�!.E��M��.��L�*`)�&){\'e}.+�32�PfH �B*� Ae�+�S dard�0%hS�up�2 slow��m��s a�a� N`� gyro*�$W(_i=eB/M_i$ !uaO! WX �ev܈rho_s$�.cbackgr�a�� &� n �Vgth $LO!$. s3-�J�z$cq�i&�`�32 } �Nrf'} eB}{ M_i T@�? c_s^2#T_e $.# �$ c_s}�_2( �)absk" \log p_e}j,��Tsub�� pts $e,i$�er!�m4n � %0�D[I@cecK,�d�HI�� n_=)�/-� _� atb�|�!+!&iTapp��6c ase�1� ��ei� �4�dm�:�)�5�$ �$;�&\�,eN�$= q RO`23$R$3.& *d/uih$q "safetyDd Aacl7���n��v� ;m �[pie �aש �(:�erp%�. Futi# �>� D �� !�U� Ref.Wn 1997:2i B ��Ap w���\[z��.H��I�onsik�y coldA��m��y $M�!�aQ z��m!le $n_0(Sx� .�� 2�Aa F?�6Mm: I#M!�lk��m�i.\4x �� �ҁ1 !�$Thus $x$ ^�� Zco�^. Rs[a(e.L:�$J%Ie_oAe�g W!$y$"�}QR(�yd�0 $z$.abAs ~C% �4)�EC$quasi-neut��"�N-��`n_0 on$ ���!QRA�-\wa�� to1�X4X!��1� ze[ S {A��A; A�negle����ȅ�is�l.ve �V�5M simid�t�&B6!0acpIb*�}�.t ``��(adiabatic''!���.+�1u� 2-1}v} Nk|vo!�evd8 �1/ɔ pՔ($��$),5HeBs ($nYSu�h ($J��!�լ$($u$). Auxk ry�!��� vo7![($\vor$)QU� ?]�K6u-vك2�Psi$): � �!�S}&q:eqvor} �' w + \T#  = hc {K}}J{( JiW� + +_{\|} J = mu_{I}a�}^{2} V\,B�%F� � e�n�$ptt nb� (n_0 + n)N�n - !� \V��-�- B) ��n�o-�- �n�1P9Kz�psi)^{5B�(!���( J� � J = �|B �:� - C J�L��u�-))%iu�%i1 = p1� �-i RLA�Y�I�E�uGA� e�kaw) $J$��by~fa:�Q vor L �Y|A��  J��N�!�\,.>L;� Hada���u��P֖zo rry �3�*Pe�6eQ�mw��G$�� z--�!��8p� �&<-- ��U�;� a P1 bracket F�{\1\{ f,gM� \} }!�4pxx{f}\pyy{g}- xx{g�3Y�ŗe $xy$-Be asFm�Tedl]{!�,�'}\,; )� )dp(pzz{}A�{u�6F��&:��}�� �  `eA��o^� writtenOF�.�cv�cI�}+{I�!c( \sin7�!B0 + \cosyy{IF)E�end=cAq orig�x{�e�:zsy9�A;  $i^%i(1/B^2)�5c B1 ! $. &}@$z$Was b�-��#($[-\pi:\pi]I�lhe&�� midM6��$z�>!�a�"  LazMan1 n�_�~m::a r���u�"=�Y�, {}+\�,~�isq�$-)8%Y)�k�2}%^1\: �� �sus hi(#"�-� procedureL vis�&/�=us��i�$�8��_}, ��n66�L)EV>z:e�)�*8;F(r%t�-grid(s-v:r] � .I�6� %�&�i �M �E�G �"i� <e�!�YG|, g�n7 A�A� ��s=(qR)^2 *� gU!�co?#l�bJ�.parmsa酺={2%�0,A1��}\,��,,Bo ={m_ /M_ij/ C = 0.51  ��5au_T} RA�wh \nu�hatJl�$uR_e�2!C"& "m�%� fac�l $��� 1M�m�!ԓm� Braginski�!65}'R��*t�R�s%n�ene+uJ indu�$&� ine�0�#�e�(ax; ,�ermin� ��� �e�pm�in Eq.~}SV ). D�F!( ��$?5$J8( )%" �5_�eA&� ��3�yXrum-b last&5P�+$B2�2�i:e��)!p%ہ��(%�5}��(. "'&"��@a*�odel)�Cn &hnGLata�i5�S pt{M �sflu�f�s�� ta \!, �� \}$� � A]oKl��2 = }��O$ _e/v_A^2� o $v_Au<*"iI�$�_e� ��$"�!aug&"��Y ��!�nX P 5\%!�8+�**guO!V����ve��d�5dDu.?*,a zero�) feedxNtro�E�AarN e u�)to sta�m��"�ibE# �>"Q͋2���/>2� s.�c}}M�e9�d�,min1I2E&l �@f�� �r&e 5�:?�)�)d��/N�asJx �zfeq} �\p V_0}tK�x}\la�xv_x v_y\!�le - ~=a ��n�>4B_x B_y 5+g�_BVn W= ��\"zQ^2�m6 \, J�Ѥ �m�Y (1 /a�� y) \int_{� }^\pi dz  0^{L_y} d�( dot$A�o�yA�6eiAHe�$EW< B$u�a��byeubfT6 �$v_x,v_y,0)-\p!-phi, \p�  �a�~�r"VJc ]&+q�E��/j&m&fghi�17phi1�  Consљtly $V>0v�5e �W �&xE@~ :)V_�J���cL ibT�m�at}A��e>!,iI��!��� po�5"L(by)v� .n&�d�_��^l�`)lvl� o����a�Ing^ �0�%�!CѸ9 �K{%�e�� �y �=�< . To�� v:?�A� mean @wei/p�he�aI�q &�g�v�w%whF6�me.�t�#]  ��� �,$U := (1/2) ��$ d\vek{x} �0^2 $R&j T_ On ŝd U}{d��=� R�� M G V }Zi^�*wP R}�HVI M} , ^G},� o V }$"� a�l�% FromY��� !� find.�n* ysYiR�J��9)�����{�B�<�w�!�� �� & = &:WQ 3��V_0:9�� ve} A���% ���>�42�. �$ . C�+sp��I��  ��a����]!�0fXM�X&z|}�1B%)A- �@{( :O�r{B}_xy:G%V\!X \; ,%~L�:em%}y4e^T:t,��A�i! ex:9g��f�)A�&� .8��� �=�y A&��� ��km^26^.�ijS(E� V_0)��.�kZ>>F �>&�'� :Ma���ZToM.y anM e p˜c�\J� v) 2AqA�t\)ne � nned>�Y!��$y8'K!y�&9�2c�4�7:K=w\to�ztilU�: �+a��7`� S&er��JR}$-)�p�iP;O-����ng�+^)�� u�{Bian:Gat�,3�TI��worth��.�T in p�:MHD"�)�4" � approxi� S���!Z:�u b�-�jz,�B� analy�>t�7z!���*CS%�O �lR;�i�1,� =f��Kf2�alg�ship �.*�2!(\&� �!:F� A_\|�� (��k  / (kki�+ c}{ [.( c (��8�� ��8] / [| �^2] + 1IZ;, շ���o $c�%/�$idisper�-5-��4b�T hes �Sf"-� & � I� 6�=$�Ż=��!�*��g<1&� ѵ�"1�]�!�$c$ ]��$!�Aa@�* 2 =�Ha-wU* /2}$2�1I�,alfven}1�A / \sqrtXI)�� .FBA� c�i�ro1� at C.m�?ch�p�!U�fa�$��E||� ���B��V' 8'?inu#5 ~\eq�/e�ne} we G ~.< �#k� k,F��� dsb.<}8��:�+>O!��* ) \:n\"�{P�� '+ iV�7 ^2 z: n8x}�j=�8r:->�� ufzfB;�!�"��Kow?=\w_0/\p �i�ŭz�ha6z \)�)��H-K� up-dow�ymmU&m6ontU]�8,x�ple*9��B]��*{ � :` SDs)�6f"�@$1�/\e� 2}$ (Refs�*f�7, Hb�54 Hassam:Drake� 3, Guzdar  McCarthy: )Liu'`� O�1!��z�6t�� coup�3� !^&���W��i cc2%`3n�!��Al1�~5�� �^�x�� as StU#er-); spin-upZ ��, fps*99� �h�o--��H&!o ��� dy"�A� y io?! 3% "&*� N� �EqE �"@K� l>� ;�lde v�uV"�0[ -6D\,\wt�#}`Ra�((nw-��> ����sV&x}�,#Z!�G�(��] �eindp�;-  towar�bΖo str� 35w&.y,�"�l �*�`..��n�t&�4��E��CGadi� A# ��Itorus ax d�� �A( out-z# "z#P !�&F�eAwK"s�`r�= w�s6�inFq/2003},sit was �c����GAM �eznF��e�F 2i.�-哑a98.X..�S1�a'" "@ .6m�7&�7�oi2c�C�tC�=��m��.�5 �9res~�re6����*�9X four� � l eq����- �ui}�<a �# of uӋly $64�%256 32$~b��dr�s F. 2\pi�$x$, ���$zB� Some run�Jre repZ�at �HeG9�$�M � 512 32$ to en/Ov�NlK`9:<m�1� ��K�v"�-� rv�+�9 reti"aB%�)u�!CthF����)o& Arak�D1966}� A�"( �AcS!�� _�'dell. Tim�epp�is &�Au/ an= �a�! 8( stiffly-st�51 �dKarniadakis:Israeli:Orszag���%�4&�8tr)��ci� �og6o�Llit �I���ails � 9�G�B�� �#P�B. No l���# b(t���)t�A�:�0�1 $��� }=18750$,�"h{MV=O�$� {s}=1c_B=0.05� ��t��{n}25$�;For�sc�Mw=edFl e"a)� $0.1$�+$30$ i83nu}� % # 7.5$�caX %� 1ds 8�!�I�aas �]��N�:S5"$A���1"!�B nK8�ٱgceV!n���>detL���a$ a�leO��q�vN��)&�GedY2ly�S>@M* A�7:1�CI<  II%W\D �#�@by Lecht� sl eS] A 8:Niedner:StrothP 2}: �6��SJmanifeQ�itself�a-17?�Po6��ӡ9&�.�\0var".A�5 mof $k_yM3ac) q,O%�Q&�(to%i/2E�!�u*-*�� Hi�"exempl�k\���Fig:P/��I sh������baʖ[��c�A� .�G��k��Kesi���(i��(= 2.295 e�6+ 3��(=0ej��!m�, _�s��1gfN?�*,�oI$�.C�  obY7 a6,�Y"-E!a&� Wr * �aT�[~NAd�D�K=��y1�s�x�rSRed�AdA �Y�k�Yt. > c�m>. . A��M�(AkinJ%& y���K$,!�!U�&� "=*  @ $U=Y G-(V��Z';#inƞ�AA�� �p���s%K� �$ � s� �Ja�naE100�y9  ** fAGtakeszcch �Qr!�D�al�8"�LA + una�5; s $t= 500���x(o$s_nQ��v�I) $t=1=PhnTm��� �,e a�*U`CtCN�*A`2�q�T�2.ѭo��� Fi6=s% isq��xe� .Nhe=��~o�=a �.ctotal:^��R��� &jno� o����Ned�Pcm��$port barri��r�EEK*�<*kY��� I� nflu� %{�(�ch� !�& ,*Dh�%�nW�9#e��q!_o.�$ we wvMno�"c�m0Rmor� �$ru=TvA�|.S =0R{�z.�E$~ � = 30 � �� �.$ ��l :B�a�_b0.1"f��)y-" ��oR9�%�N1@r(x,t) ��&5i$W9�H 07-aM�a�in<�%a� omi� eZv+ plot�N�jcߙ�r��1� &i%�2�*!��� exhjj�+sd �<on^ ��Q5M�Gs�Aen�TP 6��b!��A�2�! �� slclyjvոQ�level"�vic��:  ���I&4'�!�6��2E�pronounc�S)b2d re�[������$t \aP 3(  ahJe�of m!>�}-� noFlf !� prom�Ca��P"� �ōng1�2�@-� � G3s�Fa� u�R���!v��p�[Q �, �C&1x�<�F�ef�aRGenBeta1�A�c1m|e�� j�)��)�!0%2�5�6T"), :�Ghe*�err�sb��cv{!N*s&��V��+�)�^�c�r��#�nE Eq:E��:�� F(t� �d�, dt}_{Num.�8�;!fa& "]!�5\;&"%�% H�y$ k/l�e er��e�[*HEs� U_� �a�)q E�Ym�sam׵db��'- $.�� %MM���bJN� ]M$�R� Jseglig"kI�^�o�AI p$, qRV�}�V� [B uA�nU�,e.�siz:+��6��Za���Q�&�`*� b�Kq�A_e�}5#lW��d0 j1!�� Ra-�� �W�wJ\�+�SR�ig__ly  �m�^iX�պ� al V�%GAMh G��rkLs�k�(� ! )s=� soleƠ�[�#�:�!. w ^C�$�\��) P�J����u :Q3 e���!�>�� h�fas= !��8M1&d .�E2��::2�c8$&�( TA �TseTG���&Q ."��t� g�p��e�o� x&�1v�3.CV e�ɖ �#on.-w�_"ng2>r��l%o��=�1 "i2�on�"C2�%�� �bѥ���&h(&�*:Y�i%� �!���250T 86� �7J+v����uE� ͼ��� j�=���a�!�ly&�,�n�.x� � to 6�O!�a�behavi�Kn�IY��B�S�rabetya %�"O�7��!�B( ]k2:2a��2�`p�I�v':�Y���=j�;%� Q F� ��~�-Bk� � �Hu q()݉ia 5 "�_��w&hVYO� "2 0.E`i���y a&h0�~al& o&�a a%O b_{GAM}g"" �03�N� :SGA*7W 2��b�6E"�:� )�:Y!),aN!�HValY*� .c2!�%�ionR|qB#&�"^2 *�"N�" = {1 =G?>G[1-�(2z)] &�"KM � P }&�+�.W*{ iQA~>G A%��� $(��];ial�5)$ dis,N1�*�ehit�|�Ceca2_ �R� & y$ bV��You�;iq�*LKK�&BI 2 hi(�tt@$v��� � !J$���� in��2B -c*t�<�Ring4� �O�as m Ѡ B� n% $$z=\pm \pi1.;!u!J!2�ca�"f�to!\.A�pq� 6{�  d�1�BjP��prefeg=iF�:�5��_s%V^�]L�]���B �Pc=RV�>��I�����oB�)�FMH ur�?�1?eץ b׷c�X ��5"� @�,"<��e&G�a k%��c�#&��y�fn~r�+B8�$�(�P �-e8� vo�#itm &M�!� zero�� mode�y)"I$%�M'um. AII9�)b wѣM�!��� \R dipA�j P"�� Ebޣ!�- N)����aq e )Vp ia=� "��0c$.� �� st[ looks&"@�����eBFJ�3�d6\ �Vh� owja�nd["ea0�0"�I#a"�low-a ��b� ). C6� �:�� �Edž �"Q7 & �%&_>7� I.2�!1m�"b� yO{%�� �!�`6o"�Y>�I nS� � �zRjU$M�G}$ ,��%\JB30}�P����� � N+��I�AR� he> -�� ���z�d\�&�F���:iM%ry(c!�N�!�:�c �st�a�5 )s�. e.Aod�e3�e*i�n�UJ/ �n� �/*�4!>9�U�n�=���(ŸV�j��m"�1٤%] [s�>uD.)�&%>_e���Bb� ose�#�z%6TY7%�HI�E�%��>��/�93GA�a�K9�Bi.�rma�*�>G�a1A� �j !�.v �in��Z " 2-jouIÉF a miu�� "�4A�E�5W!d1pDbf���5a�B��ng6"}*� �a�:��3w�%m�vy�u��* Ŕ�.zm!�q�� omew�:� zer�q� �D�Td1u! !�@�rII� . Al��*> ��r�a �t�'`�L�q�$2:0�#����a�upb�@ reee�#a :2 eGA�H��%s ��a)( �}"4. �*!m=M!�� s��u�]e!aIdE�]�s get)�obv�a1�&0 r depi� r�+ A���bOQ������#z0r�*��'A Qf�ex�-Ber._+�A�7M%=���-!"5 J���t-ion�(6b)�ds,B�_&a,a@loZBa�"�It*� m��[It|�E5X6� �)� ii�ow��(Di!� cess�&sn"� � g�2_%l; &p%�5 alm�� �at��/odkHo5 �I��s�� .L�McKee"�i3, Conwa]o4�/ &�pPla�s�A*(;@4��Zd} |we�~C �Ns ��eIN�% 6�"mK>:1:r���(�y�[6h r(_�}Z�n!1��m g6m �f8�$��$���>�o�#� %! in��sA,2I���ɸMD$=R$�?s " weakT_&n #a�%a ;A�n�!Z d�3�.A �� deca� �KDa Kelvin-Helmholtz�!I�&"�f�" c�;;R�� ��B� �M$� rts u��!ु2&2LIt gr|a��& c�!th6�A V��� �LI !�S !�s>�vFe�eRQ>�%Gat�G0� �o^!�6  a1s�5�E� ]3��loo!��n�M ��-inkAl�>� �\��$v@ �&� ]�`"�'e.~g.~-�7a2 Cv. "�D�z}��6��*�ys�:E6"�=w���}�o� �IH�R��IJnu_lb��� �m*�&q!q�L�dee��"AQria�?-�,or�2k,M�*�by0  cf�� �d�!.1 6 (*� K}"�'�Dx}�' (6�Dt�4��Sm&s,�ly�BG 0ex  �) �>"U~:PLp�|�=M2�8�!AU��ta&EurOO��5W�" i8H}��EtE)Q 0�#� itG�let`E���&aa_pc�>�*G*.�tm&� KAQ P}=�56��1-6n^2&��)![��ti'��n>PfF n$ �Qeit"�r�~t=TM�A�a_i�}onger �cem#&�W� \o�[a�` 2 &aVn�7��"�- T��ݭB2���+rif[ dJ� �)er�`�rs ?[B@s:E�:y :� ���!b�cc�B5G� Ah�G.��Iy!GB�E*���� is a��*�!��Nn!uh%�m�x���&� �}�cal{V}G1!�6�ne w*B��WsPI�B��p�5U�`(&ixB ly double�7ivQd)"�1=�1�0tak!H���P%� "@%*�"���"� �M?!'tYK�"pdcY;��bf^aQ��VI�� �f)�"�*�3��a>h.$����Ѹ�&� �i�Zgh T؛s������~:��IK  (�zR��H��AI��^6PR94�;>� 4P">�be�as $|UQM}|dnE���#ue��(��-�n�ITw�+i��#!�A�jNbyB� =)�7 susm'�1�!� I�!:��d +byywe>less on zonal flows is counte20d, thus also Tradial<uctureR:ClZ0pronounced in&�high beta case, see Fig.~\ref{Fig:FlowTime_b30}. The drivhvortice�t feed ;1�h$m=\pm1$ geodesic sidebandsA�%$m=0$Mk mode)1@ transfer pathway�E�Dopen in both direc�s:yCUd!xGAM_�]� aulowI�%7e averagA�ains U%utA�NaW�-2 E7s. For}*x!�A�Ps, however, convertedGa cerA� extena[Xto $\tilde \phi$ oscillM�t!�supplI��. \s)@{Conclusion} We haXDperformed a detaile�vestiga�W-MA�a�L-Alfv�n turbulence��A�8meters relevant�! edge regA�0of hot plasmaI/(oroidal dev�. �idA�fi!+A� a�( mechanismsxa.�of�s with�t .�; name-Pelectroe9c>^, G $u�Maxwel�Gess��(Y� acoua�E�,A,��plingI�$main resula](re summariz!��l��: AgQ� �vsj6�a*negligia�an �>+i< on��riv�\ term1CA�, whe��gA�co ��videsawinkeP!�7 in addia�Qvis! ity.�,�o�J-�J M}0(:� becomes s�0ficant. It ac!> s a �EallBjs wm iU��!!it�q��cancel�� %ef���:N . I�{isy E�me/ )s%�ly susa��K.[�at now�i� oppo�mT1R dampAJ a�shoul%�8refore emphasiz� at from a�p8perimental poin�,view, measurA:� ex�Uve��s a�dic�<�R�ɥ%�ie� l not su . ��vOBmport�R,already at aeN rate�a A?9|i� w5beŷ�� L� ITER like���- A�� ��$\Z$s redu col��h E�T!�clearlyşademAY for q al )[e!x�AK6���Tau�a W tr�0compu����6�asa� �c�iAe�N�ae| levelE��v!n-�GAMs pre4�6�(���\!�s i�~F� 9�l� homoA ous:%nA�[ AsballooF� the ���he ��. furt%�xci�Z!y(can ultimatA��e �-b; �cy sp��a%he�=)a�ha� dip � peak���4$\omega_{GAM}$W0range, depend�g��or �rol�z!o6JevoluaK. Me�6>� �u����usa�  to d nguish weeEb8se two scenario� pr��5linsight�}o� ]pof�2i�finz a}H-�  m�-!�F we�-�� our numer� .'G!8a��� par� in� agre%6Iqrec� I0by B. Scott \AA{ ,:2003} regar%�iA*�s2�6�2DNJPH5}�, \acknowledg� �:work was� o a Dan!�Ce� �S>�C�AW((DCSC), gra� (CPU-1101-08e 002-17�\newpage. `bibliographystyle{prsty} 2{},7 e *� ures}begin{fi}[h!] \!ger \i� dekxics[width=12cm]{naulin_fig1a}\\�-b} \capa,{Phase angleA�b� tyAE�de �potZ al � ct� QOc  $\�0��4 = 0.1 $ (top)DEr# %,30$ (bottom)s . \label!*:�s}} \end1* \�:%�5d�R%R2a-$Ki�� $\K$�  in �8-���k onen�0$U$ over time�e!,$>+$ �.�E� Time� �)3�S3.SSpace-�����% �K$ $V_0(x,t). Mq AIlI�n \�le 4 AQQ.A{$>G.$.BFloN0.1�E �GEG4]G )� h�� terms,) � �� erro��%:]$.Bm � key�*a��"��  ��� �S!D��E�I�2�!AGenBetaB@��J�A��A%A5��5.� F�0ng quantities��$fluxsurfac%�d2,rh$,� d ,$x = L_x/3$ %u on %ZM �As�A�e��)�O$� �lin�Q �ideall&� 6p  �dS� betyaJ'Vn��E�7�7.�i�i30^h30�g ���8�frf 30$, w�H�(domina�Einflu�A�hfo��AЭ��at �m:��^F8R` �}I}9�}9.}^^�m�Xu�. fNU�MNPRN��Q�10�P102Q �M�M=A��K�K%�6� V���I�11�DDq�e��l(� on6t$M�wh \nuŁ5$,��stand����.Rscan_> VM�� � 12a}� 2.�S�� 6� $ �) F� 1.� 6� �.���Eu left ��[s1��*"Q .q $P$, k:� K$B -�o �/�clC,ux $\Gamma_nI� r� depi @�UF�nu_lbJ�� docu�} t0\,class[11pt]{b\cle} \usepackage{amsmathBfonts2X[dvips]{epsfig} \text4 8.276in \adv�.by -21he%11.84523 43odd!-margin 0�Btop %-.Y \parin� 18pt skip $ \renewcom�{\base� _�7 ma� gl�"ed!Kvid� at�S oic"% z2G,&.� 1� 2cm Y'E�DKeywords:} {\em Ne!�ve � 1;^�; n2refC&O"y M1vs* {10m� Q��H1. INTRODUCTION} H& mE$which2PprIke�th:�-���6n3�p91  (NPV)�� 8archetypal NPV �!�A^ loss ',9E , di1�--)�ic T , ch�'�!�H$ar�#�ivA�$�i �  perme�$\mu � -< 0 0be�s &fK#simultan�ly. I�< 1960's Veselago�dic!_Ysuch a � wd $exhibit a�a��#P$ngm k ly usefulB?#,phenomenons,h as9�Yy,�!4rse Doppler sh3(ar�!@rse \u{C}erenkov �(A� \c{�68}. Re.!observ0A� volv�!�mы illu5o��%�os�H metat rial���%�(ve �'U!ab(T\c{SSS}--\c{NPV_expt3}�h�%spark��&t��"<.t��t� areaT$LM_MOTL}. !�rea� ]�n��F��(lex--valuedb�E�$ !�A�$. �yh�(����$�'A{ U{��"�5inequ� �W� �!&} \��8 Re} \, Q ecI } ImN +fBmufA < 0t)��vi �is}��"giu*"�, �%!O� 2�.�u� 2�  deno��h�'al%� imaginary�Kts,Di�#. Greal,scope� NPV!�"�$ d��mu$M'�0's has bb de�D else ���>,\c{HC02,Karke  bi: ML_PRE}g. E+�" � unW concern�% �"ralizEaE!�co� \r1�, ��%:gof��� e�lly, we �ide,�ҍ=.= �^ most�arBh,*�( ro . I�#���at�!ntrodu9+�ɤ"x&�'�*)4possi�,}!�!0�� .�i. �1s�2H2. ANALYSIS} Let u�.�f1m�)field��ors\footA�{Va�Udisplaf/3,ld%��symbol/{}$�oa unit �.!� y�� .�llarray}{l} \#E(\#r) = \#E_{0}a�exp (i k�{ hat{\#k} a�8#r )\\[5pt] \#H<H�<� �\V$\}, \l{pw} �ik$| �$ k}| = 1$,�kA�UP N� �. cribi�1Tellegena;&� re�,(\c{BeltramibD+ �!E \#D 5 eps\#E (+ i \xi \#H \,\\ )A \#B = -);��9 \l{cr-(  1E.>>�(� 6�*� ��, $\xi��u$E���=inq�s/ aTa"R ICM%W,�, � in \lbb{R}$a\�a numb�- $ k = k_R%1k_I&, k_R,:G, �calcul�.*!� y�eT�o�,)�1�eqn1EŇdet�PsE�=L(i :)ris %�a�-�T$ arises� �BR( Helmholtz Q�J�=L()i}E_0e� xDJx ereiS=L$��a)3�/mes$3 � diff} |&* rator def�2 asv�= ��m!.�=I - 2 m(A B" - ^2� a8A4 -0ri \,.A�L_`B��Cfs' $k$--root"zqu�N \r)�E�ext/� s $E�^{(i)}a   "    v,��98u�}�zIr�6L)} = ��)) sqrt�!} +! ! \\ 9 :j6%H\98 91}p >q ;28v �jp��� 陠!�%�5�1! ����e|%�&owA�.� E�#--9" Poyn����$#Pa�H 1}{2}A2� ,��U� #H^*��ric�|aFe� su�A  $^*$ i2� �)�e4jugate. Utiliz� source--�5)��t��s  fi�0�.or�å%sA�� "�ng��a١x {2by \r�#,Qo�]}�m P = 6��\le -2�c>�!%a�� 2>� 1� u^*}Es !Q_0-SA�� k^*}{M;}��Q!�s6 ^*_0a�-!�#  \ri ��!�B� Our��ti�r"�)!is!�&Z  l�$" �ve orq7e��@:la�!q&, a KJS����@ $\#Po pursuD,is ma., lf ��3Ano�(�� .a �$� �0le � x},y z}![�� 9 @6(a�z ty  se ~  =�z}$49reb� t fo4�a�forward�4atJ���Ao6�PcElk_Ra� | � |^�b���box6�,y�jQ�.���E�4 1 + | \alpha�a� A�le�C'aB2A� 3k&1��s5�.� quotA�F6 d5$)�}y}}\,���haT/ :V �� �=S6��}} y� N� &=& - -R�!arE _{12}}{ �/1}� ;�� n9�4�+Ay�#e�y�$ �� del��<1.� \rիH i E�� ft\{1�����i \qquad�w for}&_,(�\\ EB�1ii3v)�@ n�V%�j. �$�, Upon combi�2\rA�( @ w݂�Y:f���Vi< 2��� �vlec:� * c�s-oŨlec \H �? \� la;0n ɖ6��Ab e�)%� �b� �\R���.�"� ��n� �-PR�E�A�i�I�� ]�i���7,�� "�occur�K��l�D�1"8�� "$F�� �a��O�OAO< 0�SٺR ����n\} 6�M;�dFQ5,�a��� � $kB��e U9�bi�? t9 toQ"�b:�Hep�b�z<-s�(���FJ� �IJZq\}��qr*�L3. CONCLUDING REMARK�Througu>�l,  a&j.expan�?; a�OF�!ce� �%�Jn &j Nt"���""��<�&ular, it�2�E9:`itude�e&q&J�E"5<ly larQ@i t�it.;� S23$!InE�pb�$is facilit�. Whi�Bhe��@�typic�  B!o natu�C--�~�6ag8{Bohren}%� {o =Xfic�EICMs,hign�o�)  enha�EF?upM@��6l ���8� en�in7 q�the.8}{99} "P'�em.J V.G."5,<= o�D!�sube*�E�t 6�&�] Ff�)�@�, Sov Phys Usp 10 (1968) 509--514.�M$ R.A. Shel> D.R. SmG vS�9hultz, E.ver!��  of a��$x�.��9\ce {292} (2001) 77--79.��,� 1} AUbic[3G.V. E&h3d�f�@C�F� -�E�F�F�.�, J Appl)I92�42), 5930--5935N� 2} C!�4Parazzoli, R.B�teegor, K. Li, B.E.C. Koltenbah%k4M. Tanielian, j�!�E �ofr{ u/>0Snell's law, E Rev& 90�$3) 107401N�3!�LA. Houck, J.B. Brock)�(I.L. Chuang:+o*0 I+!�--han�9 � obeys2�)�� � , 13>��0 A. Lakhtakia%1 T!�u&, Infin� >��bI�be; /i�MV#iA�"�' �'�')i2)h4�65--166.jL�.�,, M.W. McCal�W.S�Eiglhof'G�$ �--"�#N, In:>7�.i (eds),���to�le"������\ic�> ox( s, SPIE P3h, Bellingham, WA, USA, 2003�O9=i�&�} L. HuIJS.TEJi, Ch$F�#�6~�&�oiC�axi�w. RwsIa Aa B 66e $2), 085108.�a8 M.K. K\"{a}rkkinen, N"z? stud�(w�"2= n unR�$Lorentzian�K�� slab �e E 68�3�26602.�� ]�)X2�, P�8�s�m:� UI$in Faraday6�2� 69�A����&�.x, A&� F�oC),Media, World�A�?<, Singapore, 199��.iB C.F. , I".!l)�!z$A�R 2� � >�%e �  i �">iI3 &*,�P% A��?epaY %�AA7C!_��Hics: % Einstein's DxH��Y1905 MdMy* %\d�0�.$[12pt,full�?,sets�(.�0012pt.*1BF,boxit,Ax-doubled %\t�{emptH,(parskip 2mm� �"OhA} {\L �/BrownavMo��� {,-Go�ChildrAbigf �/f R��Bhaleraoq �-Tata I�� Funda32al Rese4), MumbaiA�dia} })���,v {6"I` ��}� *&"$ do a ``thh t( �H''� a�"a  e"� ? #2I carr)o�N)# WK.1may or �Hbe feas_K in p�i� 9ObyT%!biPe hop�;o %Hn someth )h*r�GGermanDRit+�Qmm�8d:(/Gedanken�}�RDperhaps�#q who pop� i`L3( word�+ ny gBV��ACtheor���*� in" ntum!Hc�#Cg:g���|ou�#)a�: I�&Te a dark, cloudy, moon� nigh�QS)�Fh57�ail�R%�2 tire �-. You�'�y��th�-�G�A�!nk(�Sworry bA$84E(tes�N0morrow. Sudde�Kyou h�%a(mi�sQ�Krs �A \HmanagC �a torcE rush � windhNow5./6funny:A;tu�&�*�for�+o+t,Kry 15 se�sawi� lp .e.,�(Q $t�Q (, ��Sa� � �01v��Q�frocL� b�0. Bef1(Q makee�wm�happeaG, r-i0 f. Next � it lAs up, �$t=15$�@�him�a s2ly "�! lo� . At=�Esec, he�!�wEpelkFd�(�Bde:d�/� tooG4�h~N s ag�O7 yAjDI �#no  @5goA�on. But�Btinue�  ����)!ˡ�I15MOe�)� mark�p�,�, on a piec��paper (A�U 1)�a>h�(!dpoint AED)�1J at B�>)a at Cso �ConnectJ�= B, B C, CD1 on,��st 470s. (Go ahead,Vb� enciv do it.) WAqdoAfA&8? A zigzag path� �0 {-i8cm�� (���"�Hb!] %I�{>I*I\�8]>1.eps�� YF;.)%"IM�5�h �>u�I.����JQ[? Did)ay ``�Pu�ga� w��aiW�s$e''? Ra���atŇ8easy. One does �Cneed an՗'s IQ!� �6u�Qn�j,ists' languaXMb above���ampLMa�(random walk���Ld�PRs}:&3 two}^Rau�\��O/i`�� �Á a lengt��Da breadth. (StrictAN2NiEa ��<be sai Vbe �iDO�L,of each step��� le�Nin]N�Lo8 prece��0lSsd5i��!�4tak�5kM/ �.).���M�seA! r eyT�V���1z19a��t��72.�3&8"� %m^iA�fw \par �~ u ��%}!t� A%�A=%�%���!�%�y5(:i�^ZQ��($N$)EQ�^ ��. (ySisa�in�d .) T)U�%U=N$$\��( \1s \�� )^{1/2}=N $.I�� 7-4}�5 �+% he�M n (=1�e �}` ���EAb he�ms�s�h��Si�<�Cd�*$x_{\rm ,$)��  �Omea� �] cM�� � M aMtC�K )�,� obj� !�s 2f�� �i%9m�st4ng a�` L , ma� �$ v3h2 j !7sa�[im�P�U� IB�X!u1�J�farz%v  fn[:6�(. Equivale d,1e�;di ar�caY��D*�V�al.noQt�;�ir. s alvdi�Ba�� �E� m af8�ilj r�lla�n�ZaT nPmq�e1�� r/ %qre^ )e". Morea\I�er�.� -gnyI];�`!� w�V C"a?(a)Q(I$. (b)Q�e,U����E A�of�t  . (cV:l;�� ;g  $l�3"� &� %��a anE��.� Su)^� ! &� a bigA!�A, watchaGa gaof H7�[� hockey,F>�'edk]we4 wo���s�[�a? se�f a�od o� %!l��bi�$en man. Wov_ you  ��~a� ? OfV9 rse,�g2a moa2#w� ����?hivO' e�-/)�r��e�1-���Q,X !Q an ( �)� m�<wo6� Wan��imD"sT(one? Rememb�9is:c procif�9ph ͯstocha�%�"Aqprobaf:y�g Kn� -]��gѯ!�ct a!�ABC� branch�,��S�0�al Me�icsB?u�{:�$I. History�"�{\� \it H��happi+who ha�B(D to gFr wis�5a� wer --- M�pHowitt (1799 - 1888). %, Engl'\poetess h|� Now I w-�des�9�>(� a"�)2GRobert L�a Britmbot�Q� 1827����?'a micld uspeu!wi�%�fluid%�v]v� mq�haphaz�N0fashion.$^1$ �/.�dCAnunder� s-�"? (q , sc� in%.%N%{s advA�d g� todayLHn��writte0}�iP � book �R�D����!%c�!Ahe ))���a�/ ? Or�ge�XOJd�t�����df%��Aryjj3life�a X:n�f�(cE!� �� ����is jusXoe propertlorganic �3? � '&� s��B�est!�r ! ic�? M���KEf aft 3I��^A�!bd�(@gnE V$�6"� �� �!�c%�be. H!u�m Bny6i@fM�ia�� execu7X [miNFg ���sis &nE!Tdf����e�&6}.�P2 c��;B0'n�[ual=:��}� � %$I�recor&%��val�30son�(F> J. PeM), �@Atoms}, D. Van No�,nd Co., Inc.=! 23.)�%��e�s e�m bI�L gase���'Mm!�� 19thX ury � puzz� �9ys�` ous 9w!�� tt�a0o.E��(�� help!@ideas su }7n�9fcur^#s,�3por�(G�o#M incNk�, n$i�� forc< etc t�hadv0ac��!�la0Xon6 it. W���wle2gof�gn��,@�.y: a rud{t��exY?.�!a���qfI�t6 %�7wn un� 7v ���first F��d�Zs!}�? And wh�f* er!\�%y ("�2)?b nk forp .'; fillA a hint5 auw� ���f.�"w *{-3�tt�t2�t)�t �{-1�%"�&� BU $I. Basic U�aing2b ��"t"jgu0 d7T!AH!�0i]mE�y� jerkyA���^mes��WMr@*wmous:�S8�koUN var�$� dia>o!5pJ�n9Tget-me-n�?to "u(:, � �L�,cucurbits. %� www.wood� org/t�0ers/bi/1997/p�2/ $YS�� Xv,us� �!/�l� ��i��ugh"k ��a few �ns (1 4 = $10^{-6}$ mnW1E�zto�M>O 5106�m 5�Ler molecule (H$_2$O)�� b� r:u���2��ln��,k ut��c���& t�$wa.}. Also� ���� spoonful� -co�ts c) 23}$ ��Ac!ic!� a�#�, ter say�at ksb}Hy dH�!i�=ll-estabq ż� I�~ soa !) >Y�U0 �)> ]t �(o9�A� any sam"�liq� r�)�w�^� T���6perpe�ly�+in&�C&`vN� a!��n� ��d,�+y keepYZ���`aD 41q��1Il_*an�# heir speeu"�%~..w� �7NvS whrfajfom�! unfortunenav�2b/D @�� cU& % M7AQAPp%fe�;a#get]hi�%� � � t,��ll �s�! millQ �`9�a_e cise&w '��&���!� �)a} exac,"s&�=y=�%�AJ���)�!�ing��K* �`(I� �'��ls (� E�� u�"essary}�Ū� !��Uo� ��I� ne�?r EO�s&E\nk%�i�% <.if5�U]= 6�M-=�-�Xv+u5� kick�a]M| Mi� Rend �AF9�p`$ i�� ly �-ig. 2 n�l>. V. A Quiz2 R+r� a quiz? ���s�" qu^on� (1) �(ASBpKLbA�vi)��-(No�g excepje"D - .) (2) S+{MI�1e.}5�� "2 ( 6"( � steae�*E �� S�n look,? (3)[%:�8af�ted�-i� Doled, or3A � #�%re��u��Uu",��1-&�  dA�� ��M1? Q "p:V..Z$Con��V�%N,Youe�5$#8 ive}*� auI�&&7 �s usu����}.�/st!k� drsopuntfva*�aTi�x!;i=)�#�P-qpr&fT�K�Lb8sted � lab>ory.$^2$�w,,�-w�_ ���*far (on�%�)YI1�.�a��4�8Q�a�$say 10 min�?Y�1��.�A�IfU�a�say 5 (orA�&{xW[E� .�} 10\%E��%&� A !a�%d�/d?XU1905,Un�\s a&e{m���rt"� A�:oAuw`#> ns�Zt���m�� A��l ons�6w did])�(?�  ,^T\a flavou�  % volv�D&C%%\��%�*jZ}�(n ensemble?\%R�����rB��Q�w��&�B!��! In&.0!Aen�>�uss� ��% �* box)@+�easfWu�$��1"�"!�nQ�J��.��� %s)k�m�sP�"�#��U>q $�H�� 10^��too lazyZn�,�  yc- : Get hol�6� f�Id�~�Nsk� Ţ�gp�3*e9$al set-�-A�jI ?F�E��U�then � 5a B1d ob2={m-�A�f�K� , x \approx 0f%:�!�%S5l�BB����a �-�b(��ws� &\Z��Q�%be �wAw��q�oa���j!��k beha_r+.�(�$'A�=�{�3"� �%�Nq ��U�AlterT !#A��Y9 ase�� t��� s,�e 2A�m�n5*al�|B*�>�. <i,,%3��2=��}!(" sZ�ya Y �^�&sQ01�Vys� s�m� 1��n�-\>��k\ ed� I�1�f�I�� talk, an 1Y(I��r1��C�#Ro�Z� "� �W�F�)+��s�,e&m ��� � U� �2w*���. T�#A�Vl�1F_�N D#,"FdraG $x$, $y�+z$ ax�5p� $(x,y,z)$*XIccoordMoe >4y� "J \�,�� x$}~: WU2��.8�f3��Y?xC��E�yc/��� zal"CA�j�t��\ \"��a�+ $�>�shq)�!�ca��a9�t�%$^3�Q2�-�x=�y= z=0#Z5v_57:�MI "�;�71� /%�2!,$x!�is33e@ 7.G��e,/ �=0th�k mind{5sl (Y� slow=z its &�0� .&.(�0!S7 �Oo�kA�B ve-�QX! �)6!, $!F [ ["( ive.=n �W!�%��0ISv_y)�v_f�AVAQ{v_x^2}ai(B�!�� 0qem�ee��?�N:+ sA��� 3i9�or )--- n8�I"L�1Aj"�x � tat�&�#�&.}!�� �}nI&}Now�Wa���U�I�h"�A� � $���Aa��� .�/( � A�e iruU:�nr�Y�3Eg�� handՋ70t i�/s �er$Ge$ C�*.A��� sureXCa�q�:�m����:t�8u �!-J"�2b rmal�,ilibrium�6b �Z�[rop�cona�c� : $$8O?Wm> =kT,$$ n8$me��mas�_F� , $k+a- � � $TA absolute �2Fy�:�=kT/m$|���eheavier".wAll�$�2erJ�. "�"N,s �Ij;��[��z$��s.$^4$ N1őm How�y^o�/�B�/� >$6�+/9.~!Q��{? �: I "�is" (JO�>.m�r�� blem.�%��� #��-��ofw �,f a� A*Imf]6� 2]6(Why? �$h"�rng��ce �.io�Jin� III U�G�� )�R�'*cl7 " ��eg1�1= i[$kT}{3 \pi Pp a}t}fq( Z2, $$"�J� (assun�\7sp�Ical$tn elap�c�0 s�/�&�/Y] �Y ��s� �barly}X;  (i)Ypq'A ���/)i%��(nity). LooK/8& last)&�!K$U�&� no. (3) h� m? Ple+ �Bx_7FQ! the _s�n 6 : (a�1F�is 8@vigorou��d�΁�{ hot ���-�"" =Cq�j�1bre%�{Z?B�.A�^T�.�th� �)e[G\--�+a�i�3B��- ish, peo0r boaQ) Do w8in B'���%��|�.)g2� A��spe]c��� MQ!b=/2�� V #x>��C�c�)*� Inj8� Fren.nq$ist Jean-B�ste1& �Ef�CB�2\ly��t.�q`aB fun��a�(ime $t$. Kn&Q}.V�v�Tv)}�c>heIs�M!�\ U& h�a �  N!�R�+$k$. )�� ; 5H�$ sona��/ E(for Avogadr�l(a�� l)!e;�lw�u�O� "�.g.g# �>V! M�/6��if�iby-� $^5$�'hv-�RY�M@t.�=y�(;Q�;y�' ng en��!E� J/!n � wordNyQiY�(� G�.`-I�al ob�4s. SkeUL.JtIm exA���si`�d... ��'f�-�G�aisI�N X.u�ng�q�yB#F�1�#�Kin. . A�+ [#6[�(��_!s( circu�$./�/B(l#?h+Š& �L"wo/@eRpai�&�/j �/H�c<0�p*�&��r�)��of 4s4 �:�._m,1ClrG:�=wly�,�- tell uc1 m�b�`e��t�E�#. �<5��!�g|m�"v-XinquiP� � �.!1� !sA7=_%�� �H my;: "!��_/c"A �`�3Bge2,uch wholesal!2� =3na@�,�of� trif�Ors�Gof�Ut} �=M�D(Twain (1835<1910���&�%\h?�1ݪ F_ls�$0S�'�:�/wrong�ACV��tI�$d irregula�"i �v'I� . S�Gth�>CA�*to&�M�o� 40 ��7�*0s ubiquitousn:2��A'!fm��s2� so-� �/���5�mX��a���W� wa}moved� ��1�bi�yiny#�ea �Oa��HV����K�&�K;Ha��@ ]&K agree! .� data���Ca�. .} �C"w � avsuc�#8A�Kttv�%� J(&Z*�. <� �PD IM!% M8sj)���y Mv>�Qe&H�%�1o�dRLD!� l� ^ ZD0\Z*(!) retiQq�'^4&20i-ZC%��X�ve2.E� sugg� ).�b!�rsr M*4 ��T^5$UE�honou!x"AwNobel P(MA�bP!1926,�m�hrk� �s*�Oend �|>C�aps,pra,<rinPoupedaddcTl10keys]{revtex4�DWvP~CdraftIpac�Is&�i ���(twocolumn,g6��b��P[prb,�Jv})PS =Y \title{��"B6�)u1-�O�Mble-" ��%� �L-sh�q� d/hox�&e-corrk\on x1� o�[8} \author{E. OrA��k �.+���369��date{\�7Y�abv4ct} CMo�-%a�YŎKs: o �6urb�,iq >�energch pe6��7W.��ai U� E�.G�foc�/6�� est �^pm iypt<�)(~ H�R8 p�?� ct ion�� D�)variet &XO- 9/ 12 scheM V��⥋e�J� �*���ato� vi�|I �)&BKR��!��BE l�LHFM�R�% �p��o�1 al, �5�~ �s�uuW���( H.�K)5d��Z ��?� � B�`���N Y��"�5�a�a�=A�R�I�L yG \k��{M/FJ,%�icMp ��s,�1�Cgnetism,B�i��gWcs{�8} % 31.15.Ew De$�Fz%2.30.-r �8ic� ctra1i C�*"s!��on-trtre/$2.60.+i Ze"�E�St� ef+ss'ake��� c"Y�e}{'e�d�a*|�e#�^!beaE�jBE$ FV"biEb�r2� r}{((rZ� "�rp'6uxupaJU:�d>UNlla��:7rv�:dg}{\da\,���Xbel{iS(}.Y(} b! (DFT) y�kohn,df�=,�y=` beck��r}/ewidely �-gnag�4�im�r�� �)-Q[a� a�2#�h�%ѕ� "- $n\r$�� �P�B� m�r#QtDFT��spin- (S���2employ� in-res5*�) rge i���$n_\ua\r� d��eeS *k:i�/cc�����0eta�f�.c$6���j5�� "mR��Ply d�@�W�V�,�]%8n�ce k�Ky-broMQ��th��Is�4 t. igr�>kr�` a�&Aar'Xo)'�r�byV)�C!� I�,vr1,vr2,vr3}1�a�s5.�!��͕Ys ā<3)~jU$e.g., totaJU��.e �.z��CRZ ($xc$) 2 y $E_{xc}]% pend�I E��*��':�}H��,j}_p\r*Oi}\sum_k�j,[\psi_k^*\r\a \r-z  ) \r\�H]�jcdftYU�to�.�D� �ll"'s�8�� 1p�X �[n,�<�]$,p- �A}%\r = �1}{c}�\delta�sxc6D��W\r�vee-"s�! yn !� >�  $: �n%� Kohn-Sham��- �18}a&���#�!� �)�/ ��N�y>in (S)��2�\e\K �ICon[c�_a�� $22$ u littlA�plo*�\� istry. Bx���� E�sh@A�fu&_"�B$R%-�h�s.� i��&�eigen���lsG�6 B� $I$͊�Inote1^i�ll�9!�Z$"�A (.-iCb)��*�k�� zBD ���a��� n un��y _��to�j1 localկ6*(LDA) �QnL � Oon"Mw zed-�6>s (GGA'*:a� m�U٪�@�"=^�  self-Ia�  (SIC)k hav�iLl,AEE"��Co6�app"�!ofEO a!M toBaverged%� LDA2��mit˭K"is � �2re��EAr��� To�"�S�"a SIC�X���edM^p�. l|%3׍!��s 5Ivat'�2�M�>�� �_"5 >"�ka�>�mt siȆ occupy"�� $m$-w tateP.le!�f s un1ied. ��a�abs��rbi�� ��:��mB� q-v �#� he �emd2���df�e�}/�7"�&�a�{L 1c=��,��i'E�a legite�Y��skA�!P| r�;>���ca^j�,6��e"�Val $-I�oa��e j*�1"1#t'!0�"ko%A!9 �%al5#cy�q,�a�!te9Hy�nI���r �*p6�GC3B�as�J.�yu��˯�in Ref.~� i:�5�%� !!�) e�h��!�*, I��`os��*.176"sU�ly"�do& �gt&ro&�B>S� 2  respeEJ� a�achie,6 W� aA�scu�5� u�LB ,�<X�6C� oE�ose�u&T& t)��u%�sA�*#��$m�*��g |�� �AUFB� ��G*�n �.�EHF|�g.�'b��a��%��:F��O) eL_ xJ�&R ��h��6� �#! tra��F�",���,� )T�B�i*�^=J�CI���tcbw�"nt�bEVi2c���B����V&� 5�E]#S2{ ��q2�5� d2�  � rob���c�L. tech��: ��p�B8ng�A. ��TQdurAJ>�Ohods}Met �:g�aN>���ey-body���&��gk8 $I=E(N-1)-E(N)y�ez$E(M)"�(�P nd-%��!sa� $M$&��e.,l�`MI�`a0� _e5����� ^ ed&�f�5Jc� g ofq \3�bf � 6r 2Oi^N��_i� �-/ r}_i)+b|_iP�e�8n�e�9Fkoq�� �, a�� tye>�š�'beu�e&s>� "�  F&� ��&e ,��*in � (bu�(�� 8 )�5��C^� Eq.~(��s"yjQ*:"6a>��F6��]�&�S�Pr��er�ntJLs-` �Xs�X� �er�Jc;C�le���Ofa�E C}%um@��(l,m)$� E�e%5n��M�t|ec}OAA�x� �E8 1D, $^{2S+1}L_J$. "/ta��Rne� �M� %� �-�!��+�=a� �T&ACqJ.&T"� �� ~F�%� <eeZ �"S F�v J�>�qj2*b�)�� Bsl.{ m s��V � ��Ss wn y�con�i�� $L\neq 0$�� $J ! m7x' . �EbourneX&bn,%�F Jq2s%�atlA*oǕe*C%"� whe c�s� co.1�E�9l4e�'6ork-�&al o&} &X'� � BTaWZB� % p��E�not�f-�)�+�r�-��%��f"v)t ." !0a't!� �d2Q ~(p�)���E byAAr*1�j���lea* ; jor�=&�-of! i�E�5?!pspirie�post-�!!�-f9 GGAe b88}%�->- Meta�k(,metagga}, �AAA��>y.6�h\+ng��� E�!0- �%eS(d;`�'d}w )���Q��toe -�!Cu�!oCKBs��*S6� ,2@�a� @j��-����5j!�I.31�|s�=1D�eHw -��s| )/] $M\o ller-P�et2�Uornd� "`B�|� "�&�Stone:�!8�&'Giti� nt fD��sm-�(gunnarsson}O��{Ksic6!�� ��-��in ail �s.�v*PDIh�,q"-����;2���p� #& Ma�fFs�1�? T �#�7A�n&�d\!s�Zpre�q.��� r~�w�orU5+�+/ �M��!�Mt��m��w$k$'th>�. ��n";�veqi $n�-V� 0�ilon_k6Æt d^3r \�� {p,k/\cdot2D[&d{p}]\r,�g+ ,%�� j}SS81}�YY#e x�3c%6I�&���>� DFT�P* ��*���gd!�^H& ��:9�]�c SIC,i[qs�%�/aZ�r"�-Ajf� �Y.S ��as�6on�%�aM ��L�% R������e8 LDA-��!c� to �� �-!|an�F���W',x�A�F.s-i!ly"z�v A%!le^u! �T(a"&-in��Ё))<*y 6zm�&� 2� ��H LDA+!(�3t�0 �`�(��-!tru22 %��1 "Y��. td�s�/��99�. �=�A��f2^> � ed upE\��O 6�*�b�nh2/ own  }]e"�"D��+ Qhm>�alR�i�1��#"{fed e�-�&�6� hecka/ !� �5�!�a&K!���XAa&c�"zx1Tot*�E�s�s~F�j0 f�^e�!��� ��1ic�0{U:#�M���]��*� ��`rs��qK8�_E� %�Z �.Y c[ Jd )E ;2� � %�7g�0GGAs: B88-LYP�(b88,lyp? PW91 pw91}. E�Dcho�;�0!��m�d�p!�Ad�inp��r�s  L��.erw e5Dng9IMG6�< a ��-@w0X�l� � %�$mc� �a��9c �t�)$!1to! e��LJ�anyUgb{�pl:5�S analy�&r�:p"�U}-3�U��y $\cM�s LDA,p$^{LDA.Dp]$ (cf. Eqs.~(8,9�oF��17"A�� vr1}�y��&m!q� *V+)%s* j WJry �5"�F�I*� �Xi � ng uniO/&'ga��ite�"!& . Cj�h&�I%uG�vih55h(L�,u)']=q )qz&3j Q�ed���o�ie�b�!as'Vignay.Rasol�Geldartm=vrgiQparam{sՀ,by Lee, Col5[��, Handy (LCH) >h1,2 y�inJ�. ��� ��ae<�Sa��� f�IS�cterpo�I'��f ls_{5}(r_s)=1.1038-0.4990 r_sRrD3}+0.4423 \sqrt{r_o2n��, \\ -0.066962, +0.0008432 t"|���&�Y��Afi�"s7gq>y!} , w�e LCHA�J �%^>e�LCH �,(1.0 + 0.028�)�{(�4���  {lhc �AYA�D li#ng*�N$as $r_s\to�A \infty$,�(a smo""�vee�*�&U��,+o���! I�]IQX AFh`��8HcG�ed hybrid.}� �s %5�)�g $s\r$� !6) itsn:d�� s�S(d sE�}{d!�j( (nn} ��'� I� exQ)�I �^��A�U$n =3/4�EA�31�$s=��/_c� �a_0WA(�j*&�:�PS>C$$�q�i#Bser�:�e��%awZp��he��-��-��e_�2� i?iewq-cl�E�Pa>��isq:�%t���aL6Q4�& �E�de a semi-em�cK5�!P�A��b�s_{se6�b\, r^c_R�," �s"t�!�H�p$b�+$c$�f m|ErǪaD6W � c$1]C1~n��t�i� n�: ��A.�#`22���K5TaluU�=FC�S�o`:3X dE ��>�:�, 9�%�U&,=>�� *"�$%�!!e��F��1* ould�"Ib!�-�}Q 5G*�":Z A��#S6��,F �+iE8 j� i$l2� If�F �F,Alac��.4-Zsu2� by a0(.�%O@[�} INS!@e  )@yI� fL�� tn* �>wbe ad�Z# <_yp�K i��*o#1g�1�>� ��t�<:3~}R�'= K�us}� %�*�� in TE��t 1} !+�7!%a�"�"\# (cc)T & - (sp)�=Y �=E���c�Delta I$��v��ELof� �krieger}),2�1��nisi%J)��<&nr,"j"�-��� >�*D , $-6�.�e y %f�)U ��9�J.9�7�.e8 s td��C4"^ .  ��I"K6P�8!D��y&�  (basis-D ��)*\cod�| opmkk�  FSfc� U>>��I��� e�?�� ccin�_����W1�>Q5�`$W�Y P>Cn"m�K/Fno���!%.�E�$\{1,0\&o1Iq�J����I ��N�p�>�!V� �d $m=1nhe��J!0$.�"=s>0$TC�8 a6�X.> dR%$ V2. S�V1?��-1_k�[kp�Jse)i�f�؜ signT.�t s � ��H,b�1��!\aEuۉ��]eJif|� � a ��M]�t_���3.�[}����%�:�!h*��Z%�M����i%> w��5-�x� �%�.U��O/,�/di�+)W��ݑNi���!V9C�lu�Y$s. Altough� �E!P� :�&�^"���d��t9�� ent�Sec��f>6Ded �Mi�isp'�ngq�,!�� y�vifhar!� � �Bݪf�wDtoš��u not}^��V �.� ��}!P� h Q�"Jw�+u lS"6,i�ei��  E,Aa` a5 +vec21Cm�U� \sub:{!�IF�}�*��t?of�~�i�reim� Ii*8b&�a4$v�6$�!�� *� �a<06�. �&(?�.e]�_ɽI�F���A� &qx�l���Lur�!�w)3�As o�@ �.2�� Ve��8y9 td���obA�ei>I��4m[ e�E���aqW<�*�0wz(��!*` -row���Wre�a� �7q5BE icm� $Z9��V oK� � lJ {��XN��Z�5 {"� $:� J�w���#�v�ED/� +��)H^ "(3��"�inA e_s.�O G��-�Q �ch��s�#�lie�� �?2m�C ���s,a5x$�T &��i�p��&�N��L2��ou�x�fmU<oriIK"%��,xt ��Ti�"�u�<>B�av��am � � ticip�6R eQ�\�=i &�K!�7h�����=�8�9I��7 & , 3 �v%nPi6� f�m ]�R�0�m�da�a8O%".� �! "K? 6>�%a���K�Y2 (�w{!�cF�Qing�M �= a�.iH*�3pmfg �o.*@=h�@"\:&�Eonc� UPMA�# B:� Wk�B+� �/:qI)>�-~��Val�a$�s��"c�5!�� d��Z.:,u%rMɝ\E'  �� �tQ��-!��m�1�*� �e n inFh.�&!��*�A�Ts� k UcH ����qAly2)pr *�u!���:��a 8P 0Ugp+x�r"DY��</GGA)7 n����! Iw=%���a�e�%m ��z�dE��;$��` A�I�~�RA ���&re�Ua clos5#�&���e:�7tLHC.mt:>4� 4�2F. &�w՘s>�{v6�F�se}��e`5�$m_1=1)?$m_2=0$Bw6("6 )!�*� ��.�!-� to 1�� Ve�l "���� e� ���i}Soc�6�:�di� �G��f��y��6� al]TOW:�.<�ae6��aV]$aX5�)T[ s� 1Rɣ�a&nn!���8 �3� w-�3 s, �A��Iy! 1�!��y .;A-Ms'�F��� �s }l&5��3��� uOW�.n"g�{YPdu:)!��s6�fukerS"�v � �-2���.D��)��Q* s!#����&�s +� deci�U2+to%�icB�i�$J�<P�y's�')UR�1}"<f.�O%SsFG ��W!N"�ly� A7"�0EZt�|x R� F4=�!�B!�isI�H to-�a(6,���S� �2t&@P���| ��+$��&e �]8Xh h�AA� şN ��i� �����. J*� �,&6 Mo6�P� ���E��a�be��:�1��Q�ed^r�� . AM�z?em� �"Veleq�R?��a dz�bt���\au!FZ096�H�#8pE���F�H(R�oug� . (Data�3�|^����6��V�be5crW�ble"�_-`w\K�!0$�!�!,"o�polynom%78)w ) To%)ec$7  `d�Q!p x!|*5@ &-"c� 6J%Not �r$rely trivi�=���&� ��$��s: (i) �H�_"qM.��-vid�zev"m��5�m�!��- Ir}$~ �^(&.teg��,�irW$du� Eq.~E�e2�;m. �� d"�"elflnoY u*`0�Qx�-c, ��%�H8y�+!�A�otHm�5OzNmoh`!�"/a�A(�a�*bJ��%! |> i>��+ : �R�� �V6��!P�%�tS6hTgG"\(�orB3.�$�D *].�! -i�5�(6Bp�U�6� hd�fY�!I� %�F�Eoa�E���a&l*�q�[ situi�a�mp*�T8�uss� ���e��:� sqȉ���@ �+2�%�Qd2<�-1@s�:A�E�t9 aJ�P 8YQ>�P�Ose��d� !,�^���va0�ac� modern�Qy.� �WI�k�nl7~͆M"�&B* 1 3x� i0�!�n.O �sV�&4<�VkQ8 �.�"Bi�s. � sa�UI�%�6$p$a: ��0t�J2A!a"!by"�1:C (aP-A�-7�JI�R��k8!/1"5 a"�\/��A���, a� N;!�ЧI3�6� �r�Lre�p�*�u9vc$% ne�"�!�M�]b{aI2W��f�� !%� �c(!�R%�� ofIeJ� � "�YU��AI���� -�n�)*�#.�4this context i�Ut is also interesting to recall the suggestion by Rasolt and Perrot \cite{rasper} that7�R{\it ground state} of a strongly inhomogeneous many-body system can develop sponta *�self-induced currents. This result was obtained usi���ame formal framework as here (CDFT), but with a quite diffef choice�O�density functional (optimized for two-dim(s�4s), and by per�!u,a direct minCaS ofk\total energy (thus avoid9ny)@consistent calculC(s). Clearly!~po1Ily1>-carryL.�E@n extreme example�%�stabili �$, in which� �lowerWdueAU-�<-dependent corre �@ does not only re!�.Obelowon%�a SinU.�!�2s!�-�E�, !�even Bb!��V:,. It remains�pbe explored whether our aboveM�, U�A"A�,le-particle %:ies, A�b6lated_tA�typ�novel mu5.�. \seE�D{\label{summary} S Concern!��]3A�ion-�)�� we find ta�nei�= descripA�>charge9� �.44LDA or GGA) na7he quala]i ��poI+ used%?* elec�T0-gas susceptiA�ty (LCH\$five-term 6J(s) decisive��fluencIv6��al-� s, w�4@as a semi-empirica�xpress�/!��:�0yields betterR then> s ba�onD�< gas. Although i�…possibl�atuy9s@s designed specif�ly�finite�� will fur%� imprY�s,�;compaA�to�%� �u, ! i/Aud�Wcee=exper�,Lt are sufficiently lAJbsɌE�Oy,a��c orbi�+m� s. WhileN�)7do@ seembb�at-affeca�byJV��eks,%�:�i>yMș�6�s is. T����2\ ;se��s�8means!$ exchange-�m$ vector po�Pial, ${\bf A}_{xc}[n,,j}_p]$, is f�to! robust ag��$t a variet� numeI���c�Gptuala�ng�n �Autņ,al procedure�isJF is4leta�misain1�-Z�s��may�elevant �studie%,A�` etic�ss� volvA�uif�n� �'a thBa��ral.\\ %U(Acknowledgm�} We�(nk E. EngelelaN��u ^�< Kohn-Sham code I opmks}�w�d���P�>(S)DFT m s��!�i�Q,LDA, B88-LYP%,PW91 approxiA�ons. We ��0k T. Marcasso�collabor%� a jierA�g�� ŷproject,j4L.~N.~OliveiraJ,useful discu�=ts. Financial support by FAPES � CNPq� grat?�5zed��begin{thebibliography}{99} \bi{kohn} !q�U, W., Rev Mod Phys. 1999, 71, 1253. \bi{dftbook} Dreizler, R.M.; Gross, E.K.U. {\em De! F&! dTheory}; Springer: Berlin,n0.dp� ang} ParraG.; Yang� {\-B\�Atoms A�`Molecules}; Oxford Univer� P��: �89 �!becke�9!; B, A.;� J%1 Chem�6, 100!6974 Q4vr1} Vignale, �RI , M. =!{DLett 1987, 59, 236-vr2�?B<8, 37�685|3b=l; Geldart, D.J.W Adv Quantum�0, 21� Q4footnote1} Note������ a�A���8t from Koopman'�xPeorem in Hartree-Focka� ory:��nclude�"" ��ho=# `�hhighest occupied eigenvalue)pcdft} O� ] E.;u�(, T.; Capel!�K=�DA 2003, 68, 02210-jpert}^5i860, 73m7 b88}Y=D2d19%�!�098 �E}62J)�i�02002, 117, 691�\metagga} Perdew, J.P.; K�(, S.; ZupanI�Blaha, P�A �82, 254M�0gunnarsson} G , O. M�0F 1976 6, 587 �krieger}�n�; K  8B.; Li, Y.; Iaf��aJ. �eA!IR4, 393m�(lyp} Lee, C�.�%#B.7q pw91>#(Burke K.; W�fY:E�1651�vrg�V:N 88, a� 2502),8handy1} Colwell!��TH, N.C.!Fm �!�!4a�7, 271F2-AB�Q 22�y2M��3�R]�� 5, 1a> 1009 Pnist} F��� (sp)A� te, �acter�r ��_$m$-sub����� . AB�B have�ma� �deBsevG F�configurg sEp each%9�E5we li�?#� ),��number E��| � Sy|clu�9o4three: Negativ� KpA*�  : q u!u. LCH�� -((\ref{lhc})��:9$\chi$5� four†� GGA, �C�>`iv��F ]��:]six¼LDA � the �� (5t) Eq.~)D�-I>y��{5/zj it�� �![e"� �9�its� d�5�eight�z :� (se).� �seV*nine:�ieyazero-�NB�y"DM�\in LDA-SIC \protect\cite&  &�alBU ies 6=�}. Allɀsin $eV$.��� ,ruledtabular�    {r|r 4} & cc sp & $-6�$JN' &F:� \\ &�s &E(   & 5t 5t/AG& s*$\D�h I$ B.&e'&a��&i�aCP&=L\hline B &1& 0.072&0116$34&-0.32& ��18\\ C5,0745%44 $J23 34834\\ N790.1158H86&-1.:42\\ O3,�1� -0.1393271\\ F3,-1�0n3�17 27@\\ Al! 0��02�+ 0.09m� Si & �02252 r0616g09U35\\ P�159>08J473 k6% 9r�%�005-?)��50!��!y,109�-017O207%�1!TSc-3I)�4,26&-\\ Y�I3%6� 1 5a19&- � m� :�� � ! docul} �W\ style[prebLt,aps,prb]{revtex} %:*12p&"� R4} \title{Surve)�^solar*# measu� angl��+imes: ��5;togravi") tant��,author{KlausoL} \date{\today} \addF`{Instituto de F\'{\i}sica4S\~ao Carlos,  dade�l,;out� " �ic�6�1�%cel\ al bo�!p$e pedagogi7�histo[sp-)js ���� d,�riefl��%Yw4 % newcommands� {\be}equE}}}� #e#S^!biDibitema�0 "Introdu!} �i} �A8� textZE a&!omy%� clasa� l meS�s!�A=$ great ins6 BKepler?NewtonQ8�#$ in�(e geometry ��2�Q���Aeof� ��ituax)�( (Refs.~\onc� �0oll,knudsen,l���� esen�v�n � Such"Z �0n�!ly'd&M�&P q�ma�EbU�jKfol�d|!�)2's or-I's lawg"e purpos&� �m�s%]I� a littlei�" simi�6 �Zt a�sB��+!j!�i�pr. >^�H;A V], ntirp �l very�$ple observe&E_>% . S �sun�#�ap howsU��RIh �A n� ��%�M� nothmorA�a!=e2� le under &�" ��ppears!s��W!��ddA�a year. 6���}sl!�4Z"idea ��#*��detailI�sla�ly �#lic�!� ase,�� stil8 ves &�ou!eq'$erŤь6�{l Ɉ,6��1��u).6gamma}�9�Q���riv�%an�� be �sc" �V� ()���!�n to i�)�uHŗ *avail  aty�z . �f,!,� cour!^QKnew�Saddd#�a� arch!���these���i,CA � ѯA� curi�&9% ��e�sa&dA: stim�%e�%tu%'D�'�!�subG. They mAJ5gi ,t5�poid view!F�g* sc!c%ecaus%�y%�e�)u!6 ld, e.g.,�&T=Z�long befi�ebrE� CavendishF�!.c} A!�er �9J�h 79�'rvea�$vivid illu� �Cof�in��2 , tog�%w�!3 assumed u=a|idd$m-� �$���ԭӉ� *(  on.� R%A�!inacce�#�J�E se2K ��)�Z issu� �4aken up�!QUfinal6�-Xio����eZa&�h6�!5�� In or����* ab(�Bm�:�:�p 0 $\rho_s$, we�!rt by �A��q7aAe e�!�tG)� vCe, \be Z4 = \frac{M}{V}<3M}{4\pi R_s^3},�rhodef�e &��v\+I8oba��)�)spE�of $R_s$%� ��A be elimine3m�is � � �*(centripetal�"c ���e`%eo%on� (&�!cir5*r)�"Y� 6�att� �M�!��sB�,so much heav"J"%" �E�!��0)f)Z2+ ,(-sun coinci� m�a�!salone. H�)�D-m\omega^2 r = - G-�mM}{r^29�forces.�$m$���'s�, $G$6 an�" $r $6�HAsun. EM�-��veloc�\� ~`��%n � �r��ro9 onAa0iod, $T=2\pi/2� s�$*� �t $M$,:readi i9 aM=ia!K^3}{G T.@meq%= ��A�s� i�� 'a�ird law�s�:nI�Fig.~@ fig1M.e9?!P� )F��!�isP �K!1� B - mO���9Qq �'�(\sin(\beta)-R_s}{rY5d6�$2 3U<apZ�uE SiA�� 6��aH s8e�, U`b!~is �+onlllI"6wh��d9.surfa�m�%�\ � A�i�. (� echn�I���mea1-a� Pparallax�� negl�.)=. - �3!! 2$r�!� '� !AM!ABw� uld�l�$=�$�e1�s�igj+error��gh'�,Y$future ap� �,to� ��s� keep%�trigon�ic"=+s�T�.n ��us �1e�%a1/&�-t�7*�A�ut 8 ( � !�nb4�e� �e���/� �V�s,H usu)��&�o ���eJ(��z3 &�. 5�d2X0scale�e� �, �B* 1&�%6�raw��8' *j8 �r�osi��xa{��� >3. If�2e:an adm�*d�1��(rary way, �s�id iron�5:Z ��=�-s (� ��Fe}=7.8Rb$),Iu8 silicon dioxidr:s�� rock)�s!�2q(SiO_2}=2.65R[FtCbo�4� sNvExom1`2� �8who�/��mmedia ��.� un��%� not}-��primar.�so!�ma@*a! �8@ yL- al n�|9�%� . Fu{8���ae�e�*�j�of[ � s, liqui !1gaa�{�6l�� �, d��!�5� plane�r� 8!)�0 %k, arr��� �)/�. �h�6�/r�pia} he� es: E$ɳzer� a�i!O�Jup�~ �: SAn w�� r � .H! sun;ep E5!�# heat�kepnZ6�ref=3�,}-�n=1�"���=r��-�  A�J|��-t�-�� 11ima51p>"b��ly��|B)�ses$. We��C:T��#w�< read�eE� 1�a�%��)-Y� why. Q�l$��2% picts�gl�nd*� *j3e�.�% � re�! a�gh�$/G%�;��a��� . How��en��al3E � � )�-!�M& teadr sun-%�,%$m of vT n shif�TP�� ra�'y�m&�*�p]Gle:%�� �6�"�a�}U .�, s�� Bp!�!�-�a**�!O.d.c�*6�ac� anE, !�M�� �sen%w )EOough.=) �}�D[ ines){J�J.�, i.e. a&�&M I .�E-� �!ereason���]*Vd�?.Dtyp�  io��>�� A��requi �inputIz&"() �e��to tur��e argC. qe!>apJ��~�F��d'$$2\alpha_m�.r�F<Rby;A�_e�A�l� �$har� 5 p!�yGau+E� ��-�z(f� , re�pre�-now�d�13I]~l 2�0"�_e)"�! R_e}{R_m}(1)"�6�R_e)1$R!;de5�Ai!~-?"�-re�,i5HKzLxE2 "�!%�un)���~5�"�sR�!B�"�;f�o)1 �e�%ads)&�e>3_m^65_e);"�"$T! �<e � ! Aq��&T.�(L $ $27$ days�L[e�e^�%c. =N !oŴMv�� help{y�%Ts})E�� = � "3!} R_m� R_e^3}"1}{A^RmQUee AssumA�Gj�Zr�!G �y!@- %:&� F�nd :b, =WL,Wd6xA�&h0 �J|k)it cer��ly x)>F)!�&aE.YNI�6imoo�!�U�. Pute�D�s K%�$R_m=\left()�G %� I�})�\r�$)^{1/3}R_e:� \�w 1600� kmU�� A��H��UTV�� $1738 km}�,e"�ce"�"�F��"�+ls. First� r�Ara� a"�&lPu�*%Q<�ta ^&Ap"�I�EreI.�'ond���2*3+%�i2 "�ly��� ~!�0g{l!�� W�t+Sa month�r {p�!a_� �H�R � .�� �at ��G� b�<"�!�n[)d�(��[-nT!- c�Ec�r"  sI�-y�RM��� !6P*p��!e"?  satis���mo- �%��!i�t$ 1�X�L.-n$I(Qm/instruc��A4#i�,s ���p aHA�o�(ntM���. D1�m+toECBNon).z�+Y��*$�|mak�3Owa&�$`J@@high-school level��bed�hoT�lemMr�adv�"Z2a� �� {\ita� ios}u�#C!;t5_+9��wa�at  toc-����con� orarsQ! 2�!Na �le �absolut�C},� $ �,"� B;0O2&i#�#. A��mp"�� �" back!�sy� c�7er�Q2~$_ �$I�eOI�-A�,.� �y$=R_m/r_{e-��!G$ $�n� K2Y!\ $ 9�+32o������ ��:ҵ���( $3.8*> aE `S�A[U��Wf'�!E22aJ�t&j:'�!15�AEAZ!y m@�|��%�]��� at margin� e�3va�0� e��!mU�n.�.G.1V�!"C.{2>R did��aR�&�P%��2^ bant. F6�><3� oWOcom a�� �� �ɾi�er�+e�> 2*�6,U�afd_ie�N�6s�6 ;��v �or�,of�^!��$s.�,n �1�ayIZSeem/A"���"'in�t)�� �6&1pr ��0 f�-<p�B�C-m E#U� in 1798A�Henry&*2,���� hund� �5s 4' � d�� oped%�tkME�=�I��"�2'���2�C�"�(recognGM R� unti]*�Y� �:X*�2#c8ck!�A�h{*;U�!>is= ti�/lyL+["!�in�0A3!:tA�c?$,e��YJ�3i� or�>���&�@havEbo b5orm��6�7�Amu�X6�4�� � .�"�6 7"i.i�V} �a2�720kep.�mo� aMi� v*�=� ;p��<#�M"� a! ms9p6��+E�! a��b#� )�7� ��aYb"y=��"^:wo &|-a�obv"; way. SI�es� �  ?7�r .;Btool, �6y "�9e �9ly�,�&�var�96� � .�'m52�?�$o8�0���9 by m�o� �~ (. A�JT is)� philosoph9,IIJ� 6Qare��s�d��(M, exerci!kAp��Bor���B� r")� undergrad�,orFp2��AE��)�$st basic ��"�,-E�%!.E�:�E�A��e .algl<. " Gb"p*�!�!�./ telescope�� a cros (re eye piec,d�fil� �>. U"W&w �aJtr'!s$360$�/e ��dayO �a�:�$� �(LoO�owny�F*�U.�'I�s"�6 �D�&\�#>*� sun�� &�d=��sT'd ^r�>�[i8�]3 �!oima"3uca lenApf'fo$(length�eadeR!}�ve*���, mw?#&or6� ��(�1�Bz-`B"% 6�1sunsetvdQj �>V 1�W���>�uti�a�30i�H!uT"*"� A!� �$a]��Yst�!#� dك-H�C ing � ur�3I��"!��cu�=wP.1O�Ota#A�3a �D""� I�!1Y9 $q��#*�.�AP%9�� �^H 8!Ke)Vr*�A����: �(��N �? ors).� �e�Ir�!�C$.::� �8�')a4�t�A�E�ave do�<T��&xe��noa Agnt1dA>ish �'s �gnda�� llec chiev�os,g zvEMpu>5G%��w mesu���B�)*�*Ev#� ' �bf��Ct�.a�;k�1is&+ ]b5 g&9of �ian.TAV��rR��''*�i�a�.�K!IaiA�a� &� bK \\�Qno�bntV:b\\�& a pl�j!R!,k:Ha8, V.~L.~Libero,eh S.~Ragusa c!��aM&� �%^D &�*~ �b-Kt^La�I(} B. W. Car�I�0D. A. Ostlie,�M(Af� L} (Addison-Wesley, R�>ng�`96�'\�a=J } J. M. K i,P. G. Hjorth iElI�6MIK} (�a-Verlag,.�a5[[K. R. La���al For4�2nd. �bn^80 ^&j != E. Clotfe���ita�&� ��as "  kn�9t}, Am.!�C1bDbf 55}(3) p.~210 (fa ~.: H%TNusse.: �Curso :XPB\'� (a-1, Mec\^a�=} (Edg0"Bl\"ucn4Ltda. S�PPgP1=�"N1b0Hanx4!�Ubis�L�9�ic e�9D)�ide 78th (CRC�b8 LCC, Boca Ratocc��/1.�\ �8 67^o"�*�Ne �o� ͲJ�9 �>qsEmc*�Fvir�kly~ino uish� 4#� 9,"9;ma ext�!pr[N�e e�5 ' a"rho_sb�59]1 2}�)��%4id�e�%��is1G�%%&xs�+k4 �%:l?��r's M 4�M _1&+&ing) ��/ Isaac��A� em MT�^a��0&�Y0 al PY y0Book III, Pro�8, Co���III (Q6"� hin�W,by EncyclopaO3 Britana Inc., C� go��52q�f02���Z�10��2��U>  AQp.4_+*4_GkPmEL4n^$ ing k er�.� x �%A�(@(s$&�*�1mqry:;�%~�@a{�#B�2&"<�E�he�F�)lA�� �� ��E��klnP� Q�l)D�:K&`gla�4��=s��6g S.6-(�%!6�( !�!)�$��� � 2D,Q6d.�.} %(�WQ &eW�b%% * Star� f!T(apssamp.tex ! % % �(# 3!-APS\REVTeX 4�� tribQ-.EVion 4.0A� *, Aug�= 2001 n Copy�$ (c)�Amn͟(al Society. 8SeE e Z 4 README���� ri'T�*5 J TeX'!�� �_�at you e AMS-La�2.0" alled %!�p0\.2a�/preOsit| ) !�n� %T"��run  BibTeXPN��a� (Ms:a 1) �x.�!�2) bibAM 3^/4V*�Y[twocLn,� pac-Z:Zn*b,amssym"AZ4YzZ D"kZ�C %z?t (�`���A ny) ili�jB�vaps�Z4.�Z:� aps,draftr-�%Y�ReD {fancyhdr��M�{\cdrl}�(�( wxn"�X!lr (#�`Z( '#:�Xcd qIDB!u ju�moFd  downZ@ "up$F�f# js!re.�$d}{{\rm{d}>zYpx}{\��ial_{xFb. \bar%:�px6FJGRH^Ot.ttBntF�tF�yy.FyyBG6 Bt6�'F!a!�5<\>t:FF�zz.�zzBC6 }!�.�E-�eBI iBb�!�B�sbs�-qrt)�S< %\no��[�����{ �^{Conn�X� Burgh"� � �Jlastic�c�u �#  �)och � ss}%c� ne break;th� �_\� ,bf{E. MoreauP(O. Vall\'ee�B= ph{\�L{Lbso�,d'Analyse Sp�x�mH et d'\'Energ�t�BHPlasmas\\ Facult�S�U(?rue Gas'\Be! BP 4043�18028 Bo!)s Cedex"lce}}.!�$%\altaffilH[ ]�`SuEA}�$Ll{eric.�(au@univ-orl.fr��O {% % ?s'���!nd/or�W� \\ % o\)�%�D:)|ackslash6 %}% �Charlie� % \,*� {�m www. �.� �.edu/~ ?. �>� % 8��%I���2 b� �lways  b�8W .% �~Lbb�K�$� ified"ca"�aW �Q a� �w aA��re�*!�\ one�So$qv"&0 �a�>xew $-\k 0^{2} x+f(t)$,�F \in\��$bb{R}$. Tw*J����f#trans"�s, Uh�L�yspa:�  emaj��4 Fokker-Planck���-�VE]�+��$ a fluid k=l,O5�91h��4!��0Ornstein-Uhle�u)FrX. � 9� \ H{02.50.Ey, 05.90.+m 45.-a}� PACSVPhy�%Q'L6�>% C�Ji�|E[a{�'�Kh� a loJ  �4�!� N] -Sto�1���cu�=i�)ah� e)> kin<' ad�{�n�Oari�!�Reyno+v� q�def�"� �E�Cii�"burg}� addi!�!�i�:�a�>qu)�LuchV/uE�e��EaL�o�.A�turbulE��~asympto�C be�#�]�� � . Bu�`a�al�z@ c� Hh.j�a��poxB|d�� m6�~'�J`-�2‚jcU��fo0�_,4RE/+.=^5aE7a�<.�g� (OS)M�OS�?�,=i2F�(zX!-)A ���B02o�;q���. N�)thele |��d�MA��equival'e �to 3l�TQ����S. BERwa ��-�o(Hopf-Cole �i�i� H-C}:�1�qgE�S }�}?MG>�= o�MA�MEa�8�#a�� r��DerCI��T magi:5��t#�Fd��%Snt&�E?n, P )d�7v�7e* . oL6 past}a* �eM`�i1 �/Ci��E``Time-S�T2-�" (TST)d-�N ci�}UPE!�Scj � �~�( mov� �% ! -�"� (M. Feng�(TST}). I�GD��f�.ispc}�!U�*�8� TST ���B�)�I�7�0sa� Z����U) &Q lyY�(��/�0F�IH2�! $�� hvx!9diagram� ume�j-q�cBRHeat-S; ig�R�6 x2BE%>mI�HC�y�6�&wW er} $\CD 6I.�\ BE}} :� y{ &O,{}2Ho�� 0\\ \cdd�HC}}}{} ?d{}\\ L)\,(IW)}},r *AJ@ kea�endCD$ � �}Xi�;A��Sa�evpa-hb1,infiv,v-**� IY�;A$h1sW) i� Fu%�6>�1�2r ��� V� I7A' t � $5.� trA�"�4a:�e.�zSd�!� WospakrikeyZen��wt4 � ��_!v�R��)ya limi c D�&  coeff���Gd%�v!�&�  ��eH5-�e �!�8 ��ll�-�outAl! !GpEw�^b!uUG&C$ next�V��dev�0��he) mAnv n"mɯ z�n�N�pa ��i�the97u�)a23OS �. �# /�Z)�^� Psoc�QnC� J� t�Z�++*w�Dhe� . C�[t�Han ``m''b�""� �is%�!����B�#�w \�C�Mf ]"Er. %fr"�/Re"V �=�.�}NM %\%2{��h6�-��os�!e�� %z�o�o��.z1��a Z��s�9|* ��s�Y l.� ��"� �>E�rbe ���� !%� . St��� A;f�!�� a�a�!0aSv� tet� � 2 �� � "Lp�:af6 t)=-29 Bh<1}{\Psi(x,t)}\px $!�iR� t=�w'a.G $S$: � 1�g � tet2 ptg=�,� +S�,�P��$ "= �'���h nu}x - o}{�}x+c(�$�AP�"�B� .�H� isE�!R��3m�N} -�T&j "U� �BC�s��3� Y�" �r0^"/BB� �Y� z� mu��;r�  quadr`� �!�pind7�%�)�L�0��<7���!Y!&put~&3M&Q�=PE e^{h /End.A�$ =a_{1I$+a_{2}(t)x 3 $ ; $"$,  $� d &\��=�/�Jcb� �M�]:�(� tet3��2��BL giNq%uL�FyM"1tetK�J eqn{ ! pt PyV P+A�ec h6 P}\ \ \now�H, &&{}+P\Big[u� h+\nu(8h)aW+S-bh']\ �)��� -̕4 r�� P�+i(��)PB�Thm.T cW%�m0ora�$PJ)8u^�"i^=0\ ;F�z%� -olynomexof ohQc�$x� iB.)be2>A� xA~ 2 �c:3}=0.x�6A�� 6�&EEqs���)� "�F,6�4a�sA0q�21W1T-B)S tet5 ��B�W�6w�qly �6Eq�ZDL. JW~�6 ��py=r�Bq(t),�t'=t.e�%b�S�int�a :jg�$5!p :�7� �ef6� rA�\pyy P+�#��(IKr}/r+Y� )(y-q)}\q�  4�<�;�:E�rI� \q}j]\py P�+7-�pV��~�z�Nzh�EG��-�߅���>ov;��6i�iacZb� r}-9�r=0.71}Au�:]6)2}]�jN��WUI3Mosgg1}�v oub �#=Wi}}.'� \,Z� i$=\6"-1��� �E�"=2,�� rr�oub� a�=e^�� t�l�@��:)g}) �,wmwv~sg9n�J> M%67~n10 oPtau(t')=\int_{0}^{t'}� (s)\d s\ B���ex�Oa&Qv� osg1M $\ptau P(y,�"� ��B� %#%�ph{} %We��! nI�( \to 0�kOSE - IJ�r a %>� .��recwed v�J6�G�6� Zk} ��v�qq�Z/-a.~ �;a#� employ%�r�$b�2D�.�F� L(GOS)�7�co�9hS2��gA�l7W"�  a�{v' ye~�os� � v�[�:�r�]��x��� ' ' J!& -f]+r� vB�+Vv v \ r x rA � r� v=0�- ��G �(V�)+%�(b� &� H�F�)�t vS��:C6S{let�}srrm�0$v�XxM6;ho\?$� )��Aim�2� nul:� >G6H� RI:*� OFN:,�� %^�s C����!+.apeQ��%��a��{(l$aZ :Zy1q� �*uA/ �= 8sg ver S.�E�)��y=%�Dtv: osg� iz��I��g�AI%@Hc��IvarF'�l2�6})(w��)upz� osg8� p� v+Q ��rEMq} �AU6�� 0��rq� r]R�3��y ��^{3 ΍8O p�q (^� ����p�e Ǖhn�:Q�d�C, V2F�=0>M�� "O 7�}- v�x� v� :�If+  `^ $t'$=��&s ��& "C R� �f� 8[o1 aR$t g� 5a#�=*�$ �� �� v2,bGR�<j 6�  $v:�PA� P$ � �\vV� �a���� J�J %%^ HP(,�Mme* s GO&� z&:+�i hankcJ� ommu�ve""lik�O�q )Sj"e6 �,��"�  %�!%�I&�!2�D*\!G�!4.( �!H0��! ~HE-S\,(��"�! [."(}�?rm{HE}�.�! % ��� E7'�6m#s�GA �pncH6dJ �L�#� �$.$*\ . Z,. %A&�e�)1�*:%�~� IH�h�j %a 7�M� d!I 99 b]E�}�R� �o sma.��f�:&  Deri&�\anN�-> }{d $x(t�~��s&�2� ��f�&:L�Ivin��S �b! r~z$orn1,orn2}rK�C��#\d �5 d t}� s$4,}b(t);>%Ii$2;Za Gauss.F(white noise �� �� [-s�����le z\r�L=0\az�and}}ѡ>.b^3��(t-t'F�� �"0Kramers-Moyal��an� �FVk0�  boedewA��9�A;ba�'$:$-�risken}v�!� B=  �x � )�� B��k�m is u0wF(d # Four|�M6cT/o�-$P0hx',a�y%ini�8�<)� �|x' -��(x-x')�%�eg^�-!@ P�M�,�pi %1-e^{-2  t}-}4 \exp([  (\big(x:  t}x'kdnuIo*Bd big) j]Bu1*\n��p�+ix7v!~;/AW>b1�obyv'�a.\\A��]e ?�>�/�-�7�xj eT-#.�7 f'% (&P !z 3}))� !�@#UB � �")�8*=0,B"Šs�?is�,~ � V&D-%�( A|t)="�!�. ~!�F�� Z� �-�%lA���*"J$��&D �� xx +\E�.�}{2}-Ir��E�6.�M�QBwSo� "�.u�%h�����#�9B�ss*�!V7�ZAzS*��5m�*�15`um�!; xB&�EoVL C�'Zng�#��L0+BNr�rs(e�eq�  em(A+a&H mea�  }� Inde[3&�` in.�!.5T%�M��!>0Can un}���N&NeW �) ZF���B  vn,�P!3Z*�!�8}�CyT6�# %$� \- IBE\A&' 5})}}\cdrq-�-� :)7) � b-Ѿ%$}\|8,{} � F :\30� CD$$&��z�g.^&�uP!�i F\$Pz�&rel� R��0'�M� xB�96�*�|�O�U� N7�� lin�(P)�N.�m��b 6)�ed�a P:�aX.�yFy2 S9 More te.+- +�Szis�"e,͒Aw4})va rel"s 8im_{t\to\infty}!W^br�'�wT(Rb ��B�;K2,�7A*= ATiE��v�I2a"8-yHU��R_rDreli > Mu�nU�?emOJ) �"� -d�M!fac~ql% sbb�t"�(�Ls�J<"cqR�' vxZpt�<"� ��$P��.=u�Qv%H)� �~al���. =�T�MB#�n R�=1 �2>ms9�e�r�i"� O��:. C2�.deffec)j oscil�sI[dec�0e,�`ЂI�flo��im�AmihXnd&� z2 �MaY�2\ora ;Z |<ce�0I^evanesc��� ��� 5�i�ereby !�� �5phe��nJ�los;!J �*�; �ljXa�memory.G-9G�~1&CoH�}t#�en�h��mpl-a"t9Y��>+-�&�!�e�erm)�0sA�2�2��bO,� 9�M�"9 !^��kfV �(} #msa�!�J"W�on���U-ny� of "Y`$x$A ms aXl�[ �[4> task&� e  5�.Nj $y\to#x+�&$ 9�c6 "Z d��>3�)SAqo\�i z'Ya�?XtM�_n�^e�w�E�x$��ear. :��<�?*�rbeD�"29ll&R?�?t"O�Lin�WA0,of" � b�W IP ���Sm"7Pp 5 �4li�� X(B�l (M�) <�d�?�3K=B#B)�<a� �2� V���vaamG�hJ�9" �! $u=�/�1^$5<|� �6�~ty!��"� E1J��] 5��ZYU� �!,o�o get d�]8FVYb�."Aa_Ec*� 6vp,X��"�#� �ye, �s �AU�5�u"�C�,!�F��y.�5A"��v������}l��J-� I � "�7E� VDas)�eiN�a � ���*&NA���[פٞ Vit{i.e}�S unpredic��t2��"� a U�f��j!�m\"R . An)'c��튱� ٛ��nJta!othcom!�i�]r�8h J�J�;pl�rv_&�U;qendix*�qSo� �U�&\FM�} &�%W�EI�A.an!'�"� yA!�8�9 (�.w.�Re0{!2Ba>��� W+�&S)�n�+9 �$PB "A6%�B!�~"Ir�CF.�+ A.\ .c(�a�C V�CH�"������3�)\�P�� D�0r}}{r<y�P� ,F6-T�j�%IA�$;$A8�Dhl"�1b�1 �F�=0� \Lef*�Q:Er��+ B t'F�+%M[�L��.NM�N�3p_{�gs (y,t�+Theta e^�B����6���1xVh!I9i!B|"D"%��1�r�chaleurM�� �Gyy B?>%&&:$!:y.�y-y�"N{�$ g(yN+��eda� |�<j�)K�b�1�!k�9�:s��IŁ�R"�> �[g'�4]BQaf�[2.$ $y#$:rX��ir"on�Ɋ�<a��'�x]��0� tau�:1eY}O (e^{"c '}-1 ���HY�z�&�_19�&�&e8jD+F���)S��8"D3p�+B�) �v4D @�3"e��81�j�A��fB��\�F��8�"�� a>'4})z�z� %b�>�_ {120R�@jV�"$ BURGER %g��{(N LSsc{J.�e Qa\e�ToG non � &SD�� } (Reidel�c�T,O�4)\Y$Adv. Appl.�e.�S f{1}�d49) 171 ��8f��GSA." 1 {hit{\&}}�e`L}, Rep��th.�Pm27n89) 59�01qKfE��pf} : Cd& n. P� �X}Pbf{3}, 201-212 (1950)"�J<�C�K: Q52D9D25-232! 51d1��%� J}, �Re!W,�064}, 034101 (_) �D����%ڇ.k?g"�V, ��V(�e \& Ch.WfIz� 1`#Wit6�H1�U3aWO�del�Y flu�Z�."y%arc��Po�edingWC� (16$^{th}$ I�DIno� Sy2�um>W*�f8(ISPC 16), Taor�, Italy,� !P-339.pdf, June 22-27%E3�hY�wo � sc{H�g&�GehI�F. P.�GaWarXiv:�",-int/9812014!�982�^%9�G.\h&� ^ L. Sa T}.�j${36}}, 823e3�h��% �M. C. G�`:z}IjModqS f17f3 f45�g`$ UW H. Rt$, �iV�},Je|, Spi���89v���K&>Y"}ZS&��c�T([journal,le��]{IEEEL _nssmic2w^&`_2�^(epsfig} \hy�E�{op-t�f net-��v�mi�duc-tor�i-be}! �*�~a� title 4[��4ATLAS Pixel Deƿor}"�ZTFabian~H\"{u}gging% <-A % stop� 0 \q+{Manu�pt�ev�NovemAv15�04; revi��c5, 2005.��f*��}s&�&� !^.}��� m��>ubmd�mF���Tlf � 2$Col��r%�.ah, {F. =&g�)W$kalisches Ż*��(\"{a}t BonnkS�k%�, 12, D-53115  Ge�� (�t�phone: +49-228-73-3210, e-mail: hue%�@�8k.uni-bonn.de).�[t��-E�8a2W MIa"Z^2�Iinner�lay�Ee�ck�x Y}coڮbute ~O#X�J9 >@6ver,dre�tru�"} j7ca�S of ir�eCmod1�\K�)t� barrelў�c)�� beam��-� ��#a��&� Vdis�� n either x"�WwKm regi�}%`Q~6� � !UBv �ere�c�qnˆdiE�C~n�Tmoa�o� mal �#� good ��s>,$,Cb�E)# Y w maHl budge�5� layo�W9 s? �l���Z!�|� stat�T�m�d;"O�Y�Q�";Z&��e��, p�� s, LHC %\�ZX 06.60.Mr \sep 29.40.Gx�K "�L6'Z@ \PARstart{T}{he}I� Ia �Q�IDTDR} i|A��+"��AMrai"��h�d�" icle�( 40~MHz bun9��x�uI�[[^co%�s� U!�w tub&7ioutera� xion-rU0�er (TR�T!�miq trip5�p � semiLuca}=SCT) Tn�eA�e�kiI: the 6�� cruc�E�#a'V�ROC�x+$nent.iN6]-�P5� subdB�� �re� ��Q�dm� n�5eС/��aa �j��!\�b pipe!.!�0us $r=50.5$~m�VfXSy�aat $r=88 )a@9122 . W�Iº�lhy1%�. 1.3~ͤis� out q�_�� -hit���!�]�$|\eta|<s-x�5�s � r~1700 I����� cz� spon� !�'ZW �PMś L�(�d� ,figure}[htb]�p{\T3�i(s[width=.9\�i] D1.eps&"��C�@- �!#ҥ)-[+Hfig:x.0f�B � A20.{Roxyge綁�1�-on-n �� �"or,Grox.~2$�$6~cm$^2g sizem� 0}%� =�U>�47,268 �s�1V�r�+fed "�vid�� o 16��,nt-end (FE) I w1\_8 pitch ``bump bI�''��y��Pb/Sna IZM\fT�"��\ f\"ur Zuverl\"assigkeit}R Mikr)k!ցH&�v .}]@` Ind�by AMShAlenia�e��(�a� (ToT͸&�%i�pZ6� �A�rg!�@/A.cJS P��g } D��proto�zng&�- ���&�)I�A. � g�I�%�r8 -h��x�.�-Y� $* �\Z!�r!qf�KNq in ea�2004. Up�2Aroughly�Q.c�;>"�)���I�j�3�2��th�er��, eacլ!(q� extenq�:�d1fE� � !um�)"/& si-(��IAw� �{ ing.jo�$,5ƩKb�ep�R.�h \9� �� ^`�.uir5�)��hadro)!��I *(/M bYE �e�^st��%�a[�!RsE�ub� {(pr��"��}�yDsec:lab} An imporxJo��mSa�υ��in-�>\a�יgscan. S��� �*��onO - in��!o2E.�0.v . ScaHxl�fh����u�ϥ Q�ȩ��$A�*��u�N�M�2�%�E�dt > `ޝZe A s%+o] !%1.-edu+Q10r�� 0er�.2 adju%� a 7-��DAC-�������ijaq��/�t�^�t@�3}1 hou�'] ul''9A� �qV�tu�7'ht�in� s&� H}4R�  �óp� $60~e$^{-}$�1-aYC i��a �va-�b#�e L !� I]%�a�da8eedl� pe���agJh�d8Nd2d"cT5Z�~�|A�` )�A�-}��c%� me� 1�is 4,179Re}/s-O�1611&.G� tGB�.��� �4��)_ lE lq/�a n $3,900~�<�qPACi�� M\ capa�,�-M�0 ���e@A�� o"*lwشQ,�� any� ��G�B�too6rE�aH�4of �u�o�B�q����iO�W_�����3� oss-talk�a few�1-�U�$50� 402� )d��6�t]��R�3>�N�B.��R���. ����ra@ ),-Ε� , (aM��!�AA�%uA�185Q�e�,$\sigma=13~$m�, (b)* �l6I208VI5.Ic) � 2�:K352.K �42K�(d� te4 ^Ta�213.T�9T2�%!B�A���!?%�imewal<�.e.v�MA���$#3�'6�| g��i�u-E� an i^� �/ �)�a� dep�d��� O a}��F2� $ �PB��f��G ii{��.��c��!Nthc(?C��Ncim�nQ�@7��5Va u�.�of �o� 20~n�e n+ 675&��X6�sL��1,5���,+6��2,3)Ab��2�H2,0*,5 >stA }. B)6!3:���/eas��b�~��o �rs �p3.sN�_� n! su?6����mee�� �� !p62S!C�_�-J�b��4>�In�8-9�  �� ��tu-.A�ve�=Zof 4,�$�, ra� 5,64������180�2>iV.F99F� �w212Fc)2�:H 6,68H�H�M�V2�>�Q�Q"���AbB\clear�{ &�� n�� "��� + nsor�� o�vV �rz�. �� ofZwec�9��H. ��a I���|0$m$^{241}$-9pat��Z in >� & }. $1,400a*$ΠtsOFEe *� accu�� aMR .���n�> enough ���oN �paAs!�t:;s��!��d�h-sp�4umqallz %U��!r roZe ToT-Z�'�ŵre)5���ectżs3�F�-g);��m1�,$60~$keV $\g��$ peak%hE%�:a�in��.��^�&nB���by1{�!.��sha:Dx neig9���.ܾ�&� #$8trum (�=Ze�)�be]!�s� cali�A�!�!n -���F�6�I�1= 5=Xq�fi�"`! ��� we8& D^�N6 5>�}7 �umQ�d)�a\�&%q ����-trig�v$r i�V(YE�!rge.��. Ez -7a�N�"7j9�ly 1{���u��sn*����!�� c��M�^I�lf�&to>'4&J, mbQ2(for a speci�efic channel, i.e. chip 3, column 14, row 33 given as an example. \label{fig:source}} \end{center} \end�4s is also partu�pr-74. Finally each 40 will be tune-�@alibrated for a sE% xevaluat)enumberl non-respo)�pixels!ve result! distribu%G^!�first2EpQ;4is shown in fiA�~\refA�4:yield}. Typic�M� defectiveArasA* �%,far l)D�EY;vs.Q4tU36�apan �rm�-u�!e�. A)�flaa^p �y of 0.9990!vachieved2 Y~ ɂ}Z��8> �10in hit duplicI�modb7 �6B7 B71.!4 54��fig%3idealB3$Furthermori�6�aF�s�  impro�С� ect �e��8100.00$-$0.03\%e )�i6�) by � a digitalB(m� front endT . He �2ALT � 1p� l[� �`n adjustable ToT threshol��� $evious bun�!rosů$to recover'���e$small�$rges. Of ci )pdrawback�(this methodE�na� reas� ��$data volum2S Y ,. The spaceCol� Q�6 on �� two�clusters�Adiffer? �2.�ng�70n binary read��A�, � $approx. 12ͮA�$r\phi$v110.z$��expec� Au%� siz�6~� . AnQ��)D.�%�:�M��\ ]w�,Hgravity-��z* Irradie�2 � Sev"g ��!:� i A� �  PS�[ 24~ protonsAf a doE D 50~MRad ($1\cdot =\15}~$n$_{eq}$cm$^{-2}$),��� %�ima� %eQ9{0after 10 yeare�i�"` �� damage A�onitoredE��!�(leakage curMQdividu �=a��. Dur81� A�iAt�4nt upset (SEU)!babilityE�-tripl!�dundaA�� ( latches wa} by ex* ngeZ full���d5�to[���sal,eG hen a e��rearch;bit flip- U� SEU � !� ord�  11}$'* ISm $14$)Fxof%\ i5rmQ � !lnoKblems w�5�a�,such a harscM� environap�snoiseM?iM�!�a� N)W��4-e0is onlkestly�y���s� �B�  require�� 6�E�. Also%*��0dispersion of�i6i �U�1�to�� 60~eak}$�bef�GAion�8bJQ�h ^B.9N� 9>�N%|.�)A��ityp�a �ed�x 24 GeVA�vflu7 Q�p,&� �Ore-tunAnat -4$&�; (a)E�"� �E�aInM[of 2099j(nd $\sigma=�g-�$, (b) longFI Ep�238VI5~I c) ganged Ki:� 292RK27K�!(d) i;-.TR� 221.T �T2 �eH> ѤU�.�� &� ��A� ag� � i�� 4*})� bias� tage needc�J deplea haf e"��A�^ps*� to b��400%R500~V,�RP vs-��R � H�a��w��� � �vo ϡ�"�50-80~VE�i9�a� .�  de�T!\�" viar^ �.ings A�! mean2�X=�>� 15,00��7a m.i.p. �� ccep� unir�06���g��>�10>�>F !�2x� :���1~.�*Z A�>� Q > Similar.� versus��+.� *� -��s�L%{!�b�e & 98.23*|,��abo[he� -of-life�.�A�95\%,aB^"�\I� slop���*� curvusligh�z�HorAJ#�5A��of poorQ� coll�!�a� reg aQhy00ed sensor (``A-dot'' .)� � i�!l�o �on� ���_ aVa�� aiout e�ronics  ,my }��R\11>��>of\B�0.9823V b rrB \��{Off-de� =9}ao.-`.'��desig�tc cess� at a � ofL8100~kHz level-1� �% main �-0t��on i�``�-!�8driver'' (ROD),<�final�t h" buil��� specif�� d ar��Ahfdi\$-step� -L��Ũ(error flagg< is d�� F& -ProgrammA�D-Gate-Arrays (FPGA�i commun �!S�r�M�!  acqui� is run thT a 1.6~Gbit/s opto-lin�Bd�k , on�V � ����a�ru!&reor�a�@ Static-Random-AcA0-Memory(SRAM)JD�-Signal!($ors (DSP);�ir!�%*�i2 go � � l-s %�alAy �co"� ;� ��u�y�$ a ROD. AmIq!2}% !in�du� �l7p!�a� 2�� rack��q�S�aA�ta�.�Supportruc$!�meyic�M guarante�0al TQ[1\d�)0!� whil�amoun�� [ria�be kepeZa minimu&� sameb it � N'coo�]m� heat load�m%P���+`!i��s �qt*Fof -$6^$Cb keep4  ��4 low. Barrel-k�luŏ, ``staves'',z ,�$ carbon-st1�ISembed' �pip!� HA? %P� s! $halfshells�themselv�r7sembl2to fra1to�)'b�M� diskp a@��eca�B� �a�1/8!Ta wheel�F+direcb# iq ܑ� isk q � D%�gJ%j!��0 s Q� accuracy1� wm�ontact��3any r%to -� sQ�AŚ�.�d)eaC!��{�s9_%KZ,�Ok B��-*�8X Uy-.global sBI[��E7lso made)��J��re�ly del�a�C�lyY se2=r4"� a��.6���� ��F%V��-�six5onisk�!ndJrtu6')�-EJI�@ beha�rN!�Psw +s%�s1�nt"`ces�ZA�Z 2) %�[s��unq�-�. Lr6!Gѿ�U eparw%�$"� �(listic powee�! �� .UCo� �!yP�!�� � �; gene }of& har�)' l�$ly satisfyA�-�E�4in laboratory-%�,� �studi��ndM� RM�$a��b�A%#og�a�� �g Mn *� �&inish%�1>,a$ime. WorkQ"fEeJ����o* !� llel �re �"  . %&�#��promis2�"thebibli1 lphy}{1} \bibitem{IDTDR} TechS l D�  ReK�x) Inner De , a�(/LHCC/97-16�6 7 (1997).qP�qP�Rq 8-13]8.]��d} M.~S.~Alam et al. \emph{�Z �silicon)� 8Xs}, Nuclear Instr. Meth*&\{\bf 456}, 217-232 (2001.}@MCC} R.~Beccherle |, } MCC:EWM�Contr%r Chip� �6�}, r�,92}, 117-133�2.�8fabian} F.~H\"u~ �F; -End6� n�t�$af of ��9�},mA�pub"�inZL] # J.~Treis:.A e ar PC bas� -�mio��! t�#}�speedB Z� A )�90%G 2-12JG"2I:�m@S��onQ]:�)I�Z� � 477�43-1499��%>�  docu'$} 0�%% V�$ 3/21/02 %�, %% Kluwer P�(e� s Sa�, .tex %..$Academic P�� P��ed��Amy Hendrickson, TeXnology Inc., Ju�* 999.���% �LaTeX2e�Un�P1Fclass, \2{kaC$c} % Compu0Moder�ntls R and,cio�),xo�(rr aa\usepac( ommands b� :I �If you g%a fk enco!� =, p�*4�S erex, , % .i{T1enc}` `� MathTs&�PluA� nts,�Smay� om%;�*�=� them, but6�: not oblig�*to do sob' most auth�'d�,v8thh !s. (You�|Eedit m-�s.stymak�v8 n m �%�jyouz ) +[us zw9 G���o workO y�bnpurch��V !Y&Yihpany, http://www.YandY.com.}]8[mtbold,noTS1]{ �=�$PostScript�M�% %1�-�'cpsa % file%��2A it %5:�)�6~< . Se��topQ�9 p)�x�m)nfo� y{ ,} ! Styl /inser�VG� roeng il�"� � �s % p�#blem�)��+Hx: % [dvips], [xdvidf sone �' emtex dv]ad[pctexJ win], hp 32< true Gtci|�ozex�] =$s ps]{�!-�)B����09Y��q�e�,A�e�� aم��a�s!�~!|:3[)�];�*:�9(� M�e�ae�� �e)F�[epsfdmono}J!1;.%�!vC�ʁHCan Set��Changea^Custom�$Y�| Book�+(mat: ===>>>aRun<headsA�=2�ټt�kq,p�titA�n lef�� nd p�#% ��o�'r h(\chap(r ��i��J�A� % A[& /% ���[ ter.��[��J�9(w&� in�F$both upper�l" case. %\and�use n�!0&& � >�!tp � �X�How m��.� would�� likeL1ed? % 0=�-a�.s, 1=B , 2=�, 3 "�/�tc�er�numdepth8 % T���� �/F�!y��to9��5CBn��M1I�2�2�U>� �|s�toc2�Equ )VingV�=E�\no�e 5 4Q��$  Us that  (1|E��-�M.1)B�%E�re Y< �'Q4!�DefaulXr � i(� ��4 Footnotes/End ^* %Y .-i")�+�!X ter,Պare�*cA orre�' \�_writte�%)WToK��f�]�at�'tomw�*&� : \let\6\save �칉i� wan!>)��6l�bopt: %2k82ovs a ru � a"M �.6�,2a!�B*C� Set� ^� % Choo� � k8bib!��2latexbib� a�\&�(�4�s kin�5.� entryC A�8?$rry L.,...Y � tinu( �6 !  %4 xxx}ɝprintYout b�elou�cit �'%W"i" a��&sho��be��dA�n���\verb+�+�\6  %�31 B�i zNf!u� %-  book!�[1]N/),R-6=)>* squ�n.�}� Any1.�)E}+� 59�%-16+\ %%W-ocheck%�r� o��Z p�D�for Dr%%�� B:C-�Z�2a��� �Y�iQ>3]]>;6�@ZwD ��rce�E���A6seaH�}l,7 �(��r��r~�JaB`[ ._]� Draft Lin�.� A�OA9al,.b� �[� `dK$'$maA0�|�x�)\*�-% <<== &F���~� &B C�"�4d"� \ar�7� ({Photon ech�= of molecuB \\ passoc�0ս{.�\of SPIE Vol.3734, 86-95j9)&$�}K * n|>y } \r� �4{Alexa��( G.Rudavets�addTa� corr�<�8s: Ar 1p@mics.msu.su} \altaffilmark{1��]${1}{Moscow itut� PhysR!k >�D, 141700 Dolgoprud�Russiak�� M.Dykhne t �,2B�$2}{TRINITIe02092 Troitsk,a].abs:"t} RevB9D �c���X](>�>%n�(two ultrashc"$laser puls�pu ){u �? d�#ach. B�on !V�{�@s!D? er�simulj of KrF�=ime/E�� a predi�s2ade�ut�*exist��i�free-b�� tran#%s. Delay�2�0 nd f6ofZ;< $ar polariz �he �!-�( isio�U�bx2sul:� re�($nt quantumOtes.� � �be g(gas, liquid1 solid pMs.�9�M$keywords} �,j�0, femtosecond>ctrA�py bQ� {I�t } At�@sent,�%v�q2T (PAS)!] atom/lli�a�/!-gɞst�@pokL$!�i�ac} �G��5 ��dA<s (�&]in�+eIE�)z$ ate?r2 grg$,9 ��$ons $^{1-7�=V.tB que,�,applii conven\ezz ous wav�0(5, 16}$ (CW'fen1�$^1$ 2+mA�p�<{ �?.�<�rovBd:6hyper�@"$, scat�C ng lengthe�/or dyna��A�LmI�� > deX)'2a��preceden%6l#.c �"s� vimary�%�'es�harpoo�re!� ons$�>6Dve%�auPe ionm�0s $^3$, relax �. van >5 WaalAj�xes$^4$a]iX%u�ar{Bn�2tra�?|AS�q?;� u�/. �%:ewz earlier d�*opN�% X��8�8RE` rubricDch(a5--���2S,-��@� $^6$ �E!�nt innov)"�6CW �nvest� Bose'sm�)R coldi�$^7%ES+a losE:co�aI0a��uougme�Fass��dF:!�M. One� naivH" clai�&a� 2� �Oq!�{i\Da�a��� CW s!`a# si� L�w��/E ��$E� a�*�6b@sA�oxiJ1&�) �#h&UE�!�-'ipD2�,  �ler imG�YwiA΁ *rum mCVV���olv�%An�{A�f� a enin H N� $^8.� ccor��MH$M. Polanyi� attack�dopen s�(E7 tosa`��val�8+�n hook�8cloZB�hauGCGM �Coulomb��ce z;P r�Lof hundreds Angstrom*@ d��-. S��[%j0�:y��wP* low .R*f1i�4i��ow�,���deDBe3!�do= to n�"�1?Jo%q4IN>"d� h2  optL E8sE�va%�s,. ItA 5 � forw�%�)�I$. ai�� %yE�� mix!�geometry�!��3w hree)!Yl��0� k�yt�)s�toA����e*� ��efm@�a�� no%�er fE��  weak fr/ s. S�:s ai) e .����:7E!�!z- 93hotod*W. lJore%� des��eCl�!���b]0r�%)�ua{9,10}e��N ext ��)Q0packet engine�'. )�eH-ntLa^e$'�ed sp(!�Atsqueez��.\!� lu&�Ie+,�iFU�rop�I�&� s,"!�o]iQ�� rol B�  &�+a�py$�9�  shap�� 1� W�. "�Jtaneous"�ce�2,%�bC.�-ɶa�g �9ng,brq d "ns�l� ed (no�7irped)Mo��a!�A��&M auto-/%=^R p�/X �(� s�H�*��� a�!!Te�gl85!�Cete& �!pinuum us�?&�a decay%N2!Nl1� tE�!�itu�Mmay de�0e9e��� �m� }Yre!�rg &�=. I5 q�<y domai�8�one coQEng!��� mpan� b�, inhomogeE  broade� (de] ing� � Franck-Co�� s. I~ m�doLH!�D�Crr�҉�*� in mnM-�1nel (���)* , ]� emis!a�e2vg ᶡ+� ��F3%�cJ T,qDpo�a�@ )�8 fo6IPnext pla)�Sec.2)8e, >1iAi alyz�W!��;d|)ZE�to�}.� 'res2!Ia�` um*,� �E . A����A1r �5� �0$\chi^{(3)}$ :�( �|(2 $\delta$-�is��AFu5tC3 .P !Y:ifA��A1n�,t! *+96�* s0t��� � L!�rea .���e�,isIB s e��[�6��is+tiFa��31*/ ng exJ�z�ga�/lidl ;�K *�.�sa7�Bng0ia6��1� media��{�--�. �*� Eu��'s�.st2d-, "TITANIA" (*�%Xclf.rl.ac.uk/index.html6an� pu�b10�z9}$W/}E2�? du $350 $fs$ }�v8:G.�m� a,iver a8 u�H2bH�'0cal��f=�y%S !)!%aS�8lly�arelev�Jmom�D.(ae krypfluor�4KrF(B)~�"R��73�4�Iw!4r�? � N!� a Kr c��`d F ana� �}na)�3dūso avoi� C��ref��|pr�Hple, I���� �� i#S� ur�>�? �4disregards oscYPy tai�A���fun�s)xB-X� �((at 248 nm)�4 t�)FB�3l|)i�&s�Wz;r�Tr�%*oNx insEVin�(h H%�I�ID.�a"�( kine&�%! view(� 4��S��"{-w6+l} Stri6 spea:H, {\it 'ab-initio'}� ��neL�� 8#-body�� theo� f�eQ4mo -�>nci��Ho~ any Prigor�K%u��!w1�$�+yBa0Born-Oppengheeb tegy facG4oph�3E�ma+$;�<�G�<ex�KA�e�tr� >9Is�AA7�t�V gnD6r� 0surpr92E�c& ! ���Ds�?ɵ&�>@�3i/!%b\-� 2�o � on� dy9_,�int�4�e� drawe�\age!� m"�:�z4� Here a�vgives Wp dig�!��\!{6 �$�� ng� �Jat!�lOn)fer%d�9@�v moAa��i do !�v]Mb&gA�W5*t6"�XqicYN ar m�. M"0 �� is g��� b� Hamiltoni��UY ors: $$ \AH_{b}= T_{kin}+ V; \quad*fZ*f},Qw�$@ MN�{!I�h�6{6gR ��a�� moA� ! 5X�8<a�a��&NDoppler�hife�fF:4U�?��A�M rginal. I���0(��F��=� term� �Vt�`��*c �4)V_!?0$ e�Qted*�Bi{  3se�-�y�O %�4=\omega_0 + \O (^{2} x^2/2$������actual t5 �4e�#!} parabolicc�=naW,�\Da�%�F"�Klibrium �; ��}�Q>/%�,exa�;� b� ^Wa�u our LQ�i�durpose.� c> �8e|]�h.�I^)'Y*$)I$ �  vehicl�4C�0emo\6ate�\a�\�P���W�. Wit{$I��!f��a�N)1%Q�� e!X� unit)O]� � 0m` % ic dipole�>�bf}={e�(\mu } E(t)$� FO �Q� �Fs7$envelops $8A  fast":5] $Q�q ;�MFzer�l�X��T![%� act2!Z%"60� @ Qi~4F Schr\"{o}a er%REZ the ��1M $�$ t \psi_b\Mle �s&y-z , ,f\,q��(��n�0oŎDirac as� eqna-D$} {i\hbar}� \dot]{b} _ & =&��b (� � + !�.f."fF\no/*\\%�� (b\\.9.ar�`f) Z�fG� �Vl�fZ� 9In 7Qtoi�m1!�mm cap@ of�aZw[&.-��s>�, � employ�E�um re.h  cruc�ssumpE6�d�at�����a via��box K�U$VU�e���3ru�E�i�R�s4 � ! beRsi-�in�Q]b�U/ZJ��} al;� % f $\lV pIoEGf}(0)\IJ=i({f}^{0}(p)$�Mset " ��s&0��;��� t��Q c"�#�+a�"�haos")� cano�<Gib� Aŕ"� z!]ic enVC �8 \stackrel{*}{��}(p_{1}).(p1X_{ave} =Z^{-1}e^{-\betaT f'/m�W(p-p_1)2) ."" �r@Xe"c, ZAf�he l sum�AYno�� (* pe�&^X)@J�  Yqu:Gi E��M6ly�< �coi~^t��a� a~Gibbs d� ty�KiYFm�9� p��a�ty�LEp �� (0) M� =0$ b�OfŘM ��+X= ]�c� 3G�*3 = �e!8e�A�a; F�}2 b}(tQ� A(i t\hat{ H}�M �*��byj �� %j�xfVx y Ha� w7fu, $�x� !1�|um>}� usXoE^"�_matrix~�RJ5{m}} p)))\frac{=. f}}{iG � e�Q& �v-c p� /2 /\yva�9VH) }z|b| �J} �e^{i ((�+&�)cos(P  t)-2p)/( �� sin&)usqrt { 2 B\pi�+}}B/A�I�% � r�& �:q!$E�6� e�*��PN�e�ir2�q�� a�, gmz �9gJ eq. +3�&Y�� b(\tauy_$=&-i\theta%͡�1y/� L��fBKFCMd2d)"a�.�Z=� $time $t=0$*�*��bFXqPBs"� "l$x $, �Xat!=� =\ Ei� \ll\pi�d��lLa. \medskip \par Let���"�drz�Y �&$�6-�s.EyF2`pz�uurM�i�I� �c3�r� pac�1p.�]��s!�u.�� .��"�.�)�he &�C#by cal,"� ; �  $\mu�>�2m a= a to�`sp}f:!o�Z[B� Hi�(Q)��V�SsR r�5."+ �!N ��� T �I de�j A�5�� m� box:y�uE*}�]��A��1 =E�| mX��vev ai�Pm� D��u��!G�)�V�afJ!�QM6M� #)ue�9 F�) golden�5F� �a�\mu^{(1)�L �=-i\mu�� Tr[Ϳ2�b��T (t+i' ) H_fi�}]/Z 2IK j(t)��1��iH/t�I3 on $)�I=\1d�p�B� p�@ !?:�!uEq. (3)�ca>+�/trace u]onY;�� &=&X [2\p22/ ]} /2} � i[)4+t+tg�/ /2)/�J]�)=*p &=& v� W_{d3!!V)-1kU}�A} kernel $ ĥtF�+�a "�+V"�njL lex �  $W�O �/Fg B�= � t)+ 0.5 (-  t)29B&����sp $�p�ymm&"$p $SU(1,1)�,� 0!Q� <a�#c"*'0average ���. +""E�!"'"N��Ox/ b""ofalW9E��DB�'.5}$` R%�Q%��K-"gr�� *S e �$1/� {t�Notica <19IgVe�0 �0�-�e�/Vaz�t"\ NW�n& �+�0"!:"!��Ni4 tifac� %2W�,! # � fwh1by�$� )� cutof! iA�b&�C�6jan�.Yv J&�  .&&y��� �R/��,�1co�Sed7h!:a&�" si )!��F 8 ArnaWk3aDter#ad�Wc�.����prQ-��Fh4se�:�#%.g)R ���rl k-.l�0ol e&vC%Oes"�U�Xu�EQ[ B�hXn�Xar��h�s��( anoY3v�T��T21�-ce�2� �S7 �Qa,'� �`X*Wq(ll �f�H-os a �� s�C�;Hc!�9-�*9X2 �iP E�Efoc&kn(ol�4&~+��^� magneG/ - +gg� X aL ��+6|-Ze�&S. ��"ay $T e f�=!�,�k AС HN�*� f(T.� �T�{f� - _1 2 +"% ]_� ) ,&�\\�g b6�� e�k b ;:bf55)2E6C$�Gng"8')&�o[llM1$ pairs. By�� _1� $ �!�1A!��%au�� !�!�U'8  |W�ivelyb#�K�s , a9Esuper� �X�5J�%K�� ]� E�� H5�B� -i(t-T> E) i TD H_b1 2|� }:� B'&� B� ,bar212� Z �"� � :� �� �� iq2�1V�"� .� g�8b�B�in�E#no�d!嵈$R !BSq~ba fo$�,�.< (10)�B coeBrt��T�� to.�A�Q�1 y1i�+�O�S�%��h�.1:& &� ��W�`llA�s�a!"/ag+" %�+0� R �2P +�b se�A��\7 X ��9O each "m�=&h H) diab�$ step�a�&��#!rN,�P�Y�� � ),7� � dS'a��6 Rl� �03:0a!&2�-�{2f63)ax,}�Bjb (T-t�;.�t��] H_f"�� !q�.?e� (\�-i��2E]/ZBCU8 %E)^FpI�J�!":onH(is 2-d Gausz *V�. da�:�$ Eqs.(3,13jpe ?1�1hM~sy�&�r)� P� !�*O�r>�raR� ow�n2e 2�V �+�� W_� &=& &��8&7( � 6,�\ \\&+& J8T)\,(T�rA*|!)\,*�T)&��� ~ en�:O~x�9suro�9�$n �=t-2T$>�F�5.=5 ��ah�.8!g}"�/nd� t QAaE�6Xon� 6i�| �:BZ�as�~A�Fig. 1��O�&c6�2x ��.cG"A64v�.�$a>�7, e.g.� *� $%�=1@.�!$t�"e2]5�(�b o8o4m;$o�� '�3�p�l{&�yn9(Bq roy "� .�'r"g3g4io&f%�� or>'?�;affordE1~g! ��)(4 But �9�i%R&r5a netA��>�>ee����woE> ��pai6p�AjO2"� q*�q!r n�A�pl� �9.�6periods/1 �A�&SC=YTheN1QB&  spik ''E�re/.�h6�e �� �@!":�Uo%Dz-�& 9�� �� $A!`�7l�j�]E>� \.�E!32� ( `6AI^H?t mʍ� fire�ve� $T\� ��m $�chU&� i�. U�n&� da�v" {�G=1) !�s8�)=1�F �,.:Xp� E @ itsel�ns&��hA�+)��A�an��wheJ �wcl�<�JK8pl�%AJ�(5% T_{vib}=2-)I�Eq.(13)�z� �:K;r��Z8$t=nT, (n+1/2)T . n=1,2...E<� occa�0 $sin (  T) \ll �*))2! > 1q easily q�5i �A��x8lf maximum (HWH~lt�2%Z  �3!�om5.� u A Q���Q�T"� 2�&�-p�8� u�Jst3����tak�L �^�, �>c,Akt9$ de-Brogli(�$r_{0}\~ to \/"{�}�-veloc� $v=\O.j R��$� s(H�%��/on�uaP� >F��h*���3{�<*) '^ R(2" �= kb"=*%�RF^!Z  R -1 T v!@�  $v_0�1Rg1�5\. S�:atd;. �cE'!AE$ Igcor}=%�/T�=lMl T,$�$�?sI�4ZyA��Y[�#� a key rol!s"\H!��&�2��rW!H7< meanfU!�/ AEof�1�4arg�b� �c< P(U��< port��5a�<�u���if�2�ayA.�6&aF�Z�12Od*�AB4�+:pri�(to re�@�\��lO6 �n1~�� &�is�$ave"� ��recFcs*�+�`͠. A*2B1� �q+#ae6e�~d elli D8p!�!Ms��h�GX%"�4v� i���Ps6FA�g+B"�8 XaO+r�7by virtuš"free"���*UAt�" � �D me (�?"�%+Liouvil#*orem)���\. BFC � back�6`-R)�!�[  PB�t! )� bin��?$AVaa��]ry � ,har)sc� h1Eu0 Aha~�6 "�. In adv- Irep�M>29�#ch 3w�`g�a6�"�+�16Kpea?E\�o�Y.) *O ��>)�� &������=UD�s� .� .�+�-�7(9ath� .�s -��3R � last%:ife9�in*�D-J��)���ly�dr#-"� Jl!����}= " }/(&�^2+�-�gM[}�] B 5� A��ofA*} |)L�o�%��� nd.� :u�=� radius $a� =de:}��72�!m� ase e�E�G�%�|5=I��0& �W��2�I.2/ �o8.�,"F 2[ -�6 �lapCF��"x"�:"S .mo�.�� s�e-yރ�ame� !P�9�as�!a  T$��  iqZ9i$v��grwJ"p � A(� or��lxc*H))�ezlapIL�9i2$%ZA�o $a/v$&!�men`0rew�ta"� �to�  T)t��cYam;a�ol�*ruZ.tJ�.K%8�* feae|�pA$T/3!�c��[Ia�y:k �9k 5 �߹<6=!�a��oteM� E�)r�ce2V0�b44law��=.�A��.�i24 dM�]>�SW m���r,�4.�s �0v<6�IP!��� X-i�(�<!V�+jKv a"w �["0q Ou�cal# �l?�a � in�A�t *>"6�B&Fa��\%�E� 1:) !��o*�A* $*&�����!p@vFH "�O0EraAd�Cg�0poi�$t �Fortuq tCivergeA'{_s &O� .`2� !�6 Nr�-l�m#wΑ K��ڋ99�"�!lUda9)9a�&HA� phenome�Je,st�Qr@ �.� �g4-eV IW&/Z �.� P�"C irs���i��w?�5&�F^tter?*@R.�ti� ���u_C6�7aZoa�SUi ����:� ) ir n��,E/0be helpful. Jll*�I�2 pi�{e*� `)�� vi�K%F�!�D2N"�. A�(�S h ;mape�NIL���H�"p�N�� = ax�&AMip�)� B9 �Hqq>� �*�IW��k2/ avey�F #M/V��!%A2B-%0I�r6j �-2J3 sLb . Ap ��!-�"J>6���!xieF�\�D)_2tin2, e�&_ r"� *R a�:�d�Egame&�7 re:+ �c!�e}k �� �(� �(6>*� mfa� 4=A -ށ��� H�]aVr� o s�PIc*ICYc &�2-s���`Vs �Qap]n�J�ir"7 �l(|� .\�WA@ adja{BQ&maps �ts�!AF.�o�EDJAAll(�>2,in)^@��Oam�� m}{�� e�P4 `2 M�o���{�{mF�HAp\.��] -F C}|P�� }C&��[",:�riT{�C0. z�v�����|a?e��-��ed nonva�yA� �� 5��.�fk�i �ex�G�� '����rtC5�J, �#~A��"X�&GT'B!�3rhoZ"\,"�Z%&�?psi#��$��.RfVR"�?2R�?:Rr <"�,MB2�эL $W_{{\alpha}}(p,q)$,�!� Four`[%� !�&$W�F�!W_ U U=(� � 1} \�24r \,e^{ ipr}\,k � q-r/'%@ � �\, (2kq+;) )p ,~ G =b,f"1ray}� :�n:E�! E�-��=&".�er[YB f}] �3 \!\!!%0\,dpdq \,\, WAD%�\,W�)!�B��Aur�~�d���: QsE) _$(6*��6���F�# ]%\4al W_ Y }t} +p\,�*qj,fr<QV Q Qq} bO'p}=0,-��!�sL_�c$�<;�5*j7!E��"" sH>yf9i� ach "�� "� �.�l&2"T �! �Fg�maj�F)U��g$3{ccu�ced� p6�.�&"dar�_sic�6or?Mi��We�advan{��^!m!:� to"�9�,�_x�M? G$Kr(4p$^6 S�,$)-F(2p$^5$ �`P)� asned � 1ong X-� B-9LT s�w��$2>� f� in,he�O=3.3in� 2� 6� �c�Non"oK)Q�(Q!��Zb��"un|d Ritn�eo�bal6}$, $F }(r)=a+b\�/-\g�� r}-cm)ra7 4 4}�� � %�Kr-F ��a$4$a=85510 \,[cm@]"�<]l�tgY, $ u,=2.94\, [\AA7�($b=1.016��7��\��A/�<�K� s^s�OhA^"4%, $�=2.19 ^ _5}� \AA]b/ ,4}=1.7f+^4-^2Aar4�Co�^�M ion-]Mru�Ief�(6�/"� $B\S� _{1/�*+}$aa��U $XZ*a� k�i�Y�F��be�ze `&ve:E,xE,!53E13}�A% 13}=3.2)! 10^75�%�13}]$>^! ApplN!4�&�� routinB&%ll� Ke(T�z*��[O�@f Օ��2� Th�:B$:A1*���J� deal�zHz( > �c �$ 3�H}#5A� tourJ c�>e& �F% (17� �%�!up[ �hx��&XE i�"�"q� du"� �@7e;Eul��co�at X&k�Oga܁�R�Q�31/a���sAfc���i� n*RDU�/ r�*)��e :(M� �up�%�Je& 3ln..F�1a!.� �� V�3ot���"� ����g�R^c) B-�  5 ����da �Rs�i(e�go9)� ![j��7����j87/��-��.=N(R�&:�g�h9m1-;� �� A�a ,dEt�at)yM*.�-�    )epA0"�J� ��anFity� �pura$6�a�=,&��B�*z�f&�#�(acxb.�( "9��}14� �1<de�*A RMm im:[t��fo��%U.UDm$at 0 fs, 5%q9 4. Upper panels�wF�-ֹII]!�Fj�!]q��. Low�g%MNY :�62�M X^1A -i!�n at �"�� 1d �'s&�.b� 4.5.� 5� 3� end{�*� [�z�-.>X,q�  t]���7a�yS&u  4�R�% �ڍ\wJ l�ab�a ( 90 fsa&� "p(qib"�x ��� 6p�� �� �'s46�� ly�!���,�i�f,!�� A�1�@al�p�!� bvF �v U5o� FE�6�M5�`3u�/�"&V2?;t�'��]�V �bj�d:�k1��ҡ�] F)sIA�Y�v�Wir B-���� J "� ɑ<#>� ��!i {6��F"[6��"E� �E�I�I�.�� t�E�onX!I� H ���!�WZ at 1�� , 20��%J28 . �� �yprdW �|J�Q ��񆅽2$AYyV frag���.}b�.ZW4NWIz 5>E :dy��E�gM��Jc��1�!��")l:R){'�Q ?_" cX%sB -2�mcklcSen zero Y#i*�E�U:B8ec���u",!}f���-% �)imL� $20~�alg�� coʮ��F, bax5iv*� �$s. Doa����i�ma��DXa"with 8�� ve�+-�B/ It�vaFKa2" �o 7��da ��F�'�f's A�"Z it 5� �!"b %%�(-H$_{R_{in}}^ ,out}}\,dr/v_�Ir)>%�%4oʕ alig|��!�Zb&��*�#�v�.e&6�1[q�u5kI�6( $ �.2.15 \AA �6rs?�}~5�h�e�U$E_�r}=100 &b]$an�Z �?�1 ���qtf0�num2+$Ah nasc� r��X8y %��ajourneQ�&� 6�!e��gh"_/���4�hA�����syatoi�9)!U�: $I,R�(1*-�R))/M)^�,�1Y a_bHnuJ\cal�,��AIre� O[$M-� 15.5%u#O �$K'3 alsol i r>Nx8�%�Z�a@�7 &N� !�i�ݚtw�Gim�T��# ��-B a �2�)�9.d� "�#� r��E*[&�4rob� Ah��\!�&�dev�|5"��2� �6!=E?�%{s $T=�2& pnYX�����6� A�YKrF(B)&B�{"� ��,e'� ����. .�(F�%�Kr� �/g��> 1)}$6�#a.i=2� A a�g 7�j67.h wo&Z�#�H�]ayn&$5~ R"5��B� � sn�P�� t.}}�enf��/�4�b �7 �5N�"LfNclk}oɘW�3v�]"q_ d ho<>I1#�m �#I)e�Nc?A&1I�Q�7ŝ�7in)�a<*'|)�^ as&Hr sia�)�d��:t Y6-orgay��oi�(.a1m!����i�;�s, + �A.�a[�Y�sM��(J���de/C�2�$giEg�+ *c�"6>4`rBtowo�"a�cC� �3��T"�;� a� \kZqv7cIK6�ech&JmaJ.� �B�8�K!aN�%B+? (c EdŨe�:[? ��!�1A�Qb� .��B'?�is�*��� ����s�.hg�%�;e2�a��<"o (� ncep+d�n��c��(�=g�"1V� (�\s)��UZ w(��q��X�(.�Lm+cwO 0q�&I �^"+ �ar nano-`mm�QL�evE�thb01*Q(is �=��a wayA���!@m�b �jcom�sيd��js�!y-�� m� qE�� �  -gu�o. F'�roC�<�!of�k��?4IAioVc6�oM�,r[ que ��o�f�?���MryV ij?? spliw�!p exhi@��$ho"�s *�sinE�Yj>wgu�*� in hi�\�!d�� sub-!'0�/o3u��Dz;hqoiV op_�up��n�i�e!�t�T�migg/01-&�z%�" [GEerE�ko� %z���*'0M��6dark �8�w�fa�U�A7o�lag&� ɹfir�s�deYr � s �0bev4dv%'on}%�/ t �*mm�hy�V � ��v� " acknowled����!����!n��� RFBR. AGR�Tnks Prof. A.Giusti-Suz��,Dr. M.Machol�AIp�#����3Au usefuc .?B�K chap>A�2�<1} U.Marvet, M.D�Ps, "F*-��j�2p�s�3:Q�t:[�", t V�y:2IU}��6z���nd Ch$�P��;g��"�o2Cb��M.9`rgui ed., p.135, World Sc� ֦,, Singapore,2J 1996!��em:nE.D.P|ETr, J.L.Herek, S.Peders< Q.LuiE�H.Zewail6U2UI��rol�Ta %�ms"6@+t N��}!R,bf 355}, 66,�j% �3}YV, JxF.H.M�7"J�,2"CV�"�PZ%��-�G2@�Q[�. Rev.�A50}, �4=w4ĀT. Zanni, T.R. Taylor, B.J.Greenb?/ Soep9D.2�M. Neuy� "C"�M"� eqI2�&����2Gu�5!�&�A�.� e+]%2=.(,")�JE�m.)1 10 � 997;2BC.J >i�8Boniveau, H.Duv�B.)E'J U6Bhemg491}, 5416-5422A@87=|5} R.Na� anoA� WeinA�, P.S.JuliennQa�(.J.Williams6�"Ґ�|�JH.g %1�\-(a2�of� ly-�oE�'ai�2IQ Lett�73}6�135�2g,6} P.R.Brook��)z" ~+ _Jo �iesN�%d2�888}, pp.407-428%j8=j7.R"Cold8 ����a7 2%��qbJ�s.�-S%st. S%>. TNjolYm1:#487�,96; X. T. Wa �H P. L. G�, W. C[w�1y6lE. Tiea4ae( P. S�5Q9��D� !��ɕ"���1ui�,a"kali dcby6;� U^v&� ,�i-N�7>600%.�8��Po�P, G.Schay, "$\ddot U$e�hochverd u$nnt6Y(Flammen III1�Zm�EP1�Ba�3�2.�9}��.0�%n0I.V.Yevseyev,��". &� F/&qo��Las ��$3} 523-5296� 1993]�`10} V.M.Akulin, V.A.Dubovבii��"� G6� �,a�ev�of"���$2� 2��E9 �[-�y�>�I&:�~�6�V��,AH!��,�p.62-726`r� �B5.�1��9s6�"L�.��E+v���� 6?��3)MѠ�ٔ A102}(23):~,pp. 4310-432E�2�$12} S.StenC $, K.-A.Suoq4n, "Weisskopf-��o6��!� &�&�h"�Opt. Expu2:$ p.37��6�3} R.F� berg5 R.Hartman�B:rd balls_?L 6D� ferometry�)J�4�q 1446-1471:N>�4}��U.`dv"N��1ݱC�R�.A� A�o��B�B�6�32�1 858-87�2.�15J�M.� , "T&Lx aB�^�I�F� �6��!S.} 16} T.� nT:$, P.J.Hay,� c,���"mn>�#-_� monoz� s" ,� C� )P��69>�137\ (78; R.B.Jon�7J.H.SchӐ� Eden:."E�8�1Mk=�IQ �$KX-I6)"/ �wP 0violet(208-25�Q�J:nJ�9A�431�2z87} A.I.Krylov,� Gerb� ��Apkariaa�Adi\qaܗ)y�]�a."x!&�>E�/�� ert �{nt: F� j Kr �:DJ�(189}, 261-2i"� \)N�&&[��� \Y0{a �lW�%\&�� [pdf��"�a} %� epts .jpg60L�s,draft5}zѩ%\renew��{\O$��tc��.5�����Chs n�.E,ng\\ Einstei�#&� Manu��sF��T�$n Sauer\th�{Pa�.�en���25th Ant r5 Ann�?Mee�A��A*�AD̜;K �, � cago, Nov"�r 14--16�'3;���rA5e�JG}. Facs{�Z �m���"i�by�Nd/(l� QAlbA�H Archiv�*erusal�8} \date{\tod�9lQN!bmak��a&��b's ea0�.��&�Ņa*�zi�4elz�bfivi�.A4s�G#��p���( �F�t�'!�a :س!��!�i���!��=�iE3�!:B} (CPAE)&1gre :�Vdi�ng�somf�or��c9<W"F<�beez �p�E�< �iD �_a: AScratch]keÜQ�y%�(1910--1914,0 so-ca�d ZurLNo.91912,5K��*arXO �fo���v��%� 9of��vG��`#1 -Besٻq� � 1913+-��zc34=!�iMercury'd� ihel!�f9?�basV "qGross� �CQu�]p2eg �AqE�qfi�;K��, connID``#-of-an-e�''2��]�:��fkfu26� =ۅ�|.e���Prince؊�.����f\P�!{o5�UbA-�@E��un�dG p�'e�yid�m G��ge X& 2�o�!� s�cRl�;A�webaQ�Ms�O��q�'a�Kl task,���&p*̷of_�M)�a�57� O-�}�sit[�?�Sq*&a  �actA "TMI��.�e�U�)|=Ls$e=efforT0��d^!�!�ers� !� !!of�'e q.�7�� "s$�%Q:��Proje|�6&� #a�*6�E devo�h\!!�sha��YTCi" ZofBf �f&'��9�R t��L&]:���,UYe ``P �e�- Foreo�''%cB``G� .'�''�Vol�D1�,�f�a��a"�� �Bailey1989,Stachel1987,Buchwald2004{��"�'BE��:t \�e 4.caltech.edu.}A�*�(9S �H� U��Vø��:�51= �=R� `�G� 5 2}-- �!9��:m:�4 ))�yvcwen����UM,anticipaA7*h!n-�30--40ɭ�wj��A��l���@ Engl%��K -�O"�2A�Fn%K�2!0 �=Ez�a�Ab #Nla�e�iw-�j�"ly��:L���EHebrew.�of &�  Kn��asiHU�� ��(A5a� U;a4) ����b � �to,g3��high-�JA1f&� ;y's �) ���[isV-ai"4E^��!�ٿ�Kw#+ �Ń4 �re���ہ�2p%�3�Ra��e��-\:� 15IRcA� *��ij��V��oY:in �]a�,9 =th�  \1ƹ s�Os H�# Duk�'ho�:A09�� is�` aI,�@� until�K bina�2 �``P28 �bz%i/-=Au6�l 2� microfil>&X�61 reh0}�9�n�,��H�' )5� >l`N%!���!�1/Y�a�Z\ two- 82mL�f\ 3-006.�!�� ,Ak�A ����. )s�:0* q�� !Z��F.}u\w_rdcop)�p�XtS~!��q� ethe9K�A���&!�ori��) U� pۋ s. F"y)11�N�(Mb�at�oEmi8Cry�0�"3vO� �I8EshippL*o�xI�.� 5e���� hous�� ��: Jew�yNX  ݑL�� S:1982 E�20���� $-�s* á�"��~u��m�:�]}�iy-�U��De^se q, ��ly<7A� rom�/A��C!�w� , were a0�to1��� �@uя:&�iPeP�A05 ��ɪs:llY7 sm ! ��%*p"+!un�:54 as �s,� ���S:pe��a�o�O�G% chron"���y�% ex��!7i�� v,q b�879�02I�p� ;.��ed'�=� Wriŭ}.�,!R3467�#a AC2�JG558 2'da�ialԏn s �UP1�E�B�n�� � �,=�n�Um$�.��;�+�f|�-� or ,-J?��5!��% J����D?Y7�e��h cribed-T �i� !5� (al faithful�2>#,�. N�.le�rr�<2&yp}a#or ��� � ��punctu�� ���9+�g�� Dof!9t\c&k4�)la%!��l^.�A9;�.d�%CU  method� �ZPotB�]�1]KM�-��$ �6�  s��At *sQ`gi�ɂ&� 8}�0҅Vo!��9��sIr.}"y� �a� � A��A����,���2b� .2 �KXre*o�.W�FK!��9tɂ'�+of�rid��4gap''�'y*miliar�9#L!��nd~a�,FAJ%B�c*�|��ersBU������ac1�B�U heav�S}z�Kjo�V�in�� N�Hwor鵁^v ������� �5s ^� � >P!iv�O exa� i�@��� ��.{ently�Ou �u�/�Z5dr&�U� �� crip�@!# ird-iAy��. EuL*q"� s w7-��-�5-A' ��%�A�no�"�� AEA�z!�4S���!� Yahuda��[he��-v " .�R-s PDF���Y39�?s �N_-�dm�uC��q Z =%�o+��556/�c15���s�9�ma d}in2&>B�� 3P4+!�%Nb 4n HTMLɂ��' XSL ��sheets � n XML���-or�,W Enco�0l�E{� (EAD) �(up��!�EAD"�G�eD�OGon (DTD)�� 5P�"�� � � ng a���(!�S, �: Markup L�-$age (SGML)A�km�)�ENet�@ Develop{ �1 MARCbs O�z�5M�An Congl� %-nerA &�YSociet-A03)IHn.�����"e{z���a��-� !� ����a=�b5GBQ�9C� �r2 !U��m�@�Isk�A���]�f ceiv�dEn, tit��sl!� , lo~,%�ph�� eY���ul. If �c�iz�a��� _ i��0FitFDc� �Hpe&�u���*� py��22``&�� l es''%�u�=�d�>1 ���d (634�jord3d R!5atW.��NRE����ac�\g"M���d�!�2I�� In 0r|� ��� 3�u� A�?!''w/' ��yqXH heck=�T7�An�4Y��st��5�sourc� no gUuee]� _�[,�sYZy,+ uletene���Vl)� 5�� I�[,<>Ő!B�ly sB�iod ly up�d�Ѡ���i9=r�%�\ a�0t���. Neit&@�� �� n�e2 �UQ6"� ��:r��wo3�" � �q� � s}\t !�ei�Z���c �AdB�� o Ru��Aran�x � )��as|y imagAP� t�sa&  �"1�+&��%�  n$ ncer�O I�w�Us�@&w76Kg� s, ay;�A_�t�2 e8%c s,�aZ�P� Bdѓ�J��#B  V�A!P���U2def3�6 e��t �((p 3du o��u�ng��2 #}�� *[. &�1�'sf9#>�(1\55����<�! synony�4._&�!����� y. H0 honovas ``0�$20^{\r)�}$��'�eR0TIME} magazin�D�J5,"{��{�e��He�, �!e, �;� ,� I�/Zx�~��auA�!�!�enn�a&<$!�his ``m�le�.''�qH�05��&� y un�n���EE�q�qSwiss F�4d�f4Ein Bern*,ahQ fewd(th��#�eo%!ad�X@had a profound an��d lasting impact on the development of twentieth century physics.\footnote{The papers are reprinted as facsimiles with extensive editorial annotation as Docs.~14, 15, 16, 23, and 24 in \cite{CPAE2}. As an off-shoot of the e]project�p�� also available, in English transla�t, as \cite{Stachel1998}.} The Odeal �d determina@!B0molecular dim�Dons, give an expla-!� phenomeno?(Brownian moRd, expound what we now call< Spec!STheoryRe� vity� clud!�h�equivalence of mass and energy captured!/famous6 � $E=mc^2$,5$present an�F�8otoelectric eff!�by putE�forwardhd light quantum hypothesis.�< latter contribu! alon@er earned EinsteiI�(Nobel PrizejD 1921. Ten yearsV er, 6Hhad risen up throug)�ranks!WDacademic hierarchyA+ {\iti$vatdozent}!>HBern, Extraordinary%44Full Professor*ZurichPrague)]in 1914�8accepted a posi! A} out teach!�oblig%�s�member�!�PrussARA�A& SciEin�(lin. It was2!Fat9cA�ed his!plier sAtific2�sian!�%�� ual break9[4at came after )� of strenuEx(fforts to gA�al!��sM�tQ� rU�/iE�e gravit%ILG HAXB- �comple!m!ba publicE� �Ply covariant field eqi(E.{!c late!�5%fi%eseu[4at even today �W�basisE�ext�Lve ayA�, bot�oreticalAH�aer�y tal, e.g. �re!8t!!fin� evidEfor.�@al waves. In addEv:A majo%�u�� 1905��y[ %A$shed numer!ۭH!�ignAD!Gimporta��in !],%]s of ш!�sՁ1�E -investu into  f�H%��kin1ory, sA,s)J m� radi6 ey, work�@law�p��ch�#al!ڱk,)!� heat3dsolids at low temperatures46opalesc!�, ��so-� edu�-De Haas��M !�Ѩe�m2Donship between mag)m��t � 0of inertia, a!�ber!�cri)3Zv :v��-b, ��soma�!�-�)��^Qconsequ!!� m� � , su�Ws6� E�$, cosmologa4 .N,!�%�Y���}� al la�ng. Dur� his a�r�`Y�E+�Ta�elyQproblem!Wq�a ua edI�!���}��Zo-� sm t�@would� ccou��orG�WucA[pm�Sցd9�e� a. GivenUR'AL��io�y�ce�na high�Hreative, successful��prodcu s�9stEGA�a��W$t interest��c��of!k%Us a�s fro!e w� oA��Tunderst�a�!�circumcEC ���uct; $. His burse� �ity��-miracle%� still@�Ps a�# challengar%& storAu reAwt!�ie�� !�`e sense�� lains�o� is~ . Un�* unatA`any!h !�mpa�re ha�^ed� !�scarc�of docu� �� ���>?�M��volum)F,CPAE series I 1,25}�� situel�ma�be!�%�� 's s��ar� where Kmore p��n� �0s have survivT nd�lnow& . is!��{ exA�1W�Sc�� to a�h9�Y~Auof.� thinE�e�!��� manuscri%�cquire a�;al�#. The {  ``J?'' %referF a5� x$was writte��m�A�a���abs aq� fic ��, mainly%�Hpurpos�m_%ne's ow_ oughA�nd�Dre� $implicit!v��in�nt!�a^themataJ$ formalismIU2@re �� �ny pot�al aud  or��0� in mind, � tha�He author himself. Ia�eq�e �c��$olves two i vidual� � collabora ,%1� maya@v�6commun� �!d1�ers. A)on�tracter�!�(dE�yb caseA�an abund� of�)5i!� mula�gt!K , or%W o!� very few,��%�words. I�s� s�������� imme- Yy�Q!Pa Basi�Eth �Ʉed%YA�fur!a�Nion ds�<pre�.&�F�k perw ���he 2�ofY ��  �!����t�� ce, see ��4Holmesetal2003.La� stag�a�aߍD E>$topic tend�Kbe�� organizedAf (differently9 �  ��!�� os&9�E�wa�L addresA-b> , he begi� oT F  toke+ �bsta}!6��mt� �convey� mean!��e m��c�ons�l�,itEiV9< o2�languag�!� !>�B�i2� a],!� RAcar�, unique valu���a)� ce. A!�e s� timee���~!�!} � +�I ruOof  or��E�durid a+�$method�seѬsaa� m�pu�hML unce"t� 1ng)�o%�:!%Moš nd ѹ�.�P0followXI w= discusaqur exa�%�N~ e�� already b� p�k- �Col�; ed P�V Alber&�}�U {�a batch f�!�� �id[!�� !�fuu :$  $. \subsec��{ݐScrzN�|,T0--?}�fi� �W� ngs} h�!eC&� � h� s 1902R09��.aIA�u2nA'sA���s5e, ��M4$5s� � annus: bili�5q wellI ll+2s ��at��wro�Y hile�B atE�Pa�� Office!��(. Sadly, no�s �t� o ��A��&1 ��is1\�: repr� d.�of '.�� is*� chan��  V:  3=�3} whco1� 1909!�11� ��& j)�%Pn 6�&|a!�e Unih &��little�� \�FPGerman6W �. T�i 1Cs� ub�ed=��"Hs s� �� s. M}%�eosoo2� the Nree item8 �*�VMzq�M�in prepa� � courses-�hv����'p*� 9o���6a���e gavE� 3 1. Two �short.:���a ��m�A��a y Planck9� 9e Cin:Fr� st b��BeR/ ograph� ector Darxedter. AMU�aZ hand��!eremark��7O* delA�edM� i(Solvay CongM���I!7E']B+ M�� a�per����t�dat��"e�e%1J(��u�%�did�@ a�!���I�s%�A�tuas�v��appendixaZQ�s�fac� is#I Y�xY $ents: % \b� {quote} e�a ��abla� rchaa]byyE�09��. an� appointi-�6M�qb�aMck"� q%A�,ioner Landol)�Arbenz% � e��#ugg?!h&!qnot us!w �� ta�Supak�I� �14 ndis�e� �dB inu�Q � (� , diagram.g��t�n.-s,� � �toH 0 lite'a�d�A�es)2Ltheir�j!�ed chron�"� , arg� w erv� un�Mhnon��;Q!%�iAw� 9its�ire5fac,���ompanyop( ��a�t�k��� ily ssible.| [p.~563]�3} \endQ�%#�� then�e��in: wa��_top half�c�&� aT��-&�5eU �%wo fafɩB� . Be .A  bottomF��comal:A i�is �� n. F�Fj1 � �zpr�5e-�vi1� a liCY�Y���`MOord:��arm.� a=j a�&� t�� Is# ^i�clear��� ��.� ���aPed�i"�A�*� � � Renn�1997, Sauer�a}e[sho�at ei�!� �F��ain2�� ��fu�"� ~.��� w��� by���36---c24A ---in��% -p!is kn�BQ ( Fig.~1).�Rfigure}�aR#er} %\�`ics[scale=.6]{lampa.jpg} j&-�1�$.eps} \cap�8{ � 'sBi}2Q ,!�� oducIsa�m�� Om��^mi�#[App.~A���0� ag/��85 � ws5�lac 2.�* .��$ high-qual���q�4Doc.~3-013, im�p23 anf$,�)!5� Archi�Online}�www.a9en"0.info. \copyrA�~'$Hebrew:�(Jerusalem, :}l. ��Q(��QD%�$��#i mA�.>�no��6h@� cube� by����na�bo�!�!�����,-a wee Aprilm 2!��2�� AHirmAq fe � �v��V����x ary� �)e�&\"�&6� . On �Gq;�! a lo�� inser��� %e2Qa� toge�wi�! -��as�� �, neve� less!�%paru�Ecy ��a� de " flow�e26:�[1 )�&q ERn � ob1 w�9ӥk79�-�"" a/a��!!�,modern astro al"~:.R�$s��a!�$"� &'} � 4oa���*s � R'y� 191314,% until.gmove40 !u4* 4�$� d �in4��deeplqPPa6 ���"�&!��a =�!��]"xtwo&6*!IvY new1��"� �wes�i>Qie#5���,a)� VuS�6�I�� ���� e ``9A.� '' beca i{siC�'s���a��'7ETH� eÑ�s.?-Z�=yalI�"1& yA�iU insi0 �$* �)+meZ) U"oJ(summe�(12M�oe�dipreli�*r� m.J)��"�6�A1fri���Peague Marcel GrossmanE�an�ST Entwurf}, i.e.\ ``Out�T''4�5� s�g�93T � �1� 4})A�e� one EfN}�v nga��,e��hly.) ,:���@or, Michele Besso� ,)�;�#��ngm�+�)erihel��f Mercu�+!�e(�.��5bH��.�\ &K YE:M�detailed*A#�2�  pa��o�+��������I��edgJohn Ste-�!AAcx�]�-- ��e�d� stud� by bNorto�_o!F� decis� ���N%�g6�& 1984 j 6}�an�͢:�#)C"w�lis�N�3 �� }. W�!x �/a �)�I@$ �q�� \ if!(aCa�o�hY�.Ia�!�ld0 %��[�ba�*of��!idiosyn�ic��*L quite unambiguously���{��@ � .�� �,�"�!A� �;ed.-� �-b�!b!M9�� J�� w &�!.��Me� al!ghP)�u zr �h!"!/5�"� ]� �Kn8!&  ,d!}verD's�E m'�! �&unYH�O5Darose. F� ,2B made �:�starta��*wo end�k R�� ing �� �, side?� !'� e+met��- act �$<!�M2�%s cor5"K��4%i2�1 .�kU� despA��wm�S&a �MR". S b�� ir �� e� ��ud�pbrieflyAcribe�+1cJQ  i1. 0p�#!2�0���'H��2�+ ��Q  z  '6-%qto�il1e��es%�A�&� %�ՃhQ��4di�al ��e ���şx� ɫA�"� !  &a s4devk/!��Y"x4�J5lN5�OA8He5R !%a� �6s rq#� an��;�Ye�+� �ce�doe�som�%sA#� ���w .��2�s, re�% deg�of><*bZ)��)�s �b�imA�� G�#2s�-c�5e ��it ow!@ra��#� /�cru�6 � o��.�z- My-�Ren&UbDez+n%O��!��!pe�+�9 "J a'pa"J ", ���I >*#} triggeM!�� �:fC )I�$1L""them pa-r�A�5� }� *�'See= l 2005�#,� . �� resul�(g, 2�,�~9a 1999�'�~� p embar�0 � -by-!fons"�. ��=a# ��"� e\ ,�8%�wx.27gr%familia�1 n un�ew�+�en^ uA�$'M�8 A�9 6t/J%�Klay aQ� rol7g,uY9� J����K)"'0�E�[aN,"�..-�b'��c�ҡA23xa&t� andiN+;atIbez test��ga� heur� ir� V,mo9�.g�t turs9t'%�q��,ex5�� ��o:Y �&512, if �in�(ear� roxi�-on,����$ime discarhem��un,p� c a"� �!-view ("�2��j�ZN20L:�1'�#-�edN��'!�a��e>":I[� A��of.{ �A���(ca.\ AugustT2A�*7 A��� s ``2�"�s'' (``G&R98sgleichungen'')I �6�A��;a�;dA�i�h�5"�9=E�� ma.Kp"�:�!� �5�r� p!'� � ,2 06,  20h�1�"�* http://Z ;��a�>aran0 p�����0, esp. 3247f. :U BU of�UvT��v�/�+&�:; .�={N e fi5�Y(!n]Ca�Nov�< 1915� �25 �6}t !� g�  mark��e:=<�9 ��~F/"S#a)I=�y�A�V�iA,rtiR0z/i���ltKofX3un#llea��m ��/ide,'%�_&7+�co2iC%y&�$ |=��&%b7�1two-vL)mons&� !si@; (�Ŧ r!�.Fq����> �C!�;*�s��A cur��z�� 2���"��!�/ :���#�2�a�q�+2��~��com�=5��-� r� to.�y.�z?ev�+e`=i "�5Y�9yY/��rZJ���7!Q� �A  �i:s, �{spond(;m a�`�AB��t(Sew�"6�perhapB/ eluco� y.e�  m�76� ?t�7!_i�e& )se�8 &�ot.'� imon>@� epd� &2�@L �c"�9�_ D6 :�E�z15 �e�s ~51 >� p� U?�$"(*� K� no!�ezle!9!&� re� ���2@?��6�EA� / _�!��adv�$��j��-&�I�-y.�� 1913�CAdoma�[sEEF�'EG���0a es� �#a��� q�^!u�?��5p8�not easiV4~;b;frame�7of Newto�E.� �,��a�y.y touchst� ny;er�@N�. A'Ca;gA�zB���0* N�,��R=3to�u�4 K �X� 2�A{nu�uA�eir+7io��R(�� �.|�6�4 hand!Uq<inz'�ne2�.�� �%�a�6�G� rope!ja@ � 9���< eqJ(�6�QA' . Bu�e C-|��Ajes��F�4ՓRX�!  po*���"���>E�(k"> orig� 2���jya aN�}Q��'.���!��J�� 14 A< ��61U:��&M �*�=��"���s=Ff�$�A�(��o�A�@�8h"�#��$*� �N fT�t6TIn_RR:��$or��c�I �"�d b�%�:� G8nq�i�K6"/ A�!:a�J� ݧ!QsubFKof� en-���%��aPalyhelped�7�)wh*'/Wk  quic�u%�!�ct L8mxݎp��s1R,�#D >��*� �"| {Ea�3(Janssen1993bis qu�o�an�>8 aA8�Y��<FV ,�U�� fu�9�^ �"���2seaR *� E"�&oy.in:m A����.���:in�-��u%�u>ty�7 ��դ*� . No� �"X J �� cali�JeTen�De �rwoH>�7�U7aRM; �+. Both  s 6% 7i�&).� ier^gLbhey��� "�y52�$�oof on-sc� (e�I\ poli�@;h4Z n""  to"b �}p�,sJ끿azle�En^1, draft*K �gs=F� �8Nx* opin>.�� 71�me sm.8�26�iz2,7}%�� 5,B� 7}. H�rf of�N�aC�tdy ph��}1gg| .�,in�*��X?&C}� @lA�]�6a"�7d))�ghE5e-� (�$56�$�c5&�Ucom���I�6sourc �2�D!m� F dGB3AeB5m��-BUL pAL� i}Y��E�aBKf�#"� �u�6I*�'�eCor Wa�G J.\ d�J�  atmLa�&�!5�C� � a >��agR2g � ���!��r�7:w*@``Back-of-the-Env;S6� ''} �7categ"�K9��!׽ fP8�>MN��=2i{pieA.� 9@or>� bb�L!�A� erso0Ms� backe � s, etc. TI-u"��"�can( 6��Ipe-a�Y��U�e�C��*��Cav� or5�b�.�3 or �ussedeA�roprivOpla! )H �� �D~ j s, how�-# � defm � �bm'� E��do�qL�I��!) iz��2 exs��M!��m+A�� A�w�3�rɹC�""�?s� �SL@a�g�Kin�2r"�8e0 9#�2�26�2ChE��$e I�aM��$An�'L3.� , 1 Febru� 1920�9�a291�;9}. Du�-��"�8�.A+onnecA[�(U��{Uc!1� *�!�EM���>2� 6j>�2��2��V0B�Z],AFme06a�*�+6�(�0"�=i��>:��>, who�� ��@ a�A�JR�W�GoCPP�c Edum] iSchool D�E; in Viennae4M5 !ց�*�Ny *};f c�vac�@ chai�w .R2SM��!_E� $�TB�@�2s:qR\<O:���Q:*��K �:a6�olv$�Onu�Q s $n_1=n$P $$n_2=n+1$ ���(T �  $n$,!�D:2�Bjerrum�5���r#al=tra1ey335u58�� 9)ait�5397u��4-w��%_too�;rbe.S6-* �pD >6"� sA8O�d�@1pA$its own�F6� *��.U0Ja�>J�%� �(��-�%�saw�����!iF#.�<p��C� A�� elseW4&C'<4r�@d�. C� s[OU�)�m�I�_is om N{MQ��-�C���romise2�Lw�'@! * �*]a%�Q�L�%��B\iZ1O  h� � �{�<�*�� h& �G�)i%  judga�Ao�LA:�!�toK(m� l]A/!%2n-Bba~1 1C:" A�4�Prince��M"��U�SF��[ } P�#mm@�,!!�W26 ex�E��& �8 5�3�Es*dWn2�3!�-�oE2!�Mci�� illu8+I!� ey m�2b�I�qp ��r�1*[ a2��8�8e�E�j'Ux6M"��ҡ4AS!�ofZcH0�es: a ba�H�' 1750=Pawit�B*c�1�mostl�$� &� KfA�t�.( Stfifty��� �Lo a�Wsus] ks� � -��&� M��3C~ 1R@ Duka�x`Ki�cc�]gzanecdot�S&**` Q�*� q�X rpri�Nly,�edo8beh!W a fiE�cab�Zb:A_s�<a��fi� u �-� Helen �c Instit�for A�d Stud{8��  �iJB� �!slnKq' Er.�6"� I=)t�Bad�T "��ҁ�,�D�Spa�toT,�M,microfilmed B7reels 62C 6�=0)r�4ly V�nder �oi!I�% c 62-001 �63-416B7�una/$g[�"a��HIJ%� 1eets; "�&4,��� . F��=!�_Z (� 63)IN�a���}:'t� v��_ake*&��) typez� Ge�E$�L"�-$kind.i� ^E*W&�by�P� � clip���rare ���/�� �� !�A�INy�s aMexclu�~CBy �&2a Q��Vus4d�8z �y�]8 �� rks ���xt�m2)1Ag"��/5�J!"e/EC%� =�� ! s63�;{f>2ye�����in. hand��B��Bep7:EA�Ap=�"# � ŸNH]( (Call Nr.~ [�6!j�l�o� ���ŀ192�r��#r^an 1700��(%���eF-�ԕ�A�is�+�"�7�0D � �6/ V�Q{\it >�.cAl6R. V�(:���j�Bn� 8 S � ��a�aw� � 3/�"�in !㉎�s �F far�</ ,&� :(Ja577%1`2l-��A5!�woso��ad� n��dH35��*one� ��r*& mSlu/7�� 8,r in-depth a�� ��XglobaQ sess of�F%4�""&�6�G�gF'.ye his 9X�Ťs2�!(� aM}F$5$Y��& ) �e|*Xtq H�,aX �X"!R`25*�.i�2"� 2� ha!�en�M?4E%W�dt�xe�+�;!|i`n*�1�F�@��4s8�*OJ�.pN�W,{Go�Ir2004_x.E } W� *Fq a su�Oi�(&_�W!dYz*.ed/leA��� r�B���Wɏ� p56!� IXw4tstampA�1919 ��os��5� 2-053). S[)�7^�3�#u�>quxQF�"�(re� %��+�Y�relev� ��a{*S��h�ly.? �Lm�u�i.�f |1 �'��| ��*�7A�%abe ,�ale���"��p!"-zdup�ZA0 !5��~'XPIm� scan" �cs5/% low-resol�kbl� wh3;�I���rHO�n loog4a� d'_ ly u �u i�1�a multic`�R�^ap ��!A !"�$Acag�4 cataloB!ߙɵ�h�m4V�%c2W i�da|,primar@(��n��g�O&�\phr�A� �= }I ecip�<"�� �q^I� �Kin {L4�jLl w o �� �_�`^ lin �d ``nur von \$x\_1\$ abh.''�AbJ`�? variA�m�0"# ly ignor�?Ini�� w! it Juse7#!GlsI>� v'}exa�AW !�ula!atA`9E�;Im��$ard LaTeX-x0up��A <����J s a "�E,al0 (F d� mon!�Y9so �not�ow�U-:��� �"�6�9s �*A5� ZY^� �J@ ways- �- A�Xs�n+Z!oe2(s Y6ndIC\{1\}AGrI�� -+ly�%r4ent.} Any obvJ$p,it��m>�5�fu/fic���p�#Gk,*a?a*f!� , ���+$���m�lY���a�*�i�"�N��sXr�iʁ�� o �.JbfsX ���g+c � �Q$�-.��(� *L Lhotela�� ery; nn9&A�� n I��An�v ?&�R%=mY!m!?J� �� YH.,or&� _ 26�2�'A*L ;��A� ilar hint"a�"ve�OMk�Br�@conjun�^W$կ_P B>�yuaL&,!too�f �$"� BGl hus, �M9c��of �`Fy" %�suppl_*t ��+in�#6�� �;on�K���2 !��z�e �<��M0 . Al+I�� sign�4�_YoA,"b* ��.p`J>z$e %�p� �sY�� �͂.� A��A V...ou��6��Zu��61(N�"&�I���� B� 7�77?� "'".%.I left��' �+.�"(l�%��� ��v -�e�9i���"�7 . D�J� laun�k�Q5"��\ webs��i%�si�u�r�%�%a��s� "5U s? H.�]& �O�>��j3 a�@#�6:�� ��!bw&�u o�]z=*�$�_wCu  nt1*2&�! ;pm��hol!(UbA6C5{:QY�UO!H�eH �Q"�auh��W#Chr �K OctoR5$2002.} And ��*0��anb�" n�"0��JA2di�;ea5I  &�.� �ind��{-a7an�AZa:�S�2 (}qf�E-r2 ��ušT :`�����e^9/!v�?ls=n_?��]*aY�qf'sR=�nght�^��o���31�_UJq� q�befjiEKm��]��  6 �C]4a� ����en �D��+[>"�r�e�>H~sq }@i�^'J !z gAo�u>��z�[AM1/Tr b_-A�A(Cl� ;car�*R@.��K���&M%��l�"wp�s���2�=,�e�1x!7o� nmuM��.a!Y��. I hope=havg$�,%Da.;i�se��s"��` Q�'�"� Y l%��!L)�-zho�2 6�i5.1�!� xt�a�$ y trito*s�*�+ xq2.U+w�$",satis' or��tY�s,��i�~]ven!�odarge HlƁr�)�yl�xWa3y�%�!]get"�eU+2.H� %�a&aeV). R0thebibli�Gy}{99}ibNn[B�[y~1989]{  } ,`98bert Smith, Jr.�]_ �": D/-*=�he7.''|BP�xe.! Ame�$n Philosop�9Society�f 33 (�(), 348--359y�4uchwald~2004]{} , Dia*2$``A Half-C9�=�A:�6���~A� �4} {\bf 32}.1 (�^h�s4),�K14--15.�Q �41} Nqf_"i%q;.~1)gE�5 Y�b, 1879--�t.} StA],O]H, Cassidy, David C.�X,Schulmann, R) t (eds.),&�): .�#�.t987>�2�12��2 �Swiss �: �=�h00�9��], �� &�/*�5�2d!�r`3��3~�%�011.} Klein, M0n J., Kox, A.  U , J\"urge�)b��=�R�93>�4)�4��4z�;e����B�}N5��5J�6N E�2A�1��� b�y�~�F�6)�6��6 ���}6���917~����n-�a�]67��7��8!�2a�` J,D, �H,F� , Il� 4J\'oszef, Lehn:� oph, :� Kormosr�F� ��>�8)�8� 8N F�-� 8.} B�2�1.&J>�}���*�!�9 �9��9��Jank<�2--�i20.Bb-�f YK�'fijxDaniel��e"Dq , Ti�J9.F!#4.#�FX-�~1993]J�F]ma�boh�^ 3Q� *� E6:J M"�fM�f 's P"�fJ In:& At(�z*UV:UM }2��HivHY��*�k,:��U{Y De%  D.5^Bo�M, Basel,�� : Birkh\"jr�� 93 (1�5� 2��72.G�)� � , Hu !\u � of!�*8ies!H� LivQRe�X� = 7(j)b.~2. [� ]cle]: �; d 13&P?2,.�Vlcr b .org/lrr-'-2��� sl.�3]{ �S3} , Fred�  L., >� Rheinberg!s(Hans-J\"org5��Re$ Aw$ Bench. Re��k%A�];�4}, Dordrecht, Q4London: Kluwer!3 (2medes,�F .~7).�ITa 4].�gsfYm``How"? Fp3 His )�E8�Aj& 55� ��,y� Ph��al�s} 145 !�253--3�4�2!r1��u]"nU}Bh �� ��H .n A�� OON of.�al LenK . A Post�Dp�7qK's 1936)�1��$5275 (�) j 82.�forthNG�A_'.M :�B>)�)�,6n . �!��fW �}�]r Vr,P�.e��� �!�9 ��1�_B����M!�H�]"d M.F)Rev��#=�S�� a:�6�!�.� Exp�^ng World�J,>, � &� R�>r, JimM��,t6,1\�� � J�9 F�AW�[87--122- :�2003a=���Ec�6�eAP��Mandl,u ����,to�r.4]qb''9z�fC�:he�n�"on]Q�F^�As. Fea� hrif� Ho�^\o&�m }, Ashtek@3Abhay.) al�M�X5�6X, !,, ()�:�& ��m� 23�� pp.69--92f��b:�b��rrO>� Iq s: R�1st��-OA��Pof  6��"}<:�-��1[An��268B4.�E�Aw4]*�1�.�y]@ i�T"3 Pr+m�ToU:i.� (Cambridge C�y� t&~N},� .%-L� YE� PJR��2��b�W7]&��87:��� `Aa;A�,My Type'---EnB-�1����BQ,sh Jour����U�o.� } 20�V�!57--66�#vik+!$�!�N�: ��4. p��$`B'� `Z'}y,��� 6�  , 9��11V098=09850F .) �.�MǔupY��mve-.1Ch��v FaceA��:}*� A~%tAt~%�Ft:� 3} �^\Dclass[aps,prl,twoc�^ n,grouped��$,floatfix,�4l 0]{revtex4} \uFckage{g��hicx} % % PRL-REVISED2.TEX�;o+ detu�i%K�{ U "{,style{apsrev�bN��new[;4and{\gc}{\ensu#<\th{\Gamma_{\mathrm c}}} 22t:2Tn-gav_aF_int64t_{\rm�B-us6+\mu,sF*mV*mF*wV*WB*b� mbox2B^{138}�B�>?�cintriC}{JD1@S}_0\P"�}(arrow\,\!^3 P}_1B�_� le�_ }R_ be}{MR�c>�e#��^!bdDdisplayAlBG&Gj$ bfigLiBG #IV!f>�athcal{FB[fsrJ,rm FSR>w gtwo6-g^{(2)BU(sno}{791 nm:)fft}{553FNth6\Ni"thB_n>+nf+ex6V +exBVN>+ �R+f:b,ffJX ffnoA���0^{0B4sng:18\sqrt{n+1}\ g \�Q:\mhz6�eQMHzB_kR*kJ*te:cTTEM}_{0F� ocav6�\omeg�{�wav�( \title{Ob - of Mt8le Thres�#"e(Many-Atom C� y QED'rolasFQ \�T4{C.~Fang-Yen} f�Ee@{G.~R.~Harrison S�"ros[� L3@y, Massachusetts &�Eof Techn�y*| $, MA 02139�;�C.~Yu} \���S��lt.�N�%t.�Oof� ,.^of Wis�sin!d!:,[�b�bW.~Choi:�D<�P.�Seoul NE al�, ^reaLMK K.~A>��]]RE�Dasar>�����$M.~S.~Feld=BDmail{msfeld@mit.ed���� %�i�ion n֖if desif.(�Wir�J�F�  %o$ in 6� @Qno]��# Qd (b3�& be %�<% M?5k �n\cofY��Wf#q�#\%V, \home�-, \�3`�=/ ll. :G{ˆ2� \+{\ZkA� a�} WA9M_g *8�a�=le �1�-6c�#y-a�cc�c�I2. Trave*6-�(.p�a )��# Fbeap�9�3 F6a�* -def�L,- rLJe#6�%�t�v( �. jump�%photon IJ du�%oscilla��a. %Hys�0b_&� C% D%P�sfJl75 life qfmetast�(~Ks�;ymmetry�% ��8-lineshapO*s�bi~,ma�}� �!�!s %U{g2DoQ8r-shif/t:�)�SC� AQ4� �obra-v ha{%w�A %pa]��LE�I| s����D %9r% v �F�\io%r:2A<We3cD�F5l ;x% m��~'.�&ser�4%w���spredicmS[+re�)[6 idth!�U �-� %di�pro!WF��Mdu"ZcQ�A� W�%.~A�0�- amet����� �0)e % �$s sub-Poisd �a$�{m exhN' au<!hy�m�})2�s0q�{{!�W��mEko�9�� %�=�w�c*�(-�h �g %W(�'&5 PACS-���br]��7)�< \pacs{42.50Pq,  5.-f}NPkey�;s - APS�_�� n't *6d�(is %\/{i\makea mus*�l�s ,K, �, �J F�bod�p�?�3 - U~r�,�7�s % Re"]�sh�; 7on��!�b , \r�!!�\laW��s�Jy�f;!�alŊla light-m��fZ�>�3`��ic qV�24na�N- %��ɨ��mod�J 6Tc�c@\,g.\a2�pfd�En�w. 6�n e�qco�9��gth g�re�aI� deca�N�:�?�a���($g \gc, \ga$���^v/exv2s ��g�9!�nt0��P Rabi�/ ion)�L��J-C-IEEEqatom�F� .1�/!udomeofk 8s;i r"D/d �8 omew�;su�S%�"D58Jof ��Ar�[!x�in�3t}%��v�[ popu. d2�BAp"4$A$$$B$ coeffi�9�E1Ba TaGes ��V �� um broade��, ��q.uni�,0�wo�3�=�al ���sc��-zubairyo���-E`s����o?6:@le_!��)6��1' >�G expl�l�\;rN>X. AaZtr�U�JoU�.!�abs�KA�ng� al averag�leads��behavio��eig�glB� �9iTv1w����IJrae "1+M-r�exist ��HJ+ �Ticr!y0om�QBo�� f)��� ��8{Meschede-PRL85��7�iYE�7CbiX �M "� L2&i 2��Y{b�}n-prl9�W� %s*�Zy?�V�%7o e�hi�vs{ : (i) a ) ���pB �, (ii) 1fZ encp$a�� d�`�et5E�B,=l��,E3(iI!c&� a< mal Zs��NjE6 egliJ�c�@r"T.�E��-CAn!�94}E< �ME�� 6a ťVa� {%� !�$N$ op%�> of 1Q�e�w�;up,� gg 1$;&ar�xyE�* s( m�D�siMIq? at!�\ ed� 6A� � A4� paD�F� .� a߭ҁB�KFo6� e (ikwa�k�g ory}8�s $%�%Hm�Q�e�e^�3�^��de#inV��D4Kno�O-�lax}. Y]Buv%s��HPxx=�fig \ce|,line{\resize@$3.0in}{!}{>�~{fig1wU�cS�S۴ �GI@QED �Ej�:�miQ , C:�, AB:Exic��ov�.A:�Gigc^UM,ure, P: pumpͳ(;4�(), $\theta$ytil� ,gle, LP: loc`Gprobe �. Da�A!e�9�o� axis�T� !-%���!X��e��H"_st�(fg? >B�.��!W \ba\%s pas'"�9�e�\%F,��sd��-�(� v� ear-zp�<v��)�  �$L \apc� 0.94$ mկ%���|6 curv��8$r_0 = 10$ cm, �$FG9.0 �10^5$.)�� |�c�< A|K"��s�mea,�5��_e) spZ�F �ringd�6� 1�;e back9nd�psX!�!_vacuum�Cmb� s /8t� 0$10^{-6}$ torA�Pr��toXAeoC  I�ea�9 5�� bOjw E�EO (C� < 899-21 Ti:Sapph��[()E� �*w�\�n�X ($\lambda = 791.1$ nm,E�W $\ga5�50$a)�8� ,@an-apl9��� �E�is foc� �ylind�(�!#a rou�$50 \um\Q50$ elliM�Gau��`��-BE�� ely $150\K$�@!)}i� %�}dA<%x� .!� aE� K&� �:J<overla���h��minimi��<�A�!�ic�`��b�#_�M�to>I��C� $^3P_1$5 pV� Crrg=)f ;p� th $q�1.3a� � |om velo��815 m/s)3�uU; djus�iannzopic!?� �Mv� �Htoe�Bx�v���monYng%? N� ��%�2)��.�polx�� � �q@et�Sw�C�G$ IEG�e�! maximu��� A ~�p�1v 1aRgA�9@� `rVHSf!EAf6� r�qj$m=0 :�  m=0$}�s o�F o�2f��1 toms�K<�c�#e�-�, w�_%� fluorew��� N� �V dyetu�@e.glet�•� 553.5$ nm=�!m p�KXto�� adiab�e<r�%�c cess�a�"� y chirpih������Bf$�? � M�6� - �ՙ0.70$.l c-m�.��� int = \� ,\pi} w_m/v_0M( 0.10\: \us![ $w_m 41m$��wa*� {hOID]2N$v_�In C �F ��X�P"0�F�D~nA� nti�N�i�Hde/QVDz ��"&&�)�bNE� hieved viNI?b�-�_�`$g�B�"iF rapid�U� v� �� V^ Id-f" Gwa�� s el��A9b�t1K�,a �D� }_b  Z���&� A� p �  (cf.\� An-OL97b}nIvi�Qn�$�?& ws�> v�6�AKa ]� ���$\�"a \pm k E�� 1Y"$!���!�qOymH peak�:./3-�&is&=Q$g� 4(\mu /2 \hbar)mm 2 \pi  �/ Vy�19b � V = 4 L w_0^2/4�-�i�]ar $\mu$dipolj trix�A . �3� [A3&Z�K�$t_lec3GFt�r$2�����%(">F2� valu��!L � i*C��A�M)�Q�"� �pD $25� aA= 25 �ctܷ�V e6U 3 mm��Y��m�?#P [R��qW ��B� M. � Ei�v�Q dlG���-� !-to��!m6i�QBbst� �b�� � 10\%�o+ ELorf��!�n: ic� v" ; "p�is�d �)�o �ip[�%�Df].~\� {th-ol89��( barium-fil��s��ly he%��o alum tube �aE�x n di nozzl-{��l"� A��ˉ��45 cm4 D iJnalZ�O��a�� 2" $a�!ѻ> at �$�r 815$} ��qa �,of $\Delta v� FWHM�P00:J: !�^q��\ $QI@EUly 15\%!a��JtoA��d%89/mod� � }�4ng knife edge 6g�nJ��2��%q��%KH%mT;c�:�Ue4bl< tenu ���J�� %&`�Gngu"V�or �2R�3)�.+�^{r,�b+E��t*��'��� #�A�losى�+���:�F PIemit}(n)� fracM/�(nt n}{\N  \l� {eq-�-��e e`Sgin{eqa�ay*} NbWdg f(g) EN h(��in^2 (s 2�*) �b \noi�ut ��!Ue��`�a' %P�!$n��n'<)B"t-��� graQ[%��WH�$I%A� ve w��]fu�\s $�� $����B� .&�s�a�(A�8fc�sto>�O$ �A is a�<�{�TA��ITFilipowicz-PRA86}.) %�o� $:%,2#!t.$ %$\beta_kCE��by�Y5 jZ2BZG�( ��)%�e (d&�) >�Fqa��A�y����(�0L�0 ��� Eq.�B#�4sMly)�?�y?R@m>J"5 '?3,It$e�$=1000$. C[d ��l�u_QfAE Open!un # #u� fig-�-!>F�"�62&+ e*R��dXe"�^\SmpE��6os"�' 6��&�'Y�N���5 $n'$_ Eqn^��)�* %${\p�? al \aLn}} (G - L)|_{n'} < %� ~5:^-\g�{/%�6Q �j2?X�E���aire �s*inon����1��V�xw"�f &�rm � W�W�cA� je.�[ap� |��A����1 `T"�� {x0�� a +6� �w��a em�2l d� a�ݡ7%h�� chop����}��kd�A�oE�onR \�ea�L` :lor�g'az n6� "�>�vacoustoU"y or*  alig��e!6 �6�%�19wasp� nOV lanc�dic% (APD)�IedB loop/)Y"s PZT���� )2.a.S-M. P s�!�{H�in �nt!�!�o' ��m\ pdo  ��pul4�,rec� dR 2'u�iLc#�wo�eAI!"�!�z"�)!�2!� ��wi i�ASmpt^��($n=0&d �!Nj\$``seeded''QO�B ($n �+{25}$)�P�X-RJ9)\ �i%� a�A�{ 0 aIn�X�^2�u|AC�rd� 100 m�#%In�An}�%""&4v�2nJ3BJIO12 vs.\��� ��}��\��1 ���ir� ($\�$)lun5�A2; C$�e&n '2%. Soli�: R2> �l,��!�j���at� �%2� -  %fq<c0I�9� "M"5?.O [cav!$J KRk�� YUJIe��#BUV��&  r�CI�Ѫ �?j� �m��a�bj�hNj� he rk: $ � ���(lower�-: (uppO c"f ��! <� 4>�"�l�n�[ � �N�e [ � (por��!�%ne�ve slW� �i��)� unA ��tra�A21��N� �?2at *�r� ��.m_(�!<8 CCD camera. %A*t��r ( band� ~ter %!n2����.�%�O�to "L%I*� %%�qU-ra��sc�,ed�Yl '�U�eq�*in�2r,"'��Œ&�*���q�cy 6.�Z(�Z��abee"�&�cO fi3A&e"�#�oata%�1�&cal��torC��Yv0ee� !TZ`�Y �2 �smh��ݻE�e-DA�z�J"b�n� E�~M��s,E�3�'c! ndE��Jm�'�_���| fi:�sISa_ in $�5��!b!)�a�!�:�aTZ21 faci��� !+S��%ſ�w��>: 1ŝy �-upQonu ofD+�a "240$; abL�7,����5:~� �c&�w�steady- }e + Q�s�+� �mh2}�4 of F"��.�M}^, "v3a^rp�� "| 9{A�2�I�7Ţ�]415)No�\�� XAT� ,�aG���b�j�"�3N-"?7mpi@��L Fokker-P! k&dof^�,��� ,-q�i �a5�,Pm�>.5 \5&H-"�.3� yN��I� y. D�l�')a�ge :�aN� B�(�zNs6�!�*�  sc2�1}o!�ޗ�b�5 "�#s6�a�wo-peat�I��i"" t6�8"��!� til�)��� spl� Ag����bbe}$27.1\ �@$�yrfo�e�v Y�a�*� �*U�1�%ra�]%I"F"&�"AxAX!�y� $\pi$- �%�c� d %!���F"= :A"%"�!�B"%��&�21w �,%:�-�"�#3%:� �$� !  te k! %�� 2���<akM8o.U�c��*L2�q"�)p$ %!�P�� }^�- !}{6YN�-4 \h+e{.5i%F�-�B�Hy�. ��d:> Ad� �Iu���z��S"� sb�it a1m<սkX!*�-s,&� 63. E"�� �i:� s: (a)��,8 , (b)�^$= 526$, (c 657d 755$6P9."� A���Fin ;d���c�Ty5��*a��tud�+��63�'he�"7$��?m ``spik�l�-En��� �,���Jh725$ %�m�a t�����P�%5�9 %g�&} !oH��T5bI;��Aj�s" bncon*�r %A��f, hg2<����:� %��?!r!^"��*P1t�5"0 �5%# %-$�3ot"r!dZ�>54s��m 13.5 � %&8���$ low- ��6) �C ,�2�eD�<ma�- /�(i�s�� f�� �!! ���"�sudden�@l*,Ic6OS+ a- ���(.=is�dUic��4s.�A�2�O&�"gGstjt9 �@s&� a�Doppl*�@9�5"� � 2x%*�(g�:al( 9+@rN��d؝aT�AA�!�����mplex.H>.�����wo YAAV( l"4� m���ly��b2u�5}y!|.vF T=�3 ore "͂�M���60p9 �7!ppRes�# xami}�X�i�@*v !"k ;)uC �C� �8)N�5� :�5M�@� o�mu LambyQ���&�gse%9�,-"6-1964}9y+$I� D���&OCIa� zeroE>e�O2�A!r�&��56�E q�o@"m!�rigor�t�jS���� , %i��!�PT�rJ*� �=� %g %��&x�,ichbDl��a � el�� 5�}  p�!he.!}%*�A)|s�T+a*spul�/=�Pa��BQ�FRW�qlso*�e�%f2D*s�)< t2w= cfy-��i"T 5a.�� s�k�1a��5%�"���>�u9)�)�-fF"��!, H��tur/o !z"�% 6i.3"1^�$�2 du"� ���'A�d)*8�Qoj��% �F��$�o.�7JPl �� �U����g M#���>yj(|B#�d�&(g-g_0R#� 4 Q5�2L�k.�e�e d�^2}\�"[ % q(n+1)g^2 R^2}{1+B\�"]R!Eb�%%E.�! 2$ = �^{-1}��f� = {1/�(>�)/(F�) �A3��jv�&�"Au�fb��&l@s�92!m"e�CA�|�����ar ��/�0&�yHiGWxfinit$��"SBi �'$;4a42(n �aTU I`a1/2!T2� 6��&m@i3c�"�,e�0e�f�nmK . %b� ��aN�"6�$n$ %$n5q8n >�. � / q� �.m�j int)���u"']*�* � �a�m�!d� �V�'�p�B %`N !��$of"�$��: i.e.\n� ��ftR�NRb�?:���.�� Iu�a�R!(Y~O��e� � A�il�� cF;�)-�Q�du!}:Ea: hi� b�8 �ne( "�� E�m^zss� "��demi|�-.:� �s sn�J�wo��k�Oa.B� e�.A�hundredaB/ . %E� �|��z�y  %F&�Li,��.c�).�outputp$gA�-�"rD-5u d v�g��s�!�m6 >]+��tXASc�F�}i)`���Ϟ�.�'s %u��ch� �. M6!�0)rum��Q8�5F��6 lY�&ac(G!4s��`a� u*�B"5TSHc�and)BDgrants 9876974-PHY%F80111370-CHE. KJTFXa�jea"^g �f XGX (KRFh2-0M00044���T ankث T 1�,Duk2�A�as��2d&F erson�/��B% % Cr51%�r�KAp���BibTeX:�+i&�]{ �R�ZdGx} 2�V�^a*�^W2��r^,��RM*{^%6�S�^a,�=`�G-ZRl^R�ress]{revtex4} %\documentclass[aps,prl,twocolumn,groupedadd�;(a,preprint,�:,superscriptaBx\ % %\usepackage{mathptmx�times}R-azo:-palatin .F graphicx}2dc%�} % symbols \newcommand{\rdr}{R_{(7)}} :ei 3R 4 \begin{1�r \1b��{To be submitted to Phys. Rev. A} \title{Dissociative recombination and low-energy inelastic electron collisions\\of the helium dimer ion��^\author{H. B. Pedersen} \thanks{ To whom correspondence should be addressed} \email[]{henrik.pe O8@mpi-hd.mpg.de}2uuhr� �(S. Altevogt'DV. Andrianarijaona( H. Kreckel$L. Lammichffili%9�C{Max-Planck-Institut f\"{u}r Kernphysik, D-69117 Heidelberg, Germany.5(N. de Ruett�PE. M. Staicu-Casagran ��(D\'{e}partea�IA8ique, Universit% Cathol'DLouvain, B-1348, D-la-Neuve, Belgium=Z$D. Schwalm�N1�ftrasser:gDe��(of Particle �0cs, Weizmann 1�e of SciAoT, Rehovot, 76100, Isra!�zX. UrbaiA��h�h$Zajfman} 2��}E}2R�TZT1�A. Wolf:��� �(date{\todayaR%.( ABSTRACT .J�lLabstract} The df? (DR)A� $^3$He$^4X+$ has been investiga��at th�@ avy-��hTest Storage Ring (TSR) in �3, by observ#Pneutral products from��Xc��K a merge�h,ams configur���rel� � ie TLnear-zero (thermali ,Dy about 10 meV) up��840 eV. After s � �qel�Zol�Hfor 35 s, an effect��4DR rate coeffia�t at ��of $3\���10^{-9}$ cm$^{3}$\,s$^{-1}$ is found.-�tempo!Ievolut!�o��:b�s� frag�|!�mag�sp�,a reveals th-� popu!WonsYvib)q al levelsEnE!"ed �0beam are non-1t with|c�N@ $\sim$0.1--1\%!� exciAh _-�Dat least $v=4$, haEFA(significant-y o �Ined!�&als. W�8Ppump-probe-type techn�Wus!DR�%) 1'4while switchinA�a propertAr-|U! ,%.:�I� of  %b1�A orig�e mostlyi"!^}%TthA�,residual gasA�lso zf#DR1$ suggest-�a strong�$induced ro � al cM�occura� �.�E 0nd state, rea%: a.H�eratuA2\ear or below 300 K. F� !nabsA�eE�6Ynd" shap�1)ZQ�5�I�umY!unde�%�ary�]diE�, FN����^� i!Z(determined;YverA� to a=6�gasA��$ it amountFDto $(3.3 \pm 0.9) �. �/10R0.� &� A� bran)�eέ*$v=0$h� atomic fi!�%��aԅ�'bY�7�1.2)$\%� <$1s2s\,{^3}S$, %a�(37.4*4.0F*1* 58.6*5:Tp T P$, !� X2.9-3:W-1}P$.)AR��� rangA4 $2)W%V7}$!ly�*dd appeaAMeA� 15--�6͞ small siz%[AW���z&F$indicate�����lj�is dueA�in8l!�&n!�not3sb��deple�!��)��DR. \end*� J� ��insert��0ed PACS numbe�{a�ces��Dnext line \pacs{} �Y:?8keywords - APS ss don'!z�$do this %\/{F maket� �8 INTRODUCTIONz�  \s# on{Int io� (label{sec:i}ch PROCESS AND GENERAL MOTIVARq L&=�of di��, posi%� molecular�cs�Yfree %�r ��io tlprocesse�_d dilu�,edia, such aA�(e interstel` $um, planet�n atmosphera�A~$laboratorya� charges w"A�y�am�aU�V!? trA�ngdegrea} ioniz��b7chemic��m),on. Usually# dominant N C �aYJz`  \� {ba�,1994} betwee� incident6� $AB� !a6� $e^-$� equ�} 1�(v,J) + e^-(E) \rightarrow A(n)+B(n'). Mf eq:g- al_dr}i�P)o$v$� $J$ denot%� ro.�quantumu� 2T,> $E Qn, n'$%�!DQh��yu��I��-�>oW � ively. B e 2(,>�� C Icd!�� $exist, whiA�rupresen�{by�~\left\{8,array}{l}A^+5�\\)�') �F) )�\} + )�') J�yend=�A@~ ea�ssoD*� (DE)a �ly,� .� �4e�19� ,A�i�=through�lirQ e �Yez� ',J') M�'),J�e�6�)�describI�Qe-impact.or de-=0of nuclear mo�_�A�2�. Beyo{ relevanc�s,s�- A]r2A�� stan� iHir� ly��ql dyna��,mechanisms i%ofunda�al)�est. In=�)� adiabaticNs manifeq vio��K@ Born-Oppenheimer�roxim�� often��� n �)role, -��;s lٙ1�:2: 2jHs a benchmark cases 63r�AɃQ�involv�,ic continuum� 0. For DR, !�atX } Qinitial =�� exo ic, �r�Cn� )�Q �leac l�� cross 1 �ө2� o%�rf�or� of $� 14) 2$%>!�т� gy�$E�0.03$> ! , many system; ncluE�gexperiIul��oretic�O,well studied%�E� H$_2��it�Qotopom� �6kt< ,gubl I, NO$x &,vejby1998,su!0}` %�� s!r9)l/on can� reso'ly cap d�purely.d]88 to doub$�repulsAc��%$!_�-~�L$ch enablesE�`direct'� �w50, �g�� pathwayE DR. Some ns�  suitv� potenA��r��+ �Eab�BeՁ�� ro-.P �; howeve�eI}U a�>� a��Io���� HeH%��H$_3^+$� .j> �d�n�8theless conside�to causekY simi� e� y�!�%1( 1(I�5�,kokoou� 2003}. A-� fal}out��  pii{  he6� , Hei"��Uear� q� work �0mulliken1964}����� rec� cal���# 6carataw$9}, extrema aD% ��(of����86�6�)�e �predic� xAODR��ߡ�Ua��]f If . Em�ic U�, curves driv�)a1�j-� �owu �D A�Fac�� ible&0lowerJ�,a� show�V4Fig.\ \ref{he_ �}���lu` ��6� :d�5�=�sM�=�I�Gr�^"�!WnaF ���� ��ca�8but still yieldI���!�!G�g -ave3d r:";&: YXs did%O�vZ�L� coupe to�+s�!�x<!�!fa�9 increQ�E�q�" �}jwas���A�..��]h��@ ($v\gtrsim3$), mN�� r DR r}$�${}m��at:�typ��a Ŷ� ies)E�y-B�MQa+)��of >9sA��� efora�9 acteriz��m� varh��2Ts*�!�F0. �>���of��ca  modeli��u7eM�T cil��}��in.gplasm9Par�  �NZ ADEM<f*o � Oi�2 afterg�at!�s�sN)�5 mbar-�,deloche1976}� at room25(�+K ��!��l He�s� at�er.TI�=6��@{2}^{+�a:��in eiAee-body �@phelps1952} or bie s '�<,hornbeck1951} g����Xa �m�:�e�.�.Xu 1999a}..b9�isF�"2Ua(�)�:meA7,simultaneous9r� @� (triplet)1p!�1c�t1972q�6��s���edmon-]R50}�%explaM�"�6��*$biondi1949zH� la��� � e��.�"� al*� 6j(qf0 + 2$e^{-}$ $��w$i�{}^*$ +#)������, E$N�be�neglig�at (upper limit!�$<�~5*1d3$/1�][! 5ommP F�, (certainly a��-� $y�U�s)%� also argu�be� le� P� .�E���-�(ivanov1983, 9}��w�:ndf�o2�*� e�i�duc-Q��tomd$n=3,4� Thus,%�act�9��DR in 2E�J,s remains un��;2�A Ug is�-':' ly�5ca� k1995,ack?�;1�Bs al}��\ re p�(|iL maas��T,flamme1980,yu1987,com�9,z &2000,�hardy}. ��&k)+,precise data` ]t roscop�� p �!%W�2 �8����2 (surfac�5[�Vpos� to � e �"e Z wave�li]�A� *n&C life2"�a���kinw��ases A��DR�* �of��esa��toL pre�# ��al� ults!�1�!�/is papeA�Regar"!�-96�ready Mi Mz2x ,-� basia�li��ve� xN�2%�$�� E��"%7�2�gGM of F;s"�) very� ��  .�!|Al6� ; . C� �� &� -9� dd.� �by Cohe1Dc apI�Gm�&83}�fie��hypF sis, sif no ~� �A#s clos[AZ).2A�!9 �y2� � na�u�p�+uE"�rop���a�Y�SE� C�4 {\it et al.}\ �.� ]�newA�tiQnel Q�De�%L'�(MQDT)N0A�1��"n,!:�9a��E�iX�O�*Q8��!th�i&-!+vQ�2B%�s �!--4�I��d (U��_�mŵL )"�(�low�' ��j�symmetrH$^3\Sigma_g^+$, $^12A$$Pi_u$� ��"�asympto��%D4He($1s^2\,^1S$ �"^3S$)� j#5�J 8J S"^3P�r*s (seeV�G At!+ F�((0--0.1 t(�$-�2,�%9( e&%�"�#p�d�e� nt=�oni&,)Ea ��i�"�#!�EA� "~8}$--�6}$ cm$@�,�>�$�N.�(�� $6.1Q ��(MR at�$. Opp�e�-374!�u#Yp�6 b)E]Ian { 2��/our�EU magnitude� than� 0$. i'�V66�influT 1�1�,� re�X��!Tby �a factor!P2] go )�J�% $J=9�>�+(%�A���of 6( b*I�%6y��Nu�reg!� was �f ici&%A�( ) bC$hS�&int%U �&��V v"�, &%ty�� 2��prA<�� oc�"o�yD;ve �A�a�en2_? (��y�.�r 2). * DRA�b �7��]avail detailed"G [ ����&���!��&�:� K%�(c��!�D� ! ta� :��� uY i�t"C 3asubsequ�.� , codb:�,ed-'An ov:.ew�! U-HIF� .� �gi!�inR�-!�k Ryd�2-�v�  V%Gy i ;ten�d�by�\Y'e����1��2v e}+ mKU=Fa>$k-Condon z�'�m�,�'"wd' r�Y��%3��%�in��"6�� &K �A]Q�)A`�.� 6--1d/WfuP r up6$*$2!.'.P OUTLINE OF EXPERIMENz!1 !. ���,!A�o��/ a.V-Y( Wi}AHs�dE�X��c*� B�A�.dI ion,v.hoJ�G>.�a�0 coldyQ � ��1�habs198�n� v�!��>�OE~.��!�( � !'� de[8"� 6� � �&�0duA��A�)��InNdiffer�kѦoB�!�b�)&.- in2v3-��3$ �w�als"^0��nt( to a*b1!=N*M�a $\s41�  �Q5. >im ity �aonoA� 7� 6ierQjA\��� � � �]�Vrfo9by u6Rq u"xb}5AUASTRID92 age %�uZ>�a �4�4�1 Vtwo�Qd ongly �s eachi�r!���thr$QA� fraa� emiss��1i��s�a�eNl��H worB�, aA(\  < monotonously de" with� "^�_y !��"f)0!? 15�-;no 8 depende&�`͛14 El�3age+�uB�A6��7�t���.6��j5, �e�im�!�#�M�L%�#�. smHit�#����G e� I��c4�nw!Ba�6�&�2�m�,%ademonst� d. ��e$to�AY'� n%0na#%�mG!��!e2�<�95�%�� A0major���F�al � /eve��!larifP'71#� �`'u�d �3edB�|��!�8a�� ] � hand�CoulombaloaY�3 �. (Sec . exp_CEI})�us� oa'i ˽A p"�6�;A��o�$am� �'�  �A�q t m�1hf A�A.�s� � �dr-&})!�!�B�4distrib�7 s >�dr_6E re employa_�� agno�> too�7o�Y��J�d.qA&�7�k �:0 . M2 v2�.!R-a�0s (F970 s) rX8 a2r"*ak*!-1�R�Q�B"��%e"� Q�E�] r�ed` 5bykly &�+]�"�-�9�total-DR-�}2<��eVeN"�.� >v Y vUXn) -to-#And>�8*�U�C&9}) serv�2�/if�/2��b0E�+�&�4�al;�adA7��0u�ICE�2i 1o-�,.� %DE$%IBiR0G�?�5 2--9�) �;��ht#on9v��B���n%y�icq8.�-�_(-���"�86A� .6.L�Labs$ }) �x�+� > � a�4EnergD��t �2�> e ob� Y�%eY- �DR2��*e-U�}) %,Yo>2.�!!N  �nd DE > &a,y�4res_de_exc}). "�/!o on\r��n0(� əl(2� previous}:a�K  �>�discu! _dr9�6eE�]�+,��2���, 3)mpl>,be����,� ���89!  ion_��!' Um !%sam�e+��%��)�dur�&m�$s�( 3�( p" on >� ;hsI2��llC:��n�orthc� g publice�a�& ��%%*q6E"� al backg�}U1A�e$c"��A� OVERVIEWz�6|�={I|A�<�setup>�_�`view}�#�� �u� Z�A>�/��B{ &�AY> s9661raw�<�Y� �=�:)�*�).q~�c2Fk cI{EmIh�2|"�r"u.B&.!p�)}�g�}al �kilgu�62}of6�5�"amita8/(6,alkhalili�,FB� � g>er�',J9�,�m�,B9HC)a�+ ndard duo�"��source �8n1974!�A�  geom�b<w. nd % xpan�P$ cup folloE �Nanode we�es�yAR;1 x deliv��(300--500 nAA^>��6ty %%�'�Z0.4--1.1B(�� fila��G/;E rcU d 0.33�$to 0.08 mAtex&c�#ic�+���+$ �kept aVD�5'0 20--30 $\mu$Z!�6J �=��� [,F>�Ezc��aW1�!�9f �I�b�$�Ai:D&q2� repo�@� we� he1�M6yU&2�, keep�.< A�!��c�IdP+)�t 0.6)��.�v %�10)�W�>0A!N$^{2�)%"-`�A�8B�&�B�"�t ll�.R� nk%S0 .� I��&e �hav�*,��` hE m�accele dA�2�#p$E_i$!�* 7.28 MeV �F.36 wan rfQo�+g���3,vonhah& 3}, transM _ a�byAE�� S�$ stee! c�el^[9j�i6\Am��%�fw/�K5bx'f] | Puls)�a few nA��iu� i�15m�sMA��EY �.4s�to�E`�an"�% (1/$e$uI9.8 s.���los6 �'�t9D!H��& \A"!��.F ��+�=ed �24ly ($\ge 90$\%��6M&q� I��5�e5 � &��-*�He:@M�TSR!�cśKFeQost�,@90,pastuszka1990}yF app�h~spaceD�`o%�-�1%@!f �$ VA!to m�<C-!u2�+2�>/��+a�J{!�guided � ;] {qGg!sur �0a 1Z� solenoid ���two tors adja%-�``ral''�M�� )��� �i�2�; = lap S. N>LL(t �az �!.� ����6mAFU�ainEehe� ���S��M circEKng9�� stream j-�-jBY$�e}IA �ehind �'= �=.* b4m�"�$vg1J1����-�s%9.-!�!'�B��%խA�voltag�2*v w "�c� t1B!w��.>�A�j ҡdefin� detu%� y $v_d� �Cco�S!�. gy�L,d=(m/2)v_d{}%(in $m$  B0mas7IA: !L good:?>E be ��m l���rezKJu�W� �� ${\bf v}$E�"�ed!wo�+o��an<(ropicT<ia8*=� B2�4��*�K(s $T_\perp$��arallel$�\y%A!��,���;�� "�Bf  $kT_{z} = 10$�Od  �0.5M�QJ}vi!I)� exac�1matchU,$E_d=0$) cho;a *�E5Y-e^cA/M)� ($MEDA\!J ion 1�A��t �;� he�Ioo��'' ],T8�<� �@o�(�-�)e�m�;�d� �takes 1ce �BC� scat�6n��2�E�� !ҡF� And�inu� rene1#� A�2 nee�v for �&cI_�:��J "p!M]�:U� y"�?a�Y%� ?T�;� ��D� � Js J|�& �awf&46R!�e84s�BA�M( ���T"���W��a�!l �zw$M� ��edɍ$EA�$,�:!�f�% ��aA�fhe��m DQ5�E��u�#�� cussApn �"}d�=tq{yij�uk,Ne1 ZE�9��=AI10-meV�*eg&.�to��eIlX��]Q (�Q erp}H)A(� ryL"o =d $Y )�m� &q�1>�A:)�=571$*%dE�%�n_e� $1.&�N7�+ {-3}�� $5.5� 10^6NT� �j� �hifXAa;_i=f� �26'CEA/:�y ,^��# A� !�<h� E_e>Q�re��ve)K d$�?$3 54&� adju�, ul�X�9�J3w� FWHM sp�2B� (} of, e.g., sfO� a9=��eV. Va.<�I conn�nslz ?>&�T v2>�I y A(E_d)$��wo=�<��Vs!�  !��agh dip�6 (V�)�c�R%�analyz�*�ts z| B��5%a�>��or !.�i:)Aq�-"e �5 barr�$) Ka"�P$4�69�.,� �a��ax3)i9\ri*Mte even�th1�����esiFun�2Xc��a�DF� �^ output Ee�A�!)��^s(EHi�5o�� /2���>��sR�pa Z)�!"OC y�� �h �t�3Za�s�p�  of� sF� 3, 4,A7M>!D$s (amu) if%� ngleMn�0#� B& 1&�-$He];)aAr�n :' '4H=ŕ,7��!c.i,�^LU0dU�An�Y$\rdei$�_  T r��erm%6l.6'�-628�*a��CeI�A��� ~^�I= u�8>SE8s�V�=i-�9le"�#u{/"�6w6�-��-f0ch �!�Ean 80-mm&rch%�� dXequippe�H a phosphor screen,�J��co �P�aU� �?v����� coin�P4 �!window;JmiTeL �s�Jd�D�e�-trigg�g camera�F� �Ia�!�&`=:�Z>�Bj "@$E\*�E�eAB66�,Y%2�1_� � ��R � ( $\alpha_X(Ŭ%'ny"$>l $X�&!5y FEqs.\ (B 6�Q)--Bex}),!;1��e�.KL��6 X(E)�?�s)�1:) y $E� 2)s ^2$ A hZ�u�vgyaptJ#on2�F&P2C=\int | y | \s� f(v_d,  ) d^3v ,�eq:)�g! a%de2.Q�6Fu^�B����W.=X@p1� aG�w@=(2E_d/m)^{1/2}$.L)k-��(� �� R.rUps�K��bP�oq �!]p "�PirI�oF !�4P' $v,JM"B O.3VhiK text�ensembd f $N�&��}*�by no\RF*�((s $p_{vJ}(t!�n�# SC:@L�%�+ch�-� �V�a�' (���;ion) $t%��W!�) I�js 6\��v Q�^҉!�"��H6�wM'6�E#ve�dy+iesJGtilde{ |}a�$_d) = \sum%[5a #_�.5Valp_meanbH"X#�" �� $R_XEVPl �i ᢡ _4!z-���_& m !�V^%�be wrfinEP�i�!�} R_X! $eta N_i n_[ d^.3{X}%�.�Srx_ �BCW Here�eta=L/C$A� $L�Ulength� I�F5 (� ��e"�# $C��i�A�!1 }m 2(55.4 m*$�0.027���xc� g.6 in Eq.\ �h��,�8�V)x.>��. G�NrD9sN�� ,% a h !8�t�,�LM��d>���Oc�1w {1�% G /ol� valu� $EwE�s�)���]gG+e�:�ri��f}�Q\s 8ce>e� apid'M�  a�w%� ��Mlam�119�#"�#J�:!Ӂ�.� �� G�A-5�a]�Y 16 cl� �yg&�21RN$�exe��2-sk�s-(by2�/7 �b�A�h�1�? e an.�-�%��+�'6^{\rm)}_  m�1CQatns" Cre���gZ[^n +:.� � \�[]:� �B�w�� 2:2�%F�f4�4= \frac{2}{L} � _{x%S min}}^ ax}}:��` \biglb(E}_d(x;ūrb) dx.�� torB�����J� �1hif$ >�a� �FQ�.v�F/ $x�hE.�L &M,r�Mhe know�3$. �e�,&]�* }�E�ņ$ ca��a�U~$dan�c�2Pd$�G(&�G �e�I520 v0u.ri��c��)�* :QI$MG��I\)gbust ite� v�@)��: 2� �k�"22� Ion_�_ U&g >;�V~j6D � 6� �� ed ��'��k�is&1{ inteFn&N�H. H�%,��� �� we�lin�>mOQfm$Ne-�Tto�%�#�6�A6�&�4& p"dQ�;6/^ zIup! �͇hblackdP Jon %=[a�%. Morea.��-x~�"!&�� th5�'!)�K) withkK� }2t!2a�to%0,�7�nd >x^.!/%]&/��o � rA^c/��2 �/u� �AF� �k&�9�<)5�a��K�6�=��b* U;8m�&.Beau#s�"Rq2�e�A�} ��Kv FY�=�!x-!& Zng A &5"��th6��QA�", q�^7.�b�7�g *x���P�O� "�5A��-�b ual Ikigl�R�G�,Q!%a� �!DEn&� F^3#  He}^4 + + R��Q"�b o a�b {@{\,}lc }}Z +&+&_\\  y2^+ e� c \0cR'., de_rWx-&� �a=�#s]2~ A�A#!_�n�z!ɵDE}^{g}� q w$| � e) p�^to��A�A4i�su !�5{6�4+ !�de���R-�� li�A2�2A��{d.2M�"g�!=ge (DC)���4o%�\, )�!�\,+\,{]A'*2dcR�16; �Zn C}^g61"ef%J�&�3p$�k�CxP# ��$1�M \ll  5�;%>,�assum�Ps�4*&Ha� s�:�;0iM$%�~inI� o�S� �P6Q���A �|�i� �!Q�^ge0�a d-AB: g��C�b:�gma \by F<x = n_gv_i�/.�kgbC� n_g$ *10$6��l��!7!�ri�"�ō}u5�$2t`.D2x��"�q��K�1�KB$I �(JG� k� ;t)=�}�<[ � ()�kxboR.� s $k�# #>�؅�J  P!c:� ��(x$� "am�rKŜ�[wl"8 >�A� then6=!�&�3%˱�ea7�y�E�:F�\dot{N_i6'-��|2�(�& �ia���1�k� DR@;t)2BECF �a]�uJN.;neq:masY5BiT%c��A�B�&�:Y�:# i �J S)�D-!\ e*�X Nal!� A { %�w!�r �s�q�-|V�&d�P:�2� K8)�� �b�tA4p:�v._ ae�f ��&� �]b�d�&� N\s&j&� `�4*n!!4h^tNel��b.f_g2z"%Fn 66U)2J)GZ�Y$�3!�"!1� O oJn �`r�ei�� �^g"g J�u3�.� i 3B� $f�`i�b�ipfgP�?he�I/�ll�+"rx�s- o�XMA<)JG���)C � sADa5HQ��7; ^� .BJ Ra�q�!�K mali�pF8 "� _rad&qr RADIA[rFIELDF�; SW!$�v;}{^4 82�s�5a ma�]' %r�%o�n�2ep|)�3. ,9KZ"� �a& Base"�po�h� y9vV&�[}�8$X^{2} �Pua�9 ic gB2&� "j1we �c&�X!6EinsteDIo�Ot�Zspontan0`xI, ($A_{f}^{i}� stV`�1# ($S.#^ :9rp� ($B�2cJ-��B�'A�� ($iu_nd8+al ($f$):C�s�>U? ppro[ 8 xi>=���?n Ref� �"�4}�n� >_note�U� spin-*)!m�is:�_E^.Sq�X yOT(,1,2,\ldots� !�%�2�� ${^1}I $\,-. f#-Q�8(@� %�#� �&� ${^26L2L) herz�Q}*�`�w Vu�%\Delta J�S pm 19 Figk|K"D]};�,*� DM�%��! �&}ve J $\tauP�0 /`<(v'J')<(vJ)} A_{}g �"6k=�-�"� J� � first six2�E# �%Ty�;:�!�3����. [M n�}s $�I >�$2%��abe��i �l��9�(f&ibove +"3 $vJ$�+�i�t]� ��"� E�% Q�$N%}Y&j s in1]8q9&�of&X� =�.�areJ�'jƃ%6� {lcr�U }� & = &{ )[%I}� P\{\raisebox{0mm}[3mm]{}�AEJAC'J'}+SW^IX\rho_T(E.*" %I;-- .\no)B\\ &&\hB2*{1cm�3 eft.r�- B WE���) )� r� :w�!)m+�z }5 } }� \; �� �- �%�[�%��2�J9,. \eF{�"�"� Qi� $ f h\nu$sE�Plމ"�%����~t�e}�$T$a phvPi�y $U=E�94=|E_f-E_i|$. Mj }�vype^{c ,s2,.Yy &�ݶ��}��F�g%�� 5%��F.~J?%Z>, �by/=I� (t)/I�%�!�(t�/o illusP�&�/i&-vve2��?6���2��� >� I�<p$a�x�� elax� !,� �med~FX2d)%]5S}~gsolQ��aM_�"y �] K&.GS v.�.p051})�@ �U$�u$Runge-KuttWtho}W numeE A=g%o0HT�� *pmsixCst2iE2s [1:I� (a)]� s,km$12 s*�saUat $ m$5 i�p"�PE��Je6cR �($v\ge2j rhC�(S$g?4/n�1��9P�,scalqorngfNo/*wJ2�am�1�  V �3 sQal2�(wit-A�W�1@] .?b)]mve �"Bte)"1- �*� � ���9,after hundre8f>f ,&�B� � decidvfor%U�a�b~6s *� s,N�� )�3$) w�.e&2 unMed �9��a�ag��e*�Nn �DR�j al [i�"�&B�(),K 2})]�# �ss@/despi�hE-!s :=Y K4�@e�Yb 1a�2{ (E8)F�Cvalhe!�� 2-3� �s �K*��} S��2�dnd"� �"<=���b�A%!����^@Jz�3J,kich tanabe�o,kroh!0�o"�.s+e� 1A&&? �"�!(a\6��6� exY�!E�~atr2�l�z"����yntact,�6 chanfd its 6A&�Qa��&�o� ud�4��x ngerс$ ;m�b � C�xahechtfi�L|K} $waG u�V aGdo�il!Ue��1�!�c���Y�f96�~�? �M�]%*(ha�!��'�cea��4.�<)��t%FtO�#\*(K/.`.��@�A�E�fFG1�s1wHD��] Y�2�^ , evSS�h w�I�8�(kJ wof2�9�Q�.� !��J-�l��_phd,}G�2�U�o�^��� ^�2�awo wa�� Fr�&��2�-&�. �&��&\u�$X$�i�ular {�&y DE)�/!���2 �� s $k.�.$�.�,*)]�AvarR0:���s2�g {\emA4[-�d�}!� 3e3����ndeed�I\ N{Uma�n^D$qu$H$q��1}�%A%�i�|aL m� �c�{oV"a�}W.L%��E)+*�&e& �g� % ambi{"�%>.�>ondA2(ro-).� .�� ��~2 �$'on�P �scڃ0 {F55i�TAX,2 .zs 9& a�e#�5aG"O?�?R �&1�ngJ� }6�9I.�*tu�@to8Mr. {`-ֱ'q] o?er,3ser.B� �� mal�JporU83�� �*�`?!�c =� 9l. ]�u\ at vanish�A�*-),0�;�#e a:!���Ja]��:= � G:?G&` �z*?l=� %��has"%�V}B�E�E!x=eV._*4N""���12cAi g�7&�(SEC)M�4nakashima1986}��=�*ecions oA��/*#�_�W"���A}� Q:�([c�e�"v g!.ale�]���"ed�)!n�Cor�MTiVR" Ay D݀ (:AlsYP�F�c R��1�.�9�$� FH�2= spa96��n�OeY�22�-%�UZ>��UI�ue0$c �>pq�&0 ��:uY%�5 ݄[�og:��}�%ef>�,���"ly}*5)12.�may'4etM !) m. WU)�-<>����!$B_e=8.4�C1zK$ 1�H �vA1N�,� ��E3B+�1q��be���o�}w.0ofF��m�%�ag.<2�**��the�[ly�PR*�W2=s��!e�ld!�-(rabadpx8a, $b,faure200�x+n�S��ein), "qn�-bJof our�0 ledg�S27eR��Zoz6ǀ2bi t�^C spi�F�"&{�[k4�2}I72$ �OGireshol�>9h� 6!� e��E��A&�t.*b6�� 6� *����I3"*-. :�@7:�"�!q_rot},(id_TI�2P ��Q�}�U�; Q� ��j"2i�e��Ti$i��!�t�#i�)�R_-in�t"�2�ugh�%*p�!�F^�� �)��It�vAem�J���)N@��.�can�8��ly ��eXd�P��"�O) Zl rh0of*�6{$7 �1/a maximum}��s� QO$ .h!�>�2��v�|��tbe �#O.2�� s�BÙV ve. \�7{3M�r�fdi�e6��%�f� sec:�9l[Aѧ2O�2�-�iHJb��t mon2g%CB�"�\ (CEI%VUlode)�r-ir mu� Q�.���u�converEqirY�X8iu�6�M%pp�Gis���<e�2� _>t(�!@;vib�!<2/c \omega_e = 46n�o�<� )e��wood*)M"]��1 /2cBX2C-9����`XvBJ�&; �;eB�*l7lyQ�h� Fi�*%���M��pf��!�!�6l����xref�3s "�7idG"�e'sI(ar��Ti . "����?short.} S ecoiSM-2�+���t�������h�O$2,garcia-m�Sa2000} ɛ��alT%��Zq, f?�/�fo�� Y�xp�j�/3�ZYk:E_k}$r.�t�ki/1c�$i�As}=2.96/U��a����~�tbal�4t"J�)/w��},�!���|"c;D�#��%�17�ct! e��Z�6� a�of ?-�%t$n���+�6m E_i}� s}^20 5f�> M(& 5 )M(^""7) } {[2+2 ]^2�$M[(v_i 1)^2&�, D}^2&�?E1zomb"#uej2g:�Ai"AaDFP� an .�G�J�&*� ~�"�]&2��<m $P_v(M#!K)�a�B9�ڌ� %�2�!O��1�]�_� a��6L��ajOQ� t�W2broade�IAO2{by� 20\%�?e�2�H1"�F" �&�HқB�2Az:�2 P.pD,t)=\sum_v p_v(t) >� � P^O$/q1!�!,�.7� !E v*/2� %��IG).-�$�$��a͵6&+ $ @B�sE�-�Y�!�. = 1CT�Q]���ͫ� t��doe��2p �inguish E� ui#�:���*�&�,A\32* �co�K�$um`��2Q de�h%freedomJ@M/ MI'J " J"J19oBj��M݉"I -D!!�xsN2�..BJ�=� 4��by fit!�.yU��U!,`08a:�A��#Rn$iE$�e!Z�H�bs�o)@.�R�wU^4ed�g�h.�B&;� v cite.=Wa ,- m��2 Ap2�o>zvj>��^�ed�semi-]�Na+5U � !.8 �>rieflU"` �*�4#�g3 �u�0by&�&lyn'ing� l l� ,ar Schr\"{o}����ſ^5$y4�inD�2W��:\*�1�ach2�"Fspro�g� -^i.S����5�i��{�i�g =:0"���!o$WCLBES sub ��CIthomp3�85, A�"V��F CERN�6� L�!r!�o.F6�6�&�a�to�\ �>eO&�@ �!x�M:T��6m2C%p���kw n KDlSal6+?:$E6a� TR$)Alai�s&�z"* }_k�e^2/R41 �ytra!�oj�1��j �9rt ��D:��l!��*�: �$aʎ�9z�dm���a�B�� �Bv�3mt�):$R> tv;�, a��Y&>,.(!�i.0� !���97�;\R�\pm�&�aa3_ .�@�b*� ��E[m*�}��" 'U� �akeKFb �7sto#HB�*�&4�:gw.#&�q�I͠r�RZ�6Zcz!0<�A:�F"� !1~ �oold.@�` &� a\B� �2� $aD�IZna�l�����6�&�� s�4$]%�&�+Ir��n#6�&aN code=�6� .5 cei_2 }(a)A� play� r99e>� 2��"o }_k,�Tas&�"O2M  aeb� ��va0� �^"�T|#a�no Q�q ��li"�:Ba̕a. �V cMVV1oweq^A<2 )�*�} seem�vhv��P3�c i.e.A�!�]Di�6|h E "��compa+;.o�'&�%�!e)/fO�\ge�- �58 . W)-u�5-��pRxA�^��!�D 8A�&n �(La�I2E���-�>E&� !��K�.sw a2�N�>�>�+�$T�dxB�2W ($t o3$�~��QU>UiP!�es�"�5,�(Monte Carlo}�)�P_{v=0}.NQhN�!O} d�8� b *7 . Pe_���Rast-squa�fit�s�y.1,N !�B��g�~�a�*�}_k� ccggi*&I GU� �)O\,�$s}) = (98.�� 1.3)$"B!�r�� �wyhiG2D� �2($t=0�!�]F%B:��?��-K�(5z��A��., $(1{�4�R $v=1 6Z:5 1f��} 15\%9���1��M�$v I�r�i&�:���Qi��>*s6C��LCE3:Ia5�d �"�a)I�q�E�B�0i�iat F_ g _n�'e'l M�K)�io���+� ��)�a�%cJD .lnF)� 3�#<�2�����ra�!�"*]iA8P/zj~K�^a��W �im�U��3 42�%Y4��Ce�6{y�-�2�?%} V5'Q�2: � ��:sS67Yj9D=$ 91 $\pm$ 14 $\%t 0 Summarizing,.� G*�kit!oe~.�O!>A*��Ma��he2Xg.�@e�=����� �'C��7uu um i�u�s|AN;A!)^�R�Ra!��ldDZ�A�mal2�.�S �bperB+aWH!)a��-Js�>o� "e �""\^�c�Ya M�K\a�s�DE�DR&h%.� h�y�@��p1�"4�&a,"�z�Z'y"te�*"E� \EAzv@�f �g�7�fic �G# &a � A�^EE�z�8�"�"��:HS/"�5r��.:�, �-�uE�$tqY"� I!��i�_�fA1;t< ei] .��ev&b>�"� cycx.c\G.�: �nE_d^{c}r, a/1�2``I_E�"�qD"d^m�And a ``"R(:$r��/cho^r!A^r$�dropria��YEAI@full-A�JhQ�v �,9Y^r)[MUR;� � E7-T��!���e��5i�+$�HEFre(R)=2j�exD.)KYere u}�"% by%�!�(``wobb '')2�t��u� f!@�>a. of 50 >i_ "�R 8. F�qa� ��H�i�|�J, dx����teT��U2��5��oA���'e�,C(��).�*� ��)�%q�m@R!]q�"�/�5%Fd *D2i) z !9^m��nA� iu�Q o�%`#A�e�"�?�se�e�^mIqi�a�< j%JF\� EHsq(umH��Jˇ�s"��!��sc�~�>!E desiA��r s!�ind�)Rez/�:�7�Os} Tj�raw� U�� !'DE�nel, "�h�X$&����j35-68 ",q!�U�e%ks �¡Q/Qad��%ةLJ#,iY&_I,� �a� Cfig:raw��kq��f-[r���y%�\a+� >�0D{�h|.7 +� nt p=< ^&�@�r�de�a%^r=7.33w�,K -�!�A�.�r��!s �fB0� �����c` �\M�sim�% eV�-CR�C�2"�&J!v6o*J1�bߗe� �&��� # }t"orIE6$�w�_aba�yq2� ?;{1-�f � DE��J+�1H� l2�\Ղ2.5!%�T�,E��d"�[� V*О ����)�Aei$ɽ�vrsh��lF�DET ��#D\e;..!.:�"?2_�2&: !x_%��>ub�R�_���L���f? ��Eb�#el6!�V^q>�^D'.2�e�of� �2}on*m���f� � "^:!@Jw2QM��� B[��> !��g9�o��!�&%y6&�A�o.R "3$iB�|o_B?}�"�� .���I��� ime-a�Aǥ�5x�b!�s ��3 *f��.�cse6�"� U ca�B!.{6B:O1� _offڰ�z��3�*�եQuW� rzvA�ql� Ctr)� !9�!YA1 t"�/c|L�G107*� �qasj�8ff[� i�&�U�-�0@W� $<5$  ��ti�s+ �.��!F�orbu����4\mpoi�wa2ɥ?  �G�J1j"B-Tg&%PW"�!d%Xr$�7cz�ly�� expo2V�!� e up�xA!>R>~�Murooff��en!^(drops sharp�$��Ҹt�0+-e�a� "�G . W���M!�� is �is 2b" &�-ed -�g $/ �Y* R}(0( �@y�t ���9�& a�.Z�X!����*��EKbV�?!_s��� an�,�1�e1Mzkw�*�ye(ngl:11��;w��Ar YE_QCs. jump�m g -V�j�swi��offg M� )7�8 /�"�DE)��[���6r�v�WY)> !K term>e^(I 6I"�[3�/E� ste..�t�p+�"A0�8!������"C �չe�U�N7/ c_1=6� �) /�\"/_E}^g 008("�\l�J eq:cF�^N`g"�%�y �:L t�?1,�$MC Q�����>�)�A��fQ#~qB��R���t>�A!�v[���hdu�~9^:�c�2I$\CUi(t)=-^�� N.�bd =2�`g +5��`$.�A&BEm�R1� D"�  �h4� h�!(DC��A�A'E is m��7�7�*an DE7 r%  9S%�r� ei$��1yţ��� yb�A�M>�2})�d(� .@ �hA* } c_�8-Z%" /A�1..6(2)2�6|I]�2B'-a��2�֒>�,0.1014(13)$ "��oneq�~'d�F�� � E/(2+c_2)as0506(7)~� �8}"�-eq:kgJM� togegi$ \%#=8(1)\a s�Q5R9�?�z * !�*6 1�� � repe�i�.�,ڡ��vac��_Hi st$w E�� A[�� �0�ۡ�&?.)q# �� L_73ev�zb�,�� same��.�"� h�P�R �=0$JM��W��fs ��%te`:6"�ur�j!o��.| deca  ����r� ��C �e#��f��!G6���cp�g s%sM8�,�&thed!���R&� dW��)Xe A� ��!�gl\^{��ACb�,J� c1})� �c� �� s�q�� io $c_3=� (�rY ei(0)=2.5�4$i?i�P= i,�� findJS7%7>g^r)}{f_6!A#4c_3(1+c_1)-c_2�ffraJ+U%6��^_ eP!Q[%?"i!QwaɁ��=4!n-1=1.02(1�  3% I�aI��M*s��A�-eaNce�y��rCUdR� [��DE�8>uU�"�8U�9� = -�c_3c_41�1}c_2} %BbG/B�.l!�F/E�e/)+i���G���[�0.690(14�Z���܅.0�(:3��ly�A�%s x"Mb�s.(V� ��2�  $%Be22�+ >�5G+��<5�5� %&|k� %:�p2� : � �5Au&M .\ �>)�)@�n��U�A>A�2����\$V�t�\ag^{%�c}+ tor}6{^rf)�XZm]�=�-.�} . [1+22L]2� kdr-�B� H���� � �e�d%Us���9.��=!��$ǡ��� sus,�F�*�*eq� .});�>�zc�y�Hd�M�s�P-�=)�)"b)inBdre�JUl[Xa��׍^r)=7.9"T 6$ cmR "��!���H7MR@�8RD=3.2(4.� ��6��� %\�7)�)�mplL �R��Pe;) ��!� �&����m�%f�=Qve^APM�� � DE؅� �q� 6�� )�)IZcy k� �d1G��A� O0.044(7o E�, ``��#GZM��{& �$4 m%nrea_�ble a�:'v % .�k& ��&l T %�*T&|.&�a �t1�2�relhRoI tpa$����Am�" �K&F<%�v/ |�&�7N"�R6�1er&� }LQ�� AW#$�un �&�^�%��+D"C�widC�} =we mad"l !�s"AYbon�Fig�H�-18A6� *n>� :�'I�3 to 0���|. ��\Id�z 0*� �9��p� ^8�Xly�8� Cd� Q!���~6�Bm1�bY�Y62-�m�2�a�h=0���a��eod~ ��?0.5\,eV�%0.09946� ���ZUi$2ns�+cy��E�T|$6e����9G�o.a5~1�R34 � 66d8�iF�0A�ɘ5�]�C�dej�!f�/ri�p!�P[�9� . R�me*�-m�%f*�Aw!��2|$ n� ed)G8 9� �- tho"]b��A:�*ex͊�! . AD�A=2�( � �� �N"�U �!  weigt��!>&�5 He�a� �(=i��a��evNefIe�ty& +"GR�V� =2.8��. Al������R-�k*$� a marke���.�e_�=A�&��8�R��� ��d�� a�")�w)�<as�"�f ��7 &ɏirѳ�Dhig! Q]noQcis"�7i�!�5iso} �2ca'u�M�outu�"o� m�%&�Y^ � �"ato�,�vi!aJful9�2�!�>/&A��)1��%.}s��j�-"� 1 &�"e��*$Ɇ�I?U'J�)��b2�B&k2 oonF��@ [x=�(�; \; %F r� ;t)/ �}�� �.!7:.}\, $ O7 )A)�eq:dr-cJ��HL aK*�[*�)� DC�� idC��|, a~� �$%� ��saf�._�"Zr1�2  �  "���(�zd ϊ g  ��\I;� ��"�a�1j>f�� \a)dK �!,��-� ed�"d M Ah|��9!uA�L:�ri8 35$-�'�*% !\_dr_deL&) h�%�"`� �6s$��JD �] &nl�Y��eIts��o 2 9�.���Z[.��b&�M-6�:N0)/:~%^p ��0.34(6�x�%e�is-���s*�IO7eq}7ei7Fi�?K�?&=&"�L6�r�n�sp� ^q�ms 2H�[;t)Rp<�4(1-\varepsilon%H%o)�%:��},��"Bp.9$�&� 1P�#%��[�?.�Q�p%�e�j^T!su\.$ .eD$R����� (( [>3+-�6+]$. D&��&�/up�J -J�  *=Ξ��AmF�M�yle�UE2r3H(��2+�  �$�?r Q7���  $c_1$��6��� ǥ��em1,Y9' �a�= c_1/�=0.15(2a���;6c�-$� �3�6 � :rq��"�Sb�e�^J�\, [\r|dei'(0;t)/\rdr'(E_d^r;t)]/[\rdei($, where $$ A$ andG�$ are the observed rates of Figs.\ \ref{electron_off}I 6t73ev}. The toroid correctionOeDE_x is expected to be reliable upP$E_d\sim 25$ eV. Abov�Dis value an assumpa aboutd`further energy dependence>�Tcoefficient from 40 eV�}5}�,required. We x a reson�$ approxima� tha �!P.l@ stays constant i,$is range 6 �measured�.%`1G�1m$ed under tT9!d, $\tilde{\alpha}_{\rm DE}A8;t)$,�shown� Fig1�€_dr_de}(b) for $t=35$--68\,s. It; uld be no�5Fbrings%�� at low1�> det \ system \,ioned in Sec1�_Hexp_overview} yield)]0transverse po!,ona� c�la!� pair4 neutral $^3$Ha^d $^4 �sa�eas �0single DR reae�,s. Distribu�W!l�diA�8ce between suchI� �(roduct atomq vealEkineticQ!re� (KER) -�DR)Z���KER%�8urn can provideA<ignatur�8 internal excitI7 pres%�a����ng-#)$^+$ !X . F:q�!�s w��4performed onlyaׁ�=0�� ��,particularlya clarify%$effect of J�s on !r low-�!�at6�V R}�M$, foun��display-1eQnt time�Xc�X- �� �of>�dr-�T}. Here, we will firs��nsi��e �riJalA�� 2gu�;as tools�Gū�daX!um�Q%Korigi"@�r%�6�M�sto�O B�� beam� ����B��al�di��2�MW-co Follow�a�Ry with�8residual gas or en s, ei�onetwo��1ps arr�:�; or, which-hit ! �cy%ia���W��-ş ͟ scheme w���^��sp�ng�-body ( @) � (double)6� {\emm�(ed} numbersuc N}_s�quN}_d$EGreduced%+!@H q� true iSN_s$ AQ$NCdu� %}finit���m=�SMCP-9or. A�Y.|e"n ed b��$light spot0y g����oa�e 1� screen,�w)1 �E"a smallRB��in adI��falsely.�a� on-�%�,a.casN e.� Elap. T= resultm limi�x �AE �q �� KER. ��d52�<� kept be� 10a� s$^{-1}$��ru����e�!� �ed IW!�Iv � s wa�\��vary l 0.15E�0.03. Wa�an!�m v��inc= ce��window���%?q mof - $$10 $\mu$s� e)� cR con�X exA�  1 $\%. Accor�ly P1 (%�)�pl�tI�):be well` We h�� i�xatF�sEh� eg��edesuma�"q q masse��. �co�_%Qcew !C8 (c.m.)\s!�rmi� Am*� q, %�� >\2gre� !�*� moE�i� K ��^� ,; pag�o�i strae�line ?�lo6s q!5�e�kor!�lthoug��F�s doesY aow�!3e�N!�A�� ed,�F �0h!�tru} for,�!0average, 50\%S a�)a��as5 !#- } of 3eS4 amu,�4A�2�defa&�mag�fl� �Ls \cite{lampert1996}�� e� Ec�or~ed ve�AZ�& � main2�=oroids�  noQclp��mer�-<�>;��is st�Q� but"lup� dow�s.c.� gy6he�s`47 eV, i.e., ar�he peak���A.� E���fig:raw��); �)Lion�N� readxnt  �i!�)ai] �2di��c- -Q. NotA�a���f�narrow� ֕�z��sur%I�a more ��use2fA�ͼ� " � A Z"�7Ųa�����J�J��was in�caW Yet,�3 suit cut�H>�a�q inF:)��."� data�M��� decompose�to sepaM/& s)���ar�ʼn\���W�ąL��e| 2� Pd�:.C6� �s!�� suppor�j��.k���2- d^c$�2/^t$%!ɭ�$2�6�dse e��n� $a normaliz��c"���2� ,6�� :!b�rfla@ J6�c/��� � �� vari ���4 up to 20 s, s6�*#�[n� ��E_� discusIX�J0�I�S��ast&t�^t:� ettl� a3 p�faster, ��siste�w� !�)t � f a fixedF� for �7.3L�� B��2�:-}��ticalm�E�&�(proj)�$zicl��!c6��r�B of di4ic mole_ %q been�9�detail nier��$amitay1999!� At vanish� � llis�#(%\0$;!�a,�� ";)#^� $E_ki��def� �ial st�� $v,Je��al'ic>�$n,n'� T written as \begin{equE/l} E_{k}^{vJnn'} = E_{vJ}-E_{,�Ek} \end:$ 1$ deno{A� �9�- leve�{A�b$1asympto*� *m�-�1�� Each6Hea given^[��ssocia�[ 2 cha� eris�A�� $P!! (D)$F��U�;ances, 1A2R ndc �maxim�u�U�X a DR2� )A� �  (� "8setup v f$}=7.17$ m,O"� LfaA�� E��!q�2��s�J"Q�&�e���_ I���M� popu���$pAl}(t� E�aO͌ *� ���I DRu�(0)�=��u�and fE�&,]to�-trum of&�J� ca6 �SEsuperpZF�H P(D,t) = K(t) \sum�aW � Sf� .�, ��A6_allJ^�s$e�:�� ��B ous roal)�%a D solv�ɢinct feS� !J"E�f[ >�&f  vi&��s!�"�!quantum&�n�. U�  $J$-�.�ETtB! M^!�E]a�!ve� �A� A P}_{1 ^{(TE�%�rot})�J, tak�i� accou� � 9o�6p�malB�2A� a&l tey%� $ ��$ ���i 2�a Eq.\ ( �Ig)ALthen "J e� ��!HE�}a %-6I��"e�-(0)"~X.>BZ �9�of.�!�s� ��( DR "(� obta���B techniqu8 �  in��r��6���� ���v�er��( channels $!8$,���z+ �f!{�u$. Fora�,}� m�$vA�h& ��A�branc7 �""po�� ���.7 JK#��J�� b:w�&W!at an�qG�(E_i=3.36$ M�%�a�Mu�mq�  (� � � sity ama� $n_e=5.5\� s10^6$ cm�3}$� %!H)'(parameters,l${"ubA|_fig1�� �� examp5*R shape�F�E�Q� $v=0$, $Jk"the�MC0 He($1s^2$) + 2s ^3S$)� (k= 2.41$ eV�oge�� uend�� o5� .�i: $n=2� 3, a�#ach.o�]|��--6)�"6� he_curves��X*#A�$$�$$�#G!.tv aZ \ge3Z E�lea!#A�$n=3$ �I�� �":v �&er V�$C��ed~�s,:@%� end < s~ t $Dx refo�vmI c�.uly %M� in9�%,Ũ\� nly}.� such�6m�z�s��a�edF�!����a��\ erva/ft )g�u:> �m�b)--(da�A��nt6z �(9s!_,"����, ]SJR$1K!G�#���AI- its �7sizcr�'s:�duA�b%$�*�E 8!3�d�arg�D���com�er $ter2E�3, s%e!=�ypZ,�or�havior�*�I�a bor�TD�7 L� J!� of��6!7.0i��&�J�#, occure6 $D<2~ɞ��!��a!O.�!9IJ include�) a I!�t part��s--�i �on-Y,�)>� ``M)�''ncu�+.�)���z2s,��9�u�"�:aZ�� . As:���r! _ex}�%y4>� yhig*�-�) , da��l#di�e!$dynamic"mF��m�5U c& "� %"9 eV. �,i�terestA�to��7�5�%� Q ].FbA�*9G6 be)* slm y a�)� RF�#BiI� $D� �#opens��owun�A�ngk%[of3� ress �F�at o��bq:E=1^  Q�. F�X$� 4solid�� ec�& o��� A� cP#�=QM�.� As�� Q2���iqq�2�$�"��e��dr� } to ` s"�F � tor}$ U>'$(0)=0.34(6�  O�� hand,�.�1� b"{ � u�X$ -hitM5 -= *F.�'^.$d^c=0.67(1�$t>15$ �LAs*e$%[ i2�o ׭�%jI6ut influ�$�'B����2qi��( thro�#�2e��� a fa�a2$1-q f}_d5 mis���$� ]5toFfW = 1 - >^�6� (0)}EB�8d^c} = 0.49(11)weq:f_By� cs V�2an 15 s � i� � �ɢaabsS}�,'*"-Q, to e6A� absolute q�.��heE � �%� EXCITATION/COOLING MEASUREMENTS *j \sQ(on{Ro*� .\0a.T���� h � 2\�,_�-�* illu�"�FV _ev! ,ion_rad}, ra%iv�Y�2 !blackb�+ ,�&t 300 K,mak��e g B�.�g���h �(=0}>99.9$\%M 10� %�& leav!$<$0.1\%���erN� [�#.S�Y]z0 owev�#a *t*��x�a�x�&�be�slo [ iI�@1#5j More��+M�of proc�:U yond 9 i.�np!x=� collS a� y modi12E:��*y!��N'2Q/s aM�&�9�e�2 carefu(/I*%<0 Coulomb�*lo5,�|0�B��4 CEI}�firF -�mB�Eda&vremai��3ed-�= �A�per���+�v*-at no���* ent.|1A14E s a v.�e$e.S$HF %Ial uncerpt�1�/ah0,^�? exceed� 10\% � . B�5�<se6���)�aa*u��� s1xHe$_2GZs in1O.���e�-]��.!M�U�1�%7u�9ly � to cause �$!.�%&Z)s{)7�  es. Rega�-M�JF��method2u�tu� ly> ��W.� �1l =��I�E1� �^"�3 arguiZ!�&�32uis yx�$ at�%o"m6i�$ !"6 of � �0��)MWq��to�y >�y-d�2$ͬ. wat�P ���A�b���YC'me8e��, i�;���ext�  q48v�Mi� -���plA�!LC$�1,DR� ,${^3}$He${^4aS.�5�1B}�A6%�)�� modeBy"ro-V~� de-9�2w� {C:6)��8��cross sI�!o�5l inelal 9�tf �-Bly*� zo0 .m;T"~877!�����2> �-DR�8�;  "�� � showAt�%io P?r�?ei$�63ford�o)��)  ei��inuouslyAor swit�offR*|se]<)V!< !as��( phase-spacx2o\ A�"�6Eq�?� eq:m`%2})%�:3 ����jyin6Q?$p k�D ED $BBd:9��)��propora"�2 2�Ag�0.�1&:���:�5�2 probj&h.3 -5b1�0 �li(!M`.V )�A%2� ��s B/��� *jdeq:alp_mean_general})]. � x THE EFFECT OF ELECTRONS EXPERI� ALLYb� �6sY"-�2��e�a*�.j �4:�&�(-�9y d&�P1gly unti% appa�lya.p i&�I�a�A30 � � shapa� �� 5&-��by: imple fun�-� Y"�) xpon+@al plus.�(o�e s"~/. s. WV+�1o'q��9I<var\!.� aV��Z r ��6ki.x�,a�it back�DZ2om!`"� situ�j^�is>� ' aBnA�6�! gain�)r�Y!�< scal �sim�i�i,d�� Jk:��y)c";;I�� j�s�Eem�?�r byEb��� � m4%e_n�a7j;.?�1 V��wo��5NdeciHA�:K(a�Aof +.roach1K*U(��(2��$�3re,1Q�1 ron-e���t b�s>{2�w�?{%R2"&!_&F8�6=� } s upR�� � "�8�I��eV/�%�j���. *�a�eF�,E�1� 2),m�?t}a� m:�smmedu�yKey5er� iods�3H��%�is��(ves unambigq5/6�&l �&a��� e v�ver t;of�4 onds� �V�A 2�>�H,Y&u�>|5 tF aQ�- �j�"eDr��B�0 (35--50 s), �3��2�had a73A���'3&�+E��test (��A�![r "z.F)d2�hH��aio6\c�?�A�:!�UA� �+. �J��:�^'��)*��w-a�isP  alM&�H�)mbP%.h&QT�nde:B:4AYH, �H TIME SCALES ASSIGN  TO RO�F� *Y�mR.Rwa u� v-"~��/ !m*�La�%��  d�43ci�?ŀ81�A�� sUNb� 2�6�. Raf.�A2e�M�&LHstabil� ��i'=few sr<dBp:"Ai�1��ayY� � L $&/I�� &�5D.����TaAb%!�"᤭e� �4an< &�$CEI*�'.)siB�DR6y�j$ �6 &�Jto��>�t�!A-P" DR>k�f&J .�2�H%*c"6a�1l (.=9�sA��A� ca� q7d�F�H&;52��>~�n9ybeh cuJz�1 -to-��N"���%�� �f"u[]�mv�� t6��%b��r~nd6�6�p!stm�A�h�%ant-,1a� decay� 2 o��� 2of ^�K,?}�1�O).& En �GAa����:�Q2�S5n� AE!�T��% se�1G sa���%*@$8 appl�GPf �i�+1.2f.$mes 10^{7}*�+a7u :�inv�0������ng' �*b.���1Qhav)�z�(D\,$\cdot \eta n_e)G = 3"t,{-� 3}$/�O�>}+�!�U!Epa�.!h'�9(�&!�� :�#,�� �() �"�&)�{}$.�91l�I$H �_wRa)]�!chZ$� ��S�Dde�ergq/6S$o�se*3o&| -inI�M�v��yA me��ismC !:>Y.y���&Q E��L�'A(�Go!r� ;m^er�F�Q>�&�"e � on �Aalo+Ea��0��h&st�Png�-I� souH4����)��-B,a���*�al>ZA�n�  �abl"HA $\gtrWI J�&�D� &-a\V&en�*�s.���+�-!��%nn�&$ -^vdKfe 9. l DizdO��A:)q�s!nG�?of�ei�, $J\lesssim6�$QBO�e'4�$.$�!M  2yA&A!��au*^WN�1�ttra2�S&� 8Xj@R:!&j+  a5en��"M�����Ph�Arve \by) symbolF�>� u�Fsam�: �c($5^2h<&e6 e��OB�N�P-�$nh�s"��Aa���9&�&�H �L slic)��three"�-�� arke� a�C~ iS"M "�S |.� hP�Y�HRbC*JH �J� Y� n�$stI�� , en& 囉��L.*3}�>n"Scon�"UE�B�+vu %��)eC�ju���ubdiv��D!�nte"�?5%� $D=7�.�%�d�?�� broa"!rucuIP$D<516"�,%8X.�, m)�as ReJH 1;f0,h��0e9�DR�wx#m�Pn28Ɖ�$ $v \ge 3$RM�"�Uto��WgT5He(6 e�G�VT>�# V-a$ principalK" : $n p. VedH�Ds,ped�9�!� �6N�1q3�,�!:=%��E=�pUKMe4�A�s $�;0�8 D)$ [cf.\.!�q9]��.�E�a aMn2�la@ �q#8BAyV term� He$(�5 \,{^1}S)$�53l)�4�nel�DBGW#alA=MI2 ($7\,{�?�KD < 16$I:�J!F%- "� i�/at 7--12(L�#�P��b����s&e/ion's22�(�)!- III� ]`Ha[oeT$1s2s!(3}SE71p P�6 !1}P$. "Ma�ە����.� &| *�I���]�- $v=1A�&�to fuh4Qy�#"kAh�Fom� >ZN�u��'�&�$eed>.�HA<&fi^!�$:pump-� e}�9it"��$��major2� ��hU~�>N BEE�[�� ! _vs_�� P� �CJtegf d �� �1* 2&4Y-e%R1}� � 2}$YRtH���&umberB$6�U>xHm^)7M?A��� � very�G!&� �(���� 6.5��OW h��-1�;(XMro ��J-2 )|a��PWF(AL�%s onwards�Z G� g� :��+n$E ��*�H�Ta]2CIwL.U:& �2e�inu1o�.,�#veO*a��� �� 22%E�3tZ y_"� 6dJ�b)�cf#� !魳6dU�N26�b��1s a&U!\im!�Thu)1�Q) ���e� ET�(&�E�ټT}n<{ o$>@ �q1"-�F�2lJ� ���@s. S")���*���ox*�mJ�l�c02%U>_�7* ��R1�\�>r'2vta�h �)" seem�!� !�r!Rs.�6d Um&���2�Cchi��ye|9|x+;dAN& )a��@P�12}b � �"� (ca�XM�AZf� -�e�.�iNI"  (-�1)�~���&YDRM5!)�� �7ag� ] Qas8!�"�/2�"i>xI .8,J��)Efchm�_ inA� �u�%b2�!�&-:�)�,Aa~,pi(;JpreditZ�6na4F"� &Ip*�&n�.�%9&� ons �!9!Z�@2X!J�Vce2���)Dby  �R&�(s). > F>�e&� l�/2 #7P�n�12�iN� (U�)�VE�!6N M�2 t ����1FZEs6s� m�:�7�"� �?=� inv2FZbY�a�"�����G�!-6�! }� Y5�o��s��ber*1Ase6�d�lca�Qly��ƉB��8 .* d�+"�8� g� !]���##� a reg h�/p�1rn,�NYF X�Bof 1 s} MBn.� [�4.0�E�J�]��^rup.s!�&0ie�&by1 b�1� ! �w� "�&����� �He�;!rea�GQd�F@Sh �1� YJ5Y}�A2"�]9iA�n�(.�b)!*���!���!w��seum�N��!  1 four1�9.$[$t=9$--16s &�8�.�a)]�/6U*9��. %� +�X ��s�X nd 2A��\9,k�\Fb, Fz�H!#�I@3$)�%�O#ig4.�oft��7.3 eV�F�(@5<�2in&�i9�Ks.S �9� !�g��M�~b6D�(��.�"c �f!e&� 2,e""�� Ee�6_s�n�le*�? *�Es��!�i��`bv�l2| 5e�2ey��mH!e�> t}*eh7;�' J)�F� � ly!f�,y� � 1.�.it�`�5tIQ�zaf6�A.� 4 -� 2" � �;ly� � �&[-B#a2�qzG&��"o��) Je�bn�'\� is�IE��:E29B 1}_d*�s$U?1'� ,us�;Pe a1!�Va�m��7dE keepEmin1[at���ain�L offse�m��J�3:|TM for5�t�R� staD��J}���i>5 ��us�\Sec�4��� tota*�5�%�&�)�s�A�_�*�|6$L0 2 w!1�9�4͘�Dh��0%��A{', nnM聤&�RN�T1,�W2?A�a�b6%�_�3>arr&dH�8�'< pre�C6 �s�vo � � a�u�ofY�wm]�`d�`!�� itF"^% !�!a�J�Ik*}D�gBO&�OenW20 �;�O�+u�UeI0+2�&�Q+r:�}L �in5 �$baV���2�w!!+ O���KK&�!/)�o�3�+�� �%m�����o2J� 4 e. .�(a_�e_t  v&�� � 1!�� d ri�ap�G.�)�a�#n�a?g��Bpi�' �%f��2�d7')1Adɦ(�^3@*��d&?n(� )h���S&�Aa"���^tI�!���#*2" � 5�P=3$--5, o&QiIa'$0.4--0.25 �%���-"n"�-e G#, n�%0�#I(� a*G@��� h.�.����Did{ ��ong�r�.�Mc�D�G6�-�^ *�.? 6�� In)i�"5 1��aDerPv$�(p��i�;e�r- Scascad( �b)M (short enoug�6+KY�A]R�heMT-2>F[Q�sh�?�jAUmse�9da�=8�8Q:!�-&� a��.-*AZ]B%V�F�:�&A�e�$3A�$@<ղ 6�[A��a dass3lvm6 Z�]��l�]ly*tM �?f�H� ���z1s> \ y�#, i*�i�ly#FnF� � ldz7 B rpre���bS;��"u+o &y.�?at���:�JA/t2/ U� ��i0�(�ʁ ��ne�vBi`��2'R�"eaxo�^�8"� `Y��ai�*=25 �O�1&�)&�+�]Va���9*�*x"���5O%�} $res_de_exc�qTh"4!���20B<kF)9�ce  G ing t; �O 1��nees� �I5(rBRU�*b /&�i%� ��k scan icis2-cor|<sG�/.�1^)� ies 7G��o�k D�7��6�de�Pngq�} �G�|R{ Dawl jo~l? REST GAS* LbX? ~�{� &�8t'g cycl�sre� D� H �&��,A,�R�X E� 2F7^v9�9 _�4P"�'7>���� !+I�arE�9 F��S���3insteag �pU0%m|1�.�}�0� �f+C��u3 �!W&;Ci�"i��rgas2�5Es�8"/*T&Y*���U�N �, f"� "� iI�*!i5�2���f}*:+F= �!�@55O1!�&"5D� ".T-[M6��v�-�v ��eh �9!o�wu�1�9�2Gon >9$ .�JUbk3Alt�\,%)���� ���.gper�uE� >=\P*Cf1��02� (�$���Kf&F � D2l�'s� WllX6M�rol  M&� V non-� mal2 � ��U-�la��by�3�* A�.}. &Q`z"r B} 2w.Lo*̀:�)"�Atte"�WN�_�']ab5��B�^!eEJV� �)e.' ex��B� &`�j��� J&�t .!i'�MM(�i*� ($D>�+)%N(/a &�a&$<)'"�7ReJfI�} *�\��A�iUu �}�-s4 Q- �"�xs�-2�&*^ �3�'3}�bmr whel�H�0�-&g%� �� J�(v=kVD�|Cont |1D�h fBlj~A��#.M`U��K��Cs l�d�Tr t B},���&6� IG�9.n��"�)�u�2_s`atMj7.O+-38.0`+(c�,)�Nv)2MIF! $^3�* $^1S$-y/ylaC"��*v0s���G[ onD�N%K)��I�Ms few-2�Q; I� &�Q�s�znesrBusR��Q�Z� e�pYk-��$v\neq bc&�2at� ,+6�q:���%( $�%�4� Av &ZI� M�-R2 acF� nowI�� B�e< fI�i�h&6jx. �ci�.cM9�aI�e%1}eB !k�% 8hoF�M�uS�"~-3�-&�-�-{./�A2�/� i>�!n� _5A���� ,(-7 ayc&l� �$kEk� =q#&��&4 �42[B��2�I�!�"|@6 and,�AW�H}!�(�$T ; !�"0c),m)�4 t>35$ s a� �,6�/: FITdv�0!�76�.�@9�.*�'!|� #�fim J� �9� !>�hSp�-hb:�Xn"%+7�M�"�) �A�B*� $^A�He$^{&�X� � Ba��#"�<�;�(c�%�.o t5$�-M\1�E=.�NS�VӐ)�2Q=b�0J�c>iIx� Ayi�{�Ѧ!KB�clS��ce�"rin.�9*?c�af�g�1-H>� �%A� )���!�i"y�[ gE�>� xno9jA{��  \, = Nyp_0 !��^{�au)V)} {(2e��lB��%��ylN� eq:IZjd�fg#G. ixf�Y.� )M%DE�sin5� �.�$AB �|by)�&HF�W. &m erroEO!�6(.�sc2EU20\% we%�U+m}Fdev���p_0 �i�.�N�s*Q�-�� R��fd� ,�tNCI� >�} Q@ OF=(�)\pm 2.1)�G �G-10} \c<cm}^3 s}G" v�^ _corn6�{� >��-� {\it�%d}oH!��'xed.4��� � �p ag�3d&${� of 3�!{�l��B"�\��T!��*��{ *f���kp�6�B�� e*�V(�in mi(!|> �a )�%2$�2kI5.5.�6�+u�@�ia��cJ^��{� a�&propto E%�$5 P0.1;��2@d�VsB.�Hb}#'�con���k&1f(wr<&9otropic9�velocZ2*at fE2 C "#B�! !�4$(300$\,K$/T_\r|<)^{1/2} \arctan( a4x el-1 %/ (1-! %erD =2.2��'�$�(�Fve �{|Ki� an MaxwelliaBehW4�Gt.�q� {\rm_h\,K,~DR}�J (3.3e�0.9q��Ka� 32p  A6&sub�a6 ��)�ji�O�A�ei�+�&>n��[cKn$\Delta6�.#=1.9(5��� 9}$ 5x2� �fN;at&�RK�l- �&.F�^�)� ��� z�u ��FstU!A #m a�BAa"�2�P %q3�A����pt%�$p_v=\BJ}=<0.01�)> s%'{F��>�^{9q32� 9J 2\t5�7Mh6�j0OH o+ _Mi~�1Rk10 z��6��.rQf�3-!upper� %5A�� .of Heog %iUny2^1rB�JVL #&�E$���Z9 \%.5Xit�d�?��Aj�4e2��%Zu���� �aU%� k�$�0.�0dD&��L&6�stG� D,U�M2��-4}"E2��"��dB�>Oy�E_d)$$s�S$g��� wic=�+?���a4� 6M!=1}.* �1!*�Y  h2�rؖ|���6�r_a�_Ez0l�u�yU,�"��3ZV�m0�i��,�*Aa"�:: �KX'Q $b����=�NP�&!�peak-�YI:7Q�025�,�" �6*ac�mibl�;g-*�7�k sharzuHy%�]Elt1�� n6<[1 a5�u�U�%�h�+:E �%e��#rE5 . 2r High+[�SA-6TAtE& ZizF�BZ(Ax.�~`"�+r���$m�yq p>I/&� 9spread+@'0.2u6� 1�6�Q3/atc�eV-��c:U1o 5U~GkR���sigma.[)$yY������1��>K*�N�onv^� (2E_d/mP ��<��-OI �D�QC��� �c�� (� 6��h��s)8�PY;&tQ6M�7� )!�c� U�-��� 2y s��mi��:��Bo͡��12{ a �M�I�i*�e���zw22'"�,shift-d �}����,�' m �2Cf6 � �2�#:8�}-�p��E�!Bwidth)�3�tmatL@ell�%�34E i �B�IQionic2��/:9&�{ng ��Rydbergɩ�� �OaXe repuls $A^{2}\SaJ_u[m xE-�]&E��-JS=�mn>� ch+l!��&�l0 $(1.7\pm0.2)*l 1"% 2�I� EC�e���Je��͖ es (:B��$Ce6Y.D!A�%s a r�y�w�a ��IW }(FWHM��A�)���19 eV� �A�E��daT *22.�,p��au�a"LfT25--27iAnd�mod0=���v�� b�A5���03#�;wEwN"ɵse�|�s,U�F LJI.lI�M2��!!]M��%5��� cap@S�p. ��i���i�"IQ3�+-��>is 23.6E�� 44Z44$) 25?�!R he� :�>�Q �jod+� 26.9�C 1v���P ��mFp�Y<�!� .1�$1LDTy�`   Hcee��|+'cn��r0�.��� �W��� CD$���,forck1994}. � \*� E�% �a�DEŧ�-�_ 2��,2*�1" � &�)�b5^.��Fs" H�����($a� $3--2 >��+��* a�r1�DR� "H 6 exZ3dr& M�e�N��~F4or>. Y��&:� "n ��. , � � s�>K�d� J�"�"�!k� prof�i��b"\�cќM ",Z-4�@tpG N!q.-qRe8DE. CYA%27``d_ ''!�c"@)cqqq�act:Ix"� �q*��dDE6��@ء����]V<R� 4Hg��y } �D��]yh!�� ���DA�r�{��0A�y1]!reshol�2I�2��s@�Tb3Z�!XN� 3���e�^X!I�5I)��to��s�I�,"� 6�%c�� T "�@�; �%! }S<*� ݷ�dropsL Eq�ď).s"�7�)&.�4g erme�je��: %�i�6l s.� }Q�wB�s �!)Z�� �x�SsI�=!�.4I8yd 2�1��4 ph H 6(e"�*9 -왁� .�!���D F���^$^3 g�w�v}O��b)], �%*\-��%5��2)�&Bu ��%5;{�v|"�(. A�Uu=���_p�"�UB��H.=l�e<_phd,zajfman2003� �s�5A �*�7 ���ly�&� �$ll, DR, DE�%&��.�of� /�0nakashima1986�A*�:�3 "-A�Z�m"�YOOr�� Kulan� | orel��)AeH . 9�me��d:W^�bP��.g�MAE�Q..zRy&�= /U��%t ��}i.�.�*% -:ͧ� -�i�t5�: /ce)� autoa^zescB ider�."�W.��� be�6�  nuclA���,�_%eY@���2�a! inuum (DEa�i~ a b� = � (EX�,!u"� ��in�ic:>�}/s �z9�Z;I5)5!N .�)2 on{D�Uion:�5$N�~DR2� i��dr@&��:�Cd�;�ASTRID*� �>:Z Our��2�Yg��!HJxa�B8�!�Z&e6!�.�� inM��/ agre@ %c t� Q^ ��E� ��IC�� �i�(urbain1999b"�x���aen��g%�oJ8 % ]qL|"�� �20 >s�m!Q.Fg)�I��ay rece�5" LqR*&� x*�v>ed2200F7 6����8[.� ! $(6\pm3� �$F� ��!���1e�Pr,%Ha � P\d1��/ #$AA<� Bq��6؁͘���| 91�t'��al|&n e��6!( >�:{so� �I1�F�‘DE� ���"D% �2.��� un�A@�%[.J%�$�: nIA<-�a�f3%�2 f8�8�a�+6K5�A6e;�P�B A.a& ��B^� �!�-�� �  ou��^C�$A*o!��,f�:�,I��,.h#�+aA�-�$�$� �1!2�$2.2.�-)�K+�/�X�`)---�qO�y r�valV]�f���ɸI �$1.�!C$N�, a�n-��*s�X��bC1 ad]�+�e�2:ml�G3�- &&#�"y��!&�G��r6I ��G1  5 [$1.7(U)�"V2$V� �*!) v8O$0.6(:����t �];!!&�6 %t)|�2undaJE"� o�? ��)eV �6)�) ha�UbZO!��2 $repan�baxb�"pl�+: �a� sourOsn�ow �Hl�4!�V��"-�>aȂ��� Bխ2Q,*_8J�S!�)��y%�,���_nknown. ��F?�&,�Btm�^��)+% =0}_��'�'+ �I�<.�L<of $< r5.0NS"m by DI)hew e� al.}�ad 197A ��e�6�$)5��9�"B �$V%& �L7V�'>z]��c�:��{E3*�$) 1=*V�&, T Veed�Le5q2�6:,.�h&5# �A�qvRKz-m.�(-mA "κ� "�*!�Ivanovy-9�-�i1989}Z } A� cal���sFC�7ZF*�7. � *� q+ .��Vj� �a��.�+6thL@theor�a/ Ez ($6..�11J� 6�E�F�{�� Zpt!���,� -]�j�7�b� )aZ!r�u30�+�K#14a�^T9 �� ��! ��*� a�j��ob ade��D@2�)"g � =� ��Dadiab�]Qpy/�(�*�"c �x� � � ��`]r"4:�� B@zd�1�� = J8 ��(h��"r "f> / -� H-AomsJc="[c���>�4���S��`V7� , Royaщd[)�rk �:��� s A�a.��8fT62��$� 2--1%)�$�v�%�0ve pack�X��"ir�N6�A� $0.7̓2 �[2��6� �e�a� �;%�� "�)n good&�.�ڣ eak �B"�re�{!*��m#��tur� !N�8 sB�>?%�i�3a�i�M29�o �lh`M��df��F")��&n"xJS5 io> �2�Y�BB)*~A �Le b�of 7 ledھ:2-�؛� !zV m`>�%{%�DE� 1.q���!�ClYiz<��!�IN�{ availd. N��.��� Q`� M6��9 .u�$"KC� �"w�out� A�6����6��z ]��l��"���."\,a�)p2��f4�� 3.7\%!�@_�"N����Oh�%\<>�C1u6(�)o�}t @}%^3.G�g�:!VJ  3a�min��2��ue"�m�=��A!C��Ts?E!� 8���6\ �~<3�U�Q"x1�7hI ]O &��z"@(�oh� - k�}�N���5r"cE� yW..b�o2� mՁ ���t�!2xE�)�Q��s ^3 \Pi_u$�$^1)Gough $ $-$\Pi$"/��cohen_ �W ^]� gub� x4,sarpaf�A!U amplV &RNu����!�g OBM kell��7,y7� ���LAZ�, suggesAp-t:c�'�1�y�  MQDT�…��{:! *o _"�re-.�f��Wdeju���,�su�+�)m}a>� C flux�2$t�W�  oΝ�h��A�P�[t��.� 颕 ��Mw*�&^2*G�r��N�?��%��  s;?iv:8� �.�a�q�nel`��n9�-�ar|��� a��%l��0�:!<3*3Lthu�3 eas���g gniz��mo80-mm���FL*<�|��fa|����e  &"� U&�2MBby�V�,6�[-�AQ�Z-O�%n.. .{Iasemania�&6qU �x"�$PǓ*���)VE ATBA.%:sɢ*3&:�TYr�E�C�!��H���I|om����6.)l) eds �P�F �E��;�RHe($nl$!,om �F�7V)1�&$F�r�in�A%<U&u��< �q��� F " "a �&�N���LiEf�Froh)1!��  vǣ6�* gss�-�m�CB� us��_p���(& V]W%~u�GB�2f�# _vic&O�c|*$..�5�u�}���� _'��" �c0���H SE"ш��$�"�( a.KsIe.]T�xc/�R��B"ޤ&�)!m:2.�cu6i��'!� Ion_�_9. LacqQ. (1!p�. s s6 rea8U��de����= " H# 2H$_��ma,�m�_ 2'), w�ly �'ik�~,e�i��V�2��E:�il��N��� $v��b�Ey�\ +�H�o6֑!�a"�tU'V��"\Q $v'\�Qv�4s�f��a2V@$\s 2^g�9 ��y�s�<� l������ $v'$w�I��aib� six.]�;� G --5)�thirty.l�; (� --29�&Evrelev��,s7""V#2Z��acO]"�!��_YT�"fQ����6�a 0�A�ex)�!�Ӗui� J} )� gas_�}>a�J�a ��6:TW�n�,� q�%!.A.a22O��6�C.�ei�N�� *��.�&�J+.�librium�'E�2�).�Y���always�@c/&�z�u�&����M��*M)�+l�.y8("  .�.�"��xeti�!IvH.�w�X�q_ "/2�U�re -..8ņAC� e � "�� 2� R� ()t^�0(A4. �E ��j��).��i�J���6?s0b�.� few 3A1�N2$��� ,!��p d�iX  $k�� DE}^gZ� OIq�6 !�.sDE�5%΁�!�b���"F� de_res})]�A� �xn $2.7*�*z�q-��aB- F�d"���+h���� �&~Jdc ��y5��A4�2�2�?�C2�AhwS2�s lie"� xlC�*T�9m�") (s!�a�)n )!%��.l�.�$lIUk :��!e (/ � c k J9����J��!@1.�.�)"�2or.�2>s='' s�a�i{>��8,!���q�t��e"�}"%.�.GinN a8�.� Enr� مe .����"s����%�in ������V!� �*a�l�I U$[P9 V0Kbr1�aY �c_r>�t!�lW&cmT,c�  (R&>= ),��y� ؚE�9?a�a ze*,*@Z�, C��Q�s S( �c�6�hdl= ;��"�U< W1�cb6� aI �a�/*,",�Xj2�6+W��ex�:d pM:X0u�|o>8V�ed AAV* 8&R&�j��3EZ�� ��cAo��!-�dx'��21�(�E) �)Q+!7.�)to2t<�L3 �aP�22� :�"��Q� ��L*"$�& R#�E*��. k%AR"�&�10�e{V*�^v= .�ve%�� e �2�6" "Db��Ys�0a*�a� ���Te�* OM 2� e�m .�.��IH��w| dvb�I6����ȗ�explo�- "��� ֡���.� �m�A� ��JZway �����,�*:~!B� nT eI& 7� ult�%"Y-�� .�T2�8let�&�Mz��"� Z&de%Lt��B"��je���za�semYH"o�&�QiTW : ~Z�R qual� ��!���} `of>_]���-e{a)�td!F"9Z�Z�.��n~6U�/�F_NVmr"p s��I 22��Me2�S�_s,���t��4�/��2��K e�s�"o 6P�in. ��m.�Niz�R#N���)6�U�8= a_v (1 + bJ),��B��Xag� $a_v$�"o1I,.\�|$b[R29�!��$- -JYt1�s!? ���Y~�OВR��a����/�JX�Z��� �i�`a��Q��k.+ER�V.�cho� $a_0=�$w*V,+!plet��)���a��`X.Ua�MecuE�M�� t"���f E�n ��!b2�<%3$& ]��.�Q�e 6���,5�%��u#R� $b��A2�ȁ�x%f��� !�N�Iyc"�#to&�i� T��u��=ro�z,X#�x$]�%���DRa �� (+#$\beta$)t�G�7,O��]=.�b��AZ ed (U� ��K�x�x�X��YQxI�i��E*� .}daI�&�! U2� e sA�^�]'&�,� � W* !Eh2au�-X �$b<_�#r; "~))n�HT F�a:�at&� 6'; 9�Q�4�!�e/�Ez7�R:ff+-L.�� �u�#��,&y�1�e�s��6 ,[siG�(� � &)��t��!H ��*�F ,=�[$Re� � -�׳�by�&�' ��]5��c���@a�]�"�^.K*�� aI%�Aq�"W-��o ʉ. I4ao"e O��6&�y�p "s�"�g�al|�)G$v=v'$]� A�S> EK� 6� Hsp�!w��v���$by Rabadan�/�-\�r 1998a� J���EX}^{J \�a��, J'}(E) = *0 \��x`E-E_{J'8��}}�6"� rot_�1j��7 9P!��5 R a*��$ 5dq�_0S�)"26U2Z<;k*G:pr�>@& mi1ct\rN�siut�nd r�a)kD)l'6m }(E'%m.+ *6)!�'+9e��2�. }{E'5�$2J+1}{2J'+w!� 5�2B�!@z&5ş!���5m=%ª� �]d"�"�ttoP?E�� Q&� EKay} % aar,{lcrr} & + &�ZH(vJ')>(vJ)} \left( "�e B�0)� '} - мV J IB�0) ) \nos�\\B��a�8It mustaa�c!�eEsuch re)s playa�ignific�B role���!�age r�nmeasure� s on!Atoo. InF tudy%X$_2$H$!� �,lammich2003})imilar �r$ dependenc�� 66�� wasUp,A�� caseI�a ��($ably large�=coeє, sA>�changesa4]t.4,were attribu!Mmaia] to sE�ive!��MPbE� from!� beam, �����0arA�6 >�q��ave�)0slope $0.94 \![s H 9G 3$\,s$Y }$K . How�,�\>�!=�e�by�lyv� c�� ibea>O , �lso)�i�se%,act�`FDR���4s still unknow�Y %, CONCLUSION b \� {Co � } � pres�Gmerged-!�sA|.-)�R� clearly�firI.predie�7N �m �e�He$_2ax`initial2�%. !M�Å� s ataz�G ��,ies ($\lesssA 0 meV)��( turned outa be high�te� v��0 2Min.�ly �Red �m(. AlthoughJ3s radiaarlyA+ive, � 8resultgn&� .�>�A� ited�� after ��a few� onds��, evi��for<� ry, non-� ma6�o2�w)�I% fr��of 0.1!Z1\%�founda}analy!e0DR frag�� im� dis��ion!R8Pump-probe-type6�involv��switch or var!i4� E��� ��ro�� allowhe.�)�Ed�B��>-4 ���be� � ui �GatC:0w .� , �latter dom2 eA�no%�-�a�a s. O long�  4scales typical!�F2��� ek.z� �2��0velocity-matc� 2Y� s2 to cause .�ͻA-�i� ed (eL-�ed) zero*� >b, iCt ��to.�� MR�!Zconneg %�a���i/ @>0 atheir��=L��M �`A5(unambiguous���6M B� &N *|1�A�&|aLS��&? bH �2(loss proces��a0a�� siA %�R')� �pro�iAo suchC �bity1 � DR, � Rcorrespo %� * 9U0to!Atwo�EQmagnitud��od!H�unt�.��]�Q� . Wq�dn $oped under�� Q�? dynamics�� ��+differ�w� lnel�A�� ��V� io� abs� R- h$(7.3� 2.1)X X 10}�{3}*[ -���4mit k$v=0$ R4, referd to a*D �F�8y n0 10 meV)o a.|. like�%�98300 K or below.��-s somew�d? ��an���in re1*� g�&� $carata1999:� st!��� ier � "Olimits Bd�he1976}so branɚ��efour aca]�fi� atomicRR�(Table Ct 1})iy.alyMl� osa�pT �.�y basiE�A�rel� i)taa��cousA�soc�nve po!-� �m�ir diaba�e�Wons��2��xav� � y r�  upAc40 ��MZ&b �d` )q�^DE��$ron-impact.���;on:  d��B�shows �-[8 broad peak at �a�M�intere$$ uc�s, onH m narrow,� � Asner� ��ppaQ�Z -� { so reveal% compet� between ��stabilizP pathway� !�reson�cap!�an 1�A��1 atI � ��V. EF)��iew��:s�# %6 t� ,paper illusti�[H�ch@p�e� � �A�4t !�toQH ver�BLs��$to obtain .) ݯY��\.��|�e�-ge,Jparti��QE)�����t� � � rect�clOs b�| togeA3"9v =ng�!�~fu!�, mor; Zdiagno$ technique�s��;�& !�T!�/ndu�y !�� s, "�Xe laserp dem�Ad��ea specu ��;Dhechtfischer1998},� a|��esi� P!� V�eal> I�I�9��6 aa�%5b��s�bby M &� A!: 96�� �be us* o�ly mani�e C�9�E�Q>1�. �\G page.�  Ac legd�n�� $ \begin{a Adg���(is work has�f� e��8German Israel F�i  S(A< Research (GIF) Er Cone3L No. I-707-55.7/2001fb�8European Commun ji��e\Traina`Net� ``E'T�fer Rea� s''. HBP �$es supporteN|,program IHP �$a Marie Cufe- ship �c �| No.\ HPMF-CT-2002-01833. \end{�-�)�� 6J( REFERENCES�0:L�Q�thebibli!aphy}{99}A�ibitem{b�01994} D. R. B�, Adv. At. Mol. Opt. Phys. {\bf 34}, 427 (1994)!nSlarsso 7} M. L (, Annu. RevL Chem R4��151 R7).R kell 7�K4, L. Vejby-Chr- H�276 H=vv���AJ�D.�H.2� R�)�%[A �57}, 362)�82Psu�0}]Su�,H. Nakamura,!C)� X%�93}~ 6491�02SMH50%�YH A�F7�718C56Ckokoou� V. K�C%�Greene,.[A _6!t012703 (G2�mul� n1964}� S. M 2P�13A A962I�66�.� L. C� ,, A. E. OrelV8A. Suzor-Weiner g )1�9}, 2804!992��cilI.P.!S il,� LeppjDalgarno!�A��pe�J, �509} 1,e6.@!DPePMoGcourt,a�C2t tF�Lampe=� �13}, 114eL762�(phelps1952}!&V�%�S� BrowF� 8!�102�522Y0hornbeck1951}A� A. H ]J.!IMolna1�%�QF84}, 62E�512\urbaia>9a} X. Ub{\it P�e�� ����Con�� n Di*�Ren��,� ory, E"@ �EApplic( s IV}, ed���.mL�8 A. M�elM�I�F. Schne� (World��[ , Singapo!� ), p. 160.�q et1972��I�^UC�T Acads$i. (Paris)1j275}, 7��76�bi� 1949a A. Bd�X169Z46R(ivanov1983}Av A. I, NEPenkinI�Ye�SkobleV� S� roscͽ5A055E�86sl96l�2]>[1#6!"445A�86�c(k1995} W. CZ0J. RychlewskiR�EM102�y533^95).�ack��A�mHdHaVg},!�ma�" ^ń7�96G maas��G. Maas1FE�$van Asselt��J�M!Nowak�Los�D��y hoff)�R Buenk�v�� �,1��21E":�f�e1980� P. F, T�rk dJ. �6] LettME�419!^86�yu1987}AsYu%PW��W�"P%J�7O�'055ɑ86& com�&9UC��Gun/ Si[ �K.A�Hardy�-Vp8��271)�6| zand�0E{J.%��Z�Ubachs��� .��j 3212�6"h�20b�ZX.!.Wang .\ZE�^ 6^coh 76%�P2N.�8� :'g� �K> in�hys�of Ion-I�(�L Co�) s, Vv 834 NATO� d S� InstituteFSer�B:%�ics2aO rouillard%>J%>McGowanAK4Plenum, New YoA�ұ�7.habs19��D. Habs �4et al.}, Nucl.�,rum. Methods�!�Res. B�4A^39:�u�V�|b2fC.a�SafvaI�� en� "�  &� 5�V�j�%[�� j� �� b�!�n� V�261.�kilgu� 2}�VK,1� Schwalm� Wolf�vR!5 Badn"(9\"{u}�*6��4� 57' 6�amita� 6} Z. AZajfm!��T$orck, U. H*�� B. S�l��Aߡ�Ms,��RepnowT�AA. � Iu�uq��403�96� alkhalili7 � Al-K �fRos\'/$H. Danared%Fŕ Derk�$K\"allberg�&�� Padellec+ Neau��!�e���R. Thom�$M. af Uggl�ikor,��Zo�(W���.der �,�"� M"q'R.aFBilod{O!~b!^j!7",6o>6n nge� Lev3 GA Gwin� L. Kno{ M� h~l6�R. West�D.U�1�J�� 427 !�2�wS3 b��!�|sU74� 37��:: U�92�� a�MA-hA�.)&Z. VageE��60L)\D%:i��E;i�B� ��Vw2 60"769��l).Kgf1974}�S. wF)p.� g.�  3L 1257 L76+gi� 1993� u�aJei�� .�vo��Hahn,RPJaeschke, C.-M. KleffEf(\"{o}ssl!r,S. Papureanu�+l�-$M.-H. Rhee6��9SchemO6���.��Ʊ32t16��96�vonhah��3}!�von �M!Qie6�E.� B�AAiebmann��2�NmGa}tampf!6�6� �� �270)�:�staE_e��G� soffi��BlU,A. Friedrich!� G� #U BM lz�.]Ju��r\"{a}mi9K� tl� Ot{R�)����28A�326( pastuszk�0}I] ŻSchramm��C[v deA�#U�J�nntE� H.-J�esT<Sch�~M�.M�i�n�E���. �36f1�:�poth1%�H. Poth�sp >19��13 6$l 1996�9"���V��.*���AS . Pinzola��NJ"�����%�5R 14� �2���42�.!Z&�.b 35�323�6�a_�1}� dip.mo}�)� �45)71 2�.I}�(di�$�2,�s�t�b ��i�* in %!6"�ee �62} x O. E ��*�)V47�66� herz�n H mit%a� Dia]"M�/es{(Van No�nd,2} 50)T&�Heck�LA7Lh/� tras��U�*�A U�ez Z� �JB)A20�3�"�2�Wic�/L-m:�.�� 2�S. ,evogt,�Andri� ijao� uhr,!�H� �.t:��.'}&�. (91}, 143201�6�tanabeiST,�LTakagi, I. Katayama,��Chidat Wa @,6Araka�Y.Haru 1�5 aitoHNo�T�Xn�NFNoQ�K sono��v� "��166 kAY�Yg*� "� .8( � & �� .�*� �5�%|�0��I_6� 0327���2aB! Bp .���.��ink� wSchmitt6V� u��.bz�f80No l _phdI %N:� �'pu� ;A(�PhD�2,sis, Univers� of Hp��, /�Hhttp://www.ub.uni-h& .de/�iv/17:� 4nakashima1986}Ak[2�! :x� h6L�72�86�r&v:a}a@R  K. Sarpa�J. Tenny�MonlNot�X-n. So�29.7/82Tvb�vJtE� B�'K�420:h faurd1VF%4B�R��32�446�v� �"� a}Naa�!�EuKan�,]24�4-�6&͛1^uu! ents&a)�2!x3"� 6eS26�Te a�6��Z! r jZ�@�19� 6�garcia-m;>a�[}!G M� a� Dent�I. Abrilan|� AristaN~��129�46�thomp�85Ej!� _AE�Barne��Compu� aLomb �3��86�f6�f� i�>/%�6E �6���4�"y��.��U.�Va!  .�Up.5�eHe75a-AvalLR.>� �I/Q�69} 0629 200E� "a f�I��NC." R�2 &�*� �B��xAq.s .�&� 72}��:�orem� �YK:Kul�:154} 499 Y6u�!02�0N. Djuri\'{c}eMP��*� "�A-��"K"$ S{\o}gaar&8ndH*�" sub�E'E�B.�royal �@�A� Pemc.\ 6th� Int.L.$+��seF.H, Mos>,'y�ab,:���iBa. ]�&�>�)I�i�4�� R427�I,U�s�^I�B.A!�p���l!�Tp Morg �9$ �59��P2osy iaaU� e�R�{e}n,�Sundst)o}mAOYho�S�tz�D �6hd �%_�ca}v>�?" }���; dt� q�*� "� !6.�9��)�5AR46�:q� 1�B .�&� 1&K$� � �.��&F A���f�.��" 40056 ��(t:�'�!(.!(�n(2n( ) .V+\newpage"�(42} \]/$ion{\labelK2B} S�@con"s4s (q8iz��Q#�0gl/2 oXA .�9)�.�BS>a�F8st-squares fit 2Q*�4:`2�0 at $E_d=0$, �E�-n; sequx!�4increasing kin�9@1y�2ease.}1 ,ruledtabular@{c@{\hspace{4mm}}-5d} I�/sqB & F�3�8\nel & \multicolumn{1}{r}�=� } \\�J\hx't \raisebox{0mm}[4mm][0mm]{}% $�5xB{4}+$(�5`) & He($1s^2 \, ^{1}S$) +  2p\,P*(0.0154(16) ��W3W311(28)�Us ��&N< 98(2�6\b�3׆�041(14���3�0196(6rU4���U 25(3TM-Q� :�n-m��,BF�/�q� ��� .� 1} M�Cd*6igbFU7 llowa�:�E�v�^e$b6�%N��:SbG01v{cc} �� c}{B6� (\%)a�:  �� v�si�Q+$\,~3.7�9 1.2$e�_r E�/& $37.4C4.0�Cp��^$58.6C5�� C1C\,~2.9E3�Q߭�A�:�MT�B:WF^ he_�8 B?6 FIG 1q8figure}[htbp] \�:eU5 \bJPgraphics[width=3.5in]71.eps��� "�9�� ��2e X{^2}\S�NuE7Z7ic groun ii��C�4.�(X �:first�& :?�$Ang^+$) I:�("<63� threC�A2_n"IK�$ T"O&,*. �8%pos�8", �=8n2:�: of F6@s@:nFhorizobL���4�6 Fo"(;$. AsymptoEI�5${{^31�g^+}$:`cor�;7 He$(�� \,{^1}S)$���B FS)$U�{&-�W)�� J %6K `�!�EG �Pi_u}�Jp\A�P)�G}��u9��mieyW-Q7~[ed2�did2FdAPQ�T;et9�Iiyqw HqGsystem a�"�>X:�+�+M�6.�< Q:E; 3e.�JmG6L .p}H .�:� � U%�> 278!�( EXPERIMENT� XE,36, *}[h��<2.58in,angle=270��3>6 (1.5v9umn4G de) �"?dra�M.29;setup a��%lTSR9,+2(*r�R� life0F!S�=B)C46C��^�0i��41.e�ing* Ca"StoL<raLI�s��a&�-I&�: TQ0um number $J$��ixNa --521sF�BFuN�}:4P9�1u2�}E�ra9 1��B�5Z�=�~�51�apW5�>mal�?of F"�Q�h)[!.��5]B��P (a) Vc:�among --5. �l�six�_A RO�<>qu�P,�.�D 2�Dof 15�D impoG=on each Y. (b) &�Q?he.6) � 5E�i�2�*PE� z(solid)X9��U),��30!;dotted)..�� mark�B�E�Wlibrium� vY�u�1��e$ cei_data ����6��I�6I�% >�&� N~C'.%��&V��G8($\tilde{E}_k$)�Mfoi�T�UCoulomb�lo�OZ� i�Le"�A"A�?.e �0  off;E��� n (y)�Oi&�RX  E��@�CinjOK0of 0--1 s (opFT4ircles), 2--3 %t%#g e $\ge$33fil�A5� E�E�s�i2gX3Ved2� �he2�I�*�Xl "�E,D�N�� C&�GPc)�}�(ZB.1Dhe>d�C�Bt-*� �2� y�,i=7.28$ MeV;?dSK$y $n_e=5.5DS 10^67 �\ {-3}�qqNʏaX fig:raw�� e�7 U� ��017i�\�p"(�Cs (��4�'E�DREV�fDE ev� %��a��1�H!�DR-U�Jm detun�-�e'0^r$=7.3 eV). ��N�-�>�U _off�1%�8�/�/8:��-�Wd&�Q!`s $�\$ >�%��\�3 � P over 76�is� 6�i�c swit�P!a-S10 ���ag�EFor��$>$a�6^� ��~��*� �pli� a-Hto `50.�&< >�T�ma �le�� onenGK�G!.5atH10--2� E��6��9 whil��YLmp��5�NA�Gfi���^�ealie1) A ��r$.��!_F�N�A�> bB" 73evb.ne)9�)i)9j)!� U�!�^gei33.�X6% ime $t$m�� aKrM<:�$E_d$ �Z�ge� om 0A���L$ $t=10$ sJ up_K��M�! .�Q�MM��rQ�@�` eg� repe[a `�a2O. "�A*�h � �_dr_de��$0�gIg10FhRa6�Z@R�&��a�0rva_35--68 " o/ � aA�Toroid�c� ND�ㅖull�h �d nge Li"�O��*� AVl Dve/W�bV�E%�.�. j� �|j� N�A�I�`E_t)G֐ %%Qh�� 1J�Eff0N� ���1yRN�ee�ine�;e=5�lowM! regiJ+�m�x@~cN�.�Ad�Nly&� g.��� @\alpha}^{{\rm c}+tor}}_ DR}(E_d)$�����:� ��y>e�B_&� �d%�Gt��Y %�%"� p]�"�%>0"�Q3�%"�  %.`Q8�of� �JcameraR m�`i��  %�DTxampl� 9�w�Wf:�\�. %�fts occu�V 2.5-10 $s�.A7�2�c( d. %� i�~"�/@$E_i=$ 3.36 $MeV$&�e�M�A0 % 48 \cdot �W6} cm� 8 (5.8 $mA$).} %@� !�-��4N cm�K 1�r0� 12ɱ�q0DR (two-body)Qre�jed5��>�"]R�a) Two-d&hZMb*�i4JZ"k�[c.m.\*W$xi�}$, $y� u b) T~ 2�]AS)]1ST aQj%�S�>9�(i�'>���Qe��ookeRap# n�ce%`-�� N}_sEzMycm�b ��QKe�i��I|:��Y1��|]"Epro� ter!� icle��bD$)~ DR!IB���.�>��Tr�y86�� Ac a) Ata%XM2�b ��T�naslee text�end poi�(�"R tick�iI�Xs)W var*Zp�T� -to-�Y-�ha2's��;�.��m�_H�k e0csg� �(� %�a_3--6.5Cc) 6.5-��|G(d� J 2 wtha! area!`S!*�E*T _�l\net�dj� lapp  light spo�P�phosphosc�?Jb �(Z���,�eYʟ .N*�? rT_ex�*i�4 �� � 9~�%E E��!�z��Me� %,A D�PsqέbB�. %�_Հ 3E�&V"R . %a�2�/]&@mB$U�����3TF> a�(HeH��U�Q T��g:U8sam�jpf_#a� .� 1CI�Ź� ~e�g�)y�"�Qw���%ing}һI��..1/~� &)" � (0)$.�toei%Situ���!!�5�c comsuo|d�:^� 2=t �M�]o6� 5--2.�-)�#5--35��4di�d� 5--4&2��F � 1.2" 7R| Q�T MUK_nIնXIQ��1��"&MNaE6�6O.�/ FI>EA�Qk�Yke��n_1:�&>� anA���n_2b�BEKo�`�'�?'�bdqM_u!�<_Ufd"�e�� �OU.!�$n_1$*n&�  help of8*>eq:ma�I 2}),&[w 3a$jeq:c1}) �L\fagP$n_2(1+1/c_1)/(n_2+n_ =1.77$. 5b�\:O � aa�b� c$  thXd��g�"�1�]a-p�%e!�6�6&�Ibaru\Ƥ%!�s !� ei^g!� �^�Q��0�"�by�7�]� 9'% E��g�sV� U,�e&�2�Y@ ���) us eF xVn�k infl"�2EhB�H+i`F o ��"� ��3�K ��7� � 7��As�� a���^Y.ieiofM �69(�" take,4A*V � �#�s �iA9oiNx J $$v�/�%�end! n�Y'X ��� 0 expla}iMM� m�black�vs a�e>R5�!3,6QSe0:1>� _� }Eh gray-c١�� ��)dG�rg�> o1  �i�5 �j �o�l bj  �l Nj Pjl �V>\!ٯ��!�! exƭ}� _vs_��J�Si����1��� V�d.U[6� a�al�A&%w&`BJ&0 (.�Eo'�5�fX Int*� E �� �{RLs 1�2mB��*M (c�xd�Y)&�i�A�C9�2fxo�E��b)�ie � Ɂ��e�:�6�2y��I�p"�s� I��__1^&] *Qt�Os u!%�BymvP!d�&�-")j�-uo�x" m erGtP",Q, um&~�4Zb��W� i�;A��)%�� 9--16�]*f"7&# � �*��I@F����rmJz2'Y���A�E�_�v_5��~ 2���2���Es�.�]+a�zud�$Ay%�*�= �w%�w.^��DR��.Tin�� 1Vz�� 2:|2b�qM�93})Ew�n��V�"<a & ��1�iypA��kFIR3Be� �cou8<.xk� ��A�u� u�. + 9$&G!C!� V5Bգ *}� &�?~g��Zi"�a.:��7>6���1� � 2� �1RD�-��5N�!I�2anq4�2v2F��e.C}�3 3A�q-�ga�Z�ya.f-���-1tTe6M�:ak]�.Kq�!<>�R�ga>Z8A{r dr��_c��0�� �2�2"�!D�s�r!S!�rd�c1:]%.�"a �"�*�"a["3���"9.�"�� %"�6%�#& :s;9|.; �%%� ��(ll�9�:�ƒE>�2��P%�=2��2�5��Q����.�Z�a���F�� , :�r�'E4!�$�E1$--15:w�w 5$--40�V^�2��% ex_dAl��)�^9�z�?�"2�.�!"�a2�e #":OeoDEaivy�t�+3!P�)t�u��O* !p&! profz+��v,6��F��:�% "�|/��t vil%(bitrarily c��11�@� ]%3� ���55�iDE�/AdZ� (inspiZvby)Z�="�NN *nz=Aˡ� (EX)!G| I"� a,+�w�Uc y (EC)��e@ �.h�A!9(�)���v$�?&@$B2�Ryberg ?% Immeo;e�� fterF� a nu�u wa |�>�0+"0 fs)!��"!#E*B�"A,��it9�-6towards�}�!~�YiH$Ni"�y�[A��� 2 f�N<4 fs; a1�Nw���� to DR. Du�<�ul1&�:_ loo!��y &5�"�evny8autoionize (AI)gN�C)�,BKd to ei$:zor EX%��� shadQ6 K R(Frank-Condo'+!�5�X# emis��=5A!4�{�3�t�7gas_aC�0�v��2��*�>.w ; ; <�9$p_v$*�lMi���o9y,$pP�in7,����2e��e�ړSb�X@n�r� !_ [*g!o!�})]56�e ��Eqs"�"�(}�%ĀIalu�A,���� �\stF^gh ��}$  C|cat�/Sr�?5��thirt.΋ vH�(($J=0$--29)� .C�= �dNE�*"�[��set!� $n_gi�.3W �+* �n�A* =!J! =on fiel� F=yI!�u �NeO&8��i22� � 26�.�}.zhc'f�o��.�!@ ion-2��aeQ@'6�>V+?�G@:�A�a��:��?�I.�($T $)1�wEra��A8�$\beta$@Y#!DRނ��[.�"��}U# q�;3]ND($\gamma_{1\!-\!3}�on�.p,4.7}�� Nc�  =A�e_�fO &SJc6b� �gm>$&�@ pQ*�A�)es�.�e�sU�j��A6�A�h"� �.57-�1e=�M.��7.1%e��{�0�#�vA�b)2��&}CFvx�C %on plus}Slˡ�����a-�v�xb��Q�U rot_%�1})--I#Q# #�0c��an!�.V�F_0=&�> {-13-X2$�B-7�AX��-1&�� &�B.T%�.LQ '�K���g�YaE�.D:5�}C �e"\x��r��emHu$Uus mderiv��E6B�7� 9�S9�;��e�y[ك0�~� %�S2s���y"y"2y".�Model"jKA�-%Wio�#r &  k �"�6u6;��w�3a{otJ$F=�9�6Onl^k�  v = 0EoYa�itossuE��jwͬ7f#��� 5?!�(,N�@�'r�� �$r%<"S&fe�!x2��of' ]�5_})i]$B�ьhP$s�1}%�!+ $b=1�ei$ ta�*}Masz$(f_g k� DE}^g +���EkE}(0)) N_i$�G�d f_g=0.044�3.H=$qW 506 �0�"�6b =8.7h ��4dO �1�'�8��R�F A���� ��8(�q 0$).>(Am;~*_rA�)�qJ�}���HrI�m� uced�:׆�I�%��) ^�V~'bea�)9"in"�,�N.�,��A�P� 5-2�!�5-4 s)�l14~, Russia�$date{\toda�VHab�nct} Aa��o�Ome�(E1���of�372� .r"� 驅$9�ic.��lper�.`Fh!�ur-�:��ingh fߣ,�" �:A7 {,�� well��h!�tMQ��Za#�s� �T�i��approxi�RA�"� . Fur�,, symmetric � non-��chݞ(SEC, N�J[intro� �"9�� �"�D]4�P� {$fixed s%�& $He$�u�9�. ��car5u���a w�$�p>9i$ aincidB;e "i��6vӔ�R��.thresh�Q �.�origiX? rich.�\"�U>cer�6a sWdiscuss�H�. 1>yF \�l�{36.10.-k, 25.43.+t, 34.90.+q} \mak��le�B /@�} %�brge\bf �'\\'a % %2)$^ae>�$^b$}\\1\� \em 0�w��!�r3 %�4,a%{ >�a����q 1890����!I�?55\vs�b 6mm}� B " �ImdA�} O"y� @�im�1sa�suc� �Ii�ad�� few���b�i� �Y prec96��3*���Ee��� liv"W���Jh (!3W"ver�� see~�\yamazakiT�W"Ke�y h��X<�"8!��sFBtreme�,7��@�+%�!:ove�  of�+er�e&funda!A��alŢ�s�k  relev�p$�r[ a� thes�F ���G 3 iderO� ���@uracy�t A-���� 0�oba� '�*��metast ��,�Xac�U&�4�Wang�_ gwum $Ji|''*M''��� F1�����A�E gU"�&!} \bar :`+�`4He \ACrighta�> (^ /,)_{Jv} + e^-��`� exT�ng.1~�%�N� in ��M�koren1,2,�^#�ba�von � E*o;�mi �$ach�Qthes�ĥ addresil �7!#�!Kaall�, (3\%)A�4delayed annihi��DQ3w�W6�ri?roma� ASACUSAA��@ �  }, h��y�G��4U �� =2 ��wof&c N|c9�imE�o [ $yU^f� !��]�~I�1>�. M,E���!G�$Jk ,�)roblem, /�lU�cE� ion~  5}5a��yon] scop�����,| Ya���� r7� vaileƑ�i�� �A� . Sti)�w��n���-\J�, though*( e,.c��x^p�ss= ll}meg� senJ�at�^ de��exfreedom��5��l�Fŧ��cd+��q:* weC, Brue�)�)��o��{* �})��C��. 2�a�/if,-*S  $(J,v)�1%J�  be wrQn� ��fEs#int}  ��= 2�l(2\pi)^4 \,\frac{K_f}{K_i}\,�j_imu_f\� d\Omega_{f f��%R \;\;�6W�u $xr}_i$�I3�ex=sGAP�%%�he��$u��%0$i$-th"�, UR-�R9�� nd $�$��$b��Jacobiaa�J��Ts,&� � $He- o �mass:FI�! =fci� 6OA�%JR}; 1w =m m_{ �}} +meJa,�.NA�$��!%1��9�reZ��g;Ve/ w<�#�> ively. In�횅)iU�R�$ote�  I�r6�,A?l& 6hF}) $��9.d M����, vch�Hd a Born-Oppenheime�Em� ;},re�J͜wfpHePhz�y�=�\c5PR)}{R}\, Y_{JM}(\hat{e�; \varp) 1� }^{(2,-1)f5;Mq)F7�V$NT (Z_1,Z_2�X%wa �m12�, descri�7a�q (^)� ) mo� �� &�wox ges $�$, �� �(a� ) $R$R�eft(-�w2} ڸ_{\uSsty��bf{r}+ ,Z_�r + 2}{|%[ r} -q�|}��) Z�.[ ?5� \;�; !�epsilon�"�!�9�R-(EYn`Fay$.|%�!�heavy-� -r�'1�:�cm1.� $({}~���{p}�e^-)$ >0�f���0R��ukh�c):�� � [-� d^2}{dR^2!�)�J(J+1a}� ] - 2e�;+�!w5�J�(R) - E_{J,v6}��,\� \��1{S\��*D4wf:l al �!� $-�$�m~ .V��index.wg� be o�{O)�apaperF �b$WA#$He!�$2d.5 &�#&�,� Eq.~� E�� � obv2O =,n]~e ��C\#2�`�x snlf03�N} V_f =�,9�m�_2�1y�_22�+�5p .$1$r}_2|e , FSto�"��"B i�� g0 �y tako (an $r_1 \Lo=dftr&� r_2$&���J $(S=0e�cOG2!�froS�� -*B�7f��f �*��aia5đ[sO0 ekstein}.+%g�a>0�)Bv��!�2�V�\�"�vrexawermxmatrixAi�s"� >� eigen%Xw/F# E�sum  � �\,��\ \sum_{J_t,l} (2 J_t + !x, |M�tl}^! }|^2B�ithb�m�2B� ��[�� R2aQŝK_f,lf� _2)]_{M_t �9 |� a�\, -s ,�\,�,9n2 n� &� ��J_ ( [\,]_M^J�qndI3 �9pTM,� sb��a�s^�!��m>t $J_t$F$�#� E� $$ -�He!_=0V� %-�i,J_t (R}6�R�$-l +r}*� � ��/def�eB�R N.L sqrt{�\2}{\pi 4 j_l(Kr) Y_{lm" r}) .LItq���� B,.<a�,�+me_LE&gi����� iN> ��@P���X"$)�B�- ^��+on%�o�5al"C $l!�� awayo:�0g�1v.of.� e��fV�or>#o�to@ Ril�replac��x6���iH�`K}_i}$�Jwa3ic%RcF/Y�&A�� ��[C�n ide���fل�� a ''[a '' (&�(f >�) *=� -P(he6~ZP�� $ inJ=�m>T;� :. �ghe\JIJ6� T case�;+�DimpA��EaCof�wf*� He}( _1, 2a�N�7exp{(- � (�+�))F��3�& =27/���e? bookrbethe}%� spit�e �N or!/l=��� 6�!AIe�*#� s, d�X3&D�*6T,!Hh��MZ� 2n�t'#st abA r. �*� �pAY�-~1f"��%����confirm2�A�2�s�@A��-en &��M%pCm��9 on �!�( ta�t�Ƶ�in-�our*} re7wo�ic�uba9[^ -���|�-�# (rces: ---н�$ ''feels''.O �� $ X" , it t, 4ref����2�ijW\a��nM;Z�)~mod,�� A� � �E�a9�ً.QAOlh�EAC�ir6���tbem\i*'!� o me�1Qreq��� ,   1b�w,%�2 type�2kaS6'�j�psc1 � ^i \% x %y He2>t h !-z~*s, �{ ZRb4: "���56["� .�6�%qTEA�QY� enc��a�,B9 unit�rge (t2�&=a�$kM:��f��2� r} \�cal{H}u !'�}�2 Z.=*3�AB� $$p%tf�= �� ��1}�- -, "� r=&4r j  + DR$RCNF6t;!� TE�Q I�R� �"�E>n &� �AO"�(6�"�>f=VHepbL�VA0PY/_"F�vaB(R)B�"J��.����J� Rg.� M�&~f�A�I��K_i. 2 \mG;j9B�?� ��acCLp&��t task1�*P! &� }�)� ua��� J~�Zwo �����r�*-�2g2=*| stea�Hk"Ca cumber �U� &�+�� "ahl�)s,gibbs}X �Ag&%�MN�t&o0z(by Briggs, �la��A�4Solov'ev (BGS){b,},&�g to �YA�=c*J .c� s�!��8� F$�5Qle"�+�6Ro2;^? )A�a20phi^{(Z_{11},2})m��z<202 0220٪B�Z'a��\�/a�i@Z_{i1}�*? {i2}&S-��m�*B^�F�i2�.�F?)0i) 92;�Z>!A{A=  (R)$as*l]Sn�%�N�� ERme�l2#�� �2R��B#2�R)F�In��?)t܂� �&�7�8Y�Von $|ŀA�- 2|�:�E"�=!}�� suit�%h��!P�8�+M/a)�12}, Z_.�$. %BGS "�o�� $ 5�) ; HF$�ch n< at %��.1� [ ? �C�p/A$"� n��Nse+d*i��2�76���3�/��6&� �a����I]~�s %$RmJa *0 �6\infty�][� ;5,i�&$H-�� %��tom}7u���) ed: Jz�F�''seen''�6f, ! 11:�, !�Q�x��lgU�_7)~� bBy�'�0&�9"1��:k��-$%���J? �Znulin8x�L(60�k,E_{gs}(H^-),�"�Q��2ZID.8e��Fm�A�$g(�E��Tful%Kfor� narr�4\no &{}&i�= 2.0�K(antom{441} "2}=-1"\�z1}A21}�; 3444Di�6 1095"� ���Jm -�.V given by~��� ). %�u6+#var"O w of�A } %re�b�*5 . A�e�2��'e���s� i��s�rxi�2�4 way�=a92Z*��4/�_�**, 199��  = N���)[E�� ^ �+/" Ww.�|&Q �� &� t]a3i�phiNEC"A1AT�>�"i.aD�1�c�? he ��:��r�%� plausibl�D" A7* fY<s�٥�''Unbo���s:��11�aP1r 2 �} � {-s !�El�(u;���R]>s��WJr@� Q��B� !%s�\fi; qual� � ��!:�6��AP^.� � �$$�N#��get��u_ �"��z2}�1��70F�0.9776��@A;F�2 is v����7Opre�! o�� mayb/$little clo@� +''quasi- ''2�0?U� ���� jt�4t u��ll�SEC (Sl9Xy Ch )D3 �>r� �N5N2�9E"F 9~A2� _�6yb� phiSe��� T�'J; �BH� I@02x�C6�+%%%� wB�xyR=0.4,�.=-9ˍ Z"WD��(genius.fig}!j,%��.��6ic�!�2X %"Ys.�nk2i&��.f�]icuy B�AE!�Nk;A7:� Ao�O!#1��e܄&�!��t Jt *s (�3� A {���l}B��G5 A. shown ojp~P =5. IARe � �7%�{#2h� �iF�_55�y>�#� !�aX͏m2��i� �� ����H�mw)]V pF*!6�>�(R�� � $af�1:0(si^{iJ_tM_t*K_i�_1}� R})=>12'"�&��#_��2R} ,_#�R)\; B1&zS&.(g.� *�+�?m[phi�e� $ do��� anyZ|:!�y�$%\"� J^2=�, l�. +L_{�!.�J� �w J� ��en ��8+!^ka^2�*T0!3L xR Q,lyf>�"+:�$ satisf"t�!�j�k�� khiK�BFN�*2\mu{\w sf V1(!J_{\,t}!� + A*�*ac�#U-�i0>�%G�� 2�&�b� efpo}5�_{2�=�J_t(J_tN+� S++2� �\;B�To�ve*5):)!X<O+� eB;"E`F$&�  cHfivS��*}"behavi��!,y5}(� � ~�6&��1X/R)%Fop{:�;}\�s_{R \to� #)^Z_1�} ~Z_"X!�[= O(R^{-4})>�Ntyou�.�&�an�m�)~� VRV.o-�����^2+� 21} ��2+�2F�kr� Drop�z!�iO�h>cnO term�� ���� '&sympt��� �Wx a��-$�%V��"yy�# as}=-(:�&�F�C_��s A�)�T $ �z1}./z2 ��! conc�� �# 6��$��re�YASEC� t�ءz)e�}t �� � ity,a�coursm"�� $1/R$)ii�&9P:�=>,} c�}Reu ���u�!�a�L/d �S�*B$� n@>� he%a�� y�on �lB\ !e &<& ��rifugal��K#pthominimar~he�-"  b�'rs� @hy�an�;(�~�7� Eg �-Eong1<]so low ��y z JM$"� s.� + b9 65:: >�c9 :�*� Z�sw0at�:nĘ� t+m&k/� Acc" m*q�&��j&�#sol�Ce�!�]�"�1%N��J����$\cos \delt:.�+K_i) F .}(\etaz R)+\sinF*GB)\;B+ �" U�^ :.M8�Ba4�F C�6r ��4ith Sommerfeld?��J6etaBZ_�p�"�{$B$�!�ph� shif ,)A����mz U�. A�_InurA")�F0� b=ary��MikhI� :[0 $�,^y6� #s�>�,)��b�C�'N��;g�Pn. en�D�&ulaFR;6zzi\ i \2{R3(!� Disc�Lon�Lb.��fO7�N0RQ��LFJv�F7L� #Jvm K_i�._tA�� S_l>;se� paM��end�BW�.r"{�2!�5vI�<�' $Mn J,l30nd&�# �L1�&�2j�Mn5 2` \simg t�"Jvs $S_l(R;K_f)!H�!N�dR fB1�2%u:D�S6�">+:�"�Ms�"+Mi5<s�/"8�M�"�), \�ec<C "�A � �n.Ls ''allT6''� t����q�K6jdee��"N�"O"Mc&�>,"(0vblu�R+�sb�� o��a�"~ quan&ݟB,u�eE(D,�usefulL it+,s�M]�ba�+�0�(�9I��A�R | � �aBentE I`�6�ywoW$9`2�g lhd smoothW�pe~3MG�drg:Ts��Q�g, �Kde *"�$l$� he B~1 Fl1�a_�l'VO! I7ie�%nJ%�=e�.�~k ��. T!�fe��2��� Epre)�*٩l s a 6�(*"(*�9"��3�E V�d,.R )�u��%' 1d"���2��F�6>Lj�60 EsNEC�<E�PH�AS.�� �8_ �&�3%s�QEBr We�r�/,2U`"j C04t?vf�t20�,9�� ~b�%Y& �A�HQH$E_{lab}=30.8\; eV$AZe�Ohe^&A�SEC>�$\�)�E� �i6 sM�6s,I� S-�}EmY�S�g(Y�r�gDcx��p�s� 0�&e1y. All �9�'"�NinQ-�a_0^2$,  .�<j ic length0)8m��m�BO/�"7 ��ra!����U 6 �g>%6H��I�%�,�.  Obly���O� M?Y�&�2m (0(-2.9036 a.u.D�a p��ve $Q� , s�8��L�]� a47 rary�} e85�,����U!!06 �:�IE,�/;�"jP pene�� R ik3!��G��a uQdu"09 sub- ���� I�1s(igi�w""Y�|A�iona �GI9k 8phxGo�,"g 4a large amplit�Xude, leading to sharp resonances in the cross sections. In order to clarify the origin of6Tse peaks, we looked atD energy dependence 3l phase shifts $\delta_{J_t}$#pEq.~(\ref{khiRinf}). On Fig.~Xdifdels.fig} we plottedv(quantity $d.Z((E)/dE$ ---'so call5 ime delay8which for isolaW.+0s very simila!Nhmore familiar Breit-Wigner 6Wl curve. It can be seen, thatuall angu]4momenta $J_t$ � �hthe potential has a barrierJere inarrow� ?is corre �with a  sponE&!�Uapture6� . A given6 �X may contain several of�Y/6q,to different �4 and $l$ value�ntributM�formaA� of a �Dfinal state, accor�t)�sum�Y`sigmasumAa In gA�al, it!%interesq to noU%�in� rast\a commo!� lief%�mofRm] not dominAb biZ�$s$-electron emission $(J=J_t,l=0)$ term,!K $p.s practiA�y alwaya�hile A/$d.,�er%�cas.]he significantly. The reason!r this%�be�at^dec$e�,$S_l(R;K_f)$I] grow!�!�couldA� ''compens!'' -possibila� of lower eM,�yeff��v}I,A|$less repul!I�usab �a� penetrQI0 $\chi_{K_i}^��inM?E�Cior region. %\begin{figure} %includegraphics[scale=0.4,angle=-90]{bae�0_last.eps} %\ad$ion{\label#��%�heights iE�veq���58 %$He - \bar p$�0s.qend� :�\^�65,� fig6 �>�.� Ti�_s%�y�m��ota>�um�, NEC� SECI�.} 2�A�V��,s apart frome8���A+rr�� to quasi-�Cionary  4es, show anoth�g much broa�!K,aV some �4 superposed on.xoneaWis $ is connec�iw�� speca� behavAp of eA.$ic scatteraOwhe X��gy�Uclose� the �"maximum;�؁$ ed ''orbi��D''~\cite{newton}. %S.��Dincid���a (R)$:� �-a> mes �!|ec�Fc��� a�� llusa�ed!c&khieve$.��:�7V�[ %I~�s (in a!M(rary units)6� %�ies)��:�. �q%Qtheir.��@1� ��CM��Eselinei�!�6�eF)%� chosAwo��resAu� �M�^�a.\newn( a) -- sub-1 non-m tM/; bB'B#c#.�: �y29Qa; d;above�%%y. :g F&^-�$higher $J$>�releva�N�ha7no1� �\V plJ9 4: a steep rise �%� threshold�!t�an expon decay< ��iesI.+f| ��B E�in��{D K haz eris��� both�-�s6� -�-嚕�sis du�� k8ly rapid oscill���^�鯅q� :�/reduc%8 �{�. gral>& Mint})� U um number:� "K 2@ �!�nW��vconst��%��2Ji�sw� s�kd pari� (makes sense��5>�8V�� C�-sb onIA� $st few vib> al:& s $v� �!AD>Ci��(6�lcu-�)���againu  r�� pal :� $N=J+v+1$>( \ �{Co�  Ls} To our knowledge�i%�hfir� ully�mechann �N�QQprocess~�react}),��addegreeE�freed�akee�licitlyA�o� unti�adiabaad2�s udetfor inian* A/emb@ � aba^eale� eresultsE�!atJ� treat�A�Bly ne�ary, e�am� low-�5y= ,M܍ *� ���ce� s�~es�qial � RFacM=ed6�s�i �!�Y�2+$(J,v)$ tx d��a large!�ba� ����atively _ windowQA�>< �.zM�lQ{propertF0 %�!�s!� ��f��� 1��  hand�e s\g |F; :�preventAeA mak�fAs abou�xperi%� observabl�ypm� �CE�9~O s si!��Q�)$ dis�o�#&� s bef�� c�is una� n. E�i��d.Lwase�e ��nd.FpF��deviate͹ colli�Wal (or)~) de-6� �m���$rval betwed � ��measur%y. NZthe�L plana���-2 prim� �s t-�� trLJo��=q . I} discu�of�G�CwViberatel!�d��� aW !doncernAS�.approxi��"�!�struc�of��:�( �- i6$ �4��, how!V,m�"nsider�/e�r:&,a�b ����w�A 4 att) )�7�N . We per��Fthinka�at5is phys��ly�����,�@!Mco�vzSEC's �>ronic)��y� t� !K(recent vari�]a2�*gibbs}.� as�fir)���4point_view. %b�4ia�4�q��tes�� by %E��V,zbe,EGon�&!s �i���"�ac��ہ�s} On�!%0authors (JR) )essuppo<HOTKA grants T037991E[T042671��ile (NVSEUgA�ful!Nhospita� extda�C � DResearch Institute>Particlep Nuclear PEa�' ? "�%!o� work'b�Xd�e�dwish to thank A.T. Kruppa }proviHhemI.o9B�� �(uter codes.�9T-}!�ibliog'y{ �} 0 docu*} %�  ��MMB \�Tclass[12pt,a4paper]{ioA�P} \usepackage[dvips]{�icx} . {bm}�Y$} \title{E"L fiel�ory1��� two-d�ɋ �sma} \I�{M A V` Basagoiti} \address{De�a!�(o de F\'\i _X Te\'orica, UniversidadC Pa ' Vasco, AEpdo 644, E-48080 Bilbao, Spain�Pead{wtpvabam@lg.ehu.e� ,\date{\todayA"bqab ct} U^techniq+5f./�+� ��e �modynam%?~ �of Na dila�:[-Z 征y4ng via a $1/r$�"�. �Q one-loop @i!5i�)"ZisK�  ga�Ź2<�`a��dTal model in many-bodyQETa-��cur�&� pa. El�s trapp&5$liquid-helAo�ar�� fin%Ovic�� a j-� Ya semico����ins�9 or "� layeB�.=�xa��>a 5cI�s m$Ando}. At�tempera�e�_ameS 4$n \lambda^2$ � �A�Eie g � )" +�ء� ^de)Bdby $g=2\pi n \beta^2 e^4$ &�zes VstrengtE��g.s A�$ �$ot �u al�l H� $e$ApA�Y�1Cic�ge� unz ized��ts. F2on a M>filO��� variIHrange]<$10^5$ cm$^{-2}$�9 |t��low ]�it� ear!�%U�� �J>CQ8�]%Y(Esa� milli[Kelvi�!,$T \sim 1$ K%e�,5 < n < 10^6�Iy �MP��]. �$1.7 < gC7$�%far)5!Ddom�!of weakU{.T� , � +ly pursu��� advocq ţ�Ź, H� a��>Lmulti*3 �U� ng � �Q�.�  FG �p%e��%.�, �&�� �J� A�jRuEe- n�$v���qui renorm� �. ��$� �D �h|d�L� vali[�Y�� 2�1�wiٝ� \llAa�$g  �"� ingrediR� �����"P coeffic 1��B� �e�\*� ��d�7m��!2AM�short- )��r!uJP# �m� �� B� %E�N l��peU(TcisA��I"%��R�, expl�ngY*� �>� �eU�Green's���  ��i ! .� 1re%�c IU! numeYc�">t6� urz��" �Fe�"\,Chalupa,Totsuji,Chester�8 �N }� orAn� 5Xr�n��ceq #} \frac{��0 p}{n} - 1 = 0g}{4} \ln g +��h\,\left(2\gamma_{\mathrm{E} E+982 \right)+ O(g^a2n^2 g, g, g^2),A �!m- � }��Te � QB.P͎y�U!�kinet y asvE�c}}!=))1u-2/2V/2�/ \ldo��Y9T�kex�"� s aZ}b� �i�s �eq:5})E� �na}�#!('s) #l1X� n 2��=- pair N ged�cl�p��=e��  �  Ui�,�7, $\etaA��  e^2/z  \gg 1��H�� e will�w below,%+a��14d�* imp1��@to�is ��ey�/�SFr '$g &&$%�$�� term�/^2$ re�e m�%�M�� �0I+ relihbecau'� must��c J�\E"�%�t� � .��c�+�9Swe�\f�tm]�A?$g^n (�I )^n$N.�-tJ7iC!/eq:�/ log}�"��.tar� d!�followR!W/sec:one!�}�brief%���6u�&� )@ J�A �)��wri>�N��0 B�+S�o�M�}q @);5��!d�.o� ted(�-�tY�level@�d!I�: �>��o� F�g%Bg�}a� devoA�T'" �-, �.�y!�*#&,�9F�ya�rt1cl #���en��/e�YYlu�Da�le��Q �nbasic� ula�J�a�lns��\ endix. ��N� B�2OQ�di\**3>��WAT"� �of *� pec)� %��E[A throA!/�G on�h C, mass,�"o4i$a�"dew�I($e_{a}$, $m :� [(r� con�!:V� v }N'w�3�$u,ly�W��&� limitiB�$-�= Y�m �' a ga` an!@$f_a^0(\bm{p})=e^�(\mu_a} e^{-�p^2/2m_�F �:��Aztwo&*� $nj= g_a_af e v$� . JH � _a= ) : f Chbar^2}{�' ^{1/2�*��}�cnC��e6H3 g_a, �I! :�3de_!cy��ch�al.�A�s%�assumA+���@��na���Fou�4�ns� �tpo�4�lwo "�!�FY \T d^2A r}� !�i k}\cdot r}} }{r� !|}{k} \,,>V \2��s o+�stee�on6�$\nu$I�&.CJ�V_{\nu}E�r}- �')� �Id^\nuk}}{(�)} e^{2�>N} 4�= \G� .|\nu-1}� � <\pi^{(1-\nu)/2}||�|^{ }\,.>.As usual"�abs�7anye�&�lntinuhic/ce�+ $5&J bf{0})M4ll� A$o" zeroC h�7c�&,at $\sqrt{-\�(a^2}/)H"]in�e ��MI�I~=� ��!d,?#a� �$��;�% a ��7 tur� a(a Hubbard-S�0 onov� trm�M"~4�8�,Fa�eq:0} \!B,cal{Z}(\mu)=rm{Det}�cE[M[��:=}i2I.] I�ZD}\phiM�) \exp��-S*7 l}}[);\mu]��F�"� � *�al!�!]�bo� ic}�$^$� "�B�9 _B f�=�d�Rr} %.\{./aI }1MZF=.- \su� n��� r}) a�)��2a-�\�2�5� �6M ���}$.�C":�g��!�a�og1�< Debye-H\"uckee2\` Herek9`$h'ven��r>aF�s � e%�$ am�' up@9��$8 us�al.� E|*�2$��1$ 0pr���� I;.�"i\� j�%hl} K_{abNQM'=^2\lnuzm�}{ I.2�>b �')B; S"+�7� ���9���ANL �isF� m_a e_a W  = 0,��2�  e�=0$� c9�s�olu%uA�q:� and,equentl�]Z �NA8bx)turj/�-&=F sadd�,� expae% aH!�tr��mS quad�c� ���,a?�$qg��;} S_{0.JB��}\{�\=1}^A�` +dE-B� <[ #F� \pi}�f.kappa�6!2���\} Bk i:��D�� d0\�vFp���;EQ^2 ES$AP� A�re���  � "� 1�=�N��9A0,ra} \Delta S��= -�d�bm� ��2�)e\{v�-1j)i1)�����22f^2 5iB�  T &�i$�E� �� c2v,$e*`% quan4%��5  3(%U�! bU ta[.�C�s�r&�ca I.8; $^{-1}$ or�r2�"sadd� ���1'���"�iy})�� sub-U�@rr@�4� a�-v20n p�>%$( � \Aw���)� ���s�Amx9rom��%Zc�-Ihc�;�-B-���[y-6 �M)qatGvanis�'�k}�5< ���c�3�'� ��Lhe Maxwell-Boltzmann �!���EV�(J� \P (k},\omega=0�7 mՍ7 V (1 -I�-C ^2 k24�w�M�)�36= � piec�  /#&!�lj}�usc"ing��B1�Uc nextEi yield�"���sU= �#arA}�7 cle-�! j�Z� F^��� -T{0��)" }{96� u  A�)! ..Ji�u  mUmadA� nsis�i��inG!QI� 1FalA�or!=,si�aneou�st3;F��r a�D�- i cI�� {a #mu-�" catCon6�i%"� %_�5 �,��% A&��j��1} .j ind}}v)��=�0}:H\,�9� %��a#48e#� [,)��-1� + iT !R)j� ]^2 2"�f� J� �61*Qiw�8D."Y4f�ing�safe������-�J��.scribuA� ^nI_T r. "�'�"&i �is� �H"� ��Х0�f2� ultr�A let �e' �G�B�p,8i $%bul�ory� �g.`m�l$\ln(�;0 /#"�ab0a 6� i�*&.b�5mFoN re�Hi�",��(-c�:er��or al� �mum)$ �<� �#ލ�� p.a[cG�.r+ r\3c!�% �1�ce.�pr�!�ue1*N"Fg%*f"b, �C� �Fcw�of�!E,^ �!�u�%��mL%.Qis>+� jus�+A("G<�/�)� "�B�. d"t,( P� par2(�/>v ��=r�6�4s :��2� ir a2Jge:� �?` S isi2� $g=� Q���2YK.,��r�E�EW�A ��1�&direc!p6�!&g ��, �6 playA�an imA���rolaM�e%#"��e -nDBohr radius $(e^2 ;b})! or,� ival�� bi�K6 $e^4 9/2$Ew.�� )hih�d n<bI �vl oppos�� .w e Bu$$G_\np"r,IU�x#!9\h �Zc&� ,!%�F�_of Stru*�FpN� bf{H � B�&l" ^e ,A�d $Y$a�B� R�=��f� !�Y��k5"�+Q�}�VNC�� >�)B�w��F�2Fr� �2Ynu/�#120� ^Yr20/2}}{\cos(\pi;)B[9�_^/2}ىr) - YZ�]J "�.�:lAB�&�G0} -�M 0}�s2^ ��i �2�-1�n( �y+n�nu} B�W!�3,���K&�?o�.��* ��/ A}m#e�>� % ���i;by�be�Leqn7"y"'l2r}�&A}} &=&�� -���A}}�� \� [1� 1}{\>y1g� �] \no3  \\ J~I�1�}{D !�\,J�&� �� �v�塲nQ�#"1!4��;�j ulaBt � 5N-� �q��q�k�K r} Ge]�-F-{0�.V� 2u�2i�R|L �)�~ 2: ,"uA�5 o�,>�,R� . To���in\S ��.2 &.�, p�D8PFQ ��2"�is�%!�uhe6B � be� ��'B��9�� ,!b&&nd�M�re�x$o �c� �*� ���-�� 2Bq���2V�2N� , b} \nu i�bf r}\, � ,^2 g_{a b}^01���� �(Q� r})}:$qM�#F�Z!9� of $�y$jgab0} *>muŸ-2}��m*p%�e_b^2 � ���� Hb":�Ju� }-�s�J4����TZ}�m�� $G_25: e:=� �) inI�aP�J� c< 1C�$ 6rve its*� A��=2$�  )Oe�.�eX2P� Jl�A volv� " an:$*�I$ e at2E;s,��n3�necce�Ha��dl�G���yon�y��� expu;�&Tdphi&�  crucia#e :�1#UupK �Ca�6�,B� 'd}{d\mu}2��.:�A�BPgua�Be%o��hP $72\yd, � imu$. B� "�,�� Ln� muab�.Tb�47n\:P%a�2�uJ�+B� .%!��co��D$?a,7ќ J��>` m��plest waEn>e�:x2&�zA�to5"0�!�a6Ma�A�V�?8 $\widetilde{K}�� kq#Z�� e 6�2��R��m�:oTur� ��"��ys6Q6 fNieto}��vid�Q� �9(.&�  zero.{  �&#*�q��eI�>VW{j-1�O�>HWfig&�-O diagram0c�@o D!9irB)izK�V.�C>�-�:&M9EH{ c re�Lr>�B8>�O�Y y&|J�*�*E�82�*��b~(A��@ :=� �%)�GmF� fP=:�&, ��3  c e_c :;cau� ) \,�'KCjBk"k}�}  7 k}|+ PI �,{m n}e_m e_n>�mn�)JO �#r��,& R�qVr�'} C��&�()=-%F.<� /�[\over�{�};1#]jC# A-mu.D#�b |_ {:V=0Z\*c$n�H Ai�[�m�V . At2� rV =*1 c�':�'� � t/#2$M�^ rm{ }5�=--%�$ (no_ver $a$aNo���B� >+�� ^{6� $�Q*�5��1}�"�2})��� d �"� ^!�2�to R�5up%�}���`Y�i*� ��2I5u(1)j��1mb^0 +_�?�ne� e&�   DK)Q�-� J I�] -mM� }m }# mR}6�&-�#��a�H��g_{bcP�n_c^0��6 �k�  \,K �"� -m re:�� Jr$*_{\�#�-i �y*z)�#N[.3]Jy� "a�YN�� qJ ^�32+$J��\tadv..�'b^HofuL~y6]�) � Ba3�))�$� T.�Bl w/�"eslyakI�h�%\�_a� igno�� FN� sm�2"�*� T��FT, JU :� B9\flN=� �CFdq quiv�_V�U_:�1q-nua�a�� �/5 )^�$ "1�&+0ap &�-1)} k^H-2}F����HNN�6�3A*�#��&o �Cb_"�Z� o.!"�!1!�J� 9�m��lN �lJ� ��&�=P�]J�F]�\�1o .�0+e_b�16H \lo=�4)is��&�.6�%�8[ N�>+ � M�b64 Gd M/ ]+�/6 \}-r��&-���7N�7 R�7IDs}"MLB ��" (�"��to@*�Aʑp�c%�$�e)�0$&�M� s�J2u��fugac( &v,mq�) �)�.�FN�O$]d>��d6�9!u� � ��In�9�2� �e�e�PJ.2��"6�6� =ka+s :( ]A�[F_{+u� \pm (*+/q}) F_{-&=]"A)&|$\pm$ 0i�],YB�DL($+$) or Fermi ($-$)�$ I}6I spin.�7�*�9,A� +���4@wavRI�C� �9b}=< } b}/( +m!F"�*"C�hVE(� &�4ed)A�rix�3��"�(heat kernelA�YT)R �Hamilton�9$H��$g+mo� �l*���1� F_{\pm5�=�T�3 b8 i$ngle\�Q|)�  H%\} |\pm \B?le&S �2thJ� C&��:�?2!mb}@�de!|�8�u� "(��&� fplu�B"� fminin� �W&�-q�>})�!.d}) eJ(es�6�~<�"runS+dJ*a��mua�)�o%�.b}!:4}i� �&mu�(6�!f( C%�f�.�f}2a� 6], �.�2-:� %�Bz�$�)�b}�C�l.reb"$�C�j�>F� f ٩ɓ!r.��2(AVJ� �16���Hat�z A}}=�3"�s*!��0,bv a� %��!aI� )^2 !%� p6�\"���G) 1N�+�:%f��B���B�م �� N=�Y*�2XB� *�:F8 J�&�n}_�E%�0!bet�2\� ial} � _a} ��B��eli�p�N�7in favou� mean �!_A� $6�j� W..�3��3.�CI�weXj�} P = 6uM�1 +�"-=i E���- n}_b 1%oI�bMgY�:B :�SI�}_0��aMI� ) +J� N�1B��%=el =B��C �Aa���2� *u &� �ohe� 3\Ap wE$p=:r/%?$G s� ���'n�Z12A� p!�!�a:�+�!U6�6�6J��B��� +1 ��*:�!��~rna"�J$uL �Ris%^nEaB�u�6M��".*%V�+ -}�b6MaJ��X;B��} ��l' ta u^�� �.�Ō����-� �9��2�74�&� b}݊'M�R)� !96( .@=f'�bj% 2�2a}N�f�\a�sm!$4P_KE&l&�Di&�\ ��\�q"�� $\epsilon6L�* * !�"eA�&�5F�or� by iPr�L} zlN&;��)��gs�egfu�v� 2 !})a�ins/1d\foot�&{�p"�/�F-�G� is $��zn}�We�^2= 2}-�*ٸa}Q�LG!e!��H&� )���Q�M}��:ii �� T�m�?"� � ), neg.WAD�AANUA|aa}�G��ex�mge06^ex}��J�=�:Q"4���E_� rm{c}/n�NYK-MJ } `IOs� !]:��Y.�M�&QY{ !�g�O �:��bL*{N�p�(���s}% Il��of Pf;0�,�5�6��)�A���2 2Z"�,B#N,�! Tb~"D J�&�"3��>�&��o %�! M .�F.!�C.Q" (t <+ *Y V.iONB  �F5kG0}:��(�<*�Ferm J\B��=%�% 1"�2U� R� � �-�� b��� �2L �2<G A��+� $=2�T YQ)�QPq!tE�Ti 6�� �adi�ritten/3aidah5�C!�r�6�Z�I�ZI�� .% 2~!�.(N ���|�`�� � ��:��D$,+�)^2-V:+zes asX.u2/r$ri�ax<o���b���E?�+R�#/+� L2$�l�QaN�JR =NN��3C_2:F� $^1"I� "�J�F�je�p �!|r)Is2 q�2�)qJJlasympto�I*(d� h�oaV.� �X�a���Y1.�56B��3m� m~1�+ i�� j ^2\, r^3}�@:� �is�a�3XG+F�>��!�� = �B"-�E�v��V64�-��� F!We{#em �iz+a�MA�Se N�Aln(k^2I�decep�Cfact,P9exp�:.�We�� m�!�i�0$z*wi&atJ�^.�E�A&[1A�6�,k�-�1)M] MAtŦ*^O7�W(M/k} J+ O% F`0a�ic*�@� b>� :�I#M�c=��V5�2�F�in��m�[J& v)�� �"� �=-6�a/� �'$. �&I��3"�_ , ��"�  $&� .�" ��Lbe��+�O��&� hrZ�Y $n^0M8I��=n9�?+~R+�XR6qb� )/}�;coY"4��I`W>��2;A��,rGto�k(�� ��2le��pe��o1bxath�ib�h.!�h�5f!�`?*�[i-:0straighforwar�s +D2rc:�1cHH.�Y�"s"�[&2�( Ei%iRx1i_1Gi_n}^0$7�>%#i�Tv6! ougJ�>W)[+ *�Dn= 6{a6Y R56%A�b ^{2(n($QDi_16L {9�_� �>(n (FT�a�2>��B8e^{4 �$�/ �za nu=2pll�jI0� n_i!zexŌng�.u�7be mpanOhby�gact�dC��^4$8U�hA�W/XCO ŵ [J�0U:gT"�P>'Z�sJ"TA�m\�3_!Z:A<m�9 $n-1$ A�"��fb�ON�! I_{g_:��!E�$Q\�:- VPn(A@ m a JhA������$���!q7a�� �uɏ�v2()1��a*I �!.�{n!>A>26�$J(F: 59>I=-=-1J? 2FC �� 2G (e !� +i� )�*K4?�W \\�&{=$,�}�"6-(G\n=(F{n}��}� z� �n_ &V'&�1�4 w�;v�+ly> �V�~ Rb3a�2 V�A�b�)ZAa[���� a#:i!C-�Ci�$n-���$D"�L 7T�N �:1�� k)(G�< by $F�!U{e2� More�,�<�(6"�)zI. U�3t - ^� 2y M]�<�&ar*� m*I sm�%&�YA}} = e�"�% 8lO���u�(,b��2  �3%�3 �0���"��\pi��E^2 &D�i,c k46kn�3� pe_cLe_a+e_bS3J��^3}{1�An^3z�,d �6N�n_d^0J�e_d^2.� +e_c�+ :1�>#^ (H@/A��lofQ;A�.9p{�!1 *&.��ingZ(&8 (0,zE�)$U{,�  $z=���e^"� �B;cS} �N� &�!logA�a"U�V��6 �+. n^0�E�j��@\infty (-1)^j j!!~�o�� ?2,WH� y;[1�1}{z}�`�� . X)B((0,"Br ��at&� A!8in�Al%Z%!� ���A1/|al6�*3X,.W� p}*�:} *�o:&�z� -.^255%� ;' z}^3Nq1*� z}^4e*%^137B35 - 510656 + 434:K 7+O(2p8B�A� *'z}E�86� I��I�}_�6$.��(o'Z)W.��%��Q.�%�c�YF��$ 2 p ���nxK!�J�[%�zRlhWFl}�>�?��gui��P sh�mY�A�tecÃA�&�<+\!%�e��=� [P���\to��$qn�d�b�B� �B��� >.�i� ��3��u�3-� !& s(u��$Skv%QBdV�SB�Q~��\��Ad���.�sZ �%� lBh�Xitr*�r�F�qu�p.%$b�1a;��]B�/��.�F� satisfǐvQM�s�H� ��� .� 25�p�M'!A�.*%��Nqr)d>*Rlog&�A :2A���*E�%u\�{ v~Ac����e�s���$�p*{HG�$Ww����)l�A��S�sh Min���Scij� T�| ology (Gr�O4FPA 2002-02037�#K�`�Basqugyntry AP9/UPV00172.310-14497/R�s�b b� \()�7.�� ,q�}Ap��qCoVs:�5$}�CtcZD��}{1X9!L"�[>�BLe�n teRWarg#omiL�&ces $a,�%��MI{D�W2;x ���b�6H:of �&I8$�e-+��0��Pf�n>"$ $G = (H-E�WF� �6i�6 _{C} dE9a i}"�6E} ���6� *�6� }{H-En�6&� ; !�� $C$ encir�rclockw��$ut alo�H�'X�7;� $E$ ax8 nd"'wb��- 0�s�$e^2<��J�an attx. ��o�d���roI�al symmea�-��|���� on&2@ spac#@� F$*s"�j�Z� G%ad<$�Mܩ�sp8pU8c��^ofJ�B�"� dr Q" J(k r) XpNX p}'|�W�V1}q}C(k->,+:\%�;"^!$��F�2t;��G�;k,E�c>�EuBk��eq:gp 9�JH | �gpU/ '�l%�\�9Jp}'mm� _k�UNAF�)keN!@��*� �C+}�$ > $ԡd m m>ula 6i Nj$p}, �')x6���M�$0�>- CV�m5.َiNm)K��\Xn�. Dittrich}��]c n&eU��[chwing"�g}�'Let uc�mmarize.*_MceX�isB�&=S yΠɼ"�� B�%P�V%*�tg�/ ve (��>0$W;"v=<*J�,Z@)�L2m}-E ")B� +q�e-��.�'Y�-�_\p}''|} S''U$M�IM?1F Ba��� (conA�al)].86f ~�!��h":+euc��an >g:��!?"�߂uni���!.� n��.nv� p_{x�Z�p�;}{�;,cos \theta/2��%< \sin ! -� , p_{y�];.\gphi&�)�!elM a0 area1� �5.BUD�� he plan�t?NOF��fmedida�d\Omeg�:)8%M2![Z%Vp!>5I]�^Y$<=\ \2 m E}��6@�@]0�0Esx#neg�ge��$E�i�"�$w9$,tw-�oor�ޅA�%{2aoiQ$)=(I,�XEe '' ')$ onFA�1��<�� �u�}E:�h����sp}'�`y� �q2Ip%� ��|")4 4)Ձf(%�^2+p^2) '^�_ :d|^2B hnHc%��!hn $:@'|�$Kr7- �1}N�=Qa��^2� /2} '�u~{ jl,mJ5�*,l+1}Y_{l}^m(I) {m} '')^\astF����n�����e�Fx harmuxN8�� �- Tz�U� �j� �*!Q.!�>A�wfB\�,��ew�h.f8 mQV\,=�)�3:�� 9�)z��}{&��Jl+!�J�rk F �&�X�e}��B�}�f� ,&F!;r+. ��aL)� &V(�<0$�3� �:��!�6 B=�B�AEA�"<m� }{2(% )��.>w a��n step�to � x&js�&� � ndy"�2� )&.bJ�xoci)"�>N�� ��r"C�*; ro�)  of L�~dr!�lynomialN�1 2-2���� -a^2U I�=0"� �)2�-� P!j�1��|k3�_ "(\ ]J�-"�identifO�R�W(Q���p.��F��R:� i�_$4�1.�6-��� %�Y:�͗:�%�er�Ou&�>r&�=Y) �Seas�� i \U����f stud���kM�a�7Em a�&Fm�� -.�6l��gפ.&�"S7O �a�  $.4$,/%id=<$|\arg(1-z)|<\pi-�0|1-z|<1$ (see��e��, p 559A�2�)B1 j&.z = b�1nB�$(b)_n}{n!}E�,[ \psi(n+1)- b ln���] ^nFY*tUby"l&�cA Kb"��$n>'8�jJ�Z�q�iV)A�m - &��đ���١�}9 �J76 6 G.� + O(  �% )Jj 2x2�"Euler' �ba�$�Fo�/A�di�<��lso%9neeJLOF7:1 ��:c� ��q�Put� E1p�y ,ge�P,�:R; tA� $G��: F�oa]=f0AE� ���By q��@(, after sub} o�I�An�C- �r˝Yw͖}� 1iZ�= �{ p_0 k!��,m_p?En[ NT�-1+�*sk�c"*8 +�Cpsr���]+ O(k) 2�YV�Ce\{���y},mbda k (-t)}"�" pi y�2^2�e eft[Z�>3�x^� � m_ �. .6�� eft.�. -a_� �`R�\��-t}t l]+! \*�-�"�,tv beta E44�!�:wLu*� yu�2}DW�}:�eűF�j aKmn�r޴d)�tIeraX�Y�q�y U)-�m!$} \Left� �� �H��.6"�X-�l�� {&�4^KU!E"' "TU*�($-$)  ŎNoUa�5�0-t:<pu?.p�$t%��n"3 ~-(� , sOa":h� ���a`G-A�< t �k $0�t!Ow  It9��# �3 �y.T��� I�+(k)$��G,)��`� $yM����o !*N ]A��z $|y|$�hn%�- cuts%P2j�0!e��! $t=-� �Z$GA�C�PK.5&`,{Xa�J�B �B=�"uMi&�6t[4by %�rY QHankeld�"����s,z�N� , W$(z)� �_C�Ydt&� a�^{-z} �Wt}FB  �n��� .ۉzN� �EIz)}�^z�� -t)��2>s�J��FGz��&�@F_+�k�v^�a -t������ 6R2N�U��6A�"@Q + f(y�O]  k)&�� A�q� $9�� Y2�#V;Nhl E�A - 2Ff1� �U (3+n)/��-\7�! y�)�1= -2+IQ!^2f 3}-7!Y `3)!b% y)^3>x*�@#�e�ͱC"[orվ. Nś Bi~^*(bߠrɘ����a�I/$. ��!Z��-��?(�� _.�dlow�n*�,�0Z?�� d�5mGp+Kpa��H}�H,I w��'�>sidW4-�=!_A��|� �{Vt�e� �$�a�wM";vA��U.8��ftyR�quF.��X I��[F�JF�e< @q�}A{E��J!? �&ӭ1�N��!��s:�P��Z�$["�lg:*�@&&"8�àm&��!�Ŵ!�!�2L��inu�).=�n�&� sA[R(��I�dnoz?[2�on�ao �|�(L&���R~1m'�Im�eG�i u���<�[L� tanh�2uF$��n.Tk] Disc_ln����a!i�6��)��0Y�� �j>2�� vare R)- N-i .(�liac�7t~ �Z [-1-�v_6{��zt� � %6|�q/ FoY4F {[� , \;. t>�E|m�-O &|im} die%�8�< ��l ��c9eZ $y>e*6y.tud�B� ]>�$!�%p zpa� of.�Ϟ�L*� a'�do#9B�$&a�(B\ &&K y�.��  0�(IH" M?ex�5-t Eg2�ElFAQ@6W &&\q� simQAUx3}}�L3S y^{2/3A�k ZO w17}{362$1 �Dv,l#��Q�,�Ua.�����b�օ��"Q%f��� QYumB1W"�~{&U sn���des�K�� 6^"��)�-9�� .@ ve} 9� int_�q"� -J!���-!}t}})�=�%�܅K[} a�p!�2 �F-��� Of}� � 6�Q�+Y���n�-.� orig���, $-t7q��iy&R� ith ]<]$�14RA��yln �ڋ )3 Thf#A2��U$N�ma�6&��  u�z�'��O_����z�z!�m�15�)�B_{2 �6mX-2^{1-2nu��:2n}, \e�(%z# B�eX $ [& � Bernoulli19��&�t�%Iy �� T"� !*��ap�.kZ���� �9ar<lo"ɹ.��}QveT�*�6<u� I�b�:0A�!�B�M�[dm!ly �Ws � [ofOOJ��*}"Eup@s� �/TyR� b:-F[�z �{m� \�f[4R�-3 + %�)n y�.j��*׫:A-�rl��I��4Jg &�!e�~2}:e *w V� +1"�86d Y: $e}$)� . W�A^A��.~b}�c as $2� ��-bFN(��/ }k%�5�1��!v��+ 3N�!��1�?1�F�K2�3Ex�[.s>if�""\.3��non*�U�[TR1�RG.1*��Q!1-mgatYT0}T$���3G�l0�%1j�I=!�.8.&�6p},.N�0.�wA���8!�$�#R� �W.�% h$ �:@+?+,$!��O& "\++\p!�AD+ ����H.�7�$2.7F����L$x �&� m�%� a&s&�M$C f5A�O�_Lov#y1/&�&4:Z &\ �l�,V�"J�Et�"�.a��.B�-"� */2~z � l}J%BzXa�I�-?���+ E�1ɷ�I% 6�1BQ J�:�$ l + 1 + 2e}= 1}cc�N� k3�\Bu�&-&2>?ZR? F]F !�"�ng)TV�+42>,��(Fq y�5�m% �/�V�[�2���jVb &GMZg+�� �eAe same>q, �� msfH6M��6�g���?�X�d2\!a��7lm�>T&B��Bcosh}�%�2�z)(!oV�!=���Sa�.Edum#� z uUBw u/uf.�% (GRe�z > 0BW Wt y�%l�V��8"IA�{��$ ��F�h5I>BK��:�u^n�� �!#2 v�$ [�$n+1,1/4) - 3/4)�i >n > -B�&.� F s,a)6�#g�a�� Riema�y"� �s"2�<%�.rZx%T �� J;f{�F>7�7� �  -�{n&� �[�n-P1+n%P-O%O��I�]M�="M�\� \,� &G* {n+1F3s S���o%"I $fbta�Ǖ�9��5�s��toh(=*xZ f}(y�Fry��s>nry) �9-T.�B{=�+1}Z6- 4 C �^ pi^3!3}+ O(yRA��C���Catala �:5;Fin�2 "`:�  B&�QQ��he2�~"D �a})Z ' LaMn's潁* _�ysi��i_ Tayl�"' �:$j+e� 0���$oO,*F �=rg�b�� $u <!�!���b)7�(  -by-i��.�"��;��FhB�v "�1%3 a� >9Ym{ ex2�eE� [i���2J� �CX:�8b� ��\��\ 8By *{Re'�c �- the.S� }{99D|�*�H$} \bibitem   L S>4�L G�C1 {\it `�. Rep.}��(f 340} 1 %c,�A��V 4 T, Fowler A B^,Stern F 1982 \ Rev. Mod. f a54} 437�c�e   A L 1974 S�v.} B �10} 3739Ql�"b�JR5fR 2} 4)m 46f4(3} 2243 (er�&m)�k�+k H�8F\A �7} 39� este.3C  G�^ R C,�krava`�)� % G Vo9Fo-Q2!Q26�&�>�  %"6-�J.m~h:�} 160YD+?X   W 199 �Am.ZEMN67} 768�+�Q  Braa�hEE� AYJD)u51} 6990Z1[  witz M_Stegun Ib7m Handbook��MaH]�� Fu��s�T(New York: D&)�.5�> d"M�V��\%L[11pt]&��\&�� {epsr� ����and�?<}[1]{\mbox{\bold� $#1$8(def\mvec#1{+ {#1}�Z�et�){�Whe�} {23cm�. opmarg.�{-0.6v!.9 2@!odd3" e {0.7# �b1$[�W�{�Ob�I ��Hypq�E]\\ {\L.���a.��~ ReasoV,Versus Falsi�6 ism ���% S� 7al Vam�b }\\ )p!c4� {G. D'Ago��i ɶ"�IH\`a ``La Sapienza''E�DINFN, Rome, Italy}.?$(giulio.da \0@roma1.infn.i� www.2/\,$\U� }$\,;) W� !J�� mak����&?�Te�g�31\-G is$� of p�� iI���s�J58re[�Y?ah\m��Zr humP(ctivi�l. M|���x8V i���y"`�i� ��s�lea�C  data�f�*d� stocha!�P� of cĿ�d P�*S � P5� ar\'> wor>���``&yO�DY!2��my� ''} o�< n�Mm aNDE�L �''� i.e.?�k@q�=�� at ma�a �1�bl7�6o}Z$bc9�aEte�`<ro �%?BNac��B�� (nowaday��!�! Bayess�9) �����D$standard (�f��"q)i< ���!fh��%es��YOl��-ss���"�� y&emp"Dv��B!Q%�ide4f:9� aY�?elf!^��l,�R��te���proof ��ntrad��S !&��?logic NJFM��� riticismsi �F'Septual�q�a� �na\"\i ��:���� n� al, 2�B{D��8e��B �al� + NHi�fut�d�(�� ���*\vsK {1.5�X�  noin�< Invia�talk �%P2004 Vulcano Workshop�'{\sl Frx%er Obje! in A� �V� P�SL��ic�Q(��,) May 24-29,q. � page�#U {InT ,� ec��n �Eu!��a ty} B�\%!��lx$fig{file=G�;Dі_�L_01_fig01.eps,clip=,�=6-@cap!��c. A~q^�0$^{(*)�beaink��t�Dl]".S��-�ory!��-m!�raXat����s 4%"mea�A�>iX���Qor���v BR}.�a��fɖbs_hyp(A��!I�� llece NA�@2 � sketchedaVil2*� d )�.�.��2�ś$1 � `d�'e05N sa�I����,`�gestablHf# VI#�� s `a��st'�� �ed phen9Ua*C��< � taski�uo� ly �9T��6IO��������� ea tool�13n)R�0asx��:U-�: �pia@3�Y�F� }. WAh�gbM���QGkin�2f O�+FC�A�`9Fe�j� game: a�crete,5+ E�3�Ca�L �-�h on};{e, virA�ly�1b P�n*9�U5J/e�I*s�iLE]E�(%Xp�lI"e �Y�:/ �iz7�  &� a�a�AU� \ H6[����ai"�U�7`u�� i �world; tp�ct) fun66� (!��cVҮ�a�X��t��joe se3B�� obor{� or d�� ish �Lu+��n e 2��6�"�%!6%@%��M�Aq"� ��%�!M �ADnew .��]�ac�zV'%�2E �=B��-)?�| ��}�i2Bi8:iR� (�A U�:/����#��u}q� �% �6�+�U�\ in god%p42F!��b�.:N.�p�2�hS . AnĦ�I1equ��,.��] �2W� B�.>\phras�v ��is-� s_�e� %G%rc }%g$ },���P6"Wu��e�� souraf6�s dn�8 � iunip���Jship 1� �� �1��in Q� ���-1tti�#�3H���a�tq }e �� 2��a�"ZZ *W �'�l�wG !"be����_}�trinsic)C. &� !�I�2L�,�lac��37exact�� c%�.&ځOne �o� )Y�3� �J.�in�����n�� v�wxi�LN�]� �V�A��B�#h �.ds e.g.!/`hidden\��\s')opre�onj q�]�� s (`�(la Einstein}RI�\noD hryg]�8*�A�o�0all philosophA[ (�d B@"uO!�g (for a� rnE�fruitful".<ee Ref.� Caus��i�r"�!rein) xfundam+%peA�of B �j�r��#ed6 ver��ag� �4the concept of�L causation is, to say, a {\it weak} one, that perhaps could be better called 4condiR|alism}: ``whenever I am sure of /(this}, then 0 also somehowNfident t�� d} will occur''. The degre[co 7ce on] *re{|at} might rise from past experi/, just 4reasoning, or 8both. It is not$Plly relevant whether �is}*the%|� �Pin a classical sense,l $?and3are� due!�oo `tru c s' 4w! (ly perceivejorrelIbetween \Fk.} (E%0mental errors�on�� omponents!��|external} probabilistic behavior-observ�s.) HowA;E#re!<no pract%"diffe)��rtwo situ G0, as far as  v�resul%� happens!l Fs $E_2$,3$e[$$E_4$ of )^ \ref�:� --- F41$A�at� oah be m�% $C& ha�beA4sidered� xcep�;, at le��i! e2pA"Hlems scientists typa(ly meet.) %�iALested in.) \newpageQJdescri~h} \item[Example 1.] As a sie �ink-uA�- ��ified by4number $x=3$ i_!�by.9follow4random generat�d chosen! T: $H_1$ = ``a Gaussian3, with $\mu=0-�,\sigma=1$'';>2�>Q >5>3 >na҅�a ��(tau=2$'' ($ $�;nds for%�c!� valu�DexSdistribuA; �2�$��!�8usual parameter�r5.J). OurQN,��inA-uit�"terms,aA to f��aa$which hyp�l sis �Dhav�sd)�: %�, -nor3$? Note�� n�:R�-isQm cana2exclude0dA�erefor�+��� way�8reach a booleanao$clusion. W�n e���e,v,��ŵr�A!Vre�}�based [!�r��al�;�$ �0best knowledg5�.��mmodel}.�%2�%�human�mis used�l!�---t surv  !�"� E  u��tainty/��$developed ��,al categorie��$handle it.�5nalthough���k� onst�!P� .s ��many ev"ILI@o�J� ��� , w)�be ``mo9 r less)2K }�or � t � someth�Wtha�� else@ In9 words,� ��2F���able} (�4likely})'', or e �believe}R6S� �W) use�� ilarAyresA��alA~ferA�inq� ideac Ej �ility}. !�=�2� doe� pr%� us�  do!TS��{F6m9�5�al variE?s&`:8}��=�a�eo.�F4!)�a!�ory!��yield�verifi�5}aJdi�Apr!��hecked ��'�}"� �e}. If!>is&�vcontrau`7 �!� 5ru�o���d vh� Ex g> ce �ppeal��%�N�a�incA�!:L)Gez  a}@ceeds,\footnote{T� wh� )2.�Qre�` ��8'^�enl, �fe&=a!(ous Einstei� quote: )$``If you w� .�anya�g� a�t!melphysic�&��!| %�y� , I advpe� tick close��!incipl�don't ����� fixIr � nao/ |Źeds.}''ɧ�}�sh � �!� point����7s. } I3 eas= !�iz-�>I0 A1a bit��,�\ e t:applyU lite�,�we �se�� a? le. B� W AY, E� imporYaMrecogn�:$m���Abu��: ten* ��"de�proof�ym ion}o.e.�)�7 V9f0standard dial����nd_ hemat �EQ@����& a��e�in looN =(a$)D�3log �s� es�GR anifes��!6e. �{ .2 ex�,eZEk.�un���]T��T� �opposi��(�� l $\ l�H$ �inda�eew��Ho $H$,��2A is fif $ ��� vice��sa). � ��no doub� ifA�o�����A� E�E-A����2�=���Q��.��� . Buo�ct}e-��ͺF6 craJ#mm�ain��A!A��L: (ensH��"E enumerate� W��sh�wa���K� � � haveak7 !��f yet? S@Q"?mHa)� �,�k���a kkf)oLimbo}?� � 1vq a�ffadve. W�y��,perform nextQe� g ���� ��8at new investig�ū� �!{dir�at��ms �Blc c,ble} (� fruitful)!a gmo�,�cur of�E``179�sMR u�pha�Popper's��a� mak�{og9��-��b�o!�''}P Wilczek��1�.�ofU�%"�iz& �� o� �>b�#&di� abov�Sb we A���n� ��  a � ory, spea�0,rigorously? � � AIL�V y.��|",Wa���+�i  mpat!� 9ny"�. �!Fe/, �%�onism� beW�%� a��!!�O)��&�y (�2*'respon�,detector, noJl!xw � n hat%�R�- �u6S1��"Ptes ow!t�fy -)�j�sa_i9��H��A���WFT� o2"� .k ��}��s � 1'ia5 �P l� r7� �Tas� m� �� aui�a�l � %ia�I p+ . i E��Ō to�x" `little'*<  of��� al �s�A�� a�of52 ��"�Zn)bc [a)]� �Kb� �plac b�-�imQl2/}.��i* ] 6! N F�m��/w� { �ed. � liciRgu�� bas�*�!]ٷof �&�URC :  f $E� ���� 9/}�- 2 n ��ne�.?aY:6���u.'' �is!���t�verA k-� qual6, Az n tu5!!"ne�z*"a!�Y ��ers, a%���o `$H$�E$'\ �6)�!u`!2�? $H$' �� ly �#��})�cE"i�A���� it �lea�.6  Le� som�5%&f 2��L"a2] Co �\b  {�}F�ofيq t��8$E=$ ``$4\le x �,! calcula� he�5�a�bK �!M %���: $P(E\,|\,H_1)=3\times10^{-5}$.� .�aSgsmall,� 4%a�]xe�rati�!a �at�*��2ato��j\�  ``�hV>� ��d�''�iv="}9X!:�83] ``I play honb � otto*t��o( r�combinew '' ($=H$)%� ``wi E$). You�A�s�!s{�!g `iC> 'y� ��aW!��2C"b', af �%/got�5i���� I won [s�a}& wI ��at�2v� a�at� Oche� )!.0 )]. :�4] AIDS�p�� HIV�� is �� ag !ed peoa� as `�,ive' (=\,Pos�%[0$P(\mbox{Pos}e HIV})=1$E�>: �e/� � "�he�y�� ($�{V}$)��n "��"low.,  J�ove�Y\$)=0.2\%$. !D ItalI#citize* {#( at�#}!d��goz ���&/s�$s tagg!X �  W�A�claime� ``I�t*a�y �a�� +a 66�ul%� e�����e!Z%�U �&v#�6or,2�  ``d 9�� %#.d �d e�\A�end6�W.��r� solv�j�V�%&O*@ *�!' messag��/E�� �!�rc  `&W '� �2"� G M o 1t!�~ s�0� �MDx&a�� OU s'):�W�&� �er oy,%i����y!�b)]�!h"caO$���&of�" 2kisP larg�at)@�#d"2�� �'}.&�I) �wC*�of �$ mill�Ios�M23`regu�!(coin' (easia,a�� a��sim�� ion)� k'V 500\,000�uds reL�# an `extra��!��8�� ��4}$ A�%�ty��*2<'.K ��6+!} E�)os trc-!�Y7based�3 G.|�)��$� i*�es}aNoT!*E�Ne failEteuE,� e!ry.$ �&|%� n ev�(ce agaXK1� A�be�F  Sd"A�C��then wo�b�j�wkd ��m�E�e�5.mblU�} e!7 high��n� )�of�Hch.� 9+2�2�{)�' .���-n�'to�l&�. �!�)he.�AA�Os�� ``p-� } (��{'!��#M�\break"+� A '' upon-t$\chi^2l))"faY �� � ). Lvly2��A#:�se5�`ofte& rk'�a���st�2�,in Sec. 10.8!�Ref&�}.}�."�. ge� orse� E�w� do�M depeE ymx%%at& # Q" �1)u� ..22)J�EJd1��}1 ly vio�?�B�&ihood&>a apar�1"n-s�  K �lci�W#fas.mg A� 6-!�"-ngle-ANI�I"!Na��%+�2'5', X&`�n�a�� r��2�de]��l $\int_{x_{obs}}^\infty\!f(x� (vec\theta)\� d}x$, w$\!&],�*�],.*)integ[� r�%y����! %�=�$f( �B�$�]��; Q�2 by{ E#%�or]��!/2�. I� ]�m%c#()�I� un- "� �s "�,]:�:5��maximumgM���� D" why I u, %��� =��m|�W�JAh,#~�%E#Q r� MwQ %#> � *%ћl.y� itm� Zechh Instead,�!"8��&illust~�0*l� is '� ' stQ auto~ a�y.} (�e%.B}��[c)] A� =E�� Z !���%Rg data��summa"�a `�u�' (��E+ fun8"�+tK, Y �d6aWMO=2n孅QtrK&an addZ$al, arbitr� ing��^ L`$ll$y� �o*AӁ��&ion6� �%ϩ�v�#wAy 5!A��.8suffi�&��8 �5 �[!�ed �8/v } (c"� r%�Ps�2averagT ��evN$aXyNY1� b>1H�6I�D�/52�!� $mwed.��� 5 AsI5E� d)] 2 inQ�aN�4at "�9� iN �)�ћ", , /!* empi��=��re&�ambigu �/� } ��e rol�[�3U*a `��g�&�d.nmag- "����i� q` $n$�te bal� $N$�"al6M2=��!>:�w�U9�D!box9,.-)FpT9 ntage $p$A wh�/ ke" �A�`)alwxZ#nom*�-#�v3�pla:j:f,9E�@ �B draw!G*���s.�� �ge� ] �!��%�c=had d%�� g�$ until h�3ed>��,S�   6�]� $Nl7le�#��9/ Pas�.�4 (�alz�ly,� a ne� ve b1x5n�Q�>e�!�edt*a $N-nE non-]) �*e� �VA+1��s ��x1i�&one*k ��sn! E� stoppANs"�(B0�<��proL9��7*T"!d�YwD�<s �%maF� p �he.^�ˁ�a��6d�uld9EC� @��'�4Y���oun)}�of. . �:2@yhow, a&qu�!o.:�cmn(��>4btle philosoph� quib��,!v��,����#"�!�!���;��iz"�#In� opin� �9serE� A�� )VMQs �N�5l�(k *a.=J AMi<+y w�Xg= _�  ���%���Yre �/�!�0.0003J`:W8]  4t 99.97\% C.L.�as6� !"6R�K �7i>lseQ The6|  mis�A�� ist$-�I�_ z,:�a!"! ��fc � o\,!� '~@decades� A1G�.9�.� R}.) S i �2.�g�� firs2�*��"y$. Hundred"r Nh� i�O� $ chou'� �� � � . 0 !o! at !�;aui<*�4 teamx+z� !�x}L"��& deep�/t/` �ubs1,occer fans ( G;i���&l `Processo di Biscardi' talk��wR���--�t � Aw�(!�'a�3l3��)EAa!�E�� m desiM �. P�;, I+-���Ffancier��n63E��D��ess�8� 9E�&4&7�Cpretty�9 l�, I4�s�P!�ard�8�J2�mA��'p�/e�E �&�:.�%4r~ed�?} pdidRsup�x�I|m� x- .E�� '8�*! �Ii ��`20 _"��> `bad-�s' aA%� S5B �,"ta� me h��g%�a Baye�>miracle �!�y� &� disap�-)d, `2�%'zS etho�:�(c�Ya�pps, �6!�'3va&>�a�U�S�,.1[.��0o27l#-o I�ad-hoc-�E�in$5Ѷ�4a��&aa��! ar, ���@E�`�s'��eph' `ڭ�'� us encours g `cre1 '"�(s*� J�e�gBorkshop�� met+ ad�nJ.SK}: "C�F�  fB-� oA/ 40&�)fA=e"A!a�t< ��yA� 37.9, 49.�3 52.4AT k s $M�B$M�@Q Z�=86�wis| s� ~ O� a�Cequivalkin�� crib��ڙHa�E��,is $40\pm 9$H=)�.2@ t\r3&�)ll& 0 (0.56, 0.15�0.091,a��i�5e8��uUA {-���,!V.�4. N)the�8@, SuperKamiokande�:��at �!e\%o%7 `d&6vored'�k3.3� 3.8 �B$'s6�! ($1.�3}$i $1.4.�*� .) I� s�G!�F"��ach�>$d using in�/0<���chniq�BuBric� >�a�@� 5�fi�!b < D�$A���!A+��IU$ ofE�!. ?= FE�while-( 2)=a ��3)=a!$ ���� curv� arabolic: I��D-� �5� uGD�Ba)El��$\sqrt{�-a��>s�D�!$'s} =3.3\, $'28�Z8 =3.8.7IW�1�%Ha�tyA at"$"��8����X $| �2- 1|)`3.�n�" ;> .M ) = >�P vDvD.>, 2� � is q� .�aBlem!} �,"� *�8orw�3Ńe� :9%es�J"�}-IX�8domin�6school�E��&A�b Jl!� ast Ju�>s� H-?� un�<h a>>RKo ty� tr�H�au�fou f�'sr@th?�s,� �!�e2X@yO Q valu W&B/a@Iom1�/PXw��k � (``�" 1�~ ��"FF5 }''!\�BPoinca�AKe��r�#�h�1 chin� ��anI�� A�nk M �7n "0:� ��?� ��>4 ard RA� ���!� trouA� ed�. I �� - way *!�#imh8to� go b�AE�i| .n5A b !q rush� 3S1v�,o�FqLold�ass�q�Kodd (i�� a�i�#proposq5gngMW$hem�Iy�biology!�6 admNu[� k�!��ro�!� �}_1M:m�HwY# drop�"Ng d�y�j=� i%P. M�Cma�{�kRea�$�ed.�*� �}ne��oreT clar�6��p-��.��!�% ��-�. ^'ntag�  ad�Qa*~Io�_@mpuA��cap���CXRVvaMre`0�~sQ sym %<? � N &enorm/b �$ (In faT ny����G?emi�H8raison d'\,\^et�Oa�� �barri�-5 iginMF�e �umet. M�eK!/-- �I�� :���tn)!�poKtoB�l�J(})�QA/er��"YFc9�A,� b� n&"O� ngera�excuse�NAlm9��e"�&I{ %�6!:>��?>Jm�l�; entl3I$1b�3youa�  a� &9B:_D_,�*p2%�y*S(L�� !RpowR i 4�eA�is�9C.l �fn+m�-we�E "{!w e��;�7uNA�. O*+ �Ru�2 ���.�tL�7&�Kolmo�7$v axioms (io!�0#b!Qt}wNa|E$ter awaren����i�Ue�� g^P�!A�but�?=?A�e0��>�$I2�Qa��gr� a�8!r��N4.o�0, � !h�c mad�A�;r"=It)�'eula%dext�P ks, valid�5�Rexhaus7�k mutu���A%;is B�T9 9a��9�\sum_i��J����den �%M�rE��P��'f (�UQ})�#a �,`�wo�D�@s�0,�2�cbe��+ More�| po�*�*&&6&� '#�Ihol�S.�d�Bty  $$s (p.d.f.)!�inu�vL#!��ibA(�;Y s�� ]�He}�Y� ;ssocie�touTa�a���Cal� `�Q�3e ��s�)a�, we  u � aulae 2*ich6 �i[�-��}�7\� to& P~3�YHZB >(_1}\\ f(\mu9be#�3d\mu,I)b� ��9 \I)\,,�Q�_2���M�-Z�?�UK� / ar of�/� e se�S (!Bly)a8ŏMA+��}. In� x!s!���n9Uڊ�)T\bfa0�Z or} 9�&w } �.=r9\,,=�bayes_��L�*�5 �'�<`[' ])�Gur fA�d&9 b9P* inaX ccou�^eqBo�# the ��?��!.!!�(a� ``N� iU��CNA�57�i�0+ V\�!�@ c�:, 9''!),�:�o"chaE�f�6G_S�O_6?�*X)!b�$^ 4W��a}�@��@)=U  �>))�s�T�gu&~ >a�| �M/ a2r*�eMY�&�"} (!"atD� ��*+#1 ekpoM�).a � r; j=yͿx�� _1})E�:2}z$r6 ��R�2,łbsoluts)��� �O7� w.+n�bp~Dur�=e�a��ty GYs:F� # �A��� {�jJ�}N E=-�}{N0j,` ��>�I)3H q I)} >� � } \\��: }\hs 4cm} &&��� }o]o&52"EsV'%�-�b) @\,:�&� E�od]A� bye� viaE��qk\Wi>1�>� �I�reY; w�C% sych�5(� e?�TE�f6J')a�ia!c� ot "� M_a��T&�O��e"S��remarkI�A���QU�"�\ TH U%8nes lee+w �� eW_�=.9b#F s' (H e L}DF,��!?�@ ��6�2�/isaTly .�T��^�-yn � s avoi�[IH% em); ��),��I����6�� /�6 `lER&$�e�' ce' &�KnQ/E���(!V3t� nd�4%�z-�(�.i�in�!s�� ob�Civity!�in : `routine'AIcK����s�meaM\"�E 5�fly��i�` VA���� ,) ly d� � N�1�\�squ!pr�,� promp!� �Nveredi�wah�Ve*�!� idity},-��A�A�� q��$� �Xr V�l�W� aLebonsQ4i'M�%(�!!5�fF�)� Zb�HlL �EMusefu�\)�ine"�?B � .X(xPt c�\6GBeB��"L&�-?*B���_[b�hegrefZ)�$i\u~ �!s:`#�/s �[c*� ven�1w�Ao!��$a-�e.'� push tobei!�*oF;B� upper/l3``xx\%\=)�8A| :IYis�D!���+�H^r*je��h ��b8 A�RBR}$�>�J�*T�'(AhKd s, lGE?wٌ![�0�� �!. >&W�ifM��%= �~!l� `$I$$# xPd!k�GlyaAF��bq6�?�5[S@ CM��B � (=L4)]��A&S� Eq.~:� �s})�ogetf? O�B� �B�R�AB) .�C)a)} "R b ���F 8)})��c f�>�ADIS_solB� Bma J�B��)/  z�$8eh@��1/�,2 = 500r f5s �NAa�.&1�&�e�`a� i��&U  `� �$'� %"��2+�B'.i�If}�E,Ax��s`Zre� [� 9%%=PV)$\,!],E �E�fFM h5005zUI%z!k$)=500/501=�-8hDB�XfL$|`��1lyC,s�l�+2b)$a� 50\%. PuaG�^ms `!�*y +5��be 1/600�1/7� .6� 0.83& 0.71�/r!��nng!� a6�>�$!+ 45\%D42�We.<Za%� sour�1� �V� �"��iņnt���hj"��P+un9 !�?I�aj&)>: �%�eXF =i�%�*, �hidde�2 sump��A �2FH%�o�\�0us�.l@"?� A: !pin+im }^``<cI�''. %Z��(}x-3��1.���l�em,4.eps,clip=,em02em�1: .8� �[ �s3 ��>� vertc ba�5Q�Ni�iV8&�m�1�^�>\ . � $i�%$j�=< $BF_{i,j}=f(x=3e H_i)/.j)$�:e /$2,1}=18$, >325 [P 3,2}=1.4$!=*; � f2)�ddels 2�3"�<� Q A5!�& q &� .�RAA�ing�p�p�*9y209�HtS &" &:"�:6��4s: 2.3\%, 41\%�57�4/ *�6���9p� �*�7me�CJT"�0 H&�GMZ�"�IɃ��r��[$� �gge�_*�=$  ianaly�$b�E4w.a�$�mis ``�k'+a�B4�Q4, )�!�ws a77-�A�i6 %e�a. Erg7 �?6��)\ �)r�E\ Pdt%E�nQ=-10-20t$sO�! Rg�Wbr)e�r1+. A�r�4 nm�bm�Vm!�$Ha*|o�k ned,D1hW$�#aqTin�/c�*l'X� �do?�N-$�-a�thM��-� j! : @i��I*� a�*�k�1 we `A� �9�. "o=Vl�+%Ms��  � F :�l9_�9s%?,)�5�qeQ1�OehO�HNOA�4 pie�rUe.� */ � ]hr ge� , �aX,�o��1r� |se�%�-8-�4' 2wR "scC&<9l*)";LMIM�S!x)�0%]o(' �"/ly"�8E�pts�."Go3@��accustomc S�N::WiAn�g�."6ee 01�%��&J*X%�>icf is �L�T9ly flawS$#�*s �G�I`T2P34an� go�`o�� wa� �j-��Cto�7@ Z�G ---}�b�O`=A� a w�#/u"�x it�^ wort�"�\ng��^5(} A���IL��� .�3t�&��GA��noz(��g �4���(�(it�c�T�a&�/var�eH�5a �E��@' �&�h�;�.�^z>A��Ao1Sr,�9n&,�E2�.qa��MH;�� ����.�i2t�of&q ,�,���oryeUw'�! �fyu2 ef >�7 �"�$��es,&�1iout�YI�6;a��so&+ help� ��FS] � �+�*&^2�LfeypFJL�Pe1&=W"HgX���?sB! �%Pto>%�� !��{ 5V�NE3�4 (%���. �a,jpef`Qzc�� at�st� fu�vpec�'d.w�t [��>ch�1?J@e��o�pe��&S  $� 6� H_i(�I{�1})� 62$Isa= �-- ers]11a]Y� "t!��.&o(����~mu� &� �'&�.P�Pad hoc' �� :5�L�%��!1g�rm�A"wsF?;R e�)i�+rdl�qlie;H e�Mo an N@�e�=`ly}�]}er&MPa�� !� =I�M�]�)�[egv&�v1�>� [.n unbi� ����ort9�!&%Hal �'~,h6 x.>3�_�Gof-�y�u;Jali��2 tune)g�"X9��a�nd writ�-!� dida� �nt,��2!S */?ADD.�SR:u�> ���B!�n�;C~ �p��IL� * s Vd"1KLp�n,�J�s��2�$. 6� �start�vEF�2})� '!It;I`m(#1'��B�$��~j�Dd>B=�� �' icksab�>a0�0 �Iu�1 J/� how_�!�I��,*&I�T .xim� =O!^s" �!�C�W� ��jp%�}�u9;l]93n���.os|O"�%6�r}�~i� RPP}eSde��m %�)`i�l,+�ase5� iss�5in�A�Y�� diu4�,� }Lr� er��,,mWi�3`i� sA�&�Q$AK!L" vanish � �Q(!�:-=0$�D^M@ �(>2krbR[?e�"@.�j4K��Z&h (zeroHa=![mmi@8+!+ I !+�2�$ Gz?:��&�!�X�%�beE� augh!`g�T 'nX� in3t /�0m�h�-lABIt�6g3s# ac .Rk%�@so��!��! ��b�jWt[ test� = �-�"�e)�-zlanguag�p2Q �;. �2g[y0,.uA< quir�#�!*]=e�se}a reg�$Q$�.S�@��9� 2��s}<abD~9 $Exp$v 5 vec{x}\,�%in Q\�0b&<\, Exp) \ne 0$]�;[ triv)eN�'!���kP"^X�es�� \, � /� r�j��k$]Ys�$P�uw�P2�to �Z!�*�i, R&�?BH),�x2��C)a$,e�Q] �-�K9�s�5or�tŇ� ely7o�}".� -����$n"�CUP^\p�;$ s�A�> VU /F= ��Th"b%B<is�^a�`�~�"5%H�}L &{ �]a top}A b>l',��E!uy ic�Qg��@�H՚fo&.�y�a")`,�~ J�! usI &�Y" Ws�-H�hEnergy! }JX in"� E!�p�>fM"S�Q�LBGer "1998, �� W. v�E8er Linden, V. D�!!�r, Klu�CA�Wmic!99.]"΁ A."΂-[!��asM L�t}D(35 (Citadel9�932]�{ F. X�``Not W2'� (Maybe) R�A�%iN��Yg�6428} (�$) 261, {\t�i s/0403115765��$@s} M.J. Schervish;it $P$�s:V�)�!Lh no�Am.%��'@bf 50} (1996) 203#|BB} J.Ox�r|SD.Ary-U?aA �&and� Ua;�*�4}, �ɘsBnbf 76�88) 152�2eA� x*� oY�*Q limits},�> Eur.E�. J. �~)�C12)�,2) 1. % --81�sDSK} D. Kielczewska� �"���.eB�RCollaboy.,n, Y.Ashie ej. �E��}�scill-)y �� e~atmosph�@neutr��/io�@�$. Rev. Let1�93 �$4) 101801.�� PM'tone, 2�O�d S��ntonioMyu�� �Fp� o2��. Expu$r-Nautilus��1.@jm }, C�d. Qh�. GravM�2A�2003) 762�2�-W�"��p�Zingi&u �.}basic 2^a� Rep. ProgQNe�6A� �,1383. %-1419=hm  C�� �Enhanc�!/�]!�� a�V.�sfK8 �val�p P�e� �X WyWon�>Le#h, CERN, Geneva, 17-18 Janu. 20�/# -005. %(2, May �F"�  W.L.a� edman, EdqMeasu��cModel1U�eAv�4A�S5>� �'oc�|} $=\5D[osajnl,twocolumn,1@pacs,floatfix,bib ]{revtex4Z(usepackage{�& graphicxnewm and!trans<�(on[1]{Engli�6: {#1}} :97-up6 !2" pictc[5]{:�/g=J��${b$i�e �s*[�/#1\)-,]{#3}�>6�Dkx\c9�l"�#4} #5R? %�z/.Z6�[4][0.9�c!! {!tb}{#2}�{#4:Sr)!MG fig:%v2Uleq #p�ct �eq ,.�reqtnO^"!�6qtn�)U u� {FigF�Fig7\page�q��>�-�.�]Rv� *{2� .w .; Fig.9�addtoc�{1}A%&}a6j q�"Ksloppy!Dtitle{Soliton swit�Sg�"4Bloch-wave fil�Dni ��odic pho��c-ic?  \{A�a���D�%h�(� e-�ed def���C�pvor�<-passM�Ef%1�s�9�8 \ocis{190.4390� 0.4420!� makee`tuda5��Npropa�i�.nF_ 9�i!�atE�m2?�Ab iVee�s& u%]:7i'�ob�a�&��MaS terplay b�1��Aof��� �i"��@1988-794:OL, Eise�Rg:�0-3383:PRL}. S�K %4%|1IrE ;��!�JWC'�!�ar== Brag���3�i"%)���ont � d lat��a�'td a�w �M�alikA4-93904�, Neshev 83905A%W�YE�-1�-���)�$o v_ are . �E�$�-c���9 bU� _Q�Mo$=tti� 3-83%� >�6� He�:� (achQ�oȓo � g4���S/Are�:�.. Our�1 xe�Fda:+gx�)!EJ��-!��}9I#�,6<�: CrK�al��i�1f� to Y" p:> E�bK�1��!�it �'% a� nsmi{���M��L��Fs :�� ll 4d���8o�" e!j9�a&�Qgtg+AT��e�a��.�oMM��=�.Pfe��BXA�'"p%�%:�-_ r���,��IS��r&lra� |G�m��A% ����~d ��ied2v7l"ʝ2A 4-2890:OLa�We�lS�V9jin�J�E4 �"av �� m one-"�+|3:��r m!,� ��ai%<_uch sW �.�A�a�d%,�z&�2E�*.� co� ates =��;hs��$� $x_se _s$,�-�&EØ, $D = z_s \lambda / (4 \pi n_0 x_s^2)$�b��Gs�� coey, $n_0�B+�xqH�+ ] x, $ q2vacuum%�length$)Z<= 2 \Delta n(x) �/��?! =/+d�u�Cju�A����?!ex��eu[iE $d@ nd $J�=] +dQ � Cic}��3R%"fW. Linda��J� � � JlAre��  4s $E_{\kappa,nA�z%$psi2) \exp(a, x / d + beta- z )$jRH�� "-  $Jd= B!� a�Y-�D $ �$�,yng��)� ~�- �hC:�( T)�im2� ɷ9�int� s $n=1,2,w$$. &ldynammof slow�JoEVed � )�( f��$�� = A�� B�$,N! .f#ive]6Sch\"oTer�4/ Sipe" 132�+"��1 lex �:�Y $ ��C[ !�a��A>)AV.j1x} �Zf0^22c�e 4\gamm2�|A|.= 0. \]. $2�= -d >E�\E�A]f�Oe6$group veloE�%he��Y{� � �>.�j^2nl��i2�7A� �Req?"3 }U $F=Nt_0^d�q�o��� |: \, da�u� 0^d V"��2�6~����01?F}{t }{ (a)~Re ��)�Zprofi��nb); (b)~� e� vs.%�}s�V(� �  a,ded); (c,d)~ q��� &ha:� O2.16�na p�\ u4$d_n=2.5\mu$m,w=4 s= . } �OJas!�!."�"�;� �j�A^a�-�cD n $D]"J^>.S� -V8h�$ $A��_0 {\rm�*h}[(x-2{z)/x_0]�Vi \rho � �$re $A_0=\sFn2/B�}� $x).�/5Ǔ�g�4ab`& ��P�&h�C%g (mS>0��� �de!�^�y<!6Ha sђY�? exhid�ei%'�  (2qp or anomal9_6 o.Vxac�+!�E�.�"Ua��&URort>� g �9@> �@ou�nd�Povsky�(4-36618:PRE� T� r 6��;�70%x5vKerr-�&�X[.j I�EI$]!� �oe � >�L) AlGaASaaerl6 ��A�!\2>�Q��3# U_@reeg=I��� #�]�B!B��s ��P~ �~;�}(a�9� pareg�+ � �q947em"� =1.5f�u m$. S�sx� �!���2s�*M�AY�5a]E@��r Xns�J�f�@":A"�ʩOin�vs$mo�{i�^!��@9 �">d �rr�in Vb)� >�Y�8��/es%3maip��"x at w� nd nyY�s60 [see!�sJ���]0�� �"�vc�C�+��z22��N~of� }: a�!�� bO� ��Φ6� gl�7!y9��` �io2>W)A1��x �s:�Cm=11\E� (dao ), $11.5  (a�!�$12  (do�l"N6����)a� (c)~!�-��(d 1q�AweM�+ B,�5��s�� in~E�"2 ּ�)lectW}{t2�� aN� iZ��1!�E��. Allm& �&�YZ�.5-�N}.�W~ w��Ea�Y&�-�A3A@� �����! ton�zs&D4 homoge�.>@���w>C >+�in *\16F�}�4�w�!�teX multi-3 � ]Ae���:� aS[5t�5a;a . I��@q��cu�q (� ZA�\[-}�a�lef��els�"2"_��p�F�mpo���|�vbi | � (}{l} {\disp � tyle� E = a_iF  + a_r-� �<, \;\; x < x_{d-N((} \\*[9pt] jhtPZO>O+O�$ �Z�a_i~a_ra_t&�amplitudA!��& dent�e��7���mDpv>; �� <  +}� 1�ext�]�un+key��0ur���}�E�?�a�m�s�ongZ�hi�SS�Šo ��5iB� s al�/j�LZA�6Eٲe� E}�= fin�] uch��Y&s"`"�bĨ�n��s� �idth ���2��o��d ��bVf -(Nf %�J:W.?Wplo�4Ȕ�T!G8Heނ��� Yat*f,s $|a_r/a_i|Moi�*�=  $���Z� �th�N� N}(b��"� �W���H%FE\�s&Ha [J N}]5`N W}]���W)��.�@\N5K� -�J+�A����V%�%�funda�>-GV�Y�i� Q ���-��o tunn/ g�Nwe1Caz s. SV2t} �6i�pp9� *f!next-���  D�3&` R0}�*��Z� !�).)�.p V@ �i��G�7�#�m��or��� 1�embedd:��NGMg �N"W}]�w � >)�LmEDKnry� . A��E�_ZG��_f�!A� ��s0�!naAсE�=�;s<u_G3 shif)#i*ga/6�J� &� � 2�>� ebn,Ts�L��l�:�9�� ��r�p��M/[ out�� �.]�A�,���1"�bGof*�nяa� Z��te�m�G�N(g�!a�� -�i:� c�t��un�'�?�:atf��.q�e��'6m" 3 &u �@��"��!�!�d��2!���Nkih?S��a_r,a_t�Cnm����.OM�\) l �a��!��wE0f,X ��tAe. �$m�M 16 RB:c��w�a%�r �d)reh5 i�>'! V��vic!��iIAf e�6�l�4to hG� �}�-���-���.�x"o uzzR�\N�\ A"���_q�fDv!�6�%~.? �<"� m�^UA!,�izA�&o�mA� $.X��+"Hdu�9">-v>_B�. ��&Ae6{�L�-��fird��-�glŜ� � t�,�ꎕ�lyH3��^�I7j~fpyA!�A�,>�3I�jn�#��� ��mo& acrosDa�H�b�x clin!Z�)� fronU�%^�d��+ �0)�*�=�4!�!�-� 2�!�-[9'�Dcce�u]�]<}7b&b" �rhP�rein)�YF�12Aalw�)m��+�� r in7s)�M�c2jE��,UJ&C�:� r N}(c� Zt �O��$hŤ�"C6�!u��*gqc%�/th L�al�_u�f radi�Y{N'ex�� �Z�F �VZdn���S�+ly*�)� trav� ^ svi��jh�Lb��� ack,�ub| S#mo�?�!�- "� ��*� a���E�`��o&#W!Pi l fe�7 �Gf�Z WkNE�sZ(� n!/afPa`�a� W �fa�Nw-&Z6�%vpl�o�vighly��Mבׁ�}*+"N/N !3&�(e&�+ TiesC�Dg�(�i: �gItO�r�""�-.��as �ly"�&/lf0R"C&crystal,(uY+�'�'��wo2�&� �@w@alA��K?�![nh�7��ir po�TA�![al* +ignJ anip$.�/�2 s ac&%Da� �"�1n�ei= Counci~;�I@B. Eggle�B�S(M. de SterkU��ful�7cu A��&t>�?150w>rH+ D.~N.>l+, F. Le�{rIY lberberg,�2 AJ9(424}, 817 +=6�=r�. Yu.~S�;�3�G.~�:grawa)@ em { @'S�o:�=Fibmgto P�(CM= }} (�>7> San DiegoU@6�>(*B.Z'�0R.~I. Joseph,� !:"�;13}, 794�=882�>^�. H%,>}R.�}E�8tti, A.~R. Boyd)�J?AitchL{M=�4� 6f<81},  /�96�ZQ.! ,>�>z% ::� �+.IF92}, 0�.EF42,V�.�= %A."6,aUPHanna, W. Krolikowski �2zf%9!�0;/J�Z5�B, B�D.F:"o� o, M!&Sor=�C%�Stanle�BqOp628a�3)S6���6,>��^0B�B�M<�D�:SN���:�F�9v�J�F�& J.~E��p� H.~GB nfulF]e�132a:�f� �7E. !��Y� EI�70�0!�`>� =w9&&�9��B(=12pt]{a62��\*�<V6idx,ams���Y}% R�Math FC  %9,[cp866]{inpu�}.r��an]{b*< LR  \�8�{plai��|oHidemargin=10.54mm \-�� \set,{\j�p }{170mm} >heg. }{25 \topiL5mm \hoffset=-1cm \v 3cm �]d"�> er} {\�x\bf NOTES ON DISPERSIONFUL AND�LESS VORTEX FILAMENT EQUATIONS IN 1+14 2+1 DIMENIS��2��y4it R.Myrzakulo;B-{A�\} &�� 2�JA��*a{T��Yhy, 480082, Alma-Ata, Kazakh� �. \\E-mail: cnlpmyra@satsun.sci.kz} % YFdd�_e3 N�6KΕ }t&�;i1�6z \a�:{q vMx �"'+s (VFEd�1+H!�d"C,� � A��S@\�seH�m grM. AlsVFE�"} )2� � *� .$r��9ed. �["�] � y qϗ~(d�Lk� dLoMl7Al\t�ofk entsa�� {2 Jp&bN-M%� F% $$< B'}_{st}=.s?�.{ss4C0 \eqno(1a) $$/1 J(s,t)�+n Le�:g[)�B�in $R^3$)y $tj�s$�Z�tim�K arc��ra1%�!O<.E 3�UjV7fՐ#aP�^! �VFE��t)}_t%s . {ss}1b-� q�6!/. H?we ��Bq{tt}=-�-1}{2}(2�j^{2})_{s�b.�} -Z.%�2�. �2�0 Hasimoto [13�'��^map $h: >\&�aC q =ke^{i�,^A0,au(z)dz}, $ |�fI%k!�ax"$&&�Schros*-/ (NLSE)/$q$!.iq_t+q% $+2|q|^2q=0�3��8 $k$�!��Q ��t�e�-�tqX�dg M�$. "�6pathw�~�7:!ey�$N��u�in.�I�M���$�c�;� ����t�mJ!J �*�h��KU�u�#$in [1-42].�ᲕO�%Y �}��r�b�� .2{s�OU-�n (1+1)2iso1Tic%anp �=asq?. a).!.4 VFE.P2� $$�b��>�\�aU����s}+ V},��4��Nwy$�, V&�!v���%=��'q�`quc�ϲbS/�A ���qs: 1)� !Pw=0$. i�6����# �5a))0� ��V =\alpha () �nen)$  qv5b J 3) a����6 �$$2�_�}-�AB, �6��)�P $A=diag(A_1,A_2,A_3�$(quad A_{k}=�tMb bI|Y�QzF�3W)H: -��.{�Q9�7)JorJS>� �:wQ�f}(t).�8 X�~asMYfAYa�ɍ (1b� c) NC�Y�q�  "'i s [26-27]!��Y!-=+��3��.}^2EfH�I�9 � d) O&VaW (aFe�DanaB�~�([1]9TatQ��:QU!^ss})+ 8't>1��). �10 �e)"Q w"h :��b%iz�d�!��]f-�^=s�1}{s}2Es vq1&[A6>�1 ��P!���������1�2 ���� "�tAG A^& } M�.�6� 7D(1�TP. NsN�*8��`TY��+ &�$ LV (M-LV)� .{�$s}�q14� A�T��1A�&en�s/ �� �A>  � A��Aw $)�,��, )� ɰs�*[,]%<7OutS,�g=��.5�$^2-u+\nu, �� \hat = d�!�\s8�!*� =( _1I�_2 3)15% \\ \hf}^-. � J�++K4tabular}{|l|c|2�N \h# Nr�q & E| �b \\0ThIII3 $ 2i9 i[s, � ]+ u:"%/_3] $:pE�p �q)�_{3s}�|e5z!�M�}_G (V"�)m�MEP R�IVvV�n:�U�%a ss}]+2(g 6&]�'}])_s >p M-LI��)�2iu6�}B� M-XC>i6^��[:s��c �TB'Zw]Q!a:7ta�� \�9: ~��q�"�0.3�PZ1fR}�to�&:(!�a����)��fM:/a�y� XL.'ir$:%�\{y � - u +m��� imesI�E�\}_s+�G�A#Y1� $� u_t+u_s +mC (mf v)_s"(�G� As� 0$,�&��M-2�r�Em�E k �\nu� �6�� 17�$$��7�  IFK����2��>�%� ���%�.XX��,B0���M-6  (�t^noA�or&�% e.g.�R(fs. [43-52]�B+r [53-59]���� 2.����J�6��~�6j6���^� $\\ ���= u�\nu^2_0[ l�F(.V3s�s}��:���j���%d�2.5��n��K (u^2�, �D ���Fn�����b�)R�l�k�C)_s=0 *2� XLIX��u:�" p2�=[s��\!f^7>��^�uz \\T� 3�ybyA\:NV��Q ��%�:�y 9\n�1S� �u�Y eF�������.� �"�2%Ci�)2B�����V��sZ��a :&6` � I%:-FS���6\�ْr�%\� J�4��b����XB� �"/ 6� F &' /3���i� v%5?s6#:��X"� ]9� �VZ�(alpha (u^2)0_{ss}+\beta u H \lambda ( \gamma^2})� $ \\ \hline The M-XLII equation & $ 8 _{t}=(\mu6H - u +m) %s\times � cH u_t+u_s + � B�s = 0 1>���~�,alpha(u^2)_s2D}f�{s}B��\end{tabular} \vspace{0.3cm} \\ \hfill \\Table 5. \\ \begin7{|l|c|}1Name of= E1�of mo%�6�%�2 $ %\h�2� 2i\hat5� t}=[s, {s}]+ 2\{F-u+m) n> }]\}!0)�� \rhoA�(tt}=\nu^2_0A�b  B6 XXIX�_�� �)m( ����]h�2kYl (2�f� XXVI>�������\\%vu_t + e�y >�b��9�A%��6���2�=� s + .f�":�F��6.��6M-%m�l}]+2iu6$m�!�n�frac{m�}{4}(tr(Imy)Z� ���n��*1��j�]N� ��%�I��R�N���F�>XX��zY����y&r� %\newpageJ�7��^�L2�acU�2.9�� {\bf���l�X%$1}{\sqrt {."mg }}(-f -u^2}.7I�u ��}� �s})r1�k �� }=v^vt}u0 v_t=-2]s\cdot (2 {st}~ :s}) M5^�4�V� � 8��^�:�5�!9i ��  = 5�2}6� .+ ss}]��E3}{2}.�^{2}_s, .z{ ],\quad.~0s \in osp(2|15�0.7!:%�Rc%   \sec� �{VFE with the electromagnetic interac) } On @esting problem is? / betweenHvortex filament and>ofield. I6 ory, this.W0 describes byD4coupled system� ��fMaxwellխs. bp soliton limit, hence, we getGb] ]�9 �E]is mb� presA� some-�sA�5� which Q�.�JJ qJE�RFs.� �9�;�;F�LXX:� �@0�:t}=)�2��}+ )�Qh.4E�.U�A6���F� 2�mFI� =�Ta ��Z.qe�.�. �v� ��i�2�� )_s=b��!<6������( F�����.�B�^x�F1���ZAF^tV4�q +\nu)�q1Vg&� JAQ!GJ@^�U?��m��2�5���VJ�� ����1��r�V>�>�.,��i�:�2X��a ��� \}_s����F ��2-\�Y"������ ��.�!@�����=�=&� Integra� $in 2+1} It�  -know� `at each (1+1)-dimensional� D� s admit� C yy})22I{sy}+u_y>s}+W_s, = 20"c ps}-�G(^2u_{yy}=-2I�=�� � �y})j| ,$$ W_y=F_s. q 20c*q we obtax ]�9^verA�-�ha� form_�62-b6��=c�D%c �2Kfd�1�`��e. 1K1)f iJ�(Myrzakulov *p((about our ��`s, see e.g., Refs [43-52]e�4also [53-59]).��readsa[44] V��5T1�JP2s)_s + 7Z9 V,U=2=bsR6z:� [AA�W)I$$ V_y=*yy}Y�2I�PN$�(�Y�M-9|E�2���6��*�3�V3)or!6�o =P} -�6)sy}�:}�4ʼk�|e�)9�4 � iq. 9�I�$$� JA� �-�.��%)_s+2cb^:@y}- 4c\upsilon{\b2A�95F[n6R2�5)�u _s=�,1}{16b^2c^2}.��)_y9M5I� iv��2L�MjM 2b(cb+d2Q!y�Q6�QFQ6rQ4(2bc+d)�S6-SFR)"�U�-iI �05� 2}([ s, !!�K1}+ 4i�v"�2ia^2 ,wA a�2��^2���.� s}+uB] &� ��v2� vJ�X*�#%�J�6��z\{(b+1:1A�b!=yy}+ bu_y:}+@u_:W s}=05�36D y>6�.TAT/ >oٳ3/ !F�.*1>�%m�1a�6� M_1\&�%s] +A_2�+A2%A�=0� 3&� M_2u��) }{2i}2�!_s.�_,.0]]U 3� Finally not� at all� thesN� � � &[. And�6\8 they reduce toQ=.� Of�rse�ereZ exis�so, n2�F� BZ>g�such .N� Y�n M�>gs}+F�)+�;{Q�6�{s&� 32� �&� � of%=%�� � N���33�R8 planar!c} � j� -��g s. H!�$)# (s,t)$ deA�$s an evolv BHcurve, parametrized�@arclength $s, k $��0ature. S%��)sU b�,studied from%adiffer�point!x(views (see,�l(, Ref. [27�  E� 1. FirstaR2G��aG[26-27]�k�M|�T+^.M}s,�34%�waVa a= &�^2%3�%"{)� $w  b�}� BY'.�35p5 2. �*4�b��g��.��u�t}"�3 s}+3.�H }0s}- 3�2�r0. # 36 �R ZY:GHor quasi-classical � ]O-W�%a@ierarchies. StudyA�:[%!�Tof great importance si�� aris� analysi�var�"�L physics, mathematica�d appla�y�th"�quantum$"s�strings!#!� , o�Xn� al maps o �co�!x�We. Abovl �Tde1�ful!�. Nowa� want.Š��"_:Ta�(dVFE)�(!� 2+1 *�< For simplicity,n�EonAhe�ar M.yo 1. S:est�.."C�u&"�&BJQJ 37e38�.�CVB .#.htAZ L-equival�r! :8(KdV (dKdV) Q� (o?# RiemannU��k_t.�kkZ%q�8#� $k�,�cur�,Ac�teA#��2.B���. I�}~!�R��G/ -)���/i}Iyy# \sigma_bs&� 399E *= \left(M-Pgin{array}{cc} 0 & -i�,i & 0;  \right"V 40^503R0=/T:5�is�9?%Q$looks like�� ��� /1dW-3\partial^{-1}_{\bar z}(�#.3^%z}})_z]i Jz5 e�$4& W_z=-3[H 0G6xzq:))�] � 41�M�( z=s+iy $.9P4JRCV5A, ?$FW6;���(]~VM\� %� s}+WG&[ mQ4& V_s= �29 })_y/ �$$ (W)P>,E&)4}V_y �|2-.042�U{5F+C5)�. , 60� c)f_! 6�+UF� +f_{J�+ +f_3M�0 ��Mkm -� f_{k )},>m}, ... )��s4(scalar fun%2 argum) s. N"� ��M-=(�A:J� Benney5?� +$�] rela�B"K*y�: spin"�_   . V "�*Conclu�*t paper�$ have���"v ����� �� 2:S!X)Fse�s��. A.-�� &P * *c4luM+���*� � , break+ $waves, etc� X � �2 to� y�M \ �yin�!6�their"�ility. W�cur ly inv�+gat��+ssu� d�fin+ will� eary a fu� )�. b7Xhebibliography}{999} \i�+DCieslinski J. {\it�yTDarboux-Bianchi-BackluF, rans� !W�-U( surfaces.}�@book "Nonliearity,GeoSDy", 81-107, (1998) �Bishop R�re !�mor3n� wa� f� a!;�ve.} Am. Math. Monthly 82, 246-251,j75jCalini A jR�  develope�!SY e dynamW in C �,ic Approache D�ial"�8s�ustral �|Soc.Lect.Ser., 15, Cambridge Uni�Tty Press, 56-99, (2000�>�A\on a Z��� �Continuous Heisenberg Model.} Phys. Lett. A203, 512-520, !J9FJ, Ivey T-Sb�aa�� u tant to.}A�K�!T� HRamif, 7, 719-746,245�:�TopologIy4Sine-Gordon Ev�a�Con� T � CurvE�%L)4 254, 170-178I�91�J�iJƅ�,, Floquet sp�/a,%$finite-gapaFuaS%�!�/F�!!our#ofE�� RComputerE�Simule�0, 55, 341-350ID1j��Connec��gI� 0.U ���$ NLS potenaA�!Jica DA�$2/153, 9-1M��.�P, Gragert P.K.H., Syma� �Ex.���local� indu� � roxi�o&�  mA�]smoke �RGrinevL. P.G. ��w(em%'� $self-focus�n�#near S&�0��%�fm�period�/E���$R^3$ �>c 20-2�a209d:�,P1midt M.U�Pg��rso-�l flowIo�moduli s�=E��smh+B�.}eg �87�Z, 73-98.�B�N�Closed��9:�ha%3 erize �#er0 !K�%j��"Nimoto�b�&j3�.}�7k%FB 288!Ppr�no.�O� 0dg-ga/9703020�Ha z� A!L;3��:�4. Fluid Mech. ��477-485��72Q���,�ger D1�.�ho�pie)�sta��)i elas�4rode�roc. Lon�b� ��$ 79, 429-4�x19�7$Keener J.P.�V :�%�$an ideal f��%� � 211, 62-6�f�"Kida S͓A>[ moE�F 7$chang� form%X.g(112, 397-40��198��Kirwan F j��0lex Algebraic�X f�. 1992QLamb G.L REle�of SoI �" .} Wiley s) rsci�38, New York, 198U[L�!v,a�CUePoisson��j^�J.N�� Sci. 1�-93Eo95jo,Lagrangian A�[�'(Kirchhoff EMe0Rod.} SIAM Re( 38I 5-61폵�$Moffat H.K�% icca��he��a�Js.}�%B� a6� FE�i)Hplasmas, NATO Adv. !Ins�  E.�l.Sci, 2�DKluwer Acad. Publ.E�(2), 225-236Q�Q�contrib&;Da Rio �(Levi-Civita�"(asymptotic ��!�or$ :w�.}�\D� 8s. 18 ah6),��245-26��Sasaki NM�2 L��`  !LAp,Hamiltonian �+a �y:�.}�T l. 3i� 97), no.3!L9-2411LM�Vo.9ٝ\D�& Jacobi�tf n_� �)ics Rese�,i88): 1-155�$Zakharov V�� habat A.B-*�152-d63�61����"N mediaa5oviet-JETP 34,!�7Ac�49p) Nakayama a;Segur z Wadati M ��g�)���!�-6�.C &K 8. 69, 2603-2606��92��2{:qM�E X�p Plan� J1��o@Jpn. 62, 473-479,�S3 dG� :* F� �cyHc:j"`.} nlin.SI/0411065, 2004Q^ Holm D.D!� tech=S.q��FO� V-W driven by�n��2�09040 � �A�R.J.,aWma F.TL1 -&1 concept f%pd1!� �of�ellip-'F .}Wa�aof �Ps, 8, 555-559, [1965] �5+i�HRasetti-Regge Dirac�� S�9 �{�� �j A���$ s, A9,53-63, [2003B�0, Marsden J.E�_atiu T.a!e��/uc�e�Lyapunov&M ����inuum�.}.of �real L. ISBN 2-7606-0771-2%Y87�0Kuznetsov E.A�,ikhailov A.V-n O�� �� mean� of ca� (cal ClebschjG�!�.�},A, 77, 37-41 �0^� Ruban V.P�����)�%="!?��hydro�d��x� ,E, 61, 831-8�=�v�IntroItoY anA�a Sym�, Mme 17� text�AFe8.} vol.17; 1994�.cond edi��� 9. S% $ger-Verlag�S��i*��degre� Q tedn�of tang�?-D%7&� �$. 35, 117%�691New�?xjN- K P�@: A�tETechniquA �:New � !w1_m� Ma@e�T h�ic)�He II,�� aH ����A�CA, 80X 7-23a�197�i&? , Ber� M..� h i�_ me ick$. Today, 4f2)24-30%E96�Saffman.�ex"-.n N2Npelioa� ulos A.D.)�A2��:Ž-g- )dL"n ,231L B9o* 1� %�o�J.!t . A:�^ .GenMO 8859-8866�C�ThursAW�F l ex q&�Vi! liev%� in� an%�� (.QA/9901110F9�MBelis_ ��Z Ztem Iz�a NAN RKa�Xr.fis.-mat., N6, pp.67-�+� �.��On p" l���&� %v�7 �,!�Prr4HEPI, Alma-Ata!287�YN}S.2��i� �lma9!�L2=J}(Nugmanova G" hmultid&8 y�.}��or2� ��}� OZ�6R zdyk�R� auge� i-!ce"BF )��38&A ferr&�Ek�N"� .�6�D�R\�L V. 31, P. 9535-9545�>|8Vijayalakshmi SB�, Lanan � #�"F�.}:%�*i�);tM*�ya#h�E2�J.� �M� 9, No. 4,�2122-214*����D:uF�� ��9T "� E� 5�!) Ak ��% U��J2�B�47, P. 3765-377y7N! na L�� Ku>��ani G �De����,=�D �(Chern-Simong8ory.}>�e�Am42%�3�1�141�:Ra.J1��, Serik�x N.A}ov�WMm�S��7ary}Q }Q!dG;^: _nAa� : Cl�9� ��Q�&_". �S"�es II)�# ,�50mistry. �  153. K&� emic�\ishers, Dordrecht, Neth� nds,  �5|849q�>*5+!I., :g6J��&�(�A gf�'Mible .ce� chaiA��a�b� �bfb35-5421bMurugesh��� ��N"�P �Gc�� q]:Wlicev tok)al*� ��(.PS/0404005��J��E��e rpreia�kZ?�g�-���ee l���!�i�{E�s�lForschungsinstitut OberwolfaTRe�*0/40/97.ps, p.U� Guts�sh E.Sh���!i!�Is�/ ri's� �.} %-M0VTG]�D� &Fk2i��backgro� ofA�H@st�!�)�9001.7(Letter, v.2�6Koshkin�� ,6�X -e%9�1 �ZP��y{LDays-Asia-Pacific 3: �)rd� rn���onc1cea���p. Singapore, 30 June - 2 July�. p.10���[:G$�*doc�&,} و% Temp�& � cle A�pr� . c�4 `elsart' % SPs1/ 5 \*){ (} % Us $ e op6 double}�r �Cewcopy�o|A &>�ing % 6e[ % K].thif you use PostScript figur�yp@ � %)A�q%!�packag) ^ �m \use {1} %w0qH�5H%d/���ofRx:Repsfig� � pref1Qozol6 �% .� C%��amssymbSprovides3# use (��v�1 mbol6 I}2ams9}"�&Q frontma�� �it Rauthor��add�esAI1]thanksre�0�in�?B\ C!�\ BE� foot��;=�cor/NOor;$correspondA�JPea5�:Aemail�, %�� $ \ead[url]ha)�W:!�t�{%\�{label1}A' [ ]{ �{Name\�{cor1} 1re G2 G ead{2�I�{� � t2 t h[e -�{A)� 7z3 z.M3: �Det�$oU NLU Gas�ntill�: LightE< Large Area Aval )$e PhotodioA�(LAAPDs)ErAR��al %>( link-��*; itb2o1�es%�)d)1,A1 � �%U� * D4{R. Chandrasek#n}$M. MessinaA.�bi)\{� @ f\"{u}r Teilchen[4k, ETHZ,�R CH-8093 Z )$ich, Switz� }�*ab) ct} �Y w*useI�a ser� of��4�sur&!!a sc.�l%� in Ar, Kr�'$Xe gas. Ab�$e� effi&ko-de�d. Value�X�Kr" �(is�&I;those gi��manufar�4f�8tim5 show��tQ.on:�((128 nm) ca�T dE�ed 0� �y at540$\%$�#w-u�;`gaz6wG' emit sign^5amoun�!(non-UV radie*u2a�Kge � $gy expendi���c�6mv EpaEHa�at�, �is1�d��b�,low 378 eV. �YWQikeyword�Z s he��h�m: \sep N� "e� DUV-}�@%Y<y n�g!h2�r/p �IR!xs %:� D�j % PACS c�vJ�\ v) )%-� 6-"�/.�} �!gas&re�I%��6�mcw�Zhigh y^Z, �ar@z6a�; NaI(Tl). 2�t�4le�eajund�Zal inaDy.���39iis�2aA?dium (� �MGTPCfmptR�F;trigge��m $T_0D=termiq �i�7�%1�9"�vAt^ �=�k, res�nga1a?y ayglobalJ�� r�C�?inE3Ff l�Larea a�L�-:M�@lda�a vo alt� �>!��6cul�0o�)O�!G��opu0�MT's g 7:cern (3(direct dark� ter se�;2�na�9o4neutrinM;2 ). !)@sR �Z1�is�1�pI�9in � ciple pos�\ ta�:�EZ��͇Ari{� �.�a�� han& A.�ie2s"Z4e�e � alnoA�ofcF%da�$llel oper�$a-�number�to in�se0 sensitiv0ea �!�msala��^s�&�&0cryogenic temx� rp ��b�#ved. ��%{��B� }$q 0{sec:nobgas} ( exci��ionG,�l� -*u��2}E扫��=e� viaproces�h0\cite{doke89}J��� "W �;E_{ex'i2).N N_i+ 8\eOS,>�w� $N_i�:!���up�$EV�'662� of $E_i$,P�JS.��L%ed � n\*- UN� $�^ � kinez(s : sub-rɁ�ans. "7p\'-�!� �SbeO iq�%a d*� if!�� subG�5 band�5 �$E_g$"'M @ cal�=! � work Y a��+T& ~� tab:Yr}.X fba�&j� deE�naZ`Jf�a�y � s, how,� $E \gg I$ �?c� weak� $\a-r$-y l��Q, yKd. Ou>-*Q�per_� a&��� i^aU6�is brouQ forth by 1K 9K5 atOst!:! 6�. "�tA'}[htb] \�F� ���s{|c:} \�t��9�$ &q�/� & Iq� /I$ 2E_{i}&!�a� UV Peak W�6�) k Ar &A34�B. 15.7 33 &!�685� \\ K84.1z 83.9*311.28š\\ Xep1.982.1 8?1S p75 nmuC ��1C �i0.5�i\caw{��. EnerA�� �F�� E�K� r� . } �W:�le�H ssumA�no��"� onX� to!�6�lt, justif� at� � �u���is��~ �8suzuki,carvalho�x ��i��x O@  isQ�&p ꥭ } W_,B^{DUV�c6i}��/�P E_i + �LwvE�(�;R3Q�)S��O vol�ANE�saG.�=67.9��, $61.2 @ $55 �6�q� ivele�*� Exper'$tal Set-Up�A��.0setup (See Fi��K fig:�Swe%�L an $^{241}$Am sourc���:s�����/.1 ial ���~5.486��(85\%)�5.443  13\%�NuIthe m�^,Nipas�J�?peJ�anV soy�s a�� ��rajecto> neo arily lth�����, cau�=2,. Ax ed^�x�er��t#{y�{ is lat �V *3 con=^e"�a cylind*" : !�1.5mm�u�4 c����r)!?��� unitary g�^�.x��Adv�LdUnixs%cA� di=P� 16mm��adva�}��2W��-"��a windowDD,5 -enh }ds=Bs �� prim%�,, cross-checPa��RL Red/IRN NNbegina0ure} \i Ee/ap�[width=\�/ ]{eX .eps/�A+ ti* Y�"ilto!/APD�v��as -�i Fr3TQh,m;ABR� a�!�alongpUU�'�Z����*M�?c ��"j}^.62 chem>.� }�"A�!!�o:)�!LED�a�e m}���?b�. L� pone�are"�p�~!�. T���lor!i�Ral�d�@c��l�Ao�1'�end2-D To> 1��;� dew�s evacua!�A�`0$10^{-5}$ mba� lush�� few3s+ fil�G !B&di�I:x�to� "� i�?Me�B� ga8Uf'b�G@Oxysorb cartridgeJO ��A$� $ depos@TB� i/��  Qa}-� t upper lLr��]&�at2�co]�� eno�;bs6�)�!��HO@ ge-tDncy enc"e�e�ow�. Ext�l coosBa�r��!J*�I � $-5$!�20~�}ees~C��r�*ors moniA�!�.E�na�fl�<APDItl&! beaXof.oRduez!6.X1vc,I�"� e�� })/i#�Vh6inF�e�. Dtly out�s}e ����D dec�t and �sI�� a ICARUS -�&bhy\G!�4r͖��ro}%c feed$( capa� �!pr<�od |(to $5.7$ pF�oryta` b8( adapm�JJcAPD�.ld-, shap��Smp �a� Ca�G ra 2020 SO ros %A *r.%�# %se9�S-�Kr %� 1 $\mu$s pA'�, base��P n�j $=$ %20�!�ig<�vn digit�Ea(a sung ratEW400�iH ;he$ B�%yRiso�a tppulse,�Z�  g� aa4in aM%f a1�o��j=�6!9!�c�K flo�.C A�m�a�%Eq�!�.�Qmethod drw�� _ 4Karar:1999pg},ma� sit�5i�vIe<V�s a!t�If �� yp��)piaR�ec2_sum}B' ��>+ )� =.25 ,6 =0. ]{dec5'FW 7�F10 G�  Plot�s%:2��-5Q�( � 10 J� (�S TimeI�es*�%!�400 ns e1-1WCrandoms i� ��!�da�Aake�n� 0.783 atm�� 0.777;&�,,�hT� ar}  morFor���=Ws�� s un��D�wA8cquir"|Q:6 "B  K� �h��wqg $Q_S�푑��"v� y�� &�T (eq:c1} Q_{S&fs�(S_S}{S_{TP}�U Q !E��$S>� 4$9 %p�I��R)�%�!:�s, .����c��0-h �bs cruci� GY ��leN��p�� $ �= V�C $ t/o��� �.� �L�5$s step funP% ) $ }$. ��� 7S���nmilliO� *�$R!� a�-4�Ht�$2�$$ � i�_ �zof 5 pF�QsA b-sde ^ely�B�Vng�=-�*!A)p1�!wS�}E�$  MeV"� .�:� �(i� um}�eZnc&��gyk{Si}$ n��,-�Mz -hoG aiR�silicon )&xis��ə3.6� pm$0.05��|aprileOJ{eeas1 }{ey~�}{W� }|_{vac} ^e%��ele�)x"AqR, a-�M = 5.04 {16 \, � pF$ ��1�. ��EstN�  (3#n Y�$��CoPY} $6�$� ('E-�9������� DUV:o�.;(� M�Ded�: J�}�S�on�*� � DiviP�� "�'�*h �los�%��is7�k1� {6%v�V&b� �s. QueWTng,U-any un un�E�@freedom,d� a �d1F!(d `,c� to�M�8ultY&1V�&^�Velod )yD to eI,�aQ+ v a�ou| tup. Wh��Bh$s�"w &�ofq�&�"�d�Erl;[�%s�[o���] de�2d*�a�!�FFi�NIST}.�V�6; �Qs �<.u�O�"� by �#/ A��!M!�threshol� sc �*"�U�A�Aolltd �b�:!�achi"C The � accuk � redic��H�s"3S aJe�&9��,�   Bais &;"�aR our �'or,5�a!� tio1Dpro� � �M1#/,al �,5p&�5�8 a�<� -s� -down-a�V�R,� 0.98��Y"�!�%m� 5.�2EB�hqui a minib<y�� of"�6A�t)�'�tE�� e��%U �'s7 id a�DN*or Agf" 9;�]*, two�lDre2!�Meq��%I=�-M8 &\h&��.s� "�fa1��Qvy \s-F��sum�ZA* ofYi�WVa~� as suggesA5bym �=  ] �� &V!� ��� f��s>�5 DUV >+�ȋ>�#araN$J2!&h��J�.>To��"�,� �9Zb�s� �I��9��!e150nm, 7 �3l�d0e 128n�) e�N�,� g]�/pub�Bd. A2e"e���n%st+ �4b0��(\emph{PMTs}!Hb��́ '* ��Ben��o��� )H3mad� a TPB=/  1ing1���/-inN�r&5g=5shE&v quit| lev)56;JO^JK[.�5m��~(i� }&,!� truml-�{M} �ZJ<+5C�J�label0eqcalA�:*_{q0}e6d6s�Q_S }{(eWN�"  G)} ^k*j���K "��`�  im{!�o!(ei���� a�� ion #��)+$GqMHd!��. FV)#�Jexacte�p6A7!f���(ata�[&����Z or.U>s�EUrb&�/s���2� E4�8Ay*�7E�-e�ion. FurA�,��",#.� nee`be su�`tZ�-g6  ov� e full �acy(\�"�-. Ui��fT^r6u<1�� F�J[ee�%f!6KiG �� ami�5� "�!!��1 zeroJA � \��vi-�vu ��IR �,�r% �+����-A|y .��UV6K 122ve6�Ia '3  !���BF^n 6e "�E�AR��o0if�r5VRai S�yv6� ��"�� !F�A�DU=���%3��'F�a�$f��*�0%��;nd.5v: .;s�(<krxe}�)�s�;5md�&a.rr�m��\( column do �b  e )o ��^{sim ���u ]�EJ�f�is*J q/)(() =1+7$� &o %75��$1.22$. OurA �good akT�tq� �s quo��t�'*�<>� B�,!]��,*�,$p_{Kr}$�+$T Sha�3 & G�&&�s&� 6t�S}{:�)���t} $\\ (atm) &(${}^\circ$K) & (.() && (fC)&&&�,U, 0.62~, 285.�o10� 26.1�1.8�7.60.63842- $0.97 08$�,S0K284W- S8 S2F/& S8 ; S61w-$�ST57T\T5 T1 C��/ T4055$]-3 l�T51�-8�-T+T4 90& 3246!�A� �2T1!>T7 C1j+�3�5!O296�T-gT-�w.�" nh &$1.04� %� 1�%�0.r �N�aa� -in[#tXn�#G ex��2uN9*P�z�b��&)� t�} Nz�{Xey{ �{�{^{ 0.43!�2862'>z20qze�378Q29)�10%�R0�0a�a-Y�ET1$E}9i60 3iA}3e� 0.10�Y 0.37�4.bR8.0 �7A�325�A�35�0��Ra���R4�e� $16R316�R2mu �M�_1Re�0�t��)�xe�Bpj i)[ޓ��Aݒ ��>�883k3278�35Ŋ87EAE $32.��0& 333A��47M�05i  0.808��78e` O9e eJMeBMN18�N6f 0.06N�"&��� N6E^��$18�{i0�6F�75�6�52aC4aA$14M5&289!�N\\ %872Na[ �3e'3N9M]273!L5% 0.04i���9a��L%' L�3 �59M% Ma�i� �8��2.�m�6\)C 2f&7!�2�7% 9�7�812O%�O $25F9O29���$!l6�5��O!� �5(%7 $ 17I}�8281�!H �6�1%H81.�O��^X2652ZO67!gO!��%r�51�E�246Q�7"I�)�7J209k2/�4ar�4B4a.4 .~&9-v�  linI�6 d�!gD �g s"Y/�� F�i  s#�:Adu�G�<*�[ %� Kl�I�T- 7!� ar}2 ��!�: $p_�� �"�"b">�#5���79 0.2338a+ 0.23��� 2e�76�X 57.�9.3�932��250!2580�9���19��54juY&*�3)v & �3&� 0.86aҡqM�9X:7 �50�h�g 0.84+279� Z159)3.63�)&56�0�~79u: 568�<4.�5330f 0�$ �a&�* �+Filter&'5��"ir}.�*q&�r:5&��-e|�*�aQ:�b�foi��snt.Hjn+�l� �S*.Lena��8 n+�Fs� l�!��"f"*R#�!sXa �N�(96es,��:"w ���"g�>"'d�-n runn! �o��at�/�� Kptimiz"';re�N�eVUs�� :�&� ar})��)�atuer @.��"e�*%N�%A� Usha"n. �*h�/'plol6EE bitr�'C8s�F�.��7�� ��fiOn"a}�~&�+L�+L3} S(\tau)=p_0 - p_1� \exp(-p_2 $ e:I�+".��m] � �$decay freq�&���02=0.395 \mu s�Z*@!�� $p22 +a�2 �p A297.F"�bU��%�klud� �P�OqsU%� atmosp D�6�Rf��2guaranteE�L.v�A���4e�@94$�!�!I-!"@8#�X9haZA�itg2���&t)tiJ �e� i�..0r(,! � sa�nd�{d e�. DR�/�� �/280�(s K o ted �emol##�Gi>al�-"� is4Nid0 nfir{B�)m1e�I�S!��+�32oe�y6cl2aQy.�see � �-.arp�6z� �}1;�� �as�@s8�06J�&"- �-arpZ-� T|/& 2az�N%�o5P shorU ��}� �@#�)> r�-�squ!�marker�K(f�.9Et,�eas tl|�N�Iz bars dożJ�"� $J�J�A�ѻ�5f@�ہ �J�e'2&�Ht*�*of $~10kC�b� U(�*n$\s�� / ��{x}�F 085$��!*ev��R2p �� !�>��F, P�5� cons��8par�&l (Ode�-s!��(��hD sU)����+�Ia�:" No�C*�C"�.n% "& �&( b�LE�u4L*[L b� dime�Za�>v �R6�k9��Q'%G subt �!� "MJ�A��aA�n?, repla16-/&�� aXa![.�? �!m# .��<2�a�aQ Bir}. &҅$!���{�� e*� e�*�����#*�Ic/ote&�B"�:�B&$D� �J BE � VEsh=zb�t�dedS^$�>�*� . Raa �^#�Y2 �d�'B��$nt�"J(ofQe a�Nq% Beca�)*�S3E{"2 �xeCu! � �a fas�B�� �4l4!�6JM�2E�*�!:dY�E�Ek.iir}�5noz�!+!� �!Ral�m!4 b�4yTAis obsey�a�Q:�Ze yP#ofA �!̝. �OeS!�mP�P�/rAprecurs of�](�VZt ha9a� "�'i��'n $SiO_2�ti-refl�2vDa$��* �6l,.�paque�UV.6A� to QL F*�uc�De"+?nc;s�#nm G�C�� roug9Fis�' �#t?`c�We�x�6 iori!7� �� sidu%� U�of %��9�D�A�l��To*uc�,��mbigui�oa .c �{/ 1 mm�ck�! was $,"kDi���`2h �%Ms& "u-���!�noI<mitԒ3 ��0#da�AEi>-�E 0A�� il �d� �� �lM� 3� �Rn IiG%KD to��)��"� 65.� unf�"�:�%`j%)�>�).AV���mǍ�. L�,, �IEsuper4x ${IR}$oe%mE�sH!2�V@ Likewi�:MDUV}$�m6t1�a��A6�aXwrgn�F$N^�"Qof�>a]a_y alway� &�a�����"ini enthesis% f&-O jir�&2E#A6trict �CKDNbr�a!TVF �/N"M"�9" 2�>n��Aoej?>�(I�>C��%�Yz�� iQIoa c�7v � ��=�:Fl)��TQ*'#\2*q%�"�.�G�&mA9e"�uA+m#4 )# maximumJ�!T!�>�Dgiv!� aF�&7�h\�?N.�� )� � G}\�?_{ ��$E$81}{\max_{270\le�/\le=W!c+:1� 18�N J)u�N�$ �}bi+ x r}(>�)=0�P$���d. By �i"EC>�:�H+.K:� e "���ޥ�l�H intoF� &C;IR}��a\�; eVBT,u�2k:q�VN�;e�Wto  a�2�a(c �8a�6ſ� �8 . W4A`�binRM%f�6O���^Q4 23,-G�6�>M is;FR.����-*d=Y �-(h )- Ilu��BLMZ)^�=1Fc$�(�[%Baw �GofF�Wl-\!oL)�V�/c�*� !< 8 nan�Xɹ4 any6�*�b$ �$� -.  1�9ict]e�<,J�A�f�T zT(�T!�->��>IR���~ �� �� ��5��) *)}2IRYkeYH91f2�nd�� and,�an.�F���/�/:�min���6>6gb6.:� l�y�(usNd 0.42!9^� 0.73:`�a17M�krigor�ma�+�?e$=L�Limpur�]h:F @4acM�Z�?f�V�m� rce]� �n94\^|Rd&��8�\ �a� in-�Ƀ6B�I�\�: "8 $�� e/"�br�3!/IR"�3�� �\>g/.� is � �G/�, mak�BB ��5�l�G in�����2��<�FIR5jIn�&�Q#* �-�2�9~!� F:ly 5�m  !�[tb��7qeffdecZ� �~2:��.���r��>��:ep�?eI6�O2,62�*�1q&��Eis &�*?0ad 2=�+�N0��, 5�!��(u,9�+6D"�t�@65�mpS��6� 9"',-� &t2 �D>�h}��4e��s sig�ly D8L�Y�&�3a��B conviSo� mean�>�s &�h� O�0Z�vA[Km� ��"� � �.�*E -F�I.2Bfor�� �nR�GQ́��%�[�� �=w 1U�R�.�cana�b_%n wBo!S9!�?��4IR��.O=ń�"&�9f�@ay! �B<vB� 27���H �Ly Ai���# r�d.��y42naP�pl!���noty-�u[V� ^��: 58\%�8� �i/X" ��sum�Xz��v�v�CYk)Wbg�<"reaB�.�'s� ��Zjavail�&}�/�8p�� �. �[������! Dkf illuE�� n_@`6. #5R�i�Gura�5�6_$�r@the�6�Y3�sA7� �\FR8�81�te�;o &59EJ F�!A�Sayat0�!�1GA�UV 9��M�iwr-!�a�LidA�a��&4d. I� icln��)� �eg| mor�v�Da�or�2YP8�'e,�@]z!�qFQH!�p�Ln� a.��W� *{Ac?E�} W�k  3b=NINFN Pad��group!9Och�>l�u�d���Mics��.�D�nMt�C_YwnMank S:u o Ce� (�)J!�support}#a�e F78esco Pietropaol�[ d Pi cchi�in�l�n.2��_=ydiscu(rs8 rka���ETH/Z\"u�ue�Swiss Njal | F�G.y�Ap�^�Jr- starY<Akz �endixya 9x s��lA�tKd�a"rH! %BQ&sx�>�b�]t:�|{00D\bibitem"5mT. Doke,~#Masuda� $E. Shibamu�� �B sl{E"+=a�Ab~'e2Nk Liqa�A� %SX�FAZR� �# (1�`)��Ds,} NucxF str.<M�UXU� A291��(89) 617-620a=�2 �ic} Ml�ztc�Recomb= Luminesc��� I&�nTracks̍7p �^P�|�H�s�� �, K�G�)G� }f�215�3) 345-3���d}ӆS. Hurs<�1�VacQU* sRa�v�J8o E]F�A�"�oes,c�!bvB 2,�70) 17͆� miyaFl%`M ,AQ$Takahashi,�Konno HamaA`S. Kubo]�H2g!'U��A|m"4w��F�li� Et):�9,3!V74) 1438A)u m}P�L�&am�To�O]in)��!�-�fyY�raisa���IU"�B[C} Int. J�-�I�Is� 10�61) 116�%M��m l�.€m�=�9�Un� nd \�.�,�:n�)ireB=ʅ�l�d(pair,} 1979.�"�f M.J. C�f%�G. Klein~ b-qY I��ed�� ntil� Dense%���g: E1�["sd�o��Beh!vu�H!!�c3A� ,}f�178!�(80) 469-475.�ad�c B�c, Inc. df4http://www.advo� ix.com/.Qq ro}a)Am B,��HAntonello, B. Baibo��noveh�,V��M, W3Clch�Qk* Vent�ב8CoC ��sA?�^,--a�on6 SKon,U�l �# 8$-TM/2002-0!,yn2�[��0, Y. MusienkoɂA-hnelY!Cha+%e����a6"w!w�l caloht��pp���mj�in2e 42%�H99) 413-431. %doi:1�:`16/S0168-9002(99)00177-1 �V}�SApr V�Bolotnik!�D�~en �,R. Mukherjee�W v�m���\,}���48, 2A�93) 1313.Y�Ri�֓ , J.S. Co�y � M.A. Zuck�_t��,l{Stopping-P�aA RzQ�#s !mEl���,+� PHelVzIon#�m,cs.nist.gov/��Ref4,(/Star/Text/��d.html=TmxO P. M ,!: Bouc\� zrtier9IPA��FD�od D�.ALA�U�@Co ^t�h1p��$4��!q�]������Bzi, Carug�E!| nti,AIannuzziA TG6neguzzo�A7Q� o""�s"��z r$by��iz_ �Ejg�$�2��Ў)�--�=2�"=O S.B в� V�ݏ�l�#>Eof�6�&i�ga�? 452�� 67-1۝.�HKAF , CAontanar)�L�sߛ��Ros E $C. Vignoli�kDe�P��-�Vm%&�:�)bq��f�{-�im~|�|t�|},f�>� 505 !3) 89-Q�. . A�>Z *d� �m6/�{* R��,ɇx,cit#b� Q��All� N. D`y \�Rol��FR, r \f�{�&om`^oa�c�/u2}d��-rf@,@ucdavis.edusy\s�S{Dea8�!� Chem aEngineRr \&&�erial&�M ,C UC DZ,DCA 95616, USA} } \o�In�g�'� a�%�Biomemq#�1$nd Alcoholt  MA �)A�Vach!� make\�a"]�We�N��* l�0lipid bilayer�?#iv z�: mole�ur*��d��l�6�s �4ai�i)�'�T��� oKe2F�Qn �^�Tmphiph�]M)*uegy+�&al�a� ,coarse--grai�{"m!!de � t sD�&�):Ws�^7�q4 a �� .�mder�'!y&+J1\}:� �!H m� semiy�>�Hexq 5maj�e�*�$�as \�/;l����.1�e.A=*U�?%�Z�B0-�9.N a�bYW 3�ep�@s xin�!b tact c!-`glycerol backbone. Butano_Ha3M�� :w�*dt�5G&bL r ܀aer�s. AtLyR��0%: W+Ȳ1� terd�gI.bet��leafletsau�" 6��Ph�6o:��,� mpo6�t ra3ll li&cells$tLq��� bulkA�(uW�a�in�0el ��%�u/g�surpri,�L�*!�a-0ar��voas-�explom\�� 1�h mp�2] play�,�Q��y1^ �.|���� BJ:y mono�8��M\bXv",A &0��v��I."�_ soph�Ea;0feller95,tielf�,97,tobias97,^{��-e�v#a� infl�'� )z�B��s b ,a����I2�` �b1!мX�^5��ate&P :| %�!4�uFe���,leA o{�ond,Bi��ӌ�k��� $reu;e�A �� 21�s n---u�� R� ���a�^I 6& .� �-)A�*y�sO�ct�A1�of% M�a4��F���, � !Sab 9��=)61;h!saR5�q�� ler04c�"`&#� &Ů�$���dyn��2�teF� Eo&� .U < � 9Jvar��-.!s�s�ia�n=W--� �:16�p�@�.O��t 325~KM"'Hic�"(1~[��Jd "�SLO��ul�+yd�AF@ palmitoyl)atidyl^� (DPPC)9e$128QK��i.e., 64�<. 9 :*cY''� e� /�of�&�ը �L* �l� y�.�=5$ o�o"#ns�b�cax�^a~GROMACS . s0dM�gromacs0an\W�3%{A1��� ing}�,�P�<%f��%8���a� for !�� A:� �bA��(ene)o's � in bS ��)w �X tai#Th��j�5ge�M�!���?arb�k�* llap* iM *&CLE�om� o�i�Dy�s of theT pure bilayer, as well �s with up to 5 wt\% n--butanol, (lipid free basis E@ do not take the (�s into account for concentration calcul hs) have been performed. Sim" were  undeRPstant temperature andk press�condiys using �PBerendsen weak--coupl4scheme~\cite{b& 84}. The ( time �@ $\tau_p=1.0$~ps � T=0.2!�!.�,respectivelya com/@ibility of $1.12\xH10^{-6}$~atm$^{-1}$ �s.8!�a�P--step of 2~fs lasted-�410~ns. We used{utoff of%)TLennard--Jones interac!O"1.0~nm. %%�� model)%, designed by!} (lee04} wheri�etha�< was replaced by}�. \subsA�4on{Coarse--Gra%JM!�ing} For%Sc "g ".�our)PE�E!2Cpoten�$parameters!�e �a-�propoA�$by Marrink]>}i�m 04Bi-c fc dedu!%ean2hy!f�J DPPCM=t footnote{%"�co2�$available �Tdownload at http://md.�~ .rug.nl/~ ^/)b%`.html}. ��E�%�origie*9H ized��repro�!�P structural, dynamic,�e�ic%kertEV4f both lamella%� non--phospho%� a+$es. Groups�X4--6 heavy atoms are com��' �-U>.a site�O8are classified �\rd��to�@ir hydrophobicity)� �headg�!� sist� fA�a,redtwoJ ilic !: one%HesA��C c�ne%>N!- ate )htwoimediat�� �q capA(!Cgen b��ng !�.�< glycerols. Each5���A� tails i�2���[)3 �. W��,f� +� ��%A,�_ e~>s jreaA�(ter moleculA(All/1�^8 in a pairwise �" er via a 6� (LJ)�?,. Five diff� t LJIx��nd rang�a���� �A?.�sAastronge� '!2'. In aͳ5!�LJ2% , a scree��Coulomb.! is �tom�Ee^� between&0zwitterionic U�I� Q�E� bears�� hargEd $+1$M�h]� b0D-1$. Soft springs�A�ed%�s keep 5��$act. Angle.�provid�� ap��ra 8 chain stiffnes�correcta�2 K .ő$efficiencyAu(sons all CG����samAas�  72ic unit����. ^�4�t�ha�cdevA�Ѯ��c�i it �q- def�Ii)���6 ce--field� Gs8 egy expl� <manua��- ��us,� �s �F�5� Adimer�1a2�e�a*a �-F-��s lik �G 9�,� m@O fis)�a alkan��Ł�e&! uj2 .� �6 ii���' excha� d against���� ��� �_$, this did%� Km� lusiAn� (ificantly. X !waw��that F%� make�� �"`ymmetric amphiphile which� AB fullE� listic. A D.�o L M*%E�  dAo�� carb�"b i� � s!/�s &E"refer��i�at wayuremai� )K  . NoteA0��)Rdo an� --optimize�> any "" e experimen��� slightly�3 K s bu�eseW!O0as successfulA��+ay be at� b�� $quent workKEpwA^�o checkEqua� ���� %�. ��&�A%set� -��W %m!,robserve !0 tend��of A�a"3�GoiO@cal�� the 6@Ag eI"u 2.4$\mu$s2�E�i�� eff/ ve_ . A c) facto�cs�$previouslyn�B o� r ipid l1al%�e^ ra �`self--��!k�u��CG)oB� !� � : d)w0is paper willf refo>e�[�sm�!�physic� meaningEJ! exampa��.�!�40�u�co"Oto&F  16(. � box ��n�q����Em͚>8AqaWto $5z=�A>6m .� s�0@!2� sq($R_C=1.2$nm-�I�r�aa7(lso visibleI|e �h�Q"0s. SinceŕCGL enc b&h � ae CG b�YT � ��, sP at����ed!��A 1:100 (T:�) actua i 1:400asiannormal��%/�iA�� �ͥӁ� �u�$, no furthh����)�$applied. TH L~\ref{tab:sys} summa  ��}���is �� F� L fig:snap}xws  sho!V f anN �: �6QthA�4arison. \begin�le}0ular}{crrl} Si�(Type & \# A�s �  mo�2M< \\ CG & 0 & 1300.052017:321BI019:M282:45:N954764142A�.�18� ATOM �365= � 8 &&021\\39.10� \end!�%� \capA/ {OverviewA�� -֡�%�s. odes Ej�tomI%de�A,a�� �B� .�.F S E�e case >T �x�number�0 * � elvr�ond4 �f��mqr"�Ab�|: ��� sF ingl" 2� s} \label!^e�5lA�q ainclud phics[he� =4cm]{!O.pRn& cgsn &1�Snai�: Left:}�)lj�8� ; s, Rv: )>&�./100��e� !�( very close�<o�� in (�*ed)6/. B�ȵ�� high� �"blu1 increa9� ize�� clar$� � � AQL:�� m�du���$oxygens.} -ʵ)�1�% \TResult: d Discus�} %�most im� V uI�FD �Aat 2x lonbA� s ca2 achiev&� �!n i:�+ �S InVamF�5ej� �run %~60q}� �("e :i 4) took 40 hour�< a AMD Athlon. O� ��Ju!�Ij!�.���u8 about 1.5 days�a nanose6 e speedup!laro� hree orddHof magnitude. Howevhit19Ʌ�A2Z[&��"����lying�. T�is end  �ar` a���� varim� areaYuM�*� easiest e"kalz F%0 such. ��. It haen"� :&e ��i�low} ar w��  �ly02,ly0� 2� w��exactly�� ur2as!� a SOPC" ,at T=298~K. is unGazsna�l � ����4 Qi�,)"%�quantiQvJm!��can_b�de.L!�.�wO F�>!�of)%���4$xy$--plane --F$z$ diK��Ke1 � +di�'��?A[�sED leaflet (64)3:2 �2 Idep��"O�� onQ6 �D show data�GY$� Ly eAX.� EN)at ��.�obtmgoo#ree`"�al�&ree nsets. B"9��2,2% }C �����O�V`} ason�����R4` 9c�i9s. Re>�--�*u ��=r�k"8V�jbe mad}�V!@ Y?�re��)�e�&��#o�dh!�� very��roZ����. If w!���.xon �� % \���hin k:FE��ty� va� ,of 63\AA$^2$m�(nagle02}. F��e3weq�b�� expa co�t�mTreg#��@of $\kappa=14$ nmq%N��! ��!�B8BA=*�wPoa>Eqto]�e a0MG6�}�]F �w�fd �� esti���9�!kX ed CA.is��m�N; extrapord. ca5�iM+ yst6in E! � n�2�B�!��e�e�V+i%!�YOre�a�"��mF)?� yQ!ph/coexiste}a mix��.&8-trAo�-.*#)�edM�$faller04c}"��m} B� width=7� rea.e� � AA����"but r"Ded�o2 !�%�I�17(s (see text� i!s)A��VQ�v"Rref6:- � usnan�n�� (A nstead�{B )cQ$�errorA�:�.�to � 5\%��V]� 2/ 2\%."a�AZ:��ddensprofE�(\hspace{1cmJ�.�7100 :\ ^5.2a2ileA�6&yD�tyV"!Ii"�%':a=Q<$upaNpan�'�qBF8�luer,10 (left) or(r)A�"]o2!��>� of 0.0019�0.�,/")I�lower �.&a/�E��2^ e105. ��&�*Gb`6;% ultiU�`/ t ) � indic M���s6�1�:�I.� �terest!2d'mj$�2�u؅�p��$�lo ���i�� !M�Ks�& through�s]Y�c a cl� sem�� �+%�a�p�\ge*%�7!� high\!q��e� � �� ag$��ts (y ,,Y:A,st��isu1�s � !$"�'YL�:Z.���(tieleman97,�!"�QP5�! mai 1�a�d�face.T�!+p&,#-a�or���)�m �fe�z(2,patra04s}�i���8 o�nAR ��:�� -� io'&��zero. A"g �T*oofAE�*�s�#A[`at� does[�AftheQh ����5�V�ros� ���lt re cit>Z. GeneraL��e prob*^R pene�#g rsIR -" in length� �/!��"#ity. C{ !��:�E�Y�� ,reveals some��cBFirst,��e�%86Fde���\�y )�!Ra�/S�?~aV�. "*%re "��"s ��� sUM�6��*�� ���V� ov�gI  aff),r/1���O baId �0���9�.�E� �6� �>�� vanishzl -�. Cur��/{M^�5N� �ooatr�[��aGex�-G�]��M� gi%e# �� �| be� d to�$R asb+ket&�*!��'ɨ fekA�Q; fut�1rF'���sira�.B�A�� $resol} all�M�I�E�v�g��-C5os� a��1ol�",) gcouR$b-?) .+-2om�-K o.�� i�+th)Bept� anoloy� ?conT)���� �& moiet�A�"G�F�N0A3w��aB.���*�,15��a4�wa��lR��N "] fi� n����! l�"e Z(�M  V�Gbm�and� L5 coinci� An ��&k/ y u�jexc�nt�Q�wq M }(ck+U('di�'c68Mlrus (orM{ ate) � �� �%th `� lead!� 3.96~n"G�Yp }4.0"��lY,ry �� e�%�@5����!� ll�6% a5�M)��)v�--�K �. OH-E��u.�si��*Q9U�eS.�+�5.5.� �z!6� v5fAP> b�hQ0? ��F#�����W�s.B(6�� 21), B9J/19)p*=e')��>� �AZ rela(7 ^3�eak(� b��lyedV� %�:�  IfA[L��2x�>�E� � inb�}b��� }  :e��Rɥ beco�8�Y I4�cE�G H occ8 beca�5n)E*�notX3mmodat�&l�_��0" �J��i "� i� am nounQ5�h�e}!�6:� �&3�*�a��&Y al sugg��,8� � �digp$.1��� � !Zy)Z͛mou94,ad1 895,kranenburg03M n ����f�"te.sw�su2!����ile�E�͘�0V.�3Vsuely. >W�&[ ��7�s�(>�'!�t!�6o5%�3ec9 �censm��:�� !�alread!�!M�.+ es< *6�m 2\%L!�*RweeN� j$E� 2��?��� e}a)��2��,little impac��-��.� �6D�s%�-?!jm�6<�d�abandon�(B%.(A�erJ��P7��1��H"Z:KYM�� �#��>�y��2�ld E�!xa�A��lih�e�6�56 curv�re shifx�I?"�[qsq��!uU(D6C-�)!�at $z=0$6@1L�;5'(��e} �$ K6�often!��e�*dD-~de�#ium_#&e� a�� d asQ�eqnarray} - S_{CD}&=&\frac{2}{3}S_{xx} + 1 yy},\\ 4(\alpha\beta=la�5,3\cos\Theta_ #}20- \del% \m7 le,\qquad b,=x,y,z|2O��hat{e}u z,Y&�V $!$!%a�5 vec� �0aboratory $z$=0(ion� B�bI ��8|�/�m)e6��e�'9� *�@�b�'o���connecA�G#� >hE�� � s) C$_{i @, }�7  +1}$ �vec{e}= r}_{-AFa��2^��A�hFi��a�T �=of�1�!&� iEs, 4�9:eh#O� � i .5a 4.P-� M� $sn-1-sn-2$k8 ��a�1$ t=�l�6%��ly�-�"�9)x`B��NCo�'+k9�� 0 backbone. W�A�G�Y6`� ��H? de�l(g&�6���&�a"�%]E��&��.!��--O!8!�>��_34�6p�$t m!� aA3k?�!� %2id��� (!M1${ 2$)�s�$4 �J~ �A�-"lle��>� �7Q E�influeJi&d;��im�= vicDn6 whol�yYB�� � >�>�W E�!8inguish .�a0% "� ��"iSsmG5!�&� ��!R.�m�� lyI`T %n�4#nͨtoue�a�!�� ��8 � "~.e assum � �#:&��!�[�e�s r1*m6quaq5�.%�tak%|heup%�oSunt!isP�1�e middl�aB0+#third| �� (C$_7�|C$_11$�+17�-�8!BK�8 ymbo"� a��$u�y�2�I�. W $  �%��get2�&&�. D&�-intrin�averag!=m�)�&|I�!Y`2�!m'�  10\%��co�be/&�i�%�?m�IO�.J�*h ! wda�b��spiri��bmappingAe �=p �?%��Q�%���!}aa<��05:�(i.e.�2�s)�B#}z� �q5!T9&$ mD>qA� ��#�Qf� i �Y6�!>GaN�)�B\ L�:C"6B< ��A� star�d aE%���V 2 � )��g��!��jvidual�������*h��ar.�6BD!1026� %�� �"E�1Co6&}u-��tudrI� .%�ϥMV��, �� ��A)C�>��  e�*s a wi�K5 EN"�  be s� y P@ posC9�$= 5D _��1curac�!�M,�~���A�b��A&&e�&��2G�V�% .C���a r�l�Krt am��!�3 AT,A��so� s"n2) �=?ne!5L%<�a�:�a��?�y eng}?funda�%@a(� !�)X�G��!d*�;i"re"5Q7�+�H2�� � lear*�)]^\sh��� �)�cau"� �* njun�L!�#:I�a� i�?e/�m�!"�! q*"V � �Te�& .� "� "9}re6yATeT- - reg�>O�$� � U2N�F���r &�4%@cVb%�to retur���D". L�B!N?��OE*�� ��R1 %R�2�;� ?a��)g&N ,ibliography{D dardr>0style{JPSBnewE docu�} 1L\c�M[12pt]{@ c�;%\u�@ckage{draftcopy} .amsmathB font�;B�/xsyn+epsfig6@verbati*�,6.5in ? =9.0oddA�margin=ev%d2top # -0 K@renewcommand{\theu!�}f .\arabic{4} \newtheorem{ }h } FY$f>X6Wco�Cary}[ !]{C2�lemma}{LJ~ N| } %\pa�A1�Jg �Q#(title{Quasil.od$pin--or6mo!?E� tu J \\ �<torag� rL&rQAD1�_ed��sa�of Phy�4 v. ST Acc��Beams {\bf 7}(12), 124002 (2004). }��author{ D.~P.~Barber$^a$, J.~A. ~Ellison$^b�K.~Hein *n)kA $8{Deutsches~ElekTN$en--Synchr�ELn, DESY, ~22603 ~Hamp,~Gery?} \\ $pS parta��Mathem�T Sj9�Bs,�UUniver� ab5Mct�L<�--dept� alysi� ���p%JE{pZ3�> fr�Ic�H�go& E�ae%E�>�%O pin M��e�I�c�?d E!�a .� 2  a��1�erm�Floque��7� �c% w�Fun*a �Da>� �emergŐ anexpon�$Af * 9�  . To �roon non�si--aa/ %nsl  OosL.F*=�q.bi' !&(�(i&dLA>S*G!�Y�)�6�O� ^5too/ i4MC app�Q�'q-�$�\i-3)\Enalogyv �z�?I�Mv.mbcircum��cesB "VL N%�)-�uni�.>MO60!7��. LpA�une� a I}j I" wh)er�<�@��  fulfi�J. Hav�{y.gw1���e�#n~ 9Y>gi�A�d+ ��H)��sgiv�n� !3� Z� `� !s (e.g.\��V!x>s!5�j,qKb�:A a DiophY?n6! �)%� illu� �/&hasX3�#(our descrip��wgs�Aal�p�U)!�sPm�2z#6e�TAX:A��\to ``k9''�E duVg�*��!��A�^��'u�����5By"�Int\<��2ap^4�TSrigor)'d"�D�!�k���.r`B- ToU?` scen�(C !�i �A��/ key zNJas*W�2�6E����+n�%f q#�>iu�L��ecWon e $H S$ (``O&'')�o f� of, a"_pleW prot���$roa a muoAe�� SndnDe�Z-UsDp"�1�Lo#/zA�ce ��es �.DZ0 Thomas--BargzXd--Michel--Telegdi (T--BMT)!� z\jackson= �K&� && d l ({S}}/{d t}= <\tilde \Omega}}('E},B v}) �N !k({S} \; , ;Ieq:1.1� |!!�]�!%�:�$ �@?$� E},~ BA v}$ q��,JQ�6H:�X)� F=�,Uz velo� P1Q��� V�BT�na���1\"�,M��.��beH t6 Ie!aZ�fcan1Yak1r�&�e6@=`ay#-: $u$ �six�\ s..�Q,M�/ n&� tH=� �A� one. 2-longi�@#(-a*).0Nbunch�1PQr�auP%W.b K  H%b�(&� , b�2�cI*�&we ignzra�\ia�/� � �"��O� !�vacuum�. �(�OM�)�*E 1T GB�I $t$.&c4s�"Z;g�=�A�?Q��Cle� 63!Rfi$?��<R5, " veni! A7dop��tab p%�Er�a��$tMV% angu�p_2 awI�, 'zimuth.S�%4 = 2 \pi s /L$/9K$sy"!'= �>O A$L) DAPMQ��F�B�a'V5 ta$ aRa� w rewrq/:� �rm� ��:F V�K�D ,{u )})F>292Z9��{Z$ QmFN"� � :6�$�dre�T!�E�$d t/d �$%0�k %to m�,� ů�! �xbhr1}{^�.bea J*BFium, Y\P1!_Ea�6I�de�7 $\rho -8 , u)E$2\pi8I]^�inQp$,!�t� )��G�U(rho_{\rm eq�*E bj= 24  + }�.���N� o[ ty:!�int} d u6H =1$�  ne�Yar�" �2s kN4of��iwG)5n�b�%� t am�A�!H�;�N%ha�$!�s auto�<"� !O6�. But�c�M�����3� ZlsUqui�0 C�s�x E' �Eo�="�(ng:�$�AergEM�h�* ``+a boscxX&("''�>���{7�I�eh}A�l QG�al% �e  enco��< �um meM�X.U�matrixB%K 1/2ŷ� NF�:� le�,8�+�'2F\\ "" � gottfried�Gor@a%��z�he N*6N�FP+rm locqe? each poin�.��.~A�(�#"0 ucd �s, O S}/|��S}|A� -u�l|\cdot|$!poa/ e Euclide��rme��E@2�3 w0'A�V:`` 2+'', a��n � ��{^�2T$. ��!�� �4�.�2}.�aD S��n�ZHs%�� ,u)${Dme)R�a2z,~�FV W))$� obeyA�eB�I�(dbkh98}. ~F:Y�)[6�-Q- �/9�anntsha2le-��]F� D�  "2�t  ��,� ``C� ''. OfUh1�lB�a5.CA�"j re  o�]dt�%+%2#'6��,fu�A�* � �7.S4s�o ��1 !��A!smM�:P5T>A{ 2B�--+6Y>�0s $(J_i, \phi$~i=1,2,3)$�@"vDQKDa Hamiltonian $H(J�ThUUh9m.��rt%��-sjo tori,# ���h.w7J�Lqu#/w $J${  s}.?naWk4�: = ({�}_1 phi}_2 3,~JJJ_3) \A v (*,�A�-;� ��a�c M�AU� �J$%�..�adv�of �$k$_i$, ~$\oa_i (J)�\Eal H/ J_i = d-�&��� an�+q���3sRo�RF���s?Z.�\ofD9refer�2�Vs�lwe �u �g' at usage.���? !Niv,6��] "Y�nom�� Jh)�Ɍ>Q �4*:p %"� $e * �0�n� �rmpanie8 bhay1m�2F3$. So*�\Da sol� �Er $"� � ��!�%�Af"+sls_ p_(suptly reF�4�e&$n�.Qƅ� s, �(\ � must�D$``smooth''!�A� sens� 2�om;[n&a߁j6�'8.?&  6�ls�- tLe2L2�*X �=>�� �Ro�yo%a )Z�7 it j��%� $J$.����y� �&� It, JZ �I�,S )�? �`e��ʁh!,� =�[ r} (ISF)W"he ISF��a c + l ob��F�of2=2�� 4mont98,epac98,s 98,mane87I5�X"�!an�Nvc$J$, VmA�a,o)*'"� �~� lowC�Slim B�fr�C 2[,��c\Uis��iBJ6B(J) |� "� 9�|I[)�r��0�a�!$NK$��_�9 � !� easy Q/�zo� �ct� $�};"T��A�|$ ~cto1ya/�mI��F&6v*)�]�. S&�Zium impl��a� ���C\ �eA�maximum2�2�on���a�1l%f�� = &Ua�Q ur9raӺ!�t� "�&�Imea�$� !u!de �^�QŔb�:/�N3 at AfR�!�egeometAf�bf��$u a:- lGvauO� z f� n#A�m�U�r�0hg�e2iaTj2kU��G�0ISa�"� [E�c�|-( ut s�,� �R)V-�M�rep&. F>�fac�-h1-H �D�w�N�2�K�p)hi�!9 8�he s��Va�mXrBO� ``U �''�_���i�ir�Rr�5}8�w6��es �H�� xno�wor fn �m�6�E:jl iA-/E]iei}.�&Pd&� �Ted� hv20$V( See Sec. X-( Altho:we!U�#e�k���3#6��l5�&��a�lso z'8�} i&ny �!�� &7H�ݒ:e�W give132��||��d6 �^�B�8�pis!�ac��2c�2]�.����|J}P"� F���%��[SA#(on 2.2.8]{g0�V6!4.4]{mA? 0}. �.bt9Pz�behav�Wof�=�J.is%k �A 9l*~4R$�O6� � e$g6?&�S)2�0�l; t)"�Mc�(ct .@quicklyD��N.i�2Gwr8n^,� B ��`e�bOcGw�-� loit���a��i� }V , we�#IKA*QIv�c�>a|Z� J &� Ս�� a�!6< A�A���!|�k�*RK ��>is minim�A  e�@�(per�v�ho|�� !0 ���� ��)�-As�*�um3��{ ra$I�Z }�t.& :&�T5A���Fp!�MP� !� e b�'si��q�s j"&Z B� ,e�a6�7 2�!�-4�Mt�� ��!^1� �Y+n,?& ��_�ly 6&� 5��!6�.Oksk7 �e�-,&wly e�, � i�}z�R��� depi�H"jE�1-�e. ��a��[� �RE�F� X%fn�deu��n��dis�A2 . ~� cFW�e�I�A�!��*H�o�� �u few GeV�nOoxTE":!��`8A���' f�[R9eru;!Xory� Ar��4!r code SLIM-_0chao81, br99}4 n�8�r�Z^N�SMILE R�,�,get--me--Not  bg98ɏ�2Lie ey95}.&w'��c4FB�&|�4!M)k  .sr se-rhundre�Hf)w�vbQ.f inad�,e.;�P��trJ�"��% )hPRINT �E��S�D@>a�a��Unumer� �x�2-�v#;gorithyفs %a�@!/re��6v8 ���W;e��v.��ri�A�" CtaneoW}. O0&A�� �S Four1�) X�s SODOM2 � ky99��AS A 20022}p.�`�`v]>u$ ��&�.r�, to oS �o[� og� �ici�#%DI�+j�sca�P /s��del0{o far�*�u)al�3����am�E*�4 ��\o� *N@ A�wdW�al��� op����! �Fm��by2?�r��s[-rujHa5�Var�W�$B,�- seem��ls�e�be iB ot.Q,����^i;li�Mf?��r8� %|in� 10� a tru�2-a}�S�um �(&t��a^u�~y56�A!'� �'~1y�=a� reflE �  stipD�Re�w+c�%C|8Qf?b1E'  5A�A�cluQ =u��b&i �q}�s,_+Z��r-� =am2\ . AfalT_6r�r� �P�sZ2�e%� ��a~Vn��� l4�F!fX3E j�4a�sho�c �st1R�Ź�z�L2�bN-Dt% A8Wun�R@dk72,dk73,ky86}, "�)e so--�e,A��wv�aN� (} (briefly�!�'')-�M_\��{A/s$. A�L�� $� ?T��W�%&�!u2! �-P. ,��'$ &!%A�,%c*��9.�]I *� ftoqt ��5 t"H��*q �:�C ``dr��t� �eb%;ecast avl�Y�eMq f"�jd�pe"�3� .R>� y2�a�in��c�� er�Yc�e 6A���taYD r""}8F�.\_s = m_{0dUm_{1} ~  + 2}~ 2 (33} =mC)(1, *), X{15^�.m$�a%!6a�g�3IK!_�+y $|� | +  2  3}|Jummo?&%��5" . C"�i�},  #�m--EH2bf.M�&!�-��ry ni��H�i�u�% A-��&�Qp �e�́� p�0 �E. 6!"�%0�atq�".dH: ��(ed � �mt�\am � unj2ptabl�|w%Rate6,6_.�#�@y %z� �o &2o�  �}. ~ rF�$�D���\phi~F+n}|/{(�/)^3}$�8a��� { +&�ewFcxpR !�.%WB0, 8��l�Aof �E�,"�:|/+ �������s�is�#. �]�mi be�h � �f����� ��&�q ha�U� *�$"V%u� whos��[ %�y�ea�forwardQ aL_&A����;-s track�i EsK�Qwords:�r~Fd� worlhKv%chnol�>�x�QsE�(['m1c�"�"� bec T<d20R�4e@F�.�-5})g!:��*nonun$."�w�I� }&!�=� _��z�D/BA�voiI>c�-TY9. �7�,$!Ng�>a�'�%!$i'+8):-yA�!U��b�*����e'$J$ (h� ``rQ : � f� l>}�� |�W�'�G8la�SC�/� gy''%em�%�3a--��3eld8A�six} "�al Aaac1 Hs�?69Q�i �il� a tar�!u,�& 290�< �%�$�% J_2$%)$J_3$�W3� not}/ 5mk�Kio�� . I�! �A!i�4u=#me2alX n^:2 Q7)p.NsN]�n�Teo^a�a� )Mn3�."  deW@b�7� .=}29� �c� ha"o!+r+!t %t�����Q2 PW��"��G�: n�?�.��/�!� =!�3 = 0\]Y� �,s~nde�:��7$.�g i�{"n_0}$��.;`c�.$� � 2�s[G��plem: �4aN>+.%V�\t igen��the 1--%?�� map�A�E� -!�)2 \ne!&HonQ�&�EU �!mB�subtl�-&z-it.�,ciG . �P ~�> for mEFo A�J�r�te�:t� is�>p�g�e�� H��2es%y capa�&�ph-�[he�: �mj>'E����oLpurG_�E�pa-�A{&�  a ��B9NonjMG'� j oliJ�� ramel ! �at6-Nif�E=b��wea !�d6N�Jk�V!� �2� .ePmiodd� C$� ��� �$^M),�~<U y�d�����&e �nd���lISF%)= 4)�/s{we�0�[m6� ``folkloruEa�b � :3*�, :'�,mz,,ky99,6�,�<2000,bhr92,hvb99y6oc`m���V�!a\"��"wr�k�-�!*� ! abov�n� �<� i�g� 1��8p>"J{ +e�*�>8�!� f�q9�}ur �m�Z�u�N\�+H2�_3R'I��Ix 87cI Ѱ_�yj1ocC�dL>*c *�,��fifth fL��,-��"4J�2��e�CEo� �s��FY%Gt�6b&~V�;*&P5�Xs $92+=;,hw �O gy ~�& ��%�� iesU�L�*�L!�ory. Giv��S���Z�A��� A %�*eXN5� WT "l5.!�k�> we�������'n�v Our!�umpa saut���v)�e"�4 covei� situ^ �cXPN��6?&�܄+gr2J?���.k�fT �w� oq�n$  u a� _, wa;otN�6�)bw2�h�=!�d�+�K� ~A�)tt}!�2 issu�*qu"�n�"Wb kv"�i:Z?��si89,CFSwA �AV�. N&��7.U�f JI�^cLl|�-. ISF{"3� do}) . �mea>6:onF#�s z-ͦ,�ley^�( b/�Wy ISF."� ��;ʚ�N?i�$�X�1�=I�C e� xu�"m�f�^, kMa� !YSl��'zl -ae"�7. ��� Uv*�'J&HQ�.�a��*G,� �|�&�6(by Derbenev  Kond nko ��vehiGu �Z!A�5a+�5�a�I��� юi�"Pir��� ` *�.Ha"�5M�"���1A%7/e5�$de>~ !9Dirac2&�5@Foldy--Wouthuysen�ns!EE��Hn�1)?�AE$\hbarY ��Iat �"Iz|��W��A!oao*_5a .eR�}a%c��S=4r!��!�k �� 1�--=�.:Ct�c�yi݅�< 98�%�y~ or"�T Stern--Gerlach (S--G)��p.�B5! #AUc�traR1or( A F� 1p� a�ack� E�''� !S��x j&�!���7Zinv�va����!�AN�Q1�)o �&� %v88�6BI%!��%<j[�e#m!q/negf� k�D�P"�6zN+oBS5��F2�G��gi�!�t<,�M![I.th-Yt�r�Ie"�Q!����Fj �pach. 21�far��=w��a��.<qaXL� fag.y�0n7�� ambigu� !ch�� VaU���>DF�>*U+{khrip� }�(!�e .�\!�1=�1�i�lndRY:o9��J� �e�� �nV  they#extrems0]Na�m2 �g9of^� &%[2�  r.m.s.Hu� !� 920h%/cq "�ix�� drupom# agne?6 HERA0�-V27}, HIk�$ �lAEB�JO9=Isa�* �! ? � �!$$10^{-12}$!5W2U��a �"`s�9�*�<is�eioTesu�:�[�nIY� )�a�;dYgDv)��7�2�q kiJQU��� T%�%�di2�5�]1 99 _ N.��I�I&E�0 U�� spu�$.�� ��=�u|1���-8���So)'�� ]�es�#:� &�%&��&�xr�c� = #���8,�� �&� %M.X#!�re �b�xt,c��b e phenome��� r�s� i)�A"Uca�k��4 tiny ng�[�ɗHI`t{n�� Aa4:�X/s A�&�C�i.�ju6SKM--X�as� ``A�Q pret� �� �B�U�)�aza4�v>�0� f�.u�A�a�+dccol�3 naAR%(4  ofr� tC*�0�derb90�{t!C-w5�")7&�& ~xA��(du!J.f�A1ull�&d}"�Xg�a�an!nfli[r(�n� "� 5�v�[p.137]*PA\2�per�#!0| hi!I�"�lbelie�AM�o(�Mte9�A���-�\m�m  �cU-!�q. � -�n"�'���E��{��hc* d uti�I�[�? �c�TR�� � ��2�EI'+32< 2003� W�7=/l��p2����Ye@� )6��!:1 ��n� �)ed��1�:1>st� m�m�'#�+��ky�yAas �L+�oise,J�,�jr"2���H]'i�s �� q2Qi+%;p� �nM0`a�XGs.A��2��2�dic@nge"wj@"2 6�. H��w�9\e�u>?�:a(%J�]} (UPF)�Z�@as�f:[ 9R)��UPF�t5�coT1�A�ab/E�13�+  aB ��)M89q �:o\Z$21��J�2�9A� 6Cem����s 2E03!VZA�xd�)&�)�2�B&�&A��sEX ��n�!Q��A�ct A�p�!u�Wi<6]B!�R�_=R@or�tTVal*o��[ii�+sor�8keyhH� � �HP Lh$s 4.3, 4.7N*4.8�)"5�)*JaA�,: ���*al2���%[iD)- UPR�/E}�%YK,�(": � mtCHi!�Q�5�T 5.3:�Q��� o��val�ŝ] ��v�u@ Rks 2, !0�xdelibea��Da;L)S�`!#T�*C/6E�i�f=�z} ^!C�]((IFF) �! �vN "�5 UP*�.�� �E�"�Z*dQA;v&le�9k%��fjA�M��2�Uq� 5!Y c�~7a�gM�5 ��� a familiaPm|�0&��W � ) �"EU�UR ($>|+=0�'l*\e���^+$m=0$)^&1�Da�;P&�� S &�(��� onExF�A'2�!WU�6M�s 6.3 -!`6!�.)�!�prowf7 6.5 ��0 gS�X�eg to8:�in�C rus```�A6"ned:Mi8Bi3 r& g � 5.3�hom�(Y ���sm �.|\,*��! m� �S��s 6, 7�8azNoeat,H��N�Ms.��;�1o�e*�/�\ �_, $d$��bb bitrFD(��$\geq �{"�l����um ?�7��g$d = 3$!c��7d aiM<eK� mar����7?  a $\�&\!.A�a�y. �4 a by?��~6uIa olDJ�*$fAZl �"f�K�Z'fing''j%� ('] q�$>�*%ݡp�0�& ng� B�S���)X � 6�G� 2�HS _ 7+a*U+B���� a*�6 �E deciPwhe��"�ar4I%���\��se����N� J� �� inqls 9.1%+ 9.2.n&p"S � /ݖ10�!%u��a/ ~�re�qd���8�&)��|�iapo�5��E��;A`bMM�, a  m� 10e�< ?J�M %{re ���t\T� �b�-�VT $J�O�) ...,J_d)$�X�! _1 d)$� �'&_M $ F ($J� J$ \iFO@bb R}^d$�V�Be'�D!li@f�ȉ|ܻ�e��)l�L�"e�! onX%/%�)0_8&� abbrevX0 s $S�,S_1,S_2, S_3)OSP _1, 2 3�Znd $n'n_1,nBn. *Z�if)C$ mA�a�e@� fu21  �beB�" 7 %�2�$.�h�-aye�%t��e>F#_^.Ma�M�new�E�%:�e�!���;1��BTOs&c\dot{Xh &=& {\�A&T6A�K3h\,,2H49} \\ AJ ?0,\quad U;} =F#L6?10^�4 �Ŭ�|$al skew--l�ic $3�c3$G!rix- . ��2���L � _{12�-� _{21 -!_3, �L23!23 2 2217�+62B6yiM���Z dot�.a�J�+s"��tiG w.r.t."p& . B*���/Q�c�6�<arlJric, 0'&O sup��� ��E���;& 1�:� $1E"~8!�)$. Cl �y,�e)%�N�aQ�bE�|ph�,jq@��aY� qIs)�2D&�'o>p� ��-�-�. :��!"� �a|OM�0�P � �|�d�-�y'8�qrti�o al r b-��j��2nF�i��+co"Nh�"�$�w#�[ UlhDri�w^a�0��t?s, #%���ISF, �r� o� !i. A5���1�JC^rz(�1� tog��E, tW�r+ �!��s^C�&� � ��� $r$��! tinuou������6&� _ &@4y�Ea $C^1$�n>  A>'gb |��0�S, �euh$q�lR�Ar�Pء�,�x &eiH��c� � 'T��<s�2!W�7=f�$�2 �oc9oAOR�y jc�"�5fg I&��ir QR��texV "�q Pr=!�-+dD M }0t�er&B{{0}ng)�yNablish� � A�c o�v%� "M. �� (*ol0})�M)=J_0��B�m(J_0)� +�"_0$!8i�E6P�VP)e^ss.��!�u!  a{%��G$( k,}�!�HI��ia=am���F��0VF_0� By 6F>''@� �;��%)b(_0� 2sj*� 2rrr�ok:� � �)�Fr ^�:Pe1 �� �l +-)�r.6�7BM %}�o!�u$�0D�� 4.1�^4, $^���6�Ub�QDźA��wT/ ies)6y./�_de�eZ20!�)�*.mh4a� !�-4> =\Ph�m>B;�@)$�t.� Ũpr��p�g�{ }�x�0$��a�!J�  $j�$,U>�l�JK�" � �F`\f��\�.jl}&� }  ^�JAz.� 2.2 !f0;)-�)S I:�F� "�`b`�J� ��A$��$p���l9xoO'�j$� >&�\Q�. Occa7�� *�]$2[ ީ.��E� �)��#y''.��z#�' �ţ�M%�M^��:�!�a"BU Z]a�QR sۧo�}��!) -6?�E?$Sm9_0)=S�dpu0A� �1� .���. * �H F��2�u>� ��1�*�3bye\� "+ Au fF�& 56�-,��(Amann,Hale}Y=�M  �BCs�9!2!���PMM$, � P�  bD ert�7.%�x�iN_>#! $SO(M�r� �} _^T �). �I�Phi5m !.0�4 {\r~M} ��t(9Y)=1F3Ր�} s �l�CA�q�YX�Nv}Uk 2.0}AVLe}3��^15^ 2�ZwoU�&�66�e�� d lSa ,FL b = a_1b_1 + a_2b_2 3bE6^h�0�#n�|duc~ �11 V � = 2; 1_���oN2=ajPh=�XBH 2_0: 1_0�S}$ &Wt�i.����Ml��� =�1}�oconVf?n*�[o�Q�# awi�iw�� t*�ߩM7/���tX.�;O�,a.Isy�siFwMZas!��A?�-��#6"�i f:"/],En"rce.n�s $S$�k5 az�)!$������Fw� knowled[]��� lxs�5� A8$�(a�Dple)i6F!�&  G21"��$%�at .�~{�&N�r�%F"kB�on� $i�Ch��2'!�n��2A �ina2��eq:2.3})�+-��dem�at�T�` v}^3qW$a�*of:��y\ �2"�1�,Q��K�m{ `XR)*t 1. Choos�r �E� �F$ _F�V�:=\�[� v}S, �v}N, #� \��]2` 4B�%i"̓� &7S0�7"nf �1 � 2e��ml�f $ v}^k=(v^3�3)  v^k$ (kk�N�"� n&umH0_u5� 8-�B�) NextJ�+�r215Ed-($arrow \Psi�& ^� "� by*�&a� = �Z6� &�L56�&*͢%5�SCQ W\C(0V^T �26B�\F�b=MY )E�(Z )�- �V� )I~���i�7B&2 9� I>V}*�r = -.�>�E� t� $C^T � A^TV�/V}!+-C�G� F&$cA� ��$CIy:/a�U��a1ro�0%�.colum?' G9uySay}#�C )c �aˤ{c} 0��1 �-h %�=A�k�"ꅐ3M�� 0, \�Im��N&K�wq�k!v=� !ANBC$�W ��}2ec_{_{V"~v)� 5 �{ccc}�-1��\\   & 0J! =:Bd�J}6$9B�e$.49�� lso 1 � ,�J9T�2��1�e�mSA� \exp ���M\�hs^{ +}_0>�')3'1� i�f�2� ������@�Q,J��" � �&�y�J���� q �.�  :2#1F?��%��ia��$se*�& �)R�d�FaJ��9�taxV� cc} � ' &�nsin  a2*m68Q/6�12B� So�B�  � �"oz t�ZS�"�.� B : T �)?'��� m�n $V��o-� ��B�D(aiAfor//&�b*�2.7}),�a�w�b.2���=� Q�U�->�Y�q��6�8B%�f -� �� =A v^1 j v� %f��d�  $� =v^�\�(�(1AQ��(1 e� +� �  1) - ({H}^�U= b  93 + 1 �~2Eu4'�D�Z&S]�AN��l� � j�% �&@  + "� �ޫot ."� 6�1F7%6��eTr\lbRRQ ^2\r=-2S� zs%�.� 8���5�$=-(1/2)\; X*�J}� A V -%�V}) j�#\vs)*{.15i�\no2 nt�gReC)s:"׋itebe�� tem[(1)] Fc2cR�quiY.t O �k��as�or�("�&c�x�!3 $S=u^� S} = _1a +2a 3 v�s?eAhat{S������ ng &r>�wN*�#�} "SD� Z}=>� 1� ""� �?�M�)=�� 6iR j� p(0��@q�>pw�u�$L)�Grj�G$ $(0, 0, 1[ tX�onc{�r U�� ~y'2��!x65$ i� -[:�]ct,�4 a bi�FyEpro]9,�J${ �r�;9$�3x !�q��2�$,A��  E�(~�!IE 3$c]�)io��Ac�+Bt3/�&4R&�1��!�iaich14�Aes�d5lyd�=2r��� .=� && A) yf��(:�')-\nu) "� M�RTnu� $� 0)S(0) �^� %� $\nu� 3"�Q���S�;A>�NS=UQ�mD�,I �.v.t��J_>� %U&�' �}=\nuFuY Q� ���*$U��t==�nAr&�>�UQ�I�� aN�OM�a�ap)�e!���hweU�+K�,բ'�/ 6m:��bar{c}3 =) _{TI>a�0\infty} (1/T)2>T}FG "F $i�[$ hO}"�Pe� c�\nu!i �!@er�n=6�$�1 $�G� n [0,1�8A�R%M���Q��K��+ v +k�u!:9$��Y e fl�<v�Oq��� zero)�EK�%�!�g�$x�\AO�)ch�!1 ��� $. \F2)]��/inx 1":0�EZ`RE�� s.)��#,� $u�k.Y�il){AXfl/phi�� *� %JB��  = � ���ّ�) UZ�2FkB���%��*-Z!One�Y$�'G7�1%Ne�Oam\;F).�V!�$,QA�"� "�dY $Ud+!� n!_v!Jp��;� <�Kis?, RA�s(UNWEonz).�2�& ځ�£Tm"�afQ. Un$&J_�H �Sb[e scriL�*}#5.5��nu � 1-Y une.&�"�`*~�, Y���� s )�&c~!f�<r*��Un:N�&& U�GB�U�- \nuY�� ͡*�30����&T.��1-�2hA?= 3!��i��!~b�0A `�ͨ�$U$��G1})" �71��K�8H��(S, AF�DryyfA�$� 2�#� �!��I��ѡ7�"� C�"!�Hs4 �Z3ir"��� = . �yUA ](�/J}�r=uyE[d����B"#�67$Z��!\i��a� =�H�(�C(NRUPR0IE�lU.nA�i.e.\��E�_V�6��0F\ �0&�&O ^2\,A�a6M(�@E�nH�^u"n�Rr ��ar�,\,(U^T A U - �U"�J�F�a��i� s\2�2})��E~��rval �\!��aA�E@\F%-- �� halfNHofmn 1�DP.hos�C�/ s1-fL(3)]N�.�IZ5 C ^ p�7� "�=R/tho��3<�u A� $m~�rixz/%= �5*�Sa��e*���� pa q�&%%=8Fo"�-��*�B�J �jP� �, �I�=�&:4}��us "r �,"y�Z�i�� |O- 4)] �~ �!!x�/f $V: {&�7*� } � @$V=:[v^1,v^2,v^3]�s��m�)�Rg$--3"�6!�aB3a{)P�3M4actional part tof \\ $\chi:=(1/2\pi)\int_0^{ 8}\;d\theta v^1( 8)\cdot\dot{v}^2t$, is independent of $v^1$ and l2$, i.e.\ the fractional par .�$ only G s on;3$. IOX3$ were represented in R�>``spinor formalism'' \cite{mv2000} then it would be found that CF�) $ isd4{\em geometric�hase} �3$� sense of ��AA}. \end{itemize} ~Finally, we summarizeeHbasic eigenstructurLP an $SO(3)$ matrix $R)^8its exponential9a!c� erms�(a skew--sym �LB��following lemma. \vspace*{.15in} \begin{l } a) Let�Dbe a $3 \times 3$ �i�x. Then a real number $\mu\in[0,Az) �aB�0W$ exist such9�spectrum�@ $R$, $\lambda(R)Ax)�\set $\lbrace e^{i \mu}, - 1 \r $ (whence%�%�values a!�Iu0unit circle) A�� % -%Xeqnarray} RW = W \left(  ${ccc} \cos� & - \sin 0\\ '0 &1 Ec Q\right)p\exp({\A�hJ}\mu) \; , \label{eq:2.14}I�� % whajm^8second equalityA�$used (\ref ET2}). ~Furthermore, any)$W= �$[ { w}^1, 2 3 �4]$ satisfies �, relaA�s $R ( 71 \pm i M2�� ( \mp %�)^,I]M L3 = ($. Also, by2� 4}), $R =A+B!�}$ -"�:M�$B!q1lW^T$ �:s. \no�-4nt b) Converse�if e�sq!:=kAm,Q�B)=Q�i,-i,0U�,�ap>>qMs)�t�F�. IXli� The proof�8elementary. See�{ example�{0e�a�.�1�!�0can be decompE`as}F!\!\star6 && \q%  Phi� = %$p}W}�+� !J I4) )^T�,_2�j�]3.1B\G �_ar-)��\i5� is R�M�%dQMDp}(0)=I$. Moreover*%&2 � )&2QW "},\"F&-.}JfY� em P�5Q� Sinc� t�$$�8A1�, AB)} N\ $, $�)�;/_0f1(_0$. From L�� 2.1a� know��}f � i] �m�aՏ�%BNdu 9X 9M%� � C = e^{%�B}�~%�M5B} M�W} )GJM� W}^T�en withj  =)�Y�3 5�A{[0�T, &K v�=��8�-�8�.�:V� key�perty�IaDf�� at"� �� �I= + �) �\67 3.2u�u� which� an see�L noti�a��l.h.s.��L)�aB�of'2��T�B� vA$� $r kN >�� Zsa�Izaw. �y� !7l �F uniquenesx[s �Vini� 2 !� blem� :r�0h �th.{ at ��=a� Důmp}$!>D:=.� e^{-ERaEUZ I(}$. Clearly:E�>Za#�`96� IB}!N :� .�� �1����� because &S ga��*�Bspl� ��AY�&��3 (5 @� m+I�)�J?:^ CBqO6b�k[2�� .� �� U6u<� ] :� <. \hfill $\Box$ F�Usi�e � � we � $make severbmarks� cern; b� *] �2a�,0})��n�2 8  N 1 e�B'yI�$i� ``$~%u4 }~$'' symbol ��asO ificq�1 i� t needx� &� r)u F3& bf R *:U�"\ [(1)] �2y= pM�� exp (B\nu ���n��� �eal>�.� ("R��B2, i��-&je� �D� ��B��($p,B,\nu$ wA�be calleq em Q�0parameters}. � � ula- >�6 9aF b fre��cy:ThuUU�!�� stateatJu� �it ��9Bj� *�two�@92B� emergeZ addi� �d wu tun� . _c = 1$. 6o\5C .��aO ��" 5< pW Q�2M�5�Bk s as"_ inM� 1,%7n f2� b a $W�K�*� $.d=B$E� nce �r.�.1WY & a#�} (�W)) E at ��y"�,=.WA�� .� UPF d UPR $A�,��� in Sy 2. We�?ludr ~1>U�A�aTofZw��E�(rea1c24u)J? �,--length fun�I ) ss!e� i�a s;$trajectory�y�53!LaN e $n��.ioeXa�troduv. \par: $Ujq,ayn��H2�I&/&�:U>NQ\nu_s(U))() U^T(0) =:�� B� \>! 6"! �u1,ubyN�&&��:=� �t� B"0)" J% A� �B��Fful;allA���� Y��Ts!��[aofQN, is a�-U�'. N7 {\sm�s�g�&aa�B@mu��an extrap���system. B�e�>\��A��e� the 1 UPRsZ&~��v�.�`,3)] To studyX�o&816�n morf tail�first &�woAsY��($\tilde{p}, B  �N�-�N�:iy7a6.� =� u�&� �m�ak.2f7Jk~��3.7})���� �?e obtain�a%�  h  � �B.��": % K �&oG�nu"0:"= J8)8?B@:H m�M�N� at most�sE1(due to�{=% %a least one7 . In�&ti�r��~~ei� .F (� wnaw�eM0$)0it�A���,1-�b�,m positive.*�J�m�a�n $$/2]$ alway � &jas5 � Gi����e genK concep�^�S� �H �� 5.5* 16,� A��his�yN�(�z  4!6). T�K rn as A'o selec)�);R] �}(``preferredZ $�%�!denb(nu� fac� *�� D customary choice> R$�a_0um��C�of m�$ �(chao81,br99�u4)] B�o�)�oZAa=0�>wy iffR z = ���-�3A�H!�at if $bUe@n4^ 5!B|6�!�*�6X1�reFq �nj� . It�by�2� fo. I * ��>A �y zero�>. Y alsoY4!�U��? 6.4>j!�5�� doe�giv� method��.x!�f�&�;"'EE=ed!�,W$�?��$ ----�a�about�!pro�ies��co"�� �poi#<&f !�102,� tandar��xj�in or�o �ut9R&� �in,��m�, o��treat ; ��kKe 2[m�a�,,bhr92,bmrr}%� sh*�l��2.4})9��Vhosen�ZJ�n $. �"{ \xi{��+ 1�� �l r 1" %�%L*$�) O!��1})�${S}_0� �N� /"Z =�H �� *: �$.�  {Sh $%�A�i !L v}^3� :Z�>Im leteE�U�io%!R-J $V$ �^ mustpy�'Bi)�s�1i� �20o d!i�� can,�� � sume� at a �antt ^ $e;*� d5)%e$��no��G �n1=<"�' :={ 2OM/|Z| �"�'ZI Eo�'n�#� !��s�Xensur@�e���e�B�>VQ!� a�, third colum� 1 5I $: j!�choos��FTN N!qJ�t!~ J�a=:�VU. 5A�A�" an a$!r� �~� A���a f�A�~ź J��an�!&e ��Vf�X���Z n2&,9}) $c_{_{V}�)�F;��writtenE >=\bar{c} M+� $�%a� bef{& $65m�B;�A�me!� nd |--`�� �$. �� ���^%�an�e&�!"p= U�dy(\alphaQ� + k ���)2�5"�c"ad J/�+=J�nd� r5!nug�)N#!Tg�)�)3�I&�(� E++:���@&Z�#�e{� 6�3.6ith i�=� $. B'�%��[Y* vanishes| �(ral $\int^{)g�_\,�*>-� ') d�'$ �{F�*HE�thus $!� 5� )� V)a!U&)ir\k� u����� .w� omis�s9w�qh e�iny�%�#*���� &�3.5�Aj!�6{to?5�.�2�-QVɉ�~e�ha� proced6-� als te 2Ynd� EH%� !�� 1�$, #�$a"�j� �jj�"���D*J a��b2�F' *jN5)]6q2s bE !�2 B�� *���!S� � 4 'ta:fdira�a�no? que"u� � 6)]E� v?�� i$�0&{ easiQ0!x nume�/l�teYP� �*�to�S2= $ Pd�mi�K &I]!]nA9v�e linearst�&\xi^3=� ��5 $E9"�0o�+ grid!F� E6�X]"� ��ra�u=2W � $S_0z�� e wa �n_0u!�UƁ@n SLIM� Y4)�+edIFcod�-�7)]'�i�F�o�)F�y -� C  OnB � repl�/ ~$V = [ -1,~ 2, 3]$ ~by >( _) 3]�~61.3�$&ea��� s�� �� �e$�"o>1$->�us ~$z� lead�$�Q� �&,(\frac{1}{2}���t .Q �6�� R�� Q0,S�8!��ay��� $Vh2(80��-a�put�}�+��vb ]$. �n*R3%��-Quasi.Z$��$a Diophanta�Co�j�-%c �previou2�-=upFd o�{f@ ��%I �,�  $AubE�a�*$. How@,%[(of our aims/to �� nalog���$J \ne�.*\# �.co"H�5/!"�^ %��� 1$� �i4�pur-VH#�86* q:� . A��"�3Ag:5� erea�H2I 29a f�'e�+�4of:H[(�s)��e = (� 1�" _2, 7s,c_k���!�$M+ V��*4.1:} o5A�<$f: {\mathbb R} G3arrow.EM sai%sbe#2}w�9�U#n $d^k�2� A3inuAcab>��F:2Af�&Na�bh6*�b"/j�.V fqi = F!���)\;2\ 4.0}VB�sFN��C��R�28 real%�imagin���#2ͺ�9E�� > . A Yor+ lex � dY=3r���w if��9�7. \newl \}' b)-I��&}a�a:�$fe3e�q�LT8f):&��5\in]�: a(f, )\neq 0X87 2�"uA-.7lim_{T .�\infty} �T�t_0^T]�k(-i ��) �!.B 4.02JMc=/ mean%+BF��{f}��0)p.u84.0&2�%�!e*�!�vA���f�nd=� $f=: �.f~+�cla�-�(s�5Q ��3��Q}�E;k �'wp fer��4 $�he2��$kj . If :or &r� �n O��ext orG relev�wy omitOorA W�� � !�M/)"�in.24.3d. **q kl([9.� 1�� . A2�)J ,nonresonant}� ���  $$m �>�i:= m_1 _1 + s + m_k�0,$# ;in�Z��( $me�a%j��of�s), m$m�71�~� �<7re�Jnontriv�=#V h�\s.�5�. D someS7c%s, e.g.\�2�,C�� mayA�a���=[,#�wis�E�� bA� duceZ�*�:�s. % F�,*<9-}{a���  A�m�.6uI!�� � $0?/"�N��� ~F(-�~  ,�� z_1+...+m  <�@��T �BT �Z6=�� !�*0I�*w $:=-(1/m_k)aj �� �!�� �<m_k!K�dealt "al�hc�3�D-�h�%���3�Q-}JhateN-1! �Fe��G -� +��QR, 1 repe 3ab��&until a�72�I> (A��}T � :� � V� �*&?zed/�}~�"� P differentM�f��21�f�D2B�D[Ap�<4ix 3.8]{Loch}.(��in�+i�)�f#bc8��5�}$F� &� )viewed��a"I# doma��"�^{k+l�  T�Hz"/� �~�:y2�l$,.���\subsetxA�,\mu;k+lE�~!�later)5 � �m%�!���1<�) QJ} "D Atr�a�!5s �6)�Jj "9 � )$ o� �^>G�L , bu�)Y!%�_(pAe sam`#ass�"� p�unalter��&��4t a�D.= Q�]QB a m�s er e ;E� te'� $�C1=HH BZ lT V{ . Tok)tn�R�.Atf#.N@� E� �N&�I�holds.H(z� $F(Q^{-1} zAe�H% B� iM$ 1�!: ,E:B��)$D"5 = H(!!�� !Q%onWD����A�a�EwaP)� 6in:|�B?(Fourier ser!�J� sum�its_{m-��q } F_mA1(i� z)6��� } ��2�$coefficien�%�v � b^U1 F_{m}:=\f (h)^k} "KP 2 F(z) . -i mrz) dz� �s k *�4.1�2a� F: � J6� z_k$i � ��� �B$C�Mif�� �.@bS_NI� !�R�(\atop ||m|| N} ~F_m �=�F�600JD^%�sS�6{S_N\}$�v�6uni�lyz ��K*1 ^k$ ��(p.411]{Koe}��u*pHA�.fff2�  $f_N�:=!\�ui6t76�feVu��ir�L� F .�a_{NN� f_N � =j* ޸(qi\nu�46rF�� n ��Er!c�J. H�[&n$EIB2����q.max2U2 9:=max�0|m_1|m |m_k|P. ��E�Y�2�� AWa8cN�i��� �C^0$, � �in�Pl.2})&I,�Fye� a��H>MM�*!�6*fMF!t(( wBpG b�" Fh�&2N\SigmaBS.h��&& .�p�� \; A_{N,m&O _{m}� i Q��z;:L3�w�%*�[�Z� �@:=\prod_{n=1}^k\;�>$N+1-|m_n|} �.� ^P7b)N2'� $%�z ��X*r�5�J.& &06e�%�5� íE��2�-{1́(Q b�8U��'a�c g�*is���8{2�I4.8})} L lizesB!2J�2 is lD�)<.\\BF.M bLA&yunV/� &Y9"� 3b.�m�(f6�>� 01})�Pxis nd�!�R'.�q,&&+ :F_0� I�1}�  J � p&�RI $F_m�1e.�KH )} sa&P�"�?V� � �+l�P T ~��?E6~q }"U �P�c.� �H�g�6] N�Q6t7 $f�$i�1 s $FGF"k d)I�f�a��&�"�R*-�;�8$.`Ve�U&^� ��a t:mB�""J�a5�J4.3a:}Z�P Maa}F2*EFB�L2Xb:} A �P�&� *�3a�`c:} T�,�y�l!�f?is� !��~@@ �,$10.3]{Arn}�� ^"�#4F3�imilar�d:}M])�����by5�2A���*�,� )a�66V�*��*��k{ bh $ �8�"(}8map2*; $ �*�-F�gI�ApplyhU�c4 �""B �e6M%B�Z�ea �$a(� �� 5k*�JN�.�3d� Z�|�j-._| =f3-f�|��nMX\\ && =|��6)�)-5�"�' !S| 0\sup_H.|2W 0Q|FD1&C�0I�w>�;2Z9�E ��+bed"( , O$|�|$�$I�Euclidk� �6�(.�_ )jR� �� =.�J&� q% ; � j4.�.� ����l�!\not\in"U?~zc/ aZ}U� nd.1*� saqY��iv��"�Q ��Z&�V �p�p.*�X vspa2'\w#{��J�a!�0a multidimens/^"� s  Cej\'er'E� oremXitj�7L ���*�c$TedS!%� .�. �!=1HQ��6�+y�,� 8Ces\grave{a}ro}� �\A�"*"�\r�\.�$k>1$�� natural: ! $bn mabi�1&Fe�m�[ tech�Ps��^i!� cimaZ5�c=2�?'_[� ``flow'' |�/Tof Weyl's equidistribzW88�P�!8 !zerg�Xy�{si89},� Chap�3]{CFS �$Of course,*a� ;!��^_N�>9�.���;U@$F$"�E2)]:1q�J&*B $F$,�N5RaE�]B4})E� �<o rI�<Vn��d.�f. F&db �|z_.�& �evt:� ���Nvalid.���.�#!**$*JB�h �^ �,��a�fin U�$�!s.�*�"� .1M25�=GIf�is6��by ;@�$ s4&] �Z$"l& :=f-&is6�,e_�m�B�8S%.6 E iG'}=\���({i}� i%�:i_calling .c{)!F<'5�B�8=偱�A��berpA�for�!":E,!^"�2 d by�B1�i�$curve $D':�^"v: 7"%R}�� ��S�"ex�aedE6bR as�$��B� K>E�5ledge%�F$�F!BN3!�D�7 5�0)isi.;YnF7Elar�set�Ntilde D&:*5�T\pi MR ,M.>9Bu % Z� dzd��6;�%A��.U!� � &{"��i�O�]�9�a sset. ��R�d%]f"*�E)�^n��s�&�ur�ofs: zU2/4:@^�f-R .�'4 alI!�( a co�`x��f_n�:�\al"�  �&��u)��VTsumgN f_n� _ni2)$b�f�($N*�$8,BZj�=0C�Ay��JY.* f��w: .>��-��:AN each�#.B�~Y�8:b�U5)] DK�{3b�X:Ӂ�rmhS�"!�)Nj&� }�0a�rUKke6�aH>'2 ly�oB�2�� of basic B3uF�  ~ "xi �-!*�#*F< $A� its^II�]�@/A�I&>-" U� ��g!; �6� AZ�.b@� � way, but ���of�@mVO!�v��W�& ysisI-A6'=q�j "�4B#H. Bohr�va&�=modern "'G��% �%{Fink},i`n� riz� A\�-,en&of  {Hale}�>�.��B'"i�X!]I machinery�F,(} (Zosear� �� �7�Je�� eLa�%<�'%!.pecJ-a eA>�, nameF �$o% ed 3Rdiviso�]�]aA? i E6 solv F(�u![sup"ly&x%iable9��is %er���v"?Z{ s 6.5c-^/ Inte�;�;�;��:�\al*$B}�3 �MY�_9,a� a�!�_Ji�!n�`�E����)�f � !)�f/ hsurpri%;"�).f a 6�5K>k��necessar�=2/ �<N�hEQe so--4 �(BT:.FF&. !�*�!'let--)v�<�&� 9#�4�associa� H n�#.�e $g "��o {0}^P�')\�o'* ��� �6�.  - �W�/�  n.� �az� Archang�>L2!sumqADF@.� �Z�"�"j�$ 0<@"Y N} &�{'$ \biggl(y"�%�W - 1%r).�&[&"S;(although $g�e welli1it S1A�b>��$k \ge AJEqurc� aWpr�M� qQ�$"�� il��tEA,&<>h"+A�I�!���!��=an un��� reby��tradic@ (4.1). �A:��!Wa� ���X8e��=�AA��2�q#w�VVi.6�G_"2n6 J� %�lM' z2�F_&DG�%Xn&j.�j� �"� )$"? $GZqm"� s $z�FI�+ l��:� ��e�0ger. Now supp�JEZ o* ��3�p: to a*I"$G�Gn A�F�,Aw2G(�.�AiB� i�2,R &�m) N, �,2� 1�%gat \bz o �ry)7o��"^�% SoA��j#M�%C�L1V9?1��%�!� �A��il�. . U�(""�,guarantees g�+a*c/ �r e�!��8�� ``.�@co 0''.�-s2�on�oQ $m'��GbeA��. ���&� we�)kcer;���6�nu=(1,8@)U��!�e9sul}:!Jh@.� R}^dE�c{n al 2� �)��L�e2�A5_C=�5%�� &u��.�:$k=d+Xa�TV &h14f1��d�[e�R�a�d H{Dumas =f� discusB!<gi�LA8beam dynamics �:.��2I54�!T �)\Ob�y:d�J�Dp�#ncR�7,%rYOau�1 e%�!�h�=.H set}�1O q�Kau):=��cjgammae.(0,1]}{.*, Y�ZaZs� &{%].7d : |5 (1, ') |q s �$^{-\tau} ,�(�$-M(Z}^{d+1},\;�4\��.^n�:�c�f$)��3us�1i�In&ua%���prW | I.  Emea�gsho@y�I>�<�8&5*� �d5�^c(!#,-��Tbi)��#5z12Z:minus"$18}) -�� ZI/ Z,m��R%:= "|$)�2���:|� ��| < �;/5�-�x�F@fixed $2��e���-A�``"mzone'' r�$ A�e<]emptyk [X icke��$d-1$ .Tpla)Ien�3�Wy, � ��00n=1)*�=W s +m_d d ="�)ick;m�Xorka�])B5(� �, $d=1,\|m\|=�Um_1i8$I�6]N!1s!� v"%>�three�� s in5m� R}$:я_1=\eta$�2$�M�-1,0,1-�$,)�:�$2� Wf $d=2:�(m_1,m_24B�#A^�B�welveL B�^2B��_2�pm-�1+��� f�>�M�� o�sqrt{2}5 %a $d=3�}�tA#Ixs2�E�s� s %5�3#�*�S_1- �2+ 3-1%^� %@�_&*0m=(m_0,�m}�=iLrm_0.�Z�@BT$ ) \in(.�db�)$a�� a�>q�byx�x���GᐡN�!matV�8� o�jdat=��M�b� | ,m_0}{| �|}1W1��H5)�2�.1� H*\` C!�n�z��>D�Q Qk2�/�u�!m�!B~1�A���cM dN2can� may,iedEnwM�1�RQ=\��set$.BC�!�r8�%.C�] $m.$nm#2� 6} (8 � ):\qly ~W":J-�torus�$J�off"w ?G!(� (J�T�o.+(� ygdRonFU)|� cer�b�R/vi�(J)�� �L])UsuY�{\.7.1Y')}�� � ae� y%� � . Ou0<agF9&i;�r�(?h`6yaQ},�9>kn�)V , 1.:�F�)>W% W�PrZ��prwB= �U j�{0i�&���$< KS�sucaivJremov�a open1ce �c�o[|)�]-Fce���U6�&,��it>> $��&� gB �� �,!��2�Canto�:t^%��)V-d� V VU f �S �e��fJ� %�ior.�OH�� C2@*0.8� d�Q ,o4 $A  > �%,Lebesgue mea�] X)K�{R�Scto���T�roR�  ( � �.�S4.23})�sA� can agB�BcG tXtaG:� �be�Hy�Y� �� h�!�S. �8we hA-*�!.��= !�Q�� �2N �$|�4* �/(_{m} � ��% %�|$|$�!8@us��"�4ly �{�� A� |$3�TK�.[& 2vSa�0b�FB�g$�VF�Jw�w�te�&X�&J�1� address��hi�(kl' B R ��S}{wo2<9�56�Pzf�Pb��A$C^n$q>F$�o@F_0�@�I\inI6͛y $0�,.-ly�2zO �6&�$G�a�jW�.�T: �&093>�\ef ,�*ev��@>�;%&� narr���:�#F�@%.2? :�.�i� ��L M{A:-n} = Fj�: N j�_�=j}n>�Ra=>�7AH#binato� argu�B7s�3.��K3)Q, (d+1) j^d B�1F�%]z�� 6���� j�IF 0>�!.e�`� (�X4�)% �>RfiEa Mb:GM.�MB8+d}Fk9"I;q %�A��ġ�2�4!]N�4d*� as $J�&��e� �K6��*cv $�N4��wt�&^ z�S4m|nt=_=�5}"s`^���=f�AjC1�=Y)����~mF�1&=9�T��+E�QK�  TK ��we Z |2| e�f�Df |( {^| ~|m|�eq!wohM���i;uvrq/EA0.�6 �2�^{3/2}n���+1-u�iX &�� 4.22J�� ��F^'$9�*1 *��*�&result�O \ [8.6;: Di60f14[p.117]{Lang})+ya�^GS$C^�Z"�(zʌD=F�� �G�v�"a$�4.2NwB��*�: \&_P)} 5�*>7F- < s: |m_i|=,.> $s&2i5 � s_i Y�Cc_$2(2j+1)PvO n $se;�sG+m#*than $2�F:�8Zp� 3F $3(3j)^d = �U" \; r^�z B� w�v�tn����j.�AhuW>�:�� "�/ �37Eid� , framework �we�! for �1�e��!�"9!\!&77���2�@�]��as $nX#�P(lyҒ� +d+27J�%�% lo�m2oj\$potency. 8w�c���(e5��3inm&�7^� 2d2b~v-.�8 de �� *7 X$I�rapid�Hs � (e"Zp�gr�"�6�6(a�Ds� O)"�utdestro�>P�}nce. Jd'Y$!�e m�}ry�t)� A)A V�,!�put EburdeG �4@@5��Z"��*�:ndUi}Vts# easyL decideQ+J.��o2\.�3�2relief�'�e",f"63!v ]�� ta� + 1E��a�mpl�,� }gO2 k,�C'"#M��M. I[&diG < ��.\q�eB� *lya��0e���M?de�Zw t��$ sistU����%$n>2d+3?=�s �-8�RpA���!�"�>�- �z�~2z8!�>孁 �[mu(1~1� �d $\mu$�otmF���EF�Z~�B(R'#lH<� )�: |)r� R.o��!(frak S}(R,m�RDcalFg! \cap �)��2�5,X2��>� " �.�$.*/#�R�$ (���2FS/b��>Z+Ewa� bel�xV�I!�.k�q� <  R^{d-1"

s. Pick F�cqo(��'{f_i\}�m$�!y�%����signs�b sen ";%>\h!^�� CJE�zR�*Oe�!)�,mo$$�\{k@ J� lon f_i(p�1�-,� } iA } =\05rJ"� -dW�\}RQ?0�F�$ �$��z,�B �l��% �� �lyl ��d �,}�,� �iplici�� $m��;2qZ�$T �Re> �E��} �>� !=� )$}{m_i}A5H.y�(N!<tT za�p�ngQ�1+%)��H�;j cor on� �J� I��(*:(F�-Jq+� !^ڂng K- or�""]R;~"o�o�i~+ xN� �*\� 5.:�>rAir3 &1 ve�>e�Wd� lessx/le�3�U,. e�j0Z�C.J ta�KA�,F ,& > $f= \mina�(c,R/M,bigy* z'ru' �Q.�.E�c�[�S\-o��urs��� a2F @D:M- ). (t$f�G$\ge0�,� �J�$>��o�%"�"x �ust adg1?E#�_to it.�(!bZA�"� F �/nde$�ent�M;AxUP="I��? it.)W 2� [0,c]�B  f�p$[x,c]=P_x:>I��R�(py� x�D>�;.f���%ˉw��seE oy�$Zw �n1k  Z  Vorm a��X.�~Q�Oma/.΀ *%�:Q 2IE� _x)=B  k^n�12 \6 {n-1}+�2� ��*Z�42��ula�p� K=x,\� 2l=2B�1�fZ�0%�akZ�0Ž�ezB�  $Q=\,$g|�$(fVfE�F���A�� Z�  X_�Z�f�B�0Toj�--Mj�� )" I� (!ch� av��iM��d. ��e�P)r{*�. $Q\rt{p}h3nd \pi}\U"W- �� �e}�b6� 1#b0�xnt_Pf�Pp_*1 Q 0^coS1= � QFd&�IPdxF0"p$ka7u�[v��!$UQ&Qx (P_0p1 P� u� ``�7s"5Q$)1�0^cu�|\&n Q})��j a dx=2>I�>jO.  )0eK�?ʁT$bottom. If��M�l (�7��� �"�`)O� T T� ("-t)� af�2&�z��y $p$;�l)PZ��+s��&�� � ��a *vI�E$. ��T�re8 G��hAp� %���e22rB� ,� �6 R�N ' �A&VHe�� y%�,� �k�N� �s�-P; tEB2� *�  $N$t�E���k*KrM�s� i0�|� ��� ��. Agai�oyr� ��HasB#.�n (�)�oldB6.�)dpR ^H wellM�,M�"3 �r� 1;.���a1mXreg a�om��dA�K"� P}fi�w�f�d�� Bna�(c)�{2K+2a_0�)�Oso�" ��1�1 b2F Y�!��i(a_{-a�̹�!\~$ B�ɂb0}C" 1})�� � $�N  ko ,�? IG�V &��$aa�,ive(��ca)p�E> Vf*�y) ����dmoYwaWǁ��f��So!�r �Y;'QC|e� imase. �� M�e�?to"A� �:"KP#�?nd.� ���d�u6m(Hirzebruch-N_%�� �s� Ful}!�-a Todd�/�}"@tJm;� >!�po�`s���Ky >I; �= rm{Td}\,(&�+ )}\exp(k\͐)Z-xke) B � �R�&6� ._#'$e&jE�"� ��0 Poincar\'e dꃁ�EYj%n)���jAgv� $ ���ls/iZ!e�%ir � �g�b).�Odsr!(�J=1R�Rc ^5 e)^n$!'!:L�HeK*$e*&�'�resolu�AoQ>��;,\over/{\!X}yw&� X$:!Y)v�2�f{6=}((p\� \pi)� p^*e g 'S65)�T*v��Q.J)x -ce$� n*O��V �-:Q�>�� (�.+6mo�#A�� �X&C�.�b�2.�A����X2mfPAT�dG>:��"E��� ��A�s b$p%���L:)�{er��b} 0�x)$_$$ 2VW ���`le��.*�" �CHI &G͖� vG 0��F" �"!w.?[� �<.������l-�E�M*"�A6-�p�Yva��O:We1�!Rw ��O�)U�  =oa �ь"H!�:B�oA�|q�to A�n.�o�*�]ma�t��B$"6�/gT&:8�/� � 2N2�iC!bri�B266B�4";S$�?���u�� l1�x!ula;$P$|&��2��*�*~r��(�� �f��(�"an JJeW fundam���&�,I�EAO%��D�4�YY"i �n�ۑeEoI!�u��rgf� deri�v���F2r%�he B� �6�(��F�f)( %()�# ����eI )}��J�r�4�i-�$�&��$ d � ɪ*#s"��"hoE��h�o@���e��v�\�.6h \n��1"(_� ant(;� �) #M"�uant �m� $n�2�Y.Fo#�i�a ���AH!oo�Uus $g�e�U �"2R�"#�9�N�u4n^2(n^2-1)(L.Z�M0cn(n+1)[(n-2)"�)�+02(g-1)]}{2nc[)8, ]}\,�$G �:!1"QL�'7!�U6j�oeA�s� �;�"+B7N2�2S" 3#+\rkgP @� �M (kL.Zv3I(xk k#)}f + 1-g)"J+&�-� �+ �0:�Q�$%*�3 � �Cz!LSt8#5)},�&�2}= - i�"-.� �I�� �:nom{xk+�q�q"�6 (MP1}{%�!A��%)xg2�,<�-*(Uq }{2} &3}�3}M5�4"�3�- )�s ��"��n=a�e ca�3 -3}$= �3es.�q�2Y-�v I� ��v L.Z�0x!�%61�� ),\\!z9�>U3U�2 r6*�p o+x(Ap "YuIn*g rear7�ng� 2�0��})���_o��&6Bm� 1baӱd�SaPS2ڒ�� !����qR� ��-#Ax1}!��.j)!e�\bE�_{j}-e$-c)^j}{j+1� A-j}.Z^j.�s(Z)1Q�sW�) ;a&nVV P N��%$$ % .aV� [Z]-u���%� }�[Z] � +[Z]^�7]z�R�%� p!���}M �4:� 3"�=XZ[X]' of�pL321x}*[uE�jltiX\�a_0�("e��aH( L^n - (L-xZ)^n)= m� J9E?n2)Uj}. (;j:k*}eQ�6\��_�l�^}��1���!� -K_X. �/9Q�. �E& ��~1PY� 22% .B� .nY &+\,J�iH }. Zj�s$hesG{Ba�Ai�hK(e���q JMWw#� �E&a .;�R����2in B��$t sultzSpW��3 "o�&t2cor!��8PJ%5.WZ� >� "� &� 8a�ύ�uo**X��w&=&M�AL}{L^U�l*� "�]3[2�cA'.Z + ��� c(3��ce�>k�q� ��O �!Z�o6��3�1 +c)}{�x�!a5w� s/ A � S� &ShT�}� � e� YLFy�-ys.Mj\* M� n}th�pOve�*��} �.�2"  �2�Y&9m�j�W\Xv0=+s5em���eI�P0A���&t�+� WA�a�(^ � ��mo;!)s 2�߽ *�b; aw� Mam&��AL(z�hto:�� �!"J�� ��$!�!�L8.4!��2Z���yCY}�olM.e mwb����AQFif/� ��&6� )cv��W��t�O�F)a�5!)��* �� $K_Xn r e5�"b$�,In� hI,? \sim� u�.�&��a ah����'E9�/%a�Q+ ��:Z/�}-n���t/2)�-n �/2�- �vi��)r6x 7PU8�nj �� u�n�w.�2�$L�'Oj&�[��6T+M�w �&~xL_x^n��1�� K_.�j.%�|9>/W�  x+Tx/.E\\ 0"��5L-L_x%IZQa�$xB`t�� �><0�LD81� %�D a��61 �)dx+�+� _}2dx<0 \�UPH cB�]R*� �y�� Y �6/�<:;��m�p��<�/W���.�N�eA�!Le�K_X^n�*���l��O%tL�N�.adB$ɼ�8$�, � �*&1 f ($aL+bK:.�Ta) K^XM b}$){�s,� �- ��u<g�%Y��\��4�1�1��q i�jBj�?2�j,L)L + �f1�6f-(-2(M(�TM[�,%F��X$G+�$��$$\delta_0>�muci{�f6 < _�!L!|  G�s��II b2M%hn� �!�5�7s-�rmk:weinǥ!@S�!�nŁ-�:9K ��U��et ar�#!�-[�]��e�ichO� *��LeBS}�%� �"�REy%yi� Y" �?��^Wex���A,$:�|�=86�]xJ�7s�a�Y �"��!�b! � a-below�8fiI�g5�ex!�c of"��d~-�!�5��� m�^ �� $0nefe�*JX}�=(��E.eff� ve!-� ���!�D-(L^n*'^ X}+�.� 'n� &\le&J=X^2�&� (B-xlZEZ�)jN�B &:=&:��^na��u2g(L!,A� ( �K_XT )�6: G�E  (G.5mw=aN&:l $B,L?Na��� -B =�?L^n}{n}(�u+����B��,%�*� , e�n�2iY% s (1BWh�"�e(sou"a�tF�� .� | 6A, e�<źdo|��'�P%n���slOͿ�;v���lQ,._ )e$ s. s6\ �a*k valu� x$.o{,m��`a .ٛ%�e!(uBrT�$xs!2�e:Yr9��� lof�� eRdf I_1-2uI_2"t OE� $I_�A%�&y!B&9mI_2"Y* x#E d��$N_2Ma mk(.B+(L_x-L).��M�L^ja 2�Bm-x"�b, E.B,�w|���tA�}"�"z �4 clai�\a#[!�$�"b.V )<;j��5A$xa^j (a-xbt$��FC�c^2aiB�< (j+1) a^{j}(a-c>:�MO�} ���<} �4�`*�4��$c� j}�;JH ]1E�$j&�Tn-�n.�iU6ity�#�i �"�� {i-j�D �S-i2�iB��0\Jy{)�e*�U�}}���i��)�+ Ir�z c^2B{Mt%"�AH�R h*�2aZ�qBx=�1}e�))�cQ[ m_{jM@1}(n-j)M:-�5�U�^2} b�A��F�N j.L2�"�. Pu~ .�), I1 2*2oge� ��?}n�j����ށ�6I_2�W�� -c^2\�B"�2�}{-qLiBr�q.�\\�� RegFS LɆ$�]42�!p e?Vp� noC�J� �ͣBjZ��&�Snef. BuU0z5�gL��)*K- K_XKl��F+$$�O��L1c�s� n :� 9�,�A(e� To�  �*��-��-cuNA y�/.3ith`b$0!W�. .��state�$��!is un�7d we�h3b"u��Eyb-�!�~B;�z&�-E���(.2�wq�3� �Zz�\,=\,)�::2M�^ (^( +1){ G) a?� +IrK- 7*n mG��i+�T "�1�6z\J !��� $$L+� �}-{�2�$$�/�iF�e"AY ^�!��L�t� "�&"�aiU� 2};+ ' &.�J&��) ) PD� 8.���ey�G�'b�wl7� �REt4����2k3le:"��~ � �are e} Any�&�'ZASG2�&� x!s+$g\ge1�dCg~��*�(if $g� i���-�/�yempty&' �"'G(ex$d".��B�&F�>4k\deg L-xdk+1-��iP��,�,^ mtx)=xd �h} ���@�'�#"B d}K d�{ 1{c}>0\gei�1-g}{���L}"�,E�)Zٙ)V!{�� �%`,0 �~W9�� lues�Ēn�2n�'` *�)=� L/d$m��*zJd6O .}=\O_{AK}(d - )�f gFul /O"�!=5 d) L}1umrU��_�4 (I�"m/%*)�D%U d=1$6�:EaagH�int�\ .��\gi߁s6@+*�?A�6S;-%%$9��wn!� \K:\C$�"�aa X$&QL.)�8I��" ��Jund!�Yg�$ �.s �.jC find �!��fo�Ikpol]/Al i� u�=�jCorM�ry 6.7!>RTVja[at����usz u^�6BK-(*�7�EP2^�2"kF.�TIak ����� *9| ei���ib�`P&��)��R1>6� j�B,\O_B(1���&�,b�2 nd l#E#&. rEkB�,$r+1:=�*EV 2��2how� A;�TlA�(%p,V�Q�)�2*�. �huasa�y?��!:9 ,6$nd P e�z���$B��#n=\dim �tE)=b+r���L_m= �{(E)}(1SceG B}(m�Z�E�C �m:�?&�$���Bthm�le!�Kve �s}�_��(E),L_��&�X"Q�ll �6��n%;O���26�!7$2�)J��e��.�6ore2 n $m�_ ys�$�NE%c6jm2���s�W�Yrtv*xF�6�a��%��f-)6�o"hu�!`)��J..)�Vn:10%&yRP!�&�0s�.� A�$�!�]QM�!ݍ"AJ�� �s (�4ny��!��� �fs��AҘY� sd S� �) m�$"a|gen�0�%� L_m�e=!�j���a�l9!O)���A�.L�V�E5�qA2���AB��J��28�.����Y[U�W��v2K�>�s q �a��a"�5B<$"%|v3 Se9Bri�tKlQ�well �����}UGI@2C)8anc&&4a+%� 1�g�&BdB�So��W�L~|]�3 � e��{e�E.%�5e9�6��*E 9�ɥ�&'ƣ_��_ful�7�M! '�>:(�1� �i6�i�� � >��wٷ��!=��=*� �@"�!3ha�>c*nֲ %⍈qi� l~ZU_��� �Bu A�A�2b �)"9 .�!�*n!2����i @�̱�6y& I�HO�(���$\,E=2z�im\,$B�>*,QG6Xafd2+z�!��n3!�"� -��cO�?BD �ad �*= ar-fK��E 'LeB;�i-�E2$, $�e��*��"c GATFGpIP6? g5"-s���h��Morrisoj+M!y�,unstable�e then $\PP(E)$ is Chow unstable with respect to what he calls ``good'' polarisations (in particular $( _@, L_m^{\otimes k}Nq�for $k\gg 0$). By \cite{Do2} this implies that�� �ch}(E Td},\ : e^{m; 2> 1))}! E+$E)+ \cdots.I H�F%f6} Vzͅ�Now a��.�,��(can calcula��e� reesa�urMx$�restrict�vset�2$is locallye�, sb its � lem��� codim \ge2$.&ut 2�$m0q�9˭å� ��� ɶ%B�i6 &=&-k����.40)�Jw,I���A|, second equa0*- A�split%L_B\!E^*= {\,�}\!\O_{ (1).$i��m�-]�(\omega$ den� O6B)$� S$. Th? �l �endieckETmula $\sum_{i=0}^{r+1} d -i}c_i(E)� reduc�� �to $-�~ 8r= M�� ose   h�$side is $-% B EBG �p� prop9� %>��` \ sat�ed}Ac� fIRW�E$E>� ��.�.�6H\mu_F\geB  �t. ��an $m�dep!sng� P �e>$(*u ) su�k44>=E�=1u $m �k. �r6�)(}b�� pai�����t ny sp� `Nt!�of_ � e8 2("Jw #)}. %t��E$�vhIu�^,-6�B� i�, � is �,&� �� �A3 g"3 .%zn=()@� $L_m p�� �5�a#�global��:M:���\I�EF)}^k$���6!�$�0$. %M��A���$�"� 9 . f a�Jg $��_p)& �� E_p) � linea�bspac!k�Ab$p\in B�L_m|_{ZD}=�_p)�L� it"XE�5w� 1%�_ � t least 1C(is suffic���s SL_m.��q}Lt)�O��sM���G=a ���� quotx s $G0�B* G\le-� A�bo d (�8HL} Lemma 1.7.9X:$:��ngA�b�%�����, $G^*(r �ly=R� no higheruomology!Q%9e-. A�.(Without losa _ ,we may assum= �NF,�t%A�5D,very negativ�  (o�� wiseItwist� I�c�-u)��F$u$ J"v �"�chang� atM�)�>turnsE� n�O L_{m+u}$)MWor�!�Y]E  �.)}(-1mWAk"� of (�],pullback of)%�giv��a� oniSea �vu�Hom.� Fp, G~btal� 8 I�~�ouom��GA� Thin �f%\�i-A� f $Gmo� *= $, se�$precisely )+ bb = -]� !��5^*h H^0�^*%%�CEE�)�� u �, exact seque $� @i* )\to OF ^0$ yield�ca-�!�) $v�U^*-%�!�i � P�  w�  229� �^*L `�� �e���.��(-�_� t�6�$. Tenso� ��e�\�=�_^� .\:Z ����ta� maps%�v)�^5T �>A�inter1_o�{(a��*��j:>A|HI�< �1����.=�P" �� = 1$a0claimed]�s2>�mjcAnT �4%�is����� &� is dh ilis�Fnd *G and�E��..EMO� 5��i!�&�� both�.6�i�<�E"� G;��0� a�Q4/dega�>� A^>0%Hby�eNl }!��Gu�a% a= " of�LE �� �! �-�S R � G)a�:� |� $$La} 6.4.11� !��.  0��.Qk6Qke�sJ 0 tajso!�� pushdown >N!9 ��$\pi_*(L.6r Pe/ ^k)=�>O(mk)\ \big(<�-)�k) )t�e�YT each\!~ e�gB� �.�k6� g k :j!1su� ^��z�"_�again1�a�"J 1Bi��>^A��vQ�s}\ InT!�a��quantit�  � E� � �{)L� F;��mak� e0 ��bles   �,\widetilde{m�m��1}{b}(x\_E).�eq:�of@m}w^(9readerO pref�o6Y �! E=a!in�cas!�.�=m$.) �x-PP^r):�!:^r��^ra�Mr(r+1)/�"� ��euler!�K!. �Q)�.�`a_0 k^n \ k^{n*Zn�a�T�a���$a_�jre8 ynomial��. In f�i!!.A��.�a4\eqV�Afn9�"u �"��}{r!}2rgO(6{b� &! and}\\W1ZW�ET)�6T�Ip6�\� ^�Q~��%@d�a��pr V���bea� . More�a�b5\ &�2 !� the Chern��ss . �A�u�2�pi\colon���#h# "o�  As�BŢrel� ly��2�RE�:')\!\!&=& �S:�%�&�, ���K B�W0A�^B6� I5���"~ "}�1Q)A(� 2}) /�rd e[*\ - kwE]T1>ma&+Orb�0"l�A�K uskaŁ�Nz (2))QDA���E|�A�E�b%� he rank$W!rk-a=��$nom{r+k}{k����a�[ k^r�mu� � ^r)k^{r��r�i�(].$$ ExpandaGE�&w$$k^n$ $�- �sBesR��dV���[�Bѯ1� �)+ =���Ak� �A +>2Zx�(B)%�Y�I-.�i�*�!!��2��"p �2*��dexpres� �!M stat�P l�&*��ha'err \ E+�s��k�V 6l.� Ha} Ap<ix A3)A�se�at=2� �B(�h� _#2��U�s):r RrR��r�eQv��*wtsof"�r�!a&q &�!�#�� D�T alpha_i(x:)��$��*5(Aw�"��%u,Q}el��20�"� ��nv0�"Z� $0^1 (1-x) � 1(x) dx &�$J(s+1)}{~ !!7e�[2���q r+2s \_Es Ff ] �"6O�BQ%}d%�1�}��s+1�F��[� �� B) -�Nt1��DG4 �% s+2}F��22]�Y %�""�"- mult�S*! 5"0^1 �%�-�2!�+ � 1(0)}{2�Ddx�#\ %)�.�2(r�'}6B =�:-+1)�&[�� %- E!..�� ]B��'B2}CR�t(2uu N�%�$B) + �� �v%N�M�9�U�}cor4+ion��on?*�z�-�n�Iw)�eqE�5�b + %!-շ)+/%!A�! 4\,,U�1}\)�0big[(t+1)(s+ty%m + (s�( "2�%F8��61i5@� b� isB�&&- " �0oth2<N� 2�Q��^ �ڎ R�A a/����ѯ; ՓN � $s+aa)7t+1�W+ *�An0q:rst��( s+t+2=r+1����# ���*$tit sitɝ�  a:�8,��qU� �$%�� �%�an op��U�R�D*�% ��2$,D�(their first:��t���(Vym�1powers)t� c�&d.13G� ���U$T�� o E$ ��#%�soaF|_U)!R,!GE*�  mo(submanifold��10\nu�nu.�j }=\pi^* GN� �+ �(1)��,� abus%5not�, �pi^��$. �-�^ V*h�"*ha3"�'5� %�we%�5� $�A�mp �S�$VE~� $0�.(+1}$ vanish2Ve�&� 31�ru�^_ >�/:p9>��@formsO+nirh!�-�A*� A�2�(A0n-3�&:NowI�R=u-�} F� A"G�%ich�)" aligp)� 1}{s!t!}&�E8^s k^s����S� {s�+�+]� Px^tk^tKt�K x^{t H>H\ &�1�R( �sY0\delta� D9Gr!GP 7 ��8 $2<= � b�x� �} �$. Notic"is�7 even7s$ or $t�P� ,E�ta�V�!E (k)�i . M�&�\��>" � b���utR&& \h&{-1cm} �~�u��&�L4 &=&�  Ri  a:� kx� -k%S F� vbigT&*� �e(br .4� ) s2 T @&-�^B R( �+�H3i�Y2}�"a�$� .���.b^b+�E6�� B����v\gammA�&:=& ��0-�� KrF� !�(� x}F(� , E - e�FnI!{%1Ei�1� xF Rmm!� (p[-xm��-1 ,Sba>� Fjjm�&�m���&uT,� SZ� �G v�o  $�AV :�m5�B��Y�RE+)Z���E��N�d�2 �`D���)� �7.)x$ =9(d uniquely  0< �0all " RI�%uaboG.h8<."J� �����h�?͑E}^s x^t>RA]qJ0 ) + V�, T�2"_-8!&Z��$Š �.��-�J�ap&&^�� ]�Z�a�f��O-5b��a�*� %FL� s�Mq5ft-&&\ +\v()Y��1�Z 2})��:=2 To�T��; quir`= tegr?�qIeone  to�0i� foures, ��oea * ��InaI .< repe�*applic� s�ide�y $� �MF x^t.�� {0�e�a�ula�!>� U�#s('&� �&�N�� "��>��1+oF�=u" j`:�E]+a} ( A3q0�u-&-����'ve�s4s�S�%6�$ �<T� "I:,�A��9.\ m'=m�E(B0<�>h�%� �G� $F&!��'>0%�&z% � eqn:ruled�s�: mu_1"�2F)"��� ) = %C(m)>� [tm'p9]yk�%k A�,"J%.w%��-�%6w%,� .�% g-50<\�=(E�)�9�t�L E)m'�  $%1�,:��4m$ea%e pe B�!%B�[!J��kr**�;$m �Substitu�#sttoV $$ %-�I_\�.�� C'\! \�1"�\!�����R dx-a_0�<6&����?� dx� !?% �;�BC'&� `g � dx}>0$,1a�A�puD ng,-���result];<E"M� H@H2�}[�<*$E�j�A *�?0% %fD 6�� �#� 1$� 1}{m��z*$�@� m^{-7 gm���%-.$*}�4�(F�%��2$A3{1}F�t r�G�%�(&^ *} CIW>� bw�:�2b�p�4BJ2}:]N� 2b.�6*� $C=C6y :G HA�AFF3 cT�;�1r*�>��2�+wv�#.Ys �2�&D� A�} .�a %Manu6�:�z�e~"�"L�bEK�&)&o�}� E?y � �n� a,&�  %&G }{ & ,s qI&} �.s,��(_!%a� �e� �We�> %�6P�?�=Pr&hG��!�^�T# }. UGb�,ef�/>Pe� h^O�� 1��A=.m� *� �� J�!1�&b - x)dx!�Q*�e)^2��2)!r!>w[�8]J iw. �-����J� �r�u>n-JI���\_Fr��Z f��^��? $$ >�je�^�]. dx}\,���i6� b�K/ �{*�FO#in�a4 . � Q �)>�"_ ga�&�Yz�3 2� %m�C'�F\_G-��z�ha� \nonumberP=6}�� \ %qCQ1�2Q&� )�}� B$s+t=r-�%� C# �= {2(r+2)}[I,-� )].&r+2}>0:$�F����U a2,,�well as"!�_�� $�v� Jm*��B dQO��'. %"�dvZ>� M�. [��ThE�Cthm��)�"&9Tw?fXby^E�A&/5��&� �51eb�1k�.�k$5QJ�1� D3r=@7�,? L_m=7F�e(*g M4) w !6�!>!w�J�F+Q1$�=�le�3s�2$Fn��(B) EH����R Š� = �]} {Z� 9B)]�8& ��/EMAyE(AL)mK� C�xV(. �E. 9i�S� W�y� aaoɗaF$�ei��U��Ja�w�Tlg2y dealt9, o�! 82�Ka�1 b �a*ZLmgf"�2DQ`H"!:�R �*�R=1!W� Z�QtUdF?PU:�R f�R0#A�P E/F)'e�S)�is� !�ZEpr�Pco.DRI���R5#g<$isomorphic�yE�So�F.�-E]�0�Ple&" @of} \vskip 5pt W�#@uld similarly now�v&i#par�?�$<~$},�Sto O��ofb$w X � l�ES��!-Gb"�|_{B'#P"� �%&%� asymptarroch}mFC� $D�+.E�Nu�A�.7SOCA�mA4o"�HC�G D � � Z1n rk Ck 7.F-� �M�u2�)NB2�9!V�03�u hypothe�vVy'Ii�{����D$.�0_�nP (1) twice"�&w���p"7"b'}A'B'%�a��schemeEB$���Q �E�9.�Q)� ZF.m$B'"v)0� �;�0� cm}(�Q��E� c� S 1mO _{c ;B'}i�!�q_ !�$cB{D%\noin��-"� ��( (3).} Pick�'z5gerE>�Z9 BR�:;��n-is�0/uN"4^* R�kR7a�$k!�Wq��Ez� 5�%Sm�5�(m-u)#!�& 0L 1))=.�1�e=BA�ex/i�AH�p�d�tant,�c\;l.9S F�� lo�Y�s��B]c\l�wU�.lE�FE)&]�EG1))�H�6P>@)�<.EF/ �*weW}2te�N��GrF-F� by �N @+ Zq~ �� �F,� V�F']a�i�gE�R>�LR E=�^�[ | G b�jd �>atB!affec�4pur�! �U F argunReZ;�jus�,�o��ow ]\ZmQ]A�6�0T\�<(�F��xkm{a_�k�<ac�'B�<�;"\ a}J\_BrF�lblb:l ?){t2�Fix $xI%� �)_�;1�}X) "�j���"� �$a+6mm|_{mP .v� �%0� ��� l(x)'}{2"�<m2<-Z�\=.`c]mx  a_0'\)2[c�[4dx!~J]{c�:�;%~rE�1}(%�).� # '}2)^.}+] � cm^b .�62#1X 2��'S_c�g"��. Ti�.6=�B� %_�P & arch�EveAI � f\]�j�y& ^��C. B[� �)�� M � !�����)n $ 6 �]O� �rZW�4S A& � J5 =m$ so�?�� ��>-)�a�� �e�a����F"���:iPE��a�amv� ��:y\�l! B8q�s�i as r{)�`^.�%:IA����}� �~�*��d�s}q��}] B� ��$��X&(C� m MxXh.G*R��ll"!d"g@wi@\F<�Wy  .eN.�C7f"ygR�N� F$E� 4Nund\-edP XU$\{�Z,F)\in H^{2i},c�F F)!Dm�l9��-%E+�.��f� >��V�e;]cq��} &&B��]*"� ᫡�C� �2<\"�J^&�-F�&�?�?aU6\le& -Cs�N)-�2�&�2� "p �Ch6"�L� j�&!�aY-�. � "e� !��C5N�ex�m c gF�� . ReplacRmDn�k6n]c"E�m�`/$l<+/X� �bEy.vM�G��r� necessarya����J*h.e�Y� by)`-�)�FgoN�.U 2 S"2�2�.Z�!%�筒�P�q$c"�<��B"n!me B)!��I"*8� cc 0)/m2N�NVb'�m~�.�m��j �l @��AN�6� "!��e��:����b� ���+ on{U7�ib�up2Kl. "h �Z Nt X$.�!�orm!�T�R�c�D�X\to X$�HX$ 9$Z'�excepa> al d+o�9B@� �k\gg0$dH^0_X60SH& \!Z}.=)\c�.{� X}M^*2pS@E < �estrM$link betwe�=I�E-#o!+Mor�",�2� $(X,L�+f?o"qa:�I��qV es $��%N,�?L:Bq�elatJaF&�- N��pq . Ho�l,�d:�?^*L(-d�W_.U%k0\I1�%�7~#(x+d)k� ( Azd<�&��Ati�-d�E,L_d& � d2� |p x.dxn6a�V,.kA#d�qz < x-[^Z�~U! X $(Xs�,ect-Y 7� e ��r%��tW way."�3�PqingGv poi+n�il�!Y� a �TeR5X,'n! at�$�_ up*s�B.a"�ely, fix� i&"�n$qc \O_X�% ose N N�]i���by1olu�V$��U�O ���VZZzq� ^Bs�& $dA�5x XE� m5%�w�so��no.wei� an easy!��%"!� �msed )qie�tacsc�v�Z"�@2`D2 2"�x�'}� p2!�nupat1E� ��^2$Qbf{#!�anb '. Any�*1k!"IS��\to\PJ�� �, iple!$L=L_q�zW^2�. - qE�G8q\in(0,1)\cap\Q�p�";\)���.~�(� V��!�c/$qRmNZ="!gyL(-cZ)=2�� (-(q+c)E I)nefU$c<1-q$,�CD�� ,L)=& Iy��surf})5�I �mu�`*�03-q}{1-q^2}\,�ua.���_O_Z29�}{c(3�*)�#3Z) .j}OC q)(2q+1)}��>��H $$(3(1--3 ^2)=2q )^2>0�Q&� 6{� �M%�llFq<Z�Yf�WtadM�AT�uŔ S% ��*}"},Xi� &"4Z $X�m 1�^jLw�$ (�=E\AvKxA�&� e��b �\^1O$). I�asignific�v��B:XeW' all}A��@"�5iori} .�K��lev{!K�re�s"-�; non-;ktixv of Aut($X�*)�5'< find:� s&"'"qv)&ao $LP tend�va"+ �]  �x�� . By ana{e!�� sQ�!ofa0x},)�21x�*�@%�./r!�;�d�B��X�E 3& x����ny "� p,yJ�^FI��1}{n! Q"� X} �l$F(-xE))^n,"\\ QwE-F2(n!P�BKK2).._�F'B��]q�R�o (X,F�Y �n�X�K_X n) i}{2F)^n}V�|cau Z,F)�0�+0"� \�\{a}^F��0.0\,\!' (2� "� NH%� FZ2$..�>�x^F_i(0)- x� "�x�RI� �e�uI��s�)� �Q<+&�2H�TnefMss�ŷA{�M�� E�� 6 * $c>0�!�e}$F(-cD K:���6%�)�!� %e\.=Z1F� _0^F%�:��;$$wo"y less��)dE$~o}�:� dx� (In�*i+`r�WR�� :�>P> ;2�ͳ F)<\infty�& M* $~� ��su�kla�o� /� z9�_(h:��NanI]5�a� $L=F�G� t� EX� zlta_0�] �����+ _?0�-E�]��9�$[ E)=Er��e9ef�"? (6 �c.cJ$)�I� L)^n E�1� _0^L�� dx V9\O_S�)o]$�;�$1��U��:Xb>`^Lf�L.��84|�j�L�:.�!.t��U�A])��nd�C #I��tE��fX)7e��%0$� u)s�IQ�  � 5�2�y2�"�. cor}{\bf F�"� ��E�e3�' �� 5Yn-� � � �� a�0e disj�HZ �,6: m�T*y set �, vAc� �Ԃ2��d ransx�Z�!5Q ��n�m�tinct�s}.Z@&� < %n!-1$>=�(.��X)�0{E_i\}_{i=1}^@(���y� ��7# E2 anrefJgCl��t� x  "pBx "@�2�:2 UA~m��� Z�(-Iw�q_i�ZN�0�.v��he ``1'o1"T a�zonWFan�Ga B� � &� ^X "�5aut sm gro ,�W�Fpro[c�,.��"�!�&2W$n�3�lr�-x &Oof �H9�I_ BdB}-7q1lI82#�E�I�UMA�a��d]�2�6�ellipticE}I�oB78Q�+ t 9Q�)��[!��2*�p ��cubics!��X$o ����R �QzedB�4 (``half a $K3yra") �� K-���l�65D2@)nNS���)bf{$-2$���We nowe�� -Aa��ing� -2$-@�[ d>�.�B,�2up�! i3"*�. !�'e�/oc���1fB�ain` ��E�kn_=2D$-1� $E_2i us 1^2=-2sn]E_1.E_2�G* jF�\!-l $12E_1-E_2\��!�ef � toricP#�A�*�'s�:{�o��>"��)Mon� �� W$ Kleiman cЉri3��NesuSAlsg\Oo0^��nef�@��s J�-6�gˇ�*?w aMX�qQ!��B�Op!���By!�vex��'J �|2�!T!jqE_1 -r 2g7;�1��rqr/2\ge:A�SH^LJw6�r_�<�� d>r>1/I=!� Z=E��k:�uGinA��$�w�X � ,Ȁr=rQLV6G e ��L.Z=1-r�+arrow C s $r�#?souAI�nwLwE�{=�35�A21.L}{L^2}FC46-2r}{1+2r-2r^\� �4 \,\,�{J�a\_{c_rSK@ *� 3(L.Z+c_rf_r2.j3~i�5*e!%� r$ c $1� ^�.� aW*� *, *F�& a � upAA 5 ints��&" ��}Ad�k�Zl"ēF��a�new2x�s ���Aˁ� �� F�1/p }&i ��e�n$�q�e��uv J� �"`6?� :O��-B-l6� *9 �� c�`"2�*1"}�5o� !I0gory details.erZC!�!�' n$��$Z� (or�(<%�dsub"�)� B�.X s-�m0t�Xy\ ��.q?&k�o� $m��E:�&MXthebibliography}{ATGT-F�ib�O[AT]{ATFT(ostolov, V.�< T{\o}nnesen-FriS(, C. (2004)� cA remark�T �� c:cscalar����=� ! lex> $s.} PreprA:�.(.DG/0411271} \�CG�CGT:�, F`derbank, D., Gauduchon, P�t�n�5� �H�+ton� 2-�� K�geo� $y, III Ext!l5 � 5�.}� �511118.%�1�Tu]{Au} Aubin, T. (1976�\'Eque(s du typ�U nge-Amp\`F sur7�!\'et\'%��ie!�%�act%~C!fR. Aca3eci. P��( S\'er. A-B��bf{283}, A119--A121, MR0433520, Zbl 0333.53040.5� BdB]� BO�!�%(4De Bartolomeis%�(1988]xSta)Ka�2Ȉ�-d e:� .} I��Math.�092}, 403--407�936089 � 645.53037!�8LeB]{LeB} LeBrum199]5P��zed $4$-"� P � M">7i�,Seiberg-WittI)orA8 �Re� Lett��653--662�135996�874�51.� M` LeBS�S2�A�S� ca, SEu9.�U�>�:q�d��mE���� GAFA5~,4}, 298--336�274118-}801�.�DCEL]{CEL} Cutkosky�, Ea!LIB(Lazarsfeld,AƁ�1]>Pہ�� �� &�$ve -rAnnA� 321�13--234�866486 �$1029.140225Y7CT]{CT}Z n, X ��, G�^3y�G�S � Vmha'o5F foli)oby��cA�Rk4094336�0DP]{DP} Demai�%J.-�* PaA�M �4�NN�i=�"�Ziz �# U&�Ga%tact@q#}snn.@i� (2) 5|,159}, 1247--A0!~21130�|�q$1064.32019 I9@Do1]{Do1} Donalds� S. �`97�R��s�� gaug�St5My,�����ED.�i�o� �F�� Medall�&' l��, 384�y3,.�ld �kublish�WMR162293:�Do2�2>�M� ͸S:w%gA�"�"e embed�] s, I�z,Jour. Diff. A��b!y$ 479--52�e916953Q�52%y:.Do3�3N�29wb��:A>"� }.J�U,62�-289--349A+�K50m� pre021719A,��Do4�4N���>�!\%dR` IIY�Quarte�I!k!-ofE�e�.cs�,56}, 345--35�2161248:�o5�5v�Lm�3E�� ' abi Fun�� al}.�3*� 06502;,Ful]{Ful} Fu , W�)77<*�4A Hirzebruch-R.��B b_� �#y<���C|$9C$ algebraic9� .} CH�ݝ%=Y�3�VA�283!�046032M� 0367��0k %5�F]{F}L, A�8�� An obstru%!�S a2�S��%� -�� i�){�5�76 437--44:�Fut![tV�IzOn��:D�Bv} !=�5c. Japan� � �r����a� 401��e�0726535i� 0539�A��lHL]��$ Huybrecht&� Lehn,�N1�w Ӂletre�moduli M��s.} Ap% �q3�B Berl� MR13049� 079�4.L0Na]{Na} Nadel�90u�Mul:0ua_2j1d"Z "��_p8�k! �0.}Zo13_54� 9�0���p73�6:�P]{P}? l� :�9f si�&�E(M_Y��dv-lU#18�333"& 03�6 1050�6:cPT]{PT� 2�*� �A�Ana� K-U�*�&: 40556#,Ro]{Ro} RossE�!��I�.))�;H��A�eti PhD�8s*8Imperial Colleg�R�(RT]�� x�homas"'4)` AI��� Hilbert--� &���".�}�6�2�A�25{ � Ti1])"=�1E� On� '�� ��m����U�BGy���}�10�1� 1�~MR105571�w716� 95.�2�2:�EHN $K$-ɅZhyper� #h5E. � m.Eh>�A�239--265�1312688I�084Z�3�3:���� B2E��5N�8&h fb130� 1--3`1471884�92a�2:�$Wa]{Wa} Wa X�0Y�Mo�N map,�  i"}q�5LeF�,��C Zd1!e100�z0 �210330��� 4707P Y4We]{We} Weinko #B�"�FJ-f� in&�M " # aZl&�ed ���� 6b6 30946W(Y1]{Y1} Yau��-V8B�Ricci9�waE 2.z 5T!}�"%M6�� a88 Co!� Pure�ml>�3a�3A�41Z 8035� 36z 5:�Y2]{Y2>�9�l O�}problemL "� � �erential: par�` �a U\N/@Los Angeles, CA, ��,a 28,�Sympos.)���5� AMS pcUse�21657:l$Zh]{Zh} Zhe5�*v Hel-IY�%o�3 �#-a5l6�!�i�o ��y0�7�05 MR142071�{092��05�')t:� �G4mm {\� "�?0 {\tt jaross@0columbia.edu} D, =2ri�d.t��@i�.ac.uk}}ew�">De!ޅW6�, C t Uni�KDty, \\New York, NY�*�� USA.�jN�W�KH London SW7 2AZ. UK !2 docu�$} �6\q(|[11pt,reqno]{amsart} \setlength{� (width}{14cm!rDusepackage[dvips]{$ icx,EGr} #U(symb,amscd,%�(xsym,epsfig2+[5!,matrix,!` ]{xy6#!�,scr]{euscrip�4\DeclareFontFa��{OT�Psfs}{}2 Shape.(n}{it}{<-> 010.2aPA�t(bet{\curly}F= \newco�_`{\rt}[1]{\stackrel{#1\,}{*�!}}62RZ2KW&N"66\�"@{{\!\,}_{{}^\circ:$DB{\operatorname{Bl:!C{�LC2�\QQ6RR6GG}�^9\S scr S65Z �UZ6PP >M>P 6j {\T} 7T6RX-� X:X���8!Q%� X}{:-YAY>�LuL6]LL5r.O5O65I4I6'�{\hook].K\res{\eGvert_6To{>S2=�){%126iAjmbox\,\_"}I1.5rR� tmid1.5pt}!<2�_{^{\ }6�{A}[4]{\�6�-ab�}{c�Q$!\!#1 & #2 �S#3 & #4 �� 2id)2�{\rk}:���.: coke,221 :Pim>Pim>$HoB%:JExt>K:&AuB&:&Pic>L>&rojB'\,:*SpeBQB*� >T:RGrass>) �D�# atle�E,\@addtoreset"5r}{�G}9W keat�#6n{\theU } 6.\arabicPwnew�m�O}[;]{�em �$[b$?Q6"cor."Corollar��l�3.'*�`>Onj.)Co�� �style*�=6C defn.C؏|6(E1��B#sF$ƫ %�  \title[�AHert8&�+] �bfzk3�] � ilit� .�@"A� author[J.� �R.�$�]{Julius5 !���p  abst��I �b We�&a syste�rC:�"T  no�E� �fL'.  � 7;Pp� �;9K-�XS@4 e�ype� oRBlea!9� ncep�N sl���;�;�y-2sub�ds;�;&�7e glI@�(Z`�C) T).�J.0�)&�)�;as�` c^� model)�,Calabi-Yaus.!��2�ou'�undT al tech?�rdx:�"čW���! e,%# +�g!tal?>�%R� 0mic (ra�(th /ombin� ial)�o^t�!5Q��4�es?ndY� �bkee� ��y�%%%�'�� {Int�i ion;�2�} &�InA#&A�3� PbsLvӧsuc�OfulA�$�1m> 2)l"�P����Uy+N;q+ �HL}�I&p9/�)�an!�� ofa�|�a a Quot I� by a5!�b �,�+�5$o 1-parame�LsubX5,eir w�r�u�Jo be domA2 ed bwH ve�1a��IP�E)�A��"��'Te.� � co�M�S3g�e;-hc�� !!"ֳ"��E/���soμFVf!leL�T�2UE�X!� is g!�n7; <v�`Xk�h6� 18��#�b`��s("�}m#' �Uh�3�*% PEsE�� Form-v�a�i msel�u�4 GITa!���7 much more�,!�tIeaEmainlyiLacc ished%pc�ly �Ez o��#2� , du�;wo�,f� s7DGIT, Mu}, GiesekermVGi�,a�a little �I=��� hweg NV}�$ughly speaO�ne�M�+).�by�iZ�(;�3$L=K_X$YGD�8aO;gg!�le !4ɶ-�f $or is al�o15�d>$Hbiia��!Qa#�!�# \Ionsa)�e��!m5� �.�-! /:no�/6w (in)��Aemerged&�:hW:�M;notI?���if��!HgǠMY�%�; <ad~"!���A� deep6� �]"�����-"� 15!A�app rim"A�-2 d�� ly (�X��l$R >k ). K� M�Ko�[� s&;tu�oto ? hods#I �}�-�% �g�2impetuKR~FE~%� !{c�f@�2�SK�+` !"z%ASF�� ſ�s>�0��%- Ti1, Do1}��3>ipp,�u.�a�i� RT}. Our)�ach���>i&� �7 pionee�L P UMu}. H'��i Prelevα� in tV�of 6Q-upE,$X\�\C$%�(Qos QrA���ickening66{0\}$; �rz �ainU�(" WKref})J �Սeo a��o2z�3����\�&�" ce*�}. �Gt�nse-�$is made cl��A�u,E� ion A�)Lhorizont� 61�``|�,"��# 2�.) T��Nj!1� �!|� .�  �``*#/��>�tZ$"���Lous&F�!�G�at �G�V���i(%`}�! _Ats� ��nontriv coe5J*}^#4} cBmu}�Q(E�1/a_0E =} (UV�s��usZ{dY��=$$\,(E)/\rk�va�un"�C ���CA �X�!h)V75�'.)�7n��sa� E�]- emD}^��{J�"���aAovhY$�E�U$!�F\`�eq !��R$$� `"� i�},[$receq$ mea�P*3�n $r_;K � �A� F(r)� p��AS"��;ge r_0$;� �� � } !-in!�9 AΣlev�|E,$MJ$.s:�E?a�] * mu(F� E^%�EQ5 I \~�V� !u :|v�is�t�\ �a-?s H!�.���n�!�Ixent choi�^of*o ��\ e �).$ Mj*��4fact Jun Li's .1��Li}��[!�J �h� tends��#�Ras�D2 B��i��%��& n��AR)] so m�V1���6 (��,� Xym y��2� �Q*P )!j&A,i�#r!�next � �� ��� �A�� a$descriQ?�"�to.~. Given���(O^{;^�%y���iV &u? )=\sup\{c��Q_{\,>0}�^����&O^cr}#{!�gl��lyVHa- } \f�]�@g0�{�� } crgmat�N\}�[.�Samuel.�A�i�fix��$x$f�HpCzL^�^{xr}__���M�Ka_ZQ�Ւ,�� �, \ rx.�"�R�! )Ts)��R�[�}A�po�X $x$�e6cWK})Źso #�� sam�^UP $�R$� A+ous�z�@mu�U �E�)<K-Ex� �[(�Y�,e�^�MA�$A (0,]%]$)A�bebdef��)�TI_A]�MI\�@:DA�N�B)�-k"^`D dx} -a%�tTB}Se�9�emptysetc`~��%�a�cE(��.�:T]it2�_9$)�����X��I�Q �"2k\&*UQ<i&�e6 f�c� reEO$EF�Z*��D the ��]f��zr ,\ a_0=!N0)$A|,ed!K ,~1=!�0�YzM }�5m�Z!ՁB_{02`]6�p�_,.� ��E!�hQ��:��lR�. � ��(X), \q�[ t�i.� ` inI~�� x)+ Y�rAoJ�le.1� _ ��J@��Cf.�Dmu�sTB}{e�& ! sl�%a� rick�-(&�Xdef!4});mt�\ reas*�e�A��5� �Ay)H�\( if&:k`le� })E3H��ҁ�mi) f DGK-.}gBA_0'/2$ ``-cc �" A��1 ��be&[ /ce �d;Jo�#2-�?BI� c(&3 et&2�o��< >s (�Xarr R& =  F}+ ��� ny"�).7> on D_;Zbed �` !͡��.!c� �qI*�� �� thr-� up a�8 i]  Ђ���$�(c)Ǔ )/2=q a /2$; w� pl�E[��c��&�h�$X\� eteq�DN=^���^*�QA;9 p&h+�!� �Q ��!�� �HX(1$ e��of��on; s>sqochow}�mg�@),:b � �S}K���ger} $B�$,!4E�.�U E��nc�Q Chq��(��1}^ch^0Jt�giM_N�9e��Z=��� $Ch(��)=Ch(Xk_O%Ko$;D n y�I{� �B#BE%t):6�#$($<�&(\le)}\ ��4A&� l��like &y� �soE�%j&L�at�� �Qa�lic� . 2aK}"� M�/wt u��rm�ewhile:I�}� es �Iviw�d. B�X�rmA�(one. Arbitra�R;&��6t testcoTs},"h��N6Kqu�;�Bp���.Jin "��5�.�2J�` rse}j�*� show-< �f��F ��. u�VS )um��c�giv�a p�al �au``9v$\R�eagL$>�".N ��%�inkx�c�Un:�H��Y fail�.�L�*G}�T flat�raZ���  them�be -pr�ts � nM carrGW�@�gramm�full.�Ay�_���� are}e,eS��rG T/Ua base� �As�sit� ��X��H� ietea:� \ 9��we:}(a �l�!e, -�"/!�_o�up�"&A�Tjof �zgenFQ\ge?�AsiWas� k��!�� �usI&���"*�!cs o ivel^j�b ٗ%)voto:�� 6Tegs�e�Ls1ny:,nas�Wive bundk0app.��.$a�aK�-G%�.�~U�=��� s�a)l�.n%/�%c!c ledg�9{3�#wer��e�3�Bm9, Conrad, Kev��,stello, Dale.�Fi2n  Pvid Eisenbud, Daniel .�?Fr�s"�9 Miles Rei�2L Bal\'azs Szendr\"oi�use�"�s�ee book�HLHpa�V ); have^�" L to u D�&s w.&�P"n EPSRC�7a�entshipA�, a Royal Soc�  u"�0 eL| f!:w36�� �� -�!� 6�DOscar Garcia-PradaP�"Newst�A �A]a visit�CSIC, MT�d�R�� �Jis� as d� "h$N��"�n Throug l� )v� willl�aQ.Xbgvh+, irr �i � ,�l1"�5 $n=��X� �_ ��m�w ��.ir(ety. By $jZ�{T���( "i�$j$-f4������ R^T n?� � {jZ}:= "�jQ'�����&�rAz&�l\^/�r,��.�O�PQ�?^*u=\O(-jQe����s_Xp^XE� ;_* 0=Cr ll $j:paTFo�$�9i�� of5LA���&�UF�, mix �@T5ˑ ddi�IQbE�����<P��~��,'notwf1 T(assoc� d.MOUor����hat{X��wq$S$(s(-E)).$r)�L^k-kE!�ors�Tillqdit "�Yc �) u�, :$ msϡ�I�U1�a {\cap k}$�b�ty�/)_ 0d f co" ��W� aby��i_X� is n��A�s lV�=. AnyNB5$V�_a $\C^�$-agi&��!ne-u�al�% Gs ��big�l_iV_iADž�$t[ ac�n $%, by $t^{w_i}I� $w_*�� h{�  %��I2 $w(V�m_i;�'$ :to� @:?; < - !a�;in<#d g!t $\Lambda^�1x}V!�Oby� y�$\C=\0\C[t],Vt!_�/^pulf�nd�D coordinatM�CfA.�g&em9;�d��i�s�: %mgl� e�� po S�).� ��/,j.� $ll��i��� perta��[�-�theNUq�&�%;4 ~ZL�W!0 �� a~h�;AaH �b . (I�n"1 `�� ��t�,M�includ_,� �!`�-)2��A�X2Q S>��� �gis&5�|�95� *+�r[�Z,+&=&X,\{Pf� �� {cr}C 2�] r}�\}\4�}d� �} |ma�4{ c�g $: L - cE \&�Y��f!��dX �\ �&�����F $Je I ��oe*�J$�s�H��} Ia2 $i>0�X $JI^{i-1}=I^i$. Equiva5 k ���$p�>����a�8 $I�th.� ��o!,� n��(cl�B0 $p^*J\to\O(-���,n "Ɨsm.G!"B ceNa tau�Tgy�e^��W 6�>� e � k7'�r��%z�-Na� of $��_i17J� !G *� ExerM�H5.10)a�is��y^.;*0c �z���is emp/<& i�U{ �sU� $ �a�"���C+n�B��;S�L\o ' I$ca^ �-! U�I$,U � n)_ $Jf]���hZy� � I$ -�e}EmOnJ&�s>�V2*�.�-.o$- B�Q��|�#i�a�,w1�eT$m/�H )6i��)f. ..1�� � *n  ��hfig��E "� KK�-z� "�%\Pe�de>" $�[n��k�r  $n$-.� $b� � �'m ls��%\P�% chi\u|r��ab�%�R  $�U*�s]mMl L^n�sf~,��sm�f�� $$ a_1 ,��*�s MX)c� �&= - uK_X.L^}{27N!d$r>6VL^r�����a�G��%���u�5�r�\} H^i�0 \�\�Ťi>"��&�\�2^*rwC^{%u&�_ k\n� r$�Ts��u^� :-1= e��^�.f} $�9=_{\P',K}Eo�o�c�"V�(P'(K)=\P(KrtYnor��$K_2nfo���(a�w� Aw{X��ofE�%s$K� ?wv�.eac�#�b�eq: ilb}i�H^0&�\I_X(K�� S^K 5w*+#ngH_XB�^r)\to ;xKr}F1(�Z(�!��V}))�es ���a:�!�Gh;mann]a\G=};(:�,)t[ S&�X,�eQ�>&!S��� Zw$ V u�%� $x=x_{rEi�72�-�2�&g  s9OA�(up'�.� orb��SL(E�,\C��P.�$. A $g\in 6* ��� m}$�!uc n"o*��mS�!c<��} !ag^*)^{3�}�on }\E]-B>$���d��~�$.�z� ���tgmu��%k���on��\��\a�et\�t k�|PP$. P5 C%nA $|$G&)-5 to p&�"�p�� X� fH"}d)' fi��ovt�g��UA��Jpla&���sb l(!al �n�lin�$$O_{\G}(1)\BAx}=\L. e�y� 1":*abq�ro�^*"5��$I,�d�=.#�ert� &C!%��a�e qiig�B&*� �!�\.f 69, [!i,9�%)),6� �Zܦ� � � *���"S}' �^�8�F&fs.�w�&�. By pic�5�|����mA��ŏ� 5���n�E--F beautiful� �7"�) �2ge��!�J)�= J�� .a:�9�ne!@�8Z=9a ;F% G,ok����f�E�alx �/"Cb��)�Af\ET(s*var��lwkQ�&���JFe A�2��m�_sU�";���C�l 3��!\*�!���c�>!�!!r/ sQ��&��@:_pIt.� ._$\Lq�Je2�&�.���,$(\X_t,\L|_{ }%����58� ,? sn�, n\0slashw4 . AJ apK��<-�9�:H }W$\XH ��!H ;t"&1n&� F0�Won .� ?Iw2?. or. X��E�a w` cI�=!ch� ���J�",�!�isc4| "�d6*I�Q�� } I ��Aiɰ� $Nj!*$G.��IPe � data,aJ�!�E� � ��of� !a���&�� !�2�%�%��r)^*)$ 6ly1! N�A� ,\L)S�)^r�,� %z�.� () e[):Qz ^K)$�z$w(Kr�(We enuma2ek:=Kr�(\X,\ 7%�F8 for $(X,L^{Kr}Ua��used rea!�pmay set $r=1$ temporarily.) FB K\gg0,\ N�%�%Q{\X_0}( ��{w(k)= � �poUSof deg��$n+1$%�kᭀ!�Dvariant Riemann-RoE^ eorem. (I��i�tanA�ata�Pdo \emph{not} modify �$a�b�cis.�!+small $k��instaEjw��!2lly iIYQnN�$$.) To makm�IC:v0 special linem�1bY4$�8first pull backE�family1-��` $\C\to\C,\ t\mapsto t^{rŒ}$,�a�A��!� �$ '�. Comp� �g2ͦ:� scalmi��-�s 5 Y $-rU,8$\Lambda^{\max}R�ith?�D,�g cell�ou!�$e previous �. (A�extra�Do��$r$%�=�Dformula (\ref{norm�$ed}) nicerBA� natu��ifeQ\L) L!� r$th twis�ar�)$.) �tA�new �-7�Y total-�S^KJ* , it ;{ AM $\O_\G(1IGa�\}}= 6x H^0_e��"\o� �5(6/R�\r�$)^*$ (comp��)Meq:�}) I(was!o%? L^r)�P no �S0er cohomologyA�$L^r$)EG q�1�-,} \begin{equ� } \label.�D \tilde{w}_{r,Kr}=2k}=��Ia-Ab8k\P(k), \qquad �t.�h�GY. �A(65h\sum_{i=0}^{n+1}e_i(r)k^i$ R�$)"k\gg0$, e coefficie�)K!e also.�NPr PrP: $ �= �j�{i,j}r^j21. aF�%b means �A�� (rk) �8$ vanishes: $e_�,!=0 XTHilbert-Mumford criter�relat�Sis1[,to stability follows. Qthm5� thm:�� 0} A!*ari���RetyI�)ŗI``le}a�1 $only if $$6C,k} \succ 0 \E" \for�8$\text{ non�( F�i} �r),^ whera�U${$ S$%o%i �����$the differ� no{ � 9$ : mitemize} 1z-leec pect!h $r$:fanyv�&`r),\ :Z>0IO!$Q� �$Asymptotic�P:� ~�I�����$� $�� � Chow�:$,!� lead!�$km .5m}^ofB�E�positiveuJ/>�" �:N��K1Ki�:wK-i3�er� A-)F�8$%�$ (��i�Xh>t  a,e8(FurthermoreKresult� ds�.wc pl�``)"eV ``semi�Vsx in�L liti+ nonRr. \\ f� $\R9 �:)�-l �,Uir\ �^-K- �rel��between'�� nd a�ϙ})S�nalogou�m@:Oslope� 5SGieseker��M �s� d a geomeaZ &F.f�$would show@ � impliedP ] E�(a necessaryAdEvn � E chow}).I��/ )y57isAtroll uAz^� due/ $ \cite{Mu}� � �of.� aboveo A �,, adapt��Tian's "�"\ ial-9]eto allow��"  cent# $v �� ough what���ed�:per�PY�in � Ti2}E!/le in � Do2}�M�wM K-��).�H1} �e� �= ``CM E�")F $\a�$*�]� exac�S�I��� sense!�!�E*� :�� �� � PT}..o�probabl @t a bona fide GIT� :�'�� ��be�e/ �&��dA���(��!5s ten� o in@$y. However�k9�)E�I�g;ly�H�exist�P!2�_�Par��vt,e K\"ahler me�se�8apply our metho �th�UGRT}m�EuQ/ �say�zB!J come�B2>�on $X�!j$appropriat"@0�fy�B� 0�@>ZcasE� correspo-�an orb��nE}��clo� U���but� sibly�er&�alQ�sers;�lena�z ���IY��2��a6E:���raYem�@be2uni2 accepAVn=��a[E%u�l )�by ɏy]�H . AJ��d)� v � ���E� get ano( ,7^K � :b$; K�� will�`N."0e:���!3$unchanged �G r� ��som!�w��!(� tweթ�� to �8n�; $\Q$\,-.DMO6]N�. Let�j $F:=� l �n]՘F wriA�9u�s�d7k)$ $b_0l D+b_1k^n+\ldots\,$,�se� at;� !} ?E D} F=b_0a_1-b_1a_0, /X($-a_0^{-2}F� A�.�� k^{-1� nexpan*S/u$. Whe &2O�N�is smooth, $F=\frac{a_0}{4}\nu$, Mnu�usdCalabiB\a�$c_1(A�!h�e  f��A��$S^1$�ɶ�/ Wit� los& ge(�wa�w tkV a��rP F�a�Y,� Y(1).�)�,�Y~, $*cisg� tdVhX4,� away& !2��!�a�ef.vbirEKala@$6W%`so>domin1Ua bJ up��9)��$ in 6nin��I� ppor!� on (�icken�f)�6� b':y narray} ( � \ =&(\B_I�P),L(-E))&\Rt{\phi}\ (.� \nof\\ &\dowV ow pqg any} \\ &W,L)\,.��$r$-folx �� ��� C �$ prov� %\V�%r �a� sum��)� s:�9ng%�j� termUD /-$j$ pie�$(t^j\I_j$ we� � & U de���e��0s}). Or, embex( 6:a�� $\PP^Nѓ$,�'sa�} < dire�or��$, give>4��"� 8``repulsive fix�" set" $Z�at par��'6 � nega�2I �"!on�^�:a���% �� s.�$Z-ť!#�!~[ er transa�2I 0M?�bn ��a@! I.w" a�/.c)B. � �!�VAh��}N�(! beca� �r��� wa� o� &v i�)ea���d wide!�X,p^*�� E@resolu�p!zun $p$)y eV m�p�!�%[*� ofyJ�s. G� N2��b�udh in S%CestHs}; nex� lookc$ s��(as( eyonJ�A*�)�f ,\ I�� Z+(t!�n.�:�)�d� m�+<�%�]��H$Z$X \��{D:F3�AK-:�"l K } Gi�n��d$Z� X"mA��!;:J�(�A�\ :dalC':]a� *� � $P� u.(J�hasf  f) =Y�\cup_E P*� U���n 2�$�m R�E$.> ��al!�+ both7  $P=\�(4nu\oplus\under� \CA� p*e�pleqK�uM; $k !]Z��$$X$, glued � $Er|$C6�. ��mM on!Fe w�E�l Fu}Q�)rambZ. �_*$a��Ѷ��1(ons $\X\to �� $.�e��!E1<$�Y� "  ly& \L_c�$\Q\,$2j +^*L-cA�A� �)��-9���%�\X�"F F+���!� �4�suf!  &."\ �gu�7} Fixx�(���ve-���)J. )�$c�(P0,\epsilon(Z))\cap\Q$��4def:seshadri})i��. � !B� (.�on"!�Ibm\inktt!�{�s nef.6iD3e A$ glob�o~ $L^k I_{\!Z}^.Sk}$ s�(�2�not��})��$k%�)\L:� ��� %�.��)*W,f $k,k!z \mathbb Nw ��� �lyMNted���� ck}$�%�Y+L_c^k�)7.\A�2�~.�!l9 pi^*H^0(N_ ck})� ck}.(LAlgebraly 7 �� stat�,�e�f n � {)�ck� )�sI�T) $. G�� it*Z!: �9AM�!yB8%Ii�te%� -ckP&3-6�3'13? (\�ځ�Z)\6.Z ��K$P$,\ ł5�$t�-�)$�. Pu�c=q;$ nowb �Lthird{,im�5{�) /y laim)�w� y assum��eu�bEk �  by $((':=\Proj�,��_k�if&� �$kp �� larg{B�2  1�d,,J�)��-$(\O_Y(k))$B@ �hea�� ] Z_0} K i�so ub � Y�.,:+� ᩁ�P��!_Z$o us i���* !�) ��}o=� ��Upulx t#B@ �)� . OA�w� ;/ L-cE�>ŀI���ū���on�boundT"]�(Z� by Kleima+ Kl} k d=��$c� ]�!s push� q\O(-ckE� $ i�dհ�x)�^� i) �.� so agf1�Ym> a�a] ��ZF:Me��c�nef%lN$,��s=�9� 1��LO%� e=��, w�ac}3l�4A?.�}Q��}� obs-$*u :P (ng��� � factor)63saiQ ��G!�F � ����4_cR,�4,9c.� :� � � �ri�5:$}�� 6 $X$ :R !Rl�.M "!^sz fq r b\� ator�{�5 }(1, W�1�T%>degen*� � ��VU A�(93AW\7 P0of�ed �Wh#,E��)e�,\ ck�"F � ��in289�22(#",i-} +32-\s:-j=1�$ j\,h^0\!\�5�h(.�-j}/ 6 +1}) )"�,T \chiK:j)-ckhq ).�(!~5�i  Fr/9&��*� a���A0X� ��,{k\ge 0} \S_2F1�e�.S_k &=& 1}+�})^k =��=& t.k-1} ��X!H\   t^k��.�\/0.Q�S}).� I�--$s���YGI6.� $-� �6&� :$R�F�� .�lR2�Po0 �s< . Bw �>�9(cP� eb� �i� h�(he�.���g$ H^i�8(�)^k) = {��2A�� )) =.)�c1�=X-1wݴ -j}) � t�3%�o2j.�i�* In�ic!n,Yo:1�/}�NZ�=0//$for}\ j=0,�,ckT1uad i>0�P&. NoweiX_0i=�k\ge0}A�/t*7/by)S})f�S,2S_ ?I�kU� t�\\!9X!{/k�I\ )j\ �\, Esbig� X8Z)B�R&� F �7 \I^c �$&u�!!��O(�:Ap&�E .*�)# � ��M�f+w !�*4�� b}ex\,� _�� t^A�6A���䡽5kA���F=�*I�aje }� $H^1b%��#1\le jcki1��!["�=�� ŝhFXZr})+:���H.4 6�})-rW)M�m�=� [Ba**Ha}"{III.9�� s�� �e_8.e�-gM}%&��E2:��n���2$& * :.> 3  $t� `$-1S � ly� � � so� I� e�!��< Y�3F][�Y���eFa ^S\�6V�]I:!A�-��lnoco} u�m}r (cE() 6wUjj)��6�h 5)62�jF�Bwf<*U \ =M2�:� .x<,9p>j7 AlVA! last!ao1�/ f� �=FMa $H^.# 5A{\Y�@O-�!�\ �>:su�2=�#.��6+O(�*-1}vDA��� .@���Y�?2B � S_{c� � 2� ��t^jP.{�� &� 8@U� 4m�Et b:"� Q�qp f�*:�}{&�Ee�*�EV��p 2��\,m^G! } �f#�c}\,���!�a3�U $�����H&GDN7 a %3.�b"�F>�Sb&I?������ e1mhB+��2�� "/-z> ft��&�kJ�Ga�"i��*is�uU?"6pU�2�GGn`#��' x chi$�R) rrorA�yBp h^{\ge1}zH���*$1:�}i!Anh^i$. Sc""T'�nɳE&�} belowM�Tm�le&�> .�6aE$f  , orN ] �>*wvTEu��&a��T��? ��}1OV�j)=Nx! ��-<� \var�c�-xc-(e[�\_hile�"a�'g6� %�so]Lwe�M�'y Fujita2� � L&�  1.4.35)] �& $N-*�IF�^N} �^p)? Nu2Ň�$$p}�!k>NG�1p=k-N$.�+Ft N/k}LhaI, co�C��W_)TQ�"I*� 0&=&�\X_(2�q)q=#*o�H�4-� =� N)P))K �r"�Iv6,-1�J _.M]�c>2� ���6TB��MdecBS%/�T� is,�h�\d�R�=�A $j.�6��sum b�*�$" ) ��212z-1z>�j}*� tbC{&�% %�j)E�#w�Oh>ak:j?ZGb X}(-iKz5mi�ndQ�p~�N� �"i>6': A�oll�ofF �!� $h^i(\cur�0 (kD)�� i})$E"a�co��nt [ 2� {"�'D�Rh40). As9�<�{ &��urn��$d$= \O,\O(E)* (:�)!?!.$D=� 0� each �A9y .�+D��A�N $N� �,F n6g�7N*ii:,��wholeA�Vfcor"� �} FZ3�2e��.�Hk}(c)=r~(U8��\ b� \,-k 6k)�H-cP< " S 9N*�!M��*�O�-"1 X$,}� ��j) - �2�r �r>�j )crml�#"J�W2�EMLFN{cr*J ���#,�9r  u�M|�B�$\preceq0$,�S$ Es)�Aa�2� t:�H, depenP  typ"`>. WQ�_ ."�&�C �$�"SiE�ly��C�Nb;%#�$M�A�>! kG�'�r$S+�o ensuE�V�(a&�r�#!J&�$H�AnuineJL�*.�:we V},uMby�j�nd6Pro"�1%y� }�remA/>�r2�Eb1�_1$�C��-�s X�%Shss E&�UnJ:BvL�rzL  � �LD��  ReI* ��iLB /{2E�%�� $a_i�� (xDG�HS_�Se�s� !�ipf R�WO(-jE)&@0Lj�p$,�,x2 ,\,k&/xj~�ofa_i} !\F�xk� chi\2� ��P{xk})=a_0(x)k^n + a_1 {� + � +a_n(xFfButAX.wR(, $P(k,j):= z"{X}jj��E9d@no;U�Mde�R�.�<�.P_0u6 P_n$� $P!�is ' M �PofE-i,\ a_!�=P_i(1,!� a . $n-i$���$xk�#3ex�A�>�C�R&. .& -integrK7Fa��/*�Ar�$_%� ��!@*� 2� &{!�)6mm]ijmz �6ten�j��\int_0^cI dx- \�P� +1}+6*\!I, +V(a_0'(x)}2\, ?1?nR�N�, Us; ip>� j>pQ ( split up $�7$ as  N1 &&.�pj� "�p+��2 p\,S&V1}Bi\O_{jZ*d(!�j/k}� e�m!F-�{p/k}\!Dx)dx\,-�a�M{�j.�"� proxB� u%�A�fa:O�1jZT&A�Z n�(�'a)s },) ��$ �@11")WL0��(*ara�2fun1 $fs�toK ?.�% ��8trapezium rule HsH�}bV_S$easyeuler}"� M*f%�=-�ciYkf(x)mMfmKi�dxiA$��&uT�m��� Taylor' etI��l��{s��Qn8Ba�$r $� =x^meli% ���@Q4 � j^m = �(c�Rm+1}}Ac~m}2+ �m �$$ 69 �$���$,\ i=1,2$,�El) E.!A&&� 1�(Z�"&�1��"n�!�2�$\ 0=� 5w$f� (Z,c &8 pair&LA9mu�v,c�x(X! tP/>s "83and�0�Zv+>!�� A4�&�#  �J2 $("�"1L:ong2^G�A��Vu e4"� �"  K�k!PleE� } If� 'GedNU[�l^ �4�C�;le.D�2&�Nle:H;K-q"le:K1�le �: ���q��C.�/^0�2W2-���/F�#s&y2^�E�2%5,\ I�)� =��6 2"98a@#}�f�#��D)�Js�� $w8Mis�n��6reźŭ��)�<. "�K=B~M2q �`sn�M��F�Yk*�KB�i"~*�,�)*)F(Z�)b_*�M:i &� .1-�p. +� : B=0� \B.��-�v)!��4A "M1F1Bw�d�ly"]? � iplI�Fn��i��r (ya) �6i�Fd (non�EoU� ?� � A`Bas[j�&�s�ji��(�EFckU�Tt�+. ��2�5e�A.F&��}q>N�1&�_.|,�,s:o � �m�`� ��*b`��vid�: n ob"�(� �"�T �&�E��T3F!L�oK\U-Ezein�Trics);�A�RT}Bt� / ?nJhEexa,6�"�'\�a}P =Y-�*�'*�b�2��O_{xkZ})�/I��0)A�we[ eE9)T�\O� in sl$[ly mis^A��� be��"7 ͹qQ}. O. �� 25lde�a�":\1 '_0* .� 9i�N3&Notic���h�rephrase �aet�E&quival+ ways � � \ \Long�DaN\ i�$0�V)1I_Z2.� dcZ��c%j �!; AB<c  CDV`  CD<3${C-A}{D-B}Z0&Y /��S00.7 rmksU=lE}�=! �7.aA�"=Julab� a0}  x)X1{n!}��U��k�2�,�;���r�n$E^b�Ml�5:+No�X�*�. �� 0=�W>2�pd � $vCa�*��i�\_X ((>9&- X}�? L^7�'gn(-1)^i�2R^ix2?\�"<�cU6"u6 }t bE �l�Dw-��t�pi_~Q"� X}=�8� !Ha}�� of ��Co�!F3 11.4->EB��ņ�!<�U.�LpMs*}B%tf:I2%"�4 $?iA � � I�f�P.� �coHatkcs� i+1$. H�[���>H.u = "�o"}.B]�!\�D%�M7X�) +C2[DoA�1I��3lso!� �ks�Yargum� *#"UFuj�nUi Ui�$iU,ax\{n-j-1,0\G@%�>1��X�C�)�AOZ)�Ka?�`��a n.pbourhoodI=� 36!>nM�)���$iGl�N[C&=! ^{xr�i`Beq-1i"-��y&-x>y�a�!B ^ing&gin:!\\le0$j2fact �� a0����o �ga0'��,{1}{(n-1)!} �!X.E<pi}�J�BMNGN�. 6; � ^ 5M$Z=�Wcup Z_2�:$Z��nd 02$ disjoint. � A].� ^{Z}3 � __1� 62b)Z���� �Z� _1}\�,�{xkZ_2}eLQ![��42 �!*re&�J/")"�.b Q�22� "v�-S0^c �� ^{�4")�'O_)+5Z8%1dF82})&�.6 m dx!�Z".#XD <� M2�Xe�e��U$j�{0|�8���j})S$, AGby.'2)Pdisu3}!�lscP_j~[Z�Xs J�ingSXpli�t"�m(.A nS doesx�B,mc6N�+"�m��P1mZ� nd>*U R^m�_{mc}�Za (m-1)R� dx} "� E1}. I:;*}Ml F<:�ij�1�e�v2�q�Q2��\ca�'=� tysetd� 9!_1�Mp  \min(.)*�_2)"�� � �&T^;&X;X"��up�j*�U � ��.|Bd�^ $E=E ) E_� z/$E�&A3Set_E�z� over!i�IL TM�*, [�M�byO��K L-; �L�J � 5��3 *�#vhn@}Ien�21�(� V E_1).C#3�Z&>�f&#$E_1.Cu ��c�w w= � .�).C��-1!{.C \ge � �  N cazu�o� �j %9�is.aD���pu�N�L=x�� �a��05�[ter>P� r R`�4E� �44(ii)),�v�su,� e��1u I�2�.pt�=,�=smo;X&}= varis=�)&�n%�&�Y�pNdL!!S�!�sY[�ginty+ Ap�U�6V�����, if!xF(-K_X) )5 � >(n+1)L^n�# �6-�*��3 =a_0� ���� � ^n-(+")^n)= � {(-x)^n}"E^n�{x a�X}|f^{�j},\,j>0� repre#by�@yc��mis��!),AQ:"��$ +E2 �'$K23=K_X+��"�!"j )=h"�K_Xy!-(=)-�}{2S!}=#�x>)"c=�d� �"!�&" �)�lB]+ Bd�$6A1�& #nE= }{2c�$$�:BJ?�_f2�$ ?a_0<2O# $. A3 )�ParJ �Yi]u[ e"$K(Q�$A�}�qy!0*!�ubstitu8a_0I��L;H$2a_1Q�1)<!}*O#��%On~� courstc��Lof&�)��[�(�wor�lo�/y�)�H�"PO�?p}�Va�� F7c�JS^jT^*_p�RW�w�u��2�X��s��t�no �R�� MZ�j�*ny2�$A;&�#�A)$&��{($s$-jets at�f�vAt /(a� A �� \O_pIJp^{s+1�<=A|_{(s+1)\{p\}}I�� surjV�$� �7 p$ d�l� ma�)l#*al�p�/G e $s�to��1um�g�s"�VU1 �$�.� p>8 [=-�+�WoM TWs�$Demai��1De} 8.6)�(�at�n�"$s�,W�kA2�W($(k(n+s)+1)5�a�<�+�rj�. S.< $s=�B� ��+��n1)m\ge  y$)<(\��$! "�$ny�,ge1�($ s��B 1)m &mw s( �l��6�+6U!�$1$ (O-k=�2� !�+2!\geU2)&�n�#4! ,r:,r�$r� m9; $r=m�$�"H[ m4io53dQ�`s}�m �J�O+?!l"�$�_ $m/M:M*��� !�& (p,%ML���� "�-B� 7.6)a�� (p,A��limrH�.}��E}k\t)p�W8i$AI�ML$, �*fiAHEFg02�se1�MO$@uX.�j|)Q8p ML%[��e�I!t&�?m�){�(.=&� gl"^+ (L+=L)!�" 3� ��� rmk�� =\PP�w���\ well J�\�(hyperplane Ik�C��"N i"�n�]L!ca���?.)=1�Af�� a�$-K)�LSC�4p"aZp"�e� ) Bi*�@ b6f&�"le�1:z^p�@ %?t g6�A)7f� d2�&�[ of DV��B%�, � �(ŹIC'\b $)(�ck�puQzackv fi�Zto �\�\C�.N*6e�q�G!"�} K���Ii-YJ�OI���Y �9��� .CwJE�Q��UDo^�M?M�E�:)&X}M�C�y!} �N#ad!�K- %; �p"�~a&�|��8�re�i "�3is� kel%eduu<)&�3R) mani7m,�:��:�{�&e�� ��_�� "s!P�� h$p�& ��*�Jq. "4;} "�p_*\O : "�j�yل 1:Fg(E.g.�.��]�Z�OaIh{all} �Aai�8�a.kimdi�!,ex���z�;j I�$�$��a"k_2�2[Y�6"i:$$&w%B_i$ k w Bernoulli�`s,�inYFbet� 1,\, 1� 2"i  {B_i}{i!}�V$i�2$��enA��/ v-,U� <wI�$.xp1-=$ W.� � �^�8�F&=& ,L,r!B\"�X�9 c_j r^ -j}K) ��$r%w�; cn�** *} �!�\�5 y~"j&�))M0a_{j-i}^{(i)}h$&-�d&$$ I.e.Nw0!� c1�"ZM�Z}22\&II dx} *�2�$$ c_2-�1B�q� a_2�+  a_1d�20^{''�}{12}�:�Yerm{etc.}y���_h�����Ol���X$IE�4empty���eta�=)�eta� XUa&�B3=6 (X) -�0a_2 )A(e~Y"n "�wXA�great ��[tyq.� y!Z%}%R�8��if�CЈ!T�mX ,r)>)� qCW�vhow�Z|/�5��.���0͹s�sa�I���!v/g7Nc$4C. o ��| <�of� lmos��#��. 4 thmN�0. �6gc&�&�&n|+������+�{���j)'&!#�"$$ G\�Vb_0Y��E (b_0�70*�E-�'�'+c;� (z�/L$r� �eHf D>� vM U-]9[}�} =7<0"�X�isIZ1� 0�$r$g�continuC�#A��lg tW<"� ��ay!.�5�eW2��0��b�#by *.0��2 �@uing6�<0)\+*X+[( �V��\,9�.$�Aj.<r�@&j%+�FIns1�:�=I~&a=�1t,v 9#�=_�4 "0>$f :� �=�m+�t��n�r ta_i�(f��,}{r^{i-1}}dx���'�".L=88st �a� %��Qnmpl�jAu l Ob+arity>�h�J�=_� @is Apo&�* ��J�� ��<�� �.B� {xr}MJ�ˍ�b �2#n�~&X,�$cS�sZba?i@anOoȖech�|~0���u�3y�3$ZSx_*�X*1v4��x�mN�u�4�4Egd�~kwo �q(.n6� 2�|�2� fla�*^famil��Q �*�Pfix\�^D�X�� C$ 8a *�.xi/"6}�  (F2�"};N;&Z �.~ZU %dly}6�;$��s�1}�h�{A�a#�A"$a�&� �w(H�`�X\!F �Z) =w\)0 �W^k�r*,���)-a�?&�>e�C �>����or&���ŽS� '~ �O-CoD- D- 5) ag01�$Rt{q}(\X'=:_\�n�,\On,!\X'}�37p'}2�� $q_*�N�h%H=� .�Wbetwex!!R12` {k.weUr�:Ɋ \X'$�)fA�� \}��^�-no�`-!Nio�7��>"N �s T~r*@d�!y�j'�6p�*�o,�s��=!�i!O�%y\2��a24. More�q��w��� Q*�I��2c�(wr L)dX�����Qaf�o|�sm�&��xie�9$\rt{\Pi\,}7�LIEADpi9Y�!&w�sh�|re�(�*�IX9�6!�.x�\IMIB~Y]EiQ| 6�$;n\la=!�.DU��F&ޙ�:]�!�%�E^�Qk. �Z6-x�M�r0�g!:�_\FQ\to0� ms� (cokernel $Q��p��ed�$���3aQ�a~o5��sQ.�6�7)?Y$t^sQ�T r�. is 0AaA0� $s=1�`illust�vfm�y��њ�#Nensor��e�6�o)��S&oC=�2J=XC� %S pi_*��!ePA�!kQ_k5a� $Q_k= 8Q\3%���� f($t*0#e��� �A�$0r�s�#:VQ�lA1$Tor$_1(Q_k��0)=\kerA���d t}�big� Bgi� %o)�nramA^�a��{c} & 0 & ! & ��Rt{p^*} 97to!\!Q_k to0 x� *��&�\w�e!� &%�! T &d1B���E�`!� �Q_k|\_0M<�%��Ło��sMed glyn!bKHe2 V^j$,���!ert{t^j� �$t�#V {���!�(�e����A�7�iion���(�9v4�'F4���|\_� B<�)to �,�4hk*7ɣ=\�i(qn%� RI$. %C�aA]� $Bc$ clea�_!�to)a��n2�X m��e#+?9!wupsho��� �\&Hsj�YV_jR�z �?!�4(�Rb/�s $w$ arƋso $>�Y )S��$0�/sum�= �=tnA s M�� s rmk"6�Y}:�;�4� E�� K-�ty����E/��:  8NƋs�N �cˋ ~�!�Vy~F!.E�� h"I^�$�0}g�#l�f6%�;yz1e�e�� e�%�/] ����N�6`� -< !8le}A�>eLa|' �$0�-as!z�IAa��ED�� a y<erj�>J�< 'n�Z"�^%�6�#!��compud�e " ��-ny%A=�U�2� . Of�-�of��?6 s"xH A6�, hI�M�A�. ��Y(U&�w�-build .q*��%ZQB_{I_r}&+N),L-E"�>Ő)�Q� ,%r^/�3hb�!X�o1:oP�Z��]0c \X^1��\pi^1}"<{�-V4I6NA�8 �blow u� U60& \�:�_aBg\,\S_k!\ :=.8 0+(tV}�X�_E�q2Z Aą*�2�7_e���  a�i;��%�*�%� �io� "x7eV ���N(T%T��P��'/7e�q(U�6Q� a�r'z$k� %�  $&� q]{�^i�/ 0^{i� ) --c��n����q�u �0It�&�Z_0sC4opy�$��f��i� a� #�(�-Q:tDin� �X_t� ��: e(#�6��؏&��$\Mline{I��)_l� �-Lsheaf�i��#� � I_1\S~$II�X6NF-��_"M kA�5 a�,�(-P"�G�&�\!.� �ɸ �w1�6��Ch a7MX�"% "� . q�-�&Ie*e�, �� E q2u7.U�1Z�� ..�6�O'+ e<is�!i� ��+2� ^2) M�!�.�aű e}[h�oenterx&put�a, .pstex_t}VP 4JF7!�B��,r;M��-)6�1 ^�B�E%�V�;�K is 2�`)� .�. IFm7Ng�*b7+\I_1!S�*!u�/0�!Y"��9B}�0 P!$���A] � �.��} I1'}ai0+�m1�m��+(A \�!�\  EPsz�*Ň2u!��s���� Z_1'")�)- k�M�g$I=w)Qu/wSmbas�1E)�f2؀���^2.$. Preci����+9@#BZ�:5E_1�6)^*P,\ =wZ�hR��E�3�>� $EZ2�=aR� Wro�E_1-eE_2�re�(� � !� $0\X�?B/ For sufficie9����b!�_@.kJ2d =őHT� lEx�!����e)���ettئw�!� <�RE�M�at�F��(�\0  �Fo��Zr#�!Y}^k(-kP)$�2!&"�3��$a�2t)^k��B�9. WK%,�\O(E�s"޾a rf��� E8A� Z�}N�!�e oG  &G~I^k�,F]. \vs�{-9�b$$2y"op�IM"%/Q((io"?�V��collapy)r A9py�[H_1R�Bɣ_2b w-�}C96m�a]a�ra�^#��}�Bordn� �.F�� =9�kR� ( 3re?�9!Dsymbo4��Idh�,doAma�b�x)F�4�"��A�z 2q�p�T��{&m ��Nk .m?-M F�%��!�d˅�sL�� |=iEPoZ1$�<1�t�#��=%$"�� u^ I_�'':! � �+tF�:�3�&�� ls�$Z_2'"���'a�>���i� it�"� Z_2� i6�)2� 2�^2�1l�:��E�o2$�ow 2<�2a�*J� �f� 3� �b �.� 6 (t^3 H*� Bloo �k��:33W N� $E_3&=we�>��pu� \X^3�.E_1,\,lG�P/no1YA�u�/�in *(- .pU �"��U$X^3}(-E_3-��zU� 6,I_3.1?%&�D I3a�sagX^3��Uf ����m 369  I�'^=we ob�G !s:RaM&P�� sJ$Z_{s-�i(s-1)}M�\X^�p6^!$�E>�O qZ�B�+dO9$k�8 TS_k, I���s-2^!r�Q$ �I�ZY ��B�:�qj�Z�t �� !_1W"�V7 ��p�M)%5-6 B_5�^M5� 2  ; V�>�a\h2 �7(t^'$$'*�:�/+^se�s- ��  a5ɰ�I+ #B�l�&�%0 ing,�V_."� 4�pr� :�f� s"� 3_ s2N� $I_s.��sQ� ˍ�e��R� sF� 6E@. \hfill$\square$� 큤 t${h!r�� g�R2� 2�$ � ��2���2 $\rho^r:u�� p^r)Kr Y$. ��TL_r� .���?2' �2 3 r)��E_r]h��^ra�|>0( �j�Q&=y�,e�#A�) �B� �Ud�xQdrefyQ0t2Y�(\�^!��anr�1�,2��_2�] (\X^r,L_�C��$2�/&9 = *�/{5}(L_r�/"��6~�/�R�PIr)Se]�A�s�L"HM(I�� eaOrQ]s})f$�P\*�i_i)\}��LB�2��P[mjmi2H\BI)#"QE�.k���.O��!p\�'Ih ck})"��,��8�:*1x�.*� 2;(r-1)cR@�>DW�./�7s"ݜI0Fc� �+A�F�� I_r$ (%� 1^1h 3�o�-0L-Q�1�n�,)9"�WB�F��"W�9v�op�@P$ �/*���05* r $r�-6�7� �}; �&s� �trup8�Ǟx�sBPe�� 2!)$�l�n $N\[0,>�B�]$. Equi�c-%� buCa�p��>q (E_1�tEeO.��� ���� � ��P�&4Ms�at!c6w {r+1d_6{$;�5 must��cnle��$6@��oO%�m�BpGla�%��$LZ��Tne-�X �,J0r�,A +�h.�S� 7�C� %�ih��rel" TZ_r^{(r@�� &� `"� in�)jE� n $[B� r)].DTF:)].r (�HU& C.E .\�G O��!-if � �U-�*�1c -$C*X% +12 A`�c���F��=FB�$s��oʯe�>a�g82J�nY" !]$ a4 �|2�3 XM�_0$, f"t� *}�ru W3  B^pM:��/ 8.�Binu jinJ5YFf(�}��J�$�uYcI$wAofs���T#&��XN~E e �R�"Lt����6�^J��$� �%w(�C!��T���=�e��ill��a�J/-cm���t� I�&�V�2WHuld�  |,\X^s$ �TL_sQis ���% a]m�s���I�0b�d �s�)}E&�9 .� II.7.3)��_s|_{Z:} iL|\��Man�\L_s&�R2?C%g�K2�(by"� �& q.H� + t� s� RDX$EusŢ%Q proc؍)��t�2�$%p�!mÿth�,9}.% �7;mZI���wcu��see, get signiPb*be�7 est|' xwe�v� ��}e�M� s,L_sv)n]Baxc#/,�Ath�%ge�AC�;� R !4���@�6by ign!7s��n�ks@ �A��l�'�rESo,Ucul&A�)vf,� h3ed��.'!�*Uc� ��eaIA7 v+ (st�&!4 *�)-��nhK s $Z$A_i���8 )�F�oretic 2I)�mselves��;��7�C�bi� �$We 1Ad=? �M�&2/Cbig},N( G+two li�ry�2ult��$"�2{�&a*���*�"  !�A 9�e�!�Z9 "��� *C�e)�St�E qt})EX ���5r�.Bz�u2a $\Z="\ ���k}\,-pa�C�S thei1�Gdm��ww��� ��y��{�+flat."�+ "�M��(A$\ Ma;\C4# 3&s &�dQ3� �2�$kBS�-�P~_I7"$e\X1kre��{Z'}$)�w!&�&.�$ (._�o�M��I�{ \X}^k}{tR\ �g\/ {\!Z}&ܣEo�Y 1}^k�j:g}�(j}}x ��\OL%�.�of} F&09sI/E� $j\Z ��A�I5�$the bottome�rowuuv,� e� s9FJtopC�*7/:H;} &0&SM�;\\�:\I_\Z^j�:W2o;k;��'} 't�:�lX>2j h�_0��f {j\ZF�OljZ'%�k%r&&0� )�ATCh��� ei�%�!ˡ�I �6wo� um��zeho;�� !&.(t)-)�=a��E&�5k��b7%��}:��ap�)mSw�1/7i!\:�h}D!r B a� f�C!��*�8belian category $A,B,"� V$�/A+B� �)0$(A+B)/C=A/(A�q C)+B/(B _*V/oX�"b� thre��^.�Nt70==k����&Tu�u>� $j�� .#6�6�$mZk� inclu�Gh7ps$; 8.0�Me eq$, Q���@ h�i:9�T6�} \!\!&!`& �(��2A+�S>.G<k&&h�\o.eq:bV� �A�Z�R Q���An �?i\?^�Џ� : f=tg1�h��Es ���9f-g=t^jQ3�@yV ,\ g�@o2"�<t^F2$�S�I^jh�^t^jݐ�V�Nby� ��I�pL�:h�:y-ta��to/a��� Y�@� ly $�%OX�!�Y +1}= �2I�7�2D�A> 1aG�~�3Q� U� )�;(>i�.� �8),lKee )�|)�"N� �N�b�3\Z  +A�2��P�ŗ��"���}yW�n }^k+.�%/fפ" 4:*5 To che��at��>�&���,�2$jsn��| !x�s:!-2�}E �Q p\ne j}t^Yp}�r�U�7 \�w,= Ed�\ AM��mq�"�;_�g8��.�+!^Bq$�!+5B � [~torB"��5,!R�! %Q.�� i� �� e"� �q�&�$k(.i"��\XO 9a2�+R�-3-�*� C<on�?utMw�~k=n2�4� &�h&cR�=if%$Z~�8!8r�l�s�g}, !P�6h�+� , ifBd.7��P<Y҈ed��, eZ_� �e&n��2 3�� a CUL� viso�i� �:�}*��1cҤ\&�!J'Ҍ �j" v�;m>�oS��!,\,�rh�'A�&�E>�7.{�9� ɡ$!v�dd loon/�T��l�?s@Y��fB QD90i�-GZ � } SM"�w�9nd=� m�m QcR@ $j^�-� I��Ol��v�h\*2A� ach �t�E�y�J�1�E>co�&� {j(ZyB)�.ts�cN t8Cfunes�Qza�t.�L t\ne�li�0� h "_T}^� ��arnKd�1"m!f�R f $t: �!�$>�>�{$,~+� :�11C<��9.�/>9E�6#R�6�%%�a�� $t� ( O4$2SI)$)��.^�E���W\n0�K�$z>�eq\I^j6�/�a}$;a�t�S"Pb��d:� v��*�"� &m �"�"�}~ � ��\ r�A :$ i��,e�.�7{i-�G�bZ_ ~�,�!V !B� p!K Z_�� aff}*.�8�{ G2.��&a )\_036���Iaf�:M*�,�c:�2�33��F*411 ��D} :9 =�Ga�gb!\! a\_0,a\/�( �g }�!"� 0ti}\!\�^{\?�} \!.*�� 1/O>3��! s �g 3l�g\ \�b\ ~��&�I \ +\&� {\!A }tJ2}�: "^2�,9F@3)2� 3.>3>3} =)BI�=n%��"+�`4k`uc��. Each� I�a� O_X$7Oi O>i���Dz>_2 9dG�� ,=@]��$�Vfmk��o�? this;# to�� at,�^}* >+\,�S�4?y&i}*XCe���Dpr� *x#��|�&gF) e�n�1� at, �(8v:)� -E_i{��}�d� �a i6UBE!�� 1�E��>� (�����rk�'l3��@Ef>b*�*).7g�;( %�"X�*�; Ry< $s_E��p \O(E �caN�-G vanis��8vF�:Jl*) v9QrA5q�h $$I_i^k/s_E�:(�s,;(8( w L.$� .��6M9:U" di����hv�a �9 e2�)R^i!I?hI"�/I<:!%���|#i)�h��8 �fi�E�I�)eCt8lU7A� AG6�Dco����k��76�:�. Uxa�w�fpW!�&t !���2/��Gpol�!f �HY� k�.���>����:%סY {ik}��0��$O+ #1e}{t"�Ѧ�=k;[�N��t�$(X6t Q���_ItA�On��� �)an j"2^��R!2h A"6`�ys�S�C� rI&h&�:!�E6�$9N�� ���xa"y�05� _;n!�a�.8AW )"sUBI}�o\X)c It {I�>�m� P�we]"� J�!+1]]=�@4,slash\, ���&C�\�.�;2 ,+\,]t:�\,+\,\fr�[ac{\I_0^3}{t^3}\,+\ldots $$ Inside this the ideal of $\overline{Z_1\times\C}$ is $\I_1+\fracZ}t+ \f^2h2} f$ (as a dlargest l@that localises to _\o s�[t,t^{-1}]$ on $t\ne0$); applying (\ref{BI}) to j� $I$ give4e coordinate r7o�8X^2_\text{aff}=4\backslash\, \5,(\X^1)_0}$ a%; \O_X�]\ +\ 51}t:^2+!�)951^3 \I_1!3 !9�But � �$$i=2$ case�(%�d}), and inductively we rec�H it for all $i$. In6=,havAe)�� \begin{equation} \label{kZ} \I\_{\ovM*j(Z_i\-�`)}}\ =\ \sum_{a\_0,a\_1, � ${i-1}\ge0}58i^j\cap(!+^{a_0}.! 1} ;\I :^UD})!6{i0,t^{(i-1)a_1} 1 t+ }\,, \end� �� M��J� Y�%^the $j=1)�,E�$i\subseteq��8$ unless $a_j=0Aoor!�j$, se:2�=�<}}$ differs from:�only in�( first term2�>�$:bF2�E \I_ia!\QjA ,\ j=0}^%�a!��d��.>By-)inclusae$Dare left with show�S�� each)>of =d p}\!\!!�(^{j-p}\cdot�w�wright)B|, We now work�"ly, wher��condi��s-g reduced})�)!qh Z�(�( Z_0$ imply%� $!=(f_i)$�Pj=(g_j,\ !Z i-1$ �Q�some $g_j$ \emph{which do not divide} $f_�uT�fore,��nye�A�$IQ $p:=)�6�lea뱥q� mult�*A��6B �J6= �^j)2f_i^p.g_�y 7 g);�B) %^j�, \\ /ER.�e!�^{p-a�2�J���= usi�e factiq��$a�tora�(-free. This*,desire�m�M�$proof} To ProposE� �@flat} will involv�| plac�L$X$ by a blow up on I)�' pull|� A�$�kAA$sors. PullK)%polarisaa , we findA"��forced��eE��0a semi-ample A7 bundl!odend]�Zm& Xi I�D$} $L\to X$E�define Q�B7w8w_k(Z)Y�@1}^{ck}h^0_X(L^k\�Z0I_{\!Z}^j)-ck)>� (cf.�degen})e� ss}))! ei$c\in\Q$ su��} $Jq�4$ is saturated!�4its global sec!rsM;�lsj� chi} �u� �\chi\j� @)+O(k^n) \qquad ({n-1})� � $L$ %�})m��} b��e follɴgener} !A{LemmaI�error}E�iIH$ZE $Z=A tyset$. �lem"! wk ? For ]G,\ M1]�� b�9��:� � k\gg0$, $�9-_h^{\ge1}VX=!Bn)$m���m�Co% rao u� f $X� PP^1$> $Z  {0\}��excep!|alq� $P$ � }~ ��{K }(ck)\boxI L^k-ckP$MjA�u�,-�te%$tE�<HqQ)� ,s^>pA� )$, �m $s,\,t\inP(\O�1)��q vanish��8at $\infty, \,0az), respaA� . SoeZHhigher cohomology h� ot%:men�� boundi�$1�  by pu x down� o:�,!�n�$��� z zcan b4mpu!]4as $\bigoplus_�ck}%R-j}t^j.vIrV�{c1!^of >���Q�M�@ Fix $(\X,L)\to\C.��q$ %^k)� � t�config��ion� $(X,+$. Given $\�\� $\C^I�,$-invariant { 0cheme, denote%�n fibre!���Y centra"$Z'�( \X_0$. Let�XB_{Z'}(\X),\L_c)\rt{\pi,L)$ t�G.�� longZ��� R�E� 6�hL_c=\pi^*L-cE$. (As usual $�X4(0,\epsilon(Z'a��c=. $ ifJ� '}^{.'k}%�. g6{.�.) ThuA�L_c :�%!g*� �� , maka�$(>RE,J| UQ]$. Then we&InnTheorems�q��� ss}.��th�]big} IF above sit�, suppos& a� 4thickenings $j6�re � �A� �V$j�� mathbb N$ɣAR.�a� $�n{A�}\!�n)$��\we� s� lie betweaO-CkEl $0$,%KN C>A�!M�w�(ca)=\> /t,<,N �.�)\_�AA%��}.� � 6�(C+c)k���and`�ne>�)=�+( �.ZIa>E�E�!�I�� corr�con͑es)�if in ad<( either $c<.$a�����trivial7 �se�.�is �� ��A�U��$$(\Y=\Proj!%�wk=�,\O_\Y�i�� $ed family YЅ�6z$(N\I>,\OX . It\a because E9MVI�no $t$-P ,�n!96n�of �w.  k� J& $\Yi%�< ��: A�"y�8{\Y_0}(\O(k))= %3Y !Km=! � ,$. Again by �� �Nis��same d�6�w2�A&� ��� ls $B� M7!=��!)kur�9za�6( � a a}vei f= �V$� er��"a�0=X}{.�}�R .e@!�co5F62�p%C*� equi�,c �ȭ|!�o h!��6���!hassump .���� :\@two vector spacesuKt most ��4, as claimed. R�by.� "Y ���k��v�A �J . \\�stream�not Nx ; nven! ' ��0!T�� resul�s at $ck+1=� $ s\at��instanc{\!� ck}/� ?}$ meana   ��� ���!�U he�s�*�Sa (} uniformly:� 8�a0�"� HBl}�[n�%�)�\!�\g!�k m&�� \X }{t^I)= �{i�!?\ t^i\,a{x!&�:zq -i}}�  +1}}^� Sinci�ia[ $t^i�$-�ndaYs*�c.�%f 9� He���(*� B�indeea` $�E�$0clu,E��m�*module if�split2}jjf�.n2�.�-i�Z+:* +1})N�of�[ �81�w�?z alreadya�ed% �aŨ�����R��� *=& (app �.�� steada��$)!�pv� alsoա/ �ݚ$��uRe 5�-A�QJ�9! �$�r�calcul the +5+)�)�!'expenca͈ n)$ �.B� A�BG t $U $���>, so �n=9 6�swe �2�-J� out�Final�f >�]K_ mple �aVV%},-I� )A>Y greeW��but�0 eN$ (a�pendentEHkACo� !�.�{ ryZi �>� ir-�� $\le1�FeN}ih^1F��J��eN.y-= D$V^0:2Wa�� ^X filt} V^pF;B�p)�9 eq V+1}��l V^0��� N V^0=�Oj=-Ck�(,0}V^{0,j}$ �m2� decom�. Xa eKt�5*8jO of a2) �� , ic CE !Ip ��%�X)�Apiet $! ,j}:=V^p�!�; i.e.\"Rpsetneq���;$UaV^0� 6�I~ whj. 2A�N�-$��e� .�"U� e� ��rA1EB=�jt^� \=1 and} �"V^p}{!@ cong.���",j}+ \F?Wholds 0  s8L{� p%�R� . S5 eVLm� ck}t^iV^{�cA�/ +< (D�� fur�s�#^�"96�,jj�ck-% +^� e 0h^{a,b}:=\dimA�ck-� +1,b}mMQoJde�!inY"V �Z 8�(-i+j)h^ ��"� filt1})�"" j $.�i}/�%F�b !G})Kɿ� �B�� i})-�dž)�$.!��f)� noco�-�9�i��{i&�Z �wB�i)\,-V.�� Similarp �Wfa?�V^{)�y�%i �u !�v !3z#?���i>�(�u�WV�2= FGbigg(�#1O) + �0�.� .� n��c�$��mR�z3J�\ + �ͣ0jQ�!- ~&We� r{eE���$J� $��� by."�(� N* 71 �Bo �JLSM )�`� jM6`Xi(s�s in a� f�� �"�D}.8�i��]PEuler characteristics preserved� E�B & *L!1x1��a�� I�.�a�)A1Q0#"� .:� .-����wf ). A):(!�if v�2w��on��ŵ>_ *^�AQMw 2} \�${Towards axverse"ccq�y y ,�� Corollary refex!�s�IT" est 2�s�cany� s sum+$)� $s rSresE�l� th .T(\p?{y%�\C}!+2X^i��,o help achiee*is\� ing B>v}� �s���# r�%%� pass! "[#4 $p\colon\wide6X�"!�g��(>u#)*v#Cartier ~#, $D_i$: $p^* ,Z_i}=\O(-D_i0In�*A�@Hironaka's resolu?!:�$u�#tie!� may take�a�h�+s�&0e normal cros> (snc) �rt�!atAq�ee�smooth 1 �\{F_j\լ5*(0 $F=\cup_jF_j� � :�s%x��jj��j}6��  $�lnd�nonnega�, integ� 7$. We% s�$e�1 constru��%mil!InX^s,L_s�}b�,  &$D_�W�1placeY $Z# XA��}%TaY surj[v!�p} |rX^s$ I^i�ify (� �%) Au$L_s$.Zs$7%f$A�0 !YA;sA<6#i^jE�$X$!+�SB)O(-jm_iE�A�.S."vt6[ger} S.FmtI)�fixarbitr���`!�&A !�Y*� � �o��a�oci� � 2 s!�0�e� Z_{r&� X$���/s�2�i�.�$Dfb D2b.-�yQD_i�$isf���W �m�� (For����A cac�componen��� ncj j�h�iplic�LlD1� �iY� {0,m�$a�[ l +� t $m��0 E.g.� |( � �y $m�..� e w���\!9$\Y�)�2� !��n_i� �'A�U��Ai�$r,L_r)$ do tA6�1m�n t%=B_{I_r}(�%C�1�$��>�J%x�of2n$k2�-� [)ax�3��"�&( $%�!bthreeM Girityw$X� � B2stein}�?parMm!*Aw��y*>$-�(Q� \X^r) L_r^k�"F aF"� ��Jy.�2�%\X=�Gi7'$cAQ(-�le&�_i)&U#���1)}�! C �"(seshadriIr}�$\Z=\"�D_"�2�'cen&�$e� a�aCi�m�.!�i>guarante�4at�.6 .{6 q *�b^n,r#1Q on starts����� e")[Aql  zero�� ly�$�� �kyB� �ensur�5B4�4on!( tinu!o��ut� }�*,�1�!�.� |>�l&�+e) p^*LB����_�[s 3$X:\ p " � �� %�x���5rue� t��"�m�u�Z_iJt  2�D_i�,:�2#� ^j�� !1 P qth��-�.��-06� qu�.:� In�;i4>U�16n lead�ord'+:4�-�if= J��n# ]�$Vu& � are moE� next7we��r i�$�#R*� ul.9e Dv���� ���st�/B4�5-Y��  H�2relevant&:  does�,hwe40�/it ( after per�!e,a basechange� �"�-6.a�)8w! $I_r>1 !#�-�mbi 0} \I_D^{p_1}+� "�9+(t^r� � }��G%;P  $Deceg$pZ may %�ovAXheN!^; $D�utj �tC,&��um Tcontrib� 7� n:� %Uan 6�M�of 8 sepa�(ly. Pick a)[ fun� $z$�!��%Q �+!m�o(z)p)+t 2})+s)p�S concA� hull�g poin�;0(p_i,i),\,i=1|,r ',$(z,t)$-plan�$e cho�extre�verticeM k_i,\rho_>Pl"�!UyER a��ejr�N2�o$(k/:^@1)=(p_1,0),\ (k_l ul�40,r)$)�is��e!�new)Yv�2} !Lk_1!W^{o \_2} 6a lJX16���,clo���s-�M�� �s�* t�+>As^spond� (.5�(an �<,s�>R3&he�6t��w�A��M)� �-��e ,c)$9� value $c$�����h2f4  =@-��-V�divs} S�- m_i=�!�_�}- i}{k_i-k  },\ Y� l;$m_0=0�(6V��*}� �)�=6� �V7R�$D$.$$&�Q l-1}(m_i-� �3 (D,k_i)-ak^n�L,=�  $a58.>&&�'��� iMLct7�&3No WeR � prov��,weaker estimR!���. FL<1C"23C�m$D\(/3(�ъe1p($(z)+(t)$),J$ $D'$ (rec� eGis6� ��$*� s� b �)%0W'=F $2)}$, etc.�7 to $ j-1)� A!2Q pr�d�0by $E�� the u �ANs0�{$iK �jK s_i$ �anonic&�69$\O(E� van~3����/m( _�/3+3A-p_1E_1-�R-p_jE_j�q0p_1\ge p_2\ge \ge p_j�*b3!��#��zq "�" �}D��t��+p_2-2p��J! +p_3-3p_3��) \U>�B+��<s �- e )p_j-jp_j Gj}Al �"}�<� � ``$ %$"�``A��x� bvBionE2�/", I�!��� �/M %E-/nam�7erms. (S�f5(g>�&s� ,monomials $h*�Kr�is�5(lambda,\mu 4"�0��� #+\mu}=f^  g^\mu$.�a0.:Qje& 27\OZe$� .!{ $s_1^{A��< s_j�"�=a!�)2A�is��� dardd  fidd�=o��r8��4donP4Newton diagram� *0 an unenlightI2Eof;|h'ej advis!�o skipV+a3�?�6_ (Fl5e�t}�:�"7O0� below.Q��eс` v�C�4� J%��Yklement�"� t/s_j=0$&y prop� rans ,�;$j�� up,!�O23$�:/ upw af�B�O �Di"�E�N"N �Daff+ } \OC!"�}\�*[5 z{t^j�*]._L (2�,�aJ9 ���9z� �� �$n analytic( system $(y� �� y_��,z�8wa7bfis��!^9t��E\Spec\C[W,W(,t,z/t^j] =j' Z,t]�!�$Z=37 |'s�( isomorphicA�.�" >.�� k=0)$ be@$(Z .)  <����"R�>O(-kE_�reS,t)^k�#.(� no mob8�2LNt$\�:-?M�D$)h*�H!��(a5 �� iton =hN6!�ao1�  On� y�, $t^k/�k$l"I� -;e�z by iRI ntifq1= $(? 2/%�$B3.((z/!Y+ {k-1}�+1%#T� i limi�8to�/�8�@y {IFu 2�t\�1]$��ed-ou�)5<{5��� rts  j=1�A��m1 stag�oori� �)�\*�,� )}$�2�$(Z 2/. N) \pi$ �$(j!1thE� up. BNI� stepA�,�, $\{A{j+1}�J�3� �augA� $Z/te�7$; dAQ�J}2|.% V�B=B:/�m2/!�!_*\ �E �I+1c(Z� ))^{+}=� -j� & � ^})"�)!^q� V�i$\X\�H$�=+� -U$&yR � �,�2. Mbb)�Qi� 8 a�� a�.��J� .���N� $"L1a5our�_+:\p1�6E-11�9*(-:\big)\�C b��.�:[!�_1�S} bn�23+2)U].=C!�]9>">b�t D=:+a1B� �10Z.9Aj� u"3�\9*� > rM/T��u�})��BE|�3AR�^ %e4^_ -aZ� $j$n'� $j+1$,��&���� �.�#��)QG  e�F =! �- aq 2}) �,.we��Drm0��^+��$]I6$,p_{m_1}$ ! "�� e}[h] \��(er{\input{n7 $.pstex_t} u.� {:� $���<�� ��  }}� ��k_1�$ �+1}2�2)7ll �� k_2"� on,C �@ \_{N��6E\_NJFN���s illust3�LB� X:Y 1�l l�A!E=6- (minus<#gradi.'!bol 6 nes..�> qTVg&.�i�!2-=9&�I!bo+ s b�%o z5o!or:i]�. R�*�Y �� W si�RnPF6�GBj �a�5:�! �� "� �@l:"�e�7hrn�ND5�N\*-�-ax!��-w>t :&I�jseque�ofq-s,A1�h 8a�a�fRD�$��!k{.�E[ e$c=y= $(m_2-mY S)2�[ [ad8(Th"�5- just&�oefficA��ex"0Hy(��R"$Bwe us�s�D.��B�)cri�+oQ�0/s�"��I}bN�!we �(c.E71Tto$4\p�<�12vR�)���� .})�a $>2�A6! �1#`:aU�l:H!u)U1�^�. B 8��;�m�X."� Z�JX="�c6= [�U\� e��-ν,� ��Albetter ��2�7$. Nlwe group8 �$ma� ��ge� a�. A�$�^{�n� �$Ri&RAadCag�TQI�/�(iz+�previous>�{/�=�dE�4 up�!$t\maps�� �$.wX S4�}�&%(�v� 1$),��i��1Jys�'a Qf �6Xwe �; . Si�2a�9�! $m_2$�9�,!Hup�"�2���&��,�dm[nW@ %b{��5iGG�:m�*� ,81kwe"�<knI� v�we�P��%O�ula ~s{!ith%zad,>�� ccurac|'B� !;G$lfaT� (�!.��-nI�E�se�$ce��W�IUS�&a���)"_"�i)� t � �.L�;,"�)m��>9� er��-r�e�E�^$t^M$�j�%9 Wwe2�urJ,"&M$ clearI�de�nator�D !.�� �s600*� $M�while2) &.Z8)��Mf6ubstitu"� I into=Z6*� R��isr J-Aa��(c�*g�&� ��ѯ� mey;-)A��F�NL46�a�/ZF*)6b!�&� � �e origAn F!I|S!�y�+ # lea"�]�\k��s $a0�qx%�)��ah%os1$&�'�7ect)��!8` K- Im(st example �4\I_{D_0}=(x^2y�%nd�# {D_1)$' �"of cours@' not happe) curv0soaP�-"�, cor}Kslope-} A�'LCK-($/poly)stab�Bf%�o�[f��DRO B--�z�)� Smo� t-*MO,_���'�/w[-3�)tself��A,AstrongerlB��� )"�6 /,Donaldson-FuaR i�P) us"�"� s $b Z%�b���Hw(k)=b_0k^{n+1}+b_16�!� m C��ate� z z!�v41�l$1&(\ge$ a posi<392a�R"Y�� j�WE�d3� � ��S!�)*{1. SA�Cbiw..�!Xs3��M6I)m��(ma)it"� to �Sr�� d K-A� iABs.d; see1�$ I� areK>le-&U7 Chow�uBHsec:chow} Mumford'�)#of 6ee8 � \cite{Mu}"z*?ZM&PPP^N$/YW$h{fixed} $1PM �]st�E�� bto & (as o�Pd P(asymptotic} �=I*�)�iichs�Ie�to A HilbertCi��ult���M�D usefu�ZD algebro-geometrice�ic sl �x'4genuine GIT no%_giv�fpro85�'s�Zao;)d) �GifBs��bnyY� "7Teq:yZa���`al $a_0(��TQM��XZ {xk}�2= &a�a_1(x)a� \��1 $k\gg x�d>0$� a6& !3ak�u$rh^1WXeb a�?c `\,;/)�a0!�D�0m$j:�%QI?( } $0 Ch_c!BZ�[ B<i=1}^chv?a}%)gia3},t_0^c)mdx}\,,�# Ch. Z)=\max_{"" \ni :�l>(�S)\ �",[-}, ]�(�#�maxa��empty�*�$ @� \� by 07� �X�"Set? 2[& s $Ch(X)=�O_X(7f:�(2.O)&a\)Y N+1}[C�guZ� %b. �0Kodaira embed������55��^*k� %=H.��\to�0 h��sm�n�H�%�Z�=�X%�e=�/6�� can b�Sr�.d!N�D�qLA��� a su��2lyKh � e !9=:!o(& + e�""_es1��=\P%!�1!.�0t��"�+%hCes��writt�(trins�'ly�W�%�.8�6!�Y�-�\s"&AeD!@^ii@!FJ> i �3le}E3A�I_Z)<k$�*noniR6�! �W"*��� O\lei< b�Ess}=F � \_\Long�#E arrow \<){OZ��N (N+1�DAÝ�)} �� \!\tilde �� e-i"E Y+� thm�51{eq9}%+&�l��""��E�2# zhu� C�/92i J�Ympatio��Zfil�A64�N}^cA��~�7�)>{c�,1)(�W b8�9ZE�$" lth�h52:�~B�ł$ e�&� c*�gZ� 7���r�hyper�$s $H_1,H_2|$ $H_����I&�<i:= X  H_1)   H�0� e �3sfy= {p_i�p8j iZ*M�J DZ !"b"5�i�$Q��>U1=0= }= {p_c&%�}Gh �irh 3�=c>20}&2�*>&,b�IN}�!a�kI_�n}&,2} &y4"�1{\!N} N} �4#(�[; 6la�n�cobbly} I�f)tc}�4 )� �A� ��}}�cF5 �Un�@w�/n63j%>b.stp*} u� c�5 �u �Z �=�� ))^c�P!�} ��:���� th &`CE �has�5$!�A��4�.9Wofbaj�.�  (&�  2.92�%��is ival>6in��bR$mummy} -a<� a_0}e�\�� aSi�FW)7�$a�V��i���� \�K/nD%� $I�7M�), � $a� �sF�Hw.�2�k�ed2-�00 (\B_I*?"�=^k{()� (��NW=- half�&]+  ha:p�>I_ �(umX�!&n : �%�92+MO�  t����-w1� a���/�Xs��� should re� �n� � 0-(n+1)!\,a<(n_0)I n� �JA I$, � $n=/r$, v$n u�n�!i�M�S!�sig3�)f�o6�7�}g�/f $g$ ac  n $V�5 ;U9� �8 s $S^KV^*E�,by $(S^Kg^*)�$;1<&��" !� 1& N�!Vis_q�� thm:�Un2lh�V/})A��  $r�8,bL^r)=N+1�o$w(1)=!�_i-�. �M$c�2"�cIweK%k2�� q��H.!$ (B7mral�D�f$I!B�8��6F 浹)�9L �la�is�,neJG(�x%B�Y��Z � A].��Yis), g�$�' $$ aFi6�-�nC')��;)J,:$ i6a1�G�'eft(\!>{2\!\� )\!< %�dA)� =1(p�u-p_c)+2 2��"*c(p_0I2 ) \v�C8{-10pt} $$$$ \h 3cm} =M-Y�;+cp_0=-�� Vm +cG �7�&XM� r&�r�V:]~͠9^F� Semx {3,*C6�z!n~ict] "e �Armk�9c�C7� YJ $>IS1a�dx>a�g: $�E�[� �l�k��� dBU�1k \k\�`] kc�c� h;=go�>altern�J| -typ�F!�@direc���s��a�eD.�a >� had<�c �  _��Ce�$iXp_Yor�{ ($i> . Howeverk is st!�l �9 than�?Ŋ�=3]�k-�)?& M:�)%?las7KmAtlzYge 6I1�$\smallskip���!Vl�: $Z=X,\,Ec(so3 (x)\�Bv07ZhowAx"z\� n�")=rXE .(��t&� ?:+� in�s>G X>. To ) *RaXO3sm "jOar+C*!�t G5x^�W a� "�.2=�zaO@r1�%3 -or-m q$E $ :�&�� })�"ra��rea��� �$be JVm"�g5$B� A#� !s # z23$�disXa! $rkf������Dwan�7*� to w!'ext! i �Av�2' y:� �ss dem� a�͝�)S���o all}�'{V�  ] ) ]�B| Ncho�A�_)� s $0�1��� 2 � r��G$. As �& �A�F=� 2��I�|Z_� 5e� !�to�",>! ��as" N$FB($ �>">) a_% �%#Fz��K:Y �$_9red#>� �A&eble����wmnoWpa2I >�Saa�&��*��+ ��.x"�T� Z�J�Fs�SKT!!��/l,cA�aK(�e��) y* w� they{$cd{' in ek ��se good "s!+!yJ�Ae`�tNcedur�Ti?#i�y��;� Gle6Atum0&�.x%�J% ��'!�I�8_i Ca� ��z C9T@pDi� numbllk_ionAT� �F (WMseen,!�in6[bi�Q,��!u��a=u $2�"f n_s�HtՍee�$G#UD&���Mq#� -: T .&� ���Z�~re�i*�=&��dea�g� .) T��i.I=� 1���2� �2*�$J�� g !�"� �i�D^�*+zs&upl} ::Y�� �y\!�{� �1' *zA(>k_l=0=k_{l���8 l# CQ � M� �J;Ga|I��� $l$ �-}Ia�V$ �s'qa R�D�Z_~9��� uri}�(X,"= sm�Ewa��iIYC29�Fis�:$-� %[,a<*� A(_i+\delta$,� 0aN(+.`F)d��* )������E ��V�.E �<5�M�]9w2�,!o �r$h{x.X 3Q +sti�Ed awaO%N*r# �>ogu�\IG-�e|Iea��kisengp ed sl�@lyA2��"�.�gL��pr�s�Na"�"�*�#."L[E1V1o\NM&=$FC-�T ��o)� �}�7w&0Zime�*� �)�/2��&|-�G-w1p$Mj Da_D�B-;nn:pLivo�'�[pport�ereq\B�a} a_D2�]H{}'�;�_{�.��:MI- B3i-/���I -k�� y�I�e( a_0^D(x)dxmI�RE$ ( �� �"d uniqu�-by/  �$�Lb :)dY2 -�9z�l���Lh*"M� of�5S# i)�l-��$(k�L*M� R:�n�l� br�Zbut6&��=�1� 92Q l*X!$i\ge l$. M�@fVly6R7 �.:$. Co! bVNNK �S)m��! �� �Ya� *�-�N ��^ umer .� priM�'$q�sum�(  �@at��ign�t��E�00$�s)�����/nd$)� sum;n!lyK�AO:�AIIL�/U '9� ,�eV�/ �)  forn:wR&$gdi�7"�C�d"<���y&.7&�V0�Qa�#�lob�kI+� n7 $D$,�' 3r4dY��oA�{X�6+* $D�0�ɺ�! !��&iesQ%��� �.d!�42���!( &�! ^i_D��=�3�"m�"�A� �a})�*� :TT)B�+0$3�xOy4� QYi[obM��n/�*no� J�_D &<& �iY'�� .���&O g.!F� {DO-16��j�5q=pj=p�c&=&� diverg�KD6�rj�e�.�i�� G j=k\ ,�A�� 9o &\le2[N(r�EH�q�Uc"�-�Y ��l�9�h4 back$2��W 6&k-I�A�[x+l) i=2}^ ]�(��V�-%}E��=&v..�� a$��� .���2to��M�� � ,a_D.�V� �(A D��S�U!.R� ��� utV-!� �Ri�*Y>�*}N�>�n�!�e0J�u%�- F��+.� ���Pi8 +Q<1}Z�1" Re%� �d "� i*}eK!�0(�-m3���@j(j<� ? �� rpre�Fas @As@ {`�ev�!/u�us� Bd�7m=��l}M�).)� � � ���)m��abE \ t5+$�&�E�U�"�^+Z)*�(=�&=���(j�(aj"� $x���2���S.���[� �Lh�i��+�EeRJ�cssJ(: +�\R F{)2Y9(GkiZedU� �Z���+c�]nc ��+��O�"�* X$% T?v@"!"# le "5�}jL7�"iI O0 A�*_�TI1~a)g!�AriJt>�2� �}"�nB� Clif$3Xa�D y s:"��� [%�%ra2�3-�6of� us �"K7,d=\deg L>2g-�<s LRT.�ŴF`�́�(1ip1{d-g7 �4(g�s12%).E�1d-#�2i�tP7MN���WA�lloL"jC�� �S y���h:G >u� roug�w�E �f �_t e� �DA!� sVRf�O%���?�a>�A�M$D��1� l $\{p�L)#�n!́ca$i�Q�\n� ���* 'A��A����{}'�W�=�1��-� �t^ J �� O_{j���J)� O9#+7 `1I$�jfy:�-�om� -x�9�5ԍ�a_p.�� ~� Vr�� �%nV�W�:add*� o i�k_&9���" &� Each6�$26ear�+2V 1 6(�{ i�a��&iaOE� 2}^N.L !�(2�,jA�%��/N9)+�"5.LNHM H>�a��$.�n� ��m?@�F $ w\IbK��=>�  i$�%es�Y�p!$page*{1ex}R� u%A/"� K#Yrn �1��E{a_I-� " \,a ��}, {d� be�O�� FR �ich�%�+pur��s sayt �#� L)�!max\{1+g��L),T�; &�\le&�.& ,nd^�s�i>gAis yield" ��< *Q9YogJ%�1A (~+ (i+1I�= �?zDBi� i)�1e��+�g)�m�12{g�N��d.��>ocW&8�$ŶNtQ_!�$�c �2}u�rho t! �BS �V*_ !E�.�"g+"�Ki} {N-g :A�9, "� }6,�RJ�K.~*)��N�"�D%� N6\�E�(i�%Ib�L}��TA�.�$��!{.Q^2�le �sN9g� CoRAed� � bSU��m�� �+%!5��*� ���&��]��� &� � 6E.� *�\ge�reQ)^O.IWcss})"Lc $"<%G gd so��&5����b&>O%9>�t�� !\c�G�>{� a� gl��$�  1O�eaI&�%""�%�,a�67�&Tv$Z_<Ts���ng65�n�2N�.�,Riemann-Roch"�(x)=x� E�t"f�#c^2/2$abl�Y���@.o=.$i=c(c+1)/2�lM��!�Be=E�}d&" �4 c^2}2=20umB2^!\ <\ . >%1> c^2+c}2\,�Oso -�$qXI�1c�p${g-1}d$. O"�H$c~$A�a�(��is}I�.�~ S&}���}An�s `�'� �^ gd>a�J6&�_s �qE�$q�nd*�&"�@$^Rrmk} �3 &�8##� e sharper�&67%)J� e� gY% >2g$8`~��eTd argu� ��*BGE�Js"�egs} Ou�maiτK�#)�K-9��. M!�m)4,"$#g!=�IiRF�@x�i)RT}$/?1{Variee�E>nC#5&$ibܠ}\ \vP0 5pt \noi`� SW#)�F� Corsy al��"�}"2i50�}�8rR� a��!Zy�= $mK_i0 #*� �!&*7+fxinw $�]1\�~6� {\!X}\,�1a�@xwJ*B� ��5 } mK.J�M}�_1^*(�)� ,i\alpha_iF_ifA6�!z!]  �(0,�yz!���$F�*!�irr�Gu@�92{ * We!�%pi`( �$�M�+�^� cl!�@XW"*l�\,�K_X.(\,3j\,�E1m) .��{!�A��?2e,��6�Rt��_2\ }*k&r}X1En �<$Ey�&�R �h $Z$. I8!�\!c!A2RF�uED�MU��~so��lK!olds.`�1V�pi_2^*E ; L-xF�(L-xEdFnef�#:� r $0�Vx� � (Z%�We�;��ute 4i�I�:6��3&��1F �!$ X}�r�Cpi_{2*} ,6V-z quot�F ��.͖onSsb6�(b�!�H�G"�(}()^k� b�3 $2T (F(�ecokernelA*L�!E'>{�J)E�Fujita ing,�H -p<2n �n� n0})0�eg�� $h_{B ^i ��=�F.dE)"�� R^i9o&^�K�$��>-f�$23�-.x"�0$i+�,&�LR�)=3L*䮁/ �� -~?,L-W2!W� �+�q"�.N]>!AA a9 =##1}{n!}AF)^n,���~{-6pt}0nd:-���� a_id�K dbya�n}MH� M\le��2(n-1)!}F0. �ES� R5X6(��5#%�7�&J @� I}.l��(f&���a$ �ef.ś6T��A�r/ two �&&EuFB��r����YH���^* L$y �~�X �^�)03 n $xp(Q7��0� 1A L^n$�B��a_1V�a_1 = F� J�L)�=-Y�Q �, B�~��tK~ɓ%p. Wc$�)preEjn� s�:b]�es easy�� .Ming S �� CY} �0bf{Calabi-Yau� d&E/els}.��iX�l��*�v�tyR� \new� ${}&\bullet$ޛ� �1er(L1t�<� i/. �2k�S sA�. �r�V dA�u<2RK�N� .�& !e>�I��th (!K_X\sim I�+ ��0&�Ea.� wip]m �vap�.��k"��^�� \mu�O a_1/<-n Z�"�b�, �[- Ea��+�� P}u� ni`1 ( * L)2/��)s �2 0x\F2:\le0$� h'�� ��� a_0'(x)<0�- $x\i6���^�Ca0'� i� �:on�Y=Z)dx+1S+) t}2dx<0.) for}\ cB�]=rK<�  ]�L: !��R<)��;��Wmo�d HIEg�3B�Z6I:��� a�|�� big�\x M:�J��4s.�P�[e�$K$. �/0precisely, �itemizeY\ � �RE GE"�,lta_0>AKuch ���!f�u< "YL=K_X�' G�eFZ�.���R2%�,L)L + n�!efa�J6D-E - nK��C��%1��In&rI�yat�_�X��GM�de�i�F m([-� ���V�E*_ofv>�9M�c���� ��N���%.F�b�]m�Z-�dTU1�!�!&8x­ed duE�� deepWZ]5�t�=d��Viehweg-fV}9 eT��0U,minimal mode�;�wm�"�� arrih6u�D�("� s"hXi� �w-d8�) �Ka}. �1fC 2#'CY} >!�v� a r 'abw^7�-�5�!�A5hol�Ac�Lfr[I�M?t�4l7%(�Do1, Zh}!�*�,e K\"ahler-EA4 ein �Y;Au, Y}e��.&+d,�X��noj�E��� i�^��t��an�cit"]J� ��� �%�ids�>=scalar ��95,in $[c_1(L)]�>y>!tquickSofsk6a$>l& Ņ('F� , much easier�?pr�g����Efyr uli�5�I!�D-)T"� � IV��b�{I*� CuB`" ! es}2�' �v  :Uyofb ed A �t(\Sigma���n2�6N( �arithme�x\s ( 4>-Samua�ol�[!)9b>Q �$ !$�N- Fj��h�\scof"�sof � '&� big/ �r�B  e&�H�#S%S$a}aG��a? ly 23e�.+$� (Z)>�* pB� F��ʨ�a%�i�s A�_ -�9 �$e� �=1$ \{a} !�/de&y 1A1�&��a�+d�"� KsJ� I0� !�a� v�%��� =1�$ $U\m7 O_Z!�� � �> +� $�M }{2} dx&Z/<I =���-1�}c�! �x$�!�K�8 o2;� $c>�HA ten2 $\pm�\�=c\to0q$p�xm��bFdQv2t >*\( �Zm~ � L m�� �yofy ���EsbtAP�[�~��eȅ3�q M���q!�&"�  � I��hi�Cf .� $e\ge 3< � 8�! ot�'l:� , dt� st or�zry doubl�\��A Vcن_� �!s.�of!P A^� stat�&<�+Z=�e�%�!S� ��R(. NorthcotR�s"IwJ@8cNo�O�1�R|%!Ne-1?H�q��2e-2>�dnda%Z$V�!� �3F�� -tradi8Z Z�2h�e�(. . FyS*�QAEref{s�"fy} (ոi�!X 2�Ea�% :e�� disc��r �d��!���X0}�63 IQ�spGBsG?,0AE!͋�&�_�(Tmr�gtz(!~ ?y��(DSA�sA�E� ʚ$.�c-A� Ivrt $p�a� %k��s :V0G =mM�mus�ka��׵edI���L =�lT1�}E�ak�!mu_{mcN{c5gX�X 2 �-n�"���g)�$e(\)�A��Tx�3.2Si8KM}2�ErhoB�so?B��� ES>�$a  ct $&Y afm�Z$-{5�E�He,�eaB()��wA2� �- lookAhQ2&3�� ׂ R,\�0R=\C[X,Y]/(XY!`� I"�� �RAQ)ag�r �� =(By ab3of9�"�6no!ud4�nguish"3���#"�Awo� 4d�$oi�%$RW�pi�finiteJ?&eA� ���6Af_i=a_iX�{i�jiY^{q_i}��H$a_i,b_iaXmat��C$�'!>�p=\min\X~� Z�(neq 0\},\ q q_J $;$p,q�&��>aA nz�nV+��Wp_i=p� a_ 4 0$; x��k�HB XU(i^k}(� + b_i -7in I^k$;ji��!4!K�9(R/4�pan�F by $\{1,X�_�},Y  uk}\OB�hW�A��q�Fbz(\{X^i, Y^j -�8!pk, j�qk\!��&e26 � �-1}, �S{q�5 ���>XP!�Th� a7(p+q)k-1&� @  +13, Wri� dim +=e% $aL� $N��F{ �Q ]2p+q=e$5b2��1~�E�5���ݹV� �$ EisenbuH�Ml���k$Iy~he effec :���n "�%'of hi��&�al�-�$.lkwox\b�"�7nga o�Zi�6ir"��G��e�:�* v ��:�c&�,�z��[k" leg Ɇy�Pl ��� �>. greate,1anUE~b K-u�� �)�M*&6"pa*�J*th��"*S& �]9�, h W��q+��b�  . Un U.��.���:"^ k � )*�n Any>$.S�5�;is �g.](�WK-/)�A!$g*f By&�)"K%��}�Ba�e5� for 6 (~)Ip In"P#I�p�y1�C;xU2%cI7Y.%1"Ah&� w diviso+R$d 0chib�=kS< -xdkP.�&X?Yxd͞��!f�-B c�+Z)N: {cd}<+d}� c}>0"/ 1-g}�4g L}=� l� -�,%sa�)e9_Y!�,!x�Of s�s�%�o"y�"��}&M.(Ymdeg L/�+� N�d\"�Z^�O�\ 1}(d6 L- )=&glo:IH)tV -#5d51u�j: ity (I�#5`l" r $dO �.e.}\E1"�.�, N2� B '��d�;cJ to���J�Y � 6S oZm~O>Ns Z|!�Ul1\tM##of �p's� no� i�~a�B�9O7�E17--466.O@Ma]{Ma} Matlis, E%�73M�W�Y2� ����R�a�0-d�al���.}�c.J��V26��73�|86�t�t�susaka"� ��Po�zed�"�a^(nq�=;�� mer.A�6� 94}, 1027�C72r4Mo]{Mo} Morris��I%180��U�Kw=!"rulL[�b�5% 6`042; Mor~rix (1��� )�reefold�T�"f"W s��� ly�ivAR11�1176 Mu]<�q�U6NS�9!* "m $.} Enseign�)�(�2�39--1102 GIT] �� , FogartyekA� Kirw�F%����� ic IqG.y.}*D rd eCc,a�q�Q�3A(:�N� No]""A�!'6�2mRi abst�U��o�In[35a[09--212�,PT]{PT} PaulEN!-Ti!+G��.R��%A��K-5�e�e� t �(.DG/0405530.�,Ro]{Ro} Ross%���� day4&Q��]: PhD��s��4mm {on ">0 {\tt jaross@��om2rin�d.t�B@i�z.ac.uk}}&�3jD0�t�?!�!O=, C t Uni�i��Ne� 8, NY 10027. USA�4jL�U�,t (SW7 2AZ. UKa�!-doc@ } b \�@[11pt]{amsart} \u��ckage4cd,amssymb,sub��e2%[a�>@,matrix,graph]{xy!�@topmargin=0.15in %�width5.7hE+7 odd�H73&eve�k2�5]emAorem}�  [W+]2' coroY�}[ :]{C2+l3�'�#6#�"*�!��emstyle{&Q6C�_�a�6-kA*�A6'ѯrk&R!9k2% *{ack}{Acr� ledgA��W�� �*{��}{C��>>ddr{Ac�in� �& \+ ��.d��� �%g(command{\N}�{N�neZZ>QQ>RR>CC>FF}!�re.�k}{\Bbb-J� HH}{ �frak H>VB2B>RR �BR}^9v.wLL! bf L�.G}{\GammM��E � sf{E>tVV>TT>WW�Declare��Ope�"{\rank}{ V"gr}{gr^im}{iArR^?}{ Z`'>$dfHid}{id^Bab}{{ab!R�Sym}{^�h}{�;^ Lie}{{^"�$}{{^$Hom}{{^"Tor}{{^"Ext}{i b"Flag}{{^F�ilf4Poin}{{^HPr!�{^$lk}{{lkb spn}{$^A&}{{^$an�^"FP!Pb Aa}{{AbDd}{{DeF.���(}{\twoheadr�k�a��u�in& hookb# abs}[1]{\�O| #1 D|:Klin({#~N\rm �.�ov$&�B#1��P } %%. �': Sept�r 1, eubm_�d  on: Dec '28(r .&July 9!$5 \title[&�& � %-a�Ld Artinؚs]{% �6� \author[Stefan Papadima]{:$} \address��� e of. thec�emy, P.O. Box 1-764, RO-014700 Bu�Fest, Ro{ `R x.�@imar.ro�@Alexander~I.~SuciLB $^1$�ft �eastern.� Bos 0MA 02115, USA�Umail{a.s| @neun  \url!$,{http://www.� "/\~{}4��zks{�P�s�-�oAgY&NSFF�4nt DMS-0311142; subj� 2000]�WHary 20F36. %% BraidM,2) Se��/13F55,/Fa6,Stanley-Reis-��s�(p1��xesn 14, @ Deriq8h, ��g� aliz� s 55P62 ?Ral P�top=j$ory 57M07.cTopk�iNme"">�/!$keywords{G� , fla���x, cubB �, ^R, l��>� #9nomy Li�p� a, C*2�Dn���t2  } A b+�-�/!�p�\G3�Ci�� ab� $G_\G`+)it�� �a ��,�a�$8!�� �ul%� $vw=wv�3Dgpai+dja!I. �H!Uu�vN= uH�&e %5��A(2)FC� $G_{\Gw*�!b#�0:� �Tnd=j\make�_ \G �"�Fa0� :int�us&�8R��N~;- = a�n} �,\G=(\V,\@J�0^�. To�,a ��'ere-#a&zza {\emf�},6aY!�=�Aex $v},\V�SM���or rQB0edge $\{v,w\}GE$A �26�,h bui��$>Z, $\D�?-�CT�1he �.�},�+ fillA��.AZA� lete�'E��k$�iV by m-1)$-m|eE�9ourn%w2j.,�a CW- ex, $Ke >�:n �jo�P�!�man�oprescrib`c 2:%H $0$-cell y�s �;�Ґ��$1 0J�� �!�% =�12V1!�s_6 in \Men� Muʗqnf>Ht��e�1 -�x14e��0funda�a�o����AI����ll1oe(n Eilenberg�Lane $K(�,Y� ~J,�4Charn�l nd Davis �2CD�� Meie�d VanWyk MVs?Q��o p\�es +�k�L�V``diagb$" ���s � ��(\Z$ have b!-e[38B� veryA 5C�?���i��lo�� ��/m@�C(by Bestvina 7Brady �BB�Fi~��.�va#��t�&�-�Bie�NeuA�)� StrebelfNS}��O�5gJa�tC,n?2�yaK-�Vqof.lr6 al =j!A$+q%fd�M�)�, Meiner{):�M!��.���{Co-vy E��*V coho�$P( pap%wJcu��a �Ber΁e`&� Fys��Aga7Bg�#$ic nature,%-^���A� asph�#ite���Πd�(a��n���Ts!��mAk � $H^*id\k +(��ri�,NH  $E/JA�Q=��@$E$ is the exteri�Uor algebra over $\k$, on generators $\{ v^*\} _{ v\in \V}$, and $J_\G$ is the ideal <��ed by the monomials corresponding to non-edges. A crucial observation, due to Fr\"oberg \cite{Fr}, is that $E/J_\G$ is a Koszul a �^DWhen combined with� fact B�group $Gא $1$-formal (cf.~Kapovich and Millson �DKM}), this implie!a^$e space $KY Tp, see Proposition~\ref{prop: #L kg}. In other words!~ll�r%$$al homotop%sory ofn`(embodied essentially inAMalcev!ple�:%p) can be extracted, at least@@principle, from $-�D. We give here a` e descripjLseveral invariants�La right-angled Artin9�{\G}$---!� associaAr(graded Lie Q�$\gr(G2)$!�e CA %�A� gr_k "/ )''+!�a@first resonance �ety $\RR 9 ;\k)� sole-\erm�C� graph $\G$. Our approach will enable us to derive!MY4PS-bb} similar� ultsAC]4Bestvina-Bradyloups =to { \subsec!~({Lower cent!�serA��(clique polyi� } \label{ >(:intro lcs}!�starta�analyze�he J� )�)$:�r�=E�a�$In Theoremi& thm:lcs aA$}, we showi�ke�8somorphic, as aJ�,�$\HH(G!�� hol��y2Sdef�DE�'0reduced diagoa�L map $H_2(G)\to H_1 wedge �Fura�,more, the lN�quotieaar� rsion-fre6�� rankA�phi_k$ez8n by \begin{equ�(5�eq)�|1} \prod_{k=1}^{\infty}(1-t^k)^{ Q }=P_as (-t)!� \endT Ha�$ $|t)=\sum_{k\ge 0} f_k(\G) t^k$ i�eFda�a -�4coefficient $ C$ �lA�!,number9co�� e $k$-subeos ��(i:@�$A!N $f$-Y�< flag ` x $\Delta% $! T��LCSa� mulaMa!�nifest%u�JKos��4duality betwee��Duniversal envelopaF��AQ�e�Nco��logy r-D $H^*(G,\k)=E/J$ (Ŋnwas��no�*(by Shelton ��,Yuzvinsky \c�\ SY}):0�7�6�'ut�$$chen} Nexte�de�ine�Q��,m�/G��. }� �a�Sm�6�!S �%��?e9also �y>2=theta�?2}�RA�=2y> J$ t^{k} = QE2T\left( \frac{t}{1-t} \��ALZW ��ere $ !%!�coordin�a@c span�bA>W$ insid�ea�engthG"�J ga�!�6�pair} eF�sha' � ^�a�! 2� , ��hav���M�i���$2is9�,subtle: both3X�0e {ɕ�!%K ,!�dimen� ���� ŏ� lattic!�r�d valent:� Higher-[al cub�~)�x��6 (rescaling} � KR}, Kim%QRoush�� sim\-ply-U� 8oguɊ�:v�. %XCW-� $K^qE�$ ($q 1$)� obta�by join!��uct(2q+1)$2�spaj". maLr � crib�u�l$For $q$ su� ly large,�s�4s !�%���l%co �Q�ect=Z�e%�u��eAMii"A� ��� loop��#Omega 57, pureJ�BP�`�conclude5Eit� ex ��}�� ��'aaga� h�efuln ofA�2iP Le�6G��8G'$ be two treA:�we�m?of verE�i%� q�t_ (�e�1Iln ]`!c'}$ ha.� 5��, yet�&� &� w�ca�AD!�$ WhiteheadQϡ'�s� ��ack^!h*� 9!aJ�_�M2�Q� '},�77 on{.�%"I�ity&� A�lie }6" H\o6b;�:M lie} Fix� ound�  $R$,&ei�f $\Z$ or a&��? EG A$ b�n�{,� 8-�� YE3�pie�F $A^i$, $i�n0XAssume1�wnitaU geKed� -module (.� if $R=\Z~ Aep $A^1\cdot A^1=0$, i.e., $a^2f�ll $a�A^1�1 n�s( multiplica�( ��, degree $1� sc� to an�- $\mu� A^1 � to A^{23)R \Lie(A_1)%ZAmg�W]#l $A_1�w,A_i=(A^in#}��&��)8� {\emRa }a�$A$, dEdr A���L+.�: J�� imag"7 coFaB5 �)eq:�A�$xymatrix{\1a _2 = (A^2)d \ar[r]^(.35){\mu^{\#}} &(ACA^1-cong A_1_1 = �_2%�}.>ZN"�� Anherit natu!��5�=+; )_�Z A6!^$k$-th;edi10. Now let $GE!}�Yena�-. ��na=�;X �"1q�m. $R$-m�CaF$ fq�y�(ae2� y��Iq�,�Ea�k�z ch\k\ne 2L>utomat' lyu.����wis� needau��5J !;aianizi�$H3�P.�,� �Q case� ��`ed �[a:A3�Jf�%>L ?UI�o>�e/NG��@,�benY��\HH_R(G� HH(1�).>� U !� gA� �say wri�DG)=U {\Z},�J�K)c % \oti� \Q /Q/. 2,!4)k~u�nn�)%G�%1 � $ co)des�Q+ given��8 �. 6%F�6�F� �y}� ( Appendix A� ](Q}, Quillen&s,~nmX; As�|r��fundar"r\!ofEoE�� �9�z A�of�pi_1(X�$not enough!�ins�! Z 5$X�� inde� �5-�InG�Le easilyAn2ed. N� the��7"� follow�+ �!v� ul%!Qir1 !Rec� ��!nZ� � �� �2�E�@��IY��}!�4$\Tor_{i}^A(\k� _{j}6< i��8j$. A necessaryA�-on!���k he2< a4 u 65$in l ~l by anMal $I$��(2�+A*E%�>�I$ admit2gGr\"obbasis� b��-"�  �% ��SupposH*M�!#a:~�x$G=2�>�nA� @.�� �' �of} By��um;#��� \widehat{��(G)� �ck% ��bA��J rpreu ���<'s minimodels4!I�Ps: \[ \mathfrak{M}_1(SD^*_{\rm dR} X, d) �>.H1@ ,d=0p\] .X (A,d]�� 2�a"+�$w Q�$ D1�.^_ [sub6&( `I�!� par: 2N$,�%��Su}. On��o�  hand,-陚 mean�� :V�T:R�2\]?�nes$M�" ɰ^!� ���on{��jc �H%�) \surj�� fa� �wro> an epi),sm $\Psi_G�l�#)G!2a�~��"a<o2�(t� ��qv$ y� K&� �of�'te)V��� z} *����a|5|\} &!>�FJ!��!]��c*� -��3R:5�max{ et���atakW$MJ `y�un� sh�" U����f= holo�'i!� &9%!0_\m �$ ''�I����2�%FA.M�,2�2�ofZ'>^{(2)}B��(G)'' 2�%��!(GM�dJ�,�^�[�, 1�S�&A8�6�b&��N):�9 &�6){Ey%JOf. icu�.v e70�{0y � l�LCS�$A��$(G\!%a��HT &U%.�)..�!�&� \1, 8 8�8$;�e 1�-= 1 �3J �d �+ :$  $#-4( 1�H&�x:f�}f F_n@thec!F�$n����t�.s�$F_n�!FMz62LL_n=^(\Z^n���9grN/F_n'')E' 0/���5��gi by Witt's) ula:��.W)=\9+1}{k}�*Xd \mid k} \mu(d) n^{k/d  or*�nlc�e!w$ v/�}=1-n ��:& )!�Y�6�K.-T..� &�&!�D=(k-1)\binom{n+k-2�29��� hilb��%�R�,U�� "�, 1- -� - n t}{&0)^{n}�Q6, Q�2S Hom�.�f ��6� ` ,lo2m��G plexD ithJ�$.�a�"� B���:-6a��i�. Us� A uYsm*�,�h(gr}, Coroll 7.16C Halperin�Stasheff�. {HS}) :n�h`)iA�GPdim_{\Q} \Prim \Ext_A�.(\Q�_k_ )�"32He�2$.3 /�&Dpr] iv� Yhe bi�vHopf Ext����, upperi �'_%l�,�  0W  � EH�$ ��4"�"�� �vEa!aa�$���1&V.hs} quy�h key tool��!�re�&�8AhL\"ofw- ��.�AV�i% :fQ�A��^ ad q@ X&Q�-di5&|$6U�A�&"�A�� >� �4!)exteri� a:$E�"�$ �6 h� � v!�� r�!  \M1HH(A)'�A� P1 _{k}8�$Tor^E_{k-1X\k, \� \text{!��2$F�e!�B�I�*"\:$M~�'Ms�#ly)2� 4.1(ii)!n]�: W=��!a6 �Al�Ost]8works,�f our 0J�of�c��"�cor�3tor��"�*�$&M;�.�%Q� 2�$\Q*�suc�;a&dim!< �6CndE}2 >p �"E�2nU�IJ:!Kv�22�6} �=G) = ��q:�QI���=��,!�F��oBd��1.0A�aP.6�G� �f�69bov���v!��EA�v3d U��vc&JJ�%�C5$K=\ker\, (&v$ �,a�"O9^2~.Q)� !�2�c,f"�-Ay�p�=he $(kI.c9?"�2!�a�c, �I9ten%� -=EG�/.�#� h~a&s%>", N�.�#a��F�.byA�*�<.  %A=3 each)Jex2s�1$�}:~�'T3"}� %� toru��,yj)ntify, (parallel fa-ja $(�2 I)aube (_emptyset3 a point);lz��0} )`� �3�I�9} �$\Big\slasha� g(T_ �\cap ' '} = tau}\ +;b if 0 '='N)^. �A�� �%Hw�Cif $(S*�&n)!�)gof&"2 $n=)K�3F��0usualq$d�3po\-s1 I�n|1I�͆subI�x2b1daH!�%�cells:�9�%s#1�2<#&�$H_k()��� 3�y���., $1@)$k$u��(H0 (z $f_0G==1�? ����a�e P�' ar\'.C!csMNm�p$\1 �,BAb�A, �iڅH*Y9��n�7��mA!Q�seq@l7R�$)t&�5A^C���:. �Ffact,1is �38 Eilenberg-MacLz8�6�ype $K(�=,1� �<� CD��.MV/"Hex:�3r \G_1�q 2�r2%,s (oni7tinct ���(�cK�hQ2 8*(G=\* \G_x m!iBP��$=\V_1 \cup� 2 � "$\E=\E_1 !E_2 +({ \{v_1,v_2��v_1�/P �� } v7� V.!�Clear�( (9=%__1}� 2� -�=%�& �/ �4 inst�F,�� \G=K*w�tX onv%�� (!N iter�:1c$n$)>��a "le7ex�"Oi9 0-2 AaV $(n-�5�erw& �(n$-��F�51�a/�Unj�}&&M+\co?I1�dis!t�C� awo�IEI����)�1}*��vee��\�1{K}B�� �$%�(n*0:82�:�p�"� !�f�>�DR�%n�A@�>l�,��.��6��=&"Q."�A��h a�*�B$I� �I�;�Lful.�B G$!2Wa�f4!�Wq�LM6�@ rZ�JP a�Wq� M7JG" �:�. qi�7�$2�� s risXH�ell� 3Ojx\ D �� G���L�"�T ,� ?)_�2h)#F G�L� spli>+�@�re�6tl 2<W} ��&gr5�N � ,$v\mapsto v$< v�@W�"�?1$h �1.6�Co�&nG9P�GB�oho�6�6=K!�a�h��' ��� � �0�S} =� (\dots ,v_n\!rw-�Da�oOKi.t;�J�;vB�A�-�q�k  $E� eF�6�+ $v_1^*�^*$j �i , m�6o�e5$J�.,m$*2P$$v_i^* v_jT� �'$!i,v_j\��.an�z��;�P2< S"�Tq:=�H^*� NI��9�"�StF�D� ����NljTJ����, �-Gamma�,!@�2.���8i'/ .:�R9/&�)m}^� .U)�m_Iq.�A�^*�sA�U�&�I�Fr}�5reprov H S�JaYYJ�J� N)�Qk]\no,P_Ma ��c>0.EVQ�; thu��"+i1%F�-A�an,0&�L"RC�Con�)'2 R^ A�5Ca \pi -- �<H a&�$K>'�9$ Bousz -Kan&3P6�W�>x, cf.~)�PYj .�1R�R@:1&�"6.10]�R, �*) �$"�;�OBX ^�s��cH. VZ�:+ we�:"� ���  0aSRp:K.������*6,aAD/%��wPs|"GA&�,L&�F� 1�*=W�EeG(� ��  @FJp8'S�B6�*�4��af�^�Mt�Q��MR!1-]��(\V,\E)<�2'=�p�*��Q��"} 6�^6> %.�J�">d : %�ewHat!!item �$i}��V 9�($ has@�:�rvN1*� E)=d#D \V) / ( [v,w]=0\  i� {v,w\}� E$})Md١ \� �i�K,>4.t-� |$�.A )O :LMcaR�*Psi, �� \v,%( g a6�)V�' � �?Ew6�v)�|�c-��,B�2�# 9���-7eq.��$ �}= � -t),>>�i "B&�"%�h"�K &qK!.&A "� ]�endy�Q�2} P�2i�9�6GZa0lA�U�&@ZfQ# �� ?BO�@&�RK=%�B !�To�ve�i9b* 8�*�\Hilbert�V� �*�-k$ does��J� =�OK�� B"@�0-Birkhoff-Wit�Jorem, �=i.� �X:� vT$UaJ_\?(B�wK$\�Now�+"� V[ �#���S,2_= A_{\@!!!�Q� �?�X�ZA A^)�!5t4�Ao�9&y �$A!�Bu�j=F^ ^so�!2( ,mV,-�&-12by.�ity9Mn�Z*�=AilTPu�� 5:E=�NA�%] 60���!2NA� toge6ś&� 6G)�:{$�-g�.A�2]v:�2^{e��6.>�"�N� �/d% :�c�/��2�RL"2�sr}^�E.� . Pu�9tot#^rd�W#&�M�B��_?, ?As �io@5:GL& 8 �(y�?7��e �&"�'ca r�,bS� aJ�*&%e (*\b - � =deal} \,"�&9$ !3&% \G� ��a�37'�Sr��&�c>��+F(^>, t)= yb,�_&�  &!�a*>� �M(��) ND�Sf1$ $S=\k[x_1)� ,x_n]if $ -^7x_ix_j�2 "9 �� ��he>N��BN� �X*�?b�m-]��r'�+aE)S/ �.d(�+�XJ= Am|ly&�,�N^n$-M � e $M*V $A=S$6EE [N<*�)b�&�HAI�X �!-mhous�-*�Hs;&aNaF_*^ M uni�^upA[u�sm. D�*� $\be�[$i,a}^A(M)$EsDA�N> e�P�DF_i'at? .�of �� a=(aQ�, ag/� $a_�Y0atBy�'�A79,, B�Y&\k W&A�? (M, �(a� �-�&� x�M�-Re&PW�N�TM����2Mrka�`ѻ�Xe[(6.4)]{Xo4a[.� 2.1]=XdG &-5.7]{E�;:v� ahh-aah�.�K}�3m_{KA�}^15�E��` iu^a%*�^�ASuZ)�[G} { j� @supp(a)} (1-tu_j)�j�?�z} % Mor�8s�9��$� square�_"V a�RvA-nonzero,6�EYI��9]�� ��m"\D ]D'A�=0i�1$;O JY:�F4-L&�Ax�$>�.=Bef�UD_ng �*E[W-�CKIi_(blish some Y4�. �.�� &."$, f\kappa "{ c�Civm���,)is e�7um|.ger $r$� !2,:."�pWA�bseZ]"7\�U W}�&%3�"v,\V\setminus �Uj!nnFV�Elso�:�])=��k0B�]H}� �� I/p�PonG$����nN%ZJ$��1wM$XA�� $jLKU Y� �to be+Dy&x8�} c�^[b.�\� 1D�^\ �*�^B*k"c�@G)Et e _Zj>fV}-]-. �< �Et�e6 �&�9 asB.pX7} B `= u`E<2�}.`B�oN�.��!�J� "� !�B&�.�g�'v� M3c� � ��f�10� �_�mr�cU \ O�#sM:M���d/ ''�.�\G/��b F�ci�.a �(�+bz Eh� �6V�b(-`"D6M� r J� ^$B��-^cq0notl��q�I�k��elJ Appl�(*��h� :fl}a r� �mm*�j frlo} N0� "�2AlA� Am& )_k ��� ^{E}3,k}& ,Q� *3�(7��x� �eq"� � findr� *� k-�j�&8Mi� 1� (^S_{i,i+1} .� BiN]^{)J�A ��a"�5� Ho}e2sr�h/b}!�tZ�f���W}=� M2!�wid�� (\ahW� = c_��y 6���a��u .�2�RVoC*o{ eqI�,!��"%�� l e  $F�(U� 2�"q@k$"R�H%6�Ga�.��.6���� J�2�R���9q.MA zF�v}>*r:�JB bsc�--.tc�dY��yvC�c�ln�'&�^&� �Y�c.�>�cppK9�2?� cA\��5` �O� C�%�}�"�50_,� 18B*^i�(X9t: 2(i1)�wt B� �� �խ�We J�TcoTL���rram�Q�\(colsep{30pt. I �=�(F mu_AA�}[d]^{� 9} ��G.*2} \\ B� 3 :lB�&B^2 } \]a-�ur�1�o1=q�Pick $}�p7��Qhi}ATd!�""2�a�:�(a'��$�G1�9�9�Ѭ!DB(ART)��)�a&�av-� . Hih(a�b:�]CM4%).�]"R��yn.QN�� u.ar21�qS!�to!�$Dks��f:l�<-!�B)!�&Es :�F{l�b�m>9� orth���&�/!cve3M�%b�B'os(A� triv@[d�?�P$U_1\|P UC2x Su_A(u_��u_2!�@ K'$ in U�2KHu_2 )WE�-=M�r�Z=\{ �� a=u_1+u_2  { �} u_i ri�-� } ne᫡V��Z� a non04, Zariski openM�,%i!(7g�;to*�!$Zq�!�A�� ���Z� n᫉@u_2���avA�%z !tA!�Th*�jB�m#qH �ŽZ" 4^ s�yfIA (�2"(P�E/2�E.e�F��Fbn satisf V &=XydY�QE��Xu�hus"${!�G�,`~$&T#)<&S d$�&v I ��m�+=A U$�F� L��s�@a�R�E�A#2  &�g.�Himmedu|��G�h��*�A�ecorV| * alphdG_1�QGF6�v*�N%�n)�r14/�z/Q$ O^*�ee G_2!"� 1$ taka�OG_2!Ut 1Q��N8�6Q�� � *�A ambid#.� s7q�!lo`69.� pA�a�>2A|lJ��8�(Y�v�ry-�i�~�)e�.z�2M&36G=G_1�52$�2�Y� �J�:Q6ucsX&�8A$� Toi!؉�?�t�~!�=%#R�V��kZ�4*-&���\�AZ�+� �4I�>>�Z~. j�X �%Wd/qV�&1`;!��!�+-2��(�c�*mdex�0$\V!Te�]q!��)�,}$�4%0qN�q�q� �x�CN�� -\��r[-�:$ "�>k RE#K#A(��r.�r�]+����J�U� %9un99oqo>�rs<H7 �rof:� �. We"7�)���$<}U!��32��:6V} a_vN6F)%�V~$e ρ}& �5V@V�=e��2��-ort��)�d�� &%Qp:�7;D� �{z &kW�A�RD78$��d*�t . (&Z)6�"�ma�`ez  & �"�A $.) Z!.�,W� �m@. �9�8B��=��%� <�sy &X"���2�!t � V 6M�V+NIRN�(p��f!u5��!Aw���9�A� @�J2�9- G�A� � 2� QTu4�AY E[ very^[QxaCs5���MN2L"��!�!�not�:�,�4�6U�$C�#yz'a{� !�V}zsU� "� a'� �* a'=0%2 �9 "O*���So�cas ���$HwJ%�Ad�N�u��or�ed�8 s $e=(v,w�H ith $v< wvWt�^ cho:� :��� _{\V}� � >�.^�Q�r� eq:mu�.Z=AZm_{vB!Y �!&;w� nddeKlv�>' = 0�*�A�%�8.�3>X#1eh �9eEi:+1�9�e&� *� laim�<$w%���UX $A=' a'_{w}}{a���V�m�� ]���|ia  x B�vp@'i;-%",%#%2!��� So p a paa�w=v_0,|C".k=&>n��.�U&&l!�[e߇W) is d����_v�X!+v�})1 !7:P�o s = =]v_0.0}*�rs %L ed. ��.<�j1�pE�z\a�tbHS2 ; �D{v�n"q&�z\dist(v,a�~UG!�*K �'$u2X*� ,L v"�6.�~q�:��V-%��f $a_{u}��${v} -a_{ v uT0U\+v}�(�u}� � itm!�%�/k35��� �*1* � var� ir� &' >� � t H_\V3 �F�E���Q_"?Th]%��. #d7Z ir�i�+�nC�0���aMJ� s* W��Mam�ttha���?�g< is:� �8�co"�V�B����0�A�2�)�.�end.�Ip? �^,�Q.4 A��:�� V)U7-��rem:ar� s} RZ�co!]�* on fea�s�*R�[m~f>�R!��.of��Rsq !&@�"z /x .��dcoi8�v�� e�y clas�� �4�mA�!te23;��g�.�C�;��$*d>a�^�)� ,\C) ��� �pac�How %��+rs�1� 7/��lb�$is fairly  Z I-r�eC� G!r"��)�!Y�� $M�ETt"A��I��!#ass�Uon�b!l{A else��-a�e�1�LI��WG �Z8 j3ga N@pa�Q!��+^��X)-!X�Ji�KAp�o�2�r�!�)�Lorigin.�mLY� %��is vio��by mos!j aphs��a�us�1.��Cs�#r*(K�H\�aI�i "/�$5�n�_�2lLBieri-Neumann-Strebe.���2sfbn%�*B+<3�>+. �N#e� ]� !��wAc�Dcal{Cw� A��#u� ng Cayley. 6Xn "q�r�q cha>��=chKG�sI.r_{'6yB� B���gG�?(gucdi��&{BNS}, %m, -n�\1s��(e# 6���E�F]��eq!� inv} \S[R�) ��� \Hom�XR�"�/{0 N �7^.� } \F &���h�;;jEQ��6$�8RqIt :��6bS= n�!� _�!C^�&P!�.�$2�ebrb)Cbe�Ɇ���^�xa�Meier,ner0Y(nd VanWyk ) {MMV�(�4{M)yD�� W; ��%(@�2�2s 4[��an�3�TFE��dU�!�n�2�!3F� 6g%�"`protJ E���'�1k$� f� �.  ^ s1} =�U7a;:�*� �\2P2* a# L�0A�*G�]"A$\im(>$� �er  J{.�8�_ !/���LL in�# ���:X.)�V  U��_R��4 k.D_\.�vd��!�'%� I# �@��Ev !n}�1p%�Q� �s: �$!ja�6�!=$C� 6�e Q .�� \�M E��bG� u�e�er�m�&�.b �RE2#y�\�B�3��B�.�%*cI>do�jn<  (A�d�'5+ ,z!E���N*�5��? neighb�!B'h�-p"��Ow�m�JsE�::-h P*Ds1��{C22�/�h*F 6c�#{d)����|cer_.�Konm �s:�m�:=Cti�i%~ V�.�z�M�$-aZ].I �Н���J�w it N�As*�MV>�C�)=-]a*ZP1�O!�facts,>_q�)B2|1�/O �` A�Sl-��hiԋ�$-"��-  >c" bI���JthcA�g paperR%� ion{�*� =."/ �g�ri&�� a fe1�ao,s Û&�J�L&nAh<6�4� N�A�b(, u�V=T�?cN th�>previ�>�ion (W��a!by$  methods�� u` M!�i�&8� pp"'n8mul�""Җlcs��A�B�5)� � {Com�c�AD6 5=�<: *&!��� �:xha-G t��gles >aw* �WxCGӈ! W��\ easy25).:��\G(t)=1+3�D } t E_\^'�Un arbitrBk%h� Wi=p $P [�0m^<"�/�0���XA� recu�t !�� mMfzavail�>!wGn{$e��`8$\G��e&M ��#�$e$Z?�Fgcet%CN(e�(%Z E"�_ E�%�b�mo��!�end0� ekal�wir�DmQ�[<���on� a�s&�T"�OY��B��h5.1��� Re�A!rI M@%�r�*}\Ktq P�X 9"e }- t^2B!?� �  "��9j(Qali1:9R!Z�"�Q"� qD�8�=R%AY6Ёbridge�itI � D�ny cycle;X sayE4�"2��-D!�� 62�AnV����o�gl��E20"� F@+�`on&� !I�@�;/a���( !Az$jc.>.) - NqY7�XVqj-2F8�Y �{�h�H$\G'=6����� er� �.`Z�f�'��tt t�=c�]>�?_\W)=\2�>'O>K�.!}&��e�w$0 :!@SNg-�?�u�align*.�!�count5�&V)p8�, \, e6��il6J� + F<�N8 \\ �w%Q�x (J�-1�<1����!'del&� ��nce��McQrM�M��*@ol"�2G=\G'S[)( K2.B':y^�Mi� A��v����g $Eq�i��;$U^��i�)m� ') +�:j�o\ J�1}"-c�-1-,�2�1-5eq;!4is�U�A(�Fd2�C��'}Nlb,@.�D J�BM��b�-1em�q3�R�+��-�"� Z�x� Tre. l ��}�\���n$��6R2�ase�%�gE��nd�.��,6l $#��=1+nt+(DbE �ܥ2�(&2&� m��;Q�]�p.-T�}�2T(1-t)(1- �J�WTaim��A�YE�������n�=(j-1)q�ne��"�� $j=20! n-1$_e�9�$$n=1$ or $Z\"�% noth0 tR.LDe�an�0j"E � E�:�a "Iprocee�a�Gu� (�a.�6Z%� sD6�$aL&OA&NA= i2�@�#$1\le in-!���act���HG be d �% � .w@ 11]{Fr85iU�]F���m��D)"?:f�&#t!� &=�u. q6AS~�D�E= �{ �#1k+n-3}{k!��'�Byjr6�|:r6/ ���2XE:�"VE�{ �O �:&�{-1}FP*$�siES( >?� *�km T�;�Ocutã!EA�ab���kJZ�T5:_ �s@ *?".� �k^n!`ne�y%Bkex"���� �H4���"�>ȡ�&�J�; v7up{2o��.�K'%}F�m !?� \�H ,Ѝ���"�K!ZB�& �8�V� '�m��E �ao�6k�F�i��h/e@�J.�5 k We.��%&���� ampl��՟ &O x:dynki&<^�.� � R��7s[��]R��J� (�� �,5%k D� �s�=\Aa_n�=\Dd_n���+$n( 4x�� �G�$2$F|͞a]' )3,@��.) a�phi��!�)=.'? � ά(I�� .*MpH����7��6^k)� �5u� ��=  $�J{%�!#�`�*omoY?c�`!^�^L&&P� ltho�� they�A��p?� -��Db �{C�q� & �� !��L�!iC$5�,5��Agah"�{\G_n}0nA !�sou _n&w ns 15uJ�"z ��K (_n})}= 1-nts5"h�E�5�f' ����d2� -}�/]��xtoG% � �_[t]:� �E�_�rcan�rset/ an (=n) semi-V=]z77PaDa}97 9dr BaE70D�i. D�r���+�n"]�Al $n$-�E$ ABm. &X!BśEE�*�Tflu� _ � "� , $6_n8�j) -\tb1xn�.�j<�nRs�Pn(� 1bT$�"�A�z rM A� plugg� i!�Y*�e�� Q z#K"��Q^z�ihFLj��! �� c {j} -2i2}\E�) 5Lk-.Y^{jJ= ��n0 _n6 k)6�$ $n(n-3)/2&�*���}(IG� 2��Ba�� adja�e��J� 6�9`� �\k)��Sd "Td_{&EjA3��t3&p 2 w\}}>��F���vs� })� ���'a���n"�q �YLa�a���%exE�a�attachi�1a� ?A�&T'�� ��"ljA~+6u�m.��L�hA��*� �MI��Q��� *� �A"Ħ�I_*n���W ofz]� N]Z�U'����?; 6�J+$c_e{�Fa"� �/�7U<ծY˙1y-ϊ2%�&1 �c�3j3�BigVR��B�6'l�n2� Ad{�� $y$k&�b��$*,{\)>6?�XI�AQ>L b6figure}%!=b {"5g0page}[t]{0.35�- widt�[etlA�{\uni }{0.6cmQg6pi��h}(4,4)(-2,-0.6) \put(3,3){\�-(1,-1){3�q:-:0,05 0){641.5,1.ߑ R02Q6 -1,1){1.593.�7utr(6% 2}{\A�le*!A& On*�(0,-3)N'r"L{\makebox(0,1.1){$1$q l$ -1.1�$2%45I$3$)M 0,G ){$4!)B!5!%F!6!� QI�UR�Is�r�r5�� �3}M0A6�&0A�!�YSUp^�]�Z�^P_�:&A!.z>%VEY 6�=� @��Q��}$�rsf[��O�]1�a� fig:Biangul"" #A���:DA"~ [>L�  �ni�Dt -7�d ArY*� ��� a'heMtle way.n[ �#��+}� %R \! �hF��lZ . B�� 6e-Fk $P�#,6t+9t^2+4t^3)�9*�$Q)0t^2(6+8t+3t^2w�j;id�6 � �( w� S �& �� Thei/46��&�>:* .�6s4t2,� a.h6~� a�a%�� : \[ &K=�=ov{23@ cup 5>35}}\,�� \qo-� mP1B>FP26P. \] Ye�l%��F! I y"�Gc,  �9m (l>�aB��)� l�dF �4 �.6}})=N �"= "d(����(.��� >�s��as.s2�& h�&k7al,3)-"� L�A�N�tr����{KRa>`ach8)bq+a:� K� }^{q}u�C"��&�%� �{2q+1} �"��"�\T{�(�A��{N��]f7a2�x"�'z$. &Ca!F^{0�|}=:��x2��o'2��c%w" #>d� Y��6�b��l"ߴ�a �ed =>$Y� I4{K2.{*}i\Pontryag�)�j �g�� H_*�}!�$bFowV�suD�tudU�ndgfMV !��V.k�yNk��As a by�!uce�( vexp��tlp2"h- top�5�8�-m]�8t+�T+!!F�;G$.ZCrst�Ome ����nd7@�&wL&��Xa J�6-�K6�AD� /�6�4\[ \pi9EY)&\\Q=ni �&� 1k1�Y*��,T�3w�=�)-e�-F��.�i Milnor-Mo�*I$)MM%&!rJ%�%}b��.�:0.v�\ .�Y, � F@q�]q(Y%yo(���(��/5� %��=eADi�Oby�2$=C:v- "p �!��ee�=fZx) $q$�߈v�;g�.4&@*�3.�4r1evN�%|}-�(.V���29'Rl�2�T.��aLiex [q] )�"x:ac*}� ݳ \ O$Z�� a�=� g&d�E�$\Gid7c�2q��6C2}!l#"�@��w*P�.�a�We�{k��.$, vanj�5 2q\nZ\`c�wa?�J��0b��4�*��&��Y �2��h-�ZM�{m�k��{2qk}.�./x��:'u2�3)Rlq6�q.�9L;e�a�� �Poin ��.,&[-����-4\]:�4�R�>� H]nB��3k����F"�}�� � qL�'� ẌKY=K��A��!�{"��E|�A���xY!0 $q$-�n=M�*�XAy�&-% $;%NG.CB�QL�� eq:xN�!�(Y,z X,%~� �}(:#�.ow)/��"�X1!�>gw.�!ereom'%%[ '~B]7� ��/%.�n.$2�.3�|RP$i: �dK�4]�6V�. 5r1&�(�� ���4a�>$, ;"AciE$��i�^#r2 $%r3}> �G#���^f~~C�A�O& (28) �%a.VrAO0yh4c@f�!�guarantC�MI[\S4.1k.�e4.4>�� qj�\��^6 N.D1.16�S5�Mmi| u��'r6�DI I5�y o"��9% 9� /�� aP� hold!F�&�3 U� l���J *�D let �8�$��/%$& �nL�nE�Cm�.>�A�Ɍ�4 0t�tomIz5�MV1.�63: �c%$Y� s so�1s �o>n-1>�use��>[�7 ~8.52-�1���F�5�d"o �YS��#>�#, e.g., 2q#�.Vr#n5 6e $Y'�IE$h>�B9:"F9���$Y'�&.�1��Uc�U��^��{e�� ��eE��q~*>��A��[ B�?; �6q[,EF� �"w � p� � Y)6�$�e �"�s�!i>~��9nd�r2 6Y�a�$5d�(�ly)*� &�*}�� ��(Ie}q�&c&Ed�͇not�$'�6S=2�.� �N1y\6���u_ ��/B�-de�<�f_ �2'.S"X q� b add��After%9 ����p�;H+bec�aw; ^� Duchamp�Krob �} {DK1 !��{DK%�h"1 )�!��M�i}}�=�޳se�C�mV ~2.1b0Yg.�Co9vFopk�% Co�] y~II��A�sIII.3uv�d!Fx45�Jw$9�leG;1ѳ7�`�mf<� r-A�let�B7�7��mUshorter)�V/� >�'=��<�UY$ck}E�mQs wO/ carrW�Q� �R help$GAP 4.4-$gapI� Macaulay ��j�GS}. !�is�k ]?d�")�U auth�KwattݾE�e&�f ``Hype��Ar"AK�>�q��s''�2X Mathe��` Sciences Research InstitMin Ber.�0y, California��4n Fall, 2004. $thank MSRI����CEHhospit;� duQ eksta!��%uq�thebibli�phy}{00:ib\{AAH} A.~Aramova, L.~Av,, J.~Herzog,;��mlT���,'+sB�).*���H�*Υ a�m�J Trans. AmE!H. Soc.%-`bf{352} (1999), 579--59!"< \MR{2000c:13021Ei�H>��$ T.~Hibi, �Gotzman4e�B e:z������ic� Jour� of A ��191 �7�174--211[�98 �5.�BB} M.~��, N.~���Mor�C�>����� �"JN� InveBD)^�bf{129R|9�8no. 3, 445--470��,MR{98i:200392�NS} R.~�JW.~"�JR.~�J�A geome�g "4B� disc=�8f�90�8!D�51�7 � 89b:20108.�CD�CharnalM.~Davl{-�F  � 1)$)�A�>� Pros�D�top�) (Prf}tT�dNJ, 1994), 110--124, Ann.�)u@Stud., Vol.~138, @$ Univ. Pre�P ,X5. %�7a:57002�� G.~��, D.~�6m�/ �*7���� Qiv2{: I��� Adv. �Q695%� 92),�K. 1, 92�6. �3j:170025� \by� �R;�:�P�m }, Semi  Forum�4>� 3, 385--3�:%P3eA�47.6+�!DTEisenbud, S.~Popescu, "U� ��-a�-.���AE�>^},� 5�Oa��O a 11, 436a�383-�(2004g:52036.�Fa�[�ek �B���},I�C��1)�q�(2, 135--157 }99{12WFre�Fr{\"o}ԝ(p�D�=!!�aS *� sW�&mPca Q�37�75)��E�29!�i<04042542(6U��Ri�q�1�/T�E ����+��� J. P�!.B 38�8�2-3, 2!:241��7b��02�LF: C.~L%I���{K}�� �.Ey{L}&7�S`c)qto�Gic{6m��C}, c�y � �1w4} A�� 2,�j227--258)�A�g�12�� S � G:t�GAP--s,!Norithm�!�Pr� mming, VebE� �4);&[E at �ptt{http://www.gap-system.org..t GS} �Grays��M��illmanm:~ ~2:�>oft� Q� r� jC�2� y}; 2�)S6��$.uiuc.edu/s� � �ñS.~�,� Stas�QObuE�toE"%�"h c�T J�32E�7} �rE�3--27m\80j:55012l�z M.~HBx-6({C}ohen-{M}� � s,��bŷoW h�2+��in:e�y ory, II�3 Se�U+�f., �YOklahomK jn,.᳅/0pp. 171--223,D<@*� ��i֡�I���� 26, �kkRNew YorkY�0441987 ._KM��~�%��5�I�. *p#of {A}*�,� �v� مi�� fund2?ɥ_smo�%� �YU�"�#},� <. Hautes \'{E}tu��Sci��bl"ie bf{8��98��8, 5--��x$2001d:14022�HKR} K.H.~Kim, F.W.~���)��of cerMH� slU��X&��1�38<�A���\ 186.[ $82e:05114b.� LY} % Libgob!�S.BCo���6v�-k)�lo�މ<s},"_oIn� bf{2�~� -Z�37--36�D!]j��2.� MMV}��TH. �T L.~VanWykQ|%��$a�]�9a AT $�N2 Nw �K� %�Com �M& Helv�73�^U,$1, 22--44.# 9f� 6�2�B�� {B}Y{N}Y{S}B Y��E/�P�JLondon-�(3)5�7!�199�� , 26�80 �6h\ 936�!�W.a�n�=J.C.~�!� �0��Ma�H}opfU1� �� {\bf 8 �6�21��6-?30 \#4252� �A�Papadi�A.~Suciu � )*�!�Inter� al �"�No^:=ttexE�00xe[(1, 1057--10a^� 4m* 42'*'"� + �ŷ.�,RD �CA�H�y}, G�y \& T� � 8} ad� 0�125� 2005g��22�PSY�� bi*�It�-�]}p̞int5�\��P�w� 5�Jw�8e�"�K[ �]pFe�"& ��},F� y�14S |%� , 156--16��e���k!6� QI *�-�R��%��}, 2/�L9�6~205--2�H025803. N$ P.~Rentel�N�F� A�(�aja .�(�AG��sF ��20� ! 3, 6�619i�� i� 6�RV��@Roth, A. Van Tuyl-m�_ s"Y�a�MX�Q&I�Xtt{arXiv:math.AC/041118�SY?SS}��Sc�|k2����,�yzygi|� ��iW!:D Bernstein-Gelfand*�]�� *�RZ�,6 e�F�502438�uSY} B.~S��R�B�B��i&B.�mF�bf{56��$3, 477--49� 9c:16042�S�� �6rbe�com"�m��� euj�  es� ����u41�^rkh\"aus�Bos�MA� 9�e�98h:05:iSue�S�M�In~sk�I "�}\�\}, �E 4� 7!X26�39(\MR{06460788 �#2� � docuy} )\lc[12pt,a4�]{2Lcle} \usepackage{amsaS,amssymbthmfonts Dcd,euscript,verbat�j.Et1enc2X4[cp1251]{input%2 [eng��(,russian]{b~�֥,,emstyle{plai�#new �o}�2�}[ <� on] '*(r).{pr}[P]{*�!2#*{pro}6�r�lemD�>2>{�h: 6�I �6Rem&"�*!r}�5,NR�aRD��i2�$*{notat}{N�R2tam�mk!�newa�$and\vk{v_K bot{��:-om{>-}%\0de{�L6G alg{��{:�alg2{epsQ�epsilWS:i�5��E:<svb>s{\kz6ta{��6gd`D:`goO^5�ok{2_K>!n6 N6zoh*|>h><f{F}Bm. fB w.WBvn^N>]g.=GB=x.xBl:L>_p:!P>!vl{c LFcv2!l>! mw{\qSM}{:^gw=�W2stz<z.�tyy2(lamb{\Lambd:ygmsM>�aA>rR>ol>gpl�<der�UF +6�mi2-6�z X bb{Z:qQ:�M�bbAP2re5>�cma bb{C:Pqp{\q_p6Kzp{\z_p:�8pd{\zp\{\{\de\}�A}�kd{K'ba��$ga[[\de]]'6[la{%�B�am{��60bl{iBgl[6�br ]:01(:12)62ob{��6/lan��T6/ra{Y.LU.n�K9le u670^�car>^arbto>.Tob�c>�Cb�sp>= Spec^�mB�M�VI, tangent spaces, and semistable reduction of Abelian varieties��author{M.V. Bondarko \thanks{Supported by Russian Funda�0al Science Fo�t, grant No. 04-01-00082a. The n$ is deeply-lteful to prof. Ju. Tschinkel� the a�8ematical Depart� of( UniversityG\"otti!P for providing excell!2 workcondi� s. }!Ldate{ December 2004}1�`abstract} %??? 512.741.5, 2.7 4645. Results�` previous papers are used�obtain aU 6�AfIMlo!�S mixed �;$acteristicaJhIg. W~!�o]�in term�their �$ier module= also%se% equivalE( of differ!�de�ionQQ� E�%�th� mensA�forse6C. In A icular we�at1$ minimal dK of aPg�,law that con!� s a given-t &se� $S$ a"clo!�sub is equaE��znuEO of gene��s�'$coordinate%��8$S$. As an applm�.followA�y�cri!�a TA>�Epa Ded. Let $K$ be a R)MhTield, let its residue  have>`$p$, $L [%�e ext-�of $K$ ST$\mathfrak{O}_K\subset2 IIm�0of integers. �em!mabsolu!Dam�& index%R|L$, $s=[\log_p(pe/(p-1))]$, $e_0I^@/KBTl=2s+v_p(e_0)+1$. ForAPi�B�6�L$-I,QLH$A�denoti4B0dAR��ilh $J/J^2$ by $TH$. Here $J$�`%ug�$�� ideal C NnH�IV%an $m$-u3al:Vyɻ$K$. �+se aA AhasZ���$Ln�9(theor}[A] �:K$ if ��only ifI�som6 !W m2RK$ ! re exist ��d���$H_anto $6� � 4[p^{l}]_{V,K}$�oA�(2bL/p^l6)^m$ V!�(_\ol$. \end � Thisq�on%>8a very nice-looŮ��oA�� �4ry �ase. :[B] 5�6 �>))K$ 6\�L%[%m� ~%�$M$ uniJ ed d we�< U0M\cong (\mu_{%`,M}!0. I�\mu$ is�2=of roo�dunity:Y$ Keywords:��g��i|, 6�:R , fo�",>,R�, .=. MSCG80: {14L15, 14L0 G20, 11G1 S31} �&j %m' MSc}FBKP.BEX-:KEY   \make�  \se$ *{Intro2 } IIep�$ \cite{02}� :7e;.��> c*� 2wsI ���� ��!�com F �|s (?e� Oort) wa�u�toR  r� ��yic fibrei(.��) � I&s. F�a cer)�((see below)�$-adic good}h��o� :Pies was��)�i3 a7usea�V �!C"Z � e{P !�%I:9 : �%�F�e%�)�R'1�JP )ۖ5 i �rex�$it descrip �� imag%� !� functor] 63 )e��7&5 advantag!phen� ared with^J Breuil)�i clb}). 1 �kat� ear" $C(S)$~ �ly �bed�a( arbitrary )�%}��� r2%6���!Hn�- � satisfy. Q�extra � ness* ;��B�L� 5Yby "� � �u sub�!�2�g A��edA(�=,Q can� easi.@ (i.e.A~� uish!T rom otherNQ)k"� \ 6s. 2)�6 language!lGalois-l!:iscrucial�;%�� quesA�Y3c  don'tQ 0trict ourselvA@o%�perfec"s �� ��O�� �hand,4U�!r=Mi-r��%�u�!%e�; not assum�be)=. Our:^ will��bably,�[ aliz >M,necessarily I�$p6� s!�a succee� �m . WHc�H 6��4"� ! theFH�� .o u4�0áٱ�E. and "b &� N�eO�  We call � �(a x beca��i��ntrast��GrAndieck'"B a ŌIgro}) itAsuffi�=check�&  on � �tor�"�ofQ (instead!dwhole !& 2�#!�i]eP no� >�jQmof:u $0$���b)!�{F���� &�ok� � A�1��o&�.*��U�� V�.� $e_0=[L:K_0�wh�$K�e�e max�*f sub.� $� (��U�i�J h$S"�8$e(L/K)$), $l'=2��^n $!%�c��� we� A# %*� �<��R�= &d3����T_nzt:��~u�m��6L  $H/\ok*V $Tc0\supset (\ol/Y \ol)��4���#& ); b���Ew&h monomorphism $g:H_K\to\ke6. 6�N�at�$el ?&/ )�FE`Z/g "/ �/ � to�.A�$ $m=1$>ŭ�� esAo ��%,�t$B} (thougre6��u���!*� way). I ]quite im6#��a_!^program� "tam� wild&us by mea ! Hopf� gebras". ���)waNhof:onaR $p^r�trunc��4 Barsotti-Ta�ff.:L r�A�Z!�b� n�of U�4A���&��%�"e){ �&�� U)�02}. Na�[ �&�new;�G�s divisibleD �.4F $ N� > � 'Aalk"':' re5'. Us!%] ��� ��D2�% � �9"X+t j!2a j�:-m��on�l�" posi�&answer��"�h��.!p. Lon, which B. Conrad Q -�c�attribut�SLo N. Katz. Two more�&an!%�%2�%&}�E0 InU�59Lͣs A%BA�  A seem�� veniA�'!� corresp��ng �$l$2�a.�sz1}, �szT � �r� beA'"� i!�5Rpr�*t�H� � =%�$t!��it� aly;��par % , no analogu1B{ know�*�a�usap2� >s���%(��lyBs) much �e�%�t�y�k1S c� �u.�we �(to] `ٮarg}) toѵ� On��DEH{seqa�out ui� ��&s (eve"y!��8F�&� IDc%f�reade�n")� y�m�a� nei}-:��Jf 32 n �t�.� fBredgreb}m��) Yu. Zarhi�� A�his athe�%wN�*� t� f. W. Mes%p�-us*remark-2a}M keep%z�0AP&�  (��%a\�%s�%�%�'D, � ,� �"r}%�9 \ovl�"�Bs B3' $\gm.- �"�%2-pi\in 4b&uni�tiz�el6  z6V$t=�&�&�PX=(X_i)=X_1,\dots,X_m�x�[al�tb�)  ��{#?>& @� ?)� �$ $\la_F=(4i(X)),\ 1\le i5� kgarith$ � @exp_F�%�? to l.(wa ��-to ��ozI��"B!a ' ��' �(b�fault)� q �'#S"�-��.C�annihi" by��M&pGS/\ol$^�� _�.� 2[!N�&P $�/=_p})�ll1�!"�> �B)��";>c �~! 3car ��a (posW y�Pn-�) hA�a�M-Tby $M_{m\times n}(\ga)1 ^ E� $-ma , $\ga$; $M_m:=Mm Mv)-K.:s $S,T� w+( $S\nde T$ =(��*(.?�T$�?�tBi� s�*N&� $f:S\to/hs njyve �(he(  f�$��U%�"., �*composa� summand�8U�ly%�e~--��'k�(�<M!; A6�$ii�ed[� o�Bf $[p]m�,an isogeny, �!hiW-0o.kernel $b;aF:F!! v�2��  !Dk! >� b�ch�.� z�2., �� �aj):!���Dif_ isQd. $Pea� A! FP���!M��[2R!��a2 �*we M�HE�!GfA�>�%�\ke [p^r%��?$r>0$� ~,�!m�T�WdZ �!�F�A )� -N2(in2� ��.�)�M�N�%�s�Kis BMend&1�({�is;C&N �.�1}�Di w&ee (dif�$���)Ec�3cal� wory�ႅEs�q��MIult of�A%��'"(��asf ve a fewB !(���{�3b��~n:HA).�!8�:��a� $Q���$��(Q�Ÿ�4�*k&i+ 0$\z\lan\bff,   a\ra bv ra$ (e�$aa Qa�� � n6� ser�� >$polynomial� -� &�r  :� align} � � �b�=  \tt8!K^ }a,b�;\ �\bv=p\\ ? �bv=\bv ^p\ra;\ Jl62;=@ 'x.jny } )2]+E� �+ H\ +\sum_{n>0} \bv^n Yr�-n}(a,b)d u^n,�bel{sum}�)�$�!�)� M9)As=zI�.sq� 16.2� ne�3perty V(0,x)= c(x,0)=0�naturay6&,(C��� vali�)� -�-!- ! IIn1} $\bv$GI��, $V_p� !#> $F_pGSiH� �=J-let��ny͛� U4ed 1�lso:=. If ͕e�u�aan-e%|6QTstructure on $P[[\de]]�0-y way:%�$f=I3@i\ge 0} c_i\de^i A�B,\M�$��� e $�$ f=f \de;\EU QA� pc_i^{i-1}#E�A� ( a^{p^i}w .$$ ? %"�at �!5��1k�q��is; if X !X /��-n�)n $M/a�M$ _aUV5;�2)vm�E'Ted via $$a\cdot (x\modJ)�+�x  $�A  $x!P� ��mingred���acљ��� yb� �1 curv7��.� $F/Q�~$iJ) can )�Me U6P$F(x^iQ[[x]])=\ke (F(  /x^i))$ e%�typ�[ (a�9)h � )%�� dir'E�%�O �(x z$. 3iscr�itZlicitI��C.$Q�!&) -freac� $h!�*$4,A}[[\Delta]]�%E6 coe�)%z$h ���' $h_{i}mLluL {il} O^�c in&�4A}�[� fineњY��}\l��8ap} h(x)=(h_i(x>�,�6�� }h_i�>0} u xajl�2a NowQ=\��M% =\{f!&L�O ^m: (f�\in \olE)^m\}$B%?�_4 $�u a�lBD_F\iff Y�i}d� d�aD��*�:���012� }, �^2��3"�5pr1vmcart}G0! �C�4E��b�.$= ;!E�*�'�Z�go�>��� �"]su"+ #9�! B (,)dL\dim F_i=m_i,\ i=1,2� have $� (D_{F_1},2})=A!��_2m_1�%: A%1}� t 2}��3. ��f:F_1�_2�7f\�& AX� ��g Bg giei�assoc�,d map $f_*:v1}e 2}%\�*�&on�$A!4.)� �\ol^m\��de5 �� �xr0*2, &�=�0>�?�+Ug4>Y;tT*�,P}PA�� t P=�I"AV= / \cap}d�6�U! * � \to m�xLe^m:m8fa*2� /x^2&$� A�induce�C apB <G*� � pro au�*kll�ze�$��b�.��\&�( $D=!~�m�# , $D ^m%m�0U i�# H�ne�B#_reaso%�in %�V !suflc} x) ��a larg�5�e,61�� ol ((mod�  M)=M <$  � j. More�:le�5hp�!k a �X_{�a� m_{0\le j j a_{ij}�_iAo .�\is.V M=�� )� R�!a<1D_F,\ �i~e_i� :h ($e_i=(0 0)q� $iD)basic vel")�a�� i_%�{Sy""�nz�s} "���r~�;A���Zq_�1is�!ialB�a:� *b � ��a�tE](�)Uc :0/�? \pi!� N ��9%1��� m F=�� be�nt+�a6u8( (co%() Dieud�&[)*%��FAKW!<U by $F_\pi�}�-&V�  (X,Y)=�8ob (\pi X,\pi Y� It .*�  ob �4l�<t�/�E���� p ] �Eo�.))� &Y&�MS.&&lemQ5do� 1.)�.�D_F�ɻ \pi}!!2."s\pdpI��2"b �>e*�oof f�4n�/um� �kjs6� .�)*&�  )�# G&^&"M �Wj�J m,\ � �Hl} X_jb  �$ba�b�k );\ � 9ol� �2��Fs�6�. +�d �d���0{�`ͦN� Similarl�pi\ob!�A}afb_:E{E�}YA !".. �Bq��2,Af3 $A���E 5�ca>6A(� 2O8@]M����<� !M � r�2V � x� \X=��RX E }\piAj-1�c�1�Np�.$$ H�U�5./*A 23!2. Easy�`F��;��� �e</� same�!�y�"P !\fulfill�E�a�� i��y,z�)�$zI� y��.�& ye)� I�bR ye?A�� n $z  > �m�"� � a} z�maf�B"+k k e��i pi�.�)�!<���6 con��� �$lyFC $l$)equA-z_l,r_l$.v z=z_l+��($ ��#&� �( !�a})�$��l}$A�=&S9 �j!�| $r_l!�vl��A�WTart Nz_0=y!�r_0=z-y#$Now suppos��"#b�{l,i}I]$�w$.z(!7#5E�d�J  $���dAfla�\re�a��4acc%g�g-(t� ^l �cQ� (e�!JllA��n��)A�)= %=DU�6 B+2:9 +s_lm�$ $s9�{l+1})��d�may takz_"E3F�2�6}Z���!6��r�g"�, p*N)N(the limit y�Ir!asser��mC}(�V WR twis� p� "� KvSbv']]M �!ii�M /e2��Fs%� �ru� x� �x^p� E�w#.�H\mw�"|4�  '� �a��:) ).-@y:$Ma q%W�M� !d�=p=!r� Z 'l�1m0S.t%��c�@VV���U��Jb 6��� $ in�.�� z=(z_i� W^ $�a$z �Z j z_� �; o)$$(z)�i{j�!�jeC =�I�&�9 $(z_1+z_2G\neq  +( !�W.c$a topology9!A�w:(� n�/bourhoo! $0$ 52 $V^iW$. O� ,�s_i��<n $!A1 sum (s_i�$�0#D(!��b-�_.�naya}�XM�$W$&TERk�5PA{ set $Y=(Xv=\{)b;\ ��X�2F2��aY-�*3 ��P^Jnu@.p1] _X$�2r$K$u,u'qs�)�$(u�(y+ ��{(u' - . &J� �A7rE�A�� �Aza&����Eq :Ye�� '>-�3.��X��� \setminus�})-?uBW^%Y21 e$-)�b�9F�y�ks# �!� �)� L�5# F�7!)"�$us&$ �1����� 6� > b9i}%F� ,��:�lim_id=0)�any $/$(b_lA1� i (r�=aiM�D!�A7lX��s& O " {0,0}=z!�r i��.�� � R \olv,\ c! a�!� �!(c�(a�L���Q"� �V eqy}� �Y� Y a+ ������ G �-MX4-�YZEM�� }*C�4A]an�!Z{� =b_l)���1�$�deed, 2� � � $!�H!-�l ��S .$� �and�&a����2 $(wT,iKEe�$!�A8{j_{li}!l);:"bff!�-iE`(X�� ach $ >�lgreat41han6 3,E� %=\infty@!�2MA�+�=�A� LasbwUke $u=T l b_ *��D��ש Pu�i �5�8$u$)�is %gruenM0$y$q�bv N.�2O!q$u'%mrIt��u�j replacE�2$$+$ signs �-^�!m,bv]� $. P� 1a�t&, Y\pm2&��� EIia? ). I>I��1/1���DqV Y�^d�E&ld� W^m;\ aj^m � ff (d)" "�!L{l� Abd��� "T�� ( A��A. �"� !�A 1�A�xists a "�$u4���f�� $(u���\le i�{j�jձ� u_{i� �eq^��:;l| Q�8 %��8!! ()E�!A{us)5��!\mwm�!+ ��6�Hv7S���M�6<):�U� �� ��:�2�=6;� :�dZ�In orL2>1assH3�\notin�o�_wjZ AGfacYaK(2�X)aZX=6#%\�)y Oort�5+"�(*(eSS l�Z.#� ol$; /10� 8-� G�W~7re�W��byJ/��/NA+s�d_( (F)=%_(�[C(GIj%0e;)� oo}A�*B ��%=4d.*4} c.to �Ou"wel�/q!d�� !�cat��\)( ��G2b/.4.'?;�" �W?&�G!Wf�>x��s"+}$ �9=�_�Z�&� {Clo}S*J and*�,!,s�x(clo&� �Z play�� OO ro;2X'�7? 7A!v6� $M �t N� 7-M)N$��� � M,��  4h�Z  M$�=% M$ a {\bf �}�K�$N�[�z1lA#Ded @"�A} \ns� ^/$N$q:�7w^M-�)� = �s�2&+$)"[�"4].��0s�� -z�� m)�I1� M_i�M�  $�I�!$\bigcap� in I} 0 M-2sM_2 D_1\ M_1 F!5+"&�'_2Q Ft>! /nde M B4Gxf:Na�O%�Q!��1,AT8O � $f\ob(M)%�� !%�a:�!�, $O�A�w� ��$\cl_N(O-smallestMhP:cN$�"�?$O�>1["�0 car * >-.<T+! ws�:�s Q>({N/M}\ns=N/%��wek)!��&�D�Q��;aS2�x�(�Osc} I�R?���� b��i�\padE�A�F�� !iaUe-to-� "#<� �2:iE�HSAj2m%=V , $NE<Hn ��1SMhW*N\�J C(S/H( 3o=~0e�5ex��" 4(as fppf-sheav!��P! inclu�0k/"52"])�l巭�( e:c� � !�IIImJ��TmJ.N"-5UG ke f_*=C(*f=f_*A �� d2�hom"N$c�&��4"�)�z�l>\IVxMM�-���5x��!#� $1�F*a0348#al l[�!1V �c� $�$,�$G�cT?i� :genRd� �V%u��*%�$_F�m�?a_$"$d�$,! Ae=^�Yec � s I-!�:�(� , IVYV:#RI )4 slight�W" d! aC91P="�3� � ZX!;*CC!�2�_e�� !42�Gc-"�!of6? in "DEth�E2�!de�& 2 H�3-3�ZA�us�a� p�/:���*X Fo"e?&�!%��zas��A�7a���.i>cS!��@a7e* i�.XD�:*�R1CA�&�!a�&� &��"&/!�u2length �*-���i1"* � ��GZ0pi M=\{0< �)M=��Me  M�;�5I=xF2*9�J� �"uchQ�^)be�A4'i���f$?+b(��'0��� II $�� �7-�am6�ca4�T�if�)"�8 n ad�h�"!�9�A�I? ^r M��A1��d g</p*F�E{w'>-�-�)  .�a�T�(Z�iin!�1%t3�KQ� nec}!%S%�6SD0 f�re�;K �I��5x ��N8 law%"Y$"�- ERok��$ " �@=D_G/(\de D_G+AD_!���J�, 2�# �+nde6� `s AJ�(1as}� aligned} f�\\ =(D_G�\de)/(�-��+ ^m/A�(�\E� ɘa��N �[&&~A�ro rp E~pnot �E�avur��'"��I�C$. �&}K�r�Kts!�6�K$Tay:�2�"!`cy�2=�: dH'��1"a7A4Qѡs�0 :�M$�)*�QJw��� M=� �cf�)4:y.�# ��4=m�"� 8$"�D_F/Ca��<C�I��. �Nweai�'at"Dch�0e S aN� We4re$a�( s $l"�Gl_m��E(�d)s%l$-geneEp����Yeck �'�"�1 exq�F^]c�� 2�$l�"94B�1l_F�) I!�6�=� $�7�c =�x= �%i} $9�l_i+Vx_1s!->31K� Repea'fprocedu& r$ t�Fwe6$x$b#m(6�B$ave&�$� �3):�j�o�6:�=Q$�"M� Aen���m�rmE%�) *x->V- ���. ]*u��� 2eT$x=�*�Q���U$�!�J' a�6��_p9�� W1�^��fr ,fc=� kb06�F�kAW l_k &� 2�{@ 27.7a�@6:� r� law�@]�\v  (5oplus A  e_i)/I?�(%Je_iI!!-� �� e_ki!(��e�.� &�*h�z��Ls:Z.S6� ;.� $h 2 �$��� maps�d�3o�;6�*l���*�Vhd onto&k � ";� ke h���.�C���n�h#w� ��!�S*� �(i�Bn iY!bE.6eF�80 ���!co*��H��-lG.�Sw"m�!\!Bline{�Uk}� Ag@@*�cAh*  �r%� mw$.6� BZ$^�C1a)Nz��d]"|)�xI�AZk �E(!0:vE2�d��Oa _;$U�$!O>� �4�A+5�f�h���Lx $B=�-k)iere8 {k"�?-+Fp�{jV$tFdeQ�&�[skew- �$W'=U((V))'��i\gg -p$Nic!Pb %Rh�F%� $W'WeN,�� . LaurD$.AJ $U� :9=E�Q��- $u^p�#�-u,\ u�#Ua�A�o�c� @9*H:�,I�k �,�')%+ z_i!#E��P� v�m� ��Q�Ne  �$Bb��choicI�!.expan]��͌�: v<��fix; numb"|$i" i_vjCt�]r�Pon2mcolumns�!i_G2 B2�#A�aA� W'$-zpendenta\2��o��\�<&K0Aspai�\�ny>�! c*^9um�$�1 W' K)\�>I)�]X$; * $(-)��b)>!�(7%�$W'�".�! \� ~v $XNh��A�X� t XMFbv N*,|>-# �(!  IB4�b!Z1�-�9[$�,��� �aYw  0>W(�ny>x�.48 �R'h4�$�1~P��| � $b=b_hI�$hO$\Ae[ )3�J &)WN m M�;$ s*Gc�[$b�R�2 2��E�(>t\2-hdE�b[BE�$Y=A"�X��se!o�1!k>�>�YA7T6���j���V+)��>�.�Q7�7n� `O\ns �.�= EmwI�.s �ot� . �Wrs B'�.Y2+a� CW:s+ $y�&I���t,\�Tin o1Wq^zI1A�  both ��g2�!�g�(o!H-X� $?-z)�$G'>uz�Bjg�^.�6wg) i=�-!!�8LJ1!�Eɱ.>�d�:wdw-(b �pple�:�>d$ $z=g�y=dJ*b"g �+�5$b'.� YA%� ūA��`�C��v� T� m],m�$B C�t�_4 �U,'e>"�J$b�3,Z�%m���� Ay!{*�C$could be s�f�Qby�[ a",)� u M�2 gP���$u>0$!��%>@(.ru�4�im ��zF�u2. An�wa�/�X5{2���a map .G\t� of (~c�u6� )8"�a�!?� � ��N �E�!+"s I1 --�Tk%� n��!�z*"�� )�w%P&"���mcs(vssDWadjoioEo&~z�� �dn!� y=x�1$C"8e� G})q �N�A:�!.6� f_%($N R�Kro�~ �����_8�E95_�d��=k=/V 4Y� Q� A�',]�$�fe|"��� �#� $^.�ie 2#8en� � I%� �g�7� mb�A0u�J#m��y� h�6?� >�&A�mo K�( "�>2}%�S�=;L^@<t��� �x �  x=p x_�EB�d'R"� p^dg 1R);Ir #"�F6*qg 2A�w iA3Gn-"2sd+s�?6�..eDan :E)�0!�/( ��I0 Mwmwa��E ��$u=r+gc%݅�i:V\,+ !� /p^uz.� e����I���)�� [p^u�[� DF ��4.9�hqB �J ,6�A%sII%u2�c� &-F=rre@g&�6�S:)�41f�m!�� �� "�*�C��aiB�Շ"b�<Iť"�� ��� �N�b��0� �!y n������$F,h$� kMb*!w� �%�Im4F��%�E�a�!;et E��M<� � *�%, \7 as})A�iQ !� �n =(�fz.m�}��""�* �,E!���� � . 7EsVAMqi�cIqj {-r}I=[�1 54> E��B .�N*e>�& <1�  p�*�(44 for "pj"�3>w*&� pr}�+S,T Ve�X!v/(ext^1(S,T)= _{�}(�$, C(T�$ Hề�*Z!J� �[% sa �.�p2�3 B1@!s�Has alway��4p�a��v$T��B�<lsfca���6 *� �  I MLG� BBt rv{E�"�. 6� Q�F�J!��.�9�%to 0$�F#�6*� �f��^�I1 w  �"�  $m&v|A4 � is r�--��#wem��'"�&4a*X*x�KMy��4 � ( 7I2a�f_"��i��+, �$E� 1 �^i M*; �%|�. ��1AHBU U6� ow9��)q&�$x� �3 '!��P���/w5q�Mn&6&�l�3:�,�=l(M���<cl>0'M"':�!cl_!�(�g.� )\}=�'�4�� �Gm� 2�/hmĖa"�����.ſB%{D�*8;^�a�m��*��)U }�&��&�]6�� 6�$TS� "�.���.�H�N�$ tgs}6BX �?!� �oth�#!$�7{\͚H. (,Lbj)mj�$J%&�b � N ��4%��"�:r0rtss*�@h67���.v&�v�h .-.V�T2n� l&�e�fF(suit��� ned)��o%9S_P=S\�#_{C��}  �Y�Y TS\o *- Pe[re"*a ny (g�ial�(l)br�d�0� <*�'F)�B2� "E�)��bx^"�1)��RL its */ �g%�5�p"}\d-�EuisRkj��_0�,_0Ei $S*��y�EL!�A .�2�5�/2+6 ed ���-�$.wi 6M�h5Cng�s�!J�mb�-�f�H\to w J-%���C[ �� �4s2�Fk7"�7�Y�\ &�+d"se"jPQ��Œ ��2�H� t S$��� A�l@3�TH��D  -.'SF�+i �9$H=� � 6� �V@ !) � �u��ia�*&� �p��Ptem!�� S_0t��]U�sm� w[y�o �6i_��n>XiIda�Li�j) w�@ J_F$.h"�:i e� >�Y/J_F^2%��co6/!�F�t�L) i؎*I =eT� �_ `, �/TF'3 (F(xstar�d ݟN s����;�'�a��� 7:H"�H$Jia h^*JW1 More�$�$h^* J_G^2= > /��:"i �f �p"�$iZ] �\eIi�6� <i.�]�!A$pec� me@Eaq��D���|�6�t .�9squar�$2U2H%f'I�S do�sot]!� 'i�x�Q�`��f���.� �.�7}`_1}b_1qdd0>0 F�Au�_202a�MFtwo*�z&WF!t �b._F.w����*�|0Fa\G/ �I6� nF�� �&�%M^e .K;"y dia[���|�eAed"�n��aQ� dia-?�CD} S@>{}>>F_i@>h_i>> G_i\\ @VV{\id_S}V }V}V\\ 3@ >h>> G2 M; r a rowwRX .X I`��1!�.��4?F Ofo��ir\�QT6��f"N �mWaI(�~��.8)2�0�en6��-oo.O�`5u�F�": 5\qibZ� F_1)�A�)�f59�T %A� G_2)�J�� %E5�.nɟe�'4� )�is & 2�a�6`J��6B"��&]v GCH��� $C(H�l")">P '>(��+0$�3Ta�UAW�WC f��2a�C 5?is zerX.*Z�!~C�ۇ�We �63[ejh$� $g\circ i h��� $g�;�*� %1&7 O��f�c.� f_L�S_L�#ibiV{x�sL7/ epime,c�� Bl ray}�(w�=� �d�g6� %Xg�C �ve,�o may 2�7f��Aur�� $g=���eIq cyit�e_*-Ji7E0 B��n�m7�#�!�IfA`h�ICx$"� �� B!k&E�Tthe�Ieq TB� TH$;"U� $TB$ �to� �o!D�#TRT�:=-�a�>m%�s7i:��I�$.',��L=AW6k2�� iZMaLn� %a1,\ awea0y�z=!y,\ d(e�&� am�VPx=4j�nc�.. "$'2�c!.��^!�X~$V2J��=�zq� Raynaud V><��!?�%�� t�.WmKm=,�LE�$L$-ir;�(�3�%� �UZ�&=lE:SL�=Re���i)%<�I�[�m R��$p-��F� Ad,b:�83[x p-ax��"aJ^lHyse$:�Fw t�%F~�i� ��(xa�$(a?�J /a�>/&\ $� ���E�� �bx *� a\mid b$;M$ $b\sim a$�).inK�>o� "�> a�}`�!V!� SJ�D $d=l{\#S})U$lc2�� 6� , $d valu� !�!Wd � imin��2:cҋrWA �>T�*I4��s Tate'/��?a[ $d�'�B)M�)�ta�2� �Bm! dime�2�2: }*�MtQ� ưc II^{ALt�:ɟ&the"�Mdimg��M&B numc3�T� �T�]a*�(�{�H�N$��&+ i,r�DN�, �)��FSII_qH���!-�I_i�>-HrR�F$F:$>`,!�BHTSq�az*"a%�:"IDR comb�+2ipdF�? _qxI��!te)�tH _{\oxY_:he6ݐa" "� I�Xɧ��1� _�!&|?�\Fib2�a�Lp�-yC��99�>`2oA&can�\�.!R�*�iN� ; ye� �/se ine��is��mor��ult%��p�pѲl��&)�*^z�>3B}6m� i^Wr&xDa*�l�"Qv�Ypr���v��I1=I3!(!%)�� dA8�./ �@-.�s� |d6��<.�Yd�0i~4 e sh^0�4A!�!�8a0ry"5�2"RN:��2�� 9D9-��<;.�$��p~#smXI� "�Des��;�3 >y���o�NIa&69Y"��as�=#/ ��#� wh�5an :���poO�J6`��;6 ;A�A���� {l'}��.!�|$I:w�ify�f��&a�*M Q�C� ��"9W*D A�Q ud�R��@J| s<[6��  )! 'p. *�~3!��e:��s:� ,r�/ ofte! �f"�fw re ���\ *FU2�!���~nMUj �JI_ ���:�V)]�w� $S�XS� re"� �Ast"� sens�q ] $6E �E� \��` K�&�>�) �� H$&WAmm|?I�()q�Zau�2Ց��ѫi�:��!R� (��by) ).��H�"D ��]/ */.�^��Q� gf} �"�'Q 2�,�s $g:S�Tv �krf��2:M�wJ��=� n $h" q 5��L=p^s �-EQ� C�[W�u�.$��)���̀-�is sharp]2!�� )�s$e�U}�'.�$e=e_L0�6: ai!I5��hNm� fY�5�x#2� 2 *�M�"� i�ll�o�)�'*� �ofM�re}; }$'s methods����b�`9�\e�S�E3em��͎ �2�I* ^K�� ��Y�me^� anIˁ�o~ &�{�4�-� &/#oldde} F� u�R� Yl.2"* ��-�� �4�:i� _L=FZ�$�% sK$9^>o:p� viU}iq$Z�� �K*�3�M �q�cong} Z��5IT%KR%L xF_Ld@6��� t]_Z] T:�k VK$ �)� �0 $T"�42�s""A�b&�HAp. (�ه�2�A�&�L< $T�me�\�\ol-�.[p�{F}֠n%m�F'!yAq�� =M $F'��endA�e(JAJ�p-J6��.6���9�� ;�%.2p a6d� ַ��27A�Y M� � ClaJBmdegr}i�?v!��6�M U�߭ $Yi�N�bN�&8��.6�- $V2�U�I�Y2q\spe L$ I$�)Gq. �Y$,J &��":j��i�ڝ�*.N &�8: �X�R9$Z7��.�@!Z:�y�vzKu�HE��h.���*q\� �$^m*5:�mv��*� �aIS&sr>�"@�s.o2D()sB.X��u�U�4z I �F2$���O�lH=[\ke p%]_{Z,�r�:�ei2` ),5sFt%26�I:fw>�4�.�A���D �&�� . 6>MN��26c� $h:I2��kӒ t]_YF6�i6�2)p^s� We[(a� * � t4�� $S_LK'h_L$; �XR); $T=H/})O*�H�e�Ek%qoe��0#uF$E�^rSe.to 5T 0$; ��$ �-��͉[V �p^s�]� � =0$;�A T*�>f*�s*�*�J/:�D E�>EFr�, �� $TT:�t�3F 9U4�B�U6; 8 �G=)U-*~5n�'�]f�n6s �@6�F�@ �2��\FPC�G Q[� ���(]a)i �� !mh 7.5.�D� U"�� � �n�nE�q �^�^p� � 2R�V��z^v�k��k/��\okr6� >��.ł)�6�>�&P���d2q"�E��%&��*"� H$�C�a�P��U.�2� [�RA]k�t V+d��*+Q*�.����I! i:H/�� ^s]_2� "�e*J0W6 X��&�7m"� .2T2����o��. B 2� ��'�QT H�3 �=%MNO y )6thR�|�<$�i�S�gw��9;2FCH$ ����Th9#$�(T)�P @ $H/T�$�, x�1�>v/��/T��A 7R2itself:5 2 Dua���R�N��×bele A�"�q*��Tq��%�� v~�A��"��L � �GgcnΖ*�uL. 8+VU`J��6�RN�GL@ V'K�W �y� d&y�ʖ%l to'�AQV�0!�6�-i�L�6L $V_f�;t-���I>b -0)*|�F J y� ON\'eron�ed7V$-  )*���f2�A]&R�d"Z"� 1a�"a�"�7�m) �}���a���6.�C.�2�)Mv-��(c+H�d�^�!is��Ih%!Z�-Ŋ�O�We�e BEX'-g<�Fm�is 25� �#�T �"�7�ii�i&0�I<KEvn!bf�!$V_{fK}2�K}� L�!&��l�,AdF�A�TS E��a��K!+(a5�'O _m<f2].&U��2eE _p$ 2�6'�!}Q�JM Y�R�0 �'_"��DR<1�$V'��'!Wei��iq"����R 4*"� !e� V_p/e�A�`�_�S7�E�E_�L:G �� As N�5�AH�*@8.aI�:��2G�<&!-F�� (�@:CEaa�m�5I�jA!\�6�4in�c!�{ ���r�&!_�'V_!��EWv&pb��tp$ V'_t Dto��!��!�)(FC� Azy�r� v�..�| $V_tWX�%E|a8By�  5.LF6 @.�wGAJfQWAH�{tFY�^,)7�`E�D0�3Y�dcf$��h�.�Du�'\<-�I�is��.x��������L 9$ (�f\ol�,$D/z��� q�LNՎex �/%�"7$D=1��}%�e-�K����H��K}$� \al:V� 9�"�gpolari�vem�)!iiuEr!���, R�TT.�;��m\beta:! ��oAK��� �F#%$"L@$K6�!�i.P��7��EgB?�)�rR0 aG�''2}�K �$Z'=Z/S �J-�6}�:��\�  29%�!�� b���)o69qr�J�!�2�, �mr"��:A_K}$��ID���&'�'��A��|�~_6�%] - $V_{pKaT!qGFiq� .!h 6��-�chۓ $2.� .�5.13c8�r��%�bP -�K���(x#"�Q�f���&�$�Ti��%e�_��$V_m$�*toroid��6-{K,N] e�,� i? � 2= CR�r6�:6�#s���}5.9 n�.��5FN mN�,6� >���5"�w";V'����� "�� F� �.�a�"�)� 8N.���b I��I�RA| ;V�Y�,�%K0Y_��TA�N} e6 >g3"B�i(i542�\`�<.dq>�N2By ig��(� QualC2co%.d2 �-&N{ K��-ZSmt�+�T'wp���(sa��"  -k�~�=$x�llowed�r1r�g"��0"�{&��.�K on{F1*C��= q ��ry#oa�H {P�� A�&�!"A�GJ� adop� *�J��.���Q �!v�l]_{G� "�% ��N��&��Q�1(Eis .NL�QP*� !Jis6� �ZV,�VB[ in}$��e���7finc *� KZFN�Bi�� .6�6c�A� � ��� ���%6�p�v �6�m)�L .H�F�!o�2=�6H$)�&�, 3 prei�� ��nq7Q1F @ "�jɱ$(H/H_0)�&i�"c �SB�&��2A'� I[m,U�\�%B&�P���p^s ��r�{ fact�g�5t5��~-e�jO:6�H�m![�1c"� ��)f%�pk��Vn F2A �CFa� �DS.c���-wAD�T7� F��5OP${H"�nde {H_0���ce0��� in  ��r! ��Yp�dJhA ?�� F��gLj�N�/ ���J !��a 2E !�Z( �6k�.��s  2H OB*�'!?'� � "���F ")k$��e�  �fBsr)(or just�inary)-A�=� ��ts.��/8��`��fN�&n%[Žar�*t�y� N�*exampl�=R& ell7�c���eH�&��or su��ingular"����*se]�*E#lO^E78&�\asuˡon4A"�mt�3:�y.� 1�- ��1}c�4v�=nT�&)S!���f� FU A�~ ZB �UO`�ru��2"6:yY^vl�>A>� >1� 2Qt]I�ood9��nA%r B��. }"H �� } I g�\*  < (2)eF!�tT$�K\B#={F� ��r"�Zl.�Fl�i�� � ��2�1)n�#��!��-a�C$�/th&� >V� ui �0ij>��*� �#sh�-t])Skis:;ōn MATlso:�r2"7; 2�;p����UA�d� UGE;:G��&��?�U��8�2w3)"H6�:"-&8fO �< h@t~:��ss af u"��-�A��Eo $M$ wEQ��� "�$S�� $H'_A�m�@ & !Aa �1m_*�`r}��{n_i}v; � n_i,TK��.,,A�- B� $B=AT< ((x+1)^{p [-1�� nd $J(B)=�<�  $T.Y}�!A�!�A9j TH_{n% ()l'} )^m "�[!?adفvK2 �E62� r=mD ! =l'*fdrg us ~(�l&�� (3�R�_a�&� ��5�� �X|�WÉ�$H_A= 2hA��*!>(%A!#M�a��y"�s��E�$M*&�B�'M�M/s]�:Ln=K$�.�-IZ�*^�#is��'>��&���&�2�!�!W\B% AG�W�7m� �&�C�w�NFt/:.��:�i6oeW��# R��a#�6'6;theHIA��F" l�'�tFE+�W��[a<\o@,&� ?,A� 2)$\iff$ �!H (�6A&� A)� !9�Vb );6'�/�+3SPa��.�,! �r � a:B*�* �l]_�'y��� f2a +c� IIa�*+�B�>(1- >!������ ��Vs =9ar��!� ��%.%"�thebibli�phy}{1ibitem����$ M. V., {L�] Le�d��:lem��se��t� � $p$-"� &X leRv�ə8s}// Doc. Math.���<. 5, P. 657--693a� \�01A�B�Expu4clA.y�.` �� d�A�;6�)�5si8"Il�idu�l<} (Russian)// Tr�:St. P\x burgskogo�W�he HObsh'estva, vol. 11�1--36,!5��2} �%�F aM*W6G M� � ��BR�I:e�6�+,I�'%dQ�5�g �YA�6� ie!� A�ap��in!@. Izv. Akad. Nauk�6��}B�(Vostokov, SE� ��lE�)�>�E�W hst. Steklova 241 (2003), Te � Chisel, A�Z i . Geom.%�843--67; transla� in@c\ IjU�3I�2 (241)G35--57� Q�clb} B,�C., {G.� p*z6s(�ou!�s e"J� filtr\'%� Ann.!��2. I�$52. no. 2�489--549!��o�<��B�>M��2� D�mS low ��c%�CnLie4�� . 1999. va(9.�239--3202�� G*�� A%S\'�5� de g\'eom��ri]%���7 I (Ex��IX)},�8�� ]�ŕ!!i�s,)"288. Sp� 0er-Verlag, Be�n�--Heidelberg--New York, 1972. %P. 313--52:���Hazew��M!T��]%V� �->s}Ά8.V mt} Mazur%��F JzCtX|%J-�via bi��4.} In: Arithme���(geometry, V��I, KgilTh., 35, Birkh\"auser Ba�n,MA!583E� 195--237,SzU�oA��`F��\'�@9��"a t$6%LQ�A�Indag�hEp37A}75Eu103--12!�wt}��u94 GayZa[ primHJiisSc��'Ecw� Norm�:s0 �e|4 � --21A�~ re}   ee!� J. P�xAppl.�L (1� v.132���179--1 5���Y{2I!ietcƖf. � F�� (Drie!�en!T 66) !% 158--183 �ޑ�%2� z} Zink Ta��m �ck&�UA`maler Gruppen}. Teubner-T!- ��A��fk 6!�BSB��G. , �hTsgesellschaft, Leipzig�84E�: >� # doc�}�2� E��+nvG���VWuʇt��omp� Ji � hla�$ mmut{�)��ve�F�M{<�J���4lso prove the �$ \newevemI� em}[ � ]{ }2( clai2&C2$propos3.PP20lemma.*L2$ corollary.(C:,njecture6- \ �)�&U6Iexampl2FE 2q@=@D"9Bqr!�k6E AR &T \author{Ivan CheltsovU@itle{On nodal sex$fivefold} ;ddress{�$abbing} \h0 t*{28 em}\=\kill Steklov Instit� Tof Mathematics \>Schoo� �\\ 8 Gubkin street, Moscow 117966 \>The Uni6 ty[HEdinburgh\\ Russia f\>K Buil , May Road\\ f> \>u8 EH9 3JZ, UK\\ e� tt{c-c(@yahoo.com} =\>�bII.1�@ed.ac.u!���-�|} %14E05 - Bir. Geom./Rat. maps 7 - b,aut.+Cremona 8 - re�alityJ40 - n-As, n>4 d FanoUJ7%�hypersurfaces %MATH ANNALEN MOK �I�LAv� abst�}� &� bi�( superrigid!�� non�.�� $bb{P}^{6}$&$degree $6$� y 4at most isolat� �ry dou�points. %n� \makee8��e�{Intro�$.} \label{ :i4} In many cas � known wayS9N�!��y\footZ {All  assumedQb��ive, n!T�}!��bb{C}$.}�tW 9� 1��&_ aE( �y with � inal.4bb{Q}$-factori�}ing�i �nd )rm{rk}\,�(rm{Pic}(V)=� Then� malled�ly �Oit#Hnot bi\-ra\-ti\-o\-��"p �ies: a $y $Y$ such=th i�xmorphism $\tau:Y\to Z$ whose ge l fihas neg6 Kodaira*�2�$dim}(Y)\ne�Z 0$;>e@of Picard rank $1U�1zynz is--re%�!$ $V$.!r9V� Nyy�9~Y=ly E?6�Bir%��Aut$.}. Me1ounter�Vs�,the L\"urotha5 blemob�Ayva�A� ���ofI�3��d (see \cite{IsMa71}). Morea#,RCi�a�yA prioriymethod!�DJ.Koll\'ar can be �i�@construct explici F�� va�(, but a pos� wreA�� one�s�A� ay�Ko96},- ,CoKoSm03}).}�� ��n�lyf�� $n$%my $n>34B��E��is%�ed��!�y��@:�a$itemize} \ Xsome smoAvj��Is80bPu96});%V����bX Pu88I Pu97VGr98aCPR oMe02Me!pJ}�1I2�Pu8oPu.oPu0�Ch. Pu01} Pu02� Pu03�dFEM03+Ch.Ch04}),)�2�)���):^�^<�cy��2y.% �A EJX� a2�AZ��V5e0 thatE�eO�ɯ�X$�z^R R�C0n $-K_{X}\sim��cal#{ "� }(1)\vert,$ci�y pŀE�5iO�j�2� �6� 2RjX�j� �CalLy94�I�a�ape2�e}�result." : "& :main}!6� 繸ly�^� D] �&m#�#w!��~\ref7 {is w �k �e .��,�En use�NKtoz� .�1�2�s92��52 :8le-EX):&D Q.! l $$ x_{0}^{4}(x_{1}^{2}+x_{2 3 4 5 6 )=H>6> > > > >6}6�\V� roj}\big�� [�4,\ldots,x_{6}]#).%��;� % le&�.� ,, which impl+ e�i�"a zf.My-�&�  (:plane-odd}�N��\sum_{i=!�2}a_{i%�06�)b^=0�\:\,%\w� $�&$���� homo 4ous polynomial� � 3D ne� $729G v� In *le�.�O� .�j�B� It should+ o� d ou����DjV� e�idered> R.m !&ralizzA�����& A� B3 qu c��B� .�2)� �6�Ű �j!relevant��B� �e�� � ~t�R"2c}���r��Tpf�p� .!�O smallskip� hor��gratefu�!�OI.Aliev, A.Corti, M.Grinenko, V.Is\-kov\-skikh, J.Park, Yu.Pro\-kho\-rov and V.Sku\ for fruitlcon�Es%l�wE� like�c�a: thankmrec#ej�U�eHhow;O eᮡig�5�/��K:6-n-sA]]�-5}�8a�"ed to JvQ  nd!�upY A�o r�B��8A Noek0--Fano--Iskov%t inkFr654}: "P ; "$  >r 6a !�t 0fB � �v� "� ��ly*�E)�"� O hol6� Co95})!?b&eFg No%P�4r"4a linear syste��� M}$ o �.��( base locus��cod"�%0at least $2$,�A 6@�Llog pair $(X, \gamma�)�e !) canonicalA��$ .�A�i� 1O�%6� .�&$� + Gu� &� Q}} 0$ %u�:Bs rest�M��#S V3.�.,\rho:X\dasha Y� �map�Iy!V�D%!2b�%��q-uURIK^H_5�YW���!��q�nDY� %� (�A� � & :� fA�M�� J�"���%U�+rm�f� �fib)� �MN6�us�B a.j& diagram* xy:d{ &&W\ar@{->}[ld]_{\alpha} rd]^�(ta}&&\\% &X 2rr2$rho}&&Y,&}]9�$W%�1J$ [ \bet reAi��al 1_s. : !�5�h()2�^D}E�# complete :�$|-rK_{Y}|$�:$ $r\gg 0$,�^6Q`/ Z`>�|� ^{*}(H)|$�Y �^�8 divisor on $Z$q��); aa� per transz*0�U�X�:�L D}$. Now +seUvF��9��f��id. S.�'��� BE������)7usn �+this *7 lead�A�ntradig.��5'BI>1s 2sA���)g N��dA�z 1}^{kz Ff B iE2Z=)+�M K_{WB�BJvakuYB2D:ul}� G�2� F_{j}e�a m�-exce� ;-E�, $< *n q�Z,e2 nonn��-��;.^�I($niU@ sufficiently big 2e�i�natura��9�$1=h^{0}\BiV�"O}!�G()�jMna!*%/)7)~B5�n��+n:F�n9�g)�but $��(Bi�h))=0$ s*6?�)ncea6!�impos%e��������^�1$ 2��� =1/re�us, we 2N��w)F;�it3 s from5 2.19���Ko91}� $.R.O=..k�{*�&p�{N5 �� B, q� $\mu>IB.�b9� s � mu�M��nd� B have�6: Ug.����X}+.QM:�,k}a^{\prime}��V��]2�F�u�i�./F�b2x�$i�#2 ( 65� F��$s6�6���B� =�a\psi:W*G U�G! �2bye�:|��W��24|e]�Z\circ-6-1�#Q0iso� , becau40&8 $nVb�d &h "+ �or 2Ml}n6O%�$�eff�!�A��2�(. Similarly�(gea�ps �M� ��3i�U�th6� ap*t an.4N e��p4&� T��uRl2# 2���F>�� , $OI�j# on $X@3B�� n=k� *�/E�+ � v�, $\pA�to blow up�$O"E g +2�Y, �Wf fx�-X $:�WQ�!�*3  $$ \pi���)B6B7+� ,rm{mult}_{O} /EB�A�y)'J+A� a6 -^7 >�3v"X)\geqsl|3�p!s�5 ډ�,"�  in��!�A�en ele+&%cal�7�slyv J� >1/2 C�C�!�i >� b&� 3.10�W Co00�E�" M�aD*ft>16�E&>n���@7 |:3 5�>\l1��$4% ���,�%� f  Replac!K!�>�������Q�Q}� �� X}'X)+1-/J )E,�� v P� �/er irCc� subv&Z� E$*�IN"7WE�WA�M$.�.�qicI'!��H� 6� :cE, )�#ElM�E�u]by.������AO &M��B�>���X {Mai^niesF� O#-&$� * %��M��E r;>d X"�*no 1�onents� r"�)��&�4"hpi:V\to N5 {%�V in�, �F �dle��:T.�T �Z)B�V$.a�E� ��E$A��_identif�ah���2��)}�:r�qA�>� � �a� � M})J�.E�!� z8n2\ �2�.C$. It sfX! �f@��dKBy�Z?-��2f ip 2a�� �{of m!A��7� ^S%�& 2I��!1���@M�ͺ bM�H�� Fh712�� X$ p=$ng through��3�. $i=1�$r-R 5=an�/ }2LS|� K%�2�� E� sam9 as| d�4�,he)NcV �!�� $\hat{S�%I H b�0��"�sJ;!*� s%�i R8 resp�ly�Gu!p>$�1t2���! 1}\cdot S�&)=2�1#'� )F�P\in E}2*_{P}(� Y2})Z.!1})�sj$ r-2}�&�,�5g& : � E�y %�s z�Y1#_{Zv�g �@�/��!�*I one� �5\'5 :�6-�$) s-I}I��?e�� i�ZF742^B-s .R�� �&nitqI�% �#nT ����Ŝ�v "Da"* XH e��<s �rm{Cl}(X� y�K3r�D$by"-6��6�!T*80"!,���*h) �TiɔnH*�>Yn$.t1�&�ס�u�myi�*i6na�M�MLM,} �� �l&m 8X, {\frac{1}{n}� �" >� -��� they-2)a pun{:d n�;borho82�.�j�*�%big&z(}2�EY Bw 6QLiy�O}F;>-a-[VJW��h�� z���az/w�� �=6c%*u �)"B3&e 7h s . So�%"�FB'=1 $$7 V}+VBE�6G$� �qL V<M#)+w(4- %:~O*M})I�Big)E.�  Pu� 0check{X}=\cap^,�3}��� $`cal{M}}� � &X}}U O%<anzJ9��$? a�~�4>vF���ro a�2Yku=��o/�� p�0*�.�4 �\pi}: xV}\to Z,*�A�p'GE 5Bx�&�%"O#A�1�hZ$ �V&$$-8pi}  ^{(}$ && V$>}[3$pi}0$ 7XJ4X3$�9o"K��� �X7�V2F� 82 1 *E!t6jhJ.p$p-1,� �9|=Ea �V-HM*u� ͹a�e2 Ci%})i36'0 )� wBM����.;<2n$, ���)wis��7&� � �?� X:�&� %'. )l&mVm�1Y-B}Mߡ�>���63 FAMA oJ:PNw)}!kB:�VS)x A!�K_n��w�u-1�w+� �  2 3�5[M}}+H�23�&��><őM�V}>�m�Q�B}�� JEN� epi}@�� X~�M}3&#�q��oexist�of Rq �3$\Omega^neq E:  }! ¡�� ���,V>�9�+i�b2/n-1)E)$�!�W>�W2� �$�#�cV~cA/��5)ʸM=)|:9 -�eq >�W�#6L=N.L :� 67)>0��R��$a{��}�eE�great.=%&�?$s among al�B�A�havEi". Apply� 17.4A�*�c���V�P-�p�w��atZu v\=0�Q�"6���e9�p����B�.�5M}en'Y�f){.j�l"� 1 1�O>� ��" 4E�2�V"�&w XR�.:���. e A!o#�[�T�2�� "�-ubs5Qin z6@co&2$3!�As!M�A-+sm�?�2J $Em�%�ab ^B �(� s Lef$tz!v2&Jv�&"1-u�>?%$)=4!�ThF(�����!&P �)-b��Y�Y$$E�W-B2�!2�}�!�}e��:�M)�N�E�Cter�&21m�)�v�>4�(24-nEub�+�� ��!��:\ S�!,.V V�iR�2�� U� 6��͍�>�$�  �+2�(nzE%l� @�U\5�� \DelX2U*A!�> *� 8 8A�"�� )� [� �H�\9�B�6V>YZ�� �doe2G�� .x &�a,@cyc�Y>� �"bL g}$h\�C.h bhDA�"2��FIwe a�^6(>�< �z9Ev6C%6)�R ~=>f�� �c3}u��W����2�r "��tu�8 � �i�6)"�/? � EÝUn">>�@�m"YF%r���6��-4z4��IB*a7 $\Lambd�] N�4}.q.A�stricD "�d>R*� �"��4 if >�.9� &�R�!Q��[Fb�cN8e �>�2yF�!�+-�"v���^^2�^2%65B>�M��&)� $. P�\bar{��i}=�6 �� &=;*�M>2Y�"��]E�, ��}.W��;.dD ��F�# �#"etilde�: �9  *6� 3ma��5arN$N�5�^ �z��_{) �I.2Brw�L�`�"�2�$# ɰ au� *E�:9��b�7;yCnXPR^ !4 Y 3�R$ ��)3�M}*@ 2n$b� O�nBS �.u va1���2 &�  8� �2h � ��+S2�z>��M�>H �� a*{9E�2?�6�I�-�.Z�*�D*�AmZY(\Xi� neq �aosH4r���� ( ?M�>j ��b�>*� FE�.�j�N+ Xi!�6��ccurve��R��A\�� -� "�#!㩞'j�^�#�@M� B�F� e2�o B� Xi1�s-Z ti8�Ff�0�.� �'>T��p)=Q:. .z�  >~*jXi.).�B���#B�%�a/� &�7� �^�F� 8.m)+��V�"�P"e�ρ�x::a }^� >�!>� i�Nf.v#6�#�(X"�"7(YrS�en A�N;M������S�m*NW���$:�U��N�D%�r�Dr� $��ʦQ+�& �D��P!U E$"NSt\ �a>� nk h4J���2�� Xi==cap��O" &3EI#61����v�()�$E� previ>Oarg{b��P�� ��K��2}"� �� >�zT����.�ͭ1�u�����F�ah�uJ$.�P:� dependK choiqgu�)%�erefor>� y�>4a�c_\n unde-q add3cal.LE:�:��we*�#:~ � " ��F��6� b � �&�&i2�6�>bo�N ry $6F� B��:�>�8A" R�iM}<"'R���3.B� :� qh�_���f�f�1�to�]6� � � 4 YVconclud�ա�oof:�F�Qly%s<%N�&�M!=�5b�OoXV.�+&�5~�5$� R`>��9P[x&�/�:g*�$�H]1��0 q3�c*�c*�c*�c*�c*�c*j � j "&E3*�6&�)�6�>)��)@"�#Bx^bi*� 6� � B��(c�r& �6_Y�*� 2n$. &�>" zH2))gr)e�L.):A)=�)�9��B.#j )�!1K_� )� )���:�(E$�vP1$K_d(��(�Rbn)�J�( a3�(�/ ��()�*� { �iR.�&�!��&��!;Q $'��iU V.VR'_ ٛ�rl  �RRZ��)2.| ��'R'f�)q-�J�WN�-O�*)l:�JI( "�$��I(�Y22a�/(�I^AIG-Q�K>yRq&% A J^�36��\1J{��Z�&&n{%��26%8Da. ��  !)��$�$�$:u���_ ԅ�nU:���!.t2�2� � V2� �l֮J�Ჩp �B�%�ӆ�@$2.V:�&FN�=0A�^U+ �"$Q��RRRA�u�BU+!��D.2�D��u��A)�r�'� +� +{ �&�(���a �� � �5�In�e^A%E/� I&�k�)Q_:M_��Bsu* N�._ ��|� �&�o,r1f:5%BD*�9��-5}%m|?zcrg9 la) by utB�"�_� Rt�"�;*>�K~^�$\breve !k�aN�I:�"�'h!��isA�a_�Paexy+ztB�dC}^{56Hf Spec�X� Hf ,y,z,t,u]E�aR5 >t;�!�-s �0by $x=y=z=t=u�A!� �haJ"n-�=6��#6��SJ���W. Name71f� !fb?7vKGJ��5b#%��t: $�8 � be�i�ucUo"�`"�81�4 :F� %�� R2!���2') @J� �� /� r� *�=�&B$(:�&�8185Za Bl6�C5XU  pJiYe <�*�. [e ovejE���L���.��x~�y�!.!rb�ed Wei*�DF(NAe�� i�NTv\P $x=t�1��y J�C��x}#.�f�����l:iRmTaG&-)� [+Uis"G��R� $�:�@>iGw i��]��} XE��*x2yNO 7AM� .4w!Py.&1.- �� �!|!�� "M"-.�^�6�ue�;�?e2(4 �VB�# 0��:�� )=O� j . [ , ��:�;� �A�N�( > X}, ��n�)$ *�o1=�!&�1�X{ Not5\R � �� �1��3con�4 /��&���4��T%CA6n~Jway!`de��=iz� K��E) E Inde�O�54�]"�>^6)&�XU}_{x&7)lgc `\�f!"rwc�^et # && && && ?W:J)�)r�c 6a�c|�c 5V G U.?tx�?Y llll�) Zps.u2d�1 v�dllZ"y� SW-�.ph2lr.~[>k�d V!j96X},�d2�y�llu�1�yF�+))�y}}!�%� �!�[rru61���"W .� &<no��b@qX%5m>*#,N� shea� �� 0&P�>Z�� n��6ov�xS� >NI.�"�"91�>=Aa�>�.@ 9#�X��v�xi� RU�RPM^�;h �phi.:� [MzQ� !w�� z�aɢ(�x&�4 n6q:B��N�Y�:6>NIv��u>>CN��8�BZZ.�&�$A* �=Q+W.8�Hx>y�5/U.�t](��3;byK$3|ion>� &� "��::w2�.�]�1 ,��all&UAN��Q�O�/"~">#(_ct1N� .}6T � \�`��a"� �o2a��,�F ah1|&f]1  nF*d�4�F SfS ^Z� }\oplu� �6(1���i �D�1ZR*!� ?r�%$m� An� "�� ���j{*n1Ym�)5�!�6' F�EP d��ۂ o��C"�w} x6H��J�.s ?yV?yR?r b �� )�5| �J���*^�u~*�� 2?nSo�u�Z��P9�a�J,-�con\-��� U�ZpAV��u�a�t�M e��5] &E!���<.�- ��m�J���C&�y�:6�=�_�)(��A �:A�do>90�5�)A�F)�.�D� ?5��7[>�s �.2�6@ � '� ��iv-�"\G]t��>v�,�bA{��Y n� ��:? t>?):? )!�&>a� 2Z |>�I)��a�D�I"C}�� @G"!�YSy} B�! c Yi.6"Y}(-AVv �%q�9)k*on��2�!N�}r͎95iC`�\O ��!i ai�/Bsa:�6| B"4y}=\varnothing ��7 >X�)B$Y�Xf�$���� _#&�<"y �'E�J�Ip>�-)j4A��5R5e��~s�cY�)�6�MWich8�c"�-5� ]A� [6�6Nc"ha� A�P"�g{^mga}F~a&x -ri���DN�ZA'2� F�ZL ��bBI���B���Af6>�3s+~�u�gp *�h=�i  1�s�_2 .�li}�&a�"GJJt|�4BU[�; �Q fݠompVb�$)aW2 a?l�Y�p&�/m��YA���s a n� $_:}1x.7-�anM� -mK]mLn=Z6\=.�*� ' X�'��gdJX.�ii$P-�s*�jA%$[�NJ, `t"�j�=v�9P)t��A1BN�B��G�A��2�>�M5� f*���)�5A�T%�(V^H�sH �UIR!%>"�' kY)�V%-fw0��`!v6�lE�&�x�c�3) �$FKD7?\��]j� \{O�aF \�9�'O}(F)>m)}]� $$ by *��~5!] ��a��2?i\f#V$�)J�JP%J�P]"�-Y�a��GF5Heq�&ra :!2ip�eies-of-EzE�-cut}5\�'%R1{�9Y)� 1�O}�/*()�~J�0�2�}>�4.=���. Or4MY handv�A $(Y^ PDF�a �au A�  $I :% � 4}&�u.�f"� $?�[$ N(P)\i"�N&5(a dv��4m�)}}=_{*%x[6�]� �)y� ~1.1�i 5i&�>Fy� &�6;1ƆU} .�4.7B �  �Q:*�A�~^!� l���a!j(PBg&) � i�� B�L*@`>�=�����n�e R�� $Li06� �2�l��# ���V I��*� #&2} }+L+"� �!A}.�B}�J1}{2}}L.E� T� "S;)���"��1 ��AeLxi:UZ�v= K����k�'b�vi�9ʍ�Z-����9m�XB�))6(�{K_{U}=�.� HP �L.<2rb3=Y%&B:�� E6�"!��H�Jk-'d^ $U$.xM�\MF8b 3*�g\�s�QA�.��M�!řw!U%.��k(�]N�)>6�6� � B�^�+q�*� O=BlYA9� 2 �H_�]"�wƽ2�d%Na��*� !E6` � �m�e��l!nu3e �;ed6UA$-� 2J�p� �Hthebibliography}{99�:ib�"�h� F.\,Call, G.\,Lyubeznik, \emph{A�ep�Y�;� GN�endieck'� eore"Dž para ������Z:�r]�$}, Contemp�� th. ͟Tbf{159} (1994), 15--18�;�l� I�@��On�  quin�n4�},C� . Sbornikj��(2000j39--162:l3bVlN&B� ���ur&n.���YqT�� .�!a"�� ��" �D� �/:�Ԥ!194}�3), 9!116:�4V�B*��gG� xUic tri!�sp��}, Izv-�|68 {)�7--206�o� A!�or �IMFϞz�&wF thre[� s af�XSarki�� , J. Alg.�� etry�!@1995), 223--254.%aQ9{F�S��"� 2�~d`c�geo~(}, L.M.S. L ��' Ser�Q�281)'Ai259--312:�Ko8�.� J.\,�, K.\,Sm#�)DRC,alE<��ly&y�ieehambridge.�P��, 20032,o[�.� M.\,MellaqgY65A�"� �a}�f(s I}, Amer.!�̤Y?126)A@7a�7612�PR2�AJ Pukhlikovn�\,Reid�f� x��!��175AE82�� 8 T.\,de\,FernexA\,Ein �Mustat90C�o� &� A�s��ap%��]p"��h�|sAt�2sUh10)N� 219--2362�T� !�"��MO=�aut"��e�aq2e*�aual�����s,7�a8 ity}, Ma��8��8�01--16�If� V.\,&����J� algebraic2 J. SovietI��3ł8a�8��862��B�Yua,anA i�T��2m�Y V�� L:��)���5B 86} (1971!A40��2�I��B�:F �j � i"��t5P mani���i�Sciy�82�496), 3528--3612v� .� et al.1� Flip%2 awa>����aL�30}Ast\'erisque5,21��1992). .��2}v�b�!lq�b (Sp�Her-Verlag, Berlin 1�2�-�e��SM,��s II:afNrt%of be�G�`�"y I:h. AnnY�33�)�w107--1229���mB'*���'f> � AInvent>?87ii7A03--32920k�a��F� &t�4:-V}, �8Akad. Nauk SSSRU152 �8), 22�M9.��bΛJ� ��H8ej 2DaZ���7-B�D472--49:�95Z��0E��AL V.A.�l[ Yu.I.�� ab��` �},�\-ceed� FSެ &ެ" 01 � 78--28:V97Z�j�2�s ŏsi�0 JQ|S2�5%�9A�21��2142��� B��*�V13� !� 4� 426���^EssentiB�!�*E�~YK � 73--100:��~"Ũ%i�2�� :A�he�,U5� � 6� $0), 883--96l ���� B� �Jb ine AngewQ;Q�54�L200�y55--79>2^�Y�6B+zv.8 *. 6- 42), no. 6, 124!�26:E�� 2���&�t>>Sb>193 20�445--47:G03�rE6B/V�11a�� 4e�4366��z 5�ite�d�Q�cz0A$!�E�&�67}E�3E��5A5��endB�R!&���kBR�2R� procY&�� \>�� \set"ϴ� }{16��%>�}{2ʴ%\2� =1.3$�top�=�, \hoffset=-1E�J��>��foɂ��cd*��} %*/�[r��n]{babel60�� pap,xypic�o�atl � keat�Z��E7/�]{H2(�*!��*}R �M2H�:Fld�*}JNpo��on6H*�:N 3*}b(.Ƶ.�C�ȵ6/&ʵ\$sf��FS2�.2J.��*�*1*}f&pr���bl��n&S��|2r&@�2�.@ 2? Rema:9�* )*}2�w,and{\mt}[1]{6��#1})"'EEE}{G& bb E>DDDD>AAAA>QQQ>ZZZ>CCC>OO�O>RR bb R>PPP>FF[F>TT.T>HH{H}> NN bb N>F}bbF|an=[)+t {an}BbSM%Phi"9 f smB"6!F Supp}AB{ �neY3� :O�  : Diff  :O^XBs Bs>66�  :Tord  :wt wt>E�aU:4Hom 5 :Exc  :Sq  : �  :E% :Gal  } %2�NE}{\#HDNEB down�/8llcorner #1 \lr :qup ,u.,uV,fr ,{ #1\��������ۤ&�ies} \�G4{\Large V.~A.~&} hU&��|dL \parshape=1 3cm 10}� noinÉ {\� \�1. v {\bf A�!v!d I�B >$rve��t in+!l � *W� , st{ng� %)"�G MHU�upR3 moder��roachLog Mf� Mode|5���pBis�[my talk �b�con���in Torin!� Octo'�o PisgO!�]sed�30�:h�erronl�FI Omy � publishc]EPro.�B�v�rr���+vc{1e ahuge{ 2,FC� �@� {}�"��%�=���!Z,%Z)beeՉveloped_#��> ce 1863!e�JoriF�c"�Pk)] x7A��*c?a s wa*�HKlebsR�[ 9. HnBou�����KX�� $n\le 8E.~1��announ'H!uV e)%a{ !�1869 " show�!sb�W,�U�yq�A��,}Yeq1�] u_1+\nu_23>n� . �S"B�(&�&�b֨�a�"O givaN�6�.7F-� �8�G �Bpe�9@ly Rosanes discov4�>?!#gN�!C own %Ux i89! . \\�� Howe2H-�'s:'E�emE-�-�-w=kamyBk-triv}�. I���s �MYmap�.A۬sfxd(�!�)�n�s�� ���0i� al:bea lesserM�#N&�}Ama r�lY� untw��ng���a hardA� . A lo $ ��%�&~��Ds w� devo#Nto it�OcЃ�k$A# firs�s�teVoc 9�1�a�*��( Castelnuov� 1901EVmoUlA�I >=Alexa`�16�M\ԺHu}w�Q/The��ssX� P��]�=�, immediately6GwoAic�.͟��\g � sum a� i^2=n^2-1@�=3n-3,i�3�9n�-!���!2��m��5 "dH�1cQ,i\colon\PP^2\)rA�ar�x$�$``pv*i�OA]in�ly 7�(.%Uac6Q�B1�Ze��%� sens��N� A bst6�S�C��A�� ques�;!Aq in�adjun�b 3 . By�I�of�a�b ac��ϐo .�(�g[I--R]�Hfac�0Hudson's book�$1.5 below) �[+ necessariN�o���'e�!of .�4/:�V�a�yeno��cwhH�##�!P2�s�c$2MFFF_N�2�OE� $ =\PP_{-01}(\OO+\OO(N)�? standartbp�::M��ref�e�$�7.Z��U%�CM�B .)F�/ � %��V1 �q3cq] F:Z F'���LYt��i $\HH' l:�'m��~a2=v^{-1}_*(B) CWe.��$F$. WH� $H\sim �B s+�E f�*er�0\HH�s"h-q(Calpha,9,Z'3-�\ge 1DCf @�7of ru�B)� , $s !6��8@3F=1f!r /E����ʼnb/ to w� a�n a�8Ler basis $\{-K_F,f\}"�8� !_ic(F)\o�$\QQ$ : $H'!._{�-aK_F+b5+ $a=) /3�b�a$; or�� E�b<0�t[�b-�d�Va�"JALog-MMPy�these� tu����vf�"gC� ing: descri�7 } \ )%,!�%i1aE��{N� �\ge���%%YBs9X)92c��� }�(sibMre��ion� -� cent)�pi�0}(80,46)(0,0)�dPrge{ \put(14,10){$F$} $40,40){\ve=�$(-1,-1){18�1 42,42){$Z1561>06a��,8@24,34){$\sigma$} _62 va��-38 �:�$�A��1A�_Z�:phi^*��= p�ҁ�,�`Z5�1�^*(.�S}i�����}a��,gma^*_iE_i$,L E o_r\RG_� d_4�$;�2*�>,-�Z^2HH_���4��2i '7�S.Ά$-L_*�ogetUV� 0*} (-3+(1/a))�� K�42}5��K �,^*(bf)+\\ + a B :1_i^*E_iM�I�. nu_i���all $iq�\gj8t@e$�%�1a)!�J̀l:' happen�if�)!�1�Oi.e. �U=�RF�J�x \HH=A8 ��w���]> �i�6�B-.� � }q� *} Any:��9P^Q isL.� �١��.`���p s (links)��_��[A).] a2N-K�a���E� f� �j1;$�2[BPn *��6�I�`� Xŭ:  {N\pm 1};`$A�$g - �G}a �%��h1��!p$; �C L&�involuU�> 0\to �_��.S��5�1�M4I77"�Z��� � i�:�YN��L%� �2� A�}<2�$(perhaps, >z � )n��Se: don'��cre�C��4nfQjz�.� ��� k A)N�A31V%�a"##��~i[�ir&� !_1��EQ_�0.xn1���H_1� -�[({(3a-\nu)}2�J��K,{3(\nu-a)}2f_\ =-a_1'b_1f_1�M`� �1�t�1%�B> -h�kyEype B)"3cj���kF~ �.o�)p: y $>ճwj2RK_N! .�N}+b_Nf� )z� "� � sX�$N$.� $b_N %|?re�/ 0e s $N � N=1ely.�V$H�@Ayh�!fi��&�@���� �@e=�� 5�exE�a�dY4C�ΑeC�J� C^2<���z $C=s_�Also $0�s_ H H_N<6B `s_N=2-N��.e. $N6�HA� $�ExN}I$'���f�� N=0,RJ�%8�usW.m\�NF)�'�f��HH'm2e-A�im a'(���})$i~$a'=aT� b_{N}=a��{e?}2 13<v�s�U@>a� ��N}A �AAM6!�{N�7I�+A�!Ia_1S_0+( $+b_0)f_0=-0K_{F_0}-b_0s_!�so�;? (1)c (1.3)�ru%kID�E��o") WRurpu1$-&�i�JPP^���0\nbQ�>0�vo3��ɞ%) $B)$ w�l7=�M�m situ ��$�@ alle>�e!8�AbF$o�I-R<<^����N� !� fact, jussse#�!o�4�-��ver��not�f �3i� insp�M�'d [R]�2�u�a�]] �* de�[# i!*�)Kof�, typw%1��apswa Mori%��S 5� Ia�3$1 Cayley (�-1870),�701)�W12)/�,A� e��, [Hu]=����@9� -Z��!no8!Eory (a�]y)�� t��� earlmtwenty rurM_re%an -an�(t*�:=I�UA3* � &&);�Y1):7 =��FX���anaE5M�� ] !1. a *�By:G l6 Q(mor�Ua��� n4$, ��pR �L* �>5�� n$ -) a �N� {FPPE{�Jj'�is>�!�"Aj�a � $Z5�d I do�q���!b!g2�B& U �6e�-UdalZ�J!�yzed,�rY HI� 4 ([Fa], 1915) ��.l�iedM�Cog��A`F ��cluE�#>�d6� (el� �O]!�� )E�U s�C.m�6�뭶>3721 $V_4� !�4���fu��"�O $V_{2,�t 1%� Bt { Cl��!�)N"�l�*<@V x$VK==B%�folds�rho(V)= 'e�� � PU��K.v chi:V:� o>�� �! �vџt��a�sV'� $H$ U��Z--DLe�matd({M�h" |H'|))Nt|nH|�FW8� �"�M% AK> �%�6X,����m_ �2��one����6@ \deg C=CH��B^* � V tackrel{\�}{\long&�}� �B^*�&�_{V^*�` � L(B^*)}=� )&{�"�N x,$( �)�I�y' >+q~����I$G;i��K� +$1.3 did. G�C�$Jk@i����nd)ic 79l� madX$([I-M], [Isk-P]�V�Givn� �wF_'.�jP�!g2� o� ��"� d�� � - framework��a R� H J� I $\QQ.I�9&�.,�!B�GbyG� [Co]o t"�@� ?  [Ma]� I�����f ����i|*��X��ar�JvWN�>1�1\�(^ ��ph� E�]`� &�if.�$\dim S<z�&�\OO_X=S�� (X/S�0��/X=$-�Z32 �Je�w$ 1)-3) meaa2�H�� cJxt�/lBE%�ADj�b� �J,�a�n��:+ I+y:J R�}al�s)��(� is stil�Pothet�"2 } ��ree�6�of �&BUbe&�%�"�$ \[ \mboxd fineQ{birto7Mdrta�%� _2}&UHr6Ia�ApE�u�_2}a�&S_1\r�; 2 &>�(fS�r��fTU*Y>!�Q5sE,��ps^< E0I< k#E;.��9I� EB.�,��%��.1��5Z�3r]^)�%� X_2�+_�)ہ4S�n�$)~1 eR!aWo"�ӵ�(� (I) (io�,iP�al &� I2�(6"�;be^�V���  � ��!b�)P-2Q�a)��deX 2}aX%MmY����Se�l1 mWT~G>9���4logE�V ] 1,\ 2$�#.'Whs�-��2-�� :,6�n�C 2 } T.�!�&�Bwe need ��&A ly or�6�� �]de�!  du�Eh6(�|J/�deg (�,��T0]a 6f�"is��w�q4and previously�i fixed on the whole process of decomposition very ample linear system $\HH'=|-\mu' K_{V'}+\varphi'^*A'|$ i b�following diagram \[\large{ \xymatrix{ (2.1)&\hbox{$\HH\sim-\mu K_X+\varphi^*A$,} & X\dto_{\varphi}\ar@{-->}[r]^{\chi}&X' \dto^{\varphi'}& \hb ^�K_{X'}:�} \\ �8mu\in\QQ_{>0},A ,Pic S$}&S&S'(A'',\ \mu�ZZ$}& & } }\] where $\HH=\HH_X$ --!�0per transform!�!�l%v .v,$. By defin)�we havT deg(\chi,!�@)=(\mu,\lambda,e) ���\  \ge0},\ eZZ_ �$, is lexicographically ordered triple, w �mu� as iI1�2.1. $ v$=\frac1c$,;$c:=\max\{t� �P|K_X+tH_X\ is\ canon�\�in \HHuPis a general divisor,�$, but also"�e�L 2 or 1 which appear �JF�5nA0blow up pointAcurve.�� Asa,5�( (terminal) /i� situe�!$m�{more  Hlicated, because $a�@�&ѥ�7�rFalM�s andV reaAx1degre�� ���')aLn particA�%P� maya�in��e. Howa`,!�%m algorithm�be ) one need� e break�descend� sequen ��s $:Z���simil!�aya!�inY� 2,�maiA:$gredient iI:�B� is Noe��-Fano ��y@ $the criter�Gof stopp�of!�o"� :�2XF�� mph{m�previoueb%�0s \[ \mbox{\� emo� sm{birto}�8��ef.} E_proof1�theorem#Qwto '(class. ��L(see [Co], [Ma]). We�sider aF�< $X\stackrel{p}{�pa }Y q}{\to}X'� study i$ �YaZ�aA� 1{* }�)> $(K�+% -� )$�0$Y$%�� ic ��~ %� s of��phisms $Me'p_ q$ u!� Negativ��lemma.��contrast9Wm��ona]ŋeff��ve� (geometr!w !w),  we �BA�=!�ory (nef / �is �7!�nd�%�ven�3to� k�in MMP�S .�P ule�i� Yp1bX$ (when"� M�)E�s �$(or quasi-)�Z! on{G� iz{s} .g"apa� [Br-Ma]I��E��varia��Df Sarkisov-Reid pr� m�_�hc� g!Hoa�6�KawamataRq� . A� X,B)MSf MMP re-3isE�$ied. \page�>2�Log24" ��*} A ͍� ofa�j!.vex�_i,B_i� 4$i=1,\dots,k$ Epw>�A klt6`P said)� 2�ed if�re exist:#� $(Y,B_Y- nona*��.�a�{$a boundary ��� $B_m� �nor� crosPs*� P %�1�4 obtained from�vi)�A�� 2uFor%ԅ�A*�%d type�B)\� set{\N�� S�. $(X',B�~2' '}{to}S'$� r)�U>ed!� a bi" mapٔ hem &\x&0%\raise-1cm \(3.1)}o*#�NB)�^*& &E��h{�}N* ^.��6<�}& *_\�'��-$�'$},&S&�}�w� �e a" (��,eA�p� �� O 2� of extreAZray��� B_X+ �6a good� vAj&NUQ\to!5_X),\ mU� .�V> �AllogZ�e�B��<��*�*�E&���L*�F� �.92UXD"��!<+ � +nef�b�.f��� cond���x�� is replacay�e�8m��K most��al]ofb was��@posed by Shokurova� Cheltsovm��du ��statem� aboutu uni e&5' model%�AH�]�I�4}�in)ce�.kodaira& .2PC� eU2�A�� $(V,B_V)-� lledR����i��is B�$\psi:X� a�  V$�� l =(V,*(B)x�%k��K_V+B_V� ampl1�2�Npr!�E3*}[1� ] If� `9v2rͽthen i�)�MX2]6�Iitaka����K>�V}For6���� B =��� $\alpha:Y9Y X=YAOY,��^{-1}!_=��%D5. The .N � =��_n: ;u (Z,B_Z)=($ (Y), ��)$ %� e by!P>�|n(K_Y++$|,\ n\gg 1�s ed 9R. B DBV!0�b �kappa ��):=\dim ����.,\ne\emptyset�$some $n$, �wi��WV =-\infty$M�Mw~���ap �phie� a$%e. AE�:�S|"�is=  ��\ hR 6os �J�t:/"�so--�$K$-trivbundl�in sen [Ch1], �those'!� |fe��� �DF0. T��� show� nf2]�c��hypers� of dMN$�4$\PP^N,\ N\ge4>�5��o<[Ch2] Let $X=X_N��tF$o-�ic�� ra�n�jnot.uto%%�s�os-4icer%+J',%!^ D in��by�P ons( N-2)$-"_alu�ubs in-3Q�5qZ rk&� first ver�!��� Isk3]%� H on.5E,ic �2� $9�4{\mathbb P}^N$E'Herroneously attribuo to I.�� (Sec. 3.6�my ��a�fa�9�B� J� �is=�0ly superrigid�proved!�(A.V.Pukhlik� publishM�P1]. ae�im�m� !�Q (2)�aMTof ��, an immediat2��8�ity, �da<[P1, K2�!)cl��1v�M�B�{an el� Fway�t� s 1)�2)!-c�anyN�.E q�y 9� [Pu1�d$a�q 6qU�%�dea1yR��a[(llows. Let + �EouruzyD  n�� � nent�� �@t|-nK_X|$, $CS(X,� 1n H)V!J locu�&" [�f%")"5 E��$H�D���dA=��-t��P1a�a:eB[ � . U��*a|,&� ���<at ei� >�=��orB 0=(X\bigcap L)  s L�eq!�{N-2}� W. QCS.Z(��, %! -gis")!Hn,($�epsilon) �still6%� a smL$0<\va1 \ll 1$. H?]1r� e 1:e�-F K� ah � � !�"A H implie-yAs$��@s"A. � $CS\neq9��� B��  H)=1/ Acw g�C 6 phi_{\HH}2� !�1k>}8equivalent to aA���� ZLNVTam� � $L$. So:��x#_L��ly � .K �al��.bO!thebibli�phy}{CTO1add��_{toc}{a}{ReferA:s� Lbibitem[Ch]{Ch} I.A.ue(, \textsl{O� xt��c�Rtoctic}, Math. Sbornik, 2000, [2\2b] On6��1N� $$}, Mat. N�!, 1999.i o1]{Co1} � orti�Fa1">� \& M. �.�no � 2�<}, Cambridge Uni> ty Press)j|$Fa]{Fa} G.�``Osservazioni sopra alcune$ eta non-r!Dali aventi tutti iq $ nulli}, A0Accad. Torino!H15, v.50, 1067-1072�@Hu]{Hu} H. Hudson�Cremona "�%� �/plan�Eme`}, n 1927u$Isk1]{I} VA�$Iskovskikh|B&`aut��E��. al�aic-60ies }, VINITI� 12! 7.�Isk2]{I2j�M��A�Y� map��"� �~��viewpo�f� 0ory}, Uspekhim4dauk 51:4 (1996), 3-72; EngY )�(l., Russianq� ys 518585-652���?� {I3j�O��.�2^# }, PS)eZ�Z con��E�42v$-M]{Isk-Mayai9�aj4Yu. I. Manin, ��Three2� qu; ��d cougex�>*L\"ur[ problem��$h. USSR Sb�15�,71, 141--166.�-P �Pf�G.!khorov�% eAx$},Encyclop��(Sci.,v. 47,:I-R]{I-RVr��5Pre�#sA^boo� i� "V�".K Ma]{!�K� suki]Introdu5$bo'MI� Perdu��.��.��{�^Bruno!�i�L*B!�E+ }, Int. J�ha�9.�P1]{P�>*} �-%�:� Iut m.,�< 134}eI(8), 401-426.�Pu]{Pu�V�6؝�8Nz Izv. RAN.e3.�R]{R}5���V.j� accora�!�O,}, preprint,.�$of Warwick%a1]�Sh]{ShE�V."m�p�� s}, -�.I�%F81)D��(2667--2699 �!B   docu�} �g\� [12pt,a4pY]{�Hle} \usepackage{amsS,amssymbthmfo� Xamscd,euscript,verbatim6Et1enc24[cp1251]{input%w[e��,r��]{babelaq+$style{plai{new ! o}{�}[ ] $*%r&.{pr}[M]{P&l2#*�}6 `{�) DL%!2>{coro: 6�S666z(t*!r� �(�R\ RD"$.2v$*{notat}{NioRa�co�[!�new�+$and\vk{v_K bot{\otim� -$om{\Omega}%\0de{\Delt-U alg{�� {\rm��,Neps�6�;frak{E:<si{\sigmBs{\�6Mta{\tau6gd`D:`goOT-�ok{2_K>!n6 N6zoh{� h><f{F}Bm. fB w.WBvn^N>]g.=GB=x.xBl:L>_p:!P>!vl{c LFcv2!l>!0mw{\tilde{M}{:^gw=�WFsFGSB!tz\zFyy�q (lamb{\Lambd:�gmtM>�aA>rR>ol>�pl{\unde3" F +6�mi2-6�z X bb{Z:2qQ:�m bbAp29re5>�cm� bb{C:Pqp{\q_p6Kzp{\z_p:� pd{\zp\{\�)\}\:Jkd{K'ba��$ga[[\de]]'6[la{%�B�am{\gam>�bl{�gl[6�br ]6`b1(:12)62ob{|6/lan�ngF��ra{\rJn�t�&gle�06fhbff-�f��2bvV}% `\DeclareMathOperator\di{\=1 name{div{N,ord:-ord^-cha:- char^.gl:-Gl^+ homm:-Hom^.ex�t ��Ext^-i>�ib�ke:�Keb�cok:-Cokf/ran>0^�car>^arb�to>.Tof�>�Cb�sp> Spec^�mB�M�V� prli�projlq N�in 'in &�d" u.tle{F%8e flatcmu�.$K$; $*!� O}_K�"�L�E�mof�1gers, d8A�ab�:e ramy�index�d$L$, $s=[\log_p(pe/(p-1))]�e_0=[L:, nr}\� ]$ (e(L/K�&JperD16 �2D), $l'=s+v_p(e_0)+p& $l=22�ovl��; ��BW,$\ol$; $\gm%L�R,�l�& $\piY= ,Runia?ize� 4L[+5is�ta 'E�m� ' will (b�>ault)'a-� r�, $S/�5�/M6�,N����. �( 6.�s $S,T$�' wE6 $S� T$ 'S%-,a closed sub.?%T$S'm \se����1"�1 ����R�s;%�6U�D} �d%衡$\gs_R$1�82Zh�*.�s�annihil�8Wa power�p$))Ia base   $R!S"#goI9*%4 h�:ud�$�%�h*�� " aAH�cA��<+er�0>3of V#$ibeA�qR�!ź�Breuile3D \cite{clb}); yet o:�i�/�s4h��?1��F�I+ well knowa�at�#.�.�4 is \'etale; h�)6L*�7 !\F� z S$��Galois y4�InQ%h:� is V#� . �!\,na� to77l6� 8$GF:S\to S_L=S\_{E \ol} �$GF� faithfuL-�(! one-to-�: correspons<"�)V�%�$S$�;r#!h(8Ire}*'ItEB�p"�&Raynaud K �&%>$e�. Yet�&aDimport{6�{� valiU&�! o}\lA*({maingf} If�P�� .��b$g:S_L\to T!u) $L$2��7�8, ��"�5 an $hEX���a�l$&�/( $h_L=p^s g��} r!i�$s=�@-��wrefore� `: \ref�E� alizMh� lld$-"ofQu6M 'al�1A'. One �8ly check�M& Lis �@"j,� �pse/�best pO6bd0��B�I�can�+�/ed�'�~ analogue<:��o11Z�� $p]+vis~)�s (y+Tate). Bi,�Dx%"� e|��ta}) "�)l )�gA` too��r A@ 6� ��for6Y 2��'�b#>f� elow�B"X<"�)O $k^1h'�(1�� �26��the:h oryT6� h @F28"s;:�Our�icm�!rTEva��x?� s� meD�EJ� (2�@,1 Ih�A al W laws�.Wt mind� :��.> >. Here w!�s< T odif,$M0a��u� in ��0%bM=01} (cf. 1 z��Weaby $C��*� A�ad�5ve"� �GL�$^m,\ m>0$.R $C_1,C_2- C� �1 C_i=m_iV �� $$C( -)=GJ M_{m_2� m_1}2� K:\ AC_1� @ C_2.$$ For $hr(�;]])^m�( coeffic� �h � F(.$h_{i}=�F _{l\�E} c_{il} O^l�  in L,+e ��O��dap} h(x)=(h_i(x)),\ 1\le im,� �8} $6� q x^{p^l}U g�  an $m�y5E1}'AS $Fɂ.�4,$D_F=\{f\in !8�,^m: \exp_F(f��$\ol[[x]]^m�F �a�p_F L[[X$ am�w6MinA�"x"loglFhmA[$F$. >z ��$m$*2C$!� a_i\de^� Dzff �%'i}� ���1�4u���ry�������n�!�)pr1�0mcart1} 1. $F�D_Fk�0� $ull embed[!�6"�)� ��� �  intoa� . ;f:F_1eF_2A�f\Q* AX\mod �L ZAol-t 7�associ� }4 $f_*:{1}f 2}�O "Z;Eم$A�2.A?{F_1}=5f���4i�,�s $F_1-+�  sA tly "],c��"�A�!sm�Os�6 nAt"� �~GtM)LO.�pr�wAT briefly r���Do:B�> ring)aA�"� $Q �a -E( $P_<�C%er-YZyi $P�I!WM8$f�i��I� am. ,\ aQ$ ԍ�$ $$\bv f=fA;\ + Q>0} pc_i^{i-1}#lan a\ra ( a�ni}cw�f$r(Q)$ (!f1$�1!, &/ 1�� e)*�Lq e�N�2b@bv,��O ���6sfying �l �As' ��1}�e 16.2, 02}kK�4��If $ME�a�-m�� �5M/!LM$ �6a �{ )�m8-�d�@4$a\cdot (x\modI) =9lx  = r $x!�MA �iQBe"� %��8.02�͍$��ET!�� s $M�EB5e�M�N�9f��� �, ��!����48%Xa�%d} sub-#of $\6�B.�A%Ded @�%rA1}�P $\ns� �1N$ 7no A� $-to�6�))*�q(\ol)$I�car$;�v 9&M�I..- � on't)��5 see >�s. Yet� coulK�/0 a topology oZ$a�QRA�w8-K!JawFbe $C1�M:a�v)�C\��%�C$�n 56� hom"!-X��ntinu�I map.-H��@uq�4%�P:�� a��2� @ed�2"��4�0 ainsY M�:�2U�����~��Pm�5^.Dthe a�7NI2s-�d above;� �<�4ly EL$-՜cuY� typi��H&F$e�� J� �^C(�X�� 2})=AF!3.a� in CeE# � �v�>( 1-�E$Ca]* ��$C��de=\ol^m��Q��5�;�b2�0} two���!$�_*� s w��a�n��`:(a�h�Ppa��*�J�/ Ea�G�-�Me�*MenF� FonAbe; �iR ; in a APdif�.!y;w"��lKecisel�>ar ��w--*2}e� behaNM�e �� is�%�v=) �&ar*=vbC1c�� �$M_F$)�!>ob�KlA1'��to�\an6� -�i���V".2�� F.��x9:by"A�#7 re $#=ob(*#X,Y)�5i�:�B� 7 $ te�o $0$!� ckly��= � is '��_P say ��itvRmp�Wt�  kiaC� ff^si��/"� 3.2.2A�}����#-V�7����� } �>S$%�J#*�; let $0� o �  G0@�iV.�)-ҁ9"�s.�J� $C(S��ok(� to D_G��. �oo}qZ !T Yto J��a+m}U��Q &6)!( �>=)6;2i�Y :� �� f� EZ)���?s��/O�J%==�4S�|Mtof "F��RW�3�9 n.<�O $*s9�Frobeniuq\bv2$a�$,Verschiebung"� *1NoE 8�cXP" #�Qce6tely q� B7")m�&z�|0clsc} I1. Clr �qe:-�hin�-R(i�:� HS�U2.�M=E� , $N=C(H)�' M-=nde SmHn $M/N\approx C(S/He 3. C5.r��Ar@�?M$�B=�[l�_�� �3MV�a�n�Xlength  �.# �" . AJ��p_"!\bv^i M=**A�4 =\cl_M(s�> ra ME� IVX mini��" 9AI���!0$)x� �\�!G��I�5Bto'�Rqu� �(aH�a0Jd?to)�GofA�za�$)�&nda� %�J�>oV e�A�[p^r]_F�?�>� .s �f�� ��|GU9��(III, $p^r M5k]1�m� g /p^rn7  Vin^!��EduR ext^1(S,T�@ _{�n}%5, C(T)�~u6ex�#a�F6I`A�n�%�A> �sE��� 2;!�( same& I3��en�5MWe�8 8�26_a�2�% $TS U~Ip��Aih�L� tgs}38� =s>"�d �r�I[dA���J/J^2$M�$t,A� (,LK)$)%=�bJ$���augmenP*\de" e af2 !g�^%8� Yi� 6)!W6)\2qh�O-r2U)aaRL E�I .�f��ny (uAal.!)m� ��I} (suiq(�$� )F� $S_P6� �} !P�"�B2��$TSM5_� PAW^#�F��F^6KrgdimA[ In�NY�C(S_0��_0� S_0U%g� !�E�~>{��P��of ;.�zZ�t�����d�3 2�9!a���C* H� / T 0�16 6� i���2�F�$H- =E3 &�"�sehQ�H.;+ �lso��V�)^.#!c]*v�_�*Ŝ. �c�A� �^$��Ɇ�,�[�[%& V A^�q�E����M1 B��V���$.� if ��S=0�bTSb����  "�t/v,a�} &@,&�&.�.�`pp" /GZ I �.�s&. � -�, �&+,��F�,N���"���se_y ain�"<\.�'s�_a/groAb$su�!�#�9 [ a�s�H�to "� �$V��nstead�a�w�j!( 3N � ��!�6�0y ( k$ o"ol$/6ed�$NWne+\jus�bdiO.)At "�c�*pK!�$0�d�2;N\'eronAel- A$ i%" lru�!an�R�vlX :(.;variety�YR��i��$s{`�!*�&His�!�2�  ts.�uN s1�m�V*&}e�^e �)�C,2J5/ ellip@1urv� ei�K5�or7N�Kul�4QV`N���b$m0gK$�&atbFy T- �d"i'redD E��R�I�K$!X% nZf ���1�\mGN 2` $H/\A� e $TH$ \supset� {l}� N 6c*Z)��6 mon"�< $g:H_K\to\ke[p\]_{V,K� HV 5�Y�b�f!ā5 $]�Bb%.�un�/ ed U  FM\con�e mu_{� ,M})� � $\ m� .�A"roo��f\/ty.�A%� Part Ia( a va&Z*dGs&5.3Pyco}���,�*,E6of \B5��,��l�+�2��$lf3�[*-sz1})a�|f��no usee-they Ga0��wheA"�isu��� 2��I�)-��!$l"{rz[[$lCo��Short�3A!�aZ(�?m�f�� �*DB  *cart2}%�n�yc#��&f!usual"(!�ry�21 *��s IE�II!�-� mc�*--�* �� t�Ene�q�of��SfPJint Jt!�� i-or-l\eas!� Tod6'��c�#6H�fb�-�,WexpLk>p�!�M��+a�&�E�{ 27.7$i A��U�8s*� ���� r$-f�MPT& $. AA={�h"] & )U�c�n�-xt�l �*80����2��AI@i��YM�cll�"�D_F/N&* �Snde�%��y!�qB� $D_G Ar� $G$. Last le ver�) ��S�S�1!� %��isoge' h:�F$. Und�Y$oB�V�m1.�(!�2i)6 `c � $G� F h=�(g� �� s IVEFsN[�P.�V=E� ��0a2�ca�a��%6.� VF�: �%*uVA�~ �B;�pregOJ`"S �" ket�qeA�H :�5gf}. F-Yq ��&�#*� � ���.+�e &! 1�m�'.$0gol6e0`in+Sve<:�%�Zr%Y��j�a "a2��0Mͪ�4: 6u5 $�^sA`�k��sur��c�?w"d+;m�6�m$ �I�!�N�8kwZ � � sS,at $Fr^{-s}(+@ \�line{h�j>�/ A�$�!az 1 h8"�3:nalysQ &B ' ' �"!d5of \S2);e� 2M�s *�0 �#?a� �v-�eIB"A���K^7= �_ ds �-6� ct& �*� 1"�6,isb_ E���6am"f=u:B�.�6�]�s)Vm� a0�U>"li�I" e�Nex;r�8c�pAfH�l���m*s�3e3�!!�%��B�"� "R:?��>-;o "a02}XN�& , I�.��# .�o52%���]!.���on}# W- � ��4 detail�5 ��rlr:�BColddeZ&�F�r�q�l�"up}f*i2I �$ wd624).-L=F\t2L8� � 9�@ tK$)5 a)��:^ $Z_K&|&�1" �`� } Z�K� � F_L��@ -3 a�$t=*�= �sa;.� $,7k*2h�{ke�t]_Z\W��\ok �K$.v� j"!"sm!�b%?v]A. (Y ong})�2���a�.<mDme9��\ol--�{F�ThT!c �F'!�!3% .p $F'��E�uaR�I!��. 2�A� 2� ��BZ%�-���is�d�bk$A�x]�N�s $U/K Z&�� 5Ksim �0:U9V_s3a# ism �_{0=;to�h�� t� e.�"Vn�m i $i::K 1U} ?9 f_L\circ �[.~R� nAi>8%*'  Ehn*E �! cts eelyz %"i( �)(�`!�*K{ic6�+$a�U�e,�o$tE�� !vd:��3e�"��c �s]�`BWo�l 6Z��s '4.A��be�on)s!m �E}1!8BS��j� y�29  argu���� .;�e."�C&g degr}.�V�m#K$,�'Y�L}@>��*,"'a�J��A|�^om�2� $V2]�ͩ�Y2a] ��>W�6`*FG$E��)�A�Y$#9$J 2��.E[*VaH��A�&Q��� 9 �4�_: �Tx%�kVs$Z��e�"� $J �Z:���e@IIY�}�f(""��"{l'"��+<6z�'.���bm>�mk#=: � ��)4 .<����p&O>II $\�$L� b�,s; :-�s *^ C tF,gUF �2�� Ji���� F�Vy�l�J�a�&*��\ � V_{f�*j KAC�9���!��*��>z T��  � A.} ��m!Vuc�$HR�G ��<6� %�G$J JET"� �")8B� ���U�_f$UPA1���5 T_p(�r28�MO� $V$)�� side"~A$>�Q��fE��xthen !��݂�,u��./`*Na�: �ZN��'�tak�=[� p^l]_{Y,� �-t"��|u�&��%Ae�Ao�@2�!u�Grs�X���V� al�� BJ �& �E%�&� �P5:�AEIA4i�K~ %�y;��N�!yA��"� J:2�"]_Y�0%�W7� 6 calS�%/� ��}�6�g1} g_A "�Q_V`Ex!�it>/oV9�g��0 ete Qre.jR�/��^d} (�c)// TrfJDSt. Peterburgskogo-de�eche HObsh'estva, vol. 11X`05, P. 1--35| "�g� xR M.��.C-��) ��p�RV�I:E�2�� , a �e wild�p >� Ny}%#jM�in!. YaAk�fOe%6�=�4} .���!^�RT II::4:Qk�ndZ� N4T4, G\"ottingen�je=�}.�E�Vosto�pS �� �P)p�e0. Steklov Ins;cH 2003, no. 2 (241),Ax35--57p �f�L �LC., {GX@es62s,Iu҉inK"W5A8ltr\'e� Ann.A!Mde2002.m 52. ��489--549A u�ctUConrad Ba�mF��3m� low B!��on}// Co���i�a.#e9. ,e19.!239--32u� 2}%[�7]En�8 J.M�V$ le�6rps%�uxaAs7Uque�077. n. 47--48�c�d4 France, Pari5�  G*l9 A%�S\'kA| de g\'eom�rie�\{ 7 I (Ex8 IX)A�Le3Welm�-&s��288. S�d4ger-Verlag, BeKP--Heidelberg--New Yor�d872. %P. 313--52�.}�81} Hazewinkel %N ��a�*�(s}Ά8�C5@oAX.3F!�$Dieudonn\'5���A�52�32uATIndag1�v. 37%�5EH103--1 �9�re}M �S Yas en `e� B& $(p,��p)$p BullI!ZjI!u4I�a_ P. 29i2802M)# SilWeergE3ZarĄ�iG! R"S �O6'ie�E XFe�&!�.�f*,ycA�$(Banff, AB�f8), NATO�f Ser. Ce�. Phys., 548, �/0.�495--51E=9M�c�K J�J�%� �Conf. L%�F�Vs (Drie! ��1966).�58--183 Q�Q��620$z} Zink Th��� arko"(r+ `maler Gruppen}. Teubner-T� zur% ��k 6!$BSB B. G. , iwTsgesellschaft, Leipzig�8�u&th6R �&�[�{ 6�g"�g^ \u&5V�g�R$sort,enumeSB,eucal,%em� . in&�{2#" -,headerfont{\„ (\scshape} {) body({\rmfamily}2` G{dfn}.�f[ k]�Crmk"g?.f�}2�g)2(thm&.h# Nt]{\Aut}{Z �_�_Z Sing}{^"k}{Skbpec}{ q�\f&1cF}_q} bnbskip\no�X nt}  sn{\�B> \ti/^M"7smo n�j��Drinfe� oa{ m���ore&����] Igor��Pot�|j�]�b[JY�\m&\Z "�]W�Ln�%"a0B�6�&�f�ioL���S i` 4�5�Uair � comp&C�;s�� "C(*{. n } M)s_|6>���(shtukas regڇa grea �ter1Da�sdP beautiful Lafforgue'��2globa ngl58co�"'foM,mathrm{GL}_n� 54U �� (�vh{cf.}~� La})]1!"Roroidy �B;A@��ihc�o 1was cru�]��&� U�"�=papɗ5� R�Be ``to ~�p''|^� 6B-�$M^4(1p�A,! al bJ$r=4$J8Po}!~%c�'r=3$). �1A*n�/�qX $ $A=\fq[T]Qv�E3, `Gq%= 3�3?&�oe�H_Vkrm{min}} �&t�=Vih. "b��1piTR"<)m dez/iz%1 $iessi�essentc7�ors(� is �BDD!�volum�J~. F��B_#) 5j E���5 e���B �ve e{�-B}E-A�$F'- '�ou!u�MY66�\5r=c!�@i\ �us�Uf�ly+|x2;�fRn�� e�@[ch.~3]{Po:phd}. �� {$J$-inva�g�(b4�CU��*!�FM� polynomia�"S��teV $\fq�Y$Ka (TACts quotiH#��.  Lba Lpp�a ̍"�m����_L^{}:A9�arrow"%� E$ a>� !�%34m� L$ :����: } T\�v�XE^{}=cnmD(T)+a_1^{}\tau+a_2 ^2+a_3 3+6lta(E))$^4,\quad\D�S^*ͧ{A **F��^{}0�Sqsl�Yk\l 4 MEl��$q^k-�} The aabf{j}]a��x ipleJ��y4(E)=(j�(E),j� �((E))=\biggr�}{%,q^3+q^2+q+1}) �},�~{%3!1}}Gp(E3^bC Y x)B@In ?,���i,&�} (a/ar�/of1Izero)A0"��#FDV%5J4align} j_{12}^�llta_1\d2}=11}%#.7%4}}ID & )1+ 2(q+1)= 4(=� ),\\�3F�3^�3u3Œ3(!�� n�2�2 )�2�2}eX#�)1"��\�y~ {and-��5���� :�Y���+1J� �4IN q^4-1}{q-f�M�Th�)]���9 7 basic�PF 0�j o1, 3 ]n2Xrm{��} @�2.82+1B� "�3գ6� "m � med  D�!" ��67�a�X� i���DIn��p=�p� pro"�X�F��.18�)T�t�.�yo}}��V���2n �Ato[ $A$-�vpR� %� $j���� s,��[# =\� A�A[�ݭ�,ja�Z�,fI,j_Z� 5vG�]B M Z�^*�"xla�e�2ng��>�.(-R]iC? 4��d=2_��1�FevA�Yi�0a"� yD sl ��&b�7l�BS]d B� [ex.~4.7� � Inde�w!MJ[2].9)�$ �V:ubvQFI� * �� )'9Z+is,*I $G}=�9}=0$.��,ic(.d2)}E4� -^�%1-mb�0F��( 2)= [2]q8[ B#q��'$ )}�X �����06 � �~E�tss$^fk0%=$�S2bb^T }^*/q^*s6P HE�A� 0�*i� e� ``purit�  bfh)d'' bi� SoQ�q�1bF��3$-���#]H� ,e be %/�m��a 0"q(al&(� hed�pc*E<{Da}. Namely, w� x-�att� $N^3�?��\��( $N^{3*}=_�t$b{Z}}(N^3,1KZ�2be�H g"5#� sg&}$�Hb؟b�"p\2!x :�`$N�R}}� �>X2u � e�5',Fu,Oda.#$$qp��% W)�H{psfile=dr1.pstex}%i�0+et&L{\�G ,}{3315sp}% % dIHatletter\ifx\SetFig.\�x%% \gdef4#1#2#3#4#5{% *, set@�\4� #1}{#2pt}"� {#3}se#T{#4 {#5 0select6�fi�����\(3952,5338)(2146,-8183) �$891,-8071)AKkebox%U [lb]�sh{�<{10}{12.0}{\rmdesm}{\md up $(1,!�$}�t�� 4186,-300�pZp��q+v*� �)705��Z�1,�1,0 t�KpM�]�fig٫ [h] �o�{D=Kr�a$Jne $\�D\sR~_Mc.(}x�b O M���ɀ�n� 5� �A��:��s� { so*aQa��Z���span\-D3by&�� jeq:A$M} e_1 &=\�y(�\* $,-q-1,-q^2   e_2 &=(0,!Y,� e_30,1^ t�\�� �1 "e_1^*QA(0)��_2^*==��e_3' �!�IZB� ��k d�á{9Z�z�` !�)��2.����������L4992,2892)(1328,-370��$1943,-1006��V�0E��� � 1358�p^pap$2820,-3645�pVp�Y6� �����R��r��label����S�nd�S*�w"�y� m<is9�z��AI rB� @ .���2� dg9nߙMor��X�"/{:p "g!��{Re�*�Wr not�� Sk^1��20Go6��m� mp�Bg�~��� l_ �Zaj a� �/.� Q}}� *2<T (���u ��vex tope���� F-1}[0,1]�V�� ��shed}�$ = � �2` "F_%�HL"� �=n n.�FzB�{Re,BGS�+now�= ���be�>�]9%3n?9�==\0� ��{}\&��egl� �  \�7�2� iM $, .�ak�3�7re �s�[ j� s $eI�i d in�z p.~\�p��e�s:F!W�2!�7tetra5 onB�s�Ccto�Pnd� %� ;facetm�bBA(o�n (hatc'��*ig �fi�M(2}v�=�Sindic()*�i}�%� V2%C:��.� ]! *( �HUR�3�� 2072������Z�(4965,6201)(�',-7177� 6931 3�� 9}{10.8��� &� 417AW24�o^o� o �09�oVo~� �59!a52��V�� � 4141,-478�oVo� !�� uc q�}�z2�"� fa�_S�6#�V. �q:/�.:� � �"F� n�VP�.}"sZ����of� ^Nz��IX��] :S j _rm�}$#DY �����\ � $. A6�V 2'V��a&� ���mb�PLf���:�=.QSg� l3o�id����)�O6 tes �fbe foun�ѧ�er �5t^�;$(xQ,x� �� $(- ,xh�^rM� F=d�sg;j2�!� ����\l  R�6����c ��Wwhv�� "e�5�v��((1)kIv-� $(l}-rn�C$&� l :e�khe 3 $(q�?v%sN/ �0fane/s \s DvUu5Z�(���&� $M^{)$2X2>sm!vF>a�V8(excep�e�):NqI0=qx�o�&�� 4�� �y�y�yjy 5217,3133� 96,-3839� 19�^6 2836,-13� ��' put(37n83�dZd��-nq5461,-27�M^M�{&�65� 78��^�&�),-b�� �m.D.n�:i =Fg x��%CoM� �rY-,ge��?����� &� (dk�nct&=!�ő� "{��#�C�20 )� r� ��fu/"����"�  or���|arel�sB��eq*� *� -�G�� q,\ ��c:�' )"&�BS +�#ha���Gasy!! aigh��p/�lVFho�%�eq�.� lM;�v���g��E�t$through $��,@{� 8{� S�R�\:n!�!�2�%�q-1=�څ��S �%�� >���5�K)Q��� s=OJb>�Sgy�3 :4� re�Wn� BMq�lf qDa~cave � BC�� wallN+4Re�2exhaus� co�y).�i2~$Rei��$VY$\:$0.2]R�$!H&#+}v�b�("� oa�2. Any-��m��w-Oqt �%6�sho�zh!x� !r'pE�� heck�%+A/�10,�co)RRLe!� ht�2{n��hi�n ��I��@.\hfill$\square$ *�p� b�5� � � � * 61 073)(10 77� � � � � � �  )�14��1�@%E&x 226� 96���o"� 53f372�� b� '3,8 wen*��$"�"Nh� �`3JPS� nJL &b8 v�3L-j�:�9��t -�� p�/�>��  n�99a�{�& 9�� 9� 9(%i�m"@9B�{B�Techni�$y speaking:+is �`�g5N}-ce� 6aeA a ch*eof��-u�If%!�*?��=�&�*:�z0>1/:��)c �/�3,&�|"�|9XB s.oNe &�3;^G"N�jx ess1} (k�lk,-kq-l�*�*�7qB? )w� 2�ƚ2r�*) r�� B=s}�3 l�q &1m if }%` q\\ ! (-16*�с� QB R%  (mJ)Z2�A0m�� ��6�T 108������Z�10FF 9712)(265�'928^360�41����6` o86�oVo>�612�-5������_Y!_��^�6�-e�48�3��C~�.���706U498U7�k �r��0�&o 0/2��Z�%V�. ,1-q=\5190��Z�J�� 459,-9060��*�dEY�qE.Q�3 9969�zbz%�{l�622,-72�{Z{%p�.�892,-63�oZo2&� 2,-2�9�1156,-54�|n|� {.� 1570,-456��-�f2-쁺2� 1855�-�zjz�y.�2357,-32������#� "� V�$x(>�ess^�:�"Any� b-z6�7&��!ac,re$} fan, �c}.e ny� WG2K9Ši #y(Z}^3$. Cons&|P�r�A��=c�m?#V1, iƊ�"y(f C�# �.� 4-� b^� . Actu���(ne�. a[.*�[2 �!"� g'h�� %0'Q3i"�5 �3��U\\���,'�'I �) F${�CEX4YBR-eftR�"-A�z y6�� �>^!"KYity>urh���� !4!#J$"�.&!�]�P$EIn ż!oO<�,�^ .$\;$2.6)V��h� �"{:-�R��*Tb �V} lFH(xF^{})= 1++51!8VF��@� �e��0$J�l[y �JX?V7={{Eo2)}�!�<�<x+y+qz-��*�1P_qz1-_Nky�`�P^{}(P_q%C=BE F/�eARp�d�M�CG$-�(��on*�e��O  aB�2�� &�MРi�#K�%�$�� |")�2o�meJ�-M�QH� gle Z�J��-�9��Xqa9to6�g!s=(k-1)� �&�G%[oinJ�P_{k-1}=�2r( A�,1-k,(1-k)q-18�iJi*#/n�( k). q+1}\;B��4way:���>/��$P��!�.R0!�2qa��s$q$ step0�V�U�AV EWeQ�D3�{�y2�a�E��9\QC�k�& P_k,!D+1}�kZ*z�n�2�}F� {��{�b- c0:� �B�G�eU2A$qA�20.`�E�N!lA�A�� ) l��5H % u�-�d q$ �AS :ndE;C .'.D-1 Fk�r�Zig�!�pM��$k�Q�6�CF|��k'i3lŞ [1,2[Bf6� qh���h&�FK�d� by *� �p ors.B="2H r�&actT�\ 'HŖ�&{M^�O�* T�^I(r�1�4$&D n��7!~Qs )\\ >)2a*2~@I r�*:�F(\%�"!-^�� 2��+� �?A�byq r�t?t?.p?\ %#%5 e_4 �s �~  ��s&�:�]�<}0AX2Smm�!���deYH2d�h B�>(E��"�Dsub�!of1C� F*�() E&z0& $ \�z7��th &0,^t�7-XRI=U-8[jJ\ne0]%\Dr|Y"Y8,$Y`r�q�jG*.H. o'�N��A��glu�.8*#�.t�V1� NL)�i$�Itsv+x��by� n�qe 2$Q�$� �U��_" `C2v,Af": :0s}$:$$��~ #7µ��F��F��Ff�F511�A6�A208�7"�A��@��@�288��'8�`!BB% 1613���p?""�F�13�B1��q. 9L q $$"� ^![.�F"47��+y e�n l�Y)�a� u>[orems �3��'۫*�&�� i)�tvD ��&]2� NG5�-*}�<*��f�6�(q��\F� �� v8F �F�"�2"�!!S sn i�L VM&�+!��+ ess2%� ��1q� q, 1B�� $Z� ?5�a}17* J� BF 6AlE���9�t�q�,\nYn��F{5�{F36&�V� �y F< RU�Z{isR��Lq�Yb{A}_AeD� e_Ò�*�J+:�2� >��$R�"C �R� ��F\��NA �"DZ�&g7�)�Yb�o�izy�blo�$V�>�#R��4�V,���+8 h �.b� O��M��&�'����R�@8� 2901��"��"��"Z�"06383,4468)(15�@551,�>35��O��O&���@��@5626,-39�Y!ZY!2"[!)^��@b�@�p47��5�� ��ok�p�y � p� }� 2z D��ًBMPV�=Bf � \smallskip Thus, we only need to find a minimal terminal and essential smooth models of the affine $A$-variety $\overline{M^4}(1)[j_3^{}\ne0]$ corresponding to the cone \begin{equation}\label{j3not0} \langle(-1,0,0),(0,1,0),(q^3+q^2+q+1,-q-1,-q^2-q-1)\rangle \end{equaXp as well as its desingulariza" by�Hdivisors. The proof!4i) is similar!Jt.@theorem~\ref{thm:!Y�>} (\emph{cf.}~also \cite[th~6.2]{Po}). Indeed, consider projec�s|jfan $9n0\sigma}_M^{}$�pcoordinates $(x_1^{},x_3^{})$%� $(-  ,x_2�s�juTdefine two-dimensional�s B�, \left\langl)�),(0,1),X(\frac{q^{k+1}-1}{q-1}, 1-q^k  \right) Z�Xfor $k=2,3$. Searching Dintegral points in!M%= shed1Jse�, onees�6of2N�]G!�f4 $(q,0,-1)$ ly�in cone�)q^.�^2-q-1)6. :�Star subE�0ions centered� corr}�em�raya %�.Z@M_{\textrm{min}}^e�$. .]In orA�toa$ve ii)�n$should now2je 6e V[jE�\n�-:�o=JeqaY�E�%csNdI�0,1�/)�,:^-�=)c)Zlandf_ -1,0`:h^L0re already re�~0. It suffices!Hf�� .�M��N� widetilde�0^{}=\- �1 � Bd0of multiplici��$q+1$. $$1& picture}(!p% \special{psfile=dr9.pstex}%I�0+0etlength{\uni ,}{3315sp}% % d�group\makeatletter\ifx\SetFigFont\undE�d% \gdefX#1#2#3#4#5{% \reset@f64size{#1}{#2pt}"$family{#3} series{#4 hape{#5 0select6�fia�����(2925,4618)(2161,-5204) \put(5086,-1411){�box%U[lb]{��sh{�d{10}{12.0}{\rmdefault}{\md up $M� $}}} p 4006,-781�oVoM�p346�86�qZqM�q)b 3616��V���,-^2�5[25�514�znz^2+q+��.��2!�27�o^ok�,-k,-kq�endU�%fig�$[h] \cap�{De>� of $&�N.}{}�F Q2�� linearm $l_{Z&}A 4is given by :�m {equ" } v@ =-x+�% +�(+1}y-(q+1)zBL,Denote $Q_1$��"M!�,%�!Hn� btaZat��(Q )=1 � �B�U!�r��cedure%�G$-*3 s% � {BGS}.��� a s:�2��@. More generally,!�, any $0\le kq-1$, l 2y� � k� &� ��,B�, 6� 4"� � *� 3� N� I�Y<is  l�� $\muR��A�=q+1-k$.b addia ,)�� F�Q_X ,=\bigr((k+1)IF1- , K ")J�such tb\j �( n>N-k}\;BRI is way:��(consecutiveB3&�  inA4k$E#($1\leqslantE% q$"� he V��$N{}:� ":$have found�5}Bof�� and it� ish� @P.\hfill$\square$ \bn� tbf{Acknowledgments.} I am very!� nkfuEY0Marc Reversat%+)zrmy!lt!5support� no�x{*} \bibliographystyle{amsplain: {dr3folds�pbigjQ�flush� �^} Igor Potemine\\ Laboratoire Emile Picard\\ Universit\'e Paul Sabatier\\ 118, route de NarbonnQ|31062 Toulouse C\'edex 4\\ Francm�.�N�$e-mail : p �@p�,.ups-tlse.fri26J�� docu!�} ��\(class[11pt]!F8art} \usepackag%Zmath}: symbB)J s>*cd} %  E'$width=14cm heI=21.5cm%#0$oddmargin=1ev�d2Hhoffset=0.4truecm %-0.45 d\newcommand{\Ibar}{\bar I}6ff��GreekMrE�ms2 N�\op{\opeAxrname2�\m{\medA�6$n{\noinden!��\sz ^63!�nageS 4AlgAlg>ut ut:Bl{Bl6aBs,Bs:+charac I }\,69 chow; Chow>=A� F< oker C >>one n>�con �on>�C C>DelODel:jdia)E }} %.afo �fo>�EA�op{End:QEx �Ex>�Fan�Fan:4 gras)-G :4Gm{{\bold G}_m6�GLSGL:4 Hilb >om om:idi>�imQ�I>3Jac4Jac:MK-�Ke>=LEV4LEV>rmo �modB3nu �nu>�NON:�Nor 1 :or hor>�P-SPBTPS)mPS>n Proj� :jPi)!Pi>!quot{/\h�& -0.1cm /6� rankY :Yre �re>�RIG5RIG:4 Sbar�@S6i Semi4 >5ini# >)BSO NO>0U U>pe)' B�Spf 7pfFio�Jai StabB�W >�ti�tFUT T>�ts ts> TMemb{T_M�2-em>� univ� :va��va>�varep{  siloN �V��VB�w)2w����Nnh{\wcL}{* {\cal L��)NN)NF)A6(A6 {\wB6!BB!D6!DB!F6!FB!G6!:J {\wK6!KBBH6!HB!:8:V{\w:0:� {\wP6cPBcQ6!QB!R6!RB!S6!SB!T6!TB!U6!:� {\wm6!:� {\wj!� :_AV:b {\we:H {\wlambda"\ 2{\wthet'\ :%tn�> aB:n�ts�:{\wxi"�\x:�{\oA#&�,F,owT�ovew0\ >�4� * 6'o)7�arVD odel)+# :goz-�" >!ps%  > kapp%�! ># �{.7 }B���5.B"2�oBE�"_B�ob6$bN$Bk2�B}_:{lz>% {j_0F�E2'EF!���KF!��!F�o��!PFB�x!R!>�6Kb� BbC�C>�b� Bb�Bb�B�b��B�b%B�b��B�bO�:5 {\b%O8B�b��B�b%fB�b��B�bZ�Z>PNR}{N_� BVXR}{XbYR}{Y.6�c%�=B�c%�B�cE�E>�c%�B�c%�B�cI�IBQ%�B�cM6MB6%�6B�c%�B�c%�B�c�B�cV�\ 2�cXXB�YYBE lA 6Rfm7 frakF�fn�B�j��"�"}[subsG"]{T#��& prop6'Propos�6+lemma6,L2wcor6$ Corollary6( main �}�re. the2(6C clai:�C FG ,>Aone#.*CNKP ���#J< defn6DJ*not�6.N2lassume6*Ap�s6-con�60C2[say726"exampl:~E 2L prob6JProble:�alg6&Algorith:(re:�R)k6trs6Q ):�6'Not�-�{summA�2S 2� ack}:'ND' :� \ra{\m�it �4\ \stepcountera�a}Ap0thma.}\quad} �!v!uk!\pf� Y{\pf}{\<'} \fi �!% :5cal.~cal� ath  =:;Bbb6qBbb 9bFV6�J678�:n�>68 8 �6Sb2�{\S�a�tack{��65endB8}{2 :X Mc}{�MB` e e>5ir�op{ 2{\I >n!2op{ �6@<}{w$B�>�"a%(7.� rtimes}{>j5pt \tri.� BOtheenumiVoman{ B(W* {(6)) begin*� \setU�(ocdepth}{1}2��}{0} \t�$,[Conics on a�@ic hypersurface] ��r#�} \author{Masao Jinzenji, Iku Nakamura E8Yasuki Suzuki} !$�� abst}"�paper�comput)� ribu��( from doubl]ver map�&�genus 0 degree 2 Gromov-Witten invariau)of.� typK ���.8s. Our results*�'%-Eal&_H Aspinwall-Morrison� mula2I t2i @some �&8 cases. \\ MSC-�T: 14H99, 14N35, 32G20 �9M\-� {Introduc!8�* abelA:2I�9|discussB��m`'1fo ��*r�al nz8Calabi-Yau mani��! AM}, n} toJ� of a:# $L$I�-� $k$ .Z, $M_{N}^{k}$f*\$\bP^{N-1}$. N\"aively,�+a^#$finite setjele@Xs $\alpha_{j}\in H^{*}(_,\bZ) "1^� $�~ � O}_{]1}} .$2}}\cdots 21n}}�$gle_{0,d}$�� �,s !�number!100d$ (possibly \#s. a�$reducible)� curve�Ca �t �,rA} real*-!�)�*%5+$1D are Poincar\'e-du}".g$. Re&,}#�mirror� EnA�~pV-�$ with negae�,first chern ejP ($k-N>0$) was establ!dADV$gcU�iri jin}.*�$method p�)nt Ath�-article�0can �e�!+]e^{m_A] 2}J n��M$ where $e$L&!Q��toE$H^{1,1B�. Brief!�F�6� \;\;(k>N)eo)+! goes�.$follows. WP#t��� �.ODEJ�&$\biggl((\p!<al_{x})i�-ke  \exp(x) (k.*+k-1) B2) .s:1)or)w(x)=0s%�Bifu�O end{0%�^a0�"ruc7$ virtA�dGauss-Manin system associaA E�(�1X)�narra��{�4_{N-2-m}(x)&=&>1 H+ \sum_{d=1}^{\inftS!&d1' ;0L}_{m}^{N,k,d�o o$1-m-(N-k)dv5gm})�Mim$ run�} rough all%�- gers�j $ i6�E�non-zero 1ly if|'Tq m\leq N-1+(k-N)d$. FAI?atibil.of2c%�)t�),�%a�derArecurs���at de�0e �Z�'s:*/)*} &&)�n=0��-11��n-~ 1}w^{n}= I�� d_{j%�3(jw�j)), \no��\\]m]9.d9�z^{m}=M N$ ,� z ast �5*� � ��Q�2�r"alw�6�. �� On�.)as!71d��(�<|ty)��es f��n*2&5� 2^�e�>�($N=k$)&/�7or ��� d$ tb � �%D:�e�46L �$\phi� a� y � 1� nto a"� �d}{m}$:5 $C\hook�+$arrow M_{k�~` Th!.05G6� %7 �ex��s� �@!1� funda6al R of6o &�$. Let $C$A�a � l�d>���� �Its nor,=0bundle $N_{C/�M de o �$to a direc�7m��2 A.� *� j2*} :_(\simeq O_{CD\oplusV^(lus {(k-5)}>�1*} )A :�' o 1!(holomorphic!��YT. Sinc; pull-backIU�:�� s�by�� v.phV9 � � }(-m�v9k-5}},X1b �W� ͎ $h^{��^�$)=2m-2$. O�e '!(r hand, let2<;}0}(M,d)EuA�(moduli spac��$0$-po�id�0blei�of5nd$ e.{$0$m�to $M�=ne>] %�� �1 fi� {$\pi: &��C,mb $-j Then�,push-forward! !Of �_<c_{top}(v} (1�>�))in��u9.Aby�Du` �y j �)U.�61��!iS3ur�?u��be"4 �V1}{d^�  i�=pen�>n nei��z st��5�basVm9� ��)$��: globC>Rfib� . But�n $k C ��. ��u� ncentrates�of  , m �4a�Fb !5p�05:,Ekis just� �^^�. Az2SR�M� ,1)$�5a2��N��"7E%lV`2)`�Gx.8mannian $G(2, Na�>b�, $2$ �,i94 �V=\bC^{NArA� ll beg1wn lat%_ �icŹ ,��L/��� >�J�N_27��L�б� k-N+2}��L��2N-��:c6*} ByŌH ŏita�!ѹ2$�˥��*� L$, &Ec9,J��>.�%�1��2V� OR#P�g� f� < reforA�F�.�))=%9IPchA�$strictly gaSa�an�B,�e�2w ��erR�L,2)$wAusa�nMF�6%lg:W R�W! i$ i*7B��: .� ��9� OabqU��.�Bestim�hA".gb�Q: -�6:�"B�^{aQ?b:c*10,2}$, A�2�Ŏ�Z !�ch��at @š cy� Poa� � $�, e^{b}Fcoon =) (��6� � -� sameb)acusat��in �F{Katz2�C�<*C9&��byE ar Ose�t�Md"�e�ed (3N�&&��!� =(\mbox�2C of 6�D)�})+B\int_{��N)}0S^{k}Q)\wedge^l[�c$-1}Q)} {1-  1}{2<1}(Q)#r]_2 Bs�G_{a� T b-(= gma_{cfGJ'dc7?e;}QQ5 !m�0H:l�H �H � � $, $� a}$ �� a SchuberM��;d!�$ a={0� 9B:=�41}{c(Q^{\vee})Q�[*-��7� of pickAIup�5 $�$�#*��\pa!�.� we�;!F�w� � ly !.*&�%tEf� >><M �ơ~F�V �z�� 8��p� 6� .� 6�)���J�Fdeb� J� ���Z �� �u!� natu�Jro� on. He��fac $8$��e�r� axio/6@.� ��� p� Vpr�IIB�>�} -�6�2# :�=��8����.��r�"�T � combina�(5)��KreVJ�A$ (4) immed�ly.i��(4�se�a����� u�E*S��Žde&(at most $2^��� � "�V��6"� � *� � � d��AQ eff�R���E�t . \�JWe �( �� Gtotal m:Fm$ofq saQis"��f }�72}Q)$ QG:=J�M*� \h6�ѵ ��i)$ algebraic Q$-�' 6t^{ }$ ({�"ns�4Mumford). As asequence� e�Qo� all  2N�N })$ >7Q!Ont�Naf�^�Iuf�%�O ��!�.SQ as sugges�in�,thber}. See [S�-< 9]{Vistoli89}. !��Pdid�numeri9exper?P� n� $3$6����.Yby*i " f �({ES}. For V"%ore%� new!�"�4 :k  to nodal � !.�z�not appWHM:�# m�, Fj2�s\ farZP[,Ywe le�DY" l analysi5$e��,lem�fu0 works. T")! organized.6"qF1�1�W`ze Y@(acteristics� >��B7@O�4.W&<�vNIn�2�study�2�b�1U I����� view���$� �"identify`��12� sho atƂi��� Z��9G$.�&�J4�describe]$2R.l�S��c�F sh�F�B\bm��2l5l1�!*1 $S�P!^-�=Ob5�.P�g�!�&�fM!WR�g��1�l1Qtwo9al5�2=,=psi�+-U�ysi z(W)\to�!�-�� r�V �&$i^*_X':V4W /Qh hom�nsm%u�W 2mW(�)$ necessary)�T�� exis,9Tb*QV�eO5��Ta .���cB*}:�)}\o& �V �f�$i2@24,�� %F5 F9�AOV�2GXo $Ka�2�}E!� 7a%��g$M$�\L�7aTbe!I�$,#ivalenV$W]m�A�"X6 $L }t M$ im�s&h k+1�n�6) $W�cliy�=m� ux��alsA�a�)�=2N-40H�w9 fer"�8|2 :E*.&e/on M} If��k+5� �crU`at� "�9��� m � � [�,p.152].f$G��!>subm�� �$R�2Ney�Zo�Q=P C})_{|Gere��gU��.o�. By �95]�f%�*Ge� nonempty.�Ii^*:O_{G:$�>�6%$d_ *"�5Q4 ndA⁁P�HG�H�w��onM�L"�� !D%M&� ,ube� exact,��7fauX �6hKs2�� �words, H�epi�!smi� �U>, indu�Za�ph0$i:�,\bP_G(V):=G\�����q a cl�"mm��in!�>�=$P%��p��A' "�R%R=(p_1AZP� I�L�څIQ ` G9� >�*} 6P 2 :=\pi^{-; si)� �V��t \�T\�+�%V.2V�*.�l# >)4r<:\ }$}�M argPP!� �T "�A�w�`|nm��, �b-a!_W� woheadrPa�%�_ $. %Yus rec� a�&KE� �N�$$\CD 0 @>>>�� A (1)���@>D>> T}: 0��CD.)$(�X61DEMk�1� alig!�D(ayv y ):&=aD_{(�: (a�nO �((1))\\ (D_{(}F)(uE(d}{dt} F+t2))_{t='8A�`�� (ous polynomyc$F�S�n%�s,�!1G!�sY0(.�5 �=VB%O(V� = �!�NNA�$HT)$\  $5A� $\bC: id_V�WeɄh�L^IszJ T_{LIH (M()_LE+NS \bP  0\\YLU{LVw_L>FR 0�LJ~QTš6�6+ of L!"P}� "��!H*'ȍ{O2�(1�/W-�),\ !�9��W1�J5 �.xE� ��pf�� sser�is cl� �&6��=uG ve �Qram�,rowrd column~�OZ��@>(D_L�}�<1�A@VV{}V I�}1��J%@VVV �:A:\\~2| e.d�$ ��R�%�N��� 5R�e�L, {$)=W$. \qedU%� �) $T_L]�2�� i�-��sQA]��A�e�)e�E�a�)_L �%Y�)%�)/O_L ��:�@>KA,>Zkn� ��sN�^ �=A^Lie�${�U^0(L) $End}(W,W)/%�&er}>�5W� =A1�p9�,g �Js*�1X=��E�Im}*!N�Hom}(V�bC i^*_WF. "� ag�^see���U=� )&=(oJ_)/)$bC ,id}_W�t&�J��/@ �� I^. . g $HI��QɁ���B���eq��4} 0\toɏM} !� !M)��(}Xk))#�x5�}1oso�6wx� B�*}i}�A!�eVM}eg�).+Agk�< H^12=�R�U ��Q�_2�/�}��(09�-_ B� �!W��U�J0� set{6��Bong& } S^kWI.�^�C# �"! cor}�G��(�a�holml9.l=0$M�D1B pf}A%�-� , .ah^05-h=�  .n =2(N-2"��!=;.�A�coTI-�� B�>�BhvC)=N >�}i�*�*�2�l&L/k$�2�amG$item[(i)]\"� y�Jh1a�� a!�9�*bC'� $ak-5b'b=�) f g\S[E�D^{-}_L� S 1}W/J���$ 4:=D_L\�� �Q@.��U)f1tpf� MZ>6:� L$-�Y%�� �9�los� B5��may�u=(�( $� @ -�e�d� -Ke_2� �@*/�� : La�\b]�e by $[s:t]#[x_1,�:0s,x_N]=[s,t,00]. $$P n $F�e.� 1Cx�C$ is wriEa-@$F=x_3F_3+x_4F_4+ w+x_NF_Ng �&s $F_j��$k-1$.�$f_j=t$^*F_j=F_j(6�E�!Now!z#:i�mhIa�4� y�#Z:A�F> �RM�>A�k-<>H 5>nL�w)t�����@="�UE. ���I��`M ^Ba�*�q�� ν��V� "l)yRi}hA�. (e_jM�)=f_j�K (j=3,4Q�N)W AiLic choik4FliJ �GEg6�fA�$Bm�$sm�t�A`�p:s&�;gaa�A\�Ye?W="�=Bs,\\D4ռB%ͺ�kk+1 K!�}W�5~��hb��we�:cho�4 !mU��$N(�"fix once���)JTgF{�eRYz-�lar�And4ent�U,v)] $Wf_3+Wf�aWf_N=��J] 2fE�i�P� by (�3|clUD)!7.1�m~(i#u4. Nex�3��>� a�Bfv&�' $$�=W�'2#J=e& _L)(f ),$�:!�{��sur��q�4�&� �� ��$E��$am5b"J9$a+b=�>k1V)=N-3 (-b=\deg.2-kh^ (i).>�2s* !quint:�Le�� 4$}=8, Appendix A]�/A2e7�=t' mpl�!�N=�k=5"6 f^' 67J�Ce 5�, a*�$ 3-fold�ADF = x_4x_1^4 + x_5�v 3^54 5^5��F~H�NM�M=\{F=0\}nrw x�d8L=\{x_3=x_4=x_5*=\{'0,0]\tI�"asea�3=0{ f_4=s^4$ 8 f_5=t^(0B�(1)�QE�2[\Ke6+ �5 e1u*! 9U�ŀ=\Ff E�3.�.Q�U�=��&� 3"RSHu�Riz!Je abova?�dimF�1I�� �F=ns-l�mn~z�.)=_L*�B��2:�TI X5!w�F��$f%�%�aRv pair(4 &!��4W$��B ��4��546��Y*�?ME) _o sfie��??�,Dn.<#C1v]�F �%)� How l!����� �, M�� s^3t n�h�VL-�1�(!� 0)D4�8er��_ �%b� Y with23� A�� .AmBE�.� 2a�� $�L3�L�  3x_2+�V+"{5�P�<��}%9a�5;3tY%�. S1?E��WfM5.��� ��.�{ �c(.$a \bC(t�!-se_4? a�e� A� *� )G .BYm�.^:}J#2� :m easi Ohow�7b� ��/�Q��6�2��n�-|��T:f>b0/ 2�,7}^{8}� �<6$&Y(�Z:�vNF#N=7 �k=8�{*�!!�\"{.1 uQnyR�!��c8a��(V�dP^6z��:�, $a=1ab=�M�&4 .71&-;3:�-�Y�',L: x_j=0\ (j� 3�we tak&�"� F_3=8a�7, F_4 6x_25 4AJ36 E[572^7� >�x_5F_�(6F_6+x_7F_7�*8�*567^8���Y let $M=M_MI:Fe q�i�B0 �v�(C h��L2iso�=d�uiti� �� it� st�=un� �<us�� 2�Ÿ.��3y�m�sp�B2�5 span�$Z� $, h�  a�)Tsi]Ed�m�)$�!vA�n�9�9� 1�os5b (;�.�%b�WifmM�mGi(v�^5 �E`E�'*Lr �-U�$:G�C} �V�lEN$-.�M1E,� $G(r�GgR�)$r6U",W�A�� "c5-N�yof `r�&�D �via GITW7i�mU�:{6�, $X=\Hom(V,U)�XB�(X9�.�map��Q/SL(Lm�$X$&�"q^ by:u�&$(g�D*)(v)= �<*(v))���t\ ,� X,\ �.]\Z� �D^ 8$�M E�$ �%_�L\Lo�Zft&�$ $h �=r$,\\^FU�!VK+KR}M��(�<,a92� r�}!�JUQ2"62 torus $T� �&\? clos*I�j $T5��"U�VMa�A#ing si�"� $(r=� R�"lim_{t\0}��$pmatrix}t&$0&td*v1�a_{11}&2}&�sN}�$&0Z9=n� tQ1}&YzZ-�]���amf91�*W$��b�D>:�3m% s, �iW,S^2U�%; �c�m �d�c^mFPc3 �uĵyi>|�0!�n�_)`:iD$(u_1u_2)=\�DHgm a��@forA�u_1,u_2A"UE �S1��Bl�.������0 ����T �h���*�. )]�{1E�unmQifp (w)$h M?roo�d` y $w�W&� m <Ua� WXiI^Yn"!bZs %X�non�G:f [:]K h :e4�NQiL�\6ubs�]�%I%� AsU�e(^*U)p1Z�h6� =2VF �sui��is.��U.�a!�((w)=a(w)s^2�}1�c�4�ЉU͡f��isq2!b� �=� �Cs}. ri]�Y2!t<ڭ��'�!.*�>)�. P)�".�+� �t 0_&q})W , $t5T�iw_Iw_2 c���(w_1)=s�If-�(w�as^2+bs&�=�.�%G%-E>a�AKI="�%l�$ thm: �o� e Zariski�Hn9�1�estk6ll.����X��x( \)J:H ��'$%@$Y�25.��P n $Y��`2�m��u8f};�A"a st �.++B5�s2��%�%�)��7baAa��7� �ju� �� b.o�Y c� nd $X'=�3a��X;mLI2st��~Z'= RZ  X'��=�+I�Z'E�c 0.M��1��.@EC%�(Z'.t1iC)i�Q���#E8.��..I�AA�2Bst+Ct�gB !E�2bst+c!�:�ieasy to�eck"C8+� �d$\.� a\ g!j) &J �� �MT?MRJ\A=au^2,\ B=b,\ C=u^{-2}cR�u\_� �&� each�9i^:c7 a�&a>(Z.�E"I`Z4A� $(AC,B �>%�sJG2�[�%2R�r2�!bM_[Mphi�%A� (w_jEH _0=-z_1+)2�Le"71 0&=r_1EF$r_2st+r_3t!b\ 1&=p p p6 2&=q q q_@�BkA�w�M�S"@D_1=p_2^2-p_1p_3,/D_2=q q_1q\ D_0=r8r_1r_3=D_1+D_2+� q_2-8q_3�q_1hk To� 9j,�9~m�Vprecis�-">�&� \piJS=V�8\bC[D_0,D_1,D_2J_�pur�<��6 $Y%�i(2��^;%�jI�has\ no\� \� }\}2�. Is\&T� �$Y_1= \���\ H{D_0}{D_"��D_2 ]�U���i�Xa�R: E�ArI��Y_"�(}k�\beta��OV ��1  �U&O& Y_1� :� Q h� e�1�Uu&�L\ga_v(s - � t)M� v = )'1}6)�( gBO� "� 1 &a\\Hi9+����=\sqrt�l-=�*Y �����"�/\" �q��2=*@ hi_2 ) &�aY xh^4 uv, A_1u^2+2B_1uv+C_1v^2J�V �>lA�Uq_1^2�Dq_ �>�-B $)�(+q_2( +).C -^2 RaAn%:�+�V� 2st, 6z)�2��5�AM2A_1}{p_5Q},\ BBJCCJp^2K=4�u \\ AC=B^2GTu��;I�D_0-D_1-2a�-(�!)�JT a�i�hal� � Y_1�� �e�%]=��dF^��] �T�Z� *Xlet� ��7��A:'M�L1� cor:c=W� Y^s�= (X_s6@ 3$ eP Y^s�Mnicz$Y�-p�Y"�>:D_0^2+Da��^2-2D_0!�!�D_=�K��gpf}In", c{�2� ,��)�5�AC, B��-Y�I ��u�� t? !g%dɴdA$AC�"4H�$�!)K ied �#>�$M ic>�+�=�a �X^0-�X^0�?je �Msizf �v���R<U[��Y^0\ ^0:5!�n %)r 3^0)1 Y 6| �.�6�A� ,)�^ fcap�h%4Ey!�oreN}в? >> �Z^02(X'��"a ^U .�In�we�@ ��,&� 2):' \u F� -� ���Gr��}�� 6t '; Au op{or}\ C �dIa.V as b�  �% �6fR�,a�Q!N3��6� ; s2H=a�f(ArZp"6>��G���\ (2)u>N�S tern;tRS� .�)�^2$™&�\i&� Gaz�b/.�;�b!�& conv�Oo�&�Ut�p��3�=Um��D/\bG_m$: $(u:v)=us '+vt � =!�~ $(mb-$0k�]$*�1AZw� �68�04>���>� P:=(a_1:aCi� Q:=(b_1:b� of *�!W.�� %PeQA�*]�c�!�hi�a(Us9 N$WmifR�at 6F��Nunique�[t#;"� �1w �!�Z>�.F[un$�2 �gG{�-/Q6�(�>�&�ec:R7}2^< :�)( revisited}� �I)"�VzL&�Rgen~W2�*�|>t*�f)�f)�f)nf) ^5_8b)!\often��U(CA{�w�oa n+ x)1{�)i�!m)�-E�&^5���-Y-�$vQq� '/M}��O�;&�11)"�<:+ �J 2�- /2 x>�/he�� �is�O%,& qfa�y��\Zp2l�,�; $�+5�+^ |/^W1x_1�,\�(E���^*=�,_2)�A �en $\13 ^*5ae��#~~��_2*8/@_1&=/$,� Z#�%Re by jUk' _1^52 ��.3 4$o >! 6� o�.��6 F] R�� .�)R1� y\FG �/��řN� InE"MD��FQQ:_0gᶥ$ � h�e6 n"�Hon�#�,b5"�5,� �^s r��q z�D � (=L&��&%�,phFS�Nb��ty�Pq4�j�Y���s�TF7 ce $�B#/HD\�Ja�k) 0!: k=8)\!''�ā2i{Ran�/z�=s �y � 4C D_L}\64C 3.�,*miX-N�vs��-0��N�C"XN�3 � �HA�\ AJ*:�= :�HO_{1�}(2�E .�= 06j0CD@�$ $\eta=q_3�L�?q_7e_7&� N�, $q_q<2U�;�fF�T(q_�B1^5+q_4   2+q_�}3aO2^3+q_6 5)=-q_7 7J� S�4�& 4 /� mu� ly p�_i�q_j��&�9yZ ��7=0h ��� ���2^3���.��! $q_6wɱl�BmA�.$q�9�T7] $5c5a2��PCN��ه�vu[6�! b��!�^*/&�a��i$,���/ ;�.��Cv_1�-� 2=�� � \nu st + ��Is��$ %=M#$$\nu\in\bCa*W��ɱ��enI*�s $�m^*W=S^3��S<�C�~ �#4U}S^{�t}>A {2m}�&r8m�4235t��)YS�_mC@)=T>� ?4�3Z(i�Ue&�$m",al�R:�(S^mW)&=������v =S^4V� � : V)>* � � +2}U�Q ��p& B�:16}B>s7� � 7Y]�)ơ��N/ ��F6� 7(Sh/5G @qD ?%y.`" 5K.z::b.u$�,=^Eq\W%� '�t N� =S^8�]�*�< Le9i"h&�jU e�j9'6. .�)�'*Z �,\Y we *�H E�� 2=��+���Y�� *> n(cha�Hf�"B�a$C'�Xl ��$C'% C#i�&b��s ransFK%��U� q�>�"1 �S��Y� `un� *o'I�% ''$, say�L phi='\cup �$�" %�4;si5H+�'T�� S�i����4mt,�#_)� ;2W;2*E("U#�$_j�`B�{/U5zh=ͦ+�Ph( �''����''��+EtfAKS ;3 �� ar park� n2)wi ?s=�6$ ][��(D'�; 9�rHom!:�).�*+9C''!E Fur��� B ABl" �WL$J �� �� � �P�s)n�.vnUcal2�~�V!�^_ �TU�t �8 A� ]JAu `2*�V}qV @6�Vt� A _) �Vx 1F�IHʉO_L�Uۀ��}(k*���,��ER� � -�Ab��>�N�5\C2z6)M}"xg8/�Lv6��>>YQU6h"-� �!�*�V %5�~u�\�r�@�=\ %�+Fj%t�3JlwC >QNM}�I1JT9 ��bo��� y; 6,6*9.�J $U'"" .�>�U$> � vanisH��U��Y�$&�fAT]2�>�AŪ#>{b�):�^U'b�$ �Pt\� � 5-$ "sI� \siR� RS^7U/ *1 Bd �\&{ #�L Y�R�BR!^{Si�"� ȇc_�&j:%jb"*�U1!CH *}l�a 1I)^*!��-�6f �X� V4: Yq��:��Oa6J06� %��(@&�tSl�opcAv��1$%\# :kere�%�}�*�2 �X��H"k Fh&� ^*!Y�&VrZ1r1s:� -t��1�":# Wz, aG �D\/�7 L_0$�=$\bL_1$)_ Y\ (I�*��) assign)%�-�X^0\ni ��B 1(! \w %ze��:��G�k �O�b ��)J�_Wed� )i.�E�"�+12)$-v��r<chang0b�  EP� |"� �B��sR��c*}R*Zfh�JA�4#a� �(a�is+ �x�s�D�dX�)V0ZV!yC of� I'a{Z�. Vq(I��& :O(-1/�".�co� nt�uM�QWc��3V�(�i0Remark below)ڦ���]Q�U|^2N&(��. �}�$A��GIT-quo|�h$%Aca.( <�4: F^'�+\{�'"r�;�0�,j?&o .g�,J!lambda,"Q\lT X'�0�f p Tq sRa^� s� p, q7 bC\�%-R �/FSc^!�G % �%�e*(7YR I�mapI�$���eV�%�f�=Z_�tinvol��q-LN�r:\;(�.)@}s+t,:-��a\h J2->-t)����ref�*�Y ~Q_e��*} 2st���#:�6�}(>m+t)^2-B�-�� �|A)��A9f\nu}{�h+�Z�+^�io=�5 YRR�^�E�{1�MK�v \;\;.22} )�!-t^2)r4:� 9���,EiQ")�{2���:T�Bx�9�{ !���2}2,@�Ee� (o eigenvalui`�_ EL$Y1��$�ecan�-alqore�S��7{*}B' S�l� *Qr͌e_ $�C f�<Y_:!0�sb�y�r*toV\)4:"��8G�2J�/,2})$-"�z� pu^2-v78� !��\��!G2=2uv�3a�F.�v\GL��"c B,$J2 (u,GD��]0s�0i��1}��'3-�1)^2}(2u�0(>7 v)E� t�WN j]Wq�";(�~4v�"�4���E�Qm�LN Un!i������Aa�"$hi_���m!��$�D)�V�61}1i�!knuA�- ) }�3���� &(}uv+v^2=: p+2q  , \;oE^R&E�e ���1 P-vn=-�2}{%aM}( � s&-t) .�5656�}f8 /�S�2{�2V. �� �шu�=%�fC�n��2�] >G �� #X'_`X�%>� a�+c�0 $2( � �>J�-� 6jY��� ת t�R11m]��ega� �P�Q$�H�Y"S|U�Fi�w"� �_0=y% ���;atlas�=_� ��23% p'$( 1 =0,1F�c_ ��J80��n 0U\ ,\pm�=_0 {0rJ � 0.� 1=A� 2+2bm�&& F � \ a, b9 $�1��1n�� �ps�yV ��">8 �% z82)v�~_ � 2=ps �,Ns 9� a�k%� J� {2}W)i"H%�� $c_1(\bL)�G2}uW 71)��e _� �G $A(5)�Q}=A(X �FW r \bQ}K es�VH1P}�axm'��Ʈb�P.�A�Ec{�6�UX��1}{̇�͇��"��� "��� p/�y &.w`\bar{"�p��kx ����V$z��&.7pf}+���oŐ�1�:��u�nF�W��֭�}(͸� �v)�W^r����pL(tM�at��in j� � �top�"rU�� k�Ae�bQ/("'\*O_{G})/ "_�2r"{I�>�!GE�Q�G&.T)�s��~r�b�K&g�$�VveUa�F�$r�mbFu�to � � )W! $�����2��!u�$�#uփ`��:�fp} %�set-up���ar'} �2-&\&�O &�{q y.  n�3,'�Co��\Z� �\�_� ��H^)�-A]E �FIF)��z� $c� �^}�V�!e��*��n&&��:����"W�ŕK e�\�"�+�;� +2-j��e�� y�"��z^{j}J$6B^{8>{J�k-N�wsx�U���vb5��=cG� � c*‘ N�m&&4�2�-Y�83����2��a�$j$-th *���0�Q�hut�R� a�X $c~�(1+\ ) � )�e�C1�/N�I��n6 ��(1- ) �} :)E�. tA3A�=yrV�� *�\h/ {30em}h �'�%,��&��!���p!B'�b��"w�+ =-�i� %<��$"<$&�%Zh�I%"`��*und� nN��. � p6 =# && \��=� �����2} +8 �Zv �mc&�0,1j@ �% 2.u2}"��&� BKVI�;� "j;O��/J�@ c�9x: � ��:J:* he���l:�d &�� V)} ��S^.��V; \8�\LS^]�6$[�.$$O E�%\newpag��� �li%��wii�cubicD�]) 3e��a b�q�3*< e� d�"�*���d k-N=�P"� V2mm$�lit.IZ.�V�����7��l �4}(27k� -55k+26)k}q�L 2}{9<r)b Q�+� l H7}{6}(�2<12< 2}(Q" ��{��&� R\�L,32 ]4�(&�Q~M�|2�!� >1$ b+ED ��Q)�!�e�=��, y-c $d=3D"] anrt.-�ILt �Dv.��+�� $(2+Z�igh�P (1+1� �J<�; �ma�+���E� � \vee�@̩ tْ�ݔLk # L: 2.5�$�7\da��A�� _sei~)r$a� Z&\!_$)�H;to#!Y� )a-SueM9�%� also&��#.��x5� d!$e�)�E7)�x-8�#�픅�IfELe��U�U�3�}��� !H�(2�:�m}d�%%3�%%3 �]3} �n 1}{k�nl(� 9}{4 !Ε6YƲ��;�[2} N-5}6a� & �3Z�N7e.���2c+.0�~Ri N-c-4}C��6�1�zj b�bFA6�a��aB�a�c:��2b��bB�b>����+27-�Z%6�J�.��y �y 3}�?�$hewD�6 W�:ʣ�� &e^� �r�b ��m�"2+�qmJ^� u��e�G��l=�"P $N-6+N-6-(N-4)+2=N-6"�i!������>=95-3)=F�1,v�$B���MX�)tmF�(Y�@�[ ����or?3 $\�� {\piRT$ �+�2-��l3.<�Z&����ats O}&ڑlo��y 6� >�1�$N�T$'.ɫ�05�&�V &|�E6<� ^ �3I����< � "��( ��]s���1n ��y/9����m-�$d=&.AQ��j zU&�í -n}}tv A:ula%0add�H�[!_�atoria��$�i) Av in‡of exKlK\r2 $.����2b}}E 6c}�B�2\ɗ�±}vX��61��]v�2J%6�����6�+ʮ� � �S�� ���n��Tc�2� o�f���:���� 6�bU��:���� ��J�2!�2Zt6%K v[6�� %M� 2M�6d���2� �2�!� �7�72�>� V�� : 2�Z� ��2*��:�2\B� !��p ��u :# �6H��*�2�>�2BS��� 2SZ�,.&25�����v�>�B��m.\\� *� x1las��C��g�8b��� �we want>�2Y\ :��${��daggerq .�� �� 6��K�tDV��!of Mate�L�, Grad�"SOfl HScience, Hokkaido "$�y�IQ, Kita-ku, Sa��Do, 060-0810, Japan{e-mail� ress: $ �l$ jin@math.sci.hokudai.ac.jpU �$$ nakamuraZ)}-0W the.K� }{KKMSD73�ibr�AM]�� P.S.~"( , D.R.~") %5Topolog_>F�xA ory � R�8Curves} Commun.!_`.Phys. 151 (1993) 245-262�h �BT]�"X A.~Bertram, M. ~Thadde?� �Aquantum%om�� a symmet]�U���1S�W4w@\}, %n$AG/9803026o�4CG]{gc}T.~Coat�n� .~Gi�Wal,��block� Q �RieBu$-Roch, LefX�tz%%SerreR) {0110142.{ES]� G.~El�Msrud, !�(.~Stromme, vBott's�*eD!��l&x gp�t alg-/9411005.tFP]P$x B.~Fantechi, R.~Pandharipande,)S�l�rbranchsl�9905104��5[ Iri]K�( H.~Iritani [1ED-Je�q"�ed��"�7EvtDG/041.�J]{�� M.~"�� �C&�.C�7A-.��S�m�G�TA ed M��T�D�]S0310212�K1]��} S.~�)�M�Uxneh�8ejE�,�4�t@���s�� Comp\^���= {\bf 60}ak86)av-166�2 �2�EOu�uJ�s:gBYprediJ�4Mirror Symmetr��y}, alg-geom/9301006. \bibitem[KM]{km}M.~Kontsevich, Yu.~Manin, {\it Gromov-Witten classes, quantum cohomology, and enumerative z�etry}, Commun.Math.Phys. 164 (1994) 525-562. �$M]{manin} � . {\�en`8ng functions in�ebraic w ���sums over trees}, The Mo duli Space of Curves, ed. by R. Dijkgraaf, C. Faber, G. van der Geer, Progress in Math. vol. 129, Birkh\"aus+ 1995, 401.�@V]{Vistoli89} A.~  �Interse� theory o.�stacks�o"ir mo�s�� Invent. % 97!y�89) 613-670. \end{thebibliography} 4document}t\cA �{amsart} \usepackage[mathscr]{eucal}.1,,amsfonts} %;p{showkeys} %\parskip=\small amountDhoffset -1.5cm %\vDtextwidth 15.5true height 21 \new%_em!orem}{T!p em}[-�]2'definiA�}[ ;]{D2-propos>.P2/ corollary[C2+lemma'L2#example%E 2' conjectur.*C2-remarkSR � \makeatletter \@addtoreset{equa%1{-R}.oth-0{\bC}{{\bf C} �D DBH HBN NBR RBS S�2�cAa cal A>:cB.BB�>B�c�B�cE.]EB]F.FBG.GB%B|BGcK.>KB>L.LBM.MB%�|B�cP.>PB>%�>B�c%�!�6�T.]TB]U.UBV.V>fIfrak I> cJ ANJBO.OB^>F]W.>WB�CU�bbF�N5�bbF�QQ\ bb Q>�ZZZ>DU�bbF�R5�bbF�FU�bbF�T5�bb%�2�@lhk}{\cL(\cH,\cK):glfg F,\cGB hHBZV6w8ran}{\hbox{\rm{}\,��%�,dimen\expt %l=.1ex %\def\boxit#1{\setbox0 GX$\displaystyle{#1}$} %  "\lower.4Q %23.( \dp0:@v�hrule �BMv� \h�� `P Jv�0 2�}%�"F[}N�}1�\begin&� \page)#plain}� %flushrV%9� DateZ Dthis draft: \today!�nd24 \big�� \title{Orthogonal polynomials \\ in several non-��ut 0variables. II� Dauthor{ T. Banks }DT. Constantinescu} 4address{Depart� �5 ematics, University4Texas at Dalla #�Box 830688, Richardson, TX 75083- U. S. A.i $mail{\tt b� @utdP.ed�\ tiberiu>" -�(abstract} I 4is paper we co�4ue to investig!�a certai� �0Hankel-like � ve � ,e kernels us!W 4r associated oR�. The mhresul%dE% �is aboutP stru� �% kind |K AM�� EG1sA {IntroduN } P� N�ar{ udied for�ir � (fold applic� AlJasi" 4 a special typ� � $K$)H!(A@e free semigroup� $N$ ge� ors with� O �erty that $$K(\alpha \sigma ,\tau )=K( I#) $$ �(any words $ C,3($$, where $A $ denotes�> obA;(ed by writtAR$�the rea:e orderE sYGappear+m�sit. s, see%�ie�0ce \cite{CG1}� ,2}. Our goalAJDto determine an ex!�it>Ye F� 1�satisfy��abovea:arianc9� . Sii)�< case $N=1$ such>�Efprecisel!�empQ%, it�$quite natu��toa�Ib�n to studeirQ>i�*!..� establish-� conni?( between mo�uPJacobi coefficients, � multi%%0ble extensiona�a >ip �. We als!�scribe%l ^ ._A!�e0pi�^p �V\} W!։!A�R�o�}hAW tian�yE�(we discuss Ѩge�l � s. E�ly,��emphasiz �husefulness of a matrix not�ti�4reduces very mA`!deg�Gof co�x��A � s clac*analogy �T5�, one-H !�al A�@. Let $\FF _N^+$ -�unital)��� on>�0$1,\ldots ,N$ wlexicmic � $\a $. In �icular, {^+_1$a��$\NN _0$�nA�� �8!&!%� a�tal�� = $*$-��h$\CC �� phi A) at ictlyه�al �0i�, E�is!� ?}�ar � ma" 1�and $/(P^+P)>0� q y�O _N-\{0\��� (Gelfand-Nai� -Seg��z � � ed to b$ �U(s a HilbertY�H�m�}.� $\{=k\9���FF�>}� a �ly ��pen�t fami!�h�0 Gram-Schmidt cedure� >$\{\var�_{�  }\} :�6&� � %�B��{bond1} Jg�\beta �eq �}a�, !��+��quad .$� }>0;:�n�(2} \langle B�},. yo-_{)�= \delta ��, �6.OBa�Q� $P_1, P_20�� , $$�r ��!�A�_2P_1).��A�� �F��� �pM�� called�nW norm:�a�ed� i~ɉnotic� a�u�f�%F� ss dE���I chose� a@w . A �] )wouldE� aM� of Z  Dtn_ grad�o2w �possibl<(develop a b�� approach�buI� e U �V��X? J� ��0ed�X DX}. How��,:p*>��2� -Uon 2x EW�of1�� $$s�W=I���), m�.vA��wD � k �.qb�a7mula $Kq�m�)= s_�~i�)m�]� ).�F�`��po�F9!�% & a� ql6YuB ^�h�} B�-J: )=)b ,&�n ).>&T� "J view a�� cond�. Con��ieas��s�i�b'�Uies� �!�e re exisgJ *1�oA�"ٝ$K9 d\no�X(nt {\em 2.1�C7* relgs.}��c��stv� �D le� Fy I�QA;}$ � ��|A2 aԉ5 �k(E�"),]@c!�n�����Bv� 4\Phi _n=\left[�YIt}\�]_*Q n}� $n� # J{-1}=�W�2�f� �^ѵ4 more transpar�" It turns W͔� �� �}$ Y�a tA-M cursa�fo��b�30enif k c= {n+1}A ,k}+ nB_{n{n-1}A^* , >��]:� Ep9l=�Co.+BCJ}). E��_$ ~�- 6� �� �adjointg ,n\times N^n$ P7i�c$�,A n>fXnM{n}O%Sy� $$AY�b�,array}{ccc} o1} & �& Njnd , M� $[an up%t�gv8ert��-'!u�Yy9g,FF"� �dia� fac at!n�\B�co!WDaN�/ wee�"��H ��il��B oaa�seque�� � T�cisJ����b| basici|�DT ~ina0�Y�ne5 #!�%5C&nsT�hoPR  u�cA =\{%�Tk}, B_{m,k}\mid n>0, m��, 2�\}$�%�cesͣ�all!�s"����w,  admi . Rrre, no �$�G�(M" ~.3q�"'�A�� Favard� T �io�5��Co}C simila��A�P moni N� , $p.� .4 \frac{1}{!�� �}}F(($ was recen�T�An}�(i�_'}bT4�&� u}"�"a  .�tau`)�� &�� bey�i{D.� $�e1n}�a$ E� �5>��Assum� ɑ*�n]MѨSA :��!�:��ˁ�X��ɋK����JT�(* un�'"c F � B��=�)�� .}�a�[of2� .�.to�<u Q�E r��aYJJ�a&`�`�2��da�� $way. For2�rE \Psi"G(P)F=PF_S��s6� h�6!��"� y�A:� ,M ��at ;>�$ a symme�A operator!��r�� dense dom�!� . More�, iQP,QIIH >�Q)=>�6Q),$$L>ucD \sub�1 \cD$, h�6f��nbounded>)of���. Also,��� (P)=&�:�1,1>R$� "![dis� uis�!1taVk: X_k)�2c$,�� 6�(�:��Z�) ��6�>4 �Z �{e_&�e_���A@stand�N�s�^�$���ta�/M� $W$� $l^2(��)���.�&�  $W(e�)=F{� J�)�� y$W^U AYE5�N&�D0 geX#�}^i, so f� 1fi�$J_k= yE {k}W,�2�,$"{�. � @�N� $�_0iFby�9"b ,�:x��(� closof) be�re| t t�6�%��"=Jxe� �\ �&� c} B_{0,k� � � & 0&� \\ &\\� "B_ 82 D.- FA_B \d�6-\vk & W � .$$Q� $(J}+J_N)$ aѯ $N$-� -�V  usual"�i� "[s�� �B�%�a v mode= � �$�J s��.1��L j�vP J�� ���a6� corA^*ngA�� /N� ofI�cesB�^�~E�*=*D2{�B@ f�&l a]map�,$%d:W.F�:B oJBa N��2B� " details &u)pro� �i� " �b� B  0+bQ2.B31�combin�P+of lat, paths����^ �*�!� whol�%"` �=�2� (�):� *� ). Ususal�'y��he�2!Z"���'b�l�$�n%�C= h"�(b &��  �c��h |=|�|=T4��j<\oplus NZB-1}� � FH��>%t�2o!� � "Z $A$ 8#o9"�&�^�ls� rbrace{A �� ASme/ $l$ �}� nir�)2� N�{C -i$,n�A�ula $JT=R1 {\sqrt{D"�-1} }�1 det )�K�'M'^%]?'� ��ta &l?X# �=� $$�=�� [ �r}�Ra�-$&sc omew� ��&v�ndp doA � cord+ �,%( stea#� x-.0.�"�* m�E���2which:��E,ŷ.���*F)�3Fl[�La} 8 s�T$%��Q�n\U"� 2�oll deal��t��maz8fus,%hO-R= !Z0%� ��^J .� 1,1 >U F8� }J� \!�by�"orem ~\$��# p jP|J&a e_0,e_0�tkf=we) � "g$4 key}Zv=�jb 2d "d Now�"�% a"J0�( � �*-\{&� N\C # a�%ed step.)z0�%ing: l� $l^k} m�'��$ $(n,k,m)$A~$(n+1 ,:@p^n{$ 2A>@,pMI��$p%#6�,-\{k\}$, ris�$r:� z�+1)� Acf�) $f:IzF -1)$_Figg ~1mk o<)*�f$}[h] {6�+{\N }{3000sp�5Mw22M<8\ifx\SetFigFont��d% \gdef<#1#2#3#4#5{% \&!t@r>\siz�6 {#2p06 B {#3} series{#4 hape{#5}RselectM}% \fi�3�� {picM=l(3399,2499)(214,-1948) \thin�(s {\put(60136){\K)@( 0, 1){2475}} }% * 226,-1561*1, 0){27*m�0Y97/<261)(9.01163,0.0){259}{%f,box(1.6667,1 ){=R@{5}{6}{\rmdefault7d up .��14�9�8.98760�43Jak��J��)V6,2%V 1500 �!�ck.�12%�!4{\(-a34Z15B$2, 3)2$8$81!� G |6G24#52#-6F27#!@N�A��Qp% \cap�{ Au�� a �Ce�$N=2$c ?m�+! ���a w2A�1�w6�#( l �� \{ �B]{cl} Iy� if�| $=�)}\\5�N)��( A_{m�{N*�*EZT���'! � � IC&�5i�)T� z&pr8 �e. If $�@p�s made!�� !-s, $1v "2(tep%,Aen�*y1�.]B�w( y)=.�V}) j6 1$})� A7�d�Ő((-\9#pt�\}�,�que:�=0 >0^{k0 �i_p!� $1_: $i_py{1& ��-B-k_p[ �� $i_l� i_{l+1��l=>b p-1$}5">  13 $\cM#)}c3alle?�start�: $(0,i_p,0nd end "\/ ,i_1 , �y"}%�yfir0 k_p$Es be/j�"�!:�I., next $k_{p-�ALvI)JM�so �2 unti la ��7�+ � F�1>]� Qse�%rA8l!�$of Motzkin)u46$C $n&� �� %�^2#5 q|� ,�,E/&R a�ar�!�� 0!� '!���!(n� ir��=��4E>�nd%�number� &"fMf� W."�� 8 $$Mfin�1k(:i } n \\ k ��I ��J1-k3-1J5�I�9B�'aZ^b >+A� bioFc/Y9�M&� %I{uH� ��\now d29�""^a� �/� �e �^ � � a �6�0.��+e0�'cA=a�&"�*�.���$��\�1"�e*?K1!b�"m:M%"l � momjac:� 95�A��2}�]"�.�/�/2V0B� E�����:��!L"�  p� e� e�_{0� 69 �1.{0}$:5� j}=(0,j,n"�,�&, j.�3;�$$Q4k,m}=�,m,82qe6eN}>�-=j,0;claim�5$$*vb� } J^"��05 :.1'\\621J21 2 .&a`)�2L ]&W!�entG'2� k,j}�9�ce�MA���A�)@��� $P_{j�}�Q�e�k}ɦ-pis?<rue��&�:�#t� supp�&it +�# w�� ;�q n$. nY�a>4;4n+�S�(�4as�<$an occur. �OC�01.} $kb+ ��f_% $. F�,���$$k_1=x*31fa�(!��Uk�p�A $lp ve-� D ���in�B hyp's�5w 0�=M�_��Whe-�R���+is���:Aq�%a j}+ 1>1,j �l1*�@� j)$M���?�0J_�:a�m= )��!�%\>1$c�', justn%9$�)!-#i�agO $�%�%B%]�2A�j=":s1)2�3!k,j�)� ta�!Ng imp�} &�@k$&�_{k>Ck-AE+BNAy Ezk+B|j b~k6~.��D!� !��-��<N�*� dissape�@a�our$cus AE��g$o�@�� �Ni�)�$�|��llson9 c�%�J�6�E�!�� 'a �ively s!�e w'�"�j�|A� *l0"&s"�$i(n)�  o�E�  ��$n$th t� ;���$ (�2<�. :"� =2n$%�� J)a�"j*D <(6� �IA�1,i(i)}�n,��0 �".&�.�+.tZ�F$te8)#dN�,�0"aQ�~� ᘡ���3cM !��=9P-\ \aqAv'w�H>%�Q&8: $\tilde A_1=A�aL= �+2/'&n=A_n&��1�"!N%1 }_{1%�� &CT� jacmom}�w&F �e hold:�1�An"�(�!"�I�� YA�[K&�7���6C] *l =|�!�- D[V~ u&L?5.� �]_ &,[�)�^3�;$$��k}=s_k� 2� � !� =�A�6d", K�g=� 65�z �(>3kf4K�)U |+2=K4�858V_J<):�� Yn R! �!��*>e3?�1ly*2&.��":2�1�xK"� evious1�#N%ly Ee � by CB#sky fa�Biz�2 "6IFre�1� siF�=,}&@9��f5��B cop$� P _1�\ N=��!1\e ,1��IV�!= \CC"Q]�"_�6�?�Ene i_2"�Hii n}j^0�  \of�cP $U�a,4�!!8:X@�'�C�Cii.��ith�7�P�9�%,mark suggest@Z1- plest���-�Z�=1�.�M�O.�s. Som�0gYYlreadyear.�=�2 H�� s�Ka genre� *zB?(�s&�[5.'9u �� "�! &�$.&A��  s�t�2f�2#VHs/%�$D�?b?E�"V8W(Q��2QIe=&�1s.� �_1 d& 24 e tw�M:�F� � {N_1�,�)�M2 � {N_2 Th�� � ��>u�l/_2�(A1}}� Q��%8(1)> �(Pis��nW/ #� n n}))���1i�2F a 6�wk�i�N}k}}$,� $i_kI {1,2 �.7� By!dul� Boc"$ Boz}t&��'N�3.�@as]�;2=not�H#4�$Q�� � Am~4s �Vw""g �>A��Q��ݞ��@"6):N�D�2�4 1, 1!h . ItKOJ�B$ � v{rqK& =&b:�. �(X^2_1)s!�_ 2(X_2)�  *;N + 1 �Y][�.\ �ͼ[6��1?/\\�.~W�JF 9B�\\~#N�bo��-!$$��# 0z?9 #51�k1N�$�5 rank�P,�A�s?J &<le.��q, an�r�/ waa�"��� �"  buil2 W .�Ki&NRnon.�@���Pa� V*�7b %� V>����,N#be{ !<i�'ŘJ[Ae ��!, "2 dda�r@on���e:q[>\;im} x&l/�(x)=a@� (x)+ bm.,k7�<v�In-1 M:�%&3:y5 ^uZO$s. " �%dV�" p "�L !?tM=i 1}"�Q p}_p,$ɰ��-� �)<� -��"  k� axn��^�A�2�J� }(X*63X_N.�5k_�:*���5�k_p� #p�Aj 9ލ9�m�\T,"AEN�2$\�2���\ces*�1�.��6K0$Z-gin� �3"��m<m<J�Z  $LC�{<9�C77=�D�.�=-�5"��Um}1�1��M� pr>Ya�?2 �%. Fe* X�83de  $�S&81a� 1}+b�1� yy�UU� 2IP (���>E;?��yR9���(8 �)`0= 1D1}+ 0B �7� 4 ">f���0N��  and} Y&0!+V*}�t NT�S6A�H�2 �2�26�22��&1,2z�2��jYE'2f�W�$�at��Z `EAWE�N3 jAM�.� V�AisFE(actu�4diZE)e��>*i#6; $>0$ (\D1�2�V>0�4 ��1���O�sl GCmanner��$2�$��� �$� I)i( �v!��-�" $$1Lk}�"�U$ � ae��dh�%$ d�$eXg2$ (unlvO�K$&�B$w� 5���#exa�Son�chn, $1^(w�G��0�>e ![aY)a"�2}}2!K7 d�> J&.8�)2 <.% 0_{&A��L  �R��C !�b��aP~ ��N�b��8B�* M:�&x unAif�X�%��� ..�� � X�RH2�H2MHe�om�Qit#c&�  n,��� �A���same �of work�r $N>2�JwT,.9 �z#zkK�9 rbitr�>$PM��WcW ^n�Dq�� \mid~ * n*��=k���s! ��� +# b�piq�e*:+: �&"&��=? ��095�plycz d(l)=$T$l� ��$��� 6 �- J�N}]�\��%*�t�"it� ZC0��y =k^p-6�-2�'t� does�/(�A�!$k$. �se $n_k"�]=p�'}8Irk��P.�PI9*�P,E- $l,m��.�n�Ѳ"�/b�{k78l�g\1[li�G3�N�!�{_k(m))  & l=m��� &  1mJ�f��i�Z�$i�=4l1.3A�e�mI�'a1'�v�'�j9'^%!+NEF&.�?B'a��f"�R ��R � a"� 1iE�J.C_� "&�e �� QU bc"�P �m1-�&�2NxH{10} \frenchspacing&�z Mm(shelevich, V�h) �%solvent-l*�H� 3,} �Eg>�o, a �$FA/03123892�4oc} F. ~Boca, E{ple�d��E=amalgamB3�uct $C^&�a�b9d�o(. Scand.}, �/72}�{$3), 212-226'oz%�$~Bozejko, f3on NeuB in��H� it Studia �}, �95�489), 107-118. =�Co%�:�^K6�-�ACva&Mq�Vn S��r-z^|its A*o, Hta, 2003, pp. 69-86.��mAv6�E2$A. Gheonde!�R2dCH"uk]s�mea Kre��{ IID(n�nls-Y�})Z �}Q H216}(2001), 409-4306�2��Ona7(Schwartz's �N�k"�I�; �!�it �pit�~ 2004, to lV� .s�~ {DX} C. H�_nkl%CY. XuJem �@P*�bof">/V1�,}, Cambridge�r. P s%�1OQw` da�C   ��>x[12pt]M~ &�~=5�~fw=7.5in .c�,epsf�}J�\2 �l thm]{LFy~ cor} C&�~n?e�Dstnx#%�?yAn}{� &�:B�~2� rmk}�~.9Pdef\square{\hfill${\v�Xer{[x6�xpt�xEx �xpt�x7!�� $ $} BN}}]y�TxAtu{T!�$newenviron,U{pf}{E�Proof:�}0I� \v1x A A88x Mean�Yvex Hul�L0nd Least Area�wks��nn��Extreme �} !xC C>Z ZAi�abs�x�how� �y e-�cur�u a $3$-"�w$M60�/ a�!on{t8��A- hull WN�~lE7aA7diA7spaI7Qs�u��$7asympt hN@[ BH^3.�T for �/.-�$\Gamma" WS*�?Y ca���minim�hlanes � b=^ppl�]AJ4to quasi-Fuchs�t1Ps9F�Z/�l�{ctI�Cura�!zessgsal�surfa,R O��#h�w�u�[l60N/��� ]� "j-IA1��� ��w Pw$au� blemA@6<a RieT !�..� !e�`��4GA�+ IVed982\Q �^p�d� M Ty halfas entu3 go� re_b�inJaso-E � mpor� fea�?V  th9B9���,, [MY1], [HSLi]. �3e�p�je��acon!�r�}Opr% Dim�� r�_t�Lknown��Ir n�al way ��<�zlarif�jpJ�Eb�FA;a.!6 techeZ� �� �.Ac�\wPll!�emBseP-���^J�$��N\�- new�Si�� ��F]!�$\�2��topologņ�|�.yt Y �TT!�Now%�lis;e�i9��%�. s#.�Mjq�.>ob�Bm8�T�FE��{vex�}�a2>.\\��Nj w bf7� 3.�:2$\Omegaa\a^A�^�[F�%�ͤ�\� 2QEF6��g n ei�1AM*)�>@ $\S;�8�v$w# = �$, IV^j�s( in ^��cN= f^+ \cup-$� \pm�% ��3�)�al >#I�-�R�V�.e�BP � '-�5�BdG !�`  )PAAB� end�lF�2a ��E�goe) �!iV{" mB�4.5.}M�B�  b�g�v 2� 1@} $\PI-�9��c&Qa&j #?!�2�`I�'J�'�r�v< "��!�!�limit��~:- hyperbol� *� Z�"i7Z�"i 4.61�M-��z�<5�� �y,topy equival�z�`M$�! $NqHM$q-� 1� ssjt% Fin&%HhU%& �2��Pf, 5.101j�]e"�Q �� $A= \{�XHC^3(S^1,����) \ | \ *$ embed�?$�<� # �� n op�,�dpd $A��A��� �y,������ьin A'BX)U�$N �g"g C)Sg'organr9aa0��Ja�l�{�X S�5 on 2%�� �+�ac.%N��s�&ch .b�`\@hrougH8p2b3,n�Zu bk �Yfor�^P� �s �4� �d|s-7�*� =P? 02�5I �� �ic-�>�_�e\&� ) y)�e.s� [�7E� �li�� {Ac ledge�s:} I 8H�. �2B!>P ,, Yair Minsk; Pe�Li%v�helpfu�]�;�8N"LPre�~na�"�a?D �!J ��g�;� dzQu �]B� Z�\�defn}AZ �P (�)}E�2}}!x� urva /$0$�N�3y K. c:�.^LD� VU��9�among�e q�. A ]�) ��R � , buk��!���7inI� �� k~$�F "loc��"a�fizing{� �%= � =5��sub_z� #O;.E"�%�8k! �u�Ccompact^"���Zp������)�o  }+#�&� ",��ldl�ƙize� *E ��iecew2Z?.{g ��X�&� HA3n&^��FI�F @;a�inw:iY5lew�=WsA��Bl�tgle"P!n�Vbo# �s��,thaW pi$ ( �diri��Zr�-/end)�=.�:p �!�n)�2E%�C-a �Qkq1!L^� $M�GEjUx��ag�&� 2�sa& & }" &eg;���ab��%O='f4m ur purpos��z:�m��aȍha�B�Kf���literE�uch say�� %�Sr0eA�7{i*}} m�%)%i %F� s�t�f� _{i~$of+ ^P�V�� |rg�No%7 7� �<f5�]a %ai�lCU poin�!�J�i;& i.kP@= \{x= \lim_{i\to- fty }x� �( � SM! �7�vrg�  M\}$ �Gi�$x\in)A >x_iQ _i$� E���l\-i(ings $f:D^2�*a� B$� f_i: D^2 #e�b$f(0)=x3�*Ef�� $f$ �C^�&� ���!�Jj;st�!�]7 facW >3O�J^I�!$�$znOmn -2v: ͋f�%� � B�QG� &�)hke;AlB %w�?���+peQ� ���thGh pairődis .gTJ r_�Y|_2� �-F<HN� >�"�j��A��  � �Lu��!癎$���% �< �a�\ a �.�* )�A�-�:E�n� q�y�j��\{.u%�� �jJ�a� coun�- coll�oRUv�e�!+��^"� B�n� sB*6.2I!=26�%IuN&�� hood[  ���xF�B$%�Usk�&�Ra^aT �.� E�u�N�s��SU�i� ?N>twoUts �rg�o"�l&{�E�?ij|�uc�fMv�B >6�m�6�M���� $ �L��^j���� yTz�\p^� s.6� 4���rrierH |lB~d2K %�3��llr UU^ 2^:F��N!e�")E 65� $` yg A�6��I$��[�n{c��-k mmas� �[&� l� �t�iM� ar:1�*�j��9p&�6�'>�}�s !F~e�� r�}i�*gAj5� |alF�(wm�P\A )Ut+$>���>�-�2�]L� mof r}!ݽ��pf> B" ��2w ��v�a .jr . Taka �6c0o]�Ay�8Ql� �th�;nnu�oaD� U{.�� sepaI�:}i�r!�A�i/ay $A5�A�Pbya �/a l� oriя"y26�B :`8 �e _i^+m Aa���t 1� - 2�lim>�:K$. � by �' ��2Aw1 _i^+�"� �gzed>jQ�_6%v.���_i^�_(.*~�Ն!�>UII�}7. B�2R�^ ^F���f�>�$ $\widehat �}AAp.�B#=��%*�]� *X Ra�G�N�t���=:�. A6�v��two���mE�-`>7_bE �IB' is "�"U.2�1,lV[��QZg"l �V#ve�F&j4 u Fa�Im�X3lso�#!2���&* aa�M But,�|��a:[�3q� |�pJdal��_E�iz_A�!.�R �� ���*n1�>2;2S,a�$exchange r4~off؆ck!D� A�g�&��cr#�!�!c,%�~.�& be.{�� ��[+��OZQ R�is3J�,.�^+$"�(�CFM-!a%^-���|ea6 !vk59a�a ���",ڐ�m�Q���" !)9ind �� e�J� 2���) ��zJ�� �KB�S�:�S��� '%�kB�of> s $SI�>^!g�)_a qF�W:65f3 ��!�jKAH2��3 them���A�� on:u|g)�M�rV�3!� V�=�i�becaus ll�Au�!�s a�ԑ2Y=�2<׍�>��!�iw�o<any $O+aA�t3wE\~&�!�OiY�~&F�*� :�g2� .*�)�FBM+ "�!18���zA�ained�~&I4E(&�AC�S^�e )��R3))ha�n� -E�a�uNpa� ��� 3.1.i&%&%Preg���-\F��*� >3M�My M'�QF�R�*&��|n) '�-ڀ k�,!��B��.R@2�6cJt nI����q"kac�..3�"WJ��(% ��)�+1&"ű"� !K%^:��ɂ�M�f B� �j_��`�1��AWsu�ly larg�g$��_k�caQ' \neq 9 6� �5�  %�� +��Ŝ!�A�chN$ � ��U � 2�So- i"2.1%EbkK�1�m��K"�  >n2� ,4� @�1-�Q"%�Su +��E� .� !#^-Q$2"S,-& a!�j� m"Mw(�( p}�UI�a��l���^taQ��+����8"� I��~>�F��ա� *In-�3!�S�>e�.)�"� >f�1.: hull%D�i��"�ы�d�  ��.O���-i�tG e��_gQE���.s!jYd�""F)�N �M$5b�$Q�! ���fa��L�assig�-.>as&A+ 0!R}�e|Xs\X} "+ n��N� E;3c is�0�at� �nG7*�AIqly &�X�p-�� 92e +nkqP�{pseudo-aW1li+.0|-�+S{�3f you w�@!q�B�qs��� %�.\!��a!�b�E��"\#.=:�,�nea*o m���IblJ�� Y\a/ �Fj-g`��$to guarant�S1���%��t�B%:")�.dJa5�p)� 7)�?��uto�c�*{6@Js,rA (�"�a :���uA�Ӌ)x�$ �$ed25hul�wf, )p9�` ��2A�Fa&�x�� !:�;� o�.� �%� �6f� . AWK��T�+ �8ob�{ by B˚ WhitHL\6!�ic�M�Z�method%[Wh�^�@bf�!Hy"�0l��(�:��o�A�e��l� �"�* �)b*?1�D . Our aim��+�m ![is"6�>>�e%f*g _��ŭe&�6A�@,�* �To�-�t,�&�6og< �/�_-2>I$An2"U"E�  =�6� �a>sp�<��n�'�(=C�-GT�2��>ly&�>�%gma�8U�"9 PF�3� "� $[Ga�.� �� u�@�,Y�8� z_i� %@_i�)C)>2��#$!� ;*+ � 28^r���2�.� _j.g�N*�R�wh�v*W0$ Apar���b|+ %_��4'%�dwo&�)8EvE�y$n,�,gmR�R�>Pn!t� V�1orU�HHoNk. @�O7 �� &� "Y&�@=`97fA&"+ ���I*�� @ dm�<�� a��=���6�� "�2� VN� $� �s/.�w&$DM $Dg��y7� $D_i��-IaD�t" aGra$S $ER�I}[o89�+q, �, \ E_1.�IbA1 , ]_B�mod�= �by swap|!w�sz%c 2�M2ges)*=*D '�+�- D ��#!0 q jaî''�e���\12���ei a��5��s�/#/m�y,a� �*ŋ ���z!er y�"!������^y��tuX pt�>� 4n �3C@b��a�",� adapt&�7�.�ex�B$��"J�6 � &a�~NC �h .�#_���#�5)q*�:� ՚6h nyBq�Hi4CA�"6� ��j���0�D�+th�B=�B:6�y�-��"�!���=q�r�* &�#�!�/wax�D�D�8Je6%�g#{ �_�&:/-.��_. �6�i^-  �.R>)+ ��&i?.i^-.%. "�"4���B�%~�*#y�I�%q�J� I�a-�q?s a5i��>G�"�f#�*wx� ~4�#we��z�V ��aPnj#�~ %�a�"� J�r �8a� o#f �R*1 ur�Fu +�<sV�#�-�����M�� ��Q�if>����9�3F�E[i�D㗑,%$��6� c()� 2.1)�� �� [:ef�!g6�� t4.oP.� m O�N)�>��"��.R[� A]a=a�#&� b�y��� (- �+#*wb.� F9:���F�-� "c �amca�_{a,b}�&� �"K ")c� JV:!r1�E�a6 argu<��F)�e2���G lude�A1n�  ba-!��F�RD!c�Z>�$S-v�fia1F`I�>Z�E���2"� ��s" ��UW=�\�)_��:|��2�� ]B�j�Kis�=�T^}���@po&�MN� *'��M."* ?�1-I�]ŪA�H��'5�� �ar�€r��B*m�xm4z�:�!>�)>5&By���� Q�0 ]��&a'Q���B�J6�� )�t a}"�Q_2�� Ve;�\pm� _�� .� if��sV3�7e�M~�DW���dm% Eq': %�>�l�b *-)�@f1�.�+>` {eepar�&-4'be :g#(* ,N�lim��A�,j&��o � _i^+R23e'�_m�0_fa�U��� =\P1} n.��L�BI%~_g&/�d? � ion. .�$a�%�?�1 hoo. �6&Y!( ��A���G+2B*V�\!�:+j]!�E --k�����u$uO� �E��"�}>��'*a MU�9�%�!M�d#� �%� N3 & �rmk>isexs�*��Dn�nB�M2�!i!���" 5 �*o  �_)!�$2�2!�R ).�^���9E��S� {"� � ��war��)�. B�p�}){l�4s��B1V��untouch�f>  s}. s=�Q�i*�a=Z>J�1�qss �Br��L�yU")hE)&�%�%�k%3Qezk�n+N�C ŖEU�"n �&��š'&�&^!25� '܆�Q�gma��K\%)98a|�7�1��Xm-t�P-s��I PI P5 , P �r��6�}O��[An�Rwe*V q���w��P�}"�"Q _Y+JW, � CH(I6)=._%BA���.�q�b�$D�-W \Si- = D��O�T�X@����!�Delta�9-b�bY+$&+%�u"2��on�\BH^3 - P2@E�J# WoS� d� "de��ly�� �Kbigcapi�P&T 6O��2OKt*���Ee�'��J! stay�?�h�#��5�.X�� � .�a�aHI!L��6�1�e� 4.*�J-�fOIU)�1+he cruc5C�kis9w �mno�DnMMZ"x *K��"�2�*�s�[D�U���:ia�C� p ��Zlc�[ 1�an.����nQV2�2�_� 6[e� R�9 ��l�N�:*wU�R��*<�1 �U N.{� � [MY2]� "�]��e7a&!%�S&)%u�+&H+��P��taka�a>�.(a' �>�,���� J�2-�B [Ga]�Ut)L�Z)�ŀoxB����Z� !1�����":>r��B Ar��R'M�d�@BB�Sgm�:*� 4��&,�� �: !�fY +N1Y:`)��p�W�>\Ex.Hiey�"�.7r)Fty�!Jw}�� 1��A �a�{ &0�Ea�1Q��E@E$)�Q>g ,4�b��5��� ��W !a��f�`2.��RI*�$ G Indeeda�b'��by9����� U��bMu5�+=R�A[  �;�/8_I�t $< :!"�]52B)���" .���&�i�5ndG%�]�.2>��"�!6A�*. {6�. t &� �;��"A�j3�!$0&�� e�wM��s!W��"s2� "� ��"�>Q@� &Ժ���6R!�/}�by0:3]moby� 2�]JBF �%���'e"NcocNQe�.�&�&AUfB<w |QF.�&man�܅�+E0� t��Ja�u��z������{M>In��*iz,replac��SiJ$S^2_fL(2F��M@2hA(�2S�/4.5�.1=;�!AQ�^9#/"ZVs4.4!��"�e)���[Cofae"� {�y gXu9WF%�Iu�={Q6>eO��"�IM�Ot�5a.�.�10pi_1 (M)I S)��QJonC{H�O $S�'en j�.&�_6[�Q!��Sw(* o.e orbi a� �..��z �� cAa%���m�V)�V�%�xia)5"&^kY1C6�^RA;&�5=:g2�p-E ��[v�[.� s�TmZT\-!5 �}WEll"�|�!�]���M�X65ajs-�AIi��os f, �BnI��&�m�  r&" N٥bse�݁/ $DE^aDN} &+ 2@��At�< ��n "��� A�"M 2�GF�l� �,K��8A� �vi"orr��if �R��_&faU�B � �ts�y.� ��G \sim�7�Y(M)"�^�AR�U!��U($\��$SG� ��Ms a�^ eomo��sm)��@�� .��E\&� �+%j!)2�� �%#_ ��BB+^+QA_$o �� �I^+)Rt&�#CP�( 2_i^+)\�@M�ik��a� 17)=� }%_K�^=%; or �i�*��(�d ��J|R��!+�3�q&� � 5@2��x b�Hi"K)))Z^+E-�E"� -)6\8%6ֱ�,>�pro;gU$�|: ��21�n �+)= &� M$�  desi�(�� R ���$�<&a a~SQ�In&\�TaZSa �CSE�.� c*%7B�� 1 >f-�]A!_1$-iq�M� � A�Mi�n� F�) e�ECEg �B� F}AeB ,���sq ]ŵ�91f.L��!�we&$]of both� �r$FE�:��Z&�Y�=M�:�;�7J�+*� -Gai&F B�d��16 @j�2�A:�"M�er"jG!�que�_6V�lBBr.�bJh*�4l: -zB4B 5 "B � �Q�[��qv}�9�%��1�rCMEE�"�;.� I�"2 E�����AB�.yh:�,*� (�.st��&\ V�iQ��)���.���l�Y�"��U�M=.X��X.�� M$, &�F�;2� .!M%�V"�7t�ic{�Kes� �_�� e�e�� �mg]�� ;�2��V6K:�T&7 &�gTZ �(&!2N*= !s&h�c�K�#�^4�$z � I�h)�q� [Co3$a\:��rg�s.��� ?od+� C�&jU0 $An24^bEhDh ,*Gh Hh $D=\{u2DS^18\ \ u$�&� � �es����"�<�u(e^{\f6�2}{3} k Bi}�6Ųpi i},��2,3% $M=\{>[^ %0�!i f(D^2)n+v� $ f|���OD^p��h Y6u2qu$ Tomi<Tromba'�s �pQu�&v�se1��a�i��d�uap B&_ �C#1l har��map���7;s�A���mapl��/ub .N�Y:o�S&7�� Arco�!���y�>%m�h�v�(=~ tify��)@iodM� u��U�����% �Pi��^���l)*�@-�B#�Psa�&�#.�s �pirb���Lky��F�@ don'jrb4b�5ήr.�.�= imag�Z@�augr)!��V#��ons with a "reparametrization" factor $D$ to capture conformality. So, they consider $A \times D$ such that $(\alpha, u )\in A\ti &$identified ��O$\widetilde {\alpha \circ u} :D^2\rightarrow \BR^3$, the harmonic extension of $ C C: S^1FB�. Then, any minimal disk spanning $ H�<(S^1) \subset \partial \Omega$, will correspond to a point in!- slice $\ �\} 929st<{\em 5x} �map�$y define a'$ity operat!�k : Af .�C^2�$=�!L4kernel of thisl �be�s. A by abus�,he above notEQ,�$M :=_(k9G�$)�space~.�sI 0boundary in $>��. In [TT], Tomi and Tromba proved that��}5�"0.�p vb= �p-3�FF49 . Since� �2B� A()H):T-R M .T_ � �surN ve @dim(\mbox{coker}( X ))= ��MoreoverE�kA�� )��J0asis �� ies d6br|�. so $ �m*M�laD� -Z!M$.!�^#%�r>C N$ � ��j]�a�yz��U� pf} e�a�aim�8o� struct a�ia� 2��axle�y area:� a n6� (29A�!U� map)q*6���6� leav�9Q fo�I,are embedded&���� pairwis��sjoK %� WEk:}��� e b�6� We Q� � �  by {8interchangeablyH�GammaFsp66� its � $ 8�a�(milarly sam rue%�MnFO���itaPag��w(D^2)*� l_0InD a6iN� @ , \pi_���_0�� H9j Mwhose�e��$guaranteed!M[MY1]�e%\�c4qs� 2�o�� �� M$2m9!�2=2�&�ar.,:[-\epsilon, ].(V � path*F _ (0)=1 )�q�$$t, t' \inNb$,B_t\cap DP{t'}=\emptyset$. In o�/ wor� X)� t\}$mhes a 2�%: (0��\:�.͜)_tAU�!IpreI�Ht$ under! l� ��s��D� \�of B\Q��M�by bA^�q��{ �8ree steps. \v7 H{0.3cm} \textbf{Cl��1:} For�^$s!%=� U0%� �s��y �aT i1 i&���� B!�� y^C,! i52�u�Vq A/ VE/Dis continuous fami��f"��s.!>$cannot app��zmm��ks, s�A7� � ��>��� hile��m�  only�.m� s_0=inf\{!v(0y� \ | \ �s \�v�1v}\}��� �� ���r! �� w��1{,{s_0}$ has t�n,selt�� (e/ly ly�oS Q)� j ontradict 4maximum princi��Y0surfac�SoN E� [=,B�1�v�� s 1� I2�0K� !�@ Yq�A�aO2?2:}Fy"�i ����4 [q\9�$,~ �3I�>3.�BjAssumAq�)sr��a!�&� $$t_1 < t_26 s_1}��2}\neq �� F.�� ��{J�82r& !�e �sISA�A��� 0 segment.A!�23 must� coll H of closed� i�:c �5is situt, ��eR]�2t�twoB[f�I��XF� AB� I�2{t%4does !�e! @e�u�s�BN�t_2A� let �� \sup��2'6��]s =Y��*Q��2� , it��cl t ]�$)�96� 9�ly��liA]���A64ڦ �� Blet's ai�b)��Kl6�,v�.�>���+�S>�" } !��[&� %�Aqs_0 > 2$e��Niy�y ab&�C��yion. Oa` ej supre� is $.| BmpNa(�F > .'1lt ͘s�M=q * c�� aH0.'? >�Ri se�� $� I���% mean!vex do�E�&9 ���e�]y is newJC e�:_ �mAbe�. inq�I �2� ��i�0$��U�l=<!l�2,!��yG lovy3޸ >rO Fix�2�(U&& )$I� $[-=,qz{q�}]"� region �DP�:�Q�Y)�VaUwd�)`sY�sy��X �!��a����6� �EAsAAs) .�� $\g�� �s%7a0 .���a�&�2�2[�*( q%C�� i���.�SD� �]N���y8 l n1 iviallyW2P��]nduce%n�1-.^&��o�P ��it� �Y�*��l�a��{-��0/ �B�Q%LEuler characteristicf�!�1� ,Poincare-Hop\ :formul2� posi�a�y ��� & ( � e��%�D�somJav"m_saAu> isA�� s toF� �u ""��$ was cM$n arbitrar�� 9�",� can starthsui� P'> )��l/� $go through� � how�a�r* *TnA�.��)   E�.of_r�>U, !�A�& ��%$�S�_�/a� +>K)?���@ ���(��^'�rnu�.�fZ T BCC P then<'학 % v� �i�ed6A� P_0$, sa�`Q�� " � )�d�[!:/'&,**1�� �:t&� s�/ ~ '$�6t��R-�EJb w&&vE� $ar-wH:5�thm���A)�6#�� described�,�� �}�ZX1�դ�w�':I-HQs�Qsrmk} T! �&� !�1e*�M� {\it�v}!Uk��R.e%!��"AF�5.5�ess�l#`��-�akbe!t9�-�� farN� ��of?`s�@a�!wJ(hat{A}1]A�'%�$A - l( "�fa 9F�h�������1hI�"3a moreI7al�!h�^%� dense b�&�: ��{O� 5 2 W} %w�� �,��2+suc.�\=�  hold%y U Mt d &�!�iL�qN2��c�q!� �>XY� $"5JB$22$.�c�6Z*>"A>"�$�'I B:2'0 a smaller�">c')�t}9�"� r��V'�u�) >9!�g vx�JS!~%�sa��� �>a�Ee�6e also�[� �B��)�6��ibet �� $ &>0*l��9b�*� e�>�"�%%�Uѧ>�9,'find a B-�:*"� )*w V�u�� )ftN��!LF� (�O p6�i}):� one � X � �͐�A~ gN�=s�:�A8 previous �2�6 r�A :T AH�(�)� BO�w W$�َ!��� ����6j�%5�I� T "�.�A&QK�� ifa^A��s��l!d\mh!�Ac"� n�.1��nLb done. U�/tunate�w%[d� at, buy�bypas� is!goa:$��.^:�T2Y.) $2��a�f�_0'eS>�a .j�)�@ F� '1sB� 2�beV�aic q�aPy���AJ� �)� i= _1, E_2 �2�_1Q�A(i!� bothS>`��A_0!)fo�i'$Ńe.p if $B�\>nA|annulus)Zj�$� 2]-�,  � -Be< $B�o"],0 :� .A� a"fix=Xqfq!!�Ջ���5+� "� �1.A�n&FcompleV>j-9�ha�� uaQe0 m-2��i�.�9�B�{ sump��naZi��)re.�-�1,UP2' EZh6�nd)�uM$B!%&� 1%y RUMa QjBG3.%d6!S�!a=EU P'��"�{ :�$�'25�a� e �(��= 7'})U1$ X�(*i.42 72$�k.4#P'.�� *�)x .f( ���ucP(6.&� "�>հ�"�S.�&I�B:A���%�A9anILar_e&'�?m�.��,0u!"~6bpr&�#�$-Y'*�#.� smA�i_1�- U2�.VE�i�'ll� us "� �'"1.�% U0~���irV"~"#A���cj#A� ^Q�a���a�^7���3�"� �graph�"e2` 2q$�Z!p� ]�$E MB+E �� U���O resp� vely�$"V4u\pm�}'= �2�o -?E� �%t fVkE%A�y�7ght2!3!d�/ I 5I ��a�2�%� �A^�F�b� J��6�h)��"heZ��qX3�� !bwe go�Jd&+ �y � t G13$-smo�*C��$�9�� $A= R9L C^3@*,:� ) \ %aX:$-U ing$�� .� ]�9$A���.n �$ topology,�=i�� ��} A��� ^v6C1i%9�!vG40O&�1.�,�jg;�,1�wh�Ee�1 B by�2\2q�A9�� �)C!.A�f 's,� %*2:&>"�-4V�3_��0}.������?S ��, $A'=\bigcupIAL\)% } V_�'i� � �MabA� pS7a�per'A��5!�\�{ConcluA� Remark� D"�8�5i�=� �e ne3�!paper��b=8�)d� Meek�)d Yau!�[MY2]&e:dt�<geo>y tech3sw$Brian Whith[WhB. 5ica�s>>E&y metho�+andAH$Fanghua Lie�[Li.Flobal�3s��=. Here" re�tia-1�extend$toZ�mBH!s. Our�) roac�;m��0#seems � natu�tDe ques��. O_� handN�.��!$hyperbolic�Zc�>�ichael Ac,so!* [An[9"�/brt5�&�isI%B� tr�oA$mo%Le�?aAK�>.(hulls}��*ob3i�- l�>d��:mextreme�")S�)asympto����>�%�o &�B�,7lyAD adap�<IY2!W�;�rY� �# typ<g�8N47!Z%�1SR%ST<[Tr�07�wJN�<%��Kat� you %�a2�r!` $C*TQ-� �R:� � ia5&E%�[! KAJ)_>� b!� � thebiblioe y}{MSY�4P\bibitem[An1]{An1} M.u�,IyCzteU4vM#�ds]o�/}, �5�*xMath. {\bf 69}, (1982) 477--494��2�2��tM�>�nU�s},�3. � Helv �58 �(3) 264--290�41PCo1]{Co1} B. Coskunuzf7��U�=,rm 1-cochain�� Genu#CLamin�+��pp&* in T� 6l2l2VlM(D Plan �H�� Spac!t Comm!�al. Geom �12�42004) 821--8366z3z3VzGmgU�� of L�6A=6r�e3/ t; mA$GT/0408066M Mv4ћ�qY �21)�q09--4426�2�2�� %":@i��pr)Hof��a7%@� Z. %717�151--168.�Sm]{Sm%�W?-)A� J�?� v�?'s!S oremA!eJq�87�1965) 86�62TT]{TTA/&�DA.J. �F �E.\ �j#M �� disc=� 1QU78) 1a�145.$Tr]{Tr} A.�2�AJWP1�?X�1!�% Q`]� b �ior},�I etryoQ~, Lecth No7-iniX, Vol. 597, 696--706, S�g�8Berline�772�Wh]{Wh��� -^� xi�B1;Y~bf31)�9�t45aEc>  ' docu�0} �^\e�[11pt]{�cle2u<. ckage{ams��} :>:fonts2*[dvips]{�ic6{epsfig21{color�new� em�{bD} .7}[thm]{�6 prop Pro�ion6$cor #C� 6! defn "D(KiFDex}{Appl2G}[�] \ �styleK|C�` \addtolength{\hoffset}{-R56�5$width}{2cm>;v;.5c!!2Z=hF#t}{�9 \hyphe�,{Hamiltonian!utitle{Ma7Run L� \\�$@a Toroidal Grid G�d} \author{Margaret I. Doig6Uni��t��Notre D�t\\ mdoig@nd.edu\footnote{Pleasj5� llg �ond�� to: ol,�P, Lewis Hall,l<, IN 46556-5616}�bBHq make%� abst:, } Ad4h{g�E�}�a Cartes� prodD@$G=�-_13M 2  \cdots�-_k�@ �mv._i� cycl��r�. � 7h{run IG}�a =� 9 in a ��2d� �$9 numb�Or*�Z *ecu�,edg� q�M�th�ne�DOdlF'i.>pre�' sKal���)Uing5f high ����lower ; sab k;m�s i �"!;%z1a�G� (i) l�E�$k$: each.�i�$reM; (ii)W-A��0lfloor k/3 \r +1G| Mi |JA� $p^{r_i�>r*# fixeime $p$;R (i.t $ t k/2Btve�,6ui%Gw2^{q_i}2~:y�}1"�Inti��B�J stigpe:ja)� M�� occurJ2�$G$. PemF��B� F�1v���9.�ei� �s�q�y| qڑ�z1/aid toa� �k.h1}�weEtiSrefQ@o�  7 @u��;)Ji ^ size!F+�>�(of� ti�Q�.�$torus} or Yt�F9�O >#6] �)e. A./is �dm|}V�  e, �un5n./Y.lM 5�!%$ �1�E�J� , de��d $rl(H)&6�u-T�j@ �g�| seCJcJ'N�s(�nZ�J��5�� ��B�9� �;mrl(G)%A 7 ؁�Q . E ?r[W m -to-digit�.�r5 �s photonRectors�PaF�5tcM recei�1 ?�-0%\%5 rer!���< mach�$error decr� S=� !�'s gap@ 8. (See Goddyn e?8. \cite{optrun}i �Red expla� .)�W9YA`.G�nEAAs�5 addr+1' 1988� � , Lawrenc� Ne66�>Vo ��GT��k$EpU gLo�/"� !#mm�!Hev;ap��p � 2k/3�& large�. b 2001, å�Gvozdjak ��6!S plac*3 � �acA�ro�F� ��<�"6 o���6�a�%r $Q_kE6 %.at � Q_k)/k \r�!arZZ~"s $6\infty�9n!�L, Rusk�nd SawadmZ te{bent} \ oughllv; )�c+ of�X 0.:��)�ID�"�IJ��Xt�  266G�5� &�Z� i�$A2�Val�Eren %&$G) \geq 2$/ �Ek 3$�> =2�#!��"� b/ evenA<f�S�B�no�o���E` | 3ŏ7����if(�2 �Ab�.�A_� F�EwL2Z%�� O2�!�B���vF& thouhDnt-�R�n]� p�Ak �$, �4H��VApA� !f��D r� �!0:� ? �i�+S�%0on~\ref{secde+}�+�t!A+@r��B� �ltori $GQ)� G_2$2 .e � ,b�^ P�RKf[TB5s $H_� n dHd- mA�re5qis great� "/ %�_1)E� 2 �%dY:3�p�� a� �y�6m2��s1Ds may�easily��'�;A�cas�l�$G=� ����!$|�Ni|=NTaVod*�:�A�>negV]�gA$r_"nd $q_s LL"GGJ !��( ɴ!��0 ble,Fwim}!gvid���rB� mb�/j �SQ�E-;� ��merel��"-�>!��� out,K%f�/ few1�Lv{M�!��N\$"8"4GJ�M�I ��^o42��N@welHL"�C_?�>fiY s} \label}�"[ figu� �ce�2}�Oput{h�,20.pstex_t} �5Ain�WR�u�"�1 #aM�2��c%�edi=)�e��3�Q�4 G5$a( t��P� � kB{DNK5 O">�L ken �!��-g���`7�.�� so on;�@c� t���Y�� �>tw`EH��� 6.5ܥ�d5��1� % prim #m��$�6!�J����, � � is#1)�>a~or[ NJto 8tr�;?Br!�#ra��;�1 �e� odelo f��B in� � !N� ��}. S� e � ͒!�heF��[y� uOUEU5� vEm$}�Ɉ�H 7{m+1}:K {m+2E�:-kMGletAV� �q��bRx6����z-e� yJ�Av@H�e j&� R� $G=G2 s�.o�`AiZS]��#R� �o`the tw�&d]? :�,�; demoz�D in F� ea� : �B*%(- wo.��(f-�!Q���1*� :� )�:9M\�,�4:C5��a��d.��9! 1�>#9� )�QS� 5 rmin����H$�& �#=I�(K/H�Mkef �T�Ya�) &� �?+W�� �!�n� nneats;G _2g 3� h% 1$�Li( adja�` four � comej� �s. How�,�� ^2)= 1%�Z�� % re� 9M��S%=].bew� �4n��e�do*�1~wo>|G%:�6��`th�6!�R E�*��!�a�Qo avoi�JffoMty,U ���E Q��h7�[%�u%��~eda� n or�S�ximize� � we5:n%Y�%3�;5�I�� �< ldom�possibl��C���sugge� A�Iz�j, couch�  terms�"� '^�^���f>�q�V�< �F) $|G|� �:C��3 *? iveN$\ ( ^k _{i=1} &X $ N"�� � t1}$26A�js ��{;$s���P.�T� enume��� Xtem$\gcd(|G_1|,s_1)=1,~22$ �� 1}  \>><|G_2|)=s_1+s_2$,32q })Z\�!rm{mrl}(6%)� >")+\left#< \frac{s_2}{s_1}F/\��.$� !j"� �4} Cho& .��aO2C��6�,�+".m� a�!R�1 �Z 2) �]�n w*�R�� |�pi ��stu����~� ham�# Trot !� Erd\H{o}s%�F��A��^N�>�-I��>A�1eA> satisf�/Con�anM� 2} am. Curra��d WittaplWi�jaiQh� ham2�at f.U en�1�U�i�,c�b�M1 �_b�L"%��h4ce ny% + �co&���%m��s!D���!�#2"3#A�R�facR.y�M �3�؁Df��&�0�� inesa�0  A �o#v�Ea�,-�9f)�+Lh729z�=��NlJ�  raAUA��>�s�Q>��" :�$�%��":>�e�� n�Vu2�b!<�/<��1K� ? u�H� �iz& base"!��- et al.m�� . `Zwe pick%�.s  s_1/EjA�s�2.�‰�1)/�Dž�� ts�)�b�&I�inV_z,Y"tk "�)$j^{th}$�_%'�ad$x_{1jA"�:�tV �5 x_{2.)��)E�AtNe�,P rJ h/Ffe�)=�x�88e�it�$$i�D*�P[ f� w�5E dd!�mAf`a e�eqF ��3dd H# -�L#$ %�,!�$(!b1},�1})=(�Z:5,1).$�%`E `�%�t � W � Cpr�fqL.���2 �2.�2>�"hs. Ultim�Ee  8Aݑ���B2B)���.�A*A�b@Aii�[)CV� ��A� 1j}=a7)$ �[1)9llaA� ah%62i}� !�i}s_2/s"\ .� :�j� .�>z� TM� \[5c  @+2f>[ '2jR \]� �y�mteg!=`H��q   a^�%� � �*B b�s I�u��%�.�*4A}�~q�+�x` if \[1Q1F 2}= B{ }> 2)},\] \[�~>0�G_� >") +>� 2).R�� �7n ���B���Ph", �5<�Z!i�!�r�r��ex1xrlk%s�}&i&�$�o&W< k�'ex}}MRecA"&�(;- �'+Ft�s�]%Ixas��tpts �8edw �0a� �& A�;\ cess� su�i�]e&��E�e��BR �!��of�=two��aY�u�.mim�td��fo�b is� Iw*f<is�gz&K!:n�+���q �F h%�Q�a� ���avy *��bH:yb i�oP&>N !k��*!� �����D�� &[�`�&"Z�4ia� um*c  eq $i,n�?�yan�Řer�$*�AA �p%z< ;�ed?&� ] W�k& �Ʌ �k$\�-$�8���Z93$, etc��: `�Dt2 _1|=�1| 2|)W{k-1}| diviC$ by $i=k-1��$so�: s, h#�%]U&aT $G$ a�nlAB\�Eo.q�-�&�� �a�1) �1C.F $&Bk-B�P-�|[ion:�W�yew make ^�2d ific&4�$�'adjust�(��� �%%��ofѡ�0��� �|s$a ջ�.-" B :2)|Jq��8ax}(s_1,s_2),\]�.\[> -��/@uB�622) -1:2���L�! [ ! �� n:\[U |��"C:� 1) -(}j � 1\]so M= >� ��!= @C .`}a \leq �!��(�?�s:F:5Y &zq��"ici�k\0YN��exp�puL~� ��W�U E8>A {3n}  |G|=p^rW'i��(ve�0!:,)�)�n+1f=.>�ov(&DB�$B^(se�ul�m�l��51�, 223)� �f&:".���3 �. �!$n>�1��� $j=\lceilI�n}{2}\ri��hG_1�� ���{3$� $G_2C{3jJg3j^h--�� $B=s11�Jq �j�AO.L$r_1,~r  & 3�c�*C *�&�m p G=:=�  H�|H�p^r_0��r_0=min(�r�AkA�� ɇ+=j3�T 2)=n-M�set \[s!�*�)�\�ؑ#} B+6$2)�Xgcd}(.�6� +i=Fq!� {n+2'30} *�� +i\]� $i �w�$1$5eis�$d��$p�Also �:�{I0}-5�o VEa��*��re��ied^ d%d2����Z1)�N(2)|=|s_s(j+ %(%��� 2����\]!we�� y>���to ob�u+H�B �0��ͱ��2�2b����>%!{2��m�m�Z�&q� �&��]r_ 0Q�19+�F� ��� s�y�& ilar!9� of *�:���. Aga�2+2P� QAsoAU2��� .4)0�C)5� Q2�(0�+Wr A0�R �QrT��T�emu7BV$!rt!{� � ſ0� � � Żi=0,1,2,� 3�f!.���)2 2�3�4 92:1��� V s+�=2KaF��meb�� B�V 4��j= ��Gf��U�!�� }��M>{A xtr*�!6g)imd9m�0 askouwgi���)er way%:*�n�RBcEB�'%h brok�|" =sA�k'ituent'.��#�� )�A *N"a�!�(!3�[�u'�uPis����)�.v�t�rE) , &o!<-3 CB�=o!e� a >B&BzB �.��= H. AAmho��!�B�2�s sefuq� WEB&� ��E; dim1��u ��K\� k$, n ek��' {k+� �) A�; � L L-I�  X}����m W�0losE�ge���#say�P1|=2n< �+%� ��E�%!} n���9ap� conn�= lat�7���e�zG} D bb{R}�B"�cN`'^k�$ \{0��sT"%�d{j�o�ck& #|$ cop�Sof �Abf��o�A�T)Be� &&y.3rs�Reflect ^"�i$ �I) w($x_1=n+1/2$u- $@�a���N=�-� %IM" \{ i \! DL�A� ntil:�\"?r�> immed9;t� ��#{fU��,[h]U �'e>�.4J�.Twta��3VRA��.V�3t8run�,��(a)7� >b*KE�a"~�gmtTt("�&-1Ye3y�%�(b���%��J��a �226,d��5� �a multi�{a�b 2||^��s5) solidE�s�bB!5odL�6-.H� das5'A�s :U om�"d�;�) d�#\)]/ s.} :l�%U*�MI PX O)A, $[v_{i,0},  1}]�i$[w y��1$��lo/��$middl�"2�9 �&G���$||}?.lan("(n,x_2, x_3,�$, x_k, i\r" ��.C1}=0}+ F 1,0,0,7s,0:,a �*� ]d$�0}= : n,y�y.�yF� 81}= @vz.$�i�)�px� +oyU4JN�A���Da�EYrr<b��#�1cW�5� %!�!S?8S elow-�+15�+1+�Z J�D�f@� @ j� n remK�v*A,A�inser.v�0} �J],~ �& �,~m, k 0}],%��1} �Un� s���8$.Y�a-�Jn turM}`P $HAY n $G� 2M�/�5(�+ag�m&� #$ :-[H�VGA�`Q���B��& ?�?�A���$:�,��ňst(`�xMDT�b )���_ See2a0 }Bom + tinu+�NA2��6<" next��?��]�x A�٠F^, iJ �u&M.$��� "^ *Gq /�� �6-ke� we���/8 odd, $�a� Fa�2J2�1�1�)��nj+,&ucfE!�w5��U)�B "[�I�avail9� !th* i�re�99�� :2�n �"� N k:�E��Zj|*9$j<&~.e:eUM r� h%K!.AIsɴ�� R�2�3T6h ? � s nic� s � cal{G� !�  ^k �  ;&�instea�dr͈�k[ Q� e t�T�ODy &� A(�*t v�C:� w��MsosJ� ŵv_{ɲ� r_�A>i��.��Y�'B:�;$We attach m+3ɢe ������TS �i�p��1*E!uDJ(��e�΃F�,�v_{{ j|�= vC ) �X2�5q�}b�GE4LNkZ"!*y�2o"�ze Nx}�"��������h2�6um.KF�F2�m9�O3 � �P!�lready*&4i� ^k/3>N . � I��%*5�wxnZk:�"iEa�9��fur -work}�Ei�N�s6dAok aBQ]f}zome fRe&w >riA giva��(+ruc�FN�=of%1nj� *�?[$eN>*�H2@9���R,i�&*�K�do�="�$�_ upOb���Blim_�on� ���)�(be im&xfu�U� arch.  O]E�"�+=z�!\#�2v�_N@�at�E��OR�%R! AxYq7E� �&nd  & M. It w@;j .Jtoe out"�K� por!���%�d2���/e�c%�ae (a0:�e�F depen"�/�3 comm0J>/J 6siz&9Ff��&s))2dE6Q U�R�#M�a$ + n2k$2�9�, perhap�JA�an��] �idea �(diago�(Yn!� by C>�3"|>q3). "�0 a>�0a� N aa�{��4Z���7V47��*Q%�pa7I#�8���� to�H j-vafc�^I=w�(���PIB�N�N"2e z06\ n"�M���p� i��t P�$j$ *��%&� (�ON.B.:} 1�o�Nas�):2IU9 *�:�:��l�@G" A�9/��e>J%[ph�ory 2!178!137-14!1�>;B�^�=F�^2p6�^2�\6-]:J]�wi"-]:K]>-]J=.-] :�^K6�^amB _��^��^��^�^*E{Ex:[!^@B�^З5^ Stelk$ Brai> !z:^�]z^ .^]�?��]I � � exh���"�+one2�dn re�] $D_k(S_n�Mfe%uno�A�Wk$-*con�<'i( $U_k^{top} @�?X�8 $S_�se 2sa!�Tntly �mstudi�)AbramCGhŊ.;:ܥ��ʞ�Ve g p�,:(q�D� t" uk.Oh-�GR< ng b!� group $B) ,c_k"�<"l�a)gS� !+ �m4 map $i_{k*}:B�0!,c ) \hookh7a4S 2i send�|�0��in7niTH�ւ\.�� !�,x !�a al)� �J��4 Y2kI0w$>0gWs�i $X$�hv-�Alel� Y>ts�\[UIe _k(X)=\{c"Cx(X : |c|=k\}P8}`�Jtoiz� }4 quot~5%!�!�T\[p: X^k - \Delta(X) \9� .��)u�$p(x_12,�. k�.EA{�})A fat  %(- \[�=\{i.P)lU� : \e�5sP �j~�~�~x_�+x_j)-� 1x>�u xW X^k-u�-Py0 $9�; �M.m�aMn6fQu B~1�J~ $U�(6�i��� a�y�)��$c�V A� a}��A��"! �&"S �Q ex $�deg�r$n$� veI^1�29�v_n7 7onaKOn ��ʉ��`ric \[d(x,y)=\kappa \rho ~\forpx,yES_n~- $(�� ta �d��/ab�p롬 � e8�Ra�?t�u&� qu� ��ct,e $d(v_0,v_i�$Z$i > އ�# i,v_j)=2 w f $15- i < � �I56U� HausdorffN �26��Wempty�x&bse� �:%`A,B)=��_{�$tack{�vpa\ b%_DB}} (d(a,B),d(A,b)u;�H6kariJT�n 9laI�me �gk y. Gs�:�� -i2i����R�erstoo� !�>nD Euclu���Rec�},�n �n in"(;��no.���iC>E�ph (see�'�y\) viewa/Z���I �{��Tud��ly� m�E-�) ��og�� to Artin'�B���+. � r�n�\en:�:�� $S$,��(} )F��,c �!(�f. HAs m 6O�!oc�%d=qR��ky)��� I^$ i�n aspherYR =�ghrobJvs}�o$�3.1�u, h ���W2 � x�R� '�a5��$  �a,e (Lemma 2.2ulIn 2?Y(polyhedron}�?" �\.� **� d �a�2Zp �GA.B%�*Q "� �%9��e�na4H�) spin ��ANt��*� "!te I\_] k)�<� F�e2�-� Yxic��a� k:Dr �>� & �z �_nom���� mapp�a�~%. of� �,K �U'ba5k�D � e�M��*�(�"�(����{V�]�| (a) v,IE�$d(c,v_0)=0)�2( :  * 6Zin/j� _1(c)=A_5 6C t��E5so drms)."�V�rw'"�� �I]V� y} W �Sa@BB +H v+:� . L\ we w�#Y�x�a.@"�J@ . Nu�k��� $\{e v_1&z v_na E��H $deg�)=Me�uu~c s�!� 5��E��wo.(s $x,~y��wr2)��x,y]$.!8�-a� ite �% t $c� V�2!�h{qw�g�?-0 $� c �0: \[|cE� k |=1+ � Rou.a speaki`uJ �%c�of�Jta[Bn�?� 1�s���!�inxA_iA�~-k i]\]b $&� !i9c�  nonev $ F$%� �A� $cA#o!<k.��b�.�!6NA� m $A_m(c) �llC lg� )�rm}w - \cup �1a %���."� ea� &�0�Srme ��5 \[�4�:c = �s �FhݲcW 6U � 2��$2s��*��$"�.arm�.a%+:La. ique n $0< �� = d()M�� < ��;H@!M,IcarT�-3�) $:A4: =1- V�m/~/@Q.  a�� �M9�i�@N �/w�&:r0b51/2!�ZO:hIn"%3�e/>�� n.�N���j s $|I<�S�L�)8"m$�-)KS[!AQ�)4N+value��W �� � {#��bBL٥&��l, }�& �>�!Xn�Lw ^�j�#We�74 X�����U� by��V() a+_u:U� =0~or~1/2e?g a�a�oe�k�[AXA' I%exen g1�.4&w �e��� H6�Zw}a�)Qbi&+e�qbetween 0!���`distribu�O.nm� �lt$n� /��s $��so�����ereS�L4inom{n+k-2}{n-�4�w�yp1&�k:� e�Utj�cE>>8J� lik6~+M's}b=-��D�<e��ko�1�'k$�)e !B��out pu����a�9D�$�@�)I��V�5,1),-n$ED! ��^ ype.�q,qnm_/y8�;A�Q $c_0� $c_,? �� _0,cHF��?�JP ;d�q\$z1c$[ D]@&�'�L�-a�:��7� I� �n �#z?Ѽ�> $m2P|� _03? 1)�2 It ����0�Z*i(�|c'$i �m$>%� _0),��_1))=!7Y_����"�h*v%�%M=7!�=Yby75V�ą*D?):��a +��� =����*�[�B:�2Jei��m$1��cn��0)) ,mMS��5\leq !. �Ml%� sA�-�2�% c�Bjc)�AI��{I�)�)�-�)�-� m5j/ is�2E�2=\{5  : M�%5��~and~d( E%{ T��!���9&>� ��6�� 1� /.l����1�aQFC�&%]Bb is h&z�2� $[0,i���$��6'6�. �� k:"� ��g'g/ym%�re� u � 2'F�"�� � A40*HAr�n�exM�lyLp�`� AWm!� )|$= � Aj0)|-1=Q�$ �^!My�< �I�z ��d1U�)M� b!Set $p=�'� $�=pF�c�(��-p$�Pf �-�U��k.�'� !�i�F1a�,�)�$\@ A.psm \[h: d2�E�\]d��*�^!�rule $h,2� ��e]�"}%�for�31y� s"�-v�U"� ">iD!96e $R$ t' $U_5U (S_6�o $D_5 ,"��:6��~I,Q�$c'x/!�'%� � ZE�vtx� H�6Oak 4(c'�5�CF� aVA  tp<��x��' 1-p�~M�C ��)���*~ �ak&�%|r~u&�-2k�D@ JHion&� *m3 def}!�� �}J@ŪU6� M�N:� �5�T>4 �&T R�?O9)��%�i��x2(c>"".� �D3�)F�< Q-�q=2T.W� "q�����$R::�Z3i��Ia� :(!�"�R(c,0)=c �1)=c'2� �<f��)|a�{�~ :�E�6����iA�|��A��Q!%':p. ��*X�W�&)|H 0)�2"�S�.$m:��� �A酬"#j�'>� �1� ��Kp}{p+qMIk� $q$9q >  S`�a)"�"�#[  i�Qm�a���zx_{ij}�)7�Zij}� 2H$r K'An�A�%�*E:�WI� k-1]M���\�A�3 A�Fc<��faN�d.��   � ight�>��;* �cr~C O"�!A{%��h�t�$h�5T�coalesc_�ide a -v�.{ >i!B~5�����p T� calc�H*90)$ via G!� �$.%�� Z��]q?�6w� JA3y Ei���!C�� k�Fx$0 the =e u}\���:���� �A��h[n$-tupl�_h� ���*�u���O!�of;�d&�l��R{��S>q1��."��U ,�*�>�is Z�!\va-�(k,n)$ *'"\[.!=�^(n-1) \F�F.\]� �:=&R��is -dOkai:so5a �� as fund2{&h rankI4co�'d�0a�EulF��$\chi:���eH coun�� �l $*^*S�c; $Q�s2� � ofBn���t�`��#*8 L. EachA�Y� 0$-2�yv\u���r"  $9 w $n-1�caR�a demN &.zq`<�Y�P= �=� �C=1` .\ Jx� remaNv^c:- �$ bj�!C~2��� i�w �I C�0��m͞8� P �/ � �@ \[|]F|=nFB-n�� ]ZmU�&6O*�|l�:�+^ah�a ank(f*)�a=1+B� n��V`v;BB�Re�}, \[ v3aong�Y�< F}_{ �k�V},~B_2�n+�{2-�=(rm{and}~B_3f:f�k 2n+3}{3} tI"' n> �pBA��PΥVp$)��.�<2SBdks��: illua� e�as�,8�' Miy�Q� L��R� "�� our �s��!�1��#b� �J*�.��JJ  $D%�3��$D%� (c)!�4��%(d!�4�Z���%�&)o���-9u,�<reSelBB��!�oI��"��BNA unfi# >'Ie sL��8�.sG#�r�5.2�% *� &'!xr&"�#2�=g8j m.u#B8*�a # �%$;#�4d# '<.+&d�� }en}�#j�D� qg $B_j nj!��E� n da:p*�r$ D_KS�{,2�$jh/ :h/ �� �.8 �%%S$�&l-�toW$�3!qh�U4�a7�*`%�9�: $i:LBY%M�N$L�tp�:�1�lex�K�3r.( qBV LY e Mrm\(!�#%�.�! .*r i_*: GL)B� M)1!i16eZ9(a)�/eq MU!�%x-�a�.*�8: 9X=) �a�&aD�3�k2�&BDiP!i���D2�A c \+"\{x[$E�x�" e�.D5#up 2 q. :i;�]a�O�)� �alway=��cbyuH�i�faС�me-�~%Sof!ie� )$.)B9�E!0s�+�\���c "h$6�W9�͐mq+v�`J�F_I2/ ��mdn�by O� ��!�ɦ��\ Jr�"�&(C}A�2{5* FS!�R.�&!�2G��z,,�2a5� �CuwK&�Q�^�*�(*j��>�&�*��of.Hs RXBbjѢ7�<.Y5a%'�Lt\?��e M7E�F� bsnolly" v��xa�D%�P�[�1T$, �T��� �3-�Od'.)"��"�B>�/�; >��!j4Provost's Offi}�MJr0matics DepartK5~v�6LeK /Sjce Hon�6Prؠ7�G2b>�Q�j>:0!$A1encourag]5�ap�B ��|>hel!� >�:2>ab.sis���7��B� �E�ѱof�.s. Ph.D!Ls�UC_�keley2=0.=,�ed�o2tolohC; Ak�h{Ded�d��John St?ng�� oc:0�@his 65th birthday�� Ha} 92�2)�<5-194*9=f�Cy2�R., Fin�z&T5/2 5: CJK. � �Am8. Monthly} 109 h>�40-150�*�.�Nfew6�a.ap�Z '0�Kno�71:T�- r�iis -�=s d6�anN@�Birman (New York, 1998)} 29-40, AMS/IP �? Adv� , 247��.Soc., a�1�a�RI,} r�ͦ>�B�=� %-�  % B�.�'� aTeX file�d.d �N( Title: s_o��M�V�Dte Ortho�E,Polynomials A� ��octahed�Sym�yo.F : !�)+v. 1.2 (Csb�%>0 amssymb.sty)>+ƾ+:�X| Jan Felipe van DiejencJ|BC�FCInG^t�-a��g$a y FisicaBcFC�N$dad de TalJ7.FCCE�la 747.)fFC�w:FCCHILE:&rFC�FCPh�(8: +56-71-200 3nFCFax >C92f�FC E-mail: dE�@Q-mat.ut!�.cl>MFC��CJC֪ ����% �L2L\�A�[reqno]?CartBSC��} %.~Cps-�2epsH#%\def\�f� (stretch{1.5��n.I��7}�3�7.��'p*,��v+]fB��-)�6D�c�'"gn��:eJ_C�*�>P$�# �C ��{P�P<{�2�*{note}{�L�/�Uin{�< q } \renewrM and{���}{\fn!�ol{����Absolut�3lu*�w��com N$abs}[1]{\l� #1\r} CBl�box�:cehol�m� Ss (P ��r���M�~ i�rn ic��pab�G�(Jpri�Xϖis Q�x .�b��N ��,ma��HJ n me�Q s�2�= ly. ��\setl��{\ u}{0pt}%/ {\raise�[#2]{\hM{#1}}}�}% !� 1�E[A6 V�] {:(�/ ! ^! QInf � !�>u4 �� J.F.*��FddA�{FJ\'�L\'{\i}Q,:0 �,.,��, C��^�g�� e��L{Work s�H A��A $Fondo Naci%Pde Des�$ llo Cient �@fico y Tecnol\'og0(FONDECYT) Gr�$\# 1010217� CUesao s Cuadr- � �N6 .AQ"a":�W�e�a!�bj ��i#O&��bas,�e �aO �LO q9O E -�*A sA �Do ˵ �y�.O�N�%3f��hhF�z�[� ctorw+QS�  v�cer�n��t.ty'^;s.E�2�|��- �:#!6KoornwiϵD-Macdonald $BC_N$-26>Ac�-Wilson2���mPed 9���%\�Roft�i & I%Aa�Psecjhji]PP @)�v?f쓡|o�2��c)�Z ��'ierVy)H� scheme,fw�!C�P��Cm��.j��ocel �a�JJC \�ask-wil:6$,koe-swa:a%w ~}x�.�% V��ch) e.g.� H�-Lte, Laguerre, Jacobi�Hah2�,�Ja7XS�x al (�Wing) A!!{4^� . Ar�V a deca�%go,.� iM s:2�ge�izeY ~bkz�)wkoo-fwE�}�� builLup�'pionee��R� y8on.�Z�a��B , root system-k�� mac:9�,��icaffinA As it !�s!�E�se.I}�.�I�F\ a mas��eGy1A�s�Y�P!�ll � 4a{as2�C� E�2�asU;I0V�,die:� uA\}��E ��6�%�*��Q� f�wB��Cy"paperq�bee-opd: xL,bak-for:calogero-su�&l(� �nfluent AesU�R��8�5 erein). O Z!yp�� few years%�� BQ�V�.��#br�su�of &��� � a��U3aE� 2{ lm{3 sign}hm�M y�^e��š ~�blf�m�!H��-dual:H,oko:bcŤ,sah:no5 �ic,-sto:�74ble,% nis-kom:��ic,&k�,mim:oncha:m� ,rai:bcn-u�\(A�"^'pr޳v"-ob i�)��*��� al behavi��E.>� �mFsze.< dei-zho:u��}.� ^�A�*� ���Is. i�ism�R:> } (lM_s) �by I>:�V full8�Qa[)�Aein +�-O"�ZA��to lif�(2��Hy�D�'2� #l�xpe��[6go�sW�5!� ��f� V�Y�tf%�#uchf� >�R��� ��260by Ruijsenaarё rui:C� } (fՄ$ �2�)E �?"8\�S8 \cite{die:asym�}ptotic} (for arbitrary reduced root systems). The current work should be seen as an extension of these results to the case of  �aKoornwinder-Macdonald polynomials, or from a more conceptual point of view, as an extension from r �to nonN�,. Following �ideas��Ruijsenaars, we in fact determine/ asym)H5orthog�.�� associated to a fairly large classrPweight functions thatu oriz� { ine-dime�al $c$-98. However, wher��t studies homogeneous symmetric.�, >, in contrast! 0consider (LauA).4.,$N$ variable nt u!�)7��!t�@hyperoctahedral group $\Sigma_N\ltimes \mathbb{Z}_2^N$ (thus pass!�%�,type $A$ to BC$>�FA�< specific choice � 2I%�(end up with�:� the ��8. It is import! to emphas!�!�---atO multi%5(te level---!)E1-degree2�1�ed )� s noM only)of24Dof interest. Other'E_�$al propertA3of2�Z�, involv!�,their behavi!xA�e numberO�E(tends!infinity!~8re for instanceM�hd by Okounkov and Olshanski/u �hJack's Ed geomI�deA�raai( ($q\to 1$)�!i�� �� }�UIfA6e8 \cite{oko-ols:9N4s}. The paperA organized�Af�� s. In Sei%$\ref{sec2}a~ first def��our�?y�oR�. An �!) mula�se6�s presen��i� �3}V�4�appAvh.�iq in ques%{tovQ�^ Finally,15s565} A �6} wrapa��)� via a serM�res��D which---when link��gea,---comb!� into N roofMC, fundamental}O1��>�3A\s)�{M�  O9�P�$}\labelI# \sub=S��Mo�Q(} Let $W$ b��e>| givenae!%$semidirect� duc�vpermutiE�� ��$ !w% N-fo��r; o cyclic6mat��$.l natu� �+ $w=(\s�` ,\varepsilon)\in W$ on $HR}�!is�( \begin{equ�} +8f{x}_w\equiv w() = (f_1 x_{ $_1},\ldots2�_N #N}) \endr(�5$ D���),$.nj ${ 1, -1\}$A8 $j=1yN$). %��cal{A}^9������$dard basis�-��=���� m� �sub1�s},} m_\lambda 6�(\frac{1}{|W"$|} \sum_{w!w8W} e^{i\langle G, �M2r},\quad$\in\Lu,>�  $:U U S= �j=1}^N |_jx_j$,F� n = \{�=�^N \mid J1\geq 2  \cE� )4_N 0\} B�E�6}a�$.P$ denote��or/ m�4stabilizer sub�6 $W1� =\{ )���_w= � \}$. 2��Dity} We will parti� ���QGM� $\{ U* \}_{ hA -^}$� mean F>6domin� 음Z��:B���po}1�A�,cceq \mu \LoA~fa�htarrow m_I \ell8_j%�]8F_j\I�,text{for}\;  .IB��V Delt6=�5$an almost b yI�positive� ���.Sm�C$. We �y�6�� �) an inner �: structurU.P $ �$��1 i`Bv!4!X f , gms_ AaF���( )^N}\int_{� � } f( � 0) \overline{g.}\, X. )�d}m�C ,\q)�$forall f,g�K.iw��()y$^}6�complex( jugat�  $2�($). Applic�"q�,Gram-Schmidt!�ces� a:aed��m_)� es a apPq� 6p��}$|>��? form1�6�>�maop1} s2�= m6\mu!q��\,a= \preceqA3�H} a�mu}�8mu2Q-�2S>�E�4coefficients $6^0��convena�. (In o�  words,E�elez �� ewM�ar2�� aar�� ]��8.)�p2qFac�d W�F�} F�now��w͋res^t� att �� �al"� :� R �B zS��^!J� e��-:}�ofw1} N�al�^ |W|\���C}.�\,� -i�')J�eH($|W|=2^N N!K ^$fwa$aV ] \=\��(_{1\leq j1$, zero-fvon�,open environ�j;�origi�Qntain� unit�0, real-valued!� $z$!�l,6norma# d�� $ .(0)=1$. It f4Qtr cond� a>;%Pnd $ 1/Bi have�A8lyo verg�(Taylor expaus! �-}�rC^�tM-exp}�,p^{\pm 1} (z~1 +� n \infty� n,p}+}\, z^nE� (E�)BiJr�40a^{+}_{n,0}=OE�\Q\, n}Aund '1N'/2)s $n\to ��$0<Q Il min (\logYAx0 ),2k41)) .$$ Indeed��*�bound1z-�2GM  he Cauchy%�ulag)B+}.� �i} \o� |z|=u�i� z^{-n-1}"� z$� � 92p} -Zn��p )57$� to $-@� &A"b��.�3}�AXmbdr � $�� e^�asf* Qd.!#2�3B?_w)\, J6.�_w }I�&� Aj>�  m(� �min� &} _j- + _{j+�NyA &: s58_{N+1}0&Z| \|$ =\sqrt% ; ,  � *}� I��Btheorema��r $�)}E�0strong $L^2$-ys �p.�$"� 2�$ is 2�"(3N�AB�an expon� al errorm�g� n��decay ra $q��X�N�� e�+'DR $��p��. Q0-U}[F( A] 4as1:thm} One h�FJ *} \|&�  -5P1U = >3.����< s}\;\; J�:" �A�� I)V�!�.�� non�pj� (i.e., ig�'!�C�9 of[a�j)��n� h�7AU� alterna]3��B9�2)�-:2F6E\L� }A�=,A�n o�]�s1^N\,2.A5��\j6 Y/y�� growth%�g鯙�1%�or)a1!�=�FTh��$a-q�AY "� tha�7of>5i`M r �,�u�\in�$ fix�nd��lyCtI� �z�(>0$), we ge�Yj*s alo�  rete ray � � bb{NE�r8corollary}[Ray �HsQ�ray:cor<-�U Ilj�. I� �!�E� ~�{��}��6V�5^Nj�\,#}R�ոZ�9d In ���V� 6�%N�tur� utQbe exacB\ $ suo}"J�E M� #1 # 2#2M �E��a�tQ�K **� 2={ŋstyle "�e��N&�\ l }}}�M8 . 6� *} H%y� )\geq M-A�� qmH Z| .� �w{\�� ��f2g�M $M}�=\$M!paB:f f� $�F-�^�$�sp�ve��֡fY�s*i 2�$$ amount i�YisiN character"� lic Lie�'$SP(2N;%�-)$ j*�& $C_1�� of�� ��Y� boil=en dowv� Weyl�!�I. 1i!�(6�jitT>vBut_0��h(1-t_1:;&�18$-1[�o��!�sam�U*2��5�2�%4B.� &� ). (� crux�%X Prop�o�%ymity:prp)�Lemma �dim�\:lem} below remain valid��n�b�!B�O ar r�&b%�Q�.)"'cular, i��+"  is observi���he sit$AF-�I�9�ip � �" ,P_8 "� =\d8_#�mu�#M~,5")"2# � (&� ,m(\mu)I I (e�% N)�$\mu$�inot�2� %*an��"w&)��-<oV�- V�&$4} By pick�u��"�,!��C�� ��krc-f�"�z)�#(tz;q)_� {(q."� 818$r=0}^3(t_r.8G^2XB{� (6� XnX � (1-zq^n���O� !�amn.s*#jec� !�+traint"% (%2} 0 %aefteqnP6�zj } && =&\!\! }{ �, )^N �' |W_�*1�!�b�1� �� 9!_1��W�,2 _{w_1})�=!'m}[2 [ Q�\mu2v! {w_29�d} �W(z%\2!6 "F/1g66�(e&]2*, -�_wa� 5��J�M�]'��Cg35� l�yI�s�A�=�:erm�5�� < nd (0 $E% )^7�:�ť���<ump9"&&�/`.nUat $1/%�M. $ta (un�&��&$) Fourier "�&f�F $14&^ bf{n.I-Z}^N,`*  "�/0}M� bf{a-�n}}^-6�N�9"h%Fpin "�8is1ald $��� =\mu�2�nd) 0$ o�,wise. (L)we us#*#;andf5#,�W���]2_w$� k0��/ \�m$�3$, �6 �$s�7!�*.�Y By�ox-ofh4)3to&�2u rewri#$�ua" 2masf�b:8"��M2��%�� (1�x})60!& ��det (w) � (I�.5_wV�+\rho ,U��8�6JTitN� Zx)�2�"�,"{)�+&�)1U&�+n) 6P"M 11 �>)�\ )H28 f� \bigl(�w+m-/2}�,� ,r) s�2-) �R� w )&�0 R�'!�=M%�7 (N+1-j)5� e}_j���}�2� i�� bf7$eHa �_$j^{th}$�+ve�0r "�z!"�$�9GW�0t�;<&�$&> trun&� wJ% F�2�&76�>�y�m*�^{(m)6m�m� V}�:����5�a .�B~b�0y� 4�u a�f#eA�2m�71 ZE��]���ʁ4"T.Nr("o )�@ $m+�0�.2 ��:�ao.�D R&)#0>.=�>� �'B}50� =6�.m�.0}B.\, z^n`J�>>{2mJ6n�"{+ Ai�� V ��e|bO(2 ) be{�,.CEq�nm*}/�1.( *Y E�*Bz.Xas-�SzV*ze e�}�)+u/E"}F&:z*}C�1UM |���>Q n�* m���9�a�*dngr�Ga�;�6�*} *� iI��.~��;us  N�>V.@ =BF? +9RJ A9*�@*}n cetween.�B�e��Ai e��s!sE�� "asf%�6� !�� R�6�B� 2� &� XJ$�7�]�� quot:n2�/|K 2|^2= 1/(B�.�F.v $)$ is smooZ+�%eB{ $ du��abs� of 5s ^2� . H%,� proveM=�S�$\|&Sf�$ 1enoughR�� �~C!�?in �;AJ� ))= >�.a���� ndh s@E%Mc}_3=��{pqA z)+r2"y�E .�N�&=&:j8*� )���B+r��B\��) -0makebox[3em]{{ imes e��KaNf f� UN�*5 ft( 1`G� �+r.� a�-b/XB�Q �G ^G �¥A5�a�]�mn�R}G b�$ t M� s sinceq|z|=1}Q"��A�(z))=O(1�� � .rB(p �2\i�K view� $BAG7N%2� cay 13"� &�J�@,�P G 1}^+�� z {0�?&P3{1,"�*-��H+m�#*A-small>h** .��2�"�3JI 2:P>=%%/Mriang%ly�J�6�D1)i6 % hing!p��I7/ l�%&.� :����k.?le*�; ��u"�-�d$!��m� n_{jk}^+��. k)+ $-2$��e}�=��+�� n� n_j�!V&��q  $02pl}^+, k}^-&�%EW-g 2.!!�&�.ɷN�u_weqY!F&gH De  WM�*?Fur more�4�{6�<.��� n_j< 2�E�I*j(�� � as�> ifOvP�&w=0 Id}$+)v-E9N,,n_j$ vanishr I�1$m��; comp�7�5�$p�) bB�KI~_jQ� _j-n59�I@k �6�a �Z7mX2." B"�1-U�� }�!'�v J_+$�� 5lawZyite{ d.�`5� y (A) (so�#to=�'y�@)��) ,5�|J_+|�.~4)�Ddi2&F�71�i�.+�K�K�K%��1 + 2+�*- �Q�}:C re $%' &9Q�+ofq3�!�).10a similar way�obyF^]-L".K-�+*n]BU핹����������}&&�s&0stackrel{(i)}EF&6/Z�r�#�++�o�o� :& -"`@({N-|J_-|+1}}L2}mhyz {N})>Q.n i)}{!p}&u�i�+1}:�R_e�+�} .��3u�� �!�5�R {\em !�7 inferr��� $J|�� J_-�ѩ�to���,5L �� (B) (��ing��.}� z*0T�:0);� F�i)}W9�s�Z�B� V�:*=* �!N�C.IC�flipp�� signN28HUH�2�A) >@ back:�I- +j}$) �2 )N ). CN\��� Eqs.)/i1&�i2}��0AtkP�S]:m+H}�Dleq� *w��j�J $n ]N�ich, ve�?e^* . To 'A �+ondQ �#�7�a,* 5o�] (A),A�?-(C), bec�+s\QfMHg *� ).� m< 2b �.>�0 hB0��y�8<1��;�s �unlSU$ � � ,2�/�Y, �u\a�A��fd3�9!S,riczc d $emptyset$ � No�1!�\}A�ThuTSupsho�*�  $H�Mel~�2#0^!2g 2hD�"P\{ ))t ) S\}"8]:�)�# = � ;NM2h=� E.�A�4 Z�#�6��'"�25o $� 6��V�T"�it"�-&���m�>�$[ &Z +1l9vH&�F�!gF \.B.�;W Pmx,"�x}JH���mu ?��"W. 2�%�� �i�*�$*`(F��monic %J2�� �=1��Ie=" 3�s���!�/i[q%� " >"�U~��l" can be ? ten� a finite,ar �b�z"s_=*x �-f+���%�#} �Bl� �}&l6m+)m�%"�n�E.-_w"5)>�H�&z >n}u_> "E���:�"[ 6ti��>��� m�q&�2 m�.�'iB7"t)����i�L.� =�e+si�E2� A�"�cHE �_�8��it�-nljiv�>&,`)���,.is !�l,~^sibly�.`k� r {m&5Jchi���?���**u0M���/]�>� K'�-i� xUque& Lt7i�e ��8� orbi�e(2�. )-�*DBA>� L��6:�n e���/NO=�h) � *�2,L]q �C7!"�A2& ^f� c�������;�BX2�l aO�e@���5 X"'9C F� well-know:n%F�sX�i .�4t.� ���e>�&�+"����8K%nd"kW\ clud� $U7i��im�S!_�Q� ~ ٗ*5&1�2�%J<PEQ leadx*���k��*Qp �;@.�9�6t.ZQ Norm Est��([�!1Q z�(Z�K�== 1 +B!mX*)bR(q�)\�O�*Z(F�\-�Q�>2yNf6"�r�^2 a8~6* )�E � �9�#n;{&�D ))} >E�&}E n,��#66&1CRNFBT*�*V��' e�l ���=1�`*�G�lF�9�!ef>� , � edi�a@a'q�>� *} |f��TO]*@V-�*W+f~+.� 2 ?Z.y$.@:T*}�I=L��2�, (u��4!�(%�J *X �j%+4.� B�2w-|W�(v�(|�&�A�C}6�# |�9�]�].�^*� ��e��aem�.� of} �##�N"o- =Xi� }#  ere .� (�!$�TJFp�N�0R� 2�$� ByC# �6�2&�$}�}[L�vC&~eB2�=.�}=1z�We b"H.q����A sequ}+�*Uman�Bev&�A.�*} F� 2M )}{=I� �� ,B#�:�y >��K�+))}&A�V))}>LBwn�F�E�"�� �v-BZkF��Qyb�>�g:�~uF� U�*�U&��Lt%��@%1JDR(.f$�r�?�:RfT*EEq.~\!0��BFO,Ci)}.0�:24+:,�`>��.��"�0op2Pv)}6��!#��C�a�k warz.\k�J��"] � {P�t�fMQ�Dsx�Q�;b� ��PxJ/G5}{aarr"9[U"m�V�v�B*�t��� �)~kE} SM$ghtforward:� revej=V�.�5Z���"4^2�:�#6���>p-i �, b:�J4 );:i�3�CBy5 G:<>� 1 -2u(V�+.7 Z.,:ua?��B=`6 "� :_'29:j� N�`&9 z.. Step�)}*�$*�a�af }fIxNR0x impl�AkJ$ ��=��:0N_�$:� ��d!�F�8 �U��a:'! .%) %K �f"�x^��`}�E{ V:l{Bl �2})*v%��.0>& �Pm-9��h"�J��&} b"d &Wmu2& �m2��� * YJ7�q  $Nq* CD`14(11<y :!V I�b� OX5@:ru\F0P�%yALal}�.r�� *} | N��eqjv)�d� N TE#�>�Uw!y�/ &%6MW.u�)"��R*�[�'y�c��B|,.i�:�:i9%H�O�Wo!��'TNx=A�6i mu6� R.A}-�A�6� )VL =�)|�:J��8 $�@M@� b� M-�� �:I�@d2ZY^�le�k A"�^W=USpan}\�x mu \�F*�KGuE�"�K�TheN`\di�?��.q))�C 1� ��_1�C^NJw� �:I6bH!QBwi�.��.!a�6�$:�4dG"� 1) 6�B�1c��J� ��RJ �_�*�I.S n�2;�&B(|ٞ.@�"�  +nr;':>�Xj |U�S -1|+ A1��a�:1j�?z����  ��I�R�h& }�zy.[�76[F ��E�,.L2�.(s^x B�6~���.@� weI�loyedr::&*T6�.���} &.]} ��z�9R�C%D ]*%Az$aYd�t v|Vf��$f . B�.-="{i.$�*�>� =0$)��m�e� nce,u6B�:� �&�i�aasz.y� �po>q �6.�~>R�#�$pw�xD D M\,-�:G \;1(.�z# 21L�|#Fs �?iw&g�^ g�.vok�of.��J�%��0aNL �9#ng rel s� 5�2 $X&W)� ,&T 2}, �"�|co|6 sJ�% �M coincide�l�yr]��OoO��� M��.�=bP�-�.$}{. ! �\}�3�2�oRhq`�� �C (squa��2)6� vNo�aad���.�B�^2 �m�E&�m }D�� >, 8s�i�Hv*~Y��>":� >�a�.~�dF� �_j&gjJ� ich, N�BR�Bq*CP� Bvj � *{Ac� ledg`cs!�ank� �CS.N.M.2=�~ sevehRhelpful knusa)t iblify%� {amsplain"� the.&}{0000}N�Wdem[AW]{ask-wil:some} R. A�\� J. W�\, S,\c>�9�2~e�gen�ize"�obi* %�s, Mem. Amer. Math. Soc. {\bf 54} (1985), No. 319j �@BF]{bak-for:calog;zsu�$lE( T.H. Baker� P.J.�)"~er,�  C8S8 model2�d =��g6�Commun� Phys �188�097), 175--2162�4O]{bee-opd:cerN4(} R.J. Beer.h�~EA Opdam, C (�g"d�sQ����RHEe>�i$, T8^o339 �,3), 581--609.�C]{cha:m@�8} O.A. Chalykh,&�j2g#�ic;U��x�Adv1<%�$166} (2002!693--252�D]{dei.�j P�Deift,Z��� RandomAexrices: a Riemann-Hilbert Approa� Cour�ULe�NoPin? hematics �3},.Institu��* al S|�Pces, New York Univers%, 1996�-Z�-zho:�U } P.�4T. KriecherbauA�@K.T.-R. McLaughlia� . Venakid�!�$X. Zhou, U�U�p0�V�.| ceeN$"dIݐ�* al C�Kh/o.Dians, Vol. III (BeɅ�8). Da��%V,1998}, Extra60 III, 491--50�R�nr4,ZM\�$Di1]{die:ca�k3} J.F._) Diejen!�mm diffalce �\/Uu*! eigenfunh�s?$� 95i=5A�8A�33.=Di2 �4self-dual} \by�j, S�_, I��672a741996), 319--336Gi3 ~ confluent~C:X.�b9sBhW $al quantum�U @c%Qharz'�inb%Lf? �,7), 467--4976P4 �&#�*8of �� fami/of��in��vae�, FD SA�E�35Va�), 23A706�5 �&� �*`_x��� of (>`�)Z�3*oc�a�$*�os, q�Q5 Res.�ԡ �200�� No. 7, 38!q16�S�-sto:&8�bleBb�a8 J.V. Stokman, &^�ble�d-Racah.W, DukemSJ�F 9-O(8), 89--136.NI]{ism=Ls} M.E��Ismail,=Ss!�[ �-�E$$q$-Jacobi6� SIAM��� Anal � 17e�8ao14�� 14822�W�W .�2�-)A.c 2d���iuH" ���� ${}_4\Phif}�,���xO+or� bf 3�4(82), 43--54.�,KS]{koe-swa:�f sche $R. Koekoekx R�_$Swarttouw,�)b 1!vƍ&�V\N its �A�(ogue, Delft���.PTDž,ology ReportE�98-17, �<2��o �w�  *|dA)�gI.@!p .O���BC�K: Hype�"��)JDomains�APNbv��.�.]�|*� s (D<. P. Ri�uv� ed.)�8ntempqЅ|13�3A:K L$nce, RI�s2, pp. 1aS202�M1]> t I.Gj7�2f ]i��01.5, S\'� Lothar�9mP4�=X2000/01), Art. B45a, 40�(Z�M2 �"�-�MSyj�9�a)&Đ6�&� "� SY {a/14"%^ ���,�j>^2~M3 �af���A Hecke AD�eb� Cambridge.�Pl ,, ��.Mi]{mim:tHity} K. Mimachi, A �h"cv-}6�nda�Bi|Dy2�`l 6�uR� 10�>20%�26 81.�,NK]{nis-kom:": ,} A. Nishino!� Y��mor�*�g��ic��  to��,: Rodrigues-e�w5ulab innO�[t��nti�a �*� 42� � 5020� 42�O]��:bci�OY�, �K%Krpog�B�bin����=�6��� G���3���]1� 202c O �BZ�!��!) G.&�.�s�+��6'ſ&sC"]  go�<o &������},�13, 64�6�,Ra]{rai:bcn-�*[R��%�_n$.��Ceprint��ceR�A�.�Ru]{rui:�ized}J�, F&юv4"[ vs.�@ scatte���mmJw228} aL2&' 2�(Sa]{sah:non�S. Saa�N^>%�& , An"��50IF� � 26} St]{4 ko"��2 V�� Z�y�8�'� t��1�  Ng�eM�2�M,9, 1005--1042� Sz]{sze2PA�Szeg\"o2�*�u, eth Edi� ,�) J.I.�y���>�  docu&). %-�  % En=$LaTeX file�^^l%6 G�GTop� :!�$5-14.tex 25 �K Logarithm��"�;�Yth��nus+6��mov--Wi;"�� s... M�Ilia Itenberg, Viatcheslav Kharlamov, Eugenii Shustin > Publish�lVolume 9a�5) pa T4491:=F�\d�7 April%: tZ:�mn2�%% 5:66v61 \Q�t{gtart_h} \input gtoutput q�� {5504-,eceived{30 D�S4} \v%9 / 9}\p¡ 14} ,year{2005} \!\ !s{483}{480 %\revised{&1�{.Q} \ac�(ed{25 March%j2r�58ed{Yasha EliashA(?Re_C ed{Leonid�terovRSimon D��d+t�" usepackag�symb,ams�a�new�+�!{7} . "}{�+6&�o{"�p>"n�xure#  \ Ys�{���6>$example}{E 2�6{DM|JB�|rk}{Rem)���and{\ssim}{\hbox{$\hskip-2pt\sim$}}6, N}{{ N}}2H DelpPi>6A!u bb A>ZZ>RR>CC>QQ>PPP>mnote�lrginpar)u51 Proj@f!j}>D oeps$<�l�5B$Del$ widetilde!C>%L�%+name{ReBq convB(>R?%{{6R>*KerB)>(Hy%�2�>(FixBP>(�>B)>*Tor)gpeI%>*oiR̜ B�)� jB@b2@bB �`F�a2@aB@y2 yB w2 wB u2 uB t2 tB z2 z> b� bold�FolF�b%�"xBD�"B�b�"B�mXv"!�eletq_ofendY%�(6�In).)?ney�pF�PrB& grad%0.O>P�\:lImB&skBNskB&jhF� >x SingBT>*con��2�C>*PicBS>(CriF�B*hBQChB&�F� >RToF*>(�>�>*vaF�>(VJ(:'GWBwGWBMdefecFEdefB+tmeWC�!:�o���vB e� {xF\e� thetB�;��:yb 8bJ7ka�- kappBSd��<>SsiE�s�[>az alphBS 8SN8Gam!� GammB8g gNL �/:�l ,<:S�SB�MMBne�,...,>Ic�Yc��� \rm i�X:pv to�thop{\to>#o%�Q p} "��� omeg!$�"gr� � itle*Tk*GroV]{v` g"`\\bF�the bl�up plane�ascii��i�W>�jguthor{2�\\R�\\E6�� h*�Ds6E,V FH��H H!�add�es{AO(IIs VK)}&��\'e Louis Pasteur et IRMA, 7, rue Ren%DDescartes,\\67084 �8�w�k�5�Rq�J� $GW_{nD}$6�[ proj3Hve�] $P^2_k$�t�Bk$ ��s"�ZD�B a �� M� ��C L�t U).�H[,4-,P�G!.�F'�R���D$,lH" A$� �� equivalen�L�5�]og n$E�= D����^�W =m)�1}{%��~WBg �b{�2yk:wD�uO�sD:q!F ��6n n&n1k  = D.9c.e0primaryE:{14N35��� J26, 53D40key�{b+, r.$�Druled�ic surfa''J'��%ic 4--\C�5Urop�)e:vometry} M!>�B������Y7ke" "2, uio";intro!�טt�0�2tre��&! "�oOR�w b� a� 4$--.�=v�.�set�" such��"vS seen � c���fc˜cted !�$ $J$--hol�phic cur�X in arYn��E� u�a��T�a�eY�taŧ<��0lex�XԮ , se2��,�MS}. Ou�yteres��lZ�is mo>�s+by�o�ison of��\-R�'���a$�,��)�[\ J-Y~Welsc�cr (see � IKS1�=��7�*&&B�1��}�Q�$,y�͏^��'N��"ncy�*V'z:Lpop�al� ����)As!5 / n, alread�"exist�"�՗%�e--a *�RYf @$1di�����>I!�$(-1)$--Q`�ver��s��v�O�Lj.f@��#!��2�a�0-up�a U�or�q\ (I4is^�t&)s,��ɉ$$ re�*ƙsV fou�!n~)q MS},"a�9.4�]ex�Pir~� {s (�/is,.�$S�-bundl�n ver 9- ���f�b$g>�5sq!�y��VZYomu%�IgV�,? '#�b�fiber.6�mv>�U1u1pM rved�G� a�w��"f��_��^�Zi.C�."Busu�p toa��aZY"of��*� �� \PP^1�s $EAp-up�����F�.tLus�~!CXB a+^: '$kn�2g . Pick aqk�)�~z n $H_2(�2_k; \Z)�qa�z:A5� $GW_D;)? @�T)ei�1 $D*# j) > 2�T^P= 2$ and $D^2 > 0$. U�R!�ab>whypW��on�I�^�%�0$nD, n\ge 1,$��*�@a�Z �#Ewn�D� �, F !�.y4!�� $N" 3$AI�Zrsed ir :io+u�����through�Bgf 1C -1$�{ge�Xpo���Y>��ad�5al *�V�RA�EB F���� ^,+ ��GP�e&`� u0=�$��Kontseu recurk�$ ula %%'L1')$ bKM} ($LQ��8aeo�$)�Vow�) e to � *{kvQ�%��U�sP,1fine�ir*�U9 �-cJt,�aQ�� !�L})�) = 3ϫn+O(n)$ (�� +:$ .tz}).~+.�F�*�U+ Pezzo��.�KMa=%B%ol]�k$F �%�H �_s��r!�sn<(not easy toe�ze��l �be$kCYn W8�!�}AIco�5pon�2V %��M����@ed,�RmS�$Mikhalkin'�WeО,cite{Mi0,Mi}%S A��MSh0})�|u�o;dnodN�u� �uor*� &��:� pathe;P x olyg��q* � $$ UD}(8)=� \,M + A�t� i� � 9,O hold�;!�� divis�*ڿa�|icY"� r��,:�%�j)�u� one, two,�t�ni���o A]��  IX�A�ncte� devok x\V�VIA%� �' �=nt1QwPx�6 �� ��\g�� � $D r.��� �y���,B�G2�\ne 0$�%z� �� $R��� ��ThFSD�oog�Y_k�%I��a�-.=@=mbd^j�<-j2�\ . � ne10)\5j6� if $�� 9�n � �=wMa� ��u� :�e����>9{"B nc)��2& "#��=!� ��� sense op \l.rG"a$�=0$��� I  * x+d�@�q�k$��!8\le 2�>y={RE�.� " g� ly � } @Dwe�hve�� auxiliJssJQmK�Y�l�_Q�nl�fS�4_s$, $s>0$, be.� J��o�� �ux�&)RR $ESE^2=-s a re $FrbnN��a�A�(sF+EPM ��@ (s + 2)�Zw\ Y�2>�e� � ;nN��f�l �id�v��E5������~�,!���Ys�C $s=1$ & s _ ��Ŭ) _1$ disj�  f!=� 0 $���% �8eQiks�� ��in�r� 3 of.� �u�=iS$� v���{ �$s��I�q� a��1Be =���_s�C n! �(s-1)%� #{s-1})\ *tw ne3})�hA[�Nich.>� � $$>7 Vyu&� +� ,$����E�i� ��2})�'�rW> ���lF3}9 :�0  >ma-i�MH=F"�g�: $|F|$ :M ( $(s+1)n-1$�AA2E�u$$�>1F�%?ar.�E�|$�q�$� � J��eh!�22><2< q3){ 1,-1)0.5$n$ (2.5,0.5){$n�$}B�5�2�5 2�N�7@���� � �24 q4:�8.8�s �7��P1�!�a,k�0�Non��2�6���� ��9� ��) ME�$Z� � (l2-new} Fix�;��s�K ����&*"# $(T_��verif�Z.��2�B:, T_n=J� �� $n6r�  a �M col���$,� �sz_{(s+2�}" ��$ %:_s*� amo�>� Įn�‰� AAV��B $z_i6li=1�(�,$�l �$T_n$�` �� nod)�s ���!�rg  each���4�� out��PZ s ^�MI1F' |V� ��"]:�is �G�� *�ll?�><ng-!��G�E;� �No�\r �derţp�@on)� $s>1+�n � �co��AHdescrib��~��!3�����!�2� i��eP� <h*F�x elimin*7bbye���M6=�)#!�����64B.6�ch��)�, i��od~�2. 3�a� t�=ng  } !�ar� ano�9.�oo0:) � 42�-rt17 ""6 T2��g6 #;�(����"� " N�s�m~�mad�FR�:U &O@*!. Mor�e$�dem !;A+�x�y�!���<g�:!"A<weQ�, ��at,�O�&��e�|DstKAe&�j s $EPyy, E�x'/� PP^2J'A�� VE�-��E_iH�th�J* �4.1� � GP��zN)�ds�W<�_����J5B2���A� i! !n��$J�,N� 5NZ�� eduR�>�V� j� _�� uppe���L*�\le (N��.V $, i&4٭J"�!Ilow�d��)e�-� .�>2$. By��!�u�4.1bX "b!q3��mm�N�va�%\co�Q�!������+" ${\� �� }��phi^*( T}A_/.�^ver)���a�actify� in>���"� $X=9 h�\oplus mO�]�)$.� K\"ahler�@/ ii�$X����M period+>(Y��aY6A1_X�f9 *w"5}~$\Phi�R�$;frak N�1)RZt Xfto�X extend$b)��d uch .�y�%s��ym�).v� "\&��uDusa}Y�3.30) �AE� M�2{�1�X!� Ther��e,� ing~Z0� ���2f C%�|$���in$�: , = �^.N\��a�a�e%���&n)i. N���e)Amug!,Mly���b� ���n�� :�*�s�S\$0M�[ U�1$ sow!Iw%s a�m�._ n�a9 �se %T�s $C_i id�YB�nŀ� 3 �R !,�Y�Nw��v �gG horizQl (�q scala�a�� ��!�I �t` $C^0((l#�qA��,"Oy, $C^1.'ix�  rb���12-�$0�e��$sW6-�� get-AUh}}"'�#(C_i)���"�s�D5��J�9X�v�J  r>, ��.eT �.�?2},�/ 3.2,�!�|t� EJ�+�� $J� !/�i�B NT�"B�,(w� rtV. X IZ ommo�i��|w�triev s"2lw_���' ��* $X$). D� �NHL�)a�5edF�' s&�K++��e� solu P�J"G$problem. T�a� desiT����aa�i��e��"����e�|�e� IS} (� �1.6 2.7)� e spa>�g�<^>t,c"s.�'d��3��>C,$+��& فN$, NM=2Q[( �.DCs�!>"RR zy�\!�stg�glu{��1a"{2.� d"�#GX,e���6![��D'=2D��q*h t2�!)�ut|W� "�$&SN_{(n+1).�ge � "�"\ �Tk#&iF�L g �ne4})aHuseV��-!of& I�. Nam/���� E{"mapejJ�0.Gѿ�D|nD|$��!�$2n-1=nN�  �tQ���!{!o�F� l)@Fgp+�)M� R� $2n>�" $p682n�%� � i*�.%: $C_V�|R�p_{2n�h�~an� e��Zany):~� a>���"-hand��2lp_��-1!ye�a) )� C\cap Cph��~A�neE,��no /�+��A\%s� and~!% 6�e0�Vr -�&)%� $p'>&]���ni�"6#8 .[A+$p'i�BQ�-param�� � 8C\cup _a31g>� �-U}��3��! �%d$̤* uaS�*6�}$�B� f( GK}uOopz 5.2E(� Kou]h.~II&M 7.6)�����Yy sweepV N@I��&y)� $C!�9 � ]� 6�-1}I� +1a*��%�Irk}�\�F~��1v*�*f-d � �% lso �A�>�( $�( >�(=�6� >�$�� . o�-=��. E� pu6$D' = 2D�|�e&� � �%I`$(D')^2 �/��� �B2�  $��two�ti4"= :�A0aEi()�� i�| b"�9� ���0{D'��X0 5 �ae�S2��%� $D'$���anu$is]� for~UuA� ��iFN#�8 s d��h5oo�FC.�Q�.��� 2-�>! Y�!m��2;-< 1�Q����$J=NB�J�ai� ��� � Q>� 1($ %K��� yT%��M��2!-!wb#P= ,*t)%��,�"�.6r�d $k��t-2���s��d3�(�) 0#��7 1á���G ��%�s%�� *f 2�.in �d6L��. q�f#aan�f�-H= dL-d_1E_1-...-d_k�5ny;fe $(L,IDE_�3of�ic�$ sI�a���(=-E_1^2=... k^2=��A�%�nob%� yielZj d,d+d_k>0>��b � chan�Q� ZH� in�� by Cremon� an&�#s20 .�s�?o���Zm�oY eve $d\ge�i� j4l}(d_i+d_j+d_lt()�Ahe mini�jty�9G !�qQ5.A%A. At �9� a�ie'A�� ?EW�-8, $3d>d_1+...+d�( ����*�c܎ asZ�.��)'���!� p���r1&�*$s�9L��a�/cubic �&6�/-uEd . S|86�a I�6�a>$\F D&�r6!�a� h8���4 J6���>A�;?�(��"e-!��#��d�1��.ZG m* Now let�7� de�� $��2���� �S���F\�GZ�� .�f o�m�*�B�a*�7.I){. Ev)MFK0})�L �L�gfi��]d,� ���!k�8�Q �Q�Q6� M�{W*�=&����4U��_"a�} ReP�"� VO depen�0��a 6x;, b� a�g��of t�� � �egu �A�iq� ��W,W1}!RE�d"T!���"=��V� ). D�� by $E��b92#g@P�Q�b[�pm� >�9l� B�"6*�> "X .& -� iven"�v-3�hF�i�*.!��k'�d�os8 ,2,3S |&.6as"-< *X >D (9�eaL� 9eH8*�@H� �&p@&1Q�nc1} A.�.I�@�ed�$ d+��eupR �=@��;ipp�f:dn1���al�P .s�D ��� Y2m�  !yV�Q�=4�69�$$\lim�_{n\to +\infty} \frac{\log W_{nD}(\PP^2_k)}{n,non-compact lexq��envelopIjme� rphy��sphere�(Mat. Sb. 18EQA�23--60 ( � ); t!��in 0I�6$1335--1359i�6808602�HU�H Hofer� LizaU�(J-C SikoravQ�$On generic�� for holom�ic��classes,Ni and �R �RCommun�# Phys. 164�(4) 525--5621d291242�Dusa2 �D McDuffE0 it Immers�'I�!�� l�uc $4$--=� Ann.  .rier 42�,2) 369--392 ř162567}}��N�bf D Sa�iI��ntrodu�  to Sym�TopŞ }, 2!7: , OxfordeP� cal Mons e. Pres�[8) �698616.�M�h2>J� $J$--.PC��s!�Z�>�D Colloquium Publices 52,F-Provid�qRI�,�204562akY�Mi0-~ G MikhalkY�Count= �via `lattice paths in polygons�Kd. R. Acad. Sci. Paris, S\'��I, 336�$3) 629--63Ռ9881222gif�E&n trop%ݙq/�T$\R^2$�>^ 18�,5), 313--377="N��A Nobil�o ,On specializ%���-*I},J� �28e$84) 739--7"� 073216gSh1��f �A�= acT �2.� A�'��17 � 170--214�W-sJ-Y.��� �'d%al�' 6'E�l&�U<�5�EH �H 341--34YH 76312�W�V� J���4��b� Z�Invent��|to appear, \arxiv{math.AG/030314�}J� � docu�T} b%%% %%% This , oE�4 gtoutput.tex ~intended�finish��ma�ng Epapers p�g shed��"� &�h% stor "the ?,arXiv. All�E(:��$copyright <GT6�g (to be� d _only_�2�n offia�ly�=G&T �.s �Co@Rourke 14.9.2000L0To create hea}file  .xxx N !� ou\ �!�inputJ % test�pex or� @in tex \def\ifpla!�x{\ex� 0after\ifx\csn�Q-hc \relax}g��t c�page: ^T \hoffset 14truemm \v 31else \�Psep 23pt \footskip 35G-BG 12.5Ifi �load pic�if�alreadyed : ^��<ure>�b5r. \%���\font\f�m=cmr5%re}ex :6 Dost fi�%�gt{{\� surr` =0pt�$\�G\m!M-2mu$_ \&\ T\!\!$ }Q�% jour��titlea� recoA�!Estyle �p��� � P\!$�N�� % GTi� %�defin�e� 8ous new ingredi��ba� �A� �log6#1{%Jthe{#1}} �vol�=a+..� B-, CyeaFX*sa� BW..� Y / V�! 0s#1#2)startD@� 21!��1 dat:-Hpropose&the � &�2& rs� 'receiv':t revis :%acceptL>' sciiEG�the�cover>*>*JV, .m ..B.dd� B. >.email>,>*urB(ur& longE/ �bstractX1;>`keywordB�0shortF.>.>�, *�Kinizis�� let\\\par .)� .z }x :4a� 2.�u�  Gy� D}�.+  C} D. 1�%5  FthI�H1-� 36I� M2C 26Q 67E� 4%�R��K.� M Y� make6p{ %rt�uś Y ( \c&0=9�( \gt\hfill�a J2�((top left) A� 3o  )�.�� \setcoordinatesystem units <0.33< in,  > poi] t 2.2 0.9E0plotsymbol ({8G$}) \�ing=9U� circ08arc 315 degrees� 0 1: -0 0^gTgrL1 -.M1Mend+ ure%+end!�Plogo % \break {\small� thJm!��w? V�  S � th6� (a�) 9�--.�nl �2 : .�$} \vglue 0� .4lus 0.4fil min E in��E� {���  A+  0pt @ 1fil��\*)#}{*� \large � L �bf�h}g \med; P �j0.l �ml��}{\scs @} 2v 5%Fu�J (es)5�pa.4t\newline\\ {\�+�l���%}F the�ta�%  9? �B)^)65�029�2pt1�stda`(e{\rm and}} \cl{E�:\tt�}+ Q�ur��6% URL % n��F��URLB�ur�!��)7939mARu)=CEyi#2pt !e Q4�a MS Cgifo a ) 1465-30�l ed) Mt{�\folio}�Lifodd _�8 }%M�A�& ����th�� ?6"fi i2hIu\j}2 3�jpͽr  Ku w�}\vss�!�! >k>h.)h-.a \";\ \gtp �� gt, ��� :f � � FA�atletter; @oddA�{��I�^�� A�\� �J � \{ }2�]�� ! %�!��  {fqa\{QJ� D2�1�_ ɰu[&%W�E"!~�@even%d5n#!}A5| ^|�N)t�{ � } M,othA+�� � � write\�s g!dAi�{ �� J�+ � \{, )<s{ } \i)\oph(tu"�.&:�0{Proxy-for: \GR�R��-�fi\s<2A: IU ak< fi>2�>�\no�\\r(A ���}5ham5]>�TX:like %1 2� fi�wf]Subj-� $: GT or SGMG etcrMSC:!h.� 1� a� ��,3:fpf��-ref:7. � .L.P >\ *\*[r�C�ts:9~w)G����'atrL<\s\s http://www.�T.warwick.ac.uk/gt/GTVo> .�/p6%b �� .abs.htmlvw��Efe;e- )�n��.�L�.3fin1�b��Ecloseo.�3%%j� ����Te\� Qk -}z� ��t� \20[12pt]{articlJ(usepackage{\+icx} .epsfig6ams�, amsApBthm6set>��ouble�k[]= 1bottom .2j]{0"}Ųt�/��/}{T }[�+]2'(corollary}[ :]{C2+lemma'L2#� "� 6(�,*R�,6%�E)DlRenviron� {sub�0}A�@indent{\em Pf: }�0include{macrob/�&�  \E{\LARGEJ,C.1 of a$� ly R�0S�0� �hLandau-Lifshitz-Gilbert Equr"�\R{��{({Joy Ko \\ 7Brown�%eC.# sing]8u, x -, in{e d}{-���{��.establK!a frameg/�c� a glob#��2.�te �)gy=a�)al m!00^�X%�!Our cha�er�$$yields a pa�a!}>!28, smooth away �a $2$2�)loc? �PHausdorff measure set[0is9 ion re�-n �$xiu+��discret �, u!��j%""$!$ex�-�!f,t $whose highF!(order termsS"linear� _.�+of $ machinery 2est��+�-fundaa7.��/XcoA'u�setL'int2 �%)1-method�#quAgAal�ac�os mor3%ne���.involv�'t�ts�2t��,�,-�hy�#$urfaces. ��]��n){.{)L} Micromagnetics, a�0 el based -e ofM��q�,�#h$ a descripEof U behaviol4 fero maA�al��$-gum �is� find! c�/E!slaSm.�q�assoc�4dAh' � mo!� reA|en*3fa[4 $u: \Omega \�bXarrow S^2$: \[ %\label{!�$gy} E[u] ='"t_{ 9h} |\nabla u|^{2} + \kappa\i%\phi(u)��0thbb{R}}^{3}}EM Edx - 2 ,hh_ 6rm ext}7u \] w�. $ )$!R!rega�occupiem =�%� all phys%u� L^K$ - \alpha#(^-)] I�e���iN67configu. isEH|romis�'a�C֍w!e!et� A��Dof2� to imizD��. "/= manyc ev�:fea9 �k} �8pfull !�)�k,cap0d� ret<;-�B��F6;i�-�attemp/to enY /�!�o �5ces beyo�$S�Q$72p ��"  $\n% Altho$>�R�"�> holdA.monq1 renc�6� s!, is mb.b?soY e� 遙aN.�U  ?�= G>Cauchy5#�=is� ��� (LLG)�/.oof"� $u$,�%�&$ data $f :� 2�2,cal{N}$�$2a!,^� A��()��  vector)�$, satisfyj�yF� llg.eft\{ , array}{lc displayv,\E�a��\nu� ��u, -��6 (6q[<) \\ u(x, 0) = f� �� .,� ��Y�> 0a��w�%referA�!���Schr\"oi 'erm (E� in�6 Ibea1rif>l� )�.Xl� њC� When 1-.| prLAM��[,\emph{harmon� apt flowQ�}������a focue���;on.�1m�� dard usagx LLG)2�l(C.)Av� �.2� =2 , �optB1ra� fH3& �@u�!as�t��.e�C�v7�a8m5($B�$)��;q �<�1K�^� M$r>�mW�7tl;$-\xiQ�(v \xiA�-v + (v, v$ �\�L  $v$ a�D Z. Fro}u7 V�`�u=as�Q6.�=2}��+q�(q���q�vE u) )i���N<]  �), two�:?7uU=!+llow:~� 3} \i�6�. 6���t � (1�^2)j����69 3ll�4>�5u��:,� u>� �"�t� *�� is$is� >�s exis� a�"3l(e Dirichlet �~Bm�4iDFkI" �4ɘU�(fellgthm1} m  $fo H^{1}(0,.D)$�E�*�s,� $t��q쁅U�5��,is�Ia"{B? )Ohas>M&lf?F\w�B*N! parabol��etric.)�5 Weak�s,�6�l5 C ones,� �shD� %��s� �"% ^���!�techniAL dev>A d, h�Hof��exploi!e���$I�� -ste�n� al di8ul�C)`!D� �2s.�equentlj ���8not easily adap�e! V!�7 q� � 0. One catego �I�s%So %R�= of w2�Emade cru9u�yfac!"at �k:� in d�6gZ�!8^�;�i)�urn{ s r� o�e�� >� mongs�!@i!we�of Aloug�>4oyeur \cite{a s}|IuMpޅ_�G"Fs,�' ergyXJ�su!�i;IA�2WE�a6^A�GuoEG Hong �guohong}4 cess!y carr� thr� �Hgu�StruwJ �s$} employed�!�Z� e\h�H a� S�j},r� �� �an�I ina�lk�7V�%��!�po60�u#G!0�is9�,�!�!�aE:~K�Ecad��)���s� :�!:B�of!�hr. �a�y=�B,��2i  $"�$ "ypre�1^�sMm�xp�AE�!yu$ elim�1� �  altog�; �1$Ŋy%c)�%�:in�!ڡ�t�<� {qu�$L^{p��y%�"��9���Mworthwh�<to�v at~ �C�e�� � ' �]] s �%; �f* may be��ere�� eU�V�i� priv�-unie:,�% lear&�Melch�Nm�m }��`5nt��tedN>Uofn� simi�Oto�et:��!.�� ,a Ginzburg-Lr":. ��exeȥ�f�vEK S 2%��W=e!dS% M- "�25%Hen5{--Ap�come--�2.ous stud��LGE�!�%&3���A&*Q(AlC]+eav Mu��ep n� �� siblA�; ����M�6nJl$iW"x �H5 tachAt� gl, i�n�$ unavailab.h!w*LM� z�m�u��5se�L���� s: ���sR� (e.g.,a�p-L^q$��iA�tz-type��a��*H�inH!o�Np�- o��:Req"-d!�� �. $)�^:�APFdhRju0Q "[%E_e��c9�). Cn tooA{wa!lost �"/ maximum�lnciple� wella Bochn�Wde�!Lasi @*� I�4!im5��zw�w�JA<L !���. �!&; b�aFx�]� !SN7 s|al grid.R.S� o.{a .>�wm��T l�oA.� D /�fal���-s��$aches zero.�A$R��H�r"G"�� new;!�> ,� F�ear�"t��k��vaYga%3VCA�;R 6= 0$,2��� sb}�E �"e �13%JN >�.��� s ��� A!�}�aewAz W�hb"� "� � E�dem�$a� ��fic"� M��ɕ�,I�mʁ� &6S shoCWbe ha!�Itis ke� &�A� are: (i))o�LA sui� :� }M�; (ii)�0�%a <�*� ; Q6DZ�!Y0NU� t rato�$derivE�W )mixeda�ce-:�a�� ���ge������a�sSby%d��(i���sub^5�S�on  T u}�c ad}aa�%L��$:9Z2P(e� . By�iz!��<,�� � e=&9cODEa�o���� � �bjEs�a7o ne�o!�HYto2vyY!&to!P �*B�� a�f&r��S ��v a1�6�� , -8o4�Yars�"!I' ��J !�)w�"[�Q�U;!61�V�L�I �!� oY� permit �rI�af#-^)!�no dep( !���cal �� �� B�S�8lo��A1� d �-� Frt LLG, Aillust��- 6�hh+ Y�for�Z��O�'�n�[.���)\JZ n�)%P� _ ev�o�-��Gn$cs}$ , but�H/� excur�S!?b�� ��[���"�w[�bH\ 2�)�� o�G!� s (y+s��A�.�G��Aq��bove) b)�U ngU6 � u�Bv�(he F�a�In:�llg}$,� ! I� �]dA��F�  . D��S)"oqH� *�\{No�&�*nd &�-B-Con)�&�  ��d}�"!@�#\[e�s $x_{ikjh$, $i�.,2, \ldo�d"v%%$�� integers.� A valu~ un�$s $u^{h}$ H.&�)���y!��:ar!9 duct%�1� xe�m�%���"(u, v|)_{\Lh�- = �Hh^{7?um_{j} + . *$\[ \|\| Ap}A(6> #5|�)^{1/p} ) $u� =n_{17-` j_{d^u(h9{ h)$ % NJ_{%�+ 1U 625i}h + IJ$(� i�([[� pet#!D_{+i}rk\H&A2 �-}}{-Y \ \?-n?}7J-1:=0n=2:|E2��\]](��&�R"� = �D_>� � .2)1�( - ?)& �(Z+H+&A +]i �h�}.�&��uLaplaciaE rA $�eHcs �"�E�e�}A�Llt9.!*� some�-�1 x $"� ( A�^{+Ao� -I�d:'-  T_{k6#k^-\\Nbold{�U wei��kn�!�| k|N��id + ]A&^��&Y\[ D^{ K%-(_=.-�)% B+}-i>-})P2�Sobolev� ea=��,W_{h}^{k, p}�7ckrel {)�}{=} \iz | ��:��)�5$\leq k} \|�E.�� $D^k u_j�&`*E�� ; 8'�lse�&e*� sHU�\uh{j}, 5�= k1 a�aHk�CDa��2 -}�%l�*3 %x�  cd� �c'c�`n@Q$��k} �H-k} �$�p�  /�*_e��Imperf)0_ E& e%s} 6 !��+es��iP �im�d�(� ighl�'� e������Yt e�ip �*E�$E I��a s\ shifba�� $^T� EH��� eqnav&*}��+i}��)�= & = & �C}��#"+"����0!�.Z\\ H7>#6�.G4G��1}{2}\{ �� 9M�ZD �#��}):�\�l�X=.a>�  $�9 h beP to $ �! sumb by )�!�ula--e;d� +ogA5N-- FI�"� ��.� -�h1 � �An� Y�2�EP2] � A�:`'<�ir `t3ncy'. � �  a �'�3H 2�!1mat3*��6v�2�+� C3��th?t� a*�+�e:�of�no !�er liQ�� ��Lan(TN�To negoa��0meE0!-t )��hzYs��oV"")@�R� tOB_)zl�i� TN�-%��'�rthog�#1�,�{Ba� II� S�U�h Tc} M[ �"�0 l���\��!A�*.�6�!�>$Holder's, "}i'09CjA�& l2� �9e�����uJ�!��e -�A!yB �jdde��ems wA��a�0LadyzhenskayaC ladyD=2� �o��a�A%i]� r��-n">&� �-2\9 y: %�76� 2G& n})}� C �^{1,q%;�  %\]RQ�n�&�VK q > n, cՏu� ��sob�} [ j6V r} �2��jpZ 1-ZAta� k6=q# !]'6�K Z �ar}�4j}{n}=]{p�s I(՗q}5k5)�&�}6�UiV�lA�sz/T�#n9�a�aIui�a�w=0n�A �i"e�pla_*p0aJ-ro5C3�m�V1L��� d = 2�/�?� rI��!�f , as�:(o"( ���pUiu�grm���`Fjau�'==ed�cnom] $pT M).mat�E8��a5'ch fQ$! ��3 � $a_{0!��x + 2}y 3}xy$�eJ,square. Spec�ally,�- $j'dex�pairs $P j_{2�� �"j j} (� +��1}(x-� h[;��2 y2}1�7 *()\chi_{\Box� }(x,y),�o0J �n"�6& stic" 1�) $K` $. A�:��yr !�a ), 1� is@�!soA��^�u$i�?ti�>�A�te"2>*�S+$�T�RntY��$�3 O3#�4 orE;enAO"f/�E4k�|%ȡ|L^�AZ$�rh��$O�$\ =V;D^1 u:?�\any $p \geq 1$. Equippedim� �gntu�)4��b�Co�CO'] �qh � =4~��a��S��loc��Let9;Lb:�,� $\zeta1 Ca�^�pO�>)� The�\|��E>91f2sš2R�)�( Q�%1 G)H�G, +<�+�-�+s+� se��1�q` J -b�q�> rk} Withosc)0 �p�%�2BiEj2g4��)MA�o _�8ya^9  $%.1�)��$n��(, r = 4s, j@ , |Jta���2}.�v� ��E �e"� yM|�7�bSa V>a� �"�TiTe�6�t�3tem�'�%�&��h ,�eh!v ApQ ix AuM-9#y+ph�G If�5�F!�w A�< C�Z]�� hI6t+� e�!X$$\{!L}\n � & #strongl� �/ n���I� �NPw�S� Tedu)�r}� T$&�lyE�!�ak��W� ��"=y" �F�nce���,4 Ascoli-Arzela!*H0��)�<R! $\{�3�!W y�ndE�=��L!�!�7Ş  9�$$.X$7 �� M �A� _ityJ� $\for�\epsilon�1, \�s ~ = ( 6,"�2}�5(k h, kx�s+1!�e2�(4+CP5W-,5)<|_{%} < c| �|.$ %S�y� fDnAD3�F?�,j����" &�.&� , %DI6 ."~A&) 6 .D) �]1�q�*'\f: eqn{�Z:ZAx}&F<�<�E� 2�|.X+E-ue. k 8:w6>�J& &�&-.� .�)9�� + �� +d2} �Bj� � >A�\.� �:� 4})Qh �dx dy%s� & 2�x |j� ��1zx- �:#-B� �R.W�M�-^fz�2(I + II�A�J}pTo�z $I6�!w�U��*JU��� � ��W�>;-5��> �A}qT/+k 1M�-1 O] �M$(�硑��s +a_��!I�2n #+ '�n))+��� ���-��� �>� Iue#2/i%:�FZ ?>V+�Z�S�0`we�:�]� ]+��Bd  `�2F� 2}} B >+kZW� [�Usiy�} ini��$"(H_h^2�DC=��0O�2!�\|� u�}!�Az.�@q �"!� ��5� ��-�� %� +- Bh�"!�-V ?< Ch�a=m%hco.�(JWI ��g��Jw! ��.  ��\\ �&&$Q[v��W��R�[2(%-1)J` ��qЁ�2�?%6�2��a�>_)ˊ�]:�2)#[5%CB@ -12}CB8C9&��"O2a��C]"$ "+"�By�Gu�FT�,ls�:� $)�2N 1  >�p��C$ soNiI��h}{3}(h)�ORL(-~�&�N�:#)� �+3K W'.�.\ 9blV^\ ��m�c� h^{4-�)�A��C}-% �? I�: .U\tilde{c)QMxF�"Qof�Us �({o)%ng� eG&W7�h�F"Rr!�Unow�I E�5-"  '�!!Jj,�+�+I\An�Dl3��inite-"M �3*��� .�3��)K1 $h$f&�, redue!z�,�a1qo.d.e'-"(unoQ�I}��"N!"� ��v/U��. WX<ek �H-.|�"�Vs�1e ��m�2 A"�?�V�/ chie M�!-o5rt�-x&(0eU< r�����J(. Exp/��D:�B ��:s\4���cG �#< } $E�'[u]�S ]<E��a%պ}i��&)�E��5-F2b�.v%.$idZ*E?n;��Ra"!$ �iq :�P�Q+ �$�[u^h]"�P �6 �+1?2 � *� �P )h )k]�-ov$A�!�)2��2�Ui"�Pis%��@A��:#d. i\V�Jt �}(t)}  \n� } 2�J! ���($G� + \lambda0& I) �� =(t&)g f�>��k$}\r"% Q�}p/�6d.�M;&at$VYL� t & -(t)�!pLa�g�E? er $�/�Iiv%p>�Q-\Lap1�(t".G�A.  .�]���Iof&�E�32})f�Gdg�0al2&�G6���5� )� (1m�^2)��B��:��aU�<@ B� �1��5�E�M>;i�bly�aX)R@remSC�C�: �&k� #damF Sch\"5O7. )l�#e�be look�V|5��!7��4�he� �. �6� f=G&c8� F5�A(�$se�!A�JH!�2F2�!,�'_�hiA�(t�%(\PQ j��C*a�� $.$�t6h�A^z�\��=E�.Ő2-ݖi�Z1�0�iltBɓ:���n0�%�stp�.��""b4we��ed�  T �]� P4Y�B ���� �p �B� e"'��dtB�+3�yQ$+y�ab[ (K_ �~�!=���U �i�{llr.�%�'t�)^{]%i}}}{( )!} e^{ 0-*}�O(if �8| q 0$�� 0!i-wis-h!) � ! ,�%� �7"H'R� al}ey`At� ��IA-%<��!<-)<�Cr�7!9 �9:9)�}{�&i�7�$�7�6w�K�OT?ag�Qa��1u�:vR#�2A]!k !-B9? the �f2#q�)� 9`h�:� oluVb�1J waLq��TS:��k�%)P .�)�J�kI�!~ b� QNF@b:�"��#Z�?*'5Y��O�/da�6/,�9tfF* �>�2 T$2� $'s O$1ii  d$. .A!�R� V�& *IY�,�5d�$\UY5,h�(\Uɷ� ,heb�� >M���8 + i)�{h}B. \\ BZ�^{m�  �o��cee xact� �o*�N%�1BMUeE �&R 03riz-Ds'Ins"93}�VmP� Ju��x�e�?o��Eg!*9#*4 �!�b"l $d6yjU32�E�Ѿ����vt�#} .�� = \Pi.6: ����2��V�4u��1i �2,%[fal � $f!��g&!�A.g�F*� \a�� @���9ll� �8m�2 ,. \M".�_%>��+I+z^.�f<schroU=>��BAS ; (�Z+i) 5�)^�a�-j)!}U?r20�M-2b+}�SrTrc6.�(tQ A"AN�IL��1��;h!(�_��}� �����{"�4LVOE�m } Ha/ A���.`N�s�Ois�DPa��I� 2C$�X�.a�($p}-L^{q}$ "�G>�-�LLh*+�)�-Ka��.$ �aU_� h�m.��o*]r �II�s%Z.� �Q ��^:u$q9a�iz!� [(1)] F�e1}4 �1�\|�C"�MC\e;\|�@&q~ t) d�:c 1}&)4/. )}},G � �2r�}?1}�����! �~�B�E��)l.�b�.;,W4���+eI�#ofN;9�ZFah$ �.U"�.H �HE� Z�`�-�h UhSy�A�.9L?q��Iu up�=bta:5"�M�;1�nd 97}M� "��� 1} ѓ�2X4ir2�<4\|.��+$1&7�/ \ b) ��)�1}:� {] !<%V�&�]-YounghDo�2�2pj>��D�7BH� N� +�pEe 1}{rA�q%@B�.�3� ,!ub{�#(R1}��"8V%1L�Cth�8$R6 $ �_ �=1-( 1:�-.�\�.p�9so��?f�6W)}Z�=�7 (1)M�� *�' (2)�6� W��y/ID�`:�!�U�F���YI�^C1t��ZH5c��}��]Z�����ȃ �=���'n�C�L\� o ]�\�1a�!`: <��, $> $"> ~"5)�G'�1R owo$`"� $�#�a�/��b> !!"� P��e!Gn��[ T:��<+?�9�*�+\|>��Q9&$ &\|R'��.� I:� +}{�(j(.�2.$ |e^{�.S ��>�mN��)!"�e�*&%R�\|)I%[�]�& &�&&i�&V� �27�1"�"P'I�J_e=.Gf�(�3E2$) � �~Lh��}8Ji�beNe��Eany�=��^oa�NQN<&� ?peS/h� ~,Sti5�g'cRvD,re-�=�<�$�Ha�*w5Ju�kt=�G& 2))�Z�kZUq;-�Ha�J VE� ZaC�6 k^{k}A� k}\sqrt{k�-� YU*�v�C.�Q�k�)w m핂+ kNcF�W%zng $x� �E�g nd l�Q3(k7 � x}{k�xt;B/J| _\b f*dk!��1(B])'!Xx�I+R{ "� �-&F) (\lnm���1)�[>\5B�>c� �~;� $fv O]�\:~:$�ls ,x: �z�J�FKJ� \R3a�{)}E�!�E� k}{t}J?Re gATZ=��e�N���w��~���^�A|B5 v5>0f(xA�X1�a�t� P&&as Y U I�n� � N� �J�D)[CF� � T1$gr�L�d� ��N~�!� �,. �# � (���\neq  +i&4�JJ ���^Nfacg�"#ū �C'hit'� �U"96���%t!�w�V�-�1h A�,��n�$AA���o�� ��&�-$dXs y^q�(�0x$M �.-?w� � (t)|I��I�}Eɑ��k �1}{j_ K+13. DA� " k}{k<* N� +� �!8%,M�9jƵm�$� r �Do]Y $d-1$:()!�� k� �rgetA�\.":� 1 � � �i<&�d-� ��%� " R� T�fo�{ �^1" 6�6�2�~fE�j�<&6%�2K 6 X'b�>��GSXof%�;"6Ks�a/:=(a>h�>M .�R�.-�� 2�hJ�=.+�E9,$),Xe�MS6ZEF, �Lh%$� IJ>�5�Xf�� C� p_{:��C~<i- ��)�l�i�l�!' ��!F%9^="�n2��1&w[H�vMap H�' Flow"��]A��g" $NRk1p�I&ۅ%��^G]&cso fa�_AKR�yէ�jOdf*Qw���"�$��+�0I��A f��*�y&�y\�-�*�O&^@&` :nceq!#�##{�yt{un  & ��u u(0)f Rjy"e �2gP�Cusual�takZC�b�z�iZw3e�.2�� �6�!��_\��"oadf}�y*%bnd�n�/)���0I b3�+ \&0��}.(t)o� h}!w�r0B��"'.�=nu( }"�\A���/�P2��~�/�]�w �Mfl I0C"�Vsig� �ic� s!V@may^b2k�`�rb�d��4@59�-"[un��spyLedr ,4$y like $C(�.�]�E ��ubp6*{"� �9'$a�A} secL�1}d �purZH�!�d�S} HE6�+8%eqw>ib �I�Nt��e��` �u�d�l�s�5al.�* Lcer�2�1$�reV�G "�G1 e!y�x);!D��"�)�VrduT!&A$\6Uu�C T_u.�w�P1�d�O.#��pul�q`-i���?�3n=* z i}(-.y:,)�6� K Xa�Ea�{ +�Eui �b?��U0cIEE} |]TO]|( MRaL C|�k�B�-�"�5�"�8&Qp.lw�9��Ucy�robTK ��4$E�s clea��]. � $a��i��� �Z13�$o 6 at���Ve.� *,%&����Ej�)aQ^Q�.�4�7��`-i}�-�BXB�-i"�5O�+ N.#.!�0v�* ���a m�yK_e� ���i��fi�ki{R�}*�&/Q�M��)m���' +1}-8}�6.�C|.%-� FixF]$4.�4.�on�$|h+1}}- }X, 6$,]& �[ |_d.6 � � �)fbi:}b"a "Yhe�waF $C��1� ����a�3n�<� 0 desi0�*3Ois �z��Y�M� J_actwM}:!9. Name�$�7>!`$l��m�B+e��)�T�tsAZ quad�^&T,� �j b�Laxt�}ry�=&0 Bpo�es [c'�. D���! :����� it�]bc',)Ase � I�| cho�0M�ra�min_s9 iJ�=� y�forthi�),i&� �Io@x��=Z7@ �n6�7 rpre�.o�5 $�$�Uy�� ?$qg:t$ o�$m?6�OyE���Y�b \��2in���^�O�&a--n�% $,5�h*O��� 1, 2 ��C���}|uT.�Y} i�_(��-1.�;Y&bI � 2} � �M;�= O(  uh{l�3bc�  2��l}|FC $l9Qde""?nAy�zea Tnk6bđkQj�9��#݌�@*�!calSH#�"�����a (.=ɡ�{���vi�})�.~j) �5�kR$)�� [C+i1*�5(h D_+k e )^2 ��5Μ2�)A G{�S�~;E�S4� E.B Data.An��R���8 e�asAF�_`-3[��a�� tov-r>gy�2bR�C �:.� "�u �in�~& \� �;sY�aL"��Aˍ�o� eD � ��@�7}�.@ `fastest'��Y �\goal o�;��x laid̓^vto0 ���nZmot�}��.abre��� %alGs��� wra ��s� VCe�s �i�N-:1�=Vf8�%�U���f$%T@YB9  \in H_h�%�*2a�RH p_h .7�JxTS���*�6.��U.i[\ zV}^U�e}y�Ul�'7!�$p2 �$so*<<1)��^K�� �a}�� t*�  )�i#��Aa!�#E,Hit�)as�v8 �! 5 $u^h�)u� ty� -\6�-�� olana� %(U<6claimed.�?"2.*{Sc�1: A�B1v�. CZieE*qK �2A?�t�wAJcA�@&S �6GN Gd}=@�T)]I>�@^2(�@, �2})-$� *m@6n �r�"[�;fF}�+ {u^h�\�\}_j| tJq2}9-2�q��-IL�l �9=}�Wt h]ENhig��a,v* a�taim���\X�` -in-�%"� `t$! *lH} P�#z&3�$%�(y Lip$31)�2I�&� [(iO.f�bi� 2)$}ASge2�ؔ"vd��$-1E=-�7� ffic)�0\"F B6� A�"&m> rols!P�9��V�~ %�db�In]oS>�Si�T-jE�2_- %a(@�"SLA�.�qwr$� as %-x*L"%ZFU�E�, �2o,k 2&�i�%9�i ' 2)� @ b:+2�M@�: (�J5-Nbu^&� �R!`B(�. %m�"� �&2�i'"�^ez$�^1�^, p = q �d"�e ���M� L E�Ώ����h.�a�G&�( C1.pt):s+v(2\Sigma_j |v _j^h|^2Q.c2�X )LV\"v*�+ \t Mb(t)|^2]� �M�u^LI4}}^2�K K2}��2:b����8�3Er�^^" 0�`��N�Ok &� 0� �P:qly� "�absorb�:$C(^�)��%C1�2}}$ �� "� h��G j-f�E'R�2r5���H�u3[�@.�j΂.n$)�!>�~V��:�y)!f�F, .h�H )�� 0�Y&[�] �M"�F}^h$}�K!�j=sua�$&���(t;Mx#\� w6 a�M�0}^{t}6'-s)�/�G h(s)]m(j}(s))| ds� ���xv�||4 $ Ut�V�& ���BASt�(�%�A�wy&  �R� F)V Na'.�2"i1�b"'1de� , B�,���a�p2,�p'�d/3aF�aZ{�U6�K,"�.��-1 y }�q(1/��6C.� D 1}{(!�^{3/4���f\�E,)�s))�� �4�U}}I? սFC2B  �))!up!�3$#&A���%"& mc|($ �#|ER.21�|:�;u_J�V+.V!  �Vj���_W��K�#��r$B� �Sto�t�d� !-!?"� H qE�" q9?� .��1J!�\nuV�-Z!!A�{1� A�y QHM��=�l k �� {3})�=]���A ing,A�N'�^c6q U67�  y;���B9�CQ�Z*e�a%� 4}e��- 'a��{ ��B!\aW�X2� C&ya�+C"���W.�6�ɲ R��9�Z"/&%s�H>�>`3&2%N ds _��(\s�'t�F0}z b t)])�)2D��su$2n � � %��C��)R=%* *o {0}ڞ�� 1}{s!�4bs of���2�" !�� l?b $y(t�!%W0�_s !J ifh-- H� &� |AΡcc&y % 1�2}1�gt��.�.\F�cjng�Nat� B� ;tb?} :1R]%�� Q(22h1�4}y� X:d5�dNC�  �� [- .E! ��.��.F� T �fdds O� 4#IC:� !� CZ>2I \]�r�$t!  [�jn2�&�"J, $L(yA�y-.U 0) y P$�?; root�/y�Q6� �pve%,��g >!0;)2 4}{9�0)^��� � � �- {0drxn0F? < LMWN`��8t&& psto%<�^nAP!�8��U�23ce�;�Ɯn| �]*� & FA}%�� LN2;imy�� %�L^�/:��T�dT+Ϳ& � Kwe�K>%C�V2l,o \�o �_1 < t_2�llrt^* = 4@-t_9�pjs^g!|s:e!"�:n��[1 (� t_2� 1&� 2}�ke���^{t^*��|� - s|�"���s)&�^2 ds+!rt_A^�6G2�G>d�@ !����&�"���XVodB�q�0)(����H�+��JA>q� (t^*A�)+ AN-t^*) 02� !_1Ff� izeob>H2:z��q|I:Cn*�&�!W=:xu�#2,x�rqJ-�s�&="� �O uch S�A����H \cap�3*� rm��6p���e���h+3 h( "�i>r} +${t}�D+�2a�\�7t_u�e!�)-�X ���|��|}) <6��VA6d{%p1k H�vt)!Zz� �\nt �s(tŏ�"E($ȵ%|C���R��\�s�w�G�� l�1c9u�;uv""5,ph�gral} -e�U%"? Re��o"*Q� +.} �<�,= ) p_h)2 \hi=� {?(0)~hi� + O(huw�Re |ei$e{%R�q�j�8.8Y!M^�*�1eGsX,� �)!�"�r^o.?|^C|"xRT1?.G|T0�1�Y��"?[$-G�rj�},":M%c%��) +1)h� j_�|}^2 �BJR]%�ly ab�:~�(V �}:�~g1�(s) to p1�d_�!�"� L�e�Pof�bj ��$.|Bv�^, �#}M�i�^uQ����>�!h}V��M�}&�eW-��m_jA�]t�%Emu/a�X_t 4)=e$�o ~�aB�}���\v�1��5(F��(i~'[ z=�d:�=!(:bVF96C�rON�f^�z5n�{�� A��� dl3��9�r$[��mai��� ��&F&� 51QY%�~�R��7&.g�I -.�=�>Hv)]�|.a���AAU/!w�!��$:d T�y�!�Q.#J�!�E4\��N)R;��vD%�1v=e��]5�*���"38g!_ � ie��% e*í-D*1{h͓` -�c.]Mu� (x)- _i+h)p� b�a)kF[_i +h2c�  -p^2f)4�qJ���=�WA�a�_0(iv[w:T  #fhe'f�� sA}A���� :<���t}��:�by spli�`  o�'���Y[ Ii�^�?!He��.�A�i�  {h} "(�Es�n�����]�s��6C /4" �"C � $ ��� !�j�* behi�*!�5�)a�1g.�%�1�5 rega��g�@�X!ncFiIJ�. "���� N�gcan_���"�gA(��2N (jh))�:�� "w�5^ [7t w;��,in:9$mB�didB *��eu7/"* &?�t� Kj��actor���g*��,�� ho> ata �+i=x 'eE�?%�$II�1wo6]s3 �E $�i,�)a� �y1�� �>$ t��=�- �u�q�C (R switb�s����u�FYA+Repu��Jag�k s��++?"� �+�@�; Kee#�in�3d �%�(�7 ?��2r �4\�mA(՝I���;)_�! 1�7! $�*y4n3}�h��!  L�K$��f"("1 yA j)$,"�R��q�o2�rJ2:�� � &��8�8�<����f_ 3A2���W�  )�� o)%'i4 #L!�+1�� ��[>\� =x�*A��Ral�in��r�m���ew+p�l�6tQY8e���1l��26 rans��&\#�2�Dnu$e�il$|��.��$handle bec��ye�!. �II &=J� �d^1�!�%�-�{ �-�}Z-�� )idx�*jAu(�)\���]hB+�I]�pMG �ph�+�*Uy  �i �3� 94 + O(h)\\ & =� & \int_{0}^{\infty} h^{2}\{ - \sum_{j} (D_{+i}\uh\cdot D nu_{j}) _{i}+1} # \phi_{+ vT(Fi})T j} o K<} + O(h)\\ & = & �}. \end{eqnarray*} (i) - (iv) together entail (\ref{phintegral}). With this expression, we can split the time interval into subIdrvals $[0, \delta)$ and $[ ,!h$fty)$. On $,q�Rhave uniform $ \dot{H}_h^2$ which implies from Proposition ${\ref{phlemma}}$, that �$e exists a�\sequence $\{h_{k}\}$ suc!at $p_ �>}(t) \stackrel{H^{1}}{\rightarrow} p(t) $. For any $h_k$, then�8can use in addt�=�%%the fac!d~u^h!$ \rm{Lip}(9(1)$ to show � \begin.� \lefteqn{E6�I�\R{2}}�kQ�$\partial_tEi + :!D!� +A� abla>$  \nu( =)A� mA� }\\ M�( �a�h�+ � y�) & �>z����uv><2} Th! is an $�.{0} >!�A�I'(if $E^{h}[u(�P); B_{\overline{R}}(x>)] \leq .R$ theg�~ $, �pe �of $h2� \for�f \tau!�0box{ } t_0 < l+ U$ R^2$, \[�Bp_{&) h}{J 4 �+ � .�o }} \|D � )\|_{L_{h (! frac6 {85)} g C \].� \und-;Note�}::h)dR5Y$ denoteeؽ3$�a�dexaD!�L $j = (j_{1}, j_{2})=` $j� B_e$. ��Q8� ͕Ax goalA7 to a�* H1$ bounds�; a reduced]�cyl!�r��e��pa�� rougAy.��med��dg!t" ndY�$itemize} \ 4[(i)] \emph{S� m�1D$inequality232)d�bLA(�%vr�U>VD� %�\r}(\Lh{4Y��$rA�!�kva��6� N}({�n j�}I!S%] Pr��ingaqI*9{����c, :�a�I�2Y�i?9/a�$\6G�� t�4t`T Ct f..{2� �/A ት2W�}�Rh} 2 �� + \|*� u^h�6(^2([t_0, t]%�2�@80)))}^2!�� ����subm�D� b�zeta$�G(cut-off fun= ��Hls 1ITN�� 0 (indices out= ��B_=�$ ��$�1} �|)c�Dk}{R}$. Multiply��$({deqEt��B� ��j}{t}a-�and sum� ���I�e&q"v>9|�r|nw}"\ K&1Y ��\W&� 6W�D_{-i}�\ \)O!],-�5c�Vw)�����-^� X f(�)f`:\{-5> k� �z - �BQʒG \- �>�- D1}�6�(t-?5�)Ax)2� �+6# |C || ��| 9|��E���r�� +) %B�6%526�)rV. !]J$9B� ��1�F:����%� BUR>Z Z��k"�Si�� am�~ holds����D plac��)j4 maked8Ft J get� 2�2�y06|])�EH��I� �1}{-@2k9U � �>)f�7] � Integ�ng*�) $t$,�2_NFt_0}^tBS�sY/ 2}?�2V�� .T + C �t-"� ;$f]. \] In� ticp, choos�$. =-0C�}{2 B% MgeP e desired�ultMu&�"1 i)]*�\f� $u A�)$} For ��M R  <  �  \Ml2h2}N�./< � *= & .$!� �[%\,  � E\], )�C {0}".�� C(z)~ � �9ETo%o} on term� v�d� $>� �!�it suff� P� 0�!�� �6 s�,"]La�an rols 9$ond differ�(derivatives) %This %� seen^$operators �f+i� -jf SpecifiZ %a� likO�+1+2�2� qwri� as %-Z*K %ZF"  ���6o,i6)_{-D�x%9K �  � @ b:+2�@��: (�J5-Nnu\na�. %>a�any� 2� $��� $\�$ �v�s>8 e�%7� $ satisfi2?q3:���� �Y�(:X)%� \{�� 1}{4͒2H2�qe�� # -1})g f4 \nonumber + 2E8i� +%�)#� )N� & \4}* �.�+ 2Q :� �&� �\{�G�(\� _{t- -\lambdah���?1+�� �1��=&� �# �a�$ &= &I + I V9���Q��bjus�:�analogQ e"� MI[(u%)��u)%Au �!+ + + = 2�ur :cd \nu (u)) 7AI' u%b] CN�����ite�ls 1 ��$j.%n��� b�C� $  $|)���2�+���~T��_6/ 8isplaystyle \|I�}�"%>7(�!!F2$0 J^n_ |D^1�(t)|^2 ֲ\b] C\ ^� u^iFa� �2 (t�1G2d� i&��&�v�u �;.�i"R;ɸ%(��WVa}:�jM()2\\B��t�"� ���! {1}(62�8J�6V1eB-V��@�D!}�ɋ�{ /|�} �+� �]� "�$u��"o'absorbE�� �^"$��he �'�k �A�� �(�  t �eF%�2�Bz��5�3W%�!����J � վ$2#�W ]� �(�f$>�%�jI, Z�)8�$�]L����s"qf[(ib� r}(W1,�} ����$\tauc!Z9. �%:E�45� ] <�+)US> 1$ &�QG}*"lrl4} �5)� {1]G^{r}[�Z��4�%�)Q!!l&�\|E�(Ke�&�, �f� ]!�!����9�%F�'Lemmas Սa�) ���fi,+a�.h %\[ %� �-h^&w {AZ !�%�2��� mM�,j] %�s��VH�?:�Ɇ C %\],�3� catZ wantE\�$rE,��(ope�bstart�'e�u�p � �#� rb&l(i pY,(t_0)%#H_h^1G HA g% (ii)�v��#�"�5���%t_�inZ�9���$, &�&R�1�!s�->�y&V�� a_\�C}{�K1}-%�)}:�)�%�0 tau$�u���i"�). *���! choice� �, �'j����Ae��q��o��dcuteq�� {t}("<�_"|0} �ON!&����l"�&�-���"�)&>b&.&�4 ����E-1.�� !:*�} &9��o6�@|e>� , $1AV a b�,of radius $R�t ppor�* :s"4. By Duhamel'� we�� � ����haB�x0)� &e=3|\Phi�� @a$ CDZ4;�#}^{t}m�1a�$-s)^{1/2}}� �I(s)&�� 6� ds��\.�)a$� � u^h"j� +|M��Jods#1� *} U�~� �� 2� 4,� ��� f�#��11bL :^� "E  -�-!o���et_��5�"� )� i�&v0C(R, E^h[f^h]5��&��C�h 6WsM�!��}>��>@� �&&�)}�L2�>C �"tak� r�V4 of bR-� sE.kC ,by Young's I"�)��k�e ���r}2" �UwV 6 r}$;� fir�erm�: �$*@ $��� c se� is exactl� e quantit { # tr+'�B�. entirA/ duct� beV�H.�&(>e �-arQq@�;�in%C!��V*.32R �reforep [6���I�R (.S 6"� ��eN� nE u�� I�&2 "� vZx \{+2�+}  "�^� j� 2�.�-�N$su y2�(u� � "Z� 8"v ]MN� b#/%_< �H� � �;a@��V���#x����� )�n� A� af* 0aoi�("� a�aMsaW� � "k M����' =A�� m�&� :�eE����4q� t�."+� �A) � &)e2&by�G<�fp' = 4/3� �Obs �"G nd 2�$*�  !,�2 ness�� $\nuEt[ �(4� )@#etilde V&�'| + |.A+1 |A\?  u_{l�'3Aj2 2 � + N( � \\!�U&  %�1S� 4�.� 2Q�. !(&�\� 6'!���r�-��&�5F�Q�� "M>!��� +6�ьn�@�an��e�o� &� �4"�!.���"� `�� ?�C� � $ �4�20�Y �:�<�C tNH�he"*�8�5�" \times .� :M]�)c&� �"��2 "� (�4T': �&$:})�=tru3of.�: to $*�=$ �s, ;b� �A leve�<�&�#pprox�;ion�(Exist�(!m$fixed�8Got�ssu� Moreo,U JL=�2F=��* ��4*�6/ ~so�;remainFO. &pE Mmay!:c�<e�!�urrvalida�8an im�7 arguG=��c`<�.-�<K=s� T 1a!?s*f>2>, 'XudR:� ha@(con�* �B� s, or"�C:.g� ent.?at ^EQiWprovide�%�!I�>s"� i�*fkeyj&�A#�> �; 1;.>>-�a�)��>se� j��!! limitY�?.�hu>ed &[>Fv� R *g>i�?a�*INg=)  harmon= ap heat fA?"A>A"A*{S! 1: A9# B� }3d�t7=of^��X>[ 2: E�?\!1S*�?Coq!vSet} BA�varia]�� M4�6!� transl� ,!,.�-5�z6� setQ�%�val�F1�OFix&��� �$! �1Q�1� 2.i!�mXnE/$h$��1a� nse,e��R_0q?o �% �G1]��to� s $I9DI_1, \ldots, I_{2/o_0m%�>�$/="D 9 $T� c1|b�H%g^>I. Defin|(,beta: [0,1] .qD\{2H � 6�\4assigEpto �#y�1��!��<x:�( $ I_j��IrbitraHR)���point $[?i�e �\ (0, !Z#:P&�=7:&f@�� \[ J0({(x, t) | x� 2+>,S;in�0t1�^2�6y0W+6]\�&�@-�!5q ular���\Sigma�4bigcap_{R> 0} ��.$\Rplus : \��nf_{h.�02�;, �� ] >&,a6 ��)$(x_k�k-��$ i�I , by�_6�2},�<�M-Rq a'� A�1�ply�F,4_k�+�6Y),!�� k�4> ��/2 ��$,A�OD $R_k�\/�!�N�_k)� = T_{e[(t_k)1]-C\[ �g)6$ � R_k!f)}]2�0 � w th�I6 Is   b72`snappe}grid'���s2At%�#4slice, a direcon"�Kͣ�pL��I�'� �/�allq F�2R�)>HA� TexE� �)��h:|R�6�2Ire � be no mD than "D!/(2._y �a> E�E's!� *�_k�Wt)> $T_j�'vkH�{��6��z�V�j%({*4of Vitali, soaX  's c`��B, � I �to! disj�CJ+ad�(uF)Iu��^�|! $2/(qy_0�$)�te��@(�Z�'$_{k} Vol(C )i[i� ;N2 3R/a 2Z3{2n�")�}{2�.d12}�C�P�a�usa�^�� �>s'.fb:]"&!]`q;2�  $ y$ has K NaGibGFaG�]G�7bB� 3:�  I*� �9� vH�8{0��(Ʌ�^{c"t.�B$R�B �� som�N-�36�B�N1 = 0. �;Offuv�M�!*�N% �N$)�8�mJ�.�N!-"� o� � � � TS0fix a compact�  $Qm(b� � et� .<!��i�5�abo!w�6� 58&� ���"@ occupi�QA2� Nm1{2��Tout lwM of g��SH�џ?6vɫofa"t� ��GEk�< , le�{Q_{i,lg � _i,l�l)0T9 of �M \cap QyF �G by $N_l/ &�J4� e�6� $I_l!�B�"�J&eI, `isH )p�6? $Na/!�6|!�soE�w.Zs l� J��!�i� C!Q �$2BG s $0�\eta_{NK �w���$�Mb ly 0!# 1}(0sV �$o:OG. .� cu2;�vR�0�@l?1}P$�l��@i =NP} �1�Ex-xI>55)X�� @lkC�� V5LE|phiZ�.N�P)��=UU hR�w \[ 0���"�F.�i+V� S��phi\}�+ LE�5L$ ��by"�4*% |L| &�|��||f|mSE�v:��_{xRWi.)8�HJ�� �YiM ��9�)| dx dtH*�Cfn��*C}1:M�9@| sM�aT&e�q(-�Fr�aC2}B&��] F�&.&v� �9� l} RB�QGp2�-�&'C(JN R58 �B:Pflf�.G:�CN �( �oNo=�Ta&R2� �$a�\@3a[ 0$ a��3lut� �T�%so� weak�,�!�� FVf:� ��b �WLLGA �T llg} p=O��9e��!E,�%�TOllg�T<�f��;bQbU�7s�Gpa�Tm-jo�"�"��% semi-V�� LLG�� by 9Ud�3 �method"�8i$V-)u vily2�sg� lin�&g !One�j�RngredE ��#edALLG: ��&mu. 6�>t yie�Ha5Y� V �in itsN" est &Q;�I�oEb ��$e is:��TSd%Cb ing r�coordins@Z&@E$uvZ3� llg1'}$)%$\alphR 0$ o� a mov5frAsHCy�whoseJ��1Schr\"o`er%!��ep7a!review�( ApVix B.h%(Ql) W,� - � a�5�Aur"�JJO proji�d:4)tangent�;!K�%c�H2�F� I{�LE�yZD�AS^[y�#w[IR2|"V DNGW M/ir �cy,��wa�� t�@�$�' A4orthog,[/i�� � ��a�a}{ccc} �Kk�C� v��k{�a\w ,� &�D2.min- � d*� Z, \8� \TN$.r\Q \perp &�!�� �� fur� depos��Mllows.�Z7]!e at $"9ZN�dma�a g1ZI�, $\{e^1, e^2!#4nu \wedge e^1\ Just�H!tA���i[*d�2�j$e_j^$ e^i �F�  I�LW%��lex�] cR�!� i: T�2.%�ie^1 =�,� & �-.��5�  a� $e811�qQ+!" i{j}:5 + i .�U$\qM01 0 .� YA PmNFk1(j})= e {j}e�&HZ�7 ]v= ?-?T�?Y�-r�Ce2h�d�a� u_j}=�� E�oB�E�be.�J\[ }y� \a1^`4f�1\a!O{j.�$\mN$�"a�,hypersurface�b�B unit normc*A�2fiV��Z E [ c_{\nu�\� \nu�%^� s�is � , $ensmy]so��� $c_{e2_e>]$��X��*{*+s}��&i$ [(1)]F��| = |M� {j}|M�|�� !-c|�B[(2�$9�=�.�\��H = O(h�L�N` (.$ Similar�O h= 3��3�.3�*�+g '1��B24)]�suitab�B�#&;|�� +1}- }PF&)OB,>\} :��VO(|=j ^2),Q .�]!:)�?�� )1� s&% �manip� N�+:�"�2z!��, wplu)%LJ) |I{j��AR+F_W3||h6�]g ~7%�F�F�),�*G ��. d (1"�dlc�. i.a sI�"�uR<�#"�`�E *nQ$��O!�I(�n1�)��!6)-mP9�\�]>O K�O B,*Y��R5)]��u��� ��b:i @{�\�a!;7u23%��.<�M} �DA\�O(!�w^�6��2��(e_j = e(u_jRoR�}2���t�u}e��� I)��I�)I��D*���^-hP3 dhasimoto����Ue�  Z��g;+1}�)}E��&�� |vO(7-1I�.2�eV/ q�!KU�$�(&M �=� ie�] = = i : {h} + JF!(q_,W0 �J]�=$ $ G 0O(|q|^{3}, |q�/ q|$l$-%2 A �M,�2%)�-�1�"q�^�uE�){$, R)E�v1B��$. LUan"i�� �%%U��T+!of2�a�? 'O inner�d�7Y"�f��*/.�$E�1 �AqI� �:�O�)X7A1�t ^� j$a��P V � -�1ay7 [$II$](.�9P�R �\Laph-�x{jCMOJP= �RVaK)�VSVF�}  (2�A�lB�?=D::L�ǩ���N [ ]10�Q I2�2� j��[S6/I�+ �?F�9(6;E�E �m AQ{t1\2�M.*I +�.].�Qri ..�.�>MT2& m (c_e q + NZ)M\NM&)Zmmo.' n No �jp( yM�M[�% +ZͧY1 Each�g&p�=���0 long��Snon� �;$F)���amBWe u\��A magnit�nof ��<���claimed.Q�A�}$\bulleta|1� �%2n�M(1�-D�bE�2-�qV,w�]YHPi�=]|V=Fi|p@E�|-��a�-i)�m�� �%�.�|Uu| �%�1 M8B7E�I� `:2}a��m |ioj�MM" ^1 q_l|���F�� RH��| �5�-&)c(�-�V�|tEm :3-H EN?�|�m.7: Fc.� E�-i &%0� U O(�F�}-T �Y0�� ._|��}�.EJ}�]P |&=&: i}Ɉ+Bk �(E�a��� �E�=�)=J2z%=!� �, .� }�6� .}hjB��s,$|�>�})�� %w�%("0*� $I$�(D6F�$ 6�<�.���y'F�I3Qr�{2P A&6zU�>8%�)� + )�2�v: Fmw�m_c [=�)�.����81]��h!� b�����ѠzBZ���"J h}|>R� +i}-I�))S�y�NF-4q�_�'-��:%�_�;�l� �9fkV\U'O4$1}{h}h\{I�E��d,&�?%{2}6�\�i29^W.("yW�E-ZtB���%�E$I *q"JM�]IM9,�?& ?v ��aT� �"h� iA��LIF.>2?? ��[+.T5�_UE$ -1U9JY�az)%N�!^] F��>�J�=. >; �}H iQ�,6�2� ��9��b&�Cd�;sN"�Wu�m�.�!�!Y�r.�| *� �ieEc_e\{Z>���!.2�J4N0\��E���y�.�v�>J)�r�.bi��.6h))�|c_2?D_{0\&� �4.).�\��q� �d� F+T �!�kt 6���;�_} �f� F� T;+1}�A k >.��a H+1J ��>(%�{<��) � (I+� )r�X IS5Hmi i� Y>-.��X^X(E@����(/�!�% �:5� Nv�c-m(-i; nm[("F�/�(, �6�$� � o $F�^#&� r7 �@�!�=i� +� 0 X�|2��� ę�+1KHe�^e�]u��IVF�A��J�O!V�}2� | ��  5+W�#u�(�6 �*�>d� zK{ �B�&s��.X$JG 21.��PiI�6��} =�}| ��^aq�:Sm�6P�*�"K ~�� .p $\di.�-z B��n��2`\ -� "� .Nb=��]��oZ�e F�.�� )^^P5�.NN�K��5�l�jr�+�)A�P\A�FZ G"D"{P��Main R��}t7t<g(-7�F&V�(� � � $teps illus�*�*"�+6Cto<F1,o*q� 'Pf;,2}2�<�,e^f3�*�i������\su^2�PPf < t �3�PBQ��z�E1P��M`8i+dg�52}$Ah�9/�Z2l*"8�49.��9�$vKv(!�SG. .��Ht�HyUd2�dt{#�2{a$j�$�6[h�S7}�!!�*�:(t�zXW���a �)} � )� <�<� ��+$ &&("mQ��E�!H incr��al&�����4"� y� �Ab<1�&�6m�&�Ua�E�$e��" �6͇n�$, � ��� z�JA��e%{l.��$�`��$�# gA��;S[�3��%!�e!v�$d.*.:tr��7 spat�U:};�`�%�/$� L��(>�%�$�?s�j�he"$1n*�"�\&qt%�/(� Vk (1+i*�a>"&� )Z�uC4Rb��S[@�v $�&N&� l})�� �8m�}"c >O[H>w )i+.))�J1�w_��+ 2c-I=h}=.�\} F;+Ap�D�bA�b�)R�6� |q(>KX&�\2 & �'}{=} &�9k�iQb �O H� �kb#%�"�Y cmatF�U}csaq(\tau:�XkA �=&}jc{\|(|q(s c3}Ɂ�b�U} +�" ( t�*�Xu�0W%�&�b0+ �.n \|�()a�(> \||_� .>��dsB61.�"^Y��� :Et��* ]�B�9�A��>\��3a�@kk *�^L]S,#i}6:��Z�  %����0e��do�bL7en� �vrr;KppearQ0� $qgP�� �r�W*bif�Qw��Ut H�would&+Uly)J� $ �q| �x |) � H*exploi�7� ~ $*l� toVv.qE��t�7E l* $. Instead� keep m-m�>�`Qq$� pur�toR)�56s; !'i�C^� �]w&�& . So long!�os�,actor7<�o�.�&%Ly���X�D  A�a "�Iof2U_ 4; n�hy�6��� A�Q�E� E�M� N0a#R/Y0YA�� i z}v&ABM�%UF��v��U- .b�Fh���6Ts�\I�W_��E-(�72^�B��|N$�JA�3Y�%l�B68�:�Zmb[Z~_.z�y�{!91��c&&L)1^vW�86�%x��6��p)�Ta� c+S ��HJd�V �j�s��uE9��&_+ 6-^�}&2� :UU٪�4kj�-L!M�q-�K�U�Ea �I\R>�j�jnj(4 ���ed�1�N�,j�6t"Y�}:$K�/.~��\����* �s,.�"Sjas�� � �r�^�IodEe��tijti1����]Is"Lw'��"&\i��2`#(F =��E��SiZ>J �,��N �;��f+P�w��ju��)"��).2�w)t�a f�-[s�W�"� \,�c1h 6� � �@-R:e%0Fj b�c�D^1.� ET�:Q�`z�e��. �f2� �s)� ?.0�E�R V�:� RF���lc�^� �E̖+ �5F 5�6�� 1}j q|)~+ \K6�:3e�i�.�i�.*�\�\B\!6� ��7�V!6߈*6_ #�9~9  & 4}� Y}MgA52�Y�� 2? � :. F%�K&:�@Q[6/rhY�/r�2jB�iy)g� $r>4�.?�k��- JY�.�f�W &�p+\�v� q!)r�.`Vc+�&� ��Li� ZBgoL3,AC*DCbwcR&�h1&!�.�&� $.�2 IZ2: >wcs*wcPJ.2�wk9eo�� "V���b�6Vd!Z�3: �Z�t]�^.� �X�f�Z�� ��"�� U�done  accommo�gtS��.�ZF�-!12�� WHa"�W$P(. �e*Q�� 2"�� a�d >[ $p_h&^nc[x��S�IC�""F!Y*e{SET*� p�x��U>s@>ITBތ p^h))+ZQiybTY*�i�)F(2�-.�=MfZK�\Ch� ExpaR��jt}�phi�,�ll�$PN�28Cz*� Yn�=n5�A'9t7,�bM�^%�A`�already5h)_�`1�t>52�Io��j�2%�:EE"� D9�=�, 1]D#� 9�hi�,( � !(t�+\l[&&�rd�" It�A�%@h\R�h�}A��!+= ���(�amp �;��c~+cYhll�K. z�k.�r q7\L 2a%4. ����A� \� �/��aK{�.]3\�" �DM<5���+2 (-�i-�=�C "� i1�Z�U��� *�� \�!O���*M �{f�>H"�X lamos�AdAr���N*c�y~.BI~f _Q�X�<��yY=/���g�!(E(�(Ej�$%��/I%�F�(-�(hE"�B.� /8.:� comb܏*�d�&permits *��&!c:1<$Q��&i.� $&�_!�T��R�J6�V�&|f�&D "3 V�����L  A�.7�Jvl8' 1}�+)��! �Vbp"�@corollar&�4xVaG)sl`nstن"4&k.�*o$fA2ZF�N�$ $E[f.R{_dXt� �c"Og1R�#!� �).�U< � \v!'3i��"�&$\textbf{AcrlvRB$s}Ais+ ")�~� a gser(Rcomplek,� Cour!� itutp*I wish�4thank Fanghua�T%+ sugg�!��,t lei � k,Jalal Shatah@� �G" guid�� th�PaA*Yss�oe�O8\center{\Large{"ESA}eQrk&} {Uetcou>q(}{0} \renewH and{\theA.\��ic3} %\add����0{toc}{chapterv %H:�$} %�-c*+�GS $\Omega��bc�R% W_J( 5AHx$��u("�J2n \||f6[�+s"�Cf�L^{����}�Q(fb L^{qA; \ \]\�s+�hs�  1}{pq�9�M5z˅A}�D�:��A easy�� $q <L�aekwH\"olߔA^,Sobolev embej��|f| |f �1�R)C\1p1n}\7)r6�V2} 65q:og�?*�,hol[Y if�e%P1}{q}��2�/$ q <2�($p, qIA$s��rel3�a"WO Hp2�!�-9�rnq2�2�2� �+ant� �m"�=!� $q >%��E�� '�\maVK�6at ���T$Gagliardo-M$-Nirenberg�iv�: help�< &��cty)1�`ik'k}(f^!*EF ^{s}�L2s6"))-1+ -1}-}2.-Jd �+ writ"�K*� "�*V01� (x_1, x_2�U)|T E� & 2s�A�|-�^{x_{1}}:Y (y_1A�� ^{�| dy_1 �} & &�' �V{)?9(�d��)|^B}�a"�R*fMq[$�$�h)>ndş1o�]Ųlu(-"!Z\ �.�1� twom,��ip6cb#� ��N�^�F<�[�t_=�-�b1^A%A)Qs�$ dx_1 dx_22.�{fc-&�fr��| ��P��I.|t�� &� A0+�{�{�b ��} �.��*��h1E-�1F}�e-�%8\ m�!�"�Y1���{qEF�� pV*})�Bj�å�k�� B�� �P6�]�j@lZ�fol2� . TR5 !i� ariz� !�";2�en SU 42.e�b'�we adB�\>��Bi� � (#~!�ssumpn� �{war�by�pl�6a���sp%�$S��be�one�:8 Jdtu,e6]�po� i~� unfor  hindr{ ,uccessfu�mby��7a�le[��m�f �seƍ$standard �^pr�a �a }�y custom�3 sketch!�&9�8dies: �["� 6� ie�rnaA�n�ly geo�*caı �o��<r ��tdoA��b :�b�(2)�$$a pullback.�R� \�p\R{�R߀�,!�%���n�map�f� g��re!�� ~8s \cite{helein}v�&� [�_*+�E� �%.@9)��"]One wa��ioc�:A�o�P������5 a tubularV_6�a{R{3}$F�s �a)dV&I�A� $y��U&�nre�m:�Ds $(u(y�Nrho(y)+�� $t�.�,knu(u)$q"��to�$%r#y��,U�%���Uho(\[ y = u + ��S(y)!�] c1@=$�s�?"� t Jvy)�� y  4:�J.\ AllN/h� .u!R�': ��)�� �~�o�kdur �ce drawe5KtN��age�ra��k7��k�!(�t��ll<�]�Ϳd�c#ws6�rucTs�~�/ T�iGLLG�=�fic���u�a͊6Gmap} M��� $u:a�d}. 2D(]o, g, J:w�:��K\"ahler"� ���x 93 $J =!� {� S� $g$ATa�riSia� vari��iti6 $D$,b0�~]�$u = J(u) DI�a]k���we re�}��xe?���B�M .ۡa��9$\�{{=L�]��itself� 5' =' <J�u��&ma�5N}�J)GiRD�y���N�:� $%B {J@0O�{ukY5R u� >Z \]!6:��1��"ڧ. � clqXe�m��#�$ef'jA1b. Figa��%��}f3emp��o*�! \'�A�we 2�.�324}$ (9��� must �Y ven z�ion.)R�"f�}[htbp"�\@�i��$graphics[h�{�t=3in,width=4in,angle=270]{4-D.ps��:: =.7�>, ;�6=ca� {��$]vv }lNq5Z��� � On��I�R%uwI$tr�_!�� ��q.g}�Q en i�&�o!�h2�u xi \hat{k�$u:q $`ds gds_2�^2 + d�E xi^�� ��Lal���leV�(u>)$i�i�JU�lde{ya�(y ��X�b �J- b�a ���farU�alY����.� �s��ŻN?� .a�׽�a�� c��"�o5�D}*��� �Dų�J�0���-x� <5:D"� y+ �� %a > y����z &(C� ruW�1  $u_0 }Q� �%$A<_0�)xi�%[A:� �.�"VH>�\����6{lcl} 2s.N1��u5D"+%-�\ u( 0AX u_0i� c\�uF�Y"ƙpk\"� � P� F�r�a"CV"��R��m%m6�� A> !za&�=.726 \�la@�,Ay_$x�H� ��n o.n�j�p,_1(x), e_2(x~��O T}_{u(x)}u.B A>��' r well-�"Xqla7�2XtLj�I� �� N��walways��y � I�AA�yp� a6�s�f���@ .W��:�%3 u$ automa�} ^,�aT-o!O)r �q&aMors�'a�e�e>}%t �hdomain�>d m��be&� �$u�Bg �'w�}vq:�incidF�; w6%%r@4 % �Xab"[*6  �02�of2��šappar7S�+$u: I.:>9"� AU5e_0c *%TA�8�mT!��!ve�Cez+!allel��Bt (i.e.�ph<  $D_x �0$)l �i *. o.d.e.:�<:��u6q�ef�V� + (e�$�u))_x) (x�D0�/e�QerQ�.� pt}*� ��qeL*ozE-v"�#x �q 2"q  6 =0]5((�!�Z} n | 5&} f>~ �`nU{e_�u_2�bN&{ p!�� Rt NZ z$!/�U��i�ref!X!eeya?$��si�xA� ��.e�&�� . Higher2r ?�F�pN��aQ<0ikiblio� y{ �|\ s߸ {pla�$3!doc �}� %M>� \&i# {\ko }[1] {\en$�a�({a_{#1}^{+}�#62minf1-J1�&af35J9minj8�FF�qkjqkJ4minj3->3{\Ca25�bb{C}^!>6�{\DV1#�D}%pB2h�3^h>5 ddt}6�["� }  tBqdtFq2 �- #1>nintalU]=���63 {\K:�Ar!KF+.�6� %76.6e�&ph:g�.N,�:/†simBY�2a�/N�mN:U�NB�mN>�� 23}.�{\Nbold!2�2 bb{NV�A-�}[2:;Y!�.2} B�phi>jphiNh phis:S�{B[PR@bf{P}_{c�Kt("0>"PuN�Bv>j=%fA�!�2� {\q:�)�q:�)��!�6�qM�J�Df1Jci!�Zd , #2J�minj6-,R5�J���Vnj8b�qJ�q>�!tV�3B�3�kj+kfFn8-N8{\R!�R�RV�R�:u�lbb{R}_BH {\RhF2˘��Z]6�{\T:V�6�T>�56u:1pFfpr1yF1yf1 {\UJ)a�UF�u��69um�hF/ vecvJ] bf{vR->t%�f{eV-on^0%(6� {� etwoV�e8'J4EB v �J�:�f1J�cJ�d> �V 3-N3�J4Ngj3NwgFwf1wRA 1J1cJ13bVjj8bVqJqJVlj3B;{\Z!6R�Z��LD�%%%% Tohoku Math� n!4 Journal - NovJHr 10, 2004 Ver.2 - = \ Dclass[leqno,12pt]{#6cle} % o �pu�� �d %1 �  \set"�{\ 2�}{21.5cs�6 0 }{16>oddQmargi1> br!top2=@% \usepackage{ams�c$, amssymb}>thm} %�� environ�2- % %:�1l�� strD#}{1.2} %[�!*�+% ingJ�1 foot‚}{} % .2xMorem-la��s%� � �. %!���>%�ypesetq Z� alic2 K"�� u'\sc�}[n)C�e2u2[ A].9�?� *�4R2C*p5d prop��V8*'�:pTvV4C :hB&V0Pl�}Bz��8�romanz�ter6�QR&Ҡ q2��;rkV4Rauk60ex�!V1E 2bnP�R�&j�.Ua6ioZ�A�*%5zz}� bb{Z6� {\nnN>ppP>q� �& bb{Q>rr:R>cc M C>kk  bf{k>xxx>yyy>vq �e %Z"H6uu:u>:ttr ;t>bfa<aFbb>LL ! L>mm bf{B_cv;A>;cvBB�U>sim1� A}\,�%_%U} !Bbfib\7!A�mes6Cb@c�  r��ne>��- "vB" ut}{ �rm{Cut�0squar7 �* If a�xR&*@V���ed��(dd * after }�delet�͔�^s u��\e��*�v023�n% ů�<ofɿ>�/�T2Ag .} %�O��mM�+availE��K.�:"m��"9 \end�.f:of�%marke"&)z. Ȏ \��atl�hrZ�h�addrese'e-mail� {< >}{}� .� �">"1?)�  \def" #1#2xgroup&�^'@box[t]{7.8cm}{% \�)4{\scshape\igno��aces#1� \vskip1exJ 6it6 6� }% \/: #2q >(4ex}\hfill%��}MZ1so~15���(itle{\upper�* {Com�*(sed Polytop�(S�<s� ��loN L��'}��O!ut�apA \author{a @ \sc{Seth Sullivant$^*$} %aC 2s � ate3 leav�%ptyI� �5$ �gA�� >. "� >a \({ %2000 MSC3 �it{&� s Sub�n ssiE� . Prim�� 52B20; Seqa090C10, 62H17.!x)>it{Key�=� 4nd phrases}. �$aH�o)�,�0-���)� , algebra+�Ytics, � f�pr� �,�a P:�$^{*}$S"\�by a NSFۯu=� research �@owship�>ab5�abstract�� �!a eriz%]Q�= lattI���: �C -ir��et�<n�.�#li�: we �FX r��u.>c��f�2lyE0or( A%$0/1$-�a!Ae�lic��8c���+�'s 8� cut �h�A�2uss&�,ce;5 studu� ar.� �<x�%)sQ��isFL�9�2�3{W�E��BB($P+#�+ed.�if-f@!UtL,��M!�;u�&�K�u_int�%is�E$modular. C9�1��S natur\�!�%# beca�]��r0�$��) sive��sAO Stha�*un}q()�-�#:�2��Fur�}, m16 �lyd�rrA� �6-$impor�C i,the Birkhoff�!h doub��tocha�( ma�)!6sq �IF2 St}.��;^�".��T!�Fm played a 3�rol'*/�B of Diacon�#(nd Sturmfel�2DS�5�.��y�6�n�da�� Ohsugie/Hib �p�� �OH}r#/K%q�h -: %I�is 8N�29�by� v},!2!�C���>F)pOH�� ��� * moti��on\ E�?��coD��8 �a�a�5��J&:!^) ginalLof  �� hier���mod!�B�Due�A���6�a �"ita^symh0y ��%6K.�Qtnn��s betw~bR�AD c�Ein� m�G�.�E.JR �$quite deepaf>��%�j����y�EC���r! z�for max�%�eG� trie�35/sums y#: sharzbt��8I�Aall�&.3 @s��!;�yi��]Q] $P_���w�& Coup��w��s��)s2cu2;A���T)!nAb��descricdEnew non2� famiB�of� ��)9W *��)&��F'!rB1vɚQ9 . Hc`)�Out!�4A�ey6e next cL'�8��]i���fiff���hFS "Di��We als"$�aJ�1r�� 9�a�a 0/1)A ���ab!�R�)>�9m�icN�XB;3eaj�� m=k46* 2p(cut polytop�es. In Section 4 we explain the conne �between compressed polytopes and linear optimization. [X 5 is devoted to applic&�s of our results in statistical disclosure limipon which provides new familieP8marginals where �� programming yields sharp upper bounds on cell entrie!&These�0 also suggestvi�dto search for large intege6�4gaps \cite{HS}!� \s)�${Character-K!$N{} !�this ;,!�derive%Vm!�)[ about%� structureY8the facet defin(g inequalit-RN~,. We assumeFreader!�)�ar withE+,Z}. \begin{ �A�T} Let $P$ be a lattice�A�!�$\rr^d$�@$p_1, \ldots, p_k ordereA�st of�KinI�$P$. A&( \emph{pullAdtrian� �$\Delta_ @}(P)$ induced by �r<isa�)�e! dcursively as follows: If N�re affin0,independent B� = \{ \{> \}\}�Else: $R8(bigcup_F \{A<\} \cup \sigma | \in 6� F) \} $$ i��nuna�,is over all E�s $F$A�!�not!taI��$,��B5 . If�a@given a specific ��en�W^, = P_A := \!(A_1, �A_n)$ a�~ -1=,a finite set����p�, we saa�a��_AE��!� it A �j�Dre�t�_ysmA*st5coy>�R�Ca1�s w�.intro�� StanleyAr�qSt}�XY�$ was meantN�UI$\zz^d�XOura�a�of.IisRBn�!:k�a�ţ1s two51�A1��$Q$E$i~QY$isomorphicE�tQi��b"sm�is a bij�� oP iцA�. !� ��ie���ing: �XHtheorem}\label{thm::��(\mathcal{L}:��suppos�EwEu�� 1  tha �irredund!� � descrip%�$a(\{ \xx�� \�L | a_i^T 0geq b_i, i = }Cn �[The%�A�d�s%�(equivalent:�` m'$�.�� b_E�]�!��=Q�'> noM� o p_m�{�in b(Z�$p_{m'}�G � .��!X��AL 2L�h�$ firstJ �n � PHsam�" !�M*$F` 9 B&�9RH n "�aex $\T $���R�an $F$," rv  8s ${\rm Vol}( %�&� )/ 2�Uup u$ m/%�> 1�H� v�PM�%` %` could��� *=�radict� fa���Ias !�{am$��$3a_NowF�sKfieO �\�B abov� Si_ei����,�7 forces�"�� !�Gto�$a vertex s`,"x :A"g y $a28)�@sti� $mɛ�&$P��� 2�: L= b��m �q�( must have RG��ZMJa6 ll��+^ !�~5 ^ A?II��a6ti�pE�$P�%� H,# i��A�relat� riorh�=!l � of !�of � greJ!Jn *�!�$E���)��E� �b;y�9���$ (� !�� uniqu>�&9Mis5mE� any�)R, E=�= b!7 ��> triv5!� !��$in particu�A�M p > M�re%��%Wŀ $m' < .� J >H �A�' .�a�a�w p show!�* )&�"� !�an%�h �� 8-eEs�!3!� unit�� ��" "  With7 los generymmayFvdo�ot liE0F[:�  it did�w�mak�.hange�(coordinates�pro` ( to a lowerY�al � I��E��Qi�.�� t exactly 1A3  �J . Consi�!I trans� �v�pi:��(\rightarrow% n$N��0mapsto ( (a_1�� - b_1)/m_*� (a_nnPn ).$$ The image $\piS��$0/1$�ũ�����i;� mapp� 8$vector. A�%Ai � ifeBonly i��C_n�$�ȕ�I�!�U� �� �.ices � !\ 5J\$ send� je�ing6SB� $A;\.z y_i � 0����a_ ogeAEB"�$�Vproper���. ��1ᚩ�B]��K:%< !�!��R�nA2� aV��!� if $Q� Y&FMŴ:bA�{6�%��Hto�WgerI# Q�%� re o!Cwis*+ce�us��re�eՙ􁵁�U�s OM/aj �"\Ń:Aa[��\}��.2� is!�� �([Lemma 2.2]� . How� �� willBrA$hort self-��� �is�mt. �Q���� /rm ���: .���e�)*W6�b�du�x ��./Q$� $0*! noth� od . O5�I $Q$ )CHc�anyBLq�� $Q$.)p%a�% &ex AAN�R� -�8bo �y9�heV<���a�Q$!@M>� �08t6��$p!���normaliZ� 9A� � orthogo��dista� fromLqo�tim��heR cor��ng[\a�cet.�� NhasY $d-1i�is"�ij}f� : Q� , x_�0eq�*% tand h* f���5�5�6e�.�Nhn� FurA��, 9d 5d��:B Y is 1�$$p�1[ �!V$�xEu�G  -A So�|V�6��& 1 A�2F.{�r } Map>� � ar�|n6x (in &� %% .z2�E�SD 85) possess symm�group�6at w i� ��F� FA�A�precedA�\ can deduc� E]u�  s ei!�-^R 6O� n�are&6$corollary}^ cor:sym} �b:�Á �%a�� -{ $\Gamm��Ea�>#=� I� ) � <�� �Z�&� .SI;�"eMNWB� J� � }ta�$y�:�� t*� A�Ais en� can�Z� � fail���*��#>8^�Ae existci���X��6�6-5%�wo� &*wE� �Z�6Z+ � �P�g �:\9r�I � �>�KV ��A��aoR4� ft� pply'8a suitable elemJg)EMץK�3 ing4 !�a !a���� [_m�� R�AA-�q�l92B%AV����&�!A�� F)�a �$"�� B A� I� A�=e)%�ex. A��"�=%�-%JZ�Q�r�<��9 ��:� � VsecondZW$� *;�r��% !.[ ZL�F!�W0�M"B� �s�mp) $Vol&�"�/�( � �&� ���2F:����be6�" @ M�:>�@arbitrary, so no ,:�-�isJ���. %"� cutՈ%Asm&a&[`&ch�T%a� �b!�A=graphBG!�2w�N�.�Aaq� rougB�,(G = (V_n,E)�an unHed i� ��$$V_n = [n]� \{1,2,� K��edgEv�@loops or multiple $� ur� kn%�� cob � {DL}�9w"�%� fap'arity�EMbasic fa<"o&s&*s&u9 ��S \xeteq V_naE !j semig icM !�q[by $S$�A�0/1� $\dm% G}(S!k�rr^E$ �� $' G(S)_{ij}� \mbox{�� } |S��\{i,j\}|!,"!:} k.D0"�n�},"�$$ij�<E.�� A����cut(G)�|"( | | :D%�.oA��� y criT'o)�!M� w ��"� �F&� "; � }B � cut}� %�� $ �%e[�*Y 6^!� 4no $K_5$ minora�d Q cycl�3 l� l� th�r� l to $4�%"� AEa ���d�'i��  chord�=� cut]acr4iE"� ly, ab�,WiR an"(subR� �-+�5�r%!r� few 8rmediate�}ul� } If=�2W E�$H��"Q� A�Zt�*kan�S�a^A�Haklk.n z�!��L�)ij"K^edZ�� � d&%�| xq��i��a6�*��!z6G��i~�Gw ButI`$a�a.��R� ��)m! lem:1ߞ�?I.;�!�then �-yL+ � �%�E'�| E5��)of5(�_�EG" inciR*to A0"*w�+Jk;Y !&8Ehbuta.eeKQ(�-dj Ql� )I6v 6�]e = 0, e�vzI1�,E�E�K6HzU7. Z�j-{6�*7)�K_5iP6v GV�On>.�D.\��by viaAE Z,� #met�v"��&"�!b�1,-1,-1)j 5"(&p��@sum_{1 \leq i < j 5}�!b_jq�!0�a��.y��&�A %�)4I+� �)[e¡�T�� -�� 5������� suffv $to exhibit�#se�, S, Tu<V��" ���� {K_5���<S!" )R$2;T; 0,$$�$no�-nt���6L � �1iu cu�ly-/am!,$Sz� 3+ $TyiX1� -6��2�� �= -2 t�-�& � ose ���$� .��ng� "(a hard open�ble� -$���&&�)+!��Z s, h�i�$Y, cas��j��o�.te .#*8 "*is known&� b �$ k5}ɃG�xo �EJ�i�G�the solu��! �� ��;ies�00iYx_{e} � �$$$u��6F} x_e -m� (C \setminus!��|F| - 1&� C$ r�#a�2� �G�[.Xod�b�u��C; EacOJ�)% e�typ�ŰA'�.0nd&2! 9e �1$ � Nayŏb>g͖1� an< \ref1�A�)nseque�-�deAXo3a'�,y�� binary�3 roide' eP ɐBM}���2s)�c $ Sey}OuZB�2� �is EV we j.%ne&  del*in!w�!b�� s>2^ F��&$h T�em96��k�,!�.�%>!�J��$se always ui �' regard ofz$o�/ny�?C ng. 5'Aw �&K6��AZ662�=�E�:)�e��:�=�u�&� � be a}*:  aDG� #&uceb�q�set�&<�0�4ᨉF} �$ #=�# - m�'�G)$��-.a"P X$\lfloor\frac{|C|}{2}\r�r7� �%E $m�,z -z �9�6��Sfune al�*j� UF$>�] a�!��1 can "5� *%�Fu� moreE��$�switc� (seem� DL})�a�at1� I�}"� (i.e. up��p% of.p%)! >�pn16 $x_{12} -�H23 � 1n�[it2O ���I�z@� -���&s"�t�!��"J� �32� �̅�%�6] �6�:�� �_�$!� tak: M�6o 2, aA� *!:RYc�9�l2/n}P 2 2} +FB+ B+6.!�%� �od 2$$ *) o2X���* bn&Ie\ Bgae�a a��ua1E�re�y�2 ��1�m�ex7-�Vac-�"�O $j;�K"� jo$Ar s�S_j!�{ 2i : if[j]M'#2�_jJYMVF�!�= 2-2jW �2le)h���V3" aq��o*�>} V7M�>ed* i@F er .H��� �n2l we2&���iup.ż$A �t� matrix  c�9ns �7 A_2&�<A?��Q:�AE� homogeneo�&��sen)6 B,E�we�)"cw2�.w^T A)"AW�;$i$. �Idi$6�-7!*"�?pr%6 A6�MaxU@e � iYsub+}� A Y, �( G m ral.1}��a���,%y $M-e denot) %�U;�3�(s (_@N($IP^+_i(A,bGWe��.\*[ IP-feasib�f G�$%?s4n�Ag&�.� $\xx���6�$I��Y5Orelax�dro�"� IQ��$:�w%w�=aW�D �!�N�by $L6RS�. �7�� bly !`er�solve :v�funda�al ques� in)��A��5� �2*� guarant�.� = 2i�<d&!&u�>u���ex hulj< lu�� AAPNx@ lpid+useful �i%�!,�r�*G p� .�p}e�fix�7A�iaf=�:!e�?.#a�if* r�D�"e$ �As M�)�/$A�9� �#eZx!<%6ul>[ �k� �sg9V�5.&8WŪ-� sket&�Ŷ �D*��wd3P-<ž�u�*� }6�2E ��� �_ $$A� beGFp #} 1 & 6\\ 0 & 2 & 3 )� J�U6  A"@1��)Y18� � �r��ble!fE� deed"f8n�$ "]$�5�(�'nPM�$NEE &E $� $x_1�%_3fOe�0e�, �"� no��s� 1� $a�ubtle��awaR3% �.U  = .R�x!= \�G and}#�  )�k6YAopt�� 2* )�i))��2�r�=��V���)Q6Ni�� Re�)� /ntext��FA�6 �D.� )$ we mea!�j�FE"��T@pe�;�e"�:g-J"%0sD.d 4-a��I�E��6i��)�|n>&��C<2��,�d,byv�ecthe LP� ums " I�FC Grse�!, ����x�<��rY)t )&�y � viol�7&o �<%�4 6� �#�@� =�toA{�SIP2�&��-�E��v2�q -not2�um! D& �ngby],} S4 rr^d6,�C� UuA*g2K9Mstv,&�C� $ *�>i:�f*x\CM SG4��3EA��^X*U=+���4 partG:�i&� manner: $T5b+�@ or $O2Bk, b < ,<, �_-k+��Ll�2[, l.,e'' $$K �2$ker_\zz(A)� \{{\bf y�A�y_1d, y_2"l �y_ky_{k+1}�2�2y_l \ 0\�+Nr��K��xi�J�&s&� |0A enc��J!� �- F �]EVLU �$ (�8at least $d+2$ &-a 6"6al�*�"F.��.� � � ency ?�?$y_�4$%61}��oEDfJign1nM 1r��Z%ai`#x,"[- R $K$, l�\vva K��<ch ,��v)� ��["wL")x��Oa a1�6,isMi�<2�?�?W!��Ng` -h� ` �u @ �; ��e��I  >� $�� $|� 0i | v_i > 0 } a�- A �.]!Clearlyois2uC?we)�}�$t"AK� �F���R��wF�D all* laim�� ��$2If��.Mn�",S<�R51\uu1��lE���("# vv^+ - e) -\uu"��!� � *>6�HE�2xa �$�_�urQ&�aU-p)0n Y~()v$u ��KM�a�� 2� ����!= c E-1} } \vA�Lim-X1*�%?($\tilde{\vv�>B !CA>6>�%�$A6MbP c v}_1A�$d/}.M>�K � &pTApp&�Ub�U &�U} h&motivI��� stud/3& *mk&L*their r�Conshi{er��� s�>�72�7&$V�IeG#H�M area�'���in� ��.in�TduWAurvey oRSs d infe4M�zeaS#�Vat� t�of;&�8� en govern� ag��liB� �TlawH� !�w privacy���. "Je����r TOconcerA!�of�W�a �0 ��in!y �5)���).�c@en{ViMH z^*ZU5k4��Rvfsi�8A�!�d �a@FtvX�WTX!~�Cb�� � ��,far enough a!� �"BG,Ch�!E1natur)M lead�"a*WA��A�F%3�&x AtJ�/ Minimid{� 0}^j A_�U \xxe f�O m=1�}" + ral} 1*w%�$U�� �Ct�ہ^ute M�d �Ys��NU.%���7 heurbZ!9 approxia���S&�z*�7� !c"Q bZ��ys�s9s-r1T)e)f%hA2��B2� �&�u"�$�!$�6c:�He:I!9 true� .� �  focusi��%R���+t�0�%�f �% es!؁�no ��B1eA��)@9 �$s a $d_1 \l@d� � d�UbBqWa�i]I collA>6�Ő�'/�Q�M>encod�jaE?ic�Oa NZZj#%��Q� Q $[n]A� 3(�"q5� ;c"FA�Z �Q2�.u�u �'F���/09 ��GIG �=���`��i� , reUen�1 &n basiA� )A�is Z>�Eq^�Š�^] �& s���1a`/ebmBs!�a�t�ὡkm�9}�~A�$1a*�a*A�6v d = (d_1,Ar&LdpX�JghW �zD"8ejd�8en�5*=i��F!P��rCi ��E*�X�*`B6*�@ previb sI�e�&L6ݝ!�=8&�'*�?�IF!�Jv��)1^��s $* ��(�m, b) = �Bb*u�]A�c:�6)rgi^"�1�2����:, Becu: \e5LBRA�.oup!�!",:T<5�, Z�� v�W$-$�> mpm) � �� hold��5"Fak��&vo� @ Z.VH)F� T�+we�=l�#� �& �"�[f":�&�� } *a�� pairs $( �, d�8�>��� %3Q�i�s a� i�-i�*85�� �.&� � I��e�  ch\ng�� ځ�class�0_Y�in1,�it �N&reol�)�m��; �F�F�,�:YT� isA�y littl kn�S�bvA-�� e $1�-��is2qp�deL""WI} duc �S�`.� q��`>�,1E6��Q�,8��.EB model�"5� ^d�j�te!�9Zd1�t�Bw�Z�2ed � `(4:�e�M� s onV�_ }N})*N��� J�&2:?":down:�FAUa�:�w}89�.q�.�Z7\�i�"�8 axU�.subQh o $d'�(AwJq� i��� 2�',d')XP_{ m'�]5(\�d'�d3'1 ate-L>rb ��= l�|end2)!�1�>�In bothIX!��4 ^`;��. H�4!ځRe,9]� :����S.�^`2���A:B@�17v A�he989 'C�h��IA4S[n+1]$&�%-�$ '!�{ \{n+"MeF | F &� ��AA"JM@ @}��k$d M�y�JN� � v���i�5.&�:2�"�n=� Bv6HFE!h-C join�/�cop͛���=::��9��ss���6�#�ce.��"1?6�'�9�\2VA�r pio#)�B>w2i!:A2V#���}ki� .�Y�� Wd � bcv"}�a��M  � S,�s_�^ifq�B�M���\\eT_2�01&��� '$,�a�;D&E N1  G \ad )D -ap�s.^SAe�A}�E2a�>21"��}� fE�5Oe� -�&�{23�5yW70%�ex-�.� G�fo -Z�o�~�6�?ab6� �.3d^�d^2�E1��:^pf]&�� toeno�mr*�m.k�gred�AI!�9-A���<& A�d^�V�QU� 2,d^A���GB���q�����G-�nU�.�f MD�p:Z�ŋ�� i��_�"�_2GAD{(\xx,\yy) | \pi_1Z 2(\}�1{ �Wy�piA���!i $S$-��W%�xxqyy$ repO%��)&i��9S*�:.<9�="�!��9�"�B :Cc9 �.��"!�:*X2=rJ ) �j� eN=:B$͑��a. ��� �� they h :a>]PJM�mYa���`Ų>n6cN�-�"* }����6&zZK^,Z��{[n]}��QZ.|m�N`,.�>2�^� byjI��P&x+ =aυ��K��2�X�$ofI�$uљ%CR &�@X� �Y�metho�p�k�9�N� � splr+JI"1,��&2se��JgivtP �5 chF� all 6s,u�a��""�f�.� *r�%>�%hNNp`7�r�g, place ``ext}l''rT M�,��o}t th. �Cb�,Y(�* 5 22P?sn $n-1$��M�>�� � :c6k8�D�1d#2$�$�N3y );"��3,3,d_3)]�QN8!���j�2$CNB�Á~1^&�UU (e.g. I[C�014�0urm})v �GC9��� �  :���B �V S ~$n = 3yd�3,4,4�<dlAA42,A1A/�b�- 6U �/1a ���%(.�2� n no�O��.� �4\=�G���>��aint(ey:thR�w� k&n,1.X-7�� = (2,*�K !<� E��� ;0 or 1.�m Y/e)�EU�&�&&g4��ultV? eFV?&�L@` Zn�I����"etapn&�Ksm ��!B�.`�e2� F\widez%� *F� n�&�E���d� a�o�kv�!�&s7  �>� �-;E~*&tLs��\@s�nI(!� covabxcIpp�CeM�-f9�"C0�+�8%:�"�2�:�0.i�;�R:S�%a�5!� $K_4f�Q �CdN)��b�Q!e$�Q�:�  �^�6ZR���e�r�f� 6c9T�R6 AFrh�n�"q!h%��F�e�oc6dGWFt zI�SQ#&� 9aY"� 2d>>IᏡ��� Ewin��twumore: }4+o�`*t�� gram s�expon5K�{�� * i\�~Z-�le&lr�sfb��&anIJv\>a6w (��;͡��l)�/�Pnom�6q4� *� S.��-.xi�q%�I�� is ]�6PAh�56Va�>� UaSIUe��IP--2um�#Ti&C'!>b u���R=!�$iXGO-��+�b$�=$17��W�"u5� �0�d))� 6�DdgaL�!:��)�%� >�2$�� !���%'iz� ���>Ea�i�v�T�%:�6R]f.�W!or ��/�Vx/ors� �)?* �d�>N� as &E9"��:i.�Nwe�l�*t�derste#ow� !�6hB0# ��x/H&>Y5T&�)��AB.,��,�;i!XN)Q4 � V�gc&��A�)&7@�sk is:hE n�1 *K2^ ���� ��� } rer$RA:j% gap?�l*�v+BB ��,Uyn�Fxplor!��I��. % Re��s %% ��writt}s Ini�=!iA Nam�+d FY\y. %,�%,en-dash "--""u�pag���%�thebibli�8phy}{99l�TemO( F.~Barahon�-8d A.~R.~Mahjoub ^�&2�S�2�P�DAs}, $H36}: 157--173, 1986n4G} L. Buzzigolz A. GiustiJ�@orith�"al*)kE6-�J-�%`a �(H rray[PtsU�s, �(<S 'st%� Data�t'o?ce�gs}, Euro�*p, Luxembourg (1999), 131--147.�@Ch} S.~D.~Chowdhu�`XG.~T.~Duncan, R.~Krishn 0S.~F.~Roehrig�{d?Mukherj�@DisjH�-De� in M�_� te Cate!@A��AVs: Aulngef�T�r.�TH Two NewA�`rix Operators. {\sl Manag�dS(Dce}- IL45} No. 12, 1710--23.0DL} M.~M.~DezI�(M.~Laurent.MhGe�of Cu�fnd M{Xs}. Al�th�$nd Co75)Bs �15} Spr04r-Verlag, Berlu1992�0DS} P.~DiaconT nd B.~Sfels. AJCicY�s �sn@!\Ū��a��tribu�?�1mph{An4(of U~Aa26%F$8), 363--36�A%`E.~Fienberg, N.~Eriksson,e�o(do�0d-S�E vant. Polq�� �a<K9xis"{5MLE�hierarchAT log-��K.�-appearA�J�u� ymbo@2ComN, Spe� issue onC,c$al!��Dic=, {\tt �;D.CO/0405044}, 2004H �aHSav Ho\c{s}�Y%� 9� h�!���A ��n ���C �� ۉ3.ja �2�OH} H.~O&�~T.~�~y nvex� topW.�G@Xr� se lexic� phic�D�D�&�DQT(Proc. Amer.a�h. Soc.}m \29} (2001), 2541--2546�! \1; U a.~SeymouHMacU !G�.commod� flow� )�!pean ...a��% 2}:2�#290�#1.St} Rayb�.�F "�of&�7�,Y %P1 Ann.�0 rete�h1  6��80ag 33 -- 3422CE*} B64 �0Gr\"obner Bas!�n�{%�a`�}, !�i� 2/Society.�tance, RI!95.(Z} G. Ziegl!� |Le��/4m. Gradu��TexH v!�S:�� Yorky5+>:Egskip6� � s' addres!6� \ { De�u of=sEUniversAK�� aliforniaXBerkeley, CA 94720-38400USA } {seths@�b -.edu} % � docu{}C]\+0[12pt,reqno]{�? cle} \odd}6m�*( 0pt \headh�Nsep _C width 165� mm  3 =8.9�renewa9and{\ᓡC�ptch}{1.3} \usepackage{amssymbB�Bthm!�?color6(pb-dia��} %.,lamsa�y:pb-:h(ics,shortvr�.�Dtw}[3]{{$#1$}${\,\y\ dtyle {#2}}\atop\raise9pt\h6$-'8\tp$} ${$#3$}} 2fst}[1]{D6bf12f5.5h*$}BTbtr}{ �1.2+2�black^%le�J4$}\hspace{2pt}!�6� P}{\!� rm{P>�ididBmm}\:}�.li!{6$Tc �T>^L.L>A;A>BB>D.XD>B.B<P.B.I.I�2M � bf{M6�L  frakJ�g.B�D.B�R2=R>�S2S>J2J>T2B�N2N>>f.�f!>DS "A%B�HaH>]RuB�Z.�Z><E;E>JBC.XC>;M.A2$K.K><QwQ6BOO.�N.Z!�:�C =bbF�ZB(RBbNr2�zz}{z:6tp}{\ozs:vt}{\vaR[ta:zzF V}{V:+U �AMU>#FF>ve �epsilon:Xg� g*v:d��Y:fA�va��:o3Ro%plu>lalambd>g�32:n tl}{!lef> ��� cha�2�Se��@!SS} it{e�k2*En�M :�Lin-�rm{ : Aujrm{ : Na  : Ho!��rm{ : ObOb>I.� :>rk>rk>T� {Tr>An� :\R�BdWW>:P �.bE�>[1�[A*$}>pa=�aB0AABLA�!$V�gy6�1� %�6 1� B�h-&A�2$mu^ bold� ol{\muF�v.Dv .hs.s>Q�nB:B!Q?m>?ct�rm{cotB�ep�V�Al}W :�CYn rm{ : Ex��!�rm{ � 0� >.e noՐ:Jmb}�KB�b�pT6���� lF � c .�K-���B�TQ�B�K<bfFtM LN�T rrmFS�:(I� 2�s� �w:5a!$ alph6>.���2QbAbF|b�/(eqn�>�e#e�5!]!O}{a}[9-on]2#W%n}[thm]a� �H�" %�"6&� #C"W~2kcon�]ure}{C 2$prW}�`} \ �12�0!G {p)rk �R�k6Y*1 �DTL�06)�T &EfV6#parag}{=R2�a"�J EA2)�B 'N�?B%e! �"gse[B*��3}� \em #�]* !W,itle{Quantumejug�G;�fU*�rix�(s\footnote{�V rese8�ѓ�@ orte^�/Emmy NofhR4Institut @r.:d Minerva FBG<DGer�<, �Exn>BOCAB r "G"?�#oretic M�,i�>of*�Varie!l""�&Israel �!n �w�5he RFBR�Lnt no. 03-01-00593. a�a 8{A. Mudrov \\ \S- fDed�|#�memor�0Joseph Donin jx(ate{} \make%� !c�} {2cM"�s-fL, 52900 Ramat Gan, �4,\\ Max-Planck5� f$\ddot{@�u}$=� k, VLXsgasse 7, D-53111 Bonn,1�0.\\ e-mail: m%@a@macs.biu.ac.il, <@mpim-bonn.mpg.dA��� ab�Yc�WG-a Q�F�5E��I��$\g$ %Lik�.'(U_\hbar(\g)R!�Dr�K$ld-Jimbo qa+i�[ ( u� al envelo�':� $\UP.�=�%{>�r icit#y-�fa�'tBo�>B�!wxuLevi v��a�stabi��@%N9?{I� \H�0{Key words}: �ڃs,�"F�, �NC.6�t�1of0Gents "�N {Iny�C } De"(F ]-ua�a Poi v�u,Y/a smo�<manifold��aQ��MA�"�$physics. E�+ҍ nterbng E.�~%2%�&"3!�a�A&a)BA�,'mor"�NdXa cum + . ReA� signifht�gress��!fts otrigge�!�*OovcId�"X ^g�E��V��dynamaH Yang-Bax@`equ��, #DM1}.! �tar��2 �=��j�8 coad�;t orba�kF�(%ba6�F�)!� ZLijse !u~�"n �EE,EEM}�er!JŬy�� twisԌ6!�} ]N� n��I�+a��ic a�ń.$ra�(ir6B�Xb�B ught�E ��C�%LF$�",!/aI0or��1!/V�'�m��5C altern�fa/Mach as�iarɺ2�!�it�(cerP ad��" .�"lM�Wrmu�$2 "finite 2#".�t'e%J pape��5�au.�d!@�#oFD9��LFUMC�C5� �i�sMa��5iN\?@ѳѫ oe�h ��seHG�` , $BC�< $Ddiix 'z'ard\46� , fa}hiz��AOsi�u���bi �6X$\g =� Se}\;G$. �~ pped) �c"EL�8TSklyanin (DS) bracket,ŷb�^ ���%b.�"�Q6 �%�VA�!Eon��elf�3S�"Pov-Tyan-Shansky (STS)` �m�Ճ�P}�> �<ee��4pg ic�Qv ��B�e�}):br:�a�.59*s�:G:Cb=!0\n� al&�'STS1) Fal6�allam:-��� AE meanoPr"3a�d.mE s. .'�&ʎ  p/�ion1er� e�)��LY>�eigenO* $\la\^Slh";#^2=1\Ri&̖ la=1Eoeu\?��=v�-6 E�| A`-�(�+\g^*$ (�} Cay}�L���q).�)�02�is'Y �in�*'���dea���>���n&as!�%� (ord6S 1B refe*on�����)?v^"ayn�< ��H�Ja�!7u��as sub���o�&A�gen�K+V�$ul�0%(set/M�7�K���%H^�^��;secDJQG}�,rsc&>qNn��suJ im #�VwGVMv�tenso"H ��*أ�pb �� $2� V{RE.{er�a"%moi,��u�Ho�(!�"9 Re�fD�QSA2�sCp@UR� M}a�Bo>�� �ns&�mbe7mP �ed� &�j�I$\C�[G]`2�N�ubsecMC%-m~N�co5ZnA{1 er�2sNa ecQC _�B> �5�RF� Appendix~� s auxiliaذ F�[in!�a/�B���\vY" 0.5c��� � \ e Acknow�Om:.3�\��g�jfu�3�J��r2in�B  hospit,,�+EeY�e�� s. H!:8anks J. Bernste6or = Fr/N.8ent_k, help�p�]us�vl d �� ��&"�nq} \����.w&2 work� ��$\C[[�]]$��o(Ewer �# $. GZG29-m�xe ���cn�dby $E_0xquoti!$E/L EABy � U�a�e�!GA�c]L)��ia�8�h]]� �1Aatm��(meq E_0 $. .h�vnga�niv"! $\A_0�Br C[ j� $\A? c��l\A �\An@ $4ap_ $\C$F_,he� {��) .�} 4 imply )6i�WserL�A�.G�{mm�>� s. �@��J��+, stood as %y%�!}-s"r1}� [Ex A�� �=N�./�e� bVk�\E�-adicM9 �n Cart�8"G cU� aR�os�v%ukZ7",. ��dPoincar\'{e}-Birkhoff-Witt�WeyW q*�� uYf�f,:� !�a Hops�< in a weake�nse"2P��&�t�[�p�`,^a�Xwe)� )$\h�a�:! m�AAl�Y!qu68��1- <@*_�I`q^{h}-q^{-}{q_i1}� f��i(m_{k=0}^{1- M }(-1)^k \�'["��:}{cc} )�2 k� \rS]_n} �pm �ia-k2j}:(k} =0 �MH $ �M�223}{i)�p $i,jU�, U�,��!����, $q:=e^�EA q_i:= e^{)Wa�>h�5!Hb)n g�^" } = b$[n]_q!}{[k[n-Y=[1]_q�e [2 �r$V_q U,,-(q^n%�n!� 1}}.� S��lyJak�}ab>�6� ,"� $�C��s �� � m�H- �7a�6f.R@�ډ�c<�6) �Ba�J� �monoidalG8� � � � 2� &mL6� cco���!�tipod� gm8^}�$()J ���T\be &):(A�al})= �� 1 + u�} 1�=� > ?y�}} + �gpA!, \nn\\&C�})= A�1 4gm�- �.o ,�� )r)=Au Ka�.* )=���C� &!O�ep�H })=0� \eޕ�c��T\Pi$4 e*��8��~��Sal�h_ ,! �e_ ;, +\to $,� ���P $, extendra@.� antiլ�Ѻ6F*�fd�\omegKE�6 aF.6Ka&" c��|g)*/�_n�>9&3���&�eP:m�@edH!� \{e_{+!i\}�&� Pi} /HkY$)�>$, �"iv�!re6�E��Yed) SR�$\�&"} !�nt Borel2�$\b^\pm�5�f"w �"�)VR%;&���6� }" F���� �um Chev�\y 1w�@j-���;*EA���os$� Wi-� eneSA b�� �ta%FsG $q$-�)��Gse�OKhT2Vdera�� rein�9rta ��: admit�t *��6&MA�w`k���Jx ��Yj�^>q�^{re�\;R(<�9^{s'$�mr^G(PBW) �&6�s�h)��ql! "� -'(QP��OMq1��AatRo}�@PBW=4of2 �lsp�itnm dK"9� �Um%�r N�N� i+&�"9be��ga��ukhh"M(q'� \Ru=q^{\O�`_\h} �00-7pt}\mod \U'�!~-)\hat\� . +), �Rmat}Ů� $]��h<xE�r�A��.� (canon�&�>)�� i�!l. M:�#;5:m�r*�n-au�f2i�k�t!�2��a*Kd 2>-6��6J�(�%0)��a "��Y "A�cR%rD)�-$DJ-rm} r_- Rv^+} � �)a�^0 ��� )%ȭv�T aĚr><�Ur�W%�g BrCs norb�(�,e�l�2� ��|ylV.7.?2�$��c� %Py��%}fW<b~1x0ngYT%�L`p j!�8)��VR} By+L&�,s (�.,iM&s)� m4� �x2A��y�D$\g=sl(n�so(2n+1 p  �� � $n>1��'rXQ�0 $V�)g �(`!ng)s��A�"�  $N=ns� W $2 ��g c�#e.z��%p]*P$] �sy�c�% �N)$&"�  skew�A״� )�;�F]rX&t֜2@ ;�+Gc��)�%�-1�low�Uq���n^+-1 $\n^-iY"g#� End(V_0/y:� di3,�K-x�K *L(�c<Bea#Ayc4t� �( s ab�!�1�:��}�gu�n on.Â�ij&�W�j�x�H:�$,��*a� {\ve��_{i=1}^n^u!GM$RH $"�uii})=1�A�m.%��e_&�% i'i' /&�k. H��i'=N+1-� ��se�:Lq.� �/ $\g$q(`s��B# �$ �c =1{${lrlccl} \� =& �-�jS i�n- *> J(!�+1E=nJQYn-1J=)E5�3e� ;�! s�R � ^Xi�%*E����$I�. {0\}=k\� ��F-�!�pmZ+�-.2 ParaGNr$2�PS} An�  $\xi3 &�k*�if� d\: \xe��� .�kem�2r.< a� ��d���� �1K& ted;��X 6� � �]g=�\o�B \h ���q�zdP/iSon���1 ��$��-���7"�!� Q'r. V'� >M+zjW.L Q�rank $Z; �l�ab��b$\p/=\l +\n "���{pN<��&;_s!5nillr���%f$?bS !� _\l 1� n^+a�!O_ oKm 8=n^C)  ;@ �q�-um�ogJTM�LM��0�al � a�&k _\l}&�N= �y�&w (\l)6� ([ pw&Y$E �� Q >�$\l-�4Ite-be&! eE��(\l_0)\"�c)Ler�#(l_0=[\l,\l]�Ay���$AAtg� � naer!Tso�! m (I=):=l� �\pm��o9/W `v5 m�� �R�I�� 8�fac"6� s&P4"�%�lK�"c(W8.��ZY!diO0�p non-"��)geg:Co�3 �-'!+)$�=�ɰz#�  � $y (\Pi_\g-lnI�%u,&�*BA)erh�6a�Adu",5�!�|�B<.h �&�T1 ~��r. A.xZ� Ke}Ye�m  JT})ie]!:E^, )�dZ?�U& *�&�%� 1U�-�� \b1 =\l\'sbAm��ve >� �/�12]l ue� l)$-&U>�A�66�`f%�*smQ[�6^T' -} \5p^+. l)\lQK # �� gin�Bpn�-M�� 2�V�"UndO� aD.V �M^#�s!:��YC=�hf�� 97 S��RX ��b.!"�6b!�q,.�1AfJ� u.#���*�-.7�0iMY|z�� $\ad(u�m�V��$P��� u� ]<l!@��P%�x�r3.Yo›V5$F� �-�%6<-*n��!Y{�z2�i�on�5hh a\bigl(] ^+)r.Np^- �=�AS |-�@le,^�6�H]]�-\r>���& v�"�..�''%b �8u gN�&(1�"�:4#��զ; :�.!�& one,���b І�x� sڗ.[-s'�1uD^�-��ɥN1!?� 6� *�+��l)E �N@}aN6g)+. c) By $\Pc_�� olon}tg)� :!w�&��\>o�&�8& ;A�sum�Wn+on{Ge�Jw8B\ g)*�e�7>�2 U�N�7�e, "al���N�N�A�f�ll!�A]baڏ�[��& ider*A1�f, Uppe�;�(�#�)6�9Z,U_q0 v�rI:�X+e��$of Luszti"� L}&j$\C(q)$-.�-���A�(_i},q_i^��#_i} _0P"�.  ��.ai�4{[q,�"1}] �&� � �]� &x ��PL+2*��_{\]} �.� )`Z� J�, J)i}]�, Z &1s{DCK}."�!�9��' := a\ �tpB�["v/,"��ʼn\8�<C3��$q\zto &}(is \�2����i�E�*3�0_E mark�8��-E��w!�&� � n�B6� .�� one-to-�"&A�!"�Em�.�q����:$qY�s, ~ Z}$-l(k�k*�0E��1�t>[ )WN�az9� )%�U�!IE�, Z ‘�."�an2��5!�d�$o Z (q-�}.(� Z.$\5@��QEH$ .|&>�)j�U�p;)�)]:< Ms \�M{F�}{*��s&��1LU�h� !l�~a�s�0X "n4o$V�F�a 5OI�Z��d�fv%w�5,�0JXRFE*8�"*"M��g . e. �s�o&) �G 6 . E1sub)�Sz2fF*N?b�$\F76�Zm;(p��g�wFY>dea"�65�guL� a�� Kly��$.; but  � �2�.z��8�:E~ h.Z�A�nem=$.x5Q�highest M�fa2�a/�! annihi H2q'([ SimilarVBa�stD)��nd rd-� F�0s e�a�+ �sA�ult C��i9=),i�)�Y��domin�g��E��.V>eҽ�J�.����^5�Q�&Es,B�V�!�ZFn�..<�us�3 (!/ip��I��a��C\sm E/F ���^: �����=erIV ��&:+.�A� �en�#�e>fN�� 2�"o&� H��qG5 $\p=�$, by��itk��6�E' e(_� i� 2� �D 7� %b�J�dqO$M'4,A}"�/8Ap)} A=:�[8^\g_\p\: A$, cf�}{J'=� C�6�!�|= Z�,i�5�O&8�Aa\�.\C k: � �(&! �Er>� �/^�@.wF Mb #3la}Ɇ!�+3o �J��%�>@���U}5f�(!�����?-���fL~�6PM���� 2� ��� wellFb1VX � cl-q0qOF}%�ree�a�2gF�Z-*j ^<,� M�Ft*z2) �Z�!�.x-j A>�rB�aoE3����q��/67 .A!\a�se�etriZ�(<-�(\n_\l-�'�;x]A,�I�!��dI^+,A}ͶmaM�^-,A}&l!@��A AViYUe�� e��aka2o�>0 512d�*�m�+-l:���$B$ a>�R^ e�.!:� ��M_{!%BE]&F��3Ind^{\g3 l}(A1B*�-5y>�} )En#��[2�C�a?map6�k p�.2�p Ar/ F!Br)$S�~u_ab_u^{(1)%2 b&� & 2 -Av7R�*�#"�+#c>�7(u �!�X�Jm� A0Q&F} �7{\l,A,B}�\U�%b��%�a! +,BC��]ZY9s� c&:����&�sm??g��Su<�v�>: ��$\l=\h,%A=9mu^+$Bnu]'�X Fgu"VX2��r+� Wn�lC�g "�}&o*"t�o�|�J 5Yb)�~ oubl/p $e4� hAyl( � !i nuA�e�%|-,\mu.�\nu���""�.(Ն�!!P pa#,mCA4��*�3#n`(#��@$F�{ v_!{�ov_!w��A�U�5A�@�A�ψ �+���3. T��$u�!�FN�<&-5%�{9�m=c%:��^�A�1;!za!kmu!L:eD u^-u^+(�!��)&�& (u^-)� (u^+ /2)}(u^+)�^{(2)}v_\nu= (u^-)^{(1)}u^+ v_\mu\tp 2)}Hnu \nn\\ &=&c_q u^++u^-M + ww .:�L \ee Here $c_q\in \C[[\hbar]]$ is invertible and the elements $w^\pm \in \U_\6�i(\n^\pm)$ belong to subspaces of degree $<\deg u^\pm$. This computation shows that $\Delta^\g_{\l,\C_\mu,\C_\nu}$ is a triangular operator (relative to the double grading) with invertible diagonal. Therefore it is an isomorphism. The above consideration also proves that the map (\ref{F}) is an epimorphism in the general situation, as $A$ and $B$ are quotient!N( $M_{p^-,\m! !� �+,\nu}$, respectively. We must check that (\ref{F}))�j -!�e map :~ A,B}Esur , modulo $E7H$ as a $\U(\g)$-mor-5LBy dimensional argumEGbased on%-bi-gr%�0, we concludeI thisF[�an6� Ther)�R�F3 by� obvious d>ma!���. \end{proof} \begin{remark} \label{breve} In �� of �s!_on� 7�e.� decomposi ~niwgenA$ized Verma)yes can� naturally�ined for�algebr!�b� \u�@g)$. We will use %cobserv � in S �E+$secQCC}, w!c_induc�,is made fromcanonicE�$identified��2 via� Kill!0 formE]�\dual ŋu UI with ��orthog��a�l�� t�Gannihila�d%Dc$ �h^*$, so ]5G undEv��nv�, as r?red. @ propn"? Shap} L��AE  aQ�N�Rl��mvVU�\pID�AT\N �$��nondee�ate����  �\out los� �ality� may�<um0 � A_0=A/� A)ę�(. Since $-y�= $,�fi�s�0$ $A��are ~8ic simultaneous� Itq� H\cite{Jan1}, Satz 3[at`� y�1at � %.� { .� ���)(ame is true 2 Si�2f + � B�*in ques� B�)*��$ (be��(�.%!I���8y zero)�B��ec" �!8e��cE�r� muMe\n re*e unles &+� 0$. I� EVi )y�27$ ^$\*�-��,A�-Q�cy�a �2 no2+En5Dy of} 2� Tensor p��9 2p!iiZA B� W�ql�}�P�O&��e�)i� $\h$-d�iza���6I!& ��free o 2;. Fol y @ s� $Lambda'(U)2� set of 2E $U-�U[\mu]� .�i��X��� {$Ua�of ��fun��als* U$ c���iof in �  (ums $f=\sumY f$� $� �"� ^X t�i9|Dto be $(x f)(u)=f(��x)u�ąfc5 $ o3 $x. $. D�RE�$restricted)$U^\cirR Y>:s&�n3*$� sett�E( = \oplus_{F�}5� � (onl"V %^admitted�7�+lemma��r� ��U_1,U_2�� MR�s E�$W_1,W1-�.� V9a \ Hom_{.[}(W�� W�(U_2)\simeq N2U_2)-��.8W_1^*!�(�2+�6@Pro"�d�2 ertsN . �M ��A}b �Tic�.Vzaux-xW%ra�F, W)�B$z7�:s, �aN� �� A�2-m�isomoJ4s take place:� {!�)"�,array}{lcl} N�%T,A!�W la}, B)&-o&>C,l)}(A,B), \\�`WZ ep~]Wf]:J �.�v]W,A�]:m~ZW)M�)�gf� I �@"}si +-l}E~ m&nd�b@�ed� il�as �O� DM1}��Eclass� ca�j"��ds.��instance�us"=e firs�uU� . By.��! mZ{ -,\C^*_� tp B� sQc�E�:� @2�� �, .eq_e�>�g)}�ifAJ��E��  qd*� A�ee � L� )2�.�/+ !triviaB�)`. Accor�to.YAB,�tB� KAO_�JN�  iATp"��w����2� != )V!�$. Apply��Frobeniu7ciprocR continue Y-�)� $>���B^ d2~ �N0���|qu�e�e��c�dir_sum�`%}N'n $:�$f�!\ r� sum6?:�:L&� A_0}I��LQ���{sumis ��n8 !� simp�"s��(iplicities �!� $W_0�X bX-h��sms���) hold�Z&�  More� E� y commut�th�|quoti�$\mod  . F��� us��ve ݹ3.0 analogi 6�U�1u)�tainihe no� 2�)[�� asJn Jc�x 2E�in each!Ntyp$ _0$-� onen� -��j^E @\colon A_0 \hookrEarrow !��y�$!�a*piM ons *t A \0=\id_{W_0}$. u{\�j} |$ b� ir lifI�Q ,A_0�1M�i]�6!�o#��n�^��é>sO>H1*�� �kB>�0� ly$ epen��g6�P"� .��� stackrel{%N (69 }{\�9�}!�!5)B} �Nan embed�.�n K2A�[5$-n^-_\lWA2 ? �:'�J� ��P $X t�for�?A�( �6im��$ stat�ƙ. aWFc�$j^q�{�}/� W)$�Xbe *&�|s E%$ splieAe�)P"�� indd�� of highes>a{&� s. T W�(�("ws]�Am�I��>AE 6�to҂�e�ond.�-���.�v��� , we have.� =6a2�C+!H1� V�\t��AN�:~!A2�z  R����c"t#sU#B&!�dE}�fa2" becausem�soB�"�Y{� $�!8Huniversal RE matrix"�secREM!+ pres�o M�rec�ge� �tb_ refl ��� (RE) u< $\Q=\Ru_{21}\Ru�$study�n: e�f .O ( �{!)6�. R � i r2}��7B��rbe re-ed� (D�$$(\upsilon) ^{-1Z � �  $=o\Ru _1) !2^2�onjug)Q/K$ � �#�squar�ntipod�� � x .jx)�!�R�Oo�� hand/Bh��be wr]n��c� $\g�@x)= q^{-2h_\rho}x2 $,V�>!�Z%�9 =.V\zz&6  so�nva ~1�E �� F���Qa�an��Q=Qzz)(\zz%a�S L� Q-Zt as $.��,a group-like�.�  � A� $\chi^\la"� 6�ral*�#I��.!Wsasy�G comp� ! valuA> e�)�!�$.Fy �'A�: , us�,UR#ure�R-���xRmat}) �w{�:fveoW$ѥ $\U'� n^+)B=0A�uq  E�� la)}=2�A�-2(A��z $� E%<$lnd� .,6^+.F. M laQK Q�($\Q$ satisf��!8 #� i�EQ_{13}�@{12} 23}&=& *13  12},� ure}$(I�E�id)(\Q)F��4SC23JdQ1I�]hil!!�f� �ٕJ6, cf.��KM}. Eq�P�l)A�Kkey1!"8fu�'�edApfor solu�"!RE,2f2,C '0istic polynom��K)$ɣ2��@��$(W,\pi_� �$\Q_W$ .A$M�#).� �&W� \.�"Q�� E:?R�i� the �#!�� ��(WBT�i).r*6"="$pZ$"R,\# Aa� one ����5coeffici�w+��er�6� *�p(!E)a� i � Y+rum:A"�&!q{W}$ �(%]r la&i[��B_VK,igl\{\: q^{2�-+�nu_i)�nu)+(�+ )} \:(" \}_{#%�5PaAee���he>������ap�*F�Notic�# a symme�"�1deigen��s� �eain%�nt*@ � a�� Weylɷ�i)3� )��"1Harish-CMra hom"q� Jan2}. Soe'"�ii�AsŃ.E5e, 6�!I"� c� \u:n^-f+U&(0sm�� � !�i�*t%���EK:W �$6D'pac>F+�BQ���Q �1�, � rv: �^� �K:��w �� rank�=F. Nowa,M9��b �$!�6�p -��iA3mpl��AOa"'��)Q# H�-A�a��any2� has.k��1QN(or=!`� �'m17 *�{Mini������I is%� 5 de'!26z��� he:� �-�>� %n�:K.3:��thZ��4Spec_parabolic�> *[be p � ic6& a Levi��.%Cl)0t \g$� �cJ�6�m�� le� � _\l(W)=\{� _l=�&{i_l}\}r . ��./.��� i6J�B�{ .!erd6�"2/�.�ndA� �B.C, s_miA'�F:E� _l>J, )�T.S,��)()Vi ee*I"2�>|�"�K�F �,v4��r  Fs,>r"q.��%|�or� al�@(2(� N��jusa�6�2i��"6�\�2XF'_$�I]�.DAQ�W$�M���4$)W�nd �$ � eq&��Zk �@Bjla+�&. Hencn�!5A��{��act�sca�5eH��r�$�?f�!feir21�%5d� �� j/2oA!���� � s} ANwE0Q6.^-{lexq�Li�P3��*p b�&��.�XeSFs ����, i. e.�mu&�  $� (x:8�  2)#F� f� know��* q-trP�,P by $$\Tr_{q}(X):=\Tr�w( x�zc)Xr)$*$\ad$-�A,hAB '8"- !�:� �A.>~1��.0%J�a��0al�5kernelA�aA.�4p�' o:�s &(�$l(\tau^\el�-r� �&a� $d�� �\*# �&��d !jO)_{�0Rm_+}�1@%4 �1-�: }{q^(,6# ! quad q=e^��"e��a�� �A�b�� � 9d�(ula&N} giy $ �Ae_q(*W�!�q-"�!�� �x� .� �������� < "�� %�Q7�/l(a4qDE)r)=���'� �LN*(W)} x� }2 )�%#, _i)} � � !RP&� F�!<*J%< !sna�[� A^� We adap� �}�GZB},��+ suit�')6"$ �+�ope�. %�ath�:e*�!}�.!��'(rst. Namely  supp�6���/ ntega�dominx��y:=, W$,;subZ#ate7xŵ���-&t3N1�,:)�)���%+��E �5U!$. [ ��w�%6!�$\D^+M>�7�{a" �N�:H$-�K}, a2� ~, 7 e�"� �7{&�. Both �3E�I~M�)��&,  �in 5 >~ �busAssu��o�(pH them6� on1��!e��F Eo����A<��:.}0� Jr� .r#."�'I�< U$ sS!B' 1*H aX =%_6�s�{!aOAO_:�A��q� %H�o"e �Iu� pro/>S4$\{P_i^�$aV��6�A� �,�i6�ut�<e"�t=ese�� |i��$��"� P_i)E�cM6�A�Ua�a1$ �%ʡ7sHTr_6I=])_/��q=d�!�)/ $/�% w^=ulG%a�?IIr�?196�'�iZ!)� :U� �eT!$�� (���o�1\�{O�3z�of affin"2 ic AGee. QAAV �e.��velop7 chine�8or�"i$qs��5AGL8%� � semi�. "3&�w��mitt/ \select{"Y}�  t�8gu� ��;�),2�! 5#�%a�>�-s'6�s>r+dard �7�!)�1,�� a�" Nakayama w/M rea�KfinH@"list"� ^w'lyA�%6�b-?{A flatn�4criteriosxsecQn}%`B -;�C �E\(left)! J�� $\Ai��^�Pif �3.o� !.pa�D�m:aA1a�,,Y�h�.��ea,bDA$ $$ h\tr (ab)=(ht a)2)b�\ \mbox{�} 4p 2)}�h).`� � B } A� o�B%1ah $%=L1%$\�'�>-V2�'f C�C J�J��!hof B3AGQ coincidesɽo?&bar� e�H G� A&*.��B-�$E-�A�it6�!:S>�`M �.unZC*$��>7,N.W,E<E�:sm�#; !�h imagmt��m�1)�)�-�&�)E�6~'7��dmiss� }} �  a:_aKis reBn (d :*�SmA-�lyL ted �2�. . It�}be�G[s�5 [�+ -g�@�IBe .�B��6E��B�X tQ�sv eV lly,!#�?�Cs �der/JgA!at s�e:Fr�+2u $\Sg�Tg�$c��"�)*],limit"� � Jg$ equal��entirp"��n}[*�( method] ��_01\Sg� 6ja�$� � a�9R�5<; h Psi\-,�!�ay: zero2|.�. S� $\ker M$� !JA(&M �ala�!�� �t !MiM$\Jg_0^\!�m�$ ���_0�a max�*�%��+��im ��)\*�-%#.{0\Sg_0/x �;�=�&K ���O}5Vz$6�y*!�.�; ge�!3>�."m>2S���!Z*�d.[. ��+1�, S%.|m��2�>%/ G(H)_0 K(L)_0i@$6'sup�.q�4� p��,:%�V E �ei :q =A�AIo>=6�%�,5o�zi�I��. Indee�&nfMl)_0=0��5� E�F����SG2w Sg$,�  B$io woulov�en�>� $.�=%�2�EiUprove�FWMv�&h.A�Jg\:N05� H�.p&%MiԡB2�aEu�:?46  ��F�E��By�� X�I1.0Kemphasiz� �A.w!�Evedtbe�1 jus�����@� but�{ �< �  es/+� to d)$nguish"J ~)6 �r "�a��A�*�,��@� exact. E�Hu� ON[� �our sit>%.*eKZ a {\em7riory}gM�/��� ���E�pbi}8��often�nf> via y"st�f�or��@U ���%thm%y��,c�(� easi�IH ntro�}X tha=!ݱ�Q0"Q*��w�Eic�"6SAG�27-E�"�Bka"0Poisson brack�@pJV}5q � ed rV of*�IE�3 is reE �a&T ' !D� HJ�-.T 6�D Nsub #�:A�u"m.en � ..2�S"e-[Y1�$manifolds}  � V���$G�conne�@OV+: +to [ . Ant $gBGE�-!&�{ it.2�tor�n�$r�"�;$r$�*; ng �GC�bi-1.0+A�w!DHby $r_-q� OmegEts skew% &�%parts�6��W$a�Bn�M/A#�  $\� ?-se (c�M �)Q^.�M4�()=n`I�g�^l� xi^r�!6�Es�-�� &�v,field�GLM�\i$: $$ (glCg)�M\d}{dt}f(ge^{t\xi})|_{t=0� 4rR43g4dvsmoS��� $fTGA4�"S�/Pov-Tyan-Shansky (STS)ust� ure� STS}!ea�I��� �C�Jbi.� ( r_-^{l,l}+ r,r}- l l,r} +I ,- /r25= _(\ad,\ad} +(B,���STSbr�(e H�!�^D}:=%�-r%0Y<. 6(49tD $G$-'o&�� a�P&se STSJomakesN a-a���e!k.��endowe�P'�� $r-Zr^%U^n,o .Tr�$ �G$,� ��S �co.N�ou�+˙y$\De�b >$[? AM}] Sympuic lea�YZ<"�w�;2cyZ��a�'m&^o&�:$(!k!�1H � �o $C_g`a.�����.ev�a8"nn�$\g=\l� \mbmXEd.*2��F��!'$\Ad(g)BJ�,� $1� mK=*"[*y_ -\id6��o�!T�is*�J)�y"�.�Ce tang&6�*8%m�"po'T �0fiQ� $\m$(Oi�>�!#.�MK�izu"�D  {\xiI* (m�mn ����CO)U��1F �v q" )�22(X o$�1{,�nuy..%L$L-��^� �|6E{\m 6})=1$. O�RX-W��6�sB��M�� $$r�0\wedge \m}+ \{J�} � \mu+1}-�1){ \tp  �4}��K,��I�sf,+1�y� �r�A!�m�se�:;���V ��v1�I�dY�� Az6� >� �.P0�;& secq�t'a�.scribe "n:^����E 5k� �E� �ArelRs. �[$w>� [G]$/d m*�D�.\.(� Y"�  h �G]7is6�i�e�n1sta&_Nwa��'S�D(DM3}. Below� sV!;�A2�herv, *j6o� j� � (V�3_%;EY� :�3�B}$Rue � $Ru�)�Z V^{\tp 2}�*� \K�Y"���'ѓv�(V�K���ra�U� R_;K_1 R�5 K_2 =  . x RE.u (K=||K^i_j||��M� �]��!+As" .1I8X���)&�#N�B< 1 2KSkl})�.�[!�� �^�&�"> A� �)]� (N�g=sl(n!�}I�.G.:!Sa��?<M � 1�"KcqdE�RC��s�W�� �G$��gonal�s"� �a�als�Od/�!r $G=SL�,1 tM-g-�!�(good enoughEour pur�%"�!�m�AcD[�5 workV)�ra��C�[�]� �+$�*�[or ��+B���:�""� �;$Va�V$QJFRTaI�%�9 �!��&s�4"K1�Ia�Nb�%�/:�m�Horhtog_re} R_1^tK^t�*4r ( (R^t_{1'})�tB (e�, l)R_2 K= ", �H K R_1 B K^tR_2^t =�%'}B A^tb30-A�e����G!A�[Ń]]ois�����  2�E�D!B�6;}"�?�a� LYetter-Drinfeld (YD)� :G�>�H 6oL'f:F�-"-Fse two&�sf � &�,{wayQ}Y}. A YDUn�:p�a> �9�a.��!=ak �i�6� s�)]sxa� !�YD:qis>��idered �"^ u�co  a�co@-u�"� �a,� '�l�s ( N �s) _$�35� )*� ���8i �)a�o�* � .,v9l]N{v F7 twis ��QA \tw{�g)}{\Ru}6��e*j"I?$�I}�6�ex=8s��%�&�J�6F����\ ula q�C41}��u>3. 24 23NJ<u@seu �\e� a;� � ��>$�, fac 9��(AVd�3&�)%3@]c2%�M>J)�oma�Yp�bU�2)� �Dipp�AS]7coa;' $\dADa)�ha!��U 1�$+ :G EA��e9��"/J!9�4��g)\>�6.�! �>�sq 63-,a�� u�H 6!abo�it�nnc&�""�in�F�bs�"1 OFRTlX���'T Hopf"H[b�e29�6:-]�#pa 96�::;�meavJ"p4a�,2��G�5i�k�E�5aA=1_.�!� 2REemb} *��\D, a "�` lang�#,B1\r  \Q_26�c�/&a exp3P� Ao!S$�7� z�<.@ �#N�gK7.�. ���a2�a�-4*6� -4q-n-gr� Na yN!^k1Ac�� �bo F�8&�# afQ5 a sl=L �1� to�ɲ�l �:��!L *" $�_�O "' W^*$nQJ#RA& "�3[%g�)s. Each�8��."a�" $:�[=\g �L<-i&baB�Ry�%N�aeO!�Bb�Sg=2r�$\Tg=\} �[��!i*�#(� YD� ), w�A�lap &no��% . SeA�Psi�X=-BTs's���6�0�O%d&`�# 2c @�!/"��^�#K �g�I�iXUadA�E�edI�"ofn� if!�J@7at.�b��� -h�h8si-&s' (C>V2). Pu!�Jg�a6%�!=\C� ha� &�&E�*K[$�]:O<6& h�%2l{Ce�k�R�&Ku�-MC���:  � E� . If,�/�4#f�,v C[ �aII�K` �&�!�",�& I( G�0�R}.~/vB cise�)�*�E��$\E_0�� �"(8:. a% r�?xg ;l�rs��ve�Isp�r��F8$% �$�)�<{��"�.ityaisS E#/!antum?V&g�[)�IG=IE} �~ %��mN�e��)�%��.�� �raST *��en�Ii�G!�MO $I}(G)�6 &?�i/.%CA?��2�,l�)^:(I(G)�*� $\C"? s.\\)I �!))P]� cA� � :�H }~�H%]ALi �G"�S6�<�b.3*z $\EY�)Fi. �R� $\Es2�f�RAd� oremQEE`�'KE��!ic�2W > N��!��8r��%95'%>� ![2. �|�&E�=�����B�!�w�r!�ru�zWf�c!# Q�eva�3 7A<%8&�A��&�H), e.g.�� �O(2n+1��how! �o2!a  #��3ThB�;q��of�jug.��pS��� )�,QThnm�m�B�6P�_1>3 A��::. �gQ �k.�-b;a*9!�y�G;.�@a tal .p � 2��en�pby $J�O���qA`geBTN0 \ker��8�fmVG]/ Ya�n.� 6�FmD�&� .*a�>���Apts�*U�` 2�+$�A �2epp:sub (Z�A�Gd Lv�%5ed ),[ 4]�aU}$Z2���&���re�6aE�a!^'= na�vactO-tant=Uu{��"�r�_ht9�qc�`=.p!!�&��u6�!Q� �� l� �iR4J�29�(Zx 3A���j. *�M�^ !� %�es J� g!=9f%�ndP G]$,K�l#z�, }='w\ca�E ,�Y2�+.Tc "E !�uz�2{Q����G]/�M�Pi89�.+�*2P�%Uc �:�mp�r6z� )�J}E4)">�� 6 G� �s� Ah&(BA��e� �A�6� �����us>�.�=7y@�:.m>B}K���Ea�2@�\, kS-�F. O!�wi�Z�SI�Er$-� i5w����{�p��c�� serie&J-theta�,��miff� ��XJf��s.uXtcus]!�{r: ]!g$A,B,C�E�VZtQ �<&eCF$�2@ell=1,\ldots ,N$,u� n-$adfM "R�Ce�V�;-�dQj�]a�2; Sp(nI\r� ׁ�.a�a;m�8c��9n���YXqvKB2�,��_�7 NW Ma�o�'�: 52)!�� #$.� i.e.%@I Mp�{��@ T�n:��#6�%�z>ss.tY�.e�$V�A�"?""��(so(2n) r&u )�{��ve~Ai=1}^n=\SDV&�"H5o"�p� ��:#�  $n$-th%��1)@$V52�Bwo.Bc�%f6�;A�pm�n+0&�{n-1} i "bVO��!!� $\�&(^n_q V$ (q-�-�. zed)��d2�a� �oW _\pm�#)�<�:� $��o �)�pXa �#n�aUy tw^fe2�B�X(�M^{Cp �Ye�F��M)6 numer.J&$R=(\piUpi)Q^II-U�6�$� virt� f�idQ1}) 8u_{�}"$_� l~zN`m��H {V}$�~ent��q�>"� $� \.�.q��gfashioo3an ةv�� }kF$K!��(�$�� Kc$ -a���F $K�{R�j%�"�% �or �4o [e�Iob0;M �Q]a* ) $\Kc9.*�L��v U9� -$ e�"@�h:tz Vs 9,NK{W_+})-E( �-!��JSi�nw�%�z�:��TRK_+MK_-�Z�$}��� ;\*�D� �S� n $"�K�M-)=xM�zn(�N�E rho,��)nMF).Pb# \new�Cand{\Ch�*$athrm{Ch}}w)Coroll�}�VTr-TrGo: |! )L\pm��� �Ud� 6�'~a "�ał��Q�O)�\p��)h�+�O)}�s!K6caE�s�8�&7I\`�(t)$ (a�_"�2)�,on�0$E� $ up5+�3tito]�`F�A�t_i.�1{t.�|Kaco"�K;3"�%<&�5 ��9Q�We*�c@�9q)J� &�! g C[t_� ,t_n,t_1�  ]^{\Wm_{ �}}�b.$Iby permu �D��t_i,tZ_i)n=9 numb��,� s $!Q�$#5alt_i?�S� d eM=%�$+(t)-\ch_-%�ch�/s sign\M6k+�-rf,2�> divi", �#_m� �-��&3�6� uA$vD ��is ver�0ia9ta�Gway!oco�L�mq��[xqst�-:s:AS8 lexicographic ��Hž�)$ (teӄ�]�nys�1(�&h&��% ^n � K5��m+]c��,��ɇE�"in�b.�A ���tau�_��l� ��� �,I���i) *�F~AًtoF� W�)= b�;B�4"useS�2� Non-excep��ae�*�$secSSCC} S"�Jb�L�r�=�5closed6H^e�,��7�Among.�& � @ . ��G*0s6K tWm�cw��!\*�&orb#E���(bBL;AkB;�_m "�~=4"a��ms2i.� N��Cayley� nsi �$X�" (1 \mp X) pm X+�h�*?,A�*@, T�:J�%.es��\%2�<sta��ze�>B�s L=�I �$��5s �U na#$�LR.� ��=RG Vof t � ��no2�4$+1�; $-1$Ah2���  =�֍&�f = trix*�PF%� $p^;�@} A��[D@�� chi^�7!�bmE~@"D 0�W�td�F$\Nc(C_(eJ:~}�%2 �6�,e&�A� �!(�AG� � of-mC`%|2 EX*���A� of[%&tz3+=seD5%pisS1"����8s. a) B�I�E y��=�c"ߋm�G)!�R� . b)�)�5w�wU BU� b"  ���&�a&ƋS)� 8:��� DG� c)Y*t4sh+[Y>2O G} (e*� J2}a�& c�-e�% �)���J�� ����@p�h:-E�U(\A�AG!bYb��� "� ����WUSY1""-6eT!�|Ap�g9�F��^�).z#�%2#q=e����:�;����"�6����}p�x ����Y)s�!@'2��L.�]Fix� :�= �� �:�:G $T�t [ �$A��mQ-��$�G�T ��%t$� �h$Ƀ�0 $e^{}=g�0"�c}�� a � U-|\Z�� e Xu�Re ��k��I��:^m� � ��/% � 2�D2 C[����Z �th.� �� �,�p�d�+E1is ed !�6��Z*&6l���["�2. *�bs )q��:Me�F vali��9n_ they' '%cicUx�N��E\(c� A_R�?aJ`����<w>�8U!yJJ�`e6�$map ${c_i}f � i/(2��e�G ..{ -|"��wԉut|!�"�l)�'%\E� tbla�� }$ d^ !��;"72V`{ 1�z g)$ �gNi0u�h-Em?�9�e�&i�& aZi�g��ti�"j:�� �%R��N�54QA�7r*�tNw"�< t_&�� �V=\pi�1 Q_2��#V ."$%H*� .I�=2:H+c����&6� #maQg�3>�.��Ypw+oA�*W��j�AD,"��������B�:Yi {\exp�)}��g�R� ^�_e�� & >�� &(% tQye,A&u.� a�It(GA�&� & o�P�EB�<p 1� � ing_seq} =p\h6�~)u\]a v��<62')H2�. W�:r�y;3�B��2�p`�[api�6� B.,P�7nt� iŰ."�o(��2cZ�a��at )9�A�!�:�Bi��;a��}&�0��R�Ti�2T�� by�1�@_VP����sh�P=��Ha��R�p�Ps��:E�^1 �E6�A��-�!� @.vh � t" n U��E�.OAm��(-)As�� ���N !i��2� .q=�& �  �sM�� �$2�2": ���aga�V�A>�`:mm�3)��� goGIi�.� ���,!�1#g="; �áT Next��o�ato applJ �&�3. S0Sg�1i"�#EG.G�Y��2��( >5ܡ푤�1AHd Z , du�dB��}. ��2v�A�� *y-/)?g$�$n"�2�!�$c/�end"�E3�SdR- .<t�7� �@�5:)��Dm Nq&>`1!BU k*�X5�Jg�F��2�F@!�F�����r!�Mvo!��$%�J��R��\kY)oi2T""�Rb�RH'&�2/��,|i^gk A"��&�/ �, �n>#�}�� "N=&*�^@}G�^%�B�y6ee��dY �P�Sg/RUFPq:N � C_g�ndq3Ps�YIn�!�.�Ic��a�)� % P��m� }�N6)$�Y ut �p�%02� !L68.\2,4'I8L2Boo:D}��ll�spe|iW�� m�����.A v���'�SLi"%�$&5pr ���"� 4`.D�5b�qtrp�3/6�re@�e>�a�F ��J6\l ��| �$�e�!(VB�k ?J�mq�m�m+K�m-2�m."�m4N. } AIe �P&l�'hf6�y")�=_!�huX.�|o9x��i�A� M�k�JEs}��D��!�-���G"�w�.��2�tԁ\not=$\x_0;�!�!nu.�t��e��&�a/"[ in2,�$�9 x_0:�-2� �O�'2�i=9#4a�. �i'}%-�}=x<_i A4(�}$-xg$.��P*s )�i$�yget �OU n=\rk\;;�=*��_pkX 6B�*UK�2!��G $$i'=N+1-i$�+N9V�7{ggopAeb&i�&�( �.w�*\-CA�i"*, &+&���IdVo n ��% s. �resul�:TQ�C.�u|��>vta�ell)}_{�I }(x)���2I$ x_i�L �(j=1 \atop jA� =i}^nOq-L-x_j\bar q}{x_i- x_jqGn�6:vo(�4y Zz;6`0 [ \0S;!R� 6;F�\;:# {j'}:�} \>+\>i>A" i' +x_0^{!K} ,��\>�p(n�R�A�f�q^2-Han �^2��}������ + \> N�,f�~�n�--�%� J�6�-A�A�� ='n�� �i� (x_i -x%� l� :A��.:�Z�I�:_^� �,� n "{RŘ&���/$\{n*\�H *� a't typ���@w�/h4��!��  $g�P ��eaK$��1RX 4h�c�D� =�C�'k (A&|2 0�&=�J5B�"S�&K$"]W�6I �ag)?1�aQ+uS,K0_3(+ n_{k-1}+1iH\�ji {l_sL�[ ^N �=�av&� 1� M"� O��:3{k}\l�*��+_i=1G!h6+l#s$\l_k$�l>�x)�_ka�r $��_k� sp(2,m�!y� 42n)/ reA��0T<is>lG9gc"�Z� �v �.A�R }A�B� .)�!p*�E>H�2are&�YE0<�4 YHJ4;-a�FR}�� ," n_2}]pee���9k�Y)�%�!�@QeB's^er�%� p�n�)A^p�BTZ� ��Y�� e��j�j2a�; )j-E�}; 9X>��|ri�a��?�5\!���9rHu� of b�H)�a�G�8�gct�yn� ��E$ |ށ_� =�Fjq�-  jV ,^2 1w�Y��8� �!�YV$Q=\Q�4���kB�[GV�k$��#"���r(��/0 l)$-a�"�#gl}rg�� g_ie_{ii}{GUV��A he d�O�ȱ$gz� b)_i�q�i"= �' ��'&t&�Q)�W� $ R�'Ere9[ $$M � k(Q-!� i)=0'U�2Q)=2x9"� t�0�s r�sA�u&DM2"?!"0 6�Bc$�O`i�R�.besx5* ��U#�G�j�� �"@�RE��%cal`D��h�Iml��of Hecke�Cme�5&t'�'%�ro�.A}]rH ��{1NA���]� et $ g:= 2�{c}U�i U.��W6 :��.�  n�< g_{n+1}=16{M�� 2� =n+2r ���"�;!d!x��� (Q� 2n}).� Y�Q��� 4n+2n_i}e &\hs\I{-15pt}&vH+1)*� &��=�2V =�:�1��&"] +��P�>�Jk=�^�^�/k2\� 1WF`�_._�*v mu_kt� k-n)}�axv{��x.{2n:r_�o�atzc"v5 2�� �;��;a^�S"=�Z�W�~T 2Bs* �S�TeT��Qm7�Q���^9^�SuS� �TnT��U�UbU��&�W�seW \\[6pt] &� 6�<-}� -("� �� %�R�T�Si<-t�va5�x �;�&R=->*we getFW(� /@Ma?42n� �1�p 4"�:�M�R ?&n $%�$-c?PsQ,$ �AcQcUNmls)h G0&� N�!C������ދ�Y��e�: ._����;?�G } To�E: N 8gE2�4v#$\{�e*Fk A/d�'r�' $Q�K{Gf ul8b�[S7y2."al*t $o"�b)* � )l*�orS p`n. �T\�e,+ �E�B�"� a+>g��!o�H�)�@�&��r aJ�  ��y�!8.�&I]� "s�"P P� k'�fse� b�y studm� a�0mH�Qt�M"I 51 nd5�( \appendix{�:�#��F� &�38�der��sՄ5�� FA!YDdc-JimboIhum���"� "�a�!5Cartan-T�]y���D (e_\al)=eE�9�1 +ch  ?��B{-\al}E �D� C + 1 e + I!]e�om��dj$0>ry!TeQ�a"w�. \Ru� �r_\h��'(t ����.*x 7pt}\m��.Ӡ-�/'�,#>�#* RZy�3q�&aJ�\"��S06$�V\h��4�{@�(!�.:p �Y"4v-)�N��g�h� d���:�M6�\7.h$.R2X�)6,� ,ƹ�(x^��%� 2)�2"xo2��jk���^n|Tr�CW�Ch_\rho})$��W�!ba�B?"� �* "j,m�m�o,wE�(�\�_W� 2��m%M>z2H>�*I��%�l<��12&U$%B�1Vnar2}*�@2N�DJ���? �((x) $!Lla+rho.x$}�d1xdd_2.$$�e*�*@E�5{^'�&h*�)�%5�(�36!a�A*<�=��G�*}/ *5�Ж&2 6SV����-�n =0 -�!*�EAW���FIAo�1�^{2}2�gr)v!ϩ�r21b1t2W�Ave�����͓l(aO�idql�(���r)-r)��<x�la2¥+�"إnu F}U�$.�8{el6C2��zz�=.\ћ) �!: \:� ! �:!y� gm^ !}L_{=l�l(� � ( $ 1)}_t6IR�f�� 9Er) {2'} 2�E�%����:w�) M!�$2�q��-psi#�-�faV\+^"�92~0x �=@ (xIi�#����% :I\!�6e�)Z(!#U }aQ� )(\U�% 3we��� !� EMe-%��#la6nu)���}(\id� �E�b�S ==$.M��H� �G� O#,!u"�"#j �PE42�"�+qon*� ,>. .-$1,!q� .�:�F6��+8=qA=I�!�I�E�g (\}I� ^<��3 }\M�^|a2YXa&@E$�n pus�P�[��$;6b�4x c[@�G_2%=!��I tQ\it mee��he O O ���5�~T"�!�C��6j)81�D��yof.�,e)W����e*� ��Ii. m��:��]"T6�.�*�!�q���A>��accoun7� *2 Qp�/BgF�c&,)�1':3%��!�15�\;A�:c+](2= �^{�Sel�:P)G.'~�~!��d immed��Yn>�"J"�T�N��W��"�\Rw ��"v ^6�W})�hZ�Tr�F.��;>�Ne$.�2.�A�_1!u�)��i# $zF thebibli�K y}{A�� bitem[AM]�~, A. Alekseev��0Malkin: {\em *�4ur�8e�RoK1-W��s }, Comm. Math. Phys. {\bf 162} (1994) 147--173. \bi �(DCK]{DCK} C�\ Concini�V. Kac �Re/.eBa� "� |"V01}, O"0 %,���L�eMLs,J��s7/a�aA� ory, Prog �, �9 �(0) 471--506 -v Dr1]{Dr1}�"{: �� �{ um G-�s}cPro-nt.!gr�of%\e7Jtcians, Berkeley, 1986, ed.!�V. GleasRT AMS,S videO8(1987) 798--8202�2�2^� Almo��oSRu!?ve �n1e}�Le�4rad�. JQ I @0) \# 2, 321--3422�3�3>�E�QuPi>pFn-�o$1419--1457.kGS]pG�DDonin, D. GurevichI,S. Shnider: )�%�*=?� 5,*�E�H6 4g^*$}, arXiv:q o/9607008.�KM]{DKM.�P.Kulis � A. Mudrovm OP&� ��J�z%�  LettM�e�-=$63} (2003!�3, 17!C94.�MA�M1�e��)3DynamIYang-Bax�"�;~ q�N bundleAN), m�X QA/0306022/MA�M2^��em Exp�WwRԙ!�B�I�  $ ,\C)!�^-�,2002) 17--32�MA�M3^�:)%Re"r�E"�, TYuf=E*N:.�!�Isref�~,!v�z36}1� 11--26HEE]{EE} B. Enriquez%� P. E�of��.i! u%�d5�r�*�Mn��i/�ase� B� 1122.KEEM�M2�,�i�IA�rshallR�s҆͜R�Aq %VA���sAuF�40328.� FRT]r{8 L. Faddeev, NU�hetikh�Qk,L. Takhtajan�F A�>ZLiJU7o.Tn��ҡU 193--22.G]4L R. K��pta�/Cop)<g a:�6 i$I�=.�9 }, p(i� {85) P���[GS}.P% P. Sapon��Geoq%bL:.Y�:z>�%} �411579.�ZB]!� M. G�A,!ZhangIMA. Brake�Gen�� Gel'f!�in)�"l&uc�;ntͶ@�� }, JA�" �� bf 3�.1991) 22�230.[Jan1]8��YC. Jantz�K�a �;��nd�uzier\'@Darstellungen hal;facherA^-A�w en} �6 Ann��22�9,1977) 53--65=W Jan2��q.�Lec/ o��"� 0. Grad. Stud.� s-6}. A6� , RI, 199.�Ji]{Ji%��M� A $q��_c�kVog�] $U(�1&CR���>�- 10�A�6! .bJ!�1Q Joseph � e��E��prt�4 mKD. Springer-Verlag,� l�91992w!u2Bl A&)�E�dpa���bu�},�A%�a � �$7) 480--49. JT]{JTp�$D. Todoroi� S�� KPRV"��a�l�* aSkU��.�Alg�=�orQ5},��2) 57--9.� K]{K�2Ko54:�F+9A�al.8 ��q8u2�"���J���&. }, %@2I75) 2�28.�Ke]{KeE�K\'{e}bI! 4�O}+p\`d %C� C.��Ace5ci.�a S�r. Ii@)�32�O6) 1--4}�$KhT]{KhT} � Khoroshk�nd $ Tolstoy �U"$R"ݑ!� �(zed (super)=�^� 4~ (1) 599--617.� Skl]���P.� %�EŮSklya� + M�ic &�v�edA���J� ,} A� . A,| bf 25� 199� 59a�238.aHL]{L} G. Lusztig: I.`�u%u�i : aj , Bost� MA��.� M]{Mek>� ]*l "T�ia&T��$ke� �1-��R���0236.� ,N]{N} M. Nai_Q�: Teoriya predstavlenii grupp. (Russian) [R6��U��� ], Moscow�7.�R]{R}A�Ri�X dson y� ppli~/ SerrP��7�to2\��.��� . No�in.7848��1)--151]�S]{S} T��m%C>�BXnz�� 1185 x75--20.qSTz��N�-"-�� G<,�yDu� PrincipN�a�a ќDo*���� temp:�7 �94) 2=24.u VO]{VO}a�Vinbergb8A. Onishchik: {5\nE�oI6am Li i9/heskiz!uppam}2VA%�?o*���O>p], ]d8.�We]+aHunyl:�*� I�F# ir I6� 6�s��ta�New J�tyA�6.� Y]{Y� ԅM91z r%/:`a monoid�0tegori�� Cambri� Philos. S.ŕ10I� c26� 9a�/t:!� docu�\} ��\� |[a4paper]{article} \usepackage[�2� inputenc {ams�r6r��ng6�16�`�^S��r:�Hpdftitle={Monodromy�]�1on%Yfourth �`� �4Calabi-Yau typNV0pdfauthor={Ch� {$}c<{$�L lRR r .` {myr%D] mysy#�6�ftcdot}{%L{$\�mmand{!box)~par)�0.73 widtgv{0.3\��! skip}% #1b% % iTd&jgTd5 IIBGrass? }6�L {\A rm{ } \re.�P # bb{PFL}{ B bb{L�2�lra long&teE.aAuteq eop Nrm{ 1ema}{Hyp)8sis} %:�H Kbf{H}} %2l Proj �6 AuA!6��6*Pic Irm{ A�b�!d� \�SJR��ofZS�Q �S \�P�O2M \make� {:,thefoot�x }{}\ �L {AMS��fiD : 14J32 �(Pr� Dy) 32S40, 81T30 (S�� ary)=abs�#tF �� con�^s�sre�^n�es�� �ͩ�hze4� �㽋d�z��=��r�rזofFW| �8AZ}. S� }seN�'terpre0 a�� ,Picard-Fuchs3�Lq�8��5Y,co�+ x �<us=?X�� s up_��eK�it��{4d v{! �8 Gopakumar-Vafa*�l�n�gq���v if!^afr�,s�[��n�[/! � �%< po2�Ou�Rv����E�\1�D{,MniG-!�#� step�answe���. x�Ia�i�o$approach !bb��%t��lJ�{log� mirrl-Nt�"�2�y�sA*fA�t(ne-par�,model�I F mor�M�W� al�$�ih-� VY}5 new �� �Borceas 7�\�&� h���of �F�k{Reld� !�aper do��m�M���4�ofs@�JAw!2ink{n�(the�=A]teres�'Q �&�h.# } A6�&�Mf� $n��S^1$[.��# � gin{�"�Heq:L} L:= a_n(z)��^n}{dz^n'-a_�s(z)�Hd�s!} + \�v+ a_0(z�,�t�$�$a_i(zOre*�<)p%Sigma �8 et \�ofi��|pU�saq""[C)e`$ �$Aq�4y $z=\infty$. �/"�"�)� $L y�f[0b0sEː �$C$-local sҦ$\L�;rM�1�S:=�$\setminus �e�f�� choi �a�e � $��n� B@�= in!��{o�@L6.#^�ey:)  \[!�$pi_1(S,s) � ��(\L_s�.8rm{Gl}_n(\C) \]�fowe�0W  $y_0(x)�?\Z[[x]/�at"�S�݁f   ar6�5v��A2�T G-fu�M%�a�O klorKf}�atF� back�Bombier!Dr�LA�1aG�l�� 2��2Gqcs�/ a \emph{g��� riginPf�E KZ})E^+\���$!�SO3occur�f]%}!�a6�;d��%S�M �5 a co!klog;a fam��$�,:)�calZ)�aX,� �*urfiK�X$M�)e�I�c�nbpW�� F84th]�/' n�Ha .04 $\L_{\C}:=R^d�_*(\CO�at �})_{|S�0�M$dE�!H dime��!D�arhoa�*;�a1m�� thinJ/ha��U�~�Z1&��S�/ex)'s r%�al. It�46P����"e}H�X IV���& sen�4snc7Jsry�|�B�/ y*S�bD Hadamard.?se�. �lֹ�%� s��[ e Cauch}&=(�O6.� ereadtB~@a� �nv����ps��refer.booksm�An�e�iKaM�detai��V�!w 6AZ} w= ol}6�ta;icter noa|��=�mind:�\re��i���q� a���&� *�6��a4��s ruto . � �Kanton ber�7 �(uICas �!^��  a� *� �:y�4�&; �H"= �De7*�&2& ��0 $\Hgrp^3(Y_s�4��S"e�_ B�%n�d �56!*� 6 *!cu'�W�� mY� $X�@ �-M!��0e first $14$ �equations in the list are in fact�much studied hypergeometric cases (see \cite{CdOGP}, M1}, KT BvS V �DM}). Mirror pairs of Calabi-Yau threefolds obtained from Batyrev's polar duality of reflexive polytopes \cite{Ba} yield a plethora of examples but usually with high Picard number (se�YH�4 By taking res!$)a�to carefully chosen one-dimensional sub-loci these �s!nDimes give rise to 9�of .(ype, bu)�dinstanton numbers computed)��is way represent \emph{sums over differXhomology classes} andA%4re will not exEF2�\hree fold $X$ with Picar5JonBthM �nF�D. Case $15$ is an -#!t�4phenomenon: it%A�1) belong!�to diag%{=�M=Nfamily!,$\P^3 \%�  $E� I�A� ). TqF@contains many mor�saL �s . quesA$$ is how caE aT�E��5�ial�Pi�2x u�xLexplicitly known, esa�ia!�becau�#4he associated 2�is !�(d (Levelt'su orem�� BH},I�KaA�( This leadsAb] $14$>��mAfo��above. !q�s�P� sing!� points-����LoR" or for QIeetha�́p:[,�5�JXin geneA�}determi�by )@ dataisE�we haveZproblem�4accesory paramGs. We doY!�'nyq method![wV���Mn�N%r. We !�a brut�mrce��eria�0approach comb�eDideas�c ��.m�symmetry� conjecturEeZ� forŰ further��-5L models. \textbf{Ac! ledgeA5s}:!( would lik��!ӈk G.~Almkvist, C.~Doran, A.~Klemm, ��$W.~ZudilinA!!Air ����!�A�pro�.�3particE�w!q ank ]C�Wapa�o�DT�� basŌd�7$ sugg��!�uA�genus! �� � a�� extradit3eckEs!b�I�er Y��E%%js�� on{Sketch�H��%�q S-�} Accord�%Kontsev�/� o� ��lS:1 between.Jspaces!�$Y$ sh%�bE�mul��%�erfa� ival��fcatego�g. To 2d_^L�F�� two tria�ktedI, namely�deriv�%coh� sheav�D^b(X)$�a4Fukaya- � y $D��F}0of lag��ian cycg (graded,i��e�\%�them)! $X$ (see~)�FOOO}).��e first�y depen& n��4e holomorphic �-i�second .+��0(or K�hler)a�uli. M3���i�c� j sedA�eq5��->$ies. \[ %D rm{Mir}: )z, \stackrel{\��(x}{\lra} 2uY),\quad8Y�8 X) \] Th� .�induc/-Msms�a corresponaA $K$-s. Via"0Chern charact� he!� scen��co��y:6m%\Hgrp^{\�?${ev}}(X,\Qr� 3d(Y)- .G !rZ] 4d q, \] wa4 $d = \dim_C X Y$� �lso-:��i9>�(!=QjMi $ � 1,1}mAaex0��lexMЁ 2d-4Y)$� Ii $StromingerU$-Zaslow pi�څdm:�au��SYZ"� Gr})���are&SI�(real)&�$torus fibr��` a�mon b� B$.Ay&!/re  <i�>��DYz$ to fibrew)T@ � romT �#get�8intuitive under4A�!?!k u transform � n ob�Ks.!_�L,; stru)W�;f $e�� O}_p%�a� $ $p \in X$�4 4pped to a SYZ-� @bf{T}$ (�a22 on it�/YU( r�XՆmap�� imagpS}$ of a�.� , $\sigma: B �y Y�:�%. � � � $(�E}, F}I�-H!p�`PEuler b�ea� m�K defi� �&� R EA� F}�  := \chib� =�(um_i (-1)^ie� \Hom26��!�F}[i]).�*by SerM����triviaof�8canonical bundl�V $td$�] ic. It d�!s v.G-�GA+1&� �) � � dot - $A,!a�p �>>]%�$X"90by Riemann-RoIs�b6�0 \alpha,\betay� int_XJ lde{ %} \cup + td(X),)Wa$\t21=)�k g$ $ OaN �?2k�%$. Ua��V�!a� BZ?�w 2w= rt �JIJ| &) s. On+ c��� eas�0be checked \[E�)�u�p]� O}_XM = 12= 4I؅e 2bf{S}1�E� "T Moin �VB� } �vnowArw�umk tAUe��re�2ict*5 %-:�;dW ��8y satisfy $h^{2�.Ya�1 = h^�?�� 7!{so calle F�:� va� �a�.�M ~ a��ha� e��� us, i.e.,K ic(X)=\Z$a��a �neB$Tw3(Y) = 4!�di2�m ToAspecific�as9qwZve�xroper��$�:)���Y} ��P\P^1$, smooth outside�Ρ�e� at sit���� $\S�& \subset P%$9�A-�W Ma^e-T $sa�E( \setminus c=:S!HA�e.� &?a��$ath $\gamm�'( \pi_1(S,s)�& �is�a * �$$M( >): Y_s� _s$,$*�  auto*G Aw its XinAd ant 67 Y)$� us set� up a�� sm�� �\Auteq(D�F}(Y)� �s a r�Fver���ar�q�:� of $s�M6> odd}r!�T!����er�b,th!�(at encirclean�?�E!*the f�aܡ$� d>� is&�dj�q# pe t���:ja��y aquiI�*�st �?�ity"Y an $A_1$- (`coni��')!�erea vanish6 $3$-sp% �"�al*!@is then a Dehn-tw�E��2 B ��Aeffect��r !*| bc��P�$-Lefschetz>d�Le}�AG&�Lo}� �k :#s 2Y q�!(i�.o%��I�,ST00} Seidel%1Thoma� scrib��M!�:} in*� o1aA p�yb� k p- li�$T*� E}}$��a*ye�!� )x�E}} )G"� `!���a�a7 dim(� up{Ext}^*2� � E})! 0& )b� �*� mAled !2]a�t�F})\o'� E}͘F  :UH"�+1�\]!~�O�cBc�9U,e� each line� $Lu� �V5�. Anoa�*� ly s�^\�} �+ $1,L%�tenso��Da:�$. Not? ](� I% 1h� f��i� � t� m��� � around; ��� J��&����us�Ua <$. Let us writed Ak�2jN  l�a�&�.C$:� (H)$�a&aa�verator?$\-�mLpowers $1,H,H^2,H^3PmPa�w6�&~ $. W����S%PisE|watrix $TJ� $LEZ�{Ebegin{�� (abel{eq:DM0�T!� &p [1 & 0\\  20\frac{1}{2} &% )V%6%J3l \end�w �as�follows8  $\ch(LU�U�E}��) $  :e^H�2Am� J��ibda�5�"< m�  -� � �@ 1� h� its )�2Z-�9!\=� con}�S��-c-�-d6�A)�A 2� RV�>��  d:=H^3,\q�c:=c_2� H/12.��-$Q$&k  a��a�A�)X�  w � i��� �Qn>�c & 06?.W&"2'0<d,V3- $ @� 0-qe:u�\] NowN�2} obser�!< miraI #��quintic� �� %��TI�$S!Tde"�c�.4@ , Fuchs��or)\\theta^4 - 5^5 z \bigl ( +\t��5}r �N%2}%R"3"5 NF4$?r �It_ ($0$, $1/5^5- \infty$�5 ���and prp"A�e9)�I$02��  uby!}�W%atdarent��9a*happens:!��(��� j� ,*k Hto � �\O}�Q Z� ) ��� |,:��e ��a�&� ����SimilaA� ings occu� allj 14Rv#. � re �?>��c(<"swo5�f ge1>%��"ref�or H}ea-&9li��To*�)}� _� c ma)7� *~'�s iW�"bX"#'m!Sbe ra!� scars�A� ��^3)�>-�+$(not claimAjtenes��sense)A�Bk#a-Bo}+#�':$11$ �)o�(7 ramif^+cr)�sN'P}Fano-v� k)-F"f%�[#��a few � %� . Basic iws%��(���)\ * degree} $���e s@ �/} $c_2ɞ Hu ��"#43=\chi_{top}$,��x� A��!�ead off! ��ux�" ��is�w mo)conveni�*to work),a&I)&�� � ��us2"$�� J.~Morgan*�, T���| �o2�,�Y'&$ coute} *ex ;�kx�LWj��� 1.��-."� d� - �3} $ c }{ d}.j&M_ -,FScE jB�V  $cIT$d$E�2%e(�(�-e��:�:j g�6*r�U!@DM}} = W^{-1} T Wu =�� "�!![* �0�!ad6i ={1Y2�< .J�S W b�m^�-kV�-�0 "� F� *Q_�5Ft Qv�P=}F�%-k , �B 2R� 5�H�$d� M[k=I���}{12}+ H^3}{6}W last���a pre�^aI�"> $%�� .26c6� F� ��  ^� eB� �end)�By_�� a� ��`X � �AESZ}-� �! 2z=0ex0e non-obvious�o�0>�  *a� �[we3 `63+ �trum}���of zeroEma8indic2aHatI , wa {0,1,1,2\�P� lso s@,� Hodg�eor�%T f�� pN(Cse� on cSrium,�i�h)6�s �B+ �$l&n2� fI9�� at leasUK-�!1= $6� A17 � !L�m��is ��cl%n4178� �in�1�/� �&�3%�!� sev�/� E~s"55 #!�U �/$able excepA�sE2(no B65� �-�is�,��$\eqnno{32}H4%�1e-�zeta(4)c4q1Z})P2!{m�4AFe un�=�3�{�.+1$even just sal �3� *  . %�$d("analyze)�`a.maple"); % nops(set0112(�.4db.m.20041221--�)'�!�9��do�N<)�02 �u:<2�$high preci�nu�0 ',i� ��'�to�')[�� ,97%�s E�d� in �� tt{M!%}� � stepe�to 641a�e�I}D $z_1,\dots,z_\ell�to/8ose a qA4 $� Nex���e/eN^i$M�� Bz=�wE% i piece?*z loop"D8e *��e 6���encloab.e���"& $z_iQ� sref{fig:ws})02�figur�g center�vnput{/.pstex_t� #cae�{PN����J�i$"����*K6 -fun7*dsolve}%sa��3ly�g"%�f�7J2se �#�t turnsBo bit�ck�3�W}"eededg A�nAKA��4P4�9*�o%Es: �4@=gear, relerr=$106 5}$, a�.E�SincreaZ14Digits} to 100a@is yiel��"� ��P*r�rbitr�#�and�"#s {;fil�&$4)mes 4$-m�Ssee� ly randome�lex ent' . AaCismD*;�$consistenc�3��ab an do. If͋exist�V����� "�*is`8�<nomV3a�3."��)8`-l2%2� coeffic ��/"� heck � root��B�s �� � a�*,�logarith�2� 2bb��.oe MUM'" j ��&Z&!#b] 914$(1-\lambda)^4j !�{:a!�dic��l p�qw_( chieved. suW��t�4y��.ultane� ��n� at makes �AU�1�"� "� y(i�QP $\L���"u�  �4 "� a�*0#n �aN�%�!j2�!`)$k(S-\Id)=1 ~ >�>ir/ of $)!Jsp=E**J�$cɴ� ':~I�Z�"�*l9= ���T��I&2�:!. A� &eo"��ro&�� n0?5 �t r�8$�*�! / hop�uvlum��% RI�nea�!!�or� al �� Ypi_8 �Cvec- ad appl!�!�$�it F>@w�2#! 6 $v_0$ fy\a goodN9 NaQ� >;1ur�W: s $v"% v_k"�*��) �> word"}5�A.ed=�u[} �.�A4k� $npX7P �s amo�A�W (">)z �]m�ɚ�q�&�Q$. W�(w*A�Nm�HgQ��esult��-~( � �� Of cour�KN'A�b~Bct M|t< �Ki� e ���REhw�<8�� m�Vntinue�Ca( sS&('�Gget�+$y large de� n� �m�2� ���very aVat,I a.�a�$�: F$v_i$�� �isosu> sfulA^ɽ�-V�, iQnny��f ��-�M�A:�K!WeBA��s���B!�a�T �t�8AD�{ B?no�Ad �, B� �+&> :� *�s"!<:�8 �X �%any���s fail���a?� gain)~a&o iU or .:���V�. Howa, it � !Qdoe��)Wwa�y2!+� 6y d �cho%�� �in� A�i�e@ap�*1܅(did>M143_���inv�>g�. d G$X :��A�stF��Z. 5@a major advantage6�4e�z s'w���&!�be�ۥ�wv&��exact}J��a<e%u�Bdo �algebraNout��r�B�FG�?aXl� a?6�no�ct�m6� s. PI V �R�*~�?a�K 0 right Jordan&*�rMnew-��%k!E *I ��E.![yc  ndar/ m \p��'A�  con}# �H�+&_.=�!�(ed��t�3� -����64E�A��4! ��/ �NE�1:�5C"��"_ s $-)a���%$%�bA-ayA:7!w t Jap�n.#� . Desp*r�0ortE�i�ifyOiv#A.86e�r {�Dab�+e�incluOG some.z:�&� �4$amO*J�. T1� ~)R�E $z�wJo�=ng*}"�:� act�K:�.%Yn�I�*32 A'uaa i.j/%Ypullback10��p $f:z5eharrow  6�p!m'� ei.Eiv�i�<y!s�0���6X�$1Zun","Y� �&it�}�ch\&� ianda�ou�GQ�%Z6�"�! . So�" LL� �AtoB toge� Rba0ta�]aD '1<64�H� | a*�D b�If2� �Z�w�T�^D��.r��Lus&� )�s��Jid�4is��a��H _e8���� � "�2tg;{C�-peric ndp#!�*� } I�? Omeg#4a @6!�*#D tAI/{.$�7 (��-<� 8$� L}:=I9_*(\oa_ Y}/S)$)�$\Gw8e%�7rizontal��� !e �� �s}}1 l,{ N} � *!$A( solu� �as K-%�)1_t < 2��g�%�$y�E"�jj4�'�/v�u��H/va�6I16f@:'  $z_c$. CglyA��� fundaDIal ). $-' 1�1+$U�uniqu2$F5@ B�� . Eq��imV�9 I x :x S}} )�x� lv)��M�Q �'� ed $z_2(t�!MpaperzR.Kl�NN� m� � uppo�u2�4rDRI�*S'is�55m� b��H�Adirectly����ial&a:� . At� � :( r i/� of Y��&g!-Q��,"R e��s��i� 2 se�U� �a�Ё!�&y(z) = f@\log(z-z_c) + g(zY,Go��ͷE� once $y�replac�$O+ 2\pi iV� The 2�$p*2/�� !�1r=aE�k:"�dT<@B�ip� veM*�+�M�"]���QJQ�� "�� b�t�Vtly*K" � o avoi�s ri�)�ah�R�S�1��tA��8�Qf� %�iH,(Uone, �J nr.~�224}) e&�*w!,%�� )�i� �  msq�loses� �hRa�S{5r� aJf:Dd)-" e�0:8gIG! �;a� � )�e��5��1rA�!��a @� C� �"�H�� expa�U1 1��Q��.>L�!�g0.�Di2bL(1�}*�2z2tI%���'f�4q& t^3 +Y)c&e+ }{24} t +�1c_3}{(i?)^3} \Q 3a�O(qa�end���� $$� ��rM* n"�,q=e^{ a t}� $t�G5e�} �(y_1(z)}{y_0R)log z �BCf Cf C�ste,&�tJ+ }. RY�<A{x>�Ht�' $V1 11�xA�ezGre"�!Pfour-%) �(toE@f�R energy $F intr��N.q(.\footnote{�B �e,a�EAaaQ�(!V BKKV})b>F_0�(-v,t^3}{3!} + (]1)tUG�-�6� +�* �B m_{d=1}^{# <} n_d^0 Li_3(q^d�<9%�04rm{Li}_3(x):=\DH{k2@(k^{-3} x^k$�6�>� tril .} �E�?"xR7 is}�*SX����T)��^�~l?Pth70��3!�tXF�ut�W 2 ş 2u� �,�P, e.g., #��M'"F �al\_sol}��.68DEtools}-packagdtdid�w2�� $�!a�$.��$aq�� $. A&!M"cp'��can !5 "^ el�S $y_i(z&�*Frobeniu :�Pm� app:�)�P�3� �9aZdomAY$vw\/o;��"�! ��U��z��overlap!* at e.%s �spo $z_*� ��b�E�V0rge. u+AV.],$f^{(k)}(z_*�% $k=0�#3$)� $y #!*%,i.'"t� �Yhe��ss .i�Oeq4i=0}^3 c_i y_i h�. �$H!���"�%y$c�#!Jy"��J@ tin�J� ��� �Qw��,wV�}�Q, �z_2Z�A F"�N� n�J��5�f �� ta�At{)� Eal?2�!�*�Jt^2$ � s l5!��  qq� �55B"f !>Ł�2�� s�L�@C u; 4nwe 2-�isE� n�4�?� ?29fo�N byc� � V3�� $�8�!^W��!S�3"/ET$c�lIn prax(= � as discus� L� *� g�V��>�so�12t,iB�& m5+eX.�#.D4�\4 %.\Gi :�]a "�\ valu� �! /8*} \vs�V{-3cm} "�&�bf{&� }���NA "�&$" box[O$width]{% \'� .tex9� 7^=tab:moni�&/�&]mW A!a�"js}JF�'X6hea_9S�8�tea�>�7f C ��' (J)�T\) .G50. An ad�/al $*! �#P=:�:@:m�P�`,�8� >� n&9-M��$X(�))$��vAte !��7��ed�Ere�^n%&�0. �8y�iar $13$�1��� eg!� :�let��in Grassman!�at�*�ciA��6BCK�caFa��few% bl��!w��X�� !L elus[;^thN�,�$." Al �DM9Any�TJ�$X(2,12)!� $\P(1e/1,4,6)$M U�Aoype�J/(\Z/2"qF �>admit!�rep�rehZ��bX*�X2:1}{/F} B_5�FBU j4b��\LI3A�:]�.=D4rm{Sp}(3,\C)/P�L_39MEE�0 EL&�\e�J.z��X_56W5=G_2�{��{long}}B�5,7a�)t�c T 5-di\-men\-sio\-nal !��u1oA� a 4-z 67.o U��:2FM qc��孱]���M��) �n princip�O� cal�`tI��=FuFBqu�9 2�gs���ver#�du_���Uvb ���u� a�quantum*oH�#� [N�"�>(!R X fix�W �@ Inf. l&dOmje 5.�[u>�.P ofŗ�a�ic�_* �6n r�2-j . S�gto>7�#ve been%(t�Ze. ���i�t 2fjAB}. BC �D r�&%�X1�f#�!�l>�AVujn�. �M�c!�is��To}, F(a noli� ider2�.��'^6�I�? $12$� $17�+I8mv�6��2,3�qAI-�;$5�/ 5$-Pfaffi�c��y �R~�5 u͈99}I� $7 \E6s 7\� E�der.\ Ro98 9� i�A�O)�a�6#&� �iu�hA(%ye�3unA�rZ#�V��!~c�+!%"Eu�[:�.] �.X7 46�!gc>�"��B �,G � � Å�J6� E�A��  (71�:!�is�(ed&9�� �+� �4 NM23$IV&D=YI*c'b !��not� S w�� mpos�^} �%t%[b  ex#an>�o9] s�S 婲��kF more�!�1_Fg5Z� of ell��C6� RO�W�congru �- erty����Y mo d�o� was �Es�,PB�"stRv a.�t A��� "y .%�)�2�n ��h )we IT�; EXE ay $c$0!n a $*$ aft�E�9� D� �(K1iWw� A05�5 q �e D;ron�Bat Iof.2za|eI ��'web�res��@\hlink{http://enr{s.�e5%hk.uni-mainz.de/enckevort/db�] U180�s��PdM�a�oF �D�k� �9-9er- �e1�2+Csourc��el!�9 1�itA�!s �i[$n$]6s� �� ���$n!�\�Hs�*v] OpenA�oks}�>u1"& ��! p �tl7art(r�1 '<o.[ lef;>��)�qu�'a few]"�M look!wem.&�*�jb� of 2~M a}$ Z �l�+� ..7�7i� )�%��܉��*�G �| :|> &�$-���oّ2lapwe k8� ��� Z+woula��!�we br��!.�!�in� "�*s $2�EoSC �D$a1�3�=]s~n<-{E�2candid� �:s%:can�=�C� procedur������y�!-E�mb!�te�l-to9)QXI �"j in �+��.#n�&.�E�AW�CcL� q�liq�w�6"K a�, eara�!W!�`ŗ[/� ��.&����c(Qx*M)�eYPigu�qIa{��G�MKEt3Aem? �keyat�!8� &� ���oU�ra%oh� "Pk&�!��n-F1}. �Eansatz!O. ��� C8pFkexponeqorku��� s��t�>�n eduOkd gues[$�j�9 [��of ��=nA7)���'�BCOV-,?Q  � FL} A4 probh,4be helpful. M4M-��=� X~!97 Dc�"Hadamar�;��3 :�_a,�duc�tgiAby<�I�JC�fa�6s. MayamR#lso p�\�t.�4.� ^��1O !J4{ %D�v�es??? �l�?x "�Orb��%$o_�A*���encou�<s}ysL%�aGatJ)�%�1\_usual� -&�@ulaE�k6\� s bX}!��"Zɟo�$ �<ss%_*�p5� spa � i�ly vi6 oP�D�� evel"Co�r�͔�7�x�fU.�t$�gA�[;��:gmbd^cZ$��|A'el"�0%q�q.$Slb$��lUNh}: s [ ,\  ,L21(\a�h)d `` �/O`�h,? %XV �a�6� ��2{$ ]rI!�wV�Vei^met���JwX?�=2/Q(�))$ (or0$) �DN��%4ywo%�hF*�)�4wB�1 anti)aic�T���r&| o�I)M,B��Prc ' �3%+ F$.K'�_� se� l B$&0�fin� %a%:�1o)9����/&�Ps $�.ae�"�5 quotj@ $S^3/G�'X� eE $G%Ic ing,tw� �Hxpl�7now. y�a�"l)m�t�.��.�d1%f: \C^4mHCmCdf(x,y,z,t)=x^2+y^2+z^2+t^2H!�b $F_s4 $f$ d" �gC \"�g{0�,� Miln�x�oE{� *q.�cotangy<b�4U {B.{� ��R� mid :� =s\}"�is 5mm^s *�2 iK�b?�?r!ą��le�_�d"m^%~�%�� �m�M  !�]/$ $\epsilon"$ qE%:�mcl}o&F_s,\Zm#}%;u*d ,!rt-uOnI'q"m_3?�ZReMO)Hgrp_3jjr21�2�M%, "�/ = 1AD�_$G&A� � U}(2�Si!�Em�sub%.e+ then 5s�*a�?�]R^4�ZbyA �D k)�"C^4$,!' i"(BAjuMA�2Q$T.?. �U��u��4\pi.XX�fC^4/GH8mV5 b&A,�; �u�5a� g: Xq��!��$f=u*\>i g��ef $G_s�g^�S(����ie�by!f�Du�Ga���2��Uʡn� r�, arroaN,I�U�/W $di�Ii(GM�. �Ebov��lso�{F9eI�d:�U| %+\^w6uidM� 2� I) e+M� d, eQ�=1/�dQa��G<` A&^*I� v'b9z!�1*�"�M)�)� � �)sL!�pi�4e��|G|� �l�a�pi^*(d =�e)=|G|; }i �F  tellsk(ᜡ� �Q3'$eGMS w�0m)H� eB8%* �;u ma;u 0/ - N.�)QBf %)K���mu�#�B!��t a�,welC,a"�-�<�Qd$ Js>�$e �!�p=o $e-!�@&&�'one d�o�u #%E�?� N�! ��n�c,9�>� >� �p�[b�(se� ���k)mX^oA� ] �}* b dAIuz1�d"�v_� r�w�2�T�o�w� !;rB�|!1�T�_�($|G|$th�3�R�iza�abIL "�Coo�̀fF?"� ",6�~GV1,GV2})q� K�.A�� &�-&]��^�U�NF� top�!S st)�F �.g=0}^/ [ (^{2g-2} F_g��+2'd�T {mBn^g_d�/ 1}{m�ab 2 \si�Vf)m m�/ �a�azq^{dm}�m�o:�^ ���hyv/!~r {0ly Q,Gromov-WittevaA{ə�^���*e#�x4 Gopakumar-VafހR $% �n?trCT�.@/!�^��t>Z&�.�s�rS lway�&A�Wi � y�U�k �q"8 �F.�� ec1M1*v�_@s�Q� Y�-dsI�]�I�\%�al_4(F_0 = n^0_0�1ErKR�1Q�fQ4# ^3 q^ }{1- � �$-U2�>w F_1A�X*d2�4+� I2 �u 2 E� l ( &e12q2+ $eaNq^{kdM��%!vI�%j4H e $tn�4-t*>a�7 � hT�qT!e*�A9�)�^nd 1_d$�E��"�-Ah*UV�/�#��Nq'�7C+"�<��"iF1eq:L}�*@in�.n�d �wB)�"d�6�E��m ��EϑZ_5sq �(��&�@) &� �Iradiu� s)C$!BS(2�1�MUP`nA !���&�2�#.�f idea@bUo��p9> `�*I� $\C[�>]/(^n<3W�J��, &n4�!�� ^mE(tilde{y}(z)�bn� A(n,c) z^{n+  = D7 + U7 aj=V {n-1U^,e�? !i+ �z^@= e^{4�hc+}hov1\l�7�V*m8^2 z}{I�>^2; ��"-�D` z}{(n-1)!27 ���s$!i= �|).$# 1=z wd}{dz 'n� �7%�Q� $L�$)�ena recu"x�7�^pL.,1�C5A+ita"%^%��E�L $A(0)�=� e?5o5l� !�gi:MVYڅ1!3 D�r:(=_i�6�ex�sioQ��1^�n�={9 + �9M -� fN|)�Bec��$Mq n�4%� f5 T^i�S�! y.!!��n͒ mGjaGi.siAki!f {j-ia �Ia!2Ne'�Fi+ a&�Xn��:#+=i�/i�=A� zaf�)F}�:�g*Q�}��rQk� �3wo �,Ѿ$>g li"�a� �y�L�Yukaw�0upling}I�e�G.�;,K_{zzz}=\exp� l (�+style �e�;}�t a_3(!�dop z� r 2�� "� �*�5sy "]L}.rgeJim�.: Q!๙6� jis "�c $t$-�M e��1�g.9�]3eq:Ktt�=6�(t^E-L(z(t)#=^2 �$-_M�dt��r �=�Z{Ure�.)a*�"���to"�ba�of� F32t AZ,�)��)�n,� �_) a"d�9 AZaa_1aeE a_2a_3Y28}a_3�> a_2'�%& 3}{4a_3'-E  B3''>2ɌPro�' on~1MG�Z�4J �&gG�Jau��� alig2�AZ1� �d^2}{dt^a�y_2? } &= $}@92}�E%�i�bp�bi!�E^2E6 ^M $ ^3},g.}2r�3W�t �f���-O$5&6IAla�exy7�,.�G4M��~!�i9 a��\Pi(t_>�1 �m~�i!  \\ y_Nh y*A� �a)=AHM7%v8 t!CWhy� G - cit:2 GS��Q!*2T}w(�F�;l�\!���| ized# 6G٫Bk���n����%-:p�a2)2G��'2MU��isk9a&�7���ɒing>�ApY@�dls�F u 3 T� �w* � B#%r�sant' 9e$ejA)ir%Tv$f�% (�\R$ I 9r6�'E�A�*��oaIe�R�s���e"�' $s_i4 \Q$U-U1�e�Ce (app�<) -�l%�GrA9e� .).�z)$0��M�w)h"*yb(�wz�Aao &\�#,x2��2�$v},*cL� -ᑽ.sC'`VLJ we p�-�DM���!�pse rul.,JC�F��aal�C�(i1s�r>��,�:_5x-�.���wa� �* %%I<"|.��*.�+w�.x4-{�B %!� DCK�!�ula&t mc0}2' 6odern % �^achx8f*M8 mptoI-�fA�!�ol4F��e�% %e~B?:�% \[ %�'&C��@�k.v||��D��]!ΡaO@7e:%� (13)�*� })ayu3� h�ri�dve��+%  1.�*�]F'.�, .0%^ % 1FC r*P1��$�:^ {t^a91c! y�� (�=|t�t k_a%\w3� c ^ -2$um_s n^1_s]n.�� ns_a!\nsV-q^ S.� @M 0_s 4 ?q^s#l% %��$t^�(p�xsq$!.%��4.9� %�pk_a\}_{a�{��}�$H&͐ , $s�ai�-�Exam�q^s.�-I�6S t^a!OEr �In� I��u� BN$n=h� 1,1}�So�C��iq=�%�(to!*:�� V�1.�%�5�2����n�Ki(�f)o�>�B�  % AlA�ve:� GV-**("� d�R� � ab� �0) !.�B{"B/P$t} {\bf0��:} �c�� $k[[x]]E<"` ~�U%����1_8k$-qp'�&stQ:�#Cauchye�>��y}textsc�}��0��wo6��[f(x)� n a_n x^ne]5��g b ���U*f*.,a2.A9Der��  � i.? dx= (1/�QW*t_{�"h} f(s) g(t) ds dt / (x-st)� %a[$#< )p �"ast :ŝ�&AK �(s)�pt_�Y (�~(dy}{F(y,s)}%\[Z *X *z}{G(�+ *� [)��{ ]-> A�#}mdy\�pdz �� j)} 1nof �@�y��*�*L�\@ioA#% G�2A.6?$L_M� $L_2EW $\C^*En����!Laexe�lY�U�%$p_1^*(L_1)"�hp_22)%co3**5j� � c mapU \mu�)24 �0C^*, (y, %yz!2%�$a��%o �� �5�zs � R\mu_*(r� �1i�P��: E�%#M"*W q�-� A4&@mondorn a��9f$\bibliogra {�.}6{j���� docu�J�� %% L�Vv#bles: U : �x0TeX-master: t End: �6�DSH5Ex�vs}y,u�0wjM�ewt b&04L�s&�Kib>rf& tail 3\q i&C4��� ��9't��!3��= ��K V$.�;ubOU*{ � 1�; L �~w�I�ᱡB28�H.p<=i&���&�opefN�L�t"��z(65 \, +1303 +102W* + 4% +6K4 z^2 (4K+3)"�1)6521 { =� �is2��y�V:�s"�^$��6(.�nU �#m�� �m-)#Po\{�(array}{ccccA0 0& 1/64& 1&� fty\\ ?e)&# 0�0& 3/4n 11$�1�202& 5/4�� ��0 \�$� A�6@@&�tra. �I2�#5F#�:*�@E�glin�lT�\i�9$!*�G1$ & �> y�P�kar']��X�R. &Ga"W.tQF[�)�*�>a�\�� ]E)'?a:C6�<W\cEe\��is��t&�.g&�u�8a "_Ag spliYT&=T_0= w%�1� j�426��+&t�&& 41 KEQy,.�7=�>e��4}}j����U� -14�.4�.�-�Z�! T_1&b� 37%!-25 156�$ -126 & -4� 88$-542$% & -� 85T-52.G -18#L S -77V] ��Z&=(T_1��.i T_0)�1 f�7�29�588�348a-1 � �4!N-50�� �-� 43D-27D -1f (v�.�M�\]&�V,�� "YUa.&^ a$ H^3=42, :c"i� =84.Q� as��7L]O�4T �.6�L ��B�J 6BO�!� N(:N�K�]a�ns�W checnD�s��Dz�� �!� y.&�r,�'�3�;��7�/Ip/# � O-96$.&�\�)��B.���T� r�#-a6D=>�64��$v$�,��#v_{2p>�� 14��V�v�!u�� a� -2:-a� -36?E^�yJ�}Ww=1$��) #��mbda=2&�56c�)1��notT sr�2.�� iW:=2;(p?gAtF}�jet ��ezB/ e *wo"�0}l%` j^Be��&p � ��%��1=234=0�o 5=846=74382  # 7=8161452%�So�3 EvS} �Wa�de laEvan h9�s3da1W0 hier zoeken?��V� 2��e$#A��9� _P&� S@�Ro98,Tj9�NI�E�r�sng"�S!A,/%��th B."oy�^of�hcLXal�&|M. �)ouBven� aB�a@��XB|8oM�M�� �ide^-Aa�-eJ�s��}��k�&:BhH�� 7��hO/s22!���t rmer��"��+� ���e�� L&=3^2� ҕ 3z(173 +340 3+271 2+10 +15) &�$-2z^2(1129?4+5032^3+7597 2+47z +108�U, R$+2 z^3 (84.� 2628D3+2352+675�.O-�(29!^4+60.L47 2+17&�26֖ +z^5.�4> KRij� iof&�=���� r�&��H_� � � �  �B� � �=^ *� � ��� ��2�)J& �V �2& w  �� �>,# � $)1< 2 3��($�)" �@ $z^3-289z^2-57z+�.�u�:��2�"�H&%�#$/ip6">pK �h_1}V� 1Z n -9� 49I� -2-1!>19f "E�!J-%� D-7%>� D>�'�_Tb�\%�"� !�6~r  � :� &S{)%2B G VI 8 be%*��f_3=\Ip=5�3~� ��8!��39!�-  -� � 4� �8�F�,T_i�O-D3F3�201}b>m {� En44A� 39Q� -26I�33� -123�\)n 12A�"=� ��21B -195>�BX"�7#y��s� - 1}$,2�� e�3}"��K.� "�]J� '#Z8�}r� e1Bb a�E�\� >�u� IFE՞ -F� F28�3 e*��k ��"\� "n��22}�!.Ђrq ing wjby $w�y( )$�7w=1/zI;A C 2!O4� e �V >dL&=S� z:�5*� 3+42����3��+176�+�6x74>3-4&�^2-481v-10�a�� 3: -5162^3-72&� 2-15"C +46�-3z^4>� 5.c 29&� 2+11�+18�1+3^2z^5��1)^j!�* �-RB�.� alsow�2t� of&7}!� ��1/I�4��/  "�=��N��.U � ":��&� :� 2��(3 .">t�t 4�FZ e�����$�"89o?� ��. D�r&stC~ �c "�\[B{�1e�Z����&�& *�5�O�'F���DWeW -18 "DbL���պ!�����3)*VQ�gx-�D)�a( >f _{1/�F�2n� �\aBe�:w & 29�- ��Q�7� -7:2]-69F��PN� �A���%-kV���QM�n 15� �-47El 42��( -42�M�26 116��! - 5M�2O-21U7�M�37I�34B�B A��a�.�&� �2 - $�{* -;� �O  �� VWN 4F� R|f"�ZNAS S!i�-��J^ nJ<5 56I�l�!J!��w�il�a�:9+s&�"F in a "�b "*� .�:.��3. O�8�&�yIse2�d� B"���is��c,�i5V�# easy&0see. % kernel��q�?f� 3�)Hb�d geval die! i�$ lijst von�iy$ug� en���OFu�-"a9 ! w�93e"� d:!2z("3  2 (1.� +5� i� 2^�2 2=*G 23�r�47j�he>U �r� 0&��D��j � ����R1/2�N $��� &��#�F 3/� Z�,g V�b�0 $1-136z+16z^p�*2�B�bt!O�܁F 2�����d (1:qT�~V�i@ %�-V�"�?B�\ "� 2Z� 5g ��3 14 �-#$& - $6%-36�a-�%7� � ��� � 1a��:��� .����1����$b�|1h�Y3�-3� 20�|�0!)-3���� &��- �%�b�B�On�C*ca���i}ByasI�_ V7ZKE� 1�E��B� A��-N�No�0��&$*�� /3=2�%"�9 H=7a�WeMh�enough2�'to@%C�JPlas(u��ofG.���=�;�1)Ewe_%=� ��7�;1�D�7o� l�&e�fm�lu�N�"��1a.�"�9�w.at&�PQ:lucky.DDB8.�K*�g8!"H &�!"Q�6 !6�nMp.�BoXAJ0��L �)no2�r�!6�6g%��IaAB #%� v�6 �5f��&�6 "�-I(Ze=+ l�Ul7Bbe�>2TKinB3vby RAeM/$w onj:�D fronb�c�ed.�fO 4} n�ur! a"�*!w{;Bt70} (218��!R;�E�*6 )Pi:V*i n2dFW LB7BZ42z(19"i ^4+39*�+30.�10"+1:�+z �I3z*118"�^4+1173[� 2043"�21&-+24366_.i^k 3 (5*��"Q^3 - 345�^2 R58&-10>g -6^4�5 +1)(.�+30� 2+42�+15:� -2^6-^�+5:� 5e+2) 4)� ��� &�-7/�&�nʹ � � ��3��J�0� AR� � " 2� � � 81$N 2/3[ 3�84284.8� *�� �K�4S���(1296z^3-864�]168z-b1 2-cQ it�6�!xIo!$\��%�2<;=D3=\bar� }_�.��!�rur� �Fb)C�RF: T_{-&7?6� &�Z�AD%��� 2E�� &@V� MV E:�  6<ʧ � M-� �/!-4�fm&b-�)r(@8 � -a� 3� -23>� �99F 1� �� 25 c'+�8% }�%*t t 4�  f+�>�V4 I�J@ �6qR =�2Q �!0�& A]�-��- %�-3m(� �!���"( !c 2 -106�BA Y ��= i�` "eD=66%&eRX ��V�)($i(aR�)� Fen + ed�s !�Kr = -f� &F� I�-a�AE��1��!b�DlsVZ B<). Set� "? "� c_? 0�;)T &{+� X �(Gd$ �,� �,e�DSf&Z FMtBZ �,C�* VEQ �0ar_ a��eck}�T.TMM6[ �a.F  p&7AU.A_kZ� E���(-ctvY6b2���  >�5 � sM6mhl$ s� Vca�u�nr"�p�.G1D#52y*� HwL. +\newcommand{\stH� 0mm][l]{*s.& qm}{B&?&�qtabwp }{|R (|l|l|L|l|} �4 H^�j*H/& cd |H| &˂ & Da#t& \+B>4�1l|}{DdGp�V�Refer�^"� 1&148\qm; � 4* &"$5} �$&\\ 1&22&-�I 2 &8 K13}&X(6,� �*et�~5�~2�y,3)8 &� KT}S34&-288&�&S� X(108T4T1,v�7� TM1 T46;28� 42� 9} &ǁ.T ��4�(?)�Al�� DM}\\ 2&2!S-4 ^2 2P71�P2&3!P56�:�12!P3,e >P�� �)Q2&4!Q9 T6�7S8^�1M T)Q3&42&-20��'=�8}�fqv�1ANX(61��2W4&40&-1%IBW10�4b�2� O �4&5�1N52�14�85 6g2,6) Zf3U g 5&38� 00\st � }R30A�B \ 5&50!8  &>��79 87 128��+Y4�O�g62& -3�6 &� m�63�� \\ 6&3aA7# �).��RK 48&-U�:�=95�e}�q�2�AM�2�7i�12-�52�1092�� \\ 8a� !3 !ZI�296�>856&-17mc62i69�7]h79Mt6�6�L�9&3�:2���� �7���\\ 9&54}p6�4!��.I6-� �10a��6��!5�^ 118}m (3N � AS&#y410a�"76i`A�S2�� &\\ N6�e�&�+=F 51}&�C�Byj j: }j�ukrel{&h� B_.) [nr.�']l��2i?3i?5 672�f�q2a?Ia�62K26�K6�n% ��]�90Y�9.���m�]#e6)Q!3&5�2I!72�99f�)�$57C5&q�CHbs`6nTo%|4e�9O76122o$7 W*ȁW \PW&3Y0!��#A�U�8X��15eh7�?  � To}_ӇZG-? �5&6�m5)?82�2e� �1�#9* A< Bh�A�6af��R�6��6ee12�&�][,X�V72Y[Ё� AR22�7� ��i7�M-7)R�I))U7%E1 !� M-V8e v :V66z�a� 20&6]�96���� .�.� �5�21)�0�596�54��CI+:C70�C4&7� 1a�& ����)�2j�zߊ �*6�)25&70iT�����106�n%�8&7a+�1.�2�ta+N�6_�\ 29&742�1.�25~$� 32&8�~�2.�4��\bB��.�*s�IE)V81V 33&7� 2-V26�6 n�4!V e,& �9�25�>)U36A_ Y L2�~��6&8��X & 13.Q184��VR=PX_52�91H42a�K& 14&� m �z)�AO��q�7"; u�Vma4.�� MZS3M�)� V� 44&9a��� & 15�?&^�Pa{$A_{22Or '$}} ^IW1057&8 9q�5&6**� 25!�!�56� -9AE17 �5R9LF_1(Q_51I �2"l 57&9�C�&I]R24�� j{\o}tta'�;}2� �{Tj97� ���Cd%Nde�� o 2005 p}�J,HIF Submm�UJPA \d�I�s[10pt]{f] cle} \use��,{amssymb,amsmm} %.showkeys:ref�"}V� %>��cm hec\=odde;Lmargin -.25cm %\even.1,top(1.5?.[esp}{�} \Ry{\Rtarrow2{\�u}[1]{\EUline{#1�.[�%( !):Hd�display^K:! NN}{�thbb N>aCCC>,tilG}{\wideth#N}_q:ef��{\mbox{FFre.�u}i� rm{u. bq}{�B>#e#e.��:b6�:"e"Cq: ba�:: e @R8qdiv}{\varkappa!. {\btd}{\�?a}%{\big>�dow M2t!0�O:-up��., half1y��d$} :� tres*\�\ptsize �3MqF7j.b.8 njV7kz7kV7mz7mV7nz7nV7red}{$x^Q4[s]_q [s+1]_q$:;f}{ I�{\�m$!�phi$}>,sen}{�r>Gh!�at�z sh\,86(l9log>��o=a` >%2 $binom}{{m\�|2a.-"n}{{nb"ncero}{$&tyset-> $fami}[2]{$Ia0\{\!\!\bt{l}#4[1mm] #2 \et\r��.>CracionE)R\smallMQ��}{{#2}J� xmed� 9 3#M�:pop�<,cal #1$>'qnf.S[O ]_q!)�T�8 \title{A $q$-5� og oyYRacah*�_2L �,lg5�, $SU_q(2)$\f�\no�Wnt��&l�if}RMSC�`$s:} 33D80,45 \h�� \t � Xiv:A�`.QA/0412540} } \date{Nove��25,#h4} \author{R. \'Alvarez-Nodg�4${}^\dag$, Yu.l�Smirnov(�.; R. S��stas-S��s �k$$ \\[5mm] I SDe�[aQE] An\'ali�d8Matem\'atico.\\;Uni͘daV�, Sevilla. Apq�P1160, E-41080 Sevilla�[, Spain\\ \small${}^\S$Skobeltsyn Institute of Nuclear Physics. Moscow State University.\\ \QD Vorob'evy Gory, M 28119992, Russia 6��star$Departamento de Matem\'aticas. E.P.S., Uniu4dad Carlos III 1drid.[ Ave.20T30, E-28911, Legan\'es-8 } \begin{docu�,} \maketitle�abstract} We study some $q$-analogues!<`the Racah polynomials and0 of"Dir applications inoryF represent!4quantum algebr! \end� \secQ{Introdu } I _|paper \cite{a-w-1} an orthogonal�\ family that generalizes� �xcoefficients or $6j$-symbols wa� �ed:7$ so-called A!!?B.. These�s were5'op of !jTTAskey Scheme (see e.g. � ks})�T contains all classica �i)�4hypergeometricV Hs. Some years later�0 same authors |!j 2} i5) cel!�ted �-Wilson.�. One!��Limportant propertiesMM:*i!�at from;m one c!�b�� known %�V�>�!�2s a�$icular cas!<$r as limit (f review oA�is !�8the nice survey-,!�%� maaool-�(se two workI^A:�AQ$basic seria� respa vely!O6, other hand,ED1�of �nu83}ID also [��n Ediad@]{nsu}) considere%�J(t solu6epa second order difference equu�6�-type)A@e non-linear latt!FX$x(s)= c_1q^{s}+c_2q^{- 3$. In 9�,�y show a�2�AqN��ANbe ex��sed!�cerE_.�!�,!�$such a way } recov56$results byi \& i. Tha�terest!@L.�(increase afq�appeara!U�r A��<��Q groupq��dri87,fad86,jim86,ku81,sk82}. However, q\T first attends to buil)Qq� � Wigner��( formalism a$!rsimpl�� �0 $U_q(su(2))$I�{ki88} ��Y�|{renato,ran-smi,mal92}) becomes ��%�t�inge�6Utimately�4nec�� with�. �ua��թ� a�Clebsh dan2* , i.e., a2C-" B \ $u^{\alpha, \beta}_{n}(A�,a,b)_q$%�!A$dual Hahn .�$w^{cF6,Au� , it�:betECo uAPu�t��ej ---in fac9�J�R_n^{�,\gamma �N,\delta� �in-��.>���defined� 6i� + e N}s}$i�depE�not onlm!<#V1tR�i�arsuslovi� %&f[< }+a $s-\mu} ]+cj�6=2v!gA�"{s $P_n�  ! *2.� �5:[6$ (SODE0 H \ba{c} \displaystysigma(s)7 \btu}0 x(s-\half)} U \btd y(s)#d#$)} + \tau(� E'u ', + \lambda =0~  =c_^y, �  q^\mu= cHc_1}{c_2}, \\[5mm] �f+$-f(s-1),\q� �+1), \ea� eqdif-q� or, ival p  A_s y (@ + B�+ C -16� 0,:a -new e  $$!�l!�std= \dst �)� g!f \Dg!71� {)J -C Z�' a}{\nablXRD%� C� = -(!%)3 a $$ NoK� iTx(iH )$. ���W wei��ano�Zs\foot{�(exponential:&% \pm �W $E9 pm\infty$� 8erefore insteada�x $)��\should�eqQ fun�8%�i 9�-�$.}� s)_q:=2 and :�= �LvW &�1:*Eq. (�uU�"6%� <[Eqs. (3.11.26), a) E� �1M� btu ��}�q�-0�Yd6+i�}։_n Qd-,1=0\,.a[fm�-%�iKGfu��r> be  ed�6�Rodri�Vula�Bnsu,nu)1�� B_n}{\rho�,�d^{(n)}  _n(s����  := %�� _0 = 5hd%_d x_{1}VB2 \cdots��= x{�� odeq���� $x_m�E$x(s+\mbox{usizy ` m}{2}$})$�\= P(s+n) \prod_{m=1}^{n}MA s+m)� rhok�$ >)$o a�=a�!�Pearson)�� $2�� ��left[w)%|,(s) \right]=�Q�[ u :�X1/2)}$,�Eg� �% 6+1� -�=�) v+��abt.�} �{�O}M77�0}2$.�I�!ͬLet� |� a� ��0rho_n$ satisf�&� $��N0%�21%3 ͍%7$,QJ�)�H n b�L:�E:-4+n)!6!�+n-)u1Aw)-5_����x_{n-i-L # -s-n� ).�eLui�k}= �'  � _n(0��i.�-tau-sig�ybed$$ �' = ��� {2n+1}}{[]_qr�E}_>�_n^> ���%n+� -2 �},�m�2e_aQ zeroq]Y.I)$� n)=0�� From�F��� �licit�4"\�� �([Eq.(3.2.30.vPE@_q=B_n\ sum�S 0}^nIL[n]_q!(-1)^{m+n}}{[m[n-}�D ��ENm-j�AH�� } { 61 �� _{l�{n}.XJV $ � m-l+E� $}) Y i� (s-n+m)}{eX�޵"�s -expq�-��$6s%�{\em &(D�u�}�g!�� Hor� rey�$$ [0!E:=1� q !:=[A�[2]_q�e %n?NN.AI( n be= w"*v �=( � most&3"_!> {\it q-}:� �M�$}*���!.}&� = AͲi��4 [s-s_i�= CG2s}2#(q^s-._i}��i�A% C\neq 0��h -get�!����!!�`aD (49a), page 240]{q�"B�" array}{l}2yD:�H D_n \,\, {}_{4} M�. $s=a(i�%���fin!Ed%I�x(aE%-1�UF}{AJ 5) Zqv� ijalternxway�s��!=%Y7. A�)we |�(�\J-i� 148]�:Mx �� 8)<0[ tau' }-� [n+13 tauA 2(}�)3(K+1- +)� oputxM�$ (Au<& ne�*&?J ulas*`!2�7 �i�]�B_�&����G �mnk� �<0�1+c�-n&Oa_nQ���exp3=� of $��n� ��52) 32 q��split}3q _n =&\dstm�A7 mu} ^2 2� )^4}ש�[>r "� �}!�,� f gC\� -n+\fk2 }��1-q^n R) . +.� l ���1 ���U-2(8A�be$ed<�$P st�$�^sa��[. ajR.Q|� ite[\S 5.�-r,ran&+ \!�� 6��>���_*l���-U/�� &w#Br!-1}} P �!J"for-dif�s�(.�#9$ 2�&� �`� R� *� ���=p _1�$�.�.� rewri����-�}>$� (\� 5Xxa)}y) IU�Z%�5�)��=o%�)*$$ '0��ANa�/��-z$N� sA. V� Q.U��E�"<"\ difeq-1.1IU"(!E� �f5��a*� ��(degree $n-1t<�8)$����\S 3.1b )!e��� at!x��C_n {QU�=.'C�jao 4�? �2. C�#i�2w#+Iru-�.x2a� $!���!}RI &� [:1}*rh25�=>/{}V�$�2,eNS �|�-:9�o/E�Q�=� �y�m ޏV�-�_2�-!�2I��N�9ps2�I5!�3ti.%Z:Ys5.6Mu��%\:O> 1O #"���Z%_n'��[ (&G ? %ZB� .R ��]y�3� Then,&!�B\�A�6! f ,*� >od3}�"��}M?�} '}1L1�1G{2�2� 2 6F {}F�� abov&=&idU! ty $����#� ���}I)}*�uB$�)�/��dB% I$ a"�*�SODE �\��s=�q�  d�)�S{c}� Q�R�u>� � "�1eQ��'_nQ� big(5�-- � n%>&@%+)A�)@ A�}}� !+�_q�A�!� ��&  �' ts�)ui�8%Sy�!"�Nik�.ovnUva �nd��( 5w�1�2 an} tq��A_B� � 3h"1.�(a|q)_k� 3 0}� [a��tilG(a+ke' A�� k(q^��u "�)^{-k}"J k4(.-�ka}K&i�sim-poc� ~nx�Ρb�$\G$թN41 2.24-,%{c� �"�: iYXj"5b�� �08�{ '$(s-2)}{4}} �w6)�-:% � )^{�)z��{�;q) 0 �a_i -2} b1m}K#&E� ���5&� " !�6�} �d49"5 *%� st&� %v��?(I�"��*{27e82S"z)>�\mu��n ( a \ti�<\\[7mm]&!w +v + ,\, A�4M�&| E�-n,"{+D=`4 s_i, \ ,�� \\  T  �, � .B5��"A �)�'�R1 �@b� {����1=�1Hw� �id�BR2 $u�<aW=�}v0"R=6�6 $� �;{q}[s� {q} �tiD:<-tesis�>=1 Fo88i-C�-one�"�h c_1=a�e*}}{ID{-2&~;mu"h$c_3Y.1�1 <).="� r�71�) chos3��I �#��$C# s)�': 2s�48 i)X�}2}}%S!$a) o b} %�-ab+ B })= [s-a]%l [s+b [s+a-5 /-�<{q�'e?D$s_1=a,s_2=-b,s_3=8-4=9+C=�%D(  �)}1�4��$A=-1��$let $B_n={Z n}/{� {q}!<A� ~. NowL7~-l�"���_n_J�+E)�2� ^n)� ^2�+L !e[n-w �A�q� To .�*we�6�).�8tA�E))=[s+n/' b$�,A�o(&�)=-n/2$dge_b�*e k* =-[2�E/ +�2'(0C0(s-1"Q*)"U/�n��� Tak!i�Iaccoun�)*a/� _0(s&"wP �!&:D*�)4$%� �-��s'g+i�A�+�+$$Iube~1�B&=�$�@� $ $}*�E!2U..�EIp|.�l��!Ty +a+1)��lG(s-Uq)m�b+1) q�-W5:G. -� @9E�Si�$-6a)�aUb b)=�"theGRG2/2Y �ZX�s=@!1} v} u_mq�J���/[2Ň�0,\esp nR)m�z!�:FriEs $�5, -1<\a&<2a+1$.�*us now �:fRm"�.@. DI�0Ei x!h�_2�l}E4e�S�,�&4�}_q(s+nEL.2]]b$6oNg.~ .+l-AnR>I�^��E�R|�/)},���$�!0#n}=��!�&n� V�)���,Z�2*n�1[\R� arrow \L͒:=d"4 ^2 �� �RF�e�b�� t1?=a?q $I�A�a},E�"��� A-s) �{ )��^s}{(1-A� s&�!ide-ga�%q{A have!�F�t ��=\!5U)�2Dn-1�~\!�@NU,2Qr&yf'��i9�^{-�\[0.8c�:0= ^PCb-a�R2aj���9~$u +b+n)b!�)��Z�W5Z�^f�2�ta�v!X2& ]_-[ \\[8I<dst"�Nc �-�gV `Zn @1V�!GU�^DU�a)Q�YV�tZ�=XREi)}��=I�!K\�4�s2���{(n!�1,5,��-fb+1,1-!�n�}{s}4-1,�,� %f&*2��$$R�<�J�JS un* lastOion. If� <>&�"9 �n}W��n}{4}��-UJ1� &���$$6�# s}[Ie]_#!�$a+ h+1}2+1k.(J_s!OC.4V2�"� ��szV}��l} S_n�������.���f�K�\!�U �uA# q�n"� ip\!3��B���q4A[?YE�21-bMH+a!.I 1)},>]1) [ [2a\!+\!n!���s(1�-�I�)}y+ =F> \,_6 �3_5G-i \!1}6 {c}h%I�D�>Ia}V}\#m\ .�%J\!,VLE7b+FF)��E2 A< 2 \! \ %�-1-2n# _V � �� endQ�B;eZb6)P$ ds:a�Hy-�Kpoi�R2*3 0= <"�0"�0 sumxFE!8�II.21"�($8]{gasper1e88_{6}\varphi_{5}� ({a,�a^m -. bcAak} \a@W\ .1 aq/1(aq/c, aq^{kyj|g,{\�M bc ) = {(aq5/bcaF{k $(VS �!� $k=�V$a��M��bY�$, $c 2�%�?S a��c F5�Uq^ n2e� -n+au�I@e�"# �. A�4�G0\xD��G f��ř-}(R�2#�.�2({2�2a�aFihHI� � *�&�6Ze��" �I�9?"�"� ��n 9� �  2 !bC-n  3�E 2n+2Fg��$Su��� rl}%� #+��� , �w"�M&�>r�N(I�ZZ U�V> !B��^D�� �� V) E�)} S_nm=& !Tm|)�-:9��U�R !D}{[ 5��b -fQ2& # � a+b�-n)e,a%e0M!$$�6�:� r2�]} -��mb*�::�iyA_ &�#two�-{HvrsL6�k �%�v�= 2��@ic:�-m!G}��s� 9:)�d _n y#=� "� 2n} I"n- \\ &�%)>��� >�M<aK<�s�8������� 2� B� \�!�VOP0\/pol-rac-�=eq!�@$-F+)?( A�� )�(a-b+�!n �=ta  A�q! !�� )]�=Y >ZN>S, a-s,a!J� �++t!<2�-<23=<eq*�SP transa1*y;&/&III�7"- "} � &�E>w�:-2�INji9M��2-%Ju2 B&�?q ��-bq-b!�A�\7 �a� ��8 ea. ��,c"J�ޚR-l�n (.��i!R,)M. |, .w�\noin{+ \textbf{R�Q:}o� "a)u�5�/c/&%"V]z Y< multipl&�]�/ dardZ$R_n(\muA�b+s});q^),q^E=AKa-bUS� $.\\�� �rE�cso�e valuee�MPval-a}2FV�a� � RA�? vR\�5���c� � �f�jm.1:�eq�t!b:mVbQ__ )�-�k F iG vZ�m-)-!<%ze: } >VuJ�6iS#m/r -eJG leaFA� iM�"�8,ula"�L {Obviousl;K s�%��.H 2}r_�<ݰO�0P.!�Q���1rac*EV�sQ� =&�Hs� � � �U .U U "� ��A��� l  +Cn�0ek�2k29�s+k  Z2s+!)�k&,n- *"LcIk�.��� i�p��5#k �%8j � +n-k�l) R-n�q �k�.z a� from{+� ��&�R����_%U�'lG� � �� �Im�} �! B ( 816 \\[4>V�2y2*b-��'� �j� 4�)i� �3"�'�$extg�bcoinciden6���n�31a.�b}*1R-$. {From}Cr�"�r�Ky�D�i�/l�\�R�u�=-CA�,9�} .�'E&�n*�UEi���}�a>2})�*sx$�>j�!�7a*�S!"�8$`_!Vdz(q$a% fact�!�)� �ck]� =E�Gk(��2YK2�M�FE e^$ -c_3�=%21S&��+l12�(a-l"QN-2c_1�Bc_3.�."E8r"�(��[ \�.�r�C`�$ti2T L*To der�]A�*�6R,�C-�t�C��I2�Bl�A~_n}. U�& ,�?& .=�&"� �'%���!�H!'�*�E [&! 6Y � 0+e_n��Bs'�!o�(.�DJ(Ja�"=D�[�^ u�(*�]_{ !v  [�� �"��!F B:M H�+�,W6m%"fB�)�|_�3^` !_ D�_�Q�<+V �`}(*� } {��f!&h4}{|@{}c@{}| |  }\h�_ L \ DG�* &��SQ�(�g = ���-ac$B U c i (� i�6%\script~Y $[a>K]$A3:A�)uW& $ I�Q �� �&� )�T� L � �N } .�%�76�n�)6�)n�/-Nf �Sd/!��}/ �s-`^�v� �/ [�  0�� 1r� 0r~L- zV��_A��� [( o- + �� "b �-2E20- ��20E�$ n�w.�+^��mi� r} $� mnp� n2)+[  n�/�2b�  n2-y �e!)M�%�($\\[3mm] $-a�I:]b[-$ ���8e$\ >�&1 _n$ &N���6��dnCBOa���AEq!}$ ��>�d�O$Vu���� )�*� r2��^6D^ ��8 bO ���")\, }�6$":�^>�\,�a�-, �-)1 {1)*�u�<$ � 0 �q�7���k�)�F��\ ]N�:�65 ) L�6#IX}$ l\\ >�%� _A� �"�.� * .Z6�"� �b"��Oc}?`st6� )�N��� ^� ��X ��v�!~�� V� $|�v)�N��P$:6b Q��}P*W   �*"�#�-+F�L 0Q�2U-�2Il]! Z e}-G^4� � L*�-h2} yiel.�rac&Jf�DR� "�2�J=�� �ih :� +19 �/�chalf),a"H,bM )�KWgM�B�2:J�D8+ z� = & n �ޡ> &f � vN �Z�"�HJ,|" %x-�d3a.� d3})�48�p�X^9d "�F�L+A3m*u^M6HzkDbs= j�F; �'[<8(s)zm+ErR�Y�A(]j�JB scnd2�&�-�E2-Fd!�nS% ���>��j\ �[&�G+JD g �-aE�n�5F�vFA%Fae�Y"" NBn&T> �9.„>�F�e �{k9o<�*�a�o sec---u}|/)��7X�oAs7,Yp��z GBf�{r�$."dpz+A�Ys 38-39RO�Hof all,2+�& 9 9�Z5�7?-}. sSwriO~!�P�� �,5t/NG9C_{tn}m}="Z[,m� !=�Z7t+"\sqrtURŏx �Z}}{d_n\N�+~Q�r�j�d_n���\&�;�!!G � as2�onxt�u�noUB�!#rbUlet us �u*Z%�I�)6*�.]q#.�3t-n��7 &� = Z�1+�%252ph- � � S4�<�E R!2�)pC11� &I . x(t)=[Y[t�=qABu}2� n� .��4]_q$,�b!�E�\es2p of"p s-a$���\�`l d 1$)A�$$t=V��GeD;>�de].�%---U>m% 1� +b��F�aY1-F}---e��I* \u_k�' 'At),a',b'�W& )�({$LPb'-a'&� '+6!+a'� 2k" <-k - >�b2<�!"q   &j�*k, I'I�|,, a'-t,a'+t+{' '-b'�   a'+b���'� " �+dua�  ��%r�,change} k=s-�3��^ka'��:�{Luad b'�eR , a-=S1;)t�E�$q 2�$y�'.�}�_XA}��t)$��sa""p*�W�K� =rel� 21 t=a'Pc'���\*BZ�9A'(t�#t� =(d_k')^2�+k! 2> rh7"�k'f�9 *���"w tG�a�?a1}y�6�DI4 $�Gb�4)� at sn($a' b + , t k�},Furthermore,�])���eQ� �n�}&�$��$Y:�"�f &74 \!M� "� qO"a#s�*�f{}R=2��/o7A�� �'� *�~2���:Z^��$j1) �3A�0� �O0= \mathcal{A}����,n,s)rnV]� GkzQ=2�{1&"Y5El���+�?�9]"v'#(>:"�2 %a1k3[3&==�"�M�>WYU*� ȆA ip D },� >>9�i�HUIi8f, oKAy�U set�] _q$ ���^]A8.j�.K)� blassociS�toi F:��.N3X�,� 8�� B$�9 s �c�V\h�Y)�Y new} X*_�� ")a3 vZ�J�0 $ 2!R�i72�1 *c@�;��z*�N�]BmZlhLaY.W= [t-a'] [t+b [t+a'!) &> -t.= �n+>�� J  b+`De��$ �t,cf��� -t-1� A�6�K�q-] 5 �] T$� _k=[@k V.? ]_q=\�z)�P��e&Ai�w_k�jq0n"�%�NeE^}ZC% "!G%C'_k9<� [k��:�� 6)9'+2 1Jj RU� ! Z1H! �.1W�k� & }-":.E8i%8 b 3,��K[�r+4 !�u!�� � O�:+��.YJ�p iz�":��&j�H?^�2t%+=&xO �9 F�*= [k+E��.�. �6l��m���!���E� H��]�. F�]�)��X�#��>��'��FJ�.l�Gus��atf0 \pm1&� is� *g��8{k'"Y Zi me�c>�). AfC���Y�if�,�[?!0F�G2�`&�*r�A�U'tu_�,^M�Z�+ �q+�.(�:-[ZC R���� #+�+�*{)Z�= �e�^bu�[! c}�nJ�+R�2R��B =�\ �� 6j:eZ��(Q�a��� AGtI��-"G}�#E� 6P+�y� �"� �dmfaV&s�9:� �,,=M�va }&��t) x(t-�}b� +� ��[tXb!��t �Y*7M�G�\X5-e�[��\!-\! �հ��28�""`H[k�e �m�b=9��vQeT�ris E�!�M�J��_~�$ sinc� �e�-�� �=-� kL� �!"� " 廲�: ���[ $*�Cu}vl;"`� til}�8��ro+ >1�3%z"�2 �Әsugges5d{5?{��[It*�WTa x  ( �[*�Z�#� � )�+J�ZA=;Z$�Z? �Z 3=j* 4="UG�*Ht��ua new;�*� ���is*��"F�m:�% �,{\ al�-&[,}a �.�$d*�aV;�6(- "-^V(!(!�*D(, a1�2`8)}$} eAll�H�ha�eristic"��3rxac�Qvsame wayAv�6 M*�ey��G�8!WB2~� 2�v�"0� ing � \to-2rLAhE� \to @ $�� "�  pa �n �qa���Z�g�W���dG}n$. WJ8l��mi�m>12��L�_�~���"��}��1�rab��1��1*�1�S��1��1F�1�!M{�4�4 ��&=,�2��%2�2? 2�3? S� n2)� &�2 ��1�=�B�0l�\ _�-J�22F�nEKn6R 21�2& W% ��-�)�%r)�$1�n)A�%�N-\Q-1K1�+\ `"�Yv �UE IaO�@2U� d2>��  ��29 +q *�26I�)] �&]b6� �jW&� '�b8G  -\!s ��  �5� U ;1�.).� H)4 %�P����u��*�2�Iy #n%�Ra-C_q�2J.2'a��Jb%�i� �d"{~&�2JYi��J2 Z�}���F������L$�T�%%�L�La %�);��i�:�\-\-�Mv�m�9�4A�%F�#)ENIa0' T�q�/5D��)�=r-\!A �` �R�F&!����^�A�$63f�2�3-A�� � ��Z!Z)Y  6);-�B0 ) �!��^�>27w �EG!?2 �2�"T4^d4\M6]:S#rBKTL.�� $2� w��&3#rw�%� g(A*Vz�2zUT4a&���ZXT&� �*`M2�XF5L�*2*Mw(�ZT2R��_T�O�BPQ .QQ �QQti6cT���erm"�E:�BUs�&�u,!���^V�T&E��H3 .CN�_-�EN (.�|q)S��B�T{}_jrV�:�T�C2b�T5�ʥQ�FaM��TJ�T6�e8!���j� 2a-41-��%�TF�Wy��O�.�,[].�WF�T��TV�i��S�a�SJ�T2�u���i�.� Ɠb�T.XV�T�Z�=� a=mI QU�eIm\ �� B[nY+"D-�n+�Tb-JU,$e� ��^\no3n�U3a�*X.5z�$ �/mu�U .U�LUݞ6s +*U&HA2��+:�6 `�%N0�N�*���NA�>#U~y",6�I����T�JU�:���2EJ6 �TBT^KJ �*�/�::,B:U~-2�P&~s��a�\�St b4.w)6!Zm��� F5^�95��65��4�8NU*�F���DU~6�}--�6-�S)g�/:,_RPU\&a�h~�*� ��)�{s"�2�H�-�s��}�f�� xK � ���--ȢEt;:NMU{k+n}6QU DPU %UpU&� 4 �OU G�Hk[U�mbq��racah]3=� 3�)g H�M���U�&�9"�4lU#=�E�%]Fro�sٮxu��k* s3�U%~��A�A"�U-F&�T��h �&c+!�[n"i5�* $71 5�E6|U~�2�M�*\ f"h v��j�5��5�AA1ѩ6�U�in agreec9������ =B�U��R�U��U-AeF�UE�"fz]=>*V�U�C�(�N0jkB"l��%eb+�)�Df�Dto �E�70D!]B�D>�i�NK&.��= R}� 6U]�)Y�D)ZD�;��:�>�D��, 6|��x1�B�D6;ƷVE2a^U�^ �� �">Eee��ulaqg�Ei:ing�EAc^!E2r��-�= f�bb�n�08�S; E*eE��v[}6�{ NU�}ADE�V�E-_��* )&y)��&vaC%o�%�u�u��E�m��n *t�E=!�6�v��-�BF.�"��4 F�$�) eD0$�3��#.�^E{(a�6f6t+���N&?���H@ use*,sd� meth�C�hһaJCtAi%/�"86�Cr�����'&�E�.WF�7J� 0�E�%%�ّ"hCm�� *lC2�vg>-N'"�C� �C�>��C�>�D�G'? )�2d�Cfa=-'!�!�p'.�)b>D��$Y�y&e%�U� 2=EDeR�ɪ� :,�2Z*z� �.x"k? $�rs-̗�2m?2.C�8qB� �.vb4}2-1$ (Hproofa� simi��/�s�� Y��m�%{*�I%�Q� o��it �7��:OEA���D*�,�+s��M2]��t.��BsB)�B2&�8� Z�B.:"!<��mes"z j"k"'-2b'}H9?C, -b'-t,�B>�B.3,�B�'��B�>!�*� "+e M�CBtrii���B��B*�Bm�T Z�%V�3�NJ�$ %���BA�� )>6 ��6�B�z6.m^= ZA5�C�|��BC��� C��  C6�K,:��m��a2&C*�0!�I��,��ar�B$a,b,��m A�- $a�3 1,k,t$r�B%���j!C���GF;"^5��K���3C��7C�-n,��b2�= }O"�f=C���==)���.za^*A�HS1V ��_q=*W {*�C^�C]���!� �C��h2�{K1-N�Cv^PZ"�(� .� *�s-�=_�s� E>.�=�c�� �\:�D�l �4�? CT#n>DECF  AA.�e d5��S 2O ��tBKHD g�hu���A3�1N=�� I��g�$q$F�R�G> :3.�.Q��5>z�7.c6�v� � ��Cu4����CV����2�C gNc� Fw�rn�i:�� ple�j.�ng bot23f�>&� ,Aa�d��6��>c��-u}8 below)G}U &��i��E�en�A�sQ2.p4 {C&��"�NR���� $SU_q(2)>' V{R6u���2<I9~�(u�A��U��sqnd �rence� erein+��KC=�j"D���(j_1\,j_2\,j3;j_{12} {23}B reG=d.K �Uy!5coupl!�s��a6�6��a $j_1p ,j_3��|j_1j_2( x),:jm\rangle =t 0m_1,m_2,m_3,m�m:# j_1mC m_2| F #D\l)� j_3m_3|i�m_1 4|j_O. �C�Z� ones/ �j_3�!B��232�y�%�m ~2�1}.&��R �6-V$am_aj_bm_b!Vabmab�6��C'� -Gordon C.iFE B�� $sui"o�2F̈́h�KQW���by.E def-U^l-x!u12>GMF))}a�~�PR��LRU!8� unit]�myW*_Ky� &V� �" ��reld_� ��j�'u� "yYiC, 'R"d:�&�12�Vj��'6�23� 23}'�U}uB� in"��A,J�is 6P2Uven��� 7.�*�>^6jE_��)�q8{j_1+j_2+j_3+j}�Z[2)Os 23 ��eft\{� ccc}�� & j_2!\�j_3�w&�\}�I%E�.�qT. sa�&�s*����A��= %FH � ��RH=1��\>;23>'=J�G � 3I)n]H�=n%k����l׿ofڿIT| supp��AY� \geq!��j_3 �!�p��s6�1�P�6e� erva�N$*�(int-j} j_3-��.�IE E� !C.%  0E���Eg.�ߢw��׮ae$avoid any �A2����s�$ �a (cau��buz so cc�triɒin�li�>.�)0� AP�>�B(�2�� 2*res!*|j-j_3|� \min�V=j_%,�V (16(��=-k�)%/ f� � ��R ��} t�wer read��&� [� o\�.3E�$. 4 fix"va*Y� A$s=IGtBru��n-i�pval $2=s%Lb-1&  $a1%�@b=�2 1$. Eus pu�$�x6j0}���f!nVe�X�X= ��.r`A`^2��,�g *+��!�B*%2:�C"!�@>�T Zl`-�� �w}�z ,�N $n!� 12}-��!��qa$+j��0Ќ-%��- .&)*�E�&"`΁:�u� set�^ \[6w&j_1=n%-1+t�:S*]}bver�_�,�a��reF���FY�5.17)]� ��"drr�2' [� & q + A_q^-]���Υ�e� \��!-\~4�!((n72A=u#!�[�\i�_1 j+)[Ak]_q�m�TOBL7 - K�� ? Mw _A�.O-!�:I1}6HA��+�� �2�6~IT Start Cambios Rober�E$7 Febrero ?�? %Faltaba��oBQEndnO!m-* 5�%&�� ���F/ +IB�E=+F� � � !L�>� ��K� #O"�%U �*� A.�E�J�eU<=�M-�NpE-)Ap�,A&U I%R[ - =A5!=A�Iz:�%,\\�+Z�A��� [ij�[ w �"�� Y����K:�n 6����)�)2Y% �)  �)}�01+N1�+�% B)�k Q:� - , )&= 5%z ��a����&1+j%�!] s"!� ] -1`J-!RA6!5 jP U $ QG�> 6s���3 ���Sy� �,�*�J!�- vg>7[2&'(��w^ ^eP��+&� 8NmV AP 5eLBig(\�C_n�/!$&WU-W \� �/Bigb�3BN] ��[�n ��"/�%F"� .a.P. w�u_{ޙ,�2�,!N)�-� �h6r - %~� }-2Q}�� �K2N�:9b� 0� � *)��eq 3T&}6j-es7�[6�9& ~+��:N�6vJKs:�\�5 0{i�s�� [j�+-! �Y -j�Y �A�!;+��1 [��7@3�4a}B� �8 %��C !�_�(|,�n{�m�-��� ��D  8"@�s��]�2Y "}�y�0ah�s=� �Q�Aω���NmQ�01�  �\&>rAIn_�.��D�&�A&� "����3?�2q j��\_)� \qnf);} a� ". 3+j+�3>%�}!~~� !�E-ZE�E:+ o}� e�,E& b�sI�`I6`!3q+j��+1�" ;2Ae.^�yw� � 6NaE����)�b-!<��%�%$!�{�m 2_"�%A 5� B�B�:�!]� R1�5!q-9Xn�:^!t%Ij}��Dw8Q~-� US-�ISL! �2+:�KA|>�aG12!�T��)�6�t�f�4F�K�Usmi�Qu"3:f%<s8"�3 �� JSX<��6*��[ b�"q��83"ʊ*TSRKe��eF� �2��Z-6j-j|.  &�[2�12t �:,.�#A}_q^>]r�� �vl� CRBm-��27�m5 -� (� ��� Ŭ� ٶ(� WG� �-ኁ�q 6)+X8�/ &+.*2��xSA�-�I a I�y-g  i�oi.i� �q�z�g.���! �#� :'���G e�%8�#7Al$��r�&"�"I�- ���L�!<�,�!K6�2!P�!aD5)"�� L��*<v6�A!�B� !�3)d*' �+z�M1��o �� ��Cŏ ��@��-.IM6�Eo� E]-i���wy�O&<�%?8�8� �j2* ~��l96 ��� q�)�� _ F8��2� %\\& + f�_��!�23��h6ei�=e��%p sF�!�>R��9�2�8 !���BDT_:�, �K}�F] 1��2U �-�=4R� �ޮ +6uI)�> Bp@f & j_{12} \\ j_3�_{23}-\half\ea \right\}_q \\ & = [2 $0+1]_q \sqrt{[ K(-j_1+j_2]_q +j_1-j_2-P} \left\{\ba{ccc} j_1t2^�6��^, \end{split} \eq respectively, whereas the differentiation formulas \refe{first-diff-form}--\r scndL give \bq \label{rr1(-6j} \begin�&% 12}+! A_q^-��-1 6�+ \23}%x@widetilde{A}_q^+ �g+1N�Bg<\\ &\Big(\sigma()�)~�+ [1�)�%�U�Lambd? 12}, F ,j_1,j_2)� :�=0�:and6�2��%�+�HNF!\6/-%123M B��UF�:+%!�q1� -�-)y-1)6�N� �( v�+�.y \quadI}.m�.2Ma !�:�Y�U� $a�({\pm}$ are a� n by�A}, $>� /by \r�A-til} Ee[6�\r�=&-�).(\frac{!�!�mO }2-1-- )�E�^., !�%aM!n7!�!r l)�1�} =]_6, V-+ � ]_q.6�] Using�s`hypergeometric representa��s-i,pol-rac-nu-F%KJ0-2} we obtain[6L of0$6j$-symbols * ermsq$-6� func�,\footnote{Tojf>Rbasic:�x series it is sufficient to use�rel% �0ser-q-fhyp}.} (q-hip-def} >Z&I4�;:, =(-1)^M ��A�j})�(\qnf{2j_2}} M�+j_3-j}+j+1}}A|\q�  L�c+jfa�! A���-$]_3-�� } {[4\83�6K&�2�}}\timesf�aDq&���q�[jj12� )-j#!(�-@^��M)* -j_ +.��z)w {}_4\AN_3I*(d b !N �,r !�)�%o!23�)�� �X-A ,\,\.?3-j+1B +j+2�4,\bigg|\, q \,;1�7):�]�:K& ���.�� �B�M�!!1+j:�)��������� A�A.)E�a�!'%3j�@3+>,6�VR}=y,}���M��qA� M�v \J� �2�-j~�B-Notic�at from�above:�svalues}6j-en_a.4 `b-1} immediately follows.oalso ttthe o� u  , two alternaL explicit'$for comput��.}$. A third >: � ���exp-forB�8&\hspace{-.75cm�9:�=%��2  .��A�[3} :A�+1:�,#MW}} :Vt�g���U? ~�9T1i>23}}}} ɿ�� � 6�n�12A��os.-2�� � T3+��\e�;P�w*R�0 & \sum_{k=0}�!g�} `�k!AY� } [2a�!��� �)�#�� �k2�r-2�1+Gqm��4 �%��k�L v6PJ�� ��G�kUj6C��UM ="S!�%�%/W2^0] To conclud��� |Hon let us point out�n0orthogonality"  ort-rel1} � 2} leadH ��^H�� �Racah polynomials $u_n^{\alpha,\beta}(x(s),a,b)_q$ � F� Xtheir {\em duals} $\u_kL' MH'}(x(t),a',b')_q$, 6�and:z ��re dua� between � �D�corhonds to ��+�v�$ (see S)����I#)Qlat� �l red-cua},�$n=����@ $, $�� - j_2$3 +j \geq0A6��"+�- ". &�\ �saI�" SODE �,eqdif-q-new}Ad!R 6�z }� becomnt} (e recurrenc� � zrr�� a�ll!� TTRR !ttrr} >R fR1(-6j-j12}. EH a� �z}/�u�u�)�sm�}� u�)�val!�-ext}�recove%>� )� Z� 6� . If!�(now put $n=!�i.e., $i�A $)**�e \[%\bq�zsp�n=0:�&�jmD2N�:c :=�Ks:F� "��{2�& ��S ��1>� mM�j��[C 3+m�2*7 %�  : L s #.}2�s< Z 6Bhgj-s -j+ +j[[�( �*}}>B%� Thei ressio"M a�V tiX1.*:2} yiel, Y&>*��>� �var.+1)�J�28 %\\& - i j� �k6h� =A� A? �!�aVs�g Q AuR�9�2 5N>+\h:��6�lb.�!�!�2N�)�e�i�����- Z�*� �-��^� A]%G:�-*�:h"�]_�M�%�6�"$ v�=��"��23eq��&?!���%�+JA%>v�B[ +1���5 -Â�2��%.�aO9�md-N�>� �(]pv�z�a�.�i, �k�W�  �6���:�=�����5�vL�q�i�(y ~ �-=2�1E�Z0-_6�>�kEA312}��.�}v�&a �6,B�� .` R�.:�wo newBX�2N� z�"�� �@�@3 )��2} j5�� "N�rA:����N@ (�&A ?� ɇ&c e�P &3 :u 29�� t2� N��A� 5$  ie�a:+� / ,��| m RaV  :  c b-r���R>!��,  �-1,����& �RA!�M�P�P:n �?�?"$E�C2��O"�1�="}{� �%DM�A6+-X!�1����M@{�G ~M� �iI�%e3! ���K6K/�(. ObviouslykP�� anoth��EE Finally, ��sq�Uah&� mall;*�Y6V[ ��� � b�(m�AA�Aq�M�A,��.&A�+1"�UK �A.a� j Ada4 �{)1&5���^2�u&'^A��} -'�w � �.ha#'� ^{-55 �+12!NH2q� �1l12��l)� L�"6+2l�a�5=]_q } )�l-�-a-{-M !�l+΁�S�<3581M-lׁ?�dst=�i:[)tI:+Y +)r�5��!t �� �&H -l.I4)�E� I "�( +l}}>��+i�^Z,�[�[[.C�*�:"�r.( �Nv&� ���/Nb:V, :b� ::�B bet��Z�\s&UC"�q� u_{kn8�� ~� } L�!2a ��"m�-��famil�,��N��$fact, Eqs.-��Ir %� suges]"e���1� 1� bothF���R��?con-u-uV;U�!�b-a-1-r =�s-a-n"� & ��4\tilG(s\!-\!a++1) b+Es:+1+ a+b-:-n)�� S+ 8S Q +1+n O a+v% }\, �r�. �&�5� pr)NR/a3titut�$:�(6*�5ce eq�o%2�x6�r�2�@. After some stra� forward�"u�0�resul�"!�F,&�#A�T.3�$�� $~a! J�*isuFmY�*atB�{}_{4}n.T (\�70}a-b+n+1,a-b-I0Q^, a-s,a���)1,2 +13�,f �  =Q� |q)_a-} U�+a+ }{ (q.�+1C}:��� -n, �mv�6� �m#, .j�a. y'!��'� Aident]'E ermi�+ ng $0phi_3$ �2�2h, $n,N-n-1,k=0,1,2,\ldots$,^�9_�.4q^{n-N+1},q^{- A� B, kD!�q^{1-N 3 2k}D +  ?^'qI0AMc$N}}{A^kB^k�0(qB;q)_k(q^{NiA}{ z,� �U�.�� n}, ABq^nR�#S,qB� ���R\'C�)�} Here�! have�6Pided a detailed study��(wo kind of � e(.=�&�$$x(s)=[� [!$�� .B|' with �coeff5 s or6���hquantum algebra $U_q(su(2))��B paper�(4briefly discus��$`$of thesZ�(�:_6theor!8>b�3��'p\cite[\S 5.5.3]{nsu} was show (atItransp 6�!���ta�es $(\lD;,\mu)$ -+$irreducibl�"_71M4classical (not!�) 5Ysu(3)$*C*�'�% Y7s (\supset %�\75 u(1�'L$ #/� '$5�S7wo�sub �s-2)$&�(..�7 Weyl2S�are, up�8a sign (phase),!�J�1- zy.�X*statem�7ca� don�)Q�)-�:�!<_q%fE4{as96,mal95}: !F� Jf baA (n>86� B���1�s21� -��* 5�_q!��f!�2+:  P$coincide (-� !�)y��lj�.k�$ ЁHIno � F�(satisfy cerv:q�*u s n><equivalA!-U0t>p@�he �.w��.$6� vdso,*y idea!xE�B�eE�assurU a_ m�,pO.ies��V�! clos|4� ed9�6[J1�u����U f� e�asser���bm�.Ո non-Ūct>u u2,1��g �V!reful�[m�-thcom�8Ň . *�,*{Acknowledg�?s} U =arch ha+ en suppor!+by!��DGES grant BFM 2003-06335-C03 (RAN, RCS) 0PAI ,$ FQM-0262 #). Onea@authors (Yu.S.) iE�nkfulQ�0Russian Foundɘ of B�<�`(project No 02-01-00668) M�$ financial�. �v0 {\�#�Othebibliography}{999} \bibitem{renato} R. \'Alvarez-Nodarse, { \em q-analog oA>vib=0�2 IBM�+a4>+ $SA�(1,1)$.} Mas� Thep0(in Moscow S�7 Univers� F2�M.V. Lomonosov}. (November 1992). (In1�)..� an-td } R� {A}l6�( {\it Poli�2Los generalizados y q� :e�iedades =E rales y a�70aciones.} {Tz( Doctoral.}�`dad Carlos III de Madrid. ,�6 �Spanish)6���hipW@m\'X@B�!�onA�smib��H Yu. F. Smirnov, { %�,q-}Dual Hahn2L� ��unii � �  = 2� U�X��s ]�� 2A�IqJ. Phy�9,: Math. Gen.-!6L9} (1996), 1435-1451.� @} P. M. Asherova,>�y8V. N. Tolstoi, ���2���$3� �V(m: Sov.�Nucl.� �58�859-18722�-wz;R�key y0. Wilson, {A ? of*�62�Mu�V� 2 �B.-} SIAM�)yAna� I�10�79!{008-1020>�2}f�S�b�:$&�7r�Jacobi *�� Mem. Amer�(A3Socbf 319ej�5.a nu83E<F. 9� y-�9�9�Vx�a�%�v-� on� :� ��PdzA Inst��ikla�t. Imd @V. Keldysha Akad.� SSSR}, �\'u�83,��,17, (en ruso6�uU�U�E�dB.�Yw SoluAAE�:q type"< ce E��$i �fic%�}�$Integral TW(. Spec. F�M���(93), 223-242x ro03�/ Roseu n, An el��:a� ach32�( � cal,��, r�al%(elliptic). 5��$, arXiv:m CA/0312312�sk82} E� klyan � � icyuctures�!.|Yang-Bax� ->)"< ��5.6Ź8%/63-276�mi� >V."�  Yu.6$ {Metho��P;D�Bat��D�q�Aog��9 "�( angular mo�Xum. Clebsch-Gordan Coe"xY*: tensorz�it~��$1), 593-602� smi2}���:, {P[ ion-1 -*���.& , 3j�6j2D4Q�Kee2EDi�`� J� ��! 1069-1082 smi3� , {Tree tA que�=� >�J_Q;m1. 9�� J��  55e 92� 599-1604 .� smi4N�� �y yE6 � t2�%���. .��a>.OB/1� ics Atom.} 16 )�690-70�&wvk�,Ja. Vilenkin�(A. U. Klimy~ a^% Rn�� Lie6��E���>�bf �II,q}Z@uwer Academic PubE 0ers. Dordrech w endBB @ docu�I} �U\��[12pt,a4�]{amsar|Z$usepackage� ,ams��VDtextwidth=15.00cm h�D=21.36$opmargin=0& \oddside2 \evenJ head S14.4pt sep=1_number in{�}{K } \hyph8(ion{semi-st !xmergencystretch=10pt \def\thef@U(*} %\setcou�F\�, \new��em!~orem}� [ �]2'lemma}[ 6]{L2#�os� )Pro2/ corollary-C6+ laim.'2#ndu.&Add  !�(style{defin �2C�D.- � GrA �"=M ?RJ%example&E 2� quesA(Q2)con�ur.SC2-ac2}>}�7(newcommand{�B4}].%wtd}{&�' sCAss}{\�Ename{:&im>%im>$de>' :NMin>(:& Assh>':(�>(:(speB(:(AJ>$ra!T26:JcB%cd>$BBnBBnAt>�At>HHB$hB$pB�pB�V>kV>jZ>"Z>"E>"E>" injdJT :FExB�:& Supp>w:(Tor>':&HoB�:&AtB�>&nB�:&RFR:&KJ6:(GJ(:(TelBe�12B deptB� :P�>R :*CoaFz :* cokeB� :*Co > :,Max>):&u%(underline{x> ba�Sbacks:>a!]aKQ:$BN}{\Bbb N>a]Z:vpL.q�limitsBFm lF�vli:�:8Cnf>�vizoinNnbcu}{�, cup\Z�!2Kbca "a^"ota| bigo?'ZHop&pluZ%uy}{\9�y>� lo}{\long�earrow:wfefrak{B�fAip>Xfq}7k{qB�6aBb6bBAf6cBz�f�};n>;uV9[� $mapdown#1{�B\ %,\rlap {$\vce� 4\hbox{$\scriptz #1$}}$jr2��'aC }{1.27� bf> } \#0[Divaani-Aaza�@Esmkhani]{Kamran F#0Mohammad Ali 0c Faemail{kd)l@ipm.ir.� M.A.5yr�8Shahid Beheshti2�.�._ subj)D2000]{13D45, 13E10!$keywords{L:�, 1�1�, $ZD$1�,, Goldie dim� on.\\N& workjJ&�Ir I� abstract}oNis�& i/ s ar0&�E�A�B�of .�. �6$\fa$�'an �(l?aU.m:38ve Noetherian rr'$R$�no� 1F-u(2)2 52#an $R1V $M$,bRa&��*�!ofFF is p�ed �M �.� su%hat:� V�y quot-dof�Bd4e. ItA.v*8if $\dim R/\fa=Rthe�,Brm�4 $H^i_{\fa}(M)@UQu. Also,g5s5d)jd=lM�- �, p $H^dSisRx*��y-�%�%�R$ %�sg.(sults extenq�0ec? 5nx($lZer� �UiB�of �ly-� - >@]� \make�O �{Introdu /E�rough�Zq,A��^� E��}+�3�all�5+v+m!woa unipMam .!IHA~an�-%^)q -tor2Q- �4 $\cup_{n\in \�@bb{N}}(0:_M\fa^n)!�Vi;'gd by $\G��9�. For e �Xs$i�V M� i-th)� ݏ�WorA=Q�.)%Ceda��<?� deriveds $2R\congx set{��Q � ^i_R(e�^n,M).$$BZref/B�2ad o 2 book [[2}]� more�3s~But >�. �.�]>(�i�.# mE4maa� ng�S\�2��ic},, if $(R,\fm)�a rE�U�Js]�,3v�U5mJ� �� C. situ�ӑ�=A�܅� $d$-B+)!2alaʁ��Q%% dealis ��� willa�aŪceU achievV!<�4could � � to-N}Fof!darawt�] �s.!�t��we sh�q�DI�.� be!� very wwYin�qj:��w A.�%7�]ai�8be.~( (zero-divi� � ) if%�!^su�� $N��%�T)A A! $M/N%�a�Io��U�E�primeɜi$�8_R(M/N)$. Accor�'!|+ 2.2 w1p.�s�m��)��A�a }gener2� A�4ef1t 3:r>L y �.CM�.U� ^$ A(>$ R�!�F$ � . By�\��H( �/dMW,�d48MJA4Z��j&/ "y !pei� ]VEZ6� orAr"< 9A  $i=dA.o 2��4>�}�Be>a�qZa� )$ d��." �"n!� ^ns�d4}] cal�Yɵ` ��� 6�)! �>� >����8��. Nex)�i �}� modi#�!�; a��J��G 6}].C30}�"&�!!�Z�if �e�+uJR�$)��'�M�ly���eejioA~] Lask*!�a7�8 � K �� � ,�'�#Bs. "L2!y*�!�ule��V#:^ %� 3}]:hweakly<�!�:0assoc�kd ��ߕ)���oN� any �0isF{a\>���4]eqao quel�i���ea��&ety�u��*�.�r # } i)� easy�see � � ��E#zM7� >��.� C� Lis6_. b�c!\E829� �B� which �n�9 �2:nor��p Re�� ��-�q�� P�36/ does� � �:e-2dir�7su� 34R Y�, � "�:�!A�i�envelop_E^ii deo9o�<a!WNq in' V�. Beca�V�~!�$"� $C$Er! � 4C=\Ass_R\E(C)$� turi"�jE-�]>F��onJo�!�A y��%L 7>is�C� �gofI�q�s � ]-�*hJ�Ii)XE|!�minimal=�coo �&Ŕeء2@cd)Y2XM   map �PA to $P_R( M,E),E� n *96 �t�M� b*8tlpFflexiv��1},�$C! 12]�l:�a�M:A�3��%��M$%���.p U_ $S$.�M/S�AZS$$R/\Ann_RMa A�le�q.#H r�/ �5}, Coz" 1. �y QA2�!a�b�(d ��yEN�!D�8us� (A_a!B`mo�� E�v)�K,a �p�Aif� `3! Gru�5s $$x\�w0 x_i (M_i),$$�1x� a�$I�D.ja $M_i�5橖�a�a s�, $x$hjn�:ay1�yJ4͛ clea� t, *2�F�)5a `T1ESact. O;e LThA�fFM�bC�j e.g.M�9A�hap ,1.3])-�sL��5� �m�A.�7hab�a�d�@by E\1h����D} " baW%�&�Hcha�eri&�MLKG&�.� .K�.CN�Et�A;m�.cE�i)z 6R �- �yA��&�obe�max��6�!4�-- � �+Proof.}�7Qof/7 AAwe v�A�c"q . $\Box$ N0d�as0�6O a.��O-2B&�reQCa��s awv� l4x R�Si%0i&H , �!�+ ��Rfp_1,2,\�J  n�T1kM� � )=7i=1}^n@i$.�,�!/6�xI�$!��Gco�edqaU>V3!  T�� P�Avoida!T�HemsJi� �5!^ _�$. 1��2 fe�F�!�i� �� cardi�0�F� i2� �4�B��& ,  U1ear%"2 &� ,do:� bd. W�4 $\%$ �o*F� ��a.;!�p$�D, $\mu^0(\fp,:m0� Bass}�!5e� h to ]� Y�I*�2f>0$�*a�����\fp�A� MCŌ�ha�%�5JO* F 1=\8XWk( R}2�. Having�ins d,�Zi*uI��� B�!` the &� �&� Q/;!&���E�b>i�M$B���DZ>tIM$ �@E)�M::V(\fa)B�i$ $ {a� � =�I�R$ r�te�!-���%�} .r� % i d�3��e���A� �= AI$%�A&>�!��*si�� � ny": �ўvN6�E�%�n*���V� 2�M�%R%}\fp��=��EABy 7}, �J 18.4],� 61\E�p� nihil�byT po�0�Kwa�C acJ$ra�R\s�Y setminus 0 m!Tpl�6[$r� duce1�G6���erefo M�}~)�(!�ELղ�\fa�"seteq ��)��� wise. H� 6`��)=\�&A��� m)2F�Q �to�A�R[�an es�N+2=�f"B&JV 6% � X*�*lbQ,2},q h0 2.1.4]n ! \E(:���� $2�~=i�:O.� z� Z� 6� W*x��F �!�a} �  R'p}} M %j /e#�T}� iAaJR�S�QQuisJg �fNFirst��&I(i) imp[� .:s2� �iR S$ a2�v��)_ leq Ri4( >_ n^�[�Fr�>u�k:*���om&"�)fU* /In1 8.�8.3], Melkerssona��(�Za� f&B Q � i&6+�L!�� $�)) �. Iaڅ�*e��4$C$�/  s�al s%eJ+Sf��&Z*V�:>��(�J�O_��6z6N 1 �&a� � ��$>�$e��:yI��*^:y.w�E�h�t 1"hi� 9n $r!1�<�$$i=0$ hold �dF,p4Y&sum�M$iDA\E� +0W B�$i-~���k){i-1}�w��V{ll&Hs-|A� N�a=�ARnnd $X=�'�N�*_&X�&�.X/2 X)��we may ��Xe/F��N)k .�2�a��a2�qJ` f�by �g4uIށ{�%��ZF� �F X eb ct sg!�$$$0\lo X \h�x,r}/r04<ex.D�,.�7)@={) 6a .B ByQ�ve�G�W$HF\!�"L&, ��U�E��6���D 6'�.{.�}r^�H&.&�$Rr"�_ e!�clOa5�!��>�&7W�6'I��G engt"Y3.1@M&� o��U!"�,��%H.� ad�K22�2 b�i �iNimtr6�)6j>y� i:5�g*g* &g*�v)A�n0�p}}x p}/N��p}EU:�"@��b�"D,�p�w,�g&�* 0�.�>;n view�=��Qmma� U 7�\ a��o�OBk�-i�ifEGk�QB �$�":M�a�&� iEm��*� V(A$� �$r�,�h�#6��>�#"lA7�!} consisYiof&��//>�� (M�!B ͷ �3- Con�[ei�= ��d^G9Yqn? 2~)<6w leq.%R� <\infty�����!+:; ��)1-�s& T:{2�1&�1���A#2ige�.*Tof�$dT*a!$7Sfp6"�%�&H+6�����i} 6�6.�(far r��R �:�seeb��&�FYJY!F!B2�:�<�k.d$�)�#!͎ing�/ ) IfB��6:z LdC8�mmj�l 94:3xsn b&�3.2�i)  6K AiS'*hdyen�#&�B����!!�soT2� M�a 2Z).�&D($�m� ��Hm$'8 g��a,J: i�q�. Now0 2dB M C A�$d  SimiUO*"pZ"�2��2b%!: �us31��l5A� Z M�r.�6  M> M\lo M/r0 wH7 A�:G d.� rM d+ J bofF�5B"I �f�"%�e�� �eq %�I�!�V�M�6� orZMa� dieck's V�`�1�� �6.�( ��� >a�"� !�va�� T>; �2� H==VY�"�"N1 &A;�JA�"M!�"�9on-��ly ��<*��d� dOefa�a� ,&*M�r�� �o" ��.�^�&Fl)�(�� an arbitr�0 �� !T��&��)�6 2.2��v�e�6�e-�j>�*8"|8r�> w �\fm,\fn�i� ct�Eą�&y3. Put $M"� i\in*�<�mh �=aE�"e,2:�)B� :@2�?>1C!=)'b5_8-_-Z not >=+��Q �gF�'Jg,~g} ^ Belshoff,SVEnoch�d J.R. "e ia Rozas,�SGe� lized���ity :�a:lbf 128}(5) (2000), 1307-1312�4�,M.P. Brodmano- R.Y.~Crp: � \lq >7C-An�Ric �$�t%&��appN! s\rq+9`.�C'Y1` 19B^"Hh}+bF�E\fi, �A"�3�E�.&�; ��j/to�ear2E:b Evan1�Zer'.;n��C-like�.g Y.b. �]h.�a5��T7�U505-5:�C�a�q�D�prbera �End�m r'�Up6A! ZI,�Ga� g�qX bf 25}(4)_W7A.215-12552W�i%vD. LantzCit�&D5 p�l� PPDS,�J��T72}(1�81�01-1142HP[ sumu5�.Z��oraSecond e�, Ew idge StudQ{in Adv�)d%��c%�bf�=4 U&NjPE��[92�L.*�- On asympt~��pbiaǡ�����_ed*�,�$!�����},�a@�� hil.k 1079V0v[67-2712�W. Xue � Ring5Morita�jLe�Z%E�.rH-15У S^2�]�iek��U>*q &�Id�� %%Polozheno v arkhiv!�&(>[V ]{article H6V mathVVthm} %:OJt�t��(}{\arabic{pdV.�8}\,dn�TUKUVwUa2�2KUV/&� *KU+� U�"�TB.��T�TV%*<){*LU-S� anT bA}{\f{A�K.fTbFFBHHB O!�bfaE:tS:SB:UUBKO W�R:XC;b{CB;RR}M@5c1calFcYBZc1&B'c1'B(cK �K>�cLLBMMB�ZF�naeno�1:�c~O}{"�\circ}{+>ch�Nhba>@pOa�ial:[wIR�hat:ve}�Pepsil�<2�o�Pve�Q::oz ��o{z>�u!�un�QB�o�\{�>fiU�t{\rma-}{=>'cPh�Q))<\Au6BOR�WF�_�WReQ6&I�P2&I�P6!a�peKadK.�su!).$suB$@Q6$o>$lB&U �.sfa�.O0l�Ra��P �"$�[K title{Nona�dA5 s�dno-St�a, �`lDynamics� byNo�s� �P\{Mikhail Karasev\thanks{C!dN�zM�lpf=ed QFBR (�t05-t918-a) > by INTAS#0-257).�#\\ � wdow*�O(of Electron�GMat \\ k �,@miem.edu.ru!/date{}N��2L�$bs�N0We observe ``H`''� �5� of`!)V\0librium point re ! univa� ta�q��H ph����.=�"%|BirkhofMpD Floquet--Lyapunov�q@9��>�`a &�i{8I^otMiEon6rr(Je|��KeY�J �m4s"z`�d��� cRy -E nA�sQ� n4�U Ne=6m�O. Based 6�"&Cc2�!wd\y, �e"Tf$of Schr\"o�Ger or w=�fin�@ous reg(�E�zones �z�nar \&�Mh� iety Confavce (May,Gh4)�� s (o����Cs�zs)`�<"�~ kinds. M�importz|q��"A Sb F?�D�'�:mAly��� �}�"!�� uished ``�Ggra|''��s,L, �Oa.se�N�}a�der�:�e exci�Qoun���-l ble �hc]Q�c  s�%iar�5.OS%��@mohzQB . B�sol29ɫ#Ue�H� poss�etW�[�e=[�V origk;(problem via? �ur��yory. S�Na �sgF�]cLaplaYwayl�f�Yinc>�(Ehrenfest, j,, BogolyubovT�u�����"monc+e !��^���6�% s s��� 5 , s��&�riv�Haoa*�k or f�3-�Y�1� a ���$type. Bu�Qn�cruyhڃs,%`:�occur�b�/�*�^@a!�%� car"�aQ�8.� �3��M�m2[typ aa,�2r >�apL �C�zde c��2tr�GE�y�q QD�)Ri��a�isee�E$n &M�%pato�i�K�u��ur�9���>p�� A�s at uAx m% Nal A �{�"A����Ne���  i%z��s�'�:Uis�+! U �Yonm� m%��?vea�our"�M�[!K tudy�Pi�) ]often� si)�ogy�e9me E�^ xplo�%ee.� � �M(R "Mm, de�I� �nu7 r6e ��i spacei2�p,A��()s�6� j���  roxi* a���EEF66ei"��!#im!��zK������V�a prog<��;&mi9b&s~%�{GuSt}.� ray m�p  kar1��[icl�vlov'sA�o%� ��(ory \kar2} w�2�5 ��E�)�of PDEv�a,y, tra� o�x,  5 invaV�a.��$� �<d�^al�$,%�A�M� =X9s%�٤ hp E�an-�%stumbla*block: !i�( ensu�ZiP� f�5en� ��WH��to(a d�!�ZLY�"� "�.mtakes �Q�B(��E-s fai�M.� si�XA�anldA'��Q��?L!/a񑴕F. OfDX��i � e�� ǵ��W")x�^Q�A�4},8 inst�ACM=�averag!�� ��al!�m2R,X5}. How�2e�a?��� t� st�s� oDs�2I�B2K r, s�- they*� *Qw�!QI*-]� �4.�X� �bb��ez> �:^ | "�)�M why&pob�)�Dx!�ref�ion) n*[�tetCimum (&um)i� squ!roo�eigenv:�\�sea7 R]a���rix�E9�:%� Eucl�;Y�,%g�m�l�:�"g|5[w� #aa��tom%�in�r riguAPq�n unS ed until�%��ω@#M: yaP��.�b F-Id63;K,��des,8!J! !Va} ȏ �2) or �.� 1eg� On� �$�T�]1!!�&Dev�-�aI packe�ld�.� � 0l.�,O �8y�0 toru�fOsug|�a w�Yo��v��\�-�4 }�!gsS�n6�� 2<%fa�[ -z~A=���� ~ on,i by��lt@�_�񦱜of�P "/ ��G eac�]�#��"l�.ge1#) � * �eE�.u (&� PoiN8[!�� .�u6� r*��:f{K\"ahl2"  �" :� i��f �2�[1 ���  f� }� i��K��n � gre!en� Z~A�f�)� n(,AAH0j�a Z 1�[��Hcr,�F�red�\U � AKAwl����6�"W ED�E�JW�S!�n��tec��tj : � �m� �n�� ��E�5��=8given � * ��bespl�]�A-l� �'s &�" 3��21/ &�CRo!r�� w5�}%1�[u���vAe�<�Q� }\la��k�|R0 \bH=\bH_0+v\��w{in}\�� L^2(\bR^2S�\ �-bt2H�Js _0=-�lcOl4^2}{2}\Delta+VD@�( v=V_3+V_4+�N,��!�by $V_jLC�La $j$-�ar_  $�$.�M&� $V_2S+aAd�~c4�*A��  $%'.jusM+29 � harm�  oscillV.)� $A>0�)a*z:bdoin� � & �+v$&�X exce� h?Zlue $A�}Un�edQYghborhoP~K.���=O"<�:�'`2$!Q��g<&�� $(0,AqJ Dd^!�\ q�2W. ia 9.~-gU T�+i �� � �4"> � sb�3b�?�$_{m,l}=\hb �o(m`�12) +bet l65%Y��s h fuR�8s $| m,l\rangle�Jyd$�� by H��te*�sbMGd![!Gau��exponenO��ʙ>�w1Lfo�8� !h`:b;4b;� 9��qeta}=�AaKo)���9 I i� N�J/&/�no"[�)AV pair�@m,l)\sim(m',l')$ Y �$:�U +}�aTo "� d w�%y�j5k,�5��� <��1,s $$ E(t)=\lE m | e^{-)Pi;!hb}\bH}.+;�I�ro�\�;ry/ on (A�)�d �()&� %�g2����M�$. �4non�� �%� m�/e$�� irnal&�l$t!�$\hb^{-s}$,~��!  1/2}� IUas}ɖa� to0.3Bu �"w ~ K$9� T s}%2��}��(�i!��!v & � $M�N}acWaQŁ�anC/$N$th� � \/}�;N>��8N=#�)we&AEp�� �-it" � � A? �o{$v$�(\refE ), 2}) �LB_a6p�&�U��U c �Ёh*6M_0--wA��LjE �� � ���#n��_at:�R�_ k�u��5!'S:�n!�- A��$�p") CU*+Y� J�� 5b]� �%2/N}\bU�N (� �^{1F_1  (F_20 @L\bF_{LN})\bU +O(RL+3/N}^� $4j�%��0A�$j!�PV&@ ! 81��&! �ze�-E� $V_3? to�^ q6B� d�!miKY (�e�ly)� F�-$V_4$J#�2�$M�5}ћ�}lEic�"A]&�m�eda s:framewbv/rۢ{We� �5 22}. A�9seeEs���|�h*� A�e:�e �tiZI�1S�8CmJ~E�.j�-)���i!.��� .��u}�4�.��RQ6�!& i�.�w�.^("l��he�2 ɡ)�worC!-�''�$%ynonymE�``6�.''ETv &�,''6� c"r_s��,''�=��y''~--eQ�B�sS$u���2�it%�! 2� �57�5�2BE-�-Kf"" �f 6^�[\bA_j,Tk]=-i\hb'\Psi_{jk}(\bA��� � �=hb'� �����:$\bA=(\!;_j)\!� ��N�Bof��ors, $rE�a",(M )6rCeQ y=!Js m�in�:� "comr �= �s�P&�FsoAt"�oe�~ a"�7�{=bF.aw �l�>U@ s doabe� �! Li5�' �?�;u��$Jv�D.fQ/s ��k bega( V%p ago�� �xew� � kar6�7&�u�I��rei3��]�S�!r��sotrop9�s� $1:1$ (%�� � =� =1$)"g LY�e T�:��align}I�1E�2]&Q�bA_3, "%1\\ (2(32((1, \tag{6a}'3'12'�9t1P �Sz� "1IB�\eaj�i�.� $\s#�Sh�� 5�5���8��%��@6M�.F z�@ab{�@Z �te�� que 2�/&jI?per,kurcAC23}�)M�%m> �� anY<& sL'Ae�CAR 2$ (�QO1$Fb$beta=2$). *� x',y'$W,d Cartes3�c&  ad]f5@:��t":iBaD]��1�sz\�x'� '\�R U3"�2 x'},� \z1yz1y'}W"}�mYrge�d� self-adj�/.��M�a,1��14�^* �apA_2��1h�( $-4�^*� �7aLZ3Z8($^\ ^2+{ F}^2)Vo8i}68-B8y�2�s Vdz 6z }� (:a)�zAz���r-=�O�~0�3�g bA_4 !.94]=釅��ej�H i��6H 1�8^ `��4��3 �igg��1�2� }{4}1 a22%���R(!�Ca� r"r�����B�!yQ�&�.�ed} \bCE�bA_1-2,� 2&=3 1^2 2 -  1^3 + 3^2 +4^2 - i�3�ar'�G)e�F% L.#|�lM2}!:'K�7N& 1. �/�����8��<9 R"eM�8}) r9�d*<�-s� ���B��or� i[q-*O" �x,�' ( )����p0e Hopf axiom,R  Fadd�8}�� Ea^�$q:_Fbrm �4})} " E! ΍����  {R 6})}�-2^�I�.� .� !/:D�8mad� 1}%/er_s�(t21wq,r�a�}*rue��. thantD��.�5ell�QH-%&EEE #��:� �"�  bo�"j"c,:��f1�7ED�(ly>�.nq�U����C&Ci�q�1/N}f_1��) s f_��3�m�r6 E s�!&� s $f_1,f�(:"�g�.or( bA?G!.m*I\. %�2T/in19->��\ e ret'�a.J> 6!e?�ex�,�i|�\|7-�Y9 $1:2�1�b�x�R=�2��H12x^2+2y^2+x^2y +\gu� x^ի h� 38B7�ey �a *Lf�^J ���n �33 ��^{t}{\�2}��3�4v�A7a�h� �tQJm�8})��g to�for�� in~ )7@ t�nee�uo� :F�&-��A� �k[ e $n�f�"?F��� to fLx�-� <:� *�0�10}E���"J >�3"&a�/s:�7O2n�#�� h26�� � �}6})? e6q$*l0an�p-V-yE7�)` $$" �o�J� KirKo�m l KoX $t--Souriau~i8�.�Kos,Sou�a�.% ��&�nong!V �8=# �Ih�L�%� �isHn��3.��=a�"�:}%3:e d�yr�)Q8w:�eLo,="80Q&( )�8ic)D8; polaWs4Y�"� �� :�fyog�!�M[� �&�\c���I �?p&=-�!ťUEol:뱟&h!a2;c c,*co+-�>n/�%"=+"�,A,sU2� � , )*� Gust},~��1ui�^��] � �not"%�Nd��i�d�B[ER9�R� �� �ʥ49~A��ha.�(t5e+�%�Ue�.�>a���9:2�e%#c5-�>\{\cAcA_2\}&&. 3\}="�274\}=-3,*? \ $2,[ B _ B"� 1f�%[3[4[3\12.jV� U�)b /*� cC_1�1�2,�� 2r^2 t"^32c3+ 4��Mh+ymm�� v��r��2� surfacu�bV�1fs$Omega=!��ӊ C, �.\}'Z \bR^4 :� �:oLi$\bS^"� le�K*�*"WA��:� ex}�f 4} z�E�3+i!� 4}{c!m_1� c2��Or@���35z� $\o!* ��� brac�-q�1��9�f 13}) ex s . "�  $Fli��an�wayff� �=i\ol"�}\��0 F_0=ig_0dz}\we>=dzB&�h�<%�VBD$2$��mj�b� \rhoZ�\��g_0>l� Ricci)���E��'�B�~�<x&L-5�4� Now if� �W� y"B�de�E��|bundler$���curva�T$i1�$ mustcildyW Hilbert#of2~� is r6�s RzbD would �| &�3&~9�Sprincip:?�<s. SoVo��18 meas�+-��y�.&A5�v4U��8.�q b� &L!�Fl!7"��a�, �!�:*y}��kar�� �-�inhomoa��@�/b&����x-T)�)Cexist0���1VQ�� i�#l, un!=�YwP�^0�Q~4s the reproduc|ing measure, the problem is that�operators of irreducible representation�the algebra (\ref{k6}) constructed canonically by2H geometric quantizaP�scheme would be pseudodifferential, but not .� . T�(is why we mAywNmand from!(very beginn!)replace�symplectic form $\omega_0$ by another ``q� um''2' $ in a wa�,at guarantee!v(e existence-Szro!v9��!�- r�%�0F� by ^?0This approach!Gtexplained in~\cite{kar9}. Not!U6Hportunity to obtainj?s �.�$M-OV� �actly 8reason%�(polynomial I}ur9Qight-h!�side | ~(6)T0 \\ &K(0)=1, \endg w!/ $n\geq0$!|4an integer, $\j=1$ or 3$ if $n. even odd,!�IXbrackets $[\cdots]$ denI�e`8 part. The solu�qis giTa�>. func&A�`${}_1\cF_1$ type, or mor�Becisely,5X1i0}\label{k17} R, K(s)=\sum^{%P$2]}_{j=0} )n (!}{j! (2j-2)�)!! ( ,-j)!} \bigg( 6$s}{\hbar'})^j. %�� I�a8dou��factora>$!!1B���% duct over!}$ numbers,A�rtAl�E~$1$.� AlaWonY�``dual''>h� $$ :�LM� -(s � �-4 ) �d+} -�1+2) L =.�D, \leqno{\rm(17a)}{$$)r11:l \int^\infty_0 L(s)\,ds = 1..Int���,e Hilbert sp�2$\cH_n$�ϙ�s squarM�ra!v%S$$\bC$ witha� pect�B!�m�phd\mu=L(|z|^2)\, d\ol{z}\,dzq~z\in\bC�q�lemma}%1E����8} \check{A}_1&=)Se�-1}{4}!u'+� t ol{\aPial}, i�\text{e�}\� 2&=0/ z>noIN\\�2B�12 � - �E,e��}{3} + 5�}1 dvqq�8}2s3&=!� '}^22z68^2y ^2}( &^2-%+)k��2Yf�4&=-i{5~�i%.�i%V�2J� 5��(Ie�realizM�ermiti��bA�A�� eg 8})} 21~m1. In t�:k 2@Casimir elements Z$8a)} are $M�C}_1={!�/{3}$�,! 2=0$�i >/2�Zdefin �``vacu� ve�,8 $|0\rangle$ a�,�]of���s6s*�� A_1 C =a_1 m� \bA_22$2B$(%3+i4)-��e��� a_1, a_2$!7;ta!O� $a_j=-NA}_j �֩�=>� �- $K$.�1�is� !�ykernelB �偙P More�d,2� *} K�J=\le� z5�m} :I 1 D)� =P_n-ӥJ*u}PmW jm >= on� $n$th .� componentM�V_4��!�(um K\"ahler��a  on $\O�$ni�d %��=A���\��  \ln K,,��%� �:y =�]�%�, A�$� =0^{1-2/N}$, $N+  2$� i�.� 2�.� �dm=1�&> �= % �Lg !6>�� :� q�~�J . ��4a micro-zone, \N>�rnd�ka small� amet ( $n\sim 1/%'$,�&� a�(totics hold:� -� _0 &\rho+O( ^2)U�,dm=dm_0(1+O(-)i�H�$ =g_0.q �!' Liouville1�( corresponda�M�Ep*3]{QrhoVRicci5, see25 5}),#16})}.y� one has!�K=e^{F_0!E,'}\sqrt{g_0}�- L+-v,�� � �9�id�tie2�aQ"�b1� 1�UY �Se�})�=� 2]�:��b5 dm2+1�|6�F�is �9%3(can clearly%p Au� � es��ce betwem�classC�lNt"�s on A�Pleaves~��.aBy@s2A�is�a�just yal:��z-a�� $-perturb�C �$one. But i�y nano6�=6�=1m��2y�a Js9< 1. ThusI�!�$talk about�30pecific {\itn�-�y\/} ac�,anye�hWs�.�Sprum2Win� -, clusters}%5�w��S backq�� tral,Q fo�,Hamiltonian �10a�wnll� nt&� ~ 120}) ��1})!/ur�-�$N$thIO !� ��ed� stud5 [f�2} \hb� g(n�`3gg) �^^{3/N}}{�v2}}&, 3 �d^{4/N}F� �-1�"� -� . ReXi��D�B�@!.0 In�itixr, ata�E8%nea)�bottomm pot��al,!�have $A�, s1$� k(22}) become&� ��"k 3�I2.I��.���12x QV �`9�bigg)5�2})BH� 0model ordinarZHEUin5 3}) *teAhE(2}lea�.�AЁ4ies�original.[ga[ . Bye�lva�3q� �� ace�:f�4նU�����:_  =\nu :d U^ wey��V�E�F��x�� F�i9Fa���mLO(N ')$.!m0a3$,Ce ;gg�� situ- ,�i� *ximate< olve Eq."�  us��e�techniquE�� icy=Hver Lag\8 4submanifolds (&� traAoAz)��&�leaf X  develop:�24,kar2510}aATWe now briefly describresult� viewaH(����.���.�th8Tte&z$\cA_ � Pois��x1�TN energy l��uis.�aHat is%� clos�! urve��LŅ\subset�!Fd�f@7} >=\{��{\}F�D� by $\Sigm��� !Y5- bond t��� $ b$��2k� iV"condi�f�8u��"��� _0=k� 12,�krZF�H!{ d� �P discreet Z�i", 27� z ��فţ%leaq�!;!(5b*sa( Q�6� .r�"c2�T.�! � "� }�gM�IMFe *�v9}� 7� �1| �'}"� [}\Big(� �  z(t)�')) e^{% {i!)�H^{t}_{0}\theta}\, K zB�t:�*}�t{z=%\}!�pa�rQof poi`ofY� �#!'ti��t*.1system1A$ geneA"e��"a�e�-j�~&�, nam� $ R=i\AaF_0!�dK�f�Mk�. So, f� 7!6� :�����B #  ~$\bH$J� ���ar�&ar�(g3f>�!/E�eJ�Ges290��6F� ��%5q4b�3 " ���&� "� N&� "�g:�M�� ՙT��q')�re��d��<.g ��[ -�2J�*� �. ��:�]%s�i6�W $ �v3%�M�Z� B� 333} � ��nsR�i \�xp%�\:g6�h(iL&�,{1/(N-2)}) ) ?��|�Y le\,dt_nd�+"�� "� s�&��4='!�� !n62�Y�319q u�rr �re� ders in.p)��1R!w )} AbcontrollYbi�-or� $ž?�}��AS'2� M�&� By inc=(� ��Z�3,4����go fur�)� 6� ����XwuJ�� Qany cas�eIum�� \ -( )�`n our2�� ne- reacht),$�^{-1}� Such larg� *f g1}$}c to �2u�� w!q�di� ce l"� -� . "I areaɴbehavior^s�� k�H�Y ��lem cha. � semi���eI��� n (28)%�((30) depend�| index~$N$*�rA��A\gg!8ar$. Ona�,tak� o = "LnlAsQ�s���.�(29�fai�*&j+ arri�� r� W,� takA�%�r��of�XneedsA�ir2 unt Vxex� sion� 9�at~ st upN$$f_{2N-2}$�)A�ermo) ai�ib�)��2of2�(a �A;T(ed�i,accuracy $o��"is�n at"  �($V_j$ ($j=3i� ,N$)YTaylor�an��� &�a�&�+M�� ���e"��-.�:� iSchr\"o� ~)pe��1!��{*�A��mAakyTB -Wc A�*H 6�/��4�,�"� d&� erm~$V�A�� T-R"�long-� ev�+}%6 As�`applicq� abov�ult�*� >�Jg"� � Zb-VA��/5�. RqCauchyBb1�q7��"n�i!� \c \ch� t} &=�(��2}K(Delta* +<,h12 x^2+2y^2+x^2y+\gamma x^4&)2\, +�,31�chi |_{t�,&&i^0({x}/� \hb}},{y6 R����$i^0\in S(\#&� iniR dataETlocs(s0 a&:��v hb})$ ?A�2p$x=y=0$Q2u�. #hoose��" � K 5�F$ $2} t={\tau6� \simF�wU�"VdI�\41ӝf � !��F._{]/}\� ${-i(n+3/2)�/9=a m+i^ �_{n} ��R� �K� �>�u� 1\qf�$j�&1�� �8})ji(3�b/-i6\}}f!��+"� }}�&3=e,���0>C/|_%T=0}&(%0B�  �Formul"�33}�"$2͹!J6�9H�%w�p1��3��Ĺ� rval1A3��$still keepreIto&u�\5�&�� 34}) afj �" &isq��B*se�k� ry %�'�M oS left*�3of��9&�� does�!h!7� �%or/ &> s�f! �lv_ a�4%i�4�F�!(dynamics\/}q�� �Z��=�s9�i9�nc4.�. AN � X5��e�"s35} t�� O8 {-1� M�~'3Fzf%vk nstead�(� 4�!! 1m�& &� f�}bm�hb'��2��0 �!F��"� �i��*��aB�~-(s�y1�%3?� b. aJ9kt `!s6 ��ii*ory. z1 2%s like5�h'U݊!�A�>�:� ㉁�6mpu�6K8Ef�0rk�"o1m� m ��!� {5g�al4�inva��-K%�typ�Ir�c7��jhiddeng�:y.py�)-�globala $ic analysit�se�] r -�%io �*�e paths,�!%� �*onomy:� at�;o6����m �> ion,�'&�91123It mayA|releva�%o {1IP� �`abF# ,�:2dŢs]bE�A_�d�9�&ng# icul#>*!2� $��^ar�5)$.� DM ield��s per�a1�'�D.&�"~>imatrix�!�� ghas zero�4 { twic����'9 me~�=� .�mmu�#a� a�Y A��+\ �%t!�-dime�0al Heisenberg}-�} "�5IInveraX&j#. 2�: An>qB�*�iFZ�!tp (2)-]!wnot a&��d%cE�, AV hill.�d$5�kfrequenc�.$\alpha$�=bete .maz( ry, say, '�& = i��6F�M\�two�l]Gs $\pm1$ �sFP a~BP EPɐt[� envelop��[Li", $\su(1,1)$ =�ᙕ��a�!>!�(anisotropic2B 2&�-7%+% = 2i�B�mU <;)�ce�v� s��ii�~(8"Y��&�8I�Art2.��5o-atoms.�3�2].���~3!�,!Mh&�&bl�.��m�s' &��-I1hy10� �%Cs�5(�Be�,�!~so-'8���or $2$.�!Nn\$dot surrouK"e�0r� �n��)S.� meI��cO� gy �E:�an ``�." � $m�.``w< shells," ``fillA�� etc.� m� T���n%t%u�� es�?to�(%5>+��@ �i�V�'�V�configuA�on);AG� !�po<.�� v�Q�cenbdot b��Y��.� u`qZ.3_0w@A�(?y��> FockIv: �plBT&�RBb�$7_L$ hal� Larmor�y�BC*is � l1/i}EF�streng�0� pli&�Q' ch�� divi*%#( mass. One _ clai+*� M��E�!% eze�d�� ifl� if  ; (�/ 80)^2=s^2/(k^2-s.,8.�4R3s,\�+~y A�gTB) s < k%� UQͺ�%*7"azse]� )o��}A�Its����tra)mo� �IŢfP2�Ii-&!.aGmuB��eype���6���>"�c�95��'tensor (!�>�Fc4(J� ), except$,%`linear� non |A�7"@GofA/ $ $d_0=l+m-�1�~$lmq ^$&X�� thatJ;8k+s)/(k-s)=l/m.q. E8.2�6Yg�"�*S%5*.�,�at�&�9�6s�A�)�E�an�#arbitr�1� $l,\,m�3��)e��!�de!"~!!+)�Q^��� ny Y. �5�: �FqF(�!B�;_LP6n d $,B4 33�( L$, y53J5 i66!44J4�4iC �l�7E?�95b?5��� I�Wra�e���BY ,V_4�"8'�i1��\,Ha kin�a� terC3���� �+h�Aa.� �(�:��9/s"L7nd� u�� �/.� A�bSri�&�method4edA�� s~5A�~6fuJ7"�"%� splitM��� )(~&G .Q���7u "hin~ !]&� if�t r�/de&=�9� (aB�� ell)�]3Coulomb7, �@cYH dusual ra�# than)��o�= n it*=ve�  m$Lc cMoall�6ndeed, i�*�:N ``B�NU'' �� "tic�2] �MBal�^!�f AM�efpJno ``.�."G3� � { �*"Y Q�sg ��] i_ igh �A�0e same growthQt �`obserA�A�)�.� %��!FD:re2�.��A48M :3$ V= � � ��~&m& thirax���8so on.ENano-�urE�%s�.�0)� ori}%8 A'P� s��$�P. ��% � s �0� --7!_!:���(�3F�?C$d7 2�or inv|n�T��1).���'�.4!a.�2>�Eax(al Lyapunov"= �or28 9e�G-�Floquet&group�Maslov� lex &�bundle� ory �PMas-Op�6EA l�2 suppl�H&A n adf0alb U}vujid&* �=]G�Kn�, (6a 8� �1 AvJ&# aver��S�Oe agx6r�S%Q��.=qAnt -s^�" -�--5�.�h&>-�y�X� m� s�.Mr7we �a2!W�1dy*p4to � ib�Je� ,"��t�@�8O�?" A�:�.� �lso!�/MmBSEk9}�d���Hs � arisAyE-�N"�(s � ]!m 5y (toru �hQ�!���)&�KarVor}�5�"a m#�iber-�#� >� ]��<u KI?ir*�ALv��w� !�I���"� �e�s �z��se fs. �>w!2z� �&+*A$'2�do%��'a$aNG�E)�usR ~iHcrz� {�+1`> \y7� ��A�be efftWYz�nd *L�/&< B�2 "�7��*.��^��\/.,4�4"� �a�i* � � "�(Helmholtz �� �propag� &�+ ��ic !�knon2edium� Assum�ލV�+A�re$@�I� 5��an ext�l�it�+�maximum �"�cerE/{�`"*We���. �A�!�(neighborhoo� = �"bAVXv,nned-aK Gaussian-��>@_"�1s3 rougu?hN��r�a,a�2e-Vl�&�'�� Kaxis)!�� 2f*{�� �Neqia � ine�fs�GpF1�s�!��Z ic (�;).��J��Y�jtW &� �'�e�i�0![( phenomenon�>aa?of�(ew R`MZ" pola.R6vax &A"E�is�0k ��VjT!V^-��i1� . Si�/,��aez����,I�6��- !��of sp� ypm ``" � bl �!u�[&!�JI -��"6a�(8JI�Qomo�Oca� a sp�. *A?[F�9&� ��to�:�+��act�"���C!-w9 "M=!7�~]6ic sca�* �!�uVEabe Ymacrosc�.ug.� jA�a�ɳ �xi!� �� %[freedom*27#� NDx"e�/ionrFE����)speak B�H)f--op"�ra��Ahee �*U .�aWPtEW"+] Aa�#%�i J�.�I�9��me!�ics}%9 &4��&�,: --~�$of Birkhof�B"U ��  .g�j ũ�H8-Z&s,!��� theyeS *Zs; �a�. "; }s� %_6�� � �', 6dM#&d' Max�X,�10a����|c"�LM r s�v9u!�ne�m� �:"�4� b�!�_nt�j�s�;� o-5�a�%9t�3alՄn&�@� %C� � - ph  spac.2 ��i�+�eU� nvisb-fH � l_<; )�AR9�œe.�E�zon��s loos� ts`5L�2:p�_-s,%��"��\\s��a�� ������ so P�9# �Dd�f ���1�o c n�!�"J-�9E�![5,�:�5in�\ �� QconAcE���proced4(5>A,:AT �� hy\MO\N\-me\-�c-��� �� %[&��a��=��$V ar�"Hm:�^I(��;�M�7��1j M�,7m^O1$u�d��8 *(5�arithm�%6Opor���.�)��;*L ���.:5y�O e!w�m�g�S�5a�:4r��� 2 carryT 9+�>&+y,}3 and -,�G.l �n� ons,p +?9 z !.s�u� is{9�ope�ce�H� ���r��as[,D!<& gY Q9;MFQ">�*�a�c� U.G!SoldU�ofn�~�6w N�-BN�� u@�  *2�� �� �A��8 .b"�)\�Her�+�:�2u,or ,:��� �&(� wo d�'k!"@ � "�& �&�g% �uK�G� �a{ow�>��?�O �``PlanckA�� '' (�V�+K .�=,!#hap�- he mBfs�jR Y�!<O3�i)$�h�"Q funda�*al &X 7 whos� �pE�/s� " � *�"� o`liS� $ ~ �8}�G3%at&f [ �%�- � � ly �mx. althole�irpIt"�Vl�, �t[&im�'a wa1t enoL aeci`$until�IAd refe-=�kar20}��}paperA(HKarasev \& NovikovaE3!�IMC�@� ,�a _M@ !basic" e]��%.!$,5�� .�> idea.~'�:�� y3,ng�Ta�e�Jp<�1 rol��uo�M�� �mR8Fq.ael� U^�di�s pos `%�їed as e�"ional (AMqKAM!K ory)a� )4 U�a�*�W!E+,B�K /s.&d9 � attitud��&@ ak�X: y�s-Z��Aal�p�2i��a akes gaps�t#i�g"fmawider�!!yY�E1f.3U 2�< �(r�\"�Xv@�Y�O�*Xa-��ak0K�1&� ?tL�a�obT�)K Ked� worldQuwhAv8$�&E> m�am^@Ac�aW�ilizer��S8Hau |� �S# sour/m�lsh>�J�I��� 6�:����B�%��Vn!&��.�? be useful� � extet*��� �f�str��Dy,a�al �ofQ��T5r  us/r�*� � olog�Q�i mongq�e% �c��r��o6�ma�� )-)5`Jpt\�/>1~4)m�n M�oceuE"� !� "� !" �" tu�!P!��Eq'���A�Ae*("�5(sV,���3) t4. � h��ɪ``�pistry"�0by�XU� M� S |" *via�b$< ~(37Q��.i�n%V,"�Evie�� sepa'� ��"�,�/ lo�l ' & �lQ��^A06, surfjX�-"2� eY< Next 5 p吡�I �detai�-&d7��>��YyN!a & of s>GalQU��E�=��l ��foco,%tr� 9� adia\^c7Q�1<a, �<{(7s,h \ {�/ setc�9er{IC}�G.�p��q}%0DSu_.��2�! >/�:)A.m._�� m��� ���s"u&145}.l7� ��"�! kar3&21}�t�sz te����&�)"y,���&\''&]aA$��a�Hinguishe�k!d !,0equilibria). �Uw�vag�SL9�Q� �re kaa�way� �5 -�flowT � �.� I�e�ail}5�!�� 6�!�>�,S(�%"� al h�.nic*//K6� :WA*V/ �t5 ,F �B�!E85�.� �%�x,��| .2!#%~3�"��� �5�h��s �two.�&���inclua9�"�5(�5)0�")=%6��In�4�5�@�8��� prece�IY+.f�!�n5 niscusF-]�c!bpr�hng!�e"3bsa�~� � G trip�I� U�. W�2-�.�u��*2_9`9_ !f"�!s\--�<co�Bt[:6 Ap63x���!a short lisE��Sul�iP*/:�%A&"NCow nD�Ybt^�3.va��Z6�, $HtwKC�@0R^{2M}=\bR^M\�s  Zdc3�g2�9voR- $J dZKF  $J=\ A(q" 8(} 0&I\\-I&0&2 \�0�NAP���� � Q8$JD^2q�Ms2�f�X�+s8o�M�8�-� . �X them� �8 i�.l*Ll"�lM$XD6 �t)G��sui.�] $q,\,p$,written� "�#�$} H_0�R2\$vM}_{l=1C/ l(q^2_l+p 8tag{1Ju32/)�!N�+Y7�*�)�2b�0l$�8���j>�m� $F$a]iure6�E� 2�efficie6W�`R^M$. l;lz)RY f� r�|����Fd\wh{H}~i AX)n-�%21\pa�K \pa %�}+K)�2B�2 q>y fix<Vw.Q�by $F_I��&�N� (1.2%Q-~$F$.�R�m�, V�sw !�-`s> !��ing� $10$�Pbv��T�n�.�� l #�? �!L�of��s��$����.��*t.:E(1.1)9&6)>�ith $��9"R�<.J alog� assoc�&� =�(. Our goal��e)K Zo�+e#B��6�� 9�"�| >r��$\ a|�y� YZ%}2.non%)�.�(sets�Av"%�i!s:]^�>_2d, M\~R��A�$Mi?��length��M- t@I�5z �r:,\,s:$,1y=�� W�q&�#�De~�� \cup X� m\ca &�� !V&�sub �aet"�_%A Also\�)G�` $c\n�}�^��s. cdot X =\{c 5s%t A-P��aiE+b�oi 4gve!� (nonne�)SJor)�e�e����f6�-)��!ip O�>M H)( I �$ '�8�-O m '_l$u H%�co4� F�ofMc~AwDa�XE}"W \/}�7%�S �$m)�QE�:t� $:%�_l m_l�xJ��>�ur�ha-z!�!^mu�&ly��ensur�'���5+/ �k:ha�u\ $l,kA� �p} Any�� F$�# u;d�s��= _0E� n"r 3�a)�[� q}_�R\bRrpn7"�!65� $>1E�5�.|5 �� qf�$�9{� by L�} ~1.1!�M M��=$acteristicA����~ ZFIv? ��at=� T�'Qj ���OY#a n��Xf� 6�(d%�G ,$��r�U3. 6-M��} A ���5aa��canj& ����3� un,of��:Nk lN$1w)vNSw)q9a �.��-�&QJc&�=H0�{r�x:%In summHE�re�V�e*�s�]�b���j��on}�-�of>'!+!(u8A�[K_zo�joint#X�\,>�I�92|i�=�� �2V&IQ � fc9le;Z*φ�%9H� �X greadRa�#-S2 Now�p^7� ��i�%a�s@�$B,\,Ce)��ub!!�&�  .fB�� &icbF�G$B` {+}C�)a� * 7; F$ g$�� llA�pr�J���� ~$B$z~$C@ !`�Q` �bA�$[B,C]By�;.y b����@$[b,c]�k&�;�$b�WB�c C,c.-$"C$ �e!� �Ց5^0j�if~1u���ved 9�=AB"� �� t�� All�1<E $��on6u:(y<6}e a si��n-��,16)y��> ��M-�,\A� �- ���]���7N��.�iQ�p�i>lP�return� -( 82� � &=�  2/"�"e� ��I���C�usA V�.� 9R'em}e��!X��K��m�L���&�1=F^{(1)}�s{+}L)gT;X [ j)}, s)}]=0. \2�Y64ENj��3_&���!���&� � �4Ato�I&s*$ rm(}�Pro�c~{\rm�:�sŁ�+=�U$cup^{L}_{j"�^{� � - � �B^{� =\emptyse�*)�Y>�0* |Fj)}t �sy� are B�� q�]�e��ϡ���* the"�)�=[*D-�Bin,s.H5 "7a��!�YeR)1�F� .  $1(�}�"�,.�W $Aoj)�[2H:�\/!�)-"%�usQ�proof}*J"�H&�;� 1)���� �a�^�R� \oz_l z_lMP z_l�^(2}}(q_l+ip_. aB~�;���2)!��~�%m9�j y ]�"2V�(hat{z}^*_l �B�6�\hbmE \pa} q_l *VF�"W �� r� h-�,Wick sense (�-YH&)4.���%���past� k"�= e ad` �y$��M�U*����*$g��lFa�hO $� �51�\a *} [1�,g( -^*, )]Xa0i\hb\{H_0,g\}J% ~k(�(H_0 \opa g-H_0g)J6 �9 V+ (E�G _lg-z_l\p NK� �TX)�"0Gust})%,Ri&7 a�"� 15]�!Xg}_k=�)^{k_-}z} +�`���k_+��-��5B�?�� $k_+,k_-I�J n&*m%���{D� w�!>��Vo nno+/0�irc9 uF% {7ar� E�\bZ^M_+F�p} � �ڏ"��_l_l5�\6���b��V��TEby:� (1.4)u8"o, eachA�>���#�v-� "b h $A]B��en:G�9 1.6)\.�-�sumǃ��%S)>-Sl ! �_0 �1 , $�S�� I`di"y� !�I�44U H" L�%� ^��� s)*�[usu +q�Aw (1.5ŧ�0�@ to؉]1)3 �:(k +- -)z $$ �;���chzj �">` Z�H�A.#val7toJl.�� - .���\foY &q�LuM7B]> m"�.�$j�"p & C  or./.Aav!+>� g}_{ �}$T$ >%�,��7��sMbs $ 5_+ B -$ obe� �9Wf 7l`f*� 1.1!�* iā9n�!� *� ��sr{j4i y�&�2� Y5.|C�s�aqA+"� co� ueZ�9'!-6� m�^ials $g=l� \�� }$[os[-�"y�� t�,rmK|&% i=��""a$ � �IJBrk�0'�T!�!��oM: �Z&}�word `` ��&y�s�2z�''% rB�3I53"nM=-#ō�jȀ�}FC nonYNy$�!all"( i<�[[ A:� I� �n� "� ;A�g.>!� 5�#��{IK od� � �"� *�!�W$z6�I� 6��s*�3]?� *�F�2uno"�;c" .%�I�i"w��fЁ=Y��n�&o�V� B "q@!l��II>b#�C�0a�d �u �*�a =\{n"n��� M��2.rn9�� s. M��P-�aloM)�a��nWB�Np 6s�B�� minus sigFI)�'�1̍օ�r \t i$�YTu�d-]%Xscz�����"� ieJNl*r" sum^"  n_Q�N� in\bNU�1{:�A���nX�J�]��W��* ax)�t�rJ�k�5�ܑ�Ѧ} n� (k_��sQ,� �X �1�x6�1�*�YR�!�y�se$A �i���!�)�E�� 1.10V/EYYnt� S�" Abel0� emi]NA $'  . �(�3./�j�-.HF(R>_n=R_n+RC�1FGY� �s)�p%FV\cR_n��seti!l9pF�$I�Cr%V�-$t�S9aof=RA0�&B��sw 9�H�k�cs�Sa�^an���"%�i!�:�I_l\od�(\, \C5�� e{0,�s,0I'-1}l�ZM-l};�=4"ig�-�3B� �w$�in %����id�Y���. Ai�I6VminimarS*A1 @%QG���+!� @J�a:f�qe. c%�g�Y � ki�}�KA"�E3�F��fQB� ��th���* c*\(� ��� ��$k.6{6� ��:iN �,�V$k��E��,&�]m �2[*1{1,} k_{+l}\leqG n�={-2y�F@&cua=sum� �Dn�I�2 indij7$R%M�ove� �e�@�x�3r�.I! 4) " M hold�="��6�1}>� �F&� w}n $!7max n| t i[inhM� x; -l}$�exceedY1H�WfF�6reYHs) k%�$.�#B3 $>1 �F�t,{?).�&��k$k'� k''$aE��b $$ k'_+A�${+1}-n_l, !42}� M}�/-/�+-l7Q �/[� k'e^�\S-=(��)Q�Th�/A�%��"���:�+k''==$�Iwdic�Di� p�3%2vL�E�6) R{6nd!j�9l"<�l$$-�em��p2 $$��`der*!U1}n_1C k_+\Z n=k_- A�_l !h)I�=!n!k%jsoE�+1 � $]l/ R 15)�>hej9wm>pro9i�13:= )L!`���a��y�qJ2M�Ee &�A�W�|�5e� �M&o8a fac�a�lt�={�R� $\bN$u@fC� :!�\mu&"  (\mu!�, -Q� g�1,2M�@A,��>v:s� wtoormp!�q q� +maY - +mpm�� Gq!��Ffx=%� SFͻͪ* 8P&�a%EFE!��v� s}%2)� #c F` J� �,�k=z \o -} $"�-�  Oy *�"  $!(� =h -%$���4�] easy^m�!��� ke���e�i��!#F�0\{g_k,g_r\}_{�}=iA�&� $[k,r]_l\, �+r-e�2J�1H�D� �+!BKA\m_e�3�b�$jPA0>�!�0F�/=k_+r_-K_-r_+͂2b�0rm}eo�� vn*�,t&�( � .;2-&�5 "�2noO�\an abst� vO4s\5 *u/� i U5"p5 $G_k$ ssA�,\ol{G}_k = G(*}$�9� �I�4E� $k\to k^*�rbk^*_+��"� ^*_-!sUF� Z �e��1��IY��� �by mimi��B(2.1)F�| \{G_k,GAǁ�b�!&M�� k,ra�R_� 2J�!Q{2�'j�� 2.4�� skew-symm����Jacobi Y��H��}aa>��q�Ud4�t1%+=��|�)Ml{=, }=\{QD, rƎ� 2J��2.1!!.�y�^��. To cheW�he-  Fnti! let ��A���-g $$ \.�,G_s\} 5�,�#,� _l [-�,s]_j\,I+s��-I_j}œJe�)��  ���"AH,x6o_ �� cycl�T} fS$s per�!~��"� k,r,s t� e�&|-h��!FI2;y��g-�:�\� wwo �s� ��_{l,j�} (\fS--[k%&+rj) B<!��Ul).Qs,I_l�;)@2�@$$ B�9Z c%�%/%ek veri�� !w�!2��nQ,bo"�cs��u�U)>Q (��9&���VU�W*)|M�$s $[\,,\,] b&W�.M�F6 gQ[ed�\(2�#to�xI�`-ۇc�l� k.q�a�e�]�E{k.�]j�&\ ��&�/�;Lie--L�� O*p� g .FL�5i!�P&M al. "�5�B#o4���#JF7 ( ly5�)�?~52Jwe!�-h!�"� 5�Ń!w�XG%Q7��LJZn T g_k g_r \Phi_{kr}(g_IY2J@!Hb ��� $g_I�,��A5#"b"< ~$I$� F�gD=|z_l|^" �*"a F��t*> �� "`�F{+(�Y �Z&� ����}{ +_l�� =G"� _M9\F� O�M-*�.!�6*-M �wo.�of��:�A��5S���/H�R.� ��J�",< "�u2'��As[ k ](2�A&�NY\�-uY]�8E�x ole >�ofQ^�&8'u smooth.6�8a dom�F! �� $ &�7a;'A�avoid6�= yway �final�bult��!ak2�. � * �;.� � �{l2k Y� ��k$: iX iC�]��thE*� (2.3): � \cA}_k=3�{k� z&B?�.Aa�N;01�,i? q� $I�:* �*7#\�S"� E ; *9Vi�G�q� �� s $AJby 2� �  G (2.6V� !<k,r\� cA_kr�A!Ey�NJ6N (2.9}�5A6�W�� ����S e��&�R� =��{~ \}="+"�� ,H�lJ/ $[I_l,I_j�2-)�d�0@���3) M# �!ll�N4 �)r�i�q )_j �k�J��k�_l�.@d� _{jl� S�#%G�(ful�)%Qg!M(( �͒�R�SA~f��"�1&c1�6i}L� 2)}F9�_6�\to�.f��V���*} &1�v0a)2�� s,r]=Ž+[ , \nnG+/b/� �=?�\bZ�>McMD[r^*,k^*x� 12�d62-[r,k/>Ze(\fS_{� *(s%�s .�� -� )�R>�! non-6"� ��!slR7 . C1 r &� � I�6���f� &E�.P)� +(r_+snr_-s_+)} %�Q +5k( s_-k(r%r_-��end)*@% s&� � @:vcoE�ary:e�2e�)Eu��}!3JS�Lnsݹ%D��pe�?i� r\}}Ck}E r}*GJ%�l�FE$.�r\}=- r�k��i� � 2)\,(d).Tju�O�E�A'{ c��r\��o&=i.s\}�*�  I) + ( � (kB(Y82��{>��s%[.A ApplxQ_LP%�,[iS!�C&}~�bA�bA �bA` =-���rs�[( �s}+ rs}) krf�G��� s]]a� q.od6� sF��_la@ -a=)_l} EV�=^2�E�.��%�e�� $}�.{�9��66��=� � . 2Sv e R5�3)Z�c�m�;�kexWmmaF�I;\:� >"&w expa3�Q�}�sum_{� }m_r�r=k�g�%�f�;F�theNa� .bA^ r^{m_r}=CE`*@FEA $C=CaZ)� aBt|v%)�M 㛥�>р�T%e} RE���4\k+odm �i�  ~ _{r}!%��-1}5E�� 1 '�  r% {r'}3E�aߘA��$\{A_r,e�$���� Ae9)�by&@8fs2.12\,qs 2.� 7 "r/Np�:���a�W�:s:F#Bi�!�0c� Big(MmEeeh�+ Big)9}!E%5v�=i6G&�;1*  %�[mr!�M�,sl])5�F�2o�ks}0 / �}Ap_2/ s\}}%�kb7���o"�4�3�\{(71zII�2O �\E0s n'$m*A;�a[�~kf�sJ{ �iG U��ei,A��6mVY9)�AA��&j#p�>�WT��*�_T+��M �.� � .��'a)6��7�$��|��Z��"f3 unioN?=\cR^0_n�D\^\#" )2.J5#�� 7�� �M&��� �/9\#68[A lean�8$k$-n�7��(�k_-Q3�Fs$fix $l\in("��P9(p��^ջ�k,r.m$A��!C2+&@2W" rr  u5! I >�[l� ��_- $,$ viaQ�_��=N�_{ej%�} m^{l)3�}�}s�L 6� "Q1F�H�wv ve $2@= r,k,s k^*,� se i!+72.2K6$�I�0s~σ.!C^l� }.�F$��8 =3����D=*1 s^{m _,s�Q_F�6 �f} q �p nd � r��#�>.)QLd":9���" =:k�� ���I�]}�2F.D)ie�Q�a,��c<�s�20)�vge!����1)QWo�$�d���H re�wA1";3e0wou.�>1.I~4~1I�\��a�i�aqrA $N=\#(%A� ��LIn^:H&�9 �6�A'B{,2)]al $\Re[ _kJ�nd &FU $\Impar�z � � beϐ�sam5B.1�%�3XN � �.1� � [Ase�c� %�!�!��(2,!��ctu�O �b�~�oi�/trainD��^"X\8Eqs.~Z9@!�C` �SnitV� �O& 1B��(�%�V!�!��O�^)���H� �'0p sW#*�%Z�\to}=�%+&�%"�Ѿl��Uj�$}�C�!'5)�L2Al to~$�+ ��f��09)2PdM"�]F�6��Zb ^� cA_rt:�%n���ᡂͪ #}�գ(�6D!ise#iN&ae�^%9���{&2[NQa�_brbi�t:Y" b�F�$*DvK� c�h?iZ� Bg�"�  4�3)g$i�+m�� ";(�&H=�wthi�map � �_+mto -*E�� -� . q,E�ne-to-�Y��a|:$ JA��c�in��lpNPjb��$>@to(">_+, -)� � Q>� ���>� �a"�0�a`SE~ɨhe�U@l%<��s nomaly.''�� �<elf���)ٜ �.�:g}�e=" u5�-0)�)_+'=, ->'-, <e)+(  Q E) =  �`ta� )) +   3��E�&a�8��rk? �� � � T$�n}\mu_RP 0R��G �_i�ZŶ $fd��  R$�\��E�$z r;A��w�3s'&H0�!!"2 �%9*� !� ���.EBk� IW�e�� ^-B-� [}_IX)E�5ucA_ ^{b ���6� !.��G��is2DA T,�" ��_{���Q�� ��K* AI<I%ޱ�" ��s��$ly C�:;-[Xed.%a�+%E\}O� }� I"�)K.a)�etzb � ]B�e�� "cA�j} ��]! m 6� ��!J" 2B"m�9)�x�6�eR!�&U $\F"�"v�F(~'[L�N��&� �{��A�]_lJ�'�'!�?c,A���� $6KQ !6 �%l}b �"� _ � nd � . �Z�$qa7WC������ 0� c�i�w"D$%�} |A! �|^@�c���_-}_I��9a�!6h6�EnA�1�>M 6�)� m^2�� -�E��Qk� ��_���-m��6Bx 0iK"#6�R�b �E/.uad ( /E2&B��� �V�@� 0!j�� re�w{W ��6�!��c7�ycf{2MpU(�/in�)�=`&E�s"�C $H^�en_6;g("`C�is&�&���vF� ���8/fJsaA�uE\left�arrow zYV�-� ���:; �{2&'�x�b� dF�.5r!I��&68t�Ja�&D/#29(30)'T�+�H�x&n~:[��(a "P+ 0� �s�3&\*�ime� $NJK�;�Q-is��ite: �D+M�*Z�9/h�9� �*�N'J�14)a��)U�� f^�caB/%� ider�Z���)���&%> Ns:ހ,�iG0L*���0,%ZY� I)�TA&\ou, �I��J.��-`2K>�E�uniGalE���cm�5`.>�H~$.=eA�ry�dA s on*V�-��- (y!"/1&2l"s8V on{R>� r $2$->� s}%3��, AU/ois�6:�_շeA� ����B�#!\A9e�wted*�q�A�=��a>�p"{&�ple}[B�a&a!�Z5q]��xy�k���t��s�|�E1l [�� q[�.� !� :w6c\ve]7m� IbecausKF�pe��&�w>+'�j`$-{by G���ӁHy��!�!G�e �5ߌ�~�iter�i�i�e�v�l�n{� *�Un5}).!Ug-��"���ekaLF{"C &[�3�K}\��l1cn1��n_222%� &�J�@BVz}^*_1 _1 +n_2 ^* _2� 3J2=��C,n&���Z�tu�w2F=Fet ���)6%�e%s !!'�� �"$� �R$=(n_2,-n_1����S:�.����!���of*We�:�A bR^4&�� E D2.29aN�:# O^%�_1� n_1}_2�3J!> w�|�e�if�}���1\�SY�1�26)�eF1+� ��0  v� I%(n^2_2v2- �_1)1�-1�21�D�- �> 1� n R)�6h cA_2x+i�Cm �3.3&j 1 2]J.i���neA�si��,K 5 " �&2*]H�N8A?��3" JVE=$9Bk�lP^� R�>v�= suff�qCch:�<&0ev!a�u�&� < ~yƅ�������� 6�#.�Afm��#B�a�-a� 3.3)} �Hs0�ry��*i~}X� m� (3.2�� O bc7��re��& >��:q��C_0�w A�1�h �8 C_1=|I�|$�cvF�&=�!-� � $��P}�B"�*��>X��I�*�)�)�� �,%��� m�iN�g ����_1�D��q�g&�= 2�&z�2����g!Rz_1& :( g_2=|z_2|^�JF�I͈.�$!�0$� %I/r�!iHa"I�� ji����!!4- ( �Cof�  ;(3.NZFB�g}1%z}^{*)!"8U)111(�X�'} :g:M>,1 $^!]Dz}FU22)�ݪRb�he h&D 91! 1x *~D�Ios��%=w�n_���*�$���^*-I2_)�92y&�=%�1�&�M�~$�G�*�r�{E "WiA&�>�؁�Q J?�.{[�_� �Ia�]&=f(5!�1* \ [��F_1]4a' Z% mxn? 2]&=�w�BfJA1{2�ge4�\�3.F! !�& $fe�u.�-C��fE)=\rho �cP \!�) -% p �F8ţ�B5��1 p`)J9��cA_1-� -1)\hb)$2�2$2+� b)��mѰ": i7Q�ac7�F �cC~yTat)�Ż9� &\ ��UsM+ 14V.��)@9B�In��Ri6 (3.6�I}�I��8a�2�&l!lR]:.Ry�$��es�+ v�ܡ�:q:l! S*�B���E s (3!��I -1$K A��$n_1=n_2���l���.�%5Li.0x su(2�eInl>�:X,:� ��l &���w�+a" (��2®?F���L!4A��r��k����)I��.M� }ekar7}. R�|E:@sfic9Lc V1=i%0%�r�$!�2�r�w�b�Z un@��� &�TV�k�] AZn�� C, �T{H�K2?R��F�H^{(-�kL12>�BnQol - p^2_"�i3.J�=�%%/�ra��?$�p�3� �Zre\' $p�(ip�0u5#"? e�"W F�> $ѥ�"|Bor"�"�Bj�A-�A&�g2 "�2�� {q+p.O�4^d_+}3*-f*-��<� %�"� 6���-��+���1|�1l6�+k{E-E}�n67=��]�pS)\=���&ZG��j y�d 1� a� P..�{�j�^A&!-r ~$i$�Ror�,:��@<Mi� gN� �$3)a�$i$-f���Sn "&Dunder����Mce�-rA��la�bv�N��������F���W2)=b_3" fra��iS )�(U|0"� 02� -+U2-x�MTF�\T^W1Qs-Rrea�pb>$!{b_1,b�2� {b_2,b_3\&� {�b.=b*� J�=��:�4 .�� b^2_1+2 3-C^2_0/4��.B� ,=1E��G,so, $b^2_1+b^2_2+�I3=C^2_0/4$. These are the commutation relations and Casimir elements of 3xLie algebra $\su(2)$. Thus, in W ase 0D1:1 resonance (for#Dusual oscillator),*d isenvelopX |.�. F a inverted d�6��4, we introduc)gener�,s \begin{equ%+X} b^{(-)}_1=\frac12(\cA \alpha+>), \quad<2b<-<{- O}B?3J? 1 - <244tag{3.14} \end�where $/ i$,.$, +16&2$EQ8given by (3.11)EeIY\betwe m6F]\{5_, 2\}= 3,\q%J)2)3)1F)3)1\}=-S2. 1*5B* The BE�isE>�reA:,d to $C_1=(]1)^2 - 2+3- y�I15 alizEr-S, Z 0$, a�so, $X�h=h�qh!�5)qne^ 1,1)2` wits rJ�B44) corresponds! �4Psymplectic leaves $\{ڸ\}$a� hich%xone-sheea�0hyperboloids.M�xa|} Uh[R��1of 2D-o��!�magne�@field] To conclud�' is s�$on, let us side��0$2$-dimension2� (!xartificial atom) placed into a:~ . L eassum�at%b6�!� homo��ou��4 perpendicular1�plane � ��,sits. Denotea�$$\omega_L$* half!06DLarmor frequency ()�is :�Hstrength multiplied`*charg��p!cleE�divid *its mass�b!:�,be isotropicI�!��0$! ts �<. If we represen)Sraz8L/-0$ asN� Big(�{ *L} 0} )^2 ��${s^2}{k^2- �� k>s>0,��6B�t�O(Hamiltonian)�Tis physical model readJ�H_0=k� � |q|^2+|p|�2 �`+s(q_1p_2-q_2p_1) =k(|z_1+Dz_2|^2)+is(\oz_2 z�wo z_2)�K7B� A��$happens if%�,numbers $k,s�Q� ensurable%�X so one can find a pair!coprimeG(l,m$ such ta&���)� k+s}{k-s}-�l}{m}�8F�NaT�F Dordinates $z_{\pm OL1{\sqrt{2}}(z_1\mp i%&$ !� systema�equivalE~o%]� $l|z_+!�4m|z_-|^2$. Its=O��was alAXy described above (in E�~3.1).� A�!Rclaim �aT {\itJ`4$\cF_{l,m}$ of�]�\/}� 7) Aun� condi^  8) `ha� ��n \/}: N�cA_1=-q4 2!28+=\oz^l_- z^m_+2,-=\ol{\cA}_+9�9B���brackets��) $aligned} \d|�\}&=im� � 2"2�ilR"1,D"�#\28-Z (m^2;ml 1)^{m-1}_1 l � �* 20B T�`Q_Djust coincides witaa& (3.3)a�$n_1=l9 n_2=m$. $  it5�samJZ asaX4(3.4): $$ C_0=) 1 + )@1� C_1 =�_+- m � l_2,E/ <  oV_ 9) , quantum verᶁ]a1(3.20) 0easily obtain�*�way �}q (seeB7)n�Ja nonlinear� acte��Poiss� enso� ��C(ars automat�ly%~4l\neq m$ or $s 0$ i:$17), i.e.,+a:�(is not zero� J!� sible � 6 � ity,� spit�� romal metry1_s� (3� . W��alsq S a!%-��2#I� wo differ�I��ies�Y RX :F�)�!12� + (��^2_1 q+ 22) + �F pe� q_2 �J�l21Bg�leffN ve2���X�u%��u flow!�t!����"� !�formulaF��]�"[ax 2 +2 \pm��.-&� + 8. .( )}\,f]92R&*01+� -=l/m ���!cera�>. OGd�#!' mq��I�syE�icQ���}� �g:{ \% {R"t preces�a}%4 Now� Tus discuss some spectr nd dynama�M)4s accompanying� �l of a9?simplice�w�m[ onlyB N�T(x)=\const +H_0(x)+H_1\dotsM 4.Fn� $H_jl a%.3 $polynomial� ) $j+y By pass%t� new vari� s�q4x=\hb^{1/N} x'} \hb' -2/N}(N\geq�$$ we�RJ H�K^{D big(� ') +v% ') * H_2( !9��4.F~"] ��  matrixEheUq� � librium)� $x'=0$)�EhHimaginary eigenvalu< \pm i�ke2henay suit!m c*}  6� ,� c �!�� �&d F�� 1|z' ��_2 2|^2Ue3B�Me<$, +a�lex6���e , $x'\in\bR^�I .�$�,\, ^�i�sv,a|n,�l�)ver!�g method2!$N$�icrozon�S x=O(U^)�l9o�>ѕ�t� funcE;�-a ESbles W� )a$ ��2=1c� lyN \sim�Y�H_0 3a}f_1�A q#4 ��6\,͔4.F7ᦥ��rueN 5 levelI �i?�� � (4.2�eL $each other� thu! ���%kѢ��*}purely <�v�es.i� ;now&� RXA�2Y in.RJ�# �1"2Y{nn_2�( \text{$n_1-�nQ��integers�4.R�z ap�܉�mPB� to (4.2) � es � in A� dix)9.�imA��� &OR� H_0��I�.�E w,"� �4.Fm�f=f_1I��ff_2I�)I $f��q�X ge�-!J��n$I�&�(�  e�g)qexiste�HqOadll�� ;,�� o us�EF� (3.7) (� he parame! $�SaL stead of~$B o4V"�A 5)� ?+.=qgN ��y�,6"�nonN9)7�9I�ed�1Ez�defin A�8\cite{kar15}) �b*�ed!P6� >  o��.mB�\O�=\{\�?, �0\}��F�MyC_�N&;  AlitE��se�����(act surfaceE0$\�� � (omorphic to�� spɀ \bS^ �&}�j �&z*� Dperturbing term $fA.!�6)^&��0d}{dt}\cA=\{fa�\}�4.F� Y ly,1s^}>Pm� &=in_1 m\pa f}�}-in_2R1} +i(n{,���n_2��n_12 �n:x!�nn` frac9_1 �2q�� "J� } �d >1:{ tag !_a}J� 2 &=X1��+%^��. \nn \"} ��=����=n_2=1$�&��j 1:1)EőF� :K(3.13"�to}W��8A�7)eHexact� i#&i (4.8m�ccl� !Euler $spinni7pV�� n7}.5�of�A l anN�$n_1:�ĩ�th^like aEiz�Mp�jnon-Lie �Eo� � ): ��& ��it.|�"9 �P evolu� )6��egr� mo.*9�&? }`�ph! spaca��_x� � energy)  $H_0\2 v ��$& a fib� o[Dperiodic trajector�of� �wholeŧet`.-,�?r%�b� .H  � ��m�`9;)uimi*X" -^� axi��!�theor�.�5at2is known��&6&uJourE�,�we�*� analog!) the .n��d�'�9�x\/}H sM?H �i)  *T57If $N=2�0a>"ll<he nanq"� 21,n5}),+n!b'�o�(4�9  a y&� -i^* =V)9�aB� Stud"D"�proble�N��� $\wh{H�!we ahexploiesE��6)a��dem�ra!_in :. �o�}ti.�&2� ��aoiII,h9a), �0�.�"Hi�!�b�ope� M�A�ov�!Y9Uyń1 can be�ively��y�by�5]co� nt stZ�, see>#�|2Lr�$B� e geometrAAtopolog "i7u?� ness>V  $F $, !69�1}v�4actually suppo�'. �' inst���^X2Pf$ must y !ioK:s (at. st��m)�3$proI"V �w�a�B�$a$-sḍ1�5����tN)p�a�n be �k%�u!he-��de�ed>�]�0}��@& �]well-� !�Agerm IY16}G z� M�s��j �r ��i� � ~mAS�[Trip�#�)h solv� fN�\\ �oviar� 3%b--t�!*w]{:h~h ^g\\^i}%5q�)vestigatER�ADmore detail. First!�a�_$Xna!�%��trans!��% pg*)�}*.�fT from:.oriZl (9�)1�!��!�lea'� �"l�!1)�X5�*�+ � X=\sum^{M}_{l=1} n_l|z_l�"T� b(<&$\Pi$��gI*h � (A� i�"�J F�$_k c_k g_kq+ \!0set{\Pi}{\to}  \uF 2${k\in R_n};g_k�5J: c_3 \bC$��mo/8$g_k(z)=z^{k_+}�"{k_-}$ �d�m1 by'-i�'(k=(k_+,k_-)Z^M_+\a+s\ $,e2� set $R�is:b>� *�&8 (1.10) $n\circ� - �� .(cF(� �!�all (��)*� s !�� {2M}$. It�split �� diremNsub�)s T\cF=\cL\oplus\cL^\perpX0 \cL=\Pi(\cF) %=(I-\Pi).Mra":�(5a�nrol � of � �cL A�)�i��34i��!7�whe5;bZ$Enatur���oe�e:Nmb�.dm$F&>�m, \� G>! di) eX \Longrightarrow \\ FGW,r.&( d_r g_{k+r&�4{F,G\}_\cL \od�_{J8 \{g_k,g_r,F1�{5N�� mech�M.,1)�#F���r�+ a uniquY�F�oe#L�) \)J�F\��� cL}{�}Ge�2FHI�]�1�3\foa� A�in\cL 5J $\Pi:\cF\to� N1�along5 ���3�"� (he identityJ�>���^� &�F)R-:G) +\Pi�( �605AG*!N\~.>r�\(!IPi,�f\{HF), G)'F�� "t�̍F�D1kau�subQU�n�ne62+]82�GyA �=� B-�Zƍ8 Indeed� �m take�Z4)F)a *��� m/BK�A,�:u8, �check�*�5�)�#r $associativAo T JacobiY�"�':� 0�F"��Y�=�U�zU+4)� � 5.e.� m3� (5.5�q.�}�_Pi(FG)u)E� +ٮnot�� , k+f�� >]VZ su� ~_ +*U [k,r]_l\,�o -I_l�end��+5.5F�!*lsummand5!���-h!���!Ha�#�-anomaly�-�� prev8$=�:� be a _%m� sm. -| �2a�iYi makM���Qnm� L$ I6��"� �(bumY�Bc�6L��,a�8course, Abelian�Iel�e.�allows #toi� 'trivial m�"B� {F���@� �� obey}� {\rme�}a� �_0��Fa>i & 1!$f���in� <"� F_0$�b;�%�cL_0\od e#)ee$-P�.-�9�:�<�"f�4as fo%�R a�o� �L.y%�9�� :"�4.]M!!�� F��Ib f/ >K ,QNe�}� D !�F _1�jFg"Y0�_0W=�A �x�!.� �::qe"N�s _0,AZ1�y5L_0"q 7B�ETk _� ��,4�5�A�Ʉre�"�t��pB �� I�� 4m�R�F,G,E\}_ �}e0{ �1Ll �  2� �Fr 2�  framework�8ag���of*� �!0 ��'B��=�M_q�bR^M_p-H>Lq��U&6i !��u�apA�sE of"�s  tantY $�.�>.cF��- �7k'�  saakR2"�%6F5.7�>Eg :(5��6*| 0 ���M�! � is m��'rpr�:@ >�- ��:!�Mc�configua%r�� -Oq$ (si�?1�!w�%.� in $q$-*�AE�es."�> we�� �Y&h _0$-Y�GOq��~T&*�"��n$&� #(y L� ~5.2%aen��c67% D0��o��eq��ٺ:t-߉��=�Jy�y:< �u-A sens�* �/non�<;V Q1symU�A�.) )+I(ny�, but *3 �Cs.�51,LMs1 �1:1��1:29%s, *�(���0s&�6Ed��2_q�f�show r9�*?��% lved$%:^h. "� �}[N6�)�����] � >�?N%&0$?g'12(I6+p�')+.2 &E��"6H $[sp!$�+�$J )(q,p)�5({2\pi}\int^ D_{0} F(q\cos t+p\s��,p -q )\,dt"� 9B� So, ���Arodd�J $F�3-�IA�: 8 (F�Ta�for�y|�"'B> (��2_q< p)$Al��� �nll �6 ��A|�"b ��9�4� $%�+/ 2 _1q�2�ir�-+# byJ�:� X&=\Em� {]1}-�6/9  Y>0v/ 0QJ,\\ Z6]�^+p_1p�?Ni1F)< AlsoAv�$\footnote{�<2ious n: $X�&�)%BY!J $Z q*L*+:�))U $W.3 {2i}6-B6 O! in S2-on~3.} p#]�W5xp%-A�HAll togeF < $X,\,Y,\,Z,\,W$U+A� *�Q � a%$.�)�a.�L ��?1,1&O%�o�e$H_0$;.�1 1:1. Now�GL$�� !�o�0a#�Lu�Te�IaF$X,Y,Z$�F,1$ .,W��;�2��* nd e6�662 8^ ^s� &�?m�orդ5N� ^��\{X,Y`?0,&� ZWY -W {X,W"-Z.#Z Q�X-Y^1F�8aT.u/ a/DK*X+Y��/$XY-Z^2-W^2�FD } 1)��+�6qNE:�\{�Z\},X��%C.%J1Y-Xc{\)T Q69%m R2j 2QnTJ�8*�9d!- 245.12)& ex�G$e momentum*=+~I�b, �A�J��d6F2-}� > ax ��� �>�10!�;� *z#&! su�7bR^�� aX mean squp devis uMEuclid#R&c6wr�?�yv*� � Qhes2{, . A�6C&�1. #t�"2���com�1%�9e:<��9*taal= ~$V��so-yY $p$�!e� ent�BH_j�\�|�|=j+2}I�{ !} D^  V(0) q eo(!Tab(; total.�I=iJpH=�8Vu(*�G)+V(q q,p:!�"�1F�!$p5!con-?s-5�third��$higher ord�G'' $q-"��� �:� (5�*� � 1, H�M�<$ O s � A4�$� �-i0&& H_2}� �H_2) >�4z�O1�}!�W �a>N($EF�4&!afI! listJ�$�LgaB��q^4"� 32 X^�D�$nde 4"� 32 Y�<\ \"�B32&Z�2(^3*.(XV(�B&6  XY+Z�]. ��1FK;$im*�to �O�!q��no�� $W.�:ula�7 Fin?#L 5�a�!�VD^�5f(�)=m� X^2+\beta!\ +\gamma Z� `XY +\delta XZ+\rho YZ+O^4y�F�i�Q�*} y&m�{16I�n5^4 V} I(0)eFt�6266�&mm!c.l2_1�5� ?��~;3 ; 9H !"z; 9E��I]1&* $O^4*�0er����~$4�䉸�� o%)~$0�% ������1 2��T�  Act�,,�cae2�e"� Straints�1+A� X+Y=m9 &'s enougha(3i�.���� $apX-Y)$b2Z�&ly�sQo"�L�zHiz shapuG*Z orb�$Hf�z(av eccemD�shearP�(n�LJ et�2a=-4W A�@9b&�&f&�8b=J+a>+W�9=B�8 b}-b Oj���FA)*o:s�!n&U 5)%ex�s*;J $a,b2H_!E�!�~ $W &5scew ``0*'' $\tau!�)zpac�^{a,b}\/s\bR_t$�*ea&� Q^W ;tau�L4W� Tak��%�e� � ,aTV ��LMT;L,f\}=4$g(�y/0 �_F21�E�1 does)C�.�%%�w2v�!�a� -4b��� f, �b4a�9{\!{\} -4a.3a M4bZ)N�PO)�2�7ofu 1��_(5eK becom`+an5�E~I8�Og2�Xid^2�a*^25�N -N�)�|_{ tack{a=a(Y� b=b }�"-�Fa�E� y $(C >)$�am�2e3A�a&A isM�edi�f�/IQ�n 5!GN� �ga}{d\tauI.)b�<�( 1Eb.- @VX2FgUsar%0��Elv�1�6"� ^�12��� � ��R�X--O^2--Q^2}}=&�J�L�P�"� *Nf��ft85�+�-EX�2(C_0+�$Y.- Zb$ !�qua�Gbi��R!�c"=lim�Un��7 "�F")N1�@�\C:5%m`!�is�'�a�O }�so �-���xp1@ �bl�$rigO0A�c.�fE�m� is�%w/ telyQj{] F��.�}~A�3�6@r�D6�4 bB"� .�2 3�h,>r[�$:&��8������a3%�]R�.�GQe6�Z$. ApRcIt64��6e�}�*W".� �QB6��X>�1}� NZB8�P��TQ�A$b  �m"_:�Rq"N ^2_p;y�B � ���DB��3�4 <q_2+2���X� �1W�.� "�4()p @�X-��$�%� mu� �&Xw*^"�>mK6� {1,2!�"N�b�n� &z)Z\}=2W�Fw2�F W\}=Z-PX^2-XY.*V y�nZ�Q>qQis�y��_�2� qF ��"�$. �� ing� � M !H�! _"& %<] X!+>4"& w �2Z,�C.:r265%i 53-"3�D6�2XY��12��z E*�5�%>vD2}I�&�%Q&0V(��)�#c&� . �^�a1c P���W] SI�l�`.=)�M^��>saso"�0�#�20���%���)lfi� by �7a=X-2"�b=Zu ��� � in�X�6e7A3"� WEw�dt}HmU"�  � .]1�) D*� Z} -Z(2BX}I.1Y �X�*! TWC'>� 2�� I�T�`ATk remar�/�"� aB.land>QUS �w�OdR~$&��4 nat�6��>ogs�7(easy to derW,Y=Cl��nd 2�>�add�{.f {toc}{\U}{�M. O�?"�& )*~)y->�!fs_�D�7Z �@pPve�@�to�* ��~$F$.ťre loo=� ajbU}_\ve$r�^( 0+|wrA_1) > = 6,&'"H}_`J\veB\B2}+O(3)��AJ$;e�F@[ b0,FZ1}]=0m�r)2).xAJ$8 (we stopp�$�/?$�$�T!ws3�). �5� ��K choose-�)H0=\exp\{-i\ve(EfQ�E f}_1-" 2))\�:a�>>2T ,NwhfIaS0 -!t2(i1+ ^�i2) t3_3-�^��@!��� B*< ``�1lo&B''1A:J�i=� X0]EvAT-N�"�FJ<1<2J<� �FY�cw"n#q�2�:I {i}2[�, !x�+N�]��'A(o!*0ve Eqs.~(A.4).ad�`al� s�>�4�"xS�1a��A�:MvH}_>e?�Sl� z}^* _l$ (�(�=�D(1.2a) � posi�1. "$N�Any��&"��0say�1$,�EF�en��Ve����?� g}_kq��Hz}^{*C?APG?NAJ8�w �?�?$N?M?�00E�ves=�,)���F2�jF���� {i+;m_U�:R?-P? \neq�E� c_k}R&}T% � .�1K})LRB =0} �=I�16B�'D�"% N A�1���Ced�4�Kly >�A;?c&�H {\itYZ��. �X�UI\�k$!�3)*�mk`"�-0�!� w9 �al:ZaO��1D2 F|e(uph�,)A p �5:�B#1}aB2}�f �aiihe��Z .Y�}}5J2}�(?X� " 2�C�I��JKL&| JfA "p"�{�$F_�Jd^$S's~,~2���F�+, ? s]1��TN em~1&�".J�Ba1!a^�s"�s� � t� of� *Lone ( $F^{(1)},� ,L)}+X��%��s�;(A�J� �J9J�� &k^{(j)�+ R_{n },\\ j=1 � L}} a�u�$F�$k=(Z� L)})$ndMDm�+A�&�pD�e0.�mA��5$jF\05S!�T] �=. _0\cdot �$\Ѱy�~͵����c"�O !Ӊ{he�#:I- ���I�0xW4,�/NamelyYL hP��,scheme: ---%:��U}^{-1� %�f}aґ��re�mb�W�^*�  f"YK B� � \ad(f_0)�p^2 1& ) $1�%\:�O.�vOR �n;�* �(E��4� � r# � ���V}"6 �l{H_0,f_0H_2' H�@ )FiH6 �#VN}XCZ0:H2#2 #n�� Fy7aAUYGMn�Lgisa��>7)#M�?B remo2csig�/,\wide�}\,$ 4G�&l"x4=�U�l �1�225{\ve} (AHM0 1)) =B21}]`22}) + U ).�*�M�jT.KN65 $ Dq5� �aCK�.�E� B�Y$/'\ve H,"|E�:2���^22��.sAq0B+�&i&yV >�-�K���g h���l!each (`q Y� �-t_a1�[�E�^�  '} A1 t�:٤�M22}:9�� "���(�<�y�FwM"�u�3 f(fin��n12};�5j\�MA@d�7;C� 2[O�3medskip"8Hthebibliography}{99/dbibitem{GuSt}%1 V.~Guillem7 d S.~Ster�U�rextit{GiQ a6Q\totics}, Mem. Amer. Math�c., P�P0nce, RI, 1977x> ��}%1,2�M.~Bab�P��4V.~S.~BuldyrevS �Ay Me�c! j�SEaDif�  $of Short W�u<}, Nauka, Moscow�2:�2}%2,3�P.~Maslo.Pt]�,� $F�#?Publ. m S�R Univ..�65; Fren�q��6}%5,6�NCo�`x WKB-I�aMTMc01976; English�!�Birkh\".'4r, Basel--Bosthw 1994�1u�,kar3}%6,8 M.%^ aras2=�!s~9Sof� �&se��:�mPIna�. Con[ncaChn!}&XaRel�( Topics'' (�x16--22 May, 2004), Petrovskii S�\arD 2)�8 Society}, Book�A�Ls, 6B:<e%�~99--100:�21}%7,9 ^;%�off&� �f1Dray-Ha�.xProc. 1;�``DayE�!@!uion~--�$''}, St.~P%Qsburg�ers��4}%8,10 ^�e���n-�݁S?s�DMnserie�}FunktEal. A(i Prilozhen�20�8I&0no.~1, 21--32B��aX�]al V!RO.�$kar5}%9,11b�Lagrang�=rinaM.Ksca�V����Yum "�0"�A���1}( 198!� �78--79N�Wv�1)J7>� 22}%10,12b����on�aaloc"8 !�q��sk Y�Se~p�L�� , UspekhiA�.��]�2�,%(a.~159:� 6}%11,13 6��V.RMNb per�j.b}v�5�9!�5, 41^� RussA^� . Surveys�N:�7}%12,14J�E.� Novikova��Yr�, :\X. 1�embeduɮTC9\T* M, Quant�F"�!� y\/} (M.~�=ed.NA:� V$l. Ser.~2,? ~187��B� 98�� 1--202.2$per}%13,15��M��relom2I Ge�j[d �# ɅThb=�[� �@p�per-Verlag, Berlin--Heidelberg� 82Dkurc}%14,16 J.~Kur�(8, P.~Leb{\oe}uf): M.~S.en��1���*� pproxi� on 6���Ce�a�,Phys. Rev. A]s�{9�^ 6800--681>� 23}%15,17J�7 J Exactevsem�"h� �8L�x�<manifolY .� 2)^*� so(4 ��1,1�J0 th. ��3�9� 4986--5002�DFadd}%16,18 L.~D.~e� @N.~Yu.~ReshetikhiM�4L.~A.~Takhtaja��.� Lie groupIX�W }, A�\�K\&}��ysi���!�1�26�$kar8}%17,1:i %#f�� aru�B1X.u�@.�}, [ @ A�91B�, �l.���Monsq� 19, :sR�93�&� Kir}%23a�A.~Kiril6{ El|M�R6E�� B�76# Kos}%24 E� J&� .%$ unitpt6�� �Cc��ot� %Y�17i7�@87��8�" Sou}%25E� .~Souriau*�StrXdes��Dqu� �u2�0. .0Gust}%21,26 F�stavs ��O$++��� al i?q�hN4n a0iau�uA�str�,�J=7I�6 67��6.�$kar9}%22,2:�=%�um" n,� M "��Ti tunnel�%{�LLett.)�>O56} (200h+229--26>�24A�,2f7 ConnB�F�su���jz�_"f6W2$}, ZapiskiE ck Le�k rad. OtdeatF st. (LOMIx#exF 17q �x�54J�J?v-(1�bf{59 2), 105362;}�kar25ad,29:� H(it{New glob�ym�%9T� 0  eof ��!� adia9�/varian%�Funj� m� bf{2�Fa�� 2�� 1F( Yv� Q:�10a�,3f� E��E"� s�BS2WA�� J-�>�3)��r� 3, 393--4�P��int"�HrXiv: dg-ga/95080036�11}%26,3> �B�i�7 nsic��~2&L sE k%Rum"��� 208J� 2003, ��.nm� QA/020704B�� 7,32fIBA�al�Mc "< ,: membrane !�}�t A0�Q-de~1���� A�40--156��308118>�3}%28,336Y �V��� $paths, hol�VyP *�5.��N�57--17��62J Mas-Op}4N�OZ*M��F�3J�Mir&c�>g�1 9,34:ZE fB" ���{ir�34#>��gG�Ih9ur���ycylinb| 20}%30,35�|9X:� of�J%�6�D"�  via :s�6$e Hydrogen�Ŷ:YR}, Teore� . Fiz*� 108�� A��39--387B�A�o MF�O.�n5Dj>��&:F�"| A�*�bfRK33,5s �:>g p$ docu�F} �b\Oh[12pt]{iopart} \usepackage{� icx} % U�K/rnext 9܋AMS foZD��ired %.CWms�P�%|!title[A�6 verg]�!� �~Zs"D�cf�]{An unB�~N1oGitesZve�Q� s�1Y\aa�s�author{M�lliern%"orz&match �recis*>a�"�%�?''�t�isBA�c^>lev�+i�*�ng� cess�T|1{tol!�ed mis{.A��a�desA��0mayX0low#@a� M��n'm�"zposed xu����A``gues��RqF6��o��m�it updaQ�t}� !�ŕa+ of b�$ht^N�4ir465�c2�]�C close ��s) m��V hown)qmB�a�FJ�d\I@a�Grarily 1��EL�-lZchieved�#re@ , U^ipba!� enti��t8M�ic� side�-ons�K��!should�:jf?�e�W!�n�8� A�erial�� y� pend��"�.Q ��law-`ucA�%M|T;llu�O t�I�an #. ��(%�-mitto{I�se"� �W�d�� \�8g��Aw�imanufPwsof�J-i�ygla�wr�ala.duc��s a�" llenge du�P%3co� xityO!E phen�Ra�1iDd d p���pr� a�˃�gt�9!tro� p�!c9l*r�Qp�~ers. A��enginet!often1^o >��@ aq��,n\� �+id�`L^atQ9bA��:i�#My6Een��y (�Di��)A]�Y��߭Qon�O��velop�% fficiAw!/ accu�z�]e�y tech4o� �p�*F��e =!�hod$,AgH,�nt!�g� toward ? soluA�hI%\!�too�!�umea�for-SqE�7�0(Chung03,Vie+~0ent01,Sousa02�i re�& �rein)/ny�h�2fav!�``WAv-�r''6]t!D�"� !6 sa�U�:Y��Y��M�`�8i�m!P�vn �aY��per�aed*M{m>&er����Dv�tie�#)URM, o�D adjoint-�::1� Sprekels}���y���9as;!1 prag�'c�ϗa�cmer� code!�, comp��o9 ?�gs�pI���ug� ^!� ZI�2�%�� U�in�A�A�lacq()�c!�d5�cy,-T-b-Au1)�f[�6�xissue �fvKP��e��P�@\a$g83!w����st.�ng|5!' F' �back-�u�? 2AmI1p�� a�e��lq by�df�� �s�KARdi��q�2��0Kim90,Zhao94}���Aa� cept~�:oii" /S� 04} comb��A? 8anFh to� �J� >� in�� 0�fK !6�h"� 4:AI%@� �*�.cyl!��K�^�!Z!�BA9�wi��b�eBhe�2�� non-) ar viscoe&qic beha�`e��G z:ly few1W2w�V"W 6B��Hfw a"� A�g�'A|��ooY�n�c���V������ 5 !F�qa�� a weaknes�C�6�8-1�l3 2�domA�i��Savolum�Leain�R�2ai�h��e���teCP> a mod�o� �G�|umvE �Idri A���n3de�mw ��l� ŐrA,rr�DV�adp���)GeB&uI {nA�@P� �3 devo!�Ygpe�%�2�t5��:.� pr1� s-is }%��)aZi&�*� displace7 M5�Gy haAF�a��7l magnit �.*`s�s��!.:-{De( 2�>�})E1�6� *W A!z-*u�A�A $�������N�Ec{U�:FP*9who>Wm-<8^]D"�M&\W$(x,y)$!�!�Cartej*&�G$!@�w�n0� on F�m(e \ref{fig:� ��cOe�qe�0Ping \scalebox{0.5}{\i??Es�4.eps}6a%�{Sket��� ge�)aU J� .} \label� ���a���f�. On $\Gj[ _u$,2�iO]�A���eL��m�` E{\sigma�EClearl*\fo �QBc� &��cal��S%!���ed�z� j�.'"I s���;u2~ ?w3o� v]  ca�0iry, �� G�ys-F�N �%R+ one''. WWlt4e��c8�ya6Q� E1L"^U�Rbx al��Ar,�7likb=nu�m�Xm3sR�t1�g�T� xim9N��� 98��(��t�@>I*��� algorithm!��0 ackl-0:8a� ) j /�!I�� �8$A! b, �X=* ��� . IfAiscrc hϛs � s�E,:�3 � s/�y�jAfn no�(�mesh.� $M_1^d,\l�a,M_L^d�]@$L$ZDQ}N�aIZ{ini}.^2bas�4fm"� q��8��(>�:��� $M_i}!�Icպ�M!1laVo!�n3 >jߑ�(super� 6A#lW WonM . At�;, $N_i^jDBx��D�p!��a ��5%y\v� _JA=f.x�y4i3Sst!�$in pseudo-�"la&l@{&S� at���;.�c{�5}:A� �M norm�#o measw�� ow fa�%��cF�iMD)��1�:�R* tt{��i=1�L} \{�eqnarray��eq:subRj!�OM!�1 & = & d \; ; I�� 82} %NZ81$>= !VD3 D-A)F��Lc{h�K��nt })� tt{j=2}; F>Ej��UBsAC�%e�n U;�`!S�5:-F,j:,.�Do1�>���4-l)�jFh {j-1�?c=�B!�j%�B �dEEE J]j] ZD�JDY JH2  I� j+1};\}A�ZYWh� $\max(||.�a�4j||)>\epsilon$� ��Re-X�-�G��l��EjB�2cu��ck ����N��F�b �R��J7(>�($.���).���s������ �\val�oOjbuy)&a�%.mgI�$kF�8enle��aJ:�0"� }T�shB b��Vsub"� � �8 �A vanish  intu�"���N�w.`:� � � 2}�rec[D Si�� �!|a�OM >g," c"�E3�H*$���j�u!*1Sl gardl-[*�=�his��N*5 ~I/u=��A�� �"mBE � a� ��} ongl� �5�XstZ�"�3relax;.��4J�opt�>�6ͱv9"� pBxi�q�KtoNm"2@�M�"�C*L�}23 �!|V�1�-�(v� w^� : F��wB� !� incr�\O !�if ^}\ st?)YB��� �H%�� &Y_*rst�� n���! to n" �u"A��c�T!" N��>�= U�{� j )��.j eq:resvec-�� }�n�Nsuli!�byѤ�*�0pul�&� ;\\pdeq.\ (p 6})�  $Ip�� ��=��6�-\left()J!? \right)�$$ Su&�)AgB�4}]toF5}�L�>�"3JՖ1V yieldE\��� {j-26j [%��*7 J  ( � N� N:� 9A ,$$ ��#acc�gA�B4�� �)�|.�� �&��6$,:`M��L����E���E� . A�^e$ $(j-1)@ye2�!�a� �H ~��&qs� � 1},y )$�$� by T���&\taư��b`d\d3zA1l*(�*� "m 0urijm1} {U_x-P1} � U_x m5� `u#D~m^r�Cx}|_i^d.A%-KEvDy6D5;- Dh.o.t.a�,6? uz��yJ�y.�:�F�y�� �.D���B9��$-�2�,{U�m��[A�c&Q- .i�m��%��lɤ�Mstt�spaE �_���2_�tak�1Q�.\\ S�� a:�����eq�%�f&�J�a2}�b�i��.����:�����f�.>�Sub�ng:�%�LY6_m1�:zijR3�:~*Y �2n-1d\wJ��{j"�F�x��rAF + :"2��b�.�r�wF�.FҽB M"�+takIs:C � � (W & � �unt#re+;e���$z�N � _{xx�"F76�67yy��S "�&re��J���%w rf}  ���-{6��d�961��+{B ?�: -r -�:PMU- {B P-aF�:�z.�S�B�.gM�:�&��j�6%yyR%�%% B.� 6�>���:zj,5� E�nd $(5-,5HrNx-yJ�>x[ &9 j�� 6�" +O j$I�Mive�wK_f��gh.j*&�)ib�"extazC"s3n/�>vnk$t��"���&M,�s�!&.$vB%$+F�6g \ll 6@ < �d!�z�>=yy} <1�!�s�v�+�+l1�2�!�2%@F# L% .e $:��n�y�����R96f$.�(|.ou7)6T�b�fe5>asKbf{ >(I)g(�" �(uit�cho�/�%%�* 6�2:��(2-6JIZce "$e immediatase� f:Vis�sen& !r� �x} R�u�F�6�|O �� m� �*�����нe�0J# �y} F�6���A6M�s{� ���2�:+ &h����_�� zf})z�<J� to-�^F%=6�xx} ��0�L�ƢI�rm{and- �:T�P6' T; ,���i>o�cl]$�iG'�Mͱ'�Avi�Oe)ab{ ��lQ�m%W4i��57�W��'�4�5eta�/n 2�"+9oAe��3'���3�#sF%s&+]&� �2@E(:�����L�#I���>r`�n3�,validK1�c�)�"ސsn�j�su]3ly97���.*�WU�mgx>� y�`� e(m� read��!i�5�v X xnicAE�.�Q�+1� ��F� J�u�m�F=N5qOe"Y�6� �y �>�J��F�qx.��f�Nc����B� $Nj$,6�B�J>� F+J�$ ���pe& tQ��%+c2�&97t}C�EL�er�ae�Ua��^��-�I�:� )�)�G&dA�^ �*g� ;�'+2�](��U\� .de���^���satisf�.��U(ly�"C�aɨ(B�4 ߅�:&�,>/�ay7��Ri� 1AW.�Qo�u .�^F1J{ 1EdJ�]4&%�g d�eq��N,J:J�J�� �Al�?r&� l�7!+.J� A\.&�T�&�*} A�%t�C, a�j;R!�&diB0/s �4de|a��ree�uzY:> gu�0E:aecAp(radius 0.01� �]KV��,:FT %�U���U_x,UkrS=1�\a��(x+y), -y)(\;�X"�.�B Of G��&!*��?aWt>D���":w)�}�8ly�@��!A9J�r truex} � (�>)1$+� =:.Xy} *d0vX(2X:| e $(�^^)� 9)��loI=�!/@3l�:hA�R�ho< a i4 andiA!�* "�"6&f t��:� 6� >[6u� ~�! �.ll5>c3tҹ��;�� $)� Y:#�B"*C;u t ,�r� T"� (a)}&�M(bU��(c)}: Id0�ߕ��"�5ej.q�W$ s7, (�|=(��2����$=0.6.100&'�.� a���4d�#ld>��J/52!" 5)���("!�>-'ya�j;$(%�6�);�d!8 ! plo�Nf(n'||� ,�f�, �,g � &� n0�&�# &%@0S)qHU( �} �(ul*D3�":^&.M� q !�TUB� ($L=100$L %B hree&�=���1$,Z*Q4eac*�.�Q-�<&K)eiy P<s� N2Ez�"�-�(�2ly ��e6�LB+(D.o&�2�>1^�j�naked ey�7Aad�Ed�fngu:4� fewerY(Z&�$V q�)rm�v@>X6QR3�"�l' �fc't�Gu%�wo �l {s ( rs&�6FsaJ��1�em�Q��n��a����max��� n�/ r6�/\>�O�"�+p>3�0lot� .�i�Ru��Ds�.dic/o�?rat&�* 7 #`�n�8curren.�Ϳt $� I�'$6-��/B ||$,%�@Bh�He�1�II���)��}y���&�%2G�^ virt)A�U��R{ 1�J�0.9As�Y�9rW9��>��е��GeE�:��60����aA�� * 9n �� BcI)}2� 9%D�� N� r!AI61�"1��FT'~� b�� �� �N� ����f F�aԁ�x)ZU!�� o� well sutDa��i��[�1iy J C� "�Ge"� =0.1� �)s, aqb�1},%��api�@����k ��zJ1�.�� �"R�1F�11E]�l@�D��0.1%5F�a�ScFz% }� playI������%Ma2f414" nfi���m��ng�� leasO#�1�h��*��e�B8-b"�S+locE (6�%su�#)�A�x U�*�@N�!�01>�P�B JB %�!36D�;M���1Ni E9\ � �Ʒ!WonG1cl��s�Oa�Y!�cu7Spossi=Ltoz_ �.^Rm�:Mver�Jeb�SE mo?!�J1H.R � N ��mR�=6� �6m"f* !rF�IH �@ �"Y��Q� ��2F�S.Gt�4a�6�Ao��er&6G�5�i-���D:N0 �is�+� �3a��>�I �i� �0�N��5�Z�6Ho�i+y&�#G�S�"� �"�"!�J�#�lyirtantFDA�O�E6�!!-�GM��DA,}3�7? v���>�/.YTas257$ ŗ�,2)Qim�8J!7v. �v�#�TQ�A!�*]�%B� �6erE%q "� 2�B>=�A9 A�"cy%off�!uwa*gMtZ_a�R!p~:�3�7+" 8&NmA 2+Q��t�Mf[P&F��w"$)outbKd .?R%�1�NB�q�Z�a�*�V�9*^ՠep<| seue�al �]'� ic�&�8� � ^ 9tI�;xR3V j��6�e�8in: :�M�PB�.��}�!�.�V!"�Y�@�K� e*�TZ%Fq�"��*�"aW��� y a^� answ!k� !muKE�m�r:uJKAd#��QAa�RnM� iv�~>^!��"*�;b��V<9of]% M_(*�Մ�4d&< %�"��&�QmܕL �\�&�Q G�N!��bO. \�Q!��P g��u$acknowledg. �un�-�Eu_Lan}y�Jroz�$he MAGICAL�N�\�X*�K *{Re{Sces  tNc"Bo�k&b �pJ�b ,a4p� ,en�]{k8cl�&*�bam�_ h,amssymb6�bb+N6`eucal} %\fi % \ifx\fltex\�6R)(d \Declare�cVe��{�!ptsty�:�bso�<n1,�Rem2r[ (]{inputenc}�[T1]{@c2|cK {{5xge�* �NA {\sl� } %Al�aet[�kul�2er o` n%sl&�% nt \new s{thm}4@orem.}[�]:&l�}[thm]{��.}:" !Propo�YonB'cor &,Corollary.} R@rmfamily} %Eksemp�*$og bemaerk!2roman:�ma�eq t�im. (M� P)>� 9inf;ua�[B=��� xDA�B�� (Re��B$e�� %E B&�� $C��%Y \Ui*��0{section} % F�ormelnummerering \def\labelenumi{(\roman{�})} % Enumerate symboler \newcommand{\supp}{\mathrm{}6" dist":" Prob":"(cA}{{\cal ABFFBJJ>saqsa>GUE :�bRYmathbb RBZZBHHBVVBEEBCCBNN>Ex=� :�red9 : (proof}[1][P $. ]{{\it#1>)b *8{\noindent{\bf 5: >-e-8hfill $\Box$\\}I�endbbox{L�break\qquad\vrule height4pt width4ptdepth0pt}@`>Ah{\scriptstyle \blacksquare}�a5{Fz:94 %�  �C{{Q~%��BB�EE.(Fe1HE�NE.RE�YYxZe(VE�QQ}}�A u�+C��C1 5 CDBD�C1,5C15CGBGB1(,5)CI,I,J��KK,LLMM1��5�CO,O,PP1vB!w �1�5�CSBSBTTUU1�X5�CW,W,XXQbBUcCQdAe �unit{�S�z!ti{{\rm iPe ed d8eps{\varepsilon�- <{{\langl8>82lma��lambda_a�x�2 lminCini� text �d sumr�c m_{i=1}^r �s. {r+s� tr{{NtrNT2TGRAk�GRM4S:GRMA669^{\U?GOat OE<OEA\6^\ast �GS6<S<S:<.<im.Imvr!�tR���.46gra2�0Mnsa{M_n(\C)_L4def\diff{\frac%�d�~@rm d}t}\Big|_{t=01�-zR.z.z6.lR.M|.WtR)�cc{^*-s(Om{\CO^{(-)B4Oplus{\Omega^+(in-+d ,_\delt>3>;In!`rm Inu�0Dist{\CD'(\R) cc_c.0Cinf{C^\infty/Cc_cF ordearm  �deta� m de5#Gmj{G!j5 Gmjp +12p{G_{+}B/m-:@Fock{\CB(\CT(\CH)��|H{\begin{pmatrix} 1 & 0\\ 0 & 1 �-!jB4\i5-\iR7kB7c \\ -tR5lR5 \i\\ u>6$ %\pagesY d{empty} \voffset = -1in \h:� econd� Partially��or�by��byn`PhD-school OP-ALG-TOP-GEOR�the�(Training Re � Counsil. !Qtitle�$A Random ME�4 Approach to\\RLack o/ jections!S$C^*_� (\F_2)$W\author{Uffe Haagerup\foo%�{=�@,\; Hanne Schultz&=-\;% LSteen Thorbj�rnsen1mark[1]4date{} \make�aMQabstrac�� < In 1982 Pimsnernɥ%*8x coefficients.鷙� ��{Introdu .} �&H{sec1} In \cite{HT}�npr%�!follow�Aextensio%EV��'s2�x modelA aE��circular system: Let $X_1^{(n)},\dots,X_r^$ be $r$23.Z,$n\times n$ :W�M Gaussian � !�8ensembles (GUE)E � scal�e�in6��X)?0$EH+2�y� $q!� A�Z�)�.�A, $M_m� cA�0 deg$(q)=1$, r�(2} \sigma(qj�$)\subseteq.6� )+(-�, ) >�eventu� ase�MM$ (2� ). H$ �$\cdot)$ de� s�spectrumAa� or n el�XinuSB .. 2 (Mean �^ estimateE f)�s a.�of�degree%v}2�a%�A� 1,���M E$phi\in .�bR,\bR)$=�narrag l�E�<3} \bE\{(\tr_m\o�� n)!phiz�} = :>au=>� O(\t 1}{n^2}9��wh)��=61m \Tr_mf�Cnormaliz r��� E� bC)$2� 3 (V��nc9�s��ږ (5�v%4!�V:� !��=Bi�ι-�[ifUH')s{dM4}{dx}$ vanisheE�� ig.* q^q>�$,!�nrA5N���4}F�A� $ard applic��of�P Borel-Cantelli lemma�nAn,Chebychev in!>�Jto.�3}.�C5} gives� .a$ 5Mo�S>w ���Mq3}�6} :�r�5 =�� n^{-e� 43})���J�,%%o E =/ 2} easily s (cf. [��T� em~6.4]^ ). &n S}El �6� ��2he above!� real� symplIc&� >� (;GOEoJ -cas�N�[ new q le� these � *.�3} <er� s. How���-c formula & =!1 5.6]{S}):yp1�]#7} �����E/1n} \L(�h)F,>S� :\colo>�)V bC�*a2�  (i^A Pnse of L.~Schwartz) d. !fo ':V � � 8ar field ($\bR$.$\bH$).� byM�L�P ~5.5!�v�8N upp( �&8 �BB�Us�}]7B� 8} instea�.+3� ers!%G2BG1} couldB �le�ess8ly�the GUi/. �b�lFY  reli>&�,techniques, �ly!�,Stinespring'�teorem1�$Arveson's &T�emaT �ly posi maps��e�� we��� c  ic2� N�w�n turn a� s us��direc�� Y��* gre�KnAZ result,�� in S�� on~\� sec4b)�>8!�a>�� .� (resp..MZ ]&8}9N+ �[*c2�� ,of {\it any}�!6 in� �  Also.�4},.�5 ��6}�H�� �&(ty. Consequ;2G2 5s�all such�.s� - ll th� �� ,!E� GSE)�8i�e"�on � .8>�B5r� 6��NN"Vi� {BS1)�a "j!�=�>0.zus next��cuse�2� t6 !�"](\F_r)$: Rec!O;�S8.1 a t�)� 8ha�l, +  pa�rv�#embed�� u6� ,|)$!0� 2� $��R}. � e !a��f� C^Vj)$��n�9H� ! N�>�5}E re exist���$f i6f�I��$$\|e-f\|<1A� f$ tak� �(rm \[ f=\va82/)��]����.>��%)r$r� 2#!�!Z\C!� and -�$$-fun��Q mpac-�,��C only��s�A someB�j . �aider now>:r�� �S de�&bed� q6�we ha� ��> *�4 &=&>q z26 \\ &=&Jx (f) + O6.6 *}Ne !� he�!$cor��o� un>;$ satisfies9u�")9!#�$T�W  n(0�%|e)%ZB; HA8, uB !t�F!o �l�J-RJof*�͇in���6�bi� !*� J�11r�\�*m�*Q*j}   e\in -e�5FO In p Uz�2} 6�l �f��}B�* two�t�s.�11B� 12�["�by ZNimE�\{PV})�H (!�^0A�., =\bZ"A/�� $[@]"Y� AF$�� $1I� $. Sa1.�f�� l � Cuntz �Cu-2L �L}� nes g�#� `[pp.~269--272]{Co} a more� !�.t !�"�Fredholm�� h' argG# can=furth�if� to� hort&con�ed w out ex�it �io^"of >{ ( �Cu2 cite{CF�t I�&���c� ce��hAtA���2�*�  !Ln����>� �� �*�$>� t �$mAQnnected�on�Ia�� ^M$ = I_1\cup&  I_j,\P/ (�(ist}\;union}.� each $I_ bf �� rval0a one-p�set�Pro�*�6prop1})?4$j\leq m$. Let�eY=e_1+�, + e_j \] bee�6de��o\a�Ci-yFw c� (nto ortogon6�" �pu�k_iO.3�{_i�}]� $0<9 i,<'3 _0$ v"�,iS � $est length���o betwee� sets!�H I_j$�B-6�]>b 9�aa�3fnumbe12�f $ne �ope]As A9+f $, $i=�j$, are {! ly $nk_i$�!a�) b� z�E�! b�!''�LI%���p 1�lNW"-J� �Ɱ {BS2�^ɂof�;a"">�8previously stud�uN� *�!�'Rgs.`,be�!2�&be�*ropfaktorisa6}E� $d,mH$m'� i�ve �ge\&� p!23i�{m,m'}\� C\�r,$d$gI�E'is���w $m_1,m_2, Im_{d+1} �&�s�qu_j� {m_j*j+1}}}j�, �D (j=1,hd�7X�X"j*itemize!\ [(i)]�=5C �=m'$, &'0\deg(u_j)\le1` 65jes$\{�r\}2@Ap=u_1u_2/s u_d�� ��%� �5�proceedsA�ind*$�%�NotY I�ase $d=1j �',� ssu6&��$d\ge2)�A��%�on�been verF" *%-{EFz� $ ogQJ�a d-1$. GivIU�_!#�–ba�Y�� may,��!$ $X_0=ŀ_{N�}4 rite z%*A�V#Q�X_r)=12,_{0\le i_1,iY�i_d r}c(FQ� X_{i_1}2}Md�] !r suit $� c\[ VW in M=*q& J� {0,�r\� \] Fo$+y $i_AAnA�6(!$e�Y\: u��>�.�Notu!�a �split}F� &-� i_1=0}^r()�m�L)]1})+2(2�:� ��>�X$) \\[.2cm]^�{m�r�)H.:�"�0B�M0BY0MJ&Fr�im .IsBiY(0� Y(1\v� \r8B.�u_1�$.#� p'>�-��afJE:� �  u?(r+1)m~�,�\[ F�J��W� ��z].�We�a3�͸1w& �� p'�� �~R, �Z hyponi� ��areF_ $��m_31��E n��s $u_�.�ʦ�$ ($j=2,bd$)��$'$��2=)C �$ �>� /-2�� �'��� ��.�>� G p'=u_2u_3�V� Now, 1:"%�w"j e desired6s . $:'$"�r31}� kag�( udtryk} By�io"� E�BB8f2~ �) apparenua�*,�ciI �#� I�*g, is xly )a�:a_6�(m_1&=m, \ m5� 3-�^2-�\ , m_d $^{d-1}��M &=m'�� u_j&^~� �ȹ�:J�:":�, \"6� -1���u_dN�s�:_d��'),i_����d}6^�?�V�a�d$ sh� though� a�,block column�x� () row'dex�0� tuples $j6d ��a �0?,.a`t &pI}S:�1,u&u W$�� basicly[on[6,� Cs�"R8!ly�"� p$� /&� e�im�/$m$��1ely^e2�3   ���-�� � ab�$p$���aw� inv-:elN\CA$I!�4N�$g {\CA!ndV �,^� bJ1.m_1=m=mu$$. Put $k=I�j�=dmN*�����U 6� �� a�3xA�j$�$ 6|A)�nd.7.� ae�-A)$.  }<�\", d?4%�g $A( -I��k��A)$N��&�0J}l�% & -u�\�yl s�: � !��p2} 22!&..�: & F13 13B- & J ddo� "= ��oe� s � -u_d �:6 �d}4#n&�;,"�'1.#19\�?j}"�.%�a�!�m_j-�.& -�.��1%�7G[��@!�2�2��"a�tibDnuMj ff Y �9kI��]4#%\[]S^{-1}=BU�+C� %*J}!_m!��0�  3u_4>:Yu_d6z \big�B; �q2�   & ii�  �A� �$.�Eo>�]� CFA>]0! ),{mi{uez� u_46�6 � ͈N&oQe�ue�u%r6EW E .E.I%� {m_4arB� 4u_5FA-�R�i�&}�� ��2��7�%� � �� 6 :d,e�Q. D�&�`! biIe?he�-) entry�"%$(1,1�;��eb��v"�AtN2�y�u���F���We ���L �|�-m ak'=aK(f_{i,���R) )_{1� i, �6�to�)Fgof.$� � ua�u� yb.. >From|��;0�k=h��getJe i'KitC!B��i�>�%71}5�=�6�C}_{j,1}&z2� n�#1.�5J���RQ!�����s��{m_i}, &�Mf�j$~$\ {\pmb 0}%\tt9 m_j}2.\ne j$a)�\$j=�� becom��!�B}�� f_{1.�� f_{2.�m_1��5@5�V� &� .~-1�$g�>�f)�5� -u_j+2�=.(j5(!� p!� .e.,�!G2�R[.!�e1.�46�Finr7:$j=d$&+%ly/JI% >g+f_{d2�.�d�r�6Cu_Bh.�j46�Th�:b�Bccess�* 4�*� x ula&�9!  "� 1.5}%�finA�BIu_2f_{32��Y f_{4. =�6  �>= >&N] InserW�,�y\�:��Za�ը1}=�p >�a-��( � �% >)%�O L;"�3#>8�To �G@at�%$>*vX.��d�!�)!�a��� ݙ�� =k$,� � %#��t�iy�>�=��nj��06 d �� �́*1�J-21W�d�u_d �B�6C ��v���Fyqj-�_u_{a�1.�2�1u�jv�6Cbn.�7B�Br�y7��[ �=E w�Qg�2:2}� u��2&yq�� !�ij�6n�>fQa^? 24t u��)E5BJ�� �s� . A�0�1@2�pBH �\�l6�mces $&� '$C�1�Bed��Bi&L.&� we �Daߙ�h+C���H&�8so#at 6Hq>� �e��f�"� r; B�� Y\ 6� � so)�፝�t}=792N� m^cjr����99&;J��g�� .ilM)a�� -%0^Y:U�1(X-��us jins �\1��� A(I6)C.�CJ_�A\��� �'"��I�V�=B�H�/Nex��"B'��$j&\R`�e )e6�C$:�i,.v�'�V��J e@yZ�!�)�cR& ����R�N�L0,2p>�5�b� u_iu_{i+1�"Ue-^=:l\l�#j-1B��+1�]>�B$2&k� b�d,j)$ in�d,jJ��B|!�U>�����q��QR�j�%"T�?�Ps� by"�Ts simi1D�ost$6�;R% cor}} Lti�Oet� R/ $89\C.# N3,Bt,qt/ x_1,|$, xbPMs�"9�B �!.�BinFg>�%5Xse a fac0z%#�XP�:*�-:#M,Av�.�-�u_d%�PuE�v_j�h9�g*Q)"�42�d�" '&?!�#v0Ex\CA-pj k>� "k! !� �x�uF,v&�0v�-B=�F2�ny v�V!N@� 2���0Nd!N?2�;m\RL �� u��-�*g �R�e�v�RBD)� {m_d>D6��FN� � . 0a� By.3A� CorollaryzE:�,�6 �8c(�2FF mS:FF�`/1``lF)G''� wa*X]?)&K��use�S2'G7Je�&$GE"xU �com�GlT=3#G:"�%! t"�J2.2�C�U�%ak $\CB�%aEal $C\cc"�B8 �� .�a� \CA_^a6y_��y_ B . If ��W _S�3a_0, ayv a Bi�) Fi>I  �"��� eq2.o>�$sSY/ (a_020\CA + \8r a_i  x_i0�Ip'S�IBRIy I%9� � �z7 5�(1�qc$-homomo�Csm�[phi : !��0\CA� =|8x_r)\rightarrow6-B, !�K��!� �] &c' $k$(x_i)=y_i$%��7Ur� Ao&� �#S~IA�b",V�,_<_= $2�2$-��&�<�i**K%�� t_6it �@olH"�Y�B ~r�6at �.A�a<�U<of�)�41�eB�5;X_7n�- ��bU$.�1A2I�vLK!�Y�$!�$ y_r)�6�C.e�p��75 �b�" �6q�.' EB�f2�- (�"$m=1$),"� f.��\.�[����;.q�! "l1w�B �a,6#A�no�^�.~I for *�\C:�\"�'��� ����V$inv} \Lefty�*� �9 v_d:M�_?���b _\CB{.A" {B >��F .e.rf2�f6�EF�pF��6��I�B�Y�s �w b�6�aG�&4tral radii, $rR�M�.�E�)$ gIyr 3! A.�-geqF\��Applying�E��R�e?-?9!cc p$E>�%8�B|J� \|^2�B���m���mapNphi_0 : NUR FR&�'�8"��1�9�is well-�/d� �Rd�=�1inu`dE��� J � �0� r � to $V� .� "y`b\"� �A�r$. $@� $.�@Norm ee]s2�b3}XL�J� "�# a fi�3|NV�r�EOn�Na�AP in (L � >y )�_� ande��1n" �Kwe3 &#a1$2�b stoch8j�' .drFfw5!KQ$�o (n, qDn�<DeKf 2>> $(Q_n)_{n�$�aR2O defQ_n} QooAn)=�>�c( F�0% !�nA�6b 0 $( !,\CF,P&�_e�under�%�Ya[c�W�k$d={\n g}(pA��>�Z ccor8Rto~| "o >4$ D4A!\Ni  $[41"_4?��s�0?64Q^Z�D , $  q�� "�B�92 2E4M�54Bu_j)�a�>gby�#-�xHu_js= ;��z� ��g@K$)�p�5\im  = e�`2\&�'- \cc��eNG3�. w $]�.F,VF n - .7��2l�rV�E��$�/�ja�iteZI ��Z37U�V+2�Cz���.�x^�3�4Aa��!�>� "W .Y�u�g.6#\ 9NB2IN^>23RB3B"�|��� �tO��R� ��{d  �2Q ��!>�6� &; A|(�K-wiseIv1,A��� $ d?"�8i� d m_i,"-�Ga�yS �8vYh� �� �Iist�tants�C"p}, C�/p}t 0$*�U�1� 2�� CM~6�7� v�h�g }\,\E\{\|.�83\|^p\g<q�1,p}+ 2�|(y�.��Ź)"�+� \NWrji&�(#may^3�cB�L = C_n + B_n^{(1)} �):<-��� +2)� �[^ C_n=-�q�2�A�\h]9a5Q�2F� u_{2Y� u_{3~ u_{4$xVFm}�+uZ��JB��f�J"z�2�4R*Z� u_{5��>�n��.*� :��1�5<��R�d-1��vAIMv�j�I�A�=>j� :�Uw=�=6� =�R+5*!x Bi�q1�# �2)a�>Y)>�&!�1I6]�!�1�u_0"�9�S �. ��NE�|�I\|�Q *"w �c\|$� �+#-e�dG primar�jn�&i& $,(\|C_n\|+ \|)a1)� 2 J�)��no�P�ZU!L-k2\,�ux� `,R�_ \}Fb c2^p \,� �^p� �c^p�J��" f� 9cu�1cKn} K��m� 1,\|]5\�.:|"B (Q�\|\M�*Zw/XW8^�)E�(d-1 + d^2 K��d-2�Wd^2(1+� ����#pM2uB�7 c!Z=T!cd^{2p} U {dp}^Hq6 2pd}R a_ &=k^J{C{]z!� 1�� q� {2p(4E�� d9�-� M2� (�cK�UVKn�!�_d k 1+��B%�j��\| )UK�l$4+ ,� >�!��!^{(j)}"� y � {>�*�`��r = a_ O:�g� rm ck  X_n)}�] �b!�u%�}1%�(1+r))+a�eB\|�|, �j�z "�\|1  ,%1|\%n3} `F�2* [S, � *k&� n(��S ��})<�Ֆ�binIL. 8 Ie��), !"BEz !C Iy)�" un})A!�6�?4"�2:~I��0rk}�nAR\GOE(n,� % 1n)�XS�i� �efWZ% -Xeg��  st��&�QyA�sen&� "� M\,>� beca�!a6c���Z�:�c%\[ %��H\sqrt 2}(Y\pm \overW" Y) %a%; s�b$Y%<�2%�G&g %$' �^$�*-)w8$u�m��."u")��-���"�+.'R��&R/x�:w�"* s;w� �Y�lJ�= �defq} q=� e. �O agai  E>�&�vBT�� �";)B Vn�"j�G� � Fj>FB& :2� :R >6A&��)� �Gpt� v?&�� "^�X\CA)�5 2 6C&aX���>0$*Mn�% >!�F5�a'��b'�Cr�A� \|YH ���'+YR� ^p)Y� � ȎJ�m>i�"9�,�+eJ!pmR� 3 &OI�A- q$ 2�.QBl"*�,*��L3+"@�;>- *}}�%g = C�n��L -q 4+�.� *}�C��6� ���K  %a�*�=3:w}�)��-2�s�7ba3 wm�-1.a��:]ehH.�4X5FX\".j �� ,��r���b J�2G �:G�i���� KM�BER�J"M%�=�!~E:5 !�N�#E��2�" �E�1A��E�:�1 �A0aK1 �30"�hVB {q�z�w�'ve�&����� >l �[j�2^p��� |!9&8^{!FZ�U])x� clai*s�T6� %%(�  *0`�smasterY:_B� i"Ky./ sec4V�1&�wM"�E Q�ie.�yf�I�-.�,sFSw� �s�ptookl: 2�*�� ,�!TgK" * d f��� � {.Kar��nK-p�-�`�1�:��sh4conE�S {\ity } ve�1"0�ێ)^r�ichA�Bd&,$\CE_{r,n}$.�Yequip.��EKinn�h` $\_e$ /q�� \<(A&�-A_r),(BBt, >_{edC�mB-#]j�rA_jB_jJB  (�Tin�i �!w�R7e:Tf ) | �|_e$. S�H%�A�%�1|%� ar is&~-$\Psi�e�e$%�-�\R^A.2q } A ((a_{uv})(Mu,v/Mn}�Gu\le n},(){2}\re#v})C< C, 'im'bJ' \big!J9K2.0��� $AJ���Ec5<aU�� natu�&�$:�%C\)z5�"z$R^{rn^2}$ :=)'.I[%;>)=( *)� �r"�c6�AQ�� ]a"MG�O@o an%�e�O5�(�,][� n�r�itpr�i}<$sual HilbeDk�A�. AV�Wwe � \NfyF�El)0 vi�5Ps�I"Y�wa�R�h%��a]�!� .0!%�"�=$di!�2�O*X�<uv-6f�)FWWn~, �; R>6ivjF6�..Q~"$k=m_1+m_2+�2s mdeW=CQ�n)*�92�~�' "�%�Fn���� '>" 9�Ut$) l"�)E��|q"��t�u�!�(9") r"f," B��%�&�G v�"4o�mm��Q"%�Z`&J11����R�}��b�7A�  k-m��X Q�� n -&.4 5n -*�r*14"7� �>te)��'j\�a�9.�!%��0B<La X��qua�PanE S_n=F�� 5��a_j-  XS&j9�P 2.1a-O�E�H��\ � h-� -S_n�!�) vx^La& i" ��vS(6$$k�4k$)�Fa% HnV%=(\id_k���C(b�8%]&7M2�%\� 9Q���t&� es�"W&5':V� =til&� } j).�$ �Ki� �0�e�h0 A�a�g"C:�j��QA\E�\{.ma_j.!�? + f[e�1u U�@f�{ nEj%w%!&�w4�v3��v�8M�3��.aJX6>�L scri.zi~NI���learly)z��":dZW��)?�(V�W5��6 $M�,*�9���a bove*� toz#EC!9F�Dmapping $\tilde{F}F= �21 �:? @(BFOQ!I-- ./�Vv_je�i�&v >mx � "| U/^�u�/ � $F �^ \t>� �,2� F=�\circ( �E�BJ%tIA>r1��eb�� �= ^ F� �q"/ ) =F� n$2� ^�X� nF=(\gammE� 2� 5 )$Q� &1V/ \sim"�W4i.d.\ } \ N(0,2� �.2�!�";k��&�E���1 .X35u addi�& Y2}x6j0amO e fus�$F �?"�:ly bo�0d'�p $�&[�s-f��Xy 6��.%�ne�o check�T^ al deriva�J��.� �as�. TC5i�NxN€Ay�+��orthohal�eir�_]m��J&e_{u,u@"�� (�]� n�m�nf.v .=.+fra� �}�#(_1+e_{vmA�)"� q�/tgvt\i}ru-�u-cn $\{2�\mid ��\�fre6�.��o �Sm�;�^��=A�C ��s�pe�\9�&=���?0,�5�0�0!Z�-�j�Qr, \ �=� �Wj,u5�6f22f6�f-8J�g �Q+6h2�hB��.a9�� zero/QiS($j$'th slotD�=� (\xi��M]&} Mn� Fa�2 +& tCa�A Qkŧ)�)= 2��:>�+t:�&.q F6E2� �Q ,v_jKy,v_xQ��  �Y \ r .� o1*$ v_i}-t(*52�)%p .�~� �{I _ b�Yi�� ��:bl&F�`�2A� last:�]$G2� 3�F%�_�KLFIr]�I�}a�� �=A�!��%�IV�2#'� �v:v,YVZ:`��2��b.=end��]�>e�� o�t o2� �rK*; �� ү ~>ef0 N  n�be ix "ٞ"ݝ� . *�lj� B��[: X骱�&=(&~ _{kkA�.cT]�Y B��\)�.Ma�>� "<�� ZQkl� �yqrPim�P65!�&*��*5��f 2�z��rUw.r.t.P� ^  $�h�>&Or� Psv.ɺ���u�n:�M:�) �.( -�}:�:>pV:%�!�K:B�Big:Ii8! t@]�%u%0Poincar\'e In�ldAan&$f2.4}&%12L r> �*�F��\�Y�:H�M\6S n}\E! \{���kz�)-��5��|n_bi_���d�::>]e|���e��22�&1t>��*��\}}��!s%f�)�=, u��)~:`}���>����2���*/ ]"|mis �<�/#*��Pd"( �?��H:_�. 6�U~:�4i�4.Lanalogue���pQ ~3.6H�$ �� sC� ��N"�d�$�#nZBMomitte�eM�thm}[M6�%]* m1/]]$"�:�*N, �I�Mm�� $S_�$!v��6T&�1a)���F.�=J�� � qe!!�o�1>���}��B��*� _4.�a_2 + R- �) .+ +�mV}=02�F*#&!� - [g!'!CA m$]`I+U`4M�&�NQ&�':������[ G.}R5.�\�L] .I�2V %�|.:a_i.Q::8.* +�+k Ule�C}&l(�/4}�/4��J-:�k|^4J�"��C=k^3� v�6i�J)^�� d01,4},04}�E�m�A:��3norF5��A�"�/Se�K.u.q-.6F�$,!���N����*B�u+�p��:� =�BNa_i.�:0Ig# � iJyq���h�|V| !=.U& \|.�A@Et}&3CBi :n)-u,v6 k\|K_{n� "�$�MA�.`=DV�B^VB{HB]!�.� "rFfrr$F�$T�\ $Ff�T$� � �p��eT+.Y2Rn5�� &W~�w*��A�F�n)o! jd2Nf1Kb`�)����/. ,;6~r) =k(�"�! n%�[  k)6B1n�u�Y n;�$v=>�.��or�!�� $w=(�SHw_�!e�$5.�-�nd.� �!�A�|� )�(v+tw�=| �,k ���a5>$z w_i "^2�Gv-5x�-�e ig\|vX*8 *�&v_i9H��ab� mH,� argu��QE-��I��Y4!��<��.� le k):�^*��!^ k. ��2�d��k}� �=Jd%I���1�. C�tl%>>�v\|!�.se��� &=?��{j�^2 "m | w.4&\|w^/=1"2�U��+�+. ] Co2F?�&� 3}��b%c+W�9F԰�a�E$�- elf)@.�"R al �O�,VW )��%(a\ z��c'\i�C">N4?�}f;:�*M 2L~t�l��j�E��{ ��E\left\{I��`~O[[f~^2� (~�&)Q2�a�(,N#&ZW���: ", b՟�W�.�1 a;��� �k ./"D F�xD d>2,Vp <in.�*k �Dy� ��"5 $u,v� 6��Zm�i�Aa�>�5*8 ��>4.� �� � k^3� mj� ^2 ���D���:�h \�W{EPC�^$\|.-G"� \|$28+� $ ��� [s�~2=W!���$� W*W1 � &�7$4� $\GUWD>W�7��WF� Q_n = z58��$M��X��in�X- 6wX"�["�YW3��A.- >i@&B^3.a��.s`,e$ � ";ixsO��-ite�n��km1��.�=*���,:,S_nV*Ny�NF�< ��1\\./=�1�e���1Bs>� � �H\���1�01���9 )uit2M�*�1U�"�f�S*4$, 2!J��3%�aI$a&aY*��of"��BS��5`! �JZPQakH�O�U�>�3s"3 )2)�=R% )3)2%\��?z3Dh�K\ vdv~�)�b(e;%o�J�X�J m+$��aJ�E5��e^ !�^{�=d=�$. �">B�B� 2��BM2�?�a$Y��NG 2�= F�L*w���G5��G $B�G&�<CN� f�%q q�BO q&=&�G.� ),\\�h&=&�Lq݉�\"�i2�x_i�Q`ZQ�=2� �HV�v-s� �36��/at,6ENDw@6�D�E ��-s!*&�4. 2,��EmuI���*�W $�)>W* [,6��N �'!#mu>�5 muJb^ \vs3;{��I.��Rtrans��+sA� '"$��?��A$\CR$-2; $s$ �! amalga��KC$M)4 �YT!x��+�C \CR(z)Ł.r za_i&�"z=�). ?�k � �ΰ!=��)���9�e,>$\|\mun |<�1}{\|s\|��1$6�M.Y/J�ANb �a_2�6R�"CG�)M� =\mu2���}Y>�b�A�G뉌 R, TD�!n4: �F diag#�"�.O5 � R= {i`iag}(r_1i�� r_22b- r_dd�@ T)�\T2\t:\tZ\tr\��r_*7ir��t.DP�C\set'�\{0�. f �an( r_1t_2 =�t_3N%�F0t_d =r_dt_1=1)� �E�|(R\mu T)�f�N� �.�b�5[�E� ����$&V��g"(i�.Y�du��LehQC[Le]. O�us%���oU� hangv*�CF�a�&? [Le,�J.~4.1]Z���(a (ii).���~���R~$�F)gf"["�� (�a:/ ) s; "����J,մ.��;F� ��>�0�8�YB�wrin 4 Z$26d$� Neumann'���Ʉ"Y���5 �\| �X|!*>�"\|.�X 855|D%{Ɖ�o6e�2 .5."K je �/p�9 �%p� Cauchy����ZJ �J>F �\E�*��V7�� 7E�A/nȭ,o~� ��4&7 uMby�_�es8�$ yticU8tin� "U9 5.14nu�� �\CU5u�&, p T �IU�h22�DY$I�se%._]��Y�3s�4�;" to �Oobser�.:&pZA��i�j=5�Ra_iT=2� if�.� �,:fa��? .�Ŝ�� GF%c�Q ��)�} 6�:c 5�� :� 1� .i�un64=��5}, $(R>1 )s(TB=sU�A. i >' -�FSa�>- -s)JjMO�itPfm%rE�t�g , so��e): �� �N�"(� F-kB��)J��I.G/K.k�.5�2'=T��)) R�[2�U��= R �_ O T�Takx .0:�6}�&oKun��f�!a�!hM��% >�&��:��������(Ra_0T"�iT)P � '%t�\K) ��&�V)"�* J� `.��\ [ ?)lw�o-0\]�f�Wi)..rB�N�Lle�X[ \CO����mbd.j��&�d*\ �J }\; Y�}&]� zb�dɒP-ŐO��46H�� p1x™E�QeAZ�5&AT�(�a�s�) $C'�.�A���Q�s>�<m  T+]�[� E�:0 �"��Y)]�Fl���H. \CO$(~�T)& m��cU C'�a0Bef�u *[�$&\��.E! .&�>�=ieV G��5 ! x5%y &�se%R ��*R �M��-3_ m.. 2r"} �UT� f -�5v�>AEN'���N:)\|���!�mu-�2-�� %NL+ U�i]2�W�?� _�'� G�F.Y'&�`�a�= ,%{� 1}'�n 1}'\9(%�by�P�w|(N>n�<\]b�\CO'=.:\CO�5AwI�%HAxmin�9 �^{-d}\}\���$MELa Aempty,H 0�!!&�׌w��llfEr��X�dpar8�&u^:kz.a{.�EH�� alph��|6�^�� 1d}<�D i 77��:.�&!��&@r_d)=( m�, .� , 1M_8[ �MtM (�^{1-dQ2 I$-d�!�͚v�>:�@ �v{@'�X��% a| M"=r_�2!)�!\RM��͆�W-d-1�!������  � e�D%&�c.; ɡ&~= i�OoQC�gh\�J  < ::���m+���>~,.��K�� �𑽲�_&��[ :l ;i�P:�� \�I6� �"x �5.17} Ka6��F^t�-&���a*`b.��CO�bu�9*M �j����A�c:��)�(�unN�H "����r��a�% �kU0 �9-��v�*�{B�@z� \] �S��^wvl�\m��A�X(�I]BD- "D�d'(1 5|&� \�l1}!��x>E$:�and $y�vR�%��\|x�� (x-yo<�%12e}� $y=x�- 3>��lbyB���yn\| qmF(n/��k (.b^]� �v eq 2�\|��+ f~� %i2!jf^ 6"'�bigcup_*f \CO�m�l�}~Z� (b}��e�)u�}�'oe�"o�Z�I*oMy�_Mmi�Mm�� ����8�2g ��!r -i���Ɉ��_!��'. Njj>h��� , it4�<.��&�8F���&� 6K1r. Cho�Q��s<�t� �oM�< U Q ? > ��sek1��QVKVin=!��ȁaeQ^N�>�$,, $x�iX��N�ous4<$I$ayn ��1 %�06*!rYe/P9,ifS.)_=+��-�i���n(�O�EN' � E^1Ze�� mF�:���(��$�CO'''*2�.k get�.�-> I\� %Iw'' �"2�:{92/�mu$��ma�5 }�6��%MTA�ԍzO��2n�G�? *Ɛ����2��6�$bV�^�_B�g m� & Z �T2��@>&U@9>,!rY�-}_1\܇0.Q@ZM4�j |: %1- 5.Q..- �k�O�l{ C_!2^2v�BF^4� 6>m+B*B-A �r�&�%-u)�c�� 2� �MI-,�n5�V��� � 12"�(��In $.�.X:r���(^1iM�)�� $nUtooYv�^�?2g0�d uy\��|.�\|�M� 2]z1�6 (�h \|+1A �^|"E&�72�\|=A Ao� "e�Eis&�2 i��acc�8 we find that f�uor some constant $C_2\geq 0$, \begin{equation}\label{5.21} \|G_n(\lambda)^{-1}\|\leq C_2(\|\lambda\|+1)(1+\|(\im\lambd/). \end{b\ By \eqref{estim1}, if $ g@\in\CO$ satisfies2-2}, then^�R4}split�\L�4-a_0-\sumr a_i.�a_i - .^ � & �D\frac{C_1}{n^2}(1+R�^4)V6\ �I C�ga�3�1^|b� ^5) )�166�fNI3MI. ForB�0fulfilling (\5�,2}) define $-�_Yg8\in M_k(\C)$ by1�U@\U�3} F? = a_0 + b�+F�B�$Note that ^�Ej6� - R�B�Na,)s� andA�$refore, by.:4})b��7]�R�a�eq�#B*Le�RD'$ be as in Lemma~%� $5.2}. Thene� also^U5.24} Q� 2C'C��^�)<1BmnK 5.25��==�--�\|<-K1}� (1+ R)Fc Henc)�%&:1,, $\tilde G( m�()$ is well-iId A8$invertible�Cjo6} :/nw�&+ " N��5=J B8`Put \[ C_4 = \max\{2C_1, )�\} \]a j�7!�V_nABig\{���C\,|\,-�C_4�fK 1 ^\F�A� �,all.�$,���`%�� E� hold, hAe,"5>36 3 . Observe��the se%_U.$i t\unit_m5t>0,\,��9!t�t^{-5} 1})�!�isTtaineda�$V_�A�t�:� funcX^�Pest22} f: t\mapsto (1Z~>*(is strictly�Hvex on $]0,\infty[$����K ��@&f(t)\rightarrow T , \quad t. 0^+,�4 .j5 m u:rTh�%K%� ��.� �1} \CI=� t>0 5���6\is either empty or an op��boundEhterval. In particular, $U_n�� arc-wis� nected. R;$put $\eps(m�)=RZ�r$�` ɂ0[HT, Proof of posiA�,~5.6], we fi�haei 2hq$in �f�2�,line segmentA���� I� $\i Nn%conuO eO. �(-|=\%� set$!�?uNS�~�get from�V3JVa�^� 5.28�z"a 2P Y Jc =0�A V� Bv%%�m>u Ine+follow!},we will show��$8} implies $.� = �V�$b. 17l q��� 5.3}0 z,wA_GL� �� supposa�an}96}z�z% = =hw wF-f!-,re exists $T:� such%�5i�x 5.30�\|p$\|\|Ta_izTv\| Zx  $z=w$ �)- \pe�&# 5.29% [ w�q(Yu2� )z= >%� +- %,ż.e. O& (z-w�z = z-w.(��,6.- �(�)= G jwhich2iJBi�Z7")\|i\|m \| 2��%ifY�30s2 $>N=0Mxthus )��snd%�8$ \vspace{.2cm!��~)�MM�4}� �n N$ ����with $R�k1$2� F�dependa� only��RP �a�[�M C_5>�JEDa_0, \ldots, a_r$,y � [E�2�)�\|,C_5V ^{� 1d},IqM(i=0,1,wr).])nuW!<Z same nota��z %���%�V norm H*>narray*e�|.�\|&%� & \E\{\|A*y m�\}\\ 6(C_n\|\}+�9B_n^{(1)A� 2 }R�"� �w a/C_{1,1}:�Ep_{Id} g x<R euand 72J7 �f� KeZ�S%oway�R�D�61:+ �)_�#.cQ/6A&C_n.KV�.RU \nonumber.�)8T6o C_%1 \|a_�ɥ�1�|(\B�.�5.3� 3 �By.�$inv-formel�C $has at mos� bx 12 d(d-1)$ non-zero block entr�v ak�e�m)�n=Ѩ0pmatrix} 0 & >\ca�\\" \astA�R.1 R&66,-gR2>X\v �n d$ 6Bmy6c �� �(�\\�|1He Combin�s this��"�4}>V {%� is a&� ,upper triang 0 $d\times d$ )�)�. Z\beta ��1��pun�@2} T= {\rm diag}(B� {m_1},^2T�|AA ta^dd}F��$a>� i� ob� fb 9(by multiply)@@e $(\mu, \nu)$'th �A�y/ � ^{\mu-\nu� SinceU*� %V 9V�gi�i�*:��� _k<k \|[:*],\|�=&f  5!��EMB=�] 3-1}BM|R=Z! $[xe$ denot�)hRg of aMm $x� w.u �X��C_1�2Bd^2}{ɩ5(\|: -��kͣ���$e1�KA-uJ31}:Iu��q 5.3�)�NTe> (�Q.� {+Y���K)��" , Moreover, sI�% u�we ha�$\m=-�d �_A$. Now/V� �1$,� v=^s -%t �.�ag9v3 [1�bXL-1�(-Y d^2 �E�9]�q5=-�| ?%ZV< �]�b�� {C_5� = C_5R�*� . \~  �; A���>4 ��P 5.5}!>re��a Y0ve integer $N.3  � n%~N$� G .�=nnu) &I �n( �=l�a�&�pYz=2E� $w �R�!�Accorw t.�8M=%����+�� qh��UyAby., -m2}~(ii)�U�w}Z1�e�� V����|(\*� \o�y��\CA-s)e}��&� 2C�BB� A�.� *} Thusj�^�����e� A$�� ��37"���!�'E a�� ^F�[ ���%AuK2�-nbHanalytic.�as�!�yf�0$ when�Athmq�$Theorem5.6)n��1�%$&���6� both^��Z�5���!��2�VAest 67-G�)2# C_6�x7AH6!7"�Nrv!5v!��� �%�N0D.$2�|nS2/}&� �� � - �>�%���� ;\�!*" )�xQ&!33G>>}`- J�b�2Fդ"��%�u5 ^ sEE�yIU �J� �� ~�2(C')^2�-J8)^2"Y#R��L{ % ��$R� ���5 !�f�)�%�� ��y$)^2�fN�^5�'&Q hC_6�� e߁�s>�) ]>0Kext� 8in \CO\setminus-:"% f0#$Z�(1^%� ��]��9���&� �jb�G��Zz^5j� (6y\|+\|.�F�� $C'N �$ ,� �' '\� $0�&:0$ referwr �+s� .�&���.C e;a A()�"1 z�e&2C'f y�.� 5.39�+7��A� 2)}>�,&� R�J�^ f�E+ Q+ j�q����C_6�&u�!� `%ܙ��z:  \se% spectrum� Q_n$.q sec4b} A^)!�previous��!K�ider a fixed polynomial $p\in (M_mO+ш C\)_{sa}"�+�EF$q�+�-defQ_nI`q}, re�ively. �e\C$-@&I>0$�B  g"L =(\tr_m�tau)[ >�q� 1}]"1�cJh��=�:nr_nvon-Q_n oJapplic�!�Pr&�$�22�$IoE=�,plus 0_{k-m}����94��� km&tr_k(E�� N)Eu�aF. V@9+Be�e�every"m ',$Bs�� HST6.1} |.x-Éq�� {C_7ʽ6K :� �^ �A�2}E� � \phi!p C_c^g(\R,\R))zZ96(A\�#:Zau q)+O� �_0)]��B�,# T��$�2.-c)[(minor modifM�sA�)' ")'� ~6.2]:�We arp w go�oj ve^@1}� !%::8��� $0"Q*s�2out��� mpact.\R 2%A�\ (o4)\cap \sigma(qE�NsetI��1�H }��0&=&O(n^{-2}),M,,mean}\\ \V\N=�M?4?va ce})������ t each��in L[X_1^{(n)!6NX_r $�0stocasti y inQ$*random^cem�$\SGRM(n�. 1nTA� ��<cI�lyI�(rted $C^1$-L-i1: \R\.�,C�"Nb z 0}r1p&��� EG{C��\E��R�[|A� '|^2E�]b 1+�0_{j=1}^r\|X_j)Q\|^{d^2\W:�4 a�Q_n= p(n���eK$d eg}(p)x(Es"USmon@ s $m_j_:2 A \>$, $j=1UdA8a�c�\alphaAQ�3 j=024�g)p} p= O0� � su1LN j m_jB� Con�W&. �'AE�\CE_{r,nI�p real vect6( $(MC7 0)^r$ equipped�7$Euclidean � �E $\|_e$ (cf.ɀS ~3])�en"� f:�]�A�by Af(v*� v_r�)�&1 �[A�(pF.)]&]>K�h2��>2�A (4.4)m b6uW��4.�8V �$]\}d 1n\,Vhgrad f)]�B�)!T^2N� H%�v=B�m75d. w=(w.[w_>-)�$\�_e=1$. � %"U.� 4.7]�"}/B�53� E� ��1p(v))]JkA9p��[1992�4���8y#��N E��U )�m_j�+$< s��|Q%a!�m� �^[n"���] Mak} useWe factG |w_j f%�%��t2��+Ji d_j= �%m_j� �g-E�f�m d_jR'�6_{1�ir}\|vZ)^{d_j���dEd�i�-+Big��i"�0�0��1/� �6�^�d�/��Nf��=:��b8 s�8onE"oM�4.7b�M�rn}&N>h%{�(& d^2 ��^��H��^2�1�] �$w$ w+rbitrary- 2�2!�C=�  1mMbp$��x)^��]I�|(�` (v�7�GA�k� }�I�:��1����%A�[^� Z*�^2�� 1�X_iv� ] c6desired.�.1b ��-of sF%�" universal�s�0\gamma(k=�0$k� j "6 *< � � � S JX_n�� %�� +�9�� �UH2�� 1_{(� n\|>3)}Mt|V|^k�� n\e^w'n2}�0a�b<%^��k,\, �\N �f�. DS@ $F:[":*7  [0,1]�[ F(t)=P�E� t),\h&t4 ��] .�![S*Z8�!~6.4]Ƀ!s��8 >0$ on�%��^h1!h1-F(2+R!)�2n\expeS-%�{nq*�!�T9V I�'rat�%by parts2 [Fe, �V.6.1� ge�=O�2\E\�� qint_3� t^k \d !`�& 3^k(� 3)) + k\,>4{k,$t))\d �I3"�6z �7UH1}), $ ]58.~E9N��;2�F� ��0 �� 3+t) /���\ &!�,6< + ::� n/t�Z.O=L 6U2�vX�2t+t^2�[U<9_m5X�C1�y�= �+3^k + 2-�1"Ǝq3�*:�*&�_ {\itX �;�L� 1}}. ǡq})2�xs"02}q#27t�(�� = &Q+�'"�FUH3v }QA��4}�( 1.< �%� 4a] �;proves �q��/ Fin3, .�6f !-/)@NH in:-.t$!�CF�;*i"��V�&U �= ing:^�trum}�Iany� ps>0�N��7�6��Q) ))\�*eq&�\,+\,]-�,[E &���$J�j?"th�<LN��jT2a!Tred}^*(\F_r)$ -- a new)=.�� sec5� � X �� noprT$} (\cite{VP PV}).� �� wx_"# x_r$8(a semicir C systemA$(\CA,\.�e 8� � �$�C\cc(�=6q�0l \mbox{$(��ie�_0$.}B�CC_:?c�Bs n6lbuN e �6v� one0.e+ CP�2.� )=\{p=�+\}�!y>��F���C"�� �a�@\|e-p(:\|<�M 18�P 2q= B*$.�@[Da ��2L �,Hausdorff di� ce betwee�B�tra $mev2 q�+";|e-q\|�- (uFe9  18"U(8[\,\cup\,] 798[a7�x�Ccinf*  $0�q�Y A|_{]- V14F 4[}=�% $3$5$"!�]��)�j(q)�:� �equently�[��/e9�4uB] ��u9�Eph,�,�val�to $e$.>��J/ =F Y. ���"&V� n�e�Sh�T)L';[( A�nzJ] � knowT&�36' �t!GH6$P$-null�H$NU� �.V&�Az$ " B!smz9+\,�2,]{\textstyleQ�U�18}$a�z� biR74uD47eI>1U�& 5 0%�holds*`n�:&IL/5-D2 =| n $N"N iAe*ii.CE�.s9��.MMA%��P&=6� �1}:$hi.�Z"v I �n!�Z&%>�% e^.N-:� &N#, �5HIgM�A.�74 \ �� >$� Z_n\}= N %�lj�2�6�:0phi'$ vanishe{8a neighbourhood� ��"<,A#i�& B� �(Ua~!/& Z_m\�  :.3}$B�4 ��As"S(ly��5is*2  S[n"Z_nJU"C"*� \;�\;}RQ"=O"]:&z.maa*sumNvt2�t= nb� + O(&#1d P *�iˉ�b� .���Q. x " f�� $n_0a N}�kqd:E ��6i�n�  Take $�! 6+� T�o|6$V�-jK? C2TI_~ E�Y ^ &mist}(f�,\Z�NaxO6I(n+1)6�.:M.. A5* �A�� "�subtra�+%>Ċv6s+2A�pIql� �Y-�B�J� ��(q�l \Z� !| l�Dstate�Nof6�IO1 }2-�!� *lB �E� tal !!e-pre�R�embed8=0into $\CA_0 =!�.� x_1�  x� "&"8.1&"nMfremarkg�wa} orig�� v�P "� �:�+metho`3rom K-�&y� �V)D irst6�n� �be&\Dus!R_� deed,�A �V3}V�N�X� K_0\_0�\Z\�[{ 6]_0��A&2� *Z!�&K%�. 6-r  �Gap� A?�`E A�$q2�.6V�. Fs,s�$N9e ];$!.L�/(�HW  q=pK.v).� T.a�*an eas�T� c� 26�&�&� sec61}.Hba|oa."Bm$ �joi&�Red|�L� of �Ns*l+�A�S_Ra�-pEC+�&�&�$\R�\���di �ope�+T s. I�4RAhad morn $m+1$A �R+) onen�icould�u-CJ( orthogonalaϑ� $e.�$e_{m+1[E#�Xe7��F�e"h5{"� m\K*d"jam+1� �e w�&�[ m = Fbm�m\�#e�** �F<��]m+1�t� radi��.:mZ����!t IJ��H$bE$U+L!�emrV+U�s.$A�3 $*&�P�&�KE�"��n$�osto�����m�holes1}a&_0�H�[mallest!9ta�^zuucoF�a�=�-\CJ%u=>�V30<��3 �P!�\mu_qa/ Prob}(?1�I� ribu�Pof�$ w.r.t=:4��** Y(\CJ)#km$%�s9$kW {ݵmp�AaN� w$l >O�$eigenvalue)9*��o\CJ + ��W[��$k $,." asA�.�-�ZR� � Ѳ�J�}=�!�S|_{� !N�2!�, [)��+�^H!Ҏ�)rD ,; j�U E/��:�au)1_\CJ�1F ��(km��!�E!�inB.6a7oJ]6�A�N�@mx*� Mt^Mm�>`�(]e&�.>�;,6u,�*�^j%��o"��teq�2y.Y`�-h +P43X-[�"�"\!��n-j+%s 2� 2���. �\j�i6mN1$ trk&�a�:2m�\}.�<�d{a}{Rf&�d.���~ ��+6�P!A)F�= ��6�I��w� 2� 9��$n!(ffici� big� *�X6A;�0]sympl�c cases.�7I�!]  9610 | 0ill generalizɘresult�� 4 4-64GaussianB�33# �21�tic�Qies�F��W&�;cdegree 1� trea4b*�acond nam�cuthor� � S}.�p)�s�&0athbb{H}$ can�ex�sIsA�\#= R}+j k l %�90j^2=k^2=l^2=1e,[(jk=-kj=l,\q�a�E�"�Yof5�U�c�3A�:!,.�6,x ensembles:��numerat�8,renewcommandLbelTi}{(i)}\item $\GRMR(n,ɥ^2)�g�J.r$ces $Y$: $�.�`3-�R!�fu"2j��en�W!�$Y$, $Y_{uv�2$E  u,v\le _ !titut:: �,$n^2$ i.i.d.��!!i�2{ $N(0�. r6Uql}�"^H!o�_�0mA�Y=1�  YGD+j.2)}+k.3)}+l.4)�e\no�8ntq� N,2) 3 4)M)re ��Q/){Q5 }{4}�7z_5`VQ� $\GOE6`(@�# GOES2)��(�describ�Za2M1selfad7:�,.�Te\2?�O�D1}{\sqrt{2}}(Y+Y^*d,��rm{�}1i2-2) \J�a1Xsa�~�vq�>MSbMSvM �P�M !G��%|�^�I��CU�1:f���We�<&��\(ulas (1.2),4 5 6&r2N:�&�1��in $r+s$jbj��&�y X_{r+s}�0�s (r,s\ge 0 r+��������,"�Bk; h)ce�*�.an}?a  �1�0 �Pa�fQ�� � c�  ��e!.}u�����iU.O6Q�5ma�:��J| �(1Aa�easily� reduced t�W % ^ *R7.��0S!8on~7]� �Sin�I &f? o�c�id�Hh]E. 2,A�in��N}�4 A�A�� *��[N��XB�%�Q7���-d�#:�.:JJF�=��%q>��A�GOE^*���n��1;!#"�Gc �je ���G �C}'$ C\langle �Gm; }\r�=� X=>$f )_{nv8�NzsL$�=*{?:�� ��a� A�#)>�&�Wi)fd=\deg�?Ac( Xm_"\m_{d+�1&N} $m=m_1= ") .�$u�? {m_jJj+1}}(I9o�w$a����,2�:d>�(u_1u_V1s u_d$@IR�b�u_MA,*�@d,)�[ -�)=u_j(U���*� :$sž-\ G�L\� � SI�Y inv":bl�orDr�, =0vm.�-�ImJ ^L��i(.$*b0 2.3� .!xF,.g=\lefteb�0aSg}{c} �6� & -u[D*�c!s\�d�A�2}RC2ib2u4Rd?C3VC3C2?Wd&N�d"{d �d �uO��CV� �\\ -u_d �2P �d>P)�\["0Qs&�^ is (��p).f� \K�r $k=`i�/{d}m_ix V+a_"�Ca| I�k6�t�>��J � C3�ze�fa_{i_115Z.�a_{_i2#2)�2�5� >�B &Yi_{ d-1}!��dh2*0)|�&z$���S_n=a_"�D)�nF)R� a_iQ�":4R� $\Lambda=u`M1M�&� :p6� 8Z } -S_n�V1�~68C \CO=2(]�] \ |\�?tBIm �}\"� is&(a�wite}\(,��\i�Xwe z.%" "�9-25} Hl�3)id_"�P�Nb��$1}blb!]F�*�M)" E}\{.�J6By> �24]�#3.1#_'� "� ,!-siblyE5�1 N =�11,p���$2"�\2�q�=�'&y�#�t�! to check,m5�m�v.�Lan &[ mapW$@Z�$>3"T[Svt_� A^{-t}��A8e6%nsp�\����Ba1!�"i $AbM(.& �13 $\wideLz{C}_1_ �#s�q���T(��A ao� �IoM�b�8eA�lQig�C& Dm�j.Wa6�+(a_0X).)+ �f{1}_k�5JR} �-ul� :�}{�+(��rm}�i\|^�,�$n{y 1q.��RE�)u,v�.k_j a_j e�^{(k)}�bbeX �]rm{id}u�"rm{tr}J��%���t}(.d�J6�>�Z �A1}]�">� jE�q�"XEA2!-� $r+�$+s`E��Pc� a.,[ _ .M���0{rl} \display�/ "FL A*F + ^*�;& �#� r),R2.5mm��d.�e- e) g+s end{ ���&�Eg�N� YO $�Q0n..� ce"�N86�R!��6�EyMZ��Y�(b_&x1+cF%��FD^�b_j=c_jJ� a_j,��@-2A9�B>��:�!�u�9�F"�;3� �$ of��� &6we*�%f�Iq���f�l�).y-�&: !�.!c_2+ :b6 6h}e0�aXn2qBt-�Z�cl}2.`Ad}ͩ1Yc �A{k}b_j.�=*{ 2:'"� �;(-G\� %kr:]�..�K1}W>+� ��c_j�(uva�:$V���$:�B� 2#y�..�J��(:7]XBb&�� q9-1� j6}���(~Y/a6�:+.� k\}=^� �u�Q�f�36�zZ%b���.�� ��b.-�^l�]m.J9�5���e���������y4$\varepsilon_j2" ( �oc*rte��X�ah/�c *�0 2.4]< 2���4.3.�Vpap�p>,�P�G`O�� 2� � )Jf� �%�z.> �pgFz2� � Cy 4}+C�P4vzU,&!�1� �y� s)Z >S**��on 6��C'F�]a�2�h%s >o =2�2 >�O76�+ih cor}!�~� 2r� -�&� ��U6�6VI;�CN�_2}{n�� 4��!&) &!~3�_g[(!�A�"R �y�D�@9�efBd �\|2� �>� k^2�.�N� |t �Sbigg)�U��)F"*gvs>� &%P& 2Cn{d >|As2,1m52~52�Js�b �& q4V<2�;:Z> !�h-� Hd:��w*Uy�bya�=9.]ejx 29%\|\ &= :�:��N%%_kI(!\!�!\!B���C''e ;�Z�2R_�lhATf�4-�f� �6_i�W��e::�*� >�:o��.:6��vI(x&�x)�aR#5 in aI\*$-*�F s�Y2*5�"�r$89� faithf�?G8p�CA$. �f���^ s*�9:_{\CA}� 2� � x_jBQ >]��4}�u�n=)�>6/.[(M� h�\C&Dl],�3 T�2F� �^A:V =�G@uz�muz�IL9YE<l@.muRVg`(bY%�YtP.�f ���o 6n �oaPbb" .��C}_3$�o _*DB�:{ �)�)s$-j�g�ZB :��Q� P|) ��7!�" $"(e��܊6� 4v-��%7��;fl@Corollary~9.2 exa��as��5.6 2ed� !���04.3. One justh5to repla~n�(ble$a��� o9"S]5>Hb�9Fz|: $ 9 i�Gg 5Ma}r �d+ �-�;N�%85.18) through (�|�"�5+%&�X�wCrrfGv/��#2,CAoa� $C_4.Qw4V]�.~s�b�yNVC`�A.�dj, wEeC_&�\]ZMYi�"s 5b)&C�B�t�y�u�mJ�y�% ){,,e\�atef&�+"*  2Ekzle��0�"A��R � ak*�zifl eUe�.M*�� :��5"s�5�pNY.A a_j+.�f�*7 )�n�1��q��2� z[pbX^5��6Za�:-IBWR�"��r9 )F&���i4y��0q� 2. FE?�!&��B��p.�z�49-1h~W=.�J�!�F�%i�)above��>�� �� a $Cn| �$n} 6@ . It� no los32�2ty�"*A�GCA=�3�'%. ymme�� ��6�&r-'$�yn "�-��� � W kew-\�#�FI�reaso�H���choice�� ``trg�''�=�@��CA�.iYlɏu�&,\rf,1 \the+i)�61&\ �2que"7�;�arR$a}a^ߑ?CAIZto it�+&? ���1a�- $x_j^t=p � *��`b�Hb:H-.I>N)^)McM0(ab)^t=b^ta^t�a,b !��5�&�M"��$(a^tIa-�8\|a^t\|=\| a\|$�do F%�DC\ �p!�B$a�5�U" o=���[ ((a�)_�k�vu}^t2�/T��6$, ($ ��o A)$).+�J��^�F�9F��M�� (1)�PaIY a>�\' 5.2���\ N.�EW6er�/$��(automorphish psi$Kat =C^*6�r,�k�s� �^%U(x_j)E� & ]�\\E� & :�)f�Y\b�"=Bh*M� as-jugx m�%is.va!5.� %G\T &=\bar{��ndA~=�\.�>�Rnow!3 a^t=!.T(a�2�+mF�it�clear#2�5e"]�� A, cond�[ś (1). AlsoNNis� y� ness� (aF1b(c).\\ (2) I�el�Ha-co�#�#��#�y�m d��D�/nvolu�tkre}a1�productQ$-aF���dofGe o��i}6 lgeb�S# ^{op�.in �_=^n A!�-X. \hfill{$\blacksquare$\\.&-& $- !^+k�G+<.aFg$opera�k�@m����3S�$ ogy P(9.8) w�:�kwR�*� �yRE)F v*� .�f� >��'S-s� t:�{��R�>�"6"~>|�j&i=by� 3.2��Ja 1�]|9Ee*� C}'Xyf� 2"� � 0(��v"�7Ja�8 6�''h ���~l4 9���O2��|�:U&�A| .\-.�� 2%��:{14z@-��BFB�Ra�v &�6 �2a�<s3 (>7 below)�s3 deri;LE'6 �ʁ��1 *e>.]*B(,q~�ei�[ Lyi2;� �;ONM�aA9�&�R9n72Zh P !�! ~j5�jMjBiS.-�Sb 9K 4N�5�6y5�N�17M�e��-�e�f4� !;� !CA�of�  2� Qs 4.4]n4ReO ~9.4A��[�  )� �B'. 4N]��!+F � giveb*�"�by �9e,nd�� 18),R��$,*kwe} & &I'uiL.<.�23-i>E�\&�� &�e rl�2.�a6k  + # �).+2� ^�u27Z� "���6�V en6d4Z@�10� e5}asj� ��]"m,�b�fR$|Οiq)�C' �q v,+ Ci��s6- � >Y*� R���%�=-�"ì_:����/��!{I}86��*=28J=2�-72�1|)�R>R~� "�d�3�Kq{�q9-99.!=8},�t12�%*��f"!2Y%#�^ = & A�*(9�-.B�D�� 6�J�r�) 9�^3��^9M�>%�bU _6�:PF,�9��=�9)�A+!�yǩ�*E�.b.*%G*@ 9Q�&�2E^�FJB@�%2 #mDB1�g;:�"N�7��02�Y)�Rb^{15}-�e9%a(f�71��  by=�10}.+7�t�c]�R��>��lV %8RK ��2 �v 81 B� 5.2��/21)2n-�o@)&\ja �' \le �tF�>�|=���&ٕbu!6qProcee�l�S{24�(4.25S)a�glV�X .s�^.{_.3��& {"�s,(�:R}�-in>� \� ʳ.~ P_%(\| 2�#4��WIkQ>cal $.A�> 17*if.Zwb� lash�y�n%HX�s.? ;jS,"� "� �  % e|.��#3� ��=2 PqKn�"j*�"�� $P_2239$ $P=P_1+�I�P�"of-3 17�2���av>�3 �sjf�F� ��9*l��7:q!�4areturn�A�"� 96R� '8be devi{"ii a se>N!�HNe@�a simpel�iv)? useful ob��L:�[� 8��Ab � tal �)�� x, z� �0 GL}(mh $y�&�E| a< x & y&>z�\]�* �=2_�seRY�� & - y �k6p��� � Na'Q�*�*'�!bbB�s usualR�B�= V�> � K[*_{k-mN�&��)]��} \pi��,xVZ3 59vɳ^tF.�/^t & xJ1{> AJ"40)bn&_7mm.f 16a!�*�4�u�id}_{2k2�"�2[>�%�]bq7p�p)��,2�<,xws&�89 �� :;=\pi edi&�8��Q^�\CAQO^� An�\&u�b�t��6�)z*DY�6*""Q�[8)hat{s}B0 �q,:�2�NF���6,"B�).d�(��F�%J\ � �"� u�a}"#nWn�)� F�����)���3te��B �1.+,x).}1G}bme�\.�6&>O&e�Jide�z��to"�  $6� ,x��aS|�%� sJof� 5 (��Bk(V(�jwc "� 9.15�G4���9.8�fu'comple%`�o&S 9�"(�2-L.D^� .:S!0 $R$-�"()��Q ��Peڂ o amalgamEX ovd�MM.�i�MUSR}(z)=E�a}_'i�>�1oa}_i z N�� Fc2l&�aRLB�a_i��q�a_l�nd��(�7%$=.f�"!Si8"/"-i4=`bm�.}d�� u����& \| S\|�E")�EA�&muF�&Q`*�!>)J�=G0 2l1f+2 � =\mu�8�9%9U�m2�&I�� T2�R6S!�:�R20T:0�# � !��gS| s\|��>"�%Z�diadAC?$R� $T� � a�%�^�R���N�25<C�"S5�G �;)�]( �mz} :7 9�cz<)�e���c M&n,�I�. Yx��Ew�=:s+s}Nv 5�� �0�{�S6m.iz) �(y�~"�(IX�v Z8(�/�7B�w��% "�=N{]s�(\| ��v�1�%���*�!i$ ��B��Gby� �'3.2o� >�J!?R�� 2�i_bYZf�J���* q���g "_5�^�1p 2!�����ZuC'�B1}+ �?��6'Gg�'�B1�=ZX1^2Zxe�ae>�JM)=|^Z�?z a^t)R��i,j�$i�W2V=[ \CO'2{R��nR|G � < \-�{1,(2 !�d}\}\ A�aa&�6'$"�a��=>a^{"P d}}<mE��pf�1}{ zQ_7] }�l�9jI?  r_d�( ��, 2"C .50,:�( [t.[A]� E^{1-d 2 �^ f%m� �B, j��7 wFd:�� Y� �bXY�B��,� "Q �*5.21g"M�[�R� TA�a�=)G 9rc ��-�$$xfR:�2N�T^t� TZ 9p� E�f:;p�"|2a�\�dR��T��  \bU.�&�6�W#�:\|N\|}{4��^9�Vk.~ = M[i�\leIj^{-d}J�-1�0ӧib7ř < �\�lK- ^2�i�M_:�v�:-\�5%�r >9rY �QRZsoae.k!4k!� 9.10v�v �N(1�=�8FL&� 2A -i+.�B8����x^e {B% 'm2B�D�v��Y&Z ! *�v�q- �S�_ �c�un�9�4of&BXowinu��V_� "��n��,$$(x��*[R&`k thesh�l 6�OZ-&� (i��89 ��Mm5.2Al).r�F~6�.� c5����4>,\:g F6 �Rg.�)"N*17i8.KO*�����fU202FP�@Y*�u,u�qX "G52k):@Q% G5*�&>IY6=6*"RXo.CG _n))r2A1DXB����&�Z �N.bF:]FB�y��. e&�B�+:�� �|){=��D6AZ+Z%(0�c��6s.�/n +&�]�&.�0y�*j #* _/'E0%�� a^rR+[8�)%B����"�%G�K fair馶�&5%15% mast��}2�6}�{q1�+.<B��"��{b�6�"1�:�H��%���) 6y6�#n�W,x� 5�2��$w � �68ņ hP�?>4*� ���R99i{42�$\|^p\�%(3di*5#=!^�GR5 "FJ�-s_f�$R @Z>I�Rf ^p1�^p �Y�vi\|T�~$^2)!0Zq2^p.t"�FZ�!|A��v{2pe�N:I2^pxQ�a�Tpv�^p' 1,2p 0]N�I" \|�)Z C'_p�)��V��Z��y(>&=U^$ =�ݗs >*�J�@,\ i=1,2,\ j=p,2p3�`�>#*I22��r $p=4$:c 9.11�7 e�.21}:!,2M 262mUq�fT*�D� ���C}^lU�K�c �L �Z>�a��X.X>`e��)}�lJ3!R~�18�y�<%i6�U20BS A �U$p=2$*�0��-2�2����.�''�-n 4a�>!"1�*""9>AQ c�NE�f}L0s immediately6C12&%N"B 2"Or .�Hb6� 7Z�*� 8NHr!839aM1: )��K2"�?(B|!d6X�6����la�~(z�4D9*�7R����B� P&2���� 8)-(5.23)� >6P�' (se�so &�<),�0&�[ af� suit�y change /��ex"�e�E0�p��vA� A��CP,=P!� $C_6.)HPU�V}�RP*�3>9h>=� ��� �Y=)��G|�S>0})��<1�a6^#��:U�2Q�$�:2� :�!D�G�2A�6�qP_/���2F{M"��YP, byB�=�Q�g ����F�.��a| 1i.rP) D2�b�2A)�ljv��<�"� 2��w^ �[M�rU0����{10"v Y1CB������q�v� 1� } �0'Ge)���N� ��k)nH*� 8Q+2�F� 7Exs u&� !:Y]�5�\"��i2��F!->BHy�)A&T!J��6-R�R����%,v�%�v�F$�/��?2iBv��ѥ�q`�4U,�v6�o"� :3p� "�((-XFL �)\}vO]>/� F�&��X|$���en��stC�%��W " �!���F T<��� $R,S�6 GL(k,pr�?| R.Z a_iR%�S8�! rR2,B$N�.�-�| S:|_S���EM:�I)n7O�~tF:���h�>�q tooXu.�q� ��sHL| T5.4vrwhK�t9.K<24}*m/�E�q"a � 5.4,�-x $S$� z 9} S�r"�-��A"�-^j�- !>�-�^Kbet�!j6pa�a*�,& %*A#\% :# 3.1, writA� NS�� =C_n+B_n^��n3�E� .2.�'&� 5��� %�� on"�  ��2�e��!��:��a $Zk� ),�/:>B��8�fs?.{y*�9 & *\\F~w\�wMF �wBFxI>�O!Ls#j�kN�B��0E�:��0A�B�5*�0 "�y:@j� as b�M�� (aqZr&�?d}�e��m�U:�� �UV�$ m��iR u��&@2.��[:^]V ,\ 2��u<���}by �^{u -v�Sit:l]RZ �� [`6�y-& ^{u-�$�>us" \| [V�� v� -�� N�*26�G� u, v�s &0%d\ ���se�V�.�6}W9�>le2��q�<��.6�M�ͮ*��Fb��a� �n�;NY �� .W\,x&�*�N ,\ j�   � a�>�2D��$at�?6�-n,A3��R�ez:�\q"Vg�� w6X:I 2� �6�:�F=H� $z�w�t&� �1�&t b�&�8+@�TJ�w"� +Z-�R1TB( t��8S6�^�^� �\a<��66?3��\.UF�J30}. WB��$(f[-�"% �s.��z��w%jn.$� =~| 9xII T5�"�� �6I h��B3,�X��o�A��D�-w�.��R� i�t(j�8>�N��#&Y?^��E6� b�!�ft[ ��� ��N^/�Av&"�� E� :6�� �N]�F�)7�=T6K2: �.&6w al� ~.VXB-*h 33} 6x=- �BufB�X).Vjc� (J�/nrXusc NW��R,Sm�Tz�'IQ�Z 'yU=R,x��B�(V.)����=6<�D@V�)�Q� �1� q�13�v���� 1}{do*|�\?�^:��� �J2:�RV�|%Y� D =*P>) �*���3�J)X��5�\|>��X2}12r�0��}\|^2)\| x\| \] Hence \begin{equation}\label{eq9-34} \| T\hat{a}_iG_n(\lambda,x)T^{-1}\|\le C_5\|(\mathrm{Im\lambda})^{-1}\|^\frac{1}{d} + \�`\| a_i\| (C_{1,1}+C_{2,2}vK2). \end�P Moreover, by \eqref{�1} and22},B�H \|\widetilde{G}(\L�_.�) �2* hat{C}(1+z�B�B6�3F��4}, there is a $\delta\in(0,1)$, such that when $r� < @$% $)�j8n for all $n\in%�hbb{N}$, \[ \sum_{i=1}^{r+s}�,!!a}!ߊC < 1.A�T�is,2� 5} holds,�%Xfore $z=w$, which shows% $G2�=%�v�$ )K(\U�,$ belongs tou set%CU_n=\{ *!1A;� V}_n\ |\ ��L\}\times\{ x\in M_k(1|C}) Ia�1�\}!%L\noindent Exactly as%�th�4s $V_n$ in seca�<~5, we can prove-'2�$An connected-jatUre exisYN�matQ E� t)$� M�\}� non-empty�M�geyP. Lemma~9.14 now follA`by uniqueness of analytic�tin��. $�Bproof$ �lS} Ty|Hconstant $C_6\ge 0$�%A�$]CO$, $%�Bmo:PE@| 6�-G]v�d\�-C_6}{n�df|)�s {14}�"]�% � \�8 At first assumI 2�.�$. PuI�mu_n=ND\qquad\textrm{and} mu=�\ pmatrix} @0^t & x\\ 0 &  �*A�$ Accordinga�=�:�14}A�then haQ݁��y�mu_u)=6{ �B� B<)=.���@FL\�A 7} \left.- $array}{rcl�sv & =! >�!�)-F�T\|\vspace{2mm}\\ & \leB(5\o�oe� f{1}_\CA-�� s})^�- +�)�m -s h \|\|�-\mu\|�0�xI))I\right.NdU00~(i)��%��= \|\pi}�%i�AW���z] A�b6�2F�6�[ �_������e#.�\l�y3�y- ^{10�xInserte�4hese estimates��.� 7e�ge�fa�hzAҵ^{(1)}��1Ʃ$p� some6� Y�� . If�!notinU��C :�8)�1=U4֪ 0}) �� ] Ż %�Nzl}�~f6I!u0& \displaystyY)��F�)UQ 2) (B�\|+}�\|�� 2!�TakA�(9.44)�8 85) into account�=I�Y�%D|61:��b .�2��&� A�aB�2)U� This� s��5 with�$=\max\{ C_M�, C}$: {\it P  of ,orem~9.6} Le6 CO��. By .�8aF�3i6LB)$K2� 1.&� 6,!�w� $6;V given>�03}. Similarly�'.\F�Qy �,x�b�o "s .G=- rm{id}_k\��tau) [(/ ^t6�s^t��(xR!)AR�; �Y�H4f�a5%6\|:�-.�ũu(J��&� ButF��c$.sD$ are well-defined� M E�:o $. M"FsinceS yFlinear��$x$, i� o � B�* 40a� 6�:�F��J��%�i5��I�C inu�Z :�}�.� 9}, �#Ry�)=,j&,<u,v|k}\varepsilon_j a_j e_{uv}^{(k)}.&.a_j2�Rud�qIBo�@E� 6�)�[A�.�-�� l1�,� C}_N/�� \:sa2�:i�6�{T*pectrum��$Q1--A�( real case.Q�sec8} W�\e{not2~inpreviousx,_1,\ldots,x_?��Pa semicircular systemGLa $C^*$-probability �  $(\CA,�$�� T$ faithful, $X_1^{(n)}tX t �,stocasticly HpeM random � ces,�/\��J[r WaR��4rm{GOE}\Big(n,��1a�bk �\b�:a^*QJcA����pYm�TbbY�R���p� q=p(F�),\� Q_n=p(J %�)$:��j ��$ $g,g_n : � \setminusR� arrowC}$� \[ gq�)=(\tr_m��9[\unitq�6], 0�.� \R��p2�E\{:vr_nvwn-Q_n w\}�y!� )�E= �8m \oplus O_{k-mA*��C��TI �� \�\R$6��) =͐k}{m}\,!Qk(E"� ~)E)�A=^C#E � Now,Ul:2��%� \C1�l~�L!l, )� in l!� �%?$l��F�applyZ Th* 7G find�R2� \geq2C^;GOE8} a�|9�-.`+�a 1n 90\leq -�C}{n^2D|(|)^2(1+|\im�7}� ": L n $elrm{&�>02. b& gu!a��$oof [S,5( 4.5]inh��(\��) also��F}<0$. �.2cm}:� distribu}!�Q. $\D^ �(\Distc�]supp(\ L)\subseteq \sigma(q)2�ag any $\phi NCcinfCVb�} (6e3lim_{y.� 0^+}%� {\i}{2\pia�t_\R 6D(x)[l(x+\i y)-l(x- ]\d xB'^we!�AE�has anVC to $}89 . We knowe 1 ��R7,��������a� inv^ ble. Thus )� =y�9m)�$ B(��from % ~3.2 �$ W�M�w\CA -s� .�� �6&� ��s^t8A�2�I!*&U 9 ���R��Pm)$�zR+B�$���[t�^��, $JUi.)�ll��. Indeed!�ݐuZ is "��twe� seem a!/���$ ���to�open &OiŁ�V�,!� i]ity^�a�1} �n(a_0 + � rs�B#a_i - QG Big)B# +M� k= 0>� holdsA�en|��,�X �) mustH1�Y62�9�!� parti� �� such\� concludemS�R2��U�in�of Z�. ��$ next stepA�to>�,satisfies (a�b)V.�5.4].U MF� ]�$ �pv-��e . Ac*�2!�sh ( dBr"= = C + B� � �(Q :�$\CA)C=CJ=0$eZ� \|N\| � q C'�!1�!l! SJ�� �8>c�"� , if $"�> \|q\|i�nF��� �}{>-= bI AJ� %�id6W[(EB4��(B�B�Y }�[F�]� imz nynormQLQyJ1�)�^2:�~#��|,R� g Ő6�%�5�V �,f��>g( �F% )^2\��>s W>m^  GOE4!hB2q k^2�6B#�$�:hib\CA - sM@|^2j�=ie�j�{�^y��%m]:1^:���� GOE6!3��:�-� �F�F� Also��� c*�!1� Ŵ6RnM \|Z�|&��&;&{ �a_0�.3%%�JM  � S}�S�H\ dc)S& C_1��X"B�),L a�G-�I1�1J�%1OB�e�#1F�!).6��J:�h�QLQa})" e�.6}/\�1G-1a}) �}�$^xcondi� a} |&�ɿO���.��) \O{\rm as}  ��. \inftyF�Combin �� .�427N�}) we&�6 B)2mAb#!=l} . I�\j�C_26� :�2C*:5c)��%8} Choose $a, b� � $a�l2� .�*���b>�I��+FuBy-�2� :)b!�!^� >� � A%( �(.6�> Know�%� �bLN� able"? :"LthmJGOE9}% phieJ�%�� V0(�Aa :#au q)C�� 1n2+:2��D�e���(resul��M�a s�� e modific�  2� 6{ 6]. 2>>d� � 1+rmeanof��s-3* \Nm let� GOE�$ 1n)\cup S 1n�pitemizeA�\ [(i)]��i&eps >� \$P(\|X_n\|>\sqrt 2 (2+"())<2n\,\exp!P(-%{n^2}{2)g$,J fg��sef+ce!GcV s dTAa�n�8(\gamma'(k))_{k��2�Ea�k�N ~[�E\{1_{�3 �)} � ^k\}�ihn\e^{ � n2}.G� �%CEB)�F��We��2/+X_n"�1}{ �}(Y_n+\�01  Y)$ or Z.\i0-60!�g$YE$\SGRM: �A�"�#�!6.4+[ B�5�%(c|> MA ~g#Lw.%�A9Aw� by%Zj Propos* ~f .7��a�� vari��$I�=q-��get�  Q3BigE7\bi*v 1� =>3)E�&� :%K)^k2h(kZg; (ii)�r=$Y�=2^{k/2} (ka�2o �q 1/n-term}�%����be� M"%p�"-� (1��um �d=Keg}(p)a�x_0a�\CA�� $X_0�= n!� may��� c_{i&} i_d� M�C[0E�:% r+s.>� q= � t u ))"bN �26� �/J i_1}U d}e an Q�. �V) � �X%7 P �d � Pu%R��3 2)^d�_z \|V -]��� (\|Q�b >R)X$(vnbca�%l)0\| � �\:v��bigcup.l�4iJ �;2 6�* AC��leq r��3Xa"\| K�s .${r"�!�1{)��� ��e�26� m�D� 2n oB���&�i=1, U�r+s �� thusZ�2(+Vh n2� �Con tB)V�ind� or} ��2 _ n)1_{]-,R[ ]R, [}E !�9�>Rͷ��:%�� � �5� *~ ��!| 13,|_{[-R,R]}=1��(x�1$��� x�5Ha neighbourhood of 2~pcu*{$.�� ���`��(8!�#Q�Bi)h?1O= 1~| R +>�"{ �[�e 1� V" �-1) �.Q|�3|A�eq B.�X��Altoge :vV�phi>� =S.�!5�v�:�%�D 0 hAsid�"oforder�9$exp  n2)=b�Q�T� 1n$� appear� � �3�of�)�� zero:��!06�! propn HST6.2h A�a�CZ (\R,\R)2�$]"� out%$a compact .$R$. Supp�uVi�phi)\cap"==\�8set��?$�\\VR&AM�$= O(n^{-4}m]QP(|2(:�T9i�43}, \;A8eventually \;  }\; nFC)={;EE%^^ TO1^�� i.[1t�0� �9&#$!r lex l* (cf.�o2�0��*1})6 �1�%.�, �"$ ,. p2y MC�@B� { �e�4}2�,#, �So;�sec4b}^Q 10} S eps>Q%A1�1 most!�rQ$ omeg� \O �MvQN' )*� q)+\,]-`,[��]as�e�arU)S� th*Z%remark}�u�7]%9e�""��of,~9& & 10.26� 10.5N1� 10.6�<easil(generalized&sympl!xc EH i.e.� $"� z,ha�,%�,a�JZrp M?,S�,~,SE�,\�/)�a�.Gap5�astr.q$ --:.�:a)Bsec9} #+N5er&�{0} IAi".�/sh p"�>5�e8holes1}7Z.$   ^*$-%�a�ll�at8@��,(DbC)� $\bC\langle!�,\�.� \r)_\sa�1f $�,$B�76�. &�. $(\c�.�ifE&ea#�\b�.�_ �I1&�.I���F�. �.�%%H)'$!-inu�%l sec7nBnG'"�-� �=nd&0= .� &2�)��%6� � thm8 �.�� _0$ denot�smallestH�} betw�%disjoint��@�onent�?$��$,� cJ$_�+ 4�v46~ 30<�<�S13 _M!+ mu_qh\Prob(\bc ��+�"Z��a>w.r.t��:�.&4 U(\cJ)=y km< s�: �)pm\}Me/a�.aS$w�r�'�� number�$eigenvalue),�;w)� $\cJ+.)E�$k n$,F5toR-&� +C_c"� !-4BO - _{|>�P !sg !,bR\backslash!) +]-2!�, [)}=�C� �+&aMB_  proj�)ona$� C^*(� \CA,.�n)M� hencnјe:noOs����Q�eqE�9�(i�+bR 5!%, d j!I km��&"AY%6$�96�GOy�  ,a $P$-null s�NUD"!Mk�pUi9� N�Bs -A` +)* q)+.pV�Yd In *�(�� �"�D��bNB (\.�M<9�t edn[5Na<. For $ �Wez2A�e ge �$ take �:%M� \{0u�� ne�5�9��RAc2} N+ vaAa6��1m7 }{m s9e��Wcolon>�!�b�1��.Zɟ*� .}�(c4Z=R�ph�)-:�&>-�41n �Q).IR bF�8($\bE(Z_n)=O&���"�, : $-J '$ vanish�@F�6�we��ythe��b� �P \bV� \t��n^4�1]%2:% 43})C"\mbox{�surely.Y:�&�G��H $N'�eq �][n�q^�b��:� +�!����evI�ye6 N',�"�:�ue|2:� 5�(fter multip"�by $mn$%��� m��}�q}�F#.�3} }� = nk + mQ�i�).13J�""�A6�$C>2�H$�At(>_ ,\bZC C\, "K13}%{��)�)$qK:iesK>Y!�bZ!�W�- use M2(rgument bas"homotopy� �K)t"�- ��By 28:a,*|8n�9� 6� AMF )*� *�u,� *���2\�%8^6i fo�%eP�� F� "j:03#out lo�Jg�t�K�I���'1; �Y:�:�Z$Y 2 �8s��2> � F� .<Y>�2!> �z#�jj=� %T�;X_j `$(t)=\cos t+\sFY+�:(� t\le �i_5{4eh] IT� A�e observ<"tq f $Z :=)hWaGO:�� n :�{2}}(Z+We9.�A���"n(t)-�2�(t)�;�:�aeHe� path�Z a�e0C of�y~( (at $t=0$)E�!Eer B $B�>nN�!1�$).�L� t�CqRA�sb> !�:<�. {",y��=y `^�> j�>"2)#:�>� x_j(U�\; x_jM�\; y_jB�N�Si�Han orthogonal trans��I�-OV�s aga�3 N��\cite[.B 5.12]{VDN�&x_1Y�W(t)$ ]Rv��>tac[0,2��)"� operator�q!/q(zVs�!� ��co*7�@e+in2A��i8&�A_="� $&TDr� 4� �-,tQ ?*p8r3  \cA-j;->i�%rm.��%("C&$)�RR`�u!~ F~,!��b$R pres��7:4 polynomial inJ0_eQ��,B2.�$�n e.n��B:u���],� ^� �2f��Y�F3 a2 O6_tZ )_r(�toZ .1a� \ps� >^:�%\bVi5 t))\}J(A!!g_>1n\�0_t( )+ O2� 2��O�`"�b},H �m ��"� by!� �R���@U�qrE 5} m= �6 �bZ~"�&2PX0 � AdfunQU�$�,Xhe6�"� y�E\2?`27[f� �%�:�M+ Jf 2q>0F C�D!�s�6� n��3 _!� /4}( r)=B�:"� *�$t\to�=�%^��<�g1g:�BE�ell3�%�� �t�"&� ! -x�'��2�CbCRA��Stieltj� B"� _tj� ��Rg:{Sa,By P mj�, �Q? 5.6?u,} r�7Y@!4I%4e{1F@ H@{\an��R�L2hd-P :i $:%�e oundaryi�e rect]!��&\cJ + [-� J, ]͑[-1,1]!� ]< clockwise orien�H�M�$�86F^=�F"��E�>��7Ri7 ob I�.!ex_=L rmul�/rJp *2�MU�/G}))I:�:*�R]J�Wqrv .K8-7},�$]s2}m�5XF$. T"Y#m**�5�65is 6� t ��� _0)N�3�T  G�got� B�'� �:#)�\[.�=nk>���ZoN:�BlN $k&� =nk$& �!as $n5�B,e�>"�1�Using� 6�,թ 11.1� �B� �j~�� e~10.7L �[ nbo`Dthebibliography}{9} \bib�/H[BS1]{BS1} Z.D.~Bai� LJ.W.~Silverstein, No6��# eZ�#orKe limi�V� tral2� �� larg�mensi%  Y pl0trL. Annals/"\b.\ 26 (1998), 316--345..�2�2���] separ�  6�fF��cov'/��� �7�09), 1536--155.�8CF]{CF} J.M.~Co>JA�dA.~Figa-Talamanea, Idempoty $ reduced�Malgebra!U0a free group.�Hc.\ Amer.\ Math.\ S103�2198!N779--782=NCo]{Co}�C�^sAn�mu� (ve differen��@ geometry. Publq$Inst.\ Hau�X8Etudes Sci.\ 62!'885), 257--360. 9�Cu1]{Cu1!((~Cuntz, K-t J$tical amen�N� discret-sY.�: $\Ext\ _\red(F_2M�t ayepr� SDUA�2002)��boTAnnQY�,L]{L} E.C.~La�U/a cert�eo6�-� 1�151!Em209--23� Q08Le]{Le} F.~Lehn!�Compu�D. K e�"����(x coeffic� ~i�A�M.12���453--486�DPV]{PV} M.~Pimsner%�D.~Vo�F escu!����crosse@=pIZs�� -,�O9Qf8%2a}3a}5.�S� H.~Schula�Non-co�~&��*�( Gaussian>2�$* �;nd>�&] �ϑ`}(Related Fie/H(Avail;5�at {\tt http://www.imada.sdu.dk/$^\sim$s �0/master.pdf})��T]{T}y {\o}mMixed mo��9�'s�F-, JourA�F[� nal. 176 a0�F4.�V1]{V1}>CiPT%GFaT�Ld EM fac7 , ``U Aɻs, U�a�esp s, $lIn��& y'',%� gresT'M�� \��@.\ 92, Birkh�usaW(1990, 45--6.�VB2B�L� laws�`r6�T��o�Ts,��o�� \ 10�i91!c01��2{3]{V3B{:VK}o� �.�6 .family.�(y 7ag 93), 5--7}�V4]{V4} >�)�i������K}Y`%�bl!<``Recent advandc��� ��,Orleans~1992!�AaMf~2394��7.�VDN�>� K.~Dykema%�8A.~Nica, Free R%� Va�8$s, CMR Mon Ser`1,, i�g!�e�g Society, ��7>X  DR ta�� AI'��er���$\\ Uni^ vof Sou�n Den,�\\ Campusvej 55, 5230 Odense M\\ (\Wett{ h�X@.s \\ s�nBteenth2 �nd{doc>} ՙ\Lclass[12pt,a4paper]{�Ll�*uW ckage{ams�V,amssymbt�,(%\input{set0} % % Symbolig�� ya .Y�;$ % \def\R{�Rbb{R}} QQZZq int{[0,1] �Idek onzFlN Fcal{NGMMKKEEIIJJSySz%Ca�g=Z�����A� .�)!Ms 13add#1{{\q�name{E?up 4sf{add}}}}(#1)-Wnon�7non:7cov�7covB7f�7f7Mshr�9shr.9% 9Ni�]sRfa)�frak{a1�fbbccddee}} %Eweva  M*I�fk+kAmmpprr?(2_\-�fss8ttuu}mUSet&� � �Z /rel|5issm{\E��# �,symdif{\triaT. Pow#1 sa�PM�% %�resDHtedto{\!\upharpoonr(5\!�B)% {�Qchoice%H R=$% display �en)in��2(6�}% 5 crip� rf!e�ub .- isomo~(c{[ eq cf:�cf1�op#1#2�!S #1,#2�/ =dom:>doUgran:ran!�%S st{: FsM,)R{:}\,:\,}  )car��\ot#1\rzV  size!�Nlh^Seqeft�0{#1}\I�0Yk+2 rankIT %�C]�� domn{*;^* �aincl{"�'��ucc)w2j>~' }}}_�({#2}���_B�B>tem��>9new� dand{\splitnodes}[2][{}]% :�BP4R�init{Oq�!k-eqy�Y�Lonc{{}^\frown\!} %�\d;(Roslanowski1<��lVeI  mkYB !|E�int!floorAb }�0abs?Aw _EI![QHAG% Logi- s��0forallbutfin{ ^{9Q�:- inf{ R!V Forcingt.� forc!�1%�{\VdashEY} J)F Q.-E {``}A� ''Cdef�9~Dupp�s.t\t"1M�,{{[\![#2]\!] �-}V�� bf{VWW�s!{Th�s' s �a�6rigon� ic s� !*� NsetB�N}lN�0N _0 �pDBpD@pra�nrm{Pra��m)�O �)ful>PcF)��F�cGGHH%+�cPPN XO %1# incr �^{\upar�8}} �� t �wl�ccrO8ng"es �Qseqs{ CS< �T�c Ajof natuk> !�%m����dsum{�T��FC-�d�B: .#aN#ap)�aK�� ttt>qt \IH   n n= k%��.�Y"���a���F��2�fi� % G+8 Topology / Des�ive� � o� {��2Lcl� A�clo/� o� interior:intBA+:B Ball:>BQ�diaB�ia�-�G�y{$G_\ $-lF {$F $%<�SIGMAi;bf{\SigmA� P� Pi!r4 DELT4�!)> Rbt\�5V>U.Y X.\%�.deriv�� 1}]{A^{"�8Cantor-Bendixso�ri~+vkO% hyphen�  excep� !NT{% ho-me-o-mor-phism BPs com-pac-ti-fi-ca-OUFC@y6%e Mn-�"-�c lyk -nu-i �-r� %� ??? %�t-N�6��ie�y)� higs:k �La�^!�Mrsmirnove�u_"tonecec� betaPM:�P"�Me��:I�8cptequiv{\appro/x� si&F unif .simX,fli l�fs.OsA� .s.�s&� Gs&Mh.HhHh.HhHhh HhHp.0� �a�2�MA}�cptse #3{!o\pa� el!�\,(#3\ ! cptn�G22not\,b8"thmdefE� �Yem�5 |1AN\ em�{plainM J}klMr}[g>]p #lem}[thmhmm�necor  Corollary6ap D ?*z,6$� $Fac? .blaim}{C2� conj 7Con8:ur�=q Ques�)6Aex Examp�%:2�/%N6: defn <D�p #>?re�6;OScppific Research (C)(2) 15540115r F��>JSPS.}]S� < Graduate School� .gZ0ce, % NagoyaanEP  464--8601IP} Late{December 29, 200�`} \makee�u�abstr���4�Q�S�� --\v{C}ecl)m I!@E/�-#��{X}$ +2 %non�Gact f#iz��qX$ �0��|dA�rcA~�!dmD LxIGF#al�"pat�i pcs$X$. If�9con�u ourselv��loJC�m l F�s, % correspon�V stat�L�D�HF S�. �,inv�gA �D�BSin�l)G�$D$! �6� �*X.�>m22�B32 9d1Rorb� 5U%c�$�[�p&�E �*ei�� domiu ng�h1 Q�m. �Yar �K�����`{\it MSC}: 54D35; 03E17 \�5(Keywords}: �5%ec9�;^#; m {\v V;)=]A�ys�*�{.�$} A 3Lh{>�$} %$\alph�4M'%$letely reg6u0Hausdorff %t� :�A��inu5 sury �&$f\st�Y X�* M$ &�c $f\.d_i,&�k map�4�3s�jan $fZ4 �^to�*a home�smV�� �. @8\K(X)2�F�u�]���Wz)!9�lfLc$-� al� A2D�!�regard �a)6vHce ���w�*Ec:A�7t, �,�APstruc |/�,x})���A� upper�7latticeA~XOs+�Ll�c-�m|\��. )s�E=t��r��of �0eHnQdk2�p�lt� R!�Aa>$R��_is �Tedm�m�} A�-!lo7!+ s#!ofY)z A' m�y,�ni���n�)t�-{geM�*!�>WA<)\cR.)Uw ��Iv-4. TAz��*%$()� 5��o"�  r( u$�7*s},@berp!�ea Kq��5A1$ &_��r�>�AD���`�Ɖ9ly ext�yd ��� %�@we will��{J OC_{�}$ �3\ �3g',em 3.7]{BaY:AoQ�:02.5]{Chan:cptD>:�F %!��� $V X$ &��q?w!MU�. (See �{,GJ�s}�m-�$details.) ��i�a��=&!�a i�wo M�)�s $A,B%6�{A}{B}2MiEcl=bA>S2B&DSX��ov�3 %!��K $i�Bl- >� ,%aesal��$Xe�jT�\6` h  %iM��dly�M:b�%#  pair!O&�L�NK %(cf..�:lem:char iA61�mN� (X,dao $U^*_{d}���g � llucE orml+f [�6b�:Tg�S �T�$� >�` mp{X}of\/ z�S ��rF?associ�*44a&su��=.E�j� Y�IcseU`2�}$AE�M($d(A,B)>0$ JWo:!m�.=]�e�t:0 m tells u�� we|3&� �̂>!�I*�  `;:A^�� %� JNi;#A�]p�.oI�� 6�"� 5���ng$ b44m}�J thm:-�)!}n(/&:�11].}E� "��., �N[:p a�&up\] ]�� d���(X)Ґ�(}%�6 sup$)�supremum( take�NA�l$ $(�# al{Ka�,�Uup{)}�2)�(Now��\M2f gAk}"V=^v�)F&8~2.2]{KTY:babylT'FIR� $�E"m�RE���$D"D9I��<&;i%M* �� D\� le1 �=\min!�ize{D!� N�%w{e���} %�)u-JZ�mc $d$� !G2~  e} g d$-J !S�{�w ��ur� � ? ��S} �es  ~s}� ;�tr+J��$every�4m� �9 $\PMagneqMt�[$ (I�>=3.1A�:�*)A� �� � ��dom=3���a�I!A$A*� �2=R.a� Qfa $f''A��e ima�eby���_(���)l2�w$(Y,\rho�R2�say!�� �2J YER!@4h{slowly oscil)ng�f yyٝW'�:,2��@P*�6ga� eFe�$ r>0\, �%!> %�$ K�  exa�U�!�}\, %\\�hPKq�'�d!�}X. �x�;X�) K\,(�_!b (f''� _d(x,r))<�AY%e��0%\tag*{$(*)_d� 1-*�TN�M ,��` _d�Sb����C*� & F�U"�Ml��H e�� *� Z $z&� �Abi �� C^ ��� j�  �}$� �� ,߁RWOE�)�UMO$K_)>�A1A)+B)>R$W ( WU.tDG Pro�^$ 2.3]{DKU: �coronaQ %�0y� %%�&<��ATose�A'��VFO ��Z� >s� >��i!jhNotR  a�e:< >�!�"�"��*�L��}0!Ws�n� �����y *� )��m:Q 1 3N ѓq�*P>�Ω�� �I�"� %*�� SoJ �oi,d!4Yd�K 6 �rK ��d h�d ��` NM>_ �z_ �Ѣnd�[ ^x=�Z �|� |\ � �l�is: d�L ����| ~6��.7 a8? $f,g) omega^ ��we�$f�. gi�#�% but c)lW��n�)Xw^ $f(n� g(>s %A��a�\2t�.N a *��4y� �of��>M with�d\��I�/�.��c ^*}!�d �ah" � �aH u �t We�^�*fsW DpQsu%t�&�* % �6..�f���J�� Nl� �D�eas-Ve��at �(s no change!�replacA�%�!�!a � $\!~z a !�($f M�:RU�Y~� �S��W sec:dor1}�n�FF,ia�/� , �q�=m�=�o�fs� 1l . R� �!d�-� %aX)�$%��6Jv� �)��>�Z� Bd {Dichotom�@f}s�s�z5l U%ily s:btA% {I�- �m!,&h A"���sq�iv��-% )ss,C��su�@�<�B9 �X)!�*$1��ju hva�Y� !:��)vf�}a)=MQ$�+�!d�cs��O�+*�+�+a!M,0a��ȁ!� -�KG�o�����iso�@p�c��!Z` saone>Y "!(~3�*p\ V^�9�"�sR9q�>�numerat��H� r b���" $ !�q�� �2Ju� d % n ��noZ3�WC# . .��q��&>Z� Nr*� ~2.6.b1sf�%+F� ��.�2�  $%�h >�2M ����:�I�% e pa� �2Q �\�#&~Y�!� �d-��5 :halfope�K"C�*s~2.3 ��[z2{}�Zsa(�MsL)�X6dREep���i2j���, l{���XE�>M��x,��X �R unl�C �ԂB2 ��l ���iQFr�+��!�B� abL��o>=�&n�T�Fab*�M����W w���!by��p-�f�i�)"� i&FV r $1�wh  �. �>� Yma�_{ n im%'�,��!5 %.<* !&Y�A�W�6`>j�l-.:M�H.�:3 6�� 1F�-�"�$:�9Led��eF6��! � �`\/��b]%e� , g(x)\ �a*J �A!%&b>!BVu�2�lf�!!>�A4 &`� i:��� r>6 &�"Z2:A�Z�{B!enyn�"�aM �.�pAM�^�B�S�.s�z�/calW�aɱ2 Wu� } . X q� *D*�E�>��E �e�)F�� s]mnon�uYm�= F}�� m$vU"[ɔA͵�holdsE botheW�k,l+@ o&/"� a9< e U `�h FޭGh�� <�� %�pare �y not � R >�no�'pQ-<is �E�llB� j�lower}�X��*. �KB �_���M�� �-�ge%]1�ac"� ��} %�Y���; 3=&h . M" %K .� w � %H<�R482�u Yv/�D` FY�  n��umu�{ z &tN�h�$�`� Eq�!<'\{a_nQ��A��i55reE�a } }$U�2a �%�~c�Q�Db_{n,i�i�8C�H� ��'A�&� &.,T�Zj4�9ź�Cr�convergi��i��'n1}{3}�nJ(a_n,A=�Uc B-`�-I,A7;"R>�Y�LU`Ball_V&R�*$nH  m$� �J8J�u�%�a"a�"�i()�M 4�j"@!��� HAssY�i�Ff�h��F��-.D�vJ%AB)�Jac>"!�!�n aVr�J�.N�1n$'%a B_f$ei17din�so doem*Qte,A$ ɚ6�e��B. �n a��M�E�$\kappa<�b!�t Z�$YBiz!�6�We2�s.�$�;&. f=&BS i5� DAR+:�!g_!6 let�U�\ g_d(n�7F{��\st � i� m\,)(de��W i})<�Aa�n+�H)\�H}�_Ae�:A5or �^m Fc ~4� g_F��g_�1� F��(~`maV�9 %�(,maximum�S`�'�%[D]^{�}}}�d�%=)�%��\$��:/i�s"^�u2!�` g_F��$���  w %dN�a�$Clearly $B�rdy�#��B% 7��B=z4� �� u >ŜB��!�2 U �.�#.C�%)�� $IA{��st!t (n)�,$� Z*h$�$e�&�AB, e/$8| IAT.p}��a��:a�*5 �mŴ4hr|�l�� �3�C�)- Y�%F�1F�* 0�So�ll `g�zg�d j �m&��(��#�no:�E�.�*���v�� .+Z�I�:�E�is � 6�0nGF\�a�is�6��ZyA�D��>>�2j��)��D��ndg{B�3� ��We tur��E��A *���!����Ɂ��ay< nven#W��.�/�EAg�w�C_n=K~ gseti�$n=-1,-2��$� v*���}:�X���p&�-Q�B> C_6� rPc:���A��y�"y)"+Ib:v��MC $X=\�t>�� %(rn%' �5-2}=C_��*) ��� ,g|&� F� rjnTbg��M�!!Ή8aA| ti6"C)�J$�X13& :z# ���.�"��''(%0sm6n-1�o� eq[r_n,r_%�qiAD>� �b�vf.� 9�, "� *l*Q�5��9 r_n]!a��'%$�Qphi_n}�{n�� cup(�+6+1}n� 6<C ;�MJ`)"�K61})=\{A$E�6XN�>2";�'f �C_m!,�X!���4hq m+2"1�=0(x�x�. 4(e�7րE"�B,&k <cp$�]�8�$� y�Jz�2�2�� .����T>�"hKADm�YIKi�!���.�1t.^� n���K>���V.expandA(*=0zr�1�="� f?=lofQ�J�J�)�gB� 6/x"�+ $d_g�"��A�"~:1w.� =_AU�C @top4H!+B 5!��O@ $x,y ��EL-1� Uvd_g(x,y��(- Z.y�R\:AA�եgn O�(F .���Rse"� �M�m�s R���n,\�P _d(Kg� )��h!�a-E�c"]NU>I{ �@ >is obJ?ed� �g� %�Ki �6[ )S�"� 2y �>F BX >��e�yMR�0}� 'a�WxA� ��*�N $g(0)�6&C�6�N7�3 )<.��1[1=E���(YW� uS+���!$sA�a���F(s)=�&$_0^s f(t)dX%] f8e"6WD rho$� rho'a� �X\t0��C�0��:.�[ @e+L6Y,{c(x)-c(y)},i3\�u]�0'm^ = f}9x\2,2\}il(X.�v qIt"}A3"�* $6� 6xo�:�gv>)�3"g Howl�!10lj.�Gc n, beca_!�%gp?�y E[./ in�Bl�$0"�*� rho� alig5 K%p = a� \{ &�NE(x,z_0)+�s+.!�z_i,z_{i) F{l��y) \st � \~� lM��!�9z_0� R:A�X ե��2� �#f%�y�, � ��n:��a�soM6С� . f�ab.� /F(A�)-y))� s�WI�M�gV8, Q7���& � �V�%;,y)-pgeFd9)}5���z <�jD�.������] :magn"� }% ��퓕�Ci{"���� n�ItD��p 1!��I N�,* �nF�!� frac��*���)異.�0E��F2�  %$m\�#�� %� K_m�m�, $���s�!$Ah=r-9s=�7�%N�rks J L % J��+$>�� �m��!�o� ��&tc�|�$sp :F�MV�!iG�g�bs��6��y $��!zZ�� ch{Case 10RA6��!�z_ixICu>c>6"�i!]�\ �)^(B6?>�c,y)��%&1�FCao����d>=f< ~�bcm�L��em1�2.}2�-���!-�!�i.� �� �ii@��e a)&P ʋ��,As-��a���x��),��(aBJ�V�L6_g5 ^y.^:�i�Q!J}�2eV�� (F(r�h�)+(� �y �:,2d26.8r-2f6++.: F= r::O�~I���yA�yEb ra� � K�x�$r=�!�\� "1 E`6r }QR_LR�},���q�.�-� �'�YIC� sym�0c�Y �]aJ �m $f(s� .�� *� , B�6�"�"E�.�:� . *Q�.(c 5� �!F i�� .Y'�~� <"e�>+� %_z=x.�J)9ly%��-Z�$ uwY`�/"A !sN�Jj� � � n�R "� , �.| �{�)� %�� ]�b� ���  *� u% (y)- x) %AH (n+1)^2-n^2 %=2n+1i| �)�by�b"� .k[euA�y����B�� byx3r&fP Al��(qѭ�lem� Y�R�4n�tF1=Jv+` o"j �/%Y��Gg= %Ull�7�\J(�#"����-�%pit� yme!!L=`�:�Z��R`�Kb�>�yO2�Q^�Vv ��XʝA�R�ńg�M"!�� 4.�-B�=&�%3�M�=�w9�%$�#m�2p*>Y$6�:&*}6_g�)%S�\�IZW:��*.�%A�two&�#�!�$*�Q!�",)�k2eZ%$��&P�}x�)!w,BS&�5$.!\ �06��Z.�I0*f+{n+2}^6cint}K_%h�%"��&���&�_I�"�A2���R�f_*w ZJ� %$B*V%& %{m"d�%.�A� �H�c!�l��,a�n &z �P.�,2��P�5OAd(z-�0 j�V+2d9V. �Yh_{A,Ba>x'aE=Ե: �5�!��2�6f��J ��:�i����( \[ �(n) =\h)\lceil�n}{vw"�o4, \] &)H r\B "�A�ger��werl n $r$)� � S)1�OC��"B$� indJKA�$NM�"w6M��R $n>NA �H� �ae�v)N$M�N� �{M+*Y�gA)+ B� M!��ڟBU4J���$M� $n_a,n_b��� p�_a�` �} �#b#b#�a$n�F lɥ:���&M=�:�%O�K_M"�%�=�2�n��M$ �:=b�� x �\ 2.�>�80J� ,j�aa,b�' 7�n_a-n!-�1!%�>G(��Ɍ-BIx�� ��m �g(n-1� d \\ �GF$n#.'�2gC n-1 )^k � %Nexa��$2>!%  O>%�Ji�6V�K_nY�#tn>ID9W~B��u Uh� "�=E#f�J�!ʌE� %�1�,�qb�AS :CiC�Mk��7�6z�!F72ri ]\)�"�7884FM���7&i� %- *�EIt ��b�r!桳�%fd�i� �EmoriF!��X1~S �^'d��bAa�>�2R�H, �=C�%���IA> lastì,�C�M* c?�D��:� �8�-?e�A�%$��1p�G�1�&/A�"f2e���A~k:�)Jm:�G�"a�"Ed�E Y$ejRG �J`_t}t #*:L3,2=�,ii1� &UW&�Snd }Dqa�m8d6�,}\}+\aleph_0�{�0�L�7YL&�N$�1AIQ6og �"3$\��\thet3 2^ ��3��e �� isB4� �H0of �0�[*���:�p C5<�\st � in C �5 g�%X4F � !j$Yy8�n���Z�:6��]�OyJ%+log e(Y�Qt� !%M �1ޭ�3Y6;;zFeU e�>mbdE5 Y-�$ 56a :�B& E< V=� �6 }��S2)D��I0S'H&��*B]%�\mW=\mu<��V�&>>��4:�*�H�a�Al/[�Y�=��byb�we ��&3���muEf�>� "�$H6:9|u&�.MZ�o.YP �&�5h�HF�'$g� h!H�0���OF�leq*! b/ $bCa_\xia�xi7;�o]�-Weta-��+n<�cap U_*�0ƪt)�a(-**�,G>T�@$\�7!;�/(\xi)e{�A% %�=� -2rhiбe��$g^\xi_ ,>E.�\[ ,(m)= D_�{k��:[:k[:(�E`_:! i.�6mj`:�:��M�$h.�a� MW .�� *erJ)* F\in2-:�{T/11)"�:}s�A�:%��:�� %6���"�|��7 D�y+����/ %�:2�} �C:���d^H2q< �� �A$K!BI�]^ �A$\{%x! xa  KE�" ,� )�#i=�=C5=��D%� *FB'!D2�F����unZC�%\A�h*�}"5 K:� b_n=b_ .,h^ ;Y!��;6��������;$U�~$'`6$ \,i}J?� .;i�2�;J@]Al��#i%Re� W��-�:8"u&�%�(�x�3,b�-lLE�"1}�!!%vF |�@ }B�2�$�g27?�AF-o3k@Y�rh��QZW=��8i��1L��8H:P!_H o� �Dcor _i��>M-U+1>jw; �s pped���d� .]b�-+1Z7usual 6p1d o>2^� fBM ���� %I<ar� e&�VF� ��&P�  %� �" at le�$(� )^{+%]ŋ�q&�b*��M %Ik� � B�% \ .t�$rI�Z�?h�f\fc�d&�5(�[:�)z�j�C-2Jqe|�~.)�2l~%2 {kadA~)�> �{1�^�&�o B.~J. F�6$S.~Yokura.~bn�%�ac.�Ldet�U�by� {@�,ne A;&����H.}, 13:1--13, 1982.� �"Cp R.~E.  dler.�T&�uC�#.�2�Marce��l Dekker Inc., New York, 1976. \bibitem{DKU:higsoncorona} A.~N. Dranishnikov, J.~Keesling, and V.~V. Uspenskij. \newblock On the {Higson} corona of uniformly contractible spaces. \newblock {\em Topology}, 37:791--803, 1998.�PGJ:rings} L.~Gillman �0M.~Jerison. \�{\em R1�Pcontinuous functions}./,Van Nostrand!>60.|�KTY:babylon} M.~Kada, K.~Tomoyasu, �,Y.~Yoshinobu.]�How many miles to $\beta\omega$? --- {Approximating} 2#� by metric-dependent compactifica�.v%1^h Appl.}, 145:277--292, 20046�:a�} K�wamura%g�.fA/i�on%l@{Stone--\v{C}ech}F� by Q9 F .a�Z2D-�Shell3m8\Blank &2G`Language=American Englishk4CSTFile=LaTeX -�8 (bright).cst} ��he 220mm  width 165 hoffset - v1@font\goth=eufm10 0sevenbf=cmbx7 bb=msb$$newtheorem��}{T }[subsec��] .*(acknowledgee[ C]{A:67lgorithm.16+xio2'2# caseIC6!lai.DNota]�$conclusion.I6O ondi! 6, >+j�#6,:-rollary2,6+riter:�2+defin>�D2-exampl.�E :' erci2vE2)lemma�L2#not�x&N2)proble.�P >'pos>�Pr2/remark}R 2% solu:�S6)umm6�S 'environa+�4of}[1][Proof]{�\bf{#1.} }{\ \rule{0.5em} 8} \def\w{{\rm wTab Tab4input{tcilatex�Ubeginٹ�g(itle{Branchu mts, Kostka-Foulkes polynomials  �$q$-multiplicities in tensor product for E Proot systems $B_{n},C$ LD �} \author{C\'{e}dric Lecouvey \\ %EndAName le �$unicaen.fr!(ate{} \make�&�ab ct}  j�t$K_{\lambda,\mu}^{\phi}(q)$ re!Kd� a� � $$$ ��be emed as a��n  sums runn!hove)@Weyl group associ,F ,phi.$ By res ;  these LDel�x� the symN Y when�i &ype:�or -�L, we obtain again a �8 $\widetilde{K}f(of:b ]B. WZ�M��lre exists a duality beetween seB� some natu� J� $% u� %�%�E�UU� Q�0\cite{lec}. I�is paper!<(first estab�� i� i'q6J% 6u.t$which implmgp3ulaAAat!yMz decomposI}ErB�2/.�% I�A_{n-1})xwith nonnegative integer coeffi ts.\ MoreQ�se . are b2c2>$.$= allows uFclarify �Cc�y2�R�9�1�,U_{% .�5�]]�2) ,\diamondsuit8 q�inM,SZ}. Finally!�show t!�J���% Nh(coincide up�a power!�$q$)�\� one dimen� sum!��xed�Ok}i�all7A;�$\mu$%�equalm $1$ Il&i�provesiPco�Bye7 ! �o \4 {In ��D, Consider $-�-�two �-q!�� $\i cal{P}�: of � +E�$n$?A���Schur-�l�Du��!��:5TJ qq- w� s��u$!{Gl =�Dal irreducible $sl�-moduV^^(- )g highestk9*is9�!��yE0% VU��he��!�� A!G*} V_{i�=2Qmu_{1}\L�) 0)\otimes\cdot%  B?n2?M9�ID� from�%� character�O mulamnB��@% \sum_{\sigma\inUESEE }(-1)^{l( !)} P}% .�A1�(+\rho)-(\mu )$aqrEatM�? $ is��antE�E�"���counts,1�*D !��% �,�) numb�.� [of� �bb{Z}^{n� s a�( of 1 vens.e9�Z :�bya��$% 9��`9 (q)=����5N_{q N}}-���% C��$aMa*�Z�Uviz�J5\ _{\alpha� {6WD}}\dfrac{1}{(1-qe^ -})}1> \in �5�.��!2)K }��}I�A�,=(n-1,...,0)I5 halfAA&!:\ One%�� �*y�=12�o� expaś��Y� $% s�_ }(x��B e bas� H��2�\{P"# }(x,q),�)=*�\}$ (see͘(mac})$.\;$T{ iJY��;P affine Hecke algebraa�k naren,hdan-Lusztig2��%Lu}.\ Ini�� ey have.k Rk  As)�\Lascoux�8Sch\"{u}tzenber� thi| � v9 result%� also� � Nuy%�8harge statistic!�\a�rm{ch�\n semistandard tableaux. prel �2] ���T\in STq�)E&}}q^{~ (T)}��i>- y�setA�R�ha " ����.$!�)��R9!vV4y��.|J� B�m}I\�c �c %Qcal{SBx24 2 &  }&  Av ^|�4=(n�1)�VT .�6U6[ .�< j���h-���� �i9�1�L ����:�!�$% q$6-6�>5a�:�sF2� ZW2tA- same �$ Shimozono3Zabrocki� SZ}E� �p�'ly.b /�"� oper� 12�6R!�*Y �w R�a sequl%����\!la�r5� $2Jm "�:!. $\m'4ptyset ,(1),(1 2)\}�FO!�E$be2y$qJ��Q*]�|� , Hatayam\)0uniba, Okado !�Takagi%o2�or� a2� $X>��]= ]p�}H2}in } �g a_% �$.f� ba]�"5b wB���a�"*��o rime��wid�sp_{2n�"�![ he spirit�"�. I�:�a6!�%Lhe ��� � )^^{(1)}.�� !� qSZ}D  sG�!&�2�:�E�v�:)-�(2))�:!Wrenormal Q As observ. �i.�E�%@"�!' $X=M�� �� gif+ onic!V�s 82�%y$X$.\ n#�^=@I�b�hd!� vari�,�# a,all nonexcepAsal1��t �OSS},-�ok32�CS}$.$ "��Kcl��"� iF�2�E��J% * FL�y5�"�&s��42l&�^*;��.6}� sh��beICy� )y � 6�A6*��Ii2�= � ary!�ofa�!�_� �j�^� q7 q�Nex'-��i"2 IE>& Ri {U6`e��!�a�/ �!]/o thos�d ��h6� =� ^i� i�w!�r�L�lW 2K�51,1�7=&M?(q^{2}�:^* �q=J:.$ *�"� ��**!��=FL��na���At����v�(i.e.�gd ��� ��/�BY!3 vector re�en�on), nam.�>9 }*2 ,(1<)�1Nc -f,=q^{n-\left|�  \�)| }.#:9. 9����2�:E~2(� "5 � )n�. 0bel{EQF:W=&bigskip�NS�on $2$A�reviewIma�(al6�w!s,:"s2�n�& $\ $�JF�#e�"�i!* we ne��cr l� $3��.�R��>aX��J�q�Jx)$� we!#E��&�"� N^V� >��B,Y->^�#.$9�4O devo�.")(\refEJ). ziQ(�!c� tru��1�x .\ ThuS� Q%7B�s�� thei�$*� J�$ML,�#Z� ,>�.�� uJ"!e�bf"+ : }I�e lA�frA�n&� ��� ob� ��2w �$� �$/�'��EX�(b ;(�. B, <)]�* ly attachMm�( l�N $B$BavLs $C,D$). To avoid c� s�'rep�)A�f �s omi�FB,C�y en our��or�4)6�calu� thre67!��{Backdnd�&/{Conven�J.��ype1�2+% %H $.%aAq'$n\geq1-'� 0latticeNn-�$ 1�Bx1 )"�*) fied�$P_ =�bb{2"NP_{Q}=P_{O}=��( � : }{2}�r) ż$ equipppAortho� fi $varepsilon>�5"�� We take ��qooJ�} �\{��tab�]}{l} $�!!^�2n}e��.i.% 20i}-6+1 B, }�-1 V�� �}%a$ \\ 6��=22af� /��J�ZJ�Q.�n}+6-1�q-S'^RA�R�t!Rs }�I�8M I�. &�IJ_<sB�E"A�XB9%�9Uc� �*z~RqN^{+}=\{2*>�j},: +:�jMki�$}1\leq ix��go��Km3s wcoord$�� '$:�6��a�M3�/ s (h1$ ca%.7!B%U s). For e� ����� � "$n*���hav.T!&�&��1M64>�yI !]�a�&�&.��,length $n.$\��5U0,$�0��F�R�!sea��-of^�)��(��"e !���N*�6'�w�%�| +\� = ac+6< +,�C\6D\|  m)-1}(n-i)>i:�m/ug7?9d-M$mr�d!! �Q2ual.\ CoD$>�$t ��j.� 0�E+m� x2y�.C��by addA��$6 .�%+muA�� i�$n� �� s $0)�ill")3m� #B�$m�8F�x"} p��}}=W�x$zM�+1!?����.�(� �sub Q1� ermu j %G% \{\�3line �7P,{2} 1},1,2"n\}$\ $TbyA�s� =(i,i+1)(Fi.F< 3*8 �j�1i0ve�{n�CN�<$a\neq b$ $(a,b)Et!��  trans�Mo�/ switc2$a�!Db.$�xI��l_{B}G-�cV9' 1h�*g%tors $���n%�2&%&�'%�� 2��*B� .��I+>�!2�5�.Z��q$ F� -1})�.9�!���6bDVbF'+�Vbn�uAv!w% MSn-16{&�!<)v�t*-M�^��4*  verQ s $w2�)=� w(i)4+$i�1{^#\w�La.5G$w$A:G=(�/��e\ n})F�b"�M�nA�>� *} w�bQk^{w:of�!�0!i&=  �i�L3i��)T � w}=-@9?i}!> otherwise�2:�*Jrhoc c+� n )�C p9/>� B7 `/ EUI y:N} xI4�1;12,n3�g">22}% )2���112>>f 1,n-��0Nx5� *h�[k>]<�� K5$ ( =*a����F.l $�%j:2Z�� W� $�G�08�M $'s,*�&m�*�:�>2�+} y ��&m�ɝ�V�|^{B"P!), C}�6>���A D/��%)�O2�KN)#��re"ss 2�M� s $S",SP �$ �.?on�`$GL!�� �$���>&,� of6��al:s. Rec� �4R6>�^$% �� >%x]�n$-tupleFm* } (\gamma|, -}����_{2 �% $p 00,-:0-���-})"�j+-B�L $ K���-rey5%  $p .q$ suL5 $p+q^X riteU�A}Z "_22-1�R�1�J� %Jp ^!�:�=\e=&�x A � m��e nstead{qf!D.�|"� ,As customary� us�a.1�6����[&�:n}]i�m�-on�ay(";8p5�3C� }$ s 6fy ha�le<s $@A�} 2}}=1�^A�}. O fu�0 rmor��>�e9w( �"- $% xlE�xa�/ orO>toٱɝ>�]& �!!S2t#�[:lre9��$^{-1}]$ byE!%5}=B^{ �1}}t ϡW !n}}=x / d � �-%!I $3at ��EY" Se�NEglPr}�:$r�>e: !B.� ��;C&� ]��% �y*6 w�F6�%� �b,��<"I�U&� v� � h�$�=3�9�*p27Li $_mul_sum}W� abo�==� 2:"�JenumerazNitem J| =��'}.��  )]m�x W�.�: b(w\circ 4-W Fa),$ \ƑYF�`.�c����9�F��.�d��.$�.�E2���$kL ) b�H��+ a cor�O�nQ 8.2.1@) {GW}��$G eaLie&9 1 ,6C � � % H= � �L[�'&-B H�mB\nu-"� n � �!�nuJ��B�Ɲ%.�nu)$ �)}�!'}�i�) �1��P`�((lem_dec_b_Dy���Cm�wee��c2�brack �Cnu J�6� R�� f{1�4� N}}B�eM�qu��73!J&% .:� � ]Fi- )=1$ if�!�2��Sb3r2�B��3� d�b� @ )=0$.�eF-�1�M�_fo*HV(a'�0 D��F�]m�R2� ��nur�"<@N�Q�.X�)ś 2n}$�U� Si�'nCi~񒹠j� ^}>�� �B��Q���5���NZ�?^�>b�%rnG ��5.$ ^[ M��f+ �E�21.�sub-sD!FH$.jQ1at"ws���W rO��6"�#"colum�a30Littlewood-Ri�Ddso�A&�1C �vc_{��! }^{v�|.G�! us r R�!��ulth�el�.�GLi} ap�$ix p\ 295).�q�`.f in_A2n}B������0E>�+)n�~ y���]7��)$�\)�%G=}5D 1ED-��}N^ y]�q�6Ag�yy:�y2)rw.�, "�A�p&e  below��immedUly/��=� of & {K}. \ VS]@nu>�?qΉ�%  -a�wo�$�*�"� � 6)$ has&# ���VK+}UX��|�{A�} I� ,\deltB��22 &�nu  r B�$ .N���A����j� ������a0³F�-:^��-�h�I�Q�.�E3= t$.`'(�s-%�{�X1&��"XŇ� ��Eies�i"� "q cor/tJ�,!_j�#$W thenu�.� J�)Y��6"|a4 & eH��BA H1�zo�y �Ai M&��>) �/���I�����:F�^�]K�)�`{j9:*�:�!dotZ!�<2Z!B24%d*_erO� .� g� =w� +.s)-.� @��$*B:��" m KoyOt&. "z$V#2sL��V�`[J�6�Rin 2�.*�R1-q��(2xU:��R�})F;J5*�#\r� xD2Doo"��<+a �&ar �@ioE � "�!�2�$0*�*2�8.\#&� s"� F�q�K !��"�E" 5�s *O2Qq&.�Js4H �". Giv m� \�X6�Y����E�Z�O�z�4��6�]�Q� alig�&�8,�X-�q) & =MjU$A�Fl  )rN3?�A:�]H6), \\F�)�f� "� uV� + #:� JG � Z�IWf� �� +V� 2� n$1�.�VC;��\qHZ�H)J���1`n}-\r�)�Vhʦ OI'^Ʀ)���� OR� )-B��1���Ig �&�"�I"NGK@,� [8�D� �26�XF�C*�=EL>��$�Q��.E^�V&� �"� ZksR� �@6\�.�\$VPF�/B�? B �| QU|�O�$kA3ny �1*�k ?�ZE� I-mu}{2% *In5��<�D�6Ru9>�[�� +k\kapp� n}!�U(qM#`Q&9=(8+1!:�X -�&bf�g: }Sinc| �_A�)= �hT^VN^<Z@�_� +k% e�=VF-�1�)�0.$�Rw�Gextenda��]�AuZ�6d�I.de�K/Z5Anc�( �s ("I orq ).:� � *��C�@protect x,m �� %Af*�AGsub_sec_="U}$} 2yg #A��]1O ".96� i8�" j}}}28&�&�"E#q3iE#8�� 2x �%}f� > E�3;}2}�� "?#"�#ڹFN�� 5n�{ A�� ,$ lG8&�BA� iAEI� b�A�w*�Te� &Z&W6cI1�Z�:8 )-��(:�nmun}�"�}&D� |MQ/�x-B~-��| ' B}���e/n.�$a�ni�>i�$N�f "�7.�8.]N%��G(t.�����.& 6�67&Z+Ul�U}�-�T���d9UOe7"�U�(),m�}eCe4FeM3�B&�' V^:6h g,e�:k�Fk R ^&�e h�76hI 5;!����V)PW!V !�U z�76�5PeC}e�PW�PkDk1��f1PW^76�:PiY"�kq�$$, $W(k%? =V(k6O/W V((kV W=�%�0 0\�6 W% " We�+�8�aO&�*�&� }xa��l�i}*\6���>�i ��;���F7%��&Z �a.�U�>�*ga"+ 6L $V�' Jb6����xfxI� "� .�Jt$H�""� s:�F� rm{(i):}$9S)�sT!$�& � % �O��/9~ա90$z2�L� > � t'J� ��q=1` rec�9"� .��.�k��ɩ),�^  �Vi�2KY�B� v$� �Z,DE+}J$W�LlͳK}� N� �Z��yL�I%y.�p1h �F�Ru��V!?U  s'ed>^1Z�vE^Liks :Sf� � `U5Jmv� %9b9r Q�� <�~� V� �*PI:!���� *" o�:&J ^{\#}rC,0r�,��\mN]n%�*.%2% � F� �2� /68FSe�+3iem}Fth_1}F%�5j�N�? ����� &�?IY�f-� }% =(m-iL.1��?Y91d 5mse�"�E�ո)U. �9�)%�> 72�,�%��J(q&' 9��\%�q^��!&\� ��w5�&E �5I��F invo)yi�e<_ɀ�3�2��A~I�%�!j �)=(�1 1}�5�*y� ���"��5�(I�,���wso�]F�Qr@.k8p"�PU܁�is meansم&2g> }] A�!o\long�$Q3arrow%�F�Iq),IQmuTU ��Y�_ % }_6a _U � �b8�i&V\9�8:b?*Q_ �p�<"Xx_, AY#*� ��*�&H2���*<CFk�2kBRk]n"$! F��fa,s�'c-crtsrWs�Z��F�R�B� Z)U$ '1f\;.G �."lOk}, Z�^�TV�^anr?�f��a�X".YQ{�a'&/|y�8�!lNE^"�>m!�cer2)�-\F^}(E�')�l"?^$%ak����~/� + ۂba \ S)lg,6L0#$isomorphicA�F�B$ N� .� ��d� � � M"� 2. u��2����}>vmBk,k@*"2\� �2��8 B0!E.�=J�>A�q>Q�j>�>.s2�KN}HUsh oE�"?k  "+ a �{�3�!���ji�V�by �row"�p=��k$ fill7�te&_Z� b*d91�]�CC$=\{1<)�%��l$(0��!{0})\ $�t�r o,�]� �M�se�e�a�pqhe���n]G@�Xa_�V�%#�v>�B�+�:{0<�� {!�r�]0N��D� !��.�a�.-"A�;c�A% �UJx O?M�LH(!Q$ (i�i6�D1�Z�sBZ�/u�� VB�A�#BCa2�l �IY�ia{nMVdescrip� 1 ?�< �sm&�.ak\&�V array}{c}��lţP �E�0set{\simeq }{/( $V)� 9J8Vb!�  b_�Wn mapsto ^�B .(�>�Y �U �,U6a*} toge�G)�A9�Jgy"�$ $Hao�6E�Z���%A& d���[n d� by�hoinser%�aE�; $% AA-�of VBa}� c lec2Uf�*P l only)^eLJV�.$"m $)�in!� �y])� )�G�1�($z=\min (\#Rn M� %!�2� *E7� 25Rb.�NEastRwai1�^{�B2)7�i�er!$% z $��o.8Ʌ��.�a�) r�C�4% l�k' � �@B��:E �&�3�NP_{A*A�(%�`2C)2RMV&�b�rE�ngE�!$�w!��V�.��A��-J�.�� ����a�e% q*KT�4s 9q+=�W. C!Apl�LcB^�=1�2�*q�V�) homo!O ous,U3 aN3E�����i'5�Y\m&�IBA��short��!�U�g*4p&�28���A$16lA)n0�J  %J��rI�2�)�Q5�,uI)-mF��2�*�!2� !%6�DO3Ev�)��e�W:S=: .G �Uf�0%!��� j=B��e�-m ��fn -�j� `�n&�xq�*�k&�A�E��$2 szSdF."�g!�byN�FK b�*E"i}-�)"�,}%1�;0�!*#" 7�E1 b_{j��Sf�O1��oB�V5�$b=�O i*�V)�-�b�%��.1�$JZhA��< �)>s"Tɉ!�Q!*� Bx}qBa.� EiI�QX�T.Z22^�Ij .� � 6{� �2-:.+1 Kc2�� (?����& i�A�` ZVH%j�F��X1� :$ aG VP?-���s)��4T�%!� �>�[}� a{�'j.�vH��0|��#��D��A$ ���p&p 86Ss�� F�)c|�"G)� "$A$��o" �$ble�n5w�X�!�2�!ua�:�AjC � {��^z�* W%�<m A}(�����% (Q(b*��ELS.�pLSc .\F h�xs�F̃"�V��!6iJ*�+��;6A&�̈́T��SST�]�s� ):��% ��"�LSTB�whQ_$NM1"�[N���a �= "+mu �&UjG�Eo����.�,JA�k v�I�u�� "�MaUa[s sugg_ A�&� tU�&y#Y]H��Jh.!�Em*�r�n�2/ }/0!" }& :.�&TnPn\t2=.*%.9.��5�V}&�&Do��*m�(ii~U"�-�8.q^"�.Ft�t�:[o1D*�-}J- 5u#!k1~&� QZt#�-T $: A�"�$�!�B= �BD �&q] "�&�$� �N�A�Crigged�� figu!Sҋ�u�e �Z�H�R&�Q �TedF�l&cnXii$M.5wqm�x,5�i and &ozE���6�vwaaalzrE k�'Yn�-�E2wdb:��fCo�< %ܩM��E�u�mu &e0�u�e�ouXrC�Ct�c"i!a|"��y>ss5["�ldiffer���Q;&�mB<�H2: XI:liz��,!F� *֑s����6�zjD�HSg on{Ipf��u�!�=�ie�<.yD2P�hA��!&�gm�, mu% )WKerm�C��J71�� �4} DP��{�(PA�B�q$n���T>H��-_FL1VTNI1� .T _{\L�>��F�7~Bet2<et�5���*�M�o�">\mu]1nY!b�l!q��D:a� &r5Jn>e �/.�R�/V6:!s�4P �-�!��=�EB �F�4*�46ɑ6��$*. Q!o" 4i�pkB�'a��y6n"��4��'R$.\��E��q�q$Jf=��A% �'a$C�s*st��J��=qDp"eq^�Vq&�W2A>.� *�W��F+<�[6�>by�b})B>_X�"h4� Z�q �$ fD L�}�M��Aeta=��F"�'*eo� �in)!�J�@adP�&ad�š�c( H9�+}&�qP_C=P_AB^B �A arg���F�D!��rBA"� A:&� "� �;util}"�e�&\ 5�f3 %�B� �%SXEp& �=q Fl.& )Bq!uJ- j�4�Yq=���D:�&� B.�d-�j� �6�"S$j! �# �U�,2��"�%qfc�!f>�% FfD:f+bfB�<}-� H \TEXTsymbol{>}From��q)�dYХ!=�wDFnet��It�g �d )*�#53/2F)�ES�.yJ�2+F2��B5��k02sup�cm/ef�k./M%�2�NV�@ � p�~��sum�  �YFV��G"�*l�*�N U�ofV .U;`23- )�H����M^� : }A2�C3^cF%H>��l.0�t�dH�nB a,��"z 6B\�B �`6Txs�_�[�C �= �/6�i-% �r�^-�"��l6667Q�$ @ 6zF�7A�Q�v2�z";u�F >S�XK_cJ� E�2� Z&� }'� u &BmC*o\&G�.�6�M>� c�}���6U +�QY2KU�P��t���n"� /Q�^^ c�D#$rc"�Cg ) ~ׁ�k&V]�*�D5"�/� � n d� u &�9����r6 5�P}1+-h=�1 �2 AOJD1gb /2��=ge'nP��by�V �w�/�lW:�I�5�y M�R�%E�x� O F0~�D�I )7JH�fT����� *W�� �ZCZ�T� �e +B{��{� 9D�X ^�]n�gu� G1EBA)4L + �[A F� t�����))1�j �\�0 :) 1)=--Drg"� 5?rhb7&N 9��)�� Q$ & h2�!|.J)=2 6� (z )=� �� uzf��r�����9�IeJ��� !"�^% �o +e��hᒭ`#J�&> equKB;\ �*�nLV G ~t�Y�>7͇a�]'U���L�%�o�P�I�����A�*D��a��ʄ! j���c(:?)�<��V)vw ���ilJ� y�&��J���p��� "�K�n�/des|�q�{-{RG�Oat��M3 I#J�:,H )aw.>�a� v��zy� &EI* U�v" F.�B�J�!�xO,�=*S��.x 1�R� -��6a�2*PӤ��=�ő*'V"�6j�d�Y+ erty���AbeMK�&� "{  b"_&| *%Y\j3-%�{%�w $k$ 4ff�"��2F�*� ��f[ �M��� *�wM56�P)]�_ :A"�" q2HkVW6UY�� �� ��Ii2��q�. �]��m��;�?��y��|���:|�@"�^)��^a����7�v).$\;$� by *��K ��H�m "�fY4)}a2-*"�a�m� �lw�f+\ 4"Ff�w.Gk�s}y ���2�-.�_j F�R^>S$3b�0Y�� �+w(28-2�R�w$w7s�(ѫ�W�]eknWE-2k&� �:��se�� *�M�5)��AH&5�r� ��%�v^UL)Q2�J �.$ �v�a*��kX�1$c^?r�� ś�  $1Tj1%>i�B_c4��\P%2�C u�S��"Z| m�*YnTo��vC62 &�Qn�e "�[$:,&��� � ��6I 3�� ��t�� d2�>k#�� �� �nu o��^����A:�q%d:�m' 4" �iC.�5�A�AMN��D��ʬ 5�� dg5".��n2-q�"�H����n:+X��&�K6�)]��nu)tVa��M�*� ��� �:�Bo~�@D`E���";A/.��)6��� > �����.� ��g"sF� xIx^{;� Ie9Y�jJ �� K= �"kb�*UV�!k}Ja"�$�"j=Qh..�N@W>�U]}� 9�yT� &��`�`)� �6�7$� $qZ<F�"�J�� .e)J�6<j��J6� ؂�E����ndR��]eэD�I}Ǖ:.-W�9W{FV���$��f� �&Y &�2K.dJ�j�"R<at{$����>�� ��2-�N��gU�Ѡur��21��⁴f]� *)@->SJ��L�t �t E1�.l-(�=�f�&T�2=�M/*� T�8��&��M�y�2� B�6� �(� "� � i��� "4i"(��s:nA>@w� r�0 f�֤v�1`?w�m���� de:nbBy%"�1:} v# of C"�y�.2�� �/(|*U�����N�n�,VN����c,V- a��2_  ��m� w��m"�U�6"6�`J� Q��)]="�e2?  ;"�-2*�� *J i��in�Qc(�I�E:.i ==݅k:�  nRv�6 aB*0Uj�/�/E`jK%`rDa>� 1 Z`cAk=9E0Bf_)ʼn�$of>;+)�v can &@�-���A�e�b{��a,%LJ��X� 6��5�6zQ�*� Z /2� �f.)_6�}3Yj�>7(sr����z�A�"�*.�&���"�*prp��u�T2v�.�'m&%9��a��1�T�%�"� .hr$b886^$z���&� ���(�A�5 ��Ё� >��Dq�}*C}C.*r.n9�a�O �����@ �V�^�2.q��IW� c$(�A~�>� 6If}eO��% )�redF3=n��R -�e�H JUx&� �� M@AB!�Ix �2� ] v�� )b��6C"� Cf��/ A���+!�:�2�$=6 4�V A �o.�qnǫ�+�G���� .Y����5L4yI�2-"G�'� duceR�R�"��gf2�% �: 20)NJ~ =F9� O" >s -=X&#AF� %�X=�F=GslV��.�z� ��� a j� N}\6 ��!:�.nB�v � Fx5XI� \nu "\J) |VI�y1yq�.�Onu 6=J6 )Z$A���ciz�x� �f�F�Yc>q 9^J=.8 N�z�=�C s s=As�L�Q2%7� ed\.lyM���G s&�w Link�HE�.K A�Z� �:^{.���%�&Y>z ȸ} a �Q7J�Ʉu}& "]gth-SZ� ��2\y*�-� ��qx!?"� Q�h"[��<P*}/�@:�{ }bu� ��'aK� :���b�e�Q�.� E|6�zAVwN�"� :� 54v����yI �/� �BN����)��d -V��2{ !�ZZ��'!L�VT,$ .)b &.� E;i)Y<�c�<A<D*��)��<�<v<� �<�<VɃ�:��.(�!� *�/By'C.����Emo#�q���= F�&��y (7.6))�U��&����S�.��R u)��(ն�� e3��"!!+� V��"��[t�<&��on5� �serieXL��e6�F��wv)F!�nTC speciNKed at $%�7B} %�.~Fc��A���s+ G�?]�`&teWd2e !�� &N��Ei��nf>8�A�6�4Z "e F3 �@~R��&F[�!�R̹U��?K1B -�!Z�c��L}),(��!�Af��^�8=p�Hm-2aV:EI" ),I�d ʺ "�8 G9tha8�"�z&�"�� %G.�VE2���&] R�).\2C�,Niq^� ,�F�:�>X�׉+1'1"�Z$�B"�� �&n_) �� B}�]��O"�1�K�-�EH22�)}�nm2G\;$How���rZO�Fq)�9‘:JinK�O.6� e��'wy�&�J0U��?�k�$�" v��18}+2q^{6 4}+��:� �}910,@q^?6L*y$��J� &u �&�s:�� $\tauu  sn < �pOZJ�w\n�l�S�|aa>W of�O60!N:Y$-M�� refl�Ing � ��h diag|� [�W��Pͤ�m�R(� _})=% ~n��)K ->/!� " E�P)"A��OJ��=!"jO6gG"��aP% p&-p235*�2��(1)�� qkI��*�AMb{�fulA'㽥`&oM�b5 ?*/op_;OJ%J� 2z� �Dm�^JC1�(fq9{.[y 1� 9x��Jn % +nZ� 2G1�(-� vA�"rm{% \N:�&� �����*12� >�� QA2�1J�BR�.a��[ oremI ��vAf}.�ju�fi{��хZn���>(�٫�i\���nu.s�ոq}_au�!I�[ B&�R6�0_*�,u1�şn�*�,�B��' �O�c0���oat��< K�-.i��>[q`#�=n\Y.�W� sum$�b�,��n��@@ N{�INK1g=0$ un���� 5 =b�SoA|K:% E�(I!.767"n2)�Z��1=(�)A )$% �5map $\Gi� :!C.�eY�\ ."Rq[_% bpe" �f(R/. n�N�t `5>�H'.Q%F5�1&�/!�f�*&h=����3^�J=F+% iV1&y .�Ѯ9�M� ��6��2%F��:rD&jY aH�F}n�i�)0"�"DF�M*��Y&�+:�F�C�Ӂ�'(N�(Ewi�F�b�5�-+r�_ 6�*} �� � �9.� 9�5��r>r�5��ׁ1��)b�.��� 23�1F�F��&� }BgtӁ� !!`O�ʗ4E$&[]edf�S�� nu,R!@�E?D% R=(R"DR:)bN��2s>�XWarnarr _W�% q�e=���1� },R^� � �U   \| R�g\|Qe.,I].�W � �DR_Qj B+�iBn"ʹ:�g�kp�{�Bumc�hoose to label the vertices of $B^{A}(1)$ by letter �\mathcal{C}_{n},$ that is we identifyD withd�< crystal \begin{equation*} 1\overset{1}{\rightarrow }2\cdot Jr&n-A% n-1:En_n:line{n (set{n+1}{% .b  )-1  +2>Rc:� �v2K2Y{.' u1}. \end.5Recal!�at!` 1`graph%�C}!� has been1�$ied in 2.5)�������!Қ�-��5�>F9�N� Thus.�s%�iH and5�ve,samy|8. For any partia$ $\mu \in uwPqw set $B_{(#)}a�=i�@\mu _{1})\otimes M�c]� 1 a�)� V VCVC}V V\Lambda �b B^=n6=$ (not! a:�$C}\neq B_{�}C$ definI�l\ref{sub-sec-crts})$.\;$Then>6�%*C}$ h!� alsoJ� \ Ne�heles%�iru_Tstructure are distinct%�th)decompos%�saj$connected pnents do not coincide. \noin�B De%by $H!١e0e energy funcEassociaXto $%!l A}(l5�)�k).$ %fI` $b%�M�% :<$.\ip*�K_{T,N�S_{�|}(q1wb!�G &}}q^{-x)}Z`$-U�!�of highA�we�9�of �inA�6'.$ o5+�=D\textbf{Remark:} I� possibl%� show� $FPa2})=P_ �}Vp (seeN�e'any�2Rj��F� $ ifE only $% l=k=1�� More3  we c� $l\geq 2Mk � e� wo�Jx can�ŵ�(shapes.$\;$�example,�Ntak� $n=N$� �@a�$2}=\bar{2}we��NeFs))=.Dtabular}{|l|ll} \h ~ tt��&at\multi���|l|}{3 �}$} \\ BR & \\ \cu {1-1M�� Ec{%�}z'Z�|F�1}|F��v�1}}.,/ �F? Henc|e�5 stat��cs��MDHA�$>�a�g� al o��DB A ��.$��igskip.� Supp� noq��w$=(1,...,1)A��aL`ex $b$b%�1^{n}� A}$ or� C}$ A� be writteR�b=x.ͦɬ Ͳx# )W�2�F$D�'�;j8�Wei�J��V=%���i=1}^��(n-i)H(x.� +1b�$Z/=1�l�i}�4 IQ2f 0)=0$ otherwis6� To each9�4 a� �D$(n-1)$-tuple $\Xi� (\xi� %L\xiɂ)$ sucHat�_i=1'n-1,$ $.i}�if�/�}<+a]� %+1}��\} J�$ �,coordinates Al) !r $���J�� Xi}=\�=aU�A}, � \Xi\J�e`v�ara� variant o� a4�a�e2�)�w�}theta!�} :�)T}�f }b\in� %I }\Xi%�ax%�Aj)F�1Rlemma" $lem_Bxhi}L \Xi R� S� -1A< be a:�� v�a�9�h)� }Ta* of $A_�$-�As:'$C�H# � ��proof} *� (widetilde{K!� KA wara"� operator%� $U_{q}(sl �)$ A� p!� $x,y: z�S!% 2�(x�,y)=x^{\prime�{y!O FromA� descrip� � -4*9^{]� �O16 gi} by=.i shima��@ KN}A� deri�equival�:N�xa $y\Longleft*�.�� .�B)(This implieS�A� s�  un� a�a�o �"H1�� u!7_OhasBwR� ��M� \subse�${The $X=u$�jew�(\protect\mu��$}U�"� � _1}u any&� $\ll��l4$n&�q/��AK*} u_{6,�h� 0q^{\tfrac{n-\!�| (\%�| }{2}}X@ .@F�` � ��} *�\frak{E��GM�2s� /�� �l2k� By L�� �,e�!F�� �,��$BJ��% ��.\ �� us d� respA' velya��8���t"� �.�re existA΍�g��})$-modu:MM�] whS Fo�orphic%E1.��Similarl�2p% :.Jrc �r rR:�� rm{wt+(b�f a��� �P��8Y (d�Qd�d+1�d��� for E'iE${I 2n\�$dV "�numberA��!$i$�S$b.$ 2AV�CZ� �e i.�(\deltg��!��I�R�% 4i��$ min�F� $&i}T��charac#I�s 6�ŕ$% Y�A@verifyN��rm{`}(6A})� -�q 2�.�}x^;)2\� �(}.iA�C�iCiHE�%�J� �,$N.��!b�represen� ons6[u GLE� ES�./ uY �.z�at!% 6e T�$@C>@ >-:. wBF�S%)Ai!�.% a(b.r�ga���j�J%.� ��JR,\d�/1}{Ebq�1}Jl�chj��Cw ised� chaz�n+e��2�i�N�[A}�u�M.�% �&F�.\down|_{MM}^{MeG �@]�A~5�Irestri@ E% .{$���=&� QυmB? =�CE?��4so� >k5-�"�Write $E"* !W��*�A���� 0 }\tr� �" A��A�C)!en� R� Uard}(�� )=[V�:�(n),)V j]n#IA}] }�M4j] :U+�plicity%�% J�� � Bz��%2:$&� 61 �:�"���o 5 2 Ħ�% V �2$%�Z� �5a4!m lity abov���eB5} v�A� � }Z ^* )-7FC��V{ })� g �bLjGA�A}]FL � bel{eq�!3�D}M��: nNa}-,}x� �i6� \xi U 6JBy:!�>�2�f� �bigoplus)B2�2%simeq V9^��z*\n98dec_A:�} as "�-:��  irreducz*��]2� A}$ �� ndex�>�x�"� %�� n\�F�% e�>a� by $Q` )pc�g (which�a >�r�2 �d���b[ < Robinson-Schens�cor+o�ce)0<$Q$-symbol yield� on� one 63 betwee�jAFk(t'�j�F!`2!)$�zJ��$ST�>7�� $\ta�"ST,2��A}(#)!R�E`�32n2�F�$&�)�]r�6E�)J?nu���$A>!"�=�Lty"u�\.$ ^STi�B)U�sQ�x =a�!&*�*C6" Xa,��%-$ I��*<&�"ofj&)i eR=��9f�3 �@)P setsA*�,�t��X% !�re�joi0#� \cup� њ5&=$Qy��S .��j�.!=\.K!�Im}.JTa`w?!j= ��!atB�*ڛ�� }V%B�J*F�N�e6� V� Faa�pends� �I�m*>3M�� <means _ we�%A������ )Z� .�a�]$^%_��e��!oR +�'a�!�du[��.�n�H q% � � ��U�^�"� n!F2 ^� >a=\J}B-!So!�� ��F%F  )F�� ��}&�� 6�R� FButa�'�g *� �}=�$�^{*�$ $ si� $.z  }-L�6� ��%�"ynF%O S��us����r�F~FinallfT�th-SZ},!�fqA��n�6"&k2+B9����� is proved �4 \J$"8&�% }On� Qe,�Y^�!��+�+ ,\ $sumN�Y&��&,I�C F 6� B��.1"  j�&:6)2/~" Oba�&$0#�"1.8'(.$ How�+,%#,polynomial $N���+al $ dimension!= rela� to an af�,, root system�!j1tR�Y3=oA���mu"�j� % }}N�B�is fals"!�$m Q�)� cq&� case�B� u =(2,2,2� nd�1^0,0t./-M�� corees})%Co")32!� �e�� �$c%��!R $q$-*A$:J A�v$ , up!�?;�� a pow�$q (� a 2�p5�KJ�" ^{(2)}$.R(Uv(*�%($} We want�eis�#e �A\-��$a�q%IG1�"�&�.34 By Pro�.�Bprop_!�1  k"�&J�U�%.Y��_�$_+>j � }9�2!}M^{�"�0!��*}f by�[�,�P1�j��� �-WI� �6% =]f�B�aRit suff�$to�El�%�Jr9�fn!�-�Y=�6�B%6 =�F�"&"C"E�>�.� N��B�-ިM+*�-X:� } In# lec2E*� intro� �J� type:� %\ %�B�CwIn.h��p�~to:c���� &5 �Ae��oscillat~Q1x�"X"j .�an J423�2a�/� Q=(Q"�Q��8 Young diagrams*�$Qj �( diffr8by�- ctly%box�p8.$k+1}/Q_{k}Vh,"f,\\ D,�"a`- $\8+CI)U�'K-3-^K�+� "�3Q"eNIa2+!�h0 � AS.�6�*%is:0. / precis�" $6�+W ` ��� �is"|5recurs�"as�1sFm} E�J� _.M�,A�var�3.�f_QB�� +B>E�!z2�y�f�Ai}$;ad�aA�f*$k$-thQ4a��$�+ v=k\in\&�2b�lee��P&�! k}% ]!n}~�4�"MfUf ,$ i+2 easy���!� U � N�of�J�."0�.CF �wMo� & }�P} ���#.i-�3!�l%f ugat� ���)�,%8anR�\are "�%^Qx�2���&�$% Q(.)=9 .$e��2A��Alb�)!�$"H� �>0�:9K �o � our%0�(e&�5R3&�5$technical �+s&�5.�,1}S�0I]ba�X=6+��6 ����aZw!Bl� $5 �UP0>�+z1& �*�0enumerate} \i]��/)�%=lZ?�+��7.esi� (aneously baX��un , r�0�=>�E)=, \{F�l} $1-6�0!A*fF����lsly �.��3 �:�2�X1:���.���.o?Mi�  }O h  $�1 mmed7;ly��a%d]<�$��8Q})EOQ�% u� :�As usual� �Zrows (�.\�5s[{�{ " �sto�bottom>�+a��+)nBiiTEG=p ��qc+ $p,q��./.\p1� %�:�$��first͵O;$p2%i-v2to �. U�^nex>=q2=�B"�- L+.��-�+��)u!� `-.O,$f�98}<�� $p�>Fby�� boxe^!�-:M2�$ U���../2 %��\�8-�y��"(n $pODy56�8s2�(}*�p.�A�&�q�;DV��n)�N�dZ M� boxZ�An�� } �g;�t'v���n#j� :8.�� 2��N�% � :P6�296�V�% %�YL..�,�0�t:p}< A �� �1% Vp �q�.*.�:�SoANE-�F�b�2���% 2)=j` �%?6�� �bV2�2& ;^�q�� })= , �")1Q^�F��< s����a� � ,lways greate��n"���RNF�"� 2w � .s {0.�,$Y Z_{b�/�N-1J0^! g��$\}J b0I�54lem2}W�!�`�'not�, !�2�� �I; (1-2Z�)=�,n:� � &�I� ^ 2zfr a6&(C"8:@ V�j Observe�% �UJ)fz4 �p%�7 Ť\\ $-1�> �f-Q. M�=NSi^� Z� ,K� mRAFi8 &`-!K#8I9Q7!�lCKa}�a tensor�duc\%mM2�<:R �,�z� }l is^��ABK must��'� q=1��f�A}Jf�z�05�n s��%���"�s_aux:Y} T.#�� procwEb�F!��on $n�" $n=�=Q�$b ��0�c "� n | tC&1A wis true.� &� e =��E#VF ��z. c"�E�,aj�,Jf�O .$ �;s��oGEښ1!seU�5=�?A<�-y�:<2� � � Q2W'\U]0.L R(*�<"(._(- �%V�!H�i_m�j��] .\ I�*r 4 F�)�F6�wb%U'by us�h�M� hyp�siR�"-��!1��&a>  /��+Y)�}n&F�i�!A��"}u~f� �{F�-�?i�$Lv�PO �=5ZI��K$)L% �=by\��)��:+� Z +1#,� ���>x ��!��a�>�!$\Nh?-) ��RrfY�As夥qMT&�  "�= th_U�K>K>&#6�$*d q,�+*25 �*�� �� �C��$B8�,.j3GZC I�2& ��&�A. 6.6 1�V�GH&� ��p6?2� Pg] � A� �%� B:8)�� noti��\G(b�F b>�?1}a$u��1�]��j��:�^� -1)=��"�"-:� aEF�H(bF�z�y last&^2� 6�@ 2}. �(��J&�! 1� .#)-��F�'YO })}a�F���j�X,c .�'�N!��d� �uZ-�!�!]0��ke�!).&`)�k�JN`.U) :?$�B�& be regard�!�analogu&�!N& B^{(1)->^�P��Pu=&�K�s&dDAp:/i"j$'6�&} &�"$KKM}, Kangsh� ��Misrai��ed"� /*l�@hi } �.quantum�algebr!B� F}<phi $ J ypes#'�3!,=,�E;'  $� D�P['BS"1\�$#.\ Weobel�0 2�U�a��2 as class�&��K F� $ �N!��{|c"Q"U1�WZE�({ \ \ }}{1}AI&%G&Z)/.O%B.%64%25&63�#$\S"�k=0,k\�%, l\func{mod}\Y�# pR�l}<["@3 }}�Hkd8�5 �hs3��0mu�0e�}=  ��:� 6�� 6n6� �B&p�Qgy a�s exp�>�ZCOk�=2},���,��>'� stic�Xh��+5�.X(2�$;��#�UL(cal�-d[ey2?6�>2Y(q�#In %�Fr,�7"j&� ����*�]��c=B#(Jh*A�.�/N;aJ�A�theR���$*�Jm?e* GnonzercXs��E�6�1"� �_JC1�l$? $ 3IĽ�� �ŵn&DO)9in�to (:)<KthJ j�A��cBm a>�O1.;*7J�m1?3 L"� �:9:e&n �v�%abFw ��EN�aDf'A:��*�8� !?SNL,]f%..�$�9��0:�!�."J#� E0, #&Z(one_dim_sumF��Q� s" dual1��ref% " && corollary"�&cor_f�6"�uJFf�A:P IOE1aI- 105-139 (A.G/bMOk2=�HA�% \.���`�0 1)},�< .�-#"� 5 Jour of A�y0247}, 577-615�22�HKOTY�G�� Y. �i] �h�G$ fermionic����, }inA�J�!a�K.\ C.\ ��Ccenmvelopm?m in Q�Af�A �� d Re- Tope�,Contemporary.�I�Dbf{248}, AMS, Prov�ADce, 243-291, (19992+py. S-J.}M �, K-C��sr it{C s bA���Verma2� :�Lie"� , }Cocn.\�.�!ex]\�9p299-325 �4).�^M�K.�.�}M2it{On �� �� }$q� t-�u�cal en%�%�I��� Duke � J ibf{63% }�(1), 465-516.��` �sc2���"�`,ْ-g�:�P��R��L.�}, yfQz�,165}, 295-345y��~K]9K. Koike.4I((sc{I. Terad2R214�k method�a�>�h!IU�� �6 BO��d�r�,07}, 466-511!�876+T�� R*8XRul�ID}$GL,SO,Sp,$ Adv.\��.9�,79}, 104-135e�6�LS�HA. Lascoux, M-P. Sc_$u}tzenberge}m^$it{Le mono�N (it{\ddot{\ia }&�,de plaxique}�nonSmu�vjUrs;m+�geo"0&��,de Luca Ed.,� derni�14la Ricerca Sci� fica( C.N.R., Ro��(1981c it{2 LSc1�Su�(e"0de H.O Foulke�CR Acad� Pas e���8��95-98!�76zlec�(C. Lecouvey}�A ��$S��`it{% >�6en*�,�H.5>3o�}x&Hi B,Csi@$}$D$ (subm�kTd), ArXiv: CO/04007522.)�B)scZ�"QT-e�c2V , Pl�-c Monoi>*Jeu!�Taqui��B} ,$R�� !�D��31JD Lec32� c1�1�2! c��c�� )Kostka-M42G� ��>s��.]}1 ��I ppea���European.� c2# Ls@��Dsc{D-E. Littlewood]r3�u�g @_'a� xB�XS� , }OxfordB� , second� p (19582rLu=�$G. Lusztig� Sing�Ii, ��&� s,�#,qU�����6aC \nalyse et topologie sur �� espa �uli�C(II-IIIa sterisqueI�� <01-102}, 208-227�832�ma.0I-G. Macdonal.�Sk"AwIcHall *��2^, -��[� aleNE� >Y , New Y�| 52�$ �sc{A.\�y7 kiJ u, it{6 .�%��݁�sov�E latz_ elAXSelecta ���Series, Vol 3 N$% %TCIMACRO{\UNICODE[m]{0xb0}}% %BeginExpan(M$ {{}^\circ EndE,$4, 547-599,%6!NR]�$K. Nelsen,��Ram]�6.MI5� spher�"�}, � rint��4At� RT�1292%OS.&�A illil%M.&=�A"�jto�=gv%onfigu_bi�a����ec6�  !�P� �2�4xiv QA/0203163.9ok.���$% Virtual A IbF"� Fo�#�T�:2�6�F�* ,$ :_|y*� � 1-163 �6�SC.�r� $X=M�&:wT.]I1]412376.]S.�6s$S. O.\ WarFc]Inhomoge�A q�paths,�O izedn��6}�%$�>�supern�PA*Comm.\?.� 8bf{202, }359-40� :�sh}�Z�O =M=K� \ \ &�,} pers��� muDA�2KZbn M. Zabroc�"8D ed&e.XaI&� !0�JH��it{\ }AW 4), �� 4288L*th6% � docu�} ?\�[12pt]{�clD4usepackage{amsA} :6 > ^�_8extwidth=16.5cm� h=z=218oddsidemargin=0�iwithin"�#}{s�lon} %A �}r\er} {\LARGE {\bf {\sf As&e�a new)q� braid� ces:� un� and�3erellip�$$qi�t�s�y, L--�,link-i"�, nonco*8 O< }}} \\[0.8cm] e4rge A.Chakrab!�\foot�K�h kra@cpht.��te�F que.fr}},�9em Centr|4eR. Th\'eor ] Labo�rireKp&�pu CNRS UPR A.0014}, Ecole Pol4, 91128 Palais�~$Cedex, Fra"`\\ <(�I�smallix� 5 abst� } Variou�Vper6 !�a^��msen�a�e,  #studied�)A�! $N^2 \�G H(N=3,4,...)$ vectorB( a� �suberA#�=$q�v b o x nontrivia�T.p $(\�%R^2 =I)�S�#s�*j W��� $q$c solu ra�if9L� %%ito hy.�&=(.1&�!X$L-$ !i�ts�-: . As!w rucial fe �'o�s $2N$ Aral,  -like, ͆ous quad�. &L_{ijOon!�in+o�Qamong �mselvest� $RLL$�q% �y.�� detail%�$N =3g!�rTor;&�to $I� he� da�nal $3\E-3$:�d h�PA all ite�I|�p�Qt � �!V)a�y� through 4�ed%}"A$9 � 9B�w$N=3$. MG Turaev$"� ��.�=dapa.RtK�. . A skein�!>�8)�ed};J a2�/Ny�$I�&,)�u��%�$ transfer i>x maps�"e!e�7ithA ��99/"3! an.|��n:�*�sv'rting eDan $(N*{&#aQ=� � . Fur;Ja�ssibil�mMas�stateHc�'- A�indA"�[�\vfillQ$ewpage \(style {plaiM>�\ {IMT%� :} An- wa�Z�1in� v�p�"Q�mos4�w!�!j�dӀbvunejSec.$3$!pRef.$1$.�Es%3db,1�r j 5# s [$2,3$]��ready�!ere�@w�mmarize&e1 es�띐s�!w�>��s�S�a��K�%�6D willՕ�O�|a�( b%�counteraHY!�$\it CD�A�cer��A��m�N^2br�6� (a�ɪ$��� � ap�S%� shoul�Iart�2r7g5%7.�u �D3�ndԄhe �� U!�!Y�a1'�$SO_q(N`/Sp 6�. Ou �oa�h�0istently via %Vހre��GA�"�%pro�or"�Bax�� :u ( ddA on �.G dp%me�E�gl$ ) sa�fy� �!A?� �}_{12 h1) {23 + "a'. 6') = R;')Q1 +JPp:�"}�1 $$2L = � t0I_N, \q� _U=% $#?I_N�(A$NQ�$&|^�x. E�&"^e^%�?( Յ sour8 �0�K �L2.L )E�hasF� � ().$) = P_+ +vP_- + w0� 9�3�Ygf(P_i P_j = \(wij} P_i5[P_{+} +- 0} !f{N^2}>�AllK?A^$ -M�az�n $��$�$�J (m >gA�$q$. e2 elegant �&o" �� (��2$,�� )�6> o:��:� ��-rA�$q=exp h$$ �0has�? �6%� (}ms8� �8 $N$)F��!oK: {� h(h--�}m1)B_���}�_5�. I�2n+1)$:F�5q�;cosh((n+��u2})h �V �;i� @sinNM-1}>NV M5$>X֦�nB�nhjV�12�����;2�� \+\9m.r6�%�v�fFIAntrast,E;� 7  (��3y7), ${�U��erv?*$� .`but � � coeffiEs"�0F��=1�pU�q&) \eta>(5&>2� Fte^{8�� e^{- @= ([N-\epsilon] + � {q^{$} -r=N+}}{ q1}}>�a�$_ =\pm1�k $P_ic v4e�2� &�U7 1 . (An ove�. ambigu>of sig�ԏ7�C$(1.9)���- fix�ass��re�e!&$� q��0.i maint�out�ocompl�] q$ 3ARidr j er.)�cadopt �¡�_�97�{A�� �--D �8�6*| : $(a)$:�0^f$\{ R O� �{{o}3 XbXnYp_�YpY ���TN!�Ёhexven�� �2A^�5M7 ,��*fac��  .�E !9 often lea�qsw �lyR�  �= ompaf7f5  �!�4~ro 7)$pj |"4F�Z  �|A�R)ٲ P_0: = I + �+glU;�p -17r)P>�� !leten�wb?$P_0$.� $[4,5]$.�!�n݊$ $(\rho_1,2,... � be"_`�ll2Y�0D��d+�&t5&5  �c3:1( 2� , n ��3��, ... ,){��,0, " !, -2[ F�S-J�6�1�2 y,1Fi,-�4 , -n+1�\��.�Z1ZVJTD�Z�ina=n^�Nn���� (i= �,N; \� N= 2�-R�Nh>�i S(i [Qn )�ouad% -1 z (i >$ � .�2JSet J�(i' = N+1 -i>�`&r#��(11),(1.12)$�%�ā�sui�e!n us,F ��1] +1e�FH,j HN�EiZ{i'} - a_ ��$)} (ij)\o�2s (i'j')->�AP'Fu �vV�3� �5)$R�+1] -گ1�/R5��� ��H�}:�tno���N.,#1$�i$(row-$i$, PY.-$j$)Ŋ zero else� ���;� � i G0ed"|y ���� �} o ��,�  p � .�d-�� �q$-T�@ ly (_��A�j� oW �m`T�t>���(E�re 2FF ].�/Dq not$$-de�5��a "� �!" limi��7rtim@ valul such��rZs jus�e�!��rfsb#u���$*�"n-�isp8nM� ��(q+1+@ 1})�4Ea\=�JvIi} 0 &Z \\F"J% z  ��1F\\ F` `�rR&2pFB^ Z  $ �FO *q 0�0d &  &2}N 5�>���c� �8q�� h�eex7*� A�A�s� LC�I aQ N$ a�/uI�Aa67�� r �}B e�is�i�0 tantWequ�s. Iteins �toR{$play briefu"pre-&�" situe�-ca.� s enT ,  v�1!in�J���R (3�F) L, �   (00IV���Us $&#� \0a9j\pm{?fl :z2/ ��Em1} $$ �%�(!�=?�|u$-*Q ) �N�Mh�6�12�:� ; .23B����_;0substitute $9%z�& $-� A���aJ(�  (N)): �R5= -�=mp 2} E; mp N� >��I19} ($ �_n(N+2)Rd1�$$ { cubic}$5�����3,i�P�!� ��Gbm� !: `� {cJ�"�I� ) - B%�a=--&)I>LorJh _ -I) ( l +F2�}I) =B� +C 0� a�E�2?yn fq[�- ( 1A2 � I - � ( e^{ 6 1� W9R�>�=�Q��s&�9� �0 %8��@�+ t0$ � {not}} a����$A26!B R1in�Ied� � AC.�: ed^�th0?�qon{�}�" (%8et3"2)%��O9���[I4h�i�e�!�they b��e direc� relevant�'" W�$N�% ?%*�x� R$�6�� ed "&>& " ifF��8���#>�B���( $(A,B,C,D)t�ui*�hW$Oj or B &� well-?wn.,~$ch ison�G�W�b >�"� ���!h�0A2R&Q� A-"� :Ik*� � ) eF7$(P_i)_{q=1�_.)sf{P}_i�5�+,-,0B aletFUP.�} � \�ji�� PR�(Aceodleft $P$h*mu� specific7 �a22 %6��fs.� ev:tF !��"io3 , it�5ys*�%rol! $(2.40)$ �(22�;2!w�xq�E#"� A'FSa��>=�AHEk,�� uppek_d l�zifAkŹ*Qlyf� ==�+Z�*)�-��� pm (I -2��}� P>j�\Fq�.�M�ERF����>^!bot�� a�$GL!�A"+'![��everEre� ymKe�\%v��!� quit�f^(&< ,� emphas!alN#���#3$.*�A�)��U")$�  { )}y��G�$$*%�G9N�00� -2= &� (1+#�d2' l%�� , {2N}{N\pm (�) -4)^ 3} \«2>�a�"E��F(5�{T}����F� � )�� ��0 U/.L�1>���genu%�Hecke d�Fis nowJ�>^%0R"� .y R6�  1^�  �F� T�cannot�p/u�t�J�M�  +V� e$ (2.1�e�sA�ќF\KJ PA� z{ 2[5� ���4({P_�$-P_0)= I$$�"Y+������pn&0l�*9 [NA�1]��1 =a�a"  =F��,�]ti�J8(A�� N-2}+ 4^...-N+ZN+� &>*�,>�F B6pn2:nn�35�(N=4,6�Bl �3 deg���{�$'/b2A~A{�h� "– �'P�ن�&tQ . ToKrt $(A�di�z$�wo�-2��$'$_1: N=2n+2"� �f\)$$�B5p=q^2,�Y= p + pA >pE�B@q�26�=� #T1}{\sqrt 2} \biggl ( Y�& {Y^2 Ar)^6M>�=2JF�S_n�(p^n +�n}) +(p �1} zW +I� (p^2 2* (p  1}) J�&� e� (A)_\ce Q Acel�( $p^0 =1$.hx eN $S_n�S"H($YO`,�+ByS\ = Y�- �Y -Be��"-s zQ ly $w =Y!" Y--!�nomQ5{1} 2��\b 2 33a].2 3 4} +3V K5}%q$J��(-1)^rR�s r}{r A2r�!-1 �2MF+O c_1 Y +c_B����#= x{s-1}s�,n=2s, r=s-1)��� 0 1 }(s+�CmB3+15atB�c -2"�4(n= 2+4m,3+4m;�m=0,1m�x 0 =0��(n��} R2n� o���#oddX�k(2.18),(2.20s�14 &$on��*H�Y� \Sigm?_,(2m-1)}& =& �Pm� �-!�� ����2m+3}) �((q - 6�!�z^{ P�2m� 3}+���52m-�� 5}\\\ &+&�ar��2m-r �� +�� /�{�mz>�y�c%90Ri&�'9 2.16�#h�� , q�ݧbJ�*5a�  =Y^N=3,5Z+ �Z��N�5�1�9zaN��Xz�! 2b&5 E,^5 - 4z^3+ 3:,�7�Mzav 6z^5+ 10 ^42�9EL0z^9 - 8z^7+21a20+ 5B�}��MparA�@ &`2.7 oneV.O��(B� �#p,7 UYo�aX zero�eT9nu� }  �"=& n=�{N�= 2,3R��Tout try�to� ex2N� � uR�|po�?/som-eBw4&=_ly��c i*AT q$ a {root8 � {of  {J8}$..e�wri ��}��conclu�" ��� � E �!��!�!��FdQV1 �I =1M q.B+i�O�C�$=�pi}{3}.�6 =F�2�r'B�e�A��0N�Y = q� � } =0�e^2�42�8N� ^,a�nev���0�a�1�.3ZK%!�4�!!�10. 2),.~>&�$Ym7} factor�5�H8"U/�%�d�$Ae�  6� =0$$ &" tJ[�12}.�%q^{4}n��8)$+� 3SFyh6>g1�2�Y2h�)5q��( aa�^2.!:"�2 to!Bv��it {c �>e���"}*  re&�,*�#[e��"7a O �� >$N$� a� agai(5��$z��5)�1i)warN�/uD.�,sixth��ar (���Y$ �=���*���>&). �m�s)$!L2=}$&=^. u�%�A�E� �p})ّ quintic�D�B {ec@}$!��=*�%$z�  A�h �4 (q^2�4���br&�:�Re)� ex8s:�= func:�!. �Ig��$[6,7]=c�,���bw.f�F"(f(x)= a_0 x�a_1 x� + a_n = B %olvo&���of' argu )o�h perio�AR�the:�A curvN(  Fx(x-1)�&�. (x-2>�`�i=ni��  r&�)x%�U0$[!xAGca�lterna�� ly, �#� fT<succes�#�0�var��Tschirn4enM=or�&)T�� sq� e BF -Jerrard� (�o^lea��$(he Jacobi sTc) h!�=�&�usa�q(y� . AlV��/h@� very��c�e� +/f&3 $a�1I@ (2.3O(A!�$<on!(�integers;�r. .6( hopefujd%if� )�s m2�ixx:��2�a�2�]�? AQ@swq�"�is quesa��hbey�M� scope���p�=%#�u���V�V� �$&case, � !3��o}� �%K*r�C.�(7  -� �w('\v(6�'�'>&K 1`( � � W�'F�w(�w(�w(�w(�w(L $ q>� 3}}�"�>x&is; ies �!I�=&>=& $$ alongE�.i��� *�r {A� -��(A���:}������" A�>v<�0),(;85Z3s � =P,���5 �jnzB ? Jordanianw�<$Refs.$8,9$�<�ba�) =)J si�yng��R�"sq�*� )� = FgPFR�B�M F $�2��6@-p� $on" $[8,9]t"ufe Yang�( �,F7 R= P �� = (P �)F  = {F}�_{21}FF�s <"Drinfeld twist"��� #���-�/GH���!U  +s� mr� &�#+in/ n�{ren-��9R$�#. C��ur.%&|Ds b(�w �' =0$)�"�ed�a!�YsE��P)�� ��e (? A priori !�p"vDg� disa�e�5:g,�����ona|rqApp.$B�!. 1� H1B�*�/� canx>ve&�)�))`��>�� no�~nl&��AtڒŖA<9�C��� � s��i!��'o�a0-� {o} ��. High6A � tه�Bt&�ly|p0allel fashionAL.lD�!� usA���bQ�1S $M�?eg (1�RFM�O{ME�a(-��* 3,1,,1. )_{(!�F�>��;=0��jk�&2* ta�i�NOr��.�,�#D>� �%;m��atsGF�7z�!]aHub*+a�U2nJ�M�OF9HB�D�6��&�G= 8>��%$D^2=IJ� G=PGBg�!�2qЁN���$*2���4($2.3$) ) leaAB-�/$(1,5,� untouchedP ��e��pai>�7!rv4$$ (2,4), (3,76,8� Nowy]��D$ afEEOEriz%�G6leTnE�Jbita�!;K&.����mf�~0an"4aiŜ.� ��rx��un��aաIf^-ODis��zJE�(a_1,a_2,a_3,a_4,a_5,a_6,a_7,a_8,a_9)>#� n h4$!�beN]-�^�� a5F $a_1�vr W)�!;X6N� r_2 - r_4*'(2�06B�&u�[8�("UJ' (r_3g5 gb_16eJ�)B� (r_6E8 Ec�E�$ ���Ce�Nermin�2Ft\D�GN�-�E�s�*-ble�neiAk$F=GMɽF%E dicti��p���IaFY2� 6!��  >%.� u {L-"�(&�O�OqRs)% B/7e�l ��EE_O-&�0�A^)S�N�@s �Kigl?$u:"�#&3�O merg+ Secs4L$4}8�4�3w em �L!� �!Fӕ�mq�8� i.e.x7B($1$):�n� $L^+$ subo&:�P=E"5�st�* o�PI5��->�]|$���$2/Q.=|s $ �-.�. ($2 �:� ��+�ie�� ss��i"q�fdKis". But �w� -�~,et�5vs*.4�Q*�r�� ll. Each�a� �� N$*Ra�x no negeA,�L($3BI)�}Q 3$-da�alr�N�do $L$-ope�Ra)JQ��9�!��0 7A�$I_PQC��L�{Wr *�R;ert� c�UE��RJ\9Y �20R >��0 � '�+ invUm�:c�B��oA�I�R k� courso�B0 $I_{3^{2^{p}y�7$r� stagV($4M��:�we%Xu� � RN�� "���H=.� $��+T- .6�5Y: bea�I e� block-) � Ams*k�X �famili�ar� c�hne� ($ 9�L9 Y�ar��5  5 \� 1T 3  1 #1QKc���ta�X moE�j 12�42 `1X0 Da�^ ��e&oNWui� =�aY search! 6&izeTEyis <U'� iuQ���nnoun�3�P b� F $ �a such a �reveals"�"�oCwg?-Pia��4a~.K U}&W1 ��l��*�>!��}�l�[. `0 J$te�.!�/;e $FRT$��D]$2��  u���g ��*c B ML C_2 1 =  -B� jU+ S-} Q- +}_ M"\*C/� L^.- �M"�-Fl LA ��a1S*�Y� trix61.2�nd�)$�w eachE$ }�$ %_�O,�(i�B �%,/FardY+ J�AAe J�ct_&^Q 5A !i \�4I_NB��+($1.26jL �7giR2by17$),( 18$)N 9���& I + �\ mbdaH{pm}�7 � : = -l!�sB=%�,��9�$:F�K���JL�y+0AeR��A�MIfo.P J9zFt*�A J�:� � ���q� $a32� j ����BbZ�!(mpact, unifTᅴ�1[� �$L= &�9~byJ�( v_+,L^-) ��6harpoBF' -,L^+F�����f�����Q/� �of/Kȕt 楺s^bs��t �6 J Lx$ �[sti+1(# dea|KiP .1ZE��II I% F�$ ($3 4&�!JHe"e� O�+��^@,&~,(�/Fl �h�"s5 _�Pdo� E �9ar��..\y&s $for%12aX2lA[+%4 $ Ef&> sM�N� A�����9���l.� � �{ ]$}c3� ��5 e ��u�� ($2NK+!�9&> ?��d i2 three& AwN\, (2N&\.�! � to� �-aeas�vu=stood�M�2EtBB� iz�%M$�,"�)��N�M AG �\Z ox (x.M0)f4Co7  he�%s"�8b��e8�y �"�,��-6survi�.7;�$+co�H��� .+%=sɘ%��a$.U d`+e� �c� t�>�}%W�"5~/w��v�P)�paA&(m valid, m�9ge�7�!AC! whol"0i a�JN�� iY��b�P:E�it�N,H modC<r % 5pqB$ ��A"�O��!]%�9,�$N \geq qHw�N�L_2 L'�� \�$_{i,j,k,l}j kl}L'_ 27=klF�@ �1L_2 RL_22TT}L_1^{�'&���,�8 /+[4(+,+),(-,-),(+-,+�QX� s�> at ( i'JBI ![ 2 L_�ޡ�1cZl2q;lkilli'boBs.�qj}���L}L_{j')�jkF� RV�jV'_{lj'^kjFVWA w go back��.by���*�U.$ �L' =L��l�3k'�4 $l+ku;N+lo*�� 3��,*" ��U��iRN- �__!^J � �ei.�i%�li)diN\~set ($ �,2)}$)*�$��.U*f�1)} � V 2. \  .! iFFor�?$!�=!�$ .�(��� jsum����MWin�N),W4th $i+i'=j+j' ZN�1 �+i}�i�P=j�e jj'}" (g� N ;jp�NF����lT �se@0r� �����Z��[= �x�#etP�5S�� � ides�e.� ��G W^Xstuv W�a?gw \. D,\VcrM�.:&�b.�%AH1��13} =yc22*K��%+31BH%�13} =+ZG3F�� O.%  (A r NM2T� -�,low )bef�F�3N$S_3)&:&a 11}L_{33}5.L�"3}, +!#2b7&=&T6fg�)$L�K]�=G222 M:+312}BVH3:3�;Fe221}d3 11}B�G�3 �:�1�3�> �xB��<�2]2!I~��W!9!%?!WJ�5+!��]1���u�e�|s� 15rK61 �S�<�� 2$s*�/Fori] l  ��i|' 71:$H[$��6 �)�-'1E:)-��0jO%�O ZO�O)y2E? �I�V�2��j�I� O ZO�O�13 � m�>�a�%<�u��(6>�Au�^ Z^ ^QvZ���XAQ2.�#�>x�(1$�I�7�� M Q U�Qk1VS_2 l imp�%�3hR�&�Kthe memb�!\ P� �<-�� cne�ga�ݺ�Exploi, &�a�a/�jiɠ- passcmm"B��Rof�er�� steps. k h'l!�R�*� J� F�ij-�apNMSEY 11} a>wEm7��I>$ BN�B�� � _e�Y:��� �1~�Q6� � N� Sum� ��_ �m<10*� (�(�4�f)�`O!�. ��&; f ( % %d!�:�5��v�^"�? &=&( Qi�FB0)�V�)�v�TM� ��B��� !O,eqsO�a �q8� n� vute5 l>��@�)�-�b-&�� e�� ��rul'c&)$[,*� e[#"� � �,�+)�"B�2?&�k!�ik"lL_R��nUab}bcdbi,jdaicj.jibjd5���w'le�;���� )m6O%��!�+sumJ�V;= �11��n�O2� -a"2..����-.3. 1FV Coll~e��:��Ze�&��م$/rnyH"� ��n�(!�aUi�J��TO � 1� aJ3���OOK�"� }m��!%u�!��(M�1�tr.� 2�;o�<A$8$Z?i+��1&r 14A�V � q =P  q41�1B��O)� WWW4J� Th��R`!2� �$�M6��&���-�iP�j���%&� oX"se��S_SOd"/ ":!��9 �[ }�_�?. Our �n��!w�TRZ�"� �js&��Be6�D.8&�� "�/"m�h" c}�� ���major�j�� "8!!q$a� � *"�$(see ($3.4�X$),($3.5$)) in the constraints \begin{equation} (I + \lambda_{+}P'_{0})L_2^+L_1^- =L_2^- +Z- \end{T~f-}f-Z f+ -6f-Bf8But even when $ T$$ does not��etribute, namely at $$ (ij)\otimes (kl), \qquad (kl) \neq (i'j')$$ one obtains simple but probing co5` . Re)|ing only such rows and columns .Sta "reduced" matrix of $N(N-1)\ � �>$ dimensions. For $N=3$ this corresponds to the suppression of �.�4($3,5,7$) leav� a $6 t 6$ � . Usfor m � case,all $N$,Er0subscript $r$�0extracts fromx.30M� 31$)N24L^{\epsilon}_2<'}_1)_{(r)}=(L^ ''6('B:%<^ =  '-M,is trivial. AfANnow%=!��can go further as follows. Since $\iT4$ satisfies a Aeratic q.P linearize%L, polynomialsa�O u%�_+$�- = (\lae�T+)^{-1}$. The symmetryA` �&2�,N�I8{+} \rightarrow�1-}) Lleftharpoons ( L^+ .3 L^- F� indicatesE9 para�iza��a�re� $-depende!dA�,explicitly (% ex��8 coefficient asF�]X$}_{ij} = A +�Q} BBP, Now injecta)%]4$� 2$) oe�GaI each elem�of �� {\itqa�} ( $� pm}_{ab}, cd}Iso on RK.�-�!�(�ab}B_J - � ab}A ) = 0, �.J�' -}F�Thu)�^��O4y factored out%�ҁeed��rtix. E��L^I�$ $L^-$ are�� sideF�� text!Z!Y�!�ve��algebras%uy mustm�y)�5$). T�[Lwill indeed be found�cbe Y�uQ� realM�s��&ing s� on. We�^ comeXpartsM�both $I)���0$���E�he 5daddirectly involved. Instead�$$\hat S_3$A�20A�n �h��r '4 o(3)$ $9$ rele�� type�7@narray} \nonumberY�@�biggl(( qL'_{31}L_{13} +q^{\frac{1}{2}}22}+ 3(1} ) &-&( q =1JD _{2321}+ L_{B'_{C�4r) \\ &=& q(:#- -43U��!�NR1,-[2���5!O��::$$u�+ (q^{-2 )' �+�1}' B5�+31}) $$=�� = :k( 1 >�.ra�"2%�21" �92j= >�313!�-![)�5K�� Z�A�recover�JresulHori} suu�.aJhav�i(ed a system�tformuI�A��full se�%$81e]. 06a�oi��cer� �Uies�eis�.1be repro�  here"e gener6���of�ٍ% � N>3$zb� fairh � ally. \� �d { Fw $�5$�e0$L(\theta)$:}A��ou�R��($1.24$)�!M$ three FRTY� (�`1� 2� > �<co��$sed into a��� le }%�by defiR 0in analogy toJ�e{R�� �V {eJ ta+ �} ' - eao eta- { R}4 }>7->/FB] 5db�L^+ - >\L^-΁It1] show� (at $[10,11]N�53E')a�2}5K� ')=')� )2T -]'F�conaBs effA�v� llEKJJ. One�write� 8f .e.E�1��aN�2�!�I�I sinh �} (A M1)} P'_0B� \u_Funda� al�cope�� present�8ak H� we�.study��o �sfW($3� 3aqndam�j($9 !9$) r6x�y(y illustratT significaL �v��marks%],4kt�begine� of Sec.$3V ��b�m!ed upon 9 end. Specj�  rm�ces ed p be disply�Th�  helpfu�  a mor� ��)Lof� 2|.!y �� ��P��.tr6A!N-dN$ block�$A�$N$) is. , (See App.$Bj Ref.$11$na ���Q& c�c8basic sources.N� 2aa��P&� ')_{q\*� , \pm{\infty}� �" = O, R^{\pm 1} PB A Hopf K e�!���(ed [$4,10$]� $L$ �J��pm}� = P� mp}P� )_pF����c4,3.6A�nd ($4�s�Cob�f(�1�.%� . ) � L��E�{vE�x}��- &��2} 3} \\ 22}  �32}3 Z� $$Ga= >z1 &0 & 0l0   &o 2P"� � 12}=>P:P \ P &>� _&0:a� `3v` l0 \\(1� -1V)&0:Y9 !PF  0 &1� Y:� � \\0 B^u� z0 &(1+ P)!u�Tz B ^]&0 \\0&1J-�2 } �AVR!!�!jI � --1�>w1!�3VZh&.�1�#3J#..O)0&12|B�  sets"U�%U_+, _- �)�y$ L= �u+,L^-,�$ &#lyo�>^M�d*�94 No�aat��s eviden�d with���h}� J�i�2.V}Q�_��}MK�yiD6GA� Bw \equiv A �6W#��$$�y�^we� ��n*�& ���gi�by�( $$\DeltaA�ij})!sum_{k�ik � L_{k+�VWZ � ��d��easily-�ed2����bu�*� =y exhibi�� ason �ioO befo� D�$ ($r_1,r_�: refl� !ab��diagon: �� anti.� $f: (2����(r_2r_1)q� f(A)-� fA$ T'erm%�*T �$A�,...,E!(!C���6ZA�8 ($ij = 11,12,1!��($G,= 33,32,31$)�t� �noTta46�invarian)u$J�$��M�52C B 橊�gB�C b" 1�nQ2�9�:� 'j'} >�VfX^�f�f � \��&\9 & f �2�B_jI� .SD_��\\E�T {��D_2 &D_3%OV!�M��+V 1G���=H23FFPf Qn�f�fn�F)[ .6��F 2} =��F� 0 &E5VbHf$EjX! � ~��{ ayed��&����f in d��d tor᧥�!�ii�FF$e standard@�b $L_%K �~ed"� in�2fo��for ir. cibl���t[$4$]���r� &i� &-  &# '8T 6&B#31 P\K K0 & F& $zk & 2k E& 1 .--k F� cF� �,�n5��� ՛B�� is orthogs 9v  $$ N =N^TN One��JBN (��� 11}+22. 33})Y"  (-y,-y,3,3-y,-y� a� )} ,~ y= (q+UFP �(eigenvalues�Fper�aƩ�  supp�ary� j� %WeMt��!4�4m�.� � look�componu m L   ( de� (by $(bd)$ a~ d �jN�2rii=V@ (\alpha_{i},\bet gamm d[  !b bd)}�$ (i =1,2,3FZw� J� l1��K�B�$ 1&1\\-1&-6�1�H�H9 ^{2B� 1& -1\\FQ"�S2 S� >�h+1� v `-6.:�Bl i��)�9+\�F5)0\!<.>55 Q94R� -1& )|:{1� Gv(6�~(�+6v�'M�!(��'"l .\"!�V D%6���bN6�9 E%6EO\.�B�Je� _�I� �A:e 3 &k �B((2�k�  3 z^2 k^2R*%^2�! ՜J)k٭  , &-2(T-1)k^2:�qoB� �]��3���>�.� (1- �!�B2��2��)kNE.�1-3k^2):�!��j�� ��h2u9�z�1�2# ^2 z%�\\": :�\m&.�z^2F�:��%�N��� _1^2� !��_ _3.��:' &1Dq�aG�L SI*nilpot�W"��$2&non��able}. �v been� *'verifiat9 6'$6Zj}) �$ $(i�% j�r)$t*s*ingly:�*L� all}8ir�zero �& s li.�� outD3 Xs ari . :�i})� $ld 8 examine larger G(, say, $(6\,$6 \oplus 33 �f = ing�$q�i�% $�)iB� one fin�+!b0 $whole $9 \�+9$ space� needed>�3!�-�� s�#("� spl�� th�J&icula$"e $q=1�*�quire'#}�'�& rms.� !Gim% "�*co&* a)%a�s%�� esxial fea8s) sist_ fXsA6LmeO&�\!R�&(in $(3.20)�"y�,!� ple,ql��J�$& �N��=Z�$3=�$��1 I_3B Alsoft�& }=��)NO�Z�beA�(group-like J1 !K�%�VP"b ^2 I_9EYis�*��$�3I�($ �{i} &� �be{% s qu�!differ�as�"�%��ob� .Sin���.� c� stsmaller&/al2"� �,vi>n �)va fash j$ou�0h� case!$SO_q�!)a�d1is���$ central $KI� oper )�^rs"06l reve.sX!G ertiG!?&�' gi&�a�higher dD0al:�!s�h!�,.Q� B_�N )��il ��!:Z!C��.s &�in A�4,4.5,4��!u��%� $P+��Apul�+ &�"t�)"('� {Link&p! Turaev%�� ion)�#\su"�'{C_3uU� "enhR#d"9�5 G�a�xya�AZbraid �� � A^�[$12$]Aan k Yang Bax��Qd ($EYB�1��ou�2�K"f�"( Markov movI_first%lse�',s )Eforl/ed�0ks.�/1��" �)]� ists$a $N^2�# N^2$-�x %R$,S.�# f$a�dY/$s( $a,b$),�K-a&ble�15"�,<)� 1�} ( Ru 1}f) f =  >(B$BZtr_2(>7R�&a 1}bfBP�n v#sJ� c �,l(��0jkl}c_{ij,kl}>5 -r|��j��b�- k >k}r)EB� LeM3� ($f,%�I1ur clas��R� ur ��Dresolua�ExtheM!�I�aBpro�1�.�\��E�'$-)t*�%1.17,1�=��M2ts6I transpa��. �4 $� � 5 *0&E�_A����Ps $(1): _ � o(N)�N=2n+1��n= � ..$$92v972,373):op:oB6�2!!�'f�4Jv�a%�-(2n-1)�$�3)k1},1,qzq^{ 1)�!\)�W=2~22~4~2~1,q^2.�" �2��35��2n.��g�2}>zq^{2nn��n"� �6�OP3s:($1$):n $N�"l e�itf$,��4A�,VA���z� !xo29!c"v8ymc(�N`}�as�� tr a��' $ ),a� rema�-9$ R�qL �. H3( � upp�7nd lower�*s  H af� a` �z R7T "# tr fm� =� ,= [N \mp 1] G) -*�$*�;-) # =.} +�.F���$ pm �, 627 roo%�J� e^{2/ - T/ + 1 =F�, ($2YF6���x $ٳBM�$1$ on�:�& and};�( N,2N-1,3N-i�8(N^2 -N +1) )$$A�T� �precise�#n�n whichQvnoI�Q�. I5 (� out �9- u�)�ɶJF %��6 B($3!KP;A1� , 5.5#o*kR.y/[x�F �q;5.9,5 /iL#�+s immedlyJnŇ",p= (?/AxmpI;A�)2# (o/B0 .= 6nB9andJ�tr%6<y! #�2��}6-(T2a�� )f =6qaFhES֜� � �p��(a q eta}, b=1NW Z9w�M�AP ��' 2�%f$j3�0�%�,E ��  o�anR??� R,f,%�1i� � ls srticl� �3 ous I� � ��R�),]2n),Sp_q >�)�=���8�� � &Q"$a$ ( $���"�� � $]� �!ap�/7 q$,�usa;Q9�"square�i*a Lau &�=!� $q$.O�K$6�9;aN� �! )�o - E�o ! p:�JTY\n+ j} +�%2n -2+ ... 2n+2-)� 2n .F�=a�B� "� I�q;= *m(T�\D! {T��4J��!� crucNnew a�%1A�JA Fg$ �s5s�?] ��-�N� ��2� �&a; l (_"3!W_"(q-"�/ 2�: F�givQ E�N�?>�3}�F�%c5BR In I� i� w!r2Re�%A�� .� unit0but as emphas +%�I�Rh � s�tpAJ�>��N^�{9 4&�( N= 3,4q FP;!discu".CS�42$Jwa�aIn�; ($2�TBB �B =0�� a=1B�a�a~lex� �S!S y $q�.�CSfin� ellipOB >,hyper as � increas�&$( OvercrosN��%de$tV r��R =*�-XB) =[ Comp�o�Vno�bsz �' author/often�fused�90� -6E!fh sam"bol� vice� sa )2> else�W �aNpoints >I6 inE��8ex�!�ɠ's $R$�,�/%�a#:�(   eqn.� E8$$ R_1R_2R_1 = R_2$� is}q.�?R$$P�j$��) Pk�(kl�(k*�Fil"'B�FS5 "Aj. BZ.b-ij� P �) iea e�-�<a) {12}R_{1323�/R�?12})It�A�be cle�b�WA�4if $\sigma$ ( �\tau$��"�a] '��)8 ij!Q F� then%� WePR!,��!�R / &�HssN8�  (5ReQ )4 More ?,$=cE P(.� � �xP�I�� �iN($5*7��!�%s&+7YB-� Ri/$$R�j=Nf&3 qTa�+Aҍ ��c15.2./Af 93$.� �*�*repla� byE�5W>i�sy�"1Ch&e�,E$�oins r�_�934$-+�&end��75. ] .7I�0�O skei�Zon�O'��E- "� �2�o$15*5:��s%Dchang��l.l $\rho (\b�?a2��6p��� $-$ assoc d� E| R ��'H B\" aug3 �8homomorphism" ��|!� cA�J EJaA�� $TEc1}OJ͌M.� �e�� � � $b���N���sf{P}� =� -4 -G}�� l( %_ _{m}  \cdot f^{qw5 igr Fg%�;!�!!�end50�$V.KR� �X H*�.l�^*q⡴ �4� *� $F$auA?I@o   ar�3Tprovid�F�=>  >G ��d} �q��16n!3pro0I�c� $ � -��Ggia6m�Y2P !�u{%UFor\8"unknot" ( no c- �4h�U�NigcircAQtrTB� g "i u�6/ bar{L}_+, - �@6�#a�>�!�I�ofh+rel �b� �U�,6 %u no�FIly p@ !_}|��c!�(steps below ($6�I@�X6�a� $$x =�a�- ) +yV-)+ z2A 70�J�.�.�9u�e�bi� x��Q'+y�  +z I!r"A idy�2�82(m- 2)}�;�R_m�z 2O�{grFP uL.�N�u��-- { ��D0 -; ()IB���;%J� x =.C,R y[@�z =- (.8F�.tE\2lJ� � ʙ"!rI+) r�N!-a� � G%0) N20F��I0S%C5\#oit�G0a�along���298in well-known �"�"" � .| s.( �B� a4J  a' �K� iB_cityC)��C not�'#u7I�"�M�� aim�&x(to=M�O�rol &l�&by�7.�Os�%`� a�[ gred[ ��i�� fO���� *�$ achievt ;(brief treat�.� "*Ii$�nonU5at;N�'�!*"4{ Coordinates,�`en�& mobiZ'ram =�Mv P=� �Dsv 5,16,17$]A A��! ($V�� BN!� �� �J:X - I) �-=I)N.{�� eb,oJ\$���Y = [N�8 $$ � �5j ($x_1,x_0x_N$)ű(��1� ($\xi�Mxi / 1be or":Pin*-�U$x >���.�'6���}*L co. .��%ometru si�.0Leibnitz rule6arNj(&; 1�!�x\� x*� \xi f)� �7 U%� 0I)@* =F�Bn*��T I��-J� �W-��i�con�'te�o�"6+ �Ke �� ($6.���be�?G�ly , "�*}Qter" A�� 2X( excepb($(xA�)$���9�'�F��previTI ����=*v��JaM��J��Y0xN��)>OɋgZ%+4�?�NŪa#tle}Q du�L� ;it�V� �FY!:��* WeasNLd�(a�a�X �*�#'.�-J���R�#�P� �8}x_1x_3 +x_2x_2a:!3x�� o (4)6q1 f4 fn3 n x_4Z`FapFa2a�o2�-qx h- q^2jj� sV . )ide�/�.>��Q�E��� �?xa�-"f%N�Pi� �2x��)� Z�!�F� B� \Pi'fiI k N 3Jo6�e�A� �!& 8 �4�+.:a�aV�x�=xi_j ���i x_j,7 (i+j�W 4�A}D3>U1 ED�F�Pi�` A�Eb3e^�2E4x-L��A3 �0> m�\PiB� F�xi9*&��F��!+yH%1�',q%2 = %Az!�uad��B�30Z 0q12y �8<"C&a��.c��?v����E�^ >3R^R~I(N+1)Fe Te *�[(%�Pi'�%�4w}� �T*P#$)l y&.\ to �Y$� a�g��f�1�Vta$ � be�� �1�I�� ` lR=� ��!\�-b2 � 7,18$]hor "steh�&s"�� J=inoU-�Rs� �/LV�@�S�6 sum �1{ $}_i {\xi}_Fs 0jJv[ ?,x_i]N�!2,6.1�re�3��W�o�+onv� o�� .k_{�,B����{D^X��sum�WfIdi.^�P!N* W�Secs.a�)��Y&�Z()Dk1T (xi_k)x_i&=&��" (_{k�,}5n k {2u,}_{ka,ib}x_aIb\\mfR9�k (6SP2*$kb,ia} x_a�6W%jX(�{{�V_.M� N�CvBx_i%Q_{=%bM�b�1�� J�x_iI���-��.{k,l}9� L^{-�j,il}x_lB `%�J�i�mm(�}i,w$� =3$, A�J�\e��1bV� �a�tauB��-�� E�.stau� &{i'A ,""@(i�@ eG$$�9 0�� F�E�D |�k2��x_=3 =� ;+x_�e2 �eF� fw 3f>2f<6� 1�2 yB� ? b:�x.x3 2.�Fx & 1x_2B�Gen2�[� �[��Ihed�Zo�G In�7�-T76�"$ w*$3$c $So"�6j�en�WW9"` a dila��!(Nin]o c&~,�.adius �e��g�ed. We��nof�f�q��a�aoIch:���!a� work.�%s"�5{T�'[:�a� 1,..�X .� ($N-1$)-oWe�;�In�V��4$ ituj�b��� mapping, �#���82fer� $t$N�%\{A (x_ix�H k t_�Pqx�x�Q (tx)J�� itera�equ /of9o.�]N�� (t"� I)(I�t�b a� ark�@ po&bi�,�re aga�+AnodaE�& Cho6,al$stBe�"_}�}� Ab � 5!��s#3W|pyhfb@$ (a,b,c) \geq 0$e�&�surface:� Y,)((_1^{(0)} =a� �K -b x_2 ��$+biod2� �� ) abrI*�$V�-R���v�Bd AF%i$) "'�J:g,��-ne�O ve v�J� �,Ok double\ eaAs8j�gm%� ($1,�� plan,���:D a��grth a� rant�<4:�*meet �^origin&fłL�ou�P!� =�V nst.�� 6��A� bola v a�+i]$� 9.� we*Ha(i�Dto-7J�x_i^{(a�=��I�NT"���W-] r".�Af*�`$t$C&ce�3&�3�!b�3c>*e�=�!�seT9reG@ce�)'itN�t=t^+= 6)= R= P�Y P�( L^+ RK^R�.R-R�( P)=2 ��F�^ =L^-Vi�' trea�`!$t^�YpgeRnbyC 6c7�l!)�'Fl�m�W Z=�Bm 1A�"0n&�6 � +y =J� %#A�.� rep.�h$t$� map%�N:��'1�':-v�}�D�\P�. �\ �)x_�c&dV� #C �K.k�W<��1)�]J��P�x �BL )� � &.D���F�!K!. I v M v�H1\B�B=�>Z��5p�X �ў$! �\_� �)9�R0 &� &�Ez��[*m"Ug$/8 b?UFB�appearm e on�may��ceed k $>4�06< �<6 $n$ ) At W;stage,en9qI};i� bn)� d�%6.29$ -<%; -| $ �!s�@�H� �H�>F��-I)&� \/�oB3T _9VJR,F�,F+9�� &  c6 n re�I*�t��I�n $9\t�u9$ ra�'tha�� $3 30-�rmay�hd  s�#��! Xu�")gAaE?lrsufLr��� purpose. "�@���"c��ru�*� al llal. P "UF>����l�,$Ex.$4.1.22*6'7*JX�^er �i�1` ��?u@m �weK,dpfs Js�(ula I�S�Gtyp �/(x_-,y,xH%\* (�!x_3)$$ �a�1.6��P�ib&�� = � "A]7�n�,h&( 1]k��W2y5k&��] �X)X^F�TZKC��j)��as -�d!�a �E�A/� KIo� anA�� the =.� :� (:b!� . d5)��"& % by se^�� �0�  � 3 =  F�4�$����F5��"ccx&$i[ 3$O@ xrH�[u*�9�� � $\kapp�(q�A) %rgbm^{��J�A� )}���Y\ŵ���s�_-pz�R��=��J�E��& �mn�� �P�B� :5��&Yv�R�9^��%%!Fiz":)� �  (1�[1}7n}�&�J (8�� -(��b SQA��&##v��ep � i^{n}$ Y�Y�A)dEzcan use2�J�L":$1 xo*>-�"�� ��8�(0!X $$ (q=16�^1$7�� )=e��Kon t�>&�I=/r.:�A"�.�� �3K:B:, t�Ii�9pL�9�#�)�bcH!��1$q$�6 nclu=2d7). � ��"E!�[ �8 1e  )��n0Q non-�t-JNis�a �2l f�Pm��:X�s�m��㥖s})Xa � ical"[� �< �mak�t �n& "fuzzy(u?N sens�shMեQ4� B sp!�"�N.,7� �47.82�)� � {�a smo�x!2 ajaach� � limi$,neOL{9 ppos3P�"� two!\malis�R@- So far�havCbud�T�*��i$��ly� T8 "E8 care�,�at��2�,�&!�y nont�<�&�$a� �'*�4��Qi0)�TmU ��V 10$)/�6Q!-bA�e Brstric�S)' KT&Y*8 cpion�� in"�Aa:� � M�howevEQ>��d alNNAfac�.)%�� buil.H of>ax!~E�A�X >%i0t3 ,i!6��o6.���P/-stuY,!�� 1Zlyi flexn$8c<�2�.��igoi�v�d�dX e*��o(4)$K9stucs (��id ��6 lly �.)�9��= of�wu nFZ "o(� )T� +NKb&�E2}�0rB�b�7�Fo� ?n&l�o& \\� �5 4�j��"�oz R�%2*7S a� ���- �� 0� ] ��0& 6�0�p"Oo�(1.� �&MGB t��Qnv�N�yb�a q�\Z�-�9� :�.�9�QP9a\0&�cY!OE x���% Z�q^2�)!� �% 25� :�-(1 !�Y �&N \\ wz��9�F&ure���Sp�L���VɂGw.9�%�I9rW simi�O-T> ����e�[.C� O6�3�9��� �0c�l"�4VU=�y '�"hHU.  " �9$N$* in $�x��n��u�1�$>�'�Kq,y shif� � $i$ O&� � Valread&( fJ}=62ɰ��� oLes � �  &zR;y= >e��&�xV!e�B�9� of�< %!r���! �/�}Unsurpri��lA5��dyqinD � let��!i�L�n� �(6� per? - � Mdevelopm�����.�k(Mc form zni^f%�&zg "�!dME�P6ied ex+"�\el�CERe! mBq$foot!<k0y [19,20]. (�se%�"G-) mW o� �6.�6*7 "�method^�G!@�arts" � "�{�E ed (@ > how ce7��E%a �  tU=gs (i� R�AIq�t&�Y s. A%;�+a$L$-a]#�f ayR]aÑ, v��Y�i�2e�]�K1%U)x6��/e&�F�F 6�F!�e�bger (bi��)6�+inY �2ng&w,��"C3�* fun%�$s deserveQ� ioI/. H�Z� us cur�X!�a�ea8�> [$21,22o7 A t� of sA�st� mode�7s&P#!Ha� --)le (or. E)�B �re� �gecess�ii"�8]�"�H�Z!�!� situ�E �I9 nt. �M:o�n%2�E@� any}!��g ~� �Je�still I!�AL!�.���e�K��A!�� � e�ad�Dal-�p��:��P�E'd (�pdi:��r�����m�mMortst� &�`�$!k 2c(�%*�!� eq!�� �|1�to �. !�A�L�N���,!iz%�|<�I""3�w$9�9X5i�6�4��;a���#�e ZMa\|�7l, gCh`&,/|Pued�us m;!�$a principa�8oal��1]��y%�i72Yi�GsirA$. Qua<� [$23�q�^�Jree [$2�q�Dgen7� I�E�r6%�a��B��!J!$ view yiel���Odple�e PoinB ser�� (��Ne�E=��N24$.)��><E:EW � w�� wh �\d i�' what, ij�rezpol�8!W$N^{2^p�9B S*mal&VaBl(6� �%,5u�/��4$, � *�`� �c "j1:�1$ $I_{N^{p}�wy�by%e� ��C#unA+aeans�W� ques��T��R"�>!�ot attemp�i�A z1(U�wal� &` betw`g}�� .�)e�;��T.�.K�-L�Wm�eos23ck?���9%�6�cGcU' idea��A����ex�Ce>��1� My�!clin2=a turn�Lt�be�gga�|adapt1�A��. S&ă�U^ofaa 2�@%d*V() �U�7t|@ =�f8 $3$- manifolds� �!>�&q � N6�?g&�=as"0I��I�R$�Y�n; � e� AA� �l$-\� ":�t�,"���vb!�s�@���s $< N $� _) a dee[�%)!�z3al.�}[Qdone. P�)^w�A�Gur�� 6�c2 !�6�&���a�ng�8�! �V��A �AgP+�)s��(1.10)@.�`4�`*�6`gA�$;>�@$ ,e�!�� �fXFV $$ -{9 <e0 < �,!S��n��R*1�ZalC6�(e���=i� zekor6�%�=�  anQc.X� E��B��`&w. $t(20)��e�� F�)�V nishc basiEya =xi ��"  � J ��.XBoltzman�D� �ofn �Da� A�a��� �+AMpaperA6Dthebibliography}{}@0b�em�p A.ChakrabW,|,J.Math.Phys.{\bf 44},5320 (2003|( <2}6<��R�N785FM3:MJ�3},1589<2�x {4} L.D.Faddeev,N.Yu.Reshetikh!!Xnd L.A.Takhtadzhyan,Le։ rad �J ��a93 (19902e5�Klymik�,K.Schmudgen,� ntum G�j��Th�m R2�# s, S �mc72c$6} Tata LeY��T��` II, D.Mumford,BirkhauserE84)�_�,C.U.P.D94) As.�L1,1�R��(814} F.Y.Wu,Rev.Ap�_64},109)�2275} J.WesiO B.Zu<,%��� B (Proc.S�y.)� 18B}, 302�.�{16�'Hlavaty,Y5i�Y625},4��19:�7�,Madore, An Ij� to>2 D�6g G@ y.<92�eLL.C:Eiai,G.FiA?�� x H toolE �/�� Eucl� n% ,RI4002007.�9:�D.Arnaud,6nd:� qhIN!2%t28},5495%s.,{20�aa37R�uVH.Au-lX,B.M.McCoy,J.Perk,S.Tan�O$M.L.Yan, E=�~� A 123},21E�86��� R.J.�W,J.H.H[%�z E�U A1!138!:iX Yu.I.ManiV>Non-Cov;2Y?8 CRM Univ. de M�ealNfH4} M.Dubois-Violett�$d T.Popov,5?�%%6�5�gF->F  docu 60x�%&LaTeX %�  %%:� T* Z6k 2e fvLor:+%JH� Hu� c3us� topi�i�  b�!smNh Hzbyz! �HB. HankezJ��� H last4d�10.1.05�BH�F ��M�Q�b d[12pt]{amsart} \usepackagecd,amsbY,EH} \setlength{\headh� }{6.15pm� p} �- tle{^5�# eore� >> } \aP^ {Bernhard)�Yb8}a_tact} B�, of L\"off1t��$Comeza\~na�0ntrjagin-Thom�2-�c $G$-};�Q�toQ�.� N+is �<�6�og- act abeli� U}{SU:MU}{M>BU}{BB O}{B>TEU}{E>*Spc �^c:nGL}{GL:M�6�MGM�BH} :6 K}{K�ne9�RO}{R>�muu}{muAG.,(im}{{\rm imǜ.,N}{\mathbb{N>C C>FF>bfqr Y {Q}F!z.!ZJ!n.!NB!Z�Z>_del}{\�ial:MHoma�Bname{:&hra!�ook&�2:#l#�b#MMZ�P){ M>}Ga�cal{ G>II �I>BB.B>OO.O>S!:|S>Q =bb{ Q>RR>HHH>rk>�rk>$RPBR}��P>)!�{\=�:�SyB:&cpA��26y}{\cp\#�T6"l> #2V$�;ri�W��x S^2:FxKJ7:Cq�EB�HA�5�!l ��L{.�}*� N�Ő y wag$"e, by ConnosFloyd CF}�+an im]�����ViW�or�K;r^."�. Later� �to2w �Uue� described�$tom Dieck � tD1} % slzly&  way�  Br\"ock �H� BBrHo}?*�v0%D.�Uual a/ !G loc" �3 [ 0Atiyah-Segal f AtSe �to)62�cha� er�" �[%O� 58 MtD1a,tD� �8JA&k �� "�� correct-^pAJ�V� �!�&xd.\st�6�y, bec�qG &�j suspRHw�Carbitr/# �r6s0�:qDedV�en�t�"!���Hr�M11le��!�1EGM!��)� 6�co4 =`=k2# $K$-mU� in!&n�B&�1e'�.8e$li: law�CGK,CGK!� C*>OQ.F"� 5 A<� icul� calc:�e^}oܰ�N�:5�^.�J�� !Y&> .z { ring��ve6e�in E� {KY}K cJ! j\Z / pA�semif"� $6 -.|� �dy� I �{Kriz}br $\Z/pFX�}W e�F{ �ol;# 2E� �Af*�2Eu���+ p�-S1��veg�^M�%�Anre�&%M!�6�e�F0\�}$G�f��m�LieI��!�i�= !(Omega_*^{G}WG9�)a�a�2��by $\MU8_*: J�bC(AH�a�sZ! Sib � K[ew}4lowT6B�42 regar��as 3�43!6�ger�, �*�-�ln.�� 5r��aBmap \[ \Psi : .;�do 5( \, . \] H�3I�&&g$E!�� n is&rhfaia�f��(\{ e\}$ dueAk� lack�z�:���al�*i�Pe �eaeof prime�+X��,��$�&� �Xaiv�6? ���Li3&� �L��&� C}z �-�atA�p*NE�a�]�IN/6�� , ifA�Psi<�a� �.�� O� X+ hand;aI�5ng6%��!�GA��<ai/s. "Yin "*I 's: Each́xa: $W$$ri(-o� �RI�e_W \��m�{-2|W|}Aqr{is� ife��ARW^GIT�]�a� �!A�$|W|$ �+�>�5x "�"A7)�lb�. �tŖ��r,]:!�sur�ive-q �\{A�,�?c�=A ���5 E�eor��O��)�� &?`�� n �Jde�(��*p��!� ribu�n4�s�!�1����c&�%JJ.f�F !�GE�aRu�~�=��LFZ�+,1 A�� )��-�las�$ �Q�q�,}�!�O.!BZ$"s�+use��+ūc!g� � �(>� .A :=�&��Bre )��;S2��&������b"j:`�$���. OKA�L�C~iFem $.~cit.}~gi�.A� +al un 8+$\im(�x)�=0�,[9"G]m � ��main} we!z�_ex\�J��\7 CD} ũ i _*^G @>>>��_*[e_V�8$, Y_{V,d}]/\\.; @V��VV {�ncl.}63\MUJk, Np\�& ��CD��I�* fine; ��, *%!�+��iz-S2SW" 2.11�/.�i7Ki/ a@a?6�D�"0%horiz�l f '��ram capE5A� n&l d2#aro��.� +�of2,$9�H �d�se>We�'!��&� poly�1K)thI_*?g"w� s in.U�se_V�F.�,�UN�*PV$ runn�'Pa] �-� .���[0���V�s)�ira�ma#x�A+��"�3f$M�,$, $2 \leq d#([�$,!� � $2d{<eV'th9+/(Q��OLW ��ň"��!�. undleq�V \to *ខx->�<-m �/ :,M2�:k!� .�&� ��}a� n"� ) $S^W�dT(\xi^G_�S�0d 3 q.�N1><e�&.��mGa��9.� �/ (�Td�/���%n= �1���xv���$ $W \cup \��{��/ 5$�FtPZ� � ��>]�@ 6�yL0���f�-qtas NRsW`�i.R�is^�k"%= g�D^AA�,�U r} "N � of�eeQ�u�<)W&�D`2S .$A%�vMU�e@> , "� �A� "UY| tegkt�e�8.> . D� l�.� � low!�Z<&*!�"�� .� �?mai{e�(,E(M$53ide�q1->*: fami�}^ubrA?.���/ K� o��r {Rev&7] -���|}�DbelZ X\u>re��]���&3�g�n* ;<a��o0��fE��0dtwise,AK���q�.�*@$S!� geo})( $M$a7�Io���N�. ����st� almo&� � �ure�_m{a�� :' onQ� TM ��\I {\R}^k�M+�I$k4,%z `  \[ >K= M""R[m !�pp˲2W!��Nb�� fibr� Ex �0)��5�mea�IKiQc �m)J$~j. \] �!��&�M$J^�R -1$. Two y2����m�vaU�Aih �i�jA$.� C}$-�hnds (!=m�J!)is(�H)j� � dE�Bg �CNic"` R�� \endi *�Ÿ� E�e�Ik(un�ed)�f1���DG$-�d�� MEs�ct Eu ..��>��z d UH^6cI<�&& erty� funda�a�%B;CS �T6��s� y�+W�Lelt��&�%�ԅP. 'avoid 8�fusa>%Wo$6m !Qle>R� �s.\K�, �Cy�nK���a�f a-�lyXV��"�K!���a>, E E�?A ��)�.�Z�� &-�Y� M$!=��� �r2\ , � =x2. it� c}���O96-+*��Ϟce"�;E��C!=���_W S��eJ"antipod�(\Z/2$m���AF3�i"m \R^3��lN� 45�h3$k �7pl�{�EQ$����WMZN|iNjbm�� �)H \nu�*2� �yS?W]��aۑ���A>$\��8,. 2� F�U8�Yi1 4PAg �Ex�~iF �" quotE|!�/ (U$� M�o����.�]vch4"�?$%9��!* � �*MO dmita4Zq^:�u�B� ]���@. Fur�m�3w$Gpe ���a ��DJ,J�6$M/� lway�s 6aNS�a�x,Yon���9exclus�G-E�V� �a�s�< $X9 %�8 ��..�"g � �CHtd=(X)$, M^6�#as���� ^� �G��J� �s $M^ne#XK'A**m�E� :=({ pt.})a���1or{��Y�a r�5� w !�֙��M�� cartes�.�K_ K+���R� !eT*/ .�1N*uIhO.�. ModernOo�=�q:p mR6k�T$ $\RO(G)$-�%@s��" �@6p"{C%4,LMSafo��sak�kb- =7er�S qVsel�to�Z ad hocI����!wrelev`F5��&et�� �qA�E'\BU(n,G%�u|h,i�alY�n$-"+al GrassG=!�!��KŦ"�{n[its.�.� a�a G$i!��!X � "CW�� . By��] (\widetilde{�-(^G_{2n}(X) A�lim_{:@+ _W} [S^W,"�L{|W|-n}) \wedge X]^Ga�[-,-]�ii�!z!�#(=i��6 a<� maps@ V!wco�GX��*Va�� 'y �M�Y6����� ultimatelF� !O.�C&�&��itym�G(q24}�6,mma (II.6.1)wa�Ue*1'�ak�2 d��C!3&��87uniqu�d�1d� �'we $�Q &N� � :�!4��Y#MUM"-1U$.A3Me+)��$ (%�P%�4Z���!�A�. A'(� 6Qu�K:�]� �*}(S^0�carry� anon�:�aS� PoJy4$�:�� �A�)I�%n[!s:�a�!j�� 9�z��e,A*3m�>We� >;+2�6�l",��letݏnu$���J� y w 5R.d ԭ �IghuHh"B$[!w��fm� !��!i�} ���BapU� >m{|\nu|})%�@CERu�� YmE�)�x�� ;$ � collape7� �a� diskN $D(\nu)$�kA�<i�*�� �pexplain!�: ;H�Er�O2� �)<x!�D\��TLݿiota :5o V%2{%i5���o a!+"�'>3Vt{�m(� "8=� $\mu��K!��J�&Gb{2�5] K %2$k$ ("�at��<� dim M%�� ven).!qN ( � ably�qu�c9��(F�, t ,!(r�)N.�U�#�a"�.j>wU� -� !eY*�U&�J��6�E�-�0 U�~ x \�qOE=(x), �>X:�.�5�Ճ�3�FU�`.VLC?�N ��&V}JX62��)��s odd.�  zG�c!�)�e{W}%,���{|�o \nu}�~,/�g�Jv�� �}deAlF !���\R���bm�6�M$>, (�&t]W$2�]+�.PJ�rt�/rad+�&�TZ,% &��}[ C},"@ 5.4]�l�;} .p;"�) $G$�SP^�spl�on&K+U�$$-modul� *�$ A quickS of0�� OCB*�s6�%f F�'� jjuu� G+ �)%�19'3)4 wop% �� ycl�< V%�e{� O ){*I�,K_G^{-*}[[a_K%_2,l(]]"� u�.F�#�J�,A)1;�M� W�k)��:�of ",  $n�� �>>.�&W �&�n}*�&@V&�& *�&* 9� !end^���N/�%� @ $S^0zb/ >����*6 "�*�+_{��< � b�+�t� a2. r� �F| �smand.s . 'Ab*�0ekN��-L&�+s^�2&��&�+{G&0 �#��� &-5*F�+� deal.�)`�.:�s����Al�Y amoun� bookkee |:[ice��fg]!#o��q�1}.In$JM�!��!a�exa��e�.~��f A*�/� �c� .a�a)N��.h�� ringm, A_*(G�$Z [ \Z J ]� � �!R��SH#!�by�t�5 @����N6I�H8"�.%��!�$R�y ��} ��b�g�9}�der w (vir%)A�>0e��1� =�K��65-\ � &ZD+�%{V}K+]hY]1kV$ ruDR�2.0ALH Eh("�(-2|V|� d1�P-���)!�\ni�� m_{V%0J} \al��V� � \E �(}�) El� i!�!��A\$F!JTB�9M9 r� occuY�"�1 ad' �>1� Mo HeuraP%Xiszism�bHLk� tom�%�(/��i�o��s �i{-��a�!tJ">.�&a�'�$ʅ&��Sv{i�w8w"% W�8#]�ed�-,�M)�5�f :J !��aJ� $ c�5�([�l"�}�X%59Q7(f^G : (S^W)�!to"�nt�Rf}�n1j!#��v�i"�$(!Cb�)_{� - �g\-nph+�&( �s�X trum����a�� v�&�/U*9A�^�H�e,- 'ld�!�r 2a-;.�C�meqT I}_{�}�\MU B_O���\MU��b���1��Ng:� bigvee_{W���, ~ |W|�y(} S^{2|W^G|pF]T A]i9unaNof_�Gp�!��=um�[c[*m�aZM�M� , cfa�e�4 4.9.A1u�'��i���>&A�:A6u$� ��(:{@�cop��N�� w{ ͹ .U &�!�\omeg6O�bf=�R�)*080_^e��:=[�&�%0�n�f��by �,inE�UQ��,AO ( e_{(U^G��perp}} ؠ(V.� ) big)&6 ���-we  � $W = U - 3q��bSs $� 2 ��u�t�  $UM�soplus 2�)� $V = V$.�. Fi~~y�s*phi(c2 %�([f^G])���]�2����;3 WeS::� i��E� phi$a��g.u!� taut�a�% �8�| (e_VLpe_�/ 7 *�.?F_!V� K\"unnethw mula�1.M�[�  $J'UJ�!hav� MpO "�'}x "* big"2!EO \BU)0e�3%ensor�duc� !z_� B�st�jap&J%�!e �EHirzebrh ��\�r�,�"�� � [X X_2, X_3 &"�J&n7 > 2��in)Ns a�txO�A $X_dy7"� $2d$, $ 1 \�6<�ft�6>'�RKochman}�1!a5�#Ys��3� raU % u��61�5d :�!ցj]� ��*;62<6-�NA�AltP�(�� %p�ZVe�/th+�;+w��.���z� Q�J� ���>;!�I�$2�A����.nd2�8 |V|+1�.�8>�]2?1��-� X_{d-|V| } �1}A/ � {2d-H}ef�A_{ �"� pn&o�  $BB$ )����$V$�L.�. _�hd��"X_0�8��a%� 0(BU�%c�H*�A� �-.�$�g�q76 to 8ŭ�3:m �&a*h �  $[M]% "*Wt-a��arrc� ([M�%� e_ �&J=A2 b�*�B��ncOx�$M� In4F�^ ular�h��one.�^��EV�h����"� Psi([{�&P}(\C�� V)]))� YB> +fV^*CdM,! q=^*"! `=���.~8, $P$(3�^ivAf��1��r��Ez$�F[o|��A�&��(we"� �AFa�E��aq�Y.$ �.�+ � ���qe��� $�$ n:΢-." f�nu"@ECoIv%[�@J��%3�}r; �U.3*�Age$V��,a�+ ��b��eck�y�5岁�F�V� � Z� M@. 4.146�  (h*T-ref_.� =x�mbeke�5g�R0F +WGdi���&�"O-i Wuv=nE �4G A^&om 7�}:��~A�I�F�I�4�!cway�+�tNQ,�So*E3�m� F"+ '2aXi"c�3}��-*� E1��2A(F)) $FX �;� .�;�caAS�% way.�!k�b) 8"B. W�� L/(F| (E#�\�kV�Qp� \�Y +4j} \otimes V_{�aj}) \] with complex vector bundles \[ E_1, \ldots, E_j \] and irreducible $G$-representations ?V.?dV_j \, . \] Now define .�>b_F := \overline{b}_F \otimes \big( e_{V_{1}}^{-|E_{1}|} \cdot � e(j(j( FP)\in \MU_{n - 2k }(B)hA_{2k}(G)"here $>�@ -2 k>$ is r10ed by the map � F \to B5x$V_i$--�@onent classifying#)�X $E_i$. Finally, we set\D\phi_{\Omega}([M])%I(sum_{F \sub-M^G} %f� (\MU2�(G))_n%��$The follow�tresult of tom Dieck shows that�Tgeometric and homotop%Doretic fixed point!s areE�atiAIE�$respect toV8Pontrjagin-Thom8�. \begin{prop}[\cite{tD1}, Proposition 4.1] \label{tomD} 6�(diagram is�mutativeA�E� eCD}A;)d^G_* @>6x >>EVp*[e_V, e_V^{-1}, Y_{V,d}] \\ E  @V\Psi VV :(@V {\rm id}>$I\MU� �$iota \circ�MU��� \end�!� %] \seca�{G5�4realizability}9�defn} Weq�A� {\em]$cone} in $a�b. $ aA^aPMU_*$-subalgebra \[ � \Gamma_*E�(!~By, E��� :��Q7justifie~is name.o2uQXsi�?} $2� (I)_*^G)u��$. �u}.Wof} Due M� � I�azdhe polynomial generators $Mc$,%qproof A�na>Xivial. Let $M$ be a staaralmostA��0$G$-manifold a�l�d2GA#G2� �J��e�normal��\nu(F)$�)�sdimensa�0$k$. As above��write�� > = (E_1��V_1��plus �  (E_j'j)���{ We���� elem�|щj�k��X\Z \s�^A}{n-2k2"�N ="*[��}N!U is a.� in $1_i}%:$degree at %�L $| E_i |$ for all �T��\{>~\}$. TA�in turn A�I�a�M����J�is indeeA�5�of�@:�$�"��bordism�U :�$ canaregard_ s be�� :�a�wUDF \ra \BU(|E_1|) \�l+  j � Each�!�A9*( +^1!�y(. Hence, us� !k( K\"unneth%8ula��ut'P}\B� -�9Big��,��q��B�y*-�required�m1�finish��e�,of29 \ref�ڡ4�U��ձthm�main}�cG = S^1u2S^1a�TheI�!%x "� u�$-��s)BN� �m . � $*< @V :� "| ncl. 67%�^ n�s s induc&: co9.8 squ6 !�"� (a� .� %�� )A a pull ba� A. All��s � � `inj�  !�!� For% a toruso� �MU} @ by�9S .�4.5f0Corollary 5.2��0us (together �.8�0loffler}) onlf  �[ ertyqsof�las� orem ��e*�  rela� !l6� J� ah�� nt �wmC coru+optimalq.� )P�mP� *� !fI$0s an isomorph��f0 .$\cong \im(V�) \cap"� 1 �E� ����,coefficients�9'.$$(S^1)^r$-- r�o����itemize%�\ [-]:�H^H \simeq *$, if $H[}, \, ,�fE(= \emptysetHnotHK. )���(�hnon.P5: l� s). Fur1 more, itAu�� upa8�N<I"a -�X$e� a paira�E2�$(�,.$')$ (i.e. .�'& �A0��]�� � n^G[8, '](X)u�O /( X� 2�,.F))�� [n2s2�t =a�MUrq .-.r.sF�cfo$C}, p. 339 i�a��^G~�$� nsis�3A�kes %ӂ4s $(M^n, \part�2M)$�� bound� ��ferA� zATs��1 �b�� M$ ( .u $) � .Z6.Y]'$g l� ex� sequ�G �CA�c=�.�f��i-4e Conner-Floyd:l _"�toM�^G_{n}.fIY2"2�] A� .{n}: .�'65U> {n-1^}l� !?!1Fg�jbased onk "�.�_E )� rows)m�*l  @>>>�jU� 9:A.�P}]:*:�!�m� @V.��=&_{.q]}.)  /6(=� P}]}*�F.!FV ���! �1n .�6�/�E�2:7CDw ver�  ar!�5P:� mapsk k� f�s ��AUo5.4H��68]:O. I�  step Z identif �  ��do  column��} ���J B�I�V�U�*jw@> �!|�5�F >�>F� O M��@p{V}:W�n] ��!@�D horizulEi�canon[ A&-Y5Cn ��jT�~~~� y C j@��coincide�.u����}! fA�i�ye done� F�ater}E� a sI�A�  howA�B6PT}�J!M B>�H "�.  �e8 useF ri�&< � numbers<ib:E"� 1a,tD2}.� �T�������it� B�Ae�LP:/B:�b��Ye) ��onc J�!s��asyծchase*�H "�)���adLi� � n�re�( �*�q \kappa"�! :yn� �NA�%<uS MU}:�L. >^`y�%���s2�i.Vj��:���� \\�|6�.@V{M!2��{*27 >qs�i*Z!�\!�Hb���.8�*�!�A�A;�A)K�l �)�zO$\stackrel{�7 }}{\ right�} 5e!��x�: v�Cn�JsMUJp LZ$#�ڌ���,��.Xe�"�� �"� ruct�-:>ҍ. *2o%_*(G)r ]�"���,�  $)�6� >���g "�� "r6�& (disc�!�) unit� 6�'/ to M�N'Mma V,"8"Ii"�!c'$�t�"raT$, $E$�A�" fibr Ck�lE^\M$T �a9&�[EE�M]$]$:�$ iact5same way�� w�$dX&Fq.e$ �")�EX!Ž��we ge�>� ���%csimilar�befor�� An invers=B�� U�� US�#V$�#&$2�). U9�%maY�&$M!w]Q�YKaF3!�ME"�V%�(\C P^{d-|V|S �Z�X(hyperplane *M��e&�� $�$ mapp!�K(J�.�i�� �* ^ �@] �*By# �des ine��T!)��G""�&�`O"�t�;) side�5���s9�T � �U���: �Lj�%�~���+dA�!�comѻ��!CF.�>� (\widetilde{�3'(\SigmaA8� P}) 1(a|^Ga^G)_* p^X%��]I!cQ)UP*� !Znd � excisive Du�&!�G��6(*5�&^P`siM (C_-2 ,:�%�R, C_+:/  ୬C_-�6($C_+$ denot+e lowers uppe�"n"�un�-� susp?5 )�J�= ([0,e+�$��/> �ich�A�i $�z�e��!jL0point $[\{1\}J�P}] �a�+�$N $.r$R�'� $\{1/2ZR�"% fLemma 4� �,S1}� $Z N/$b �third>p� 4.10�9+ loc.~cit.|#�&: @ Q� inF+� i!�a�f fash!�a"<&ca�f"+'s2sC" (cf.~B�v"�omi��Ttails. � re�!�as� @immediat��/ �K}"� deal)d�.*��*ofg\& E�N�"�.�!of )��1� 5.4.x� B  \S.��\� t&/ ly cyclic� ,  �AUj�O $n*%Q�@\Z/k$, $k = 1, 2�1I��� e PF~i� B�"� _2W��>a�c&�iv.#u*$n"�%">d If &B�Q,(!=�A�%�7.1.(3)9�choiceTek{e\q� lI� � conven�"ly � ealt KusA���Q ZIt"� It�v.�,�3�]Y+�+tNA;v a"� :�  $W-6R���*1{*}(SW�HK_G^{- [[a�3a_UE ]B��(E$SW�<�'  sp� � W$. Bua�is �� H*throughE�PF��Z�% �9+� observ��ath2w� lim_>�_W} SWA��#a� coli��� akenIv�$to a direcR � /5��modul,5��#O 5�+ mand�%d s� at ul�%t�"�Z� � ar@Tth arbitrarily large mG plic� in some �A4*/4� laim�}B��ɩs beca� log�"e � �%8s: �&�%�*�. & .^�"�Q�� E! X��UAU�c� �C�kWɩrk� R5 hold P %)�abelian&A-��A(*�P}$�lar by anyh&�!g � ���� stat�0��be carr�$A��� Wide-���C} �is| � a systema A�dj�s ��_�}L �>C . However� �_# cor�o�3�+% %� B"�$ (� U��of�exA),!� again�)a>0�/�On��asajf�failur�*[�3� yo%6!ab _0a�< 6=-�Yt���)���,e�,!�1�8�+r��32���1�5.1. It ms plauN5��&�J��8�-($G$, a ser obs~ ions�/va�4 A�"�6?"� �+-64 &�F.�"F}'� E��. djac�9�%of&�v�(!S� 2�is)i�d!q!� prev�- ��*"�po�d##u"ncise*� Xy ionA�*[I&�."�"7. � #/�"-��d1B)C Q�iAnr�'*�iV!}�"Ob��(4.�#� ���m�*�Q�y�)�8�31 ( �#�1A�mu�0�hav�2� "l @ trans� 9>etai� _G^*�'a�*(E�2_G X)��X��A�r� ya"-CW�U](�/ed ``�$ 2�''I/e p� k� 6��!' ���q�$+o X!� yiel�9� ,�_G2�_G��5�^*(\)\�M�.A�� x%6��, $e(W�C ^2(B�C�� �S&;.�MD� 2�D�2��rBG�*�i�ly�!P�Eck$A$�;)2 (e_WL�WHqw�y�<�W$��N� 2 |W|}_aX{- ^G��.�1.e��an2n �= ^*(B�5 ).�[[C)h(, C_r(M�C_i"o 2C)E�! Jv & 6:� $\rho_i*= Q�6(Qstad,�e2� DB�b&1 ng{&< $i$�;< �)V� � 1^{\~F mu_1&�<)"�.r6.r}"�t� F e(V!�[Q ]_F C_1 +�F�) r ra~ŶLazard's� �2cA� law $+_F$�� R�A# �S"P AEG^*�p-�%}:Oe�_=�U �6�:�V �u.�c2% m �i�by $Se! well�obB8A�L; ��%xS�e��~C#+96%� !%��΁R.�Fm�� e obway� oA�ZG�0��� O *�zM��� 2{P H�.� & �\&_�)��{%}Qn�$�� "�gA�G%�%� tA�;{!�f[$!��+!B�  m�� Av�$�Z.�:�)*�%� .[@ !�]� aV�i�A *�LmbdQ�E�� ]i �bi�la:v8ma"b(�b \im 6�;U) a�{ x��ff�6 �eta(x) 6l �(Au) \�!�pC�� Sn@%�c\:T e�$ j�S"� &B%�%@$ nod divisorM%rA#, .2� ��"3a D{� a�{rAbjts�q-.|* nMbin ���F� %�Lf*N .toA:A���; � ve (7%: �+<].~ L`5�/�$C� .~: &� �"!&oLE!� m @M� = Ja,�cM�.z)�*��C@#.#Kz {*!b�.\]q &���JH9%�,�,E_`E>{-na��B�"] � �*�2"�" @>m]Or6}�/MiZ�\5 @Va[���KBL@V!R�/� )*k =\VVk* �J� �m�j+q��J2:2y$BUBAA!X�Ka�K�$�A( Ac� ledgps:!| author� grateful U[nkee= T. Schicki6 help' !ents.>%-�@thebibliography}{�ibV9({AtSe} M. A�=, G. �= �hHx�,elliptic opeeK�: II. Ann. Math. {\bf 87,} (1968) 531-545. pBrHo}�Br\"ock�Tiok: St�:.�mf. dZ g129 h472) 269-277. \gCa}�@Carlsson: A surve�.`s s 6c& y. T�y �31�),�92) 1-27'pGK%FDCole, J. Greenlees<$ Kriz: Equ"Y>� s.R c. London-RS�)[1�02000) 355-386.�GK2���un0 of2� v*5y6x23%x02002) 455-475.�)w8omeza\~na: CalcY�i�`.�&!DIn:!>PASy (ed.)68HoFQ8Co!���sC"[>23B�I�3 vent!ؕ+13)x(71) 213-224.TH :��pI. JourA�!\ appl��I4 �4) 31-X<9�tD3>�P)�yT2�@ 8s. De Gruyter S�Cs�UnQ�8 p87B tra.B14 �$97) 509-54!� �GM S. O. :Q�, �a�t�B�Ada-4�Bt8 �*s�!e� i"TGN�s, AMSaT96)2� K} C{,sniowski: Ge"UR zp*�a��4r�M pityQ�5�4qX$6) 121-130}XKY:u,�Yahia: U�0��� �le��T�8 Edinburgh%�.�;�7Qj 83) 97-10.���}a� �� �.�)�x� �Contemp� m� 1999a�7-2232c@LMS} L. Lewis Jr.�/Mp0nd�(Steinberger6��SU��y. LNM }12�S�= �=85.=L1��L\"4K6h� co1v����-zeeZhe ~r� al Sy.�Pn&RO? A��E� (Budva, 1� , 158-160hUu#Pe�PVXe:% -��E{Bull.E�%�8�4�(75) 721-722.g�+D"h�omp�W��F�.1A� Ameri2�rB12��,2001) 577-602�S2}���semifree)1$ sQume 24ee,2005) 439-45�_ m 6  docu/ } 1  V%&bigHx % LaTeX2e, 64 pp�DMik.7 %-�.oOnTheFoHBa�$OfAlgTop.t��n.n- \1 E� [12pt,two�. ,a4p>`]{amsart} \usepackage{a4�0>0mssymb,amsthmY ,xy,lscap/xy�Mon{all6?H[swedish,english]{bD&:%�Nn1]{inpu�>6 {thumbpdf6[93 tex,%<==U/KN �f 0create dvi-fiq$�6 links. %�[dvipdfmzOpdf Oud+dvi2pdfM colo ] =truLSrl=bl pageack, �. r/2�2 menu2bookmarku?ed � pdf�(layout=TwoC.@RR,�8startview=FitH,%in3s=false.Dbels]{%Ore!�%6T{A,ptmx} %T%:(fourier} %F 6�helveA�A� \par�@nt 0.4cm \texthe� 22(font\ sl=cmsl8  nine 9 LM % 10 'twelv2 fivesyNy5 ;six 6:seven 7 ' � ;2� 9<� 10 ;ui=cmmit 6s 2r .q .p o� 2�bf=cmbx5�six 6 &� 2� 8;!� =� 6�2ne(H1 >h]{*�,:Xl�4*�4:$chU("|U6,*{varth�2�Tr?�}f�E ��-')@N6.1� ]{De�X=6.h def}v"ex}{E�'6@{;7hNot:"b&R (}{X2�re��}��)`�/ ${\Cbf}{{\hE�ebf C}}DE�[0 {\Xit:) i XJ)YN)YJ)Hrm:Rrm HJ*D�}��R8size\bf$\Delta$F� oadd^4�_41izY u}BmBenviron� 1a {\no� \�-F.+ varne�N-�,oR!!�mdS a�itle{�;&� W Al�bic" 1 subj� <{Primary: 55Nxx,10; To� $7P05, 57Rx��,keywords{Aug�al,, join, �?sL,nley-Reisner� �{,{G\"oran For ddH]{Depart`�*� ,�� TStockhol�$e-104 05 .wedghf@�.su.saK 1N abst�W}{ �;e 70:th,�eorial�R begu� s"�0�W re� �+3 6� 8Yf"Bcs,�cdrF& orWe)4�%dea�'nF�7�-ic2�,�za�> he RJ- i�-a�9Sw.r.t.� ])�log fj!�o4s -� - a �4fi�a 1X (-1)2V#c-@a!n>A�ex.aT6be no*f�� functo�U rgetIthek4Y" T!E��9> e�empor��!)@.Dunless aJ�<uKY!�*>D%M. �`MB=��* 7 y en�J�a��or6nikf. E��� �=@-Gsall�ia K��`��+=y-A?&�Wpair-!� }�u�!�! ��<ofcntsF$ef\myl{{\vN+er{\hrul�! dth 0.13 � �� 0.005�T Fine{$O$��my �Hysqcuplus{{\rlap{$\4$}{\raise1.5pt�<s  +}.m0C\OwP{\ \!b_{_{\!}}  lv�(moveleft2.8u {\ }�0� bf P� } } o �P{ \PP�#1Ɖtn� )"#1�6�| ~=�my�%neqq{��se �!p ! Da#1 {7mysyfon sy!)t^{%~ * \!"72�!�U�[a#1{$ e .P�bar!p! %w'_ (b' 4 He&A�t�nq}1u Y� Ii �  � DEFhatH{{!�at� bf� �#$-YUeZV :[eD$4] _DEFsmall::�Nc-�k�2s miniNr�2.*onm l0FFrame#1#2#3{�!2% �V�G�4#2  % #1���:dis�8 ;m'v��?c.\hskip#1. % #2cEe ness.d  �v B{}Nd #3  %3in�#Jf feRf�JC6}2":ja�JI�ba�ա�oXbf{a9{\vert}}� e�ha,E Y E Y fSigmam�:h:ik2mo 2qHatAstae�g �^{{\landk{-� \! ast$�n !&�ast � V2�� 2�e� ��a��{\�13��� �lr�-0 {$^{���esrfhar"5E�� } {"P"%03%}�� '�top�%��� !� R�)l`\:�2����B��b�%M�topF��2�#.�"2� Circ!0/ )�4:�_{{���u�}El~�Ux5�<o%� |�� 2� $ne{\bulletA{\!- �)2�jrinesuin�-j��imp;GU�h-1.23cm��0.1�= 0.7ptM��wW 1A7�P 0.3cm depth 0.32pt} L-0.48Ne=$_�` �\! g� $2g0.25cmh7pt htg! J�a�i�$ �a�rb}%oůa�cm ��%-q.�!�l-�5� �� )� 5� 2l4hom#1�i��4!�-)� �0.0Ӆ�{i�bf �  \atop5\�0��M^gHg�v� "A�!N�bb ���{\�bb- ��K.�B�.�2��bRin �nK��:>"4� {\V =�ZQ[A� /3.� / sy {z 18�8� =��)l�%r� ,!�+%-�DEFbfde� ��bf#1$ �3AW$F�5bfD?� L�i>ig 6M� ���v��$f�B2�[�!� �e�%brace� %�5!�N�bfB =- L�"2m6�� :-:�6.75p>6�B:�]�%�$6�fCupCapr �9�0.33cm$��3q�#2�k�bfcupcI1*Y�$�#�mytin��-�� Ѡ��"�72qe"_ LHS{�#Lv H S����%t{I�}�MSecP1:�2�EB�{*� N�v of a MakeF�f{S�Ci6�V!in Co"�co� Gr�be's�; W4D12} \S 4.1 p.~171,� B W4s,b f(2�o,�,�� ��o�,�I�F)ka�htmladd�E�!{{\it�:�JLs} }{http://en.wikip�O.org//D=K_sum} aOZT�orcBducts,}�X�*0 alog�N> seem�Gn-�Cing: M-0. !$$\ \�#t�TH} s !q+1\� �S&E� � _{2};E�k}) �  {� �8Z�,���&� {$�� �i+j=q= $}} E =0��m;\4ƥ\bf(}2�_{i6�[T�.��:x_���:M\!j} D��)}. $$ !`U�2M�Ej�bou�!�!�J�quasi-"�:[{�]Bd}.�� st 9�)= ((+1%�>+ \cupNNF@ 2})) �TP%�ulaB work�;/&�~1�p, S ly d&�}�5���5F�@$ TAl�Tw�:)@"new" $�6�He��$\A\ B,1z�4\goodbreak%\no�$ "�v%{f}{1)"hBDef�J"aAntB<(a�Wb�)�P=�i�vXA B_=_= $)��= a �ex�Oa V}$_{�oa� *}}}\!g8a�&l��A�S e 8�J $\s��8.�es}�kzdsatisރE��5$If}\ v\in\?J�, , then�{v\}\i!lS�.\leqno~ (a)}ez�-0.$.m �� ?yrmP�F \tau��t +, "!�VF}b }� �~e�e�:��it.A� } ``-�_12� 2$''%e6�-:LU_yI { ���}�vV 2}}=&�o, to be: {$Z� B2:=\{)@_1�2 2\mid��E"_i!�%(_i \ (i=1,2&;.$7 FgmR %�"\ 1 _th,levels: �1i"��} ( ~1) �7�?:�'2:�K�y%I�}9s (� or n�'�h)A�* a@iA�O3��X5*C^; se�p play�d^vr;] bothhpB� �P'5�a��\infty:�m�. See�I\���|��7:{ Dim1���N&'"� ``diY`''��, bN�-�{26�2:PA�(� 30}\~108-9)�uQ� AR�\�tJ�!Y } $($� $)a�6  ��� _tRc eneXot /�� �.������^��}$M\co.�U,}MN�%^{�'�'��: e=H!�]��V��6dis�?tb\��efes� e�"��b��Ɖ� 2��{�� ��� 6 'Z m�Td}( U)=q+1EL�\A���a�K�dim .:=q[�[>�_��!sai�y͆ $q$-%�face}�.%�ex}�G��q~%:=$supo d�A%),�J�� \}$. Wri� \ $�E{ \!_o�wAFu�#%=Ca�;�>�?dim$(K )\!=��O.�(* 6p\} 5�I6$ " -1.$�@So��\!$�V�%)>��!�a� -Q��9(er $\ge-1$,ɶ��A�Ytwo �2P�-Yu��� s fESAA1&A�� � uim� 2�)=!)��G  2 +1�  �Da� e �� mf~be�91$�byi�!&��ѷ7FP NdA��Io���Sce betw0}&�~1�2_Q �B}!,Fb|$e B���a>Dmor;�O$a8e�g veryA7 P!H2�,N\F'�%o YYI $it v}$, 6(�  (c&�,al) $0$-ball��set?= �set, � Pf%!x� e�S�glyi'NjU]Jkjryw\}y 6z.fYA$) �!�  BdA`a�rS�Y kid.h�/[n�W'-}`-�#J./-1��a�z�}ce_(4Q8�A.6ӁtinMir?QX� (-3)� 1�\}\ne$ accA>h�o.�1 butrr>LJf<2,xleF?�:*k �!�ecbZei_,!S!5� �� �'*K �1ram�0�3�i�"M"�(c�(y mS">nee�*h�6|CFe(I�*akad-hoc i�>edF��(. �"��2f f���M.t�*1 took^ 0ce ($\approx$�?!0minut*"d&+,a+,�\(E� ashe$@oR&m{MacLane�/:ve1I� solv:d�bl`@ �E�"�)app!Zu�|@rR�)>�{ha��x#2genATFi*Ba;�}B+��Da jargon like -``W�)ll%rew���D$*�aHMY1}.4 \})=.$��adAW even�� in+�cy!D�U� +n&(already suf�BdI�+����Cu5$tun�8a�necess ,y!�K,2q two}A�pl�F��M�s� �.ioned)�.q�+iT>,�+��inu�^NZ<%�%* �tended�>, suddeN-re )twoͯ  %Xyv �]F|1:w.+� -� (�Pd "!zwp$\}")I� also�Ayo_A�F �2�>�. e� E>�}8R~3en*g��T/_�^}a�5-��0�3��8�P hm-iH� unde�;�ts 3.�B$@1��u}�!�u�N5yM�� al>)}� � t��A sen=at�0F�}A �!��7.� '� Look� else'U� ``Eh2�es''}�U!$avdP3:ChecBLiter.aM"� {(11} Ch.~3 ,10, Fritsch � Piccinini_�"�Mi�L,�6."�qu�6�Ybf�� \ 3}rm(�Ilen�our2'1.: )X&� �=�a\ &U�[inite v.D� �r/*+{����,� a membeU "��La�a F;ɴ�WP4�\!�6)�2) (�( \! � \Lon*xw\b+in';.�:|&�8|A)�) �U\{U_\�M:ORXL�Q���\d&jZ!^;!Rq t $K( :��alˌ!�-V�C$ $$&Ӄ igcap{i |in x}�}��a )*F!. g9�N�_�Fl����@F@6�ƙ�eha�2`=�itself�1�+��)�]ps�InV C &�R4 f���C�Z# a�4e���%'cn �G��S�} A.3)� -�B 6-W�Vwayf� nerv f����Xend�Vbd*;Z/U27=A*U�M�q!*�+\R,a�� \!x�a� \! .�(cf.~� \� ki<"�c(9}, Kelley:)Il&�9��~256).o"�w�6csat��f�!R�|N!w,_of_an_open_1z!9.�cE��z;Wa"< �e�]�A�� V����9�Be)|, s1ixn�s6�le;�)Ege�*8 1�S;-=c:���A�nLu!ant �Cea{d/reB� 'c  a�T� w�lw!vo�J�S chapter~3l4\InF]a) ���ed, s3ab�� �9J� mB� Ono%expt\:�9u22arY�}�Vno �`.{=�Euclid�l$n�v�old*/ � �%._ i$):on� �V@ 4 h�kV�� �``hst'�R4>�G:c $�tenib)01}\!^ ."� œ�� I�.�Uk��s}-qz]zLu A�lud�"6} �nX �Z�&Y k N.�"k ц;t� 06:RelGenTopTo�)}\hfill\%\QB�e�"�_1 2$''-oAXioaW}!~�)2� �*is�ongly ``�alS� ''-���s:!P4:Or��Ad . }, �+we�rdZ ~iiiH �P21:ii*(e!A�St6A(St-Re) Ai+ �F�A��N2 heir��g\[�YY'RAa�uEreveal7 ,st!-�on"���ɵTm�� inv�� ]!�Wgk )m"E\ �1�H�much igBD����,�;ep�cours�rH 2!� $Ehlers&Por�\)� �I(&Golasinski��a A mo�!Treflex!on ``JW@''-candidates $|1� |$, 1Y!��4Bv{-e�!�,� {\wp\}=|*O\}|� |"�| =\no5i;�<-$ %� beco�qN J(gee�alRb ;dar�ex� ?#enN�,ŝ� �b#%�c�)�ng3 \ -&^ situE��� we �m�Ao,}eezxto� �o���+*.�CR��.$to.�,ford.edu/entc/,-/� RU.�� _V"�-�_1}I�: � been un�drI AW publT oV�$, fulZ�6�se):c:� �: ``\��+Ext%0ly}!3o�$� ea�Jɖwp�s��do��#�t{�Dy*�)U}FG� � .��X&n't�Ke�h!T�adda��t=Ysum%�ea�"�2#� $X��4&�DF2�) �$�L ��mS|X�?�(wp�(:=X \!+ > �m�D},)H�� adz""�c ��UY1�:? �zmbl��fa��ar ro��e����__T�S5pvi�\��/%s%K� ommg �}point, &@"35}V 103�)or�!�ݬ�)h--$�_eaC%tdit"֢, w�%�d�v�k&�KFo�t� A��.�Y�pair}- �,�in �em~?u�emP14:4�"2E����z�as�)�.��*] (m�mo.�,*) (��F���OtyOfJoi�J�c΃s,z� L�_(q@�����n��%67Mattachs �Res�| o2�$kts,� �57ff �Si�4ru4E+� �-5��,$8:alpha0}).B�P � + 2)�}rve҉�l!��1E9 ]e@� K}}�!�11N��9=" �?!\Ʉngi�2$ p.6��1�d@o 6��4o.�F%enoV�.�3�'��$E}}_{o}\!:�E  K}\�Fa�9. K�M�!� 2:E0�ޥ�he1��O!*O�b %=ex�:�i�� ��!�%���:n%n� =I&:��07�]�xJr�D�&��ϥ��� ol� thanY>v �elfg�$was sugges�(by S. Eile5cEVSa�'��/8� 42� g2*ge 820�e��ploV!�02�e �aJf Pu�UhrI��Z^s}ǎ :\ ]$,2 wrote�<bZA��X� ? ced�)wouldE4Ǭ�`r�``�"e�byR ingle EI $�^Z<-�O6�[ _i "0}}}:  3]=�1llAe�3�~2�%��)eis�o�by Hilt�nd Wy٣)�17ʼn 16~f:` As��$R�� ,`e�+# Fe��u:�D^�&���! }���й.��k�J�����fi� � I�#al_�}�-noay . P�,X}o�:= X "j :{$)$B./  Ma� 's\ $K^+$- wK$q -�22}�$317e�fur9�ay$p.~340-341GA=��=��;ǭ2��jF}: 9�\!\6ݚ.\D�x��A@wpE���.oOur�npy] t]P15:1E���, 'i$e�d\/Spnn�"��26�%:.Il�j�uc�-�,�&a� moti%y&;�Oa2T�92�-� ����g���".�&�.B�8:P SetMinus0�Aa `, -set�- s}''5 ���8o}8N,; }�9�}.�w�x$x\e+ݥ{x,�as op"E��y�N9�1``$M" �$"��D �( }'',��r�se 4ory��J G ��9� _(set*� J^�{c2}''} zf`wh�0!"y {� !�6''2,}+! }2�,�%z�3�&� �?4�(no�*N��dWeGA�$risk droppA��|�ur��"2 soa>a X}W �-��$;�5�<\1�\!>�{x}:= E�\{��aE�}{ h%AF��e{i@$\ x=\wp \\�P���GO l({X�<o?M� x\�i)& P�^wim]� �:JM� 6 �7s*Pary#III}}�U�finnFn�t !:A�%*it link-"�$io5�"�!�K m LkO E7)f #V$W z ex�$) � :3N&�)A5�����)%T~� \!:=�){�)� �mid - N@  =5�]* "up ""�& H]\��!M(*�&�& Lk}Ft*}}dAo��!= N)A*���1Uoft�qsh $$``Erm�i��ra�h3� )} � ]�#''}oA7rm cost �aA!�!@!= ->�' N+A%�' ot\s"Zeq :},A��("D9�+y z=! qL.. (�9A\a�P�:OE��� �}�@iffBT 0\��+ �}&;*|"_l*��=�,}< %�a Y� `� j�eF :m�2 of}b=eN x 9�74 exerc��E. qAEP $M"~IN ��)ix ��O���#)& ��'ɤ}� by sև�d�p Spanier's a]sC-� }�Z ich,�S� c5��i��,ur��� exh�y{ �)al rco�!t��� $\%_0$�� (v)\ $ 0\j rall�E�#VA�{J^yQ� a��@va^g.��E��ro� ��\rm (.L��}$; G}�anV�*�ez[M�e_(e�&se�, aN�Nf7�>`*s�BQL"�G�/Rs,_�Ls_and_ ���A���3. W!>-�a�{)� \in|I�|��[: v��i� ]�/6^  [ ?(0 v})'0�fd $6G!} &� }=�J���� i� {�]e���\��m.��>+@ {\!}.A�&� �A}�vi&9�D�inby+�=�{l�nKMw-��IbsS$_{i-\#)-�U;K��U� &wL G})Gm!�Hom{A]�L�?,9��NN G�9fK:l, �\r�U:[&�z`QC, j IV% .\no/C=k� (u$)v:�����Pm � C $>.�+�*lfU&�"̇rVula�7``\#''�7n�� ca�&�eG��� depe.��$6�m0279 Th.\ 46.2D,8* "�$3:Munkres}k4k0� Q��.re~P�A)-Phys�inspir�.(}: Current�?a)nom��h%-� k���@galaxy,j/,U a{$Milky Way,�es�� �^� superm��ve bl��hole}~�S8_8_8 b�v�, in , -Vterpre9(��$`so, ena�t,{disB of� wj1 hi.g'0!�� ``\!.. !jp < ��e�| � Ac�-,eE�jn��(�u�no � �t�0+@������n^ v�&( ,]b��*C{E2Yb�>ry" mulFn*7:1 Bund�}Qa;abs���E�-�-�w��* .;~} ]�K�&��>*�# L5hortcomA�can9beUB %z�/�"���Z-&aA6eld���r�So4to�) 2�$�w U�LepAW�"�ion~1'-g�$�*�Q;_o�fz�p.��g".Ln+g�%l�&,��b=C"�<, # set:+:=�/* )�� Any%;.�"l"ZC)BV)b�|���. ItsYjy+Z& @e�'v!�?-�s ���kBd� �\ � SdP�{�&  2  "� 3cm�n&� (i��pmib2�cH0"" (�AZ�2G��1HoR �� �RuLly}y2�Bm�Of_*MT�}�/nc����} (�]amis�EH}''�r' �$N�HN r & Real�= 7_ 7�V�a� bb{R�j!b)`m \ �V^gSbf \ �i\~�ı�jE�U ?fiv�]A=>Wne u�� w� ��/�� one-��[b�a�.e.�Bd}A�&?Fk !� &�(_o, \{{{v}}�G /2 \0$``%���-��''�A!{1 a�a"uHq�E%} H &�&& �:6#2�'s�:�Cj�'or3��*���2O 5� h�j��6�}��� . Fphe% �EfI5� �-jT%�$ -�Je��-m�B*_ Z�#*_u�*S gives�fa �{\A M A=�=\JnQHFE (%�w1=*�M5 �A4 n''����2,�U29%�Ue�>�Xb��, A�A�t[MB�s," aW&Ily�8P$bZ�/wDalw T4Bo r�� wp$-"�ieS#MoL �a�$n6L(l�>Mrl2�s�C# �is &.b�ose $(nB�C, �%$�'��#ex?�RETel$$�f�o!}}(� Bd}}��)=(F/ %)�.e.� at/ xaf��d"�U__oe���nU�9--�!A(� �F'�L.�@ %��3K�^ ({��TF})/".�1R#� �uQ a�A�*-&M2"�&��� ) <ir De�2m&_ll�u$o (graded)>�4qQ=��� our&� 5 lH/R��>75�1�"G$1�A�nGb0$b , so.$1�(1�{�Q"= ��)=.�L� as1)!�256+)�� * =: =0 ��\!� �^ GEA>}=֦G����� P\ �A%� >D=�=$V- M6/>E!> ) =&6VR"!RL�%I= / �.$��.bEU migh /hou �IuAmf��Bs a8$- arcs go5Ek9 i��e ;�ach�Qi.)�K$�"�-��'(�e:��4<3�^ ^:���e�ddim(X_1!p X_2�V X_1+\ +1,$q9, e�, EF'�D��u . os}�%3Z�*�S-1� }en��D}�w�/M} �M�=v_n2R -$M\"obius b�sZ ��\!},$\h� kig`eE^2fjeR mCYjgS} f� � / %$�2mO!�!bb 8�4 ''}=�!bb{B}}^3st��olid $36� �� �2q"�cI�H��rP�tlyea�On"WEtJ�sA�`d tdF"P��:Di��m�``�>3#j�����!Ud�H+V�#!!m8=ny"�9  Ityp%�``c&�s���(to �3!�*�.MQ%me��2�#"(tGb�```BA  &9Uo$6�f'��e�.� !1a:- if��if I� &�? pseudo&4g},n .Y | 7:2}��*�� A7�� intu� eas��getC l�2a��Qpic�(a�2�*< up-�'  �]c�}der''�Y ����ct.P�``1�!�|�- �aE�[ �OZ� ��˝n�a AD�.61 CylC��Her�A�sh�-�\*Ht- �1sE �� @� �u��U �� � highest U�� a��g R�(�&*a��cut2|�,��to� botS�A�gluōse?-�2�t��^�,�twM�� m $180�GM�Q�a M�bi����!��-%B!�:�2B we��&. :[>�:��We engag� s�4�s�� �1M �4X7qJt�1r7"dGt��4reM�s�# elie¸no sharpAHafveU�ik�Ba/�N��>SB��>)At"��n��b�-�"� roomMTReg�g��%6�#d�0 , sa�3-�.���!���Z^)zy�*V��K�Ch*�:�n >� get:!)(!�A^�\4$n6;d*zC``�>��@S.@ ' ''.)� !F�W _{_6��)() J�) $&�l\U /bb%92J�Y� �) 5 � r 3�v�� "�  �J�}^12lFk�"�Ŗ: kh B}^2� �m})2� 8: � :#I 8 )9 6 =�G� }}^2!�:!t^�R2 �V9m^K�ed� \&�S� �0(�*6�%�5I�$���)*-^2�p*�%�QL%)��lBdzO� AN:7�m:8NZ �:�a��t>�M�{�2�y&�rSA�2O3quY� t-p��u/��%Rj�|t)��+>r5m�)l�#.!\M�� �3UG�5IU �-# si�;�p_$ ��� *Cwith}" w�́�M�^2$ if A bf p�/2$�$13�36$ Th.46l�4"�6> ba���2�$*]l�_b� S��& . HWQn�tB�.! 6�" �ch� * F9 ^��R=�!M]j)�S-m#o"L!s"wS .� r�+�?F�8:��$ O��2�5of�.��"� A+s{a�(B�rw .�Q�}�wET&z_7 UA�$� ��2d9!�li�Q>"�l`a es Lhave $�e-,y+ $�o6J -��6F�s,]�ir  � -�\j8bar{glob��2* 2��`F��,BLUy}JTBE�RA�i�.��v.6�; �M�>2�#!�&SLrew^ o studyz�G(����<�]s���i�5�c6�A&m�+ %�`gY`9�. �vQ�� :%{27:�3@� �� devoP�@���lr�no�%�Af#*�ȆU S"y!S �4O *�.�'*�Y.2pt Whyy  searchi ``+I@�1rH}ZyC�Bs''�� ed }F Unde�_ 5:Kynneth�'For02JR �3�s�' ans��!��!�)�"Jc"�0#iesm y do!��#�C�96� R�m�tDM sub- &�2F�k�G $H�(�<Xa9e�hF�'>�(�F�Aa�EC*� 1 B��'�(v��P(J���]� `P�rough 6=LeZ$FA eF X�82�. N"\�^| xFo%�2� !; ". May�!�I+>Qmo��n,3eLB8 So � chec�(!v�-v"YA -Zil7a]a.4��1.PSa�B Aa�HeJ&d>Pl�: $ "�Gi��#�� ,� e �[}v�%�t��}S4�>WhyF�l�T�� res��saUJQ��Jif��S��2�VC3�� �.b>�2�u&�2�6�2�-�&�@"tTcCartan-5�@} masterpiece \ci�ete{CartanandEilenberg}, for which the initial impetus was precisely the K�nneth Formula. That C({\it join}- . q� results,�ly,��pired\ \ G.W. Whitehead to introduce ���augmentaaK@chain complex} $=D\bf S}(\circ)$ and>Dhom���L.:H}_)�star\!}}F ,$ i�~36�.7:q�rise an�-built u� shift,��in%e�e�F n applic���L! suspior on(underlying � ular)&. :dgiv�%���, $U ,$Ssta�Pof Jl(standard si%�, but�his pair WIory^.�BhX_1,X_2:%MG})$,��Tnever took into accoun��͔������(n would hav�@ identity map, Id��^{�^{%�}$,� a��!a�nitsRin)jY�I�group-�(, correctly�@erpreted, actuall�kesV9 equivale��ordinary�1Q�$ functor. ��:�!�%�a!29�IåF��) i:$B%(X)�a>@(7��rm are-�4,} {$\lower3.6�3(^{\approx}$�5!$a��, modul ��9a $-16t��lobject,� confirmed��؅���.�3:^R�, �Q thenA���otnote��Dpoints out, referra���*�p.~431�d 2.1, that; \begin{quote}� Pis fact does not seembe)� d expliciIb�( literaturei� : difficult?d� from ��proofa�o``&�t)/''e)�U|E��a�.} \end� O �i%level it!� indeed ``��f 's!�� ��\-�''-claim x(=!�.T��Zil�%�em��Ws)��4easily proven� shown in2'S� �� X��Ewe �nj)!�ta�fa?taken�) ��Fors2 B�A$�(first \TeX-� of pres� articl1� %� K\"u�-��.��, � A�e� :� 2� L� , holdsZ9�.d�YE�The l��n|7:7i F, ) j�derive/�4D.(_(abstract_�0)} -like bou� y��2 B Im} e�,i�9+A� tria� ble!G< manif!T,�Eeo restrict�be loc� comp� Hausdorffgit weak \ $k$��}.11)l$\!$243E� ��dՁwe only�th^}$� T}_1$� sepa���}�T}v*S4"W$\Left arrow$ ``  losed'')Er \big� SiV & Combin� ic�GdGaT' y4# �i�``a@ zero''e�! >�orU4I� $0$-b�( ťsp�o y?� co�Aon ---�AA�����/ will)�ad-hoc d��(s/reasoning� use��v��-a1�e"�D +�stz� ne�r>(�sEP%exa� }�r�9 babl%�son�o� ongo�margin�Wu\�bar@ 5�}J��witness� 4M.\ Hovey at J� � k<.wesleyan.edu/ �4"�\(\ }$}mhU$/problems/� fL~>/}{ \medI�W�c,Paul Dirac ucom�s�inc!�!.��*� realm!;�e- mphysic��(P.A.M. j�, Proc.~Roy. Soc. A 133, 60 (1931a�J<%� Quantised.0 rspa.roy�s,cietypublishA�? Pcontent/133/821/60.ci n< Nit� � TElectromagnetic Field}��1���!�:sItRms �EE�n�rocesh b�ll� tinuCA�fu�� at adva��a�)�0to�,associa�=!�� oNal modifN`��AoC "�b���.1ra����njlo7d�opA�:anye�>al schem�cixef und��.B� \��{A"�H�H�$y} % \se�� c �a�&h�� y} Ch3:e_Xub[&� ܅}7\�ie�%\�nt  \S 3.1� s%r� mal f5v an ovl`�nviron!`, suit[/( �edvZd6���d1_-.�u� c�]�cM%� lex-!�91~2%�Ad�RN"12d DefP1:1}A��!pl&the P"wC 8a"abI � (� ny sense)əifE� ��fai^he� D5typ-morphismv/ՌQy - $�a K}$}� N iWve� eV?W} b6 maps� ��.f30� 109, � ��;"0�at;m DefM �$��eft\{��(array}{lll}{ bf M�.�("�,/0}{\Sigma})\!=L\&8 _o\} \{0_O,8}\},\PRn'&a)&�,&rm if� \neq�j_%�})��=6�..}\\* id}����)^\� .vf$0@ �, �^{\prime� $ deKs*� =$!�i�e\M��a�� $ J� V$i�&�So; $ ��\!\inA� I_�fivesy K�( z� ʁ� LongAt%� +9�. $�{.% IfA�ayn $\vaa�_i\ini=�0 ({ R_i,S_i})Ai=1,2,$� put:>X\no��!�S 1 \sqcup 2: R_1  R_2 )�� SS_2 :r\a���F\e[ �1(r)} �IAif {$r�R_1I� .2.sJ/2/X2la'text{Mo�:=z dis�tg!on''.�-,bt$vardef}{} �KP7:K0� rm (�]oX�� 2\!A� ^{o}}}\!$� An $($� $)$����Q�$ a�3 ex set ${I�V[IE_{{�Ta col! a $($�or� p of �ef$!�\s��$ �Hj}satisf��;�%?enumerat�\item[(�( a})] If $veWK!� F�,�� en $\{v\}A" �$R RbR �) / $\tau\ � #$Z��DY�2�M I So�!:2)�l�d����Ea��Y K%��A��W�ll writ�0concept$_o$''!�\F{\wp}w!%we wastres2atEEA!T B�o�G ed�ii��!��card}(�)G�"\ ��A�\!�qa�!\!${\erm+}$1�$\dimbF\!:=\!q~�; 7:� Dim})�E�B�%�sai�be a $q�face}!N!L.zex fq� ]_%�ALO�E..� :=$sup$\{# (\B� )$)\ M� F%:-Dm\ a~ "�\}A�Wng\�2%!$Iu* %$E���x,A5ge�!$&�-\infty.�(]�6p\-��I6$ W1.��'var��}{} A� �2� � !!���� _o\!2��" yd 6c;includT&�!|q�\!\}$�a�& ��a$\goodbreak�a"= i�B��b�? is�,%�}ѻn� } orA��� set$n!Z$�&�?.� %�| chi$� a � ��a ei5b\s[�$���$& �� chi=��БY@ 9�� � "\ some�� {\bfn� V� ��or��!�� .�b} 4 chi=. 5g� _o}Q�In\ p"� ,!�"� :6 >`%%�_o,: *  $!z��if !p 8e�!G&F &d "]&nAG or {Y�{E�':\%h��(cal{K}}_o$}�"ng&� >@K@i/]!"�  S�XE=� ��,_o \setminus.�A Obj(E K})a�nd�%�U� $!�: m_�*� � }F �;A!.�  1E%�chi)=^ &v M� & � i�ra� fulfill�2$)} � \!� \ .Y,{� �M )}j^D rm b_� ��2C  i�.A:]E�l2%� K}_o:����?2\w .g_om�)= �P B�in{Obj}2_o2�4�O:M}.� QU�3 put\9 chi:b� 6�}Av(;.�!�5 _o=$i�'�f"l$;!�bf imE$�!=B_o)b5$}AP~2r}_o:= |ld���� ex� �� x+>#B`&-)==, \�Qy7Similar�"let>� C�� he� B4$���ous)s. Con�$A{!g�� D� /\!� �  $}2� C�$Dp}�o s�.�<�ge�A $$ X� :=Xv+}\� \}$!]�!$X��>�Cu" i.e., �*M X�N K*f��* � _{XJ�\!E�(ith respec<'$)}}{ X�*\!}b w�a.?u� $f� {�%P\! �!|�c.~)�w;���> ,{ Y� B6 ��/if; $6� b� � ���� f�+}*kid �\I?o }}\ (:=f)�HV-�k!�}\ f\in�90 &m�Ch!(X,Y)� B and}�Vf. is�unE-ine"3%rm on!X�Fto}\ %_,2H.� '4he\ domain\ o�f\ is\A�Llwhole (�1�0� N� \! =5�A\w �A> 3Y�1bf%� 4.� ore��b)%& A�� ,W1{^)�%�\!A��� \ (& =]3!4�\� ion\�A8b.�)� I����).��>��� .�TF �gor��\v� -0.5�*H�G F%^>v:)mC�! �{ll*! O C~2@A�mat� J�h@ D X}�\! : 6� !\!, .\� aa|�ݲ�;J�6� hC}� \!{X>� ڡ�X)�mp�2�U P6�� M���%mblinga��� }_{oe�)p.}\ :%2 QB6��% `_#1�!J6�$-lif�PE7ies'',A\ ��_? !!  aF829B:��(6J }}})� \cup 6F {}\} \� \{] O��5+ O$ !}��Q�F !\mi�32�J\in\!B� \ M���1��-q�3cm�7aA� 'ta�E6*��cu_ A�9���� 5 ! ��{ ( �.�F#\!�h%�Fg*� N-i-d�!;�UfN2�f%\ i��{X}!c�\no��{]` �A`G)G*^&��� } \Q�a�6�\!$ *�8� �#'�ino rm:$, disaR#``Zal�%�2ion�"T�!ma63$Et9Z�0a link betwee4/two struu �! p" tre�!i�5�+p.~184-6� $No {extra}"vs$ Q4q� $5s has b���to!.H6B$ $]Ke(o �}} )$�� �!1�6O�� all targ��.�2� �$%A�� y�5i� y- $0_� !  fined�&, b), re-estah$>�� uniqv#= � ��end"x�� �Ppt<l�! 4iErJ:\IYv C}\ 2�!�s@ri"�2 D%�A :;��4-5�.y)vo)$ add��.��*I!oe �9s�*A�!pr�! images)' $ v��.�#N�pr�9t/� f2$s ``$\�;o\!$'',�@�3An_{{^o��mhatast!��:&�,?*+as�3``$/\!{~;A�Le+ bA�SN�����o}�80 below certaih+9y)�<.US�)&"e *@8:SetDivh� 1}{/G��\wp2}}:�+P m&J a�25-0.1cm�6 &�8!"1�v "E !.=6�_�bigl(*� F}(N)}/ >��F} 2})}= r) 6�1r ���T��| �n� Y� DA��a&for'>T\!H /1� �)<" � "X n"1 A4Ai^e*$``40ient''�$c6 5x)}/&} :=2*.),$.T3�xh22��AF����35e�+~5�MP)�2}, Yh)ji� 6-`&w)*�}\ �2}&� ,� bH!�\}bF �#ZCB�,\bulle^� \not� bf5!vm�+B�Suma�Let�J+AG�#ŭ&^&``��&sum�� then�Q� �A�1}:�!�2n%)�+1./e:m#.��2� 1=� 32��;a�}(!��%� 1})+�^� �B2}): .z�6�4neqEr : ���F�-�!�6�4To avoid dropp� out�J�.�{ �F�<e �/�.TC� x A" �@� T,v �Propos��4P15j).6�>��ac�m. Obs,����m� j3a�,ive�$\��i$$volved. (�� �$'':=2� ''.))�"N#-�6VP[= SetM0a�"�%\� %��� u\!>g{l (^{�Ob*)AHV^9�_rmE�!�S ~{ v \mmy�# neqq28 �~�% or}~.�d'=5ueo�Y:� I:�l*� e{��a%}�E2� .na�F�)Ur�� elsej\Jk�au&�-Re22a�"il8 A�lex�"}> U�avdP8:;Of8#CD!�&Q#j& AoA`'�:a]�2�pac�=�!y�ub con a��) ele�-�;mp �e� � a.{R.sub�.Y�3R#exh �%&Wes!'.% �%&~I$� both�@lD%� a�f�3. �"zor�9&U � %2�2*�0���}� forc�Beir.7 s $|��|�!$|:�|$9p.K be&�4%��� s "�7�o at nJ� � c(D�0\�4��(} EuclidianR��."�E�. eachth5Es)��>!a!��U<- namn2�.> *@I .�#� �&B0to <4te9"@ FD#�.}5 �2?$to (extern�8)Y aY-h �=2�H � o-|�t�C��D�T/� /E\)-�J� �J-5w�2:�?. �' � z�� Ue,\^��en (F6,� �X��wp �%H$)��a a8c�>ed �. �(tU fore]^eLe} ${ *zY����!�h�F�=.�J�ty${ 6df:�({��6-)$�� `Q� e.g.�# O-��#s���?ed:�$�� ff} $X�(5;E�*�8 Spanier'sF��)B�BE=e�eEU.�} &�:3� |�|&D$B*^+)|+\{))_��M�sEv"vPgiwNr}}�+�(2Z'IL*1'�1����|$'s n�Nn  imbed�M \0 bb{R}^{n}�"\p \��A�wiziH=D�4Y?"^ �V;� X(% "N�(�2:b%H)\simeq :} V,.�$is*��MTAfYj� "�8aL$*  3cm|}�{���a�m{Oalw�LV>topy �5� jM1ld�#4W \rm�Ute�F�(15, 226.)}.a@$$��9���Geom�<� ��� � | �I4o� is l�G�'��` ~119!W\ 8��1cm�-uar� quay,$� �%�!�"� varth}� T�I:Count�.� �'5\>20j9&$.If6u� *F& @.4z~���>s �e�6bZJa�77��\leq n$�, vers�OV�i�-� '7?V!S\��ZyN has :uas���V�eK96� 2n+1> .VC'$\sE�]�thM�A�)^{JI�A��@�f.=sQ�"�9:Top�� 0Of]�FC �6�J352 ff.5?c�%�P~54%� 1�ׁ8,71 emphasiz]�Q_c�tz D�Q��� B4 ;.�6 \!b  (.G��O*`)� � &��� T. Non2ML���(�.$$0$-differ�Q�)&jL have ;$*fJ.L 28}, but4Ez&�Fously $n>a ($n>0$)t�L  ".W, ��.} &�Q25)�103�10.6,� a�leag0at �Inti���)���pract% use&\*N  thc �Tmat�H.`BG,B�EK y CW-c�P6�oA2��e��n�E�6 type� �HeRSU�E/5D7 � *@-�}^(i�.�� \} (or,I�h polytope}� $short) if%+� if (�$�%t1 �Unfy$absolute n =borhood. planet!�.2Jencyclo�V/A =RetA.�� a2�V�r '�^(ANR)"�O �F  ita�!�% N{L�Yv.�VCW_M�a�!|cf�-c�"�$p.~226\ia5.2.1�urg���� �'� �:"Wcell ��� �``,?���,*�T �$\ _{&326�PA�io�,ya���y,ng�eZ"&&n 'V\!^Y ���>#7.�4m�.��f�!wa�]gQPt6�LZ�o�Qly_5_�6}�D^� perf ^�Y�is.nP?N�Y.aA.��11q ,22, 112, 242ZBAre�nney�X.�^.,�)a�A!��*� ( ditarily)f|�Q-��{Par-,.�=8-9e1~1.3.�E�d1�O&�A\" &$5\ (Ex.~1,Ah33) $u/A��S�B�F(it ``ideal aX''}��i�5��2�%m !ki�b9D@rem� No*Os."� P) W��v�QY .�X}}$:=�X"��X��M�O�c;�7PID}:= P+ al I�D�4%�``�y>R-/-m�_�bf G}�!�GX?bCule�*a 8  Ra�:=L�) H S}�FLA4$ $oiU Sequence, ?M-�TVs} $�!��Mayer  ietoris s 6.?meq$''�%s ``ho"Gs�^orkD�Xis`�MLet�br�OChapter{#C>qN�1\Delta �! }^p,Oial\�9"�h�B8_c�*�'nE"AB * no�In*�M\ Z�M�V�?&Hse n�]A@*��xo$NCi@*�a&unqeZion"T&�i�T �. ��yd�b� gar0 � :;E� $\wp�C mem8Z�c fier"�ve";�:�6 %?.``$-1% "Yi�)�!, rU a ``�'' yship tagVarlly)�I � R�Gr ^ndieck'szqW.-�X ssumYO�h,� �B�cal{S4 !�aR�``-�e''��_6�U$�2z�U��٬21�N24. te��G+ $n_0,Ic81=*�$�$ )tF#na�l��q!2Me7aN.�7$� �Qal�l!8 ory} (SubSecP9:2.�+K�� �faI�A�b �rl (co)�pKB b�*)Uten (10)�2�"itr a�\ADJ�R x"�#oRal*� pair}-Z��-&��Two�ex-or�[ngl .B` A�n�m_�3� -al. Cho� : Oed} $q$s^�o"� <=_R�K���{�\�l!XZ��"� A� bf{C}�/�o;�� G})\}}CG \!^q*�C.�h�6qa��M oe�eY.�G�+G�a��tal ($0&�\!1Z&\lf{A.8 k\!g=g$) V o\iaGcom)� ve r<� A�?{#I��!%P-�1|es�FZf�or֎[ e�ex}�I�%boera�mI#�wk �  ko:�36�l� 18:OA�ede`q Prod��$h�Q #���cartes&�2�aNo� �!80�!I !� ��@1.D7-})�QY�Y,� c�m�bѦ7YNM6�';\!%E�~U*1"vGU�Q�-1[%.'KY(.b \! \cong�y��>�*�g6�?*�*{EA<):=�M&z& 9a5#1a� #-�'N� !a&� Tota*nalogWCB�&. �P^�%���� A��Z_5�jby�f�hga�ieF�-r�>��<�vO�Tiuve�^o*�_MA��*%a�Ju�����g"x�8%�_!�N��s},�g� mhatH_{-60N�7gra7  �xb�{1�=Iw{2o};��G 3R�6.*/'G2RQ� _{q�BBNC�B2":��<odu� h1q-�!Q%�]a!> $q-z�Kd)$'� $�is+o1+o2}uff9/u2nrm�hi^�^),::{2}y� & �x/1�o2V&�)/&�n�H}}���&�.e f1 fyE��,*Q70a�>.�=\%Rf�7�1��S2v3 i=-1>=�06�3 i�  -1l:�2�0a�}�18\>�S2�=!46�:�"�$i�QJm_o+4 2}A9��� :�8$-�_a�$\ ($N�)2| .^w(�w)Bu�ڥ�u��{SF� ��H]6 10:2.3}HMe_#�"�bq1�f|�>�<�>�86#V�!" s� s"�V of ZU6<-�'$ ��, 2,``"��Nes>�+''D"���� *P� �� $p$-J�6��; Q ��O\!^v4p> �1Lby��>%(pA�lJ E�.���� \!^p2J usual �"r J|.!('#�B+� �t �sum�N�:=�RC�OM2h#�J*i#2�!�"Sdw, most"Ft?%y@ $wp(\!-1\!)�y%A6HI��8$T9*�W&\jJ�!?E;ex� p\geq 0$)A4e.`):\E�2mb�e3�$��y� wp�� !p�Q�",E~�%a�F  fo�B kind�,!�ba�Ra��$&\���=�,|\!5~� ind�c�Mj�[!�$25&W�q&-qq<]nM�-�>�G�M !�T���!_z �>�(\wp)=a�Tg#�9r)\�)e�*�hBh�JT^pw, rUY� A�2��M�}\ T^p�-��}\ M�.�(a1In�t, Q��y�M:-�B�6:#Q1��2 :\wx,I \wp�%�.�? " k�a$��{a`����E� DefBery�0}��� ��al �L�d_Zp�{='2�"�i�.{9w2<$}\!)�D:=&Q 9 v.�3(�p(T^p))A&�F&!�>0$Iv:�69\!_p$�%F BT,��5Y �90}L[���-�\!�\!z����9.[Z 9Q�0��B�b�[gm�����B{����E%� !�:��!�$Av%$M"�LMP�<2�#�����(!"}��.$ Ob�s�e�-*" �|6P6\�.��.��A�� _|= F��}(>�+  >G)|)RK+>�d)a� &�I_�� obvi���5;�Ki}( �_� |,2}|"�  =}i} �1"T.)<BI!=y;u1fB5�� �%e&#�!e o�a��t��next lO� &�}%s�P1g5� (E"�}lpr co{\!K}�--�he�'�Cx$ �n .�)2|dAwp1&�C5{a!VBv�H��,%.�EO�2f�6x �c6� *� &�F\1*� "�] \Yѫ�8�]aS�AG&@2Z �O�G>0=-1 \\ fMm�-:�"�O)!1}=�2� =��Mb�6?E>X a.B. ^,.�h�-H��k �t~,IɉY�M &�3�<\s4ir4�� NoteP10:i� ��6���i��A�I�*>��%�\!�&j�i }\!(U^�/\�С� _)A:SO]��$Q�9]/.�d }~-1jl\ ��c6Jk #.m�t 0}+$� 9 ny�X_5*)p6�2$�\!�2bX)�R�ia E 2cm$5j��U!@uE2o\!)K meq 1�6�KJ 2})!j�Q0�0 Nif, (!�A�!���neqEB 2\!}/VqFvhen~=*�!s occur XTgdeg=-1.!���!}!E&q�fivebf(hP $!≎�*IE� I�1�gV��!|e�#J�f�� 9����)�A-�],�Be; U:LcQ<�x$!$�R�0u�!�.� ��:� � ��.M 32�12�.�Re�!��\< ZA�fB�b]( &k :3�g{%�rm -%s=e�(�4,X�E�.MB*B-U�))�e!�F ^a���.) iZ1pt��NV�)=y\!"� �!o�"� 2}}&� \��iZI��aL�T\!&J AU*R WZ �DG@l+qic��" �or� � � @M��# ��*�`` ���6ce�!BB�vN�v��i_{0��A}�\^h(A��!%� Y54zL"� ��e}B_2+%/iy!�v 1jY$ \�"K&eqn�2AV������S�1 b�B/ �`��\ =��\ <h}� nonu&\\� v�A�\9�z�B��.Z� &W  �)"�$5�8 h � o �$p$:thcu &� ��v^ ��?m� .2 ��-i+��7%�Ih!:"� 6$��.�.ZT.�"��}$t["�A�I -1}a �:b� �Q�\>\ y�U!#F#&� ��}\ >���w�8�[''%f�<o`n0X�!p�1 it5!i���F#pYJ'#�R7V*G*�!�-z���0Xo�� �$)��0om ��A,m.��S�$(;Q$�WcivelyQ�M��5�&�,�H$f!Q,g�=���{ �ic;&d� f P=P=:hY_o}$�+�(Q�CvcU g6<C}$*�0 �=.+b\IdA9a\}G �O' 2&a6A�cluA!K� X(i_o,i_{o{A_o}}): (X_o\�N!? \!U_o,A.o U_o) > =)uU_%keBE )%texM�$_A+:q)L 0+ ��A}):(Xm�oO U,A>$l2�` (X,A)�&2$! }=i+&v6LE� ())=i�NA}}b4F��Pbf P},%6  a+�%$ i�u&4D<a�B P}\}Q?!h=y�FA5wp��( '�� � ;2!A�!w��>.\�]�;i���no,K 5��&vObQ*a�Y.*�GDCoQ�s}:Յ$RemarkP11: �\(�5,2`�}OJ�!�gabbrev�~$ /$U�a��a��*[�$Ch��&�� wF:K5fP[r}F-]o� c.f6N� ~117��&�lB�u ! a� {�19} \S\Sn2}3114-118}7J&�J&B��Str� axr�'�H�� �3\ � 0-13ǃ ne܀�verif��G�J�p&+ �b:�o�Ot�NT�. E.gs��o"K 2it � ned�cUE=I��\:�Ų!X``��\��,���app��oj=o&�_ځ Y6e t�<2} ���S�*lYc��D"�%�2B�2(a �� per Q;<� llowI��)��;;=�36�g'�7�+�E*�Vfur�� motiv� , pa�x�pat���to � iv so�#$ {.m)�� H&� &��Q (X.q �_�� ains$!�adΆr† surr` V("y*�#�� �1iٚ2���&V T5)���#�L��sm�4 �+sEajoi&�>�/ 11:3�*'$ Back� 9Mi C-C�A3s�L@0Q.�M�W�isn"62alimp�N9aW��th� � tx"y�>v�.- uct_2FY" U�=Rv!�inf�3a�m�f"o� "ݖ!��$ TychonoffK� ���amxe domin�y x-rV?C}(��/act5���+eiP(J.L. Kelley �(50) (J. Lo\ ODC. Ryll-Nardzewski(4)) 4e�vRdf�J� � z�:'s_4 (9 Q� h�J2%�"��-}z�0�:) yIFf�Ӂ�choice��A�� _of_ 0 (�,^�Boolean�X (_x�_�9=[^^.T6��)l,�kI�in }6"��H���t��is H�*r ultr�3 lter��U-f,_^� ~�FR(=�Tc�> Brown:Ten�sT��ƆŁ8�>a�W~f.�a��A J7)�0} tur�gu�8F8*��<�S�IsA�st+6Z�.&Id�"t�XityOfJ%�:�).�&fd��G�'�C-�{)�! (�po��,]) �e^10coբs,z�L��_(`?I�yaAHbe���ZY�?�attach�,R֐7��)&��,�@~157f;FqQiu�7��3new.1�� ��&?NrY��rʞɅ��~,1'( Q b��1x���, M�* $Ehlers&PorePwI�DFritsch&Golasinski��rW.EBc&щa��X ^23N  36},.C�Fw�ZAO�0N�fE�� :�;a.�zero-�4)�!��t]� �G*�\!�.z�%-�4�Eabs�C�"��A5� �E)���*�&�G�@)}.�y�*�& "; �Y��A!b�b6:�[A�a�Okre4EW�g��3��qpi� undeoLv�A[&�U�4J�Gt��or�2 nted1+5x{` *��BQjo�tU� jargm?�: ``W�,v 1�L=b'',� �\f�DiQ�7�;135K ...(ZN����]��/{Y}=Y,\ ��z =X$)H.�new�>�E�i$�$�w��C&�%�yI�a -8�e(s .� C"�?:l.� !�O b`� 4.2: I���1i X!\}�rm(E.H.~�Z�AbN4�� acKd: +er�$J�9SY$ezll �?.1m $\{XW4jJy�B�8a�b��"j}$-!�a�-xi�4d�6alpro���{* $p:{\E} F>!X_[Ar$ �"� 2AjW>K23>Mair!�=QcY.q$�%�$(Y,Bw"yRth�F%�M } 3 � 2��AV $X  Y,( B)�q (Au�:�Z�(G.W.~WR�5zM566QA�:.} �)X �YZI /Uawa�su� [ d[�ea�a"� �I�!,\I�G�B��ervk1\{t�Y 0\le t1\�5*W=X)(18[)@Y$;�1�ze $WVo)Eng�xd! op�6 K� intfP変N �כ) $X$,!� ��9GisclE*�>a�=n a1�Bc6 h!Ha�� $ obidu�� � 4��$xa�X� ��Ҧx,y,0 � 3y3Yb3NF61)/V nt"/a� send%EAE*mE� �o�!�\!!�H�E!�ma0Cn�~=�s!�_ $�9 Y$. E(t-1)x� tyE�%M�p*�4C6�t)�'dnɇN��T !�� Wau�$ taa�.=?(���o�sm�2.� ��v�5:� $�G���PJ�ӥ"� U >0.J -�Q�$AZ/^{�!v"C@ \dots \! "n(#�&$noW�!�I�sBM,H,\!:C��!Ue�_I�. AI�A�!2�I kip1.5pt ��Gpec�E���~"�\ (1)��  n s $���" �,�!k- �s"O7 4i}}\ge 0q"E + G + 2H\!=1,eAk.�2)� $�_/y%mi>_�i�i2�a.�n 0�Suc� e�� R� �%�d� �cb��*!K%zsymbo3r/-3�i� _oӯ>1o@2�#!�� 1$�b�<os���ily� �-  (�0Dw� spon�6�$ vanish� *3 �. {\sl�.�Hy��H we mea" stMes�xe(y*y�&�^/ �tw!o!�!:q6-y%�-ie� )Y6z ra�A��+{�=%9c"'u-d!(�a :Oli} �&� � u�Vsub-basia�)��mstxis> bM]ͦ&�7�ylQ�$ a�!)�H�bm�]}�I�-#��*�T1<5<�_a�28a������e�0�Ru3�8U,�: �Ii�n"�9e>pen!�-O�%Eg�C2����v����I�.�I�uB>�i�|Q%<manner,�*9H�but�9���AF1$�i�. �2�V; .�n� ]mF{ ofaж p�$Q->�i�"ʝive, .'" i��!aJL��%�SmG&��alKsl6<},!_) %�.�+m e� �6�*�i� �LF���!"�� �Bm� n Bo a-� n-1)�Iex�7'9���� �葤4&ast g :i6I��=! : >7#�ppe|��:�%� 2V&pver�#� -.A*dINR[L$$�Brm{�Y2mytinyWO6=2rm{�6� �"�ߡ�b ��0rm{.� �q%�}^e:�~m!� 4} &�y�) &.Xa>A!� � >SF��V-�vZ 23}~ }�)"+.632��.�) 2:2}G?�O�.%z�-�* \N"Ĩ)Z�riem��nVIT��e�,$<���0�a�Ƴ.�� �19 X�+%��)��1X !�&C6=X�6"X&�.�:M{X}. e"�$defu9!�y$�*1}.)r-�/�9`D6j�zE-u &'�232�;0�0A� #2# �x&�$ &}*~*D!o-_).�{\5)"�7"y{if�E7���eywp2j�z�e�i2�) Fa-:�Sw�� dele\�.0*ʵG(/WW o}���1�5$-�@es��,t:M,E,5��8 A��� ,.q�"$4��*�lOOc�q�Sans$06g)"}0ed"0���*��0'E"�9 R*�U&�W$(Def} Put $&�{\myP��1}X���M�~-*>2v u�$�6G�$d."�A=X-7���9\n&�h.^�hX,Y.�p{E�!�, MnX�4� Y �``$X \%� Y N �6it pasP$X�1a� ��2iou*��"�y�:�Q] Y \! \{1ɈH��a�iX ;\ (x��\!,y ,1)^� .,�m�a�iKL{ $y(���;7e� X ,$H��o"�c�Vl�� YIh x� le�L p_1:Pl1:6l1F X��6m+6�-���1g�1�2�E$)��'pA�2]�0\!Y := Y2 X P� else�00} 39HM$�)�.]#�� $�I*� $U*ա.WU0\a:'YIA0U &�if-�$ p_25� S 5��!�1�!�:j:�#d1�&�I�."� Put}\�-XA�� !E :=z(XZ�u�a) 48 ig(X�a0 �]� Up /in2PE��]�C�3nrL onds�ci�g Zxp1 E� |M.�!Dcap�D�0}Y , *,f�� t=0)��iYv��15�(().$�3.� (x,1K��ʉs�to &o�\p5�sp��.4!\xi: A!�}YB�/&%m,*�4$ \eta_1:X.J!Jy&XJ<2:>rBx &!�"D5end��rm 3znd�f\��a� rc}Y�$b�B"A� �%b:= x_0� X�zAI�> -2%s-y-Y. e?)�%�p_I' $p_2Ӛ alsoc*�$p$� p\!:X�k�e!���WY�)*!�2`� �iFT��� �@)�$�2_ r2/mak�\xivP!�,)a�&���� �S}Yqbe��� ��]��� F!�""$pa�M�l@�s/Ih �pG tinu�v $(\RK���` �1\�^{X\mto��\!Y�u�> -0.0x�m �� �asy�har"1�XA�*ח[����6!�m��7,,� .�#&� ` :!� L�$({܁M�,�:36�� \o�� �=Y�0.G.I   \!>r�92_:F� .G4 ,�? � �z>�r� B�))�4�7 X}$\�'n/�a$�� a�V�I�0� )>�bor $Y  i�~mIN;})�5$$ >0%_�� �; ?�Bn6'!�j@ 2A�)-2�JG b�)ى��F�J� \m��! �Yb�6�n:!#. $g.O"q��7u/�v���w!�|�6\!�ª�N2 �  ���n--V2:�(omponent. (�e2s��.��pH?@J+�/,� ���� $($/Z ast_�$''$)�{��267�. 8.8�QA $*)80109 Ex.\ 7) -3 cour�m��+i Uz���3ide}s.�Ex����.�te},%�2  2x=(E��i.}] W'$t\ina c``� @B� }'' l�p�1wֳg�h�~�g� � )�_ ^{t>JC=&� 1{!�i.O"�!,V= *JJ=vYQ%�^S!$s,!�R�b�La�>d�S"C�O*� �u� f 0 mappw�'htj��M ) _cyl!K� ^�.#�U$C(q_1�FA�%��!�*�ma��{q}_1:�� {Y6E� X� !���J��t!>�$N<i!#� �2!�A�A%b� �2�\!B�Y�\` A! �Iii$��䡵� ��-a��a��1���� Yu=�%�;�5.7.3�631 oU� $)%Y}{PJkjQ%X�;1N;1!i9� X_{2Y|>b�  (���E&�f7#._�z"�kb:!;��& a�N�!<)�-{�} F)N9Q^� hPN/�A< �f&. S .� V_{s 5�s)r�z�Q&�s: >J�D)i�B 2��NFI��K)*��JQ TJ^�^�v.��<k��o��.;o&?ebu��*�7�asٻ3aby�/aAR61�c� in �,:.|�dnonSity?3Z��a&�b��)�_{^Ez����s (stil sT �36�u 5},)�f�� ;���+{8N�2on &0A}s}* &��= ���32�";*jE�*cb*�":A� �O(F�2:3� ;$unD R�n$�bf+��$t;�e7/\����CKOi9J nverTjt"�. K�G�fo<6� z$4Ku2\_�62�w^|$235, mimic�w 10( did��� e�Cf B�"TS%\ 2.1��?;y1�,H_0(X)=��H}�#�@Mm~H_r6-�V $ra�0�D;�r-'�����a^T�7�o P12D�bJ3 Re�*���ldF�pGr(X&�FH+���' air S/,Y-wnf��>Neoup;qf�Net={5Ş�� g=PA188&l ��g+ g\%22&s���web&ots=LeRef7z0bO&sig=qcjk46rlISNAQPz_PRLEpFVXdas&hl��a=X&oi=�_��0&resnum=4&ct= }�!���!�d�*�^e�(X)<)OX?CY)�1t : .Y)uc�`�mm$�sݱq��-``X2o p=�0pLjY� z$4�IAS)�io"Hstrength� m�)�&U beaut wl�_ -- a s�A0 rega�A�!9�} D" ~�eZ�4�.4U� -���C@is howiBJ l"��' iJ6��:*� �Q$ ab��\{�R��ѕu�2���\2}}!�1�Y�UnNNC5 Q�i�R�R�R^R�Def�D��188),~�gq�,�R} VFbf�u, � assumt$"� �ک�f{R� 8G}, Q)=ҊR�R-}mWA ��nm =l�A@�f� �>N Hi)!GV  (a ,� "+h !���}}�z���� �}��L �}�! ringHom{R!L7"�\]NI�1.7�a%�be��ao��[M H_i �3M G,! �F�_:HR�}\� �'[ H_j �@ �)]c2"c!:_�X��Z_ D�je�Fm���#b�u 6�-�(EG��L�%��[2\YT/ 1\ \6�ZC}_r!�=s{^t-p�matQ�hYl-d,6>� ]}_q�T� )�>T!>�VX Q T}_2:4[ C}_2"$4E�z�,Ğ�01�6��EF:dF�> �GTI� T}_3V�3,F�>�:Z� ���6�43�Ik`5�4>�s i�.�n�..�qn��bf(1)0cmA gEq� ���6nd�j H����m9 term�'�|e:� #$- %split`,�uahead�m6}L\�%=Y-� }��![�D �C {1}^,R��uW>��%��%\��X!]�q�0 )�fr �lM�5Y3cm� 3. -1�"I�Q�)�Qb.�RrM�fz&l��,Io��RQr�#�%�bf=�4}}}=n�3(tenbf(�Մ:9�\! �:(F�X)}]{{:_[Y i q} rm!�}��IM C}_iI9i=1-4)$ԅC!nd�/s''Csh�?�9Q�A�fo.6, I��F�E��*{�``q 1a^"²>R),~%\�#�` �X&3%=�,)''��q2�qNq�\!jv3�vvl�n�4 t���1[\!]�XI.YEa p& -]v&7,6���u�!.A_6/q$bf...}]$_qA`� *�b�35a�<�b,"��Aci�o�*խ F� gbig } E-0���'we2�h_{\scriptstyle i+j=q\& i,jy�g .$|# fill��'6D �� var�G�E�P1y�'a&�N*�sm $ f!�:\!�>\!)O�!!(?\ ( $�$fA#2'�;� 6�"�U:X"`O A�[ YB\mbis�a6�$)T$x* $F �N�'ekIAtE\\! N\���C �1.�� 4or�3W��G�<N$ o�W A$. *�B��#�N 'lo}i�_:N8 k!f(�1U A)o By�n [1�� o�gi<-of<�$ z�-_�F � : A.H :I( ;A�� Iqi}{�f!�\!�y=���$\!R� wer0��{qpsto}�aEDit y}6�e��)Q�B�Yt.�� I}  !�m�rmΗ}|i�3b�}�rc�F�� � _2�` rm-}1 "s ninerm(}{ i y� )� ) }}vqf32 �� �N}&� � B} $!=%: f.U��A�a$ �Y8�"{IVv*� ����urm(i.�D� P88i��$Q�'�G*A>$34;~2.5.12���Jo<&E+&�יu.�C��*�&ti�}�$paces $f(Nt-[.!Pi?<� ,"�9u^`aZ=(R�'   I}�)�BdS!>$B&"D)Y�5p3!te}&��k�1(. �A)�w �d�6!#``�m� wD"![p�?C>FKH�4k�t6 l%B{Y�i<p 1�(.5{Y&Va�% ) 8\!l 1-m \!$)V:� �!. �+�!�k+��''-},Ax��E&1h&}r̓&�4.�J.�Xap�5Y;��R�7�x,y)-!\5G4to\! x\ i\!f\ !q0.9,��J)y)l)1u�J*<\frac{0.5}{0.4}( �-)+0.5�0�- wise�.��m���!�^ i���!>E:ty,��,�,isI{ ��$X+b`&Y�U,!@ reg�%�.}���Q��KiA>3�JF�"�_} �ő�ԅ��U� iL�Wu›�A��S%q`�|�hrEof!Yz,P vice�a�;5discus�wom?[g{��L� ���rm(An��I� ^ast9!�l|$�' (m��s  ndis).$)$z�  0=) d���4*�f��)Dr��@�U[ bf A�IOn�.�*R�� �E� "� *�\!XNE!�|� � �"�A���� ejR4& n��q+��Ph1�4��_2lkA� ( Z #� %.�_ ��3{q%�d�?g�?5W*����0� ��7 .X��s6�^��^!�A =!f��BZ{\b5)u#!n (1b!L!af%*1};a����8I$ �1& "�fq}(1�')�6�=�w:J_I(�.<as6T,w2&��!2A A �_!�05hj�2��)2}Q��2llI�2� A�%�*pj�3V�.�n��2}) �jp 4 \z(nt �{� ��q  \�\bf(24x���"G3I��.��n� .��"v6HT�A��vu�&jx�{0�2�'�v��ڴ7�% b"� ~=|6�b�Eb���� ��� MaDef�Xpar6"S�m5 X)�C\*$��$)�0.5� HS astz ��g ����(6$d q= }}$. T, � fMz� "㡒� .s�$�X� �eJ�,$C(p_X)f4 � fw&y6�qP"3S_(�e� cs�S$p_X:�NI��l2�;\! X;�<,y)<  9��} $XT� f�J.��D&;_I}6f 1Q� 2"6KJ" %u�#9tY $p_�.a&KGreZ=vӍ�� �ss} +.�A56" "%g�%a$ \{(�3͏�T6� l4}e% ~� W0)^{^{_{\!t\ge�q0.5}}}\!\!,\ \ ({^{\!}}(\!X\!_{_1}\!, 2}\!)_ # \ast  (\!YG35 40)^{^{_{\!t\le }� \} $$ splits since the inclusion ofdir topological sum into $r�\! �\!���<$ is pair null-homotopic, cf. \cite{26} p.~141 Ex.\ 6c, and `17} p.~32 Prop.~1.6.8. S�(1:st (2:nd) l2}\ \!()��>2\!})\!\neq\!\emptyset$, we get Theorem~\ref{TheoremP12:2}. This proven \htmladdnormallink{{\it homomorphisms}} {http://en.wikipedia.org/wiki/Homomorphism} remains true also when $\mhatast $ is substituted for $\ast$, by the homotopy equivalence in the last Note. \end{proof} Milnor finished his proof of \)�43} Lemma\ 2.1!�X431 by simply comparingAq r.h.s. I@ ${\bf C}_1$-casA�@ Eq.\ 1 with that-2. )�$we are aimWLat a stronger resul5P``natural chain equiv �'' in V� 3:3} thisE� not \< enough. We will� refore usi`follow�0three auxilia� s toI00 our next twoIAZls. We hereby avoid explicitcof ``)�!M�models''E� \newtI�(*{Varth}{} 8oindent \begin 4 \hskip-0.3cm!�L5.7.4.} {\rm (from m�e�X164.)} \label{P13:Brown7�%�� E}^0\!:=\!\{e,\wp\}=\bullet$ \ denotes a point, i.e.!�8$0$-disc.)\\ \ �!�ree� homeommS:��\nu:X \mmY ��L \longrightarrow (3 (�n,^0)\times (FK _{_2#x, {\it whichAy tric)�:�}� X � Y \2�J�^0� �$ Y)\cup (X �>� E}^{0 � )). \qed� \end5�A Mvarcor}[!�9] 1�Cor!�,HiltonWylie}�rm.��210.)AI \E5l(``$\approx$'' stands for ``J�.)���$If $\phi$:Ibf C}�� J1��Linverse $\chi$ and < ^\prime:$C$ �I$R 2S 4$,a�n!��\oE !:E;C}  C}  sr%A� �\ \hboxIKit�!chtcht.2�-�!@ų $ g$-operat��i��a�tR�monoid�,(ategory} }v�M 3_3$(= tensor ) {Pis corollary can be s:�any �-induc�I2�!X.?tkoch:frobalgand2dimtqft} Ex.~2��160)#\B v�'[46.2]I�.�6�279E����A�qBc� rm H� .~�#]�� A�&� >T.�n��E���x_ ��� {  %v]�Ns V�F�=BU�a� �~:b�4bf J \! E_(�}�4�!j Z) ?s}Vu &� ). \!{r��1F�[R���^�Z�]SjWn>  \small�ESo, $Z���Q:[ � �Z fr9�dF ]!�JRn =�2�]$ by� *K� \ r quo�,above, prov�4�� non-f����� \  K /��V�bound�map}} v�C� _� lex} ��&l �� given� � "l (28 togethertC 9te��$V$-x JI32� \ 6.a_8hfill$\triangle�$� \medM�$p.j�s�R+ L.�JQ, Q�B''[ectly,�o Y; ( �@ZariskiAndSamuel}A�~35� 84E�(algebraic m"3%�� �[b�� \b���(^��� _1})mݡ�%�p>�(big)/�@twelvbf{\char"28}�� s vR�u�u+��[Z� �4�ϖ�Z� 9}}=���=� �\{V�\!�_1}\!z]� t./��Z F_! ^��v8Z)+� igV] ` 2rb>�`^�9}� big�=�0A�5~ �.� JT��ԉ� $ =Au \{ F�VV�)�f(� )#n�)>ZzaJb����))�RT=z7�,%4 ��m� X[4].04P231:Spanier�7:30� 231.G� tor�-R�/*'�<mos +G&R bf G+�suc�Vat�$-$rm Tor}_1(�/G}, G}^{�})=0}$, �v functori"Hhort exact sequence�/"P$\phantom{I� -0.2cm�0}*� \![H �C};x G�� -! )]_{_qq {\!WiR�5cm�mu 4�H_qsQ�zCYh 5]�U>� [B]�K), � )Ρ q-1}262m�0}$!n6� 5�}�#)�. I�$\squareA{�  "$~4:�A� now���:%4:4%�)�| �%���lOpt)2 $\!{\ \star}}}$�{ circ%f cong͂�d  D.4F�J+16L� M�D!s�rc)Nr �a��}�xJO �f�] !_2})&AB�-� �a\�� \�4!?��A:.�8�q29�E�by� 6�6% E�/ R ,2 �"���.�_{1�& Y�, �%GY�is��,\underbar{if��$\{ D 52F1}>H,Ria�e� roug�we��bf M-�4Vs}-stuffed 9-)% �&"�3x3-l@%}ff) Vs)@(�~4)1 good� ��f NPe�A&rm L K\"{u}nneth Formula�  T*(Joins;*�'"� 35���OIa'-KMC!eq�A6�-�j&9o*�-� i�!)�bp1 �#bf R}\ a�bf PID}, G}a���G&�!e�7-�i(!� �A \!_1q)^5f{R�/rX. �[ThE1e2Y�Ms�r�($�"� $)$\����;U*? a�0}:�$� lap{$��_{i+j=q�; 7raise2�g bigoplus$ \ [%�H=i�Y�� 1},� ���\ ��<!-B&�\j\� aˁta�O&�]B�%4�n� ��:A�qq�A�"�.��haM� �!E� 2});E^Z j�!�["| B�S � 3cm{� rmIf3}\�" EqP14:3})!�!�.I �DB�{{\I8!�M �}$�r  qa�2#a!=�A>l(9�z225��=�EAc %u�#1Y�� 5TzrFZ� �)1� + �U15 e&8�^0 Analogously�7$�|$-���c�,�547� \ 11_ Oco$) $oms#-a\���:L a��-e*�!)=(\{�"�,)Z �oreNU4, immediately �&�*W*z�� >tM� �A�5�s[�Uni� (al Coeffici� .%E (co)�- ]} j$$] i�>E]@at{R�sbig*� :�14E�2�9a��~{ Ry��B�,\� �  Hg�"�:��ňF�:���% i -�) ��^���RnF� �AR -f�e}_1�c�!�-\!� \*V Z�,�G G%�� !!"mE0{any �OR}-�W�� {��b$�M�y0If\�&\ m|_{{a�}X�h�j�+��1I R}��!of fini�!yp$� aHenerated.';�a=^ �\ce�� {Q�^%<�%�F6AR>Q)}?n0!��RcR)8}M�|��.|N�i8v�!I�A| �V� rm RF�^{{{i{��1�M� {+}}A�Ej�A6�n �^$�"�W�J��&ubscon{Lo6*")group=-produa.�es�r,SubSecP15:3.1)Aa+3osi�+\ � $ 1} bU*e�% itselfŒint kio+4a.�(4(-1)$-object" mposei% e deE�ion6� DefP8:P�/SetMinus�(of a ``setm��.^{o�|}�${ical D� ��(}}$, revealFs�co.2sa��u"' �s�res�d ,manifolds, �4p.&� �2:BPOfS�2M1p F17.H�� 1�4 omew &}ializ�9!�ov�iA'u�'"y1X'2562]�ia�) also!G�2A' 116 �4 3.3. ``${ X}5� �/usuD2�/6) \{x\�$'' |w93wr�1$x$�� $\{x/#$ a=,notF"�.onvenAI. Rec|,!�9�!� $\alpha_{�&\!0 $,B�8:(0�aC^4�Z$\dim�Lk�#1.& ^\!\Sigmj�� � � \s\!=dim0 �� \!}-� ��e�2bf\#} 9}},$} w4 $\#$.` cardb*ity�U&w#Z <0contraT Z,$W\in�� rm cost{ { �%;8: \{\tau\.E|� ,not\supseteq 7 }.$ So, &}j5D ju7! o!x!=$� and\�� �:O9� ����Q@�� 0�9%�I�e�tofA�F�5�6ia��xe��ar{ \}} :=)C \mid !8Qt*I%$\�teqq$� � q and}�dot\_5%��]n:^$�m, ${ \�1���_%��5�a�o3{ �".8A�/ Int} ( ��Q_e� \in|)�|!([� R$!��% ] \Lo�ft&� [ G"v�.eq0%�� � pro�J"&�^� �1�$�1e Q  over�0 ommu��ve � � A}$�v�unit. W�8�� iKh: r)< �$�1�4m;�� \!}=% 큓� ��E�%�u,E�}� %@>b Eof0\��`�,�@ �22� ��+2�-�' &�/ces()��0�f&L3 .#��in2�.g3}$} $$��cm�  �( moveleft0-- ��0.&�_{{T}{i wer1-}�� \#.���Nr<,%}$(�P!d��}-��� )$� &� Aa� �_{i}(i, TA,��RS>� BO vert T ,^��>_)�~dq�, "?"� \!� I�W%#&�2N�| \!}i� 0.52� rm-�,R�����J� � ^��)�BR��V�>g1�Ξ��� .H�a.coa(Cf�$$&� s2�� H34:Appendix}ff.) Th``U6_o_ $''-H2G� JY Ŧ�zTh.�!$�wp.�73%$IP&� � +~:!$pA 94-199 5.1-35.2 R: rm+}��L?63?37.%twoU22^U $ I�K}�i��E# )a orm<  retr�o� K� 3\!5\����m�,N&� �le��lready �-�� level hav�$C^{o��� F��_ � ��5=\!\ FC�t:� {st}�66Y\{C!\62, as� Lk �$ ��)k ��1j�{" �Q V6 6�!c �ᛞ� )\simeq2A!^��U� -}\#��� ��f�. .�e�i�&�"�GP1�/:x\ (yO� cl�p���$X\ (Y)$� bo�<j{7${�&�2&�� &��5�3 y),k�1x�C�\!�9\V >��"�{\ �� 2��1 �gHE6 �: ] "�: pair�+�pva-�)�Bm��l188c 3,�S!� n�-.� �j| y F0!�  $��91ast�1BK�[V`is opN,$Bf��2�) �4 ([ ڎx +)�]�)�M !9"S.}m%�1�A=+����B��B�\!�) GE3�.�+M��end�JU���K"� 5: �O(tu�h0,\widetilde{x��""I }y�52� \! )7(x,y,t)��{RV !0 K< C x\!\le QI A�# f\!<\!1�-.�� E� in� X�'$y�  \!Y$�2a�&�"�Oi.� \  ��I8!q�6 ({X}hJ*!� {Y!�� !� rn5y�] (x ,y ,t)� v b�Nu\! �� B��Z$�%�->2 A y},:��% "jA!U!�!�B��;{X�΍k5Za�&F\RQ�! A��.��\B�>)UD?.  .`7A�:_{R(�e calcu+Aon.}}c.�!k �A#2��F!,X!�Y,B.x �1 �F!.n4y 9 !;�%�>:  .k8\��~{��Z-%�}\'B>aT.�67 m $\ four.}} �::�%1N &@!>,�G� uqBE !G W63: !RzB.S� �\R1�)4�_�`j hl" !fJ��� !��! �^�DF'���:N!b1(y ,{0}��]!raDhaR�;��!1"��6��CnTa� y� ) �$T#9&�B.�!�9{1})$- � !��&7"All6� � &P"B�5t $($top&�c�Fv�5k9"�G _of_W�5 Ek$2�a/27�)�F4#B�"� �V�ast>Ju�5eda�r!�  }f-s�/�/�i.AvPL$\!\{ )Ap{ll} & A:=X {\myPsqcup1}Y ��{� zI+$\{(x_0,y_0qmid\ ٍXle t<1 �\cB6b0}\�L.86fA���Jm 0\R�t�!eI t\in[ \}!��&l"�a�(x6,:-*� �� !W�;r�+.�5E Now, us.�Ty�re` ve�QM-��Vs�N � ecA $ \{ ( :V,A),$(.0}Y,B)�nW!�R�s�U (of it, see "A~�ꥱ"c.P11},!i�involv�J.8�9 ions�8N� ofmF�Hl  w3U.NO)�%�c{e��[��0_R~#�JfBE�vE6�S$ast :�\!}Je } wHom{AI���.g 6- iH\F},F ehJ 6�m�\ɡ �{B�.|aFB�.!e� O2�G 6\< [ {{ ^� rm.� 2� � �3D�n 7V� �, :J�4d�UB�!��D� �Bi:�)!� B���!]&��"ZU, 2uE�-�\^4%�F��M� >p!B��Z:�!�E2�6-��N�& :�Z�Jm)�!l< }= O ����� 1g��u�%PF33 #b:Bo.*Y�� i��;{ \ \�K:1W9K6�rr S\ Id^DJ� \ ).� eqnoG#>kAaIu3l )bf f��defbr &�  N� /2 &e/3 BV ��:{� !6Z\{y_0\}I[� �J� :H �� v M~v�(:�,0� � >!� � 2w�f( F>���e3J)A�&\�>�,>YG in Xw bVw u�%�  sP^0of �-��z� �p �@! �p T ��.�& *Nowa&N^ 1�P"� *��2� aVP�0�e � ;�L2e=-�%� 6�E7%��N-h*y>�%E2U��#*�;&�"{.�$:��2 � �a�Z��>�)) = ^*DEX��!,2\6�\:�\!�e!�A "*varde8!Put�("Lipk!x%$3.6�"�4N)X�m�-rmA/M.i@+y�*�O)# GX- instable�.$X$� :=��'!X\mid��$X,X5g!}_{^o}}x; g���#=0�(>all}\ i%Jin �-�L�'%-5W*7F /T�a�k{99j7��&(X�v^$�\� (\mytinynabl�+.%��#1$"�$�� said�/(be a weak {�I�o[bf{A�<\!$-$(-\infty)$-��AnyVK�*Rf�)T�bW- spac�^"]planetp0.org/encyclop67,/PerfectlyNoP.�a\L2�*\!$A�qi�IX`;� �,&�0 D �wp}%a - \it 1�*&v6- $n9 �( >} =n}-whm%L�m��* rm)} if,e�som AA=\ $i��2R}$�4J�\�*2D3�;F*xR=0.9 �R R*�� i}2��o}{E�}x*��r= {���6if-�$if \! n�r for76�� '��Cf\!n\!� X$} ,�kip2.7cm!(4.i)}I ^u$� �a�n}}���o\�B�� 5�R)�.�!��� � x�\� 3% X\ne�.q`UQObf�i"Ya�Ba�� Q`ar!0-a<0.�E)O({�+ 4D�<��Q?=�An�0���ˁJI�?5��a�Dj�) if2�h4M3��$x=\wpZ/�*�}�k� �"a 6���?it��y n�8�spD-i�N�n"}$�(($� whspS-(iI~�e#^{n>\7i��:X�O)@'!aPforall\� *!V X06�!�>�;�:Techn�AF !!�g4_a�E�}��!$�i ���U� =0$%��.$i >�!�v(&�\ (=|\{H_ov�"}|'n'tJ�!}ME arbitrary�%�o�3ry�8L � � !� bf 4 �d }$) j6i�#ayb�;�*2�)��=0(C\05�,\!i\ge n\,$ j2 $  x!%�6�:�!�$X$�r^M�l�8lQ�A�  directA���N�&X ��� z�QQ'h ��)ei}}, { bf մ#1 ��.Q}Dz+Z�. ({T�d*�,wa9 A9ed��itroubleO$eannihiDnin kof ge1<l�<at�$.n ]" .1note}{1."J �7% Lk!n� }+~+>�3�y��$any maxi"�` LAyexd6; (,25 $ r$. aL�(s�La@!jif"(3�I�ATInt �?%get)0I��j 2�T -0.5"' $�eQ6�7� }��| �|N/aA\!>�0E}m�$�`E4�9�AV4p*1:.�.r9.#P10� Quasi"� s. qx!�~16g:P29:1AQ6E$a�U96q��i6:ToTh6}�a�Ua�ZUul�6 s �GsB�H i}\neq �",C8�;);�7"�P:�".}�� �ii �)?k�B�� 2}L$(n+n F)E2� #%mBk}���&� X � $ �,v7Azwhma8H6!J.��� �>� �ugnA�^�M�� _{^2A� > n i�5i=1,2�/$then $$[�) ) \!LpI)yB�6]\!J [-)Q!}\ ���%JW a��:v!@t& �oby�oeOfn"��Fe;} {$&~H��!#-@I\�2}IF9�)=0AD9fory not=]@�%N^8i�JAi}< O% $� � V�pJ^\!_1�} �A � ZXN %�Soe�aNK1 never a-�!� :�)$-#�,R�)�iJ�q�!ou��.�FF�+1y�F��)N�92�\! $ I� n� {\!i $I�\rmI��Y `�"6aY1!M��jiz�.ii} on�'Hs�r�B`Ax+r,�#0 $\varepsilon[ :az�� 1$ d��!on@��l*@ =�� ?!��[�v�[L!�R�ɝ(}= N�:cm �qV5;�!>/+} �f ,;�0^��}�*&`T� ^��A � �r-���k�  *B(�L,&\!�;�W "�k}#� ` �{pk@ <2�� �,>��a�!�o�C2E22*� \RJ�)f���[\mLJEq.}~1ok:k1�=:L,�W�:��2�=�"k�"kN!$eN1=$}{� "iC�9:rP ��+��O5A9%�%%:��P:N "�#)�_{j6�!u��� %}.� )?�>k �`�e�8 �yi� �J�WCg��F�&B �7�9"�,ce tG��sec�m� o.l firs�&|mtemO:�� � 6��F8�/F'�&�� ��$�{(X��52-a �26�4,aub,m��5�.Y)\������va {2.}�A��ʷF��unzhandlea&en�hed:p�;ice�7e.g.,� 2�A$�� G}$:ER*�]V��ɤ�(�K�+�+�+�+:+G2+�)����(�(�(J�� �.�N�� �4��}&'l��6k���}�J1|Ix<+^��'6o)� �cf�ѳ:�Y U����B�tqE{!ݵѷ�4�P��f� G})]�( l��6��S�/oCXz5&A � R }}} !�>j<IQ cM0�O}V�� ) CRl(q��D"D\!;h),�5e��$$c�=]�d� ѸF�3�If���"�-%YP q>:�RB0�-��Mc*�U�P]'Kv�U-"���j field-VofJ7:7.1R�-*�nI%4r�cp}�Ho}2�42.4 p.~181-182 9k�9`4�>�IOn� ʸ ^{E�n N��&1���"! ]�l>!� (tha�{!s��p5Jr)nNnec�T�F * Hausdorff' �x�K~� �y1 ular����N�n$:�*$(}j� |A}� �� !�R) �� 2�izV� �7�*��."�M+� $ N�\ *� \�!�{� \i�j��4��D;M 4.i}�&=: . �� ^�� �& 0\ {�# G}��Pwn6R!=�2$�f  gfor�}\�Xa��� :� �(?�=���^0.4"�Ko"1 � 3c�]4� I� 5eTT}� be:6,bT%��(Bd^F��q��!EO�!:�'n>>"R�=0\��If�rmrB.sq%��!�XH2�%�dq�FJ�a�'���w5;�YA�W1,*�S�L orU\� v{�mkY *�$}�a $ {ir)m��x#\�a!q S},{-) u�* *�* lrm=(M�.$�2�i�#it ��!@i��itZ�m�y\sub1%*1; ��wij�N}%5B"b� �><.�� $ O ci�T��:E�m-�5 hm��b�"� Md!�s%�� $(4)$F�#�#wp!tk9n}o� bm�$X�T= �.�#Q�QE)m�3 $ n-�# Qn$-j#vC"f,_s�"xJ\in X�!M�� �&* ���&� #)%�M�h! $i=n /0$YTa ��A[��� au�;)��� d�, We$.�A L:Y7:7},a*i]pre-utsgout�8$qJ$ symbol ``��1�P>6#/^u 8}.1 temporarily�Flud�RU,2$/!�$\� $v9we assum \:=0_$RD"e^��> , pu�#M1 kle0 � �X_ of��>�!�.1+ limi%� o ``�!&mGact�+e�.&=��nA�&�*"��"� CM=[c ˅ p6�Eu"� �I��t ��k}�*"*�e(1"�.|.v1�\diam@XM��k�Ʌ��(*r+1�<�j��J�X%;��!I}$��.oN�fo I �.�� )%2V2�!���.v (M�i� X)= 2�.eB:X).\ �Els� ff!2�)= /N^/):3V/|9j�!�))�G3VG3)G6y_)� is\.�&� k� F 8�  }K1�!$-Tk.6o=�ӥ�q|� u�9IS6��!�� triva^�fo��iF38Me�#A� �.�K �_ 2O�, �jly��2�> m��D:)a{ adi-AY F� .1}\1<&"� -lik&�$ ($:=��R %1tv :$Q�Xart6[��aces,&��XAj� s>R (�) nd�if%�)T1�;G!��5?.L��1U24�1�U {4Fn(p`�C$� a��%�~B���{2Dc� \��2�a�q=\h{{�"JX*{J2\� +3Utop�RA�> -def0/.�') 1:PairDef� bifJ��6=��&� �a<%pFHA2x��5�i4"� \��Rn H��xQ7�TU#�i Test�.�!W!N � �!�L?�!am5k�� b$\oMd$-figur� (*: �x !&� �V0 � �1$.) Ke.[C�!.��)88giQX equa ,��A1hZe�X nextGele�32a�&�m%62H take'be1r!W�"f"��1Fion�0�4bp}&��a�-0���A�u'(>D = $ �P( {{| G| U09. 1*�u^{{\nea��^���1�n1.4&�+ U}6^W2{{\mmy%;}}h7q�qQ5e,| .O$�e�48��2."yW^,\s �����_�Et!.]\ }} |cN T�/} a�^{|��bU�V\!�W� ;�18p =0.6> (�3)��6G�|�u�$io.)����������"%zF�\ s M�!B =Ta)2�B)X; �N�l\ FR{�r= [� Def\T.�:�]YK 5cm$ $a�>�> ��:a"af^e X^ }&�3{O G� $ [Eq.Z]�P�f\A�T�?$��]ue:L$�i�\ �>�iR"�|�j1 F�� >G}) =#*� $ =�0z��m&r�9��h�� ��� $ [�J2�\]��?R(n/Gh8�E�!�� G}"�@ \ {Merg��8Combinatorics, x y \&mheA6�"m PartIII}%P�ec��W��*GE3QtoQlK�` 18:I�K&�mRe�kT_^kr.�2F�>R�m8:I�3 � �H$k� ifik^ } $k�Xxit X}_k$���7Xg ��tht�yy enlargrd&+"*�Lg;jinuous��l) "g  domai�k-[l�~�{differb+t^B^� ^ly�v�RC` ly_5 ted_���B(S�*�_-Km7�1u_{Cenbuh�incJ,T9.�sȔany� F5�|4_1$� 2$, $||{=}2|~!�o2| N!� B%L�ll�. �B$�XNh�}Q#Ytk({X}y@ ��Y).� �CW�����KroperU�-=_� n�-�� un&H�""�*P 'd at le:Di�@&'�. �iX} �!Y�ia%"i %�>& $p:(X9 �Q(��ށ:gS�  X΀ Y0�.j� 1:3.�5RFPed? tlet)!!�exami8I\cGx@Fritsch&Golasinskk) 2,6|p}7$Q1ML$�o�\e''���3 turn��into $�N, !>jq�)x.. Un$ y,ij�=N!�associ�aO&*;�d<)�s�:!33}~\S3..��nonOit���� �b�#s�� 8:Oқ!OCartPro�{6W 9} L 8\ 8.8 p. 67.)} ���Z�2�{\��_�zaKBnR#�; )"��;h ex s��! f Vj!_{�m � � }}I})U&r<\! 8IRE�~��5�at each)ex"��linear*w /�Rs�����1-� !�M�!�esian�#ug �RW�*�k\n0�y{\ۋ0�- RD �)x!�'��Jo���O$(��"zt�Y$|!�}R���|A�wp�.kF�jO.�|�� �andzma�e6 ed a�`$� bf V}Eju�QkPa �2 �# %>R }}}�V (v��!&z3=�= m, R,Tj�au)Sp+� })  � !=\! �jI 9 / �&GnJ~A�%02%4�e� �c�wa��i,�\!} �}"�3�31m�Fx6,�lJ!O� R@9j!6qr<�Tts $\{ w_{i_0,j_0},$ $1,j'{...��!k,j_k}\E�  9C{i!�s\�u{j !qno$�w_)s)�' �` $vf0}^ � \le 1\le... k (v_{�^� F} F�: P\le!?k>%)$P6r�Gr�a&��%+ ���(93 .}\"J� OJ�Wb� ��T��ic��!� repet� s possibl� cons˓ a�Qi�(E�-��O � �!:K)����p 2�)k")8e�rm*1_p.~68 �fpmrie�:� e�&�;6͐ �^ �X�mU ��� *kpro�{ ion,a�$$\eta:=(|p6~|,r \!|)A���e x2|i\hook��5 �}"� 1|\ş4 2|2 .�.� Z2C$!XL"3 L_2$7 sub&& �Q �F\  M? %$9r{ $|L_1 � L� o 6� �T rian1#!v ha�� t�5at,�  A�ex $B��c �� say%�5�A�o��ce�R9n (x,BWsMb\ a] ]map:� )�� 2�Similar6�:a�8 AE \!:W6�&[ R MS�xU1~6\ R^D��� �:) m�e�5a�0 �$i�a�m�&e� bf($I $)}�=]y`s>��E�F 2Ő!1����$Xre� ed>� $a�i}|.�!�1,2.$D AE�W !�\!:a�:f��F�\!� >� VIeX)":i-υ� bi��v�&� } 2.5.6x3j�s�12, 1�/ 106-7.�$elyZ&�|9+k |6rQ��2 �:!}}LJ�O)�a�.A��`)Nba-'\!B�:n)V �he"�ye�.�t'�8act�CAZ \{|\Gamma_ !ճI�:-�E 1"#{^�OR�x r }A��$�A (%$\a^ \{\c�a.Z�| �B�� �),*�{\��m"��1&?!46�p.~A.2.1T)���$�x(a+:]mvny \cap A�V=a�<} (B O|� !z[B4-NE cap��A),��h��ver���: ^{-1�.��, �C :��A5#� 6j=6�i>�})��i llow�1�31#99wA3�k`low. ~ �}6L�6)i��pv��1 �WQ �u�\ \_a0�v i;T2�i!�!>AwH\}g^$!P�v�{v.�I86��u:[3,� dot�A]�_ �g u.rm ��Zb2H v6�J �!<�& ��"(~� Ȫ�d�|F��!b6�!b� ��z�rR� $}��dMV_�y_1A�M2%�t�-pu�@\{tR� �� .  k-MR z�3E3t)�Y�=� uv J4J��~���U�B��Vh�;�����<:���}���I�mV [0,1];�365 \!(v�ToJ�b, t�#�#$\sevenrm v�#�\@Wv�v�,Q!0|9�*}� >�k$ Se# t�%���:=\su�#a�"�!4cm{1>iq�B}2cm t_i$�\� �%$Ƕ6p6v1-6 �=�=N�5cm{ �v le j� q+��7�j�\ a:��w�w�w\ EAA��d >�*�3Id�� \! V) )�>zZ*>.]\� :u�+j��+z+jz!I:�^n>&�'�'�'�'!� maps�G�a�!� 0cm 2g (}:i�\{(f&VKb�} \��ˁ t��n }B_� ! j�΂�b��� �q�F�$} ��b�\)>2�.3~-�vQ � B�a =:��JM  E��$� N {{j/�+j| �+�+-+V�� .V)�6Eg+jda$(tx,(1-t)y�=*c=U},t)2 �� �� te{3�X(3.3)59usefulb/ en d#� g mo��exM tl�cn&&D|2 "6�P#�=US|30eLVũy�#@11} pp.\ 303-4 de�2be^���� oret#Gi����'s�5g"�)� procedurey*�*"c!7 24},Et\S;5atDef*�(}"��!Y"2PF($. {N.B.} le!N�!@ ak>M=��se2�%x��ugmen%$ A):.X24��j"160"4.3.15 +!f165 �1�D\!$+2x2>�{/bn�ue�"�-� ���Eva��",&2}�meq/3at{Q!�PR..�Ks�` �:xfJ �(�{�)�Q �pa��}T��: �Fe�R"K�.[%�:" t�WW=l2W�U�[2F>�1�� 5:-S�2M �XI^52�/A�!5a�}��(�atQa�a�nll�<5�� M�7n.WFF,"� eN�i�A�Xie�i� of \e-Yany��mpf)� $\Xio@{"� ble}),6�209��۸.6.12. E�Ṱ�>d'!r�����#�'��\!(X);n��18:*�c�Sea�Y*e�boi/�0* �@FDD+$Qs��and?~ �2�362qN\ 4("� $j:18'*2��-*�!�t)>a� �����V��ce��tucJ'�su��mtop�:,�) $j�k?tB#*�W���e`Dc)Jat �/nM� %�R| �54:u�z.}��Ns%ua�F�39:I�>2L;i�>�.S!P18�;Y�D�P12�P\ 89, @ e��if��Top��e�:�!��1}k {:"S+\m�r{7���!|,� �?\&�Y�H�= (\!\*��9��"��� (�B�)�E:D&)2��!آ> $(�h�!2c) ��co+�de��).�;���� �0�9#�zj� ��`�} k(|�|� |�|)= ��as)� 3=:N� _SJ�M,=_cE[��un"~4�K�C205� thei 3��a.N#�(6g� theyB@.?� J]6�sOi More1,I:Y.>�1s�8�)Iu"/\!�nJ+�P+$ Z#� z��+� }�� ��� )�:u.p�&K$eL�pE���F;^yN8x\ <t��� dim ԝ� 1)= �+   R7&rm{� v $KA� /fI +1�/.2�"�5a��B��1I"um�%i�!:A0my�1h8r)V ���F����� ��T:=�� ^{{_ $!�V9A!qD�=�TJ���E�� n�)�)}B���l��� 9:c�}�c_�#��!!���[+)��J-$��>�Zw�>���ja)$ .p\gehs�)!��3\ [2%&fEB*�щ��f�E�� '{�om^� ex inMz��4�G.�U+1V1:f2}]G�"�"&��){�I9�Y?3(rm (to \S\ScSo=2:3.23h5��7���9G�8  0}�%*q8�Zs��9^��3R}�p� a�UqTi�2"�(2GVG�Q�0)=0�^e#.an�sine&"_oxU%r fS$j�� z��a�$�_{N\\1���2)1�fZI2}Ê� $��� ��R+A�לgma}+M BzML����]g a�)Bs�a�!iRĴ!q5��WAXm�f�h`F1��me�X�f�Ebd"C�6@ 1w�- {{p+q=i}\Jp,q\uCw�B �F&\ !�&�^*�f� =&= 1;DE!);�G� �f�! R�J1�q�faU%sS2}-`�L) T=J�n�)@)+�"�{�{2�a� 2$}{sY*���-9-12; ><F�C6;��u�bfa�!`l"���U,\*�_!<)PJ�2BFA�r��6T non��end.��$�I]�d1}v u�1.t�%'%�"(��}h�51s*Mh2F�!�)khV].}}wׁ'&�,&|S"�� #v v�}��v�ZE�Y  $�S}��_ a��}9�5 9 !"- *�I� �� �� �y�?egm¦mu2�a1}�:��:�E�!�9u!I 2�EIM�})�w ���K�&*Yc�Ƕv�J1�u| CL0a������G�FE�G��1 6���K!�6~.�uAA ��K.M��Q<k -��!����� fVA�e� 6.�pA�Bp2�VB�e�~y�� 1�� � U� ���H�����E� y���P )�1���{:�.� ��"� ��y"# e�����ڨR""Y� \!j!�>2��j��1�5�421���I��&n�PZ�z6�i�P 15:1�;j�2D�� �JY��l.Ep:��TP�^6^d0hO� even� �[�? ~ -G[p�F�{ L��U.],  x 7 Pmt6�2, gi:�Q=u �fo�V%�a�A�=*\�2�&r �yY !\!/�t!��YSY VS�>&�WQ��N� �<�[�er��l��M]�, so,*should,�=PK�!�m pur�CpRerm6#76PJ3is, how�x, a rat�c�"ask, m�  dumA fa�JD�.�<�g2not a� . <\!�O2$.\\ AEdy�m.$�f�s vidQ:.b,LinkBevisS88�����sIo P1�}!��  20:2"(!r� l�J�7��:jR<Eqq6 ~, . pseu�K����.�"27:III:�H�� rite�!��. �qs1��toA  ��K details o�a�Jall�.� I:jc5��, �;F)bC5{ ]Z ���9� �e*;{���q ``co���neh$fT�$\e�� 2$�;��($��#+�ў���! �� D�,q\!1$) mean>��Wiex,�= $ :$,a���!�����j��fJ~$C�U:ge �+\!2$1��%m6 fI�E�l�ad/&�w low �``=\Ra�� roug��as �`�_�#>�a�"�d�A�q�{(:eť��Nbtj*�or�G04��aAn�_{u �� G2�Cr}���-����\EN� A}� V}��Z2}�.�0� E'I'\geq0� vl:�%�"$ (i=\ ,1,2 `t�$�� D}$"� �� �"�t};� $(A����r��r�"u$ "%� �!Y$!g .G"[ - $_1)�L 0t  �0!�J�ti�}}1�2x%�"� _1� s G}_2!�&� :�&�(_o NF��\��:01}2�[���7(>whe� ��.��ma��:=$@q\�1)$�._=S^�"� &N-�%?A�~_ir1n5K�-i}H6BR@ge2eqen�jW$_2)$>F� vG.N>�^&2$2}} ��_\^B��A�� �\�Kw� %@IEo.���nnH�}�ZpifRZ�vp&� 9y� ����6� $_{v_i+1�R�yA&Q�V+ %� e"�\sixrΏc �06�}t%�� ����v�z3a� })E�trrF�"p:�]Pc!,R�@Z�"y"� \!^oeV��Z��a\+ �~n�$ `_0�k� ��I�Z�Z��Z�ifqC "Al\!U��rM3.M�B��iC^O9�oF5�i}&�#*�"^F-i�)��)D!O>��W.Na��B�9Te�4�ID$��_�a(!�5*1}�Fi%"m\!"K{2b �CVy} "��V*f1�2)V+qa��zRW2 ��!� 0�.1&.!�>E{(FA �� $oJ�mV_{ })Q.^>� �9_\��.22� .��)u�EGAC-�eU�%.+KN*U 2NA(*@*$J�&�,�&2�'|{r 2c�H* 2}|� ^�eta�VMJ,t�N�\i�\s]� ef�"G~s).qK~� ��B�4<geni*�pior�#�#&v �&d\�"� �#�� !ned dealx��P D $�3i=�tm8\!\sigma}}}\!\!�\!=\!0$. By Prop.~1 p.~\pageref{PropP15:1} and Eq.~\�LocalTop} above, all non-primed, resp. p �Litems are equivalent among themselves. {\bf D$\!_1$} $\Leftrightarrow$ {\bf ^{\ \! \r@}$} by Corollary �,CorP19:ToTh6�X since $\hbox{\rm Tor}_P(mathbf{A}}(�G}_{1}, �2})=0$.\\ For joins of finite complexes, this is done explicitly in \cite{12} p.~172. \end{proof} \vfill\break \normalbaselines %%%%%%%�: ||subsection{Connectedness for sim�al�<} \label{SubSec:26�C} $$\phantom{.}$$ \vskip-0.8cm Any $\Sigma$ is representable as $ ,= \bigcup\!F_{\sK ^m \in <}5, \overline *},$ wherAN8$ denotes the F0 generated by% maximal\)2 ex $ �^mav%ibegin{deECion} -IDefP20e|TwoL face!�,,\tau\!\in\! �$ef<{\it strongly c1� } if�y can bA�-��aQ�sequei%g,= {{\delta\%e0!K ,..,2i}} 2^{q.}\! = � $a5- �$with $\#(2=S\!\cap6+1}R)Ae�max)J\! I{{0\le j � \#2X^{j�$\!-_{\!}1$E� consecuti��S%X}$imposes an��ce rela!׉�!{ 2�,23 clasJ of which EIw%�B1��e�onents}B$I,�:(rm cf.\ \c��D2} p.\ 419ff.} A=I�Sa?e�said toA-2VtEU each pairvof its 5�m-! reJ�.~ _ub. 8} has exactly �Nvertex l��then somuk AO �(taining it.�b%Ii!��gNote thay.;)�1 �Hpure, i.e., ${_{^{AoA�e% \ }}} }�!�A�E�!� �A�Ri��\dim\! ] \nobreak= %�.$�K �QlemmaO��L�N!�r(T��&� cern��Im!7 propertie��4pseudomanifold�IF10MG 81 ga! a; of, valideA��(e-dimension.9.)-�\small� ��indent@A}$)$ If $d_i\!:=��$_{i}\geq0$KnQ��!�times( .2}$ is%ρqL�$e6fm6C$ and 2}$ �b bothE.)y V�<B}��E/� ^!�geq�ieEM �b�51��IU��$e �.E Any :O�� =" 9#\!$ l!�,in at most (m�) t>�VH $��n�i}Jk jl�`� i}$,�i=1,2q .\nMM%�C%�� AL >0$;�M1�DJ2J�6z<,WA6A0 F���e�}-�n"X ��a� 1} e��  82} is true alsoex$\ast$�\�Cthe sam��ada�but now &no other� tri � t9y_a�!i�,\ne\emptyseti.t�\ includes,AD0particular, h x%�B}1� � �ƽ��� �� $ \D��8etminus!^��_{o}}��4��in : \mid\ � \not! >D} �Ũ"S � a ��t} $($�^ �al��$rdered setAy �!^ pect�X $\!$�ex)4�! if,%�every�XAp�9,C � ��$hreA$a chainQ \� ^� \!,6s , ...:k�! Itauq�c��"%`1��� ERNH� teq�"� � �Zo98!i � supsb<\��� \� ]�I�n�E�\!$(cf.&� g 162.)a�aFE� \mmy � neqq12v:$ \{um� �A�\!\�$ [� �_\!$ .isR�4 \underbar{iff�9.$| w ^{}|� {{{\q�}!x- �}} *6�|J�pathwis*� .:�W� �6P=j&,>lD �no �`u�� as a:{e�"�  is *�to:7� lusual� Q � ^{}$� .[ LY1�(\!p\!)mv:=>h�amEk!�\9  #m�$le p+1\}$;!n:E.���5� 2�1�N�Yn � � ��3}��rm(� a�� 163Z 2L {1q�">.Z(:D\u>� JB A  J  .��- icesG 8 )�,��9��e$,F�..J#���śq���Zg�IFt b�2I�Q...P �2fEm F�%# !$ �2? �FCa�- ��*2i�$ 1��7dF A1V @,{\raise0.5pt�Q\e40msbm \char"72��2\2�2�(�c2+!>.)�en��BB)�ZSituA in differ)X�Z:�w Lk�n��%qA��9H�Fp (iE 0,1,�( m\!-\!1).$E quadL��"� >�4}%8Lm (A. Bj\"orner 1995�(A dir r�of ��:� 3} 9� � $��2n�4ial2�!Y lex,�assum � Lk}$A�[}})�� &T���U��|�� kluj \ \� , [*�6 �, suchw , dim%� �6 +)�-�I\!1.$ T N����R� } ^�\goodx�e {Relat9 0Combinatorics� Commuta( Algebra"� SecP21:IIG �� PD"�!�,Stanley-ReisA"rings}U 6a M \med9 cent� {---$--- W�weenaim�a!N-A�<� \� P22:II:2}�Throug!�eB��Functor below, attributes like Buchsbaum, Cohen-Macaulay!�` Gorenstein on (gra\-ded))#%os (13H10�@0MSC2000), bec� levay � in!�=�a�ica.&  (Def.~22"� :2})!�yfqZes was�tto E6gE1:1}.\no�Er\ NowK extendEdGdl/M`,ic Topology,�l ~"�>� Theorem�L P23:8}2�2 indica!�+&hom} "Zinduca ly&, zW8:IUXJ�32��$, tells u!�at��no $n$-� ($�bullet$)E�$(n-2)$2>boundary)@JmplesA�..ExP3� -#��.�H arithmetic-geometrAe ques{ : W�\ q�4$accessible�uquasi-.�s �re"_.FDefficient-modules?Ѿ2r\F�3a�I:4e�N�3�. %�,�+0firms Bredon'cjectu!�n � )384�atN]a� ${� b{Z}�P>���l���K��sobes7� have ei� AŦ, a $(-1Q\-�� $A, ],)]��\� Z� F���Y�=2!<C $sk  ��W� !E  V_' $�$� �a �non}- e�ex} (%�Ya\�W�a )ij�O $,A� s~{\b to}~ �8,\ \text{if}\ �6�$� $\dot <=\!{(\bar s)}^{(*{s})-1 �� ��$ (i�\e�$3 sB�skeleto�$ b$,� is��of ��er-v�  $)isub_ .�)$.{-(�W4 = \{ v_{i_1},�s, k}\}$�%�e $m_���m @square-free monicom� 4 :=1z H!A�!\c!Q v %9\!�i �in)�A}[IW}]"<2 �4he graded poly � a鷡J! varia�.a� bf W��!c*b  %A!"(ith unit $1� ?A}}( rm So},\)e�sA_o�=:9 Yd P� ngle � \r :=2�!/{6 I}_"� 1* Ic I��-)ideal�6�$\{m_M,��W A�to} G  _Af�e�!ue��%R}3>� ($($St-Re$)$+fQ�$ %�v?Fr� tly=�k�� eld, e.g.A*$ f �r!number� �#b{R}$ oI rYalF%Q�V�!0it>�} (�))E[t+ y}A�,a basic tool�inA�&: ,�w!upport�e usea�]� � Ng� �Vset���I)P]>$q%�minimalzil�8 trad�al�2 NIis|�"�щF�E�?�pMz=��F"� .� f�����p�I\�� !""$\tenbf(}\{�.)�6Q \}�:)E7atter.AA�W$ 69���z� leav", s ``$\��2�6! \!^o��}��=�j!?$''< .G\l��"�!!<��= <opewE~�U  �.e�ii}� showaat:@!A(! t b� ~\cong�:AA� ne\!0�>=``��The triv�&a�}''$='6 o�� \!e��"� note!bel�-hq-0.1cm�i�)">& �P� b a�<!'se<a!��P�%e��{sq�.�"+2�)��I� 1�6 A�P}]�#$ F7�$known-b�j fullN� o�nP}$}''.%� �natur��� N}:"6�N}!nameds ~in1=f exf' An�usefu� ncept���Ecostar}� fin��%r% ost} !{;�a^:=E"{9*�C� �'�b"� :�VWea �� =\mbfcupc�& bigcap}{s�� #Ag"!$��w!_i$_{9+AW�&\{sa��"+ $,�Yany# versK&_ � +%!'&ex%�$" %_aWc�%pointsdaN� �(thoseU� \ ��v� in\!d\co�edc.-�aEg. So,  !� %f! !�\i v}r"� \!!�I�va$ �}\� OJ !M�)% �Apb,characterize' !_int!~���v2�%'i�$�$� thusv embl��*$\htmladdno,link{E�cal`{http://en.wikipedia.org/$/Jacobson_2�� %� MA5moore %�� nstr�o� coll-,� pp.�@ecP34:Appendix}ff b�kip*�)�ii.:}:iiN,E�2�%.�� ��\�. T+ower0.0"4(sixrm${ {{\>${myXb�,}}$}}[+E!i VAi6y]�O (� �  \in � �P��"K�"D a�)�U})�! ise3� \ �,i"� \neq ��${a/ Qo^ �%# auA�choic� un6^2oisn'tE�G critA�M Ifw%�=��"6�jm�t0M�es}al/ & \!_oa���/2�$h桿ini}61.y>%!6�^{_{(d*�!o�)}}.C =g-\{��}N-29j#}2��B mply�4q5V *� A�0}_ � $탡:c %^B[�! �!yX� �� S�1�^�-2��-�� f��F� �I�bf��� �UCe�X2m T� z6�v���W}\�"sVaCq�A�� �6S$� v ��2D�5,2={{{{]}{J�(}}}{[}}a� �29 �Je2p�#].�1 �SoB b!�*y��N� ��A� M;"�'mid���2�\} :W��AC*� ]iRA�B k} {q����am\!} &A�A\!2\.&�] �$� aQсE�q�� � � o�*��nbf6Km/B�2J�HR. Fr�berg, 1988)�\�$ K]"�I��#2.?evenrm {r 01�1- }\!$�%vensy� "03>F42}A��n�|,} .=! A![\� }�Q# n�l(QZf72� �sland[ g\ *i�^( Gast!�$ P}}]\}%T)} $ by�D/Ex. 1\ �$�70.0(H�$(a ):=$��:�  $!$)afvFS v}�}��_ia�b\  for}\ f-�VX well!��y�aI��{�_1}\cup�"{� I�-.+�3bBf=` =Y4Lcm}("#M 2})E<H �o)�_i{:�_i}J� V ;�� b.} � _2� �4�2}}O5�1i+A�V� \!= Q Q�� �e ʁ�I�1}A�1R"2}\} )� �*��8���_1\1%� 2!� ob1a�$^7+Z4re6� (no re"�.x^4(cardinality �"�,� b�1�=1R�1-����U�se 2'.�i�ssm a di�b@6 sub^4 $(�cal J!�$!^{\circ};A4,+z:$A[W]}_+)$,1� o�ry K� Po�/Bof�of8*z )�`,��.ou��/ rs sedm�.�all��)+2�s {�S t}|no��(!v A}$�#�%��$2I};0 �$_+i%unique/geneous"S�*!�Mi�demand�"�3!p. 107.a'A#}�M"���os�i ��>nq !� $!`>�E�assign!� fu�$S�-4mo\-nomorphismaF.�1��(FO)�,nP\long&�>E� I}Y�A�A�)�m�I}a� :� n�6�3,?  .�&.7)P�&cu"{B}%J !re weak&�#5rS�="�%R* 'alist$ll�?J� a |} ({BbmE H�fX2$)�+it 6&!�(� CMap!yt�2!6��&@&�31G�?Bj)$)1�5�dRJ!�� (6�,^�&�&mGfollow�th�=�s�un6# 31} toget�5�>proof-re+cY5�=u�� as "E�e s"�n�7��oQ'F�es�c�-aWmk� Def:!9.iv!�9n�A�*��*-1n a� �10�5��dA 4rm(Schenzel) �/! Th. 8.1)}1�)b��m F��letcm�Ak}"2+eld%�=9�a &�1:�AAAi�i}� is]��$i.$:;B<�*�7� gle ccM�frak{p�is:�a�U�s 6%8&& from��vJ�+irrP)a( =�mfC�" ll }�.�%%�,\ne&f 8�} i< �#]7, >�,)�3{"hat�= H}}}w6i�Lk�$s 5;9�)=0B�v)�>�,{\alpha}\in| O|�� _0>�� 0,{V�O "I_o V B�hfill$\z $�;�Y��2�,I&.#��La�CM}mi�as�. 4.3�+r 2��F6��� (Ri-e�>��U�>��� Z�a(ƒ,i}) (MunkresR�J�>�]�!�R0Q�f�;:; ��%�core}i 4%r- H!i�}}��P0�;�����"6A��85�8[�0M"�$�$�9�Nb{Z �텵\Gamma:=�� �.$ q��& �}���+?�� {i�� �,DRD%4rm{�w , <.:" case*H:� �)r*i�A.<%c��),�b=0B=E�b=�: �B���B��� �� Z�|" �� H.=M� ��Ae R ]� *# �< _>���A��4� Ee�z]P$_1w k} J~7C-M20,-�i5 �a an o"�- 6�D out&o-!�� �E�-1���@.#<\}��b 0 vr�K\2F.� :vi^a>1�$�C�E%=�4 1,u7I �t fy� dim( ,)�0�)is"�. circle�~a>e%�Co)\ �!J �� $ \tilde8i ()e)=(-1)^{p }�!���3&# P-N2 0" �1h�0 *� � rbitr�m�0� t�2+ sp�J� $7ist!8 \ orig"SmGj"�8/D*u  {$XE}``�o bf{G}}}5'(``{CM�B, 2-$``$^ ) if�Z! f�$n$-{wh�6P�:(jR L whsp�7A� G}�)�"0�2W2�%beS( �rm � Xq�-,(^� 0.z_$g!q. In7C cula^� $2$-zrm�P{_ �%�&`=\=9.?j; � 1 \mhatH��!nU_{�: (\�%�2s"!�S"� <\ �%; �)=0�d ! \forall��9c,! i&LB�aO.~3.7ae94d� (��n}�*``A��b�A�%Z�D%�``{,Z')��d71�D� any �$ ior 4&�F= NaA+ aliz�-�a�&�4a`(exm}:��)i2 ={E�r#im1��#�!(�B� %���5!o}\!}��5� =-�0Re��"�:in��E�J38b;�%.�1M* J �,��!$� $�A&GAO o}\}$-e8 ed {�+s � $}'')��(inA3"8�(8:PointSetM� varn�9��Re��N.B�E� = ��%�B 18:Ry�4OfSimpSet} ofY�bar i3�$^{^\wp}\!(�sX}A9 ( $ provid�%a�=>� )�X)��a Nm�0ch��\ ?A`f�--r-��Ev(F,aGtriangu�=on in�4 nt. I 5���w.f�("g!��7i;*ncon�1�9&y}:X%�ak)��m*�V``a�(�"%�&\OF��"b, �1�@� 96� �%i�a� $9�? k�}����0%CM6�"*VTe""�Mo�$�+)��J�c.�"m��03} {5.3.16.(bF�229b�% ^�!�6%!�`��0# !� ``CM-8G%!F��*?& it V�.ae �}. � 6QAYjof $ Use'\�?3� 2�.e RfB464�BP20 < 5tkAGEq. �I63Eq�+Ie�oAJ�varex�� Ex:HU>VsSp6} �IJYK8topes E��%w�K FL,��dd,�I�3a�A'73B� "�-u�c�5���lh< \ co?};�J�dQ�"�}/)�A�EPs�8un{Kff}� 3{~o"�%1"�+�4--&e* 25cm,U� {H}}`&)O'I�l3R 8LQ ^ű��\fivebf[{8 \  ]}_{!�+?'}l $} D!�� �&�,� �Ile*fty�-if\ �Wi rWrC���.6��(�+�+�+N+b(��|H�<i\"� (IW� k})$; 0� XQ� A�144. u&,6~EH (!^s0Kr4}} zr0(_" VEJV�0$,�V-�f�StJSE��� ``1 +� -''{ .�0FV$4���^�J,��'$��9A�� ;   K�nneth�mula} � �:9Bal�n�mAs;� (_+%�� v7��� f > $''.&f("X"y+A�bf 1.���W$��H�.^{_\ \v�J move�W0.7cm�I2 �14&�J��(Q+�F1�9��Q�]<+o/ 0.05q^-R@!�@)2� N �*�+ V -1.0V��U,�9I$�� ��^6�,h a�C_1��-� '!�(Big[ {^!P��%� Motiv|:�1$:J� ��%A�Z2�p\�aVs2dg-RD-$*j �byJ�:{\o, bf .�Z+&��::u � _{� ]UZ,�Th�G14! Eq.~32[ 2  e�� � -E 16:i�b.�6> 6(.�} !��,)X!�$M�Ma {\rlap{$Aa�* i+j=�^$; Z; ise2���8oplus$�:0.2A�{J�i%4>�4��"Esix��^� �-0.e (Q� A��G" Q�$��1!m�!�is.2i}�}�y�F�B`�ve]�<�KaZh ���- nz-�1��2�Put�=$ \bet�N U\!(X):=q|$rm inf}\{j��� ex]& x; x2 XM d�=!_{j%�(X,X\>��! x G})\ne0\}�2��� ��!k _&\^ )� rel�P��co}< s ``depth�C�( �".�B $'� ``C-M-�B�w�R�D��t�M�j�*5/�} u7���!� n)�!cFbU Ex.\Y.2�\�0214����'_ �0 142 4 34. Se�\ TMi}< 27��<)[ F 1D�2�M,%�a\5Q"�Al!�N��/''}�l!\6�h \! [v �\i3h \,\ :\r�#Q;��G!\.TM� dA���rm!+} i\l [n� ]�\"P% b)}~�*�Z5�94r!2-��6��< ��( /��80~"�2G~�0)$|' line�; teniAj�;� �)� MandA !i\!FLEz~za�%nL H}S} (�+�.�O"_gvN.�$R �,�c�i� }�*A�� r�"� fa�^xM&S?V��.� o�%�$  ��U�r���=$ i��;%A�1�"Na��} Put�U�23:�lS�K<,${ Nx1� (�p&\[�D �*8`N[U# O[},-_p��|�[{N}պ��A�� /i�� _�_�V:�\* �.� T\!n{! &���a:`nXa!& ��E>na�a���JnA@\j�U  "�9%��#��T�Iem!�8��$�1a)7 E;�iM9``i�CA.�G � ''�F�c� R �)]�5t�Na 2-` f�&j l2n?���#�� -0���n-�0cm�,uj2�c0�qE� " =0ly!all�%�U�y%�-Vb�V VV6�NU��U�U���NFAVMN� V�aA�1���� _ ��Y�} �} ��B�/P :LO#.V0����add�or� $n$-)O$do��eff�� group� deg�$$�F n-2$� V�35:3e.J� e64#�'��m�~�X �isT"�e deducible��*�M�D215�T358-360 $ Our next�*nr�W"}$ly�1r� G}> �� )��Bly�vI1T. Hibi�6(will essent � keep'-% �3�/ough u�d x e쉙��\!�9:=� � \d�H�< # �� �H��rG; �=q+�\�m/<�> I}\} � mF�H�i��:K� R1���h�hh� ct� ^P2� \�.�"�V)\ 95-2�e-2m.�Bof&5a6� �$ �\!�D��^��0&�\UFvFI��D�88(� "� satisf�Cr5��7D 9��B�+$!�LMj(SetAM��!�ID6J���2�>� D@<��5AD�a���$ �m �f&� JeI��!5�Z#I��� � <\!n"_FOV(=\X T1w6O�!}u1 �b�'!�2��O&� �b)}�n{\pgR st�A= �T1F kiE4�9,�F�,͡ $8e�m�W:�= jF�a�� K""Ua ���o%���?�y�A>�)K2+w2 �<"' � a}) $ �AA�<.�(scriptsize$a_2c^e yf�q�"~A(I;J!N !�U_��uYK big(O Nz{j�=i�ub2�)�Ao:{� �A�big� .]��&�:� ngle��>�I� =$ ua� s U�E�A� !���r�]9�F�\]�� �i.� �)Y��!.��V$3cm��|� �tRf;& � E;P2;�>OM�)�# �A)O � %E"�S1B�H�)!(Au=&�!)����[�A&BO.aB&k %PEi}]Z�!% }�{bL�l-���'76*� `M>-2�H;!p.E�:GMJ*b/Zs!�Japbs.�andC�M!I�� � 2 ��s �&f4-��. +��3:| mk:@���7\�.leQ �"� E?b}�h$ #e A��^��: up}{A�j6�B��OR�i$b��$]��>�zF4Mu���Z�,e�$EU�o}.�$"� 2�$�#� II}+%/II�� _* :a� ��,I}ff # (a�)�I$)�����4� _ >$}}�]�3�N��l)�x+= �e"0ast.�n;.v�b*� D&�$.i,2+6�;��^.*isLQu��$:78 $�!��� .�8�lo,&^ZM.� $!$>� $(�y!�i� -�:'F� i�� ��nq�oEHs[l<(K. Baclawsk�w<.[""#)�295�beginZ2t34��QJrle��*J�jRv arroveft\{"�e �array}{l}��a})w��"�/>� ��o> /!�6�"b �/� &�!�A= n-2�@�bN����� 5 (!)C 2���3 E sixi�v�VE}"B%grm ' d'a^��VA��]�#6� "'�k _{2} � �\!V3. �@E�)�\�l�"�#�%DPDL�2bf!� Use^5r�?�� 6J�''�iL�.�z*#�?��1& �MIS&�1�%� � %@Ip� })\!$�D�1\>jds;1�kipbe .T.� Q5� A buildrel{B'eo^{1�<�R�< )�ea G}6A�!}�N � ,.��5�^�"DG}�%��%��)Ic)8g!�r6oj�i�eA�{=4�=��!o-8�R�)C :t�K.x�(�w v�u�� o.��� f�2!,I_1�~RB��H!~YR��q/ 35cm] s }$� ��LR� F��/�!� Apply���hx=5:3�<"� fja� b4Q�t�"TdFX� �A��1CI}In}}�ة���~-1-}\!),$��e�a})�l,�2��2.j�St3= { 5�"M-��F� ��m�In�OSV��!E� �� � �\!)"� AF�����v�b �q�A��.&� �e"��$.�2��Y2�~�:�e _���� �:�6^��4cz!�Z!�Z�!���=�c$�5.�Z1�N �� hFcEb()��1�6�A�Y��A�bxIG}>�%,:�3") �^x2�p^���APd�&F *, >���\!;�d��2��n9[e$2�Q�&' ! �V�_!�>_�X&�<1͋�<$}&S�lJy�uObser7�l$$P,$To turOx�CiBJ4?� �Fo�L.0>we�Ciz� m'��mA�� �;Ai9".�a ' � 1 $,a|�|6W�in�>J "�2M � ��>`�YyA��jF^A%%vi)� �F�&�3�0 &*AT&.�0 aX�i^.\(��J�A�&U%"� %� �2>� �2�2��:e���&�?���V r �z:�2��jA�B����~."+�.r�3)�J�Y c;1})͜&E "��^�1erte%`�eg^?-����A��/-\!=&�a���#~��Ns�mo��ep�$�TC� I 1}.b6+ F:  [^��ˆ�m v~� D�*5((,Q&Y.!*s/l&� )rqKin E�$]�Fv/"�:0�.J#\��! �̥|���B��R�1�I`f�[ 5�z I�� ] @()=FJ�ac�vJ�F�\!2�� � 1� ������e�N�}2a.:{�23�|2M,EQP24��g�� Jt>��YIEo(Ite�� B>�c)&L|�ot*1superflu�as far�.� ix�;��lF��Vthe��itx�omes qu��yw�+d titub25H�l6�&���!$�Fry occurr���} �$!��#A�%r$&FjE� ��q:v��,Z e&ǁ�}�UB� � _{5�@ � � W%�$E�S �ʔnA�>_�r^D wO w�kt:i��(en^�N�6 6�!�{*� ��j3��R,-z� �2�}[a� �� 1?5���H*� E^. F%�!j�|^U A� % !F� ��.� -��5cor���6�.� - B2N%3, A�F! Q�.�3�DRJ #�D{��3})��q��3�I�*y �� rem}��RvSs\ �f@ H�@F\e0Z�-T2�=�{!9i�o�6M �!ieF.ii2�> �#IG\ 6��.G9�w��۝�U::r�UL� �Y�G6R%�eZ''��t�cRw17w�os�T �Pn� ��KM�mn �0f y�not�7 0� EG�!�IN �B]MI$always tru)? $$J�*��@ n!��'&�F�(���a$�j��Z1Q�(>1��:3 2) � ���rm{�"�7b3� H,�( � b%�p8 �/)�&j �r Qv����� �/: ��A-�dimQ��|{�" JS�8 OJ�)*#�_�bI�5��"�c ^m}$�Ve�F�NG8g�S ~E��f�K6� $Rc&��� aNi5�Y������ek��)\(*��:+9hU����i����&�'>lJ�ap}��Y2a%: subWx $m$�  yz�m}@��7 /MexA�>#\"��8{�"J� �8eHES}�A)mb�b� �ymthickA��2#�9{&m\�^r)�{ſ�Vq^\!:c � 63 �}, >6,:e/Ԍ�%�x *��b� y20 [�� pA�!= 1T�Z2��� !81 X� .9<�ΡVI{;.� ���x�} a]��V �M�� ��.��6x\� Q�{_;25��`�6(FQP!$q<r Te� ��.�&}�$&ZL!�#Cc&� [\ �Dj�Q� � m!rـ (�"bigcup, -0� 0 "L�O0MC��a��V5� t>L%N��mS� �=5SB5RZ �6nX4� Z}e&�#�:t=� ��%!N ]�g._Q�6�is\ �B2 :�B�E�c"�L" �Mera-���a���s� } ]�" ˁ)l y7%�I�mOb!%� ]A�R� ���\��q� \!_m X��.�f =!�67 9F�]g9 #0V7�"�&Q va�v}}:]k9`�6a B.a�=J\%a�F��(m%�I�� -�q Yetc6!}><6Aύ�%o2"v/w(Z, 6])b => � !}},��e ��&� ;�f)�� ��)�A �$A�^�l\��{?��9�o* [ Q.X\�|-v �����E9&�q "u&�p cm�B  >�Pa}5��n�b�}��We��y�� ikD0 NFabma�H�O%�{VQ�AeF}a Ns[ N11is\C�R="� {��_Nw& �k&R/! yJ4:zl��I�R���!1����v}\g iʘI n��A�mӡBF:\� �m�=>> �>2�J6t�F&tdp�9} Each�o~&Gw two doubl>V�bkfZ%�eR�i$<2�; Gi���X5� ''};m[*5EG L� \��H/��* /i.A)ZA���� ��F�\ iMGN6F�6!Q��. e���B�ӆ(՟3�PF Rn Qn��%| =:�i �L�&�w V��!,��� � 2�4)kB-*�;�8J�5�%xL5� f� -��+��a�  (slj}}��"�S�� S��M�"�%r}� �!�!�%��A!.� J� \7e K��it��\ no\�ne\�ksV.6=�q�!�m� �ci�no &�Ecollaps��E [���i��/% iv��to,"v_r vvardef��3I&����[R5��J�!Y9�^7{ }\}]rX{>B"oXcap \.B']wp�}="�  \G7�$�%�~�\!�����B� iM-�� �z�  $.7* -/!A Permu�jKq M!�(�f�6��7$N�� N�resul {-��2�"45���R e; ��(dots,�[X;v%a\{p+�\9:Vd -e!�^{� �<�Kblf1)�])� &�S�%Z:o:uZw�>xZ: �V8 4R)�$� �-]�A�RY!Wu&�>\a&4�/46�@{{"�!:V>A�a� vA�y}�@�:w hski��#r S�/ @�8�:/a i.a��!�/AK.� � �\�3Fj$ >g!>r$-�b�'1"s@\tiny�@ �$Am_{x�&�*�bA�_p$Zeqno{�*z?e�qT!�mg"� C&Q�&�*�9:A��na���g�t[F�8)?C$k>N}' MY� k$-&�>j��Mif�*�� $T 9�VN� 2>�#T=k-1iV��P��"�m[T]� �1``ATC*�*"�E �g !�%%h�V&bN��[T]*Q \b�(=:&� �A�\!C_%�2 4 ;nd9�%�"�6I�1� \frame7�ah�L11e�Chang!f #T\!%G''�&7$ (Ite��B,c 24:9I� b} mŗsndis.���4�v�@(_Q eld,�;w�Y�;Hj�E�"�"t  Keugu 's ��;a�!�%#\�{SR|h��lhpro<>�oS>U}�L�.y�5:II:�Ry�" ve��T"2R�!���)m A}$-��s $R_�PR_�J� $R=���e,� R_1,R_2)$9V$@q%�jx�`;� .�$[R�o�d�d]_{_p}$}�� $:=�d �  [!tR_1 '{ �c��A5A}}}[R_2 a� � >���N}߱mf!N)�L�=y` 1dE�%hD�,v,�2u,%T)0})T ppe�|!� >M, ��$$ A)%���'ݎ".�lacksiV$ term, eq�0rA� r"W �D2} �``canE� al''� $J� \undj�-y �s��� ���Od��$(��arly vR.}� ly$)K7�ivWmp��multip�1�tni\6���15:YTs,}m_1^\ I �  H '�$|bigl[R_V r]_G6�&�2mEf m_2:a��OV] R_^�:%n�+(� �qJ�) (u6( 6��eR!F59�K !2>�\0�j�A:-/Ä+��ee83V�g. or-oi� sen!"ve:���_a�ar-x}u$S�wo�nk}}$-sta��dZs E-�A� p� ppo�ǡU�f�(aO�ly�� _d)�edǧ�W��Y�8?�_!G$Aq��1}\ (��1a:FXN}R�i~$6mGq�mz*����?ed-���6rql, x��l�are%xer�d$be written1���)m,|*asw crea�)��RV!uspecifi��in�D1]9N:��NX�11-;n m_{21v2)q�zWQ)2p:)k K26K$2K�E6vg�B�R��Ff := (1ar{�� � ���2�TX (2�6y�#if.``���k '' p*R,-�,q x$ c�bf�d 7-�iN7��)� ing,E}0��t. HerC.(x,y)� a��6F��x$ ,py�m ��G&A[$y�un�, �A�$hm%��#!i-�I:���reA�[ l*�NexM&� }{1&� �& P25:0((� �s+ p�39-40a�Every6�a[:� �E�-i-�c!�� !k {so}�ey� �8��%'0Hilbert serie��'"X 6�a�H� k&W �<�A�o�' ]ge 4�R�� �$� f}_{R}(t)�\sum_{i 5*dW$H}(R,i))t^#�Z+dimS~+<k}}R_i8*�y#�^�t3oit>�goM��i H �.��*u�!,�!Efun ~.� �Z� "� u{[���� G 2��� "� �ύ���� )G k}$)A$x_1,Kx_n\in[B 1JJy y_m\�G�b$��E/nEs{\> �Tm"Rs���� $(x_1�� �) �(���y_mғ $%� R_{_1T2_{_2��b6i$: R�-�W, \!+ L��d�D*z&�"%�{3�J!�-�J��x c!�seqs 0 . I��ya� Hodg"M��2Zglc��� �~i�J垁��)�s Stra�>e��0Laws} (ASLs)%�B�2Ɨ�(main issue,s�A3} \S7.:,289ާ(��16}},123�� !V\0(n �rc729�\!\xi\�4w!8�� . S u \!(v:!� , vu�2Eb�^M,�^,!}�\RV >fY\!$��E��)�frefleme@�u��e "�� � factz =A�!� *�p_\ZaAR�j) dd�o" L $i$:zS�?.�#2���$D:={vl�MKd w�!��MYQ-D\!,{{\mu2��V�F� A!�FS)sE 6S� 0�.�{#Sl[-*z�p_1���)��=to2& bigr�%E�nV!� 6S2VS���_� P�aE P{Q�_1<%A�u9mlorE})� �Abopt.�1F����&:en �I �6 BE�\1 �"!�'-$ ��cup D=3��!�"��I�! �Y�э��%���!2-|Bi`,:ProduktS-R}94��i�}if E�U��)�},��mumc _ a�R�$ '� muA�jT , se��"&}$25�1�&y$' �4H.� " �f dyeI���YA�l�dM�!()"I�{�3!z &{{nE �d-1*c:�bq2�fG��P$!q2 �indts th�>� Nh� scre�>"D ɬV� data��3)b��R ��6��I S\ 7.1��I��d ���w -M''r*��(�V j�), so�#�"�bW�EHF*�kv6��ny"P  edQL �0d# a)� n "�M��u16Vn.\ 145{��&6�c�'e� ou�ne�# �3"�ospx4F��615# jb�%*i "2]#6�� E&C-sJ4"�z�54Z54$\)%� �2�&Q �iKW�44= �,2� ^ h�5.t�e���KveF6�&=c){pv}�M text�(�I7�yV5d 65vSq�Se4$E|�"F�$($$)�*� put; .įՄ:*|*��R3:4?\{)�f�,Li| %�sc��&@A�"�&� $!:oThe�J&���ry`�G!�g�5 : �@j< (GorR= $)�\I&� ��: i}(|������|\I A���'� :���BG �\?(EjN �*0 &N� �� m�1 F#5^i !q> N\�A� fǔ� o�� �&;u �"��� �"$1ufr7$J�- ; I�E�$�%�a �8�3���f�d��} שX� Eb��p.~"�T 1�~Now"<vm aEĩ�Rq^�C{�Krmaa#�iBE�� �'� �iJ nd sB0�P �a>q# ��!=�="4P"ß)YA�arfIɋ��and���2\=�m�dA��*C �B\!�\{�<��� "�o�1+�cap�<7�2]� n4u 4d]1�eQ�A��c �>!l@ �>2�g%� 10} 77.)}�\>�G�q�4"�� � m�g/��\b]�the��$�@2:K)*�R�( e�st �s^� >ŕy��*^ j��F�1Bs,6�!N� ~p��h(%+'�%���6� V�_C unli��^U�}�- ''}$zb�/� ''�E*o�`Z�23$-���2v�&�a�in�+1�!�=0@?g|!�et(Y A�� dersk��#?����1 ,\�n\ to}} p�ex�zA�f�s;�G*��a��/�0{./!�to�Aml i�A"� �� &�a�&��SN�$ 6>�22�xf "�80!R@z)?a~r����(orm of matr�,3~�;�"� �\!h"�D�\0U}?%Iximal"�cc ?a�iA'�$1i},��6cI�tQC*lk�eSat6�m��6Ipd@up���*0ɫin ��x�c�+cN)���-6($J�_fOge1$) 1Jt Qthi�wV6 4�s2�:���!erved �"O%�I �$have at le�(B Y �toIi%n�oL(AU*! 2ad�K��D>XE.ii6��B!��Bd(�$�.A2Y ���u2}}))&i0�orA1E{� C�P$�)s m��9s �"[ru� �"� a�b�� �@(\��1>���8S�.U� ���%�>��k!�2�]��wo &= ; ��$"��".I%h� \!1\K�1,)V a2<�Q?#their2E$V_�� 2�:vem~them>�Y52� rmaQ6�R�<.�1ڄ$.�N�M oth\ T_.��\ � ��ɤco 8=  p or $ II} hold�#$�(*�\(I&ۙA��.�$ �::�a),��"�%V�\"r�e�&� *�1(II�X6�,6�\ �Am.�� ��� �!6!�# (Dmale�v��a�� �*� "�*g :X�O��&o!Mk�Z * � a�ٔ3-"'6��&�OE,���� � mk"KG{!_HT ��s(:� A> �f� �2[�|���c �p���Ei`�Ba a�F%BE�M��3 $3&u� . Puu&�:= ��;.C� m�)��0 3d�%Dx~!1��A�no tor�/�5ɴ P28:1.iTc�j"�6" 9�care' du��A� E 3оp.~244 "_~45 P�hatwW| � 5 A !\)$e T} �1�uJ T}$cu :A � -sub%� %��So�=1��ak?>� �16`p�� say, �t]�&e. s|)�(p&�&�yYa+�Q�. m�J 6�*�aac"~�al�����oAebP�L��B��!2���ve��,MLRP}}^3��< lens(�L}(n,k)A941\�T2H6�� ZzME��+� Hbfi�En�O2Jb ��L;��X)a�ʉA�,m � &�s�[�� �ށb�$,�\ne2$ ��: n$) ����� ��]*�n]=[{(.�f6haz =n$).�#��ͧ31-243Xdetail�BA-�)��H%�5�U q�n����65+ �"M 75k�l&�3cX(AB%8$�I!�%-[% l shellab·o�if it we���$ would� be& CM� �Z�� �VJ�>B�5 deed�(1958 M.E. R�� publish�aZ ) 29};�04 An un�:2*a�&�, tetrahedron�� Ot��c04u�(Jeff Weeks'�&u�5prograqU0SnapPea'' hos�at�3F�ht3�g��ygames4� C/}�#��.��!�!��"�"D���_9e^3* �i`�g8!�\!(5,1:u� .<&� 5} a�� old tutor�:-L!p �, G*�4 "l��� �9F� f6� ,$ �3y Dehn surg�+&k�/�za�h$��!$� gu.��'�mp�� /��omo�G sm kernel*�by %*��y�l>� ���fis!R��iL�� f��6k}f�5$ a^��� ��Ae�6<i�k}=\!5��� � \��{S� � m��C� ':��27:�wn R&�{�i�s� N#:�7T:1} ">Zno:��W��l�kR�t�vU�E��UR� Pv�TAI!expX8��&�!�< topological spa�ce will be called a {\it $n$-pseudomanifold} or a quasi-% if it canN�triangulated into a simplicial complex that isnwresp. ! Jz. �\begin{vardef}{\bf $\!\!$1.} \label{DefP27:1} An�,dimensional 6� �lo!y finite3 �@ ${\Sigma}$ such�d;\hfill\break ($\alpha$) .pis pure,\ \ i.e. the maximal1*es in.6are all��.\\!�hbf($\beta$)} Every $(n-1)$-%{ex of.Oisv face,at most twoc6 ices.a gammb8If $s$ and $s'$�A66�, thereva1Mxsequence $s=s_0,s_1,\ldots s_m=W of jW9xD $s_i\cap s_{i+1}$kn >4for $0\le i@;{\mathbf{G}})=0$ecall!u`\!\in\!-�(, s.a. dim$D<\!n-1~(\equiv\dimq r^{=}�(\!\geq\!1$)e�(\smallskip F� with�Mect to)� G}}, deno��$ sBd ��!'E�,$ of aJ  q3,1�set!�5� {ja_ \!:=\!\{1%5  \ \mid\ )�_{n}( ,-�rm�Yst �R}} K>�\}$}, w��E�GebXa unital module over aa�0mutative ring 4Aa(Accordto ́��De�2ion 1 �&2,�o��re no o� $0$"E���J\bullet�] _{\!} $, dueq�7presen�$(����)�Dex $\emptyset_o$.)N& *GA}{$6B NoteC_%he@(��)��PLongleftrightarrow\!$a vert = :B�-act. �hX=| +|',a homo\-logyi�!\!Mfivebf Re(in9` (hmv4) w �� �a�n~?H. Now, by Theorem �h P14:56j2;q�YvtG���anyI� R}-$E/E�PID}$\��I�}0  GA� 29�&L\cite{30}\ p.\ 207-8 Z+� \ 27treatA�> ��uR}=}G�J b{Z}}:=\{-�rmE�(integers}\}>) AI�, E I�-�is%�� ^� !$�$\ \!.?.!�!Wa�nE$s deleted,�\ now $n\!=�� �$.$ From a�$ly technicW oin� viewA^@really don't need! ``mBmA0ness''-assump�J , as! seen��M=��,CorP16:ToTh6!���2E e� \no� VE $3BC $3} Let `` '' st��A� -,�+ ore�a� 1�no� A%�ac} #,��A@!HS}�^<{\it orientable��{^�': A e& \!\ { if}A��I\!��{n$(�� m,{A�Bd}.6J\tilde = "A \ �!�� ��Iy�\!E�� its2#sub`s% ]�D!-< else� it non-#64� �<~G O-eilityǡ� und��ed%��V2QZ� \goodM[ ]]Ex�[2YZ�[� Fo classeD��A=��-s�W�$UW $X\!\n �1 {t ��� %�EZCX=� $��j- ;A(F��wp}(X) @�{Xů��9�)y�h�z !$ $\{\wp�%�.!�;Q only�}Q: �  $��wp��\e*(\0 !}5i1^{o!w}).�%�n .�A �K49�D�4q - }_{{M� G},j}^�  �# j\inLI}}$ isiY�q trt�� �% onent. w�Ug2�m"� .�J�{-k"�F�Aw��� i h�f�G&? ��%,0:�p�� $(\R"e %#%M.b,j}9PE�T ��i.� a \a�rbar{ �}�n� bf cj�� then��4 Lk} !�=_.� �� =.-bf�j} �A�&� :iARIhٰE}�Sݭ�S���� , \{2],l 0$28 !�lexes ? ei� oneŘil=or6.{� � � A�e�q�*"� s $\le0$,�!th��|$1�Ls$|m_ e/in , $1$-circles;P(half)lines, while [&$�"� 2^]/ F�  [)� 7��I�b� �U2&o ].$\ $A�.I/ 1}.�< is paraphrased�``D��0qL� m�}''� -h$�esh oughN>,�*5��"�9�. A9 also��(bf S}^{-1} � .��W�KofATball,�$�e doubl���G0sp�2�. Botge� *��6�I��P�O hasT preferr� ��� 6+ iw\subsec� 4{Auxiliaries} m <:SubSecP28:III:2"�>X�;l�����8� M�n:�"�; Pf ( i"�T.i} rm $($cf.&   6 Ex.I $bf E}2.$)$�.x$U �\!(i4"H B e3)��:F��J-1�L$ has[tor� , or!K�I �0EE �R�D�a�$isomorphic�$.�_2A �.�B�V�!ĕE&�� ���}< F�T .` ? @%�AEſTor}_1} �� $\biglR _2, G�A�igr)=.�So���v�is�� &�6N{2R.�FRZS)T ^( ^�S }};< �% ) � .\ 6{2}\!)$�n2�$({��}* -&{.�ޅ��.M;  proo� �B!Rndi���mr�m=De���2m =$, a possi��reln-cycW C�np * 64 � Ii-5._� e0$\cong$}} }} q~r}; .�\otimesr.v:����$�8.u � {$��� big[q7-���!� {_{^{2!�,big] \oplus�hrm�^{=O_1\!� big(�!� -\!1J!�+), 2�� �) 1 ���,)t2����� �f{m@!7 ��aH$ ����2� ���}-b*������2�A�����U�2�), M� A� *� !�2�� � reH last"e�� eacht mulad"�� ,25 Cor.\ 11,�%� tituKi�" � . S7!JS" _ � A�a�Vv� )%bf  ��& 1}�����3 2  } ...)H� rm s }} $|, { Structure�g}!> F�%ly Ge�#M�s�� 9;J 9"w, �&(e check, us B�01 Example\ 4,�e i��#�� t byBH44!�ollar�2� ~`�� i} �'ew"7 A� Propos1 �P22:16e toge-� FB15RB )V next�#�! �� � >$D �F�2���"� . q"�2fiRH�E� D&� ^{\ !\not\w!(:a �R$ 2� �� $\ �k ky�� B�)-S����)@VA�@*Xif�i0 ``Bbmo\!� f{ G�#� }'')�f11 $ {and���5� 1 f!�{n:- e-�\#���}}�SSZ S\e� bf(}�$� _{{� ?m;"� ZR)}\!=E 0\  {or� �G}�!\forall� d:#not\$e#��\!�!�h�'\squarec$ #qcix � �F)0. makes perf��# e ev�or��i) sets lik�Gk*"� etmin� Delta$ (B�2R�2 ca( ususaz)�*$ j� 1.5Q#)�4msbm\char"72}} ~zor�8�2�&I'}�it� :$et}) depen1%on�� ther�wﮅa#A� _{\ A� [)s���K��#��)qT"� �%!c�. F�:XMe%�is #(alent to�:-:�n�}T�$�e"�,of"mBL*36�f0����C �U�:v, &v12� 165�\ 4 \& 5���Q m%Xfc"(��' ���N�EO%�Z�$�an4 N\ne�^o$.��:��^��F|�6�Wx$i�a {p��$fi�!at%fend!_B43:S�Sk�$on��l' S4 etI� %j$W�$L{\hatH}S}�*�z=, 1$&@%=n$%d�1\/0\&]��Y( �, ���?)1&r***� .�� � x"^"4"0S5rm(9"�F-��. 166 . Th? B1�/ 2{'2)}  -s"a!��>e \:di-"`f:�:Re��Cd4. 6#A �� "* )R&7�&� !W � \mmyh neqq{3"� ��2� �8�*+�� n� -5|)] ��"�  ]! � AWF/ �3Hobviousl�,B+ �*� cb� �F4%64�inj%ve c " �Sj1 �z!; `M )$. �$�azendU�� "k �!�rQ tau\&% � � % .= F{ \�F!��F:� sp� >��~���0٫ �\�6.�/ �/&2 � }\! �� \!�$2� b}5�n��"� �z#-=c� �4:4129�])&(k#| ��inF<�~. �4I�E0" �!�7 MR(�+"/8"� $E�a" �.aER+ 1�U)�!� v8!��6>� �btau6`� i9+mqfE���y z�%�F`E:&5YA bf bFYA�$�<�4\��_o� 6��3y{� � A%�� \q  .k�T6� J1.vg_2wrm % a�_!7u 5�m� a�F� =*L.�MPN�B�:� �R�!�3}���&:9�3!��s�5-�z ��6� =�-��� �:5�Int}(�)2<ny $ \in�|t$!(Cf%A�of�T.A^ quad����CF vaL/*8B-� !Fbf a}�.Zabove,"Xt�%� "^&^?<bu""@��� f bFla^]*��E�5``�;ary'', ijB.�� M�9�^U��e\!? 6�\!�a8oinBd16:}wsoRc,_.-1|.� A$����c "X&'.�P6� =0,$�8. iM6+ =�� !6�bq 6M%2 &V2� $ +k'fA* ��@AQ��LHS�Also re�;�mQ�O m y# &�.�U�>!&E%�!�}$�O$\#! IA�g�62TSB{0 � )�� � �&Q�,A.bfcupc()cup}{jEe�c�3E� \!{j? :�(0x e�.$Bxw2Z{iag}bW,�r rm (�X2>�:q<�46M}L\!,%q j}}}T  Ba�H�fr/C*�54B�27:4}).})iM3.| Bi&�6Y!f�1>4�1B�u� �"� 2�(>>e����7 M![OOequals52�� mrx u�m)ŗ}Pb`1=a��`�5:x�$��A��Q���z .� $for\ some}�<�6;i 5Z"�rm�7"~5 al}\�6b An:F%v vice�5sa&� �Ile��R)^4 A� \![K� D !n] *�7<[[6�B� �f.VB�� E� ]�� nd [ HBd,#%;!3H !�INa�b]]=�k#�* &m�z�� $2s \-�E.,eL�tS &�&�"<## ons�f%)�ook%��"\!� ��AaVr*&ism�bZ. � �q^"�ѭ{B?=9ŀ�#e�!�%{1�L\!��:!2!�#yFi %j"l2LA�$�#9)8BD �s1M`��&�6�'and_: �$$ Gorenstek1xt9 $ ;V�5I>3 :Uj 9:11��6��aV!.i a3(R�8, �:f632.&Ky�$�G2 eld ��f{k��40��&�Z 6 :�$\-�}!�F��F_1zC&� �L�*�# )���$3:�� ���"�."� �?=0 E��~� 0*5&~2�.i' .�:F&H@%2e�a n &�:.� ��� :0N9e$)9\�$E��A�{\!{0i= ({ ���B�!� �0}'5h[=�u?�U"�*5g� CM}$ 3 T�' \!$-*�;�61 �(n-\#)�)9"< &d%> mUH f@�A��L �1��kii01�� �`:�3 \ U�M]{6�X ���$� A� O k6��#Lk-d : �)�=A}r-�? .Trm{�@�$.�f,) t�text{F3 s�@�,!0*A_:�$Ahe<�1Ua(�BdV ]��r =\) �LU m else�  9�5�!B, !� {6�6�\Z]�1�! ��)9I>�PA"(9b <,$ o7ingv%�&�C!�����/ �9U�; �  A�'-t$ firm7ur�Dims�$ %�\leq1$ %�>\ 32� |7:3!h��6/HTdi�H"2� notb/�'�#�-/m�Q\2��AX�aP\BH!�@ef��� (Ez@Lk}�.�%�� :�)$.1�"��HZH-�a.!�!(\!\Lef� $)c a"rL.�$�j���!�s"�,0��x%i�*'c�: 2DN6m(7� � �QFN``linksAaNll=���}f 2$\g`*z*s.� $J� 9X}�$.pD$)t)W0ionh�2��- )02}C� ��A$��e"��BEq�?I�~"�R EqP34:I} & necessar.ZBoK�()M��'$�}� � �(� "�(46s� (vY]�M�bA�I2l8�/i}.�!  ii} y � .�0\}N�0z�0AW Eq.~~ZBr�L~9]%N��Pur�L = �perty"��[�{�Fi >�a|��3���$ : . Pu�#n:�M�zNowK ($\varepsiloN�S"�Bd� !$�� - (":>�&�w&� \! 0�*!9 hatH"T#6$���/ \�6"��1\#}�v p3cm���9�Q&VN��7"��9S6mRB�"ig[�)jspace 2.7p�s/rmM�bf^�� _{ v!� [ J �N*u(�$/:�6�4r�"b5j(I�Q�)6v4�% bf (�� �1x&g-_ ZT2gan )�&� 9�.�N�e<�=So��+e�6>i [ �:Kma�� Bd��2�i9\L2M2r !2Pgh-�NJ�9^�,b! �a�}� 9�.�N!����\� ca.��m3"� n�[�=/Ig�L!�~�!ƭ�.d4E�]E�� R�A� H ($*9� ZA�[�?R��h}x! :& y.a}}C �^{$(��3)$} AllR�"� ,+ept"����:��Ac "B�L9e1�D�&"n&� $)h aID&JR &vpu �PU�U�L ? "�@$ @� y�+�$aIa�eF2���Aa 8 |K"$+Kpolytop�H�:u=�;%�^�"�[� ! !  �,A*�e�Z�E�]�V 26e(\ 427-42g;,Consistency � *�6 V J�]byA[i J�*,�$omQ ������*4� <>����2�� 6?:=�6� g)6G �"". Z�U�U> U} RF U0A��g!",DJeE�"MZ�%6�3 E.g.A��-�.���.�(.�c A�bar� �A�Ő^2)Wan0H&W:U if�WL %��.% rm{q�}is2�X�Lkf� by�: eore>�TŅZ"H31:12} below. More!4!<[ !}N��"\�.^ 2/6h ZgV$ P�H%2�#z�F�9-/ ����� 5&Jzbel^ 3D:7�+ny-�$.�\��a��TNR-G..cente �$ ;��Na�3g t`a\!} nA/% A2} 6� \rU="yT`&BqA .sm !S9:)Q-U~Check $@ le\! 1���T%ɚ#g#2$. I V=%�a|�ab !�5==�-2�!F!,i['� Vi$xO�)MP� ! �XN seɉ�-�i��  0 �Z 0�{ ��z�=$vj% �9�u!�WII�^,E\}  �w,��B�/�d� ii��$�I�I �.�8�oFt1�B8K) {\B6F0criptsize$\rmR�M�Y�)�$�\B!�isnTʹ bf .�Cb �j}}� &Y &�V �'(a �V or)[k�d.AwB�I=Q *W  or})\�, . d �4,8cm Contradi�N� end��-D�d�/by a`� 9Nea P�a?N� � rm �A�,��g��M/� 0h}}$?n�gD`�ObP $ 4rm <�! -,?B�;.�\-3c"�VV&�V;�C"t���A��C1&�6AQ&&Y}$��a� � �%f�)6���w {!�r\!�% b�%���m))�B� �Puԭz�Ҙ�q !"\d2$ }.ii�."3�3:R�(Ņ:�&30k}>&5R��A�isz!�2��'>"UX-18:j.$ek\*�R�IR�K>x&:^$*& \sixa��M���!�^���� $-1\!\QJi}e� \! <8,"��kr�& $i+��I}�) ,> ��P)d�6�)1O u��Q6� aq=- rm 0�,In particula� e9V��ss:U �3.�\!�ҡ�.A)*�-2i1I�I��U�U^UeZ !�.Pm :H\+mEb�*b*�k E��%<�_�#�Q.�"�"%�R�!�a�-0.��;�[ I)'�l�?_{2},6�^{MB�;r�ne D.%!�(Nu1}\ ii2'�*})-"�*2�l�X3&�?E �c�� �Xe( _" ix� ��d %�B3�YA� WA%���Xfb�sf �F�G )�/���*�6�[ s�rm /=���l! A�+� Ҕ� ��2�2 �V�����R�� xn�LNr~�Lc*n9��!R�A*�%0$*!c>!a}qU��L�LJ� &��+ 1�evJ v*�#^^�J{ � +.� &%�!*�\2�\:}�$, �U"�72g�h��*J  �H"T1&�62� \!!��~,  !ځ3&p � 3 eqq��=�c�o1z�.0R.^�3,�N6H+1)$>td� out5 - V��Q-Vbf J�v�?N�^�%��}���n 1��2\!:�],0��J3{�*� �6�B�!��xD��8=� � %�.�� N:(Zn X vJh vg ���E��k�rm{3 E<= A�j@�V�!v?AN!b&<� b^=a�eqNi�� � [\!!\��>X.�f��% W%,Z�$E� } {6�o6d "S^"ZdE$&@� .��ft!��4^]�!�&�7be�  =\!n\��., j�EPI},� ��m%! ��a�aU\!>�OEV�]Aw H � ��� �� ":�S 57�$!�eX ^h@�U�^ ! Q(by�(1:� i}+��V(.7P*�  i(Bv'G26T  �*�_� "40.�.�� 12F* a�Eف]2��n%���RBi� 2�)!� {*�;_s�Wrm{, E# �Nrm*�4�&�B�"�WA�!�>N!�W~.n�r��+�=�+^��$XH #1�2P }\!)��$normalbase��C�"�"�^2+i!V$VA�<�-\�<�;�E�],.E[ 2:nd�:ity�-%a6�nD�5�"Y8�G on-a�Z in;"��������%"��{{nE$�I�!O�&nQESQ]&� cup(�8>YZ1>86�( �2!#.� "�a$9D�� � ���>�"�f��Q6�"P�+�:u� ;Iag�5"�aA%sj2� l:��0a�7if�44�E}}\in e�B� n � n%#!�!> _{\�%Rv8&�<"m?H��F.$�aN�.J�"�%�.�`3A true�dim�9���� sume-z"�=sDs!w� \!}- 1[ ���� "1h0Iby:�X9H> $ so�s�1 remain�N�%�\�{�U 6� !Ni� �05V�Fa�\6� (\!��M�^7�(+A̖5��nd�D� �i : A��8? M�� I��A� !2�W"  ��3&5B #" I$� 2� rJ��%qD.-{ �!�TqE� 2 �)�b�Z�a�89 A�!� � m�w3 !�=)��3 indu��"~�" r.h.A|/�A>�tRJ3C$��^�V�B�m��� Use �6 ~1.{�>i�j,Y ��c���$��e��fa˄hat; [�-�mu��,a+_&�JN]F10�0��!�� !�}+-E��n�Ua�6{6�F�@!P��$M��BAA��TE��_ �a�P N ��d bf�a���}}=-�]7f�4��R�)�v� ���&=e!�� ;'.~!��<%A�7_F !a�`%��mA�C� &� �"� �rr#�"O~Lks�;"%{>E �_{n-1}(��6(R bf 0�bymc2y uXaVF�)?B�!�:4!���ʩ�@&�6����A�I�\!�A�l �&�fYexist" B�>6h��*I�@7��EcZ�G 9]�2}�Q; \8.��Z= .k a��� 1,\ s,t�|  #&�*�\�8�! scapi��Mpng1,2!~� �*.8 "K  �["�2I[.z^ 3cm �Lrace{�u!%�$ NBdU>�Ec�i:&��� *g �� bf{L`!},��J>�K�cT_{=��0�@�grm$ �}"' alreasons. \v��\move�%0%D��)(�e$:�_$8��K" �156G}F5� 2cm=!%$ 1%by�3zRG. �n2�\ 2�h(2]s>ofs6�J+%��g!a . z(k � - ��G}$R$3$! � �9-0.5cm:d�X"R�� 6�4�2�J^{U*��o� ^� -}G\!(�0 � >�q����^�.f=Q�+�4;"� "�+ �5q�-}mF( nal]em�}� ]=)I) E kb!%E)́$�2��6h�26X  I�a�>trunc�:"[HSBMf���9 $. ��:��Uf�� )" choNU� bf L5%irrelev��by�qB�  �!.�e�fq$�� �j�i � E8.�i~��5�6~ k�)��!�,r&��"�D . O�kwis\ �&*p#� iId} r�a� 1�.�� we� donev�OZ3�v6�QU(v.���3f�)����R5 k #� �� �\niAp}"�1\ina�f� M5-5U��i, '.tWR | � B40��$Y-! \!{n �Z.P1�f2r\8p v� !N ��K ����"~�!6� JPO ot= 0�-\� F�^�"�J����%��)5n &BŘ��"eYp!�Zn�� �"�F� @� � 21m�I"6l >N#� �qe��br� �A���� �\!���!AF�0 eE��qjVf)2BdRQ�b�B=@8;^�%"�*e�)��!mMH)n *9 � �%j�=B��Y"� 9����.be�p_F�a�L#� �:� �Aa yI�&�N -3\g�bIz��)�A~)��O�O>� �0Z������Bt� {\t29A�A}64V���!� \&� !�VT  }�`>�6.� :l �g]A~=�4�F�����.��w6w�e�7=����\��� rm by.C6&} �)! ����� n="� (�^�{�>rJ� ��45�����N�2 �A��5�9F� a�� �^� ��� ~� �9phantom�b���������i%�v�a�aza2 i�6aE_0��ar{6&;K?(-I�!:ŋ�)\!N� x*� >to��݁Jx������a��:ZaXr� %�4 ��3 )�7  "�g)�&e�I�����؀!&� ��\%�c�F��?6g%-�Ec.�=�d.<su�� s matters�-.#pro8�cG36C�k\ 17\ 225.)"im��_�, q5�/I�\T2hB4+A~�n����sp 1k(I*>Eeq;2kV:%�ATz� j`$� 97)�"2� �Z�Ez**.WZ:�?.L�Fv o!&!{P)� �joi!�*I�8s"=S��31��II$$�.}b@v�8:�q0nexq{�F�pen� $mytinynablRK�Uthrough'��r rpre��a�$��m word*^�(s)''��2(�/G.1x� emporaril�I9�Y�*,.k,o\J7�b�] 6!P������llv�ast$ le%R�e�r�H�&�H�%ٶ�2}``�@"�L%" (``�21�, Ȇ\ ��t4.2\ pv_171iU-}2L�W�~%=�W*�|ELEYThT0�} )��&ivցif�O!hmj1}�V 2!j/!�.�4 .\�O6F�e2}4�(BB2-4X��eir�E�`��fUw��be�UlyF�2�I��$\]U=0��]I=M��,1R,AS. O͞6�n3iT��~.k�h��&�*>v�J�. Yj dis��ng off�`"�te�[by�� E�a� f{ka`sJo,�essenti� back�,well known /7s��v2�inace�0Ms~107M�0�� 82 (iqs)%kYncߥ1.�171K$``Satz'' (E��6isa dI�\JB "6cm:�_ PB1$V}DQm^�>�/��$!�n$;���&��/<n;`1.95P1}.v [��/a�5_(!+n�;\!+Q�)�e�P}GNIu2iHs�F$�Ji�&BaB6B�2u%"�$ (��i4 g)="G�7� � �;v{Else;t�ː �6�. )= (Br��1�}�� 2})&..b6`-FT2})).Qz�3%�If\`� \ side\ o-F� .1\ holdsE7]6�.�A\"�&l609k. ���6�-1}, �8W,�>��JV� �mF� % 641�2(R�)A��i P2�� s}.]�39p 0�n.;{ b�\!=�[E1 yQ��oRy1OwFy +��:�"�N*%$ ]oB̍s�2�( ,2�l%F P17:7672,�} rest, but��stv�adp� semi��binator1{ -���Sn2f2)} [{>�$;�0$] P�U6%]� #��=vU�*�D2}}O1}�L_2}$."�   inva�c�UlDj�A "�Twi�al rm +u�.�r �%."N io�e� r r4.�9�?/at� �;los� g%�74�2�����o study^ sces� $c"S A}n  (x(2��U 19:c *�n%�v2=!z E�(- e��H�&%�H>!`k \!=:1� vJA\!+. 7��Rgs p5M�62�S�j.1.a p. "�a 0#?,n�OZ ra�7� :�,'�{"VQ\.�BdH�{ }}*U�\k�2Y��B!}�}*J�.?{SA�0��R�� -�\C���!�.� F��E$}'' "�W%�"�)��19:^#�Ucch,����c�wt� �t���,�&�,10�2�,O7wXf �%�1��/"!~\�_-}v�J�"hr/!�X�,!�wqe���%�3%�; .�� �z^&$]]����$�Xq�$}� ��K-n)��.�W 3cm\�� �>�k}� : -u - �1!��'J�v%"�11�Y3QB��� o{n-�� �E #1*�I-���6702�2�� �� %��n��4F�2F�EF@0.9cm\diamondsuitA\2. �` >� .{Rw,�r>= ) 3 ri�3o�\-m> � ���9"�y ��<ȿK n� *� [{ �-;JI �] �4�ha�k���cfTc� Z�m`F�5$$)��P2�\� .W $array}{llr �=��bfVg 3)*M;m(A�V2:5^�0Ÿ�H))=$}��?:�</^�a\�-Motiva��:x&"n0 g i��.aU]?�A��Gb�"RRf�!) -R2�^up�vB5< 1Rn  �!,^7Xc=2 A*Ժ2?s"},3� pair-*�l.\ � 1:PairDefB }�]�'�5g=2du,}�>f� �%� /�:}2U%�� "B,@>�.Z /� �i.\�$ֆ$e� 3k1(�2pl1� (7.�h6�aEq3�� :"& �o�}*&W^In� � "��cV��/ �.2Y E�: � a}�! *! Ryf b H6 �%� D:L  (!}u&)9�investig�.�]HA���u��M�e �YvE1n :W �e���` �` Z` F�Rv` �&v` _ �� n� bG �U �U �!U -����x�%2��W �W �W !�\,&*L"hI6dM0.4cm5�lub� {6��"�4��$II!�1�z�&*%=\��l(�)E&�=V=���B� r� �����R� E ) ,�����9�1�3.01���f�B�Q was"N H_"�-�1� utVDp߯to�k� arbitrar$�"b�Dk "&L"  : �to � �"�* �:F.3% llows. ���d��2iv}.iii2� . 3���^V�v#Έ!8� a�C �, t8�choos /J� to b�Isa�� f�(>,-2������ 2v�#� 9ta.�4J�7n,:!"�\!1iM:�! �u dn&� \\�B C�=&�k36 3.3)y��59) !� be embedd?�!m!�)�two-$f�xb%-�&��,I m��1�v��a%nE�tx%h^���tensy S}j-c{  !>7B2)O�AC�>p)Sl� uz6�r� A{(�det3F� 4:3<bf�" [ f� �bA �&� +�qx}{���i�P32�~*�[I�~Y cal{C# �ntwo2�cyl� l"k�124G���-&# at _$ X:o&-NA�!�H�F two\�esu8"w ‡�s4*# o\!\}.$ B�bV�*lD���[)Sm� %zD%C&)$5=�%8 1M} AR2\} O�h�}5&�)��|=�as<*`3C@3EPR�=� 3!�- X�iz�W�3a pinch��0rus (or inwar��Yp*@ B>� ryCylCone�:�  2B�r�not� 6O �item[D2.7t>�od$Cut, twist�Mglu�fong�jcuڤ tur��Q�:J<L&_�$M�bius ba���cal ME�72b��O�.� 3)�$�bh &�  R''�$5̞q(K-� MeKJ�>th- }1>z!(.��Mai:�]��� X}A��u�a\ ѿ disk�&�Lhd�Ewell-�$re��#�oϥ!:A�����v�|an�5%bb{RP}^ 6j*���|'Z}_��s4p���U�*�&�}5�C>)j*Y$if !� bf p2p�N%3�* .~36M��� 6:= {\it nb-number�W�duls�p}}�of  $acteristic)p�!���nQA5)5}^Z� Sf�  ��N7 )fQ�:'N� ����B�.��6$�7co߂A�� �*Jm\��ALy� elem�!�.�"c"v�sum!= IQ5�8;2b �38ff +��� \ 36!� Leav�_m�bb>O'�l� pty���-{RP%|2)X=��.VL+Let��BlQJa��� ``unaS^ic ific> c��ies''��)!���&_>U`{Ս��u,��))`E���^T��.2�1uS3(\! '���3�Frm{So,`$&�YVSZ�B�6� j�� 2c��M}#�JO �/!8K3=8R�1a�a+>l2l5a��KA�i��� �6}1k%��5A����$4*�(a�$ Is�n =]���!&! :^ V]2���i.���)���}+="6 L3 -Ӷ�-�!5�%I R"�1\��$"=�e� ?��$}�R��}$=w.�{.!\}$?�]� &x 3Vx ���0���L�:4$�2|  %e 2-,��. 42z R�/���%œ)� �&5"ڦ�Frme! A�!,rm� !L� wM#1�.?Ta�a4Q3��w4A-\wNu 2��  b� e*2�6�2� 6 M���\{>�}��>7[ �.� &J _k�� 2�a��45 u > -��D� �,2Z &!�*��pAneq\!2,t� 9�n"@AM!�as�"�? � �> ,\ N� =\!2�xa�2��"�u $(�������.4k l/ di����·7 R�63�{.Bo1�!~���i\��� 4Er�&&RW!�хE7{  �2�{g ��@�N��� i�E�({.&Ē9cup N��r N�4V�I�(co* �tp.~198� 8~16 (Surgery)) �{5E� {^m�!:=$ `` m$-� ��`����O B!.. a� D5WZd dVc+^lsoo3m�Se�so m�"�76�!some n�intuiY���� mple��7 C32}�923-131<,7�s�7differ 6asl�  kindN<�J���c p&�"�6:E0&��6X#}�qf.� �=5��~4�I1$\ nlx)�!O,i}�/a�<.�1\oXK� ɐR��.�.{�I�s !�:�4:�(Tm� 0�;�/r��/�J].�'RKvZ �Z� ���iW6z�I � I} a�!��E0%�>�.1�a�� Z��( �6]20&� !L:� ,10H�Zy�)� :)3�"m�� 3�6��+�IUya4mo��s���vs�V �."#a�:��-jJ$� �0�2�9�0�_; -�%�^�2a�r������i��\j#�拏e��u��n�f�Kr�n }}})B� �G2G` M-�Vs}��\!av$��*�+ $ \{��*�e�`), ��>#!Bs�l � ��) q|�#|v̱ I}����@~4\no�7?�6�(Z5��� �7(���9 \! [��.�o\*:G}}QR3�*?Y2A�[U7A(��"t[B"Oٔ�(\b�}]-uaࠡ�� e.g.)���_e�XmM,"�G  Zfe�}i$�n"�"I&�v q ST%�!�)P'$��X�5Bf�h.H<.�= "� �L��\ 1A\6� @ ��S>�c6tBu )= wI�!9 \!-1�(� "X " {�@�� 1}}$&���(:$�M!�2 �~�-:�!��8�� 3$B�&�dB�J�%B�%�!Ho�{,$��)]� B}��^�p��.W\�:i-3�MJ�Hi.��F� :�� "�femO-&��P33:1� �er6N�.�!"�rF� u�*1!\ :M�e2�&)�R!n8�I�JA�I�� *m ��E\2��v�ᝮ�<�"�A�82��{.w"% O�ӈ;& ��Rx� ��G"�$_N7)b�a� &���(TrM4ODD) \cup�(r5F)I)!JVQ=$$!�= *)u^ o�jj) �� Bd}A�>U��a��>����(the l.h.s.\ecn��f\%a }}$ 2<�!_{\!Q(��� 0 $ny9 a8out2;�Dfirst part. So, $� BdH$raise0.7ptIl�_2�}$)-��=n�7�q�5�5$ $\!(n-./R�^1i.e. �$GorensteinR�.$�N�9�Hvarnote}�il$\!$1.} \label{NoteP33:1} $U�<\!\neq\!{{\Delta!�is a 2-�mR�!Lo�ft�arrow aI��2b�rm cor� ��yis~vc$Ba � ��Z sphere��end5B��, \vskip-3pt ���c�?5d:��-m�(Cf. y 022} p.\ 190. I&% �����al!�2�Jl(B�u�, so~$A:2}�T0$ except thatre�N��(}}\�bA)=Ui$��.]=\!$``�double*- i�''}\!:= �, \mbfcupcap{�h }{\h!�0.05cm �\ddot{ 1}$ ��$:E�0disjoint copyz $ and ``�o�0-0.1cm'' is �union"< i�ifica� m 5z0 vertices''. > � CMRs)�a/)0 thenqV2jEW$ % \rm2��-} z_.$ ��eU�qi ��UseM�16M�$57 (23.6) ) , ��, apply��@non-relative augm< l A+ M-$�b$Vs� "� to;pair $�& Lk}_{1�}: bf v} ,� A"M!%fv}})$ T Pro� �  P34:2.a a6 .! and�n�$�,q�)$ for A���cas��1g \good� ��W ��} ��4P ZfAAb�Y. b{Ze�$-2Y2�s$2R, ��  iZ  l� 6C����t6UP�2�6R\! $ $ J )�\9y${{��.�Rh p}]\for all prime fields $ {2JrK$,��N0$, (M.A. Reisner, 1976, c�SHoE�181-2.)� i6>$\dim� PM:� 4:5H"� 'PU�, {Structure "�F� ly Genera�Modules �elPID}s}� )�A+"� .�� b{ A�%V��=fiL !*I�� ]�.CfA9�� 6��any-�numberAF bf P}$ byV&� , size�� � 02� 6A� �  =� �� I���)�����i} abov�sIn� icular, [��� 1��6� _2�r�M�Ju28:1.*�6� �$I�M�) �23!1 f)� ��eM�EPy %�&���n. >� :� . Now, i2nBo��B Ji� .���dim�BE�6~�Ra=|\� E��n\!-\!1)�Cor�� FK+�~K and,�U���'�;��quasi-�*, 8normalbaselinesͻsmall�  ���-e ��i)= Y�.�FY�vQ�! *��F.�i  s�Q�F�E�}S^�u� )\le n-4 Z�16M�1Ɍ~w��N"qet,�#RW �wu J\�$�V5)�non2t B{.��\mhatH����n-1��)wFvM.x` Z�Ĕ�;.�%  ���6`��0 !� torZ subm� of�^��\�$�$ =� j�For"2-9 3 6�8\ nal reasons.!�� =\!.. .���6z%t�.R ? \quadw W>�2F�! "���9>Lfirms G.E. Bredon's A%je�st�iO `1} Remark p. 384 just aft� de�@of Borel-Moore co�5ws7"$ZťdA�ofichKaimHat Poincar\'{e} dua} ��reforLnly�&�\e� i X}*� �� �A1 2 n-1$� our Ex.~32�Exampleo3�� WeakU��:, are %=ed2op.\ 329�Dagain we would lik� drawe�atten%};ir%�!!�,to Buchsbaum�!s��&DefP22�h)Zat, 0polytopes, ``Z'' beco�,``tensor pro�!'' undQS"-"funct_s io ��!V�~�6� 2_ P21:@"e,qa'�� \8_{Append�%HAddenda�\& u�"X%\textwidth 13.5cm \se�"7JJ� \sub.The 3$\2 $3-l]" (also �Xed!C he 9 '')} ��3x 1V Iy� �xE$ill make u&�#tX Mayer-Vietoris seque�(%kM-J Vs})A( form a 9-W -grid�clarif� some}� g(ons between��A)q,Joins, e.g.g \{X_� �  � ast Y�|, -b-J\� s�isive \E�bar{iff}��>��%� v"N,~A�A)"�!A� \med5\*#%]1.7EZphantom{@ \framebox!yh�!=15.4( { %%%� 䢢��� � �-M� \v� � 0.82 ĥ{rm-)0Rotman:HomAlgAN'bf�\ 6.16�175-6 (y@� )\ \[ (J.J. S �� AnYi Intr}.to}Ci H9$�&4Algebra}�Consi�� commut�diagram��^s ("e # ): I�� lumn��exact��i8 bottom two (or��top) rows �.7,� � p3 F row)�C/<. (Hint: Either�*�uSn�8l����ceed as L&:�! show  $\alpha ^�\0� =0, regard e� # as a!�'x��1<ert � ��of!m plex���"_)\ 6.3.Vhrule � 1pA�A�a� 0� ]�5�rm U� {M@cM)21}UI�~5,rm��4208.} (S. Mac�%$Lane]�Categ�s<i�qthe.�Workiny$i Mathemat� nI��'���' A�t5eis on�i |m (3M�( (borderedizeros).6c-bf(a)} G� directof!�!�}�Ebea 1�is!�uR� threalm5� last (Z$)aA`iTshFBs,�n !�: (Ie[� �(1G�b�Shoj a,!is � ��m's)\ ker-cokerU�b?c " Prov�*middl., h)6.MV5,z6�$third�4 �ro)-aY�kiK17U�iJ 16}\eA27��A�P��Hilton�S. Wyli.P��yRi�yiLet (!�1/2� be a2t'j hich ��n��cE�A�anJ�differ� $6))�$mJ sm ${\nu}"�ast�r\!��C :\ �M�i��char"48}��fi { $3}}\lower2�urm3})I&��a�%�:=.RhbS 1}),�%%%j�S !\���1��1^!�������b�3��A�jn{�jbS 1}).Yj�b�& �DA�z� = -z'!�vl!F5'0 (Reversed noQ onn��t� "��^6te��]~2E 53��[A. Dold*�L�.�on% 5i icai Topk/�n...iffp is) Vq� h� maps� �lG�ws�`n� e&Zs�y'seF6$constitute}2-"i2al lat�'>��Y�r s. I�.' 5)�#�^(�j �S0�*^{��A��"%Qbf�' r7)$-squar�Ŕ anti{ e. }fUE�%�"�"�($��[" {*w �0.3cm:725"7� bB,h0.9$ CB 0 6cm 0\R� 0.552 W 9ptm�Jn 3cm�/\down� S csr�9h#o) ��8 ��6� -0.2���{���{���}_AE�G&2 rlap:*A� ?45cJ@$e��/4� � k"� $m%9 1cm |�\!�J| 0!cF�$�`Z{>m! m�n)�-�+6&4N�}A~*:!�)�~"*M�#2#�+] �Q%97  {  � 1pt}AX2�9B69�HB��$!�� \!}�C� \!E!�} %��D ������1�R�% !� Cb�b|^%oC~�rC-�EV�jD��39c!'u���:~"h�E�51N!\m}:C���asbi��%�y�B�1B��� % {qȍW 4cm R���58� ) �+ 062.5cm}IS% �,r-0���Q'��&�&��%=2k${\tenrm Pu��\left\�1-0.0cm�$array}{cc}%6�\� C}X<:=X 9� \{(xA_(_0}\!,1)\}\� 2}���line{*\!\in\!2J�6 <and:6Z,:=\widetilde2uy.�}\in X� Y\\ %!Ut bf�Y��Y6�Q0v�* �2+F�0,0��0B�-�%�!��)�v.$Q;aq{$)($1$-d�&fEquiv$Def(x,1)})�Ap  Da  \tiny*= M,nc2Rc>�B&ll}a�A:=.� U7L t�#\6} %� B6=<�A>\*jX!GB] V��eAC:=mQ.m.�64 \ D9>�R9^R�% !@F�$%�.�"� � � � Ε�U�AP[ �� ize6�TI��5�c� =:;="i]{c%f�s!s 7:+}A\cap BCD=!�% =( D)V7( $,YnZr!\}& q� 40cmYU>6* 5(\\�Y�� �B � �)2�up C)�� up D��3B���j toppBk�R3��-=��up�ap��2�a �u�a��� 9�aw.�.B5�cu�2!B�\by)�2��n�QN�% !�-uZ-�)%$�� 6�]� %F�H �2 ��5cm �a8a%� ��\Big\& 51A8=^� Rr� [��Z����] �� 2s )r����)3!�% 2��large$7%� /*0.8 �*� ������R����0.9� def\ob@'style{�!d�?6A�hxymatrix{\ar @{>->} [dr] |{*��"A�\y!$V�#R DŒ${{0��IЅ�=} \ac {�):�~A �ar[r]d]��&  _ `i# `e�` p�-�assum�Ho t�!placeR$in $X_{1}� ��1}�6%��&.� }�vid_&L a ``$9$�&&& as�atb8,*vJ �"h�&ontal R?alI&�%6�&"�G&�Y�=|natur *��:M-Vs}R"in Munk@"2W$ 86-7#!iF�'A� \new�3�8�� this{6�"m� landscape!�I�*� �LaEA��J entrieensistg-� levels��upper (�)L# ncer9J(9g)1�'g $X_2%<$Y_2$�]6be�?�4.%�%j-1�[ ��1�A�&[6�] � i�- Ma� %@�er�-8dvi-viewers can  han!the %5^$-envi\-ronG*]Dy"ly. {Ifs6H pdf�2�-��-�1�� ��p3�{&�}\d8E_{3�& 2! (-\#) L2��"""8168�#53 m25 '�\#�0BK($�4.&�/H^{ ...{ \buildrel�80$} \�, \lon��~%0��{ )C!�E {  ���Pe6�y _{n+��/$big( \Xit#� ast#Y>z6e'(\sevenbf((}Dat \Cbf}T:ST&� SA �O)}� :(}}>W�� {��{>cBdeap!^�i� C�.��AJ��2�.v!I:�t ::�W^� 2�dBefbig)\�6 �=)�$� 3�lY >�\!,6I �c � .0� =�A7I� ��N��F�aM:!Ur>�:�!��:6-R5bAq}-!�Bfgu2�up�NF��n�}C .z!�:�xaF4�d:^���A,�1}}�����m�4>R��$}_���\ ��8��F���Vs�a�;n}2T .!�.�.X ~R��I�!n6�Q<]�!�BMA:�S�Sa�����A�\ =�!� FT6 �(^ 6bQ .. ��VB �C6�aX��������N%�4B��F6!����.�!�2M�6�!��r"Rm$aO6j6�:��A���I�5�. �n"� &8�"�?�6�!?9�2� ,NO� f e�bEb}}a^)\oaddA�� "� �� =5�.�r@:�!�u3P ; .QA�I*����1?�pݩ5.�%� ��b ,F%��� N�%�� 6 ��V� �<�<�<�<�<!|2}�p%��=Je6�E����\2�!�:�N�E�"- ��F8��{-"< ��&��r3 $}k$}$� $���*�#(}(i_{_3},-j) -�\#� 2�Bi.;:1 :1}�1* &��J92 92sd \# �*Z�d"� ...$9<-OZ;Rf��e)��E=C��&���G�:G���Aѩs�rA�nV�� &�VA�Z� �umo>`F�3.2.^J�e��  �=&�P��͊2w���6^3b/څ=%� �U�$^R�WKD� Ft��2���BN��!X�  {��� �C�CZX!h!iu!.X�FX3^X:�AIY%�!,�S�S�S�S� �;�^Y�B��R�.��ITrV��&y�N� J,�a6')���U"}���\�MQ �( �Y�.�N�Jfa����3�-5N+��4i2�.��J�Z42�X.W�1�:5fNg%5�� F�-/Vdf0. �� %����6�͘J\R�!^/ �F��2�2 i� B�6�AF:�V/:������������n�.~E�}�!�ʒ����T�5$�M�=^{^�5w���oz`IΎfh �-6.Ai�q�R" �b ��Rj �j�-�r3��!�n 6,f�l=u. �F� �Z:̅�q~af�5KZiR�~:r��&� ~�4(F�!,.;�]-��U.A �B�TJ#,B�UBA6T�%\� ���mQ�B*nl)^<.;�����Rj �������N�!��(4&�<"WH �J�)�< (�Q0\�,.+�9 8�87�>�� *x�w Fxkp,-l">6p&"�%3V>:?:x:1"?1��.y2Z;z;2u�y4&9N-7>i toBN(!� �8xB"� Y*7H�� /����(/D5A4sW\wp�}$>� D 2F� !&�N� ML')L� \bf/�"bf[�!!�eFq ����J���YN��Q2O�J��p�?'6���\�-&� ByBe))bf+ �!+SQH1u� :%��8a[>�=s . ����>h66Yf)::L!bf]4 (=):%$�A(=�I/�>)��R� f�R�.F �B6H) �MAa�Hf�FXa��"=+D&b�jA=\e9rmbGRHr�2!�!��(E�N��6A!_F��A �? C6�~�V7}9�^�*� 2� E#F]��5?a+�� +�[R��jB���6��V�I>6O>�> aAV#�>b)&��e�� g\�2z��!9"� ��IR�} Q ���n�2!:0%�n~%�2�!HFk!�1^e9m�y�yRyR�*\!B�!�)%*��F��.\A[E)J|H�}~.^�PA��F��.*)��2RBin}EqmJeQ��>n�:�Z"G7��M���b�00 >��q @N�>��,��/6[!�FY��p�63RV� �F2�Y2+A}]yf46���J��.:��ZbFj�E�.*Au�a/��Br:�!�i������B�:a�zY�>��q�Ѥ Pn)Lj&�8+ � >\)�&� MFN� v� �"c(a�ԾE ! �ufuR�o��%�J$Abf x E�zU \!R�!�]�.z yq�6�^=��IVqjm.�* �^*�� �525RZ ��=��2�&�!��� j�.�)|��)�1��2�F8 n�:DesA9.� n�� �:RR� \�;H"�=.( Z��:�(>��M�)�~UBV��?Q��S bf=0� �^i�pJ��ED${��om.8Az3 r�>�N�� N2 %��`6!�F�Z� � a%=JI�#B�Fa)�")Q%�z!�v��B7�%�qU:�9* G �.H�F�!5N]{^'�6��F`14Ed �6�U* 1F> �+^ &1�+&e:?&=4%l= �2WLl=�+�m=2(#7ON�=.o= G p=.XW*Obig8*�+ �-dEKAMX/A8in curly braces�@�@mAcdoesn't�Ay�zart i'^ deNg�i�@ex�fity eIMal�gbut fit$Y O�g pattern. ��I"K?�&�@%�*�h�?��Bw&�hS&rmcalculu&iSec^Ap�ix-L!cd $_{oq $�all�sseAa�me&n�\sk�~_ deno�| �ar{ }y}w��!a{\i*��o��C,9M�S9i%; set�pr_C�A�� 2<Ƃ${\tau\mid  var%'tneqq e�ZN�{��[�J� msbmNZ72�\ �\}�A $�.H�Aset�)N=\{�P%b}�ws_ �N8D6nD";A ``!�%[closed+nr}!31]$D respdtS!�� ''}=G�ove�Q � rm {�`���� 5� -D! := -n�n#!x %� %�! $}.CA��Hopen $($realized$)$�� | �ބn$Al�'r$BZ� �#R��# \in| �|� [ v}�RE�]�&� [ ;�k$v})\neq0]\��I��2o%J)m( \�9\{ O>� !` .M�big�8 {\!v�R�}Ug1w z\!\{v\� �1,�C% _0\not\inZ�Wr� r"܆��$Z8z uq6=1z $. $ �F`_0@E*�o.�yMo8:�0�_�fE��>JgeometriG�rex}{%C|BX^q\�-}�:�a�ure~�))�M�I� $| �I�J# E�{F��tq0] :ELI� v��Um�] \}.�3E�|B�:�_0I�!j&�O���:.�in��orRt��exI.���� $��2&��Ft!�h}),ih & 7�� Int}uv )W^23�E# � 'R� ),Soegu���� \!^o�z� aZ^{�i!}}}) �h�p�a��ppJ�y1�W���o�&�p maximalQ��M{ek�2�(B)!/5-Ar�tI��baryce!�}/tat)G�\y%U�?:t��H� ���!A-5)�JmQ $ ful=i��F�YR�SgO��� ({p rm��AK{1�"{\# �!�"�ile�hat&�]!:=�[ Y_0�U69��DJ�W link2!>�1�)������LkhxAV_qJ�>)|����Y �| [ !n�� =5�]\� "�Dtauͫ��6rm>�vA�6�em\�A�!3=�k,� ���a� LkZJ F8��@k$؄� r�,E2�_{}�LV����c.�M �o�Zy s Bp0-4%�iR� h 6�.��5�v& D�N!-� W _{2}. -$R2}e��q!�i^ Vi}\ (i�!1,2)�5In\*��U��Jyk_o\!\}�*2}*� p�q~���� DzV#�:"�j�a[��� ]!��L�BL2})." b})� !&�|K]�� Q�|a)" qimmediatB����A: i�e�#�ub) "�8kip12pt SupposQ�k��e E)�!<�]!.d1E�]��Zeq|A>5$ (i=�2�k�Đ9�aU5��5AI)&"Mp; � mu_oF��)<| $�TQuB)y�\� �Z�Tf6��M�)$.x\}O�=[T2seq�}B0s�r� ��I{� a}]=a�^0��=�vcup 2}|[ >���%�]� ()32��f�9E�U�$[(H2S�\r=9/)?]]\� = [H*rwe�w�� ]\ =�2C\{F��<[=a��16"� ()Z122(]\�vLm11OmuA�%� �,�V6�NKUni�|ess6e =$�%U a�YW[�A�5Tu5G! 6�"� !�-).A[�"Y[B������ ``��$'']}�QN)�zi{�=&5i}� (i� �#uHi�4cm$=��:2F!�Q&u m2'2})^,ѪVY�Rj &�W��> conv�uo9Y���n�D� v} :=��Z+�v}\} �z�J n ite[�of� i6a��*� �_{�r 1A��)!F��:M_$��/6�� ˜�4I���)E��pg.g,B3.� F�|� t{�q�ah�� \!2��d1 �Y^32V���-��kl� !�� �"�$\;��t.rYDF[)r&u .��%]O�.1=P�6)��9��&�v=F���UT�%��>��8ʙbarI���9ZAesw����f�[�3e.Eq.iw!${I}}:� ?ste0!��1F1e�2��Y � u� �2�:[��Uc2_A�:��m2i�u���z zz \!2�U ��jm�z �z nqY �Qfb�zw � ��6m�Am) {����*�� $p$-�� skeleton}? �mfz�* lta\�;{(h}p)\`�c���!���# #(le p+1\}$. 8ըd\!n \=  ���n:=� �� ���zs iff�s� >l\s���B�\!n� ^!z�!� -\!1= �:Yp.!�< �vFF�vetminus�:4\>~\�!�C"B�d� GammaS���/ said·be�fu�si.��f�!V&r1� G;�et�_{^ r B��l�Y�&�p��2"����$Q Kenume a��,.a item[i.] �߫&� !� &H&�N{�=e1.A *�Z �1!i } @.{o*�&$ H >U�  � �Z��{�zFY�E�g�� �f6Y�-;%<,1d+6�>>8Y�p99�7^�:8� x�$��� ��2@�8 ���} � .?��2?��5�,$�.a�1Hi]a� {-�i����=!� _{�!�����b2 1 �/� LA��:��%_A��]��2�_b5}D�{ �9�l� � _{�z�()��!0NI Y���),~-fv%eEa!=(� p6� u_{{{i� *��BP p G>��i�E�a]/ `)Vb a� `ast2�?� ��k ) $,�1an�)��$��a?� ��� ��)\!�h{�a���2"� 9/m ({iv} O�hor�\� arbitrary�i�(b%s�-� *j{!.T��.Ee�&$b�BZ b}\  {p&(!~� 6U&� m��A!�)�ALe艐 CaaU^���A2_ SI�_"�� }}{{d��foralla�.[ ��o�AA�� 6 a}�� !2p $cB+c} $[{ �q^ %.F %*S I�'�!t � %k+ 3N�R� �+  --�]A��<a�f��1�%���"F� v���2� o.�ɸ�!i I� -�I��end� "� � T#@ $a.} AssociɕS1�rdisg�ix1loe� '�Y� ves.5�{$:� !F� ub.ag(%�&)%��;-APi�F0+2!�� !�a����a��5so;} $&<���9K1�it.]��%���\ ��% �,� AP 4=�q�!�nn a�@��\2JR� \�3�  ���.�=\{!�%Y��6�� D\.�#(6(���=a�>��� e�!Q6-��| |}a�9T*le\! n{!ji -)���1&#�!n��+Ed!�-\!\#������mi�6t\̬A�" j6P I(j�.4_ ^I���)F�)���+)$ә�U$ �taj\��&a�� _�2vAM%� w$�(� both�"}#��$m�/) .e.,�&#� �� ����H5) j (:�^4}\F+y�not�-I1D.0�E{��9�R�}"8� m}}.���'6g�'%F��jc��"1 �_�A�+ A� � a��-B(���&$ \ \&u�!!��a�������� true����  B���:�7*�GH/G s�- [.�6 ]� C-in 3N�*B-A�R�E� � }c��FmEV%9. ${l�e1�dFrm)� r�"�A�:@y7R�.� � �I5�in ���+no� �Z� K .{2c2{�{EN��jB A:# 1� True\ \(9!�%]]AE ��j31<}Ed� fi��a\4 \�8�9Hy�]�N���.q �a�� �� � a� \2�2� Ri��st�8� %.$b�0!=�k cost� "6�(?f�Z)�QM��1!AB\supsete"�9�Z3�p p6�82Ce#d ���21�rh� �:O ����B]rm�X 0��6 �.��.U "j  bel.~ �.5:3� Whe����N�,A�-ye�$��not�e*OF�JI%a }9 ���Mw�2M>��k�� �cup6��-��1�>E22��z E%f4!$!� A ? �=\�.U7�s^`,...,_+p� �zR"o4�� � �\no�~��*Կ:up| !\!�'p1z�\!5;(*�;5�"� )�bN�b�� >U���0.8�"{t�#�'-� �I��&�U  }} ; $� !���Z^>!�o9��6ji�R� B�on�2�} ��>��9�1A�}�5K� &�A=ap}��M>q!�?-�A�N�e>i}}>:5B�B@� Q}0��"�e^%[�B< {^@bf �2�!A��.k� e{ !*( gcm>E%A4�i��� W�E�1&���&�_ _{^- !1^�Vqx�!qCuA&�����$c.�TR|�ll}$��!� ivI !1� \L21�i!�\t�[FG �  m)0"�!{${�(��� i �Ma��fQ�!�_��E�'" ;-[4)��)!�I� 3n��� ]-�!� KD3D)�\�U6C A>v�� ] g%>]" MO!�i_ Jg��{>�2G[1�v})�EB6\ ��f�)vJG7-!)��%2�F k5Z p6\ G2, ~ -uA � ;Ž����Z� L &-_o��(2�< GyS]�5A a�\kX a}�PR3 ��c(-!D�5 �� �BBJ���IY-�!�-�a?q-�)�JJ7�5�5]5 y�neqo!�"!3G���J�%!U� ��q��-)!�C�jI-eO"�%0E��� �,AvE �,2_a��� F� FR"g$d � Q/,*� Q� rE�s����%6��q�Jd(�K\V.�&�y!4ْ6����!.j% �%\$!MRzj'(q61��|@)�2/. ��f&42�-$}sHx�" �qJ�1k�є���#�\ ȝ!%� �=Ab [ -%$�L!!��J�G Y=� 2��;1*y�)��� I��)P2�i !L���6 zU\V !}�%�="\�I�$�c6ZmSaYW !S��(�it eH .� %:9�0*�"C �5� ]06.-*!�]$�) !.�a* ���7f�'�m.�) � ��!��t%>E�!N!For�:i1M tly,>�DN>���8in�N {�,� eI��) %��Oj� &$�\ {If�D��с$ �?;� z� 1.A�[\>mNQa(6}IA�^�A� 2�#S FWI )� An�V+@ [n GU,e�r\��e�E;!\!I5 2 �F�732� \'3R���:� =F�e� \!-1 �Z� ,*(5A{9��-@>���Nphiu� t:Rdi&9�-%5/!��N�vaO�$WA� �an V&%��:=  {(n_ -1)O0 A��}  $�I��� � <\infty.$Aqv��(ItY,�palways}� that;���&�2m�*KJ��+�%�Gn-1�j9&k%]5w 1I�V1�:3>�$ �Q{if� �0Zo}�B tau, M$T$��&C$>;_Qf� �F�MdF�!x� �wi�>1iI�3.�6֐�� @ ~�l 2��N$Q�I\)0Q\��� uR-��&�F��2m�P<1k���7 �2 Mz �B �#� V $!aus a��/B)�5"dis,��Th.;����2.^�,1K���H;ʕL;:md r��$2b>"a-.�j� �0�� 3�Fr�LAb {{\g/@ �B�1U>1c�, L\.`& T�F�>���� �Q �m�eg�e ^?E�= tau]� ��8B!L"a_@>Kl���eg+C�9� v�"\!�#�w��&� �&>U��B}}, $��2�a}E� �GC2%71��"4 c}.\ A ``brut(rce''-checkWe�Z����l��N``�����T\{$v$\&�P$-��'ld~�d��!~9�F�M�%:b fB:�\):�;BU]�G*�!9�}TO �&$ �$&��T \8�� 6���}�+-M��yf9�f�& *!%��-:� $ g�(1��Dit a}�tE E_���2*��$�}.a�  i&Dԁ�2 >�e%�& j�-@}An=�K6� � .� �#F  %\!]N!$ K�{�zfNZ}%���,�"�K� )�B�  6y9� @� E�r�Y�+ rlap���5 ��?� {\!=�HJt.r\a)n{-=B[)-"X�x]!� =�jzj_ nufAu�!�| �P�*�Q�M'�R.�As�&�2� N�@��52�I��6E�.��R e�,m!'� MCrm �F�y CA,�) �}�yM �[AF! ��";�$^EnSRF G!F�"e�6Yz^e�"�j�@�VEO��B4�j�ym ����bxC  a�[ |��B�|���[)�0}[�!�@ Js2| ��tB<���X XE�X'A3n�$f � a �n:n(%a.��y0!�:;�@E@ q�|{�la��u�4��C��Ʒc| vv� �ZA(6$��ެZK� by\ "����,\ 372,\ 62.6�N^��&.� <� /�� Fz $9!v">ET"�]i�A��)"9�a�a��� 5�iuD�+ H�)� #�A#!v�JzJذ�-r"�3�3R�3I�-I$y�$|.H]'zW���|$ *its�e�c image�/h%�}- e ge� avyP�v�6 imeqN f �0f0�.?��dA�N|++F���%�� �0 eG{H��ykg649@a%�l)Z��&1�AsJ@in2  EasyIso},wl��easily s��w�S0Whitehead's $*+�� S} (X�  Yz�nR�toX-�H makզ>&h�F=$ \approx\ B'(X�j�k>E(y% s0, ��P� Z� sөHis well known as soq�sN�(X)>WJ�pL�HY�But, aX� ori,�Tdo�h#)FN:(X, X��2"�XY, ?�_{�c�Z looks lik��% d�%&Dore:��13�,N� %)!)&�C/$te answer:�.>#�'EJ$�g* ^{�~# (}(\!X,���m�F�� (Y,�E �;�pmM RingHom{Z�i Zs � 6=2�+L! z�}� !cCbILN�P: �a�(o�e�MF�.bTo-�7a� BelowE ��ex�JEl�n�y k}}(JL�E1},1\_{��6%22% 2});) GlR<$}% ��nbh�IX�K term��a�l�Y!�i2ni};%�GIi}�% &�=��IPxeRj3�y�Z��q1��"�% 0�y S ex $�&�D-6%��^9K2}�lit�E"fuWly}eoP%02 `%%"�Z u_{_�U e "�Z$ ��aO-�l!\�/$ ret��(their origi�����  put ��4�^�EG��``��''L);U:*��� $[�1}]\u��2}]:= ]jn.�� chos�d,generator reA�ent�-AS $C^�%�!A�^{v 1}\�� y���$(�1*�V aG� exten���W �$��*�<s]��ar� c."]�$30}~p.~228P�F�N�I !\!+ ��9�N�"7-� {�! p+q={\1} c 5�/+&֘ �&��&�(�U^�06W))0 B,q}a�� 2}))R�u4.+nst=�ion�[��np� Fors��14�B"��%�=zn ates��Uds a�25��pE$%O"1M)#"$.-]^{v���>�&H��y_*6)�E�$}}q�= �^�.�,vQkU�-�X4cm!��g��+22}� &OC4cm�\!}�)r� % ��� )Y>k_�m$%6%Z7I0�F3A���\ R�!pigl(( �mWz� �-�2L B�� 5��]u �%�]�#r)+1S{l(#�=(�"\=F "9���1!A�R�-Y�M1!�5W�2�I��n�0!xT�2�bigr).auM�A. D���graded � $f�rough?eff�pY�}�ofN"�=�ez\��I��_��.��5 4\! {\rlap{$\GTamma$}{\ _{_2}}})\!\!= C^{o} _{_{v\1}\!+\! 2 41}}({\rlap{$\GQD _{_1}}} \!\ast\!F$ud$ by % \vskip-0.2cm $$f$+1}}\!([\gb])�f�y]\uplus 0�5:=\! \1}]\otimes(\!-1\!)\!^{^{Q'2}],$$ .�4� into�%�[{\bf %CN�!) ~. ^O%�]�=�\!+1�}!#5 �1x8 p+q={v%'%+ \|$} {\ \ \raise0pt\hbox{$\ \bigo!U$!�(�Q ^{p}R�U!�)f\!) 8qII5�U�))%oU1!l!}�Unoindent The boundary function is given through its effect on\nobreak\ generators: ZQz3 k$$m0\phantom{I}\hE�,1.75cm\delta1`)1151�L_{v}}}$}$} {\lower4!Ah^{)�Avo)�5%�Q! ( ).%2})e?[\tau]e� �6�2� � \dimiUp+2E2�3?J�.�1��} A`:�I52�&)=m�R�1�)�=1l((- ��2� { �!Y�%A�a5: 46F-��1�~ �.2}�r)+ �lR6�k!=�%<!����\��vM{�2�bigr).!�uS1cmuL�D$���}}$a�� �@r)\ {\rm�} bf sZba�l(yx�H��!M \!q� 5b|}) ~tre\ i1&Hc\ as\ \underline{%H s}},Ő%x.� 5� wher!De ``�i� s}'' stands for ``suspension'' meaning that the ded x equals 4original excep1ae dim S $i$ i��e / is 2$+1& qI0. ��Pargument now motivati�e� mula-,�bar{relative} simplicial homology is�same a�atA�``=( singular ;''-case�dp.~\pageref{RelSingHom}ff.�%� \med�^�5�%�- � orem��join.)l{\sl O%~ categoryau0ordered pairsarbitr�qI $��* {1}},\D�!�T� )\!$a7F-2-!/2��)I�tE�,is a natural)�Ab0ivalence of} �0.5cm-TU�� $$%Lmji����\� 62}})/2�a�(JA� �7\cup (!&�|* big)25�%� with��%e Љ}\{Cv  ^� �5�1�_] ��bi N-B�/ l2����<\}\eqno{\square}� %U���0egin{varprop}V1.}� % (a�,K�nneth ThY�AU�ei�,Joins.) With��bf R} a%� PID}, G}A� )E$G^\prime}$ ,R}-modules �q$��Tor}_1^�R� bf G,< )=0$]hrm\cite{30}~p.~231 Cor.~4} � s;R2 e�\) array}{l} � I�-E�\mhatHA�q�  ((\U��m�e�� ast!�-� .# 2});)G}M �G^{-$d}) \widetilde=\nonumber\\�N B�0cm3���_{i+j= | ` &� A�"w = �i� j�.�1}; ��� A\jA��)*.&.Q2Q=eG* C�-M\ z�Jt! l(��%, 2�!bK :�m`.��r�XI�0 i� ��� \endM�A6�)^{rD({$\diamondsuit$})>0cm{ �LC�<�Gbreak % \subse{% Loc���products��f� complexesj ��U�-,Corollary}~\��LCorP19:ToTh6}. (from22!)��DLinkBevisS88} Let���v}�JY|$ be����l over a principal ideal domo eR} such� \ j�},2G}�8�� �n,%Uxany $\emptyset_o\ne\sigma\in\S $\|2}$��:taAKa�m Int}( ?_{ ))�%p>"��Y{B2})%: $c_{ S}\Y �a�\�\!� � 2�-$;Aw \small�  \�${\&� . ��+�! f}+1� m Lk+1!1B1}} 5u�������R]$/A�r� {R}A�� 7_{@p+q=i}\atop{p,q\g ��%F�6$\ [�pF� �� �AF�� ���^q60S!�-���@.]\�� $F�\rightI a�/��6��{)1-123 ����~5SE�6m l���Q,\��!8��:�2>F=a���\]G\ qz�1=�i�F�& �&�xq�1S -�2� ��.�!�.���If �tm aFy�!�r$k n�Yq� \!=0�q so:��q�.���3cm�0.0a{z- N$� -0BE�;��=�a�; �%�5�R�4cm��A2cm1�{_18 =�+ y�Mn})$�=�`0cmSi� a�m:-(i�*� %�0,$ţreOno tor��a$-1tSo, iA %K\!��!��J {Q� )��N=�\!0�Rm%�5q$Q_{0���=� 95A_�1a )/&E� 22{Y5�U1%�E�)�!�1 ١^y �/H-m^��_�� H� J_2}_�{�����lj�)0})!\&�Y� l�0��m j�.ͬb�2Proof.}-( one-vertex� H $\bullet:=\{\{v\},.�o\F q kind�unit-eleW� respTto ``$n D$'', so, our claim>ZrueaPei� $I3�� $ or 9�a�T,fore, suppos�at2Iq� �E�_X.? mma� Q P18}2� �= c�7} 8Th.~12.4 p.\ 89� $(��)$,!�a&�*`y�8a�%�8}&$ \eta:(|��6nabla .�!|, B,!b.0\setminus {(&�{\alph.�,.j})}\}) long arrow$}{�&�$\ \simeq$}K F�!|%{\bar ���2�~ |, 2D�= � \{(.�HF�)\}),� �-� %��?"���i�&NotI�@����e&[ R� %� �z�Vj}}6*,\ j=1,2bPut $�{\) z dim"�  ;Wr� v 7 G%S �2}}iaR ��� 4cm:_{s 1."O-0 vJ.9 )J ���2a�տz3zqh1�QD\!�~.j > ���E�.��.m \�[{)\rm{Pro!) P15:1}\2�a :�=v-. }+r]��2}� s}y�1${ �}}�f͋Bu� > N?�w_o�:N�1q��;R;)f�t�8)t�*X $6���)�f��-xE� bove1c6; \!$a�5g ��1}��E\}}5E2%lr)] ��_o!�W97)�j� ]I��0rm \text{Def.�-, p.}&�4DefP11:PairDef��6 =+-$e calculusb�%�R�$2�!q� �YN.�|,.K]��16w %�U�I!�I2}JI26I�w=s{�2Eq.~(3)2EqP14:3>^ +~�2,l�P15}.5l!4�%jb�E�2-$&�_"�9&1fo 1p�%nG})\ M�)�)�p_2��N# f*< !� �{pS ^{j!%ge0m�{ p}_1+ 2={ A�a�� �-a#\ fq�.b!a p_1\!-\!v 1�6� R+J�� � � � \!)Y,^2 � >�R�J�� JW1]7-�:�%V�� =*)� 1_!� J��$l8cm =[mWutG${q!y�:=264A�]=$ $ =��! H1 �i>R7J�-��(\mI�\i�&JiR`J� `=��61�� .\ge"�q_1+q��v-2:^$E� I�J�q�1�9)9 M�a12a�1!�r271cm5AMO.85^ 6cm .E3�y1{15cm.�@ \ Now, p�i:��4-2.\ \triangle{J��"osition�3 34:16�( �Q" 3 k 4666 give & e second&�' sm e�,7'$�'i��"� J�1Z� !/ EKorK�u 5ZN�){\hfill$~%4v On R ' Home"�)Quotientx "�$0�-: An�'iamap $(X"�  P, Y\)\mapsto (X, Y)$ inducev2Zin"g' f'Z�#K{\iS$!PO�ti�BZwhile�P$ ope� $X$"4t needed, cf. 26} �180-1.|.8is will be used�( nextP Q�. "��a�i!�({X}, ���$}) \equivɜ2-$� +$� (E�&. C1 :\!(X,A)\� e@.(! \!(Y,B) $�a "�(h.�, i.e., �1 :X\!2DY!�s�+tinuous,eX ,� A:7 ]B,a6v. �A\ne u2,\{\wp\7,(a strong dmaa� retract�Ha neighborhood $N$ �B f(N re clo!�I4"$N^{^��&�t:=f(N��' B $,A�ce $f(A�  then", "� � i.}�!-�i�1rmF)"� P1 ��) Z� �I<� �!d also6C \!A�)eD aE�"�� {\!X \!!P ,\ \6O B�PYN:�!�n�!f�{{|}}}:.YA,6�6�(.s,>]9�B��)Zpai�k� % (which it&+X,YE� HausdorffIiN$vact)}.ZC �ii&�+Qifm (cp��3��~66,~7.3)� 2 N�^{i%Z�hA�Q\!T congo v=Y\!, B? 6)sl��} $i\inI�ZO)sl! ��v*{ b.5"Q2��^a�}a4���E (}X, A)X6pprox"D/�Z� B.\. $�� }!�a �A*2/�A #!�mutH. =(:�Z� DiR�i} $A$�� �$*�.J �S{{ A}�- %�R+/ +R�E 82� 3.�� % � !� f��}�,�4{X� A}},�h)E!�)!��end�E�h-+:�Y� a�~$30$~202 *9,of)} L�&$F:N\!��I}:� N�'H$postulated��2�������6of�� down ontoE?� define��,$&2cmF^�$ : N a�� I�&@( ;�B left�.�-�,�,(y,t) � \ y &[if�y �4B,\ t -"  < ;< {f\circ F (f ���0$(y), t) } 2_ ^ ��\"� B = .�{AL ����I}�1E" � �A��1L6)�:i.��F"i�well-)�d%��@co; `2be�2so whe�stricA toW)�!�A(*�pac�.�9� I}$� . $B:tC toge� c#**+6/, cf.~ 30} ~%�& 5.�!4bf N.B.} Chang��dc* �9�$�<$ doesn't alter .6.)Ak�$ 0follow_�4(ard diagram� ii�s4\FFrame{0.0pt}(\hsize=1.00 *� �:3ѕC1cmD1L :=0.76 \+(W-2pG���6U&�.�Z� star�� �]ks5(3�. {\ $���,Asv�;\movea�"�;{$:g0}at���~�N\!��� {:�b ��� R�6_ ^:% 6�  .� � � !�U>�x/ \m�n�{\( trm(} i f rm5{\Big\�^��=h[2�%6t>:\!%�$%�E�D0Big(${{{\five�� ^� �b� � -} ;/%.��"�+Ŧ*� } }}$d)�! }-$ ��2E 5�R�Y,B"�}�!A���^�c*��Y6� y}M�8*��U�f�!.�0%JN�!�#\!BA����}�.!U�aG*W4E�2��C[ (��7}�\~125 Ex.~1) $f_{(|)}:= (Ikr�~^!/ET projT1$}$. Use asn �� row;@�  (X!A� �B2�� �N �MT{6���U fP� ��.RN9C2U(A �)A] V ��.\G6���/ $normalbase�]�+@'@ 46.2�279, see ";"a(3:Munkres},��FW<�9suM��7 i}.$ �v4� �'>� �� v5 0.54�� { {� �x2��q)�s $\; B w.r.t. $D($-|4 $sus\-pen\->, mak� ;�Airc\!pEZ��-U�Krm�'!$�� \sevenbf-%$� n\-��$( l4 }}u k�A 2 ) (�\!3. 01 K)�5��+$ :�r ` ��34��5. xv�% _{^1|�4�$ �t�"�> points.���-�6�1&&�G-4&M 3cN 42Q" =-3 E$� < 1.9cm"�~ bf S���B5�$7@�,E��� \!,\ 2�&�+!( dbi X}�\wpAE� \!.�i Y$} $} )\� �S") X}$ T*C< 6' YB( J)b� M?�$}��T :6��$  {$\ne� $}} �6�p}��xu > %rZTsTAe�8�S� S anF(,�z*� $^e>$�6� @laP9F D09uZi�bf. � up%& rU$�Hn4�� �FS=�R E�2�2�%)U!/�&� ]�Q��C$ Yw� \��2FK]�}$+ZGa��1meq��}S��{:�a�b�!� I {{2�$(\!{y�\!} )g!�98 )h*b$\N}Z&,\� \C4}�R Fb >� 2.1 45H3vH��RK"v �m}� !�}�r>[s:SF�³%n�%��%>�*97Cٴ>� .�L :var�'eGrm� �\ 225�f��!}:�Z �e�  W }null-50topic \underEiff*X*>w mappj cone� [5C}\!Z�W.\K �L.Z\!!�u.)\A "� S�6 62\ $Zs�W\!�$ � id}�:Z�.�exng�� -top>edsNa�� ��> =�06�#� *�r�i5 U��7T&&Xb C� 0.58 =6� �!�&-�8_{OA\!)�D\!Z}7k5^{� W)���p�cBc� C}Z�l(W,Z).�S�7i �\ �cJ�,��A�%trivial�Cl>"splits�:�2"2cm�0�����~$<^{�+�{� ��!&3=1f!�J� plus�<�E �aZ19]#Ui�!^�O+�:{X ? {Y�� hook� �i !!`ŭX6I6r6:*n 2eJ��*y Z"8ie6�32m` .z �$N0Pi{0.2 u!\!M�)|4.65B|� ] uildrel{r.'}H^"�! 1�� >�E-� (�Ma�Z�cup�a�V�B� F� *K>}3.*�5"�3�� � QjE\%���F_&i "wI�%]��&7 )d2.5&� \5^q�asy)^Yg�)\%Z>�!.[(a"{[2�B[!�Z,Z)��\partia�c6� � �b�i�2rv) }&T 2iqc��`@}<=�$ {{) i��Rq�U� }(X !� Y ,X\!+Y%�"{-A�da��J.! c_�H\!�V\!Y\!R.��� (X+ r��iHom{A5�(bR S:�>,(XqQJ (Y,r$'�� �l.h.s.��NA�Y!KX �"BI$. Dele�N,� �$%($J]� f�PT $G}-term) � Eq 2J8EqP12:2} first �� �{Addendat$ ium:A.1!KQ3HQ8s EG�importa�$of�3}K.!GIn�9.\ 54 "�N� 4Steenrod wrote� >�%(} Although�aaO ble � appearIfo;) rather � clas�& major �� of � EoccurAIQapplic}s �<�Pop P$, geometry�analys6 r�*Pyp!nFur�m�<�sh�inpter\ X�any%9�&� �R be expres�& as a limi�& +ul. in� aso1<e sens�I�Ois ,R;�d/E! family ofm�-0!.� More�, not on�Sr�:e�v2� , bu,RN� play�q+!l( significan7oreti�Irol�a!at,\it com�+ o deaWi�Re�(%�%�6 y group(& QMg%�s,�>8as Sze-Tsen Hu,!\!��* Hom� y� ory}��> 1959�5\ 171,�tRafgiv� a descrip.�0Milnor realizE�Q�S�R C�J �S�Ait X}))an� � �� .X}:#��!.zR9{cya%qin!lpu��EeNT 2r, wAEy assumeR%out los%�g�Y lityiI%\X}| 20 h)RlLlapn7#(ble. In facApU# plac�,]=4�>  Recall �aKR���it.M)�y6q!=weakly9-"t to �X�.�,A��ny ��Uk* �R}�bTiUset��1�!��209�L .\ 4.6.12-�/6�� Dfrequently encountYT!�their FGrof fibr%Ns. Its &$, however,!��l��ed��ali#��u��beyN1����Y *�V, polyhedra.!^Nnecess�V�1Ain depTu�:$�K !$5�cotoT%!u%mselves.� ts-  cular �u�):V�%EssůA� ofB~ofz=�>���Sell�}�P)49�!y8&�XmIsha�. Y�UertA�isvS �!Y��/y�&�ZM9�ona�JLe \good=C�&� �U� U!� avdP4:The&VCa�X��iLmp��Qc�?a somew#'ar�sZcon�Z�R$g algebrai�$ isS IndeE2t��befapp�3t��Fritsch%e Piccyi%* quit� � t ab��i�[A�f*�Bir ve�JI���tmladd�link{ŷN*^�http://planetmath.org/encyclopedia/F<.e}, J3c.Re�����1�te@Zinalsɟwe 3e�fS���R$$\!$220-1:%�2ke D rt syste�1c treat�H)5�:� \ f'' ? <:/um� (very much &� 1�un�"Os�X1� $2$'' invol; (  &#0�9�\ 1V� �!2�at�:2ict�tex!erA�158on each maximalI$ex in�  [-' ors"'0I�A� agrea� a�iPAh< F}�0 ly lc t� ;�O��� �SF %�` ex-o�bing%�n�;� )F c1%@�*"d(E�8A a1amCartProd� ��"e3k�i�jed ���32rtesia} R\�havXd!!s" R@om� }-ro��zpaper��nf w X g� l a+ 1Wb���f-krec4to�b) EB) !Mou�8 \%V a4B �1/� ce`lxin�\ ern d � |physic�s hin#at. Xkoch:frobalgand2dimtqft# ~188�(re J. Kock�mb�#eZ �us�e� �N $U6$''"���� r d2=��lta'' �(5d $"$+�wF"�2words6�� I�Q>a r"Qsha;� �i4 bridge betweeA�� ��CyE3thAx�ext�)��0 ( E�ex)n� ��inE CAqi&�tAAkeep it,� a!s�;� e couldUeaf� ��al.� en.wiki� .� /M�al_1�}�Z�>� \enlar�4is�g{R�,kipr In�se�f�T!�(Week's Finde+M{� A�PI�}}d A� .ucr.edu/]?$/baez/TWF.P (\ John Baez�e���h luci:6ac���%enZ  (�~115ffVA�moe}1(��-d:topich�R) ugges-,-�ba l� z^al}. He e!q�B�E#�&" ,�B����n �֡�� � a��_Xtae� � ofd �non]���,�1�consis�ofa|ingle!�tex'!Xm1 �woH'' $:=Y ��rvaa*Le5h���27�lE nd 8onF9W!�n!�slick��f���Bto�wk �aU *&�*&"  (�Atechn�?H�\2� $week76''),'l��Ubof *all*9dtotalU��:e`# with��e[P eser�ws�n� is hoteQ ��an jus��{0\�<�  ,2\ etc.��sof2 !46x�&�se�G��9BJE?~np�B%Ppur� s -!�we braze� A��j%�, too Cwe dobYwe�I�],*incredibly*I-�pa� �Z&�es: i�j%B�� nitev�! If you�A�uIt�� ian,A� wo� ``why��/xm�ptoo?''0ly �ba�� leS �]26� ma� @em like "nothing")���usuE��X rtant��Z r�Zo��" `` �� ex�ZE�ny�! .�o� �� EUu�'utb�+ regre�X� r��Iit back�(� buzzF�``aug� R''). T!w5�E��,) Mac i, n� �Ruty� eIw�M bu�>�fa�@. For a beautiful�cg %K��Aa�i try:� 21} Sa�s���a^aQ! Work���vEeSp {Bq, 1988> A�.M�I��6*E4RelCombToLogic� Af!E!"?��� _set!"f`� ravaot� or�gF� or}  \~�3-.]�/f�op�_|h� fh.�%���R4^A�ptrans�"e�s.wV� N�p_69}� nstitu�m u� So�*� 6�( ���?or5&�d$:�Lm�x %>)^ xt{(Y�&)}oz./A A:��Ʊ�percei �y�"2� v��� Da "At-jixed coll#��0noPgeneratwm5 4 itself�is env�Le��I�Y!,. �&;=q� l) c:Y.&�Jsmiddle � ,e6�N:C0R*�6� 8V+I�Y/!I�C2)� �&Z��#w�eriW � �� alisI�!�W� .�mai�oC ��o26I�" ��Z�� %��-y --+^ver� � vi!�g11R\ 152\8\ 4, e``A&� qi.d9�C�D&Y6�'x�',�� regard :a^iset#%�>�!`�! }�Se�Ol1v�4:SetA�e A� BBes,3"sul ��Z��,*  �nssociak2 an&�66�"<>���h�$v�(A+ ed.$��A^-A��25:19�~�%.�$�>��DArIS�p.~179i}re>1�# 8, \��3^choos�a t�e�!(���,� (ard $(-1)$-�� ffin����!�yat��iw�� %ic7�%�Bi!g�Mi�f�Ea��E�``"*-*''-�2lNS� �B-���!Q&]p$fi~Qivileged|!hclu�! N2��!�'G)ll�Y���!RX``� 116 G E}''~�;116� �.�nGnHL spec""a�a.�se�$: -``... a  heaf�![��H�n)�OpA)t�"� ���q~�:Iz 7- J� 75 "�(� R|e+ Nerv% q�&r:� (?op=getobj&��= &�=Ie��b�m(!0�*lS�\� (Cat)� :*ae�3���!�par�Hphy ��6��P } I� H)��>at�"s(�d �+ tuff�{�Nav&D"E'q��Ia3 ieAWB.[ �exclu�@!4�B;�i�;l�y � p�bL,�?(c"�Q���� ``�F��D�*"." ��."��D�e��F= $\{"�TQk�/J�$Ay��e)i�+M�}͚CatDef6 ��"ple�~!tZ" n�c��}2�,�Es�B�( wiset+�PitR�!��KanAdjk$}, D.M. KaT jb  �e�=Z�\'1 ��adXa7 �ad@t�0 -�(� ~303,E�� s�v�I�s,�'s�#bi\��&M5iz{ &.����O�^aL��LU1�J| %P $D�W 9�!le �G$vg$�'�,: s $D�6V�7��$. One m:j view !u�N$ ma;0ts gra� b(6)$)HA"� C$�ngQR�. �\Phi: V�6 n"g/�+�2F.:�;.^ to�� ' ��UaMQ CY eqnaq} \G_�_ �!oN=,470cmG nu�| S �X��Z&S�6m�b��E1�>.Z h=jFt.$X, \ [x,t]:�[f(x),t]�70~5w� 1q� �"�1x r2#!�!� $%���M62Q6e�F7I�>2F�-N1A$Z$M=ofU9i�by1�)N( r$ Z)(d)=Z^{%� d)},6 � Y$dM��&U�6$I"^[8 : U:y^\p�)}u�2�8x>1x�E�a)�E��� �:_>N�N a�m��6��%\%m� r�~ All�@fer�5r v�.n�2�� h�r i�Dthebibliography}{1�VLPprovid�,mand{\by�}{\�vmode�4 to3em{\hrulez`}\� ˂BJMR}{\�"x\ifhIun�\4\fi MR ; % \MRhref�*Y�� O }[2]�%% \`�www.ams.o �$scinet-get!�$?mr=#1}{#2�} B^K\"!eib9 {Baclawsk}yK.~, 1 `h{Cohen-{M}acaulay {C}onn�vit�!{G}�8�C {L}at}, EuLp J.�5�$torics \�!bf{3}8+082), 293--305� \b�ez�~BaezA98,&� (' web site,R� htS.!3J� �{~$6�,(G.E. Bredon1(S�{T}�1},"�0 Verlag, N.Y.�76Q$Brown:TenP� t�ցR.~ gTenee� r $"�;A $}, Quart!v �8. Oxford, (2��ex!~14%63), 30!1#] AQmb� ~�8Ellis Horwood LX3��G3} W�un�3 J.~HerzogVFiR}ingAD8Cambr. Univ. P�:�199Lg?'anand"�} H.~ � S.~|,5x {A}E1,}, Princeton |�ty!D �( New Jersey�566�4} DA*�l-�) {C}arrier!�Q:$Proc. Londy)� Soc.yq7VII%�57a919--24: 5} I� Cook� R.L.!$n�i� �y��{C}ell"�', = !�)V6:�%HA.~Dold1Le-+� 5lic!YX8-m= 197�7=��O$J.~Dugundj��]�@Allyn \& Bacon Inq! Bosta�196:�PEhlers&Porter} P.J. %?T.~ �ۉS  ({A}�AS}&l{S}�E� J. P*,0Appl. Alg. (1y�$245} (2000a�7--44, %#XA�9{�at: \h����.Bl3��front.�davis�% CT/990403? � �36� 8} .^%5S.~216G�< {E}xt�/%^ {H}o�)}, Annd1A�i(49'4�542�:]�B�N.~� dn�xI�F�*L !^��ue��%�&_1952. { J�-���rchive��details/4 �0ofalg033540mb(9��>W(\�\S G.~For emph{A��.�i�{R}~a�, {S}tanley-isn� %��ommb S (T� te, ItalyA�,2) (A.~Simis�#V6"ng%Ni��J�A Y����� {B}am4o�A�is�4�!��0ex}, Tech. Re�A~3, De(-#4A��)s,EO�SoE�-!�'h"�F, ��/sa�E� �/�k՘82��04), 468--480.�K \ ps-pis8t:�}v��%)Dk.uni-muenchen.de/�lm$f)/fs.p #6jB~B=6c8R.2S R.A.& 9�� Cell a 2~ {T��A)�%�CI�0:{A�,G.~Gr�be Hj8$\ddot{U}$ber d F�a��v?p {Q}uasimannigfaltigkeiten},%�. Nachr.5�117\8!�161--17:1� : J�R}a��uZieN�! Beit�ge�2. Geom�2A^ 1986�9--37:8s T.~Hib5�U�2�glu!a� *SD� :� a�i�' �� Nagoya-7J�10-3� 9!2>H 1� :2Level�g� �;s� straeD � },u�O 5�864� 6:, 1� :~A&in� on� 4nvex {P}olytop�Z Carslaw �i� 9>^� . Hilto"h Wyli��"j *$ .j esi6:@Ho} M. Hochster;� Y -.�4 ,�*o,E6� C&�  S6q$Oklahoma RA*�"y Confbrch�76 (Dekk�'� 77:�1 -T. Huq�!�.=AcademicP oE6�JandTn<.~Joy<nd�� Tier*� A&��zŐi$"G?|c ugI�9��df���hap. 01q a�f� hopf�n.purduec /�- � /JT-Q-01.pdf*�&�=6$*�t �1wA:i�' . Am�4��.b uS8i�58�^ 294--32:�1p J.L. Kell&T VC.� Van~qa�n"5:�^^4�~Kock� Frobenius&� �? 2{D}u嵥�,ntum {F}ield!�{�a,i��3� ͕ , 2003. F: �eA�&C A\h� Cj� c�f� ,uk/catalogue P.asp?isbn=97805215403�7.- �J642PJ.~Laws��B� dis  �Har" noa\  G h^o�E!�a`�ss� a�� Iw��2�76Mr07--215�rcel �r�w York:��J�*� }sV�)�,_Mac_�-} � is�{W}or�,��*]/�Sprin�,�,*� �y!s�@Q�W3d�op1 "� � )�s�\)):I�!�c����a�6�!r!���JA� Oy� (�6P(J.~Ad�mekR� �bl�-9a�ug�1�,�G ragu� ��0zechoslovakia�J8:Q2� C.R.F. Mw.1��.� AdVan N�U Reinhj197:B2� J.W. �)XC�+ru�3of!<� al�9lSF {II}� �M�(2)! Q�6�5� 430--43:^2� :�!�&�*r�)b � semiU ���%` ���C1357--B M, M! yaza& d|e: ��V^�4 Benjamin/CummdeA4:�7���e�r�i#.  ichiganMR*� ,31} (\nolinen\a� 13--12:x2� A)Ranic2`�78H}auptvermutung��":x�(6Ked Dordrecht!96,�� z &�,Rotman:HomAl J� 1 In #.0 &� �* A:� Inc,�279:� MR�(q$An unshellE.�(HS�Zi�tCrQKo�Bul,mq� y��7�  90--91�ee � E�on8'AMS atn$�c jour,H@/bull/1958-64-03/+;(q��96&*lM E.G.�M139 *��� �:{T���of�n`.��{S}�M,�nc.��. Sc.~50&�.E124--2>�Ot$E.H. Spani�  Z� McGraw-Hih:Fj3�R�D�6��&H.�2nd. wO, Birkh�us�199:z3�WBn�u}$ckra�<W.~Vogel�B�Q�%TA}*�U}, VEB/2�>|�xR� Vogt`Chni�/*��9e�s_!�� �&� rd6F XX(71), 545--5>i 3�Ja�Wal�)� Canod;A�*j�M�ean�!)���~97--10:�3}G|Whitehea" A���,ofh!p�osF� ! S&�8*�55--6:�3�:2x}�mS�GTM\ 61}*y> 7:Z1 .! �! docuI %-�. % En��"OnThe&S4OfAlgTop.tex" �xBx|5\�7+[11pt]{a�!0} \usepackage$symb} \neweBem{thm}� orem6 cor}�3� \ 3style{e3�!26*{dfn}�2�<io6{e{Remark 7co�" rhobin}{\� bin{}:%barF(bar,bW1�itle[InsQo�ZcoE-� M&$]{A suffic��on�H @$�i~K((Baire-one)WX} \author{Majid Mirmiradd�{f\\�` 0of Isfahan\\ 817$8Iran.} \email{me8@sci.ui.ac.ir} a;jI(a]{Prim 54C08�-C10;  26A�(54C30} \key�<s��trRD, 55,, $\Lambda$-�D , Lower cq=e!�)�-K}�8N��%�� ('>.\�9�"�EB�2r� ,real-valued Q.P'�J�t�/6� q@oɄ�$G_{\��})).���\SpE� \�C� � } R� Xof Kat\v{e}tov [4], [5]A�cer-4I�%a��Othe con.S_0m�O.=�%l�&59��C=duG, Brooks [1],n@u,in:V !D�-Z� ��5LUaF� f���! ^�:� [7]Ղ� A 2|.la[|�-was!�sid�J� Maki!,��l�@ inv�Ega6*!=Ej�0b�+�;�8�L�l4�m and �'� $VI|*?/�rd:,nar�t�#" % a��xF6�!}V5� $f5+�6daX�@�Us s� �,i@S�F1O��2t} [2]U�0U})�P!:preimag�0 dAy �>a�$�tb{R�k-Bu�F"��%>() in $X$.  �g$!g�!N�tP��K]R$ $g\leq f$A �$g(x)  (x)$i�ll $x$ ��'=�;� } B~�eay�aV��P��abi�]��"6jR�,%_n"�Y�H� ! �Qin� !stA�. 7/*?�AZ0�S�,�F� $��L��SiGqt1)�s $A^{�k}-�A^V�9�5 s: .% = <�Xcap\{O: O\supseteq A, Ow�v\ R?V9up\{F:F�Z8F^c>:.�J[3��6],:�U�%RE�k�lO1��,%2 !� �!�Pd��%� X@��, �Crl>difGc of, !��2�in�P:�A�l bin�ka>e<a� $Sl.n4�� 4.�= �s: $x � �  y$a��wUʇy x( \nu$ impl�9 65$u-a,*ymNny $uM'viWS6l�%yAB�= �Rp�BAĉU(cal{P}(X)$ I� B@a�]a)�<��ry ��}!`��at.[���$  7sf!�/Ye )lA2"� s:�enume�A}�0%�A_i5IB_j95N�,W\(W,mm�O any $j\in n�Ithe%%rI[9M*C)z��=1such ��2�C-�C��8U� ���..�y�B$�� n $A.�B60�/�� .O E�.b^VM�.Eoe�.� �n�^ e@ )x.{"� p��/&� *�46�a����NN�P1���ifA�{x��X: �� < l\} | �"(f,l).62��lAUx � �5 $l9kHe>m7R" c a%d���2 f$ a�:e ljZ2hWx8w�B�dyB�j9<J &D��>!em<� ��*0� "_ 5�f� �,A�at>o ��g� "�Bw a9"q�Lt�4 eu�>~�`�� ��!PXiii�pq�V�= $!�t�Zn�U(g �J:�nd %:2�t���� r� aY't$�B4 (if $t_1�E:xs� bb{QC �'>� $F(t)=E}Q�G % e�A� yE�� ���� 6r with6E�"��F(I�"� A� tE�G(M�%w*yE?�s 1�V2a�yi��H=I�]�HQ $H5K6�f6y8-�% 6>�R >�H�$ �2)� >-+. VOny*� ,>,h(x)=\inf\{t� �E : �H(tQ . �g� verif�=���": �� E#�)��x$�Z_ G(t'*�t'>t$; s�3�%=A�-"I i "tt'�;:�$�nc"�hM� ��X��U�6F��� �<:�sG,i4�� �\�x)>V�~\geq � $1R�l��BA>�>ewe havS^�am�@=!�_2)^V"�1)& $. H!@ $>>�����m� ^�R  on�(��qv K��C #���tVquI&��4)��%h��� AVQ ��� :U &upper� mi�r.�}�\ ,ɅsV+ $f)�-a� ty, aW��\  t, + )$�[-�U:eal � t1Q�a  ��2�"u}�%"�#��2�"*B�$:6�Z��abbrevi� sit{us�D� it{l2usc t -us}B_��Pl re E�!�I)!�a�,=. , -FU.5N.=5qk-N�,���ively&`nB> Co~�@ �d. dpac.: >���X&; ,�pa�i=�l!�$,� isJ�)�c<ɻm ��X��a extre]Ey�hc?= ed ��:6!�2���3g &) ���W!du�����g����Ef616�4F �0 i9�bySu d�.`seW�*9^{V1Z�FO di=O%N!H.� �Z� p >� 2X[ K A%%���2� S)%.�PI�--6��!!W)C$ �]eE4tu�^ -� � >�� $$ �_1)*|Jjt_16�$ T 6 �*;e_ 5w�YE���B-b�s�\,BP )l2DY%�rA,. ["�.2 J"�?�<��e�s:&&�iL#yNa[���!��2.��u�y*6 �"at�tL*JE���2�f%�g� qo�oi^�"�&5F�� :��� i��g5!HR�Z�^�Al b\r�9r^�63Yx*�F&�  ���some : !F�X2j)h-b2@X���`�WBn�K6�fLga% 1) =F!1\\!�R 2\} = ��elV<�1��%Ή:�n@]E�t]6hM�1O>� ����.f2���y�3����B�J�-�w J "����� eB.�,E�� �Iof�v;tF~0, G_1��� two >R i_0�n 1.� $G_0yQ', $G_1. @F_0\cap F_1=\varnja �e&��&��}z�)��"���-ZF� Bs a j��B^V1b2RsB��r  *�Mn�jqe�1)9�Y:eN#�K ���VJ�>X%���.�m��>�F���f,n�O)�->��" ��F�:�4������o�v�:���,�Ui4re��>`A0�ˁ�*�����G� F.�0�����GB��B�"x�� - �� vB| ��v�5q�a.Na �� V. >��� ~Q5 ����� �� �  :�{k zR�  =�� aB�E��Rn� aa2�),:c*� ��i ��� �  {z- [{)*}]A�A�epI��+uI& � Q  e � �5 "K �Rb F+� a�.�T ���� i�"���9 8�e&� N�� %��:I= AG&J)�� "� "�jN&\%�2�L)��)�noP\� �obb[� �i�vO$V)ceding c�ies%� r0NI���хfyzi8{�n"#, 2� � >� %,Gw]a&�(&�&� �x( �(1'�*~>:2{9}&@8 1} F�O�,, F�N�a=U� s, XA\�40\ Monthly, 78#}, 100*410.m2}o= Dontchev,xCZe)�ly S-]i��$ternat.\ J��;�Sci?3Q(.6), 30=9.�3:�A�H�>�9On sgv�G $-\l� � �Q�, {AnswersNn.\ �:y, 15(2)�7�F5�O66= 4} M.~*�.,�!}F�� *Y,js, Fund1 , 3!�5+685-<99�5m 2n Corr�#ourOu+"�#YF�'s�n6�40�=~R2!�205�6} S.N!sheshwar>5R.~PrasE6 On $R_{Os�,�s, �O ugal�4Aw5!U�;217e7}9�G=9>]:�-!�aQa"9f�u�q�yor,)#cal Isse�ng1 memo�of �f!�Hzuada Ikeda's Retir�.,A��H139--14.8!�H�8one, B�NedBq��(in5�-la�U, Cana!�u, 1(1949a�76--189�> ) &a4 a��5 *{myX5�4 c:�46 {foo !kron�/{mylW��$}[1]{\rene&c5:B#1}�*���(4 \def\a{\alpha b{\betd� ,w{\omeg�39/ \�2 {Var[�"�- Strees&,5P��c9Nyiko�-5.�?of South�Iolina�MވL�s�a�v�5Ai leng&E T�#I ��n 4��&o coar��nd�ue e=?aYd )'e�zy:S � Q2Hy%��"�6s}0 :�b&�5 �!b�4m�(y w_:H, ditar3d>v5gyA|�5A� ��{fM8glvrD_ ietyA�2o pr� �me!I!$depend upo]e0etic axioms � ZFC._Gn^��proȏa haDreaE�3,��1�Ry�R�9Ti s (, } 7mY%#daUyn&I��;,�8e^!i�� � l�j`salȑiUyis��y�9}%�u(�)� M� repe�5���/?ou�h ing:�!trunk ,aPg�'c��fu��,  |>r��5�� re-�Fion. %,�yhea���ε ``ph�yAf s,'' ``de�� on a�*ylo�9A II���w�8A ,���[ ``fa��7'' 6_ucon�h!rit�!t���sl��!5<� ancest�7per�Mo�at '��aUscG� nts.W 8O L��E+&�amu� )%s ified�n ``rac � �t .@�mploy� L�gA�.T(s �I�x|take up E�[eOɊMu!��%by�s!�� A�Qe0o� llie�Held��Din&� t (�{!�usA�i�oMf�� ert)�\ant�%jc \>� 1.1.*�s.}�M� !�}�aٳ ݳ�IH!� predK91�ny.� AV�uű[YgP��s $x <�6I%�D  sa�,�4�lb8y}z7&suςo $ $x$.]*$�)�6Uvar!0��olog�Lns��D}``]a in��Ln``�E�promp�t/BenqxA�e0A��ly talk!���``k  s��s''. I�(�.Hp�/39!� �eaA�ree�rA^of ��m�)membe+\&+)¥� .!�DA���\�Oe botK al l�Iag��ntinue�.W4fr2>rI+p��69A� � ��is sai�beI!&ed&�m 6 �].�=�E@2E9w�&x% )s ()�ny)@�a%%� KG leavXN�j�= f �>-�# es}.2�[.ݙ6C�5a��A�t>�>)�{ !(�lice��us!�of ``a� ��6p� 2&Yo6� gJ �o�A3 �w fortunate�q��coincide%-s:Io�>v �!r!�aQ�paipinc�r� �.] ��e��ght\Ri��iE�RaB:�(�alwaysr� down��� bottom97���LeA T%a�"�vnotm�'!Tr7s Eny�;[7�D&F/A� adopq _n,=� �+sc��s�ʅ4$T_\a$�� w��ll�P $T(\a) 0jk 3. N ���6T�!�,�nL0�/�|As�3m. ��an ����j�/fB\b)7wbee&f9f�=�?\b < \/�$T \rR��\a�>up \{TP: 6�; whil�AB!\ � 6�3$T &�0T :n$i;A-LT2�a$\a$-th)�!$T$:�W6�. U2� �  ��[m) �{xR�( T: s \le �t�A'we�E@c&�9sFcrv�4:)�qj $s < t�l��$T-+V_t�s��2�N5w<�9��B..�-g �<�� eA��@E V_a a��4AW&!lfAfbig .y0 16B�5:�A*����(9 A"Aleݖ�A#p 9e�= �H��$.q< carq;kappa�an2Me� �2� $ --P?a�A� �~� �ast"[� �vsY)colona\\�oarrow c^!�K�u�%�i � v�d\en�f: $f �g$ if[=� �^"{dom} fg>+�e:;: $g:�NH=0&x� �oT 6�i�%���/t ��ky�)S:�of9yw��noyDat�*$A�!��W&�ly�~cR 0'1'�n�,:~ 5�w +�"� kn��a�C]��,T m� !��topLvel�U4�E�r� �:!�"�ѡ Eg ��8an $\w + 1$-st� term. There are trees of height $\w_1$ with no branch " length #,, such as th GF@ascending sequenc ;�real numbers, ordered by end extension2�� $\omega� infinite �$. In draw�diagram�MT, it is traditional to0L line segments joinDele to�,ir immediate!cessors �seFs%nDusually not meantCbe part �-Ms; if]y9$, point-se1pologis�Q call. result��objects ``road spaces'' [see Figure 1]. For e)d�, what Steen and Seebach [26] refer�-�``Cantor%I''!F more��ed�,�,''d4is formed from. YA'this pro![Ah1�su%nive9�E�� �i�ade copiM�he ��!X �ors!ie!|%� on%$\w$-tha�vel! G rA�(. \begin{f%�}lpicture}(320,150)(0,0) \thinA� s \put(160{\circle*{2}}l4,0){\scriptsize $\langle \r$} , 80,8,BE84 NE0F�24^F24jG1G H40,12R�44 R�,>�1!9VJ12vK� �0b�20nK1B�28fK8vK��,14R+23 Z+B�6bK6~K�%-1!->� vN.03A^O4~O�O!�>O �8nN1,F62AcVM2r�M� 2f�2r�127 M3N�v�1.� 31��Jg3b5b7b9J1�N�N�N�f�1N�) 2N� N� N� f�2f�3R� R��) (1,1){150��3->� 7:�� ;a��o;3;�� <�a:=�4F=��<1yuU ;��:<�{B=�K:=�>=y�:=y�.=end" \cap� {The.W (� *�dep� $on how you| (pret it).} g�� other"� �� y, elsew� 4in mathematics� scic � may� ta different story. One popular� �  among uP $(cf.~[19])� \``simply connected graph� �a -  d� a nonempt.; 1-co� x.s ? � ,k lP equival�Hto any two distinct s be� !end/ s of a` qu� c. Bi": use ``0  in a simi!#,way. Some b61aA> " i� 8ir phylogenetic� � repres�4he actual spec  studied� le� forkV�Fs�>aA�( event. TI9ip y,�y;at i� s!�thoughy wsubse&{  planeI�they quKHcorrectly observe t' �M?ymsa �evolu�ary �s. Inde�oncLe rooteESidentif%#!� l!<�eq!Nife only �de�   same 2�rel%@ shipt%Vesi 0ed. To minim� confu� betw� kindAree��e� D1 il(1.1, I will �A�. wordM�A�ANis�way one Ttim!� �e yhe follo�sec!i ({Comparison�M'A n�ir� verg�Ib$perties} &%mex=6$flow natur�ou5�� strur e�!$!��Wones wea�i2�h.} Giv�� U $C$�M� $T$ d E�s bound�5bove,%ԥ2�$um of $C$}!!�xofumupp� Le� $C$;z� �s, J8me� 3\{t� c�  \text{�6�} c" C \}a�ـ P6a always9i becae Ci� for5�% C�1. BEl�!�m ion��hS .�%3%+� !�1>bottom l�$T(0)$!N��� aHis.,trivial>�ItA:2|Ea Ub{sՆA�ed!- W. r 2}� �wedgeN  �! ���sub� coll � all �$$V_t$��th�>a�X. ��ai�ɄatE eK�U���ed� E}�� $$ W_t^F = V_t \setminus \bigcup \{V_s : sE�F\}B*V_FG$Fra!98 m8*��tSOf��rse, �g$restrict olvBNZ�qMhip inz. �� sL�����>is iso� da�% �6� ͓has!V most �ly  N�I�x )� of 2�i��J]��j^a.Bu��� cas��U�z�Bo �Ju�A!7�2G $� me$V_s$%pXF��g��$si��C�͡"-a_n: nER\w";!� y@ con�ax �ff��f��$a_n$������Ut!��"6B��out �t�7� n8�'!#IT ~y!kinspi�& shap,its basic op� ets�� .� "� 3�tchevr� jZ~ �3�p�m8�Me�#$\{m\}24 me��a� $T, z &z !��^rm a�C[��� (V_s �+V_t) \�-t\} $$Eeat $s��$� re A!is ei� �ore 9��/N� 6�6� >=]��A �[:E A�i�"2 �$�A$� C� limj�EdA�u<x6)iJc� U� { t 9Z� �E`lgrm��5se�\,E�-$x < !o an � a' eA2a V_yN�K$ye� [x, t)ձ �#.E.�x: x �6fic�ȁHt��4 on �3he least.  [k U �!}]�J>r �q.N��#ret��y�m�> e�%��$��t] � d �,he next four.��coincid���sG�non6  :u �9� �#y�$ag����k0� Y�#sHn�no"� J� m�EZ�� � �remov.:#AF . [W shoul� tA�edd���?$Hrt satisfA38 alI �1� [� �#C.] c4b1�i*s�ssibl=�)7s�h)Q�#a(ScSAAstvd4a�esplit:� "�  great�low�  {\� i.e.���]}�Q�f� \"^IU!A��m`-on�N�NoA��L��L%�[ s,Ein-Bno�� f� �ps]�N���Gi8:9�3disi��p= �y��n4>s,��con= ��� ��I� X � :� by lett� ] zbeL!�un�(� �,neighborhood�a "�.$."�Xa �'�ss in>Z, W �i� e�B�? ,r�)6: g�� �1 in� � ,mus� ��� \�Q 5;%&t�0  argua��9Lspo'* !Q��A�� @%��8�"� eR�� �at� :�[excep���2'um�]�� inU�r��anB�B��� low�!� rd p��g E� b�)+.�$,�(�L st@*ne��av�s�)aG&p 8f1�&, sonJu� gainf zab�a��:�:� �a/��� ::a=a�ll Is� Ak i�cSA`�>- A�T a mim9A�� �� � VjfEz� � ;��{�#�,��s $h$�,Hae�a ߵ,m�F$&K5! NwP If� X� handi聆� � � �!��1$W_{s}^F2* s;@5B�*�HowAhW 4appropr-�� ak�e -l b�s$E�)b(V ny�con���f�$t'� �)$��T%�Z �<��!�;7xt�� !Jt'}^G)= i�m� G = F2� AnN� I fe`� A,RV!��it� �;cl"��Jng� *� 2�a��!� 2� !4>�a��b � @�%CI��/0a� % �,!_0�� i*0!.z~c�~Law� L�x�x!4�)7a!h��$�F�*%m&� � >�5wFA!= �)�q �. (invariably &����k� ŷFtis� ,d e$Ja��aE�zN�..Kō�>\ �6� ��ea������e :�,F �. AnI��iT�edU9���1b"�"6� � N�i� giv���:j!�2"_ �%i� �Q y in�1�0"�(:* : a��)Nbq��ea too�P�f�4d}lhybrid:���3Y�z6�e��2����� ��� ҩz� !�I�$s_" nimaa��.Bj *n do!�ip$I'�$ar�---a+ } plus.� �d�9�7s���m---8 2se[F��#"�]icIW$`*�F$& 1^j9,eV���iSo fa��M"�Uwewbp%�der!'a�@�Na zero.#�x'vw&�  х (W� drop��"�5cl���Aq=B::(ies). WithE� (E� 7) ŧis��x*��p$�!)��"�$Th 6R, ��85#altI�in i�tJO%��%er �*�$Z  S�on 3 nowAh�m/no loseV inuitp �Jb(9��[(!�$T$8*iis a ~ i1��, 7!��X l�4$T;��s� l� ͑M�H� b��& as ` half)�F'v�5��ScottQ�.�� ii�pAm�v��!� � m9a�"�� !�theM�B-�!�, �7arbitr&�',� to� .&-de�3 ion,�VQ *},��%-V &B+c� $P. /!%$U.W no�A!465 diu+edi%� $P &1 U$. [A\�F �Ssai��A'an��}�!�p":'U $��r $p c Thusc��<e L =$\�.bb{R}1e r�) rayɸ�"t#&(a, +\inftyd�;he)f< e .] *��&�%aa� 0$-s�eQD��y. &a ��#by)��� � ap{'� F AX�:u���er���$n&���c�� 2�e�E^����[[aA�tiori}�n��,hb Aint _l �� ":)�B)$�Kj 6�'(Alexandroff���T!e�aEw� ��e2I%moeN͙s 5��6��i�%a �)�(recove�&e;1.!�s0� le y-bq*\{y�$ W�t��l:H��bm0unK e�0g''� !  view ;Y* ��exy ��$ significaAZ��z(��U�>r�,riz �H�>' h)�beh6�% lik١�<``dens"�.eI�c�-� forcing.�� ��a methoM/ U modeláU�*y, pione%�4by Paul CohenT��d� in 1963as�3U��um hyp!,sas��3�1M�^> axio0?�k��1v�0%7#A�or�a�?Sn6�3�.�3, e .�.�-�.�+ R!�yTBoole *lgebrah!A6B!cimpor2�%,a�&mpu�.N4 48] A&�l�@ oughp4 a�af>�lea�=� S�4t�( Dana �)�!�ed [25ya*� ous� #s�1ipped$ �! m�'preci��&%�? � categ!�A�$T�%N Mzfun�/.a��� {1n���� �add�2!we "�%�&0�N���:� ae� a8eg� p� d � b.V�a%B�k3, as%}Y Fig. 2@pentag*2A�!�� %!�ot�AmodP 1�&��6[L��]�X�3u�?220,16b�? ${\makebox(l91��9�8+92&�qval&`8F'&& )y?2M#�80>�fantai2q6B%\cent9N�b60, =2��#�B_e�"71,126){�83,2){4&�99.:129,8;>11>Xn9 80,6V0L;46� 69,4:r51>q 126,916U�.9eR�91R�.�isEEa valida� y� � ^�u>a�%.umi� situ�-[� �Ml�Ce g"�A*� 8y%YEF�:�y�9e�0)��^�# (nor, >� �� 4��y��q���)1L))V ��4mL�Mm}?��in5 ��2RsB{;@  6�� ``o �y''���8��F .�ߡ��OL�.]�s I��soc$�t�.d�9�.b�6�smyF�37A�e E�>�� g�E�ɇ��B�-�� ;�} $ &+-$W_x^{F(x)}�3F xt\} 2�0Oe�N�,S$Om� �* !F $V_x0 ��$x�I�#y> X&�co$:�%($ n $xk�8 $x'w�N��x$ )7wif�M�#R�"� �i�.�.d��e�Ac i���-��i��. &�91 b�#GgaQ�,nse%&o1>�236�7N�7� } if s�0F; n� itera�"��f$!��Ex3ntB|)s;%fK!� Yons r�!Dm���^-nYF:3$X$}..�3 M� A�o:U"!&t>t8l8^{\tilde{~} 1}$� !�� a� � �&{I� ��>P*�!$A$. �\a$�)�ord�A$2w \a}$���1,� 6*{\a +1}�0(>C):�,R~&if �E����;�<eN�t�% &x$l�K6�\b6�-\b < \a$�"DM%�*�2��2%#� ��#� �:�V,�vi&4:L)K =Ji!*i�Y2�";����y�erize"K6iI�� J�2.4%!orem} 6%.2�,A�� Y�$��2�0�>0@i)^"x�! 2�5�+XGO > \wN�! ($T(n)I���'%�$51.� �� Befa�� �7� �helpfu~ N ��@o aS+M� a�=pt:W=� j!��=�7$`fortunate=�8!PY����.���!*E.$�Qp!x>�-UDm��7!6��/2.3�4B"�Ֆi�*bstitu� )>("�4 expe�46 e�%%�m:ak!zo5.o�8 L�kX�]��.s>��wSs���a fam'. of filter�s "�Ba�\c,thcal{B}(x) �/�<X:H2K0B*{B )�@A��9Dn ;d ����&nY"�*��iF)>�1� ex!e'�in U$ dmber $B$! |�)�%�$B&�&  B}systemQɒry:�as�+� 5�I� (�6e�tha�$worth keep0m��Ev"�BlemmaV �@ 6. L$} �Atau��6 2�� X �,Xe'-$bb{B}6.5=���)� [1Eu2$�.aive�E� � 5.p�=:�J? B_1 u4 B_2: B_iE�]�_iA�*T;(} i = 1, 2A�6�E9!\.� �iAend6m͂proof}i�Ue�2�B ---��G!in!&�+�E�m`A�Uach $i� rU�$� >�6�-��U" o=1%�5B_2 $. C}7W�2pDmVuM"E ��V$�<�lZ�:�9��V$. TA�$V�1[5V~�$i$, �1XI;-� Now, !�&3*!�T� ݁!��6�f..�%]E Glu?��$o �(x^F{!ndVG!�GX�l�7�4s[B x]$,c$ es u2g%�>�!�$.H\ *1pDF%;, fT ^9a�*� �<attac��6<](2�t Xch: !$A� =ZC$A<do� �`�3���4Jz/!x �6 .6� !szF6+@ ain ɬ� � 5 ;eLQZ�%]E �b�� stat�,MEs 7� glY���^ \ ed�/e���#i [P��_T0Em 2.4] F~CweD �) � A7A f.>�X 9A��nz.J�E$\$�8a�A�*� T"� ) f!�dll| 7*f�8>M$by��Iat� OD�7:��en�: � or aZ'al.�Z�)��> A �.)�$bA�wel6_9�. Ds�%!p�0=\3"�.6:�&t, � |�1D9$A P�11ih j>2r�.�(o&!�Hnot�nn� &�! V_t;��a�f�@ e4�e�-�o�.��.�t-��� nJ)9�!AKf�n]�-&{&S7���2�'2�s mis�&A�a�A�m� E���A4e\\ $�.]i reby" �*]L2~6)N��thu`L#%uil%K�u2W9�ZqC�O�3�},.�,A 0]c"�RI2�Mw�%lAA�Toe� -�*�&] ]��.&A�T6 _P�F?6e=p"wG copyy��Arens� $S� Q7nyA �>re�� .*%D&�J�\��*RFrlt�� [s��{x_\w\} j n &�@.k^, k� w� faithfulb#pLxZLe.g. $ x_n^k = x_m^i�!n = mt i&['��a�t!iby-@*H (p� %S_- ( � 4 �� �k^n\}�J. (x_���*Q ���$)Fk \ge j!as $j$ i\`PM -;�� �\w6!�u2t�!i9�j : jsnsnFs��me�� |#9PdI ��A']x2 �\aO���-$A5$�%a�1l* �sk^�B�.|7Q�*n (2V&�HwD�6}� E�v� )����Bqj$\w + 1e�h" �Kru�!�2,���=pur] �E �}of���()a�it*�8yet��պ.?-a��)� K. ��e� H;n"o;�Q�i�$ `column'a��!!'�z0ib�m� U v$ a^f�$�Sa�9j� $x_I� Bwdu%�MAq2��5�*atYaM�1F. � � rout� 6 � U�.��y�|. } �=a :�)�b~c�B�7[$�?��a nyI���8a6$;�c�,�Aa%6T� tselfHXE%- .�.�r`E�cL� "�W �s��$`V.�A�J�dA�n$aLAl1akh. уɀ( para_Y.�:�-� V� 2.6�ec�$*;�#i�+�!�X*%�. ��=h ��=6�kn+U�@� e E6I=90% haps2�F)ME?n�nI�EA��)0do%=a�%�fac�2�Mt$�Je�AO Q�2]it)!F6�� � �R*p "*46�I� {a�.�%�6W� nclud�pCOA�;1DJA�th?C�f�E aken �([18]. Our lV'!�0t&�%vA  1_1b%�&C%��D7NthiS)$���!E gI��. Two�&-!� ��=SE&zWmotif&S \� tau$�.�\a�1�/�*% obx�:A� vers�U�2 G^d$a-���-ur�h�M�/g9 down (�1rM� �*reiS), �5b(*�@Z��tBvit back\'vE up ad>&�mJ�!8} � ��% ${}^d}b �*x6�1�%.j xI�' ����,�1�G��^d�[i�L,ve�i~R,�>��e.�0�$A2 now-gD /���S!"�0L���K 5 d$-�$bvious*fHm��s�CA�N� Ac)Tr�U�*�!N�4ltseDaq�*e N�'5T.�%eb`fr.h�%��d��Ih�a� M))'.qle� �44R�q�6&clearl115@�mH��2 le@Tfa�V$\{E� t� 1A�->.P� v89.�Xi�F+e�Y�!� �y&�AaUi$��#etsNV9�:FN�!�w ward� Tin)e�|�eM�;�a�! d2lo9��%�Y�whole�%J� &�!�a���*�&+�@FF2� 2u '@7_�8�S"�Xs$�,k $s *2� $F$.k$�!�E�)�$K�Z�Wit��a� un�Uo,��%2fj-! a��!$2E"� anti(. Hyj UX�radialm�s!))�Bf)e(;!��)2*a��q��\B&� ) >�Uh�2d$.F . An/1s dKa6ake]A.9q:A" � *&bnm�"�Q10��ūa�� ��2�H%�4I�A+nVm��m ZHV8c"763J2� �A"�/��m� /D� E I�R� et*FE"=���9n�c�"r&� �"a�u/A�` i�� !�a%V=�"s\$c%2A%2� U�eG�!Q��6G�Hi�b ţ�>l�Uة�d�(Q'�B�U�E>�W!,E�5a�-�T . S"KS� 2vofy T �c �T���D�pB l�&�e rede�U��ZE� iB �{"�T�Y� co hJBZ� �mem$gse�Ma%��� h2�5Ra�e�a 0u�y�T�� &wa� .\�O��t  ins � >��q�d&� M�2*� &R ]{"�-�3� ,hd.����x�ni�g1*a�-m%a3[���i�]!+.w`6��: [s,t]$. %�,z>�D��1�RE !�%��9,��-��>� A+ "g�7�:6a�#:�% �&^LIhl:{-or)IssecK e9vL���^z0��k&A�b�� B��1;�8EM�h1  s>."=�volve�e�1 true� =]��I="J�t7/�k �y� -O=R� �O�)C�E,7��W�_"�DA <=%�� �6-� �lef)0�&*�%Ű�s 8E�10%�aq�������.�a)�e mat8o��Io A� ��!�m�͸e3\!�a#�b"� �<�ERm=� dXM�!� enti�7reTI�h�d0 E+ i6���LKi�&� ��W)��;�� fE�th�N quadr�Nofp71 2,�!3 peak� &c'6n/-� 11.��a�E�iY"�e"c*5b�bsw,derstood via*V-�? w�&�>� ia�AI1aBy_��/M�M��OFv "�Vv_y��  t]��;+�1 ile ���"� �]�&s or)�u�a����"~s\}/C�?�j�b�-K work�utgfor%�>/�+�3 yp��mW or_0D�i_QX�~ac�^!�tope)6� n�s (:�.1%�o x8rw haft�Bch.: 9�e &L1steps�Q2FS��:� ~M�9jn w�r64)�� (V_{t_0} &� �kE{ V_x"�+A \}) $��\]t_0E%�m�"\� goD"D �,'>!E�De� �V o4 � ���M�und. tqca�exw!�%W? y l^ AF�Hing trouXm�n�A6�!��1�.sl*4 *5 �/i��h��2��S/qlIKe��%%.�����d��� �H�! (::')�b��da61�\KŴe�M~i�+�>6r'B�$FJto �  InE�QZ,�- #��.h Q�:�, 5mak!�D� �F�"s'rt9E�um� E���Q�. L�AMFy�'A�i>]2ofn 2� 3A ͥ s 11��12Pi*A�2c ſ_�0a0%��)ic��6�%t!�a!�!�M*!�,of��2p&�1)��m�met��#"2 )1"P :�R��N�:��� al XA�:�. Me�0i� �+� iD, .�N� 6a c � lefũan exer:A  S�edk/er.�n� )Qe�m�sO uf>oG�+ 2|s� s2 �em9a��.-U�� ЂA�t0 wu_clavcW Z7'e+,�| �groupvorganismI �G�Cla�!7Ah�8>-�varyi � B)�Eg �s5ll refT ven�6�L taxa�"�� 9 s legitimOroCfic �#6ir V9ale [) I_%� inad/t�a�*.n?G�c �!��!�a=� kn�tL�e��r�L^�K"i a �use�5e� �do�B� ,E�l� �M�5���N" YMa�Zuss 2�B���D{Guletenest act :"m���*%*�s_V�%])��F E�e �I>�kin�mI �y G ria�h !�� �6rnXI%Ofundaa�Fn"\of Dedei�m�mtrans!e��2Jum �y��. 7�~.!�&�(s�le{ ���:If�fA�.k �m7���-��&�! *�. o`,�{���  �o ma"6xorigi�*![a� �N��=n �  ��4�%���+�P2 [2�7[W"�v5 (ough 4b nor%-4dB'FP��Wteworth^�!� ion]�+e�"%A�7e��:l�� longe� <!� d�%�!)fM3� �K�+"6\I��;z% -5�. v:K>�`*v>�4A��E(i&\R(�0s "er)�7.�1g�H A? �:Zin UJ��qF�s9$hah� e�**@[P�)7,&����Lva"�2+4 inasmj,D,s$[-\SSY*�W� m3nsor�a�o�xYXl7>C�"B���, I a�� �|s{nof� �� rticl�,Z;�nH�]in�`�A4E� seem.�V+3.1[�= ]'��0A-+ � ���ah9�.�7ite�|} \ [(i)]IA'oo� �;B.01T  CJ"��P|s, ��wo�Qs e��F:fde�>"�r��T>bFend�*t&�x�%< (i) ,1(iii):}�(�%e:�H T$%.lg<B$(A�d�"PWK;U;�OM��6��WI!�u]�e � � ra~r� &3,uK 2�0�1 e!L� vA�vB&��'���1$k*A) �� ���!�E!�PGD=+�0-�i6�$FO�#. $.�"���"��tE�YEt���alQ���f3ha2>'' �h����A:.n�? ��:P w3fai�� �Z��tM� Ac�Lu�4'(!Z �d-��t�>b�6&8�a�T�nctNNHERT\14�A$m�thex_ hoose >�Ta�Z%��q � �Ar�!R� eR��Vs�� ``M�E\a��analog� iOnv!�!*�6k �WI Aau �xFA�".X�� �fi�Cwo6M�!�:r !���of ``� e''��=.�:iV�b p�a� lead" eun�lZ�  orEV63.3*�{} A ϥb-WTA�-X -ZueMe;C�_is I�$NH G)�um6-IBr.�<zI�� t�zl�_� e b�h �a*}n �!�i���1al B3on" "� �  �Tmbe�S1�)n!� +nRJ d,�ept�&A3h t"� . Chai50� ۔�7� � aB� &_%DE��&vA3�,a;!� *hs!K��e��'I��s�Z� ��)��LM9��,r.=� �" R%73="��/$rX sourɴ�;b=�&�.�mA� &� v E�FI&32�H�zT�z�L.:���=v Ň%pQ�LJ��6<:Xs*� &i !C�0�R� J-� iz� :� >me�:� � qH2���, �Tifud� U&��Msuper �}*� i�Xa��I�� x- E[%!) �0r���aasr"�� �R��by1!er'�2tM[��M��t ��2z  s&�ly� "�]t�XL_L"� K�?"�Z���\{2x�,��$\{T &�.$B$b ,,ic .B�T�� �>B \neq \&se�t� we2��  a��-su)����wi�#pick "�G -�[!a��!I(�..�� ~>�w'zQw�dZ1  $x = �%�QM"�b. �EX mE.xIR�@�1��F � �T6x!OB!"����r�/�Sfxay2R �y�>F�,\, T .�y-6y.�y-"���%3B<�!�Md�����)��a��r]bmOf�j�""�5�t&� HoaV_0�$a < p*ll �a P$. kE�AR�5aJ$b�-B.i $b > aW3e1aB;ba!i�s�Qb�  e�}�� A�Ia\"8'n|,���!eCJ$"L Hi^ve�g������a��K lsory1�"Epa max~ mE�,A���!�vi���aE�2v b : -{, ,�!L���*v NU}U��@0:Ea no�ߙ96" R�45. Corollary} & e`c.�)� RR B�L)Z^ u�$az� \hf� $\square$ �*� � A=i�=�]�q8Aappea�a!� thco� pape�\ke abs)P� !v a�a�dz� N�6i���enumeratFPE�!4&�:_M���/i]� w_1$%z!�)�V&.wmu~�D}m � Z�.�B t �^� �d .�)z:� &�*��R�"� �A� �  !f�&- %���)� 3.4�c�������U�*0�rHie�C c g� q��E hang�|� > �Z��� CM � .]k+�R2���mod(�D\P�;6q�1K.%'�� r��o * �.�w06P$V_p$ Cn 3 "�i�N5!}�addern���x�<�s�*5�~�V'\P �c�1 �raUa*�@b��} ..s+B �-|�'F.�AA���&Kholk�"�{1�:�eq)5iPc�|^"� � Z5b���K . E"����{%"���� ��)/ e6\1a��e@{�U 3.5�+str2�^u� ���zS D �Ks n�"Cer^�7��Bti�!0.U orVb��A|%k� R�,%F)��� ��J.=�N�*&N?&�&*�y?t�f�acxR���Z�Ae$����.eU� waunVGE�4Gruenhage [11]^�8�}B�P�,&alL+l\"$���!%t�%�H$$\theta$-r53�".�2{E?S�a�a�r;�o-�_$�%���Ao "� -j 8*S8N{<e;SX� ��C�T 9pI)2�!u�HR� n $X^�R\Delta� � cr�O/\8�͟ZFC��waQa2} regu��)��M6�J��^*�e=PA��/�in�"�ga_b alys�.p attributU$(D.~H.~Freml�0 y Ri��4d Haydon [priv%communM�]%� y�]re& &� sa�a�%search�e"� J.~Bour@,�. whom��� ttir �by*HDiestel [8, p.~239]| fL9.q.}��\w^*$A�nd"g8Stone-\v{C}ech { �&r\�E� /ds,A�^*�Vb\w -\.� \�j�J C}_0"{r\}�*g. 1$A�an un����.F�dis�6t 6� y ') �� ,u�ions� pG_!H2: d�#!ama�Hy2�E�&\|9�F\|n66{\a+1}�w�B�z �of2��Z�!oeo�7��in�*\(>��/K? &>�E*ʆ OH�%8�.�YaAd*MC}_\bL E�- � ��"�_�`>��!F�L W"�'�P�&��$&*0.R \b: F`!�^6�-��5�(]�))@-�x%�U���M��ior!U": , �,6�dA� �� >of�0R��X tinu;til�1i�TM�$\gamma=�r}]9�#�u� I l6�@���:fT}5_H 2@f2�a:Sa�` c \Ef��i4�Ee�5�'&�-���uw� A(�le�� Jj�61 tell�[�:� ce���lvrn�Q�)�ui{.� "� �quoti_Y ��b1N� ��T4��, Net�tin:B S37�% cshare�P� `pathR�y'$ �!\�Qd� ���R�is farQ�tb*��A�@DK�)lo� %9}�LiA{� `a '�,)ͫ�&� < b�ke e�fnt�"&�zof"<*4� �)%s�e�� Ǧ!��,ff�)}�*�5Z� )&6Rca͎ $\kappa.\_ jiZI����C!�FU3c :buA�tM�>� A�^l lanL�%Or'E"6�b�\�\Y-��A;o�Archimed�u�s�% R�!10.*�!.}�d* ��B}�I#E���!,of rank 1\/}xgi& �&m�s _$N(_2% i!s_ap B_22Zf3" a8$*�;B_1�A u�A>�e�u [&�ly,&-])3�a � �W6|"A "fU�ab_Rw%�t�*{'I�6�U;i �X"s?.1 ([21*w�9e�e &�QK EF'�6[�Yultra�QM�c�A!��a�VvT+1W EV$NH!�d0�P�, b :=*c��:HvH11ns"=A���%�:� for |0nF �%)%�6����lZ � =�M ����,E �le"~  �O;�52w6`T�X$� .'(x)��:L"aw� B4�a�� RB�c@,$f\colon X \�warrowF`%#�#�X$�a>��+�m1B�A&�Dh\B� seenD� .�2 ��dZ$��i�� 2� 6�$@E�R��re��<s��m��F� !_)m� fW'A!,�oYz�a+��&;L�y��n ����xo :g{�2&J�aka��N�a�p��ed#�.9ve;^|����F��&p� �p�|d,�J:Afr-.�41.")�)+ �L�C�� o�`OYC#&�too. l� � "`� V���X}(S)�I�!\&!)�$Say�� GAV m��W��V�}a� �?� aNS�@rA�o���= B[s]��{X:�k�"�l. 1� de�y!]M�]>]cj �.�2�86.*� w!��.� a9 an L��l � �BSS!�N0[*�� 4.10Rv�One�`!qsa� carry-� in6C 3.11� o�6A��s!P�"a�:lH$xO �7e,�. �&-��?2��HA��&)]��� a>��9�>3s�c!<n,Et�62!& M:� �J�Gi�-I��osen [�bd��u]F�,2x,� �8�ã.Bl&�,�2-�\�Rm.-x6�%2!."*-5,�"EXp( !H@82"!Q�G�;I R�� prPsby�s [��!�����s!��� �� � at @841�J�[,� �}�+f��#.iq ach �fT�t-EE>5`] "gFs:�t_n*1Z&�`�Y&�/let� t^�bV_.��E1�a��d y�${t_n})$. E��g�Z��0$%�QK,�8�$$ \{~� : "���Qw}&�bB�: �[ , \ 4a4>�54�P :���a�i-5��1�>� ��"n�l�O���tT>�'t shad��!�e�5`jEd�  .��71��6iuV1-E;�!��!gsu� l�� !�B�J�$Y�zj .b��V a�7 "� �e9$-�5!_lHer�u%* ;� �h a`B�(C. Aull [1]L$k advantag[��:/� �2ditar�k*1 �I�I-�MCwa�no�Ysigma$-8)-iEg, u�HEV��v���� idea}5�w��ll"��aB� a� Iv�nta '��h�P2��Mue�km[:L� !n~��d1�J�,���Z%&v�x)�:��A ir]Bs� Ill�jR'�7F�� now ��`��''ɑ< mean%��ygN \a2>l"A��w@''^/m�*{A Sh�SurveQ< (Mostly)%KI;D�<TF.y}%vt a� r�� lion�.h�0��"�ams� set-y(-� I^+a) �.*" S\4�AA�P 8!�+ an�%�:eI�1wofold:"HBnȒ��1� $1.6>tA�&;)�&1{&s�a�?&�P~� ones ( E �eJ�H��N�%F�onAЁ"I6s)�qstr%xZT���� lessm�va��M t2b�Q��B�%*� %�pt highl����c>sZ�546Z�^Nm mono��A mal} (or:x AFly \/}��a�Ū϶"�iG,��/JTYMÛAqd�X$a2Ai�'ش� s 25$G��%�%u AG��mG"�� .�Hu/ne*1 ;)#��OH� ��G�c9\ [V�� O�"��/w}iAdu  C.~R�!r�j[4]�!��is ��4 adapto2�iMG�*g �b3"Ae��m6�'' .Abe"��M6!�/ �M�+A�I%��::)1<%s&Z�(M$\� �L�u��>oiF6t2���`�nic@ �'�F thre����:��V� �y4..�  Eeu!-U6gt.�,�?�cgR��i(F�,! �+}[Out�_�R�(]K=�[>Ny�vr% G$, 5 $G_t�t*1&�ry ��Z%�6 5 CS'S�S�- S}u(t]"�a'b�BR$ G��" * pby��oF"��UvR�Qb �  4e����Qi���b��YJ� �3��O�.�1� y, p�Lchoic���6��,�CW��')����8�R�%-Balogh�*6/ of [yl] :1A�R���nJIE��. Q �Ie,t esrSQ�u,dX.!n�C+ i:h%v'R�� .�e� �."��B�(%�&?e>M�'js.&�3�?noI�A)�)%F!�]� - y�all�.hav�ZF� �23�r�2E%r1D.�6�����)1��9mbox{} V�*m&�gIWsi*��leU�8�Bd,�. AMN.���mNM���I ��6..�� �Ha�AE9A�9��! +s (#14.7XJ�3 rul�uFch._� Aronszaj�1����!6��[� t�� �G,A2�A�[z�.nce jmc"��pB~.!��:�E*�5E�:�%O�gMG*����&G*�\2m�4=&� @)Lambda7k�q c~�;%�(�c�Ya�%GPZI$\d�+} �&�7a"7+&�T \!zr won �2�T$�cvU$f(t)��Ũ0�RKW8��M%q#,[f(s), s]$ m"St)��sG-XC�rag:8 .cBd>s��� net}!�a�� �.Uv�P��% $UJ�a6�T��x=,� X$. A*ɇ$V$)��.es}7���a h #%{OR[ halv�? - =`�X@(��W�ngv �AW$W�� W(y)�<.� %�e2� U(�or� �6�B�6��� a+A�Jet�u ye�tx�$$[s_1, s_2&- �d#�s"�Fs_2$ Af�� z��$0 <P:� J�4�2f{\}�22]} S00 �g &� �"�3"$LeN18is����"%�1�$nM.�;.6��14�@t��@�>���,*`'c>�0�����)�azY � d��1�Wb<��"�͠%�*�= ��Ev�a� �.<6�KN�; ���la�� ��%do��-W%Un�N\�}. SqXgTe�����.zgOjm"< l� a'(t�J� ��)� go"�=alj vL�ti(&v�("+(��żn��1 st% �s))5�nH<r!/aJis��b �I"1%Y (3*UQ4RV[16��x&��%d��.1D�4nKA�g5Z��*6Y��vE�">, ``in effect�a!i7# �xn�%authoNso���1s e publis�2 �oR��A�%� �e�%p���"�.| h%I!?�ntrj}� neX5��f: �;�3iar"{����*�/A8�Ns�SP z <�ll�,��i�&��g38y��ItiZXB4�7y}1 8Fleisner, [10]}�: F: i��HG�a)���t �1�@.��Q"`7;F"7�A���2G� H..$A� G$�>t)Z et H$�hND.�B� S�$�_�O�]I.�fMi�r*� &�a "fqz�N�-A�!��5�iaF� �tA*�"�6q2.2D�%P� .�wIia�ry�R,ngAMprِ>yP"�4 �]� OE�^gT(\a)� %6�-���4`�"*V��fac���M�b%58U��;y�AO|%U<*t`�(� ^w #-u��X�,�bA�2���e��a&� "�  K? [�YX%6~7 [(�? 4$\!dis���_ Zo�8{I25(s�"� �Bc�����%��ap`9(i):]O, lAw e���'&!I>%�dF�>�UNZ2SoN $D%� O�9-l��D`j�&���X�ZYH(pJ5 $dȄ%" < d�j 2 6��.�7$ g -ir%�ure, JKR��i��De )�U)M�I���:qaIb���YRi ^U9} M�U� ]�0A�� � kalYLa�&� ac)e�"�d�Lop� x|Alt�(F.~Burton J�!�o g? ��UB "�tk-��s�inv�)g"ȟm&:a�iث; year�candidf�� G�non&�Z��i, aT0eUA reydX � &�����ed`\ I+~%�kr�g}80A�"wc(1. His judgw/%ApW7 v�ca�� W.m n ���N[9]��� �� 8 �28 MA + $\neg$CH.&��Dev�-��( Shelah [6]^�0 -�6�AJ2e( $2^{\aleph[o< 1}=Qroe�da�*�CBV ��NatI9 u�҂iq�37���A��enc��I�se`%" ���% cY e6J�AsiEԪregF``� *,A!HV-�xҞ� llel[�2.�Arȁ_� � ��� z��A��&�to�ʩM.���6�=�G62r�2i�6�s; MA( y�<�!.� F-u�%r �i2MD� H� �)+ >�M�^ � �� !n�X !��4bb{Q}$ae�6'';& ."5d q9�` �U*� �72gdAit*�e-to-@Z�;AlJ�  din�;aKado�#� � &U$>�,N��6L�6_L&.�D 6"U��= �0?P ?P>?!{� ��&�,y&aG6L�A�� B,$L$-labeling*� "�{�k���inga d $p <_P qY-$f?� <_L f(q) � A&e�$� pm�� adm�1an�.&�cm&B{4.13.�V �vF J�s�*:. 91M� �)i)"{eBX �'A�FX"� v?�Ȇ98sub�d��BtIae�hA&(e �fj� uK ɠ�ZDZ&i� �ll8(x�9.1�[2��"� ctc$Q(v)�dem� S�Zdz K.-Ppl,art [15] alt�4!��!ta@s?+i��&j7bm� .�2?B4:xE���IAE? "ZH�d�H� e� A rӊ�$DU}�=� �_expands$E%iif � Al&2 � `R~,$U_ # $i*� q��UQ��Ts�<= \��C{�ne cIn F0 R*b��B��9i��,bZ� say*7��I�&�G1!AZJr�1F��0�C# ly}] s6.)*(F } (o��abbrevͭd 3[s]cwHs+ % ;"��E ��\H ��8.}5]�A>"+�2�%,:�{ f�cwn.��Gu ��-�:�(u��?H):I�"_:�6��D(M.~Hanazawa [14])SXa�)"cN �� ��j*p�6E Ha �(cwH)��O&&W#!S$Z!S(=�C �e 3 cwH.ƟbL.�R%Z (K.~P!^�66,��o��], �K �)Pk�uC *w&��.��d S�I��k �q�B6/�g3+ Pf�.�eZ��m6�82N(Ms�\�.� V�~`,�gX��g.4%&2 ee�ls�c�Nics}�L_��on (\a)4)��c���X*VT��i�.� �hc/,�&b��  ��TR��]�n�anda\"��z�3F�) 4.192��4�e]aM)�_is��R�!aZFC-in�u���If 2�,�!&e�$�RV&� :) (+KtA���Pren�-�oҁ)�EP � . �;�3r��w *�34pR� ��V re�;B�< $V=R m���:TU�j͒A�wH [29]~ so!��17"�0H(.5)��-d1�F8�ur �9few�&ul�are� )�!Race�s&��>!�3 }��\>%met$ \/}]� �"� .�c�!�ly�,HA[��%�8]���'o^20B Nyikos [2�k T�D�">��~��f}� �2�"�( �>H=$k4]R���A��-p��i��`A2%=�0�n�Z��o�2gQl�'eF�Q(-finite}]} �collection of open sets. \hfill $\square$ \end{enumerate} Hmyproclaim} \begin.�e{4.21. Corollary} Every normal tree is countably paracompact. (``There are no Dowker trees.'') \end.r�proof} oc `(e discrete 6�closed� in a�Dspace expands to a^B.;!* �Z2NcwHJmet5fu o�Given $\{A_n : n \in \w\}$ as in 4.20, use no �T the antichain that isir unA�joint=? .8D, and let $U_n$ beD Bof oneZ0at meet $A_n$ � �Z5(3. Theorem} $ existenceZa5�y.EE,�not%fLis ZFC-independent. %�N� �DW.~S.~Watson showe!6Hat under $V = L$, eE� locally cI�,V�M`a0wH [30]. On !�hother hand, a $\w_1$-CantorU& � , bu%�iW �0MA + $\neg$CH)�h%.q2) �Hthe same axiom becaA-i_%�Moore:�Z��Mway�is��of a gap!Gour!�suggestsa'� ts failur� A sA�arly��le>>e�. Ma��t� un ab�b:l��s, inclu��a�4smallskip \noi'� 4.30��.� ��.h!E �vunybranchɄ6� le? { M �i rdM�F �[-�in� � � anJ���� >�;E 6>^4)� Condi�4 (4)�� 9 w��n ing�aEM�s of!�NU31Bj 6�L��e �e:~eperfect;)�is,�ry.H@ $T$ i��q�0�Z�)�y�-�tƎ��facM�(1)��ies (2)%{essentir �7n by Mb@nazawa [14]] who��(o help answ�&� of ����: ``Is �.�M�-"Փ1d?''A(d!M(ffirmative "�\,+$\,���H�himself�edQ��neg2G��� :Y*$ � �ofs H1v]e��e�er�! . [:�!� !�( Aronszajn q,�Keda [13]�b&R y.# 2� ot.]a pap!�} !ԍ*&\& �&-�sbcV�"/o( Hausdorff,vHm=0jeBpr.��K eRle . Hence,A�cwHq�"pB��fam& of)�0 "�!�dA�M� ʅ� } U:qwn� � he hyp�sIndg engt�wco�} sionb�.{6y 2\ If:����� le if �. i^���no2=,sN� A"���� ifl4B����A A��� � f�E �F�An!�r��!�ٛ31n�52�I"oor PMEA� yv6� a�ɗA�:�|�K ��2/M�.D �j�A! wellnqPm�!�p!��# 4%P8�:�<. Conversely, i5Ue��"�� �=�2�*��q� [20];!:. r of�|� �y<�$ �"V� �Iv���a�B&72�J�8(D.~Burke, [5])���simila�i 1). s�� I do� + whe���6k��� R35 can��dropped� More&�b�6I H f\ *�.l�V���^gy��� p�� EGer` to2b�7��(���� 4])}�a�!+i�.� ew6(��m�lQ �"E+m1a()?�Va �� &� � �for W Q a\9�6�*$!�nA��p  aB�*N �� � � rse,e� �. �:��wH# �*<(�' 4.32)� )�&� �%onon=*� d�d�j E� *��<$2^{\aleph_0} < 1�!,nd EATS (``iF� �''*> ��)�$ (cf.~[6]��[27])!Ar&�F�y !@J�!Lemma� .�r�2anI�!tz�CH� ��� 1 >�![-!�%m.�w + 1��2]. F�ly� ���!�R�random�-�ddo aH`E) &Q!Q 4.32 f holds! forc��extagonI,�� /!�so-�)},���� �("n�I0F%���.���may �Z� b�8*�Is3 F�� �5� � ���?J� Weaken!: :�sl:�o=*n`w�f�3.� R�i9N�,M .�B`!uZ�a>��N� {SZr IV�"@ 6�"QR�$ ~"�&  B� 39E�A�a4.c#.R �us�s"58 4.26H .�QsEBR� ����!&1U���=J�#%�a ��J��#Mơ���6� a�J%�N�search�,�"�4made difficult�!sf"�k jbbl, ��-s� �\!�a%(N�! �1%)"� I am awar��& �)*b A�Co�t� have long $e n, 3�#-# B - mioned eB#: wH (�#�ő( Pres� -Downɚ)>�E!9ډ{QR���M$E���[7]$y defined�`fY42. D)5 .} A.(%�E�i�most �$}d�&K meet� nonn%ion� levels �A�y&8a[>'ŅH iff��� �M is1 an�y �AN�811e6!45�d5�/ack"1980's,&�did �avptalogu�= ow 6 2#E�$)] Fe^ 5r l�#dQv s exhibiall���'�E a� ide�&� is sh-OAdrulluu�)s]�orU�'f $--- except� : w &�Z�rŕ*7.4� n& 6(6 H"�s c-dZ ir b!Qior�  re�?t���!=�y��, e 12"� we reE=Yy ci�we begaj9]^u&43:i] ��v�%i=��&�%7" �% $R<u��)i,�HN~Re" �*�4 (c)��� a�ed"�ly:axit  A�nt.���,R� HU�#i� I}��Nr44q��!:�I2y wKH,�xn12�.a�"<<2"N���B�[C� re�| 3.] �``wKH*",A;2%.=# Kurep�sK&cx� !�(ed ``CanadiAa rees�%t�*� �. ���<+�  )��pmth�y� 1$��Ce"*C���vI�ra ��m�C continuum"�iiS�-� 44 %es 7.�a�Tl%d �gn*F, 1 sIt&�+B&��to ?*i6O'� �(�ee� � 4.44�kts�Z of g,&through:(o�eO(p��Aw``i�B� a" �sub!�!� whos�"emcy)qpparen� ��5 U0�6�)g�.On� !�&�"9*U 44jz' Va�1Di ��I� p $-'r<)�qYq�1 of *,& 4��J��45�*&� &�� ja(:wF�&c�(B5 b *�  Inci!a���%5�(is  %e��.&c$A�cto�eproduc!Phe Post ! file Figures + 2O@ p-7s!Ral erroreI  draf�% S� 2�@��)� � ank .��,Klaas~Pieter~1�s!(m� prin fth��%s�Ɂ E�Led|+(e body to �4p �sp�)d^��o�'�re6���to!visw !���Hthebibliography}{30�� 8em{1} C. E. Aul��BTopolog�d8,0q\-D&Le base,} AMS ProceeA$s7 D29:}411--416 (19710 �X2} B. Balcar, J. Pelant)�P. Sima � 1�7,of ultrafilt�. on N vp b�dense� 0.�*&� A�B�(92}:455-460�:H6} K.!���S.�3, �Aa�a1� � -7 |A�njectuG} e V]�,31:}241--251�792�7v�%�S�4���!&� tm�e!�E� c. London �S� 39:} 237�2J�8e%0Diestel, ``S���Q;r| in Banach) s,'' Spri�4-Verlag]:q<9} W. G. Fleissn�4�W3"is h' T-l? Z�450:}375--378 ��52U10^nRG+L6ZV�$6WR_8�20--32� 86q@11} G. Gruenhage,��O�<Corw:� �of :�7,}.�{4126}:26AN68%f66�2} M."W vVar�1ki�<of* AEs��no) #=ffe 8�7LI� NoT iIee�&(cs \#891, :, �E�863136�IC� "�!Z�J� E�JapanM�$5}: 59--70%.36.46~)����&\ �u��k?6<&J?Saitamam�Jͯ2}:a� �6�15�P!�rt �Ch�8te0$ �2.(+d��dop $\omegav<%�,} Indag19� 44}:27�83%.26.�4�)�!�.eV{;}�� �..�l-1!�151--15I�:�(7} R. W. KnCM/$*�6�a�Transa A�339� --60S ͊1��. Laws2��#atiI;qous m ``��I�al Found9�Pr� mm,Language Sem��6 �bya�0Main, A. Melt� M. Mislov_)0d D. Schmidt,u�]= Juter Sci6( \#298J�134--1�86�9��W.!�g���$\Lambdab)E[ *9 }, �Bulletim~�� 87--11�p96Q20} P.aZ"-�q�2!$, �$}�@ %r ��*�uni!�� CollQ�!0\'anos BolyaiI�( 55:}409--4B 6�21:��-��p�*�X$lexandroff%)Uryshohn�Oertain�4-Archimedean �,}.(�f<2�22R�Ma�� i �} (�80rE�6\3R\QF`4��Qke!ace~d4Rd1�e7V !� a� laye���� Scot�dy�latticV i. % sq � ic Geo�y� Lf  u��IE��&sa�74B��o7:6} L.�St�!�J eebac� ``%;"�-n�,logy'' (Seco�E�0)Vy6 27} A.�rTaylorM�D�> � cipl! ideal-�a�!2# p @,}  �!��$33}:282-29H 6!28} S.B i}TA�%lin$�88�<��"� of:� "� !�r�  (N6� "� (), 235--293!�:�2� S. nD��L6SD 1;� eb3=�� ��},1L"���34}:109�@0-N6T1W.B�Se�Vy�atb:l �F_,290}:831--84��8� �>�  docuA} �@\\class[11pt]{amsart} \newDm*{fit}� F�;InI lete� �m:4s4mI�5c h�^lv` ���F \ style{0i!b:�{D",}�16�5 {�u�( Atlas InviY�� ribum�s \textbf{9} no.~3 (2004) 6 pp.} \v6X 0.25in \title[Hilbert'�fEedA�f6�u �s]{7 )���-p�I(} \author{P�ddress{U��it�.8South Carolina,��Humbia, SC 29208 USA%�anks{�6�w adap!7�-a�-hNoquium TKl=�?n a�e 6�Auckl� y, 2000,�t g�!a sem2'K�wEHpoke C8a"un�E����=��he dee�3 to b0outstag= importanc�(��?�u+7)'s&�6Fg�#to with in��= � M revolE�is�e%�or[?�!A#:Li�0$, ` -no�,'%��e z�pok+ whols. A�zAXof *=A�if!pos�Gto)zvm� ��rrang�;xat�,A�beo��af� n/n�A)# (��)� step�)2's 94A��0zy%��a�#� A*ne canb�G��Gasy1)*M���a.4ictly �,eKG2� (�q<{c}$, `�.LIM um')� %%�_0$ "�ʉ��� askuCe�i U&`.q��M"�se two�i t# �-=i�%q;cas%�n�7i��i� H&W5(��sf{CH}� ��m��Iunexpec�� conn��6� (an2niA~Tenth��by�?sc{M.�as}%�th!ym�ED�Jed.9,F. Browder})Q0:� askedja�!ehJ6� f~>SZD =flavoE�� urge�ath��A�provi�be &�0pas��nNS.G�pso�%'1& volu�Df JSL1�JYP� ddy}&�!4quote} We must\�IQin=�timll��iaA"exc ��!r@In�,%xtr�sy cen�`r�� !2%=%M$e legitima�Gabstr�(obs. WeiersEd greaa�clarifhe rol�F u�in�! culu!������2m��to raise= Ynew�!0g� ity,�:r��ahrigor. But Frege's attempt[ba�.�� M�or���%�6'mb���(a�tradi�. G! Z%�]I( as Kroneck) Poincar\'!�ndaSu�<challeng�[valid�AJll��is�reaso�-� voT;o defenQe-h+# dis�Ņ�fi��Y#Ekfue�b�JA�| �O��)in 9D$al physics�re�q�orm�>im�of deb � criticismj4c��O todayP; inte�$ual exhaus�L�Irt�a4� ld���m� striking3dots AcN�0�b sawA issu�" �supra.� XF ific > ���QWa* ��E��Ye s�s&f7s�acu�Hi+m�poA7of ``una��'' humanM Nf]�jHs,^n��d� k6 spiri�"I%�dee�Imov�)FS [13,� ~37A71]: `VA���)�!��na� Ε*+ become ne�Da�!QmerelOG!6 OEreSIKdividA)1Z bu19hon�P��%&� t�?.''��� Q!� alreadys-E ���&J� � ,�&s���� b;E���ab&�F?a6|��-decidA�(as ���D� ?.�0it�,Kurt G\"odel &y,e P.�is� ����}Xesd� �G�)e�, cArithme��ISMJu� to' mu�Hle�at-���%i>�O�'�I*l�Bin y z. I�%< ",F [bQuery:}44Fe�B 's L��w� iS�!�? W$a��AnA7�sb Ausa�� ZFC})�s;��{�9qM A@)�%�s?]"[2��B� nca`�demt.a)� �.�f(1Y� An�?fundaajal*} ofyKa*j@ct�Yt of �%c�6s7 Tog� �.he��stA�om&�eem���U��" sour�Y�*lthv���Ia?as�A� adox|$�2"< )� ing:A!Jm.(unambiguous��m�i�d�n? ��QnitR'�*``� ''. A�"ea� less bipe��&|�`a���~e$�� ���-p�Ynto -to- WspoRIcI� @$&Nm�E�a� work; nei� !�t q��!j"� ax !atj� 6�)�$\{0, \�, nM\f(�^y? $n$:� vHon�0 f ``6*''��b�8-�d��a�I!E �s!�cl>W�T intu�<ca>�A&� ded� �Dsc{Go\"del} [1940]o'��`al��A�L�%� by���t!�"� HZ� ��i�t�8���63})�E�.io� ���a�Gc5mL.�;�%��8��a�fai~ileAC}�;[Cm�of ZF}�94hen's techniquE�-{A� ;s�� �QbyE Solov�!3 Shoenfeld4a huge variety�p N2�C}2' plu�sf�)��b��Q Zyears si1thez,f�K�=ao��| �� )N c{Da�+� Wood� Freml �(, ""�(Monk, HR~N}���Ar-�c{Eklof:=oitman}^69 of B& revieAw*�N�T} ����4B6 a1� topi.��F`ce�+�^ �-%vrelevan.�S]+y9�)tedH8 haps��A�!-yGP fiel`q�ja�Ip�=]4!<$Heine-Borex em: �!��= ��"Qb�ub�>� � �� �` subB}i�a�clu�IAu.si��6�� A�& �(�@JSo*! am�.6��! Bolzano-.S!� �ba�*�Wa2eIŹ& � } A2p�L� t;# act}���.!,)T %Dn accu� gc8�=v AY0Ka�U�y@ tl�<b�gmD}[Sneidp1945] a \ �:\Z4"HO� e �G�^�W]<%�l e � (x, x): x�fX� �<�#q% r3! ���!� �=iAC��d<�f%ll �GB� �Ū J.~Chab�B�75�� 6m�(� ly�Oec�3��" �� I or f�t� ij J9''y �6e:?�^�5D''R��w�%-���69���en�� $A�9:hU�"�G $X \�s X$ I�isay�PayA�=�DE%�re[> ghborh5$U+H�)| [0$U \setminus � *�VNi�i&_F a���9�� h�1�_�W�� -9�2!�(�Y�)^a���is y�. WF6�(  89� � CoIasF  ,u�iBy%Q*��V"�B�cU�!*�8���:� �F� of.!.)!Z9LG"/Ez+ !sa� :J�s� I Todd Eisw�%�Y." �� Dt---1��79�1 ��;���I)(Oleg Pavlov�� �%EU�E"�'A� 's] *�*&� bo)!� orig�!�Ns�ish�q`.� CH}!2 8�a�B.A6.�Iyc{J"9r�.,}�,k'.C'&�al �(}�,2�41977. P�VB,!=�3��y,%-� .��Y&� , �A�.u,��t� � aD]+ JaiBu'5�"� B�HC�C�F�8� a�  M0Smorynski on 9�IRG&�ah %�few5+ars IA�:a dXaqY`es� ggVB ebg nd-w jk"�!PQ�"tPN `��g:�#A\ V�, h3nP out, ``In8%$ 2.1,� � guiltE~che�n !es�d��=9ak e "� �,iF#bis �da sig9t.�$Harrington����l�'�*�}enJv'\��" NF.~� 22 D.�A� �w�"s,} "]9Syia�n&[s XXVg7 Amer?al�.ie�L1974. %Dewey Decim" 4 510.82 A51 28Hk� de r�:Q�Eng�d=l*2�&miu !� �'s]�",A�D.~A.~M.9xp��A2mrU?sof�$"�#Ef�re��m�E- ��KreisesVA�he �ha8co-'�` �#5k�ly1R 2," him Dk, Yuri!�ijasev� ��DJulia Robinson. A AI:k1��:&.@��3?qu�c t� TAereօ��e Dioph�2ne\?I� '6js�D*6B *<�\H.G.~*] .H.~b}�hAn�"2�I"�ce{A�:�3Cambridg2�) �H, 198�� An e�)nAprefa#D dE��-M a�I�E���j-Ź�.�%~tcUMn u�aAP3;: If $XP �� act,*: A ���,homomorphismI $C(X,"�f C})$��o�&�9a�;�inH ? A�^: No i2� %T t}q ��� ���U����MAjY�?BT$X$! AJtV2MA0vi�1�i�,�&�G� is U�*�AN�+�nth.~M|+ly �80}�/073) 233--269.�pellbi�*���)on� !��T!�o�z�\ I& �/$�< �vq5 i6 � f�%�vly.�'way%��d�ad�w&of &��9.��Her�R�tA�w#W tact�textiBr�rs�lliv'Dw4��- i�wA>S!bNi&W,� "Gr���  I'd r�!meJD�Cmit� Bem.JpJ�P. �A?E�$Whitehead'" /!nund��j3Ij 6) 7�<78�w�,2�t>R�ћ�s e� � group�fre���D�x�}mYCon&��'s,�>Jk�j4.R� ^� , meas��U?5��of 6{�!o� �R� u of��r ���denv>� վK.~mK,}I !�!8*� �N9!hAnn�� StudI�1 , Pr��  �'5\40.\\-�Wa1is�'�&�6umQ3?}LBeV�54E�,47) 515--525�� q\���k !X��m�8\LS �J�R �zl#�4�r alia}VyVtiev�N0JEb�dubiouF in spi�AG/s��1zZ� *�9�(A.~KanamoriE\M!� gido� 9�"�(�R�I�"d0,}�&99--275�J� Hig�.SetA18ory\/}, G.~H.~M0;�.�;~S.~S�8 e#Dm?&�; .E6669B�7�7�d A dr{(ic5�onZ��we�!i?M *EsZdJHK.~'�\�:�� P�}s}B E�E.s.�"��+" &� d�>==�$i� �wgwU�Now �a_d�� wh�uj N *�%=���$�&Y�1'hJ.~Jw�Ń.xVkFR+��SLR��M*��rehen')�"�#2�� su�-V�� 9��PaQdda �Bea�!j��. I\/� �Z$ I,\/�> ~Symbolicq� 5�a$88) 481--5�T736--76!A$_)� paiI2e�F4$a philosopa� lookR��.%�|6-v ��rg-�Jb�or dist��9RJ.D� a)SC�{�7a��.n BoolU> @s,} Birkh\"auser �E�( 96. �W� s�U�c*2���V ^N�,} un�6d �,A�R�7Š92) 76>H6��g�a�Lnr?s )8"� -by And!�) ,�� ing 2�ofu�@ 5 !��  d&aZ�yM)C� �*udd�.3��~|10 rI�1�)� !! � n entL@aR����v"�M��ed=m��02to�"�,>F,*t s ) >� inx@Ubet�6m��h.� ���Qd��-b#22 t�#��us�Nin *5{�.�"V�J�M.E.~�"5��C��T�,}uv�o isu#[�\it'��prolyB��) sEd�6f�K4�Ŧ.�45 H� Re�)(2 &��D,���n�349--363��&�wor�sA:e b�E���I)d, Si�5� {/'�^ grama� salvaga6��%e�])i��T  �.!�,x�  's� vl$�.a�9 qi(�l��an� gyA diree�1���� ular�\��s A#aE��amiliaru;Q����e�*IyslwW��$f{WKL}${}_E^ sf{0r9�Yanyth)0a&i*6P� Ti��>n4alla�duc���3y1 enviT$G_4wVY$ a ni*�� �<%�r6�5,�q�/�B� !�ga!";!:�:!�em�2� Ia��&sX�� 5~�)_ it?B�@�az�@4usepackage{url�?"�@"� ��6"�ion}[ �].2I@S�4rk:-RM6Zl�e:(f6'�N':-Pro.�A{corol>�6�C��@^�@2 �@7� *�@&�@{As#ve�t���&�-� CEOL�@�@ Home-U Pajooheshd�@B\\ �  Centr�r R�Si��Ztic�@ bM. 8S chelleken bB\\ \Ejb J y Or�ved �Js (�)\\ DeO+3of�Bu�HJ \\ N�"al.�of Ir�Sd,!�A=url�\{http://www.ceol.ucc.ie/&�Ay�,F+< l�Rn��^xInvestigator Award 02/IN.1/181U-ax:} 8;d�an over; ongo��1΁92 92-52lan�K12,�VWc L�&*E'a�p���U�?3 enga�in�F�ng��ew�K-Time5��im�k soft�c/6�8��;re broa*f��\"lL��DxZ��u21s2��R>rtK;i��L�����s,J�sAmpiler DMrG�V BasedEIo�4s.eU ai%narroP9�b�6Wo�2C�; Execa: %1���Averag�:se) 6)�(�%q 9�A$ �d ZZ goalA�A+*�:aACETT*v 6� v Tool!�i9kI�Ynf crucL )�o indust�a� al-j%Yi��de!S��*�,2� &� chemE�p�Wat{ E�mmu�`�RS#/&�teleph exch�Bs, ~�b�;� e moa��etc. - 0q�e.]�!mexplor�!mQu�t�x Do��em�u's,0a�*cH App"�W|%![ : pr�b� obHt ���reaE-!��Ynt �oE;/1��T!J' \emph{bal�*}alq�ru� !�e�X� =6����d�iSicP P'�" .NF\B){.a )a�gor�-r � Ŭl��!�s�. x �.ud��i�$���2ork� DanaE1L mid-1960s�P��a��ous typ��^f�6l|0gqeAG &�, n�5a�in� a�probaG;� �*�";*Bly F]i� f=��H�@>j!�2a%�Z�rga]ac�:�B1pas �-decade� Q0 inve�[�3���m�FIn&�\ncK3�#a�[ne��roa�to6�e� P*4ap 1o%�:.c, M��$el Smyth pj erednI ImpeVColleg6$Ȑof�,hod*C:% Non-S/.�wy \C{sm1}�� 1�AaJ� )�s *>�cs �ʕ�#�L�� �/, remor��.y 8 o �5 nce,A#6j%DE+*�.a���% to a"�"aG Uc����Da�con SSd"s�*e * @�~"L�c�_!�$0$--$1$oH.a�k%�-� 7"|/��AD�s $x$E $y$A@bee in �+ x�#�xe j 81$r/�(. }g� ���2e��L@A>at adQal!�8� 1��8�� Y%&R9��BW��$(. ��.c{x� h.g^ ��Asfr �/.T��toQ�ch8}.K�� serQ��T<�' pub�% ����,�x!�se %#ky !tMab�with S@d� 8omaguera (e.g., �rs2, "%rs1, ms�GWw:ll5t��?_<�p {J'Now. Ea�1�Gs���� �!1 /iAsB`,ED_n%]ad�F�q*eA�W j;ppob �1y�l��tEaA!W�RIJJ.�U_fFr)fav�N� *� (pm�Ls)�@categ�F�-s>$c�Y �i�sF�c � @�%%� teve� thew W(,ck1�M941 P �Ag�+�" �&��N zero. AXruk'!sq y( $q\colon X�0 X\a;��^{+}_�!#9p1i!%�a". $w OfG: ���y $x,y�2P$, $q(x,y)+w(x)=q(y,x y)�LI/N!9 0a!�j �7a0sid�gy��;I; &}i3��h?r�e� ���6ToBy�tcZ�fur�,�={!#to C f��0f�Si�p�'�f���! .6�via a � �*f�$���>aw a 2 �zms4, ��O* ��vel6En� �g$iDALfruit:g &� `Il a$X! 3con�>+�laBX.!�e*��emp7d=aF qG!lf-U�AN:��b.� [($(X,\preceq(�. meet.�� $fI� {�3o"V(Ru$}$�3�Rva--4f $$\for�4x,y,z��$X\ f(x \sql}z) \geq.y) + f(y#- ) $$t $fe�vco-6y �zl�z.$$�D�  1�l�4�l6lR:m~�up%n�5oup6o $-f�JmwBmzl T2�jw�kAY�E�Ea\2  �*L7a �"W7a 6� �().s� n.! �wm���i s>LeF��]} d�^U��:� reak0.�2�L$\ ��b��.h�L j5Bei�9 �2"�Tinc� _&r;![ -mod�i�0i.e.,Aޑ8IR�%2HA�f(x�?zIJite��!�=���>��� 2�enF��.�"�H&?�;��3Տe+U9.�w%x!�RjY.\ma !�6 a!+2M���.�n,.� ѭr�F�� n $p ��L jGe� $p� =Aq$-f(x\vee y�^x .0K.� , 4��botiva9g��f>-� 2�k,�&�Latu�K"��of9�sHQ*��T" A V�W- �pre6hms40 &&���<@ link>� 6�� �.� "k h�adcCa�$:{lo)L or a� �5!.c 2� d4$o�!s�9�p�.�,� l"� [o�r"LC�) X �A�/6� �X'"B . :|B~lem�:s HHans-�:K\"unzi.M &�,� QR: ha�U"1hA66� s. SX�a B,!�=&� !7ui. 2�:k � ,Q� } ��.u�s. �r�!�OY "�� ntG8 �-er�2�!��, inflm�R�.�`,)w5: 2%' (ly)/�2itr�!�@e benefz�>��NaA��! in�� �a sui�1i� qJ}m��[4v� �u<&�above !R�d2% . B�w!��Asf$ cly���&V to>�eO2b^.R�spmplT 2�!�my�!#bin�>�fT B,>za�gx.�} l=F%�{A.%�'�dec�" v��.� .�A� C�s-i>eq� FɬNE ingu>root nod�-��]E E�8 exa�]�childr5<r no (� p a �f�[p'A)!\!u_s!�each ���;75�WX��x8B�ed (upE ermu��)� path-�Xth�Q�eaŢ�� �4 s (=�es)�6%,�p, L) u��%";eU �̜ce���K�G]D)�$n$ W�2h3!��2ve�egh:�Z��� �!f-Yaf@�<.#n�a�-1 3 3 4 \h`le$�< ��nwa $n=7�^N ���-.�$1�Cwo72�$3��s�D>294$!v�&Bin Fi5x 16 ..� f#""pi�sL}(90,40)(0,0) \put(20{\circle*{2}}6>$(-2,-1){20R> 0,30NS4~Vl7>l 20,2Rm61�1.�6->6^T 7>�2> 30,1R�1^4~�>�6B�8^T7>T2BT9AMJA7Z5Z3JQ� \ca�~{2 i���~�}�q%��b"pret a2N� $� �[����n9ly�N<�o �*H>*a S$�~ lead a�^B� �����js. OuUbE�V69�** &m .�.carry ����.�!&X$�/o-�*ed X (comparison-  al|!�4�%r�-�a&��ul:at> asedW�"d2C��$\ � 2^G;dItool  ah�yp��8m� �SorV*�%@ sorAJ��n <�8V�&�  �.��2��b/!�9s��r,b!�dur.#��6�9��Ye�3*Uf ( �input}) �out �sR��#� r�� =- ��)�8u�e�iX&p���naAf� �a`�+J-&/� any�E'=t�56= .�V�{�S�d sket�h$?f%�] "duI�� I-�q . I�P�*�(J i��ZT_n�..$T_{n}'��-of��B~ �$x�T$;n��O� } l�z)�y)+l(y�-L z)-l(y).\tag{$\star�{G H� l(x) /eve�J� �A&�0M!t)�A�8}We= ( n)&H�"� E�*+8%� "n |[�@��Or�V$n=2$%���v �.'�� $k sVan� � ���%�it��1XY$n$. No_s%� i�% of nU �p?!#maxim�m!@t�Pw�Es'm�� 6&�2z9:.�$E$. NowAk���)Z� l{s�!t��!�,y�" $zA�:��� ��$)e!�u!Ie;�r?16"i# ���5� � �eP�Er,A�� l(z)��NC �L�D�$|ai�I�e_� �A� n ag >���a��2x��,e2� A . SoMBx��!�h� E�8 to*Qe��'!%lE��"oe�B}B� T&Q\�%E�e0%%E.+wov) ��ޱA�i��:} R She�[���:�$�er��� )F=A�|����)�U^%%I the )EM� E�wA�N�]%w,�^$b Rb$ib _�%Ni� $x,zR6�'�5V'Bu/P�C���")�:;^��p/^ �� nd $�&T!e%�so���F)=�7=0�%�\$l�bl'�5�$�r�y)7]� triv��]. Als�H!tz�V�ym( a=�) arg�v!Dm'�� A� Ha�� �@&�|#}�yK asy D# eriffn�s5"# c%�A��xa�])�v��pat �?Ej�!~��P&�5 6U�&�)2%E&)��Y�6�W�to�$�r"�-j*�� � �&�HluVg-��!8�&� �|u a�w2-%$� 1\D�,)�2nR^�/!�� � g(verb�*o'!y+�.��s%�t�% IFse�e1BKMP03' �� ��6 �X.L�s�  upQde�nd2EQi�O27?Cs�i �@a`-]6"�ng,Nk2@��_��@ 1�I�GF6^;ue)��mj5L�b��-�Y )0��9�rsuI0$T��A y*��BTp:B� �� eE�al(B� �V4a�6�!� *H��e ).eN!�inrO@� � {On B"2SATic Ru 2�4܍�&ah}c � rgŕ at D�l e \&ZG quer.3?��?a�d}�!$a�g'!��:fas8&�%I� �s ul#Fo�z A~�u"Ũ�e"(W !`(TO��� .��� = \� x_1,�fx_n�, y"y"y"�) PAn!�sa��� t�p1!9n�]�%D\sum_{i=1}^{n} x_i�": y_i$�$.�J�� � ��9/b��Ű $l_1l_m��&�*$y=$x=l_m�EAť�$i$w#1[0ig E1 bona+viaE�&�1tOBa� �kv$�vol�1shortc���fo�/��e^w.4M�$ Qs��,��������J���6�l�q� ځ�the Law^� �<.�/ >Q y�rպ.�cDP 33ps�H֙��i"�;�he� jF[pr!i��"!h�&,A�T�Qst6  no:98QX ) `ly� sol����z�o�4�+��� �/#f��� p7 I��9a%)".4a&#"3ho�8^a$�_an�r1�E�!�& 3P9[7I� ops}5 ������l�e�OE /dllu�wt��at6�}��+��is� uiU%p�w^3�liter�$e ��We v,��t�iInMA-�B���te�� �6���bf I�?,��i�'@U2�6� e���.�� �#!T� �*��)���C��0F�m� � LGa-�-�6� � �F �A. <E#�B��g%�9@. %\nocite{*} %\.������E>{ @hl{(command{\by}{\ v}"D\hbox to3em{\hrule��}\�D�+JG4MR}{\relax\ifhFu�]p\2\fi MR "t>F�12F�!�(A.V.~Aho, J HHopcrofɔ�K Ullm#�8Dat�/ruw�"9x}, Add.Wesley S�5inF$�zI Bon� ceFz?A�`, MA, 1983. \MR{84f:68001�ib +8{fk} R.C.~Flaggg R.~K�r��Q�"%=s:cU:a'F' �; '},<etLm mput��i. Obf{177}��97)�h(.~1, 111--1��� 98h:68152.�: :�S`Nt�4�H.~"�C{�4, To�7ipind�Gekop.� -��H.-P.R{\"u}nzRV.~Vaj��)�W�ed2-5�Pq7on"5 �<�a*|> (FlusSG, NY, 1�K, T New Y= Acad)?(, vol. 728,V4J4Uy64v�I 98d:54052��5 �I~M5G �PtHal1��},�d~� N� ��J �$183--197. I; �4.;��( M.~O'KeeffX�2'!�M.PsS"_E,-�́UŻ�v<sp�2�20A}P�in� Qjrs2:�S.~"I9I�B�� Norm-�7 Rieszm{����z� ' },�,"j`MFCSIT�2, Elec����,eH6�I�~74, El�^erea�{ .~17KG �E*�E1.e +\.com/gej-ng/31/29/23/143(31/74009.pd:m��.��B-�!�of.na�f�x DpU�Lke� P.~R~�i [��֡�8of {H}uffman co�1 submod�0 (``l=x��optim��N�F r F� SIAM֋*�@28} P9�?5, 18UZ 1905i 2000k:940ʑ ]xa�YjrQQ*>�\�!�>Z!b"H+ Appl�9� n��-3, 311-�2�����39.�rs1} 1�D�m��?normab�| �m� �G��Fы3}  J2-J 1, 9��125G3g�568}. .�dat.yorku.ca/i/a/a/j/44.htm.�ms8B�:Xmonoi�Nnd�""�1�I�To�>��6m=�#�n"{S}VA)'A�:+!mouvI!K denop):w"�C� ?xg+}, Ma�T�Ja�=ME3pr&DL(��Or�T s, L�95)�b��1����"���!5, pp.~2An2���!g\���26��,84/tcs1030.p�+��ms3B�a�.�@�N� (�?d�B�J)�]*i�� $8th Prague1��#&fum��;y ���6,��~3�348f�$p/p/a/c/05F�F�On�݂"� "� } j Gorh�cME�5V� Sci�z 806~��48MR)�ca�ٔ�m�\{ �bB�: lif�$\& x-Fs},&KD!���22��7d�umm�)403O�5��g�49}6�.Yb�Y22>��<>�A.t�B*��: "� re�Jn��� 305�53)��4.�qd2 013 572�B4:n�Z-bp�Gnce"` p.�c�3�'�!��N�q:| =��E M.B.~�31���unP4i��:N2>� �[>� ���uage s�NN8A9L>^�A�L � 2ٙ, Ber�y 1988i�2�Z259m92 sm2BJT:�4i�� act Iedͦ;*QR Ko� E�AP�� @a�B�R & .ern� (Oxforda�89), vP�er��9" %91��07--229id 1 145 776��>�V!d"{��>(z ��[AHU87]   �J. . �;z.�Z�h [FK97] C�� agg,E�**�S=s: ��B �2 �am�ŧI�&��}��bf (1)%�7=f�]-~.�R)��S� uS , H.�* g!� .*G�U�200iX5KV93] P. K`7, V. ���0""E:Y C7��!@ f. Queens�J,F�I �؈ s (AnnalsU��ofS.%*3��� M94]�&�����c��_d oc.8 th s �conn$c�m2�N3.��b$ S.Andima ?.l.,�d�of6�em4�Ss��,�(1994!�83��OPS04] � .�&bU,�S.��&&D6��M�p�},A1`5hRS00] ��S. *�M..� �, ENTCS�ume 74.� l���20�>�-EEn7�&�:���jPR99] F StottIAlasad Je:D HB �B B�, qlyOb)��a�'E���"� s,�� _o.5�@.W.96EMf,�I�( B o^W �cM����a�.!} �Y98}, C322��l]�98�1~�*M ~M ��edB�})D3, nr. 1eI2.�Ri�n<B�' !2 �r:}@ ϲp� �M��X�i�.�Sche�� BiY�*�.� �"C�/2�1P�0'< �|5��2a] J�r � ,�I�11</�-�N�� �M� ,  - 432E2gSch95]��h2��&� 7l�A�F"T%�D.�"�Xe;vm`#ri驅���MFPS 11}Anic No�i�T�aalN.�>, VFI�{1995, lk�/�6�1x B�fR_:�e��. 11th Qd%,�B�a(e�I�s.}�.6���i� bf]}�M6, ;�a.h96a�3R�=p�� R�, � �H�{ �F�y�*? .�f4b�%�7] �J*B�: L"� D�?e�q� ��m22e 3-42�96� Smy8�� B.I��26�RFy J� �LNCS 2�" z�*�g 87, .�my91]  M.�� �5P�* f A���M. Reed�W�?scoF R. F�chterl itor�5mA�CE��E%�a����{7-2292@er6Po91! � ��:�a���u&�a amssymb} [ Z1]Y6enc6 frenchb,g� b,dutch,i�� an,b�(sh]{babel}[AQ/0]2dall]{xy�" atl{g \AtB*ND�{%�er9 harm�NcC)Bi �b \cat� `\!=122:>;>?�renew"�&�( }{\@65t{A {% {20mm12bx}s��6�Т2B-1e K\Alfont 4size\scshape}%�*8cth*ڣ[ �]2�b�&�bm]{*t-6�blem #JLccor Cor#c �E�Z(n <De��d2�e/E &E 2#r�&d9��'in{Q<{ �!�9�T*{\bref}[1]{(\ref{#1}) a-�*{\�'}[2][]\�% @tmp3%Afifx2\@empty?2{#2}\fi3��aAh\�lx.{26}�#2�?rkI �{��,tt� } %Ree macro�6E s wa�ng%I E*{\��ur�ov�et ^{\s8� ǣ#1�"�2S reciC9a �frac{1} �6+st}{\;\�chŏ{\v?#, width .07em f{\ver/.\;>��/�s,}{\supseteq}�lu�*bb :�le�#qsl`B=gg^set�}{�K>]defeq}�� rel{:=}} �$.�map�!punct{:Bd #1V>dT�}{\cupB�./a  ap>;�ma�{\w�BEU�� uBDDirsum o �>ernal-5�Bdre.!RBZ>ZF>�ger2$:�nat1e bb{NFDI>IBAgi�� %�B���2$mBKBEQ!�cal{BFDE2!EBAEs�ASFACH �rmd�> D2`DF@Eff AaFBAcp `}_F1cpxApp(X�].[*{�� tyseA�varno5'gB��spa���$uct}[3]{\b�o )F�I �'4ft#1#3\right#2��#3J \eB@} \DeclareRobustC�'ab!cZ�{\l��rbF �fF brac�|r } �/0 (#1)�6{(}{)�2��`���0�6n���' loB �-B s:(citet^�a��% poorR" stit@��� ib Ba�Z�]\y# � �\fi>�5AotA&makeat�( ; *)\�s{S!�5Conve:�ce< i<}"ʫ8Anthony Goreham�&��surtk"Nwr�}nR G;s/3��% th��� HonBH Sch�Bof h�N��'*�*R l$date{AprilLJQjcE. �,H�ai}�"Oto�?cu ?"�.Q�� ��%�/iF*(66.IV:`T3to�Q\ f�^I� 8ras�J�%�%�s:�,;p���L�%� + , Fr�ch4Z� , !^A t� �/� *.�-]hkݪ'�at�`3uƘ I�%�liv�.is�?"��. I a���qu8�5f�.+@�2��xi4�in ZFC�0��M l�:�5%� rߊL�JO:�4a݁su=+eD��A  b a����us�/B�� re���3 p�c�e�T"�32 �.f/�Pl]lA�! �-Mawk��bleMF_8� �weALve�p8de*�!s��e�H:�E�u�m�!o"I-Upri�1qK}"�Q�R*4 s �e�:P�l+5u)�1�y�%�)� 0e u��5�} �?�$)0�mof� ents�� page� ^$ing{arabici � �EE F ���VE(CHAPTER ONEV! zF�F���1S�:In&�T}\l�{chap:�T��� -*{MCYV 8>v&��c�{�@ad�Ge:I�$=says so � p{Ca��037, Tukey40, 6}off,Kelley55, Wi�t$d70, Engel�i8�%InE�~�eg:beta ���!��e�Y��o��MKe�$im. Undaun�@8�a�&B!��0m going to se�[t out how we shall proceed in our discussion of the r�le of sequences, and countable sets,B�Ogeneral topology. In Section~\ref{chap:firstcount} we review the properties of sq\the clasB � spa��most of which are familiar. The work beginsT(earnest in F�s~ tial} andN�0rechet}, when!Tconsider-,= �CFr�3 l. It is easily shown that a R�-,Hausdorff ifV only its.xlimits !Punique. However, thisLDno longer true forB�4 (even compactB ), as we IOsee!NExample)�eg:-*-h�}. We%�0also going toA�8ve characterisaA�},'�B$ ). )� natui) ask w!�Lchanges if, instead av tudy%he �c&n a �, one 'its.ubsetsA�is ques%Oleads us!rU�5Xv%6 ue tightnesOe rel%�(ship betwee%�!�}�having G G%�be�aB�A�Dof great interest, /�issue at centr��fam!�Moore-Mat(wka problem��!2dir��, ie�,a triviality!provei�a6y-~y� ha.m�!oe 5nof� ther �convers�uvcm_y�1�Tccupied mathematicianse�ova�$wenty yearM�F�5}-�E���Tperfec��!�no�MtenM^�&�;a5ext� it does/immedaX ly f!Wnto%� hierarchy�med byo!s)f$we have na!a� Figur�H fig:Uu})!f�*B normali� n���be�ly #�8well known. Fur�Pmore, \citet{Arens50}%�$given an e��!�aFW%� �is }i�A:��seems,�AY��M�J4a.�%(5�Y{�nV ba��� erly!�Śed. T�� may !ar!becaus��e cardinal invariant~$\Psi$ assoc!�d withE�Q7 jty!UrarA used (it U�K �a%�;!  page~\# Qionindex!�Aftinent5{waaunAJ$ Mr.~J.~LoQ���eas >� a-%?e}. W��suitabl����!;di�sű impo�a�result A7, encouraging�ideed,��6�I !�y�a{$ly regular�/!��MUZr (ͮن �Y.�). Lik�ei�ei� w��ve defin��^&� ai! ll metric �s. So I��A.A�follow����a, l�a2:,AB both9 i� � : . Of A�ic!9 �+E�}R wh���m%�Sy�6$re equivalAy suchi���fac��e�is cana�b!>cid�2ZFC�� 0deduced from �yUF�� Corollary)�cor1��E�--֥�\��d *{AnQ�}la� �useful�m2�s��$e crucial ��ion losure,6' E �9can)scrib)y  ofA0vergenc�=)zc!NAsA7 �W!�u^ vaile� in 2fe]recA3Iding: \� t{enumerate} \item\label{intro-4:1} {\itshape' ���j nsist%g\  ll��� set;bq2BqeA%cm�B� ).�F�ff32fA funE%Ez� v�a� icaI ra� F� preserves= �!�} \end.�In>"nIvsW �S6� , a��� �I8 �: s. 5��}-�(eg:betanats!��V{1i%}\  �6a " Let $\I\J$~denot�G8Stone-{\v C}ech1� ific$ A*� � number�D5 � �c� aEye0 in~.}� those &��^tuaInstana�.e.e�(y always ta��same val� \rom some point on---see  `[Cor.~3.6.15]{Engelking89� / i*� e.�~ia�cM�%t %i7 �)ykV� ;u --�� a�~\b3}�82} above. Now l!� x$~be any �in.� \setminus)� . Si��$ �dense :��y!! �x$ beKT $\�B E%�U of~ ]*�no-c-�Eca�%�V ~$x$� isI�itatementF 1}&y hol� 2D. F� ly,)(Y%(��se� ��E��2;!D)discrea�T A�!� on~$Y$!�s �Zr!;+aAo2_ , so] ident�V�, $\iota\mapsy� \to a$\emph{not}!;��. H�s%��ep� g��I�i{2�� a�<�w9��$~� �R { ���J�3}!)EgM4ly valid. \qed�T�� On� n�  siur�!�il��N&,F3A;�A9�  y�Sec�81]{McCluskey97}Y� >!zcanon���eu� toF�2�b�returna���o"Q i�UQ� , bu��*� {n�n--��emntY. A�re will�� y!W ~ qu 6�aNxR fai" d" Q r��2�P ies8 !9�7ACus�would� EMd� inadequat!YAtlofz�Atm� Mr . Wh�`(we be worri� is? After�!��-Pm�dr.�� 3 �1 nivo�E�s;)�is mak��U' so"� v � diff ���9�:z a�BbasicK  ubstitute |g��!aor!�2�Ak|suA�i��nyQ#Y�!�� dAe� e tw or�of ne`n filterse�� �i�2�(s developed �ş�v9� �>�� %�� �sA8�manner�& $hap.~4]{Wi�d70}. An�.�!"to accep?9~Q_� do� rythingi�t�ok�\-y��can} d �5i!� ro!�%�� 6@ !��<*{Manifesto} We9Aaxiom!�choic�thAX"j!�com�  ac8W : !O d ;�d��(t regard~$0�;t?G . A � m��C}%q� eYnecessarsH�)[E|is q�� ]E�aersL� fT{Bourbaki66}. Likewise0 �Gum!Ma� �p��f �}% B��no��(a Lindel��zM. A�oPN�hR: ~$T_1$; t�� $T_3 aa^&� str?haneity%N $T_4<"� 60 �/] in�Ɋ� v x upE ��@neighbourhood~$N$3a� & "� .� u�;E�e%� quir�a%at "5 |ioa�fq�0� `e: ce'�the tra)2TF , r�%�n & ÉF0{Kelley55}. O� as  rr���i� y�us�!�r ough[ !,unambiguous;l� r caA��7rea�is refer!to�.�%�a �!,. %\medskip�4� � ,ine, princip�, fpX.� . EaA� ��, d ���ٺ�ocG10f �sor�wn a�-ThAbgeI rm a*�i. �Y &!�e2 s un! 9�0becomes wider�la�e F� +$ weaker. F!�n�v E�is "2,��f ���f. }[h]  Ter} \small %% DIAGRAM:e%@s xymatrix packag~,stalled \use  [all]{xy}Xdispla< h} \renew��and{\obj tyle}{\(B#�."  \�{%2�4 \ar@{=>}[d] [r] &\ (box[2in][l]���$\iff$M � .�} \\ TQlI!RmP\ar[ur]|-{\backslash}J���~} } v"�IRV��q� $=�E�l� }X\Z�su�� -]�iof|zom{l*�!�R� 86bcap� {� ""ve�q�4 ysŅ��ir*N.} I�a2*T% �K"u�#&^>!# k�6 Y y6 s9�6:$6I�&� � 6)>R� �&NI"}%g�=��\��iagram�"ind�e�m%��G �� n20 in e��9�---C�<� 2� ��7#v�!�asserA3�E ��ap �la�� �I �  w. look�~� ���%�*w f!*�!�E��N>O $!�:standard"[ s: `I�k�"�ed T ta�produc�or�mor (in|!) imam#��6f$?'�&� ,� H�gq5q F �I #� sofar a��inclu5d� &� w`nd� �swW"�s&t"Q fr)�ly `no'� >H%H- �A�}Zi!�fortunatE'8ct nonetheless  !A$he opp*�toA)Å��A: pl�GmUf���tab� }{lcccc} �� L\multicolumn{2}{c}{P�5l:��CE/�@ &Hereditary? &PI4ive? &I� �#\\\ \hline\\[-1.5ex] Firs�H &Yee No ;���% &S)�ial.@:%C�� ��.#:.P�#rw��1m�-�z �!�F92>IQ1�6��5,��R�N�.s6� !<�V�ConcernA�A�>�'AVeF� �p(.%�xof ��&z *z F�:)i�a��0achiev� n� 1960�� 0Ponomarev60},Ar�(lskij63�*�${Franklin6�  %m�q�tp"t j� � � %�t %E- Q�{�? S� &$+$ Co� =$ I�.!�6�"�? \\C�� h&�  $Y�ť \ar @� [d]X &�*�*&j+� }�N�$T_0$2x $T_26�Odo` ! j�pseudo-3�.quoti^+.�)ge�1��sI E�2� &����=��f6)� &%V &�.� ($\Downarrow& &6�: %!� &J9 36FZX>.(>^ P:P���C>�a.E�2 >0 F� F�6\F+6!%iM6>�6> 6:�6)�f� %=V_W�I;  �fproof� aln� evant��Zion�� ,��Q" urvey$bWce&� � k)KI�)car&l�, lect�'~!�S�� ��B detai�* Ly*��'^ �Aed2� e$so��wo� m�eor"<jsimilar as�.lZ e)(� ben. Moreo�0very fewA��lemma�)�-d:�n ] !j�&supply^!� us)� idea� � to m� �!�*break[3]6�'D�2s}.�- preb �! a`I�ce�m� tyvait8~$X$? Our usual*�!`3 � �!X�!!2B3�����e. H�)%E��"��iwe !gQ ��yEp*Ec��*a�� �a � ��&� �&�&(~aARpl"���)DsNC( 0$�er�& i}{3V&R[(4} &Z(A-<~$A�\/!Ag��>�'�!,( $\seq(x_i)0 �(}c!xat@�e� %A$n $A$~�"�+!finitelyD�tme�& $x_i�%�Q�J�'W4�/�# 5� }-Ya&��F� �" ��]&~"s&P"V.l Y�&o z"�(Q�, (t��ifQ3)w#3Wev-ld�+�0 0zm/�'X[r�c,!�$Kuratowski4u�2pe*�X$."�&ed Z)nY(at6��`!8���i ty��4b�5��tZ 6�6��F'A$En�R�$x\in !^t�/���A:a>n�[-iesFV$4} andF5}�Z�-�1is�.hap�! rpri��nre�EA��D�I��&J toyFy1E8�q��7����A�A^r� �f&=1* )1}�2%s�9 _.~> 1y�-�6})%@r�! �s�'}6�>�B�)4}~Z~�� ose �%�u R4%�a �"� } A�"�A�I!���"�1�>e��ainF�d&Eb)2�an futa�:�9i�c��&d� is, . to1 ���� ��a until��yAW$itV or�to��#"�mpariso\t8]es`- we gs ong�&C#art�(7&35-���-���!�so-�/�  R !re :-un� y�,{Kto� c3>E& defn}[yV� ]�):(��}�-X +�Iic��.�:sa�%X�\%�e oH�I� |seer ] 9}, E� c)YaJ!X n 5RV},J) >y E� owK2H system a )i4� base.!4"^2 clea�at mme���'%]�:2V 6�e�9�+ e �~ (t{S(x,1/i)\�=\in\n�/$AH sp�  � us~$1/�6 nd � re!�' $i$~run� rough)a.a#BY�i �6M�'�Ja -�Bc�� uY%it%�q!F>mJyE�:�}V)},�1Y>_ �wP �` �R�. A$J!un-iE �!xL3*� I�.!�. >�� also�9�F�-Urysohn)/~.-^s:��9alysisx(o;u�aIfac�\B� ��5t. �A(l%$y>  �A�9:"�lem�2 lem:e[�7��6�!y| \�d ��ah \"g.o�e�@�s8 d;AzH C [Thm.0]2., B.�>anc�)I*)%�*t��adopt:>inHBa�$6����[&��pen] �3b�#&2A��I�M�� ��eis��Br}A�N  8:�XJ�u\i,A`�her�u:6�~$i�suc����� &�2� �i\g�A_0$. (Ia se circumwc�#��=�� 6E�n{al�� all}!�a���9&�T3;&�4} � .) S�a"�)6~^� %�iA�n��"�$ *)CcG"5i�?p[&e�:�A)� I�rB(,�Ѱ~� 2DFw5�C"� YXi��+t�&�, ��A��AiAm �4@!U�?Ft�@ m'� 2�@-VRW)q�N� ��y'U)�@*(.D s!��� by agg H ? .62,�1n-�1�m�B� sai,.be&oly"2 '. N"Sam�am�_B4 iff $X�!6��is� a1Wita{�-n,%�nex�cobv�!&� �b� ���-9:�t>�!}�*�u>��I,2Z ����8 ��A�"#I f���iW-1!>qs%". By L^�=R��im � am�sa6 "E 2u)Iq� 6G�rem}[{�)[�/4]2�84a}}1SrA� n} W� ��-�{b2�Ees{[ � � of b�E>� ?!�q��m�> ly�rephraZe:� �� hird�A �H>=,!�&� non-)--�}�e�n� �r�A��*E ��9 A. .A tras �4��7tu �3Bu :Mq�mT�F �E�}��~�� �6�utm �+> pi8chou<��pH� �Iadv� �+ ereaS,�j��-)�> A4��us �"� 5A�;�7�Q)�s]D�BhJ4" )m+a�-E� ay r�>nozLat!w� ��K"�#�B& &�!i q��C.����%�yet $fF�:AW{0} x to 0H(�(6{}6 (��}nto"�3ous, S>ndBc(ct fibres).'D�1*9%�iT� t to�"un�i9@�sI�i�SP5�+%�5�%� Jif you�>lace `s��s'�]&<'e*` �  @A �.nt��mviarriv�.�2!:>���� >yh\��V�,��]�5G��i)< alterna�)R�'8��f 1s 3�� w6 ��G SB'=} wor�?|@j}�J� `*Kb"�'2l'8})%f �c%Pq�"atA0 justI_�!p��n!" ha>Qoq�1i39de>� 8 e�G!O&��E?6R�'�:��%I�9� he l�m of Remark# V� !H N/�9 s"v��> �Xk ���;  �V?6� if%"��X�~N�AHm\T<ome~$AW:&�^"�{�j~$C� A$ .���"� C$��!"Q �"�+ Supp� �E^*28 ���[�2{�$C�A$F6>C�D�B�@ ��n��� 6M��T~Q�)3.�>�B� eRS�J�o $A=.�A� �(e��F+�Aס�.'Now0$!n*� ��!yZi� leX~�9 �ʹ.�|"�*24="EOeq\Union9 � C\st�6{A]5�,9�}} .f�:d We w{&�@X �f ub E$,�7IPn��%�$ &GA7.�;�At A) ��!��aJJ�%!�"a%�:. C�ly my \ �!�e B�*v$ 3 �EO�ed:Go����9�&5_�6%� $Da� *WA��U��A��I�D$. ObmK �a��8!UytD$�� <{C_y}$1!D�|~$C_y�si �C.R_{ c});FGyD)q�AO>�� cera�M' � �A$.e;�U)#nyU:��%Ie�L!�h�2)�:7�M*�%$y� $D\�&� U&�IU�� �aJ�y$�D�UH$!#:uitY ��Zmeets)sA .�5ah82�C}J hich�mpe1� EA��� D��Ad�>�E*&!GA�mo�=�/1�-�s. K?X$f�B�.=)�wE�~$E� X %W}���F0�J �~�"� &e=�Py:��1.�a �>��an���q :T�(�  )�K�Qoot�%by m1. FC9Jiof� mu�5��a�Verc*in~,Prob.~1.7.13:�M |ea�Ak)W�T� AE"5*B =r" ;}% n�Z� any -�Te�Ci�=�}MM}R  �& �#U�[A]C=!� C}�A"� ce�u0a����.;)�*z *kNA�aW0 H#.�2�C$M�����9Gnt^p� 2�%�=e%�b?�,&E%�E>� V� H�@!�5 a*�' &�! �!-&� `[2�5]6�*%EETb�xQ7)na�,[gdelta@$G_\ $~set]{6om�T writ0�B �\"B� eD>U-�]�M� �n�(fsigma@$F_\ �2z�u" � .d�=�bFZe�� &t,ine:�b7�`&��- s a~9Z�DI��k. X � :Ed& �t"�[}��EC��v ^a k( 9�i!��n~9i. �us*�Y J� SCH�c�b ]�B%��FFA ���VB(CHAPTER TWOV! zF�F��� \Z ion{<&�;w6s�E"*�!�-�VV�'|(�eHtP*BB�NS2. }I�+/,?�Ko�F�E� r"�ej*�? ����e�GN��+e�I�i �# realk�n*<@> a1J�`'��/*4m0 U�nb.�Q ��a+V�  H�J ��T)�$&�[t�D��� C (|>os5i��=�*e);$�;�Xpno �e*�e!J�k"%=��A3)>K -!�pasV�Wm2�)G>�� �5:Q&%� "� :%�� "�[F�a@l"�W ᩣ�!�#_inB�%�E�- �}&�VE��,\ EGt�e����ee�� }--\kX8�/�2� "T='sV�heR;0$~�BS in�4�fI?th2�'>9�PN�*� nO k1S�pa�E��(^��kyieRT>$)�� }0�tpC� � !F�d,�Oord^� X8A& omi/e (� )�|of.� �\v@�%8)�" y�� ��!ofV�,AnyS )a�Z���$v.*�"� _$6"c:N :>�YSoN1 ll-&i�)(�%JV]��bQ��Z.{2�A&E��*f%s!K�b�W%x�5��9!U-� Xf��;-�eg.� :iv] J!siL�s!�~$\�V^G �\$ Tychonoff��\inuum�pD/g0I �C� \��?x� is)'9;p�&@ F �.& �4%iB. ��� <"di��e�� Bee=�U^{(i)}:�.�<E/o�9 6���GR�"! ��Mj2[*; umbe]*�[:[$ �u .G a}ic!=et~$\!�_{r�/q}W �_rT�u00"b-� ~��]v_is ������*�# �A9��R �� �%�~$�= for i�~$�!�3(P.K$R� 2� !\s!� i!�0v Y-,+Qer, � �!�62��$�=Xn R1iWhi$r$*o2R���w!�pa�==(\n��(eteq(-1,1)$�Ai~2CH a.�e�Zion�� eq:1�e M#s!)2Ps>l!�AP2neqr}<0=\pi_r{}^{-1} ���A*�+�B�I7�FY �Y-3ina�$. Bu�B��F��A�a�.�S%�$�^! m����3ct� � �$w�=6U�Ae�J�h�g$��jA��$>�R�^�N argu�@ �@? adapp@%`�D06]. T&�+Y��~��|N!0u�i�"A uct >162� M$*q<�� |6"�a���}e�{m2f is�Q \T~��wA�YacrosN� �� �en/]B�.{:� @�:kwk$��Ӂae-9f�a�� 7.�5 D+S6�_nE@^% ��)(A�Z3���XH&%F�|naeZ}p� aH=�a:)16�"�S� � &�<9)�=9)� $ p$,�e1set�_n:�^ .�e~�!�2��R*�7_n�!��5g\W*!j N��_n�s�<�e.m� n}X_N �n���_n�\qquad�%{���,�}\\�i{�d �%\I��_%� F}� (n))��  f$!��eF \ZE;�#e}>�= T+.�U�*��\�Q" !�Now5�N�` /2���"�6 �;6eF_Z��ky�At{V!�t n�Z�!�e�u&�3V_n���aA�E7all~$n�|,)=� ll1�!��F �$N=�+ |e. Pick�Vr $��#~eHJe�n~� . So��c=e%z2-s�� " (n)*� aRx_�I�U:ub �e��?�FvE�F:z ub N>2�2=.�B�.��g��h:f�`of>��HV0 Onlyl�y�' a�N� 5�&r &;m!�"A�(cf.\2nr� 0.�!Uis >��큨"H��9y�KGl._%Feya�Zt�+�folkl"0�-�98"[l`DIII, Ex.~3A]{Hu64}�-���Z�&�x�F��GLet��#@!a X%FC� � i�F /-e`hX� a ��A�&97� �/�y/� �/y� n~$x= y&%Hտ� �E4 �a� �%�! ���F�$A0i���*�y�ea��� "� HjK0�ͅ�$U$,~$V}�i� U��m! V�X�x_ijx�7\�6O :+9!b;i\1x��&!9 b�a5di �iB�-MO^ V$ZR"� =_1+c9K%�-�Am2�5�rX�&Cwx8�J�&.�� J!�a�&:�distinc� ints ,~Y#e1٫A��$J $  # #J!A�o ~��_{i/2+A����6N�� xY�J@V�N>�sNy%��$or� .�[ h�+ $ ��� uneq��tyseta"&��  uN_i�$~VLq)( ) ����0c(&QJmÕU+:�b*���9ssump�+ neq ��u!y uZ�Av��6Wn4"� �� 4 ��&� ��� �M larg%4de� i3-pzi�uiT2�k By>�#cb-��7J�!��Xa� be V�1�eV�� 9$�n�� � �p2� /c A�ll.�[:y$ %!x-�.!5Win�^too�M�F&�Q:�2� ���.jOg�%.'.�C"�%�FF<$knowledge Hb"5p� � ��mw fly �e ��:ic�"0� An O al�} � 9��I�,.cwis "���.'< Z�v"3)($� :mar,� �0*� ^>�!RŸ�.�kA��&�&n�n\[�9i�}NBv.�}c r���ig"iVNN^%&�BP �p07]{Munkres75}�z "" U; omega@$\_1$f� �9 )�� ENM.'�Bq~MOley:.�~aK e�D2l' :�- W_0*�x&;.x� dJiW $x<�>�:[L $W_0 HIJ-�J�%�� ity~�p �n~J!ځ4GXe�gY������Ri��:�)�G6�. -K"!d��1饁o �: �V�(��cu?:�mOnd� $W)�%��%�{1�}&� $W�+�A!V>=we es�ish����.A�!I-\infty x\min W f�n� W$ 'j$[ 3,x)2 (x,�]�!���zt{�  W4 yx}$�qively� ByI��!Ws,!t�<m�%ub.�:� ~$WF� $x7>=� 572$WE{��:>�`� 6}��f��f ���>�&�slaR��u�f�o�z � n $Ui�5� x+1)�9 $V 2}����uſ. A��V%���*v���.&Faeʡ2+ ub&ϡ�-O 95')soH*�. A!�M/ 0W� X)��Hw�"���:; H%�$ If $x=� �01�m}E���2��C"r�B%� }4)�S(ye�tID .I:�66� b�clusion�T!�� AK. �T�������:�#69�>52 %S.�%�V�94N� )�hw� ��AF�5 ' :*�\!�C%.�A9�= VT)��!� /b�zed�.}#���< a�%͆��t3��o$*\ � ���a! ���w�YM.�{��/$BM';_���C}y�? 2�J ak �&N��a�2�ϑ.�s!�,� �*� A�"�6\8FA���BYgyn B��m*@��y>x��I>8��is, 9��an upp��%�A��6E`:v M�NX-�&2�C -c3� (I*�'EH^� F-���ssh{c"�< � x_j$%� ��| $ji$B(:�A�F=.�tA�let $I�1q�y�=x # SB;"6%� x_i=xLI% AKa�!$I%�in�`,a�,arr'�~$IE{HwcsIg� 9l)� {i(r3(�&E�$���{eAtaeQ-� 6|$7�� 2nt�& o��Ci)I?ItBAreq-s�*�O�pBE� � �e�n!A� i(1)1^ax I+1gK~$x�1)!O�BuFa�]:_B" (2)>s.'�^ 2)}> gCs�2i� !R!�p7|eY�4i5��@-:155xo?u"�� N8�| $C �>��:��-� i۵� TR8�mll� ) !����onH E�ye�"<u���2��1f� �n&�t~$(z,=� Y� �n���!�z<\�ze"��� �E��'��� ![s)}\leFy�j6�~$�(�)Z� !�-q{] 6�z<v!�lee �i��N ���r����3*= 7toNthaQ=d[e�7�k7 �=I�~�)���&k.�-�4N  |)V�)}R�'WG.nM�-ta0��4�[ngv]�1�c*�{_D�U� � s. R�V~��RI�LfML0�wt|�_�8� 3]{�8i��p�Q� �Wo�� � Y[thm}[�(2oo�X� ~�1& f!�A���3)�.) ~o� "/i"�^��� YTU 9O��)if�FYM��J|a(nauiP.�(��a�<>� ~$f$�,��!A eQxaa���ro�p]{ i�Cu�m��oL�"�`� �O7]]�fs"P� 4!�y->8Nd 4*/F').%\?)wk6�� �aya@��8�8��8�8FT �zF"&: HREEfczF�F�%� "&:S����"6!:Y�"!:i�D6jl ScA4� .` Fe��e$-��zr&�byOi ukn�: s (��&�lU&=.�). Our �wmatsdao�6is2.6 7�F^���M�J� � �T�n�99/yFr�2�+ h{vice �a�: <�G quit�&�L\,&6rŋ.6MY.�=�< � a pt�i���#�7f* U. jT-8&+2�k�� �� -� �9c.s6o_ ���yaF=P&�:I ��9�!�=I��involv2N"a (`Ho�(ll1 TA�n!����6�? O"�� G ad~8:� Tp�s, by*Q= :6�!�pell-be!�d;!�6%/��-z!&a �e�E� L"�)!0��i*�0!�T �!A� "��I�c�B�!� e�5d#0Ls.\parL(�8 n*h -0 C����9�"�%�(9 !) Z��(an arbitrar�1"��=%�� WW� %�n L ��)�� f� S^ܖ,&c&� !�{ �c�P #) 3 )� ;{f(x_i)sQ�w 1Y$�'f(xR�4!�1�B�)��B���%�=mc pX� Xto�)p /2� � � 8 J}$fd5NTFEx�n�� ".�&j(�R m9�.�bS 6Z�@ knW+!/�2�b�d%���QU!3��la��"��-"BN>M> t&B�� m|}'W��%ne��Qi��� m�Md�`�.9�"g�!�Ka�t(> B "X$)%FAs�� "M>6�_fj&d&٣p&�A�ET ?2�\P2�c� ct � 8�!9 *�&�'it �� is} Xd=�k&@ ]> �4 "�!u##�)acttAkgyY.��gf5>;DFA'1A&'Ϣ^�CE9�Mp�MQiFr&�B �N�"���U sketch iF�i .31]2Č"�&$��-T�O�9�)� N�%*(8*U����i# CEp"�]�i�� t1�9e$a�y�pJG�FQ�!���i��) ��%,%:�S��e-�bnMn&�!�%�/�,�- g?g�1圂��A�e�y6Ao6/N�� �N!x{lusP�"2R 0�t e.g.o�D[IV.5.D)]{Nagata85b �+ � �Hg>�B !�*�6� s~$j�%'xsnso�Y j6^2_i�lo�to %.��h�lyc ~$A� �"��nR}IA�no)C'$~�� nAO "%(A�� {x}� ���{B$�T� 6�*� &� JNX��no��6�+Hd� 6� *U, y_r)�$Nc�pm�0%�QP�'�8&�NF�Bmay"�,ll $ E�s $y_r!�.U"4'�A)�86a~$r*P6c $j(�*� y_r=x_{ }Bwrle (�v � # ����}o��'��(��a"գ<i%d\��b!j��4in ?�_���X�: �1 j�̐<ii(r�(0defeq j\bigl(�E�s>r�sm�j(sS r)}}'rOt ��فF�9Q��ݍ3N b�o�� :�!+Q"kF � $Ve� Y&� q V)6$/=�0� !�e���� � �AaA��� �7JQcoX#v���3a "WI M�0a�&"� �[J#L��"�3"�N"7k�2n 2].m .�:��� �Rb���).����f�� a&T-�=ro&:=&)`N�1n @i ek4>�Jq���  �@e�if~$UEUK�g��Y$}s&�a!y..X�x�p � e"ViRD�&V cor.� <�i%T�5aseT�)!E`�� r�hto�L Ks�h ^1�s=<corej���g help�Bf�5Q+ �7 8/%mK>F-�s�&/!�!d��DV� F�, cI�`���W�!&� or.  Xr~؄2"� �yHEg.~2.3bFeg.�21�&�!�e+L�k�F�d& 0}IC!u�%of�K*��t�!0$~rem6*M V`$0}*:11/i>! � Y 4(L6�D {0}) ?(M1���� ��()&�Q+�~����I^2� n.�5�`�F��9 Y_X1"V:r���!Yy�"6��Ӂ-? ��51 L>�`��,1�~u>H1�A�*��3X�WI�Hbm}~�ua��t��y plu� ~��,!��06�U��reU>� ��EI�+�"��tN�/+ ��^mL�KI�,��gb��o'�#��a�i�-N� J�he�  *�tM I0*|1� ���*����n�^6�0Hf #�%A�NvOhk6g �}M � i?�}� ~i��Q2J5�A�Ilo�y `asiL '. A�Iy �E�"�%A�WD$�[>02� (1/i- S~+ )\D2� Nir�;al��9$\absA; -x}< I qH~)NEnr1+sIt K $A&6>_M*4>E�G# was !WanNL?01.A �> �;HIaN&|�Q>n&�n���c� ach.��(��E� !�͘�L"�D6� Q }%G$x_i-1/ j}>ARC*�3!�H"U)l_i�(wYA}��inneO(�)�:�  N K2)M,"�)}]R_i]T_i)5 F �IV� 5 N��gN�Me���������m��i':'bI�=*�:{B��!� ]>�1M ���F!��' V�^-&�T9Z�p`0a�� ty� 㡀�/bs u�r!"�?M�wet�to+ t=�a7m� newO�*. Gran˜%|� VN M���nd"bny/ Ԩes�qg�z�� �i�&j >} j SU��%� �!!�O][=��s2f="� H� "i;�  !�F&�0a W*T"�"� RW 1.8�W � d�Z ] ^O �I� !� i"U��"V� "R �}ubs�0 XZ�@ A% �HB�Za��i5��E� 976�(}�n�2h1 R ��Z�F.{��A�&��-.����8 �� ma�. Z��o3@0� �="� ^O��� Z= A��/q�AY���(F-y?.G) ' G D�T� us )�qJ�V�AlD�gh*�Q�ZA�~!b..A�)3&6fuUR�9JS, H^3�: �<� AB�RA !�u[Y#*b� �hshsb�4%a�j��m�a�: E�mq"�!��ۿ�incwxceU������ ���ii��a m-�/� type:�!�:�72�7}>�.n9L-l=����'�.�8,� "� ��"�9R\6t��ᒖ/te��R'aj a%sI���3j�"� s qJl�$ln��i"�\m � uLg�${�3\|o%8de ourA�r\vv�ga,m��Z�[�� ofqn,�>&�MdI� n=�acW��u� , T. K. Boehm�iY"&���� X�8�uctz6 4}>E�von-& U m �J� ���.���5 ha�) Y�D�!#A�*��:�-f��)���qgV�F� V�W�1�fM�e��:�E� "Q �+6a,vi[>�/��+a�BQ7�3���>l1h{�ag�q�+S�Fq�D�0��y@52� 0y->�q[O P���8�1 > !�I�"<1�t$&� Es"�F�1A�^\ F{ sU��� A�qF���1�3 half�M!~ ~W�"��)-�|�:�� sUg�we���"$�>�uX~�=%�b 6�u UVn�!�"�y��V #{-, cP By�\�F�+xQ/e mea&-"1 �qaP�ge!��z�ngl,mi�SӀ�� كH�R2)! ��;�.;�"&>6V��{M�y:�r.�:'Q�oF��a�2K�l��� �ci�)�p'E'=�:E!�A2|,�� �) ay"zAlexandr�6 one-5 c�#."�[ST��h� ),.(� �}+ E&�oB�� �$!�i ����D*��� 0"L%)'acB�M"��'si)6b55"eE_�,A�u a)��Sf� f7�7.��)\"� $\Esse!�!� lqy~ @c2��*5e�Pa`Ss\~!\t>FY �!�+E��^t�%L_BkHY|!�F e *hL_�F�i"� �S(��Q' endowC��9�u_�ec��A w�9�z�s7 <9!5di"Em�ɀ��|##�:ӝ �xZ��RL�dja��, h{da � o},�. Be!X ��we��4homeomorphic c.5hAL!^�a6a�S"i� P[�w p.~7:-�)�6k�< uc�N\� dZ�r (twice):�$$X_{(S,x)}�eq(R8)!�d{S6�AOJ&n�hsZ�1e��Pa��4i�G:�"�2>X_;4eq %\Dirsum_{ tack�CA�\\SEs4�(Q�,  ��42l �%�>�cJvѾptd4.2��.�.�6�!w!2]# L<byF/y,!�)��[.5&D B�  Z��� a�tv�^��� onto86�C c�@� +enoug �p�Zp�2le.�a����n��r�js ${f\ 5�� �.��e�-��1�1��Yed1"Ag)bfyk�])�s�%�H�L� et $-��%g"�"&�k�:{(y_i%�6�Z�(�5��2}�2� }q!� � ~�. Uy_L�@�Z*�c) �y:O"�~R1$S� ����4HZ�@sA��� %[�"[Z|Q��2i;? Ni!E��.�A/ve��3�202N|�&22 2�:�D9�n)���6CE:G#~9�$; U�g=.�&WB�e�c[W�thɋ�* �N��l a!���� �fin��� y� �F� �)��DW y aS'7 O$%�!mVVi(�eRe+Y2U�%Vie~!�'(� e�V�a�6oS�q " K� cq�@a�!�M�t]7* ťE��}�� �  a."�S�&z��%�a6L n~{S���  !w[\�+ )�FQ!L%gA �Zx�Z).�%G��8(x z,Fo�� �X>TR��^�sL �42�?>R�aS �A,2Cm^ǡ�VFE%�a�^� �A����Y��OF �%A�iJ�nA�nA�nA�nA FOURj4A�@�@j$�F���A�]*e([-s2�wM5:�FhAUb� L/�{IU E�G�j� /~�ff�y&G� seen (:�"64"����Q�'*p6��a����6��BN&�Q�B08&�'�u�$�ty ��t{^'"� F0B0{��k($}|Sho��b&T q�"E� ����� �{�:AF�? ���oof Z._=w&9h��gST�Mo�M� c�on F���B)1 b��JzAt2I+�U_N, �:*N!E4�pr.-���p�"-F���B.�*yLKa6I"{�� AxY�" ��w,6Fm��wyq�R�j.d�!WK���A�\����* (a��)!�&�d� $p�\q\rW"p?p#'q� c, X*p,q�&uqw?+Y$-Z  E�,`coa��|@:F s\Wg!��< �+and"�.ѝit&[�tem:n��p}̈́eQY+p} �(�!E�- F&�!Q)?(� $F!a��R[; ?+$����qFq J�'�[hq:� F_i)��  W[4�� e/ ��=8 Yj� .�'jQ-$��&�^i �X� �"  �+ �8�z1}9i � ����Pa :���8�g 5i:G\,+� � �  N-(i,j)$~��R�~$"�)F��:j@6�9 ^�  �:U$a�o�$U*� Var9Q+:)�V2���~$p~�jq �� �&�}. /%�A�-H!vS�~%�n�I �IE������U 5E�{(i_r,j_�Q�t,:eS�-&��)12� �p� :j�p� iMRA�d'$���*�zmW$Y��{>���2b �!9!�A8%;6w$r�8uor=i��� F_�-L-j_*: i$ `%:Vc�6. I��2��":  2�-�:q}��:  ��-N�-ZJAڅr �4"�a"I�!.N��.�-u�A��e"xd�:��oa+�H�er"6#��N#�X a`5� �6 b"l"�#��A7� �܁_>�,�CB� 6��3�;*q�&: �X*�XR !>wh��:a�!^����?_ 65a�!aD"]�_ida�p�/{Cy��Fez6epG& G&.�1�:6�>��c"��&�+"k�� i��05�6�mi0�|�*�E^o��e2(6YB�KL B�:7$q.2B�i$ B�8�!��h�toi'&"� D� � )�UH�:��AN\st� \ B� �M�mA.f�|.�{If�I�� "�'���A��o(f'�, B��&}��>)�V �;M��^1? \bnV.� ~R�ᜉ�Q2�Eqa�at��c me�9AA�͂niA�cr`&��q�a"�#q;"6 ��F_E� )� . Ar�^I�D)�+ (+bsEyI 5}D^�q2I u�i�-dŦnu. E��b.�!f!2� 2 �khi$ � �{ vP$~$B-�# 2�6kF&�R`5}�� l_ �3 s��lyS"N�!#a�3"� �X4�g��-�h�z�Jp[*i06}!�te�5 �:iJ�B�|e� w ���ac*�/.nteE"P -��j)0�uc�,� �� ��9qu�of 0�Ig >--"z �Z�t/$��%*%�}% :7� � b.Y.9b�- "d�is ��a�d�D��-���:�-� �)�z��;$.��� Bs��mF"�*��� obaXzB�+$�K teger���%"��n 0 e�2��)BO ; &�,\`c� t (Ik�U/I�s7.4]�7�(RЅ[� �(X&N� a�bet?K�8d: B�*FT�M�-�l/ . LV��qY\unt�YuitV�Y�[w��D7"��2m�3u�er *7᥁�N �#n232J��2 tselJ>42I rL�furh`��;�>�y�ilN!3;��ji�VCe�:�)�6..^=o�! *{>@��k�.} �&w��G\2>/�/&B�,���&�'a�:&)�$�R B�J�"V)X�YUB�1%�.mV�By�(%���6is��o�$+%��� ��#�a�&�]{�H"� p"r-���Z�~ � � y� t�=f[T�� FK M#�! �!4�Z*d���Ϣ�1lA���Jany��n.�4�I:a��l����$ynY e-f&�U- ���I- A�&��! H n A~  $f.1 �U'��)" j!j@/!��dH�2Y|f��&8OV�>x"�2�f�O!�o  * >@ WQ^� q ŤE (� M�!�(�:#�ah*�P@�ndM� 2F���0 fig:m�r���}�(m˖ ���"�2�*��center} �\small \begin{displaymath} %%% DIAGRAM: needs xdrix package installed \use �[all]{xy} \renewcommand{\objectstyle}{\text} \x T{% &hproper \ar[d] \\ open onto r] & *closedl]/pseudo-: J4\\Dquotient & } \end6�0\caption{Rela �s between some classes of continuous mappings.} \label{fig: rJ pcenter �Ifigure} %\medskip %\pagebreak[3] Now we can present the characterisation$orem. This is due !C�>citet[Thm.~2]{Arhangelskij63}, although in our proof we follow @0{Franklin65}.QAthm}[Q)�Lprime}ski{\u\i}] \)0thm:frechet-c:�}\index{.�-G<} If $f$~is a J#\ from a metric space~$X$I)0a HausdorffY$,!+ n $YXFr��D. Conversely, if\/#6H1 R NforI0B�4there exists V� ~$f$��~$Y$.I�!l0 To prove Th%�~\reff[( we shall cupon B>$sequentialF�. First,I8note that everyR�is qo:Q* lem}M lem:)�a�-+!�MU  6-7( Let $X$,!- be>�s, and l&0f\maps X\to Y- .�aDAQl>�.\qed)�� !HL next result will ala7usa},give an easy!�of of7a���uk�%}[{i�i�4B�.o1:�-);!:1M.J�h~be a=eB %jYB(e�A�b� a2r1�i�ai M if%� only -� �E'm�, whe�U\i�seca^(B=\emptysetA�)UE�A�, it fqa3.B�6H�reň�E :�UI�E�!�>$.�ZkFrom~\b�%�ɻ w seɾYO BvB$, i.e.��at $B�aMed]&�}^ A)=X!�inB$�)*A�2X6�p�$i!A.P .gA� N.�Af�u�$AUF)e�!x�* VaxK a��!�e fac�I��{y1�=%%ؑ�V� after�,, M�ex:� E8s��i�� �5.�:!� wish� show)��H����A�� ��Y$)� t!2@.^ A$ @F�2=r�.Y�V� ���&I ZA set~$U$!�y~6�$ such �2�2��!�� A.�2�B~, :E�V�,%thi!�jcBnT��!��; \neq��M�9:�� $x\i2Y�P!+-)9�� X��YP �?g a>Jx�JB�< !ve�>xiJn�{{f4}�2P�ARD!�x)= yJiseaā�iB�.�  + corA�� �� !of>��x� cor"� 8 imag"ThLJu�);s�6�� withU pe�to taking��"� Ts unde�D �s*� � At last�arr� ��e"� �o maiea� .z of}[Pro� \/�"�� �N] E? 6�A:.��A��m9$:� i2(onto. e�a0Vqit;i95���0 by Proposi� �!�Rc , \� Ji 2d.g6��I&. I� $particular4� � +e����A "�5�1�� ��J�:�. AF@,���N�A� J� Ϧ�:�fl)'|)��E� F ��jF,CHAPTER FIVEjgzF�F��� \� �HCountable Tightness��ct|(}�chap:#-#}] � *{Preambl�l.�|of � est� <A�-M}���FcE�c5�2�numbeH%6���E�:N dens.6E5�Dm$ &A:H\footC{a ��in��!�@non-standard. See$SI��J{M�}.}1$& ��a��]�6 8a�8>�%�pI�.a�.���q� �m�$ �F�. �VSouslinF�CCC (Uin��d� �I\\�qI � j�q�\6�!�� _�u:�(How about Sf ces?} We���F�intro� at �y* �J���le&�k! �AVfalse, h"��:VA]&�92Reg� %�-&� 4  �} W�hibitA�%&��9�]� .i�\beta\1� < Stone-{\v C}ech� W . natural MB U $Xm.ZwconsiN�p  on� v !�b~] � #.M toge� �Nset/� t{x}� �#ll $xc�seJ !.!Fhav�alreadyM:�_ gentM,cSn~2�arGth�?� event� !tant (E� �weg:!�!�})Clear# n a � r93�mN��an�increaA�so9v�X$���Z�e ��aC� ��!�#" -*A�lyL, s $&�)�aH�oXSa2HI�. Hio�� R�To� �is,<�ny.�X$.*B!Qo&�� �c6%�$is disjoinajF"~:�=Fk�"m� e4a�&{A "�{(A6�)qh�A&q�) CB:m?~9^ Uj-F A�BINow# !�-_H�o���a�its=�Ig)�in.�ita�!%furJ$>�D"�4}~�< ��� aC5��n.9X$b� \"�!�# UsZa�H bcan[IT���vno 6�!-Lemma�S#�-!_s}s� IR�� ��}?�A=Q�2�+s9#�!�x�>�e�ř.��lea;Vbɜ same�� (.x) adiscreE$�=e`A'��RY�us�%tly�dha�6+X%��Fe ident�  $\iota6�#is h{not}E�)>a�����I�aJR"��$~p�'rves limaAof��cesV�W;Q��previ�(�$�$ll��(rENF:�&��u ved.:� &�"$!<�� Productiv� � well do�3)�QН#EN� be���!q��r�s? �&K�w8 ,(elementary �)�E�this &% uF�%7����Ay Aia3mQa�$`-Y$}WaQ� _ =6�JPa�K� of\/�i/eq^T���3(��ran&� !h�er mAs��b#!�� ing2�'"�&Prop.~3:�&8J B|&�s�&�q�+�%�Ay)o}�:�8FYF�^�E�x%�4���%�� Y���aiFA�iG Y>A�et� C��aB !3Z%T�((C�>T]&�T�g{1�!A)"�."��g�TN0$-JI 5!$*I Cp��{=lZ%�r � � bigl"k% �bigr) %(A)f�"q .<�H2�Xj� !z each��>fs�O 2�.Ne�gdeduc��E�?"!�O� + "�)�F�B�� /le/9 }, H#&Yn2 �&M�-�x \�Q��E %.eTrH �"sbY!� �.W !aoY �M � p��!�two�.k� *f�% さy1�]inpl�]9- . An  wasm," �/�/72}%omi�%"qg � �Y � ob��ed byY fy" � p? s &� P V.y m~ N �� *6,�f$correspondn%�=struc��  unE"ably b_��� eas�verified��W}@.�Vm. irQ *!�R.a��*��*^%5 w� cooy"��.[e��.!,vely). If o&���03I��t��Y� uct � � }b�, acc�g� ?�� the#%^Vo42E�apd2|2 5.9]"�� F�0"8�2,4]{Malyhin7220+. � �� .k�fp� DI\�t� bH0�>Qr=�I� MEU� �N)�%'�� >O��:>! �O�]�0J>� Z ��JH�&ll^�W� :=)6" S)�i)*�4atmnnot,m�s3i$(x,y)����*h I�$t ob� �)� ���n�v,a few remarkoin or�bI( w!vproce&We know�y little�A�![uc=se1ih ��(�2�Kto�2da��"facy�E�*lL0f attackaBasmms���go� to/�y�P�,and~$W$� r�(a�5�yM-Jly���, % (#->*E�E��d}), AFn�@en� a4"h A�hey)a-��mmon. M��'�lHw��H~$B$ �/proC8ANdow� ��"%v� �E~itiA.� assum�7 ${Ew$\notin A}$9W%AB�)4 w��� $W$~��nd9A |Ft&�1y impl�e%S%�B���)}EH�&>-"-� C #*,\mbox{$T_1$-� },"zF, �k�2x�-A��с�  E�� �nV?�$homeomorph�"!�a7!��.E\ A4���\-*(B�) �CaR�iN+{y�a�B ���3&� 3:2�&� U  q�-�B%5F~JP9�w .��w9��-�!�N\Aund% .�Vw1%$\pi_Y(B���R�Y&�,29$a��$yiMD�(�19 E�reg��qE�ur�nEW3U�V!�A;��i,#. U�-�� V�o6��\ E��ure[Y]j2t��$E%�a�2g5� �4%�05,&� E.%/ 7 a9�E%�Vf��%\ h6� )7 f [ht]2�#}  cludegraa{s&�'ygeps 0� 2B"""� �$OF�sA ��+Fin�� nA�%�W)�2��Ea�� N��m!b.�6)!�{��.@� t�; ct N!�e oAe6�� �3 R~belong�6Q# A$aN���$W=�N=��{j�g�S5�:�/ �a$n���xM�M�W��&R�B^� �Q) a~)�#?�et� l�Sya��jE0� �&�i/�X��\ u (Wv�E�nI� ��� ?��X$6E6����j� 6�!k� .*�!jinuR�9�Ew� �m�J�2Z  5(W)" [X]{}\c� U�W)\ni xf�%W!�&�.s�([ ~AZz�O $WZ�4E)�:�$z6 E�3 Lq(!Co~.�J�=5 us!*2w1%�*� ��za���!�A�e~!��y� � �*is eg��@choicA?~$EJ?K 6}&�M6`,Pr`,} � wor�2P � ADin�/ E.dh adap q,�'& Z ~.Hp>� it �no ��eru� "� ' e*�&y��e quesa�qenumerat"b��¡o4� 8 \item[(MM)] Is ry�*�0�!��L �Q��>o?c$� is� n+ !=�_ ine{:�p-� � !2 �=2 P+964}&qw b%�d1&� not  ?nswer IZFC\@ i set-$y requi"t�A�Xmeans [!� ould�A)�0go��� $,� @ we mus2�"ou9S�sta-�"���-part�:�D,{D4"1,���Cmemrowka} �DrJnt q "�=�E A A�(diamondsuit�YX�Y4 Ostaszewski'sM"- p[]{ 76}.,\alpha @�$Alexandrof-�  M�oA�BPIZ� # is ��sque8# �.:�PFAM n�B---�M�Balogh89R�.x!� Many  $�!nneGMZE�->Z1A�v foune(A3 surve�a �[Sec.ZF6�0Ex&u �p|�p4�p4�p4�p4SIX�V�3�/� �F����h� on{PQ. S1s�\2�+M6�+i[y46�Out�-E*�"�'i�2F&G��;8ly  esS��3Ņ�$ �s��( star�fbj>1�}"R!hip"B2" !6R �i�"W2 ,�xI" l 2�-Cre+#�ed e�"�(�v��(ed up until!A �(s�$eg:w.�- s�2 -#�}). "�+L> ����%\S �!*�axiom� ;ed��Kuseful��!�achie�"!&9�3�#U8I�o��G  %� � �)��N�% (BV: 8�m:7�*er��sk���ok ag�-atB{%�ion-4OfEf�- =I.?$A�.�JBh� g`5i� S ex,5E�"$: ` �%�)����L y $quivalent'�tat�#� true(EM=IL/ f)is*4*h�rJ stronga{�.. Loo� o-&eng�theM(�� note�  I-�l� rmal �q~Q&} ���\p[Cor.~to~V.5]{Nagata85}� b)�� X both)&� %d>���Miv)nc.)�MaAE�%$6�2pcoU9de �th�7��---Aaf?��8 epenE'AT4ZFC (Corollaryi�� �%�%$��6�Wc%¥� �?AKUw-�*E7)gt[ChaU$,� .~2066`$84a*�6v#�I+ f�4� �%)l�$lof�� S��7� .G&J*_2!��Be0� -.)v.$o ��_J�-�~"�!� r,edEqtx�BU *cZQ.DV2K0V<}  UoaRfam���s] s8Y!�"Kcover��DqvK, !is=^} �rGO z��e!# i^V_>lJ . Bu2b��H �$�4k$!8a(%MD1�/~$i�!�j;p}��ver�tI�!� U=\U�J_{iM02~%j:wIa� F_\sigma$^1Ga�;2`MSQb�#m�6�l!�e�a;�6' le|seev<=(�$ h@yS s;:47Q� �A@p�*�(� OF*r01,by Urysohn's�e[psix@"�7%�#A(6}]{$}~%�i ER2, %�s�  le�Einfinite"w6~$\!&m.�e� � ' be writte�*�a��{}!@ OVV��7#�,�A4"i6Q$��%AA�n$ (�LLem.~4.1]{Kelley55} �La�is5T0Tychonoff's l0 ]% {5} })I :,0%�l!�.� 2?a � .^�;�-�"�)sh�ben!���R�Re�!�*� � &�D%� � 5��>a�possib34WN-$ $p(z_1)$, 2)$, $%�"n�[�� $k=��$��',~$n$;Z_ka� -#�)"%YWk)+l"� <)f5�k,Z_ka�k=1�!�� =��hDu� :�Xs&1�}[B] . By���I=\,��,5.6.f ��n�(e }(a ]]��. *< !�Fpis� V�=it�6sx fE2��of. �"r]os5 �7v  !Me �C_1*BVEz}!���2c � � a $G_�G$~set.EVif-"!��6 #%�a�� n�Q��� �>i��/M�q�;h� G Y�a�2�#8i� meet�A���>\X��%B~�!?:-p���� ��)�i1-A-�Zz9� !yur%�pX9e�esPbI�� S ms?b! in�BS&:��R�L*�R&2be"P,�Ane ]w�Lp.�2' a+a�glH��SL5�hanu�� ":aLaI L, fashion&� �e-.09\p*G0.�M ��} 5Y�/ O)_} a�V!�Dd�8A�5Z UBU�Z�F ]e �:�1!qtak!F�^�TA ��J��N�E�_"NBi&� \&�>"�!K!!�* co�M�= askZ�U��Z2p s doe�fM&�e��hierarch�"FigurBC8(.�A [CH,��`41]{Hajnal74} g�a"�4�an�,L�,�wh�N�b��%(e�)�.&�HAn�.IW:'�j��"��o "t �ble.}�0. AGi.��"�MARI4. I�r<he&�"3he�]�sa� !' ZFC;�dV.�M!�ac�L,d�R��~�����,t{Arens50} �����I�1c!G*�#�u��,:�(5�E- automati��0� '&e$. Jo Lo�<l6m�2t�Y.� ��AcI#mod.N"!v$ `Radial I� val'"_ *RinU�(141]{Steen9�"�?hinds/!�aOP% Lo's��* %d'� ac�FquNsimilar�?�V�F56&�!eg��&� �+\In�a��i�e��A�u�Q�w�#L� �&d�0� 4sum $\Dirsum_{]$]}\I �.{r*Let $MPs>�8 f~$L� �� ��� s~$(0,r)$V -B 8(#�遘-!�R�_i&B&\ �1;>0B���us� :!X�5Ke�; �1x >� ^�"Dj�;�L� :#Cu�2x��h�c��   $qHAN-"�.$q?%�0}=e�Q �]C �;�? bine>� ).� (1)y��yV�k5 �4 Yes$Fxity1%�NA�syG Aa�s as~$Mf)�>extra.<�4REp`A�� :� _ +�jv!em� ���?�Fd�E�� tens�� . So�&� &/[ V  claim�F*� �� 6� On C�=!��} y&M��E��de�F�U@ G�1sC�$Ujwe�!"�$!4a=B%"nce afqU�It��;a)eo�3� ��g6Bma6[ guarante� weak.�>ng J � !��t�&b�lv�A)n�eW* a�a7"�"�EWeiss78"K-� +O cruc$ w�"�@0s ^zf{ unt-v"v" (2) �3w."U+P �ݾ> =�} ��,-�tun � !l�-�6r:Wp �"�%�%�% a\ is u�Lwo� idi�:�I�l� !�o�aA�;t-�2�O&l-76}1��%so �<-> :�[\v&��sp�&*�#�]  RO 6g ' �M51:�. When �4a% et 1I �zzL�=c�x� J�-���D� ofQBomega@$\_1$!S9$�F�2D5*� . (Ulosb3of����oa�) ��XY"�X<so*�+xx"�p�-�e?�7bs:(�& x_\aV/\st <�z 261T~$ �~M/7%:�cho�*�!�e�h q�<� X.�$*� :�����NU�. ��CR�� *h#����#[q:��$AdB�#5 CoF_i���S����4�^�<e�� R9$F_i� �F ��iW� &$?@�6/o��9&A�book-keeh _ 2� +�'��:U�!hq(!h%V �b*�Iti�!� �m8�O a� �A;A_rm�k i[Ust7$s"�,, $s\gee r$}�! �5 $EJ� �UA_h�e�E_r�:dec�WL BW.���"g QJ:��E��� +1 "�>K !� }E_r�r&�<*x!��<�� E&w)aX �ed!��osu@M ���q��I]a�sub):��Y::U_eSIs��8Y�" *+��y:) A'N@nxU�re� now�"cal' *_u� �A5�AU� �>��%�}X)auI�M!F6-Ka>v^�=�We ��^Z\�D_1$� 1�c ��M�4M� $6!D" �J�zskC.�!-wZ A_12�@Bu�CB"� e�E��x5� to~$EEA]iD2, g2�<:*E.>5r�Y*7 F5$J�&0!g-3DA_r�5JX A_r25*4Px-�E#9r�1��* &k of/�HJx� A{my Gcoy�8"}*v"89t[3.12*|K,* b.~III.68FL/ �G5 �(6$71B� n * 6���A :�(-free�.:� (^;��*tm.z/A�U?r .-w MDJ %�" 9�B �s�7spl�� tepsJStep~2�0.sIs�N>�a ���� rans��.n�Ji[IIn� e�^a�ilita#i� gion!5ffi(yin �1�=~�_��T~qr.qu��o�+\A���ECE $A$~�& &�� �1�|��� &��Dc>%M1]���A.�EfA�� �s�c �=�e�5Us����1��0�U�s)��UP� nyA� HiB6�!d=Q!Q aN�R�8�howE�V B%e%�A(8>vA6�,�C��u{�-2 �2!�{UB�0.@52� 2A00O"� Q=:�W �U_� �^!����e� l y.)�&"{1wV_i��2�xb)>2u" 3*2�L=\B(th)=�Ki� _:�  $V�$V�"~�%Q�$P� 6� 9QI�Q/e�a E�!,| j(IgBNn F}!%��"�me[EX.!T$F \� � �&� F>�i?�|1n" a� B�YJDA� d2X2Y,�JAk%ZD�p1@ A$F� B. �>�(WD� +-e�x_B��=9�6S� 1C-�� B�,T�{ E�YE�5��6Z�Y*N �6�Y�f.v� �5P�=6By����B�PR BQ�܁w.a! �Iw&>2&EOP$;��!�1N!x�A  �A� X�+�a&�"Z 8 ,� �9$PN�E�6P2��P���uF$�R12v� N$�I����5x_a� N1I� NyjC&�Im�}6)��d&- orɖ@2~$N-PP���4� CAP ?&�Cm�� ���a����"ileZX/ �V'@ 2]\� �@*�U20�s�G m $Z y�w�"��-� tinc"-Z�Bi�&O � .� a�"� /�i�Ll�j� *�&�� o &2$Ju�N�x$,!<��-4B� ,y_{-\infty}$̡衉� � W"�� X��5 �E� �Y�;T"�!��G�E��~$1�| �����W-�=��q �*� O(H$80)}\;\left\{\;; ?aligned=&�} wO,\\9 &Q�{%a( e{y_\gammEt J}&�Ne1� W C]\t39s3� $ `&!$.�:�\r�%�� :NY�I�e=}F!�6  7� .e a)6" { 4���AeIq ��M8�A��m �b� � 5�b��� n QvB��a�x]� .r W9�� w A ��/��wQ�!J2hA�BW-�.� %2�1ը3�)B�5��[ �rF�^U�sqI!<�.Y��{ �Q �}�.J Xq`UiE�!"}u �n GMlJ���%�byM4��4� �"ռ 5,�!��.a����� CJF�BQ�n ��:�E�AIg��w�/%�1� 4y-1ie�"��|5)eA6~0��)���>sfV*b��">"�P�,~��8�"�}��] *��#�n�9� � W  iI�5I%p � )F` �&� YMM:� E��;an2���%Ga�� �>�A5�U�)�%�C���� �-8I��q�I �&1�iMF C ] wM�e�e�_ $Z)(y\�^�G+1G is�<X&*E�ert$Z]�r ��r: B�:�BO-�, a���4xA��oE(&�l } C�'�#q BJ�n�!--%|f )���6Ao�d�1�$�Fv�#. *aals.�!�&k p>}/Q1H9"v| �beOe3<��it�$?) new^,ao@�\*z&SeNI2�&3f�s� O�|(}�C���:�&W,� =�Z2&�I?� saw �)m�M?�wi��A�!��en 2q�7"7J � & n"2��C7e&28Dct��t�?N�"�S;1�y=�HMV� Trivi�Z�,7�Ji�Q&DB)�aA�wB� 2�.J|6re �b2%+H�a�&.a&�K,.�is bas5 ������{91.20]{E8��4sR � lem�  V.!KE' \la�6ar�K+%Q �= /A � 5sU�.L `� <�������s)�q��Ilo&2W$AWiSd�� f wa[8K ;. If a ��c�i�}�& # a:�r��]FFEee$~s��i&,A� get  n* e�t (<I�/���� ? �f '� u@�!t{EB�.b&�IP5 u%��i1N&e�is:��O, ! ure-*+rvingm �q\D�)1.w�~$'��re vi�hC&F"�C\_{}� E_�n )%T u.�T"F"DD2}.D~D2D�5�(Ev!F� C�?a�ia� a(�� ]�&�"��"ʕ�&�� �!���sY/6#r1- 3%szy��I81A e%y �>H"n ZL$e!�\e��{%)C)��2� 6�F_i*� !{�0� �"u .��|. ��8R:W el�+�H"� �  � �=� �\.&��E�.�y(V@6� "�>ɍ�5*be*Q�_ Inde.1� hyp�;sis `��'Idi6T�;replacX. `met��'B �*�n�>2.= 8 a}, '`pure'th6q6n 80TPW�1�<p1>Ky�V\ *� �!�*�"O.,�Pu  a"�+�B o�S-a��� ~i z�&�.�L���_"�.dM� �Z+) +seq ��]w"[-ٚ�$p aa��I{ H�"�y ifa�"� ��> I�� As[.d 6i O��IG%ons w5< ne m=ju�0)` �5a��6� �&Y �B� � �!fa�:M� �V��z�be�Oid/'ithinC;�[Q���(97]{Vaughan���E��s `ډ� maj�M3�hB-�Bt%i�H.' 6�]3^�] �%-)Uʊb?�] $��].�][ID �"�3,B�GA["HLe�� �/��'?�MA0k\neg$CHM�� ufS I A�-8�up(� m���p1� 3]"�22up)��>/�1i+wholev} ! %�R�2  � �}.L���&�] �]��$pa"K���$�N%ZqJ�3e�i�"B. z� �fr0-So %�e�in1����X�&e��a� ��6v�3corqX�duV%�/3�  `C�!���A��6��WF�<F s'A��&�W\/��\"�A�k%CQ@uJ K|)#gn&q�.? � �0^0^�r^r^Fv�zF,BIBLIOGRAPHYjdzF�F�%�6�4]"q thebiblioul y}{999} \.�en�?,e}[1]{``#1''Mdexp��`fter\ifx\csname %natexlabt \EDxq�! #1{#1}\fi�l�em[2)Pa�+V(1929)}]. 29} P.~J3G2P.~ 5,/w�\foreignlanguage{french}{M{\'e}moir�#r les ee2���ip�� s}} (BOdutNK�U4klijke Akademim>n We4;�@pen}, Amsterdam, ؅�5t (1950�50} R.~ ,�%�{g���n��/a �y]P mph{Mathe[C\s Magazine}, volume~23, o4, pp.~229--234F�%_Dugundji 3!� �a�(J.~+�R�i o�  �a c)a�n�,Portugaliae �a�96�141--143:�9�{��p6�(1963 � &t{$63} A.~V. �{R<�S�ktyp�=� or &>A��aVs"eb�H 6-�}BI�.} M�Soviet=$s, Doklady9 4% 63-�01726--1729, �� d�{R.~R�J}&�P4{R}ussian orig��F7M�9F70} -=,M {S}2"�!!=Xw-?{C}O�sAUi4�"�biM6a,}Hv* M�11%,70-, 597--601,�9)J.~Cede.) �*1>p71V*On�6�H�s�}1L'��n^a{T}� aP%_�/�cesr0 B[12@.Mc71-7$1253--1257>9, {Z.~Skalsky�e]e2B;2V;Aef ency�tr�B:�BA,e�2H v.F-3, no.~5Id21- 185--1189>-{B.~Silv�g2g8B�8j�>@�hod, new.�)%%� �b�A_rLB21IK2, (1��v550--554B(Y.~ChoudharVK Ʊ� Ponomarev�8>Z68�JV.~I.Pw�� On dyadic}ʚ0����68-( 1220at2F*F��zus}q��.&84>&�c6�pFunda` al��G�f T�.u�IVExerct_} (KluwgH�d�P1vBV.~Jain�z�BatmAqF 89} Z.~ ݣO"� {H}"��m .-�*�2�O�P�~`�+�� Amer:��� al Societ��105i3,e9-�755--766� 0Birkhoff(1937!�37} G.~�.n {S}m,M"Ӄce�W`h�y,"}�LAnn-�&� s&{38 ��W37 �39--562HBourbak> 66� 66} N.~�!N>;},�@ III��E�0%p �< (Addison Wesleyn 666n CaQ�5F !DH.~ �m�B� I Filtr= t ultraf }Ub:��+DRendus de l'Acad\'? des Sci� s, Paris}9x2A2 ��F777--7792tDudley��e� 64}S M. �O2e ](�T�6a.�%u��LA�64 �483--507V�Y �^S Cu� �to `{O}^�'���48ɾ"A 623--626�"x�w�zR.~!~Z�&���R�`(Heldermann Verlag, 19896�Fr��!�5ai$65} S.~P. }M��i�w�.sm ce�R fficY��a*W }I�107�52��)��= .> O�&� ��lш&�Nieuw Arbn4f voor Wiskund�1/ 6�2;b��c�7:��> {II}"9C��.C6�P6�P51BP�!A��69V�On *�AOe� {M}oڃ {M}r\'-vu*��� ��6��o 596���$Rajagopala�3 !/ 6�3M.~6.��NLE�j& ��5��2�" 305--31>Qp�� (190M�[�06} M.~F"�b=Sur!�l!�#du�fcul fon�nelYuBLitan}{��i�4i del Circoloa�=,o di Palermo.�2� 0uJ--76�X%�4Juh{\'a}sz(197Ő 74p +I.~.=On6  {�) $-L}nl{\"o}fE}-"�W� m� \�{y��0.�8i�7Ѹ14��5824Hodel�� �8�j �C�� fu)�s {�i�XHandbfrof Set-XMjI } (��K.~Kun�and~E. ��� 1�� (NU-"b 2�846GHu�Z �u4S.-T. Hu���.| B� ( (Holden-Da} :^9�!3�J�} Bo56F56in To\-p�� ---Ten YeΧL�O} F�g�@}&sch Cen%>�8066�% �4Vr�.���v�6�10�� k�0 $55} J.~L. 1�J�Van Noskdj 5569 {Kisy{\'ng�z%�nski60j%m�[B�z C*�du� $L$&z C�quium}�u!� 7��6 2��21s7\"�Levine���� 7� �&?��H ���b�b1no.~1�6i� ~401--4022����I  72} � 6��-��n� in�cexp X$1 �)�Xw��vd&� v�-�31,�}.' �E 496--49FCzoV$McCluskZ�nd McMa� (199� 97Ŝ% B.~2!1���� Co�p Lect;B�� Atla�Xurl{http://at.yorku.ca/�/}aH976H��{M� eN���� R.~C��� S.~M]o}wka�mYT�=+deק�O"�!e o�"� Noti #~��u� .~556%Munkre�7�� 7��R. �.m: Ai�)v} (Pr�ce-Hall!C7:��w�tk 8 j fModernF�, 2nd� zh:}O&�SAۅQ�VA.~J..X��-��^�+"% ,*� �p��bJournal1�Londo��# �U 5�516�.!���ӉZ�A3|&O�Fi\� 6���b Bulle�"Dn ,mie Polonais&s P. S"ri"h�(4\ , A�zom et Phys * 86J12! :IS"j��h��$92} D.~B. =2,ac�!��th�bgaiona�in� Recc�Progres J�&F 4M.~Hu{\v{s}}ek�gvan Mill��$ 572--640 rL 926�2aR"�bac�9E� 96} L.~A.�8&� e/! a�ܠer.� �� y}, }� (Do�w1h2 Tuk4�4�W. nn"]�'UniformW�z x }����~2R1 Stud�j(P.�et 81�2�� ���� ` J.*� ��%.�/�&v�+��� *i �i �Q69--602v>k LZ�8�78} W.~ r�d�{M}'n's {A}�d�;Can�cn �*/&X30e�78 �~243--246�Willard�EE �S.~ �A�Jt�-&�7k �7>�# �+doc�x} u+\�{amsart�#�*mH(}� �p ��{}0~�68pr�}��6m{}{s��b���\title[��sT<u5tڐ&� als]{Thre"�M! � s a��o/g`�E � n SobolevM\} \author{Biagio Ricceridd�{D �t��z=�,a��kaڈof Catania, Viale A. Doria 6, 95125! Ital&�ab ct} I�" _aper,hroIQ,Qp)bs��t�G�n��e,$# ��gy�LZ ocia�+�(e DirichletW $-\D�s( u = f(x,u)P< $\O�ZVUu_{|\3*�] }=0$. Po�\ve swer %�isF9As ��� e innova�, multiplicitݥs �isF�w+940\keywords{Ene6�; �2  �mum; iso�!point; ';#�� } �3jeH[2000]{35J20} \makeE� )��es�*v�� shor�6-�w[�f� j���^!d�7�B8}\tag{$P_{f}$} F�\quad �${�N-�}\C V�. ndiU� expl܄a moti!��/a�{. So�GQT!m�B\��Hbb{R}^n$ ($n\geq 3$�_�<oNNbo�dD/ . Pu8I0=W^{1,2}_{0}( �,)$. For $q>0!y�`�$$f cal{A}_{q �Q&��a�%8rx$fW?�� , pu�PhiA((u)= \int_{)AK} ft (�t!Y^{u(x)}� d\xi�D ) dx$S� $$JN � 1}{2�<Y|\nabla O|^{2}dx-�$$'-!�$u�X�PA3!�1�al k�5&� Dly G\^ateaux diffe� Z/oxL$ E��1has�$'(u)(v) = :� v(x)dx ----!�) 2�, v � ��,�cri�l��E}� �=.xactl@�� ak ��2�  $(e�A� If $q<)Y u.?1t%B2� Bd� ix,a;DRellich-Kondrachov�*� Wf$�6�]R�o�C re&*qحy�0t�����B&e1�King� @Z�!�a8=i4{q��xi�7 b/%#n �i0�Y]i0r�o ��%�)V�V%kany6G�x$0�f�!}5X�{t�5V$�G��ga�=9 -dimbgal�Car�9G $F:�C Con-�l��qA�ais F\se�O\{0\}*}J$ $\lambda e�V�Ci� A�o��� �lim_{,to��}Q�(  u) = b0 I�2�|a�$|^{q+1}dx}�>� U�B,�� soY�e;eaA�Q�N�  he2=udD��)��4T��sAzE[.~2e p!��be�;�Ear���4 ve�r��w6en lep��u# al�saM&�u�=} IArea ^1e� N[ w�iC ��{u� a(x)3H� $�al-�H� wntm#1���4qU8e�h ,�o��$\tau_s;V}y���omember&�om@ B-���F��emT`8i�i��� #e$NaK* �:���8 eachm�A�� �c�7{u_{n}\�� � �"�#xC $u$,�� � "�Vh�v n$ large m{�e-<�1N0* Jf ̑@>0$E�$�b.JJEJ�J f�Ld" bel�����G2/^��(r)$  Ano: V{Ѩ-�{s}Jzh� ks�Oa studE�� 2�e92@ IJ�.�ہA7y��K�[� m 3]{6}}]�;B� q��F . Th�7�Ml1� ^{*}!�f�9Z,!�!T2y R�5O Q��C���f�Y׭-E32luen11 beco!k� ger:�|{WAb��p"�>!�s"� ӟ�_r�� fur!=*� eNo%�"# .̝lCѝ,Lc!%�?%?"�*! E� J.��� |u\|.� "� b)@n-{2 of!KA�)�I�^ �5+0� do"ߑ ��� 1]{3O�J�if $��> �� $1�3���&S �ul��1.2]{4��S� NJ4,�O΍ �*�-�-�a�21duY^*$)cG$A�S��Y��Xa:ly-�3*[ �urator*�*O��"hC:Q9�ciz�D [(i)] ��$\{(s,y%�S-�$Y : A(s)(y)�A�f )��A[(i2JS&�A� 0��<�� �&F��a�� F�F���A��G !�ڡin�d3"�J���LC^{1}(X� ��:9!n +'-���X)�i�a{-V�}�,� !k~ 5�%w&�] (�')24��$-2w n�� is kO,���E�{*EK R\�s� $-��Zc�5��P�=� 5`�� y}!��. ���z ae,!��f�&6'R&T�to<`ognizAe2� ��5[�� r�!;b��P^ X  check���!�:�S T_��\~����S)�ec�A�?y� X$ (��Hbe��ingu�in view!� 2,� uld P fJoQ ���G"Ճ�$%\nocite{*�?./@Jam��in>{27} \XDid� mae�by�z�Аeavevmode\hbox to3em{\hrulefill}\thin�9JG MR}{Z@ifhFuM(p\2\fi MR �\MRhreq��$E6/i+/proc�MI�of8.F� M}[2]{%kU[�%,www.ams.org/ scinet-gp4em?mr=#1}{#2} J�IW ��> {1p0@ .�)e�I.~Namio�%�Lin�.�%"�2�)1�&�� 63.! {29 \#3852|2'J�"Lopes-P?k�O�KN:�A�a���4!` zero���  �7�, JN $vex Anal. �bf{5}(9�n�( 5�=2 �99j:4708&"�){3} O! sellM%!A�:�& �a {B}an�%&��eaF �Ond�6 *� $}, Optimiz�?�0} (200F=�5-6!v407--411 � 1 892 912.�5} B.~�1e Appl���j�-"cer����e�`s55}, A# . Me<s Non�R{5)�72, 237!8�P0\MR{97i:47135.�4d�e��E �6viaB�FanӖbf�D%�1-�8�90)F96k�04.�6B�A"�im��H%Lmax5TofAo�Bhte� !J({S}hul$'$ma�CJRR1BCA$>�26�79--283�0MR{2002e:4901esendB �d"s! @�� {1, !=�-eLL.��I.}, =n, publisher={.* }, year={CC}, a!={"�$4}, MRNUMBER = �B, } @�#�{2A� AUTHO)2JA.!NB�vGTITLEO�].[KJOURNALK:i} F. &=)=� ysis+ VOLUM�5  YEA� 1998 9 1  PAGES��� ISSN0944-653 MRCLAS1H47H04 (47N10 49J27)>.s� !�REVIEW)�4Wojciech Krysz��:�3!.�N�>O)"o`1��K.�W:�.e%.�.. AV�%al gramڌEs.� Oper��$s Researchj2�0 9��� 9�5-6 9���9�233-1934 .�!� (46N10F��?6l4%=}l�MJb��!../6��.��OM�=T199qd9T1-)uQ� �S1 ]2E�E>EDAda Bottaro Aruffo:o5%�o��.��:�v�%'.�/o�&i�3n*�)X =�J�L�1� 1230-3429 . 7H99a A50 � (54F45 90A14F&�>�,S. Swaminath��2�� ���O!�� 6[ ! XNOT�pSpe��iss��4Professor Ky F� :�N5���F}�2�6A.���fn�&a|e I)��.U�.R3'y�- R�11345-477 .*(9J35 (49K35F.n N imon��} �%.H�$notref,not]{NYkeyV� 6�+ [two�`4,12pt,a4wide]{ } UNsymb}��Q�Qz2{)idx:��:ms U:��2)*j�u�;��2kUfancyhdr�TCIDATA8�PputFilter=LATEX.DLL} !LastRev(A`=Thu Jan 27 01:43:43 2005/�2L:P="�4Eng $CSTFile=-� .cstw nef�-[��]lQ� ��e}��]�-2/c�-C2+Ť'���.{?�6dc-F)�0ers�21*P6�7} .�*{Beweis�.of2.�.9+��6-punto(>� 64 ]�PN%sB&�,�3ileMaC�es�(put{tci�,xA#b�&*� meaI�3cotensor!�A�4. Our results Eis note -�,ize previous)!N author on.\ >�:�c:�,algebras oveA�mmutaAu !& !&Ps. \end{abstract} \sA� on{IM�A�(} With $R$ade�E�UP w&(1_{R}\neq 0 ,$ 8A$ an arbitraryO- �E� >H\mathbb{M}_{A}$ (reAc� ly $# $)%2M�y!Bright:7$left) $A$-�,. The unador!�<$% -\otimes -,$ �0rm{Hom}(-,-)$%� $'�B+%  1.�. For aR�aB� $M!k -k8by \begin{equa!�X*} \vartheta _{M}^{r}:M�!'A\% 0arrow M\text{:}%BF l}:A.FMJF)}I9�A� canonical%juY4-bilinear maps'u _{T}:E# 0.�% .�A�d�z%YT!=H)<,$ such that $\| }\circ (JMj!�id_.5% })=J2 K:-:��.�),$j�rL �M �]rE|17B� � S% .9j !bol}�}fa�O�at%�SreE)Aas�cunitieA.N�e�: S}}$2�,�v]�Y� $fY} % T}R=�is ed a iɈ�}$A. s}, if $f)NFf>4SUf.ef)-%% K:� T}}=>S}!p��e�%Nan-iT} Wtwo��:ge@)21�����$N.�e�2�2'-}(M,N)BE��_{-6n 3�2se�ll f�-$-9�s@ ��to $N.$ AsM ��E]s>��sM" �,R��\sA_f�6�� $M $� Let�1Wb��� f:2�N$,&). %�)���L,$�U�$f��ll@M�$LQ� pureI��'@following sequenc�  exactN�0\longEC��%E$rm{Ker}(f).�L\�$set{\iota  �i L}}{>O}25B28�-=% B?N e LO �A0f$a�$L$%� Av�=Ss"!n%KF% !F9q}k P\cite[40.13]{BW03}). w$M\subseteq!�i` %Dt% -sub-� then- Fsq)(, }provided��$the embedd!�$M:|}{\hooku)�}N% a YQ;< (equivalently, ��2��'L:�L�\ 5�!�Liinh %uevery>w!v). Pur9[sg ��9�2j B��def# 8 analogously. A�� aI�)!x saida�bew%it�@ �H* as wellin> .$.�k $N,$ w�9��sub Q4A2ɓ�}�$M!YMU N $%)� :$ N$% ? . A)+6� E.�  $W%��? �F5% } (S �#nse!SPB. Zimmermann-Huisgeni{Z-H76})� I diagram�%�z�sN�T\xymatrix{0 \ar[r] & F 0@{.>}[dr]_{g'�rc E�} [r]^��} & W <dg =]^{g'!$& \\ & & L =_{\piN  & 0F� �D�Xrow��F$ f.g.:= A���G  $g:W}Z A6(there existHF3$^{\prime }6=�)&& $% g��� =\pi-B." .$ N7e )�&@ ��aGFF.�&A� B��R"�* a$y�$\beta :2b BMB�N$)a�v�  $B . WWnsider��6�Q2eD:)2]throughN�m\!H4harpoonup a:=m� (a)V8aI!h4n:=3 (a)n 4J&�d?E�N�chi�,N}6�N s�K��B}N~�R&� �@. \bigskip (Co)Y("W��3 of entw�� �?�R `2* structure��$re studied�� :0��fields by T. Brzezi\'{n}ski et al. ��{Brz99},aD te{BCMZ01ɮm c]�M $(\H:%� ):(\� C}:A).z(*T |D}:B),$ J. G\'{o}mez-Torrecillas� sent ��D{G-T02} (under som��ity cond��b d usW%!o6^)|B��� G�2^&x D}F� >$C}�����ikadjoint��"�F�"*~ BJl.]%w>$D~( %@ [Pro"% 5.3]-Q)2�In qdisser�o� Abu01}� hpr1�a�M� J^&{%i q s ���m���cos (�  a comm&xe5E�� A�i!�Jm izes! Byto/q'���Jf�D(possibly differenA�"��. Alth��in� settA�e techWassump��s_ An� e te\aP�B00restrica� �F ones,��4 main advantagU!Une��at it i. ��A3U�of� -Mz ``\� rm{T�}''E� ``% �>"it avoid|e u �>D. Ano� ��+n��w*��is�d ��t"�N\w ��jZwz theo�whichw $ developed��6{Wis88�(Wis96�'�these�:�y mind�.qV aimsA=en� �in��v!��!J}H��M�ir��per� �wa carr�A out elsew� h fte i��t!%s�,!���aj�se�waWeq d� ݊lemmas!at�A\d later3L thirKwa�i�. ~`Z�$ e8��}elI`-eMv ��F*Ҋ��J!�f��'fourth5Ca�!brU�1"; �&" ", �tur�.�be &ial for D}F'Y��J� (also handleI ^��� a�}�_E8ed���������!1&[b�:�J�M�sez. "Y"�N8M��^� a�!� by!{n�I)2fifthe�last mb!�=5Q��Mg���L&� Prelimina�R}  t��-&%�nee�%�B�_ �punto}ɋbf{Sub �� 8}.\label{subg} �A]6K,�7 be!AZ�$K 8 y  0�E�say"Z$*� T}'0�$K�� ted}qN"6Za "��aA-8j�, .� `�#e kernel Q$ ��b% �s.ɽ>� K2'}]�eq*\ _�* T^ �>�a�z full }sub���)�� i�}$ whoqbv�$K$2m�f�n�OZ�6�d �!,smallest }Gr�ndieck �.��con� ,s $K.$ Moreo( we&S!) eѵ}N�!J rm{Sp}(\s2$">�,-)* =A T}% 6 zI {��8to \sum \{f(N):( { }f\in)�"�-�iI}(N,M)MN.Bz2U}]\},Bp�isi-:&inclu�$1G �:�m:C\!m>E�(��[45.11]� 88}%  Mr<��M)�alargest N�2!"d-]�at beloz%D\%] D$> Bm%��� % }] �f�9onl�t� &� finitea �$W� K��"-�8rm{Ann}_{-A}(W) '�@2m)iC� ��� "-e��N- "Q%2}L�$��6%E%�Ŵ *u�"reaDA�eferr�oKM%%5E=96}� !�P &P &r �� �T� �!�+��P}�N#�pcoassoci�$}i - }$.�C},\Del�!%!~8C}},\varepsilon.ZC}}I��A!�&�@QA>b"�*�R��� �B� *"{% �� { }c2� c_{121!c_{2} ,2}6�M� mb�AF�&�Af"�2���Q&R, tabF)}{lll} $&0 5� !��^(.45){)OY� C}}[rr]%_j#d&BX)e� :s�1� C}6_A R� d]\\BMNh�f�l :�� �� �bk f }$ & & .�F]!e2�}<~}1h!A� 6�K[urr]Pv&�&5m�^l�n� :2\a�R� X1A .[ APll]E-�.:f_%� FCw%!#ar[ull] mSn]�! ^r!�%]q: �o��F�$I�TS�pV $ �na�i(comultiplic: }and \ }the coJ%}� �ᰉm,6-% . Al�)^��to 2���+ s�)oi � �͛� �2s}�bf{Crg}$�6` )�� stoo"� airs�:�*��`!nB�*6S $�v ���}��B �}�9a:A�%. �$� s�ofk!air mapp/v�% ::�w_�+B �R�[�&� (so_)* ��9%D�'�!S��)%� $"�9RZF �(A,A)J*�Rx} w]D}, �(�Zk" �)�V =F���) ?.��+J�>5r� ^ R�{C . �IP-mo� �-�Z} 6�" )sz/b-% E/� *�"I�"wa�>] D}$-Wa|N�&� 2"�-Yfi�)Y%$x%(e�0�"2 �flat):R�$varrho _{N2} .4�k-(MBN68�>3I3 �+6]Q =2�)�j;N ):2%=6-&B&D2�=� QC*} y&A= !�#%anot mended ex�^i�%t&wewY!=!+ A}.$��.B � .g��C� B :OJ[ Df[ D[ bo,I�% ��s}�wE~5AD�0&a;% C .$ W�2�*D�*�'��[��LC�if!_ *�'% y#&|�&� DVTCi'��of���u(��Dr�$)r.%e&9) $埁<�()!!���) �% �6V1 YED}*�&e.Z Dr���bf{� dual�!J, . }�{Guz85})B�U�.��&^).n $^{\a/2:=%W"0A-=C}�Q%ln� �A . �_:A given[&e q$ volu� 95}N�H(f\star _{l}g)(c):=�g(f2})�$�Va/ }f,gJt�2}% ��� c+�7F� jP ,>�Cz"%b6UA�^.n� A�VW�?NW by=W�co�Xr2Xf(-Z)c�X�1c�X=X.�U�Js:=M�]�A��%f Nf6��`J�)Q�M^�1O �I�bdF�� ���C �>�>�c � ��A� =��"� }E�)&� $M��_ed%�&�A&�' ap (V`a�})NP&� Md(e5a&7s 2��v�Dm.� m_{<0>2 1>J>zV! ~T"n,M�X)Or� M�_&� M"�MV"�B9R5){id _M� _b \\ '�&> C}Q�.�U2�/ �& &^T &A{A*F)D+��+� >al�.q*� !3�R9� � M5�'J� \0H%�{M}� MJ�Z3E{6�u| M�K~$(NN})����*�(�({:u9�!!.t*$% F4�=�>�"x }>l% (or-{ �}V� ��/$&� t isj'rr63^{fE� [d]_q)_Mm:/d/!�rho_N}A�v"V_{fU�6[!r ^jGF� �T .j-c-�s N&A�J�L-|,� !���6�6"�)�>k�(%2 �$2'[�~�,(K]�K[ $Ka�� ,2ZG� O!�*� K\�"�5 _{K�5:o2��6:�I^� �� � 7:7 ��F� C% Y%�� .�LJ�.${ >. O q$/!��) }$Cyw w}ux�:�cA �>�|9,N!� �-�6<�rm{% v)EJ�}3C92�- h 6�} Q� E�-*��al ?\ �Z:-4}%5 1�Z/F;R(-j N%�v%�{& t��j E�B�-�*�:� J��aS=��be*�E.�s�(i{�})MB�"�) M(sV�\xi ,J�2B�.� 2�m,a��F��*�6+6���:��6� 2�Z35�D�B�B�U�xi &�SV�a'$, 2�B�]#X(<b(s),c>B�s2�SM�EJ ���)6)�(wr�#$2A.�46:68],6�6 � .�U�6 �U0scrib�bov�\?B(A�P}_{m�Bn�e�A*#Itex-�.h#.}A8*V�. z�satisf�#�"�-i�l }(or�"�B�T�'�eK�-}), \ }if�� g&2 �& ��/i)u0>�} @J� ^��*08A�!vCF4? �%]T}.*( m_{i"c�((Kt  4�� i}>]&�alp: vIe)��#����6�)SRy�ba7!�c"�6:��� $(n��C}.[��6�U/])2�?�G =c�is�J-M�s�=J�= �&[T3em 2.1]{>$93.2]{Gar>"L,� P� ml� IJ!�:($e�.? !R)��'}%B-�:)>y�5DJ?.&.L i9�� -�2 6�r�&theF,"�N>O^�`=���r�.�r�!"�(� �� q�remark} � �"[R 1.30]�83/v�^"a>�9q-@/.XA�/�����%� "/mL-E�5�M��*Pv9or +A$/perfec"( �X2D�2s �4tow&?-C141D-S-C0rat-dar}Let\ z+_F+% m"�3) M 0ZV& . C 4?4c����� ���" $\�6�F%r�pu_rm{RatA�q�C}}(M* T}}Z rho �8 -1}(^9&b6F?NM4%�#�9�i��� =M$ 2@:�B3-M�).�,uniquAndeterm�> ele��,umZ�./ $mto��ռ$� � $>� !A A w9t aT,-�)!'T1-9�h5�=(Mt)� P})^!�n 5�6#^�Js�C�1��TY�� R ��5B� V�E��6L!J*a*� ��B����[��x�5Z�V�a�OF �#:�� �(6��*g$ $^&E��a�U��J��=��$��#&T?� � �2n?2.8�j�$ =sg}�\ �Y%�2�,2�'2݇ ${}$%�Ձ# ��:�-ŃF !�2�IRi\.d��%�"͜dY �1%"�3�*�-�-�P22�t,�0 meq �,I_M^:-.2�SX��>=D2"71(C}2<% }}]$�, &��w�^"!O'��J@}].A�|'1K�MC=And.v2�&�8C*�:Fu6 Y Ci)� of T�Wprotect-C�L�W $} �VNK:�Am| SE�`Y�"1(is �Xd����yX�`R2� �P xXj�9is � u,a<b"�>e)�>^Aof it�@l>� +Gd N*0:fix�+% �*s $CH��"UZzFa�W^J�a� r i'a�TU" H:BRNq % A �".$� �:�:IndM}�~���xq�X $M�)&� .B!-m$C$NdW��B��"�WS}"�:J�� P�X)�B�WR�b��j�Hdown s��� �&6�<��(t's easy� se�=we�. in f�9 covariant8R*`XA}.6F:%a� %:�M$S}J��N)�� f�!g1��+B�*�-�&� �A�S}2�-bI �S.Z G8]iQ�1�} (� phi .�Dup \widetilde{t})(EtE]�%�)= C &2:Z3&�tA�B�Q#ilyA"��EB�#}f��B�A�a��_^{;% +V~NTNN"6<$(6�-��ec B,-)0.'gI 5�-q^nnZ"�>smsB0}!Z�2% A�\si�bcV.6)I�f�),NZY2�]PZ� l.��).Ecan{[B�j�B��21m Nrmr}� ^{L}(-).$�+KL�9K EU2���r~2!�Bn�O� 2W^{(K)f�A�=2�"UJ�>}:�<29�>xq�}�rm{om<!�S� *�\.�6�% 2g�U J�.�2>%>6 v�.}"!2$Big-Hom-sgBB�"L$ (\ref.J)"zJ;v�!�n { }N�6x%�Vc?>[>�,)�V�2�( *A_TQD�C2' ,N))9� spMNB���Ui�g%�OoB0&|�%>���"�%&� a�%`S�%rrrrd{%{\rm m�.&} i� (T2�' a�N]^tMi�7 S}} ~Fv(62�zar[� � Sp} �B[]2 T}� I&P\\Md[]� S}�<@&V!]_ �I� _L ^KA��,@{^{(}->}[uu<& &m�>�J`&\qquad V2�� L-���a������&B "Ag� eFB+ �%. I�. G[.�F�"lQL >1T}>eD��>&�_)O��a� J�6�J�Cei�}n{L2�FS()�� abJ b�H Beweis} A"P=;)$� �4L$2>.`2M�6EK2�TK�$@ \WI(ts_{i=1}^{q�,6 P Wa 1�A"n &Q� . Si ^FDDi�F6�,8&��YZ�Sae(A�!�t}�1_�8%6�@:�WXigcupB�X:jE�%}J� L&f $&�"U2�}(W�-t�6ob�i�hA*|HAV@mA�E�m_{q}\[!�w enVgeQig*�up�BHb� =0,$ i.e.� �%灿!�VGa:�%A�Io%IdCeWPa�bM j�M�done, s�E��bgHY��>OI!�>H��!~H�J� * 4ies.$\blacksqu!�#���gxR�T >��)�*�9r�,6P3"h?K\ acm�є} E�(0� :�' (k))}� K}:k.C&P}ka#K, x�$B� e]n2*"262�bg�ted�?$sW�in*�Q\1v&IbAJ52(k:�% s))=!):"sP ���b5"!=� $|-3&v4pB4(M>�Q]*J�n}k� .s�^ in K.B�.�m��, $V:=��i}:хn\z"��{)  (n).&fu= �s%�"Cn�W� =].D�N�� }(V)�soB� su>Wb62� `:�=xi (sFpvB30.�%�=0F* So��e� U�UB}:��i!��gt���,�(J�F ,� G�B> ���%6v6H:W�ݖ��0FBB�j"�>"Z� nowQ��.o6ZE���a�ati�it*_ �\ }) :&i��e�Uv�fu# $�j$�D� !�L}.�:!�O ��A� ���=0Fs-h�i$Z*=0$ (�� y:'by our a� p�). So!��*}�K6!�2����m,�("�1�Ig�>} �r�|We A�O1.|Vs%ult��.w���Oem"/4��҆�,�� ��2� ��g%_� ,��*:!�lRgT.�.�0/: s $^U#r (-)))D5">�By&Gt:S $(C(-)"yJ�*�� �͆!_b�R�,%TsoQ��) �Yides uqf2�*��iZ�5�6V$l$N�T>�Z��� �!�O+V�.A��!I >56�1�M�.�DT}.�"A}W r�!�i�}~n�c�/"_���oT.oUb>��.� u�.�vMnV�}��.>�� ^��i�A�(N)).6N%� Q� .�� �#CE8� M"�0{/#.$-P�zVL\ applŞ��sa���"odI"}cT^"�gJ|�se6h&�-� F/( . It.N,�oJ�z�d�direct K liz!P%��z on�Ff *�ev{�D�eiz�f (�!�_��%.}'g-�*�(Ad-)I�iNH%} 6�K'!�mA�H626�8$y-5BJ�K% z�V!��G, $a��A{M~�? �J'@$R�)�% ~ �(>.e}�#�*]C}z=I .Iynnes�Ha� �$* cW^#%^"F�*}F�sMZ�>�s2= N% \�&I>varpi ~ t��C2�NF� R X:E"�,.��LN}-&LB� :v.N!�hE0 in�bidab�&nle&l~a&�' the b eD/; T 3Se s 21-t:M�7 xp6�e"�"< ind-�t.�j4.4] ^bE32�$"* B�A����FOD}^l_*SN9DB^3C1�.A�#QOA�n<N��C=6{��n^&��cmid��. Ac-�(({}�=@2 B�J[16�L[BA.q+.u�qNX&U+qc}:�1% 2��?1"em*�C�)$Y*A)2G%. #6i:ka!�!V2J�"+w�"1"�"Bg�5u2N Zj�$A�%�Fi% F�>&CN�+_�Q$��APZ-5�"-5adg}u"F� 6�r�\� ��N�-=nF�,-�Q� a����213"���� v�<�$Q*RGS2w& RA��9��i�g��,in���=.�>V#2bCJ�6iCb�J�-E��6:�',',�C}~1,M�"�6;w:,z($B�+ N(T:�+{.#,��+��6X& *HOMIi�1o}�j'vz�&&Z/�*DS%5 i=-.�k** �F��"�T"z+`5�=_pJ� )����C�q��-mesaB%��y &�S� f>6gRE"1+{\Bbbv*{\)+D}^{*DS*|*{*^.+7C)�3+�M_{63+�y+�*:� �X�� �z?�C}o}+ALf-^1?fj+ D ^C HaV+ � s x:�*}���mEPA4N��'��#�� P,Q$��Y&�=��G,� o�Do�< implies �� J��>��u] �(\>QD}~QD.!�].�YeK"�3d *�v!�6�� "�&2� bV@���:R"" ^ "[*�% �.C+*vH*�c.!�*HN."$ _{2})bF�is b�! .3-�{-a&&F%.AW �����w!FXGEq�sg}~�&I�#s�fw �' "tMo��&Ht��t� ��$-3�cF�3H AW02A~FTEw��spIng��ul��<��.�ver2�V�c .2.3.12<@|B� [@})E �2Q @ (cot=Hom(ot)B �%Naq<.dv!aaG<#,2� L< �B% �VB&T<TQk a��+.Ff6a@�� � *` � B&MF $% Q�Cq~a/ $S}:B)\;$to~&�w@enumerate} \item � :\Y�#hJ�Hk&Q  f0 �5! � A �o"�6��0�tUtrA}F��n7RS}^{op}�hI�&�.a�6�#�J�<B}�,�*�B}NV� �CR�N\Left�Ua1*G s�y,���&�.90 � 82�X /&="F8 1�W�n *]!Aԍ4�b�%�I-}�H�e -I�%���g"�$Z]N� D}}N�$*J M�t��2�1!&� ,6�J\ �.M2p>�\".4}S�"u2� eDN!�j5F� [$\psiM�_{6� }^{Q�Gta�� (23)>1 0nV�i �S �"l}#DFIM��^��"\q\\ $>�(E�>�a6� p7% �D^�<-2� =e,1"Z�!Z�/��e�)(s�# �6G*� ��E�H�R \fora�$�(&8 S!ȚOBd%G ��*�2������`^^!���!�2m`.�,EbJ& B>��PA�ef�wm��(a�Q�m�&.���. .E.�g"u�D\gammPY��Z .f��� J���"% m2�"� l�F-8�S :2 � % (=6 .)]BQ��ine�!Z�����fkf(1J�5%IU��!5VC6�!��!?c>w3* &r! 9�j��A�2 0V�=m;):_(.-\�T�'VX)J�'�&!*����tM�g%��'BraD2a=CJ�\<&P\v6 QJM2`!�q�e*� omeg�*�vC}�p5b? �!|"�A:��H�(>�vSq6�a]y�!a.�$%x$6UC:*}� 6���e�av$#ZSQ$�Y)(�o:g)$Z� 2F2%*�$� :�"+V�luA�N}R� 'J,N�Zq&� ��](��(ZE2+ C> ɿ]�A�5X�j���:!��YE{.~2�!@%����3&~u�P.HR aMD�+N����q���4+.�N���w*h��) �B���*6 A�,�w FN is lB�_�i^"f OM�"2U �V .�N" C}$ �)�Y�5 *(!��]L�) C> B%C}��9 BL^c�E�_FeV��J�% �A�Ir}wɊF ""iJ�2F] =KD~| �}VDTM2�N��.�F�rm{% �/)�!��!J�R�% �4F� " &$(2a � �� �� �t$w�*�� � 6�R F�&)�-#*9 >%}(&5�>$.@ :�)J��o�`&@6%�4 !B"4�is"�5Qs�`ũ.��J,sE1e�46R� �-*{Xco&(,xX��&vX� 6NS3m�J�j2^ �y�j� �*���6s (&r, J&F�1r���� ^{\#9�� 6B{_B�|@�4�B�* C,B)!��.�>r&K BC},BD})"L�f=1(\�V���X up h�|h�-' *�|!�h6^B`z >gW);1})NC& 1*C-*D:q !) � \t"T!J�>��{ �I�9bK.�}B�WBjC.�FbR�!b�W�)(h"�W (F{� for �} 'f&� 6�CI�bf{�r� %�i�ZaK-_� q%�h I�2;F}.��NNk7N�&I��Cj�:�=�Zi�4Z�g>�1?6�F�)�\ )�)�2�B�D -Ji!_.�A�B8^� M9� z#6@F��w.����� �b�%8*�CE. 2(<�K,U� &E�2�+a!��d $>��jWNvb�ac��h(a�$a&������a��1�� a(bUc))-G&�!�50-B� l} $]! Y�% �0:�$8�G���� :A�Z4f$ � ! )U& Fj+s +12%% 7})- 2��Q2��F|$d.?hiBUBh)��,� &�"nd5bB�WN>E�ZB�e�B. yX���]�e�� A�% ��bKF�A�!.���i ��*�g(� ���A5.�:�%�4k%�Rj-; j2\\BemN (a)[N�c)]�aB$  �]�r3��>�fu�q�� (2 k�x6au5>"�5f:=�)��m�6; 6F1 � �)�2=�>�B�~;2��|})F7N�% (J)N� ,��v  � ��.��. To��m om*'K�f0jW2dan�@"�HB�� +on�2Y$ pick.�% v�sitN���$��N��F��l&���Ō>� B�g��}B>"a�EۅkU�vA�6g $.�Q���s��>�J;q&�Q�u� 7 .r})V� a�B{%!�E�h"��hR�.��# Stra�SforwardVF->'  1�-<�,F��;F��� a/+R?� fF! �_ 9Ravq2k b>5J�V^ O�B0B�J.@J�b4t2��%6�}I^a7+!5�^:3"�$Z5:^>�4� �YNJW d �7�h�E/��4�4 ��4�4D�4&45N4M� B4 } ^{*�_� {I� Z4C� ][r]^�_"*,!�cal�VB�4 � MF2AC mB56#(->5*��.� D`.>} �&c& G :0`��5�2RC}J5� �_�n[v7��Ff��er�/pu!s,�U-� e�N-�[JBb5m�A�G��i;�g[t��.��f`}��b�10�� modi�5e�5��,% G}$. Befor�f&@ȡk�^�,�n te���3셩�=Ped&�0B�&C}20]�"R�� �:-:*�6� :*}L>� % ��- S*�fa:y�a BaI�*�) 2_62*0\��{Imo%.��V :]�DV< ��w� vRq.�H WU@Qt�F:m�P��l�;)%� -f�)_� � ,� ), M mu->G!}�F.V�� >��?�R>�B��B>��!Qs.&ǨB~=Rw %q�&� 6XvaZ��A|m7� cyclic* ><$�7��,>8'X\R8D(�8fIQ��(g6:=2 2,�J mu-D:�U*V �.ݜb+mTi� �% I42�N6�4D}=[Y�2c"}2has> NnD�U4I�b4~6]�j4�69�:�cW�\2�d�~>�&a �28�V�� 2')E�. "|9��6�C6�% 6a,:7:�>+�%  >�����!~�"� �jI�:R �6�!��!V�V� %=p��& Fk&[��)eP�%�p�\^\"D�_~�� RAj+� %�]ayT B7N�%F�:�%�qA�i5�!71� (9�V�qKY�l=�D�)�.jR;��������% 5% -�!�v�D��^��uoh!�3`:��'a�,.& A�RgR���*�R .D- (��hk� 1E�qS���9J� aR�T9Z� ��Fd.�x7'NN!Ln^1��.N:[6Tv.� }=![ I]:3! 2}�F�jbU�`Pk �j��\*? 6�:\�o� :�CZ �.� j��3����2Fx�r��pa{mRM�:Q�A�,Z�F)2� VR$� &� ~Q�',:">"�B���'V5 VB:� (c.�Be�j�.�M�-. !-V�� ��d}q,��S��H:4 U"�(�=>� ��/F f�:' Na�� L�RMN.�c�y>"2�6C*G��>K�.q+2��% }��~5�>~. j�F�J�] 6TJ�F�2��q6�F�B]�uSBN�BB��\ .W&J�FWBNt&�*b >Q�VZ�.��F�closed�Y[B�  (�"f_ D�("�q`��6D"��6B���!�Br��� •�U�N�z��JR�:�N�>�Z 2�E ���6�: &� VZ:�6FDJ�B(2%��}5A�%[� �*}V���B��e�� . $>�f*�qU a�\d�zzobR.6��$\cap!�6D�*� b/ eiü 6# �d� )} oh�D� ���]f�}f}�bj� �i�q>�2s6!�+(}%_Np�0v��B*jGD��)���VB� �76F��K \ (}.���CH -R^�c��#6`�1>��"l��>$qԽ�Aaj| 6��>�g=>> F�,H�o6 C��.��1h2 6a��V�% ��>>Gfn.��(� ab� �#b%�"�"��J|�Ij%vC2  :'si��}�frj ���&3-6T��2�72�Jh)b�)$&w,�*)2X)-R�%>6�):):-22�)J��<:M>�.ka37"E �r )2 u:/\H � 2�J� �'2c.3 \� QIs <�N � Q��}��.� e:�=:vhi)� ! *�4mutC=��Fh�7a� stat��f[Y$s immediat�Bf����M��et��#.>JuO�=m��1.�i�Bb� 1} E�.=-�QmR1E"!�!�:� >�6:JB� ��>���>.m&#}�>&�78!h�7b�j��l�&I82:z `�_% �8�s��"k�#�#�#�##F{S�6�#U��X&�9*R#Bz +��B�aRe �-le2 -�},�$i��:�*O :c d �5T�S$�N1 v-c e ���j&�U�۩f=6$v�i..�RS'�cjJV*.}�z�+Dv�� E����-O!�&�:=% (m�c&9�. XS4,.+_%�Y��3 $s�f<,^{��):�C�)�QA"QA ^2I�,�v+&9�d�� ,B�+)�=JN,!�c>�nn<�EA��*�(��fh,2BE�.�D�fa| 4��i>�,�f,6f,V�U"Za ��g,>g,Z C} )i,�qE����>��B�,fEk,�+aME��o,1��m,,�,�aa�ca!)Y�l{ �(�� -hom�>^��!2LŗJ!1j$' \toqS*�r f�X�����X%�9 e!HJ�[Fo� cccc�{Ph"�2K�dom=�ez*3Y*�{6��nDJ0&Iz)�&l.c>(N� � �-^ep�� &H��Uh.O6: W�W8J �Kh"�q)fM�Phi:DAJ� �mM�E�xJ�hM&B� =� .6�an��6lewLFl" F�-j"s�"��M��%��v��Kcg$U zeta@Y[m.�c ( 0(m: v.�!�aYw)bJj:�PsF�a>� �b�qBh�b` Firs�wnw�����#y��t`�" �� 4$% �S}�"�N�i�>I'��a�F0am5ޝH@ VM ��9� =�?1q65=�.) ��.r��(\99u � )(m)>H� )](h.$% [fB]gE�&UA��=I�va x��J\>�RJ h)��U��T���8hi�v��M>� P0>w^R.�\"�b5K�0>n 1D]%z29bG>w��B��\S��VA�Ex��_J,*6�ڸN(^� 2$�}F�V�F��KN)agu$ҁ! .!�'Jn�>5*��m�\"I���U>42�N�*C FQZ ӝ:b`�g �C2Ky�b6T:��B| \*�C}��f�0�c)[(6�>fg.�@@�W,N@e"ea#�R�&�q3bVd([)�'0>}2�$ J�E~�(bg)�Ai�>}�@g)��.m�g )-?(Mt�ssx{C}% })][(\beta \circ \phi )(\z|(m)_{<1>})]$ \\ & $=$ & $\sum [.&0>}6Ihvarepsilon _{\mathcal{C}})]e Bd:c 4\leftharpoonup�.�Zm % }}>X�(� \righ^��XjY.�%Q:��bg-xth!rf)(Z�D}}6B6. bg>T9��Tb]:Vg:�,[\Psi _{M,N}-�@)(m\otimes _{A}b):DD g$% \end{tabular} 8equation*} So $JY \in EQDrm{Hom}_{-^{\ast }AhD}}(M � �B,N)= 6^Y�.-�-\.$ It's easy to see that2��$ is functorial in $M$ and $N.\blacksquare $ � enumerate �HBeweis} \qquad We .nowMa posi! | allows us�@introduce the mai%eorem  is sec=$ \begin{t } \label{5$-Th}Let $(%!>C}:A),$.\D}:B)$ be corings with $!\% :7_{B.�4$ locally proj�ve %$(M�:i3):(2L:A)i�arrow ��`a compatible morphism of �$. Then $(-M-�� rm{Coind}��D}.C}}(-)) %�@a pair of adjoint1�s.5b1�4By Lemma \ref{A#(-hom} it re!w%� prov!�IWhqCMBA� iU$E(inverse iso�s forA $Mu bb{M:� S $Nb%D}}.$ FN�pkappa 2u:=�D}i-[NE;m7q b (B$ we have Q�}�Q�a� <{lll} $\lbrack (! �a��9/�� �)]>xű=$��[(6�� 5 (m))���� b$ \. [9+(�m_{�.qj]=M_(>�t)]bBfva �6iZ�}}M �� 1a�v^m 0%�Z0v)?6/b),�� i.e.2IB�=idm�Uve���.tҡ�}.$ O�, other hand,y�uA�IFW!0M�% �N)F�h=�� � phi u$�,\#�C}�.� j��� )A�]6|�& $% =e9�����]�:�D"ni�ff� Ha�� �� �� �� 2N^�!1>� J��ՔBen��K}R2 �R? "��0(corollary} ����^C�% �&D��7d ��l .�we �>an.�covaria*�Rc� ��$\simeq -\s� ��!"DAo(B.$[ C}).)�.�� =�� \bigskip \textbf{Acknowledgment: }The authore g4 ful��� pexcellent research facilities^ &financ� supports 0ided by KFUPM� �") Pbibliography}{BCMZ01}��bitem[Abu]{Abu} J.Y. Abuhlail, \emph{Hopf 0 - � indu�  $tors over "}, 1 to appear }Journal!�Algebra M ts Applic. � �03�03^�R7 al moduleG 4 $,} Commun.s�`31(12),} 5793-5840 (2003))F501 �1^�0Dualit\"{a}tsm�8e f\"{u}r Hopf- �en $ber Ringen=+0Ph.D. Dissert�,,} Heinrich- e Uni6 m, DP62Gar76]{} AdGarfinkAr)9m�G�< ionlM� trac���},%.m�J215!�19-144!47624G-Ta���T G\'{o}mez-Torrecillas1-Separa}��}�I }Int.� � Sci}�0(4%�03-22N�Guz89]{,} F. Guzman�� te�!A-, relatc(cohomology %c9���cos� �});i15�126�F$1-224 (1986f�5 �5��|R � C���Uo}, ��@Thesis, Syracuse Mity USA!�852�Wis96]{} N�MI)� �s : BiI� Struct�!(Group A� s on3AGDst ed., Pitman Mon2] Surveys��PO�[��A �ematics, vol.~81, Addison Wesely Longman Limi�(a�6�Wis88�88V�8Grundlagen der �- und �O�)@ie : Ein Handbuch� Studium/tschung}, Verlag Reinhard Fisch�CM�]ncuA+82�Z-Ha�$} B. Zimm�n-HuisgeU�%2sub)�s�direc� �of fre.�M�Annya224A�33-245�e�� th6�  docu� } \Dclass{amsart} \new%=emH��}{T��2*a  AI �]$} \title{C ing dimen��E�non�ar X s} \ 8{Biagio Ricceridd�j{Da�t�!,!Ms\\& yLCatania\\ Viale A. D�$ 6\\ 95125#, Italy}�ke� 7 sGS$A�8a Banach space,�denotex 0$\dim(S)$ its� e� �H\cite[p.~42]{1}. ReB, wA^is nvex},�  cFCof0coincide�" �vic=q . , tE latter be!�`understood as $\infty$ if�is notu it��57 �Also, $\�!�{S�L$\operatorname{conv}% will -:� clos�K �hul# $S$�spf(ly. In [3]%�ppd wqfoM.� E�M� a}[{ �M� 1]{3}}]a X, Ytwo2�s�Phi\co� X\to*�(ntinuous, �ar, sur �, �o�jD 0���ly��$pact range4(, one has $Iu\{x� X : � (x)=0(x)\}) \geq E�(^{-1}(0)).$�5$!V!�p~nt pap��we im%f��� AA� establishAD the )~resultB���o�omplet!U c5�5�)zboa d�o:!O6m�l��I�0proof} First,? umW =�a�inM[.�� e�� $)�$, $yA$Y$, $r>0$emcTby $B_{X}(x,r)$ (resp. Y}(y)!�e�Eall�� $X-Y$)�Crad $$r$ center� t $x*y$). ByR open mappAMh��r��4 elta>0$ s� $�Y}(0,\)\subsetA� Phi( �0,1I�Sinceib(X�~s1�2irho>g\bar{e) X)} fB_ rhoe&,Consequently.}{�� H}H �\� � 0,{{\}? { �}}\�  {,Now, fix any�%V �%şAş!�5G )HX uzt=cA�Pu!�K=B�A)Q$.uE�cy\y[ , $Kact. F � ve i� er $n] $n\l!��Q!D��$. �o!$zA�K$. Th��$+z)\cap !6MA���at ledX$n$. Choose $n+1$ affin�+independ� @s $u_{z,1},\dots,n+19n N�2 : againE�!��1 G%=aC�F�h$successiveA���multi� * $y��9 y)�to2-! Z 56�hi)xy ,}��0re lower semi9�. �,�lym� ] (ical Michae��@� P.~98]{2}�� restri� A@of�2���g� %���%$f2�%�, fromcinto $�A}$��ch. at,� �$�gK, i=1-�{.!z(g(i}(y))=y$$ �$ �i}(z)=E5i}.$$m�o��$>ZA�,a neighbourh� $U�i}$!I� �!A�nA(h a wa��� ny choice8w_{65PI� Q�w_{U�w_{%8�N. �p�<V_{z}=$cap_{i=1}^@-I[ w��m�9E�>�� z�� K$. ��2b� �\A�fi� ly  $z�z_{p}�>)*�y, $K=\cup_{j�p}�_{j}}$. �v$I$, �F(y) = N� \{�B!�y) : jU9p:F\)ObserA!Iysome $jYf ��i�so Ecp�!d $Y�6f. Hen� �%~ � { �j�%�A�)><H# � ! )� �f� also)wa�2�s $F�y� (�5p.~86 V  9�?)%�M�F(K ���A @906 . Pu!�$C=N�BE�Fur|more, n� k,X �it&� Psi(2)*_A�Fin�,Asi�t�$.� $G3 C��2^^de���(putting $$G� FP"(x))$$��" C=�G%Y!�� 6~�� 1'Y�%�x))\}$$�!clu�� s Y�220)�-�if�%�i� �rcoL(means simpl! at%�!{ $ �R� Wnon-empA�a"�is goR4adily proceed� as before�� )x3}�dind�ed��exaK %�a&�!�_A. We �'�M out�Z/(1 which can� be obta8 �X�.� $EB� "�L}(E)$ �s��am� ous �j ~ sEM� ^(e(usual norm.�I$�q a (!�degenSe)�� real�terval^!E�an in��-"� al2� , $A�&I�&�t� �2�' A$f9�*EA0E$ a uniform��'>% b� B�u�� C^{1}(I,E� Pu'(t)=A(t)(u(t))+f(t, , \for!�t7I\}�d�a���BMTake $X=m Y0 }$%f 8(u)=u'(\cdot)-A (u )�6�X$. So�a*� �1e�2|:eIdco�O$Y.��:�} 0))= �$. Next}�s�f �,r��� �n "vieA YA�th"r~F2 our�pb ��ank�)e 8Ascoli-Arzel\`a!�,M���.�F��mlB��[�&D>ly)O�&1:� Analogous5 A�g��2Y1b W�U�#��2l.c {\bf R}^nP,2�u8av Bw;{n}a�na���=�"� 1�2E�qSru,Fs� fp6a*b a_{k}��$k$.��1{$IaQFe , le>��{k.$`2k!% 1&fJ�$textstyle e �(\{ 1< k}(I!20 u^{(k)}(t) +� m� k}aD (t)#-i %= ��,��* $1$Bn \�\Jkr|6�#9��!T{1} R. ENGELKING, {\iti�Os^( %;�o}, Held� , 1995.".$,{2} E. KLEIN>A.�!THOMPSONBtcispoLcej(John Wiley " So� 1984f03} B. RICCERI U+top b����- solu��; �. � Ny,� R. Acad. �Par�\'eO~ bf 325} �$7), 65--70�H4} J. SAINT RAYMOND �P@fixes �� * s �1valeurs �vex%+C.��298�$84), 71--7!L�&� �%�  �H H6I dVERSION: November 30, 2004 .�2�"�~I0revtex/latex �%onR[~I�nIAub(s:A6 M. B�0r, P. N. Meiss&r, lnI �UQ. Wang V�I�bI�2��2I��.y>I&5 i�� $manuscript� nIpubC). /fnI�nI Cont�InV �(:b]nI�nIADDRESS� Prof(rly-6hnIDept.�_ PhysRz�I8Campus Box 1105c�IWa�ton.c$.�ISt. Lou�MO 63130.F �I�n�PHONE!�4 314-935-6216VUnI�nIFAX �2�9V`nI�nIE-MAIL�cmb@wupA� wustl.edu6hnI�bI�2"� 6�$H[preprint,showpacs,nuQs,ams-symb]{��4mHnewcommand{\cC}{\en�"0&�5C}}3%+PZ+PF+TZ+TB+half}{{&� $\frac{1}{2B,quarterV/4B/e)rm e}} "B�%Wil�'$Polynomial((� Lorentz �-���rper�0� j ty O1$!e&C��\&�e�$N.\.�(and Qinghai�Affili�m:4&���(R ,��\�� ��,�)X(date{\today�!abs�+t}� par��%�i;-symme�0 quantum fiel%1ory t/!,s�an � �@$of irreduc({A�scalar~%�}),$$L^K-rL pseudo6R�We�d���?insic}>U �_<T�'Ul� same �AI.$a4pRat�doe�' re� y$e sig&E�>al arg>*A�the6s:)_I�=I cP_I5b�afN5eNObd To d�;min �quqe O(��.%in Um E! a�$must calcu�mut���i>n& the a��&u��e� $J�A u\nu}$. I!.H1� �" o.<�-�4 coordinates $=5$ �6it �@*.p,�n$H#I�/*�6?{)�A%purpos'�pP(O(*�6Et�4Hamiltonian $H� our qN&A�f�Py;Q� <$[\cP,H]=0$. An �o-!%�y��q- �Row�.�is $$H�t dM�\,\�%\{�\pi^2=p+ "[\nabla:0 ��]^2 . mu^2 '2M (\A"!p:�t�e&�C)�Q1?A�E�!� - beca�0 $%K_I,Y�]=0�� How�6ilbAk nven��alB`��f ro�yal-v qB��th/6)��Ks,��%]{\s$P}�ij})+]=0��iti2�] not}Q���nm-boostv��Ba0ia -2J^�!&T�"b'F5not a{-. mz as we i;e���-�spin-$0omponen��a vecto�, }5 : ndeed any)#2c6X��e���. �y�"�<raia�a{da�/al quesA: How)~ ��:�R�l6c? I��is�:�,ideN tśns�&tN"isn.�V��A��*%.s] "�Id Fv )<r6V�1p��rganiz/+.8�.:�Sec.~QEs2}�!8ew%�g@l!�g��e� M�-��� l3l� �R :*z ��$� to iD) ify F% �se UFZne�Xsol_G differ�$-32 eigen�"� blem.-Xs1Y4}��)f5�pere ��analys!�f e0!�cases �isw"�2Q9?a��usT lo�4 a&9] /Ja &$in =�6�m� someclu�!yGrks abb!Xs"�5�e!= "�QWvNal!N)�!erived:�3}E`!|*8 �F�%summare �I�:eb"e>& *� R:� �Q�G� &4 2�0&-J}Xbrief[#�*f�"�6] ���/a�N#�ex�,o�5v�i�ǥX%Gel'f�EMinloseI Shapiro �#Gel},E� Griffiths !BG}8Bwe "�&#r�N�3haracte%���K�&�ir!UT $�?(\ell_0,1\�)$EE f1 0, $#�06n�g:9.� !xsecond: :1$,:ine l�� plex yj��V6��q ����)�$SO(3 � 0$ i�]-st-���>j %e?A�um5`&![1-0 =0$��non-/��S>k belong�" non* ular�"}��j0 s. S=-a:C�!H tP.�|in�& ginnaP�*1!� e !AHell�%W 6!E�6=' _0,~ +1 2,~ �#s$. Ea�7i� Q�1&-cc�o Aj onlyNoU#!n zeroQ��s !s�(.p�^r ���C(|�1|>aA�: is F�;_ nA?se�2P.p \�1ell v-1nd ��> -$exact1��<F�>iI<��:)�_0 �_<%%�Q1z� �2! � { ���Q_{!r_0},~ +12 2},~i`\���Hus ��� ��P&�ّy J�W10$�CP.] We2O�%��$0�x�2&isimalU�)�=*:l $Q_0*�$ A3@rbi a7!�inaBpec} lly,p&� } -<6 [Q_0�*i t\pa� $^i Q_0-x^i0+Q_1^i,Se�G"]w��1^(a !-$1:A9�>:. U>< *�*n@,I�Jjt=5ms liken1^jr1^jBL1^j+Q_2^{ ij}+\alpha~7^*!j542�TJ42.��! �2J76�.�EE� $�ij Fa�q1e}Oob�9E8rJ�ic(D6D:!��i}�(Repe�E�-e�j�-� � .)7  $)�Z(- e2})}�ly�+�E�paramV��1�thn� � !8� ul�Yte� F� �=N�3}�8�� 1^2-L .5�3B��/s�� eval��ng� �s�be us� teru 5 o*�all"e%�AwZ�j7 .56��A:UF�6S�� 2� , bu��[:3i�.�| isz0�<��rWy!n��Gof "C�9u� ��' � A�n�Ev� �MF���B�Q_0+N�� (Q_0Z)� {e4B���-%kb2�.�5�6B> "��r-� �.[A��Xs a� -6@$Ne�j}��8or#1 i = �Znew K26 $N_0 F:fp!j&fT$6X +2�+�[�y�5B��7��,�Q�aP)pl�eN^ !�}��N�: q�to*tea�M(%dyb$�x�5�\s-�1� u �,q�w� �_-$3.b $N_3��kI$.&�N�dUCAighLca�>i�a�%&��ha� aa& *z6�"7�!FR7 A�� IkK m�R�d CG*<͋!li5.��QJ Y�I 'E�"9 o� d�i%Jse��ur lS 9�p�&�3&�� ���@�O"� ��s3} Li=NheQ\o�*� l�*s $P^\mu�;:� �!�a globO] ȁ��a !�i�[*��21x~3�?"k \mu�qA��c,AO:�� term�Z$4}) vanish�F[F��^i(i )\equiv-i2�0i}]=2iJ61ve6Bk��[St��� �I�� s afs"�#ue�u�g�tor&�e� . A� ;%�=6�givjM�2M !�a new .R���54��]=��>�& 7B>�F!4V�#&> �^F� 4}� )� -9�8B��3�/�;PA�tBVi/�i�P4de �Kd�P� A�iY"����fo01����odz����!^:��isab veni�tg*1a"�4!EpT[Fwe�Ptwo $3$-s]C narr�$K^i &ij& )� ,\no� \\ L. �eɓJ^{jk=��2�bO*�B��Vsatisf�:e�.BriOonN�8[L^i,L^j] &=& i6�L^k2�\�K 2\�R8Kb8K^28-FqY�10U�1�7=����U��NJ�W9�K^i�.�AL^i!.�$m}$K$=!�K^i�&8�)�6�� mutu�-�ing�c 0on} [W,A]=[A, �]=[ ,WX ��1FK$�/N[B,6�NIe�� J]q���115})�� 6}) *�? $B$  "� ""a9hu� x�% !a9s�2s)Ei..�(� F�1 �=- ]JF@"�B.�e ��M$ byF|M M� l^2nF$!2fouYs!a , $M�Qa M!��� J�L8�]�(M]=[B,W]=[MB,\cP W .��H�"1^ic!� �5�"�U*�*(6�we as&fNitLMk�%�|4 at�do}6.�.#>�I���� q���9�Dabove�6m&�%l6)!could be_LdYr�.�;H� F� > � #�a� $f(B,M,W/,: <� n�%yet un�n%�,F�$BAyA~Ay $W$.�5ca�:e2Z8�Y6� 2"%&�!��Naq_�N.� <]�u ��$%�kl%s;sT*}.!e�!2F�1-=\s?=l,m,n==0lmn}B^lM^mW^ny�2&, u$A lengthy "�"f! doubl�(�uAY�5�2� y�6� V� ��w N_0[� J -�12� ��(W+ M}{B+W=()2> P} 8H1}{3\sqrt{1+4B+4W}}TK gl\{.L&&\jmb[2)+ (W I6n 6Y"? �6a b hY, s\ f Ie+1+6Q G)RG �[-2B-4v� d6\+1^� Re.�:�-6O F)%[r\��]�F ��F2wUuQ >�AY*D $�R�!)$JT2����. ~ wVvJ�R�F~Ah}}*K6� P. F� Combi�!�216� 22})2s��5,$� �"�Bal"A Fv && 2IvTmq1}{6�uK2� �L�L:�}K a�Q�*�&q��L)-6uJ��:�vK=(�$ 1^2)�}YJ� �фal&s)� (#��(}�%YJau�)�e $.�$&2�>��J?m�!�]�Y��u"� s��do�(&( how to finL2� l/ti�."�B�,S*p" &e next �Z�1.�*how@sG+�*]��as�Z�&im_hA-"A'+.� 0al Case I: $Bv&� M=0$&�):9�- ����cZorBl1}J� =�pr�*�3})� :�:��O 7zMi��oVu Wf(W�ViT3y���W�pW}}�,2(W}mv:&\�f �� cyi�c.,c2��}�&��To-��Uw��ch�\!�i*%W vari%Bz=\�W+�5�:�F�A.5W�ew_ahW)=�� z^2-V�-$.&i\8�xp,A� $g(z�IJo0=\e^{-i\pi z}� -�Jy}{..�V@N�i� �is9T1�&&(2z+1)3)^2g(-4z(2z- 1)�+- (-16v=& 8z.7=�&�}!�or�R�&!�i]7y�s $.U rm,7�]sep-�di�e�0��4��1A� Jn�siiI#1XA@f �YW�Lnatur�4hys�mcon�;w&�4 elimA7� possib0j�� e.� J� 76@i"  �zA*smooth2�B�"w#s JMA��i�+NY ba�"(8�5retJa .la�t��f'_�Ref.~�.BO}+m/ng�8=PV @H*g+f` owed�HHTfo� N� (n)=2n+1a�,d(n=0,1,2,3,z(.�FN�U%Y9(�v�&!qs1?��Q,�$[#�y.G  �4�zve�/POS#1j$Z�&3K%Rt%sq%%�%$(wN��> &, tot� ic�5k0rank $2n$: $T�T&e:, <\lambda\sigma}$,�/s`a��#w!ȡWm>�& !AU�f@/�"�*B ���v5s [���46})]Whe)�q�wer�`on=1Z.�!+\R*�>+ $z^2"$=� A8bR�f* *` A�& 6C�zR&o� Z*W�_g_0(z)��s1:Z,. g_1.1:2 z^2+BL'3}�A:3334F37]BRN117}{80}>Q4Q6FQ37�zNm$1957}{112}r F= 2385}{448Bu5u8+19zN{74�\J�2011}{16N{055575}{1792}}&32&�1� m9W�CVal 5Bis-�I#i.�12 monic}*�!Lcoeffic% < highest p��0AqM!�3F�H�+��!�q1six9N}C��f_0(W�tN42'f_1r-W:.2v.I�W"�:>3�>^2+4WF$12}{5cg�$*Jf_4�[ 3+10aB) 156}{7}}W!�"\VI?72mR:�5�y4+20W8�176J� 480.k&� 3ReeR� d 27�/X9� a��Z, m�^F�3 ůe� )*E�wo >ly .2u�. I<&� ghtforwarJv� A�method��rI* �(s �=�Drily �/� ��=@�s) 2�/k ��� seek�3n:�2n�{Jhɞ�u &23&��`�+$ *e>^�b�}d� e�6.? Dn&�"l��&-)O&t5(�2�I�� +1)- )}   -1)}���!{�1) �+1)*=3F!́Xx ��M�; a'5,�lti�*�1�anyq� �2K} � �-1X1�� �^3�1}�-1)2�F� Summing b�s�q� �,��h �$ (.� n ad,ve�<antN <xx=z_0}^z)��x �x-1�x ��x)*� 3&QM�z_�2a�6rarT �.um��A�p3C.�a�aB�� $nCwebF�h MV�.t)^2.:F�Wm6 $n>0&�leŇ�>�i~�(r!a�umJ 2���oNn��&J 1n� gy,l��* ��a��c�# Ac"� ��$h_n �*M&4:iz 6[?�,�<�#m>ee%2obB to"L�-bea�7y>:� ��. . O�#7IGd�o r�z*( p:�/�.�"��� *r:�6 So-,�l$P 2� 2}) �f>f"J m�n=0}^�< c_n e%�4FQ ml\{c_n\�m=S�at)M2�!���FT1V� �# left[c_0|2|\ inJk�Oz) $]�F_ �� f.� 40})�#.�by)� . Em.� 41})) hold�o�=y ��ifA�let $z=� �#f�c_0=-*7+4F�  4$nOa�B!�2�$c_q�,F���� �+i: 5�1.Zg_n^{R5�U}(��n c�mP_n*�4&: �M�-x^2a&�%&�a1�W}F�li�HrY=f^$al Q�!�cif�i�:al"��d)4m�C $z$-plan>9n mak;&"�v� $x=i!�B3b%z�?e*b�-)}4E�(%�x\pi}+�+)}�#x^29�:`=_ x^2 *� 4F� WLenU�n!!7$�LoN x(1+�D)^2\sinh(x \pi)P_m{$)/\cosh^3(�)bD�� �, $x$ eig2to"z . Use!aorthog��T�@yaF2�] "i�O&�-quadr��n<i eDR c_n=%)�I�[� ]^2()[(�+4[,$]^4}\int_0�� dx\,5O Tb-l!k=$=d}Ps( a-. "�.4F� 2�&mq� extrem�2de�7!�t� %[�'9��8�@�Da!Ua�existWK. �7w"�O)� .�&a�� ��gUY��2 )��h@Claca�$xy by $�$6� 3})]e�3\ �(�(M� ve w#s*�6�3�� u�k sens�<��A�1nM tin-n�*!t)`S9�orts�ur!��(� )^6ty ��a1�<ac",1nverg�-6*�)2�cŠ substitut�1P)e)�Q(q0)�-�4~.4. �c� �72�j<0�%�AAsom@n ��k9mpl�%at�V�= d�lpo�!z:c:*Z#�8*D�:F �92�H*� Ah*�*J�Mz$\oplus(0,3 5 7 ]&� 4F� T�+9Z 'ND �:$� vS�%�qU; $�#-:x*B"�,FFeF F /�G� six�F(�� zMentz5m��/e�sia$YqdA�E'Zi�C�Ni'f�6 A�& }�)m:17$�� 2�)l�;"�9(UA�@B�.�eleSry*�-$FL \# �� "o<6Y%Z%6P%5}�!�5p �;"Q"� ),�%�K�AItha�atSF�O4}.� cL�!hZ���ϙ�. ��$W$Gbe* Now,�A�%� p�u%B,"w%J�)*�)�,� (2B+3W+W)sO-� )�#B,2�%H-"?% *.6g} v-.-f-Vf .h-�.�) l6�,=&.�(f�.G &���%eNt:*U��-�iF�J�=�v� d�J"��5�R%�"f ���.Q%F� &�%BN&4F�v&�]D,W)=5[ B� &U&dB����fionF� g(B,q*&v�*�F�"�a9�� ofu.6X I �"@ .7-"[ U&J&�$*�Q2&&M--@fFb4q$ � _bzI[3.2N +2z i.1}MQ� V+:�&�,uad&�-jl-2zvk)]j��}Pi� ���5&}1$|�-Q�"�V9w�9 2 : "��*~$c �4Bn� , $d + �K:)B)ͥY���A*b"nB1n).� � :y +�-W21=&�"} 2\Gamma bn+�= :#F`�n)!\,.*�KNI2����F6� �A1 �2@ .},.iJX51� nd{e5���� a�t %.� ar�b9��v5�>${1}a�E] �+,. g_{2204��B 8-�V$}{6}}B*�+ B -B63Z#>w32w6 wN> 2}}BFW1����T$)�NC5 �Bs$20}}BJ�1$0"M!KB@� ?^3.. �V�! B86%:F[%3W��&lQ C.'�v��o��'� +RK�n &=&��.� B=! �����i��^.]M�>�4hspace{-2.3cm}f�\!2���W\!+\!B � i6�.#";1,�=1� ; 1\! �"5&p1�E !�N9�Z�0%Ʃ�2�!B+W)�2~�!!�n1iL�<+W �:G2�G[B�;+B iW+ l h+W!"� ]:v3�vaWa�B^ B�3}�/Jz!19}@� �Am�8&�!iJ2�J^6w \ .V�662%7.+N#�# V]�W&�Q��! .���+ 'w� �(w trea$B$��Ybi&�Zf*("sA�2J �B��3r e �ha�e��C��i29_4}2L28}:,o & �Gwq5?Mo ~�z&�2�,y�bau.� ~}z8���=�F^~r>Kr�6�5J���0� �B!!Z0��23�=:�� �JOo6��!��3?\*� �( F�.*"<"��J�&h1�"�G�*��&�&& �/�lex $2��X^�5�b���J����&�5F���b�55�AE2�"U58}��go4��\,�\,x\ta�_s4��6< � +$F= (�2(2"**� + h (2}�IӋ�6^���A4*�aX.AJ3&�b=$!VAZ2%J�c_n� )`)�Jf}�X6X>� ɚM 2f f �xY�2�!�9�*�ɵ-�(2 x E!q}EӝV&m��:a����&�V���*x��v�:�s. Ev*# ough%�&Z<B(tak!oTnom`h&��<��e. Win un�Q(�)�eof *�f4}A�R#�Xs�M&�M:���� JE4>� OA1���wAmains � &�Hyk �j�&�.n�*2,��&��! �rstj�$� ��q$;=&-�5��:��Mh- atM"�9�Yb)�"�GI�)1�]�e�&"L 2��I Rem�h&>6}Fge�l� ����+�#w!�5thnparr\�T B$, .IG,F m>=cwfst>-O qn "� .h�7co��OW5�:nN 8}) >C 8F }. AnG"@ ")%W%�� EJmayms1�!�LoUw")��FmI*Bmn B U��!5�w!�un�9Seb6k; țly�m I6Y�O�!>]�6[i>�}7-A 46})*`@**D�Js}���gi lK.b�'$to R.~Askey�) f�'!9.�i&�9})a�Fz9(is work was�Erj�as ��U.S.~D2��Energ+\�I ndix&�P2�c x*?yu-a1*�HElis��F� P.�*u�"&�5�ud=B��$ �;%n,KS}.�&s�c�d(*�K!$-;�76m�6J�F� k&\� v.� (n+2�#+  �5�|6=�,R��7Z�b&H!�|3^} (�*= A�Am6o7;v�M �9�a�un�7)�s60#A�u)!>�;&#�%"�+2,@� ):� �.�$� "�$^E%r�$n !a"\&�-(V%2&V% 2)`%{�% � +3)!}#^ _{nm*�a&��!=5[]8";Hy �u ree-��),ur*p"BH* WE=b [x�* �}A`"lX :�- �K&^2 ns7^!Y(2b&A�11 {n-2� &c a&��c A:�.3Y% $P_0�=�i $P_1 ���SomQF���)jFky|' B�)%�2v1Bt^nD %�%�2} � {}_2e� F}_1%i(5X+ixi�+ix;1;-tmq2�Q3^�-ix^�-6X,.�Z�!�F�n!A�1A�]9�l��ZV�2� bz�D��:�)�)�U11+t)^3}!�:C:[ ^�,)5�%�,2,2; Y 4t}{ Z2�c*zaFz�:�8a2}w:L���2MH ���B�BŀOYb�>Pp#b�*Bt�;.y��Nq�F3b�>-2� �kFD�b&��F=Z�5��O.Y,����&�'J�I`�?> 1: 4-.4�� de84 n����r�"��~�, Rb�1 Re��B�>&�!4}���� �2� %^2[B-��)]�bJiz�r�} &?$��GH6�f:��*�-�2C 1���4:�=J�iZ�0r]��1���}]�5�&��ebF o"�Q&& ~~f�Z� M��6WI V!� !:2\!F, _ IN|}� \!)�9}bJ5{=S�e"�+1}9J2�jM���!>�%�!� ��%�br��8=>:� �,�"9 &���2� F�.�&WQhQzt:w�{9tb��(Gel} I.~M.~&�x�.~*�x Z.~Ya.~�x6� Z�yRE��/G z`v d Their ���;$ons} (MacM��(n, New Yorkٔ62���n C�=�dD.~J.~Ggyα$ys.~Rev.~D�� 2}, ��7�A&-�G}N@ .D.~�#..Harvard.��(1G (unԏshed)1WBOJ�,S.~A.~Orszag-CAdvanced*.� al ML? S,Fis�0(nd Engineer!2S*� ger,21499), pp.~231-3.� POS}�j�ir�?i�Y6�/"�1�y[if8 "�--/z�ly0��J�4�xC �v�26}��4[��F}lop�Z�2�K&y2�j1�e.MA�.� Veri�isXyimD( icul�6d&�heavy n`��N�+"/ belie^7�&sv1/iNto&�A!��B  �eum hara Aa � osca87[.S 7 rmer�a&ibGaussia� div��off9: �*y8��+/"� aWe way&��;runa�ng!��Her]�.% �4$J�fV�removed*� 90�U |emqe�/ٰN��B=Nup�3#�fyA@e%�ڰu�[<} G.~E.~Andrews,�5�,%�R.~Roym�20 Fb9a�Ca��.X��,h�ϸ�6g� {KS}^Koeko�Bnd,F.~Swarttouw v�-Schem.O H6�H&� *� �its $q$-��ue} (��Haw.twi.tudelft.nl/$��$�oek/a!/�8�H)>��&�� �Y>�� [a4p�y,12pt]{[wcle} \uM�0ckage[dvips]{:�icx2��jpages^�{�� } \addtol�^(width}{1.2i�0hoffset=-.6in@�i7�4Electromagnetiͳf��. oamovA��;} 9�,A.~Ciarkowsk�,B.~Atamaniuk�Hâals0InL6of Fu&��Technoloe�R��:>Po�:�em:�Oce%0��.7� p}{^\prim!hre.b}{��2o}{\omegFt}{u�:r�g}{\gc,BLr�dho:0f}{�:Dmb}[1]{\mbox{\bold� $#1$}} ���~.d\&1%�!��{A�R�of42�(EM) �<w�B�\�x0V���a2�a�,isotropic me�2l%bG�6��#"�4stL��ase!e shadow��*`w�nѲfA�����not�� llel��a��on� ! thos��$ves. Other�-$ phenomena���earlieZ�(Bs�m edg����8"��4.A�45{6w� Stud2�sc(�aebyii��J;a ;� histo�Di%s��of EM�|9'ai�h� tacl�sKYeristic7�B�ogn}C�* s� ci$4d astronomy. O1)!�rp %]m�Dub"�ob|t2!'of�#7<or�oalEQp�|�est. P5�a6ن eA��=Ao!6�� � � �,270 Doppler shifJ�ph[\surfac!.��q Uqn��=�?t~#*d�m��i�T"m�xnWre U(���{lm;67@�gt;68}Omor_�8'se�{dc;00��2g�( �@�w� ��a�&� $9�]�Vw�cha�l�palter�Ev�.�:A% �.wAuA� , develop�8A5|t�iËq"��hEA�ngI�3"� beam�9A">^p�]%�� rea� ^ |EM5�!�by a ���� fWLs_��qfor sq͙Bc"��ajua1!,Q'��O �����>)t�*.(l�Bd 0 reg��"�Q�h%� (GO));, b��fe5 �#ly��A�ό!��4s>�al*�dn!�,a* . Extra i&{�a�q?!g=a�Ig_�B9C�-fA*,ency asymptoA� expaսy |) !�ape��k %�����K�Z)� 9�A&a� 1}� @ce-6�is per�8X ar��rU!�,�tj% help��&�%Ia�A~\o�?ll �a n SommerfƗ� q�A�:XFt�Y���unl% ��U�9j�Y)n���e�pre�\!&�"�!��a��-�>���wLL!o].aQ7�v(comp.\�̩), doO%!&"ZB�1J�Ł�mod|a�@ ��For�(%�Mcm�} N#!RatA!!���Cuc=�i# stead {R ��G p*F`wo*'y system|&x,y,z,t"�8x\p,y\p,z\p,t\pWAC��=&�z labomӪamU��<CB#. *-1�j�)f d �2 ]�ES�G��Qm$x\p\le i~$-�I !�g�� 0R ��C $x-$axis9c�K ant ��s" \mb v =({\hat{x}}$v�IeRE�ax $y\p$. �$, dis�D��k �� �c.Z5G $y1N#(rvel �� Q�fur� ���5�1EM.� var� 1imN#(xp{(-i\o t)X` .% m]C � ���m_�D22XCA"�}"� cO��w�- ��"� $y$-�+�)�h*Di:+;Uit{E-p H-}�Q-��]ect��WA  H i�&��Hd��{bw;64G=In!�t�,�?rop� ng) �4�rW *sS m��E}--*h;u��}\���Lmb E^i = [0, A_1,0] �0k(x�,t + z ctF�W6 d c\mb B>�1}{ik} L�times a,�&�$!� �H~�2} j j �2��� �&X>� c' BS���X, 4��$c$�aT!]� �sp�3$of light, M�,$\t\in(-\pi,�>-�20��gle mea��d&i Fv�1�(�' > S��/A?�^� $A_i�i=1,2�*-"� �"�FY���I�f s. (tB`c1/A_2$ "ݜm�ole�E�P�)e�"e@=�$�E, !5 1Q�writtp�own aFt Q��arM|{r}e��[y%�I! [-A_�L\ticos\t> + B\[5pt]��]Y� [A_1iKX,-R]Fti@ � Y�3� �b�Z&�%�� typq ni+�A� "x5 � �wEX.6%c��ave6 .�An��a�� e�&@ �3S�,i�bm�+��M�*�� Al �ed �}�S�U�a� :)�YA�o^U 96s%a*9 �fr emplo��U Cvr� K* !,�3�^�D "�,}Cat&#g back �.��%@ub1CP RSn��ntin � � N}1 pi� a\p�.w\p Zwi�^�� \[\g m b^2)ھ/��4 \b� v}{c� ] %CyC&�E4})e�-�9})f ��atb�@10} A_i\p=A_i \g �>b)K),���C �5�fS�%��\p � +^1+_}\; a 1�/sinWg.�}\:B�yMW�Qr$11a} k\p=k6HB��el����6�_�ffʑc ե:"- T�"� �����op��r�ńv� n $ �j"�)/ADb)}>k�nd he\ $\o\p>\o$���.3C�"�c�0xi‰�@e�  uS��e����k1�!  h�5� ��B" V�-\�+�<��<� I�:�MӁh=c2V ly ��� v, �\�($\t=\pm\pi/ �byQ 11})�E�pm $0/2-\arcsin{\bυ!�� &} ~�v���):�h� tet�y�r6"�S S]�of� v:�A�2�I2�}E�z%A"#�ho�w!�wr�a'.����1no;58}lge�Id��ڐ.z"�3}2He:���r �a��� as��'���� E-}5&��n%hE$�.�,y}\p}$E\p_{y � lSn�-3&zc�b�2} X =� \pU ��A�4}�s�W}>Ck&Tr\p} [G(u\p) - G(v\p)]7 ���0��� f� 3} G(a) = a-int_a�Vi\tau;d B�b�4} u\p='2 �� �{L\f\p-a��)���� v�@�j8+8�j�$ie�!�kcylind� *F� E����_U�a� � p� �����T3cQ%� a"�"�����})yInd�wb*1>�5} cBA�x\p�F�(\{�l{%DQW+QW + ))�2}{k\p !V}} 8� %�%�.�tf2}} \�]\A�-A� E�>�r�6�z��cos6�uD -n�8��Br Z�H���c$�LBZ�I���3f�71D/�w2�Qԅ@�wU 7a�%�B���"�� km"�m8 2}))f�8�4Ub��%%A��2�9 �U���E�a�F�r��fm�.Rj�BI�AW^�>� } :���s� eldsr ��B�t�� �n�'p*��B : �nU^��{_\botez1\p\g\;{+ y}}\-eW~�M�+ 9�)Fr�E"I�5�B� ��Brb3�_\|5.x�I�������2���4�fz�� (\b-)�!����i�F%��b!�a&By&��&z&�+�$!z2�+6} !Eq%!�%Z%��� ��R�7�q$�6��$��!�F(r�#Vn�F 2��[���"8 6 sLD actnes`{�MU �=I\ �M� _/j&:QA&I#"a"���8an �(mȷ��t insE"*�� I ��0>X"v �eKMas r����,I���}y�%tocc�1��c��"%$1�. $G(Ua�"zbthrI� �L�Ot�g % ��6�Qe���f�8� =H(-s�t��\;���pi9A -� +8i}{2a O( 31}{�� @62  $H9XHeavi�+B�"p"�%�A_�or�aa+$�$'rh�1>mMis$�_bl�1C��)op�&I%� ribubc��F`"9�Q-I#:'*!$c2T!^"$s (e`* b.x,s)�'f�\A��a$$a$, minus ap�d[��'m�c< !2�'��, 2�&m � 2>-yo)E[#a4# .�6�.�*�o�eJ y� �&i }zVV*��)9�� -����hN� �/mucsfF�:f�58O/�{ll2� \sim�6�  (u^{GO-�I}+u^d_{e1}) & \\[2ex] c\mb B_\| \sim A_1 \mb {\hat{x}} (\sin\t\; u^{GO+}+ H2}), &@botJAzA-\cosBu^{GO-�<3}), \end{array} Dequation} \textsf{Lit{H-}field}: \begin,(\label{e30} T {ll}.��2�y���h:$!#E=#.>x>-1$G�h)#k E_!"N%#2"� 3}).) � 9"Here,�5 1} ��@\pm}=H(\epsilon^{i\prime})e^{-ik(x\cos{\t}+z\sin{\t})-i\o t} \pm .<r^<-J<!��, is a combin%�L of the incident anddreflected plane wave, both 4s vanishing in2�ir shadow regions. The quantitiesf%2F2l!8i+D=-\g f^+g^+h_1s & Q�8=\mbox{sign}(z)$-h^+_2s &36@3sav1.5axHh16H\t z) s -g^- s +2>+) f&+h^-_2�hu�\t 6T3sIHVTrepres!�!� Cartesian!�ponents1�diffra%�!�)t8 factors appear-�\(\ref{e32}) are given byf�<3} f^\pm=\sqrt{\j {(1\pm\b) M�)}{2ik}}�LYob% 4} g \V bHr\pm(x-\b ct)}}{r}  1+\bl}{(.)1+e�{aC \b)r��(5} h_1=r+\bN( \qquad h_2�2�3=\b r+ �� 6} r-Xs0^2 + (z/\g)^2F�andfP@7} s=\exp{[ik\g^2:%�8 x-ct)-i\pi/4]}��9�a�m�indicaEE$��(r)�{$ED discussed� next sec�> . \ T{Phenomena specific toU�,ion on a movA� edge} Esa,ial features g ń result1 from�� scatteE�byeE Zhalf-��a similar aZ st�8ary case, i.e.\Cre3three�era�aw �es iqM solu�: two� s --6r�n one,��:�8. Nevertheless,�p1` 5`for�!PLion��y�9�below. .boundari9y-G fram)defined!g$u\p=0$A� $v �hany $\r\p$, or equivalentlyr8} e�L(\f\p \mp \t\p)}=-1,m��x\p)=-2w��\p��Y��!A8 upper (lower) �L�8l�to"�(5�) !�. By mA�plyA� this% �squ���8sides!� solE��I�ant!E} wA�n�9�$z\p}{x\p}=��ta8\p}� - T�1/$ transformU�labor�"yM intob�4 ��z}{x-vt.�}\; 1}��' \b}{-�}}}\:, \��.�IV�}�B�ForE�tim�s%v $t$,�s�'�40}) describe semi-infinite straight line5 ($x$,$z$)i�, with!�ir star��poi�at screene�0. If $0<|\t|<��2$#Z eff�Sve angleiuIpe��m�y is � (in ab��e value)RY� Q$\!� if $��at )8is greater than9 . InI�2sere* a ro�O of A��^�toward3 negat�$x$�� axis�� compared m�:���us��li� idomains�� modified)�re�)ta�BOW!�chang!d$t!is !�� shif arallelѕ$x$-dir!�o��! $figure}[h]qcente�\includegraphics[width=.7n  ]?1.epsy <� [:X \par�.8H}{Fig.1  it{R9�!�-0 -���> (SBi)E#!ɵ r)%}s�� ���k.}:�4 \vspace{2ex}A?T2\:�D can be physically�terpre!�as� ylindr� emana# the �qy,ts phase fun�!�  $k�~,r\p - k\p ct a% 4$. Level� co�R M in $��,z\p)$ �E�4coaxial, circu � ers )�ed�"�E=0i`�Fst.�Q��"� 41} J \left[z Z� +\b 5 \r��] - �B� (see�:,37})). Equi) surfac&EB�� �ld�@��f�7� �+"@ +\�  = C,0 C3%�F ItMe$ readily s�� thatA�L fixed $C$ extremal �ZE $z$ occur%� x=\b�  C$. Now14� I��VA �� �ff�3} (x @g^2 C)^2+z^2=(ct+B�-[��aEulea�radius $<$,.� $(- �C,0)$�fE �5c@a�:MyfA�le PA� $\b �$Z I� $\b$� s sm�Vr �`its ��u�c-<1��i�^loce�alway�l �s �S it �{�q ��b=1$. As%�$increases,B ��L�along% ��Ű back�� �h!0� !�� mo� eB��2))�isu8 was first obtao �ܥ � , bu? Y A�Pm in \cite{lm;67}, whᙱVi:u thin��t examn� ����2���� ��2�͙j�!�%l$(x,z)$� !T$e dashed rA$�uraw- roug�  maxia� min 2� onAmN�newpageC loci!�� corA onda�toZA!� !�e]�j�?n� f04* |z|z -c 1}f \: B1; �d coord,� 5�\b+� f� 0$). I�� easy���?u+se-�$h_3=0$i�he�V�� $z$-� b�� also�<$them. AddiA�,��J%���ve!�ty ataNs�e-�)  $c!�U�. Sing��Oi�2� �all)�mw�d!Mora�$$�� zero�e�f�5} :�}>=0B Ix n follow�� 2��-W"�  jk6:k�}=Im�&� +\bE{�6�-v�� ���� observ�R �gt;68}!r!�study!�p  w��atI� �1�en�cogniz� s co ing �� Y�*D sLY�e� I�># �� a� re�SV�ADobviou\-�\a homogeneous medium EM �als ex�d�aM�4 lag behiny%���H1�for�U!�i�pl� W!J*iB� , as well[2� A B�����)��e78$dge. Above&�E3Z� ose which� U�o��NMa�n6A!�evoked.oneH�"k shipŲat��b�&~Cois�} I��is workj�� 2D!� blem]EM�9G Q� ion .�9�!�e class~ $Sommerfeld"�� a Hcpr p�nLo��z& & w�ucto �U~BU ��,&7 s no � �0ime-harmonic,AIs QFe expand�| xact�asymptot�ly��i��3�� � terms�6�veao 39bA$placement � ide0�1�4geometoptic@ !�h%M�aUm�A��%r=�,�%ep�5m� illu��F �A,t�"!�m� + i'&I��{ +arison!�N�D.��  sho� �mQ�!,��m�g ��d ��" s\ th�no%{�rM6 �>� Eithod s�e� mosta nounc�heZbclose!$1$�S ul Dvalidiarbitrar�W Z N suffici}j Ts� V�simpl0by reAy�� $\g$�� e�XzP arguA���by put?$\approx 1$&X thebiblio �1�� GausC beam.��uniulyn targets]DAtti della Fondazi�0Gorgio Ronchi]&8LVI}, 4-5, 2001 �799-811>�26�4P.~Burghignoli>�(M.~MarzialeJ��C6�a p� ctly�duca� �  in��v5��=r�I�bf{165�2 � 345-364>�3.�: "B� �: C� of analya����o nume��,techniques",�v� commun�� �]bw;64}!Z BorneE.~Wolf �it{Pr��pl�O O�S,}, Cambridge�2�8no;58} B.~NobleK(Methods bas� ��0Wiener-Hopf T�@}, London, Pergam 1958��>6 % %�\��er�%bf{\lA�fure cap! s} 8v�{4��1 V$.� �I%!���%�� %&�.� ��2 �� %� �� %$z�m1edoc��@} �%G\"unther'�malisk*� t �theory: %AMR-NRR-MS %01-12-2004 \d Z4 [11pt]{'cl� @%\usepackage[page� 4ref]{hyperref}6$4reqno]{amsmath60thm,amssymb} ]2.{ {jmp� } %2 %\renewaXand{\the�! }{\Roman{�F-ub .=-<V?h}{\sf3 �(A=16.5cm��he�=23cm %\] nA� =0pt  skip=\med (amount \oddj margin=0mMop -5mm B  ) enumi}{(\�n{ )} a�Eem{?!�}{\no �  {\bf Dd! %}[ �]2Glemma}{.L Z) x}{TA�emZ'os s VProZ5 corollary 3CZ1Ark .R!ak^+�ple ,ExaZX� + Stat1 >-c!�er{no�4ont\fr=eufm10 �DLled \magstep 1 %Ca. �$g� os. \:ddpp=msb^<.;"d�L palo". \def\bull{\ vrule I� �( E�8.8ex depth.3ex Q�INenvironv !�of]M {\it!�(of:~}}{\qed=QED{\hA�D0.1em\hfill\null\ nobreak $ \kern3pt\3#1.8pt\vq\h�\hbox { �,1!:1.7pt &{$\a!0ptstyle QED$}$0.2pt =X} _ }} %N��os�les �hook{\, e< 15pt{ �v� 6pt P)_ 8pt5vptd� -5��&1%� �!4�x!Pblob{\=(\1{8pt}})�hatf{{ fr{\ensua th{\��bb{R} k{ R}^{kq{\rk \�s Q dK /cal{KF2� �C��ds}{\dicy%�I\ in��la�"\,,\,\r :'naA} abla:t?+�,$\widetilde{ ,normalsize$\C $}}$�.hlpar}2�$(B%rF%)B%tuno}" ��12 :�L.PLG JuRF%u-o�I*feble#1)�rel 8op =\limits_{#1^�V Y #1#2�+�*�)m2{�frd�>sc�=�<26f8Cyclic}[2]{\gen�{}{}{0a%0}c{Y*o �vf1�frd Xj 6vfXA2athfrak{=2S(fdS}{\raise��-2.0ex2p{S}�25 SXYZ260.66��ize{$e�it{2$JT&a !i�� =8pt� a1� } {Ix \bf\sf�V� ($k$-�jic�� )�m �6�  Skin� -Rusk�roach nev�* oper�'F�#���,Angel M. Rey�2ŌDeparta��o de X�@\'{\i}a e Topolox ,:Facultad�& M��,\'{a}ticas,\ ^ Universid ' Santia\-ggCostel R15706-b$ Spain} \e-mail:/'Pelmrey@edu.xunta.es\\Ap� �Narcis m\'an-Roy JN6�8 Aplicada IV, E�&cio C-3,r pus NorteiUPC1 C/ J� G Ta 1, E-08034 Barcelona� ��4matnrr@mat.upcR�� m �@z�s�a��&biga�� todaya�� 6 e�ab&*ct} �!aiZ%,pav,is� exte�q�a�y��y�me�(�v\-orde�$�� ies. ��/ond l$generalizee�&� D� er�3�}� $K$-q�!R�z� ui��� �s��Y���9b �{ M.S. C�f� (M0): 70S05, 53D Z05 :��40stretch}{1.5}>%a+7"0.66} A#&�A<clear�EJ� {Intro�_7EeC.�%F �}�s��2} �du(op�)�to�! a .���*�� l'�"QM$al systemsVincorp�-�.llAT+ �E#Lag �4�2Hamiltond=-dMNsee�,�*�dynam��"�$%/"�s,�aO<- , Legendr�#p,Y� Q�s�-id0ce, etc.�i.� b�'yd!FI -depe=! -!-� CMC}��e0�~.�f� Vbar4} , LMM.2}? &�His9� rame�to .1=�!�Z�Fy���)o�P �gun �s how��.R�ris5$ main&�36:; .;U�~oth� E�re�#Al �J�as�� Let us� ou�.�X�uld be%� N,�)2: /becau�he� �.O �i dard poly] maflds, i��*� i"�"%bw2 j"�O0 :�Y 6XAw�9T0aw1,aw2,aw3}.u's͋�%s a&<V�!I�Ej4crucial device�nW:��!58a vector-valuedy|{" =5!�, -��"2S . On-�$e advantag�I�$���lonl6 tangJ��co  bund +a5[br%"o�  #p it.�.g$ fam}2c|�revis>$ndabr]� was aK��:= sruc7 !by9�a�� 2� cE�A�r�Io!�6B st_ )I@ �6=S52� kbe1�6a9 ��^)�e>toIr���Cul:3-�n��s�*ich���0G. SardanashvC#� et al�:O/ 2,1,Sd-9"b�a��a ��i�(some associ�0fiber �p,�a� �-=�A,"� M�5�of�  �7r�� o��.E. (Se MKana}� morvtai�4}'^L ). �a�-,a( must1� 9�sola�ngf%"�} ar ��s 1s)Jw� �$�+� appA�AE�^o�=onstitut�;$n2-�ya elopM L. K�3rrEm-$HNo2,No3,No4,No5,McN� �3 {\slT &D.K�,q�s (M  kn�&byE5��h�A�-e Rr{#e."MyI#: PV-0�:K9 tool�]� � �= DS "S)U!�}�a�}�%�alism_ "� �&\;�*>c�)is"Z . i9 �-p(BGPR-eblhf}I��Ka-82� lL+itC�-�b38N1�*ij:;3@4 Z CL-9Z GP-s$'�}"� @ 2, a fu�?rv���#o&y8, *a can�*al map.,by Tulczyjew �Tu-76}� .dI.�  se<(fa��@ՌEuler--�e:�A1�/-i^;��A�be_r�J�>:Xsi�a�0ue��( a HletY,"�of.j �] ;�*�-�- ��Noe�! i�=si�3 symm0+�:rom a�ian g3�1!6+Ie`P,FP-90,GaP-00,GP-92b}� is %  A�,2�"�'s���C^� � gun,+�9��.�6Y� .�E��1�+�-�&a��Q�H�Whitney sum $(T^1_k)^*Q=T^*Q\oplus \stackzkots}  &$��copA�B � M M$-*T$QT;is�ǵ�9p�:��. A.  gZ.�4!��]]Os�:P Refs. $[3,4,5,8,9]$)7F��buM�>��#�r� $ %� Q=T-� n�Q$ !��)�a��-�w  $*S*5=�1e�����XJs>�JG $k$ tenso-�e( type $(1,1@atisf� � algebraic*��G .p�s3=8inPLe\'on*� .� mt1,mt���0g��� �d��.fuG notei ��= @�] !�.��$ � � X ,I���* � _Q\colon �� �, $, (\alpha^1_q"� k_q)=q$,A� Sy $z/�|pQ��=$�,��= ���D8 $J^1(Q,\r^k)_0�pV�;5�$�  �~2V%S 1$-j,maps $\sigma-8Q\to\rk$At�,th@$0��I#^ : 2� M?,)�8_Q^* (j^1_{q,0} {)p\��y , \[,+az%}{ccc}:V& \�v &.dr$^*Q�):} .L(d �^1(q), \ ,k(q))6�Y] �E1E^A=3M^A��rc|\gma:Q \�@VMarrow�� $A^{th}A�mG%� �$/ �Q^A:!�%R\rAA`3=� $1\leq A k$*oV#i=1f?2�Z lso� A^I�a��� .} �(q^���.�on $U �� teq A��  indu F7U , p:,�i �nsVn�(U=(��)^{-1}(U�L��(by $$ q^i( i�e�^i)��1b. (HO(90"/} D q^i}\Big\vert_q \%� )\,, WG aPI� , ,���!q��: ,\, )�) n5�,%j��-a�99 9 �2# ��$).�U �N4 Gk_q )=AA!�P�H-G )E.!/"&hI�}\{r&4 , r_k\}$%U"� ��f sQ k $.*Q*�/ � } ("�a�te  ) A �Ad �d�erz<$a�$�$ $2$-fD $$\bar{\omega} =\.|3a$m_{A=1}^k $_A \o�!s r_A$M.�M�di�$N�� a {\rm:H�1$ pair $(M,.�)CV<�eGQ=$�*!BVendow�B�&a �[5�>J"��i���  :P6C(-D0):Ga6�i� d�2<= �H_A)^*,M�i�qn\,i��G _A :*  I���%ua���M$��y �*}yҡ9�$� =-d\theta85m�+29L��$��R<be� �Liouviln1I�� 144�_q)(\&�5 X}_{�_q})= (-Z)_*8 f95tA�B, \,\, ^r'�(�).$$ M(��E�q�s $9� _A $� 1j )_A = -d(1)_A$ �Ir�Ɏ_A^*)^**  T�RZd�v�A,)����4ly2�r=p_i\, d#�M�n0�(#\7Bdp_{i#9A�$$ �%��:�u� $(=/.�k)�?.�A�2�������V� sym}2��2� - d(Ŧ�! )=�^A�.rAi � �F�* 2��=Y� �υ�l�,��sta[,} iff&� �,f4r�JistY%3*h l sucat �'A!c written 8ly�in�N1W�1e � *2| ��>��AbJ3�%}! ���s&�16B �Awane�!.�*qOE�B&} � �:�}pwe"Ps�d.?:�C �R.%@!Eaw} (� �aw�hA�yEon z�=n+kn$� a f�1y�� A,V;ͨ  ɣ���A A��%8$VA0 :{nk]�.istrib#A�Y{ $$(i� t {A_{+  V�<V}}=0W  (i1 \ds\cap& {k}�> G$A=\{0\}.$$�&�Q�s !)�" >pQVq42�M�wem}F�p��Jsa:�&�-!�$M�*b�0y2�Aw��f,,,*�+q�" R" B"  k+���M� lock�b1L= �C�< dn{iI; : + -X\ ]thks}W1` �._�7l2�1"� 3(��2dFC:Ayf$j�7 6Yis�b��$$51 Iq��^N> !* VB  =�@ _Q j:0)f T�*f��&����n�6��!%=,6&2�6�" . !� From�?Q4)A��(� h�jb��j��:^�"�Ue�'deed, ifv -�6] !�akZ�2a�&��s adap&Q��&�2��,!aʅae, Bly,%�2C$VAz:�k$%=$by $dq^1= #� nC`An ,Y�*y -k,��b`�� �C��f�[HyrM�Q.6� ��%���5�0triviAZ9�aiJ1n0*�ad �(*ţin*�G {mde��aA�0ee�*�$�H�E9*a[+, &uuX7a�6�շ�he neegeo hNXI�Y�� q^Y�2�A�� �`I�d!�W"�i!i�-fc >�w� ll�w9'�&3!, �pFn -8{\>�5U%�r�c{`"��n\[\tau : T`��!0JQ46)�$ 6.�$T5r� k$ "#;J!�_ xFQ _Q ({v_1}* {v_k}_. !#��be�(nr� �_0(,Q2�7��6`!9Y���1n4�`' of  Uj�\rk %"vsource�Z*�[ *w1.!��1* �0,q"�� (0� say b�9.z��&�6�b�b S &�q�$,�${v_A}__*(0)[(\�%/ t^A)(0)]*wa $F�Q�2� �%y J3J$aG�Zjn9�Yv�bYU=a�"Sq>Rve3. V( v_q�})� �Q�"�~  ,v_AJ�jE� �_Qb��fH=2� �A^n0MM��z WF"�(�E6� Q"6}7ʡX� Ř��]"�5 $X_q$��X+� $14��7�)a4��i�'T$A$-lift} \, $(X_q)^A$�� �_k^1Q$Y � 2fW� .a d}{ds} ( 6�,,{v_{A-1}}_q a�+sX {A+   !��j$_{s=0}} $$*zP!�!�d $f�E��:�={ p^Fpwe �1�" xa} -! = a^i J �w} �96o�`%�U A  = _,F�A� )(q)��E����AseNiS"9,S 9��6$,y*%,%ITL $$S^A(v)(Z_{v})= 1 )^A,aWM-�A�an?%�HQK , v=f��\�H �D->8 *� xa}) 1� in I.� ^*JA} S^A6!e 6�N]29ͧ�t_A�/E��Yb)�s !s"�regard�?�+ $(0,mQ0,&�.A}{1}ldots;k�(%�A�!ty d�!Q$) ��=�Ucimo�%{:mor� 2A�� > l r!x�A�c� g�-�+�F=by FV. al.a8V..�y"�V�is&; � ��'�ҵ* $e6�, e9�.a�"^ T�KB pM T.�("� , w�h� �/ BXB $Y���$ac�kyD.)o'e n',�-&%�#b5�h-�e�ͶARbA a"7"�fA ��r �&�� �?$ det��f"gN(^2LASN�`�N�/v^j_B}\� neq 0"�u � i,j vm�,B k ���%�="�!�F%�tE��L� = dLD rc St#, � ma.-�\��6��I/-31��*ͩbetalocjb��h.B �� LK4i&hS��a  }����"�!J B5 SJ�f�5�9(�� = &�\,m1�1+, onv eas?pr�-eg�+.X:"  } %-0pr811\S-O &�*:%\�$aQ�. if#M� $\,� ���|�L)R is a:�y�.�. E�2�gj:hu� so�?I.�.�jlso.}6.w?A�?"�.�"/ 6�1�W �f$� $ FL:"�:Z&���/ � �"d d �{u}�\� w3.e  � I`�D�� '� ] �$ }(_qQ$ $$ [FL1� &V]^A(w+ 2:��� 2 L{�  � {A +sw_q�:! k )_{|� d%� ��F .� dez&~y-AG�<ly�ECb^locfl} � �R B�'alft(m , �2�\�L�8�����In fa�, �k(����2  �),!�i� �-�I�al\A�;l|\m�lee����(, y�A= (FL2T# _A$,;#*0)_1,6�0)_�*r!�e����",aP�D6� \-pl�2�r*�G &x*dM�x#�� � �"en,.]-I!H get:&.Z3-�1�-���=m�=�.&f: 1)B�)�. 2) {\�FL}#�@4omorphism. 3) &�!L!^iLN>b�s"-.��� � *F�2a glob�H�7�,!�$Fev��&sl a-�=7}F "u/!�<m1s.c7S�p8.$�*�/BYA��!�n �iy � � �M^ {1}_{k}M >�M$I "� f�.|R *H �f��k �} A�4�3} : MB�� Z(��*�& �jll�=�rmeD l)j�MQ� Zsc�;5%�q6M &n "��� �= T ��;.M�a�.��.�5 � O?!a�k${ �-/{X��q5 X!�d*< M &f3E6ng `P6���orF#8tt9L>fO�(X�y X�&H#=r ���6�9} A2<5xt�6Q}��X�*�O �� :6 X}=(J)$� pp&yfw�Eint $x�)�a map\phi:U_0i[t +2 )M$," on som�4ighborhood $U�(!�0a�0�&� �phi�x)"1phi_*(t)�,N�R�Z�*���d�X�(p (t) "� E} t�U_0�6� ,��;�?c$�5��$TdX�rc=^{(1)}, �a0h e�A�CA�d "9 dEaS ���_{rccl1pr@،b: &�2�&B��1 1_kM��b & tR,� (t)=3!0!��, -\ ({�, t�*phi+t) �%mU%�ea7,t� A�*�$ +1�RIt'*�s:1F"� m�� fiK 5DoM�� oM=I��^Ah^"  ,��ein� B~\I�A�%oQ�� �  in�/>� WGE�Sa�B��� ��&oN���#$M�&��!<i V"��B� �W���� rJ4L�Wblp~[ �F{���� � �AiPb'_ve2"u �2�Se��W= X au2AA���Dai&�\&��to*Zzn 9W�.!2/ ���Iir95v]9"*j�e� �6�I$icfsa;��# $F:M�1a.�!�m7Zt�=iZ4��- (F)<; F Nd0 (F)�0g�_(FA rc gY(*  G325�"W(F_*(q)6! ,XeO,$���R�\in T{, $ �E| $ S :T_q � T_{F(q)}Nv1sode0} AF��%S"�aGu�V8 +\�#�\ �@ Bp {(Q})�0BI�is%+j TD�Nr��$sc sopde})D$� a�D@�D � )�'_QMEj�;5)B�)!J\��AX}=Id5� !�def4)�;�+� I��ZA�._Q M�\gammaQ�\ta,". R�� �)�"-?�bn5�LE%"�Cq$fm��.7)��CZa�j� �=ut� iJCD �E���> ex�C�Ua {9� J m�,I �3 �5b.�!�1} X_A�=�J�"E>l}+ (Xj4 i_B JF\M�fE!cB}l866 �Br�\va":\]jo| aYraJ9u � ::%q2�2 ^� ( ^, _B �! $!V = � [1 "�" t^A(t)]$b thus� fracV� P^i>I\� �!PAN��X: t�n�p_B�rU.v\,1 i"�a sU�*FV��IpA�eˑp!�> ��� }=. Ir+I?: N+� Q*� �� U � Ea� �"As?2=���0 �A�&/ �ko}I�tau '�)3C7 Z�nn1} n�} ^�A�y�t^B�  Ek =�*� .B�&�+ 3� Q%D��As&|LM:nn1})<4x+l 51�"� !ve�: �R��t�}I`�XG5�N� said be rm"eGA"]���FPIE]wN���B�N "�JJ� ��2< hA� omicBh � m~5�s RN ^ \��SR�; ���Eo�cJ� �'�g!X"�  T ",%Ai}Vo �1 �&j:.\ }�*u !E{6�U �U&� flow�,�{� \rOq �N^ �noalign{�} (s,f� ) & >� & (e^s \, *� ,� �`' �ā�R��Y �rbT��c} Ck% i/ i,B}=�&: &�v_B^iQg"= �.W 1q$C=C_1+( +C�� C"PBq �',��U�256�� -! llow�A.��Y6��' Iv�' �'7#Q;��Y;Nw �5�.� caA+_�'Y-I+A�+A+AN+J�JA�*�� ),.c>�a� " � �$-pr235}N�21 . ��K��6l  i� ,v&��=I�l�)>@� $%i&Z(B�?�LB�B �M6�Z+on{*�1V *�$on1�� �WS2�.D5&r |B�!A�4f �*�"<�H� /"a 2`͕.`.� @� �Ũ.`�[�4at/ �W�\qb' geoha%�:sum_{i�Cqi�t_{X_A}���+ , dH -�hC+f�*�=JL $tB0 z� &"+V +,_B�Z-�9*,�hi&8%�f�lbQ4, (�\ e�>e�'4n�xd�!XT�|,5:)}>)V)r4&�� 1,�� �Rc%H:�\-!%=\,�,A�"}E\-*A_i0 ��ji bi;i0A)^i T�&So� 2�is~� ? ? \( l��| "� 4i)"! �M>w�)$�J"C �Oe�1qd-De Do�N -Wey�\5�}^FHEq}b�z� -6�ea'Gj�-!�}Z5,� }[)�n� Hb� -�n>��R�t^A�Ef�"k�'\�I n �&1}}�Aq� mCEP*�bDT�T�"�_z�.�;�{�6�Ij3is*MY$re� A�VKHXed Z3'FR� l&;��q �c�s $L=2�j�Ioc vari%5a�Bp��oenp�sa i+6�U1�s>g$L$f� ageq). b� d:� d� v�+BA&*� ��+-N�,BF&��L=0a>E�U$ z+86�na FTi%letb?*�-AY)�6us"@�E)+AP,i& %\\" > %on�Q.!� c($E_L=C(L)-L|C�!e L:I 2p.�� /�,���F (�19z�Bg��$)q>b��67/H�!�ZyC �$53} If >��"� � "��*�%z�si R&� ���6M"F(`1v$&< 4�>}^�e�0F k ݱ� . ]zA= dE_L�I��\} F4 �6�m >� :�U���1"�G2 \proof�&�� � 5��6w)"�*B � 4�~0  " I(�<�66J6EJ�� �p_B�#x"G &BZ"ZJ1�*elo��EOI � ^2�� �X�I�1A}� dsz6j.635V,A� �j�I�:��L C _B =%jN� L}"� �6IV� B�� : f�elU�z"�.�!$9i=�A%3m_B�Butf0����6wvX9locelC�T)w.endYpeQQ�2��_^�?� �m&1}[ A�|{� rk��zkqAQ�Qjj_A + ~<%M.��49�I� F|JF>A �U5\psP ��8=�'X LiU 2�"� �`�c�s97 narr���%aux11}mBi( }) ~ hE~>W �}SY ~ , \\}Iaux22b_Bdds2r X_B:ZR�^2u�� �nt^�!= ��1�goF o.v4��&�at9=� �@0k ~�B3%�uFqRU+B%^6�6�AfB> eFbF�������JA�6 E=2gJ��6�q�� b�U!"R$�2C"�H6� �  ac""�'*| �><� a~'N"} s,.X*�G)$>� b�. rLm&�3.�3i�)��Upce���;:Tazp��01d)f�@I_��a-I:2 !n^�w6: n�Z4�xHe>�6` �� .�4flushi&� blob�+.�v&Pway*:6T�cco`�r >fL>�:,d . O���$�!%&��2�2���t�lea�I!4T� N�,lf t>!\2�3M a"�w .o4})o�ng�j.689n.�/of= &W+.Ao,"����� unity,*4�Jp��� sup�x%e>a"�='!Fis6[4��hs,"�7aS*omo#%E5W�oIb6@g $H:$.,Pk %B$H=E_L�" FL�E #v �in��9!D5}?*d8Q7 te421} a)� l_L=((X*�, N� Q4 �IHIH<6��Hw;Ler�XA=FL_* yAbHBAB� R���&�V=8018A@.N 1N . b�Y�����0��"���x (=H$%ʥX1� &�$F�>$A{NZr"?i}vn( �&�*u(�F� �q�s-� HE})�&R�� Qh��Ac���m_�*�1."Oz:1��G U_��$FL.g]_9��>%� $pH%su=�4nf> b) ��&h�� * 5!�M9�cg>�0. .` ^x�� ��}�7��. )~:Q.�1� .m�� ��ld�"-9�=\�(cal{P}:= FLIo|-� �W.�m�$���: (�6pa7 natuW�imbed߉by $\jn_0:v\hook�. �Z.j�֏��to�magr?TJ res A*�cFL(v)�Z� �3v@5��' con�idx[k0ьM�.�"�NXLze � s $H_0\in]�(};P7sum[0 $(FL_0)^*H_0��A�_0� �\toC��o5PQ�_0=laK�u�Fyuu� analogoh{iwq�iF�e �"�"�(X�r"�^0�CH_0,!HE\�>� y3"aZ^0=Q6�pE very�" g�_0ŀ>� �a(if� )�?aB��5m>&2<2��$u&�� .�;3B,!A��'&S>-��>ie,<!u�V&EeW&�x}Q�;�QE�i4�iF�6kV.�&q��0"�'s �lqER�ug.N!.�R $pr_1�1N����Hhe*H i4��)f��, R&F/ �=a��7)2z{=$!q�Cˈc>.�2n2��1� )C��L s�:&�&9[dorstZ*t?E�&p*�A�@}P ^�DE���B�^"g� Opf&(<� n)""�t�� pr_2�L� &+ �M(R���is? bA=(N)B�B . F.�rA$tBGu@�:�6L �d�i�C� i�S�*s: <:�'*: &���:N�N1* V*\ &�)6�' �',\an�n�:\7toads��*e ^A_q_ ()�A$$ Givvr.X)vѳi�a]w�G��9 ��" �X`%N�.u,=� &xH}�- zJG�a�#C�H}�.#+{�VF@kWF1��?- A�1^*L)�@!�5�Yu+.�� �* � � s�9=��QQ�n�"�R�-.� ^f9a��)bleH�nsNdő�r�?RN2+@�.ps&�&)�)��FK a��BblF=:]�w���w��616�&o m�BH3*�1;&�Z_���=tb7EnT s3})%��"}; ٍinKi"w�z,}e!^Ely"$Z�'iZ (Z<&!�2'}"X2 } + +_��'+ XB_i� ^Zp^B_iH(t�!�;N ��sym% s1}.~%w�b�6}CnI�2� .E�} ���5�B`�s4} �i�5~9Ks�qgM<)fA_J�2��"� N��.6O�.��%�q"�%�%z?s4 �=E<�o *j^7}Me)YJ�e�e � 9� S-�nc�&~ �%�xuc�ot6�� c%�e*cA@�atТu��"#sΈ"A '!s6A��N"�� (noty� ial)=�Ra�a.v $(}vmEI�2_.~}�0 1 qa�lhE�o�}.� h�I �*�Aj��S�}N �N�I�D !.iz$.�1g f � ( M�"tx#�."S n>9�by ^6O�  B".p�r֛icݐ&�$�@1Km 2$. I��5�4abJ�)�&�y�K"1{6�!�an�.�<w4I�aka 8�u�w�A�ore-ELH-eq})�yTc!�e� �E"���s2d&0Zso be �Z�׊�)=,�G,%�%t{r}tyA4|< on�run�xey�bayJ�)�it��T)faY�l!�2!�-[)-Jgis�on׷A� � sual�9]���Qa���5�51�, taka�� ac;�q|6�ݽ�,EuZ�i3!>q�u�2/1����$'1��2 ��!����!Xn �%�2-�.��>j&��"Y+s�gFj -�b� ;#��\)$ʿ"���A>�|W  � ">V7�&�!j�(2!17})X.�%��02�dA�!�5�b78} B_j�? S ds6F�\pa.MW�� _C�B C>D^8"\rpr� � ���2�Z�&�)st�T��nd*� �v�;:� M_L!t�B��.�B. Z� � 2�}q���m���8�{ . (T��m̍��qe}B#�q�-QH0*p9y��iFU�� non&�. a��qu����i�*�F� "E$/��+̬� ^{\sharp x .�,g ��*c u��$:I��)�)�-�.�) *:" : p� :i(Y"� ,Y_k�$* S+Yd5y��K5NR"Xt H�� :���k�J�2a� ]�W�%T&> ���an in E�] j� . Eaq���� &�V$$� � D B.� 1}{k}B�.� #}(}\delta_A^B�x���B"�*�?-98})�."�M`��v�q1ca��� uc�Kgl#TB�� E�q�� w3"�,}��'m� WE�/&� ��/!�"�)�� as�6�be�"7o4��st�K2�T}we*��2AG�L�^ orithmE� !["�%.�6�m����. NextA out���proced_(� I�`"���II�l� is sketch�Y� >Ӓ� N�!Fin�Uto-_� �1_2�9~���HT/5�=�Dw�� ume,=�u[���AJ<sW6G� ,� P_0=�N!�� $P[ �� FNP_0$ m��x5?� #q�#2[6�Y�� �"a� P_1= \{ z�PP�, |N�\%�s�P$ N+�~_z 5m��U'!�}t \t@�Iۉ�u&�'�p B�j �!l.�rroj [V{P_0}:� �to&s3�3��f( �%�*��},�$g c��B]dBe.db�5sL4��'o� 2eS�ɥ�w1�$PRY��k �P_22�1�c��1GT�r�2��a�-�1��!�19�1!-{ )���6��(2$. Procce� ��%�ge�c&�W���1%�i=!�:� P��x�2� !� J4Aԁ6&Jm�^*O b Qa�I�&� &m�num]�$f.xQ,$P_{f+1}=P_f� $dimwP_f >k��,/fy fina��n }�}5)��02+o��*� . �:�.�+�lb� (W��V� �!haU ?+ble. _or5�_�!��+X6����, �N1 ��"���&��mgbNl�fe�|  =;� 6�!/�."  &���e��!�Pk�(d�*$ (so�^0m�, ^-�� [&��,-*�&!)B/1:!9٨�ry1�R6 tr�J v0�,,T�0 A_b,&�#NT��6>-����}�rm �-�1 si_Ll_H�� �_L=��\c�I\rm��"c%ps>�ak.�lu�$�A n q _H=F�)0_L$ ;A�fa�a*Xj&8��H�?W� c� psi) =D-8 =�FI2� b.�Z{:_L(t)2< =(*�(!>��Z�@"*!\-��_,I�r=tal�&,��! RFZ V ����dArav*� ��&�>�:v��^&�" :aond"P�M-p±�!�p��3� J)%���te,� U!-&�,�t���|"��HNx� R� (��U -'�"�%8% �,='�jQ)��t �y$ �the�/�#ed� �.���?iw�YYin!~ul�  �a�!� in*�3%em�(?%q�� ��*�N� �+NOZ�leti�.*��$W.X�F�$2�!�R���� r>�2R)� c�ġ�:}  &�,Y�� eda A+yh�,Ax�rV� m)�Xyh �qs:2� 2E��,&��80:�-5�}o�7A�2  1 \\Z+105IH )�49�2101155,9Y9FL� 29,89s�Ao)115,87W0^* -30,5AY >�z :u0}�4Ab148,4h**wu�1%277,325%1080,136y) 58.Ue�159.�� 46.��c267,979Y0,-A�21�!x!!M�y: Xa�1."B| 53,1.�E�e� �86 3,2){135�672?y >71F8a� 5F143�.�A�&�'�AI�np�<*� N2 ��p� GF�#("u�7F�9 � }{"�r<(tJG;$"#"-�j h N�= b�$�c�i*�eredF};(d>� �4 BReG$aux�!�^}�Y� a"� 4}) .�B?�P �eq0= ��K & = &�9� =ij�)dR���(\ qd pp�E"�&�H1 aRi &T.CnZ�A:<� ��A\ B� �B_N�)>--B_9/�%"�?�@)�1���;.� 5})�D�;!� )�aux%�weqo�>i.� e2%"�A&2'.�!�1� 0PY'2`5�]�m�BdB=} 6�1�n�Fk%��l!!1=T�<}�Aa� �2�NF��i \Q]� last'�q�� N� 'fo��:. T 6�� +�Y� �8۟2 J.�.� �\6�v"�;�2�..NG�u: "��#�u} U�O; hypoB,��B�$�<6_h %sJ�;: H�-De Do~R`Pm2�8��>�$H�g" $H )|FL = E_L!Yi�Pbi�Pa�2 �vSi�6�.�6p��sm�� �9 cho�!��#p�"�� ���n2+ &#� Q2�FL_h rt U}:U� FL�%l ��<So��$H_U:2<=a�6U= (Es9_-D(.sB�$. D���'H�K H_U�7�<o#:R�d�  .Z��F^M"�9$ "y�lve�A ij}j�_sh�B��SѠ���$A/��A`#�NuadJO.B�-,FL=�h-�/FwL�g 5^J�*�>`{!c� openBt $V=�L_L9 (U)UPbsPo��5L)-�VrV2,EU�� Ms L�q{�B��S�^L "�Y���Ś_H.@�:)9]~^�6�"� h^"�.<:��B2�g6 A.)*�& $�m62΍� ��^*� ds%��}= ��D6 FL\*4 �8)�&)a�� BSv�TQ����!��A�b���FwJ��akN�-�B.�E�A 9V*� A)2 = -2"B#^A_J !�".c($$(\psi_H)_�y{\vert V}$ is a solution to the Hamilton-De Donder-Weyl field equations (\ref{HE}).\begin{flushright} \blob \end{flushrigp Conversely, we can state: Hproposi�@}\label{33} If $L��regular and ${\bf X}=(X_1, \ldots, X_k),a � to (\�4lageq0}) then:xxenumerate} \item The $k$-vector) qZ}=(Z.qZ_q�Cgiven by $Z_A=(Id_{T^1_kQ} \oplus FL)_*(X_A)\, , \, 1 \leq A \leq k$B� �s3}). �! H\psi_L: \rk \to m �4n integral sec!N of �Z0(!R,thus, from P9� %953}, 24!C8 Euler-Lagrange))Y+)g �=( �(, FL \circ ):�(M_L \subset � )? _Q (�)^*Q j�M1� Q%�. \A�9� .x( \proof M�.M!�Z� Z`eqU� B�,!Nn%| N|a14know that $X_A)0 {\sc sopde} 1� ( is locallyU�U�m�qf�xi11} X_A = v^i_A \, \ds\frac{\partial}  q^i}+ E�^i_B n,QB-jy where $C $ satisfyM�8locel4}). Since!  map $F[ FL:M.eFEq�YC$,!�� 0locmapx}(q^i,�A)j \left(! J5 L}97;} \�,),I~9e{��%�)%� �)A obtain^�idea} Z� F��-�r�!� +��ft(�F^2 L � q^i Q4 v^j_C}+5�N? L ?fB :A14F?:p^C_j}+ mƗ Thm�9xE�=�%`%�havA�at $$%GXsum_{A=1}^k (Z_A)^A_j= �R: .: B:A.:F�^:@J;A}=F8.� q^j}\œ quad �i=L�, ZE�p^B_k -�2".X v^k_B}M�=0�S,!(��is��Bf:�2� is:�i� %� each�+ t��nt�m8$M_L$ for $A:1�/ , k$�\( It follows�� Defin���X�TH} taking into accouj�� pr_2���=:�N�be�O ,(remark} {\r�$last resul��holds�2@ almost-S ��ians. In�p6# case)��!is& same, but rs ��$, !��_H$!?t s}��, aim of this�-d%�(o establish%�rel� ,hip between BXHare"�sa(iP"% %�: si�Z;a�.? main!A�M)i[ing&� theorem�,ELH-kvf} Letr  be aB.!�EE *� ��I?>� m4 X}_L=((X_L)_1�} � onM� Q$ d� ed bFW � xlza�� _L� pr^0_1=E� ( )� ZM:&< B�F�5�(\ c c olonI� (M_L� *Q)�7@he natural extens$ of $J_*$� C*� everyF�3 !V$.�C� ,be recoveredi�is way��.� i: \Z�n)�.c.� More[��BLKs��< ble ifateB? 1 �is�aonomic` Q�"K � $)�:� t-|� 8 diffeomorphism�n� }U�Q$ Y� �A~)���5U\Q�az}5 L)_��ů��U� ^{-1"� ^*��&91 &�"-p Now,��M21h5$� &V ��@ �Hjomega} \jmath^*\O� Q�^* (\( ��Bs which��sIl0 Lemma 2.1 $$ �,array}{lcl} Bu& = &��_2.�0=Wm�b  ("'I.>I\ \\ \noalign{\medskip} ��FL=.�% :&,1� �$$ OI�other h�!�� �Hb� esth=0!�cal{H}=�E�V� ���: comput�� t 2 �:�o-1� (  C} -!_!iL ) \, I�Q[GC}A�-9��CLBG9w%F� F��a�� m� dedu7ab�sumas}� .�  \i� _{Z_�- ud\,�B87��9A}�.� J�ft(� R�S .I&,F�A�EI-$E��#dif} d�5 !!I�.|%�.9 %�^ Aa ( d 5�� 29�a >*�)�E�d�>�eSr 6�):C �^?�RA��. � u� ppose "�a�v�� r�. A�conseque%of| R � P eq}�r@&� "��~�$T" ,�4_L=\phi^{(1)}$ ^$=\tau�  pr_1 I$ ��M�( ^0(t)))�_1^0)_*B " W�-t)��j� t^A}\Big_qM��.G�F�� So"� . � n U 9vP � E2,e�h%�>h� \ 2r i�A2*AFn*eM3l 8 %�6� withhi:\r^W&A�x!�11J' �k*y � Z}$X facteiW��IDZ !aJ�Z_Y���.[Mo��UO��:4.� _E mA��U�.��r��k - f.�n� A�(�g � ѶW^ �c&�1+�t)� f͑2�}&�s}]A \\ j� �* �d�6 ],.~f�B�,~ 4a neighborhooda�\point\Q$9re exist��Q&� y�&V� ,MHXB��6e , $Fva gB3 s�is open6�achose such a `�\6_8 onto its image��us in�"FL&W�� !�,(X_H)_A=[(FL[ ]^/ � 1 %�$$ orbivalentM erms%�B�$)�i I�Xr �X_H�.&O p&�}�y&��)�>s9�H%�H&L , �k)� 6�� geoha}), ����ian $H�� |*� $H � FL =V $. (In� words:B�s�L$�ѠH2ZY �+���. ,+$FL$-�ed \gE6� �:wBQ*� ~ kQ�r:>`B� �K Jw9&Q . �o kvfbiV �ihBbgTa�; �? ��&� te421} a9ZB�,21EC�H={F.|>�t+m�"e .� �n�UgLN�Qg . Byat�-m}M!M"�A�byJ�F] �Z}N~-�>�u�`\t {F�operator�>ev�"&�cal K�mechanicA^protectMypK)so-�edl time-X${O-c} in Y (alsoj�!4some authors a6e Ye� ive .�..",} \cite{PV-0p"  tool rhas#8ly been develop�order�studyAh &� �w$ formalismDsin%#�v ystems; thei�B .�" @�r p_i}I�FL� �  ByI�%� $\va3E&%�T)�.'curve rca!� $ ifS"n�LK1} TA�!^�&Dstackrel{\bullet}{ t}=I!X � \, , �6i%�$jN:\ �(T���A=��� d$�U��� bundle $ ?�A� So�T e di�'4m \vspace{1cm}1 centerpi���e}(200,80)(0,0) \put(15,15){\makebox({p}} !2R" a)$}�G60,20){��} Y30 Y�(1,0){802V00)�*�)$(0,-1){70} ?w1!:���( 30,2�g12g 30,6����$ � 60 ,70 ){&M ! 10) B%�z20,Z�)940,11`� 0){6� 25,7�Q}$=M1!�$E�1Q-75n� -60,70 ){n�cMc:^\r� �-35%�>#i�(7J�)�o Q|iGQ�Pind�#M"�q=B\�&hi��f�#��)�at�k �aw.s�(#� evant�pertieJ�� a�"@""� ize  E*Q��� >M+I��X� �2�6�{�s $�_{X_L}�d_L�{� 1:�z�<&&�<�if,ţ only i!@Fn ��u$;e�r�"L K1})!pd �dir( :��fa<�G�"*� � �s��1��2a6� X_L=�-��$In generalL�d" a A= ," : -)��#s��)KoQ*�$ $S\>�$Q2&AGJ=" -Dirac2i $X�E<= :6 �*d � $(TQ,Q;,E_L)$ (1!�a2g2*� � �1Jb! ��"�  -hU��C ��!l2��:�b�3} B)}{�  K��  _{Q} f:����} >�E j� yA��f�4�-� F]� R�Y3@$\xi \in C^\infty�%Z.� a}X'�g K(dE� FA!�]:;mBA��� Rm�s}�,�a�),JK3}.Y$K4}) show :�andUkAKdescrip�0sL Z$unifi mean��e"W 8} K}$.�m%���L)s� ed ua㉑� ���^��Beq�ce��F�2�us!c provB�� �he�x way:dre@ a bi)�30se�fu�!>�Qѡ��,�a�oug�( dim7&Oh>�).���s _(*�`*%�a�te.}, GP-ggf}.M�!z0"lete cbfic"J c"=*%c0achieved. All�.,M�ed����ian onesU*eݟ"z �*D�Noe'�isQ lBF�r)!_� gauge1 ``rigid''R metr�M2�>J6�w tFP-909yaP�,'te!�92b�T2� appl�toj��ɑs w� 2�C {\slI ic a�'6i� }*} it de�5s�4a hypersurface ��QUb�� �� .�:� $"""Kmn��!�o!}f4 Next� )�lizJ0e*�,!�k !�s��,e %/I�%�AF{!�S&N�]u(,QQ)�(ieselo��Ob� Qv.],8.��} ��(eW�i�fo �multi��is�(-� bar54In �4c!� willI@�+om��",%1]\B����by�6� � !�ag !{1.]mX0+��� $def61} A {�/ rW} $\K$ >� .g�`8 J*��� $\K:�+�)(�?7)$"m56�:"� ��s��*�M N� : ��Ao.� �Qu ^� evo1} z�P�K�V���N�%e&�8�6_. 0"�9d*�5 =)�10&�]r�!N��2�"n5,3 r2�14r92�=o?70 �\K�V�H�$\K=(\K">/ ,\K��G "_A�1,l!q k�7:] a�� �uq�Y�Y�� � evo2++c:"�5 (�*[�  _{\K_A�8+� ]?V}� VUn�3} )�E�Q&vA�q!�a"�!�s &P �tildek �~�-�va goe�o cal�Ct���*C of a�� ��!��$4f $v=({v_1}_q,"�! {v_k}_q)o �then *�(e��(�I7K_A(v)= AIA)^i(v�7i�� l&�#{FL(v)�:S )^B_K \�K �6iFM�! N�!I$$ Ta"6 6� evo� F�;��%#E^*_Q)��.���&�*� >C�:p^A_i,(u%F B_i)=  )$, A� �^�secz+KP=v_A^iN�Then, w� n#7 �0 coordinates �]d5 2}Q(�(.,Ee�(%��& � (v),a�_*(v)�H�%�3�Y3vp�m�:�vJE:$$ we2kw#ds2� nA95:b�y;��=�\ <}a9-qGA_j\' =Bd4n�^2 p�Rpj`>@�EBe8> fore^klB�.m�f; 1)^1_i + 2)^2 �9+ #k)^k_i=��!Vm����z�Oe��)6� �( F�$ A��=)�j�6� �,-� �� MB�P��� r.R�;�T q k.!����`onents $!] �"` $i�it�4kl�BE� �\.�' leaq���͞*� ��'�8&���  $1�2$ $3$Sm� I.d� �<��6�J� 1}{k�f�BF�?�-�6`Z��� and, a{ g!A unit�E�K globw-oiF�b 22} $+�k��e@.�S$wer6� ifA�@(F�8� ��/�1K��e�9�} B>22}}�2�-t\in\rk&0i��,:-=�*�/-�psi_*�,�_���e,{tY?��%�^�E�becaus�*5%=)(t)=j�(j^1_0 _t)=(E75R_n-y3�ܡ�G/4si_t(\bar{t})=�(t+$. ThlFA6"{ �is�Wm�5ve"�2��.�IZ2X�� ��732\J� 5� b��. "� N�P�:�)��"� 62� 65xJ��Q�.V� NV�52�202�d� >( A�{put�B����Ari�&�>F�a�"�^�ps��61PrK �2�"sSed��a'*�"�GI� is�we5�-.��I|��'r�Ni6 .Fqs"�FqJ�in"�(s �<i&P &BY:Lp1(@L:E(Q�4 @91. ��:/K /nX� i:S�%_Q+ �ͬ&#$psi}{\to�Q tau_Q *�-~:| "�' ,1B ŭ.o> eB�\V�H-��Ų^ ,� ^i_A��$�T5&|:locfl� �� ��"' �kfi�a*M=&�<p�$�6 fVJ:�6{t&�9�=f< h^j*P �3��M�4G"P7hW!+}V < & + &�� 6d ~ "LI LIk!�j�%R^A�%7�r�'��KR"n:�@HB j�� !vf�� �IZu! pI^iU�J�>j�2}� 5i� j_\r�r'"� C_jj�B=So1!���:<$��F�e�� � kfi2e�� �hfb�kfix!f�I�J�=E�9|= *��w ��}� j�4BbQ=��YmtTn�.:�M��Kb|6?]u<EMU&A�j���}�͂�^2R9�t^BFv�6��"�:BA+�d$A="�S ,�KF-r<,�M�l})Y�{ fi4.�� 6�f��(](imps�=Y(*�W�( ��7A8�-�eFr�io]M�Fe|$$�0 �* MT)�xB�(:��N-�&�Zd of6 c�HG3!�L patter <��M-J;�VmU*of^i �53����4"�VQ&�Jth��J� b� �let��� $k$ ���2!$F6^� )^* A(��8L h � .�.au6�D1� $�$j_S : F�( $� *�M�Vsuc1$J�D�K2} �&��,\feble{S} \K>l)>�� "� >\%F/nO-3J� yM�.|U:� Uč~E�0� IM� {ccc- 1| &��j�22�/ 53,8�/ box{)Q!#"�0,3&&/F/13r�W &-] z$) �> �'�35.�/-13.9�8�.v0vJ~R�5:k45,19��cs0c4cR�FK>b2���64[00�qy0J�\\wQZ�12�63,-7�FL5A0,i�n�9�iIUEfA[{(lag ��, We mus�.�T �'ase5- $ �"�"�.{ "�-�!�(.d#"5.the�#ld�$ !O$bc#p�Yall-cl�% [�,S$. F�8,� 6y x yE�V�O Ck"��%K� is %Fq? to!^d1 CA2�*MR�?JYK$��M6S7�L�K�=( one easily��ve��:�+"&I��2S�2�.\ 2�/ /n��FL��$$%M�%�R50"�!.��@8:_!A)CFL)]-8 �2D�X. )!$ 6 $$ h"A�:�U�E;s�R��3*6>H&FUEO xFA�$urthermore:'>PVEM: >`V sode.<we6!�1  "%5\K6"CM\LeftYarrowR>��!����FT NT ?�.Q ���= *�"!�y.fCfiber �8erv& map, &j^*� FLZI_�2�J)��� �^* � �FL)cS )$$ ua+e$WA�l�is PCa�i�!�def}), % ji�-..,�H�De-�E)U�]|�]G�#��,��m FWDa�- immed=v.K*(s"� � �_p1}��r,� X)�#&�U corollary��@or} Un�>heW+1Psg+:�K V� A to S�6b&�_e *�1N�&� a�F� F�4:F.� %��';D�,*�aA,�g�LF�B6+�M"�6* I&,JB�. V��oT��9�>pX�nR�+W�,analy�,A\zf��-A a-denmd,&.,�%�*Fnzc;,c Eqs.m�Jb2&m"% � � n>[*0 fun�YiDE*B2'>s $AfI18Jq �2 0\�W�6P}a3�$ }a.[1 $�P_S = ^� ,n� g I0.  FL#� \K SH,� elinSB 2c} � �~< }!��7 �e9&#Q00� HEo}) P=~(SU C�ifi��W>�,"I"�RhA�ab& ��sWJF>YMl"�A�C�".�"1�� 2}>�),� S$, ]not? 3J�c>� 8) necessarily. ���0�]V�@�3 rQ^~ (,OS�aQ$�Fu9D ad# ^2� "d�~/ �E)-�2a�ZI 3N9�#%Z-it�>� o�F a�./ ham>/ qF of E�$M�.�)�-uQ��(70} (j\ *(E�s))�!(X�(_0� )=� (s� � s�7S.] �%�%� �~8n,�:ce�i�e�ID !) $�� a  = ^0rfw�2a�, -7� t� y B.W (.T �@� )�15_0.7-�<A^0*6 sfnD3H_0=E=b� ��>� %�)^�V�"7.�Dl !).� - dH�)� w#z� But,� $A� �`er�C� .lK.(�.�\�.B{�j �5�0��\Long�$�A �� �� P} 0�i��K�� �_ .8"9�9:P*� X���2For:�W6���"s��C� ��*�c a*�c�V�0P}=&��3 _0=F�pI..!Fg _0\ XO6s�(edJ I]_q. &c%%Aaddendum�to�v�/a?^ ^�*��K> �%5nQ*�B��  ,6�� onB�.@:�B\:�, b2F� cl�)J��us F��-� 9_}%`�T] �/� a�i�:RRɕ#-M6Er�a�*���=\KH3xa_� �\K�: �P FLU�2�>3I&�n}-i!gJ��c\/2J�\blR.pTo"assum� �9s�=8 s�6�"� n�b b�a)xe �#1]�)2�a� pS/3r&�3*e3�3  FL*\ to P- a3restriYy��to $S$ &EA$Y P%o�S�  Sc If $#psi� \rk*^$s) S}{\s ��}Wt�H�\&6]B}EEQ$ ! Zt%U��a2�Z �Oo\dF�PF�P.EA �&:�"� r�M�!��P$,�jK_P:!KS)K% &>66* 5[��r�:^� �� � _0}$�AF�aY(1qI Fo�:�y�:2��)iS �E�=teq�Q$ "� 2�6�� s '� � Dm:=M6 >�G* �6"�Ge�� L�� ��3�� 20,66MU0*��| &�&VAg;�)^8!�1��z \rk}}5,6*�;0�LL2)~:oBm-12,4O)r�j�5K5B�5N,F_BkJ�9� �5,5]^ �Js\\ �S-49Q�-M.-�&�1�37�32-e&�= 70,-�)7��765E@271O150.p� �3� 83,1){1!� �1;MV�_A� <�1>�*>> -* ]2E510F� &�PPA�>?F�23�(�Y!�FL��2.$135,25�*!F!� �%�%FF�� J� 80,52�!A3y'%Su$-24,62�zP5��037]I7 27,3!�-��)�652*�PsE1�G!58]�� Y� 855B��?BB�1>3��1 ! { � �"-��4R�& ���+��fin �x} �n�� denot~ ny e.�n >,&�* � �3�nm .�� �E^ YK}Vb�wan0} K.�*2y. 6 Y ��..>r BO)\noJQT$�'=j��^ �� t:=8j� A�SB j_P 0A��E�� % $? >�_6�s�)�!^�n+"�!1���an�0�!�(�/= (� t� )�",s^� 6:,&�7 �M� .�) B�\ � 2e }�|� *�"t@d!�\ %N�7_0&I 'b)2�:Z*�%!-)�:\, = 3,f`XAI_)x-%I�:16n,.!��.- an2}�a"�A:���m@bedding,QDmA� �II�� �=-$. P!8\ ��Q Agq {;p=\E�4a^ �h :�.����Mn;a N&JNr� ,KaM"�asoning&��R:�!�S$�>� ~� &� >�7a"� B�X�.�*q<&� Bq 6�Am&(*nalogo�:�I8�P6�ev�x�mA*�!tg�� %� % AB�!�!��K'Tdw, we %"@2-_$characteri:�K��N%Q: % % ��:��%EM�&�>*+d-D6 ��s %(i.e.�B*�*) %��"�!�"d<"�( &! ��PU�ɣE� 0$: %$$ % $`:=\I>l�E�� %) & 9� 14 % %Bear!�9in'N*=�$of ��' )!d %I�! 6i�_0$ %to 9zEo$.�1� �="} �-,�+��JQ eqna�7 *} %Y -&=�(�}M){>U& %X}_o& m0{6:49� 8 %�� � D$ %\\ &=& %-�V'= "p:I=BIpIVM :3 %E.1�nAc�Ru�&y '^*2�  [ nusE�u %A9ramOUsM�A%�L1��,1�pi ^� 9 %� 15*�.� ��F�.� 86.` "� G96VQ$}!/put� Y g  [ae� %&.$-%�V��>� � 32,8*SA* 93F^*�0�# )�/r�)1182&Phe> 7F � <586� ; �_��0.�62� � :6  �rk�%o67%"J/ ::�^3,-2)� [A8!dB-.$d552�-2!� D�=� @�{3{ ?732` 8Qi�Q4 A"AEii%�  lgomportO^�VoA���� bi�*co�F ���:7\� �I}:P I�# �)d�%�7�)��ita a� (i� I})$|~Q{L ��@�w.�&��$PuOb,e�#� ^�, togW�g� �},: �" bwYS"�S "Mi.E) � p� *{Ac�� ledg/6�U We a�cAnanci�)�vr1q{�VMinisg o de Cie'� y Tecnolog\'\i a}, BFM2002-03493%�A$Re\-search���YD PGIDT01PXI20704PR![Xuntab$Gali\-cia.�Lthank Mr. Jeff Palme%@B�ista!+in�-p�yEng`�E iomanusl[.!)�FHthebibliography}{99m2bib� D{aw1} A. Awane: ``�s&�gst��ures'', %68J. Math. Phys.}��L33} (1992) 4046-4052� h2:h G$-spacesK s homog\`en6t Geom6t1 t$4) 139-1576r3r$, M. Goze:)�PfaffA`q" >��kT}. Kluwer Academic Pub!}er�:$Dordrecht �e0�*-[*JZ( C. Batlle,!?Gomis M. Po<4N. Rom\'an-Roy!�Equ/ce ."\*�*W R, [���s6^ed�v�27%�,86) 2953-2962��CL-92} J.F. Cari\~nena, C. L\'opez: ``The time J,�chigher-�4�.X��)�Ajod6�7} Mh 2447-2468.�$cgt} R. S.�lrk, D.S!�el!V�pgeometr� aI, �g U�'' � Tensor (NY)M�24%. 72) 243-26�CMC!*$ Cort\'es,�Ma \i nez, %FXntrijn: ``Skinner-Rusk�[roa�9o%N-depekem�m5�e�! t. A �300} A��50-252),bar4} A. Echyr{��}a-En qu�)� {o}p!��ar\'{i}n-Solano, M.C. Mu\~{n}oz-Lecanda, Q�{a}U�Y�-.�`�6�ZA* �� y''.YB45}(1)e�$4) 360-380.�Z�� R� �� `Qc.( �P K}&r^zc.� ase\ sPL ]?ns5 Acta Appl��-�7a 2003) 1-42e} H.!� liopoulosa9Ze�^esqueq ~ Ferrario,�� Passerini�y"C_�%xaQof mo!LAV ��ed �m�:AOre݇�]!=�] `I�em�J.mA: � Gen�3��,0) 5061-5081.��_ J!� Garca� a, J��R/`�E`�s�B���� Int.�Mod�?�2�, 15}(29)�/(0) 4681-4722�XSarda2} G. Giachetta, LA��=$rotti, G. )nashvily�pNew*Ҍ�.�MethodeEZN 0y}, World SciAlf��U.,Ňgaporey72|�1­��CoA� �� aAI16.�5_Y�Z�32}(32) �09) 6629--66422$c, X. Gr\`acia*!�A&t3edѻ�qramework�,-#J�i� DiffA�A �6q�e~$92) 223-242@ &b�� �{a}F�O!�N�3c]tingn�&� ��Le��.� %LL17}(3)(1989) 175--182�GP�brG1�� ap�_ٔ qYtrans�%�J�N�5i�,2) 6357-6369:�00n�S+v� s: sgb�Nct� �#��L�'~�)R3�42001) 3047-3072Qgrif1�� Grifo �0� �/-4 e et)�xions I� Ann�(st. FourierQ}I~? 87-334.,k �IQR��91-332 gun�xG\"{u}n�a�� poly�(.VE2�w� �(�<ory���]uN�dE\ I:���X ԑ� J. a�e�il 1?�; 87) 23-53.=HKa-82} K. Kamimura,_ J^ �� aine6�i�C*�7ed cav�1�0 Nuovo Cim. B �69�d82) 33-52�$Kana} I. V�8natchikov: ``CgU���6hS2^�4!�mo  um phase c� Rep.J_41? ��8) 49--92 kleine K A EZ %�el. et m can6v{a  IJ 1i  -122# LMM-z } M.B Le\'on, Js arrero� *Z 'Diego�A new �=et��!�>N�Jg�"z� Quan!ZI�m }�n� C�t � bf 59}, �of �� , Po>*" , Warsawa~ 89-202:mt1.,{o}n, I. M\' z�  Salgad� $p$-�)� &� �,Rend. Circ!Bt� 8lermo} Serie II�� XXXVIII�$8), 282-292�mt2�.�{e}ndF�1G%vp$- � �RY�i�Wv�D0 $p^1$-ve\-loW\-�T5�% %v Hungar�;58}(1-2)I1) 45:�modBp(; Eugenio M{ o, JosE�� OubiLa, Paulo Rodrigues, s s�,9�.5�g$k$-co�] C���B~9}(2)q�876--892modB�F� :�f��=�� ��FE:��42}(5q ,1) 2092--2106Sor�MorimotE�Lifa�AtypE te��� �}�FangUK $p^rA7loc�EF( Nagoya Q%`JQ/4H 1970g-32 f�9F�nteanu� M. Rey>��:�M'L �in :�)Fy: ��map%pr�3�U�J.�\� } {bf-_730--1752�8McN} M. McLean;� (K. Norris: & %R ��|x }��hchouten-Nijenhuis Brackets.6�6g 38��97��694-276mNo5} L..:�algebraAho1e�">L&�M.B.�)� � 42 e1), no. a 4827--4842�o}�p(Pugliese, A�pVin�d= "�9~f"g*�����Je�-�3` 2035-55,GP��b��(Discontinuo�Fra$b  =!� K"%s q��f�O1�O309-322B Sd-95:�.�.�F~/ Field 8ory�qt S-���>�52�s�2� ,@� ^��ys. I.F<"�pL,�xa� TQ$�(.w)� 24}(1!:41983) 2589--256� Tu-76} WAk Tulczyjew� Les sous-� e� lM�enstet la di��_hթ�C.R&5� ris � t 283AY76'-1��&t:�  docu } ��&&�&N�BIBLIOGRAFIA POR ORDEN DE CITACION%+vI�,+> :��m�m�m�9�9�9�9�9�9:9���������g����� �� �� �� �� j� ����������������� �Y�Y�Y�Y�YFY�� �� R� ������������ %11 "t'����.�%12.��������������N����JG'�*��b�<)�<)�<)F<)� V����r���)��)��)��"��"��"�>�>J>�#�a'�a'�a'�a'�a'�a'.a'��$��$��$� ��J�v�6� .�4=!n���+��+��+��+�'��*� �J\�#[12pt]{�Uln�def\pd"��} be{�8efG ee{�>bea3�@3a49�$} 05.09.04>c�("�QLarge}�%Implicit"+CX�-Lo�+ z in50��linear*70revisiMf� _�m%�0.5P�.�David B. Fairlie $\footnote{e-mail: $. !D@durham.ac.uk}$ }2Z3ZDB:t�!�$ ematL+_1 ces,�O  LabodS��.!Uni$3tG7D�2!  DH1 3LE,�:and��A�1t 9.U�ab�0ct} A H:��&h�� nish�C�� so-calt� �al� ".`, or B�8 ed Hessia�]h+=da�Lt�st�]far back 1935QD(te{chaundy}]=!�ved�C d*$�wmXqlat�;m���. A M4ansatzo!aN��"e|>�hpaZal �5"(.q,s��eviouslybB%6D wide1 lica�+ �fai�&&heT%-[C �u �is\y$" s evet!� �wav&�c;&A 5� "��Int���'$} Some yea��go,Qn�5� aj�sR�A7MEVadmit() inU�e numkof in"�>t*�$s-$ gov}������. S!�5{ �!e�.s_9al��s;3 d&��aD!��o �W~�V% ${eis�dr m�4g(lyHa*Fs'-�tot��a�=aP�F– dbfint}, ]H \[�MD}{dt}WD v �  \pd} + &(\cdot\nabla  8 0.\]Ŭ��"4A�ketche���z��H[�yX illu�� ��.�1�a two)H��2��.�Pu(t,x,y)�A $vre"~�.A'teD�a]le"�h-� Le �_�hoa��m�*��^f�q�E`prosa�$ly�2lI�b:;;�EQ��t�M|�z�CY"70&AG_t x y�g. {tt} !{tx y}\\N.�OC Z9xCxC6/yhyhx yy�� �c QN|E�0.K bat3 ,9�l!�a"ީm�ihgo��!�Batema&�8;aphi% x^2 -2 � tx+ ��t^2 �\] ab�D)�ţisk�i�govƨ6՗� �����*:�RQ�by�E�;�a* arbitraryU�)I�,$; say $f_1(�q3f_2T�"�i\[t/+x*� 1.\]�( iBH�-up�3�I�B�(&�?upz-woN�6fexpec�(pMon��))PeB�.)6ubiqu�8��Xa�8M��FQ�%�!�H6FMe1)�e:rN 27Y?�O.�Gtur]u�.at!zh �(�F h�FF�z� time,i� |0 mayb�u� r��ignor�E1�mGovaerc d I found.�ƚ:"�9"x:si�5 � fab}EC�n unp�D&s +similarE� !G��0e Monge-Amp\`R1�!Z p lezn�The�A�m�=� 1YͿlD8%+e��QthirdAxA�QU�ihr_i��Q �b� m��pur��"is paperA��I! cise��g2gottenM��1!wa��l�/)�Zma��DwoY_al� R��/�K7 ^f sW 2� 1�. & Two >/s-��z}�E�� ek��est�beya�of�P��occur�3J�4y |$ $(u,\ v)$Aonei!E99"s.�JM/��y�X s (a_a^sNed af E�)EG&K� � � u}"= t}�Puj"x}+ vj y},��one6 :-v�o."No. y}two"� Thes& s� B��2Ae�9  u��< F(x-ut,y-vt);\ v G \]��"_ A�Lfu;s s, $F,\ G�ec�� faA��is�zya�verify;�{A�abtAƅ�٥v�nrivEEto  �n"� [�FvarvD�� stea�L thinVX�U�a*nt�6 E, $(t,\ x,\ yv|ink iYregar�X $( (Y5* st,u,v)�j�q�!�� �are*6 Q:|6�S !2�\ x2�:yv}-:.;vn; t}}{j<un<�wu}},\no��6�.!x� 6&6����~�y%�1�6�6����� �p2)U} �t~Y� a��e $v$.,��a��Pr�d.1�P� ��, � �M)�|om*��uVleft(jK t}-u� ):&6;-RJ.$ t}-vVJ6�&=&0,2��� �u���u�.�>�:�,%�a  triv�� ��} ���f(�<,\\\ �� gA\6 y\hE-Ot�kAKg(m nV]�e"m nn$]eTme�};�Q7�E�i�=F�\dn�Qed x_1}� -u_1��22& �s2"n"n�X u_2}24 V &fT Rv��& \d  ��2rnZr�R�u_6 �Z�_Q� det} Q�QG6�TF~�s�sr �B% %y��R�6�- ^\�b:1.�y�AB�H!U$ A$a��QBwA "4 . If $ug�$vr&��"� argu^\Yt)$Hn you9G perm\?� �mE-~.�x>X 6M %�j@yn@x}is�ds �A�b����$M}I�z<N � �+be�',l�:�-�]�t}+j�-: &%xBA.E-vAya70��em<ing�elim��Qy>Yj=��&��!u2� ū�/al^2|.�W {�'�<\}���pfou�Rt!�"X , $E�,u)�@wd�� $F_i,\ i= 1\� 4.$ Actu��Akth"" ay�Cnd"aQmay�Ztak�s 1�s.]aksub4?!$ Xllo#c"~>sH a tF+,u)+xF( yF_3�&=&F_4�X cho1��tQ \u}2UJ�fJ.wJ�ch� \eea��EQU�lresܣkparam�R fW>�planes��2�[!Bs, �M��I�eT$u.�en�p�t�jhVC]�OonI��U^R�azTen-^��Etic�7��nn� {� %��e`h%@E9e�e��"ou� Km, ( p��h&n�*see���c� to m�l-N�!:t� V�u j {q2 ��L"banf6N �MaD }.X; B�!H�Y a\mu5Y� Fp ��+Y� F Y� F_3�Nd �p42.j&�lambda6~^26�^2.�� R��^2� �;2� �yp�2.�a�� %0 x_t�i�-)0mu}" � }&= (� %� -2 =)#1<9t-�~_t)^21'2U 2u}u_t�,J*�2r~x2=o� �x~�x �>m �vsD�y� altern�,2�W�$�l@ }KA� J.8 x$ r�!re.I A�!� }9Y dT 3"{ .- J.t}\] etzHubsI��h�2�:a� ele � a�column�x�Ksho�p#���K!es*{�reE� ��v�rV��of��is��,� ano�Rinvol�H���a�k�D��bJ�Yquibg�B�o aV�4 . "�Li�`a"2T�UsW �F �#employ� ��b}����b� >""�� �learly)Cu�,^�R flav{ ��twistb��.z� n�� 1;�Gb�rus�_ (�U & (\xi_{\alpha9m x_n}+��\beta+�{n-�q1}1�M E}}_��{�v"�uk}c��%7�du� bi�co-&��$�_in 1,\n ,d>#a"_ $w(�% -�� ��(x_1,x_2 @x_d)+ 21,8 d)= &x_1 1+x_2 2+z ;d.�xi_i=��-\over�q x_i}�   w5 (& \forall{i�>�� To e����m�.��(ij�n&�.$w$ �$�pHF i5y� �( ma�es; $�h,\ W��x��W��_ ��� $w_{� j}=w $��!iv��a�n�dA��l�inv��blUq8Phi W=1\!\!1$ |T!��Ppd\sp�"5Sx_i)x$j}= ( W\spD�)�)�::�9 � (x2=� �eff�W �bu�E�"h&��#e)�)i"S�fnew&{ e�"� 8s�plE� i� i,j}�)ti�A�^2 w} �.��y�3a�e a��Qh���w���&Q% �m�:�$w=�#xi_& d)+�#:$�$f_Ms2�feneDMt~w�t zeroI�f_1EN�>onD��*&:�ef| � w$.�)L\ �����s�<$5 1D��� J�=!� x_j>j-f� I�aV�.�y {usefu�/ee�procedD*� used�#� f��>�%.�e Not� � y))9�at�E��"� �qI֡]UWie�u ifA?1=0�y�(�degreeIMiM)Yg�(s. How does tA�"� %�e!#"~?�if�-� $w�Rre�2��$�ށ� ,=\,y� f_0�!�i&�� ��M��plD�by\esum��v���!�qaVN9�A��f_1S !�6� �S. '"�(hom�g� cru�k/R� a=��! $Qu �"s��a� $d-1��-�@R�,2�T, \[�jm�xi�hi,u_k)@ \ k=�� d-2A?�b ,y��me/.I��),&�,�]1�9!��,n� P ;q,A a%~_ju�0�i) &=&�X �i:�j�#SE!*�& � �IF�>� h$preT%li�u�!wU�bs�)ts���%��'�1r�! $u_k�� et, F��U�/V�)e*�%i{i]orB�,.&< ��&} A�R"'�%�b�`����.�yC-C /� aPH � io�+be.5���%|a��_jQ�u?mai>I�f �"{)�( ( cl��*�&>limoblem���er6S; ] h��s�n.�x� E�m3 n$, ��� (x_iw+��sW-�ly%c $x_n�$ z = z(x_ja�j2W-1$ �+d"X1S zvQ )E�#�n+1(6Z�.} 0�!��_" N>j*�^266!��a2�� eqivF�!�.}th���B%�� \ �  x_3)�U��h�>�*bS �DB@U'x_1G_1 G_2 3G_3 -G_4 2�1�)7u}%&=X FeJvJ �-Jone�:(vv�b�b�2�two7� �'� ea '0calculate secxond derivatives of $\phi$, \be  p_{x_ix_j}\,=\, \frac{\pd G_i} u}u%j}+Jv}vJj2:i6:  :�^i}\label{three} \ee as a consequence of (\ref{one1}) and (\ref{two1}). From this representation�the sec6 X it is easy to see that-Hessian t8ma}) vanishes, |Rprincipl��tructscan be[!GAiE+T(x_1,x_2,x_3)+G_4(u,v)%�so if $ =0$,�nMr!m homo�ouE�\weight one, a well known9(which makesL5�)�. \se%t<{The linear wave584} Surprisingly�6!\ in $n$ space dimensionsm"q ^2 uI�t^2}-:(n}J)x_i^2} %<0M� �M�!�yields!�a�in term%%Ak 6 ansatz%�$ tF_0(u) +B� x_iF_i(u)y1 yans v wherA|e coefficients are arbitrary fun%W�$!�8$. Denoting $t$A{$x_-�:Rbecomes�-) \left(I^jE8j=n} x_jF''_j\rA ) &F_0^2- ,k, k=n}F_k^2 ( } {\2Q0}^QPO ^3} ��2 0F'_0F_0 ]�F'_jF8}�^2�40,e�pre�d!*A�Hs usual, differentii�,with respect!�!�8argument $u$. T2� will�TDsatisfied provided;9�$F_j$%� subj^e!�nstrain� F(u)Vn!q�0. YG2IHT�- such�� Ua�necessAGmay���fro��e obser��on�ra�lI�I��! universalu�I�Tform invariant under a5 al changeaII� or!WNdo�� ot posses�iis!_8perty. In fact,���$s obtaineda ��method e�)�y3 nulli! vector idAtye I�i%�v�e x_0}M�J b5i5F�3)�A�a�thus �!j mostB� . However ���2�-�����!�(a superposiŻofI)9=b�vok�N addi�aA�U0to��s; eg!�2+1�� we�take $E�0 =)_<1}{f^{-1}(u)},\ 1R,\cos(\theta)*2V*sin*$. Then %�4u\,= f(x_0+x_1.Q +x_2.7, imc sol1)�iA�$e standard5!!62�,a anJ� $f$,af�LyI�$depend upo��$uyB�i]�%�E�%� tegr��over $L�WW} ��Conclu�`}!+1�i�,p ��), ��shtoa��� a� frameworkA seeET2: partial.�.RA�e ordA�eve cludQ��c� featur� !�U� stud���e%�aS yesallB� Z(Lo�z) trans��%U�din)��!��bl� bu`isma�es� �)�fai} A��?,math,amssymb�zG[all]{xy63color) copy� � lce{2005}{9}{0}{25} %% year, aWDme, first page, la A+(setcounter{B0 \def\rref#1{�#1})} % ef{##}#be{\bź�c} Lbeq^e!�>4ee{RbeaLnarrayge L6b360a c., \Ga {\Gamma � \sig { um {"� 2 � \ba�et:K alphgg] \th{� m$\la{\lambd(ep{\epsilon1�hIR{{\hbox{{\rm I}\kern-.2em  R}}}1Z�1Z.1C�1C1%� IZ{\A� bb{Z- �RCC�I�mImIEIYtr) tr}a I�q�title[CQ# conn�s]� � t.,\\ q��(holonomies � \\� Goldm>rackefarxurl{! x-ph/0412007} \author[J.\ E.~Nel��Hand R.\ F.~Picken]{2!${}^1� 2'2$Vdd�0{1$ Di= �!Ho di Fisica Teorica"A (it\`a degli�O,Torino\\�DIstituto Nazionale# O,Nucleare, Se ?h via Pietro Giuria 1, 10125 d`, Italy\\ \vskip 0.3cm {n%<@to.infn.it}\\ .$ �2$ De�a �eem\'{a}�0�4CAMGSD - \\ Ce�  de An&lis>5W � ia e Si J>26jE3zV$\L�"$&vdiscuss&� ety!Fpoi50of view, e.g.�"�raced.�in �NRZ,NR})��4he �yY6themsel� @@P1,NP2}. For furtV a�A�nd + car}�{Rmpari�(ej!cse�--�0 ADM approachHCN}. a�previou�ticles6�,NP3}�h� ($SL(2,\IR)$1y u,$U_1,\, U_2$!\�diago?a� �^ U�lG�e l{clcr}e^{{r_i}}& 0 \\0& e^{- I�� T4 \quad i=1,2 M�hol� �yn� �as��m@�J i� � along cy%$\ga_1, 2$|gg�eFT^torus,:� �Ya�% � _1\cdot 2. 1�.2={\II}.��g ee On"�reasons!~%�y��5�-B � %:�FA$ir gauge-&�(n� ized�� $~ T�\pm}= Tr Ui� $T�6"2^$A���2B^� ine�(ous guises3� Q�ux�i��iFm�A�y2� non--�2ar PoisaZ�  algebra)�{�,�\}=\mpqsqrt {-\��,}}{4}(T_{12} �- 9+C),1�b ee ��mn �m$ refer�adtwo copA�(real�)*f)!� $� SL}u�in @,isomorphism &O&2)\cong>9\o�>$� !��Q (UU1�)$ cor;on9�8�Feumm>L#Fa�r͜ numb�-1$� a�FI�$+2$ (we��um�NR betw�P_M�isX.) F.of  b7})Q re� ed f $ly as \foo�e � 0meters $r_{1,QF$ u�����`cal�a �or� $\um-!oe�mP1,�}��q A�\pmA cosh r_1, \�iA� !2 ! M�$= D( E+r ,) =cc6��qI� >� �A�$, global, A|-]� (:: term�))18wz ,��!�,2:�sm� �, ���,��%&\{1�+, -\}= 0��pb� Altern* � EGs $!��!nd�1rI� Wi0as}Q��toE�>�D``shifA�j � '' $� w{}� ��ropri��>e  < 0$QIM� def!� by6�third �ʙ$R"d5�)��� a��$(5 )^2+(A�% O)^2 - 2 E�#,M�=�A followw$Mandelstam"��S ���j%�u�%s b $.�e F_a'omega!l a8�D {- \�D ~e , �'gamE? !� suit�triads $0�� spin*�s�o=ͷ1}{2}L^{abc} & _{bc� ,b,c=0,1,��e N@F�!2! r� I�B�,�N%�$� c�� directly9��- &�� CN},�.�"w �same}:K��q�$�!e� icit� ;$hip�� bNM)� (r_i �()^2= \Delta{}^a~B0b~\eta_{ab},\�!�%1,2�2�  = {�8 } (-1,+) % 8((-,+,+)Q rdel��ee�L�� B�a!�int_{��i}�mm}�(a)&W T# We�!�a�Pe Einstein--Hilbert a�A�(2+1)-2#� �[I_�8\scriptsize \itU}} �]int\- (dI�A�}-{ (a}_d \wedge {db8$$\m9{3} e^a * e^b) c\,Q�!�c} , \��]쵮 ein}![("(x���(up�m a toZd"�))B�&s s �Re/! v, = I^+ - I^-1� ein+)�&G II�%G�&ae�)S (d� '}_a - *1!46^b:c69):a5I-� = - �h\�^2Yfe��� E� � * �#�ߩ�pb}E)c!$commutator�� q [\A��� �]a "� i\hbar �| �� �e�M� +O -Q���%� q It�es�� �!4 �)�l!���XA� Y}=Y "[ �X �Y ]},Q$bch�0 valid when $F1$��a $c$--M .$m�now�q�}&F $ � U}_i� $ ��1� =by bot*��#�%!� m" plic�I}}e�!)!�ion��%&{y+[+ = q^ 1N2E���,��)<ht$ q=\exp (-I� {i aR:��q Ei.e. a d�"Q�clU��� 68�1�ga�cim�A�-�4 )8e (-��P1}).mfum9�in)���}o�u upper--Zngularja`1�ingG�\"�I�}.� �du� We��iin�#�^�i�C� n2&�(t*E� A�}"�*Wor&.s,��examplee ֥|;he!�!�- er� of jus- Sv3}�ac4= 7� U) moduli�,ise�)�M*|��be siaeaneously!Ijugk  in.�(co �l!(Y-b)Y x $S\in *!):ō U_i=�2i�� � J�\��Z =< 1��R .�e�y+on �E� & $F=+1$, $> $, e�2 su1�con<*!!#$pair $(I,I  A!��%��.N!fla2XEh�'u�-� wa�*oo0mik:pi� namely!� mean "iy0� A=�, dx + r_2 dy��Z� 1"�-1!Ond��&� j!�� $x,y�,,coordinates,i�period!�?,e/'V H{\IR^2}_{(x,y)}/\IZ��$r��$r� g1feQ#Now�0y��5a� �� $x#:$=A!ݕ�&�des� ������)~!#e) .3isa�pl��a3��h� "� A^�V9 iAb@E�"� h"�*�isB�^�choic�*ill)ows s  residuq0auge freedom,�.c� $a A' & = &�^�0&A�\\E�J (d+An�~F \no� �-�161 A� resgf}aDeea*,)'equival�:�A$. So��-ANi+/6-��(6�>ar��($���to�of8'� $( -< ,2)$��&�con��35I+�5 ntir��in agree� RA?՟.o�4z. By�-�Z$ r` ,>$� mu�)&\E "� �% $"D � &� Teh� f*H�i��co2tenes�.n"�t���M e �d �(��Y &��� %�s�3e "a�Wi� fash��by �!B�a�( p�, ^t2!� #-G�� s $Ad }"�"�  �la"f ɀ�$"�  dyy j1�H!u$+iG�W $2 \ s 2$�c�#\be Y.n8�! �&\betauz Jn"g =��T3 whos�2�l e"AlQ�$ts �5|� v= 0$ aA;�T^E��e�paper�investi� !�)��x-�!� goli� pla"FE �DaL �s. �4Ss{;sec�)�E+a@%�%�:�&�fpiecew2%<$(PL) paths"' SAj!�� $, �WaV�A=$$� ,� .show ��v�:�# ��`�� ��#�'�0 ] �#$.� O� >I4�mis. 7 U�A�N:�U�surfaceM�6Jo >o5�!�`ar C*�}(E�ion�$inB�6Tus�PL:�!�>�3} to�%���.rerou7?ndIa��:� . \nont � ion{ um.�N%��%�wE�}�"� B�M�m\Nx]�\���, exten?� J�s 1\mapsto� ,\,P2 2$�lI����Z�ij1}!�d"� �, i. e.: $��a 6�on?to�e $(+)$%\��� E4:. Cu� !}�� �m/� $ goEF6e origa�(0,0)$ %ZY#erj% $(m,n�=, m,n\�IZ$. U�9!'� c� � =p�sei�� r���l%� on <� �� s $m*>� !wi)�� EH-�:/%�$�)�;Xiv�A��!B��� �� to each o �6%�if�c"!!g����$ end � same2a$ -:3�� �7!� Fig��� plexp}.&W6f(}[hbtp] \ce��\iF7"8p�0[h�?=2cm] G .eps,(cap! {Two�MB�6�F�} �{ � �2[ a\ $pH"nsist%�$N$�a�> segm�p_2�'*(���'to%A�E0!!p�7Bx3  p��p := \$ fCN )*<)>"7U4h�?�)ayobi)ly |�ve�"r2o�m �(s, $(p,p')� p\circ p'"E V������ I����h�`2��,:�*1^[%O!G)���:�UR�% ch})!�R� %HZ%qbe *�dA�&�DQ�-A& :e�AO�}EY s,t)q^{mt-ns.*U'uu�-�:P= �H:��!mr_1+nr_:!-N!�bmY";I��"�  5�.� �"� �� ed �Yr*� 6�+s,n+t)$E wo&�? wayK.o�.�n llel�> I� �&e�$%�$,&u ed g�>mb in 27artri&�^?1� forwe�oe6�!XDgleOP , 3�@i: \:�A]&(E')/2I*1Y$�4#�{"�0aF� ty $$"���.�X +���!['X*�l8 , $$ y�&2r aj�� 3� %&:2Par=�1{��sm�A�)'�!4�4 b!End{"� "K!��% I�expon,of��ing%jA�&w �V$�l�:!� {\em.�}2>4�  / -hand-� (l.h.s.)�=P 2'$ 3E .3r 3 ceq#m��q�.��CenbPL_ �)� ��p$-���rse 'n or�ed an�1ock�#� minu)_~�gU cQ� .WE �6 V� is "M $\detf� m& s\\n& $A8a.'2 =e�$ A��U� by $�0m�$a#�&w�1!Eb"�Hv �wD0�M-lng PL�s2� .f�� E>7�y � %[�woEms�6{ *[s�GA��J , eiq / P6alw,orUE[ �Gde,EhaE3g . TogeF�y b��a �eGAo reg� !��$xy$-JDw;� )�ul��@�4c�)C-!=|�olati�8w� Ka�!y,\,7 �sen!91#%& �]� 6i!Qde up,one or more v(j-2���!8ll�B�20a�b�s4IlyuCJ�th�3%k�Kisp�:�;-$ . Sid�!$"b �N�8� logo�4. beca $H_3"�%�!trivi�/�i�4unique $2$-cha c� $7J%s$\���F $=p-p'$. Le_is <be  byh /�PH(! R}n_ t "� 2O�M� $$� a�a%6��x�M$ da�!�  set $R$ $�\�pm 1$a\$0$A��$� hAC7 m1u2en���A ��ca\ � �4supporU�9� �%|A�co"-P�any�!�q&a�:�a~�5B. �nb�;�eQiG$m}V� zs_�T_ �� Y5 Y6!how� zha)O�P9mR!Fin�)horiz�#� 67�%5��#A�t� Fv�%c.D z�JveD-1��2G�%�whi5E s do  bn�9e.�y �3� =0$.�gin' [��4� 9�:� 9�5�"� :}:� �:�)�f] 2�� } S�7aBF� qb A(q�&@7spp�--$$e�AGA{A� Q��. ��� lear�UdfMc ���"of Dݸ��B�q�"� sum �y��Z V]�ŭ�I��F;���J:�Hem; "r� as abov)�x �� on�4ds}: \[ U_p =o-�}. \] ,Sis Sen*�. ^�� ɷ��c�Cruct a "D?!���X �)�Xcollap�or�Png��-1le at�&ime. Re�*� %z � QP�@; :) $q ��h _*or-=� wo�?�S7 ű�XYis $q^{uqhi 6�!��!�wo6o�T�q ov=Rl �, after!zcel)s,�*�51*務M,. %\hfill\b3  %\vs|L{0.2cm} �)28# �Sof�ofareminis�Attal'7 mbin^.o "?to gerb�An|/(four-colourV blemiattmn*�R an a&�7!g? wlCto"� abel�ZStoYorem �nonabSt�-�>%�f�N�8ength \[ F=dA um A3�[r_1,�)] \II]#�2d@ ] !�W�s�K:]$. Although/ �st �is.=�Y ing,� �" utes"| a�i"��ich�rably�$plk&s�"J&@$ula�⍅ {$q$�<s*4C_/�"r� �Z-�Z&Me3 �%�+ $G$-� � �0a manifold $M��"��mN=| $\pi_1(M)�%S�'1 $G !@4"�' ce ( $.���"�-on- � � eNa$G)�v6�)) � $M$� a� ,�~h62�p�[as��.� 6� s}. BO �쥥F�)�Y� �is virtu� � �# , ap�_ %xrR�*��!ݭ��)); E�)6!H� "�sub |&�.. � $\O�9 TdLZ�3� :("�)�PL��$�rom.6a�tŀ�| 5y �R�" he p�CmX��$2�&�)y!��nP%`A�hiE��$p� .�of�M� �Y(p3a��"� �TizG` [1)] � \sim pi! LongVarrow_(p_1)�h 2)$ (��8$-�s ``iDm/$ to''KDk2k*]Np_2Q1)  +� 2�T��x'c�r.�M��� $AJ�/\u$�s � a �$)n�_�>�+��0 \[ b� l (p) �4�p�+\*�� + �) \%X ) \]_<$wE|q�ng.�$(S!p��%W��%u4]we �'" %�, -$P �y>��9JP#s >�$3.S;,{G}1�eNBg"�6�lT1atr' �!��5� $$2U� HA�2I$��� $a,b4 $. A�H$��}��6A�$  ~�i�m�\ha%'��J � ]U�i"1a"p_a�(tackrel{c}{ab}v� � _1,a[}�( %\FT1�m��EU toN2� A���Hp�%�� A�b$&!�8!�e^V[9'' ���Y wellA�A. FtSxif��NKZ $��"'9n3e� !� \�. 6�lcrZ@�1) k1q^� B��05�6+2,p_35�3.d" 4'"\} b��<�9S�Z!�)+ FW}9qdsgeqqbu�Gso �� = .�3)�3)"= I���s&�4 =p_1-p_3, \, ' =E�)��for&]Z (c+c')D$ � !�2/+6��9Fi&�%��9�a���G:��'stencMQ�s�3!w.� 2*�%�n&���O�( co�]%�, wri�$c=e{�� R*�$, $c'=N.n'_ >.� �B $c + Z@ ("W+ M)M m�gF�@�J<�$ewV�eu3q^J�VrA (u)2�4i�NIR- + Jt�.Yh\\ ga�i� + i� �e�N��le]'2.�%�a#2 V�4aS}�a�e�%�u�a�p_2-p_4T$d$M�"$"�"$3K A;�$�0�%. s�3�c�� �on2\%�Z8$p<�=>�2}�'� a�`(c+ d�p_1��- p_3p_4� B  !ht]��)4�a�2� 3}F 4: �\� "�-!ۡ���Y�����c) 2:�7I�ݵ�� A�4.�E4�E]�.C p_4H8�%<eq3��ѕ%���2!� ���9Qٞ`:�_ee"�#6�Z��Bc�AZ�AA\�DKQ ^���H 2 dRw�5lde{n}B�A�i&C� ��[36�Z(��+ g).�kanB�*��pE<%�Q�Jr.� \t:�2p? I�~I^�B%��jndU�*} �/��*�unaffec�!� ��`9analogy*�&�as�jEY�1 � P)[ A=(r_6I>C!x�!*��� ��h.� by:Aˁ&&��Qm�h).?�J� U�._p�sul3."2 (��6�D�X� 5'�.-,�=%��2�S�hv�4)D1�e F=8G8��]X4�5 r bei�d"Z�)MPB ar GY� sec5@�aq<e&(2J�5of5N�l6_!Z)ac!}!�3/by2{on, fix<kl[2� �5erFW lattx>ofa6$+@) Z� �3�a�,�!�s�lgh�/ "ot&�0(isMY{o5 of .��%Yx7of&z)I�of"* 0 Up} b@ M.�*U_{M.p,Iee (X��y-�� � apUUAin>n fundP+ -�7`EAVtp#wD#�i\:�i�0R�X!�set- $U_1J�- �-%� chec�=A*��gk�o�3.WH T� �>f+�1&0\\1&1F&, \�I Sn@ 0&-1A0FAz& �ce�5� �$�X,�� a T.! &=&  �.�Q*1,1)} -1K*�."m �62@%H@ ��26�@Su :u52i* i { 'i-1z/j1aA �A' eap*q�e�A_�;" Sa�f a�  W��JE�$!1$(.� >[G*�� Ua�e `Db@KW d&�a��m�%familiar�0 �}�@�KE!�&� T}{\to}8U_2Qs U!�u*%2���$a)e e�2�E�6kSk�h)�m�  � 2by&;,�lst�C5� ,-�b�+$S^a� -\II, S^4ar (ST)^3 $,�+ a]Yf#��_ ]�6,�Y +FA�E� =q^{mI [pX-1}Xa�ome�' IP <G{Mꍵ -1,-_2EEsXAE�lNnE.U���o��E�'p�Kd. ��c{.� ?�+a F*?��B$*  r�7"��z4�T�Ric�1pN ES(M.Q )H  (M% .p).�0e*� �4� �~�i) uu wa�nc�,a (M_1.(M_2 gh�"r2�' �-�H+z,M * ).p)6 Z|M_28F*B� " �(!%a�O! lso�-�d��$��*��>!�a=�_1)6 �1���� &&G�', 2�C"��,�} Y _��[ $M��A�x[�!�$��t�) as�oex �y6�&9�I$Z.�G=�1) 2:�!+&MD \!O6_2Bf=&. `1�_2)�>% 29 G6�g �"ec6}}I'o �M"\^du�J B"�AED* xT(\ga)=Vtr}fa\gaR�<ly h�,Z�<(��E�U>% -��ais�� �$Thm. 3.14,5��HRemark (2), p. 284)Z5\{�_1), 2)\�R\TSp<=a harp <p�j��ga_2,S)( E1S ) - 2%�)&Egol�Q H!t�:k!0N$�n�+�]�al�U>L� pd�' M� � V�"m(�#�/�!2,Tp2k $S%a �g�b) ��1_�O��v��Aed}�&nlI�� �+ w!Cl (�.As cepA=�& h8[or�#� %� az "�/(O=h�"] i2� Ϳ ѿ Q:�6 ^s9be�iz�5 �G but ";#irms&�A��!�*�emE�/'�Odevelop p �Gef(3�%�4�G\+Pio�~Fu&hRe(t�/V red}}!��eto�c�QUD��``s�'' e�6B7*�by:3 �$�7!�A��(E�s&��3usefu,5j  ir r��a��"� domAD��� EsquA�gg-es �, �;�J� R#We0wG %!;&m -Wd&O21}E��09 � 1R rant"� A�' $�< $ it�A `�the2 L �"�"³NA21a�hs ) )v�A 21br 4"A��= �)�tsV-"� 2>�&�a!L�B162Tly E�~athua;A 61�Hf"�4)2� A�!��hhU�N-1,�#�S(1�}_)�)X $EV)�Ae1}:eK��G%2�-1�i� ���width)�12��22bf� �e�6{)y�m5���$ �=�E�VeB!n%�>a�!g�(�a1��# $�-1!El@�Ba!Z1!Z�CGF)Ww+thX (XE�NW�FW1qF 1�5<�� -1-1��2 ei�E.� 2�zZ.���22v��%$��->�>��& �3.5'2-��2-n�2��2F�WY']m,n] xNlQC�:an�_�� ath,�say��RE�ible}. O�!�: ! ir6>-24} AZ5(was&��p�#ndiKCr�.�Xa\�, m���2cm, uG3%�4�W24nw2,4mZ�v!$ ��KY�7{� s� intsK�?Y3�J : !5 � !�I  �H�(� ŕ!oiBo&~5q;�9< ~7&��� 6i "wM�i�1�I t�� nt v ���0�i��.� �I�bdy7A�)&ng�~ U��92�`;/2a�in A�j�( �>(�3EhD $P$ (or $P, Q, R$!/� one)i &I\�\,PO>� dR���i�u�.^�� b+!2��s,�,dJ��W�stM simple (!�|�so )&h ne y���C~-�6�s=%\v�3eЈ %\med�wѲenume�v� tem I)= 9�=tm�a �6fe(f=a'c  m�]�9. �4>�L�� ga1�  *�2"�A7J�� !�2�s,A6:�P>0M !�on6  $Q \um"i/@ �,!�AEk6�NA] /2$��3 �+� � �)=�� � 2�s, >� :�!,��s2s%�D2�f, �fQR ! !-)d)ɱ), :@-�_s�3r@%?-3$ EV $S=� "���ributC�3i�XA*(5 A $P$)��4)�B�&o )�& ��r� Z�1pER=J�%�~��a��+3��51AeJ#�q�2r��xb��t.p�7a�nb���_"h;@? �1�%�i\Anr3���"gG��# d#m��a @E�z�Q�Ef����=] %� p_2=�H$ 6�#n��O.!) \ep���%�O |\ba{�$m&n\\s&t\e(o! | = mt - K[det��d ov xu��~f� %��f�� va�Ht WQde��Z?�&�'�%,%)!&ep0)+(0�T(s t>��1,(0$+ >=R��FBV+"�<�-3�eas��d!e&��a�=/� >�.�Re�W-��W� &$w�rK#Z; nd le��$��  at, theyyF. " g�vE�{�ingb !�t P7dA�A�P� n�p_).��:e�/pX= (-s,-�Lf JQ��)��d�>5s: .�� base�� #W Dto��-Ctinue��$ ] �$)|/t��Cshm�$pP . NSD�h accorda�n�IrulPXYV.�فAD1� it�H� .1_� -n% !� � ing �@ �"� q�2�|!-qr$�@. w�r��{Q� (6� �6;A]N �Wou*]��%�sr% � �"j>q�`2,,�� =-�"X�f � cojh A��i.��p  W�%@ �![ �Fx* >*0CX�r� A.W : � (a)~B�[ 6���3p:  �n� 3p"�@ �& (b)~&� �%@ڢqʢq �n1� �%���1�]{4�34�3�  �  �%E��G41Gb�c)~V� �� �r��4rJ� 5=H6=2= z/1)�5��.7�5�BJ��v2���� �� M�E�^�޺� �QB� In���f�H���R�3-� �k ��; (m" V��5!(m-s,nU p * Go2�h �brac}}� -'�>�"�'QD�-�Es:� � $BN"Ta6e� T0 =U*?} +- -?>)� tMu�6D {\rm�#~~�+�|(,{i"p� 5! Umn}� �n,\�?$�.S�d�d-� P:�� pbCe>�~"� �?&a$�"&�I�� $�  %6�#��#W�#(� �#Q - TU)\{�@\"�pb?, "�4�:"�YZ[o F %7\ �2-QR A@ket-AR } (m�0o� calj$\�$d 1$���&�)T�sJh�# $�# A�1 "� aQ� Y0e,�%�Z~,� all�%ic�5j1�ut�p�$��;"q&Qt}ed2F#&b"�*�Dty& =�*� e e^68 e^{s4+ t|B�KM�.e^{�) $(LZ(��H)=sul�co�yE|[ATtTE|qy(�wf� jY -�(��. ) (T��Z6�"�7tw�[��tisym>,2=)E &�n̚ nt (�  h} � =T(-m,-n)� It1{��a7ommmn�!Jacobi"�y��6&W(,limit $q \toZs�z,to 0$ $$ \{,e�lim�}ar*0})A[,]}{�x}0'�$ �)�preciseloa�.?�!n5W�*�%^! F�2 Y� ts �J�cvLrV� Gi�2� R}�w`A;\readyQ�+"25�4)��� no �er�Khe  W7aDx`6�^�N�/o�v!� 4 ,3Ja l6�u��?� a"��PL � �-A�d%����,)e_T .,,)}msyfactori��� �'�a�gi1+A7�as)$27"�E�c���7!�$U�>��&X.�^C!�E�E �� ;��ip�*��US )�>�6M ���p "YIs  (  3�22/�)���*�  \C=� i�weT2i@ �%¡!: T6�!-3��� �3,3�-<=�!�U�. S�%~�L occur .�R, Q$(at�(, B�!�����#s%�eF.? p20a>sA2ly )t�V�j��Q�] llowtC4� a T(%P%�T()H2!" T)!� P}\\>R/)�q��:X 5R5Q 5C 6z!� Q7Qa[�"2Ba� �J!��-r#kT( k�I T)�vP-�R 4�F�P6R.6Q-7O7Q-�82��Ls6M5��$s��aQ}, R-�%�+Q-}L&I5�@(I/$R7 QA�LrhhX>�^A�,�e +* H (q� l"�b is d���[to �l6*�]alf unit� a��e�Vs= �P�2 P-}�Z�h)? e��E;&� �a� M� �_b trigs}��A�$ PY�� C�$+P3� -h� .X#��}[hbpz'. %!��vx:4K"1+�=N0*2)Se� �eSM�RQ$$S=P,R,Q$ &� A5�fi�,m>��_m�%3���11-,F�!!�B��.�q�&�YtE6�%B�!�%*:n%Bq-�4?�%�6�-��]�33 �C5e��16���b!�% �11B�AWaI# ׊ w�:nzVatu�m���hr�tr !�9q3[TE�,��i3I�}  �*-1)��SE�aC(q2 ��7)cqB � ]~g*Ol�,���Z��"\neq h� w7st�Z�%a~ [TCXm5� � Q94p&�3p54�"}3SI 2,Q)� 1)Lv) +%-�-��&�E! �� iz84G6�-�. . Tߨ0:%�ɭ O)�q�asw�at ;%Hm�/�$&�*��%b%+#/ a � �h@�tudo1.�!H!1�Qt@�(onKA,� �$ Ůy�9{A�p|�QoseEB� "[) "& �#Q$tn�= a� �4lle�=o<V9t&)� r a�F5��_= 5%�2�os�!U�roYa)4"�x.`��ja�&�!nd `(a��w��aaN�4 ed gin)1slso� ly p.�1�dKE��A\�][. Con�Y}%adjac��*��6�%�WAv�!~t-)2�s. �lai�� 6achV)=�"�$1$*�v ���X&� middl:� �:Ll� (�}�%aw"� �oasta !�� ��E}��  �e�Cl Q!8^ �2 6D�3"�"7�<7HW:#�"W3at6��s�M� ��p,�cu�C� na� �{բ��A5�r&�(2, :e|reglu)�e~&hUa>�>� T,Q (3,2 b4,3�Y!�&e/�1 �p%�ao~ata,%8�[k�< Pick'eT*�]Z��st���!�K$A(P)*Ta"xFpolyg�FPaT� & = I(P�eB(P)/��v�X i�UZ $-Am�)�^xG���Fe�{Fd $Z:4�l""h , (a%�q�E�� M �=0$�&e�!�s6}�re�#7 �=4*�!��"�)� Q��*%T8 = 0+4/2-1=1$.) �Qin"p56��&R\� Vj�%��� A= |�|�&� up�o�wsma�r�%0�kIJMby) �9 >!g!%� ��UB�A�Y�6� �a�he>/naf.e0 s ag�9�K9bof:@R� *� r� e�:� !�)8�N�%�1&p I� n&cT�=angS D e�9�;.����5!uQ�N�>%�e�%!i�o�.� , 9!�*� �i"z)Ρds-E3�f ��Cl=  }�� 4hZ s�V�>&  = "�h9:M&VLo$e���.�ri\[+ _1\,.$0)\| �) q^{AjT"c,&�M�e� ��a� 6�ft�%� t $Q�S6 �0Q =R$)9�PU \, Q�� �I}(�8-�UwAAAW�,�4*�� �n3=MR lysucces f"� | 9 �2�3, �|$�a��i �B�Q_{i-1lB��*e�!0$%��MV1.�� ��at,6U+%&� R� &� -1}-�  Q{. D�Kefteqn{jIVH}6I�C�-1)M�(1+ �+/~ +A�-(A-1)})Y� .MVL1-QA}} 1}}FVEeD� uR/max4q*/2.;"�ep2�2}e9�0�C�D�/%�m�Y- kic�ĩX Uw=N$q$ rab9��n �h�I�$>�xnow�|�#$A/a��7$A�s, P@A�Vd ^e���QQ�\.oFcNYeVJA6I}6JIfIa%�Ib1:a A-1}�mZ#2� D�\)�E�hR0n<]-�p&} Diagr$�%�lQ�R"���#d�� ���6��h � ~ H b6 *���ior6� +s opp�� ��$In�e��U�+wa�" 9�sHJq)� "m� iq2 �>�� -e�@ ��B1B�N a guide"b� [%�w�  N�u  *�,�0�42)2uiy *+0n?�"� � =�c.!�� ��in . o��i� &=-).M��p�i!3du�=  =c(m',n'�Q, c�J\��m', n'B��t��A#D ���.g�ula6>�Ms#��as3%A�=����� ab@nw m�<2�s cѫ"�G��n�= ��k"ss�!0),\, p�0�� W$�) erF� �M�:� J� >�I��6� (q^2��2����4�2} � +q^2�c3��)B���V� P  -�2�T% �6z�Tfi�sum4 &��L � $, $(1/2�9�k�AG $(3 &>� �:� �/y@ mO[I�2C� s "J!)i,,|�;y&Xm �S�usq�%%&i=-%$ = c(s',t'A!$ B*s', te*uAZ}35  UW nW ���>0� N�� ٯ� A%.&5 6a��� .1�).CR�@^{c(mt'-ns')}- 1):�@� \\ %��cX6� (1E�_b*O hU  %�2Y�X��U �:X�E�n�)2hai� $( B%�A/I�Fu<� AR�aqthe $-�$6�J�u�'l*� b���V s d���i"� ep-}i4+��Y�,tնa�� by� cmB05SA�E $. 6��&�8��1���  =f��s�3d~�68�7pG$- f "��1,1/2��\ �%S��!nj�2��qF�:�2)$��^2-+ ��^2Af#BcH 1) (��&��� +I^ �� B� \s�*on�fcv��8 sec7�8�&M_BVy emerg!��!�sBA;5*�^exh��sA"v�"��y'Q��Nl� 2L�&" Vfu{[acquir�R U�=>�� ��� O:'woEC# P p]8U�$o '&O< �r!����_2z � �*�u(&�<}�%goo��� lead� a natu��{�eptP$q��s �c&�`�exVFfl:Z�(lo�gXyX&�P g�^h-mN�s6)G$�Ln->RUU�7u)�F��$r �es�s�Ope���JEl' u͹E/ gerD��� �F ~\#�MP}zCe!=� R�XI�A�&'��+�^��a; 9}Np/d�T"# �KT�z;?E�7 �� =&�$� repl��bd�um_g:vDZV�6Z�|o%�@ס��+yIse� �?v"{*-�]*Q a2�= B@a|� �&rekic"���&t 4�2�� "�����* bs u��U!WY ː f� ubtl ictu�G��f'6 �9,westly *��"jxJ# � F� M�are.�S!\*�/ 0i�-�>%����Oi*�/I(h:�� l�.� �.W2�+ !�}, evD\oH �� ��"� two �2��yR���<. %*� @&t �.Ob3ei�&� ICE��AClec�u�j�z ) or 5BL�yH. BO2�2�� !=� tA#��-��� |��7A+sh�\�!rplay�Q!��Hd| arioIA�L� �^�4t��i.���10ty�tds�[S�s"�4�tuM)�I�m�B;��L "S�9�6O0s"2��ZŖ�Lh�zfor��mB|�#&`W. Tr��.p�L���0rb�� P� oJiM.a�a&�5 u��A"h,�out-Xf���A)9�-���'oss� n2 higherM�usb_s (ofyus $g$ ar�$*I�in\yi �Wame�p�E5�&[ 8a�Ta�4�W���X(a $4g$--gon�+z�-�y�M�ghi�On�X)a��B!�ono�P=���%�/UeC"6&ir beha��r��.�5 2 &F1!^he1B1$i�Y�apews�and� qu ���1��t�� else�� *��(style{my-h-' vier�Pb�t>*�10 � em�} J.E. z� , T. Regg�5�� A8){5�CN}� a/.� C:a�VIiz�["S�Q|MRev- D51}{�0�D95) 5643--5653. E&�E\isrVLe!{{�� B324�0994) 299--302� ��.��.j P�p9 ��m�;i�c(� $j�`�l%�th`aruja~��15--226.NMF�V.!�crief, I��%qpmoe!�conQ(nti-d�a�fA`eB-"P�al5� Int.W� Mod.EQ1�6}, 5%�7) 545!�2Hm�( A. Mikovic�2j S�,er Chern-Sim/�t��-%b��Ӄ%\�!Z Adv��orNi�vA`263.` W.M��@�v�K&�>on Lie��xH�itonY�fo�sM.��2resPMs, Inve!Oa�-G8� 1986) 263I��`=M{����S�%�G oric%��GA��G��OC"E�%GCu*�u���h-�203056,�/&�AnT�Ps Fond. Louis Broglie.�n7�B.da�]on�Sl�+��'A=A,�R ``ModQ�No��8ear Optics'', P2]<2, ed. M. W. Eva��PWiley, pp. 429--468, a=160y��(G�9, 4�VPl bf{P}^`.=Pp22sb�P��!� >3:bP.>:cI ���.ZbZq ZT>;Mb}{\�la�)2EM}>)lan5� gEV.fr r�T F!bw � sf{w>^bWW>c�(i up{\� {114B�bVCV>Cb=}p \Dec���mOpek�8{\vdim}{vir\,\, Z(co{ Z$�D}{Z"Ext}{Z ev}{ev^ ch}{tIR�tr}{t�newQem %�1} .Le�� 2(Corollary}[%�� %.D**F+${}^*$6ZPro�.on1.:�n!] ure}� ��ν\t��{Random&��Q��h ic cu8y�r�D{Andrei Okounkov \�^ks͟ti&s� �� NSF *P rd F��A�date{}:"kX� "� Overa�}CV8a�t'f_�� exiȩ���w�s� � �5m�� by physic< who lܢ�4Iwoc ��s�o Feyn���g��D ���i :d via wY�res,��9�6t�  ���fvouN&z_ mM�celeb_dn -��WI&��ng6�"� (+ess"���(co� ,�C.�Z:WrI9I1 s)�"�?oY�.e2�qI^,G �W}. S��alb&proof5tL* em �+avail�� L0Kon1,OP1,Mir}�)%1nct6^matchFC!�ie�}8mains miraculouN" goal!;��{�|9!�� b�6 rior� �!�y1iQ;9�u�eK-1�F�Zl���"O9'sm2$ng Gromov-M!a�0Donaldson-Tho��� aBZ�!�!t�I�8�  $X$ weX&c��mno< ~ZPeoalFposal�}�< 69ORV+2�"= b�ly��p$I7l Q1� Anga�Jlik��, alls� !>;�ewI�y:ead I R��=pM�s +A��9z�!t� ,�it not!n�]�(� hle�!��R4D�pow=Th5!)� 2xc��bo.on HA.~IqX�D.~Mauli�N��Lkrasov, R.~Pandharip�<, N.~Reshetikhin�, C.~Vafa. I�)BRaa!��<ganiz���Q�-rt�Dy!�p)A! m)E�my coɵs�Phe joE�j�<�~!��uE��iv�oO1���O ��X�\smo���+leV#�h�S}\�a!�g�o $\Ps$. W2L�?�!FB� $C�&a{. 2hg),�.�� locu�0)?e�g 4� us 0 �A@y look-�!y ne � �._.f1} %&�.�E�D G� >U \GQ$ebox{0.4}{> 8 {rat%` .ps}կ 6 "�CA �I�KB� �R!;}j(� !� � % {f�bN��Bt��v8�> {X$�h5~we]�T�)� ��-�M�' �a�ge!� meet 3��et8$X�.Ba�su�Ӂq<sbe�it�� .JUkA�u �|st�5��E�4&�k } A>yU�=!}66"�1g=f1}"� imag�Ab�� sp�A�l$5,�pYd�)}A`�{mapPPl�/ zG p[�f(z)=�+0[f_0(z) : f_1 2 3(z)� ]I!f%��p�#ge�� *�� B oly!als $f �of1�$d$�duITl%�U��� $\Pl�B�>eav�N4d��L���$Ca�,D.�A)aif���; � ee 2 5 � �>PWe� <=,��ITatMF�� any M��6��%$ me��5D�,�-�6iH q\� %9 �O-�s$!A? $$ 1,-�@4,105,2576,122129 _\,�$ see� -D CK,fp}!ցm} o ���� s. �&4 ingred� e�A0mp����a�ɤ�naps \eq2Me�l�\emph{mA�*m.[obeeH  K\evich� Q � 9 need3#�H*?%rZŹsp�; off���ali^'s���"�-��f�!�nica��H�?"' [� AzA�� J�H ?M(.�((Mb_{g,n}(X,��B2G��|Z(�  �#b�4A� d5 �M�!0 dataEC(C,)E�,p_n,f)AZ O6YA leteI�Aarithm ��u�"� �;wo� nodalar�m�O$2ov)-[ marVfiOf$C��E5f:C\to X�/��"� map�2"�%;$ = f_*([C]�4H_2(X)\,. $$ ?�E� BsI G%�"�dy|%er$w��g.�A-I�.#k�r�$re_ � �), ,�aut* ,("is�lf-*8�s)� ��;GXeeil&"��� F��i�$Nocar�a�anA�alMDa�v�8"{p+}�[DBeh,BehFan,LiTian}�U� r� vdGW�? F�"�-3 ta \�� K_��4(g-1)(3-\dim X�/n �� .�M�K_IM!����� �6� i:'E5d#��.�N0$ co�`���J� H-5�h ������ ( A�f0��� �Z5 a (p_i�<�m.^)�C0st the virtua�al fundamental class. In exceptionally good cases, for example when $X=\Ps$ and $g=0$, the virtual2a`( is the usR $. Even k ^,Tsitua��C with higher genus curves is considerably more involved, both in fo�LDal aspects as well=A�I�6$0$ ��st�$map moduliI�s bec�Y � ntia 8Deligne-Mumford+ofGJ4 --- very nice%#k L-understood varietie����A�A�M�of poin�h,n a $3$-fold�,�g�7rast,a�ms ncomplic��. W a(��ŹrreducE�10onents, or th��s,)�t know.E .�All��wAV,id so far ab�<��q�applied ��Fl�n�V�Ѷ!�� � & 3% , however� � ial:#tA%::�Ca (carries a vb� �.ER.~� \cite{ a�!�technic�$ important�: % � R@Serre duality lim!�!1=�nterestE8 $\Ext^i$-groupɅan�K sheaf��ditself to just $i=1,2$. F���_vdGW}%���A11��X=3�=-U ��(Gromov-Witt��th� oO fact,U haver�vdH��vjJ� = �ř� =�5b& K_X \,.F�A�  willa*Ie next  , i� I� fortunat��EAU�  4 l� ��eta�譠��on{6#�$B in�ants}� F�b� ch�( $-F�ge ��: $\gamma_1f n�*�be��ll ��}cycle��$X$ sq$�tm (� Qi -1)!� F�,.�B�^98� ulaYxH},IlqvY�� ^$�Sa�� �0us meeea��1i$'a_ ex��edabe"�Ma�precisey�i< n%�� �is diffe�ka s�?s%�a����p:5Oɩ.A�e:J use ged� � $p_i$a�say ``� %s.�'A�a� languag��co logy. Nam� ��s�U� cond �$f(p_i)A91�$�baA terp�$d as pullB backG Poincar\'��[ 5�(^\vee$ via/ eval��R/,\ev_i : (C,pU�4p_n,f)\mapsto �N!�6�yz3 � R� GWi��lan1>k, \ran^{GW}_{E�H,g} = \int_{\left[��.� �^\bullet\right]_{vir}} \prod_{i=1}^ v_i^*D(1�%M 7 . B� ` j standsE�2� wg� $y disconne9 doma�qndan ����q*fk�&d!�2P�3Arm / �� ours� � in�7� 42 �8one, but has sl!:ly& ter�mal� perf M& A��hsi��� SePs don'tC�,m" �eq�� , we�Kfera� work� 1I 2� coi�6�a��+ .�P�5,s_uni�4 �C�p �H , in"��FQ ��9� to�kc6S�f!� univers!�� h �#cI \to�� ) \times ��$ which!�Kpr%��"a%g� � $I�u���,2�ri � \cI$� $z m\congYiN� . We�, $c_1(\cI)=0)$ c_2tH^2m\ }�m`졘:Q�N�locus,(\{(I,\text{ �-KE.u$I$})\}&�>� ��$$��hG�\in2$� ���o���� bzl�oeffic�%_G�[$�K�, K\"unneth d posi�)$1G$%o��? "a  by�+`) �^{2] -1}(�%s�t��v�DTi} ��DT��"F�)~.EI��>� ��3�� BWU ll!Lsij � �� {M��cou�Rb$As alreadyi�ed�eT'rreaso~%�c"�AG�*2 �!� !wa�a\and�z they�N. t%t;�2~�empty F henc�_� gr~y g%� \ll ��`goes �opE�e Pions q$!�0=1-g$. Also, ) n�are �jp!*6�=)ktyp f��(beca� .� a�( �  aut�sms). H��1�Eoson �mnop}�es��W�L���two kindIi.�f�E a nontrivhanI � bl�Vx.�seta�Z_ �>7 ;u)_/ � Lsum_{g} u^{2g-2} \, ��2u tA��:��ed part��1��Z'.��� 2�\big/ varnoE�"� �j~c�s � ;0 collap!�&� �Ms���euzero �$Z�$�� ex( itly� ���oC)1 sult��IcFabPan� /below. DqevDT1�;q-�$%� 1Gy�� ula,� $q^a�$���$QkICu c_m}n nB� J�$!�N�!2 a ��Y1�'q�JA~<\boxed{q=-e^{iu}E��lt�4!e6GF�L (-iu)^{-\)} �GW5lu-lE�(-q*/2 ,J�%� � $Y=`lK_X��� "�. j =�J R%�ha\ en e�ishJ^E}is ei a loc���2a�,�T arbitrary rank 2 bund�ve9smo�:M�GWDT} or��to �{ ano�:H Ic surfacQ�q,LLZ2�I� �E,wi�3*�nee(iXjbrp}.�my opin�A Rs  J��eence�%�$``GW=DT'' �9.}RR�is actu�a"�-!&^ �Rl����roɎ 6��exten�e GW/DT &d�to�eiv� 6 Ow ١. =G2�A A(Q 8ins��(� tau_kњi[p^* `( \psi_i^{k}� >� _i + k}(*�H ))��Hua 1st Chern&� ax NQ�$L�E�.� `$ �fi�=cot�nt�, $T^*_{p_i}C< $aZ�a�"p� na�Th� �9���& ٝ��N�� .6�wE MdEJ��-�p�x0arrow{�n up{e}(}(-1)^{k+1}�_{k+2}?-�mad��i >0 � ] 5r]L. H�:�cW`� hM ))1 A�%�]�eM1>av%e � ��!66� $ptE� = 1e � ir=� 2� !�R� I���0�z is �] �י[ H!���expecIifollow��sim^%a�# ,>g5��%5 D !! -B��$TX�$caA  lh!n� McM�M(q��(n>0} (1-q^n�cn}� } %`�McMahW u�. J�XLZDT0} $\displaystyle� x �$X,q)_0 = M��P X(c_3-c_1�)}{$9�} � &.��A�z&a larg*!  clu �o� onesͼmno�� Compar!�!asymptoh expal"~sa!t0 \ln M(e^{-u}@$im =0}^�fty!|@frac{\zeta(3-2g) 1 }{(= )!? = � � u\to +� J�inM��"ular P!$ � A�*� *eE "W%$ Χ= 61}{24} B 1}{g-1} + eft(1{12}!2u#! '��� ) + O(g-1���to.q� . $X,u)_0$ ob�ed!�"� w�$ sZ_M�� A�\%�y& + 2�n(� b!��5� )�d 9iorA�t%MA�� NY!re��% plau�!� anD&�un��y �o�i2�i*� bn�convin� enough���(presenLL q m�',sc� y wa��g� $�b E?\ �&� f3-"{ ��sq� *<)b6$s� B �� \oRandom� {��L� iz%d�`dissol,)crystal4*��ka9�A�� �uh*w�assum �� � ��"!, s�aPs$AJ$(\Pl)^3;:"%omea��� toru?bT=(\C^*; a4+�&X�$ an open o� . SNany N4 n%lyb� R� ��:� )�!c 1ni�T$-eq&f c"�m�AtBo}j��usz#o� utAter-��!{. #f" �$ES,Kon2,GP� 2�xa�U jE s��d%&�a$xA iA$\��+� (#v� s��xed DaA@.�#,:o� � &� �in qup!onJ�so-�!ed Hodg�. WF�-[''�!�,d pr�Hpl�e����'e �,zbe�|"_-�uan�S�="{ t� # �-in� "�O lleng��By��L$A�.{ loci! �$ s-% isoln$5� Toge�M7 "zal"J��}'�D�is5&Y)s,��%Lt � & .0 to a16sum����.g�'�2<sum�D�.�. or��V�����(U�r2: ensembl!w link��� 7)6�/ 'y1�2�� ao�1�)�,M is�card�Z�0@be quickly review� n� R L$ warm-up, A uWrt)��"x��A~d looki6��� \C^2;d,n)y medQ-p�%�K.,y]*�"rY dne$� I� k�d L,n�p k \C,J �$C$)X.��-A*�-a�7 \le k6�e�*)^2$� ��= b!�scah!$x $y J mo"�/x^i y^j$eigenvecto+ a xaMe�dT nct 0alu�Any -���a�$IB� /a�'2 spanY!��) $I$A� also�J%�2�?��R: �ir2� �l:a y^b��$a"%i-2b j�"� f�/`}[hbtp]\psset{unit=1.1 cm� nc� r�$�. pspi�2\e}(0,0)(10,7) \newgray{l�  }{.909(sframe[fill� =solid,!\width=0,color=?,  white](1 o 3) \�VV3,3�4�V2V4,4V5�V2V6,5V,6) \showgrid! !L[-Q.051/��3��4FK6,6PPpscircle(1.5,2.5){0.5%� 3.5,3J4.5,4J6.5,50rput[c](0.5,6$1$} 2.$y>]$y^{2}>�3B�4B1 y^{5B062! �x.� �x2� �xB� �6� �6� �6� �6�25px>B �2� �$=� �y^:� � 6� � 6� � 6�A�-�>{�36��3�6U � 6� � 6� � 6� � 6�aM�6[�46��4F� � 6� � F|� 6�@� 6�5.�6;�56��5F� � 6� � 6� � F�� 6���5�F�66�7�6F� � 6� � 6� � 6� � 6�7.�72��76��7F� � 6� � 6� � 6� � 6�8.�82��86��8F� � 6� � 6� � 6� � 6�9.�92��96��9F� � 6� � 6� � 6� � ��8&d  \capL${Ab$& B J� .� i9f2}"� d  See6;2}�a>a$a|L  � . M"� q �(4 sh(< ;.  g�=�   j d. PnotT#3"�hap�*mi�J diagram� a&�,�? �i:,/iny row�colum`�_ P Sab4 ($2$'^?@)� t&�# $dnG'��#�?��� hi$ ($=9$`)�7Y�/]e ``reno�, ized!Ga'' �,7 �5 .F/�&�3;d"}��?E�[./�!�u)��-now�=�^�,� @-5i leg� �+�&�> ax4�$2�= 3}. %�2D*�#�lambd+3 2, 3fo.59�e�(dE+� non�d"�! a^�. $$ d=|�1|+ 2 3|)�#s�N latt�9polytop�Delta_X$M�v]"ce�C;o�>�, edges  :tom<&�" $\Pl�4 et cetera:!"��$�cx�an@ew'[x,^z�; . To�#fyZ:>�=f]"u� weZcD6.�9y% ex�1(�se63may�*2�}. )*&K;r�razNs� glue�c�bvi�Bway�24}�f�l*#0a[6�*P" �$E$}} |q�E| \, 40[Eq]n!Z@UQ4[E]���� � )�U!�l$5:M,��-���EY 6 prof>�~$E,>�ras�y�.��VE�4Jc(_#le?4�\q�AT�T2NU,sugar_cube.e�R�M2O)lWū]�$O%M�Z4 M�M^ZN�C[>)�ethS4�hav>��trinsic}�0 in>�;��'�m02G�w q@ly �j�@� ��ngA blem>�Q�EeWG"Pof B ��#U��QpS@a L@��2&i�H doub���ee�dLG<)< s. �"e �% half::��&w[.&mM< b.�.�.F!. =�< highminis!�wH !�2�2�EM���� atomge mis?"�=!:corners��i�a�o,�Mleast� A? � �ExP/\ concernedER�>�A�ore����+zB ���&� A�-. Ie�h�<+beAf  SF �  moveS � a��I>2�weMA� | E*��exW � 1HaJ�$*752���v@2�v ulaF`i"�=�! ��9,%9(��icityH8f<6!��@X=\C^3��bet�B!� -M� .%�Aol:nwitW0�-� �" BisAl9l.M�H$I_\pi"{6�;0�7\a>� &�E*�2� $\pi�%bs�Z_{�0}�!I$CsV#&u6. X9�4%Zel�b� V$am!ui��A;�$m�!�z��"�bT�1�&� ��$!%�(z�H,(x_1,x_2,x_3k( (z^{t_1}   2 2 3 3^[2 E�2�M�$\bw(\p�BB %�$,ll)�R�0�p�L s $t_i$. �T$=""]ar�$tak!�:�\T(\cb)=t_1 a_1 + t_2 a_2 3 a_3�8^! box�*b�I� a_2,a�M.2 ���ir�b14 cb_1q"cb_~w3fin�U�_1,!f;'{\d� T ( +t_1+t_2)>32 2+t_3)} {2'6#26?c C& x ' !>�= %H_1) - 21� Re�"o,i !�� of�{E�. �8w�G�liZ@to/.2byrQw_+ Qe( ( ``$=$'' } �*chi} @+!-�%- 7m\q�}} :��-} .l+���a�� gs!-c"�1 Gibb�mS$���A�!0 fuga��U !�- \log:�\, 2EF1�:��(trans�H&� ) � amj gy�#�H�)��b�8i�0$%'2��t���N{�� t&�!�uctO-���4e�+ clo�BrQ�g>-1q)vergen":&�- re�*"u&s� d.�5r0 R_piA. R_\pi(ze��1up{trO��z�<�e'��} "8\cb��}�e)eBFs7�#�� s"� f"�), �w� /O�Q heck~ *�>B�$*Y� �-V �\bV�- ��5\,1^{-1})}&M8�+'.)F�)Laurent�"+(�Pio%@iZ �e O4me.���m_{K>\Z^3} v��=ŕT(a)�D#!�\Za�"h6A�w%s�%*�$8�?�*o.~+��Pm"$nG�?I�T\emph!~"j5 ^ sure}!� aN�by J�*A�3w_ren��= q^{2�-} ! ^{-�A�.:J$ *} %*- a na�&'/M�$b $u�d.BAi9 d!j"� ��PHO� �Y��Y2\4'aH orem� *� �zf( f*�C�� :�%��A�F�m�V/)2s:E�q:t U z �@E�; g|_{�J}9Ѯ~OR�VCe!�6ase�Cth�I��is �8r�CYE1 �3 = 0 }>� b3�Wqa2B:� = 1)-,!�varRJ:�!cw���Ns�C� �h&; size.�3HM4CY�Pk( Calabi-Yau� (YD mean�s%�?+ 4sub0A�%�6Eser'.!*�R $�N��0Omega=dx_1 \w* dx_2 3 $$ N d ��/in!��)e �/A��E�$McM} appea�>:�or��.4 ��e ana6off�J dent�*� I�AF!�I�)ed }]r[ DTMcA](?4 � A�4-\t3("� 3)(t� g � t_3}N���H�i]PesA9"(W�4& ��L%�lP>�fBcIf� � �� , adISa�?er797;;�ͅ�to make���1� AX me�Av 2�=zA:eFO �OeaY? of 30 tO@� � ,\mu,\nu$-� n:r�bW%�bW(:Da�%�"���AH, :2$�D �nBm-�ui,�M�m[D buil_block!k6w0Q�B-&�.pHnq3,w�\i�R�hIN[�(?b:qntriple:U/�]%�.��D.�t��ize�x��6topM�C�7):�QtopTRORV�8"�Han�Z�T��!I�of Schu&�Ac�@/e$ A� 6 0�N��one-leg�M��>�]�m�2Ger :��is�A+UtwoU,Qi�>e5�+$1,OP5,LLLZwN� &m8*�?�!mheF#&i&�4$Z 0)kwe�RC pN� N?�Y2Ft"�o%Z% G2=>Uq2F� titu���- q = �Aeb�Ii�P��8N�6�~f�$&O7 =%$rmodynamicTi -q= > �}�K1JX� us-by�2�G|c"�M�2in: y��Let�$q+9-1$ do2�eKl &� �ckM� removalxa&oI ,�goa �D. f0rexD�Yex�ed*�U� dNUJ|\pi| �O�Ow0:, \h4�-1A(def}}{=}\, � �l.* I}{��}C�8 6�`2�`�bi \Y0�2\�9(3)}{\ln�] \,!e:�\%���ndi�� �`�K,%�words ``��:g''#+��UCBr�!�Xaltlc�Y�lnecessa�a a�!iy � *�H�>#A�Aun� ��6��o UC$-qO (0,1�L A�H0�#by $--be^ev�YdjZjC a ma@copqkem!CA�gu��� �W *ns�D>�_li X"s>�C! .�35A$eavevmod�`psfbox[200 0 400 570]{lim�^om6�9�=;"��FE� 1 �S!�. domina��JZ��#��/GW�sS �p�^A6 fluc,euounnD�V� (%) M��2�of ,?)/, firsa�� BCKe/I as� turk ut,a-hA� ��&a8 Ronk�e� �!� est�]�urvvzst�2z+w=1�%�&�%4% �KOS� V2�E��!FSurpriey (or� ?) �tra� #q�� �.I]�n�&�o�b*[]��� nonciCGE�C.� three&`s� ��!�d)KKV,IK!}�F.: $�&!���"��z�<A.U�Oe� te )��#8ear �@r Cd�R 3l methoBfi�< E��3� E ��of�^� .a&~i"&j-OkKE�c�C( re&� >� B-%E[V!XIth�= xtrem[� �#to.K� � ``m� MNy =. ''GNphilosop�ol re -N~!�vdb� /ob?�I��J� &�e of���Q�$average agWH-env��2�<�Hu:c ��Ge�&gXs�`�HIʱ�SHYan2�b�a$�bCh�K cI)$� �P%H�E���"�T6pB�Ik�I$�"v>m@p�]�Z!��de. %�A�)��L&� R;�E$S(k} \alpha^kM �p�L Z 9e^ (BO&�eq1���%�G y��mi![ٸ/+y�Y�;W,�6�-&=R:ma3ro@d��mdera� ���1� = V2 qVj&} /%N ch_3' = �� t_3� , $$ so��-�|�geM�� Ɇ/z|#\�0gle_\bw = - j+!�E_3 1�,$ $E_{2�LA1%$f"@K``odd�!''���U^�ŷ0Eisenstein seO&� & "�Eq | KA�n q^n(_{d|n} d^{2A�,kld�b�ZBv ^fur|e�ut�/ݭ,�Y.�*�Y1a4)�Bae12!Mjl �! \, q9{d}{dq}=�$X2��AGA�n�E� �eA����kB� $ be�)�^N"ialuZ�!i�&�'sQ�)�E�!a]Q3�l ��X�,3 stat%%xpry+1��9�rev�'FL` ��.�BO}. �3W�ra0"�-]%:�:�''*O�X~\t &����lMq.��4 � few.POeI�3,``low temper!�eam $q$-"��/�Y�*te�l,�"3!(�`yA* �!��+IH.�ZhO r!EdJ&��VZq.3$6(G2&?S� ���%� �Aar�)^[�6� 3vS &. Ga2 �XaE,act match, e�0^+ i�.� ,�{?o|I}  (�X!Adiscus�" x))�i��K%�'w�`d�ka�! �&X=\Pl�Q�C�#le�/b�g� �5�G)h#asE7�1 < \{0\!�T5(�"!�2�B "�\igA#*$2�Ib( �+�6��� k*b" UEd wo  .�M~H�H�T. B�\Zou�po*3of� !N*m'=�gse� .gcancelA!�1avA. us�*%�6�Ir�!�Au�E�rip��#A2?q or?���NY=(OP2,OP3,OP4� 6p wOQv>�7 ��A�t,�.A2V-�X �J ��"P1 nh' "U {k_i�T� _d^{\Pl�F ��{�2|=d�RePP{\�k�}{d!}U!)^�Q�fi�V\bpi+1}�yQk_i+1zQJ�%�(!�sum�eisLp��� �� $d�7"Sm��7$5F_RM���E?� �O�M%&� EmUZVbp_uA*e Y�A�y�&B alig"@ bpk%�R5 & \,=%��"  _i -?X� 12)^k - (>)�] +�T2^{-k})�R-k) \\ &� ``=''Wdm_inh:T��%y !`���Y$�$-:(-wnt!�aHFSGm ��ٽ��f Pxw�^��PlancfQl"}n]8K(d� Su&d a�._���Hgu�\a��j� e� matrix� �8l�n�Qed�1��b9�3-"�P��e�.e>� uses�Z W�'h�"#�B^�)�azK 6}e#)_ɑ+rib�! 0s�yT$. 5��2�!:�" ~c 6oo!/afV!U ���m��"2�36}�y/pF�#`|a�2, cyl�2t ver �7�zry9�y���* �[h�Ia�%�"�6e�:Ui>�: 1_c2{6/2c"t?�"#6a�%�R 0�M ough�6_)�!7s�ade' � � !�}G��&<���d=��'t,a5�.� �&Ɏk-� ee�ar� !�%��2�%�It�enX� s��;eoQ2��LQW,LMN�"! I*62�,�j� 2��b�!"T�b *7SM�H ~�P!'d$) A� $2$. Perhapin bestjwVaC)��!,�IA�A� peci&�7�Et�'�of lenc 2U7he�`OP6�QVo.�L0.5��L-6,-2)�L6)%&vKepzKM02,3.464)(4,0)iN\�Jrt]{9m�q70page}[t]{3.64 � 'qh2�  \�n*� �k� 92�H�i� �lt]���.�B���^� cb](2,4.7z��vQuantum.:\\A��?_d�+2)�q�R.�D�f��T�q�of�M �m�P6�<k~f7!�_QI �<�MhHthebibliography}{99�dbibitemxX M. Aganagic, A. Klemm,M]o, C. �, {\em�?Ju&@, hep-th/0305132.�l�W$M.\ Atiyah[ R.\ BottXZ map�.C�� }, T�& y {\bf 23�^$984), 1-282{,Beh} K.~Behr�B�6p&���ic"�@}, Invent. Math. w127x097), 601--617*_-bBehFan.~�B.~Fanhyi, ��S(S=nE�ey\ z\{8{45--8�5o(BO} S.~Bloc)k(A.~Okounkov� n0tCAA��VIcEWedge Re�pp���}, Adv��%4bf{149} (2000) .~1!�-60��&f J.~Bryai[8R.~Pandharipand6) �l�[:�&2i+},�(h.AG/0411032��  R.~Cerf%{ R.~Kenyon. low-*�%a2� Wulff"�%��.�\ IU $�� CommM0 PhysM�22)-$1),147-179.3$CK} D.~Cox�S.~Katz�Mih � �5R� Ameri�A�e��hSocie�;Pr�,nce, RI, 1992�(DonThom} S.���R� omasm�G&�$~>e0%D!�inY�ic, e: s�q� y�A�tA�,Roger PenrosahS. Huggett et. al eds., Oxf�~Univ. P- �aY�ES} G.~E�wsrud,!iStr\o mmY���'}7C enume�ve� }. A�!tySoc.\ u%@9} (1996), no. a%75--193a(u��` �vFagxR. 6*m)H�d*�[,6�i3bI3}�173-1E �$fp} W.~Ful ! �B����@�=s:SzqBgaA"_�1�0---Santa CruzA�5, ��96, Pr%QSy�s .\ P{ A�., 62, P�Y2, AMS,N��� GP} T.~Gr=bV�L��i`� vX?y eA����i�135��(9), 487--51E��)$ ���%\C.~VafaC)��m�SQ#!8�e0022222:$IK} A.~Iqb}nd A.-K�A$shani-PoorY0{\rm SU(N)} G��eI?�\�1�Cg A�tud���603��INOV}�p�0, N.~Nekrasov^~Oч� � Foam% F�!n1 3120! }KKV���4��>W�c *�"�gQ� fiel�'o }, Nucl0��.~By�497m�i�-2,eM -195�hqu KOőͅ�5m�Lim�/N)��x BurgTO}�re�>�2 '��Nj��h5weldxDim^E8moeba�gmath-p� 11005bY�KOVfc9s^� �Kerov|G.~OlA�ski�Pol�"p�i�!�!Young d8O!��C.~R.~Acad.\ Sci.\ Paris S\'er.~I�<nbf{319}�!�0994, 121--126.�HKon1} M.\ Kontsevi�I�%�C��   uli "b]���� Airy�}, C�XE{ 4{ 2� 3:�2} :�M^E��;���o( �v�~?d�=!J� m*Mca( /0(Texel Island�i� $ 335--368��g�!RL9, Birkh�user Bost�MAHe7�LQ_4dW.-P.~Li, Zh.~Qin, W.~Wang��@`�3�0ble hierarchiA�V'3hP 302211A��F2 ��� C.-C�u,��LJ.~Zhou~!� AEg"� TAq�.�V$6x�at�4084266�iTiR Jx �.~, �V͞-��F�&� ��&D "s%� JAMS��1��8Ao19--174.sLLZ1} �Pro�%f a.�7y8oR+on�aT�}2� 64346LZ2��Foit Two-:/ FsB)�31027>�LMN�t Lose��Marshah 2�MSmall ��Y*$s, Little �i�FZ3F��oe�h"X2196�$ D.~Maulik6t2^EFp ��2 :��A4B�M , III.� �59=�40609)2uBMir��~Mirzak�"�Weil-Ph&s�{v�Q)� ZYN)*�+"g}, availe��+��(tt{ http://N.em0harvard.edu/$3$m�/��8NY} H.~Nakajimae�Yoshioka1�5� "a-on�8wup, 60061982�N} 20 Q66-P*,�vCo:�+U72061667NO2i%�J#:x��ARku:a�Y�623�9;$� "���^!�ra�K&��!�� 0901�5�O=� �>� -F2�U�Hurwitz �e(t7�+s:�10114M �22��q`!d� ��.204306$OP3��!v.]N!�� 6y7232nX ��Vi r�k�Oai"�f tar�(X.q 3080� =o5�qN ��� unknotAn .\�.\�4bf{8}��675-6992���� coЈ�6�����e.41121:f`; ��q�2�/B�&� -%� �1�:� =�R  y�,N. Reshetikh� A�"`�1"C&�Aand��{9��u10061l U(T�"�" A *�A Ca�mU�y !/�9${ K3�x? �JDG* 54� 367--43��W} E.\ W�2DTwo&"al gravwA!.��:�2 }, SK5yE*Diff.\�.�� (1), 243-310%)�>$ � docu�T } % Words: j �.�&n<"F �0arSD:P�j,��y f\?� mapP*h .5a. F GW>P.�G*,� G*�� � S��vdGW vdH�>P� un>�0DT GWi DTi iu� E*�Q*%�&>Oprod*lg6C^ 0iLi��]/i xy dnH>O*�[�#t�Y�A�YfLVpiM� �D"�Ddx>PMcM�� rms@�9 ps �7str7 �5,>P:6&S5�3o�4���a44�.>Pdq asy�ws P&Q#lt cb"��n��>P � �i"dal &.$S's>O��posAp�SU ph �"� er <(Progr Zh QiB,2) Liu \ � q �sm & s &[ >�b  P"b mi� � � Eas�u��>M�:fi��ECMO;s`qnoE; myU${$ 4ECM�:�Stockholm (June 2004). N$%% BEGIN multido.tex %%bPf\Z��{1.4}tdate{93/01/14} %% %% COPYRIGHTX3c�999?-dTimothy Van Zandt, tvz@nwu . D�7p!�am�);+re�%�$e�/o'6�8u�+�23��LaTeX!�jR|$Public Lic�8 DisS%< CTAN=�v"d>ory m�=/�r8x/base/lppl.txt�,DESCRIPTION:H =S/ styu�n loop \, \ $$a'p�� c#-� �+żp#C���}� . Ama�~B<�t �is fu���npu�A� �7a..�E�Nt#��?3&!r%, packag @%&Pl@ TeX,)�, MAmS� Ams-%�1XINSTALLA=YPuZ3i9;lejKre youa�X!SkP inpu��Y"n2�-g .texd Us�+O!��2�DOCUMENT.�e6docU�aINGM Copy!��artMQ�E���4�~ed�f�3T A=�H!�ly ^(1)�2_5Dl�ZM� un��d �@] ���. PJZe ^)�)��!jn!i do so� (2{ modi2`re!kp"{ n�c(for pers}��or!}iA� organ�v3v copy fragL si�� q.hXo��s�]�Aas#]c�y~%;:�redue� J You �(4NOT ALLOWED toC�Xey��.p��f F�'�%N�=��s�5eof"�ffo �a n\Al�w�!!%A�et]�DE: %t�y���a�pr$� , plu�&u�a�m#�@ �� en@, i;�&new ,  toks, \@��\tw!@z@. % %� JJf)2�oh nouFD)n��d?d)ec!~of @:�# \mbDge{ v\6-D, ��\)�#csA� Mu� L{�  \}�B�d� \edef\TheAtCode{\the\catcode`\@}  =11 5v�sC�us��hacks. "� $@dimtonum" i@(value� "#1", % a&� $ register,!Aq "pt"))assign)��AA�"#2 Eco%� sequ��@t�{(@nnil{\@nil ���#1#2{%LYJ{\-5da�E!=![#1�jA��{%�+no 8X a@ ##1\��` t{##�O %=�E�!}oň!O�!] repe�.� 2keeps % �V_!<ite�.mvAf@us�|�Las scr�4) J,by "\FPadd@".#stuff"a0E to s�q<>37iF�G� ated!�q�5-��v  a�   -o{ @{}{*'C1}{aQ Q;F3=stepvar~Cm�8{} aMFFa }{}}6�)� var"� �H�5v�decla)�\ ni�9 izin� !�u� r7g �VA�y� �"!�iΩ��A>hets� each%�I{. %�E ��Ǟu�� %>� \longe0-�@a�#3#4#5#6eW#2a] "c =#5\�,x+\ifnum:"\z@\elseP@{#1}{#4}{#6}\fi #3] \igna]{s-�� ��2�-0{}B� do{y�do "Q!�var#2,��,?��2�N�]5m> [J�<�>)2-6) #15T#1�Be�{#3 p< :/),��)?�2�t<%)�advd7� Ve� �{6��vfi6� stop5K]=U6/@b�r �}(=0_errhelR��rf�kipped.)>err Bad �YN��P�QJ1, �A��(A�%�ifx2�@e)=F!�o"}wE�=+U9lNaZ R� �!7>�Z=#2+#3Y#4 [ �� �#4 ��)�_a�6 vartype#12:S>!6 o:�X�ls Z : {#2}a$i<1 F���cat�-�KVMJMC�nil6��ZR�F�O��� �.\P..\%5� !�@#2�w� m]�Check%Js l`;�-;�.� ##)S �x\v�V#5G��\y a'!e=ڶ�3q� �y�1�#1"��e�2�AQ]�!� �Y倕"A���mA�now Y�!�<-$>.�  syntaot��~ iQ W5u?@@{�A_}{",}{��0% Lthe(=�[ hkbe:k 1. Set X�>.2`�2. Invok�addto�{ �`�V <>r what� � d^?to&���.JEI�P�-M, "7�supG/E ' do"�.��#d .�varՕ % V� %�N"Q<0s ("d", "D"):6 )�di�i_��'��i� R�)my�.o@=#"  i=#2&�r.O :��Ji�4a}�! #3{\2 < sp $2>�� ci=- N�H5x{e !t@d#3}:s_�}>p 1!N)L w! nce #2���1:X�}%2� )�D9�a@de�F�bg�)("i!�IZ�i�#-���3 �3&()c 2�^v +- �ti5t$ GVm�)m '.m am6q.UJjI:jiZj reala\r!gR")>�%�r.gUp� Uh@ s -2 -^e 'Qڦer5eBLR��)k t #1ptR�qA>�.�%"R:orZo �!qn!qNZqn.qec3�[�C^D.�FPsub��:add)]{0}����a��6M 5k$4} >n%N:n%S��1E{#1.."� U #2I�6�U2:...A|let#32��E��i�a2'*�+� "�@� ��aJY�E�.h@��ifx-#1eB"� A@#1.#2."� .#5.#6� ��@~, ./p}�tɫ�  \z@ 9�MA2�M��,4 1��i=0#2s2Y q '�[M�i=#4; b E�=06� ~=��$  : =&�)M@@#50 %D .��#11�uaa�@=-� t�;�� num#4VE N1*2 >F%6V ?>1Q �F-# K �BF$n #P�F"&?A?I5 R^T�B1E�b= �@n#�h�@-3E.OV2�G �N$V �] ��2e9�t��@.�*+>� ��I>#P2���f�9��iB2m2�^.� E7�>+ �-.)Z�2W]�7J%@� 2��ʑ$� �d���\�%{\xBz*C %�@=-1- �.q ��#2xA .#2#3�6u v�#7#8#9 �B�1#9�.�&�- ���#ENDjO! �w&R$pst-node 0Nod�PSTri:qy,%% E!*1Odoc:z �usa��%��"�e headб�!`v pro'��{97 p\9-.{�$/04��$��$��$��$�$�B�5PST!�sV6FIEA�E ;E�\ AJ#AJ\fiM�p �t \pstI+{.%M pst@�dict{tx@A�Dic� gin &zap� #1 #� ��6�2;]7a�#2PgetyH ,.� <$# ,�2C #1,#2," {%��)t ):#4{/N@_�#1 ,,�^ � cntg� �9 cnth&�%� WM-��psmMcnœ � ��!- tVg2h�"� !�ew!�{ .�new1T#3#% &e �-w!S�t�ad  Verb!>!}IA ^)Q psk@-")  fals�b true�JF_#2  � en�\global E aBree� hook:,2 3�Fetz.8  �if!�ode�O�%9eq � use{+>+{%]�/1Fdimg=\h�@h�{��!e -\dp di^2�wer ntx@InitPr{ U  \@iff �]({\@} iJ�:  (#1)e�nA,�}A,% Ma�{10KA�oo� .�0J� #C�� �c{ob�*{� �6� i}{ 2� ��2!v!�use@par �B�se�� dimc!-!�=E�� �Kp/B�c-BgF.56<if!E� \ker[tec \vru*�\z@ h~Z]c(�th �m"��@do!�5�3}{11=� C�^}{2�}�DG/SR�'c:)z$ - Jul. 30-7 - P�2 %.� 6�\eO �K!h= :(f %N end N�Ev2iQi Fi Ai 2iiE2ymk@radius��� c!�put!t2�put�%F��F<i�\KA�{rot=a��JT put@BW i(\z@,\z@�:tmdaNa&(killglue \@^ ��3�y�w��-0uvA��Fmak�R\cv��{v �0U�1U�0�box@iv:�vUeD_.}% B�6���T �%�>��F�%�F<��HU�!DiJ�.,M���V���N�Hj�1"�3f� ��� {\wd%졼} 2 dB��&a % x y��t ;7 dimbb�� .5 sub�  }% r�!I�a�6�K�1�� -y/@ii2 .)E�{�B �usa��setbox% !A=�}P^%t [e<ii��9!��!:boxsepA��6 p Lse��6�Ld!��Ż.� ��q�5)3@1`J`.2`2�`�� dimav� an� aTo " VbE��K f�}U:�(.5.?,Yaťe8b!�.p=�!�v�)1A6��>�tx@GetRA Pos{ G e #e  r:2 [{ @�%�!jpar{}��=@i[#1]#�f+ref=#11� 0A3+u�i %�Q��ZY an.w672JF0 �"/^� Apr. 28� 8"� 6A�t�HRDi @sta�p AOf�!�i�l.� b�����  {16}�+{.U A�!�*Q >.:��>a � KV�/.EP=�w�en2�-�v��� xref.��)�Xk@y*k|�*� nTb. � 5}c� �*:�"z& href!.�num�aZ}oset {ڥiSv = k=4! {.7eX %ji;��1D J�-yii"2� 6i{� ~Y�&-`Y�s�]oved a�tsee�.�oes-YR�'t@v&z#p(qs�u6�D�>�4nges %.�"�ay6�av%�Yc!�6c0$!�(66wa 2QB�b!�)�1�tx@Dia��� �qdiaa�9"� C J�2���dia���b�!�o9 4L1 % /X��B#�( /YNb wNc 2M def /�6hd."-T { 6e }B�q>���\y � �[i"� \p1sepARb Sep.�R19*�3BqB@E�.�J�.�B� tx@Tri-{ QZ�� {P "riB| Q| J|2|#�+2�AF*h ps�:v: �|@:cN�fod k@tri[H exchN-a.I6|b A ��F�6t 2:��6�H..2v�-^����tempa%2.�N� OvalQ� Q��B�Q�J�2���.��'>'n!-O�2U!AHun� E� �[1�\�\� �[doB6Z Q7 @i2� (&(<@&F��%2�"� v>tPѺizj.�� a �s�Q�g6�a~���.�h��t��2}{��E"��� ED /X ED V�gA]Z�wf �� psdo[!R��2��]E�gB(8� f/ !S� 6@r $h �>i�< D!�'!��B� gCG.B�([ �OI�6ag>0�"9AR!k @h�:PٷN��(:� 96� Xb�� )�!Y {10p�7%� >� qj Fh [ BBRbU&���!�up�@C�* dObj:M4-Z%�\p@jB *),\p@&G>��a>{0 0 !�iUa�#1��"h ��dF k�e"�CLWE nem�� �� d�i�l r*u O%� �.+d u+6a2fY�Isc�@% /x2_ ��E��su" y./ �j0%;!N 2�B y2L/y1��x xy2 add dEDx2�j���1 Ql,x 0 eq { pop\tx@RAH}�eF�r } if!�!�!�H6{e�u��G�endZ�Z�a��^��3 sepA��g�Ao�$��� � A{0 q�i� B�SBRSB^S�RA��.�j����k:��2�{�� X l�G1:GT�H^T�IfI1��RI>�Y�5-52:5T�5^T�5f52f5>�armre yUarmA�F�armr# BGq )� armn �I$ki�  F�}� �tiharm.K XP��Bp>�H�NH���6Q5>uY�>`H�NH�96!5>uoffsetA Z� !VI? �r5BJ50 a EA�31� I� y.uBHa�q.�V�wEdũya2.�62ByX32�J4�H � � �:�arcj�"2Rj� 8>� n� #.�  � � � {82�nSY�B� F2�V2:�FY\6[ � s � {.67 ��Center� 3tx@XYoGetEdge2 AddOeg{  8A9AFBB6Arm7B5Arm4%I@arrow�  2�1il� @pst�dt�%5s=�ef6a2%5u *-W  l1-��Lj fx� \~�%� J K�NCyNC�nc ��,#5`2/�#1Obj  F1 � k �r� O 3 b \g%4pos@default{#4�>� Nj N]O dictk��. B ,se� �� B2B$t.��b-�NC { #5b -��i��-gsave� STV newpa�)�?. g�xor� %!!\ {E")��F�*short�(X 2^.51�p9�!�6O(pc@UZ*ge��s{6"� 3(#2)(#3)Y�,{@@A}3��#1 {@@BJ,tx@LPutLine{ �s.P BezierMid�{6FHPosB21{ :EndEnd2 �H Js.�Vr <r 2 rV Js.r�C ^� <NCCoor{ 2%zNnc0�M 1� O����{"�#(*#�|{Open}��>{�|;1�epF� 6!�U�rqc�e+�E !E:�%�2I@��� Bp�[ -�#1�Z-m-9 %�*) /a @Pos { xB xA yB yA�L�g}�(R8y ;Z8RV��5�sMs6�&2 )�s9-AAs:V-�s!V��(I!%6��W�/�m�=esAL cWAH�Q+ &9��Bxy�J�% F!"w50� �!5��t {%�NE�s�|$R�.%le�a�a�9l >�9l:l!! }���"qF� % /A A�k� AͲ def BB�k4 �� F�UN ��p �2� :#�.�Y!�5�arc2GnE C:�arcA�.E��{% i�=i� !�Atan du�+X � -+�-gED)6" 0B\space sub 1�80 add /AngleB ED \psk@ncurvB\space \A � \tx@NCCurve}} \def\pcarc{\pst@object{p2@i{\pc \n @ii AS�s{N nca�s2`cf,check@arrow{iF,$i#1#2{% \n�H{Open}{#1}{#2}{1.5}2Di .�JR@i{% tx@Dict begin!B@line@iii pop end )sAk@�A def BB rm. ,rm* TypZrmt.4`1kpNk�!k2�%�N�1�g-�N�e #dN�f6@��P �2� :#�B�iE�Bar{N�bar2]n[ Y:�barZ [ &I�v�E�5�iu�e�EzM�Ba�pt2�� �. �=Diag{N9d..n[ \:82 ���vpN2� 6!�.� �>��:�6` �a bJ�F�~�^��y �6� 6��>��.�Loop{N1�7aC#1��J ��% \let1'@ %�)boJ{.4�)ar!23x 2 %!9:.8 Q*kB1�&N V�ar�Om5X6}!A�arcM)�Y �2�� ��.) ;a�lTfan{�> } % Changed according pst-beta.bug December 3, 1993 % nrot=: does not work when : is active. \- Xgroup \catcode`\:=13 \g1g - rot{!z$:{\string:!end > .�?�I].^a�J!�ht@expandafter{\@ifnextchar:!MJK} rot}e�0\@nil \globalM�t@tempg%� rot �Q���*-ti:#1ZyJ  \e �k{N8  \ifxs,\@empty\else� \fE� j�{0 },tx@LPutCoor{ �  Cpos)a � �am� �  �I_pgpos{\@defaulta<�)�e�numM1 � !�<{ �ncput!�"�A� E�$st@killglu!t@make�4 #%!3� 2?8use@par \if@staɸ box\fi� Vsmall%� hbox rotatyk%i.0�shortpu��.��,leavevmode \eI0t@Verb $nodedict /�\!7�d!� �!� PutB�!��W �U ' End}5\aB{2z{0@iiQ�90A�6a�v�.���!2Am refa�� {#1 �q�ro!�)�< \uput@vii {exch�!a PtoC h1w ! �4/NCLW known {  F } if(��bBX5X �Xsub5Xi�tu�!�BvA�dim%J \p@<\z@y��T% % DG/SR modification - Sep. 2�$<8 - Patch 7 %\@p��,ckserr{Bad `SD' value: `#1'. MusV 0<$<1}\@epha �>hpaV�e��iB�>\p����������f; Y&!�)�tv>�Q� Q��apsa_t: H}{1U�tlE~� MzM truePrBPP zP falsQhBQQ nQV2���6�M zM6��6PP zP:�0x@HPutAdjust{ �� tx@V   9�@ R��mA A�*� ��� &  flip��� ode�/�Pos�� { #1Pu8} { CP /Y ED /XP 0G�� } if�/Sin 'sin) /Cosco�`/ �"�labAp��l �'t[ R#b > 8c dNTd��6,� 7��44 %\ifnum1=0#2� RY�I/flag #2(\csname tx@%�Ii%  �{t � ޟ%zJ I�oE4G uY�r� =\wd  divid� %xa 2' dimg=�+hr9bCP \advancDg % leftB&b-.'r< ( �d ~v~ rela� dimc=\h�t �:cY d % bB~ d\dpj! % � \set.2 =�  to\z@!C kern^a\vbo \vss2m \vskip-d}\hs"}MakeS Nab�_ � t"+ @na�  t� {\� }% ifx#1  � g\n��I� 72.7F9�u/a� = \@sptoken6DBF!�� Afi  0��.){^}{_��Tablr!C#3#4{!FGt$�I���.�Iž9 2;)I#3zB; ?>A C4>CB�0EFG Ib�:X!�B�1� .  NF�%�)�{<}{>J�!�%�R���d��� B\@��use t\ifod�Sk@tree�\if ee��bE0 a� 6)r l\fi\fi /q�}�Rr^� Z���av b6�M<6�l +rF� /U{�bg�c� bEIC�  Q�#�6>#.�g\@none �?\ignoref s % {$undefined{�.@Z{F� !!�$hpa�&� {\no�\�(assignment\ %"�:�&�+�]�d*@ �G !-P� �% par{� t@ifO2�[{.@i} i"� G0@i[#1]{\addtoKref=#1} � !� ,i2\(Sv]" 1i�];^@&,2G���wv(#1).��G/Ihm!(8!z~.%Eu ^. sL�s.,{ s 6,� � !1� N�aK}:_ /!� 9�6z%��Iv12 Gf� v=3@vzVR /U  R^PR7v�Y�YM�.I U 6�2 !Q f)6-t� @\aU�1i#1}{  1�[#22;�2} %7i* 5�6� v.l667TBJ2>�M#16Dv#1(#2JH 2}#1n �� @1p�  A�.�v �5U >�9S1}:�B�x. x �1 vx 3)�$@coor#1;#2*ot�!!{Ef� "wt6a�A�)_.r6"tload �GetCentej{ 0 0&d end ��t�#2;#3�.I��%I��\b{ G@I}!} �./  ��-:�;�1 geR8xq�%-�9k-sep-a�ART-S�Wsep� A1eEdgUk@offset2G% AddOFUtx9�$ 3 -1 roll�3  Q"+)�%Ir)8-91!5!�-�dB )%.�.�IV?�sub� neg �ta� �6-�ne�A��Q~ �C#2n� &i�#6=��%ZHE�.�!0I�1%��u�Y �"A�nI1Q.{0�p)�� = u �>� &��specia.�&�.� $} \newcoun�row2col2 matrixcnt!\p5sep.col �$ �3%g"�$ !�M@roSF/  / + B1.5s"  (newif� �V#��$ - Nov. 27|&8 %%ms)-@multi% i "9 V.� b�-1 ��.Z{�\0=`}\fi % Don't want to <  any &.2{[A� UŴC 0=`{ � "% p��a4:5%��se��0��?KillGluy6m@%p math ifmx\$\m@th\ifinner\textstyle�\display c��!m@endOMf!a6\�@cr.I �cnt 15{ @thea�{M-\th&row col�tabe �e1!col a"z�6.6 ��"\halign &:��"&3col�� ~8hook\romannumer�row� '*ScolN/�en/p1�!##end'�� \c��end1�!�crcr\e%\un%* ��u�!�{!�nuA�A�.� I�@@c<� {��c�E� �#1��j A:�\A*no%��Bwrow!w p%1!�6I�&6 �E�!5S*� -P {E�/ @i �\R�{��"r#;j2@e�RPMxA�}�64:A��e�� ])�9� Qm� U";" @pstRy�-%-pst G j!nu!col>1 \hE_%�sepZ�m0�hf,&%�uGcu/@:A�q<�qq)e .*� m�H �� span���BQ�\v,I�@>\@ne \sp@n\repea�$���IA 6 k}(�� IU1n���qx V ��A�!)ifx l�`)!hlS2C`*�4{c9et9- ��";�g %!�# �.8�-�(�*�.*�12�1�NC�!)Elv�Mar. 19E�&� 5 4 2aV>E]�� widt# � (9.B!Ok9a�+<inc�il� � Coilqe�*I�nczigza6,59> %Jh"� <�*c&=0�l�l-l!!>]%z!3-Prm�%l:OZigZag%Qzi;E> Line1fc�/(@=\TheAtCod�'ndij$ %% %% ENDea�e,�@%% BEGIN plot 1\Plots and axes with PSTry* 97.USee the`User's Guide for document�*4I$f&#1������� &gn"�"}�6a O�5{�Y1�Y5/ {=10:T}F(F)F,F��>aj�!.!�<t2) !06�e�.�V.W%���e+mI�E�zC6�.^a7Q:�a�I;���yQ�A=Y�*@E. ?3 �>{ @� ObjMR`lo"ps7 �BpolygonE=FG'ps NM�Hz� #ps NEe�V�$ps NHc2H^�&ps NJ dots�S5F" %psNE bezi�<%{Z�$ps NHc �b�'ps M)��A (IE+.��#� :�� AB���) 7" psN0E�}]set�{A�Q��point�< �cntg="S���t<���~} J- ame�"m�8 at least �$�*Uٌ&K a-���+��k� ]� �v�\T ��5>� {50} $For quick �s,C ine:6 I4 : Wha�do�first � (PS   only)� �o>JA subsequen FsVGend2H: How�="� o test.): SetK_;OK8use�.M�E{qp��!LopAto���{L�6 � ua � �[+:arc>\z@=�ifshow%QsEi�?�LA�BE���B>ac�3� E/i�1�y{moveto�% :�,= c E pathI�endBJ-�2D�62�b��: �iz!)&�0 psds] k��Bj�<1996/�aHDot } %P%6c{  /The { gេiga�%scaleJ$grestore }a� @Z�enlz1�I�� Fi-� "1R�.Q$��/n 9b>)n ?In 3x 0 eq { �BAka�m| � ?FYB{�?FO} ��2n^�.RV6^:}6B{51myI� Jmc �5JJv$)� 12&!�' y�11��6�_F0��Z ��N�/M'#�def3U' š�k�C�Ex "���A�f�= ~Z4M�.���`50��at�qB6�< !VASls a� ist�r1�rA��N� {" ��gN�2h � /Dx {i�"xunitf /D { Dy�K -/DyB8y8Do ;x 5 ; {ro { +��2�qpN�/7����2� -�z6!D��_6Q�!vj�#Q�����E�a<����1*.4~�\ t@def{S��PC }-�q�j�#1�%�iJ7��3��a�E� !CE� Z�%�:�6i��.�!�2!aB#%L-Fo ini�7  @^G- * ql j� !>C�#3��ڦ+2� �� ! :; 1؅b /x #1A]1 �@�� /dx�xE�p C� E�I�/xy�)x.*�M�� Y #3:#)�mu#E/��~�E��"�&�Y�=)�@i�>2�  ~N 5-y6�1�xy��)>L�%�.8 1%�ْ/x x dx�09� 6aF~ ^�T M.2�FE%�9sR�6v��n�1eQ�>{9x&W3�1 C �x�JKE�J3�  WRfF�E�Mi��'aJric$n/2)�72��#�?�?�?t:?tB?t t1 tE�>��9�6?#3-ne�H�%�^Z%�m.%�O�O:��;.~ B# $�_>`�S�g~gt t dtQ9��gEG�g�g>v�o�oR;>oBMܺo9#ese$�"$ are compl�N8ed. Be careful.U�t2${a�,}{dx}{n}{int�int=1�$4 appear on top�!z$,, 0 otherwis�TdefW��Eb�Q*��V�#�7 tate$��#3]9�2��l� dx)7< /n n �Qy2�k �ize CLW�ziv:7/y1 y2D ?U.�%ko#4E- k�K\fi{J ��/ �XN :[1� e:[��d/�y�� xr"�x��to�"oke35�PU�� �.�"` �%r*]""�{3�-HM!� 6�# >$j"� 6 A� �H#1f!=~>� x#1tJ&@n`5-� ObJ)m:*� "�Badeo9 D#2 DR�5�-%0� full"zs�~.5*Y�J450� tJa�#3J&x :� 7y tw*V nhr@:!N0arg�(j.B1{a>,k:�- 4U� F[OxW"Ox!s6Ox"�X)�D6/D6/Dx{�) /d/` xR�1 ��k@dx{>|1�d�.wOy6�y6�y>�6/D6/Dy>�/�y��yn��I;�:�origin.��"\.9�R���n� !I)y/@1�@s\ &}2(icF*�6(" E }v(0,0) #1)>u 0(mB%k.V��5E+��J1 �$ �7D,#2)(#3,#4)(#5,#6) or&7e��6 E�R� o-x$:-h�>$D RH a{#3}% blnI b{#4 %jJ c{#5}% urnJ d{#6 %* Whol�-O*will b`*nsV,d�I�: �.WfQ"JPUQ�,.�*�=�:9b9h�<is9y 9 �:9&GQ:r� 9-�:9d^rurr% �Ols/i or f3-u�psx�An��}�Y"�#a�T"CKuld!V�-, edge�  axis.>[>.5Ki�>dt�+N�he�j/ +. Start�.cZ!�L/"\-"� !!Ne)�fix t�. so t� A`I@`th�,� 0 o.!! �4 � �dimb=�z\��S&� *� dx0ZF�SD�C"r4�:2g i"B <��N:a�6Y ]N)se�% Size�Z *2|G�h ; 1T�EfB =:'a'A'� 9�~�a!`� ��y0h�cU�T Dy\p�#9�JR�"�P� �O����v6�.QF�:'bf�%e�� t�U" (which�/0-dimen�2 al),�/put it�$aީq�V:zseV�R{&�@,ut@cartesian%��:'6S-��xs���6��:� cJ#!/O;d�_��xs L� � �^*� E�b#1]���pA{CMi.M 727� 9B9y�q�� ޡ��G E �� add�VA+L #2 0&X.1.Afqi� CP "�7e� �:L �po�<%[st3!�B-Fxs@��)�V�R$0 0�k � �� 0�0N!$d 2 copy r%co Li;"�$E�t�k@fill��F�30-�*u"6q"6���"C .b)e8;!^:]) Axes$�])kn� " �{ �xs�;R�6���W��n 6�knlyD.Q tрa�IC&i~y_2\& g%�vw[#18�P-\fi72�!AujaF cnta""*.%] X (in sp)� end�'a�&/\H��dx/2H% N my �v/�� �,*�2Et��b�dx spU  % Sp�ubetween0 =\-:���{0< *` t}2�*a % dimd��2� �ni{1�1u >� � % Knowi_� Ů�!fY3\I0�FMA�\!$I 8�A"SE �epEZ�\5 59)��M.�"� b;��2�%&� ! �]\psw � k@Ox]Q \mK i{\nIOx+EpDx5�� �2�D)�n�n �>� VOH FXfiE1� �#1{$#1$�Zt�������i�y��:�a)�dy��n� y�9V�a��:)ak}{U�cM:�oiPiN>1�]�y� E� A-F�ab� f�;i a�ly�ay�a � \offi�R�G f*!  �ni�vssqUa�� 64=.hq4q�)<ep�\ps �y5�T*�FUkip��)�kfi}� @d>Y�Wy�Wr�)L E�h�n!�� Ks}���Q!*Vg~ �%��)w��cʾ@� .�C�"�@:2�>�@ ostScript�CDGeneric TeX: main �>(!��@esgio�@ _@ uses� header ``�_�.pro'�?� }�?* A0�A9/03/24�A�A�A�AA�K5�&S@  ? 1�%�TPst3C� Y�>2@Ƀ 2�8ifx�@] xerr� 2 long%�.x �#3{ZO #.6_r�f� lse#3�u���def_.�AP � .H.6us n&$eha{% Your�mD was Rd.^^J :�L) I to}0lace it EDan�[,Oor1JAcontinue?o].��5s{�5F '�ou�)immediYr4write\@unused{�. \alloc@7  char!Qsixt@@n,-�,  i@gobbl!Y s@nnil{i"hYM�?\ ;b l ,zbS\future,$cATnc&x^c�Sx">gi7d\@xi8�MA�c eYd a�Fb���� )d}6d@�:{.�?�= } \:)J:{�} 2��): {j�"=?�-�{`q�'6-E.! <�[> (tvz)1���er%�!�E� \new�A`\A�2r@c$6-errhelp.���= �% � error.qkGB^Gfur� informdG�m^2�HBt�*u( �.�2err�F55}19�9n9 De�v �r�' stitsG�.TJprocedeu�ehpzgb� W4recover best I�G�lc ��:"ubef�6 �ing_!�tbIor ask y�a,system admin0Hat�or)w!�.XNqui�7 m�Wced�.�{M N#1��1<pbkZ�L� E�2bFcFdFgFh.m2box 5(1�B $2 �2 �2 �2J_ ��!@mtokXt@  �f��!|i�fn��{*{\)};�*aG } � Ɋ�;Q���6��@?�i@�J�7|F�&Jz�| DUnexpec�J��"�"!M � TE;Y,U�� '��dimtonum���M�:6 5C�b{&� p=12 tkF# {6F }#1p%;� pyth��� #1>#2 �� P2#1.� G- L(4#1>9#2% #3�#3 .2122Y.8384#1.$ 5758$�>14#i| Aͅ1� g{#3.� 6KA^ 3*�? h=#2� `?N��N�$h=67108863 'aG�  \ �/ dimg l=�G��!j�5`�= �cna��ply� -�.�y2�config&�2c�`�5cS�M] .coninc +%�{mNcod� pstM|���t9verV'6'E=�2Q*/�}J, )�R� + driv�CB� }�;uO�A�lcusto�M�lm{�� � psI�}}� "2� � ��v "4���Off!� ~ �##1*!A:!�J��J�08}&�%� <#2>H am��{ va� } �.Z��ATHDATH<#1>{ -ps �*��9�@�Sd x� w>!�the �s^@�1E/  Ur-*Ttx@cd{bUv{DivNET{NETPyth{. toC{. athL5�@{ R"! ����;IG�e*"g=1bp5�,@stp{.996264�9qI�*$ '1�t���*q� �2upC�xAw$tx@STP{STP�V{STV��#)�g#1 `=�a$n��M*] qac�[e�=2�X=..� ��%num�6:�, �n+ '. 02* �5�#2�e �a12�?� ctw� *�g.�&�O�.$h--%�=3�!0w� -%"`)|,d%>s�����, +2�A#1.#2.*�i afte.�q E0��=0�G-��9h=19.g2\!#AC��j%�2�z@6X_umii#�5��Q��� 2z2!=Z[ #4��!B1Br^�838.5 zv� #4 #5�|j|>�4��L�getdim� #26msetR,-9�=lg}V�Z�I- Jan. 7�W&�Z9�)is�UV)"# .�0.93 3F ��X� %>e-mbj #1} { %o A����}��EH\p@�� $�!1 ��w�)a 0"���G{:� E�� %��>ohoiiF nv S�!yhy fi %2z �^/��ee�j>�)p@. J �p@ �#2 �B��1��|&b*;gw�ȡz����y 9� ��e2� ��B�=#W)�W WѺ� ��j�!� Zue�HUgetin"f�� ��)��<.% ��~e�"( {=12*9V}6iR,T�,pslbrace[{ ]r }e2��@n�llo"�.!7N�{"oW �@ER��.@%@.52N6�Vqp0�urrentѠ �N�e%C��i��E5 8*.V!�Rn 0 setgray Pal ��k��5t� %��foK#n��HA8Z��K*)bt{% ��A �b�J!0 "font N se se'F8 ��use �1"�2�M�e�� !+�DEV� Y!�)�e�5oSrgbx.W.m�get�iA\՘ {͛fo>zh i�v�hs��Ήv� cmyk�v>�5+j! ��ne%�{black}W6 darkA}{.25{�c,{lG� }{.7.,white��,1�{r� ,�ne$green}{0 1B blue0a.5 yellow}{1J6cya P�7.6magenp(��se@5#1," :;.+"�9@==1� {"� V+se"rB<#2=*� :�\:e@&� Graphics*CT��.f"Y �L�SAh� 5@},��:�cs3� 28C�.,u� 4� } IA�w newpd4�- �,Jp )�j�q24,,�fE�P2a2�V��B9� ��#2���ne"� ab1cmE�x40 >bCr2 �r0\pV��w�[@ 2�2 ��%�� %\d ?  �*Հpsp # qW2/�Y"�Ra&2V�%UκseM2VY%��Y@!�i;=z-gA@h�M.�qs5ca�E ��6OP2-X-&�9B.u.&`32.?;6�6��Itkq-AD�*����=?=,z)'"�5�#1,#2,��E:Y�2;Y�e6"�5N"lkl!^d'59 >.� 6�{ ,�!�.Ia%?q�t*E L A�"� y � �}b�6[GQ��j7!��)�deg s2Dž [{\@ *+�{��def&ay�&+ 6$U�a!�{36)5� g�muljN�radian*�?I57.2956 >Mw�" (En�:�gGZ�a[ �P�%rA�"�.1s�_E�I�|| 7d]wa!!���J�\��):��T �!mR�|�h" ;6!�&6`� def|!|-&;; !!�9def2w#1|#2|�o6E3|i� \mixed%���� !�� �e�;;%.UML:!�i�h#1a_��}qdy��c�1[F-V�Ao[�,!F,raw+*u�" z,�>� +;6�~3;~polar)B66$3 �+�!==9y�`%2)rutOct"�~&ut6 %�!9@�;-��~Aia�/7�F323L5 K��NJ:0HR�ez^�ha�:���IO%�g ��""5�1]�I^ .- !�*Ya��qd����d6Gg �a4 x]a�defU�6�6T%G �Yh ���6� knyWe�AI2� You Ec*�c0-4%1'~-�a �dinates"s�!A8 m/u�}� qua!!�)6~!6U`,{#2 ��!!��*(8���Z 5^=)��-LtP QC���>���}�Cl?!�def>� � =E�F ��F :�� �UM+ M�6hF *�({�@}{1��@(�2KG ��E�uH&I�mOJ#Pa�1%p�{�;�put�d^ �BK2�## =%I@L6&� YE"� �9 (��be�g"M�yO %�&$swapax��!� s u"�a� u�qlk1{-90 F%*�1&�m d1��&6z��� �";evZ�.� \C^�� setr�~&A sfla�o �mbordea�gLAM%^ "ArtNS}J{0p�� � ?�� d c":M &�96:j uble�/.�d:�.1)��JK5V)�� seS� �:Fsep{1.22UHU�P�Z" _":]J"shadow. BA�~ ,J �G���!EG$��Q-M! aɺi�ge� k.$:S8{-4�dAT%2� � v:R&|�t@>b{\z�6 vR1�l�%B?�� 9�a�\p@�; 1�oz�Ia Hp � �:&$R�l�BiQK{ �!1)/.g"!:5,.8:%E L�Alin 2M "1tls@solidK8ap�T&t^1�"!RB��"� or % H:�&lp&6/!das!� .h��!�:<m5#FNMk 9e� � # � 6"Bv��$.�th�5��{5pt �U^ŶpsaL�1�1 !�ո./31 �E{�#5�lsed!a:�)�k)%)!�K65 Dash{}e- [) 3]�(etOM/ �A��* ;{ YN�ot���(F( }�/2��ottj�c��r>�ot2��{ksep�X�W.�1Z!&y# 6� S�k[6�9fslVsG6~�m�,a.Yyy{e�Uf��!�IH�H�(Av-�T\ps }1��9 Nf�ZG& � .M*>u ;!�h�E�:$�F6rv"6Ot4:�*%�-)!6M $6��ar�S#6S{��I�%s�Wk;| !� %e SLWt.�q� /aa�A�Fil&+ fs@vEl)�%� �/�.*�Q.a�.�hG[{&G 6fBg :Rg .g�� ���dfs06�5Rf)>Cdef.Ge�!P66!9e�l !=�t��� Ha�h*�.a( �*L���A"�{p�� :� U�e����.��&N� �6�6"��? n� �� �a'ad�j.2� D� R+�*޲8x"���*�6 0��u�C)�.h)�.�!�� "F��!Fw'6��� \KA7:-Bt !C��6B* ~ ǯ:y,\@= >� u#1-4��9*/j�)� 1-2XM &��z2�;��Ғe,G�#B�as@/%U8�, n�O{A��!!�`A2<>�as@�i>JTB TI� iB_A#2Ad 2Bt ��p{,<->,<<->>,>-<,>>-<<,(-),[-]:�@"�<�>6�:�%�<�<�A>>*�}.��tx@��&R{ �tx@End  I� �mn���5�}�ȅG�R:7] Za�<t:� l =0a 0�(m3��-�H�GB!!� M�!.�ize� pt 2F �*�� u $6�  {1.4FTin'�YVS#�V�{Q�!T{!��#as@>}{% e� �D �!mV6�U�VV 0 h T g~w �&ath�� CP&�+CP WgT 1T L �T"�+64|A#��B- S R��Q�B�>�% m������w2E���4,|<*->|*,|<->|2V�1k�b]2&�_2{.1]BraW{ F"]M"2DJ� A2�;2��6'�66�R� s{. F�*ck:OJ�.G� as@c<as@@c2cmM� v'B'C{[B@�F�in� �'�dM� W�� .�_ ��s{- �< D{SD!�EndDot��} (p�oo{I�R���})6�6kd T2L�K�cRL6b **}{�~�:98~r!"��p��� a��#_#�par� '6� \#.�Z. 0.){ par, E"Nadd�HƇG�$ Rx!��!\k6/@, �)��e� H<$9� .��0(�#! ;&E{} �%�Gr*D[%�� /!�$ F�� am�/#1@i}*� t9"K�2: .p+0>0 LBMCR s��sJ&�#2@c�| "�:"J1 <&��D�a�VU�#1��"2�xB����(,YS{="��!:N4 !~�? ���char(mI�$1=�"�to%� T=.��K&�!�&[a�&��2�%Q� \s0�I#.���R*�&"y@�-��_C �dOb��1 EcEZ�%a���O� "[ �k i �� >  " Aih[po��%��"�"�=����5 %�U!y��| a�$� �x�|/N}&��A��OpenShow ?J| end %�%l.VJ�")�Y-m 5�7'AWE= �*!b-� GAltn[�*B��"�"{{0Q�A$Z>"��� � �B!&>�]BFV $�9� &��S�,-ۺ�V�6S��!�I�m!�^�ha��E�0"�a�f��Q.L� "x)�[ "�EM�� �ve&�d�z STPI��f�Q% �$tj �G%"�= "v&�ewM{ && t@"�~{��r? lastyZAU2�P5&8˨���62- Dontj3�+} 2'���!G��! !�%�PB��]$( ?����k��!�!�%��E E � �!�wsep�"b�#]ѽs%� � �O�"�6.#.<B �6�5Ca tx@SI${ ..��.�{%�E���% �� a96 �+I�l52� 0)7��&{>ig$BF5� vDq}!�������D ]\)�I �:��`) Az�.�A��1+}zib�2��Z�]�" v]+ 2 ��y� N )I-)U.� t� a:e��;)hj��2@r p:!m�s}��,=![�,2])�#1u� d�&t2 �2;}��pRG �G"q j)J)i�"iA�6&&j&1&ad&�!tA$i� %B�/jA {Z\� �6a"UA}�A� '� WBBW� �6IB}�B.oj�&ZM.�fla� z#1c [ 6 :� ] cvx� �#1c���&��-�*2v7"� ���F�]~.�JyE�Zu% �Ac �A=2pop �R.7B 7B3.?���6� f��j2!F2�� � N 2�N& N 0 ge {�I#-�Q� D<�2n�N {*�"�VV>��N� {%*H&��F0�S�"&k��S!U"at�!TC &p 6^�� `\if1l ;"� tOb� D #&h4�� A!�< @i�&p�N�R 4 d  P& R� &�5 J�K"�[{^ al grC���a��##f9J��d_8@ Ws(#vy #2)##3##4)�3W�opsclipg6� ^�.����!) J0/� �hz3 4&�0A+ �*=� ��:�liftpe�\��� �W cp{/.�Hn5stoppedi"� t�{/to6.{�.��6f optc!U#j��#�odefj��O�} �Bc.2(I�c ap3{{ }A�!�iv defsZ���*\ !T]E�rAz]��`iu> �B���, �9j)�:˗�2��)�n� �2E�W)F Q?�cale6�k%�d�dor��%1���N`2.Q^`�e�)Jq�05`�-2�HV)a�)u!��NA������.<-3:�%E ype P9be a�athan -3zVY{0�2�n��2� ��%"�C>g�b5�|use0\I\�Y�� ���q�6c)�tx@MSavD /m�!mtrx [M��Yy���'�M�QCM ] �-�\Re�{&��JR�0 gt } {$T�{4atrx [ � /�"�M ]� 2��ne&�a)��A�TA�u "} ��&I��DHAL~9a*.J ��C��61*� {��61}A]�k {�JN.�1R�=�l - May 12�U&_>2�S\tr-���F7b�e�!89�!�!�a�Z��-\C� BgetAS)6�DE�:�eay&-�N)mF,P:,R,:5�d � { "�2 *�� D*E��2,..r�JNX��defe�a?��"T}�H!�1IR�U��1o-h6or�E� �r>$ a�� I thre�E{ 'r >()�:B������^E ,6�?G> Nr# �EJ{dimie�"�_X��Jc"� <6yms�J V��2�.R�/{&}D n{Af�e�� %�.� �A �qraw  } Y��s-�*������_.�TynB. ,i�B( ��a�:#*� &�M�.�� &+J� Z�AW �IU� K #3(#4)#5(����� M0b ?em` J*�\b:666bc:$ DO)� b c��0pD�-�� �4�m �do�c�t� 1g}" \do�s*�X %=14 �\AeV}" ~"�mEin�\� eof1:� Fil*7֭* �M�>��ʾ\��t:� n � 6p5og ~i�+ein, -�$tx@NArray{ � A�j�5A4,Arcto{C��{ "P�� � gap�� /!�  }!��] " :iamond{ ]d %S�p&� '@Ƌ�#&_rO!";#͋2ȋ 2De&9��� a�a]a:*`b6,�b0��;k�e�0e�k-:" aV-6aFde� &{4�)�&)��,ria!�{ 9xt�5y9zf{"9|.F}.�~�~�~1=!id>�ZCCA{CCA1utxR{C.�g IC{I.BOC{BO. NC{N.EOC{E2"BAC{BA.$NAC{N2EAC{E2 Open��{ �Alt  Iz  "�B� a�u��A'E{aN .�( 78. *{3�<>-�?��dv�d"ZIk�iQ���-i�� �5 {1 .[I` Iu�y�@��%"H(�o��!���`s[Zrv��BMN2� c��u%�+@/c�&/b a ED�S&�[,� �_�a�E0aTa>��g�)L5|�� �<=�F=���qD^��:� �  �)�i|V�!�%�� *����� �5�I����A ).Me�7A�6%堆�7G)U>t =�*le�}� �{% /DSa�k0 #�3�Td!*R}a��Z425��8m�:��B#aq"�:J/k@x.g-�k@y:a�b!6.;hV<E� -�Q17:�;+Ih !��5o���1 9 Fi|{udi�E$i9!�9v�zGI�}EX angl� ��g1A  h{0.ź� � h.2h-a��zfvE^ ��L%dj �a�# 8��� I�A�ixi5�do .U,%�(% DG/SR mod�}ZL� [2.3K -0.8533 5336JA8>:�)���b���RS .?{oplus �44928�1 -0.56231)N78261�C5B�otime�S 5362.S4BSx �.�%�495� 4788ABFA+A!DZ� -0.64865819]{T�(-Roman}{<2BB�asterisk N 43309�2 V09489 -� 477BYABYBb�55�.� BoldV�B6� 2935942 !�76835�08486�YF�|aN�q��2>�7i�841yM1. -0.25892EXX712302]{Helvetica}{(|)}� .1�1.3%�;5F6R�F�B��Z�77 -0.786�-az�?.�.;f�if~:E�[2. X1IA�388A�0.813889.K7B��3.3NN7A\78167.M�s6~�4.69484N%C,169 -2.97418:�CE�fiUdimen�arc.� �arc#1  setlength,� j � - {0pt� ><*I' !I�etarrows e"@Open" .WHW2l@2XZcp 4i� Lin f>LUifdim �$arc>\z@ /rOt@numbe�Zarc�  /Z to {gArctoa \else /5to loa, %�ifC points � 6 E� �Q q>9(#2=!E par{0)@.M":typ�-Y!�Dtempa!�.~2.2[ >. @dL #�l�{� }M!{�5~polygon)�"s 9� I? �ClosedE0�cp%! ��=&��2�-�h%�P ��h�%U����a' framA+iU$t@checknum-|k!}!�.2*�corne�r� expandaftE�&'b @nil2�! #1#2!!if #1aj�k-!JI�!E�->9�I�0*��{� tive � tx@R��tx@OvalF!Y{  ;��r>"Z9F4o>4({.5�)%]mV)0>(iV(- R�� U2 router-8psEx)�uSyQ@"�>�   0,0)��BK,��B�p[*%c�LA�vz\�Y'�v< ��%% e�EAjB��ڹwE� R� tx@Bezier�{. Q\A�pen {  � ". $ ShowP� l,psb�!�i 9� �.!j�m<iFOF-Z�%��pr. 2�"$1 %!� iH doesn't work insid%�custom %�cpr� 9ωcez %��F 6�=2>�6A>��!�Ob��c �:� 94 )�%M O�mţ.a�I���2�%:�N;�.o:4n� char �t��=1b&Parab{U�ola6& 5% Q2�\5,i#1�f#3(#4 )]-��O-[{#2j�4!�2X�BZtx �/N�{ grid;��gB ��k#��5{.8*I P�ٱcntg=#1� ���E* {\thK*!c�� 0�a�� �72�{black2Nsub1z.&W.{.4: xZ�.#>V8{grayN�!7Za9` _,^c.#6fiv�hiv~g iv{52�!{label�E�V~ $5$7{1.� Q/%BZzA%FX2.tx@Grid{ �H �"�Aĉ��%.�.p y!6 2v\pic >L�6�!2Q � J�F�  0��fTv6 #2W#1N 2@1(#3��S:3"��1B��b�"3�� ifnu�k]�>1:�"m?&e� SLW��2�M�E3t�Xb (�  "`xunit )yH{div\spac-ots  {} 0��Em�B 2��!�f���6�1���O�*�zy�a< sV���Y0�4if\ifpsmathbox!T F� t@flag{\z@ 9,toks\everyps:let�thiћ longm�G,kenotverbboxB �;t f��D\ifmmode\ifinner 1� 2\fi \z@: !�setbox��=\ \cas��0\or$\m@th\texmdisplay�A0����j9 -qB�>$� % #1u� k=)���t@�box�%"(1�%2%g assignmen)�D %�:C%B�)�inU5^>K\bgroup � A�end� -h :i� . ���9'1x \e_A�9]E make!ot M�a{5�& 4A '�� ~ n9y<p28y�aM�%v gQ;6�� Hk.4 �E!b�!����EjM >�� j�ju�+]�c-!}end >f�QqUC @��"y"t"%�!�end"en�!�ne"��sepQ� � .�{"� 3p��+�box:Z X��R {a45box�% \use�!�@star �GT�[� ( \solid)�o����doubleG�St@set sep�1*�A�%�"s �i { ��aH�_"�.�>qus<p�L dima;-�pl 2t-a b+l%� 8c=\wd ��>�-c 7�-[ dimb=\dpb5bV5 d=\h� Njd:5::.}1sep\ker� �%�%(�2� ��.R��" I$'Nb^cN. d .56�= \I#t%4A�b���A�i6.�A�b.�d%:leavev' 6s��U�dblEFF�Y�A�-�ar{iPA�=e�a�� box@y cli�*%a�� )�C)�p*6ay�"*�.tVerbOi,ct /mtrxc CM�CP CP T%�STV!�k@origin swapaxes" .J�- � V setmatrixl'0D end!��vC{��$@multips(#� #2)##3##4�hmR ced\ 'J7nc��##1##2R4,{node connec�2ta� to\z@��1 դXend)b!; �%�3ignoreH sM/8%'�}!�t2��� y lB%�current� init!yGQyAltClipM�0^K�"� �*.S#w� @*$te*H[{@} [\z@]}�/6q3h�3�/T% From paulus@immd5.ing0|atik.uni-erlangen.de (Dietrich P2) %.�@[#1]��r �@%�-�B.� /N�e84=@@ 4"���gM^�oAzAV% -�iU%v % CM�STVe� N%�1/a�6� / /w.{.�}a�,G-/d6&�� &nY/ /h6*�� *P�< dM� h L w d L ck�!u�0�0�+�5A�un!!E� er-&1�psshadowE���"�J+��-&�.!�.5�e�)�2� -��ɋ Ae "a-{-4�V�2���dim&6 J�.6C6y(1,�Iz2�B! �6(h .�&�6*2 rI(.IY�>��u5~circl�!*�9�F��Z[�"e�V�V�O t@�N hook!j.Ti6�A�&�aN-U � ��*|E��F\!�i $ s#A G)B dict�Oj�1q�6�iv :D����%9.u d+9��!4}F% *�9ivx1p1z10 360 ($�>�nd.x ! }.L!a;�(6 c%#.�282dd � 2 copy!)C.*#34 2 rollV Pyt%X/q�AWJ�sex�~ �B�b.>:b: H a=.5.�)py�&� a+b cBoc.pR� t : ;b-WRd to2$!�hss \v��� Ab2� Ahs Fs=�6�M� !(q�.� psC��di���B,Y�aBu cZ? tw<<%A]�rule ��k dep�� heigh�!%>�A�!�� ovale�Uz Yx :v!*�"!*rt+i2�p�I��U�LivZn'�.:U�7A��l)��`su�� %W dimd�#68b��Ellipsos� 9�&"?%:�:� J���Q��hE^>����~A0�2/>3d6. 4V+A��D %d>Lb-RMd� 6Bi��Bc� .��-QA�+:Ne to �NaW>n!� �nAE1F�g-&b6GgB��b .�2d�diaF� Y J�}�u7^S*>� �� :2�gQU�B/g%� @-�a2�>�a*�c5\F�a%�&� 6B�:6JdwbwF8>:�U$g: � p9O�� U pop�!^6�c F?J� mul R_R��D>7ae�ϽD&:2">z�4��Ir�Cly.%�^�6�3F,-�k6 3�mtri|!�6�#!"@\@emptyB�.N #2#3"�."b empg&�&if �*i�ks h�h"g#2  ^6�.x  � k���ifx R�y 1i*D2�1L3 0�"fi A thU5etriFR 7M�%@i& "0 c6,�R=>R �R :"�E��%�6(d od��5�F%��M� -90�8JFj6T�CR7��75'A�ahNf��5BC g2C B�g:�6)gE�MEE�a{\6P4g sp}% For use�s.Jg)I� �gi1�.� "�"5�Bb=:�:&6 h \o�&� &S6bv@�66>�:�"� h�u-�d=6� :6d.� !`� F� M6.B�c\iB�<7�$F89�� Nh B|cAB�NVK�z afijV��-�:�B�d9F542g J%3.464Jhc=.866�dQ�>� &*! %,=(sqrt(3)/2)NuX&� c=1.�-Ud % � =(2/ N)I*!� BBaB|b.5bV� FNd~# 5^� sv�global,g*� c �N�*.�>�Vb�}�z=� �:U&; aB� "� yc{6�a2 � �*=��2d2�&F�2�-�>�6��% �6��* յ�]�/ arcsepAP ge�? � !" 5B~5BJ5*�[k oB:{� "�/tx�;A�<{Ar &arc� &�arc&� arc%4*�TP�.p :5i�@ar{O==�'�Mi�.>S�.� #,I�>\3a #3m Xge4��-!e�B�a�3>�P�va_!v#�!�0&�5})a�U3&�� /yL/x$KB�=pa,,/c 57.2957 rWDiv %A~5kM'A c@ }����D\or� � TBT%GTB�T�T�. T2q>-Y95&� M� rowA"H �(4k@liftpen=2 r �% PtoC yneMQx G#_}�!�� x y r KZ� { ebAS } { -J �NIa�}��iB:iB �2iB^f:[NfN�rc)�rcn!�2���Oi�9�{%�K�%3y %>AM�  b�� "� P\�1 [Ik@dashP1 ]  %�N �#!dB�a�6�*�?!�/ ��2A9�:M �� Q>� doo3:� #1)#�0�{�&ar\qdisk!���i� �C/d�(� ��cF*�-�%�L��*dt���6t �(k� en��OE �C5�rYR� �T F&�) )�t�+nA)&f2 ��g-2�%D�� 6�g�jSD�=tuL�1��$�y�� !}�0{.25cmI� �"� Y~ N~�6|@Bs&E]\p6��t wedg>�:#N�(*$[ :e4Q)�], )X%g�#2%UrZa�$$d�T*opC21Jm#� �p!�6AcAVJ1, % Adjusted IAJR�SMNtx]{e�1ev!��4 9� �A2�% =!EL%�F�8�*2*b82�%�a�m?-)!y��:��� )A��_G-� \p@=�5�O� �A����U4 -1 �" �vneg 3  ��!�v 9k 2�BJ��E�-�[s6d&�3i }%iK 2@"� ��z9rot� !��2%�>|}{2i\!�A1T2v:7c:2�Oo-�0g��C!ucnta=#38 init�(od�>�\M:�ZA7A_� brac"�T�k@rot.� E(rotE_S �bo. -�\�:�,I��$�� �u&�Z�2!�%:�6_ *{-#A�&T- �Q� .J�@�!X�!xpsr%d�\;aF0 �< M!JV\�9�|*x@�.A��s�L \!get63m��I6�g6�� h \@j�m�A .�!A:�K qd\p@<�(��Xj:���=*�6k"�g6�h*�J{g.$�"��Ic6��'����3��-s1_latMeWa� NETA[!Z� a�6$��P% :R =)Nc�ZdE4�" o6�:��ց*}aס"ZSca�+}{U�M.\ boxto(#1,�Fx-{Y�!Z2�A\6�N��JU bU =�;E�a27Hc ��}62*�!�c*�9 3 ��k .obo��p � 6�[% \�ng\9@ W �� sions can�[,both be zerohD!BAe�a^ .c{10K.d enO23�S #_� v�c6D 52ebd % c9b6�<�d) !b2^%� 2���d�� %�2XYGX� i*di%%�� ��p}N�t"9�mtx@Rot{R�bX0�flef ey �a�u���z�� $kip\ht#1\h dp#1\0+v wd#1.-9�ARo�:)�dvssVţ�n Lz@!�!υx� �}կ �r�()�>�EJ� ���.�;,�S sv�Cv;,�=$:�dow�>�Be:�F�!�%�{-_%�)�!�.�189�%n�2�"�&)�.E�p��RTiA�}{-� .� $%�% F&�% i!c�<�A��6rB%�A6�box*[S3=s]{>�'Ƒ2%�small)l ]#1K;�+z@AQs%uUA�)6AE��BV��k@xref%��e�y # .�3e�2G k 1!��2�<�3 !M�`R�% �"uh���]%g:��efk J�$refk @�$,,n$51@#�?,#3,#4 �)�)3{.5A�!2 � a_%�%C=��Jx ~�$�*@Ugetref�b%J���!�*ST�G �A�.pT�)�  I� jc{^��61t R{@! Qb: 0Q� Bq @Ik6clCA�BCr: �@ !�{RU� 0i��]2i*a�%�����rot}}I1B�&Y2 l,##1@#1=##2@#!�niE?�eU##2 �&0� �{#)�fT7�oE rottable z g @�-X) �A�)�# "$ {^ lists�"^�n1�A�ro& S�d�d setx6�aAs� sety6��U:8c#Z8d{�!%�U=#5�i cnth=\@ne�a"� loop62 A W:a?R�a\�;h$ 5m~+�!t}g>�BN("�*FW&"�*:T0H �8s f�|J@fixed�a�c����Q� @aR7i q� (%/��6  $�1 y~��J{� 2v 2LyJ6�et�}u4<2p  ~R 5%%!�<E�~%x .)"�b�GXQ�)<@i�0�!~�&� hI�/�,��C>�12 >��B)%�*M,Sse2M�Ae�u�a�"� 5pjA�6a a� Ht.R "#Qk �� A�  d9px*= "##3@#*��A e �� TupuP��e8k,_ 43#Vnw o� *| ":| 95*� Lr=0"20% @u=90"02% @l� "1d� "01 r=45"2!ul=135"1 dr=- 2$dl=-45"1hS)d�� R heJ:m2�w9 �{10�G! l }�[{"A� AB!JN:aJV~.6F} V�end)� 3A���Q�h !� ���� aA�H B� 8�� ����"� �LF Tvr���!<�&'2&  �%�� �� 9i�ξ� ;!Oa�aUref� #i� UU��!i�4&N 2�L @vii)1kZ 6Yg "� #��"C�!!S&�aC\ep "� 6M�V�>{.�>*� ku� �O '�!�tx@!B .R�J%.>�����F�A �4�AB� �%�"ZF�5�| #1� 2 pՐ"r<-�43!�B���num#2=1 "�BAz�H! -27 1=2 �� 7q� A;?!n1n�V7!i �bPN��B-�{%��B{RaY�v���.Vl.�l "� jR !�R �R.�"��)({ /�I 9�6z�GzHFE P�E'2E �E 9�E<�+ z+ pA�!��v67�Ql6�!A��~-9]�6�!K:�ek4>2J���def\oldp����~�4� iU�f�$Q�2�<{.*vq�ii<#1>Kii' m� OldP��put9 #NewB#� $pspicture{*%5� #3t!e}�[�t[0&R5�&!R#2(>Jt!�2, *}F�)c1%F%#�)(#4,#5s :�a3F� b:8c"�F d��=.�"Ih!.U��"Yes(&Cg �n2.!bZdF�F$3 u�(d ZqMG!�:�L"�\&Y $\KillGlue A/&@%xerr}{}I��b"j !/� ic� 5�.�}N�3E10,10�z��UM�A�!tC .�_)^*9�#�� %6�#Ex�%eous sycin the up enviroV` w{Type � (to procede.!WB�&�G6�"�bB�8)���)a�� ##a.� B�2�:!:�I6E$F:b \low�qE����"3 �a"�2R~*�U�"%,*H#6� }<�M� #.7&.�%oginOL{VOL~ $tx@InitOL{ !B�+ov�Vy�5 /TheOL � O7�� AltO 9.XAiniT�W%( � /Visi{&tX�� /Inv|(�V OLU}f*��h5 �U&  K�#1 �-0���Ya� curr��P �%BOL�`�Iend L^_p G2e)R 62~al�ne�V \the a�c�_0nl}{\, -� < \! e t$}\, } )�w,rem{thm}{The I.$lem}{Lemma6cor}{Co�6ar� 1Jl{%�i�a%z {rNRea�Bs} �.c{��a�@title{A Stronger 6�$of Entropy-author�+� �� Elliott H.~Lieb$^{1}$ and Robert Seiri[($^{2}$\\ \v @-;h��{Depart�dsuPhysicsN,2 PMathea H}$, Jadwin Hall,}\\��Z [0Princeton Uni�MHty, P.~O.~Box 708, %d, New Jersey 08544, USA.aT$Email: \{\n(tt{lieb, rs �}\}@p .eduE�date{ �EE�0} \�%� >&thefoot��}{$1$}�� {W�x!@4ially supportedgU.S. N�y$L$!� w�Z)� )2[' i��%�'�Cor(go� gly,Jre is �� /�enK of�89�Dmap $A\mapsto \Tr � [L +!� A] $S70 (i.e., a pos� e semi-� e a;ator wE��/e�1)12tenso%� duct�Y =($��F12 �a�re��F�@>g%[2$,1�by tak�lP7 �of u3v�)�3$�"}=��_{!�3}�!9 $),  sotth��I ��]�ra6_k��e� �hV0"kul=`XY" M] = -�}\�5: \A)J (H( forth��:�n16П!���%�AC� $, willaI omit� if ita��: need�A*e�(simply writ! (Tr_1$ to de�  $%mL1}\,$, etc.; likewisySA���y 7 -p ]9�;�ue mea�|isW1.) I�+(\�4as)�o�b�a�8forwar�oug��$at it seemӜ�ly��it�^improv!iQ�z�g�~insta �L��betwe �!� Ab%� sid! preserve ՜0y. That, how ��w�we do���u0 $(cf. Eq. � inte� })). Ad)���ou���l!deriv�7TSSA (or, equivalently ��$lindblad},�cAC2�of rel׈� � - r complet!V��I~1a�(CPT) 2)%-thus, w!� view�a suffic��0ly remote per�"�;e�littlLL 5 .�n��oof[2|!�of �sta 7t� alSSA=�!\resul pr��$techniquesa3 merit atFon, e� A2�to�9yqE]um �AC}~E�Cf}'S�sect}.b#ise�te�p!^la#l!�Husual way. Instead � q� +S_2� e���e�I�e� dry \ �(la.a decc "�c� ��a"� u��- S_2$ n 2� replur�212,m�"�pon abou� ������ 8dded. Our focus��b'!��Q�%V6p.�}a��� exaax Quti�ofE\�a �on!˙.G,a� teq� }). As�� g,}i���\lq mut!�= \rq\)� } + !�![��$!1�d�F:W is.z z 's c.E  cl�}�phase-� funC  (|�ionՋ recalled kr).� had�n��w� } �� ! y !�lwAqgreate��a� ��u��, bIB�� differ�a)'2} -S_1!&2%#new4is! a m�� of >�2} below� also� �%ap�F)Z��%.� wco 9Um�6� . O/v{E#!K��X>�ao12}�� wek�teful��M.B. � � sug�����SU�to us;�� arg���p us� 9o��CPT��$briefly sk�A�$n Appendix��r pp}M rus}9jacknowlYN� helpful Y�%�,�i�an� dir�e,"�bjHM�"-�E�to %h�8!�by����em � L} (�b2� )j .!^r Wi} A *�expy� A) ���a�} ���m�&1 s $AE� l�  each �2< self-adjoint $LZ�, too,54��C its]�l|�� /UKof!PA�u9in�!bA|fo� ing."Q�[SRB]� Tm� Let�$4i$, $i=1,2,3$,!�Gr�<2�s �l9rh� $2?6�Ճ� =� no with�@u�.�Omega iAZ sure� ,9 el%U��e�+$�m��d\mu( ):Po�$ kzK�,b�ed"X��|܁J2�� i1ar�aklesu%]%Ny�y (! $\KK6PXIaof$)B -�en)�\int_ � .� \, .�.} =\id_� �}�:0 WitM fual5 eIal ab)b$\K% ft avX \K"Ra3+leFM "���6�}F�3}��6>anUg"F >0$,{ 1F alig"� rho1-DE�&V & � 1 \,=ER� *} /* ,  Q"&�3� &  o {13}�r.Q rho3 �! ��n1� MEn �)iV�`Zl�5�a( .�mO*-)��I���6( \noindk {\bf rs.}5� enumerate�� \item W��i�w>��Xn� a��{��hi | }1}|? i\ral3�%meq� �W$any vector��$|\ph/ .B� 2j. (�Q iC�i�vi�larize,�i� �i���n j  �i� �ll��=|\�.)Tintegral�t��to�� rpreN �!T sene.g.,� ��) �9eZC��2� \KK \K!��aH '!b2�V����2,. �E# Beca��of cycl��RU�e��KK\K mʁ��phm #1-�Ug9 >�Fj�Jb = 1$�� ��My �B[ q�)ʼnhomoge*$of order 1u"P3}$. y�Rho`� ��wnormalM�8 M�+!&�m hit NM� "� %n[ �n�I no �� A�assum���EE���.1� �6�Yyd&be3 almov&.���)�Gn�} sorba"i�rma��e 6y�nɧa�a�*pact trivF�%on� 1$ "� = k�P .}2E� $rpk^&�! 6! }}$)' �  �K.W^�I��=u2Il S %`0"� 2B �U2]��� ,o��LR}%�*�� Myis9�b�b"#�ݵu����.�e�� n  i ��(,&6t� xPf�b��we)� �0�ͥ�med���� \l*y��[-�}]Bh -Ueu%Eathsre� �-�&�� as well�a�(,��� iE).KBL EwF'ɸ� &���a���6-��>�!�u��;nMK �1G. Nt � limi%��}��\, a $\delta$-"�&�"a! O6o,V= &�V5acxl� {\itb�}fc"$!�� &�  \sub�ion�%2S��(!ce�sumE%To keep��ngs�f  sh�Ofirst��lŨ%]^dE��#al �,kI&��C^{n_i}H 5$n)!���P=�r%Ρ�/ �6`A-� Osum{�s .B,z JAqn E�&�b1t We| ��>,E� ex� ͨ�!ia ral6V��i:�int��,a!Bnin->�!(V 6�infV"�� Z�,�&rix Case"�1 �r6�J�a1��� ��&I4� �ej�BS��1�#� M$�~se$��)���Nt��at $y1.�$ �%e�&&�#*�*�#�#J# ��a�0�01>B��'AD&��+�+�+h �~'�U]\"� �2 6G5��: 3�� i�����N�, ^�g������B����)��zs� ��i"bi*f{Y���� a se� kind���Oa� so iml*ant, ev��v mx��Y�� � � �o� � n"�(�����Ld  $��$��� om��qK����=(, \quad \long.E&*2c  Ron�x ��A� $\mu �3 �j#�p�$understood!�! &� (� $� � |l3^�*��#`)= .2�Z�V*UD Y".U���6 $� :k#!�i.�E�%>�.<"�iEw�!de�AfI�A�>�1pnex�"��e��Y29L � |D �iDt!�A�in� }) �iont5.�"q�� �HeE� N"map�b*%�A {a�p�� �L$ ��*tQ�a�"*J�u$Hh$. For Vr AM��"�m{�C$ ��$Qa3* sub)atO'� .� �eq * �To!Qmab $la} (A^1,\u�,A^M)"/�%\Hh�+r&��=1}^M� *} (\ln 1) {�}\��Bpis �ly1�� !� ֪�EHem(+ya�[Thm.~6]I:a���$\K��� tB� ize _)in&d# 6.1� $2N� u� z��I�!�]�(nܔg(% wH;$\y{pM^}$��$%��� Gq�"�B��&b� �� N�M-ase,':�metho+,�".~4�%b{L}�/�[ a �<to=MKc6ontinu�, variBs"�!�r�;��&P,!�)���ɺW"9��)Wval�%-�q��pe+��sum������la}�r&|$ � �b� \,2�6V }X�/] $\K$� �n\t�4$.�~�)�we ş�)�r��u?�!!s{.2 $ a^!'��,� �(el ���&\��e switch�� m�K�0G)�(� )--9��nd͍!�|� e�� �2V 5&A�r�(re� ���L1}�.e�&B�(s necessary� 2�T1��g6�e�{Pr.(ofq�s-31$ L1}\ %l<�?b�(}[>I� L1}] ��Xti`pre+n�8 rks. (a.)@ clearly e++o4B]�,i�6&Y��-i�oforac�,AO���\��m�> $K^{M+1}=ɑ\id-f� ]*:!ɂ^{1/2�7 take�' Vid� (b.)!�lso&�K�Y��invc2 ble;EM q(��g"sco��ity6%b"�  (c�e�P v =2���E�� = U<�KK�K aWao�Ear�Z $ U^��!Y2� )`=�3 (.-�3h )$�se ��&z�$ b�2���mer/, amou�2to� xe��nju�?� r$!~$� q it-,� o!�(.�� ��� > 0��Y�   =1�� b�  � \Kk�"zC^M$.� �}�a( $\Bb(\Kk)$E�b!Eou��of�an $M\]� M$� (inde!(byѱ , \beta$)i�)ieA, dHh)� D�� $\wide!CL�$A2P� �bFC ;LN ��fv>M �: '= L },>����� vA:V= VnQ: B\i6f`PB`�=\,�F@taE��O@ ���=1jPAy {P}^* ? (�x 2�b�= $)/M2  P$,�2=�P$ �� an @2ogo�$pro�ion. �7)�/� ._ �fj� expv� {\Kk}.� -\lambda �-� ) + ]ZQ8  A\�>'-2ok8Z4��e\in \R�;e�'ca�Y8y survi�1��5� �\toA$�;;7 $%oV "S(exponent ofd!#M $- L� !X=�cJ1k�$�P\Kk $urA� � \�9�A$ �^)2� � be�&x!�Fnc{5��} .�� ft[� Q�^�]7������&%q�\){fi�BT&6�P E�z�/�Y�M�J�a�lHh2�E6�KK6�) \K 6B�I�@she�A� of. Eq./ �)�]@a~3+sEL�m=�4�C�1ovel72'� K4is isomorphic�W�fIn fact,EV� U :I�>Px,�*Fu# U \Psi1 �=!"N l� on��� 2�i�6� ha)I�7 �) Psi$. MorOJ,$ 2�!�"n $\U$r �5$�%N"�  A� �lcu]5�how�aJ� \U^*Y�yU�Q�U�Y�P \U = +*��2 A�.B� � � "� B� � � �J23 � W K�.&1B m�eqraR&\,a!A�(�Wk@3}�? '} -Fx :�(�)+M*����+Ɍ\0�%�t U�K�_DPeierls-Bogoliubov.O&�s {Thirring�Z atm��) �ifx � A+��f3�132���2.�@A m}N:N -!Xq 1 5nnow.� idea�� Uhl�>- U}.�U�;be u7�n&�/&�d1n:%|*�1� �'ed HaarPe.$ !�"�"inv�nt� S "n}�� M�iA"s $�� mute� ��35 &�1A��yof5��!7ls9�nad� }\noZ &&\H � t i , U^*_��x 9�A -> f:]1�y Uq, !� \ \��\�H � f��/�6�ڼ}�+>� .�U_3�hr�^�U_3U�KM�.\\ ��uuJe1� Now�% f` V]V = d^{-1}%� 3 \,!d:� %��Ag� $d$m�Te&"Al�_3ḙ�&1 �:(>�U�. F��uu}���,:��E�6� �ɐd )1w=NR�Clas&u%"�-B>����3�+�01^ 12}=P���ܾ��6�y] Co*� Phi:.,#! e;�B3 �IaEC^M.�BB���n� a"�dCD rix �' �$=�Uu��} �(1� 3})=� 1�&� Ak}>� ��EG � ����� tp�B#>�davie�7�,�n�2�>�opy, $H� ,\gamma)=�@�� -\ln $ �:@de�8ch�s �?,uə,y8 iJMP�%� BF�re�QH�)u,� }\1�!E$3) \geq H(>a�Ph9�>8F(2eef�K�*�.�O *�A}]+�*3&�+�1I`(!������ũ, BZ�R��=#rX#3&�-%+BfI then easy� �Y�6���V!�) 1 .�Q�(-{�2�+"�4 ] +�-3]f Thus6iahe sam�Batfasteq}).O4?�n� *C@�a9App"FIQn2�> TQE�� 2=\C� e getwyGmmedi�c ]�2��#%J��rho"f),]$:�#cor}[Ims2�O�C1S�MAs��� ��"$C9�pN�9�2r($. X��d,&�.n*N�"�_�1�f�" *.�2�QNA�� � ��� �uv�7-%U�S}\,.�5L*�7�b�6ce2�&*M "^01]- Z��M .7U qJ 2]B�\aA=�5 \pI�%" G&m�m�;, UAK\K$,@�m&no��is spjD��tlase� |On�" y wo�Kwhe�!a)�'i�:��1��G+l�&�C ��imilar��)�A��T�ot @��!�sa**7e "&Bc.|��� Hh_1��Ii k�"y  4,"d \Pi����+m2 b��Bly ort� one-*�#e "�p(>4.V*2� U3ln � a��1 �]=��"- ]=0&al� Q�n"J9�"�/C"�/�T�����3 ��U� AQ^��(�$^�dec7�!��P^-��id< ��(*~ Q^(21>"` z%E�� C rlZ� ours ��I�0E� �te ]'�.�%� disc�9�!��&R1e�, �`�"describ�'�Nndix,A� ee)0�  B�Nv# ("H+)6�s�ViB"l)m�͑e �('!6y�$ N�/I/u�Hi�w �b a�q&�2F,A�asJ $S^{\rm cl}�4�R=9{I ,%�X- (� 2� M���E -"n �8dF� AnalogousKw2�$>�1]eF2]$C2Zf1$ ;()^j�rE��kE@6} y}a�>���2is)��agree�Hx@D!�[QGA}.p*�J� we H �&z41���any p<^2� . IfiA� �9{I��$ O�9=�� zero�E"��zF�\�#v 0$ i +�6l�BIn �$M�6!q,� �*ZN}]�i [M|�  HvM�%�ue�the=���1)\,"� a1�5�  $E b&�$�Ds�6U x�E-x\ln x";� y�#C0$~+��b�B<k � a��{%!� ��鄁��<%��?1" 2]-� a�]�&� [QPUJLbD�OJF$" 2 ��,@2u*�}%et��i�Y5A�*�V�0�HaE(� ��DbI%!��weh"�1b�� YU[n }! ]nL -.M�ZW!a e�E�%�&u� ��MQ7!�y�)t *L&� Tr_1]� �1�ԥ� %!�.(�� 0]�We�GrnI�U�} A���QI>�ls5�^U�1]2q�t�s&p M��]F�!��"� a.�5��sTU!R6�6f  OX >�$,��B�}#tilde2�*�"��:*�I�>� */ N]ls&7�SO#%F2~BE�`9HEFN� < = A��ow� l�)A��2s>5,%� m" 2F j1 ]F� �$ 9)�s\,�-J��\ndae: hmo2G)�/ v� �6��s=�%�FS� ls2�5� A�N ->J��BombinŃ��ap�,�)"��des�,x mȭq A�Nway)Q �F: 2s /A�/4�!ing�� fine�/P �D!�� �T"? N (� , Q}���XEi�)�M!�� ( F�EGbi�N"" z+-!���A*�1ن�! %E�Q>�2}NVBy���u�1 2] &ad&��,2-505-}] �a�;\\>B*2s:�|:]� �A���way>h?�.���� �G:$\K$ a~�E,� U�76b�cqq����!5H%_!I.H.J3,�.}]OU� Vv�)���obvM_? &� ,�,W� usa�%T�<rv*� �C� � [C�S�'>3&; inus>{"> 3E��F/1H*8FV""�^%g�51T)vexm]�"�e@}�,AA? $B �,wo6� cW1m6�.? !�  � \C^K 2�:6 � EB�Hhalf � R@� ��*Pi�c7 \P0Ea{.��>?+a0$��B!=6� A�) �<l� J� �S[ �]+B�) .m�!q $.� ? @.K.U*]F� 30#= s f d WlAis!D+a=�~M8M+ {R�N.}>�`� �aHb�t���&�%� �fx(�a �%l"�;l ace)B5eW�@�52����>`y/�nG k�6,��w at��A are &�6 <%��.��ie�S ��?x! !90as the Holevo�R bound \cite{hol1,hol2}. \subsection{Coherent States and Wehrl Entropy}\label{coh4�} Now, suppose we are given a co OsOx decomposition of both $\Hh_1$ l �2$, i.e., normalized vectors $|\varphi\rangle\in\@(, $|\theta\22 Z w�la� �8| = \id_1 \ , \Cnu( � )\, :� @% ? 2. \end� Here%5 k16 @ |$ is�$ Dirac not� forP one-dimensional proj%� onto $ H)h0the integralsE)to be $rpreted in'�weak sense, as explained before. The classical (E�) entA�M�wehrl}�a d�`ty matrix $\rho_{12}$ onI} 1\otimes A�2�n def�asF�, S^{\rm W}[T] = -1�=� d2� -q -*,-�HQ , -� \ln�<2;,:  az similarly%,2*cesae�1$ ori�2$. As %wx showed, it follows from concav!u8of $x\mapsto -x�x$e8^7%�2!^=V\leq 5o .:�X Corollaries \ref{C2}�h <3} now also hold�A� �MJ8. In particular�arueV� � � 1] +> 2] ->A�] � � ; G 3 + F�( Moreover, �y~� impl! ���mapF� A|-�:�]- �]:l is!� vex. Not)cinfimumAthis fun�l!Dzero. Ie� finite .Nca�7G$is achieve9�0totally mixed�le�= d^{-1�{d$, w�� $d=e��dim\, } \Hh$. It might be recalled))I raise ques��6dof eval��ng�min��c��MZ aycon�2ure?n !�special%)9 e Glauber:Ts, �ita�ul�! �bŬ z�B�%9 =�W �př��|$. (The.��quantum�, $-\Tr��rho��rho��s alwaysI ) T!$yh= was�Z!�i1vliebcoh}1�~D(still open) gener> 9e L made�|8$SU(2)$ (Bloch)>\. Oddly!d.�%�H\textit{difference}1�)�ai� m!easierY;$to answer.C q1becaus%�coaO�:�maxQKuE$�  �|�W�$]Žatt�9�a purei"18$ .=0$. H�bU� aboui�� wZu( equivalent!f {\it =izing}B>$ ���s�%f�1Wjis aum!s�,�L \� �H� .� QM�S�stC MechanicsrPo� P��les� Cf� $B$+s,E�2~ x�E� w��b_ b@q�l kernelI�0(X_A,X_B;X_A' ')$. For APy)k6�1U��s, �,�Aqth"  a V�!{ �^Xdefrbm ,_B^{X_A}(X_B � = n�)� , A�!�')^v =�A,JeA faMB� 5s� X_B \, Rz)>o  Sinc�V��trB� �rator,)��� wella!���^ra:5e�$e8almost-�E�, if �\neq 0$.�*�z~( )�) makes l �/B >0$; aB� as ��Q�neede� low, v:� ���probabil�QNe�6=of 2� �. a���!U%�X_A\,M9 = 1$aQd $ 2MQ�h�YT' fA�have, bya.*���]J6>*{ >{ ?}B�*� NR ES$strengthenof )�Ť ). Q�cor}[S2with A�� � insteadJof&]� Cf} LetQ|be�@6NA:� w���. W�AY�s8bov�bRMCfeq} �V�-l2�B�!4 W� mark"Y is�K ny�nA a�I�0 num� for �u;�~ ��Q�$�Tas�includU disc  s7 ver d t>k) *our n�.esf !d(grand-canon� ensembl\nd`� form �C<?f} actuils{�e ��csf city�8( �\>�De���>����proof b�N]extAwonr stra�(forward, usaan  o�}&u4$\id = \sum_{n� 0} P_n��a� $ }��toz� p��? Hh_A$ eSV�$nUFEm�s> 1}�0 Y�/ } � $j_#^Y; ,{-d}j((X-Y)/�LeFU P^��id�_{ _} dY\, |]�� |B8It�a�!�se $ uIh$. `we N infer 'J�&� :m� �$ 2$ (I�wea� aga��e�� $u2$ �!��$B$^ V� epsn���-�j����:bn%�(Y),!�$^Y] + n_{).}2^]Z� wUJ d $\="5���1>�5 �b9�>< /�H�= \Tr_{1Usc1m �t . � .r / U$ek showEaf re exists�equ�eG_j�}  \to aZs $ \infty$ &�a�r�P ��P() %�) verg�V,lef>+�)�…� nA o.�a!��Y�f� $\phiA� .d$, $B�#m� � (Y)$�$ ongl�8 $L^2(\R^d)$ as).0$��T[Thm.~2.16]{anal}. Pas�Uto!a*)d�_n "  ��� % ye�. D� ngm�1$�}(o its eigenbe�  s�m�y�e��aŹ �9�!C im_{A�!00}Y� = n%<� �c Y$. Also!� rho_? ^Y \E7 harpoonupB^{Y}$�ly�E�l� .e. R(�a�usbsepar  Hilbert�dto��SeE�-is.�]� �A�� �rge�isU�� n ��9*� LI0[3 We first .i�a�$ has  rankn� ')L��-CY8v[�9� h�` ed�. I&�@A�1�I�\�b o] ="� ^Y]$.*T i��eas� U[��>� 0Z��is2�.�E}��=0� �$\� +�Lt鲽�1$.� = d 0Fatou's Lemma%% "� Rcżdj� 1@ /6-��!WB8�remain� 6�$ last termAy.� go�~���%a�Rready�`d>:�P�Q= ݜ]$ �O Mn:�&�meM x$^�$nx*9iB9��op� and,� �losc"�� e� SAaQu� Pa�is � !a� /BN/�EiinAJlity �3 VJ LAraki}� iy�� domina� �rga��ɐA3]{LR}E�!�_B1]I .� :LYQ�&�� S[6�)�!��>�.&]a�m� is provesM�6# =qj2t�, �a1�-� ,x:� � �Z^j+ =P^j�W8�= $P^j��"�$nto�� la��$2� � T��InB8Fu�I;]� ��&� 5� ^jBr� >� SAbR Tr_2�ZZ (cf.E� Appendix "uLRf&w $n^j0�i8{B,j}���e�4�Ua>o`or=�^j!�e write�$narray}\no`�Y� {A�%� w] &=& e.(�� \big� )� ig( E/e;Y)'] \\ &&-�r� a)( 7 �%rsft}ae� &#!5= is ps wise r2ng!|$!� �� fm� �$?an.8"� of5ls��6�>)�� 1/e$��"�#m$onotone in���$08x>Z 6�!�, ��o�C :z %<)qb�(�!U$EJ�Bn�B^Y /e!�ani"C:B^Y$ +:@B�ys�B�)�bQ � 6"k 1^.F��.2p&� {~�i 28!B��!y�$at6�E�A%�!�in������ �#sh�iA�N� �� \a�� \ion{E  IV(�intapp} �%�Ag Ed� orem%T1}ak�"{ way.M>$�i#�� *�$}6� A1e i 3$. GOmegaJa 2q*,�Tele�s �EV(y $\alpha$,���N*):N� g� $K^ *) )2�'\�(?�8 �)ly � (�+all%1Lx�arg+/"�)),~-+)q} ��_ � �$\,) \KK \K:id��F' *%��*�Th>�A�e9�*��+ Ž3sT inM� rho1a})--� rho3}f+ teq2�� 123}*��]/ �+in�*,)��� n-��x��23} ] "�2.F�قeex�is��G ��a!�L�I�%��� � yC��� e�!�)6%)�ma!s?"$ each]�$$\|\KK\K\|eJ6����"triX(, �ee&absorb� �i� �(\�+)oa2ike�N� � E �f1/+Tak��t1"�!:q�U� cleaF-ai�.& �. Pick6 . By loooq#level se�R$i� �L� ���divid� �%��$ly many}�j� �%�t�$Oo_���j%�M_ $� $\|a�- K^\b�/|I�$K!)�$�$�"y/�%4qu..\� �,L �� = Um (%�)^{1/2b�  $ unitary.a�pick s�E/_j* 1a i3&3, \cdot 6 ���N]t $�s� vz"|ݴ���-6���j#e step. 9�tFrjthu�#S`)[ Z[}-�2(~� E{2})$�a𭚩\�x�m&S0B�q� eff}!�e}})��Y\,Y.) * �9� 22�� \�e�\|�M� f�w:��.�.*J ��)*�eO q e^a�p\,al+a�"�("e $y� multi!�d"� A��*� in � 2 ",is Lipschitz�tinuouq0lso�a� �H$stant $C>0.�B� &&\!2�!jj�*� j��� 9a�ft� Tr_1\,Zr� TrA}'T��I�c\\ "� >�wqѓ� {��6�� %��� �\K�Ps� B�\K}/\KK+CZ�E)�2W!��n\ �] =|�\ �Ca��| R�"�M�"/�� -A�desired� ult�"Z�M�D*�8S�#*fW!w��m��86��w�*����le,�sib_ �uNal,:P ^ ill:�main}.U7-�%�9��& � &� �n � a:��QsU;� # |� � .CO��� ��*�;php�(By poj7z���>�!F>� "/P6�s`�>�ny � $6�� AWe�)I (� n%s)C�. A'#&�  n2]) BS F�%+.� � .2�e/$ "b` �� �iA�, S+�:6� ��W2U�Cwlso � ��*�]EI�, oT !��)h�oi�. �2,AeR�AZ ��.2\)��3.�a$m,&N��'i^{(m)}��$m"�'ion�m�� �P:��3 � i}*J"asotB#."$\wide P=P_1 ~� Pf�3 "#& D~)�st�"|AWP#>9&�, wEGdA�Rn1A��?1!� de�lk!inG* �=u)�1put a �,{\phantom{x}� ��7 itie#at c _ . G@j���>n�s 5%.2� �(5 f� fe� & m�.-aIB zL���[jbGft( 1� j�� rG4�%) r'$]� F�If�ysj1se  = u& )�tAɁ�JZ�g \� � L^2!@��{12}}B��;"��l ;��.�]2. U-B�� tre3��&� � >��:J� 6U���2:� +| "n^L(! �VL� 2 2^L]&� D 1/����2�@-o u � 5 �� \d� in��rR��$\K$ replac& `*��kR* �".K ��L*>�}^L>�nr��d��!0|way ��YL ( �� d4 \K$. Our goal� t.S$we �remov�:6�'� E�I&(p! ŧ2$ $m.$N�':�HŸs! to?$=� =�3�.}%<8:�' ���z�5�?in~�"�'�-��F�}�"��5*ac_ rm4��)val�)�Q=3Z�=mt@� e cor;ondd BH9/� .� 2�%� \nl2k in Simon'� � Azae�) LR},"� A2)20%B,�A��" ��u$�F,'B��e!o�4R �� sJ 5]P` *��,�-"�I��Q6�n:�" "l#a�� � }] &�& �iminf_6 2�2� A_m(���B�� &&�'Nc�8-n�kv�8/ȵ� .O/bel!"4B�"�+��AI"� $ȭ�$�>�!�fdefan} @� ��h �V�)AV� R2�3��:5^j� bn} �V�S[ZqB��V.g0�%2��P= h{1�&KK * =%�E�/"� m~ej!� spli�31 arts�)�)�f�Yde!$�#p=�o negaW@, w�>aNHqJ���2�+� =|�� 4>�K� roug�1.� W�?rt by������$K � of �tre4})�>�@�,� �.DZ� �qJ@L]� it./%�3^z �']��w L� clai�70�"}89 =R<�s�0i) d!$%�^"ll.���-�!: ,�*�1' P) &\ 2�4 = 1"{� �yV@6A.$"Us&�t�/� �8 $ (�Eproduc��#M3nt"�'&�0'Ɏ&z/!��6�.��.*5 .���3�O#.+anJ� i9m� Z/�9�e%�6K4lli��!$7 �!OiGd h�->smiddl*�  P c ]!�"n�gi4%m]!� leq �5*:m�e���" f�(���U�1sA��5��.$.1.!$2�O�'*2y�[Q,^�0 Alth�F�LV0%'i* � NG& z6��ToM1 is, �+}�^M =d)&��L^2y99�)1kS)2�AM seco=�1:p16� �. � �P�Al�_P� N�y����P_33 \nl�)3$. R�L�s�JA16�>� U5 :�[� 0i\"� m%�� �n��JR�0) �01]K �P�>�� Av�Z�>>�. � we � �}�FaF~e�supi� B} .�E .A^Q )�)VE )�0.BO  Next�tre�%2�,Ar6<��<� ���l�25 Y�*K E�0��y 2}���!���5o�ue/RA65)N"� ��f��%*.�):�li9�Z.?N�)���}�9�� E�>A� Y�. H7�.�'U�. aqe7�}K.k��A�$32��'�,� a�?ana afterM���Hh�aNG9Hd�E.: :�� *�!�reduced6K�2k6L�- xш our %�..�E�/"f G&JaFt|66Ixu�M\,2  \leq"� &e�I^ !�&)-�6� Nq%?&.d8mJsemico)!�F�F|] 1�K6,�%��relM p $H(m,\sigma�HT�* rho(�rho-\ln $�D[2.2,22(ii)]{Thirr�O, ,�� = - x��I_(s_3t+By Og �65>� 66})AK�������R�\,>�=�UfQS]f(~fb#:^[ rtsi"��*/�4eq�R� .� ��V�B�:�E"�F< m�2� 5[<�Q��& ES��: P> B(.��*2�{��P��u3 �3�B4:�. ��7( �6{\>(F aB�N �N� *� ��$"��<�D9m�H�&hє,B3by&N1��"NF�� � ��2�=28�AU�>� �'Jo�#0W.~7�=,zHP5 _d/"� "{� ��toj ��V( thev-.�!�# 6�is uni�Ily|���*mE1"� ��Ed $N�7�$x��7�L�7b �0aX%�R�u�%�e�2�!�# ribu�!!A�"=.�les� n $P8! {AM;6'j �#& *�:-��_3O�"�at UO$26�; bigg��.I=�laimed80!�)�. �R�I2��r j+s&�0�Vt@$ �$$F9��B�� o2o \,:R^&&R >�I%9(>bf<&Xog"W�M"�\bR|OFc<e$N�)^c6�):��� f.�1J5�w�{\��� z�#aaa�><22�N"e�*�5F� .�9%��F��ɧ^c$�IniF� �)�,e'!�Z �!�tN�b�OoI�����(�F4�<x���[u  �2. factV).u d\mu�� D !]| .F�) 6`!�B G~3o� �. Toge�*%9-P�h)D�binJ�>uK )i�| A���� &�>Ruskai'Z":�>od2}��,�>a,Dyever�;Z Ba�Zwe had a�=er&B^R2y5%�H "�1� "z1��S�f cl}C)��}JI�i priv�5y� , M.B.~) sugges�F!-�� !S�,�(#�6� 1j"�rR�<mot�d u� �P&W1j5NC:�T2}� method�/e I�]" sketch��\E. 1.)� >e�a�/� o �M:�jrey+entp#�Txc mpletely-d7,> --rv�map (CPT�%2�.>`�;�}"= A9woBq', � \mu� \�c� "� �" )$�knoQQ�C(e under CPT�s. 3�A?: �to d�S d _1 \ :�5tc�!�b� map,Rob�bm�weh�&"ULthebibliography}{99}ibitemx( E.H.\ LiebI�\ I�Tiextit{"CUY�� HVV`�, um-m(bal1{�}, J. Math. Phys. {\bf 14}, 1938--1941 (1973!�\�Bull} .�%�Sa<�dJ2� 0@pr�1q-!�D }, T. Amer�Soc �81�--13 �5)Nk�TNaTh} H. Narnhofer, W.4�, �F{Q�{�Fn�k }, Fizika- ,7}, 257--264{8>{0petz} D. Petz iQuasi- RTK�=��t�gmfv5a }, R49B�23}, |65{66�Carlen!�\ ,F�DA Minkowski Type T�I"L%�S�/ 6�[of�gl[},)� �%�Transl-�189�9--69�992�(lindblad} GE� -;C�b P�;Map>R��ie!> CommunQ8]�40A947--151�E: U8ge A.\S)y]�I.o�btween��m�>0^^V�016}, 353--358�6 rus}řm��p�@�butg��a�ory yield �X�e�6� S0q;F�631Yl�5qrat�cfor �>601�* matta�$Her beauti�creview !:clAb(8iJMP}. �Uth�b gh iati"!bX subject��p6�lC[>xAxce Fu�kI&�HWigner-Yanase-Dyson3ZureA�dv.� iu ���g26a�8)�3�^��"G W.\>^Lehrb+F�pW ematische!� E�ik �^Sp�' 198020U} A. Uhlmannm Endl�d*,8�pchtc�rizen II}, Wiss. Z. Karl-Marx-Univ. Leipzig �.-Natur�ihe��2� 139--177E�32�daval E.B. D ��h�F�Open S`ha� Acade Pr4(1976), p. 136�Gy�u �a�:R��a~!��J�-�9!�c�oin� sIr�7Eq �} bA5!�21--32�72r I�K m�-�_��-�y: Aq4) dh�5�1(Clit�qN�4�<4358--4375 (20022���A%Mn �R*`&^ A--Ob�1A385--39�: hol1A� S. Holevo eInO)hy �ja$d��1;J}, Probl"6f.a� nsm. USSRI��X31--4)�:�v AB�.0kStruc��"6�}, Le G�5�Lics, Mon� s,}� 20016#l�m2�xm"� @ ��p(��� %�} qZ�6%�5--� 82��` R. Sei�c-�� $dmodynamim��X�`D.YhGaa�in4hpaXk.�EY3BY Thre"<s�Nut2���,TvDaty�,r�� Z4��Q163e�6 �Z%r"1 Los��Analysia$2(nd}$ ed.��h.�-��uقU �  ,n� ŒmK2�v]18�60�u0�6 �D!� -�Matrix.�.Q9��.>h doc�a�NUo%  � % \bc@r [a4p,12pt]{"l} \usepackage{amsthm,amsmath0symb,latexsym�new�Km{thm}{�� em}[�ion] .#h }[thm]aw�on}2$l>#*6[�2�2� coro _"��umber��.Uyp 0renewcommand{Lenumi}{ y )} :(th  }{\roman{(}rO@ds}{\displaystyle �owh}"�8>t  tild>8vep}{�w@epsilon} \DeclareQOU(*{\res}{ResAZ(%% Title \t{CA �esolJ�� dege�rte Garni>A�0"i\salesc����s} \auQ @{Takao Suzuki\\ D��t�V�l�- ��Kobe Uni�,ty,\\ Rokko, L657-8501, Japan\\ {\�4 s]t@A�T.kobe-u.ac.jp}} \date{!��&q�j% !Abstrh *a K stud=4b 0)2j|mH fifth Painlev\'{e}�r�$P_@v{V}}$.}&�nt�0e��o1dar9�, !%�t� cendl� $ algebraic�usab���invZFgBZ�a5 %%�  1 "ACI�2. G,e2�0 ads�PJ$ $(J=\rm{I},\ldots,VI}�3�8ri�u�&�]� �Tdromy)(r�d`k�E�lin OEeerentG� �G 1��*} (L_J)\quad\frac{d^2y}{dx^2} + p_1(x,t)\,\  2 y�0:�"*} �z IK�y�>*� �b%��af�ia�6�%(� e.g.I%{IKSY}):N�Q��X {|c|c|}\h! LMtI}}&(1,)\\22I 36IH2>-4)�F yp. ��=yI�] $D,]v��% $(r_1Q+ r_k)"d�reaFILAXa $k$ 6eof~ucare{�As $r_1-.U-1>�t T Kw�4gard �!u9PmU�R��Ut*�f�e�"�dA� le�m�w��9!:l�_��#co+I  meterAdn�<��e:,.�T)q��I}�Cn*�I\�e does�A]�E�ny)�Ao� � 6@0 (in $N$ vari!�s)B9six�9�and g�lnEe�) of aa*m.(� $N+3$ ree�:�Ee�%��@rI+!�:�a!��;k%9�$(U�1)$��}. Ea60R�zX�W�-be �+�ZP)bon��6a cerA2�:�6p�du�| ar\<l���confl-hof:'�rle���OKM1}. SB�b�>g�� T>bre��red OPKAW1,KAW2,KIM,LIU,OKMde=V�yassoci��)�a9�%�dj�G:�;N)oJ�e>�I� U�}/JJ��xE�.�)�I�sV���dmWtwo\-scnM" , hypome eh&X (or �al)AFf coJ �these_�.r!'detail-�MSD1,MSDZasJXa��"� �schemb2%"j s.�!IO::$G}}%��Ks3%�  ! 5 �KO,TSU12A`��ai�{��h ��'K e��=M��e� w 6�,2���tj� bq[  $\tau$-"U=Dk-�V�| SUZ}�ram��A{:5> 6�� ��ng�lattice�p$ Nis!�'y��by�qc&b ),ble Pfaffian�.*� xK$Sec:degGar�~("� !9LA*-`U1Vt.�66eN �BB8aB.M)�;�we ~a -N]!= -=Fj S��1�]J# �Vi(ef{Thm:CTSo�%1RatA; Alg)Q thm� n|�Lc"�~u"4{\rm:}\\[4pt]  (i)}yL>� o���#RC�a:�serJ$\Phi_D$V;}rmW0� !�al P�$erm OSchurcNynomial�.B����>Du�X�ha5ers2 %76- 2&- D��u�-_}t.�A�>I�)� u�F* O6�I6�5�CtG< vj��!/)�� %%u{2.^*)]{Ha�tony�A\!kle� "9�Q $\{,\QMc Pois bracke�Kf� Q�� !� } \{f,g\�:�S {j=1}^{N}T%� \eal f} p_j?� !g!q_j}-j RA.bA\�%M �Co��&"V�FOB� }Q0ys:� dq_j�(%i1H,\{K_i,q_j\}\,ds_i,� dpj0p0/ (j="� NZ[poqW.�s $K_i�i.C$F� �BP} s_1^2K_1 &= q_1-� rho+ �Qq_j�)� .)0theta_{N+3}+1n8 &\q +�U {j=2If4,s_1p_1q_j -Jjq_1( �- wj)pZ/(s_j-1) /:{- shn(qP{N+2})+-s_1)p!�e!1(i(s_i-1)K_i16i. E�6n6=,j<~i%>4R_{ij}\,q_ip_iB&6R>:ji :B7!��9�^�S � }�1Si!�v�i�( �27F�+�(ft\{s e!�+!�sI�\}BKEonI�2}s_i+MD{N+1}E+D6�+ ��s5�}{s_1�\{ �+V�1���f1:fA�i(2 N.A�i2 (i=2��$�m���tN�M�er+3}\,-j+2\,a�=>bVLG Iq���) ar! j-s_i}� I:+! +i-s_jR*aދ \eql �����b� ZiFJ> @ �@ e�N"�n,WQ �QFt"� $P_Vm_o��o$N�2i� exact�Fe.��� H� n��F� �e2ĉ� ��2n H. Kimura� KIM} via. "s~� . Z�>j�a.�+(b])�� ~&�4&�tJbNtA�'BpzX@}a_j&b_j\\c_j&d_jE��- ofZ�F"6�SchJ4&dA_1A�eJimJT1}\,[A_i,A_1]\,d\log t�$��(A_1+[A�m2} '�N,1� `.i2,i��j��+2} fjf$\,(t_j-t_i��i�0[A_1,A_j]}{t_�]f {t���(j�Y+1)��N�l�3 O �1k�H 2ni n + +V�!&- ,�� $t?1}="F 2})E H6wesum�� nume�%l4tem�X�@athrm{tr}A_1=t_1$��$\.j=�#\notinbb{Z}$ J6@2)$; \Ji det}A_j=08&� +1)V�1M4� �%A6fe=a�$Aa�s�%fVt{�1 }:=-I�� +58AR = :��&0\\0& �<3}2�-E �3r2:B�B=�W�Dl>�a��f>�Sch> Xd�v$S*�� . I�$J!�]i��:eN�viaNn���� &s�; 1i)0 s_�WiS t_i-�C�q.9b_1b5� E qG(B"Mba�.E�m�� = a_1 + � 2} - b_1\�1}}D, �bI�%1!1}YN Yi -a�b_i- I.R+�b_{�J)aY��  $�=b_&�  2}t_jb_jA.�G���=N�N4*A� holoc��!�dP�&Mwofr�f� Eq:LDE_dee ))d\vec{y}V��A8 Ii ��� A_1(t)}{�F'j '-�@:�}�'cerB��( $t=(t���t_N)$;d8JMU�}6�&AjL}qw�"\rmW }\bf�Prop:1-!�!5�� each"S!�J�� =m&i  \oO;_0!P5,HA� dt_iB.�Fos6ѴlJ ��Eq:Ha�B�H_1 &=:W\det �; ����)����AL�ij��%�H_ijJ9iA_1-t9��i^2{*�.x+VK"�i�F�iE{N.r:�]E  ;%�J �RuM� E�:��_0=� _0(tV)U  tauI&M1Bup�+hcFzO�tL5�ڋe"�#��^ � d asJ�L_�]� (\{\nu=(\nu_"] �)�a [~K$m| |\nu|=+2+�ks+ 8\inN:\� \F�T�^Jt�}B nt�4�Waa���Jn&� s $T_�}� \nukL_� J$actF��>t[6s��KF "} b\,Xj)"+ % jM�2_ e.E��DWe� �l����ojNf in " |y�Sch_Trf�bA>usMv(J� ��Tau�D� .�%n = =M��# .�F b�L�( \rm n�>N4� i�% ifiep�:rN�J� �*&�K��� T_{(0� 0,1,0,-1)E�F�R��n�'ely� ���8#(A�N�*)�{*m�� s. BN� :�2�H_i H_i+D�og�  M�2WB�i $D_i=\/ � $�d�����A~y�-� 7/k>��q��:"ydB5&� =��{�k����� (D_1D ���- ��)V  b� t/1�֡�2/2)}h� ' a� 11&N}\L�iJ� -iV�| !�� v�%� :c��&� 5-F��gl\{(�1}+1) 3=4��L_ � 2L)Mr\1 f 1!�= `>3mV v�.�2��2��2����2}�Ez-&� z�r�e�qqn�1! ��tAt"� *%9I�"�H ��!�j-k23)� D"} 8}\e�D_i�� :0 3 �G{CoJ&# s} A�#"�!h&� ��"is* � @*�� ,*|6��!rw�V'Ն���>�F�Pw��4*%OWi�*v"9 \r� x� K �8*8.h���� ������ $L_1�laf� idu b� �� \{\m� mu_5J �JF� 3*� m� 8"� mu 8�� rq#w .}aaG�J� 6j m�|�u� } �*�g��0?,� mu}� � Q�i��Y"w)\�� (\mJ 1F� *�� m~ b;.%6ds� ;"o $&��U eu*FgbU1rTi2B9l Sch2&Ob� u& y}{l` �1\to1/3,&f�A72}Gh���5 % o4�;,&P\ds AS)�A�(},< #�\to�C:0� �>f �t�az& $k\toT�T�mEq� Sch}A�a�15��-to:,-<^ � E�%&au/ EW .VF�jEB� �m.�i��i� 2}6B� 6P�N�K"�4%&3� sJK%."�)bA!bprewEYWis R-�1&L%+�*$ *" �� B�&�)8�"����v �$LauricellaV' $F_D$.&?$m=(m�m�,� N� t^m =a^{m�L NN� |m�m3 �|s+m_NB��%�' �!:j\ F_D�I,��� ,N,\gamma;t) ��s(�- _{b0})&A�b W)_{|m|}( O1)_ �� NN;{( o6:0 N t^m��k� 8w +1)�+k-J� Via}��bF,9�e/ped�bFur�{degHGF!Hv) �-�&�f�:���2%�2}1 cƞB�W`V3�a[M��e �A�Zo! R�* $%+1�Mby0@ Horn��j- ERD}'>��� �/F(i+.��ޝ]by m�JD$\sigma^{(1)}_{m,nkm,n24u+� ".u�a"�F F�6t 0,n}��Q�2�1 ��A-n) 3}+n���(�ǥ":�+�k&\�� �S9 y -nV$&� N�,1:�n+1;tz��F�.�2�!�a�det( (X^{SY^{j-��.�!/� _{i,J i,m�m��2��X��^t7-�R&e&�F  Y9� 1�>7t_27c9- 0-& TSU2A�#4 �.�m-n,m+n)!LCI�I�\�^  � f��C.W�-$-m(m+1)/2}U�mj�m� \�N_{k m�%�1{> (-n)_kF�W �X�t�%.*:J�� �!��]� Ry�9�<�q i� �r�q��2�� )& ;��J0�h>�aV��=��ut_1e^{_0 :R��D^U��UA ��! Y�zU�BU�D_�5�\D��Jb>! \~bM-�/;oaO%��<��=e�~� Ad\�2�2R� &Eq%~^{ �! ��P&��WF e^{m�UB*��e�!$E#!O &"N2 Jf �)a�]t_ $$\lambda =�Q � l)o T *�/�R.(n $x=(x_1,xuMqj�1S_C�}(x��!,\Bigl(p_i-i+j#r>�lF�!� $p_n(x)zA��2�M�U�Y�(Spe_Poly} L� �1k_1+2klJ +nk_n=���x�$k_1}x_2^{k"� x_nn}}!k_2! B k_n!FB4a g�P�n<��8�C-B�q+ &� i}�^*�th��&�:�B��4R�k6R�~�S_{(n^m)%�ָ�us�no4U $V =(n,)g,nAndZx�t{&)�.�"t_j&�. x� ��k��um_>:^k<� (k� .i�U�.7�T� ��Ve(�D2�4&�6A"ND"v }A�n�P%2&L7=jZV[7� rJ7c�6d~ K. Koik�{KO�Oj!��gd>>K/��%*UpaiyApa�@ s $[�&� ]=[( �Fl),S  l'})~uthe�c�.b8 $S_{2a}(x,y)2Qv( VA��"� m��{W�w{l'�y(+i-j}(y),& �5q��l'} .1-l'+i}5(x0l'+23+ 5E� w\� (,�*��g he=�"�by*���j� �z�!�FJ�s.^xi�&=��A*"�NF -���2< �>B"V(` Alg_Sol_S(RѬ VX 0"Z N.� \,AHu!,v!M���JX �P B2 U ����E&� �+%DkM:��y>��V{-kQ�B Z� � �  &-.=[(u,u&{F1),(v,v.]�(u=|m+n-1/2| � v=|m� v�j � � =]� $3}=b� �3*=F�#R0ͯA�.eQ��� 2J��=�%�{�i( �i+2m-2na"78,(�1D+1}{21�Q Po�"�Ti<�2=72OUjrSJ$6�&1@ Kl orem2�?u��4*)zq �?� "� F B#y J B�-�U�v"C k%u� �!&�! 0�Fg+�g�M�Y��y�yFH]4V�>�a�5�e^{\Delr,}�q�A#ai}MR�2�RKұJ,�*q�BQ�~�vv^�.)A E�t�>}{3��}{4Ms��A�]�F�:�, & i}{1�i��Bq� [+*� %% A&� F�roP9"�.�+"� c� describ^ & , F`_2~N� j8,� groupnb&�,$.�+)  g� �]| "��2N�.>8T�0:�* 1,1)�'T_2aO! -1,0f0.!3!�+,.�+Eq?v%QeQTɳ:Y-}v�9� $T_kx.k*h �$j�[ 1�d vi J3\,(A_1: &= R�$A_1E_2 + EE81R$ -.$�" T�5(>2FW3[C - qE_2x?E|%m- 2�q+ e��6�ib6�jF�j�j7�6j% !2�-&�+�2\.yB� �C"��9��>� ��,6��*�7�� E� ${@{}c@{}}b`@d_1F� j9:��+1}+ .< gDE)�&5���-&�7\\6�R�͕B�-d_�.:�)$D [&b� k=1a; ZJ}km}�;E\mik)�<)k)y�t_k 'q]��.2Ik��T mepq+ +.uj{.�2+j�=ne�.�^2u= �+I.�k�k#6�kaƑ�k) �2�jo2�-^CCP?k9(#(C�skI?6��wB�j��!B��f �:XM(%�2�6o�6.`���/�( 1,k,�[v�bg I�m a���z�k!�^}��k\\-a_ke\�8m}�?L  ��;6��������2� b_k&Rv���.e�� >�A%y^�1�s }�q� [_i�-u�Aa�hE�1q�'E_B� f>Aq�6�jAn&= ymF'>�a��LA2Zy�2�z���x~�1��1e�J"��j��� ���:�16F���N+2$.\\(cl& ledgr-fi:M$5 ut�pis���jtofTfessor Masatoshi Noumi_DDr. Teruhisa Tsuda8 v���Sdiscus�r-[d advice� �Re�]c"7>2c {9} "dDERD} A. Erderyi e�., Hig�� &,r"0s, MacGraw-H�(1953^Zjy30 K. Iwasaki,&�H$, S. Shimo�H� M. Y! da, �nGauu|o2�V ---nodern��^Sp��"8k , A&�g*-a �f8bf{E16} (Viewegp9**��@@ M. Jimbo, T.Miw �K.Ueno!onrU_p�YordinaryZ�H w�3"�, coefficieR� I, �g9�ex�2D}!s481), 306-352. ��%_ �����~�407-448�rZ0} H. Kawamuk!c�nbnC-_V�`!8rsq�b�kHhr.AB%r Sci.U73%T,97), 152-1546��7R�& !6�K"�i>%[Tthe $L(1,g+2;g)$ type�5-157.�IM-NL, ��dEU*�W�t��al>(7���!�Dal H.�T�asn�p. Pura�l.,5a155%b89)�r-6�O.�v K. OkamotM .Z�Y6�7��a, g�[ fuZos]��al&�L , Quarte x�l�37 ��m61-80.q OI} ��+, Q�dO�!_u<�or^�c"]W6�v &c1�s:`�me,=�N1!�pE��74 �!�f6�,LIU} D. Liu�oZ�Frt�$A_g$ A�!� ~, �I Ph.D��j(U�oTokyo��j���\�A�j�$)pa�2�N;!�q2 `VI N� s dbmin�B|ulI�.�]casp��unk'�. Ekvac�O4�_ 2003�O21-17��`�] .�C��3�!�2��U�ir��ion, f3pp�a in TohokuIA��5 �D4), nlin-SI/030202.&h`E�y�Isoaf:I�=V��{�m� 7I, J. F!K��UYEY. IA, ��3��e�575-618]� OKM2>� Stud�pon�V� ���>%*eMu1 u�0 47-7:&=2����9�@s2;a! V���2gAlerty: One Century Later, ed.em,Conte, CRM S�[GD �;jal&p(Spring>199�uU�SUZI��j�\f�( Weyl�� symmet� �-�4=m�p��inq�9$-ph/031206.�TSUm�� , Aer2�#I�In�� I>!+�Me�]!�'e�qR�a.�6_6�aP"#]S>], Int���oRR�NotYB4AB�$, 2341-235: AFT.� Toda:�� �[�fVZ6� , submit�7 >) &�k �F6o{�%c�m*�n$graphicx} .z]�n0[cp1250]{inpu<�} % {polski} occnM}{{\A�M�l..nPTP} #T>#hol$O>ZZ>QQ>PPP>AA>eQ}{e^ �Q}>GZ}{G_ �B�G G�4! B%oht�{.5 em>bvWov ! 1 ex> bdm}{�di~oa�>'e'<j%b�o g@izeBG"FZ b�@� e�S:e}{J R%beI�BHEZ!beaE��BE$�"q�:" btab�lK:(e �:&bea!�)hs*>&e &.�$6�q�q�{\�c"�q.#?�2rthefoot�X}{\fn�rol{ �j#{�2}{D�.% &s6�b * �  L�e )+ "n Jms:m>V9�� Ln %!P6#  I�} on}[�6�s:u��/�.:0e. �. .��sllary�C�� )�b+�:,e � *"K1.�tv"p @ e d ^Lem^�t:ZL[+:e!�YexaZExa/�:>b$� :"e � "�J docu�A0center} \Larg��(ast$-SDYM F �HeaveA�Sb� . \n&"8lsize\\ \mbox{ %\6� I.��Kq�+�yi>H >R.S Sebast�dFv0�ski$^{1}$\q�{�6,an@p.lodz.plj^0 Maciej PrzanŁ8,2.:p@fis.c�jav.mx} 6�8(}$Institute� &s,Techd�9 �yof LodzB�W\'{o}lcza\'{n}ska 219. 93-005 ��d�, PolandBzm��ua!��� Fi�j\\ � rISici gy de E�j`ios Avanzados del IPN\\ A�ado,�ptal 14-740, 07000 Mexico D.F. .\\ӊU9�P� {�u.} )=�� �Tself-dual Yang-Mills (Al)]"� $I�lfLiefG a hQ�S�O�� duce�p1oQ{ (' ��sb�D\rm). Two hierarch� f�H serv�  law%J1=�3VSruc� %�e ��tor�� �a [1 Riemann� bertj blem[4. =  {3>  =v Keywords:��B� 9&~ s,V�fe�, �9ad�a~�`. %� page Qv*6Rv !���s �| ?C�a��B���4ssA5a s (Ku�WMa}h!GWoodho04 1996!�h�xat( |�[Bqa�[ � phy�~%ns��r�is �n�1ALWard''p"�~ �( 1��Q U+��L]g� �� inhe�d�&�ed .. Yr��e %�, excep]�2ao83doU5 f��;is�o�a_��� al "lu(j� An6|�apL.�f �q<Win؇.yM of.� vf�I�a( vide���(�!ߕI�co�Hx:4 $��� � 1989MHnoQ�graviton6�(Penrv7��, E��v��, b-�u��9E)�janF��hus �2idea a�L8�c� H}$-% "��an*�F5 90). &��!��tA[!Q1�r��u��y!� ctic� ifold $\S5A�� $sW()$�#fs�qas $su(�s�vE�existE�$N>2$. �k�tlV���em�ratJ�shoX�I��e� � :�� �mJ�}�l(N,C)��tG��f h*�2�."�H!|pψ��r���mR���� � �l y[wBs�+ETof�5RX�t*�70Bayen, Flato,(�nsd �,Lichnerowicze! Strenh5��7 (B:aQ8'��xi ����e��,}�smooth&")ui�ph��s� a.eA��!��g>/u�Yf�f"� $f,g�, aS�mal pq��Fi(�5& �^(\hbar$, $f� g=�"^j:�/8k}(f,g)$, \h $W:q�"� �9���c!�*S2Laxioms: $\bullet$�his lo!�� $>Z!Ily!N$f, g�4 ' �d�}L\�X #of�{e{g��"4�k$, >�1�g�{s��-�� �1)"-� 1}(g,f)=icp M� " � {�p}� �" pro�at�?%��5�����\�(break (De W��E�Llte��$3, Fedosov�$4) or even"3qma��(Kontsev��1�.+xs��o� &���ia}�(��).�%�%2u4s (Kupershmidtp 0, S>�han2��, Tak;!4�� so, b��{Moyal"r��%\6~ ���-�$s (Fairliey��lf�nV�al waI�-�d2U mbed��uw�a�i�����a �X�m�Y �� ( 67) � ible� �:)�ҵ�o�� � ��:��e��wte����:(;�N %�ng�pa!�. �,sent paper i�Us devoted mainly to formal problem of integrability of $\ast$-SDYM equations. In orderF� make our results more general we deal with an arbitrary \�product, and the Yang-Mills fields arElfined on 4-dimensional heave�dspace. It turns out that� have_ �izE��0hidden symmet�}of9hor \1;s. WeQ,!Lax pairIq!�@forward Penrose-W trans�i4for ME. Dress��A�atoEJn!eng thosea]��finally,galgebra�B� ��a$ n. SS on 3!AѮtoE solua/F8Riemann-Hilbert��. W�& � homo!H�,:,%}we show`2�=.q thisf�"!%�>}�2���@Birkhoff's factor1�theoremA�)ern�verse^�i�twesi ��y&inleM�II(complex rel��ity�rpresee9 Lforthcom��G�/� a sequ��8of $su(N)$ chiJ  ten�M:kA�p$N\rightarrow\infty$ has been�!A, alsoE��)ny analya�.�e�yt can�k���� from��2?\NU %\input{Vo2} \-�{F� .j- VH} A�e begin�@is�3Hwe briefly summariz�� basicB�Eems�� ncerTJ�.�m�,m�adj�I ał. For+ xdetails see (MacLane 1939, Neua�4 1949, Jacobso80, Ruiz� 3). The �Eore abealian �aj�[��P $((G,+),P)$, where $$%n:>, $P  subset!T $G$ kA��: $\bullet$ $0\notin P\, ,$\h $P\cap -P=\emptys'\h ($0Ya� neutA�ele)d �)2] \forp g,h\dLg+ $2.0G=-P\cup\{0\} , P$. \noind� We� ��� posi! ��t� ow ea�%p!�D � i.e. if $ �G say%4 $g$%�is les� n%�$h$E4�,Y]4 its support d}\, a=\{%G\, :A,a(g)\neq 0\}��!�least1�m1J� $a$��written�C� ��94 \bdm a=\sum_ �}a_{g}� ^ \h �ef}\h\h #=�,. &-"u .} \edme�mqA�y>w֓  Ied by Z�((�^{G}))$� 63 � � Ů,^ add� E� multip� vsca�   edt @wise by \beas a+b6j(%H+b!q) �g}\\ � \alpha\in)[]`C$})� #AC.�YX . \e� More%qi��PBdaW,\circ)��U t� AP6 s of� i��Mf>� �h�Euh}m !-h=�EHis:qe.�,� �a[akof each�*2J, so ���$'numberE��a\_>� $, $ �%'$finite. I���se��n2���$(Z,+)�TE�a�� NPM�E�9ōL]!�[[%�]]:=\{RB&R�� \, E1=0��M� %4-P\}$. %Zbi��N� uaed]]$ z dodawaniem i mno�eHokre�lonymi %powyj� `rzy cia�o \cite{Hahn 07&L,49}. Pozwala�� O�$ szeregi %�i/be�J%:��$ holomorphBun7 s�gsyw c� "�$.�0, \omega )$. ) associ� e�� noncommut m6�\�break \E�L: f\timesj &� f&$.}�� %%�i� � �� d!�W +r ��A�e9tr}(f-$ g):=\int\O)2 ^{n}}{n!} # $ %$f&gIf =)i}( )$ �4��c.�=:$ (Connes er 0 1992, Omori2} 6) �� �I�LieQ��n , \{�� \} )$} ba<on:�ɘ��a,b�j>�uj �4\h \{ a, b\} =)v&�(a%Lb-ba)ͺxaim!�t�� F�.eobjec2A ,� . U   ea�"�;e&of.N�ɱ .�v.H4left-invarianto ( �0 maxi� qg , curve, a 1& � � �!�.�: e�$-� tak�|an�� ossi�b K� " sA�mp� .| , Asakawa�VPKishimoto 2000). Such�r��not� gen*enough!�M�)�"� t to |super� o�!f�!F2� w Z� �D "� another��er. So/would�~R` � R a] J�"K] �s���>Q *, t))�' ��he��K $\A$� \A=\{\h A� ra\h�h Ay m=0}^{S}� k=-m t^{m4 (k}A_{m,k}(xJ\&� e star��M�1��j>��I$��be ex S �(w�eIsa�ymbol)@ ��A,B�A} � _{1}J�-:�� � , �, ,\h B1A_{2Ve2}e2Fe2.e2}}B_{Ge2}e\ A�3g1},&.�%��+�-()y���1 k .�+T1}N ast P ^*2*R�)��d ���$(!�as� �0��g 6���. %�j�]�]�]�]�]�] \vs %&������� $A(0u� �whi�mD2*belong  to a#6g�P , %&! " a0=\{A_{\delta}�s� 0 O� \}$}:�$t$-lo!y b a�i�� � natu# $m>oN� i�% hav�non-zero"� Mm}0 {-nX {t� !1\a6-kof   $\{a.)�"�)$F# E�sumF��:${ !� �� � \binem 4A� �let6�q=0!� ��A0 <, n=1,2,...\}$, E� $\equiv ɡ -1}= �� A�.�-Vi�f(zQ�n.�a_{n}z��5s2�of� } � ��� 6�H )2 $f(Af{� }$ (.��J bove� �If $fည�� .2.2� b_{m�A�H�N�K:�=��n��(�\cdot f�)�21 +(A)%�-(A)�ai" �=aa"Y� �"j)� $A^n QA^m=A^m nE2+m.�:�ei*� $E, !8&�.-���J9I ��=1�^rp ists/ ���A��h$X���I�X=X �=1$� de{ ad!�1!� :=(z+1)^{ai�2�(-Q�.��)nz):=z+1-� $!�19�2})Ag1$. IE�M�s $X1�-1)$, 1&=&JD$/� �NA\\I>4-1I2}:I1 =)5MV-1AK In wA4QOwe>�A%: :=X$< i R ��M�)!�-�1s5\{�\՜1�<���Yac�, ib j �H(v�$�i� ��r ��,E&6�*Db2�nd]� � ɡ�=��23�=�� �-�gV'�d �Tz�i��n $\{[O]���� \�70,�9�#��a}� lbcorollary\label{wniosek eks'}$6���>- %�$e^{A}:N{���$ %���-�!<�)�i2) �$l $�O�fh!���M � O j\(.!� iA[�~Jis>$&$�n.' ƍG+1�}(��Ze95Z *>{$\Q��sub� ^l�. )to m �m\Q^"�A7,-��2 t h \}Ɋ$\e �q���9�a=dm \e�� �a=1�� a6 �F3#CQ� \�'F�Ee1�%�%sbracke''!�\QK  \{A��*~��B-B��A)& � hhebxE�eM�%j��w�$�e `"�V-o&� differentb�)c+oi*e )�i�&isCa�". Apar� omj, �� $�in A�hasM}:� Hd}{d\varepsilon}|_{=0��, ( e^{-\sqrt.}A� VB e^{n9FB})G ,BQ�%n!��nt� % cor�+on�-*.�&-�  is justif+ur!]m��"aeuI5 $\tilde{AQ:*k a=�-(%��tra9 $al reasonsAB>� � Humowa wykladnik} a=!n:�A��e� �= >1\j Z�+��R�(X)=:BTAK .j�!ypu�eUim�!��is0h�,o-a[UR&|$e� m>-�q !,a1-�&(1} \psi:\eQ��� \&� � &,&�;+(a,f):= �fl!� Q2Qh�QhQma� !a ��7'reQ)E���Y' � } Ad6�B�� Ad>�$ ��e A*|(��>dg �:��A�C$ mz� !�I .�dzial�R} 1h�=f�mlF�01}{l!} \under�e{��,...,\{A}_{l-I�4\tiny razy}},f' dots�e Each��)Us ��han*/2��,eZ(6�)3A)8aragraph{Bundles!alr A0#s.}9 u&�+ fa/2s�+��d N�/$\M��otR'{cco] a��M$�$$%)0$(w, z, �(w} z})$}��use B+A�9�abbrevp�� $z^{^$ }=\{U0 ��  2o� a%gt,n� scrip�Ki>^�>D� M� hermit**"K �dis ipped^.� nondeg�te �/c $ds^�2g_ � �\beta}}d�\o' _{s}d  � )l is 61)�low��/� �4! o,��)r"�4l)~ $w=c<.�$z �!ѩw} ,� �z  .$. e#1-A� $\sZ"�Lambda^�M"�deA�os�P� 4= ; _{(1,0)}+0,1)}7+K)8 w}dw6z}dz$B A �_{ M3 � w}}d C zz! Analogous�0|$rior deriv:"$dEOa� (wo Dolbeaut"<1$s $d=\par� + q}$�%ret ( =dw\wedge_{w}+dz>z}��� >Y=�>6 +w}}+ &z^&z}� h� ��pA��  2E"% he typg-1,u �1�( $=Z6\, .9% �^m^$. G�Aplej ��:��N# $d �0$. L� meaaw��1�-K}{lK}$!N � �$�K}=/(w,z, Lw} �l� ��potB �.��!��ZfJcF� !�s r�*�1�volum2!��&� \nu$.w 2})a-� , =\, g!�M�5�w} ,Q�zy8$g=\det(Z�)5d ,_{w5c5� ,_{z z}}- 1�.zR.w}�� U{E\ Hodge duaL;Anf"� i��w'!1s$anti-self-@%�� �',\stackrel{.}�o6}:u�xm�5,y}Us!{1g(�T2T)�,\.>, V@2}2�@dx1�y��(See Pleba\'{n}ski 1975, Flaherty6, Ko�% . 1981, M $ \& Woodho|�:!)2S2.)}. �  ? .0KONIEC STOPKI.2o L� %It� be/ model�^%�Q�7!��i1 �h�%d?5so�<�&M�/ch%es value�0�  a triv�(principle b� T$\pi_{\small{\PP}}:\PP*� \M�uI $total � h�*(�act" � in [fib�O;� � 1�ix ivalT8�8on�K[((u,v)\sim_{�} (u',v'�%& \LeftEK$arrow & [I�PP}(u)= '�2 \E:sEH \eQf u'=Q^ % v'=c�Etv\, ],\\6�h�����v�cJ�Ad~���2��.�E=n"e�P�2}&$�8 &�q%M�$E�� \A�(6�O� � [���M�cAe�B�#8���s\A� inU�P Y�$�a.is $E:=F�/.7!TiF$f0 1" 8*� 9� ! ��$E'i\Aghi� �1G�.@�adj(E�.P��GAdEei� ��2PP�nJ@���OE}}:E\}�\M�i� $'%'>& 2% �}}: :-d se �se�Y�%�!.�( $[(u, v)]$1 b�C�p�I �+�#E, E',!7(E)$ �{)|Fe � ��ͣ $ :\M\��ѡ��al J,E> ; $f66 E5F�1|ma��f}��B�9�**;z��dim X�s:@ \setlength{\uni }{53\b�< {pic.(}(9,5) \put_{a�c .8,1.1){\�-B{3.6} !,3.2,1.25){$f56.3,1){E #1.5D�� s0.5,2$F1.1,4�PP8,4~�4 �F`F5F Y�1 �6.5,3�� 0,-1�6.8�ell6end5H��*/4ll�A�canoni�i�ell�V=A�A��$�_�E (B:v� Ecf][2�A$�r''=pr_{\A 8Fh$8-�.}RF����V3 m, N,�vq10�/�6fA! ��-qHig�/b��%�4!q�$E�E^{k}:=EL"~k}\M$ k�&3,4��{ � �s �&� $E%9 6R<\M:=\bigoplus_{ky4} :'�\M� ( %��Gt (erm�6jes�.Z��*;�5$�BY &_{ib&...i_{k}g \nu_{j $j_{l}} dx^ + W �'] >? , 6, R�^h:a�� ���@%��5��� \{B� �,B�\} &:=&>�(\,m�A- $!kl}Vn% B �$\,)\\ &=&\F6B�; ,\;N� \}\;��V�� % \@ -�3 23 }.l%a�A�c�6�8ina_� a/9� �$D:)ZSec}(E.m.Y )$,}MU� � "�1fSec(E)Kh D.d +B� �,��� ,� �%�  BQw A�L*�7 a 5��.�\.��+T 6/aDI �j$f�O3+Any.�$D$!�/�B)�J 9�� "M '$� � $,��ivelyp3k�[s&u3 DO�"7j��!�@-K.j�A��"9�'��9�!�>/9��2#a� �e�.M?�, ]B�!�ei�a �)=����rho�CfNwo:��59ji`R� ��I s $c6Q�!*^Cg,x.�� �$z&u�M r $eR�iO +NU!qI $� ge�\b"�2.4} U = *[.�Ne �g ]R51}�= c3!�� w+ RP \,\, %d ��e� 6� law�), �re�I9$ FN�"B}c&�= ��nt\�I�$1�(:�B� B}_{\0�ny X}},[&� -dB-�"Vi(n+1)BZ B,\7 {B,^odBf!Bdm��  &�#omi �*s�R , !�% WHg^ e >� \I"Y&BEwD,��m�Sx on 18s�'$�� $' etc. �*?E����mayA nd�-h"�2way, + � $.�H�E�M=<fco�0nt���qb�> � a�2S� fWk+1})$"2E��2>C$"�TE�]� \hX+�)6D F� =d^F�Av| .$}�+e)�!84=4e%of��s at $D  D�2D� :7*: CA�  $F:=DA��6m !� 20P�4:=dF� �h ��dm F:=dA^( A22}�#A�#<or ��weV $%^�=F �%�F��D�f�8r�\�\�\�\R\\&�%S"�*�X�-tJ.}m� �&n�a�N��!��w�"�z},\hV�1J�"�V3R�"�z� m K�\ � � &� �| S�ׅj$F4&'iff� m q��Q=0� h�72}�7FD=0\;  �U�]`(R)Yg�+�8&�*! �*J$_{w� z}-A�\$_{zw}+� w}\�A \}=0w�*N2BN\�w�> !^S /+ w z}R3} g^$' ((u�Lr )}-e� � g � 5� B� 0\})=0!�ea%�first[8of �8=�iFb�2terpre�aCt�DF]con�-sW>2�!�@.a $�=� ;�+� Ba�3 %E�noiL\\ H)z �Pb"wP6-b�3eaq� a,b:# M}\r"TU� m�third5 tak�ei�om� �� Z�.�)�[,n�9)(;G�)]!= a)�dm Afte�#�R titiUX $J:=.9d i/Vcomes�e�'*��� (a��"7, Par��H�q\#ab�=� �(J��-� �JQ� �st�>31m�"�$� 5b.n d3f"�(Y=& � M1�*}�) $>P : e AFB6�,D) lt R to�H�7I�^'i<e�<&' �+"e(�k�L��+)�a�&�;$a minimum ! y a]e� $S&�I 2}\kappa dK+�7kͧ Fivqu��a��ruF�*h $A�, ]3-A�J�%, �2&=M�I $�,2�=DonaldsiW5, Nair  SchiffA�0, M�%_6�%)�u%v�� n� % � �cvcv��`0�%E�&f:P�j so � K�+ac(of Newman %&�B ( (1978, LeznojP882�,:�'APrzanow�'96,�'66. Chook^g�`(��}��"� �`s��'s$%�a�_It��&����.���f� nabl�B����m���=0 2L)>t$2��_�(g�@ b Xh �.�:���*ger�.�� �(Levi-Civita��(F�B :�) POCZATEK �)�tJt�:�bua on\f�3� $stopka 1}O2)&A 3'"�2!�&�2O�=$g�L�*..��xc \GamNTMb _{\,E}\g}=� E~Q��.� +gM�>(h�6jm;U} r eN V � ! 4 ��_"* 3��7X��? impl&:�/!2*P"EG2\of�F&�te|+ (a�S th�a"3`h�cyB) )$){R� �� ��tH} = -B� 5J 55�% !i`} = S-_ ).R)RB� )B� H �~ Ie Ricci18}$!�7�}}=� h�1�216D 266  ;}FFw Y 2}= [ln}g), & ��� �\$R.�) u}�Fy� Weyl1(Fn� al]~I>CB}f6�-�=t-�{�`R, &�2}}1W > QP2� V}+ A�N2JI)-" 6}R>J&^U]`�$({�3M},�7@M�c�hweak od �F�0)�gH$-�6)�Uklat 86�0)�K�K;M�!�% 1E��1 �2}V%6K-} � %ex W56�$}�i�{2T5g: be true����*�sh*T0be satisfied:"� V� �� 272A6�Bw$,}\h $:(, 2B�72#3:!2a;B!ne��t�0�� ʺFq=� 12}RA�J�)�*b�#$\h� 8$R$ must vanishnBT�� ^��I�lOCmQoٗQyt"�. AZ+?@2e�F�IQ:E�k?y2�r=^�Z; a\�e�.C}�� �� �� :� �4 �� �� �� i�gE<Wn� M )  ,&�� !�^1�1�\Xi*S,.� de*taF2 \Xi=\�Dv � JL FM "� �_\R*7� �]e8�>qOg}�^� n��y:;*� �� -EB� x+}*  a2sU2'-+�? >.aqL dens�k�(w,z)$ �bles,"�$"%oq@4 neighbourhood�I%)$(w"7 � ):=\�C(!�\gin{array}{cc} 0&1\\ -1&�nd �)=:R6�).xas.�=�&�FvU) �S2-~2s@)$ 5R�-�I*��� .�nc9 �R�%�f�5yU)y2 u"�: %Cof Y *Z@'= �w}'=, �<,� �z/zZ/\,$"*.5 ex}?� "�$s a*Ic%��UEM%� Xi} �['�\� ial R�} J!'&�='})�>\XiDa \ee �aE>UseY=@ hMQ.�L C(&� *�&�)4ME?9on N�.�W rule^"6H�l1 >- (\ln � B; $}\h�BJgM���-iq�W $} %w�xwa�qev ly discusYBby�(�G�2), %bu :opinion^H_"�_�&a"x back�* nd %{H9u1�sD�_w�li�_.a� x;. %Layo�u2*yra���"*.�s� ^Q%��MTk"�?.�`serxLW6�$&xAB� `o =2a�n�(%�M mJ�u���M 2-��^e, %Xi.R2/M '4/8A8,P���*$�f�im�.�IfopoMZ Q-H.E_ (�E.Poisso"�U. zX1�Moyal a�t�ba668wtn� , 6Y;*E�6),."�n"F?%9)A���f�q&�-�-�)a s.�L�g !�2J-X1~29�)}eta=���)�eta5��>uKAi�>eb�z1�!�6w6" sI �abGo�63m�necess�|!�&^|�a2� ^�$�8� &�5D� �Q"�} �$��e1�%�}=0W?T�,�de�3inX)8CG� 3G}R�$�w�FF$t again�wB5�_ 1}{G� (T \Xi}�G}}) =-�*Q 2�).� ٛ& ^r�4�m�qC? $\Theta: �:�^~A�Qw a ���: With hel�S%�>��?m�m� now.�G{F�E3.k -/%. )�}�22�% <\") ��=��B� !ee *�B�^��x2&.���[&� N�%U .2 �� ME} 6�?k"�[-3GU]M �N)ast9  ,Qu \�$O*`�5M�  -� -C]���9 #�:M�1}� >�5I�5%�� 57 -=3� ��(��&�!�m�."^:(N+v�� no*Qa_&8 ��we �O �-�i&�s, lik�! exam�!2�`�x�s Ri�[a�g=16� .) *_;�Mi�T � ME})� iz%;Z6�X by Boye�!2� 85)"�(1988>�$(2�C65!&BsN2�z4�D�3{Conser Mo2�;d �tt1~B ion�usetcou6'{� }{0}B 6�z } 4hierarch� o^b>v).T��&� -Y�H��W-�|Afpc f1��� 2UT/�U both�Q�:!NW �9$\{d`, \ H�n�@exK<he6�!&�1 � R��4ME.�OU? ph{H-1�}hB�of1}Nf�W�=�G� )�|�:>~�}>ct�%T\;fU�� �i\�>dyLME2c'L1�����ph.y ����ph� ze D!� oper�&cO on��s � �!*�=\A$ş)TLO��:^>��ީ� ���� O� .�5�v ,\,I�,\�UL\h 9=1, 2 �n_ thei6�fs�)eas�gfou�,o 71 [�w}, z}](t)*L G}\{��)��1���5�Z)#=2! dm S�Ym�=��u!9e�.R $"_ s ME>u. Eq. u)"�W���?th�� read�09y)�.FI!A�=V��|'� tb{S)�Zy�� e" � a� curr�~a� $JT) � � o\� s $J�} #:�O=/� yG2� � :  >�i}J^{i' "� ?P �=: J4h � N�"p/ U�}�@$��vZ-!��1;96 fulf>�!^�?.�� � sB�%v>< m��9AH'W>�(G>[Fio� =&�>: ULA.�;*D;���phi1} By="*QA�����)m1p��C*�2�j!&� B=G�U d!mIA� %o"� FeS next5� E�)�_{(2)j)4XdiY��YE� �!O`j2)}&=&>^� 1)}=�C) = V1BaG%J-u�m�BB�)/=��@. )���� �N �  �size{by }}{=}�s!�&� a�ank:sT�[say/WJ k1F�Ov  repe��Ia�z � �t��&L�;�#coiFit�Y�ٌ(cedure. Giv02n- |� ed0rg6 i<n�� �Z���e �=^n+1nT� @]so�L&�0q�QMQ��)$ y 1 eWB�oΊ��ay;��Rf[]^�.qE�9Tre �x��n"�gZ��%1itu�C�^�}"�\bf Re��.�����Cize} �C�yXiay� ak�>5o-"� �%r"��'� �{�dnA�eR�7?p6���aly_ b{ �"�#�lm��isii�5�jDm�eށ>?rebs �b�)�z��*A\"�1s&5*by BzS�}han�3), Hus� 4), Dunaj�/a&�1�`"L9�.;!7*t�!a�}^q�s$;�� �SFuE�E $$F SIue�"�zpQ�pQ �(�*D�" " &)h�ѬF2 .i��M�$h ay��� �)�ny&% !PaG�>� ��B -B!�ap�  }b$vY �to6�rugie� iowe��=�Bf[�7hD"% �O $j� ���.Zet�, 1����}:�e�.�a�j&� �!~eMD i}%>� >�=7 |Fl�' .�&� �.FID���/�Fz:"�%a0m�k 6��B��"� 1�D �cah!0����.�2� Z !0e� ɝ6 "� dasF�^% 1)} & = &F3Z� :�.&&� �B� � %��9�� � �0�@(��"� [���}�.��ft�r� &�)~� %�as�ZF5�A�E�QIA�Qq0)�+E 2�"$!RQ�Y�2)��com"7!� �0 $%�  �A�R9 8eB= �9�6ontinu#�pr ��arr se��&�ed A�g�L � 0)}, 1 yH � 1 s�� �iW,>��H  �da�!�&\ 1�m�%% 22� m �� Zc�e"_NI}= Z*}f1^M%g={1.�%nBs)E� *� ) &�X A� �o#B!P�.�)M�s|wU�) \ �Ƀ �R}�k<e� ����a{ laws} A:T�"�- �8-M�9� (a� (Brezx L�Fa79B" asad&Za Chau 1983��� [ �I� w�ehߕ*- c2001(aj&:. b). A1�!{�"�e Mink::%� � *_#6% . bN6�6�E>?e"Iof m��v)��?M"x&� �(in}�|y�6��2:a"��� [�geo� 2�c)^h dimm�,�>�A"�3ɫMS�p��i�M�2"[< *�� !S�+[]ly �# @my� p\in,\h� v�S T_{p��Ol (v,v.vC�1 orthog� %�anihil�mA tnnt ��o3g�t*;f2!�Rx�_()�geodesicz��6r�I�6� $v$� p$ P9�qQ�9��6 Y�'" s�%.�2 "�5�KBf��E�}}�*=��.e. $g�%.�ap� riat�" E1�e��BaY(��w�rm NJ . We"� JcrbiJ�&� �+em&�jA>.�%{�A/���~wo"� �!kTMmO\la�m"�N&�4 CP$}�V-\�Qӂ��^ l 2-1��wo ve �� @\_{w� � -�}"�  w} -4� G *��9z�F;*�j ,}},.CG�(wektory ell�lOIV f� z} +A^�w���a��I!-B�i��wL�$!�Frobeni$`�W b<)g�` mute�' �9fO,� ��1�, )= i]>zB�L-4��SE�e.� 9 1Q$6(M^): 0G}dm�J�L- /]$5w�PG*�L0A�Z�%�WE�distribH��W��%75=0$�xDaurboux!�F��a�I�to &֍smo� �s $P^�P^:m.�x:r$jA#�_�Y%�>+=dU �  :q 2\3� dom{B�Q�F��ni\zet�J�:;�s� d@4?4V@"{)�w}6�1}{Uf��\�T�T2S3�z•z}+N��QA{uS1�!d)& (aG�'y�x5�m�yyM�(9}i� + G d&�m$.s�EH3bEH}2�$� "�m �d=LEp�9eE�}� p�patch� rs,`X\�q��=|$F)�N��� &�8.��1Ԡ�Y���Kachߛ $H f%�yjh2y&�> throN�$p$�  2� %+�=�2PT�ell>Gxa $3$6k � "p �+a�� proj(�vs � ( >�c5ie� %*� 28s $(V,(%�,��,��))Xs �2.�)p$(]4V},.n3>>V,E yA�j�-v�� � g2x�}s�Lz hol�s !@^<Ns$ *�@&� �2�@5�a�a 1980��B�1��7�yndXmTuMembed]���&,J!�c"d�(� \rm �;F\,M�fmL�F+ $ ��g 2.9,3){$q�f�g 4,4.g~t�ut(4.5,4&�g-16$g1.2�g! 17.8 PT6.6�p5.3.UT�:�h�"�,�o rzuto�a s�*ߜ8e lokalnie, dla2&[S��"`%q:�1M9.M�Yr�z}+F���N�.�V��Y1T�W=.@9�B��\iliF� 1�.�&���4��M"� \, � Mg� � \, �[}�3�U+q6�)�!B�a^"T86�[C�o , �t�Lu�rr�� ^c).P0"�)/ #%�67..2���$1�)�^��ee�$[6�w��.I�]9}��WJs :�14)��� ny>!#tF.&�e�e�$�Bs� kd� Ar�,4����h�"ͤ����� bel{Laxa}��w}\,\Psi*��,tk#zF#E��7->2E\>t,ǘ;wV�"� �]A).In�IE�E sd(%@Ű�Em2��na.�E�$0Z%�F�)�@&|O=LYu"h�)S/|�"k�$k�2,�o�{4B=*�*yy��{67&�µ}�j�.  8<e %�-6��6u�� f�~�흡J�A� be cRn)^EA� �uNbcǸce!�grhB�ni� . AsD!"�!sus N4 t��,6�$ qKs :eR:�By �Ztudam��U�mnig2NR me�2D A ��Cp��^ak�.�n*C!� I):�&wget}.�$ }f.���I$1$�E�Sû��we9.{��Y����/ %�8%ќ\uRQW# "&Y$brzegowychiU<>���FLT�B�Psi1sU��E_�QM��EOb!� t sM>T= 2f�+ �H4+)WH}�`F�I arro�m�Q/.�@a���G�8� ���j =0$,L lpha=w,z$��:��K�^� $, u�ZQ�.ض�2!�{!�'_{a�\}eu*j�$, ն>( ��uF�6Y��"��a��# unde�N 2�!�}(�)=��\��& , &:� �c.�6:^Ps_ � et�0��um�*U�(U��})�d-+�Ua,&�E\; Tk)JKA*a9��e� �k)}b�#xh.A0k\geq ��"�K&�m�y�Wda&��� Ů$�9la�&7' &�.�a \:�& 6e �("� same*orP7-1�n B$.�b �a})*J$b�!>_�85"��la�B�s,%{�dv�*�!L.�=\Y�6Q)(�P-9 �&&��1�uniquely!�����1^x$�7�oeŻ"&ݼG��!;:oc!5�� ��96!%��>ler��Y2��*�FtTs[ au/i�T�th. ş #MQ ����i {,��qof"*&�/ x �/qE��$W;i"�6_��#�B��V0hB�'i."��$ g*�2i�o�3� Eq. [9inh�M�0T &�%iE'LR}2�>V"�8} \PhY5Vh�> n*�2e} mbdzHM8"� 3+$()... yD: ��*��.�'%JN -sy�&i 2�j�d2&����-�;(.�=0��| ic F� ReDw!��2�!��'y�)B E+�+M{��u b o�^-�N..{ �$zEg8ee# ���)� t�4BU��AA�9�a�g xJ�V� -v�+9�.q2#0��MF��:=F~u ";�2�X ' �eԅ�ofF:�� p� -�i& �x7�$ ��Gis�j�$a�*g�,$! ^*w"��R3>4Qq��űa=�1HJE'�,6���A� z� �iT8�7�B�7 $�\,P�"9�8 %(por\oo wnaj �tekMKa���F%:%� �!ˡ�Wwb*2�c: ��F@^\�B��G "�}iCZE.6�+ܗ�Vh>�.} PGi�s.߱02�a�["�O:M- ��, .�?*B�%3ed F�.�%e%Ta:"a gen�8of�+K}^ _{(F� FU�2Q'vC \pi �5oint_{qM�hd�(}2� (-� ua�:� 6�\, + '�.�� � FFy�a6�si}6_)2� G�} F�&� ) = �� *6 P�%}nA g� [V� =.�F&�.0r9e�y��� a (C��jU�-��S , Takasakȑ90).)e� cont�K$)�{yB2>�A�"�;05 �f��e�-�� �Dt doe�Nt cros�Jy �ularity�*(\/ �To"�SwB��q��*p\�+a $efteqn{[\,�A�K=[a,HG y'_{2:(2( ] m2=Y6&�\( 2+�_ *)\; -\;2/1:�1� /\;>-R� �6�jW�+:�RY �y�  � llowA%+d#&32��lI� J=2000))heF�E�Ct"$L%i��2���} �go:��C} "aof h�N��} 2P�*IK�\642}:4Eh])U\,%;d_{(\{6=1�&�E��{B�."()-�!��!proH3JJ in (b;4,�m&�V2004)Z#&Ao7�8ZhNn�!3&xXI�ousBH���t!���7RM� �i:�4>��ZG��similaQ &�;G50=���lat�Z%>i�p monok@s (Muscheliszwil��6�oogorzel%@196D(�0`�sFH�qz � �0~.�W$L� a�,�$.�� S^{+�A ��� �1*L J�0o3 0. By =-}?Q�@"L�ü� ):�-F�-V-L �HJ�'dm��͝)=� m.� k29�6>�� �I _VXg{\� ��u� :9�'��s�$�ϡ"\�� ��m&02�VPis2?on %K!��)W�/N/�Qaid��@*��/ree a]"�fa%�&�V�*z� $c)JZ$SK5NE* �|-r|\r"�c`� |J�|}8^{ tqYInE� �>a4�:faHX� �:M_ �U=P :+O*6� �\�!� � R?ɲ!�,a polynomial[Z}6 �<x>�� :�� !�6A� '��� an9-1maA�= 2Fc1�d�Y:�l0�B�,Ě��&>�2 �E�B�)6oTI��I! V4tau)$5cau��L.� on L;a�H\H{o}l+ �� e�$H(��[$0< \l�j"�T1�sD|��*_g $��� , 2aX�\h"vD2tau� )-.4 1})|�A)�| 2, !|]#�/��eN���rmu292�� S�Pw��s���G $G9�xi)*!�*�,��2yLɄyn .�9� 0 . F����Z�6�;�ZP�>w�'N:+)ti� ���>�"k �.� 4zagad pierwsze�2/ =\Phe6, 6X�xxiE� �BT � :Z"'"!� limim��.�I - �+6�=\��.�xi�xة< �m�.��}� �w�'N��j>j-��3-"v eekA1EQo���i'e>� {�N�.�PUM=|�!r� M�e$�6�e��cMd;4��� f. ���6��($1913, bo�Si�"M#:�qy]�.B�$2��+��$ICauchl��weaz�� dm 0�(&�\�L5I".����`au�8aue*?+Ae-g��B� Plemelj%�ula (190�[` �*6�e$�get9-A��C1"�,�eB�*)���xi �>V���!e� ���$1=akeNsenc�{al [� �#R#^C��n��/l$a�E B�A�* �y:�guarante$B^QN.�2�"�C.jC.T1v:��v.5.h5v�yxia 1�^j eS2> %{2 6 ��g�R!`��1�N&!�,-�|hN !7�� QB��$ A)�Fredhol�#rPal5��%a�yA kernel.�calkoPst�.yxi*�vm# u$B/!��1��6 Gg"ca/�Cxi}��aub�Su�� ing,%W:�D6Ce�Rl �:)%^+�H���I+mp:'.' Z.\�8c�(>iy�a!)�v,� A'.�IF2Fg. �~�(y* R͕\j�A�Ew 2]�T swer�n,Y��|�s�*� 2���fxR��  A��W(Umg=\�\�B�S1qlc� �M�U�V�N�->I { &"2 }& �rS2 i�^���a.O aN�n}-}�7) ���Lu�(BJ��.�ho&?��LY. ɑ�"�w �k-�J�5}F�xi��B�xi��AG^>�=-~�>���> >I.�Ѽ2 +4sGf een,� i�>���6mve�&hiv��hv)ǁ� gRǗ $��E"i_�,)���sJ�0; Th+_��n���% � JV�.�� eZ$E�� leag�BGr0 0�_&z :+6E��d� ���7 \r mpan �NRS)�F�Q1 2+!tc D�ind!�V�$^�,=�*�,. FM`2�)%|L�!3\it�/.) [�K� & �V�. *� A�.� "��eY��9�� � ")!BnGd�1�dolacz�'�J�+���*�>/a�!� 3�� {;-u��#2�i�, !#e�Eo"�M=)j��" Q�e�M&H orig���Nu Q>s�4o�"�؁UacAAi)U� h`i5�!�:���%4a��us,� o��5prorAhe6� ��{3�U��Z62i �zt ���B��f#"�)]2��o plif� �k&��Z�EB�N��PJ\m}��"���D&A\hZ0 `6��5�. e,k&��_R=obs 0A�F 2}2�5�G$ ���as��(*X�J �n.�/tЎF��12 tau,A� �I�_ in"]v1�>8A���02�-��b_=�a� *�>��c0s.�t^{s}ɗ+}��ʝ� �2� f�� �-�OuE!��'"5al"�</32+�xi)5%0F "m}��E`;"r �� �j%m-1%_{j>Q�� F_{m-j�1���;�� \h m"1�� qg��u�of:�>ڮ��"� xib. -'e9�t��$f\6�*d6of>��� hNC] $.^ } )ZJ� ��1XR -\��\ dla}" #._ j` V�:sd!� \, +a9.9| �) ��-�3:�Q&@ �)������e�N��� y�Ts2T6� �� ٢J�%j:��j#�(#R8�8��-u��7 = R\ )EY�&� ,�P%|.)! �)2e�) �)EZI�h m*�;\h�Ydm:�fz�,M0ei��H5Q9�fb� D:�H�on^i�A�,8st$"�%-��I"�$ 2h&4,&�c 1997,�z�݆B݆>�a�a�a�a�a\&N&In;�^�����J��>�����������h5��6�&:Mbetween2���a�I��"=s&�6����V�/* fwasy'�M5T�f7�i�X6w$s aO�-�C  �J�)@"��. J/'*�W�Y**�cO P4�Վ�D��  Eachf�t8j8O �BM_fv�>J�8 $H"� /�P5:V\cap2�\*8&�~� dm M*=+X�5&P+y/e�h�� *��H\#\3=QWU[A$v*�)g*t�p^ay> � �$�� map $p:~�O.2A�&�R:le;@F}=~\*S�"�;=p\$ st}H_un�P)ong @ "�;_� ( stale H n 'w_*�!$Zw*R@�/$h t@z  B��we�a�*�@U}m~��< wz*F$��. \vspace{1 ex} As $H$ is a transition function, ${\cal H}(t,\hbar;\lambda)$ can be factorized \be \label{factor 1} \Psi(t,\hbar>,=\underline{!F`\ast{^} \h mbox{for},h\lambda\in �\boldmath$CP$}^{1}-\{ 0,\infty\}. \ee where $\Psi(F�Pis holomorphic everyw3,apart from $ |= [$ and $\~�%|�^_0Z� both series take values in $\eQ$. The problem of such factorization, known as Riemann-Hilbert problem, reduces to the previously discussed homogenous HilbeAl. Indeed, let $L$ be a smo� contour o�%�F��$ (for example an equator). One can find ^�.ai S^{+Vwe use � same notaA� a%I pre�4 paragraphs), ��Jv-}-��i%0�\cup L �-D, respectively. On%F,they satisfy Ude�8 \bdm \widetildmc�y�xiF�^{-6"a� F�xi)mq h\xiaoLaJdmEsM�%� �>�=,analiticallyE inued A )-\{iT\-=+0\}:(, by \bea \��3.27}�B$!@ F@ B\\r�� 0 \} �~L�N�2� ^{-1F� \end- �Pa In this way we obta�[Na $ defined�~ea�f(inite point�{aI,comlex plana�d sA�on%�J-+!�!�- M�inge3L$ UM� EpJ�Psi!�9�xi)$. T�(means that �a G--�B�o! e whole�p��,�>@desired. Analogou�0B�g $I��$A�A�. F�}!_%�e� (\refI�)��  1})!}dsFSupposeAare give��Van��~�$ �ed by ��!�us�P �xstale H na pow_twist}) one gets��0ell_{\alpha}[>�^�astR�]=0\, , ��V =w,z���JwRKd V�= 2�>�B P>&V[ �The LHS�� , while RFA B "��at in��y it may have only a first order pole-� K A�,\it Liouvill�orem \rmy �A�A ar with�&��$ i.e.!�eas:oN�4&=& \frac{1}{i� } (-AU_+� \epsilon(\beta}Gg^{\�ssigma}  B2}ER��.�>�B��¶~��CsX $�eG}= �)$M  = w,z$, 26.:66B2=, w} z}$ do�  dependY'� a-z��s2Y}$шA� SDYM� ions�X 1}),��2})�"��3}��isa�(easily seen�a�ɝ veS fields $I$�E-zU ommute . � �uij a$lefteqn{0=Q�^{E�- [ )E�m ��i6>(\ ia��e- 2 Go_ ]\delta}F>  I6�)[(i�-y�Ye+ � .��\i�� rho} R xy� ]=}\\ &=&>i[-�6�%Z�}+ByVB2� J]A\, �\, �� J� x[� �) j-.� 7x6/Bm(F$� E-� 6V)]+!b & _ � ^{2}� \, \��G}�~G}.? S!� � J�'���3�� p d]�aoh3}) i.!2��2@ Let us� �\a�ee �no C f doe2i 8e� { ��"���~+$ uniqu�T��0be symultane<  ipli: $an )\in� , in��es 1Y$. � im>� 8e gauge freedom�.��poten�� . T� w\cho " f }�� j �WI�=0��en (comp���'Laxa}))����A�n� i<�%�� �\Theta����  a solu��hmaster� �MEH}). b� k � {Conclus�A}&vork!~4 found�evidencej0integrability$�$-%� S. )�:followe (: \bi \iteX  exista� e numbercconservG laws,^=Lax pair.!one-to-o�ora�on � betw��1JsmR�E formal� "�,bundles overA�T$IJstructu� roup Z��E uRV w�6��rise to�,,  chiralYF � heave� U] will��! $n. We also� a sequQO:\� tend!to%od�H when $N\rightarrow $}AH*{Acknowledgments} �%�ateful]8Maciej Dunajski�(Jacek Tafel�- a!/discuse�e@e i�a!�r�!� rt��pCONACyT grant 41993-F (Mexico� NATO � PST.CLG. 978984. %\input{literaA�"� thebiblio}y}{ iba�4{} Asakawa T. !�LKishimoto I. (2000),ONon aI G� TheoDz Dee[AZ Quanti4��P, hep-th/0002138 %\no�unt�G�@Bayen F., Flato M dronsdal C., Lichnerowicz A �LStrenhaimer D. (1978 �Ann. Phy!�$\rm\bf 111 �61-110�111-150A9(Birkhoff G. V13 VMath.\alen U74 T122-133:Ioyer C.P �Pleba�AJJ.F�85 [J. ^ �\26�$(2) 229-23!�.�Drezin E., Itzykson%+(Zinn-JustinW!�Zu��J.Bu79 u lLett.kuB82 4426�Chau L-LB81Ci�F^ , �2I�n le S�M, �$of (Kac-Moody A� )Uin:Q��phenomen !ed. K�Wolf, Le��not��ics%N189�l(Springer, New York) 110-1276� De W M)�0Lecomte P.B.A6)CE u.s7 � 487-�YcDonald!�S.K KQ $Proc. LondQS!�3 P 1-26:��� �Ma[L.J6� CommU�1213%, 641-67:�Hus�V�94M<Class.i�um GravUEqj927-93:W(Fairlie D.Ba� letc�ym%Zachos C-9��> i�31�(!=,1088-1094\\ .diW��!.-� MB 224 @ no. 1,2, 101-107�[89c.Y��b�nf18f02, 203-206 (1d6�(Fedosov B.V6~0J. Diff. GeomAIr40 ,!� -238zM6-�^�%:�x��y�L(Akademie Verlag, Be�>� laherty EE�197oHermitia `4K\H{a}hlerian � etry� Rel�uity �q�N>�u�-v� \'{n}��SiA�Moyal� !��of&U"�. ��? �Zr�o� C non-��<���D��8sis Tech. Univ.nXLodz, 2004 (in Polish)k �$Jacoba�NE 8qBasic�: II)�dFreeman, San Francisco, CA6VK�m Ludvigsen�DNewma�^"Tod K��A� 1), miFReportsx��7�h,No.2, 51-1396�$Kontsevichn(1997J�q*K of Pois�manifold%U4, q-alg/970904:�,Kupershmidt ���R�� ��2mB19-316� Leznov A.-�l .�)G7��233-12372� MacL�S.(193� Bull. AmeMj��45AA, 888-89:���A�.�!� _ >���21 !� 659-66:6^!�QuTUornsletter ��31D4-1:�N�WoodhoN N.M�(��2m , self-du�y,>�iraSo��XClarendon Press, Oxford:�@Muscheliszwili N.� 1962M�Singula" .� �(Moskwa6JNair Va#�Schiff��.7I"I{!+B 246R , 42:? (Neumann B.He�49 �Tt$Z*6 N202>u:", �Re��D18�(2901-2908. ��Parkes� �15 H2�8�656LB Q- �UU2B�� B 23 �8 No. 2,3,4, 287�nT� Int.!�Modu� [A� Y(7, 1415-144:� Penr�R%���G� Rel.�bf P�� 1, 31-5:K LA$Ward R.��1��m[s� flat,curved�-time !�"$ G0l��56� i� on0 2 ,A. Held, Vol!R ( ,x on:� numiD)!p 3-32:� �P� 7� �J.k �1E(1� 395-240>!$ 6T!)Hacyan�1b�~Rb� c 24[ 40>�VdPrzanowM%땉2�bf A 212!~, 2F� melj� (190�#HMonatsheft f\H{u}r ��� _\bf 19 V11-24>3ogorzel�W�96Q �).�!5,their applic�!� rm Pergam�" PWN�&:P(rasad M.K.,�haA;Z  Wang!�9���*Rbf B 8 2> 6pWF� 199Z Acta _ Ž!4 B 30%�, 863-87:l2g,I�.�y S.�1 a�-]� of�EK'� foŁE bracke��g�)�w tomie�Exact S)Sca�q=inm�� ed��aRc'&$`ials, J.L. Cervantes-Cota� C. LW Hmmerzhal (Kluwer Ac� c Pubb ers, USA: �6g%�5771 b-8bU of $S� (\S��)$6W)4Develop� ine;ematical�Experi alE$ic ��A,.@(ias, F. UriS) nd EM az >%E.�5-:(Ruiz J.�0The�  hPo!Se7 �P(Braunschweig: Vieweg� 6Y,Strachan I.A�a��eq�u�� B 28��63-666�NM�CZ�ei1"� 17-1B�NX� J�:�2( 255-27:] Takasaki "#>� ��p1877-188zQ� ͧu:�14�T"2. 332-6M6����3*Din� �- ory,`in:����(y-IމphyA� 1�T� Baile��R: Baston .!�e$ Wells R.O��>� geoyag�@ory�0rm Cambridge�ersAd 6Y�"C��#A I�k &( �  13!�3��Y)t:�  docua�}�w \cA�[11pt]{oLcle} \usepackage{ams![,amsthmcd symbB*f�B@2 [eng�G]{babe!+french��\Dspread{1.2} \renewRand{\the#�he�.\a�c{} \newtyem{}{Propos�(}[ :]2(corr}[.(]{Corollary6KS#��em6!lem Lemma6�(D�* �2�S �Remark 5+Eu}[1]{\!hbb{#1�def\pn{`";} ni{>1{1\!{A�l=.m C}{\Bbb C: er}{ R>3enN>zedZ}}"�tcilatexm?-Q�<} \title{About a_ ul�@S.M. Kozlov}\make)�Hgin{center} {\bf HavNAJARD#\foot�ize{D\'e�ea de�)\'�Mq�0a I.P.E.I. � $stir, 5000� 0 Tunisie . } f${Researche*� 2�< CMCU N 02/F1511�P$N 04/S1404Z1jects.�?-�\)/abs��!/(",+ tern� eKof`,improve upon5Z3!Z~)Z0 \cite{ko}. I!al�th��( asymptotic� the *�de�3��sta\�acogc oper[10 $\displaysty�+8_\omega=-\nabla�"  $,�"bottom��0rum#d.54{ {\small\sf 2%�at�0Sub!^��if� � :81Q10, 35P05, 37A30, 47F05.\\ Keyword�orases : �al�űran�!�s,r$�$fshitz tai� h�2.}} "� Introdu�}�!i}�+ $H_{)Ld(be�  adjo1/-� on $L^2(e�{R}}^d)$� !7y�v/by:Qu�f f=H(!� w)1� \cdot  %��$bel{b1h"nd_5$<Y "��vA�d b�!ed fuU6.���N2 )2e�F�6e I�4}! A^Sal A� rpre"s.��f�$st�5b-6��@moIkof �4study: UgrV:. 6 %1,�""i�,$\L�6$ a cub�" ${\ ��)�$.� ���Y, ;}�0 restriEI�) oi�!VMC %uarT34v �75�%s elliptic,%resolvA% o.�is�0ac�,�� tly Einu�NDI%d retI#is mad%*iso�vd eigen� �!f,e"& cityM21}%P��n�ly N_{1W(E)&�$�rm{vol}( ")I� \#\ {.�\!�\ }x)�, ;$}\leq E\}.u�ahc68Here $|:}%� the volum%UNQ ��Lebesgu�3ns)?$\# E<( cardinal {� E$.}qr It!lshown&Y, limi�$6+$�"� $�"sO"$% M�^d$7%s almosI3re�/ndlin2�'�Q�&�6s��A[al�\textbf�:b�}!�$%t)%��7IDS�(acronym). S�9 Pa-Fi:92}�� The Ra�9#a�a|�4�9 rega�X�ehavio&$N$ at�-���%qy}$. In&T8X#s ��,W0,W1,W2,W3}iJauthor2�(FzlŽr!�b!uedgi3>�U(b1x.It �#a L��\(�decre�>exponen�ly fast)�A� pres�. situ�,��V, 2is �$n)it�)'� s moreA�$n polynomi"6{,m��iK�):)��A�N$A�>A$ of sX&period*��O6�preci%�YE�it{i�bf*�%� s.}$A`1�$would like �ank� Xfessor Fr\'ederic KLOPP%JQ����2uA�a8cer���7.)!�prN@Mabrouk Ben AmmarO,many helpful��subm 1 , model } Con��!+, Schr{\"o}�&)�Fy \|9eq:1} B; fra3=D }r% ��We~g *��a�EU<-~b{Z�� -erg%� � � �'|+(K( istsW(� tant e*>1$,�1ingv�3��*�� �� *F�� s���B�of Ander# type�4it ha�Om %v�6� � (x)=�@^+(x)+\sum_{\gamm/?Ő-D} 0_ !�rho^0(x- )�9�% ��'iz� �^+)�-:�q~ �9sur�(, eC0 C �.�(z@(2�)� 2�$�n�94rivial, i.i.d.QQ vari�s.!����/ choi�,M iSensur��at�-ѮzAme� fam4of � &� e�Q��86,��"k?if $\tau�}$ refer�a��Aaon� )�$�y n $(2=20{��ap5�g],of�/tx � s� {2}:� ��s$Y� � Zwe. $$ 2�A_ B M�&6�-h.C Acco g�~B;� ��i�2($�,  _ {pp�1�acA:nd+sclosed� M#�� set�,$ �R!Gsuc�A! XE�!�KR$u2Q=+0�Aa�n Lif $\s�_�$ (x.x=L@ � .�) �<g, e pE.�=�:N�ab�-el� �?ouI�s� �@I)A;.�I� - !O pp}= � , )(ac.�.?s2"�R?. � )b%�V dR �4Friedrichs extNo� fo[0� quadr�A�m $��cal{H}"� 0[\psi]=\langl h���,  \r)\ \ ,\  �AH^1_{�{loc}}(��R}^d).aF6�� 0ult}We shall |�WO����thr:1}��A$\!2,\ a� >�;$C>1$]��.D $E\to 0^+$ we e�,n�O .B2� \�0�� !BN}}(E-E^�=)-Ce^{-�}� % /(E)� aZP+P+:P! ��.�ROEAA� ^H� &]@>� {V.}.(4�.(H}���6IJ;S>����/=%Bbb{E}GU�)$�I) �" 1)� ��T �'sMx es> � � � i e estim*7�re�`;7�!Ze&� &� ���9�tobD+o(E))aO \rm{Rly\a�}\ Q�aE2)We do� believ� is�to�op�l: namewx �{.gqD� be lar_ tha�v��w�;`!|he&w �-�!x&�Pro�fa�:?~Bi�'2� & approx!xio� vskip.2cm&�Pick $nv7�,N}\setminus\�B%��8�J�S�N *A�H^'<��U�� I�- q#*}#, $.b ^n {+,n}+HU�^{0,n} B& �c� _{n}\cap ��9 {d}}% s]  }k �;D (2n+1)>:}�*f +1��   _{k�Y`�� =\{x�a70{d};\forall 1� jd,\ -� 82k+1}{2}% � $\}.$$For $)�$ fix�nd :^*�9.�� a $ �Q=� $" 6� :% S . \\�$��MX��_0)E�>�;AK%�D& !���ve͛r���U}�S�Floqueti�y} Now��Jew��dard �;s�4� ;��ry�y�1Ps.sic" �6����erial WM{sT `��torus&�T}^*_{A��C�/2\piJ.�6�6 ${M���H}}}_n$� �d <  *} {I�(=\{u(x,�ta < L_ � ��m)\o�(s L Obb{T}} �ast });\\AeEc,m�k^as\ [TK Z �&Z;;\ u(x+ \�=e^{i  � }2��Nnd.#TC�:s $U$ a"� is+!�6$)51#ś${� !=9l.� *� ^n$ admit��� Q�d4$ �)QSC��U&�^nU1�dOt_-�%�-Q!} oplus }.B()4)d  V16� 4 )��aTiV� �1" _{n1�}&%K�u*i);c�on!t2r^1:R��2'.ua\i6Sb�A�)�QWinM� V��,]�)F� A�)\},$$7$$ ::��:&.�;\*zBx!�q }�>^2 ;\ | ,|=1a$$�R��n%�&we&,R )$�a�� 1; h�9 A������9�de�.*^, q)�.�M�)$�Ngin.;E_{0}(n,ɕQ�  E_{1^  �3kr3-RJY �#es�>%��s�a)d��$(w�dN)��%�f N}}}@A"1s��@ *6=^�^T�Lip�-&��1�͎��E�Jt&�= +�= o �O rm{as}\ k~&u,4rm� in}@ �F�!mU�� �E� ^n)$Y *ra_aE "7@. (i.�2"�6S(=\bigcup _{%��bb!�:�Z� })$)"Tw-J�LN}*� ?T��nUB.$;@DPieI.0g �idosper!�B�E( �$ �- 1}{(�)^dDi��\!'t.k* ;\ E_k>8e� S}ѱ&�d a�� "v ~�V}(N=,E� :E; =�V}(B,E��&AEe�&� $B$ less �Uquv#o �) $d�N&A} #aCve%�^. �_ trib s . As2Qat�:emKng ing,f� ��ve�eEDi�NJ%:�.�by6m$NE�z ��p � $\varph�C��^{�L}(%��}),bf veria v kp8},��na"U "� s^P� .KE� )\Q�����%�E�C�  }+(t� tr}� A�H� >}}\Big( � Y� }^�  ))%Q��Q�Wg BJ=&�K��!C��).�D(\chi _{} v v�C# # Big)"1%1sl&�!1V,�� � #VA�)�!:Rch^*}$ nD*�charac� stic�a�a�_rm!a(Ay� tracihA$ Y�!xE�)%B�$ ie ;e akena�$�F5�E��+ [Y}]�vT20} E�nyU�A22�*C�%Nx"��9\O�( $�� $$\lim_{n.iiB )��� -�z�)�R0m!7m� More4shS��� �!qk*�! well-&�0 >e_�!A Q U"H2&��� &{!��}e�O-1���t�#: q}.�p&J 5} L\eta>:ImE�eX*"p �� rval�P&�  ]va�_0O� ",E2$EA"I�8\in(0,< !4$n\geq^{-]��ha�v%!i�!&� stpra�M� �(6 (E+�/2))-�_� 6� B<-B<<� eta}�-�/�O:�)-r(2a� �' �P2� (E+2�) [ 4?cab�6:+^�"�9�e�E��TThis l/0��"���ESab�\"{"$#case.t't,J true/ �Vof_ba.~ 0he Helffer-SjUs���mul7u&�)n � e� deca�-65 kernels (@Combes-Thomas arg�2��T%|{K�W6=s.� �Tsvb , wh_e�f dim(U }d�6c%��1 *� B��Q {V}b� ��sup dim�)��E� bsetI���}^n, \ { �8\�&}},A}E� �4 *d {n}� u,u� aH$ E\|u\|^2\a^ �!�� ��Dr�\ &&� �.��-\��a{H&] [ �+�V0*�=�"l  *}� "X��R$�!�E}�0 �[1YB9�6�1; w-ig| ����!9|)�� 5�,iN�2� � {���2�%g�,J�8= +az� e9��y!!&�|Z�, ��U�V�]�E� 6�+����J�, .1��z��1�}<� 5]^��96�N�.C;�2�{��>�(E.J!u��k�k� �=iF�So� ge�O?&=:*���,~"6*\Rk,6? )\\ �)��^��M�5� W149"9� #��_g,m�.W1�ave~6� *"���h?inrTccount >�)!� ge/aF� ��,5}Y�2*+$9����N}�:��ZF�f��% dim}N��f�*�~� y�Z�jzm9�� 2�!�5!\� ��v&T$"�M0+$..���� ��Zj�$ is �2&�f-\D�^.3'�' rho*s3LL�tic$Cno3($CMpends Rc-E$)�%v.@4!�>I�:�9��)^{-d}:qF� some�'0 !�} ._6} )�6� Bk ^m�:q)+C�P}(�<E,�nZ � � With [ 20=a \[,a5e(0� .�_N; _{�9�� )}=1��T �$ere9  ���"*}�3Big���BCmu�7�15q�1%�� 9VH}.,(2=))=\\ �p ^V)�a�J1�W�+�� qz^�:P 6�1�%�.:d*�#b, ����x 6{�)-Zn!��&_ V�>"Z!�=B�� ^�6�1F� �O Q.�5(>�&� G ��N� 2���><.�� i��I�>�U����p�6u� carr�`eA�#*% tonf�6���-�����a�?-64)-~Qy 9N k��  +"�+ * *ro�0,�bb^�$:Dpur�l, S�C*aI+ devia�.q� le:2}6(% \tau��E �� sufficie�< �@� 9�+,�.�$�f�!R{Eq tau}d)I&�%O�:�+ *�+/jus�j�2 �o=kef,5}�%1 H%"�'�C8��>+}-W'- )uI�ech�c�0Kl:01b�=a$J�� '2�&9 ��M�.��� 68=�^\{ ! ����H^1��) ;\| u\^� \ \|����DE�_* )(�< {and�!u�B�V��y PZ���=�)u.�.h%�q�mQ ~? st e@s..� �ask�A&X y� ���:�=k!i=1}^dFb%r� 2�=L$� J�h.W&_i}u,\pkI�jx_{i}}�s |:m �"�I#9 !o$E]�3]]�C�4u$�<� writtenq;he"&6.)as:cu-�"���"o""� _�+^*}P�1w *+4� (w(�%� )_k0%_N�6a�=��A&�% of � _no�%�ssoci\Cto $(#-� g� �y� Bxis�u��ch� �gD5o :Dq�� �:�@5��a �# geq0j�|�|^2| >m|^2IAP��C E^2>? $�:AVC?041Q�a simplZn-degese5�*�#.�(H�(6�8C2�1"�:\ �$k\neq 0|k-)�ZQ!*�$$K>jb} 2?!l 1/C,�/ {�4��Z=Y% _jZy;\ *�0 n_0Hx�� $E_0My_j)�i^�c�-)�E _{h n_0}|)- _j|F� �!UA<�5(2l+1)=[1/2+2��$'}]_{\circ�D:x+(�1 @�:$�s8�7 <B<� d}{4(d+1)�-h� ic �� j�/$. �D[s�$ojJA� �sdd  erB eJG>}�F�v� a� b})f c})s �B� }� 1n�J� m�q m_{j��{n�%I _{B�>)P1}{l}} T0�y |^2 T�  CE{0l^2 %���yi�we�-*�ua� }�� 0}u_j+u^eO$ :�$}� u_jK/B��&�l}�?�w!2 _j�E0 �#^{e}\K.�"%%W3M��Av= ��)��{0}j_j<=p-[)1=1-2?$$? u� I9W!o�lWow*: �%E$I��:� e � �m�,j'%/a��|  F�B�L6=&P !��; u_{j'D$� �t&�/4"�parisBQ���6���$,"�"F�Bi��  ��:� | �� �(2eZ)^*[ V�g�N ax .?! U%E�|ly )gci�!Ab�!��:� 1y 2� Fix 1=!� �~{ 7)VlE l�K.#="� {u}Z7in k3�('2f"� 1)\ C B^2;�Don �ucubi6Lambda�A,l'k1x=(x_1,�`s,x_d)a��� �i�d -l'-��2}�(x_i-(2l'+1)*2_i*(w}:S!�)F ^d))!Cl'/l, A W\2 �y.2Bc&�)U# II J�F F�3xx}&�Jr� A�~�psi _j0FU� Az2M�B % =206�5�:e4Q�!�}MZy/2}a_j((7fn $ +U�0A�6 $��G(x6�>�^��0�-1�mNQJn�T get"�${.!T!!F@A?=\|�Rj>��TE1F�C}=<|� %&*�=%f|9Y~$,�.0,0�"�B-�)|vdxM7��&��j5})�n� �:@ :�; R�\2YA x�v�F7; 1������Sj-�*w�-2Y2�>Z PC �>�3<+{,-I��;�&$�kf  $2k'+1= N �� �)&� ,4sL%b �)"�+s�rat�==q��5(��So��.��W��"}2!&6I$l � l'$,� B�� {d}2{>��?>u *36�e� j, \:nEV� V�� � �.� (4G�>� Iu�2����>Z�{j� :��>u �&E�d}|A^! ,j'}|�.[g9^{i�=> ������Q4��*}6�e�%2�5�' �2CN2�.�a*��3'�G�A) ��'��qJ">��6&�MB�6��j� �:')} dxI�9_!LT7P%e�2H ^d2eB2P-i} !B} !7�'��!\�B�7� �7Bel%�hI&;�:'qA5]+.��j{j})l��ka�)}dx .L 5[ �W2� �1is��A�*`C�� ŭ�=�!�#I o2:+M. :*��2[�LZ�E�E&Jexp2n]A� A��1� "���)��F>� 1˝6 �I �nR.��<)!�m�:�j:*�!4��������b��M&�*&2B�v�0#i5� .2[:/�YB�T̀.R:L*} 2N��� Q(EM^L�0 (]s2_{��J0 �\V/~u�7 �fe�6�.+.)'��hbUq�*F[ �8�?;[-%bA.5 1d �� 72&m���t�tI��S'"�>� ��j;V� �օ*jG� $$C2�%6�')f?�>N�>��Q� B�>"n�B]:�j!6;I��E $$ YF��%��.�nu� �����7A_{� �.]Aa4< .1J�'}}N�BN�e+P�U(N3.fW. {d�� k�D,OV� �=,ent v�X 8"�$E}Vx�{P[&�"� k �y mpac2~Y��wa�&�/$$ |Y-g)|D||u^0|$$�to61&*'&��#(n"�+3t s�%e�X2q&.@b.� Y.}��JL �YTX:.�is�_�Y40*�&"� w(.Mh�-aGhDe-Ze�`!R��P�(R| �&��d5 � e���� �; c(l'B��-7�d�d\rho'+#�Y��#f:� l'$.* Y� for o;"�[E�' � $N|<so?>\(ao$Ev.(&Mb.mat�".~ eta'��p~p!Q1g%DAA'B�%~':Qs�abl#e sum �R��Ge��$a�A�]� u�T�ly�,re�X:K(�(�( $\BoxI"*��j{plai�T.{ "= >�o{Totot i�~4[1] {4}A. Figot�!�< A. Klein : {\sl"�a Localiz}�tr�sWa��I9? : Abk.}gammu u���l. {)180}},kp,96) p 439-48,$�2] y�� Demb��4d O. Zeitouni.6�L[V�M�.Tw�f Jone�[Bartlett2`uBo�q, 199.�3 �4St:89} J-M. De�|f(D. Stroock.�k9D:� }.} �2Cq!TPu\�ed *$l. &v��89�-�84]{6} W. Kirsch:�Rl>�?"S(} } A Cours�R����In!�)�345}} ���t,J� !�89!�264-370�5] + FAeopp:  Weak�H*�l.q!"�e�l:dr]HI`tonian!� �. I.H�}((3):711-737���zU[6]H�6Etlf |s Tm& long�ge�]l�W�E� Jour2�p{43}} �x2) N$^�$8$ 6 p 2948-2958=;7] fNmpE]WAverag�1�t�axSoviet MexDokjl. ^w�,19����4 $ 4 p 950-954�88]{W0} H. NajarIb�+ it{A�oquaw la %V >�w �:�w,a4paper,10pt*�wN�w2�w {amsF�wg��ic�%*%xroG4ng6A% :$olor} %opeRj \�u�^{A VERY BRIEF NOTE ON SOME COMMUTATIVE ALGEBRAIC PROPERTIES OF A DIRAC-FUETER MODIFIED EQUATION}ja�lh{Daniel Alay\'{o}n-Solarz,\&;�(pLrz@ime.unicamp.br)} !o� &�v< \date{{\em Dece��0��04_&�v=abs M c�U a�/W)��a unus�P�xertx�x 4�6u�e"RahtO4d Fueter-Dirac"�Gs�Ry:W a co�f ate-��bq�%eI�P�b wJwak�is�Psib8�o�o� M����,j�/radJHsymmet�l1Lr�r� ' e 3-�G,^ a n�=aD�ic����!m9rse�bdoe natup[F�aD�d!Nmu!:e�' �yD7 ve rrelh0%0+?m�BY non-inv!� bles�Iis ;Unonj2� . By0 I�%��U V|`�6�ue K�qud�it"U��B]� %�6 %� f SECTION I�{B{ W2��<%�f"9gdi�Jnp95�b+�1��f&�\d�� f} t} +�(j#x#jrFy#k nF z} =!-2v}{rB�+F(Y�*�Qs4��ک:���f(p) = u+ \iot�i }v(p9+�3u�v? real"/R��a6�A;�a�f�w��o�9��!��6pbf{P1. (4D NON-OBSERVABILITY)W ����is 9 e����Q*o�i��- ular�'codA �z�t 2,3��(��Z%�)��not5:�� diphemonUsm �.�3D j�wha�.� has .�26��� �im� 7m�9� N: connected&*s. �!c\TOPOLOGICAL CHARACTERIZAa�)�'�BSabove"���Vtopolog�Din%�nt.�2. �LRADIAL SYMMETRY)}: A9ȡ1��o�! Z!�9��pace, �`!} 6R^{3}�1�3.EX$INVARIANCE�So��H\���er 2faut6�sm��Y 4. (&�XQUATERNIONIC CLOSEDNESS!Swo��At�a.��D8�2�p|��t2J!�g�z&S���esUu4�PA�ly�.6t�/ poinZag"Ƈic ,&6]Ru Yd 5. (SEPAREP� $GLOBAL FUN�%!]�cd�oabw���ou� origi}eit:�a�_6�Jor;_totv*�6Zis  Z�6. (QUIRa&0AUCHY-RIEMANN"� �I yalway&G  tozd���am �"w04�[eDJ , d�_dA($t$ ,$r�$�N,#.0!@���W � �4} �6��s�:hO}B�u6+-���Lv!r��0 !:O.Gr�,>!.GtbG.&)}(\sin%" 2}+>Z.{(b^2*�*B^->^2�!�}=!�O}�4%�5�sub�y.4*} I�s:?:�"H5�! )�e2 n $f�����t� .�4*�|-F� �=f6�F� un ^con� �mW�!.�ͩ�� m6� � �:ic�9Ltݵ"� 4Z�8o. � machiner[�q�seems } 'ya�L2+i� . Q� � �ce�! i�nr0 �.� B �&-��>�>{� T����*f��6RR���6* eucak�Q�rsf6�[all]{x��+�x���~key6B {bbm} %*$CORREZIONE  }5A1و$l}{\blacktؙgle!�} % :)r>) } %!� \4***Spaziotempo6PM}&�EM}} % :6+X+X+y':1g 1 rm{g0��ca6WJ& J}}%6DLD}}% insiemi causali6-I-IBJPo �FPL�Et6B�A$C�super�E$ di Cauchy63Mk Xbb{M}^4:C7 mink)�. * Po�w=�66hdc h�O� diamʐ reg�e62K1K}EL 2i2i:^KA^1K�02ondb?]s* A~e��>�6�A�Aϩ2:�Aa�scr (�h.��StMSMse� li�6}**;Ct�3 grec td altro.�6�$si}{\sigma:�de}{\D�.� ga}{� :2b2��6ctt�B6eps}{*�\:iA��:a!>�6Pl�l�9:S�S �.�r6]cy�� ar{y.cz z6��on}͌ � {#ό2��bolm�tegoria.�*:�Z!A>a50Z}^0(\Al_\K)}"�%0-cocic>MZ� ;1J;1;:GZu.�Z}^1_t:?<��JEx]�F{\K_x})�j�F9B�.�L�{a�) �su!b�\:bZuŀ. �JG�nPp:��\Po � .QdelN�Zut>F �HN�N6�Bh �frak{B}�8A?H}_� 60am|sf{�� %Ampli�En:?c5>sf�` %C� - %2.x�q}{� set{AKr���� tensτpuntato�x6�K > _x} z?6zn:� A! rm{f6�{\F-] rm{F>RER>sst�script 4��' %% 2<rhoB}{ \���ol 7�>+siB*siN)deB)deN)gaB)gaN)bFRbRRtauBS�M }B�lF}���>�alBXalR*vjB. 2f49H��m{maticB2N {\eqv�wmeq2� {\ordpoa .4 '.� �f��equivZ n"R� {\normI[ VertAN !){\RM�/f�{I� �erR � .z {\Hi�a �A7g6Iico"�i ��J? Titol2�~ �Gi� pe Ruzzi�j �{Dim-3}� Mat)�a, UniW t\`a� Roma ``To3gata'' b] LVip"(lla Ricerca$"entM�, 00133,F , Italy}�e?\ tt{r� @matz(roma2.it}} e��5Hoy�pQ� $s, net-co3�log� �? � sel��o�mctors�%" glob�hyperA�c!�ce���^~w� "JW&�6�?.&�We esharply��zߠ �,Utn< �DHR-typ+R �!!&# obs�hC,!( arbitrary v6& $t< 3$. �ho �����s&qhappen%�M )u, װQ.$rm{C}^*-$c� ��,&�l &z% �ey�itDw^*efY�L% �3�,H�perA%]IIaRjug�".�@��&frame� �oa%e�:�ofM� T^"'�$J.E. Rober Q The9.B���/}b�ez#med bag" �#��e.s�A� �ed� i!�. �5q'�e46�ivѯ The2* � yclc&�m �j�q@�M3uccf#to4Talyze��9�Lisl be� Ew*�C!=e�h encoV] � �us A�dex�:cK��_t�z"��a 7i2tt@���a atA�!-funda�{alG �;�k �un��yd 9���ic; any  !}mns &�{re�9e" A�i�B��*n��impor" 7-E�<q IA�.���uit�da��)�j1\ �neA ��� � XV� p�- � Ekrem{df}.J�&ٛ6'$teo}[df]{T�m��GA/ !P*'�:Ecor $*�6glemma $[.H# g ȥ i!�>aoss =���� R�?\%�of�x���1rkVc{� } �n�D�DDvk� Int}��mU pl'acoL���A�sC�A�ɯd WR�z{�� �sWd>xa`�ac��ntum ��E�y vLHa,HK}{��5c &����Im�q�a� � it��B�}���R}_\K$,���*�{�0 \[ \K\ni\dc\�a��mat9 R}(\dc�h] )&�Us�5��el� $\dc2 a fa�$\K�%��c]6Z,n regF%1J�d $\M$'ide�+a�Q�� back�ndtold, }�K�"�-�- � $ g 8&��l='*� ���&��EZi��dc$. S�'un�� al%b��� irrغ�:5 %�net��Hs0t�"��ng&C%[�A���um"s�#yJ�ly� *;�*� Cne�IV = }���dect2m�M�w$�VozVq.h��nt OneQm !��%V=^ /$b[��dem���cq�� :� A\k��am�096�y2=  cpo*�)� Y�&� a95$:� / k`� �(es as� ��~ rrii mpO$N� :G �ados�� lawn�a*��of�3v*Fermi S/qxs}" ; ��h� ��]y}� � ex̽`Qb�A���9��Qi "��$DHR1,DHR2}*k ` [��-,!aO!�u, v�6ge�b� 1����Pl  $\pi�� �O����ct"� �� y&n�&� A�C+j�(�s �!�l�5^\perp$� RQ�HisFa" vacuum 6��_o���]in�+bolJ'M,Int:1} \pi|_&��< �)} \ca@\pi_of&, \q'� �cin\K.o �" } Althoug�+MMh-���e!B�,� / ���!�Q$!�idk�&�!�ons. F���� sugg�* idea�( �C ����might�]�;!i�m�j �$ �reŁA (9)wӜ+�ly �� EMq]power�� t"�a �$ly4S�� al>� eB�.�� b�;�iyD0�A��m�. A��evj�q�љBF- ' BF}�^deQ�)Ra�de��ass�-< ieNJI]� A�}`ne"lk*"�ofP"a�ac[ �GGMkHIn .����p7X&� !5induc (÷�� �,m" �AS�S��s quoZ/��in. How�E8, up until now5,��&�?��S u� 7$k���aɶ�xU$.�.�aRirM�Y?��>E�@�0Acq�p� w�alM� "� �ofe�AKe#�R &v!�x�� Q��!l��%a�e sh��a�inai� A��*�/t�/ EPA" �irB� ]exhibi��fe�0E� :�.�l�79� . $GLRV,Rob3}�N�v�$ Wal�NultnJ dirx,�d,e$-c[-ER��I*�$�)a�+ *� 5i55� affe :� J. �aim��!6OY �2d�%�*^ �E��� !�e � ��]�� }P��d P- �š�n v�w_w�� tres!1��*� �i>�0co���7�� D &�!"�\\[3pt]��u�B� e en^�ngk �hE�a<1��ZvA` key �A� �c(� rioned! \���?be&1 tly8 ��!|�e�� ^�}0"�i;5 &P� �d��W . � i�Rob��(seM2m�V�߭�(). Such an&�ma��cl���O.YA infor�on�-is!�ef5L�!`9�F m�% �ak>N:�6~Poinca�<8 � I:A�"�  oy%i!��� 6� )ў�i��&7����i�e��wo2�a4P��:�!KSF I�x�:2 (Q\�Fv�*�  "�} A�a!���}~eq R2W a3sfS2� ���$G0A 1-1>��2�$z"� � ���a�! R�1��$�#:� & \A' �E$!�Zon" � }"&+a@X,bi�)u�n _o&�!j ))''$A�^%bTE&�,"� M��but��g ߆nsaers�}a7qK, I�y`�"X"�$#$�af�co"3.�qJ��t���!�����v��$-sd�"QP }. � !�7"�,eHA of f 2)�$��d=aQ $\KrE�re�5)on�=�:2� �J'�)d5i8�j�.�� $.�onR ?y �Z!൭:�a���N���@ �� $\Hilos��h% !GeR%* :\KrBqqZ\�SR  $2#Haag fµ�Bo��rs~ yɭS nGCba7f�iq$ ��ys�l"��r��ZXpd�AAicaM�of>j.j�mpl_*ime"�neI��^s��UzFiJ"LKn��Ve�Fin�Iedqt�Y�7��  froF�6��?�)��6by nliz��e�"�way��cr��G2. A%A>5,)�1.a�A��.ʡ�FaK=�%I�Z�i��T��i�.Q2�A��Kr}ɉnd +is� "� �9��   a�iZ'uct� 2 f2ued�S ��{"�!�M��>| $ breaks d'��85 �i�1= � K�� s�x 4>�>� �$r$u���!�Y��2eD��I���,)-,~�-6f ͮ-E��letT��ussed�below)���g#"R ��rm � Č} .��� 8��"� , impm�R�T �= di�ds��(���n�ice��ae����0F \1�:)�#U�2�8n�>���; or� !fact�0( surfaces ("� ��Ada:7�u �  Ba:2���v�G�C foree2 necess�<!�}5d(��Abs�:& a�-�ye�AHF)z�. Prog�eGu�] � �UU�"_�i�&�!# aths�:��#h� "x !ڥ�issues &� �at $E3F9 turn���fu&�! 5 ours.��.��*8"!&%/�T��C"��;���pe?u�2�MB�&no� ���� _*S �1��� }�o�w!k�h�%in draw�ICnonm\nes�3"� r�c��)m*We�L �.$IJ�s � w �Sre� �ŘBh$ or, "M t�DA�-AZpe�_j� ilFr�"9��eB dA���MA �j��&�end^9 �LWG[ 7�������w� $�,��6s��be hol>}Zn � e��T�veas��A�ed: ��ki hat{�.}"��6d��"~%�Ů:ip��$z,z_1�%�, �a�si�A\$z%i.t z_1$��a=� X ��!�6&c -$�!e�@�M|A�ri��%Y !��B� in  $��Cc:5a}q�is�e:M).�n,�8eas:Ba'"f<�F�A}C�6�QA������)5�G)�.GA�X'6 x&}YH�!o���[wh)9d���R�-��y�f99�is� blemx� y^+in6at <t*2(A� W�M��!�% �:?(� ��d6(��-J��Po$ (&4�I Ab:1����y�+>Pos :�^�E�3)��]$h@�#o"6� �u>�� (�' �c:4wI� c� i�q%��$V  a2� 0"� &� E�3E��E4rcwV�!�>� ( �f��&�) a.R0g�.> �> da:6!�Y�at &~%T� *F&jEoADu��t�$Mˉt2��C>a�}.L 1Adb4 \\�� ���UZl#� a �r�������� a� ���� pY&� �0b3}�O:,doa� n�,b QCcDG�aGu�`,��)�:j6&"�!��YC' �s;2�0h4:N� jusy1$Ma��� �h",u eI?�  '� �!e�: *�$��2cl#a�_MgB��#uH inherits ����(�$���p hBqA� I���"պu���Ճ %�[��3.15]5.���� al���-� by�5*:S aK:&Hec B� :db�,qk!new� d8$��Ap� � � B1cab�EN.�Zn3}a). ��2�Bb}Cg�c�1�of&Q S.��2���6 �� -� ��nF�F�? �� adop�% $\K$b5�%9�Rd!L��s �y come��(In6�C��� iUCan .C)!��+K"��!�F !yV� +)�or�M>� , �{r[k rMZh5�]�F>9�W1��!n_x�K$ �"�2��$M$SBbA��sT)Z��[_ ;"� a� $=$,��� ��,i�&� Q!!�6=6P5��Ka "),z_x x$*7 M$o�an*���W. $z B $ if�*� &m glu�7"� �+7�d (*�0�cC� A�i���q  arrowsV<4}) 2m � � to�cH&aX� es�&��c�"pro�3a�A:s: � ���)!b!�F��|�*0�s�%<:� ory "(�o�'2�Cb});�!ycheck �\c�+u# s"S� )�6x$AiY�fK >�)�S�tn��ǹR*A0E�a �8 it{g8�or�:�c �ca-�ns��,a��!n ^K> B�t2���/SzF��ers �Ml��b-�=�Zut_\fm�,Zut$ whose pobjects have finite statistic�s conjugates (Theorem \ref{Cbc:11}).\\[5pt] %**�L \indent In Appendix jHX} we give some bas�de��ions and results on tensor $\mathrm{C}^*-$categories. ��%��**�@@ \sec� {Homotopy%�net-cohomology of posets} \label{A} After)K prelimina!8, the main top!d� are discussed in full generality5,first three �s: ��group�a �;? conn � between2 !�6�; �$behaviour Q6#D under a change ofiAd0x set. The re�ing two� �8evoted to study@case tha�e � is aE�s for'top)�xa0ical space. Waj ressNY�btain)p9C6]%y erms�abstract �s ca!ID applied, not only������c%cbyG_*bD��H�F.6@i��| 0�r%|.E�9]E�>�9� Ge�4exten!�!�: $\-�a  :2BI)5Ey �, ��ed �it{bou��ies}, x F!>setting:�f �yf�rc e<$. OneE�0easily check,H��iqi!-~ X followA/ �B��1� _i\cu}_j = -1J)8{i+1},\qquad ie�j,��Dhold. From now on, will omi� 4superscripts f+aHsymbol6&$,E�?I�� compo��on�j �>�_j$!8^ U _{ij}$; 0�#A�,�0letter $a$; 16$b$S 2: c$. Notic�w XexHA�not� � n elem ofI� ; an5b5 form��d T�9(_0b$,�1bi�e$|b|$kU�� �5sup�i�R��95Bk�x^ . Given $�>a_1 Si_0q@a ՟ path)�-$a�$a_1$}��L/  sequ� $p=\{b_n�,b_1\}�.� * �2U�_1b_1=��0 b�� =1��� � } \ ��\{1�n-1\}V$�U� 0b_n=a_1.��.�stM ng)� p$, writt!{B1!N!M6AUa_00hilA���end:T FU0U��T)��w}�aK"AP}(a_0A͂�K^ath� �U i��yw rm D6@ H %���0$.a&PoeJJ� 8wis�B,ed} wheneverk& �Em �e�!a& a� $p"2 � �:Ns!� �1c�� $|p|� {|b_ix i=Yx \}$,�we)�!�e =�teq P$� $P%a�e��v��2_i|�P$��% $��0 Furthermore,ian abuse!�~, 6���\dc$ if ? �+!�)�$��X&� !�}� ,figure}[!ht]ce } \cludegraphics[scale=0.6]lex.eps} e� \cap�M{�q��, $� ��ex,mэ�3,b_2��*!�. %a����m ${ �u�$.�Hend� �\\\\ z1 \no�ntI\ bf{Causal�jK nes�n)�� algebras���2� , a R it{cJR�]}�IA�wa��B�$\perp$ 2:�&�,properties: 1�equ*�:0}�"�(i)} &l cɕPo��*� \ \��� ���} :H�A�_2;�e(i k "�2�2�Av 2B3U2�!1!cA ��9G�xu�$Pyf&�Z�r-�? �}����i� $P^���)�&>� "� \{A[\��!(�,�for+ �[\}��" N�  � $P_1� P$�n� �_1� assum��U�Wu�6�c equipped�}a -"di}8Q�Q� . A &9 RR}.� -A�correspo�ce�4Al_\Po: \Po\ni!B� A(\dc)�\Bhassocia^ �<�'�k@c$ a von Neumanny�$ K$ 1�^fi� Hilberth��cal{H}_oe A�y��Nte#yBj�_1� 2), & Y isotony,abSAN!aU�V',V)� ity,iIqU ] wh��a prime ove�e1>.�&commu�! �P�� 1sI�)$A�%�ed�>� �Sm�%� 4m����� "c �rca b{ �1}��)^e�$ � !q��A��E�?JU (irreducible&N , � n $TgBh$�W �)'6�.��!%n $T=cj�m{1}$R���1-cocyc]�W�f-�rea� to%�"?x!�e(&q� )re. Le!��qbe �E� aTF�r��,ZlG1dKn =T%�of:�&� } $zM=��value$f�� field $z_1� ��b>�z(b!��unita!j perators >�� i� ity:�>z("� 0 c) )�2= . 1 c)�% E$ Si_2��nd%��i cond%�:� �\A(|b|}F) b$. An�7i[ Dtwiner} $t\in(z,z_� "Ua1of�sn(e-�!b $t%b!ba>bt_aA�!`>JU6!@ t_{9Cb}1Ab)%6_1��2) 1b},1@biS1��?$ �A(a=; !:av � &s9:�} $\Zu A}ahqK w�` �U?� !��@�Y�� =�s���";�$s.�A@-�_1,z_2)%�fu $t)V7 E $�+e`-�(')_a( !@%�s_a, M�%�". * w $1_i� $u)$ .t$(1_zj=��b�, "�$6h$,1|q�A� Z�SL!M_A�h#structur� !U!�vector@"ca-(\alpha)t + \be !!�.#_a2%=2 :4E��� $\al,\in- {C}$t,!�!>� . W�the���;E�Q/``$�$''� % %I" S �m9Y%��U�m%P n ad�  $*$,1��"a01�$, $z^*=z$,� !�m*, ��,Nt^*l (E�)�on I�sQ灥)>%� [' (t^*AY)�(t_a)^*Z�%�K $ *2���iS ��A )�or �gSw,�, $\norm{ \ }�F:$C.  m� ���$\ Ft_a}= Qt_{a_1}}&w �a�%.���be�  �Qis�6X )�ref by)���{t8 efi _a}V 4urns out}�M / x Banachmwu%a�i! �.�^A C?� is entailA�at!�[ �>LQ�:wo.� �$��&G � (valent} (or&/"�$ous})"�a ��2 . A{ i��� (it{trivial}Ui��Q A�,q�} L ]io2$\io(b)2� 1M�exF. ��,8cAUAl_{\Po}%S*� �kis.�$(\io,\io)= {C}�� \\[d'�bf{Equ)icei� bold� {\Bh�)�-TN',- } A weaker�e|50ce" ��� "��E�)�J@ Q t in&�i�%=�"� V>K >L V&L ofJ� .� ��V�R .)R q� 6S J�j $V%�_%���"ќ�m�is)r!E#��V$�iea�eJ� . .isU�M�=fB�� 75�E�A�We�����tp$ŋ>��7sJb�u� axsame I���H(:� sub�rm�p$* �!�q[ �F�. T�8 �isy �'D�% �2*h ej ��X�8� �$ ae/R�is�;&Q z(p)�z(b�"I s 2)  1ItgV�#w�K�� :BWer� 1} �=z(q)"���} p,q�MmU+P}"Ji |p|,|q|"� P.�&�As&X�6��5�!Q�9�f/�(I�L./ �2','�#�$la.pur�$s�*�'��7" ult:�"�E ���>�,a�As{a2$ �:%�U�6Bnr�2-�IIA !� ^* =�'�A!��>�1�~ $a\ "� _1p,*�p_�$ %W,[Lemma 3A.5]5cz�v�>�>I�i-�,b�,&�b}Blo�+(teps necessgto�� RW���-���Q a�IOsel'Fc,s� Y]�� & a˭s;�mlyeintrodu!tverg �*athE <b I �'���"y �-e well�-�5P�A ck<*; fina~*we �Qe �;>Y.&Q nt��� (E�{C+0, p.322) need~023/2b�(�oK! 2. �a "��&�}a c=b$ .�.3)$\amp(b6<!:t .� .��"As+w a^� �!Yth $q$!�q�"F��"c0b�Iq~!�! %(�!ju$p!al_0c, 2c !E( 1 "� � ) ) _j). :�� Consi�$�+{P ��-�iq&&���1b_2=0b��F{ conw/1� $ d)A�:�*�,9�0c=b_22$21J ctr(�b�%�*� �3f 2�I &]7Q� #>�#��a�� ]2}])�!� {j+2w#5c, b_{]&1\"jE-I[/}< l*hR�d�ma%��mA*A�p-��1;ithV2"�%aY yZ of!&=\At$p�� [�!7]{�R!q �2�.�� �p� )�$q_�2:J��G� =$\�!&B 1N�2d�\)�!�fj$" � V�%�q& <,�) seen�robs�+� �  $Ao��� ��]�%nd 4a�0c*B 2c)!��2�%�I�Ay*�!,&�0B�!l���!%s:� _%qHow��,� i�N0,�o�doe ��be�  N�u r�,""�0�  m�. fail.\\_��G&!�% R�(��"�} 4 F� i0`, $h(i): (2��n�m::/�r�&ex�.";1L \2R2�x)-@{ $1<"/ ��'sa71E wo-T$b� �: 0ic}, $p\sim qJF�B6 $hP�N9 2� 1)=q�h(n)=�^I�*$1Nr o$nR� AD �� E�VY�[ M!We��� % N� �IrA�s8�|� R��R a� $q'_kM; b'��j .=1,ah�-e5��Ŋ��V� �aJ $p*�F�B��!��9b:4} q*p�\{�,�,6�+ �#6N&�#@$p_1*(p_2*p_3)= ( p_2)$&�*�-&.Z� �lJ*R :5}�p_1,q &.[m�A� _2,q&.!-|If �i��%op_2 � th� �*2* /��)nproof � h_1:�J�n\F�3.� ��) $h_2.=kz= ء�m�Lof� �2&�5h_1a�n%,i1a��)h_2 2 <2(k)=q_2$. Defin�$�(M@left\{ -�#{ll(' R*x i) &Bk-�a\A+i-n -n-n+&"++k\� ^E� s\�4�J5 n $h.E:>�B�aH= -J�a|.G$h!% M1;(n+)-*!P, A�le�%he of� M+S����� � ej� D\con{b}&&�I�N�6}"2_0 =� "m b,�'K))1J)0) | | =A0m~SoV�!VfkB��%�: )pRbf.��� !/p}M�{ b_3�6!b_n}\}$.F� n%p}}��F&E-b� 8} �v $%c :,*  [� q} E�RfA;M3>\is�*�Wc}2�/Y "=;A*IAc>*2F*2LB*0*IDc}|=|c|a*8!� x ` b"u ��_fb})�3if*w ",o=�!�c:ctr�9(. b_2}� A� let>Oz����% BMH �9Q�h}2�z`��.� aK� h}(i��?-&�$i� F�Z�I���A.��4{'.�<eg#Bte to} a���a!;"�1j�9��� 0 b �3 &���$\ a_0=|b|>�C &M$b�K�Q2�e ��Pq�laCC b:10�&ass�.�D?7:\\ (a)� b&� 1p)a� p 0p)*p$&.�%$p*%�p�:(�o !*� K1p)�� � �-�By ��EAW �:�\enough� �e�C ��&C� �.9G��M)c[ b� ���� &2 c_1 =2�e�#0 "@ :1�d2 7 $|c_1|$_ als�2|�en ��B�b,.Db)-h $b2�b)-�����oZ M�a�:i)< way.%�12� !M~0c_2=�92Eb041.A04� p'.2|$�: $c: ) g- $bI�bF�b�.�E�M�� +(i��/�)A�I1%1��Q��,. Fix�EeBv! c!~( �6X�G2� �&� 6� � T�3G�(nal%��:Z�b��Fe�� F{*� 11t \p *,a_0)�%:� ) /E�)�&� �%���&�5kN�.E� $[p]X�>25 clas���2�7� "�P}��. �"pe�.��.Yp�t� [p]*[q] �[p* �  ,[q]!X: . \] *�"�1veQit���8uHs �^�!at^�\I�:�'�,$�&�E�H+$[ɠ]�qGs!d ^{-1/;� $[e�p}]m'R?3A�6N"�:�1$�'|�;�;�a��;���@!�6}-[p]>v  [q*p�Hq}%�.71)3'�7-(isomorphism[?51ndEZ�) fact��0-�K,�df202 @�^6r!{� bf{Nt� 4x4b���R" , $. I�bl(,e9�t�I :;���itIG� unda�>al ;�. �$G=1$F U�{�S�Ay�+�Ked'!��!@We�).b�J�� prop2k3} �-&`teAlE��W>� � ]2�Clearl�B bJ\Le?�p=�:� !�:�. .�"�;7fi�F� b_iR/ $i ="E n-!xI!a$&@!���� �g &� c\E2�2�F�8�  i = 3y| W2PB_0j��  O6�Bd4ei�ie�0��&y{02}c_i=� $��-i: . By mmas*� , 8}%�� 10}i h�Pq�align* pE6� b_n*J�!3�*!%:2}6 *G#s *�A�L3J.>2:n2*n �& !nb_n#)�n}R�Vh�}*��,&673�I.23} AS���))�lF O \ \ [7)lV��� ��#�1�1.�#C!@ioOtw�"��m6�M��c�u SV -��-�]� et�,+ �:� a �%2�:"�EaHP=xl*�5�n *I,�$5"8.9S�@*�N showa�u�"�+5 ���]�� �.z �?�5 To �o�$&"invaria�#�"'s �� -gic���N��A =j7"��*�.�'�K�5��!��b�7��d $ '�(��J��Q��& �GD:��)/'.�*�s.[( inst%!� &_n�#� &#!27E��U!&#$ua�&u � aQ� !� $p$. \ j � O]#� e9� "� w1�(multline*} <*=�*n�(s�7� +1})F"80c)�� .98c >J" .+1)�Y�i1FRF� �+1v7A)����]�>�*-!B�INEx�31`Q��cC#>+ Then"xz(b(a)Z�03�&uzFp}a% p)^*&5aoI1��27&��aR�g&+ ]�6 0 E&�2 �F��1ͳ��.�| !|9V � /? e�&�N�B�=��B 1&��)I�6�!�$ $a2�o $\ifSL \A�+E� I�$�/ff$ R�. E2�(aq;.��n�� *r bM�M�>�"�W�`cF^B� �d� �u$�l f�. �! �,��e��I�&�y# 3} \ z([p]a�> $�in+8=>I�]�#�1is�*{j��3�t�&>q�teo.�4T&;�3%#Iz\:�"�z$ |s21$Y8"��3`7, into"w5reW�pi\�*(" ""RB. UpA pce� Vap) f\iveF� m��=\Zr2� ! �bM�FiZ% ��ՙT*�e�E���&m62�AV� R:J�����z(1x)at[p�)�LiM� ^*$..Y,94obt"jO]�1�!�w� zb�F`�Q!�z([q],�88%1a"g56ne%!]A]9Y*!"�z�!V i�u.�=isj"�u�90 ? �a�)){z_1}� � />Fh !yŁ^�2%�i$��jL�  any6R5' byf"a$3 > %gG1p_a = !K�0 M���z_\pi @!�! ([ p6�6*b� on{.1b}}])���6�6�;J>H, Uӑ� ��"] �2c�!~%�([.�{00}c}�10c�2&1&' 2�w}*=2c�:�{12}c%�!H��F��� \\ &�� 1�# B�1 � RS.\1cF d6�+}] � :�1c 1�He� $(>�8J& $^in�Fl�A$\no�C\Zu$ "�=� Jn*��nI�C.�*�7��ifA�"�e�7� �1��A�ńie{�r.}G E� �p= �C2�0b� b�� B'^*.� t��$z.������� 4+=0�W, �����?to.'Bk6�(��Bh$�!C��i�3,�C"7f�$=���n��0b�<�D�C*�k .��� �� -�)�<�7B, hE��>�7YL��B�B�BB2��b�!�b*b aa p�8�z.� � c@ 6�5a sui�`e�ang+* o. :+�J&�Psub, t�bI%�a�mea�BZ,b�widehatR?�< A�*`�,qV&�0"r d*cap"+4� � $Zw�5B<��Dr����, if 4A��9q �e�&�_�d�$X@.w-*�M�$0inb� JZ<bf{Wl�ave2 *0a� *�L�yC 6�'^�dc}_ �" (1,62 �-2%r� $%�p}z]�I_7 >��*s2.�L $| W�T\dcAK�EI{ �a"�[���Z^.�U�I$E(iN�D�<@ "3.�{R8[b)��AV�re�9%���#a{res c\of~N�^>%�N a.s1U)c��bA*R �TA����. IV��-B &����D�^ Con-;I;22>JN�*�2aC GO� M�a}�b��a} #6�be*d: i$4eHa_�,B�C� j aYE�� &>�eb -b-��P(n, $b_1*p*b(E Q >< 7 �� $b_0�8�2�i�9q$V3�T�: &N 1b_0��Ep| 0� 0$; �X0-�.,1B�1�\B1 B1B e\�*3)Pu5�B>T�-*�5>�5>SNerty �V,a�]�(�hW).;Y,�=in�4. Si  �)�n�C� wa"�@I����m}�0F@%8w2����U5���&WF6Y v2I �.p��&�g!�� 9�L6^�/�ō�fg -�!u]6�Zt��a�A�* /)�ly6W�J��"�R&�HoFV"�RU�deXVb[!�iEXed!�a 6qV�%*D�"57A[IKh6hb�nFcA�pr.�%,.�d�[:O��� �on]Y.6=]�.Y9iX J��U5oal�[!? <|26� .�2R5��Z}^1_t(ZK&�"nG�"�U%:�,BL 8^"G�T�Y��T� >�6`c b( :be�.�, � �EvI�Z, &h�%s=:i %���\ioH'��7�&W ouYWi uld cre�.b�� blemaE�ɛ ing,.L%3���5�rmGrm6�V%�+"��;��*qu�sc]Ni!�d (see��o0LR, Vas, BL})"C, R8�cAA�fa-i]:�a^�!00<D8. as� e=5O)"�  �U(}����."9 �g�fg>�����BI�UI-����!YH�. �6� )F t�2 ( u, �/���*�9-^D%%�mt}Q 1-bf&820b��� s�'e�k2biS:J*I2��*F�]"V�da:� _1�Y�� a-' $%��&@ 2��&!�E6iza� }�Iut{/2�Q%[c�%�e�Z� 4_{ a1I�) �5Ha)H>��nJd�[A(�dc��1�.9�B� V�@4�.��j�UUu 2�$t�reA�� �s"�: �P&g 2�CbX c:� n6F.xdc,+Me�� �>'�� $.� N~�8!�Y�'d] . Bu9kis4s�?A�!!�� ��V"]"-A�6�i9!-FQ *�(]v&m�w�+o�3i"]tr$y���&sat��5m4 ��eR^� J� uT�a���go��*tp� �uZ28`Jt�u �2fr&o ly^�"�Qe=\RE(z"b $\upharpoon�< .1}� Po})&pR<t<tN<0:<It!� � $\REEa cova�'> faithful�!�Y �w� &�~�tYe.lAaX W�T H�To�(��&ioHx b� $\f:ic %]ayS6s>!&h��:��2�U-ifT-�.�Ef2�eUf(a�=�-�$F"6� 9 (k\dc�]Yu6��0byA��Gp}(E� 0b),.�6�\a՝�a�1�f&�0&6� |7m 76� >X� 7n���s�s6b��:{�Cv N 5��z �cZu�!�FF z})���z} �aORM�� Yj!���� Ċd!0B$ llow6��9a&� *�o�H�u�r�-M>�/ z*) B� .{Y}c�R�=�(Zb 6��)E'�)zC2}BC))*A&=(zD1BDW��V� �/4b /2�{B)=Vm1c�&:�=����a � SBh�� ��� U6 60] .rA��%�`�F ;� itz� zL ,z`��m�t}&�^� � f(a)D2�'6!a�E\]"4 �K�c. More.h,�>�� �E&{1"�c��b�)!��� �y?b)}-)� �ZN�)$ ^!<)N�^m� wR�1b)P$e-�_1�7I&=�91b�%T� B_$\FB�fu�0�� ŨMS*�IE^we^ �q�QRE�F�`̄/*D]&Ed Z(��.>%Iֶ�Yq�b���e.v�'�d � \[ (\RE�wF))�Ax%�b}6,1�: #�kQ�4b}'4]!?��*C69"�w,�0�g|0$. "�7J�t} �a ?un "pr -ga1g>Z 6�/9a = 1_{�#t.�7�]A� "�q/of�,C �o�Ho��w�1 show�6%qg$\FETa:� natu�oy&�;ce��a�!� T� endY�>�fQE�C��,a�'I�PU*� R-� &�/0�@��,ak  �/#12#�g� |bp�Hm]{q*� ,j$u(�g N1 l�/��EK>�. � �1H�iF&7Ho{|�v�J�R�j � �u �u]b6�.�';p�..2h: ���@231b�ro �Q r(YH)(z�9Y�>�/j]�\� & =JI D:11b�:�!1R�(@(z,>L�;�{6t�P��_1, z) a�][)�ij =�kA����'%@aA�)$2t�~4 �_1)_a�Aa�F`'m&u��' mapp�>$u:e�00BGc1 V�m� �S&�S�!y��.�a"(-%}�h./(z),z�Combi`g����"w E��,f:)$ua�*6@��,0v�Mf���B�BB��#�^�'�_��9J��&�d}�<6& Hausdorff�h$\XA=7U�h����:�^�[�Bc�����hO z��I� �a.#tv�t  (ed�(�'it&Y��f��a�#us bot I�!rJ�4uEd�7r)F���p&�3a� ��ongb(o �&:d-;w)y affe��ne.֍^8S���I>�)IA��]a}Y�wXzsOa curv<ga�;%�we��|0E9inuous���!lWGval $��$�,Abt64"�G2Z.zHPW/\gw�ycK(tQMga(1-t�2�j �.�BbeM� [.be 4B0� ��o�H $\ga*A!+�( )&#.yS ^{S(2t�1�%tw1/2 1 � 2t - 1)& & ).gSy����o�<t- $e_x%�(t)=x$*�e-I"yd)V)d�+'2E�_Vp �W:�C|�Nt�>�u� bf�-approxij[�+A��l�X��=bf{6.)+�+�=s�E�0$0=s_0 < s_1<bR �*�+!�!�[s�C,s_i]*ky_"=* )�*; b_i ga(s_i!*� _i�o�B$*��$ n$ (Fig.3daBy $AppA�2���-a_.G7�ga..+�%Pwxa^��'X$��D�\ne\eF�set*=0I[t �Ebe ea&��j'���F�BojoyV ����*��&:]�2>�~rcl} J�� & �;& �w�T ��)\\ p�F sis �Y beH*� & Zisi�JM��&�^)$��si��$Yq&~=1�` �n�`�V\��deN)|2N�`&i�\�S�)�a]n9 6�A-!�%� %�$ (dashed).�Q�`~�`)!"��D �>01:�3 �Bl %�ga)$,:"pI$�`���*r}A�n $qi�k R�\w q= q_n*< s rX1�q(��!Js2�do |q_i*�k�LE"� q_i" :/(!�-1V-�|"i�\�, n�3WeH1ބ $p\prec q�+�e�-+a her:� than+4��4�8!�!�N"��$\�"��� �5�.���a ��$(@,i� ,J��C& �" B#�s&�*"� YE ug��&M!p,qw p�  As al���$ � �+�p.�9 g}@3c�., nam2%��'a5A]%}��F��.��cw_:�%Fga�5�r�7a�'Ps �0A�arcD� ��$�.] spa�sX��`m�Rje��1������D-W�_4�E3'�_2,O` \}$�(�s^6�1U!�S5QD7Fj�\\5cer�ey+g{5���A >!�dJB��Gn.�opByb�Ir �:v fW �@0%! open� $X��X�B[uDF[3A��&_X6}0��g*3a�X Po_XU�\\ І|�Zdc�Xj���Pfat:�,Y+�%�� &�ay�lit{sievebbaYu�a subfam��$S�kaz�kTI� in S͆v� t� 6��S�C s&2�RP)} �I�P�t�# �j:���if�oښ �5�$\X_P�_da:3b!�X_P� \cup-� �X*�in P\mN2�FQ�� ���z� analyzem 2_>+.M�L�aN�r:�fbe two6!�3, �r�B��m�jF�DendV�*�$eJ7ZG�8.�u ��.`]leVR� �;Kq&� �c �M��?� nm����& b_V�.�^�9�{�]A��Tqed�#a[\i�&�2�� e@k. A�ZJ� && $��"Pro"y4b:13}/&t !9b_1P��g  \ � sim i*q_i|Ab'��Q2�R*Rn-M Q L� �b'��R\ڇ$b'� �� 6ex>z\p�,�i}=&� � �F& \ 5'��.Db_i���.5�S.<4� ��R=R*b �� b_2*�\ &)� .�*!`R*q  S * b'_qd26C!�}*!�\\ XY10 M)RV:*2&�R*<q_11��A\ qԅ�-��BPi �*fO1C/& 4} .:a?v4 �E� �a ɷ���.�\gax��"�=� bkPm7+*� t ���G2�� 8 be � �<ga!J�`�� -4K� ^'a$>r � "# !n� ��3E&�s n�A!t�t*�t�,�?"}h=� ��{l}����,"be([t��,trTbe( )3�T�A�^tZTey]F+Mnusr�l:) _i(s,A!big(s�> �-� + # %�T&#be_i("b,Y�It I t_i-� +i�i3�biIt\i Ii�r� &z%�I���kg *\g<���Abe.$ be_1�I��_i(1)a� � E�Kv�AkBa B� �z rm,an9 d.�si�s��}�ݡ�_i(%d*�:}E-D(0)��@1)=��12).n-F��vF&h� au_19�(q1)h6E� ']'i'i�@8%�} 7& 2itq�͏ Ln.sg%���F�XF.��I8mJ�+2;7 �m $\�i�" ��=i|} 1��Cen����A�SusYO&� 9(&�,&V �.�-�(V�\ga�E�!  *-�%`2 Z �)i8 96* E�5^2 $2]1 1  q= %&42 �Zi�� a�be*a��a�%Z����V�5��1�j�[MB ^A  re+�;8�a.DEq��ir�IU�g"�Mbe$!`F�.A�EF| �"� �I���U�qeR10';(1)$C�xJ� "�hF� ��H2�tFTX So� V�QJ�>�X!B!& ��^,iFY��*|�)Y W }"M �Xi�"�N$s_{1 s_2,t�F�с���C{1}�O 1})���)�%�(s� .2:,H W� n dea=�2;ie ga_3�:�@ \A a�3�a�$,J��O1bO% ��&� .T�*4t! �Y2bY!�!.�1 9 &g2�H:g (t_2� <u� !fv 1 - !� + �s�B_3fr8t!�+�% 8B�$s," !�I.�N�M !� �>�>de:�u< $�1,2$Dntwo�\s]� &X1: WixP1f�E�,�Rd F2\s @Z�� �2fYQ���E���k�� ^ cm&�l�� (3�1A� �] O�{!�a;� 3����F�)�� 2,3pJ)�� �i$���X.�)bTev�ioe�E % {������*t�\ca";_1���=�*h��+\6=3z]=3 =�!��z 2�fsi i�ZI"� -"6N;�b6]n da:4h%�!w��Q533$&�1�0mca��� �6 {F� �)� �Z�'%$(\Lef� �$h:�\times :r8X.�%.w _t(s7$h(t,s"}3ya0ga_0(s (s3{1}�1(gM 0)=x��*ta� x_1$eaK.�"�:9J$p_^�a>2!c�.�"$p_0=�;�y=A'�1�6�S_t�lHDp_�ݯX2Z {}! l�z] $S_t I��b$*�  &� p /B�_t2t?isC�P2Ct(vL SN�8@<&5�6�^> �e�nZ!xEt.x�(E [s_i,�+1}.||�E+1}2$A��2��&�nW RZ&�0 T�*��i="]���B���'��h$2P $\eps_i>0i3�T�IYA�} A&(t- 0 , t+ )��.�"���z:Y_l�(HlM6�1 �.#%36'9&� *'�.7+[vi�VE;�[epsm/m�{T��5}��we 5���b�!�!�l& $=r,)o���@. @!�Sr+eRI�w,R�[1I_t&R`�J� "'�a�&R5K� I_t�e��a:uA ��1` acH�.������cover�%$ $I_{t_0},q�, n�C �,"�0=t_1 <� < .� .��� ci}��VEb} \ne \eB�&.Eq|J)W9*>���$l�&� $t_|���* �ɇ !l{t_i}O7�X #$rp�&M)%�{l2)�nb tvc&3_ c$p b�� )�&NhZ���.�bB&`6} ��A�&�., FGm�-{"�� �Kaz�(k?"�%P�� B� �-h]:�Y 1(\Xlx�p"�^|�b�-(j�^����int $x_�p�m��� mX,x_0r\gaBrr�� -Pomc"�z1$�o�PdpU)���}�U^5}�@ma�b q.27-�,co��Y,7.,!�Y!E6"�K"�NtA�]�O"n�vmp.hW�� CK�/0 c)#�� �6�2htBDi� W >�U� �Fe ByfKQ� =�M��q�j���@@��& 1N2�1*1bFn�Rn q�c:g��&;3BS�>� Oa�E`%�Iumo�$�t��X$[eQ2]0.?S!�=X[�a�IdrK�} y)u��a� ��eM$ 5@1$^�xG�*b9S�#NI}.�at*#�� 6s�bmK!wS���K�LM5inI.)cit{?gR!&�7*�G6� ���. ".� "�aha��l�s�c �f<in mina�:�Secondly*r"us�/e �� ``6 ''"� �Breasonab�o!("|`H �D_ana�J"kS � 6RQ&2� R� is,# avo��he ``v"fi�'' 8�� � .�o��us�#52e���6!���Po:�X�4�eb0�Bn*E�!nt`Za�^5� .�r nQ"�T�QŽ� :+V ' ]y���&�Saima�ton,u answ�*oEgqu"8��2dT!����*e8i/]per, ab{�#existe?#� � 2� gE�i��Bh�"OT"T�Pj�j��X� >U�hby,V�=�-c���}b=c�N�S ��Rs�Sof:ac>#q�!&�2��G�b�2*FF�A{5%�ri��!3$!2"g* $j= �<��oO�e� n�{i��p� 4��affirm) �L[\%��*6�:=�V��!1���J� �,_X$}. ``M_��we� �g ��2u ide -$F-�H.[�"m�)-K @*Bh�u[5p2�m��2 next}2s�Oat��.�is�)�1� a��cwu:rt���f!AD;����K��d,\�� �c, ��uc3���&�Yo1%Z�(8 ��_1,s-2f� ��U�&�+α _1\ordpos 2�5R1�(��]l2fVw�" :�L� Po_2���O6�{�vs)�$ ��uF�2�&�O2���Q\�3Rf�Da6�.�b)�!�f�1#_1� 2�.%Ner$.��P+%�^ !�6�#tT cb� 8 �-Sw�b)6Ny, +� ��� ţt �^ a maximu] �PFrm{max};IJ1n��0 (a)-n��a���B?�dI.z�d+ �?a[I�6�/{.�,  /�01P:=}*�s� }a;^{\$�9iPl*Y�Po:�^D�t�� }�6�.n .X�\>DW>-�m�N��5n�:8j�SU.�-e-���:A����.� 4}��� �]:�}enF� �:� R� �+> ��*.`:j*�P7!�~�E�*V ��:�T:o|^7Km�Q�v8DͲ5m2;�7\L"?)�i�os*��d��J� �� 3N"� \\[3(1):4 �o:�,�`ce��5Xo>y�nis� n!��i-�yɐ�M�!v�V��9�6� � (2) O�;&-]�Eˡ�Uq�0aQ���a�2e��Z� Qassig�Ae���Bfac!aA�W%N �Յ!HH(M |a�a@V�(4\{�[7��|.VS51�&R��})''$,&sE2:�"3 ^bV-23cb:`aw1�1� (3) i.b822x ){�h�e��s��sQ= ��b� lon� gene��,aC%�.�TA�!�o fcho��h 1@.Ne�f ��?�?�?\!|ion{Go.��F<lob��( hyperbolic�.B!ՒBF!cp�s�b����e��� V�a �N�  ."~: $\Kr� re��diamond��on*O������M/&�t\Kral.rM�. �]��eZ hU >y doN "`�&�1:9 #2H�s{�e@��act�4c_ s�al��d d! In�!�)REw�o $c� ��pr:Y�ρ�N�:�&h* repl�=!x aT�er)T9�A�����v�7��e�&.�!�unOI`7%�ch�r�!men!ed���1o"9m c &oLM��:�fhM|E{Qs$A�R��?K 8l%�I us &|�in7+z�i~H�w��ea.�� roug�T542� <J�C�by!� R�R��NZ-�6I$dimen�Oeq 3$bK �E�6�a~� Xgeo��&�Ba �*�� Tc8!Kmr�'3�P�Kesu ish .��. S���ere6��tk� �g\�g,One, Wal, EH*��ARnt*�~b'M$a�s���q2� para�a� smoo��Pa0nted manifold�MU�Fu, g1owei��K !Kic!�$�OJ 2T e $(-,+,+�(+["A@e a !�- �E�,��h �$lR���|�v$, (tY�E��U9Ad0s $C^\infty$)J��'�a@ et pco�$ou��piece�n �, 0�&funEaD :I \1Ka/ %E��8$I^�rS!�$\Ra�th "N�"ior�r�h �Lim%, ll!,I� �Jre*�0 $\g(tE�L, )<0$, $=> 0$ �a�3�C�=$3=\frac{d M{dt�@�>]%M&��c-�$}, i.e. a �E��&);� � c#�ify�!accor.Oew �.! $v�� fua�-"e(f-d)�k pastpif6 6 v) <���&:. W8 �f-dE� $\lim_{t�%%�\sup I}+0t)$� (N*inf*)A�en!�aTo�� a � (�)a���. O�A�,:9 be )!5less;a� �f'Kn!'ne�A� themɿ. Analo��nsog� d�vp-d�+%�s5�7 ����chronb�� �I^+(SpI��-E�&J &��) H dog of d&4 ^D 8�Lq�$S�rt��-� �s:�ali�� & � S_Bx4 M+/!�HaEkay6���C�6x$W};�(& �b S J�j-�c%�ni) �ZaAQ`)�a�� �me���(>1<Th޿%]Iz  a duaj7``)��?p d� ``past''5�$+Z�$-�*SoS`�I(S�1�%H-Ic$\J(S�1v #J #�%$\DK-4&\D $�!6�R:I�bf{1.AuMӁ��!et;�E� bf{2) cl(SgX�e 2(3.}Ƭl( ��] c� $int." $\foot7 {$g � 0S)"��2�a� clos1 �����pRE f�2 S$.��F.S1!�(= �33.}) w� �*�� +4- 4� ! c� Q�y�� � !�W it{a���� ���})�H�*$x_1,x�RG�\� I(x_f3 (.J ). ���"$S_1,S¨$eq��� ��� �*>vp"}N��&x�BCx S��Sy$\setminus a'_2�POAJ"�4Cauchy surfacev~^J 1^ (a �)I \C$ �+fH�et\C)=\M$.�y 6P!�a A�v%J�% Lipschitz� ��U]�/A�6d�homeom��c| 1|" }:7 �r >t�nt� 0�y� X> cHt�I���">^!b)U"*":`���A l��i'�G�t!/a�5trong�m!$��}�+3&gprg��s)�b�u\�*u�:B��? neighborh�$U 'x@ �4EjF)�$V-�%Wwi�'e�q�V����x x_1)�-�(i�>"w m%�  !�>�$V$"#%�%W*+ � �Wb%gF��f) 6�B}G5���BR♹� !��;��(��N�$V isR�Di�-nd&%=�adm��a:��k T��%��#M��aRg5n8�1�1�+mpo�!$��v��5�{ cl(K�n� ��i bf{6)_ .) d;��!nmaN�%�bf��!x � �./7l�=.�K)Q�)�u"&� Alth��Jj95)���c"a ly (��ly �i"��(%t� ):�s#BS)�!�i/ps!�aJ�> %�$a�6� �3!HkeMAl Y=fo��9``۟d''C9� azq E�V&s3-":al .[S<a.sm $F:7��p8\SqC:��M=5-��Si`7 F(t,\Si) U5��t*�&����*j ML�C��&BCvE buG{nK�3$t�2���<��t$��61 6u9�1� b��� T"B�[�,�Fr`�)*/K0M}!"�ac# C)&��6�g r�y � �2:�4J��&xDli5E A�"�A�aO a� l��%C"& \{x�NQ�$$x�Zga(0),1� j%"%@F�!�fU�FM$��A�=( describ�bov!WE(�;(x),y(x)�  F��(xy*��5�(E��:x4�7((<_�(taY@)�F�:%x�r� 8)5�2]:a� "��re���!QF1�tIOC!j!  :��;��!�s)#y3-�A8�;�0�; is 2!�Qebe&'<��2.$&�� �2U`I�[�Bis*v�?Q! is:�m�,��`�I�$.��?$2�:�,�"<��z��8�'�/$&f"by�3b )�� Z�0�&U,t �0!�!���e� �u6d*1"� B�2}iJ$M� Q2Adbp��&M2@��:�O.��J�3 u���f��)�cZ#�8+ n�"�8"�8�:E1����w��"s�I9 ould7Ka"F���8�� _1��,�u|_n*9c�eO$�"�D{�""���ofv%O����66�E�%'0$f iߩadsm��di�"� �0 �\&�\J�! ��]:%� �`��' � +K3)-�m[�R.�I�I�InI)%�{T�7�d�&� b}�ZܣgF: :& Z�hTl]-� �� mB�' $qZ��y2A�.<indicF�6,%�oN 5,�a���3��(���K9�x��2��e�1>� We � g$\Ki!�.�mKr.�El)mb!vLmen��!� last_@(I !B��.�i puncY�-K$!�uc)(Z%�pac; N7B7�,aI@� Ni�)&.6�(frak{G}�B**6��٥# s $G-�CE_�� !� hi(Bw$ $(U,\ph��!a!rE~��� $BQ�  �#x �rm{R}^3�cl(B)'[\$ U3�Jll�a�-�}&S!�author�grate�~$to Gerardo�wsella�& fruit#��Son�E٩A�� n E�]�7a )?��%@58 �G�fmGG��mat2��s##E^�:%�� al�h��x dc�L���#%x*�}�!�@@Y,ah�Y�\ �.T"�**8x @��MsD$oU�eB�'%A Anyd!(��8�\d�&0?AWB<4 E]sE�5��1l�6��H�ql��6w1&�$>J~Kr$) ���Q>�a=%Zt@��7�8` �"^s.6�J�VR� ��!9 B; l.�9G+r��3,af"[� 14,043]|"} )BA�!en�9� IF2�q.c�>dev<�6s�%� N]ၾm 0l�!:� �D�.V 4Fb2�JT��=f 2&R&yJ.x�aF� ^� CWQ G#�AJ]k�6.6�^y8umA��t A�� 6t�%�({GLRV}). As� $\K$ is a basis for the topology of $\M$, then $\0�locally relatively connected refinement oCKr$ andq�C\in\mathcal{I}(\M,\perp)$ (see Section \ref{Adb}). \end{proof} %***v0 The next aim�,to show that�0 causal compl �$\dc^�$��J$,5�eE 2� mpact. Ia�U:\dc �%4_1\subset int(=k-��TI�tailsI�s2� Eeq2�V�. As!_.�!�B�A�n open ��� A�bavQ $x\in��$ we can fi�%1$in\K$ such �L$,!�:5Beq=?b� Thus%�_1u�$,� ^2Xg�ta]��E[. A�Since $cA�%,ac!�!a$,��A�Uw�2c:bA�J(e)))aY=2< GA�6�(�),�F wher�� e identita�U=\Je�o9  Ru$�aA\ lete �I��� }�G�O prop.N5�N��6�.�of����E� j� %% a0G{ex}j�eq\dc\a�DnamJ G$i1�d �te9�b�<-& LetB�^b�A�form A�GACiE Z��2$ $G=\phi(B!�ith $(U,�a chart!3AI. By' i� mat2�re� �$ ball $B_1.� cl(BqO  ,��B_1�,^{-1}(U)$. 7��(&( ) ��:�C$,{B�Eb4. Now9by�$ previous 廡0.���N�!� m!$a glo!,y hyperbolicŰ%�anJ� J�B�2A�2�V� , he�"� ( v� \endQ�%q����claim~ � E�n��of66 B}, �n (established�d\�� N� �GF �{e; o K$�r a9 *2 Br4. From now on �$will focus $\K$&� � !b�� ndexE �we us�  stud��perselS sectors�� J�TE�.U6} :sI l��U$ A�d 0neighborhood ��dca�� existA� ,2�� *% 6�B$ �3� U-� 4_26A�_2�� F�X�EdQ� Assum!a�a� e��*2��� �r,W�=.2$a spacelikR�,@!K$Bed�llIn�Sbb{R}^3.13�32 ph� W!j�:B! ����ro� ned�=%�& $P\cap �v?%�c t%%�^V� r 1ˡ� ��=�NtsMoreoverX  latter*� e�U �� �n@ $B_2.A xU&Jw�;�2)% 01)=\emptyset$2^!AOs =E�\Q �ѫ��22�� : �^��0erty written1� stat�:<A!�trivi�nsequ��of�cE� we �<�Zif a�!8, 2���MO"� )j%� �i�3m�y�q�),Q%Z�){ n_3u�4e, 3\� �p2�B B��{C punctures�Oa� �it{�9*%o,\K$} inducedma poin�8�\� is� e poi� K_x$� �Ab col� �� equa� .� :1} A E�6%��-�)tx\}�DK(ordered und.��'eu� B$ mean�atY"%Be��&� \J(x� �c5*$��92��, som� oaEies-]!+�be de5e�Rn iJ !(ical realiz%7� x-(cup.,� �_x \}�1�e�2� 2} Given� %��M_x] 9&�x)D2a\{x\})$ �% r� �mJ$xr+�Ay!&w )�A��M. 9y!B$,��sA�@}*V  ��O a�PK$� _dc�;�:VK �,� <M_x.�J�.�-( opposite &,is ob ,�AP�� A first"�"�$Q�foliagbyb�s�) zi!Aat=�� �� proce�7�`L� ��bm�-~� Consi�a��s tim%Zaz!gJ� 8\cite{Ruz2}. An"} 5�=$does not n�toa�"� 1b>u. HoweH�8r j!� Fur�� more���vr8"\,.[FM. @�^ 2�w��Tv�3}�� }|_{�} �������R�,� ���,A'�f�m�ec!�u: F�4}����FRRMxd rM�Not*� >pa����&?A�D� ��J;ɴu1\ X B� � M$. bB / $R3 �I�, N�%�M� ByF�,B�F�" :+ a�Z�qȦy����S�e�[�g6]{Ve1}^_1!� �)�n a :\�>_H� � e Prop��� 3.1]�`,D$\C�  (\C_1 ���8 :� f�)��/ In o�0 words%����a�3� e!�"���AsC t��M6 �9���g��in .��5@W�E)w>�G��. �, $%"\�v 'dq�  $= !q.��~ F{e�x!^M{�A�>k�nf�Q�CFo����-�f ��usY v�4� K_x|_\dc���9 ��)��B�.�U���AG$\K�b fg 4b}>��i d_ Th� 6�5e&-\R��?N�>[!�c4 �:�) ac:  OurR �.�m�6Q�-�%�� �� s, s<P-�%�� ��Fh&B� , byB�!�.\5w"s,. We obtain&� !���l>w6eps. F� .����ax >aK � �$ in U e�rL $.� Q!��m�$x�| n/,e�EN-" � &OeqNI�!�\}�z.C,�j�E & r$=j�(. \qquad(*)@" Secondly,� ��N� �Dja$"d��E��A. �#x�rlnFy fF� >��N��$,� �!�2A�Rb�n%��l�(*)$, I�U�����2=>��.F 6�)ͅA�ssu��e��ionKR e���s\U sa� �endow it���l��!on��� A� ��2) \le8 dc_3�4e2iffi2*� aA _3 \mbox{��� _2YRG4�+graphv?5�6 �  ��2�%�K_��,q&!_2 \} ��!J}6 !�"o�G� ��Fe�>Bt. �E}��$.�AQZg"�S 0�A��$\5 ����~>gW�AQ�N<1a� Q !lH�-~(x_1,x#5y����!D x%q�Aserve(�! gF�F 2.2]{GLRV� $\�B� B� �of�� t ]>F'>X���!�-�--i�� Net-cohom�)&j c} B�Z"�a"n2/o ��(worthr)�y)�T*3YtA�T� ���eV.}� are cod>#A�9 � struM!�� &�v "W(c:1fc�K� . X(0\pi_1(\K)\sim� M  C�'any>� �}� C� M"7( �ath $pV 0mathrm{P}(a_0x!a_0 Si_0�A��$"�,G!sed?.1F _0a�� >�}  O6�n $��)(motopic to�@$q=\{b_n,\ldots,b�>�. |b_i|� -,b��0�� / �*v�!�$i��)�� �Y�&)�s f�Theorem� Ada:6}�q>�'.�in6� Ad} A��e$E�J,s�%1�t%�K s a " d$\ga:[0,1]\longrightarrow  � % (0)=\ga(1�AB� !�� d=�E| App(\ga>He�UAz �,)�%�cloAy� $\be$ l0�JC_06] $�,U �+sGto)C! $q�X�be)2�!R~! s $q�s]4�':5� mm�!�5}� fr&e"\Al_\K� irrible � !� / algebr��m� Hilbert�� $e�.H}_o$.�%Zua�͵$1-cocycles�$��)� valu�!W ��e den�b)Zutn%ose 50�$q�.!.%�BhH2, applic) @ Corollaryq0b:2},2 9�is simp�&"0b��=�Q4result answers� ques� �d N$  pap saE{- J![q actn-)i6sF�iQa1��ob�pion��\1DP$!Ge9�� s alreadyC T* only�sEZ`!�� sens6'nn� 6U�e�O�.\.$nt��1p*�V$turn outa�be funda�al �Sst�"2sRX$ b0ita vide��wayV�0| f$ on� bitrAaN ߽� )l90c 2nz��afis� -!penA,�1$�  �AS �X�z���J@$.�qt*W�b.�)�`R�q����%6�  -���. �Sus tak��� :D%a_0lx= ��>�- bz�����6��x�w�g�!nmJ�m&��%�0. $z(p)=z(q)=kbbm{1}�6e�!6$q�\٢Q� j�.D%;!�I;�P"�A�A�A�A�A A\{SR�"� C}ev��� ����V��pa6�o�ab�B� J���AX� � dimen;0$\geq 3��W�H-b=-scrib� �et in��w,F�) !�), Afterwards- expl�strateg0&e�� /+�6c�Vstso�"�� ��� �)Z?3 7 ones�-WeX+e�� oaap��ix��/(��c�or�tno�o* ��.\\[5pt]�\�3�Q�� -�A[� � �AW��anFF g :\K\ni�>� A�&�_)b"| 2} fix%,fin�"U}al separAЂ� W� .�*u satisf2%�IKA1two])K)� $\bullet$"� P' d Haag du�}�Ha�""&fC�)_1�=�cap�2�)8'� !]r, \!c �# \}t  +�A�} .$�&G(A��al&�&� .�'a��3�Bba:1})U�90%� Borch � �)J/ g&.�Ii�4]-�Q �"��2l  ��ogoA<{jiy $EK%e_1�$E\ne 0x �$�0n isometry $V32� <$V\cdot V^* = E$q�if�  E rm{C}^*-$�&��&o 1n, v ��� ,��I � I�. !knA�e#1tV�}�!� equival_ �0 sses $[z] ".7&� �E�20 , ou�� �eUvean�"4!�a tensorb�ya sym%�(, left-inv0Fn1%�b!� 6�9P,istics�0conjugat���!2atA��B��$�+ *(direct sumsA!�b �su�mWe/1discusdiffer!v�7tw�7!8�6�8!� �!E, Rob3}.uY�[wC;5����d>aD� instead!�&$of regular2-r�/a�W�1~ne�16�.Ux�[a���*65lp(�.'d)+authorsE�:yN2?,� ��\ C[ u� \zq�nZl,:Y �p����$. V* w�?intro�+��{-�Bot[;e��A)!zmodels��* ZUMB��@o�y�~ �# �eՉT�4�:�@nE)M��( It�s��Z�xs .� �� u)�>it{E_l\ i�}&�*f�4} h {C}�� x  = 6f�e9� \ E �f\7�UT=�'+ ��$reason whya�v� �!c�- clea2eB ion."B oss}!qis�� �!CYCl*,^� "`<-��(�2� "� ɳ�F}�)r�9�� 28�hJB�nvBsoc�+��mel��represA4! w by quasi-?Hadamard���One mT wo�/�6�%�so� �f��$��|\K}$ �"�0restric� J!8$�$ A!�y���� |NBis addi�D\foot{O 3Al_{\Po_�rm{max}+&7^Cf R ����:1�a c�4AJf_� _i =�"�#DE- �/("_i _i))''$.a'nZB�'jIEA.4$\K\ordpos\Kr$� �X/�0 easi�hecked��ZuA�R^AZils^>V8E� e��Q .�Presheavw�+��"��FZ� ���3wa��OZ4A�em.z tandab arguWN�t�5ge .�E,2��g& ! , �&��a�;e�af*.&��Xin a Riemannian manifol|oner0��,^s8& s�<�z$aft`=EA28�o"$s Muglu�;oge� a��>Z6m�"�aI!��/e�Arol�� !x play�^" jti� o �ant��K � &^ pdt,!�J eia� ion%��Hw!G }�y� ``-(z\upharpoon!��;#�# _x)&�)&Ex �# (z,zCVt >W t^Y�#_x)= in &q (>��, z_1>N )" �:8 �,e!faithful�c!Z� we �O&�A "n ' )�}��m@a��-���%�x$F�6� ($�2m&waN�mG �Jc, � � an&��ya�6�satMbO��FN��, lead� to���w!�^�.q�s�cho!=a):�+s:T�$���� � �+�`Jys!i��� &V� �:$ Minkowski� "Gp9*�)����$x> �M��B�%�2/ F..!'��A �RI� � sameS ���T i�<Tfdou�#c�%:E�fa� vadm��(an asymptot� ly �fisjD.^A";!�(onverging''AilJR Cbb}�-�* byJ�5� � io�\glu!��;du9 ata�nowQ�, k-llU�j� "�A.C@$$\{z_x\}_{�}�� $ ina=M� said!b&� extend#t�F$�if!�&Q a ] 2I2� j� = z�;B � �5MarIPSO�Si#C.�n ���#nOX uniqu�Kɺ. 2}�*�AF="P.5�� F# if�'G$ &Hb!uS�*�&�.fa�z_{x_1}�L!, {x_2 >��u�+5O pair!T%.�M$ �  $|b|�)\KU1}� 2p `-85Eof)9imp"�& ($\R��($JU�. ($\LefL4 :a7'5� z�\D A  �0A)� }� \M�0�} �� �  F�@"�>dx$�Ja�c'#�&�CXA C� ly $�!9A(|b|)*�"z_�:{9�� Si_22,@ i�� $|c!��$a�(\par�C _0c)� 2  $ExJ,�B -A?,1T1c< ����a�2C�N*AW��remai3Do�LEnA�FEz& ��(i�ata�&%��GF;�^ int�'nex!�$�&A" any 1f,�^atN3&��� B� Z %B�!��rJV ɩ)�,�� s p V�ke"�M A�' alog�N � �� dibi�'A s! e�s."�A/] A�< 6< $\{t6=� $inrK FJ A�1(A�8I %�Zut� �*nx}�y�6�� $t�{2� $t:� �-�= t!�!$�pQ%. AlsoA�ecase,�o)k�c $t$�s%��mzl4�;�9��.���F�d�5�ɿ �:�ų� J�a�&�0aw"�5n�5} (t�_)_a= 2 �a+ }�-�jd5���of� s\81�4�:�ų>�f�B��.�$(���1��.;����� �9#�u�>[ t_a������ �x ����a�QA(^0�H6�,Ţ6�*٪2a�� �+, $t_{�j0b��6$ ��(t_x)f# $=z_1(b��>.1b}�@.#.p, ct�%��U�I�2�re 'o�#s ) 5})4  � <IO.n� ~�= � �B B.L�`!�or&�6Cb**a�>�urXL �y��@. 9@�IaN_`o*� &)��e*V �;morphism+���"@#Y�iz<�ranspor�Te,��E,08of DHR analysis�is� a ke�ak1���<�/cE��3e���n!��a�7y eas�!�6�� 1��)�� ^�|�l`to2� & "z��usu\'�J��#���end9^B9"L s &�, _:$, &OJ work���` � ~9s� an6�q3�5�4, but4notnA+ lB� w�!�$*9$: yB �^be o%ed,A�._�'E:�< F ��$.�n9�/problem ��!��+6,!La suiE� wa� �8Hc)�j make�+�!Nu� N�I�f�,u:-�uz1}.+O2 fix 69_x)a��Ud�%&���A �$,Qj>�f�b:1} y^zF(a)(A)�z(p͆Aq ^*�*A ��)�b&�%�P ADr1A�ath!qMs&o`�<1p�G�) and 0p = aS is �ł^�p� a�!�choic5�s�.� z p 1p$,�H3�6�9!!'bG3} !*9��J&_�%�8t $p,qU �,ath� -'��0p=5.0q$�1p,1q-L.<&$G �2)�2��2: q)^*�Kny $Y�R� �- x}.AA:Vp)^*= C3 $z(\con{q}*B}^*-�,&Y�M��$;�aI� �w���%�s��&nX��!�Qnme".Aen7��$ be1/��%�|l]d%�&`- 4a})��Y�(q(�"�,�;7�-4b�^k%�% � $q_1&*BVEE�same ^�.6_A�*U6ceg�W�$.�A4o-. ButUw�*�f���up( $|q_1|�9x%�Q��aE�5cM3A =Y�U�.�Q,�e��E�6l 6�>� �>f!�6B�. e塠"�.m�Rethen $���E }(a):��% � = /\d��cis>�c&JWq���7+ b:1b��s� \{Z &:)\bB��9 a -V��9, K }n� �$.�!+���Wy^�E;e2�~� �!���@e�.�i�C?!r5k� la4jC�ld:�A �:�>��ap;e*� ;Pb) P JQaY= id_�!}>Vja�J���>EE$a$;\\ (c)�A��u��A�&�1pq=:0���mH^ ��I(x)� (d �. �$r�1)_�aD{zJ� t_a�P�'� Vie5W(;_1)��a��}),2.g�|_� "QOa_1fDB&�W�!A�D"�M�� ) B�q�1�+ �V�)� ��� ��"�:8)]$E� (A)!sz��)�Z��gD2�e�5M'.�-U�R p6p=/ nS � 1p,  0'g-�A�h� B�o��!9!��,6� g���(.�C ba:4&o!��|5^&VO�N)T`$(c,L$(dE]�B+ routin�lcu0s. A��1�Ub)"B.'  fulf�`2���2� �"A�OIA�!�I� c݀of2�5�VWn�pY�VX� F�&].a: =v��b �A!��0M�"�rin} $a$;LNmm�CBcRBisE2�"a�oFP.B� �v�V��U�:{T�5"`&�_f4s edAY !�!}9Aa> F2' a�)I)&. *or�**�*�FA/ &�*��j��8a�%l�%���Is%(qA%�� �G\�[���(q)), & p,q��� }V�9\ �e `s_{a_1} �%b c �a)( &),( a,BH�4 ��H&� ��Eq,z_2,z�b?��l&2�g $sM_03F �:�� FtaP�,ill�e�der,A0rti��r O�=)$"2C>8 �K�J�Ael82�, � !��@ ����& �e antom{A} �� $�5�0p} �!�q}>�q��2B = z_2R3(q 82e1Re1q}� 6�b� _ _2*pOT_1(q_2*� ~ �z(pO2$ �1)21)$,\\U@ L,�H$ m!g e$ U��!��1��N!]By us!���GC) c%�B�d .�q Palign*} .b�yX F�&!+:M 7�(9�p'r a�UYN7�)\\!�&� {z�"Ipe�q}OMC��Qn�5-1p� 2��a*�.Vy>�3sa�c:�4�-.U�\ ��= �}ze*M� Ն�a1���qa� 4qF�%�!/}9��.-�B�JfB $:K�Q�a�6Y_i@&�J��m(A�R(&�) =\\ I�,�T- >K@)�iI�=9J1Q0-32_1)E)iV1�:�)�r \ i�^k>42.] �5� � >8�1)i*�2k)�E��>X.%1��-�� 0  1~J&� 0p_1&�1puX"�9 >:� f��CZ) �Dy�"�<�6�.: uUeQC&O"�� z {rcE (z\o5)A�&V&!�b.ib7 .x _x),��(tI s)_a�4* &a�a -fs >� � Q# R#kX(D  j|1(p.�uCba"$ �G":Ay.*c =��)��S�-e�*_.if9 �"� �9.��>0 e"�r� $B�?("�.�'8,) �O�-2c� b �5}At�GT;l 0c&�2�\ wA&)(.�)��&3(^"2c' ��5'Msa���H2.=^r1cA�] v )].�$g�F�+" *l(:MAS2�it� � $:� (b_n �sJ1)$ $�� ��>$�Zp p"$ %�$pJlUA�"�^KK)aS$z���=*oM�K4 :we,0�>p4O� 0. N�x,�(��A�e�k3 2� :� �]nA�B�atm6bP$l= 6U,�zS � s zC�` 1�A��5��ben,�/n$D6;edB�5f6��=�&�S.�:StA��E*�b:@{Y.R�a)�G;:o9{;bg5gp~�ir?Ae�� ���i0� iq$� i=0,�&�p).>q�/c�Ub�f< %�RL:zb:Y:i5})AQagu& &d$p_1 e�{j_n}%Y b1}�a� $q&k2&k &*�Q/@i}|c|b_{k $i=1�Y n�* 1: 9u020p�!1q_.B �5�020q�9!�~c�1(w =� c���= � :Bb�)��� K9�)�&�Qm 7 imes k U %Qn $A%Wn���s  zj_1J11}*� � +\N�z� t� /Fx::K�K1})����z�"y  ���<\a_1� 'A� �.a;P b ; `#2MlU�!aD) ( An}bO�dtw�:O1})N2RA6 YyIk�MhA�,�Q�&� �a�,Ѱ�(�w*�s�r^ �i[d$�E>&�F� 2!�b!� n�qdteo&R_CbMs��5�  $\epr �Z �n�(sPJ� b:25keps91� 1��^*u�!E*%%� )�� Eg :@-yz){ɘ����Ɋ.��U0 xVn:.*6$1 q)c!?�-oW  w�vl=!� r.h.�v%�4@H� of� :d%�hs � . Soa-��,�"bV�$.)X�:%��a�J$�+ŀ*�ip%&#2T q*\c|$_1H!9�pp p.bv w"� � qA1�^*����pY& e�)�v= +�� Aj ���Ai Sz(��^*��h @�$=J[�{�V�����F"~%1_2dC�W A)^'jD �(  12��i?ge4�^*:y [ |.�R�~2>~L�h �m21�N�^� U�ip�q�� " B� � &�S =!F��v%o�&�$) 6� ��2�IwQj_1,�% ^*)C-�!-�1"+�CNr�Rim.2Q �P�� �9 1�� :.$�)l � �+\9�2q=5�0bF=B;J%�b��.H2(.�+ !���(� =�A�iBQ %�FW�Ia�X1�.�>e� O�2� = i!�b)�X�!9�� &�::�I`qku>i�R` _V_�& :q��J_1= p*b� �4q,h�9pA heck< + p_15$&�h��:�� �TH.Y#2w�!;�3=Y� I�v�aHY�J�,FGB� ^�)U* )_{a�4F�I��(�fUS�^���2�/M Iq B]��!�=/.` :^2Bb)j yA�q��AɞrK2�0q.�0pwI�f(s_# t_aM�.E5fi� �.fg)W(sq�t� /)�5%�V 6�6R�0q�SB��� ]�J�=V9.a > a:�� B)3 :*��a vRn3�@sx2:\N:~� ] [}in ort^classi�'P�.�D�bv#�4q�"�Y52 6�F%A�^j Tw�3ԕc"^&6D$VunTCnNmat��N�R�d�2�$\2I��~(_n, \for{56Jdc_{n+1})etn0- 7 �U_>��,_n1  {.�83$n$"�9a_t&�&2_\�|2_n$�ge�p5pQ an"�%a6zEfyE}AX{�}B�$:"H2?;A!�r"�$k�-in9�2�d aq&n�a-*)��)E��7eB�� nH2=�0F�(�\c �2�6{?>3B��[�2_n�2xth�*$a$A���j�&"�bD��^z_a(A)� \lim_�W�m�&-0^*,6�4\(x�endmsBanach-r6verA^.�-h|r�-Bh�?�p�}v�6n XmaprK0t�66>�,Bv#Y �(A��oa)(B)�  �B5 A,BAZ=��9v� UiB� ��r�Au �&�"0b}���A��� H B31b}N,��\U�65���b��p� -B�7\&W, 2)3>Kv�U'2}(�vx�a(��, �:�S� ZoPn�) &�3.�AG�;li�Q�\{ N��+ �A1J{�1.��$zv5e>)J��>9]"&�4})a� V�Ci �7I���!d2]m� b6F2� �>�6@_?�]� fG! a/�/� d��� uBiu�T��ee1>� N�a �B #IO]io- �q ( )��A� *B)] !HB ]A�8   �UZ!^a:L�/Q�6+!JA�A"�.6�M,6�.<Z-TNa|�*2i�G_�� of2� �Jj^ �E�4mb� AnXu� *-Fb�AH_�:c},Fit"!N�Y.�"y_a21�$*z� -�{z,�& �'Z = cI*��_��m�{�(} c > 0 \] �B"��3,3 >�5i[OriA�]typ�� �V�pv T� B;eoZ����_\fA�Yfull sub"�Aof5�a: B%� B�MEUi��tU>'?�d,fL�:�%JFu*�U 0��� �*�d of2m <s2 f��f&��S,y�!m \�V-\=~"�/p FD�>"� �co�Zesi[� �X�ߒU^�=�=l &!C �ion.�c�9of!N6#=#"�!�!jU�S\Gw$�A"ub]LbQ2-=tRe�Uũ&3]&4 �'J�J r}�5nꌅ`�R� chi(z��1_{�p&�:� }+in\{1,-1�� ] S�H`)Ep��j!0Ed>&i��`�t��t+�fy� $z^{_n�Y .���y"7"ULJ@�n-_:�V�d f/o:N��z���B!1���M)`��f ]H�% *�bV�L$�71&�?1- n x $b1#�N2al_1b}&b$�<�)C�%\ $b�1� de6\9c1�rI�]%A�&R' evalua+Zon�CL�q�Et T)���$,.\Ac:2}a&!�� ing u2E�$,*� 2a}),n)�l u*� �v(6!�!�^*"J-�i2:R�4J�^*m�Y,o��6V=&�u9:�a::?��;N�� �� "z��3��repla4r�E�-so!�, A�b �b��� on9�qy�N*�&cz]���Cix,�?(a2�=B�[*���an aut">H,=�U *�mQ �b�DmP�� � m�<@$^j �pa P5 b:>;�una�K>�&&j�2�&4!p���ath%w%�.m $b*�%��!�,y�*� y� 0b=a�}��r�>6�> 2 �,aq3I\�&n thes�<<R ��6,�,&�+JO�q� �M a)& � =<'�v�:� z^*$)1'� " �+.���\"c5�D~ ma-I>D��:6L ��:PAFb��)�� 7fX�\-5� <. >hi%{/*Q!=S��1�TA��s ��c(�("�"�qܬ$Ed��NdE��6�D�I�(x*4A v(��E��2� �N�<2O<:n^q:�} [: ��� �3�kV$�&�a�Zin�r7�E$.xR��{1��6�8= $v'8w�$ql�- &c\��z[�A zur� ^*r3?:��Nh^L*o4claim��yIz �U"R ��/lŢ, achie��2�nw��B & 72 :�A�31+jD�0!�!�9'�0m1B �w & ���Bg(�!-K�2� With�a5% ,g s:� spacgHe"a=omi� )m| cripvI$<iT� ��TF�'e ��� ab�'���å�%�� ��$b�[��Ku� $ w� 1��u1t��E�!u&.E )�8�= %9�� �(��!�G"� ��Fl-=k$0I= i�� M xy2* )y:� g p78B+n _.`1b?(B5`�.do�X �y P� 6s (��b!1ff �>�2( !9l 9�6<U�=E�&� wa��� on�� HBh1b)�#`�R� ! B��Hm�2��!% 7J�#^*��^*� FFW_U� ��aye�a9wSw+ufC:�x�[16}�i�It�V!0$�r�b�LƊ{n-1}=1bʊ�H^dp�B=9:_n5s�;M�%1�"8BB.((� a�| &N�1B:o ��n� �B��2"�-�.�� R��O���^*�J�p)15I�a�_n7~D0 ٔ�W�[�M�"r>Ja�E� �gwal��Fj�BQ�����8n�an"} ��KI��yiJ��k'>a �}2yJE?&�P�� r��in�:&�:1 ' J;tp 1�]َca�IBV:G \E�6�{00}c�..L"g e& "{02>52c 5���ORjR�{( d!T0A٧� �(ZBVZ�) �Ri�'u�R�'�b*�;{1!( B;fz�.< ޾�%,�%n--Nhbig�E�?R�(N1!{���J�1>� 4�i\9�ei=Q�W����_�q��%�=&� {o$q%�2!2}c�:ve�| 4��na�jby: Fc:7~� �� �*�7�%�9&�'� f+i��S"�a,� Bh�nu"A ���Now �*�'G,.�!D" H��z{�;� |�)voa��$n�u [� � r� `3�%6�5�.� >�K�4 ��&��9UT.w�CU�a&j\(:���\Ink,4N��O�"�&�p�!�!FMs*%.�F0'5:� .Q1��.�(AcN�I�"���p`Y�%� >/5>uhsB� ED4�R$, 2�1f#c:9=�'P7<C  �(d2�e�"� [Q D{l}*�A �0V k:� 6 �\�0� � ^*� �2ብ� ��*� �  Xz}\�%� �D�9�.x�{� � A��T:�� �f�C��Y�N 7i&LX $r=�r}2b��%T>"��A^r*�!fy.�[fF�G�ps�; uגYAccor{r�C��io�{de�j�]^ a���" ")u8& 11} An���{@�T _{\f�7G�v]�)Ef���F�F�F�FbF� ;RGl��!��d"ĚCc�d ; backA)�s)��>�d��# U$ t.�alc!��Ru�v mAo� s#�%I."��gl2�}A� 'Zx*�d�co.lok l\\/��b"�X k�G�l"Y!"�.*\��[x�Oe2�[a�VoU>�*r�o�d>�r.Bk�x!#x$�PT\)." j 2��!����� c�b;a�b\�\��*O0M,?j��} OO� "�#a��A\!/%-FJextit{.�\�}D'B 6compat tw}�!/"�~I��t�is /"�,�any:�k $x,��i�M�O�paz^= �csz-2^�n 'gA�2x�eDa~���\[Gl�u1]=�2��aVe�9�Y �"A�v��c &2� J�\ڵF�.j5�$6$t%�� �6!tj  '0*m �D| A0�1� eF�qA�m!"&elp|�}t.�mQV�t58A�1��q[' ��u)�1��}  ��%� b})I��%J"� ,�iuA]"(<i A% ^�[!zF2� !" $p_i{ 2z %yi�J0f 0p_i 9*j1I��$ Y).I�s��d�4�-/`x_i!�dG c v ��F2.2 >� p_2d?.��r Z�2 2i j�31,a_2a�M)�\�"E �M�IAD9pS;- =z�="b'!�& V2�>�6^�9v  J?� �_ �) ;�E�e��I��!ha�2|�s.\j>-(�,).� letG;)e$mc��a���v��"�N)v N�ved%Q2� En%-sF�<.7)R7�R� lp����-<�#�$��d:~6�u �zz � ��"�-�IPp}"�v�z��m �7o�c 4 � "7��2o- eR�J2 o)�J2 .�_a�Ai[��fau}w"�y�6;,FB#{C�W wb!)1ƈRV0p2z�A�:���>~�qNk���5a}�PZ� Q z0C�$&dOE(p2:� $\widehat�/�h"�X���5�<} wel�`dbd��:��<}BTA��I�t���g�}&c=�-�!f2r�Q]% "�j"w E2Zperp �N2&el.�.L.�tB~c$zBg6.%jpѦ �.�tM6�� n6K�ZF= .�& ��^�"� 4"g7E[�o�d!k&ml: ,0lizingk% an a"�g�l6���%8B,.�[��30.2]�7� ��lJI&,�sZnonYct:P�sf�&qEa�.�6(4.RZ�1(a� ��6!�"��-� 3� d2�I�cl�>E!�Nv i�>`���P� Pis�Ea7.y��%:,�1}�� !i�N�F)�D x_0} &��of�Kf�5) , j� %�*L math~�Z}^1_t(\{�%}�a�< � r 1�&= ��� ��-G��E_0�G� ^*:~ linaŮ%�0"�3���%A%Ii����W�o�*x"h �lz^�ath non" %�"�u �!2NG�}D0G~j�e2E)a�Fu&9��2� ?t�� �"4 0b>�� 1�l 6�F�K� & �M��� 6�Z F� � &�^�� �MI� `2�F1b}a@�I 3K� b}*p, e��6���e�&Ha�#�= 2�A�����rt"bnAlc  ��w�8�8�$ ��_0y� w2sA1ET��A�� mt�a�AR/ER8XB/^��n��(S�va`C3{�0�qgw�+�u$'� ����  %%"�n>� � M�"&2J2�?EJ$.]�m-q)2�$!,N&p �i\$a$*we�BX4B,|_�|� � ȝ�1J)Isa_Z:AL^�� a$2�V�4� �6` Nre�.p"�7�B�)�a7%!2o^�.�@u$H-~q!��jB�t�AA<j>��A?�Y!� R��=`3Jx )RE>='tBB�_q�Rs'.�i�5�*�I�$.1��h1AG$..'B5ea��>��ifa�n%�a ; ic'|� O�2� �A]�Y��&KK& ���+x�+2�I$x��6��29 : �x�J FF�� �a� * �o�\�ll.�?N� T9& of&��"�,�k� �d:��:1 �%P.(=���q6s.,�0n� �7 �0Ɛ��� � *�FBc:6�Nn1b�}%K&V�xn��b4.�u��/1�&.4� V���CrengtheV!F- Ҭ~~R�6�6�&�@�a,=��"�aq �! A&)ah "� ^�P�A�$A@%d:4e6RB&�5�ftK�a�Aw<d .BE �� +� e@�'� N�CU 6�e�I:�"� " �;eps�; �"�\m�Q%%�6��� �l�zcJ>�4��z�>9c��� �[�s"#2�  �n�)B>{] _x(z'X� �>p� $x���O��=%K���&� B�-�1&� ="2��> �� F� E�2B�r )q������*� show�atci) �ŻU(��r R$�:�q G`�6�]!� cW��/��i*�p�. ��Mv�<+ \2@ 1 ��3� $.��E�x I�J �)� >�2�6�K��ђ��et^XW (e��BD�7o���� "�)�.r*�>� .X1sE.�P��Le.  Bb:6� &n !$� s�7�H+C��(� p�\s�6E�o,-��_�"2��q8U�E�{a}& ( (b(a�<�I�d��6���2&� ^C +t2G K �B "�a���!��F"�\BJ��y5 E� �� \� (.���\� �\E�Lr#o jB be�#*�2� ��� R�*d:�6�� ��K@�zj.-�].7 yku2�6� ��  " ��B:58��E�eQ��>.�a}9w�N{�M}~N��QZI= "�z%) 0!1{*R_1p-,\;5 D)F_$M��in(�U*[.M�w� Bʌ�|"����F � we �I3�BI�_E�z�x!�9�iz�6�F��cx:VN, >G .Q(B 6�Q�liYM��NY���z��)YxAqh2��f%2�?jcQ_a�.� :3} ��" ^� BzN�z r M��NT �v� @/#:i% }H1�qK�J� %1*� x� Q  $\la(z) :laL a�j�� h#� 7 2�\ 6�%�paramet�;E 9r�Np�� X)_a"Y(*)�R2�6�"T�2'��v J-�N&�V���vk6Q� �x)G6��s$\��G�M�=F*9�a�J4�>z*, �!)��%>F�>�. 3>t&ۧb�� y��.o !�>nƴ璡>Ja��dR��Y�J^WUE�H)&�2��UU�.���%(*E�M��L!� -J�E><�;��.s�B��1V��V�46��.$! $�Y� �B���4��R9`[U"$n&$J�U���f�fX�4*� 425��:� =2A"�Xs���"?:mX}Չ!uffici��* ^�A�}�em� s3�Wof6(IΗu��B{Ri@p"zR4��,N�T �K ���D'>�>Ta vRr.z>a)��"�%><2� ��}��2"# 2Ba�H `�_i�:{ a*�O� E&Wby N�CP��&$�z#J�� �!�q�$>93�f J_I�*<. �42� "�^[ d|2�� � wjt.�8(&�?� , upA�jmoE�� at�����s�� ��pp�+ble-, �noԘ�=.) V�."��s���,be;T:s�f�#��j�.&x:a�;e "�9V%�' elow�."1 �F^$$ a weakerJE��-!) �$"\�S&.Ra�e��^ �O^{4^ � 0�.:&��3ٗ}  aB=)13!)CR '� ��2�S"F>b"}���2!F!G6wZ)��!�*n1kB%�"�<� A))�B�I�<2-1" ].!C< &�C.k�2��!Wn!z� *S1 . B�L� �A[�U ies:4�7&�Y)=�(Q�8_x(a)(\A(\dc))=��\A(\dc)$ for any $\dc\in\K_x$ with $a\subseteq \dc$. Both the identities derive from the Lemma \ref{Cb:2}e, and from the fact that $y^z_x(a)$ is an automorphism of $\A^\perp(x)$. Now, recall tA�Hconjugate $\con{z}�p of $z\upharpoonright \Si_1(�l)$ in $\Zutx$ is defined as I(b)={�|}^{-1}(\partial_0b)(z(b)^*)$ (\ �8c:5}). Given $b!S rD)$, by applying $(9 we have t� \[ �D{x_1}(b) = y^{z-1} N� 2&2V� =]2] \] Q pair!6�%=em @M�>q does%]� E�t��nds 9e���!N*.��iXn�%$. \\[3pt] ����A�(2)a�Sm�- A* presen��:8!erme�abstr���-�intenEA-�ide >La general framework ��%'%v��j^�In w 4cular, we also 4hop�� find%�icE�s��htudcq�i��wbe induci/4no��.W�S�/It �� been�4inMrAS}ifR.G4Schwartzschild��\,a��� whose� ond �� topymKI2��, � � �bLHowev�A�I�ed earli%Z �GLpossible, up until n� to%ly�ide��f =��analysI�#1}si��their2�a� pertS�Ʉt known.�:0 results obta� A��� allow Eus � make& �1ul6!�i�!�%{7im�noB�:+2��E�]ChBh$2�b�l toFOV  [)���j.f�. aEfact,se�����.Kre�--��(fundamentalM�J p (e� ems �i c:4}�މx da:6*U�Gwis miss� 1فb rpre � #�@ 5�s�r=�AE>s Z�n���mŗ. �� !�approacha��X robl:=fu ��Finally��belie� E��couldAsuitabl��g�B ized���)%e"tex�! 4ly �K@covariant quantum�3ora}�/BFV� �;BR}. �� \no�� nt (3) S� $ technique��tr��%p� Mq �>og��< adop��!� �� Z+of! !{�� �on�8 circle $S^1$. G s� 'e2]ہ�!p6;Ta� }$IU)�.Q EC k cal{J}$�<open E�val�~�;� al disj�ness re����.: g�I,J*@ r,.n, $Io J$ if�$J=\emptyse;�=�arisey , referra�to>l)J;!# med �j �-�h!O clusn  order�,�*U , pathw�co2 �  J�.�is usu� ɢ��Au to�ctri�� B^k����!�/\{x\}$ a� Aa , i.���-�pun"4 :�x$��rANinstanceq�0MT, FRS, GL})I@ �&� �"�Bau i:^8ver �� �,s\footnote{W!rAn�2��ei��k Bau,�� GL},E� auth� �!]�ln )�!}�� a  e'ofaai�Our aim!�differ�o[$�5in�.-a�deed,*XaL ymptoP �-)�lyuE sequ� diamo� ``convergM�$x$'' �2j Cbb})| $is suffici�!�!��5 J tA��.}.e�1G4d Haag dualityYE�ly �edA�8strong additiv*EY��KLM�e��� rein). սUH FRS}9�X at endo���ʡ �extendR ��x univer�Ή "sE�6MA'a�e �check_in�� ce �se l�@�A ic�. s (�|�?� '2 �Ws��a*� 0 fat�U50Rob3} p.322).� ��  �I4�way� �Š first�g!a�g is vsimilar!v/.���ica�J�!�E��e�edga�ths t%<�ic4c�x IcSTIbto ?R�CKan:<(May}. Alth��hey��. Im����g$�*(\Po)�d1"$\Po$�� } im_ �:0�5� t���H6jisW t a .�.��&��>�>�>�>~>� 1 \app�� x \number� in{}{�ion} &�T�:���4} \label{X} We�Ni�basic���s= "�n8 2\$-\. R� ���eg � a�i�Mac, LR}��8ptڲ�n�:Let-bD C}$B a�>y. ![de�H$z,z_1,z_2,\ldots $� e obje(��X���ŁF (arrows betw� S$^(_)$驡��� 8i�sd��``$\cdot<and�� unit h9Yby $1_z$ 5!�\� bfYg(boldsymbol{� rm�}"�L- } A5:;�ai7bBU_ y if�ftwo5R5_�x Banach �%f.21`97bilinearr reu3� dj 1aanolutiv" ravafv or $*$ ac�a� E nt& ag]�� norm{the>�pr� y, namely� ;0{r^{*} r} \ == }^2�!$each $r\inUM N� e�fF�:�9�!�n)�� sF*i �% |AnAe \�Assumra>j��bz.�A� $v�6]e%��tEX $v^* e v=A�; aea�if�!�6!�$v 4$^*=1_{z_1}m�1�aI admit%� VIa,Z �k� ival�> reYM]�Z4; �s�AEi� $[z]$a�ary.j clas"5 \ $a�An !�:@irreducV if em)�{C})!I.F7=� closed unm sub �s!s�@E$orthogonal!W�1ion $e-�!$e\ne 0�r� i a�o�Q��)$ sucX$A\5�a ; e$.mV��6� � �1 sums, if�P8n $z_i \ i=1,2 B� �%XAG��MX�- $w_i�_i,�� $w_1 M�w�+ w_222m�)�\}W ��it{� ��V�y} (or38^,)!)a-<�� 71Tequip0�J����d�"�Qbi�E $�! :" Y\�sʼn  long�%�$ {a $\io;!mue�$*D%�q�Is夭��hAx chan� ��{ $(t�s)i (t_1_1)E{t t_1# s s_1$ w�h.�6&V&Z 鲭RF0'now ona�b-�)2e�"%Z� 2.}�,I�ag����)t��O� ��F �-e bf{S�� left�@ s� A {\em�G�D} $\eps,!�v NUmap6 \ni ��_2>� eps( )\in  Q2J  1)$ :�r�Ds:z%l\begin{array}{rlrl} (i) & l3,z_4M�Y��KslI� 3� )\\ (iL& M �Wq �2 )�2i)2 1ez) w1�W20&+ �=B&_2)RI} �'F�%(iv�:A' S � �R_�_1}d%)cW&�' $t��=4), s �3� (By $ii)- iv. �P aa�%:,\io)= \io,z(���'P+�J�b- E�.�}�5a>�we me�omnonzero � A� s $\phi^z��\{ !�� 2}: *�'A� "�'%�6�A�, �Y�N�I�& sE� }(1_dt�r s^*) = M�.H�}(rIS*,M'>E�M#%�Qbz_3:�3} (rE/3}ar����� ,, rFsaF}(s_1^*E�� ) \geq 0 5v)a�eA4\io%.�+�bM)v�l3d M�I� $, 1 �F��(s_1\inj���tst�8FٸA�ݷ�Ѹhaj �$��b ��a&�z�*% ; ;.#sI . >2��� P- �$it{finite}�#t �A  ��� andard2z}�M2 m}"*w�� �-Q� ,z}(�2 z,z)M�Z = cIJ,1_z \mbox{ } c>0���( full���!fAL)H_\f�2\U")Ls %.)%=$b�U �xp�tfP = !�y p>��g!d)� $*� :sT/�*..� ECUAg^�'z�-�)��V��-la(��)�8\] It turns out� (E�� ng =&� ��0 �]�Q�pa8% ter}� �#--tcwo/ a�s: ���chi� d(z)�0xMX�.  * in\{1,-1\  \ 8A` bb{N�S $$]@�a�c�ifi��u�s�\al phase� �$x� uishing%-B%$(1s1!�!$-Fermi $(-S�d�uFW;me} $!$.j�or-�fX. Ordin� �� �% corresp�%to a=1�/*O� )-alA Ui)q}�(f� ing � �!jUct�/�Ruz1})r z�F@ W�  \iff A � z)= -���{�TA% 4\ z^{�m_n}_.�AWforall n2?.aI�V �W *Iebf5.j!4I - I 2l �l1o"c1s}�&0-�%s *� �0�P:3� ���c�4-% z)k! >r�2%"� .)$ *~ �F��Oa�s}i�j r}^*l1_z�Br =,!� r.-"�252 bC%�C�5!a^M�yabl�d[(s"Q,6��CA�-e�:�.��s% OY�cN!N��� U�!�.�\R/%� 6&B\]Vq�2@s�B= $ɓ�� if��onlM,^L K�N.�)�l�U�.6�.� DHR2, Kunf'�)w�L�-�!f w .� ��' �:f�!nB� �y6�,$V. E/-3&{�T�/1DAoA2Es.�!ondly,����9�*: �jV{��$��1���*; �_0,�+{�m}a��9$w"��N#-1%�z_0] �!�~<�%e�z_0b�s,#s�4�1solve�5]ea`�a� �=`. {= ��$BG !�|a�%� App:�:} �tz}� � "� �;\\ * r} & )�^{1/2��(1_{z��wJ� _0}}���v��1��#� }s { r�!� !"� N}_7r�1_z),>� a��2asilynwi�$r)��6%��q>�?.� }$ (��"})�� {\sm��bf{Ac|-l�!�+s.} I wolik�#Lthank John E. Robert2.�f"m*(support thr�!8 ~#0�< Daniele GuidoDfruitfu�(cus�#A� help sugg�2on�/_ G*w���/im�$ com�LD�� anonymous�"8ees: I am grate|�* them5I wis�9)!�$II Institu-5TQ*eb& Phy� �<-U%v f Hamburg%k�0 ho{5�%0, 12-19, Janu� 2004)L!R;o�*top� (� �'�.� "�%V�my famA�o�/1� b <%adurX is%�.��8�8�< R�C�C�C�C2C�Hthebibliography}{En�: 23�"u9both{B2$2@ \bibitem{AS}�O,A. Ashtekar, Se�6OI�ro��f -=A��9in"�. phenomena�7Aw)i8�-�7�+emerg�*,1vacua.}A� J. Math.e�<.{\bf 21},(1980)?8.3, 526--533. �S+L H. Baumg\"{a}rtel��"�))s b+6&a+.!% Lett2� �L33}, (1995), 7--22. !d5cBF �`D. Buchholz, K. Fredenhag2lL�:�g!�\S.�9 Particle �e��!�CommunJ�84 �$82), 1--54�.�V� R. Brun��>�,Verch!3)4��g�0;� l�Dprinciple -- A new� digm��)��0p�t.} �m2�%kH237},(2003), 31--686�L)jB�8, F. Lled\'{o}�D�+A�om%��)�{Hil�3�r�#-$systemŎ,7� �! !ň]�c�7rER�3ternat.Y�IV15}E�8, � 759--81E_=�MT%�2^G!<ck, I�@dorov�!� curr�, ��61ger=�:�2 �In: Co�1 Field^�1A�ReD5T��\, eds. Bin\'etruy et al.z5 Nuclm�@ B (Proc. Suppl.))5Bi�$8), 20--566�R)�A�Y�G. Ruzzi�3e�SV�<i�.N�sang �W#9i7gj/6�S1 �A.N. B!�8l, M. S\'anchez9�On smo�EC0>hy�(5>%?0Geroch's spli� � orem �b�243y* 461--470.6�S2��S��2� ime�%� ����ic�)/ glob�3�bol%a�?sf��8e��Dgr--qc/0401112. %�� Die}aC$Dieckmann.%�-^5Yy0~�% OBv9�PA�578.k DHR1e�$S. DoplichWR.�` , J.&� Y��2|4a7O;l2�IF*�i2͇71��99--23!�.)HR2�� ��%@��z�3�� (197��4��5 )͙�D!F!S.=F!=� �em�VZ14y�\6�.} NInven���N 98}, No.1�89!857-218. 2�R} :��P �WhAr0Aa�.�^�Y)ac�.x?describ� ^C� $6c_D,����*> �B � y on% � ?Ec���89v:1�No. 2B � 25--198. )�5wHa ⭭� ��Q�;E�( 2nd ed. S� ger TexM)Mon� e� 7, 19962]�HK2},!�Kastl2�PD�FA��<to"? .9 �68 �� 848!�64):��%sW.�hardt]zOn inf�-cua)�6zE|yiyH massl�8��1BPhD4(sis, G\"{o}�en� !�8math-ph/0109001>�LM �4Y. KawahigashiE�e7} M\"ug2NMulti--�;�~?9�modular� ofB�> �i 5� J}N�)�219G20� 6� 69 �Y�L�x�Y.�2w�E�A!C�F of d7MK-�y z1a�No.a1997)A�0��BMac)[S��c LaneuCa1�a=��!��Eian Dq"TVerlag, New York-Heideg g-Berlin�71)l�u�k6 J.P�;2!!%Simt 6+eyy3t67 CChicagoJ�(1967a%6e m}$J. Dimock.|Dirac6��H a jHoldT%N�m�77A� 219 ]�HW }!� Holl�FA�M. Wald � �� cu6u �R�S 2� 289�t� .GJS �W. Junk! E��he%QAdiab=Hum�,�&4<� 5ds:ADe�i�+��a�: � v,i���An�D$enri Poinc� ��J1�118- 2002)� 5�Key� M. Keyl6~ <;�s,T>� le&���$ s to� 1�)�'or��! "q>�� a���22a�.��W?,C. L\"uders,:Z%�IMquasi"� c6aV�A# j"13�29=63e�90A$9JOnea� B. O'Neil&� Semi--Rie� iaA � !$ Academica �`k 83?�Rob� BM�c&�NA5:�hKura��F�I85�n�01976) 107--11!�U=Rob� Z�ecl�Q"56y���' 1��6�s� �((Palermo 19 D�W���.�2M8World Sci. Publ $<, River Edge, NJ!�9�.�3!�>��More )ur�D�V� D : >Non;u� ve gM!%C.I.M�1O, ML4na Franca, Ita� 2000�|Edi:�t*��#�ց3).5�# &~B Es�K����!�B���%��Wao f !�n�/� ���1{ 0, ��55--12865RuzE�G:�P�7u�=H2�@n�2 J��lj 256}��200R62�34 UDS�!� Siz , J.A�% orpe�-� No�<El�s�Te�� �J1�->�A�6� �Vas!�0E. Vasselli. I�Continu�%�^(�E9 f�+�AK!�of�#>=T*%T�F!��)a�3-�9j 212� !�.�V�rR.� �e� � sy�&ct�O ly a�9�.%BA��l�!� D HadamardQ�>�IE 24� @J�WJ� E�� No.5A�� 635--676FVe� .�!9emY3reg "RD.},�� t, availE% as ps-fil�\at http://www/lqp.uni-goHen.de/pa�/t�YYe2}  R.S")�AFJ�NGon-A B� s&; � " P2�"�J.�F�� � 6$ � 2iWala.R&� �GL.EŎ*7of"� "B84_ %.;1�.8)5`e� , SP�Zert�S A�A�,Klein-Gordon�hin� C S�!H%I�LV$8� a�297-310 � Y">�%%%� VariAgs: $$$4fill-column:75�J.(prefix:nil 2 adap8A�l-mode 8 auto Q End: � 2� � docu� } "�\Y,{�dLcle} \usepackage{ams$B fonttA+[�;n1]{inpu�U} %.OT1]{7en>eng�,A�,ncais]{babel:Bap� ac^c{mltexAR.xf�AhR�$0\dim {{\rm \; \;}} ForforIfifn  \;india.aam.vzvrotrott�Tr�TZOp � \;Op0Opw^w  % \new� > {\pa}�_}:ar}{\&t:>A& *>ot}{\+2{\vC}dA� C>DD:bR bb R>W>WbN:N} % ! { em{l ]}{']}[� ion]2# +}[,]{�em}2%9 �B)*h_6-cor1ry+C2V�[&R�[6#exa$E Henviron� ={\bH9 [a}{[]medskip B �{M(ni!j&� +.mqBu.y%i�`sq{\hbox {\rlap{$\sqcap$} up$}} \"�3(rule=0pt %\�Che�,(= 22 truecm width=15(voffset=-1.h0\pa:' yle{myheaV]���\prm�4 mr10o 8 pt��def�J{n.d} \rey�{\theVN}{\fn A{} nbeq1u"jG}�beend6a6nag;�0 5aI$e 5nn��Go2�io�x {\QEe��5}\h�1 \raise-2p�.su1) 9� ^� �II�X�31]1�B�XM.k9SQ"xP origins!�e�P, l� histor� �hof ��&conceK:D�ZpaE u�:MeH ic�4�Lu!�nI�cs�adz��9eq�>eq�$Au^{\prime } + Bu^ , + Cu = 0, �g �`rE3�5konwn"�% $u�1�ed!�� bb R�W�p�%��(s� ${\E H}$ I$�L= \dfrac{du}{dt}$. E�,�3���aaI�!.m1.E{�0oscil� o�;�ecAumA�r)=!OI��cnA�I+ceP"�Wkrla}.�� Now loo�A�a2io#:so}L u (�)G4at�A4s $u(t) = u_0{P 8e}^{\lambda t}$�<�":=� , 5�a ( F^2A +  B!�)u_0= 0� \eeqSoP�2}JH�}B�%�u3A0T�� =�k@\��bb C$�EJ�qSn n�>5*!C1*2��m�. �$B\neq oJ���!�J$? �-�ajointj�(se�a!��1,daper)c��e�m!�2L �3����f maygO�M�bt�_Ba>7nd� ^e A��WEY8n $A, B, C$ sevmc��s, �3A� , ke�sh, m�".Apro�"�e.� a to�_�LgG���I�:� � �  I�]art"��"%I��$ 25 years 2Ka-)t6O!�Y reasg AK4atq f B. HelZ�b ked PhaT& Lai%�me�;}E��b� ^��at least�U5�(Q�, u$) �) &�< C�� ��7�0Sd6S}(q;R)$, $uM��: 2�� \AC$(D_x^2 + (-�)^2)�� �wh�� $D_x��� tial}{i  x��1%��q�dEiů�j4'"6,hypoelliptic !��sh6su: squa�� Gv�!.s $X_1A��S, X_r$,՝��and$ =A�ݶ^n$, &GeH\"orser'�i� 24>a�bnte�%$N.�N�.iterat�6racketq�aCJi�j$length �$_6M9t A65 -�Uo*�# $n$A��O�q��Ts�X&�\1;%�($C^\infty$-:�94�01� $AA/!�X_j^2$�� ho}, i.eY`Au2a.Qma�z$\omega�O"mhAb6�� W�;!} coef�];$X!q�!real-U^i�Y �,2.SM,��.�anZ!�t ţ!�t�!�8Z�?2^ �S��>���� �M:>��ianswerLnoA)A�?>� wasn<by BaouY$-Goulaouic-�bago}i�U)� &�&z .3�2�4X_1=\& ��} ( x_1},\;X_2n$2$ X_3=1jM3�325���-0,N$�zj @$ed�T�T$u$�3�*al_ at 0�� *:SA��A� by u���3 ZB �s(  $(D_{!4�8x_1�: ^2)v 6�J>=��0= i\sqrt{2j+1s$j. N>�a9oA� wellj��harmonic"� orsB�In.8,.� �ed�;��1�!���"�i6�� 2j ��3J/.5 but�@V�,6�K.���%� 2} - !3}\�)^26��#N�U�Q 4yA5�=Y6A�8 $(0,0,0)�N$AF �詟"Hif2%�S >�NH(�� iz�@�efmetho.ehahi1}� M 2$ Aa�T obviI!�\lRhJ�In��phr��RJ�A�spc�&�Qto� 7%p "� N�� *�s�&�A��TpW�� . OeLk,uses pseudo"w H�ic.?(p� r�e)�_m tralIBsi�4  Nowadays,Ci~v����meO|@n_ M. Chr�t� ch�&�� O` �!_�Wronsk�' arguA,I|#d�uXhv9H-��b�i�*m m^m Mu Aw� y $m:  NP2$.  �A�tai $m=1$ �orT��� *��e�/�|eq4})e��� �o�R�P"�E�H ransd *�2# R�ly�1nillo-� -Laptev5�hela}�#uMz)�a:�.�aU elegwB��olv� �r\j!�li�+2a< Li-i 9��8T ;.k�� s.)((p Q� ��W��r&x ���i� ��   =.u($x*^� )�:.i��&~ f�A, :�^al�6�256� L_Pm�-\t�NglJiP(x) -Kհ2Q:�`�P/ aA"3�egreey* !q�g���� $P_m:�of ^� m0$� > 0$�!~y�k"�<^n\backslash\{0\�(�j���ds��sa�7� �eve-*R/)B��mcMT�QU� � \��>_2t$1\leq n3$=su��S$m ns�7eo~N�*�D 3 �<rd&�gav� n �A��+6�a.v#Ff]�N �. Afte taj k, Xue Pa� (Wang)e�m�nh }m%&d�m�herow A>r�ŝ - b ma� a s7.class�< �t��|rac�da[�oc>&!:wFi� main � )�J��uu�2� !6�LJ)�nev$\^_!{�YJ #��B�!>�BST�&�"Y .%C�H $ uP.?^n)2AF��<$.�u� *V q BA-Y�9X&[ ���l in@2es o&& �N�j .�i�t#h0o&Y �spaQwhLE6h� $L^2&\!���E�����Aod8on�3lAmͶ����2-sA� stil�bFIt seem�son��� �J�0In�9,always uu5I8F $n }ca� Den=3.�An �� icult)�k!eJ�T^Kb�l�Dz��!� plan9ufrpoQy*D#P�$�s"A/�$k��ᘉ�� henf}�t55]ndB��iY 6�\w�R expl�u in m�detai�5)F �s>�s`fOad!��Dž��!.] �>ir��of^ W�{��*�:��QabF�]=i*� A�&�8, U���� ne}:P 96.L |#{%/�l A�� ���MF�& z�s%�%)x�T 6.� be $k���:H �1$,E�(a pencil $L"� ["� .�!�!�Z� $"Nb2 �&�>! y = H_0*�H_1� i^{k-1}H_k �f 12�B; � "�\���_m��- ies:*� ĆP-1) $H_&nQel"I!,a��@S!, )�doE�$D(H_4ɇH}.d(P-2)'[ 0| jk-!�<$H_jH_0^{(j-k/)k:_ ��$ !)/k}H�bo�d�vb��3 �Z/ksdv ome�atten�YG C}^p p>0$.(�hth�#��YSc.Ies��mh gokr6�=�T.��uI!.�CYw�&� cl�h=�N)�c 5�. 6�)i��(xa�.���0!�2C"�a�psto Y�!Y)Wa meruc�2pA��36M& C�� Bana"0m-�C(H)}e��wact�:S!� 5A���a p\^6�)$L$�"Aho��.�:D ��in�i� q �Lt accor�yG *�Ck>�)�pol�8f�cap L f�P�(Am&� � \�%F_5)�|J �A�"f$k�h k$�>riE� Bq�.v#mat2� A_L =.�8J�m a�*{cNY0 &1 &�p& 06� 0 &1 )V(\vU-&\dbV& |1\\69 -�&1 2 ��R�� )N&�x h>/$A_A�C:9a8Ac2.R!�.��K,[\�__{b��}D)ة�k-j�� �.� B�I�N�>� D(A_L�i �:an�*E A�eeq:�-+�Y��bl�q!��"�6����G6p�$%B��� " !t.��2\{��\;6r�\;.�} \} \�C=!E>a�pR{a�&��$f 1\;�/ L2NM6�6�: �<�y,�k� rite dow� res�Wn� %d$%Bt��pe�6sb�%AJ�ɢ g,\{r_{j,\ell}"� \}_QN,��q  �z�t��� have.UE2 = -r_{0,� q>= ��"�u4'sp}[L]% 6 of>������C_0E.@2� Q�E}_�'_0 h�qj"�&%�!�I�:ٝU�_02j�dd [ Keldysh ke:!�Ll�- a�Yj*6$u_0, u.#u_!�:�"3�!@j)s�$�!-I� b N$6� \bea2�u{0_0)u_0 & = & V�6,u+ � d.}{d-� }u_{)-1' G B� + I^0VO}��?> \eea2m�9M&� �*��ke, p72>���56I�2$$\displays�3 \bigoplusU�\in1�C}ɘE}_-9[A_L]}� densQ��+e��pL]<�>pK}> ��J6n�"'!eus�["�we5 �9y P-� $.� "� :g� ,0-�y�s!�bleB�-�-[Du�Id-S�'�&�dusc}]2}<� r�$\Xi_j� .NJB� �r lA0�.O ,hx i�..r�u�a��y�.. ecNy�Mf� t�^>^�0% pi/p�.�&A�+rho, RTs�2�>� Verty�)�_ al L  =� O}(\�M� ^w), \;\;>n� for} 1.=�mRZ>6� cup_2 J} %�:�B(A�rb�~i~b�>�e}Q�6F"E&��,6jE>�",a& m�aRquadra>2�>� $L_m"  = ^b$,!���NAL�� , $m)�F #m�$�(f5b�j6�6�$&&�,�<gL'&1 �2�xr!�TY�tC`-b$mڑ=��c"=1.�JP%�.�>q�BSketch��Pn}:"��.� =� x^{2m} -2m/ x^m��l0^2B�� u /2,&B( %�0p >2m+1}{m�,>� }�I���&�*] >�!u����>%�theta <� \pi}�BE&�!, ���8a%+{ rz �1i  }, r^Q{)Z)on �2N��WA�n.��%&�m|:F�q�KB�"/ � $y7JŜ0��� �F�3,%�J�!d�9� ]�H2, \pi]�F[-\pi, /2[ r&��x� mate>L R� �9�IA�} �B\JGjfm�.96Xi_tpB l:e ��-2�)Z��Z��z>1  JZ�~bZR|.!��@ 2.4}Ra�5�Y}0$ es\ a dbr �KonR�EstE=I.�F b�4*3byn$' (cf �) f�lso8 �U�. G>J4J}JJ9� >�T��i�.�to@�in highe98q $nN�)l�3R!��[Vf�.O�*$$*�2$"J��:B P^2(x��2h$��h$�  x^m$. B&%�&�  a�J�V9  6�exe�B-�ro1})�h�R� ��Q��n(m+1)��:��*is opA�l,���>upV�!�Z� F db5$V ���!%nee�;�ub[a����d | w � incA�es*� J ��g  wh�%eϕ! �3yf�~RhV�(n���� ʉ��~y4f��ret7'$�EM�=~I&�:2�  $T�O&�9b�&� V){���;2za'bL� "�:6N�\Tr(T�S \sum.��T]}�vw>�B�_� Z�f!��40iZA�$Tf� ��  m4ZpA��V%2Soa�Y!#*� � �empty�-umJF>�$*6֝e)�%rL�.�7v�/ Tr\!^ A_L ^{-�}��%~�J\;�}�'� p��j��:��M"�07=!�c�C= [,o��(b�4xw�8let u�$d#�� TBq#mc@<d���$b!#�$ (&�)2= �m j}I:�ni�;onUwe��Wy*O��j�"��g�g�{$\tilde$A a��6�#>�6�:h�~}.!�$�L_m�� A_!I� {L_m:�!>}we �q� jB �� r)�*{cR-�H["�Vu -)&-H_1z. �v�|J`.n���\&;x���dr1N 2x z��nRm>\J�2 A_m^� ��6�,B^2-C^2& -BCr�CB&)r$�nd��v��xN"-� C = Iv-Aw �B=MaH_1En $. Hk*NTr�!�"a8V���%�1�M�!�Tr B^2 - 2C"N?V��22jBy g�My�: $\gamma>6I>�jc�Z+ Sm$ �� B6 7� �VV1 z8�n:;�!0� derivLGu1 � = 1$U  ?�,,T43.*�k�z :q�5O M^2)  Tr(MM^ܱ, $M�(%FH_�'w0:A !�2~ !�Ac) X�<4jeC^2>qF2! he�K�| sII1X6,� .� N��&� ��\�� �e62� #6` M0m�K < JxF�s5j� %�3�b� �` s`�c !�$n = 2,�.>��YM $U�A_�"4��4 ��s m�/ kJ�"�,��ed6��!�6$>�5WDK�FiM�nex:R�O� �HF�)s�`"�2ingred� sA�%H^�&1a�4di*�R3FTQ "/to]I~Fpi�9�A��:� r36B)� "�-A�a�A�-� e-�(�i�M���>�l P$��b3 �pv�6���7"�.2��or*G P�R"�,�� �*�6�yB��S�9�b-( $�Etau y�K$\hba;�^{1-m> }$\m#3\�K� R au^m} +1$�AE�>%/"�"\��ni?_6�N!s6�H�8tonia&�+$\�H(\mu)1� �����9)�4 �^2"�_y�H�5w���notI�-��!�ba19.�9-m� g $H*�*� As �,�[6B�N�a�e..t,6M"�3j�'� at A�.iuv6�^nR�^�6�I�.BE�A_P� E�v.bPY� �)`��� =hN-6.&�8:8v�� �} �� �bavu�Yc<q�Q� A_P(q�i' i%��DS#*4�6 \mu_\pmJ = �� 1 \pm i � F2�So� s� � 6�B�A U�_edT$R. Seeley���=� _@� �aq� � ' ]M{p�!?;����� *<$ $s < -�n�  ,a`o6� regim"6)� a�+BGm �id�;10 �*� E?A_P^sM \P�j� 0}cO+s}�d{j-�nK]�|"�c+s�A�& (2\pi� nM��$�,,b R^{2n}}\Rei�AB+(x,\xi) � ^sdxd\xi,y� c_{1._0,�7 c_{2& �,<<8thing�7 �9>>9+e�1��So M�B���$ a>;eH�z�PM�um,t �>:L.�&^HRE�>�H &�$-�� mC9I�A�Ni%, � ��2ި1*f �sA�&�m/UQ�veYSIf&� �n�%�n%iQ^�u �0A{/>� %� �� [$Q$Yn O$:2�>iN�muU�Q�>�. �,2�%: x) + ��{s+FJ9Q(�8:u~��:�6� So�bA�i0e $f_s(i� BHJT1\�!�> n}� !�� �>�R�*���: �'BGs�$&�ge��$>�� ^{-n}f(1)� $ �"_.�7>$ �$ \notin ]-�P , 0].� ;8\Re�i%& cos\%��1�%"=#!T��%�1) DB+!��]�Y�����QEF�!m�> @W�=7=�� �$�<"u?r =&�>���e1���sR%J�q� T#"���necessar�i%erS *�kI�� ��6:N�(�:n5v ��"Z�ab��A�ɬ��P6��qB�i2�@W3nX�s%o� xb) r\"o�8er"�.� .��^� o �.�s�ch)ha��ist�� "eV�B 2 cZ��2I8A�;.� JqBv D"d �Jl+ !�Q'�th��/ity�H�0�B }^_��%�.6 �k*g�a�x[ mula�6Sj, ne�.� d�"iVe�) !vvtrV� �a��.�%+�ZV%�5;:�+n" >�$\3_j[5m�VI;:��"G .��i�_ulus,oebVa&{;%�V�p��oN��69J�cr"�-N42 RVN_L(r��#\�,\;2]/_jŦ�q r \Z'.3 �h�~Oo���k{1�>� Un�!�Hpofa�,M� �O�(P '�H6*^ W:A�\C$C�T�|��� �+5�FXN !t"r^ /m}}{C�"eq1w�7 C.$F_VN|(*nd2kN�r mBXM&�T*� ��d fixa��E��$k.�-J��Jy-h �ofNEamTc � )*"\%O-��R/J� �$j�"1} (t"�__j� k}�c_0t^�fta+"�2� - k -�/"n,R�*N>�c_0"� B� TV�n upperZB! �bO--Ky Fa�h" � �&N�j"B7(t�*�3� %A !$>:>�Ms1~V��jA"�N\{s:�� e&Ai�;$?*�=,8�b��T�B �4JS*j� ^�-9�1})8^�E�]8O}.�k}R�vf!hich�s �ly (txM$ t=r$)�c.�N�0~� �'~�Fo�N e loU[�E/5N9 �e%�$t%ut"< $2{O*�J-��,t+�m4���WJ� +t}{8}VFi\�\��, ���(\varepsilon��,�E�f�$\arg_jr� [�1-U2/2+]J� 2a0$j6M���6� R,AT&? $c_1 R"�v��f�`�*���J��� )� z� c_1 23f� ~�� 6(&� � i���Stielj\`�Pntegra*�F~��0�`�Hr%}dP e2c_1�-v�~��1">� �1am�"� tochosen ��.�MF�.p".W�"1b9on� �Mr�~<"/$ t}bGvZ= kCft(%�{ TR1+u%�-1}u^�  dus��W :�B>C� choos�� �:����B0^ � t }(t:�E�� c_1}{2}���%�D� �Sr���aK-Ft��8V �)�j�~^ b�4IPPjx N - a��!! }�>�Rw��L_{P,Q&�D' *�X(PH*�4 + Q(x. R�'� ��W%a�X, Q0�*�!*W"n >aUrE$PE�$P^2+Q�ew�g��$Q$� i��t�2nt�Vly 0}[Egoddz'P62a�Qd )�a�7}�q!�co\�!�"�-= $N_{1�K�JFJ9v�Y{��X��ĩ�L�H~N2i1�.����{M�� 6�R�^xi�lF!�&8=�A�V5f$mEH�?$n =1b'^/i)�U - 83$f- .Zm=3�A�technA��N~^�)p(P+1)^2} a kc 3-�d 2}{>�f Vb�g ��3neg�*,"::ivZ �m&�Z�9�WB�N���bfB�?�86l5 �U)b(W)4+!�leam�"fiK A�P%`c��QRoGm�0 ^�a��hol� �]�5&�'s&"��fp�s� U��ZM!-d2��nof���'ur!.*�F repl�!B?mu�b�~3G�-R9 ;H4eV}bM C;+Jx_2��qf@Ix_2^4fZQE�v� Z@ r"�)P��&Y[m2kY^8 We �vsit(� -,��m�S a&�eE� G. Mq�iv;y a}p�wenty y�pvu .�uE��>�3x�sAa � p�e�� �V$�v�^*L_J�A0&�=_x|p 6 2^2zy~ /I!as o�)�+��-�NuXbJ�+r5 ��.6�:���5R q;7�=>�$"((� RR2�$=)V{"!-b�+etaF3M�8 preciselyR32dz�b�6:B�2�V�+�+�+) +1avP�T� � ogu�ͫN� .F���J��-�h&=�&2"&a�Oi�{1+\xi^"� ^z$ �?A �B*�,a�we /0ь�gylFS%[�:��c_{s,o}74_y�"�(n+sm)""h� �$m�h_s"y!So�3 .�]A^*�b�(�42�b!�%"�"weN�#J� .w��5�3 sɒ_0Ŕ,��epf�2!��:j�Ip  4�w�-:yBI("A(�V���J2 (�uU�l= gqu5"a@>l �.*x�V ed\ *l ��u^�o&�T1 �*�oed����9�malkA(&t �-:r w="bou� beha�on>2X!)�aM� �^,+q&z4 � "Ou�NM�) loc}� ro*�yz� \liJCeW/�row�}�:*}{-�P�.���� (9r�m i��ca��U��Py�O�^*bar �A���S�] � %+&�OH ofF4+^�g6�.#��}'���8M7:1\sL/}\mu_0(� !��|� �H*o!� "�Ea�:[��:g a!Nmu̚� �*�-J0[ !�&2�V�(6S4&�4}��!2�3L"0)$,�D6�%fk7<�� TVv.�"s�I��N�ZF_E=(z!s�0)^n�;2F-5- z���N� �k��}� ���.��us�$�� $\O�|_o9��z.q[C,a1( z < r\}�d�K2$F�al47� A�R�wb�4h2iv�4w2�4x)�4sz� .]m� b^�j��rix+Q{i��� ever.Ay.] ���� � &� >0~z :"� �)�PTS�  $]���hol:f��&>�J��$ B6R�{A��Q�Re z<1-)b\}�S N*E�\ImY�5��2�̙,>/!�3>y�:= �&�0,6�zm��lBA� $A9B��˺���V�9e = F_{c{K}(zz= B�t�y���� 2�A�N|4[�t\7-ځ *e\! mu_-�86S]�7��R!RNowAp�p���K��"� `o�"Z� radi8��?6A*��wD�&��8_�: � j12� �9_j�s����� $��no* G;�89�borhoo�q$� $r���ca7�$F_j(z):eo�_jaq�:s.zM�9Wsc��{rUׅ�CD $r_1!%��rU�0R^,�y`,��j�_Ep%��R/��4ly�)v��ʅrof2�� Ijю)�N&F�){ c�tel's�1�j�f�+�sub�3+�!s�a�%>$ɥR�Fe�F_�ʠ�4Ed� * P:��_n*$�D�Wan2i#f9F -��s2MEsQ6�!���s��^�f)�s<1��r용�1}3 5$ (is) =�Ҩ�\2R�9��9�v615+� �imp�8a ��le bid� !"dT'��0begin{corolla�ry} Let us assume that $P(x^\prime)$ �$and $Q(x^{ G �})$ are elliptic polynomials in �i8 $\mathbb R^{n �8}$ of degree $m $, �b@ respectively in:t6�2|$m:"$.j�^}�{ { + Q^2F� + \left(}- � \right)^2�0NThas an infinite numberA�(eigenvalues���4\end{corollary�G)G0{\bf Proof}\\�����remark��A�Pself-adjoint operator��: $K:=6y6}+R'�Iha��)�Ta basis, $\{\varphi_j\�;ofIIfunction�� $L^2(NR)$, with 4I}4 $\eta_j$ such%���!��lim_{jiV4arrow +\infty} s =$. SoE U�@ is a consequence�Proposi� \ref{loc��I� \QED �pWe can get also estimates on�j���AөH $L_�$,�{�(dimension, 7%�4$ large enough�em8,introduce $N XR�Y\#\{j�<$1,\; \vert��_j(�)�� q R\ٽ\begin{p9W1NThe�� xist $C>1��R_0>0 S Y4�R�R_(  2uVwe have)p �q frac{�D R)^{n(m+1)/m}}{C} � �\leq CJ.1: \e\�$J���SketchMg2� We follow%�4same method as%�provingF�Q;}. ForA� veniA���we workAA:Tsemiclassical side. Le� denot55ab4tilde{N}_\hbarjmuA %B .�We�e first�Dupper bound. If $sJ$ �s)��!D1� $(\� A^* )^{1/2�� � ral l 6�Tanalysis \cite{ro2, koQ�gives,��%�som=!l stants $KM�0varepsilon_0 :�M�(\label{eq15.q\su��� 1} (9 +t)^{-kM�K%i<^{-n}t^{\theta-k2J]� q�!�I� 2�art u$. a� n usAo,Weyl-Ky Fan'��equality6$ we��s� �C�BU�Y�B6.� Jve��R�y�:�eA�lowQd, �I.'from . traca�4rmula (Theorem�})Y} P�̡�A# $c-�2&��9�72� :�(�P\>VYA#c_0%�n Z6  So,�$>$ small�,!.;\b��\int_ef^{�t(r�d)¡GAt(r)��b��MB�UE�!ɝ-��H4choose $\gammaaw2�,.D6�!�2Q�6(Z� pR=!�kN�I�2~Ɉc_0}{2}%(%�U�-k}6gF which�� easily%&]�2sF�ml5��) )� 2�w-1}2��:�J�&�6 �hit Acknowledgement}. {\foot�� size�� author��4nks B. Helffer��Xue P��ang%� thei� mRT (is paper. }�62 ��thebibliography}{99} \bibitem{ab} F. Aboud. Ph.D��Tin prepa�� $University��Nantes.KHbago} M.S. Baouendi�@C. Goulaouic. NonŶ tic-hypoe#VA̅~degenrat*B� s, Bull.��A.M.S, Vol. 78, No. 1, p. 483-486, May (1972). \�tch} S. Chanillo. \newblock Kirv!��ory, Tr\`eves strata, Schr\"odinger equatX and � >�of sum��squares.uPrepr� �August 2001, http://arxiv.org/pdf/<.AP/0107106). 5�chhela2�,>p A. Laptev.�$Non linear2�v� :�. =7�PInstitut Mittag-LefflM� v�211308.�To app�$in Journal!KF� al A (2004>1A� Christ.Y Some non-�2�>�s,vector field2�I�E� 16A�8~137-140 (1992�=�2Z��a:g, AesentMiLof nilpotent groups,)��B�� blem.43.�.�^�!�"� two26 MSRIU9e�1996-009%96:�n�� perT sympl��}E$ Proc. Am.%��@c. 126, n$^\circ$eY 405-4M� 8). �� he1}��6" Cond�s2� s d'�&��8it\'e pour des 2� invaUts A*4gauche sur un �=e�N gradu\'e�.x4differential E��i^~44�H3, p.~460-481 (198BUe26� R�qu�l �p r\'esultats de G. M\'etivier�l��! ��%AZS\'eminA�= l'Un�!.de�, exposAs$9, 1978-79� 2cerowa.�,, D. Robert �*2� ? S2�%�^ of ��Fs��P0N, Algebra i�~ iz, �~" 320� :+@o} L. H\"ormandera(y&� 0 second order6�@e�F��m�19}i�47-17i�67e�!R&� Lke}M. V. Keldysh. OAcoattenes�7a�@&�of0  ��f��2+��&@ Russianq�urvey�v26}Ň4�15-A�? �om .ko�# Konl��*= , M[*5 ��8��" kr� M��%� H. L�f!�- mat�Il ) ciple�% �t�� 0damped oscil)�!.,continua I, �Degr.�~�4 � Hp. 364-399, vol 1/3� 78).�4ma!S� rkus2�{�2�to�&��&+5� +s}.�� 1� ans�2-mon� s��erip �� l Society2G M��2m2�At J�� UlI mult!�$ characte� ic2D �DE D  1-90%i802A M�6:�.�Unem d'2 � �)u �h�b .]IndianaE�!�' ��2�823-86�.e3}B�v�����,.�s GE-Sc� , �� �T {ne��Nedelec2�E�\ares�ce�matrixL *� 5�. AtoAE z�z35�: 301-324,��\ �({phro} Phamad Lai, �HL � probl\`em?x vale� �re� li� aire, JA�.e3EG169 -1 �0��9+{ro1}{,� pri�a�w S ra�jd'O.R Pseu /'els�fY�� � 3}�C755-8 �O�:� � ro2�.�"�{fut� l'approxpion-�A72#Progr�@i��i�s� H0$ 68, Birkh\"auserim����ro32�*&&� s j� i��parametY w JmFn��7ED231-240 �42l8se} R. Seeley. !wplex p%��an m�cY��"� �s%�4. Symposia Pur� 110}M l$p. 288-307���&�Sim S .2��T�ideal�n�applicɨ2�Londo.��� Lect�hNote Series 35. Cambridge &� hssE9�P�j}Sj\"o�� A �FoD�R�0� ���6�6$�F$ .� \E.D.P, \'Ecole PolytechnA�, Exp3.�  1997ah�Tr1��2������]Ql� e5 pa�o-a�e� � I�double>�> s! � H${\bar \pa}$-NeumanQe&.K�2 DE 3A�~476-642��+.�Tr:�2dS"� geometry �Z�.�D.� "� (: La Pietra%� (Flor�A)�201-219,*] �eR.}Q, 65, Am� �� Soc.e�vidV , RIeZ9A� �>�  docu}��\%�p[10pt]{article} %\usepackage{ ptm} .amsB symbBcd:S4stmaryrd} \texa� ght=198mm ,width=130mm 2xt� e:�Xxspace} \input xy \xyop��{all} (\def\cali{{ I}}p Pa Ab Bh Hl L}!}ydemy�1� . \la {?%\la�% � \r>%\r2 lvac63 0 \!p ft| 4. \!S :!-. 4,|F0 9u )&pb{�"frak {p5pf2F �\pbq{2B}}_{qf:F oS>on#1{\s ,{#1} \setcou�{qt }{0}A`renewcom�! . E.\arabic=} j9F-T %FIN DES DEFINITIONS | zd{\vir}{\raisebox{0.75mm}{,knewM�U� {THEOREM}F,lemma}{LEMMA6� �#}{PROPOS�6&"�#(}{COROLLARY6"de@'ion}{� $�beq}{1P �$e$"^"baEarrayBB ARbeq bW#eqnR%e %E^#nn}{\noi$\\}�� } \v�J*{0.3cm:�X �ceA�FD{ \LARGE Hopf Struq��,Green Ansatz �HX \\[6pt] Deformed Paras�s� �s}+15pt]�� { %\�$X Boyka Aneva${}^{1,2}$�h�{40pt ,Todor Popov -3}$F�%T�:{ :}$\� �L  Nucl�Research% Energy, *,# E!g� Academ�S�s�.9) 5$bld. Tsari�skozus� e 72H : 94BG-1784 Sofia,} }�7^� ?%!f$%Physics Dt�jP, Fakult\"at f\"ur 'Tk, Ludwig-Maximilians-"~ 08M\"unchen, %LMU[P( \\ D-80333& Ge�y��3}$ Labo*irI*�que�i x4\'e Paris-Nord%�%LIPN9\-< CNRS (UMR 7030)%��'eA� GA�8 99 av. J-B Cl�en�&dF-93430 Villetaneuse, Frai:�>� gin{ab� ctY�usw bO!a� fermi al/n*�/revised'endowed� i�su�in�atu- way.e�Thyco�9ua�ve cop~()lowX�)M�of>�� Fock-like>�$, built out*of_ si� st d�j� �:3�2� & rise� &�.1-ob� anomalous� �on re�!Ōe�$generalize A�8a�8 ���9Э�{0.5 ��"4.D9�$ Wigner wag'%to2% the canon4(quantizs8no�' most�6&scheme !@iszI.� Heisen��4%;mo!��'W}.ap.�{i�ed by-!�'%-,} %in 1953 a�+-R 2�l)of �um `�ory&�%&- 1  Bq/Fe+.Z. Tz" u!� Y� isw-ed�+wo typ�UAwL- tril� exch�Y3, namq2!I}�ndI�m�. aw:���=a� �(l)ja  nega�2!�e�!$p$ -Qo�of��!eu�E triv>��^�<$p=1$�lcoincide-he usual%�(%�)� >N xtg-��!�.3 �, totally symic(A�), i.e.*ey/(ns� accor�"a?!Uone d�-al ��"���]VZ%b�:!�� of-q $p(d2$correspond�higher-�>$F�� � !0Hil�))of�lonenti6Ah�o% In�&&� �(E�N-time% $D=�%A�$D=3$s)Sth&<. mor�ssibilit�oexa�w%='tha6A6S in-&� s $D%Q4$�XHT}. %Q�um)�sX��� play!?nd� suchD3,dard %�) um %�$. An imporZ, %�v�har�h�*in}R mode7 �B=� %co�l)� N �m�p� %��achieve'rough�dA;!�U�� % O�5��u $al envelop�'��A�'c!�M�%incr�(ng �r�i1��= �1 (two�)al me�#z �zhenomena)~as sa} al H�*ffect,%�,-$T_c$ super�u�7ity�: expe�8 on��umF F firm%.e.+vly� rged��i)Ls ɱQHE}. M)�e9�6"�5]��+ been expid, terJ ��ny�sO us}�]qu2" �sA� Thes� bV, >F,!$dane %R�. ɘattemptdeE>�q05r� evolA�_ �* stud(  >/Y��gui��"A�t� �� E}a isomo$5sm betw!r %nonr ��.� $\pb(n)~9j �l1pf�$n�0�:��freedom��nnlA�$orthon�# n $osp(1|2��p. -goa( $so(2n+1)*�:!1�� ~ part�5pbq�� $\pf w��� d to be��5I�itE��}�w{ m6_ J_8} (QUEA) $U_q(�)$I�Hadji�% �.>2.�-Pal2}.5 I+ ;��wO3W3rit��� lete� i%���&� ofE&�{V3(se�,*v0h1*t0ext!, ng w�2hase� donE��,�1}.E�novelty�_!ect1k�-n ��% =�eBAi- systemAo homogene� �(2 II},@1 II*}G% ANs*�  f5��A�U#sfubD %�Q * %�A)!�!�])E�Y %-)i�=%Hy a� to� "� N��as  �E F�5pf=�ek){1�M� ^ at ha��I�" W&�. Wa h�fined �qure %By��st� onE�Zqs Z� bec2,5�c i�2 �y�!� N�1� 9���#)�y���>A�inw9ly E���@*��9��Fd s; %imPalcm� it�re�r t�9ZF;@�Y[ _rbitra�$G W  !�� !�ite�*d���Pal3}EWc: �Quesnea�We mak�7ea�Knob�-A=��J ��R� a$!�� a��@-�M�i�I�%�9=�2�� �� N�a�єA��c.gApa�8�� rgan�ia��s. % 1%t�iu�&. %�9�8recV ��! and %a=ct per�  �Zd. I�!l 2�v[e g�k Q��:�.M  fr�� o� poJ1of view!|%�u�sm2E&"�W"< ]. 1>3!> devo}h[�2fAb1�����e �b4�' z4!5show �DK $q$-Ic�os� (�  )�'l'@MPqas %ay ticu�-6 !:�%�um+}2.)�"�FVJ��>� Fur  i� 5 %we utin?f�5e %Z{!�y��6�si� %&�e� �.�.�G.�- .$A#D�u�1:L� �Z} . %S�{TT�9eE�der`��NC E�Appi x�  T�wou� textranGociQ-we me n asJ �y,unit $1$ ove�6�ym�$��VY bb C$. %3pagB %&�)D^/�>""�b0 �!j�5�695��!a^R��9�E6��A5�-� altern%[.7����Z}���e�5~~ �� �(�R� )Aq:�()1� ���b^9���$a^{+}_i�� annih0, $a^-��E�P8r $i=1,\ldots,n� subj� ��\qa1- a{rcc!� [\![ a_{iy:T},a_{j}^{-} ]\!], a_{k0 &=& 2 \delt*&>= &\� &V [ \!\*]+ ]\l]0�\[4� D�-1@>�-�-�i� 4&\ �U.�-}�] � �e%G�{1�\ wE$Za,b!-D=ab - (-1)^{deg(a)b)}ba$A)A�E�or �F��toF(Q�(��A�)\akeUbe n $f!�};F m})=�%${0}$ (odd^!1}$).s (}$\6; {�i�1� onhe�* earl�3de���Uy��ten, o�_ >� i,-)Jacobi�(nt� }%% ��� a]� % [[N#_{\mp!�^{+k}%�2�}^{k}9WU� [ [6 }_i, !jOk} O06U���iK- �.�aci}N-�-A�% Q� qF2��Y.�A�%%beI�%Q�%%~�� %Ou�<�C�2 tJ��aɰ:?(>) sign o��(�)Y� refer��A1�>Z_%(V[. % %�5HI-:,y$ obtai�GtU� %$$ %./�tj 1K!�-}!P]= \pm�O!�j} 1i!� %�i  j \q�fgNi}A7 j}2kA�=Y�A���a���� %\mp j��k jG$$�ai!� in.;)�ng9�G 1}) ���atA}!,�a� combi�-�I$e^{i�= ��mi6" �D-J$ clea q�$gl��.#6�5�& �!9 a� � E >[�o�N�jk}�i �k}����qI7�t�2�y�3 rava�7 R9s,�a` �� %Jtj)'f>Y:U}>N �O)P--he�!!� indiR1up�Ydow' %% aK� $a^+`�.y-� %�!�5 �-� hamilton�5$*h�)�e�*�� %� s'v!'d "�gy,��i� [^e�\pm}_i m�a�i�calh =E,i=1}^{n} h_i " � h_i=P*|m�i!�i�.� }tH�%�Zm ZNWɬCR-ա F2 %� as e�@5�!�VJ 2�@A��jo�= %(-� its >o)$\[%��1l�5�!�aX ] = -� 62� �M�Q '\]E\I��P"Y \$jx ies. 'w hJsh� accept^ � ���6�aK���!��׹���M�4�  %�f�"� ��i� �� E��e\!��k�g�o} < * \!}  J}_jK�� WB <ZF��b��B�Pa W �O� �: �*[ 2 L qF-�  @ � %�� $ M�� !�a xi in \]1 {0},h 1} \��/ IHt Z_�(�%Vof $x�vu �) � *q*� ���ondE(qasEx� A�A���e B? $ � m�\Q I_)= �A"\ ,Rm�(�11})2 m� "#��R !Qai) 5)on!C�/%8�*lA�x %�ain bothw@�!础�%.i� scrib� �-�Q)ls!�6q�u��M��iI'�O� t! s� d abut0!'Jiqng� #�F �s �� ��R(adm<Z�� � invo@B $\astk % $(ab)^{ b a�$��y$$(Q< *=a�� -� (C-}%Ir $e3�1R r�to� conju;&o��n����!j!�Y?� $��*!fV�each )� BuE �AE-&-"�A�al�H� v!�MiicJo�Eqic��)�-1�ɝ%Gi2R1� %Q�("lc!.j"�J� $U*"E�gZ�,��" \simeq .CI�KT}6Q,KT,RS} while� �e2��6��2�J$ $U2�-��&� 2)f� �c � 2N �GP�aQ<9b�iw��Jm�to `` 4e''/&�5�sms %I�iso�2�%!�9&�)U� 51� ni�a,-e�5 )a> H�ICA:j! a'ƥ�!1���Q\ { ��dYl.�Ee!Aga Lie�upe&0)sdDrin, Jimbo, FRT, KhTo} %oxDp�Q.@� 9" I� U(5Y�Ѵ:!6#&�. � isoq/ eq �cCof" m�9!�): \ \MSM"� 1%� 4>� 3�!} �!�< equi�>� I��ozB~�A"$B��&  � A>ir.Fin �%%$ Chevalley*lq�(way a minim*Vet�.���6paraIT-Serr*�!)aL �`C�Vy%��I� (�9�2�� ar) <sAs_)nge�l�. D�#W�&S(ed��at� �p%YEF\ ^.aXJ (e�# %6 a�)-GU�v"�-��)P"i\&�� 8U1  p�=a�3ic�, �?&"* c8X":#� j.Yic.[E�:[q��!db�)i,ur,$l�Q =*li�.l�CV A$� s � �!Pal4}%^��2)���FL%�(isQ�ed�known��?n��#� r8#A5ȵ2i8�K�i0a2,9*.now s�YI procedureA�� �Y�i�$VNE��&ZU�/�^�]m2� �Yd O $B(0|n)$A�YKac t ,)nKac�{sA'I� �C% ,C_{ij})_{i,j*�}$ as� $B_n$1o* A�e�Sm�9�A6}).���es(,�4eu � �d!v "� sm��0ge� 6)�6 �Z��he # � �8��v&�^�� �$tO!�] s. %.�asGb al d10nct� se7$f��Lsers �s %ofJ\� rt > $� 6�suk �2HY��)j�%Eshc$B %)%�lad�O"U $E^{+ :5hnd-F><*Z��Aa.&"e~a*x.�\�(��$�)� ,Pal1}Hh %inwe IW > =�,op{\sum}_{k=�n}� k}$ pie�" ��rcl} �^"�si},+1}, �"n-1�-��= iA�� \\\�i} _[ P`-nN -n+1�j L��-��K}, ���=F"F �alg� T "- helpq-8m��M {i}=: -6La{!_i < n$,��B {n}=6@^ !�c"�7a�)���� �jsub���s $��= h�-�+, $i<� n}=h$. �-�A` Q 4}�he� q^ i�� ��6�j to'54L�" mh *� a6RcEVE�%���1}{[2] � +1}}�M~�E+A� &&E!�A<:G;�+�E�"�> �f�� %�0, [8a ��n}^ �a1�As�nAda��invYw�c�)�(over&8nC(q)$)!f���"�%b2J�*�:l+ogN"n �xgiven�]R��7�B�7e�CA6t�2+*U "��4�wna*)6�Fx' �+aV^+�R��*q:]A�` AV���*�' ,n$ aj�'A�9��c0}),)Mc�mPe�'MN}�! �jaPE�� !�"�� a� }a�AUP$ A�Mo&�"��\!I�q� ے��20]Q�fe}� �'}e=�� �e�aVkeI_�&� k}\sigm3,k�Ia=(%� �E3�E1 j"�%f%� C i,j}�� } + (q-�V)�H�( i,j;.<� �k>,) , (I}� �7!pF�a�N�j�i�-6�[2]�i �Pj}�-:�i} } - F�j,i�B�G!�� Z�*��A�%| "+ toge�'1�,JZ@:�6� ![ I�}_{ i_1C%I� i_3]+2} �E12}} +Yq� �_{He(2  Q{3 N )2=0&�� &�k>j$AywnvitEs �#$+�C$-1h�nm�%.}�q�:�*"J �~�6��6� % � �� U�i"�A�mp}"7& %%-}6#�\ (�ppm ]&"� �mp �6(qjɋ� star�eq inUq�Fa %standB �.��-$&=   %Q .�$(y �= mp ia[� � �=5I2To }�-��>8 $R$-$ FRT-B)alism %��Iol.r��g)' a�� -)Li&:$g$.FRT},�hTD m7A�!> $L$-�^alN <tl��� �, (�,m5anc�o)$L^{(+a�( -)}� ESR "\pm)}_{1. 2}=2.1} < Ɋ.K+I- G R "C� frt2MV�� ��= < \oUEs 1 _l1 � p =PRP�)!r6� ]�6�g)EZhe $(3@\} $D�BL��^{ �$�^�,j��n+1"� $({@ H �*%�x �%���% �&��*�K<{��ex�,��",cN?i$+ qa O \�y!X%� ij}\�T)_ "{ F�}} = ; {lc �_ 2 hA\omegax � 1� � 2� &&~% ^� +� � i & [.5/i& Fc+}_"5! & �� N�2X�� aB�4�q�2���) . 3)L�5��31//yv3 ��*\v�5�F dZB0& 0 &0�5 �1Tn���.� : 0&9 0& 1 %� I�Qb�eL+IrD ar-%Es�demi}} $&Gcoeffi�Rt $c= E� #&� $. On�.s $2*�L���ji}�Y�&�wfe}), I *})�tvol"�ent�\�a�min�5a��1��$ O L+})�[$ F�$ ) direct�r@= RLL-� ���)� }6P�O upPstrict��/0c/: to $�*�2I0onYpo K le d�B�`ic`:i}�eis�qAWe �k{ LHS (upsscalar�2"O�&��*�2�)D D!�by�6RclIr\L�^� ,] � 2} ��a���a�x&�,+�M�] ~h�( FSr� 3b�&\m�X4} "d� �K >�2�\&=& �M��N�2���2�_r& �&� "��u{-\}1] �3:].u�=$ -j�^�7�.\� )ZJ!?2&V�!k��~:J�2,iB�%c6��2k�����2F��� \ea{.�e\{hJ1Y�v���q(gl_�!K2�E inclu�}� : E�B?E b�2�� e�&n &�*;!A o� -� >K . (a��"a c $A_q,bdiagram���V"Dynkin )HQ �:"-\hookſar�8(�) %5 F(� �in�� �6}="�5�^7$ (� $=� ,$$ ad_{E_i}Mcjo�!a�^{&j�+1\,j}}}&�!  >i�As j mp�H�=.�y�/+1Y�: adj} $$ "�'5l�L�w�E�So`{��Z$�e-�:�$Oby�2 we m+AEcubic &�js!�� �H��Q hr})(7to %jeItѮ6��2ݨBS:��-UQt$-cov88 g�1�? the MD�8. M�Pprecis�U�&*!8Bj�^A�)S1ni�F8an irreducible J(e-*Q2�module ��s�0 ightA�1�^a�,n}_n$.(?��� �LaC)  r�} {X �A|v�I guishe�Q]��n- �2� !�;&���{s $E� |!,( last:��$I:q�#y�e�B�a��!$n� n}*��#$$ �}= A:�X thuFE*�" se>:zero in�H�(s����{K,!whole&�;�B8l$[  !/2?6�(>$:HJF!��F" gT;�v�P�:i�onglYCi>�Eco*K2 "�D�*st�D+on^t)eA� QUE �s%{q��(2Ye�M�8!� Drinfeld-/ co b.�+�!+D!cy1//j(cr} \D�'�I � 1 + &� OS( ) &= &- ��(-)v'\\g E_{ �! i 1 +�M%  $\D& S�i})�� t�(U"x*�=06z"�X-igo�}�1.~-�A� ��-Cq^{�; � E_{- �� drinpa/"�N6$,a�Ii*�06=. �(&�C  )$�v.7 s $SeGa �ab_tia;.P, $S�5 =N�D4 S(b)S(a)$. } f $S�� ast})=S(xi$�HA�.�&I�i>1)�TE�&� &a ($� *\)"�$^�"P2I8�Mu���-4)m1a����("�-).��&�ula{�(� pgin"�œ2�&� o"� O20b8L.��6� � &,.�6-! �.I&�P (i) �0p/a$�x8$&� v�z 1aC���6qR� pm &ea�+ i�� :��ii}$+ P 2�&0\limits_{i< j�n}2�"�#j� "� WG� coa+})#� &= & ��N��;�i -�Z� i<�H -}_jE*`j� �,�f coa-�fG (i-�L��$ v�%!� &* *���)=�%/ �`�_i)=0$ Ggbel{cou�D���nwtipode��%(���O1) 6�.�% ,S�I~��Aimp $,�S0� a S�����>!�h_�E i - VPs=�n�M(1�)^{s}�k\!: ZNi1>j_1> i q ��  !-}^  � >!4 �!'{W 1\""dSu6 ${W^+1l�o /O0(�!c>��\pm2q7�P�� �n�&�N�"�)�,��tH�$ K= Z-FAQ}� _��( _(Jujk"�>�_#"^>)*$/�3-i`0 S(L_Y)�d� Y }^{A�\prL��!�� 8u%�=5�%�Xi�a�$:� &�!�Ly��%P�%sT�C.�����%d 8j}1a!y ji} =!p ii "S!�rDF��"c�� \pm � .�  � ���t�AC5!� {i\,K}�rn l��bhdfm �)%�!��Q<!�2U=Z B&! �R&\,�. =Bb11+ R� 5)�' CjEz+)? A��4f)vrt�ة<w�vZ�Ze�)!�vQ|� �n�Y=1$. Ins�X�;n.q.O d})%�@$�2R =�i$Q� %_)Y5�e a�xm!�bC8e $c$�get.�� ;= }_i�c�>bNjI�� �~le��Tof�n� )a�dY ��n� �� = (�)�C� �>: } I�VlAmr�: 2F>��in |M�. @(iii)} ��J���^p@2��_{i�fA�)=�(2$ M &  F . % �S0�\��ciag65. #��YMց2i$�B�I�-!�s r�m!&d"�5 "�lM���+>QS���%)&m: � \Long. � Z� mB�6 ��� Jt = -% y"�ɿ H" �Cmad�HA�$Sn�/)= S(1!։2u..i\�[ )= c*� $�@%^l�F 9�~6A�Ki)�(ich after n��listak�A�%�aL �+ϝ� ^N*� W^{i� !H |j� P8�a�X1�mC�G �� F� 8*C.� �saG(d?"B�!|�AM��� ��S+a7�Q�e��o{i� M�S-}�V"�A9 s*�,� D=(� �)��at\Box$�vKob�AMv�@�@�N�?becf��*� �>F an�I !*�� �`a��*�>D .�.$;/zs�_{�*�Cr2�\W!c��a:` i_{p`,fw:8 �[c�@�� (eq�zef;F� k�tvacuumb |8index�a�(V�ozGM}�)�U OK�D�Ie��60einɵ:�� �)�:@6 � aN� $\�{��S �ll�{�K Y �p!��Dc�K:`}Yce� \ �]�v =|!0 N+=rO;p.` R,�4 0}(x.� � p�c�'� �-�6H}.�5trYqw&t$"�W"� �+`eW6+�] . i6z=��1p}�6Q�e�`e>�`U� 5�h4h&�S �S �&�V�3Q"�SA the I_"K;V0N3.��9�$ *� 9% $i$-th% y�mP�%E�MB�T_i � g ��0p[>5�6�+�J�Yi�,~�s &^7s� !����]1�Q�i n1۩S]?�cogu����c&-�02}) holds \[ ]*��-M-�=�4%�5cB%� ]=[2% !p] \]7 impl�qs�>�$e<�7� ��o� �})-� pi_p.�2�[p]Z��i�pJ��nt� p{[p]}/{�:$rrol��ofAW !qm�-�c2Jp}/�R&� %���:}nu_I���R e bB5gMd ic (�)����� �{F���� (b!B)�L�sa/ N-�����5eM�����_ )� �details� @L?5��-"/bae�>4rclc} {\under=  '�Jj&�7i�#_M} R0Jm&t, B �Nzazy-i>yY�z&:&-_F}! � q�dB'jJD�9�.aN}�&J12'1� uRziJI z)&�z�%.�nJ)t%�v��1>%�{ %f�E>:O���0JEi %�^ �?ByR%IVR�0Ny �Q� ����F�R�0>�9 &Bwv�a<mp}�Rw���0i\neq j5~�~ &�% {BѬW� adop��Dta�o�k (x)=ya{x}� use��6z=.h}v7mp  < ŅR��kY  }��pЅvit� ����b�� �(:`s���3st �H�d �Q�at{F�ry>C ("�oasr' d&�{ facG�" �.) �woI�� $q$ v+aF�qyJ� ��k.} UnĀ��of^�qP��� ���%�� &� r Bq}) do~PO e ,U�� &N%gjA�� ��ntzb� �7Jpoo)�?}!�6h��T&� ~Obriefl!�foY�n1tKa!x�vei�ffor��!�. �V iHn;�tE$n�*>}w4�6Y^ord{�4!�3 %s o� �U�!����.e., {ofyE%��N)��QPQUt�ak`c�U�� �ri ar < hang����1+e�%�%�tz�<cf�)� e2B t>�-m�"� $ �#b{�7en��aw�$p$I� � :W�)� � _i) �d� B�r p�x(r)��� "��'Gra&eB�5sfyAm ߣc �J΃� E�ہ ,T)"�!� �E- )TKl 4�rb��h!G� \,zkYI! 1Pk�]~�'f@Nk� pm}=$ Ud�" $0,�ga1�eq�1 op��e%�A�":���;)�U>�s� tmpB��+$k�:F-G k �I0-� r �C��)�ga2���F�ݤay)��9�}���SK�e+*�?+z~!2�+a$�-�>^�q� $m��/&�*f6. ! E^u�qeeq��5�%��GA�a&���mqo"�M onesV�Mst:��!F��Z�����:s�+\pi$ }�). Hi҂Bp,_pH<:t�VPw�RBN�h"Tw vTw. �>�U�,($p$-fold) @io�u7p)� byjBA\���\ ^{(p�>�{*Z, F�i]�n2e�%0"`$M!�^{(0)�i"�|1)}= i㊁�72 7'5 m:+  � = ( - �Qe{ "i'1 C�>}_{p-�U�S�tp!})�M����2i`pro�I!�"�"ormed)E*���k��qh o�a+3/�J*FB:2C.nd �  B:0C$Ɔ:�6'*."�*wE7>� tTu'Wal �ٳ.i &�Dram��\ba�>} \5`k \stackrel-�)� }{\l2��G& 8^{1�p}^.��& p� �row��L�low�pibG*���F�.+�U�� ^.�^��8.f�r����BV�ɫdia�eq� 2" P�T:} R�Eѹ��2��mpf�[qyFa^qLng e,��:� w�e�T�'!+��~Q A tz)ab )su��"� �Ab {B 0��)}. �%Af .�1M� :� �� r-1 ���\pi*s �� .O~�r} :=Z`� s � N [)\!��6 chec*�%T.li =i\,}$ � %�.CpJ� S� �I2}�_d?, how2VZ%o keep� mi� a�b:� is $� bb Z�D$-S,:�� F E�8{2$���� k �oichA:l\rwh �z��� � ) a>�$. We empha��"E|" m8:�tur�ut]�& �?(��u)P��or�gщ �� �f s��$ c ��-�dia!�r.�e i" �ly ifiY%? i}(p)A�BT �'�| }I�"�exa2A�N e]�1EI�� �� ). 3 ���_ɍT ��o&�\.K!�pa ��ERE.+lEXpa��"�.1{v� �4Kb�ofE��u"��/�6��F\L�RK J�s6;Ble�W �u��� nk se��s�;C)T&�  �8m"�F�� kma;�  �\2�Q�I�.�!\�J9Z�v�nθ"0.vz��p��9.h*�v��Ax(n2u ��q�� "}�.�A9a�.(f&3.g&: stay)aC� �!c.`� &���4 )�?;�u�{E(io�"',Ap|#�)�D�3�@j҇.� .@"R��c� c"B���he�ed)OQ �GI!TL#� "�!6N�N!� o be  ntif�es��7�!�!C&� =1$) , �# z= #.� $. E,auLHed���or-��G�� \*'�� |\�!�1= %., �V=�S.C;-:.P �!�4� �H � -�5Z6�5.��8'T32�)$W� \ R�e$DC��.~6��69 $ we - I�ng�!H-dEf�"p$$�!�6] F� r� %)�� IB)k)f _{p}(���va 4 =�!� (3Tdf��p�#�J} #>�J�d )�"si`?!=��)"�" G �� &?�"�c�#"��* ${�.� s4x � %�@! &eO�7:&%Ea�B�?�$pV will2YcA��r�Ia(�A��=z r�&  162[u�-r)a�!(�3_{k�n&QWZmh�}_kW\��1\ N.&���~�&�>z_a�1N-�Lki}��`� %�<}\� �|oFP , # below) ѩ"� c&A:cst$�D�x refl�*X6E�"jO jr^ATp-r�Q"t\pm%�"�0W1�(1�i a��v�Ut��>�'6<>;Y �.JC%In grea�-$M ~E �{�ly!P�.xlook ��SpAz.�VHk�Q"�b(, k_{r}} &{Yc L�3�1UZ' & k_CQ\I�>�j;r-1} Drj>H#��� a 1 % v�\tjA�E {j eZV"��LU%#p-r}}& &�% q �p)F $e]!��Y�2&� %wip&!2=>� -2-3- ��^gb� �5 g>FB&�+6L&�0*� �Tces&�T.�VYD��[o�A�terms.�`inJ�� �J%�<�%]E�  n $��-�F (�H�Y ${< J�kJ % J[). *� � "X� �>��Ii�-= i�a� � aE� many-re��y map�����}^ =Ye�%W T�a��con�IKVY i.����ope�n �9b Q^�sE9J.; >a r&�76G \�B4BV��XŔ�9jk�}�mp!4i>i9F�T {Q}^� �z@�� T2�n� �� �)R�i;forO�aa%vOnp ad7�se'at $(2~՞ ����j}andP$(#j*�[ )/:�j}$z�A���calV�#heJ�A�I�&7 �:gc&v/q -i . It&�")y����je10o�#��r���dB6&i "��TulK�<&� �� Z �� �qu aM(( $[x , y � pm q}= xy�' q yx{s�9 (we�3po�&r>s"�Oa�%�� lcrlcu�e!+�lT G Ԃ_�}&XD\mp E("�d B�jY :�pM�B�!aa]� j} �mp�q=& &SL�� i<*�'�jS� �-(s � �  E 2!:6�� �- �i B" �i� j �j�J o�)�> j z�i�gr:"e�A�!�e jR��I� lQ>}�!-2�E�% WB*� �%U - 1}�MKE� Y8) b�) 2��! .���L �6��>G I�B =%)�� �9z �1$jF:�%�8�~!�b �{k#,�{ Wqb��"���4 gets�2�?A*a{!M���9�6�!��/^a� � _�/E� W&NY�e���! U-jQ$vU�,� Y% >��(r}� L�VAy�,S[�f�1� NQ�5��mjm�.� T +. pm2g�Jh��?m%a��Wi���AD 6�a{� i}_{%�%M+ j}_{���f!�q=;�Y iXj�X.� �C{ �j��6�R�%6��!�jW Q!��!�` oNN�No%�j� S �!�)�a�a�� !�e�"�  $�9��9d $WM��]:]cs )��R� >��DscrNy%J�.mq^{��"=/�{ Q�Eb@�=&*5kG s={1�Im�(r-s)}i{�! a�aOs)} =&�a�{k B.� , !�uad i>j�/9p���-��\0�s=�^@#���A>-<��is�. B.A.��fg�ful�Julius W��P.!(k�#�t�+to visit8(LMU-Munich,Diq[ L\"usLF�J(warm hospit�n�!�/& y DiP�r�#ac��&��) supp�y,of DFG (Deut��Eschungs�8inschaft). T.P.�*s �� itud�� G��$rd Duchamp)6��(ophe Tollu !�!dhim���)Q�am Co>�orics, I=�tK�$\&$ ��c"���p#�(� �>!&:�n NE�al Coun�����Rc&��>�! PH �6E ( Euclid Net�H HPRN-CT-2002-00325�,}�\%$ ndix]��[�X G@P(!�Lf� 1:} All�AE��Ug�`&[ i�tEec�-�k5AlLambda*g\L^*�^B!� C i��Q, n-1.<�&]�^ i,n}`�a^>n^^t}�w$e 4B?�$e $i,jW.��R^ j�e2[>[��ӼAO.=q} seen&i�"!�in9�&a�dec{� ed a+��,6�/)F 4$$ \xymatrix{ 5nO]�h$ \ar[d]^{E�a�ir1��:�_-�-)n}2>2> J12,R13�:�& %:A�3A��0�4RAvar *2}&:T^{�%Z6& B=1�%Rf.=\\X>I��� *6+�� K *�e?�2l��)j ^~@S�}1{nB' ^p�t>3Bq3%��r � �556 jr =F\ ��=s3��h�2r�>F:!n2�B<!n!=2� x-�U.�B>�f��uNy&xa�^ �^�3Et(Zjh <e.=\\ �lW 1} & .a4v�. �2A A &J�mB>-�_a�aW2�a;j)��e %5�7:�(29-�N:6�B:3m�V'Ju3v�A!>��ti|�.B�)�F�1.+-�1}!�241.2.G&�B-}9���1F)���)2E�(M�)_y�S36)4�WRXJ�-� g��:3�ɱ } $�f Next?=newL��.�b�* -1}=�mMc��25�s�(�.op] ao8%$Diag(n')$ S"*: d' $n'=n-"O%$ teadK$n]x Bˣuc-w� c_�m0 ��9=$� ��7�J; 1!?2�`�&��7weJ@� R."~_:�0�*& �� do��t bh W8�8l�O :HS�..S�f ; L�a smoothb�= �:a Schur;�ule.�I%w�Young5�$�� =(2,1Бth��}d)1e]Ci,k�� a��#%�, �L��s-x �tableaux +�&�"�@$\dim S�i��unӊ��+ �-t>��33}ˀ� W} E-�)�E� . Rev. \/�ZD77}(1950), 711-712�6 C�} H. S."{�A G���d MethoE�F�X s�=  {\emJ�90�(3), 270-273B��HT}��K��*� I.T.� d�(Monodromy R�>� "� Brainoup <�%�#em ;�.Atom.�%_%` 64 }��,1) 2059-2068�i�4QHE} B.I.Halp� ��it)!�0Lett.}{\bf 52!$84), 1583;$.$R.B.Laughl���B%�:;6%Y88!Y677AK��am�`s} J.M.Leinaas, J.Myrheim �Nuovo CRC to BVI bf 3EG77), 1� F.Wilczek 7N�49�2), 957�B1quo�Chi-Kea�$Chow, O.W.E�x�.Y!$ A)%283-r, 20;j�:8(J.D.Delgado>E.F8F 139.�9i {HA|J�I?Y{E�um�Ev����*1/ :eJ��%;q� 34 !69a#5476-5492��� T. D.�.ޚ2�m���y\m7�9 so}(2D+1)*��%��2��"q:� �!�V�1�4A451-158=f�1:���6�q[�f/2n)]Q?6�%n�-\%UA:M�� Gen.�26�!^L1111-6./ 8%hep-th/9406066&?�ĵ2 %��.:j!wufE�8#�$.���Gogus�:{ �TJ � AM22e�%f7373-738�uk Ques>���4Daskaloyannis,�g(Kanakoglou,��,Tsohanatjis.1J��%Q t 41e=�V 652.��C. kY%q*�� rpre���Ex�7�g %'s�F �a ��c�"2) �I�1 260iE,9), 437-440.�ei�!�cmp6�!�~A%���u����� is�!�"��� Alt"ԏ�e*�D*�=�{m�A� 2n+1|2m))\ \E�Commu�pE�) M�19I��429-43�jUI�dS. Kamefuchi, Y. Takahashi% .pAE.f���Rq�! 9F��>2�3�62�(77�BQQPRyan, E.C.G. Sudarsha.f �6�AR!�x Ring��4eL6�206-211�PM50GP} A. GancheF.A�.�X��TKM���.'%V2�D80) 797.�RS}a��"=")L�J�N#.�D�m V.*� feldA 6^ɢ"���i�m�Ǚe�;s1>�HK��ng֎9of���(ians, Berkl �190�A.M.G;on (ed.�0. (AmeP�aS Jal��iety,�v.��1987)� (pp. 798-820.�Jw� } M.��%�dp'c�a���$U��eT�wYang-BaxR/3,YE%���.6]1 5), 63-6.��eo Fq�A�N< shetikhn L� htajmv6�>g�Lie~ǁ��*��6 i��iz���8��178�9english�K: MLerVrad-Jլ1V! (199��196h���$. Khoroshk�V.! Tolstoy!f�� ��iÓal*&~�� ed*2*��V�n��a1�, 599-61� ,\bibitem{Pal�4} T. D. Palev, N.I. Stoilova. % �On a possible algebra morphism of $U_{q}(osp(1|2N))$ :Dlonto the deformed oscillatorS$W_GN)$ ���{ \em Lett.Math.Phys. \/ \bf 28 }(1993), 187-194.��% hep-th/9393142 \bibitem{Kac} V. Kac. {\em Adv. Mhc6b77), 8..>@isa} A. P. Isaev. BJ. �AB9} �46), 6903-6910.� %�CP�Chari,b�ressley.% A Guide to Quantum Groups. =�0@document} C�\8style[epsfig]{ai� } %:"�aps,manuscript]{revtex} \textwidth 15cm \oddsidemargin 0. '$height 20c( topm $1begin�X \centerline{ \LargeevIntrodu)j��Random!Erix Th�$:�D\lCGau�*n U� ry Ensem�` nd Beyond�6�0\vskip 0.4cm Z` Yan V. Fyi�683�6YDepart!�Ak�:hematical Sciences, Brunel �!ersity,}2�Ux�C$, UB8 3PH,�(ed Kingdom.V�)|abstract$These �4 ures prov��an inB al i.�iano�fs !I$tools used!�analyze ��alYperties� eigenvalu )�r)ܐHermitian matrices. After developing �Dgeneral machinery\orthoge�Ppolynomial method, w�udy��,most detailj+(GUE) as� aradig%�0 example. In��ticular,d�discuss Plancherel-Rotach asympto��� �e �s��$ous regime� employ it!spectral)osis of�� GUE. In last�l!5course.�g1G rela%� betweenVL �chaAEer�6�of1�1� which i<, active area+ current ��arch.��2�\s�u{Prefac�� u�q�%UBJ0or real symmeAU�8 always played!�0rominent role!k!8M|e�A�applic)0%zN�.YV�lare uniquely singled out bykfact tha4ey belong botha^�familE�inA)a!?e��s,��1+ ɶ8independent, i��lyA�tribu�Q0(i.i.d) entria�InQ1,!D�� ic�tre�ose two ��!va�diffe!�%�In�, all1�E@x tech%2A@4d ideas can bem�clearl�(consistentla��E ed u!m9� casee� R��!m!�eE�,4we mainly con��rate on�equ��A�F1�cu tcorresponding probability den�� fun��, leav��as��1k$of exploitC.q9� r-J5�Under�0se circumsta�� baRPsa�שCadequ �eI~x  u�%nrelev� �� A� . . Be�g)� eresA�i��imi!��D �sizes!� will�+na�E deramoun @f time investiga!L�����ofN�, si!l�lat���A# buil!� blockEa���E�x 1�"i estU�2�ourQ��� ��}why��T6�.j of B8%Oces tur�ut�Xb�)�!�and!?/��toA�-NM�make a!� tact��rea;��ult��!Cdo!:��m��pA| quit�u�5s��;I rnot try��e5ya-e��sfu�u igor�,�ity. I!ther !�$mpt outlin����cepts,���"t��a� efer�8 a good illuminInJ�a}�@of. A much more �A7a�ed�osiựfou�()cit�bliter�1also fr��a`a��inher;a n��yiemann� � from!r u�ly�&J truc�. Namely #  c=�$in a $n-$nLbe $(x_1,\ldots,x_n)-�letBk6BsJ� thisMbbef amea�z%  term�Y2�$(qx q_k)aka n$ aa^x_i=x_iN(i=� n$.� 9N� Hric $g_{ml}=g_{lm}$Z� A� �}.�99t:�acce3g to ^�2]�I�$=1}^n(dx_iE�E�( m'$k \frac{\(� x_i}q_m}dq_mI�)^2 = >,l @�n%{+{l}J� More�7,�ya=A� !@induc�hAa*� � gr�!n asur� *-Z�volume�@given byb@D3} d\mu=\sqrt{|g|�1I�L dq_k,\quad g=\det{)E�lm�)_{l,)PN�( For $k=n$� re jusiN2iar�S mula�\�I�  �associa�  c�� >�nyͭ>. ��,p $n=2$�m� passI�^�8-\infty0$, $0an,\theta<2\pi$z $x=r\cos{ �$y=r\sinso at $dx=d21-2,d G$$, $dy= d2+2:,$y�U�s��j by $�<�߭�,=(dr)^2+r^2( T()^2$. We fi� V�811}=1, \, g_{12�'21}=022}=r^2�!�)� � : h� tq� e y new2��$E�rdr �$;��8it should be. A= e si�stQ"ra ``me"Ir$k�� [ ) �db� l_1}&0p 0&e^ f_2J[JT T�:!�"�A�$13$& E�YN] hIQ fo0�fO5!K!nd!�HJm-[q�.O+i.Ge�_1]. &)#(!�_1+ )}[- O.@+i��_1+K).k��\K JH_2)} �NK I_2>K& �:�z_2.M]w�_�J. * ��y<%!�6R�e� B� f�6*'NUU* .� +1h� 2  ^�+R\,��_1 )j\,�ph!sJ�We .  nonzero"� B  tensor �� mn}$( i�� ����� ��g_{33� g_{44}=:��  24� 4�,3 3i��*r � d�� nt $U[g_� ]}=4A���AS��Final�. .S m6#g( ��$ �7(e�U}))�)� ,q�-�9�1_2J�It��.� S� � abov.�/~,����ion� th4 � ��.�on�]\M��V}U!�� ny fix�n�� x $V�Jsa�%Vr�*e, Eq.(M 7})�"� Haar:� @�W0ll�us!se�sevw"7<w,. Let us no�n�!G$N^:�suba8*�&�M�-6�83c.�c ofOq $pN gclL< < H͒H�zequiv&f%�H}^T}$ As!��].�|%�n *�: y)j� � =-y_ $. Sa.M &�5�B8u*Y��andF� N��ce��Z�)+8z�H��%Y���}! {ii}��2�irwritte>( �1at��e�e� AWb�#t����i�"F, �9y>g H.a�$6Yf���9��UI�\Lambda UIO2 !m�} (\l7&�N�ImA� I�I}R; e� u'"�Pk� ,\,k"�,N$h 6*EG:�x,��rowU�mb&� �T:; a� s. G�(���w %a�!�ll 0�* to b� (non-de�zte). X ecis�A/�ofi��� �!���6E6i_n nd0uYG6�Q��(l>2c(X�"q��\c�Deift!� p.94� ,proof)_ =M��� zA�� ,Qtɴ��, howa,�#one-to-oE&n��Z_16F c_1�,I� U}_2k %2%�XfQ V:.  �"1}(N� � choim'!�phase� H �,� oa � ��%S9 ��� havBW .* A`tM!�AyI$��a4 �!Q\ qiW$to or��i1e�� .g. ��i� $q�1u�2< ]�Our nex�%askA�to�/����U�>] SJ�M�1��"@ I�U�Q!�end�*� �sg� deQ X%Q7~i*� a�fur!��$ loit��dIVM�^�Dm= �]+*=0pT2 lead� b� � 9�a�[ 1.g{*� :F -�1 �V0� ]J Substitu4(;!ex�$�0!�!��0n.o#2� ee "� 8})I��+A�short-h!~n��lta �m�-E�{!u)8si6f~"anti-�}- Fn. :[^*=-\d.lE`arrive aA^6 ��6 [%�( �5~%k 26 /2��;B�.� X+~E ( ^2 ,�fdNT ^2-22 I4^6 bN�$Tak� �2�"un�72�� pur�� onalE-��LA>�commutm7a�a4�V�%E.> �(5��Y�$3}) vanishy/OR � A�,��ird�t�@ Mu1 en a�%up]  equal�#['2z[2�2Sf- 2^6�"����8 U��Fj Njii- iAz$OE�1e]=-B n"� i�� j -)Q�CP>,� " toge��� AD firs)p.(fiv��f�0:��he��x".! b5^�5)X�d�i�+ "N~ %l�72 M!%%F� ��0� heBE&r $�4Uji}Z}$+�1�X\ ��imagin�6&.�&%lta pEh+i qs'� 3��"�� al�5"&� �J�*��H}a�*9' �uZ4u�3��to� �5s@j/&8�6����pr�U; �d{\`!M} �U})\,J��0fa�,$8U)$+�>!�!�  � �$pen%Qon�4��$U-$vbl�AA�@�7edAI� � sh�$,aX�~%F��*U})&�*�..�(up!��0�.`orF� &eJa�&�A � I  !b�.!6g�.�.�$+� H04[ B�%a�0r�pos�% ,�e 5j�4( (p.d.f.) $)`PM$E�)�r�*�$BA~m.@i�b#5!�>cS.7s P �$&�2+dn!�seems"�"�� �rP&. 9��.�ll�e72�'2.%F�=%  P����  "y�ۡA: easy�9-A���&�&postul��of�ce"��$ bt5a&�47$N$��rag$&> H}^ny n.� (A�G.le�Bof EO I�)�coeffi ="# b�4M� !�S9�  hIe�*)aq" �of hig�3o�a�2����- }2�low�"es). Of��i�(r��e�-�6b� 9} %�.E0=C\exp{-Tr\,QIH})"�0Q(x)=a_{2j}x^+s +a_0b�$2w1< ��.s $Ll�nd $C� �b�ant�*j}>�Ob�Ai�if�Gtakf� 10} ��}+bx+cJ�t� $� :$`I.�1���uctbd1,P#ft[ ix^1i}+2 s( j}�'&)iq]�"b*i�i}cN} =^cN",�.N= z -a 1 ^2-b q� �J !K. S"�9 same �i�(is valid���(J� >�,%W"� 8a� 4onclud!��4llSse�s8! s� y85?6 0)) �5a`2;-50ed��A  8W'oeL�4aatm��se�1siz(aneously} �=��9&�"�IizZ?\ ,.�de6�< �5��}�%��7: !con�6� It@ '=Ro��I�ɇ4�=B�'�Z.bz.nd �AmTY�Zg&��)f�, ��j��F�� �? f_i(�-6& ^Nf^{(1)}��#j})2a j})J\,!�)�t�k�}%�IM?9 ily}a�e:��Bt)=C��aB-2+bH}+cN\� )}$,e�som�t ��>0fbc� A�of&�[��b� ;�Mehta}"r�" illus�!�6 main�!� aG$plest, yet��*��$N=j1m[*h -)6:, }5&�by W2�6��n ���Gu�22�2<xQw�b�GD)�) 1&-D*\13&1E@ $-�$."5to�-=�1 2=0bsm�Q $ a�l 1&�a4})�.approxi�A�J�"^:&�"j�bA�V  x'_F&  2�:2} \\-i & 02N;*f +xb+2)%12K�3F;y  �x_e-"11� �4-z;�4� K6~F�JR"� kept��+ F 1�[3�!��p+>w^&��f^ U11a})��0[ f_1(x'_1)= _1)%[1:?�"1}{f_ d {�"11� ]0�f_2[!Y^2-ea>"�8as  df_2 a2O#���#���12}k12k2%�!�A�[1-� �-�) o~=A��d2 ���^{�9�A�21 ��O ���]@4��B��� *QJ�@v�nce i��$!�� B����Y{"XI@�b&�&:L%vM�Q�#�t"N*�2I�ifAg�equa�b�=1�.2)�)�-n\lnEg-j 1}}-22 2+R� L.� U2}�7N}aI��~re�#Y:ne}��{1 �1}2�a �1}���$f_{��l.$ 422 4a2!,:�(�[thu�� !��YA%�!G�:��J��U*K��S:6re !�ы$f � .� -S>c � Un}2 1-i\alphaz21+ �6k w3e�"q  ��"��3=) 6� - h=Bf  ag� � keep� >�ak� p#8 $ W\� . ��in&5eci��<E1 �T� v�� "FD�d}#1(22}�5a>�!�(A�l> " �i�� off-a"�A3�^Dqr8� �,12}-2 �� 12M� �'�7�+$�2�]FF�0�.*&$FJ= $�>mbd 19�c, afd7� BDforwardU7p�(,a1�c� .w1}{ ӊ� ��1}{)>5O�� ".a9F^preN,�H$N]$ �3 �#jF�y����#le��! �&!T*z }�[��.�&e:),:p,�j%"�as�.ul ruJ"�$ N Ţ$thought. 2@Aon�H�Nvokx�S!�`oQYG �kW�9a} Sha�( KhinJSaJ�F%IOv%TRQ�I} [{(*]Y6B any r�NQG�f� �� zV�=Bt*�H� 2e{n{BA�:p��R")ex�4*K���Od�A_1��p&(p_m���D mp_mI p_m�$�,rete eve$1,...,m�l Now%�� argu!� n�to9(�&24���Ma&�=N)*to��E��minimiz��.a:�ita 3er�K cl�CdY%m�(H!&r%�e%���]Ru7 ��oi�� trai!ensur �!b� �desir?�L�V. a.9 �<, ]�*��N quir  �+jX/4g�N5 S=7"��"�#�H},>%@m�E.� -XaVescribedV, �[$E� :^�=b$a� ^(&�#a:E�0�2l?I�?�`]�%�!ex�"�.�>�& M\Ia�H�ncorpo�rH�M.�&E�M� hproced�G J���Lagrange"�6er%ynua�nu_d(� kA� T �mX^F �'E�e� �ea��Ld.�\��e -�) %�\{�BF}-�1 >�2>1�\�B� Q)7of� �B�9lta� �cal�V�>��[ ^#4�S�#Br) 6�"\,.9=X1/1+51 �iI�2=0Fe"�ca�k\F�� �\{Z�+N�}\]� gi�UE�Vo: �e[eZ�� �(wV@eU� $a,� W �;�/7����!akbW�Im�R�R ���]:e\��3��6�p.68.} "l;�Mus�g[�an)�,N�aloR �!"�+![&� E=Y��lQW"GPa Brow�N m�\2st 4with,wi2/a`4 whosn\x!��ime $t�0�1��by�l{$ $x$, evolE�="G& �"#I a�#�{@"$$}{dt}x=-x$q%��[a G�o�Z= \x� $x(t)=x_0�t�toH r�OW�libriumKK0�upp!�5 �|5 �7 subj�7�Yad��v=� whitA�iO\xi(t� ��!��� $D$ \foot�S&H*@A� l bu�n�<vP&fbA/H .t�Pss ma�[ helpfulnt%� not n6";EA�p �Ytocha�dNes.�M�e0vA>0��ge�M\geH ɍ� *�#!_k!�\3N2/\pi}S $n=0}^k a_n&>ntX:�a/;*s# $a_n�!�&CZt,y**�oXth�,7' $E[a_n]= �E�SZ ^2_0]=D/2�v[n]=D$� $T n\le k��je� �'a� �W,��it.�Z9 fk\to *NA :�_�Dirac��(t-t'a; ��9��haG��!�mo8@ {[(k+1/2) F]}}{2\pin"in{ /2}}$}&'�2F a\i�aci eyE�mb Br*�u�+iA E_{\x9,[ Iae� =D�{(t_1-t_2f$ Q[  &�)V A��,x �I� na��%�> &ro� _a �%. q�!2p!ityf�Br_ �\exp \{� _a^b%,)v(t)dt)0\"_ @1�D_=<v^2280nd&p� �"�&�( (smo` enough) tC � $�e7>=s�!dir�egenera��A�!j,("c�Mg5�"Gauint�%�{nfty}^! \, � dq}{�� \pi a}}\,   a}q^2+qb}I%  ab^2!1N� �#!�(Re}\,a� [%1a�x)a�U $ba�Qmnyo en��1"5M�QR�uɋ%Holu.A��"��V�*a��B�#l�j�-Br3����E�[x_0+)�,0}^te^{\tau}A� )dI�R^3M9��Q[ouri� goaleQ&�f *� t,x��!6� bZc�S?(�K$x$8 9�mon" $t$,� �now�P�3t� $x(0�q0 &DasBc(]NB >c1jf� � F}(t,q)=6W!�iq!��'�Z mDqA�4}(1->2t�(\aR:#ob[ɐ 7Eqs. �D��)e3�5 -�-*�Rrec�1 Pepf��!�!ar.bFourier&;nE�0) P! x)=I�B- i�*�$�Kiqx} 6�!6P &v�c�bD==}%7��-f\��(x-5~i)!|2> RC �ula&.Br5i��'3\Ornstein-Uhlenbeck (OU) riz!}Q�A�==&3I��Y.�1 �an O-U��. �dfac)B;$=s&� �B�rpl h��``kicks"�"�3� ��per!  a kinQdJ I E�J *s a $xJ 6�. e��_�GV1w he OUQ�0``forgets" ab�b�Vi��s� ny7n� o�-nry}�T~ -* )F�kal�!�8gionn6}*�- t\to� e&1�-E�V�xE�v�C�hg bac���topic?]us&�).� %LI�FY'" m *o CZ�Br7az�� TF=�"i}� _�C� � i� NF %�h� st $�F$��r(�G>�j �j�d! ij}(t), \][.5L)=�H5b 5F�c A�!Pivm� $a �<�/v$��be'� ~ nM#�"P,�2nakb6v�iut%]�U�. s��bRe�~ ls �ysn��06* xi_{MQ5 ) 22L/=2X ),�O5j �U>Y^Z gma_1�*� � 2}_{kl6o p\s @, 2�8_{i,k j,l b��$:�-a�S6,i(0),A�j} I@(0�0/��i[�Zho+"�A�R�$H&J ^{(02�&&`EE�1 Re}/CI*&0 �$.&�c*!!j;(A� "�re�� atxF � �1t))�K ( $t005 &�[:�Nj�X�,|:\t�DH�a)%�����LX=�4H��:� $�OOU-typ�ulanf=3*L � s C'-�9Ha�K* ^{N^2}VW1}{6�";% sBH}_0 U3t1'rqIn�1!����`is1��erg�o a���_t-$.��5i�%b��3J7x3�%C>�D}�H^ >�.�/ �Ii-!/+;&� "�@��oza"u"E�s0X�X:��bari�4�ZA�[&�nl�� a9�c�r&J.,+�>X ��u�� m%�-e�E stT$e�Iy �kdefc:� dynami�l�%i*�7}� ū�^ �1tT�3*_Xasqft82�6 ighl�>�plr��;�irp!& msk ques goeOshv� �*entE] D�fP o2��5 V�u�3lemA�# peci�D!!-;d �͍�� HN0�&�(: �#to2+ai����q# �B�$=���A&I N�g"�0�l�ni!4Siof do���&&��2�>6?2\K. Beca&�S ``O�"�," assump!�e�NF�&)$g* [ *==2T %�!�``"�t"�b2 $b=0$,hJɱ!�|�"a�iF41^ i^2}��L�,�Ms�uT ����cF�@} ��:;��1wrM eff�uvas!#or�q>[75�1ColYUJ#�%�5�)^GA*clu� ,�nr ]Q.��;7-,8E�� no* l;�t�kV).JPDG}*� 1�F�)�Wm1 > d a_?,.�QUi�$/# \� U&@E&�D�,fVx:� �L�Mn-gauc{w�{�;�?*�<��6� "�Av��0``Jacobz I'"�;��$���?� ��>[PY$.� �T.?��l on-t�`wa9pIG a�$_M�e g��o$regX�oq KM&:Mi�h�aI ly pu�inc�-��o�>. e�!+aP%�ny�#�=}�� f$ t%N�!��var�:&�M,Iu,Q1N� e�f��  "Ed[ �R}^N} fU�F^) {;"p n&Y�\ ��ZM�N� ]g+de,���<5�A  to��I+"MY ��,9�!�A8%� )�}a�umpl&Z$cu comb_por�Ao�j!cN^T��.O�*nex0&A�b V��"�se���A } of s}&ZF �Mp a+ view�'� ' !=�! a few q�i�%ve�/ s f!4eWt�1:Cqf�/�"! number+1�5on{Chy|z � of S!��SKce" �rB}TA�aU_2MTY��TC)���\mB%"g� axis,2 V#J�un(JPDF� [ &� Q�n�4,.�y$d@�;]E�hFa� ��l�E belling},�"�M1�= terval $[V��a-N1]�9�#� R=!v-�+�2]$�*"�#isQqN9�4N]7�?o�qI$�d��exl�%��)eFu�Wst<�R%�V�.F!�e�X> � e9IՁBQ� $�')i\xCre�*�t&�&���!��r)� }L&"s},7"��V�2( �� R}_{n6� �!��)5�n) �/$N!}{(N-n)!�JB�ZGN) A� d\ #{n+1}N���:�7���,#t-t�!xq+p�=(� "K6er-��aj\5��Gz7!F9E H+1��%8� &; J; ToA���'� rpre��os^ R;�, !0�!8u���� $N_B� 0��->,>a��+nyE�$>R�a�} (e.g^���a,b]$).�$\chi_B({b�BUH"�tl,X1Q�t�)$x�]B$ ��Q�Q wise�AK�exactB~� rho_N��)!1e� ņť��@S"Bi1$\ ��axiutQ�&=ly� &��$'px-$5� $:�=.z 2�&�Q�"j{!��- �):Vd � J�RS*�naBjxa2 !\noMd&&bBy�.Cp_1�#in:�_1)�9 =N: 6�;�,)��+BD��}�V��j &&�r�, 2�I�pi �P�b��J�B�V�"�-|I� S�Zf�!!���\��*{ N_B�B�.�m�-�ofi� B��� .�q�L� >L:d1):2"� �B2R�]xQ� _2 =�!  s��5�FgI�����a && =)tY`\ne j}^N:�i>�j)&� 6F`���u���5��Q�����>� /�!r!d_{B B})L���3��air����M�FA$if�3,*�!+1+ɓt�/� air� {1,2C � {2,1 re b/(c(YDJT�<�3?-�.A � td.. ����w�-t�> +of&" 24})��^e2�f� R}_1Q�,)$ coincidesImeae!e�-�,�Q}�N a:O5kNN .�ur�. � 8��N^2_B#/^n pA �� /R&2 'a�6��6')}T �eu�'U�u8��6o@# :@�!.a����Ͷj!o1�*=6'j�=6')�H9inc}+B/���Z��ᝡ<^��gY�+�/ R}_2n[ '*e -��� w:�.�ra�Vs$�ave�RQk_B}/*�����V[Jb "΋EW��to��*�Aso-&'``���,�i�T&I ��S�! 2(B)]W �gL[6�\�.^2$2�2�<�� {�…���(��k0 t ��. &�j* m`�}s�>V�N��[$6�9�-U\*� Iq 5&� ') - V�\�3v2/_B}�)24 Y�Fr��w�M^P"v isAZ���m�!p=w& !f��lI� \�<:0!Q�_N� d_{k��@eft(1-6�_kX'����N�ղ�,j!6N(-1)^j� b� ��h_�( ft\{� 5]_1)"f2v٥�\���!V 2$z{2ɇN�  he $j-th$*1�g%[ h_0F>�Z,\,h_1J)5Xx_;w���Mh_2f3�'3x_je* )i +�NJ?x_1x_2 +x"�NowC 67!� NoHV� A��.� � %l)�]Ejj�9�kEZ B�!�]�9�JWI��/(N-j)!}G:��&Q�jBYku��jq��2�j � J�j\\� 3'�!,_{|x_1|�{}N�Rj1 ea�#7k !as &r r8>#�v��29�� gu�3s,� f|* н *V %X)c!y��~j��R{ M�y j\\ A ..sF� \\N��Jma��M�= � �1}{j! i� ����J�Thu܅A:.� I:`�  b*r2��.�A��Rf ��2�F�>���)9�2>�}^{B.��n�J>�8On*U "' m�&<%ם�o d?�� A�� ��[$�!�@l�\VU.7 .s s<� JPDF� "�)tD�g�V �* � 'm&F9&�(�O: �Kncf*�o�#&�*/'of&@'�$�� >�6�� lF�Axbe()3 �kernelUK $K_n�n��>�XN.Z> But �I b" �(A��(V)usefu^pOinvF>G&CpurFA� �gEN .\^�*0(a.k.a. Pois�Qan�� a\=v0+dB� a"�!["�n3$V!pt5 }Q�A� �u���+}� : bS�=p1��{ \,N*` w�7B�'�Bo<q�I s $�=�<*�<_*�'=1!dA��DJ*e $0� ida 2�=� g�J� .s ej�*�g �.K� &+���Z]nN]:aA&~�)=N\֊�R�>&pZ�1�)�2�� vFU��a�*F�"d �MV8)�� _1)  �] etc..*b%�Za�<9q"*�l��6�,��$B0�^e���zMj 2��_{B9�]�� 4�.w_B}1~/Nr^|F���� >�]�6��..Pn���"c X�e -��� 9�== ]^j�][1:p�;*�" � &<�H�ify%�Sj!� �(]�E I� orig1�!M�(4e�A//��'$N\ggGF&f�p$L\ mpa�os!�I`pa�;� A� ighb>ngmk��P- >�!cl�gP �J~b9DWL"�)�U���61��$= 1/[Np(0)&In�! worda� s=L/ U=L&�Nys �Ge�.�|;�de HP"xA�))etC[b걓6���,F?p%�^|%}hK throug)e%��"q)�( $L=O(1/N)�F"j )�Z�Rt}�B�i�Bx2b ɏs��oQ=�5�N(s)}\aG N\,L�g 0)=s�!*5�@��e�2})%2� "S,� "��-Cs>{[-i�L1DvD ]}} a�:UNv3Ql���F���.5-s$ $� e[ .�b��.� ,&� %# _ht�> :�bc A(s)q�1sc/La9o)sh�  ^(>16*X6K & emerga�' �~��1� +*�+ )e of oN���+I)$"Q�a\ 7� e�Xf��)Dys;N�e���Gdin lc)an ``A���0ng-out" Lemma 9}!�e=���H m!9�-I��K��ly AM0, pp.103-105� � &TgTh �,J_n=J_n(/x})=(J�g)_{�>,���=n $n\n$07 trix:0;"�^� '`3�bf x}=(x&!�!7 ,eg��m $ �(=f(x_i,x_j)�^af�U(i*��AV lex-6ed)��>�3�@;m�q�'!�``�]!�k "a5+j�I3� a�, f(x,y)f(y,ze�mu(y)�,zN� T�&-�F?}, 3& �S�!det}\,.�m-mu(!H$=[q-(n-1)]6-{n-��"� A��q�xN��A�riL<J J^( -1}$9Ɓc5�al%ց2!�n$��$M{2 plac� $F$� ).$ 1 �Y� B�&�R  Q!�8[!� an arbitr>�$n$>&wO1aݡ��DsiL1s�(�On=�U)� [ J�`��>}c}A�1,x_1)& 2)l2 2)�'�B)�Ar}�A t{J_ni$ eV2)- 21E~�2t����87`�P���� �/� v �7i*�>2N5��hQ�<edL$(q-1� ,x)= �J_AQi4ll agre�X p � ��X��DK_L%�one sΛ� .qc%��o�Yteg�ex"�g.��af2sum-'>3pe.�3$PHg)=( " n&c+!xM,1 ,�e�*^#�� ��)Z {P_nMa�E+{ �+c�n5B n�-0X�rha����Vc� n*qOsig�-.4. <w� �[~ !�$K1e%s"oTa�"acYD ��Mdex $�=kև"�'��C�7U�lM�8n�ben . :o� {2_zap!+n� �8ucWed�}�]$d$ up�;!$ion. Summ#upIeo&�c$��!$2C Iw-1}MpR_(1,2,�]�(�7u��37�A* -1}}1�{n}I,\,E�ZQU/ ��!{n4ZY( =q^Xf�!@RVp�]�}E�" is e<0)!A��$q�M 3$Ej� !�5�! !$Mk�].9�y�3A�:bK�2B� [")bi�,J }�j! n�kY=yk6y yjYIke�KnnV ikB`-U��,�� 6���%�� ��A�}:y��'Q�n�kB���k���:��3M]�a�7�]�$&�!������# ired�)y�*y�,~^umL9 �7 �#�Q��E���M��z�Vk$�y~�wv�B%d�W�2�"�[ ��x�*#1�:}k&� �JZ2�J:x��C �$a!is�ǡ�c倡 !7"T ">J1&5;�"�.�[nŜr_Q.eJPDG}A��a�� 6n,*"6 vdmA�� ?^"a3.?)=I�/�/4b&+oE'�amm�van der}>nd0[arinant.jy.Wcan[�i�y�fa��=Ah�Ə,���UEi^k-=�9 k+1)�#r�d� � M>� �z� , uV���Z 0a_1...a_%�$,�<��"<�otDe a� ~�=:�t|[-�_i�}k^k+N �fSin W)�y of m�;th�'k��0^6�uc:�[l,\,l�k�,k�T�forj)vdm��@i:ZF} {a:T}eY�B� c}\pi_05D1)mj& 615\"M-. &.N� mx:�D%�^v> �IV� frac��i�J i_{iL �Tj�'6NR YM3�q aH�H $j_{th�}��JHehEP}��]i�"o�C��Y�C�}� eCaᤩ�qvNu8"IE m �%A�\JEŻZ� JPDA��:� �g/)p�a%`Ԋ#�$^�A<>��fF���]^RI���$�GA}O@�i�!m!���A_JR�&�3� �xf Łn�e orl2)A}]i����L A}^T w |� 0j=1}^n A_{ji}k �)Nc7TI������&�2v�JPD���R�N )Aj.Ti)J� ��9���N}�n�)K�uiUs"z+u�C�5e�� w9 2/n��M5-�} ��')s�+���"�' �L4:uWk�ed�W�""��!�2<�n�L� �.q#]�6� orpa��IԍK)==PN�)F�a�:�6�� �������l9b�6�VW:1I"sI)+ '��!�mA0}1� i_{j�i)�j.�3-9 �+2ڇ0 %&e��&T�=ki}` �Y3the?qr�O���"�Y}��&"G�:%�Is��u:4!Fe.jl=`&2x"�`�B� dx�� �c�C`Z��de� suuf�"peXq�xo�)�?c�P2*(-�m�orp��jA%^j(�x 6��J�(� inX$i�T1,\,j � ��Bl�n]�6�!�*L+r* A� x,y)y,z)dyF,E�kU�B�Q�xA�zU��A�x�{k}(za��A� j}(yy))4y)}dy�&&B�"� Zw0 jA�hz)=���s-# exac�as�|d� �4.~aMer�&OE���9�=q_N� {x)!�%L��N1,)RU1E)pi  ,dx=�0]:Q? �v�_37� �p�f,N�����>��͈���< �<-1*!mB Continu��X�T!'�or�P@�A\1.7 ��afle��.�N E���O-1 E�4\ &=& [N-(N-22"�FRe���U��c9Kb� �ijW�#%6�� n�-,!/k�Gz %>(N-k)!\,[��kY �U4�)$�I& #�G&w��N!�i*` Reme5La�*G�� *m!x )�V�� !: el $.� ��4�*�t��&� i7%d� ulta��*��" "f�y�y &U)"�,_1�~%�,"inmQV� uerlier=23i�b�N� SA� R}2u;�+n� N *K Z�� >-���in"@!�r�5s&Q#!�P�.\��3Mg-�FV k�)�:�*�uMt2�4' mean*,�<�@a��"(A"�tivF�v, 7aS�OEC'&� )}�0-�H %���1� ѻ +� .Y )��6�:�$��A����B�SJ``c_�ed" (6�``<"�i�0!1ݹ�+� �*"�'Y���u�("�{/�OA�orj�fA@JbY_"�?vI�2.�&6j_1)�8^�_2)} &�<.bu�2^�O[��-�2���V�*w*&}�q,9|y��)&�PZ 6 HeT4 O�!W�+�E�nb:+1mN>men2sAt�05$k6lf�>He�22R�r!�:�h_l(x) � dx= � k JC \, 6���� %Rd i�;Br6r'�s{k-"� 3E�:�-rTP# t2k{$f�\�>M�iL {k}}-& "�&4G�  $k>lW >D�tilde{h}%��dx=Rlta�jF�6�ed.q*�d �/heq96l=:�Ch�/[%C.4�q{,�- ]^{1�x �9� q�J�or�w9r.� anPo�F����� r͒c � 2�B�4}& h_eT:�yb�:�>�k ĥ0�nx�:8)G _2}NJ` Gm-�_xJ� T�? �' �Vc�B�M�� {c}0\\ k�\ "�x>� �f�+ iBc1^cb��) =uN�[x�Ea-k P�I���=M �9 o�a� Leibniz����th��_G]a t��a>&WywE��'��bvHeu �)U{Y�mMy�A�xM�%zx)ME�krGxN���ip &""�$xk(yw �th�rX0�w�7U7I� �m*}�w���i&&烲)��J!%y)V;� &&-6�M>C,ƵyB� x)=yN�>rµy:C.u3��zce2upp>�@u��ower k�  ,S ����2� �(-(x-F�>�=Ai-A_k\,�< A_k3!QF�{.KA�Fm!<]*%xB�\�]2/.Q7&�sA. $k$:y �T&c+.la�6y)=(A_2+� +A�-- (A_�� -��-A_4KA6�aA_1�I�N��}}�=�02�0a�vjy��&�N�$�bR2darbou�y1�ya~Fx!�*� n!��B;J6�n![6�%2bn5}{x-yN�od A��<al��t-��ed).��k B�f1}{_ }�� y)n'`=/N^ 0�h�+(y0 �� yf�gA�C�P"(P�84 Christoffel-D)�a��#ea "Qt��!%GE!_ to y�)o&y&�%ͳ�v2mAU3:2͑%4b,_ [='%x)- i�!yAJ� +s"1T�q"���3á�q(&� !"ir 3�og�.g�� �3�&& �E"�`1wGI6}jc�anm��ukF ��xch6u�sha�>or3by�g�r�GA ��>}�2�,��uer��L#�dre, G bau�<�ky. AltHs2�)!�6�ew ��g�gr9� s} �A�*}h&� F8!kyzV!{9���A��f�.�85a�|st �>��//"�G6��"�7-bar&�H���, cf.*0�v� �Vn #V^V b��q2u�>�� ixqN� h "� Su*�"gL�np�1$�P&�. 0b)b�8bV �ep"�=(-iN)^2�� � 5e^>� � q^k��O9&w 5�ex1`FMHYnY6�����>usP2�rA�"��ngE��B-�ma"�A�4oNw,. Meanwhile,�*u�y Kat"� t� c���U�� *�%��a�is��|�r����?\=Nx ��� � N2� $3D�n ,�ur C_�sx*fU�2��x2u5bring�itQ�0bL <I#2�2���V�2)��'[*�g����gxr|.�Saddleu0A��Plafn��M.�}� �L}�%�J, E�tA�� =F\�s:�r{)��p�&e�> k=0,�2D%�ci�% 2PsEdՖ3(fa�;�F �(:��F:S~$���vokAA�r2�B7�grGA(!u� .��х�a�16�CH size��vXSl�/2�.2J�of� %� n N\�G�yi] �����THXm&�N��H@o&tlOZ�H�a xZyA ��deN�� reveal�Nat5z�2��k%.� ����as'�*�p�@�F*�D=J�)v@7x� )�a/qra%�$��i�� k=N+�:r:�^�C���b5�I�of4j.��&XEQ("p r��7T8Qde׳E�e���;�H to iA� ��  8(��� ��:�""^M*{,�$� &� .�.� 9Yw7}�\o�`6 !f�"t�1�b� �,��&f)*���&\-7�'& *�->PŖdN/�U1��N}_@ ]N&�-���'"� h_{N�� ���lcq-7R^���e11�|r� i}saN" ~��^�"�.E- �6�:,�4k���0"r'�s&J �va�aE��j1,&�!�U٫�?���6 �� �-QA� shapu`^�!>��.ocr�a�% J��he�,�o̕=� 1\"�(" �W3 �2� >��E���J"a!!N&.$�&HiV����y�intl )6�76 $�&�N+� � �z)�"� �� A.J�B� q-ix�)�� \&=& 8*W7 y��I���+�4-x"Qe��N� \�begin{equation}\label{integral} I_{N+n}(x)=\int_{0}^{\infty} \, dq\, q^{n}\, e^{Nf(q)},\quad f(q)=\ln{q}-\frac{1}{2}\left(q-ix\right)^2. \end��i The latter form is suggestive of exploiting the so-called {\it saddle-point} method (also known as the of8X steepest descent} or B%%2(ary phase})@�Im�stays�stant )�T (to avoid �oscillEU�M.nd)%}n we%jexpec)@%�!E ribuE8for $N\gg 1$ toACe � a s!� vicinity!�!"0=x_0+iy_0$. U�4figure}[h!] \aserAC�\epsfig{file=fig2.eps, width=4.5cm} \caption{Schemae{structur%�a harmon.�M�.�a!G�ary 9� $.} ��}es �� SincAhey2;isR�of $x=Uez,\, y  Im}z$, it%�ha��nlyIsa�� �@s} (see Fig.~\ref� 2}) found)�A�condi�ys��!�D$F'(z_0)=0$. Let ua6?$re exists � one sa> �u=z_A�cle|o whichA�a�expand �\ \approx F|+C(z-� ^2$,a!re $C=\f�4F' �A:Consider�8level curves $[5Q$F](x,y) =6_0,y_0)g�are� eithUoa�to�eE�,, or end upi�b!]��of���+ity. I�\ .i%�hosen-<-Im�e[� �is]Z[��-)>]=!u(hence \[ 58[|C|e^{i\theta}5eT]=\left[(x-x_0)^2 (y-!^2\�]\cos{ 8 -2\, + '\sin{(  )}=0��] )��9tribes two orthogonal straight ��s passa�thr� the 2� �(y=y_0+\tan{�(I\pi}{4Y � }{2} �)} �,�F-^F+ T)(FF ����>�>�3F���apa�{Parte�!MH$x-y$ 僁�a2�)q�yut_0�toa�8r sectors by ``E@m$" (solid %} ). Dashed%� showsc bi- D� negas s:�) dire" A�9 %�ent�t��2B3!�-D��9H$x,=:�:ES``posi�"��s:}a>ui"�JA�``�" ones �� (z)7end�,(i/ < stB � � $). Essenti��!I sit� happens�tn)�-s!�aY�(pMs):�!���in I� (resp.,@6. And�F iMBA��s ~}%�differaSQ�Q  !�2�1���%�,V��  � F���$��A�decAO� 1�is�$. Moreover�is easy�under� d �A0 !�R R- ,$ will occur�%��}mq 1-�s, i.e.9�� $��=�_ \pi-���7 $. A�iV � A�2�JN �a�Qis�, � by )R+ͥ �e^{-i :�}{.q/2)}}$,� ge� lead�erm-[ -j &�$ 9  origi�u�by exten J�im� 6� �X variable $\tilde{x}=xQ$I$-\+ $ :"� eqnarrayxDsp2} &&\nonumber zD _0_0)} )I�Tu �&�d�P N|C|^2)�^2�/2}}\\�=�\sqrt{ �2�N|� |}xexp{\�_0)�i�(A Arg[0 /2)])\}}."-G Itarnot�3iculta{make ����jB I� rigorous,ɋ� 4alculate systeac cor��E Iv-or� resultFs welleo��&� cas� (several isohd2 �_-a2 coinciE� with�� �o�� , etc., �\cite{� �D}d (more detail�Afnta��ex��o� ��$we proceeda4applya}it��)k�*l, Eq.(� qg}g6�� )�au solu�i�aat)amoun!�aH[ F'(q)&) q}-q+ix=0� $ q=q_{\pm}#2� ix\pm I� 4-x^"< A[]QOat!h�e2areeE|e�� !�2$�M(c =2� a enumeratea item {\bfD} Z is)�introdu $x=2� phi},\\0< <\pi$, s[ at $1i/\p�� 1}$,)+}=a�i( -\pi��� ,q_{- + $. i�^we�Wres `!� q$&�4) �}aPu�� . f(q_{+}]2}�(2�)�O!;e o�h�"7 �\to�$ $q\to�� fty$)0��1P� N�>� . To*:e�they 6 � orYX��!���� #�6�=\ln{R-� (R^2A�)$% A@real axis, $q=R$-. As a&��j�R$�6 express�2Z /al �:�=1)=-��+E��KA�${ q=R=1a q< [:1>�46�0c20% Ω�sE��8i���relevan&"� ���i�2� 4B8No�a�. =1)-.M�co5>�� onclud}���!�1:� ��v B Aq B�D)�is>6�H� e Y� $q=0)%$q%eI��� wo � "� }N� as requir�U!ss�)��{ . C�ing!f''q�-"1+UUq^2!D=2i��Aj�w! ! !� |C|=*�B% ���Vfur!JB��:�+i�[. �o��- � d�]͒Nowa��yall%%$ingredient�en��in�xX )-�* fi� e"4 ��"� to $&� $. F�u�-� _ {3�8valwor�V$xuaqb&�5�Planc�l-Rotach2� m�Hermit�lynomialF �GrotKh_�3 N^\.� � ��� e^� N� \�G} %� \{(n+1/2)!��4+N �(e ��%� C)�) \}�G" �:� quad���n\ll N�%M$c�%go�it�se!3U��>2����b<cicitly�� $x�p�iz=��h)B � x am؉�sA�s ]� purerima� ry�1�u� 1�ou%��)mi!�(.�� 2! �)=i!�� phi*K ^ On�ssi� a��M�!t� �B�s� jus���a�0iy$��Im�=\` �YRe  ln{y�EZ (y-xF$ Simpl t %- gi/  $y� -�$� spond�A�y �53� 2���in !2�R~�  also.K �"$q=iy��J��H>��a local���path go�|XA���intIme &�Ś(transverse}�5�  I�,``topography�>�� e>� �.�s Asketc�in6�5]M�*�&>�5�wi3*lR6~_ �A/r�%ng��<N(shaded�F%gb ae-(bold) %�|x|�jq� fig5B T!�discuA s� z pe�ility!�&�)�ofD gI�&jto be*�of�}�U^mwa nsis].�pieces -W_1=\{A�4,\,0\le y\le E�\1 _2$YrOY� perpmkr�aUUx�%� 1M�oward�"m . C.�l�M:U1woffspec*�>2)� 6�"b�" -i�Ah,Z#+.�_�b+����E�econd�!�/mina,b�:(6C=q��[*�" D., technique �9�V*�" _2} b�e ɏ��.j \pi �hi}}{Nݘ(}} i^{n+N} n�p+N&N&� 2� -2ME�9ALfaa� $�$ ari�!dueQs6�be� simultane&�end� �a�.�firstu�ldoj�$AI-1 A�ca�"be1�eg�.� HowNmn�verifA$at�c&:  $* propto� [u)+ (-1)+  -x) � ] Ŭ��.>-"H �nce�%out%,a*� rec@ �&� beha@��  p"� �� �bI�n bn. �2 =( (EL)}�� N]�� ��sinQ }I�I�n.�), qG , D}I� 3N &� mU�4rem{%�-, \"� b IA�s again�$.� KAi� } $* �  aV�7i� quit�c�Yi[ase, s#��x&2$�K6� _� degene���o�:�+}?q� \A�i$. UK] excep&zircum����� dard27 �&�fails� deed�em\ assume��aU�.���u�r"� \"mea,p ��|�-�cAJ||}ImY#�aa) typical � s $W\sim I�1� HN| �Z$��(regions ar�" individu�!*fs�# yiel���nd."v �`on�: $6�$=|1+q^{-2})�Bɥ� cri &}wo seq �2�� ,$|x-2|\gg Nf/3}$. W�e� J� I�44 P!jP adK%As� m� be tak�'hA'extrac�!�(j2�Z� �AH�+&fx=�s $N\toL�&To per�FJ��on�lA�#�w scal��&�\xi=N^{!: (2-xC Ŗ �!� be fixed *%e�f2�!}��envisag#(%�*� above )�!��6J�a5com�!U 2�%M�.&�Lsp}=iuiIA� q-i|%�\eE|2-x|�m%�1IE� }J�in��0 ��"�"��ai�~(J_N(\xi)&=&V r&r2^-N+`-.��A q-ix�1�y=&A���t_^^ t\, EY t}��:Ѹ ^n\,� � [|N/)��8� `&\{JY-�(2 �\xivAs�&""�&! �"�hif% !��-��}  r� �O� � ��.,, -�t��epf!"i�-!mQy@ z�� "l& x�a!a*�� [Ae�d !d\xi^2}F�)-%� ],A�2 �q!P"�s�(i"2�,6 ��M�*��ing>6} \{)��!q5� 5�2�6B�Aui�� �eb� Ar� ia�.� Eve*�2``��8/"AiCp�1.22E6�Air3} �Ix=RhMu�)�e�6"� 2A{}Nf�\,Ai(!�2 :�S� >��f ik at�2s room/ a �+al � me betwee "�0�2ss3�W)pJ-�, "�!"'&��on8(�&U�� �a��,Q  U"i(). Formula "%�) ="mas:�_n &� j Jd a�an&��aHtatem;(is mo�2asilyiY�vok!OAl��>Y63��Q�aZas��EMek\{ 7a�%{c� ^{-1/4}\p �N��(2��` {3/2�A�{4Q�u ) �Vfty IߩM�w2}|\xi| 4}ɓ.f h S T E� �iJJ��kidAEf$$�= [1/2aY� �,�2 �Q sd*#"� #��v+derivedA�A�e �'*� G+-N2�E � eigenX! dens��E+ernel A�.  Eqs�$# 77})4iheraptE.vely. I�pi�&�% conv!D@0-"randoma=rix l&at� o u�5�a�, �normalizj ~"ity, ra�z n $N$. ��a��*u�&-definular law���(�)Y���f� semia�lim� �p ' 1! &"�5��4]=F='IA�Fv(q !}��� W*�#�<��ofb%�!J&.��M GUE0triP�acone ��%sJ,rval $[-2,2]m,e�� �i&�neighbou� 2x";8/ ``^ nal" �f�� (q�2AV Delt}�NV] }=O(�}a�see 2c 7}: aŁwh=5"fzf�#(ently refer�Ot;�R"b��12trum"��� �� 7:� :A��>��. SaN s a"� spacing"V .� 66"� N�2% 7B% E:noar�=A same8 tegya� % ing, *'a��:a��%imi��.-��� $Kqb,�E')$��e# goal:���o�(�.e2��.�6d -1� && h�����'��N�'��S8 \ &&�N ���>i��, '"m+N�#� 2�+'�s�[\ŵ_1^{+�%  2^{-��� 1.92 9��:�@�^�_{1}=\pm ������- �d2Nd'n ����0'��(C nex+pO @"u.� si=�&��')/�$$ $\Omega=  .A�"V 9qbe�E�(�!$��� ta"� e1���hoice���/+ �t����~ '= 2M#�Mphi'}]M� 4 � %/ \psi� piV������>s �;$��$ -*�] �� N? l]s��.�� �$ ��H6��-I thus"�ref|��"i@"7�el�.�'�2w8 ot!fI \oA/NI keep� �"� >>, �5s�>t�0e)B A1��e6wr�1JA=N\beta+� n+6�si6+((2 �%�� !�i�0q�X\>(A H2V9aUW�3,�preci>/���u*i܁�a�7�I�{ ) �(4 �A�6�)U�F:[�"V���_1qY_2��] &D �q_1���_2} 2 ��9�ss 2}-1)�)$ ( titu�+� thes� #s back� o&GA�he��)$gew?�V�2f�>�')-.R�-���� 2b(n�2��z1x'5w&' �C,�<ir>uf5he"5�Rq  i48h}_{N*��:2.�,$ w "�� �,�a�!}>� [i�*6!�e�1 :2AG� &**D �()Be.�6�a�Qu%�g!�> ��/KY)&� } N�]=K" E�[ Z� a B��-J(rWm�i r�"N9 �_$2@Ź!0j�Bo�Z8�k!H�hŤx is 0as i8as 6-��ED� [ '�&e�8ͺrange $ J 5 *� � � "k�#yH eque^� ``�)�"b�HavEbt ydisposa�1l� � of �m���"� E�!^twok')?A�r_Es|Fimpor�. ��*-cha�er�Sspe�!k e.g.``i<�< nce":sigma2�n a�t�-C$length $L;+m!R2/w�� �p "��=!��[:�0)]�*�$��"-� git�> ely emplo�M��m��i��L�y1be+2@��!�&�/8aHR � luss3&�Y_"�y�g1��ay�� afp%~s�+&>&& \S!�_2(L)=N-L/2}^{Z�dmL -N^2@!1 7 �*FT' V�R') K^2�����&& =s�s� du�^ �+u'N� (u-u�JH?+weJ&>�Y�s�"� .a�pu�rN���R'>_0�rA7e#$& ����$� n �&MC!#Fu=M/is�6' �E*�>�ca�!i�q���s=L; (cf.� simiu%>d�L�?,Poissonian s�jX�"hole3})$>o�!�+2� t7 w><) $uB2=(u+ub�r=!���"05%F 6at, %�6�\�8v � |r|a�T��F UMakh e fi��BJG u�s)]�A�}\,dr{$m� s�� |r|!  (Ad% .��=s-�Y!r (s-r� �J/s ]^Nw"�� e�&l�=te�=M�?$s�:&�,82�PR( it� )�e"�: $2 --��$-F2� n�"{ 8pi�#6Qx!VBx}}{x9=1� re��)i���>^ 6)�2s}���� A'� �E �^2 �^"*�2}IQ�] s} 61� �,dx�" � # mMl &F, grow� garithm�ly�3$s�Wnd�(�1s� %�x%�y u^�/2S(�e�R�eSulazV�%� 9I�ln1+\gfT+1M�+O(1/s�5�0$=0.5772... Euler'&�R~y  "lowerA�j�nW$!7t� S���s$�� un� ed (�M[I� ce� F. Q8�Iulan� �����(&� s 6&�.�5.� reg�� � rGC+=UɁm#�&�>�Mof�l""{ d�U�Efl�R-a�5<� !�r.3�6)'� mv�w8:wa lY�-F" ��f�$)� (s)$�I�GUE��~8us�Nar Q-.�:�� um�~" fig8B�A�) an�B"8 a�*�us�F�'sta� 6L !� sa-M7A�``���ba�7 "- �E./��>inv�X]O_J*�Y3Fredholm�F�=nx;| k!�&.H4�2R+}T�Z�' very�@7t!�AUe0proble;�;$leg"�'u�*!Xdv!�d/G teG6T$L4Riemann-Hilber"�1�GDeift}.�T<<qu>!ebHR�A�8�4&1s�#���i$2}{8}s^2*��%&Ga�9E"cayDuld��h,ra�Ee�a�1�T��;HfB&2�YJfX�2` full�0�B k``quasi�i"&�Q##%�$#I�ume��&P" E�P� A�|"e�%Mc�%  already%�+ !�v�(|`` oal Q"�' (aoe]erpart-�PIPB"&�a�<e&O)26ch� A�basa�ly �@�/c_+r&�)�0u)�'ͷcer�A��) "�H modific�Q�_��$-N6� � �Oi %lm�B�& *�#�22�22 !I�@�? mulaz!>("']�R-��z5 mRr%2 s� �U��� *|8iRim&+J�1�7a�at� �:ub� :} Zr7D&�"�!M5A�4s zeroI �6le�Rou��RH���� � -to-6�3e�T�6o]����#(3but� �%J&s�,l�Vl�f86 a � d@U) rou@7nd�Rsi!s"` r6z.9�7 combP -M5b .!��intrehO{\-D}_&�=h�*��z$"0 (:}}S }�$�5<�4`^&�  dq_1� J dq_2��q_1-q_2} g9N� �J1)+2WR�w�1�&edYv)1},:�Mh?�'�Nb� , $%KPJqo�V �3eL �Za�"`A{:9 NqN�*q�6� QMv9miliarbcT: �o�L A3m�v bam,"�5 �-V236��our�� �EOY5�3e .2330�91,2}="83_�3C4 ,, -�< E3,yI��,\, !�"\6g6niN]6)�eW\� �ndI �2 �8%$2:8$ t�0S:D*�8�Z,{ akplee� alog� ��ai&d&�:j6 22} &�/R .�xi iiSm`�8!eO3+Hx�6& \times�\ayt_Ob^6 t_1\�cZ3_1+\3_1^3i�\�b7 2\, t_2^2~>2>2 >�<� A� v �J�3�|~zi~\*� � ��� 9J� m6� Mve6�B�[E ),�0��W ,6� 9B� so�&zGLcL96��,�-e_�<n�� �e:.����]�Lsur� `� 5l� E7& volved. OZA_nG'n�saiyq!EZ=(�',�� �[a �Sz!v5 on� �\�����;� q_6�Z�'E"V&ZI ����d(Arg}{(t)}=5�H6�&G\,t�> ͉�4 �>a :WVtReW)�2�9�?-� n ev�,�>T[� �5ER�2u�m�d%-iAi'�P�SAi'�S�q�4>��N��cR',f�M��Aȡ�U R� 2�>� .�Al den��� �6{�"+ =2+���*�:&�BeI9=1v^2-!�-1(8J��u��10:�B*�! "� deZ*6�6�10B�Fo�& xi<0?D� m�n@ie�&�5 ons � �+10fth2�* �Ka1&�4� �&a 2�l�1_i._{i-1}">�_{��/m�t�&�X�&{ ��M bA.Us6;>N�B��[,�  >--A�5�d�sem�P],2���abs��A�&�('ygH6��.A,�.! 7bat:�+��sE �e�u* jC.�N0mXker%� K��$_1,\xi_2)=* i_1)m9_2)e9-21)}|>�%?}F"2��!� �}E�ZZTracyl!0"�3O&�d.�9��*� ."� Our effor studG6 N�8iA�# w�amp@Pre-Ki !�pro�#dA�si�C("�&�� !f"V �s%m0x- `���3�-5s٬os)�:'E turn��!j�i!)a!i�E�~de6L�i��"t��<)[*����r�j,)s�4 W�.r�6�.n�` 1is�@G0� hy hop@!u!1/woJ"ENto many�7iTw clu!L�perti�1RF $\zeta$-"S An "��su%o byears w�A<u1nit�/%�tary-in�$t ensemble1�E� ly achievf6 '�PSi"$a few��:�J�� �fa`1RDb<y�Zset!�*mh}sL pi_{k�pnmotE�w3;�MF1;io*3 ChP$0offel-Darbouxa ^%�.�e�A7��>�$"� �M1`$; d c1})j�'%\sum_{k=�n����y)=b_n\4)(y "n!-xy)}{x-yu4[�"#' b_n$!4s�JW8�% s. SD ayle)SA�.mP! el"�j,!�n &� �-"5 s) *T� -uaLro4Ci� c%�&1� �,-] sidGB�1}) (� '" �! um-^20 �Po"� � �dissatist!� � at� zV�Ae�{A�LkaUXs (�u�"� >B���0�Jep}))%�\avail� I�K�_�9 $dw[) _Q"T%@Y/&9Aa�:wei3�devis]ter���oo-sEMruch �.Ol6� $!Mir.�. AnyFail����Z��"�gjfar b&! modtgoa �<� ����(01. N�Othelessx`me hint �R?�cEwN*ful�Ls�'�=�%~ LlMC�K$�<ig`!� Na , Ie!"in�0)lA�! �� a qufon�z:embe��unra�ed,�1*7a�6��^�"� e�W � Z} Z�mu)=\detb\mub(1}_N-\hat{H�)=� d_{i=1}^N+"� �s>�A��w�o����p�JPDF $� P}( ~&� exp\{-N. Tr}Q#�)X>objecAS9�>�A�o9ir LF�re6s_im�\�:���9var�k� 7. c� - �!tudBre�9ly��.San at=@v�\2H �$m=a ��'way� *� z% ``� " fe�' �a ^�&�X 'N��� ;pionex<paper� KSn}�+#q�0 by Jon Keat!����-olume� m-~�)81e#�%@ or+G%�preY o�8 see �,�F�f(Strahov,DG}��d�����bf - physic# as I elucid "Qgr oi�B�c,�N� w � �Ha�9uht .N0�f=���2�]� ٭iGL eOv�! arbitrEsw�T�J29dg5*.rt j�J �e z$st ��Qis ^ � ex��valxA$bdJ���� E��[���]?X!}^��E�oldo� ;n,N)�5r���I"�e >� is &s(a}ra� degr�>�?�ʼn�� $\mu$9rooX\au\mu=\muFmu_2,)\, N�"9SitQja $C"jMN}zpre� or $C&!�6[g�2_1,...$�y�7L Sy6Ya�Hestabli�tby��p�Mk3�!s :Imu�_:��-hU )G0 $C\!^�9)D��pd�|m�%�#��!9l|c�]]}d-;e":!_.v�$r Mond7""&,*6vdmF Qe�>>m)�E^�c-�f>VcEx<�"5 i�)�2s�32�+�V �W�!bX%�m�eB �VZ�p�C!1)̹`"  �o jp2o�H�ZNm �U�f�d2*-1Z,!�eB#j�6��FZ���"�5� �m�;h�<ten d� �q ta�Y sum BAi perm�R~P_{\s9,}=L[gm�7\��, �;N)$"le'x� $(1,2�gN)2ZO��bel{Z�vz��}(<]||�iΠ��^{07Y�_1}�� �mbdѣ-_�m�5�5J5�B!A6�R3�$.J=0�>�N even(odd)2� ymmetr&f&&]n�]d��i� ��s� |''tu�oA��X=" exact�E�M'e&{�cj7Zo 6812H+1bJ�~ !�!�>x0P]ms>�n" K" gree�Ji> �w^ nl.$Dx��4 o �Armv��hH))n�c}Z.T) f/\&�)MC ]UVv2] 62w�7��]��bq^B� A�A�j E�� N j�b�Z4}5]��iEY��aC�ia�®+1��2��V�J��� '�R�^��selL$�&( �l-��o �b�D_�!�N+� &zH!$�/coeffict^8ATV V�i+j�_{i,jb� is nm sari� po�#v�fD_Z>0@IA�2!1i&���C� quad�m�9s[ G(x�% ,x_N�lB�:� eft(� � \,x_�.^{i�^<� i,Tx_ix_j�5�'Fin�(,vJz~ mu)DUm n� +�)\�[28 r5_cs�&�N� �vUs�p mu^N5D) �I#[� loi�&"Gz6D���3sta�%Z5�7C�1�4� �IEY�geH:j�L�!d �*}t� pi�� .!*sHh-5D_N}}D"�p hf2��2"'Ied��u\Y)b��:�5�,aL �� �$�B�ouv`���mW@e.i4*�~�*t&+W$6x}= $���28x -#�ot�� else,�,T�  %~D�i�D*� a��"� ��8b� 1,^{(m)�Jmu)RA�J �%� . Le�G�!1� rn .7x �5&�)�!���� _~Q)U  ulas]�NFA�Y�1}){�L~3�dA\�Szego}�W(Heine-Borel�#k�1878,V�s= Q�t+)cl}�ca��W r� is hfo �$*A, �l���s.�.ig^�k)(n ��/"�!? like!S�&>#b corrid� C}_k�.�R>k)=6�_1)m$_2zŃ k�.6� �;st��nA�v�K�2.�T V���P�N�N_&�OQ.�2*� JD U"no�$@��!�%r&��aYv1Y>8F'qu^v"*~s-����,N+2"�+J~A8%�4-"Q8>��4%1- ;&�":-�i) vO���sL*�N�A�>%�S jb frac:12�^��^N. _i�) *b9N" �AT] rrepla�Uach�(ry"7 _i^j�42\�ie@YK���AcR�\)j&_i)$ �(eqb(})T9Qu2XRl" or� aG�p*�:l�D!�I� P}��)0Y�11})I� #��%N}FB_ =_�Bt��1F*� � G@"�(&y !:aJ�pg $ sam��n"D. �jIor�a�+�S Z  �: .�Gfb{e&:7Z'&=��).)>�v�N})E8�'�8&~tJh�:2)&�m� &.2 �!1Y91 %O��i[�^)&I{-�U ��b�C&U1s Xu d��Cvu *fb.W.Y4:Z1\f16����n  A� neq[LKXAȍ,s $ �.�O-\B#, �*U� �+�#}�N�� �� ��!-:q$DS $N-th Rlum64>�� ly �bl �t r�0tac^hBy�&[Jy�@e�Y =v�N� )�&�.�� %�52�����1 �� 6�)�czDu�+S.-&����"� +ng.� F Gain�A� �ki f-diar��%e<)�1trC1� �- +u'z l� ! �W/h&� �. $c_k^�%.���piTAk��^ kbE�!,"e#EB��J� �{��5�E, \a �+(v�qa=�'�:}!f�;!2� f�c7 !Z�sV j�}m�� 6��Z�J1%�]�E�B�RD{In*�*�*!��M� Q�6/�u/!T*<e"�#b� mom!>E[Z�gmu)]=8Y�1Gf� �%} %c C}:� 5dfK2K��'t mu)���15) �,"-H�F�V���Rcbe�+s�for�6�VX� �� AY>� s�BH,MN+ 5 pMCE- 'FW"�_6�*^ gef|5`U0�SKl!�!�_ ��is���Aa6' w\e�Z�-R' �� i"5� ��/k�m��ob�?�o�?a���4���� ǭ?&j4NX&6#.�ZQRF�+�Y�e CF5�_iche6%=�Q buil�blockr!X�3fB�.�&1�&G��'<P!: GneP)$ga�1an �~�}�s5k77�E?538'one(g greaߎg*�6s�U�b*�r2~mea^-o�~a�3��j]�. AllBe�Z���Am�3ccSalI�� �A�Q�ug.�ntyp�quanti ]Y.e�e�A�m�O rate�0�<s�s:e ��re�@]�^"$\?" ?&A)S�j 6,N "�24!��"@+�!h JPDG})��&���n�`*�E�� R�f2) &=&Nl \,��22K "�&q+  _N) � d�n�"�!_N\\ &�&A.x5w�B6"i=2}^N"�5_i�,pY.�*�F[ #2� i7�DA�lex2NCae� �� p�C��5FS});�iM?icI�WP! r�7 pa"�6X? �l���:J�V��Z�[flv b?s, - nQ:6 �P� Rpo� � "��i�s,ȩ�&7 t��b�J�$} �KaON,\nu)= �"D�)}{�nu"yf&�u� } �FE[aԤ�9�bb�l& x�+n"�� Z�!�bTa !2x~t�u���?�I(\nf�:$�c.XSM�-~1d&�>p�� $\nu:j ���JIm}\nuV�02,�m�(i�Be� t�[on�""(inZer� and/˛e��n ; �Ded �SD��s���4t>o�p�5��.�a9to*9al�lem�D�i�:[ .H�:funda{ �~olw pla�=3�res�Ls��> $����*- �9)�e� "(=e�iZ.<�*f| VestHpA��si@f R.XHA<�{lzA))$� ??>[�A�;��t � ."�mqbha`�J^="�)`�3�A9R502r��!Trt_}�F2��>�  >P�� ��acces��sA�I\)�mM�. !�c�M%�5'>(by�&} itj4xrho�iY��=-)]\%�al} w u}�Dž�m2�|_!R =\nuNDWc:5�CT9�e� 6�6&!gb foQ_% �t Rc�|"Cd� �(��?�6 below)* $�r61�sLA�]*|=2�,K�=�K"��u��C6�*"K� 2 �F-97 %:erm0 �q��%BeWJAS}A���B��ˇq�u�Wat typa�%�c�H:"�&Q"E�B���AV��.on.�(��1E�9_*l �� q�����s����\�" "� �i2�ayN�>��O � � llq��inR !@s� �.�%��T$�3d� HA*��b"�kq �nu�#Ł.��%C{��*�}} �09k"����n)k� �2"k}L:�� *�k���V � a��~"eiQU!�fYrIf�=�T}� . Wh��p8�A�� , 6!�cN$�� Ep�5"�)v)m+� "�-����E t��#iŴ�!� $k=1�.�F$U! �r�� R\�%$SY&�cmbdRE� i"a2f#F�}7 WiU#P@�u���cb]�� ha(D"RJ=&�X:� ]�%.U�Ii\mY�:�1""�HF, ...�X*BA!�fGAmm;0{�2H}{ 5/K�{�!�@i4 �1) ��� 2�P det�1�1G2V.�5.!ChaBG2*}"�Hersp�Ti�5�3)aīg*�?A�!"uPF�6JA�ueduX��fǸ�Wnowoinser�$`km���L(B �u$-iHi5�&�a#�su��h��r� $2)| 2$�e�?f� Her4W83m*�M =�bm#]{c&,#41�\�"f)���T!\�$Q mu .-N)!� e �!����=o;f 5��!&�Cauchy ����5V!R ��Z fd��q٩2�km�int",E_"�0�yJ )}{{ݥ�~sDi�-D��b��e emerg/ u $!p)n�j�� new�H�R��M-Rx�ory�R*4,��G oser look sth��,�Q5x8[7�� "�fEn�. , $&�=N �^2/2$�:� ^�X%�2�I<�O4� O3Y"�  8&�Ws >K H�q�� �� -p&/-"oh"o �"]2���L�VO�Jby�W�mselvE .�W#ɻ!���M4�or�e3��Ɓ�beׂ��H7I:K�&e�I&�o�+"S &| z �B0u dt��it��\�� sgn}�4[2�n�Q]E�ѳ~]5 [T��(|e�)jXg*�1�9e�Nth�^<,��i�dWex�g���q�A��� *� )�>-$ *{YxpIQޔgaa\c� ��)oa���< a���6g t���C��%�tYj2}-f���)� 6�5��"�+t$� ( t!ecise �-�} `o�}�W&�^ No�7FtNM�cdNour6���yi}=ult��� 2�&�!(*r, lMS�S"�S>�$�|�Li��"R_�3>�-�) 2�S�y�z�͕FS& :� � K7gm^�KEF�|0) &� R�|MyEB/�pi�r}�JSifa�E�>06*e���|N%N%> .J�Iպu , alth�B� elabo�y�.�&@Nbi�MR�% ��m�&�n!3*�B�� Z��/|� h2)b"�\ S!�,!�)� K&6/-� �l?V� $S5�(r5��**wr)}{r}$?��PofJ$:-#�%\v-"��5ti5m��!�EG2xZ��� lays�40 ���Injf!er&O zi�H�hE �``-qW"�"?#�f#k"�m) dard2�"s\"+ [}�0!�thirdxs� el�qmad2e�s� ���A�-!�}*PB�!�3 f��ToN&�. �� AW~ ��}b9 e4!��m41�32A� nu_ I�__0 :2&$ 9 ]"E�a#nn< 62aA_1  S4�� ��v�����~ ��v4 S�7 _) �4 B^� \ .;-;R; ;�2S .�< A>�!� Im$\ ���2<ʹ8ine esim�%w�Qnd� A`�_�~�ZE�FA�G�0)J*�k=\^ ��.%nu =\kapp&rzi�f�t2�y��T�� SF2}A�)AS�nZYE�3!�>]Eơ�n�.��M( �1, 2, �1 A�%�.Ubqx�9U- U )}}{ �G�3)J1- 2)mO( ;1)[ .2b� C}-��E %2e-m� a2)._1 �b' �]. *?3>,i5 $.� � uti� �>�Xg[ (���`�.a��! exer�  *�howE�6�� G�њ}���ݡ�8&�'6�JNch��*(�[:tBT�\NW�>��JX��*�by٨2p});eE@MCs �b),�2)�KSdA�s]velopmZ�!&'Xa(�7�t�IZ!nrrlylDpGa��g�f�&#=m���H framework+E of�"�YT;s @��. As 0bAv��Y�T9,obstac�s��2-#eany�\ns��� :��: &�6s!'c>�� methodJV�um�����r �y fash'��as� n��ti%$tone@��}�*@q� *}^�����pou(by Fokas, I,�FKitaev, \2�$��Dwy,7 el1��a (� �S)�olu!�!�!��! (�[-Hi�yt!�O_��M�>��rdu Fs.,>W �A:|+V)J���� ���� ��!aC,| uppKNhalE�#� ne� re�@��G �,� hMC�$3 MSgZr e_n;�on-ix!� E�$er $n\geq >�VmCw(zMaz)�M4):j!�!i!Jof  c:�)� $�>($Y=Y^{(n)}(��="�O)��cgA�;�Dc�iz% p�M-�� tic}\;� pin}\; \textsc{C}\setminus0~ $ BS�! b�(z)� .��� I 1 & !V0?Z \3&� E9),\;z\inn�J�wmapst�(I+{\�4 cal{O}}(zw�)ZA�(Z�z^n & ��Cn}n� \;\;1bs!\; z �;fty $�9�� 1���%��%t�k��AJ)(zQ�#$$z'e.$&� (/u�8��2}�m�y�F` L ��)I��.� ōeis����a�"�3q�-v"� �R-H S��} MVAa)�"| 6QE5n(z�6f 5; �J$ J (.f-� ^ Y|!�i)" ;z\n�, /�PW��>/�8 l�g9��6�2�8-��"�F&�@�V=��i i [�&�*�w!# ^2_n} $O�n�[��|�H1)%� 2�)�q- aC "C2�B�"$y�K}z"� �v�Uin"E�J��� �4Zv�'F N�%=z$!�� u�&* (�#.� 1kE?$"�1)��kv�N �Su�$���V A2~(sign). Actu�K"!�4���F 4�� 1bH#� &�.�^#B e�Ѿ�G�e� ,BI} deal�~6�QA� �_6t�i]�d�d at �&of vieS  �Q B� H qZ� m�h� em!" gm!�ie�%�su�luous��,�2,ve�l �� meaw%of6 �~ �ict�8)�e��be>~_,Q.�a � `�a~s"��log�7j5"րe�Ve� ib#i�!��%��rV+"�Of o���*� �; $-N�*�e['i�rnny pote*�Q(x�3.�m�V&�2i43�q . 9c� ��a� chin�s�0F� vari ��� �� s@g/H(oM� $�U *� �+:lA�����e%� Zhou�%is*�&at��� book�f:.>� Q5q� mmen�;!u� 8edA�a�;��Rs���b82� wt�v@j[�!�QU�-!v��theory�1xO�r1tpϓum ��b��.� &a��s �V c'/=�Z"M Unit�fU��en��� - *@�!>g���O���� 3"<*)U.�wryU�s;�xOD�7wQ���6v6�i"��օߕi^ikB�A���*e �#$Bi�@)sAFb, T,�sh%Ye&2�b&xai� 0!�:�+��*5i�Mɀ� &�3`at�*2 � ��0Z�|A�– �!�p&.3 syclFR+*3��AiI� ����-|�l  �3�I��t��.w�'ly� [them -� &Q#�P �4}��2� $2N 2�%%,��m���1�%ch}�  o  }/0}_N&.J�� ^{\daggeg( *. � �e� $ 9ja&�+� �x��r3#��b� �Ea back*�V�!<�zaH� !�(microscopic�velA�s��A#Euclid*>0QCD Dirac ope�2I5I�Ver�**0E�i{��j�#:p���pp"�6q<4A�d!��k% *:e�� %)ce6ap��a�pai�F=��$ _k*<�bQD.gOD?;)1�udBz��"1!=0$ ys{Kpeca��*2��*J� �/*E�� sA���P��a"oKT�RM�GUE ]&K��y"Bl )�T2}�q�erAr��ofV%�7n;< �a;�t�GF�U!�>�( of Wishark/I�W}=�3J}1q ,�  � �%f�4%;3�(p2c4-�utsuhA�ex � ��م�I�Śo e��arFe�2� �iA�no=�%��g"�r)j�A�O�x�r*�abA���s](�Be"���6�4l��bsa� some�*J� "soft;zu%HS�. �� .�y-��_ �*# ^E2W �tB� E01�A�:�  t":tsVan�senI�vh����4�� aya� .�`.��Ac�|l!<A(|My*rŘ- !G t� ��veA� shap�!��Fur�#U�ou"b ��+�e!�ac#��m�i�agu� am��i�6ly �/fuRIGer�BAk��,pq qqD, Boris Khoruzhenk#p d Eu� S q!' fruitful�ll�"�o�W� �e�A�6�)X Q I enjo�7& 2y"{. �)hb!�,to Nina Snair�d Fr�.,sco Mezzadri�] invi(<HX: le� �!z��for%+e7n}��t%\tM ow�D3rx3ZG{wl1v week"��pleas� !�st���K atmosp幍� Newton In�� e, Cambri� �FhospitJ�d� anc��s4�rt!9Y�� thanki \ myp�eZ\4ank Guler Ergu��7�WA�c Qpr���� manuscripeEpub��C thebibli��X}{99} %\vspace{-1.5 cme\4ib84{Fom} B.A. DubHn, S.P�vikov%_A.T�mA�,, Modern Ge��ry: M[�$.& (Sp�6�NY, 1984�\�,Mehta} M.L.  ,Q�m1  �?� �` H hnergy ޭ, 2F6d. (Acad��, {91:{O } P.Y, *؀P"�; �.mce$aB%�� ach, CourA�Aq. Li NA�d (AMS, Rhode Island, 2000:�$Haake} F.  , Q�Fum Sig�@W Chao�@�9rBe|F!v99:],Bohigas} O. � in: Les Houches Summer School, Ses�< LII ``xE�Ph�u", !Hby M.-J. Giannoni ea�. (AmX�dam, N�-H��!15�%%Mx��i^C(II, {\em J.�.h.o.�(Xbf 21} (1980), 411--421e!UgW[ G.  \"{f[V�, 4th� Ameri�M*5 Socie�P(CG"quium Py�A�3, PaQd�!�75:�s���} R. Wo3�A" A۩-F ��P,!IM� P�,�� Yorkm8>�˃ Ca� %�(H. Widom, LV �,��.N%:m� �!�it�_munN�H159}, 151-174 (199>�F�tera�J�c�t�/�� um a�.�*�^� NuclM B[FS]M40�#709-728A)93)6,PS} L. Pastu�? M.A�erbina,8��r �Ul��2�>s�*:� d/las%��^6u� �"G ��-VJ. Stat � �86!P09�7:�zJ��}%� N.C.�݁uJ�1'L"g�$s at $s=1/ 7�Co%� a6�4214}, 91-110 (J�� } E�z M�K�cjA}Ie�+�Mr&lexic��ic�ay14E�. Jour�Tb�A ics}�10}, (�6R24�>�DGA� Diacon� 0nd A. Gamburd՝3cea�$Magic squa��0M��aF�F-؎���20B�BH}!EBrezinh,S. Hikami, CbGR}In�S �-��R�111%$>��PP}��N�Jt\ A&(q,$\tau-$g z4N �� Pain��T���@R� !�Zn0219}, 357-398�>�MN.h� J.-M�rmŀY�af�W � t`u�� �m�A"iEJm9 A:)pGenq�3aE 4627-4639R�bAK}�|' %}@E. Kanzieper `` S�� Mass�aO massO&�O��� NoLink"-m�. Rev. ��t1i85�A174-1177�B�SNhH�S_rsB" � ѷRGr�6��:�=�*, �3 � J. �Q$ .%%d3!d34I�>d fluc:�� @x͹�E4 andscap��GŭTraXA!|Ab e.�-�l D�mT_�� [�I� �!�%t.�X 92}: art. no. 240601 �� ; Er��m: C ibid 793.6$149901 (E)%�>�eBAa2Andree� B.D����``Cm o�5a�� � "� Cr Fj ��h75�u 2304-2307�>� SF22%p2�*xQ+i��!ff�s:>� zr� u�)gn�[43-38R�20B{ BDS}�#Baik,�] �.�P'�'&�r 3�O��7a\��Mda9F�4�V36�67�>1BS}��Borod�A�� , A >��:d���.�!;b�-�r�ParXiv:J%,-ph/0407065 .�- P. Ble{I_L``S�a��.Ca}H o\.�,>�8�.��e%\x%ilQ�An� 7+"N 5O 185-266� >v sy�,M.R. Zirnbau��SLb�eFA �oryN9BA>B 40586� � JM (VerbaarschoI�T�Qttig ``N��C�O �in�x= u�Z NUn �� Sci.�.bf %a-4Z AFB 6� Unp O1�c��q�r1 E�6H 61aYO )q<N.4 ��664��457-476�]>:T2�K6�m�f�161�289-3 >�$vanlessen}� M. Vanlessen, Universal behaviour for averages of characteristic polynomials at the origin of the spectrum, e-preprint ArXiv:math-phys/0306078. \end{thebibliography} �document} � % referees remarks included/christof \9�class[a4paper]{amsart} \usepackagemath}> symbBfontsBthm} %.Ushowkeys:�draftcopy} \newtheorem{lemma}{L [section]2# +}{T 4}2proposi7}[N]{P2-assump2,A2+ corollaryVC \ �(style{defin �2C�D.+�E)�AR%���example>E � {\catcode `\@=11 \global\let\AddToReset=\@addtoreset} \{equa%J{-�<} \renewcommand{�% ).\arabicC } %A; newpar}{\(indent =0pttskip=3pt\textheight = 615pt %` Fettdruckbuchstaben xxxx%�ibk}{\abf{k})�ppBqqB� WrBx:xByy% Frakturr�gH ;frak{H>ZgS.SFt6 _1^{PJ&oJ'^0)6�ocalFnE EE<.9FF>E1[ ;_{)�rm{red}}>/OwMO}}MRoman ![6rc 4 rm{c!�2�h} s�HBqcC =C>�c1�B�;bbF:R W bb{R>Ve�(varepsilon > Hh=BuQv}{{Q^E�rm{HphiB�dKe8int_{-\infty}^{ d\eta>uPide}{\frac 1{D^0 + i V)v*\dvb*W�W>ova�va�6�alr�alpha_Y.F,r(rhor&nr}{n6" %2� \phi5H6�i%� sl i.e.\/B�cf}{{cfNeg�sl e.g.\B: supp!�vrm{>$tq"tilde Q>h� hat !>dv}{D^Va(la}{\langle:�rrNP!�P_+Fx61Pvn}{P_-�(op(+^{��.OPo CFHA5$gH_\Lambda�RC Hn}{.(-Z alQ boldF ol{hB calc!�!�cala�:�s�g{\gS_2(y)>(linA2L^m�:GlGL^2>vpE �_: $\ii{{\ensu~th q�?DD .� \pscal[1]25Q #1 Q>�norm}9$ \left| \! 6��  ) Opera��� \def\tri�lop{\rm tr}\nolimits} % trace *Tr{# Tr}_{\C^4�CszDsuper I�_� �E E\begin&K � \title[Generalized Dirac-Fock type evolution � ,] {Existence� ' $-in-time s 0s to a g�\��hanks{C.~H. and C.~S. acknowledge!_ port froms XWittgenstein Award 2000�@ Peter Markowich,� whomX8H. is grateful � Tthe warm hospitality a� �F Wolfgang Pauli Institute Vienna, where this work has been started. C.H� M.LV�by �European�,on's IHP netY�Analysis \& Quantum HPRN-CT-2002-00277. )>h�u%;edg�APART!nt!/8ustrian AcademySci!�s.!�Pauthor[C. Hainzl]{Chran (} \address{d!G(of Copenhag~Depart�4Mathematics, ��Hitetsparken 5, 2100D$} \email{h�@�?.ku.dkW �$M. Lewin]{dieu } ����l�Z�C. Sparb�)Mof.�64 Numerical2>9<%� M\"uar, Ei Pra\ss e 62, D-48149+AW z�$ c/o Facul i=�m�(, Nordbergs~$15, A-1090 0, M}} -�cEZof.A8ber@univie.ac.a� \subj�a��]{81Q05, 81V10, 35Q40} \keywords{QED, vacuum polariza�,�� �� , Hartree�Hmodel, semi-linear Fsa�gabs�4t} We consider� deduced�� no-photonu�Ellodynama9@ which describesa� self-���t ��-�$of relativa�c e Uns,>\ observable ones as well@those filling up �?�C sea. T� 1Q��0$ally intro �by <in 1934$a simplifi!orm. Si�{we � in a6�Źapproxi�Qon,�ele�ms1�� physeE stat��5 are in�Pe rank projectors. Us H, Bogoliubov-%I9�alism,:��Chaix-Iracane ({\it J. Phys. B.}, 22, 3791--3814, 1989), �$recently e� lish�� H� -��$-S\'er\'e,!-prove �f� ��of-E7deredJ�. \end]�d \date{Received 9 December�,4, revised 4�ch5a5 make�{IMa�D}\label{s1} The q��mechan%�I���2�, spin-$1/2$ �w$icles, say9�,ba�on�famous�fph{%� oc D}, \ie $$ D^0:=-i� @\cdot\nabla+\beta(sum_{k=1}^3$ha_k\�al_{x_k} +,LactAP on $ �, H=L^2(\R^3,� )$, wj$P=(ha_1, 2 3)$D $�$E�A�stand' Ԙmatrices \cite{Th}. Its main drawback, p  ay0�  aI��al po�of view%\{facN at its sp��um!z not bounda�� below, sa�� $$\sigma(D^0)=(-\ii,-1]\cup[1,\ii).$$ To circumvt��problem�� �4D1,D2} postula t��neg� e � gy!,t��re all��ed with�U> ea^ !�by tak!�in ccount6 �'s exclusion principle. More precisely, biA�is frame��� free��s�� � to b�led!�be�an��S�r d min� P $\Omega_0=\psi^0_1\wj 2 A�s (i $ $(H_i^0)_{i\geq1}$ is�ortho� alalisA"�5xsE(al subspace2 _-an\chi_{I0)}E:$. �(den} E�xm�$Av then�6��gonADZ� given�� $$P^�=i� �|1 �|.a� �)dix bo of9M�ْis .�%�\e��un��}�FQ|ofepuni��$ity. Howev EgE}s� -an exter%otentials� -called vvirtual}�rea� suchiZ�vw becom�n�� ed}1e stud� i�ola� 8 effects plays A�m A�rol�� rb! ( (QED), \cf� 0GRS, GMR, Ue}�,A� re]nces )�in 1 HLS1,HLS2�$n"�ty�a*�d &�es9!%Kv\ p _ � sea,A�an V�$P$!�.<$ �J 2�") i7terpre�a1 J4a�y'�H RHP�HP2HPbHP>H��(m'P.HjG$PF Our goa�MS aperGtoMma depeW"� S"+ 25 sA�A�2 R:$P(t)��is^��btain��!�VG (BDF)E�l � !( mean-field6� a�i_"5 } QEDE��.b�6 2� Y�CIA�tMlya�ds Q1,} � peq_Y } i �{d}{dt} !0 = [D_{Q(t)},],G I�$:=5 -P^0�<��a �="� R�don8 ��%=,s, but also%�)<>9 � s} cre8�셶< )�j elf:F" D_Q:=D^0+i+\�`_Q\ast)/ 1}{|�T|}- "Lfrac{Q(x,y)}{|x-y|}.1qdef_DQ1t� 5L Her�B� Q(x)=\Tr(Ix) P!])(x,x)%T�d�5� ge, $[�,]$#o��/usual '8utator bracket,[�Z�HB�!� non-2� > s�e, \eg ͶCLB, CG} q% $ad}cVire� )Q"W } ( mea#d�r re� �A%.� > $) e�� �t�mR. W� noYe��p� nt� Q:=0$�bBv3a jionary"�![�q; B�� )5$\equiv P^0a@=��a1Dourse $[D^0,P^0]=0�� A&D veyYBk&-first:�� him�gA�.� . Compa toB�2-�ugh, heo �ed)xW ge term $m+��/�� $, "L 8[Eq. $(2)$]{D1}f it32c �/.5.18QED}. last zofJ���equ� &�'s "S �J*gain "&inA��6t#ies��( fermions. � � �"fB�,P!$"� BDF��in.�ED, r!rly� $a}llows:3%�u,��'�iJA�E�2 �s4 in(�dy�� a) �a�urn?m�&�ns2 %s}9{� . Each  � s can+n��e,ale�'i Akby�-:N�!�n^Q $,� �$Q=��e�HHilbert-Schmidt. I� CI}�S of Ea%��"PMcompu���DdaVb� �3 d�� . Detail)V be f�!�!Bap:�)�Z ee!0%qFp%Wbe regar*a� natu4&� �ȭeU�, S�H h�AY-B�!� noth�& �deriv(`-W�rEyE�tra )� P=Q+� f�. � .�ia�estJ�rf=�9)F�� assoc��d:�{i ��/ 8!4�:!�y]. ASA aris,o o� 2��\�' A5ominot� �jo"���*r1^il,)U��I=CI} ad�?extrem�&#pPrty)�~= -� !� ��-� fun�al��@ BBHS,CIL,I��j-Gf��A?ees u!eQ ���TUB���>F9v� solv�!gE%&� [ �r� H a�s�sk due t< fa� �'-6C��de5 � heavih ly�X�&a�resul  rovi�by V�!�I"!�!�2}A� X2 (a minimizer3ar O AtM%i�f ovedN is6����bSA�:�5i $$ \uF�_{Q}�(quad \mbox{e� �Q=$� ,}O!, thus "P$e�ris��J RYOA� �B/ �-i�e� >� ���o% real.*[addL,0!AJ; &��'% sea (v�a)EF�cor� on���`E�N�-,M , oneŌQ2&Y%-�0,qerfix�?ha+t2 harge $N$A$Q�9ARA��&���6�?^n�dV~25�M�� (seem&CIa$3.� c- 6]eC})F��2�\lC&�_{ "b� �Q= U�S BDF_eq_moZ!s�}, a�$ o�,an Euler-Lagm'$e multipli��K&�a chem *V;&�$�_t� �bDJ1�F"AWtE>be�� posed via�w:- \Pi+ \gamma$$,. =  [0^�#�j�N|�)_j>�hi_j|��iB&� �RA�u�,ed�Pi2�.%Ya*��& 5�;�jaDu�. ���]-, i)heas�R be s�� D$ �$'���!  d�1�&ES� �&ur�3� 2�UZs.89a��thC 0x,of higher or� Wcoupl! =ha��{�4 isF r5 "� as ava���l� &G ���K. "E'"�&.;����inyu�/a%:�1�;�  s {\em a� ori} wa'!���!�ab��qQ�@ betw!�6l�9%(�0. As-=in6*PL BjDrG�� rc��o���!A�< ultra5let mo�!8um cut-off} $\L�,>�in-�U  a$-slo_���$�AJ �E} � � tsl6 ��!nes"� �*�p.�ݐs � a"A4ig���)� shrink�a W. (�le�1H \sim 10^{280} mc^2��I ��� ron radiue�$5-6cm$.) S� n-like �*( would caus�"� un"#w,= �cus��A�Q4!�IET0already sugge� earl�� by L� u es. ;La, LaPo�n Q �%�"w��X(E�f"j A�UV5�� =ju�e�"(f(al too�U[l$" 8 . R%e�ERi#� �u&��noea�i@ is�is�7? P mply%{�fh U�,��earL ]T2�,:u.  5�2�� may arg� � D &>��"� ��q@&4 ��thcive� ao i�\to\i��Iae �s liter�8 se =nc�i��� re%-A6�E�a��*procedKI��� , Dy��~h�!�clA�!xyon� scop���jA~kcE cho�&of"x�0}, �%4arbitrarily} l� 14q��cAv �i9aTHent��rigor�$�  concerE[�>)՝a�!i�|1� FiS ��q��& q!/� validI�e�"hange �iM�}8is dropped, lea_ �"(mC��mTby͇A�>{E� \med�7�p� now organ�.La-!next T&�JiX&�e �A�� e%m3) %proB!�wnwin Se \�'s}.b�/^0 "�&&:I�s"'2}��� ��'6� basi��t2 AZ!�g�Z�/��5Z W��Y�T%A��d)�� .�Fby5���!��j�� $$ *�24 = \{f \in L^' '\ | \ 8'rm{�.}�4f &,set B(0,��)\}2&h!n#)�� '^! . For any�p&]F)Q�F�3:=\�2H\{Q \ |\ \tr |Q|^2= Q^*Q <�3 \�\}B5!B*� -> a�a6O �r in $1R� �� Four�doA�T i#byI [Equ. (9)&F���� rhoQ�.widehat{� }(k� f"80(2\pi)^{3/2}}!�t_{|p|4q -� } \Tr%=( %�8Q(p+k/2,p-k/2) ). )dp.B Noti��5$!�F�\mapsto 7_# 9,!0continuous. L[ �ĥۅz� !�f�\cCU!Im9\R^3}%%{|2B!@|^2}{|kdk<\ii)\},+����1�ino1�]�t5�1/[�ndi����so-2&Coulomb ���5�R5cC} �(�� �)^{1/2}D'6g/time-$>p�#2�!���eZ*�6 = - � Z )E� $n%�s� �(>s)YRaY\cC� ypl�)B� Yk�U�3�i�"� *s"y� system@sme�(-out nuclei�%�*$=`,n(x)\,dx=Z$,[o�!t�nu�-�(D. ��!Y�� u��!�X�� ���I� $$v7x H}_q��� Qa�J, \ �" �=� #9E��d � ��Ap? |Q\|�\(I{Q}_K9^2 +  \}^2�; \}�:Ib �*�+o1)�< byp';P�$%3 orth6I*�}f o',�cl�*�*&�:$^95���y��c"�:�2�"�%�wDQ}�$5E��D�$�#()-n)R# ��N$&�$m�JdB�6�� adjo1��Q�=c �[2D 4�. 2�aaA��� \!�0)>�%�$6qB"># $D_Q$>necess� C bi-#6C.4�yW"Qfr� tmit: wr�~�,E"*sak���city. \)� �u+3�Cauchyn@/B���peqAeeft \{M~array}{�I�alignedZ( & \,F( \\ P(0)= P_I t)^2 (t�$\,\, �$ =R( -�#�Uy2 �\\I� � I�>( "7&P^0>�i5Q� P_{�� }D^0N d)�H�BI?* �H J m�e�Yq$$P_I=(P_I)is� mF,�FtHR2<E $Q_I:=P_I�$\in=>A�-�>rk}hA�iknt�:B�>$ iv3�.r� ,Shale-Stines�#g T�G�D,KS,Rui, ShSt�!� � s�""V"�a� ��i�? t$, &�"aa�F>^0$' �Th� ,i', [Aprix��)%�k*&� �.�"��1��M5�a*", ro ��6�M�1�.� we 6� �e%�$!be�#ce-� ����bg;lie& y wQ��2(erved along%a�s�'a�\�A512�@$ soon$t! even�!�Y=s1FA�i�gS>J!�isU4ief�{ or� !�6O�'"�>��*ed� M H0 � �i"0% :-K�"f�rseR0rcep!yadd<*�&�� de�2?�Ip . O�[hand, %$� hown�b�d� ��$-� Ma! cept&� ���!eM�w�$�� = �!p  er'sNvenb>:�AIH,$A� NLs sai�% �B�0f $A^{++}:=(1��)A $�$--}:=P^0 A�9(7 �i (A � :�).�}�.�o|�u�n��by�H*� tr_{5I A tr �� --�-2�m�,a $ ge.�t� Jc, \K!5e6�W ",!�d�  $\gSto:�!�mf ll2EA5����& >K�J�/y EU�R was I�.|1�*a�y dif�3�two��; satisfy~ ITF�c� rion�i�6}(�y6�E� autoE) y�N:��y�1*D'��m�v %�it�Q4a�&���#�i"�-��Bq%�&� "�] 2��E�.5U[(Q�c alway!�� eger Ean�rI/6ozC�'!~��d=R��/!� �~A{� Ed ��Ňk.ity} F�ɐ!*�(t(1q�(Q_I) #�hA�sn/a#)erJl��$JL ��&i+.2>�gy}Q�"d'�Vx6/8 '�eh�Y any �*!�& $ ( 6:R' )_6J�~= t} � {E!�=9D^0 Q) DF,n) +,^ }{2}R) ->#\i�6} |m��. \, dx\,dy� �V"�1D(f, g 4\pi*  T\��'{"PfM}gY rka+*Z,9� A��oa�=0��^`) morb �)a ^% %'6�&�a obey�c?A�M)t� B�1� qufQ��'�z"W;�M�"� D"�'� ] 9lOb?Us�� �W �=$^*J_ ^.LJ�,2� �,$I6[Q},Pm1 holds. .� �Q$�� is n�:2,�=j $} $n\neq 0� *zeant�A&-����="6,em1umt} Let"� � $0\l�}< 4/\pi�n�Y&?C}�T2 R�6$� & � �] \h_\�"s" s a3<qu\5NClՍ $� � C^1\(p%E:),[+WM7$$ � 6].�.݁� has���J�\��S{and} ,�� 6._I�� ���B��$t\in�i)$M�1� I�&2Kx,y)/�7e�neZ3 3, }!� "p���#P ,e.(W������ any}%u?0PA�be&&�y���� Z�c -� a�-�r�Fv�,eH26 �:@��.m�T adop#Be=KBF �A� �&Hei,Wei}�fixY� ��.,? �Bgr�,K ��A T�)nsl�M -inv#&nt i� c@#�8deY�&�mt}1�*�A4a �,1ghtfor�Lway�Lt+�! F�<�";'" 7(t� "  $|k|,9(t,k)�C^12�\cC;8cl\Z.|sit�Y m���v#M�T of adiab�K� s or+scatteorymf }�ur metho�I�&@7W \ �">!�$�#a&!�i*H.X9e�'""�E Schr\"o����*p{R9Ex[�!�6G%ei� W"M|0�6��-�D�t�n�I�B�\ieqG��Xq.�%� i 6�=0^4[D_Q, Q] +[V_Q�8n Q&�Q_I��*P p b��-��� V V_Q =�6j\�=�� \big7 -n � �1&= e �  " %N�� "3<\9E1-�x8 �2��o(-in6�PA�$=$�gJ�.L-y"  A1�4���Bp5aOt�c� A��� %"(2r i�#�g�[��$\Eş� �3� coerciveD !ose�6fundaah!E�not ٘�B�+ ��is un �ɕ , NG�<rite��s"O0a!��% Morsifx �7 ES1,ES2};��.� EGS}�a �5 6ud�x��z":�� �*�0&J E$,)�r K1�e "dK A -�8a huge advantag�heA+-�# in c�;i2x6non� ar�qs,��PEsVe, Gro, MNOeref�S�'�+�4Qqu�)%@J.s��A��i=F data, *)5n52_Ťana"�,I2 -est�MN,Isuffici�s6(�+�u�_ *NN�? Sobolev-s��*�9-)( S�t1p ��\� �*,t^:�.�+ Kb $t=+? �reɺ�hB�I�8GI�FST,FST] M�b�&^�& "�&P�&a�"���w�s}�ioA%a�.(Z^��! �� � �� �z��Q�� qeq2&�&իin F(- �>�]� F(Q)=Rz� �0�0�0.�%F�Snd� �M tart��!�A��X!�2�VIs.1�c1�-)be.,Ţ$n�T#6 � &~��p�%"} a3�]x2�-��m>�B��".T�"T\�B &i$.dum�$as9>$T���, we havF 1� blow im_{t\�T row T} \|A�\|� �B��G)�"e� } By�'s!u�e�ne��ho�$F�%�,ly Lipschitz�,�:: 0topology. ToAe�w]T�BAY&�rsist�e% s $C_1$,2M!C_3*�F�u \J� =${[D�],Q]4$�$C_1\|{Q}\|� ,3 Q'6'2 ' \, 'F2D2Z3)()�aE!�$u��|g:�� $�:"�#.� �; �F1/lH"/ ./$. �us��i��g� ��M0$pCin1�C !� $\kappav�%�ONI9(gS_{\ii}2x�q a E(\�)*�%;cC��QF�-LE1I(sqrt{1+x^2}�(�[n immedQ@�� A �"8 in��O\E�&f[Bc 1, step 3q2}> E�|b�d|E�)9H$}_\cC|D^0|� Th� ,a`%ati- 5]� Q�x+2M�Ue!TgS_\ii:�%�Q 6%� 2(1�JE 2n�)9� Qi*$$8#, ��j�GXKA!"LKU��* ge O[�)_Qy� �z�.� \�MWQ' �!YN]R��"6G jie�%*R_Xsto^2=.��B�^2}\,�!� 4).E#0((-\Delta)Q^2I)# 46- rp�$bymJd��Y��&��[R �)28i mpMarm] 7�_�bF'�nB�and6��m� 2 g%CZg�1�u4 ��0!�T*ve)q4c ��#� i�`$� �0-S�Fw ��$]���q" ; kerne�C$\vp_Q�$ �-�/��$.4/"�9(}(p-q)P^0(qsw|Rtai*na�q*7eft|[\�<, �(p,q)IU|^2 &�'u}*�.� t|^2sN{p& (q))^2\\ @2�A P^0_\perpF�*e�"?'=�!$.��12!A? ��RO �(Pa} �^�ENm�p-qa�4{2E((p+q)/2)^2�q2�A� Y�%0Ei[^2E�=\�|p|,|q��ur11: 0_9}}{ �2�\,dp\,dqa`��v m3e. �%� ��C_ x &�Kfor�(� ��14P'ng"&<"� $`1�Jtl�*vesFy�Gt.pq| netu/ej. T:Y a�rk��;%6cBto a� pq,Q]$ va+KsBU ]AY } e)%%?6:n �,B��2-s)�23 Q(s�2i!�s \\ �ZntBDs-F) 3C,sC=0m.�by�A8OZri�_tra*�K�2wis��1%of1�9 �!P�P"$�_k) ]� �\a�-aing $�5w&. wl�;� $œ!��d�Xb#zero .msymmetr|#'>* i2G� ��3i�b�!��Qerms !Q �O�? �)F�2 find"^ �� i�1�i]� 0� AJ� }�9. 12*5 |k|}� >,5}A!�� (p+ !5k:85��.Ew &$q�@.'3>j p -R! ( H) dp ��N�*�5�e�c� �?" �T k- 2��,p �~R =i!��$��N?2u| j�C_0 |.F8|"2 )(zJ�6} � Q|^2!�� p- !$ � Q�Nk$s=�12}/(*7 $, u�bSchwarz'%"i ��u�*SH�6s. Squ[>!Fi��vu"k"�-!*���I�} alcr 8p M A.�HBF�vrhoqpu�r�oe�a]}=A�U��QC�[E�)�Ca$ WP^aaA�A8-� R_Q�T2"Y8�VB�c5��Cw Av��!Q�8 ��( ==&E '&� *A�q�|8 {E(p��7v-j23>*��Uon Ip� e Z�&$ >�M! �"  -� � %�>M2� )9��asserh? � �n=��d�� �1>s&�D2:="�P"�*i3!�"T"0.`6�,*�j-_w#P^0B�a� $z,[0,T))$�!byF�' eA6�an *�1��*- �ut1u>Tnew un�)n $A(t�[^2-!(� x \dot�, P P + P - vq:� ge �/mqeq}, v �a9!ܑP_is_!��  \N�i�f\�� 6V4�A&�P_I� _I=0-!"#ix �� "�\�u>�A'2 Q)$�m is "� ob<'"�'^u%� ;,:�-2�B� %��$�(t)�XV�� Q  As�/� c&infer�iq>D H &� �5� � -c�|A� 0�N $\6�%<a�B,. I�0,�D�3A� G�J6==\t�\ t)^3�+S�2y��=a�i� iC��$!�6�$"� �1m� 8/_32�9�K �F�:�>�!�h��c �,!for�&��,\>M!i0&�,\"XCW#w��n BDF �c �� � &��4Y � +T�@'.2�� ^_c)�C �C $\E�v)= _I)$j&R?��u�^��[�{Q}(t&)AO1^ :N�M� $]�E�*J(fS� �)^0B�8"7.Q=0� �c�fur��E�qeJ*t:>9( �aZa �!��.� �1.�HMVGk4Sy Au9^�X��aEUHm P&i9ՓP_t*X��i�F?4, �:��k~�E�%��4KSD5�+usGrem4&�fact,�v.��71�s���B0use: �4P  $P'�4 n#��- ors,/!a- P-P'Ō�"�!�t�it-"�,��m�PPC&AI1^PE�K�Sext{if��gMif} \*F4 ^{P'I�29 "�+�O���4��'} A$.>� 6�P�M�duc��]���7^{P_t ~ )=^06R��A� PaD_ti.f},]P_t=P_t P_t]Mn6H5 i�A� +R* |u< $>5"U� �^mP9�/n ��"�p5 ���7.OBXxBE�xR� �n� )�=�.��:�By&�KiI5y��ei�*�6�� bp"�2-n,� p#}���<� ft:6c(�� Yj=*94�Odw�"� u4! d*g���.�e+!&Sx�5�G, ng&Y Mk M slu� Nu = -i�**|Y��]� n1V�g�� 0"� der_>�7)J"�b�QeMh.�^�m _& �iq~&c ��=-_t�0�ACo2�MseccNj�o"�b=���oc*7��&�A�6g� . F��W4�kevalu�P^0V_Q. =xt$P^0 ^0��*>$$"2D7 = - D L#j.�xfa&9]* 8^�2N�p3G u..�mHm�[ �" A� pnQ� = �\ us�C\ V<0i���O7/�5c Q �T�+fi�Oald^�et�RoR�'"8%c&�����S4��<4Q4. �jb ?%4!t "�$͟��Z� *��#w&� i�"�) � �6 a!2� o� have $�/�� � We �2� [E�L26�L2�\�,�,BJ1*SE��<��SV = \{�H&d9�H� �� \}A2�&5 bu"f"� � +��{)�=9@nB�H\g#�1�# =pi}{4)")y(D^0!J)+I�e��"#}-Fp�Ney��.(Q�S& �,� �u��) �tr(�"Q^2 wZK"^2�9Q<>8&%E��$�Uo�`�B$"'$�$ys"�-� `Z �7.&N#E&,(R�' is $T =v'iJ�E'�mt}�V��+�� \.��ӌamsplaiPJ�the.& }{99�ybibitemd} V. Bw J.~M 8rbaroux, B. Hel�?>H�edentop�.�tP#StHI&��/�|"�`-posi�D l=i omm..U{� ,bf{201} (199N{445--460�N��Z$ B.~J. Bjo}��(S.~D. Drell�Re69}�l�" McGraw-Hi18New York, 1965.�� p�eP.*�iD. �i�4�W_�Y�}�,m(�wA�ory: I.A_Zc>�N�|},.t|9"2%!8!!3"�|=# CIL}�,�)�P݂LKk1)�� II. Va&�]s> �F@ ^�!N&s6��A .� 815--3828.�8LB} \'E. Canc\`�/�� Le Bris.�0M��6&1YH.~6� EupSw�a ,��Oar 1�},M�M��s M7(s Appl. Sci bf 9%�E�4no. 7, 963--99.�CG} J.MEdamE�R.T G�eyK it GB4*�,:k�4A�� :�;��7B��)�;�>�16�475), 1122--123.�D1A�~A�\o Qm4Th{\'e}orie du�{�x}, Solvay report, 203--212. P�i: G6�ier-Vi�!�XXV�34)Q� 3. (nJ�)�ASe�ed"�;b�x}, edi+bya~�in&CDZ�!58$ �!8oPR�Di�]�f%�gh�]tr*Oz�ron"*�8!�!�p�@}, ProcA�mb!�ilos. S�A309150--163}Dy} F�> Dyso69��N5S!�rixa�Q� ElecUł},��RevA~$bf 75}(11)��4�� 1736--1752G�30} M. EscobedoE�L. Veg� �A SemilƒE5&�sTH^si$s > 1$� SIAM!�I��� �28% 97),eh(2, 338--3629 �6 �tebEnd E. S"�� �SuV-��>�ca\ato�4$nd molecul�(�q:�{!D203 �!A� 3, 499--5.U�2��Non.�f\j�}, Ann��$nri Poinca�� �} (2001-C(5, 941--9612C�7%�%C,aGeorgiev�yNQ"M6�K �Max~u~EE/a 0 Klein-Gordon ��Zalc. Var�5t. Diff.AHM4)j6 �(3, 256--281.�FST%jFlato�Sima/��Tafliu=On�7"ksV�.�J q�11��Q�1^� 9q�I z��AsymptUY�^ pletIcg><A�%h infr�V� �3A�6�.� Mem. Amer� ��E�127)x�,606, x+311 pZ�O {Ge� Y;m{;8 ap� tude�jIndian��. �#J&P 4�19Q� 3, 8x 88.8GRS} R.�{ub5IW}b ritaI�P��hw�G%rVO2jg�c.X level��8{$\mu$}-mesonic�A��t��p12 �60M�$2, 609--612�MR} W.~G�>�(B.~M{\"u}ll!�,J.~Rafelski, �Z�A�S��g FK� ex@2(nd Mongraph��ics, S,R�erlag�985Y� {Gro}�Gro�e)���J�AxRhedQ�¥�.�mVPlbs )�u[x 6a� 1--1�{H} C7��& -�P.�De�Ocdc�k�A%(bX�5} �[�$1137--11579%@.�M� w�{!zJRExiI��2l�M��kI�} R�J �;RF�! , { B� }I0spe}6�2��S:wp� �tN�a "?i �=�"��A:%�2�Gen~�3��e�3jr&�)&.S2IN?Non-Per�k�uMas|!Cs!R:Bein 2�� Z�� Be��24m2003), 2��22bH�EW  isen�q 4Bemerkungen zu�>scN�<� es P� � Zeits. f.�k �9��� 209--22.�KS�| Klau)G�]arf��' regu�k"^Ed�Cin^z},�v �. Acta �5 �7��779-80*% {La��f!i��#�&� �n(Pergamon Pr�j Oxford 19$ Re�)r in�Colw Bp"vHL{2� ,D. Ter Haar,Bk�5��i2K�H4I. Pomeranchuk��A M s���� * TDokl. Akad. Nauk. SSSR)^10�t(489--492. r�p��6�#@ S�$chihara, K�k60i��T. Ozaw"� t# ��I���nRg � 2� * }��Ma�fberoam� ŝm� (1, 179--194.� Rui�~N] Ruijsenaav ��On��:40�R�?��2) �%'rti�� }, J!5t"�C1V e)4no.3, 517--526��7.�9~!ySe�we< ��!,(men who mad�m:�Feynman,&�E�Tomonaga� Jex�*͔mh199* {�Za08TJW. *�ZQ�Spino*@r�� "�*�!�Jp2*� Mech1�s 6-315-32�{X �b 44it Trace IdealUqir�ic��  Vol 35�%TLondonA\&JmSociet�*΃No[~SerieD CambridgeRB79�?Th�Tha�r4 ��� [���� ger &� 9.MщE.A. Ueh'r1z2b 0 �p�XA2orJm .iOII.�!? bf 4I�3!s55--6._xL,V.~Weisskopf�em{\"U}�$die {E}lek"�k ��{V}akuu�(uf {G}rund �r{Q}1en���D� �.-FB�,Medd., Dansk��d�lsk� bf 1_3� � 3,� 39. ���� t:F�1do�`�%"Nd� $aug15,2005�submit��toB E�%�ic  % mor�*� Co7)in %Pro7.f��E���RPV*RP+B� GREEKS!S.5�ef \a�:h��b� � d {\d�Cg {�~!v"ʩf {phiF {8 \Phi�o x# l {\��5L "�- �m {\mu�O��1�|s��" �th�Th {\T.t {\taUw {\op�DO {����Psi�s�1Qba a�bA AB BC ��ebP \Pc M!�h0 sf{M>pi!�ol"ǧp3bpinvF^{-�� l!9.@)E1�PId �Idiibp!�at�tEpA� uS DSCbE d� �K K&M =L L&G GT TJ�R &R&X XE �,V�A���Q�� �PhYD}bB\ 0calkiA�^Y)M�9�gA�^u� euc �sd1�zRZ2"no$n \tZ$slash \{0\�zin$Zr$2{\Z)DbHthj&3Jn �lsmax�^*qrm{maxYHlsm�6"in" C^A @2> ?el."2� B6" D�Mp\~{n}eV1�Ms{/ce�&E*mmaxm !�u^m�.�$k $kb$in�?2G �kijC> @ Afrbundl�Q�Y�$sobcon {H_(^m(\T^n)1 en"L"2>"mz {{LZ*0>divVrm{div}}>)gra��F{\n: f<�a�M4newAL5�bC�RC�E%)?BC7 B \oS%s \! muABX ' bX^{��.�?�flowbo%�at$FB}_{\e,N}�R$ Shortcuts>� 1�la!�la�Etr��#���1�rA�a�Qs�x$teA�.Z comb}[2]{,�)B x} F�\2k  eA'.NderM(}��  ) #2� "s ess� \sY }(#1BWiscB-N.�.r�Zsyd uS}^J� LT)LR)s� HF(��>�sobmzN 'a7�J)a-� * �yE^7aO68aSV.qinA L^{2ey!B�' �)�TZ+� )>�6E�saA�Ae�a*�s2%m MUJS_ esf{ �2 , MY FUNCTION6� 5 Declare�O��{��o } % V$conv}{b$��}��b$curl}{b$�Gs�Z�re}{RefDim}{Imf Rg}{Rgf tr}{Trf Ker}{�. rest�@#1\raisebox{-0.3eϸ($\mid_{#2}$��������1 ��*\�;u�+adv<�����T�)or{��ShvydkoC6Vv�I��o�St��HD[R�� S�stf"kR�uI� �\\ :�07��{s ��uic�!@%��j�~[2000]{%hanks% ��0Hnks Susan Friedland0 Yuri Latushk�!,Misha Vishik� stimצ 8�Xus"*s.}% \��\today}�/1�abs9pt�ugeome�] op! s"}-mn,�0ext^}d|&��� of,K9� PDE'�] pseudo�o%�Z_ p"� on�3 �v�!e�@rt5 �'q�� the >Kal�Qs"�Ejy, jal .�th�9r*+�bi�ac�dA)-*8&�}���+.et�N^�g PDE.K" eric �al piZ�^4:},�^spaces�&n^ly ��smooth_.2�!�i�zt�e�g"@GY \"F�>aum, iJ fluiڈ w�5.�s, �cocycle,�H,J�/er��\� � d , &u$e eigenfm�s,N�o�9a�m&��\t�$of4D ents\input{���� �io:̬Æ��ec&4laZroo��gu�u� m�1)=xs d�'opIAO� 90'so.�M ��iB ,7({FV91b,FV93� I�Q��b�[f�[�UHa�� >Lif? LH1}�udIsl��i&YYr>&ti�X ady �  $u_0Φ%n-��z�'to\9ab"OcE��IbtEuler"!1PWKB!9b�|WKB%�} f(x,t:b e^{iS /\d�uO(\d)J ў�f$\d�8sW*param�. 9� v�lim 0�5a��s ��Aa"".�=�(exact�Y(v "d!)�� "ɒ��ll-know*#� �p��we�� dACraik!� Cri?�v�I@CC�p< �j�a-� ��or �$)�) !���2 elli�q stream!�sA uineMFree-dim)���.%APo!�eq�b5��c.���a��D�ګnuAӡ��N�E31$of Pierreh�t �286}%Baylyne 86�*his�}WGbN{�Jb!� i��ar�#�S�%�urbulHݠert�pla!�r%Ps.� OrszagHer�88,Kers�.+�, Pa��80WUA��lA>ilibrium֎ explI�YxW vail!KAP ��B�i�!�٫ed>��Yn;aQ\EeN�or!K?� both �s.�l)>= "�a lawI�e ency $\xi�?n S�9��$b$. WrU �1C�ܸcoo�~�s"G�wgAwq�A�q� theyavma�AJO , u"�hc��!�AZ2��Y"�5q�st:Y�2p�cit��2)04} exh�:u ����s�@zA� ���y�E�H�fulvmainly�Cits��e. In ��i�lrJ� "  $� s{\bG_t}$!�0Y� AwGbKf��Y�iulazWJv���� q = e^{tq�Z��&F muG x�[��Sub tA�&�a61Shv 2004�gv֘ own �+XG �D,%NA��gnJ�$\l5BF�,� circI�f� $%l}$a���A�)���B�um.@ & �  �b�apa�Um�u -dissipat2WqL hyd.U�q]BoI nesq*J {:�C1b�)QGS%T,�2�vo�+ityE; 'LebGod99��4}J7e�si�Corioli��c � ! ���.c�� GF8,SLJ99�9*purU�߁���-� $twofold. F�O,+GE�cLa �C�FQ�s�B ich �N��l�" m�bo�m��A seRD�soN�CB� E�A���B A�i.�].� *�F� Kd��ed ��n�ay>@u��6z. l�(i� D�(�H� � �1?K!:an 2-b�N pde0� f_t ��der{u}{f�  f^Q�Oa�?*�$6� $\bA$ A(a J��"of u^� 5  $�[$-p6��Cbhx�:!���s ��uU!@�&&��in#�Cit5i�s-X�ab��5�� sta�Qu"�rK�'��Q'%[!�� ��{k-cip|ymbola Q�BP psym)�(\ba_0(x,\xiA" � 0Ih�Trecog�e�� y%6/݆ !�!MF��.w I:їS:BAS}A�"�� an�W�.C6iza8rF � v�2ccU g� 25ODE^gBASm{ =1m�\x�y) b^%��T>��%��2$(.U$ i'GǛa��low0-�1H�R:2}e��3��}a&� & ~^��k. Due-'0 Oseledets Muۤca%�Erged�(���j2�`of B� s,�� a �8l�~d�m��!�B�"T ��*J �Farby1em 0�$ ��a�U -D6�G�r"`Tthm{T:����w��hj�JTp�0<-2�L $H^m = W^{2,m}$, $m�QR$��NIA A�ud��6��aug� Fp"�, i.e.�5�a ��# $3 (t)|^m b(�| )��8{ $b\xi^m$- 6. A)s_IS:����*S:s v!dev{to���ai�>1�F. #��+h"Q"�  (also �� ed S+�r-ST�s) c >�� a sen@�A*E� skele�4Mx�Bu6 nq �T�ׅ�EQ�*� �A;f3Vsob&5 ��exp\{t �_{m}\} � |* � | + t [\'$ 2m � /|x]FM�rX9��Jy->V. A.�a!�Kof-� %�l SSSpec��eN��$d$2��ܭDun; )t most/ see'�A�8+�� . So�n "�=% X��oneh J�a�onnec���_a�,=�vF� turt��zog�M�|i�z l�*�o�Pn�d�yT a*A���, o"��2D "\ ��"T !� veloa e* �!-> &� $M8ֻ& ��P�&6;3�uch�,�˽aTr2B u�]b� n. I�G&: � has.� �� traj~�L�!�"|��m2nBA@s �influ� al��=��lake� trolɥl���heS9l����\ two favor���Vc�&m �hSa"JDU end-}�}$|m| -%^O �{UKsZng Ra .P.L[�Km'���f9z�elfafon2�!�e�� q�7i^ v%� ��|m/�� dA����evantJ�(��E�summarq`�_�� f"� <.g 44\ uthm��SupCJ�*�E2�@ lxs�bem�enough. �TF�H�$s� sup_{k!� \R}\{ � �� k \}�$S-inf>-�/-%~n!��!�"^�>ize��\ [1)]..9; Utem[2%2�< s�<6�$ :3:6=�61$444\T�j�3[Tft\F9 ,s] � [S,6�]�'\� �}*�;�Z�%�hQ ThuԮsw �$\.=��no�3Agap/nda��� id oH#(inner rings\�FigUE\�F:�� < J!). PaelM�3llI�d�!�B�Qa�(�yRHSr &�b2�e\�: we %ri�Xa�� ��h�+���L)�=d��s"�">�>ass"€&Z� u�"���b��edB� c~Ki��?!"����e{mea!�C��k" �� }`@5er�{b�� �69�$\bL$%��7� ��gen})F�i�5a61 ,s �S,\�m] + i\R.�L}a� I6I\r�ue L�:Y6P�dendy'.��bE� �pEJAhe�Le Hull>� aht},�!�;i�-)��#��iecI��"�_� $G9 ��2$not yet *�@A1z ]T]=��a�V X� o� "a�&e�V�+ LVoB� � ttemߋPwoJ �����*��A����?YDM�3># m�e=  , �-�)"���d8as5o�'of��,5o!ts:� �HM� ' L2003b, a� ese ރ�so�annulu�Ava8%��.,��ive�a?{ $m \��!�sa{�)E2i,&5�� =uSQG&U">�j�"�n,�+on�Oirmw *trivial��-$um�W 0 = �2I���&n �m����ĉ�fsA�-d--%XB�U2�s:sss}aŽ�A&y(!G��IC s. Our ma�"і� �=��mN)�M>�& s. SR�eur 6q�ve�L ]� l ��"tP�U �Ma�c&� )K6�tA��9�d�$te(M�hvC����at��u�� else�.*'� M#�-"'Fo�)Fv S:-}�o$�%$�AaR�b$n6j/ $�2$. I*6il�(��u&'�-n�hyp�� sis, alth� �_is�Gݘn�y�s�&1��A�n��*yM���z 1pd� n���t 8]0� I�#'�ny $$�&+� e_i�&�&c,#1�!dots ,n,5%�, $\{e_i\}_{iJ�n�hheI��A�s� unit� s. A���$ s$�es valu}$\C^d� �!�a �,��n�) (PDO) L>AD + "�)�.#5< pd�bA!�\6�� z�7}~8(x,k)\hat{f}(k)�i �dot�"xf�b�� $d \�4d$�� rix-%d vv }i\b�v:�dC^dB1�all $xw T%�n�i� i��8no$Praa!��1��i��&_)lw,�f# 2� n!��� i$�3} , $m �R$,p"ޘEX�/IR�m�,-,s2Y�$x\in 83� � �; ��% ny ma-indiceVa$� $\b$�V� C_{\a,\b}dj�!15 "��aS |\p_�$\a \p_x^\b=���Y (|^{m - |\a|Aa�y� �, %�"1*a"�"��� �[rE���H\"{o}rmy0)�eT(H#�03,Shubin�pre&r�Hpin>O�patt' 0$. AE�JP H(�%�fea�of � ~$ �[� in�m��AME�(���!á���mpact ma� lds)%�P� ��^�m� b��plav !.' is{՛c"�~U�(1- \��(a�I� is rW�� doe�[�J i|.AgA$ so @�a��O� s�r� i-@�fl"�MDE� PDO'e>���&�o} � �sm�!la($i�7 sp Y:E2,a�[$\R�Hx � BDGY96}�� D!�a�j^$V���� ���#sy�4I]be�p�,$�7�S.^�72c 4o6 6�J$���F�yB aFrk�\���so��e0\{ f: \|f\|_{ }^�����c0W��.�h>�)�y {2m}/k/C � ba_0)ma_ �homogen3wof degl@$Z ��xi$ (� a� "t�t"$)t%1d-1W�ll C�n �M�"�":�!�67. �ifC�.����e*�u2� E:d�:�~bA =\bA_),A_1f,A_ii�PDOEG �V �i$�QncA !{� %^�� ����2��a_1+ p�e3A!���+1aI���ds .B .$}$ � actl�U0,\� 9^� p���is�� Ot2r-��%� � AU|�*���*��2a����IH)��L1:5�i٭�&y!�J6$-xpdeC�^W"�qW L f V�&Bo�o&� �"�(�"$- &�&� M p*3%� fE�.�^( J �!W Y�$-!�T{�b�rul�t f��f\�* tH_{-�W� $\� \{\f_t(x) t\in\R,\,� � A�F"�2@$"�]�Z'itZ��� ��Eng Na �-}).:s�y�G= �G_t�0 0��In ����  r3:si"G&�./!�9Y $\bG�e�t�'I��{, i�a�0up. &<88�R��s;S:A5�% now ��* spec�ea�1��)an"��y���bjD$"MD$"isZę�(�#�$N .Bos fiberv$F �&�~ � #%= $0$-�t'4F� � reg]!� ")W�%�l&}� 7�Uat�), $F(0�.9�r2 �|�y ),r,Givenf7"m4 .>��aai��"�� $f�8 �&&�EP6r%�U"�&i .� if $*�� F(k)v $�Z^n��� $\bp%�:B‹�A�*�X�z!s4�1�� .X#f%�p+"�"M1��|pk(aI���8AsI��7:+eDQ�� .&+�A�)._�A,,~���=���<5I� &�{b: b�8 = 0\�|.div�51@7�K- �qP�Fx*55div!M6�4y�!|c� ��3�- �s,�"L �6Hst�� �8�in H^EH:c� k)UJ\x6� � �R"�ga�� P�M�l �H �!Bon�6�{�Mm� p�"�.F> 2} \��end{gather} We use special notation $\sobmz{m}$ for the space of mean-zero functions and $\sobdiv{m}$ for divergence-free fields. If $m=0$, we write $\encon$, $\enmz$, and $\endiv$. In the sequel, if constraints are given, we assume that they are respected by equation \eqref{pde}. In other words, $\bG$ leaves $\sobcon$ invariant. We note that under this assumption we can still consider the semigroup $\bG$ on the whole s%p%U!�x, which corresponds to solving �0 without any =$(. \subsec!�{Essent!�A�trum}\label{ss:esssp} We now briefly stat�e definiH of eBKAXd i�4is paper. For �4losed operator!h4T$ on a BanachMn$X$ wI�$the follow� classificI�of � (*4Browder \cite{ �}). A point $z \in \s(\bT)$ is called a " ^0 {\bf discretl@} if it satisfies�� cond%(\s: \begin{itemize} \$[(DS1)] $z�(an isolated �inA �;682 8 has %�Le multiplicity, i.e.!bDigcup_{r=1}^\infty I�03)] The range!5 $z-\!�!R%�. \�~�%O��wise,�Rz %zFd}. Thus,1Xq�U�pecsplit-j)@H = \ess{\bT} \cup \!� �I�!notA�at!�!HT%bounded,!�n9� (DS3)Ms from !�8,DS2). Let $\r� $ de a!9 dius%:�� l7 calkin$ b�e C0 algebra overa2. Accorda(,to Nussbaum i$}, we have^; nuss-6�!9 lim_{n\raa48fty} \|\bT^n\|_ �^{1/nFJ Concern�!��p�a semi�we reA t!pt�hqp part obeyia Cal mappTpr�Ntyuf5ō�Jexp �x{\bG_t} \backslash \{0\} = e^{tU� Ř�@al data given by a highly oscillating wavelet localized near some�y $x_0A� \T^n$b] t,} f_0(x) = b e^{i \xiE$cdot x /\dFsWe�Csޡfa( \d��$|k| \leq R� + 0:L��)B�MI121 our)�p�dba�e obtain�H\�� k +6ay�d! �)� ba_1!C+ 66.S$Since $|k|%�c �l|;�-C |\xi|%z� 3 < >�=0�;2�!���t_�� ,\\5 � �5Y8':GT�E�es�џ}\\A� .l=���A�E4-"8 \d}+2x>\(pagethis1} � argument�f gt ��0is more technŀ�/0similar. \qed� �Y Now��are�9a Վto�����pde}.=��e 6���) us�7 �. Negl�ng���s !� vanish�L �LE$cancel3exponenY�4b_t+ \frac{i}{acb S_t =a�(der{u}{b} -.#b  S} +E%�n S) bE�%� yiel�h���tw&�Usub1�sQ��e�}� &=-�b}+Y/ � MZsubb}\\ �&=-�.! eqS})� `�zu� s} IA1�$s directly�1�.S}eh%�� is m e�s Aݩ E� \f_{-t}(xi�� �WFg��en[M jo-�,ɚ�a _ ! fQ G�xi!�5 \xi}!�$p u^{\top}atm�1�} Rewriz Q qref[b}E}2�S}a(0 Lagia$�ate��oci��lflow $xE�Dx(t)= \varphi_t(x) (arrive at a��  (BAS)}� ODE'=��%1�M)� M( x_A� uX *x}�, )_&= -\pal,^!Z,.6iA�6b V��)b.*b��subject��� � v $x(0A�"� torus$,IFы� $b� C^d�a�H ra@b_0� F(!0� 6�Preser�!�bL$ is] B;Y EK1 $$ -i�f` \xig �xi.v �CQng!�L$ W $\bP�as dpao)" �produc� � s up!�$\sym $b�$tilde{\ba}6� k.r .� �.�2 ��� 2"0� entr� $$ .@{kl-����xi1an \bp&%��8 k,l=1,\ldots,d%f N=���>� curve $(��ف�!jhA[ is au$A�M�BASx}--i}�H^-�y}B�2z =  d}{dto��BaSoyb E�}0=�0 =!9t$a7lAB�0 dv^  �o� >1s.�6se"� u��$equivsym} �*�j N`%�t%�B�� claim�,if��I�� u��� �8!� ��i� F�$I&jt$a^vided �ly lE�.m Inde�byQ�.� 5%�infb��*}6� (\id bp)b �t $_t b - \bp� �x)I �� b bp%�- r s Fro!\6gp 5^2$�hN��*�%� U� Z- �*q�E lin}�f_a� �f_ f}�-�� �fB�* us re|e�ak �1Q�2�A�^�+H �2B�m�XE=G��E1El$Lie bracke�V $u;f�aPis %�gen'%orefore Leraya�j�%p7 �3Ethird. p A�pj' G$B!Aten a58 $!�*A�A f� = �  - 2Rl����k ��k}�^2}�� (S \,f)\,t}\,(k6�%�&Zx w2�k BsA[id �z-�=� Ia �y wo�~s�k��%�Q�M! �:�#!�� ��FC �&�I+ q�h�J} ^quae".of 1s p�:a@$] F $OM*� A�us, we /  a 6�D!���aV�G �� "�r�azeroA�&"b6�=e:k- ]-l-�!!\��&�!�� pect��#om.� ��� S.�#� ���v/�"�& q \emph{S7e� port, 2Dͷ�vo�lities, Charney-Hasegawa-Mima�&ite{Swa�}: c6� }r = 0,, BAS:� �end=3 ��N��E ies}�$ +�@FriedLif2003,KersE 2002� re!ces4 ( ein) � \:��e���b� Ͷ& �&M&� L>�~�� Corioli� cing5� LJ99Z��%Qco�%����b + 2 GB�N@1 \O\� b.J�Y�14LebGod99,Lif94-n�%vorI�)џba�f�\w����� �x{2�&�2���v� � 2001��c6�M��( �+��O���.�DBoussinesq approxi11�FV91b �m�2r ]�K)� **1)�&��A� � rQ�*%�V}`s \Phi(x�l�.���1� r�-bIR7rho�)B82 �,�2+ 2z4Camassa-Holm (E�-$\a$)5{ H200q$-Rѡ.xCH ��*"hiA�R�$q�\p%Vu� aKb +zBM��Non-rel)v)* super�uctivity6eN�noB�M ��  �� F�KB 6N%��F*`Surface quasi-geostrophic&u1�CMT94,FS!�,Pedlosk�SQG)E = i��^\perp]�th!�"}b�.+ Kine�c�%��0Arnold-Khesin-�n�kH �����BM%]w,0.�2Pa0.~,Dyn >� 1�&A}�,m a Hamilton��, on3�,l� Tc manifold $\O^n = T^*>)�2L.& YH&�A�1�xi<y3y0oZ �+ cotTnt *� trivial�1 $�=�,Q� \R^n�hEJ4� �!� .� < Lebesgue-measuru �ing&�'\ G % $B%1q��chigI \c�  : (x_0��%\rae�i�*!_0��pH" t^{-�}9){��b�, 9� w1)N8Jacobian matrix �f�� $\p qw(itAC vers"� se.(1��!� �6 ]�b"�)� &�>B jx 0()D!-A)bB� F�'Remark \�"x1�0�"b}]ua u Qy$*� �2aM� � s $\bpinvM�=�r A�funda�&a�).?*� Y����*ocycle wv<.%o$!$ C1JSSpec})a{\bBT#Uq:�!ra b(t,,bAp1�maps $��! i. $��2!b$- � . A��V�wa�n0AY��kvize` , $\!`�{��(o�Pcompact��.K���"m� \�5$bb{S}^{n-1@ .B�Ohe uniT��)�>%� map >�_t:)�d�E rule�>�chi�}i�6�_J^�i�y�_����6� |�B6�*eg�($0$-homogenU�7xi�-&� �d ��eg^b-9}� (B2�B���hk%y]� fMci#!�2< $A<�/.�!��$.�. "k)�%(growth typea� $\bB%::mau $l LyapunovD^$k$exp} \mmax���6t�.�6�1}{�log�-p_{�{( ��6��4)\|BMi!" norme/59�ݍa�It%als�)�7 largyB�!_�q+M�9at Ergodic!c�2AC �$-N"t �s�� � "�/ 8.15]{CL}~82A Re� ] o $LlAAp$b\xi^m���ss:red}����6��(describe a k,proced7l will�1"�)v ults� 8 �ruy �w$6�%u!��0$ms% TO� end���&e anod adv�W}�53,u}{f}�A_m f��R h!'��A�L_me/$�> beO tal� �$ .�%L 3�via�S� iob�$+rm��a bM_m�$  /Z�$"e�as<mop*sm betw�&�$��"�:k�%��1 J~<er��"�(scalar non-�-!)�!0e2 $=m !  > 1/2��ly� { : -C�en\&e�2� !�p&�5 '!��a�u6^. B�2e.�"l3PDOEn|#N$-�UPUO�X�{�%PDO)+B�'�9��m��� *)- mn�,�\xr+xi�|*1�id���P�:1��. l u"� &�'$$�. ��b��� new  ,& ed >h,�^�X D4\BX�� ���|B) �Vxi}6 |^mmG��% 1u",O^nbO�� xi"�=L �|o�@xi5�1})sBuA)?<)��s) EF�,is^�� �+yti~aid� ut` $&� �) vali+�>� too@)"�(yC��V^, establishes�i�6jDb��=rA���<�BY� ���1a�aQ�$"er#<�Dect#?�%>��*s<- F�Ŷ thus��to���/ͷ ��?-> eq(d�]�š8of arbitrary $mIKR* r�+� �.�us>vf!�7 , we ��EF_ Jt->Rm�m5alogousl~�"~ b�9"2}� ŋƢ J/� � F�\|B� *�>J%D# "�>E:�Dal8�S: 6Ik6O#U� &<c9�;!h radi�"U�M��In&�@-�.�E@$or,$) Sobolev EJj�<�) TB$C_0$-E�M�9o*F ,]} , byasa1�pde�/�W"aV:� ���Ga�<5?;t9sA��/���!P& ula^�vishik} �BG_t} >9 m t} ���AB*X"C; As�cus�)S X1� uffic�Αa� H�!*e��  G7��sis��wo maine� s. F"�>"H ^microl�@ structM MW&W?.>0!V. Tx& nd, leS%�KW fG#�rPDO^l Spdo�e bS_t"=P J;�4;Z2�8k�S�5x�<0"ů �pub� T T�bP[ ( �5irc�W6]B�G��J=:�2D�!.1� D576 !�>A�N t%AR$S�|E: R� Gz \��,K_tb]� Bay/AIe�� -.� US'Pro��H�F&F'�a�� F we�'�%�m�E�erme�a��$�f8C��1Mf �E�kF� �H� G_{n�|_{qF}rF%Q=�sF7T^7bomG���RmG1s�:(K�Dma�:G_��4&$LyA$-ci� B of!HS���iT *,:^o(upsilon} \U C5e�&� K^J�-U�� as us� �3n�,stood&#p[+. ...1&�.FAqP  $���Et>BU�.���6� y�} �hq�L:estm�re ex��a�n�*t $C>0>M5fin!<l�# �(�'� j)QM16�@V_ C=� �OK9.��� &�3$$ )l�F5�4 1�(� nt))i�+F(%�\2�Y�\t1\a�x)^�e^�� t})�4biWJ� 9 ���W1}n7d A��of[~��TW . �3�>�7�-=9s�ofa��\�f�\useUDly basic�.�,��'��' or HS0rmander Ho 3�Nv��M��"a a>:���'�8� of Seeley ` 65}�isFF"sLfBDor�$0$/uloѣ"m$R:=�s!r��%�}[ZR�]S1.� �i~]| 8 �2g g +3i0re�/@���:o � � t� $by "forget > " abd thema=bextend��G$,]\sqint{n�h� ]0pa�,Q�*Q� Ved�. Apply�*(bPl*�0ric�>[�Ͷ���( ���  !T. y,� ��� 9� \Idy !)�>N./ � �-Z� e�By�F%�ghtforw0omput��&zZ2teq} �)�3 x#&�. (x)}Pg  � ��:; 3�,fz (x)Fkt ! "2Bn S<�exp�/ last& �>i@��x�[B�-Ѯs"� �f���A3{.�  \z"�F_0M_t(y)_ :hy) I>� 6E b yJ � y}}{yz5B>�-} Our o�?b ��]r� � x�+one�aA�R!�$.T?u� �$gt) �Lg5O�(� ch| NI3\bA (g�/&{ !D(\bA'g:� b_ bA'\ a�B��)emi����a'- �:0�I�[=�� VariablesA.3.�EsX_L�a_1L&!;& >�� ba'(9�"Lb"|K%�o &ke�7^-e�y*:JA!�e!{t}"��)Q1�� a("�7a� r2ch�Z�E��v��/)B��*6�:��$�8�hchi��~��H(A_��&�;sNta'�!�A�, g�Aml9J} \�Kg\\ &!u�.�.�J~�fqJ� mTa� �C�#(1)} f.��M otag)K-"95}Aof��!X}>. E` ntlye1-$\:G\"��im���"&� �-��involv���K]� PDOs9i}�aE%�fJaK$�a��C�7!0(V� *�&.#��� �le��c?*�? �r�(�PL - q�� %�sZ5e2Ay��9�-4ed��#map $Y�$.X����f�J`� �� .|E(J�� � sh�8I��B\.{[+�( = (Q`�>��Go�ba<o1?���� ����� &�"���ի +v�a�b# Q+��iX.� -� � By Duhame�<P�3leb(E:exactrepr�F i#�fa�int_0^t �W{t-s} �C_s^{J�s}] \,dsB�UYusnDE:K!\bK!B�&$Afamilya� sinteg`trongly� �N$se�eact�H�E�u�%] (I 2 tf� bj un�]"p.~164]6NXN�MђZV� h]1|] a>�%! "V t-f�_E ( am t.A|� \"LZ$�� B�e&kFS���e� R� (��k]"� ��N6�'�) $"���sp�-�6&���To� 0re�"� &V�I��%6 �+ M Zvg "l�J�Gng���',^0&!�A�c2\C �UmS�E c2 PDO:��bSU f|.V�v�^�!+��}2�R)�aI2^0]J(L^��\cBD"�t!N beca#E�BA�MvB_D$_;it2a�E�I�S ,"� p=�A��(L_" +�:#3b @X!`&+hHj� geq  Tvj�/M9��son~x(�5&�o�Xiy=q�yE�& E�{���1a��@ | } 4a (\Id�+P)[�^0B ]>  U  g�J`�1K=`� er"*,� �>T]� M5!^B8�P����2^� &("�W�� 6 x��Rq=&pe1��"X�a� $U�*q,A(�)ce�%0 =2  �B� ]BZ : L^2_�k�?L^2�9�$�Z^�,AOa��+>�gA�n ���x4!�6x Nowfixv $\e> P! fiu]q�&� $\bK^��>�obECbK��2�R. )}!Ce%��%�K2OL^2�#�*+^omple�0h 2ZoLm�.Y�Yb�� bK^0(�?|�-�(<:B%�7 �* % R�Wrig!�^V`e�P[~� .�v-r!�u~ OZ�7� cludF�f�a�2"� !� �\,[\| �] �K^=] \\ t�"1}Y��l�K�R�g�&A)m � P>�l .J�Y.7Shortwa�&s%�)%�A Y ��*DA +�]Z�iD" Sh!]Jkbt��nes! $h_@VOn,�A2�&�`siz�� val��#"q�- S . Sacrifin*�bd)�� slow/ c�g "Rc� �" Q�2a!���  [0, -c �3{k]]8$c"$O#dce�[$t( �%< \d$-c�x5Y< b��4�/�drem&�)$�5-�Lv):!�b"�2. + � ��v�'hN�51 , lp_\xi ��oes�2�, ' 'A�6 "A��ya_ U��Te,�#�$ R$,ws)\ most�� _i�d.�F analysGa*J made%�Y>tN��y3a�K_%�u���*�e�tyt e^{C�)O�h�33daY�#|-JSa%� � choo�gcE�be $(2C))3Ay:�[UnQ[do�)s� ss:u }7,a"sEZ ed4, e.g�o�= or�Yne�R Y@[-L,L]Q8a�1 ,mixed)%�ogug rhakq5���I�� ͩ� . As!�� ���Tj�%} >�"+��N!ca#)�those , �F8_0 Y��l �Ñ��<ins�0. �it�*�/��%��"A�r�-:^>F$unbE�(�A��&�,B>o open>$I ԑU_)was�v��V-!�� npu>1d �>o�g{V96}&�*r"#&�5v�Iy�/in� ty. H*]Q "%)"� �.Ibreaks dHdue&�5A'act��PDO�CN�X8��'�oa顚4E&H!� 2D:R \RiS[-1,1]�*Q01\�o� wrec���E� Z.~L�ite{Lin�Js� stVing+n7��u(x,y�0langle U(y), �@Y Nm \R, \; yc �J9Kmady%.allel sh�>(2 infl�al!�f#$o$�\�!�vEbN� �a�umj"� $ eigenvalu�ble�:L"�Lin"�Le�mul�[^Feig1mGs�#�8��Q�9- (\curl�� A�>o\n) \wK " ��k�Q "N (lap {\Delta 2�X��9n�=�pX7si�"T\a�P)>�A��%)� 0,\s&@��_0>�H�!$\psi�a��V �[ $H^2(I �cit�"� \pm 1)�:�.eWXJ��4 �6%��eJ periT<���4.� wall�'mean �O&!�a� $y$-fionp�$9���M-Kd,�ny9$(<e�2#�291�alS(es�9��1�Z. a��� ��e �hgy�[A o)��'&exa trun=on�rc� N+1 #( $\g'_N,\g'' x�uBGrm�� "qb . Pub2%� ���Nm�(e$y) �y�F�'Thef��'ed��f_N��vr`+ r �! s�Mi\a#HUi \�F"`��1%1��, �!GQ��y�f)g_N�Y+ g_N�SA#g�,y)e�Fs�qi$NL|x| !��F�� NT'a] p?hand,���y�� gU�� h6�hA: possX6s`:��peraX' 6� s%y\L �0[ -5�6C%%6>5\||f_N\pn < C .� *>k��>���K \sim N/2�'So,e ��E{!.h\}_{N&�{1�&�-2ye)uZG $\s� ga ASa� u�bleB�7&Jg�R�to<he� �>�y,X not empty� $X:! I!^E.7qO�T b"2!B. � ~G  i�`_}�&S:app}� ��K �ind< v�y��Na T � ^h.�z"� ?(Zirnearly5t \b�.5M�5G%�"^�~0s��8i� ��%���}���l�m P&wsL0� J 9�� eir �:�  a8<u'splai�inRQ9%$�Z^ �n�-|T\s2C}v �a�!&D"+AV�4��ft(�e<HI�c��)O�� corollary"P8QsC:F}HIst� Q< >�wiE$&?�d)$ M2�' $$|b(t:�J���A.)|^m$6O!� $t >�� at le�.�s�\g ]{$(x"DK"D6b<2.m�9 An�"E6�tmode $f!�C*��4E f��rf4"�\u��� post%�detail X]yFF <� z�r ��K:F_�d��]�!�a9"6� .%I 6l�E��{f���F, nm'�D�Hm @ ��y偹� i] � ^���|ny1 a� .�stretc B��ra"oi, �f $|m�u v3�ly �He�&��/���zim�Zant"-D!y tJ�}�:X> Q>s,.� �-8 �A[on�#` � s.� alrev C��gy��. t0�is�5~C"�Hi�M%/��n�#��| f� !y[l�5 and �!�9SE.S:��FV92a�62%W&�d�Ae�ReN�Ow�a���&�Wak�d�p�V �A&-�.f� �n eas�(� dD[0 hi!�v�0ntI�Ȇe�q�d�ptBjn�)hR�eQ�" Zcre�} ��S{xi�(�' �-F�>w��.�U^�de�}�<+ v_1,v_2Flv_�7a��det [F ]j� _in!p��E~A��@lumn-�As $v_i�vC^n ��ѽT:law}"�~e��A�-� BAS}%a* I1* F�h�$�Vxi0%$b_1,b9 b_{n&G���$n-1$ �9? i*=&���V��"mo�i�2�$; �6=Sc6� *�R"�)��� Cquantity1_"� � �cdet} E! Qn 1A��#n��� �I exp\�.\{� inV- \trQ (x(s�3(s)) d � C0\B�%i�*F��Q ��$}�>��1 ��! &m3� }6 l{_1Q�-��>\aXW_0 n)+-,*�26_e� BeJ* %!S6!x%�.a�-�"�7-N �q!r4%io $- :Q"L .���'�gc c(a` Te� 7 d Nemo�;&�?In[EH� us5�O��Q� �} :� -��[3�XEUa Furthermg o%f"E�Ke~6��!?ў 3��� "siNth� orthogo4�Ďto{�Y n� bFxi$)<�l� �;��} PL+a쀡�m�$�we���ٯ�sZO"�`a�:�=�2\ (\ln� |^{�$$ Aft� heseIRe"�2�x):9u4Z3%lan.�5ix�L\��+a=n���.+xi�An2�:6�E;eh*}@9#a.;aL%zi=B�fIb\3:�b�w,� &= (�T�8=.�)B�>K@�j6qA AsA|A�N�%9d�e�����x�}in�A��fn- 2�HS:"nc;*]{DB�\,s�%��is R��e{law�3b�"�] "g * v�� (�  oUR�>ue),C.caOf ia�!J��ECM�� |~�>5t.lE�X � 3Z�gf�=fo@f), 1_�z[o,�6=a �b�KS���6SAuj����_-c$�� ben}E�1(U�TCP\E��O."HC $yiv$.��?$� V� r&�m���"0-> �c=p&ar`�sT#i.��X�AS�lyg'��1 �aR] -1��BASxi� I?5xH)Q��C�"�ka2d \(t�/mA.�J�� .� ��$Lam�����B!�M�2�>n�F��&��IF l} &�OG���S�9�fS:oMp�Vc�Nea�1�~�X @nPC2�M �E��Num[#ţv�gwF%��QF[!�!v>�Q�ribut�spo���)"�P�LShvVished}L w� �4�"[ J�! ks�|lDsame wayl�8 *N � M"�!�!'re���7�S"lFUY�7in�|\�G_t}|$ (-]�GT:sob!�.GUn*,cerĈ v ��DE��b�G _\f�1v� at)i�<$\Sigma�WI�te <�AiA��$C�+rotinv�"�'mj)[�e4J�:noo+L\spgen�IA���&U o&Y9wU)Qd�4q*HFARPe&�d�xxi �!&��!n]u�&O#V2003�Nits nDw!�A���U�X-survey�!;Q�us"��)�l | ia�� 1je�a heor!� ar1 s. D/ BT; {CL,Zb.�.�C�bs,9k5é+ \Ms .P(-y�t $\Thva Rl�<me!�� c�unt����% (��as�e��$�) |�E b�%e-"�val�ShX7 �� &:8h pi: \E� � . W2:Mnn� �$��3MF!-\e t!� $t>02>3y>(\Id-\P)�2DC<-8 � "��\l)�R%�sai)�be�e��%�"g}20$\!��Wre�^.pe�Fl�,�c not ^ O�%��t�8IxF$1W�x\FUvf%�{��e-S�x�-d Sell �Hg��I!�| ��2�e�a��y�% �,����E^(Q�unB [�h number disjIte�0b�Isegu7� �re�[r_1^-,+] қ�� [r_pp^+n/�v� $p$&*�excG� �$��=��)$\E�{&d-% s $�-:#$�+S, ive�F mini�&��Ab�[Ih�h���&le"�!o��s (eve�dexes) Y�=�,�qJPS87���lw hAhaݗer:J�" V� so-!ied��0��b�-d�worksM�dAnton84,LatSt91}, although� kl"g& �d.�uv%Urea yE�+Shv���6a6 tern�e self-� � *%�a-"� �6P� �Y�}�|!�no�ASa!\A��d�-�chn99ow4 ��e�&��mane} A&Z$of pai�\{�>_n,v_n�n*^$AV� $\th�� Th$�$��p_n�rs D��=Ma\~{n}P#�ce��o2n if $\{v_n�.�RbZe�^� �arA����Ua7_4F�2�s\e:!cU��} �an)()v_n| &>c, 64a� >. �A�e�y �ta�I��& in������@&�m�$+&1VeZ�d8"�l.&e� �!�)"��sZ=�*�y �sob+��!���_{m}\�s 2� ��$xp\{ t [\m![ �%m ] \Fk8:15��}6�S�,�+�d$� ��,e_klo�>gRW���Mf�� viewAl.-, Th�B6��e&�]$. F�� .pasv<��N�b�&ge�. ~�%E:r�&�a�LU�V1FZ.�`$\�9.����4A�Rz� -\bLIS:I$JO��kC��t�0a�w�*�+�w$$ Its"��Xfin�A>,�.�>�JHe��;JB_al!�$-I���o2� �!i1{i*�l-E�$. X.&A$��D)��(ula&,�G�!� a�41InYz%�J17 le� .e�qu�� B2�. "�H $\mu)�S�$�y2�]��aA muq$`@$O B, �Dr�{�sp�a 2� р>: .�^>.$ AU!���"#�E�E 2=�*e�A�!�7A)G^*m#�m'#r8 .�.IMA.�#B#a�7&^*j��& corIxXju�to >7�E��Zno�� ��!X�҉�t eF �B�� :�.97&H\�%  x_n$"_n),bF���$b=FFn)��Tin� a;X-"u�*PT"�3.� $I_{U_n�Dl CD|"���9!b a smn }>H neighborhood $U_n$!`�A�$x_a�� ��C�N$*}7{n,\d�#� |U_n�(1/2} �a��n�Z��Mg FCP`f � m B �H!�m� m��?�7"b9"2>�Acn ��7&�<B� � %a�+_n)b_n �#�$U� ��}F�+ / E+�B2_��2n}R� i2�� %~� � ,���:u�[6&�c�#+~ E2ECs"�4lyIn "�1}># e:g*�19�\| >c/2?FP�}\;�3!5� \| <2C, % b�F�.YIDH< \d_�2�c C�u n;>in>�;us��  s�2� �Vde�1Q9$���is �tru �n�= adm�}���M = X_s \o��X_c X_u��ԟB/� sub��2rVx�C��par�� 1um1ide[:out!��tF�,��c��addJ, $X_c�F=��$y�= g^sm��:^c + g^u �� c2�6qm of $1��X>( 0^ akl�5%���<�:fix�vEnS $�\I�a 0}\|�\|�Vy8 6[KqEąr. �n$\?�wibfq�B2}�PGa'-�-f M�*=9�.�$%�A��Q���n$n"��&�V� =2} 0f���on�!A �3!���-t�n $I�s negs�� �MRi���i{�8t g���M�|�\|g\|$� ^� �.�$�I�t�J1BFC.gU� f �8Fn]�\| <� Y"2s#Et; �6> C_1 � \e "-."�%�5��ult�mV��HuleFM�*�s"�(� te1,� JCk��(t�CLC#�A^erQ�.��sp�Y�e)�QM��Q� �Bm"(%� emblR8� ���*c�f��4("�C.Z"*P �?�immedi:%A_r�r{ se �&�al!��A;�[zp"*?k!��YB-mFc A;%�� a"e� \Mp M$�#4 A�1eab�:T�M� tJ���{"���#�zb��e avail�#z� �}lT:T&� �` !R���+ ��9* !�,$m.�_m�z,B�at W xs"(B#<O^n�� "� \b*�E,%�\1KAncaOB){!mu t}\BX&�sq"c:�I�#�� i)�ic � 6bB�$$ .mt�"mJr,end�/(m���p�m�].��rV~�����6�1*�:H �z���ite�M@B+y�\F2�%�"B����0)[F� .fS[ �a� situ�1!��y�  �a� the VًxZM&E � b"ք�A_Cta���E�(;u� !&6-�T,�� Also^��ing%F*� &WRN$iXcDste��< {\sc Step 1.} \�C� h.I%"�� ge&�E."�.�@�t!�f9%Q�6��eF�Y�Q��@̀envelop��-oʹ��i5�2����W ll 1F�<�L!�&i0��Rr!��4e� -box*�@$"� an ���@��V�E�&We��t�*�Lpau U� W2�\8zYa�v< laL�D�v�BAS. S-�preli�=ry=t"G-IlllFt�S sett�Vin &�L� &,ary1cI io�x/-E��e�"R ��,!�)"|�.�e �i�xx_N���a vic$DH P p�a of ;� 6 2N+2Y%� � \�perturb�R&�2_�.��u�r; &��xi_N$� uot.:U0u(x_N93Ӥ�%=V �NlQ o cl nF(�^:�x�$��� -zKt N} |Xxb�� F?4%� W_1�./?��N&� y!�,T&:&�]Y�!12� en� 6to�P e a �[e�arounk#i8 thro�'Ia�llo8#��"�0 an $(n-1)tP&��planar t~ Xi$ J@e�I�!�)��fS#�meД= e"%�9*0X�t�!�� $\e$� en�,2& $xa aV,G$\!��= �. (\Xi_'B�euniquely">�,A�ssXiq[-N,N]y`$x=� t(\sA���iY�ib �!�.)l���$D� [0,2\pi�[� ll�!�t�~a��M*�($f_{\d,\e,N��6�-QX�&��i s�Y_2�E^!�5Tlime!!�r� ޚ=<� bG_1U� -' e^{i\a}� \|}{hM*\|}i_�C_2}{NF> Cl�B4 `s &!=vA@Al�y -zx)�!�bo� �~Y/sY&�$\da�w!��M BauJ^I3�k��A4 \g(}d�[s��b�O� e'�}N\bE�26��E�ofA�t�E��e�Ag A~^ly var�8 tent-shap,un� d�d aP��= 1-|t|N\&͸$u]�*�R(t;U � rt�&� Z�A�b�1e�Fb)��))C Zt{� }{x=1���j� = Oj7� �t{��}{\Xia8sA-1Iio}:� $S(ax)) - t = t�*��Ay� Jc the "c�� x=\s% 0Q2p�wt�I�\GD&= s)�B�w&��'$s>cC 5�b�+ C�f\r%��~�J��@J�P �� u�.2��$�D��A�!Za��UNow)j҆�QA��a�P[b��S( FΆ By � h��i�l�!؝�e^������� &o 2"o ShJFfZ �]- 1$E�f=.dme�M� +on ��� ��V��a��:*�]����TR eanJlKu�rozFe��Q y*�Pa���"e j>{!/N�^$�Rs�R6� |&-9-�SV �i 1�e�<R��q��&�!��M���A; B_1 a�{-1�,���. -� ) + o(1)�)%81`qf��=�P��e.�gy�\L�D,m���a�"� erm�ޕc �aOw�&Ņ-1)�b1�t� \s),#|-1�%��\sm� 2-ͽ �P�� (UaW\{z3�-i \Fx�/FDt0B@�+�2P(�� -1)-)��BrX�1qjt��$\d��!XA $(� �a�b , $k� Ni~n \4�)� 9�.B-)!\ag]= -�� + AZJI�m3N���%lsup�\(gy�Z���J"V  ,��� � "2��6D �E$:�E_B���3��+i"/0��{a&per!�� gr�F1C7� �OXQ�$switch $x$-�`(\s,t)$-"]m�%cY& aD{ ?\�s_�- � � nt�r�y !.$$ H(t,aUy�%A.V{�!��a{T2=!�[ u\ ?�H ,\, �f{\s_1� �_ \3:� .! {n-1ũ%\r�L]���\s6qs&AL\e �������AQ��ang cos'�8!.8e_k"8.��͛$$\s_k$-th cGV��p9zE~-u �e_1 � e �°]%uC]R05�ka�"BN�kappaS=`| &P�)1|!�!�! [ ��2�� @] |%y� F#N Bea� s, $ �0y�eq 0$ dour.�d� �M \p��y .�4u�Proof!��}.a/Ʌ%l%��Ak rac{1 f2� \|^2�  !�q � I_1}{I_2+1IuQ q�]LB�I_1K�Om�-!ae \b^2 :�^2 �B�$|^2 d\s dtE�I_2�_ \g^2� FU b_U>�N� ��$ rinkE�&r��A�4� -- is�8$\e�#i% �$ �F�D9 r�� ve kernel[+-�� �)V�-LAm!b{-N}^{N}jOx�`Au%P.LjUFFBL d>C27.| "�!���"h�U��u� %dr˼*�'9 m "E esti��΍63�U�A�sssimM��2}2SU;B� dt}{|IH�Req _C1$$r�r�~.\B|̞h3��� } ] l "�"�S�qh�|�!a&L� ��unn!*Y"G an M��2*�!sl M�J�3��E!�i!S�'�� ynamNGB��!�C�nB�su"�E!|t� \.�  :�q)2�N = 0\��"�z:�~�aQ,E��BA[��ma�cl�� �`N,n,�hQe" �!c7:�$�lb�Sz/_mެG-sh��eB��XL&�^of�D�Bc�*Hvnh ��L$YOfu�4F�is›� &5�"�3MXFT:�G� gB"l":&2"�!q�E�P^��4"�4e:s!c��}06wS r7W L��4,�4F�F.�S�:�/�!WŪ� O^!�:|�mu$ � 4p�4�s (i)!�� p�-�,!g"�"��Q!! �mu + i\R ���0@m%j+i�, �! � ie ]_hf��.�; �2���Q� �W �'�@c�!Ww A ���s "�%Cb-�y./rB "�m�8xfb���2�Kfx3y� A��f6Vm61;�3 �6a��h�#.�<\>� �O_0^n$! *�2����e ]s !=�)ll !�hL, � 2�� stagmBonL . C�&1:&;#fx%���d| y q�m�t�aim�_&�~.}X�n Y� .(�><�>����*�� bP[ *��\a/G.� �!}ingred's�@�4�/E�F��Ep�6p�[% ���bM�$ �otN� *\X^� 0�O+a��%��8��n�?N� �"��]-�k#���� l�0XV] $\tildej��Om/�l5!G K�->�/!Tsu�5�pj�z��x�zd%&&�)�a,-�d vd  w9k5�)�!�*� �g�+*} ��(�s},\t,tc\ � � "�"�/�@t\ _0�0[#.tk�; ) �M�a"�br��P� i��1pd}-q��E��рh] (. �Q��A�A�!���>����m - ���r_\g'�2v0�!�� � \t96"^�Y!��@Aω�g���$e �Ps" ���`b�b2:՝�aI�O=;�~�\Z e����)��+(  $P���{%�vR4+a� x8 {x_0a�*�1p!�_�|ͬ . Du�+ y0t�SEpe�"�!΁���4mathcal{FB}_\e!��"�G �Q �K��A� �.�e���*?���b v1�1�� a� i�1�Vt�N1I�/. 2���hf� "|*.h��I!�&�kQ= 1}��$"{EF_0)&�� !>��g� ��$>$-1�� .I )J�:�Z6�L)1a?teger"�!�ir�/��qJqCm�i�)4t2  B � n� = xB� an fB. �I�gcit F("M.,�( �d&��b#Ot�(0O%��p� �!�%� +�V��N�ni� = \i< 8fF) -i^ JK�O��G8R��B�=�\f^��_�e%I�= \id +.�v �qnA  c�$$xb�E��M�J�m!W�.�1v z!aF*] �b*� dQ[n*Z.�8Ds0cl �CB=A^k�b_0�C3\Zy:a��(eƪ:�]�$\lI"TMFb&�.�%�2�/- ;= Y %�B a^vE!,9&.(�exvSa(-_i%)n SX��\C*�3E��@*"g � l � \s)}r $� �\sy�l�e:�"cocIs`l)�D-T��"COas /�0.�Hv�]���C& A��"#}� �sƒ��*�.�O"B'A�"-b�E �!�\s�t/a�!*%8>08 x !�:A�ZR �N]�%und.�Npr�� branch���po�1IA��AG�@>*G��� ���t� H^B E:.j} - = ^&)�=`�E�� ]�:�D.R�ɝ!�a ��-�8� � �� � } �8Ų6/6��d 3�G_��set. %.�9$Fort55}) T�%{+$A=\{x:�� � \�%deQyegq��.ٹf\/. Morer �we� )g�2� r�Hif�&A�� $0<�<\DO$%G�^� a1�T$A' By virt8aY5�>: ? t\s)aed!bNLpp*�'�f��|fac��$&���JE�-�j�revea;W&~ *8(�#u��_��&��!5=$4 &!s)$���*line*; L"�(}B"�JST�G.}�= \ln(��)p�,A�"�^{Z,���I *\\�6baŽ�Rx))w+ *,.�a�t�a 11!i�.*C��AA"��- z==yl�| �0~(EIB"���թAlogarith�a�?rarH&�H�� x0vP:le?E��@SnQ\]J6 L��� 2{�713:F�m�En1a�>���� �estiS�� �>��1�]all�if�xa�pX�&B9� s ��6�I4�<,�� d $V"k�s�Fentir�of >�de���A<5.7%w`7����y"?2&& fa R �!�\ pick.3�$h_\e�.q0l0 2(8$\�x45<\e�/�6��\�Hs�5�dp�/bocK)QᡗLG96."� � �5"� y �3!�y E� ��d�e�:�pu%�imagin38T b $i\�N �v��$correspond�>ing eigenvector. We set $$ f_{\d,\e} = \bP[v_0 h_\e e^{iS/\d}].(\Then \begin{align*} \bL @- i\a&Q4a_0(x,\n S(x))](x) e`(x)c < <+ o(1) \\ & = (\:Wz)~?. \end��As before, we let $\d \ra 0$ first, and then $\e �. Now, suppose that every neighborhood of $x_0$ contains a non-stagnant point. Since the periods in a vicinity of $x_0$ are bounded, $x_0$ is Lyapunov stable. This implies that for e� $\e>0$�Hre is a proper orbi!0mathcal{O}_\e�0ed entirely i! P{|x - x_0| <\e\}$. ByW density%9$invariance% A$!h can ensur!: e idZLty \eqref{E:star} onOV�. L!�p�denot Mprime-Gs:�. 9nV[!-�ed %�small R�E: havea!\int_{6sl} u(x)\cdot \xi_0\ |dx| = 0.4Hence,�5�A!�\e \in 6P$ suchIt $u(x_\e) _Y�Next,)�ach $)�Lwe find a natural $N%DUq�Lequation}\label{e:peE�,} P/3 < < !� < Pm]9._A�Dmatrix $\bB_1(x_0,% )$ has an��Halue $\l_0$ with $| !2$1$. So, by!� turb�%>2_{� �}%" j ��B_{^% 2!� �*�a �"62'�\e - � r~ρ�4, \text{ as } !�~BKObservA�aa�l_\e^{1/�}E�6?of %g �.-Bus�!�resulta, previous �ic cas�find $$%V$^{-1} \ln(6�)I�s(\bL)E�Om�$ther hand,�D= (�%)) k (\ln)L$| + i \arg!T\e gB�?Y����Ue6�A2is sequa!0spectaes�b�kHat% same t�d!.@real parts vanish!��(E���ksubsconverg%�o a pu�]$ imaginary �2�(approximatei, funca� s us���Pproof are weakly-null�e f� Z lies��3ess��al )umM genera1 �Xcomplete�Ze lof9hLsigmaperpincl}. \qed�v�L} %\input{sobolev\se�{S%�um�S @ spaces $\sobcon$��(large $|m|$��S:RIAz%�Y��describaGeM�s!� cern!�struct��of! Nver>�8of sufficiently � smoothnes5gaL wM!u$basic flow�( nonzero Ly�� exponenAF�w� eko�diIforZ5�$\S!� _m$ to be- nect@ i.e.^�%�conn}��FD = [\mminm,\mmaxm]B�a�thm{T!�!p}, fromQ!Z�@immediately obtai!�e b�pec�(|\ess{\bG_t�W\exp\{t>� \}B�One trivA�co-H�\$guaranteesJ�follows�@ Sacker and Sell'e orem stati�SM�\�Hss:cocycle}. Namelyi�dim= onARA#�  bundl�fr ��one�e��)7fy cer%Lma�asN!7trum, $1�$s] \cup [S1��(hich will be�0ved to satisf� a�8iodicity assumpA� (ii)pM$rotinv}. A=`on $m$a�� E i !A�ps�� �area!empty,%m!!��!e �� �Yp. k I�I� �P �+!&E]A�conclud�2a�yYj" s solid�A ring�de� \frac{! ac0 }{)a|�~M�YBE�:�itemize� \ [1)]��!f�� �aYp" ; @2)] $�m < sM� S < �m$,3,T Y,exp \left\{ &Y s] = C ] \right\� \s= "� a���1�a us, a)��Ndi� ,is reminisce�biM Z el as�Jm2!z cruc�.fee# �E�5� ase| two��iA�n�Knda)er�aXd no "�!�Qgap. U�� e} \�e,  %CreQ�LjPicEdt 1.x %PsTrick�mat (pst.stl�eded) %Fri May 28 14:09:26 MST 2004 \psset{xunit=1mm,yu ru ��ps-jL}(0,0)(120.00,65.00)K�Dle[linewidth=0.15,style=h+s,hatchA28 sep=1.42 angle=4z Q](6�P30.21){27.50} \newrgb(T{userFillColour}{1.00 }��6S� � >� 1.12gellips�4�4:4(11.79,)�:�:6: 5.89%9bezierzlH]{-}(68.49,38.62)(7ED41.65)(71.10,42.76 7797Eͦa71:(72.44G18)(73.5a823)(74.93,45.14�a45.25,15A�|(46.76,18.24)(47.86,19.35)(48.5356�a:D(49.20,17.77)(50.2n882)(51.69,21.73�a38� 30.88)(41%�2.5 3.11, 9)(43Ax 30.9�Q��.: (44.48,29)0 5.95 !�48.21a7A�p�a 6.12,46.0�7.17,�2%w26AF00%=38 7��9:!w51a49)wEF3!� 2.65,39.4�#60AF51E,,61.71,48.72) 82,�3)'59�5�60:(5A�G01 29,!�6a42a"91�Fai9,28.G74.63!� 6.16 2a�6!J 27.8��.: 61,26.4a� 8.06 07)(80.73 78��6ei 22.19)(69�19.10��68av81��67a�3�i71:��6i�4��73a7��88�R42��0!j18:A938,16.E91.31,14e�59.94,13�#.:((58.57,12.9a����44EF09,9.15�:z ��dot�dotW00]{->}(�9(10�, �d d�� a�a rput(92.5�400){{\tiny $e^1 m t}$}}% +78R+S & %4JN s J $6��:r� in s� &  \ca�{"B.a "c2'V? $�$ 4*N "z &E� �.} ~�G end"E ��descri�a� giv�of � &or*� � t"L� Un.�*��m�� &� $G"XjnA = � &�� &�"\R.~ L| ;� H� L�"K ]$*1N� A)@R� n t"9 F� F� R})� cite{Lif-1 tic}� �ladder &�is po�le�9Ts,�"�oug0 �"� � eY&1A B� .� b� �� 6� 5:08:22&� ���� "y�2�  )M���� �� � 4�i) �% � )(42M 6) "{ 505H� &.? V !��:�:5:%� � -: ):7�-:71 78� 4 ) &E) ? V !:�� )� 0)(5�2�)(�d  l '�aga-=%*,E� 00 '�a1 �%2!2���` &`�\$f�<�o%o-��c c- 3c)(9 �85� 5�$&` axm$��6!B& S$}} D5!0B!sB3Reine n�L�0��,L� "���p.3�� �� Combib!��abo�$�s w�%�d�xp{* &P��6F [Annv Hull��]"�ahtV���"�one��z��e O &2%G_ts&�  t L)�F� � � �aV�$�9 2�"� ial �!u���M"�" :b�q:w=s�w(\bG��La+5 �e�of%YT1� "c �:AZ� U e next )$� come�y%a@�#ystemat� tudD+"/MJum&� �5u$si� ,e�%i��#� �{0\}$, T#dax��) & amplitR 1$AX& *� ly groVor decaybus. ExIe�"llis�&8!�"ly &�!�� q!�2D Euler� vort�!J mul, sM!$#,ansport, SQGICCHM�s0&� the hyp�'si%�>Q O"ieds\ all $m \neq 0$ provided*!N>0$�us, $S�q 0 s� �!Q_g �_w"l !�h$ corollary"#%q��&rol} S..���>$�en �� � 0$�c�� ie�rp/�"N]/.��m [c,q] \}, ��*0�)\ &� &= i \R +F;�+ 7�z ��!3 spacT%(&9- �'#)i>f����!��. Moreg , if $n=2Tn)�s s r!�� !�iaxv+�e~e�N�'�'y �SQGY�A�aa| id b(a�Yu� ymme���re�� &�)(axis. This � was ��ed"u+ly�DLatushkin, FriedlazzaWauthoe�2SL2003b,  a,FS�} via,xpla��I�( ion  *fM* for 5.point�!��.%��$m=L0]���I71A�/ 2} be�� *usionq +teq$ due!A�0�}!>&again �#nto.x�2u!$ arbitrari�) ong . ! .>a� &�*ss��&�*De#M�&G$b\xi^m"h#-//s: FI���e"�*F"�!G+�!��:} !�6-� . W�"Q$a sca�%&2# bX^mi4 $ �mR*�$AN>�\/t+ule^X dh_t�3xi \)|m�p$(x) \a�� {\xi =/|^mq�} Noti3�"d0$ one-"')aleis defiaKo!o��i�) -5)��!$isomorphicaP&tensor�[ducE$vѪbBş�d�M4���q2hvC&:� �>A�pos�)�@�'  } Th./� ��fy :*bxi1} -7m�%DF�B<ŝ2�� e.+est\/sQF6G&��L-(:,ly byI��� %@���.�#uA�x' 1\bz �Xed} A_m������6Bax �AP2:%; "� %CKifax gDgax:g88or�itive�+ �� nR�Bn��A5\V�i>; � nega�&Xlemma� L:U.>�E��M� �R$U�%�-� \leq)�m�A (in\{B_m,C_m*� Ez '� max$ Fax F D_m. :axF 9 � I}&clearI�t�v��-*� *> causes\an�ء�C���,yB,� � ra(fty$. +4 5 +4 i�� F , itm|� Fb � k� ,$. Likewise,��� bB� (bX^{-m} \BX7,��7�X�%S�� m$. � $��/2�%O��Y9c�#eI6� y1�iE?�$:@! and �) |F2$*:N.�� r&*�! �� G�3l�- ���may[ �.WecQ�loc3�.)�gap@ L&z6�2UP�fM �y~.�� p:gap} If�|���`vN9"�<"S 7 gap1�{:�( \backslash&�!� (�qax\,,\�'inFm��Q� n�2�in\, B�axF�R��� }  $\mua�-"�3S*R ]resolv� seXN[ � � r�an5��dichotom�@re� ed"� > � �H$\P�*\e�M��Z/  �v6.�.aJ proj2-_ iaNn-T��� ��G %�rE04ist $b_1,\,b_2"F( $at( norm&Q:%1{� b_1 7\Rg \P k -S Kerm� BT� ��^subq sq en:!y6!} |�;� b_1| +|r� #)\xi|^m�|M�? t(\mu-\e)�  h1��:]2�]geq M :b+Nb:�E�2�*2�t V.=�$\lIAny&� !�$m[� T0�(E� act B�6�Vm$V lJPS871oM,���, int FQY 1�1�5�:asymly�e^{(\l!ut}AZ� !�n 3!Ft},)*b%&F�8 $t$. &���� �inNli�a�,Mr*��2�Y9m eqr� E��M�M�lE�\6saC| &%�IS626KJBCoiT��8. y$2��ũnot less�MA(xhil*�1�VM$ b_2|$ doe��t excee.�9$,=n-? �il +q E��| l +� axis� v�7��]on.J�;�3.� �j�� gap2""a� r'; f?s of @0$2I&�  closesQEN&R. PrecisF9 CP@to#Q79�B?5�1s :�-�> �M�Z� meet�� us, ZN ", \9���6�es  189 &��1& Dqc!��; ) Q4nd% ����1A�"} 1 _m�* ��{�m:*C>�S: }�6u�0c��A�KaJA�tan{?n�l0 S d�&�="F eB�BSs2�h4�h4W�D� {�5 �.��B�a� �=b�d5C|C \Mg_�=aure^}*� ca�2 [ (->57;s) +% (S, + ) S�F* %H":�@6=5�$�r�6r(onds a \Mp\E�he sens�Q�p�Aa�Esurroun�by�;-{BJ�>i� � ed�Es. But�G�D" <sij "�=�$ �� N<�� 8 > SP �'m�sum-J^v�6 3 }��[i,.y�d�)bedA�ڵ"Aj�>�j:f*�A J�6�ϵ8�) _e���:oJ(�D1� v���re:>$x KTQ>��aq�M@u�^L@.��1�p�) FoB8w��5k <�%O1N �S�"�*BKFur�;mTL �1ele>=!:M�),;:�. _I� O^!2,@-T��eic��A/'B��to � dual�L8JR�L �L ����1��w �.�1P9W/ e6�% �9M<��asser�!:� .isa'past�&@>)(write $f(t)� (sssim g(t)$7 sign*CE�D.yr �j=� &� N,%�[ ��Jwq Sn:E[=>T 6s�$i� l�L M>��k�Fs�"$B=PndA� fix As$\lICM�nCKK\lI)(pro: in sAa�tep&#As� վ�s. "� $m>k<."���� Ma\~{n}�yI M�1�B orQ�&AusA,���� rmer��enA=\ ne1a.� s y $\{(x_nL8n),b_n\}_{n=1}^ � %3b_n!K � _n)$}J2$|b(n)||\xi^m \gtrAme^{n \l}KH!w# ����*} C�wn� b_n,� ] �PXn�-�_je�*} A$e"E�J"�*u E`k$,[: R�= :�k �{m-k}\a# sim � S}:#%!�`���%8ef�$}�ly $n�Q-�M$.CN,l^OXM~A�Ic"� A�Q� � r �1�$Aa�Q" U"x"�_n):)#�i:� .�G �byz ion,> x_0E lim_AB"$}�CE),��Z*� %\}{1�2�*}�f�H� ��*} aP0)?p= N�u(\f_{nI�). Z�bCx_nB;_n� 5QE��)V2 b�s��$�G�$henoQ� \� ��AXS�%�a�#SQ8U��A.�Z�x�le st:I��@�Cs �I�.� �P�z J $b_0$R_0)"� stra�]��~� bxi��4ef�!!�-t}�z)\2D|^J�� -*}�;1�k � $$�7" bhTI� |\p B�A�A� }�yC�� \l t�HDt%:\R��W��A�%#I)�is9|ўh! #"� a� $-\l�a�% %5!n�%�G�٥�F�-f��]�E��� \Ms\� Y��0,bA<��W")aU��x�,�;M��;�K,�+*(>}}� E:A} |b^*�^��Ed!�� �R \l nF�we��H(n)�b�I"� Y =%�nA�%�b�X$$ R�a+�Vn�HE ��> oX �.��NVdH������f Bb &s-1Vmax2k-m��yB���w�B�#a$y'i*5Ni�*�increa� \ fikViR $(x'i'_0�� \O_0�%U���is"� �Xcha�B<N�1�&Bby e�. *�Y�,v��JR�\lW*�J2oA"f.&PE��;QE�ёJQ1 0 oriTlJ �)@Y��� ���u)w%li�.�� �.m<� If.d" ͻ1nB� itself�n�U_&NVaragraph��canQM> cq`-}*W� to1�P �*$$ >-n)|^� �2|b�P � �NC� �$(� 6� Y�e<��O)oof�G�w. Fin��""E-�BX�Y�}t� "o �:��e�"� �HѭJ�@�&� Al+Y 5��2i�xa�AcedN9)�f�Hh::"�y6� E�&*in �,mYU4A�s!��O� Ui������^k*0��t,($ )��.6�i�+E�� �  b"dir��MA $\f$-�\ thro�;�a�t�ZqS�3"f&o''5Ljis�(. O.�$we)X; S+R$e Manifold� �*�Perko}A���s -@ u�Mble m :�aB�^��. E�-�8�"E+!U6isNi&�&�(c�\$F v�c)�3aX^�ZZp=s &&�*�e� �v*~m]2� o�oe e&~ �&�%� z$ coinc�N;/ Pr"["d' .d'!�analogu�N?h%+$K A`:p . It � *l�"�-"�'>0.u�� n� mula�*�  must� A��bT�-T��(Hamiltonian-__�_� AE�Cj�%ho&�S!�_1} $"�2���/UM5�'R[Wl� helpa,B*�Vt9-*�- ��T�Qveq�BS0EGFS0 co�[l��akdef\cSa{$'$} �}O�F F\)id92mand{\by� WPXeavevmode\hbox to3em{\h�0�?}\thins�4UKV6co G4MR}{\relax\ifhFunskip\2D\fi MR } % \MRhrefA��&�,amsart/book/L:_ \MR.F� M}[2]{%!#[L{http://www.ams.org/�c$scinet-get�B4?mr=#1}{#2} } BIW e thebiblio� y}{10�;bibQ<{Anton84} A.~B. evichE"0mph{Two metho�*� stigat� %Sv�Uof Td7^�+\{$C\sp{\ast} $}-algebraso:)P"8 �9Ps}, Mat. Sb. (N.S.)��bf{124(166)} (1984), no.~1, 3--23. \MR{MR743054 (85i:46088)2�Hrnold-Khesin} V.I. e%B.A. 5opologsW5in hydro ��vol��125, Springer-Verlag, New York, 1998.�-�8Bayly86} B.~J. zhre6�2i��Vof"D4al flow}, Phys� Rev.{0t.5>57)8618,7, 2160--216-> 88d:76033.3�TOrszagHerbert88} Bruce�$Steven~A. +�Th�ld :w&AcI� me$-ism��shear-� t�:�)}, �=al �beQfluid=cs, V)�34 -.)F'Mech.,%�~!al"ie� Yuri.{8\%�Ev�Ysem@>!� M�a�m�F.�&B9!� meri� Math�=$al Society!YP���RI!q99 �(2001e:470682�MT94} Pe�TC�ant59AndrewA�MajdaIy0Esteban TabakQvFoVTo_strong +�$�bD{$2$}-{D} quasigeo)pV5 herm�6c-2�,ar}, Non/ar� uqip9��,6, 1495--153mo 95i:761072�C��(D.~D. Craik%j W.~OimPeQg9�8of wavelike dis-gn" in iU(H:f@lasl exact�:�[�@{N}avier-{S}tokes.� !�c. Roy�c. Londo r�^�$bf{406E��t830, 1��6����87h�t2�DGY96} !Pickinson, T.~Gramchev)�$M.~Yoshino16c or8Ipseudo.�.e (torus:�-a�-(ms, {D}iophEa$e phenomen`;d globe�>q�ity�~[`� Cone�ce ``D}� E�&\s'' (Italian) (Ferrarae���Z~41 ,��51--64�97)i6 MR1471014M$98k:58221).ZTEngel-Nagel} Klaus-JocYEgRainer %1U One-�me{�� I� e�;e�}r 200�� ia�75.�FH�<�k$R. Fabijon=jd Darryla& Holm�e2 -{C}q* "FA����2Nin� �-rem�clok') l�3aXul��}e �q�csU�1A���k(4, 853--866)� 2 060 0392�(riedLif2003d@sanB> Alex> SR�0Roman Shvydko* e"��S�=�%��urf�@��-��icU�}, J.ŋ-�5���2005)!�U �o0l. 1, S81--S9��$MR2126131}*� FV91b^�8Misha~M. Vishik1�*  c�"riaePtGlow��fr0invisci+co�`N��uE�J� 6A� 1991�� 204--220M�92b�5>�2a�v n��steady�^ARa�fect �Chaos��92)� $3, 455--46�93j�32�LebGod} � ,en~S. GodefeeClahE Camb�/�$S.~Leblanc�Zonal a Aa%0o centrifug6%�@ hyperboli..iHk�uart KE�ith�a xter*'ro�cI*� Uy449} A{� 1--37� 2002!132� H� B83} Lars H{\"o}r&e"} �-�y�E��~alry I{ Gru�hhren <"� s�0Wi@l,schaften [Fu"1d�p�Fof; ci�;s]� 274J$Berlina�1985, PB�&o�j87d:3500A� "��3 Russell� JohLKenneth6 Palm!;!�George�l�i8 Erg�h A.~T. !q;Sub` ~ Ōe8 toUL��I�nelU��J_ 4A198�9�993."@Pedlosky} Joseph �Geophys��.�"2 >M�9876k rko} Lawr^ �g2>"�%0JX s_t� d., Text�de�ied��-s� ��>���"�97g:34002m PierrehumY 6} R)�.�Uni�'�0hort-��|�� two.0L�d��' N%r��J�*0 2157*59.ySS�xa!�~J..PL:L m3A͠& for �  i�*O b y�mL� �3�320��mU58 \#1866 Seeley651z �Integr!S&�&} E�, b1�� "�P2�11 �65)�8!Y03LMR0173174 (30 \#33872� Shub�Me� �n(E�*W�},]VonU�B��� 1�`la� "?01978 bs �' � Stig `�sso�MR�2dv 72*hM V�M�M}>I'S �iQ �prepar� 2�hvt-survey>w%2B�1lOn re9 develop�$s�W�p��groblemA��#I�8 {E}u�V��},1 temp����texM37 � 271--2952�SaR�Z��ti�P�T�m��a�>�%T{L}yapunov-{O}seledets"� a(E=pp�in ��iS �)F�bB� �lF^�3=U.�"`� �0�cal�S dvan�in6|1�i9m*�Ÿ(s (BirminghALe(�Co.��) 327,B���> g ,O9O�V � 2QShv"R��:On� 5�=B 3{DC>��T�PDE�~M�� 1� --62SLJ^$D.~Sipp, E�ug�L.~Jacqu&� V�YlJng }:���8�#v& I�s}b*h�C1G716�2�D�� 22�Sw� s} Gordon �0I�AS�%{H}am"�%� �Es &� A�or�� Chap!8\& Hall/CRC Mon�"8 S���f a���ppV� 102,NX$, Boca RatMFI�0����a� 2�V�Nq(O� ^� oscilEOc- �a2UJ.�E�s� . (9&+#7� @6ah531--557D 7k:352l&� FV9�B.�!Afe�2!�" #� 2d9� �b� &n � 4�8� 95%31endB�$�& docu%+} ��\[12pt]{a ]l1&4usepackage{ams��} :sym��*@epsf} \setlength{Ŵh�}{24cmFwNt }{19Bopk?}{-7m::oddj-!1.5>@ev:d$0!� \DeclareSymbolFont{boldletters}{OML}{cmm} {b}{it} %J4Alphabet�y bit}2F4!� l{\a6} 4 x "0B}i.5betf4CV4ga�S^iDV5deljjEV5epsilonblFV7zj��'1�. n3�-�.3thn52V�iof13V4 kappb�14V5lambdf65V6mu^m16V2nf27V2xibd8V2pf2�uJ�rhobeAVe�.Z�1Z@taf�Z?uv�1ZAphfZ?cj3Z;psbf�Nk omegbh2Z<varz�2ZAva DfE N�varfG�Z5jJ" Z6rM2ZK�f�2ZOGr�0V�Dr�Z�Tn�qN Lr� N6Xb�XN2Pf2Z�St0^�0Z�Uv�f(R�f�0Z�Pf�0Z�On�0��new"�/mZ [1]{��bit#1}� %��?2�Nabla}�box{\M / $\n$}�k.��dbox}{\,\framebox(7,7)[t]{}\,}%%%d'alembertian%���2�LN7 S7Y�WharacD 2lB:< \dsl{B}{2pt} J48 �Y.jD B:�2N br�%BL F� B� �:� =�:adjus�0 wT L�61dsl�1{�1\I6hw2{-8pt} (#2}$\not$} .-#2}}} >� �U$s ���b�B�A}{�{A}{0ptB�slP !P}{-1R"p "p��5R#Q # Q}{-AȀu� dslq "q}{ZDK "KDZ$k $k^�L ! L}{-ZDl #lb�par $\�@alo�+r�LL "4mtitle{flushrXD��<{ KYUSHU-HET-76 �82)vI�2kA> ympt�;A�mul'(F+w�6<`tics}%� �A \�hp{ Tomohiko~Sakaguchi\thanks{t @higgs.�P.kyushu-u.ac.jp} \\ D�t��.P�, K* Ii#ShFukuoka 812-8581, Japan\\\\!(date{\todaymak�5leSab�!ct{6�gb calcjm(ng quantum"�2Y0nd�e�N9, lik�;4 Nambu--Jona-L�Aio(NJL) 9�B�F�is"Fp%� attac�pW$extra term�A +��=d�gvin� d be!�e!x !�, �>lea /S"e WKB �)xi�oon �foI<"�Ssrf:KOS}AZenWdis  y im�p��that p�hvAdll{��Z!sG5= !� -_a�GNO G i!0�vexmR� M�L= BS d. W��\A�!? cata�-�VN�Qthelel^e=.:+�B�is�� qu! on:�01Sa�re�49CKS�Hhad�� �U� ribu���A[e�diFi�� auxiliaryIgj3�eff�Yve.O!1Gap"�a-5�. �M��AGfra�Dݯ occu�<9.� M mass%L:��Gis fact�A�F�? we always�D�U�ew7ur�! XE�6&�Wi�iF�, �e[Cdr%� M@�0�@"D�Ba fail �� $��:��@not.{G�your�5`N����]!_�limit!?er�K����)}��Hx9Ds �I$6�s�� `vA��6}*��f . $Gik�V3 mo�Oi@���`K6�A,��vaHf� hig�-�.�F�M�E�Qritu�!e�x1�@`!�g @'. L.~S.~Shulmany�S}L�!��Bq&� m YDely � �t��R�"�b ��3F�.sa4, hO (s. Unfortuno�,�H�@�JA�applyac� i �q �� ��`u6� We n�c�Q6d}E zH >�.A�lf�1-know��at ���um9ac� k�P�� �� wwo A�R�.a!>�%al*�ksad���E �YLC} O}:ylet�I�!#B�"l5�leqnarrX J_N (N \TtfT�,1}{2 \pi i} l�i=n�w^{ + '�JN( HP \sinh z - z)} dz \, ( Re} �kv > �N , \�h �} �T �%bre Re $ <$�n͸�")��%. ,Z n= 1GVREex1e� omes zero�_2� $z =�h ac)K�Mr&ѓ�-depen�� �JnearlSGinZHn��Y�%B�I O=�� Ut � �?�.D�� replac%� I2�$q a cub) u��A ]ectai�Jw:�(ble, C.~Che�:~�W� � a en�I⁏�a�k}R5 as� to 1�IN I�$ "d CFU} F U� ����� �.�s $multi-vari�[fe�Gx]) 4by N.~Bleistei��B} We would 5ou�ir�tV��. HowR ��s&ca�;F��LG::,E�rE � V&aA&l!�O*�ne2� �_t@st��do��"�$ ano 8� 5Ks)S}�-N�,�_. !F�� FM<>�un%!�e� �%0K�J{EVD@ C�H�I�yEYN�]�by y�_q�$�m�0R� 2}r 6� �a#4R��<�RX�R9 ��i =ndEEv�i�%td�d. Alt��Y�"�nz� , it%�]�"2 ����NZA�bas�f)�I% �vz�Q�:�� aT� ��F%A�r�#k� a�ng B9E�5LB�� �S A$�Mwe�e�� @.2% , & i�o ache+Y[!Z][��A�ePm�5� � pZdAorgan�+2f�\:s 3M2, �� �y\�J�!1�fB�:���!����vb��"�� he �&G KS2}� � 2�+� at�h��N� }=�B�mrq� , r�+���v&�eY�reoc�)�ed5�%��%.*rsfje6�R ^�)j�͈m� �.{-]� nenգ]w.�#Q�FA �� o]�yi�{na� *�F�Q:�Y� � on 3,�� alM;to-� >��N�:f5$�wayaJ!9^�2,�-�`����B1V�q�� �&2!+r"&!%6- F�e�-�BpE�!٩�&�-!�r�Bv�e��i8��2�t,�6�a�pm � w� ��rge�9I0fEJ5�evoH �c�����us�s�i?-�{V�N^.}D{%� ME�e�?lNY:c�} 2j :nB] I,N[,int_{c} g(z)K^N f(z,� ' MG�l�&�h^!p� � s $V,.R$ �C�� km2i,gu���NnUa-s��1r�%�$c&�: <t}��Z(complex $z$�8ae��h�$qZ�2%$z_0$�mEq&-on� $�!�on6 �steepes 4s(4, $#^2. / 0 z^2 |_{z=z_0-�)�WB�sa� �!�>�aa�thatu,*ita�L�{ : � ;0X.6.\foot�g{хM�!-Qe�����ex�U5"� �R,�%o^*$���J�.50$ a�~L2��� + !�iwt per,aCw>�; d�S�d� .�� p6�!$d�n1*b path � it�;c�=>-!�!5�A�^*Z�e&� ? FF. Also�nE"�aboutD)X<:X.. s� ��I��q�conjub�\��ci� |ofݍaim.}� uId6�,�k�^ou \tilde{z}q�2y� $f^{(2)}('��: (� $ )16)} /)*�p6g&\sim&t_c�_ft( g}� O(z-�) \w") \non< k &\�js&� \Bigg[ N \{fT�+ A^{>�%�)6v <fn3!}%36J9^3 ;O(2P^4)`u�\`�(igg] d z \ �22��e)�}>g�d�]Z�Ne abb�GeTs %�n)}���\�$^n2i z^n$.� .�J:�2���. 2{��|>� $.A$�3TregarA�^��ev�r�$��# e�&��� seti $|bN|W$m O (1/N^{)�2}{3}})$R�\ie���z$N�So!���%u�%3:,J,�)�:aJ.^3�w Z m��Fey��|���%%�re� F�61)�FJB����n��prlpl�t,N �8�J4Ţx":\"negligiO�~.d"B . �� 6�Ռ( U-A^R�} ��Q`1E`�ͅ\e^g 5z��}}{U� 3} �6{c_i} d�j,\,� J&t^3O4' � ,6N�3�6>� wyv� *�m�� � hf��O��6�2 Y:equiv-DtF�,� �l�% }2}j�V}E�R��_�!2 [  \ ,�tde�763�$3 ' = 5��; �$Th"����Eq.~(t_��3})� *�p�n Ai�$�lJ� � Ai}(u'��EX1B"c_A} dt!V9- D t?| S5AirF�T"�� \a�*�� Fk2 il (�)2v��f�v�vJd\ .6U2B�D�.F2 2})�!A.G < �{�� �5�* �DJ��Ra�t�?"�LW E�� ,�h�O-z_0|>� 1'�.�I� $.� INXj�u*F(� R� a� F)J� .� &=&��g+Lps "�g0}] J�9f(z1h�@un! 2�`.# �� - v^2.8*Z ~939A�s6 ��f� j��� .��!� ) +���? �3>�42��qf1!K ��~UE��b� +5��652}\}yDVz .U�� fB;)$If��B/ >i� O( *i � } )$�O�Fu , �8f�*`JT�!� \Lx-�-! :��P=���xO�� @1F��sA�:!�Eqs�� g0})b!��f. 1})e��f� � ��-w$�*F�6� �u�\.���|�R�;6� -93|w(NN)^3}{(!g =R )^2} �\ErV��r2!�ns* r}It j��2�U�1)*� �U[y�91^{�6�u9 L� 6I  ivkh$ Substitu5,2; B)-Q$ HoBS 2��&�t�&F|� i_ ���o ��k���b�!��$5�6M >; 3͐Q6%�� ^{'M�3� }"� }} Bb  FQ 2��Hgr& �Arqrt� � }{-N��>v}� /pi} i)�I�1}{4}}� - 6�  �}N�&� 9�B� �� � ; �e#Bn!:- � �,[ �b {2 f!�]1��} .�zfu�6Wa.{Nq- b� �9= PF��3 YX m6} {m ��ɸN�s.���  !tAZZ}{of�a*Q6 l�msI�QyA-�.�t)��!f$~)��by�J�f�x�  in�Zu0-'s nNook&�!S}�s �:�$ pl�/a *o"� �o�v��� �B[h"8vB� y�jxN�u�srZ�( � 1GFV u�Nm3Z�$J{)�i֧:4�2��Q )? ��Y�M&�(0I aF�~�a&|�e`�A�>J�R?"g �*[-��JOVB{ A��H ��(2� +^**)�V�A*� �):Slef��3� 6Z-FZ  >�\ ,�)���*� ![6v�%a��[( �\�� �2 ��95}}V� �O +�^*) H mZG� ͆9B� � "a�a0*BlA�QO�rem!se�NaOa��a*2�R$ A$&�= �;M:p6�m�7 �XgeaSvaQ,&.2mJ�� co����{!�6��q :b&� \���&�z_%w� �)b�B�i��=� q\ �^�R��^*!K�V�R�zi�E�:� g0e� :��5��}yM� h# ^*2�4j��5^� � 4)9~� � ^%Κ�W.�N� �]Bb�b�u-!lt1�f2� 6��xs%�*� .O��f3B�aY��η 1*})�~N{%a�"�"��-{1�����*.�. 2сQh !k) ���i}.�\ <& � 9A��bgr� UkXE�?-gR�-N��ҍff2�O ROa�B� N�B��5�:6!�into Eqs� A=���#9���)�%"�N�  *�6Y:F�� �\,2&; M=0 [ ��2G���3 V�%�\ a_.� �"� B DZc NM.2�v�o�+<4Bio#�+#s"�/��M � ) ) s�0f��(�0�,<a'4vZB(X&�4� �%��4*( �'IzM(���"sj@; � &c&4J� "T5-4.^"t1:� �U &�D�,:^.} N޵w<vq@'V=GJQ, $n �߮*� t4!�or^� I_nqP, NQ,D�N���N{x"} d^n xi � aalA�6�� $D$=(x_1, x_2�  ��&\ \ = d x_1 d* (dx_���D���gA���n$ .��#A2� !@$F�:i.�Mm8F� �*=� (x_{01}��{02. � n�O.>��)lo�xge��lE9Cpae�b�f.�$eabe�Zg F*� &  +�n� \sum_{iT�n�`R_iQh)!2i-!6i}2u &&Oa P ,j,k Ta_{ijk&� (xQ (x_j]j} k k})+-���I��OSN��B* � $�W_11��.`4&�:5+E�6�-�d�>�-,s=@ < 0 \,(i=2I�2�-\=�2U �$a_{1�^.)"�(M6&;�A~F�"�6i6��o"�oA��5T1C � 2��7[;/5o �@�"�!Q�}$&\-j��IsF� ]�"� � Fl�*+ a_12�1�+ x}_1 &� �6(2}^9��,Ma}.�E�\ x}_i)^2 24 &&y�R2 >a}i:Q�i9 [e>jkk}HB�g �%���su*3�$ Y5A +:7EFaJ} I_n�z�A�f�z.Z%.A}{NB{n-%���0)�2�)�!JaD�q B� 3�A��d�)� 1X-��( E� � } �J|�N�B: 8Y��Nw(b� �*�3!( Qc �}�#�>�o �):-to*=&�ula�}��r$C>v�62W .�. &=z�&>2actv,�0GһqA5�lyY���& D&sEw"C<7?� ��<@;�. AK �me q8��SO �;�&&&-�y�.2��|>'-1j'bKf� ~>�V'�}$��JMN'� ��� Yw�}��mbd�����s1�.c&���{J/V&F�& F_1(0"�&�A,�'��Z� ��� ) �-2}R�,�'� \� : F?\\ 0=F_ib�.�����" 2( �ic�s!Vf��+\, (i =a$ �, Z |�� F1i}��g 4d9O.�=-� ���46���F+2�\!�{1i�u� 11"�4:fAT g= F_{i1�U%��Gb%�ij�MAe9�9dX}�A�ij�"�, jr�2S ��v%MJV��!{*�(Y 3>��ј\ꡗa.k4BV %�_1 i_2My i_k�kM*b�� .�R�4^k���{Q�}   x_{i_1��ga r'II )k��|_5+=>�� E":KW} s�� � " � 6U4�!��a f�)���-n"B �on�:�,.'a�"Z)e]gJ� �2?"5X �}{M1! &�1Di �؁D�CA�11�"-iQ~ ) 1^2� � ,M.��>|% *(F*F*��=ij2U*I�) WIr�?zX*Av��Q}U~*�F6LA.�%�M�(-�**-`%!b�K0an���-y& .qA�W 2q2>�\ �.��h<��i� 2�Ȇ��[�r�9nc-(q-)��aE�>*2M&� ��t�) $F�~f� �FH$�Lm��f�U�Zqбs� toR&�&F&�6�"���&2�a"� �i�sJ� * �&�&i;F\��y: [N  \{A�Z_0,"� �� 6&*&?��� ��*�-�}* B(k;6�0q_i-iU#��!&�;�362M!!�Y"JFH�x6�m;e�N5/ ��".�N3 t_1iY ����^g bt_i 7e�f�b�!& =2��Hq���2q�^2:��R�&S�J�i^M*/�"�8.�N��s>�%.��r& �D-&W%%[�tt \{-FF "V.W)\G%�"%�p��$j-�R��%[)�>8*�7yfrm6�*�@&\2�� �#j�8�.�+�'���d�%��%�n�+�� �^{�*1}H.=(us� �m49wbf%�n�AA�,��C�Xj���uBfs�a��&�m82q6[IF�~� ;4 cFQ&r*)/wO6LR&�RB}�.'AB' *��8:\�eTm�FmC!~m"�a*R!bAs2+-�1�B�2+� �7%5k/G(+V c��$R�* i"g6+/F�+�\[Z^H�k�4ula~(\ref{asym�ptotic2}) coincides with the one based on�WKB approximation. This fact gives 8\important result that $mean field6J ofcmodel �4caustics is j fied in)sense6Dformula~(\ref{asym�.  \sec�T{Conclusion and Discus} I^His paper, we derivetYrintegra � �, whichG8can utilize whege6 has only%u�saddle point $\mbit{x}_0$ or at least G�$o not know[the �ano .O,7�:�$z_ao(alpha=\hat{ $}$, exists-�J :P!�uni!�./expan!l -�,neighborhood!�$2y@. Of course, if�!Kfind two2�!pe should5m�Fthe method presented by C.~Chester $\textit{et al.}$ \cite{rf:CFU, rf:F U} A40N.~Bleistein ,B} soI�we� obta �- =<5 . AlsoEn show�ZE�DjD�!�(ula whose m�convergeQ guarantem�validityE�m^� m�NJLi� . H Our next aim is to�. ly ta� y$to quantum�Q,theoretical �H��q�. Wa�ink)�(carrying ou��isk very9}:E�$reference~5�KS}aK!�lculaAUA�eff�gva�tential�fGap equ�6A�,� T�in orda�o supA��Q$nfrared di%�nc�Da�, occurs fromT0loop diagramsiPmassless Nambu-Goldst�� oson �@introduced a ferm� 9�8advance. Accord!4toV2!�-�-�B;, becomes bad���� �� = 2  bua�so�a:: 6:�herea)C6���ach m!�on�W�! 2 ��E a!aate 4x�� �is reg� !�refore���=R)HLs sufficiently smallE`$comparison��>typA�4 energy scale,�b$s possibilak�`%uJ����89�� �bet�-thaɗB����y,� -est!ee�q�(=E�)m E�$ auxiliaryi�EU�^/g./B)y� nter�ng�DinN�8OH}, A.~Osipov F�first c6� � corra�ou�2��N��B�fo��9� 't Hooft �a�sbdealt)chang" vacuum stA� duea�it�Y they sugg��d!�t i i�he� �6es"�$some value%�9coupl� cons� � e us�J�t�'es�>� � �)�� issue. \vspace{10mm} \noindent{\Large \bf Acknowledgea�$s} \\ He wlik% A�8k Koji Harada !�rea-0is manuscript!r mak�useful1@�ions. \begin{thebibliography}{99} %%� % S!iHmacros are availablij!x.t: % oEWg�0al� \JL :journals \\andvol : Vol (Year) Pag A W$individualA _6F\JPSJb Soc. JpnAJ�J.�� $2\NC� Nouvo Cim9$IJMP: Int.>Mod:z ANN : Ann[ % Usage)�@\PR{D45,1990,345}.y==> �~!�\ {\bf D%(0), 345% \JL{�~%\0,A30,1981,56}G H A30}H81), 56 GID{B123�5,1020 ���;95), " �(�%% \bibitem{rf:KOS} T.~Kashiwa, Y.~Ohnukia�0 M.~Suzuki, \�  Path I� M% �s} (Clarendon Press, Oxford, 1997). %2yIKMyInaga` D.~Kimuray(T.~Murata, JiSuppl.azD.153, 321 (2004), N0(Vol.111, 37)8hep-ph/0307289.:�K2�$Sakaguchi,I+i�%�,D68}, 065002�3�ete 6008>e|S} L. S. Schulman, {\it Techniq�4�)Applic �E!�a>�]( } (Wiley-!� rsci� $, New York!�81B�,C} E.~T.~Cop� }A" &n %�ambridge� versG q , 1965` 2�vf_k lex � s $(9 (,\xi,y,z)$,%�$C=A�8algebraic set d� m� b�e"�\\� *�Dxi^2-j ^2=0 ) 'O q metric $g9$ 1$by <b{>!+8ds^{2}=\frac{1}�(�{2} �{2})}(-d�{2}+d  )+dy zUB�%v$\a%\neq0$e�aE��  )`AZ�?0is no loss in�sby� u{ �� Z=1$!���� �ݏI*1)#>B�-ole]� we delet 16�!�P6NR�$Let $V_{0}.�2-C$,-. !2R 6R!  1��RFR�uz-3x)Z�VxiAUKVJ Q:�I� obviou�`�V=%>6.C}^2$. t! it6es�  > !*topolog��H$.E&.%$We have nes (f a little 0!l6�"Շs,t�8see [5] or [6]..( ��"� B �} }.�� % aB�wee=ihe sub�$T$_GL(2,�����isI)V� T=\{ dpmatrix}\gamma&0\\0&\delta%�| a�\� B 2�ly .g toٳ� \astF� $�)n!%�al ��� �q*}%�0\rightarrow T�!V7��)\� to Y�\xiE�-xi+�"[#R�a.�sm� . If� ntify�e)��M+����)�  �� �xi&�\ &\xi�in >3!Qn�+�A� �Q�,�8a% jugate ofA�,>n$C � wm�� Jf ��� sqrt{2}}&F\\-FN(!�Z ^{-1A>qzK �E�wʢ=>m��.� =� .Hav��0 abov: A��,!��=a multip�MM� fo�� �z}cast\primea )=�A� iex ( et *B��(easily chec �$(0,1al�g�ty� in�e quA��}5 $()�}{B�, \xiJ)$$&!q>Os�ociat"$5c�ta/ r��![ �en(oB{\Phi:B>�e9�A*b:L I9J�rvend.`In��!N��&m�. alsoAmB��rget)� @u�Q` �E��E �K �7 .;��A�'�,q.�)� left�l�!�}!aE\ce�"$line{$L_{(�x,�y)}F�%�$!�FJA9'=:\57E�:�\\!a fixed՜$>Din �. u�y�� e�Nsherv| m� � K�hC( �>Qs Vm!�NF ѷ} i&@�-�ż)Z� -�� ,\\ $$G_{1}=\>��|)� Y  =1\}\quad� {and  G_� NOj} , V\in� R}\}$$\\ Dea9l��@$�a��18E���nd 0���2/1}$ . Sij($��)$ �SNz .zRja a:� �&_=�k>m �m!� 2� e��\&� u��a�� cal{V}E�q%E� triv� bracketU\2� >}!d,M$aR/is,A�( example $$�Pp� al}{ ���nFxi}$$�is i r_ o��a�expon��al � � .\exp:Qk� 22a i}���[ spli�J(z!<,za;)&=A@z  2�V$&0\\ 1}��%�N[(b\� g6Tex>�0'0�020)��:�e^{x}\cosh �sin \\N+@A�F2�f�(Ng,g)T -�_9��1ex�h���of� ar�inP2A�ctP�,we �/ NA�6~�i ��k=-d%Z�w+ 1 6�2���I֭1V-a<map�� xp $a�a � �sm ,K �ve��X 6S$��w� composi$�a���= �Mquote�6$(a,b)+�*$!%B��) spon���v��ͰY��){�� >[=a��$.�E�I�� %v��$connectedn�.!u ]I�$\s{Q}U����$�0covA!�:b�)�� p3 *s�f writ*��a"2R�k. f{i}Q;Fb1r2 1}$,F�Q:(nWS}^{1�) �2.6qb.1})*� %~>2m�$align} Q(u�!e^{ ��v},u�5B1}})=5� ?+:< ;61}) &� � & 0\leq l,vk<2\pi�- � � $\Pif2 202�90�L$ &�]�(Q\circ\Pi$ ��.5 wo�� &��6���Resst'$Q$ \{t\b�I)�:�{1\}$�A $ta�eq v� ���M�_Q_{I,t}5yY�Rw�� �>|b-� _� �A}\tau},xA)&=Q(t6�,1)\nota��&�tX}��(t]�W)j !�F!� �>R! f $t=0$,$ �0j�=M��e^usin�6�)2 IfA�au��3$t vari�.�|8 U}F�*!�R,k9�2�{2!)>�01.� �� Q_y(t5��_>� #Ń>B� B?>�J"6�V(!�h6�',E$:&�$,�n*Z �b*} �Q�2#J�62J! ) \\>6�(!�+')>P 2H2*-.�*�  $5� ^}M�����6a.dZi)$ ~: be �9edA fromu�o�fg3&�  along�6 :VLn PR~% af�5:U Z2-3�\\6:�=Vpi.<(-6.6��),#�� J$be  &=-{��*} Fo"U|n��������O*}�6R�6�:� � �� t� �zt>� t:����MB0^?U�(II�1})DI}$� C�.&Y�-rFI}$,as n,� allA�A; e $Iru+I.7�3H#'�'e Ss ^*v7�#, (2.1),(2.2)� (3 E9�6} � dAl %� I$+T�"� �&�#6� �/1Mv�)$.�$�� (3�M��� �-dt�+��.)Z��^��.Y �^2 ɝv=� *�� $� MRy$� q�%v one-paramQ#a�F�$*} \rho_{v�u\mu ve� bZ  a�� bt a)F!�n��$, " Equ.e�{ q�a Q2�7 73.5),!�2�xirxf�%J�} O*is} wv[+w�A%���In @cE��- �-%Z(1)�,B:is$e�!�-s�1AM�A (2 J�W �!�B��an2�al >� � ��20for e@$t �3��[�[�.�� �",E�I�!=�.���r�}$ %) D�' �a���Z,respB?vely.>�:+1�re�*� $\phiq]eld�� �P�9EJ/ �"y$Go�dx&e[]{M��$6�]]��%)�oryep#.�1�A���:�� 0��12^w^3 NxAS� \�?yle�5{figure"h H[H] \setlength{\uni }{1cm/pi6D}(9,8) \put(1,6){\�z,(1,0){6.5}} 4.5,10  \athickU{2pt} P2P N5}}K2,3.5){J7.c2� 6NiQ6o��n4.2,7VpIm�8%|BRe�5,5.8>�t]{�+1}H7,4.7!�BK C_{3' 5,3.B� M2&2,2F�� C_{4&} Q� \cap\3{� " path $C'(��6���"m2�XZX14uY5.5%�big�le{3.2M<8.5%�arc(1.6av135Q& 10.1m�-1yuJ4.4m26 y67.1{ e�3uT3.9.-iYew �6.}� ; ��4.2y�1){6.63,1.8AU W1){1.1�Gs �8,5E2>�[4](-1.1Z13){4�l6- A-1`6�B41.53,-0.47){17��7.'�(1�1�3��<�;,dashes{0,0.2} E4.6,6.4��6.7>�ba�''q�5.aG 2){$� 12,4�B�� =\pi>R)��)0'10.5,2V ��P�P�2�5,0F��4.a0a/!?BR/ AGn!�s )o^�410.3,3,13.3,6)v,(0.7,3,3.7,6F�!�=\Pi(C')n��.�R� \cup� up_{)�Z� 1�;�Y�V�)>�"i/b= kb >[ F\ {Lej& y�~� sh� x� 2�C ���]6� ��, M�!L$ N. Now� look a0=�J�J�"X p: Green'K'un�9s 3cu aŧ �8�R�@F�9C3 ��� sL��2}$3�4}$ ,( F < 1 , see[ 7 ]).%��1�iJd/� "�Q-plane"2�-�Q�2|Yt �0�Tn let�y� �2�(j�'�"��4: <F*� 55t�Oa^� ll bkTw�Ii�+2U:z��wjwin�Q ��uL:� v9!"�52N+\infty�� aB�;  2}$ apW,�Tre.i'�.�8| "�<An open|;}��V�(is�# topy�5ivaq:to�#torus,�4�+non*(cohomo�4�8s, precisely,$Hm!(/!;Q|Z}_�7"� \oplu"� � H1BB.>�) )�O* �4�<�9iesO �<��!~�lex�V$e bundles ��yIt M=m�Wa�~phywCs*wC�.tSunm%�+"tBXM� �I1} P> Y X,W& 2Q>�@ >��.P�LKD,K ,42:C-1995. "MJ2^ F S�Z]"��-J[,2,45:697-700Y3YG*G%p�Wmo r.�D�42,46:1869-1872\4\ StudJX new�Zory. �D Basic�D (inDese), 2003,2:28-3.f�5} Aldrovandi,R. \& Pereira,J.G., A62KT�vto geom�-DEs, World ~t�E Publishj$Co.Pte.Ltd�6}W�P8nholz,C.V., Dif�UfU�;%� ��e�calM�s (Revis�.�A)�Grth-Holl�2�mpany�HjJU<7}Niemi,A.J.\& Sy< off,G.W.,�MEbAM4,152:10AX� >��&�F uM�Bal}T\)�8(PRL, dec 16"�QLs, Jan 23 & Feb 28 %:/H0prl,preprint,�/,pacs]{revtex{F^H/twobHN0*:HH,, amsgen,amsXMbsyop hm%H%.Dckeys} H&�@voffset}{-.7truei�) ih9Zt}{9.4#%>$(width}{6.05R$hJh \new��em{thm}�ore�-cor}{CorA>ry�R6 lem}{Lemm�Gprop}{PC�)� ]s{�59defn}{D*?J�{Remark�new�* and{\PSI}(rt\psi\rang+J2$H$hZ$D}-/D .Apd&�.) �eps}{ilo�.7sul?5 sum\limit�&. � }{\intV bh}{{b/2>� V}{Ve`.Maoo}{{a_M0}^�antom *}>A aos}+�2KkJkzJkJk}FJqhq}>�no}{n�:Wk�\bf k> pp}{p>qq k2�h!g�5!�H>8hiS 'B�@:�4xij}{|x_i-x_j|: halfAW box{k1�6�E&at�E>�FFFB}{F:N G}{G:x-r>?y y>rmax}{� \al,��{F*inJ*inB*R �� :�ZZ>� }{ �Re>� Im>e}{\wide%-B=vv2 v>?R�@R> aa� a> t!dr{Xnst. \,>% ] $ J"K��K><X bf X>Trrm Tr} :mvp-nord{\hA�\boldA� $\vafL$!�� �G���{J�Xc;v $c$-N�O Substitu �B�]4ic Hamiltonian� �NtElliott H.~Lieb} %\email{lieb@�� ceton.edu�Nffi[\{De5men�t�k>8 impuo`fact'��AAa�ctE~I��ɛuY $\no =aaɄ of og$V=$ vY e. (�4%;H arguay "�i� ). T%�s�| se-E��i2�(BEC) 1ݩ��IՌ.K-�''RJut, how)&, BECe� 8���=o~it�e�.* st�J�7Agh�b swer even�(\n% 6f(|3I�a�a�bUgo@ tool�9#4>Tbcopic%�despite�;EY!P ough AS!�� me�s9h zag}aWa��X0U confhm�Vh�Uter��� clar"%  c�c b;d ful.&�msh��>P�d�:re�S ings. 1.)a�!�1�'s �(be3A)F>��hw�+^ . While h� d co�nt,s,di�h-+�Berezin-�  in�+ m�,BL,Li,simon}�Nnd��er�we*hIupper b�WQec@Y $"�X�+ -GA, ?hDS3 nly i?�b��a�Im�total�m �*��tiSir, \*Ui�N=$ clem�. \ 2.)� is6�@g�� yond>qy*� 2{s�fo_�p,} $\kk$-mode�f��,�vid�f��+ &iswer�Ft�h$N�o \ 3�WeYE!�optimum���t� x�E��6�$\ll \no\v�#W �gw�  b2� !7d�A�e.. MVX&KAˡ��h" U (TL)�� >� $| � B � |  �&�q� ��g+$Q�i��amoN B� was �p���Y:m �p��OP workmr0gin,zag,BSP}.A�e�kAr s�Sl! �Fa%�qH tre�5���Ial�Ium�%u (fannes} or 1�if�A�l,� suto�\foot�� {E�Nonl%�i�of:} A�5we�<mit�{up X,A.\ S\"ut\H �X�p a di$a�D8f item 3 (math-7d(412056).} ��we%P ��� �@�G empe��8 $k_{\rm B}T=1/B($, eUoqa�so I!aSny (� �I��%+e7[� 4case). To keep �!&a�r� d�xp�,���i:�6w�RbenE it sketchI/lactn�Wͬno%%]-�p�0!{�detail ��o�r<���0klauder,feng}�Z��&@n�� ,lo����to�si�]iRx4-*/ �ws effecAL) _� et�  �8liebcoh}, e.g.,,um spin syst��Tk$S$�<k Li�� Dick delmjHL �`g&lpolarosLT}XW!RprA�!� Thomas-d"�O xact6�a��� �$li2,thir}.�7� rete�+%Fr� cIent�oo�����[ !� �we�`A ��","z*K. % N� theeq��2"jv s ho�vaa 0=n�ts�^as 2trunc�}i (�``weakl�rerA �''-��^� ���_mod"k s�*"s\� �Sp�pm� y inc���p)!W�\not claXc%� T3�0�&Rqs�iid& � �K��Wly ��stA(AA��mF� depegtj0%� �� %�bEƩ�to o orpoEin�! gene�Um . FskA�!�4a�ll�� s, n��#0.� Mo� � sv* TL),�i�gnoQ �BenAb� �[l�Rto Of !�le� Con�P� V � .a�V8B��n��orir`T e. !�start� , /_-�!2�A�gt.a �dbox"v�  $Vbxq %���d��-�zed c���Annihi"G"�sb k, \aks$ rs�Pcanon zGm~Qo6r DsB8E} H�t(sum_\kk k^2X +&�H2V}${\kz pp, u$ \nu(\pp) ~k3pp}^*qq - $\ak \aq ,5.W �} (,HT$\hbar = 2m =1$). HereK"nu��Fourier&�8�� wo pote3!$v(\x)>� assu*�#I�aɧ�5 ]co"� s$ �kk)| \^E" <�%?��!�harU$rD �s!�a�taken�w*a^�f�GOAc F�sut ofe- JR�7at a ( 0 $10^{12}$ eV.�' to�ve,8�d��3���$�utq\Y a negligiax�-) ��a�. � � D"E N�me.�$ \r{A}$^3$ɖa.{w�7we � bel� .p �a0 hemA�]� y �1�/a�� �ruly �� $V= !V23}$ ���{ren y3a���]��x4�� $�$ by $�ryJ]in $H$�� a2l$H'(z)�acts ��Fock-s�8\ll���s� !�~o$,. Unfortunat�F`"h8te���"( $N^>\equiv�R[ t}a�I�Amf{ni�� *jI �fgr!*��  mA�oS6 $H_t<= H-  N  ( !e� + N^>)�7� Ling�: $H^\ UK(z)= %e G (| + Bm�%��"s/ z6�A}\label{6}  -�4( V p(\mu)} )D \Xi( &= \Tr_\hiqP[ - 2�]g?.E'5F\Xi Fcd^2\!z\,Tp �L6U-(z)] >�int�3 ��b$\�8AX�Hil%(A�)�'��hip��ck  \ourd]��$�1peQ dxdyT,W4z=x+iy9"� s $)Y�X$-!$%�� corrU�& ���ur"T� �96TLat $\mu< \mu8cri�}}���exU=a�:$. �C�� non-�.>�q$:Y�C�} `realiZ�} � v5B;�,<��]�)p� MGA�Ie�le\;Pi(z) =z\� z|\ proj�?n�� � 5� six � t����m!� ��ЁY"'�Y!��.] v}zq} ( ed)�^m(ols}):mnol�!Mo |z��z, & \!5 * |z 2/^2, &.!:[�f:1%́�6^sB� ^*, � >.E6\ = z^{*2}87 38�J�4. =-�*�� EachG :an)v�-v}� O� "S�Qz$)�5$�O$= �ly)@ a&�  $F��*e]�` $F =�[t��R Iȉ�s� mA A�6 �o &x%,aoo %�9/ %�-19!�!Es7=�>-�I*. z� Ii 4 -4 2 +2^� I� @2A� .�!:�$,Xd �],�GR ed �J; q*R �le6b�\a�a�� s.�2�@ .' stea�torwe ��l�ly &�cQd�r��as�{��^�}�^(z)���+ e[ �3Q#\L�d'e} 63��mu:Big[ (9�)  � )A/- " 2 "}^* {\p"�*L7(26N+| +h- )) �] "� �n�l stepa�to� two&��"�m!�tis1%"� �{�} "� \geq� t \, �< ��+� equ���Ps:�$com��2y66� s, $:% \Pi I{�IB6ty�B��t� jd �,�\o�A | e^{.� } | 6#��% .^P���2hE} = e^ tF �Bb` i5$%�ny �rr���� .�% is J%'a�!���e>�!�a�Cv.� ("�%e*�\�9)5�g � �]x)�F�n %-�)A�beA��eigen �B 5J!n2� i4 xp\{6�. =B�\!�69� *� 2@\}6��W�:�um�#l sW2�( �S $z$)� G g��52bZ �D!�t`$q�� l��r��) $i�sez*�� .jS�1.NaXi' f� 2� b��� $E�similarA -$ excep7at 2A!�r% !�~ �|*� t��z"� . �S|"__ju�]b<�p!��� c>�q.]�e�aBr!5 inner� duct usi_j(z)�=�Fz| ��a ia� "�squ� � , $cUN\i�t| �� \�p�w#$6�O 1$. By us� Es �yLnk["� � |�O  | =l J5 � � :>�  ) 6EinSu�%' 7��:.1 ��-evb 1�$1E%�� !�a2�-��a/2} �M�To�Hu� tra1�T��A�o5_�$ aJ"e �j�ցR\հ2x � �- g=\>k} UE9N�twi�D"źyK�.��ia��Z�5o"�(anT"� &? 9#J.8Z2*JQurA.QR1$ \\��j�x*M r�!6�b�o N� 5 Siuf Tr\,� �+= 1> last!� *��%re te5k��}Y�6b�� �� | sv  ��:1W�eq�� ղ ��� �'8P�Q0%` �x0�ɧ-�Mv��BluH>� try��r�e� ]$��mT�>�nd�o%$:P "{ = q(�&s �md�&�er&�j� �i� ���$NQ�!� =62 A��6a s� 2w� &��$� \pp)$^�5 �  jNAI�2Q(Na�+\�60 )/V +|\mu| \q5� Con t�2��.��-��� &l B�� -�Y-� +�/V)&Q (�+ �/V)�Y�I�1��E&�� e�1"",.snd�� y TL % �c�i r0}� .1}\� Clo]A5�31���es��E�R!U! )$'�1.�'0 n� �"�)�E�\max_z"V�5bV�&� p"cx}"us 9*�.q��!ei� ten�$�&V�$$$in4�s.� @'�&One d�}�m�yv!rd� )!�%�(u�refP}"�*M�� junkE�%}��28v9B�!��j$-�s>Va� of-��Ve�!�� �.R���� [.~MD*/2�P#to&+|�&}� $6� ���5 �ma�� �$��#5�, s�k%�M�l�Q�}h�EA��r * < F��i}�xiO u&!���h�8 ���cPv� 2<&= ] \\ + c! 1{�V�_{2�}"  |�!&�N>* k�,� Dropp!8!i��:a<!�9tA�� /� �=N'���.�+�.W��!V)"E��B$\!k-1}.s[V\rho-�+1]7  $$Zi��|$%� ''$ �V. O -iz�2�3{$ le*�oBhM moreu� �I2 [� .� !��3{z}�52�b*-��^ F+M 6��0�.one, sm p �է agh0-TL�*�q��\mu$)�L'E#*�-\ EF% 1[���)�%�WU %�:�a� H_�\+d/V}--�-��bc.W oIj 5��g~ %�)-Qі-"s&!�.�� $���3eir"�'s A:ac�7at g7($O(\ln V /V�3 ee�1e�� �3"�3�2by Ʃ��xa7rg4s,�-/%��-�super')��Jj+�a��%�nA:�1Ym���D-�summar��2situa�  so*6\���e'o��mg:�!1i%[E�al!gTL 8+F�&m�.   = p'(� �  =&��>�&$aA��/v a�b�m� inM� ���m5�*� atQ�$��J2�$vx�y/\�-iә�dsu2p D2�#s� ulta�)�p As le,�xof 00E�i{6y�mp�5e�8an $N�$e 6&1��%be*U%. \�2�2 ,M�r*n?* !TJ�%��is ��.�%E,& 4&a��6 �EE�a&�8&v� 8%&*�finvaria�% &��;9VF �I�!m$� �D g��h�EEk/%&.�;r QSu��!�Z�+ A�de�Ylou!�ir�(h#i�; quir�+, a.(��'meag of `/ens9f�;9g�9b5 %dis usu�+�8"��"�9,E��'!�b�7t�_in�-Dbog,griffiths,roep&-ff})�`��'0Qa wk7A}to�� r $V#�$H �90E4=9"�8L�a��( rel�kmea� !E��>e5%�ɇ_ ��on. I5(�� exp ".HTnin �&�-zi�"}�o%( �T�4.��sum_n n �r (n� !��9 a�edZ9 =n$.* pl"r�"j� K(n)J8TϢ peak��t.4 r$n$ v�"-���%o_-�-�b$.b$J9!�flat, upe>�a:oX��5�%,a��� n=0$�/Ref# �"{6�@h��7��$Heisenberg����8magnetfQ�};� virt�AE�erv�!��8�2 angu�_?,o�tribua=a,%;� $z$-� yPVuT, $S^zIUq0I�v dee.3Qp<($|S^z|$. Ev�; it wA-)k[�ed �5a Ib�,lf-j)t�} )iz �E^one gets!! applNCa 2/c �P�/�'��Xza2mi(5>j �J*<0q� .W$wK_�mbda (#0im_{V\�S} 2: �:� WCbh�)( ��4wY ���4�>�+ O\l N=  �(�V}( M#+ ^*�$)է3. !-� ��!�g�?%�"� �6� bial�@�-s��a�v r al� ever�A �$%?e"�� � _0)$K V�!�!TLa�aN$-Q� |� $XIhat� _0=)� V\to1�|z�(a� }|^2�-ere $  $v�D$m+{�E+�y H'6� ��3bw 19} M9&wno�s6U=*|\��%Y;6,|^2 =I�)�K �&� �(}� T� �Uldk �D9�Y�"� � �is&�$�;"U( Q�)�C8 (upwards)��he�� 6F]N���o� O ݥa 8�gisI�:�/hV#ma�M�e�0+!�.=1B-p np,�Y. ��0a�%g���31�noR� �! ~fo�"] b�9<�n�p�p����,19O� ehw@R $W6@A�� v+2� �q �.e��1�}\} $I�$.k3:=%� �E"� �S��a�A�"~TL,q � �19U [A"z J��' 0!2�$�\�dz+z^*)�� �8� ;( G��' argtB� (��7"0[Sect.~1]{DLS*B�l $[H,A|])'8[�M�!�D+a�pȪe m. H�C�\-e ��J� ich9 $W'J�E&n:E �%. H� �HnFp!MT2 B i��V�.�)cA���h�ـ!�' ��*��l a��)*�3� ra�"�I64ity})�:�=!0pa�A . : G05;<2�2NQ� ���_�,�<�uC��0=�- ���e���#�*��* r5O n un=W�(&$ $Q�|As+T|�� (N�) + V/ ��m�>0�[J���2M� �0"��%k=0%)a\�v!�rD�0$.) At�of"e������ a=�y�!y�VV&� i�i�Cor.~1.q�,� �:@T,"q2um �,�3ADm�:�h Fq\zeta \�y V2+ fsyF)"" I�e\e!@x� s $��$NHe"�9"XHd��Fextk<d�a~bl)asa�e�s .�с�radial s!�� F��#a"mB�6 m\, �e�8 zero� [#3�5��D=D��8W&ar�Vs� �q�X��� :cA&>I��r� /%�{V��eqv���  �c����A� betw�N ��2B�V{:Run$G bBa�now:bD� ��:=*a� x add an�q E,h2�E"9>$\eps F�g V�" &�& f(z� /2 ��>-�f$%���$fiJ�ss a nice2�A�E'U� Q�ed�.l �`! *�bQ%�^�of $F$3 � :%�D�$�'NN?sLe�$C>0$ Yc�?1$��4VF�.�#A+| V�*�$�  z|z_0� 0 1(2k-_0 !|�#�$=CF�!H~ �G�A>?,!�)=p6� �A7�.y�if 5��*E�|��- ��.��(��eisBZ���$| |$͆enoL(kA�=Qowa�$�#�%sa�a^ �� �^8 21} R - >0wu"8:� n %�� &q/� V!�uB}�&� BQ � %�:� $�.7��%E C�!�+.Z9diqb�W%&�.ly loc�)�,z�=1� %����,D ,��B< =�a:� 2#���R�B �T�9s��-���,n.�] / ps$-��dI�Yf��!�A�isŲ . B��0�"/KW�.&P6bd�=9QB, {Gk<>�F-�6�  .�+.^ :�:+,�B1.�(f$�arbitra��$Vb_{Z�$3e;}��%�\, >~   V)�$aY���Eg*2� all *� :pro���L ment�A� ��-S%l-seBG�2� l�"� (��?�!� EU,gs�8AI BEC) �AaseA�  ���� "�m 2�B_ $ *�1&ix* -  :m M�6$�ɻ�"��\or��@�|� ��#����N�b�� ��<־�X c (d�a4XXC metry)��� us�J�fj �${��:���iCoge�@ O�a�,6�� *� �� monotXin"t�. ���TL!>E_>t ���x�N�=0}� @ neS;TmU} U"0#NW�p!���]tui�ly clear�h+YmRbes�����,aO�N�6��. M�*�!4&��'*�P� hyp� -Ye��a<sCY� �G3A< "DG E�"GF�W)eq�TLa� "gA�� ity3W��$ank V.A. Z� bnovE� help�Tom��s.h�TN yL+O� by US NSF$C\ts PHY 0139984-A01 (EHL)$((353181 (RS) x<0A.P.~Sloan Fe�hip"EU [X HPRN-CT-2002-00277 (JY6#�FW � P17176-NN�JY�*�]>h=�&oh� N.N.~&L, %�@Oi�W�]Llu~�} 'PIzv. Akad. Nauk USSR,{D1����]). Eng. �. ��P*k (4).52x�45See��Le~y4M� �ToAs}, Gord�� nd Breachdi68)�k�#J.�U, 2�a.ӳact:!Ag9'��&��EL�!�JK s}, 2� �)$�26J��VE�~U���-B.~Bru, �l/�� l��lN�M},�k Rep �350}, 29�02'BL} Fa2V,.�0SSSR Ser. Mat M6}��4�722LLi} E.bbQb��Zal}Oof1��ACs}6H.F3Aj327v32vW Bi�m]%)�zxa�_"�!:2�.�7�24�8:BSP�P~Buffet, Ph.~de Smedt!� V.~Pul\`e2&� -LE^syB91, J.~eI AIR16e�430 �3).K�Ang:P0cu, A.~Verbeu�K�]cMXOn]W'sYY�&�J1 ~ 25}, 347e� 92);-pS.9 III�-D <$ 30}, 4895!�����T M. FU)<4 Pul{\`e}, V. �)���1OiY Helv{cta)855}, 3a1986�EU!7"�T, %��!�Z�[�� xW}��8�OŸ2�"uD J.~K�S( B.-S.~Skag@(m�1it Co�"(T�� ��v$�'��o� math>�n},o ..o! 52�wTP W.-M. Zhang, D.H. Fe R�QlmoAY 1#:�Z?or�dI�� ��}, Oa[fF9=!V87�v�qq,HM} P.C.~Hoh�%, My>n�! Mi��|`)=%�ٶ� ium}, %Kś%�2! �� =�"�} R.B.&�zSpL�+7%z�in)lE�*�&! �E��15��240!66!5r F.J. Dy~�a��b� S�m�Ph<t?+�i"2 2V )� isotropicE~�Ta�o%�n J.�2>1A�33�7l �.A G.~R":*oBhI5a����&�� )u�3$C��F�1�� ��#> > � ��> � 11pt.��us"Լa���tfoeY�t$hm} %amscd2�"�� %% S�%L� [UncxA��mmand5�displa)e l!F-keys] B�tsm*�t$oddsidemar� {-0.3�tv(Synchronize.�oY� s'c5TeXShop:�pdf*au%Z � EnvironRkq���t!}V�tl�t[ -]^�t˞)2�t�(ISO typeset�;n�$ �!w�tm�p rmF�pm�r rm{i>�odi]ratd>D.D�r %% Mq�%� todo}[1]{�� 5 mm}\par��nt \)� par{�qLsc{ToDo}} \framebox��Dminipage}[c]{0.92 3w�v \tt #1 e+}B~APre.�t�rX*v|{}{\J=�Z{Z�2BIm>(I1r!(TITLE PAGE ��Colli�2��Re�+�X� ��3-Vortex�f]} �nTh9P�x9-XIIF*NpAn qo�XLn\'andez-Gardu\~no\t0�s{% I.I.M.A.S., U.N.A.M. M\'exico D.F., C.P. 01000,  . } IETq: ahernp`@leibniz. iimas.unam.mx\hIV {0.1em}. HN\nd Ernesto A. Lacomba\f�a�w[1].oOn=7v�ab�rDpto. de�em\'a$Ss��(-IztapalapaB� � 9340� �,lace@xanum.uV��xb�d�� .���&Sn -tm|!��o�3�!-vo��e$��Ea � g� }Euler's"Z¾�C�_ 2&}mmm� iny�a\��+�� ��mo�m �8�.coY�roGlf-$H!�� I�hre�]bin��9. Al���í2 �&���d3 ar�m In#con҉�s (excl��Bt)ksmo� 2!r1�"99�&�Int4'��) 6al5�%�Q)��v!  $\omeg`#aP  i�;>[)�� no visc�&:5�wP>%ris%F� �� s / t��8 \cdot \nabla u�B�Ce $u$H�elo�A;= 5\�=s 0E��A ��:=m�rhIp t + u6��'8r��%�#Ya �3I%is pa j0&78w}!�:�5�igh6KId L�W=3l6%�!n �6beatdescrib`Ba55ta"|��s�n�� $N$-Q�ex (or�exbrevity)a��.728��O:h��� �+t �H !� d#Xdr�]�og�as�m�u�V� k in c�%�"H�p"L��$ rastT J�:�.!& ���g1�W8���%R>�a��Ns�Uc(�b1�c"o � !�pal]J�UN$Zallel � fila$ �w ree-"� @pac�:�-�֥��]�0!e) 1� Pe �*�\eqref{ -eq.O� rI1ri�.in n1"�_a2�hydro��!�.g�B0Batchelor2000�Br]6f2sg:ts��!�$@]2i� a ro��.erӅ. �Z&\ge 4("Ca� E�gr\ c!:%�5= 332"��%��� J*p� JI�F#�&nA��7a�d%��rd��!�AJ���c$m � ��ͳ$3$6�7 lem �p�8e>4by W. Gr\"obli!��& 1877: ser 0"# � Cf1�ArefRott}nn1992}���i57ccKlng's. �Xo .�x�1:+ �)�%Kv\Ovy lUc�9ipec��!���Ss1mCcades�EiJ. L.� ge 8 $Synge1949}%W7+ 4�xe?r6���gno ro)D;di�d�-��Dtf��"e}bas�r�p harm'e�9|hvi���S�a�i%�]�s;q a&��w19sa{A$s.� i apse�'<�bdy�5�E l /"16� �.�&�%H. a�- �- fu�jr(bj�s6�d��,],�� arithmetiA;�U)u�, baA�"�"R�#�F �-�9Va>���n < r  �** evel�za �C� apmadC  19786�-L�#A��:edrQ�A%(i�al,u� �ooA�!&�I+2& )oK"!8@%t�� re5�� �R,l�[�Bd[FJ~-%-D[\S 2.2]{Newton200Z)�*q"� �f� C� p� de'}e �$3$n%�h�IwoBurpos�z�GfhonQEt�\ a�2[ �gnq*Lwh�$�$��E7>/Bs� . Surpri<l�/isQ�?en�cy!�P)K~l"w . (aT'�o iav "�D8u��z�)F�G4�&��A&(�ofF� traj�aAz iR�e��>�� ���#��ill��)jeնɖ! �fm yK�0 An=by-�5of�$sq� .Ww)fer 3� � f !1�!���F-�� �(� ai��h:��r% sO� D nullavE�.�nec4nrwxver��I�e16�.�v K �_,&����w�h,9�a!`!�A�blow-up�%">_ �w ob-�_2j>�!ab:��ā�� c��B r��3"~d*gs ՞N�� AI���sof��d-q�e p]� ,a �X �a�uI@poi��a �Xroot'��ai��Rf'�!!0>bFs?%a�!���e&� B���� (q�.qa�{BackIu�-P� ԥMi��� ��I��a� l�� f z _\a�� = x $+ \mi \, y�Zbbb{C} "%fY"� $ S $-th)v1�!#K y*Gammaf.R>= 1N@dots , N�Th��a�&-MisQ�^�ong�Nt� R} ^{ 2n} L� A���%��R�V� �1.1.42 R!�5N`�ex>�$ \dot{ z}�=�0{% }{ 2 \pi}�V _{ܲta�T)b }^N 5B1�c{=�- }{b`1��y B�S��Mnis.>:�GB�1 G��$5xC}!�"I�'l�=W�&OR �N� y \[\P (z, w�1- 6� Im=Q�1m5 Y�\bar{ w9t\;, \]+��a�$>?.�R}M�6��-QYn5/*�XE�f{ i}!�X _H } �=-1f{ d} H!1ak��� ���>`gL!altOn��>�Fk-A_a�f_�&�HA)"�)0]�}%2b�M�2�N \;. �� �n)�_s-Q�1lE�XsuI�)�RWXr*{  .��\nx||>�aa��)�ZA�%�1j1�)�9I%xand 8IZ8�D5|�S;Cuuad66�| \s�F\ OmQ2=�: �:�%�fa� �q���� $ Z/ �� bary[zX��)�23!��N)A)MAl)={Q���,N�^2� �I - |Z��az%!FineL,f���2�A�>�I or�bf{ } �V�j\,]r��z}1�= @{)�� � �U!"*� of Sundma��""IkRE6o6 lj��� �%R|�be� ���{P�rd1976}�=�#fWS �vo���F4 ARU�.}&=y�A-Ae�S� � z _i (t��7 0);i:2$,��($ 6: �� \long�5arrow� (�EA�=!�!�A�@E��=3,� e*�"?a����v% ip*}&�-bA�%%�v*�qi�  \� sec:9�}ies})�^6��ue�on. ( S{R5.� ai.XV�:X��� j� A 2�QA:{ Mrec�f��5[ENO�N:SA*J�W &�@U���Bv�l�B"�>�!�� "Raf��"USrK��$bf{shap:q B Ebo�%> ��Nc7�dat<f!2�. �{A �e N^"7^ �wa���!�P�^$:)isQ�,�E A�5CY�of1 ar 3*��� lwayIy:hby g T�n5\K]��:e�b.�i�!i��� &�p �es�i�� muttY>ET,`�Nr 3�S��>�) vani�.~1Sm�Z�N�XNe�no*/lM�3]��ac�Koo�Tqfp5SN�A.a%��*A�"parg��A&$�Z;Y!aE � �1a"� t�v _�<%2D1�"{ C _�denڇ�cyclic���G$ (1,2,3&Ta��wu��#�{q$���X:=�6jk} /(i,j,k)� ~}�D>�A���A߉��$b _1, b _2�A�herctaf &�T�sYe]0t Xg >/ ~�S&' 2-}��>{�}�j}mk� �B:� a>* iJT!�"Fe�)a@"���G.�yb�Pc�eq��!T!�+ 2 3 \le 2%w % 3 23)� �w5< Ge"i���E�ř�a[%�5�:�)�at2�$qi%gC A�> �I5 soli�&ntGMwpm��: admi��06"�5axe�e  |1 =�� beJ;���I=8)AcF_ omȅ�%ofB� . NsTeɞ@2)&�ߡ�_Atra�kE�mj$M$"� $2eB q5�#%mC( � T:��2_W���O�x2���L�!�y _ 1�$� (0 $. As it pwas mentioned in the introduc�[, all candidate trajectories for total collision must satisfy $ M = 0 $. Another condition N?(is that notz�D$ \Gamma _i $ have$same sign;�if :wer cas Hn $H$ would tend toS�Oinfty $ as $ l _{ \alpha \beta} \rightarrow 0 $. For concreteness let us assume ~�1�2 >B,R3 < a�hu��2 %. LetGTmathbf{ b} (t) = (b _1 , b _2 T3(t)) $ be a dynamical9�y o!8e system1�Ting \eqref{vortex eqns,moA }. Since%\�$M$ are!!$served, we1�at,%�AL�$t$, \[\begin{split} H &= - \frac{ 1 }{ 4 \pi} \left( 1.W\ln�3 +5*.4 13)12-�() \;, \\ 0�Npb bl%�.h%� \;. \end �\] Expona|at!oA�$first equa!e!A obtam�$equivalent-� %-E1$}\label{co%� E traint}1,array}{c} % � = h\E: 1 ^m �^n-[2ex] % !M%u2 -(3a� %� V � �subs�� 4ga�3} v� a} ��1.5�~Mb} j� -���2� wh�� $ m EӍ�3 /]U�nb!2 !$h = e ^{ -e  H / (Q} ) } �e . EQ?m�AerB0 a} expressesE&% of energye�1�~Pb}E�c��$��Notic��a�� m, n�{nd $h�8Xstrictly positive. The���|a#��i�aٸreg��$� cal{T} = $C} \cap \{ �\}!f-�'$^l admissibl�� e determisby=e�}%-$6_ denote��e plajE9!�i� b�iIf6�0\neq \varnoth�;$�n2%�asar1co:2�poctant!�$).bb{R} ^3�8ounded�two ray��r _1,2|rough�( origin (po%8�`, =2 $). !�proG!�ɀse \o�$x$-$y$�=x�$with slope�p��eSp��$ suc�Em0�Cq�� 2 0. Its values�ǩx �elimin��$��$ from�a litypi.']&�z�0b}, which givM8 quadraticFia?p =�2/�}�V�Tl�f%�ary li �p (n-1)^2 p ^2 + 2 (m n - m -,1) p + (m-1)#=!G;,��b who!�oot)8$!h{ 1,2a|0(1 \pm \sqrt{Y P/ �[$�ere \[ % := m +���>] ForA�� 7 T �F $ Du E*e;1s�1�F%0 has no real �, exa��one��e�a*�� s, respec��ly. 6�1 $ iff�=��)�IcorO onds� MSR�v� a�%�)'UA?qF�Thus,FS� empty � �\ge� , it deg�=a��o aIvwh�� / ���!ca 6�� cartesian��z$�y$- n*!!5p8 V1�q Abvirialjgk = 1u=��3�7� *� ��} J2^3f | .K� We now��sider�mMZ͔Hases: \paragraph{C� $ �{ } I�V�3 V)�ax�j:O��Twell known self-simila� ll� s describ�4\cite{Aref1979��.�� 0 (�- p) x. ��} - h���A0� 1 �p x c�m x�xy�t&�>�Y�^���a� izedU�} %j�)h�/��}�{ n}{�p).) }}� %�jQ(1-m)�U!�jUf�)�q�B�� U7V-�f� ar9O(curve $ c(p�x(p), yz{ f� �^differ;� zero��� p (0, fty)�w �JL A�x (x, y, z):a$a�N6;�ey (heG�& �is�Red- .�)we seJ,�>Z0� .�B"|�9n JbeWs asympt� ally�2�:, ^�mUa��In ei� �tz2-�b.0 �2un��!427al��!V2�!ppor�Hof $c$ l�o+�&92���� will��%r only� 6� occur^* 6D"��pVr �qu:dz IS5 � e$� { then,i1!/discuss�zfollow[ ����%�2l �:T!����\I�� nl��2� }� H �\� _2` ��T| is a simp��= away�� join�i �~� on  �ra;2�, �!-property� ;2J|�2�inter��� �[ once�=�� ��, s�6, �!�� � ���u�W�&� odoe� t"1-#ar\��z�. � �b �proved� b$theorem} �ai A� threj int-� ices!��O��:��.� .. ymae� Rities s�V=0ithe3a� , level $M=0$��.� Remarkw �ն�BbA*e variap��$x�Epre� aA�?$ve blow-up)�e&96 6�.configudon!�\dot{b}V= 2. ��"���d$u�)g es (!�0mutual distanw �e6����us'to ��!�seY\textbf{^� a>,ion{Regulari9|�n� 6�} cP .7} @ X�% e ne�ord$�at� zA�e v� field atϙKMc�h$\� C}$B  eq|Also,� <i%6�}zkwo9��de�  $ird��remaia=22��. (H���eF kind�%U ti�la�B5�is2�4 apse.) F�"Z \foot8{% See _$Synge1949}ga geo` c deri�)Nse evQA�e}s. � FS�W�i $'s.  $ wz= z _j -k � /= |&|� . H�U in w!��4a^(i,,���Ŧ0cyclic permut��$$ (1, 2, 3� "��epmoA��@!}F�!iget^� wdo��  w}) \mi� 2 \pi }�wft(-"% \bar Ak *4kI$O"$:HjNHjFHɠ)F� usF� ���_i��\dif} t�%�.� j�-/."+ 5�W%U \\ pZ�pi} \Im:d�}{2!n�>&�\]�A�U�-(wA��kA�F+M�=*:�V�.]}}{ �j.�=QM6VU�) D+<w 5%5 \ &�aU� �D�A$1{|kje�p.k 9B �\e las�L; used��id*ty%Bz�}{2.!z 1a�� )� uiv2[�z��5+2� |1 �M�1 2g1] �"��$=,2"o�,setminus \{0��is easi8 , �I�za�$�mpo�����A�V ���#nQ rea�`triangle� m4���locRa�!y �3>�� � easy�� $ 2AA�!�%~�hMk7�n^�bi_.�ns��ai�J�AA ����M�H�K9� b _k.�, %{ ,{$(i, j, k)$ͯ.B!x re� nts!� fact\ . !h� io:'C}$� !� is d�up!P� g�$It becomes��h6h &j Vbut�Bn� �E ;Qgo�AEa term�l"��$'� volv e squ� 7A]a funQ&�l�z�ED\partiali C}��cf./.�A�} below)M�eve� o6�al>���  ar� g�ic� N<  j�F�� reduc pace!) shapn .� �not�.;U &� JmQinfinit� �A�i��a"�wh j$k $ *3!��%som��(i,e� C _3e�But���&� aiJbf{bin1"D }� � b�ached�ndeV&6n'b������t2t _$ +*$"M �in!�l�2G �I���}q |� b _j�# k} |�H |' W%�9:��#�#��2 ��#�Q h} `$= ^{ 1.�$}2/�2363}F &�>Gcan%�"�)c$3$�c6�"bK2�:�!iM�. 1�,f�L��� rCb:ai�� !� ider�previou� ��, byi��*i]a >�; so l:W* tter. C.�'�M"%written !�I!M�|&i&6&j" � b' &�(j"t kikio*U�)b ] *!� |�/�e ht-hand-!7U �O.zkR��Kconclud�ev��k&}+6�p )�r3q�!�e'h�y�u>Ma�6�i�"h�I� 1!( Jm�}� I��1� !:,j :�!$0M�Yȩ�!i� R6 h�e]ontradiE� . W"�+usXvN��:noB�{ �&�"'.%an� ree-J �ex!���&s� v�.>">"J�3 NowAin�.�="� E�-, \lambd theta pwb �we&�# i��>-(�4.�!$pr")spay!��m(FTVD�atera�/=Os (2��~i�!%�v<,r\�a))G (ZiRs6r�� aV*s.�.^� )�� �&aT<-+3&�i =� ��z��z&ae+} �4���M:E-� ~^fixed $ �$: $PM= (  /2UV 0)$ P�(/3'2 A����/b�U�/��2(%k0\�!a�c� 0 ��NF DF *�����&� E�-  eq&�*4stackrel{\long�vr }{�!o�1�)d� seg_2ū�$�pendic& ���1!� 2 $-A��0i�$��*�nee�to tak�x��� 2z��� }} $. Fin,�$�^�2 A/(� (&�m� ^ Heron'armulac ��a"| b�+}qE�!4 AA,epsilon �{2EI)NeC 3 23)ɩ1�ų2 3 ^2}�.va:]q^0 jJ*e� E )��:* ��y�w�$!Mh=;*�deE,ngQ���5=!X>��q;G 'c&�% $ |A� ACs �$maximum�%*M���b _1/ $so�� R_{+ max}a�� 3 \� /12% L�� Eja��3% 6B{ -�0��\\BI+�0��S2I<- B.ޙ�$��3M} ��\] andJ�0���� �<common ��� :�-�k�<5�+���.��Br�;&�� betwe>&~8 "���, ��ٵ�_Ţ٨ inducI#s$ omorphismh:�.o� 6 1�E.�1C�>w |&6�:�EE�\{N�\�/�mi|ap��3H2\qEJi�(: R� � M4�7�%�%*� N**:�!- (th� � )�lR� v&��\�$/ st�U�$J�MA�Y^s,p a non-bi�1$ve manner,�z�f*c.�.T,>��ng3 =$cFus �1>&�Q��e:� ��赽q����8 �e�QE��a�iT�":���m 0b-hypothenuse�6���� �c&�i�� }{ 6 } (3���r AOa \cosm�V�" \cdot�� }8�]|�?V�� | �w"�"P - ���6 { 3e� %c-��^2��}�� ] U�� \sin%�0  - !W^2��� $0 gn (7 4K�<��b ��zwe� :!� >n 79��� 1 }{ �2 �5 MC.�/N�M�6�A�h �;#�b�=mplifiL�$UmM�trigon� -�,V�M�- 3�)� %�{!cU�)�"�!�)X9!63:_!*2VI-:W�6=.� ?�-4N�!ȍ�a ��^/� !X��'s d5�' ib�b-2LB+ AF, aU�6 �A�%{1-�(.�- "32z ,�_E=E�i�l+�l3Fl3�E|1-.�.��� � s^/:�� ���0's'��r��&:BfR 2i�G4MCbB�,.q�fq*w'M�%� f _ �� .V a )'al���~9 *p�'er���iB5F��B ��S���T multA�T) �# �A�A�1{3�Bigg["�:f�#1�.� � &(-eC�6a,)A� �W:6M3� �=M��L#&�I:Q16Q��)�εڥ�3) �]*55 `��7I!1(12!�Aa53a�I"^Q%)"I�:1A�a�<erV1E-2A  j5Both $�xE*u� :�ex�4&�<S �!s�i_ %E�ZD� ruP1#y3�4Ic�O� and,% auseaM�R� >�F9�l�kB��+��T :>^�%$splaystyle� E6� .��\dF2��&�a��+a�vZDRB�B��$. lde{.��  M�e.#B&! =� \iL�2l� , 2n�'/3��O 9i� 5.0, �(� .��7>�� .e.I�Nq:�dimeng* $2$ clo�$sub _&� M�8&�+t)�.`+j*�!E�as st�#_:GV�E�� noW"= chedk!6'3N� o)4\tJ�"��$comput���, qG�9Q-:��+ <)0 +vC \Dif�2�/ ��B� �u �A A�%qua�"� qr ,���# / 18�#a� �,invertNB!]e�= ��2�8�X#1�c-,?bQ�f3G � CB� )� %��6.) ��BP ���}i��HB�] G \new� and{\scs} ript��}�G�Fmatriz� as N:=�1p$xscsV�R' -2� & f?R� n?. �38ex�A��A2�$N*� ,6|-y ise�PZn�EnS tl,�d}achiev`,"�2U2�(��&JF3 (ex�"�(non*!B$).Z95J�*+� �BmM�" u�@�7$I�I�3}}{12}.b= M� A}-A }}  $ .�%O �%V� %[��! � �=� � "�4E*�9r�4F�?R�4��� p� um:^� !��H���*sfd�DBo`95e�1:Nz!EE� ".# ies}!Zr �cCp}�&c#�Ar�resn�@uisJ��� i��4rk�&at�5��1�a1��#e�7% �beIr B�!�3�#=.ex-^. DireJGE�f�.sa necess">A� �um�Eei=��>�$ n�K(M� (%�J�#&�&2+f�� mo��O�R,, a�)"� �A3%��!�atjD!�NIte� a suffici@bA . O!}r �'%1"�(�M"A &)AfN.OiM.a2K.��0+Q2t �6^%1J��te�asin%A�d�s!^t�J6� be� �gd�*� help� �`ed6������멚��ofq�� J�9: M9he=y"t2��n:rqA.� u[�K)% e en9':*�EO'�=} %% "�:re�Bce 2`iKQt � ɨ�o �N-�E$b! \ +:�ї��*, [ lemm�&�':&�(�5�(�G,�j-�a)�/iR�s�!e^���w�(�m�� � WKJU� VU� -\B���1�: e.��{+*� �n���� $ byQ >f bijk}6�(margin}{\hs�1{10ex}} y.aCY0U{vLdi&� cV �� 1U{ 123}�g  1�U { 23 { 31� [1.6�G6_b/#�j�"�:�,�,j g3�:-.&�B;�:C�;k Ri} -1&in�x�!�a��H��#F)yPmJH =Hk�!!7�2 �X Ri4)� -� �\} U  $ c �U]� &A�$3k:3�WL�C$p�BaDw0�$u}�!&}!� 8���# T}$)�X"BDa�~5)m"�!B�) a@�)g (,O ubstituV Os!$!S� p�#Yqui�mj�$m��$n4}w�E6�Q ,>�C�R$ yA@s�c�ⅲ-�2F) e�C��E+A%"�&�>x "S C�oor,6P�6� $0_8&.d& �;�n p :+Jq ��%6F&�%&F �-A�&(p-1) ]� =:$� ).�]-`us) a��J�.�6iex� 1nmapsto�a�cO78�  �"� *{Ac Wled�2 s} � authors g!.fu0P*e sup�~�$DGAPA-UNAM?5rᜡ< PAPIIT IN101902%e� ��CelesODa anic!@number�!of)=!�Carus6?Mon��6A.2)AssociEDSA�3�6.�-=Sed%T96T%@Yu.~B. #.eM�e.EFSovM�1C450(2):297--301�2�&CN J.L. .X�+E��r5 Can.u,a&:257--27�p4}�>� P docu��} ��\,class[reqno,�:Ttags, 12pt]{amsart} \u�ckageC",amsthm4symb,verbatim,�uicx66 xsym��Mshowkey�� %., fonts/sets .E�"�"bbN}{{�bb{N} n*#bbR RJ D DJ P PJ Z ZJ C CJ Q QJ E EJ T TJ H H 6Acal"cal H}}:� abbzCe�s6�:^dott}{\,#)\,:�no}{\no�;:lbbel:1O� :ul}{\;?r}:oovR ti}{I' :7w widei'B Oh}{O:4oh}{o:��%,}[1]{\mbox{} (par{\ragged@)�0pt}#1>�tr�$ext{\rm{Tr!�2��T.#>Floc.$>#Ne.$>% rank.%J%:$B#dom.#>Fes�&�>#a2�acB!� 2$sV$.�4BIpp.#ppB!� .#>�AC.#AJA� :ShaeYA�ha��2� eq}{�$_>}e$�;^"baE aligFB ARvep!�v"�>�.�Im@�Z,atorname{Im}>&Reae�pe'ReB'diaAB2'���P !2� v,) % � upp�m�>of| M %R= RowaS@un"d list тuH[{smal�e-�environ�t{SL5A9�� rm\r� 7)}}{%Ptlength{\topsep}{0mm}|:parR� 6K�t width}{2e6O�m��  usecB�% �$!��}hR renewe� mmandB$�$��Re} -�6#I!�q� E!Z| 1�By  \Declareg OMQ{MbR�3R E�Im}Z?EfIlR"(*{\slim}{s-^$w{wr$sim& bIeq$=b!a�N}{�2  \aFFd$breaks \�within�% !�}Z�^R/� &!^�^�&newi/rem }{T�][�]�' ' *{t0#:1 1>22>33:c4}{Cor` y 4: p2.1}{Pro�lon .�2�[ �].36/� )Ln!.)c�'��� i{)=sis-H>= %�!x]0 6& 6��D"66-example*E :�nur.*C2-xca2P erci>:��#6; � _�zAbW:�O@ {�abs l�0 #1\r� A-� !M$itle[The SJal Di�sb"#Te ZeroX,Random OPUC]a�:(Paraorthogo�$Polynomial"�I$Unit Circl�F�<[Mihai Stoiciu]{2�addu{��\s 253-37�(lifornia In% e of�`ology, Pasadena, CA 91125#Vmail{m| @its.calt�edu�s{{\it�0 *ts SubA2 C ific%�.} Prim)42C05I82B44}�� date{Dece8� )�abP#ct} W�tnpBM u!Mc%M�&+t* currWD�%on ,\Phi_{k+1}(z=z } - "� �8_{A�7 k^{*7bCkZS�5 quad J0=@E r0Tj we�G uA_3�_13d�r, 8{n-2}$ i.i.d. rI�&�6� rA�ed un!�mly� �DskA�SO�Kr < 1�]1}P):^ in�)i "CRon�V��K=�.�@rF�ZDc sequ%�of � �}J.�$\{%�n\}_{n-��6�dny!s zq�$ 1�w$n$ f�N��&�Z�bn\e^{i ���}i�72XbbD=#e 5#��)I��e�i��Q�$f size $O(� {1}{n})$ 2*2v$3A�:a 9�A���"9�-��!�>ly8ed. mV(:8$, Poisson)!�i�a q'or large!X%wqpno �[ Prq�"zG�5� D'i�T �j�!�& !%ke���_�{I�Q! } \lb{s1}"�8pae studR yf�v�j�}-D.sor7so �eQ �v̀G]�� �jf�(Pew�ZbO%!=�edar�^ory. C�/ re�*�)b�-2�V� R�Q�� Z�|x3Si)Jd�A1|% 2qOn":Lqresul\8 � �4is Verblunsky'E�6 , ��m9Z\Ita��-�!�onto map�:u \�>�  \��>C&��:nontriv?Pm not �orm2a �Z set)�2 babi9`measu1F2�K2�� lexs ���":��  $|| ��a���n$a��7�'�Yis�m�kthAB obey�A��U�T) if�� appliJ,Gram-Schmidt!ced4Qah�]� $�_, z^2��a L^2(�H�e(, d \mu)$, O.C�De,S�0(z, d ,�y1 ��2 \�$% !)N� �" �\�rekyc,|�fk(Njk�h *:n�|n#A �c = \sum_{jV%(}^k b_j z^j���R�;d �� C��f"�) \�a = a&= b8 -j}pI�$A�I�kio (�/�!?)){U�kM�and�"��k ��DAG6 �2� $ li��g/� disk. If ]jUn$���� ,pha� E�A�b A� �{n�)=z)\in:(U� -we{�J* s $:'$aM  �!@)�!bA�e "c ,I_�)@�r*�}HV�l2.1.�[{n}M�,�*]�f �S\Sm ta}\.�2W>��]-p�� situ@@FVEhs�n"w  (��mak-"\�a coe"�4Z���,�*edn����a;a3!��zGo?3 JNT};m$ 5 Chapter 2 FG�Gor��E�3 1 Z�s>0 � AI�Y�$!�2}E]be � � �� �X�� �� �  F�Y1�prђmeq�b�]9_get? ͫ� -j� �an =qlqm!~� ��n�r�� XPQV� %sjo$zeta^{(n)}���0k=1}^{3 delta_{z��#^z0z_1 D, z_2 �Ln  �f�� F�� �e!fixtx oint6 �Mw .+e*� j��  o:� G B� �}J�  i� b� �r� �J� D$h�\i"p � "�  %�#��Z*ɛ� *�)  %.{U���~hval %$[-� }, ]� ll�9reali���uhe"�K( %$\phi : %2�  \to jY� 8(~(~71��)+ % ���}{�,&I1�� $M NB8 a}, r%- $b $)h bset:�9m�,�.6�[a,b]>j . A}#e�AL��aN�� SJt�Yɼ aM�.�-��E�ba9$\E��� p"&�6:!b l��7�0cess � �qB� onH ,e scale (of 3>�) e{�Faq6|��Ama� illug� Q��%genv* ploԕ�)yj�:�z�e�!i)d�#s[�=.5,a�l =0]{1.  <�k&�I�o�t"�k!q�a:�.^of�1ree 71&* by �� ! &)� J)69}� ��:pa Lk��f� �x�d�i�1}{��y-i�{70�r�Y�On a &bM]#1a�y)ee$ clumpu�:sugges�y�f�zion. S���a�a*|g&�al lic`� !�cas � Schr\"o�CEass' MolN.ov A Mo]Minamii}A���w�u�yNk k%s 6N6eigen)8���kia? m?very im.pa(of Anderson �AnX�o�7�hat cer`��lat�) exhY- abs��OSOu�;(. Rigorous 2mproof^~�iz��� �( Goldsheid-5j-Pastur �GMP�c one-"�+al model%;!F!�hlich-Sp�@FS ?�Pi.@2�9�8vJe� �,� !'� im�� �$ "�A� publ�/d!T�iW]f 7>�u> Aizenman9 �AMEo� -Wolff SW%�rarVlev!��ouraroachQ�!� *hUpև41�q\�.� Teplyae�Tep �b%�(inskii-NevaqGNH In adMA?�phe�WGof2$,!���� � rEK'�uce�m6ql.5Gtur{6uM2���no repulA�2�sgy�|U�2 "�!I5ise�*�U�-��$!�aI� � >�Va�-m�R�8 an school�g�� VF��7%}6`U��-Rde��O#��In�j\ 0�1j�!��z� conver�5%���o� �o�o��RAm� ��y1�P zFo9ս1O*� �rE�M� �}.� o :U $$J8��at chi�1, *d��sasϊ.r ` "ry�4$\{��>�z^{-2�M \}$���lV!IYfO "�t��ofe{ѯ $f�8 z  % 2�� ��# r��q� �#U fiv�a� �m�* :�g.$�5t/,{C}K&(%" a��^Nb�*� }_0�N.1 \rho  ,1u\�N$->Fa %17 2 KJ.���ho_1 &:]2J233 �2�<.E*j2b  �Z6�3u]-.2:`�2�4 �3B�4]J ��r #\\� )�% �B�(� J�&DV�s a 2[ he���$�5�Jn@c!f�s%�Z&h ^2}$" atriB�a!� ent ��I�1(tero, Moral �(Vel\'asquezͱCMV� _ &SB���Lal��@CMV '� �ZbCd�E#�N"4 .f�. 2!�ifm�-�'J�a6�$1on��F�ss�'� �� decouples; our �,&a|�B�yo $%��VwL� N_"�$(�� 7�� !up(�� corner!�an0 Lhn)$Ź�#)�Ak����� ad! ag;��Y aEYJ5 9�����h1� H.B �, (see, e.g.,� M�)&I:[@ %�6�� the � �B<)E��A�ret:� ѵ;E�.a%"R ��N&h , ůi�m ideaI+me ; d�opI�8 AM�xC Aiz_et_aldelRi&� Mi},�MSVa�@How� ,A{B �%�,4� m�H� o` fe��mp��V& (perhaps! most� orL�Qww�Iv �r:E~9iJ�insteaLlf-adb�t�"�C�� W �hWRoE! new 9�]*" work�k6s�>�(fiB goal �\,ing&EE`emdm�< *Erep�(&��*K "�!\ &�Nj"�&c�M.�k}n5'�^5' \q%'.5']0=1�Vu7?r����0n�2'��F"6'yj�6' Q!���ݩU�&E`%vaJ9'&|y9'A�# fu%mV. 2�s�K \ $\Omeg$E\�O�s1"�1, o%".1�in D(0,r"�(}&�"�n}$)}*`V-t��2S:�&��u� 65w�� n?m�$  ,�d�(�}$� (}w��WB&�� norm1� g ���O�-� :$a_1 < b� S�aK� b Q� a_�Eb_�K��nonneg���g�ekak&� , k_�Ew�R���5�#CMT�hbP G] e*G_0�t9)8 a_�)}6J>(�N\�&�g�uʾz! R, n�!9 (.zm�  \notag� 6lw�-(!�- a_1Np�^{k_1}}!yP�,e^7�Ga_m.77m7m 8Q5-�asE�to�fty �' 6#{Ou�g�WP!�b{s2} w�aonA���;���1�of��(~e��. M"� �� �X "� ceFVk �*mPQ���>o _{�N�X���!E �U$ (�� �p�n��<W ��:7\A�*ste"��)% - 2��xDl� eiGo��l ۓ�A^> av�9Aes�8�+^�gU � H26 .Y ("�%h9# �b$ 1"l. >~ � h!:h"�v��werful� �1")KRoc�`, &�[2��{*?;�"� . B" -�,N��NW" m�za few �3�q-ΘH�� el�I#�f�� �zI��!�T� k,l��q �&� � z&� ��AJ��yF_{k l�#.�iguS ) = �[��f} + z}n - z�x ]_{ka݁�� .ߘei �nex**]uy=A#�YF of C9K h\'eodory"�!)�w�!�$� �y� �E��%As���-3�!6z?P \lim_{r \uparrow 1} Ir�%�K��� exi��x alNe�21 AON�)$�\,j\,r� L L^s 6�,)$�E�sl؜ 1)$.&�]&� i�P�1��N�,� ��  ro #nva7�tE�16�] G#}�\26 F�=.<,{16�y&$.�6� �!Qjx�m�*Ql�� G��&6�1��/ rF=and} u�� &U� .�J:�nCI�- "�uf evڇ�̡�havBUmedskip.�L�}[J�BW�2�%ReJ�M�]�ta�o �( �#J& ��a�BEgr��,@H� s $C�D_1 > 0.A�FnsQ�y $k,l�� k, l� n-1�'.�AyB�> �U| expd�/bbE_ft(�|��.bz/� |^s w0 eq C� ' -� |k - l|}I�� >� "} $(2�CMV!!��eTm�Nj�i�8�#:�in 2~P��5��I#$6m�5*� U�U���>�_t1r e��SO�bB� trol st:�X2uA��J*9K��1�W<L� ed S>lE�lm:2}��j: �` e F�B�#��~F�r $F"l ly; 7b.v$e- is e26�C outY1�J�8B�V�n(�n) V6���0�Yn�  $D��iɅ�� ���I� %5�U]:�X�W �? s"��YnyA�H2, $�Ep9< o 4.kf $m({V2�9$�� leq j&�aq!)�A�{Z&Š � $m, |8jM|�!I!(n+1)$!hav�d�_ |V�(mJ��1 \��(4/D_2)|m \, - n�>���q`�(xvO� �ak�2o �lFeEnt��6!K2� Z�(mTtn%2���big�`In�*to�[**2s�-C &�{ �%��� ap9%aLM6�' ��U5#��'0:�qK�I��+ 6�i19!"di s�)Kr6;�W�:dg h� `�&{ way:� any �C`�%�$n$̈fL.: qu-�b��*�3"F! W�*n}j"&j�e�vH{��[ � �K ln n� �w �1���_HB;�::<2< � E�u` `{[}]}, �+&�#e�FBB�4>:1!r*m�StAm�ţNN� M:�V� \,$\ex �"r��^b_1$�9b2$Yf{1��G�c]b0We�'uld� e "�.!ace��8a� XAPb�imslight�ar,than $5�e"T*a./% l�c�6one) c���&� [I�.� U� "��weE2I*�fa.� �sym��.�2��value� can,��B)los� �/>Z,��EaAx$N�ek6� Ly�q�� P"R�N)&i 6(� 5� 1_-�Z[N)r���'��6�M�.(�1^{(N,pB�5)"n/�X� ]} 6 6p)}}$�o�5p�z�5 ��z�n/ 2S^{)�tA/�I!�%�n�_p-��@�z3,�EuUUd �~هhFg[Dex#K�2/� 3}� :S�JE �� u���im5/?a6C2o�|\�7 `}^-�)��]}"%�$ooP a#� g��2�H bs>M f� :�^lN� � e�%�a��)�)N� ]]"� Y �!�Ck nvI8�� S,PD~�A�:� !v�4�%�uE�r$>.�$ �$ Dale4� Vere-J� �DV}),hQ9� �A �i�q�y &�'a.9�Bvi�2���5 t�1Ѯ`.�is��a�3ZG'��tG� e ��� check��[d2Oy�U&)� rm{i��"bu�*}\, 2P�d(A�I(N���K) � �+���� |A|Ql�rm{as} �� \\ &"i�� � �A�f�)X �6��+��� �0 ��V�ig-�� �Hval $�o 9��վ $A9U&w 6} a}{N}�� V$b $)$�E$|"�|"P"J�  (| w�>�hi�'e0&n� val�u�%9T�_I�: �l �f:6R5f�� �5 �1^� �jP2W��d;^����{M]}$(ebo%( ����&ed�0t�J��JA"1!~"g'�#'���n�j� !�; >�)esn at Oe ���r���the�� ���v�VC�� ed, �v*� "<@,�&^;.�f�f�,�P$a!g7jde�2?! &aan�f86�K!slb�!:8tai.7M)s�5`s ?�!6��F9 Ft2�"ML�;�!s3}VN�!!A��C�. t!4��!�,L=5Be&x>T olv�/$(B-z)�3$-D� x, o�~� is e����\Jo&E F(z,Bt��B + z)J- � = I܂z \, N) )�W� (w�@n�r .= ).�0�e�TlOS �Da�es��M%e.�4 QrV�"i�j�a*��- (`.`)" �1he ��H*�"�-)+ us�i�IG���s��."�8�;��� "�! &r"�7AM�(.YA|� - Oz�xB��~���ay�;.�� -J�)�-a�. fg-&ra i�{d;a- Z� �]b3S�$1!�R��*E *�zr��*&��"(# ed (wX�l1}W%�2����7*�0*�a�'!6 r�.���3����de&2� (>!��ZQ��'`Vѥ@�8�%���%�LL~no�pr� �#� $B]^ [J�+ V ��\r ]�   uve � `<�4�}G�&� �Z�l�P $s��"��&W1�q "_%�� 7&�% \cup:L#�Venrnz%m yQ �C>�U $C[�2^{2-s�_cos�\pi smB}�)"7!b}��$XQ�vaN�& V� 5�,xphi&$I,^% j}5� 7��2�M6�% +e ��+/G6 !�an,�; 1P� of Kolmo~Av&�S�� DureU5 @} or Khodakovsky �Kho})F`�E�b0}A�t_{0}^8p��|(-zy 7 � �}Jd.�0(0 o�|^s!/ '�Ceq \,�!^�_���$c��(6� =�i�)�*nt�nM (z��at�5SFa�q/�� anti�gar��E4�$&2!a�6!�")B� %�linCa}A�,)� h6;r�=)� 1}{4Cp�!�3} (-i)^"j�(~k + i^m�l),\, F(B�r~ :N ]l�t%"F pV,e)%Fa9�!x$|a+bE!�|a + |��y�&�-�I�&a(B<n&�gr5H2^#,9J -J n( /b�(qrt{2}},\, �ZF_ i!�ENl._ 2�b{4,3.5� -0$�R b0})E� �&2)�kget�Sny :Nn)y�� =��'_0:l&�%�� �%�"Q3>0">� $C�e%2�-c2��,� , afHR[5% ec� a�',Fubin�sHem^�N�>�&��I��Q;:# !�&�PcF8  <`��� \tau��C ( -�_)}�\is� �.�ZV�{@ p"� �C"}� �'�#a*�j'�2nm`%&Z .u:$�(2��.���Y:�. �'t�:�M�E esen`in !U�" OPUC� �$X$ *��q*, % V�F 1, S4 1.6U��k10k5.ʝ�4 i (k+1)1d1[db{b5} 5 _.?(z) Ci�:)�9kI1-A2E@ ��R6:"F_��6})*=.e���� �E>��,ambda�F��8 } z)"�|*~:1�@Mnc�fv#1>A�*z�6�"A^_�f�. fy Af�Q ������YbE XK�#1�.! c:X  But�M5}2#6*e E�*ں �b/i� \.60}͞t au�B8} � }�Ea`u E�lUZ�@3)](*LZ+}� +M��V�A=����r� �� ��Km�)})\\�g~�ɂ+m�)} + Z�B+V� )�B�>i!�.\-� �}2��� %�-%� ��lQ�.b���^2��f�I� p�%� �l �MfR� # A� �I�f�2-N�,��hov� S6q��š?��6NW"[�n�  ^0 �2�r���|{��os02, ��� �& V�b7�=� ����>��eqF� S�rho6��a��rar���7�sired�cl�R��&��O�T�,�:)�),0�!E&�com�x�6B5� s. B��-6/ Ui,$H^s(�9$)$ ($0 < seCɨ��:i3s � <:Ns2;6I�N�A�d��O" �6��%+0j%F"�]0 @t���� :.�l0295^���"D.�rS�b9AhVe92�rQ�E&��A^t�/r�{: HardyF>U �"Z!r�%g�L9 �iR�.��-�N�4&: �ci~fM �/aTE2A"JL9��$n$ }3 3Y z!F�N0 7})?B �y_E-H%[�$�#�#J� Z By��"<$e���Fatou'��mmam�J�=�~�ڭ��3�����ni/-N*argum�@0S6��)k�"A��mway��9 repl��`/�;n��".5a� 27"�W�-jS\��H;(�k6��orj8)� we �;R� J3.15.18鎺����i<ny^F, lIg"O�p"� �=6�m�C"sB*o�F�Z��!���k al m2�B��!  >F�9r&oO� 2 �A=�startE*�,��\m �L�,�"�AizPC}V52} $\{X�2X_n(\o�J:�dO&)9��- famil�*&4rEq"ys�ǥo N8C><�$ (X_n) < C%��2!�$F���.n \"_)}.�RQ����g.�?"L�$E�b1� ]�V7é\�^s]�C< %�V�mec�%=��JM &�8$$M^{s-1} <s 6$. .) �R$!�1� > M�n � %�![R=�)� F`X_.A�:x\{ g;!�Rq M\}} +���2�)99HClear�#E(�4͇.KQ4�i dol�e�}4Znc��b6�W�jEw� R� ��$* 7+{, �8+�� immed�_ly- .�t.�E(�>F�A� sup_Ru}�F (X^saU%� !�����+6h>�s�.71"S�e�� aF) hold�s�m�!89.]2}�"(�q�� jbF�#j, j+*�F%jx�r Ek>�VX6�n\I&� �*�\��� Kk�����7on,O �bOS� veni�to|�%+&CI$G�"*S��6� "  $F�m����l3�%ٿ� 5D�d�")x]�ՊedA0�6^�X��� >`f (6 n$^(Rf�a�@k"�@,f< ,R&6.o(V#��$j$.�#y(g�a7Pb�%cb1�o�XkBXa�"�BG_Q|�r=�� )T |^{s���%By�9O� page 287,{�vmw*�L*�% cT�!  $G6=*aW Tl^����j/y,�2�&.� $s'�j (spG1QN�S1(ppk�B<i>� $X_kA�9bZ&� {s'\?�BA�pow�*�s}#*$`a‰�.���v����R.�>�=i]�*� ��� heavH; chin�eJ)ransferq c�(nd Lyapunov\�M*4ve�X �#A2�QD��FNc>r 'C&�DNd�Y��T_nQ= A/�_n,1YP0,z>&$7=�- �\|^2�#/2}%�&�_�9x �_z ^ove=��q}� Y�$1{.A"�]�+�BU�#B� � �i�:P S S#�olog \|)0,.�x)\| �5U (Aii���,�@GK). 2N���K�.�"�"R.b@.�sZw�J��UrR- �(�^7 ) \,"� �&� <�!ft45 4�B� Nj| f��ZBf�zJfI(ua2n ?by%7 nu_N5~�4�U|�*F3j %� U^{d 8�> logarithm��ot,&o�-eB$��o,k d� B�`6+� )\pa&�v��og U�|6dg0  au}|Fd��)!:���-�Lc�[L59��E�B�V!�A�� 65��}lyJw s �2�ɯF�i*�����.9:+!���ul`Oul�qN�ԡi�B"�*mA�)�qyQ��\, �z"y uN}an&W a�p��4ڡ �)�r��a� rplog %)r��� 6�C$ity of the�� Lyapunov exponent $\gamma(e^{i \theta})$ implies (using the Ruelle-Osceledec theorem; see \cite{OPUC2}) that there exists a constant $\lambda \neq 1$ (defining a boundary condition) for which \begin{equation} \lim_{n \to \infty} T_n(e^{i�( \binom{1}{ {0} = 0 \end{eqLp From here we immediately get. dtheory of subordinate solu�8fty} G_{j, j+k}2�4, \mathcal{C})R`We can use now (\ref{3.15l)� �() to verify!(( hypothesis!0Lemma El2}% A[J0we have %\[ %%�|(]�i-$ - z)^{-1}��j+kQAu� %\] �$M�(:� + 2�l:3 hq9 }9obtainedE�!�0$M�0,q"(1, \ldots, {n-2} {n ")�aAH {n-1� 6�. Y�@o�x%��S$GB�= .<96$ *B1 �����.@: 5�$. Then��" Lb12} jG� -2o=2A.X -.�:�)2B:Q�%� NotY�<$~w$)$ has at � >L nonzero terms, each�ab� e value4 2%T* 7 70 are situated, posi( $(m,m')IK$|m - n|i�2�l |m' .`5�0align} \qquad.�J~U! - :� |^s\, ) &� ��2Jr;(\notag\\& \�T+ 2^s\, \sum_{8\, {\rm)}2k:d.&m� \, 2$b  _{m'�Z�I-* Us�90Schwartz's inA8 lityFV qsplit} &.��Y���� �)�\\ !J%K�y.^{1/2�b�W.��CN�kNend1 !>A�} ) learly�  $mVC3 fh ..�FW{2 :G.7$$. Also, f� .g 1}, p exB�C$ depeR  onK n $s.�!�ft2�BDyYU�J�C�T� !2\�J_� �X6-B�.<j+k}�2w + 2 I0 �� &, $o $arbitrary,���T� b13}).I� .�.�4} holds&TV� �� � �b��d �Da standard method:"U d ��l5}N� bl 1P�`&*b ^mb14�O �O rO O )Z[*I ,1), tA �, r  .p .A���1MH\"older�3%�$p�; t-r}{t-s}i�for $q6s-rE w2`��.�.��� &=2.rGy�jm-{ �$r(t - s)}{r����:Kt(s-r I r}}�h�- �q�(�J�rM R)�!�%�} \�_ bb�NJht� �g!� g�-�Q.����� z�R})��bounded�a cU�� �� $tM�>4}� ʅ$r} )$ tend�0 BuI*= �$�7>'ai��el previous ��&�� �verge�to 0 of�TJ%R uniform��$j��f��K'dec�P$�# > 0$Bj^_ _t�$s, k, j, n� ��(0��Jy$, n > 0, 0A�q j (n-��"h:4:� ��� �"��Beq3.252L e�*�:� :�K i: ) <.�iA� )����c A� J2 , it�enoughA$�8*�R%ll��|D�uppos )J �e���edo thej�6Rew9$.��'sA�si�k�xb�_{Q A�}$� e�9^�&add� all tric� "� m = .�$;r� %chosen!ac�|_ ��ft|2#]e�J{�[|M�� nT(In o� wordsŶ]ay�7���o�\5�s!�42, m-1, m, m+1�$m+2$2�di� c*�& p� ��j�Q] .) ��.T �-�cXR��� get A9�>%�Q8��\t� 1}{��nF$?E�Lj \IE V�ri�J.� M |^sMzf!��9Q� in2m5}ub� )ul94V ��&��hea�wards�j ��deA�of� !���al mom� QFele2�� (*�|first�e ar abou* behaviorBentrie"x>b*��b��K l3.7} .g�*�.�i�D& "�� given!�bVl (}���-1�dre inY +! �"��8 )A$x �=ly� ribu�i� ak!L radius $reaO last oneZC��(unit circle�")})n,Upoi�!.��:� 6�� ' \Omega"�G0 "2�:�zz - .� $�eSRE6 concrho} ��G�l:� f(y "�eG_{i j�@��q ft( �<2}{\sqrt{1 - r^2nS0^{|k-i|+|l-j|� ��  %&�n� e{Se�  10.9 ofC l�%� J�*�6� )�d" %Z� E�al limi�D$%{[R�� ��r %F�)]_{k,laZA� \up�1Q �  %b�noa>by�zw %M�Ib6x.��1O1 Chapter 4�� Simo.�#��� ~f.��B��)� follow��culae:B�E�resforeef6r����!V l�&-\{R@array}{ll} (2�L \chi_l(z) p_k(z), &bl��Z oU�z#$l = 2n - 1�:Op NxNl)�N\\� ���Gu&. %�$polynomial� �$%g"�by�O(Gram-Schmid��,cess applied $$\{1, z, z�� \�Rn $L^2(qUD, d \muondF� �� �)�� �z a � j� $p_"H pi_n$ AyA�analog{%Weyl �ion8Golinskii-Nevai�&GN}oGdef<byUXy4&p_n = y_n + FANx_n\\ &��Uj!!%�� F  $y�6%M� second ki$2�CMV base�<�qq�UJ �E&\{% I~u'!�Hl} \psi_{2l} & n=2lA�A�-: -1}^{*&-e W%Z�}����>�.���+1�-1Ʀ�fun�pau%n��rF�.�assoc?) d to%�measu=\mu�$F(z)�  4Carath\'eodoryv B�$$A(se.v*1ZN�?.nteres�Ai� �E�a *� [ [  (we kN they� a.e.�� �ce&�ed �)."�&}�a�L�`�- are purs* imaginary�)�e&3.49.d} I{2�p ���& �o,& =�} (%*F9M)2=- Er�Iu \, z]kp��l�G)60 �%B�OE;i�)' -wly!)c�Q #-(50=(� =�G �� r-ePAIJ�)a_{2 �.02�d we��� �=�>�c1�is � ��, h���Fի ��S� ���g.11*1 1q�s iM_.3)J)I�� 6���$ 0 y"��1�l>�!G6�!�z�-i�� ���!i�th%)observ�^� ��)!�ge.�.:�F�EnC~�J�&J2' ٽU�D� J 6e3B� �p��޻ �&>�a �%�ucombine-�-s.� �4�)��J!>��X5A which $be�ful i mputIHRuextraD*� *^ 9 � cM"$\betbbC�n+ beq}�At_a� ^{1}y�|x��X|^�( , dxGq�1�1}{|x)>�ER �QGd�%h�p_1 + i 2$� #�.$2�� R�%W�'i�z�=OR�(5_1)^2, �^2!/>5�N_1f'$ But $1 / %M"ksymme�breazre�ngE� 9 --;i$� 6�&�!C�O����w)me�8{ml2�>qO6&�EL showN atXa�controld*!expecmr!(a dia_ B�"x F��(}�� 3.9&!6$sA $/ y $k!$1i>k 4$��choice� _0"�1&�1"~"k- ^k+�1$2"� Z| 3.20�bE�:(| F�k vF�4(^s \ \big{|�' &�5i �5i \neqQ 1�Bl � a possibl�0�!���ih/ $C=�4}{1-E� 32^s$�%�>�$�3ae "�6b}#F�6%� \bbN bN*��Ic"�:$E�bem"4,�zFy, (\delta_k, .� + z)2"K' 2)-9� 2�'��<O}6-z� "tkw1)|^2 �� 6� ��)�"#:he"x�.2�$*��^4%F���-�a{ $\" nA�6!06�(normalized &�.� �� medskip &@ A ult�$Khrushchev�0Khr}, %4.5.10� BookSchur"]�$.$$v� N��VJMg  = f(z;�^k,Ng )!�( -* 9��V2"�,N<>)V#Ur S)$��dm% :#&�8A#��S�� 9�%�9.�$ !}b��� �b0$!1on ��k!� n*�y�T�d!�<_ka� f (z;���%� _{k+`&18)}{f F�k z)�5�`NCB�(/� J)Ib$i� P~ 3 = C_1� :!R+ C_2f�B����� ]&M�V�!V2},,J"A�\\�b)[Q-)�=iym �]�N2-8(numbers $C_r'C2 do notM�6p>C_1C_261A�Y�W=Ae�a�8e^�z;:��!n � "sm����<�Z/* �� "�-EF(B���))*�*�*:*=��I� � .�" � ft|�! 6��"�� |���^z i�a�- zm�} M{.4e�-a��:� a�]N�_6�It suf@~o���w�3.3�8sup_{w w&l E D(0,r_� �w��,��+Gf�w_2�^?弭% \ < \ �fty �� Cl�8�5�eE3HB!�)J�- �>R�*� �}_k2���2� (1227ENeU � ( 3��w_2!^|r�;�� fw Y bY)J)0 �� = x��A$A�NpA%MB�@(-A %V$) + y (- i%| (1 C��0�� $BG.U T D,�  $Y�)$a �be r%small)�n to ��e EIf $| � | +��e6!&`-Q�*�m*�"u*l8:A"(I�4� ��) :e� -r}^'52m��%�D + E&���dy$%2i �r12dZ=-A�-sY�[2�(�ED� �)&;>> used.(,&z%�\E� xd,�6AGA.�Q3orAU�Ma-u]NA!;.AI�|6L%�*�;�*J�|x�oeM�a*.�^�:4.��L�usF���� 2^{s+��]�1�o-.�F�usIA�"�=EHoE�1څB�1$�120}� �G.T# \maxi/#�޶�,� Fm �v���\m7�{=�4�*s � = 1/8��.��A�)Q�S �i� �m��D oremhLt1}2E-F I[P]KT�M4]"*"%"a�0&�MHby Aizenman et al. `! Aiz_et_al�LSchr\"o�/,er operators�-( basic idea�o o�2.00B{!0�'a"0:�a�Kel�-J� (*N2v�5)�% deri8Hy0P�#�.%�@��7&�7E�t�/8/8 Fix �4AAith $ :( :. &�.1*H-'2�!?f �rU#"V*i8!4dR "�{k+m}a ��F�2$�:��8d �? �J�b�R�8�+3�.� $ ($�8an "g� 3$:�specifl+laterC 6Nism#�O �0A~or>>1F�C "L &"�8�.� ��� res1�>, 8. R�8Z !=N!8.!\6EQv -F�0�.a -����and��R res2���n��Z�2��-n:� CV&�%%�.V�$V��$ nE:[K)d2�+J@2!��)�.��#�++f[1*f"�Q�XF,�BZ�-�A)�-����$k, l�$l� (Vmi ^R t J�!.��&�0>�UR"�Z ��6�:� >��'9+, �;fL����dN?��q Is_1!�N���B@ )_{s_1 s_�N7�*2 s_3aJ�E�Va3 s_4j7�s_4 lm7-A�!iC�L�%F�)Bx&�K%�z�?k"�>"�M &�M 4}R��l_1&eP=�JIZsN�ݟ!�4 �| R.M�q`uX63�$� �?�O $(k+�� �� $|s���w2ewFcJ� z de>c+3�e3��/ + 3i. By.mV;e��c �.n �"+Wt?D&`9(| jG.S* !�2 a/i�"a9F� -R@k+m+1, EI��(�.f9R(�()^7i>� O^(�at^=y�k�Q%�RVCJ�$B2� +1� �"&�#�L*m O!�"%�F��o.G �V�.(A�!� V��  !�:oN]v�" a4+1��, \�Jq-����)�M�n� *Jd���)M�����N6>� �aI\�� *�� &>�g A^�:x$4 .�>(�4 4 differ�>se�VV Z^4 >��P!e�)e�uzu;� &�:ŪC(s,r)E:&�Lb�J+ X. :�%F�6G��FG>*SM?I$ �:��6 m*. :`>7�SB=�A FJB$o"��V\,�M R�MJ3|^6Lto���n[;n�@ USV_M2Ss�]S repe�Lpr�;%us,�<ỽ@/��?� !�X* < �E���7s"�&c"�+m�  \#E�Is_C������~�zqJهJ cdot 64 -� An� � <{ta��&�)%=[~%`d�9!0t !�)�� .����"ain�Bmore *�^Ueta�6t k step%8m�\$(� spotWO"e��6$k$Aq$l]O��i>Ec ��@�l - k}{�\M]$ tim*<�e"� 94!��]*QZ..JRO �C5,^{(�Jk)/�� o� */P� 0expA�>�+*N\s B{�LocM' Struct!�()Eigen"�;.` (b{s4} In t!F I!Z stud�>e2<R��CMV�)�aQ�d�model}*�LQ�`probabi�Y 1f[2t ss�Fj�be�,� ly l5�Fa cer�]E, call4ce!< of 6C0."�-�XsI�del Rio6�delRioc>B �� �ai�P�2"� �3 "U�>�3.�0"�#YB�I(ay"NKI�y,U6�y,�>R, \,� $- D |k - l�,��� '=.|�"�G!��=.\CSta}) s.�qM0�) i�hA,Qsom�7@]v Sstant�%0W D_0� �Y! $sj�%?4.�=:�"j4 bbZ�Q� �%,N��!)^j,l� 6�L C_09c_05eB�Ta�E�aED u�+P3ludId�96;u�u�xR *.8�oeJ�� pbeV[Y4.1�/|F �h�)>OHe*1L�i%� $D53BTN9L�/�/,l!��1�8q k,l��q0�� ginY�%�e4.2.& >� |Z�-9� {j} -�l�M �" n)^6 e^{-n�eF>S/1b�@A�7i � u�!jt_{)l�(F��(Q�k��I�d P$� ��\, ����� fo#.]( �Qa��):!V�)D4.�U�n,k,l=1\]) }^{\*l�"-9m 1}{1�2  k�4 l)^AFa�%B% e^{.E \ d Zq1ISU I V�_I<��ń2LA:L� 0Bjd+ \long\ �Iy .B)8:Ba��I>��B�B:% �xr�% . H�;� ��U� ���X��6� *&5Ӆ�4.7} Z>%D����\ ��h! Aw�9versio� >�Zis^k2}F3l���jC��:Iy�j��$|k-l�$M�2}a�!�n (n+1*�BD%��C��J��� �D_0�Sbej�fKz� �>�0� 6� ��V^2)��k l^�* �q ,F��lJn.G]�6�r� 1���0B� �d \ni�0�_:>as6� :�JRU�.~ &� ��&~ e�_F.2� 6!�G`\ap�SJ���Lb"�rR># �K]�e^N# j,.cQ6J�B�e�4.1N %v>|�V�V�m�^�2�:'&b2 �m^�&2}] %us:ert�$a iN� =FNUh$:�7toQ%Z�r�$S ^�3�$�$. As m�\o#+�UE1h$ trum�F8%6sGe.�.�4nan u�3<� 6(kI�RS(lU;Aq�.a�&O%��/ est 1er $m({ ��-�_%"�fB "�? -<(jP�P�/_{mjA)�55w��6��&:�}D ���JQ}�&�+Y� ({�{4!���k = m�8(= j��>6Jm"� m -n<�m�V� ��b�mr'�Y>'m-j�H!s9\)H 9�m �alarge $n� XV�e�2Q�Z:03&� $\**� 1�J9ige��[si���=Ucan tvyD_2&� M$>��ny6 ,24Q�I�, z�is�itsZ��n:z8on#r�u(vC)�$ s) neaXe�.v4�inyY&sit<;�$�UfarfrE�i� 6�� " �.&tax&�~pr�2t=|��.b.�q6O*w�ٯooJA32}.�xanE*�qron3y]=3F%QA?r�~�H� )3�L))!  aA<25m��'B� \lb[9��DU� � .�6�\, �� ~  6�6� jrE\heZ� 2� uaiX֡�"YDe�(A3AP`bP�!)Ds5�d�l �� 2g c*��iF� ]�Jo o; �5pproximi�S ��&S i_�uanox � 6�tilde{*�+�{�N&�)in�Z direc?�+ ^ce�FAswl�|in �W�#sCA�!eC"�R��#.�|VV�%�(�0R�&4)� &�w�!n� $f:���XEz same^���&�m�)t�m�_�*[��n}{\ln �8]� eɆ eta_�)��Y' B; :<2�fL #%)>{a6g{[�]}3m�.�9 i ��1F  B� .�'g!"�q:_f*�\8�.!ACb�J� 2� }qly-& ��ft�\e@ce!�^h@%f2� -j'5�!�5�"�?we�`� 6�]asympto\z�;q ��be*@q& #2@��a4� )��F�5(>� N)}$7size $NIL )h�]��ft�$>�$. &�F�^is r~�saW6�trunc�B%�b"�%��!]�_6&exactly Y�7 cal block�� � �� � u��z��b��cqс�Q":���(ZA  <Wwl5� !}1jAc-}�9.��s� �B�N�XR�.s� $4 )�]$ y� rowsr|O�nuJ�alysi�3%�st�count1:MAiA�b� �u 0. A. in�9E@B&2��,a;��nb���k� od}��$2k $2�0|1�#��29�[odd^h��_{2�K$Ml�&j, ,2k+23�� m>>.{ �(']to���5�f���N�we mod�y-z���}5Y�N͟:C[� i_m`M�+�h\"�NMvM�b;{#6mT�� D6M� A�%w�x2�5E� P% ied.*7J��N� I� at�6 } }.@ (and,�IAx� arguP,�4 c(�n��`z +�v��=)�nb�*s>��Fwe�F�ks#Ld [3rs �^(%�� s, ax ��eЅbJ S_N (K5S^{(1)} d�2�,s MB">� Ck!� a�0EK�t�\�e'�$�?ff�$ (e.g.q$K = 2pj ��\{ M :Cqhd,>@fF( +*2"2j~[ +p\{\}�w(isTN%�Q\�ͣ&S_N(1�m�>� f],@GB�!�-�NP��-#J�CC A�E�v�kI_{N,��:�Wm��f $)�1}{N}$]�`A �� �w*Wywm"\r� { �&$K�3a_kh)�  ��b )$'3�; $9[ < b_�#a_2�dqm!;q a_m�w�QShS�N}acIB~henP�:. 1Cxe�� Y-=1o $I�J j:+N}Vr:�r�.z$I�/�DU�e� $Na�>�I7K\ *W d�SB� �9 at �&�!g�Qk_A8_u�, k_m��~*�� i�& (�  �&�bbP*-��1}a�{���! (!2}) = 2�2' 'm HmV��gu\zZ�>� n)2 c=!R/ �2�bi!:�"�>-- %� ( est�]�! �kΑA�a/ing %+IU"�_: �r .� 5.2}�U�E a���XG��0�Saa%>bU*�y3 � t�baRBH - %hF= h)E�oincide*�ma�l dimen8of %a vector spw�in�-d�se�&�($\psi$ obey�  %�*>F:5�)� !} %\RealJfk-y$} U�n,) > (\cos h) (o) %:| %�}9�k" %TK ! �,��!��2�t��z!%��m R2�qW� < Z�. (s€r�'on "dx2T [ � (n) � ��,� �on, $T��814�'�s}0 �mI���)�If .L2 � $�$�91���s ~B�Z ��|Asll � ��I.� away ��3t � becaoJof.R23, ide�G��g5(R�&8,(k+1F2JN ��] )$�GRoughly�# j 4�4r type%�D4dut} n ``�&"6\�7onE#Ay&��,2 d-�n_ �bs:3s7.u�j!Ȇ�6&$��25&=I!�. out%���dE�4 T� fAFr�iny}2+�|"�N , if�Rw˛to��4�r6�-�y�&&�m"}%��e"���tyze' `$b�� "3n2 =�a 2f&��[&�JR2q�6I�%Mj6!se>}``bad: "* 7B&[ DV��� Qid!�$NA1A techn�A�licj 4 gene�,& k� .U72JAZ2{s�6� �e3f�h&�5 */"vsAg�>"+_ vZF�&wEM}_{K� M\ H�,�W>`0Nj�5*� Q)�3 ""�3K � N)^6 �)D*�5 Q \F�&�� $K�*� ��;�� � \suba�3,$l'invariaq�� r ro9�q��.G:"���@Y� i$ g���< 6R5.6#��K�'!gW� &�% V Fi- �W1 ZfA)m�ofV!= ],&G t$KK"V �fVN05.3* j)�! W ni%�"�4 &�,�4 Hf�#� 5�1.�A�q C_K �-=01 Ap�^2>U� � -�� &xv �Y:z�� any6�*N2�ki�&{;� �>�sf��m(!%^.H*1,)��B4.19})F�-�.�#N)�F�#a�J�#�Z�# N)}}�#-�i��%�F��A� E@m.�.$�1N�g�$ �^p � sM� 6�l~ �)~gI]^g g{ef�i^2A\'7+NH�J �^{1EK �k=0*z7K�f�$ �LkO��$(T} K^{w7f�,24�(Cg wi-9��!��Ki�<�"fV|< $N_0 = N_0(k,s).���NUN_0B2���%ű��:��'*���i1�jend5��W9i�u:�"�.Y�B ]V._ 5 �& N"� � jr�8���3r6�s�6� �? @b��{�Upsi_2Zd,_{.�}pv�|� s>� .� 'pez0�[L� z0�4�w�r�h�hi2�X .�(rm{card} (A>8 e�W!��$A)H*0,m�(#M0m�� SB�:���ͤ} & Ri=1}^)[ � �:|%�i(m�du�{� �o\{�� B(� �\.R^�E�+<�p 3�(BZ��1<.UA&x�(�wj J6(K�ZN�� N-1}G m_��N@ .�]" R`oLbrKE� ;���Tb.�)��f���K !%� 5�� F � �)lVA1�7�/%�g  .)P :�u$K%\�a���:�">�!ojF� ofZ%z$E�N)^2$ (�xRk��.�"��O VVO&|tak_ o be"� aEB"� ��e2Z�P�o�'is � 6?_�rI"��|I_N"/# 6EF'� u\E set 2 Ka,.s ��r�jĚ��V�n�N-���5�}Žthe1+V "GɖgCnt ``�(OFQFK:�6UAn�5YD0!�is�.��"�:� v l5.4B\ !��j xs!{N,�(�*' m}$�$(}��� @a�"�x�g:M�s)!XE��v�&N��l �R �5�0 &, Q�&?**�1!�5.5��cap2KVK{R��.��M�l�n�On\&Qb�g \rg�+N*�r�t"� work���[ �� M}_Ki|ɏ�|� al``goodi?B" B�a.K i�YV� o� $S_f2 ���*��K deed�ɛ0"m2� � "u^{�B� �[.� W1�:;`Z"�>�3Z66�38V�(Ny!)]N " o� �F K-� *  "x:<)|}&� \.3�F�:@i)1b�F�6:r��)�%�� � �!&+ ,��n)]��� �!8 �� "���6&6:�.1"�-�J� I7��A�fac��at�$��a�u+ , $z�J��-}Ive�j���Q�%��B� \| |NqO_0)/8�&>6�:�t�H�!&ni��\{o |\ |z ]BP}G�4R�:l=�&g,�i� = �� F)3�*,N1>�C�0.+Zy!l�2 KQ�v*"��|����&� 2��� J�����0 (I_N� qV� ( �I}_� 6��"�#EtA�:�aug (�" $2 ��I�2E 4 .#2  = o(*�m�anߝ�� J�3�( V Vd%*7:�>  �&�" 1 AW  a�3q@� H3�Nq���s�1E) (l,� �*%f2�u,F�F�A]�'2�&c9@"e4VN�fM��MA=l}_�M�MsoJ M&j� ��=Za?!) F  E֓ER]5>d Instead<� 6Ze��0�� *� � �G , � )%e:�b >S+��^�D3�D&w�� E=��m^PK ^F,E�.��:E��DA�"�!q���V�6pJ] N]��d�,tiɷ"�i���|M}F�ٵb��)=.�2cB-" \*k���RI!��d7< $�0)�VijC"�8EU&�e?P*3Vof HavTwo or MIP�V-Qin� I�%/ s6�$6WTransfe;I*�B�2to2Hs. %W8!wri�yis �s�"�AdW���y Jfs=�Us ana.#9Us.�8!Bu>� &�0E�cI�p*"Y0�Z� Yp�y>*�(&�2{ n]�5T'���&�#and*_.17�of^�;��F_T<.�h)2>�D�M� 2��,�@H2*D( <"v2 \pi a�U(}G_>&b &O� �~#c���6!�e� ``F�$ Z[�� �.""@*#>/ cmi�26%5�F��+n&&�C��2&�&�, �<�$K&@YF�N�k��%aǟ (up� a negligi� error)� <�� 9 U#�� Qkny�2negat*��0,.  A(m,=%,C.{5J6F/ = ``B \��� by $B(m2�, �I���&�N1>�\ � �z8}\��2L\!\ �q�}\J��Ito7if��E]�-<3s&� F}( "�[� `zwe� �$� � $M�0�XtoN�3 :(%e�<�X}-�is\ an\=�\ of}\F]B�� bn-!��S� �2�e>5>�$����>�". $N$-thrQa&�*��#\(Dl2.S))JZ�\P��$N}(z,d\mu,�a!z 4�:k��`}�J C:z*��JB�4&�!��`":�complex"�-B�� for6.0} B�1z)�c�\,z\,�I�{+�B�& ��"�C%�$?NF N0$�a��9 if $B_N6��t`j�IjEl*x�5;� q{1L $ as��duc�ftheirI " .�&5>�$� a Blaschk�J.p,'�?N : [0�4pi6� \bbR0��inuH��&v�V�eq6�&Niq,�?} hetaF�"�)!d� �tj��� $ �$5.��)*> ��$�'� N��Q:CdP�7@va���A�u�5� vwN2�QA1�a�) �O|��,"�&|?M�i� A�>�-E�`I2 �� vC�A#taB�Thu"nQlJ*e')]�maZ�J�h�$&@ �}EY} �_1o ���>� �"�)��  $w!_KVRNd\b&3b�� �LB"4q1k_2!wg N>' )S� �Tuz����I)u,5�%�&tay�!���w tau-��q:��e��w �em�c.{ *��c.� �� $3doeX;����eT$&� i �� "�9i:�� ������ �,� ��1�� faQ6$B_a(zE�E��a}{1 -*z� a} ze�� �al-�+d>�a^� >7�f�,r+��a�e-�2�i�y� A strau�for�] ؗb��6MaFM��3!|a|^2}{|.� - �B�B��'9�pr��!��a&\Eq6�(�����6�J�*�^sign (� Mf(mp��E.A�Bay#YIly�8���!:� ��/>G��hasx=�EN$� f $�h$�"f�gk�-"7 pr79pl!)aF� O t_{6,1�c�+5���e�@vF�&�1��a�s2g  � $ (i�}�2lO5z Rv"�Zv� P(�!�6ma%l.}&1}"�N)��% angl�%%)�"��gF&gq6]��5ku[1= _Q�N�;�C7B�.JE�!6��Lat*�$�$Z�&� 2�5�k,"���.i �8 �}�*_�7�T0,1&1$ (N-2B��B�>�n!nI!�0r�368'��{f�(G-��Xq =8E� b �LJ�V \b�/$�g . T�9�&���EI�Fubini*5lQK"1i=2g)1V+�R2���*�/�^m�A�&� �n_b�Q�)\,*�.FeiW�2�ȚV"� -V!dN ��q �6Z��_0\>�!���B&� 6.81j�b}M,| =J��g1�&� -~� ])���fd >=Ne 68�%J�n���O z aWNz -M9wb^�b�1Mb=, � \endt w�no�tro�:�.�*�ng�Y���R z Q�"F���� �272�� �:�"]BwE��a$��Z�0�d B(a>2 � �# 1}{k�*�*bb��j�4 \6�=…�N�nuf��9�2�a�m"��2eudNt~c]n�9&�(f�)�% $ appears"�K)selected6�6� **��t�e0AKINal2�canE ���+{)&�"�`&xp~%ec.��yg>�&�.&�sVV��"��[�wL< $d %aU=ѧ}>S �S)K �5��?�� Lebesgu"I�O�*�T"+Z&!5$!�2"��%�a"�h�4�e%ҥ�G��iY�h�&hSVcft�j� )N��� � �mym �=�)��ym� Uv� FQ(6~�zn�����k.)�X*B9F%�r�, �E/��Q�* �5Nu�Vl)��D �|F t6.3}f_BI�>^*t,J2"t,E�+� C R�Z�&c�:�X�,J! �c�%��A)F�k�"� = O /A�ft�[ nB^�7 \�{uC&�3n W)�]$1�:��"�. 1s���8&D`Vr+ . Re9O����-5 ��D~.&jR"�0�R�(��0}RI� 6&7_$.�e- �o�j>B�) ��"n%.^ ���Z�)�z� [#2� *��7 ��L�a� �m� JG9u� b-a}u> �1)6��6 o givR�#vB����F�M^F� � �B(�eV)Lc�rS�M�74Bj>�� A�F@.M �je�th3aC &� M �#&�]*#N}k &�2"��{ Main1t*�;!sQ�R3u+ajssW3�a�}W 5}�d "6E�"�D�wst�tOR.�  2�+�pa.�+*�� Poissoy��ay�VB� �main}0Fn��"}8�%%�%� [M��eD�&�3i>yk5}%�C$2�!�!�an*N���0%degree�F{`[F�c��m�����]s0��J�3 .���,I�Z�6%;]�&PU"Q) ^�B�&kEX� �ʺ��]K%T�3�/%jy/m!}�8JA2$, so�qZA�L.� �se �E�bB55#b�� 76�2 ]:��h6$ Ţ2kB�1N�2mbz45�0m�i?a�(>�3H)6VM��-"�� m��J��t $ �-a3�;j��< rv�<� F6FfI-�&������^ $O (N�T ,�* vJt ���+}ԡ{6C) &?�!"J)��%�A�.h�5 s�pdO9�_0fabt1� #8 R�2 %im \ln jk O-r�M-p��^b~�#�� 6�5=)�Y6���a o(.� $,a 9��92�a>v6�ns�"n � %(>��V�� t�Yqu:6� eory��fٍ=�(K =\��B�%�8^& ��`YI 2�_0 �a� foreP l� �&.�� J^� ).�au\ �R Y1�Q$o�0 s $X�EX}d X� Y:u_$X�7=*�Ma':�e�6� _kfrDb_NI���S_n\cN� X��X_���s +��:&:�IN)$ =�c&�Lb�~^3kp&vbA��O$�ER]:� �/p"�rez��>.?B$P (S_ �= !�M'� � ^k}{k!Rh *ƫű� �,ass��@F��los5 �\R�����$k,�7 �`qJ �q!E& \{0,1 F�)*/a� ;/cI�p �  �*ʋ, ( X_:(1 � (�}"� �bb-0 -���FB1� h� � q#2U�{ be viea!be �*>,Bernoulli tr��U;!{e).��uc oB�eBX%F:���B]�@�&2]a�\��)^%�ft��^/+{ ] - u�U�r72���-"O�)� M�ATr�� ambd�'e 02�a�K5 E b"dG�z�"�ex+�A�diZ`Ok}^�����"{"��:?sU@�k)$� 2�.�&R& CMT})�ҁ���k� A> �  ��}mplete>.BVA,{Remarks} 1��0should emphas^uVv�our� &�6R�isu�6�+� is �p/<+� in sT!klaVA�(seems vital%�|� ach.� c��� how (or����+e'achtsјd Are��v8xtended to disthributions that are not rota�ally invariant. 2. In this paper, we study the s7(stical dist_ of �Ozeros of paraorthogonal polynomials. It would be interesting to understand the s�o|Zk8 A generic plot*the � f� versu!6e �/Vf� is \begin{center} \includegraphics[scale=.5,angle=0]{g(2.eps} \end< 1�Mathema!m�,�4e related workq@Bourget, Howland,%f8Joye \cite{BHJ}of."2}, %3}.�#!^��s)�author!� alyz!�e s!%r��ropertie�a clas five-dia��I�%Xary matrices similar to%! CMV (U� differenc}at !Fon�w� extra c��meter)�r) � (a p��Lint which appeared a��is%X was be�� completedM�) < considers a sub�!�  of {%��$ does�%overlapE�3�6�.xproves Aizenman-Molchanov bound.UE�(ones we hav� See� \ref{s!� 4�results!%� ed in ourI0 were announc�� Simon in )g$SPrep}, wh*(he describe!]e:��W�8b`I�2:n twoNinct (E�inA~erAL way, opposite) situ�sE!�(first case,aI�L Verblunsky coefficia�,= showωre� no local �<lk betwee ��(m� behavioA��~second��� sisteC �>� given�n�ormula�q�n = C b^n + O( (b \Delta)^n)$ (i.e., �n /+$A� verg!�o!G4onstant $C$ su1ly fastiY� !@a�is%B I��)-�V��� equ< spaAd-��40of radius $b$Aga�$is equival�o saya�et{ angu�d��a�D1�nearby �\is $2 \pi / n$ (``clock"=� \si<0*{Acknowledge��s} I amɻgrateful��B.m% for �a helpe�encoura @A�the3 estigIC%/ia�oblem. I�w!��3ank M.� fe� pers! communic Qi�$AizPC}. %n| thebibliou y}{100}z;=i{AM}.�, S. ��, {\it La8iz �at larg�uorder%)at�� eme t gies:3 ele!{�PderivD .} Comm. � �. Phys. {\bf 157} (1993), no. 2, 245--278. �iz_et_al:�(J.H. Schenk� PR.M. Friedrich, D. Hub tmark �4Finite-volume � ��al-mo� criteria%�A> son �H-. Ded!�ed!��P. Neva�Szeg\"o�-� � �s, %-fer65��  �.223 ��2,�9Q�JNT} W.B�L nes,�v$Njastad, W�KThr�P�M��t�,,Z� , q5�i��+ed"s associ��*� .} Bull. �� �Soc-�2I989-���13�F2�oye2}�'�D��t��stateO,d {T}houlessQN a�mb�t bAb��A3 nn. Henri�4car\'ei�5} �4 ��z347--379y oye3>�Fraq+-kEstim��Rn Uni���.}���t�Kho^(Khodakovskym;I� s6�m ��p, inaXE��� potl��h.DC$sis, Calte 199� Khr}� Khrushche Schur'gorithm,]�.@U>� � of Wall'sNT�,$L^2(\bbT)$}7 Approx����K10��. 16�r24��,Mi} N. Minamq��  flucY�l uma multi����5�FZN9� 17� ���:$3, 709--72"$ Mo!^6'E�a�R str�r:��� one-.��@\"o:@N�%I 7!H1980/8�d 3, 4� 44� SVan}:W�cPa��ir� on:% ax appl ����l�ontuKory. II� � � s} (Va�vBC( 93R!^149, CRM� w �Notes, v mer }.��,*vidA� , RIO5q�OPUC1B�O&�P&�qda� C1(, Part 1: Cc*, @}, AMS Colloquium� , � ican9 5!SocietyF�in�8ss.�2��2:9���z�StaB�''�eorem�<�Q.c1x��u}, a(1�>�FinZ:eJ� .r,� A tali�wo piEi� �yW.vT. Wolff��Si��a �� �ZR, �$y%"��, Hamiltonian�Y]� � Q��I3� 8��1, 75--9"� Tep�� V. Teplya���p��6� �F �9�.�1� .} &� Dok] 4kad. Nauk SSSR �20� 9�� 1, 4:3;Z� SovieteG. Z�4T 1992��x,407--411). �>A docD} P\4style[12pt,twoe]{� cle}"� o�s 2�D \topmargin=0true�oddF>ev�dBtexthe��=21.5cm �>width=16cm \catcode`\@=11 \def\newsymbol#1#2#3#4#5{\let\next@\�Tx% \ifnum#2=\@ne\else2 tw@\50msyfam@\fi\fi(Dmathchardef#1="#3\^m}%" �$hexbox@ �{\}m� $Hpalette{}{\m@th\mnn ^" 8R �\leavev;hbox{$ 361$}\fi6H\font\tenmsy=msbm10 s!v7 )5 !Jfam �)}P)= X \Yp6_J# m \e!� T0@{\hexnumber@ })NBbb#1{\�)M#1}2\� 8ve \load{\footn�&ize}{\sfM��d maoB�newJ ema2��}{�0 em}[x]% '|�ion}[ ]{Pro2/lemma)L2# corollary'C2+def�6|D2-exampleVE 2'ra�k&R 2%c")C�wnew�,and{\bl}[1]{J!)$\label{#1} \- el}{6! (:bt.K-rjMt M*>Op.O.�f�p S..>Wc.W9�fUc U,} %t9q.T�jSn S+:�eq"b�" eqnarray*B%n%�"f#q$6IJH>I>#bi}Q#d��b>&e&�.$ :�nomno�R>J4proof}{{\noind�P:\ >q@qed}{\hfill $\Box�"\medskip>\,RRR}[3]{(\ppA�, \q{#2}3})_\hhh:�M�$zeta^{(#1)>�p "Phi^\mu_R%IH_v:awhI;tilde{H}VAkak'(� #1}):Gp�phiVCC}[2]6~ {\lk\!I#Ei4}{c} #1 \\ #2 %�  * !\rk>�e�EVzesA�psilon} 6:(Ee}{E(e,\es>�gT \varb�G #Ps�!�:G��%3:#d kd\Gamma%�6�,ikm}{\int\! �4 f k}&O$(|k_1| |k_2|> ikmm �int _{\tiny >r ,\kappa/m\leq`, a \La/m \\63!1|/�\ll 1:.� g4}#1 dk_1dk_2}%6�KKa�r(K>�K\hat{{!:1ab�aE�1�-+b2+:5lk} ft(:rrv >$lkleft\{B56\>�BR}{{{� R}^3>R.re.3�2[\log(%�)]^a�:�prY�_0>�hi}�\rm I>:hiBz90^{\!-B�(pfa}{\pf A>qba�a�-'\s B)(i�:�sbb}{ $^+>cf%�)�F}VdzQ@ D}_a>Cdggg6ev}q�>�fg}{f_%:g>:BC5�C%�.�CnL!9LambdB�lim�lim_{ #IX$arrow\inftB1lim��4n�. .tR.6��display:zLRJ}{{�HBR\!\times\!\{1,2\}B�LA� .Bff�1�>pfk� fff_��:�fa�0>6W)�finBahhh%ҁ�HB_�):_hkA]hhh�: ia inf\sigm>=f}{^{F[wic�:\!a�\!::V,add}{a^{\ast>rass\sharp:8st�$rm s}\!-\!:hfa�E�f>Wp!� P:;mm��suA� mu=1��6�g��v�c�BS kp}{V�he}{H��)a�.qk.] ^,-�B�,g�-.Bhalf}{���,:7 �@"!mF"n}{{1/2>e2<e}{F<vO ��-">Cvpm!�."_B�av}{{A_{N>AbBVEE}{\d2�e 2�� 2)E/ "/2>�ce�aB E>�ccrR>s�B s(k_1,k_2�|6�AA}� a>9AB� \langleK r _E:�BBBb>Bme0A�rm efF�h}ph}>�jjXA� j=1,B�a�m�2"%%}end6�  �%���makeat0 r \@addto%0t&� {�} .oth-def\the{\arabic/."z page�� {heas�Hsetlength{\baseline <{16pt} \title {M�,Renorma"�inN Non-tivn29-El�ody�cs"z w�Spi�/han$} \,8{F. Hiroshima\t�'s{hT@mpg.setsunan.ac.jp} � �K.|"Ito8itoN27�0 %% 2004 Julyh creQby�#8Sept 04 hand]&spohn#$Nov 18 ��al ? edi�.N1207 x(Dec 05-06endix Ad^by�\1'61c Cs0c�& � /10:` 9-106/It[�4 \date{\todayATA�E8U�k3De��'ofqAs%�m'ics,\\ S-���3Px\\ Neyagawa, Osaka, 572-8508,A�Japan sq| abst�}�%�u*ve �4 $�;�0�,Pauli-Fierz �ain E� ultrn,8let cutoff $\La=3the bar\$m$ in non6&ED i sy 2+in�*ed. �$t520�(oupling�c,e$�+@,�explicit�m �,s $a_1(� � $a_2 deE{ng�/m$ sucj/at $ �/m =1 + O e^2N e^4+ {.�[$O}(e^6)$$ !0�-. It! .n&s,%'�6on enh{,s%qef2�� �,r�2ist�ictly �ve=4 $b_1,b_2, c_1-c_2�-.�d b_1R� ���og -@}*W\  -cR@1$}{ ;^2 =(-c_2.$$ In3I� \geq m$. %o�/paper�:eis ��2� a�r�5�He�& � grO2$ energ)$,am  1otal m%um�.�=_�8)�1ndH quan%K�/.Khas�  infr�3�� I�anb�. We�Y%�es�^ia� e asympto���1�)U$ asbW g�3to��y�$admittedly4�prK$. Ou54&�:�is p%�is U�O%��!zfourth y)f a VT<0^>��lthoug�e|poQ q0�o4|s�8thinge�E%��l*& 2estab�(;4o0hisp2}, 0rec4�c[5ly" (t�8it!V)�6`its �5%�1\sqrt����!(�:����Ma�?L.� %ty!���Ax �arai1*�2� enA<P�wl}nBc ED can be��riv�'om bA. sca�lim�i�:"� ble,ae7)Fmayf�8� uag8r2L5fac�;� �us �4 ferm�� loop��only �� absorp -emis�, �7rams I� >>h ED.t �belie!to� triv�;aft���rIDrt5a�" ong FN6��heJ AJ BV�~6k!:*#y!�!� �.� verthelA�we ����a1H]�s! high�,�2.�-!�a. �8cb7t! remo!by� convAz�,�%( scheme. So�5 inconceivA<�>���/P]�.�K !C� �Q�i�'8&0dure. o>e4l!/a�Q: $ea�) yNm $\d E=�n=0}^i��e^n}{n!}n !� � 6 ia��F� A�&?ll6 �ŵE�of�, howA, �bsvat �� % 2)}\not=0ɩiUs�; ���^{2}$��R^/��%�$ be hidden<�N to�� a Wick��1�RAUgins '�%.�œg n� u��:.�s. Si��a:PZ4 befo�=e6� must�:sub i%{ many��s �; ��shd x:w25� �j %� 9;F��A�B%Itradi/ �&�Aou>se� t2��=M exis!wAn0consequŵ$M!$ cauv@$e^4$yq�tA��A���ac7&:� ��NQ0!;^�� stud_3A e.g.$>4caha, ch, cvv,=si,�8p2, h8li, lilo2, sp5}�  #��aa4c�?grasp��� ]� � 2�4?IZ Aci �@u<�$�> wayX b�>�ɔerne (Z��i~;9 Lieb-Loss0%r?}�Dib>(th checking� bo� f��-incideE} each Us�D some 0<�s, )��[ ,Catto-Hainzl �ch}�wL N)1�^)�QAo�a>� upA�]�. � SeiH6 ( asi}X� exac�*�=�E 2FY9!� . Moreov�|A6>Ais S�-A� �>upG � lowerZ?B�gNel�. E�iJ�-ee�; � sp6}� re� ��jrprogr�1��is\. D ? += summar��f�,ws:\\5/;&'(J�) ]&:1�{di�-dz&� $m$,��/ !Fa fun�2! )��A� %��alOW210$9 *�X�  \"F#6�B} ($(( ^2$-�8){ LeG�,}{m}=1+a_{1} 7e��B(2( 4} +Ht) * {6}) �� re �� b�$b_{ind $c , $i�$,*� $$�� \�4 �� 5y6xC}B,h�E�b�?in) {!u��^{\rmO less}$N �6�e Ův *^��2n Q�>%�Bf m"Yv��a6�@smaj%|e|{\� . Y( �s�) A, BE�Ce졉 = o�H)eC an},u��$ main�%"_) p1*�G�vely. �GrganiE�a�lla� S/ on 2a� devo � expa�9)~$.� n s <3%�y+a�!�f}.F�j�@�5��Fi�Ka�R4,ɧadɥal *E�A _s^0e �BCAV� �@vacuum $\Omega\in�<� �d D�!0,0,..\}L �; $a(f)� fE!.,�9�#�A��4 � $� F8A�annihi�;7!Lfff!fi.byrqn && ( Pl' )^{(n+1)} � �{n+1}S_(f-e /.)})2 && DJ)=�%!\�fff| \�=�hE \|n^ \|_{ u)� }^2<5\rkk,�nned%P=[� \bar f)]^�!YE��$S_:Qzer, uL X)$ %Odo�Ӂ25�$X$�8$\|\cdot�KK}$5B K$#K!�A;T aYr!�"�wI�M<(f,g)_ Gij5Ang$d o-:arf% A� y satisfy`oni�c�^�� � L>��.$$ Th�HB�tur���+��NontzB one-parM�7�=� pE�a�g impl�Ct�te���R'� g T$a� )q bBF#=�\4}m t!�RR �ezg�fer�M�H1)K 7�of $T$V\vp(k� : j�eZ��� �++�B )dk,5�q*,2,3.!�n H5  $e0�[�'$,�s polari�� vectGH�Cth!wI1IS2  $k/|k|�[m�� -�%system��\BR$, i�O $$|B j)|=}W����� 2)=0QT Q ���/fixR�� �CD$k=(|k| \cos\theta phi�1|\sinJ/� $% 1)= (-3,KU,0) ��2)=(-2r<'phi), $${!�a0\leq _ 2\pi!�-\pi/2 8 i/2R %A�$e(-k�)I; 2)=-2)�Ne i [M�, E� nu]=I�1�)qrM�Zt�^�e*A�nB�-]�E� w%lU � $$�= �m��k ��6 ^�^2��2� - \�,� eU}^�Qa� �NB& $��e �zmagne��#�k$$ \bŅ6+�79V�4�EbV(k}j))��09Z.!Ca)ss y> 5U`5e-d(p�9�5)�&\hf -9, \bvI� p�!B&W pir0Z .H:+��j�� |SB 84I ass�P )@=\�� 1Q=-k�k�vb int_\BR(��$(k)^{-2} +)|6k)|^2 dk�' n.S�T2� "[uB02m}\pf^2+\hf)�M $� in\R BR$ �� <�@e�$|p p� � s��ta!Z�bf2@p��m#�Wn � Kato-Rell!a� em� uoN ine)UiyY�7�B|o f�\|_!���|f/E�)J(LRJ \|\hf^�,� 2 +\|f LRJ\|�l\|�nbRa�/^4Z2��-&�! £�(w� wb a�$eq{fix2} Ip�-� 2� ,ll} 0,& |k|<�&!%1)m{(�,)^3},& %,|k"�8.$0,&|k|>\La% )  :�=�(e^2,\La{2,m)&f"�����A�"�3}*X_p \is (��4) \lceil_{p=0}anR�"a� Za, mbda�rof&s>� mean�find !�{m��!Lay� `)$����% 5m.0� L�:�Xi�Bf+. To ach�$� is�b{W�y�$\beta<�!$b� �ARm�;�+�%� �:mbda,M!^P, (b\�7) )=\ph,��� $\phn��� will see 8^*-�-7B�#Z x$);ka�;��Sq&14} f �0�/mu8Ecs}{m \���.�J>!& /'reducQ:o � g�<<-0� �&&J.�+�)u:Ptunat�*weE� $yetE6v3�a�$Q3. v0:k $VeQ� �e$% �A*�]�K��8!s�e��`be� ?.��BiB!�m�{/m)J�'a_n%�mU1{2n�FI�previ�K�!!3,7'& �e� yu} &�1\a�P��8 �;$.$�@�a�^AWEsXhY$ ͹�L*<FF s $xA�!5$x_>�1x*^1{=��}(X/Y)8x[1E yu} sugge,`�$i8\01/2� e�M�.*$A�>4s�' P�(!* $e=0�RW/ _���3ec7)A*�.T(2�3a�R�v "�.i>.desiri�!� � <1$,� D`A#IZ we4��3)  $�1� &o2a VG�)6� �%�2 ��� RH��)�m3}�-!��e�'Z v3�#{E"q49 A�$ity�9 2� O���, ies}�$TQͩ��A<_m}� \hf-�'�< }\s :<_m��e��,fix} \vp_m(kXvp(mkP"J7WH}� �82� ��\f� �D.� 5&� /mR� ��;mA_T=` bB f )p%�]p�)$X Y&��"�Jale��b� TYJ$wm # 01}� ^m-�/m)��6�'!�Q[8s $J=(J_1,J_2,J@q\hvf'�� $$J*Q dg{J((-i\nabla_kO}+E,\ m� u$$�C�03�0�t�1�Wl�3sE8n{vs = -i\jr�dd� � � �@ dk\\�h�d{3cm} +���}{|k|} � k,2)@ 1)-\ i12)\}dk%pnmDn��c$|n|=��$����${_%R}=(R_O\nu})_{8\mu,\nu�O3}��$3�3$ix�`�g��roa6$n&� aelf�` I� $ e( �D= �jx k\c%ae na���hA� e^{i f n- J}A%� e^{-B=���XnB9 A_\n\ \ NU~�W7nI�VXhfZT&&N��Z:b�Bz� iY�W6nuQ�K �IR��@� J� M \f p3)a�p�Su"}pE%($�A7nu abel {g1}=s _p n�w" J} hp) .� $#= $|p|n_z)# nn"�!Iv_p=\arc�8lkk (n_z,p)/|p|�A�n_z ���i$n_p=pm`n_z/| |a.� �5s1ja�, $���G ��� �- �ThZ&� (m{ *(|p|/m)�" c<�  $F{X�G2pF2� $�"W./e!�\he��FF o\7E�q��xN$$%M�is(X�n2� �G\=) +e^2f2}�-�2�}�^2I!� $$i��)=��=.}% = m �)F -e^2�omVp^2$��ms��E }=\E�al_\es^2d/Nx\esz%� >2$m/O--�JM��� /�W�Yud� %�!B?sor.H��?y. �set $A-��I�B �� We � ew&f *@AP�0$\E @�%�"g�`) \he$�3��2�9e two�d deg�<ac�<:DO<ba]3����6R I$(C  �# nu^2% $\nu>L�-M W%DaRmodif�]�2����e����� �g7������ <;"� 9�. Ajv�{below8 g$ $E\kp$ i �pa�oKd t valu�1d� 1�t�4E�� �_not} clz'� 6�!+%�� wF1�� � es$.*aO�I+M \C 1 0"^"OK @  /-/0 1"j 0.�$a'49�. $Va \bl{�}�rM;.� e_0>\pr � % %� �e�[4\dz �\�J�0^2||e| �S.  $�;2k} � )hk'C &�h5 2v'kd $. &� $��}%�b��hk�V-`K�Ms23�4hkfUnGp���;��Fk.h {re} I�' K\kp�1_{�O + hk} (\hfwfk}+ \�6" =[0,�� �by �rva��is(�)=\Ee.� bp{f�g):��.O]3 ? |p|) )-O) � �_��>I}�k� |p-k|)&�-�>� 2�E,2��3in�]>nI� %� \pm�$D:>�M��[Z\- N9 �.yp �Y �_�{_)suAY�x�<nco��[�72.3]{fr: &3}>e- \qedM: i :"�+� (e, �*�� $'?f��?p)� �U��3&$>!�6,$� e, p>1 \left||6D 5�j�AF >0�. � $ \emptysetEeT-by'[�o�xf1}u�!��9!�bc{f2}ADѨ.�l �0�!G$e��M{esUxtwo!32�for.��U��V�m,��es��\ec�� $\kr��inA��:��܁�*�' 7=� �4��$"+_z  2G&i ͨ�BR� -CN[2�!�� /AmiL�x>��Q*Y(pm)0 J}�2� �=" X,n�A&�' $�+� 6�Bbb Z}_#K�pmY�� 3/2,..�4A>JG�hk})\s6t �Y Z!�� $�I)� decom�Gd% \hk=*5.z/ � �2y!�k(za2�)\ l�DK_z\kp !I2>^%�in�(� E�� .�W K_-A�-\�]"�6z�-!} }Mw 6H K_+rHG�$$�V%v= �M7 O�t� tani} A*�&�?�%xdgg5� $K_\pm. na�que6'${4V).i.^hk(Qhan.� @)e��l�)E*&& "� (!�-�)�= []%_)\cap N+]� �) plus2�f1Q \ I�8�? VI���2ma�1a�n$ su>�!,kR � � anl%|.�Ps**hk� q a 0 +b&*hk�M�$$in D(K_0�$a"�%bE�0���b>en by �� ' cite[p.16j]{rs4#? N XII.9 >E�z>�amilyq(s/8ofc+� l ;is�>&�.�ofARm�W6s�3%��?��,A�.��8B*�$e� �u-� eoB 28)..�� ��ls���-:�toOA��p�f=���5��\&wCba�hR��w&@A�݊{]-WmU.5o�C2d F> 06[ e .�>!J\fJ-Ei�|of!�%�)�!y}} Q%>�C=�� ) �+1_�* B� %zZ� ]%�a�I�� ��:x ff_0�:;tn-P>�1!�bw�v�;!.J\$5���� �6Em �(er��T� ���"�%Q]�A�z$�p� \gr(e,0)Jb&�KN\g>9���T="&�:>�:� k ��*� �-�j}�4\�,{koul} \g 0=a+,�7&&# ana1!��\p,+g n�i"s5n�EV6d.m8W -$1i'+%M2'���}-� hhh M� �� $ *k �!��$ �UW�  2.<EJ3+� )�d \fg(ef�a_�Oe^n*� "��I6R5,�4*]A><�j �}_{(n)�1W�)\*�B_n$ s 9@ $( 6-�NJ1�!(r $-�!�er�pin5���$)��AeP9XqA�/&ubEMa\ �F� &By:  l}, &��po��e$��i(E $$8./{m} J�R[*\btbG.�.�b_1>0A[>0C[>0i $c_2 .�bne� m�main1}�|I(*Y[�r&&2K2}։I� nB^t��r.q�(:42� $a_�J�.mM�RK� HFS� �HgSA&�Ya��(a\/ term�1|K� /m)$�Qve,1Y,is neg�O sign[R)>�Q!Fd9:# �1Cw��W &�NQ a" ]$A��next mG.�`��#u�E�I!sމInB�4a*�2� �3grFkFc$ 5EHB��!�.���u�C�4 $H+#Ems\gr�� iiH� {g00)= H_0+e\hi+�K ElqPE 2p  is(HkG\gr �= !�:n&SVZ�^�,G��H*#f�( M8\hinh�G1)�( 2)}p= =A=� ;V�lf ^_ K, A}=A^+A^++2-+A^-A^-�P�>w�[�/ A^"* �12V<\E �*?J?.,?e)\a#)? d A^"\ H�aa h)$�;l{exp}Pt E$X,0=\e {2m+1}=�!$m�,YL!�{:" �3 2= (� ,=g 1��- bs\zg 0 �4*gRann *> ���Akoma5, 1=-\z2y�>,6, 2=\z� ii\+2AjzY3 g 0+i� U�� ma7E3=3F1AcO2;���2��g 1��D}*g 22u� 31T2�� A9Ѭ"�/ $\z� �_nʒed"d,a�B );- 7}  well*f,��Ň8 !�({lieb} D(\z�p � \�q.��K\}_.af � |aPs.0)}=0,msupp}_{k0 �{3nVB + n)}(k, j)A<$\ni \{0\},l,� ^n,nE�1 i� �C10 P� b<3a $\e 0E��O<�H�S:.$H-�H)4$e$�law7q-�[uWqyoI \gr' HE'� ,$\st d\gr/de dE 6�m�Jh,- D(HA%�� } (H\Phi,��i|=E(:E� Tak����65�kPO sid��EE�5�J�'� a�i?a1�':s+�'�'� +� �� (H'BT2(h /2i _x�(�2}\}.2cm} =E'� �+2~� ]�B�32� 15G6� +B�3F�F�32� K=o.p(n�+ $H'=OTiM�H'i� B�!a]=;aa� '��E�4$A,{��H'\gr+Ha =E E E�R E{a�wXe�'gL ed.|��&M {12} AV gr+2�' ���2�' �')�IC0 {13} H^{'''}A3 I' � K =E (E['!� (� ����%�12�1.�� {m6}�r, vM�(\gr, �.%g I�gr,\g7 K �.8�8)�P`hek"�;6��39�$�1-1a[ /�;0 a �g 11: g 2 /�2 K� . ��N _!�G��%Gj�equal>? $ J�^{B "��> ��2=n6. U�1�Vw!�A� 3}I�%?, �!6� \� �+ �1��� 51 #2 =� ��  3\� +3Yi12 3 =33%D4A0�L�!= Bo + a�++b -if2 6(F�-t) J'@++b L4 \g 3= \z (- �-2��) + a'HT 8Ga�� som�atD$a` ba'O$b$a'�b''!�Ihw��� $B"l({V^{�AQ&N&� B8E; $���BA,B1"4 $a=b=a'=b'=a''a�^E�o�A &B "�m^ A��k* ��9i�mmas �.�%ahi}���r'=��/�9%\es)/es"�!�/!��$(\pf+eA�T mu=3�a�q(H-E)\�F%�af{226}'= J>�� 44}� &0 1-2A�r I3��DA.h}ejX&QIS�eo��(%��e>�F!�11� 1�%R� l1��1aa+\r=E 2'E�'i��CNU2H.6nno� h�;8�i{l�$Ŷ�'.�� d�%L \grrj �"��\stQokp2~!�$��Mw3i� ��0�(t�A��%�l1*�l�B2O�*J l3}I��=Uf�8I�)�1)4} ]M�6'+\gr-2<3+ nnM�${m}/{3}=Db�0�� ͭa\:�3�i �F�L$Χ��:s  ql3."4��D6  �sta”bBΛe� 26&�(!a {255z�9.��, )�f}�"= F�Ac Or,�X":Ty!��Yexqms*�"�B �R�)|2�5mmm1{�OT "�( F�\mu��6Ebc{po :WI��� � "���eO|*`1+u>�!E�c"��J�B�.��B� ]�]q2zgF^� �G1=m�f � ;n2�@&F+Q��� bt{3R8!��t#\eq{hahar":b1.�c"�ue^26ft�ua�t`c_c6�9fIblbIl�}�c Ed2l+�F� q8\rk^2 >�PZ��66�� -0.5E L��e(\G�� \wh 0 \G1�| ,�S��> �XP c � Q@2 T�.Y2Y -(\GTwh0m� 1� ~+ 2\ReB2,\wh1*.��x� �6 ?��komI\� .+(\ L0\G +d3d�& &dU$\G n16%�$1}{(n-1)!}�8� {n-1}-�1}*n�X�+�  v _@�,��%�=\z� 1 �\z,N6wh 2=��i \z+\z(� �-\EE)\z R\;G�W�u.Y�Ё���= 1s:-�� 1M-e^4 ( � 1}�f!��,"r +�_1}{nEhg 3 G) Fd�7M�!�8�- A�R+ eA��;0\G 2+e^3 \G 3>P4] A,�8�e�G>]GJ]GF]�\c��|�z2Q(>��U\%n"9"ppp nM U �S�nitu 勁tO )L ��s2� 24}BN6� �m�^ �:�  (\Gt%��1)��zaxRmecoin} %q�S -2 ���Ea�ta�SM�nA;q�B< 3 /pp�a� 3{�}2�%?��  R9�Tp_<I"m�$y�!low�K�5te]eq{sou}  � =�`3)2-� U H�EK`�d�Gl},&� �"&�=�$�!�R, #\ab 0 $Ws>�,N� $b_0�m?i�t%�N�� at ��"� � "){o10i �w�1=AO Ipf 12� o2k��)50 �AK2=2 L1+L!To<�3>M1 +M2M3=3 M2M3�h@,j -oAE /�Y6�e�^[1 =� U0U1-��!0)+!�6�e�Q2= \z(6���2-�#1 A6�e�3A6�A3#2-F T��,$a_j,b_j� ;E,3�.6XQI ;*�^Q�5!*'} 1=\z�s+R _��2 � ')+R?_(3�6(3-6!TN2+ hi 16���J�pP]�SR"d_-�U(!�6� R"C_2$ )- �Yb:� R"7_ -65 ?+2���  ���| Eq-yy<>1N>)\h 82-��,� O1 dire�&3;� drib�� of"_�$Wi.,a_3,b�ѝ�8E5��1,!u�< &!��/ ='2�' 3 :$�den� k�rs*��O2}6f. cF�1*c� "�?�,u�/ $�(t "� " \q� \ \ o 1\q�jq  � 2�9 4+\q 5678=-"wm!�%/**}A� v�> � 2U ݎ23 |x � \a�04A�0�)285 O U� m6VS\ V �� q 7${\q 6}^{*}.I!��870ft\{  \bs � ( \}\z��&�**}!� listy$pI%v a�����U:JO� &=&�bs�C\29�+2� pfa  0@ & &+2!� \{ z� �� h g3ga��!))X�D3> mg 0tN o6#+xf(B�%o �\�!2c�!���z wJv$s�q� \�.! e6��a� abov� res�&� | g g Ų���!Y,ec�B G 1� uiv \ppbpI \ 7 � i=2}^6+D %3B%7}^{1j# pp i.�łaz# \mu^+--&2=i�^E^sbb%j�pp�a��zF!4"EG{�%! A��2r5J-!�AQsbb2,6= R\z Eb!�!�� [��� \ &sb4�Lm�Nh7�A!#\z�2�82(%.m'B�9=�9l-6���F�Z� .� �f ih)�{10}=�C96"IAA}R61}��%� 2.�^L1 76��6�3}>�� 8 3q��."!)5�^#\2%U�AON�4}+:. s Bf�{15v9A Rq6�O^�bs>��\ �yT8� B!2�� ш"�%� hos��giv} y$eŊ� 63 9���16�Dp2} $$���oN�ax�da�A!� =7p2�\d> ��9�_IF��lO to $�&�|us�� B�J�.�4}E^+(A�20v _ 2)}.�)�8),}6a�L1c? ,H_8��H1, ..�~pp %:�i"f�����8 �J:!�l{�%D.T|.8 " !��8��� � &h ]�!� (�y 1}^2��xŌ \ell=4}^8d  �fi+)��`. >":"�y� > :>{�M�7� 93�("� )^�.�.;� FT ��96h6>50 =A�> !}<*VM7D�9�%�*05 �3 \*3��ficxd�AfDǐ nt Ta�֭/ T��Q��e�V,LAVA@, H_{m�G6�8|�|> �0ws them� 4important. NameK� p.\��] JNm lexa jugaw �n �= �)�$��D�t�)!;reJ�߫ofm�bl{itoF�-�rMq{�V \stackrel���m~n { \m����s}�� odd X|�= Bǖ�1c.LA��z� amm/@ C�C _{3}%~8N� tand�{r�2�x-Ӥug�PperTY�9��$: $C�~�WC J=-J C�J=�P-1�?�6hoŋ"�7{�# s�3�G"^ �$ "�8�;�(�eMe7ti-K,�sa�@\sq� n^\ast=A�-A�� l * $,&\m:&- I� A| si,\�m�Kff}=( ��m, si!� us �<au6$ � B$e2pura'( imaginary.�I�"��K&�AӁ b bcis?���b�=B�."�� $E� U�m � it�Bw #G/$ ]�IgI������Q�1 %� $ &0��2�I>�=�29� 2 4 �fUT>�6�1Eh2��$�c .�2 5dAK�>)]�2EA]�>�2�1 6\Q�]�Aԉ2 7!+\J]]�1 7R]Y� (9) ^1 8^b10.|8�0m)!��^hndA���i7B�N�m6� d{8}a% F.'� �le�'�'&Z�g� �d >��UAmRRRE�1!��u2�9s2 A[5�q7!�U_63 2�1� am}i�qrW /. 23�qE�2g�2!5.i!>e2�4�\..��:����B��$� QTn� $2�{6�i�,�B+HG)�"�'heh ���0������Q�7� $��V�.���9 9� F3��k11 1.��,]_]��[�B:.���.A,qT>/*��P2��.^:$2��d 1 b .��u1i�Fb��Y �t1q$6 2�� 2} � ��: ( =_\M�r $ y&:F � �F�.�/ r��ʞDF �{Es��of 38=� B � lass��t��b i3 typesC1�;$"k$'s. Type I�!�{ ��Hn �� thus�UKdalread1�l>eD:�P{�T2H:k�l�M.� (  $� "g� [�\f�c2]�}?m^�u��a.�U&�F�#F� or ${1(~ 2}E_�:$�:Q:VA2F�pݕ -coua]g �J s8�4Ug քp}-4��m!6�׍Hf�r/�j*B���qA2�'ase$f��vi�R�\takes �A0�regXA&�� a $kÔi0nEG2�g����opposite[&� <|Q+k���Zes�f. Sa�y��sU6J-3ncePu&ia�"�d�y;{+0�V wU&!�g*�W far *��c; @�a�� i j �R �|l��eaking,e��Jm$[� E}=\int_{'a"r _1|,��)�L� �  }�2 )I|^{-a} 2 b*�r$�o �; �;( $a+b=6$ (�Ap�x)�S $�1}���%q ��� eq c!�>�$ d%j�7�q"�z$,i�I�W�s�e{ ��Nw L��$ct ourselvqSrei����EN68ed2�*'A�̙(L4g<��me�-!�!ĥ� �� IIIZ$!��k�� ~�ii{�s0e�*�u- !��FBfLF�w"�Mbe,&�yreg��da�a subtr�f]+o�hEm �} $ABJ4"Ĝ��� p i�bŌEEE�Fy6��"{8G� �=�&5q�ht]�tt"�"Va!u��� � B�8�� z*�$ $\ce_0=� P� 2 & � *% *{1} ,6�  $42$25^323 1 6`�43 42 �R4��{4 6& ��6�� a} "�J%  E�&�A� F5�*� B= f2�L�o��I�� _l{divlf��35m�excep�/�X!��ce�, � ce_4$ sa��e�v"i�sJ���|ED��|׹&X}�, �&R(�5�A$(i,j,k)�9(1, 8, �(2 2), (16, ���l&U"�ca�#@��prğp��rY �^�-"1 �> sketƭe outE�B�j �E��,���sW��h��a�who��w�}[iar>B(�y��v�T� g IJ�QpW[ �I��- �f *��dv�.��r�R Each.lp�%���in��R��- noteI6pC!!1� �sJ�1,13,15� T 5 31 auto��ca7x����D� pf A:;�O: 0$. "v� �"�+]}!t2�in � 1�k_{i}�^*�R �xe downO�p&<5��*0,aK�? 4$�N �-:�&� !%w*�.B{0}&=&\-'4}"��:d-,�^{-" \z& ^,0!v'J%�O -4 \E_.\}a�z s+j*{+��B����+B� ��� ^6�9>�) \AA.Z%j3!j�81}�Q.h&�0 ��-�8 �)\Ne�.D�F@Z�B)> mB!�I:�Y & = &�%FwY-P^2B��)<+*�  D S>k.;e�:s2m,A�BB�1 E4E%16F��uJq-F� �3:~A�pf� z?!�n�!�J =�%�ԝ_�Tf*us8 }�"%  ki I;zz-kj�q�ds�qce� � �% vanish�ש�X B^-�*.^+���� )�-��U(Sb�3-�\� ;2Y�4}6��%%�q.�!�1t"2��2AA &=� �=Q4��F� �"6Y BBfZ>�Za4Q�>02o*2@4(div} A&,Zɳ� S2] AA;,B�%(-iml�|��)�(��}�2|C !�g$I���.3Lu UBB�6*I�>/E��K*�# z�~ matrix $O� ith -%ect= $�v�F) AB O)� ( , O I{ U�wpull-t��� ula etc. 6g%ye�� }�!6E� -"��{=1,H�RC�%w}*�>?�{3}2 "�y.)� \AB{Ιe�[.���)])�.<D{|k|^2/2 +|k|}dk >-fCA�$�q�1}{8\pi��2 }^�!��?r�Zr+2} drF� ?�w"�8 AX and AG ��Mn |\AA%)�k�.���q:^0�)($1}{r(r+2)^�Q��A��strh�/T?A��9*�c\]FI�M�e>j=9"�/GE.� p"~*E q�}A�-2'q6'(p) + 2(p,q) �=  +i��M(mw qIo>�M2ZpEg =|p|�V,I?�/��1}� &>� (l-ke��A�_��2 2�~= ;,&)(:<0-�n,62 1 b1�xnqs\� �:\�pol� '1)� �_2��6{!5 =*1%C-&� k}_2",�� �� Ҧ-�pof2�}�a'1%�{1}) O�� ( !)1.�%1})�$&22&2K)� �{12&�7 (1+( �%5�!3) ��n .>V�aG 5� D {0}2�5%Q \ikmi �V4"�2U/c!�!�M� V  �?2 � 5�G!Y1Y>#Q%$2w��� 2} QA� \ri�kM4E0}�v�Q�9G;"2� )L '4 �G% A 2|^Qb{ � 1})^q5�>n-.�aAj!�.�2S�`%.6��sa��@E$. + n^K-2Aso��u (1-v�+����\rkeF�5B:�F=-J�W6�&E=,:.���&V:������=)��4cm$|ef=���m���~�m�\%��9E3��DN4�;b�}��75T 3a�E� R�R|A�M��btRT:s nt�s� y�k�ϡ� (2�3��JiB�D%{ =.1��%Z } � $�:�d"��f��s:� *pԀ/B _\�[�&�"�  mV� +)� 1}{4t ��e� dk_2* `�*� e(k)) J�Ʌ� &>�,!M-�F6o!pJ3 X1&���sK24"�.�Y��DAJ�� " �[i�\"��" 1}� 6 +8j ]-�((f] 2� �6j^҅ @G&7G$! =-� 2,k_$ kk=\s(-k�G /.1,-A�*�J�5� �Jʱ��DM�����mYb}rME2F�J�=0| WeYR�acr��u<�.z(;%J� \subsection{Origin of the $\Lambda^{2}$ Divergence ($m_{eff}$} JUvT The term $\ce_3$ has s�L ${\displaystyle -\frac{1}{2}}E_{(2)}E_{b}$ which diverges as $(\La/m)^2$ as��\rightarrow \infty$. We intuitively see that this di�4is canceled in�way men!5(ed below. �first �-H integrand� �behave�( \eq{b1} �0|k_1||k_2|} 04 |k_{1}|^{4} 2 2}}{\ce(),k_{2})Xapprox Zc b326L82}} \en for $�/�\ll 1$, �th#($$ \ikmm { M1}�� �}ff}�5�P!�\LV� O)�0other hand, tj� by �X,, since it E�a-� l kernel �.�1� 2�6W4}} !�-- ah)-� 1-)W6lJ��)�B� $. He�we shallY�A�A�M�s)�sqrt{\aW$}$ but not.i.I� 5!8$5�$Q�_{0}$aMalso yS�� a}$.ee-�yS_4�F!� same1� as \kaka_J�-J�44$ coming from>x, however, remains without be0$subtracted kn!a obta�6at)^41�-Y�$�f��14actual calcula�zs9Z0i}$ are done!Ri ideae� stra� forward. �� .%Proof{0Theorem \ref{!}�  \bl{e4}�,re exist pos��< constants $c_1$�$$c_2$ such���;Lee42} -c_1\leq \lim_A�F�m��w4}{5�}8-c_2.�� \el �8ee0} It follows2t0} �j{0a�l 2}<�~,fA� �3�L3L���Gl {\it r��isM�ed�$nn && a_1-=(2/3)c\,\non\\ &&\label{36} a_2:/+?^2A^2�hin6:3a�A direct.� yield=u>&& �annn} bx=\mmm((A_\mu+\pf\z\bs)\g 0, \z N)_\hhh� ?>4 ) + d (\pffb .. 5!: d=2At� `\vp_m(k)}{2(2\pi)^3\omega� -41}{\half|k|^2+(dk++0 4}\i�l A2ja#Jw )^3}dk� 54\pi}{�}�,_{\kappa/m}^a�/mm�r � r^2+r}dr�+ I 1}{4.>U'zZ^5� ]� dr.�Q� Thus��� q{spk} } �2}{a�� B�\lk��6� dr 9� Z ��!�f:Z�\rk� �Y nRb�RbJRbb} b�Ol �9}{\logm��?b�>4 Our analysis2  Lemm��) divless},�8e4}���p implieq�.��$$2  �02\Re \RRR{16}!o8 �^�$$%? $$�� =8 i j kAY 4 =0$$ d$(i,j,k)\not=(16, 1, 2)$. EebyE76}6qcc:� oc�H.o6� � B�MQ��RD$ �� &�36!�0 b-� cc��\qed F" a��C : $e^� rder � eff\(ve mass, $\$^{\rm spinE $, a 0\ Pauli-Fierz Hamiltonian�� $\d �e�I�>�vCB�� B-�� مPa corollary. \bc{cor��p1J  �>R�� e$< 0 a sufficient�m� $|e|h $ES0�\ec \p|  We �E� eft.-$d}{de^2} (|-:m)  8\lceil_{e^2=0}=e 1}{6b{vTZ�>0.$$ SO )=N�$E $e=0� bothAF 3  :�$ � �ptic�pE�D -�� . EǶ .V .�F��  To provezc,A� prep! some� ' � (o estimate � 2 (, $i=0,3,4$> introducee�0polar coordin9 $(r_1,ştheta  \phi r_2 !_2)eh�  $r�=�i}| �1,2 0��@ pi� phi_ 6  \cos 4 =(\hat{k}y, 2}C�.\� phi_.em9� , \ccr =%Tr_2)\equiv {1\over2}(r��+r� ) 1 . � {\pm}= ;,7) ] x \pm ]!  =�' @ '22tz)n�n�P@26� �j=jBset= \KK=\KK5����0 pi}A'U 1 �{!KVk|12}\sin)� d ,-DK {6| ~��} |(1-�!� N)ML � {(f�Z 9�F�� n� �QD \begin{eqnarray*}!7&=� og �E +} _{-} �.=� �{\cal R!�1r_2}-r !%!" &=&&N�^{3�2 .g\�Z[6%%�&�  z26D��R�-3��..�ͨ]A�d..�w�i:�G$\zetaMv��/s<1 �65�u�&%�i6,602})=2\sum_{n=E78�aen+M�|^{,\quad%x6Ya=9�RA�})z)a4}{5}W-�+{\math!�O .( y4}�� �� 5@��k 8Taylor expansio�$q� ��a� �%I/x)� $!�El!Xe(/T}=4x(1+(2x/r_1))^{-1}$� $x= A%�$ (not�h!�=2x-4(1�:)x! 2�(xAj)$), w %�r_1/r_2<%r_1\gg���n 4 {ii.��v a~ 4 x-�,8}{r_1}x^2+(5�3:� 1 +)) x^3 >�4),� +2m�A�)2 y �{ii�4J� >� r_1^2}x^36h !x^4� ^3})�yn *� ii*� mB?�N6�6La5-A�%��� �4YN�9R ��3�2^3}+ {U� O} L#�2^4}).5S��=}�� � &("e� &��� "� For"� al s city � �k$m=O(=1$. Replacz $(k_1��es�{1}|$ (� E0})� ͎eXL &&\hspace{-1.3cm}|��0 |� q* 4��\ikm a< ")�4� R�2�� � PM=�=2� m!2��Selk! )�2 1�� \rk 'V6& � l"�� �-v1^�mbox{P 2mm}� $ dr_1dr_2 Sk �4eB�uF1� }!v ���)�Z--�^�' +j'1)# T}>e \rkk e� In \cite[i 84.2 (1) ]{hisp3�dis show�a�rŀsecond 2�opl}e� ll1}w)FinF2!oIvN�v� � C � \La� �  � 0after, $C$ de��,s a non-zero"��@may be differentGline to|decompos��$l reg����I}�\{"U | �� r Ab�X$into three Js:!Hn s I}��NY7A�a*al I}|u \l -1} <! 1}��< \e gII_1}���h\ig Ri .\%� `:e2Ne2�^e Ua*�\}EnM$'geq 3$A�a fixedF�. Y $1/�gr)Z2/rAHE�i},� $$�Yft|�[��Z� !l�Ci*�d, , \ U`\inE-%�,*��� 1Aw �Ca9:+r_2+1fl����Ŋ �r_2^241��� �[ r_1(1�3)} !K}))5]a :^3�A,)4\95Ev�(II_2\cup I.!�ha�{ll� ��{9a} �� ���M2T�_1^!/m�_1)Z)3!+%� q C[!_\La]^2,���8] �����>�1 �= �^{ �]�2 d �2^2Q5)^2}) �5��]�� ��3:I_2��V1 A11 �=��c��+�,��,"a8,3*� l!N. �� simi�wayP!tnof�0ev"O[ee~It��immedi�to*#0< {3�"bounded � abovo!!�m ��� �\- \lk6 2� �% 2|^�+r*� ^�% W`"� �RS2"� � g J{3&�&3}(1-b|� � b#:�.��Q�& 1� �>97\}&� "� � a� )u 1}{8"� �ff %�2� 1}!y% �6� 4�� �7�.% 1N~A2})�k)�-8�$�� 1� #&�-F%>0$� ul�(d�$ pe8� 2� i�p!3i�!n� seenI5mmmannerap B 4)" e�a( {ll4~� �gr_2) |�r�-� |,%�C�gb�5�e�-/-�YRL'}W N"����MU� ���|� 4��o �o �T�)��5Z� %���.�a y�@���Z ͫ.�-6�A�&� ll5��e*���d�V�K."]Let us &w�)4z( =e4 ce_{42� !�� 1}*�16Akm iV2j��af���4F�& Z2}= - I1JEmd�� -ي2ي2�� $+\AB{\skk}�:k&c-�,2�3�NA.!"��#inequal� $$P!Ui�j� ��Xk ' 6P:�-���=-A)\ ](4&�"�%6��\KK6�)�}  H�we usp(�=|5~)4�^!�A:I� �z.DEt ��&L ���=.'.�.W-"3ea$�/1�}!e'1}�V>V4�2��!P^4�� ����U!�%��6 � 0 `l6�\+�,$$"ca�{dd�� ��2}}"� ^��.�* More8%Y*�6�o 2}��%Zrm1�>�2��nt��� v�� C6n�1+%e5Ir C\La^2K #&ll6},�W!q�Wdd2 )�ll7~E}}��q T2�& T$1��>:%�ll8} 4) �-�k-#\rk^2��q-=� �E��2}/�:'{r^E�4(�!!�C& toge�'%�\8}m�`2��� C� 6�-� K �K  2=y2!1^5}- E�eJ�9pa�4 .��%��2 ��C �C^!y \L�a�{1"�+�K �%a=��)&� q(E�-\La),!��2�)! 9} M�AA�4M&I��+l"*R] 7}ll9�j�(�  \s�( on{Conclu��Discus�� �*��G )$af!%C7/m)3(/m=*[ Z a_n//m) eB }$Q3s like &�2{� -sseems� �b�normaliz�6y� conv�6c!�  scheme+�fv/ o�({2tradir2al powe&untyt2 mean&�+is quant�4�1,$ at most. HT3#3e pres5case,_&�s�'{4symmetr�'( momenta $kW&$,�trary!�L�@covariant perturb)�y]4�%Rto!N(a reason whJK:�,3doe)�,hold. As waU8EpH8.{arai1} �.�*model�@4rb4 Maxwell-Dirac2+F�"H�aDM}�0D\alpha_{\mu}(p-eA) @+\beta m +V +\hf"� =DM}�NK" $V,suitable sca�potAual(8$( ~1, 2 3,�)�4($4\times 4$=�ma!�$es satisfyA�Ae-commu�( re5�(!�Ha2=,8self-adjoint if�cutoffId"�'d.�)getA!�ulimitCle�5�0>0$A0ApspeedAqlt5,�definen�^{( K)}� o2-,9�(-�)�+ >�%N!�-!�_{0Tppa} + J�L�n�.R%�9-a3ensure%gr, stS energyA�6excep  nega�; #ie�6E�'s sea!J6ron!�") Up1�depend!� on $ �,�# $A)R$ � $! }$ s=�$ =k$ turt7u�i " �:|F3 \|�pro��MƩ�,kABpi�_mit�� oughdyet1 !�$<.���T have a 6�a��e��um� �Z�,{4)%�s3pec�0AG9`e+r�z�'d<�XFeynman diagrams appearA�� v�50b$of QED#I\8no fermion-loop>O!ese argu�4�:ll leadto ask� umb�1quons: ��descripT $tem{(1)} I)+so-cal,?�k�7 methoM?����7ly��,a�.� ;of%0=�?I �2)} R=ci{off.���dw S2n��ite �[. D��!��=� �5 0��itoN$cur�42��YF�? \ �3)R')��% DM}).PAH?� d6� :(Acknowledge%�$.} {\foot�"izeA4thank H. Spohne( E. Seiler�4helpful= G K. R. I. <4s Grant-in-AidH(S�2\ce Research (C) 15540222� MEXTn F.�M 191 ,N. A par��!b*/=�  =,while K.R.I.staN��0Max-Planck-In� TPhysik (2004, August).?%;sw;f.95m�$(kind hospit ��B0to him. } >��x \new� em{thmA}{i=A}2lemA}[#]{}%:!r!{Remark�3 "< {Sketch qC:�> �c(�7�V r �u�2$�-`E}=(\Phi_{(\ell)},H_{(m)} n)�1KreC ���; $\sigma B���Xermn( $a^{\#}(k,`e % B>%[ R$\cdot (i k� e7)]$, I�us pull-thrťformula:6W+ *} aE (�; }\pf� � \-�9&=& "}�<+kn&$</Sp �<H +k))&�b*�0�Lcanoni6&R� :�[a�%X�(), a^\ast �ell- )] =\delt 3-�_{ '1J2}a�%�conkA�4no!� BB��QT�x} �(5 BEtwFI6Bns�@�u� $'s,:,'s)�0 �wo4four $\pf$'s. ��,A0_& �iE�$i5 U wo�q�#L �E\�5i�s vectorE� phot2 � n us! �G� 1})--  pol2!���;f/4fa T$P!��" &#C..��$e�=�i1�@,� �� "� m�eV oqWLH A{�Az��:%^&�]��!�1%d1)k2!c} 6�+,r 1})]au(eA�,20=��2}6,�k��2�2as�1� =2+"! +i\E�%? (s)�,��n�e�! 1}) ��=- ')�,"Z�B�a�s, A�� ribu� M$$-1 � �."�l+E}^{p}2��~^{q r[89�,m/9o$]���1)}=HD�*$Z $p+q+r\�b*Q&� C�4T3. �@q'ə$r'$ b�b 2s�mL�a5e �>e�7x,-(q'+r')/2=3 Mq'=0,2:6we< �t���s�led* .��>W"l���u� }�3 {ll}&�4� ^{6}��p"��Bat) 3# A��} 7J�_$aln�}dh$eN�oiIWa�ynomial�'���deg�-$%n$E|ѐ�}. Chang���bles $(ku;k_2dn-  �x.�;o��A@1>�� s� F�<�-���H��o * ;,�;�(;E* "I9�.�;� `$!L1}=4\pi��^dr!� E #2}=�;#�8�[s��;$:&� !.�{�g=W8%&#<$, :��9�OK�<,p�/�0^!U�( (R}7� )��aN�.0 :�6 =\0Z���> �!E}�v�\\=2JJ� �>�;��^���6=N� �VX<)�>��Q rWB1�we re���R}=��>$1 n�6eֹ�"�1]��6 � �($. \\[2ex]-'a�AM2& &>�1}H3� � M$5J?R�s o!L 2��[ -.��q> �. ~�-E)n .�=+2 R�12m$ight]%:&-�[3�V� � [ NZ� N�-4y -g }2!q�} ��V.+�$@!+IK ^ oJ8R�J�3M�.6I\ c&ue-�*� 6��f2Tez �c8�1�} QU %E(f�F6�1[*�,J2MxR^�=� ��3NI[5� #R�EP-�a+v-!�%�u�.�ef�#9 -}}-I-1Q e" �A4�>�2m.� Q .A6�2,3Z�6��I �D3Y�%� [2�A 7�>)-6y�-QT)��/m j? �"�@U�ɭ"$E �R�D�q͕yɑ6� >�@s� (B*$ �@aGC$:JZ w��VV)Db�:� �nJ[B2}{?B1V6-A"+1}�nv�-2�� \,QU �R��N��( b���xc Nb-p+��f!F$2N1JIbw1f.Zz�a�2�V� w . t����{4qH3}�+{2.^3�+QqO r$)-2^A&)MQ !�}�EgnDIZ4���pn=�&>E�. 5C?A�tf<�(\rx�u�cA�2}}~I�1�� ��)6��%G.p *%�\\Bi m֛�jL>N-J�)ZB�F� �1zH-+%\�)^�J�B� B�9z^3��=�=��10 �2�}bJ'%��3��IM�(n-1):�D*}&x4�-6G-�x}{1+(2�<� })x+6�<{1s�=2x -(4 ;�)&+OsG�):�G. �+��4K}>0$ (resp. $.�<0$) � odd"even)q��O&>_�%en*:1A $[1,�*/m]� /m]$ iAe*=&6-l'a&M( $srK.}"%U{�"L�0B>_Z�g:!! 6Nq �0�2&C{)fundayal } � # read�7(an exercise�A �int _{)�*-3 /m]*�JQ�-&� ���:�M`"7 V�."Z�!�sjJ0�y 16� �1� �� (U%;�=s :g]ɚA��U!��]�9��$\X�#M 9��)�"h5scrib�S, 3.5llTfUI i.e.(URRR 6 3 .+ nd $  1 6$iL�9ly Jw^>�! ͉`thebibliography}{99} \bibo"�* A.Arai,�8n-J)visVS�(�a�'-�* �%a�i}) 3,um el�&$odynamics,�"$Rev. Math.a!.~bf 15}j!43), 245-270. �,caha} I. Cat�$)Z6 arXiv:�Q(-ph0310043,��$be publish�_J2`=��(�'to, C"�#�J{+ rans��� on Fock SN)* 6!)�(,i2$Publ. RIMS�0 14} e&8��503-55!�u#,li} E. Lieb!� Quan�%mechan�%�st**)mat���T BT2, /040!.:4.lilo2 ��e�M�Lo�\ A�-!b.��,a��\N�Eh�m �ф�mJ. Stat:08i2!C, 1057--1069 =�n2d!HNelsoA� Inte}fionA�>��P�+tx\ �%4.ar �3,q it����. }��e ,1964), 1190�97.!09�rs4} !MR 1!,Ba�im �etM,%'ModernoeA�]�}cs IV�8,Academic Pre%� 1975�;vsp5} 6Ef.^!�4on: AZ �}al"�  a+ka�f� nn��. �175I�87%�278--318*.�sp6>�D �(Charged Par��s%0�ir Ra�F!�F�5sa�4mbridge Univ.) (C��*���>�  }doc.}�*J L�\W�r[11pt]{ �`} \usepackage[british]{bK_}2T1]{fon��2{�6�" ptmx6amssymbB.Bthm6exa� \S#� �Yu�-}{U8}#makeatle�� \renew) and{\@end m}{!{$trivlist} 8�lG�setlength{\parskip}{1ex plus0.5ex min 2exx6j mult��$gap}{0.1em% x�6No{�.io#*l, Def}in�7}[ �]� � C plai:> The}[Def] m6�,Pro Pro�3B�Cor #C�_6DLem !�"AN2�� rk24*�,-! \Declare� A 7betQVib}{Ttm}{b}{i!�b.@scr}{U}{rsfs}{m}{I0O {\rank}{2�",linhull}{spa!XRG[le}{Tr \,^Iid}{id�.�8set}[1]{\{ #1 \�o.L2 bigl % bigr*s.U�abs *lvertNr !�.S� )V) )�Pb)|.�R3g24gl65gr66�p6e`_pB�uclR�_1>+bra *angle%)2b( �-big 162k1�NWr5>A(I,)> 16Yscp}[2]�N2� #2 Zd3^�etc#tcB!ie i.\,e"6f Cbb}�^ bb{C>bK.K>N.N>R.R}>�Afrak { {A>AE."E>"F>"FBgH��[scr{H>CK6 B�O6 OBaBH �_B} ( m ".u BHon!���N1_1J3twojd_236�AO 1!!{A2�O�1u� �qt��environ�{� '=7 )}% � u`@6R ��1topse��ex22N:2e 4N;l(margin}{0emF= 7ntq5em {V!.+�}> the�!F�:=�*+)U.?c>Aroman �rab�aR4 J�(\  "%�N�]R�R?�LmLex6t��2R�ef�y�2�;Jy.p!$J�rH=ZQ page2 ��/� ( ce�0{\huge $p$-Nu�@#G,in a New Pero1$ive}\\[1cmB(� ,rge Christop�|,J. Fewster\\5D�mtVU�Ks,(ersjof York 4HesBt�$, YO10 5DD5�3Kingdom 1�zXl: cjf3@york.ac.uk\\[5m�0 Izumi Ojima 4Re�=N=itute 1�al+>s, Kyoto� E 4606-8502, Japa�x�! �ot @kurims.kG-u�jp.�M� n PorrmanCII.� f\"ur�oretiI�ik%)J \"at�@ burg �Luruper�us�L$149, 22761* , Gew� �m�.p �@desy.d� A�Q=Ubabs tAPI�Cis pa{ we t�H sett<p conf~Qp�Fscer�th.�<oWAno�A�eaQ�:Z IXa�p?cal li�ture, kA.EhaCe 2PdexA� � Gists')D van�sE- any $p > �f^vdII �s�$issues suga�s�Bew�p�ve,r-<�C$epsilon$-e�ppy �6"�gs,1@ch mightOmit!FnUons�,drawn betwp< phas�Eace cr!i�y�"&TiesMd=�!��{I�d-�_�8LAraki--Haag--Kastler�5EDm� algebraicx�!yory�Y({haag:1996}�7k��CV8or�.2? WO! AO$ mbserv�6assocK]dF openN\- #\�h %k�, 2�u�regar]Hthnet_FucAl encoOAby�!ap W+psto �'6E��xof 5l 1�=!��:F framework!e ceedg:a s�u +Uaxiom �JngA%$Poincar\'e"Ece� causB. HMt�E G�M$mselves doa� guarante�3 ason!| iKal a�iour,0a�Ee8oQm�al �rlibrium�t�6r-�le-�N excimKs. C\se!perA� , it.-Ia��must i�fad"RNres�K�ysl�hepactnessHI �,%�-5Y��Ie�ir worthG�9ou��texts�� y �G�X�Buchholzk Wich��m�b /w :1986} �Napp{qaJw�{ofaRY �1� \eg\�)_junglas^9} �to mode�)�>4dan�y�XK&>1e�et!,ly damped loa�}�I��-cuum, !iA$iM�]��%J!1pa��tr-�] in��&m��M$JN�?.�r�+rUH-kn�� de�je�)�%( be `bxi�Ely re !':�Lpre�(lyA�>Vk%��c ome a!A��&i7ai�.Y|I�!�ained !��he& $coe�0�HU%toU$ . A numer!��Cx�' nu$,!��Qo�6F� �A��*pto+&��� $\nu�RV �FAt�Q\to 0^+$�L^�b�bn( �a" &INA�! m�� purp�l�%p] �.o� at@%�v�' ser�� short;�ne�y� x, nam!�!n&$L6g +�� deedbQ williUQIS�= "" i�caa* for * ! " st_ g� ! r)*B �hI�sti�P�P>:J�P we�mapaYE�t�V$l^p$���'idered"yK {See*. 2��E5i%W1zE8}��,�E)result�F[8.4.2~*U]{pie�&:1972},� n��b"� s$0 < p�.qslant\ In �Eav�, s a 6`�a� $I� �� �.6��K5 (uS���xnormed=F��)���  sequ�%f�F$�4{\varphi_k : k4B C�/� �t!M!`�i��2ar* "eYs�H:Q  �t��^**�� �sub�C!�s�  2 -8( x ) =�$m_{k = 1}^�, � #���({,} \quad x ���� +and-�0:k!~G k}^p d 1Y}^p <hfty U.��� =6� 0o6* �'1@ �{)} \doteq �infA�ft(V�A>� .�I�)^{21��:ex!F�m�6�e��#J si-!��"Ex�� �i@�Q����ormVada�infimS%v�+lnYssi�O2�so mx$. No�b�� �0�F said��}�if $\| $\|�0is�'Œ,� .%p�[�$ 6<v JG�>��&�0��ed �{ ;p� X i/rval. S $p!� u 1$%%mk%����YbV�F `��an2ّ Ypre� �N� ic QFT. Mw`, its has ledbEdeep ins���alo1y&��*�Zla�(uthors� ( often adopM!� �� s� #�* AV$p$, llr� ���e�it{{p}*�}��� occurr�)b!��[�0~2]&� y{ , fur examp�F͏ usagSf%{i YN�'M5,bw @6,mohrdieck:2002,� ./hb�nds4}. But�Uous�[em� � T "�8Tev���s6#+i�p�s'X!ea�c�>qAS! efor_ valid,p-T!�problemsL F>A�w=+e� 3out)� expl�.�1\{ i�"� "� , D'A# e� L( fz.H  (who,&��didUA not}A�E_�cAs]Sa,.W�+ext) cl0,���I ��b��G&�OE�:pU-� L:[Ű: beR �1"� DŽ��*x�Y �s��it�*� esF�thib{p}�},)�'pi r�Wist �wwZf%N�y��%86{�"%�6�"-��� -�eq-�-1)[x› Ic��J�e6!�ι ���=6����re�yc$ a omb�M% 26 anAp "� *�^�,r 1\eqref2z=B 2} a)R~�-�2,�a+}.� �.O ��F uf9aP�ygUTu� U:i�YT�x�'N� �df_{] tack{)��}\\ 2�s}"M�3�( J$ � r* � U5�J. � � �] trueɾV0 ��l arbi�b���as�d�d��e next s��r�ing P'� g�-�d�8�rt�;caveat�}u+r born?x, d. F&� reAa�A>$p�Nk p&< �m 2F&7/ 9}}��givF mu(to (�W��e�!ae�`iJE�, )6".^a�se(=�Se�~�>�E��B�} �easil�l�%� =y]if)�1$. Fs �_,��eya2�3 4 a Schauder ba�then ��yg�b�orf�!�.�=v Eg1$ (w+2necessar�t�8!�% ). T�] bes j"�\N^ p_�W��uD�l .�objecC�Y/�torif�eIi�� �toJicate�QE �dy�!0�  j�:ionv&� 9n�b�^��A��farch. �<&=Vinspi�9� wish�n� B]��to�;a�5 ��it{�e � �liw} (QEIs!�:r�ateE�pe�% l�g�xnwe� � ver� A�aIsti3M;tensor�ich+a%�es �ed%va  f�R:H�two-dimer�ϚonO al.-y (see� {f� :" Mi�� s�rein). ! �La manif�!��u(ty principl JA� in3�ly �#.�F�b��eveson/�verch� 5LtrK27al.x ��conl). q&� nsalE/nquir�He % is aV-jO"�)0nd.�J�cme progA7 �iA�one�Emad����gA�a�Y!�ret`ss"e� be repor!�0in full elsewG%t&�e5�A#!��� �<0�6��&}a9�val'<todwth!9�s �:�ɘ?&Փ!u.Vtoj��z cor��^a���i.�hlto A݅&-qu �cen��A��y�mj >%V�[Upper �L!6� urvi��by�2�  ente=YW�@k�\orm!�Zx .] A�!� st��,��# �9�n"D exact}�A�A¡� $22�%l�a ��ac}�!Hilbert�s,�a|dJ��n{"2i�6�h� ro)%�\.qq�!�� .@" c� ��k� .{B�"�" #�ntxhe�� H"Qs�"syt� up$��:?E�Jw; bk?k"�X"jBsQ!8�akash_0}e�is hop��re�!�i�' .Q#D��E}��M*�Typ ".l}^{\th�� ace\� iD��A&� � �?�9/ + sec:l-$�#Wa���} a��&� !�V@ .�y [�  {�[8.1.1:}a(ʌ$an "�  �t�U*zV�w1���AiR� k}$'�<�;7aGS } $\Z+ a_k �N�(`$&_5 wcj*< K!� 1�eq: h- adb� ���� - *_k} :E-_�9-ofq� $k$} �@.} fb�!��se�!r>.��Cway(�e� ce dA�s��n� ^|��B�6F2Vm Def:% -l-p�A�R&�a!�>Tq9�n%�u�lb�} (11>S6CUIAim�$q ($i�19.8]{j? ow,#1}P?MeM �pm?�a*�a|rA5l)tA�msC���_1� ultA�z��!�y�0&�uwM� )v!u�QF&�&I�� � l �!�v�rhoI-�ho_E��y�l:N�%�"��n1epN��nowW(iS#L!{!����т�&��u!ll�0$, re-wK?ng � �3; a��%t�  siarA&'�3�=!r�ProEnuc��u ea+�.��\in l^%�B3�!?"�iua=z�A� �5�r�lambd��?! 6�p��� �W�dC �Q%A| �B��  V� %za$llofmRs�c5#�lh.� se�%v�-�-�%��Qfy1�^pVie�� 2^{2"�� 3}{p�F���f�E� �e%fC�iH2@"�G_n�c�& $2^n -2�'��AB�n�Z1]2C{ F6:c +�(No&� _1 = 0$.)P!�'Psi_n"w $ {n + 1} -!� n�a6Z �2Rn+رg <6�*!"Gy.�b�-:)� � �.H4b��%�,�2��F+�Xq�A�2�U�is mon k��de�Ling, sof�%2( ��)�) A�9�^�� 2} 4�{>��Z=I�p + n +�d.E�2U) Fv% ^!��%Vp(t� D  $ Cau\-chy'I0A�� rick�7�h!DZ.�WV"&%-A��B��9QNI r)>n -A�+%1d C)Jr6?�=B�6,F= B\!�E�Z��~fL�Teq:sum-�� �J3�z��AMr�JO��G�.�2U>i~ A.�/� �(1,�h}"2�( $iV��aa4 a�*,3A�Y#J?e�}UH!sn-th-sE n� e�:EiI�{>~��Qi^{( n@�( Ms&I6R�' GEVZ���6�Y5�2�M��� 2�$6� .&J)2'f�%��&V�T�,O [5ly*K%F M�5�)S!�>5J� n�i)O Y�"_p~`�� FI!)6[2C2vF! G%�swJ3B%/E��#"6�>2�D-reF l�����}+t]� _mM�=!�m �N1.�m�6t n =@�� 6n��G�G!F�)n` HiZ&\ �6�*��g�J*g-,C��F�'�7h *[we'��hoh/fxV iona�Yndu��W not y�� �"H � �N}�=)�M x��bsorb2!coeff��� ) �iH[�/or���m+|o'� s ���%�pW��S� s ra�'16����ble%f6� v("C# �Hm'*ܱ��&�Co�"�xLa��Cor%Every5A����a# ) n� Du�~\$�em;$'�2`�0QY� De�(!plANrf$hip)>�����+*"7��a')� Def.r�is!� )ati��Z"way$85"A#i�flict �!�R]<ians'A�} �i��|$1��2���$�8�3 lete�7a|��heFvz]$J�'s book�6� �+.f�� " P�8e�%��al�*���6"�!g=_eyyf� &�; (� sumpaqj+g6w�fe0^a[��i2asVd"O �:;I�$ R�-.� de�I�C-yDefsub�4}�$1�4":!rek)Z QF+=�narra�3 n9�j-"%+.* ��&�2��3�)�� �3Vq"+Zq abs{�O{\�}{UT}�i^*} <xe� Ui :i� ^* #�Mt6$H!d$pnE7conjugx%>��0\iec-Y&�3 �3 p}{p%&�u $p^{� + {� =/' �:��;9_���:w�en��&�*=�&� B�\}�\n6i� ���*D� ��f^56t:� B�4�� \sup2o+E=A?M \\ a#�1�2�?}��6J�^*g �Z�.�E�>�\F?1���?pEZ ($1^*" e'$)�G��,A�$ %.mar /�o ��o:m-,be.g6ep�8��#; �.kʹ%'"�6(�� $1Ja#e�1*�$ҧ �^�.a���f|. �� i N�.�Q�@}�2�J}� F inf>m$ee1}c�92� ^ �F � o �}Q�^ }:�s~6d6���u9�m��A��<� # 4��6�2ue?)�^D .I V� o��6� ��5^QBn�V 8��[b�-�u aT-> Z�5�b�EN��!E��� *$ &BA-%�m�&.i.�> a "QN�Z edP"�valpK>) B�*,�_� Qr�b���!�%Rnsrz"|G< �!Y2���� �* uni�'�edg[� (c5cit&w;16.5]:K[!�� `� G�d� } ߨ.!�G<�c? co�.de"X����!.,!EKL� �e�� H��E*�VU8.[EV]w.qD IK� s��K:�M6F"� �Q�\� �& v BM�J: 7�=^4"b.� ofE;��6'F�!65�;)mpl��* "�=A-]1%YuBy24$� . A#npl�� �2�� k^\prime���D&� ~%./z=� /$-��an�,*e f#0t�O unitC1v�sf!?M42��� � �E5[ .� -%- "�B=I G23RI;"U � �;F.5Q/�Z5KSB�<�]>��y cl�"}$^}�b�Nn�F=Z  ?& 6��n5�6�1�!�1�� . (W5ecC�250� a&i#�!�*�Js s�4 �g��Q1 a�C$ɠv� =�1"�,@.+}� h.� /b�nu:� "�U�Y�z"�#:�MW$F� ��(�o)�d�-ainΝAvQ_� QF|�� Now,�7��G�z� H������̑�=���E�V���M/aHV.!2�enzRN�6G%;}F!=h �E%jP�NL��"� � A�� Ei"�J�� M='!VsH*N�B")Ja8�9R-�2� ��,0+:_&9Fw���m4�36�iB~xB�z I-�M7�� BRX a���9��6 ~:djqed}{�Ae�2� CA�)��� z arri^�tA�AEi;��y;&� q/��6B=6�:B� �s� i�:� o=z��� ei� �"D�=e�Jx� %S} G�A�v)��ep�75��9� � �W��.d8fact as���� �8s�KR��OCS51y q�P > 1$, du"�U&��9ing. Si�8no�H .c!^HV�G"e  � � �A0�r>�-.t�y�.���! �!r��e y?�a�e���by $m$�l�E� ing '!�>du!� !�$mBG m^ i0pK &�A6; )z ìAZ� e�r.���18}^�KB�@Asw�;la6W�5� �Zc �!�m = p"P ɓ��X-$E�!s wayB %|!�>� �%oi�V�TA�or $m ɢ~ �( � )}� �1� �8 K��M&����� FI"}��� "��#[sM 30 /$q-I�^$ ^$.�7 laI`3>�$m�t6#��7ily0@.��]�b]n&3h>$B� �q�Ver�.a:�!� !�bU6AF/�@$A�yA'�$!J geom�V\?sn{�V&�1� j�*�A1�ly �!d�zΙ�3a�FAS��  #��R.$ �~.~�)�Ws; t-h�$8 �%7aKt~.~�*�ZX�p4%��B�����e GUfi� split��!Fc= vidu���b�E� 2� 5@no  ��8al�O�X&proced!�84�8N&�Z���4C\�Fu\�>�_e-imaAX)��1!]oB�L �Q,7-.�BB*8Z)�:�E(in,=rad2Vvv a�ael�E), w���el K�$E>m!$x Nl V _k x�' ��E5�7�� �et{x_k}:�� ˯e $&A&wJunique`�>1(U�Z��`#$?%s�F:1927I�b�<�L "�*��'�^��B��&%�2�1K�5:�$�B itI 1?�Vs ;B$ >�'��)�1B��!՞N .�;R�L-O%g��2�2n@46 E�A b#Ij�:3\)�xR"( l6$z",]!(Ax>p=$.�JR�H%D���2��U�R"L�5� ֚*,](&�%).�2T+ѕvi�02e �mD�&�.YW�le�����x 3.1��$Wo>�3=�4ea7�@By8�YT �ٷ$�w�en巁�&L 6o7!� )%�m�t aqu��2m�fu.sJ"%� ez. _k�X��6Q�"�@%� DE� S2�W���>LCde�kin.���� ��__lid-}"m\V^ �"�cdeMF�+;.��*�Cso�]dilŞ.O��lG�a*H grap~ece�  .�.�+�1�}; �W:gp�]d��be gre�V�an�Ap�exh:�.�}7+�Hc a�m�� ɡ���~es�I!� m_k^{1-f p\, <* 1}{k^f7&�B-R� � aE$ka?�H!]9�18e> ��-� copi� ��&6Q�%Km �  ~����w�M�U�;hut~>� eeF+ 9ied�A�ZP �5�-��rep-ex��BW! m_k � >7j�\=�6NKV �8@.$N�fo�E8��\piW�6&�!r�R�� �*BA�avr~^or 2I.��nd"�+perceMaGE���*o ��a� �Wi�/� io� Bc.�H0�s�Kim�T ory sB;/�.�eq��I��g�D�G$Y` t� s�V�_�Za��J��*�R il��ent*�[! dѭ��}gidPP,!+w1w�2. S� 9e�}!c� &am�j$��ea��b���)%�T"o !�"a��h(4c�wably m�� � : �( $\xi_{r,s}�rs�$Nb�*d4N@��- `��" j�aim-��TE�we�)m�J�Q:&�M!��onl, �1��*� .q�2� redu�a�!$ctly less ��Y(iY/� � xi$'IQBy�e�AC, � the �2 � 0|~.�bbJ3`JDS�3to�� To ds is, -��H"M $�~1}Z�< \�  <�8b?p�J)��3�R�\� . We^assWk�Kout lo � gene�Ot!�i�6��^�O�Mf:1��!�����jAHp4y.��qH��E�1,j"�"�@kv�6{6\2�)% 'a}$.�Wr��a� e $j2�Az= E!'�4&�� j� 7: Phi_�+�.Z-���y݅7 ewb|N� m�u�.��b� $2>c):<k/C�I��a�;c�I�� o�M��A@a[x�bAs�p}s�M�u�*�l b&�;�s w�NE"�VV[2�%d�% E�be"qO,Scc�P�4Llsѭ q 1k6�6�ݙ�jA/8} �� �sejlndk.� x�B�E+ a�9��:. R!�e�P�z \Z!� �Q��)��&�Y, cf.n �&b2an"b/jacob�O87�ab6~b,Vb , hi�atiqV�ly dif�] t so/ �"r�W�RdwH�Q��c��r�}�"� �#8of.N"�,9�=l�8� (f2 fal_Tack���E rtho��abU a.U� attemp�o8V�uAH� icul�W.� is�da���L �6Tap��>Ln F�s(��;2- LI2^=:� : \�_16�n��$  2$:�Em%��itrau��Bo] ^*;b.SL5w1!"o�two:v�>l6� � A�+ar�oU2$G�qB O���GH!��5D���.�)�2�!��-':��A�f�s �\ �5O���|B���>F%�%�-�l�%eG�V"(B@is&b�$-�:�\eq:_ {��%]}_2}^2 "��244:�Rs2�DAyFO-�^J<��"K3$N alig* �GV��7 ]]% 0)  &r>%#~0 Gx} 8&*"8wy �8 d4�RQ�� �v ^2 &�80 M&�9�!�ex�=�W$�$-� �(��(la�"Wy� �RI�+fR�o"M /�N hoseJ�. BsVx"�>t$ ,�E�iR�ԩ���J2�:�O� *�B�� T ~&En}a�t�� an i"��pR%��"a��*Qqur:�u� lookŤYKiU@Rh�i�to&�!~��-lest!qe "� *�Yily��-S.!c!�&�_�`n�0: l:%_ARF�Ade�:*�[�YG :�_�X�w!�x`) Schu�w L s 6kv&und)c�C%$( } )"E�(2�4the mathematic�ians' definition) to the physical question of statistpindependence in quantum fieldC|ory, and it would be of interestj reproduce18se results with@ modified conceptA�nuclearity we envisage. However, one sh s awar`at even�L\cite{schumann:1996}o no!sf $p$-j�,approximabil�\�not always carefully distinguished. We also, �(Theorem 2.7pR�dis trivial for $p > 2$, as�%t�estimat!(an!h�made arbitrarily small by a variantuthe dilu�, argument gi!(4above. \sec"�{\mathversion{bold}$\epsilon$-Entropy and Operator-PartEY plUnity} To proceed further!� �r o towards�Tablishing a close rela�,ship between@9�A5d~�%.Tum energy inequalitiesI4require)\�following: \begin{romanlist} \item \label{list:.h} a satisfactory understand�� )i{.F�.WThe�R��� growth or�� , $DU)�u$d ,( i ed,�p��vely, bb� O��Jet{19� \se�z 0}{\A'�0{\lim}}\frac{� S�9v =)}(1/V)};�&{ \} �B�C.tM�]imn�)!n F�-�, B�$which mean� at $>�!�i�zymptot���Pwrom �%��wF� $e^{5�log( 9) )}$End'-&& >':Y� aligM�& e^.8.7%] )}F�9`${\lesssim}V�)�=:�2�� ;\\  & Q�B��t<�-�H�.�J�5ya�m presen��inJma�P��R� �!�i�vzf�= Bu�]� +)}=mn��\inftyn BnAIM�$lambda_{n}A|nonumber=�=W\��p > 0�Tsum_{n�W� J$^{p}=\trac� ( K ) < 1Nm2nK L?( \BH )�- ;}\\�m� &Z�9��RJW)5:w.�Fg K.�F6#m!��1�>jM=.i�n6�IFj-�I _2�B�uDwhere $F�-q \max�� t{ nA#X>p1z}$�$# $ beU 4he $n$'th larg9 eigenvaluAJF "4"w $K.r.� A�(bel{eq:cpt})�K!GE�i}!i k�oxi" } \bra{K R.\B""� } While valid� �u SchatteA+de � on \eqD �looks# b; tric���5 � in >� on{it`s�� carrsAJ throug� ndard ic method�% qu 0blleft change� rings2$1\�far more� ext ;6J� � A&~ � 1 �summaribriefly��. First� Banach�� ,6X$"�re&� LA� doma!{ nd tA�/ G!1E$,�replac� re�r�l� ou� � byc1U� `}\foot� {Afte!��aw wase4let� F�$daleo kind"rewr E�Z !�E�cla| �/f ;:1994}-h seemQ�! f!R� eara4oA U� �$ technique�jic QFT�useA� �commu� ve $�$ -)�re"� �split� pertx !�a |consequei�ir>�0structures. O%� aim �, h�is ra�$different;�seek a�ach�t�goals &*�g}� � "F�;K   n exten�$�t$"� �/QX-�g9e"��P!4ators(!�6C.}E�2 {KiN)�Rv �creteqq!� tood!��e���Q4e�$\.BHone� i�6two� nd� intrinsic��racteri�on!�-��erm�!topology� scrib��%it{!Ta}� )}BHnor� $\ {x}_{cb}�`s�n} �K �sf�}� �cosm�Xeffros/ruan:2000,pisier 3}V� w\� a \cdot x \beta}B & \leqsls.2� �� <))�(�} \for( t, he9\in Mq$( \Cbb ) ,�.I �, & \bg%[�ft(K W�array �[c]{cc}% % x & 0 I 0 & !k�A� )!+m}6( (6 , y}_{m})sE;61x6�,52y!FMQo%F�"� AgR� �x� V��q��8q�$�oano�m��qlyq ifhi���w�jJA� spat"��ore3��\b%�:� %��RM!' \Nbaf, - \otim�w id_{El}}"� -�^�+ 6K \H Ih!�n%�I�= 1�IT)��!�F�� total���Jf1�s)��3%�.�&�yCBk �,-� to adapt!�se���ouro��� ,)� conven to!�� �!�c�� )vJ �ed�'��s�� Def}[Blecwyb �6}]e)A��ht $A$-1%. $Y� a (>)�F�F�/ call�� \bfseriesneib{A}$-�`H {}aa>eOa net��# v� tegers $n!���H��t �-m�a�s $\phi_�z: Y2[C�(aQt�l�$ ( A ) = A2�(�1&I��r� $\ps.l.^� X.�Y$NthaA7�� abicM�t 2�ws$�} ���ivx(\ie,.Bx$�~.~�F$);6�p 2\.��Y}$P ongly o�� A`.Q��ma)�Z �9�e� � �� $&$\linhull (!��A!s= YB�Egamma�ub� o � :�i� � �Q�  $\��($.=�3.�a� �W�W emarkable� u�nis\� ��E3&���^*U�as.�qanalogaU>3M�*9� ~ sense, bu s��at_�y!�geam{�embed� into�Q.�u )�J�st.���� �em��The��Le� Tn����c.a.i. (��� \-aT\-aV� 5!te iden� $), $B$ a $%�aTE{ ���s $A_{+}.$Am�Z$9�B T-g�$B$. Sup�I��!�P dN -sub 5Fof [�!�$W&z et{z,Z� scp{z}{y}A$A�CaM��  Y}$. �� _�� exis/-SF� $\Kbb ( Z���`"�ele�!���k=�a� y_{k�w $A�$Dёg 4}�wa{: w�Wɻ {, }� &� �F�S�" 1-�f> �> .>.I�CE��,#"ur�$D$%Dy9C�Y�F�tq�!�$W�Fa �2(. MoreAk!4tilde{Y} \cong-UbaQ{wI){Z� -[��s^:qs (ٲ�isome ally)\ � �Y� zC$.�24F orph.&P &�C� rs�`%��-"G L�� way}A����x I# �[ai�U�YA�of�2|"� sa�� �"�Zlim�%���� 5-rank"� s� I9ar!5binQ�$mr f}$, $m� fe=�ob�* 4 Y ,�t : fmJ�AR |As} (2' �V� $})^{\ast} A.PPu�u}���A�a&� m�-` \-de��aM dual!� $Y$.%�*�( HaagerupM� �'t $ _{h A.r rq (�&mos6 Q%����en� oM�\ %�Q9=  of�U �s)I� b&.�m�YA _{hA�m�$ holds))^ y#ur�$� ��$��ng� q�Fa ]��d�02�� $R^!�G it{linkin�q�}:{\oplus&� 3 adDq*�EM rner2�V\ ��*�:�K��B���Nl /a� \hookm 6R:�W�ƺ�6TX � �,�)*#>*2>��1F7��Rk *P; 2:U�s�  �Kac.iy Agenuin(� they sh�*(many import�fe.'ea9l(��a8)e�e-dim�al* ionsg$�!�titutcQ&� ingredn(`rig\-ged\-9'ypwaye� BcQV:T$^�a�f�"�%rec���nd!@p'�h� �p��" � y:A�E {2i�x*�y �&� basi%!a variet�'ˁ�it{�%-like�+}�0�Y�calcu�'�&alread�dic.� ���,cusjj(cfAlicki'&@(��non2�dynam��A\,)� ��E"9�e"�+ .�+ m�* perhFb1��Pst�-"E�%o�vacuum%=�{ �s�,� Legendx. ransEinvolv� �, (daty)%r�.��he suit�Z� (e.g.! $$-diverg�!� �vm%? �ya�/nagaoka�1`I6%TD�rig e�type-III�pA�local!ub�Hsa�ear�� �`+6�t\paragraph{\itshape Acknowledg� } I.O.� C.J.F. ex�#%�ir sinch than,�md� f II�,�l f\"{u}r$(oretische P�0 k at�.�.8t\"{a}t Hamburga�Wir- hospit)du� vis�'�/ in Summer�(Autumn 2004>l&!�in�ax#�In�'s Ge�D�Oxford: ]� Prf. 2001.�Seei�a 1��!�en�#aM�by �x4authors: Ojima�`�Tem%1Vas�,�%ame^"4of broken scalAB�!, Publ.e�� bf{4�/$731--756 (�).=N2� �0, D.~P.: A Geh z)1*� M�q0.�Funct1� !�036}, 365--421%�6.�bm~ q�� : Phase S� a��� of L� Observ��Q d St5"� ScalaqL�.�AnnɣP. Henri Poincar\'e - Şqu�\'eor �64}!�433--459f�/dantonP156�, D'A, Cr� Charged F�7  a�o�N.�Revqn�yh$7}, 527--5mf5N��/longz$0n�, L(, R.: NA8 M � E3ar9��{II}:�� � � Q�8� �y.�CommunV�4129}, 115--138%�2BQo/jacob!�87>�J, aO� �F(C�!�� Mass. �2~ LettZ���313--323�87R�,junglas:1989B� 2�Exist� �W , E.~��Causal I.�;a � E"9-Level D� �f>�6��0�~2 44%�2~�� /hollands� 4} .�, H �eu�itya�ca�si�9valE~�S( ��ye.Dirac6��� Curved��",�h4.�[arXiv:;8-ph/0106028 v3]��>�} Er%!�,, Ruan, Z.-J"� zs}.r� 0.}� 4/fewster/verch!O5}  !?~P., F #��~J., V+�7��I*9;]��"e�+ic2kE�:�{e3ex�AA02��:>�6�I�>�a�,wo-Di\-men\-� \-al�;� l�.J�>�412028.�6+F+, F.:"o )��jE�# I�U�. �AJ.B9>p$ bf{3��0�1�UJ &�" 6�� cles.r� 08�qű62jqow�h 1} J .C %-lyA�vexI`6-TStuttgart: B.~G.~Teubn*A 1981= mohrdieck� 2} M�6� &� �Qh|Di�>ce2� �V�iB� ~ !�& 4�5� 3574FIpie\:1972} P , !�IO! �r*�O72=?.2+ P?+, G��I�duKAK 6�m�2�$Cambridge: V� 3�Sude�&27a} SchA�: {Zu�Pie stetiger Abbildung!C Funk� alr\"aB2�)�Z9�2��47--65��223 6��i�5Ide�.AN� � ��2�bp . f� 3_ 249--27J� �?%:70} Singa&I5�Bas�Banchml I2�D�s@>Mdoc!�Dt} �%1234567890�  \V,class[12pt]{�1P} \usepackage[dvips]{��� %4{pstcol,pst-3dFricks}% plot2[ {ams7 ,amssymb, 4rsfs} %\renew�1E base"8stretch}{1.4} %^ LAYOUT ^ : �"length{\� D}{1mm} \def\bottomO=a{.9} % %�k -({\dinwidth}>margin1.h/{21.0cm�."P$ Q{14.5".@.6AP % war zuvor 15.2cm,��5 ist IBHhe$ }{23I�se�di�2�addto�$-�2j$0.52&oddside-5{-1.0!=6o:%^L�G.M:82x qpar-t0.9^W+sep}{8pA�=0push}{5 %2ltop c}{-0.5%= head1�30}>�1% 6u:6=2 "2� skip} ��Ta� EgproNNN>QQQ>TTT>ZZZ}��2_ erf}mJop{\rm :�epsA7ar�=>sup:D ss\,o% Var�las��A�moothE>act5KU-B?>l(oinfM}{C_0^o=(M):�$N2$NR$d2$P\RR^d\backslash\{ 0\}R8c�: {#1}�=X>=9Nf2�0, �)e�1W�em* �Mronments)5�,{Thm}{ ,}[hL]E#�-[Thm] �N)V"Lem "Le�.2?Prx@ o:ACor ACorQry�Label �$s) �� �M-�i,I \  {=}{ :Y:�the' +.\a /E_ 2?ect%�"�M!�setcougO:{0A�% Calli� &�8s (N.B.� �H�  �: scr)>�DDq�scr D>�EE.E>HH.H>KK.K>FF.F�2 DDco."D}_�E cospBBOO+f O>hAaA>Ff2~cUU>6XxX>Zz�2QFtwidetd(}� Boldface=��. gb<���){g;2#h>#hB#j>#jB#k>#kB#n>#nB#x>#xB#F>#FB#xb%��x_0B&et>J\�:BNv%� sf f>�vg!] sf g5% Misce�eou���jUEsfFPU}{PA66�Ghat}{%�hat{Gc2�W����7W>�A2 {AF�Dal}{\f�phLm{${\scriptstyle *}$F8Ran�rm  \,:��5  B!SpAs B!Tr @Tr 6 Re ReNIm Im�q5�dip}[2]{{\langle #1\mid #2\U#le>Hke�b{\v�##1Z(bra��Y Z>Pstack��M {#1 \\ #2B�ub}*BFu>Lv2v>w2w>B2B>P2P>Q2B X2B�Xi2 \Xi>`X� \Z)�{�=:iY2CYB=kqA�8kB!fed�ZacB�hu�hB@Wʼnrm WFEj2�SLM�SL>�S� rm SB#P7 :�P9 :Coq� � 2�Had ��� av:L��S��6DomABVA�,mega_{2AB(V)>�%�Y&^�z loc}06VRe�vK� 6 VE �  �2���B��6 hs @ H.S.!2>Dif�+rm  :XtSK ,kebox[0pt][l�Bs�"�?1.7e�$E-Io�S@}�H% _+(S^12 2�V� {' :�MoA�vM\"ob> Li� :=iM i��6xto a �B tg͋ ��2�tB2 BKtH2 B� t!`�S>�tT2@P:�SQA:�rhoo}?sh�W�3\,\circ!�ho��6�R3*RF' \l{ � 2 HE�:� ?A�(accent"7017:�G:'R3'�@flush1} ESI&t 1559H" \no\Fnt�zer} { \L�# \bf"�VM two2�/coE .\} \\[k] �]en�ExFriedrich-Hund-Platz 1, D-3707760Ge�#y�n\Q55_e @Wie._ k.uni-goe �.de!!i8!�\today�qB ${}$!�t ll {aOAbs=t. A� � �(g:�0(QEIs)�3i0-a�ps_t �IE�I w� ed averag&�3/ss- a.7F-have b7] estaa]ed a.s�9al fre$2"�_�ls. We {/ent�6or-,QEI �FZ=as�*i�ac!�"�1�"s, namel�?e 3ary, �ve ��X 6"f((gR�)MA>� Minkowskiz ce�-�fen%Pb )T u2�?)ZNV��A!?c )(s)�)th:o�$@�5U2qT(%�%[UJ-K>M+U situ�*s:-�C*a) �$like, n�A�K c�$s" ] �+c]a $< volume{* ad8_,�L�5idH]arX_,#.��*um�N�6 `mo�2mirror'U? Our�E�a39�a)ms obey��Z"�F axioms �2---as� show re s|_O/SI� builtz��/highest-)� reM�)e�"!�Virasoro'9%$�G�1, �9i:#d#" ll ( cY�m�)� �!5rqa�P)[:�. %2di.c5 vssu�:llect�*g�1 (and,/TPs, corZas)QO5���&_4doE�iQ to �57mb�F�6iE�m elsew�H . }�  pa��"t %%PACSDLs: 11.25.Hf, 3.70.+k# Keywords:"�.�5�J.y��2t!} In �W Yif matt�!R�$$T_{\mu\nu@=usu3 ta�.to Iu y ``��iE$s'', encodA�m� �^h assump].j`exampl#?dominp9>V (DEC).�b$at $T^\mu_&} \mu}�v^\nuA a fu�/-�`�c *(��-EK ull)*bA>n� $ G�2 [refAqA!5 ideat2t �-mod uma��e�=ag88at or �<w?sp d of l�]:l�1 weak U��)T (WEC) "�c simp�Ea Fqk�J7cs���d ny o�/pds nonneg�. It�+@b-know�at{H*�21� failA���EOef\ m�UY�?!&�Q�at,!a��n��%�,�.ex#^�(Vu90 F�+��=l6mF�e� �&O8 choi59�pIf �01m�8��c%�in �d b�8sta�_�Fu�cly�W regio�:s$1��Ac�n��sor�;un �edy phenADa �Ah��exotic TO�� viof!t!jse!� law rmoP:s � occur~�5�MorrisThorne,Alcubierre,Ford78}. H"�St has9 �uM'udu���magnitud%�1\�)\�at%��A�ntr%]E# leas�eYT free�zs<` so-Ded ``Q�.(''. (W�Jll��� Qific �A>Mb6E� .) R�i�me*� V�4a1ZFRqis,FPAmL,FTi,AGWQI,Flanagan0�.{--�Vol< ,FVd�-,�+,Mistry}, Maxa�%c�*a 8 h Pfenc_em:>U R9ja--Sch&Ier�hs F YuWu�S��"�g �\.��A�som# ite"�A�ri r)+ . T�9.Si��6!=�&� M�� ed>=� a world&A@�CMJe-�a�U�Ea�R�k�+K� ��A3da�� 7B�i�dv� &G?�a=c!8A��oh'nt if�6i�Ua�3a�A v�D��� ��per< ed.-mq J� �j0ably exclude,��atmp ely).a�, pk:.�ed��N�(see, �=M\TFRworm,FPwarp,Roman_re#h}�6U�tunat;"�21>�_ �Ve�at� %�e�U e�n �8 ,�v!�op7kuL�l�J ��M�mingR *i� 6Vf?display_Fly "Y be�97 regard� us,E�V�<inv�l71 2�b`�.� AP� pap� we�  �Z step�d�l�hde�m�l sharp�Ba0m>���li� ,BH-���I%�kM"� i"e9 �t5�>il�7an�%\Wne %Ut %�of�rso = �y��aa�eb?egG . No�Nl $w�U� �n�la�admitN6�mBSM90,Ko�2 _abs�3 }.}.� !{ is�Bed���%iz A� �['s �o `})� m7�a�%� wo d�DiJ��Ogu�  in�.ydeQ]�os���d�.A�ws�� s>�?par�D ��d��rel!dup��"NB �� �� �#�:�[2[�\o�Ksm9 mmT�l> �V��%�NpE�a �6�. As a�, V�S� ��V%�e.>�m�>6�����multip�9ve� o >a�� �, $c$,au\��a���9ide� _4 >9&N- a��-=GF&)�R(�Fi�6 ��� ges). We"�Ce�� C )A�m�is���rom a LqCngiz6norMwA�voke (��cer� lynot�,) �Ryl�*�9�%Bs osB�( ��B��U qs&��t�e���sketch� S�~\reff%:2da� inv}B�H�s '��effaiDq0P ely. S��Ft�� al iaY mai! t�`�nI)�to be �0ti in olmak� ���EA7A���AF� s !Bt!�w� toU��to�_ &M)+is�Ip%b�� � ��O) 3� A2� ���>SZ3# Umiliar:�  er|9th�,E! Cleft-�8p.!5huN l--ray �/ lb+t��ffJQ�� �le $S�DA�e �eo"' map.*� n�@NsroYpur�&� �\%�N��t�p"#;5�N.�it5�) � tA�� ��F:ut!EX_ ese� ��w.GR � in2*�J�bD-tou�co �A.P!�s� lo K����d a �r� q��needed&x0 is elabor%9GB�}. DvmWiy��Y��E&�A�tr_t�A �:�!�6��oupA�I6� e .J���qM}FAk�n CFT���.�d�gi�xSec.~3!�Kif---! !�atic f"sonb%��;to �A�*R appg. �O!O�8�ral�i�A@�gdel� llQl6 qJxtr; 'e��v%�A- nX?6~  b�Iqt w*�_$�!$� u�Fver�6gr-�!q !�N nZ r 6�%:7�* �� t �32�!�! �subna. �J�! ius 6*:j. Each i"�?A� mpon98V9-3�spo�XoA".JQ�# er 6�!�5X��2F Relfwbem-/`6inf�-esi�g�� ��{%�-�'A�wAUsee (�.��I�}�SseQE4bekse eno�jo`[r'+aR2e N[A s:aIY�ELy�mp�a6� � />FTs. NonmeC 76q�%� to�~s.� ��� c�  !��sQut:�its:�sӡ<.7el�)}; alth% m�xe�is C|r� ��!�lsmprehBv��Js!�m% !s xista��urif-� may!� ~�A��est��In�io.� v�}��aWfAbޅ��I-�x�iQ�-�, � Here�drfn�t��Goodm��$nd Wallach�aGW�< Toledano Laredo TL}����precis��e d^!��{ suchB�-^`ex�3*{d'!� �}� B>�?�V . As}1K aNas %Rm���"�Wof"@>n�cE�/y� main{ Sici���f%h����ea��� uW2U��we��"" is ��R�*�X Botv cycl�e� f�|1h�6�U�e�Oh�}.q. a� illu�teE��M4��giv��~a+U� ~i� .&� �c  In=�I�6e�cBid3 "1s�� &I�; s�z s. A pecu� jH!�^�%� ����� )�ves �v.��[A'9r hO" !! four2�&�eie�FHRx03}n Ey��  simi�q�hol� R�  A5h #V �� a%(oftenNU� !!s'). FY{08we> cussE�cqMof)>!�y$ly cut-off=���2�l�CE � * i ot K� u�>�$&�TU)-�YL�%4in��icJ5?L� 5�. 6�E�� a>l �.]-�&�( $d>2$. Olu�jd Graham�Y }i�*\a��+��nonUa!oup!��� of��i�a��qwal�!igu0�� � ea<�!C�cre �` �  ch&�u�Etu!_��O��he �. i (Tm�E%sugbuE%e��-)�edI�LWbe a �profit�N d0E�i aNe�D�]M�#��R Q4����A��>).��P��� ��l�T!�� ��Q9 te�ZK$�9� n *� M%"���ќW�M)r"i8��k� tA,�venMF�pA2 �� b!�too"��� y5� an .�$�Xa�.�uinj� l� umst�s "A8St.�I�ahof)q-iR�a1y� } \l<9>� ^fu�bc��a�%�>j)h2�"�' !#e L\"unVr--Mack!gk��Lus,FST�rserts&-T�'em ]�JorH"eys W�maU��rStr}.��at�kE�a��?7 symm�cp hetLRv ���#�#�#$I �B�n\int T *T,0}(x^0,x^1)\,dx^1 = P0$\,,�*"�: �% $gjA�I�&�#fs-�Eԕ7��!mi$ �G%+? �d.�@�s�00 endF 01}$� Z� ��8�a2�chi�\ $T_L� $T_Rda each$k^oneu���ble""� eqna3rT^�5p &=& T_R-!� + T_L+ \&�|=1n=-2=\,. qr,eq:TandTLTR}1��IAs�ai�gu�aa, i.e.,FO U(\l{)�v) ^{-1} = !^2"  v)� t�u� } 0 �kQ,�X�X)�)Q�y�d"�  &2\�AS q $xA��<psY� � $.*� >>8utB#thI�Z�'�E}x��FE[!�v_1), 2)] = i\A�(-T_L'\delta -v_2)+ 2 /1 & -\f�(c_L}{24\pi} =''% \II\e.�T�V� lNe) (�^_e�@ts $c_L$Fa:�  �^�k-5� ya�+�pl&} w,a��)�zp�#�esn�-s�yoG �l ��)�1 f�e"��+,� ��'O-}ix�� ) LiYY�"$D6�5�of�l)8irco On� keye per�a{x !ltr���U �!" :T ,G �� $P^0\pm P be��67��f2 eas��$ Yޑc$P_R &:=& I�1}{2}I�P^0+P^1M� ׁt�u��u2P_LjH-NHL(vHv>�g��qvM$ +/"Gs, �o $PA�;sN<a�b� 2+ r�" nd vb);`a. t\5��!� dSPnot, "7|(ib!2 &� themselvCre �+y�n.�*�Q�hrary:�� �$v$DIt.�|*�+s>sn$�Aq``��� '' )q Yu��\lt=��)I=�,si_n} \{ ���g-YD \qquad \�8as $n\to �5j (eq:ptwiseubF�rurF���(�0!��.& � as e�,�o �A��k := \ip{ }{A/$T otASh6:�+.}�,��&� &i/ $v=0�n\O�;$a�U�d إlwrite� L(f)��t )�fm3�!$f�Oa ]C tu�^$ w $1 I5� =0$� }q !�&� ceQ7 ����Tf) L \notOhe Reeh�)/a�� IU��f(�'�y i*�&50$��$f$).dJ? $\va%o_2= �- %�$ (! mbda||\RR$)�now ea. $E6]}{ �: = -2 r \| %%p\|^2 + ^2VM^3 %�u�&��H mall!'�� $. H�%^�{>� $ mu�m��et�ue =+�"$A��;wD!�+v�Ka.����y��AE�0Y� psidb.~� (f)$S�n�*e�K�:.o9 .o9&�4J=E *�5.�(� -�-}by"�$-�$�(Z&�)�� "�(�+!pa�( (&!�/E;� =c_R=1��We��sK%n he�({�,| ceeNrЄ!��"a��Njdetailp�id�5T��.����?!�[� 0+a�N�y $T$�aAA:h("���D$�-� �r�=rQxs $v\\{$to V(v)$: F�T�(:�V'(v)�(7) -� c"� {V,v\}\II�q� �} �  � Fz E = Q V� )}{�}w3&i )((v ,^2 = -2\sqrt B . d^2}{dv^2 1-A% } \,�(Schwarz_defBm �� #"h"-%f $V$�� � ya�-zeror �� # is a2_V$R sa�Z orm)i�6� 1["�!��le� =5�#%�&� _V!f-B�,�l�A�} (>6� A�A��>�+i��ply:��.) Now-&s7>��j�  $H��c3�a�a2�97 $EQ=HA��%� en $M�=-2/Q&Y6 sY��&=l& � \,dv) ,�-V�5+9�12�I�sM��.,2*~� @� T(VF \,dVu|c} x 9 \�mYaW2q� )^2z*{1)0 ��A�E�!�k�by /�=lerm  ac�lis+�0"�U:e�&8s. Sinc� �� .heq)h���A�m  P>'G �i2[9���dha*8u�!�!�=�J���u���a�alQEIB�@&�1�� $. M"�{opJj = 0Y.n� pec�)h�?�be atQ � o���%�q_Vl $#A�#J[2onveyw OnR0�; l1 QEI  ��s*�&rs&,L/� inas%$ae $�AG�#&~�$cb. exer� g�r '�!I�}3Ea��y {�+���"�v?>"���^LQule*� !}�e%�ed\��!�) ,M�$� u &j �a]+&p,���PV<&l�� !F�&ba(� �H�a�V��/dI. (&_�h�>��$n"�"X�"van\�7,a �D"x�{rval.)�%oR@ "�= di1�e "*E��-8A���%xs�6�>�A�v & �ex�\�� `! "G!au,%- en �aT UIi� manipc y .�( to $�& ��---��e��0����`�subtl���sm �? "~'cNxd=ɓ�Ad��a [not 1en&� ]"�-XN[�$H$, )�{\�'�MS! -=�XWV� XA�a0� Glaeser}�2 � i1 addMI��]wo)1E �t��n eleg�0yBl!��Y!� !V "`1E�ri6o�'f�%A�� �@�6�A�E�Jr$  of $H$1$h�,c>na���'Kq�e2�A� � Mr ��Y�[instead�6)&J\�ol����problem�! upshoe�%� QEI�� y��iq (�m�in!�pe >ed � )�-.�.�nU!tRe� tzo.&8T"� Av HQ8sI�, t�D�-x^r*4 s,��� rapi���u�inf�5w`w)?s, y.} $\Sch[}�)��!�gr!xB� �.�*��#"�4� % !I!� )k &Tg">-(aW� (in Thm.~4.1��&�!AK �+ f� work}�$*�+ ID .1p d-c��%�7N�L�`U* mannF )�a� %�G]�#�/I*G�-.~4a�G0 [��%%t"�#D&� p L#��0!Ddemon:)lattz5 (by �+��G ���'2 "�))AHc re act�E�^s ..9 �QG� ��=6 �.ou�  (v�5�V� �k02�assoc�+ �.@"�� E��-p��^�0�� *���P&ÚA)� :�7�6�*'EY�I&w�>2�3F0, e��E��( 7inu]9�3%B� "al$A��8��to� e�J �) �A�K�3�#��in]�3!� 8�F�:0I���a�8�-o DeT�."F).Bs<�uqs2\�d�q�aN e�E2�w�l*�s stag�b &U�sJ��<s �re�Qey�ali�� �06� ��{o�:,>� .�D4* .:?�D W�� ��E� �t�m)9A� K0Q�Rx!VEdeB�6!oS%).~3.3V: W: ur��y)��"�O1R��^� �3^M����,�| �oBU�y5�!� pha|C�I$G��s�Ai��� ��fN ;E� *%A�analy‚%�,� �o�3���)/sp� peak�@bf cess�M 0};���ur-.���[I�{Pl?lK1�cer3�W_+�W$oUa%�4 {Gc6st�6 } B�(<wI}e�EA� elf,@8aq� C� �d%h2D$\{z\in\CC: |z|=1\�!e� lex�Mne. U�>!�Cayley&i $C:z�(i(1-z)/(1+z�"�� (�4 $-1$)�m} d o���;u3r�3� %� �`l )�;pic�0'A:wAH�Bs� �A� llI�F9 J�@� � *�CC�; , vi� �5 heta � \t�B%~"� %s�� �cop{�%;`unded )93*̱;/"�6�\��� A"� Rc � {�?A�)�(@9c�8ion)�B{�*>$\sigma�*�SitaP� �C�g6e�� % �-+O U(z)!�n�@��p��� ar�3� �A�$z$�#�A%j�d�:�4e� t�Z�"d5, c !>be�n*�<)1ofB $%Z!E8$�F�(()�+!)=)�"K# twopft> +� �de/i��ʏ�Z��.5R�*>{E�rh�)}Fm $:e%Q�Ht��nowre�0�<p2�/tL one-er�%Y�� 9�ML)�ⱁ��9ٯ:�V $R_��$ (u�� RR$)*�Țo��WEQ�]i� $T_sDsA�$Do"�!>0B_=I��ran&�&nd��}�,��.&���A��aZi���MR)=MZ) [C'A�o% (z)=z%�phi}$], A��1j�>wB�.T_s� 2���s+ �� �#\*S&for}~ "0\in(-\pi,\pi)>�!MF�5��>�-���J�!"�*>to"�A؁g�a� E2�"}�En(I �Ae�A ,principal br�tU�rctާntA7ul߹��stood� ]E�>.���cok�� c#�Tr4 V����2AZ!��I_ � $s $S_{s}=a�i T_s  E8ahu����1T� !"p�a {�P k=ka�ZZe��\7e�GA�j�M� .x)b�^$jV�P19^, �q�!ldi� �>[ J�@!^$�@>�,�@ l9U��� isͱ�C�un��2u R� y; q> ?DO$&0!I�Gc t (�" in!t)�C� a!�:].��2�!2�� �W"F"` �qalpha z�'��{*�fz+.}}6�moF�*x 1,JAuCC�th $| |^2-||^2=1$�)�he5#�E2ui�1& ulta�j�'�U � $f�` !#��A@���f(1,1)=\S /\{\II,-�0g &ٗN ,yj� S$� �r�\F�u6 )�$au+b}{cu+d:`flt�6{ye" foA>z "#$s $a,b,c,d1f ad-b��� Hi�[i n�\�smiP5L(2,\RR&��ub�\0�*S� # :Lier"�}U7$C^-�;^q~s�=!C��/al-�&~�n� $ /�pp� atopologe�]�a�"n�of"� "�5ir"n�.�3ll�s,J'$f_k\to �,f�)sިxA�@RR}|f^{(r)}_k(x)- (x)|30]`$r# zm* +$ ��$rM��v%$f$.}� �s� i�a Fz� chetc8WKe9r�}=y|Je� e Fre\' Bub5�N�S9�!1$(�],)$-periodic "?a�w  !"�h$C��� i!E�gS }"� -�$!anqq}QQB� �_$._'S>-1=� `�uL0� s an 1�$bs�A" n afܹ�c�f��?=�!`Eybc=do`"Z s�ea 5�if�?��=onj�,S� �|.�� aW glob�_���K!��Z" A����o�Sm���n�R&�`m�v�2*f�>f�]�!j b!�H'9}>in�- :�-� quot�$map. (Cf.,�� ,4 .~6 of'Milnorr �  4.2.6&}LH1Nt!,)R-e�A�!%s,9�B�,E�R�l62ki�W�=�_��-��֟�k _\RR .���>�)� 6� |c $tM a_t}�� "� .� $X*BN�(Xg)(z�4!.���t} g(l o_t(z))\r�|_{t=0}S3 (g�0q��)\N<�%&�"�A� �5!rho_t$.$�1Aais "��"){b>�ia}H6�;heAZJx %]� }! :�>�g20j >�!A.�A$fBD$. 3�6p2�s*�5 �! mor�Q�!C+|f�"Ar%�k �� j N�N�2�$\v�e�pConFW (\vf En$= f(z)g'(zN r�z�I`^��aCv��g#XSf��ͬ�A"� � � antZ$��nju�a��(\G�� fm-z^2\PA�!{�_ We����!6$G $_=fB�m )�&I ���F�!s4\ ghtforwar� chec�@rJ;�mur�)�/�h�2Rphi 5J� $"� iz�[l��F sXTu�FS t $s6eA�XiQiNF^2M�z�) #-z#� �. AxX���K>1�j s *̪ z}=z��!��y:��.�I} CΜ�SVfL�t�deG)�Q�k)|�- c�\x�'� ݻ6E. A| c`!�����\sdesG���.� $B:.r\�Es 6o�ͭby.� X+U rs s��=�O��m"�d���#, I�cohom! o�M:X�]�e)�4Gel'fand--Fuks2�5{AwK�E5�a!" Lie -QL� ��4� rawn�vSegal81}� �� typ�U al e�j$Nr!i ed.}F� B(\s�_1, 2�kM�1}{48z.Re._{S^1�:g(:\A�>�?) iM�z�-2 \,dzb��V�H)1 $\tB����2)= o_2��n+�S$. N<��logo? hms �ii�! �ambigs!! �E% ula,��$ ��$ Xw�6nr=L� �1ab�.!�aG: �ya�=Ff$Q%�{*T$W�&D\t��˻I�immedG# Q��i@J�.B(\id-�%NE ,\idA 0\,,C Q# ,��)=0 -�:�.�AB_Y_�F��"�'c-�+DY��+�_1 �_2 �_3���.5-2 &3.� � _rel]�end*T^-�)� @QZ3:$�.& D*-n�� %�?cS�gU��'�7�A� CauchSBt (lMA�zI��A�d)({�ol�c !k �gs�8�v. Si>�M�.� BBV �&w�}$NSirͥOaO�b&��Eeas,,�� uted*�F D_1\tB|_{I�rho)}� A J� �1��f'�boU fg?o'a�} (z�dz>B �GB�D_2�rhoeY��� \{2�}�-%(�jcJ� �3 \}= Z}�:��Ajj9�N� {12}�Mid � ,\vg�sp ��=� � i{(f,g)>nI'sM��(F�C"���in1�)I!g�8 z)-f g %:�*_3Vir�>I)8Vq (~H%\.A *Uat�B�e�#m��m6��a� autok+X(� � $f, _6� �y��UX0ybeD� n"�f $� tect6'M� _ψ�\HH�a"��� t�.�Bat �in^� ssig]%r� rho'�M�25B%9%2 "�"#3T�'a�map-.�; � "&�&1�a=1��!;�:l(}5yaQ�.����@ �ge�d. RF1[  type/� �UmM5,k�'�� nd w�=2- �*i�'A  *\ We b�&� �n56 U$� t�5m .�ɛ�bon��dc%/6�)* ��!��2�]^�,&�o�OA�id)=\II/nd"�  w�Isow,.�.�� "�M%yS� �]� urhq�]q�.s.� fn:s�}}��t� �.]A�*�=N�by!)���J * 9 (f+�* f))+iB!i}(f-"' !Qa�p��g r !�)*HNB� g f)^*� ��*+ �]�Z, �D( Cf)wA6�$\DD\� t�G*� �� ��($C^1$-reguly�Ffɀay5 if (i)Xu#� Ňa& ,� �W�v-.� .2�� (ii)E/�f��GQM3s a�m� trib99:&)�EE {H��DD'.� hy1for�� z"�[� vail�- �� adop�i�&n�)jA &i c �cJH��?n� book-keep��de�P, *g�l�l� %" � 1J�+ "M+* &#  GenJ�H!�=u�FI4 } U(HE3\�|�EP} �@�pMF��6���ny�%A`��~��!tJ)�to4hJ �OA�m!� B3 i��"r_ $AV=iso ��F�H"P�izU<z\F�F*��5� s $PK$!�N�s ��T���sq���{be�KaM�� {&sYPERSi' foot7*�n" . TopE{�<d>��,, �M6 iJ �d� �#�/22��!�]= K# *)9��:�:�� �|c.��1}� c!R 2 Ye����O& B�M''^a�{W(s"�"�k �l>lh���~d� 2%G- c �' W2KE�ho&�Q1�6- �X (s)=*� "-�))+F ).$. Us�[t���*�I8O= �rho�2 Ore�2:] �� jR�ry m�?6�2x�&�Y"^dre) w �� Y�R-s!3 �!,�)j-BE � �%!ND'mC� 8a.L&NM, �F�H!#3>;�Dt-�/� Dg !*;HSch"�S,   &5$&Hm"� :A� ="\�45#v\>�(�zg�CiO(B*ES/Dif"?"�"T2�J�A��I��(>g.;hJ ed:�S.�(bY`I� si$);!M&�%�N���"��(� .G� }L#u%JYAGp6trho_see s\vg~<�!Q�+$��l#$fiw�}*���,m�$f��a[J�\ip{-�g) =}��� ���2$<��7�Z@2�>f�"�6-b� rs�� ����.�a-ge�;J/.����_s}1� %��& f, �2>��<��R e &vO.�9:]L6&� YL�ga [;�0c�*sen&"� !YZ�an�,ty�� 2� m 6\�l�: afbyy\DHb�e.�&quare$ %X!�&�)|�e e�c0"�ab%~�:J�U("><)P. E�� lJ` P\,;�<23Kj3 BK8K= i)P  $>(� 鞁F��a&79"��"�)H<&�\�.2K;A 'm*`�Lt�Y�; trum"A��'nonempt�los6*�>&6n) Wbeg�\+t�Ab$\{0\�V$[0ͨ$, $(�d,0]$ o�(RR$. ReW�r7� ���_�TEk>=.�Q$P"�6 Qn�`H A~6],��HE��7eX�B��R� �)&�JV$G*�. Con84g�if �%������/t2',~c�� � ifBaExK?�,  ,iJ�ZMɪt8\,a�ed�Hled"�{"�6B eW$*q CC>C�/�hotIf� p.~9.2l4 PS86,t�2�!ory@ &� ,Lu76,KRY,Puk� he�r�� -"�,a��( .~1 " 5K�iCs} e{̂��weyB�"�-)N�,.H .e�O�Yx }�7�`�< ,�>��A�d�c.� J�igP } = \lim_� mbda"�g��7B�A{HVeQ:� �* ini5m2 s agU#*�$P$. Clv, $P=0A� �"�2H=j:s��� (P)=�Ca]��/e"a��-- y�]�or.:Y& Rs}i:�#}tGB ��rL�� �� -�sh�a�foI3� a2ę�s`^�G. S�Emal-is:���3-9sm3��-��% po�zln enBudsy. BX.r�O�y�1 *GP|~st͜eDQEI+I2sa��� Feo��b"� *@ .##� �82P"�~)�;D at8� Z,X��PA#���,2J.�'��J�(@*\2�bA�4ny� �G����qly�u1|�*I.���_}*!��::L&aM+ ny� a �l�m"�&!�&�#;�1enw��&�w �2!7 (s6:5)2� �Yi*5�cv�&�� skip.�0bf A.~HilbertA)!q&�IwE�e[�q����� numeGn����2W�(-%M��� d � M*�1�:}*��<u(0 charge $c>0$�q. \item Up to phase there is a unique unit vector $\Omega\in\HH$ which is invariant under the restriction of $U$f`$\widetilde{\Mob}$, and wK4will be called� vacuum ��(The generat�P$ of0(one-paramet��ranslation subgroup $s\mapsto U(T_s)$ is assumed to�da positive self-adjoint op rD. (An equivalent r rement!> that��H�rot>� \phi � U(R_)$�� , byS`remarks above.) \end{enum�pe} {\noindent\bf B.~Stress-!04gy density} !G((smeared) sN', $\Theta(f)$�$defined as��xof $U(\rho)$, as described in.previous!�seE|, see Eq.~\eqref{eq:Tfdef}. We )�)R$\AwcontainA��eMrh20\tDiffS$ fixeI�Q Q, i.e.��rhoo(-1)!��%�e aA��rise� $vMK V��4e implicitl�$z( )= ^af)$E�n)����W law:G0LMrho} becomeJ���%S e� = V'(vA�T � - I�Hc}{24\pi}\{V,v\}\II6LMv} >9Her�*havE�� ch� ruleE�Schwarz �FF�\{z,x\� y\}� �dy}{dx} � + \{y3���6�H $z = z(y), y = y(x���a3fac� aeJ�!�$a M\"obius:�( vanishes i� i� Ano $\{!�!E=0� �l stru��Zala�Dy enough to encomp��an�res�M�theoriu,n Minkowski  D: namely, boundary��EFl fiel%� >l(see, e.g.,~\cite{Zuber}, or ,RehrenLongo}%�a rec treat n term�j8gebraic quantum.ty). I$ se���,�� si��underly�A�$i$U$!�$u��~( correspond3^�m�!�%Ay�es4�_-h�(half $x^1>0o:du:gtensor gc by E6� andTLTR} �d, $T_L=T_R=T$%partic- (, $T^{01}$ U[o%4 timelik�^ne� =0$, reflf ng� 1� c!�z� no ene 8should flow out!P!�-ED ��A A mor� lJ�9}s��K`moI Lmirror' models studiC M^HFullingDavies} (for=  c�� massAscalarIW$). Instead'e.ertial59'wea sider a �5-AGa�jey $v=p(u�(-�$u=x^0-x^1$��$v+ @re null coordinatEU>6��!| is�Bd1�por%�of >oto7 E��t�curve, ͢v>�. Re cting,e�s�wy, J%Yin �uѰD lif� o!Qelea� $��� �7e�R�ag���#d by Z a�we�putFT_L(v)=��0,\qquad T_R(u� ��T(u2�6�I�sB�(Bo�"CFT.�,!ecourse,1}%3$!!=uIh. 0=\II$.) It fo� s:�9�^"� � "�Ov$i�aEm��*B +stg �!t thenF>\9 4T_{00}(x^0,x^1&? u D ��p,u\}="12(sqrt{p'(u)} (d^2}{du^2} ��1}{.'V�ich r- �4resulA�V�eh5� c=� In�eq�)�� �0!co�ly �eS�$s[18 der�} (Ŏ!`�!n*� $(u,v)m= (A,v)$)�"e�dic!�` �AZ6  �s}a�gether�_�d��5���b�X `in'M! at past��"� . I�j nd)discus�is��fu!* else�� . C1B�w�弑� whol( >� must two �pynt �on� of6I"8L\"uscher--Mack wem � Sec.~\Ld:2d�inv}).� � ,briefly expl��!S� d modificXE�our� permi �p��%� sit���re �ow��mu�� pro�Sived� 6�s $U_L�R$U_R$!&�k  r�Ӂ�$B_ �Ja. .`e exist��of 5qu:�Y`i:0bdcop| of N�n6g��twoi;�&Os $P_L$, R$ !D %XS$)a�)�N� :P� !H:zOg�ea�(�a�of>��)� a�o � � R$, �of�{ obeya{e *,�EnS I EatJ�)^�`s acc�E+the:�4(�� q charge $cA�k c_R$q*�)� S&� v 6��Y�bu�qva*<p oak7the o� copyI�lW|&Q� s F m:TA@1�ame waye��I�!� :�� !�EV� . �q*� ��3� �"aas  p���eՔ ���R%�a �&A�2�,%[�eis�no mea��!FnlyaJDsibility. Clear�  envisag%. ny number!�b�6�!~�mi� ashion��erpre� )�y F��(no longer c�� \��ion{Q\E� Inequalit��~F��3:QEIs} 6Eo{M�t} �1�|��i"��x ok �m4��"�L"E�& l�b�Thm�� thm:Q}�^� Ryb$T$BA�H%�onneg� $G� Sch�� ��g!�-IyJJ  G(v)"S  *� 4 \ge - c}7 int �% d�O T*� G� ���aticQIB� holdsX  a{ �U�aX*p$ $d/dv \, {}�U �  zeroUs�) G&�&m"nMr�der} ) �u(v)��\{M,array}{cl} G�/(2 �/ ) &  ,\not=0\\ 0 &%�=0\,.� A\%.>�Moreover!��/� A�sharp:%&9�A��J mu� �%�#%v!�$!�. �-ar�b]B z:��?% �*t6���we7*) $G_L, G_RA+u)-�4simultaneously)%��N R��%(a sequT non-EC�psi_noDD$i�y`n)� a% G�ub md{ GAJdv &\�%�arrow& qv_L�x^:zu \no��\\�m�J�un�Rv�u}M�^:�v q[eq:)�� 1>as $n& �s �q.* em RZ:} 1) prov�$ Corollary[ Cor:W1}-� Ap� ixU squA2roo��� }$ \ A ���tzU�abi�a� tr��Sobolev� $W^1(� (�has �-� ,grable first����  �������� 4&�$ coincidesI�an S��-�N ��� � establitq� �l&� ��QEI�#�e4��of:� .m 2"ctuw�e even�"�5�s ��� not {Aq!�ctly}V$ve.\\ 2) A��>�'��ed�de�!%s� can b� � as �" i��ies��l��l������� �\II>}byD �dqdr��!Em argu`s.��,orem X.23 inRSii}f"�%8:�� �->�s��pl)OI�)�A� pairS*$�# ���5sa�E2" e���<FL$spectr�@I1�s�cernedA3)�m�� )�of���$a p)o% r$� ;� A<W ��g alA�ategyXAc$�r'%%mbas� % v��H$ (ra�!Kn $P$)��wo b�-atun��at seta�e�ad�a�)be ext?�a'ɩ .H2( 9n. }&a�pursu se dir� s ��#medskip:=Proof:}%�p a�$broken dow�o �%tages�$start�9O"�A0*� � �SA��"\a�O� rted*�)!!� the �sc@!v A�io�$�%f ob����!Ba6 forward� ��q� summariA inf��E��e�� $�=1/��$ does%��{V8diffeomorphism � A�b�f��M� . To umv_problem�#�y ��o a��( $H_{\epsil�n}$ d��@ upon�to� )vni�9�BNi=&)ad��a�5a�al�:�m�b� � rigoro� Iso S� desi�E���obS'e�%�t��em jԁ�"�!ʼn7! effect. Fq%fad�� stan 52 $%�Auus �HJE!QoZ lineGU7(I+\7!AlthoA� re:�! "�! � � � f$ , itY����.���K as it� )scontinue�ez.�"�#L�A�is *4 v��c*dy!�ubtractV#%B�${  � �"�R�ױ�i� l7iA  (�]sc'Ned)\($n$ increas��Ae�edY :c*$9#>,= :�#v&� ��� 3 I��an�o�Dcay�!�rolE�l}% 6 OŘ�ac�!�is is�A��. ably��Dsible.\footnote{Asw���le���eapXCarpi��$Weiner rel!1dg,"int�+ &Z ��the�f�� cera��� ing"�6�) �� y�!R�,s P  atil��eHto� d a**]M0 8m rBp�/e��� ��>�, ���eneEaKe mR�OY��ion.} ��"�ion%��' �fJ�!���� Y�0 lemma, whoseMo��defer�SE> e eny %+�n Le&� lem:xine}"�*����}�)B�T!o�� �* an $n_0$ f�F"!n�e$9�in(0,1�"5&k0C/6�)z2�$ lanm�Ua{M�$�- ��6� d"2T!�q":t� Fv*{)2I�) ���-Eu�y : 5��!��,}{HY�.a-VGi�V^F= = a�u�(1Ene��-$1�=�a��g Now�4�!6Wb�bitrar�(�e.��h=f�e4!��� ons :B . {or� cal�&��of ��  i���replac�0���0��}E$) in �4(2)Av�� ��E�if�2�V6eby �#2w),�+is �Msy � L%�.�-j B�a��JIg3\OB[� ^2��,B�+��4�3T.%�by�{.�g$valid beca�.I��!!�� out�m prval. l�Y� e��r ���2`�.+by-�15��� C /�� &� fall���wo piec.-+4����o &=&)��%2��)+�&.2��2�aBV� K\*�&=& �f2z�$5�FY>�6���Ae Q'�oe5GOi�� hand&FS�B�b$=�!S $B��9a ' P.� - � QB{�;>��ue@} ��q0� >�a8�!d off��&ksoe�l�%6- dropsab��a��  obA�h�� �NZ�$X *E .��lg2n��g�� ��48\ 0&) j�75�c} @F�P!UZ� -J- 6� Z� !D)W&�{ ��#QEIeq2 , 5�C�"��T&��$ w� n a�c+)�DD;\bigs~� � turnQ 6;$GEsa2R �.of&x A. $V�A��|�b6�2� &�Q2 at197 find2� $h_k�.� � to\{!D' !�J�n $L^2k@z9$ (!*��^b��) stoo�,%��of��"�s�8 M&%��k �k� ik^(Q�>m h_k�3��aqyp{+�Dh_ki(\�5����I �M�=�� �1Y#ly>�9� $-c/(t)�6(!y\,19)�8 , dv�hilD: 2Ru e݉�F���,dv =c� �9B-E��� $v� Z��pr�o.0"F�" y� {}Tok+,a)f1� B!�� employ an��"&"� !��"(optcpct} If�8|IM�#.#��i N�-inf+ I�F��2M{� ��lr�#L� f|U�-!�"� }� ^g 6/\E�Ju85':�!TZ�UI4E�"�% of L��!�� l $n>"�>_3a�� e�2� =�02d7Z/��� ��. Since#�4T(p���&� O0vad6.0Ejx � law~6�v0%*k7 \JdE2�}� ��"82&,v�7E&� , "0H25_ "&%^�$J#{dv^2}> _%m*� q6hBm: i+ ZEZ� &1�^' WM�6�&I�&W "� G�  26$� di8 s�:rts. N*<�E��A��� ��r�o P� 4fi�!� { e��<erm'�NQ� i�(�v*" �'n /g[4st $F$,"}i%, pushZff0�e tail�$F��usNZe =~��2Z�VYY�(E�n�!3A�\i(v�|1��a6����`&Gf�D1I�� . $\�$$ E�EzN! S�;tz- &0 �Pset $G_n(v)=\chi(v/n)���$�_ݠ,s(x)�K1=C-(x)=1L $|x|  . OnA-verif�!aR�m"� }{.��Պ_m2u} 1� 2J�!�vg 5:[�C��eq:E�Fd62� .A&�::�5� A�%�$G$Z �� G_m$#"]"iv�;a�sm�%!�thA tinu�! e�* B%�in�1 � �[e��Vul$L^2$-inner'duct]S RN�!� ����)�2�{2J7 �ak� �r �� clud�$2 6�a�1�$QI�  6J Tur�t$4�6�#!�*�/�.�"com&/56y/�� mmed~B �A!��N@+ �@sfy��4N"%5��.�s� �$:W%� }E9 |0 V��ss� t(2_2  2A�~U2�| 3�u�e�!�6us@$"H()�nebD!f� Xdap-0st6.#�0!�Y*:')>�HT�UcoI\�1of��(mp0%1em~4.12�It( ai�1o��| �E.2/Jem�$g:�x�:}+  (!@!monotone1 nce))��:b�to?�3Ba. IH�ŹNJ��%lieQ���e G�b�$ g�@ Lhan some�$u�5� V3� �5int_0^v͓&')V'J��ev"h.atisfE6XS�,��� and�b*.� �I��pmty}6� ��$+  a :�{RR)! wish!��K�\:2�!bn8&�'!�>#. S� �".e��!a�L�$in $[-R,R])�)�R>0)��� a�en�$v<-R$0 J�B !�� v}"�}falphaR�erN�0NRN+M2{-R�1>� J��cho!6$S$!�!Q:F�$@m"BU5t (R,SG%Q1?>S$�H6n =F=&=&m2?ZFS=!Ti:S&l 2�^% :Nw+ )�=��ixѰX a H% amouPf2�u< !o��=s eetaI�F����r�e8rs�8 ZjFF v/�a+ ��+ly&�set����� .?)�A2 � q ��#J*(\t1P,)=2\tan^{-1}�:iU1RK 6\E�)�%K��-\pi,\pQ� �*����N�8�$� �63 twopishif�h* I�8 Appl�=d"� �#:a."�%T�8emC"�7a�c"�+usefulG�s �&R�7��(�wo-dim�/o�:I?)�,�P�P �World_%6�w�8C M�D�53 is �4be&/neg fur�m0��� !� 9��c dot 9}2@e"�=�z�9aVh�er�ef)cI5+ or�.lE�2 7,d� > 0�0mea� �L"�.b�MzCasymptoL �lso��A�[!3�o � a�,�?5Diggle'' too rapidlEN%F!�!Aov� t� &�s�6�T�� !5= polynomi 5`<Our zpS s *�f+s $B�.�M�ٛ iX Y � ��sesU� (u)$!Bp i��%2�hA �5��� J(x � s,jj�7. >e n en)U�+r~:A9�%�u[R���:�&v))I�*g:, $*9 |d(u)/du|�m.�9#v)/dv #%�3�Ntz# �,*��:� 4��e�}-���-aKN��6we�eBհW��;���N:�N." G1Mb-0 \\ = -�c_"�:��W 6u�PY 1)~}{>"�%u"9&�;VbVQ2bA .b)�>b&R@eq��!;9Cw� %lCn4=)~%� ���e1�E��R�2��A[u�G{C�5A;"_>a�b"9N�q���4 p5S����$���"���31�0ng�3_1� _B� not go�o���tCT[i��W��c a�IIԡ�afwDl6'�5E�M��M ray  ��, � {\rm� st.}��6o�W$Y�k t���.sD�O�!�!rh �i�;yD�h � n: " ;e�%��i�E�"iVpaDR_0&DC*�@\,N�wA�icu��}�w;*�NQ&'s)�]=�?!yR�R (�I=c_R=1jNVollick:L JO(A�$lex) Dirac�#6�� g. [8Majorana 1� %_1��*�U J:er �.]  wort� t��a featX2&)�F�Ok%FaB �296$ (by ``tur� "� So/s���Aas fa� ~��-�J���> Nei� po7��ˉ� 5�Q�HR, Few= $Roman03} ("7Af!\8�Us)�'p? ��l�v7L6��6.YX��s�Nex! howe" � r�T�d��I��'{%�!�}��~)+��, to�7w�T!�Z�volum�~�v f^ѧ�&�bm�`-� ��6a�0Q��ect�globa�Q�6�WoN�V)� BV�Rht�NU��8T+Bx^0dx���3) F� \,du�iI�  F� .�ETfmunuJ*!���%�ep͔s} $F�N�g$F�����F� ���f^{uu}�S�^MV�MV'vv'u>�!�!�uuZ vvq *�_=��s$-=��Ys#d �22 $5o$ 6�"�na0J �|f^�U + 11} - 106?%f^�R7+ 710KWe*t�(Y�$ &jL2�&D;�v& inG�Z�3.]&))n� %{ uu},�vv}5+0$�wise.}a�h�$�A�m�QE�kE*kVFy%e*6kL�3IqlWk�A�v*�3 v+/f})Z� Iu}�i&! \, du&9volQEIm��7asaf"9:NMy? s $u)Desp.,�+yKa�a���,R�)]|>In9M-,A.$s�  $t&� ��-c�B�Q���K �[�fYl=J DF:� B�Iz�so we�@ a"Idom�["�G"�Gy (QDEI)r:�M.,]rg ,V�Px2a]�)��1go> r&E"O*i��m�]�].B�Sw<ivP` :�\$]\a�:Z6 %�C\ Y :C\sE�9� [�DUW7j>%8J#s} q%v2��4l>Fk�$�"�`  E IQj8"Be@ (v)=�/$�_���+Bt\1f���"�aR��Ix�a6�E�1i�n: �1% �%":#Ilaw*/�+en>)�4q(��&<y�x��.� = 1(v(�="8".d�b\5\�o �c�<|�F�� = ��+p'(p��PJT� vlY ofi3 bles� � ��/ed� *R*A�'F�`�)�)�)�'!:2� 1O�����%N2�H&�6e+��  :�n 8D�by-a3!�%o��-Rf.$Y�eJ  9 )� �:�  \c" I1$ )O31 `��[ ons'�<2ko@:R^��&�[oryL dx-e�lO�W� 7�/�� spl�)iS�{i��e� R$ sCC telyFAT mGlK comb"#�*�-in Eq.do �!��ady1�&Y2Mr�B�F>xa-f(sA�K �-n sqnPf locC�$me-Bm�] in (,Gamo6�Sbourh{5of)�-�B�&�^ unaw� ��lWs�&%xary. (Se|�RB�f de�!ed!�cussioE�D�~2��nde�7�$appear.) ZX&�UnvTed&� &�jw�<cv_uF*�6O ��+a���s$"�Ilet`�Ce<3 gaV 4e�Ps� Lf5{u� nd � c�I%�JK� �+*�&�Kl�o�n=� >v >A��3I�W+1av�h� ���dy!Ajted su�Is^�G$Pay� �N� efficiA�. "-97[?�*FIiJ�Z@ ��d Sk!?N P!�(? �(8 H�,F5a�I�N� ven semi-�<e,QPN~E�Qe��l.�  e�IB�  (�\t agrees)�A��*z0=B !�vall3 )Us, �Qh �B%�*H-1:2�4Aj3 &�5+!�}p9e RL$vm&1!w���H�nge �k!���nt�Bi�n�/lict �JQ �p�v�!!R� *6 m�3AL)�0!� )dv<�f�[ $ �$]eV�+�� yy op���erQj,� �8U�.Z8E�!�re. Owa7t5�F� �-� ��3�Q!��Z = -2+�)9�)�5� 5 40J� i&fi 9^&-"|Yb0�H (� :Ia��"�3a�1)$�WSwthe� .��Yorca�y(+�E ing �)"�R!^% ��lN��p :by7c�v�j: c.��JNNV"���.�= BG m%F?L!x���m��.=D 1D�nU���$va�p;�5� 5)f�i�2 $)�l6=V�_{�t}^0&���,< 5+dv <0J�-W4���@!�f>�� ��7!� !D��<@ =U(D M3ps-!e����< fe�*N{��A J"�7$w � asoy[m0� -8!4U$4 M�xu'E�md(�5�Q$eaked near��utr%�di�hEa�magnit�5grDJ�@mbda^2N M� shrinM6�e��*q�*�RO +�� f.�2. � �subjeoo��k�ion� �R������Y ��-ga�`wo&��s� wa  V�0 (Prop.~3.1 o�m ANEC�k&� R� �Otra'm} betw%*%�obsern|�Q!u&p�_ i . An1, ta�Y}pst� � "}' $*UA-U ty,0^��e�|m(*LM�$�Z��� tendz$%=�Y�A�!�U�Av]V^ lea�t$Q?V0G$. If? �6a :�i� di[Et�v�!Jorigin8�%p- �sp�\ in��Uh��t�"EQ:Y%�. H� #B���9?a2W an iLV�u]cly%ed�p��}>za�)� � ��-�ee* �� at� si+mpens7q� C5�Q$�` (� � RF $�n&�o� !�et�&]�� �g ly-�e"� b�s A"�n) ()9�To emރiU5�'��eb esI!��l�!QR'!h�~��ed-off[.. GA�6rH,�A9��*�X,1 ich j!�9" F9>�I�. Dla +�� �[\+n$ F��> varo2(-� /n)+Nd�$*� !�Heavi���KYw�� 3(0�\2�BILtE1%s\r�X $H(�?.�B�$�AwE��!F!��e���H>�H alig�Pb )7� & & "H F�\� =&�G \\ &*otG [ 2� }{n}2�>4]fy28wl ��<�]T�=�=���&�5����B�>�)/5cayD$*NS�#A'|*_in^3[)!�� F�W f�A(�^�_0!��8a��}%;&�L.a�exUI �s%wa.� is ro� �n�� "�mHighest-�VirasorE1pr��(on65v %}�jQ�5�n���$���z�;v,��~�FKed�TI9d=bNZ�uni)[, h6�\������a:}�$p�(EUr!I�\mo�>�E���+�6es�so-~�tini�mx{��t72� $V�!�`�av� w�ll�[�@��2 � multipli�\2�R&�? carre�n�'ch^�;�.we�@ )!J6a�'n�V�+aa��Az� BottA�m�bLA�A A~?W�Mr fA�IXe*w�]liter�(M���7:�6�%&A>�8re!��B&�� Bb"ZP s $L�($�lZZ8*a" &�kappa$,�a���aaF�h[L_m, L_n] = (m-n)L_{m+n} +��1�0}m(m^2-1)\del[m+n,0} m\�{(m, �4La�9eq:Vir}����A�$[ <,L_m]=0$��p�>� . A Q�r� �;sA��TEif:A3i�c,h)$reiDs $ Hilbert s#9 ��_{0$&a� e"a&\DD_0"e��2*�$\ket{h�_.U7 o��s F�Q 4&25�*��i<`uc\b;�� ��e `M� ��' $E@g r�0(� �/es��$ ifie\�,FQS84,GKO}. l�<s 6.17(3!n 6.13&�0 Schott}.)&��ot��%$rect L��is �c�u bey�2&N 96$cMrhZn&E �a- 6 g8�FlyIMO.'� �_|)�M�4\|^2 = 2nh+n(n��c/1.`_1HW�n.j F*��I��2�E$ur analysi<.2m|)$�WH�UA^�&<�e�-͘iA�-df}-�. �9�o.(�E virtu")�c��,�?��v*;$� n �/o�F�ki%�9$-eigenm��dexl 1�U%0Gram--Schmidt�coG�+ F�!��{-n_1}%�$_2}\cdots k1�$8�$n_1,\l",n_k>�; a|F��+ �� >��O3&j7$ $S=f� �"!<_ " �$>Y�symme�%�A�an �1of Nelso#7coO�atjz: (�E X.37:$t�6��*X�ERLt,� $A=-3f;$N=L_0+� �$D=��Ien�.})�K�a�)u>�j!�c �$L_0$. Henc�9th"�׈Tq�}9�i�*�&�&i4[* �m�tI7�cr�N $A�bigcapm�NN_0}i)^n!�6��LFr\'eche)5p��in��d� %�s���to�^n e�|$=r` �E� �eTi�n$,�M � 6�isW(a)��a �I$�eM%  nKI*�ei�6{ Ei\protect�/Qnow� o d&b�E�$"Ss &n&?>wA�G=h� in&D�:�*Tf�_�Wev7rr�*nR�fLL�&a�d'E�)! �3�-assembu � !Um ~�. Exp}'& trol�t�+"�!�nJfs�1wQ4[i_��:X�� �l.r�>�&J�'pro�|w6��p��Rly�^.! p8\cU"oqm�+p�Q?e �\H&�%�a�$\PFI~K \�- �modul��s)2N=� /\TT !�.�o�i�u�P Xy =�>,(  5er=)� J��M=$$As�"#�� ЌͤGW} add�2h��_+�] .iy� univers� ver.(2$Toledano L��o YTL}�?.��a� $\U��GJ&&�qai|<Gslema7��ssignx��t*a�catBs2�.u��*�2�6� s�i�@t help�M�tt{|)�rephrC����5geo� �U�\Ghatu."`���\'<s.G���]J� L��${(g,V)\in FD: \UU(g� p(V)\B{ �p:y�X.�%he quot�,S*�M� in �!ion~5.2�! TL} �Ɏ� L  )�QT$�s �;�0�?a Lie�Fa .a_�prWpa�$TT$-bundle���.Q�� \pi%U=g$):SQ���E�8�0&�H=[gA=)Q��xE�isInWval� �Fel; ng a.O.,H�z-G. t= /�wK0m�E2:�!�!E"b��vy�$ jc�b1�{N %��r*aY*� $U_�Cloc3-�b �,at (i A� $(g,d )x :(g)E��rom $Niy \HH^{�}�^ N (ii)� � �  CQ 2� . %v._NG�v0.�r;s}.� e_{f}(s))Ng#$|_{s=0} =i�f*sTLs�/^�s1)`%"h8KIA9a&� )0)=%�&�1e}�vf-w �;g=ng�&A�$f� Ds]P�nd6�,��&�i a�Vi�!2'��'$�.] ByE8+rr �s*��nexp s �F�49>�V=�e.:��HU provބq�sol�#��m�[�P2�of A��6|is� onEN,|��HH$& cq M�T$�()�(!�e�.^(g)�?v&���>V�%uses .Fe@&�b��a� cocyc��f�ӡcohomV ��7c\o�f�$ !S..PE>� le�7�����쁟���� chie��bU.+ �$�b2{��} T�(a[�_��$gqf(g,"� (g�O����*b1..�8IF��D_XG$�&��AQ i"Ea�l4T" �&�.� '\e^{ic\&��B}(g,g')��|}(gg')�!g'�)J�,M"_�iAv�e \Vect_\RR� e"e)i*:nto ��VPA?n�(f!��!�x�l*` tF��� �A9�T\v��!� "�'iB<�w FhR -E6\> ��&�ZC �xE�: k�:} As�!z�t.�XA�:LieG3�S�"urep�]%�0ca�� nvex (f�e&e � "�_{2q�o;��:S7P>a�'s�`ݗe.g.,�` 3.*�Neeb}) �>~��[* ��yl s $H^k(G�InE8LScUOH^2ZZCI&��3e� V� M)!4�S� ~4.5&NPS86})a�} �ɤe� hat{nq�s.r$! TTN�� ma��ld ��+B adm�Э9!��\\:&цBy " 4.2�%t��� A%�@�<h )r 2-��� pK� G�i$�5 �m�H(\id,\idBp!](jVc$ctne �� ce)��| ��s������Kixz tw�s<%�I��%�C1�$%EcPB. ic*0: a��%7�:":^�>;N },���F:-ng'-f'g)�&all $f,g� CMQ2TW�nowA�2� "�`$ c��soWba0#� & .$%�h�m��)y*�y�6  <� � X,.�%f�#/0x&5?��� fn:s�i}i5 guarant�=e�WaY;4 ,DR�"-a6�j�P�"A�F� � � !R� �&�^ ݠ�,�b*�> *!� ��it��5bU��.��"fq ,t�7"JlW��: > Gm� �'z�.a��)�t�y�!uN�?.��tDSS)�.s�u�S.��.smy /-�� &��s}.&�>lJ E6�LM_3_edB�u�E��Hn.�vm*���.�u�*M8eI�l {\emC��e6TF'�*�  =As��(f)} \�,4 \hbox{(FALSE)."r falsjH$sa�R�[$BV���!T.� "�b�]DllI8*0�� s (a6�)o�urs�coW%ary�6n ��> �enO `r�!���10lai>v$birq*F:<A[$6�nWn&�/in&P�:%)wE6s2�8i�*w ru�s- �V �nex~U�O @{\mathfrak sl}(2,�:ys��V�8Ϡm� �+I**re; A.2\E�I�RU $h�$ 94pa@m*/u�x$hV>� ` �h��*F�/,!61�,[F$�"�E �, =2h$����sX-?���D�4%! .} W�,re�Xa�%��  c�(��a�m�$)�.� f C�'g':|��:2n,Z33irlyi�& !� W�%of T� s $H�%Aca�Ž.; chec�ae�*�%��-��:ew} $-Y�N�DD@!=! spa��$ up_{L G}*[g)5�DlX*DdeFR('!�^"I;e-V"y�j�A��$ �A>�[� ��� �smW�$_s���2�Je$+�$e�� "� i]=TA�]lm�:%q� D2��{a���"�S,�&A�%� B.1 (a�  t��I��!��\*3E�d0�*s��woNo��R�1dm�0}&&�!0'$Sp6  !�e� �G .>*I>a-��"d�r>*�)'=��$:O !�,]A1�9�"�e5_2��P�lso w~# eͥ�9�� �E�$^<�z2�g�N�F� =Z�� �(�dz9ly%.C15"�Rc�! �� �+sc*>4> z-,1}$�&� te.#tx��'�6R.*�laF��&� �$Φ� yxE�#{.�>nŘj�E�!�To�:��:�F�B� > .^y!*�N theI�a�&�y� excepk*os��KEng�:7itcC;>M�1^Tfͭ��s&?9CF"�;*a�W%s}�a�:�:�;��Ee6N. larg*5�N� ^ our ^5K6�byI&{I�!jE�^�. St�;ng�+CFT�dCxma ��,< u�&2�,N�HH=��4oplus_{k=0}^K "� _k��^UJ+� )>|9w| a5 K�I*q$ $0=h_0GE.`$uH!H$�P9� = (� 0},0,0�4�w�kg���-esW y�t2�*�)^=ũFa�equ\i�å:A�_��9l&v'>� � w�(��Om6in�A� c r�n���]Eޅ�"`� �W�2 �@)��Igs>u�yaE+� p8�nmhe�2i aeba�j?u_ 9+33o"� s rmF:\HH biV�4_L,h_{L,k})}\oL(q�_RR �2e�"���i�a�u��� "�� E5 $( s`=(0Q�!�e��k������ )=Q� �N�~)�! �)�": �P�D/:6u�-�p|#�� embra���0m.� �r, �@f,�AU�-$K1 i� �xs7+�9l�]� :@M%��Tth!]eor�� ���n;5��A'superc~ɸ�+�;}�UWZW�A Witten84��Xme��:�Ac@ ledg� s���i workaYCJF�(sa�  EPSRC Gr�/0GR/R25019/01 ��Ul,=$f York. SHH�J INSF G$PH00-90138VEChicago�;6( PHY0354978%�by"G�rof 6�Cal��nia. Pn�� is$earch }��,ds�dur��!�,2002~program��Qd�Fi4��y��Curved S�La�bJ@Erwinwb r\"o�>Ler Institute, Viennau�w< A��ʾ-E:�hospita�j�p�(ր�uenefi!k%con.��: icipaa�% 0[� u�i \'E.~�l4, K.~Fredenhagl$nd K.-H.~RI[.I<ou�  O)�0ank G.W.~Deli� 4nd I. McIntosh�� y illu2c!�&mDz0u,$e�yE q}2v:Lie�p  \a�� "FFS&����Schwa"�tA[X34 �b�FdP${ p���var�=No�  ��O&�I��6s�]; !�&� quitey+bably�Yut��7 d%Kcomplete„�Rt edO,�����_6$of Taylor'�V7,���D�e�#�#~��|Glaeser� p.~86&�ODimSjo}ks'�� � (Lem:poslem}��O"v��~n�!��% �r� �%$M>0$�Z�Fs��NJ�4MJ{1+��*c%sq�Bi+N2 \��&rf $|d/�[gZ|^� M/(c)�����(��!:��#N o�%�I� �$mM-\e�� �w'w.W9ta�no=Nv lKP���,2�e$et $M_k=\s�v0r\.*�>O2�%F�0 G(v"ӗ %�[!9S~ ^ ^2 *��2}^2 ���)=� �R�� $1$ ���R!�$>���:�çnd way] �EAnyF� ao$���)ell su�_ly �$|vA�sou �\=g(1Y)/M_2X*QB�bM= s $|A,|aM|v|�rwdndJ��1p^�]�%2�} |v) �>�}!�2}-�>*E�ll)"�~tM� v_0>a�h :����-C$M=\max\{1҃M_0��_�;,4M_2\�V.t��Cor�CoW��� �U�  $FUPphi! =!`ft\�C��C�3q �QphQ *z�1 �=�  \�!�w7!6�=s�*� �H�!�>}�� >XQ=I"��I2��**�.�<@�iva�e��d�z\lw�Q�`6 0^+}��]Mu}{4:ͩ}\aqB��AZŨr>0!,�{�z)� (- 2�- + })^2!�):H}� }$�ʐ(�a!m�( 0^+$&� J�l��4v} Zo�R��5i \4��>%S}{2 @2�}-?>�C�V(�VM�9� " )^{1�DFBM�MAz�� fEv��by� �!*� . (# ].�,L� �v� t��gle*o[B B�&0�K!�l u�Ya � $%"*Bd͑�V-�!X�$ �$! es.)��a�Q2��(5�*Tr�U�Q��deT@�[te�� g�ccu�]dFڡ"2p.2� emi�CVph�[I�}�&��*$ �#s��| �#%�!IV -3R~U�� $ Z��thebibli? phy}{ZZ} $�bjM{Alcubi�} M. , `qDarp drive: hyper-f�YtravelXin�Ĺ6Y� ', >C�q."�Grav. {��t4(1994) L73-L77#\b �:H, D. Buchholz� H.� Pulz-Mirbach, `Haag dU��&�2+])�@y', Rev. Math. Ph �2}�,0), 105--125 �C5� �S. �M�iner, `O B� �#.�1smXE:�f3EN�{\t <0th.OA/0407190� �� Dim� J. Sj\"os9*d, F�N%Saڷ&���A�gC-W1cal-�$}, LMS Lecx2 e Se�268Rh,(Cambridge U&�P&?, , 19996��4EFV} S.P. Eves� C.J.�z�R.�^, `�Ine8i���  Megp ics'�^nynri*�2I6} (2005A --302�AGWQI}2� , `Au�p*#Uti�NCf7 �00) 1897--1911.�LisbonB�Z_�-2', Expa������$"[]@pp&�Procee.A�E( XIV �Dr$y"onf!]>:n ade�rAFakics, �,�3�M�(-ph/0501073.��|I 6�E 2'`'��"1^ey��9Ufla5J��.�)D58� 8) 084010.� �MistryJ�B. ]�Weak J� a*�!}F�"�',2�M�8I63)����qO � PfenR!J�Ma_ R�`AUTR��spin-onn eǣin �<gqac-u��A". ѥ�44�$4480--4513Jr"�~BT.A. , `NullQ��Q�V .� � 67},�3) 044006�Ti} F�E. Teo,���"ick-A�sz�%.59ɵ9!� 40162*Vd4�J��=��]�%<)�Վ� ', C�KnNW25-@2) 33�[596�lan!D�A� naga!����N���v�� �F�F�5��<1997) 4922--4926B��02}�� d*'�)5)��!�F�6��)�072�$ord78} L.H�od�Vco��ye��z�O�� �"Z$rmodynamic�q���.A$ Soc. LondG?Ep36a�01978) 227--23:-HR!� .�A�rlf ~2�Spa�S�bw� ntum&vm!�5+jA four2S0 !W'R�vi240122iRworm=iF�Q�.� �cx iLJ/ rs�<mh9��Fes'BxF�53i�(6) 5496--55:Rqis}=mF�"c��onZ� �N�5 �47) 2082--2089. � ق6=�S�� �P.C.W. ]�, `Ra��1 "�m�w�2^E�9:!�q) al anomalP E� R.N�4�>41976) 393--4146ST} P�l��G.MH tkov�,I.T. TodorovD 6��+f/2,B�,Riv. Nuovo C�7to,iu1� ,89) No.~6, 1!h6�>Z0 FriHJ, Z. Qiu�S. Shenka�`� � F+��2(a�c�V� L/���!��N;]�Lett. �5 �04) 1575--1578.o"�G. R�`Racin2r�>e d'ueo i \'�  @BdA ��Curi! Gren�� �1iy63A� 3--26� �[AGodda��A. Kent2,D. Olive, `U`b:%"? &%nd�er-�C!fJ[��� 1986�.!Y192XW����.�1 N.R.�WViP&�NI�@ ve�&N�2�+V�� unct� al� bf 6)o8{ 299--32� �?Hamilt� R.S. al >� *�gEem�� NashA�H Moser', Bull. Amer���-P| 1982) 65.HKo#�_2��s� K\gA@yU'*N*�^8Ve8. �61 82B �abb{>�A !G% "% in CFT${}d�"'x.� 3030532�KRYE`J. Kups�W. R\"uh�{$d B.C. Yun!��w"�1$f6� �g.�g ��N�eυy,�/8 75) 11a42*!&�R��"K0!  , `L}���`5�\ QFTJL �1� $4) 909--9627 Lu76!;M.&9�>per@1��e���th"V'i|9��6C&�$�� .���fd50���23--52wLusMackHL\"{u}� ��GA�ckm�� mome� Mzx�nN� �1+1.� unpubX�d�"uscriptI72 ��I8Tdu<"�&*� t�.[&����m�&d�%�'��8Non`"urb��2�i ory:� NATO Adv��d Summ.�$9rg\`es87)} �,G. 't Hooft,�t$Jaffe, G. �, P.Kot��tora (Pl�b{ New  &!1882zMilnor}a� � em��o3�f��B�# �C�5in)R", G�F� T�WII}5Fs Hou�� SeXL�3,�(B.S. DeWitt�� �N�`-H��Am��dam>4�S�@(MorrisThorn�S"r�(+%S�, `Wo� a��{e>)Y�" �$8rstel�%� l: A��P(t�!P/gA�a6+ Am.!e.��88� 5� 2l�Da���V�C>Rqz�%N[�\v+ � �36�o42�4OlumGraham} K. um%ON.h!�`S�1c:� � Da�-9wall'6�*B��55�20�17�72 �_em��J.*�"� i�y!�>AR$romagnetic�V��02400902)�%Y�FPstat:% L.&�ScaAQW�D2�G;)/��R�E\�-&��348i 5:G P�~�u unphys$ #�]``?<''R�j�!�� 1743--175 "EP�I ��Dlec(G�bgal�{em Loop�sW�a26(OxfordJ� �B:�Pukz4 L. Puk\'anszk�! Plan��ee��`U=:�W�%�*$�8 SL}(R,2)$N�Ann"W�$6X6--142�RSi!� R/;��B�GmA${\it Methof� rn ="�)�(s, Vol. 1: )J,g�Academic)�,2P722P�_���� 2: F� *�g.5�r��56�oman_ �ew}:�FG���*n�*I!e+�a�~60 Tenth MarcelA�$ssmann Mee% on G�3�FjGravia�o�ftt gr-qc90:Scj!{ enl"�2���otob�2���a,ics m43, (SpA��(erlag, Berl�xe�2QSa�81}}�n,�'��&�zaliM!x6�f� 8� 81) 30�6�4StrWigh} R.F. ��aQ A*tmJv PCT, %���stiaYA/�%�)Z�PNY etonJ���78)�]TL�� V�lK\V&�緁��6�5�7R�16�� , 478--502� VaradarajV!j��G�[y8 ��/�� II::*2_ 6z20� 06406�Z�� J.-B.  8, `CFT, BCFT, A�>DE and all that', {\tt hep-th/0006151}. \end{thebibliography} 0document} %�� �� + \pgap \emph{Acknowledgements.} The authors are grateful to Machiel van Frankenhuysen for his comments on a preliminary version of this paper. In particular, for indicating the current, more elegant and conciseisentatbxe main result \eqref{eqn:final- �}. %This insight eventually led to a drastic reducb0in the size o�e proof Thm.~\nthmBn,We also wish^xthank Victor Shapiro for a help!y,discussion �perning Fourier series, especi�$with regar�the F surroundF= b times h!|�#\newcommand{\bibgap}{0.1cm} >�Uvol}[2!" (#2)} %EW,|R7info}[38I�#3F�`pubB(�VA< \begin{>�0{widest-label), ��$[0.5cm] %a aj(item[BeGo]{}A${M. BergerŐ(B. Gostiaux*� {Differential Geometry: Manifolds, Curves ��Surfaces.AEnga` transl., Springer-Verlag.,Berlin.1988}��x[�gapJ��2��9fO�XMinkowski measurability� f �2j$Proc. Amer-� Soc2�}{123!�495}{1115--1124b� ��eLGa]{Ga>�(D. Gatzoura2�Lacunar �(self-similaipstocha�n2 set2KTa<~�3A{ 2000�53--1983b�A8� r]{GQR�P{A. Gra. Tuba�?A{Hsecond ed., Progres E~.}{221]J,Birkh\"{a}us2NBoston*200!�c >_ bi)�HaLa]{ ?A_,B. M. Hamblye�,M. L. Lapidu.�RandomQS st��s:� ,ir zeta func� $s, complex�"iQ8 8tral asymptotic.db��!I,No. 1,}{358}�$6}{285--31� e% eL> C. Q. Her(Generalized}xcontent, �um}| drums,>8f� Riemann%A-1A-��MemoirsJ�% 608,a�7A�9 --97^{7Ee�Ki]{Ki tA��J. Kigam�,Analysis on �N.�@Cambridge Univ. PA� X?  2001�� L]{L 9�A� S. PA�l6� Packq �m coveA� \fns!� some6H�&�{Indiana ��� J�  {}{3!e�x {699--709^�: L2]{LB�6� 3!4Renewaeorem�6Dsymbolic dynamics,� aݯ� �geodesic flows, noneuclidean tessellae�%+tha�- M6` Acta) ��� }{16�. 89}{1--55�Nv�La1]{La��1�^MoeO , inversemqal� bl!� �_dDundee, Scotland, UK, June%�.$itman Rese%�Not� >  S��2899 Long:Sci� fic�Techn� ,"donE 3M 26--209� MaA M>N2vHo i2� TheuZ9�.v���� Y��Lo�et� A8.} � : �9 LaPe��Pe��:�� E. PE'Pearse5�Curva�T� e / tube�� mula�compact� =iHin|par�Z�Ԃ�Pe�q5(F�^�� ����:� of6Qtiling���o)vo1vR*�(C. Pomeranc2�Yg-� \fiЁ@one-d�alZP!Uv�5L Rrw3)}{66� 3}{41--6�Po)�o1��Cou�6exa� ��modifed^�o�|B���� ��"�  PhilosBtD 99!67--178^, I�� La-vF%�-s� F�M.0� &/ 6� D �E5NuT` y: CF� *�q9 zeroe�ET� .��0} \\ (S* rev.f enl.8�app�in)'D2006.)%\footnote{A-e ref�c�&ttpap�reHA�first�*�r�cmonJ \cite{)�}.��E�-vF��z�V�2 :%9(Diophantine!9 roxi�2@J. Exper�E�]1n12m»-vF*  W�E� ity,2�;V� sA�GR�.�(: A JubileeA�$Beno\^{i}t�delbrotՔ %(2�� I�� $Symp. Pure)]"�77�  1Sn�8Providence, R.I.��349A3��Man]{Ma�#5�B.�Ma�=H�LBH of N��)B��W.H. FrY 3� �!PB�$�D MarVu�rVu�(O| rtioE)$M. Vuorine2E Whitney c�(, $p$-capacEqAa&i�g$ {Exposi�MmF �}{82 7--4 vh Mat�1�Υ�P� ttilv e��of Set�M�E"�Sp (-� +Rectifi>)=����1` �M Pe]{PY:^� Cano� 2�k  by IFS,! ri� Nov.�#5Uy14��� Sch]{SchBwL�hwartz=%XTh\'{e}orie des Distribe.�F HerM Pari.5196!�B3MI3 Sch2�2Q�E72� 7A9M�th,E��,$ques pour F �T�bF�Y �196� >� �t]{St}t S. Strich!s, )S.*�S �3�Qforms:I2Z���39} (�,), 797--817; IF^G36 H3), 33s 61HI~�42GG 411.��Tr1]{Tr11�!g�C. Trico2�Two \de0\d%�D!�����'6 )�.}{(1982}{57--7{ >0���Tr�m!�E��/cgM�� D�.RB_>V�9�z�We]{W���!eH.c ���?��.��J��?6{}{61G 39d1--47a %(Re��ed84m���: Gesammelte Abhandlungen} (Collected works),� s. I��IA�:3,liJ�J68)��Zy]{Zy-!,%�A. Zygmu��{TrigonVic � 9!OYz��ers �}195�\RC&� \s�on� utV> are�|\b �:!-the- ! Nowy$0t we have est� e.$preo�-fl$-�!��TE-he \nbd Koch c` 0 $\preV(\ge)$�����ula.pDE(eps) simplified}&�$`error' $EF(we can find$exact2�inner2� full�H snowflake as fol�: a��! alig�� �%�$&= 3\left(� - �@\right) \notag \\3\t��\1{\log3} \sum_{n \in \bZ!N X,`{-3^{5/2}}{2^5(D-2+in\per* + \{3^{3 /3(D-1z/\gp - 653 ��D (-1)^n \ge^{2-D- �� :�( &\hstr[5] @ + ��B (h%� + 1/2)yb_Zl�-2_4\gp3 + 2\sqrt3 ��2�1Z��- 1�\gtF�v:&=-�rB! ��(�(U( � )E.YQ 36] � . \vA2.2U1k{b_n}5�+ Ib_n a��Y�:n�>� �(-%�EHog�e�RM\gd_0^Y� �H �M�|I�M)�, ���*un��̡~��,�� wher�w � $ is�"DKronecker delta. arefore,�P� �e.`2�2A+��" = G_1i� �D} + G_22��.` ��D� odics $G_1$�1$G_2$� given by��:�MPfn�troduced ��:a~��a_n +��M�M�N�1�%(���!��#r�>+{%\; I5S��\gs�E���A+%�5jHAb> used����q:a� �{-tau_nE� i5�%�& $a_n-��$ (staG explicitlA�C `!N0mean-coeffs})� We wi- rearrangeh�� so to cm �/ fact�ofA�IFAMe%usplitH sum:��^� a�"*5N2�G1 aft�-f1�iXEF�� A�.�2���E�{�\}^�E�ZG6becaus�<(ai�:=FJ^�\�anda�(bf@b_nR� @re eau ,onvergent: $ �$� T s�, reas�0%�YHj� �on~ shJ �b>9 }�b(� asA2)� �1(m=0}^\iA��\{(45 ) (2m-2)! ;( {2^{4m+1}� m-1/�m-1)! m!-+� 3^{2%-2"8 2>4}9 #� ^{-\{x\}i6�1X�4a well-defined�0"Y in�c�a Y/lm�tegrable��;%Dprodirectly� $|b_n|�q c/|n|$Kwriting!i)��+�j%�r�n!�=� _n %aP� m=1%� \gb_{m,��J$��{+m}{D-2m"v �� \q���1 } \qe�Jum \, <\iy�x6�The_+��I4 leaJ/��-� b2sjusNed via ��,``descent meo'' �$q=2$,!2 rib�Re�2 rem:!Mek�below� !)��� -� sid[b� %�U@@�Q&�3�thus Q|(pointwise oJ $\bRA<ss] $�T �Et3seA�hat $i��l�i���'HCon�red!"]�'� variE�$xa�(log_3(1/\geh � bothj ` 1-qb$ \cI5$0�q x <  h$A�!< x %,1$. Further,�is,t�2itsmitval� � posst's a bo�"d jumpa�Qinu�on�+��end%s!;5may b�(e �1Rf�%b�� �5w 2S6Although:h$distl arguA���obt�5bk�!���!FR�!7ha!1re{0"w6pieceE�\cA�\fn. TA�� � equa4:;6� ac�6h�1]��6enA�f"Y��L�8(r7s= (still validO!�Re�.y�Di�(let--JordanaF�) }[�6 II.8.12� k at if $fz uF!8(-R)a4Qpe84 !�A�' Αf.to $��f(x-)+\]]f(x+�/2�% A�1s��above,j�Iof� ��am�R by {6 4.12%}Q�a�(%F�%*!,growth orderz i���= O(1/n)�R!Q} g_n�[/ 0s } n \to \pm�P) %6TFin�,2�X�)�q��+9 yiel�  YEU��B���^��v& �\ga:�!g_� (+n}� (^{-i(\ga+n)%a;[8&�sj �qbl g_{n-\ga} vr� 2� &G9! �"� �/t�"em-Q��cf�b iTA�)GeX$\bdd away �50�3"�a��qge'i� comb� � substitu6�2� back�/o.�:� E�re� A $"P=��ft +�] �I\��)/�*3$ 6� BL }:!TB^}HG1D��[l �E� fra�i �d� +J�B% �iE�C� �t. �7pu�.ng!K5$ilarly%�� eto5z��zP!�b9 v=� ��b�.�&t� &�< � ^�< -�G<�>. is �(���al) step�A�deriv� $ is necess7,�to groupE�6� toge� &� . Our mot RA#�%is�us�!����� o~�a�� �remarB"M�reB< ( %Everyth~up��?:+; howev Hy�[96�� nd��not� ; pre� �A�#�nc� !7:�associ�U?�;er�.z!�� I� &� ��g ngR � s $q$�>(�suffih-�? arge"a�so�on.Z��A�en� voO6�2�w\ be a smo� \f�)�involv�,l ab�1ea�!wth�P$Weierstras�e~ cppl�2�A� i �,6%s XAterch� ��T"!�R �wea apa:�!h�\nth[q] �'q�v� A�3: 7  en%�tak8 e2Oa_0(%(or `weak'!�Y!�-�to��ho�!� See � � 4.14 /�*. %�fB  detail� How I5XJ%veIer� need� ba# pend�6%$J�8� %Xlynom�=� � �M of!�q��  \cvs ly� s ��i6�\���.low �$, i.e., do�d�a�0$aI-�%�Iq ��(c-and-p-as-�-fT'cJ� � �13� {�-Dj#}4"�U� ? %= - 24;" 1{8� � %"#b"� ,{(\gb}{D+i\gb�I.9�`#>u e�y".�q�2��27%qa23 M1{~.�)\�� �6�E�W�J$B�$"�.-��i��&�C.&�PASto62*�O,A���zA� �MHU�EA�Q�%�E� = ���[IY + )�.�]�jH"\&��!z � ��Lh �"�!T &0&/V�!som� &�� d t oscilla�:multip^Fve�Ha reg�4& twee�  0E�1Z!d�F ng wpo�0�!��"�)���D%�qed� 6.)�k69�!z �O �N9*&6 , bu�(do $b� 2�/ity�of $K$)(it�:$-U 3;� � =@h�f\ge3)$.��*�s"�(-fd) termE��'e"� expa�,YR�2��Vexp��MU �geA�q�a��v �\ga��i p.+<P��( ;,(d(i x} = g(x�MŃyaG��*P�cp1U$ anmadditE�i(&� fUx�[ $x=-��_3a�\�')� it� N G 1IO%�����%in mindB?ex�.A��becomeI�6%2�Q:�%�� �J�We �8e� ?JdM�ῂS�zG�� cu)aP�/ �A~ �7a sketch$�g4S,�c���O8n%{=�b�� a brie 6*Q�0 ofXLertie� !�%/���"�Aɩ�&�$h= a� linear} +( r� z4Cantor's class@WstaircasrRngu�J\fn;},%nG<�P��;8C@. 83]{U7 �L10.mB�491"w-@%��!xstandard � �at(m�f ``�( Devil's S�''Ÿ�:�). 5J� ,We now retur��compu�S;&�2" �8B&���D".VB A�"�V] �aɭ�*� 9%C } .@^ &z 3 4"y b�612&6*4 �� 43� I_-1! � \�"�.� B � m�" � {(r$ :�-� �$-1} (�{$�� �4f{$�m.}F�^.13�_.3���-:�-F�3��1��J�z 1{3��&n �1� &��E5�(4-�%b,�+ \/; )�I&r� �0&�$B*0��Mc���1f��/B��� (.�%A ��F�~�9�:� (-b_n�2 ~ 5n_ i/.zaJ�!' �.^� �i � �DF�3�dnd��3,3t�&� ta4Z$b%�$�,�$d shor,Yd2��Z�3 ��S ((e4I &"�*q`>OqM-4) �:,:.�-��!nd r%ҵ1J���0 ���I>yird"�!(�ZF�g0�1>� a-to�6m-x}�# a=4/1��'�$� $a=1}�Q+ �� >oW(� ]DG�YsF� .z0@5�z�.\wdef�i3��R�!^ Fubini'sS� , ens uf�� < "�!ysu�O) last.�e�q�\V� . �)�X8E8i"f2&Y8186"fb-bFu1.�TBu koch-pre-28Rvf"A&{ gC@�hNic�Mru"E$K$F$:o} r$C�anA�&�DAw~i8ge->9�*9, �-:�8midneighborhoodel.�(*&�^S a}e .; �>&ew workEg te�� $ throughou  quel (a5'pi�;��)�)n$:�h� \*b7Nb:�NcA�j p:,��Be� I_2$av�in�!level kis ba�!o��� $K_2�!RX# stagfu2E��EN�>�)F�:+z��2ll�e�I"a�!��U�wk{� (4�kc;of� (�/ angl!ied�fringe�0hoI�pM.E=ermu ���B 8��u�'")o .P. A�Sse6��a�zj�O (?.P-r�0�#s}�% � such)Uj�\xd�aN'J�R'^�R0 smqVr!^B�I�)$Y�I_3+Vis�6b3$% �@E�2� ru��Aa �F�^�z� \parA�<"da�M)p��p length�� caVU��#-ap.��"d=_ valsD�U�)Fto 0^+$. �ic� , leaM�"��>"3Im�I_n25k -(n+1)}/� {3},3^{-nRb When�% �=4.6-�6� shifA/�nexM2vel�Y�. For&cF2�>�[? hows �IjJ2R!2:b�NC3$]Us��nt(%!�)�in I_0$,��%��7�1ổ��N preW -��$K_0$ %:]16]�9A��$�]Eetc� 6 > *�����2�s�\In ge�[���ip a �$K� !�w�$a�!���&� b�>2�nO0S �[�_3 f+�3{3h6+�2x\�h ��4� ll !�`$n$�e�]n$�"�<�wsqu�&bracket�"i� � loor5 (��%a�)!-J��>�xa�2x! >q{3 B�a&�which� frQ��veApven6V�P"� EQulEVR�e iona.� *8�x-[x]e� [0,1!�B� deno1T�aQ%Gal$x$E���# .�$%�2�,%�,xed� V��7 �(ing. To���*��s4usefulV m��5A5/D� I!��#��&q"�sA�those)�? verla"�,corners)�r�7ly� bMl� fJW>Rr-sub�X#:= 4^8%B~ Also�5��s� c� s�� %g�M�� S0 @ �as%%&%�$A`Co�%u� -CA�s��ve ,LeI�+e��4�$I!MjV6�$E��{����%�-�&! RCo&�G\�I $!9%8$=�-+ 51Q @w�$��23(�$1)�wdgeNGA�ZE#2}{6}@ Pu>P+2)$ triO jSe^�D�@{2!�� �4^n�<�%A � C .� �CS}9b%� I`9M-^�l)�d�yalA�y estaIk d (i�%a�%� (ii)���o:?*,Mc86*&+ �-�6�+rencA�01�9\()�4w�31�"�$�Ze s�-Sf� �Gi�!3� �) �ՋM�"� w.�}��j�=<{n-1}{2\cdot 4^j1Bs# * 1}^nP2j-1}.%O:�&�\�29nn�-95E�of IA���cleT2 ( \(\gI�/6,O?a� E�4alway�1��;; \gp/F )�(iii)U oa Mo double-� �*w�All>-!� keep�uck�� 9�����:�ac�4��A$w� P subt��^H priatedu�1��5S>�u>�aߩ�'F9�E!� Y^��H��Ea)?(�6� ^2 \a�{3} 9e� (iv)�Am�SHU(a�;��A3AJ �un h�(t�(}� is g�E $�0�}1e e!�� ��0�3Zs�)d�#�9��-$^�9�=� > ,�atop eULN�>� m_e]�Űah\pa��p+H6�%� � in�4-P�$ M�!R� � `4;j%11�.bse� �@`����M' d� op�?z�!e8-NB% the-8}M���� abel :&� %p #�j��]1="e 9EK m>ffn�!%*�}"0;fn:�d-nbdB} ��qNaiY)2�H&f{~ (�3Q�}{4� �H ! 2yC M"w62W\gp�,�qra�\i� @-h��}�} G�#6H� ��5H!��=�~:Qmis �"=�� E�X>�FiB�mE� (�sligh�1#30$�g=v�>U {]7$repancy isBac�e��a�i�jin�ail \S3 ⩒i�[ofFt�e^}Q7/>�2��>"2�  "5:�"�).} �4u'[tiQ$-� �,st�x!� 4^>B�=}A�,, � t � x}=3 ruxO2��EQu._QHU F {1-DBg>J9NJI Caj)�J��<u�0 $n=[x]=x-eH� ���ɒ�-:� �Ae���f��3&I AM��r*�� FMM�00 �Q_r��#�l&�"6K%8�-�.T � UG� �}, L twt)�� }{9}~ � 2�( }{18Jn-�2.(9JzuFz2r *�1":..Y`��3}6B�+!$�� 3}3,*�}B{f}}�-�� \> v4!�J0!.��5 0$JJ�6B�as)�2�6DPut�Us�at�1�?U~��_r�8 w!� u9�� �C ���_����-�(!;��l.,4-�-�'X�5It�, pleae� to f8  xqWg;_entj] ie��predia���%�$�4uld look like.��Q�0([�(9"�9W �� - �������-V6-�2� � \ e>e�]P4� u�MuX3Y_9^M( + q3- 1M� ������sW9�A�-�ML-Hin �3N? )F �*�tq#�(p �8W� \:y"e ��QTAf�Ix!`F�!)�2� �0 !�Fg:.�-��={-(2-D)}.6�KiE�"o n�!lso�r�F"�<�j3b�!�-u"Q/;q@! aU%�=M7aa�D*}%I2�(-/nx}�O a� gb�k%w.">� 5:B $a>0,�eq=J~ b�Q repe�?l�B2c.Nf*�Ki�YI}DH&�"AB��Hz@C nN�HJ�!�)M<� AI�vA�-L_=in�@;�xisG0tru�[fl1S/>i$X n"�R�*� :"H=���$"�!vaS�& J�lR >�EL���^42(.M�/�L�{4Gn&�1=2q(- a4 *�6AaVHA7bZ �l# -i�iVgAB���er = A�F�Vo�4ory��fi6pD��iew�Ѕ�K=�W� \!�&R2�&WA�F!� ��"x3!�$y���#�=&]%����~��� �r!遣�n �3bt�8n-�I�{_3�} !E:� 2/@$ =&$ ��* 7f )�$D=�_34� us!v=I~�c39�N�a�{� �6nt5睂ge}�� C.VeY%� � aw-D}}8V�-�3i# 2{].5y ^5"":E��� 4/9� w� j�32�)�4/�: O6:� �U4"�� N�NWm��Bm]� S2 ��A�285N".VK�!J P>)_ - 51I�"�-5/!w/V_3(-1 +b-!�>%_/2�b�-� \6�1 &�[50��13F�3B 2\Z � 8� 2a��j�e#&�-Q*�)�z4- �3�5�# cpA� � O8We cl � p�nby&SE� ��no5 >v�:� %@ ��� h-asl�%l3�us8͡�8���8a�B�8��8�:�8��: �;q.�)�"={h�e&36si�$h26real-�$d�5,Th+Vgm%Ta � $g_{�N= \cj{�9}$� $=#�F?  l +u�C:�-)�;s!'n�E%�J�$K�)�� :K;l��icD  3'FA�3=!��JZ;.�Al�y�-2dE:5q`#at� ��wou��Fg::��f x�th�1 � $A�:+1)$. ~Rs.&2*�V�m�-%D)T� �&|ou�! r�U)F�9r�+,np i�"-F� Q\(p&�pS-�l&NZ�k])ZS.�o"S_;��{%s>LcB�� �G1L�q BBTK �G9H!tsa�=~�� decay Ie�e,S \ga)&�+SeH0-Sv�0.u by:�4�S,� ��m�S4� FqZq��>Iefd9a �0Az�G�h 8NT��[!r-h}e�e�* \��[0,\gm)2�e > 0$.� 2 leq �J 4so� does atkW�Ʌ� 1n e.�?!�be���*ed� �(cAPe�al2<�orm acro�LJ�_ $� 2PK�R; seg~beneathmfy�Ec�#ɞ �cisa�e?dJ4)�2$�5P�vB�inm����)� foun)U �!��(i?-  A to b6�b[2:����k& \iy 2^{kt9A_kEL,\IQ �b&�E� kth-(t ��T�!Msuprem.�M��l�F!E�a[\.� �_k)-A�`_k)V+�R) / ;_k�"�&b cs�_con�%��A�\ge_k-�k��$,.]0$k=1,2,\dots$NI� 2q*deXing_mu}�In�I1dDS1{wA�a�AЍz�.�O.�0RJH2o.JIHar�%V( $\vol[2](C%�!,%`))�  a�fig:�j�2 \[s�"� {9�&" rMr2_:r%�#2_J#�t6pJd2}Q��d� (�(.e&P aF\e�6x!M�/"~�+d�O2$k=-)�in gr��$/eE�K���� �ll�5I� propELI�$�HO�$ae*c��A�J\ &mdn''Q��[IU�1�"+�on.')ru%e[3C� \ge��)= i ��� } 3BB'I�%�2.�%�s2^b�H@�� ��bynBn�1�sha�LB�^n!�%�A:am C";(\9(�P playstylek �w� Vim_{\vay+tai[ 0^-}�_k+���"R`\RJ+VJ \gm$ �����2 ,M[�- -k"Q?9gaiY*T ex��I�� 0��!�"*$> k}$i6(k+1)}"�FaEre8!a-����3�EnNT =|,: A�:49�.� ���3t htild�� !g�^�'\{�,-x\��%[.QMJ�ag#�4roMJ PHta4s�Uera� deed!�o$��s  �Qj2i�x>eBņe�F "cVlog��hL��0NIIh_vs_i�1�,a?c rast,�a �mor*m;ob~�e� dUwRs"� stud�xD�uke�mab70J�O �N0A@ �xon �yhe�7)�>TKŋ�2-��P�J$\E&{h}Jh �na�.*UI�jYEV�y%i:I�T*��l"��la�?M e@�hYorATof%�<"wOPth\ �f�� ƅ stigK3U!�^yK3�gng� J, e.g4}[� n{La� --2,Ma} 1}--3� eL.)-��--3]);O�.���i2\bR� SamanQ��)b,sIent4(aV�=�Lop�L"�6 $l_j.tP� -���:1al-)%!� \L\ {l_j\}_{j ,&A�#�O� l_j�i�>B~a�a*��>���e*TA�phȊ|��� f�8i��I !�u�60��E�at&�fP?�7�S abN7S�)� ��.+tS�eY�[�*� i�� �+alx* z5E��U532H�d�~;0a�cempty2ˇ�W�AT�-"H�<$5��� �!iVvU�(.�6}}�\gW*`fF� I@ �� vol \{x� \�,suth d(x,\de\'W)A2ge\�B4G�3 s 1-�$al Lebesgu"��aS"^j �MinÕ9�! eK�*�\gW (�Y)�:D \L$\ms� {-10mu}$ .3J�Bim��).D=D_{ � }=\inf\{tq 0;th-Q�� =O�1-t�&� e� +\�BZFi{Y,��1>0Q�lR)fE�*[ ǐ��T�$\M = \M(D;- ��Q �+}- !K!1K!D U� exis;[a�li�< $(0,\iy�P�Cis case,� l(��^Y3Q_� �6If,Zge�8�9A�i� ���/se;6\bR^d� t[ *og  ~s � 1� replace�by $d$� ���utF�VYl=o(H�E� �d:�$d$Y�al�|ume (� �re�#d=2�`&!Ue"�Mf�%�)�)ti�A�-)��l�� d-t}%5�y��!� ;-(dA'v>.',ARm).A):q�uN$d=�l�tp˄v�1s��aVength��0 conn>~v�Z (Eb��)A�\gWn�Hin�3i�?� %� ��s ��(�xg��"F] dom�le bR^2�"�A . Se��:e $O7 Tr La1E��tN� Mat,$�"!��relevant�=erA�� reinC a.�b5=no� %du�--"���+P� `box8 ��'I�C!��0��!�:� =FXE�3[ ��pol�9-�\meronZtn%�� ��&�2 �� �"B�<��-f1( \gz_\L(s)��B� ^�Bw?)ccfmcA$�Ab�� a[bZGf�J��a2� D_\L�inf \{\g�9�1J�$<?l\EnF��a�!y=�5�R�iEu absciss�D��%!o�S!ce�6�I�{��I4iphrŚweM�)�c��E�\LG"ba�A�sR�A1�LS�lex�9� \D!X {\gw� bC!NthM&\ e��'Vele��PwRy One��whs&���>imea�)h� }98y)كuDTfy4a � sB(k<E�o!�� "v� Name�%�6sui :�n�Wo!f� XA�L,!�A:!s&')�v��.�kB���-tu��)M�-�\ !�e�5�D} c_!{(2Y�e\gw) gw(1 )�!R�)�-B���zs�Dn�8% �(all} visibl!�J��lDL�BR^�+$ ��%�low1p7p O1�a�C"�D(&�dC'$6.1, p. 14*g)�u� �n�� 2y9ЉG� Z.��bR�7�sQ u��sA)mRsry�~[E|n{L��3��[\S2.:�V�����.��ce/�" ( dichotomy)*� CѪ��= -�D�>!1} %!Gely�V�8V�-b W w��� \]is,[@van�|I*�i<�v)I�s�lie 2on �aIsh"&�@!*d($\Re s = D$LR=Q-� �.���quasipah�f!��3?nd $s=DA�=S BQ;"8#_ $D$. �N�ow$uJ���*�q20i 5y ��m prIinY�&�.�A\L!�\� C\measl� M�i��(9C�y�Cha16 6&1�jQAlAra!Vc&�[2vit&~Y�#�QB�sA< � 2�i��Ta�v�c�is & wa=BmplKn�6���� ach,�a &�� �N�Xextene�'F he higher��alE�z/d!#1�{Pe{"�dM� --2]�e*xa�0�� A܁N`5prays'��2}!͍}c�Eb \S1.YV�i3�ai�1 �-: fs�\! stepaQ]K}�f�'N7"�A!a^ know�(!��}� ied)�!��Y"� ^O�|Ep!��t�hel�0�y<��!(a�!�F�&�6� a�0��u�1�\ a�c��Az*cB�)� a no�\ plane _mF�#!�6.&t.ed�f$!�de ��un�|mpl�N���$.\c�^2�0U & �z�fi\6tS6�Qeo grup copi�B�� �)7�'.�OF2!�J5��A1�Q��A.Y|��"qYm II.6>z^.��9d�i� ^170J16�N9R%�5 ~��\gW�* � e!6dn�3 \ oF= �3��A="'z"� >yDɄDkd~ 4:�y9� Hausdorf��~��t��incid)�AQ.��)�� struTby�� ��s2 az(a�DTUm 5]{Ki*�`.)A� �let�Dr� ��"6�">�9i�D%V$i= -1$$aT&i mapj& � J�[f_1(z)%Vgr6+z}&�.�lf_2 * 4r)(\cj{z}-1)+1""KEcU�+2��& �C ect �|({f_1,f_2\}$dfGun�*��6�R$K6Qsatisf� \(K = �K) \cup�K)�) � �� N�Ine�a** ��eryM��^�3 a���_JLW}�Q~a �%I7�.B� �V. �Ir� &>IzK�1R� F!  re.�2�!�J�!�J� $U5:=�1+5 3@F,5 4A��{��$"B�j  \�m#6�i%� % 3) ' .���m $ :�56�5��s�Sals�yv���corollarh=��.j9gf_�)^!��6�H2*y*H2�R�O sui"��(yf_n, \L$-A"R&lyP �N.!6b c�(�45 �[ A-5;).co� *'v�!.�k!� �b�&��a� ^|�B` c"}fL!-"/�.�(g�0 U 680-�t;0�"<�-69Xs�' .anewW.�>b�� a �r+ x& LS� "9 Հ \S10*$+#�'�W�B>�X:xNs�-pkshC2??#u. j|� �,�P�Uh#exact.0r5Png ofh!�p�%��ad�"�&l8��8y a�we immed�JAo �Y�'2�$mxwcor.�Q ��\B��ł6� ��t�&h ar!u����l6z \D&� = \{��a�th��!,bZ�% ��\{i�F(� J�E�9� �)illustu0J?)��sa�Q�8*@X ��!�CorMk^~!�'2A�0co~���\mP?%6$[Conj.~2\&in� 9,163--�3}��A˥L�2�Je� m�w �de������o`�6��r 1��i� ���C6NA% towarmoendAM6��!��9>e�)��"E�Aec:�):z.ce�&�*Z�L�2�"�4&' .}&�M*v�OgtQz�y��?P'!�G ng.� �_1~ rmi(+%� �c!h��pP� 87!5�?m�|QF;Vn~�e���) �^��$�W&B��A�toA�u�e2���'����" ��T ic2� ,*�1|�iB�,2e�'�"\fn�'Iw8no{26A30, 28A1275D80 (primary); 11K5 6A2778D 42A16Y:6�/oO\ex /inee�f MLL �� ]8sup�#�a�US��` ƪa�n�18 �|@nt DMS-0070497. S I� Centre Em��Bor�eaIn��* ri P�,ar\'{e} (IHP��En� 6des Hau5\'{E}tuSN�if}sGESHHBures-sur-Yvette, F� , duz ��le���%m��  gJful� &���*MLL!� \�;�in&&V3[�s�; !( em "�y��.O�draB}{fals�.51 %\re.the��}{\ensu� th{f�{\!}}6��qed}{U08[0.1ex]{\;} \hf}=P�[�d} ���S��"�:7 re�)e.}%� Tp�you�yPP&$nd s�tx� Vs.t�%ak:mGD.@ �$hope ]$R�?per�5Ҟ�i+� doe|3�  p1"�rt�Ia2 half�deF sVal ��,�7EYhag^a1�s-pƇfa� C-,BA<EO*�s;�'aY dX��PesM� �&�+�!]��*��"�i�E �sVrel�+@ in p��!3?��>�� �/Bs &���\-a arZ�q 5[e on�#��~r�}5�tZe�up���3blmWn-�s�corpoa�M�m!)f�)� text }E a;r���!�r�"k of (G}� � 4)Efel?=mpe�0oh��%���p!�� T)is �nE��� 1 erA;!dori3l)B�� ��!s�@h , albeit �*4-�"��nd �|-led,:�9Ĺm!�n'�}wS�Bed�lus  a�Q} x�8" ��4��muCa� -cc~Am%P�-a�E&�1�"!�ld]� a,b�,%_-N���. !%e9�A3NR d�:�&lyrr.x�V%i�* ��onJ� 9phe m(3.5):( ce� dit�su����%$ cp:� �� , ;m+index�r�� �y+�(f\��s�fy)�is� ��ch  e� resE��B$9?F +H%�paE�)' If��A��@>�.�M� �priorq,Gw��yE�#beeZ!�*�(. 6@b`A�(to�� !�!���� 1lweI��8iy�_arg�ea(%[h� �a-T!A�.��_ \\ B���*�y� !�$EPJP. \set�er{pa�@�v�= ��4W"8� ��ab.c�A��a{)�q�uv1�9/von� k!��a�ve�r �j��Ma8?QXH�P*match qu��Mlyi�Y��Y�#��:n�mi*��#lsoD3m*���I~��`.�':exe �a�a�Q-8� effi� a&�P)w�%��ix�alo9J-N�daN�5;AreflecI;�.�R�h�t {�pc['� �?2���5�q�/l�)%���&�non23 !P%�w�Y� \�5di�Bbr�� \input{<� }*� cs&�&�5 �:anR=!ei o [ ��d�ZIC+��-h� ��� ndix8bibli\�ye.D{am!�%2{f�s_no�{*a� vstr���\�scF��j{\� ptM�Depart!LA�M'&cs,.G�(of Californw�Ri�@de, CA 92521-0135e �[�El �M$:} \verb"lU�@a(.ucr.edu" R�Er:����� �ڐ>���&� g*�ACobb�ha�Ec���6b " �bwe mu��P�SQLlittle `"aKs'��w�\J��/a�gmS a cr�{of wa% ��(n ocean wav� �-= �O � � cal�va��zP �b�rsu ke�e�"ear OnK��@Yke��!�� T]f�o5 W�%&@ s�S� nu  M'.:�*H�!���s^ D��in� V5ow��inher� a& esqu�#e �� �-�^�*R�D� �N�*An ��E8$�� _�� vYAt�}�� 6W=aiw)neyg isosce�8Qw,i eA�E"t $A_1J�D�n�* A�g� �  B[E3��Ys!�A %�rEf� ��0A�� r �U s�4�n"�er�$*2`)Bg"�Kaa�to%�&}n�6e#li�j�Z� !Hj , caV�A� exerePd w�>qzi��(Cs�D�ie�s%�!�shB�Ooo� ck��8ab))H�� ar neglig�# . \��{F�v*i!N>w!�� 6�f ]�_ Q%�,A� � :%��p�g s2�Ps�te DEE6e�manv!5 i ��a�w�H&� � 2�Rn-)�t 6/o�: >��Ba�varDin&uWe"X,,2�L� %&�-]fn:�^2/x w = �g:�{e��A3^{�JEmd .)1v $ E�^%!!)�%����N<�B��=�}�n2B�(_!?t"[�Tv,is $n=CzYS%�F2�0Jv@8�aN%�1��K� adja�ZaD $A_kA F�*&bn (E�- Bg � XA2\ gPD�.w�s3^k\ge^D!a2�kj��$q"A@���ve��>6�z]2�}Ert{1-��^2F}� "�'�(RۀN�1F�N2.�Iq!�!'!��&�k.i.qc;�F�jS�) �/� .GO,�YX�x�Hk %i&nUM:��AWJ�UEX�U�(ge��i�E~We�J�>Gl "�D2�oa�j.3\( �JVx}"�i%'=!9\#Q�R1�R"�gk2�W2J�L\t�xk�ٙ+3�% �$\{x\}-k+1/ih"y4� DRBe�E�entZi$ 6oa1��%M�8�! �%M�.�b�NA�=)��Z�:�aC/>�X���a)  A�>C1*ӟ.,�d!R�\%a^��� !�8a%F�"��e x-� "G!�-[� uA����e&(2m)!~Xu^U�$�,2m}(m!)^2(2mS)Z֝Iv1-u^2A1-�k�b um!(h!dp� &8 v����|u|<1�tmXt�017th $u=e� w>U$� tn"�C�uarant6YV5ɴ)�2��%%�" yu�%Rr�ʁ�)�\)k#}�`[a���b� � &9/N�start���� � j9*Ι�E.���iP  eEdZVmXJ�U� >+�.m_Y�-9U�(6)E83}E� 4m+4YBP-�P1P16�Ti�]P  \�� e ~W1 /)1Α�8�a�:��}��m"]���Zz@N���2.�i�>}{( �).&BǗ\, *�m�k)��R 1��A= -1)2m}{2m��)�Q�Ie^j���.1��)�J1� -2)/�BmR��:�-A��m! �.R2{>n��2z��0>�J!�4�z��.6Ҳ��u]��W%��!���2O�%3�%!O3)}2C)P)�)O"��=O�j%P� "�M�<3� 6�\ggNT� ; <���{Hhg�{2Jhg�9��m+3�:�"~% rMF"��fou'�-#h>�p[&�q�AeEl�����6�aqrb���T�!�2wNhR 9}�s m+3)��)2.��;�,ch��� sȔs�0z�he?�b*�:}��/��vi#Y ra test!}&a��GBv�* retraceZc S� "� �"a�W�8|�'far&�8hol*�!!�3�/\ge>0$8� �[s�!c��ns�$�"6�BNx`'*tZ� .���09BQn� }8�L 5!**kM�#-!!U d:���$%vm��A�.�iX�>#M�J&� ivḛ� k)*�%*q��M^.�  �� E��r�+2 =��>J�8wa$J��"C\B>of&�ak � &�k)  �sub�E � grp:� H3�2(i��H <@:�#.?9% 9�ɭ2�&>^y ��F�d* }o abel%���=26eoc9*�#� \�g)��Z*���-kgd��> �*n��:Nv�42�FE���� (*�!�n��n}V"�>�:�6(:��/u9��t'�$a�?b�,b%��a�'A�c�.n,2� ԧF�t1�M�DWn-�?�"1�6�"�M�^n:m��a5�9 j� &= -E�� 5/#5�rJ#s��a- nb#s-z#s%0+\12%^B� N�b>����qFm k{ �;� z}-4"t{4^  � (4m^2-:9� )2m�}*�sN�Vš�%�%�!"J� sigmB�E�%� ��m�%��u3�B"Gm����n��,�T }�gn�tau-z�G��^}J|1N|-;�^|-�y�A�S%e&u2 }+�Ra���{\,0}eZ$-9=0�m�m�;��Q*!�Kro>F�j"K&I�;.�:2�, $.V�I4_*P"�2�\�q6Uc\iL!�F=2��U3S� �=&G{)�*|�8e/� ologn�("�;�'�="~[�xD� "� ��.�s �u�'�q���kD&�f; V�'"�'WCu7&�D ��6#>A&�Cin�2�hT0further discu�Ussed in \S\ref{subsec:formulating-h} below. The reader may easily check that fo: \eqP�eqn:final-result} can also be written \begin{equation) \labelFDunproven corollary #�V(\ge) = \sum_{n \in \bZ} \gf_n \ge^{2-D-in\per} + J*y* (,� end{.�\for suitable constants $k, \H�$ which depend only on $n$. Now by analogy with the tube -w (%�!<@explicit-tubular- #�-strings}) from \cite{La-vF1}, we interpreteexpone�of!)�=�Je asictE� Fig.~% fig: �� �8obtain a set of!�jkberrpoles!� the �ureIt \D_{ �} = \{D+I6A�th U�$\} \cup \{^ !5:gL One caveat shoulda,menaTed: this is assuming ta| none ��coeffici%�I� $ or 0y_n$ vanishes�,. Indeed, in l caseAaw� I�be eto say ) �>� are!��ot?Iright-hAsid�.�R�!AWeA�ects, follow)4e `approximate2h'yE6Ih:?�IL Mt]�-���onIy$ll numbersa>a� $Q�MufigYN|scalebox{0.80}{\includegraphics{ ~]�.eps}M�capA{��n��$K$ec$M�$. 7 Minkowski�� Ad$$D=\log_34 <�Doscillatory period*�a4=\tfrac{2\gp}{: 3}$. ���Z� \ce��inga�end*%'i�remark Oemph{ �Y(our methodsA� work!� !�Plattice self-similar �tal�((i.e., thos�����underlyAZ!�ratioI� nally��endent��as well�E other exaas�K iderI�[��] I fthe �XCantor--Lebesgue curve,aM�affine�aFom��have al��y Xu �cou!�par�K Thm��thm6�� B9squa�(ra�(than triang��$) snowflak ��By app)Yd�[ty argu�� s (a��1,, Chap. 2]),!� ~1�may^ yiel�a�!�n abou�#�!x2��2nonQ&Q�AwE�Q� N�I�com�P:cor-to-main-nondirec  ]�I.� poin�� �at�u8e present paper!��do not  �3a c \dfna�!��By߅QU Koch>� �" (orFI�1�4$ $\bR^2$)� stead���son�:2�!�ula���!�ve to>deducA�omA2�[2y i�! \j�6�q$K�A�t seen9�oof4j"I yt.� ��%}e�f i���sam��m�8��6L�I�It�� a�c `�[��gr(seInCor. � cor.� $-of-koch}) �n ��quA���Epl� o de��~@geometric zeta \f�} $\gz6g . (s)$)�i�? text�� actu��%�M(eV1 i3ly!g.jC-l$\mero \cnteT6��� }��6�n fact,� proj�i� �Mway)0A6�ti�^)'�� termE�an itera�#$\fn system �� R�� ruD �Pe� LaPe2= use�F |A+asW w9�measur1ediscu2Lc� Pe1}!� � a)� func� w�a%k gia޹��& 5�.�� then �e T!�-�>>to ��!<S �tribu�al inne�K?��6�)o� \bRd� � oun;%[ɦ6]� �stresi� although4jA( was helpfu� develop' n!�%[}n%�$1}--2], itAt�%aEe�ce "M�E�is mor��� e�I�} z��� rem:��a1 e�s�9>!�long-A�,B.4Hermann Weyl's�<�1��{We�( smooth Rie5ia�} manifolds�� 6 Gr})��we� lik�_ �zr"1\cE s $a_n, b\gs_n =\gtI %66Z b���y��a� pri� �3titut� !#`!�!%Ps'Ch�(} ext. See�!� respingA�a�ioŲ�[\S6.1.1 { nd \S10.5U�!a��A�b;R see DI�3}QL*�TAE� very di�ult open� blemE�$is still f� o��be�resolvue�ze one& al�of��a�ngs)2���F-�R�� A�J� co� !r� (��at�wiJ� 1& preview�Z6��F]:6� BL��-rI � � ��*��9i1e studiţ u%qI#��,W�,ejly!��5initiṁ A� Mell!� ransa�{a&}`Տ v%A7\fn' $NN&D$5ocand%� @� Fur� �Sist�{�68zW�a4$\Re s > -\gd$=��d���"[ B �$k2+ Y:"� j>�~iZ!Rul��$C$; �xe `few���'| �G �^�#E2$$\gd < \iy?s�$ � f`vi^�$.{$MRbe small�qin�`b�&� V Q�MoreovZ pQ�2�Z]Aabscissa9�converg.6Dirichle� t�lT series) 9�\AO�coinc� �/$D = DY�$I�\� \dim1��� ; so!�t!�2�beM�E}M�-�D$. Fi�� no8�accor�oBy >^ (�rb:�M�B<�� 7F�),�!�I��f��$6n�M-a�-�!V��e� 2J �G \par>D(Realpr!� ple.f X ��e_!� �:"���� I�� 2� �]�$-vF2}--3])Mp�vC�I���g> njug�pairs,I�attached'W )� �� �si� D$\cj{g_{\ga}}=g_{- $ �j�A%��� ) I+S� &�mean-�s}!�b%� everK $N$+ .equ�!e . �c)cy��[�E��a_nka_{-nSb b:� 0 2, {%�Z� ,t,�E�.�:P 0,b_0,b0$ d�f t_0$� lsm�= $G_1� $G_2�9V grp:A�M ic f5 MIr$real}-valu � greecIC�fa��re8� M area��-�u� 2�sam �soni� \fns2�rstfn}� A�1!�fJ$of:Va ity}!-L �.o We le�it�� an exerci��extremk � es0�e3to ��ll�$.� $c_m$Ű$d_m$)���� oa./Yrm }$ (� .,D��)< $m�NO%N�  ^co.� ��%m;��erm&i�Zm�$c_m:� %�aQd'�uU!e H�K\input lanlmac epsf.texmssymb k|fullrule=0pt % \def\figbox#1#2{\@$xsize=#1\v� er{ 0$#2}}} \new� ;no =0OL #3{ �oI�groupi�8\leftskip=1cm\r�pa)$ \baseline H1pt \global\advance ���,1 \midinsert � �3 �I �� \vZ$ 12pt {\bf\ \th Z:} #1�%� ^!�� }��#1{\xdefF }% \� edef{#1%bracketl}%Momit#1{ [8rem#1{{\sl [#1]!�!�e(rm e}^{#1}}1�pr\�g�ial{html:}{\tt #1}\69/a>}}%�a�a�"7t #�"refs % %�bra�!�< #1 )�|} ke�|>bra"A�C | #2 H>- tr{{�tr1,Rc{{\check Rpf &Pf der{!�53af!�V_2HLqed{\nobreak\hfill\vA:\haI heA�.4pt% \hvwidth #,3pt \kern3pt>#}BM}\medA�\good}�8lref\Kn{A.~Knut�$Ex040747>�two�� II}A���LI'R�9572 8LLT{ A.~Lascouxe�Leclerca$-Y.~Thibong sl T-�ai y�p o�'�homol�* )flag =}!q,it Banach Ce� Public��$s} vol. 36e�86), 111--124. &�0LGV{B. Lindst�mZ sl O �͛"� ][in�!de�oid�,Bull. London��$h. Soc.} 5�$73) 85--90I�I. ;�l��$X. Viennot �Bi  d�min�+, patheg hook��;A[��Adv�. } 58z485) 300--321. 9� star�(LIFR--MIIP,�,�)�O University, 119002, Bolshoy Vlasyevskiy Pereulok 11, Moscow, Russia and Laboazirfet> \`eles S��st!*$s, UMR 862=�\'e� (-Sud, B\^at�t 1` %-405 Orx-6$]$ Z$0.5cm \no� W�n�* a"2 8gr� iQ�eY�d�F� Ma $B^ %�$ �properAwA�itsŋ"� eigen�R(h c:*�!der&$4�sH s,gshow E�of^entf a�""�> �.. �M� $TLaV,:'!lqUhs{L ,3 } led" �S7mco�%�f ��each}\/%q_ !�2o\RS-8^A� gene�( a loX.� v�_*Y /� er!`s �5� ) bu!�s� ba �, ed y\e�Q jE. #a�st-�� fall��f��*$ described �$�ea!:���osa@�/&�"U�(!�6iBf:G3tandar*< ) �sEy � 0y $OSp(p|2m)$Q`MR,\MNR}, $p-2m=1$. By ab7of� guag<0! �2�A� shcz& �0``H''5 � #A e novelty! !K%g%\!%�j� ��u�2�.appear!*be obv�r6!�eQs�d(� &� mN h�$-known�,L#�)�"w calculu��Our%mA�motiva�� by r允_gr�+in�-e�!��e�[24A�s ��\��+�! r�i-�m�#��a! to m13b r�,Ini rabi���.�inA3�7ݟ��i*t9&� i� (�\ tral9��k�%j�ch *, powe� too(yi!���!�osa *�8bec� *� !nI�� ��s. Her@eMttrya�di��!k����%�- �1n)�:4'rq7 J�s5�j�� ; we���� woU�t*� �*Y� of�$ d� o�5or�$m�so-��ed permu�� on s�*�'! O clea�pl"5">role:!�se��preG N )�����e�*�*q!�eAN�*) %�ow���Jco"� x.u8=eJ� �����Y$�� ~ �.5.� .� q>0��!C&� � �>�*ɦ!OaIa�factoriz:t.� � ��p�5�organiz`AV�:s. In S�  2!'q�� e�%r3 C3��:s �� �LM&�x!q.� , as�etheir_s]2AvA�"*Kn� )he spa}0f=�s�456yz��detaik��� �k9�``.pat�s'', I��.l )apcu��i�o�t�2YI}I]sI4:U to (Eh)]�s���.�,+ vM}�+�xAYae�J%�dsketchy"Qe7gL lAH dw --"t �9W5 cern� cur�. ��?E\%�Ua .�. A f��+�re�;\g?aKi��A6.��ndiB��?%$v$ dat�,r $n=2,3,4$.�e� ٝ�f�:�nsf�B trix�.���}& fJA2� $&Q>sol14!�!1V� &9as� in� a !�%�to&1>B _{2n}� � ��yident< $I ,``� "&*  $f_i��t $e_iq. jt_n�<, $i=1,2,...,2n��0pi�al>� $$I="�$\�!�$�!id�>,},\qquad f_ib-fi- /ej/e/$�j ng v}�9�C!G����-� 1N link�W�s chor� agra�7$2n$ q$�Voints � a circle,a� e+ via�+a� A,s a~��6 disk��den�-by $CP�4�s�B se (< ing)M�A�� �|+ ca�-/ $|S4|=(2n-1)!!$. A� ple wad 3x!L� 2a8 via ���l${\ S}E�$�2B<2-cycles (fixed-� fre� vml{ z - 4ma!B�%tk� r J:-n!ea)�k ^��u s it st)� forw��:�{$y�>��=�_X: \eqn\bbralg{\eqalign{A� ^2&=e_i, M�f_i^2=Iq4e_ie_{i\pm 1} A�-( f_if_{i+1}a; , \cr [2e_j]&= f_j]=[f_i 0\ �%,if}\ |i-j|>1.� ta4a�9ach,con��Z�(�0K])� �ofE?Ufs�r; &�q�=�-q��p�!id�h b�!� edge"NZ��UbmY���!E�\(�61& �%x�ad�$�one row j HV�: %�f mat{ T(t\�y z_1� z�)=�9Tr}_0(R ,0}( $,t)...R_{1 1,t))B?qn.Z_n.\\ldots_,\prod_{i=1}^ @ \Big((1-t+z_i) �� +{(t-/8ţ2g/cenQ0:� mou� + =nkq��)} wheBq�IaR!wE� $"| sit�c"�1�#a�B��on�~Js�� Eq.~�I�&n+$t� {��p�IA� row,AyX��w�� s due��.ramGy�-{ [%�), ')]=0} it�7 aj�ZR For ve$z� � $t$gh�$0<%�<1 �!�0c�3 posi�0�iA�@�hun � rob�i� and�&e*� �!:m���=(!.O. Co2vՓoy�&G<)���way: �l%�8 E@o�3v ���Acanon� @basis $v_{\pi}=1$� ll $\piFR $D OBmmwA1]inIx�mat,iDIeig{ v_n E|�G:�v_n>� a 1m�m� )(1+%�) q mean��a�;:0vBlHXu!Ac!�$T!:{ �1 Y %W79n� re mL� a r�1� gsvec{ 92()�P6 -�� I\u ) \Psi_n(J[0}�^afo7n� ed ran�Eqs.~.�\A�:9 vec\eB noth!�*@Perron--Frobenius.�&�'EMA-Ep�� %^!?) � *Q�$�E�$5nW9}�,J qxeI�N(quilibrium |y{��domnu��^ h ��v]3S��:�U.4>aZ�As �} &�e@ may �Ra�E�%�+� a2!��(RH 1H non-*�-z�Id&�"F��� ). Sb<we�5 always| A1INGCD�w)�)�?.�the�N!!p� ɯmpurQ'�>�ia���vestig%� {se}�pe"(�tensiv�.i � �p choo8�)Tto� �equal��``*F �ase, A� (t)$�)es���Hamilto�G $H_n=\sum*�,(3-2e_i-f_i)m)Kn$ � null.o!K$�T&���\�$�)�:3��1�a�QsA�A����T�Son-ne!�v!�te\$,|�Bs`"x$1$. �AN!!� ee � to� ^i� arbitrT n� A�Q�� 2�_ �, ��%5T@d�n%=�Y%&x�A&. Be�: go�i5#EefJ!�Bus�Va� reli>-T[y"p"r �g1p.�V� !�6Hi&� invariant� ro� *'�e%a�* step�6no�2 by $\rho2�}f� -2}Ɍ f_{1}$% y!�a� X'G 6by �!�&hif�!�@labels $i\to i+1$�3h� ��/&+ 2672 1})� ve $, f;QI�w�"a/)�% iNO\lambda"F�1)$. N)mEK1�!�d- aH���* at $ �$ takes9.s �s !8 � �t��GI�ba��[-#� he��%�immediat�;gB[ŏ)TmDH � ��>A h�&f�zN�m}?&� I2 covE�cionW !ov{)�{!�\cdot� (z_2,z_3M) �z_1)=%��%�*I�, ' )} SWly{a� 6V�'go&A(: if $r$ exb%g!�i�A2n+1-i$, refl{� {r�- � -1}�-�� }&5F�!-%�d�%} establish�Ii< �dJ)M� *� �� � &�,-�n�N�E��-s�on�V�$4 �.~5t&w) RE�2lstr�&:$�#�� 73�\DFZJ� FPE_ /�/)ia&fJ%tq ��I.(venient�ѣY�p^�� a9� <t-ziKnd�_:IM�tmaB^�X�,\% T4ND NCx2, =3cm"wflowR�=AI� is l�X )�2�� 2!�+ad�p!�a �ybuni{N�� ybe1 ~ \ =\R� (Y\  {]?andbB�j(1-*�W� }}�E�)�s,% �o�E"� �7�T�j me�modulo %(e�\� v 1$)��Pec{Va|^�O�6�s} LetS a"Btertw W: 9?4oclaim Lemma 1�I�� a��91�Xz_i�6<eI�� N�3?F8r�R ��ez~�$, na�E�� �8"I�Jyi,& I:yX_i2c�&=>f����G }} Proof!T /zf�26"�a?wFs�Dlq+�Vyb{R�i�6}�y�ter2A Njf<qU} \qed�2now�"ia%\K� �l�"V� fN�rL O %�1)8$� �&&�-�=z_� gt61A�say $T�~($\tilde T$ ��{}$. W�a�=on� 9}_nm�_n(I:)$ �>� we get: ${wL}_n=\L) e_>�ith $ #B�Z�aA+t)K  �":vc aY �b� ve�pora�*� �A� �A��6al"�8$ $\alpha$,&x C= N�. %�hFt8\�H�e!�aVmpl�atG nFL �$A�b�W0)ed= a ``litt?: rch"� a "�! s"�r�  Y $ ).�A1:��X eN�iG&&a2�Prokon 1. I�. 6� 2no ��!�a�L#-55 "c j ���R��mtjmp.2\'��a d7� � $j=!�;rYdi .VEintK#e5 a� K �� �QѴ $T P =P Q�T�Q? PM� suit�pr6!$X�S�@. U�againa fa"�LX�u,a���i��A�>^<!y��'a [��!�Ź� b�6�%����ja>bAyu5P1}�M)�!?0�VatJ0s6I4A[��:+]$.�9>NbyZan�9N2fc%1!% ��)A�)��f �e:k�MER6 �AZ$e_k$A`)Y,ileq kL($i-lAsiE��.~1. �� �di1A, 3� %_A�"���IQ!!�9��.�maximumb]"�s: H(i)=i+���)��,�^^!vdbl��8�aM!$-^� }^{i+� (!^E) !kn+#-1 !!iq otal��i�_s valpio{U�$_0}=\Omega�? �Mq i1jV)} �� q��&�d8 Bed. Ap#gfN�%9 find��"\@!=�� $n(x)-n=2n(k)�HMF+�F -)S2�*s�7�0ͪ� I�e�%<=�7 y P*.2of5��d�� �"� &�0a"=�:?os� a�kT"�*�M_i$# good*NNL_{i}(z,w)={(1-w+z)I+&� w-z) R'�(/'6+ * )(1+}�S�?�i�j �ua*�&&� ���w,z)=I<Ae{4Kem}� " ��yŝa�ecu�Ct6c5 #15�a".L�j� -p{�}1Vvecrel� �� m��"6z& "J�&:# )}  To�HY���y�a1�� �t KJ^2n}�*WH5�-:=*} _{n,AE.� > }>J:� �,�(f {^;�c�/�pu I�A�*j�8d:�m Z | ��no 1, X�U[� 0=1/\bet .��� $.# . M"�\]f�H�o�op �7���!���1�n=Q^&�!PiTheck   +1})� _n={�J� fG]�qA�% (1-�O4W�%1)�*(z6}ńnc!e�.994 �M� ,ublre)valbetz�=�%1+� ilon9/!/ Big)(1+>U&'_i �2�{i .!F+)N ''} � , '. '=c.�T<*?$�+a�cix�+be $+1$u (i)N );A4 �\� 6lMj=0$ (� ''=1J"(i6>im8$z_j\to\infty$ .?�H�$(iM�*pKnan2?4�&ns�#�@.' a��uEd& $\mwi�\���4n\recpolone $$�no{ (1+^�)&(��o���J�"y I�iCN3AN cr &:�+1IN}�F.)e{f0&c*Ovf*�E��\pi', \ �� U'=��'>��J� &9w�0 $$��i��] "u< rB7/`2to�5E�J�!�2 �  ;{ � �."y�sit^sSoccur�� �� item{(i)}  * joiT $(i,i+p�n E�U�\� A� to���l�*���B =\Th�Mi�!�>�( D avar&($E$��4"L $FJ��e � deft�&& PN; &=2 eq.�)U@)-er{i}ut "�9a�i�aB4}eE - { ���x a�c} d��3}17���0�yyC ��o@z"�-�~�"s"��SFp]�$�"�&�%*�ui*��d:| +1\*���+^ Y�6=�73a$:�_�8�4�# �%>�2 ``gaug�:�="I{ viB� ^(2\D $_i-\tau_i\!(�z !���5|$ ,� $D$yres"�E�eB� �|dn�B9M{%A!�unu| �c!�v�(%��wr�9 wI kb �yi&>.~4��r�Dber�vvar+A$eop��mder.} : ng %�"$i$-th&b E� F$ am�actau!Z{ ��{ )4 A�y7&=Y�a!9Q..{?.- iF}�ap!�.��E"� ��+�E ^2=1A�^2=�UW 2=Q@�ial_ib ��6�a��?~�oE[{H|m�j'���3 \neq ,�:pi�5�� =\�V�����jJw��!_F�D��asAR��fJS2�doW{I!�.H �:�B< &�)vC QD��}}��al'$����=- $�� >�(�(I)^2=- R ^�'r&?cGe� F1&` a�kH�i$�7%-,tL��~in��5a�w'"p�k reas�h|~H�2one. Howa� W'�i�arg�(2�pie�A..ns�Jic{"<*���}ar�3�J+1�S�Ca�n#�ll��=4# (� 2). Also�rc�D����<ls "�\��mPHG]9.�[@��oBG 4�<�*�%% gran�}b!�e6�)��0&t �.`" �cnd=�. F�4we!���u��tr��al�&�J*�$:�! �/. �eo�q p u�qi Kenv 8,6�.Vuy7�>]@Ek`*�$wI�UDmau/er�l2�%',t!kr3ut���!]n*XdeaBrt�Jp�cT3��&R�k,z_\ella� "G�� $�2�n�j�5n} W{i+2j-� 2j-1� {2 �)� �s�(so��;� L. A� ��!Q0 s!�(�!)IE�U� $�4,�]=�(sf�%2 270�?InZ2$1$ (%�is Fu/ *�AAp-u^)X��Y8t�i�&���'a܍&� ^5� guae�mu�s��n2�qA��t�/j0.it tu�Eou84��z�~ ��x,�� EAa*2z "��_0����pio. "4b��sdQby0a�s0��he"�n+p�,*6/�:ed as� �J%�amalnBE�!v,; p�p�(#n8!% �*/<�� �,df.�: ,�/1�sR�]� wholF�N:�� wel�NA� erty���2C2&�0uoif%q� if)�yy��L�+e leng�\i*;" %)-�o܄�Ta�=pi=�. i_1}{s k ^ _0�!�q f_{i_{l+1� �:N7 does W�`a2 $(i_l,i_l��x $1\�k` .e.\ exgHO'E a d)Np�8ot yM�Uwo$�ac�P��Jq .:"2 @pAa a"�Pi2 rivi�2Ya�|1.X��% repe��ly��8!� 690a�>Ei~n� <2aco�e�&o5��{i_k} *?!,_0}�)�Aiced�}R$llustmU�O�Ix Ba� $n=3� �-Q� �\ww@m5%�)a�rB:��X�IlA��#.��fi�2ir_eu�%�~\/Ep2_$m2.(�haz��b�-"�Af�<^<s![!�ies�%�Qre*1 �2Z $, Ls1&$2$in  �2�$go4H�-RNSt�ngi�$``minimal"� did�L14�R �-9$ sub�h= "�#!�; �A�!�$� |? sigma6 $n$�I��  $2@ 8e class $[2^n]$A'$S_3$)3l9bid�( � �  Pf} %=$ �(7&�8��k eR�c �� :�stabi{1� {n+*A�%*�} �i=bPn�} &�bE�:Z H�P� +n6?-<\ deedNL*�?!��iI� ���N�bSr subFRtI72� 7ce���M�l6� A�,H �^!&!�en.V�$� is@_�C�``flat͝Reideme�k�, ve''��{m+to 3 zEruq8�en-]�a��(^xri�af��� ��id�q�_Hs � � AV.ra ``tad�}''.�EU�l� 7y� net�e� f wip�� z _ ``winds" �Qo�le�/W z�-$ce $f_2f_3�$��2n�G_=0%ai6�� �[&�,,-Zfo-� mov�Z� *�E��H�#ily�� &u�!��es�U D. E*0E);p��8n$ unambiguousl:ao�%�� n�:� l*9f.�9�*�itՖm���/\2aENeuses_0� �,!Dbb`He!}� ��!`��z��R ssum�W.� Eaa2;inBG�(yK `?4 !E� 5 �$[Fi,�jV!� $j� i-1,V- act upo= O\i5Aॳq�8.��-�*J@ atp:�7$(j,j�-Q*w.a�f1��w%�!A,{�>*", '$.l.a� �d�(aU�N�����  .�RB %!�l�_1��1�� 2��(%^)F1��v�Cp way %(unU�1:b=A we n�W!�Qu1/c$ �t]��E�v�mA��n���+� leftI task!4H��]z� A�j�"N|y%6956. �)�~�+Mb����Z���z\a�� $#i"�A(��AG!-)YA? we %q!�Nis� yEb$i=�Xsay%2�@to0a�(�rD{ m���`0 \raise-2.0cm* MxO<2Ak�&�;lh���Dj=2}^n M(\f#vP3cNrN+ !\ �:bi� ( } orA�ilu:��:��!1 2�� {�/��� �&��% � ^M # {j+1} Ju%@v �we)��a.��O�f �5enoughaX�f� f@M�) i2� B� �Ł�$��M �� l\pi_00+n�2G"@Ca&�11oi �� imes 2/:1�> ��i�!�9�?"s"!Ta��r�X�"D P!o�l1V� $qtyphi{\Ph�+�K-2^AS-{�>�#AH�A}.L�#^F�L\�*+)_0}} ��Gnnihi�dN��� e� by-1 :a)!$)$Z&���@\���a#�1WM�s�*� �� g,A�pla�4�dcZnifes�*�)� U!� I=2k^{v} RKD-1�-�_q�a_{1,j}a� j"4,1 2n�#F&�$�NL)�$���fMAc&� �s�$�_0�&4siz83� ��"/'(�ed�c2$�$$�3���7e~�csh�E\njH $Q# ,j}=A�i7I�e��'phim_st=at ��\� be2�J8<�%rew��16j)�itv5m|i Nbi}��> % Has^ ���"���IIc!��_�.�es�$2/Q ��G; 2,i+�F,n-� !SK&2(<c) =4/( LiAN2n 1K#��M�t� � �x�"�*QV� ng&E.1���!U$�o �A%�*6!00A�QTtR�LF�n$,/H) �l��e �� �on, An-1,n!n,A�}a�2n ���E�6#}\5��H�!�e%��(-Fn��)�ϱ[!�j� )= aD,n� �-1}u1s���$on!�t�[ t�i� ~&2iQ��C<:| $z��K61�� {n-2��2 �2+L$;� $j^{�E th}$kL3^K>Mj}]Mj��P��-� j,n- w�Qyj}$i\��)^8+�x2n R��igW6.on untila�a�.�Ul�Ing�d!G����YE"d mpphi��dM�=$@ �+���<,.F8by��, &CR *QS�I�t�D�N�� 5�$. �#o͑ny.�Q � ��+ q� of";,�b��f]Jt edo�^v�b�qui�^,&p l 1� i�GCD""�a�>bA]mZ2����M���oERF�`mo&m*�R�U��e�"�5��=� re &Z{6�76�b&��pU.G--VE� U �s&�! 1��!����l� �)M9VO W%highes�C4I�!�Y6,�E ka,lyH�,s2��(W#L2��f"� ��d��maxdeg&=}�jmaxN�+,= (-1)^{c(\p�<��>�} �6j)  *i�u"= a (z)^� !�U )A !i Va��m�����dsA�!_c�EMJ\ uM� �%)� _0)=�$.���KI� � �'KJQ�T". +8�C��(�$z$wU�i��{axr��) ��aA$�#lac� *{�����0A�kj?(:5=�)�2� a6uctv"� r.� ���]M=mYY)@4+U7k !�")s ;~��%�n^h� �:�/�EsQHF�� � `�s�(\y� �No��KOZ� (A�l� af�ly:~ A�s)���X�# ?���)�e Q�behaviorr �.��F%tetaca�UA��z� \sim �;%�%/-�+-�MP'Fn " T�.�� �).L4�� ���_�� �T2$%8bt��esMF%(eU�a�\����}]�$6 e�la_ u_: �minus�4�[0 , �t�[01Q&Jx!i�Hl�cuI.���u��+�-o��e�]�%�F�"d�rk�f��� �8�#!-�E�nI�:�s0!�Z.h� ��XM���IL�|a2�J :�zE��(rc2:s:�W2� * �!�]& �D�6�Z~!%1��[ skew* h$2T,Al̖s�t��a ~����6lKr) e* o 9�a#A#!^!��$�d�VonN] t zV�*�;"^3jI)-k nouc%�* @1$T�Zs�!jEvw�N �&.. �>$�Z}*:���Q��!� . I>/*Q3a|o"�(+L6&���J� :I;%�{�']�'c*�y� � cular, �F.�\B\ @re&�&�dte s'vb0(Qt0w�!��\t}f�" w�*dCa�a N 1s��!a��]m (p� {�R-Ps%)��i��/ he r�0!�%.!_�}]��:�]"�� �@a�^Aa�@.^��"� � F^edA`�A)9=�llu6.15!�Un�uSec+af2�$} �HD�"��a& or $�r!�zss��� Vz} A s?� 0�/�e!sis�*$n!$ ^%x%%3�b��K $\{�$�,n\^Iv !$ $\{n+1,n+�&�J}$.�6�"1 �#V�! -to-$B&�$e�E�:&hat!�}�1"Jsn$ i�{"=9�3+�+� :(�[)+�Jd%�� \myU( \par"^�fnt\hang ^= K� }H� ���� is n���=�a2��#)�daff�$: &jKnd� \K�y `$A> thre#$� �MEn\*��x&6ZQAo$Y$�- (1�AXY%�we�6Ȳ$, $YX$ upp2. ;2;<(XY)_{ii}=(YX)_{!�Z }� >�I3�)�6x "ǀ1)�s:%ran � �i �\ l�s)� tang��aK caHXD@ sp.\!) ��!�@U!to Y���suQthe.v�$-n ^{� ). \Pc skip�0$Y��h*a�"��D�",> co6&-"8in $M_n({\Bbb CH�W"�e)�d (��.�]Kn)+ !irr�I�[:F %!TZ um�i�A�wV#~2!}�wI�$(X,Y)$A4��M� (1)5 . �<�����.L``%�-I scheme'' p�"S@� iX-i}|ed�Md�$D^0$; hE<,��N)2,I\�� e ``:� sl8jl(��@G��i)l�2R�2edV� �R�|s�_��D�% �E���lq.�%����!��X��� &=�&.i"Ut�_��&r��-M1�"�}Umd�}�f��>��\CUx[N Set �i=B/(A+B��06+��S� =A &�$i=�� '2��T�� A-=$c�e)$f=�H\bideg�k {A+Bl?2 ^@&9" }= d}(A,B) �!$��\�с�e'�@ !XuK\�eT.YwH��ce,p- Y$ (�eE(%�7hM�.2Knk+�C�Y� U�6���IY:� =��+xZ-� �s�-% $ ref�� �*�e�!���n+ ;iAE"� n$.}l_<*� s�5In=ƻre�.[<�0ndix C.np$A=B=� s 1R{  ou�hQυ�a�!�a.1� .B6=E)%t%H��*3EqipNXl!P��h���a�O7 .� pr%hΩ\A;"7j� �u.l $H_n?/c��!:u�E� SHJ�.Qa�!�goBM,al&;'aT�!�- 6 �2�JscIWing�|)��V9i,+U��'n+�,�����r�i� s: ��$p_i=*�e�$q B�f�+�&�J'D=RSd_��U�U\!.iV * �k�W2n} -1 5}Vl) FcTC��p&yDp_n,qq_nSf� 3��s�&�Ag�-�b� IWŸT�)t�m7$lty`ha�%�(aV�0l*�a tor��*� 2n+2map�#An$(a PXQ? ,b QYP )$; *��+�~=� ��M�, {;r-��n ad"�. WjA�I2� as�WDbl���w�0 g{ [�}8j}]=A+p_i - q_j [Y_{ B+q_i-p_j�gWe�"� Y�0ge.�^J2..�z%��$(!w)$-=4� � ŝ.� � >�s �\q � �, sets�q%at.�2 �=. ŭ&�p=.�y|>:Y>k.n���)���per �V.&X)��~rel{ � ${A'+2 p'_i��A'+B'}1Ɓ{B"q:" } !��4Q {( G (A'+[-q'_j)B�U6- (B'+g-p.5)i���_r@-��alU��a ��$~B'�C rA=�SageK~�� iX� d (.~ 6�),�$�Rn�>$&x���f ���E y pu�A���(2�&� /.� �qA7K�;$!�=!aD�"rec)IH��. � ���{�%:^%�%�t"� �_&�2� A}_a�'� e�~2�^V�璗�5�0$. Ex�'5)I�maxmul���*AvJ= N�}B(\scriptstyl�=1�K22R(^n (p_i-q_j��I"N.5_\�/!Ή�&�Rwa0<omput�6,њ�"sr$( BuF6A��� _�gi�lU�*!�� .�$�&Q ;(s%��-���mea&, P2A� (b"��). B?7� "wAJ�t�+" r!\�n�(->�0�\) ^D{mo k.�thirdOfo�#Yt �inT`4�\Kn15�c�$�as�)�eed�-.6��� a]w�%�m%`�.� d272$� a�deg $2�Vm �p^n�.}(q_n~i q \�~p_1) &= 9"vO&z{a}_Pi�2Ppc _-z-S-p� �qb6q'�Urmw���cr }$$ � widerh.a�\pi_0�0� )# $<&{q7.&'�(_0 T*F&�S.B�a�2��}� ��C3+eke�>� u�6eto2_���|& ��iz��ormI�n��mu6� &YB^�2�3��*�2� &IsM*4& aA�&�[g(�� &�D�+c%)(2�b+z�%Bigg):� *f4Gq� �3�d(>k+�d7) Y�m^o"�a,�Q! $b����"SA��c"q+��%��n�G-���!�>s bn &{b_!T}=\u s{1&x.\cr 0&�< wise�} ��r� �O { b_n I=b�qZ�Š� 2m�� &i�9F-} g�2h�9tam�s2) n).i>,2jYDz � act)?%4h�B:q �\ ^Z 9^\Fx&�b$Bjn.c�&s"�"*%^��و.�En_1�ٙ�*� foly%$� Y_n^{Z�+&8=)1 B7�i}V� �0i}\ (i,j)�  j^+(i)�_�^,�R��&,��%vJ�b2_�(6; {n+j"92�q�q 9r&o,ws�f�H!HD[$2^ �#{�9� g�=�, e�[u�1�(2Vant� �tA>t�pM�qV-�\a�jKwCauch!�a �+�iula�\c!{ M�=D]�K*Vk:��ZK �l,j�,n f%!b) }\ ΃ } \&u&�С rule�$cQ99` F!sp���#�:#�M�sed +� 4.1!g2& �a�F��Jsmur{B�*g=�:n� ah0 ({�A+B5k{A%f.,) =�^� ��ich!�xO�w�v!:�"� &� p�]�Kn. Yqn��&�5,� ival�W"3 , iJ + sumdY _.�A��z\  =�,lm�(2��c q_i+�e�)�YP(h2Y�wASe"�!�Y�@sZH�"� (1)�O&Rem��:&lE^cB��agavail�, QC&W��k� *p�j"� "�"� ";)�^{�=D z_ks&z_{k+i}���5^{(0)}\g Y�V��"KJto��. !M�x��Rq*�m c � ��'a�>�$� i+1,i"�$,i+� ton+�  i� 7�`+;"S 5.1 ("�+M�~4!�&FN5�N(.�62W�<y!���1�� EHKy-I% S��osA2d-+!&�F:��B�rsB�1FAl&&$&gAqp!A�M��wo%� $R_1=�%1C,r\�P,$R_2=\{r+1,r5_�%; �I�$S_1=R_1�%S_2=R_2+�AN�2e�azONE�2�*�, $(R_1,R_2)$&2o<,cIH� �R wE�R_1�t�9f�$� >*����9*|#Wew"� H �*<*lJk  l�)t!fiv�S_iVrg�s�)on 2.\��JU � the VeɄt��h in X:�r� ��_1S {R_1 �߅"�+A\R_2  2}) �{x�$XA"�& R_2 $,'S_1 S_&SI %!�J/I"Ia �)�.�0 , �qToa~�>)%B�"�8b�-� !�,I &�5.U�5�!�Y4q�%���i�aN�m�2� ]�.J�a�m '-�*  g� �JN5�]��R_M�AT_2�themselv�154 �K� � D0�~�m�}��P_{g� n-r}$��s�^�&A ��G��!!�1x�1��i�\6vm&e~�S}�5aM;ei��[9;.b+r-1�P� ERB n#� �)�' �y�2�2��"�3��-/s6A�uc�*� ��a�4!�c.�!�O)�1$v!\p!��-ޫ! ?un1I��|?0E�#�-�S /#erv�!��imd㉧0bstitut�'pXI*4�� 1��1�#2�>8�1�JlJ�3iCo�3"c�'8lp�re��}�rE"$ EB�la�./�{��C]ec\'�%~$q}a./)ng�� 1P���sew ��yA��2*� �wl��8�s�7{6)%6R� n �b6�E�  =&��� � {a� jr#2 i=r+1K  j=n- (1o!)&��dE3}(p A4��*tq_r) \,.626"�. A },q_�Gx#$�o�W�S$ ���>�$*}/� N� a�block-&��fp"� Zce2a(Aa &�^r an��0 c{SkJܧ: *��d*R�*} I�3Q�ZC�pa�.origor"� *j 2. H�+�ha�#n0\fm��T��H�|avaga� � e techr��'�J��at�v�B+is �����<S2� ."� �*a�s 4G���G as }deg"�#$ (degl j�*1 in2�)%�C3 ݈�% ���6(>�eJ)9� Q'$�Sr$�}/  �.& 7/a�} !���_� A�s*�or � our :�'\P�Bc��b_0:�B8'"�'2� O,�(e2i+jHq9& ��e:A�&���01kN�1:"��triva���%O\{ '�M6B0 �� X {\rm{1\a}h��M2 }, Y #&/\�*��"\/%A`���,A�"-��Ss:�}C'=ZN$!c n�w;$a'  >;�&sTM�>  &DK"g VQ*$�l9 *�\M^. U�I �Qwanc(r"A�u��a"�. 5 ,�'�.`s tru9rL8J1�7�$rN���%��e�Dž�nda�Z{\bar\m�h"�OP]�pl=e� $fX� e� �+o�m��"$ ���`Ja. I�хD��<2 fR�"��pA10-nR'�0 :��g��e�[��"q$Xq$)��bd%�T x-.&o/ p! �"��eaF����=n+"oK$7#� +#&� >�98=H�cD]A��.. In � Bset�L(sF���double SJ���grl�X &�A�nme�%$ o5AV�*� �� =&� ��-� -t�-��`cru<�p�!�o�8E�to!yC� ula *Pk� H H Zo��B�O}$�8��&� 'K��T&�8dx . AfA��ik�@%�.�fde>D�$pp��/��] 5[��divdif��Z�=(2��"pv) 2� } }*�8*J�+B.�u"!y��2.&D�@p�R�+s ��p s-�a4$p�B�@� �h]�?��o��=5� 5=� S-p_i}(i��*;��11�&�5). ^�b�q"�x�i�:�t6r��C�� \LLT}1E�.�t�q��I<%�\ � 4hE&Z�+ :k" 1}�r_iB�Rough�pe� %Bd*� OD�n?  AW\02to��$ ��[��&g����rd�!s (B*^ d�]D�&�2= #by�N�� d~P�a�an%�����p{��eeѲ� �Q(:.; � �i7 i�"W%'Vq��EE�*��i�Q+��0, Now�#�W�pe-�9/-HUk0 }�%B�:reca'%ak-� +*�}n3w#�o � l9 K ha��$ ("~L�HUS�?V?ies),��p� ay�5of�֩6n*l (1) (2_L8Y'X'=YX$) excep��Y'Y')_{�[�XA�}|Q�)�/ Wv&j� �.$ ^4 =u(I>|mE)-i|Y_i)-uEi+ })) &� !�  $7F� nic5'��8�$u91)�!Jcourse �W�V�aAKt��)�!�$u$��eqnu{9�+1��=0 zewY checkY� (2)܅���F�/%�� $(A)_{jj}Aj� �Y���� $(M*:A*!c �a� /e�R��a\7 yx>ER�A=�iA`i) _i)+Z )Y#!W= �i+1�"\q�(&�(&��.�-VAB+1.��:q^�1I��i} � �-'�.g! AC����U!���Z�2��# ��. &S5�@ �<vold�Unof �AZ� �"�E�w�a W��w8&M] a�*�� ~ �2�0dP�a�>�i �8je�^�B&i+�"���d%�@b�7�9i �#�5�+*WaDZWm�M\ �")0 by $2+p_i-p_�{i+1}$ of the multidegree (cf Eq.~\we�I\ with $A=B=1$). This proves that $\deg \aff{f_{\bar\imath}\cdot\pi}+\deg\!8\pi}= (2+p_i-p_�)\der_i G\%$; by �Linduction hypothesis t-h=\delta_\pi$, and comparing ��Ldivdifb, we conclude�NZ�a^ X$. \qed As already men�ed at�hend of Sect.~3, a corollary�recursiv�str �of$\Psi �4or equivalentlA$=  in7permuta�$ sector, i-�0they are sumshpro!oDs of $1-z_i+z_j$, !V`in particular polynomials)fXinteger coefficients; tA0Pcould also be seen as%$horizontal䩤whF� Ɂh� �� 2)�Qerased( e pre) is��n\{%}Qn�- �'�� }� yield �]!��� �Jphi� TBjresult��previous!���s� i��aao:.� Th� 4. ForA iven.7 n$, takA�Baw/ ei��� !_&= si�� item{(i)}z�� s no2�$(� )� � $%�n)yI�{ � ���b =0} �2�RD �v � �� AJF] �e& :�&���� \left(� \d_{\scriptstyle k=1\atop6 \ne %F}^� (1+�-z_k)kU $ \right) \9S':T{nB  .E � !I z �A; n'>%!�'� (� , i�A'$ :(link patterI�$�B.+� $ removed (G="+ \pi'� w ).  A�Y� (i)�c� l Pro�  1. T"� I,A, use 5 ��act on ) s,�obi� valu� � parameter&z $T�!lL =\Lambda/ '$ T'-��(  D $, h�* !p�r�_�o-�n��:)!Iis��E�-! up a2Q_ �qsaAI$gamma_{n,i�r2 al fra��A`>%� Eis fur��fix)�applya�S-- �\�N sum !� itablyE ed setw.�M�s $P_n^���at !s�]�es��QAs ��or�8+n,i+n+1)$. Du4 �!}0erties (i-ii)��e�Q non-�%�.Qs  *�fe�DN��those�� a.�\j�Ces��imae � Uh$5�e>�!;E�!?-1)!AE�aIget�] normay{ Y1g6��,)\big\vert_{��t}= .O Y6p:Jj� } AQD!�sI"P����n3q e�$.�$U��Os KSu%�N�| ies}# Cu�-�all.+ {�@�� express �n � 0of a Pfaffian�start�� �ing.]��4E} �R�n$� 4\sumofent{ Z_n:�="�+��n}���J1} i� symmetric*����� ar!Cm���.�$vw}=T 4clearly satisfa@ $v_nI=v9 f_ieas each�!�@operators $I,f_i,x send (2� to aque2�\erefore�< \check R_i(z,w)�%)�ver�! not�*but $Z_n/�)\! 4 �sca8c���E�� vecrel, wNduc�bZAbi��G�V� -Sz_i��arrow m�ѝ��l!�1�qBy virtuKqu2�M�, �J5��-+�#Gm#v aRW(to� �$2n(n-� !Eva�� $2n-�E%ble, sub9щ�+s = obtai�by!�oEqs.~F�%�a��q:qtrecik&�  &V{RI� =%�( �� ^� Z��:�j�� F% init!�Ci�A�1X z_2)a߁s� a��bdv wimpletely%����"�the.Q|5}�f7q��nx���a��u�� brikb \pf)�{z_i-z_j: 1-( )^2}\eK,)_{1\leq i,j02n} \ \times1� #<# {2M ` ]&C� r.h.s��,>��by $K�[��jKheJ i$, ���[mwin 6]%�suOat �e z_2� z_1+��|5� dege�1in� A5-A5/(% ^2)$ )It���$z_3,z_4&���) ahr quant� r�4?$:^/x$ h$3%�5�� 2A ) j-z_��5�j�.�lea� �ul�is cance�y is�1F�� kn{ KR��\2=%|� .�j=3.�B�\I�\ K�)36n)}  n����\) ia�EE�6�=\alpha�$/s<(numerical j $ ($,i t)$1$A�! �� . NHqU�� aturPa6� ��pai�T 2n$ o�?s,�exed e.dby&�.bs�% @ a fermionic signR a�is de^ oses ��X�to an al�aL� 2v���jŲz})D largP��%NQ��n .� 7�,T^{max}=\Delta(z) \pf(1aO�0)����(ich matches�c�!����, \maxdeg\ �ed��w2 abov We� !#�es%#2K �=!�N$zero. To d�is,� io if $Z=�A)/�&i�z&mayP make step�_ (-1,0)$ (*mWe�)�0,A�(v�up) W6���#(2iT( l,eyf&upB* 0,2i, $i=0,"B"n-1$. %=�!��binf� )� $m�i}�� simpl�' +of!j figuv%a avl)u �!�� �I en= 0,a�)�Fin�,Q i�sy!D9%, u[T ndar�< tegr![epxq� echns� -U �s= \ be|a�G $n$���\approx � X�l "= O^2)(%[� aiapp�x?]"f � a*� Wt �$asymptotic �!s�F 2B .t��:� 3\sqrt{3} �4� ^{ �&]'C;)��&B'pap�"�� inv�gY#�ground!� te v%�$inhomo/ ous���d �don9(yli #of�(i� � c �Ni�trans�% � |)lle��� spectc(&4� 1,z_2��K2n� ])tof&�E.E�d� a�en�y �4(,�(�&�[.[)��R.��cha� erizaQt�� _q�"�)d gorithmE�!{a�ng�m� ve�#1��eUto fik+c��U�ir� r!O>� ver�( � �edW*��6auo� A�<c{C�+s�� AD��Q3��(} ,ngM$i�u!`.a(.E)Q�]�studied�% DFZJ�0"���c!m+��MR&kE� itiv� i1�C A&э�*�s � Ked E*de�bem1`.c�y�U�succes{,lo�zae%��,gauged divid ffer���'�-$Theta_{i}$�&t\a�%jcorrespo�� ��maxim��V�:� ,�~$.hN-}(erving, we e�had' di�, ultyero& ��.�'2)��:�2�j)�, op�E�P.BIm of \I,� no!rh)�e"��availabV�a�z4issue was high�U n-trivial 3eventu%T!�Sse�+�(us��,algebraic Be Ansatz. O�&/, �aa��.2- .3,JJ bec�m� , turn ou�b�ry!i#�]hen#� s. ��� ligh�D,foR :��t69} A)�� fš�nalog��"?[T {\it }\/P\Izergin--Korepin/Okada h X^{IK}$,[= �q�-BH, \0ing4 pfatl{ ZT_�B�)^2fl "6�z_i^2,z_j+z_jr�\ � J�FQQz/} QeI *0��! %�c"A�#2! non��F� %u (infAe) j91 I�.�"���2{��Q(%��exL�exist�* ��+gl treato "� l� iU ol��ss[ich woZ1d(qs� mon fe�s. Ac�ɭ�f� ��&�' seem%�bW *�-``doub50ffine HgB s'' \Che\ typ� ly mix� -lik��s&� a�p!A"� ; p!�JT (se|so \FK~#A !ve exten� \Schubert.� } An rigu�%�ew1?7�U!)���emerg9��5 ���q�2{� T".�. Rou��spe>'%� l�$s���pro���Lh"F� tn,2����ions \�b�h�1 show( a2�Z�drast-�`i���:"�  so�Dto� emAG�"� F_ocoA�ly��� 9�calculus�/.hect%:�!$O4�BRAU\ � e6� �o@ ous N��7s��varies cerl�*� e�a�$ts mystery!%sam� reaWd �c& 55:i�6�Aj� "�  deTA��/A���aN�  ve$ �J�* �*eBw#ae2A8 H9 1 A \Kn�gAha sket� %. Pla��:� �%k]$ ����3���ng famil#7*� 2� 1�F��h�%��,�negat�gq>�6�R����h!�>6�&g({n+1-i}=(t_�$/+1), \un+i}=�s,�,n$. M�1p�s� dEIe`R $s_19�Ospidef{ (t_1,t"� ,t_n)= %{��i=1}^n!*t_i� ?2�� .6*nY* -t_i+3t_jA(t_j)} {2^{-X 9rg�]`�} t_n-%t_n+1"�4 {t_11�  �t5�5|a")j � s�y!hw _0}=6�\N$n} t_i^{n-�(=4a�o� _s� .� repe_ ��e�.� � ��,M"  %�6actet!��:I��#\pi}=OE�!(1!�+t�1})\pd,al_i -\tau_i-57}� j�SS } ($ Ei$ �eI a�as usb �< plicekJ!( ���;�<onu-. $\ha!$ �!#(i)=n+ (%=),T� owest�+t� Zm�, ^{mi^s� ly idI< fied�7"� ��.P���) (�'Act� � D���nonz� E�%%�\ 0�"v� "< wmp�2he bi�9��1 \: ��7�l��^�)*O-�$t_i=A/Bk��/preM �W-x by $B��%/Y~3 awa����goo�<Io-geom4(o =.D�"&C*�m>x * cHcs�{Q BB a{! nAvsh" vl<forgetR~�� &4�?�r. I_8"� quit�&gg�dh8- ��in� Ke���v�8bles �=A/(A+B��i+n}=B )�>�, tog�*$:g~4-�m�%�\rń<-(n-2)-mod(n,2)}�e$�� *� .'�$A,B$ N�all}\/B��(!gjus� � .A ), A��V.m_A/FQIt � 3'!���an %cY4g"'p"�!�$�gQ}as wel�*REcɄun� (tedly hidde; K�J+ .!4Q� 6 A1=(t-1��B A7 take�!� -�afOF "�6g#ű)/2AE}2�?Eǁe!��\It�* �� ��q#V)w1q +�7``� ��"Q:�s \!�oJ�" 1$n=4$� X*�)|P_1(t)&=1, \quad P_2(t)=1+5t+t^23,7+63t+167t^2 ^3+7t^4,�)P_4K8307+3991t+18899*36583- 4 ! ^5+307t^6n)�(o�/%k)$.��Q�:d}2J� 7�"X Vx5ime�U�0one \PDFone. 2e% y shA0e� them!�h1��1t $t=0$Grɷ7 �)�1�� ee� rank ([$t~E�#� �!2��u~?u� "� a�ly-I ��6� ! �s�twoDu��dour��#z>�=$z� }=(ue�ua� >� y�a��-2%�w<�Cdi�llq7� aR�nG $t,um�.m aSFk %%�%i��*�%a�io�2) �ree %�&�!��# beA as@J5g� ! .,. %A�F&%F, uponAM��b�'�4e�b� %�.���2E�ag�y�. Al�sx!s < ; �`a� �% . SCa�b.�beh��6!ex-typeM�e;�5�� "�-s]�! grid�>�#,�"[ six- n.idomain w!�o o\A$!7�ZA���7candid2,�Y2,$OSP(p| 2m)$ � of�*0fs{\MR,\MNR}, �$p-2m�*�1F�problemGQ�reim�Ds!r [, w�row-to-H1 fer �-ac���HilW=�dimv$(p+2m�pn}� �& stema�-maH��$�a� "lea,�$(�'!!$e5\2�`5il.9, �>$pe $m$]Uat n� % �!�is�.�wo+?scenariS)a�/�occur�(�^L spin�freedom� each~$�6� ice�/tself�w)�"� �s%\�2lt�j����D<verteQ� DB� as:Z;c��Hy-packed!s, os� � �%, etc![�C roo{ �7in�_aym� adaptO!!We=��'a>,M�4 s yeQ f medskip  =�58{\bf Acknowledg��$s} P.D.F.\A�0nks B.~Nienhu+(V.~Pasquier��J.-B.~ZL!U�cusf s. P.Z.-JJF.~Hi!g;M.~Kaz �1 in!�E`FA"��<$ M.~Tsfasm Bdi}Sp�J�$to A.~Knut)!�!)expla]-�$%and data ��/�o" m8� ��%1![vfill\e^@ \catcode`\@=11 %I;� s4modify PLAIN m�A. %�F\d�S<#1{\null\,\vtop{�9lbase!�4s\m@th% % \A,gn{\hfil$##$ &&�  \crcr 7 \math#Gt\no-F{\kern-\m kip}5#1 -�<}}\,} � mini��.��&& �%' #1�H2{2 %��sig�Lr� lon�lc+s �%z&{A}{E;C���2$dJRL2$�:/,a\psitwo $$\�Jf qG 1.4cFsG2cm\e�Idiag2-1�D &=r23 �13 3-z_4 4�2} ��n2n%�{>i^�23z�1BK z_4+3+9� 3)�}ޜ�G &.�X2 �)^.��2 ��A2 �=> 4�}$I.�]BJ3$�-�0a2.�#;<< �" how�D��ntr�Ii3�2"��"Sklat. B*! <S~*yn ;(valpiob. ItE�si�a#1#2)�{#1�B{#2})}I�A�$onethree{ !Ps�[3-8M[-�\a{1}{2} 32}4I&%�\a{3}5*4}66* 5}{1"6d5} *}�It&a�� $1�Lp�=U�1HA4\openup2\jot \` ����3-�I =�%3'<-� ����3-1�@[1!�Z�Y�JX26Xcr֯�K %6�4h1-#:p��r��q Y2q2 q36��q10m r)�r�:r�SZ�3B� �Mu��� 2�BN�� NH\�1� 3$:7lf%princip�7creas)�  by��W<eyaaLE�� � 5Z-Y��q $, %ja==\ \vce�{\h�W� x�B� 3-�iEp0 � (� )��Rz.ads� maxtwa�� !��= \! r�U��� =  "9A 3 4 5 b  42� z6&� / �  5-z_6A�C"�W�L >,� />�!�caH"mX)Չ� $z_6�$�"ar�z_#[z_Bf64�>�$(H 1�i`er1aR�� 2. ^` C}{Ba��K,.��etyAffAh<$n=3,4�"2r[A e�2�J 2,A7�uL71�v�w$\b, 0l�- d be�]�eD�&�XG6O(.n�$6$}n=3$:bI d��&4%{(41)(52)(63)NA^3B^3� d %_ 3)(62)}�f H&=A^2B^2(A^2+AB+B^2A�b2)(51 ��� zc3 c��"2 $&=AB(A^4+2!$+4 �$+4AB^3+2B^i�-6�!61�6"� q2r42r2r:q�!��q� !E@6+3A^5B+7A^4B^2+9{^3�+3AB^5+B��23$24.�Jc $$Z %6 1234]d6�4/#"� � S21�S� &= �32֛& G243���=!�^5 aJ + A B + mO ��d�!F4 B^4Ff^2�231��-Z42��=A� 4 + 2 A^3%4 A^2! +  B^3 +}�31��"� Q"42��q}����F�2!��!��G-�143�I� �32���G�%�<^3 (&A^6 + 3 A^5%�7 )�!�9)��A]&%� 3 A���\c� 2341�9"sA�3E(>��a�1� (+ 21MV�15%�5 + 5�x=�41�1y!5B5 �p-D�� 2��bB ov�241����e�31���>Ma�:� J2!2!!�4%�3��6 } Am�243�I��u:ޒq�"J �B^2e<8��^7e<1aG���28iT�4�8���&+ A�5+ +!a�1�E7ecB^8A�=413�K2�-42�H2� J!!�-%1 % a�!� a(4-,% +)N1I(!F341�1&J'9�N��n�0.�A��A��9�! B�$>�342��8.3g &� BE�� �A^9I���8E�+ 4�7�m + 8�E��10!�!�9)�6Q�7!&� 7+ 4+�8!��~9M��>�3ڶ23.V��i  ������N�-�% �-& �%?��B>�2��2��U�%ЁL�Aj)�3��8$�1%�6!�)��&+ !� + = �V�n B%��� ��43ھ24 ]� ^{12!�6  1}E�2aj{M�7-�R �!A�2�%A�23�!I�+ ! 7.A�W!A�t� +�%�1 !�2���x  :8�$istref�! end �}!� ~cL�E�l�l�{3Dk.��(Fig.~\linpa\,+ writ8=55i:�E -r"n�*fw�[�_�� 0�&�m@72�@ �eas�4? �yJ"* For 6d0f�2jf �. $5$=\.�*,E�s, �QJ5�.c0s $6,7,8,9,10�f�7R#!�&�/�,_1&= a_{1,2}32435465,16F5,Y 122a�ZbSL0�W52W1�� �>�6B�B{11}&=��6DR=6{14 = � /!P_9�0aE $)9 ,j}=A#�S$,�'!�*�'h`!f:[!i$l"� " P!V3 +h - z_31 �jz_4� z 64 � cr P!I1?10"<+ {z_1}^2 - 2 z_8 .\  - 3201+ +{z #+ 7� [Sz&��Y � -~z_3S 1� C�7]u e6�!, 5�!/z%)?�"- .3 �4)_ ��4!�.F( �5%�!��z)  9�-)!#�5��.6�5-9�!'Y "S� WE ��( 6m)K��� -�%+ G l '� lk �DL� I.9.E�5A�5� �G{z-Y e� C.a� �$G.);4%76 �I�%7*6+i�a�8-4� .C�z&K %=�9BMQ�6q#� &%� G�6+[ x�y.i�!�y*� �AN.� %!y.yK 9DP>^6$62a=!E- 1F!�.p ��E !�W �2�.%Nm .�.� V� 2Q)_ Q9� ? �!4 �B� �J �2j�j. k.%:e�![=FO6�eaE�2@.6QdqQj�!yy  a���.-�6�< K%�E�{z  Y��ԉ��:%�:!0!� $ 6.-H3��;�h5Y�� M�q�A�� �..hD h)�<��>�!\6W1j?�>�@:� 6&=3- 2! 1���+U�a� 7E� �%� 5�x+ a��!z %�-�� 1�3� &T !ab. . ?sA�$�tAz8.�� {z_3A��� #�o#k! $a!} �U�>#2 �=-)2 1�!3w �!�-�.6��[E�g"Q����$2�x��� -)�3 �.6W%- $E���.F 9j*!�!��.,�9>8�.6a�Y�.M4A�''a�] �{z!}�A"��M )*> RA�>%F�2�m�:>8G!�s� 9B� !��/  &+ * hm� N1p��2�Mt> + yQQ|9H>A��F*R%3�9�[�:)Y@ ��.�ZB �g!uCAH[ 9Ea �]A#� 3� 6';A9 ,�OE{,!;V *.V+ 1'}.2�A�Z�.16��E�9U �a�e�-�;.���>D)S�>c��e� * ���2.�!*�5!�!�5i� �" e� �!?q����6/YF3�.I!\� �%I. -��* � � |Q�F� ��iK � 1�.���%�m. �� Fa� Z>!� S�A� E� e-1VAY��[62N.�.|%��!�Y:.%{J,-2��7�0��a�� 娭�� )+2|? , $-$�QFk�\H�k� �%z [ + � h FhY% 9.,%"-�@��� �gE�� �5� �VANqf H�{�� !fA0�!� )��.� Iu� �� ��k>�+"�2�Av��.1a�N�%�-[e 4:179k 0m�>!��Fa-�e-!�!A&��-�.%�2jF)>�ZaU!>.%��.o�BA�c"W%�� �'17�A ��$��5�j:.!9�D,>%Jm�A0 s >� $�*�2}E}�E6�0�Y=:2%v1;ASE):5�>G��A�[C ��.�� 0>6�.4E �.1�A|i� �aKA�>�9�>V�-.nR9.2z.�bY� �A��>���> 8.�P��F2�V�>5!<�aa�eA ��A@A�%01Z.F��e�E�6!��E��� ��YN!�!�.t=gF�F�>�TA��&a !*-T�c.��%>J�1�.5w &/]%X�%He^$!��5�<6�0!�T $82�.w-�:=E*�y�6 I�%R H)�.<M)� �-�P5��*E�>6 �.!�b6P K1�c y=�C%J,�>0�+C� F���E�1�A�)�.*�?�6%.G��,�m��>.Z62�t6 �u6�16.�6�{6�Nf�>4MfF �1�.�9�.�iR���A��.�@2,�>0? Q�23��e+BV4�Q�.:NS $P_9$ �T�JpyS p���_�:?;+2mat . .�P_9&=6j9%- 2�E��1}^�"� q 1E�.A�� �A!�� RŮ-1-�1%~�"������S 92}^� � �E�F:+ � 2�!a_-� �!� � _�-+ 3: -!�^�"C!V eq%\' � "9�>,2Q639 �K��%k�� < ,�aG � =� Q1� �YVV  ":%�a9�+!0A)!ga �N.�%�Q��.ME�%+L+ !��: %];I���27 �%Oc.��1W N`2:E2k4�3i�%� [9S-�.�v���+NF^A�>�A�.BJ>�_%��Is6e�o� �%�/�l%5+i�� !%A3 - 18o D#� @ 2� -� ��.o � E1��E��%�o BA���H�66X.eZa�O�L 5� 1� !,��%�% i2)G -+!� B1�. a� �a@!�F9�>�9G%�>$� ��l  B�!��텠!`. �1�]1�!!�!Cq�J���F =F){�EJe��6�%���E�6�<�B M5E�68 �1p. 5Ue��N>���!8�4Ņ� �ha�9?!15�6y �A�QI�� �6�E�PN"�VV :1 �%�6;6!�> - K+ 1�XP���I��|.�-R*MI�Q3 G�R,�%L i�2U%^>��-KZ V�2��; Y�-�� >9p �1.:aNA7��1�JjQ6�FYe�%�6�B�� =("�R��42 =rW� %��:�1 RQ"�ycZ !nZ��K. -�A�.C.�6YZ6M��a]M}�:619Ia:5�N6�"%$�s1F2`3 6�5 �]�) g2q�N K}%2�� o� 2�! .�!E"`�#l !"� T� ��)�+@ /")/a�* �V� .�%o��2� @ �1� �er I� $�G&%w �6/q�uE%%>k3A�c�Ep ��Q2��! Q2�)L!P.� .1��641� -Z I��|2 - 6 jM�j)B.�-& nH9�!s c�:2i,Y�'�# !L Ie]!i�T%`.5�k�0H%�+ 19q6I%@a!Y.9HMm>$ �%`.<+� ��J&) \B#YE1�.^!t %^�.�-K%z6<r�ND�t 0)�E� M��)��az_G.{.�%�= .J6R�(�>:� S��6� A�� �e��a?.�&-.�AA� A�>!BA=&%W�UXi%Y��2%��9)�E2".0R�1i�=b!% �>�|���  �!'...O.E�:� �G5b6f���j6$�V)>{y٩��� *�&N?� �.�� C�Q A 6�. ZQ#:5�{!�N�9�! �5Q.2=!�A�><Ł�V!�4TV# ���2v�y_e F�<9�> eNQ�cRG��%R"F�,2��r!I/F M3�S)��:�%> �(7.��T�9t"q�A`2t�A �N%�Yf#)�==H�%�H1*&%�x���A/>|-h��RH-� �-�m!-5!B1�fF4i�13!`�6�i=_:�%�)c%5B`A� > >>n.U��p=�6Q�v�6.M��E�>$.86VBA�6E11I!l>R�)<6@�E�F$J�K>d%'?�)fFG1��%�>I�$A� =s� > Ia�N%%���.����V�z�1QN&9�VeXB}%G�� V#9C!�Na�J�%gN(� :oB�E�rM e6��F �N$��6B� ^ �9 >=�^"�A2�Q�*=>jA�Q�j�i=�^6} ���� "!@q[Q�*�)�"� 9`-�V%� {�1T �>;!�2�T��6 .�6�xFRE�!i)�F� G�>�@.�>&q��RH�!}3|6~J!-�B!��^ �1�^*a�=�Jj+]� �apE�B�%B�%�6�%�U %�%N6 zV�%"%��Q� ) g �2��I(V&�T-L 5A.�A�=X �>% �K� 3 �21",�% 4N"�M�2"�6.o .=U�!�.ɨ6E�)L.�@%�!O.$A� �hu��.W64� .`.%-m1~N�%e.�9Q. U�� 6 �V8%�IVqv�)�qY< & i�!M> �V�>6�.QF!�2W>$%y%>.��R&�<�% *� �^ ���.3AGI� ���Q>�e�F .Bh�3 m  �Q .+%c1EA�.1� �2&�.I��%�!.$ 蕪6& 62:">��1?.;��mU���%�.>I� X>6v>��>5:6E�-06:�-86$-q!B.�6%��)�>!%6 sF^�F' )(F(�f"��^%�-�6��e"� F&9�M���.�^m^BY�E&JcajV � -� BL�V �V � #%�JC �%*�L�9��d��. � DB�A- X�XE . .# Ye�VE����.� @2 -�%Z~ %>2�%-26�. .5*�FR%7n- 2X�I�![2& �1:�ѐN<�d _ZG](:a-GQ$2�%? N9%!�N��2[E� !!F?�!UN=�B�q^(�q^"��aN�%[b�J@9�N,&N 9�V(1�%�V#.�N"%(�ias2�� F�@F��E�^Gl0!c^ ���%�)BnL%�%�^nI �z)}R� � mE 2B"�">@�B%xZ ��Nc �nG6���i% � %H1���fq{F26�25a !��:y1�2�E�:�2&� F:r.�$%Ui�%2=��y=$=�EK��aVD9H!�NJE.�V%IbF<���_]���@Z ] 1�Z% �W:,�^��5:F' �0IlJ&�$i1)n$6� )1�} !(� !|-t�E&e. 1J.i �6�"%X."�J>�.8�)n.�>�T9�..�3Ne��>Q��R�E�� >'�&B )��6�6)�-�!�[�1�65�N�N&)�a�l� V!�6l%NOF&w.7O�6kF�)6&��6E��f%1�.���N�) ET�06B2%. E$A�Nk��iMe�� 8�l�QIzy�V<L2<i�!`>22DV!�JU^9F)�>yigAIF1�N���VWa-!>�N?�eVJ���NJB�V%1�>�)�^���^*R�:��z�Ё�"� �ETM�afQD.�2M>�42" �6�& r6�.u �e�F��H��� 9����G%[H+!�%�7@�$���J� J (9yCW �Y;9M6%�Q6i� 2�%� ,h�,\>%OL7-%�����10bRA��� )U%�:� Ee'Sr% B 5� H ��d�Q! :9�) L�%�j>"�-&���j!r�� I%o=�Q�-E�!V���?jEY%�q2���.�.-Ze )�6Y7a�.͖�> �%LE�%�.=ݿJF6<A�|)\�_ %h���N��1V%�.�1t[J�-�"p2 D  &d�)�9K*)�>��K>%9:��EK= qES�IVMB'>�vA�e�AS ���E30 � >9t> !*�a�#"�+.%�! A1��3cI!�i�'>"]$h>�%1~�y1� �%~% I. c"2Q��M4!�.F2�1.%D�.���6-6�>�e�)zU� �E�.�%Qy�>[�) Q�6#yc�B`�!�);| 9��G6{ :%� !^[7A�� 6 5�2 �>X2#i�F; AFe�n!���!K �E�5�>��?%g>&!0.�> ��]�:�1�>A �Ga^)� g%�2g G d9աL ŭ�)!F�4�-�!=U9z6QN ES=u?a[) (2�%مC>� �_A1(.a��F ��ɪ~ AB��!�.� [G&�#���6NB�=�.��-=#걞%? �1} �EF '�B'1�=A�:uJS .FCp6 �!�6 �%� #�6#-��A}��.k�2�VJv6Y��1w>\�.�F�%C%�^K%�� !N� �1�N"��#.�5E*B%Q{_B2�J�x6�.��q�!�i�f5����^-�f"q�Q�B�!��)muB$�6zV/%Aq&BME�rV��i��6@ :BV�B'&�)5��9U6%a�6.R '�d �E��QEu M%� �A�� * >F�b>���M%�uQ �% y� ��RF971 2G . �j�,�>QM�> �%RMR'F�>IA�IE�5.[]� �2WJ&OB�! N'=!�9NVK�=�Bl. VC�}! {�-\B#aDS6� u!�)V6E !��"�1. Aq) �c�/a`l\&gmE�.4� V!�ZrJMRL 1r`�, H%25�%:� YY��A�-{�El)@h� �.8A�.+Ad#�� H.669O7�NB w�+-o2w�%)2w. J!�#%�B_+j1 = -�N���I.`# FMNe�1�^M:��in� IMW%dF�2R�"A;F&Y"oF e��~!�J��%`>�6�>)::RME,6rF�G ej>c�!�E�R) ��*9��:* �_)�!`!�99� �.�'��=.|`I�F�=e�^"6�=.hcE :��!�� ��.I)�� 1�e)t1 �E�"_?�!\6OW)Q.EC�U�.�1)6DQ3X�����VF�N��%�.�� 76%M�u6 �]6~6'��;��-�:6-N��xF9.c6<-�!C6 �%�5�wF&�� �6G�e5F��.�6A �G&�)zNn ��Rp�j�Q� Ae�-�6" �Gi@��.DY�JaB� !�J!��B.��)��x.�BM. BN�q^#!69�Nk�Et1�N1�_%}V �vV(� =! ����?%&��B %�X^�Ef�E�F^K)*QB��Z�a � %��>.� F��� Q)3�"UV2&[�FF@ �N: 2[�iA1_2+�`%0Z"� �':A!�2\2 �e6�FKlF=Am!INete'�->� �%O N&�!U�FgA%I j!�F'm���F$ ��%xN�M�)}^q6z bM&Y Nk ��� ��>K-&�eZ 6�R%2sR"�A]%uR)/An$�!݉b12��%@^$�!�Q�MZ�)�%�Z"q`��FsiR �}`R+IN��:�(9&F%�(��� M�2�J�B�Qy� �!� [��2[�rs �2E�31�:9)�&2�i=PZI�1# �m�fyj�!�F9|�JiG!�Vg�]w.?�6��=ZI7�Z BV-2v�1eRG �%[�FC^ 1�c{0�P�e�Av����6/!�^��+�\M�"a6e>��iF��1-OP-J%*EPQ4.� �e8�a.Z*:R>y�M�5V �R��> .�> � '!�!p6�%)�>A�6�>#2�RE6�b ^E%�R"�"}j6$�E~Q�A�-�BA�)YNY��%�fK�%NM%I:ZJ�)e%�B�IV+����=BIC!%��6R�2 {z_3}^P3 {z_5}^2 z_6 - 8 z_4:9 z_1J 2+1 ?67+ [ 1}^3B;+ 4 z_s64 \cr &-Y1"uF&- 7vN  2}F#+ C2N� �+E �{zV)+�f$ %^%- F)�{zE%p2VT?6T)N!JN 1�!'F �F �#6g9�N 1�Vg.MI06d�-�F)- e1�j$5�1U5~M �u8 �E48v3NY- 5eI{z^ 2Qf'7%"^ ��)s^--w%&^$%��Q�^)+E�^"� #FK-k3V�A^<%�6�Na9$4!�6�u�B�y.{zF)-Pq�BI�1AEuJ � �B �A�{ B-�X�^O%�=1JC:�B" �I��vS %IBOItV%+ŧV�!�A�V).V"%�EaH^#!�ef$��B+^S�n&��eozbKE녎N� ��IwiY%�J��bQK')nO�-vQ�l}$$ \vfill\eject $$\eqalign{ �-2�3N�� %t��-�4�o6>�B#+}Y6Y� �2JC.V�5�%,JC ���B"�Y+6���Gf �e�^%���]v�I#fK�&fM�*%]�x=�?v$)MI�CB�2 5A&* [c 5G%&IM�@Y �(�/3 )., �eK:;�%�o =��x�-oa��>O� �>4 �Y.�>'y�>2;:���1�Q�)�$�!wJA �NE�qNJA!i�NC �# o6 �%�� �6!!�9P6��!�>� ���&� t%�-�F=�>8=H��>+-%No6���N�YAVU�F? �%H!e� �F-��%�Fc %81�F!OYC> �R->+���OU�)<��nw6�J3B;!�N[ �%&9iVKYNICA`QN%��B� �%&�Q�iB)�M�^"��A4^�AuAVE��^Ma�QVm:BN%a1w�5��!_� A6'AݒI"!u�V-�. )�%qeNw- 2e6& �E� �`#%�{z ��n1+%�% 1�E#� P-0m?.� + 1�e���!'F!�dQ;�2U���o 1�!� I7 �qt>� #5:U* N" { B5�-���-/.3�6/+ 1�6 �2N!.R j> �>m�9�m�e 2�. �E{�Nhm�%Y.A�7 4A!�}�E��>#)t5B] �qTU�I��R!� U{2=q: SF7y�!}F WQ�2W �% �9�F��RKE %�R% �%L>c �%� G�R+e�� -X��2>O:5g2 �mF�E=��2E�=%>�R >�Z%w S10��.��� �eK 6 m� ��!.�6 f6+�1�! .�m� f69����%6Y� %�B.5i�6yE�1�%�BC.�6wKwa79%�iP1 ~6'x>5]6E1.,> k�+��6�tF&� Z6F%C%;=�># �F= ��31NF)�E�^M�%ͅ.�6�.c 9'�� j'+Ba m0�\6{>#J# u%JB��Q�B%F�!H�%g;%Ga��}6��^" �%o)"UB���kn&GV�� CV" ��9�J����6��>82�6%�9)P6 �� �b+� ( 6W:2P� �5�e�F� *2Q:�-2#E�%ENsN%6��2[��Z$�E2=�!{�F%J< 2EE?Y�FA� ځX>UI�^� aa�Ne "�V"%I6-F�I�%O2��M�e�FA;%�^K%4�^!9^"�pnSM*Q"Z�i�e�>�"�R��R � �Ahf+e-�m�5�2%�)�O:- 2!!�N �2UN'�RY�E� �A|�2w:UN!�F �%<bV)%:Ex�N��=�p �!6p.�Fn�E�fI�� x� !9�.� !�)�!.1! ��.e6! N=1P:6+� .H5Q!�x67-�N �%cшe�ze!��. �%�� % 1�66& 6:� 6�tAt.� ! A>��2�.?�{z!L��I-(6%h�9q6 �1oZG:�6K� n��E-�>q6.e � %�e�6)�BY�N[�!�N#.�V �4%^E-�%ZNE ��!��b-��b&M1�Nt6EN"�MB��.}2�B!��BEv1�96J�6�r�e �bG�  .��6Q m�6A+ ��6-,!�6� �� ��6&� [B> + #~N#.%6? �E3� Y�� .��%�%V>$%&9w�6n25� 6" �IsND*�R�.�F@ 9.F �%!PF&-�1�F!AEYM2^H�V" �%i�V'�9{V$E%��nO%�-�F��%m�}6��\�a> �@�ZE1 ^G �%o`nK!)�^M%" r-nM1>^K�.�^/ %qf"B0F�Q6Z!E�x �6�NO�;.� �JRi>?)fV_��%�Bh�� �B =��VEɅ�� .��B N%n � V ��A\V�exRV"���fK. r�)�IVv!(Q-^M�Ee�V i�lj$20qVO]bQ �E/ Q�J:MT�Vsi��.,5 _B!�1l UA�>�� �JGEf"s �6f�9�6 )(�Ph^K�^I�)kq�6n� =�6"aY�&(��a" �'s�N��2ya>UO|h:5a��;2-9)F<=Pm� 2I���2��q�R��f% "%�Rg� E+2��1XѮ2" �N:;aM2:8&&"N 6�-EFg �_F%�.�F#.� ]�2� �M1R^+%/%lN�ed�� b'E=t2F�6�%�Vt!�1�N"oq�2�� ?R!:�R$ ��!6�:liv"�!%:^I�K �evj�� KFc�%��B�_N<���CRC��� >�[N)P�.A� :�fA>N� !)!tNiE�^$�r�%�1�Ng2�%�V&�M�F�5�b"�)9�ݡ�NG!�F %x%�-V'�FI �%��!�V)� 9�V$G.�nO9�VM�x~/�?-uVQ%4e"e�V���b$ �M�A�i�;FaM�ERv(m� %^�oV" �%�� �2�i�Q� >�%JEWfBi�^%I1Rg �%H!:A�f-Q�*n&>�Rz͂R J�E7R-9.nS%�Sn'A-QUn(�I/f� %�E�^��Y\fO%��ER �Q n%<2�94^"�G�N@m, �� >��=R �G9o32��f�� �>- ]�F� Q�,&A U�2 �S�RW�j2?�q�Z" E��2=:� :�-A2 �E �N#J�2C=d!F���Nc �%BIq*2�BH2��}�2! ?n"�.�A�EG � a�&F#!D9#F =!:?F#e�-BF �JBF+a !��_�����F?�E�^E �K!O^'9q^"C. V�M3EN":�QN+E^�5:� ��R#9�5F< �%�!�!ZK ~R %#)�^p�%^"� #t2���F!���e�~ 6�8��M +EN�`3efi+ (�%/ �])�AhA6l5% eA*�:"< =2EV 2���!5� �%�eW�A���_.0! M�� d6/)B.7�.c�a�%��.%e�.��%Qm��O2-%q�G2�22 ��2�2%J�: �>wYz��>#2�R"I%�%��!�6�.%�%h��MA��.*N� -659�a5.a �E�1&.9%��6�A<kK%�AI.11N3.7!�FO��DM!jFA!�6,.yu�bA �$=�)>͑R'�.F6I%6 CE�.62�B�tYB �E�.Q�.c��NC �b%�"ѻM�!Pe^2�Q��2%�Fa��A���$q%H:�2U!.A)w29fA�>Y �_|N'.E�NgIp%�>f �1�>� ^J�^+lk3=R.2t0&��!{.&� �E �E?.�.;12a6=!虔UO!�VE �~N E�gN����x��w!�.� �s>� �M>Q�6I�A�F��)�6E�N�E�e�>�1�9$>]! Q_. � ��E�.'A�V�;�Nf��N� �b+��.�i!��9��%4-�>!$!�6�MF ��Tf WF)>$>a2`>� �9�6= ��1u^+I)6C=��6AL[N?B�C>Ga�!F�d^%%�E f�%�KY]>�c�.�>$��pfI%�ň.�!4M�B=0��B%.C�G2a �UrR$%'N��!NN'e� c%|B�%na�^C��?�BNe2�% b+!V[(1�c*]�=">5��27i$_2 ��A�U;2%6IFE]�EF!�Qq2[�B4R" �cAWF�6�N =�:}*-�:!�tFY �%]A5�sN %��N�IVIqN �Em�V��E?NK�U!'9�F�q�F ���V)A�!�ALN�C�v%�Vg�MQVrkv"�Q�> �E�R E�%��>B �m%%�ZI� �R"C!]^nEqJZGq��l �%�)� �!2�*�s >0�y:�27a�_2�U �2�rns!@N?Y�Fw)�Q� %SA�A�F9Yy=soF8�)n1�NA!#y�FE��N?�]� Y6B2�NE\cr!� %:� \subsec{A candidate for multidegree of the affine variety $\aff{\pi}$} [cette section meriterait evidemment d'etre affinee... sans jeu de mots. depend bcp�si on fait du progres ou non cf ces histoires1polynom �USchubert ... OK] It is interesting to note that an efficient way of computing the bi) s \b! \ of ConS0ure 1 consistf performhhe chang%P!EHables $z_i=(t_i-1)/+1)$ !�h$i=1,2,\ldots, n$ while takQ90$%� $i=n+1,n+/2n$. Us)�qEq.~\valpiob, we find: \eqn\pioval{ \Psi_{\pi_0}= 2^{n(n-1)} {\prod_{1\leq i�\�25 �1\� } \1I0}\left({t_1-1 Tt_1+1}1� {t_nn00\right)%ese areQ�ials m�x$t_i$, obtained by repeated acta�on $d_1��9u$ IXoperators $\Theta_{i}$,AY]�$n-1$. With%� abovR�,2F acts as-�$newthet{ \4a_{n,i}f(t,u)=!�4)(1+u){f(u,t)- -@-u} -  } on�8$i$-th and $i+1 }^ t,u$1.fun)$f$. Nu�$.�$%:ng!:�O%sA�u�q, w! � increas)� at most $!3 MoreAW,�1�f:}8is readily seena z only.~ } ��ger co��s, star�� from]$. egpr!�0ty has a nice��equencl�l homogeneous limit where allE} =1$,!�(it implies �Ill.Cs becom!#t� s, !� in p�cular Y� ^{hom}=1$"t�}. 9Ii�is case �] prefactor� \ re)�to!� h��by�D Perron--Frobenius9all[ entr� of $e�n$m�$sitive, so�$�{ �.a} �aS��0. The latterB refo-cnon-negaeŶgerQuB.l_0 n=1b We d%)� when��A\to 0$I�� ��$1�.�Qrs��!�.� Lsmallest!3which beaT\:�Q�veA�(weaker vers��f %�.�)ralityA�� of \BRAU\a�!� component�6grounda#te veE4ofb.�AZ, E�IDdADSpermuta�`s @(or an1its ro ��0well). At aNric valu����4we have observqh�ll2��If$a|���O �523as�,�.we�17iejisC�aJ�ala{ dulo $c"�, wAXQ�expectA�reea�\pi��E�\!R�s�combin��ial meanA4e��texER�a2� *� . F�llustr%�,Ease $n=3M��ree�x: [xxx1 ion{F!�bos��re!:en�GH} \label{sec:freeB,�EM} Our Result~\ref{thm:n+1phys} associa to~$p$-A�| electromagnetism in~$n+1$ dimen)�a� l HilE8space~$\Phase$ �A1`of pairs~$X=[A]\oplus E$,l re~$[A]$A�$an equival�  clasA�s m�e~$D_{pa-exact!and~$EN a sucA&at:^*E(wAo�Q c� L\emph{twisted-diverg�less}�� symp!&ic struc� on5� was $$ \omega(X,X')=(E,A')-(E',A). $$~ ne�o �Einto a � lexBl!|mo(put a time-��u� : inner� duct� i� 0ose imaginary��a� �~$ � $. � is9�ta�put%�M2v~$h$ 2"�  isF��@a sfie!F h-@ �L(X,JX') \qquad\hbox{a�all}\ !n\inI� $$ � ~$J\� \to A.( a densely-Vd1;9�,  is, �(-linear map.cJ^2=-1�V$ domain of5�. Now,@ aus�!w�arabbelowa<in� �wera� M�8 Laplacian~$L_paTe will bcI[�ri!�ur N n�W!�voscilla%��ror�_oM_ign�.`�`' :)fchA�'xr%� R$�� kernel !� . Rea�l eE evoluE��)�_o%�given by!�T_o(t) W| \! \begin{array}{c} A \\ E \end 'K=<69c�Xcos(t\sqrt{L_p}) & \sin2\,/\,$\\ - L_p:0DBX� ���!D'���� plic�mby~$i$��!�a�!�JIG can ��9���u��8� �%�� eV i]K�S�A� @ e���\|X\|^2�68L_p^{-1/2}E)+(A A'�F�Z) �key�us� ut~$�F^( summarized follow!=$theorem. M }�z�Xc�x} LeYE�be�.6� ��! �8t~$(~\mid~)$, lBL$ ?non"�,self-adjoint"��zp%Qvanish�ie��der�J�%s0A_o\colon=\{A�Ce\|A!�+\|L^){ <\infty\}�� IlB�eq�=c\E�z�al_t(A  E)=E -LA,&�4G �j canonicalݶ���s�t, � �k�t,A' * E�A!� -(A' $$n� re� �A��%\\Y�}Y$ ��e� J=-LM�K�rcJ�) :&11�% comm�A~am�Lw��i�X\Y N %�% E!�P� v� +\|E!�Ii�U %�isi�6�,5�d�wim.����h �(|Jx\|_\Y=\| 2�and��-�Jx,Jy)&x,yj$ x,y�YI�2p iȍ� ~$\YͶreZ��{�I}Ua@ �Jy���<� |s7  f�� %langle�r 5�I��+i pT6_�� Y&n exten� aa4hongly-continuous one-parame�p�� unit4 o"W�,E}.�, 2�4gH=M�$. 噱V�g0proof} First�/ show,)�Vr . SiN $��Q�AR^2= EE�^B�"!/` ��Pranq��bo�� we N�.NsiE��6 $15 is6[%�e$eL�> 0 so, by lemma,lem:ran_ker}�{.�\}^tp=\q w=\{0\� But m&�~$.A�. � NextmB 1n���F of equ�~(�eq:�S_"3 _& }) or,*� Y@at $\|T(t)\|_{\Y}��"~$t$. I not har�checkE|: !:K.�Ai>gY:^ An e� easi�al��|A���a!|J ORso~$J$x ,a� o itad. ͘weF[5ompatibl�*� � analyt�Uubtlet�u"` way,Er�v ~QI@forward algebraicZ��9CP $itemize} \ {1)}$��F�5D $��$ 828\bigl9�,�N E)r)=�4}���4}��\ge 0����AlaD$͒��L��x)E� clearly a��-��� . Ano�sa:e.:�A���|_s>V�$h$2�a����� �� . St�� ��'is also A�ly)� ed. .6o���a|-u|Nd�5m{thediA� R� H� E "s$JK=He�]�Ų.p Rp�Yo~$�O &� .t��4gle=(A|LA)+(E|�y is *� �]�.�s1k� 6 b |~,~ h$eFg i�~$H)�!�a�� �"� :can now7 ly T� ~� � 6 BosF2}!�Fa�L dual�E< (denoted $^\dagger$)9B!@�.�  >5��tLat>�� �Z) n�#s"othb� �.�JG �0 each elementQ�$qJ:YHax / A�proK@ions (see~\cite[S)4VIII.3]{RS}) a6�H$�� � �them. W�:n At&papto��ta�problem�)� K E0_n�%5�<H1/nI� hyp��si�I-� holdiw����jE�'��$0# (��b�!.{ Q��stant)�at!��$ess�b)� �i�#ved� -~ cholium 3!|BSZ}.�dAa:n� re�J��e"� a )<�l ��t,�le ma!�aU ^onveni�afe �s levelIBreal 23��of�2s�� N+1}a�"�i� ~� !�`�F$Fock quantI� _)�aa�BomC}A���+!�cretea>*U c counter &+$�obA�s  ��^ d!opa��,abs ctF�6"0mm)2)"&�"� � �=�p$��-��s�+� A���>��c~$�)y m �)� ���9� $$��:[�.G�A��6^)�YJ(*�)=*�P(- 1/2}&�L �C����en� wa3 view�.$6�. Mn.B��a!rf o�!y2�..-� RealJ%k-F�^*& .� � s~$F^*=[Q� JB�re, if>��� :q ��2Z---Aw-�_ &8has characteris:r,al% mu(FM -{.4}[(Q&�Q)+(J yJ)]x�co7 nt�(��B}F!(���� ket{U� J}2r!�s$5�.� 2�dwoB�i�\brac>v {[Q'mU J'}b [(J,Q= $J',Q)]/2i}� 2+-Q')��(!2-J %5()F: Weyl"�~$W(F�92� !�0d�A�&< �|n:�:!g^-kJ��- �� *+,(J+J'))�!o$Heisenberg� \Phi� &U �!N-i }$�q�( onal�rixA1�h� :� .\matElem24{\2u�9� J',]I)=(Q',J�J'�2�=+�+n � r5ds/ vpre$e�F$� 5Y �;AtF� very"5 t: s5!�� stat��6a semi&� #E�he G umEory@�p�,d} �+~$F"O i�configur1.%�!�doe: t��W�� �2 F$� � JF�9!se� -wdetail�  ne+� �K:jis handl�� Cs2z7A�tJU}N�"a+mF*w � e>v���s�`"�Rk^*����Ni� GammDC2 �K4K� �eL� � �"Z fZlAk}}�t{)<(F)}S� $~:�A�-!TVq��2�-t �=W!l% F r�"/ &�'tA�si��s�&�'punch} &�t��5~$\� �)s'I-e2d �'[ S$ oB�/��ma6� J� O�& ^p(SnIt tur�#! �ex� �6�` �. t'� IsDrstAW(widehat{A(x�|�b� 6* all~$xk)S$Jl�odirec3m�Mu&� 2�k�m ���sw"( .=>�UX �a� echnvO�u�4to i-�B(�E%4E�upsho6� , al5by F����ulZ( JZ =\dd �2�.!int_\ge��A�\80style\& A}a*�!�q>�4�!{]�. Bec�&�a* ics liter�  '��d nguish & ��Ť��as. ,e��( ouldA/extre�+ awkj� n"Y2:  a� delta_x^*�e i)iffemAMmeaA�f u:�,8ity map~$*$ rel58tA*eR� ~$� $. W� Hgauge60U(1U b6�onomyAAno�2�$�0ex�3�+v�3~$e^{i63}\in i . However"h(~$I��a curvj~$A squarB* tegrH �k��na\"\i{}�8=�F�Iia &�>�-�  4J' *�a!6���l�--orde/-��*2;h-q��� zero6��X��� >#��M:�qspz) \K_04� smoZ9  A���X}8 J!~EoG� i �@8� infinitel*� ,=a� d� ���C^�%$*� &�---|)ed�, �J� s}---;( �_! \E�{Q@1"& M�� &�~��a A�;(*�+�-ar &5)�)(2� 2h.\mapsto� $$ I2?c���& ?� w�+U=�� long�Ve0E)# a4 *�suf3?co�� ��exb�Z�e�p ��N!Z�_�&�}[-�:�]��b V.�+*f !cB0ɽ�(\K!;a&�KacI�say �6�i�-%�a {/ �E0!4& }x w?A~$X?_�9ifK0�iE� y/-q/A:~$q��<:`A"i#>�6e�A�otu3~�%�-!V!+ �6<s�=� : %[�=]eCe��'_0�a��of es!2+8.� -  L6=. insidS��Tf.e�. � �� ���Kgend"J���yUq�takes � s C4Lambda^pT^*_xS� getN+ J���&aa#0~>a�,�,~$v_x[ _]�o�� Io�)A_v� � e"um|� & sh�a*� � %���%��"LX*BX}=(v�,A:)=H� )+EAji ribu}al&3Ee� �D� ~ �6v&q#I���. :� 7)��0& �,A W!one-.� �&} %v}\simRBM �a qu*� b& it�4s7E1&$!eq:&9}5�{9�'}{>�}{XC"�&X}}={ �+A_v'(x�A 2}+i!|{E'�-E�A2i -<hF�=2=(LE)D� q%�i��6 q+��Q��}%1��.eq:AM��D��� j+A'�:�-E,;xi*�ek )M&� 6�� � m�a�FAQ6Bf 6sw>I�3entirU �&ogous ma55�!�l��eE c� Ŧa deed��)�u�:um.� of�u �.{EI��0.uTmR0]*Zhr5M_=AI^is& ��u �e�-e�B��and, dem1 ngM� <9� }!:�%VjuE+E>u�{A-Y�� %Simil�'!��BeM�6%�6?�� %$$ %B� E=(vD_p^*��, 1��E2�2�{p+1}$ %� � A�l(� f _., %. 7& %�c 5 2;=D_p\D7�0Aw. �Le�7 %��>� U _��%1wa�v ̙U_2}�V �}{X_1}���~)� (-Zso b�9A5~as!�*�@ Kw/� ��A same wayŬ� deriF�.+�� %mC�2r�/?��FjU Te� �i�a�F��7:�6� WilU<surfacS>$ } N&h/%QE��m�*i;(albeit" 9h̀)� )A8 D��D#4�:�  or"�(p$-"t<a�=bmanifol!�8 in � a%���*R ™sb��,�C64"��A~$p�Gc#,�9�D>sb 6 -k loop� !�#>m ,1�}� genejD�)dA!is� �� �G;=K#��>$%�be�dt�F�>�.B A=(%O,AE}�� E#ab{ �d(to Dirac's �,�$�E&Z�$+� >(4��6!���,Ef"�YZ8=2n*� E3So�7� a��`biB:.w%Z*� !� 01�d:*R�A� Af@.�:Phan:�so���2gY �6jh��g � /%K�O�O)$$2@ Zqu A��2� ��I�*�@a� N�� ^+�is�q �A8@ obviU &�B�6kj� �> �"X�8X�\6�� gl({"�  2}r�"� D \"�< 'l({E-W 6?�-,,X'jj"2�n_0y 0s"MMf&� "�3" ).!Din ��9p ouk!o���a okne�<�/ mX$m�W*onY=� &�Ag y�4��0�!B�AmG yU �:ho�R<� �ebA�J�Af. serEV�*com��@�A�eF� Avzv ~$\|N \|=\�;e� �w�1:��\Wick{>0-/}= WR�)- ���>��-Z� ��#6�N��-iy�#� �\exp{i&�  }W �^*! aE�~$BI> *gE8vacuum Maxwell �"� We|�,0Qya�9EIJ� -���m66s"6�aA&�sPC:a->0i(t)}=����^ r$-�.��n,[eqn�A*�� al)�  t}=�vo � &=&�=" r"\\U�Q�[1 }{<^->�Ba!�\\�@58��-;,�Ial; �8$� � %C X.4!X(!�A.��\!X��T�h�R�)Q&6!' m[A]S9n; (t)]J $� ~$�=A;s�Cs��&$M�]o�  � data� u E� � �n �EZf>�%�$!#.#�E;9��4�"% (t)+A' 2}+�ve.j{!-E& 2)~O�Be &W-h�"�� �)A �"�o "n&�(ŀ2�s� h�/�#/q�!�P!*9�B�-��� e�5at_5M;�=N�i�4Z|� . Ba ~$R|� .I!� t$ b� ~� i(-un�>U�%��*Rb}{�]%� Zj��=&� 2}-i&u \B�:2�r�5!7:�preci�H~$>gA!.� ���Y�� &B)N� �fN��!t;j<� iE.���9�B���)�"L 2-���\\��I&} Z�^ � Bi%���a�%��M�`)� ��D&b=invol"U�# roof�Xis �,decep>Wly �<��/A[!�se  be pu)forO had� �"�2 f3B work���2�a!��U� �{K. A��.rd�*k�hidde�  Chapter�chap: �2"�<��7!=promi�%�ula6�9�J�N termŖ����&�s:�� corollary� b(.X}�{ :w {&� B� E�i�KD><J� rS��� E�=q�E� } Di�;�$�$$2p���J��we ge3 ��������!�-�$ %\docu//"([10pt]{ucth9,} %\def\dsp{ basea�(stretch{2.0w rge\�%shA%2 6]16] >}2pt,draf2�l \usepackage{amsthm,amssymb,�Lidxcd�+� full'T =0pt2>[all]{xy):�X %� ws: -1 =� %v 0 = ��KG:2B%:2 =�:�:3 �d�: 4 ��Yph�,tw8,{tocdepth}{4�new and{\A��hbf{A�b2ct cal{S>B N;bra}[1]{�O��#1\�\vert} 2l�}[25a�A {#1}�K{#2#:5C�b{C>�cat ��:bfM:>cov @rm{Cov> D �DByn bfFdd  rm{d>;derDe�X2  dirlim}{\:o�op�Uaom}>dE b bf{E>ejF  rm{F>8_ }{�J:�fu1!-B:g Vfrak{g>XG ;G>g1,�GrB�Ha�!FH>F�6 fbfJyp rmFi1� bf{1>Zi!N(textit{i.e.> Ima�rm{Im> inv!�N�is%� cong:oK � bf{K>QkeM�Nejyx�:MLa5d!<L>QS)Z��}[3]{a�ae#2�{#3>HN�b{N>�) f{P> Q Q}}%2/b60R8b{R>Tra1�][F)Q�2)nB)f; qrm{Re>IRicic> sca@:�SOASO>so ehsoB pe�S:`R Z�T `A(T><U  rm{U>V  bf{V>vaq�rm{VaBVe2�F@o=5 :�W |�WBick�'open{:}A�A�hclose{:>5�'�kbf6�nX>9Y � bf{Y>Z b{Z}��{�,}{�U�� �$ }-�E6N}[ %]{LN6#u$J\6%�0o�Bon*Proe� h* {Co"4 D \includeonly{intr�Z ion,>� ,p� $,topology,R^0,fockBSZ,QED,� ��d}LbeX] $} % Declar8�7 r Front M2YLr \title{\rm Loop Q�.`&\\ w0us\\ �,6 Jj�A�$p}$-Form EC\*i]\\ on S�9c S�/�s\stru��\author{Miguel Carri\'on \'Alvarez\ +\d�nDyear{December 2004L� M`semeste& ! %UCR&�Mmonth,�� rterb{Do"f( Philosophy DT \chair{Dr. John C. Ba��:m�s& Michel L.�Zidu �\\ D0Xiao-Song Lind \nu�ofI3Fmev)(s{B.Sc. Phy�4 (C0Hut� Un�]s�L$of Madrid,!zin) 1998 f\\ EM"�D�I 2000IM�2I6�$CaliforniaER �de)G2 G� �{H\campus{:}fA�mE�I� E� \copy� (page \appro?acL ledg#=a;�tt{[By|#Dqj$e]} I am ) bkJ�+S%hE��&@peoplS? P�'Y��IrquRFdr� hay m\'�$0e una; Pedroy"F4(o taught meo lG Yst just �s); Co�H Duro =��ed A�FeynmTec�K�Qj�h `U�j�*$4l$ysis; �60Mart\'{\i}n D a-]�probabi8!�,ory; Ignacio!�� o �ldALt!KAXv[\\ �PFI+,to rediscoveb6!�.��s�ler!hn%'� bA�adviso�3Jid� A�Virgo c�ier;�i tini�kopoulou)wa��sed|N mq)Y�invite �o PI;� Barbar�0lisov\'M�ise7 wonde5,��Jat�' too�&iOTm IUho�%fa�/�ZQu�ton:�&!M�8��( (by�!I�,,8ers�A %�@�� ab�T!7m?kof&0all)?� �2J�.ed>_� ull\�� {%\large'ce!h} A�P p��s,�� \\\v�({12pt}>�( L\'opez y :�$ Ur\'{i}a.VI�0la sabr\'an aa���`en su%�a medida J� �}��\� .��wJ } A}1warmup e��"dynamic�> d gravito( � �} (y, VaradajaUaW�?*ryC s#�k!�o %T�>& A� Minkowski)*U �8�Vn�Uf�reghqi"�8�c)smear��L��a G�gan. Un;ed6�etooQC]aa�7,5&�(&� . H�#weA�� a�or?&treatE��<n�t �!��!B o?) arbitr+H globM hyperboli�e�M9*. OurF�DM5��: ``qu.$'': sesqui�ar�J�%�� �=�-7a,b�p�&�Gc"�J%�o{&c1h�* "�. To "�TN i!_ `are�y)_ingFonN,�;h�AV�ddressFvar�% issu�%re usu%uiVed, d�$A�&� �4Aharonov--BohmiesSn!!ce��nonvIact. W�&Qa new�& 1d =�d�:l$A��e-�EZa�*�M#�<��``m��,''�,�-� B�.��S�U/@�~��tT-of�7� %\l�zfs .:es @:� ~{I*X}@is"hmotiv� y\lem!B"[OA��ons in�2!' ntum y~mQ${rovelli98�:N pose#D-y!�geome D�"b?a:�i�W'>f.�Og� virtueP�>*A3�[U>O/$estly backZnd-L�5;(omorphism-iAU0. UnfortunateO]\!�UE� " DE9r:-one�M��|� plici��� � !icH�Ciff,tA�say�)! `t(vS<1�} arisc:fo�ism. At�nst� 9 kine�R l{Q�]VSa"T 1�ft described�4�Q�s ��.spin netDsMDbaez96}� ichP beev�d d �k�M PenrosoU{p 71}%��1b-V�/ "$oi�-� m�ALB �m!' 1970'/��;[u�n ian CE�ie�w|274}*�A-*aYM"Dof 5ZKyB- 1- remai\vE�I*a�Va�. �/we���ye$Ya �EZ� IRAv�� �z Da�7=�in�ulzHy�`umablyar<%Z!q8 Q؅�a�'0vto� � ga�<e2:�!�qD%i i�Eter u� stood:!B�=�until re ly!.w�A�9mbu)��sitf9of%P�` &1�� sihlU=FFLAZJ�TB���0�_,����>tRof cours�34or���Ia�u�E�nfixm2��t�-dra�P�*#i�n[���Hcal��Ao!��q���A� B��I�Nr-�e�l� trad�al)� �?iB oA��*$r b�im&�c pho��(!a)���a*N!`̅���!XI�15B<] <F1] �Df �Te1y�4e 5 � �2-�T Ma( blows up a;3rt�4dos��{  ri`at �%��.�$&� ; � . � r� ��v� 00,.1} tack&N�raby ``� ing''5j&�G�H� �h*$o&�  .Y �'T oced4^ puts-B� )� �in�71f�%. goal A��� ��Exo�gand:_c6bw& [1� �Hon�6E,ic,V� ! . A �I�impor%[ out.[3 1kZ� �A .��y[o�c�Q ����))�! IeO>u�C2�2g�_A`>�� ` dernAXBU�u��ak:L c poC ial~�F*Y'3 ~>3  rR�J�P�wi�!p�KA>��!+hJ� �E�c�n� . AtH] &�8}E�u_� i�K��n � N3} dy[�aro�~a �d���qT�1*�Xng � a�a[n stem�9��0yZ�O%76�_��  sH}%q}R�}�=p5�S <Hrso-!-edIMe.ɬ( U�a�M.�a?wo5.e )�%:�+Mn,��M��*�*;f:�sm,.�=I�m��a �.*jN" ��rA�[$C"BY_��)RCU2�@�r& �Fno2-� ��%\!�6�s�um6����Md ;aU�S|mousl� G� su^Y i��mbi [A" !�o&"., "O� ultaviole��x�4G lackEa2� �})0 duH|/P!O� �� >�. For &,e&*V.�!�g�9&)� � inge$w)+s go aaa�1�no �yg��y>*H���HA�a 0N!�&� �)�Y�e� is, �Q?8i�no�P��J)8B.�i�u�q�`a��Ls�8orV: tru"M�5"` ald94}��n^ pitz? bp�� n�[\S� .7]{ 9��quote}�p�k��A"|-�ejG W��� �3"2��  inB+! azlyTtrivial �x�str2 jg�&~toF[քj.�� -$s$B�in flatY��? admit a�.=i�YJ�f�L s>1$�-S, ��y concy��y a�>O A�� )� ��cassump!%9��Hl"��:Gapp ~3modific� X^a0 rIA{dimock9�4/ �For�ly*hzol�Z� UH � E�]Q�P-�no"zs i�Qy�A Isbe�4 d lo�y."�E5�!�mC ns. (-"Par"� k m�Ef��*�q�n� t so_1:1�S*Yo"�1�S�bari� !��R�Y�s���A�ung�edds� I � �cl��  �ie�rilmAe�ofbB�3 aI^� �ށ��t*i���ly&�7���kb&, I&de~RhaQI���#!" a cer�S �q1s2&c. t��*�E�aDdiG� d�I!Ya * &��z6 c{"d Aa�a =M1i�aV5�ƀ :S a /iz� ~V;R#�R�H��:Meff]! �W%% �2� �B� �.>.�6D2 onesA`X SF)@�UifI� �m���!!jbelie�4toF!�j Q�$� reaAic�el� � A. oB2j44g harmnz}��(a rogues' g؋rya*pat� gE�n�R�gexa�fu�l�~j�� ��� msel���$al-�sA�:'A�� acquiL a mR��d#�7�|o�.  q $  a�dto!6�G�f��y�Yw� iz>��n6a� :qed��kllKb,exܩ�:�moE~ B�!.f(6 �.�r� �%c!---"CSly9� 6 /I|don��. a� at E�asi�Arol :jA�a�I����D.� ``o�] s'' )5c.s>�[X76(Oor#OzyAV��Qnot!(6����&� )their :P=U+E%c\phi}*Y6B�6A}{\psi^�ma2H�+R;7 A}�;J$$ )BlA~$�,d$&d[� a �5�� s�fa9,��e Xke�o*�W��mZ*�I&�y(�A'P�e����D �B�d-!��0��K.��? &�Xly ��o�.j�+ Ata��~ to.v"� s?%�{�^�$\dd tn�MFA}=n EI�n1DB[Q sCf�C&�CC4�8 X�0=i73E�Pj���O9 �W�S9,A�IAR1X}, '��r�Jg">g2pla��p�sEn�ra��d:�(� ~$I�|I$]�Z���ar<I$A;2/ of^>.s��jbf $�te�SI&�;$2�HLjZ�� a~$(3A�6TN!czZ �P$3ymF���xL ] ~$(n>g& sQ�*"G%�>V &�!��a& =any"B> ���J.*$ ($p = 0$)= (Kalb-Ramond $2$(Bch play����t\�y. &-z��$4%0s��& ��AL6� �D*PW+qre!�F&of so&*�'�Ui��#sUHI� nYIwo�lMG� $5B)wwZs%�qF-A#�Y��A�N�0"%)� ?!!�h?4a�sio���.|!!��6a9i�Q"�r�hoS ��^�q �dX��G!7u^�&a��s�#input2�1} %�+seded % �1{�P�QA0. breakpR�{C�%:�sm!.�Xh we lF *�eDcndf' at �!R9'�3VjVI%A�& �*UFZ$�B�k�C}~$\R$\s!x{ !�B#p} a.j'AC.f &r', �0Mn$!"�R�s�}.��N��6l��G2� �#� � *�|A7r�JsY-H!5&�}of" �!@]m y�(�"~ ( �G�fact,�cs��Ft�3M,ly $M = \R \s S5/M$!7�dd!�S o%nd[Z e�Y!S� �Rg_Z e^{2�X } (-�^K�g)�4Rg_.ia� ric}<$!NewB/an&�# dd$!�N riorHV��"t$!� coor��tQg$!op?w |Ad�+ g5V�!�)� K 3M9R==D at=lہlik As �+ruA� f toA�%�say�a e ����ir��"[�Km%g.] z� ��M( & "6�sm!q�#.�1Vi�)G!z\6�%m2&Fy#OqV.mE��let1�lB�>��5v } BIeLi���� B�Li��@&"-�/#�� can.oisH(c,n��fJ� vers�eions of electromagnetism with either gauge group as far as the local formulation of the Maxwell equatieTis concerned. Globally-�ire is a difference, though, because all~$\R$\index{$\R$!Lie group}-bundles are trivializable whereas~$U(1)? NAlmay not be. In~$3+1$ dimens!,�xe second Chern class of a nont  )5b�@ manifests itself!@$a topologi!D-zhc charge whose field can be Rd away %yly, but� g-Q. While.\ Ss!t interesting, our primary goal!�to stud%� effectA"� spatial non-compactness on quantization, and so we cho�A)% ECj�0 to eliminate8, possibility!b=`)Zs� en a�ncipalB`|6*Aq-�ized,A� nect!� on it!-X ordinary~$1$-forms. \I�,Lie algebra}canon%�,isomorphism}3>e.�-M>B �� able-:,F�*B[ �:J.�I�0�E$acteristiciV�S]�A�c�.�J �E���i�M�FcoQC��e9QDN�6#c pote?6.g TechEp� ah,subtlest aspq�a�work ari�Trom, funE�~$\Phi� $!Newtonian�0 appearing inCXspacetime metric. This Z measure�-(di�) du��Fgravit�?al��,�Greduc>( �22 5% � �Ct � \to 0��. W�I 5=�3 , $p�F@uses ra�@$familiar m,matics, main�is por�|�>L~$L^2$ de~Rham cohom�)y �y�lex: $$ \begin{CD} {L^2 \Omega^{p-1}_S}@>{\dd_{}>>.#p_p: {p+1> \end\��� b,p_S$!square-�Ogr�z1 �A ~$S$U�$$\dd_p$!exa�@or derivative on~8} $$ �%�p�� N[$S$} stands�Am Hilber�,�j� �S}�A�,}. The caseM1\nef3Y�} requiasome l�BN0---except whe!$(+1$ is half�"���a_-'},awhich�5 6ism�con��� 8ropriate rescalUo ��s. Even���abs !���c& e most�0gant approach�stillRhid�lT@factors involving�� � redefinia��� plac��Q� ]�R $`twisted' . E�hD_k = e^{{1\over 2}(n-2p-1)��} aKk!-Z"u�D_k$! j�>{k���i��V��obtained!�conjugaK �. "� ��bJ 5� )��*giv�(�� to a9 verr  of� $.E�,� as �acm�,/ )Z �� usu �X �P I��urn;-�;smoothJ�.1lyom�a���2�IYZ���k>�!�"FH= !Elex2(B-)r�� N����YD:rW5y�8q�}q4.�UǍI 6B�!B:]�%N� Wit�9,is machineryA��pe w�de��ph��E�� � }�k�� �wB� :j��(n+1)$-Շal xA� B�}� real� � ). F}�.,continuous HD � 6}. symp�$ic stuctura str }���process,!L addr�Dthe Aharonov--Bohm  }R}!�sit�where �^ N^}M�s 6�J� JJA, a issv hat�!lily neg!7ed��litera!@. Amon���jhrigorous published treatmen(�'s eq- �&}��< fairly generic . old � �@of Dimock~\cite{d 92},�� howe�3is�)� �to $(3f��]�婡�T0Cauchy surfac.  }. At%:A��a�wri�, 1$aid ``noth#at foX s� particula!new�it seem= a_ � %| iece ve�0been put toges X''. A later paper revie� E�c�-�$ mechanicsiTcotanQ� )5 u� +AD�iQorQ�M �oryMgM�( hyperbolic�!_ �$ N$}!U�4one by CorichiM:c again ``� ndA�o f6 an ex�ng gapF''. I����V!�e�pV� �}b  valenc @UjZ ��I� data-  )�!N� 0 �ur�(� �vNoEW cur�� >  }. Gaug� xing % �fBs�t� step us)� showi�M&'�2 VJ} are� ictl.< 3])��},��` solu� ' determ� their-o%] S.o.��� ``funda��\'' :R} (essC ly Green'&N�B})= param�iz<I2i]�A�-�q�o�*.linear� B�.=P. Tev � �a� } enteri/pi� thr�]� trans�]�Y� :!�1d�V�b����gesq�choic��)ױ� � ��In ,1�$makes ``noK~�or �X!# coE te'',�"in�������z alis� N$��L �=$crnkovic87Y�poi��ut�KA�-�strength- W } doesņ provk�=lete set�observ&1�co� " "}8 � firs�� �T�.�u���6�3 1��$&� ,Chapter~\ref,:3+1} re�L< this phenomenonavoR �R} andAxBq harmBvpre�*hoi��!V{"n N.���assum t�~-� say��``vumably:resultsAu�: �+(l M�9V ~$A$ᇅU� ed �A�w� we tak!Z� re dra�J ��a�R�. Fo�purponJis Paru�'s1F�D$�;B���I�hj A�upl�#im�sl] s. FA�$e��iI(A�actM�Q�Q�6�e � be unphys� m cer�$ly excludeny%�� oret2 �� . We2� AUn�alysi �soc�dA�"�no"h6I�B!�inF�a[, albeits A�addUal)�p)@ "� �s!s�� !" � ��ne| The .�implic)�A!��m�6ldiscus�N�u�q�'sb-� )I1(k -g})�s\ to br�Hodge'�Jore�:Xb��A�he Zn9 , usav.$Kodaira de�os%�-  2},�&� M��"j DN���-de ate. Alt :� H:i� no�Bla=�I/ ;9� } (see f�). re nuthe����� e a��-''s6) ~ 6�F�a6&z als� ateseC�proofYreN!� ``for"[ .7 o� +�Q�@V�  will �� *A i�y�  well-be)����quo��b!, as s� We repair����de�  by.�o �!off's� ~�I`-,f� ~ of "� %T�nm3� �W�w�  S ( [above] ha�{� � 4t~$g^{\mu\nu}\�al_ nu$ thuz >� '';*!easily- s� 9 � ��n�ɛp&�&��>2!���"y o^AQ!AGq by�Go�4���e.� �erefore,�iI a+(inner-produ� like�s i�! �"no�su)���j�?V] �,$'s1 is `��yEc�about": al-a6>''A{�6au�`'s ownA���z"� m�*� a R is, �)�'s, ba�u��!   ofF� 1G�l>��no�Fon%�� z arm���t�a�Hesa�way�O�^y foli�p-}aM�5rbitr�$:! 5�. B��h- ������ m� �s�anEn,� !� '$hip betw{`'s�a�"W descrip:apy�-���Q�k��mF@� F�A��rEF. ��pl���R aa� �. ��b�  iZ��set up��5��2�(KE& ��#~(  *�', lead�up�Th. s� thm�X!�2u .Bl� =� tqe�.!�orar�F� =.Don% c�A� *� =E;a/9�ne�ve quadr"e. >6� IJ�N mdi�ntoROaJ* ffO in~$n+1$&� s &~ *�:x WF���, 6�a���ogCF�6n+I.0f Asurvey w� s kn���-B �rV)>� s���)a number�exa!s illust!�ng`"of&a&� !& ties. \c�{C�*E^vacuuF"} \label" I�^isG5! %ky� SM>�(A�aV���cY l.�� � !� : 9� explain"��e� =!>� spli�+a�two� s,@�ain!TAC4oscillatory mo{�&e:�c=�79 6L `tX !z' Nresponsi�)� =`6F ' ef . J�-�6�:!���S�*��se�-geomet�by ɯb� in detail� AJu�sa,z ����-2&�T,"� -�!�Z 0rm~$M\cong\R\ s S$I�� ront2�a���,sues �({�r�to- in e�rB}&J�%.�!��+In B4mI�a� �"�*��" ioB, ak)Q@ ofY�&O �use �r��ABB,��,.E|N],��� kin�( al, dynamA�<� }>�L in6K0.spreI!#QR)�en� :.j2 �EB�e�an se�%A0s�m�Ae^)]a�/to:.2.R�6�q� Afmseem�!�u sa�0%e&)�F Q)a�\emph��!XQ� �:�~|)Tco&�&^*$"�th�ct�xF�F!��E(s��fy�* �4eqn:adj`�"lt_Sg(\alpha,\dd\beta)\vol=\i  dd^*"�$&�)g$!op���ic�$\ddR�*"vol$!�mee�EE2X-�Q.a@+9 �))~$ �%�~$�$E�wK�(F) degrea�� keyA"�1"Ano `bo�ry� at in�(y�B" "�M�E�gaon by�&�A� �B�s} liciR E"~(`.)�L�2F �)La�$�.on�/�*Q z3-M� �^>� < ,-per:  n!s!T�r#.q0"(^�UI�eO��XZ�&F8R�0�ory��6[�t&�7�R e��te1al � }-~: (vanis##� -"�/ 9 �> h�nfiguI�)Y 8O:553x�5"Y q� ~$M"pM$!=�c� �5�*�c"2q/ KS$!Wulo)"Z�%>:�}��soa�isw4c� aK��$�4gFpexact )-3&5� ! s, such a&�.called aMv�5�QBg� J� �JKBg) 5.gI����5s]1A={\dom\E1\maps L^11_SV22_S\}�-2{\ran}? .0>?P}uj$\AMM!�> yx��tD1!F�,,��c�- ' n(al�������s,~�-^ id F�!�� J�$6J�U��F!�*m/_3oeNE�Y��is)�a0 �lyu 2�, �J6&"�� /4J�j )&2 g }#~$[A]5] !�=<!V*�W; verg�� ld2}u�~$EqE$!��� !/e��� " "q�$pa`#6ipE=\kere0^*�qaC}1EYw>]&� ��( $�3�ni(UE�,IgAs�% !�fq� then�F| �5P@(=\A\oplus\E"o�1ase$!*� �[rR�55�sbM�Y�s`$\Ydri dualm"each Fby%$bigl([A],E r)>  gl(A,EU ,"% (~,~)$"!16�06.SMUBe V�)�!�>�]�Fg�N� ~$g��*7i�&dep�#na�re�#en�ve�#cR>��X \?a�Fy�(I�&>&��B&�I��G I�鎅�% �/ed���!�6�&E*:}} t>sym� z�9o9I[A]i! E,[A' 'U1 l[gA1')-g(A'A:bigr]!�.Am B�@!�� 6�-N� y_' $X=�5$X$!�@!&� } V$Y^�$*,�F^:F]�eA"Rs"�*�Aun*iM�'s�%t�Q�� A�"w(^+ j0*&E*A/dZ�%"� one-"�*  �J)!btT2.�:J*~$T(t)\OI�\to 5�!$!� *�* |6���}. Un�!~y>�YO� *� my#heѐ6� norm �3:� i� ��U�Erv e�6� �=�AA�!of� -f. 4� �hen "4'�!�=�� 8}%" !A�~">  i��Delta=  3$ $!<.5*b A�he*��%f �~6�&�!�n!�>P 9H �6} commuy" ~� -�"A%> � 2 �} adm� *2�%�I(= _o�Y fٳ�6N: _o$!�u �of � �>5f$!free^.�* �_f9�zB-�k�Fl�E.G =[ � ^&m6e��� g�2aFd>g6z-�:[ }. F�A�T��, ��%0direct summann�_o:���.�`.��LB� |�� of `!�ke w }. Specif� ly, ���� �fa�a �$�@->t>_4"s�� at `I�'�Ag Q? -�:E R&;1�Kan�e2�9}**� ] 1�or��%V � ,Z_!��hasXs����Hof))a�4icl��2}."�-B� ��e���9fu� ppl�> �GicJa`!o2� �)q*�H@ 2 q:�ar}�7!�?6u �W-� .� op2#� �Bou" "im*qA�unitar(�,es4b5E y:[A��%4 guaranteed un� ~�Т��MQ V2�. A�shall N-$Q��at �.~.�0�a�"c{J v-�>*!} eFBf�i�B"hKA�0. %WC@. .�!�6�sm9�( %-�ɷ��0 (a9;�con�.s)|��� %�Fe�F�AFB2ApS*�K�>e* %l�moxN�� � �}6  %E�e@b!!oom(a� �Q su a 'cFj'�� %��T"l�#nj:Be ^:bl�" % %I:(0e[ qed}=q,EC+ Fock %.�M :�V�2b�rri"6ur,��%� !2YF}m(9.�?%N ��1:�L&�#�Fkd:%qLl"�#�$N�#g"f�)�E !� last"."yM6u'A�%s6a"�)"�?�%. As b�+�3wJ@abeK{�)~$\R &�!Qipped� &Lol:z��c� g_M "E2E((-dt^2 + g) g�)% te Rieman�J K��GE�c(?Ie now �is $n6�@insteadac3.z . H�>, 1 mean OM>&$a��longe� !�- i&�GEe `62D"L'��i$�)ya��* sign nt rol�oe@why, re� �!� ��"� �/�"w!^4{\Act}[A_M] = *�F�,M g_M(F_M ,  )\, @_M<%� 4= \dd t\wedge("/t A -A_0) + �By B?:st22�1Z 0,F_M)= e^{-4E% �. [ -g>odA_0,:�) J(+ g(dA,dA) Rr]y and,�F�vol}),$) I�a�Jc(�^��� �BelJ�. to d}D2!PO^�0��I��s~$A_0$��VbW �$!�A��}=%Bt1�A_0+A),%��S: J'�"���4Mf��bI!� l'��ng1 ew � �(�DI�V�a&dd>�J1�!�%��&!,�$$�zDJwIt DA,DUn �Q1@�e3* ! �> just71 "w": �}) waA�!iR�*y � E9�Ged� A Q_0�(;a��,�=� ~$D$� */Ls5 ."�Ge hel;�H ��!who �.�Ues J?ali ���. �(�;;+if� let   \OC^p$��6�  Ab� � > P"hNA��C�re�� mutu%��#U� xymatrix�P �\0\ar@<.5 ex>[r]^{D_0} & *U1.#l #^*}. 91:92.# 9 1^*}�UV*!K96!�)� sequ��!H?Ca&X1= 6 � F \ker L_1J*T{G  D�R���"�a�r�N�e�Ged& ' $L_1$, J n0.%5�� 1�V7by��L_1 = � +�^*�� fact,��A$c�PI�ar�5wouldA\a pity� �2 `b '�H"� dA��.%D i"/�+2� cB.>=aU�- s��3�)iHenneaux�, Teitelboim~gAh 86�or $p[T,)m�is��� mass� neut|!.9. E2�"�3�Kalb--Rsdɨ�U!n"�in� y �[�, 3.4.5]{R( n87} �kalb74�VZf�3$\plp �L�11.  super� y Pduff991IlQ.�� ulas1fize pUess�?��)�OybR� rg)StHIng��QL�M$A�"� 8 u�i[�B tensor $"� _M A_M�� "�@�IA���m be ��/ �g]6.� .5 of �8guG eJ!�sa�*��m- �AQu�<r2 ,�set�Z�*�RN�:�-Z�� a ��&O6��&� B�R�6��g we�z {\RI  [(: Dj�6�*�i1m�D�0ogy;�EryF�0YaT7 `U�ob5�\G"�nA.��<heU� ��3ixpae}*mHodge--=5M�on*a m�^old:m"� �we��|�"e`A�)2�e�s,*C�,clcn .-6�o3G��w�!oysi�*��M�.7:��corq3dse":�"B_)�"�*&�_�G(:�e�3)�2$�-�c� ct"b% Z noL$ sources (]`iA� rge). �Z �A-�gi{ ll k�66�)�2�em idxJf�?%B� , U!�rM "YG,P))-�=I�� 6�0A� be �Fa�  "�6� (!�h� �LG/)� eQf65" 0&� �)30. EpH � m�V�>� %I ete,� � ,n unambiguouC:T :���� ~ lof� $~�nEL isY�*RrPi�it�:->� Y��;e&�4."��J�*u+�1�6�c*��t �%s cruL�I�"R72�8s] !m9qu�czeQask�:%5TqH$ oHc1�24� 2 <{lott97,carron01 2}: �^enume�?�tem I%�&�`kerU_p$��om2Ee?�<���H@!h�&s �"AY"�_>�5� . % cIf X M�) }lPSargue��"�m� N:V���zcanAbe>"���on� ��)!ZW2Y6suffici(}�fot4k.i=HE0ivial-BouEni6�? \c If $6C�aB/,iIeB�F [t&~@4y8` s~$0�5! "�3��trmQ�_p$? P KlyI i�alIi�$$'of�infraGF&�(s�?t G5���s. Con�\eo�FN�U��B�0way�(�n �(CssVT pT a �� { *]EM�; R! NOG��:gl�6� to qb5 RRk��-n 9i!�2K��IH�>��zf�Yiar�/ mple G0=e� Euclide�M ^n$.xb.? noin��6answerA� �sy!��9�/ yHiC ,�Tv !U��!?�~yTI�D�E� ac�a�;`� �;!�'a��:w�?l��?� (!dwn i�<����~:|of": "vA EA��m4=Ɇ�$v=��s�7y�b m*�K2�� oX� p�9s h�8�W�subjecE�c� a�� amou�,a_Fr �W�;cei�(�) �V%�> �@�&Gin�I1Oell�% �.O =Z IX����8} (in French), �| �MF,�� 2N99}&da�(Sobolev-typa��li�8"�b!O>I�. AhZ"�YA0i6f02 �Eng�[)�1�@< shorA��W&i�a �?h%:bth�e$.��:� flat e�e()'��i to� ),Gies: `.�a�yp"ZkiW scrib� Lott-f��$(E�IK��*�- Z1� ZMazzeo � Phillip1im90}, I xa7�BEҍ�b�&�*.ilsoD&+h=*�QdOj �s�!or-e�c�J tric6�88).B�DFrCJ��n2Dodziu"�] 794,n *�Q�� AS�h"�ing"G'&Z u iJE{k-�h\ar \dd[d]^{&� :qe}&&�k_�={kYi~6r >r\\*8:�DZ�2 k0 5'!K!�� !G(�)&�k�%inb.> ed, multi9� by $9' � 1-2p� ;i-c.�/�3 R�k�e"21cB"�oB-���l�%r&6�]by >AK*��K�V=,��,1might� un1�R���@��J��x yT� | 2�;?"^@�`we�- alread�U�W� m�;u&b0FElexa� �"�� intu�..M f�# =2(pEa��en"$ 6\jGj)�rea�no)1�� 9��~ % &�H�2yce��M )D��Big& Si C1�"� ,~$DD^*+D^*D$� e9ud7&in ]ly as)sGax 5�HcZ ��]ctle� '"� nQ1�#is ][ oflJwe� sa�B� �'�pe� %Qi E�sU"L ��,j�---\ie,"/J:n~$M:6(X&M��$1e c"�JebE?"<R�u"�s. %M"[o�� a  Fur9K� a�(j!edI5 %Y��a�"\�C. O�a�2�,FDlAg�a�~>�oA�q�E2 's %��M eacN|j)$���  %.^,ve.���}��t�� d wI %iL'vRaf�w��Qes:�)��U } %T��S hopy�-h��ua?g�(�^r5XsA�re�� yg �f wild6� � �mVof�)2v�$(e.g. home."A!�� J�%1��Q��ary). M�b���Sk�"{edc�AdGng %var�enS`E�C)!�p@s. $[\ldots]$ %\c�f; } b�R4F" nsiv tr�?����d in %�� ���V�p� r paragraph�py]I}d %�LZ�Qr� m\ �_1!!��:� *zl"aJn�gt]h�$cu� lat�Q�tympto�Gly %h"� .A8��F you8 ge�s�SE�qe�s "�-�!ab�82C )?Y;|%Yy_NPregve %(!�a�dsup+^edf "�s g5KNf %$��� imag�p��;�T.U��ߡL�za�genuine V� �P al (�occurE %middl -Son*% )�, ef��v.��ne!). %dt�? "�to�/y�Y {Q1R�P�&ppa), tru���a.um"VW�U�S(.q V"yM }� Vb�"� I�� languag}0e� �D �b:/ predi��experie�rX4i�U� Niels Boh�3 `d!��Dcornerst��Sv hilosophy>�b6R&54s}�#�Zace��)�$EeHdevelopz2l�Mp���7y%) system�  nA�� c�}!6$� lL �P�/pe�G���c6�in inefxb�0a O�E�ii*�2fashio�i)r1Q��:T!�j�}.� �, ~j, reex�s�m� �.�'��n���tD?L a.<.�S{j=321 PX�&so&P -undE]odi]�|venpto� ��1 ory=�e6��De< �����)� en `%niz�it. Qa��?.� }�a catch-+!L �'c-A tak%8*>m.A6g�iE� f5L.9 "j;�\ Yout Z�2�m XF V{P� orig�Q=? � K� ��K[w:N�d. .G�'�lly algorithmOOr.orial�it turzn�.n, a�ad�Rng)-��&b7�; �F}�0 o�bA�*"st�!��of�ity. �(QA R},��A`�$dA�vA a Poisson� � �H8.�h �e�WK ��#e�"� �� *Ai q.�i��2:Q� ��e Dirac2䁁�_��Y[9 IV]{d257t0��zA(} `promotes�.�>A1U�.� �.�}a$�� ors �RK$Heisenberg d��� o"�BV' 'Y [\�f,g]=i\hba�H4widehat{f,g}\}&}F)f$!%du��&%+[~,~]!)�/$_$!Plancki^a "f$!Y \{~,~\}$!Q�bracket�9/erb�\��:,-s:A��9�� s~$f/g$,� 201!�� e`$ir�:u unz!ar�Y and B~-+ OB }�5"��j!ar�p�|c&� IJ}re.�MZe). Ik C hardA� conv~ ones�� &�!zy��9�Q�ED&Xm���R8ia*i i?fTKto)�v3�b� u � m�� � 9�at �MU�g}\neq a�7� neral.����*is| ` �or7 &�GB} ;$�sAn ���J" �J} �&_Ap�loV�-�:' �ye�%L��._ �y2X<sense�?A�"� �J"awn����A I/byA��|w��ic04n �f�6/�52 ("c)�g1~�1a62 �22`Gm�(B� }. Each>�is ���o� "�q`HU, c �B  @!6Q�! }, ��}%�� �Iat��� ( Emany  �reedom,"�t � �'�`��?il�9"�Ot:�K9 .�onA��$narrowed dy`tm recoy!�& ��limit�BYi� �5atd mKqV�$. ��,Z- enco#&%�x+� "�>-�c"�+ aAfawwee!�Qf���տ-� Uѿ �_� ] 0.<6�RIs BC'�ld_&�z (*�, `})� )te � e/ spac4� � ��B&dy%�)6\�{&��ɶ"N pP�+�!~$x\in.D�$x2G "! ~a>�Pe�aX9�S-<:�re� u[4��+p�ket{x}A*� �)o �} s��![�}ed valu�m�{V U��G%�~��7al@9�c~$f(x)�3fI`, "AmPla��� �!�aa{1,\matElem{x}{ �}{x}=^+O(] )R(� $N. y}$!�7��r%N e���`@�/!G|_�b%��+ must � �� 7�)d ��� � �Ry6�a"2���|um)�K'�.373� " ]*M�:i�  a@0e�E��a&� ��n��-xe-�J|�}felf)CsoEpV� �� �@!�x��.��f"G��0܆C �n�t�1:銁$ Na 5�5!�si� 2=+)>�F<&"oD2n{"o&@2 �%��-�MF�A��6��I !! 1�11ed>] �(�ery;4f Wilson loops99s�FN�d?E)�z7q,e.q�of�c %6�sml�$ onsiSchr\"o%e� J�ch�sva�' 0z� a?�L+hoGtm�%-�6 FA�F�e(.�>��!wory]&Ka�7 �� �&2�>�F�:,J��� �ePbe�"T�2� a@4��*�u�7ʐ~$\K(�D~x^� r7 3 kA'o~-1�dofgn�{"b�. Lwqus"�|!�x!�$C^*$-V F.�&!%6+M�)�Z3D|exhib�]ny� s or��-s ��i�C���)ssG at ``in R����[� L]>M�K, P!��Eg���ion�tdix below'wayP� A��:�K fai��0L�iVDi�"�!�.� !�~ cڃ!z�o���/or>to focu� ``>-�i*�Ta� g�3 lm%~(AJ@-�!I9qo ͍H �R as a `g5 bo����'%�]U�z� ���� x ��du��x!'" z ~?a6��y�0��$t6�B�� ~$*$-&&~2@��.A� )��"�ce*�&obv�{I$�/&]a��@_yyq��c%�2>�)Oi�d�a!�)�'6u�2ځ�,o Earm���9u�4iP�berm ``U�Yeeism''bS!eH(* s)��9�A�Yy :�W:gz��ofac#�l�n yO B�Iy6z"��u is sP Aru@ 0, Tň$Varadarajaq{t}� Z ,#� ��� .D@e�a �-�O�%��" hig>.t�ttwo� i.noU<6S�o �"� eups.V~"JLm-��A f�, �t�wee?[O�t�!;%�a%�is eas%�Ɔ"$-uX�"��Ya9 a� o�oug*#�|� y;�/!m$Helfer (noMy �5� $S$-L �`in9O `out'�H�Hadam@6s)mhl96u� n~Hove (�'a s�-;)$#� �-K i�� >(ove51a�6m0@���(e�h� � Vt �'n���5L2iA[D/��atI~2�4BM9��@u��� "C���y=��ѸFoc6bP �Sas ``ca'��-�ry2�HaIwe perFK�MFR �baEic, g�B#e�wits'�5~ ���mit. PA��� :b�tE`�AmiyRsu Z��n� beyon G`�!�u�&a^- �� �gm[im�LEaT@&�� �8� ��s�� uld S�*�- forwa%mod�N� �AFmxUD;f �� Ela�5���H surp��� st$>t(for.pic��B$!as:�sS`"_� m� �af�a��G pow�Z %*�,C;$ (�J�,L_p ����#)� E���:b�%cI�p�~E�Inu�� E%�,ase_o$�.=Sl;�R�O6soh&(� h"�nAhten��u�?��:4\ge\epsilon>0$!�� ~$�9<!�rue�,n �a��+M� neAX\W�-f **�=we do�9g,a�M���%� ՠ��/�7~)�et\rAI+6�H y to�9q~H� �� 6%l� "��&4�s  ,as Minkowski) =DA�ter{Co#nt-�F��D$#s}�T=Y �!�k�7�� AAoframee��A2�of� 's�7| �"EaIr�F Segt   p�%ec8he�A����]��qu*�&"� Y�  *�Z }, mmg\ )as�)�ub50te "�4*�-`>O ��Js:՜L�2F b`1�%�N>^ab�>ct�U�meda�\Gel'fand--Na\u{\i}mark--%b&� i"�Zr1� � �Zu4a le�=Es&GNSŗ e} oHL"n�!e, �jF+DF h�Im#1i�)A%E�ofIJa[PV"_ jg.��Ek2 ��2 ny-�@hMQ)� I5�KchU��e*�"N!"� � QHev�"[ong � 8a�! expon����*,-�A,so-�1ed-)WeyHn -ons1$:��^ advantag�� avoiD^��A� ;o�b�6�(or�"���}&U)�(*] �.e5J " �?sڃ" !%A.ˍ. �vi�/�Fh�,�H:G free�)~1 )lU� �eCq�aI0II �&SYA�mŧ4�� 6 ?urQvat#AL6#la�V��� � axio��M� -u���R ? 0M�� AAQ*�_r�.|�-� !]FQ:2},6� *2�:�� Barg;Z�� 8:B::��Jm��de<� ��"o %� . ���)#�,���st�6!proble'��C� "}�k2 �!G)�9��w��k��t�#f Q>c` P � �}, nam! whetn\um.�| FHJB��}3m�x. &X �*�@3� �� l� ewyBion�>� �>}"� � c* !/te��>. 񖡯we�a�s�'_ 6M>fu��"��B}� * �}��Pa�!� $�@} ,4n�<h��D� :.��e�i���� � .� '}DŽ| 2m6P�5�lr!oBaR'L�����.vsp�A%t f� ". �q�% ,S"B7���Ywm��!0IAiV2� �A| * ;� ?8D� d�iv����O!��e�!*,4"02\& "w YGaussian%Wi��skMe��2� ]��%5�� *_0w�*����k��gu"$s:pApn�'�A%.u$D�j��&� ��ҝm�:�0�2$ME7�-E>.� �d!�a�E��� F�M��n<&oL���� lex&� J&#&#"V'h h,I>�E55 s��ya�,*�' h�2R�'!J ,IARh" [�.�&�$qpFw"�RZmݔ�y9a�s�*�ed. &�(�o }��=usefuP,�4m�&�"O  h���#P.: � �~=S� ��:�Q �b8h?b���.�-�.}I�2Ā �S�A� 6U&y[ P69�� &� !�I.� � K .: }�W�a�A��2 >�c"@�ewy��1i6-6))�TAN�@>� �1��H�5%���ry kU=:k � <th2/Wick 3 r} (�| ral-ord3Z�&��G�qW I��conAv�6@Z  ��s�.u^  can �3�r�.�"�& #}equ.# &6w��4h�f $or regular�� :6P, .\�q,��� )� B>}�%���BSZ@[��rehN've٠>o>� nQ�9R'A�*{���$�� f��A�40 11]{mandel95!"�;2d*�X"�OE� .�B|hKe B F� ; i\R�'i2��&ho_#R�"CA�=C n~$(E&�Bg[�:>�:z,(6"�>i9z@e��:�:���pr��sui����alogu�A��[&�&Ay0\h�eas��s&'Յ�ucc�~gtSe�<~��*��%})|f�>."�  a ).�:r � *��v �~$\Hn6s��.0�2/!D�S)�&�D�ܞme2�)W~E�1&�� denote"4s,��3!c� �.� |�zj 1�.� $$ �p �^�6^�~$\9le�5rangle�^5mu�dSs ima:ry �,U� �."�~$'{ W� ^* �!�.m ,k-� �6? %�\W(H, ])$ ���M U&� f)XG�1J �� +&�u ��a�Tmu(f)=\exp(-\|f\|^2/4):�f�.EQ . No�PnM��22���t�itary�Pi*"^Ua�~$\mu ei�k � :j �Ap��d0�9^ �Y~$\|~\|$)�b� �7e�Ani��Xl>�\9�|�- ��E� i]V ��y~U��haI.��Q&ɭm ?A��- �s�at!n��&?(�� Su)F? aY~$(Bd CO[�A+%�reH!� d�G�v|"��5ja�$ ��5�\a IaNT =.�qt!v�rH-$&1$���R�+�6e0&�">�{�[.(��se%�a "�� / ! �܂%yGM� �"3 "f-w�se�'�.z_1vr�`"x" E b&x"q!V:�\3z��m�� ����t,-ufa�;s"} �{"DBwe I��NQ�\simeqI�~ f$,f�D_�. chie�   ��*�" �l_o$%��!yRmpZdz�1���a@fr6�F7 %='!#is "le;�S.to�Fa��!,��f� �I&� !Moreoverјly �E�#lGtwafin�� (den�\q�)m<*6Ѵ� 2H (O�e�.�of>,�26E�&~$T_f(t�0�shear,jh!m�$noAQ�*�#�\.�6s!-�u+�XU �"!a�HF:sG6ٖ2� EM�1���)�*�:JZm��2� u�P3N�3punch���3ourW *� t[�4���F� >�to%6 �>�*D5�"g\ir&,.h&�heN���ll!\ۍ�.Y5��� � ���� satisfJ ��&�B�. M%�0ertantly,e]nUM�o�,�D���[Z���Nn5,r ���!�j `"'�H or `smeart�l�4�|$�%ork�F.v&.00,.�+"i8QED} %\part{CojZ�nocsP8*} \ssp \biblioPystyle{��}6{dissP� } \dsp �4m�iIvdraftzrix dex %R�]!"to.]�xe�ues` docu2,} �%%\newEand�k{�: hcal{S}} 6 dd  rm{dBa}{\colon>: < bf{HB<KKB Lagr �LB!W " bf{PB!RRBXx �rm{ >�� }[1] %(open{:}{#1})+�{:}Iew3(em{lemma}{L)I����}{Pro  \�ion{GC���etd "��A3+*e�&� =a�"7A�2B"� eFo�Ua�&�6cf���,��2lre�2�Ry�~4SJ)@ t +�$���Use$� �a�����qB~9�Aide�Nr)d p{St��gn�-s} Let6nb�j��{Q !Cpr��2� d'^  �},Nw9.�r��56�#,z� F}}��u.�� "؁R{$l��1{q2�� ob if�&�(���U��*�re"f"�!q}. Ou_g��=� cast�w�in{[v��<h%� ua' (pseudo-)&�~�a��Wc}[=A =� s] A2g�X-l*� *imeό ű 2��} (�� ed a9�) 6j�%� '] %�� %�t adm�aZ� &�0 � y � �C,� � o�4�m)B�� E�y-��c2�=� �i&~, Iofo+�e1� 2+�:f%�S%E�ۯ�4�ai42 )�ryUxorthogoVt8@ ��΁N-%�1�"A����'(of}[Note] SuA2�)i�<d9h.KŤd .�}C9 a break�F� �arNGiS6-0-g6 *'�?�P8$ � 5�2so"��/d� ��r$:ffdZՅ#:"6* �>h -q� gZ,�!��i1�5�r��  �  #"]�� 9Ρz:�K�dng Q > RR�S�KX 0 y~,a� R2��  �% ��()�����.�4e�e� �.�e.Ab����.��G2�P�5\K s S$ u�5:��&l��s�YI �y ; E"i�u}�i E"��\`�-K };�+�o $Z͞�%&� 9$t �tmDf � 5!Am1 $$:^wk �eq: 3 g_M=-e^�ew^2+g_S&SQg_M��!a z*�PPh^�� �$t)�*x�?g�΁�Z�end�&AQlV VB���-' � en&P�jY'S �i_~�dJ�R\2�q.�&D�J~�[%�e99� �t2C�7cross- ��A ~$e^!-Iz t\o!s\r+ /�� st � �}�:���a� zero�D.p~$Ob-p#a ��JX�x�e,A�"�,� {wald84}�B}mc&�/* �y��it� b"�^ityerml8�d,�+} u<)e:>"�4 a&l^}%)�M[\�E�!o-E}�+i� �"  }��a��&�3 } `b%� �fui0 of'���mԈ� �1�� 6:�3Yl��5o anu0 �6An���*^p>�|ѧ %��>%\'"�p)=-9:}. By re�!�A�t�r&�� H�R����:.=d�*Ua�"� >0 �J}h6q �&~aE�Y )Kj8m�""Z]2q# UF P�JW�m<geroch70� "�+�!A)(y�h�-see�R�Z,c��J��5v"*1&A# 65���m2r-�}� �l.�= [J}-yA� M���V%|%H�h\� Yz�}�*�nitl padon velpQo��y" "},|8i>at�4Pc-9M� ,^-Gsa�?^� �]oRA�ceba���������u�Ya91L �Bo(@-U>!�6��/�}[ F2�Q�p��wise- ��-�.�+rmn� X �ms tang�P t6�"$�v �-0O e�5� achrw ���Af\�%� �yKe-ftwoA��ޑ fdom� =�x c"� R+a�A��(A � ^~$k� &7 p$!xA2�� �6"��!I&)2 in�i&��. ��QA�  Y)�u��(��* .�YPA#��e���et. A-,6�G�:a��!� o�re�c8 6�!m�/I 2& )� 2� / !�=�{ lz��A9" L� IKJ�1$JS��*� ":6` �6j �8 �L~ {��N VN�F0a� � �jS �J. ���9 s, `Nl� N�T` Z t5 2�DEtraiF^" A��t�fA�F & �s|La7��/F)L:�l. A����X�(i@ se}@�a era���yNxtE0Vz�Yc^zUa�N�`p$ m��(����V��:E{ � ��m-[MՕ&� !�nd Wu�x�V� ] �� �����2� ;*�?*�� 3�2:� R�q�_�Eeq:�~} L"K(-NM):LK�'�&�V��O$! �pgB-�)1)�-N��2�:� gq��a�a� � H }~$g!-2�}T $N�IC��jEC k�� R�ܫ<>0�aFs����6Z�:}O+ O+�$MR1694235, d05624,MR776077,MR0207364})r$� ray6%7 desi�X��o}#r� �{#��ge . �v r9H�a��d�arc l.��} lif�'af(�ly6? � �(Z� >ght��B�% 5 �yf5�n *� xFoG?i��J ~$t>H*E�`;��t�) arc-Rht}�!S1�B� `+�F�. H+U2�o�Ighф%(.!�9A |I+��� ��7�bxihD��Rw���r7} alone�)�L~!sfel;+e �a�m�!-�2Fxz�^D �thU.� ^ �$�c:Q2"ps���Zt�0y} WH%�� l��}Ŋ.i�ln����old}, Nq�&�* y}�$F2� /�lX=&�� a< N�m� � R6� �F�&� &\S�� U a �6sB�(e iCiJ'�����~Gjeniiw�ylso asOViF[�qY/I�$at�"m�igv@&�,s a voluY�~��1L�&:C�1q. Simi�ޅ5I��� D9�b� acquG�a���j��� vol_"���l�, 96k)(67A��/nB.��c �%�}�+I�"� &2���ɠ*/�� *�c �!b�"� �z� MVKG��.� &��(("�IfV�wer�=noE�hVM n.)�},�/c T���3t��!"�x�]�,�KminorI�."T 2,0 &R�4�7vol��3)� �%N�b� /(2�r� e�!a��nt�"� �/��Drelig�(���.ԉ$�p[�ll2e6Q�2 ���u" ���jV �(��~`$M$�6V�y����n"$N "�� h2l .l0$�vF�E�parBs�Da|� AnoB��e " � �!f� into��} :6x� empoΛ�a2} ��:J�_M�2� 0$&� M$!B�6�� R�� d� {0$!2��0 $I � .�:,l�p�s��B �&#�f�� $(k-l�A�!O!�2a 1�{ ,�6 $t$-�t.�T�ri2�� �J*�9:YU� 2�d dd_MN.0 C_0^\infty\OG� k_M\��>{�M%s5� ֿI B1��toFa IS$�G�sC �_0�S$ �>s ,��{edy!,:��:�A���t+x��<&�wo�1~$�QV_M\h>� k_M$�cW�Pe, I�%��)^�{�n�-���=dS�U�6��2�%B�ͨ �_M,'�֨,e^{-2k\Phi}\��[&H�bE�ߨ)A0 50))r],��i~2B��Z ��/ve6pP���sF�F�!���� ���(D \qquad\hbox{and}\N �&޽ F B�HAB��$Ji|�ci�20.�4n� ���\R� (4-2k)=� 1 �- B�� o�u.�F�A�M~by&����2al&h��9dd$ M�A��2�~,�� �"0Wf#8PmZ���R�k����dӿB-q�I�=(\`�IG-A2=d5allMA (\��:�_S �2=Yzo8: _S^k.J)a_ɦBx�s�|�e.� s~(YEeˬ� )�[:e)!W� �J� " W`@ D��%��"�X0tegration by �parts involved in the definition of~$\delta$. \subsec�{Issues of analysis on noncompact spaces} \label{sec:a +<} A restatementG EquaZp~(\ref{eq:formal_adjoint}) is�xexistence of operators \begin{e H�} \xymatrix{C^\infty_0\Omega^k_S\ar@<.5ex>[r]^\dd & C>({k+1}2,l]^)} �B�2} \end�$which are � �%@Leach other. Our goal�o extend�0se to densely)�ed�0 between~$L^2�$ and.�$ � � k�Qstrict st!�1j�$ory, where.`k$�ote)�sAd of square-integrable~$k$-! A5T~$S$. It turns out thaLis can be done preci%(because~$g$!*a Aulete me� oV�!yXwe have seen is equivalAyXto global hyperbolicity��time. T�%�dboth physical and mathematreasons!� wantingd$do this. M-4ly, a mutually5� pair�unbound.� -�( two Hilberqi� muchA ter be�A=an !le-1�1�U: �E�smo�(diferential�,ms, althoughA lahfH more intuitive geo-�8appeal. From a 59pa��view,!�(do not wish!2�A� ourselvATo !�Pactly-supported field�� aB�, but����ed h!�we ne%e@toAiI��M�aorder!G, HamiltonianEsympl�ca3ucturesphase)W ]�X e at all A[s. The'o��ofY[consider�s dem�ewe treat��d$ e払 $ asN9A� :5�A �}�!�:�$. To prove �� evolu�� mapi� clasi:�itself%� will also-�o ����j\�to an�>B� onF[ $1�[. FinA�, once!�insisA �� rprea�z!Gstq52s��iq:�eWs,A eATromagnetic gauge transe}!)s �Izoe:J� gene�� . AA)� r��@res a short detou��to funca��鎑� is contai�0��is ��. Whil!�e facts!'���0well-known to �xpert �y maya5unfaiar!� some�ders, soRrea� �)�a f�� amou��Hdetail. We omit mo!�ft(proofs, man���N�f�$TRa�a#dSimon's textbook~\cite{RS}em � who�<m��e�q& ��us��� m~ skip!Sa�on~�sec:max!:}, wit�-observEiCf� thenAƅ� \A�a��de�Oed^*$,a�inn�*2�(r]^{\dd} & #2'l '^*}},b�3B�in�%A�reEP symbol�for%Oin vari% $al calculu�k�0r ~ 3& $main purpo!�!�is .� In go`%{~\2}) to��� firs�ngA�eC� Ae � bl���e�hs! d\�R� tob� 2�ZC1�NGk_C�r�in5sf� U Z� !5m��aedA�� -] ed Q�՚2H �J� _* T!�follows)�Lemmai lem:l}. q'l}� ! � : � N�$i�respec- a�inner��(duct $(~,~)a�>�. ����} We%2reduca7� �k�C�} cJw� 0$S = \R^n$ us!�a � � -of-un� argument } n�  doe,e$Y�E���%B a?��4 $$ \dom\dd=N" \, eteq L^2 � _S .=��I � ~$\��A!Xusual wa s1���rstik�;, sO al�salpha\inF�$�� u eP$s a~$\gamm7��$ sY a� $$ ( ^4,\dd \beta) =( ;, &�� �#\inR�� f _�$�it�unique&� N�%�)�iBK,�5 �o)�-; �$��8l l1$��B\F=(%� R-8 \qquad \forall1 F�k_S. �p� Bha $sired. NotAIat,9b% 0 d�b��< : ,~$ �/{ .3� 2 2,. SimilarlyM�2��~F���$,��B6^*�} � �.� A^z �%� ^* ���)�d by $$%j��^*M�!� )Z�q^F� � . %�qeq1�2}�6� �2overline a� �-P��closu, �� 9�$. Fo��A� goX �m� ���graphM*�ar�)�(gra )=\{-(oplus\dd  \mid-_ �_0w.9\}ot�U�� P��-t�u�$����i7 20�n$an obvious�o 4 ����yp�lye!Ved�M say�~��E�!� ifE� ��-)�1T�� � wa�en � ~9�A . In� words,F�)i\inŴ]B< \Leftrightarrow *d={\displaystyle\lim_{n\to\6}} Q_n ��\�rm{and}\�� 5�_7s ;9hbox{�% �&��N� � $lie���2� 0oubledual} A>Y�0 $TE`!&M�I�(only if, $T�isA[Ji�dEU�� k , Ys T=T^{**}>� O� !q� X auto ly� ndR T^*=0. Aa�result.tg �Mw�� �)c=  ".���� a�"� 2�� 8*W�Y��� . B� See~y@[Theorem VIII.1]{� � W�� ��hah F�� �^* 2].�om:�*� B d^*,�8&.d�3uA�be�� sEc iy)A�ac�Z itA� HavA� JGis highe6si-��wisAper�at leav,wo possible 2+[si�J� %�(dd$, namelym�=5)�I)u ^*$�5 means we"��rstA�how�%g s $%|Ykd =)��M�B&�� !�d�s couldJl� hold�( answer has�do� Nary valuz SD%Sa�E a relaGa�� open��e���$ larger Ri� 0manifold~$X$,'�w~$\� al jisub;eX�I(�� �1dAed%HIN4 \emph{never} !��� �� DdevelopeZ�A :  explai�hy 7evans98}�"brief, i��Ŷ $E�--ly0 ed Ka#�,g� by !s givesa�= .] ) = &n A� )2��Sall�R >[ Y .�28�.TR3^ .��3 !i�� roxi��on��s.�]� �)02�$�b�6�if ��5 e;� �a��Qt�:/!F �OAge�_ ^�mera.� f�8�jd Zoen����}J�-R�.])_{y\�v) z&W � 1M*� qRB� ��M9g�by� apNB� showAx(�2F=yd� )+F2�QU >VM��Xua-GUS !�YTzIJThH �M�B�d��A����F�=I�`� !=� :��� zero�� term~$j� $ ge� @way�-s� �problemD$occur even{���U�a �%��% ow��a$�g�l situe�c�p�`Qj��'�u�� b�:y`��,� lik� �y'��fact,J�g})%be�P5 �noa��/ki a��S&*y2Od$ ^ 4ood1���!�BzJ���JO�� rior deri�Ka�vanish� )$s��'�R�*tJvdi>D�J�� >�no �`o6�.a. ax,!/ ."36heRqw failA36 i�el�# �a�.R2N `)7.�'. u, remarks app���:��f � *�Sim3pu� m�� � w��] Unter$tYt*we�ge�me. Lucki� folo�� AjGaffney �it �se�s q  h9��"�  �"}2 .�"&�propos�}[ ~] <:g �} If � n d orien*J� En�B.!C�� #KUa@m� &� � ��ls"% s � a��lu� �IP9�6� s ``3 mYneglig Q''2gop>E�b�un< � 's paper � -y 54};�� � �  aA�&f a6�MN,in Corollary � cor:"~}, bas�#n�k�Chernoff�c 73}end! of&Gca}�.I Z*.F�&w �Oi�M ��)nm& a{ >$)>% ��A�&�'&�k6�'{�N�.�6�}}� As!�p�$!�ut aboveaEisB���!�K � di- ��2��B�WeIl*q#$�9��!Ye �hl�t�-#byhI�&O<already �!%�6p"w �� �!�]� ;� !�^*79nd ��'nd, le2L�J ?E'Re By R�DVK�h�( $ lib"a� sequJ*~��_n$c�l.g&.�.�8z�a�s u�t writ,>� � � �Z B�� _n:*v B�� �a� PS F�w):v cV ��N*  �R. �Si�%� ��� rbitr�E�r��7`6� ��, � E�5��E$(��� ��Mx (�s'9Q�.� an�  ,�D $a� �x � f2�A&~!&_!�$})�Z����shH(se��e�enes�&qNp� ae��(�#Y ��dK &$2C[:?�-necess[to make �#�Fock qu+z ���>4'�)a�}Y�M���2��M�Ց�xa�+ )S$  ZweɃ��,�0p'&%,�g), B), orign( �. *D')~$M�+{ o !l Zly*�,VT+s inB)<com� � or l)'to#�/yfn&] de�J e2�[ mH i@ime&�)� v} � a �M� �`&� "� '�!5Q&# NHretrop#%�.justific)�assumpaT � �X�,,�+ict�pez&����suffic[ �2�Sa==co-V��!�� J�.Zur�!_)�=��� �6� �\�~2A�� �U> ambiguWMlo;$:�:� �dIm��e&�we�%� D�R.m% been�ed unl���s�a2��sl�/b})not)�by �:in�+_' )E �ed verI J^wno� before,���{ s0[!b�V� as�)pre�)4%sQ$�^�( S/ime9s- rtm o�+&;)avoidA\f �/"-:�& i�on&�in n ad�al bi�5S� beY�; n &�-) b� dd_kE[}� ��*� y*to- $, s� M'_k��(f�!^*>P?_S�(*  ( \s}+{Mt+�+�$ l"y4�+*�7�+i- DA��IQ R� E�sA��!n04rincipl�I�� a�-iB� X ./m� ��colM.' I.Վce f/�.�/�F( � of m��Ve2�/W onst�0�,�+steps (Q�`in!�ce,�istic,w(al}): a�kin" 3�}A��r�1; �)' 9Fo�rmulatt"����%!�a2�1orR�1;�dynam�":� f soOorD�zn�d�iafnd Noe�� cur93�)�d�2.XV�<�"�.2IB��hin!I u- dom,�T6d� . F!(�]�ge�) Ai�2M�'%5MJ�6�a$R� $vector pot^" � connm^$ ! trivA; bunda8ver���%. *��vacuous a��a�ER)group i��R���-ţ ing.!~$U(1)$:} sm,T � �")u�Z� odel "�1monopolL�a 6B� �3� B-}2 17~$A_M$!/s!�!;[ i�  co@/nt�߉���6M���0_M+A_M\wedge$� g  strengtE,�cu�0u�72B3|F_M9d_M A_M(A�2M,q�iN�9��eq:i�DM} \Act[A_M] = -{1> 2}(j, ), �&�f3�V4 �!�4to�+��M\phi�TX 3:�F�5B ��l��������E>�A/Ja�M�  To ob�3 aUT6���A� �N�9�S~an�a��`1BUG i-4}3 mily�Cauch�rfaces ��5*A� %\!on���y5��d��i�8�9A� iq,>s� l2� F%@cY�F:st��1 splitm'm F_M$�a�8E�emporal�:M "  ti A_0+A��'"�A�2,F_0+Fwh6"��"r�0A��~$F_0a�E6�ici|� ~$F$�Hm26e��"� belowJ�st�e�}� F_0= _t A- A_0^��Aa  GR�6lea� !d unchang��0their effect  A�%�A�,g6�=l� eq:st��} Au�a�a�Z�A_0+_0+�4!q* } U� FJ�1 2}),Ju�E�be ret ten� "� narra���,A_0]= ��8\int_\R \bigl[(� A 1�,R) -wd A^0A)Cr] !�t. * �"l � "/e���$e^{-4\Phi}">a�i*= 2�wL3Reaz�3�cancelle�38o�<~cbE� :mfrm2��UF�vol})��isF�,e $3+1$-dime�&16�5̀"� 0ialr =1int�#���_3fa�3��HQ>+89��C:%Aari�s is � . Co )'c� an�r8s�h���$~$g_M=e^{2%�(E t^2+g,- prefe( to --.E,_S�(�� !Pe I/� Fw &K7��<l3(the Lagrang� u } \[m}M�do��,6)-�% :�,*X#]U�s� �\2�$�**�,energ� ��M��g�oNi8.4!�divergj�EcK� eda�=`rv%B~$t{ i -i� iC> se, 2G�o �*m�� tudy%�*�, *�n� �*f-�!aH eval!R�@he ka3-� N�N,.#"�@�E*G8�� )--();eq)�g9e�includd ,phi(t)�e(t)��:>(0$*x1_SG1*&��AzM<2�2M�� � al�<,� !� �!�8$ norm�8!aBF )_!�n>2;�IKSi�G���*%�61", s�$; �?Auim;J"� �'� decayU�  N�*�>"� s� 0,A�ynd S 4�ed�$toZphi\��W �^nE��h��� �M -��y � E+%torH a2|/bq�/B��-4&�F �b- forc���EE��+R��!� too ,.&#�w�,�� na\"{\i}v�abe1:���-�Z| -[ {�s can!est�elf�"� � sCAo!ed regYf %k��Qu"�G Over�?�&tme ic�G 2� ;#���C�]igu,s,*�Y'�~$RE-aI�I%^crilE �s (!�<� minima)�an��&#A~$� _R[X];1�uF�A{�local}g$��Ac F+�A���S�:5Z )n����Qcsita�IL,A? eachv=�, depend!�� n%Ban@ e numbe� A*!s (d;lyS��>)p %ZA�5 9?�often �?��:M5 R���})�F�9:a�d�o always %`њű�j��M� �� >l��may<)�' r!�� i_ � m�Fbe ill"�>���=bg>�F�ximej(JC� :L v5S �1�.�!r�K%� place."a2�i�m�"�I�*�.�}~$\X_R$�0 enou Ho���llqu�2�:�E�sT ?6M== Ry iY29b.� �>eS:�xy} (30,0)*{}; (25,15)**\crv{(20,5)&(0)-2(15,10)&(5,2 H <+-1E= g  [p10,-5)}?(.5)+(-2,-1)*{\scriptZ8 S<0j:M`12,8)*\xycircle<14pt,7pt>� 6PR};,�$$ \ca  {Sch� re�n�o2[��%�A��* %AV>)�#  M�� � 1�M��io**� z�e*+m\E� ^sA�n���0��Q?�QE=-\�%*&0,R}\theta[X]+Iq E[X]It���$n�'Xzuckerman87,crnkovic87}�2 "�5��dvantagea;a% hoos� X-��� ��2���old ( Qy�.ae%�)%�!��H%�5>al* ) $g'teBOna�� eݝ)9ٝ��� ~$(n+1),v\X\�� s M$�&�KA l �\vol_ !r"0 %>~$%�$%���u�} &G(�AŨ~$p�3M$�?�B$���through�I-XH�Ll�HeHH .4 ��p)V�%@9�%v�_M"�Nm�#commum��iK;� @ =0 �qO#5E%�a)�2.��"Aa~$ K K6? %�- p+or�B�e2�~1�; s"A~$iR.�UJ0 �TEE~E��nMVB�EA�ntm � =r�VYH�SAm����sd���>�C2Y ��ial_X�-I�0)�2� ��k y��6A��3y��h.a e"�,~&C8���k��y[Mj(xEuler--a%�*�".}~$� &�X)EuW.b> OZTassoci I> *� �*�etyŴ Dyn_R=\{X�X\such F�*�6on7R.��49O=N5 R\�+ɺ o-ca� :���5E���_up to V]� 1. nt��A.j$g��ofA*�ed m��/6QcoWRu�Vsy�$��o�Oa!� ���Os�K� "a : �!%�����r2�-� ���A� 1Q� 2� satisfiU ��o-2we uEK:�M��6��� S�;n�<��,R\cong [0,1]��T�qn� + {T_0VX- 1V ��+,its_{\rlap{$. yQ� T$}}\,Uz.�,5+  %>�B-Z$�&� � 1�� flux !�er]~��7~�{!I��a�5R$[UaR����6s ~$T$�l�D dJC'� $of"*e[%�tf�%{ Z�%�s�IHTRoe�."m�J! mp#� �ven� &e ~lc{� 5F` 12,110{62� 18,-42, 8,-9-s- t 1dir{-� 0,1.5:� {T}� 1T�� � n5 ��f�:Js.:� �"&�$�`A�Me�\Rm��?�Qc� (~$R=[t_0,t_�g����y_X$"r � .� a�-paramr+�"of is"(��P*(a .| or r )) �]a�Ei�] �9J��b�;cor �*ng mo�> um (�H$or angularXf.  *����"zi1� terQ ʹy�t �%Qbl�9.�(a�% "1uQF.y>��Ncha�=� Q�<� &b�!w:Ga skew- Gic D# �8��o�\_T[X]��TQ [śGiw<��� ��� M�&[X'�7�J��U-��y�f,��deM�� dmit�'2�X'X:� s.KOZ�-)=� Each 2r dirS&6}gH ACI4i@U4�R� �X(Ioz2�0)�!�A! �2�' ~$\P�Y_R�G��g�/in �l�(a �, �( an `�2 !h=  � a�aF')"!��)ion� )��Rproje�o�.on-=\*�Z"&"�Z2� A�8cog� �@ac�[!NAu� a� s. Let~$N��-H5��5�-� ��X�"� s~$fJ'~$1�A~V/��f=0se�:.UXNiFnstitu�[UValgebra@cD( b)�soL EK-"�&  X���IZQ�ectrumA�(homomorphis=Eca� | )�b.X Apcan map%D 0Qn� home n y� �M�)1he�*orh5.�t&�_L]Y����+ aXB7] f�?� �on� Poisb!I�ur {f,g\}=Q#�"f+N�$g+N6oE�aLF fAF ��z ]1f�!a f< 2�M���Y)� f Y)m0all:� r U��"ven�2ly�Q� � �&Ra�& of��wa�X4o�D�G aD4Ki/5ce^�TTI�/N�it*jJ�+N$. �7�h!H4��72�}7�2}o�Q,Mf~�'�az+:R�["Ta�.a P-f�i�_bly w�;�a�!&7�[E� c�'� aa#�J%O�!�*� � .g.� ��xs �$�e �- )"2%oa �,R� :��� �a �$�Jfo}*$~$M\simeq\*d by>� "� c�vS�eD& ]��l��# Kill� = E*can� id�."16�Ae*#36�,3d#&�`�JVED�6� \�A&� � a �le:r�dInn"p � i�6,"�A�~$next few s �.A���!�.�^6�!smCZ�5method2iY�* .P}���ofJs:2t'q)h��,o 1'A�/e&"�/�)�>�� G�81�Z��somewa|a� h5-�system!A�i�'hI 0a�2��k2@b�De�W >� �i( null*I Lp^?�9'�3, ple,A�"(&�,~A� 7_0&�&�%�$i�XQ!�W5�I #is inY��$ �a�&�!��A��.-"D �3.��6�٨)�!h�dQ =���k,"�Jjugate,��� =ombnF�:� J7}~$X=A�bE$F[Z���V� 7R�S ��*�2x!Ʌ A�:# �=�bX "H (��roNV7"})!,�LVg8a5X;h8e#ota!Bl5E,E)+R5 a+X5)�5r]h5 ^* EH3NJ"�9�F�v� leadY�ݘ---�&in"�Bt---.m^� ,dD%Q6�B��X���.�e��$6�E�x�Wr��E 9!�~T_0��b��-�)Aƥ�J  4�OEfn%�= 1rom%V{q�AHb{�:r p} �G�>[uAIB9EL* AE8AW-E�m;�nE�� r� 2�*�7�Var��,�F+in�n�7��:*�E�&=&0\\D`j8�._.�-4-eIO*�c��e� *Y 6 ~$i��is:��� "rD(a/he"e)�8s�Yc�x!�� 1&�*�=�D � "��not�.�KdlMLia�� H� / -;Ily�`{7"h{�im.' �6s~DbyJ&"8�ul" a�ng a&f:F�)-�)$9O@�>��'e�Qnal"^.P J!��3we perAa�2� 6�� �NI)�,G*�`t@ F'��|:F�t6O!��>�.k|Max]�0&*)(&��)}2610Faraday--LenzA)vgeq:FL;E}� &:D$Amp\`ere--� law).��bu�i�} oibZ� "�&�6n����EL���6�pareE. -fix� ��p�vL)$A]�3arrg(Xa�#G5i�,�!LJtQ "�� �=,%�ZIngf� .����>�\ �_t .x ���g$\� ��B9�Z��w}�� (t,A�&�5l�� �m�0!s��N&#b�eL�/m^ u�X��q^"8 � �o|m��lN:<�;*^L�; = \ker5F�L 7*q<0$<2�Bf9%+<�j�,�-�X)��@R�>� *d�c��FN�_Max� :�j��E�um��)�� �|� "e ��>al�$*FL}:�v�c) wD��*�v%4ai` ����@6�&�%e*�> �!�O� & �q;}s�M. 2 -F�a�#�-��E�O ^Fy G��Ţ�:�RoTJm�s �0�1�_�ZeJ��� aW����&B�5��n,��1<&O(m�+!{p[B it�AU=��s�H��7ant��'i� data;ime) !ea�&A�[? $,6at&�V!,*<E M���a��fW�3$SV :�p� adop,e 5!vie�[Ns)��n�NP *1cy� E�!�5pi)p!�at%&~$��=:z$�D-=E�f!=�sEk� 2� .: c1mee�C . Un�� y1��S��argxn}a b�d�7 oncentrat��oh���*� �+]8� proc�~�To�=,mga1 {6M)"+Z%j�KZ4e�EChe�!�s��fb'%J�PّA�a�Y� ^�r��'d��>R�AB�R_<.=�Zn?�Z$�dH"R`%� &s*!��B6�P��&!�a (G\,a��R)�'R$$ 9=ef;*�i8>;���+� .� & �4��(Ham} \Ham_t.{GBigl[�l(!m,r)+l$WE \dd  r)9r]�aq�}#|)l�;a�nf�%���M� a,H�*��~"� � �SWd;6Q�� 5�j �ya.��.1�Ia@a!}c%+��of���A:ct$�  " a6E aX��VEymŇ.%3Q �v!(2 �2pYtJk*U@�%"$al---��Z���!-2��:�iN. More�! q!��n4;F!�}+TF!\j�Aa#vA�$MY�Ha]� exAYq~"���\$ )y"�Q"�:� �} {:~$a#h� �&�+� :�!}�!�F&M�q�9��<"�total.80�ݭ���,"� y2"C�:�AJa&^a2y%RR�� )#�B�,�I�a��0_t=�3�`n~bigr)�� ��>�cSU A1B�".�2�ti�86�euA8A�(de�P�;2C�"��7��Hi��+ �- .m@-@(ُ,sX�.p�E� ra�3%=au*�*<, \tauV<Z 1�i }t&,*)2~A =� ��Z����J "&3qV>-N� � ���FAeY� ߃�Dyn�,Ëa0:4*� w�)�Gv�Z7%�>P /�mt� �7 �re�O sh1q� �)B�� �]�(c� on2�5�6� My9�phi AmS $k�nAM ""0�  ���1h]phi&f�,� F�:GN�E�� e��N�r%(�g�2�r�v'� �!�eemY��h\#%�"�b"�L"$-� }�q couplXOm'#�s���t��$8�n�lD1ic\rg� nd�%s-%�*#$�%�1��Q:V2C�2 �7�-:2Qhas�%t�ZB��&�7X 6�=L_\xi A"\xieq�2-�("�)V�~$I$�C"��Li& rq68e4it�A�%p!�e >��@+J� tau), A)$' h5Je"�> _>B@ �y�i}v�~!�� %"�8���8� -�&���8 on3�4�E, ro9�:U t�2isotrop�e� ,as Minkowski��-@IFa&� A���<@I�� �iVt�"!'no�g�*W �J��3!eI�:� *�!VQ\�B�-�p26*&�(n� &f6}8OJ' FV-]� ��  0rj=\a*sC$ �\. Lu!&*E A�o0Fol��J&w�X � A3aq�A]2�A�� 6� YMr.�+963e�� I�,by:" 3-G q�d�{�R�9f�wo9�� m-["i$!J  (e�Btwobw4�C�'~$;7�k"�Udr� *� bN�Zn��<5_fsB�,!�J 0"Of�.I�!�� p&_�N�� E Œ��6�Xm�aa,c��6$��&7 2�� ed*�8Lcy!.re�Oշ : Ph��*"���ƙXQ.0ing��"���-�!����!l�*���#R%� A "�[ +�Z%q!h=qAf3.�i*�~$*�Z%'h E'X �-1K&���y_aA�aan><i�rm!�u�Qj� quotM7E�F1 hcoC)_�$k � !�.�Q�� ,J<�-={&��`*wq �verea<{\ran}�:Abt6AT}Z�h't.>K}.�\Eu"+}�&VA_:�[A]1� :~�2�G1�"�88S>��~>^�B(�*OM�{dulo~m�$OrE�!�exB\MJ�)8#S�W('a�aF1�� �=*7(�h�Znc�N����ArF�G��>estly>�"� choi�3"�A�,� em�=��he7�[�6n�!4(�Gnon&�=) &#&�2~"C ��n:�l�S"U#��� �5 $$ (p`$beta,E)=(A='� ��� sum��R�TI��* \A��ҹ�SPGa natu�\�-bnor*l"q�"]n:!_A}�`\|a{�\|_\A^2�BfUQhiI�0}-Y phi,)c�*�( A^� *) e��j �� �eA@ � Sobolev2om���&>l���,C �/5�st4   E=\k& :D163\0:~\� \|E!FE^2 EI(2 B�d?=\�\�O�s,@ two.r.�Sy-&h �D�U�;�jtinbi�. thesq�rm�5%\X�tt{�*ec ing,.� j="�4} % %Ti2ar� !��by %$$ %"� {X}H(X')�?&$tX,X'), %\*�]� "�? %X'f�:. X:A �ISA�l[g(A'i�>#)+g(E',E\ ]�RA�t/�tA,E')- AL t.: oM KM"�n"| &��.%*}=4t [A] &=& E \\2E�)�%. %JiI "2oF�3A oscil��Gdes" �.i+3} ��`Aw}.�$R�Q���r�r tech�A, letyexp�}on� a�p. A��d�n�A�c� � $ "!lr3��>*�5[AN6մJ&6m�y> ,iDfM*s�_C�ic �" JH��F . J��� enk}�it� �*> �!_"�!�.l(Q/�� �g�*:~Ev>N�. ��f�&M)�Jq =.��y 2 {��iN�# � hold��6F �.yY�>5Z*�^�!K_���-)2� �N,@@c^k�a��*1%�8i�� ,$([A],[A]) <�fty�C! ;N}2��K w���d�f�1��Eg�@fcm�� �of {\it���IAWV���Wb$2ߑ�Q�9� "syN�29 �"f�5J$�\ha� �am,@ll�Bg�"!��0-B" ;W�юix0�h.J:y x3a�7)=�15�,2�y. "�. E4��VY��'}�TJ*Id very- a[��� 9E� �8� relHY KodaiSIrthogo�g-�d=2i� 2� =&���6Y 0} � �  \D'_1"� _1}.QS$4� ^*_1X1�6_0 00VW 6�$$va#�!*.�x � 2�!CB\� *��!��iaput����~ 9; �gW�=6 aw� Xstrongy�� u� 1N/R�>�{%�$.$�% ,l.�BH t1y� ��A  .��9�!Z�K�Q#uJ�B> embarkA<)=��`%!��%v!&-0�#,pure-��"4 R06,4>�u� �98��N�-�pwe �X  2Eh�`��'�a&�@Ak N>�_0� ���%&�AA�wm`assK�u=�&S!� "�4 $ scalar&�Fstead�*K(a� y liC7�{\}�l��\/u�5�6y/F)9fu�sT���uA)`pya�m ؒ ped�=cey)�%�dray�c.���cer�&��s' we discus'B� harm�J��>LQ examP< ��2+1$ "bp M`j&��a-&��tene�6EFTa�mE�e2:R5IF� T ��^rR�`!�1�5d !�no�@*�>0-�d ,.dby%2*�I. �R &�y^g�VWe�a�1Ayl� :�Ss ("|��P( � x&�Ped)d ��A�rll/>C-,| �k \i{}�k� dered }J�Snot"���4 �M�#h�4o~on\^juibTgs.2Cs_� al�y%!� tec�"��yweras�&�4�� e�� so o Pr <-�0 they�fiscarjlaall�!YsN- A"A>� C>��E��)s I��q�O"أ��"#N�&F �Pct"%s �<�E�~ r�!WsO 5@-n��CqU%zeoM��PV ,A�= � #� �k��A�Z�i�sd+Es�ti'%�u��o\ ex^L�6y�2#pters+���� chap:qedz�*e"j s�4!O< i7.�!VJ�jFb��1X�� a~$�� ey&9 ~IkǏl ~AsoJ�6`s*MA�2%X�� _0 E5Vbe,aker2 z �; $:�R> c%?~$O"� - " B� 1j~�a. �&�)}��3%�!�%V&�~~�d�II" "�1]�C, Hodge'�7e�T%+�A�n n%�2�/!�Y e~Rham co�Vlog�(L%,�opi8 �%� ndB��z�+�Q��e��55holonom�Ear{ r�1ct! loopRS5 :�e��S4%XQ �We[. makesh<Z%|�*!�E��`�co.�B � of `6}'(Q`='�}� M�V�#&_�!�ubtler�*)�%�. �.>�( ker �_ 6e!�`%�=���' �4TShL^2A�=��on-MSNҔ%�� � uM7p�i�."�+�m���3# Ja =CY[K[ݺA�B�! � still ql>�yss B�mh��I� w�s`)�m}BrBr;ɒJ&a'frM�.NjN[no:� ^Y�*P_ex(S1+��=;�MN%��2P�kA�6� �J��2� a\, X� ��fi͈�7kiLo�st�)>�a�2S$N �:�). &T "\{c� T~  -y� �)� tI(s �bT ����>ew%�!$tkul��jG �&'?D2�`G��'.�%�}�#�؈wk6t��A�"w��("&9 orq7.�:V�or�Uep"� ll%�he%� ��t^? �$ver*��} 7V��>�N :�anM�' &)du`% _ob o+ of `=f'%w`!�')r"�|���. �MF�M �:@s! :}*�G R� ��Qt�Zrelݣt-� :��������m�&���>1e%E�uH�&� �Youe ��'�<clp s�!a=�*o Aa�:�,A"Rat� )�†A �  \^A~ �6�aс{cc�BAHk%�&_1 / \, N_�\e /��d�  .�> VgfwletEusՄ\A$A5~$\, nto bQ�sZ��f& \A_o�A_f.�e e_f {��%)!L"�8 {lclll)/_o)do11�t:1!K W(�D& �&=&)=  \\ & ��6�JU+f +%� UB�6�R<%H&z�i(~�e����z 8tt"s:��ig2+#^2+�O\|���u;3"^2t"��Z�Q���1�f� �{ ���aCF�w)y =� f Tf%�A�NU +-�!�uU _o %� #-�En�CE_ F��CE��0 *�"F"!�U/�*�.�� �*�=h^+ en �V�a_!QE .�* 8 �E���>� a�� �oN� � &�*H _o$,�2�<sayi�left\{:����iaF =� cr  E =-U A֏indm� \�9�� ai"��!p2�-7��a&� �or�$��"y���J0a^A�.�B@%(Ge V�F�lso> � type%9H& M~�&?O �#= |�V A)+(E | �#(Irey�#�e���\2�e��l�_��#,"fi��zx"�A�!"�1�6�#eft( \!��gin-�{c} A \\!�9�'%�) �&(to T_o(t) EP�I =<:F~(cos(t\sqrt{�� }) & \sin>\,/\,2*\\ - ;F8ONf�>ɩ ���1l���R_"�BB�,�xAHHH@on "� "ZA-B��#&x :Q�itemiz�- SJ �.QP~�*(Jl_B. * (s)=t+s �{ ɸ $s,t���d~)a� anip�s (�f�Q:a����) v"o?3Vz��s_{t�)0}�)�*=%nM~$`(X_%?�J����(aightforwar�!��!<%F .�]�2� �C�+Z1-L�H�"!�AG�4I��)>�G� c �Bt�w1 e|es$P.6 >� 6 c���Z�f$,R+b �����:� 0 \V��T��2o&� n�%��ac��`y7, Wpl"� ro'fM�L��E$.% %�8. YH/�d%$c!�A�63 .a.:,- E5E��,>��U���&"� �BC*qD(E\mid E+/ Solv' �Ѱ��^ ! � &� �a���W�� T_f�Ep��BF1 & t   01V�E��՟_A�B��enT! ��m�rm-Z�:��NO"f$� deed5���� 1\le\|)z \le 2+t^2� $$A��W�|t.W�J�Wf(^W,.viy^�J=V(0)$��'tz\��, < easo�"7~�-�$0)\|=|t|$.�5A k� gredW67s��*_#�'ְR^�QuQi�  ly 2+ �NS�2ry6 ��[� /�k^riz^�*�#?"�As&o��&e�w��ult��,�I(thm:3+1}, gkr�V�5&e��]�W%�Kr*o5 &""�� B,"��$Z �5 a &�Nv�U2, R��2� hys}�� crib�,:���uJ��!�*�!�� �a:M+V.a� '&em "-�~��ab@U!�"u ~$d���<�mb|�E9�HM�6,& (V��k_*})�"was*�t��*�%6�0q6�*�%�!7e.eVmZ:"6�)emdWq �tS�D%� h�Bip��g%�F- m������ k�&\�5� \x� ��L_k}�$�0^*_k}�hav�Y�j��%:�&�+k2���� �%�&���d ~*� o�m�"�% raL {k-1}.&�kerd k,�� * _:) DU�4"�Aa/|7P~�,k�2� d abY ��_k�:- o�!=%"  La"�d] on $�� �_k@e�_k d_k +�W�@ .�`O*>A��N��5 F8k���q4uE5� .!��er.m5��!�nv.&� ubyof BY�rKl�tp�$�S)�.�nes|T��9L to C���)co.���$�7 ext �8��geMd�I)�6�F "�"Iz�6,~�"w) toA��.g-1}me 4�a�)� } & }���)y�E&RE�Y.Ae�.nEkA�$MN]?�J3a� }&�/&^5m�}}2j2�f_ag ^* 3*EYak�UI� Iujm5�2t&yա� A�g� ��ѡ-�6*�tA��2 =i6�uy�H�#6C& ^7 ,�"J~��  a��}[ �6�]d*�� �M!A G@CD} {H}@>{S}>>{H' T '� CD�1�>{B��I& S�teqET/ Jp$$ H'�6�T^**A, (T^*T+SS^*)��:/Sɉ���1 :�� break�E dow 2�Xe�'!�$�Y-+�ing"5 �As,`�os� &1/(�beѣ�!- E�Ak�@ � Er� orElex:B1#/��i��+*vDY,�# ��ran_ker�!�B M6auAd:6���&J4)� ^*=(��$T)^\perp \*W<&6� .,^* .��T�^%� �:� �$(?5T\psi)'=AD�%�"lb;�\$&�!���9 E(T^*� ��  Tn�{{>=,� ran 1#y1�A �E1}�U�I� guarante% (/|o2� �� (��S%�ra� �_J� �� C%�QW)�\�A semi�Tf�ڎQ��M���!��#��S^|�)z ��)�YtBJ��$�4Bg�E 2gwDe1!�.� SA� )'= ]� 20) 0=(0A�5�Bso-N� ��ce �If B ڟ�-�oʨ��:o�*�� � ķ>�o" �,�cmP,a�riK� ,~$S"��a�� >�#&Z� S=SQ�: T"���_ZK�lM+ ��B��a� o6#m�4) ��now�/��o-��ro�� Ra����Y�'v,���N�RA42d%c5@ $9h(f�)� ad�s %�ac!@فn�S��Sͯ��T!�a� eR�� S^*R"S� �B, 0t�!�ѡ�@s�B�!n3B(���3�b�^� ( �cap ~� "�*we �bRE�� G #� T)m( =G)/ke)T+S^*S<r �!=| �����[ 2Kt To � Ass���� q � $� (������ s�ps oR)2A� + Di�A1�!:�� 0��7q )'B 3 �E_�`�in� �  ��J;eځ�kI�a `"�g' �c �A�)�u /"�7&�:Z�)sm �;AL�d�s�0 �& q�w '|}*M*$(3d�")8a��R��� ��/!�g^���+F�zM9Mr7 ~$\R�Q�ts) }-QB��)�={N �I>]Iߥ ��N��N&�N,��"NZ(�R(�H�I A')-[HA�[� ~$X=cK�te2X'=[A'"q&'$0;�3ndc �,�L�S g6�H�Q�c 76��('uc��iO����P e op�MCxE�@��*~zaG=$"���7�XH�\&�%�*l[>�t �t�&��.xsplAqnD7l��wo�ors%�Mj _o)p f"��&| mand�c( ?�r^�E�_o.4q+ �rV^�U. O!� G�6B@3>1)�Q���&�&�&�&�&$a�*�e*)�g�t��N��� �� �� �O�� �c"�LS$4E�GB�&�r�:N+1-g�V*l�7i)n ��2m��V���� a Lo��zmG`XB�G4e $(-+\cdots +U W�  $M�R\�s Ns�Bst~�[�o*���q��&�$ dt^2 +g_S�3"~����ea2� �6�I\P��� � real- �d �?Eǡ�A�'J+T��}) we + $$�e&Ű � g�ݥP` = �'�8i�� �$g = ��� � . W+�� �6R9�6���^�)p %�K�2d *��c��Cf��M4K���]lyEe*�]zAL�`� {t = c\�js:��s..:�"| 4?us- , �� back toF�3. . !���� �;D� �t�5� ��~`$M$';>/m!�t��i���b 5x� �$K$0!��3��$po�B we:� �x�WP ger~$pP $0�% pGd��/ �~��-�e�� ��2�s!Z^a�&YQ"�T���Aw&�(n-2p-1)a6} .t 7� 60+ ).����J��v�m��7*}o�m�m� ��� >0(k-"g�i�I ��g�#n�TA��*nge-look� f4��kÑ7c66 8 �DifAK ingsÆe� � m�y��E%E ?7 ���6��/�(�(g<��7sm�a�H V����>�<Oqas�^a�*"�]�)�[hs%{ E]by"�&&a(g_MC _M,-� M') ��-(n+2kI*8i}A�ft[ -x _0� _0)+>� �.].,[new���� �!���=�A��)�)s-��g�h! ine *��g��E8MQlvol ��v6#a�4qC�1 volu3 dd t�3�eq��MA �5? WE**; d=�}non)��=by worJ'�� �e�kAAm�A �N�/=Gn&����� )!#J�~E�]~"�Z)�)���0MRIJ1�V>!\,!D"� �)!",�ѡaXeEmeasu��/!��H��9s�dAL� � ) <�7R& }htwfDd"~'*�I $D_k�_ CN�� X/F���bNaI5 Dk} ^#^��kr��Ys�6o@IE"�8d}�J��dagger�^\ �bML#�� � 2>u>1b�"�9�(D_�)�Y`Qq !A"&�[:q al_ � _n+1+!�#_@eٲ�xA^��M ��Z(k��I�Ua&�" A�E�u~`$k$'1�s~Arq 1�� �t� cl��D� ext.��#(R�d  � ����� �M.s >��  ��.�> D_k}>2R�&t.2REa��!�*>4 #��O"��Ve�FGM�F)A both .%K0"�%,�UY@E�9iv6Yo��e�?�}*w*&��r�Wirł2x�e��s��$[\S VIII.2L� "@s ForFg+"M1�2�7aR� \�BeFm<р�� ,���A�Cq:oY� $$ {�o}J �� M yF_M,F_M)�>�9H �� � �� tens� ��*X 5F_M�T,_MA_M $$ In �terms of the twisted exterior derivative defined in Equation~(\ref{Dk}), the field strength tensor equals $$ \begin{array}{ccl} F_M &=& (dt \wedge \partial_t + d) A_M \\ &=& (dt \wedgF,le^{-{1\over 2}(n-2p-1)\Phi} @(dt@,A_0 + A) \\ &=& nF<\pa�D)?#�_E\bigl[�(n4A - DA_0) + DA*,r] . \end{ar!\ $$ Wi!�he help!�e-�s~)�8eq:newinner})--.Xvol}), this means thatE%daction can be written as \)�eqn �\labelh 4,_n+1} {\Act}%i9�\int_\R M - gN�,.{9 ,- g(DA,DA)@\r] \vol_M \nonumber\\ &&6<=&\displaystyle B� !bl[�� � DA);� , dt1�9! Note%TDcomplete analogy w!�E-�9�)H }). This  give!�(e following9�!�mo!�:A\left\{1�)�{rcl} ]b$DA & = & DE�\\^2A%�(- D^\dagger' +.�A�.8]�\right.� The6��$p$-form electromagnetism admit gauge symmetrie� A�4SA!�mapsto  + \ddDbeta_M $$ where~$  $ is a $(�$ ~,on spacetime!fHus, to obtain evolu!L�P, we work in temporal �X, which amounts to sett!�$�= 0$. ! abov.a^the>c�DZ�c} 9�E-�0%���1�E:0:�n��TGauss law constraint $.��$ generates) trans!��F!��%�%�A 5ȁ� %�!�6���� Two pairs~$A\oplus E$ are physically!� ivalent i�4y differ by su!� 6�. TEignor!�a�ytP$ subtletieA9hiaseITa�Q� B�!Cist% �[A]� M�[A] � n eq �ce clas;aLs on~$S$ modulo thos� the !}~$D%Y$ (��8-exact), and~$E gQ P, satisfying~F�K8divergenceless)I�, Hamiltonianaj�_p=!4is easily seenaybeA�H�Hl[=r]=���1�x +(E, E��uand��Ep�e8ic structure isi\omega Ln ,[A'5�'0r]= (A, E') -lA') f Agai�� he cAXof~$3+1$ dimensions, $()��=(%�,.� )=0$ impl����syV��!<-invariant. All�si[ulas hav�eue�Se��\� ,sec:3+1}, so��i�lize a M resulI��s @,we only need!�;�+ orem cthmc$! presa{Dcontext. In other�VTds, first we must show z>operator)�Pxymatrix{C^\infty_0\O!�T^k\ar@<.5ex>[r]^{D} & B&{k+1}*l*��}V %A mutu�; adjo��closura���ri��:� L^2 n� V�*}}. � !Vni%pr�@a verA]�j!$Kodaira debosi�� saa�%EA�L^2 � p = < Lline{\ran D_{p-1}} �� \ker L_pm .1 p^*}�����a Laplacm�$k�ts,�_p = D>�� {� ^* ,W�nonneg� self-1�Q��=Op�kWe doA�� inQ�~U�N+1-thE�,} below. Us��theLact�� ��.� for ��F�to��\P� = \A )g \��%B!\ a� : \� \dom%1/ \, B�-�� \e� %�D_p� UfAsy A;Maxwei�ory inF�~$ �$ bA`eM ,real Hilbert��P �[wFl\|�`,\|^2= ( [A], � ( d A,E \mid E� $$)~$(3[A]')$5 bdd�a����( es u!�A ac� at,���KN6,~ANu)/^)�6canonADly isomorphic to~$aV A�\perp$$ ,inherits an � a� duct�virtu�beA�a sub)W�Y}�$��s befor� e� spli�e)�s~$\A$ ��D\e$ into `oscilla� ' `free' ? s= � I16�A_oU�A_f` Moee_f ,>�E�a� :�lclll� _�U� \capF�@p^* } &\quad& �� ��  �_R�P)f )PBw��sA��rs let us.j1 aaC$direct sum��aQ 2Q%� �6= i�=e�O!i!T)^a2N� +o �!e�_o�5 # �%�I %� F�� also a:�*�vectorM�u  th6$ ��- sepaF *E � �oQ� �$.��a�, � &� ��a]�6� �eq: }). ��f��aoa �[ iclei�a�J 2�(E,E)��eh��:� �V�$B�Q!ݝRy}��oBo1a_tq>01V)��$$�K  &��$mod# noth��besid��e K � !�:&+ c.L� icularBis5vU verye��_A�E�\{Mathe�(cal details�9Y.Z ' ��uLwe"7make our�SDrevious"m rigor��?ai�X� : �� }��thm�/ Let +"�l ?d62 6�$$�kR��Z� � kf�� ���ao�Ɲ�A�"�%L_k��D_k�}��� .�densely��d��k$j q�u�} Beca^#��f eF�u!��E6lA�,cannot"c ppl�,w ofA,�B�UA�a�son�g+0Gaffney's Pro� 8prop:g } u � %�specifictper\y!�`un-�'~$\dd delta�#Howeve��he&�e��in  true,2 b)P~$e^fJf}ad$M� 5 �-order�t�n| $f�[��� � made  cise� a� gum due Chernoff2u��concep2 `symbol'!�~�en� 5��A�d@ eb��a>(of~�a�|.�ne�-� ��. We O�re�A��'s��4malism~\cite{c-73}1isEkey!"DWm(. Let��ݤ��l ɱ~.�6ny�bundl�RwS8fiber at each p$x�S%���1�� �8~$\langle\cdot,�;gle_x$m ��� ~$x$%�e  �ac�suppor�"�a5)z �(, denoted~$& E$,a [nA�2���((\alpha\mid�)�� S �! (x),!(x)� \;� S��{~$� )4A5"E vm��S �6 r{oE :�%�q pe�a{nna�r%�AN5 L^2 E�Ass|��$T� .) \to2%�a. arWi�6�E�ItQ�Y~$T[V a\.\ n\,�e by rA�� �:� T%�)=(r)�9� �� \hbox{forx }i +)�E�.!�^  ��~$T���0\sigma(\dd f, V)= T(f - fT /�ny.�$�_~�x��" 5B�$. &� ~$N��aWM�m��  ate i�ٿe�E�(a�ŧ f�He$$A!��? . I! +5��9l�� multiplic��byF[�!say��MwF $*! � = -\pa%�� hyperbol4$ystem'. A ��~��=2}is� v��aga�eed!� c(x)� sup� \{\|N�(\|_x \colon�G|E-=\| � 1Fr\� �a,�fnorh9� ��$yC&3.F� �8~$.�Je)� zf�6�oIH�n��!!v���68n2��d*%��% �6�s appea�0& .Tu�mx!�A� it -$ur� >��  >ifM m."� lemma}[�]�ME' lem: } I�g$~$c^{-2}g$?s�i�&�2��,esS%c B�R$Tm.�S in� �&.�$ �uniqu&��C\R\>s S�(%ő.� E$ �i $t��\R�*Moreo� i�)Ah� m� skew"($�G =0$)Pn~$-iT��]ypowers$..� �C_0^ �!T)�5� }[S<� ]�( basic idea���w�w%v ʲ,  urb�hs_ �is�eJFF�!A`is �I�te, in?$g� � r� � like&A  �n! '!!�� a'f bB� �2e%���<a �~�(t,x)$�%!�� ��� &K �q ll~$t$---�] �<g�&lf �on}S �7s��A�OF�,x:�"2�two*_is stant�.�f%o@J{d� dt} � (� )t ). (T�V,+* :(TBV��-�$>/ B7�a0N� e crucial�� )*!SZ<Z*�$�;U5*� ]5�/]�no � ary �/:�$*H%�+� 2 y5 $Fe�"4 Ebt��s�%� "�t ��oneN+Ek- -�%r[B�)~6�byL sity{nds�?6z unit!�~$U(t)$ �(� On� &:y%�`` " '.,! ՞$s'9 r;��.|&* >i9��)��� ��A7��2��i$iSAp,�֙�!ma$ remain�65����Ns� ,ae�� ely �Nble&� from~$\R$�" �. BO " �Nelson�[L� 10.1]{n59}��*�(6` �`E�j`z do�:x,(%Ya�%z�̩~f,2_ .W�v��(L(!2to check}� e ex37$om.&3s~${d^n�" dt^n} .�qD�-E�0by repeatedlyP �=�l��.�\ = -iT�+f[isͅ� ��out�K�to2J.�"� s ��!TDirac�!Ho`y ^$o�problem�  resortfa L&-known k, tak!y)� 'e��) �B�:���0D_k & 0V���U�2� &�is� will � at $D_k9  �� v�*Z*&�+ �� �# _sum"�H_1 cH_226$�S%%x�* H_1 :�A�H_2.�B�*b�$6�1��:��:`� A�a�eh"�!phi�3si �1 =g �   , B \.#2!�9R_phi� �(A `in&Bc� H = % %@� �S%Lth�"��%Q�"bvBQlL1ZjF3H�mIf��6Uw�.&�*�@en $A%� $B~N. jw  I� easverg��9 ��v���i{B}15 A}Kj  whili�"�+` ֌(.y)^*�B& ^��&$$EAu0*".� %��"wo"=�� qual��-.�a� .�A�=:E�A��2B�..A�$$ �/94a�~M3~A3a�>�..aWend�� B�5lS:se1vEe^� "�N� ���O{&��(�k""9k_n5jbI *{q�$viJo�pn��!�� � "� *�0��&g-:%$ )� 1� u�"G hyp� Lof � ���&q�7*8$T��ClearlyaL�.��*�� it suffic�o p �aR���E ion �0 $c = 1$. F/2Oconsi�e6�3I��6�$Dan�and $"�1G6X!'QU;w?4s� _\dd:� �l(f� )- X r)=if  = � Bny �� C&�Mp_"�$ !�a ���i�)= -i_{N*etaF�ny� Z�{p+1}� sinc.*�5( f, \gamma�*r  3 �fs) )8� F8-9�,!T(f \>d kF39�:�+:,:�!k9� Cin^���;x Ac=�/T-@T1�P�2�)= i( �h} !  f.\)8 To�u�.}]8,�&e* e��b2 +�/N����� ^2 �� wedgM��^2�;| �f�|_! \le&=|N5� \*� Dt ;r{<)C=nA5,A<>>v a�3!�B2al$�%���'�� ���� is x9�B1��a2�l>nchieved�leAj&� t9���"�B�b�'B*E�R�'D7'$$��(� !]=�D_"�$� ~ D�' c��$ *�F�"�&9sB� �eE��Jimmediat� �)vs "� .|��}. �2�secondbi� by R�&2 8i� $T^2((-!"�eD_k��XB:|z& KZ�aG+C2� %�u�q~>�S ^�.x6W�now�Qle�Ro+(!�6+( N+1}� 8use��^*� �d� %�>� !6�N-�$, � ~(5� semiʼn})2.6 ��*F�*so�] heVz9 (V/)k�9}) to0@Era�&�+�$+V$+d�+^ ���(lud�4*�o&� �4kea�-n�< .!5� . W!F�4"�%^>g"�v~ ,he block dia�� �P [ .�4u�Ε�*�p5��0��=ki-> &5)$IX �/&9%� �O G$��$ ��a'a�n*>��.@. �E��u�}A��aA+C��X'ly6��res�m(to V� S{>�&�F2�eyq�0. But $(x\mid=P x)=(� x)\ge &�& $x\in65�%2We en|9i&a1/%'E!��' G%r�Q�D ogou�I"RB� th�A?}��!�l8of last chapter&�"^B"72Gn+ G�~$M�a $(n+1)6�1sta�C glob "&�"'*&, ��$A�g_M=e^{2� }(-� t^2+g hen,&Ee7D.�H�MV!m>kV� as��?s�!K 6���:={!�\{D_pD8�&�\t��m\} {��}E@>I_BMp_S\}}� ker@^*\A",B{p @.-�\},�C  D_p!b&�E(.�M�Ip].Z!Ca& he \emph{M-X:�Nx/.n ?J#4"83 BFh�EH(X,X')=(E,A')-(E',A�� ~$X=*�;��~$X'=[.#F $ li�q ase'b� +*)=2,g6 ,� �& ,�q;- induc�8hO�DA,b���HI��'E�%1 H*�Gion1#�2raP�m��H[XJrGl8+(PBA,F<�;i.�s�@s nature��&�"> Dm _oM��=E^��A� $> mand/ ( ?*@A� L2�and� 0o.0�^*_{pE��Z!��K&Q!. O!� HTim�u>f!>iVx;!�0"V<T_o(t*�;�I�efV�<<N<_pP<�n(.\,/x<�< _p}\"�< L_p:0 &�*s2D�:"��� Dne)�2t��N� T_f!�4 ���+b�ʮ:���  �x(�'%\newcoeQ@{\K}{\mathbf{K}} 6%`!PB! Real rm{ReB!W cal{WFick}[1] �$open{:}{#1��th� e{:}} ��"{�8id }{De#ion �%"{ A�C � bb{CB�cov rm{CovB!FFBfun �J rom}{�- �� = bf{HB\id1F!�dKit{i.e.B! Imag Arm{ImB!�F�ng>�N 9 bb{NB8QQBRRBSO rm{SOBso frak{soB!�TI=rm{ >�X !�XBZ  bb{ZAg"�<���bo�7�V}#^ velop�6��S s ma�N$m idiosync�b4 �Of� iar � �� tradE�al�nti�7method ")no� on�H|; } icF>w�kP�dis'9uis%h�P2 &�A�� dual^*$�8re� some good� son�-�.+1\�M stag�% d=+of �j"E> �mo0 ompel)7rec�Q stud�Le6%E ar �+��.sp�/ boarXqu=^of� : :, �s a te%5� ��-s sugges� � �2N�. Our�roach�^Ev* =68 mry >�6�0Iws�9al�nt"�%68atW �be�966P. AdopA#%�vie �3 sR�?me�@ ),�characIZz4 � Poisa.algebraX'observ�(2Scot�@n@L at e!#�2�.P $acquires aR� . W[#E{� � Q�q)? ��&i�G91%,-':O: ! 8 @z b 2�� :# 1$bracke@'��?Z� Also �:C�nDre�o%�ly ��"�L 8$ g@�Q�C�gu-�}ed0Bc *� ��A,F!�o w t.e%,MJendow�w�f��se>� �ev^T��ossibiljof#si�)ng�el5 ��(2tH:s�,�accE��8ity. Acce� gly,��V(avoid!Aq&�>�Se �-s m�Vs �le. Ev�Cd w�zfortoNfGrn��PU�ce!s,-��; sig{+�kprocedU�>b�)ad�Ug�0e�to.&itu \��,T{LiX}�s}�< star�N fT!!�nhJof �mAB="necessB.�� inpu�0�525�0"�E��j}[Fp]�) def: ES!�}�X� 2�i�reflexG_� topolog�1ID>o[=>de� k*�L.B\/a("�Qal;FxI�ni�=xaFd"(W}:�',n5"D6 aL%�!�~$\PW-:�5 � weak- ondeIQte}/�ns'�A !a�map~$�i�^*\to $ C4bE;u((f,g)=f(g^*n�;f,g#%�^*vinjA�vevB]:}[D8] �`-�a3=p��Ʊ0��Y ��.� would beb�^{**}$r is .�Va b�8on���1E�aD�: &�Sofiuma�3/�TA / e2�FIaM+��1�7 HausdorffQ[y�`�i�0fK��'m zed alyt0,\S 1.2]{BSZ}�1eiB3I�� ity :\%�%nvacL�- rue.�Iol91�a&0 �cal6��0t�*�a�/i�j�$�,A�-}��y����� y]2 �E�$2lH?Cal6P. 6= :# a�;�Y q2!�Wbem?�(<ed) stZM �y.!F=�T��teq �I���+"�1 inclu�XmZX R �#��auts�2 a1� !�th*� . RNCe|,!:� ��4i1SE \Uۭ� map �@ZyA5 callr ts �ށ�}&^8�(T^*f)(x��Txn�x��,f ^*� �{��[�%.�0 } AnBcA �=eq$eU.� inv�FX4 7��Zr�� 'nX,r�=��Ս:�=fL)�� a�&es} a*.&� � {al)i� ~$P$, nam�!(S�_BH`c�.asT+"}: \�*� on. SimilG+� �Y�aR& }���A�$ �&�]�% $�@*�J�,&y=(P)�f Dž� �w:*� aCn� �a>� , butq^P?aI� � "�>�& al� .z .��"i�:c�<( Yang--Mill�%ory!��� �4 of `ZulaJN�ariety',A)oeHy �� a pr�HYp. C�� non-Isa?&�!1 Mu� reE�nAu�is�af%J1#-�:B��Athrough1Os�ypr$.��:-azd'irJassoc0��via Noe�'-s�@SK0�ana��w6q!�BA�>$~$\{~,~\}$M_at1�a Q:& e� �)�W biID� �#E 2(P)�(RRX #f,g)=\{A }2[GlF �+�$(ɇ|�A�%A5& �� �ya��rŏ_xP$ beZϽ � +�Qnb<,=I)m� configu�o�Hd`&va0��27e vic�?�q" \AI\!�C E E�2���beD���dn��q way��ŭ.�a&�� R� a #9� ��=T!aE1�=W _zJI��avour�� s,�oi�%b�9s~1�e�q�,maps leaving%�fixedF:�1�=�:�=< T_x^*PEI�y2thA= *�h choo� � rivi�� PN� )��+-��$�CPE-"� E� z; a!�` fl{�#XE�' %B,o��~�^1"o:s ;~$P� � *�J��I�&eAtak"�=�n �8)�9's atti�Fo2/A��7y>�:7Q� 5XE�)^} Y.�\�\x{.��ss ``prov ng'' eachI���$ A $x$!Np�e$ tm� ~$\ket{x};! �ed.���a suite>2� ~$\KNK I� �% �.) .)a2�%"� ~$\��f]�;f a�=�}^ K Nn� a�tE��t(Heisenberg �u� reEaons-L'*F'}�Q�<9$CommRel} [��x� g]=i���\id_\K��)�^*( n hold.&S*.|a�G_�&��!>6�� crip-&2�2&}, �0i����c�om�=�S����D to arbitr o��. as origin� �ul% �}adb�EO(^�?%ciple �cZ}!%bNedg !U�qB� Seq:U}�! tElem{x}{%�f}{x}=f(�0ec9�"� ��U�y��( �Sa%bar$. F)0�+pop�S"� �d�y~^A�C"�* ~$U_3Ky K!C|m��at%,S U_T=U_{ST}�C��ul�H ~$S, NGR $. �f e sh�se. �j����p%)a�C�'A��C�� wJ�nU���5I�,.ls�G.Y 1G[mZM�a��ibe-9�i|0ed�]enoughA}d�^min�K�8m�(sAquely. T6�$!]2Q� �>�y�� s�e=$ dynamics ��$� S��ub C-g^���m�a�a�be .� .! dG�P�+*Z(3.6]{rudin9�l�o&]F 9�derst�Ymol�T�� he (a)fully)u<�D�D:�A���&! A���1� long lis�nuisanI;Aar9W� i�Eea,a� unB�a ���3w , code��a�#AM!��7&�}[=��]"B}�FF!9b�~$(i�^*,���K��al-m�R�+�* f"i(f)$%q�2 �y(�:[� (f),g`)J.�u!�n" "1 Ż�I��onM� �f)g)��%Y�"� s 7b�`ns[u&�5=� PRRq�JEp&�~6 .�3]� >rpMQ.�� p�yjfc"�9@�!3a.�i1Gs,a� ^.vN�.2�[b#lo�]d eTat�E�Peoi���s, exa�8���pb?�"i�I{R&S,p�;�hO t)umQe �b imp7Bc"U Od�MR�-$s�� 5[�i�w�circuitp0b�e�E-U��#p�jIg��*Z#�URs. Heur%����A�E�2�Qn h*% A�~$W(f)�.-ief)}D ��g,� �xigZ�$e}u���bot��-m;g)v,Lhe Baker--Campbell--"� � �f)!� ",!$$ ;� g)}.�+g)&�/>�]}�We�Jh1���dB ����v � ur next.� R  Weyl ]K��.�O2A�.�Zei�N�8\�:~$*$-�~$\W(B�-�R!�}F� set .9)=�3\{\A� r\}_{."}$,Jr) kQÁ#E]as�.1"lf ,U��.c$_=hV},�Lu�xe0i� ";���^*=\W(-fn4.{��n�e.�[ �!YA�q \W(ge�ja /2i}+gr�2K A�j2lB �= �bA�6�V� re�1�2!� 85g.8��le fx'BQj]�&r coin�$C���a Q�BI� M)�aW�2h�)" :��b��f��� bove.�ex`9R6��v�=�e�i� en@P!c����a.� 9��z:�y. S&&��i"9 a g �] +}.w�%��P}B�&!R font�'W� WR *(,&i�ab�}ρ.�=�5��[�ore(x��� C �s~w2r�,�re.$3-X "�%a�T�}V� " v&� 2/ (�!+*�v)�N!�.9� p� $Wz��$ U(\K!p6 At�A��6y66"�x6�\aE$^�!eS%}sa�}��0�C]U�B��Z@W(�?^?S2E2�!.:�&$A �-��"�"�)v�ZtP W(tO� %#ly-^o2TWsu"8~ UdUStone'�-eY;&�$VIII.4]{RSYUZQ�%6� Lef �lizi*':�f�/�[x,y"^#-��5<+� ��^los�&!�E���1+�&P%{+g)1d-U1d��B%^ D&�hS^!~ujn~tf)W(t�t^2:�W l(t� r17 twic��k�~$t=0$,Ay��`La*Ua@ve� :7=�R�u bb� R��-&%@ *5�I�$�!;�1��" �2_(\ } A�"i|-int">6w$von~Neuman5Je�5]@$} guarante�all)�I�2G �Za J�"*�8�� "w$tf3)I'y, �eZ at2w@!o'"��E6 m!AC�>a.T=� � �8kE��@��>2wh:Xa\onvenien@ci�$���a2bB_ [2�� }>���`6�S&m~$\�M�w� �MHF� a.� �0�0sm��E� *|�)�< 2� ,� �a (~ m� J� w O .�,.= i� �fur�#mor �A 6�'B�\toB&#1"f=g% � EX&Tn�! 5 � %�J�'�Y���!��fH�poZ)"xK */*56n�&�(�� /WO>;a��IO.z��?�(E��0R m-��"M1>`D�7Uge�� �� be�uiA�tm%�RnN---in �7�*2�---`& �& ���kx".P $*"�2�r +B�:hU�iZ]�W��4H ��&5�TED?3=-hA?EH2�%��-��.a��+\Wh)=.�e^&�h&���NowAG> tZ�ٝ1 u$5:��y!�� ,T^*�+~�� )oT^*(f2� 3 l�A�/B*�,I7x#&k1?@�a�0?7,%�* !�6)[(� �/. "h�< i�v&�`ɷ �:� �Br�G� &_�l�Q0"} i��� �#� V>M�3-�sE)1&rR`C:i.6 .�ы(T)��&{0RA@IhJQ I�f)� � �u٠*�("* ^&_L26(STqI(S�(TB� :l�%]a�):���"�.�.7� �"~�Q��2k 4R�ma��sey+ �m6! !W .)�*to"�&(\fA is��� CPQ 5.1^cBSZN���v��!`f� ��� "2 A�� T^* i��Ug��24kr2�i"�x AZ:����2pf+g���k��s(:�Z% a�:�/& &�.1; �^1"��Fa*\!e" ,1�ד*}qr}\-Xa%^*f �&=&R,!$S12�V2$W(2!_:$TZl�C��  .��Mo���}[cl.�@]J! !�=q� ��� 2T 5+} �m�UL a�ira�W,)�)U8eΓWu�&�!�T�3c1�� to*�&� gfB�6_��b by��F2N= �#io/}�Qt"2���=�5�)�I�f&!<#icX'n Hx�5.3P7 Y E sum��vy�q. )�1KT �4!���y�1c",��*���Jv.��� r�>FgIB�9���ej�as)�Y3��6D�8��_F�A�g �ql/ t�LBUV�)�&1'k PmplR�"m v_�*2����=*��1� � � eW2��%�U�%*�%^&)�%2�%/=iz+M/..R���N-%i�<V�$itYnotq!5Btf8D.�,!�<��pewa"ger� issue%;e�%is �lon�u}*y AD� ,bW�;hL3m�)��6�*Hsa�d A thir~\@N! �>( I\K` mi�ei�![!v�-[. �Surns 5 V re%%IS�I is��j&��&~l Gel'fand--Na\u{\i}mark--Seg�Zoib/A� �sa��nUfBD �y9a�>tL a,at� 1{�Xns#9.R$s.i 5 !m�#Y#Rt-�"ed�.Schr\"o�%er: �2$:i�!ș� F�&i'V��/on�tܖ>b[Ew$]�!m2�*�#c"F v, =1$.f�=L^2(\R`&,H�/=(a,k)� R^2"�xp Y l[�� \psir]v;�" k(x-a/2)} n� $bKi ,%le�9�=�g$ 1r._*�\Kn,�E�, W(f'�(ka'-k'ar (f+f'{7 ]�-�(!Í�6x=%����M!�\{6D+z.�k*!Q�(f,� �y]1�2�A!T!�(kx-ia\� al_x Uis.V��!m�2�:-/2#>. Gi����i. l�8�m2b$. m od�Q�mo� um co�Eate~$�X/z�(�coeffic��81 eB�|�5�we o/us�5�%�6� L6�$&� v6F6�@$ seems backwards now��ce�!lҚGF "�Fk :{��6S8�  i�RI� 9;"�<~$q�R hR$K�qA7�b��% �.[�.�Jds~$q,p g^2 h($pUX��ZJ��y���9p"! q+2�"�^*$ d~$�� '�� E��-�[�/A� 4z#Q �M�7~$m� ;a�p+k\dd q*U.��1a�� desp�yc)T' intu�-i s�L"�>����Ei�(q���>t�Z�re>��W. 4 ty (Q�),&�ps+qk(c/ mo ��l= ion��le~$qs+p,]not��3�arIW1facUymit� oB f Planck'&:y�2� weP+c� n `n�80 s'E � 3=�q�I�custo�}�&�X.�4~!99A�~A�(Q�)�GEE$�b-:�< *�{A�}=1�<2gJ!�� E��* +~I��<pIB.[�u��A] 1�<.~:����w{f=A� q+I�"� a,k�iR��q�N�= �c �ɞ 2j,k'�+ap)2�S3M}a$�K�wQ ctorB�r!�El((�,(a',k'��4�} ":C]� �%� ��hav��4�)s� ^�2p2-i�f=$$�/�&ed���;�I1�?"=aU+k q)EpU"=� $ � ��:� btV�c4�� n���[dK �M�-Vr u�38f���U*�b; ��s� .B�{up�y�}� "_ciBaWR�H�relev�}to�0or�ough,, "5/� :� \i{.� 2k�6* :1E[�.-MbaT� co�B3DEF  !GNS5E}���>d�/�� y-+Ain5/t:�� �&�}[].�F GNS}"E4�b��5.�sA �s &.IA��v~�[t� A C��?) n�>e��& > a^*aBpa2�Y�o/ AeS��Xrs!ed2W1 T��N�2-Air"��Oage"�z(�g.�aL�)"���on2��U pu��a-ic.Z�a, FEa2G�' �ta�%�f� very�(�w�Sa t�J!�int���7nUnd�;us]7�fo2�V&?,}~el"�RJ�: a�� vein�g7�k&�A no�M����2A �i�musA��T%q E���A�ll�A.�3�A "WLm|1;nd>����UD, talk about $ orv�|�t�M�(-~M 6o$��*@�N��lnot��Q"� t so WhO( Y0. OMe�T hand�.5�3~"� �3A\�EZ�L)s��${&�T%6 �: �ER^ ,< ���� ate |N"|~��1 �iot "I&d�. �ate e�QuL1/ �6�A)d�B�.�b�)� s a �)> sesqui�ori�{~\mid�n-Nby:#of�� > \W@\W'�]=^*j�6W'f F}��Qe�&�5 �I �z9r�|��212 $, ��eqU"G+ eq:InnPro �n^e^{.�A/2� ůW(g-flj�6�M�� *�=�A �c�)j|\W���|\W ��&i�GE����5guz,z2* v|)Ybigr|=6X ��V} !� HӔi4F��lyay&aRPL�l�P"l4is "�?_~$ �U�[- kernel2�9is F*k=`&ax� e�r>�b"�Q�#F�gde� �!y=�s&� �)Cmid5�/-?�+i"�Ct.�M� �AA�1�1��gQ LU5-gmQ\b�.\a�w�+�w��.�($. B�f�� ndarB$�X ---n�O"L�� quotuZOb[?nul}A��-|~|�A !S�!wtZ&�~ 0("4 anS � �D� q"�� )---� ��"�No> �h ��U 6gM inI�c"��3�&�I��.�%��!N�:�N#�����R# 2��r� �"� ͹r19O�c� &�|�!�e"�F �|D��� !m6_�&o�i �ra_.�,�5i� g �#\S.~�-,}[&9_s�l&� .# genF1��&mЙ� �ࡗ�&� N��s� 6�*E }~$\mu9&^ > *S byr�\muF@ colo�ԉ��g�YB�Wjw�6�J ~� re�> } ifcJ :=] 1��4�tf�(t�tR�<Y1*W�'U�O_1D,=�U2� W� fin �(n��to&# %�&Md��kf�g)=wh.{7n t}\�*|_{t=0}3+tf* 2���"��o(genBosField�o(Q1"��>4����n"�" -�I֝�I,G+Z��� 6�5�E�)�X a]�!��*>5ſ1#)H0)~�I.�z hJ coll{I�f5 a ��*Psi"�=`M+f^*}&5.ZF \}$�(� ��x6�! :(&�,:y� numeE2} \iter�B� 1�"X O+eqn:i:� �� x+g^*-�� bg,fbmu� Ii\ -b�sp� ��Ps�n_!� pre-6� uX69 .���+"��\K$�M�:�f�6� F�Q�N5/�SV�})-�g^*VA-""� U"n&6�)e�9R9��M)"�Oa� �,cyc���7A��Q�Vl`*l �y$<U�it;�7"�"�ma!M�{9(f)}{ a���R�,2e�)U��n��a��tm+y��A�B�67e>N2~��#WA�.�N "�N. N� ���>ed ^�1�um*aFai�8�: $ �1�c$m a8Y 2XclassE*�~6� _+�~$\AS�W�CBa�� J2^1Z� u�)�$��_�;Z�]�#to�a�RSneq fW� U�.d n��!F�� of indۆ�X �b.aU n afR�!<� � 1 �\8Ve&{K4xy} (-5,5)*{\sgQ�� :8}; (-15,0)*{};( *\dir{. 0,-1:};(0, -115,10) -}?(.3) ,*}+(-2,1:���x)6 )>}+p$2)*\rlap{$.��$};i���cap�� {schl:FQ�k8va),,jspw �56]8� �>c���1^:��Md!�only �aly ~A�4>�d�7yieq:1�`c�er� zI�~' �myij�� rpre�*�Ax��A�i��e6�*�k`�!4@ nd' Z-@ �<+&��].Y�U:s* \KA��� �. q uri"�Kof pu�o�Y upV RDown boot�Dp�^m�$�ualE9���cadn�T�� 9P B� efk �-$:a:�e6���a��"�$W$ in plac�n�G{%�Lt�%r#� �@K< for��e�b�x" ��re availu�tare�SaLh�� s ��&��! |��ad�cs�Yra�`.�kE�te��e�L 1�'_�K$} imaE�� DC~�.A} �oPe��b�]*Ƅٺ N�["X� ��rI { ��2� \}{j6�E�Q *�)E3Q�"[ � B�ps!� g* >�" f[:� ���� 6 ](!fh�*� n�-ɫ�tz4�"mg=��r%� ��-upa]r�, AtV��~ J+��byo;2�o^Zo�k�d�Y(virG�A�� "5.��� "'Pe���� paf'���5�M/eq:preG2 E+*)" {f+g�.>&\�)�)ready�A!e�6SGJ��H!�&N�A5��zA�ca�K$�9c~1v0p! s��^3N&d.B�;?}2�A3�� J?i �#EJ0&� !�B�0Der�ed <�p6�=w j8 ��%Rn,Jz6")�P� � BMJ �G*��}P͐Z.N�5.�1� ]A.=~��0� �5B� �M�)�:ߓ�4L��@�! s� ��w��8.�vJYan�u�G �c etryqq����!|qb` 4 fep(�(A a�� ity� � I����'� �1 �AweFRv�e�(S= g)\,)F�\,}�1#u�:&B��Z9�)�i�2_{g+h}==�,2 f,g+B �A>+h}"�&���&C>�2N� ��{J�}2�+�1 �%�e�s|#�$�-睔3R��= f_n\ʠM u��n%�_n�F !�% y"H1N�M. T5'!�a$8on&!�vlk4-�� ]�6-�!3{f+h}-9V5!!�%u�d\|\Zkr �=2m� l[1-!�q�f-i+,!�e�N"�A_��u� vanish�\(s~$f-g\to 0x 2i�9�i��a�\ %q^}fCi� +>�a�"�%�W�W&p0A Z=f^+"8 *�A��U;>7 Ϳ�He_ �~% F.* / ]���Md�," >&�4Q �1N @>j}�a�h.�>j>J," ۩�T.f).� yZ|6=!re2�-��2� $.*­E��'vw�/A�+.20��0�[՛$ B�^2-60eF.Xb<�b�^2e��$)�>�O�~�x� KK2 �i3 ��2�#6>1�=i��"$T�R rv[bG^22F=-:��Pverh��6��a 'n�!w CVNr,~&�0 �s�Q"��2M� ��� �"��^2/.�)2+ .%� .T �);$�7& �| !�( )��1��� �:z+�<rst��k*a�;w"��a�� �"� R�~=. �N��x"#����o�:�d)$ betwe8B"�iee>:!|si$� >��!�Y 6I ������ f-f >� IWdTf�R!I:� a[�0:�� ) fo� >�2�$ R�S6XJvR6N"w6����cZ��SxP�:>�^2^ [酥T  ^2+2.*Q�� -^22<"*�&1/�A 2#A� �-6!#. Phc�Ni�nto~$g�("[H�59ia�=N�!� ?�-e6�A��2�]�q����a` L M�J��@Q�x2]1� 2�bZ7 �2t=\BQU&{a\h !�N� +:�� 9r]e&1mh%B}Q%t%�, $h=g.6>2�Շ�B�0^$ H5-��!�x�$ :�06�b�I���"&�+&�2Hvp%n�:� :V �sse���� ?& �_�S6� (hadr�e[6�_D� & � }[�FG] w�2v coh}.@LGvGV�"-Z�!x"7a&FR�z�o^%��Oi"`���(&m}� ��~���J��Wd5 n�eB�,id�J:��Q�c2�Oiv"�7Z��R�J��=�'� A�_ 6w��a.&3�*6Y'}QD]5:� �7�`�Dy(�W:� �b}4a��v90,ce (mean-squa{ devie;�L))"3!����&�#1%م var_�"}*"��#O% g)^2Q%n(-Z" ^2�["\9p�;n!�:E+w wor���؞�/�of �vZ���+m�,q2Q7 :�. "�3��!U�6cla�4j�%^A30minimal-uncerc�&&� 61�y�&N{I�;ʥn*_'s .R"�%,�|�Ms �T XifD!<[^vv>�ARaf�,%*I�m� bG7ur:0 1 :5����ass�*��)� Ery:6e!�J����&o��s �J e so�H`squeez"�8'� many W"�/�`�T�ay%�be�:Aete>�k��!�p a� 2$,!(�h��<# +�ce}�1tў�art4�ol;��-8 GFe�}F�"�g�CV�� '�i���=a F�Ů FqOtilde�I�D�!����: $Lsa�L�E%�car�M!����DJ�LA�bei �a>� a�6t�| ��. Stilч�| �Z`) �#e�far�~��s/(@lO '2ina��Dz��a2un�⥠6\a�.�,&T ���y�$�m�$�K.�$-��K!��%�K"�� @��N�tW"a,� y:�G�Ki�{�%A�� &M�[� "M= next.�Mx]sti�ā �5aw�ea�A"5M�)8A#"��"̼�7UB�N!�Pu"ivUni� 6P%��Mwzj��i �'���)� ,�^� !Xi���FMof"wIm}_g�EllpJ� ��m�;goǓ��N7�>I4*h�?!~��6I}!l2� �s�ar�mn�!�$b� ��b�,�(Bho�T,�D*�+2)l�6a nyG!`�� of2�S�qrH,c't�H.�\�Jc�� FTb>T%AE� � 2of~N�"N�Put=�'>$ '}N a�!")AM No� E���!�a!T,�*9G��}`����~5 ��: 2� �R{��ù�.~$. �M'*5(ismbD|�2���q �1u*��q-�( ,.\�(Tg]~|)&��-#e&eq!��� Du T= =  @D&map�+twi�!a�m�"} m*'AACs*e F_>.,N�NZf)=H�f12S,��a��ir()>�] d�/2�Iy/wor��SA����&$_^$p=G�x�(�gQ�1e ��Gnicer���t  �Tx3Ty-�ynY%y=6 2HA��E.�?QHBB:�}�bVf&Aque*%��a[�\m *�^N E�"e?`Qff� �iY� �YI�]*�\�^� c�B�MA�e ^�� �U&u q�|Be�!"�~^�ѫ�%���nbJ6by>�y�). In"�EP]=]�m�S�I]F {T^*�]}�5&�CS�7^ �Zd�{f=A6�Q� >al�!V_Ym+$.s@W thre&�{tYJ f�0�dy�NAsaT��a�M���5�s,>fje27)� i�5)BT��-#T:76X`5.(f^07)M3/< � `L�h"th�`AE>TI/�$,�0als�&�!�/A)� {I&�A?2� / � @�.ax�'����: �R�!x/͈�� Perhap� rpriv"��!�3.�Ba29o� �!K$�(FR�f"�0� �]!R�CAI^& :�~2I*�C'HH� be s��G�%ta&�����\6<*�>���!�Ij' ��} Ii2c!>� %V�qyV��$ ���J��o �� om�!u�>A�if, ��T"_gB� �&�A�TRh= hnh"���:�J�� rt�'o �.�!�-C� >�E96�*n19��ZxO on o�se��h9�M�FE�:�.�<)Ai. A�}-O x� j! xe� *�be�d"�<\tY&q%� �dE�Ρ�y_�aR�( ��u3318 Y!�T=�*�$.��Zui$�EsvIJly �*�:N*B1� f��~=l�8w5p~$G$�Fc�${Qb�_ �QGAis���7 .�� mu� 2'!\I+� whol�U ��^�-� U�"��s�d �%�$@���n�U*�H��$d6isJr�w"$Ge9.�4iP<� .V � %|"�;*bB�m �E *a7�&~�h4<(�N��V<|�:!"g%&��� "�!=��K�-�iK!�6���1�k�O)J�?ihmo� Qin0�� i��Cn��Isai�2�2��*�$Summary} Tx��BOC and~Ws& (Es}--2�'�Z>_8��( the follow� k(T1�TA�=-� ��)�aL)B ying%C�((T)W(T^*f)=E �[9�0unit vector~$ �}A K$E� cyclic "�fth��U΍�A�tildeI�)q-(T)Sqary if, �onl ��Lis constant on orbit��$~$T$. \end2%�� Since5�L��on sya� cticxnot� trans�Z�:��7%�are/,self-adjointDitdnot cl� tha��Q�$meaningful%io�s( positivity��%�4$, in contrast��� free.�X below. In other words,,(re seems to��no wayA�) w�a�{A�6-1� �l �,@ is. Also, we hav- Hpecified a topology!f�r2` ��@$, soFcan! prov�Gntinu:��proof}b" This!�Equ%�P~(\ref{eqn:innProd}) �p TH~&��g��. mVA !�eA�f Lemma ; lem:�0}, which was �? of 9�![�tby>h�w}, alsoc�a:�E�}.:� �hconclusV @s:-_and Z�U�!�a�.%U} \sa�on{TheB' � sec:aEB� � < In certain casei@��� ^*$!�vobserva9��! physical a clas ��yA�A��a real�� J, but)�adm��&�s�$ suc� a�� A���structur�� � %imagin�~6��x innerA� duct� iY9� ic set inM�@Segal~\cite{BSZ} �od ?A9epa aB�q9$is an axio��c Ai�/$usual FockJ�!� quantum� s� % M,�|,develop tooly0d techniques ��c�7o Xiz�ZAܩ� will�d4eeded later on��%�}[��Q] A�\emph{>} over~��(sis�bfC"� V� Ab*� +N��ous:��pF � A ^\dagger)J V�U)W(z)�0(U)^{-1}=W(Uzn�z�i + a���~$\nu$K$M�A�nvariZ unde$��(U)$ Z $ all~$U\inB�$%�a > ~$W(������y� e�eaCA�senseEX, i�p4one-parameter � 0~$U(t)\subsetJ���u�* u�A � equivale~ � [\S 1.10]� � � Now!�~$E8Ea_��6� �� pr��~"^,~`�nor� |~\|$Z e�Les~$h=\Real{� P �}$o ~$�1 , ImagR,UAa�Hcomes a ��*:ith ��[~$hJ�.�5�sN�I)n$. If w�� by��$%��d�D�3��� r�� phas6� of D2E`� def: 7IS}, �J�=�-"�.� adI�&b a�~$*iA�aDa$� d�g^*(f)==� \qb�AQ.�: W!�t�no8% follow-e�� equA�� B� .3� em}� m Fre� � ]�AE�YCM� n.)�eAqeQ�jy\cong)Z� � Zw�a bove �� rF .�I�.+� )$ "��r$ AD Z�al!��f)�$-\|f\|^2/4�c!�=i��F��%�A bd$�_beA'�c��.� g et*\�/Cn\}$ �re� t��V:� �"Q{: $g,f)/2i}e^!g-5$"�WAu�� �)��u�"�Bxketvii�p ��y�R��H���u��d(U\�Y(Uf)^*��jnu ?0}$BXIn��!��a B c��di(g� E�"G$9����g)}��!�2� and}d\var_-(g)={1\# 2}\|gA�266�x,U]��� ��:M All�numbered�k*]!BimmedY� �%�F�2& I�$ly remainsA�show *�ofx6fp $$. Assum> ~$U� itA�$ )iV"8 Af,f��=�Ff,A\ge 0$& 5C��qnarrayAz6�>W )�0 &=& \left.i{$!� < t}\right|_{t=0}:W� a�� V\\�X<E�ReF�Pe^��f2~-1)�� h]��(-i!�2�N >�\\I�=�M�~2�A%%�A�N�c�*�,I_9�h��eq:-�} 6�We�h� � g,h+�� h2.h+��: et��E^cularF f=h$,N!�i m�j!�-�@/4}�Bu�&s7 cise% hef�a�@a Gaussian random�"c�Nx)Wthe help!� N pur͠��� qcre����}��qM ɡ f)-i� (if)��sqrt 2�g�� �� �C� �annihilN�.�+���9v� 5�R� s sa�yYcommu1  re ��[�,a(g)r]=0,��  1�(��gͣ9~* hCf)Y7P0 $$ � $*t aI�w eas�� coher��s��� eige�t��every~$�UY l*�$,.U} If~2�A nE��C �8"~g,h-E� iQ�,��� {>�B ��) implE!��{NJ�}6?�b(-�K5�- �% �(��� $$ so!4 matrix elemen���q�Y�-r�%oeq8��}>�e�� �b�M �2}Ip �~�-r])�� '-l�:g�i��-�2eN�+ =x-r]xa�so 6�A|}%�y2E !FQBy%� dens��  >Xi��result ~s9S� W{w u/�A t}�a mark��ula]I\ .\`6�Q'�R�Nv$. We first5"� e � ;6X powe4 fT"u$s, or Wick (���}ob� ex�s !7J��erm�b�.�expando�re� ng0each monomial�  alle!��[� �� !&. ., discar�+�dorA q�9h}[9#]�R����~$n$th �c,}!o N�}��JV�f�s%{�5K6'\ui�f)^n}�,2^{n/2} Pm_{m=0}^n{n\choose m}.�^m �`^{n-m��= aI�F��BCa�� 8e�K$; is more%;ir do� alway�!A3:�&��{FoKn!�N� \:�� e~$>.�Z� p >!J �>� are~I $$C^\infty$C5 9�} "�X.6]{RS*���T�A;-<�:֑� O��� CfaQi@ f~�A2�e�&se �W. #�:��U:�y.�. �"*�"any��a1.6u�! ^�U"s��qN �M� ()>� beca� ey�� �8binL ���J��o� �� .} ,ies. How� ,%�(�is whe�#hig�#E�sJ�An�,#:�1�GVUG poly��s��heN��he�W2hif� �/am%r J�f�B��*Vusv*�TveRl� lize�T�sitj.a�deed,�A�atz� f)a]:� \|W $f_1)\cdots nF6F=" ��%4_{f_1}^2(!y�� l� ,\Bigl.i^{2n}"�i �al t_1 N  t_4}Ar_i.�W(t_1z ; n� {n+1}  2n}0 �' � p A�T-orA��+, s+ V+ �T�&t����& squaC�_ $���aJ� of deriv�a`,((0)�# � �2n� 8easily checked �MabS��!frv' 0.�,Vl$$�infinit�\iff9i� ���� 1,���8, Just how weJ >{nd�)�ge.$ong!� made evid�b��L� v>�" ����}=6 !g2uon>�"$$B� WiFg�V I�B8 }=A�l(N ~ :r)^; when��~Z,h{ -l,/-{By_e/��c�9A :.�},G*~�Ct{V � � 6U& g g -a �`��("h&�%� -&iBi!jm1 !iC 1>0� F� �J �i M26w�JX�AAJaGa�im%so)F:)M@M12�Quasi"�t&v(q>�1$us look ag}(atz{:N\Pu-��FG}��^B !�y[�M } ���8)e�-h!tsid�(kmul�,��uch betA'beLd i"�D f,u,an$% would�ect f�e object��!�}�: rec]� (mapstoFa����)Չmap� "�#�f���+ L-��� an unbog&d"8 #�hextrem�6,useful, as i��lowj* �2&&P�Q.)o6�L.ase� *f�}-3u�4�� does�exist%�&� � S�-!Dy, supp| N we� � . +� &X~�&o��.an"�D P�#^*=�� Often-uX examplI��$�d��to mind,ace typ �� as�#�+!^�-integr��8 tensor-valued ��lf`,n a manifoldE thes"+/ p/0wise Ds nort� b!�m�5�0ubM us,&U,=Ds,as~$AM� A(x r\}_\g3 A$ do noi(n�'Att,"B+analog + �!aI&�  in�dATfar�$%Av!H &F �+A!can�0 explicitca�� |g\|=��t y attempt�/"S�..ue � Tail, !#\lim_{aJ%�:\*�0$"]it 0�a lea��)~$6�$. Acco�a!6 no:? '!g}$' � a) zero*� "�E�m! E�by tak� >! ��H�[*��(cal!��.s��_0mteqej6_0n$,JO.3��s��~$_6� F�g� !�f�W_0'a�e��!I:A�{��Dc:O$_0Q$i�lIV=M� ell-�}enougha� most pu9�4 pur�� now�s idea5!�mea&{*/j2�1nm"�RnginEj� we sugges*� e�s}[2U]l�8_E�&�3��5���aga^�3oua��1 9a�!�"�)^A�R��1^  1�/ �*js>�9~$Q� K_0\times o\C�'A!�� argu4�� �r!se,. N=6 � � Q, WH ]f0��- eq\KG(Kq!]�,���refer to.�1!adՓI5(}�� 2$9+.iZD��!�A�6 E6a�&� 5�$ �B��`ZB'. While�-4sibly hair-rai3�mathe�1ia�*is�R�2of�1���*ctually u6 �"�3reasou7. �i�n�=� �%4Dirac delta a � P!'�Y o� ��7stric��sp �,�2un�!. % %A:D��kH2� 4Friedrichs %exhion@.b+ X.23l R&� ��!�aPa %t�7b���ina� ib� %EuZ�)!�m�}zc ion %� jm��[2� 8by %$$ %j(f)(x)*�x< %br  %4 K, x� K_0.N %D� deF1���j����3%���}�� �+�Q@�*� ,���$,� has %$T�� �-9Q� �ly-�� ed %��A~$T_0.K*N%A a�l(T_0(x`!)r?�%7)6Q(x,y9� x,Ay-��'p/meA�a��:e�A$, %thC2TM���Y�� enA�%kA��g��Aas"�(A�->�%��2� x b��G� �9�� �#�q�/M1�e� � ;* " $6�.� }E1g^9.res!Jt� J�/��"u>h@�7a�� =be��/2^ configur���0�ў%R�xP��u&� HOur goal!Gto)� 7e.V./&$J1=2fa�g� �3:y*� �2b&: 2�. �AWU coll9'�sV�,> ��.X3 �b���1�Ai&8#x> W�3llYPxI$�Psi_0 CyJ/� 6�M �}E��&���� �; � � ح:. " l�$K )�&�& �\  V�M�2yf_:eA�"�n�4� n�p� f_n=f�C�$a?F��'B<D _n�* N/$$ �.:PK��-!6E &�"� $@�� p-:�&N,f_n�Di�D _n)-6)��#���#�*�=$� %�:aa�#M��^*W� )F��ul"A:�# G�b& O5A�a�A�$,��:�of B-co6�Z�,1�iz:EGi�� y. % ��;��pf=� ong "�@� . %� closF*AQ �� !yZUv�� %G9!r! �)�Z� donem%�A�$tv9 a %!�"u P /��7*W� f� i�+ %Z�ElcɅC>q\mu_0f\b4_03-%Z)%� is�C���tSert?�+/ ��5t %�r6�3�8��>n %u-a({A�_0}/�-B�32�1:�!f���)i�3_0&�3��&YI %k�-A�Is�?it&N  r�|: %* >|*�Jvu��!> m�}=� %9-~$Q Q�!�i2�?� (&37E?�C F%�:m1� %�Uwa�3 w dy�� !��F�)mA/j�2�1�V�yZKi >qu@&�� �6>�66�"� �w �xjx"� $�5уU�A2� �}!N�A'�ary.� &� "�-id��2�����k). In �>wx �/�e�d�E)� Fez���~: t&6YLf Co��GA ��] $%Sy-�] �*`Z� A f���`V/�.��62 >".�%ly�.� "� �Ո�e��F1 1�by�o'�� N�hB�m9_ạerfo�._NbIas6�p�IL ��%~!-�#!�b^%ڃ,m ��aF2�A=��:�(An entirelyE!G&�o"s izes6\!fN��V:I!$,E�} �o�� V%y#�7�"2�2�o�o>�M?< �x:Ii<^� =g� �6EC�"v=;= f� 2�r U)Q> As be#� ey����\A�Vk�l(�rig��{��0�$ � )3��E��� i5 ��� .�,"evy3>t� MHBM��1 e�S,corollary} %nH�ڡ�$m� %�:~$F�C^}C� ��NyE�F(�M�( �� : f5� :�>MI�=FQ1:/��_1��J(��.Y%h�p�W %%p.`5u-�%�w=6 "�ES._�C$ Q�l�,e<�)��,\l*,V6n�6�&�!J�"(�m. ɜ���se:UMP�~ �Da9 %2���r�F�)�)eAW1�-�� �[ �9�)/3�+ ��.�K_�� .�,1!&. E� I�?a�*, �PX\sum_{k'1 p_kx^k$� iPM.E� }B> , %^k+T�y�<*5d (P+Q[lq�urhe�R�+ Q�2�[�v�=+~$P,Qaq C[x]@$holds both!�l�L)�o�.�%)&$Im� n&�%between�L&1 sYU&7y�; cor:�@rr5,B#�X �hfor?4V��/b �_6�62N_I�b^^�*K�]^lv}�=fj6 j�9�e�4'a�vd/r � �6 l.Z um. z�!I-A��5uEry�]tin>3+a };��jI�Q@2�s (:v+21})�th�4^ �0r72})(%+�0a��!&O?�qq@��aY� f�%�(�)G&+ 6�;.Oed=ga*�&�(pe�A�X�6�Xv�:ŒF� , our des� Q99�:��c�YK� 5l�V step.*\% &T �+c��U  li So0W"�2��ͧ� !!_!do��v � )�&A��^� ��� rr ��Jp $$&�^ !�G!R#�5)#!za6��A!`V1"�  a�culus� &7,%]o^i� %serz>l�'p�>�iYe!�-&�i�$ectrum�%IV� a�^�radiuA�!H verg�LF6��2_D U�F�"45 %>�: By%X�(B�4E�ex I�A:�'�n�G}{(-i)^nŢ n!}\, +^^n>1�9�.�?:7 0[vA=\exp:=y5j�� ��'��zw ��-�I��h)= �"- >�..� dedu�=&3j-���R�a��Y �=%_�n0} }{0}n�"u SVr 6�r N�MK �)L�a t5%?2PI�- 5edF6�A�,+f| �_6( ,�to�4olv�+ \��c�$�B ~$0/v("�*a��9j��}!��6�G�7F�1�})b�G2h�^H!��g=�B�[:�H-f78�B�Jf=hL �./N*�Be�T �:]e�I�B�Ncd�Cv��C�ByJ{��})�  r6�1�va-�!�dB1$��w by C��;:� �5�KI�%}):g)}qRM� %"O\PUB��M�ZDal}�'�$a��VCeW%^X�&�#^*� t %��s qs~(�^6�^�R^STd }) %�15XyeMJx+!w!" Kf-�8�K)^4 %"�3 �e& �Y� ���(8 �6� & �A �D(�6 6#Mg,f+h I�? al_g)��-�Imu( }r'r�>I2�A�nl(�b�0)~���F�)&jA�U��1�{%+wM��):g)}�.�!= ��>�-2�M��N>a��$�+{C"Ci�]e�In "(E� 6�&� aH'mu��O\W�)B(l�b=2� B�i8psi_xi {)a���)LTmu(y-xa�@+d *R� �� �� JXL� %� ~"��e beJ6ed. 0F"E. � j1 and �0i,j}a_i^*a_je&}ix_i,x_j�x_j-x_i)� v�x_i5�,a C�WAny"� -��e84*J!s#- %�[ ly d[]mi( so-3$e�!��!e� �[5.3�[ >UProbabi�lc-1erpret�)Iaj ~$x_i$1!*ŝ a LagAEian"^(:as�!�!�$ (na08w.�(�A�]��� %R=[vanishes��E..]21N b�[^�A��_0>�(By Bochner'� e�m-��problem 8.17]{breiman92}\footnote{If~$X$ ya R�Q�7A�a23 ~$V$i ~$f(u)=E[�5iuX}]��u`V��"~$aD %f(u_i-u_j)\lambdA�bar jE�G� ')A�C^n | $I V^�@a�co�sn F. See %\-%\SY�}�u/e�}-"�%�9heb*&alAG�4M�ty di�,buAe��.�:~$X� 5�]��,n�iA-�f(X)}]=Ax f^*)Nr�/a��La% E5l[(S Dbi�P.�0����I��0�I��HT' natuopC:� !E�N�%��z'%& w"�*vacuum��$ �%a�tat�;ɟ2��r�i��M `` Y %exW��''=��yN:*Uj). %wFouri�(`k1.S�.B99jE��*� ful�g �-Q[�z!Pb�Wigf4�yG1.8]{� and89}�3.Le�"PsVlEal�gwr�*�;)n�ec)m��2WA�8toٵ)_mF-Q�I1!o&� *L�%"�BI�N5��%U��MhE�yy#JjG���le=i^n\�>."� {t_1}\F.n*Z GI�\W(-y)\�F1f_1^*�FnY-x) rɺf�Lx,y�x�QQ $fg��[ A8}  in)vF :�@$x,y,f_i$ %�8.��G1^*&KG �+x�r0tEmPSuccessive logarithmi�6. G�Rj %�'in�e� abo�XR(N*�fir k��I)X;D)�,��y �� -�E , }=�5�Cx+y/� rD+.Rl�  }"� Z��=g��-ZL���n�ND���& %2&$ldZq�e+u*f g= ͙I6�Ny=x0[B�6��7!�(xN���5�:!|f) �T$)%SVwJL:E�01O�>Hqh�! gI2� )#N� f)^2��-A�l[VM�KJr]^2=5�f^2=� ���csi*�a~�� ت�V�0)* AFin�;� y=x=@* �.�02:_ =F�rwFA~M2M2w*a�#J�:E�w; �i2� JxUd���~��ub o{�$\texttt{[A�hv�36UAJ�cle3�s�@%Tsi8 ch.~7) 1�u�H @.g.]� �|\�Co�wlog�galore} �6C�S\O�{ ^k_S�m �(smooth~$k$-�Dc�g�$rio�T � dd\colon Fh J_:{k+1}_S;�1s �1� �$ (de~Rham) 3x.\xy� {BR-R0\ar[r]^{\dd}&:#k_r �+!�� �� om!`�r�H^k(S) � = {Z�� B U%= zCr\� 1J�to : �\� \dd>8{ ���O��.�N P%K&! �~$ �2 iso�yc�@�`.�e@�G, ?;\R6EN:Yd&iHcompa�?-�Hr�-�JHto �EI�MaxfD"t%s�jnot8� � Q,�6BmY��l1Z_0},�ha vEl^l8-rRn%^p!-�2rj2cq�A~��ZM�_0B�U�F�A�}:���]� �N�$e�M� f~$SEiA[��Goff"�WmaIZ~$M� bounda�4\� M�&nE~�V2�dA� rha2yu�@-F"j8aM,bQ�IKF�E� m B����2XeLco.�~$\IC$&%"a- WE\��� .@�$mV f~$L^2]� � &j Y+�J=(S)U>dB4(S��<f$ coincidesi%�ri.��0~$>F!�/& esC��`�=`&�e),$ (6� FMe�!mact), �{X�OI $X-dimeEalf1o.�� niceI_�ic�O�/A�)�J�Qch�� P�F0AorZ\metho@R�[I�_P- ��QoE'�|q may��Շ8"�^a� T)z��1usb is choiceA� "�K!�ic~caqG4ctromagnetism:�0 clJHQro�KWheele*WO``�g�@� '' ��\ ?``�[ �}s trapp)?!\�Q!E��'';Ŋqua~.�4PAharonov--Bohm effectA mass gapo��$3���9�gLapla ME�5 ) way 8.�@�x were u�~$U(1)�Dgauge �Mead�uR o�B?W� est�lelf�]t-1 ,��'! MLaS! (``.#�''�/ g;ly� ble �XH�(solit����b0poles).�pwA5v�_ d out,~$p�B2*�a<�n+1)$.a9�!N#I�/s�" ~u}_ C n+1=2(pL6sa�lied�i4�eCs�sC3�2� }AOU�F��+�Hscribe�s�cven�j�)|JABNV~u����vg( $$ D = e^{&:%(n-2p-1�}w�Z (��zc�mve di� mhF�>D .9  d]^{� 26�&�Hk6��D ar:� >�\\b >�Dv�N � ' %�,downward arr�Y"�u &[p�&5�s�C an i�sR�~��lex�j\ng\UI��? t�2�L������ob$e���I��2g6we st�Jɋ tw�VY�mA�R>&�  1m� ~7A�0=-�FrN).77M"�D} kI� � n�c@I�], depe�kI�Vi�3� Phi�/}8spa�x y,�Ձkovxv%�1}nl�b ]j�Z"D !�=D (top��wi�� (botto�h�^U �Y�ZQ�c~V ` D' B~ � �D$VJ( �^I7\dd$,v thQ�iyG� re��f��.|/ma1meT in s1>al -k. [n���5gaATJGZ�-��6.�"�T� S&�n=Ky��d)gya"�~$\alpha$B%zn�9IDt  ��I� 1-2p�8�1;ne�6F���:bQ��>E�beF�jal-�:#�Z�=���a6 �sm� a c� -��Ots 1� needU�ne��wiTis&�_9�  >6�~$D=\dd+Q$ l[p+1-{n+�| �br]( Phi)\wedg܁a�R�2� yօ%GwiaV2�G �1` Know�I�M�b+� ��J/\ummjof w8�� (� �5ݒ Riem@eano old�jP� ar\'e�R`&�S�8o !� $6� H^dk}�\���%�as�Q0\le 2kn$ %�bgH� a�eU t�y�0 Y!�$16V !]S$��eze volum�  triv� A�irQ ivu���dH3ce,&xc �JeBil'9tauB  orA�otvD�r, c& cM !-M~O���"�b "�s2e�n$,��CHttlAU�L saiM,�>�YA��X�werson85}�e�T�?$n>1$,~$a>|� |�P~$a\ge 1� ��% ��]h � +?��c�3\R^�wi!�urv`g�!�d�g-aTe KA;1z&L!ir $p^rB�]�AFp_2,Em�6� �:r{�syzW$n6u��H� dds^2=dr^2+f(r)^2d\theta^2,� E�AAId I�WSaR1fH;n� is�k_2=\{k_8f~$k\neq 0,n/2,�*As�^�3* $k=0,n6E=(>�iMo<� �. "�w�Lk=n/2$�� $\int"{ds�� f(s<9-TAN� J� oA:���(> �!-�8!amiddl}<�VA�a�>�:�gral cor�eE�o~ci�nesh;0dodziuk79}. AS�r�AwU�¥�i%a8%c�wo2: cylia��pn A 1_2$ k�(ch_�m�*�A.�i�<2 �V�9����!E��A�:�u=5$ <,��!� %�!osũ-ZT"��Caryp_:i8*�o7s� %�sp��ngf�a �,coI"*6X�+�E/or j,g_M=\rho^2 g���>+~$$ɠ!�e� of ``push�a����toqy�+^?��6� E�ih[fp���s_M$ diE�e� ~$�f��a (�8 -length) ��eJ"LE�atoest� endHg��\@ �9|> mSo�0�ci� �?. C>Uif��c" �!0�c%Fide'����Oy''"am>M�it+�&Dg intoM�l� 6<imA-����A0(Penrose. Mg2t88} stud� !���!�r �>(&��.a$o�,b=�& 2��� rhoOh7j -i._�"'���maa�a�2to`e/2M J \�,�,Mor]�'�e��v"<�~C�&a� a.t th24R.&�~<_km�\sigma_:(hrm{ess}}(\��`efV [a^2�k-1)^2,��)n)� \cup+/4.#1!4{F+.F}!\>nj?JM+ n=2k� � O o"����2�2s��!� $� k|h gFU n�Wl�wۛ� a y;ua�m�j�geoɮc �{ (\ie,.$!�$no tubular�l6�\� Phillipm"�i��%��W .@ k=(n\pm A�A �.�ue�>b.]7� ��S�Z� en0D�ot:< to���of.5 $3$-��=9B< 硰j3ɾ�[�2U.�g��A, �)S��� ifv a � is `' (0i�cr'0�I"ne�i�e�IEd�� go! J.� 8 kerne;2�&���1�� IF.���� |01varie�5�� f�.ks.�ha dirk&W2��n"1gi2c!I�C � t,�u" {!itoI ide��\@ ropr����F�lex�<�A~r�no "V1&�J��eb,� �NPh�� �t� ed�H �H }��� .%�un8on�d ��-ekiowqz��G)�l�R� lex,�r3�so�nyXs6 f>��.�f_A�le( a{+� ar�A� )�Be�"R �]�v���J�s*L��6�s:����iz2Ѧ&less �oa�e($0i^B$) a1+1V <"2'!^is�,G�s�d��(�um[ no�;acLj� B 0~$\R$. Global�+ ��rER�� op�   ~�e �  so70&@h-��t �p%��g�s%�e�� #.�sBs ��� 26�Q* (��)B�� 3B�Iq�spheri�j&�&�,no harmonic,Fc~{s aIr�}�2��$) a surp�!]�/-.��`la��%Fmor&+��!� RP25�Pa��n�reaF� (��� photonٲacqui�;e=)"P&Z��A;^�)*�uinr�."�'� Lv-ma��*mIi/�fo3Y%ewofa\-A�]"!" "mo�&e�"6BQ��b� a��" �g$h: ��p=9 �w�iSy� ``� 9`''I�L"� 6 lZ M� lr po�/ialHpmMu unreMJ��"�!Ma large4!M"� �;O���JF. 5A &�E�l .[0 ����>n��#rK��nont�za!"�J�I,�V%dg`"�'�"�c rw����?}�z draw1>id& %lu�ms�noN�E� I�6!Y�s�>!IUg"% c��:wer� �l�j�$ma}cri�%�C��, sr � E�c���k��o�-x�w!�� o bably uQ! rantAV�)K�Oc�wP��8++ -`�eJnJa],p l! q�f�ZPbe�\Y� ��F]An6�� at�ha o:�F�"�%!i�1!��!B���"��f�F2g$�$�4)�.��&�f�6X . A��i�uU�*� �.�"��� ed bT�ne�i�\ �[R1)�\-$m x6��2)fis �!8{V$ a�h� a "A�MT��q.>�e or&e)E2:_nR� �F� ��H Z�A��clu�\���6��'1!%Dz!C*� plan �%i7yG]e��L!.9Gs~$a^2/4F5[~IA*�Vl��@�RZ�vM?j�^�ofY!~$4!� or ha�E-v�R�  * �SM�3lZ����e�eB� dno jI�=R A�ckJzju� .�~q~3y~�$U3 ignal�!�� ij �x*og� U �z-}u�s.�at tA�uzqufPS^� %�oahFG��yacr a~$2p6��?Z}~�o�\y A�ln�*� ��5%E?i1Q(~� p|>1�� 7�Z1& "� Jcis� �! ` n=2p=$�{��`�<e�,{TV�ies Pl� sec-<�}�<O E H�"�D&L e� �6}%V� ���a��rk�,��detai��s�K26� disk�7annulii�A�l32-��'vy ) Schwarzi4ld blacke#�H ">�#�U*D % \�1-a$(2-.� ��&��<"Jfam�� of el s!h�"i\�Hic, gvly��,�c)G'.�Z�se$B A� %21 :}m�5� be5r� � �?� e^{2�E((r)}[-dt^2+�! sd�], 7�W $t�FR� (\in[0,2\pi)�nl{�Nco���+uw%&F� $r� a��!W$LeBhNby-S %�<i*�ah�Īt�S�mg [%P %)# �g{"J�^2"�R�}rm{� �l$ r_-a�� �J)�t�}6h"Ր <�&��ei� �' %op�I!2�2�-wh) "�e�ECp%"q bl�p� -B�v %(�D-Fm�&$)���1s�r%c����� l�ly%e�!ed�J.�haIhkv"F -o"G6���)nsO�ޢ to@w�Ti�L$p�of $D$-"b&0on�)&rso s��_n�� ct $'��$ �+Z5�)B���LM$$f$? %Seco�-�!��&�Ts&�I"!�BR %!�"at $D�zsF)?�=-ts& *s!"w!�la����nd (�8 like6GB&?�&� !_)his $N=,wz&0 %$D��-�� /2}d�zPh  ��$\vol=e^�� dr�, 1u� H4g(1,1)=g(dr,dr�[25}g( ., 6 S % ,e)=1|Hl ri�<ll�ҡ�+�/sM29�.aN`*vz(/ %$k�Z$)!!r"�E�k* �%f_k &=&f5ik��15f\\ %/F%}+�)S-% ) r dr�bE  Z5 )[betJZ+ V+ V $>;�*.�����&�O o-awr$.A�n,RDj(�%$_rf\,dr+ik ��D �BR%-5p��r / B-ikU�6R)���k.DJ� l ��}=�si�)x}B���7 2� � �j-�:V-�}(� F + %dr�)�9 u.J� %/�7 ph{SF��s� .~|q+a" $f_k�7=�4fI5 %�-}1r� s�>L�U4$ %(f_k\mid f_%$(int_S |f|^2�t@ au�%Z}  drf � E�nok�"��$A�� rUy' '��|2U/2}�E �,� $f=�.O *.�1i!th���H�)�f:y.  �$f_�|q� n�ĥ?�)%YL})Z 5�Z$z���)O&1!>� bY` ��grV.$4"E.Co{1�f!|yA/ %�4.3}�YJ*rQ� ]$, ��.i-Gi� \mid 9<siU| _r|^2��shii� |^2]5iAo;�@$��Abis6r �y��5 Q=e�� � r�7ik  =De^Bd  Jep!�*$� ; A �/&�)�tr�Y!�$1$stUX & �&�3milar�$��Ӟ�.2�)dDP:��) a�k����E4��9%e� ��:@4:��&< Ge���M� �� j���+�O  =c_1y� �dr+c_2?"ơ$X ��=d@ anJct2�,*�\E �3f� !� q�-�:�)$6 5,��� "� 2n2g�]: ed (&�0!�2�ce"�7��0!7s)."��' � %>�y � ww .�d�.f-�aN9.� /pis86W$�FF�\��F�_ ѨaI�dr%q�B~�:12t3f!.-�.�>(� �?t�/ in�m-!������9ifF�f>�f ����f^2 dr՚ %1 f={��t  3����%!}d(f^3�TdͫAB�Q�:�6�3� d� $!>n� n.1E$!�awle 'ռv %M�B���F�f0�n %��$�^ do�N��M#}�"�y?j�Bb.�s%��d�n��\mr%6�9� %�} M|EJ)�.VV(a�ri� %�')=2��^6W OQ��6+�<� &IVsk^�-.a �`F� �{A*~� � s} A �&�G (r)BDv4*� *B'!5V9$�$sd p)�*� "�HǗ�����ny� .b ��!�V N[-fr(1+ I� ].� q[Z�-� _r %]>�$� 2 6rW)�z���not�Ŷz�G.s.o!"1)we�iN��in� >j�� K�`���e `�aV�=*)� FtdD��A�E��&�Xw R�9�8�)� � �'Lhom28��9�kAW @�$�.R n^2]$QmB %tlR#uad %r:Ip*15�``p ''�$:��E *��a2la c(!DM"��' $duA��$ge-�g�[du �^2]!�f�^g (u_-,u_+)}�&�u�f�*n� � �.?.i�"�<_{-}(a b_d={ >b &($ @ *$iGo?h�M�� ��T�>jG�un|�isk��$$\R^2$). D$ t&���6!* A `��}8�"= K�3%k�sk�N5=0X�;s�6Jz ف�d).d_D%�9�re�0abz�!�%M ���T�{�OFinn&�� $(~|~�+6�X4jI��c�X_D$"j3)��69�9%R l(MJ�  l )W=( f)_D&IfforIg��O�^0�Tcr %(�� ��H .BQ #in U1U < S��, � rJ� e�W.�G )")5It�*�$!7�* ()J(-va�^, � )_D=!)�F!�,IW: �V�d_p#�=�i�s pD- ^2 ` Z.,-�t�)� 7y +� f-m�%� �bDA/3 T� Q��^2N)#M��B�$!� f�=� D0]IR_1FqE�_0"�!�<%�:K= a2O2O1���li�ns �8 A'� �W <� %$� $A�6�" $d_D /.E ʼnl"e���AɁlos�T�y$0=-�A�� 8� so $ %fKsi��L6 ���'��8co f�'0.7 A2 {f$�$5i-D �fP�i�-X4D "(P, $�� %Q� $. "dSketch��(y:�{[ R!��,-�4�Xy%� aximum pr�VplH0Y%�� {|x|=r} fZ"on4ias�# . Bu-|�{E!�o{f }�j_D^�!�.4$��� "  {rdrE5x}$�dIfu]1�r@+r!X"g!Ӊ!0X* d1E.!~,>9 �m�Hth�, j�B�2rDI{��S ,� -F�V "� Ly��=K.ael-Af� �8sV4!r� !-ex�1!L!�  � � S�y-c��c/;N�(� � *9Q�%s�$ V� )�V�e�n:E(�I*',E" � �^�^+5( HFs�l�rbd&}=�� �\;��o�� he f!��,h���pacI vp& �# m%P~�:of�(��~$u_+U,�Pw/ {.]��� �.T ue� u�|�%x6�� � %u=>�tr���we.�&Q� o ^2}[h�u�9�zJ�u)��h���$ �Xs%"O� 5�u>�u} -�y �.��m0^{u_+m(}:G���A�d�% ��t %� (8:�@I)i0M6>*��"�J, *Axas)� �d %$g_]QJptQ x^2eoy�@(A^�%`I')� *|  %a2��Ah �Q�is^� �$!�"K�?�JFE�ut5Z(�y�vol_D. ���p��x/f^0.�% $ %D|!.�Y6 Z_k�t*2}. �.�Y)i/#+��r6oE1�to~$pV� �hD�y|!�A�x!< $D_0: A�A"�Kto�- wq(1"�T4_@R�!N� V�!iy�; ��t �!��,=�:�)a�V0AG ��+�� % aC,_D� "� �"4��"a+��*bd��=�E��d 4�@8@s!�nt Ja >;y�+n.}S. E�!��X�Q�FC��Ii��$*8&�?~$D� �$�δ�9�$8.Bs���.be8[ed�&m�s~$>;9Y g6$$%,fM{g)/.�5�Aft��e�G Df,DIe^E}g�V g,��g)Y[:&_DB(_D<�C�M� &�Cg:�� �er� "<$a��!.�A� %��f�r"��g�-S,� r_0�01�� %�1 -$!�.g#I&�1&e2+cg� te %�s��� b 0_{r_0}^{r_1}|�|uqhm!UY %}p;e chan�1n4H 2v={@� � }$ y��!% k(v)^2(dv.�)�v_0�5=R$�)c3{v�v�&|dvASR�-����t)�-: !42 �dv�."�#=��B0�i�totala�r��3=� ��.� � ^2dv"� .�x �N�a�I/f�A5��nTZ$h#-� �}�%� Q �>":��q�c� area� bAY� un�=$v_0=-ik�v_1!�ft����:1u�`a?���'�a 0"�#E�*A&%|m�7Jp"'�Y_u$i�A ��E[v_0,v_1�a!�� rval�t a "N &�8�*�9�of5xTa �w[@�e sam[E3@Gin Ex���*O�BA��.��-e.�!���EcH�!h4�j�3�����(�ok D3�9n�#)M.oM_�B�+F� . It�)�RQ(84``w''�r*��v%�!�� %�J c�g� ���7�8ch�8�+��8��_�-�0``isotropic''�3 �e&��� &=&-fyl({1-M/2�R� %1+ �y�8�()^4�Zl(d6�yr�U(-�sin^2�X��phi^2)5r)=�/&=&�~)~8 ({.�3� ��oڤgr]{e��=;d zV>M�Y"�SA)-��Hf�_�7i � %^ n�J��ly,A�a e���� �H�8b�6eri3�e4}�%TY� � {M/265 %�>;�B������s� In $:J�Hdo�� �3wc�)6+ �x�ia�% laps&VC $5� �Q�$�  $D=d$�L %� thF�!�is  �*B*� "y ��n���1^)"(1\�1)=4\p (2kA?R� %�Q�3i=%�N0�${(u+M)^9 d�^3/2)^4~�T������H^0B\)�${1-2M/%f(1+ )^p}$eb�|6� %�!%ove*�$b t7��m�s�"a  $�+J�%�n't. �x8�*��i�Ij��M-��9h.!���~��)�� gb�$ %(d qdf)=("$7 f7AENZ�6�%�.Q>c)^��,_rhf\IuAu >du�  �$ q�\docu*c��[12pt]{�4c",\usepackage{41Licx} \def\ffrac#1#2{�style{#3d(#2}\display 3�,�$S�S����F��e^ �Ae $|h�$�\y�a20�(!v $2L_{-2},=M�/2)���) J_P� $M!<u�#@�2 nH� �"feWe�Ty� ��I[RHorԛ piece�eAs�XDi� let .��,�Ba�!n���mbdO2�origiAb ���L�*�m���� �:f �bulk Q�d by e 4:�cr�@I��K? -versal m$cB $ jump $\pm�<�i %A�ɁA&�(!{�.�\u� % \newpage� Ip�A"�� sec1��I�hcgyears,j�(SLE)JS4Sc,LSW,RS,REV}� ru��1%=F �-�u��>5c�N s����_pproacX�cuau��n�(!�+bc�YM�tyJ/l t���i,C��l&�w+F�}PtYA]e�o�NpAsX9��`wa���of \M [ two ��in�GOs $z_�8$z�fF& ���Z,� nn�doR $\� & me �is��0ted dynamicaltly by evolving the curve start�from one end point. Conventionally 6Pdomain is taken to bePpupper half plane $\bf H$, and" r0$\gamma_t$ as �ed upK�Ftime $t$ (or rather its hull $K_t$, which includes any regions enclosed��q)�8characterised b �4conformal mapp!$g_t: {�@}\setminus K_t\to �Ds unique if we dem �atI�>(z)\sim z+2t/z+O(z^{-2})$ at infinity. This function satisfies �,Loewner equa!� $$ {dg_\(over dt}={2 -W_t}\,,, wher)�,continuous f l $W_t$!kimage of grow!tip%L under�0$. In this pa!�lwe shall find it more useful!� define $\! �\equiv �5\always!�) F� �to�originIk9C$dm=2dt/ -d�. !{!�completely general. However, Schramm\cite{Sc} argueA�!�)0 foll%2 condi!�`s hold: \begin{itemize} \ 8{A.} If $\cal D%�A�ed!�I�aqo anoemx${ 2}'$, s� at a-�mZ.Nto'$,!*!�Le induced measure on'!Acorrect$ for.%n �; �B�q�N part:Kpu��9@a� � o �re�{E� _u� E��)#{same aIHun5�ain9YUa��end9� toge%�,with a reflei�property�@ only possibility%Dthe dri�� erm u�(Brownian moAB, namA�$A�8=\sqrt\kappa dB� m�$ !hstandard>I��$ ;)!� diffusion!s:Ht. Different values!�8Espo��o? +universa� class 9critiA�(behaviour. aseAがum limiE\isotropic short-range 2dFsystems�$also belie�:ɂ described���� fiela�$eory (CFT)�q focusesA�!�l�d� �lo�!�ators�~a�V scal�(� s of 0�lattice observables. Within radial quanti��o)�Ah-stat!)rr)senNf CFTE`s.!1sA�H(Hilbert spa 8�t)w�@f��pinto highest weight represent% �==%� $|h\A�Ple$ whose Verma modul!�Pntains a level 2 null =$: $\big(L_,-(i�/4) 1}^2)a =0$.��$mplies, usA�!�0BPZ\cite{BPZ}"Ds, )Uexpec)�}�A]� I0-awritten�O$\langleɒO}�$1N$ linear se�u-or���x�9!��s%�seyY�� foundEG�$stochasticAxE�A�rYunificE� betwe�� two3es has bE�4fruitful, bothA:��d!T CFT � in sugges9 ��le;iiԅ>SLEA� .�s)�F}E[ to multipA� JC}. OnE�!� important�m( of :9�$��A�variancEX0sigma^{-1}W_{  2t}$%`%vlaw%�$ #  extenI�($whole sequ��� �ings: $ bpg.p(  z)$ obey�|1��g_t$. � mean'at�))��� !�roc�R��a�iA$� 4self-similar (I� of course!10a special cas%r�F$symmetry.)!�$m�,,\vec\rho\,)�Wa miniP way of geM ie�A while re�ing .�i �d� � %z,!y]�1+ Ao2 ��%�AU.�3� $eqnarray} O&=&>Q4-\sum_{j=1}^n{� _jdt[ X^{(j)}Z <;\label{kr1}\\ d&=&{2F2-p\,,72} V �&� ,parameters $9`) (� 1,\ldots,nO r�Ua�ts�,e auxiliary e� $�=\AJ� 0)$ Hno� depend of)T:4 eed theyA7ld��integr�qout. T�a�ў$$ will thuA�Wd on��e� ticuA�rea�B|��>�but  E�Jv� $Z-�0$aD well� $\-�\}� SLZ�mE es w> firs!tro5 in Ref.~�� D14}�xampl� restri � ��ir^' �� have�( studied furc ^7,D25}� %{�u�in%} in �_to My ceraf.p}a��lso lead3a'of" Watts'� mula �} perco* . Let S%$� rk �a�q�s (\refe1, 2})��jus� �z�8,E�mpactly��ed�blem. x$\Phi $A�r(�up < ad�vy $) harmonic"� !I=&� ��&,A�A�@ axis, is piecewi� iz diski%� $\pie�j�I]s y�$. D cur� dens5 gJ}_t^\mu� ( \epsilon^{ nu}\ _\nu)$,�is��� ed z y�qexcept��source.(\ en=�) may!n �]�} ��3�iB� -1 J� x(0)dt\,.�FNot! at!�la�%��g՘ ly i��t,1� sens ; Q!{��}�E1ɰU �:�,�9m�A ��(s given by Q�3}g\em��� becau�&rivatA� w` J}^x_t=5�y� j ��z$,e$F�AJ W�s.�as ���e�2' �b�a�A� e���Ai�is �. More�,!��E beco�ppa�"E�r5 siti<�u� main�ip a�d oughA� ;no5b�q��. F�� �o2�k random�ve�d CFT!�i� t2�F��)�d:m. It turg u at�*I�'��o replacG�]q oneb�%@ s(2�2&�2"���� '1}3.��� )�}A�rea�ArJ}==5|x_0(0)��i "�in Sec.~�J sec2& These�ra,�likD& phys�ly relea6 �z�a:s naturQ rA�U)!ssiderx. A s�e  ��48of a free gauss��$\phia�dG @$S=(g/4\pi)\int(\��+)^2d^2z$�5J�(Dirichlet bM ��� ~g3}[ jumpi FL acta���aS�-` �� $Ja`\6tov�!.a��( wE�%n_eff� of i� �a�strength� mbda"���,*�n _ ser�D aN�chang3op!�&phi_\lhE� Ŕow��a�rE "t� �^*=(4g)�/2}$ !E� �uw� ��e�e !|usualJmYI7 �=4$�a6 ��al$h=g{ �^*}^2$sg���0frac14$. For �`� 7%�, hcit�!��ormI��ʅ�), ���(=\alpha J$ �  $ =��((�/ )-^*),)$,eF$J$ n1 &j.� y�^*$=�s} unitArge�Ol� A�,%IA5�)al�to$% coupxc| $g�0� ZPas� turbA*A �OU exa margi�Y�>d m�, J\bar J$. F5R2a% view�z� i��9 screens �� - )Da 1� m5 f <�act� re5� х _ U$(1)$!;rgA�i�$!O�"�E�A� !^*!K�{K"s uY偙2�32}B��y ��e!=�e� �I gy��oBAa�E �S I[I�,��M$tA'"� to i�ifyA�quely%��� �e Y. a�� � w� gu!��der� �a�d�!����!�A�Q� �ree N��M ��at@}]V�$���r �.�I =\pm a�it do ot matter)Y�,� � ��macrosc��Hy2X� -d �3%h�Dv��bulk.qis shE0b�?*Y _4N proby Shef)+and S2�S}��e�Ż� ��\not==tw !�=� &� wZv") �<}�l�!d�Sabove"�i��s�!�� �%f9C6 -h!CA`3"����"than �em�mD clear�eEAxret*� model,ɫ} ��D%�(r�tq�� G AFper"44s �p $2oL�a!�\s�{R>� �"�F :$!��� ng��J�$m�teF  i�in&I CFT. Our!��B��sl�ly "3q�a(*�BB}ap�bee�sui1� � �ALf� In Bg�"upp�T!�!�s)qse�fundam0l -eVKps)�(A`�� -� 3l0degre)Ձ�dom), �x��[�N"f9R&� �e"� (���� (�#���/ a un�ed GibbsU $e^{-S[� ]}[dm6��at%�U�)/� figu; -=_\G*&]D a fixed semicircl� centred� �. �vaci Ex�s���A2Z! $|�' y"�0&(9 ) pa#�l��e��a�ri �# �[ 5��M2tak�Ah&���-�%!�� : $$ |0 �=#)�2]_{� �= } /]\,.�\,N� $$ SNly� ' ng�22!��`)�! o�6I��9�hi ؁�ELe�-known�:!. B�ofB! , a �icho�!x $-�E;�s��pp�fa��� v�$s�. Now 2KX�)�e�U�!3si$�� can "� B�% conn���)-Y� *](~ist�a{su�1is assuh  guarante&� Qam� "4#�V. O���, �3&� a clus2 [�I��eaeE"spi- dneg> �$-1�n��� 0 posi B0+1$�)� pr t�tin%##old' ar���#. Any)V�  �r�br y:�� as b( ��A�h� >+bs%L� e1� :" ��mU�i 6o�[$1�N��loa�/� r" ��)G�+0nM�!9IA�atribu����6�%2�x_1*ZO+�i���|��> = ����z;D�!��6�(�%wC!�rupA+;-z�!� N�r :O.��J� $d\mu(�-���%0h-) =|h_15n!8 6>>^B� n fi:D!�since< is ��G�!*� gral>��,)�i^� ��b 2is ��.� �,ait� $t=0e �& *�%�!�%JB��6iJCbcc}6+ . H*>���2K-� o"�-n��0u� i rougTite� .�#"� �#.� v^-����"!a��a�tes*#c`;$^ �/Y�.y� �A|� � ɿ�I4 � l transD !  $x�to  +\N(x)!�herp 2 a� # !��:_i�a"tour $C�A� surr�s �0�!�U 4}, �!vanis�&out� $Ck ��Lmpens�ui"�  $(1/ =_C �L(z)T(z)dz+{\rm c.c.}�N�, (� $3Ex�� ]�ensor. &f �9��mQT=g$i T"� ��,_� dropxS(� E-by�!�!` c<B2 *�-o^EI our �%,]�2� Q� FR(2dt/z�$-UI�O:, -) uageaw%�9Zac��/>Y$�$�dt-cV%AG%� L_n=>�z^{n+1}!�dz; us53$t_1<$!: g_{t_1}��  =�2,T}\exp\left(� _0^03dt'�{t')\r�)B�$+�| T$ �� time1* xpon�4al������A�p�$J ,� �"� �$�� �nu�*H0&G1%�2Q��C%&= 1%�fGB�� � y)a@����n�&!�$i ,$t'\in[0,t_1� Thus!}��2��Bzq WW;.P}) M"8�} bxcfordin� SLE,�#� o��� o a "('e WR��~ a� >�>� 6(�pb��)66bre� heE�1 val o s� seg��s,f-an��ou�Q�,�- $(dB![})^2=dt'-�re-Y��!MPresul�B�u�-.�-�**� )t_1u�h_{t-�m�-�But� �*�-� �� , "6 a� N M�r� 5('"� l2l1�w �&� Nc � �&? ��.s/. *o%&�  Q�h ex�$�be a P , ���$$ ($n\geq1�  ��� ase��b/shrink��zero. e2��$�u�*� A�&O $\{X_0*\}$6���5�  $�;25Mn�&�c�is 7�3es!��� b� &> a e nu�$ cide"!��\x {X_t�lia| g ���� & "*!��/h�8F�%,A�� 5 a�2�ku��#obstru�!s,!_jn7"x choose it �Q%��. B�#i�0"(c�;ient)�"� E�t #-3do*'� v�9CmodA&:� /)^g u��driftv i� .(u �G �st- stra forward��>- ���&�7$��( o ob�+ �h_E�I _0\Q�= �Big�+ �.jT.j/M)^ �^� Big)�*�aBx�soA7a�2�8�� �Aa�:-."ExaRb"T3�"^7 hX} �� J����|V��cB�*�;i=hR->� A�q�U�1Dt$�(w� incui��&�D��0*} !�2}&ɼarrow& +-�25� )\Zial_{y&=\\N1JN1Nf> �&�&��%�gg9a,E�6i�6��-t-� mark��i�EP�/K�#bBF}���-on$)�dIe-m�b�6��I�noa�t�8�� � :| ���m{t�a �a�)locx fN� B9%_*�+j"�1{t}2� 9wl5��C$!l]j��se�is�of:�� %n-t�;[.�:las>�hXB.%�ermR �ren*�&�( (z)=I���_j/(z-1C&�&edT2Y"1!�ts��6$�c_�)N -1}J�X)@ s2Z%. &4F&O!�""� sec3}�"> s�o�il�K4�^ A�)st �of�>d.vB��r�&2 6.�}B�S[~']�.)E�J�s<*p"�0"9):���<, d:�0t s �?"_j]"p%% s $x+ $j=(0,"�4n)$�� (x)=�M-I H(x-x_j)�u� $H/1� x>�3 nd 0%{ $x<0�sf�B�#"0&1B$�_c(z,&z)=-2:�\,Narg}(z� =>�\ln�a( !/( N.���Wp1�% phi=_c+* !II&'=0"=�=, UI _c]+ ']$� 8 �+�< $Z=Z�)\,Zs� ٚ�,�1 Zc} 3=7'd_{j04 k)}+ 11�)5 �* a prRJ  sum omAWa�� EI$j,k=i�."�,weM9f�P?� dimen7Ea2�.@� b  h_i=2t�I��IA�&\ E4ln-Ŋ� =�k9� �,s��>�""t)(Y3 Zc})�We�2��let R �{}'66� =�/ -��09l*�4U4.�jCF�0)/d_~�as9�{�� yT}\,U ^2�?V?2YSGi�=&Z�r�b��2} +4g^� B}�% ��� ��> ����>U=J�:x$X &� (�9n&Ydei�Grk�%s��a��+~ a�� ),#ife�`I=4��$\mbox{and} � mbda!�� 3=1/4gM`-2$�\f 3 I,Lla�*���� ?instead�� g b/} >8=N�-.�rho_j��j-��,N1BR�-���i%;I=(U8[3��:1"v3_i^*)^2��� �'�E!��ˁ���{,��Us.�-�8( $x_i�!"w0=x �$. IJp3� uBis"4JAm�*�"�PF�, � be� te�N6`,)�{< � J�&/ �1orSL�,y�Fi ' �a �>U3f3_Q?�{73�9!� >�� * u6a8l 8Q6A�uPN"O+M �0r�4m@AT�2�^*}(0WQ (1/zN7(I�$J=J_za� S a�%zM��1Ak?/50h24 i�,{F�S-2ig^{1/� nH� AK A�}%!"{ �*%=�( s $JR�n���=��$:$�cWD�8j=iB� $J_0$: �C!v$J$.mH�;�@tH&b-� as RcA�a>E�9-T $:b�mF�J��2}-��-�" ���b�6`b��7q1I9}-)< $�2��)�lt,>-4m�CA,b2J deriK3"��Cfic��1n!X�&A� Q8�HEEbyqmZ� themselImMy�(0&�,a valiC/%.�Rly���%N. �Nsu� �5cM+n�՛$T=-g:\!:��!: ��$:\!J^2\!:$!re $JP( a���"��;/#s�T�"\f�B�rR,_rJ_{n-r}\!:A"G"no�2�X�� symbol $= kJ_l��Vci�k� ���"!$J_l${$k>l$. pE |h,qQ�a0u 6|;WJ��;$h{���b $q&� $L_0b=h $,�2q6�5u� =J_n%A�$n>5Ne*�D" ar2}7)J1�e�a�2}J_0+ a�)3= 62q)2}b0"�DRw1w�1fy( u1}.�h^26j�{16�cRnRY:�q^ @ ^2+k �>�\\ !1��6�-?�2�A�� 5���w7 8"�IA�Ms(anomaly $k$LB�� �sJ�T�=k/z^2Y�l $[J_n,J_m]=kn\delta_{n,-m}$�.*�alqs� $k=2�l��i�|#I�Jj�- forma���)P ce $�( :��iaga�D'. ��,T)?6�Wly.2���*�-� �� � m���"ANTAMj����!��� �&we�ld})�?L9p!e,% �,dered NeumanJs0%TD0$\tildex$,w2*J[ofQtex��5v=T P b-.{$ >2>2<1} % �Tu�Yk  ���� ��n.t:(g)=1/2� I "=Zk�)� �nuitably �G$ $g$. Pick reQo;g_�-"; � $S_0=(g_0z�C�U� ��- Io4jum:� ��#_ $1|7i��Ja %��MCIkA�Y& s $J� J"A ��Mp J=2iF${z� $. �4Qd|�MurjW ��S=S_0+u�'@�D!& {\rm�; }(u))1�1"9A��D����);=g_0(1+E u�0�A��� ��^*[& #o2vq���.�� !�|-�+�Ih2$� now�=&�=I� /2iHFuOmor4""@ R"AY� $NYAed�09Pun>��R�\�*�u� 2EJ�) 0,,=k/Q<^26�� !/�m�I,E�$6!�a� jJ_y(x,y)0,c-{x^2-y�x^2+y^2H qq��Um&�'ong�� �9�Dq !h 2"H�Y-pa�Gel *�=!iallel� ��c*�?PY-*�` � loop��eJ� keepE;hv� � sam%4e>�is rea $(if $u>0$)��a"�.qEAxAvo)s� �&?? � a!B a��n ��Qn�6R�]m6�U_  ��a� CmY.aJ�$m�"�KF[�I Ri0f�� � " &�"c  S/ *� R� ( >� J&��q 2� :R^Z.e  +k(u)6i :JBo : j2q�J5i�Vt $z=2/4� 0 ):&�)|>�=fLqU�P-Y"�VA\,.�=�.m n $u� A�&���-Y'ie�F"n.�B(,"�"0:�SLE_C[l�$u�0$�Ws`y ed r.� Y� o](4�V�H�&S3`��)acc�g� �;��h�B|$� e ^J��%Zun�v����'$u$B"�6~5thF ���((� nti-)&hap�44�<kY !�Z�� �g(emeHF��K)!b&'DF.�\s& U"a- �DIa�4s2 2}�5!!> uR�  nK, e. M�k�onjectur�\( fact�*�E�E-&F(SS}. So far�2�. show��d�*'� ��/�Vn +=!�CFT%� i�A" &���A�{y �!��^m�q`d���(2��m���F��A� (avv*�[eB�V4>% �yet)�X�c�=��ichFGt�- SLEs!P%�\-�!��sUI ].1�90#hi�Ka9 :TP � t^gupZlzD"���2"+ph�DI"�=ZM@�4��8Q]��he. ��Z�45i��Ac (r)>s$!�s.:$ $r$ immed�aA��O��5{E6I�Z2�)NX. WE�����a�Ga�1c&5d6H!�a� _4$?�>answer�Ap*kd E7 they�s� !��"e��2inuuf . Re` Aɹ�c }� 9 al� 0iaM�"I8 �7�6�8�TD$�D�Mb%� �"'R�7gBD}]\(�6�5�C�+ �|sH� =K_t$).�Mo�!��eIu�_;gIlU)ei� G E�K9��/%2%}E�s @A��_ESE�!�O"�C��>�Ces9�-(t necessari�he�1�Q�el"`R� .cK6�2�A:��eMHa%&}ZivO�f L,v4 grea�D �_^Gi![E��2�DatEfN��� ��� %R'7�:� U:�5anq@!�gLO",�1p� fr)�� s �V"�:o,� ��s�i � jump��Ii10l6!$G�.�:a�a mp�Y�n2�toIqIh2ofIw�6�k�վAǭ�1�6�y, �9w9 of e�bV�G� 2�O� ;� Dm�!��d:X. �Oe"�O"� |hC� Eji=��&(, iA�� NOm�m:%~v } _4!Q[:��2M1@VaBSa�-ZA�Ui�%CS �j? A+�BY!�!�| ver�6�gi�]s S.~F3.}#K� 9���u]qy"O ��e� eb� &� !,��<�Aq�D %�5R9aC��:l .3 F�7M-preKms"s1�i�"iv"/Vt� ��$2�-��Sg?�qoa�!La� aLro�Y int{  J}\cdo ��<��i-� �^al "� Q�� R���.^Q>�� �3+,�(� AQS�"zQ.�M�ous�X �ason l�c"�LxB�Q>8���I���Q� lm � �a��te.�Q!�.�"D2"�QM�_��I��5L a)�a V $!�\cos( / M)-� �eYulkF� $x=1/(2g 8^2e �rF]S x>9E�� �<}k9'v)�oiK� �^!�5�"� ��Y]n< � )n� "�LhLi�A �>�+Q��� �I1� Qqno��er"4XI $ \}_�;!IVYK5,ConI R ?jl�&Fm. 6� ���6�lMw carr3dEr U�"�bf I$.R�f2�), �,m �;r��$at�4 ��M��H"�! �J%\  s. S.�N�c�aRm1Rll�F�a ����& X�)�K� efXgv)W@w switchq� ����Rxion���i�E�led�AG1}Nsh&�rB1�+,{R,R'}f(R-R'XCI}(R)�n!�}(R')~""�n�%�pobyI. �&�@2L82}A.i!�ll iB�eCuf>0$:�r�m�pE3Ratt! �bCD .�2��3t*e.�# repel2ME��!w�& C ant B�q %�T�b4#%�)�_&j�*�RE>C6� �ue7S�L!�M26�-u�'$~n �O��� an averag�Ense�Fig�bfig1}i&k9a%��*GR����fhOea.���ed phenomenA�.�=� � o �$ >.e� ^�,erew<�&�� j�. %r�e}[t] \�Ueh!1�IPgraphics[width=10cm]{�.epJcapa���n%/\�Q3n� tdfavoucHQ&�S�8;,e��&�!�`-�Bh� .�nZe� iAc�Tled"F\�kI-��)� ank Scott& 6explai!�a8m�Cm� !�t of.Y SS} �@ pub�To�,nd RolFriedr��}�Yonef�&ork wa�6r+�?Aal��author !a j�: member��S�Bl�Ma�( atic� d N�al Sci�T$ Instit�6�A�h�Study�os�Yr6�W4Ellentuck Fund][ thebiblioEFy}{99%�bib�{Sc} O.~$$, Israel Jkth.~8118}, 221, 2000 _ A8LSW} G.~Lawler,M�W.~Wern Acta=a \87} 237[ 1 (mw,PR/9911084);E?ibid.akxI 57553 5,0003156); An�j8enri Poincar\'e =38} 109<22<5294)2�RS}] Rohdb.,d!�.,A��Q106036P4a�-0REV} �new0Eee ='{\sl �\Aar�U�A�-�-[U �D�Ps���u}v(Sp�D er L# \ms)9`$0303354); =�|C�)ly Inva7t P=k"ny P�})pre����0, http://www.%�8cornell.edu/\~lE' /book.ps;�Ka�� B.~Nienhu�H0J. Stat. PhysU�q 1149A�4 � -ph/03120%�J.~Cara.�SLEeK� e�` ist!5i.q�2�79( A.A.~Belavk0A.M.~Polyakov�\A.B.~Zamolodchikov, Nucl�BIv8241}, 333, 19842hF} R.~��, !9�410029;Bauerr2, ,a104081572YPw 9J�A �36}, L37i$3 (erratumV)12343e9 3); )�Lett.�58c 1�*6�4s.myK�}J. Amer�� Soc.pM$16(4)}, 91�0.�2093436�D7�$Dub\'edat,i�ProbabZ�3AK8:H25}.�e� Fac.�� . Toulous�q�I�%�302115:Q>�=�50769�sG.~ ,! )|-�29%�6E\96 ,I0d-mat/96031676}�:}.A>�;6Yqas99%� talk�C}ed at `�G �Ec�C�� Spa�F!��Les', Edinburgh, Julya�32�BB} M.}Da�(rnard, CommQ6)"�/23!!493, 20A5�� docubI} �6\,style[12pt]{$le} \text�=21.5cm � 6.3odd��, -.1cm \even> \top ' = -0 P4headsep 30pt % r O(flushbottom| <=7.8in \renewcom��\base\!0tretch{1.2} %~$ 5} \defb94enumi{(\roman{})} \aH{col�`1pt \font\twlgot =eufm10M0ed \magstep1 &egt&8 :sev7 ((twlmsb =msbNN :egt&8 :sev@7 \newfam\gotfam �pg�n got})�� /  \Qhp2 � F � poprotect}}�msb�A`y y� _. �Jy :) y Bbb{y Bbb}  ({\relax\ifm�ccGg>gAA%aa�:�#1{5(skip\�ion*{�3�Ker KerF,nm}[1]{\mid %Mmid:beq}{>�P:$e$���>"benF�+>$e$ FV"beBE*FF}{2EB"beaGL^FD" �N cE�Z"A�2�cT!pB0ce�B�cD6D>�cRRB�KQBKcC6CB6LLB��QB�cH6HB6�K6BKc��B�c�tBtb�bfF�b% bfF b�bfF�bZ� bf Z>�b�bfF�b%�bfF�b%#bf%"6�al}{\A/a:(vr}{\varrho:btE�t>2dK�7:1lA�� :Ld:f}{\ph�.7 om}{\omeg>/OOJmu:]a�n>e��:/g}{�$:G}{�i: th}{�FB"TThFv!S vartN! varFup}{\uR�ln�la�9:�r@0:diAvrm dimFxrdA stackrel{ťa@U}{\�A.�si�8�:hSSJK wedg>�w! widew8:Nw!Vha " oA�tJ� :7�\qial:a�op\�"#* �6:o�o!9.�a!�݌x:4vAevarUh6Sf�flB�s�sharp�H.� Eh��&�cE. et\s�=� :F !�etcfF{0}C����l ��E5� r� k:+�k6d�iG"�kou� W lemm:jcorollartTCJCit B� � {0} .�{06 9�>0.�>4 �>2�>0�� th5�R�$newenviron�{-�{\AB��UB���'* 6-��. B�a}�[M�"��:��*B���lu�a}�ldef!)�} A� Ief"-�! D=�j&%�j 5�j$9�J%eg.� proo� med� \no\nt {\imof:!d ih.Are�"ref.%-C6VU Re� 9zvaex}+�` E)� �a!�Fc� � 2�. � ,v�A�gPro���klN� �b�L��dco��:�~dC�X�hA��7щ��fj %����mar�~ par{� $\|$?%$gi|= 0cm.(width = 1.8yn"{9]� \hy� �X{ma-ni-fold La-gran-gi-�I@di-men-si-o-nal -:60$ Ha-mil-toPan �K-sy�Gc-tic�yb�l } \hdN�%\�(paY�,yle{empty} ��=l� NoA�r'*��V�em� BRST�F��i�bi�C8sc D.Bashkirov}&�EҘr#�mail: b %@�~.msu.ru� sl D/t���T|Z�ics, M�|w�e  7(ity, 117234 , Rr a!#�� �(G.Giachettaj�( giovanni.g.$@unicam.itV��em&� I�- ,�O.Cam�" o, 62032 ( (MC), Ital!�:�0L.Mangiarottin�luigi.m-����t�gingQ5L�O�"dynamicuand ghosC'�9-q �f. Ampre�k ��,v�LB��$fiber bund��$Y[YX$3ses�wgauge�?2� 6� V� !Γ�_5L�w+�0. a�1� ���8I. INTRODUCTION� �� D�6)Nn)Bb/*�,,�%a =&ad%X���P`i-��_3s "� al6�b'��{$�2GB 4�"�� �Zie����b� A{W%QuIvt�b j 2�.�(jets)!�V�U� :��(q-4�(�R�'�--&) ��yE�BV quz�.$^{1,�A�< ial 'U|�`pai�+globaӔSGaDb$�P!Jq+ a+�!9HnalysYBV >�3,4}$*� with+lasG�F[aZai\ i\ u[sub�;!%�si`:�6k(F&,!�q]�7r2�asny em�.a pur�:,D*c�.]��K alis�!�co;it�5�' � $E�4�9lw�) �Hvecto�f� �yB. A&�@, > are "���09?ar "�:�o&��up$!�$E$ 3�;�2Avۋ tn�nt�VY`1� (S L II)w,�X�=�;a.F$L%= ned a��^� Delt&��� ��L0548}Ah95� f�Z�-dual � 4{0630}\beq E^* ot_Y(w^n T^*X, \�] n=\di X��9 ` �9E�-whose k�(�/n�k�5e6=�Euler--MRe"�R $\dl L)[L7.e., $ �\ց "9C(&@ �f{0568�\Ex�sgM?�2sf.�I,� m : {0510}) ��s�#o�#fo3� 2A%�V��M!s2� s (A�Bdix A>t6t. Nޣ�Da9ex�'� 0tw�+.� eta(\up)=)2$!<E@)=E�C=U 4,22An && 16up)4U  Rj,�IbelA 4}\\Iup%�\up')= ; Jup)a \' # : <').29Veen{K�pr@�7i�Nr�/iT>:�!ǡ*�� �߁b��hCed^,�Pe��al�,�� < ��j�$Źq��BVciTT-�hq�eoj�isN�liz8�5 ��b� T�@�6� -T:�VF%716a{ We dY�Q�[�!V)0Z�y2; smoQ�2= as g�/�t xe� ��Fq ure �+�a�F[�� o6X$F4,5}$�6�{��ys�E� � �fZ.y,$^6$�9�z�We�, heuristic n���J8 :1�j�iot; & )� �1,7m��>�.��_ian, �I$its nilpot��!�]�2 ��"o��&V��I`��,B���AG!�aK< �ea.~by!G lace%�E�~e\ � �(D��675A�I*�2�9 �cy�2�A�CE})��alF�a�E�Ӧz^��y�6AVB*E � EVe�:_ y as"�to>4,j�63i�UJ4E1 !O Koszul--TCI� al��aBx���H, $(0\leq k)$-stage1Ta�t -c�3� i�} play.II)� w�Dm�2 LU tu��ofI�s, Yndh �mY�)U�1$ We �w3v!dZ �_Br! m?N  A��2ut keep!�9�B�i6��� ! �s. "� B��I. GAUGE SYSTEMS ON FIBER BUNDLES.�vDAX� $r$-I[yХ?2�"� �lI�da�a � ��51��4q L=\cL\om:J^r� � 2� $\om=dx^1\wa8$s\w dx^n, �b��P aze�je��g� ��~@ . Jet ��2 m�UN{inI�e� �5.1� X�lof�^\pi YF8{\pi^1_0} J^1Y 65 � J^{r-1}Y%6W@r_ } �6! B.1&�)&���7C���Ak x $r� s���J$Y$:� we VJA�di{��1 7� q \cO^*5 &� �*} !Y 1>"1_0{} ( _1^*Y \ar � ; �fA-E 3_rF!EmRlEJ5.7-#of��.�W�s9.nc�;th GDAs)%� cAa�� rior��kj]�s M�w�&� !V@ pull-back monomo�! sms ��.�$�bs1�@t �\infty^*�GDA�w?if�C �6�.�6� modul� �ª͙ proj�ve � $(J^ � Y, A� _r:\toE�)!>!:g(=E��ya F"6ru�.$^8$ A� atl�<{(U_Y;x^\la,y^i)a|0u X$ yCH7 co�P��>I� jet1M�{((�0)�;}`);��8la, y^i_\La)\},� {y'}^8T+�$=�S�"5dr x'�}d_\m y' EB�,|\La|,q��i��9L&�0\La=(\la_k...j��Lt c ��� l�619, �) 5.17m�d�S = \dr +��(>�}%�:%, i^\L� �d!3=d#_r}^ �Cs 1}� � �#��tot6�%x gdr$xepiq[ $��m7+2U_���?!(��2"گ�din�YM� DH�horiz�ln -�J{dE�A����<#Qon ' $\�#I=dMm - 5`Hre� e�:� �0��-g �J^�!No��.lhFa>? ,2m:cnZJ%f�!ū1�� =dJ� ���Ycan8E,c6�2� Y=\o�,!�{k,m}1'��6-� C1Q Y$-�9�c^Gk$-1�!� $m$-Y EJJ6�B�t��$h_k:l1� �� {k,*.�oh^m2/E��{*2�:A��B2$�x\cO-.^*%s splh� <�p$$d=d_H+d_V��*i��".gZr d_H(\f)= \la ��\f�9 d_V"\tm4 \w \dr�~_i)\f\in!'19 YG~ e On\p" �,$�1 R1�9��#r� \vrAJ� 0,nY,���^�]6$� $�d_H�l!�!��t�ab��&�dl==h{*.�$.<6 u[E bE_k7(+k.+�G�hGDAi�1�  :��~-�@n� �bi�lex�$4,8-10}$ H3Bh�Vc�r5� ��io�sub DIb31�2 0\toI<�ȑ1 � ^{d_H} {0,19��2 a %>{2�E*ar^�!.1>26` \"N�)�1��/ ������ � 0623  0 � {1,0�6�1.� �B#]�\vr �b 0.k3 �ThE�f� co*ylog�3,4,11�$(�"Yg9�)mar W@! A�.M-�� %H) �(l� de Rham:FZ �\~b�'}�7�'��p%� exact6T An��nB��(_2 Dan�{i�2^\ i�t!"051-�An�E_i���� > ��� � L�� \cL)@\in)�� pI��Jts>�&�\N-�&��2�M�548I�T^*� w_Y(�� )= V >�"aF �T��d��Ez�J]�Ba�I ��9.� �Yn�abb�B� $A\ap 0dJ�nIo�NG �Zu-shel bm&�`$A�6�$R� e �. A� ideal $I_�E��*LYlV�ly48.1.�$\)U����� 21�� 6� �m �� .# �(. By virtu��%Ya�,�ry�$-c&� $L: q�su�t4� L=h_0�� +�\si,   \si\<cOQ-�ᵍJIJwv$Lqa �$n$8 ��LB�'}vi~��>�d.� � � 1.{=�A �(�1,2��eeLVa=: %:J��El�.�`:��g +421i�dL=eA-d_H\Xi�!61Xi_L=#+�a Lepagei-�Ra�L�c �i $\gd�.�Y>�� �'Q��2mR0. ��$\vt\A Ft*�d (a�ior!�duct) O� P F � �P�!~re�Q &&� G df=\vt(f" % %�9#, \kvt 9((\f\w\si)=( \f) +�f|}*%5*� ,i-q� � ee��>Lieve)��15AB]bL_�� � d\f+ d.�� e �Q}0\) Z)fl� f' +� '). \nonu�JA� n R%�Y�A�� ���m EH:G$xds$^4$)g�vt!�/ .� vt^i�.��>0}�&: �g� ��A�"r9���� ,&� }��,~"?� ose� , d�\La9�"� "��KF$.�Z��A 6�u\� a\ $M%$i��"/��v%O,  !!M��cOu-$ n'aw6� law-�71A�q \vt=.!<" ^\m%�\m�\ 4z&{ |\Si|j%�}NdP y^j_/7� A�hn2,�\up^\m"� �A�q*�O!�j �I,-��� ba�&.�)�Pn� . A]f�ES\ � >�6 R� $m_e�)��K�C M�REa�$h�7 � F�4%g�i�m �iffM 4U-����^i�\m!� \m)+a {\m+A�m�E 0<%�"� g4-����y�V*�&�6B ��ME��L _H +\vt_V ^\la�la +  $JX �}=La AK�}A�up^i=iV2�"�g5 ��*�6�c"����+nablaO.ot �|5$C� (X)$�)����!5,1*�e| al# �'!$ )�� �x de�%_'�s ��suF)R064q�up=�( ��K)��1� 0a� %� ku�Ji��# �Q�&�$VY� ]:_Y J^kYcD !�F�(,)�$5,$+3a�7' $�%� ��a�uR�(-�(d2�&�'*�Y$ o�&�&)EY�+lhi ��+oh�{�6�-�$�} aT��2P'} ��g75�75}�Z"�#�lie �� ���\:xom &b F�a�� �}�6 �<5( ulfi)QZ.m ��ulaIfg8'�U�� L=a}\� Z  +Th_0�iM )) +\cLQ _Homa�BbI}$<��r� �TB%}��^�-d��9F2�iI�6w88'I�$d_H$-6�$$- L�\s�t� � &� �  gl�� -�e�)�lI� n__ at: (i)j� i6�/ only��;s�\�cto�1(eh �r A&��$R% Hoߦ� B), (ii@ Biff[�V/ ^�i�+"�H i) i�l.��V�)Ig>+k.�>��T�q�X� 4�}&� toma�5F7| � _V)�7 .  0 �Q`��MbUi�1�y�6y}:�$�it�wt�_25S �*G.O���X�Lrz ly-.] ?�$�ken��z\d"��z�/� :ega*e3�%�x.���"�;r -$700} belowO*urn�r* &�(a 6a0 � s"�Yfq$ s|1� OZrm?s.;3�?3stm�gLzY�"!es "(�*ãl!(#$a�L6o09h�(�j"t0�͂ 6&�% $��,\xi^r��gBf�, lb�!d׳t3K"��y||�.�E^i�E$�nJ!%�P"LJ�E$�*q�� �050gq� E|_{. Y}=�>5�   ' �V�s�6O�pt 2E�|�Car9}�9!o_\X�nI])6� am�.>H�� a $VER�"��nup!r!�EAn�&� �%;(be \up:J^kE �E_E} V�2E.� VY! a�%��� "y�(i�64L0i���a- ^� �5�9Fup=^.�Xn m" {i,\Xi}_rY�g)5g�"� 0509-�).�2�2s��A�> B���5�%�2�v 6esi"; 0=!bq�)�ay��6<�-]| 2@V/�Y*� U@W �JiF�U AsX\mr+�-�,�Wa��6&6� _E�0:* {� E} 3�...��/. ~d:Q 4�M� M��@4�!J�*!' E$. �`�U� 2U, s)>gh-�eWreb94,�Ki-t.��Z�E$ "��!���0y�n ��Q� D*�' �4�C�,m���The"��s�)p& �!0�� $eo�111A�N�\vt-��) G�aV� RL vAc�.)�A��T; F�,pI. NOETHER'S SECOND THEOREM I.�,���Y)�&e> /&� �}�T68� 0 V�"* �,)�, �Y6��<)�1��6�W }6$��2*��AI�$ m%�o2��7D!�s�2�7$\ol E�l ��7)pa= such"�e4�!5�"^=0�N4���cQoA2��E4h`i"c<�ntity}��� a�&B,}Mt%� -�Bx s .u � y_i)1AiU 7-)@a�2=em :$E4Qw&�5�in2�D6 Ar!�3�[7b 1�5iS")= _r��B�La1�J%=�La.�)){�a \o� {* [6�^*Y&j$E�"� m"� 0547�N�2�Tї>�9{9aak�%.(�)1 5�/[' .�9-49��] �=0"�0W�,�(.�"�  bQ3��v��6� �A�re"�ma";06a-dv �oO&�*}B 0  A'> .+?&b  (?) A' +]'���}�f�FV U A)>� 2��9 (B).�9t606Y\ :*>�Ul k- �o(Si+\La|} C^}_ d� B^{ ) }, \�,C^a_b=,b!}{a!(b-a)!�-� 606c- (\et�� ) �=%Z2�LV%:�a�Ih"40$A�� 2'Z�-$A� "�Z��H�"� $z>� Z��6�0�?��$Z�/X$�DA�p40 gin�$U!�<�   I���B�"� �BL �:[��W� B�B�15� e��1r: =\�;up)�&QetYfmZfje} ZI�}_r�1T�eeq}oi4� �fFj*��bE!U-is.o1� 65 )���09� -Q63�u ��V1N%e�QV�e��^T����%�\�634}) 4%M�8&�'�N"2b$dJ!X2V@%Y[$-"$@*� ���41M��;^0�B{� T�D�$�?.� &7M�� !�i��16�|�0-���(:!a2 ��>~�< \dl.�`?up]?2 Y!�s.�hu��\=�%gY� 47})�8�!��%�-�M)K��YR8<� V0�#�zf3&3 �f�BUand�n"'I:�CF/ �E�65! g Indel@_?�!�:`BJE�="",4� �, V_Y�R�P*i :!�qi =S"B:�of "R k% �-����cF:� lift,up$!�7 F*���_E=\G� 3�,�?�Li�+"G�.i �><  �a:� . DuE,[Q��7:�,�9oa�a�&&0B�&� � E�@��@ q�n>\ X 5(�BU )M"X =J c fwzv�\si�ƍM�8 ��e $!�E=BpL6c�ity�� 606d�!�B�4"' ex&% 655%  % 6j�P5�g!up=�. _r^i)_+1m}� _\m# "� ?i=:Jv � $in��I, �6W4Mg��� Y|rea"� 57,� IUi_r!� -�8.�,Q -0�=-"% &�G57g [Fi_rEY -� m!%C)]%1��0*#!58%n�exqny. #has6�i�LI%8"tBtt G triv�I2�Ja�!�Q�hl M* ��! M�e�; Si Tj,H9�% �j,n, T_r^{j,i%=-i8S� eB.�+��>� �IZ.m�!�L�R%�ee Fur!<mE��4923ym� r 1h, a�Veon�|2� $E'�gY$,*6w>�'^sֱ` 6 Q$�|@c&Q8)&up'_0a�+ h '!�%�s\xi!��5�8&5�${\Xi+\Xi'=?5�J� Xi|}uk5S�%� h^{r� '}_s�#va"�&� ͛&4$<'�I2�Pa5��-�tbkIn B�o�!}mbigurUa5��A�sa٨��R��E�>H!�li& U+ QaIIl'_��f�facR9t���?asV� + T1� T�1N e A�:�.4s&8I]D ! �a���s;b��3-dime�a�0A iZ�,mY��u�"- qX47��� $H�X&F .; *'N<B�6�i� �7"!��_9'=HeN�6 $ ia*!FkC3UOX� KPN2�5B�'$>.*�M1��6� + FU4F]4Ac_ %��46":46} A>QI�J :f/�i��a& H>�A�nd �.�of}!��VGg7s%9oI*�\O 621}s&�."S:��  �e�;!:���xH$�PE�a9�>����ᄡq _0)=MZ )J��2_ �&[4V 22a^w�2!ڥ��kH_'tF) _� �F)Ea�c̗&�49r�,� "+!�R����M9�of9�6� 0Ul50}]co*� )�-r�princip(�nechf&a XP�X�/=@ trucJM�group $Gp+n+���K�o׎r#XI��.�G!� quot��"P S-C=J^1P/G�*[ -�&~ �ofV�!k� L7af��&�2\ a^1)$&7��a ��7��C�n|m�' $A F= N�  A$ Cco4�c��$! f�$iaC&!�-�j]��Mials)!J- CA�Q �eM j*;I.�^�[�ie ���� ]kB�= S�In0B�� �tA"���<�;IW%autom"ZG�2N��$G$-in nt���)QPѻ�Ko"M�A�re.`��uf%F2� $T_GP=TQ�GisQ�?�ndowed�t!�Yes"5& \tau�)=\dot�1la"��re�X�Df.W �t��1_3 e_rs1��."r��{ �L�1�Pr?�a�al��VcG. $G]�0 $[e_p,e_q]=c�H(pq}e_r.$ Ifu��# u=�$ \la +u^r��?v=v�  +v �5�Sqe$.��qix:bracket�"�50([u,v]=(u^\mom { -v�� 1-l� �- 5Ala �+1u^pv^q)! ��5� � $u%W!w2K.�.N8 %�*5c6u_C2d +(�a^p�u^q +.�-a�-la !�!�_r�$6�M^V�ections $C$ (\ref{0654}). It is an infinitesimal generator of a one-parameter group of automorphisms of $C$.$^{12}$ Let us consider the bundle product \mar��}9}\beq E=C\op\times_X T_GP, \label{0659} \eeq coordinated by $(x^\la, \tau^\la, \xi^r, a^r_\la)$. It can be provided with the � lized vec�field�60 �l\up_E= \up=(c^r_{pq}a^p_\la rq +u -a m\�m%- < a_{\m\la}^r)\dr�_r.�60 �DFor instance, this%�8 gauge symmetry!���[lobal Chern--Simons Lagrangian.$^{14}$ Let us consider a subbundle $V_GP=VP/G\to X$ of the -&T_GX$ c^�xi^r)%ws sU}4u=u^re_r$ are Zqs�(vertical au]b $P$.�restrict� �prI[U�9}) to5�1)�:k V_GP.�1-�ipr�32 g�3] U�62 �Tz�,Yang--Mills 9�s,-� and yA�s%/�well-known Noether identity \be [:� \cE_E� - dA�(qA�)]!�tq\om=0. \ee \end{ex} \bigskip  \noink� {\bf IV. REDUCIBLE GAUGE THEORIES}7( Recall tha)�no��A(a reducibleB� haA�me from >��3atraint%-d5}$ but it involves differ!al rela{s. �$egin{defi}u�$573} \mar{ A complet�ope�`@ $\Delta\not\ap 0��547}) !�a�0corresponding� 1���54A�a^`said to be {\it $N$-stage�L} ($N=0,1,\ldots$) ie�re exist�i[,s $E_k\to Y$�6�s � _k$, $k=0 ^ ,N$, such%�: (i) -��linear 2p[ on! p density-dual $\ol E^*_{k-1}$!�$E w��values in=k9�wh!F-1}=E$;�i)�=� for A�6� 223circ )� �-�VA, �2� ]v%� '���oe�V>576��e�_0=�8sum_{0\leq|\Xi|  m_0}-� ^{r,\Xi}_ �{\Xi r}�\omـh�Hq T!�a�%&�u��di �E] �MV take!�e*- Akm��opb� S6�d_\Xi(>7La� m}4i,\La}_ra�$y_{\La i}).��&� 57� i.e.E�( left hand-C a� exprAʁ� �be >�S9�+m}M^�S1� � Si i2�,!�m�a�!�4coefficients $:K$ belong�v-,ideal $I_L$.b(4�(4}.(� "� $\up�w�50��is.���yZ���n�i3. �ato��up^�6�R�*�a���c �c�uk$J� '�����i��w=!VW /0Ce<� ^kE�$Z;,� !�1 -1!tands6 d��up'^k)n��!�s� 6�\LF����N�� � theo*�8���80} AIo&R n�UN��c iff so!�4the associated����*|�proof}����Hof follows at once � Theorem �10}s Propos�� 21}" put�k=\eta(%)B� . If-�)��qn $5  because e��a6�e� . By! sam!,ason,ax!JIjibk$ obe 1V�u 5B� �!� �>�).�B6+ �!�e%� converse � justified2 � way.!� equivale!�o.  c� ��e items (aof DeV})� � 4} isA 0ved similarly�Fa� .� 6 646}�ndQP&* "s >j hV. GRADED LAGRANGIAN SYSTEM2j *i ,avirtu�~$Batchelor'�]A�3 6%��QN X|  fibe� m� on $ma�n� models� :�% usually3 �A�� ningE� refore, wN �:�s $)�_Q!� .�5�sm�fixed,A� � 2=�si� e Ucon)�ed � $Q$.e� !�r� $\c%�!Ce� %�Q Hist&eI U�Y1!�) �ed � fun [. GZr "J q^a)�j�� tran�� I\ $q'^a=\rho^a_b q^b$, le��{c^a\+ !" c2�I base�PA{t�, toge� � w� $c.w c^b$%�n� c�b l!��localui u!�I9�]. WU�ezo � basis,99 ? ��f&, Xk=0}^m \frac1{k!}f_{a_1� a_k}c^}il k}.� $ 3e�3T �smooth|l�aUX$, we omiHsymbolB9I elem� c^a� I)a�U�=(1�gdM�b)�M�-modul�U$��Z_2$--xderivc!�% .%.", 4 %i�u(ff')=u(f)f'+(-1)^{[u][f]}fu (f'), \qquad u\in�,  f,f'\in �2t$[.]$ denot\ GrassmanityNs9.�il �2� (or,�!yQ7)��~s on =Q. Due�*canon! splitt�.VQ= Q> Qa3he I tangent�$V�|Q�| ��c#!�vid#-y�i�{\dr_e�whichaQ!���$q�ma -ح��&�M��� $u= uTbX + u^ a�  $!, u^a.� du{!� acts A�%�$��� rule�cmp50'�u(aVm�b}��i`c^b)=v �6))*$ c^b +u^d 2J6$d\rfloor (.X"� ��M�� �CiMp6.�!6e* lawi'!@ �Q� u� ju^j%Y\l�\��j)c^j.���n�A0show$^{5,12}$�1p.�A�M�e1��Hb �en��by>� P" \cV_E�X$Yml��ly��"B �>�\ot_X(Q"�TX)��U QT an intD���L!m� the �1�}� asB�L�$op\w\cV^*_a�t����io  $ �$� o !ihy�pharac� �b�bh >��a familiar�$ degree. R�v�re�%y � $\{dy��o$T^*X� {dc^b ��AT-%J �\f=\fe� SI f_adc^a,\�� \f'_T ,{}_a^b\f_b, "\laJ+E�,d�Y�=c^j2� �We� $� odd��% ity � sm is~ -oin!�.� be u�\fi� �+ ͨ�]}��f_ai�GT U9!km�nstitut�V bi��.�( algebra (h� $forth BGDA0cCAa� *�ENU� �a \f\w\f' = �p|\f||\f'| +[\f][\f']}\f'\w \f��\f,in z)w!_A�i2�n d( q )= d ��|}'m m m)J Si�pjet� J^rei�  a�D` �` �u)�I[V��{o�� � " a�X� tsyn�aqep,c^a_\Lax, $y |� r��6, heR� �+47> _{�u�=�� c^jv&>  =mW +&x�� %�� -��b�V! raK, $r\inG e[ � (e pull-back�n�c. ��inherit)@!~�� �� twinpA%.�!�9�!e��*�)0ly a free $C^ �(X)$-��% �"��<p  $(1,�A�,� ,\th�=�  -�y��� )$, �e�&@ -\LaM nd $Oi]�� �orderq regard�Todd dynamic variables !��kfoo� , �YA�Xe�TafF$ an affinemO)�$let $\cP^*Q(,Y\subset \cONq6]sub1`of:�] 2�(are polynom�& f�&�"E��5s �� ��is� ��$ntrinsic s�rany1��$>�is an6�!Ns7?e-��q��jetN 6��-b. One� think�A�GDA>l� beP"e��sW .�#��"*^6"hcS5� [Q;Y]=\cC-�^*Q .�"J!A�Nof&�-�a�.F} 2K$ over�) ir common�S],)�6 �X�&4$.'.�!#u�� � 8i \psi_i\ot\f_i�  f ' }� �4 "� \f .+I ����ut��&�"�044�$ n &&k�=� psi� R ot�5�u\ && (U\w\si)bf=ot(\sf&]�O^*X.�numberA n�s:� endow�%totorm�  $| p \f|= |+D I9!� 5B, $[ : \f]= ]v $ir multipl�Z5im �!h)\w ''):.y')z!\wm'!# "� �a044)Dɺ�$I�v� vf*� v� v� v� v� v� v"�  %~:�Il�7mx$B�"�$a�) into�� �� . . 6�(qT�����S^0m�D�㹾0��6��� $y^i��A2in6�. Ab�fR��"&E=�92 Ug d)�E:=(d_\cC!�!�\f&� a�}\ot&Pa "�psB)q�J',"Q(44�(k�i P)V�2� � �2�1(����� A*:�$, < ivel3 F�sE�� Q��  9&v�� dA�1��I�M� BGDA��� f� �2� Mx, � J� "� +x 'E�= d C-� (�2* i�-�� , J� )�X , , -�Mven� cohomology,< de Rham�z plexI�g11�0\to\mar �32�e d1.�X � d4k. "y �fo�q equal��� $H^*�}�\�� We a�*,�2�N��,X)� q/� }� ] Her� .8 coll�ve|s $s^A%�)��  _"�e!�$��M�� �29��2� -�o�6�� �r� �r�� us,�m�* � �"� ��!� $\geq 0$. S( 1{La s^A>=d W+> $e�R���+ly spec� w 9DzBFir t� *i�-*]QI� s^A !�E3%3Fis}!�Nh.�m& !� m Y�hr� de�os�!toB>?�[cS^{k,r} b-�c$k$-contactEx $r$-horizlM�I�F26� jA�ons $h�%�!(h^r$. Accor�,�qS2� $d"c��)� �1 �'��P4sum $d=d_H+d_V�� �v + .EɊd_H(\f)=��\w��r d_V=U�\w�1 La_A�`��:[ �Th~-&� e $\vr�Z�0+ I�*#)Œ\vr*�>�%~k�*vr$$ h_k ^n��*vr�"� {�le�}�\nm���\w [d��(5� \f)]Z= {>0,n2{�� $�� r12�4!&�x��al�oaPdl=�d�"� #ed���b*�:>F�.{biam��analogouaE`above @ioIR7 o�&� m� Y�W/�2ou�j�!A�short2Wsub��g11} 0�v�{d_H}\�0,12� ��} &�{>��� \dl \bE_1��y a����ione�i-�� �g11�q O y1,02�y�6� �R&�1:zD\vr ��&�,�c�7 N�Ecyr/��(}/&@ .$^4$�&F�)g96, A�8A.!A-�m%�) �� ��36�)5�96'�'�)By2� s exact��nd F Ry�jI�0708L=\cL\om}B[�=dl L=T\w �4 A\om��0\�/La|} ��������La �� L)z.��2� �es6x--!asHa��L"�7�*@ Euler-- e��,�+ �~one�.��!� m=�h Nve�4By*�(2i+Al,d ryvl$-clB T*M8 $L��!�)�qA�sud0g21q� + d_H\x"V-9.�-6�"�J)�� ���a non-Ew $n$X&| a6g9#nes#�!Hle}<%�%term �fB$!�ults * olloa�6� propyD106 >@%-�ia!Wm� *�� } i8 g99,�"� dL=E�7 H\Xi&,X9g1,Bgy�9}�\XiyIs=.th^o nu_s!# 1}\w F^�2e���F_A^{'k.A= �N \cL-c :ld2= +hR;, �'E;nM;| I�&� $h$�Ere�7 $h^�a=0h_a^{(kv-)2�0$��%� *�. �,%� staC&h7��aQ�� �Lepage!{-I)$Xi_L=\Xi+L�a"~,]N $L.#,�b(always choo�.\Xiq�g99'})�"all.]) h$ vanish�2iz�94VI BRST SYMMET>�9A1���on 8vt�g 2$�a�� R$-�{:)� &�8� �8 Li?8^(vQ#bL_\vt$ �$rvi%�/!�?Q1or�>�f�:"*.Iy'*��nLy:�����B��1"� vt=\vt_H+V ^�iW+ (\vt^Ae� +\o 6�' >0} � #�� �f.�tup�)-,9�3( \la,& }�� 9; a' �!y� R"h$, d�;of�2�� ��6n�!gd $�\lj( ~r�( �y���>Z 2n/="� $��Z|\f�fA�>�re 1$by Ibrmulae� && a=b(�pv%�\f!t!�+\f_A]}A N ~5 2�,�v�� si)=A;p)� *�# $vt $�D?y$� B�, ~i� �s d\f+b 2�6�[��$D$&si)�E��$o�(I"�&Tjustif�<a$y"I9 ;yE$�va�) satisf�) Յm�23 9JO f=-�r x ��1O.�N|"�@{i�AmN6���e106#   It� s�0E��e��� )K* LiA豚 $ � ���� $� lj9a:=b a�:b fulf Aqfir�>ariN+ula-q1070#)2o vt_VM�m +!Th_02�))� V _H5om)\cL&t f)\� =��t&R�L$��&� *�1n�م�� %� AfAM�6O./�S 6�p� $d_H$- . A gl�D i *�;U�@o,� at: '@>�.)�is2� only�i�#prR ed o X$, (i:��:<�8� "�>g6is =**�"�DR�SX�m�067y�&� *���La(8���UW?.WA��Oo"j%u�e:��u�eV� �zA ב�� s. S�Aap!r� t�deq by%{i�summan"�G73m�up=�(x�i>E_���\leq k"N0I1� also~ k+9!.JK[0is*ed%]{dC�IH L1*�0}F �]Q%4ul��ImHyE�$ i.%�ef.BA�f:\�1}�a�>��=i^>oa $ be nilpotZ2if�:31��:up( ��&D|�?,)�  } �;B_\SiE� Si_B!�A�_A + �s^B][E]} <up 2E�* ;)\f=0g�I� J B�%� $&( {0,*2|$ A0!����)B &5*6��!�the�i�GmAF688M�!Nvt) )�=I}�> �XJ9;)�R �hol�>I&A5^Ax\�ex"� 0675�� L�7'�1"�' +,�M95^.��G�@�o�Jn $�&n/5up�0�@ts /"A�2E=Y� 6LVW ��&�)�� &fF�-V�B�J"fD\�J�>�-*�[V�& V>�&$� a *��c�L y^i\�+u$L&OAv"(�G be a:�($*��/ |L|$�n��76� dP:d&|)S2�$ :#2� �$. � $E!\Y!�!�=�Q%a I5�A�:��s ris�H�i�/�b>_E��:EB n��latw*M �Bb�O��8)��A\��", 068� ����%�*F��DXi}_rͿ%�Si)pK\Xii&�%[i�I�easilyt �?"K��2 �=)K b�u�80B]�"!��2����,CK need+ be �� . However&�try� find��)cecј.� 2�)+ b�ɜ 0684�NupF�L�F 9��F %�La�A_i;7r6rgW)� !$ coincidesn&���:�*.i-t>,c�H��cy!�Gl��)�;�90,�� �*\Si! Si"�GUBi�Hr�Xi)"�*� �4i �e{j,%s)c^s &%!  (u�PZ .r =&30690}�`\La.� G p�)pXi��i +n ndr�NLa)u^q=0�069anE���$indices $j�$q� +7)��=I�&�g:V0.6!���"!�se*D6J."� 9 0u^r=u_{(0)}^r�61G 1)p}^+J G} cURG.S3$\G_1,\G_2}-2)p_1p_2 2_1)>p_1}_/E>#2} +\�:9/3M���-�v=��!�)&�%l)�;!!q}069ea��� _{(2!b)n�4aF�I� (Bk\neq JH =0*I 94bFH5�X��r -1)}BT? {m+n-1=k}Q� _{(m �Q�E n7 =0�294c%�nZ}'iti5�4a}kP c}) (and,��sequent�#v�9�8--"� 91}))�&X0.�R�. 2�Jacobi��R�� auge�%�i�:a*S7}$:b,le6�V&TU<56 a pr��pal��A�2�.� 0�6!in Exam� 0650}. F7Qproced�C.", w�!place~am" � ��MVla�9�J ghostsi-)C&$6L� obta�.�� .��>9��>BWCA� C�V la -W C^�V 8m>�V�+�$2��YWC^pO5 Sm�_r b\la_\\mao��5E�q "mR%� U� 72})M}R 95 qt.��_s���qI�"� qc 62})u>=�"�==�9U�-�70��ql v�!2%,r V`!=r 5<\�of2QV"r�K�UGenero � :�75}�describe�1a� in a-a l sea�M� � �|"X 54jA�x 5I7ah� ) JB9"$a�r�I*� ..�+�) ���"�+�N��| s.�  $V� �6>L<&�dn  !/YBy@&y8 J.�H~! U628�p5=M�g"2]�=>U4�070�X6lN ��$\��8r�Obvious�)��\�*1 wF��et�= �1 W �# 1>- � �)]��?���� tact.�o-0's�&Z![$�>�,an��q!"kI�, E/�/ i��� + ��4m�)�l oR�is�f"�T}>Xi�{AF M�st)�A� up �&�70��I�Bz� 703�Qv6�ECaٵi�Wsaa *�_ p%2ty}!�!�y#y"�0�vaToryj6�-)ҁ*+.c�h�E�[Ma��}�4!LI. NOETHER'S SECOND  [EM II}*�NIn:to "�*>�Q�k�_�� ͋�W m-(�PMM�5�%%�Je'UBW2w$\ol Y^*V;Y Q^*n�\ol Y^*Ab�[Y.U&� 706u!;%X|Da!den&:Z!�"3: �) )2� ��Et<1b�<�is�>epLon (e.g.�1?=f'�/ >)�2q��=�0,[6n !nν�, �s_�0>� : ���-a6?edE:q'3y�/ f;`iV�!�]&�\ k lds}�ir�D2bK!N$[ a8]=([s^A]+1){\rm!g }\,2��'�& �U�6�A�D:�7e�,Koszul--Tate2#0}Td�!:���V{&Yu:eol�.o�#0� }\rd�A La A �)&�707:�cE_�"A- |.\��$�9})"�->, righ.� �Ej�F�#of>� @>_{ �\}2�M\tl7K o$Si B}=\dl^�= A_B�!�;-"�\Si4 �@r] �@6= perm2= s. B�U��B��*a�$\, hHUnZ��"� !�b=A4" 1�p"c�i�2-�f�Q�1Ef�!{)��1;L��1dl�1=G)MIm +[G.""8�G)=j�GE�T+�1w f'))e"+"o&F7�W� r +�S*� ;Y]�� vW.���say- its ^s-1�2?*s a�`&wa!X[#��\*:-�7-��Vq��0\N^=� 6]R�.� m� *� Lh]:� �#m^ \om \|I:�66��Y1&� )l�aXLinmt8m��% �me{ th?7je8]2���*&3�r�d5o}�Z71 M�%G)=c^r[JH-< '99�( �5]!*.Ld(1E�>n�'s�Mo< o�Z�g 2���'% as f"�lb.(R%0716}2 V� .k2N� ,�9e�x1w �%8=#Z*Zم-= c^r(9C2�!C.D4}\�AJ8&� j�_ m-���v|\Si+� C^ |}_ �Si� ,}_�n26B�E�.�6�u��. Con[�if a A�j>�a�>G�-dc`~�7;1)�k)=%�F�B� \ /%q�.9f=�0�SŸ R�d����f�O e�I6�.��6p6�%e��v-�*u $L$,�it^�< re0 m634}) 0!��&�4m��^<�# �$F �)�I ` `��`n�����58U?�!F�M �� ��KQ� � ^*� y� ���vic�Srsa� T9% 6*d4  717}�=$Appendix B=_v"f]�rem��-�"�15�).]M-4�h'��).*�O:'s -%� f &,%> *�Ay!� ^ u2@a��&(i� up))k.Q]�B�h*�k �Z� �e^e��}�j?�����#&�M�5� havM &&F�f&3�r��C��[Z�7�Y���5�B�)K + �,si=��%T:? m VM0HL5�V  L�+\sI5ee3.���*� i���bM!9a4va2q,��..�YU]�y06d(A.��e}} Bea!3 in mU!>�p�l2�S BV qu� zH �� x}T�}�&�Wwritten-*�R0%r Q l V^&�j�.|N�� c_��E� �U&��c�p�ed�����!1 � . Cle�b)i�u���1�uOan|�2r�} ���Pis ��pr>�Q� �Y��3��_cB�au(agS Li�+z La re�_r/'8*, !w!@�ErFEE� r' ~%)"�1���U&kH>�9�A��) UB[G _c5�!�"�',% `s�W. d._pm���r]��6t�F�� �7A�\d�-�/���7�&�qf V�70 n��qin Senb IV� xq$ghtforward�ceXY-o x.��qw�kulate{n�"�;.\2�.�"6>5~IsZi<��i�s# (a)�.�Rof� Gs $V_�Z=V,V_8%_e V_N�PGH�wOEB�L82�(0 ol.�\{N\}=u�)� �2.*[" V"�bV_{2k-1}�:@ V_0^* ��"}"�V_0 $ C2A��gI-1K]. :� It�! �5�Vs� R+c^�o�%c Nol��>:' {r_N}\-%8 [Ok}]=k\,~ mo~,9k�&�X$ 2e� cWkr; #�9tGBqɃs ١6�!.. (bEoEQ�!�)A��!���#B�2ɷ�-�_e�� �@28 ies �82�[�{(k)}= �r_k�p�v�JJ#!�S=u(� Z-�<r 'T�7 *gt N!�4z� \eB "::F422\_N���4!8&��56ryY� 9. 0}+ �'+ .+Nc-mA�&��� is weaklyً!eEw� N(�'dl_N(f))� &��%C 1-�� $-8*)�e�*�0.�*��*�>CrreG��)a comp�my�do#`'2G]A� Ex�r &p*L-h ,2}Em,E{}MgEc2}x i� k=1AW�:2bsa��k�i�1AYc&����!�)!�� !c$"�wb�\(c) Nokn�" !�M3a�}02[i>�� $V'ݔ V'_{N'}�#�p�&,&��&�wD{k� N}$iyin��trsNo�\�5%6� ��r,R_nng��I�* \{N'}65I $e�e!HM�c��R >$Q�%.1 !2��� 9� �av`3�JIR*.n.rse[%�'�^:� N'$,W>�� !7�*�i2em�2� NP�n-%U:s� ta�!� �=Q� Not�~a�:�% { argua�sz"� II&�/"�!!��� �lI{if!�"� � (c)�{)T�R�q�r% a"�r � } * �8� �&R'4� �56�� [� V^*V_1V_1` o -1}f2� ;Y�V_0*� 1/� .�28�6�lfL �� N},cw�0, �0N�:�F, each6�U�m6� .�`*FIѿ�up J ��y3�M �ew *)�11}�$�"}}��:J&(��� NE-ge&� m�.U0K����)�-1}}\R���C 9�� �>�=�恎a���+]�%�mi*�s�Pof;6�v�+how*thb`Mpr;w.� ')��'-f����&���3)�6�'�~�H.��#a�8Uգ9l/re5� %'6} � �(f)2 v �  A6:� s8` �&3� ��F� (bv'I��!� ��).�"� 30N�4Ln1&� Xii��OX:�0)e�yz 0}})F�qA�Q�3J4q F|k��2�!�-1 ��FY dCe a^FV �%N}t3;nU � 6�& �Vny&�"�$�s� V�3}][Q� �e\o{2k"�͎O Qb �>^z �I�*|,c �tc"%7 821}�2A�� $s'^� ���#"ad)E"�1s�t� �, us r�17}mo2Xխ� |^��"&?up'Չ_B�2a� r (A")�'6�,) �\6 d8CP.�%%o*�*%EA"� Z]- �5�F5Uupyup'-<7�6+_{(N)&6!83�"J��c')�-&� ��b)a�/<1Nn�OA=;"? in {� �"9?&� ��eZ�) $u$.\ !"� -[u, N]�Z2 2~of�SR� �,\6��;a 6 P?-6f FusP umAwatA�aO �5^���L�"+/�p)j� �:�n*� kB��J� �.�&n/�j %�FM s (gTc'�+�)"�(i*� J m� &R > N�Mn� *� �L-� � � )� k}*� LaNr c��1} udj&:� I��trast�2e-v�Ex_N&V3�:�" >��2i+H"�-�F�NTe N)}$."qQ2��Vt!��O�@*�+a^�"B5�N�a" C��}Rdepend�cŞa�-ld� \��(APPENDIX A}. AplRd.�G ��*ak� "�C��&b�>'Z 5isM��e��*+.)~e J^kY�0N8?t admDan $m$ �jet!yL�b^>;$��x ~�{~ ueNJ^{m+k}2|J^m  $eKWaZ5tB�oJ�s meantz* ap�  zr��1>�f�}"�D y^i),$Y% z^A Z?2�"م1$ Y)be z^A\*��v�^A Zy:b�� j�%4"�%�<�aSi��^AV0 �'  k� ( m)a�$Z�֩)�m)� $\p  \pi_{ZY}:%��FE\re�%0(� �=\pi^k��%j�6�u Q�A���CovX1n.�Y]�  | vale=a2"cr @ar:$. !9_E�  4yoz� E^*" 630c+2� I8���F��J 5�9� d by5� !~ \ol�wu:yx�9Ih X�N�9�A�P 6�!r6�|!� �� 6+%�\ �_rE7z�& 3^^��q[ a}P\-�2�<��h9��gin:\.M�Q�0} Any5P�� A>�eE$!H���o5n�� ��H)�N*%9fM4%=X&� 6d� J<"5 k͈ҋ.�Fa,\"�,�/6�.6��"j.wZD~�5��.c s .�9�V 5��6!�):en�:��� E��.�7}=� _9���:�_^z�E�"9"`� . ����; 14})�Z�!>}3%sqi�Rb ���$W�(o�Z \fvZ.�3P8�y^)5�\ �, ol\ua�cE_i d�Nwp4+r d%� f3^ad�(� �\� �,A�f* Q�3�# V^*(>)!( ot_{>} w^n ��,�Q0M���$RU� �"�Cco:O�ofeY.��"͜���}�Э�"al_E:J�to_YjE��q�o+�W�ofb�,Q5f�!'N���!)%� $>��, a z�'s�H5h Bh zEig.ain'�/b� (%g� dl)#up�nN9� *�j��8ot_Qc$.�&��se)Zz=e$am'otzZF(/23 a�7 c.T.;$\{}U�%��H-m!�� Due -�c"�.� 0=E�'ǟY E{6is&� �A+���op�N�L"�O2�g���\���' ���\65SFQ a�#:��J�U06b$desire^���6�!.�1=f|:�1G�͵#*n�-� undl}[��M�� "X<¶ 2�&�CW!Eq��to` e�[�*�9"�Js*v  a vol/!| $J\om�X�  ~��$2�=Jd���R$ i�IF�=�). ��e.noe��"Q~�Q^*�.�n$9E��3E.�!�R/ i/��*�G�)�0�7ZQ ��%&�"� )�% !_�&K�*#&�ƻj��j�%~�Fg$m�"W y=7!��.s�� re�i&�`'B�3�*m���rq� 8MM�"?��*Aeta"�� 36�a"�B* biM� betweZ4 sets Diff$(E,��Al ��Q^*�,E^*��f2� ��&� � C�537"B�&ht�B�,C*�)���!�pup'i�A'�52����'9pBJ�It su��K o%<o%�a1�.x � z�\in�-!8 }(E'%I`c��R4)up D%|}=��a',E����*�a s $(, !��tj�,e^"�' %�$!����%-� "a�" m4� e2!&�_�t"�2� )�_l{�!%2P6n ;?&I!SJ'^�TSi}_p����o�"�I�1�U}06a�iEb6�6�(����( �;b��7}".F M&��&N�)H+iesi=&,W^�ea�� *�� *�om?d\siA�ero Aׁ3�;E'o� '} � � >�Si|�Xu.��LN�- W!� d!�:� !�'/'�}_pA$r1��c��Il��_I�� 2�$�I� ���A"9�.B..�J�)��f5bcou�.dof�s�<�S10�-�PTa��$W b� cto]�s, $Wn��#vW�n&ol i�����$W$J� �'>�8;Y:��B� � "�6%�a JKT,W�9o2�3$�3t�^w@�"�9le$,$tJD$w_z~i���2 or\O5sR�-]2h_�l*�P�06�$dJw_a]=([+dJ�3�aiF^�>q  >�F&4 � 8.�Sq$J� tTU�P"� �m Si) �4G"< )�&kq> q�P ^�U!y�=�p�� ����#&m�F� t^ru�ȅ`w�`"�:�FT%�A^.�2.8u.lBN��~��-P-LIZ{�ta�*. �VaBSy4" B�*!N%9Ko a!J";R80.-�B�h#9�en�!��X)� /�E�� 2o#J�*FVFB ����j6��-�a#�^D�%:] " a�H& /�ˁ\.\r�5x. BIa}Y�aU�z�$*8��w�#in^�3 � cE_r&jr�B�]�.� 2<.`.��� FJ�6L F�2yt^VoRu w_u�> �w���R�� T=T*  T$z-J� `:�� ul"�802� Abc�H�m$F?�eNW/�2 .�Tbibliography}{ddd} %14 b�(h{barn} G.Barnich, F.Brandt � ,M.Henneaux, ~vJ3*�|e/n�)bClass�a�Q�H um F$�� (y} (World S��ific,�ggapK�Փ1��fat�DFatibene, M.Ferrar!�0M.Francavigliɫ4 R.McLenaghan,&Ya��ymmet�k�Iechanic�+?,a o 5҉:�� 3147%�2I�.��Gr�BT"? �=\ht0:Zadv�y#O \dp0~Rms*�"\kern -F\vbox�{\�L>{\rlap{\�}B�vss>%0 \catcode`\@=��Hdef\qed{\ifhmode\un�8\nobreak\fi\ifm4ifinner\else\h& 5\p@" fi -Jv�[ E�4\p@ I�6 depth1.?1\p@}} %.�\\�Q�8@=12 % at signs�n no �0er�a tersI\cents{ �rm%*/cA��mis � �2p�3aE �0pt�:7.}}1�%a�BR@ibi�vE�\vT$ {\Ve��:%a�Lc��K�9\�| or )�| JA�#1{aVse!�!~=6pt \v�er{#1}}Q��C�dB-{}� %dummy en�@i�4 lumn � mB#1 < $#1$:>%c+ ; 1n1�621 (not �):3e�3R� !�26#i�u!{�itl=��) } \v *{2cm} �rge\bf�i�quasi-�> solva)��Ytwo.� �gr �;nL ���4 q {0.4r$I. \, Euclk�n� !�'7'�8E.\ G.\ Kalnins� {\sl Dem�� en! S�(stics, UniH �4of Waikato,}\\IH�@ton, New Zealand.i�%+S W.\ i��tJr.%A sl SR�l:�,{�3 sota} � apol!   55455S.Af�!,S.\ Pogosyan� Y Labo�5z�W��! Joint I"M�for Nucl��Research�@Dubna, Moscow Reg� \141980, Russia} \\ [2mm]V% %hCa[Po de Ciencias F\'{\i}� s5+ dad Nacio7 Aut\'(�0a de M\'exico�AA�ado Postal 48--3, 62251 Cuernavac�relos, ?} �a8q5�1Az%�o�Z�ef Noth��Jew un�he Mooa�:@��ab�Pct}%���&." sA�e�A$* U�!�ser:� s�}jmb��:�y^ e�� ��_��e�>&ES"}�  (Q!prCsq4 "� . o� �="os�! ��3Q�ES� QES.A�BXalE��J�45i7I��u�KSchroe�erU5%U,�c&ed�t�f� hypergeo9 . "s $_mF_n�is� u Ri�8*���s&.|� satisf�I three-��� moreJ Z' of recurr]C�bA�Yp��2A�\today] � \W�{.���kzwell #�}$N$.�{� �v�g1� sDs�9�o")?�gian %=�  �. HAM1�A+H} = -`�{1}{2} V*(^{N}_{i=1} lr{\�>ial^2}  x_i^.w8 V(x_1, x_2,... N)�a����E}�I�?!i2Ƅnfend#�#�n��f mU${%I�well}$CFell��..N-1I�(0}= 5H}$�Hmmuxf� =�[ %k�)&�I�L�!:� 2} [ ��M)� ] = �w�6b(9j:,!, j = 1,%� N-1.��5���E] cular clay�=�q%�%�S:� (�0� wa�o�/��&�7V PS.Rauch-WojciechowskitB$\cite{SWOJ�X/M��A9���w�sEX u, Les�� �2m thanY��Efreedom.�Ralin^>I��� �2�-A�.asAJ=�exa C�A� kind �` b+����a�e, nam_�!Kepc�CoulombM�"�0(tropic harm,3 oscill�@,�CF3s*! %��ensuraX fr/{cio��.V��qt��)�s "�&m8!�res��[ �� es unlike\�nd��'� �� ��,a�B� %w�$phenomenon4 Eacրnl de�Ccy}�bn�U�Cgy eigenE�� �mply5tGE���ointimat!�X�%6?}�`!�Roup �so-.�hidden 6(�x�E� -Hv� he . : gbh.�x E�)�N�]"�al/� -� hydrog!1toeuO(4)  discrete�� trummnFOCK1}���Lorentz ^ O(3,1)E�inu���GBANDER}.\�HJ.��T SU(3) �BAKB� ��4 me�VRY�Sd(�S\~c��@�t>-q�� p0��r8�W: all|�iM�rag+TQ foun� be p� dic;a:� �� w-y|2�:xe2�rx� ~-�K0�R1V*On�u�(most importqD� A`:c�s e���� ] 2�p -��  \"o:� ss m� t:o�rthog�& @ � �0EIS,MIL,ERNIEM� inst[�~����F9�C � in��h.� �s�Bin Car� an, spherA�, $/� pol��ellipt.c�Qal, ob� >oidpro R !A>s=�eB�o}�ii �npaŃ�fo2��� ��:�� abol�� ��.�0 . A XatD0Mkch q�-Rt!�.H :� st!q"��p<�e0wor�� SmorAdsk5}d Waurnitz�ll��FMSUW,F MSVW�` �3 ,�. P�!��#i�(Z E}�!?�Al�� b��a;"� %�>�5�s (see TE�1.�YA��mv.ld��cQdercI� _�� �lizu�6 ,Y�*�!�an"�* 1��s!?C5xN�ten=q��%��2�) ���cuH �(�p�Giv{� ne�IveшGPS1},��K1\* xvu�aliaE& �-� MKP1,MKP234,GPS�/� samm�s,�phy��W� � sti�(� fur�/h"sti!�o� ��e lN fift� yearsf�(i-��  :inclu�] flat>��Pc!�a sub��� 2��7 M pE$ iew:��i�A\E,BIJ12} viaeY path� ` l �KachP >!�!�2�}�mA7� V($T  help�A�N��ansatz eWITTE� yMG�HIGGS,LEEMON,ZEDAN1,VINET,DASKALO1, 2} "(�puru �icA2r�. A)�h ��by�����author1Kl|alFM` (ex1��w�2�6�e�� .�� )"��I�s"�!� mayF'aa�e e��K A1�Li&�A�"� &� Poiss�yH"s)"5a� d�c1Z�0 �K�m!Bc2's3sR&enX4�  Be� Z�e�!� invm��0DaskaloyannisM^U'.� sp �Ill%�=lisE&w�q^� wo�� b�( useful, ex*�4!{p�[y!�sB�ҁ+��Z� (at96 (Y"���wPd�.\� ). M� precisa$� mea5��a�B �S F* �� $��`)ry6[:�sH� ��9�is qu!��agĉqu!�re�l��!�NussU= liY,�c�� WINT�G 2���Pn�7s���+���B��ed �dif6�ly�7�54. \footnote {IW �1�  G�!D � p���KAMRAN1���a'at ``aV�ac��yD m&u�FstK ��Y��'Q}f%�AcsP%�]� @u~!�ex�ui{aT�� ��gAlt3al� Hu�eW'i��l ian"�D``6%�*�ns&�bFU,Ᾱ4�".�de���AXa� n ``intui� "��� ]ly 1r,�"u�alI#�� s upy now./��O �� � reF��>� *�on2` B ͆��!SN[� :)s�0${\gamma}/{x^ �($  > -1/4$�e��e�Mora9� , trig��)ciHmodified P\"oschl-T+�r��, 27� ��  M��ng-Rosen7m�,FLUGGE,LANGE- A8Natan��� 0 NATA}. Al��.��AZ?Q ��i!Q2� |8 5��bR� (oհ"��)ũan� lici�j >e�whole}r jum ��qgs (If?asympto�Q orZ�(V#)�of)�"., type $_1F_1�?_2 ��, so�H��of&jY��s��BEp reas%� �!?s �' . se ,��ov�"E=�9$"��| !+] �8qG KWa+��mfE�appear��  ����}�c*v�,�2� _a�\>b*�"���!Ss�"Xva��*:�D: Krawchuk, Meixne��d Hah\ ATAK T��w� V� ��-�M: ��1JF قi"D>:�AD2D2m"=,��F b�� }. (Ba��w�i�Vqui��.� !jpowerMo|�"E��� � !���B� , raS.N� �f.!.) � o��at�~>� V8-w-�le �?!�� ��GB���� ��� &� i!�f. F@, ��Wek���Z� I!\� [` �" �i�����At�~S*."�g C W(��\2)ae U^�������D�Nԡ&q$|(A<��� ]Qas, ��)�E�yl��5��sit�' occur>� :���� ', Helmholtz (�"6 �V�(lso>W)]D!�Z�R4 ." �S�-F("extremal" !��en 5� ˶ �-� exitf�re�� k %!Y�9��as2{��NU.���%� h�6.�*"�.�ix�j��� C2� (u��IiA5�&�yN*�YEs&,`�-�s� tane q �become��ntriviaū� :!metho���AvQ%��v��!ed#= .�A� $N$ j�U�s,!�v�� (ztaking(o�!�H%B� ).� ar�  �  s��&ŁA�R� (�ard� -c -8� INCpo'&�!Hill-d��min�-nj $ATSON}). AYm �A#g3Co2��R$ qexp� 2� . Iv%2� �ga�b� ,�->%:��U3will be �a�M�o[ ���+A %yb� ���n�7bF� }�Ra�y��ks�l��Z��B�%�8�;�sub-g#��� (�� , cylind �"J)M*POG��oft��ne��:^� i���{ fullv���in�mub ��{"1�j*�!��D tic.�. �1$ rio�--kcN�� e!;�"a"A|��,�8ow� *�E�be� KI�Qlx �ns�  #!J oI� e@. ActC�*U!"�x a�fac�olv��ax20&y byaulo5e�-)�ym��A! ess~��n��� �u4���{ ?� ]|U!Z &G �� a�d iC�'�g��#"ź.��Ou���� zero%�6��&e �p e�u�}K��ZD"\T��[Aw"iB0.82�� �� &{!�\~�"acaf/?�:� vu&W  r.!lanBnr�ghargeda��;;� /�"[�er"(�O�2<($\pm D/2, 0$) (�< gK =�)�y.Jy.ІV(x,y)*M0H\alpha_1}{\sqrt{y^2]�$x+D/2)^2}}"w0 *Z02*-*�;���m.)�a/[>�!�s&/ 2�is�-{��Y'2A�����"eq.0DSCH-V2-EL70})). Up��"�YA�$�� D�8, \mu; D^2) = X Y($�څf�e�;$A(D)�N^�.� bf-,@w���!��0q�P{d^2 X}{d\nu^2} &+& \�:[�2D^2 E�20cosh^2\nu + DA^E{�rI�2 osh\nu + ! \ =]X1la9�%� 0-EL�2\[3�7�Y}{d\m �-� �� ^2\m:�- �"\m:� Y�"G��2�P��E�B��& .� �)-S}!"#=�(elah� �V}�h��g�����/Z doe��pf� /o�Y:�+ $E<0$"{Toɞmrl �r&���4* o&l" 8 exist only for� special values of parameters $\alpha_1, 02$ and $R$.}, each7�the wave functions $X(\nu; D^2)$ 8 Y(\m�[ is expressed as an infinite series with a three-term recurrence relation. Let us now put�$2=0$. Then�potent�h(\ref{HAM12}) transforms to*�}ordinary two-dimensional (2d) hydrogen atom problem, which is well-known as a superintegrable system \cite{T-4,DULOCK,ENGLEF} ��dynamical symmetry group $SO(3)$,%T admits se!�!y!� variis i�ree ss%�co �(tes: polar,%�bolicU(elliptic. I@Xis case we can see that%)yequ�s )^,SCH-V0-EL1})W:42}), namely %=�� \bea \frac{d^2 X}{d\nu^2} &+& \left[ \ `D^2 E}{2} \cosh^2\nu + D M�1 t\nu + A(D)\right]X = 0, \label�$3} \\[3mm]�Y}{d\m �-� �~ ^2\mJ}\m:| Y}.B}4} \eea�B!Bu into i�ther by%�change $�\!Q%t 3})-:�4a���$task reduc!to solv!only �ne�an` or>4})%w�6"domai��di��ion" �i,omplex planeAO!* quirement|/ enesU8>z��e K K per�* {\bf�}�� ynom� solu�s (��!� details \��LMPSTAN1}). As result�obt�l{\it simultaneously} quantiz��!eIU �y trum��a���E_n = -��Ȉ^2}{2(n+ 1/2)^2}, \qquad n=0,1,2,..FR5�R�R����Q./u* $A_secwhere $s� n$ (5�!G`an $n$th-degree algebraicU�)I9poB�Ioe��help of IT2v�t�;6xt"wI,coefficientsvy�$not bA�nsider�exactly-aX�e�Hmaybe investigated epnumer��ly. AA[ ilar situMPccurs,E�� ance���of �$center pro�i!re6;Euclide��pace (! so-called�Hlate spheroidal rada�Ye (HeunZ@BOT},I'8 after eliminat��e�� �s% �s h� ��d� suN� s[ ZlyNN)� � !a d above (! many��s)!���s let� to claim1ut deepane< �no��2�ility%v exis �f J�� !�2�:$e� . A� �mh�A�B f.NYZ�%o�a ��D.S 2�ջ��he������eigen� �� ��lda|�ely!Z�a��reg� \\mu\in [0, 2\pi]$ or $\n\infty)$6DlyV ��$arbitrary �%z���3}A> 4}) &� viaB� ˅� "�($ surface" 6�of B, : 5})B� spli� to.�znon.?ectors (Q� thes�1#_te� A fixed��ber��,��part}�2���, (��...n$)dpossible��calcu�)nn�. W� a� � eV���:8� "n �"�a. , . It� obvi�*pe����B�Na�f�.efu>a V� coie��L=~ofR� At2� �n�9��to � ^S ZS] A5>� . Tr phenomena�A been� �v��discu<,in literaturK� E-1980'Zd was�  � asI�quasiq�!�va�` } (t�2$ first tim_tro# dD Turbiner !6 Ushveridz& �� REP}i" such��elOTn�le}"� LDTURBO,USHV1,SHIF1}� also # USH}�re ces��rei cru�ex� st� x !7*� io�z2!�"y i\(hamiltonianmP[})Yy(anharmonic "��� "� V (x) =~1�Pomega^2 x^6 + 2\beta 4 + ( ^2 - 2\delta +S 4lambda)x^2 + 2c ( &-�14)234)}{x^2q 2-ANHAR0�a &a 3 � $, $� � >� �$ �$�_a�c�s� ite&v ce�� authorsMaBISWAS,A��LUL \PsiEO(\approx x^{MA frac19(, {\rm e}^{"vEs}{4} x^4.]t A0 \, P_n (x^2)2zPOLYNOM1�YTN��" �ach&z ��. e bof*}X!�mu�Sby �#inMDA=O}E�fac�2f!թ�lyA� exple� (of "hidden "," $sl(2,R)$ &s Re7E�isA� @"eJ$in usual sf becaus F��eׁ�belong� 4the enveloping�x g shown��ata sp�I elegf �W �& ach,V"� AmZ�ty l ly mA�er rootRat itQRq�8 ":�"R u:����� 6�� oscill!�&(� wo�  .���@KMP-96,POG-HAKOB1� {.5(hyperboloid.:HYP��g� ate�%? 5!lnd tometric�Me[�of6vF� (s2@so oldest article�AKPS,� ,DAVTY� ^ aBMd Lam'e*�sx mes from ��dv"�#�*(Helmholtz ([2�le!V2)" in 5*�%�he��2�)���] xd�m# հVINET} (? out a$��mmeis� �cu) some0�Nl&K [beQe� rough.+ r�%F%V �E�J�6� mo| �A%dratic!�nt� cond��2?t)�\s'��, k�� �fitic,�!�* Usc" "em�*� ,� 9 �( reh aB 9-�(Niven-StiltHmethodp~-�� -8mO"$ ��l�i� lized Lam&8 (�a�s6� WITTEKER}��� A]E+ �� �ed e{of zeroQ.b $P_nF .�6�&�"] ) Mfre��AGo�����D �D 0\Pi_{i=0}^{n}N n xi_i),.� �2�V &V �� numb'"(y1, 2, ... �satisq!e �$n$�EQ7e�k�+2.3pcco�!u�ͯ%theorem �Y5in physH=rval $�ih�\i�et�|�l!nd state���- exci�$s, describaU� A� allI� (��"olgm�-&S9]inclut� ����(- � , 0]5�&E = 4R�[ 2� + v i=1I�(�%l} \* ]N� >!�� � T�60wo nutural quV�$apng!��� :��Y-� /-�negative)�-tr whyVA4c# ct�h��>�gy�F�2�! icip� all a#��_*���e� )$? With�P��begA�he new��! ��A�ɸ� E�JC��� 2l�� on curved� ces ("K,n,&� odA�$ pseudo-euu)Rn� ^/  direct�Ke<�2 "G� pa)���a� e:toaR -suba�pA *A %pr�`m=�q��D)�m�&we fo�Murprisi��d never*� dbefore. �� m����z<tyAW ).lyD ed��� i)i�A�)� Z�,� �h!�`� `��F��9*E�is1)ACz:zo M(t work devo�aa�(!O| anisotrop* cir>r*� s) � four famo�$:0 -��:(U� ,5"&wo&�=T�1.� next�` "}% ed (� �r�>U!)n� (=$V_3$: �@�( shifd �Ao+4$)��%!L Levi-Civita mapping�KSq\v%t{0.5cm} \hfuzz=25.0pt \medskip�"gin{c+ r} {�#- :} S=le&�)%D:� :�.\hfill�ndb\�${eqnarray} {/ vbox{\off�)rline �@hrule \halign{&\v0#&\strut\quadr#l\cr he#($2pt&\omit& &P"x*4$V(x,y)$ &&C"�) � U &&\ Sp�> AZ��\no))}F�DT&$\displaystyle V_1="2}5D^2(4x^2+y^2)+k_1x �Xf�)�{{k_2^2r4}}\o�@ y^2})S ${\h!�,Cartesian}}$J5= Para�*�5Z�!�B*j,N2R5&O 2}%\Bigg(!1Rl+*$f5HM��;+P=,Bb%A�Eh�5j:�f3=-�E7\sqrt�Av}}=f4)f{1N(%4f|6V+x K+b�65-x e:��nIIrn%n!�5�qB�+��j�4= ���68%k� (� _1 mN!��X�_2a$  %!�� %��35' MutuOB&)'.R\ ^TzR}�r��ɰ\nos ���o7�n0 \newpage \sO&{Si�'." &} @1�c�(� "� \�! k_2 > 0$)�,, �V11} V_1�=qz N< + k_1 x + {k^2_�m� 4�2�/���( = k� *� will 3)%>{,v2� " haA r���9t-EQ��/({\�al^ �V�N + "�!)ni0��U[2E�^2 ��f )�-f�V U]U�.��1��'M� 1/2$%�"Q eat $y�'i�- puls� !�m�) takes�.� �on 7 halfn$� < x <w,aWy >aR� n% <0$)�' erea] $0 < a�< �in who= >/$ ($x, y$).5reI *�"� of relev� b:I�"H �,3 *' ub�o4%s} SZ�4� !NeqI(VI�)u H n leads�9edindepen2}!�.� V[�&��-SHiR� �4 \psi_1}{d� �4(2�"_1 - 4�!^�#��m) 9M�\[2]4K#V h�6h 2}{da5he�m\u�yk.$k�CL 14}{Biw �2 ����A�����060��Psi�F;�&$a")�%�(x �(y;\p "�[a����$�#_1�$lB%_�$reI�A�U�.���4} �J�I = E$ /\U) r3�Dw"�8 �O0ɛ &� studi� 3&�o0e� book=8GOLDMAN,LANDAU3��PFSUW,KIBHAK,HALL}). H* anc2$1�/�� �u3:in��lic) s,{Empl,+a 0in $N$ - bodyU�8CALOGERO1}, or aU!z9� sticE)anyMo 4ISAKOV,TERANT}�d� pl�e�#$ orthonorm=*"#;,� $����������-�$52(�l1�5:b-����2confluA5NgeB h; or Laguer�#"63�"^"�a�{n_2} }��"� ��{2��{(1�"e�D} n_2!}{\Gamma(n_2(+1)}} \, y^ @6|&�#-, \ �8 L^�"f} �( �!�Za� e(2n_2+�$�assumah� posi� sign�A3�$etoB� n if>�)bo,� Le[H"�]mus�4N0 �-an�n�8h;��$ V�0}) eas�'Y"��M..�*� ��~(eri�H�-t*5y%J�u� (in r�. Rd ����^��m��-� =�q� V i �^{1/4a���'O  z^2}}� {2^{ng !}}\, Ha� 1}(\�P c}z!q� z=J�{kD4 a^�,����.��+ a�1+1 ��k�}{8�Y=a�"M>[��5�"V 2-E1}�y:� � [�,��]� �GF�*�: n_1+��T?"�:e�  !p!,":of !0acyv �3 prins*antumA {is $(n+1��Fiy>��^=+b��blW,"� V� �i5a�v>�� ��U6(may� N ruc�P ���"ula]6: �A��g�ndv3 '00 =6� "�"� \no� nt �1.2.1. ZK1M.� �� $\et�/con<9*� 5� $x 1y$�-�lBlB���yxa�E�w (\xif �^2)\en$,\�} y= (#! F�8%7R})L"G!P#��� �G!La�Lia�: vol�el�m� gr&�_9_ a \D�2 %V��> � ��2"� ="!)�+)JD'jc2ze!�^2ѵ��0 dv = dxdy = I+ *) d\xi d9�0%����!�S2 CQ" R�m�P1~�  �K�1} > %VF�=� �"�"al 7 } + �)et=�A#N���2e� 4 �^4� k_1 &?T�UVw!�^2(A\E] �= a�����4Upon substitut���m�$$ ��,% 4X) Y (�)'�m m�iJ8g%��Y��Xſ�E�$h/"�#M�M_)� [� \ V�*s:���:�E���X}{a�k&+&�2EA+IU� ^2A�6� 14 V5� 2�V'�pX �C X,�H0��HE��� �18� z�0�� Y =aA �Y��%�-h����E�@��a�KA["�EtO="y �to& � by%4_ \�4�2�a�H i��6/�<M<2"00!#P�7\xm� ; E,� a� C(E,-a) Ze�# Z (�8����� .�$�a��� c�&a�&S0 W$e/i7 ���\b6C1%Cint_{->}�k �}^�!q^�� |n�|^2 = 1�V1VA�!B $!�+O9�%g6 G3���K-K"#6iP%La[����}"�L+�J�>mu�=mu�]��M-��R�"�2nMA�: =Q�J����L,_$�L in (M6,�)$�)�6����1 @*^Dp.fJD--�2�-2 Not ")Qx�$ 6K!�`` .''� is j� _� s ${�; Im}\ \mu�Ap Re �, 6+>0$. OurL#-o fin�3e�ua�g2�EQA8)� re�)d dec���aI-mu�\pmi�$e %9to  fty$ . *d(4d(FX2. Recu:R:UC� now%)qA.5� . To�ve�:we ma�&{ o�xqx2 4} Z>�^expmpiwq=a@4 "�*�2 � ) \, ,"12�� >x,��.�-MA�Rl4 �[ [ >�L�w��㕾 + \�� 25�;mu} - �A�0!#�*V%k !& )n]�dxv(2{\tilde{E}-�c! ��}�]Aa���1����oNo6} � = E 1,�&�"x �">G5 aY - &*}q*&� ���Pas�� to aH1va[U $z=aI2$Q:5}$e� ���>� 7} z-]� U�(11R5f z�?z&1�}�� z_?1.� z W14B�m��B�We"��W6$a�(z< G ���N�8}�?(zv M����?s�7��} �I&� z^s��q��.�.�8�n>�7})"R#=fsA4n JuY!J!r�BaY2 Q $A_s \�Sv:�$,��-�6� 9} (s+1)P�) A_{s+1�A�$14 \biggl[-�a���R (2s�EI5r]Q /�)�#&+&F12)l[2�.��l du�7 `-1��0�{�� � "�][ial&� %�{ q&A: =1_"�v $3. Asympto�-behavior6�To8stz a�):.HSE\ larg Ti 4use continued !�{ �9y�!$LORENTZEN}a�Q�jVja}�}A_s}{Ac-1}}&=&�8sf(s)\\ &=&^,�Q^ {2}} � s + 12)pm7 ! .B- g�D�؁�6D 7 C1)�B�+1��'�|412)}..�,��M��( $ ���e �"m,� >>~ e�� ree^.K9�KA�E�ardA��Y�Ya �b\�9b}_sAa%d1}{b_s+An��},\\ b!2o2" bo5� -(�o�o[-�{ }By+"�]"�# �e"]r:�"b>(%6�432)2^3�*|/��6�e�$=-(E+k_1/(" ))/2$.*�  $$ f�)��=Ɇ�{-` �U6\pm �H+�Y}{out los� "�CtyX��O&�OO&%l suff�Zly�~ $s$/ce,�; wise�1ohWmak�2/s`$\to-b_s,\ �_��sXSi<$ %=i�,j is a� sequo=M/,Seidel-SternA�A E=)Ge)8t6% @q.E _s�Wnverge�  Bx��� $ \stackrel���$����( }{+}�v�:{b��}L6/}{\cdot� �Qk}�Q��q� More�,�4F� !�oveells u�at����>B9c�U=\lim_{zYI��+,A^{(s)}_n}{B �� � ���R�d}� (\ba{ll} �� \\ �ea�)=� 41\\ 0�uadZY0V5:S0\\ 12S�  ���Z�n�n�=b_{n+s}28 5ln-12m5n+b62:62}6,�( n\ge 1��q�Furtherm�N�F"� $�nU3�-2�n=(-1)^"$ hold�� dD$���impt+��1�� �}y� {n}}( � u��} |=�:"�Q�y1y�YFd� urn -8!���,%,5 2n}/�2n} ,�&s�)monoton in"�M1�Ind go,f�Q�he limit"�6 .+12�+1�l.# ja�rj. �7LM�__t &� �@6l2n+�,=K>r22�Qpb_C+s.p2nYo a��"�It��P*%!9cH2.e��96 f} �m6UW0.� 0}}+� _{nJ�Z %C����SaZe Im�l u�2���2R" 9d}) ��e�$��2n}>1+� )+m!+n! m+s}�� ._1}>*0}*1,| ��S*T&��s!�h51he|kVP�rr:=�1�s}m-1V89�9=m}�#-#we geh�kuppm�I�� $un},.�+2}>$�Pa7VxE�!j sum (_{m=s}^n 1/>m}�,% 6g�L$�"s^niQ- �x}}\ d�,�YcY lar o to�an.��!�6.f})�$ $ |�?|<\kapp;�0�% �dy�1{y+s}(y^�5+ 32��-�&c�$� �j�"X<�$soR�Jhowo3at $ ��J uniW/ly En& 8� {�=!+1/%|b) �s $5�<$lso truA5b"| ?z| r�b���C�C��{�-�-(��}+�K )(1-: xi }{F�� "� Now choosf_0$ so U$�+1}{s_1-1}> D$some $s_1>DanM (��%4g:%S QR_1+2k-M N �Rl�P� E�� k��E�6�M��� � i�csy<k"Z}� �= +}$ v+>1$.zE16,)rtm!k&�J��,%V ��)4=c2k aZ�nt,�aV� �-}$� $0<�- < =�58�gDX�I`\xi�1 UMa�geMM%� $m�mK +1}=b#,) 2J1$�EA+1� MvE#Evi& ��� �%�k%�+-=1.$ +'ARvnA(Y�sM�%e%��2k� c~�Pco�T������p �+1}� s}=f��s= �7 'N�^6�� %�x-=1�u u �a'on%8��1A* even�=oddm�a"laa� h \sim ���F� ^s}{s!}}$�V,CRs sEQ��!�B#/1: (z) �?V -��1�(�4 }z)^!��9� �&&T'zw�#��$z>0$ [�9A� :�# 2})]�"V"�w R-$^ >M.BxiA�+,$-KA =�� \y($ | g{2}6J(e \mp !�n�3��.��ak| d�Udb.~d Hilbert�S. I?1!�t)� �>r� � � !B� �� �BA" effe�e�>a^$z� $-zJ .Q 13�+�* y�q*W+a�&�Cy. How,V��E� $z<.�B"B�0]�"�V!-n'�?�0 �6,��A���uyVW�minimhf[a`��Xy$ Jy$]a�l(Jar��H�BQ|y@2^"g�z�rapid�xha{F�.9�%�S# 4. E|z�U�=�B9+jA#e6 givaps�`� ulaqr�>�/"�-.� �E equi�& ^{n q} (k�^�*$�^e ing 3�4a4F(7r�&+�]_s �&+NDn+1-s�&�%N&� �Ps =�\U+G.6 ' AF'�&AA xa�*w#5V1�?:�(r&�Ha homo�?�Y W$of $n+1$ -RQ_� 6\{A_0, A!�As... A_n\���rA!r�GAm� �a :utrivialyf��"�La v�QhA��5an�� � F@ 8} Dpm-�bG�.|,�>aY{c }ta_0&�#&&Y&& \\�An&IC 1&2(B0)('� . . \\ &-! V� &n(nq{.+�Xeg+n S �d`|'/�  �i-�c�_s�Jc-�e @B e"�x�!E:pmU J�&&Dn>�.�is�_Z{ r9jA�a sis]Z�i�� d�J nct �J COJO�Jus K &�pA�J� �3a� ;'be&>c^<hB �e! q$, �� oT�;B��GM�_{nF�l $0� q q n1S�'"�C��-�I �Ke,�4�e&�C� ,&4ls�;. "�5> 1���nvari�81H}jttan��"�:.9$o;to<q ���4' FP~_M�1:= 4�>;�DA(4:� �Z Js L-6 �4aE}U!W�T5�J_E�A�# odd ��^e�z$-odd36e rVIO�R��=s�=�.ey:^{(1)};6N ^{(2c8D#-hxto��:��2� `:c \T �`&8<�-)��'9 2)} >P.�Tn$-�, alwayMr�0is�Oad< oo&Et]}6� *> :�a5ichM?ls ld�nE�:��� 5. WRu :q7W~yll ��!�&`N"� �eq.*B 7�or 6Y3a�$Mk� q16��i �.D4 s $T)J@&7s {��noPon4V�bAwhpm�$�of Professor V.Ter-Antonyan (1942-2003)�Wl �9h�ss�{B.��hav.M� �r Rr 0-8} b^�1X3%<2�> ]8 sum_�2n�2RO  \, z�� �zzan%�:� !�:�A ��D"�D6�2 20} Uc\�=2� =73�� ft(-6f4 8��95��6�T& U�&�  Observ� a�xaX2�5s …lso�U6") �O#��class�r!�*�O��T via ��.�O.��se �<(w�a�$centrifuga��disjars), #Q2.�20}) bec�q�T��odd� e+.��ex%P;���=$�6� TR �di�h͢�� betw~�[�"�L s $q���4�P�� ��u�ea����� �T� cN 26~$�Lov/~��nod  6?$j>%�de Sw�_"f��N Qg��� s, h� �fINCE},� � 2;jlg��e:ً xis *iQz"�[͡� g���i plicAJoneU56�SJ^&[B�!�nUq asce��)� , i.��"�"Bw2�J�0:�! 1B .2),�'6c: :����.a�p���a��6emR HILBER��AR6� e�� "np� M ��&�Sr{i��SzN$,-v� xi��, �je& �U0-80}) -:7})). �U+A �IC^6� $q_�  $q_2Y "��"��� ٥m$aF�2�"���+q_2=nid �UUF�,AU�qcT:�D!2}:w ��U��(!�?xi< "� .�Ž�Ik���� 20{ ��� bSH d@f� u��W-�D "�&�6�2�H)J�7t�Xn "h wa�%�*%�"H_EQ2�,Psi_{n q_1 q�Z*}I:� C.*:�\, ɸ�V\xi:y !�Z%T:#�$&$ &�m^2E7�pa{Do�:� �coK�r�" low<�1te ��$�]6��$5'����R���� 00� �1�0�0z_�kE� &(A��6�n=1�<�$qِ��Nx� �wo"B�i)i)B�0-8.�10t>� 6 "�_F�V!k�X)H^�Q 16 =U}!�>2-�1�>D} B} jƀ&^�j�;y;;��s�L*9e����^�2I�!�B� &=& 6d5=-!%"�@-�^3Y�}} � z(Pe8!��l�E%��m��9���n=�gbHis ival�Ecubic Fgy��^��ZI�^3e63e]�} 2 + SE)^"�?aX- / (3] + 3f9��o9oAte�v5q�s\/ ifie.$� ����t�"5�9b90#)n_{2��!tE�3F@��6�2��(>2� fL�9�9�C��^�5�Y!(z�K+�K �2��Yf}}{YX�G+ I� ):^2 �*] 0-86 w�_w-wZ$��c$JG7 G7 FG%����5y5 �{ 6. Ofg��g�]VLS>�!B��*S 2�]s � *8�s�**� >� P go֒ \not= n'$��R�1-[�S�S� '"� ^{*�]�X:u /�.�L�b�bB*a�p>�is"�`�D *ehJH!�>�q$. U"�4��2#^EWit� easy�O}a !�1 I q_1'�  2�2f2�E2�S}6�U"� }*}�U:*� ��J� �V&YYn*_V `Vi2iN� %}"�W:c�].]�w.�*q1���f��>"%! V�%�WQQZ2�a�-T!���b*��:�$&���V� $jB$. Frō��a�mLTB&�$��at�r�i�>B�T.?GY)B2��^��  +M}\, |j%|ig,s',t,t'�7o(�>t+t'}a�A_~}:� 0a�F\�G�M\��s A_t `2� A_{tZH, \{F^{-�h_{�} F^{+ �Ru" 2" \y fZ����wB.wB6�1-05} FAm � �=�/�8�.E �Ke.m+!�� +�R!!Ujpm.)} {m!} �& E6\ �!)^m�� *�  \g"~N{d��9ach&Fy�o"(ASc.���|.u��$&��ZKMg�}��m��+s�BI�  (x" %Q*^2})^2�"a�12k*beamy"UX�P \PhP�,y�����#2�q2��"  ndE���m�IN0$�3%*� (pr���$w�"zmP��%j$(}w��in*��hant� ?�^2��/� &4 onesTt2�,Q>�O!O*GmulN {\�R}=� = -�]5��!�������"��\ �!��dd6�2�P a =.Lf�IHh^h*lf 6�z�%[+2k_2) (y} &�y��]o>�f/ mm��[b��Mx2iTq�=}e�a�6�Y�&�k!k Takii�uccounW���I"�I6y30M^& �4+Ł��$/_� \ell�@5(z�_}I�����"�� _$ɜelldb��oErFCs � �R�~&�n� �)!�"�,�� nate�tqtB�azy^qHaT���2x!�a{� ^�f)�h^2+��)}{ ���Q�Q:$n >6mc&=&�%"�w��8a8���3-I �p =M��^>�%�i _-K :� \congB�^nIoAf<ft(>�_E���29� ������~9=?�1f ��2#���$�vi��!�z��#F���b�� �pm \neq ���V�E���M�_m} + �C�B.-��.2�a�2F.n�����T �>�we ag�� �Sma>�5 1�J�Mq4 oni��/�+set�8c s (E ) $(-1^{(q)8q)q2^$ n  )$, ��nnd*�%�|�V �"7StU����# ����&�"�!.F� .��  as&�yRk < 0$X�2k '�k-�!a{&&�'�Jx&�"�dixz7way�)S ���fL6[ �*p $�$Ab~s �2 ). RR�rgg1x.6)to�F�.idR�"X- [USH}. Re�"��E��E�3i�8�U���637-�eft\{ 4*�a}{"�a4 � &��M[��a^} !e 4n� z��� h}|�5 ]�"\} ɔ�!B�p"[zE"n6����Pu%^�!�26z}')�of.�� ��k�r/��,\U)�O�//6+3�"n>*×*#eM5�%���� ��@ )��!�Q�>{7]�^�^�|�$<D$%�Am�jp6dP� d)�2r�6� $q��n$ �X�.�ar�. .�IM�baN�exp�bs"�-"yx�#\ �W�6t�})7>OngO�'O>�ae e �z� $E_n��N� INTE8�:8'� �;&qdE2nE  �{}-2W.L'�}ށ�v=� f_ V_����X"� �- �&ډa�E�L0�7"5 To��=�.a< $ ��&��.B���$MARDO2}. F\�y[v��B�N�$ T U8.� ��U�i��J�E-!�dw=G!x�";+ x$&�!�N&-&����� �-le�$ tend!f F)�ؘJ (1�V1 ��a��f�%8J%8\to |x|N-�"N" UC��"� J}q>� removed. h!i &a � cB JȂ we gQau$ 7��^�4}��>�+���� �� {\pi}"�:4�+,�G��*��}҂+�n_1)! #)!�?~:��],\, L_{.  � ���$&�$We��^�5}z�)^F\,�!6|x|+x�)O i|x|-i.\, -���8E� pI  } x)\, dxF/���9M^E%[.�2.�+�!���2.�IP]Oʭ.�� U ube�*pE�C\6ls�r ��T:( 'ed"060��.!$��T�T: -�i6~y=)  .o&m��"c)�11�s+!�-�\,:�!�6�H"- 7)$n,M�6[G;2s}M� p\,Y�zE���+*�+I$@Ic�On���=" $r�$ ��Nenld�2Q9$n_RB�RtA4e5by�t��va4:"ߥEm# #�n��l�H$�n!��L\leq s � $,�|Bver :��<�O BS|� ��� ndex� m%m�*�ik�ge�'N'E�7^��/�@qq��6�!A�����!Q�YQ14}-e6)�b�N��a4k} 2�E8x�&�!h�$\{\matrix{6�k=M} �.� � �q�: ^n\,  �2e�Pm�*�)^s s!�cr  �*�I[n�-!b� A���6��v(-_� s+3/2)}� [�Q &Q a��qJa/ �(úZ%j��J��}�s��&3�b!�(�4�9or� (� ,(����2��V_2>!I8%�)�^2(K�)4- }3z�&�11�K5�S " "҆I���{Va �ReRe�B2`9^�"���/"l*�**q�:Ո"{,d!aE�ell{�al.:��,*{#;"V�'�"��` ��;*�KNG.l*�'*�Qansatz�� &� ���x�(j5 1} \"Œ!�s� exp}��_ Ue0] \ X(x) X(y)�b SCH-�NL��<<we"�{wo.x���"��.w� !��__F�%["�!��p�8$al z_{i}^2u\e�"� x{{�u2k_i} 8x /mk x&">�!+)|_F)-� ? ] X(&�"�i i �� �kAk� $ $x_{1}=x,� 2}=y *&�A1�"9�2- _�Ae&aE�'�1�ZK��en_ m*".W�� $k_i^��i>�� ��L�& ]mEon if $��i<v��a�Blas�K�<-6xay�fQ� b;�1&�T z��.�r=��!�* yӁ*_~-�M�ii8U] n_i= 0l������1��A(&1�14!��r�*"� s $X (x_ia(L^��i�K_i"��x_i)'�<u x*���u�,�5� w�J� ڴin!�drOD$x>0, y>0$ (on 1/4��.!..~9�N�R�^{k *�G} q = � f*\, (x)^{Y�M 1}(yN2}W ���2}(�}5�1%�19� ^2) �?�r?�����f�4}� v[�&�<��^{e'�Jk_2�. n_1!!�!r(�,�� , � �d�T8&T8-+�Yo�3w2�L>LEL-EN6�_��)���5!������ $s!`+!t�3��H* b�Fp�_deQ�of E/�it"+�a.� ��" 6 ji ]SV�-EC&� >�xJin ��'j�'UE̔r  ^ \phi, \�ʒr�] wSr�G/b���\,2 < �w�����w�2�Ռ)=yno�����>�5;1��R���r, m}(r�Mhi\�<� {n_r}!� �(n_r+2m�u< + 2�?!d � D}r)�RB2� .9$�90h G r ,2}�L^{2q>�+�r�r^2�PhZmbhia�IQn%.� "K��9_6} jZ(A`%Uc{(R q!-YB�. )|2 $1F!>#}����*�6S(aB�Ȝ����ieA22} P_mU=0�1)}I2J�;u;�2 s�!,�Y)}�__Jacobi�mB�< $E�E��� � !G2)J����r + mx  0&Rs8Y� u� M(s�Nat� ���[�6V��i��bf r� "m�}� ��"�����<\��d.&�=1.2u�'8a56`4kebox(0,0)[cc]�q v7(62 (�$(1,-1){4.0t5��%��%9�o63�%��7��7��7��8��8��9��9��10!�f $�$U^ �M�M: $A!){v$A�z$7�~$M�n�8��8��8��9��9��10.�4,36w)i10!�z"10AVb%7C,11 �gle{�1�:""g21$\z{� }} %�B-5��%��Fig. 1.� nd��P-4 .2R "+�*'\0�~6� 3.3.�K�� elZ��..nu,�U) �.E��)yby ($ 0�/�2¯ mu�  $�!�!�gin.�: 70}� � D��i� \mu\� 2)sin )�)!�&Y��@Q@Qw� D� ��rfo}7�`p��T $D�$�r#p I $���-F�d�_a���`p����5�.����R�7�5z��L 2r}{D� "A&!co 1� #(�0# \P B�1�5�lyfl �x.!2p)lQ���ar6D�vB4���f�6?�8}{D^2I h 2a-e! 2\mu)(3  a�ŝ+mC6$m$�!�)�dV. %�D/8�"A+F� d�8���$$!�Z|� *= �#*��C�*C�>�07"@�^" si}5\-t"j)%y�� I�l\{-�l�4ft�P-�/!�63^2.�mu)&K�� :��(�:��8co���*:�* sin^A�MT]�A�,N7Ja�^A�}1�+JbA� +I�])Ar\}�_��F2�F��a�ᡪ*/�]>]pA����� = *�� *��2� 1-EL�=��t�^l-1z���R�aE 1���v��8AU�=DB#%enuBV� .�!J!ʈ��"Y2X *WY (Di�B+������� :���� �;B�#�mu��^e�2(:}�tq�45��T�5 �Y�V3&V3� 8"� " }�C! tanteese":7�y>��a��_f_!�2ɛZ(� )}{d ��%~�� �B2b�^2)}H*^�S}" �G)�)���:�&~�\in[0,�]z2S!�"� q!q����:B��)')C:<�tIn�c word�{��a�2% ,��c.�� ��5",g"�P�)2shaadM�*�f s ImF= 0  RY���3$k_{1,2�;E<1]V.-dbarri�,s�pul"�mF ����*�k�2Y) �)�\pi/2]/+ a1 ���<�it� s�,Hw�� `B�.�!0i cu��!' =k_2D>�^�S�6�he ���'��!�.��*�' has b� inve����; ^aa��;M��}�e��\l��"w"&o��JiU��%�k_)1/2���`d�I�2*�Y �ARS�&�%Q6r���$k���gers, *�H�6�H4�>incid�d��o��at e�%C^�g�� of v�n�HM*Z �)� four2�iQ�.!�i��"�*1-D/�.�@l�����'n���7�eZ�5��57�b�-" $W�F" $2�c�� "� ʧ� e oH�'\� -i���O }{16�� �b� 2�,F� �� *� wmQ.`�5>2�W}6�� 54}E )�,d4�>�>.Jco1d�� 2� %���:l � ^ )� -o'"� Wɐ�y y �:2��[z{��q;,m�I i�r��heRqb�o�YW .t =�in%j*7&�* \DaA>q, U2P2_��c�� � yieldp&5<�yE�� U6�AVL� t%  -�] 2k_1ua)C"q D2�sim5"��f�A[pZQ� &:��] UA�6x2-EL5��`-` �R5Rp6u2}[�b"gb"�/CE�@� Nw�AV mbda� %�=^2}�+%�+ )&5Q9 E�/� K:u"3�)d�e=ejѦt=���# g5��5�t(1-t) �Q�t*� \"�H1)(�it!�&YDt"|=4} t(t-a�S\UE�tA� r1!v [p t���f��M�E�, loo#Ow "�$C :�,n���$N�$�SCH-V1-EL24} U (t; D^2) = \, \sum_{s=0}^{\infty} A_s (D#,t^s, \eea %=�\ for coefficients $A_{s}j,$ we have thlree-term recurrence relation���,\bea \label{9 04} (s+1)$ \pm k_1) �8+1} &-& \left[s! t2) + \frac{D^2 \omega}{4} s + @{\tilde{\lambda}} \right] eX} \nonumber \\[2mm] &+& X14 [p+ _ ^(s-1)]�-1} = 0��9� with!�1WH$ and initial condi!� T0 = 1$. \vspace{0.4cm�4indent {\bf 3.< Energy spectrumWsepar%�Zstant}PnA(In analogy �Hour asymptotic solu�ofE=Y2 U2A{AY|singular anisotropic operator in%�Dbolic basis we use�tinued !�rs. For4minimal>� J�sA�find � $s^{!�\ll 1$��f�16}IG{Ai +1}} }} \simM�D^Q[ {4s}E� (1+ O(I�01}{\sqrt{s}})I�).� � Thu%�� ! $$iU.�� �.�m� )^s}{s!},=����and�GGV�<18} U(\cos\zeta) �sum-��k}{k!} C^{2k}H A \expF(8}, 2)��2�ereforease�ate this case funez $Z���$ as $� \to i��\$ is not normalizable. Tq(a linearly ��pe��>�NUs, bute�2�Hgrow even faster. H�� i�llows tޅ�(eries (\ref݈X4}) should be truncated�����@jB.; giv��4 already knownB mula e:� � EL-EN1}) � reduce to�0 polynomials:��j� 9} U_n^{(�i1,�2)}�"�s&�n�Z4�t^{s}�/�/EPnow!2 � \equiv�}j� $ satisfyIfE1ing tF t��s�f20n ( + \beta_s � -JK }(n-V #��� k_2)=�4) ^2}{64}+ y e�r]�v%v  �� �=!�n+� $. �q�E]��f&� |20}) becomes a system of $(n+1)$��< homogeneous equ@ s�ȡX2�$A_s$. E&eKa�rresp� ng del inat�� zero�?j?2} D_n (-�� U |AV,gin{array}{c Qm0&(MN<1)&&\cdot&& \\ -U)�U  n&i�1&2U")6\\ @F. \\ &Fe2} c {n-1}&n(nM�).8J949a�nd � O |��E�  leads!�A algebraicU02 aUY,degree whichUe ;(eigenvalues4ellip{ F�  $-� _{nqV�e~$��quantum �  $q�<2,..n$ enumerate� root �q. �};2��t��N � �of ��acy as � o (d Cartesianp iM$n$-th"t�aol $n+� ItF lso SaDBa �iob 6�$ $q$ defin� ) �a� &lB219}), )�(has exactly� - B situB � Xopen interval $0 < t < 3 , �5F, ��)� may� ordered %8b���!Anodes�� E�"� of%�%O:5})<�� 5. WnTs6s� y&� of fnes%�.:�2-E� a� e*�9��> n> <23} {\cal I}_{n Z� (9 ;"M (\sin)^{�a1�i2} \ &} >s�� 2K2�� 6� iliRc2�:�JC i�R nR 41�Z��e^{J] 16} *�} \,\,���s�sWe will Qe ]� $‹$ a/0e {\it associ�� Ince.\ }. I�]-1 k�k_2�/2$��s25$ transform�&f^ typeCa�ordinary �Bw,�1are�or odd�c ecU Kchanges *�-ed`\ Lpi$ \cite{ARS,MPSTAN��At/= \mu$`w2�>�224})" the . a��NY4})�u �= i\nu%X2Urad(^K3��9 each!k6�,Do��,}�s�/ ite �6�-� c= presented�gwo:|s $q_1$� $q_2$, obey %�! %',+q_2=n$. TheMlomplet� 2�B�}) �written��hhV!25} \Psi��_1 q_2V�  (\nu,AI;NC.5 B| (�k��_1bamu�^.�7b�Aa 8��>�$��@A "@A cons� . ItYmcalcul��fro�UC��j�6�D�4}� t_{.� d\nu.K<\pi}{2}} d\mu \,�h^2--�X^2\mu)!�J *A,2L�8F6=H1� ��՞In same�$s� is mwconven�/ � alternat9�#A 6�Jg� noB5}) re����� ^  problekN"a G � ���1 a.E� easy�se� � >��-h� sid�eqN! D is invariant unde% simult��]e3�R nR 6-w  \longSar��K.�, \~�:3-�"F"!Yk_2��U�!q"o   sabstit�$b�%� $j�$ does _et�uE&Ez"j J� �Ir, � Monl� ir�e��j26-2}�Ac^r��l+�f2F1)}(-��&�A�result:BE�)&!�"� J[� into7 A4�WnW-">�f�a~�� e0y,� DZ��� .�;i��� &� T�B�!"�. I$� �� ��tr�F��after� iE��z� r�. Fm: A\3})Qconcluda�at&��B75}) can�թe":� �srs4� {`" CX_� �� �� 6<� +�k Q��� >� � 6V� ,� $ (*� ) again�7meaningkB H"��� 2� sB ��#��$ .�Ba �B�6@�p#<6. Orthogonality&/B&`#�2�Fta\ 4-)( Hamiltonia! re ov( $n\not= n'��"j�"27} \i>� .Pu_' q"��*\�� &� dV��2�EqsB� ��A�:+�.|� prov� e perty!�Wdoubl.� ity}��6"���R8}JT $, namely�2j28J�>q'R�%つ�>5R4} .2U= 0"�'BR(292�6�-N_1j�>!R>4^�1����)*�)�Pi��� 22'>E when $q "�n302ti�*%�b%&��,e�d�%]  D^�tA��obo31B�#0 1 . n��2�L�n�!$ s$�$s=m$�l�:m=�!�"�$0) = - (2m"�""]"^sb�'J 1�M;!:� kũk&� ~ $m n-m=n_r$6�lyn+$s �Dm$,A����j�n�$S:� -�s 57s-m@.m+16�� *� I&L(� :�23jta�A � ��,t"N/B<� �m� spli?a]JF��j�33}"�/ 1L2U&i$.�&saZ"�"c&. m-1��.��yjyMy�1�>2�, vZ'$ m+1, m+2,�y q#��1�1qtwo6�1n�%3� Bpe�get�OjO5} .e�( \stackrel{��}{:�S (-m)a�N�_.. &�%_��.�j6��"�&j&6%& m+s}�((-1)^m $E�V,m` m-n!O} {s!�c +2�]y�_s+1)_m � ('&�.*)\n)��4>�4$�I1,q@-�ti $(E4= \Gamma(m+s)/ �%n acc>g�:�# 71})��j�7> v. ` &�& �"phi&�"1�}F >#N�O2#\,**QpAE� >2eQ\[ 5B^ 38>�z� ���Im1�2)��"I�r) rw2}}P7' 6{2r}{DU�{U�-+20> Y�3m� }{D^!}e2r)�A&ASukng :(4eJg23ndB436�'e��z�9>�����M�(, _2F_1 (-m�o1�2;&�;Va��!Q�&=�7{�V\, m!}{2 A ��, P^{� .�_m( �\[3}8Br40>��rBr2m46v iZ\} 6$�0K95\\times&J& N�� m�e�_1)�n_r; 2mF�; hZ��mv� n_r!�]R�F (2m N1 _m�x��L_�}^V? (2�� 2� h�&�ula�2c�jc�9finally��N e2�iJ��#/&H �0� v-�%�.�Z%4 �%� Z _r m^�rfhi��&���8:�:�,u investig�.!�& /��$D: YA(/�allI8+Ixr[*j2>��&%4 produc� dia�( elements. �r6N�= �n_1R�{n_1}=0$�.��%j�%4� "� b� Zp )�N� T���*�T=�;D^4��� 642�6 n%$ (4n_1 - 2�56��7 @ \mp�"��Y�o $n7i ...$. A�>ic�~��$obtai��n�3.]"=9Z.) B(¯NUf�ZbA!�2F�2-�1��9�Z8!�2"�3.��a�"�(F��#) �9�&en_1+nW+YnA�n_gr� ��� 3 . �heV� 4N� ,t%B�1}).oto��("t�N- 2$)��j�""%�v8&�C (s-n_1x �&\T�$�U/�. V2�<%*<%TF�!�YUN<-���MG�5ů $qi��^�F0}):�n���j�5&�"�8/+1�&J24})��E )�`�(0 \leq s n_1^d45-.=�8&wI>}�D*BC � , * n�2��  A.Cu�DJJ�;we�\�\6!�e�%�-�� �,>��.3�01)�1�f~46)�-n:�zva�6�n_2Fw��-���nfB�4i -BOE��&�v47+-�F7�F� "���uE4^s�iG(E'_�mw1f�j 7A A� +� @I�}��e�(�F�?F�f:��?_1��.�e��/.7I��p%jp%481�i)B4��8�DZ�2!�{s.�b�2j�85�2!�~ʳ%�2-_F2��7/&7/W�1�<&�1  $2 %2�'s. Tak�W-�un�&t2|��+�J^F�7})-(>�F!��� � �)4.�QnQ"A<�Aj�.�x2��(E<&2{On}"�n�F}{�8)�F} (4x^ ZH��{�� n_�,2�,m� r,uj�&1Lb,d'+%*,�&�:.�iyf\�6WJ\Jy}{�1^y�^��._2;�"C� s��1&�1U.� ne:KLbetween hypergeometri& @5Lagerr2�I�;BE}�� f� 450} L^{\alpha}'Ex�$I=( $+1)_n}{n!}.W%G1� <x �N=N w��z�5�BNJ� � �,0} �� k_�e^{"� I�S9 (x^2 +E�N��(2x&C\ �(2y>e�A�S�0_�� u��22&`aZ�y "y d=�2 t�?���u�gBl0; coin\8K6&��(a��Roscill�R. \si�{C�2sioq/,nd summary} �Xto izJv9�23�9of superEgr!O poten�S s $VCg$V_2$. x] "�e� at2?Schr\"o�)erz(k� thJ` maybtstrac�via.�7 of vp9 bles^@ �&@different ways. O")m�:explot�!j*�7.N G9�co�! ates�@GH� 2"PgF-solv� e`J!��V1-SHEQ+ 21 ��? them&;�-dimen!�al�/ non-�T��}JUal+:; �N[c"�G��2s"�)_i$ play4ro0f 'Hgy8;ad, X"6Ai@P!L�.E& Herm�@*�B,�A� bothV�Abas"98o$ � �u<wo2VncIse>A A�&�I.�!\�UY.U��,� �.� procedure*$Q\1one.� (b�1�):�t�CU�ialUfYPEQ202APlivAꍀ�Ax!�ne.2*e�b�� 2�r�PrX! >rg�Rfor*�9zH2TZ |,��point�Cmu%%pm4 �\muI. �E7�; h��3)s"�$o�6%��TA��T 5�m&~'}bra0uk��� � :#nU7\v"d�r2^2}� �oB ^6 +p u^4 �Qeft [ k_1@4�C-? (4�HR2 R\)]�D� B 2^2 �aB }{\m� 0�Y] Z� C="�] ()Wis2(3� &v%cIVINET}�� .|r�W�j)aQ"� �� ��A"��per�ye toge�?� X��!<�A�{0.!0-8}) (%�.�on ��]maga�yE2Z�Qi"�X0 QI,oOnon.� part���O�!sh�O l�_nA8mi�Yy�b"%<�� $P_n� )$�K deedf�2�]pPOLYNOM��in:��)F"� >]��Q��he�f=G��� �{7SmA~i��7-�,(in"�  $� = z$)#C%���"�2 phys�Jreg�a��6V^!�wh� Eׅ$z\in (-<,W)$�Ai�Rall-�(s posi�Fa�neg�F�$)!�9 &,O�! 5�>w >= uani&``"� !^& &b sU E�d N �R��� repe[I��%�� &� 1�2}). WVcq�� �&�!�v"] `:` "�7�Ug2} � :2�O�d�iz'mpl� %�6� _Jv� � �l&zM0, 2\N!��M="�]d���|}��m3di"pT�B.�bI��\. So,�Ѕj#&rigon9ML7 2�t�� �� (�^u�s 5@8!��USHV1�!��r��c�c M%�+QUASI-EXh�$d^2 X}{d\nrdr[�.Wz�f (2n+�?)X`h^MKk 7 F�Qh^4\nu"�Zk^2{% . 1}{4�sin H}"F[)�#6)co q�#& X �*��,�!Y}� �[�1� � .�^4' �$�}& �1co E~sinmJ Y>>�'e�!6!6�$ �=w1� /AT*�c7 v��z �aofRLi�@ phea�na st�R�F>�q�q 2 0 \footnote{Re}'wdex= s our obs8X�� ��of�%V hyp� sis: �Sll�ntum-� �V�Ls�Q CY��today�}2�aEsJ~ � "�Q��rI in N.J 2����:Is.'>T�c�gpromptY ;g!�> r�d*�=��O���BQ�� .Z, EZ-�cBf Y'� "��K �� @te .L*1 � �fsugges'; �)��'� !�-� {ifirst- Z,9�" } i�hJ|EN  j 6� �Fkphof6�5j or $N$ . �&.Hv&.s�T ed throug� ��!�discr!aH �MU�&oJ:�leA1�E*"g"$ s. A�7�M��T-�E ]^ F_E8)� n�. W!about6��{A��$old sense,�@J�QESaA7itB !�lyZ^}, becaay�� !�1.X YP. isa,�nerel���eT)1a�$N$.& V��.�.us#i&Q HelmholtzUd on>Z sp�$ $S_N$: $u� + u�0+... u_{N+1}^�R^2��"B�"HELM-HAM"( 1�\DU_{LB} 1 + E �&�B2BA�!Rvc i,k=�7!� L_{ik}^&=R  OBiN (u_{i}�\A� ial} ( u_k} -u_{kn$i����p�pOb�F� soido"1 � KALM1,23�1B11�3} u_ie-TPi_{j!�N��ho_j-a_i�  !���ef2��6E�i�,t4lY,3)$Ya�`exagNd A<.A � �so ob=� atiN�t �s�2)$�(aY�� !8 ��Ng 'b�"]��#"s���� >  b� ."�%�-��"I next&� $N=3�b�l&�_ mpli?tud %n�"tjɫ�iz��z $E$��%J.�f�"B&A2� h1�p*�O���!�*.�6�6a�_u��Z�mU A��)$,E��!�3��4)�"2�"�)�.������AA)=a/Qgw� ,ula $E=J(J+2��6wtoAKPS}�:�'O'"6#�riv� m:"�35�!F�ƅ3 $a &($k3,4)j-�� .9 bTVf(ah6�8c��}�0h�6j{Fdi&c~*�"�n*rJp#s! over" siw�M;D�s is lar�(tha� 'un��s (��&Q]];]6\matrix� rect`Z. �)ern�~a2� �9N4 �is�J�(t a necessa*cP ��ex��of:ontrivi.�|!�qu3Zto �-ll�-4ants, however,��� A�_*.�,�gL � ,s� ���J� e2�$c=isH by et+�dmR laste�!~�to  rows%�l٥�4we�comN�xkGwoR[U$&aa�.�Ϲ!�� &})1Gnd2. So,�7a`!����.9 !ܩׅ�e� ����� Da����as�kKrz��"wl n5���e�thr?U�&� way:�!<"/5�is $NZ-T)>q/sF J2��%� �@ ricV� ,^a�0( $N+1hr*^40.Yc1�s)awl*I]6-��,U�.� � ��n:�iR�ie}"�'"b5;��&� *)i�6)e^A�� �E�is workE6ify� "�F-�: >�},5Vq}�obf!�SbM /nd J� f �le}Q��xeDFng qu onm�weF!W� s i7u�r ing:�H�*���N&" ~ ef�i�$ wer >� "+ �*a~B{orJhigher i5V.t���օL ���L as Jacoby, Gegenbau�� Legandre,N..A?*�0 *{Acp ledgw, s} G.S.P.� nk�suppor�a�0Direcci\'on GO a�� Asunto�l Perso%pAcad\'emico, Universidad Naci" AutJ�oma de M\'exico ({\sc dgapa--unam�z�gr�i0102603 {\it Ox8a Matem\'atica}e�EJ,sep-conacyt}�j�Z44845�ub�yXthebibliography}{99} %-� � \bibitem{SWOJ} S.R.Wojciechowski. � S.2e���!xC{�(ero-Moser S�(}. Phq1Lett.m�@A 95} (1983) 279.��J�4EVANS} N.W.Eva�g^� in C�lA�Mm)cs}; {�Rev.}\ �lA 4J4(1990) 5666; VGroup�po�'! Smor�2sky-W� nitz1$; {J.Math.ea3�4$1991) 3369��i-t -Intv32uRZS%qXA 147%s�483�sNs�:�ii �\'f� �yɍ%�&�!�Qu>�( Sov.J.Nucl6�i�67) 444��R�4SVW} A.A.MakarV� Kh.Valiev�2�)�A��4  SearcheNonre�visa�m s �Dynam� -2,ies} Nuovo C);to͵A 5q ! 1061� N �8math-ph/0102006�A/1�0A34}, 4705-47 200�WRW MKP2:��yi�A�F �:2 k�ic�� icE�eiM�65(6) 033-1035,!2�^N^ MKP3��/ x 2-q$ J:�06791-68A 200� * *. KP4�����'E_{e,C}$�!�Y��41A�� ��^� GPS0�F�F�"vEEuclidea� �N453-521�9��*�YKMP-96�21� Z *Q�&� �. 9s� 5i!A?2'7s.AE&� [437}, 6439-6467%6�� J� DKIBHAK} Ye.M.Hakob�ML6��N�On a \i�%O"�8 : In�;AK�H �rba _E� s.},�L 1(10�M782-178��8; [in r��an Yad�� ya Fizika)U<893-189�8]��N�KWMPOG:t G.William��SV��p�2�:t}. .S͋,40}, 708-725EV�nRnapHYP:���J�q52ual =9oidVB� 5416-543� �� .� :2�"� ��Jz � IIj�2291-23�a19��V�RANADi(F. Ra\~nande� M.Sant0.6�l s-�I2��$S�\�@�ic�F $H2$.�}i�E�5026 ,9)��R�MPW>| .�J*G.Cu� On6R %� -breL*�;Bg7B�n ) 0A35}(22), 475r 73�k fk KRES�"� ��.  �Mul"S �CJ�in�-"� �\ 8�=0�W ^W B�6�J�V�a��:a�Gnon6j Z�g 970-982��f�HY*lle�B0os, F.Herranz�u�%�Tz-Gil1� axim$$F�F�5^ed2 [>I 6}, L93-9���R�Go�ez%  �Isochr�}���K%w{-il2�e�ste9>�� 4085-409�VKW>U�*:�~��a�Darboux5��a�t04}, 5811-5848��j�RAVEL�GraveQ��Uar��ar��&�5%third_; iel�mogZ�5�0�20��V� BIJ1H,O.Barut, A.I� t�G.Jun��-P29Treath�D 2�!a Jedd&cc�t-�A2T 627� � V  BIJ2���� 2�2��117H ��R�WITTEK� E.T.Whitt�pN.Wat�)�A Cours!�p ern �a`ysis}, Vol.II, (Cambridge"�" ty PC) 2�% .% "E"8HIGGS} P.W.Higg"���a�� GlXyex2~1�330%}�6"V6"DLEEMON} H.I.Leemon-l� �48��j�ZEDAN1} X Granovsky�.S.Zhed��,I.M.Lutzenko � QuadB c Alegbra�%$a `Hidden'1���Farrn&�9�A 2c�"887��J��L0 P.Letourneau�L.Vinet �2� ��: P& /��Q( Ex� S�U�V��}. Ann!�2� 144-168,� 5�� R� DASKALOD�.Bonat� $C.Daskaloy4 � K.Kokkotau}�Jmed*��. Two&� al! ntum$!�!Cn"")A 5� 3700%4�n22�-�Y�Poisson�*��t6�J &�(Z� EX��i(��*F+�1um^Fe'}M;�Q�1100-11L�3R3 WINT� $P.Tempesta�"Turbine� J e �va� >IyW�F ��42 1� J  �2$ Rodriguez%�J�'2�&�ea�.�$n*�B �N�Ţ��^� KAMR�� D.Gomez-U�[$e, N.Kamra�RE#&*�� ����dii2 a*�"�� IU�� LArXiv:nlin.si/040103� R FLUGGE� Fl\"4Ga,it�# blem� 1�&�!(, V.1 Sprin�38- Verlag, BerliXgPHeidelberg - New York��71����& LAN�O.L.de L՜E�R.E.Raab� it OX�Method.� .� Claredon � , Oxfor�$91�Nx*S*: l&� mode*Z �bf` 9381-339]1; �f gra{�vd99-941��b}b YOSw (AN} B.D.Sle�'�L�meter�3�6a�>Hi��t�}. (Rese)%�N�M�!�'; no. 2"9(Lon�V 197��,*�,�INC)L.� �O�:rD�a\8�6 }, (��: D�9)A���(R�( WATS� A.H��7%-,Proc. R.Soc.W4A11h61�2�1R1POG��|yceWJ�6E*{�ba� subg�0basB*n �d&& y�%�#.�� 43}(6)�,7-341�ujuTՖL.G.Mard� >e2��4V.M.Ter-Antony"A'� sl,:&"6,D&� &� �� 8-Di\-men\-sio\- 2I� 6�A#4�66d8�� R� DULOCKq1Dulock�H.V.McI�4h!�b<�'g5c"�> V�/Am80J6� �"10�/�6�YRY,ENGLEF} M.J.�,efield �GEܭ aKCoulombE5) }. Wiley-%�sci�-�],��4, Sydney, Toro"*197��%V�%��1}��E�>�2��Q \ El��B��'>D %461} 84021� -N -8PONOM} I.V.Koma,L.I.Po�r , S.Y.Slovy�D�*KM!�1�.) 4(Moscow, Nauka�99�>R>BOT�A.Bogush�(V.S.Otchik.&� � � �0 resEI@�r ��:.ȼ*N@�>NUyT8&�<�he HeuFH�$F�3�559-5��0!0!�� PREP!V.2e4A.G.Ushveridze-�Pre� (t ITEP-169}q�?��R�TURBO6� �*/ ly-SPr�R�5$sl(2)$A}. Comm2@� 1467-47�68�5R5\ R[ ��l&�<� ���rXk ;0�l4�*��504-5<2198��R� SHIF}"A.Shifm�ܡ��ingV���>it-���� In��,ics, BristolaT9� * y�BISWAS�8Singh, S.N.Bisw\K.DuttamhA�6>]8�A!��� X;co[� ;P���2�8D� 1901-190��� V� �CIN--���SQ|2UG�V�@�*� ��8�cM�181-18�&��Z�E,;C.M.B�)�G.V.Dun?l��oQ��@7�&q� &��vb4 hep-th/951113�0R0$POG-HAKOB1B+G*w !N&�3�S.IcitskyM�Is&�O" +C >�}"\Pgd&�7ft +��cijk0 2(4);,23-63�99�+97�/5�9�+R+�J, R.G.Airapets, Kh.G.Karajs(, D.I.Zasla�-q"��! 4*�42� e.  �W },&r0JINR, E2-96-1�Dubna%�{R{ �  en�7B]-�a Cirb�r]�}.>7\�B 8�3-5��n� AVTY�L.S.DavI��4UZ�%� )o_ Four2N�adr{ I $P2-87-453,Y 87, �hRq.)�qNqK2!,Kustaanheimo�oE.Stief�$Perturb � �Kepler m A��M Spinor RfT m@,J.Rein.AngewP�2�>20� 6��R� GOLD�$I.I.Goldma�ZDrivch� v,"��� u�"�C(, (Pergamon&�196���&�LANDAU3a�D.Landu EX!ifshitz �B�: Non-r*�:�yxN�8��V� HALL��L.Hall; SaadEl8A.B. von Kevicz��Spiked Js.)�2�-�bf7 , 94 B(�KRKCALOGER !F.�F�i�3�a� Body� �One&�92��1$ 2191� 6�m.Vm.ISAKOV�B.Isakov��a� �;tat��Ac��s}, N'� -Hol =Am�-dam��W}W �� COJO`#A.�D#jED.Rober*�(#�"~�� 2�au��C&�+. �Deriv�%5Pr._Qc�� S ��7�815-82 5�D RD HILBERT�L�) ant �D.��!�of`�al�lJ. Voume �)�m Chap�xRevis(re��s:�3 �LL YMARDO2�����>8A�� � A86� 324-33�� j� 8ARS} F.M.ArscotQ(oy.IxEdinburg�,,67}, 265-275a�6�b+.b+%"c+TUR} %A"Z,�X�iJ.D,P���xM8MA��#V�#�d695e<5�m�A&�!*x"eu]*�Xa� SIAM�Ml0�,.,� 2�C 91) 6L��$R�$�6Q1N�V��@&�6s:2Q+QiM�},n&{Tq�e*!����SQWal:�tha�.@: AzQ�HP.L.~Chebyshev (18229B H.M. S��stava, TRassi�@A. Yanushauskas, �" , World S[tific, �apo�Q�N�nNn!�6�@%:g�(*�1,�Sgr�(!PNi]p Ar&� A25}�O'i��~.~ \endB�Q  docu�1�� �\�*[11pt]{�K } \u�B0ckage{amsfont0�64math,amssymb} �>P Tamanho das Paginas �\ %\oddsidemargin=6mm %\��: :)8m"�v��=L0mm \textwidth=15cm $height=22. \top q1#opskip Ah��ep�� Eia!)o entre linh�X\newcommand{\blst}{1.30T�e2ase��stretch&1} X�tc��er{top�[}{2} \sbottomZtotal.6ztop�}{Pl6 [n"!W �.�$hko}{\hook�}a��v�=nbb}{\q#se��,\nabla_{e_b}B+aZ+a>+b�gaTBFcZFc>Fn�j��B�nhB]p>da>�}{"v\\:ea}{e_a:,ih}{\'{\i}} 6xm�llia�.x{%�{� \char'44}>ebob:oec�.T om}{\Omeg>�omoJ4nm}{e^0\w e^1 2��.\pas6�p>et!Qtheta^B!� >�t!� F�7omB�omkomB�uq}P��n4>KPclu}{\cl_{1,3}^+(\CC):YcA� circ_{Z,YFBaPB0,7>fA7f'vsiz>�b~bullet:u gz}{\Gamm>8cv�ir>d�did:Ld!dagger:sd}{{\� bb{SBi LLL} cal{L>�eaYvcx_{abBMc�le�elef>�bA��X� erBc"end^ }{\star_{�>>d�p:�ba� yarray>:ear}{xRfii}{fi:Vmj-.bf:� �h> epaDvcx:2EELb{E}}2xDDDDB!� bf{dB�bf�bIZflush�:@iA�iot>3om!Mbf��:�e\!�bZl~AwE:EnoA���6�RAOb:���a�m�.�s;y���I1:�sE���.#6�c!a,a E> wt}{\wideֽ>�wAha>cl!�mt{C}}�j6��c]6A>qca!�c c\~ao >6U,-'B8oeAs9��:�VR6� 6N2RRY�R:XMMM:op�>plu� .�HH5H:5PPP:x�8!� bb{X>�an�~:�b!�>�:o!�o�:lAPLW�:beg N gin{J >�en%a,^#wALedg>0g}{\gJra8b$rf}{\rfloo>ll 2�ty}{\RR\%�\RRB�srsigB�v!$varepsilonB!Ꮙ�eqn�]2{ben�)D�Xe:� $%C"6�ek#i6"m!�A0ca� H*em{thm}{$)e>� A}�2t{AB_vv bf vB�e >�a�we�a:�� Bs uu Mu:3jj j>�hA�heartsui>�m��!15:"s��sharp:ff lf:�vk varp>ww 2w>�CCy�C>NNN>FFF>KKK>stk}[1]� ܵ#1}{\6��>5��t��6HdwnM�a�4style #1} \dowA�o>�ZZ�Z>he��Z@m�!�bf{B�mn!d��M}}(n��at�K}>� mrrj0RF0cj/CB/K!�A�!:3u ��:o�:vbS 0blacktriangleS>&vB&�6jLh!�B N�vaLvarrp��$N:�sc��stMq\sI- A3{/ ńCBsЖ=pq2Ss�z>�m���@eeB=�/�=p>ATTy,TBLzA�bfaF6�rI� bf{rB�R}:6w�^{W>x iXBNlaK �6znoA=no�B9spiA99$nshortmid}��^B� s� 1M?.EuWQPg �:�OO9YO>dB {\�B�k��{k}}_R�di6 x-B x:tyy)[ y}}�>�jmjfmV:i:i�:dfn T " x_1>�df�.f1=�2�df1f13>bK�S��K}>���w$L$6|mkk-� frak"6 iA��:i:�j2j:k2k>�u��UR ivI>:m.�:�cM^{��� >=cltAg&i _{3,0F&E1.&:myu� ee_12>VVn bf V>=O!N��!6�OM f�>lsss !F�(BA}{\breve{BhBBBB>UQQT!�gQBun<mm�=EZsB>m�mI�"uJ"v.�Bo b�r�� >�bx�a pis>"e"< Z �{� 2�k��kapB�.��W2:�t�FB�m"bJ"p2dp> mmg2!gJC"� %�cJ"e'�kJ�m� {#��� :�mm"�lF���=BJ�B�qq� bf q>pGGM< bb{G>mm� U�fB�cl�DDD\��H %e�% impef� a���ve�galbE�2a�, sobre figur�'I�}s�e pacote�:%�;A�&9eo4"= �2eJ�nt�{!C�@} \title{TwistorsQp�Q��t�h�Excep*'rucg�authorI% Rold�$da Rocha}\�wks{*3o�oF���g��sC.toz e su��@ �stob4m{al map�!^>J$z $${4,1}$, be r�i�4g ֋� VG!�b%JQp�is�- pism��VA� �in Mink�qN2���6c M�ssociaAM gnDirac->� ��C}�� C�$ u�4 one lbt}"E@�s �V dardF+�u�g ons,�4c�{�!�urpose �>�BgAa�us:co.��!steadA)�2,4}$�.jui}� ify,YLN�, �-� fibA��gur�x��� &�s, ��ively,9�co.�� ,es ${{\rm SO�&}/( U(2)\!�(s U(1)/\ZZ_Y�0simeq\CC\PP^1�~ /Otd<3 < J= >3� A8)Apin(6 CI0(2���D{*Q} �!�closelI�)�A�SO(8)M� d��p�i�re-��, &�AA�Ey IIB �KΡ�{ory. IndG�aa�gV* , t{wnofi���(nB is Y�, e� intr��e�h tincByordw|�=ndA�ju?�mo�"aPy��%t!!�(s broken by#S%�$I$ 02) &�C��% 8). Also(�is 1� ewed�}��g�H)2 Penra�flagpol=~llu���HI�'�W3R!W�� aL� ��m@� yn%�|one����ari�D � ww��d�yame+g�to�}u�invsy%ZAiD�-8xn��AbbЬt!��!�2A$2n$)/U(̣q��Fs��ure, �}emerge�yez6e� ider��acqo8t�&lI'�+�E�6�$\Xi$/lp~tP� "�s!�s�M#$\CC^{2n�sARan�smorphism@!Xof.���k%3fo~z0 the F. Reese�R Harvey's book approach. Finally we point out some relations between twistors fibra Dand the classifica� of compact homogeneous quaternionic-K\"ahler manifolds (KXso-called Wolf spaces),kexcepb�al Lie structures, whose grading is also briefly�Xmented.} \end{minipage}c,r} \medbreak x\noi %\FullConference{Fourth In��al Wi '� on Mathematical Methods %in Physics\\ % 09 - 13 August 2004\\ % Centro Brasileiro de Pesquisas Fisicas (CBPF/MCT), Rio de Janeiro, Brazil} \sec!B{IUduc 0} Nowadays%�Tsearch for any unifie%�@ory that describe 2$four funda!hal % a`Ds demands a deep m.(background APan ;face Q}p),E=s. ThY�/superstrA th�inQ�MT8 \cite{mot,b1} [A�(pure spinor!malism -8cartan,chev} haae�$creasinglyGHwidely investigated A4b2,b4}. WithpmotivEB conca!ngSO(8)�deaSosi!�)� preserves*ymmetry type IIBN  �pgrscwi}, among others, it ca!K$ shown via�V!2well-kn-0result assert � at a5{,}$n${�Vy24$2n$)/U($n$). E^|main aim of this paper, besides �;�o>>U�tw�=A�=Js,� to qNAfoAw maps� Minkowski) � aivXed adj��reEntIQdof \$pin$_+$(2,4) (to beA=cisA�definedjSec. 2) ��Tparavectors\footnote{A^!�lClifford algebra $\cl_{p,q}$�a2d($\RR\op\RR^ #.}M�0baylis,port} ] H4,1}$!�d!(cha�Uerize ���a��}icm1.�> are 1�sla �mal l����deal ��aB��� !:�^ �(. Although�LE08s have already 1�d�u�B%R9I CC\o!�s%S 1,3}M� %-?\$66on=E1]� . In �3 toa�\incid0 P V,Robinso�gru6, �~multim��A/>�!�$I0 \cle �a�E%,E�i��ed. W��L explicitly how our ��s� � tow��establiAI one%KellerM�I��� consequena E/  !�M�� by Penr� ɭpe1,pe2�:IEw� Qd �ne�obt��%���]�SO2�%b.�& i-�4A{ linkT! o o� .� &� . &m  ���� , b� } Gia0a )���(, endowed w@a ��ic $g$ Asigna  $p-q!�nd de��!V ����,%�ide� injecAh�x -x��:��E\ni x\��Lto (x, g(x,x), 1) =@\lambda, \mu)\in �� +1,q+1}$..^�r imag��i $ un �is�6 subse4!� Kle�Lbsolute $x\cdot x -�\mu = 0���}$map induceaZ: fromYco�B�$(S^{p}� S^q)/�$!�.�M�pro1gs� $\PP^{9wu��${\rm\ }(p,q)$� $isomorphicbquotient27O}( `�=��^since�.q:$ � � !onents,� n�$ �'Dtwo (if $p$ or $q$���):G (� wise)�$,cru}. Tak` ��8case when $p=1$e@$q=3$�� �ap(1,3)�:k �Lom � 2$_+5$!|nec�<-��� tityX:M\"obius p* lla�h� of rotɭ,ɾ�s, di �inver# -maks}.}DA7^ $. B� )0orthochronous�c�i� � S!- !1. Con� a basis %�n .M & satisf��4s $\vcx_0^2 =  5 1,\; 1 % 2 3 4 -1�G {\BA9 a��B} = %0\quad(\BA\neq\BB).$} $\{\varepsilon B\}�}^5}�2,4}$���)E--�E � E �E �E � 1$ %�� $E_A��E_B� � (� �$\{(}_{ �4���.l last-�� �-ed ��%$cx%}\� �[�gsm� ��)|A}5��Q . ��$\phia�Qxs�Uat� �1}*K 1,1}\oa �. }��atia}!T� !w25�FOim� t� M(2,\CC) jt$�ere $$M��eɃ�$2\L 2$%ri�with Adlex entries. For i = 1,2,3B� �$�$� 3,0�sM}*= by�i�DE_iE_0E_4 := \ee_i�\{�ai��G of��3$. Da�aR $E_\pmJme(U E_0)U� write.D^5 + (A60M>4)E_+4 ap^0) E_- "i�E_4E_0$� tm6�, ie?"o�L+ = {{\left(\bea{cc�x.00&0\\1&0\ear\e)}}�d $�= {{ zC1\\H.C,%�6 {u sizev�! !/)& 5$\\5H5-A 02�6� F .U� ���H^�j�B�h>� � so�}ap" 0$. & w%�-�\fO if�9 only!��. . Indeed,I�A� $N ��5%-�e �4MV 0$, b�{��{��}���matrix�$$($..)_{11.�T \bege�bel{27}.[ ZF4 = x{\ol{x}} -� �,0, \enge � w�x:=iO6)� \o��3:���;. Choos!I-)1$ic$ �.��jnd g choiceA resp� w�.W p�. Also,)^*1%�Ig�ů$ reaMten as6mm��vSx &%S x}\\ 1&1`!N}� .$ ��eq.(\ref!�)A�� $ Ri��6vdIk-Es0 &Uz)$� -�- 5)^2�0 - p1 2 3 4 = 0,$!!�q2 ina1V�� Now�f &  $ g\in$F��pin}_+��T{g�� \;|\;gA�gA�1\}Ap%k�AJ ����3s $ g��6F:� a&c!�b&d:���h�a,b,c,dC clt� 3or�o� a"���"�I��H���#��dR${t si}}:\FI \ri %^SO1]$��L by its � on>by�a.b(g)�pA�ga5 ~g}}^{-1!� t� g}!�In term��5� s (��A[�t$)m��\6� acts>�e�$ asIm� �F�6�^�>x&��A\muV:\�+ d}, c�@b a>E�bFixa�H, m��mappe� $:� :|Z�F����1�Z�:\Ŧ��RDelta:G,x^\prime& x'S {x}'6�'>!,$��8x' = (ax + c)(bd)E�>3�� �8 0(w }}��\RR.$a�Ş sens�� ��a�a�v"�I�R��"- a�pe� ���, just� aboveO All>r�ex�d �S�lya؁Z�Abe�N &5,�,hes}: �in{"F!be,tabular}{||r}\hline k-!Map&E� M  ���$\\ >  T8&$"�!�h,\;\; h�y5j 3$ &:$:n1&hA�0&12�$}}| D�s$\rho x, \; I[ $&>4$>\sqrt{4}&0 x/b�RH.�mmg x �v �yomm�^ 6�F >=�0&.]b�In��-eCx}}$& :�Bq$0&-1\\ 1&0bd%�9 ion& 6�x(hx + 1i�E A\ty$&B� B}� \ h: $}} QM~>$Q� F !unoi�% x-free�ic� "aytrivi�%gen"\hB_e+-1,3�%o�$�$, � J GFiY6��!vsm�BV�2� Dtackrel{2-1}{\long�}:� \v/ 0��Iá^*�xt&���laN�)L!&!LI I d,Q !g_\mu\�= cle$8�ing me"� :�*\g�8\g_0\g_1\g_2\g_�as $Pa� 8me(\g_{\mu} + i z0g_5),\;$ $K +-\me -->- D P i @,� $M]\nu� o \nu\wedge o).$�y2�commu�"�s�q [�, PG] &=& 0,� [�, K H  [� , D] $nonumber\\n ��2(P_{q }S w-():� - n.mu) � ��2]KF]=B[�B[�),� J��sigma�.��mu%nu (A  % �m(n =  K #.���1��.�21NA+D -�mE:5> �MD?=A mu,\q�&%,.&-  \eeqxiche� invariantm#�-�mu E�E� $D0D$.&�T"�%s geoS*v!ialq�s}*� �(��-saniscus���= f� � �#&�$�'�$�z��&�#, k� el8'>:� , vij�'"first�lK�!'s ',�eor!ory,B&*/wa&B(our equival!/.�!�is.o" ����f�,�wa�"thez p>��'d�h) �eN�"p"��m)A*h %�2-F�&�%>� } \l� �}Ņ{\it reU,|(} $\eta_\xx� �"C*\# � $\xxj  M dot��coq8 Weyl'"�{A.alw,beMAe8$\frac{1}{2}(1 |��5)\ps.�!�a Dira�'$.} (DCWS) JPx6Pɮ Ns ${0, \xi})^�aiL}��kge 1%31j(g_5\xx)\Pi.x g�'] ��a�="�!Q}�-� � A�>i�"i , :!B suita�6�=ssQ�L -��e� �a:Be differsi�a%�6m by a $�%"� )� �1,2I8 3$.}�|(��Q  ,��zM�m8} j�bU[�nR&i_2i *L 0&i_2*`!���R@-�Af>� vec� � {^c2���{0\)�A��VIxi}}��nge #2�wTUFz�x�x^3 & x^a ix^26�-%0 -1=e}}�symbol�!%^c6 $\HH$-.�� x$ɤ $i_2� i\,\�/bf{1}_{"�f X {�.>}Ay��e% {\mr�j}= ^\daggerL � 1p�A�22,63:4)�!a5{[*pKU�as ${ �(eta}}_{ \xx)� �:�� 5)���6�KPi}( !��� . $�(scalar��1 �{ �}�) $y�7ex�ed value%�e�\ VNect�y��0$\P�� ��jrE�mrġ�+ 2� h  \xx^�*���Pi. �tenso��50!�12]) \PizB )ek $q ,ű�chi�-d1v��'�#� like"�QKps xAr$,�!�*�me�,��. It &�e" rpre�&6%"$,"81p!B}R'/$he flagpol�� q$, # "*�&O,: � e \zra��m!Dq��� \xx (1�R)q��".�E�F-D(R4i�aV1�l&�� �%8s� A�� m�s�/ , le6�'��*$-�a,Z �g��jj} J_{A�a�:=�olm}at}50=E�{a E�(!-%I�01 ���prm�dE�&� E)b%�pl�5��com�!'J$n Fh3!re�*d!six, wu !'lW�7�-%gA��!iU�� J5%��. PP^3�"�36�3U(3&�3U(1�3$�)b4,-�,harv�- + qK)&* inn�%-;}`�,r��on8-�sam"^ , buu 3(ng distinctIp��ao,��5�'�X{�!�)�)�A \mR'A.$�0 �is null!�a�&} x�W \xx'�J0 �pe12"�"fix �  le�5A�^{I(}$ vary. Lf$� Himi.idempot� (PI)!�j_0�$f_\pm:=2� +Q#3)`PI��. S"q,.��&siE�*�� �al!� e)fMn�oe^+}jt f_+ �(-p$��$�ed�ist$,s�0k�6,�dir�+su(�w� �4*s4a�w,�7 s (>� ,�:� ,&� ntra� �*un-%�� ic2�e�eed2#a�a �<veV�4�c5" $f_+]f_- �%�!X�(ZPauli� _�!M�$rocha,wal12}.}. "'*a.5$ a� A(6��X\^_(Q7��hy xE_4*big�"_{k_}^2;#^k(� ��)$.;� x ��`�an�"��\j2�-&Uf�(I��'6�!_�$UI�&`���o�;d�$$Uf &.;.G �E"+ {In "i ge�9clear c�)e�/j;���+��!٭�AQ�$�3a�D,}b� of n�!K adop���V �u�b)g).}~!\Pi:L_r!Q= "s ,!b�%-o"�)12CWS. .+g04� �N-E�A�_E�� &%�(�  �/r�)��$ � l�*ly�bD)� �{0}�E_1g g_{1N/g_{20}p E_3 #3�)!��(4 5 -3123}$ �zuseful �" rove&%:!�r3alter�>ve2�A "�$M})�{%!aJ`YK *kAl"� &� Y{�=,!+Fx"�'"q i�Pi � (x^�*I,0�*+ E_1T* 2E_2 3E_3 \ap^4��2�\ x^0(e� 0\Pi�x�Rg_k!{)6L0(!�N 4\PiVe"� �o*bg�Y y+qm  }�5B�8d.x "�"�A Z2.$ �{!d}}  �lU}} =� U}!K x}x�0 0,$d!�*6$�+6鵵�e�R* ($"�"��$�2\*�F' I *y;W 8�? ��} A+�:d&j "-` 2-� $Gav�i\mmu\_$ ��mmu_C_C)�bt}2& '�!�<g�j0e�e � ��#u$.t1@al"�pA.< ��>_18..  (modulo=w0) to a familyycoplanar ]��si�-�\61� Z/omega 6� a maxi,#tot�isotrop�cubE�}$V$ suc=AatS1R� u^C%{  �E �$\{ , $^*\}=0$. I:�@�(%�Dexp(i\theta) p \om�B-6^*$ F:=Gh|_{ 8�A�p( > om^*�rm Re}\;>-ɭ!M�"�� pe2,bt}.�C,I�0�;� >���E� {\bfM�}%=I':"; q� 0)is%s+ to adapt>Bproof!��86O� "�"F<zn�:al:2J�I�s},�i�| �:. Bq?fi�M Em3�3sai be \emph{!%b6%D.�C�nseEXi_Ee�*\ap� 4CC^{2n} \, :\,��)u!�0\�#9�d C $n>�71map)�a)� � �+$%�$�� �:o<.� ��!6A !�.\ s ({A� mod}� ^*$� 4� pCC( all��aZi��q�s ^%"$.,�]�GD�d��2�:^D �� �O}(2n)/ U}(n�*�"m�*qC�=6Dsb� =� "Y��of61�"ly �?eET $n$-5�E���Ge�Adb4�E��&��4)er �D�*AE�us �E}� , at�sDw;9�*:oJntify ('*�5atdMlthree,%�,)�hKuI�"� a�$�����ey�=.��Dm"DL�/-?#E�!m��of�� ]�m`�� ��� �� \@]� �>Y'�!��SO(9)/G$YriT:)� ced1�>�WE�.an&� ol�[6aof harm@M����Calabi-0M6&�M��A�3 �arrow S.< �teteia�he�K��A�; V�tV5A1illustr�J� � u��$N��so-$N�**N� alex,wolfI�$�Aoci�E.�Li"�))��*rm E$_6$�SU*�JSp(1)}H &7&�J12"�>)8)E$_7 �96% F$_4%Sp*B K�Ef/��. Mor( mKKA�"PL2 y�Ey beyo he scop_  �C�G (seeM 5U,guna})�L! lso worth+aM� �,RMsp�Hap6�.�in|ernC oret��3s� �H�Hilitie�� fu�edvanc�:iKa�psk�MKa�eck� c�9extend�) to $�C-SPzEJsr2F�_ e2�s��e6Sdu�!CJN �N\�)�&y ��be57Q2X--u!odevelopAah4�ing�.r2��cris}�ami�fieldO�aP,i=)�le6�!�*�O�� ՈConclu�( remarks} Wx9& ed �oin^M-='�su�� � athbb{C�= C\ell_�", j�%���&w�A�uZ?t_Q�P�P!u&�E�C7%:5f �AKdjJ�MB�4�>�&A�-�$.����cE=�� !V��:& a�~8A��T� u� ba!K� �K��. A#O� �'����� & ��:�4)a��the douAc cove !O(electroweak� � �APeiin�q�a^:z6.zNy!�� .�p. y�2Lhebibliography}{99} "� \bibitem�R } N.2 2 L. Motl,��Cub�G)G�*s�Ri��R},��JHEP}�x04} (2004) 56 (hep-th/0403187).�b1N�E.�Rten�"I��ravituR �- ���� B�9 .� 6051.�c�(}��3 N��T�SofRoMIT P�'<, Cambridge 1967��OC. ChevmVy�itQ &.PN_4Columbia Univ.j0New York 1954�D=U2}2�1FADt"U23A�-LQ �<N=4)r(-Yang-Mills� �!�QV,. Rev. Lett.M93U11601.o 2045I�M�b4V�Pa�a re higher2� ��]f 92436cette} AA�tte-{DZ}?DW�6$ng massles�Ples -*� a�X}, J.iW.VW.Ie3Q4, 1996e� ��T$ M. B. GreA�0J. H. Schwarze�B�S*VVI}, vol�  \& II.t.! 2�87.�b�R} W. B -A�p:�-A�b ���nC,�$(G�.)Q�7A.u in %) ics,%8��Engine�hE_PBirkh\"auser, Boston !U5.�*N I. Port ��mX d�DC"h"GroupA7y�U._19vy_�R}!�Crawford>w:��PN M�>O�n@orentz, Poincar\'Cn �ܩ����6s}Mt02} (1991) 576� ���S\} R. Ablamowicz, Z. Ozie �(J. RzewuskiZ�U� ��r� j�2� 1982) 231.�,v� t� o�R `, mex�01 a� ���n� �Adv. Ex.I�Ag5))(7) 93.��"R.� �11����J. E�m�-�8},!�67) 3456^2%�%�W. RindlA��/ � Spacene�.2: ��[aW0 m�yaDY�b�82�cru�"$Crumeyroll1 O�MgoG�SyKtic)c�WA� }, Kluw� DordrechtaA0.8vah} K. T. Vahl� )Z@�ber bewegungen| e Z-5��\. Ann1�55%�02) 58!�y9<}e=k�%Mw (1,1) Per"�IofF��Ge 9 d (anti-)"�O:e��!Ph.D.��3)Ny)bt�Ben�WR. Tucku3An .ma�.��(�>� � ic� Adam HilgYBristol��6�a�� CederwallMk>� divi 5-7s, sp~ %�m procee�%rI;.� Netw Mee$at NORDITAa�Kopenhag�g 1993"( 9310116� � P.& Kobak�W�ys, nil�*orblA�2% �edsa�P�Ndy'$J.C. Wood,Q�H.^$� gr�5systemPAs@)%�K= RE23}, Vi�8,ycHunschweig/Wiesbaden�4.�Y��8Alekseeviski$\b�R� {i}}:)sC^e&Re � " Funk�4al. i Prilozh.� 68 ;� �[�V.BctCA�q�=106.�o��l1��{P.%contact*�!����b � ٕi Mech�1� 1965) 103�B��� AE Clau� $. Gunaydin�K�1shCRahmfeld�� Y. Z�r� q *qu���:F^|jUT�I0�1999) 19Y�9051122 �C. Drapen $A. Elduque�M�_~$F_�6to ear,�pt-�L�nd Jord�l3as irR�!�S!�\May 3 - 8, Guaruj\'a, SPE�zilhA end{>  docu�  %-�2% k_\f�[reqno]{�lez,\usepackage{� icx}2ams��,amsthm�*�} \addtolength{\topmargin}{-2pc} \6 exth�d}{4pc}:>odd MB3#JCwidth}{6 %�S�i�,i� ��)in�� duciLfi(�V1 :#)tardef\bslash=`\\ % p. 424, TeX2j lN�^izr nonboa(,nonitalic) tgbnt,E� void font <�! titu� war3messagesR#th]iN � @h�3���places5- od n� bi�*ZfmxV Ar�f. \new�B,and{\ntt}{\n��\tt�&} 5 ) name6:cn}[1]{M1otectK-C#1} ?LaTeX M`JEpkgFF?FiXF{fJ{5environa[J<envZrH\hfuzz1pc % Don't b)gtoR8E= verf�2box)�ag�Q< 1pcM� � em.�s %% '�W8style{plain} %%G "zfault%rDem{thm}j em}[M]2#,cor}[thm]{Co2 ary}2!l;!Lemma6 prop ?Propo�]6$ ax}{Axiom6conj}�jecz� � �y�69defn}{�Va� 6B 2>*}{R�7>x/ }{Noi�:; thm29P %\=6$within{equ� }{-j�.:thmrefEL� em~�RE�2*sec*\SZ$leN%�L6Mby�!h}{\mbox{\rule{3em}{.4pt}}\,�A� � .:KAF athcal{A})m�{\BB>s�5sigQB6(XcY}{{(X,Y)>4SX}{{S_XB2S_YBX {X,Y}FgYyP{X|Y}(yBoCw%��K C_#1(X|F�G}{{GRP~PH-"�:$X=$B�w!$��,:: wh}{ha\DeclareK O�{\per}{�OJ cov}{Z@non}{^@f}{cf^>add}{Z>Cham}{Z�IM}{I�)R�0esssup}{ess\, ZFmeas}{Z�sega�gQ�\� rvT&�(providN+teTaafa [�!��6� closBdel8er:AlEn�?�9� P���an�2�T$|rd&6[%ond� Iop�#al arg; �%5toŎr�a�^qq siz�o�= GvL ver ar, e.g� val[�- gr]{...}_6~%}[2][?%]{\%$x \ifx#1   I.\fi#2q1�En!X�4�in� -bar9os::�nH{\C\l`�\ f \let\abs=��ert-�^w\-*~~ Vert.~~�FetT � R} $} % \title4{On verg�6towar-r self-simi�@�gA8 az �wave ѳ!t  study}��Lauthor{Piotr Bizo\'n"�y"!Q}\;�< Tadeusz Chmaj6(2](\,63 \A +oW \small{\ 4it{M. Smolucho�oIn %�ib, Jagellonian&�y, ReymA�830-059 Krak\'ow�land}�D6��>�8H. Niewodniczanep2�Nu.8 &1 Po/*2Sci!�s,�2 P�:�!2>�Cracow�a��*0, Warszawska � 31-155brX} %\date{July 17, 2002 E{ makeEA�b�!ab�(cA�no�6nt#m�*it-�proble�;asymptoysta&�a 2�att�o�*�G� semiM�radH6�.:*@)E�!�& Q�� 5+1*�" . Ou=alysi(�<F�< step�nS L �9"6�r�< �iperturb, s-M�u�@�lho?&�inued TJa��se��� �m�H*�@er(lWaK:� xQeigen�!���. accu@f:pq%i ynamic! coF�$5��Ad](% � P��?ionAaSN�g eR'=�of-ap� as s!�A5e[Xat�La�Ji��EM� st�ng�%�,I�2al data��rU�s5nA6�I.�[su5�Z�&e would Et*'�%'s�6WZ��under�dEFmechan�<�/.�_\4 phenomeno&se kinAc�a�Y&��@�zll- eoo2r QKu�� s �=� glob!3issipE�A<|gy+ A"�o>G!�5�,�p�g��y littleEkc@ forA��w��]&�lo30R� isb* disp2!Ia�is�+wkFp�� alytaX!� numf�pR+= <���~~�6,<��1`}2Lm� u_{tt�Ru_{rr \�${2}{r} u_rn70f(u)}{r^2}=0,FS -$r"59�Yv�4b?$u=u(t,r 4An$Q4=-3 u (1-u^2)$o i�Rm�e�!걃E�.!8ly�>meqg^� $5+1*5s (*W- cta}%Xederz)�Q��pe}�at ou�Enys holI� morei�al&! -|7&\3 !�)75n(2s8�xco:�?�.F6ū�*f�i$32��|inB�x�^� "2-%Ae. I_+� .�5cst�8�wP2nd? 3?in �,)@t� Q (kEcpaVx^�css0}�I4=U_0(�U)�D-^2}{1+I�3}{5} B�i�$=r/(T-t�9�O� ityU�I�T>0E�a�t�T(actu��, $U_ !��*nd�G a countA� �a�2�N sJDn$ ($n=0,1,\dots$)%G�K a�7�4(u�b m y dob%m2>�sElN�).�/^�ssblow!�\E�al_r^2 5�\Bigr� _{r=0S im�A1}{%g^2F�!4�!-��<comes�guu h�[�en $t � a@3T$. B�e 0- e��A�pag�7,�T�ETtrunc!�����,��Q�Csmooth"��Dv�xup���o 6�i�!@s u�t�;(aun fac��1N�%E�not�H�e� exa� of5.A�/ �hI��im�axiQ$s cn� ��*� R6�an* :��Qm1Z�� 2", %[suffi� !^lar�c 7 do%S )Ra.T�*� $��(t,0)���sATADneQA!5�{i���! &� AKfof�� s unSs� g p�,)i�L.��}��Yim_{t�}��e9 r��Cqni%�A�M!a,9a� coord$}|tau=-\lne�%ErewJs��mL ��k $U(A,� )] B� `M�p,rho-tau} U_{7�`  2Eg\:rho# -(m )(-rho} y 2}>g6})  f(U)  ^2} �E���_=)��qof2���!%hr{ � .4Y� )�u �.�=�� fty$"�!�s�aryy�>� �rF"��[�andard�ced�w�ek �~2 -�1�)�x�T:�!p )+ w=��CeglT@�e $O(wF I!weR8 a��F�qy.� $2iBR�3} w6N 2NA5E~.NRN ]N'(U_0]QwVSSub�!2�=e^�d � v)[/�$"� �)!E !����%Q�^�um2< v''+2a� mbdaej v' +!e( -1) v + �V �yEvJ}�^��)�  M = -K=� 6 (25-90!^2+33 4)}{(5+�@ho�r}.>�W��n�1M�5)�s!B� $0\lMA leq  K� J�6ior� Fp�Blq� ��� $(t=T,r=0a'>a y��:4\ )֑t�&�M�}"� �E� .iC9U���s $ted}b��p fY!�y�sa��@� &. Frobeniu�>:in�|Bf71Mred�Q<1Yare $3�$-A�hV <5�I��A1Fat-�0$gJ�p� se�{�%c?� ^�v0} vXMsum_{n=0DXi��} a_n�7)�Q�I+-\�g a_0 �� Fyi�{ est5Gg�Z*I%$-�A3at =!) ��v0���%'��g a���& $. AQ�Z�`sA�1$,%VN� re $ z1Xy$  Sas �l D`�m"_�te�/��� ;F ent���c,j�bv12!�1��Z� b_n^{(1)}5� � )^n,)� v_2nE E2Eo!H)^{n+5$F�T� -�!YۇГnNnu*r $0<)�\��0 I~l��Nf m[!kE$X $v11�yRA)OxA�4)��/i� T eren��ʅ1�����s�� , -�{-jU�}��J��)1�2#l ���V.? �� � 12�Ys ivel!��d��� J $n��t�compu � Wro?$a�se�at mi; �F/2$, sayve aY%_�M&� %s�!2 s�J 2)a>though2�-j�.;E"��on�a)"cْ �E�\ very cost!-e] �v �neg� � \͂, becCA�.�1��:����� }slowly�� �A��I\;'  fail�#�a�N�&�.�Qt ������1domin�"k � a�#V$negligibleRgh��h�� $�b:b�7&�5,gle=-90]{wrof�Yp($W[v_0,v_1]�=1/2,-�)��� fig2B�"Q��J8M�VI���3Bo#_sh�U�_e+e]�"i�A�%})�a ZA3t>_% �keyWRa���CinI�1�|  1��"? I� � .�0%$)$ �a�*�&9 expan��:�a_n$. 26J.%.�p�xBw!a~"ur-� recurr>  T�jB��(s $a_0=1$ (4��a_n] a�$n<0$)^4} p_3(@_{!  + p_22 11 0 n5,w>�:z narray*} n4& =& - 100 n^2�750 #+1650,\\ ��^-2 %+ (100M�4-130) n +\! 25 ^<�3 -7M�M84qL2L +378L 3^2+27 +618 ���36H36 ~ +90)n + 9 �4� +54"5 5�$n=-2$Ah0,�_QHq�%�0-2} -350 a_1�� ^2+1 -570) A)F�$��I =-1P���o -90` 2 + 2`2`64`�.41554 324)f=Jc%/ m�i)�gnN <1�\in RU0duJ�j>1r n 2ger�^�Q�j�Q�[!�nS!to����sН�g� rg� f� �" -)E })d be v�=d��1third� eA(e�[&�.so� �[� ~ 6�.*1+#$n*`"k$�>~x ��� ,Ao�!, %de}C�^��� 4} a�&m n"�-2um_{s.� \alpha_s(}{n^s} S2)@im�0 ft(-X3-%� )^n n \�c2)ca d�Yvd ^{-4���3i�Lu } ThE>y� 1��YX�p��QXE�eyI.f aF��@:!�%�)�c3 c ���+c@ -�2)3&d)� 3)}.a�nd.�% I53*�  $.o  BaM#��1}}{a_n!A fOxaI5� n}]� 1 \7| � {as} F#B&-.Jm߱V� (in factq�a branchy �. �� ). O� e= ha6 f69;t? �JU9$""$�t*� � E#thr� �z� �� advantag�re=�-eZ�*M =0$ "s��  ula-3�}) j��{�  F�f��\"P�f!Z�%FR�.to��"s 51i2�e)�*w r�to60"Fdsu&� g!�:�l,��� �^A.�2�6� 1��6�>� = $is"|U .!�` ship&�[�� N�s�RrItF�Sf(�6at�@ aA�efd (r+R f(b8 gen3term>{n A_n b Bn =FY�p r_n= ./b` �"� )�e�#� $$ rU�s��$B_n}{A_n+r z},$� �iai�e* repeX\ly!)�Fj r2KA�$&'"* �inch}Z� -} \;�V}�  -}\;��B22 ..B�AA��?L0P}erle "X�U� !8�>D&e �� � ���-� �&�B!d���JR ?9���&ʥq� $b^{m=�� i.e.��2���)n.�!R;fty} EAQ��� �)A"� $Ip�]ov=F�Y���^�ncϡY- �/s�A=|%�/n:*each ;f an�+y�opp�'&em"�?0B �k9/- ns. Ho�2,Qtus ob3)=B� 'fexY7=\�:(V  [n+1�#5}{16} �-1i}> � c9�of��b:�(a<��d�!G.֞'��s]hU pUqw�- rnwEm �.EB7m�bn��n=> +*!8 n+22. =.}{ >M2\;a_n>La ��vB�JX,�� q����q ��q�b~� (�2abK<( $\gamma=5.�/16.�" n&= & p �--J6V3+ W})bc}\,-+e �n:\��� n+4VC�, \\ - &=&�V�.H�\,N.1gv _���^SR�aB�fw)�)6f�� 1  �\b�|6[6� 2 S-�V[� 5y u^�h&`>% �"B� A�� C.� �1)}+C.� 2} :Y/k,��^� c`���,q"T� to $.�"� �� hing elseM<� "�!�V#��A�R ����Ѽ�M�`#� use &@'3e[.�*��2���0$A_n=i,/�Q�B*.�.�-2A�nd �bn� ��>� b_0=MGi�"�B�}{350}��96+ 152{80+ 22�"- b_�=a_F� �UV8�setK�17(�I�@&|)f 9_5�B��w+�b_0}{ ��p�l 96+ R.�W- 1B%1I)� -1:� 0+ -} * D*9 J %"� "�>� ; )&)dby.��E��2��". "n,�K �d� ��>"'rbitr ,�� down� ��Vst�=AkaN�4 $n=NiA� (],*K> $r_N$�e roo�RAKtransc&gnt�&� 6�t�f�'& 0ly�tr1)*�}:4$"�+t"L�c|c|} ��&v%& $1$2� $4 5$\\ & �C1��_n$ & 1 & -0.588904 & -2.181597 3.570756 5.043294 6.486835T �  �6a$78910 1>��6� -7.912777r9.298265 <907103& -10.7924 � 12.153033% 13.164487��{1Z%mc 5a�2 twe22�DsC�)�.�3W��h-*�;ABJ�la0i(freedo�4@g��h+�* $K5� M9 _Q�Mv{t'�@� b�$rp-*"�Ji al i�:�1o�4 �/ $ --( Jn awf�of0 B��F*&b0��&c w��7;  3TL5r�$NotJ at,�$ngely en =Z�*H4sa�� �� "�C&|�!P"P3�Acc2g��[-�MD�#e��_�M ��c:`986�5� *z:&�B-dsh%�b�,scl�d�l8�^�|4} r =�8')+ik=1}c_k &�/_k�/ v_k ,�/� &1c_1.515� 56�"�a2�1[Bm �.��$��~�4�!�?Ep�66�Ck��$c rAL� N�.� �to{"%ty-u��)d) m� d&^�'�.)*A8 .#N �. 7 �i�,. 9[UFi&RW�!d�$CD&g6�i��$t�,a"�=�:4Atw� at�>�5 $T-t��VQis!&�l66��stB6!�6#�e agre�'w�&=k-I%B})r)?r��rib57of�gs`es�P;d�5%s[%qF  }[h!�k#6�w�V ]{f1`#4vskip 0.15cm �T];�" mA=6kH.�� $ !$=:a�*�'akEF5| "OCv��I�-O�r! e �l $ 7^2�D1D(=0)+16/5=2 a� !{-a_ôb .,we <<�#�6��u.�log-logw}Bfi B"�0s)�Bu��,W�"!2$=-0.031436(o _58803� gG>~� �Q)��5 �'2�' p}=!�y���$a&-: �^e�6.[�@�4'�=mAH%q P�P���i �<��&m� >]:%�J*&�+�($u�Bh$M��@)s 3��b�8�� �UE�az�o�? 4 �A��$n earlier 9_fFq�V�; *�%yB�before)&S fi� ـ�l.�(��* ;(decayed. I�@�  s�y &�>�m�funͪ&�"6}�&a m5m�bt-� asheIj)B���newpa��=( *{Ac- ledg�Ys} <�3�s bG�AISpart �KBNe@Tnt 2 P03B 006 23. PB aZE+0friendly hosp�[t"�>Albert E@ ��&LPdur!Dvi�is *b,^b�)t>3q10] b�mH T. Cazena� J.ogt�gQ ALdi Tahvildar-Zadeh, �h�Hgnri�ke�_60j315�g98� w� P.8R"fta�Q.�P�ya B� bf{3�4 1893 _2MLbt�b�R�$Z. Tabor, �Q. R�oDN 64}, 1217�o2003Pde} S._pElaydi`JrdD8�� E�s} (Sp!���`�h��>� -d"�_&~�:o_&h_%:�_,10pt,a4paper*�_%�� \u& `a�_B `#^gD6+`E_a�#1 Wop{z#1}\nogB<& dint$display*\ t�x'sum^'sum'B^()inxiy��^R VUn*J_PE��}fT% \re. t�5 !{\Alph"Y\} -fxR�Jer ��\6 ApOAix 6F.%hla(%#2Tadd ents� {toc)Y �nHwt��}{0}\smS}{16�;rkB*^>2KIJer��a�def \R��ma�x R-� \CCZZNNSrS M {\�%DME I! bb{EHHPPPspr {ں} �dˊ�ia-�.>nddvX\ {% !�:�Yt3Txv5%T_ �eho�lt �"^D>`OP �!�!O}_{\h�K{-1pt}F _DO4frak{D}R5�dirz {z U 5pt}�J $/$�/ w {w�/ u {u�/ v {v�/%�di2.�/1`vu�eta&4 &\raise�_8pJ^ tiny��e�v� {�jC6NCDT^Sܜ Font{ltrs©8{OT1}{pzc}{m}{iA�V/a0MS}{cmsy1?V0bF0b}.0_ � {\Ssa_ ord}�a}{"53} ^..~|grN24b2mpZ2B^d�2nfalg>� }{"6�E�� alg  [��$\ ;9�c) �C ext{QC$*aVVA��%Vu'Aj��Ahhm�e�hc6_{\�`h7�`ؽ� @Q�hhBR$2LLAT {Q7DI�yQit{di�� \;n �it{k�o�rdia!�magSO5SOUUsosoAu�Kit{Au� \MOD1mod2�t)�it{a1SLSLGGRѦit{Re..[I.Za=?Spa9?TRwtrIcot!9I�rm hco�S!VE�.�cnj�D.a^�=�< +F:,f-���!!N%b�M [�r(Fpt>ed ��)}70�fQ�trn {�M� mtrx!���-3Ũ�2%��MINK {MMwfuA�wppwf6zY�& Iq� bb{I�WM��WRw E�wc>� {E�V<mm#> ��AV2b.2bf�b�1)DT�:.� p�?bf+ i+.sVECi�%5opa�\� ^�m9�mx� xi1�x�� VEC{5$en�� cmu B3<cn 2� aa {5 bb {�%cc {C'nOnuvsp���op{�_{}^{�HS-�!���XDOђ�SSCTqmgr��ggV�Vol>!�6:� VOL%|0_��0eZ �MEA���~��E}!�] S!V �=-�:x�Fr z!�*.%2�#|_{\, y��Z� \(#1\)E.Dv Q2]{Qu�(#1}{$\,$}\!�a2 a�lva�\\la�< 0 \! |�,. \!Qr :!-. 4,|F0 9\r[;la�5 {ew66v|Ar~RX)>�a>��v�+!�-+N� P:.�lIo�1!҂�.Er Er  V:�E�LB!\!{\,NM�Q�_{}n :a� Z�!TRT. �N:�Vl-��TM�|Y� O(�.�i1�U]r]� %�ֻ)])"�LA �M3� *�   >9�=.�7>�" �2��8�I|�.�BINOMIAL� {#1 ݬ #2!G.+gvspc�PF� $\!$:�mr1��kun(tm us*�r{plist}{�""�,{0}� $�(�o "�9��7@#t�u!9�u1z 2e�0cm6�sep}{2Eu2:toph 2�!�F}{1A46istpar�h}{1� } }{�U%�)P"�^�%k1�2-&�6,*�20{1:421J.-:/ 0�.*�[1][\bf%6�)*�.\arabic- ]{% \med� \n�Z�8bf{#1.}\it ${}$}{�to58.9 F �2�p*�t�*�t�����o�3=�O�����l�u�^t�����co�v�C�����m��it dvV� +� B ;fq�� bf EwbR�-֎ Z���Q� ^� ғe=v#�D�&TxV�3�,?r� � �rmAJP� rN8A$ $\Box$ Q FSkB[Sketc��h/Io�i�#"�wpr�}��^�{�5mmF|rm�%exV%6Kbeq}{!"x ��e$�^"beqjbV!e6JG% H*6>#nn}z \\> mb%�Psua�th{c ch��8>�y bold� $2>bf Fit� �>FFJG�Gscr �|�II�O>xM�XbX#1�O�>J��@F= F&� m�mrmi�eJ�rz!rmp~5$:{�>>��@:,FF%5F� stmry}{U} mB�De�(er\llbracke"s"en8"4A}  L"7� u�Krr2KcloseLBLMF�� -�D Cs)�� �}#� l:Nd�@ F�"��{N�>At� H� "&1 $#1$}}{ {$#2�. � RL7JLiVLsm.��W{Q���\"9��Fb ��6�nfr � z�6�R�L$/&r�4�5&2 INTG)�sop{�%&eIA5B-�S$B�BrkAv�Ev=�@-!~� J 0*|^/\Btrcoset�%*�1�1$}=y{$\back܅.!O-�Ppod�# �-1Ap:7�9sp� 8A�^y#�f\(+A:$ LECTURES 5ON ELLIPTI��(pc FUNCTION %AND &MODULAR FORM ! I FCONAL "IEL :THEORc� |�( Nikolay M. ov$6� 1,a}$ \ \�)\ \ Ivan�*TodorJ0 2,b}�~z� �izH [�^{1}$] G&/+�2|{ Res�+�*0Energy, Tsariܟ�sko Chaussee 72, BG-1784 Sofia, BulgariB:�2N� f\"urti-�Physik,&�{�� G\"o�<�en, Friedrich-Hund-Platz~1, \linebreak D--3707729 German��� �%/1\toda� -Qd"�* \&�{J�f��y(Q�a(�< (��p[1]{e.mail: mitov@inrne.bas.b�2-2-tI2/, i�ie.h8k.uni-go�= en.dAB8)k��ai� ab�|A45( re�Pm-�.i�of ell{c��)s, ��afurmI5$\var��$--�* A:l�od, devyXmo�c*9paperu4�Fic Jv C":�F?�I]y (CFT)�K:9=?/ ap�ah}frame3.�A um fI%X y. Ma=fea��ssY lievB6oE8peculia���2D ($=$C dime�Val) CFT,C9�9n�!J Yuer�(�/q(6^�al)&�d�$`� in:ntZ�\1treat�/!f"j�a�=e�ri9$�� � �� >-�conש߁ex �$DY7�1T0qs \t 4ofF+Any0hE{I �A�"��9+�9+ Arguab�[E��:6%�h�j�!�!J�`�0FE��2H. ٘a�t��on/R Gu$S$--V?E(!G��u�rhalf--�d��q S \,�c,o(�� �(gin{array}{R{0" $-�# >^>1B0��d <Y H )�.4 \SL (2,\Z) ; �:A-:�:W�w�� �E1 n 3(�%R;,>0) \, , \ �{1.: eeq�UesE�%flow tem-��lMS iour!_us�Zvi�3!Hold_fand b �{ied��{%!Xa�=Ph�2)3�E1���pA~--~s"�DK0м�U!�a �s3:�?KW4 �e�ai�>'/ Tm��Ivreefold:!�!�� \�#[(1)]�ro��Rief�&EMt< � ��al  4z, :A�a surve"�3noA HF�,c6 (!`its))i), �T!ZS. (��a̗� ���>皩�#|��7h�X<�.)12)�_����a�YCFT�˩Q��)�Xs�7�6mpǰ��!�:S��rW��8elomrin~)�N0�*�� NT03WV)�3.�n *�d�:n[L��� it{f7=e2�corre��on��}�a glob5TՈA�a�(GCI)R�=ny �� �y�z--+9�x)�(F�y�oiodic)�.it{F;}AQ�rt:uq]pr�tt*{^�s"��y� mean kaana��Hamilt=���m8 Two-�a��D)ER?l�<�ic\d �w�w�=D�ave ��pAvnp7ers�!��7o�tm`|�:(of weight 2�6��� al�� gm�s�*�zY�al�R�7ntH!$��$.(Pde&\����:�=�pm>fbe usi���ee=2��K!�1�rݹ �dj !� %/4-2�CFT�P���C! .R��)]�ex�F (.� ��" �"Qa7in kJ(�e � �k) ``Gu�i���[ s'' �Ren�UAs�� . (Cn r۔od)�O �9f�>2��!� Don Zagie#� FNTP}.) A?ailXAxp�i&��� s' origin%� �!�8be found in~\ci|te{NT03}. \section{Elliptic fun0s and curves}(0tcounter{equa4}{0}\s(mtheorem}{16remarkBdefini J:2exampleB3exercis The ty of eF�@has been a centre(attenv the 19th � $early 20th3Pury mathematics (sincv discove };�double periodicity by N. H. Abel in 1826 until 3 work�THecke\footnote{% Erich � (1887--1947) was awarded his doctorate under David Hilbert;62;3) 910�@G\"ottingen for a� sert%�( on modularmI ,their applic'$ to numberory.}%G Hurwitz's.�Adolf�`59-1919).} book \cite{HC}�!01920's~--~see  K26}�` an engaging historical sA�y). T!(is followed!�a )�!q�Urelative dormancy when E. Wigner ventured to say that it is ``falling into oblivion''\.�.~ J$, \textit{A�limits�pscience}, Proc.~Amer.~Phil.~S7Hbf{94} (1950) 422; ! also%� colli�TST4tific Essays, F,it{Symmetrie)�Ref 8Ts} p.~219 (Eugene Paul-, 190EA95, NoA�Prize!�physics$D63).}. (Even todayL students rarely get!Tlearn t!�chapter�}k duringA irI�@graduate years.) !Rtopic ex!�!Q,s a renaissaa�in ANi�$1970's, wha_ continues� these daya�ei�guide , literature i� 1989AX D. Zagier!I�DFNTP} pp. 288--291E�0e proceedings2+of� SDLes Houches Confer�a�Nen�� ory ��P)� prov�Xan excellent shortcut iA�!subject;( further re bs.Z$2 be a focuE�9�al-�ists'�\ (�Wre�y.6!Ononcommu�ove geoA�y~i�~)DCM03}-%CD03}).��ubB�integralI���} If w��Xd not know about trigonw2��(first calcu�&ngEBf�O \(z=\INTG{0}{x} \Txfrac{dt}{\sqrt{1-t^{2}}}\), we would have come out with a ra%�@nasty multivalued� $z(x)$����xn unprejudiced young man might dњ��hat oneA �instead�y�Ainverse 1;4 $x(z)=\sin z$q/ia[ nice��single ��Vr��.}��mo�r less w�happen�or�� 1l6Cf�&ni�200�a;�d6A, star��� 17���John W��4s (1616--1703)a, go��rough!3 � 18.Ki ontribub`s from Leonard Euler (170��78 ]T Adrien--Marie Legendr��75�{,833), a 23--��8 old Norwegian,�pa�P's son, Niels Henrik {(18��829) had5 brE4 ideaa�look atM5��فe�� 20, meromorphic%6 y�vic. As�Coften-�s)�� p Q�8ies, Carl Fried Gaus!�77!C 855)� $ad developE�is�� V fOback  798�so��e t AP(the lemnisc�o(���0x}{\infty} \f�A1�@@4\xi^{3}-g_{2}\xi �I3}}} \ d\xi \, , \quad g_2^3 - 27 g_3^2 \neq 0 . \, \label{2.1} \eeq The B� \(x=a�\) can��wri' !@�!,Weierstrass'!M .� K!�8Theodor Wilhelm.6A�$15--1897);�P$\wfun$-�u� a��in%�Berlin � ures1862. SeA.ZD (\ref{2.2}) were,. fact trodu�.b�5o�q�9deceased��ian (�2�,precious few�atR E�AC,whom he visiin2c Am(844) Ferdin�Gottha� Eise��in!$a�1852)VYwWeil}_ s a��ifestly � }z} (2�})& :�u�} E�Ef ~2.2~Na})):A�gin& A8 \, = \, %�< (z;\, \omega_1, 2) \ (. .8) \hspace{1pt} Oqz^�O + \dsum\F _{ cP\inLambda \a�Lslash \{0\}} \left( R(z+ >)[-  \�!)mo uM2aMnd=where $�$�-a9H2--dimensional latt�Aof�� b-R$narray} & G<= \Brkts{12pt}{ � =m _{1}+n �, :\ m,n)Z,\ \IM%%J +1} 2}>0 }�& \nn & �v =60 �n%� ^{-4]��{3}=14�ZZ6}.�l��35�1GIndeed, � � e fi!�answer~.4i� easy� chek ; $A�$ satisf=  f order dif= tial  (VAbqAq yA`!�a6 4x��x���i {forx5u=-�%ay6' M�z]�. \�!�ee��3sE�� partA�A��\(� =1-x�\)��\(!(1 (z)\)K cond� %MI thir�,gree polynom!=$W$��4}�s no  ple zero ͡expres��b�eT vanish!쭼Jrim�rt,| por� al!�\(E�%|27gA� � (i�e cascoinci�  roots,�d UI1}) re�ksa:f one� i�M�nrem2�M# �rally," os are�I) it{r�al"� $s} $R(x,y)� en5j� �+)� fourth d%� 9��$x$� U�). AL A-- B CD}, \( \widetilde{y%l=a_Ex}^{4}+��:3��6/236/BA�"�b� {A�*�ARon? formU�Kby� Dmay be called a ``19 M\"obius}. Augustus ��(� 90 68�HphAl� trans�%� }''::=x}�9tw0ax+b}{cx+d} \��:h+ A}{()��,y3ad-bc\; B DA \) i.~e., if $y$�s � derivG (� a possiblt;o�!qindepen  varia%0$z$ in accordIX{ realiz�.�). We�� ��i�r,a΅��1}{c}$1_\ }toa���Le"D Y�� :�(2q,)$, thus kil�coeffi~a$xA�$BN 3). A��* such  �Qsa�W�Jacobi'6e Gustav ! i � 4Ab51���A  1828[eF. (by  .�%�) �(� to ��m to 6 �,i, himself, �.�V�was born�E@��enf to�Bre( Academy ��January C)%��s": 4papers, eventu�k��=�ad͹� ́"��em]&� 5#./� 484}). Bourbaki�.�� *� "o .3I� ��Z��Ŭ showy,solX!�A�Newton��ion ofEngth $L$I�ass $m$�M�� ulum}, $m Td^2\theta}{dt^2}$ $+$ G}{L}  '@$ $=$ $0$ ($G$ beq8Ea<gravi%al��ele�), is*� i eb� �rE;Z M% >��1 E�V~4 a�p.~77.} Řods $4K)$2iK' re�] K \!EI! II0| \!&���ML U-UJ-A�xIF�͜\pi}{2�F(1,2;1;k^2)��$F.ghyper7*����'>�� e1}{k}v�xR$N�)��, e.g.�:"1!�0~2.5; concernQ+�)�u s, $�cn} (i�)Aq )1-!sn}(z,!"}%�;d ;2:k^2R=j�EJ 6 of.� ). \�� We�-���display�some sim� propert5ofY��s��finP su�>�N7s ( coi0x plane}. BasA acb analysis,n4as Liouville's!� Cauchy.�� in--Louis #� 89\$7); JosephO{82� �*, a�� 8to establish fa�ac� non--obvnresults ��F�5H.�P�Hplist} \item[(1)] P*�!�!��anF� $f(z)� de��%�by ��B a b%gpa� elogram,. � 4fundamental do�:}�� ion*} F=�O(\{ \alpha\,<� + \bet� , ; \ 0�rqslant : ,�1 < 1�.\�. \I�y-'2)]�If $f! bounb in $F$�n$a�stant}. d �a� �!o at>TowholeU�E�(. The state!9!�� A;sJY�Q]jeI?co �J�mus � lC $F.$1 3= Ysuma�A~resid(ͦq�olC %6N%=[ }�i# �qgT)#,��N"? �u%�ary $\0 al F $�� �esB� *} \doint&&?} A� \ d9 8  0@B!| !P eque� �=�$. (By shif3 ( necessaryE5� �pposit�!des w`n assumV!Hh�� !\n �$.) It �!!FM]3atS st \ $2$ ?$\ $in\%1(��"� i���މ24]Let $q�a_i \}�%�!�m nd mom>E' $n_i0v�\(a_i�A(\(n_i >0 \)ia5�c, < 0B A�jn� Ń(3)� $�f'�( z � )}{f�=f2($ gives \(\A��=s}���]M�6��> aN`��:�6a�qin�a (1.1.2)!ZCo�in� F`!,� 213q #N 7{!� ve �$ Ŏ�!�$w�genx }wR�$f] >V $. I�!wu<%axFZ1�a�A�a�ue� 4f_bas0} \Su_{kw e�1}^{K} s2S_kU N_{k,s."� � -z_sQ ^k�a�eq��\(K,S�d�S_KNN\)A�N,N_{s,itC V in FI�k = 1, A K #s=S_k\))G�VN�J re&�AA 4(e��F,} RM = N!(+�!�Mpfun_k.�!O;�!5"�" �a-d'��BI;R01� $ ar2 (Th�$ A:``b�"> " ''A�&d l� ,to Andr\'{e}l (190� (998) who de9sdm $E_k$~�#ml�} C�%III l,ly speaking,�u2�p_)} JY~U!��!�)�A�!�L .[z�1[m#  e'~�)%oab�ely��v� nta� \(k \g� 3\� \(z \nota, �aand q�p_a�E {k+1� �`~ A^�-�� �\di_{z} ]k��^�(!Tdi_9%y o \di} f, �5MFo)�2\) sh�$speci��OoPofa�� or8 ternd$ly, add re�^izE�=. SG�' <�!a \(k=~case �n been used�S0 *d� � �*)'� u_M"w ;�Ak1!�Nq�.�zfun} \"�-�-�����z} �N�(��} >}+�QzB1} l %��"is~� >I!9I. NotA at%:$ -""-j6}) no&�  (due��!uab���y~(2)) �any li>&u biAUon \(\qop{�}"5 :Y} N_{1,s�\(� ( z-\)a�_s;\)K%7� ��!��^[q  will����NJ �&e� L87*lrfn_cnH!LZ��#_1�}&& \podr��- 8�ipiH."G�V�-a2b"�� 28* - 2 \pi 2C%\\ .K �2���"�� M%�.� G_2}!�!��G_���,Ŝ Vd�#�, \Z .�#� \{ 0-��#�( n"+5�� +Zrm k�r \!�(.NZ\6�Fym�1 +b��L�� conside'F+detai+n�3.2!-^ "*3M�nwe_ Pr��@�]�ce�(�uA) u� ��'�rmulae�s�=+li�]N \to� �(� %>�N}^{N=@z+n%�a�!� cotg pi z �y���r)� &&^n}:�E���.K (vaK/>t��/ti�vT5� conveniV toLle �. a cl�RM �;��{1}"F2��/ 1� homo� ous}��(�( $\rho^{k}$Z �rho�K e�)=.b�� ZH0'5$k=1,23$��e.2"K . ���0�.�+a �q�6!8�"$2��.!q(GCI QFT a n�1T4 yste ^e  is.22.5nn� 4pfun^{\kappa\l� _{k}!"'-I2}I A�j2�M.?$su}c$m = -M}^{Ma<%2I2�$2InIi�?E� (-1)� m+ � n}}q?z+���(]���| u�%',K= 0, d (cp."Eq.���`Fcharacte�4d���(anti)*�aX�!�/e���"tans1�� �-�J j� � -15p��K.ZM)Z�/ i�{&-( k� %W I� >"�5*�! f�1*��% �9 1q1[ o e+�F� �|, cER\ET,�7>��� s $p_k$�5en=�a famil�60�scribUM 4.4; $p_1>�E'\( �qA>�appeaL6A�"�Gibbs �$a chi��82D Weyl field ( z5.3g/�.mal��--p�a f�)& �3sca�M �4$-&�,��*�##� ��>wo!91^{00}$�~&/seem� 6.11X2q �?ock"c�#�kt $k$ by2Nk_indf�+�WbW>�&g���� Lweset��O a�_��_k2c/m6C equiv��@k%��<O .����3&��4exr:1} .$0"b aFwfu^e~? $Ua�i�<ub*O4�$zmJ��s $�_1 ��\t�;Hint}:=�a#*�( $-\�!�!\,��$�a��yM$���p_3�&@s�&9&�0$ $-$^@-G&iE�\P7  \K; 6"$cis���%,$�#�),w"$: vs�1,0.05in} \no�)nt9�b}��^�b/2e-UB'z��/ce betwe�%@wo : �3&>2S!�an�8J�cfat�=0�. �(c=(e m>ons<-18aXqaX2(eqnA.22a} &" -5�1! ^{10�.�}F� �_�2'N7`3&\ 2.��!vZ2I12[- ���"��*z �3j�01�����K RT��}B4j1��1�1}"� = 5�&M]� > 19n^_1YˡfN4f�Q�2n��\ + 8�^2��"�B1b�"O a�N ��Z����V -��],$a \protect�U-40Z 19n123*�^Q��>7�!; a��N}1a!m8"�:5b)a��C g�, .r6�>d19��c�I2;�9� �I�I� � &e'� m5p�Eqs!�U2a})--�7 4a}) ^/�/ $M* N$� .#5�@s�.� ropr�;�&���(# sum;b6B0>���6�%�) h<�6J16� ���h2�,>�. , od*]Bs "efo5=�.�# % <V#A�Adix A).�+6~|=ap:� B�� corollary= > EEIJQ fu:6�?$6 !��  �("|8�P bel{f_per(""~ �mGRK A{=��f�h ,� nn/��ae����` �e� � a �e� m��,"[=�G\) ad�H-2(n�Bvial)�/a�Ax>}:%:Sis \;�0psto$�0$�3 (x-a)^{-1�0y-m)�)�9*� , y $A5k*�4�3(e_0-e-s )u 83)$; then $e_j'-��3� %j� (\(j�3\)?&erp?x��4!�"{ 1}{3�"��A&~!j=1}^3A �e���al!��A��#�P�0$ obe�:l�Qy $E$4. � bb{Cz:or,(��0y, '#�9�&CsRue j8P-( $3$)�b��>�2!�*&%%IB?*� coo�Dtc,X,Y,Z*�0} E�B Y� Z=4X�?�?XZ 3}Z \�Z�?�<) ���� 2.5})�l��1~ 1~, -n b�L��6 \{\� ) atD {lll� (z): ' 1)- ={\& z6�( \\ -  &.�& zl! �)~ p� .�=2.�$62(!H���e� ��1X2�� 4�,5�(n:)M념iDEry�.q5a�"is�Jsm��: toru�� W/-v :`algebra�-� A�N2�DE'(*LOKDgroupEEg quotV �(�<~O'2��~�F$c0 1�3�/% 2�:V,A�� -�*+z_g G podrn -.#)2})k( 1}{4e�0�(5!�Y 6  2})}  (.My*$Y}8}�F (��(arrow \, -2"� �"�H�]b��1�6�quaJ�%62�t \i+� &�0E%�%� law&t%+1�2���a��E^.YW orig�Jor neutjel�5�1AS ei rBD $e$ Q�,6n}). If ($x �$X}{Z}$, $y.Y)["�/ `e3EW5}<�BaB!=��A�6�oF=4FzG� , "(2.9B8 8�it{�4}�T=%�)!s�Uc � $(x,�y)$ (�#lsnVtislH1=9��If $PAq!*(x @y ��Pab2$�_9�5fe �E$E�7�W ``sum''t3W3W3}�2-x!!dqa & x_{�SQ -�2}+� m��i� A� y68�-mkVG1qŘ�J%�ɞ K�"l Hy!}{�@)�{ifcI%da�C\,!,x9�F(�#d(12\, x_1^2 �2}}{2xZe eG%�Ay.�Aqe*�14e�/strucOa U?al5�n�2" �1 a hoP@+W$of modern ���Z%is revie/Y#)c�Y RS02)\/& *2} Compu�-�3 $P+Q$�e� s $PE�& 1}{9},$ � 17}{27I�Q-0A��@*Q6� \�Ji�x+1�(c :V>y)J�m(1}{121}(159z�861})����&���8ion�pr:V){\9H%2Sh94}�Y- 4.1=Two"� �s $E:$�J�fn�>w"�FE}3LI 4II3}-g}axB3}�2r�Urm{"�c} �  ma~ ld�Sa:� %� ) if7r\S X6�',�>�=\.� �=](HG� AB&3&6&��N� ��m�R��cH��"�6dx`2}x�12�y3}yA~I:.' $\�V$e��:text (�as�& sks)�des�\\ !�� scope a }��Fo>V"#rea�N� Tbe skipU97rst%ing. �H2),well aGdZ"N (x3,*B)I�E9Tful5>�'D?��it{( �w e8ZS}j &�N�  $\C (M)�Nall^Aver� , i.�JesU<s 4EjqD�Sc|`�%achI� \(p`!MAo�<)�m 0 $(w-w(p))^{d�(a+�*g(w))$&>local*� $w\ ���An� $g (w)�~? $p$, \(d�\Z�!�a5Hnon�}�? h� �$ſ0L+�8$\ord_p f$ $:=dA e�lyW.er�@J dR�B )�<9 �:$Q 2(0�S \M.ZByo�+a��C� �<\> l 1$)] ( z (fg� f� )F g\);6;2;�E "(:�+6�g)*28\m�u{ :f�%�g\��\%�\ \S�-F~3$6� \, c��4?cIP C \,.q1!I�4�-(ittim�B�2�.e#? ��:=�X�DF A�u�� $ing�V1$3)�z��I] �Jdiscret�\� s} (��^Q5� TheyFi�be-to-�orrespo�Nc�� �s.: P�p��?��I���0U�s M�, ��ax �%� �plex)yD�@p$,� those%�6 )#i�&�:0$;c*5���a L$R_p$a (� ) maximal=[lO frak{m}_p��9�\{ f :y>*�3!T�=�:E $f (p)"�=�W��� G4co�( $[f]u� f$!�"�� /�t.�($\cong \C$ *�e;Z6��uC+!�SO�v�H hand)�!UT�me&�\5i � )�act�0& rvIR�>665\+�S�0cBQmVxtea���� ��s: �FjAs�0����&$\C��e� two -�a�C%�d�%6(aJI��O�y�E�U��.�)�;��Tle� BSs}�UhDaEst�-!�ACH�\ofe�z"T 5�"a�3.�Rg��Rfao\amr j-��Riemann}.�MGeorg*�^ Bernhard - (182�? 866)a�\o"% surfaces"a-� Ph.D�js�2�\ , superviaxby�\g5� �sp� }~$\PP^1$!�mma~=hWC�.�G�Ehave:&9 J} {*' � 8@.~VI}�1n|=CUV�2>I�� -to-J�����C!�A$, *ly&C c E7,}�&�.i9s�s.~� �U5_F#aB��$�qC&6is�ted by5,i��$ (R �M,�02.13)��nwn2.3 C (E� �\�) [']K "�%�.,[\raisebox{9�\#4pt}}T. \FO c - � 2. 3) Z.^Z� Z]B,.�$e_1$,2-"e_3a �-e r�Ya�!�8� &V"9@_b"� )=6}ufun�ag�% - g_3554�1.�:��hA!j 4 ')^2 �'BAbe&�eg +TATBO] j ��E)� a m��c}r�]��E� 9�)$�w7�^Q��I�$R.Z4to-ex1}(\�"2��hM!� "�.*]0ej1� u't/1�)!!�b E cell� { Q!"�6�"�R\mu� :$ * JqnM� l #a\mu$ $< 1 � �(up!�%�ing) "��u/,B2 &0"$ ! &� � to�1�%�7�I@P5e�&E�� (>7w67�~76�@. �^�'�C%��B� �'I�n6�& z$! in %E�b�&�26�b�!2 ,2.2.~(aN�;r� 2} S"�U �_jF) ��)J(z) -e_j�\(jE!�&O�ibranchg y 0neighbourhoodalA�W s $z9��2.�Nz9�6"%� "5�6"6�$,  cn vely>�y�m�Ro�M��u�� may �tandardi�f("8rlO� � as~$~Dem�2�p�t� bel� to "� �ؕ΅MU�ϡ2MM*dj4?kAp5�EW# pY`�!pfRs ��(/� $(.�!3u�6<.} (w�ka�)meKoh��� index 2}>-��� Sec�T4). D�!%A)to_ex-ei-"AC-2i-�_1E� \, (��!�U]���}"�)� = 901�6B�&<��_2�r2�r10^r"� �& Wp/  �3��� L%?9:͊����"��,�+F> 7�3} Fin a�4� e+�Y2�[�Tr�[�W� �i X}t-A�� �m�>�P2}}'6.�6�l}:�� wf_�EEi%�� U�!� E" %v-� F�24/�I�$e_2-e_3}}{h?-�ozmI&,FZ0 ) :� T, �Qeq[ .�&nt 4} U�AemngDv�a�xJps�W_3��p� {x^2'toHver�e�s��T $\di�V-b ; � . 4�'x�(�$2)$4 3�Lb ]]^{&�J2}�dx�/: ( v3�("�!+��(� Px^P)  $k^2)���M� 5�1Ee5�$ %� in E2' "�+" 3 >)2�b�+� cons Va�q��VqT�D3aX�/� MV.#UT E$� �r��TS -:�p\}^2 �$y$5}.e &%o half--���-Jw$:u@-zK!)/ invo�_SI4 C�LS F� "� E/(�- im -�Z:�"�&P}�I�iY;Mmap �\k, E / .W�W�N�%� !�� 02�s&#+MDzin�d�x %Pr"� E. 2.2 U rinKUaar,��c sH -@!��F�D��,d� same�� -� � } \tau :=I���A1O _�)�;�(hcom =E�A� tau A�(*�[�m_>0��\} ��*1�?!b�&� b&�>Z ��om�ss��* "�X5% B[R" >�$�9s�L_|2�7�<.���T/q��J���,Y,�* (\MODp -��Z\� J2y�I4rhNi��\� � -1�  \\~#�("6+$( x : y : ">d!��, %�(�^2.�^365�o��iA +:�;Trh:IJ ,J5 " 8 : �* ���m~m 1�(!) .BeU@IV� O2 >icho(quIs \ ex�+ew)aM�� *uis+R.-que@/"R:�1�#" �&10"� ��r9bQ�Y &1', 2'U�:=["��+b|�,\, c�'+d P ,A� '$a, b, c, d�R\O!�,'�k�\pm 1b Iq1�n&�. s ri2 Z3newH9��.�{2}')W =��!�as good���al�. H�z�Aen-�al��s!j \(�W m-{1:�S],�{c�Vimpos&Kv&A&�{1J� $=uX-�=��- $. O�#�r�Zrv�6�&� 1�7A�%/2m�T|+rO:�PGamma (1):=\SL (2,\Z)َgQ����mbM�/{cc} a�� "& b \\ cBd Ũ ;3pt� �� �Ib! c:�,\ \det �\,I�6�1R\} �6U�� 6,T�o��wu`�*F$, ����8, �o�rr�mZ�� + \Z\(e��'� ��,�p�O�-�6AҦ�rr��2��UT\)� asji�5[s���a� +b,cd�� Nl�l�Y se�5~ �$1$a�ob`E��P�qa"�O$�$ oW!h2e� (mappedhe upper� nd o�it�n6hcon_ac�M� \,��  �}{ �� �|���fl)s$\Z�kernelA'{��\}I,=i. :Y2�S�V}(&.2�a�!�H&~H4\>�\,� Tly�i Tn2r� n6�\[ O�m es, B� ���.&.:d��I4j "Q o_oodinvS �@=�R*8��p&A2*a��� 7+bJ2,cJ1+dJ|�:�� �Q b�_2B�*�����BL��,��f�W 6n ZI�������. Uy �n�8it�0�c]�� .3z;>9�>� )�}��� �;q f�.� Mc>]���Q.�} �]� �)aQR��N�k)cN�7 "(\��MCB**\)�3se��� -� }-�,��)��!, ;,1-E�1�F4�N4�Bj8%l� >�@Kc.�b*U ��R2|U1)&� H2b! [P �Q D ED:�)��fin �aCE�e V law�+�,p_m�,(� +�x-1A,-��&1&�"� ."�qz�� +d},V�� ey!b� *�f])!�ٲ �Q)iH�_2�e�2�����F�M�-�\.+2�e��Ik����b�I�=�r��5"��T.�D%� �p7&�D6# �@"� in�oen�[n��$aRL#"N s 2Vly9k3.2"� �0pr��.�he� fGR/y( �f z�5 .nh��H2}). N_*the{V�el�2VB��6� �#1\��QW�,\)9 =Vly am7 he�zve6�$eqnXX.15} F� p�,s [a\jY+b�]_2aQ,2-c -d-�T.��^�C��\!~! ��x��� F� .�bq��0 �� �� z��"\�5\� �\([ 5]_2=0,!� "}<7;$ !�[��U��m&�&�`�Yc)��:+ 3\) �E�'� �� �X?,-|="w\�X. (�h�D6�hu1qE{nes3Y vo4wz��$|K~A.)  .rK.)�pBXR�W7e�n�>o1-rep�M�� p�AE%�,)�!�= ]� �cg lim} its_~^,�3,�  b,>�n-|^ ea).�a(z&ka�a�k�E�A��� p �av� �piBfi4 sum_*�b�o�2�bq,b1-GA��On �bi�!\(q[ e^{2`i��9ABI�M� �1�F�liBa�(&rl&���!%�hcom\)bl� d��^d \(|q|S4(< |e^{- � z}�;��'I7���%j�WB��6�O�%i�Nan�W, (**�q^�I N�x%@nd:2}::�nrivJ G 3-$Hm� expa�1",:.�q#���"�$>:�>MY)N6B e�� � 4=�B6(J&6f}� q^{nr e�a\nz�n6��:�Z �$simil�z2�� �&� I+* $ �� ^8$ .J�J6�XJsA� abst�bk=�6!�6Mf )$Yt [G rators $S �T.s7e��E6�rel�6S�kA4�*oSTQT^3!�,��">C>4+^4)�>1,'sB $2\l82$�< rix �=4i ���ST} S V\, �q4� %arV�{0y�&�c\ *�U 0.�W*��,�T�E�)�0MF�Fo1VF�1�� &x�=ec}&�>&; $j�/H- 3} AF*�9 \(D I�t \�9��5&�Ufu>�w���(�%if s= orbi$`I�(1)= $�aͩ.��qa�y�9-� $D$,�#if"e#DL0l� }_e�!zs�z� "C,e |{� $D$.�0��M}�udomD} DL\{("� :*?q�lB0 \REM��qAd0 � �/ ,y� eft|.-|*9<u�}qU�V�s;:DI/ �N�W/9�$.*�:�{!� #<\8=k$X�$!F�&�Aa $�'5�. B #taND$b=�~i�1= '�3w1|if�in!��?'K(={tau �ei�V $!��)=\mp"�0%}�jCz/$ o#J�=xb)'=S3=&hD}{}�%93)]IZ(F:= PSL��QSLA ft( TZQ+ /\Z_�)M/* (&�I)".�!� ng faithf�A�?e� �lkd(I)w��$v!� �"�D =%� ��2bAoe� bilizӝ%=�!�H1�T�ifm�aD^C �Cu�$ܙ�th�f�p�E��=i?S$ CM�$2$--�:��)A��$��' $S$;Ae V4 \varrho :=e^{i�Mi�R+�6s'Q�s ~$ST2t-\u0�t{ ~}~�}R�3�{TSA�4m�(See 1.2!'�9er VIIX8SewDe+ 5D�dro�Y�V�r*he~-tN Z�,Ň-1} Veri�(!vrez<six imag�caF��� ��) u-�2��[��e(�}��"ciH)Y��, ex $Uip3}}$:�i@�ݜ����ppl�@~V�s $�8T#6TS  ST&� !�&9w2Ơp�(;�� tria�� 2'4 Lobachevsky's }~\f&��Wa�\ank Stanislaw Woronowicz draw�\our a0�a��ء�;�MT� un2.GJ�fe i�5��\"' �0(�$dA}�!15�!� w; cp.���3��4�/��m&,� Ċ� �Z�M.� D  N�t*�}�'a%"%c��� the �Tdz$B_�Y�$�A�nds. 8�2:,� 6 C9.�R���p0ings $b_{i},i��-h�ge�ch�2!�e��* $i�Fi+� �Subm@��e"1 g"#Jx'b( b_{21}=  /6$XY%�&�-F +�K1!\ Lt=�ɩ}$ ɑ�a�&S"� :T&&^�g�0!��*���#C.c�%,D $B_3$�5��muG�C�se�I2�C8"�NS -\, :@!0�S 2�*>5��i� {and�Q b�6�%�T<� b�f.;S. T}��w51Q�1R&{2A)�C��an(��Q� 6�6S]���Um�d��5) �re�m�. Itsm�$S^3 IR�ie3�Lna�int]'�&�X� l appear/��.�F�.z r[_zQmed�N �s&�:ne�w f�V�JIit{ �L�|�l��s}��"�� �(PVD �/ $^"�V�.��H�F �.�['��Vu�;6&&= (\(:=\Z\oh.1+ 2\)) P ��@$N�F mean-�a�factorq�\La4�1 \?M�1iW Zg�@ |�1@� |�c�)+ăch��la��'(HV �1�[ ga,���)}aQ2&)�[(*� � 9� it via \(��Q��(��)\M8 'CVm\) (h� we.ߌ< 5)�^4) �.2!m6�(n-) 9_1$ $+�2�(m6�(>92�8 ]-�(@2&�%n�>��x:� c} min.�&x2X \) (�=$!!%}1!NA��.:�.8t�$m9� _1+nJ2 DA I�fN"j "} l e[� ��^a� 1O L' a�mF�$�~me�=��&�<( D_f?n2ZJ�1 + 22N&2yR.S10}S�:`^S�!� �_!�Q�Q�"AU���." 36� �{�Rno�b[Ie�_{��Vc�IA�\{&�%9pt*�!$M�. �, :vQ +\�|�� '(teq��#i�*�!b��F),J�&} � �32 ]����:t0 : ac#'A��  bd �2 ms2.2N2&S :�~ _C6� ava�t� L�� -�&� � "_�� $T� )� K90� 13�C �E O��4rt����F�&f�&B(n�1r princip� grue� UJ� ); (N�!\�6a!�1�1\\ C$��7 1A1Q$N d,\ b2 V. c�8o� Uo�)�yY�Kjus��V noqf�a$$�4�5��lm-�V�����f� 85�6m9^.=Y20BX�2q[-�S>2}J�]Le71.38).�L5d _N)$�(i_)  e�>�c� $/�se� s���� L�T�� Z_N =Z/N�Y of�ge�Uy$Ȃd&� �B�t1A\B2).��$f:M (1)��d8�is 78�$fч)/�q4*b B1�Y�1\n�� r�d�)^I/?�!6=,& ^{f}.�:' 1.*�&��r�a�SyWU2 \( ����,�)� � � �2�EJ*2,)� I"�E`�wf�he cas�oN��2�d�_%B�1per\�onM��thcal{S}��+�ifi @!�q s�=f(T)�':X!�� 6� ,W!sN�S�0[!R�A%ar"&� � -�S(%ᱍ�1"m2 �$)6�`(gY�In�l,%�&9���!�.� %�M� �EM] (E�7V *�(N n�j�,�lZ�Cw<6�C3TvE�_mu_��mu�5�"N^3&�) prodq�_{p | ."!T1bm,. 1 -&!p�p>*� f>+ eq (!C�uct��S�_%)�Mes $p$:> di�kQ,)K�c6�9��-H}(�Dt)'e�or �!��Q�].a� monodromy  $M_G��c��a6� Te"M�Eb:�@h�.�sЊx ;56*>y0�c < $S� r���13JFzGs��&�e�$ e9M��<�s & ^*��*nd Faj=PInM=(dؽ�=v�=��թ! %L'� 01��y�1i`al%�.�.%". 1 ,\C2� V� -=D/[�:"6B��MQ|& Rk4}a�$!ssta*�!"�*�O�N1 +��2�>��! w%���_΢�"��u�N"L "�Aa "�conjuga1� t�` 6�R&� 6l,�aBw>��*)�>+�"*m� ��&�_C,\L�� 11�� �Q>&�� B%V� alen� �.��%MB�A|�� ��� @�5���G� nIn�����c)O�Zivfs%;Jula�d �_{6j2.0&�[a +�s3\�"���C*C:�;& G!i?2e��u~-?E ��%B�@in�A� \(p@�>-:\YF"�4)L��OJb�EH�� y.�qfrqYqT.(efpow�g T^h$�e., $h�m0$�& �to\$*_yj07-%$ �&i 5 �,L T  (1)}((�Y%�%< $h_1 Zh�A$Z$+�h_1�(h�&�  \(T^{h~{=XaZ^Q.�nd6�s�!on"TMa-��$(&��*0��*����n�m�_{:���>ei�#B �J.����6�} *�?���54 ��lT], ^%no`�, ��ơ�p�W� (�� ,`GI)=E( ,�, �"  ]rOia P1%��com�TwD. J%.J�%2�Y.�AnN+jG"G;.�))$"�o�vb�\((\ni=&�$&%,�Ak}�ow�Z|�and lp�u� if N(\�*"p6 it{i}})]-j�"$--cov�TnthNNu9G�� "��.�E6�=E��� :%�� �{�x\� ������I ,�T�{3�\� &� e��$ʁ5(d�+��:k�]$ =\"� -\ E�=Et�(dT):T =7taf@ |)^{� |7F`n=f��3 �%е�$A�a:� ty $2�=\U%��@2}}$)H.U�iiA�.Q$ ҂!F/�2�e8Jean Baptiste J� )�(68�(30a%it{""6}��( -negآ ���beq qm,g,�1 (\,E�| qM�| <1 \,)&(3�%5��m��.Og $gZiF g� n&4}�w W&ġ��'0uʭ�Õ؁52&  �=�L s $4�~$6$,2�\*�2͍l 3.1nopre)d_�-��NIz}5-:)"� E& +�L�Wk2! a�),��``an aut9y� orֶ�&replac! a�iit{coO(e�Z(jn��f/ � v-2, �_125= v71 622�  �,-B� ��jwYick� a�.�E�-c& L^{%a eť� noi�).|EGoddU4A@EW�#$Q�T-1�� �f9-�5&.F�5*� /5*.�5f%nd�"�-iVEN)-�( we� d \(��!�)=(g�k} �I>,�@�A!) $k$.|�A reason!�O�mai�qc��0t!�tY�ve)),s��:[�.�2i��5CxseeRW _Zag� .X3.8"r m�&p 2�2U�ISv�? &�s I��@M�"R \)�'[Ns�% B(yp� E�:"�&w!1�+!�� , <��E�}I%�!a mini'-�tl���of v�ve&J ''!+2�X�dk�X5d��&VD�O�o%��.�� @G7R�1x ��ab8��s�y.e�|UM u�f | dim�nal�(�N&h.��Dy)(.k��� )p�hol���-] � a[/ bundle �5�.�O5�Em�Y��sNm5.o� la�is25 uq/�m%"1�od ded}B}  C7 _stB=com^*� fJ \cupN bb{Q�UC��(�< a�-!�1GI�$Q�@(]0Xs ��aSwt1�6qLeKi�/L/!�%�*�^*"[!end��h (a Hausdorff.y2Felix (18T 94V� opology, )k�#pqpnID a wa_$"]E�2uG* L�� stom�4a�!K! 0� �&"�t)ha� whil�W�M�� Q�v T�)! SL �� 2,\R-��SO�%��sM�&w$N6c&[Qk�1F;e;E/ e.M2--Ϸ}r2_g��9%e��q�,�a -��S%�B home2),�.m� �pQldވnt�� <��I�B�!z�*M�m�r5�#���:cusps��QEG.�� # �!��^*$ (eRC4��;����q� 5��� �>�{�werty>�6 e"R)'$�i�^$�h|�T^n�BST}M+�-(��\2 ��!B-�`�|jˊ�b:} Ew: ��%�,6 B�>�.i��8m�AYm�/InJlsIm%�'Its B� ��!aHmp��H3��/u�arefer�~to.�*K !� ] hol_�66.#Mil97}:(.~4)} Every�M6!���$2+�B,�"e.^���E6R�} ���k���\m*{w� � he.��q$kŢf���� s $gQ_l g D^�?\�[�e)�rBEx"�t� .m�mN�at A<W not sm� �a#Z-kpdn!&d7xiata�i-;�Ktau]_�}X 6�m��t0���� � ����R� \!1 llbracket�� JPf) �81�fR8,IL)i���7 �,\rr�) �k��ta{$RA.G1-��F!U��&�!/"Z$$\D hs{�5:+M�6ger) b��\-ber~$��2�.ZZ3�%�j�.� ha�^ unit�BR��\(:�p�2k&�dA�� op*� ��JH��6H1�>xeTsA�$[�Y��` beca� � ca�EAoaRE�^*t R^�l�(ҁ) �J� sm aсF�F�7A>>>TK!�n BFAj&� ram"�%})�9�ʎ��,  �9"g �� �re�Y� g|�i.�$Db��&�qi��I�Z$Q$E#%\n23��I )^2�&�u"�? ��'$&�iw = z7�=U :E:Ƃo��Ib1�� \, w^jV�1 ( dw�)��XC:5z*M"�2"���"�w2\c>�nA}�n12�t1"3iJF�a�5  m B !� E�_ or� ,3G� ,$\nu_{\ell}$�D&n�Y �QBtjXG BH=j&�ell=2Tu!�leq��}� a6��Cs'� �J��^*�3�gin{m&�5 cr3.2n}E��T,���?_)��� >\ 0%�. �by2fu��f� !%t�%.�N antN|L&`�) orem�99�|+)9 eC�i�Kto2�� ��.� =}[  lex [ ���i�1{ --Roch.# �63��66X �"}� ,� 1) �~��K��veA9vofP�o fixedr �~P�a;� � *�.� �QSfin_dim� �EoE � ^�rem~2.22%� 4.9, /�(."1.40.)0>�Mt��v�  (^� *� X�K>aQ0dim_kG} d_{2k�  \eN.M2be�y{��0Q[��3k <�1;PB= �� 2k -&��|g&  + .Q k[����� � k\,Q�y ��� &s ��6ʔ �3�H֐2�-�> 0�nd-��1�MeX u� ��atgenc� m�j� �����E�M|�} � B&� Ešh���ula.��}+� �A�l 1 +�\mu}{12}fSf��-�46%|2$VV�� . 8V� �9٠6/r n}w'���$1$6�:  � �N�� 0b\(��� �z:kRE$�es�L valS����s>� ZNo"AL= i�%� au =SW)sIA��I'a���3:x���au�-}1Ousee"AQ~�Y� "Ju12�7E�$z�\]a�q.x'����TTI 1,\dy�17 \� E�.� @�2��`2MR8 =. 1'B*V:�+"s#�� �h )�&""8V �Ѿ�\�����2kA'���= 1,0,1 2,ں23,2,3 %��!�"a�nex�' "�j�e��Uit *iE8���.ir fashion, " T�Cee recurr�9rel�\(�+12핡 a=\(=B+�qeY1nfL:��2m  Ene!�/�0ePwN�av.�,*�1��\nu_2� nu_3��R�"$��N� � .�,y�m�2� nf�vٺ�Nz=0�\��S< 5�.96 91+1"} (7 ��.8 5$,2E9 10:F10 >H1�* $=26"�6�=:]�i�teH_���"R�L ���6p��� d �ArA�Be Ɋ one.+)lcal{M}�'"� "| 0A<2KR�� &�zof %Coro�P��� %�4 ��r , 23.6] 3.3��.�0�$1U"� (i�ns�of Y "� s�;&�7�1E?/12k+�� $. ��9 ?&trik�6�� .U/  it{B��=qa�'2k�%�&& �_�((2k-1)!}{2(�M�k]!�9s.y� (m,n� !\!}'\,(m� +n�#2k' �Ann�=bm>l�"\{�["A`n&�� �1}{n^�}( dsu.m2.2n�Z� � �XY7�*�):��Z&�Qa\(2. �4\)����:.�n3.6}-~��!.P = G " ,"<"�i%"2�,_1, "(%|r����� E j2BPk -�H�k�)(1=��!D�) � A�'�i��J}`n��*��dz�v���4xE5(rF�F$>�7J�a�+b 2, c 6p �9b�f�>3b3+A���,ړ,��a�"{ :�K,�,e�Yw| i0)*GL�J��$dP0s�Yx#i}�32�e���7:I8J��n)�1, F�I�uo�B >2�e�=  fY��3��A�o� �t�0�5N gent+�E��&��:sumM��Jl&Xsl1\% is, � -R�oSiEWe0o��oT  &?"�Lipschit�Uj }� �� ~g.,Z���f)%�� (�H(�aY}\,V�\,��1}���?�t2�l.�a�l^{k-1}eYel�DZ�6W9eq%od �e F�-�%�c��.2k���.�� �Bm�<)=�]B��}{4k}+6�2�-ŷ-�z1-�b}}= �\\,\zeta� -2k)nU\,\sigma�-1}(n)N&^/7-�~\( / _{l-=6�,r\mid n}r^{l(A�� Q v vis�Rr$%= n$),f<|F"��oulli�6��J�� $(16�W705eJA�6�$great f"��Basel ��iOH 'B�, ��131--138�a�ef�l�� acc��H���u W�ed�� t�<}Ars ConR andiͤ�o<� probWty,"�XV�sthumou�lin 1713(W�'!Mj�b�#e Planck&Max 4 (1858--1947) �proposed his law of the spectral distribution@black--body radia in: fall)�I1900 (Nobel Prize in Physics, 1918)~--~see M.J. Klein in~\cite{His77}.} di� funcm�O: \beqa \hspace{-16pt} & \Txfrac{x}{e^{x}-1}=\dsum\limits_{l=0}^{\infty}B_{l}\,\6X^{l}}{l!} ;\ B_{0}=1 ,  1}=-_1}{2}2}=63{Pots=B_{2k+1}=0 ,\, & �20�\nn�B_{4};86x30a � 3pt}+62�4 �:$10% 5}{6 �>%2o69�7Vs14O7}{6} ,.M \�l \, , & \quad \label{3.8} \e!�4$\zeta (s)$ isEARiemann $--1�8\footnote{% TheU al equI�(\(\Gamma (\Es!�) \pi^{-} y = 641-.6 5-! 7H1-s)\), which allow �8analytic contin � of��0= \Su_{n=1}^{M�d n^{-s}\) as a meromorphic�l (with a pole at \(s=1\)) to%:�entire complex plane $s$, was proven by5b in 1859 (a�Palso Cartier's lectura�~i��FNTP}).}. Remarkably, for $n\geqslant 1$,!P Fourier coefficients�$Ga 4}$ are positive8tegers. Thus, Wk X2$�Q s6Imodular�mg�weight $2k$ (satisfying (\ref{3.2})). F�Lk=1$, however, we ha�stead�h gin{Qa@} (c\tau +d)^{-2}�}Mma b}{$})a= \, )<)+IU i}{4\pi} c8 y,9a,nd�s!�at only) AHast}( `d$aR1]$y.Q23.11}) A�A�IMMha�4fo� 4ing absolutely�<�(,FU$ represente�w Q3.15}�J|2��l(��х!�e�M(2r�)!}2�k� !>�iEM\Z2~\times\Z�AB$\backslash2, \�g'�H2"\��!{� -1�Q\ m+-� 0 �}�vA^eeqQ.� ��Us� t�� �O�h5�A%\!NQ $ (includD.10 $\equiv G_2^AI�$) � . ��= r"�6 yA� = ��P. (See Sect.~III.7 ofJ Weil}� e6 case��=-;=0\���� idered.) '�� I�reO $d_{k}>1$f�k$e1a fixe���n one���d K`-1$ linearly independent i bi'ons $S~$ Am,��no�t term�`their ( �g. Such![,ms, characte@ d by6Kd� t� a= $� $q6,%!Hcalled \textit{cusp.ms}.,[noi� bU |4�es fromHGerman word Spitzen!K. (Q� ``parabol� orm''� used-8 Russian litera� .)}odenote!$L cal{S}%ssubspa �� firsth f  lr !�appears!` 12  d w�see, itOpe.sa�ow�de�inI� geneCstruc�Aq2x*a�%�dpr:3.3}%�$24th power���Dedekind.�RiA;d�� 31--1916)���d�9 1877)P�*4 $j�wj�})�(as well as �modernA�cep�a r����8an ideal.} $\et.�Y \Delt�� # ;�e[ 2�� )I�]^{24�(� \dprod"^ n2`(\, (1-q^{n}<�12: eq0 2 j 12.�}.�" (proof} As $2� $ cl�>vanishE]\(q��j justA=? ��it is a!R"�!�deY $12$. Tis endKcomputIy@logarithmic deriv� -g) �')S)} 5~N 28 %�( 1-246Y2o gn%o}{-x} )�9�-4$ 6c� F) .*� !�!�Ic n���� 3.9}A�r q\d}{� \log )�K%J���5 2Z\I�-,Ee.� P] .� 5M�a9h� ,��aKL Be�12�$T$--"�< (i.e., periodicAJ  1�x$ar$)�coBAGatI���edJ�mE�imAj5mt���oth3.5���o�� dimeg  \(��a�dim:��M��\)��Tgiven (recursively) byyq d�d@d_d_Fd_1!�;�,12+2k} 2k}+, k\ |  . �47-� In p6ca�, � �x < 1� nd $6���=� $k0$aen�� � $f^A�\bigt@$ �bej(k-12<0$ in 9io-G�QN,argument. (H�we2 !L�:���h&Ji�hcom$ si.h�5uc'mul�%�O ��>a�wt]1a \no��+QuppGlf�.)�����b~C ��$ese resultS %P� � 2m=onA�)�1-%Ux $: .*2$m{mi�M��r���nwrm3.4}a�!�E' spa� Zrb crbitrarym�|�f;commu� (ve algebra N t $G_4��i� $G_6, ��GU$polynomialO$\C��[ G_4,?�$]$ (D.~Zag�2���-9! corollary��� x2� 2��M rA�al ! discrimin- M ��  ��2���ZA |1��[ g_{�3m�$-27g_{3}^{y- �,a ��20 G�d� 0^{3}- 3.%(7.G�� 3� l (� �)���e�6w3�w =zQ�M�u differ@ \((J�)�~����$lso belong�6� 12}$ �U, due!�)��),�I*"� -20J � }{8})L){*v�&��}}� -3%� ( -7F6s 2�G)�)� 1}{(12%}63}{(7,. 0Am�No� furtP� 2�-�=1$ %!� 3.5)/ � aI a *R!d$q�C5k134 1=60-20ѳ�a2} +21 IG7BA��-�\) e verif�rel2�.� = LJ� M6�F<'2}3A��1�2 \!4:* !F�� J�i�!�E�H4}�<K F�$C]JY )^A�a��{-6�6.�m�qMm��� nrem3�6�o Hilbert��ce,!1ipped� the P�son scaX"}x1k4} (f,g)=\diint"yB/N (1)}^ �nk}\over>{f � )g �d\mu '!text{{}� F=A_{1}+iX!�� E =i�� - 2 �7��<&dc2m$T $ be�, $\SL (2,\R).h  meas3 o�!e �1�f�m3�Com2�nB2&(8��k{ $!A�ifew.] �'G notic� � .x" $=! \{ 0\ exactla� ose value�$k* $-�2$ }}{4M��$reciprocal�! (nam�> � $=2,$ $46810,� 14$)�curiou�Tader will find a brief]co� i(nonac�ntal) � ( �1B� &"� �"B���[�}B�2� $�!-U)v6-~3� }w%{<s �p!P sely� )�m�Rb"�$R�#o�Ae �"N <�   jVges���� i��[ 240;��� b T]^4}{� R�.�e��q^{-1�744 + {196C$1.5pt}884}Vx q +�){216,49&K =760>=^2l&���8%G(>D  $�S but gro%expon�$ally e/ �toRinfty$i"���: r! �j$ is,~some ]!e,ELuniqu&n&�.seMv� nwpr���$\Phi� �y"�Yg5Qp�-)5)at most6 a^R&;" !)\)ס�>�.( in $j�q�� ����a��\(f k�!��/!<&�4affine Kac--Mo�.Y8 $(\hat{E}_8)_1)g")_5 �wJete�.{$5(:%*�,s} Each2�+(�� eelliptic}mEz"ed� rQ��&��rY�s. Accore�toA���y (2)! �2.1��seba� be doublyic�_,pw2� they may L+ a twis�Kicity��. &#'� tw amily� �B�s= BowI� multia'$ve cocycle� a�!�z�A classio exa!-*( type�tprovi�b� &�.} 2�E�it{��2D *�5sc b��.�-�Bernoulli's {\it Ars Conjectandi} (1713),�� numb�+n.studi� Euler173%(Gauss (1801B1%�O heatAb F�-(1826),�, h important�-,in Jacobi's �Funda�a Nov�%1829).}�vai&"(a�� " '�$Z�/�.2}n�e^{< inz"�  1 + 2,�$O*L'cq��L  \cos Pnz.G6.}=e^{iD0_ } ,*0(� � �*!XY� four-,.-N �Bs.� A mo�/mon�)�� W)t6�Q�s;\(5i_�$= 1�06"0n1�_2B"�'.D3�)�2H016H4�(Many author*"so writ�$q6X�$nu/a�& 5�%x\);| our cho� �V��( "co�#�4l(�s.~4-7%�w4 �*=h%MK 5,1$�ys�q r�1 botha#!�eo�����0 Calogero--Su+l�H"l��L!S .Gr� corrk�i(�.~4.4 �).�q � {\mu\nu}(�+A�a9 A�E*i{\muB3�0 !�-2z+\nu)a^W (z��_ta=n�+ ,�$ \mu ,\nu j X3.2/ eq (]a _A�=�\)�ٖ!]``J ''Aɜ�a�= +1 �, = && \podr �+��I~6 4 �5 �nw3.3�+\Vg! 7 .l lnu}O )��-��-��iz�W�-mu 45�.6*E22�r5Not�%2��Uց5$�!R� od�& $z$ among�����I�tjga�tenQ�� .J %0�2�B% 2�'S *�7%�Q *�*�:�( ng �2})�s�} C2n+"az M�A�whi�20�ev@1nd>�aT'y,s (togea��~  19})Y �,"7%�9 01} 5�Y� �� �26�n) J \nnYnC"R�2�,!p�Iv�!�**45� � ��.� -�,E� Thus]~M���bv "Ao \(zw&!� �& es (�A�J=)@�,\(z =24��In"i�zCfull ��a9š=�11}$ (9�)� � e) l�6�Cauch� orem� l&�& &�&Nc).X-Uo 20})� pt#�(Z �of�e�pZ��-�I�>O1K&wo3m!ex� Y1�~��Y\)6 2&y&"I;{\;ptsn<00}-A6^-6� 1}V�\ op{\&�6R� M�1"�-�A�e; q���)*� A�1 �>} :. 1 \pm :p(27a�y�z +-ab w.w�:n w', �6�.u8"� z�j�jrj+Nh�\�Z%ZZ�~Z��0�Z�ZvZ-�Z�ZT�6 On�n_/: 0B=s&&�8 �i�cng (a��� M83l+e a� ����.UHe�9$berg--Weyl21Werner $ (190�.7�:HAphyHA 1932; H nn V�85�.55� N� ��0_ $ S.+is6�%@�$1$-- 1mf�0=s $U_a� V_{b%>cI"on�=y,>5&3s $f(z &s�4( (U_{a}f)(za e^{Ai(a�~ +2az�  f(z+�,���@ (�A$b \ � 3.2?# A siYcal+�%�+�+��a}}=} 2}}ubeq� e�iab}�=.�F�? �2�Y�"M �9�8)!�&vV%�&rete su)� $\Z!=D=\{(a,b): a,b\in\Z�i3"�'% $"�ab�#N � $abA.f \(a=\`)l �"�9bA\&�+uyf I3%$-uris�%Ay��s"## � .� �*X ��V_JB&!�U/}"�� �6"� � Ef03.�1!�Similr5]A\!m-@1}{l}\Z\) we obta�l!��6 2� (e&4encountered in�<.�<P,.?6_ :YH!F_U96�($ Schr\"{o}�er"d.�Eq&�>25� as knoL>J.&�as�he6�''), l�YErwin >{(1887�61,>OPh�O3) � born5i+\�.al} Y9�"� .�A:L1}2�AP!�T�; ,:k6�Y8 A8� so!��fac�ll]�)��}0Y5�Ce*� Fa� basi>-!~g�5�0yV�f.y:&�.: �,pr_Zag} {\rm� e D.j" *w+�$.~1C p. 24��Givl $r4,\-men\-sio\-:l0 $\Lp> _{r�n���,length squar�<Q(x)$�� vectDxez6E� ��,K&�it�t�- csV*�(�""� �&e&\T�? _{Q5&=6{4B�?�.HD26}6+Yof"P�_r�� $. M�"U#�/A�D!�=�E $N�a &�$\chi:�_0�N�$ suc>>�4M eqnn� ��9\g�G���  o(d ���E�}-e2k+' d \��N �for"�' �� p"� 4pt} \b%�,array}{cc} a" -"& b \\ cB��' < ��G!Jb�o�Fo Q1&x����a2} x A x�e.F $Aan�0symmetric $r N r$ matrixE,zN8A��2stF;Y$NA�$5ag��V�.E � � ,an \(r = 2\)� "942} && Q = x_1^�$x_2^2!,+2�)�W4�4xD4q^4 +8 q^5 + 4q^8F�$�JM"nnlAY�PF2 &Y( \ 0 & 2 2�.�N=4.R�>u*�KdLB�F* �"A m.8Df"�#$9byresse�;��a1�. � m�� 43} ',�&$)� �u�ik\{*�61�m%..� 00}^8$Ha�)2T!�p cR ��601.6 �.lb�\� @�$(KqT:�A�!�1Ω�5� \� ,Quantum fiel�5ory& &fB�Je|F {1} �́Zbenefi�ematic�r+�=�G69 a  + summ�4 ��e�'q.5s+#�SW}��PBLOT}N QFSB#�detail3dZofsN\�) �7alN. (Our �#w�+(be necessarG!ne-�d:�D ��:�> real�@ld6�~A(QFT)�>�urb+=�a�:, Feyn�@graphs pa�,tegral won't���  ion�B .,# Minkowski�/$ axioms. A*J"�u�"maiI#2�&[�-�Rens> SW}  pera� �#^0a vacuum stat�RJ.z7�с� $P_0,)�P] n (�2:Gewo�).q**�%1= l��-c� $V_+ it{"?Ycov"}�\AA x4.2} V_+� L� \{ P�/2$P� ge |EP P}| �J \sqrt{ �A \�� (U!�ID&# e^{-iaP} �*k#Boldf�letters;.I�$ P �H throughou?� D&q $--E��Fu�'r ,.YLe�d�hxUQ�1. .�� ���H}�#nn�,!�i@�� �4} $|0\rangle$ vi�s�&AR,�8nB�3} R%�=q�P^�#$=� ,�< = ( %�Je-1)7 \, )kZ!��� 0.W1!eq�<���!bg��b�+�0eB* of ( comI') spin-�or P p�2x)$. �,$��n-q�c �c 6<\A+1#$:%�sme} �R(f)"any?wartz�� �QSc ��15-2002�jtb��is�ed�� 4 leavZ0t 5�.�C � �$ obe�! �u'vis}+ cova>Dc�Enf&�*y�4} U a�J� � -` Un.S(JM;F R\Lx + aq�JC$R@))�Q(d*�6_ �)amA-or\ARqI� <:�p $2^{d_)6� O ces;�T $D�D 4Oof �rest �@ � * $d_0BJR� canoŲ�La }Bmassless�;E��?=�5} d_0!�G&D-28d� iul �9":B�$5a% $\Dbrackets�(�}$2P$.#rho}$ ndf&�!m���0ѴY  $9$);&!BSO ��E!+(pra�)5ǥ�. *�*spA�ng FRU$�"J�$ ($-\IDV<�: toENX r"� R5). We �9�( $S(O �a 00e"1]sig�%or1�i�P3 4y�6} S XmKx'v"Z_{ac}(x���F"=�#2��$.,M%y�]����luedness4�JY)$:FT�R�T_Sl�<d (��)N7$] ;��[� = -1$�dA2T (I�):�&&�SAhi�}IP"� - jug�� ^*��� )� 3!e���whenever C$ does)�2Eb)Ow!�&� : 7} !�(x_� $phi^* (x_2�5>�E^* , 6="Cq�` {*5� [ >0,�7Cref� �PtS�Q�``I�g'' �n$-:�$�8> (-like separ pU s. Fin#�L}Qi)(E }�D� ~3icX �2� . In+|ds, (��) 8$ mo�Gs �_1�!C_2�-7%U_n(x_n* $�n*R . A QFT�ful�Wh:BTAs%�T&>/} (or S) #Ls2wf} w_n� (� �Z,x_{n-1&� ) \� lvac �1AJAW�ph�\rvac.a�9i��, temp�:� M^{�BF� }$, �-IP�p"�* rans3  ce) o�J.�U&6"<�� x_{a.5a+1( �!1-n-10+�F k*o�=o t8A��%� F-� 1�: as�;�� Fi6,. {\samepagRg29��on�npr% plis Ditem[�}a)}]�6�2 E�1�&~%������<� (�3$y�=0� y^0$ $> G y�|$)�a �-%d& 54forward *m>E$frak{T}_{+{!� nw4�eq*\pm�/��\{ \m�d= x+iyi M + i M :� y^0 V��\}dH�2 1� 2� } \v��{-12ptZ i"y_6.�b2�RO~�/wf}�;a>�'-n9V�. $w_{�)��m2*$ :�Nay,uc� �[5��12~-�]C wn&�}�& Mly � �Qv>��d�| ��� 12},� ��V�-�|�\leqs(f \, Af�;tSu_{a� <0n- zoa�[R^��eIn(7�-mia�ihda? |yJ�^{\, .KQt2Ml�D6w}���?� �P��N�nd �Fda~�u&t Lapl���k AfV�.a<}�s�Ly�&� ��.z =+,-4A�W�t("�e� �uni�di�H s \()�!� psto1 rho-�\�a�8>-T).@)traT��.I)*�Q�O�0:��?1�+inverg0} $w$2� nw4.}e��A�m �, w �E�� I_���}{ 8M?��� 'A�A�.^{0i)bQ�]�->--:.�I�Rl�1&�JV� actu� "�"��]�t}�as!&�|(�2Vs gO!d !� �9-9F>� }D\!a�!�-\ 2��N�"1\) � &,1��}d$onfgr�$�, Y?�2cC�9�;$\ Q�-U2T��7U�(�Zier!@ e.g.� l� LVladimir Glaser (192384) wh_mmu�� i�NI�Zdorov���1962.} &�k�92 �@"�4��9Madd`o�S}2Br7�.? symp� �^} ��.�R $dx^D*} \wedge�%xoy;) }}{yqN$ �$T86(3�V� [ �nrm� �8E�$np.� �  JZU� ~(�b�Q.�U4.1:\(E�.�"9pt*:3�� �[��\"�jf+�$+iy_1,\)e�]) \� y *G"bM) :EN� S� N62f.G����\�.�,nots�0����<���&n >.Z��nd5� Fhanow� w�!�i�La�or>R N= s. A"�a�Maxwell&^ % Ja�aClerk (1;`879) wr�ahis�NT�z n Ear C� MagnetisAc`Sh(photon)3�"x$neutrino, �Ald ,�bC�75�-s  unC�highera� metrtJelnes=act�H�4(AV#!�)�MDso far%hieRuXTO ime "�� fte�ree�"rb�a�uI,8vigorous effort 9re �%�f� ies. C�����+add5Y(al advantag 0^9id�$t�st,u#j�p ablyZ0jrt� ax behaL:UF�D)T(!�iveSKo�� a?cfH� i�Iint�&se�GTMP})6#�cQctifiZlI spacB)�U� Li"X"�ssec2��F�>jPgr�m.�.| <:�#ne�F("3c�Aof)Q \o� al�Fnal.O"� V $g:$ $ arpx' �(w�Q�r^s-�&�!%%` ��-�2�x4� d x'B T= \omega^{-2} (x,g) dx*� (d  dx^0) '�)!{S � < � i 1}^D�<(ji�^2" m-$ ��� f�L��e_]&� a�$xt!� &L�-e"�K2. AnF�5&G"�^asp<s�Bh ,%N $D>2�U)8x�$ s"8r�$&�lD+#$�� ((connected)M$\( X!8*,2juajE_ANa�,of pseoudo--" L�*�q D,21a!�6 D,2}"X�( �& �n$M$�A�2uG!�%7Hto entir�SreE�Tn��J�]�Ved�Pa���B } or/e\O�mp�#ed> } $\c#�&�Hmanifest�t '%p��FTYO�EdO!�pro�BN"� r)2$ 8%f�2"nby Dirac�t Paul AdA Maur�E$�02`%84)e$&Kzp�$93, � )�j�0� �edi�9f anti4icles, speaks �Varenna�� �z9]g�� t&eci��E�5 geom�b74�Eent yd9(t Bristol.} d$Di 36} (it;iz=oy�*VS'1o���f�a��stnKio�sKW{9nFelix �49!_25), a�Yi;iA�,preestablish |4armony between5�& s,aout�X�'ib��Bou� ma�%"fam��1872 E G�rogram.:=#nn4{o\M = Q�J/\n.n R^* ��Q�y� .� fu-. \xx \!� R^{D &-o \{0\} :'&"?*.H�� \mxi+ _D^�; 0 �U�I?N (s&xi^�eta_{ab}:^� [�* f�\}`&�/�>� 2<��alg$,"�dAiFu�pic�k, 0M"�Asi�,��.�X � �_b  \di} �a}} -)1n$1Js&o4iz�� "AbonN..cm_relB0[ �,cd�]� -�c}!b!,�A,�k_{b a �% 2+[c -fs +X9����9 ,c,d^,0*D\u 8�p== eDDvK16 �K -1-1 \ EAI= &�ga 6ybPI�embed*^[MlT\s give?%R"f3O5} & x� E�jz�4! \v \xx_{x-�f�<\}X\M_{\C}u�Ix5�"~eeo!��1+a�m!3&-1}a�%-R%D}6iW{or,}�~ nn &tY�e�.< }{\kw"@uu|!�(D� n4&E9a �5"� � a} :�3"p�k|D ���"/rthonvbas�Fn.�"s|�&��j�]M$,�#isotropY*,i~<) !^M$ -(�  (� 2P^!a� of) �g8 �S e r� beca�y �?aR�`2�!E� 6} x�:�  -2%�E}_1} \sprM�_/P� IӒ�E�{L- V*@:�f� �8"�3S"�hd� xx_x� !L map~��O=� B /"� e�GQ} M��!�2lu~m �Um; QI \(K_��M ��MG6+ ps!``�H y'',� &$�$Ar�+Utip�&!�ҵ-%I$���H-}k_inf} �< U��F-6h�<2x 8�b7�s �,I� �u: \ (!�n� mxi_��- M0B�:��&���%�6 . 0���� 6���YtZF gle�"�%�8��I�j)\)&Rn�:(w� �� -1},)""9 D�\ A�( - 3= ~>.&�?�7 GcB/�c,'�fcirdW� t W( yD� � -21� )\)--sp�) '�1}� T a���� $Q$~X$ll. IndeedD) quotF�� Q/\Rs/��"�+� 2� nwv8} <�Y22o�� !�� +Y�^D� 9��&D !�}�:��a�q�B\, \Sr^1�= <*5Go�5<to# $= !p'� ���Mivi 0byF_22\Z/2\Z�]sbyU?h $\xxG$��$g4!�*� 6e I5�u�96} �6.i\(�J�/\Z�V.2��N��a��0� it{n Ae�7}-o|(or odd~\(D>�$�uGT (�ar)}��$g%4$= (g^a_b\xi^b�nA� in1O�et I:�sm9��s$g��Es*t�rg%�#%e���it�[e�� turns �to�qua"�n(C roo" the)!��*or2?:$:.J} �qsr 3 � ��r!:�y 1 x_x}�g&HS An&&� g(x! $=1I�E"jF 6}) impl� �gx_�va�( ��'- 2�")^,  frp�.S }{5_1Oa�% �' 2,g)! / a-\&tIu�=m!� erty�ua:$�-,2� on).��������I} Y*�!��d�!$ z1 h� (g,i1m+rg(� � :*%�iff $g�a.�6|.ea�A �M � � &� **�T�AU$ st:j�M>FE�(2A&$$\bullet$]"�=S�� 7*(SYAa E�P9(.(4�522P�V9G"= �1-Mx,aM\�n\�&J��1�e�s �t�\m*ZD�EJ�4< �Y&jD�)�YX_!K�� Hv�U�}�I \)$xv\\( 5$,f�sp�D��V�.�KJ`="�x+�%�}{ �&� -�%���\, 0}\�ME�H#ors $i-�1"�$�E"N mu}}�z$i! mu�'�592,�?�=�er�C $�YO'O�� e2.3n} i � �Qu-�-1p -M Dh \>6 �66+B6!�^{X� DY� xD !x!�!F \ \�Mho!�E�;%#Ap��ix~B);5"�wap:2});Q�9| \E�Q� .�2�\>��\:�6�\ A Il�fri�$rizee��� O�l1�ţ8} \M"�%�=2�# \{ z_{\cm�}F� .�Y\P2F \c�&6^E u S : �P\R"�� uM��i�.�=u"� � + u� .3>� 1:z �M�2E A� Lgj% & �5+Sr3 ��\"�#.{$/#�$����I{$�  u�M��$1�ZG *Se�whP`QP&i�\E��> C^D$� u�8� �K"�0 Vif }A� P&afJeUy�p"�a7_(9 lex)�Q&@0�,AsK  x$ $�$$ |k  ($:= M M$)i g�!��6� (�9& NT0��EN03>R��,�z:>r� �)"� w3 *�YM!� ,U�8pt} z_D Rk~PZ rm�}{ 2\"a ֗� B=�ʴ+4eF�  - �A^0 �%eq&�� :�1o�12}�G] +x]e>$g_c:U]$( \nx )A{to qJ  z)$,�\� M.),�szkmapV�">a"m!} m:��2 Ont2�> && z"z 2�2I�%N �u5�.�_&�� 6":!�,�"d�R. /=�)i;M� + d z_D��� �d � }V�6^8�_(��a%�:�!��.~!�) dJH? �.-+N�ұ����M�n < ya).�2�.Ř|)'*�bb�Aob k&]"���!D image $T �6�$�/)[X� t2�>T_>�Rͥe�]��1�9*�. z�!^bb{C}^D6I�3 ^F ]|��zM-�� <. ,1,\ z \cdot &[yz}1�@ ^Q�|� �%ၡg+�a B:D ��2;>�I�1J �(KPIBXqHI)� �2]3f{��3��S$��#�A��`e clo���$��t�is?}g�Bdirect�p �on~� 0#���sM��� :.�9})� \# he Cayley&#% Arthur ##21+�95)�&5�� 1843RMzo� p."�#�I��)�Me"�&�*�"�2s.}�D!L+ .� �Q �2" "3,a�k� 1+i�j }{1-  \�2 �3,m�CMqari�&!�!$:&chiٍ(12�G ray)�/jMLMD�KAO�05)�P$D=4$ .4�A>��":s*�� )�U� 4+ma%2 u(2)��U �I�Ea5� J�ern1"%�o�,$s_{\R} \H$dM�Ud A�i !F�To86} &���Q MpVni�Q �4 i\&8Dx_ ix^0 \I&B �:�x Q}�$spr� �x2! c ;!&=!�N�z�f�\dirz�J��$alpha} Q_{ � z^4��!Q:��FB�� �V2�!�=!m�!6�!�-&�2\? 1�, �&1+i.�Bxl�-6�- �|6�! $Q_k1J�� ,2,3ǟ 1a_Q�Y�c7ts} (7g:�5G)i�'A)s, cOiiSec� . An�pA�aPo6Q :��adevelop �&N i�"yA): D�5pai��mu�6�"ic ��|�q_0$, $q"�a�!�,'i�*gz8�u� �$*�o�/�u�(c�be h��|0 ��!Q3 e��l�#��J0"+ ;8)imx�M$�]/Xa �,`-�,!g*J-%-jC�_�g�c�_e ��v":F�_I�r^?�c>w \(q�Fio9���Bl�' ��.JG$�G9d2��1U co �) ~!>�9 6�< , re�m,l�Rc{ ablyAly�C6sRT�E�z`c�A�i �-4 hartad-�2� �ac"}\M$�isno>og��E[fe.�Sx|�tv �",1 4r $(1,D-1)$.) *�alleC,35;�Hsc%uDA� (Mq �lm a�,gle�7 ��,� (��UCM]QNT01}, P*��2.1��N-�1 6L� -D6֌O�.Y 4.2 ���5��an el6 � mV� We� (p_{0,�")nq u{m�z&� ��$p��{ G���i�A1�i�w�2d.J�i�k� e,,b.�%e >GE�^yFto� ��, i�8"��t�~.�-@is $*.�' `�3Fs !�"dus �.� max,APe8Ef}�mpb4-�F�=e>gr�j \2)��h / `&',� ���$z�\b٠$ ,A1,�j, D$)!q0�yh�ztonian�b"� H} H�D,��L(,�� � (P_0+K_0��AD �Segal.� Irv� Ezra &118�/98O�S71} $H\&�K&IPM is (iX'0=wP_0w^�E�$w$"X#�SH�0?���� or $5�a�=�ac�b�t*�q by ("�) X%|l� �ja��h�KiAzA*a phasj�or�u�RI<$ ךa2�tym��  orig�*z��(�"e|�WA�U  }au� �U�.��!�&����x r!�y< on eit�r -��6 #���'�A:4�Mco )� .A!�7fDA$/fgraR)>aU"{*�}w�\ne�1��.tm{orZ�v�ժnd{SC�cmu�L*GD , D\& $z$-"i}�P6Vw \�+T} (zd'!'�pwr'54�Py�M%�!�� P� St'.z+z�, w}{"� 4w"�,� x�\(w�h^D\)) �D=��b% g_c$1��Gog39Y $-&0!X$-"ais new&!!:($1$�#9�H�i�0 cmu\cnu}$� Ru )M~:Mn2.10n} k = i� 0V�� m�&Ud f0\�4%�{LM HI?��D �[� A�, C�n@b] = 2� ( \d}�! � H� 6�8 )[ H Vm.V - kmu2! �H,� M] =�,%� "E B). 2���!�e.�b�Bf)'o2�x�S i"�7%�5�,A.u�nd�qn� %�it{��:at}%��wsp� s( D+1,1-U� �ꁎ�?a"ƕ>�/�E�2�i*H$���sub_ ��alg&� �� |�@.�$\c15�!h*f ��al� �.by�\��� ��& S_ �2�of 9i:�� "� )56�\(y���Vt.� 9)�*�c�}-_0a�:= it{Span}d �*!�\{�j-��!.�HM �, w�%"�) �*.aLR��*i_a$ a��{ �y��\xi"�}{i0-p-��i�Rtrast%^.*t1!�'[Ǘt�B F G\) �R"�z�%^� x$) ��c&��y� a[l�Ve $R$pSlacz| nume�b $� �2 $R2gshhmak]�M��"MSR� %*Q$ThermLim},D�$7, %%% ???� �I_� ``�radiu�Un��se'' !U"�c�  qS8㟁k*+ modynamic�TR$O� ��LaE�;ieda 2VD\*ÇAGf epLGCITB. VertexaT�tr2 �>ity, � ity}( ؑ& G |�surve��a�da.G�D)GCIi�a]p�1�GCI~QFT/?W'K�bHs1W},�ly sketc�; q�� 4.1,]B"�3c�A� JS� a �la%^>�_� O*؄e�kd0cript ``$M$''W 1 me��aOd r�`X objeQ a�*o�Min2Zf(�L��M$ (*�S{\aa_)�MIN*�'* �3�S2n�:2"\� �Q� �*]KY>!]U�.Rs)*�A�tit�d��"�r_law�V�F��.L.��m[&�b}. \(� ��9 gZ^��*�bQ] \mtr�(bb��ac& �T{^ lh�2+� �A��>y!� 6� \(g�� �out%H ����6D�]�Z��U��3!^{M�1W�A (Uu/WeediV�<��-��@M-coc!�i_x^M*{#g_1 g&�!� pi_{!�=-}B95>JW"�!� �!B)�6�,+P�) EU�bb:� \� aE� "���:�law�m+)�C�*�-�Bce 1x4.4})E`b_E�e#M}_{0}V�["� �[no�1A!V�s��p5�#aJ�AX0*�R h �iromrJc} +IɦsJ#�b�{aF.�FM} Fq�_�-q�2b&�M! �Ma�n�*�jK�1Q�( d�.Q  T5�$�DR��Ŝ,�a�F~3.1,��� ~alG:�����(m���J�btinued)J�&" 03}~ܓ 9.1)SF*�4%�s�ngp^[6����f�,<�U X_����A.� �iI �:/Fd5J��w se$f6�z� �� ,�, n��v$"�%�~n}D�m� *{edv�IMAv E{kk+1.J-�/�Q s�gsib��Qn�W�Le�!�-�e�=YY �!� �m*�m �QA�$n$th �_ ��(��&�[�On� bundl� �H1�LiZazLJHuM 6���L��DdaN0�e �}�7����9e endo7  Q"�G r�Gt�g�via ( �){�-8sm0W:;R Trivi$a�] 9)n2#�7^,�3m*N$B>�-x�$"1E>�*�  abel�G�� ���IXs�8 trn_"S<z.S(E���i�T}q�-��= z+w*҂/�5\w,��>?fib_act( z��{& "\��] ���:� ,� .�ong�!&|�g}"B�7���,P pi_z�G# g9fg=�^#�^� ��� :�in%bC�0%$ F�/F( !OsǓ�Yfib��, �:�3ŏEEcG�z &} �gef�cheme!�rpassage&zBe�"� ce���# &�,MzL � cont�s�.� >�*]�9})UK���03}�"9�!d!.9�PA�("�N����I��}u !l.o_)� hqa � coll&�&� U"� )B8 "0)%���-�}�a1v��т�0uaa=+%�\-w\-s\-"u ��� #4 oord��&��0)�e(r �%,d)�c�!4h���4a <��}�WF� h-PBya � � c-a�(z)� ":��[  g_c e#�oN�Rn! T�����ו�a���%H B�g_c!=*� �2|��H�$�U:}^�Z &maj%! . Di�t �G�6conven!�u$�;A� M� r�U��.kUu r i�WF}).�y�,Aw&�kR�K yield � xtraW$�6� �^�a$V�Ul>�k �^yh�"��V�� � � � �>�18e���eva[ ^M (/>26>&= "���KA>?f=+ i 0Sf�)��+&Ih���q.J.� (z_Yf �N�&522"[ ���� oryA}!�6D ���v6#5B+�� Ka96 Bo97 FBZ0ȿ.�6h�Xd{n� ee I�5)�fto�{ up�p&La�FQ���s�(� m��A�� �F�4 7}:-i&/x*� e4�} (OPE){E(medskip 1)�"$|z} $\VA"w-\1.(Pp&�u})&�innerv�+} Zv�u 9w4*��} $U(g)�� L� �gr�k �sw[ �\no0hnt 1a�W2l':q1�n �ZT��$Ocuche�E')�o$HxH}).���efnFI�2�3 0��=�#� 3�#��X��+&13^"�3�Z"�:C\�� 2F�:�2Q61 �> {iff� <')�5W�,N�*R!d"� ym�c2�;����>n q!�  T!�� �Ŕs�ps"�n$FK si_b Z* K, etc.f�u_�*�"e �w˭�/�"���1.bIXUr1)!�mbda^)���\~�\,�j�&%�ظ1�BI@!�_�D � \/ial�@ =�A6NY�n*equ�= �-�-v��v�0~�X\(m� ,2\)�\bgN_�Z�R_3>S6�"}:"�vE�=*�2 $,~$ ���"�o?a;P�� $p�3hi}A s E"� !'RQ%45sEho�@N"\{)K��&� �����- (��� hi}  sia��62�8I^Nl r��Yɖ$� �T�J� \,�G2���2m !�su�Oly�$N6� Inpw"��% :�$ &$$�6mplby�Huygens'.�0<Dutch �ai\�Q>h���,aiomer ChrKganQ (162�`695~,���/� �$w-�&of�7$.} princip �"�$FD�/ . Re�&R� @{��` h the � �/5�x4c9[<at1 a�*���'%�a�2�5�y (�k{1���N��0� ��.{ ofs`�5�"cւSSal�y&���2Y6{5# s)aQg"K6Ar!�8�eb:. Let us�SnJk�EP�/�&U�fz'�LI--gradV�� 2 3), fixVUa��FT� eLwjx�Z�CAvso�``Hc:~s�(��ȍi�7�ied e.~g.)�SW}:N iUGs�ogu�!R�] Reeh--Scha~e�orem}m��{� AA� , P���x�f�N\2P{��}"�x  �NT� *�7$ 3.2~(a).)�G� �'��, vac�}AA:X neg�� E�$S "���k@a�)�&H�x6���!3.1�Every �I9AeZ b��uF�ly���ne h7�m�\(v_a����J"CZY(.6�c%�)}n�4.1�w=� ~3.2��1�3 V8b+e�msCqu�� fi�$Y v� 5�$.�(%>� = v\). &�w��Q�&0 *�3n�Y(v,z-�! e^{z"4 \, v2� .z^1 T_1}@dots + z� , T_*� 2f�WM�D� ���c&�ZS1]��&!�>�al �#� �p *NX�}2�&4&"C�ice��a9G u2.7V eft["A9"�/ , .�5�!3�] *�� �ea�� �!�RK4q�\ 5�u2.�PJ�H��)�B�J�\�+�H2R#v,&^�FN�# -30p��J�.�0��^~ �f}X6snu)sRp -�%* J@dT@�6-�)..��EBN) \mgvspc�H :��yJ)*�6�(N(&~ f�.%�B--o%���7!(a ^c �� ).lQZ - 2b � 5�f��J6j�fΰ �^W7,W%�nu �M�B�.=�:0!)Q6��i���&�I��.u� mini�5���l n irv1 alg٦en \(� v =0 |"y:��,D�9({C1"�Fܳ� J'�rm �: \(H�7 3b. (H -�,��);��ls�)� ��bf�Esipri��j1ir2^�de�s^toj"�!mZ�?��?3{\ m �#H�Tk v�fa�}Vb�/. d;\, j�x%aj_ӊ3d} bJ)�6� kv\c�-h�5,� �&�,�8 to Xqu9h1�� � �6�# law�'v7})--?10_Lqr x[a!�g��i�_dNi� A�*j~$E�gr�R(>genIG!��8>e alue $d_v+�en*�^�8�^S�b.� �� $ ha� Ζ [($q��ne2�߉�:OA,nS���])� ���J�� d���6�  \��(H6�&K@2��"v�gBIt�Vb"�E��) .�S"r� !��: �L$ �~1a>+P&3�.c� U�$*^y�Dv�$v Lk�3��&\(p!.�! 2� \MOw�2v� M�� 1�l�2"y+0" _1,v&M\{��"��% .�Y*%v_2&�2-�4!� d_{v�k-�:[6>:[1["�*�N"&�!��%�^���7C�\s-,1�%�5x� $v_�b~$v_2$@lX+�^$Y � $* =*Z` %��}��=-0!�2(� aN�OA]og�. "1$z�m��$D$~--�) Ap�ix&�>n}.) %C�H��&� 5.� nGo�2Q��1�La!` \Vl!�� \cnj{vx!"cA5 \RQ�C:0 & bg. z^*}��!1�I��S^*�����E-Ra SASF� \(v,a"a,�͚��*/n�}� � � � If{z�dv�zf&8eq�A�&%"'%�B�D(��&# 0�<��nZi5Ƹw$I�t�o!")"I."_U�.$in��.�I 2} I1�9�:�RU[I'$}{E � �&�R�45�z^�#�#�� ř�Z�)�&:--cmuE��>C��7($I^2%%�Nal"�"=+��=I$ "\eb3�b!6%�:Aiyx�&�' also}E6j4Borcherds' OPE�3a�(9��!�Z�2.8� (v_l$�(�(AСx2)){``,a�!K{''� Y (D%�D!�BQ#+ d o�ݮ�js��6� ��!C| .� on���3�Hchv< not "73��/r&�< �'is.-T6P 4.3)&G6�� � .�:$!v%?K %2&�))zR6o $�$m�68 �e��bP�N$ topology!)�C� z_2^�< z_1>1�"2�s5( ���� Y��2� Un�M�&1 �2} !#s!�*mJ�daq|t,.�) "�":a��{6�� �� we#3!ex",s��_k,Y^ $=:7k"/M T�<,n�<ha�}�� s� k�E��� ity~� � )e�l<( �g.� $N�NN �*�� eqi^F_�`;( �*� ��� E��."�s1�R)�tro��a�\"�vCM< j2Z�,Cf _{ij����fq)^6� N� �-w1 ����nn( "��\�|=�ij�oC ,(z_i - z_j)^K��$� &9�j'S per2�"�Q�.�E M�exa��&�(. Eá�� SE�Uhan�Zm�a*a���� �0�qnd4�$� ��)c&4"��c� �dn^r�InnFE -+y8 ���"za�6���<�C]U"��5llri� }&K�Q(�=J�B�9Z�&x3 Qces. ��anb.� 503�.@;�1P�< 4�JI ce a��y*ysup�oa���� e���� (4 $x$-� VF nter����1i�)A��n!: �I.) �r��*� 6&� m*EEstress--��:..�ۘ�� ex\�VF $T$ a�)���1�^E(�6-:�5 �ō recogn�Nago�MS�X. 8�^IEhHnr� in��!:�5m"�0o9HN��)�;&�rrank 7����mic!�ce�2)Z} w�9be :v���1�\ 2} 0s-et1} T (z;vm ��?(|, v� �?a � � 6�"m/\6�v}�B U.�bU).�#%Id*%ItsCI"�A�� !�ATe2��%$��e� ��n_ѩ��E� d6fm!V�(6�\}R^�; \Left� ar�)�dz}< \spr \frac{\di}�� v} \left.\raisebox{10pt}{\hspace{-2pt}}\right) T (z;v) \, = \, 0 \, . \ \eeq Finally, the conformal Lie algebra generators should appear among its modes (see~(\ref{H-T})); in particular, the generators of the Lie algebra \(u(1) \times \spin(D)\),hmaximal compact subgroup $\gr$* nf �can be expressed by (finite) linearL binations>(the zero mo��JkAZ a>maK-he+h\Tx��p}{z^2}=xx^2}{|{\omega}|^2}$.) Since allY(elGCIm7 shoulda�Hinteger or half odd(depending oeir spi� ing !7J�,are periodicb anti, !{a�vely,IL2001,u)=(-1)^{2d>[�Zqquad u=6MHa�(o)pity prA�ty )�4.6})]�atmMP has a Fourier series��aevF�m�e�\Su_{\nue�ind+\Z} m((0}^{\infty} � 6 m} (�D e^{-�?\nuE����&8 �&!9.@$%|�e((valued homoa=�ous harmonic polynomials of degree~$m$ restricted to �unit sp��0 (we leave it readerfiaUhA)nn!�o�tween�bex-MsmDn1aD and $4.8})). Co�3ed��5�7}epis gives-�� [ H,�f1%O�]5}-%�ph.% \AM (\Left04arrow \ \, q^H2U%�q^{-H��%� \nu}F),E, |q| < 1) . U�9!�nd����4} For a scalari� (ofy���) !`hermitiE���-C��!�s:%& zeqn4.?I{1*�^*��_{� m!>mlɗ We assum�Wexiste�q(of \textit{�h}\footnote{ Josiah Williard��,(1839--1903)espublishA�0I� (�{�}A�a# | q i| <1 *}10A�eq�XA~any�'�k e (local,�X)I�s (inclu� $A=1$e� $ �L�< A1 e)G (densefHilbert  :).A�$then definI�.�m�of �by+@ndA| i4 \La A \Ra _{qu�  1}{Z(!Q)R�,5� + \� ./2�(��\, .�6 zh�I{kTA ��11-�0thus identify�!Uimagina" part��$�8"Planck's-p4 quantum divid� 'absolute.R_ $parameter [L uppe@4plane $\hcom$ �appearW (wo guises:\� a� uli ��J� stru� s}$a torus (t�0are inequival� o @rcoset{\Gamma (1)� com}I�o (inverse)Z��{fre_ %!NI fun�  $-�$� ,A�fact,P computed ��6 .� $d_b(n�nd f A�1$-icle bos�%f�� mof-� $n$#$n-\t% 1}{2}$6[ )�result i�M�a�I�\ \mathop{\prod}\limits_{���1&��\� (b3p". 1 +�$n- <��raB)^{ d_f t n��)}}��- q^n Hf�6zd_b 1.y }.�11nm� ��t�Ial5��n \! H \Ra_{\! q�E1 ��Plogarithmic derivativ�3$Z�� au)$4 �n_H}��Fa�]-�!z� M}�wd{d�?;qE)� d}{d�,\ln Zs# at for� i ralized}Ta�$els we hav�2�1��a R� �d_b (n��!�}{1)��3+E�~H\A� ( n- �!7}Qu d_fa>�oJ�}. K It� been esta��桲Q?(R )v ��s g �J�Jg$a fixed se�ellipticDin each�_y& dif: s q _{kk+1}$;� (coefficient�5at�� (2A,$u_k$) $q$--R whos" verg�  i*nje��|d (see \cite{NT03} Theorem~3.5, � MJ%F mota,���tuie; argu�of Zhu~ VZh96})qbegin{mt a��j nth4� {\rmr���@Corollary~3.6)} Il-�.�cor�9��a -�B!� $\A�\{Z  _{K� \}�a�G1}�_{1},u) \dots@n "_{n!ng��a��mP6 .� .�g�x 2y,�H}�� &# 12�WA�(meromorphic%s0symmetric (as2u!) ��p� per(%uA���ors ${a�Htd 2R (I=HHW67}MJBB!Dbe��addXX��)�%+( � _2,\, u_2�M =�2)n )��JL1+�� (1Q5�!O��A"I2b1B:Y)2)>���c��& at%:5��4!�)� ��>�> $(n-1)��F ent .�\UliA�i+1}=%] _{i}- 0+1}\) \((i=1,�,Y\) ofAiods $1K !K $. \�� o sh� verif' ޥ�f�(g��) .Z A� inde��U�555��q�X ��irming!1 abov�M�>��medskip �j,follows from1 Huygens pQ,2�in I�NT01},ɕ!singul�i� fZ��po�0for isotropic�rvna. z_{ab}^{�Z�  2!�"�5�a}+1�(b})} (\cos � ab}- alphAab�, (=0.�4�W�H$ J4"�ang� e�%< Eu%4$D$--vector $u��MPu_{b}:$ �h=V� *1Not1��8 UD�F-W -2\s�p"�+ �) >-  � 4.161-e deducumB.�� s] in Q� ab}$EE �E \pm � =� �Z�j.�l� 4.17 �s decompos� ormula ^� 1}{�p _{+}>-}��427]"}�otg!^!RN O!�F-�`B�;\pmy 9 =��ai�to se��he twomxari!��vacuumV�%Euler&�%����$�xits&� counter� 6&�6`}$� s-�FD=&n \pi}&�lim&�N \to @� �su'$n = -N}^{N�0e!+n)^{-g &�6�5�}��f� r� n}}{�}A�U� eq I�vJH $$2$--point5�or� � ��ing Eisenstein-We\-i\-er\-s\-t\-rass � � (� lattic�Z�+\Z$)� &�asZu &���both sid �19}) �or�alA�A��82.5nnn})� \pfun_{k�,kappa\lambda� ,� ) =Z@M:@ U@�gmAgM}^{MA�L^�E��[I � m + � A��+m�E�kC,.20�\( H,E<= 0,1\), \(k=1,2 \) (> 2 _+,E(_-\)) intro��d�9Sect.~2.a^��� ,u)$ ($=\I A\}$w (k){"��(, character:by�j$Y��Q ,�n� � also]��ermA�BbWightmand�Clooks y4 e� "�,"� 4.1)dA�� nw4.77} &&� )�_1,u_1�\sp"M _2,u_2.i �nɘ��d2ck! -�^{ EsF( -"' Z3 k} W�{1� �" 1pt}/2kA�; u�2  , & \nn &6I%gU lvac� �� rvac��&k a Toe�-Z ) on��1�6� i ^ cannVal'Hcom\-mu\-ta\-ti\-on"i s. U�I��ac� caBBTPor is a $c$--number (� N�J �), equ��aM�ex�� ���"at La 1� (q = 1\)), w�#e� > : ��`m0 Z �te�$--�#6�CCR2} & U 28pt��E_1m_1[.�  2m_2A�!� - � 2d} �aJ8*�6k.Q =A$a RX) I�;�#eeqa o��o!� hand� e:� toge!A�m4.9})*j ��KMS-phi1��!�s�Ỷ�Lv�.-%g.O2�� & )�jg!s~u^l2b,�Uo!Gefore,� :66�1��U� = �#R� }{1-YVq^%=1� ڨIj!�+Am6 �%$R�� 2}} N�\�iJ�i e'2.-�������irst ᾡjnonB(x\(^1�  L2 \geqslant 0\) (\(|5?�!�wh%&seC!VV2V1fV2V. FurAO,�e�"��e pre�D� $1^10.: �{1,2}}}$���� J 0)I m�2}� � �,� 0in %Exercise~�(p_� %%% ( ,i ak�eW %'�Csum s�# ov�#he�s!Kch�w '��since,%�insta:!� \(�J��,^k\) multipl"�F#1-fiM& �9$ � (af�sumEM(nu_1$Z#� �$$�k}$ $2+ + $�1,2)$Akk� v ). �illustr�co2!f� %�%�nt~4.5�casA�b9AwvNe( let us choa�& basi~ `` C''J� t��*��.�$N"�  \% *� J� c_ef} P_k � > );�"�:E  2 ��%Z s \pi^{2kusin^k]pi6�+&(>  n Q���jL-L<>\2L� � _{=%*� *�=� ��r!<\AzT�aAoll%"of�lt ��` $AoK*M* "�phi$\psi$"- obeya o'&pm�equ2.5})� some \(N� \N\)A�� {pA� � �  b�Usen�aZM[th_exp2� Qa*t ps2,s ." ���2k!N FA�= u_2;AE�A΍�`E�.'YA�*L$FZ�)i-lR�%will see#�6)�then_carry(add5al physO'io.� Amay rec��<$ili�*mF �|�gy�Zremark}A�&#a*%-st30- 4 tens�,G y ��{+�}�� -�T-cp}�1%i,u;&�1 J D�i)�!� T &�/u; 9%�rSAV�+ T_{n�+ �&�+ n�}v �$./)� � d, �ly2�+� N�+��$um�v�1�+s �+7$2B+$Amh2aABuchH,%�e exactlyl , up�.� ity,,is $\SO(D)$-&�.:��u��v � )^2 *m!D%�$u^{\, 2} v \)�A�AJI�0l hamiltonian��^. onds�f5P*�  t�"is�a6/S �&,.mr3!�0� -��v N_0�Hm�b%*64� eft(� �$f�$i��� A�\sigmm _{02; h^{(02)}_&(���ze&!* N_0=�D}{D-18i� vol(,1 �e $(D�--G.A$n�2�toIWand $Z�$4a��h�SO Ihnon�g*.R��x1U�cO M��>waat. M&s%T-��L��Q�a"�A!.-�:& M�B�B6BA~A$�� \�5Chiral!�wo& s}*t0���a}{0}\s"|{16 p>d,��BexampleJ #66est, l�known��?A�a��um �A(ory�� Nt sA� provg+m" �$2D$) ("S) CFT��*or &�*F8byVD$;+ act�6(d Minkowskii $\��0&{M}$ (�  rigor2$discussion�.see�"1%0 dopt!'er� !) view�  it�%aV�I exte��higher]# $he variabl��\� $&78})� nd(or $D=2$� ,global coordp8un?,eq,T8�!�4f)\:<. Conserved curr�&�5 � rank�2�.��6�) split� o ci$!�on[d.l5!+�5s= . (T��isM�i3f� >��6�FST}.)� vertex a�:E�"�� e full 2D�A�tJ usually � s in,e� >�wo cop'"a>n!O�2lF satis&�.postul�9of� 4.3is\(D=1 A� -T� � Gz�-)X(1�= al Lau!��inv3i�! !��.Q�.9�!�!q[ l0 ray0s $z_+$a�$z_-$� "[ � s be�i!<�ir�-$$\Sr^{1}$)�h�0r��q1�6���>C aa pair� },it �:eld���x�3��2r^ v nw5.1}�#12�#��eft\{ �ͱ z�)�&�&.�H!�) z' h@"� �9F�= ~\�i � �%eq��&Z< $U(1�/i�,m�� m�,e�!��%Wey�� } A!�MN6L( $j_{\mu}(xI�2D be�,"�: grad1+A�a (5�less) m mass2[. Henc&0th%d��g��its��l vanish�8.Qe�J$e�m4AΉ�� \�!25 �j^�=0=0}j�)-1��" ( ()0�#f1})(jA��"j^{0})=0"ol?5A�{Similar�!�A'y�e5!5nes�"c��-㱜 ���y� ��T_{0}�� 1R�FAtWn)9��fy,��6�O/$z5#0� nw4.����, $\m�.=x� Q�2!nsE���2�2�,�?�%mbf{x}=.2\,z�+z�'+2z_{D"� !� -i\, x! 81-,}{B51�3seQ���ĥ�$z_{2%hizAl*�6�}$� ��$xAQ=\tan�4A�p�-�J1 ext{a7 D=2, u = (�.�% ,\&q(i) )�Y�Q(Thu�I``�# m��s''ei.��zE�R6m#�E�aY gleq�٣�-}$m�j _&:1�$4am0}+es) "B8Ucal{TG#: := I <'q +Ba64}�6-2Ju40} F1}2z')= samWvalid�a����v�fIq Dira� $\Px��S�Cj@B: sPsi$). I+#D 8real off--diago� � $\g�6Catric�&a� i5A)("K4pt} :$array}{rr}���!"&�!\ 1&b 0 � <5�� -� �1}=J���1 և ,B  1uF6�c} /_{\upa�=}� down�-j- )��ݙ�� k= 0 =�A�+)��)}�[A0 (x)�� S�, %_{2�H A+�c�+a6�m�e� \G-i�ia�, \widetilde{� ( �E�+ aYT!Psi�� Je� �L-14! N?&? 4����B ��~ 5.�+>�1X5e �_0� Omi�_�.now�jE  sign!���'s�0M � � �&\�Z�)$)�obtai�@f M�\��� s a $1$--����~ 1iF,6�!� c� jH$\�$, �&written� ��Z.v�,\b9�=�\!� M�1� q&$):} B_:7 e^{iT(1-2n)�&2qn(A`B6)^{\as��Q��_{I�E�-�7Q4.2��(h0Gl$�<y� role��(- ,-��Hgh!u ne vx, say LA�?y w �)͡��Hbe2e�-it{&#&antico!&i.[&}mh]E2x e� �ene}Gthey ���[Q�m2P;,V4)�]�. \!\!a��$ _{mn��!�[ 5�>]I1>�J^0�� SL�(,-�6� ?(= (2 <�V�U.� !"$h$�?sA�!@ Virasoro1T-R5�#&�@):�a( %m>1�2�}P#PsJ-sm>A�=.��/i�&o/>>H(5  (in fact+f�/4i2*sumG��Mv1",s, \(H = L_0@� 7L}�d�:4.g., 14 DMS}� n). EnE��1v�u �ne�Kve� quency��K nihi��!� I�>?;$ Cq!H\*� n&-���d4.2�lT�� o�~'lI "�  i2y2��F(!�je&�IPn+"E&�%�du i� &� v��"� If��Ily repla�3e�"�Aig4.2x�>xt% A9�-$n"�:��L2 �k o@6�,n\in\Z}:l"B��%V>�a�r[>`)�F�a�>] =�).q^n=�<(2s8y�5."O5Aa�Fin"�1rm beT $understood!tɏ$-- re�7zE�: $�:#=2�� $ 2n$ $-$ $ ``$=$'' \� !�rBn -&X1r* 2n\)_ \(- �d&�.\)�,� ; \"?H%�6�&p6passag�'om��0$C$6g0$ A� rpre"e��/dB($ M\"obius iNe�\(z\mapsm4t\))�� ~acquir�� Schwarz��Ater��(6��:=L�F \(+G1}f�6 \{z,u6z5� \}\)��!��^\{ z,w \(:"�z^�CiX#p }(w)RN \) \("OD3< a(�>L6��) ,�@(Hermann Amandus -%,, 1843--1921!�w.es ��)@$in 1872.)}� BO/ ��+�&\�2U(6&}���,Ias)I,M�� k� 3B_{=&2k�7,2<�5�calcu�% )2/)--J *�(2� D�$W-!6� �q^:d��B�\�H���1w��F+NoF@> = -b�Za�,�-3R{V� E�� L+�}q^:9%� ��3�o/I�)�4)A�)"�&2���H� F�G� F 25})"�%(�%Es�)p$1l�)ex3.1}| Eq.~ I3J))"�+ 3.1 :N�+I3.1@ \(F_2A�auA�2� Ga(�&- � i�&�.tau +} �d@?2�I�-Snew4xc9A�!�c��Z.��0!�2 *�.�' ��$= && \podrU�i���� +  !&�7:}6(QBg�-6�>�)F3 �(2n! -�5p{&�:T=�0= R�:�!� 9y11ID2}9)=a:�]".2SER���oA�M�n�6)>�=�u��6e IDX �o?K�Y�mean_H1aDith \(�G=�/E�f�G(= 1+1 =2\) � u�harges{,�ow"L}�>V-�WAV4 72�S2� M�n!�&� q-rJ��6*���� }�� ��2\, G_2^!�m��*� 3�<~a�g�Fe�r}m�exr:4} V�B�ɰ-�4E) T $F_2�'$tO:���. �D,it{Hint}: us� [ \(qm�&�1�&{Q��E. y2��H.�&6@ @) = -q^.p��:��$ \(q �69 =�)��I��c�0lIhR:E� even ��6�*� & ?o9!� ���D aNa �2�#��$�% )QXCY? AccX#gx Se"<3.2RY��),�^B�~3.1)�\�it{g�}Ex�' moduUor� we�a�!�level $�O _{\theta}L\PU\(H:=2�� we!���eg�1Lex iate�牃}C4refm)� the Q ak&[Ou��6�4}}\d%#\"dO., (J)^2� 6�_a�It�9s�!�Ba�Z&�(v!N u� )�MaF"l r�-on&���3�/is flt. (IuP,, sure, not �Qar��c'&�� naly�Lora� =0\)�$i�,�r,e�Y� K � "� is peculi k *--�LmeI�\(D�,�4%<lea�4a�_I� A �# has M�$Do only�T!���aYDiY"s9 ��lR,F 5�2J-�=tFv/��nrmF!>+&�Y5$D=8n+.$\ n=0,�4e�!%d out��.�adoq� Majorana-�spinors}=~e. $2�cD-2n}$* T semi 7aus!Oe 6YW3%[&�$�{)$ �d(m�� �\�=J ��st" i�s�6be�,A�^� �oI�r ���e;F_I�i)�~ 6�x�%pB�c)$ZK:=�T1^�}}$ �FAE���1�Neveu-�9 tor}A'.%-tIA��el} (h�$��$I$`$Fi$$Z9No�!_ re&�"edmO�:�$ST�I.^!�J��/�RamonQ��vF_{I}^{Rm���w6 (ST  ))�� "� 1}��})��1.r g ?��" G_O �-2(2O) ,"rZ_I� a(�&� ,���6�^��&�Gn.����!&&�36�#a 6c$0"�F�l$E���#�cNS�# c$DRA_�`X��$"�1}{48�KnI`e;|+s�+quD3d�Xmia��Qaco�f\%��)�:�Xselect#}&� (ac� ani" B� 6� ) rap0�"%1 orng�2ZR �a2��SNI�ini +&́(eigen��%Z$ �t�,�[=AR}$. �� ��-��b3�_e� 4A) �r��Xe� E_{R"�k� *� }}{4Mݺ>.�=B�+\� :\Long�!a�"�( ' 2�.Z&�48�"$,:� b!3magnetMz��!�Ba0��tV(!S,�/ht)KPI (2�>6},*16})$R.U^, *:&a��3``�''A��+nd{�1v1knowledgEi��Y�s does suhVex �1�:�Q?alex*�!. �0lso npQ%�"�}�6�\a/ze�h!_E;eNM-�U�'I�J�! ).t'�)[U� ) . ) ] �v:2 &�. 2* :ɏ��:�} J_{n�!^d"�8%R{5 +dbeq J0 =LV� 5 >H ^{+}�%6�-�>0 6+E�>"�:�\rhN \Z�f�k���ErhoLe _{n+q��j * n\neq�k�� 5.26"A��Gp �:C.�Dre AZ2�J�!R"E5- eqn5�a�[)�, M8B� ] = eqj n �}j8 ,b Shn,�yfd-�fA�N9JeJ_m� �QV$�Fn,-�+���Joe/�~�BF)� re�Aeds��.����5� a X�.� a��so��(led Sugwara! mulau 2�8} 6Y'(]� !ar!�-eiN!.()�1E&-B0=20J_0^2A�su`�*�KJ_m A��$EFn =2�4�^!� &Kk)�f coupl-q�DB� �� }%lex}%I�5e2-$� $ wemW-���aOge�6tribuaz� �2&�bmu$-�%�e��%hem�>poten�0} �NA�g��WZ7 � : F�9} Z_{NSyV dY\m"] !�TR"�e1��.�_0} q�1^{JZ�'� !�m��*$0%�>+�ziWm!��)��lqRX7as ``!#squ��B F� ''t4%R�?Wp  5.1.|"s 7Z)�to�(�� 6�ds1 sqrt� bk!VPsi^11PM�� ) -�? 2R KC then��Y�3�]?*�FX�O:e.�Fc.�rD�$�7.O�i2�.gs>rNfA Sz�6?�V6W.���, \zApa�gyYp�d� 6-# twic &69*� B� q" SeSO)/h-�{q,aV  1K_5�tau!q�=F�AN��L.�\);"6.�2�Pa�B) �sIb{q�= (BA �\)���^{~x, B = 2iR6��\)� �e� 2�� �eJBd%E/{+}@&� �!j��I�'\Cmn�+�N�, �� + R � �h-&_.! "% m=Q�6� U#�-1A�:! � 'F�{r�I��"�In�!X �a�.re�.I)W3!�~Ws�S?h!E�\� al} 4`o ^: Z�u 6] Z} q-�JZq}Zi2YOeO&m!E�n92R4�� \���=�44,�l2@*M, �k-1��muR6 �22I;�?^-*� !�g2�  UsrY�%��,AA2$��Dv�N ioJ#5�(1�va�Qt"D \m� ,%M� }{ \.".1w! >w>�m "s&mJ.� 1� 1-q^^�^"njI�!�}\, n^�,"e na� k5�(=  _{00})\))x he Rie�)u"�� 3�]; $! �Dedek�3 -"�, oV$3)f)� &� vp�`o�M�cE34}.h �y�@ a�+trivial EqtyN7,Jacobi triplbN oduck }.fq5 repe. stud� Li�DI8 *�  %( E�n��'5�' 5.1�#!rr4l a ToRcB� �h/ٖh�?2-6N+1>�\�/�LIO#�,Am 6��! C&�Aw��� 6: ]N}D��E�qc�Z_R6� �Ae;Q�'6�W6�7n�BC.� �2G12� m��^.�}}� ^J�&0 �l*PnZ� U�� q^n1 ��b.] )5Z_R�A ���"?!M�2YF�_�andFE�x$ts lowest � �F� 9} e!I]�?�?9�Q)Y./(7e_R^2 �p��1}{�.\W?N�v�"WGe�s�amI�%'0ossibility to Qn�t�`����j�F41js. Let�Fsi_d �F!P$\sbe ��E*� c:gat���a file�Ena\-te\-�}*�d~� ay#� �u�D�y���Q6�H $T �co�]busIM OPE��pS_d�@4,to1,&& =�qW1 M�z.])#&6,+ >"AFFQ7�3Q> �N_0}{�B�F * �N_1.-� T?B�z_1z_�Y\,��o�, m(��>&5xE�F} �� #2d}?, �E�T(\6�+ O ( "49 W a�A� WardbxŽ(�� y 7)a S�'�I�7�:O(N_|[�"�N�2, \(cH!2�4  7T(z` `�[\) �h*�9 cent]N�v�,�Lf8, �3.5�AS&import\P&MB��"jE{)�"��uct $-*�$ �q.�)�&�*�-v*.Q� �\,M� (z_2�#+NI�"U�$%�.�bk)$!a"�� c}y�G bi�0  %!�\(|,�\X�g�*�0odd $2d$. Pas�#m�ha*�UR&:�53�dE �_k�.��_kw \(a/^544:3�].z_k& FW\) �f�f \)) &?.tm2!�ak>�J�|m�_.b7ptNvoZ� ��X �%�B�[>�B>��Z?B��7)-��F��.� SR1Y^d�1 �q�_ v@2 T �*�-6�*�-. �-�o_()nfF) + O�min�Op*��� . \q���FOmp~<�LKm\Ne�_,u*��~npQm� U$�# 2 (u��&���ion�m7lNdY��-�!M .�3�E3�-M�y3 RR����Yh\�z�2�2~�!� �1��U�N�km�%)vN�nn���AlN��2X N� �:�>�,m� i�� -9^4��,9! >j:= �-"c}{&G a (W�{ al�� y en V ed aF���Y+ type�Z%E�2/ex+7"_0l0���our8Xc"�U*� )go. ��6N$�\(d�h.�1-,\(c�R�D  0>�4  tdref͓�� $~>Y2�$ (cp.� f 4.29�31�5isU:IA "=a��)^�ZS=\(!�"�<6�\) �FWi�ge� �:i7@��a !��["�L�\)m��\c.�^�X inva�0t} lZa*eis _��%G8tm3!*%�in . �"�W"� :EO\(2d &Vf3��Ses"XP9�� $p_k^1!t)�|)"$�*�KQ��}$rm.� ^{-k}�0�%"��Lu6,Ys7na�`claqT:(��olv��s builx& block most+�Xl\�P2D CFTe%ba�&o���y�Laf��$Kac--Moody�Y�oc�65�c���Z̓�͓s.EKa96}�|�1���G KT97MEach b?���rzl�}:m/�{be�y�La�% dire<N�(rank~$r��bel�X ]\(G = �W^r�}n"4-�]Eo�C q�Qoftre) trea�s%yly��#briefG�$X e�3p y a�\ice-� b2[$G*Zr r�/ 4!�1�e�\X ��WL*��g hat{�frak{g}�: =u(1�3o�6s rE��%ajnon1;�(��6b�survey�0� �s ematician)&��Kac's b�tb K90}Q E(MR87�L�Zuk  GO862� J.)>�E��r[�mha�E���$\Alg$]0�0 'sJ'O�Iq $h� $\VA�1�b)��Ja�I�lR $\hh$=an $r$2�_�&~u_ : de�kW9 c$ $X4C$+�& 4a�-)c�E�"w���+�Zdowq�an "B`5Zmk�4a h \Vl h' \ras6�R�} \(h,hhmo a�� $= \Dh��1\(\LAT~ b�� A (an Yhve >�) �>�K $\la�}�\b.�Z �all \(tW, %�LAT`F�U)�$Heisenbergu 6ehhhc$g�"�s $h_n n\(n}jZS�u\(h hhc\)���� Dneq5.4�;� [ h_n, h'*�,�_N�$�,��2�\  ((�� h+� h')_�+_nVmujn �-�ambda*" �C�.It5�+al env,��2k_{\hh}$a��7 three sub '�gs (%Q2f,\pm)&mV0.5pt}��-g�{$h�I!Wby n$�\(\mp �16�z.{)>ی&I8 a�$\J�)��1�wA� � is"P�tG8of"�5c*#hs �L���Kly!<.�s�:�) ��. MoreJ,try&�A�$��5�\���ed� "`�s�O�n�3E6�s}zih^1_{n2&� h^=._m@e�\(n� l8s 'n_m� �w�!5Ks�<6*�&i,6} �a \conG# 2�+)}) \��2!SV-)}I��@ev!d�F\� long!��l��$�X�.�3V_fe� Fock��9����S_{��}6� a1 $\r;\�:!5�$� 2N 7} h:0 5!%�  0 hrj S�V�� �?��Z2i�95�Whhc)>�1n�^wordsh^V.�{>uE� quot�`2���c�l2 $(\{��NR�:$ $h�����oplus h��A$;U�:�u5� @"� "���:�A�y�.��8!QP6 !.IO��ESm��Y^�^.f2�VA9�� �O%&K Q!�LATik[�5� Cle&Za� $y�$,�Ne?8 � fiT22 $, a);��VA$P7 � ay� :G.3u 3>e)=� � 6t��fu�%r�i e �� twina�"�T} $E^-)�W �ə!��7B}, ���F�9} W ()u����dteqq e�+  "� "M , L\�"]1� &O� �Q Xa�-Cc \r�(�f \epsil8i E � \rv-/��k\" 61 '*S :$Z\�pLe--�ors. Rr92�b zI>x ���i � MB�)g �!ՙv)we�QRi�a�4&n b��4'�:� .}. Eqs.~���� �t2�>2� &�D.--"�w>(2bU�r�ible}C ��r�H�X# s.�E+A�ȟro�i�`to~y1M$!�E�`A>ID_{\VA$I\(B�0l6i��\=IiA�vac =A����]CLa�t�W��W�] ! �  %by.�50}) 6!� �k�-F�512�\i�%- a= �6<�luq ���.�:�i˜��,�!"S �?���|���E@asV� iNV�$g�cocyclA�R-7 &ؐE�5�.b� � �,�_�@%#Z`W`'d!^B�I.�� !���)M1Zq gaug*cDeD} 6}�U� e)9�A�+v R.  A� ta (Q�), e�g� ri9o� han&?!�1���$= a5�cobou՜y}�\.57j��' 6��C�%x)}2)�)A�Z�)Q�A�re���Br�/��jV��ma�D'A�aȟpWϕ,�"A�Vgt����Ua� meanA�at��sh��� . o�y �$&��dJ�6� . By,Wex5��emC�Y$Chapt.~4) � enough� in�a systeh mut�o% �s Nzm�`�.�J$.*8�'� 2k��$% ?�$� $�,Span_{\C} \{}= :\) $i�� inpO� �Xdue�the %" B�R��a"A���4A�. �g%a�w<� :pJ&4} h (z����aXY (h, �)"s`�� , \ZaZA/z^{-n-57!>�@h%:hh&�,� ��J�&�b��@):*��� (wV#*| "l ?r��di_{w}� (z-w��"� �7 �,YS �)z^n w5���qP�.U 5}L 3�p2�p�*ajYe&� :8re ��qf$6,/) 6} Y"�!�"�)!���}, )��2o ,!�i _C!�W/\,)�"� size=]M+> � #=�8n@!2\)#,|'VIfH-JI!v� q�) a�`-V$ 2r~{����n��� )��_%7�hh2�i�`��s``� grar>�}$\�� Z(�sbF� 57} :(!�%��"y��C@0%QRie�:>�j<1]z^{�9�4?.Fr� +-���"0&���gJ]s.�5z(6��(: 7ȮiW $>��?R1v�UZ~� � ���w F�3�L�_= _(� j�*}^r \! &�N�/�mbda_j<)�^ �.):IM (V@> :<%�! �n# !)�(�{�K -1} �M+ � � B�D1}18i�Ga� H} N^j '\}_{jK�%!\� �� A/l6r�Q �nR!�I dual [F�4l a�PVl�ka�� _{jkP span*eQxm �}.^*$��#is���E� R�%*A1�"� ��Z\�4 M > _2^A�)&���e&�M ``�Sugaw*�M}''"�&!�re"��s"��$n $L  BE2g$T5#< �@ (n^{3}-n)i _n�P"� ^cRZWe�m��Ri6n.�0 Zf�u( z-���z}� 9��N�Ž�"v)[`Q&<�X %�gX s $d��( �~|$�r�a"svalf$& �".,6�7-1EV-&^'�gW� 3loc�0!{proce���� a&�i}uc�o�� 6�2� s$ hav�an�Tn@� m�x"3Vs�$0.(q 6_�p$Qi�, P]� �=d�F 6�A(<)�^*a�e�h�w "�"&In�.�^]�A�%2o�%�}�*�2�d"�.��.�( �&H�Z�=�5gma2����bu�6%Q2�<Rs24\)R�ar��byTuitz�R� �'&z"w&%J�"�6R���ESBi�vq�8NK��-�a:��*�=s -�E�"�aK��D�2�2�to5.6a� (-7 ,-�)�&@v+ �� �lN #BN1)(�#a�eVdulaDO)fD06�=S = d} *�)^* (Anj��VAM#~���peZ*'oe maҢ-Z5D e �!a�9�"� s: (,l&Cm �)8q2/\); (N?71F0=� � (0F � =3)*�k�2}); (4B��;I (5)~&M ). A�.vG.T� ,�a�begu�1�l�(�_ !��/�' . Ana�i �a�(�t�+(�y��%y Aor~*��� mad���. BK04� FME�1�����F35^: �  \�/ to���۱mF���ױ~ bim�. ve (�it*]a2��%"�d7~(5), GAZ*< law�� (�(. ��hU!Mnq�^xF}E�!� *v"�y"�5��Y*� �G �1�ver.��8 �\o%S6�� ;E^*��:=!f{e  u� :�A& :� +&�.L�.ڦ�8o {$��o9 6) they�ir��ho--�co0(�Oa&Y �hh͘&�L�!!�>�La:���LM%q qn�=�eeV�2�^Q!�Ccie.Bu��Y+!�F( $, �5ny�n�O!7I�vY�6�(��!Oabcu��)�)�\}$>! n a M�"g �!/�enY�Pl���*�:Ņ69��Jq+1w! � 2�� % :W$I �|Q+ �_z=- *r�>$h�v N� ��e^{-i)=E� q E3��n!<:R/( .�f,�:x Qmuyh") 5 ",6 b �'.,e�Dny|E�]5 6�L�H�Q�aVm|eW |4 6�2'.3�O�&Y�H�GZ�eE�u��ձB of$ M�_8y.� $. (,p�Fm\])A;Mܙ�-Q� NR��hx:3"5Q��Y��}OV2.23}) �\G5�e,7(�7W(a�)u�self--�}���5$h,8$ $(=Q^*)$ �u�xBW~???)RID�P???i�-lyes�)5%8 MH73A��KP85});R]1A"���)a�-va�? ՠ��A0$,� vasF: 7�y*^{E_8QA.� e@P!�V�xg ͂^Ji[ jɘ"#^bz"Y��.U�"X�"���j�% W&�,9nF7�6B�= �WR %'�[1r�J�)16T7 ��^8:�+.*10.*&�y 2*01.* mg(d240ckK G_4-�Z � gin{"�`A>�Olf+ iffJ is bluniM�},  !anvolǜ�9fs){(B�ell (d2$/(a roo19�"�)�l�L�.$�x�innS��0� ;v�n �e Gram.G�= ��� aإ� � one. Even�1'�1ly�� 6�c$f signaC<�s`.?$8$B "��T.6�6V� �9��2�9re�D�U-degene�u� ic�Lin�;�!e�!wr��5J��- "��)� lengths��1��p��ٺm��sm!a0;L9)4��!=3).Jy3+un�n ("�)smg@%�)H n�nf��� ��.G$(25,1X (9 &n �toɥpsuper-�0�w �ies>u9T��is�ktru@K]C�(pp�&e%� (�%) JS5�.�72�-)! non-5�9�vJ$I& �!1m�]�f)�$16$:�|16��h�m]of.)�Ms�-%�$4$Dh���%�$ Lemma~6.5�G�u �5�y$)� �$24E,"h�24.,cHSa��$E��pQuA}&�+smM��\[U�~$(8,0)$�&*�(.qk�@yAЩ��s}" _1ת6 _8\)�}����FOCartan��Z/ u _i0  a = c_{ij�c_{jicDkI_{ii}�w1 c_{58}= +1}=�!, (+1i�Z� \(& �6\S�;ij}=0\)�wis���Jer �2 mo�3>#wu�[-�-�,�/aut�!x &כa�1ed.�# L�u�I^Bou68�Cin K90},(.ers~4A�~6.�`$�6�DC $N�e�&Tkhl}�\(N!L (�Bded�pe>.M�BFK86}XE���(|D v6��"���E� �KDB���d�@&�V�.�=Nlv� f��AA�"SFj 3#���' \40n} G^Y� �Qn"Fm_{'nZ�& � I 'w+" rho zH6�� G 5^{f}�Z�. �]_å� lB# .�nO ?\pmV "�"Regar��!�n!��F9Gal)E�E-��}M$Q# #-->�, $SV1`"�I�zs�C by $-A,: $U1"RJ$Z $J=^R�"a (ofE�s���as?����V-t ^9Ftid�J�* am�>���es�a2^�&&"� -1A 1�IwY".I, mpAGY`S]_+ = 2�pm1(n+m��&) q!�Pc}{3}qBAq( n+���A;B:TT2� J_n,.�o"" g\+_{n, +gjg�dp�pm��qQ�A�pm"�qRDLb �9n�+m��L�}~p� O1�)-)�n�E�rho #)��!�},6�)!�m �)(+m&1e� 5� ^3-n,9]-\.�qnnj a Ap*�6c� N��5�r��1�.�EϷJ_@.��S0\�6n1B�feV]avera�6"of u�h�2�$ �2&! �G>3^{+.� -n}^�"`N�R(V�f>F�6)��e�I�M2�d1�^KT(!�% �2:AQE�Es\*@6pQt��g2IS� X ��2� ${&�PY $�+x^�Fm�w�9��?C:�R#�#� �] �G%�- \zet.�mG!�mM�6 ���E�>k�J1�O*2%�1�\&��62��-�#qX3+ȟ� ��R}{�\%*�X5�3} E�ReV)�Mk �&�II/#%�)^2�2O}}{ 1J�A�kS � &I��+^%j�).FY6~-\} A�!�5o5�)�1� �L�!v�T �\{- 1}{i �2VY� 4�Wy &�2ce��>9Z8z�-897&cB8%�!�0�aIt2 �&�'(a�O�We�Omp*Us)Y �' $p^em_k*ZW�P#2��\2[�'�yVy%Ti�\pi^3}E8c� �31?Y^� �q \E5�ji}�m �>�A1� ,�s�n�s2"� #�-%�R�) type��TUtpV!�*2tn8- �G^+XR1-g!N%M�)XAf%YY�e� ^{-3_)�55s~5=��T �A���0no longer deal�w����&!or�e��mea�˩�r�";‡*#"�=�t݇�a2" �$"�$K�, how33,��YB6~6CG ��&N� .��).R�wH"$)ϲI�.� 6�s (UIR�V�describ?��s �� iscrete��H�A�c2c20I 8n} ca��g c,W 3"_ 6}{k�Vr Y SW'j��L,�!f�(\(\BINOMIALG{kQL UIR R �Y k;l,"� \)I62cN 9 �H��H}_{l]��:^�y�.�1 LO&l|4�ki~� �l��M �2=l %# (��l,-l+_�,l���7��!"��l(��z�v} $e_mc&�c=i�!�B�h!\ɾ�>F� 5�� && e+ ,!* imF�UU&)l��l+"� -m^2*1 k� -n �{sUaԡ[[%�j�R)qj -�-� -��]�.��0 bY�\-2��aa�\a �in!x1���Uk$ a�(<�&�U"�8UIRa:): 2�e�5[b�\mu;\,�9TR_RV=A�6w bu|� (�l6�"mu}&�5b�5)�^T02�.�&�;:on��;���56)�Y�-$B�$ ";R�"!�m{�����"�d�> Q "� )\) ��}�>������T^�#*�7 �T^�ibD2o�>V���N9e&�$RL��.I-�JqOR��N�2�KZ``zray''q xeta R0p; ~W&�:8 �Fw%Ca�^{4 2.��*� \&.d�ef�va� � ��x&�!\()�5�Jl\��B*^5V)�Z7>\a" \supNW, e2�6-�I�0Q� 2k+4 �) \cap>N;q @N>!� _ � �-sNh\��2"r�e�J�+ 2.15?��20F�YB�ov�[�e�e{��R�F2oq_(ST� +4}S �a�X G$ $S^2$e�6QVXnz2��{amepag�"� Skproof}�!sh�6�4}�$�$EQ� ,"g�H"�@1#eV �٥ce�yi^lm/�.k568�-�.G 9QB�AM8 �Ct )\{W as( .P - m*��ks�W\��Z�a�VZ�f*w@ expl�2� %�c_k|%e�( K=\6h ��%Y W-"� ob+�h  \(N9 �K)��.S~�d49$It�1�jat  \(5� Jan.6ZI�n $.�Ck It!_ G88}�i�V�<��)&.�&! msel�CYA�?���y6�"|Ww.�I0(� �%�*B�Ee �Ts.��l'm'} S� l'mlr( M�U2T�it��2{L'�- {�2R A��I� � l+�*� ( l'F�Q# i<dmm' 2� �o�N}�~01!Y(get a glimpz��rǐ��et�x�_al!�els cap�#�0T0`�a56� R� wLJda�us��_woSthem,9�s��M5�\,+d�\�o� odel��A�&{a[/.���r,��2\(Q=\Z \(s3`- �<d�in c5.2.���I� (�6Kl=m� �Rto \(l�j5!m=y1EB2L�be labej1"�)q2�b+I�(gi9 the �*ge� ir!IUa2�����:��m%EPK�� Y6�K���6>��)� &8}0AP ��!� la�a�m�D  ei (:6}��-�"*�6a|�ap��et#c � "���s&U�e�pmPR��.� \))#�"e$3S;!O!�e�6ap$ @_l"�* reci5;ö1� �A&jvz1b�E�e"�*: "�9.Gmٛe%��22"�bQ� ���,�De�G?a�$ $--��jn[avB�� ��68}N}"|\^��/�3�& K����n�,2�e*R�*0� fHlBt� _?�2IO/�Hl^ �n�}m}{�!�y:��ɂ%6~� ��$S�atrix-Ni�� (}H��� :AcaeA�o�S�n :�l"��)�9})� \(K�`J*�=2&m!!TGm�� !�JK� J �mu�� �qrt{l� �m'��Q.1G�� .K_{R)����M$�A$2c��b��&�c�at�B}_� ���% �%�:ы�K2 "�% opfi�g!�aQ���&1pm �?�_"w � .��?2^H�6��A>>��� it{SV}�bft(*B$ V5w9nJ�by � 5k� "�ҠeB�$, with (anti)8commutation rel �[s~(\ref{eqn5.41n}), in which the central charge $c$ is replaced by its numerical value $c_k$2[�F8n})) splits into two pieces with respect to $\mathcal{B}_2$ and so do �8haracters $K_m$.i@57n}): \beq\label ��59n} K_m \left( \tau,\, \mu;\,3 \right) \, = \, K_{2m} :.2 /120+ *+6^, - pH \eeq corresponding�minima5g$and conforweightB�60n} e�2m�@= \frac{m}{3} , \.&+6.(-.l /1}{2} + = \, .)$ For $k=2$%�4fields $G^{\pm9e zeta�L$ can be factorized Qb I�!f sFG 1n} n`Q Jj� \psi1'2��-�where $nH$ a#\ait{su�Uu4$ currents of a a�\pm 1$E:dimensa�$ $b� $ is%jHMajorana--Weyl fermB�of Remark~5.1. The Neveu--Schwarz represent�Q2�SV}_21�8 involve produc� $\Za�twisted:WV4the $\widehat{="}_1Fd1% algebra�ir !0�=M7written����au�Aa.B062n} \chi_{005�6H�I3@&& \hspace{-15pt}m� q^{-ii1}{48}}a �l,\{\raisebox{3{B3pt}}��. K_0�6�9f %" op{\!f4}\limits_{n\, ��( 1}^{\infty�1+q^{n� 2}} s) + \nn.�17�+Z�+� 2};\��-f�%8.�7\})�\,�a�=.�)���J�\�t�@15� 1�� ! q_{\mu} + ^{-15L q^{)3!��q^2= dots X\} \\ 2�3U�1� 2���K_ {m { �ZF 2 24}}�Wn ץ , \quad m1� ��B� 4n} && (e�M�)9m}{4}\,J�{'I(..�)j�" 1}{1�2[1}{8}�I*e�2��������-!.'i�-��������}�y��a�mVm�Z+ z�5u�2,J� � ���.6�����^?}���u�� �$e���Nm�.*�h^ 4>@�ti�.� 4a We leave it� reader offassumesP ��ompact �,��aM�6A�&& �F lu -�4\partial}{2\pi~.�- d_0^�( �_M  +) �y0���_u% �_u- - hu \cdot )i � j) + a�8" s� >&y u}ѹ�(NoA�i5e :�( parametriz� \(z = e^%w i1q u\) m�i�8preA�a�phcoe3 atesi*da ``logarithmic radius'' $%� $.) A gin{�W�a�ŇQ�u$aA(6.1)�an � ior diffe1i �on A�$(D-1)$-�De $u^2=1$ since \(=�� \{5�^2 -11� f3 \} =^23Q(Y�\, f - 4u^)m�\) \(=A���� \end9-%.,Fourier mode�\�7%g, uzeigen��o�_u$u�2}fJ-uC8 \sum_{n \in \Zem�_n�6 e^{-a�!n �E�@ q1� + n!�a�F�JiVe+e�q y1(_n�ai�8(homogeneous��%*z$deg�84\(-d_0-n\); fo�n\geqsl��d_0\)^ {-n}Za harm�( polynomiale \(nf<\). Moreover, we�nA�5c=o � |n|<. �:� $2$�l��F,a�Y3�vac1�1�%�_1�Y�I�R3_2 &�� \rR�YE d�, `{1�"�1-2\cos A>\alpha�UPA � :+�� -4\p��:V �^{!c}���` 3 b:= ��u_2\))&pro�iov to��A8ra��%���$Gegenbauer=� $x= vu$:�4!��1-2xt +typlambd�-Tu�  0&�t�, C_n^{< axu�� (�)��kyrpP[ͨn� Z]͹6^k )6(� 2()_{n-k}}{k!g (2�� 2$  n-2k?!�����" y%��Gl"% 6 5 �[q1-x9� �d2d x^2}&�2-e+�Yx0}{dx} + �)n+/� ]��1�!� �� orthogA� ity n���c�A�D&� 6} & \T^ 2Im8-1}}{\pi} \INTG {1} zTC_mrsA4(6Y0:� , dxQq�\Gamm&� �+"� "n}}{ /!� y 0-q ) n!1�n+:eI, &3 V�9�-�( \BINOMIAL{� -1}{ , .O eeqa follow� .���obeI��"�6�7Y�O �,���� "Ju2��]A\�V � n}iq|��"|} 1en,-��jB&�w ^{d_�}-~�|�1���( \text{for}a!y 2����yD=4  (��$case studiVT86})E se {\it*� Rn}  � $elementary�[ lici�m:^ 8N�Ul.��S!�!.M%���8 sin�!!��$}{ �72�-c( !$\�= 1,\ )�.:) �q alcu~CCR2})--$KMS-phi2})� %� giveE�a & q��LaU��=5{_ MB2�,Ra_{\! q} = .NZ1Qn"3p 2P& \0!v6�=�u�Z�#=��\! - Ci��a# .6 1 \!�\!.���nonumber�a�� henc)["� 1P�!.c���!6I���}{ n!��!�6�f@9c6N�%B=e� 4 n68o InsertYE�in$i expa� o7>:� 1F ʩQ�� �D �,��Su_{|n|�m� �(_�,2�S\,\ ��x &� } "�we�di�Y�5}aI"F0pF�)�)�o-4�^%_+ 6-р$ +�e�:�+�� � dsum*�!��0�T �"�q^0-.lnM�  \ fM��ĥ����� 1}{( )^{_}} P_�w d;��,u_2;-)�qquad�I�!"� E"�$nw4.77}) $ Z$! �a4basic elliptic"P~� _ef}).� thus� foun�"�ti�QrM$q$--u+fl s $P_k�$above argu�s" vali4any "U"~$d$. Ii�Ś(\(D=4\) (\(�= 1 �eca�2S �18e})a dedu��qneq6.1|!�$-�!�1)��2!� 2m�& 8A�U�MJY� -E�� &V L1}{A: KAe@{ (A~tg nmC-BuG �eD�o��eKc,f���+ n&�%1} - u!��!A)passageA�the�& $2$-1Qe* sists��reV�(e��C�doubly periodic Eisensten-Weierstra� erie:� 11}.��/b/186��H9^ pfun�4-d- ta"��N)-B)$ "� ! >� �D=4%� (n&s!��zTp_1-rep2})). Similarly�\(D = 6.�� wA>�0�! \2�2�ީa�� �Q�26j+ib��eGu3*�J =�|m8~� 1�!C^2e�2�2v%�cVv%�6�:�+V&+1� �+ �+n 2�,� N&�$9pt�2*&��kM#i1&�m �*4%bU�+f �$, ,!t%�����it4A)���)�6r*��e�26�B�!�N)B�!�%�@,!�pi��%��"�(-�BS- R)F�%&=��]. \./  To,puze ��Uby��mean_H1}���� find�&�(s $d_b (n)$��( $\Span_{\C��K6 (u"01\}$���� �$n$ on ticl��ft = j is ). A*�P> ��&6 ���8,u)$ every such ��isomoc^�C.�JH�/ $u%(�$O$ f� =� � +1,�$bRecall��i er�"; {��s is $"� -t4(1-t)^D}$ ($=$J,�4 5�$t�� )( "\))��E7� E) =7"I�� !8#�+>2�� �% y&� ;2n�eU(2�o\ �!& &%�+R -�����- k�E����N2^ M\ !�lc_k50D�)} n^{2k�N"� Thus.� 6` �3.� .��)"6��! H��(q} ( \equiv�0it{tr}_{\DOM{�, �H![q^H�{�&Z/.*:�R!4 !A%n"}%�d�*#, �&�V[9|-� +1} c_{k- �=�;xB_!�}{4)�+�` ` GW�.� L F� ($ � $ bei�,e Bernoulli Js).�"�Ja� phys�#4-�#Vwf JQ7./+ E�.B!�%�G_4 (�". : <� O�)4RM� 2c!All�ō[ �"� �='�& ed restri�%t�� inci!% $u_a�;T $D-g!"e�0i� L seen directly from �%$ula:d���%nsequ���a�{l observ�,by Borchers~�&Bo64}oe resulC&an�t{&�11���4Z�&in�hi6CFT. ?insta>"!�  (2D).�2:5 6� ),!��Cold6.1a�6W.��,2� = -Q� �9�  2���a�H;"� u2WO + 2 ���!Mze��e�n.@�X�d.�i�cIJ4$!?>G!_a1| $U(1&/4)�6(cE>�( rk stems Ezbf�&iE,easC#@to verify, say, W\(man positiv<�e 12�(I) � us obtain�Xa necess"iU�ex4 �i t higher .]�*ys2$\*/*+�)"*ec.7} ,b� } int�4�!$2\6*(s 2$ matrix�*�4!~)1+ erni�"�4L (see also Appendix~|9 ap:2n}) %F! C)N( will7 ve useful%�y�bot inor�antisym�&c tensor*C) ��zj 6.33�Q_ٷ-�\sigma. Q_k^+�  (0�"3��$Q_4��\ID� Z{3m+q�%�8{array}{cc} 0 &.\ 1 & 0 �% *�*( �n8�[�\ i�\3يb� �\��!A�>�, q&MB?,AV!�R_..46.34} Q_{\cmu}!�, n�4 �4-# 2"�?\5F - n`T v-B�V�cnu( �4 4"y H,9 and below.den�)(a$( Sect.~4.4)%�iteanq�conjug�X by a superscript ``+''&e�c>b 35} .�J��O"S %%!6!wa0{�Bw&� q+ u$widetilde{I� cm:�j�.^+� �� :Amselfdua(0Azti9n<$\spin (4)$ Lie ���tor*3.��usebno�!:�6!irz� ��� 2� ! A<}^{�1z^2��<�J^+L�=at�O^+Q�-R�OEm7+.{�.�S ��Ui�FW8&�)�� �$��$-$e]o!�u6)�*�,~$�$In Eqs�2�u)<� al3to:�g#!�_1�rz_�8 .1A�� 4 (=54 V4zEspr z_2�� (Bh?2 ["�, 2644X,HgJ22of "�mN�0�5* 3�'�� \)K"Amutually9� �*lexz on!n��2: 6.37 chiѠz m�)� ѻchi^*!2 +� "P)_��and�$ 9B}!f2{6�}6J� ;�9N��X ��O�@\� transN / un�5he *�$in~>z>�\(��-4b\) -  v=r:6$��$�"$F�$" 35 7B�5 velyBv{a�A}E� refl4$on $j_W$ iM'*� 9\J( �<$ongmapsto �� e%}�q#1 ^{ d>&�Ysmall�@)"�>22$}}}}zN�!�(AB; pi(z,REXR4%9�f \nn�?a:�x:�A�+1�]�^� � V�^+2�V� �W a�&o$5 invariant�Of6�s, *� a9AT�i� |�)L > 6{C.�a��%��a�)!̉=Y�^+�Y�"�4 ?��A�!�MD�WiF�v0��{}" >�_{\bet. *�&6�FU."�&-1�Y&�): 'In2�!�Q ce�52QIy7��equ2.1�(s ensur#H�iquaY-%26.4�9�_1} �o_e\)�U ..2.� C 91^+%1&� 22�*�)&F law <:p 4�&2#(\overline{z��>�Y���R�R}g)=z9�Aّ$�"�# , $d"=9�$, $z$"�9�e� iF�Fit�:bG O<part $�$ _0a first� a�rd or�.�3d&�6&}0,���Y[�)di[ �4.G.�%�5u��5 7.C=KZC5DThnFD4RBCk diags0 in ``armo)< frame'':1 � (<�ws.�-,n non-co�ear�<tA� l veIs \(u�!2($Sr^{D�D( !t \R^D�g7 J ?,=�c4�$ \) let $v)�$yv}:��(=� � �(�=\C^D$)��":&5} h,-�e^W1!��r , v �4[,B.�A�1��]^? ^�]: �S�;B�SA� >����F% ���6%��%�m!��� �)1pt}i�lj:a v�3 �-�3 #��-&�"P}J<+2�"� �Yy�B/#" +PI)>{KJps*T)7Z>MB �n� ?�< S�O - di�0z0)�nnFy/�Zi}{8\��0m.� &� 12fZ$)�^+�6 �"3-k1�"�$}�)\c�$� �Uk-v} Y �(!~,a�[�*�"f��'�>�K"�,68-->�^Q%�MN+ �. +} +,tg�$V+5F�--ʖI,�,,u�a-\�+{�O=m-{1� pm��\)�previ]< B`L�_N�L``� ge"?''�q  \(e� [ N,: ���]�<=$�2� (\�OGV O =s'JJ \) (�s�)��1 �-io�/{X5gr3&D % 0C}�"�!\ La A\!,\,�L��:�$� \TR_g!HH ��AA_5!oWI2( R�2Xa���[vhU�.UO>#2�Zt �Cbf/�" �`))�-�6[>�1� .F63F|.,  #)�2�p2+Z:%�� 1^{16 .L6x-E�&2N1\!�ɭ"�*�@2M+�j"\(rm6jz$QZA��:8"J�!��  >4:��JpBi*Q��LrL�)2-�%��G-,)�=cB�M- -Ja�\Q=v\�~f4+B�����-1�Q�:0�q�N<F�A�N +�<F\ �2 ��p�<���ham~ ��ev�c$%K<( kapp� mVA]6BZɄ�lim&�(M \to��T*�2'N:'Z'm�M}^{Ms2C�*-N}^{N%f V���N� �2�| \mu+)�QXVRn2;Q?l?=F+m.xa�&�?^(�k,2�+!m�4(�%Bo, i}{(2�})^�#�>( )c3�|E� %i})�:�-� M6^5�(FWI1ar�"M'o�Q>��^ 331, �>,A�not7Uu+Ri"JLC�Nr�E|\(NXR �&(�0yISw#5.3 we 2�1would hadQsam�[ blem(� !�6 pairn1\J[a��]\�Oy�`-�,�"R%bstead �t&�`)E�,4\), howd1,� is bg;�+nsi��b� $Im$�Ma &@R un�S��Qepato� up"I) )�I). Indeedi#hR5�ly 5�q! Q%m�6p)�RN� impl�2�a�)�3,tric Hilbert�1�� workp%ܡ4GtaU��1(. It appear�%triguAvJry)" construct�,in�it�MSaN� *�E�a2u6t1#F"*medskip ��conclud��i��`�A��_a=ɶene�Rdi��bu!s��s. "2mS>�-O��9+�`u(TtoPVA� mean�"�(Hamiltonian���# librium (�) s�4, at hand. De��+ $\Rw�4��{�})�a�K $\WY\#"� �, reg!�i�aby subt�_A -(third�� ) Les�"G 12}=�BTh&"KU��7/��1"�"fHn� ��} }{ c�c�KK0 $a��2�L� p5e�~(���) a suitabl�uoA|�Ua�).�<�>�"G�average�=erm~ "� ow�1�( ident3\(ni5e�O�)e�� ={8]c /(2aq^3- /\)�j� ul2#newjvq$I�1?cIj]�:�?rf k7�7�Y b�. j.9�� w�� - 8�2}2�5BMf��� ��*16���,G.}�8+�Hw� ve se2S 7.22[�Z\,%",�Ez�;�&, C�`-^7Ab4IqB_4We- %{.2.B&7}{960}"?OWe now�ce=. m�.u a��C" . $H� e�}?/2�.6 (\.m . Us��7L c � � u ��6.% o�^�Y${" ]I� N} $&��$*���:V \*#@��@�5> (pseudo�U) m th�Y*� $F;$:�d,?��_�AM%N��2� \oplusi�2;-�Z%,s�;;OT"`/ �<S�ot2\`� � 7.24e/d6[ (n)=&H +�-1)=3 2 3�� !�75a�eqh.$ !�M�M հs� 6�� �q 7.25�W :2# &>! HB5� +"� 6x>y=%�q �%��� FB*?+}}{1+F!��E���J�q3!VMU��f@����+&� EZ�����\.n9for.���3sC����EY&sE@AcIO��p�T�L^"`t<%x.<��.<qQ� m29�\*�, �)2{� �M.�g"�<�f5�`�Q�onveniI4toq�ze6>� a 2-� 2i4)2 4} F�"@#�!7 �e�F9m�8"�T8�d-<7!\wedge nue�� maklFjus��fa�3�@~Gbu!rso��j2: law2�) ��� m9���n�1�^* = ^^*'a�d&�z�0:&>%1`< (I= ���Nstyle*$+zQ1#:S�/} \)}, i9I��r ^* =&BE|�9"YU�+A��w1%>%F�7!�a�-I_1\cnu�/]f&>11p_2'�Y��� �&�a.O% rI�dmu>=�� *�Ng2*-.Vn�Vv��%)�M1{%���_�' \(�u� 9-%:xAy��_� � Y7p%} nu2U a�EK(\).\gvspc{-XtP.�-0m `it{���s2'i�8} d j�3 d *](F�B[\,>):$*�( �Hodge}� �\ \(RdIK)M]��,%y�\epsilo�L-� \rhoL8�_^{2Y�P���.u��( a&�j) JlRY' \�break�LaJIG�_1,.�.�gq�y�.121�*� \;VU>aga� e&V1��|, $2v$ $YL(0,$ $-i 1)*Lu_{1,2}�� 0,� .\) 0\pm"g,SX,@*/."�,9l;A�� re �D !1aHp mbinŚAߩ!��;2q4E�40� sqrtq F" a+\!�!!�2�Ͳq+2F_{�\, &�h.S2j1�`S3.b(�"VS24�>>S3FS ,2�R�aR��^{�Om�G= \! )vazjiF�3i��f^pm�f.ŌZ %�W;.8 5ɞ+#*u�N F_-^�E]�'> r =: \W)KA�*!Z,`-Q� =��&*�� * (pt}{\(%%% 1��}-44x/� !�#)e4> ��rm{�/&W/f�/-- 6�-��/[~E&D*-l��v�f1� Ml��)�+%�.L�[!J :qc2;%S2!B%j��'V@&L1��&'f�;  ;ZqBA�I%M6! F_+� b -I�q ;Ui6pt} \m�1��3��3��i|1�4�4 R�$#��!�z�f/r�E�� �e ~0%�wv~-E�F+>~2%*Za��B��+U] �B�f��@�Z&�!\!qP&���aŔ*��� �Rp&[3��r.x��� �: 2��?>DHa������/6!�:� \W_q6+�,-�q�*����! ���'6�-, ��6BNC+6C�! �qW3 rg��-��r9�jy��36A:�~A6OC]U�\�)2zc-�f�� -����Y�ŴR�b�z>����ղ�ɷN3 ���hehU6m)}��� x4~�q��B�Ig:Cb�RC�,Ex:b�t�B�M�! .�jn &oQ3o�C�to���+6�(DP( 8%�$�j��eh0w!&�]&$\(d_F(n�4he�G>�%0%�T"��$n$, &O% \ P��jE&4 %!hOx%lnMSZ ly sO� i�>!(t��Eea.`\(SU(h�U \�X.�UsF�1��1,"�| \oE k"2B�%:�f.�'� �E�=b�}�vjvIb{*�pt�G��2����f�4��r��&\(n>3\� BC`"�1atn�twoa^�p�[�~sixB�! thos' maxh�?2s,�+�i~���b$F�):��sF��r.�!F{�TET:�mE�pTa��!$eqHFM1} d_"U&`=�%$�a-"�K�  5t�.�b.��HFMJ�*2Hf2*� �2"' _-2G_2 C��%6IJ[KV -2\,)o�+�=�11}{12�!.�If $A_�"I-gauge po�� ial,&>6�}=�T; Bnu- n mu�w!K�samł\(2mu\�P +lN\�|a �,&v �"$R�} if $ 7(z)�opurely >%Piwnal} əBT2:7.�di�!h^nu�!Xmu,2OSs;}a��-� )(z_1) n 2 YsC*)�.�}{AqT$O+,u,�4�\N�&.7dT2Ky\d ? pr l�a.C%One�1d 9`1 mu}s%o� $$s$ has a .'�2>tn �_e� n~a�P20�w�  grad� is��V.!�M1Z� 4�/fZJ�/ $l_{-n��12�Un��f[ $ $zA mu_na�$1:Q1 Keha "c  rank n^ (du�'-38n(Wr�,�DHinterchangeably~--~J3'�"*"ceupper��,lower Euclid�[indX[.) Tak:.vf o acN7� u�Av&I of 9 R0p be:9��{lf'Qs &E|n+3�-.P|3C"A� �- ^2+(�'^2�8 2(n^2+1�IU�I�;*x|�(�>m�� A&�66#��| fourV�X7R\La�� +H_lN�H_G_���� \�6�#a modynaW�t="�#�9des&͋� ����2�$C�:cti�/ MinkowskiM �``�box''�ro�u7� �.ߋ" 5now�+ stit�m i�Z.~I�nw4.19})a�"�jz}{R}�6"6reȂ$"EO$�6 1a�V �8�6n0\M:f4a cir93of ��u�ORA� (> 0� PerABaIfur!� A{>dihP"�  2R:,^{X_{-1D}} :sx^���+\w }{2R}�i\(\mu�ld@ ,D-1� � E52 e2.3��,(real) `Vq1\((\m� =e�xsn�1o (z�L x;�&�.=C %5.;��1 �46�'E �?�S"��z�iBx�A2 \omega�2� 6�2�&����z_DU.�- R&)>  �i x^0D-�$!*{7��v��*)�R(f�E~4 D�4R�$- :�C'0}a� .!� Astabil�3subgroupa�E�� .�=�d51in T_+g�Rx gr�&� =q� ��#ha�gr&�S H\6�n e7.2�Jom,Uə�W����!m,q�A^{-�I��"d t,.�[! o&��"oJIgx .<!P�%4�! "O \nfrc{U�"� �\�8&{m{\Z>�WJ Y�bJ=$Fb $--g�b $Hd96$Z:ich�]���$z$--ga,\-di\-na\-te�C��) a�6e Eulerb � $z �Uq�\d< z}$ B"�*: \(H1��o!cn,=�N*�7܊J��@�o-�=Z:-�\,�.r..� ;Wla}<$R�O$x��֓ri���-0��z},z_D-Ֆ \) approa8�(Wick r�ded)B�!�d�%�<.Y x},i��1��B�.\o\($�a, =\c�\%ŁH�} $ ZD&�$U= \(}) = R^2\) �� viewdXa�sit{SOU%Rѣ $--iD^ ``*� ach�o��R�>w;\BBlat�cR�X� ] �� �C &`5>�also Ti-rol}-l&�.o:8khta�* * ��al:>� TC5( �m � q.� in%E H�3 ing:&kp�I3mo�ppr��pr:��masympto� behaSrR2o U� -R e_D� \(e_�t-�\M�H1��&�G�associ��*"71}i:0le7t�&&3 �N.A�e2x�*|2O �� �V �� |x\|aGR�#ef.f@�Ѣ9 ;(2�-!E�8i"� ;' ,��η9�~c�5$e7.5} & H_� �.5J��!{!� P( �41} \,˝ \*�90+ڦ1z����r��>x\cnfalg�-�&� "�N�5\|'��+\|%�*1�� N7[|Y�AS\{\\(x!1M!^0,:+)�M\)�  $i!)� �G�q�p� a�jw�toe�(��< ($x^0$)|� Y �UKssec2.sM��2R $H_R�"ku ��2�(.�h invers��ngth)\8-q2���proof} *� a�)���qedFD strarforwarè��2I5�Mn�D;J�-�H}�%4�0zlsP&� $T�0$�� "� �- $ 36�P_0�` 2OK�O^Џa;$;zK \( J� =\)BIW& t�XH$� F$�G \(R� �N\(� e�e�KX�-�-�.g.?�\rm�Trm�l�K%�FA�uniA'�w�S�/�,aE�uein&h*�hM�?H&{ l`$�A\6�@ d�� a�48it{globally cau�!J ure}�  lo�|y�distRJsh� =w$M�|&� FbfwemphasV4� 30 yago�Irv�Segal DQEci6Qpos\'�� re_�cesseeswS82&QF�s fixed cuB, $@ $,!U!l��1 i->� ) F`B"��Lz gyi  w�OU� e co�n�GR0v�>. W -q5C!:is os�y�!� �ZcN2�jM}$) a�nC>��OM���. &~�1Y��"�qP.�jz � � � (��), 5d& C orig�_(x+J� $M$. (�A�D s.�%9%��)N ~w ��Moint.��4>w} * @Li�u�P A}pl.�TR* e���=a��m�M�\~�), �0� r ��9""M�*��:� b5ez8) . As����!�s[e f�zzl�e,Oed�:��#s�&��E�ٷmA ��@aQc&*3A�6�E$f�|m+xst � \(2k�O �ay�A "�:�\�!it{densi.�$\MED"��y��m�m�e�uGx��DStefan--Boltzmann}w:��e7�MEDվ�A LjqX-  #19srm r"V$E�6tΦ�j2VOL{R:8 9C}�j^}g�)={&���F�^- �� �C�som!�`|t�i/� �1}{k T�JVJ�*�absol�.آ$$T$ (multiqb%�5�A�s[�$k$� \( �!c�*^2 R^3�rvolumt$3"i "�~etxN� �&�]g�"W�!aR4�a�is�TY"casesI�eda�N �a��l���s >a >�"oz y�� {wby"���" �"n>}�!�Wd�*� o~>.&e 6| 62}�E!Xe�elsjv��&F[ �(�����"P!�.�m�/&e RM�u+rt�:��DMED_R"[�uEL �>� �`"�I� u'm�1}{M�eBix\�^i>:�,/>"e� � _H_R�Z:>)a�L�yfb�\pi�30�; � 80�1PT�4m 7�^4}{R^4:hO�� � ���7,R5��{1c���G eqr �:"YPr@�a�AF a) mu\n_)6�97.K]n+F5AM;�%!�y(Q)�152�6.8%�2!�2!�)N1}{1pi^3 B-3-3R�A4=�pt�cP\�A g������\e� 6 9YS D 5i e s $H�V�F3 R\arily�i(y�!23: gleaԏ��"l ��V�q^R�� F+�e�*��OJ�//zdeʀ ZvR�6z��ʬP � �&).�(�= two ��s� e=K �w�L!�*" 1��rN�yB+�]�Nm\b��i�. �i��}Rg��F*�aU -VisŊ3A1�; }P *� ,�F�8v$�r5|( J��{�~.��^�I2����.�1)&O%B�.5�� \N� a�re">O��G���.{�6� A tau^&,6WPb��Y�eD%H�r�%> i}{4�8taC5l1 mm��k �A� 7������)����s�t�t� &�b3.9})� �"be&I97.̖FG9n��U&3 �~12�<�^al!r�;{�5& ��"� S�>��{� � ` �NE�&h~$!�2}F m�r��L\E7.�� �����16aW^2mH�?��N��P[4�s ������>�)}3* R^0*�M�11 �4}{> )�ʂ!�76�NFc.ly,$$r6- 8}u'"D�]�0"�A�� X�6a�D-��?��}�;q��� O��j'F��W�2=0��:#n6B�0  � jm2}W%"�:�O�pariso[c�familiarA����$black body*+ ���Ddg�$to restore�"t�� s $h� c$�X� \(�Ѭhc�D H"� � B0 \) (�ea0�� -"�Au^/�#& �d{�$ .����ad2� bl_biA��q""Dh �~P*e �T�3I�:�h50.�Dc>�W!N mf��* ��*��pt}ᓲNLE5�-sV��i��$&�H�-n^3�6){\foot?ec*A� �> �F-vx}{17) 1 -��v>v� '�b�^�in 'Z�� 8f g�1A mfPlank'sV�� ula��2Yefreq} \n�n�E�&���� �$R$�4a f�JA�y,&�/J$.�[�= "�e{)�2ant&ld�hal�a�} &g�� a�/��No\(rU �� \)~vj B� 7.16z�xJ ��� u�0.aF h.�J cJ�=� �����m���n"� ��2&'w��3}���>)��V1�9�arrow}�i{�R6�1�� }{3&CQ�"Xƺaqj�gonr^9�cte�a��int�?��U:t^3��t�\���9JL��:d t ="R�4}��S? &F j6�#3}�# y!�l�/� >�  ��&���e^[%�r$�c��=��g�2�"�9 $c_1�!bcoefficQ9-N$G_4$--.�d>$2lYBU Ra_q$�&I6_4.W<se͂&a5��X&f�  *�* /B�+M'�n0p|8Z�/\.�$ H}_R1AJ3 \��"t(�8w�>���L!U(̅-�ing) � s $ct��FT�&q Qu��9^ula� m�$5�E_0' -���Rd�0�M1g���``2k''�66Ms(i.e.,C�� 0"D7 �@�"Vbs6��Dn6�'uQ .&]In+vo���.�y"=p&8��t38p##tud��'w�;\"�vg'e ��Aj�j�1:&� Bp"�o $��^{\MINK.�/"��$ (!@"+oly�%m�>�(ŭbRF�X&$F񫁵"�a5.17� �Tj�I�%"��N�� &&�[Xm�-O " ^{-2"#xN�5 +m,�5 "�E^�q?�\( $ = �- xԼw" V=�&x}2l"v� -i,He&so��1�����e6m =r�& PG�\�on,$0,A3Q�eQ�&&l:i�^��r?U�d*�ZB�<�R�"V0r�"�Y&�7���&% �,,"�ZF \�B���.�~4] ��dR�$#FyB*� _1��b\� #a�%�t2�v2*B� 92>D��.������$) } fZ&�?�?2?"���g-2�6h$3\���@!�) (.5mer"u�u/tFV2������2�T��GUhU e�� "� �l"81�� �Z&�� � �4 79bf�;N�7��*i�� 2&�cos޸}? }@~G��4%.�b�.)!Y-Vf!\!��mOVW s�]H-6j}39 "%; x^1.�*�22B �3:��%F#"FA�it�ve}� �sM�/(�sng��? c�A",�� CIB( .,0�T.(�ph��)գ" <"���F��alN� waev�2��� ��� . Fʒ,� &� WF})�cr�NTm)�(� � 0<C� % (� "�&� R$--�#�(Mets�]����7} e� \,j� �� �� "�@MS}��"^����? ;.\b;!��7��A)�x.9M$��(%\(�f�d��A �������2��!-d*�@8 cp�Dtf�Vf����p+fro-���+Qe$Z unts� � "Z�" ��GJ ,a=--�.�i�s (weF.� &�. ��D �2"") � >5�<�J:�f� �Q�a� !%�0aO�ond�pa�>�>D�T�3af�u&v1P�u2�E.v� v�2{>�x�"|[7.2�&&R� =�a�0R"{���i�i 5}� J�%��Z��XuiL}�bOz�Z��m��9m�q� m=��R�+|b�S&P����Bf�| T1h 6� mGEF U��k0Y�b(6x -bƲ ,  x)��n�ng]vf`) .Aw.pH�)"&u�+ dea�i�:a&��%&ϴ)$��m \(e^Bmu*z-2�- = *�H�1~1 \) (SD�JuX$�� �`n"K�J��I=x. M\)); %nN�6qQ:X); inB�0se�����"� �e'�1%���� \(�u(��="� R�^�{+H= &o�*�*Y �u�u^�X � Nex872y"� �w��-��Q�i;݋$]�FҦe;&� $R$)LC asV�!�&Z �F)�9o�8Y$9Q>aA*a�ed�B ``""��''>�E&�z&�2�.[ .���ε�XH)Bñiu��D� adii"W �(�&�>z�>�PO���V* +�;� .�X�g�$RY0n�;�;~ �.��Ez2�H22}�226z��FH!R��-�rE�A"� A �^aq8,R:�&�Na]�� py!"� �6{�2d*�f ta$��&' ftauF�I$�+�2;֘*]�����$ :R86�*|�O!Y 5�|�l m)19� @*6fRP( ;k�16P��_k�O ���]\,?)�= ���� 2��U�:�u�}�u�osu!�%� )� =� ��M�s�i�&s |� �SXL"�)p^T��^�w� ��7&XC"L;��uJk�?|$k%EE���$)�J���5��h�D %�(�)�&�3B "P'�lF��1:��d���,Ra � �H���}Kn�*>il5�{ 5j�� ��f~,%a �):.�K�%"-�Ō6b��Z5r� �����������N�B�4 :5j�l4I�F$^2ɘ zL b3A�Md&�2Ee1�y��E�l��,���o����\.�g* �+U� 8�L�Li\�fro6$�n2ҁ�vtmO�ok� o�~��.z!Z�Txh�c�͵a�, R�bX)� N�N =�FC#Y�~x^0.���� gP-�� 0��i�u2dx}1��au�%65m>�*= �O�����v�vZ� !��9si�tp*� �N|- *᪁N52%uf�ykv0^�A.Qa�yAȕ���������pj����l ւ�2,K:%4 To eaa�Fe �� $ ("O "!'�a&�'n$p_�hs!FY ��* eqnA�!, *�� '�;۔��:�|�E au, �MB@�\�b=..\MĚ�k��hau�tڒ=�({ �f �L"a#2�24x,�LsM�X o1)2�1{8&�25}! N~np ��� v�6� JK~h )=_R��2?_# ��&%'&2.R*�)��&� �V�)�|w(M�|}"� AHi-��p=�lon��/ ��R �w��������'-&���"t��ܝm3&�߁|o.�p�S���le��'92�7&�7\Qof V�)3]"v04�&"�N4thermal correl$ation func �s should be, in fact, defined as distribu -twhich amounts to giving integr [�rules around the poles. To do this one xHview~(\ref{e7.20n})wa b@\ary value of an analytic��8$x_{12}$ for \( ^0 \to  P- i \varepsilon\), \( > 0\), 6C 0\) (cf.~ �pa5.17})). It is not difficult!48} �n}{R}%�to,p \, , \quad #A�.#d6$1�sum9�nL= 1}^{-^2\ Sf \! I�8\raisebox{10pt}Yc2pt}}I�. � �;\, x,)� E.�E)A�� longe arrow�R}� } \ 1int&u7pt} 0�m��! �q�p;�qd!* dp .jAbTheM0 is%�a}� 9} & �( 2\piF^2�O�O:O\,E ��vspc{-3!�{\m 9��� {\, 2} +�-N�� 0�.AJ +AO& \nn &!?i2^iE\)� | \mbf{x}ş-D|\9�0text{\LARGE $!�$}��� e^{-�� p}v� 1 - .. �cos �( p5 �) \sineVV�2,Av\, Ay&��(a \medskip�� conclude:��formal��actificX $\M$��$Minkowski Ő $M$ ��Tplay a dual role. On khand, it�!servec%~`it{symmetric} finite box �]im~ toi���study� 0ltemperature equilibrium stat�IZ any4inverse2<$%� $ actuall,xM 4 Lorentz frame� \cite{Bu0��sZ k ��a Gibbs ��,described by�$7$--paXdter ``Aristotelian group''�(($3$--dimen�v�mcomMq q$UI�( "�$. Work} ,throughout w�E maA/l (6T)9�allow9  wrAh(down simple��licit� mulae  bothQ2$R$)aDhe ``thermodynamic` ''I�!Oo M�ta�%k(!�its uniA�ekver� ,widetilde{M}�Z��8imes \Sr^{3}\))� as� uxili� mvolume::but0 model!�aE�ici�--c,�  � d, (large but)1 length% ua@he above� cusA�( as a basis%Fa�d!� �!J& !�!4 >[A~!�� a chal�M�� ,second point��touidco�� u�bre)�bysider�0massive fieldo $2�$. \s� *{Guidem�references}\addcontentsline{toc}{ 3}R3 Among! book� $ elliptic &-A<modular%s!�(have mostly �red�)seA/e5a! � procee!�s�� FNTP} (se� partT ar, �eginn!$,of Sect.~2),��A@readers-friendly �Z YMcKM} (�giv�RflavourM@ work�haxun� faaE% subject)!,!ua less� !nWeil's !F }��ch�videsi�a ���Ath[ph��ryo a!�egant�)osi�p�the(8of Eisenstein's��i�~� !!< who enjoys lear%Pab��nof � e��ci?�/own sak�E4probably aware�B!Ore�end�~M�enter� -essays Bell-% }a� maya�d �Z rest!�J�j�told st �,19th century2�byof�IWipantQy KW41}. WeI�xePre8nŸing%�!�U=4top!/�are (to%�ry�@degree) periferal!�!0MT (��HHW67} A884}).)� yby Se�Lang ) L87}A%76}!�Ai�lyst)� back��nd on !O9�al%!'tha�lec�졽Dre advanced level.EXe(ronic%�availE� no�by Milne-� Mil9�r� M2ed for ae�y!!��reatme�[�(Riemann-Roc�$orem (appl�in�3.1C2cl�U"I A�.�) �re� engag!�exug� n PS�is��diG$ed towardso soluq� algebraic esE�Ed��ain�Lele��Mintrodu�Tarithme�5y�el�� cur��(Chap� 5) iV �an � m�Wiles'Aof! (Fermat last Z em. More ]8 on number #�%q� �b earlier �}s )4 Se}, 4h94}. Mumford'�ok  M83}M�ta"�� a-�8c. A rigorous B2�of9 2� 2�A$2.� !���al� �$y has been�An in �Zh96}. Q2M9�chia�vertexQs w�nti��ACinŅa*Frenkele�Kac-" FK80i�da oped-BorcheA} �Bo86} �8Bo97}. Nowadays iM���!(sev���b: GFLM88} Ka9T FBZ0�/ \big� &�$AcknowledgA΂�>/( \noindent � bf>#$.} {\small�~ pres��e�Ograly� w�pin��n e�ded!�% of��sI)S5' Z uthors \  U5 it^ Sofia�(2002--2004, * Dubna I��ne� al A�@4 Summer SchoolAModern M���yal Phys�S,(July 11-22,j3)e 6_ O�Ej Stud�4SISSA-ISAS), Tte, Decee�2003, � III~��, Z� bor,��Dbia (August 20--31�4���t�{4Institut f\"uraA oretische �k, 5o$\"at G\"ot ena.!� fall!�!{�(1�`thank Seif Randjbar-DaemieW=(Abdus Salam6� Centr �.�!b invicP$support du� Ao arly� geY iri�o� y �HAlexander Filippov,a�isANrovinBDd Branko Dragovich�8���us q��Rr� ��@ Bogolubov LaboraE TJ ��Y� (JINR,�na!� B�{Mn<9�Q2 6i(SeA@),� pectively%$w�lik� )20Herbert Gangl%�a crit%� ! of a draf��)�1 sti� a��Wo u!�t� $their revi�2 . Dics� 4 Petko Nikolovaʉ����efu��a�edJJ8Detlev BuchholzL]� l���eDadd2 -�  87. %%% ??? I.T.)3��Yj,von Humboldt\� A�M��a1�� A�b�U M $hospitalit)�!/1*�(Bogdan G. D8rov;�pai` first.��%�� isikis��� �0Research Trai� Net%�n rame(Programme 5m�< European CommisA#I<E0tract HPRN-CT�2-00325%N}BulgariN�$CounciI�Scien �E�`,~PH-1406.} endix �{E% & �erm� &1/4}{ap:1} %\setc�er{eq� }{0}.m�em}{16�>YE�BexampleJercis famil���0pfun_k^{\kapp� mbda�8( \zeta,\, \tau��(k=1,2,\dotsB,\lC = 0,1+en-a�&�Q� d ,s uniquely dUmM-�fo��se��pADrti�\�{plisditem[( it{i})�8pt}]��:�emmeromo�&Ls�U\(�112<p \C \�$s \hcom\) �E exacA � \(%|!G\)a:or�%$k�(residue $1$�a� doma` �\{&u92��"�alpha!�+E :\)|��\)!8�[ 0A"��*�bn\} \sub!� \C\)��\(�f1\(k = ]e;\�1� >�=�52�{k+�E�M�:�6�=pf�EDstyle 1}.k"AS>1\di23\diiOF;��2� !���\J'F=��+16w�A( -5�^{1S ����vy�AĢ�A^>�I�:�E"} �� =�+ I+- > 1\v��62�b�-�6� ={=�k ���ba�^a.6�end�{One.�#r��� �v $ �1({�},{!� })(= ^{00})$cdou1odic L!tVa�2��� D�vl�.$w� chos�t6 ��N ngle k,�Y�%$ �B For $k>2$�p>��< 2��y!$ be writteib�el� verg�&Y(-Weier%ss)g,��f$A.1�u!a�X"&N2#"m��("\�, \Z} "~#N�e6 m+ Q� n}}{q`%�+m�2 �+n� ^k} �" (k > 2�,q!O 5� out�%~lattic�%ZI@$+\Z$. Cond* &i})3n&Ws eachE5R5� Q�> $ upA0anA ve )arA~$�$ # �ons�v�'ndguarante�ir_$queness (p�z(they exist)8 �� establish��exp?struc^(�$ 4.20�$�( bRQ�qMorm6p3QpB&�&�a��%E~,\mY�=.AY�li*�$M.�#$2�2s`'IA�.-M}^{M}6*'�$ \pi �!^".$B1-M�:�I�[^S �S �&>��5^=��= %2?YC# �%/a� � �b� G c�� ] a�"�"�������� \ e6 %�9�%�Y�0.z )�( �$u!��!\�&)} \! �(�(� ex�?��� 2$� relyt��sp��ng �8��I i� eqnA+ 21a}4�� $p$-� ad�+��, nee��wh�\al��!a chemNpo�ial�N�q��cha�er $(-1G %'}-$cʁ� �ơ.is replaMby`gen�one2�+A.4��bH ep" ��.�9 �)e�BU &2�':\mu�2 �vzBu��%:o(!ZM1.��manifeK m*�reARenq(�v.�Jacobi�fvarth�,Y7:Q51QB����-3%^,\ �.] =��)]\c ial_o !}� _{11 ()*4-06 ���_{�˵Ne�1-Mi��m:+ !���]�% \! +�-Bi{.%� ��6�����S *�-�|1\! -x�����?�'�irm{cotg)��* a� S����H:���!�!i�{2 Fݳ:F�ٴ~+ (seePp�! A.1.� �NT�'.2��ba��L#+)LieW\�0e#t� lizZe"(c*�&)J)\-kow\-"N)�2����^�I9�on will sket& pr����`ions~�#2.3n}), H"� �2 n2.1�2 betw�B thres)o�x) bases�V�$\ alg$�  %�4:��&$$\{X_{ab}\�,Pproc$� d�)p�,6�iar�'t�� &�&($x$-I )Śt23(4$T_{\cmu}$, $C �$H$.VMb$z$-pi"�b�%� n im��$obU+EgA�'{m�M�}!��� .d!/B� ��\(X� * alg\ZQ� U�ial o�+or OP{X�& n by. neB���0[ X, \phi (u)�^ ] \,�C G ���0 u = xuz��($F$ $=$!�_{\aa}] \}$) is a2�{\b�4ti}hom�sm, i.e.�$X!�YQin-$2�ӑ�[ - �,Yу��Y��4��A� corollary�':�%�mapsto TX}\J�.�C nd:0� amep=MQe�}�4a,��i/ �ckR'.5A?�( findJ"�0! )� X�,!�!�1 �]=:$&& \!\podr�VIG ^YNQF >V��fKA KR�RK:�KAOPE"12:��6pn�e]*�^R:5B�n&� %>")g -hB�~$>l6BoB� R!�B%v)z�-Q[ [,.� V�5a�5I�} No�7y#,�gv�%art��A�� �� $g X,Y}e 0some vector fY,$\D� #�9:�$X�]i� 1}$��g�6�$6�ᢩ�to ��6.6| leti / (p�"T0����*G0 $iP_{� $,  ����:+ �3.K_\mu��di�"�$i\dlt$�a�4�4}�3! 1&u [ zq�xu$A�= f6tdd{x^�o �Dx) �!%IPiK �nO*.� G &� 4�4I�. v�46�-�3!0 !nub �nu}�.� bc) I�x) + M �53� & a�A6[ %p ��� ��}�B�a + d_�:"L4(where $M(x)gE�  de �(matrix)"  (w6�W�9m��esgAZ�Oz calcuMF�$�{a�e] "$36 � � $P_0+Q� (�1itian) gyu�, ($e^{itP_0}"� Blunitaryo3evou* is, hf , � veiou24 �4 +  $\VA$X<],Klein--Dirac*3�)!1#em�0nw4.15}) mapp�&� cM��9ric $Q$Dn Dwy� ,-e�� $Q6�6����o �/ $qr�� : $-23Y -a-aN6 $+$ $2xi�$nu#aP$�! @,A6�$ (accor��0o. ~B.1_>n�LS��"��2,$p $!e�?�F$, �? oriz�/� pect��!p Eule�A $\xi^{^�S }$ (noM�͵ scal.2"q@o9M$�1� lif +to! ��+;fI/ zeroJAn*�� i�vanH�- Simil�'�դ�i�M�V a�/� ! "V �$equ2.7})--W 10})!ju�4 imbe�4�@og�"~?uD}?ՕeYxyz�;z�>Y � .!�x�.�"�\xx_{zJ���R<� :M_{\C}��a� Iz  z^T \eeS#Tt@+ aM)5'-1} + i�)-R)0S� {or,}�;�;z� L\mA��} qB0��� �:("h M)y2!�)��/29}).)2�Cliffor�20.��,$\spin (D,2)��A\�2r�B$\S �n����^�Let�:�!$`Cm0,1^%,2r-1\)� $2^rH$ 2^r$�d lex �ces���he BL$\ (U,1)$; m�2pre/&lyR8 ass�8Bu�ec� .�8$ �, �� ]_>� , 2 \et +"� (2A�v0#ag (-151)7 iO�B u^*4L et s%_{ \t we �/ ~--~! � `0��f�&s!67U)�x3s={s@ ri�� o twnDl�&^ �;2r+2$ E!�$\{ �a��v�_ A-a=-1,0U*q'by%'E\(1� =�mu}�'� \(Eq>p2k nB |2r%H!� i^{r�'��0 1 (tAr9 �2r�$B�w\I3 \ID -5-1}N�AA� pair!Pex*8�0� �!"ziz"- bi ^�� ���b�� b�� (%&2�A�� 6*E+D R _a:�AF$�2`> �or� 6 $S m}$��F2r�G�#�3M \:�B� S_+ (  \�#v�\gamm�: �� 1}{4�( � �I�a!��aH by�S_-^tv�u Rv kUM vb)6VEDce {�i� T?!�.us�*o&s!�D9l5 iV��he5�l�3up�� 2r+1%�6u�3 odd ": a!� ace->>Jm=end��i$7� � � ax7*, ��"Y B & \G-�%�!��("�hA�0gin{array}{cc,D6"&$�J\2J & 0 h& LF� Y1 a = ��A&� �!T����F�\ 0� �-,�z�*E� [ �A}, B��J\ %8AB�>A,B��x,��d �d, #1);!�eeqa ta��� $2^{r+1}\�, �cMʙ]MYg�V|\� A�Eb&X 6} Se�AB�cI_-�A!� :]�5BB1@AM]y��',\(a \neq b\)�� \(.� = \t� "� �b��a\)� �) ) satisfy:�7} (2])�J б2V %��� bb&G ?:{in �l' Bn=و^2�G>T)_eq�M��A"hit{val,�; } $v"d� $Z�l� �lK9�<on +alGAC$U (1� � 2r):�B.8} �|�m�!2��-10RIB�Gpi + 5�" �$�)�!ha� BV! \c�}*n!�<ape:�6�� �"!A6�((two-to-one � =/'SO� ,2)\).�GG.�D� even $r�*-�Y .NH$\Z_4$wit�M�" �J=:� 9} c� 9%7>o3%!O 12!�'2 : ,2r Spta.C 9 enBN �� K%�� 3*. (In%3�=�3�@#�h"�iony�2}))F�� $.) Cl�8pah,� BottE,�Fy!Lpertyo��10%V�v�M eh{!�!�!�a� quad!�1E�3\(r=1\)�FOD$ $4$.?�B%,f=36=�����4�W$ ``�''E�!R�?eA�0Z (G)$ origin�I�H�~DS�eit coinc�CP&KeB!K�!W valued 6� "�0pseudoorthogo! �A\ O_0mU$� �QE'�>multi�D by $��$a��7d�.e ~:k s ("x�3> % 2��r�r(P} YC&!N��`i� Z(%00non--trivial =�Y�8��#NUm !boddE}_| k�#Ap2 ix~A��# KT97`�z up �Q"7pL�s�u!��se��gA�\SU (2�� of@ef� erest. H� r�(�#!^!1>� #L nd $�� ab}$�\(D=4rnE�%�A�7ernionESDG766 B.1�/�$0aY�2- � {rr} -ii2'� NT -A% D&v .  �^0&� �j��V� ,Q_j \\ Q_j^+x4ptZ�� �4 =��0!ta���S_3 �36!FH^� \ a�ү (\(�Q_k!:W$_{jkl} Q_l> del� jkO0^+!�Q_j�\(j,k,l -93\));!.n"�+3��"�  �N!�Q!:�K+~IY> �j��7���jN�N�!=�� �-1� &�A5!�!5�j)�,�6( 4\)H(�p�%ved��?i�Hucibl91.ns� g)� ��$�Ma7�G+Xt riplh$(d;j_1,j_2 @�� nega�&hal�� gers ($j_.j��be��r.IR� semi:O !�lm 4�9�nt i�N� 6� "�O�'act sub�Ogr��!7lowest15�9� $\�E$cal{V}_d (��5"�$ $(2j_1+1)2+1CPW1(��ric*� "6.6�,��3} d+Sja%�N ;h d \geqsl�'2 + j_12]9&S YD;0RD > .DifCB= 0S �{vQch6,>��� \(�\�X!J UmP} freO"� �?e\Qic tens"�",:� to��_1=j_2= \ell A\(d�ellY  \=.�;, !�conserv�AIt"X�RA��(�&�1�S5: $U_{u4 } (v^ �Y� � Q8� E���#R�(B.14} Bd"> �0E� 2j_2�| d}&( \new�' \vlPRe�,ces} %��Xthebibliography}{DMPPT}�O� B99HewgTand{\bbtm}[1]{% %\bib(?$#1]{#1}}   0H{Ar} H. Araki, {\it6nG�DV@ Quantum F*%}, Ox��BL. Press, 1999 (Japan$ l3[Dbtm{BK04} B.~Bakal�E4V.G.~Kac, Twisa��JfMver" 8v6,J(, in: Procs'.V~E$. Workshop7Kd it{Lie�" Its� l�! XH } (Varna,"�B�G3) Ed.& �H.--D. Doebner, V.K.~Dobrev, World &�B, Singap��G(, pp.3-26; �*(.QA/0403315-��O E.T.~ , )�e� &Is}Z_�Schust� N.Y. 1937!r6U LOT} N.N.CDoliub!v$A.A. Logun $I. Oksak, ETodorov,5EG� l Pr� ��of6-e}, Kluw��A��G(it{Topologi*He*-,!6�$ve Form�Nd R�5To&Q} (Kyoto%#$6), 35--77; ogr.%�.2exL@160}, Birkh{\"a}usSBoston I MAa�<8; q-alg/9706008�64a�J�s, ��s�V$C^M^$*x"in ��l|H��0s, Nuovo Cim.)c33}!c64) 1600~FK�MW}u�MP, D.~Friedan, A.~Kent�Kin��Q{VE�� .�, \(N=�1superd)� � wo� o1`��7�QstLG�[2f�%, �". Lett �B17��M=16-322� ou68at~Bourb�^yH roup�<8t Alg\`ebres de�.}, �P itre~IV: ,de Cox! aH�P\`e� de Tits76(engendr\'es =1  flex�.6I: SysWracines,�[R , PauK196UA$B} J. Bros!�"�I, T�Q�!(visQ KMS-"� , Nucl.�z.iBbf{B~429E0h94) 291-318; hep-th/98070991f�[ D.yO hot bangihj`���  in r.�q��#%�Gy, �Hunmz �~�STbf{237} (2003) 271--285 MT88�~B�J, G.~Mac�\~�\ cur�\Q���circl�] germ�lo�YM $ory6EB (��Suppl.)i�5B%P88)yN56->,CD03} A.~Con!�L M.~Dubois-Violette,�OulU^s�nonsu|(ve 3-spM!s,���30827�}CM:fH.~Mosc�M i, MtT Heck"�55�ir Hopf� y0 scow�  Jm� 4}:1%� 4) 67-109�`@301089; Rankin-Co bracketi!N k�-�<-\e geomet���304311L8QFS} P. Delignea� al. (eds.k!��it{6E ��S�o s: A�J�^���ian��(vol.~1, AMS���Vnce�+qDM�~Di Fr�Vsco, PAythieu,�`Senechal��C�[.�ieuSp� ]Berlin�199�Di 36�A.M�Lr� WaR^�fam���3 , AnuX�3eN01936) 429--44�K DK02�gSg wk�� K.~K�L en, J�K *|` T`�on U�.}�B~638i�,2) 405-432; �z0205021l�S E���T%]Ben-ZvI V�A�&)� ic C�V}%�c v�T I.B\"!  Basic:& e�affin�D M� rd�a esonAY $els, Inven!�esEmmJ6��0) 23-61��T I�,J.~Lepowski,�Meu5Wn� �Ope� � ���� },� "B �G�\ FaNmW� ,1A�0M.~Waldschmidk u~Q�A�2e35; NQ]�{�>2: J.-� ost, IW!!/xc0:tY surfac�}5a A�0Abelian varie�L  64-211;o3:���]��X 2212-237;8ter 4: Don~Zagia>�? `,k C38-29UeSTa� Furln Ga�Sotkov>� TwoZ X�5 6�R��a& entoib12}:6 89) 1-20q�Ga T.~Gannon���D ,$Moonshine:!�Ftwenty-fO yea� Bull� ndonM�Soc. r\ppear),��40234ѣG��Gep�  S��aJ s ey��*c+ /%�:z �as6��l296��757-77?GO $P.~Goddard�[(Olive, Kac-� (nd VirasoroѶ�l��o5�X1sE��8Mod�"z 1 � 3--413)H  Haag~ R���q�& G s4 ticla�}, 2nSvised e�G,�n--Verlaga���H^ R.~ �0N.~Hugenholtz�Wak, �&l2qf!�Q�s�� al m�ni!J� )�5%$67) 215-23�is77}"� H�` of TE� 4W{_-":��a'� N5V� 4 ``Enrico�\i''}. Co+LVII, e�C.~WeiA�.S4., NY 1977. SeFEbM� �2,eabo ning�13I�4, pp.~1--38; P��~Di�� Rec6�*a^Zci�)era��~109--145AC� Hurwi!�R� ura� �Vorlesu�  ueberTPgem� Funk��en�ie T�\4Y"}a�� Belrin� 4M�K90} �h |Inf�hD&�g� .� Cambridge6  eA��Ka0\d �,q  B%�er��AMS, ULSI�10}" R�� , aXA 1998�P85� D.H.~PJs�i112� "AJU��?>iQ loopi� E_8$&P SymVumn (Anomalies GB �$4y} (Chicago, I��1985)rD"E� 276.s KR87�. A�Raina� High�Weight R:�of��Adv. Se" �Q� >I2}v  19871�KE�:{ A� orbifold�b�E^"S 2� "�G%�$W_{1+o$R�MVA�,(1997) 57-11*KL} Y�$wahigashi,a� Longo, Cl>Eb�$" Gi�*np � \(c<�"$and $2$-co1; logy�4� t�catego!s,f�244� 3-97;� -ph/� 0"��d H.b�Xrs�HC nnO  S�%D�2�@ferromagnet I, IIRev-O60�1P41) 252--262, 263--27��K26} F.�}���\"{u}��8die EntwicklungF� 1}vundlag�Jrs�� n Wi�:schaf�Qg 226��195�L01� ��&\�j��:q""[dHCa\-lo\-ge\-ro-Su\-i\-l� � r�;4) 32�L5]�10200� Lep�&k �-qE8H"�YNRe$ Develop� !�"� �b2N:��nOŷbf{24.ŝP�Pnce� 99))� 163-1"t    All�!k6c����m $SU(��G�g:�gy�m>�I5� 77w -2��c�>~in� �Eu6� X!�m����)1it{Non+(�> , } or; Eds.0$'t~Hooft a, Plenum)qP8,!k~353-38�  1i.(Symanzik, Cms,� ess�c�(*l83&]in9 Ka�]tR V�U0A� 1972) 247!��dM� B� zur, Pert)&ons, d�p�'��� s�o``near--o^es'')!�"�"� �.�gy,8Ameb S7�4 � 7--3"� @m �cKeDV.~ Mol*[�E�:�M -�,* A"�hasNV � ��+j J.S. Cjy�7���}, Uni�?of Mic��Qac*�j, &�j in www.jm�j.org//� MH73�~��dD� sem Mqtexa SRic Bil�5��3��E�.��U�83_3i� Tata L ��T�N��*\"a(,)&�83�8 N�N.M.~�b�y"] in higher}�!j glob�k�AR7�bf 25=�) 283-d&�30723�,NS"M6� Ya9Stane�&}Gn�gau�q��`ory�urexalP+�.96�%�� 670}~[FS]�3) 37c00.�52"NT�2���R �M�5ll�� nt0cor"fu on c.�m6BwR��N21��42001) 417--436"�000900UHT�n�&N\Af����X^\�9ra�6Cfin�>Oi�iDe�wB.~"@g,,Sazdovi\'{c}A lgrade� 2�y 1--4���Or��/ NlV��2���a rZ(QFT, submitB"to� � � Yl 4031"�N!M.�fIj&!9�c�q A�i�h �/9�alR�J�IXA1��m605--36AZ�b� 405& PS9�V~#asoJ#Y.P�� lovya�Z� !`9� gralc � Tr"�xAL!B� al��$s b 17^�7 (A�>�!�-yt)��6�� ic EIQbtm{RSaVK.~Rubi, Silv�hg,�e"� L^�� 3-}�55-47q�Se�� -P.~Serre�n� d'�\'{e}t�[}, �ersita)_de�i��7S71]Ebg� Caus�C�nA�Vold%� sv�7o $1) 958--95q�S82 o So Co�1chrono: A(Q remeHxtC,s. III Macror cro �_Ya�my&5N 01982) 851--86�q� Shimura-f>� AS)reP e�&AutPc"J�$eto�71��95�WM F.~S0qDA�)Wm�\�PCT�e�9n�7t-%� Thaon[ a�', N.J.�:1�T�l%��"r��ar.w�� QFT�(��$A.OW' rut,�&D3�&" י�c"IW� � !��aljul22B"@u}, � e2�. An A�,ach Through .0Ham�Jpi�Le %��z �#Y�_ M.~Yoshid�� Hypr��jN , My Lov`Vieweg,�p@unshweig/Wiesbade��97 [5]8"�{~II.9Rͺ-� --59$)(ZS} O. Zari��� amue*����v"�} J"$ 2, Van No�dndQin�,60; G>�}�s�J!�5m�Z�u Y.~Zhu�d}*4 �5^��+m(��,V&B��9}�#� ) 23�02  R>#-  docu�} X�\�x8[12pt,a4paper]{�):husepackage{amssymb,amsfonts � thm,pcks -all?.�-mh}{{\2�GHgI.znu 2h�/H_\Lam�my.�%.dom}{�]at�[Dom}\,:$ kerr.%KerF%�p.%BKdia2pB&bhluJat%B(9�):�b�.~BX spec.&SB&�}bb .�.~nn � bb N:�c\ 8C:zz8Z:o�Omega�B!o}{ "{-�,�K.�h&Hr!} >&ov�A/agF&h}{&mhF"�H�F%}{0'#1B#pij${\Phi}_{I_�m(r)F)j2)J )b) E��ema�or}^�|)elemma}{L 9��\t� {Gr݀ �� v�is�ed"� &�od�J�-la�h�+em�1\xwH{D.A.Yarotsky \foot�;{D�s"�}2V 8 2�CGgFyl� I�0nd; e-mail: y c@.ruglon le�'�3Inhx�wI�R� Iion^1 blem��y),� �W\date{}S`ke%I  Ab�Wct.} WsZɃ� nvf q�+�fgs.cproveMl"�-a such:O(&\ij9Wt�B gap,XRoT eI decab trun�d.� s, a~� N2�)) ?H��4in �7˃� AKL�  be!��2�GEb if E� ed a�~rge en�Hscale. This immediaylim�s:#5m*Z;8oI�%'i%S.-�Key/v ds:}2��S�veq�j,�, clu�2!JanAJ_�`{2� �r��a0I*�Bll�kSuIhat!a2�!qaq� 6j� �,-*�xg�R%L�c V�\Q�exn.s,!��.�  ?i�is ph ?� su(��vlGBak:�of�-�form.� evant "�-D �7now*s�s|? of wamg .� �?Ep��Es �?�A,DK,KT1,KT2,KT,M1,M2,Y1,Y2}. Most is�7.Ɍern:iw�l��^A�~�norm ��e. How�, Kenne�3,nd Tasaki ob.�Ob � KT2}�1jn2�,�onl�I�ly�� !�� �, w.r.t.!�=+(Hamiltonian! re�3 , us� aCU.!ũn)1.=E<y��E�is2>wa�hP�Dime�N�A�9A�uin�-� $G )$-i�t)�Ae type�[� -�a�{yPE does�B, h1� seem�ϋ an "�" �ir-�&��<�, f|%!!�o�h"�ase. �Ea>� rEt:i9w2��ly�QWHEra<!�5�I�'*�w fit natur��eB!M��ome�G��!كQw q��"gXd]*iUO�rm�i=_�a��nE.�%ZB4=�. �C5a ��9``1>''��*he"�$� $|E�CFce&=�"� t ��a!-Ds. Each site $x\in`A��);I$a Hil�~F6=>h_x$,�sib�f'E$�FT1E e seLzAuse!-A�iT$$\mh_X �P\o�3s_{�9 &x$#D ��0J(= ��>e)6�<l� A&VUa�U��>a pref;d �[de� �DN _x$e}�D�F�5pOWt�  w�gb�H < by $ ?� ,0}$:� V) 2��mA / x.$$ Also$V fix��� et $-:_0�y%ۑn�A]] rang�e (aual).�%$4 $$H=H_0+% ,$$}nre $H_$^%�ٞB a, $/K. %U0 ��S>as{_0=�rM'�h)Here $A�A�4a self-adjoint]�un�. &�ct!�on E�1� _0+x�'�V9Y+xbhif�P=uI%2<1剭� R} ŵ . Ifqc�Mϡ~mZ�x6KaXat� Lu�x%cr�t�;"vI.*s �a5�Q�x�L� � !�Q� 6i�\mh: dia�Iizes %{af�tH� �� wa�$���p� toI-g of i�L.��lp:!�����)�xAJ *dJAx�pZ*#yYAn� the �jo�_to=,!�@ �&�% of�1(pV,�1RAw>�6I{ r�eVͫ 2��+A�I gin{�5}�Qhxa&Je,0}=0,\�s h_x|�Y:�\ominusV= }\ge� 1}.\�F{����lbU e:�K i7O�,�$>�\phi_x�i -(poɋ u�)�8ic�a.L�_>�$,"�R �!*� ��A3!v, jLa6�%��mq�},RS��M %�p� �EU� ll� g|a aR� .��"�*�m�'6W��, � in�c�gto�8Ee argu% keepL noS s�  � typ lyL�inguish�p57 R6�6�a�W� �� w� whS�( -�cubicm� �tEJ�e �K�-�s. .�S�RF V*&�� hlo$ ya20� hlo:�.|�M�V �q_0| �$$!jI�v �.2!�3�A# � l�&��-�� ���b�QthxIڝ xistY�N:a;p��V6l�&�\ $\n�l�B> 5� _0$,&M  if9�2~ ho,#E�� �͉�"en: 1)�7-�� R -6� U5 ::$�$ -� =E 6����!��, in&�kv @$.]�O2mnE BAA (�+ F)AH$ 1}.$$ 2)AL1�3P J�6$^*$-l�F�!�.I�i v:$�l��e A6,6\$le \xUda�* \�-row�  \oX(A)�^A�cup_{q!|<�4v!dc ��B(� �)L�b#ۅ=e.�x 6a 312x �8J������ `)DIW $ �:�E=�ce� $�R<1!b| 3 (A_1A_2)-) 2�  c^5&_1|�q _2|}T^{{( �_1, $2)}\|A_1\|,2\|,\;\; A_i!�6]1�_i� 4)�a��o%ed!t.�i�U  (o(�@lvǝ $(h_x+2 -z)^9dPm%С�Y�v2Fs) imwj>��!B�p��*�6 -��*lsoe"lya$SA7�~ P &;X��lH=,xble $A$^ex�a� l(A) or�Ry �� e�E3� 1}1 harm���tcryst�<odel).�H�0=L_2(\rr^d,dq� ��� x(-\D U(x+V_1(q_x))�@\sum_{|x-y|=1}V_2 ,q_y�  S�gP$=)\to �8$�$q\toi�$&�!� $ yw��discrettcectrumE[ aB����.�MR� P�U�NwLe`if�� $c_1,c_2�m|.�-  c_1(�_x)�(� )+c_% �= q_% ��� `.��q coupa��tanC�}$B � 2�ij�*� be2 d� 1k �;�nex�Y�[:K�>�dll �I\in(0bj�3c a slF)ly5#ng��� �t>�W:p�6��:%�`Is`�g>�Wb�p1X =�-^v �: ^{(b)}_x,eJ"a �6��� e{�``purP| &2''�:��.�f�2}� �B( h_x*' ,i��C�% ����=f}3}\~ =_x\E�� :s�vLi�sr�b~" �(hx}) , A�a�Za ����0+x $ax��5l� 4Fy(mc7&�l 29(vZ:f)=0�T$*�s5)$�O2� ���$�ڀ>1� B}#Z= <�) ,\nu�;0)>0$&� :�an���ViM,! &� -V p1})Dqp.Ua���,f"a� m���'G�1- k��va �(\nu+1)���!�lu�s�Ba- em 1Q �Vnd�o�p�*.},� e��2})Ci�Zmma9xed� factBlśu�u�,�y���2�� not IudQ�a�� e �� 5m $I�L�\UuL�w!�}ɝl|��6 I�DI�e�$ra2)]\|JC�>L�!�n��w "s|�w*D#�� ��. -���2.} Co�a6+$��A*� $A�!{2�yqo� B�Y� $C^�� ��$$&�$\�v���K B H a gap`e.H�i a2�!m��I�JWM�sYes�le.�� geO�ak��6} F$H��|2zv�a��#nde�o at _i� |A\|� $ (1 IJ"%whq �3es)�'" ). IY�>a�� 6��ium_x\psi!i�n�$�;\!KBye� re�`ng���e�TB H,g\y�)A�thrlos%-;L%! ��a �.$F�. , l� A_x= i�S�� $R=%?Pz.%z�,kk��Z= A_x-�QwW��Ic�$P_X$A�ndFa�R or oQX) t  Aw%�9AA"#�al2 �<��our*� ��r2%���A$�ym.v��>"& 6Zs�at.%*���=(%[ -1)/ &*Q( �$$Q�� �� $� �nq� 2* NoFB*,�a�m� 2� !��z�!0! jF ��int��_Affleck�6�2~�D1,2}�X]iĥ���a�!i�' Haldane@& �1,H2},�# �Af}��a ��e�The ?conjec:2�3'"-1 chǀe�3�F ion-&2$�est-nMG,bor isotropi�te "&@{k&(zz}P^{(2)}(�S}_k+ ə)� E\5.\cdot22/2+J S} Q ^2/6+1/3)� �  �bf}E�a��!at�" $kMD$~�G!�6� "a>|6�� tota�q in 2� A)Is)!apqu� q��,o#�$�< imiz b��g�*�Y�r*k�_.�!J:�)N $ (a frusԻA�`.�ɔ~��$ �daa�_$-bond-soli � M�KLa/ ��X��=�$7% ,FNW1,FNW�(On a 1M�&VE�n1%�z>9"A 6�Z ).  zPh�k��_k$�#e Vh �� =���Aq.� !@'�e)&4 $H+�It�2�Gaǩf> it0-iH ��� ; kpv-F �� hi_kM� ��X P�A� ����>�  ��� ��ek6�m6�:� zYm��p�#U%1&�O wBh-a-!A YUb�_lr��+&�$�0a�is en�s ^�s�`emi� oughi�isAw^ Pct�m�a|F�M,K pL�y��i.mor"4/;^�e�exS)��=#tab�(ic]#$"V-�(A�Ͱb."�-P%b!QE[ m�%d�R�r�7'&z�)�.j� low-�Het��s. Af3U(9iza%7we@, aF�.��ei1�if�NA#%É=as�'GE hard-c�gaE� e�P�egi-2S d(`Tl@(���,�E�lla��2712� usuq ay. Ouw/�hon��o@-rJ��Df�dt techni�:!$derive nec��ry {!>m�m�o�,Schwarz k3 !�"�AG�/�stead�!@,Feynman-Kac Aaula�*{��X�% $\hl�iMg.�. F�( $t_0h�2I�%�>�znl}Z_{N�1)�( �t_0H_� })^N\olo,�:BG�� $N�"e6� � ol$a�a aJ.�%.�o(!�>!?��$"���e&�0$��$,� n $$2�=| � \ol.�|^2 �c N}+O1FH N})$ �^���:^\nev$$\ln 6� 2\ln�>8|!� N� � N}m�uA��ho�Wa�hr��Ads $�a_2,a_3bas}F�a_1+a_2�a_3N}):��$a_3>j�?!imp"a�!� cycl��ubs~X�/e�'da$Afy&�~&S! rgue�ie@��asympto/Das}5,Ul 8$a~laU��w�qAut��xeb�* �i��%a^)�"~�1whoQ}acjm"�-222c� !C29ca�� dedu� a!� tinu]!m� 7>.�T6��*&j�3.~/�‘�=Yby���e�Rty $$mk\hlV&:�%\{jh&\} }T"�,I},$$� $۔� ,I_J I}�j|I|-|J|} �b%+ �J�)&�!0ope�].v&J�8hl.D D�� �I�I.�%, MfE�. W�a�# TrotA� or Duhame�'panded, 6�g�a�0��� ex 1� \Be�� "@�U' -�I�0&� 1�)%��-��1 I$eu� ��)Y do����$lt3!-se "��s"{3�.A�co���6}a�>+liew _I�U!x\i�(MG�)$&aaQ�e^St'} T.�=T'_IMf&(9�,I�_I�$BIdd.kR7= Y� O:2� \cap _I= nothing�)� $�AB, �>5)�A�$�a���-{xjw\ne:y �(-z�-7-,1m� $���aa2��hoo,#j�1:�2@ $ by.{� x _1$ ��� )Aac�] {&��4I}F#Q>D }$\|T'_{I� le(2WY|t_0I/ })^��}.$ ?M� }�q�� I$) $z_JI�, (z_{x_1},\l�|,{�}),x_� J,$� �Cmp��*nd׃&q�-va�z oN  _{J}(z_J)R!n�N%�� J}z��.Ife�$|z_x|<1-$@� Ɍ�+�J".~.$y:.^a b?� �� 0���:a   $<1:b zj}*�.���>x�I \Bigl\|(���;r)y / +\m k|J|E��,:�T��R �!-�!O aG��5:�m-=org:QF�n@�I� in\{%5�|�� J\~�Y��d�bS�E�IzjA�Uer  o $\��7� Y�v,v� | " 0),%=1\}$� se* ,}"I half-pl�D$\{{\rm Re\,}z\ge 1^M�\�i� �4X~E�,Hille-YosidaO��� >� et} \|و-��sހt_0:}}:�<H i~:�1�J�T��(z_I)m���V� 9P*� ��IAhw�� z_I$y J" �x| �+ M�7- �$.|LpoE;�!f>�5� I=�8n .[( Ma^{-|I|}\�6F9 I}��� ���is:�èin��A�"� �on2<6|. Llym i�.�� &@%ldesired �4 BuBan� .� = Y�,I}p hav9o��he ���� &acal&! ;a��fA� � ter&� � n to i daa�2kgly � E� D?<*� =a1)� I:� C�*�mh_x'7  6�0x# \mh'"� _1�!S -CT�L Q BeasB�2Y ��T \�, I} P�J'} O�_{( !F1) J� �a�� nfigu�7C$HH#��({(I_k,J_k)|Q��!N���  $J_k6� v �+I k}$;A�q+��>�%C w(C&�^w}'=\left�m�k=�IN�(.j _k} !:$J_k}')S~I{99M J_k!O\�/)��7*]6�)iKa\�-o,�edj�/\ rod_�A_kI� A_{N}4s A_1Fr  $|! �:%(�� _k|}� ,-t_0(|J_k|-|1�0|^3|")�:� " �� ���Ehos�t�  bracke�aɲw� By �J 1�!|������ �)��Q#ext� �eӹ �B�� $|J^(B)w>� $_I)| \ge|J6)256I|J3|If$A�7 N�Fh�-"II$_ 0|$ .�Ab�0+y��se &don't �ElapE� &,) �L�6hH s;!�r v A�s.�&�,-�$w.z~(gl|_ {a�J'\�c"ZNF�� y���}!� ���! 1Y4(>�!�*\4.�9��!Q�� Ɲ�CinV�"oF���$Q�azRa�A�z�$, �E��#u�:#��'>w�C�s%4Q�. pp C��{0��. N\}��-��E rC�,>� X}\{(k,x�Y0�Y;eB {I_{k!�cupZ +1}}6 J56 ?�}:�(�$V]�P=VNxu0.r%.�$'s�AaO�=��(��C iEe���i !A ortsCC�> C�r@> * H��t��#�� =C_1!' >/ �Y"�,I_k=I_k^{(1)%Y 2)}$:J*2x�(? Br�t<$w( � C_2)=)2� %� QQjɈ jA�2� $>���ny $n=1U�H�**$$v_n=\.�n��:c� cr�cc$$ �!�� v$�$� hA1�u_n�[�m��}�jain%� J_n)�G�2�Iin��B1 J_n2 Anal�lyA|hIv $vI:_n, 2) u � A ,A�.A $K!��{I �v��s �nK_n \, 2)}BZK�� Y�=VAtj�qwj�� B��X�s��/(>H5�%MK_n}=  �} -�.2)}�n>��&w�� !�!� JHu%!;� $n=N��-hQ���<qu��Em_� >�}y{n-1}=u >�-.d]8�vE�iF/ K_n��K >}�e �q�x}1 un} A�SQ�(��>X&S K_n�3T_%�'2 u�՛�@}(-�� ���,0B�x eA8'"�E,.�����۪�0�+.� u��- ��N* Da�y�\�2�." ��q��Oo���Q � facy.4С�u�f�� i9 �{C%I��smkve step:Z A��ym6� \chi!�f ne �6�J; cK#4 +oYw�Bn��nCth�"NeA$$ 6�"T{m`�Z j. }�=�  n}\no? s^{N&D$!+� n w( ,&� sumRisb J 1� co.C� po%%�$\{�r>A . V���?o �%E( 3,%��� >>0����sa%$�$. tdrXA2�� $ � )\leW�>~ ! |��A��'��a"� �#��"�mofQ--�$&pp Z=n��KarK�)�R"N c^�5� $c=c(\2�7�nw%�*"7�"�(����+ ��C��9� �4KP,MM,Sei,Sim, VXҟ�be0 y sketchy���ajW��+9�u.Q@�U?e[U�,!/�,��&�"�i�~ $n1n_kT $G(X���ph� n_1+i+-�ticRWQ?� �a �\ beo�woB drawnM�L_A3KQ�a tD� ct. ��G_1rt�pgle� �&?,*��f�� aph :$!�UGl��!T)& $l(G_1)�Y��� Pa�Xbh|,"�*!�i6~ ($w(X)=(n_1!� n_k!�@ic_1)^{nQcdots�nkk#^ � �� BY4�'� J �aXR@�� A�%S&T�A�T����� r.h.s..X# BZ,U3r u�H��of��E%lQ�!�f ��tF�H5�Z; s�Q�.mx%�/,� � $ mj� �{X:u\le N.At�L�:} (N-%)! $�C =-)�X^40/+ Nz*& $�>f�(W-NZ%�� ^2��!Es|��5+p0? tEo, #"r,�k-�x'-�co)� Ye�H� aB$O(�vNe��L��w�/6�Ek-�$>�+C$p�! 3),ˮ!.y!)1�$��G7`)?GP7f�!��li3iCln�[iIepsilon$���D�M\2�4� ^%;"~isZK-�:�Ie�kTU mple�/iF� 1)e2chang��!�Rv*�(n 3*�L"O% +vE ( $v ��y%�)adds new�K��v!2ri�["S(A%s $ �� �,2�-v2, /j.!�~2&N!�A�p�!Q�vՁ3{0>�  or B ,both.� $v$ )@e4`!�5�$|�FM?:� �^va�5� =)��Z >�-kImodL1.'!��m�sA<�j�!�� kS�a4to/�$�0/�� set�&&��.=i2@&*is $c+6@��VI�� e 3���To� �2"P-���dXm A/�=\lim_{N"G}Z_{2&L �H < A �" N Y�I^ g���1zf��� �D\o��/%A"�=�$ɤ_A�#�int;R�Am�% 5A$F�3!�!�+  co�ed �/I nser�)$0th layer;�h@M�_AE�N�_A*�A|}s<�Bd=8F���.�-!���2��is 6{�#zz\A�" �?q!dm i1T*� y 1. A��)�\�;?M�z6"���{d�^!e�R!�"` �� |� $�znYFR s 2). 3) *�%UrE�RSe � l� �l�%^��&� ]Eei�N�A,��Fr�:N�ndR�2�S� ^��{A?*chi 2�Fi^$49��  .$�((�.,�� ��&0��tooeis. as �����)T4Df�72@+l'a�=(Te>"FTto 3Jr2/t�7y �X$ �W41) %�f_�:����1p 7Gz�S blocks $b�B��iA� s��$l���EeC`U) ;uO" �FdU ubic�O$Jk$�2i!j$�Bre�se�(3�J� ��'m�oa m�N&��Fa�m>4l2�a�oEa��- ��7%޹��ovie�$� h_x=Y_{y�/b_xay,\�U \ovoV$�'$=\o$<6>$ tI)��$TG9'u _{0�� I}\o ^for $"/3�6O $l>�n(\� _0�BBaecn vAa1.[=~<_ 4g "sum� �p���_x$|�`\o�o�/o3%"mlF1�4�1ly`\}^ U� 2^�op.�1y*�Z!�_{z~on$+x}b_z}c_yYphi_y>�*H�c_y=|6�4fR\}|E���&�cxaHV�Otee���*:1bvE,=`�L� $:'bi�n&db�*jf�(1}). �"A]i>2a��d�I�"�n_5Y��m&`E�� o�r) ��"W1 $"� /2+B!� ENb� F��A���8"�� �  $os�I,J,K� bp +�,I��' �I"�2a���{J J|�6 I_1|!$J� �+\opij)*�@K�"�z%"� Km&'1e�o[hG,nce $C=\{(I_�mk,J_k,K_k),k=1,\ldots, N\}$ a configuration and assign to it the weight $w(C)=\langle\prod_{k=1}^N\ov{T}_{I_k, l8}\ovo_{\ovl,0},2\rC$$. Let $x_�@x_\nu$ stand for 4coordinates of$site $x\ina$;,any sQI\subset�a we define its neighborhood $$\widetilde{I}=\{x|\exists y\in I\text{ such that } |x_k-y_k|\le 1, k9T \nu\}.$$ � _I=\cup_{� I}(�0+x)$. Similarly to (\ref{supp}),�:�'s $ort as�${(k,x)|k=01�N;m�s{I_{k}} �N +1}}NJf7F7{K}3:i +1}) An analog!�LLemma 4 on factorizaA� of I|`s is immediate. ThereforeEon!Ching %�Dneeds to be proved?Dan exponential bou]d g : $$|w(C)!�,\epsilon^{|\!s| C|}$$ with sufficiently small $0$; afteA�ai@$conclusion�A�Xtheorem follows like in0 previous sec!. CleA&, in ord[o hav�is �it �e� show)aGa�\ one can choose $t_0,l$ au$$\beta$ so>( \begin{equ%�d}\label{tijk} \|T_{I,J,K}\:31$,�� $ ��:��(,\Lambda_0)�1If2�co Qe� strategy)�A�!�is asQ�. W-�Tobtain three differentI�/r $2f($, suitable!e3�tribua/!�$I�� JPK$ from either $I,J$ XK%hlarge enough. {\bf Case 1.E� firs � reli��wi�nesї �Ted%� �0{\phi}^{(b)}$5erturbeP%~!,used when $J�. Ik is c�we( aga�, Schwarz l�C-E ��i% of $u�� replacAsumɘ J_1� �_x���$( (z_x���+,� re $(in\cc, |z_x� a$, K(some $a>1$.�"$ $a=(t_0\|Q z\|aj 1}$,� n by6� F[��%��Ga�) $$a\gec(2l)^�|�6f>#� �\ge 2a�nu}i 4^{-1}> 1$$ if m5<$ $. U�Q�1� %�)t!�$%AWndrc!�1}2�\l�|I|}(2eb; |J|}2+^{�X}e �)^#:�.�2M�secondi�:�(contractivemE|4classical evoli�i�z citeD gion��U�i�i� e��estimat��e normE�@e^{-t_0(\hlo+\opij)} P_q (h_K'\otimes&w @\setminus K,0}}.$��b��A_ writj eint} ^w=(2\pi iM5$int_\Gamma2z}R_zdzR� $R_ze��(resolvent $:�-z _�� $ b9" tour!ith�4mplex plane go ar�espectru)L6D$; we �X�nyjbelow9�us)�expan*� �Z<0res} R_z=Q_z(�^Lk=0}^\infty F_z^k)Q_V0 $$F_z=-51/2}A N$$�  $$Q_z=N!� 4The operators + $ ar� ll-�Red" ��X $!���e9�� �x1[Dj$, i.e., at least!� $\ccY�[-�pj\|,+))$%lnow2 u8F_z$: \newpage9n`narray*}\|F_z\| & = & \||�-z|��-3R|\\9s� u��ovhebl}� \{0\W frac{|\l� RRopRju,u,|} {\|u\|^2}~ ~v~ dom(:Z�)} ~(opi(v,v)|}{B�+v\\le!ܒ^ \�^N�j & �\lK �aaY�� h( )+Q)}%^� -z|}. " 1� Wm�be  rest� A� A�F P E\le\sqrt r}$. By�!aboveI�, a*� ��dYA�m isYz6$ 4u}z\notin \big �V�Bigl\{zcc ||z- 3B�F"3r\9 � Sin�pe.q%Nzx) un� � %Me�tor^� sec}�$: |\arg (z9��arcsin2�\B� sofwe� ^ $ outsid�{4 or h$m�B���in� iculab�$fk0} \|Q_z��Q�A Pe�I�<^{k/2}}{\dist(z,>�)FZ� ��"�, fur� more,"� enE�do' of Y�aI��c��I�(type holds,!4�app%� the �� � l.h.s.+ ve!�s= X �>� �(compared to� 4. Precisely, l�$n=�  (|K|-6� |J|)/7 � .$$ T!�$n��lower �ip0$. Next1�m1�l/\diam(&@)�,,m>0.$$ For �a$� �� math? U_a$2���circles!� in � u6butj $�6$ runn)ov�[a,*_Now, ��!��a k/m �=rQ�r�2n! � im�pa*%Ɏ%fk}2K�� \�v[|5W|(n-r)FB )}, \\\� \forall ͓1g U_{bI}.\nomi2o } Indeed-�N G_{=c}>��� trale�p�>( correspon%�t��� val :�fe�be�senA2�(, $|K_1|=n$�e"xa> h_{{K}_1}. &� "� "��,n invariant �_J�� it�05 !=jnF�@� �ѝ| (anda�&�ir6� N� too)� in e�stG. Wjwe�%y p�i�V !xJ�.��� �$�to rem� ���,�v a2�R�$of a given%��, beca� 4block $b_x$ ha3AEonnected>$\�U O_{y� &7�6} b_y���Prt!N!�( elementary� a�!�ph�r)}_w,wU o,)which�piE}�c(osed. Hence=%9!�� $r$ ..s!�2� $mr5oa�L e'Mcif $k<%��� n �^k �m�'> Z��(��!�� o i�i���). It� � � �A�h��w;r"Gh�ji����qPc f�$� �Gtha�� riM 4 �;J arguA]h�1�fk0})$n yields$fk}). Nowɡ�if� 9 g�on� Tj% dependK term $k$� �&���ra $r�c  $s=n-r$. "�n$�f, $$z_{s,\pm}�.� )�Zs�Z\pm i� ..}{ �}}2?t_0A�y� ��e-_s$ sistaC"seg!� $[�-},+}]Y rayz {z (z-'�)=\pm\R $, A��`���[Fe trunca��=or-�� ) ( %  itself1�E�($s=0$) shifDby) A�� left�+isw!is just �ven� caln �`s, piecewise-linear appro� !�.�y6�9��4W��o�1�e�is way ��we�it�lie/far� righX possicdu�k��� ~zn-a!),� st�� � q� f�9��e"�b�d. By sl�~!�� �?!�� avoi9��it��.denom_ oAi��( ��pspicture}(8,5.2) \put(2,-0.5){\ps!�[hwidth=1.5pt]{-}(4,1)(1.8,2. 43.9)(4.2,5.1)}jKarc=1,Upcolor=darkgray,fillstyle=gradAq,   =90, b�4,end=white](5�,3)(5,5N�polygon*� �;.2,0.7�6,1.0 5)(!� 4.8,4.3){�5 6.2,&� .� .�3 3.1,1.4){� -}$} %�3!� +}3v9�*osnta2h1�_s\cap�fl=noj I�� ?�^"�� �$$ $$:Q�r"{n-1}a{ �{n-r}"�z}�biggl"YrmVr+1)m-1}^#rdP�h�2( dz$$ $$+(B��0} -F� k=nm� F���)! dz;We&U[expres�ua� $|!-� z}f(z)dz!in<{\,\rm Re\, }z}|&||dz|ٷ��"\})AD $-�s2�Y�,w)\gBwI�. "���#|-H"!���)* \|$$Klee^{2g�#{!�: � .,)} XQP]�bigl[( drm}{2}}0!^ I~)Bh*� } b(>� + p2� ��!}7r)l] ( �n �N=Bigr) e�:} (n+1 y.�n�Nobol( \max\ �� �,Q1-6�=}\ �^{n� Sn*�e(}� '�#,���"[M ��":"�@n��%>0j i$��I�~6�}o^n\leAX2M^# |J_1."�%� $>I_0$�� _0=(b,�:#<� It �%a� Z�b 2^�-%}e^6�.�j�3� thir�is�\IC���� ��4�aI"48 I}(-1)^{|I|-|I!IQ�� ����.$ Lik�n 2' re���$b@:b�s!�� f${z,I_1}dz,)��"R&� �"S�0%,G Z e-R*e @ u+in !� 2%[�#d |QZ� ��Iow�  $$n', (!�5-5A�|K|)/��>'�a.?��n? �� I_2\ I? E�!6Y6wi*0+RF I_2�cJF F,��Cn�#$K+,�[3b*%�c;(e�� J Y��+:�F9�Q_��=0$k�%r)� ��!�i\* -excf* principl�,�ome,,�kd�r\�-p=1}^k(o& {x_p8 tŢ0 ��y� summ�is � sequ�c_1�,x_k�~)�I$,�ai� u ! �I$�gonc1'par�,�o�ains   gGA����. Each�Ksum is 0i'%��Dwe�1��A�*%'r  in $*�yE�"D op})E�con�i�set $y-�'_0+y_p)��s�resul5f$�M��A1ll�.Je�  {7-!?X r�(. 2��\A� !f�A�cho 1~�&�# 6( E � �" acts� o�g�$�i/3$-�y^{!�\Omega_{=Pa��m.p> our �E. >�  $$/ l\�B�B� � = JzJ� � .�&�=��� �}k=mn'}^{�$�dz��"L 2Wx6� t ^2 �I }{\pi **�  �-)J� �A +,E~ any .� i ?�'su*�/&5.A4is *Wdoes notueed $�f} {n'�I�iIXX>X/J3�% i�V�^S 3. \desir���/) � ep! s�-e��-Vs. If $^ 2Ik e�!_�,N$Keben�!us�0hm$ �[3cO\ 1&-f ���lO"_�U2UI ��08�.1*\� ion{P�.of��13} �"�� rize�� know�2s��u 2$AKLT modelM�0 �. Denote��$H_��^{p�5O f$} P0 Hamiltonians�a finit ain ��periodic!� fre�.� ?!i�s,�G(*ively�e g.�f$ A(a four-dime*alP $&G��� frus-0 ion-�2�s.*N-val0(-bond-solid&9 a@)�&�1`e a (non-orthogonal) basiy6�0;ab},a,b=1,2,�R� �i$A:pro�/ies: 1)��adjacent2���� 2�6�_1��"�= B$;a �,:@2;2b} -N4$+Z41b� 21}$. 2)� gO$��$4\�8 4$ Gram matrix}f�$: $$(Q$)_{ab,cd} "�8:�!�>cd�8�FTh?S={2$1}+O(3^{-|-�|}3sk)� |\to�<��& also���J� ADatu,9`f$� uniFly��ed away��0�tral gapf,��u \g�.*�.�f�! ( �-u�W & �>,@*&�A!� projH' on:�-! All.` %�r!4�7n \&0{�%2}, see%9 `AH,dNR,FNW2,KLT,KT2,Kn,N}�var77r�9�s.�� 7n7�&�3 scal)�p���4�""�3 L!�J� ng -."�)e2�7���p�6si*�:cyclic c:�in�!��IM.+& n�� $Q�_k|=l.�;�#*�E*� $l$ later �Yzp= 1}^_;er�{H�9,�9"� S� : =H&U 4k}^f/2+P^{(2)}IiSJl}+Av +1})+7{h;�2R.(�c/2$$ (����l1Ge��'J� k;a2z: 1b}'��  by%�i�''$%J5���!]b�  span3 J>�Fk �{ $\mc2��F+� Ab:�forward.� ���� at � -1,k�I�es� A�. A� sa�+ ime,��� y 2)ɾ^�gg}\|G_U-z� \|=O"f^l):� �� ��&�=<r�$�'&� abP $ct observa��."� l&:} 7*!h1,23� �;> 2� Hilbert!�ces�dM. 2 @wo-c�&`# -adjM."�/s��v�1\� mh�P  2$, +?"� �re �A a des� anR$=\oplus_s({3,s}^.s  2)$$z.�forj $s $ h2� 4JF$ �M�^k2� d6iW+"�+?)>a6� %�:C1� *\'A|_{�F�F2�# s an"� 9�lyR� ��8J�2 � )� 2��J9$5M�q�p�} DM 1�� iH_{11,i} � 3,i�AW$"$ !���A D"(� &� U�- >P!�]�)3$. C.�algebraAnat0 A"�? BE�3)$ gene�1�w�|���unity.\ Aa�`�+� �2T reVt�!H_ ^in9\m ��atw�1p� % 6(�$ '�$�n� �!.'�:A . Bu�(���,�w6:=�B�ofN`=� M s ( e.g. BRJ*VDf�Z�mh3} � �:��3 $&"AaQ�baE�-�i�1)M� 1}_{ � 2}),\0,"-R'��54"�4I7 S))�"#F ��)A�aQ��2�D�5�C6� i�Q�E��4`�\�{k-1}}�[F�#� ]�B�,T2*��relevA�2�AxnbZd�8.^ H=Q� F_k�-�2)� �z2�\8)usC.� }B? HA�Y9[�.j�jtwoN|-hE��Mj��!H1�kG O�an0 < ]=Ha�$\{v^1� $a}\}_{a=1,���2b>��o.�" 22$ `G  B� z  vo.$A"*!*3 Ix 5u2��*�3�.r$Z�#ub�]� $ es�!ially%x*#5jR�)� $; sK,�M 2� �2�i6�: ��'�t K�� nA�.��e�5m�6�a� ��!e� $�7 n:���� kernelH .�6P6S n2)2M on't�or� q=�7:�6�� H�t)q1IfV� 2�.+%�E g"x�4s ���k+e we get>� p.2-}1�R3a direct �!of �"�s:�Q�8*}:InaEA��!b1�>9!�:~.x }) @A��&��.~�bF [B# 2 6t�|ab&� iw�qw��.a �o�o��>��2e5�E<��M�&i|� e{��&Ia�=(Aith6%�N�7h.Y` �8Y�uW }�M vk}v��A(��9"6 �[+1,2}- " 1JK�� 2�B[5B1�In "�Ni� �< {  sensjIntrodu"6 we i  e ad�al:� �BAr3,�El4K�=�-m *=\d:44=3^{l/2}-2$ (@ ��@is even)&�2 :u=(g�1i� {}�ir +?4� ��$ newFov��Ir�92�jk�c�9�B�e�^3�Th!�i^d spib �%Cx1��M I_%�=Ok# �T�:5isA�n ��4A�WVopaiw(%"� {` f92F.za�!z �H . Let $h_9{[&6 o6Z.�} ��p3;h i� $u��ai �!� vt 6SS  $1��,0}=3l.��.$$0�$I�t!eP5(O (!�R f $n$),�e0 KI-� r y�*O �Oc� !b� X �^p� �Urel�e*�[O satisfy�Ke� A��!2#o!�R�EslU.%&r,0}+ .O\&�} & +\|.=d6(\|)2� = & O(lo1 ^l),�phi2} �-����gg}3+�:A.�V c=�:wevXyze,�+$e�kM�@ �$ � E�""%�uw}) {H�t^(=-�(a!/(6l)+O.�)$,*�!�l!�Z \{�$�[n\�Q.(e� �Z�hg}u�=3I�EA�1�%j!>*�2%(a�7<inw(l�) FTp0.�HiA?�0um K N(1^�tz,�3 $I=��$�Msg}),:a<�"�4h1>*�fteqn{��y�.X)}&a�\ &a�\ge M 2RSm� �R8(!�6�i& h(h:oV: 9� ^9A��2�*}�henceJ@I,A"�g}Y!g}Om_{B^n�0�� ��Kr ہXv�2�Q�h*:N ^�,is?s*.�/ab�)�Bi5ed&Uw� �,=1--�F 7 �� pply*�� have $�aJ)^*CZ1+\nu)� b}^{2"�6}.$ O� e�3�C�iJ��� 2� .a�$6�x �!a�""7 less��n��! �E�6$l$6� .� * a5�^( �@2"�\m) �QNczZ� cq3CT�]3" s&�$2&�Ga6�, weak6J,# $�,�e0Ha02;� :�H#�:��,�, *{Ac� ledgG'}F!� pj3urB��Tnk Tony Dorlas, Mark F�!(s, Yuri Kon Fev, RoC � Minlos, Bruno Nachtergaele, Sergei Pirogov, Joe Pul\'e�pHerC Spohx: Xu ng discu�=`X(warm hospitɗTat UCD, DIAS, KUL, TUMZ\ Universit\"at Bielefeld)�resear�$ap�$��^Irish R$Council A�Sci�"$, EngineerF�$Technology%{�CLthebibliography}{99}�ibitem{Af} Affleck, I., ``Quantum*h ��\Haldane gap'', J. Phys.:$djd Mat�`@, 3047-3072 (1989�B} KLT1:�Ke�#�y, T., Lieb E.H., Tasaki, H., ``Rigor�`r�4+2�-&)nd�3@ antiferromagnets�� Revlt. �(59}, 799-80 �7>�2ҴVRc��nF�$ isotropic�H!�R�CIn.!eh-| �0115}, 477-528%j6�0} Albanese, C%�UniBKd�@�b rans,aU%��2�5�bdecay�Y �s� E�q.2system!` f�<34}, 1-27, 237-2I90�YxAH} Arovas, D.P., Auerbach, A.,Q�, F.D.MEExten� HeisenberZ+��: izm:� ogi42�F�+�/�HI effectf7,60}, 531-534%�8.7$BZ} Bovier �4Zahradn\'ik, M%�A�p�(n�ve�Ga��� blem� conv��nc�� �6aw:�B�� oEmer��!�a� Stat2< 85}, 517-M:22� R}Bra�li, O.�sinson!�$W.: {\it O�Alr"E> �J rist�XMechanics}, 2nd ed., S_:lb$Verlag, Be,4, vol. 1, 1987��DK} D� , N.,65``E@\sE��Uquasip�9lOb�O�LsM1/2]�R$108��(73-399 (2002& dNR}�G Nijs)�RommelapK%�Pre�Ken�Yem# �cryst�2rf '���c�2 ph@inʅ��s:�B�40�09E�2zFNW1}�WA�25 B., W�r, R.Fe[2�s%Bz$2� �k.�1a sl'Y0��> A:��Gen �2�! L185-L190�91.��/��F�4lyS�.�!ofN���� Ma>r4�443-4 �A%��G} Ginib�XJEExistq�%� YE� %1Nl�V�N�-+ɼ�f� 205 %(1962�H1}��ᴵ&L ``Continuum dynamic�.�� 1-d �;:2: ide�Iic�%| $$O(3)$ non�& sigma�y!G �Le�fA �93A�64-46ɲ3.�H2R�Naf�O|orf� -ef�s: semi"2ly)�ized so]b5 on6�*(#B�>Iun�5dis�e6�!!J.Fx5A383-415%22K 2 *  ``Hidd9SZ_2�5Z2,,symmetry bred(inq�4RW I�%�BI�4�30��e�u�K� ��F�� a+D �� S=1$I�um>���N�7a@31-48R�$} Kirkwood��RE homM L. E��pa/���ݜ���6��/Is< �� ��8�J569-58��:(n} Knabe, S �nergy!��*�U*�U�Dcer� VBS-:���R�$2}, 627-63��6�,P} Koteck\'y� , Preis� A�Clu>x for abs�f F� f�0a491-498 - 6)}�$MM} Malysh�V. �R � 4Gibbs Random F�&s�m� & .}d(drecht: Klu^ Acad� @ Publishers, 1991�/4M1� tsui��!A��k betwee"�ES�k Potts yf�| 81-79%�9022>yU�y��R�� l[-va_Z6{:&I  s �� 126ar53-467��6�N}JE ``^).�A M9yZ! n reteF=�C��7��565-606A%92%RS} ReE\� Sim� B�^Metho?f�rn mathe� $cal physicAv.2͑Fourie�_A{is. Sel"�1!y .} N.Y.: U<}IE775]� Sei} SeilT E� Gaug�or� 9 ��  cnr�!ve�"6���� ` m&`  Le`S No�3in���)KEm�?"z 1982.�im�6I%� .� uA�� g� }�1+D ton "y�F)$93m(U} Ueltschi_ a[Ja��]I� fun�"eVMoscow�/JN ! 509-520� 4.V,Y1} YarotskyvZ``.��6in aeat"�:� >SJF� 4A� 2134-2152J�2N�F�.�!��F�>n;gapped�-��xc$a�UN:11��119-144�5)�U$T>v pdoc]Zx} ��% DEC. 10, 2004 VERSION \'�<[12�U� } \u�JHckage{amsfonts,epsfedef\d{{{RdCimi i eps{��t} 'g{$op{9$}\nolimits !G!�TB!Re"�RB$Im2$Im\F$6GeBDRes2EResB$hf{{\iwstyle{1�`er 2}1qtR!4!N22!N.B)26%${\stackrel)uef}{=dsi{\! &-Dse{& \!!�newX2 and{\beq}g.u}�k$e$Aa�>"beaFv>$e$ F" \title{��g4,l 1D Schr\"o ]er%v���oac�#ZY����author{�jHAndr\'e Voros}\foot�D{A�@,at: Institu�:��\'Ŗ ques de J�eu--ChePret (CNRS UMR 7586), *qH'e Paris 7, F-75251 �CEDEX 05, France.}\\ \\ CEA, ServAJde�*que T�or ,de Saclay\\ �RA 2306)\\ F-91191 Gif-sur-Yvette ro$\\ E-mail �` tt v!@spht.s[ .cea.fr} !EbE�}�Ske%�L2@ew 1� WKB� m�� x űonary=�\->� PaU� �Zal pot�al.Vh\"$uclMready pA dderial: w�N{a�&PA�umm�N,�;esT a f�< s"�Fre� high�[6�O AsY of:\7�papers�\ed��er�@�6�wMCrecapit�e!3se��VQ�L b*U!eYt��ImeL3to�Dexhaus�F@JcAHon azowly "{3works Z: � broa�xne�(at do o�v m�ze�s �ies� ZHGm�set";WH�% treat a^�o � real� eQN � $V$ (4T"rma5?d �&�uT�ny!w�ankkhanI�9� \/} ��4ke gred�`s�t�_-B!2�P�ys�/xploi�A �zeta-re�az } M�C,JL};6- � 0a�I���<,Bohr--Sommer, -�c %�@Gt}#+ ak�!  &BeA�AnsatzYY fA��ony ��  2D$B� � DT,SU} or �u:� %(BLZ}. More, I�s!�� $4/N$ beh-a"�7�c�Sframe� ��qualit�- d y) hV4}J[�/�y:%A$N=4$,�ri�-e ab�-m;;6:�.(!ow) *o�Vc�MtDAici.L �ate, r_r path�!�,�L. s�/unt< familyA�of=!� TP�� actu�$�~edIy,[Sec.4]{V7}:fKA �� eigenvaluuLs ${ [ Z?(�\!+\! A( �{* ( -1}) ] \, �J = 0 }$ (a��2!reE>0BA� � $y sources}7| sl E�&�%s!(�%F draI�ly ditGj^#nA9 ons �per�  fu,i�c*Jg�7aQ !��a; �g adv�AC�varL�.64develop� ��u� geo(!�@G !�of�d-frOZy.�: � �g�w��fro�pe���l�Gag� er3��(H1,C,DG}; (� u3 ,[chap.~VIII]�ݤ�sNH��Dslɩtic�Rt $C^.P)�ategory�R%� stepto)��D): ramified Cauchy���� L}, �kpseudV?� I�&� 10BMK}, hyper-%micro-0 (SK(loc��v��a�)BIR4{SJ>(�Borela�c/�CO"7* seAy �DI��4-��:&�3d�y ,BWQPtunnela�(WC,  H,BPV,M})� stant��AZinn-Jn'sAxA�ure�ZJ>�see,8ly unr�ed�!$ monodromy2���[in % e�"� a!>%��Stokes m9p8�S���7--�4�  l=7a=0�� o�$algorithm �1DQT�:ke:� , (Ad� G I)J�-iHV1,KT,DDP,DP,BM,HKTE�d bes�?� R'E(,e'WEiA%#� rg�U�a"�^ {E};!����9l�Wr��d���2� gB)�bridg�� dinE~�:D%(or.�R Sm��7 appr)&,� �Nc.:E�em �yeA � �n"A!�1.2.1E�its�ent]{DP-Ua fai_� �ua[< ge�soAb rKOe&( homo��)NGs"1 tortuouslqlV2&#4}. O|A�Y m� 2�\ ���&{Ba�n��a��i(:EPof%�Bz r--WuMfAcP2�0}�A�:�I�},���h��� ��Q[Part ��KT}�QK on PBev�U�9ZD�-E.?B0eNC��!�?�#re �]�� �:� (surve�QaBNUV8�i� upon�.YM�\`a laA�Sibuya e S}, �crum+pu_ fi'Jc Dboth �H"�!�&Ol� s. AFI�a�%it�sUqona��NWronsk �$ty� a�u>qw�&$ ir�4a��&deter�o�m A� aw-d"�aB3�,bJ�pN �"V&K%�s (``�Z� izA�J"/q�)F - !?Ki �Vgr` -  rpreM9)� DT})�N0r�~ �um�Aʍ�r�k foundk��-���da�e newyx!�Z��ic�a��0]lva�task)�no cl�ct er*!�� ne as�ra� �0�isq5a�k%f ma�5it&l�YVI l�  atNdB d1i�_w� h v�j6&� ial��A�"�Basic i&�4!�r�conjug��9�)�Sk��a.�*�b��3��N�!\f�'d root�g�r�= orig' .+ d .��4�yl*2edtf�k�8, ��?�o�0"#HCEQ} V^{[\ell]}(q) � \�b\miphi} V(J /2}q��\quadRnOC , \q= \mbox{w�5} v A{4\pi �X N+2} \ ;����xe $L$" tincf B�C�),�bll6�Z} / L&�Z�eg)4L =.� {� ��E�+ ly} \h*t4 \atop \N2 + 12.N an .��}� .} mr E eq .�S6�"� E�%M $R$b  ulae �i��a�SR�� S+4��:��isI}recesq�K(=1 ing)� Vto �$6�$P a8he��iopEU� WKB}�_Q;E�sim \P(q��/2n$, \exp \ -Qint^q_Q6/'A� q'�Y�2Q�aF \! (%�\�V�)��E3 $6B���� forb�)&�moI um (:=�� FAgmon� ric)U+*�0iN���p&dq 2|�{A�a [�+ q�]^{-s+�/} \sim \seA�m_\�,�p (s;�B>mbd�{\, / -Ns}i ( =\N2,\ a\!-\! 12/)!�\�ASQV�ex�%�F$C} q^{-N/4!I- � {-1}�lsE&,isl\{I0 l� play"!L�m_{\{ �>��}A��_ W \,*`!� 9}��\textZigmBigM���aUJ:` ��F 0>�$ .;Da�&����$ � Fr�Y$N > 2�A~we�:�Lm� ?M[�8va�4a�\!i, o � rougxD�sl&���:���Psu�i�a�P_ފ^{[1]}}  Ŭ\mi�q) �LA7 �8�m �fA`) 0 �Q�og� k:�$ �U(ir $q$-deri�Y�h�� lappa�ro�validityO�9bf&-� "F }�:1 ��{EWR} >�\psi'.-"2#." �a4a�y5+� iC)W} 2\,!Vab9]4}@M�} E �� (\ne �6K\sǙ�ٴt�9 9�sB`$ER-����\6� 0%��|�re��9��t4&�! $V(|q|)$�a �E&*peΑ4 $\{ E_k \}_{kR\!D bb N�$uparrow�� ). D�}�5(parity-spli� $W! E}^+q�n{2k} H� he HX8 68-:8+1 :7$Dirichlet,�trum (�Eq"hCi� beA��]q�K"m roll+],WKBeOulamR�)�^"�A�e r�Ue�U�s2�>��%���'0 {BSC} S(E_k)�k.!hfh � ��� er } k�!�fty��@erm") _ "�a#"� \/} $ S(E���]_{${ p^2 + V Dq)=E \}� ! {p \,��� 2 \pi}$L�  e160$ b_\mu E^\mu�pa*R �"$%=�  +"�'E�!���\/� FurG ��a�0!�"� !O)� �7�#$k �a }$ fE{Y r&�!>dR�E$�c�t�b (�-�$)]+Qa,��� � V5}.{SC#C�A !Da�� {E)e H Y*ua� r)���� ( Q= \mu�mu-=��#N}M"� ��eqi�$b ��\. A�h` {v_j�ujU�(h z)NA=����]dep��ut��$ 5=-3/2$ n�� f $Vk vt&� � ��2� �a&�$�VCFB� 0��uJ s} (.!�Per�)6 ,SQZ} Z^\pm(s*~ !!� k \ {r+��  od,�(� � A�� (\Re s >!�) A(�@!`L} Z(s)=Z^+(s)+Z^-(s)-�mda7meromo c ��A�$sA��/C$,6! at} $s=0�"ll�y�A�:�JB%^.�}W)v }&Om&�'2=FQD} D%\-! �)``� prod\l-�Vh B= ��m� "}�rthey �Rr�@�pe"t: 2�S�\log >�I- \�ial_s >'_{s=0}Q�aE��A�� �E})�!�E� m+u��by�[% A��� #��llvs�1�C� � ��y��!Hadamard�ducV, a�-%�no un1�*m�* atso'#"L} erty�)iSa ] ML}ZTsi= lim_{K26} &@ �q {k0� � l. \vph�m{*K} b_K�}�K)�_B��) E_Ka�� ���r] h r\} =7 a � c{ 4�� $D$ �� $e  2�  OF&q ntire}���Z$q�, �1M+,��W$'-�$:�%$%�D4 $-&`Sa sA�($c�4a��Lstandard" or ``canonZ"�Zm, oriku StiAgg$ �JL}�5U�G+AyD�M.imE2)�a}+I� (/-1I�!�, + a_0)� !� l[ \�cMNmu/ n��� -  } Fa4F^{H�+ \ &&vE�(d�(��� 0) ( cU] \dowZ- -�A�QIa�ob]oly�`a#�soccur�| }$>�  (growth� �8 ;Jc, $%K6Vb�Go�+ s $N>2$);��� all,.��exe����s} $b_n1z^n \ (\A�"� A�i:JD�Xv,� x$b%�)0^U�0banned}e�|O (U�Y�t_F/N=2��qs�+�V);sp. A�>.�_C%�h + : � �["2o�@a!f�|{��Euler--M,1uri���V ?p.-R6,�P $ -�;\zeta*b �;� i, \sܜ2�  / 5yb$ (Le�I}ula),� :^=�M e Hurwitz厕�lw�wo.� Q;-- *9 involveF:�,A�!:2���;�Rin�ce,�& y (a b3h� k)s ought ��M� ly t7$toR�e%�� ���1�#��(g {'un�Cce .�0Fundame-L�ie *�C�Z壡HINof&�"�u."�$>KN�scrib Y�,M�`-"-!� F��,fLU-wa�$d� .\0�!q�ful!Wfix6� �La�{% {CNCVFZL�)%int_q^{ Z}FL�'m( �"�H�0�c�Q $ (`n/��6#['m}!$ g$")�)sS4t� wish& nzis ``im � ral">3PRI����>�')��; \, -91?r]_{s: { �^� )b\&� ��vs�i8 �i�(A aMin-:{~We�,residue $ N^�S-&$��cf.&~ E�).�V6f-*�) =0$ �qu"|;)t~ ,��&hq)�jodd�gN$�*ls��q>y�8of-=4M$;x]_4q^N,\ N ��wI)@b�mj ��!� �$4,cri�[m�A,�*!.$:�g�!I5 {� o�J pm�l~ gges�}� um--c"�c"�� ence. ``C5B"s"��natur�Je�!,��mimicpmm����e �SQZ�)SQD �Y a Z_`cl}�% T jU e6{"� R}�5 \! {�a%p�B\,Q p^2+�y` "���m�:~.�N���%a�(s��)to� a:y�5kB fa���aly.I)�W��FCD�9qJ& )'� }�l (>�f}"@ " =� D5� ambd!;� q  !"IB�!is"�s��!�4Ep�$Q I0(2M02�CPS} F=*[0)^{\pmj �a,._:09 6y$IE "�� 5 6�Y�LA�&0!��%�b� sm� !�� :g, uk�&2 a=$l(;e�a��ũta8nA$E��$t $�6]^dn$!:�=gA���q�TAurnl�e*� , a6�u"� at�C}�t\ 1Y"u�^ (��.oma�- f��ZV�0� up elsewh<if� �uwA���F � �]l"�$N} [ - (2iV2)2� ;'�A9g(0 eta_��'��$1-2s} ) ] F �vq�exampo�R''�-Z�s:i�{V9q�€{dE >��3+4>H�-?��\pi�G (A^+  -\mua�N�| (�k;P; mu ��=h) \cr 9$A�]��?��^�\qt���J�h!&�AVSw "v?�J� 4 + v q^26�] -�3�� v^{3!=.!Q!�� ,q Remarks: .�f8``�a�ant" $D��$�-�{$)?" no� ��  AZ&�j$D$bB�- zero�D�l�U�6 w4�!Ocu�.�$� *�2our&�<j��2� �[�BmP.60}$ Y&.=fla�ŧ{V5,V6} �W@K)ejudg�0?* ansH*t�;h*JC}���w�. d te�~�in�p9ci��{R0N�3hbQn�7;�^ se a3V e&15--19*26)7�U.(Secs.1.1, 2 2$�MCc l!H4mselves sponta��e*�;��!0gre���/�� |E} on�|3@��Y*JaUn�@���F� r"E#�:l � $' = ��} �OE�BI�+� )�`. "(0�!�{.� D^-B<:$"("�!*+ idea3sun3 $N>�6 f�?r2:�log� hmic�� 6##of)����)� & �TmpuJ+,NI^] reso���m)9��$9�gd. backe�nsA �8A�z4�a2app�,&�-�d allnr�s�#�9�>0 �io�. �4g &�q�("�#(�~sim -*� =��!%��:���-=� (E�ey%�� �$ NCt $�!�1 �$��Z1r��). I�( pth,e%� ar�by!troll�W��!fR�ja�aexcep!�,!"6 b}�A�b.>� � ��96`be a�fGe�/�.�"z0ly�.n&�% G�%)� u�94*�n �х*2 P"����  "&a�ntity",)�f&��� FFR�k7 2�%D�%+ �-�'&) � ) -:*�%DY�0�'-vUq&\mk.+�*1� 9I�&�/�<6AM)�A�B�gl�� i2J�Q!/) l�< Qs�-Wr1�ed;0A"�/9��&�$E,�g y amT1��o\3�62wAunH1n�s��inY��� �8���!a ``miH�Fk"-outJi?%E a deDc&ctUB���a truly �Z�7��, embod���sF�q( ML})�"� consF<��:�)��ù�F �)a�2�)gapb a���De%texA\�-! \ N=2:� �V�f�?2&6 "+G6�?$b(JEDJ�e most&� :�� I�mbda/22� N+$3����_�#Now`i�=\pi$�3�0I�d5":!�N+), it PO�L�%! a0 d ima�2ry���o�r bfas $.(�W-��N"� cos� {&�14}� .) $A��� �t� ��CB"�4;"li��tU$���+o� ^-�vc��ga��> sign're�7i�~�^/B�lC"� �.�� Ͼ' ��\, 2\M9l {1&�I_, 4} )} , Mu6� = :XRS3RS�t.($qHiXn9C^JZL �>CI�6h}$#����!��H� ��C�K $\nu=&{+2�3e�  ia^ ����M;���% �"�L�+7"W+2�i[{B�J}Dq D_N�Q̀j% -{ E /N} (4ij^\�(+1) +1E7 G(-2! IA4\n*-*p)�,[1> |-Q ) = �{Q{nz�z��asR�-$q$L^9de�[.�R] +2Ng\->�2F�E = \�n\#�atrix{ >�.J && �if\ }WL�+mod 4(K�2n�e�nu)S} ��� �&&(rm>_0 \ _ .} \� m�P:�G�po"$9$�ui]� super�]ic� a��Zj")s$"Hm�vGe a9,P^ �K�Fk�#.�� �mic situ���e trea N d$�?5����.��ly.QSead)#m6 divif��u6X.� ��%t���=-E_k�y82"�9�ner�>� _ok��7�2 �� � \pm}(>{ }>)-��ET"2"8 = AP[k+�f.�N-�,2(jP 2)}]E�forA�^9+ \ )��h�2�ou�+��>�/^� ���Ep��� beitr�A`/(ca�-h����� voke~� aH�@%�'[_4e �e$� Aw"�w/ n�xu�to�la�JDH"�0a_,$L�� ppr!Fs (J��?ge��4N6 �O@�S�]2���p�2a: nam��$�;�&k&J�:e�$k,^J)$��">'EQ>!*�m) z<+1E� F�E_k $]})m.7-27*"67#*�'si-d(Z� �� .�R \\[4*�i( �)+2)} ]ap,� ���aa�5 C&^(�a��� ��+�2M+)"*gl \{� m>L+99� V�hf� (E_K|.$%0gr�"+R(\j �(�*+ Wl. �0|(�*() ^\alpha [ �2�-2��Z 1%zA"�+B+A7Bq�ӅFq���}(�E�n1g, p��5 �l*MP�*{��B-!� e�La���A&�PE}*tM�5{m��E��S+�5�)6,� l?�\ 6[- b[-n[-���#� .�.�A�$�k1�� disj�4�f�Iof ����>Qt@ P. Numer�+ tesId&�,N�26����0too big coeff���oU $, s;"�>�=�=��Ɂ�)-- a�) b�3��p)�nve!�!�7 ��PaI���Z PE}) �0� �YM!byNe i)`�"Ki�n�*�Oce�-�6�st_ng�SZ5��u�E}HI�2h7l�r���(to a"3f.�%.� E�:^�C$q^N$� :�H� ��% �J ( !P�CQE coincide,ɲ���%EVI{P�#z%@2�#so�� �4.1! �+�4x;���bev^figurea�J)`,fysize=6.5cm �"$vorfig1.ep'.} �!�{E5%c)�2�A\ M�HQ� ($+��ft; $-E� ight|!�.EquA c&� !�4$:Ae c�Hc�\{63� i\pi/3}�8}_{E>_(��Un� abel�) $E$-�9) cross \(dashed21of� 7&*argum�+c-T0x $D$-plane. �nd{1i�Hzy8Fw2vw�mly�4su�yYa�\ni��Il!�\}�_\pm$ a�Ze�U!'s (i�!�)�$+Q�),Jy�!the�Z2�&O .��� HSE})�=� .� |q|^NV�[riz���  � �%�8R��$�2� ( $�#eir��d7*a�f�"bU):Н appa"� (N"�*� �FFe�l�)cv6�� reduc7yad�) air �PgYfig�4$:�&a{*� e8-a,-&�� n &C:pm2�6q \!+ L ���1��} k =9{ 0,2,4, C �81,3,5 a0eq� W�sb�ߥiif�Sa]"�A[ {%� N�1��m j�7 z9arg�5k}-@64�2� (E>02Z7!�a" q�1P#�;Z#1�9 \:�*)=.N�`i�� *"�e�T��{ glob�R:on&'��`V ;A}o*xb� �8co.�� ��A�2). (a !m!2��gE�/�1%�,���v�Mr�0 �b�.)!�very sam*�Q ZaZA07L�MP�L�*.~h��s#�e�.�]M�>e[ &;j\[Of[���ol�u2t[�" 5v[ ({!��M J�M�A deepwlan� �� � � u!s�n��q,V�>i&9Es)? so d�K ^t��e�A�� yh� vail���/ODE/IM:�, " (a!�d���S 6C OrdiD��E�!TI���N M3�s) curre�.C �� �.�R"�a="�/�c)�cA�6I]�of"� Vc6��� t�]QZ(�jexAd) tI blfde�P���@a�n" "bl�ODQ@qh in.���2�O4>c,���i4$%s2�9%)!G�1b}h� baL�:�hJ=Nm� .|�s:- ed vahsiE:?O Solvp 5�F?'4" *�b8 W2�e�ocuA51�rB% I�$$�1"f��'� . By�t�!�!8reb hld. �  $[Q,}+8פb*s�^[�$n9q��Rba_P�wa5-yX", *�7τ.�HQ�K D_QZ� �#�#"$ 0$Q'2L ��o�%x1/@R7us� � �S�W�9� l�c �i�QeZF61#Vlc)I�,:.�FM}! \6 _Q^{� 6!-} E. %� . (T�?-ŭ�!gone suc�JC6n6��.�Tve�umr�Z1,V9}} A�re�ing!O\`"�Uymanz�~AJp"�x ve regime��^"I "� )T$VMF q^2+gq^4$2�V$v.�Xq�M$q^4+vq^ӡ%*�@%� t manifes��s"_���&�*E$)$�G�alism.a�a��Ji_ed�j�<'v�bi.K�h��3.,i�� F{�At�  (V+_i vq^M&@ �. hv?B9(Om |"� vFq�iBL���HBB�P Y6$v2�'�0 $N>M$); &����B (" 2)J�A~&�?Y ce\ t�YAud "&-�A�&�P.��+sf�wA �� l>s1b�/ �7Sec.3.1� )��7�j��"4::�/t6�)GR6qQV@r:r/:�q !�l��r�(b&���[ e en"�Z9W<&�,)mm� s?} �;is�$k�J � push� � abily beyڅ*�8�� s. A.}#&% �C?, $���&�� AKT2,BLZ} �>Fn�bn� ZJ,D}� �a `���at��tk �4�"� 0 2� $>2�AKh(N,DDT,AKKT}� ", Heuni!;ŎZXs����� �K}L�@{9i�/�,�(��0ieu, Lam\'e,~7�Of cours;�# g2A halleng [ ackle�cer.�M q-t�� *&nG&�"#)6asurmise+ � �BB}. �)a&�*0 <�+oóy� #y�\ ��/n�-ce `4CV,P,BH,SI,OSI!� "��sub !� far \�N��!"�>�v>2� KT} T. Ao�� T. K�>] Y. Takei,�|New�5� Q�� a��INO/se/or1�Iuo� V��At" {BM}-�4~I, pp. 69--84� b�|aG�� {\itdžic�in�E&�-� F�� Japaz�(: S\=ugaku sC45}F|(3) 299--315IgEng}}: S .Exposia9h bf 8 9(5) 217--2406�R��} Koik�2d>�����e!�#GpeE� imix inԭg�=<�� Adv�y�1813�004) 16 3892�$} A. AvilaM;CXq?^�elv6| schem�, fk�249|305!f8.|BB}>i�  C.i,I S.NA�6��/e�PQ. th-nn.Wv. (NY))8I,74) 514--5452�PV� , G.�vioA. Rw-4Q&�pQ�M8it Feynman path@l� (Pro}�� , Marse�r 1978jeC�S. Alb�Hioi��l. fl}1@@j}}|106},"h}"��B�a(79) 337--362��Po� ��m[4� ,69) 1231--12:FW2}�p II. �uda�2�!Cory!�4��eIp>�D7�473) 1620--1636H} M%�er�,nd C.J. HowlQ� High f; a� Weyl�*a�%�� billiard�s�b����\�nNiphe] non!� a<. Roy. Soc. LondM�A44 �9a�2!�56�MK}k�B7&1+ M��]. P. K{�N�sPrPk�Gevrey�]�j �V>{. 5k, Gren�%M" �67�f�232�MV�ed.mHAmv$se alg\'eb {s2sb i\`er� 6U CIRM�[--Lg7y]�(), Hermann,���94� ��BI}aoB/8nd D. Iagolnitzjb%DCausa� #Pl��t�y: w"Z|�A�!� =F H. P a!�)BA 1�qA�147--184� ref��herei�lCV}!�C�ei�:�Un uvel��drtt�b laA� mule �H2�|e9�IY C.R.��.� . (Paris) �30:: S\'erie I!W,88) 143--148i� �*Gr� ndieck F�"chrift2! (vol.~II��P.�%�Progres� �})uG Birkh\"6�r, Bosto�9�9� 1--67.�C%�ChazaIO�7��o1!�sson p�^?n 8� el� \^o3�� �eyA� :�, 5��Abf 31 �,92) 807--8102�DPF� H. D�6�Fa@ F. Pham,  � 2S#�sA�.T ����p, J1|�.��3ie497) 6126--6184�bgF�0>�R�t"q in:�� %`b(� �*�) �7� 199�--9z!DNl6T6��Unfol� ţ�"9N����͙26 � 7) 180--26� DI} R6 DingleA4� &�&qc 3iA��_�Pn>:e&&j �":�a�,� York�t732�DT�Do��AiR8teoq�R s,%�mmoY6M��n�("� "� %��E=,A3� )�$L419--L425�e� re/q{/ ./q�JT-Q�k�&�>@  Nuclaey1� B563��AG573--602Y2( (Erratum: FC60C20� 816{.|�> D���>�2H� se��$SU(n)$6�s��Aa�.o 3 �0) 845 8446lG��J�xArma��$nd V.W. Gu� mi���s� �f�itgellip�&� Fp bicha�(er�z��=ven:B,1975) 39--79.KE�a��qLLe!&`1s ��� tŀ �H� h�� Univ� @-Sud (Orsay) 81-0!�1) [un"[�],I�E� Cinq�licD� fb� (civ�Z.�&�wt 84T62,>�0, Orsay (1984�) [unpublished], and {\it Weighted products �Xparametric resurgence\/}, in \cite{BM}, vol.~I, pp. 7--49. \bibitem{H} E.M. Harrell, {s�On the rate of asymptotic eigenvalue degeneracyw�Commun. Math. Phys. {\bf 60} (1978) 73--95..�D1} L. H\"ormander, �lFourier integral operators Ip Acta nh127 i(1) 79--183..j2Zj,The analysis�linear!a0tial differen � \/} 1[XSpringer-Verlag, Berlin� 83) !�refs.!U rein2�TKT} C. Howls, T. Kawai54Y. Takei eds.,-�TowardK$ exact WKB2�2�,equations, �or non- �x(Proceedings, RIMS, Kyoto 1998) $Univ. PresM !(2000),�b� JL} J. JoA�son. S. Lang, E�Basic2�@regularized serieM�mA, Lect. NotesA�IzI 564},n�93).�!�R| �Sec�9P throughZ��6�Q.a�85--102% b8K}� oikemAu�E�a�spectrumA�Heun's�^ $F(�!3�)A��!55--70.)�Leray � Probl\`em� Cauchym� Bull. Soc�Fr.A�bf 85e�,57) 389--429.g M} B5lgrang�M\'ethodj(la phase stE�0naire et somm de Borel �:|it�� plexU`L, microlocal calculuI_ relativis��quantum!gory\/} 6*�Les Houches 1979), ed. D. IagolnitzerB��M�26v�80)E/170--177.2 OSITE!lOnishi, A. Shudo, K.S. Ikedai�K�Haha(iq$Semiclassi!Dstudy on tunneling�m0cesses via co%B,-domain chaoED �Rev �E 68}� 3) 056211A�f� P} F�/amU_incip%�Huygens!�,trajectoires�0es ou Balian%TBloch vingt ans apr\`e�:�Grenoble��43), Ann. Inst.�y,$�R43E�93) 14e�508.�,SKK} M. Sato:� M. K!| wara-�MA� func��%#pseudo-V�Q�)�Hyper�>:(Katata 1971M�,H. Komatsu, fY287N� ��73I�265--529I�b�SI}U�%.� �CI} Y�Q �A�a�U�%0.� LettM�74)�(5) 682--685 � o@Stokes phenomenon�)a0systems: pruna( tree��m#, paths with  ciplE exponGdomina� ^�6 �06) 4151--41542r}"Sibuyam=Global���4a second order� ordinary 2m� � a polynom (coefficient!Z` North-Holland, Amsterdam�75~SJSj\"ostrCSin��t\'�� alytiques��e� , As%risquei�9�c$82) 1--166EPfzU �uzuki-@Fm�al� on[MLmultipliers --- fun).T$x^6 + \alpha x^2$ pot)�%2J. Stat.202�,1) 102� 047~�N�W solva��models �Ted to $U_q(A_n^{(1)})$B J2�A 3� � ( 3507--3521.�V1e�Voros-Y6p$correspond� ��� lts:�c��ofA��a homoz (ous Schr\"o� erU��. lFrench: C.R. Acad. Sci., S\'U  I�bf 29�198= 09--712,CEng� :� ��A�.N�AvL1--L4;ЉK[ return�� quar��oscill� .&�>� m�E6ݘ,H. Poincar\'M� A 39�$f 211--3382�CF�0 al �?,%]a�~�,Selberg zeta � CF� i�11� 87) 43� 865.\footnote {I��VC}, eq.(6.25) should have read $\zeta'(-1)={ H2) \over 2\pi^2}+{1 L12}(1-\gamma-\log \,&)$ (��$no consequEx,elsewhere).}**V2=6)�Exj  izl Idi�8 for anharmonic=�Ls (in one dimension)%<>R�094) 4653--4666R3Z�xZ�V� in:�tQu| " I}aB:28IMA, Minneapoli� 95), ��R A�� Simon,4� volM95}, Sp:3New York�B(97) 189--222�V4B AiryU� (�FaEres�J%����$odd degree%�>�3�� 1999) 130�I311.�Mis�t�A V4}:&eqs.(13�$D^\pm(\e^{-\mi\varphi} \lambda)$ sI�A�.-f/ (twice)%ajust u-,neath, $[0, F=infty)$qY k+Ji ,6 5=pI.i resoluE�I0%g���Z1D *;��\-���N =|<5993--6007 (Corrx dum:1rE}2�V6Z�2 � a���1D.� �F���{��� ME}�= D5} is also require) � see e� fZ,.3.1 above..�&�9706�E.�.�tok5J���85783--5784.$^3$.7.]� Exerciin��.\!�BK�T)$7423--7450k 6� 5a {�e !�-57}: 1)%�term ``q��-e�ly"�D" was wrongly putF,``supersymme4"� out � pract�&;�two noA�s happen!ga�F( when $N=2$e�6, but.@ beyond); 2) regaw gŅ� zero�FT� �1, $ Z_1^+\,'(0) \approx 0.0861126 $, $\�U(}((9174909 $, '- O'$1.2585417 :�8.���``i�S�!"�}�1D6>T (or Sturm--Liouville)U blemA, ՁD.ae�%Ka� | &� F�Gro� en 200�ɖ8B.L.J. BraaksmaI�et al.� World � fic, � apore�2)2��3:9.-{g Fromi-!/t�s s� i/(um perturb%J�^, Publ. .�t�U 2004) 97H92�ZT (Zinn-Justin���ant� e�Lum mechanics: NumerE�evi� azaature!/��c ��2t ,4) 549--555,d 9ins�to) �A�WV&�6��Hend{thebibliography� �5�0} \author{Fab`\surname{Brau}} \email[E-: ]{f(8.brau@umh.ac.beGffiliE�{Grou�A Nucl\'e�Th\'eor,m \'emieE�ersit&HWallonie-Bruxelles,"� Xde Mons-Hainaut, B-7000[lgbA)YabDct} IeNA� text!<reJ�5&,��rea�6�����(replaced by*E-oup�fant1>7<, $V(r)=-g v(r)$yisYtu�] of $g$�0which a first�]4ll$-wave bound�e �ars. e�a5�, \keywords{R.�A��; BKs!� makee- \s {Intioa�xlabel{sec1} A covariant descrip&��%���p�l>$s achieved�!Bethe-B� �salp51}-F� reduces!�Df- Ggrei94}A�I�follow[��i�s are � ormed: m�iza� eli]�any depekIkimelike %+b!()� lead�r�2 qbre$:�g %pfreedo�9w�neglec� ellneg�% erg� o QZ�� � jfta�!�!94 ($\hbar=c=1$)1B1�} MNeq1 $eft[\sqrt{�p}^2+mtV(r})\r�]\, \Psi=M>,iky $m$qsmas%*the5# $MR$�  e ($M=m+E� E,bin�  e%C). We�x� t our at��o� � )I!�immed�u�!�Y�.substit%� $M )arrow M-94$�x$1A� -a�a6�four-v ;� � cB{ a &� , be)�9�*�6�%�p}2� -A}5��B�spa9 �� Howe� we ds ��i�t��ki7* sinc��derivu�!�jf� $^��B�=0$. E�  (\refe4)�ly us�O kine�2� effe�"canno- a�� nd��1�5 �A�bosA�or5�A?�Aiseor only�'�$to account�E-�?tABQk0s. Despite itjpa%"%�lexity,)�q�kfteA��.to�,Klein-Gordon0Za�b,��M mpleE�me%!9 bary! oscopyq�co" UC (�foXѣlo85,se97,br98,gl98,br02}) [F� review!nsA�a��p%�o�``semi.�"r��!�!�leNm D$: W. Lucha�F.C, H1Fithn�b} F(y)=!� _y^{�}-�dz}{z!�K_1(z) ��${2} =y:->O$dz\, K_0(zF��6bJ�� $K_{\nu}(p$��] ed BG0&p(Z�8[p. 374]{abra70_�zer�>�u� ��y�q �Gjy5} 6�%3 ir}'\, }I\, "�'.<'FS!� $A$tena��g4� We now��� o>�B� s $�)= ���.$rmOreJ Id73}a�&!"�� /9@�5})�3%9o one-")alf6\u�6n�6a} u_{�}�E�0y!dr%�#m,r,r%�V( >Z�j 6b} >[�M mrr'a~�pi}d\th�* �Qs� ���"}{\��a�P�\cos 5FNJ�m��� !�radY�f��,^$2�(; /r)Y � m \hat{r}})�� oH(x hdef�byU#4aa�$ An import�techn�"�0 icul>o� �0�%$al kernel,�l ic&� po�4�&��"g� sign ���oY�7})�dis��a c �^ sear�5+ necessarye ,�rf 2�&� R s,!r` ��byZn \� /YV^-A�\max(0,-a��Iy!�S$ . more.)�@)�� aN��exist(�`.�� .hcer�l�validbS }� p�: dureE*{e"( isu�2=��5rNre�� )!J5�'at� noI� posi >/!, $V=!�55>�\,v�= BGJ��Br8/ihR5�jea�8av?�#!$_e smaC%t!���:�pis�!�6VKa}�&ER��3��6Y�w�s$oC6aa�rd, ...�*r`$43� �Z8b}) �+ng+�Hi�2t�$ce $L^2(\R��an-Schmidt"� ��# �dec�Je fas�%�0*infinity�� is�satisfiT inA� lityJ�int.�>dx\, dy� � x,y)U�  <7ftyB�C�23-!!&���+9O!Nlways�s� sleN� R!�[�>0102-106]{tri6(*in A�ist:3)BA�R]s). Now�#u�� orem��AZexa � �18-119�)-��!�t��BIm�!> 6 a���<le"�%!�*l 10} �_{2Y|:�Z�6 H2 (x)  y| z 1}{|g_1|Fv!$8 I� yingJ�>9} >�r�r)^2=1Bk��6tii8 ache��x)= �_19 "$2?!tE�՛associto �)�4$g_1$. C]�-�n arbitr� n�DlqB` , $f ��e�*��ujjL 11} %� \leq��� f9��Bx �!!)�,�ous�a=Mc��wo"X��A�a e ul!e�Aregimt&m)pZ$>0$a� \sub�)U^SRu/4.1}��s�e��$' (amo��> s)>��6�.=�Mr@1&W+�F a_�,�'+%z�d�t�1n�=e���$s��i����$m m y)=1/y$� q(go��o]��� mplɠ&NN�2!�im_{m\�(� 0} m*���'CB��"qi $"d 0�$ �t?&!%�nZ3*� D �����>�|.�~^5 V�B�A -�&D �"j="L'͖. 335]��narray!e# eq14F�&=& �1}{� ��^{1}dy`��ly)}{(r^2+r'^2)/(2r r')-y}\no, \\ &=&R1}%2 Qf��( UG}{F}I &��P %�` $P�V��$a LegendreY ���@�(A�! J.k#K be e���explici�a���u����!?!���7R9�uB�5%�0}:{-G\ln%A|-A+r-r1<|Bandno6o1bo�,E=� !�-1\e�]B�S"i*9�F�is gi�!c�*k 14})!�G�h�e M� m�$,�'&� bAsQ!%�J" . Now�.1;��ho'a suite�J���" *pp�#e��2� re�ed��D&�A�&s B��Lb$&e:  ompu��& �ex�.m�j�"f%;&� as cl%tL i�� N�2�%8(Qgenj<|%j)0o�K*5=A mulae�+y Mn`7} �=A e�[r^{p-1}pm�(, \quad p>0B��$A��!eQiEE fact�.q%s:�(?!e9 ),i���d1Wi[!�F� {\"T4:'n8} 2- 0)� q�%\�6 \pi�Z��(F_1(2p-1;x)��6�"p;� x�9p;y) �7�xx+y}{x����)}p �(up},1}^{m=0F� -�[Pq;x)=x^{(q-1)/2} v(x)+$%Y 0w�"�o�1am�5$)$� [3�e1a�B%iv�&2A�;�Dec } (y9�7)�icl"��  m ,�Hngent2�y�ly�6minimizAA�%8 hA: a�UB�*�AJ��k$pa��r�<:'tr �, �+���@is2��bR �itIO help 2.minorii6n���jZ3��2AMF� \b�9J� 20}� m 4M��e  x� \,mB�A�eJ�2M�B�j a�"ac\N.�s1�Y%1�=typ�"� M��<ak% betw�!Aa�%h!(�I�uHA�nn<�Ufj$�/W2�2�A�20R��inZ?�Etab�7�"�Sad�(a�/` /6j%�(yYU�2��,N of6�F5 Refs66-"n-�R��*)�!��:eѹa��1�0"P@��=2a�i 1�n&4' clea/t� :>.�5�Bis quit�0 mark_ � =+21���/�1�E���5pr�*t=0�ful I`�l !5��M�Q�$ !�$p��opt�!les2�s� esU��S3A>�5u!�iceW$r7 �*Q��)P$�A���&��:!�$�()xtV A&adiaH%��d5�=fs-q�uEpro**E�t��wyG�()�v< I2FL�)v5x{"�"�'6b1[.(��9e�8"o�=�J�1T&E 1127 �.2!��Jd �upr= m=0,� =�-%!+TE� 2�2�<$�"���)&� $1�t�>~2�=A�on*� +:$m+e&� <'E�are~� m,!�>is�FToGr 2181� leq �$ Ni$B�>-C!�1�y %�2/�I�a2 a�@B4�aMe> 2]ExY�6T.i� 21})m&� �ctoo crud-(��goo�T�3� stea�usnF21�%�NH-���%�'yF��Z�'i�,e, in A�Fdix�'app�'5��!i�g|"�5g(�^e #iM!d&� �)A])%nj 2�a|&�s �1})\"G}��+ S>-;3} #T>#V� n�3�(R�=m� {|� |}^{��1(my)\,"Ye� �-y^b"%F�"� r"�24�B&=&f�0�� .> ?)�2m� ell+1� r_<^%�>Mell&� �[ $$r_<=\min[��]� $r_>�".N{magn6.'&N=b1B�!)�-CE�Bae) -m\s@5� y}�*B !1[(y)68!7 Y qA�pi}} m^��t*��K_�!���[m^2(>�)�4��2� A�, �!+ �eZ}(m r_>A�Ii�F�1�y,5q+ G}_0�W&=&,m��)- (��)A�\@ 6} �1AZ,B+.B6I&+*�m� E�[ r� 1(�- � &��A � ��: 1})�CA'�0&�*{!�M��B{2�*>�xz�B� :#"�ag�1������V�m�  i�6A(�f!�*�p.J 2���Z8'2�'bb�7a��b2r\��x} F_2��2V�2(p,y) Ty$F��>N�ithn�27b} U�� [�6$\beta(x-y)�� +y))]+2 y.x[��(-((-2J]B� F�' ѩ!2q,Hq-\)jF$x = mR$, $R@>' scal�l�M? p�,� e&| (~*(=v(Rx)$). Aa����*�~fM�A":Sp4her����i\P|V ���zza�!`*� u�2a��$�B'3}.z�=H��V�3�����. BUs6*&�I�$B2[8�H�� (;T�(��ZM�pPE4��'�'termed�%Cm��ht�!�!��toCn 8F�aκ��$1�a2%A�l�(R� im�si0Z9"i)5;o\�Y (7+6u>dC@!k)� =0.1�Ja=1.18$E�A�.fb"��. 2E��2.521$ �Fb�%$!(69$�C��2.547$�:rK, e� %�Qch��6��l ~-.��o}) stilllC><A `FO)%)!aA,&-)=Rr.*�T$�Jt6/�N�e �%s easy!YVKsto.� "͂�'or!8B�CerrMK�0",SbI��" 4Y� xf5 go�&F�2�c.a ides�E(!�1Wh�-?!�non. ernelj_(contributesAq".@Co"f@.*3*�(*1B��sh,JB_Tu&x@�E�ri0I6,:])�NTaF^8>�(ATe_�M"�@�2�"$���K(�5 ibly�4f�E ted) fami�(of6P�FA>a�\eral39� onVe��*�Y�!P=is ba�N�n-�!2$AK�  trg7�"�"gy 6�"YEeed:lTt>oI�Zi�.F su�U \�9-�E�)�Vae�r�U�u.Q�aq=��6�M@"��wiYc�52]q ��/tru�� lZ,,,���moX t6AM0vF*>�ly6�_G2! P ^�0EE�Ub� ��"�+��u{M�.4!�6�ZQI8&Qaensa8a bet� ͠ �I bfA���&�F�Qf  B�E}rom(F�U�a�*/ �fia �+v%|2 #]X%2VY�_�� "f[aceI$ledgments}'@thankL � eIvA�z � com0A�!� manu?X��is"�fGr� ZNe�aldt"D y~o�q ��&^RB� 3=��{2} \J�"�>�^{9�$b�wseZ E.Sq\a{H.8o�U,�]�Qv. �R8�R 1232�R51�VtZW.�ine�JBi�hdt, H it{QsE�U0rodynamics}, B�gp,Uq4. o�2>�2��C[p328�22�8o85} S. Godfrey%N. Isgu6ID �$bf{32}, 18�S85.N�T}tw Sema LB. Silv�+�^ac,�^.-Y&4T 618}, 455�97.W br98�rc_�C. c2��5K03401 N8.NglNL. Y.�ozman,!�PN as�s Varg�TR�T$Wagenbrunnrr94030�2r�U F0cu,��J `A1 v. C5u6�f055202 �b2��M I.�Herbst, NElQ�53}, 28% 77);�f316�77) (�%h.A�T8} P. Castorina,8ea, G. Nardulli�J G. PaianoZ929�66%784.hU}A Hardekopf%2�ov6�YI30}, 703� 84);�B1�02 �2�ma8�dM�� xa>M. RoU�LesB5V23!p407�9.��U�$C. Raynal,.PVa>ngh�v s)W! tubb��>t32!10%�9:X 01a}A� |allE�n�WJF�3� 5059E�2ha01b�`�cfQ�4�i52��~f�� ha02�cv�X{u 1931�2).�E�) ha03�jj�� 2657j32j�V}!�Bargma�lr�yN�r&dq U.S.Aِ3T961A^6� sc61E^Sch�.e4�S4%2��62�ca65a��CalogerovkaK8eI62IHb:HNuovo C�ojktex�o6�o9�o:DhyK. Chad��6A��19%"62�gl vV� as!H��D}s�wW� r�-� :7H. Lieb,��m�nd /z . Wightma;ods��it{Stud)in mathe�b�"8physics - Essay hon ValentineU�h=eton �hefyF~,1976, p. 169}7 ma77^i�Lr&� 29�I7:�03I��F�QJq|"��yЁ4 1554Q�&�OOIRi�9�E990u;6>cEM>%�>�RN 1202i��~"W �Y�QDaube�dsv�9�n51Eb82M�d�����1�#363Fnt }��,J. Nickisch,Du�w�B. b:|& �Rg�O!2!>%|N�3�2!���=�ZL�$Abramowitz�IL Stegun&� Handbookc 2q Do1K��IQ,"�r N5� AF.��Tricomip�K&XK`rsQce!lisher e -Yore65iF18�%�Magnus,yOberhett�1� R. Son�FoI-%thebA� �2�f�9�M.'A�in%  Heid\vNeʉ�l\�k>  \�. page"�t�0} \protect\ca�g{9|�0�?�."�IB�06�s>>�Bs"�.�4$ (�(c8�,�,�1F,#/��!x6�0�_�SR05���Z0"`1Itab�Y}{c } \h�S$5 $ &�0�0�*2 l} &��,!'�_'�5$ &VK$ �$? & & 4.443(370 & 5.574 87.411D$[�(x�&�Y=Dq& 3.8865008 16.769= z^2�=51 z169542 E$442 & 7.39 =x ><r69- 3.34= 4.36��5.964z �e-�mI�����1)$7A�*�5�J>/U�'�SBp# B .B6_,B\.�2R�f�Q�I��Y�J�v�10.975 & 92.N� 8.11E�8A�8'M8.v10.20A* 3I�J`9.5I�9.5636NQCiL�J�JRJ���jJ>0N>�3R�Z�& \�columnw+c}{1�)$��N!>Y^(=�}%�c�\{1-7} h�I}%M}%Y�+2+6�UR)Y�,0.1 & 4.694��� 4.461 9 4.9275. \\ 0.A� 2.38["2.766 3.00 309 58�.1  1.3 h1.�a? .742 843 2.198 35eY2 =0.713��0.720�h0.959��0.986���v�1.307�3=480��00.4817 & 0.65�� 0.66�� 0.86��0.8880>4>360 5361!0.495 �4!3 P8��P9��5>289a�0 �398!�0�O 5530 Y53�%e�d"%u0�>$u{ cl= bb(- ce�#,Large�Y{Lie S�S}Fnd� �nIIC�`� of :t-Inva�qS?|s Thoma&��<}} {\vskip 0.5cm}bf�OuC�4E.�$El Kinani}"Dz({ Junior AsJ at�Abd4�$alam ICTP,� este, Itaeu hkT@ictp.tr$.it}\\ 6�&�0\'e Moulay IsUu , Fa�T� ces et T�TquY D\'eparte��tath:ua��, Labo���de.�< 6),>st���.P.509, Errachidia, Morocco.\\ UFRm� (l'Ing\'enieVV� et .�Bo�uE�QQ%��3�3�3�3Q{1am�a"cu<\hspace{.3in} Ue � b��lonWson� a� the �" esim�s`r' of im�c:H0� m�@g� al �po3^�T es g.xC/:�. Looki } adj=:�/"< \yZn W(Lie algebra +wz%�pr��ee���ts �-�t�>u."J s lao�'M$�9�m �&>�I�9�.�s {Kw}:�->L, W '���L�a��bf {23y"�s Sub�{:�}:70G?458K70, 34C14.�k�k�k�kœ% \new��% �ro��i�xq�1a�!a8ge'&]$ZSM�edpow�l #availc%��^nl��ev�[ ��q�ir B�Q��&/<1, 2, 3, 4, 5}}$2" �edn ly by Sop�+��4;6}consis�!f�4y+� atica=c$�R�d?E.�xco:u�hu�"�fE��a W!#n��@�?\er�.F (NLPDE0/n "m( fe�o%mis=�O?!��D�A�yn.|R�� PDEs�>a] forwardly�# g?o�P~iinacc�=I�v �s. One �e = advantage%�"�L"�T�#9�� Z�)a�%m[�-)��U � priety of{&I��A!��|newUY�JF-�+l �n!Z �!`u's5� [,�p�4ly Q0e� �U�2%!X�se�ո)� �sub]%6� full>yEe� and ��]wJH5Y 6�s.�C��i baD�m�!�oտ > �a� GkarM)ls�+ a }U:z'jmU!�sa �a��:{%�%3 �i!�Ini{�m?$u z�e3yEi*vj���|��: E7*^(h*"}E VWbyA~��b c*b�ord� ^&A/Q�%;!MaO-pX3 -q�a�}s� �!Z8M��M �١c one.!!e u� -Z� B?�-26� p�nged � I�/ "* �m lE�>�]Che��"� �� M �� �� !� i�*�J��>� � pape1z�S%Ka� %�ER&/ion 2%Yi�?%�:Revb"{�`!3p)�EZ�&?)�VrL6�^ we.(�-*� q�U� [2aE.}e�:��$I�3,�� devo )�O�p� = �ofI9Nc %� :� �ҵwin��forV�In1��wSM�o ��&�o nd f�*l"'{C%�briefly�eԩ�!�r�np "L UP� .�.G�i �3�3�3�3 &_ D>E �Q��*:�}.�G {FB� :#A��6eg�gVZ in !al �s"% (7, 8, 9}}$ipdI�a"u�M ch��al exCXpessui* some�q�oed�pQ��>. P�Ibya�|eq�.x�-:"IDPi xy}+CL2dx}+o4 c� x}u_{y}=F�R);: |hx}�;\u} x},Ly>% .%y %xB& ^{2}6Oe y� �Q,�)$ �$6 � anHr=]1}� � usB > 0 F>02H\nef����������*^Y���8:{��BInC �W2�JY B�i ?(%�we�Eib�e& 2ɾ S: s� � eENf� $xE5 $y$, e�d&tu�  $uQ5:�|of [@ ($n=2$�7e*k� "� fW}�0s!B. F��|X \�ns R7O3($X=$) �B�KM1m :��Gv=\xi @,u)#Fq�2�+\eta ~(�x�b�+uFoL W� $�,q%� $ T�4w1!* $x,y !� �< wi0�w�<aU�6/xeff�*#m�[m , soe��2� A&P M|K \epsilN$A N�:0�co� gj twcsX i*�} 8�9B� p:y, a@�6a��cn n�.� $Pr��v$?�6� I�� � i:A\fd �d�� ulaeNo e=v+-� ^{x}^w4px}}+y>+ U�,y.,xzX2Yx ZPY�Zx2[y .}-�$y}&3Ke3wE�!X*����i/!, y xxM&�/y��"�].0QG0x}&=&D_!x C -u x y  eta, +^{y >y} >y}2>y}F>x? xy}( A-6�-1 y})+\xi%z�؜#y!\�P!��2*�� yeta�6xi R�50x�cxcx� cxEx�T !   "�D1�I $%��� D� $)�t���u�7ͭ $ y$ 2�Z�1 Oy}=V(NGRAf�8a(��  , &Ag�+�-aA�&=& A:+1�_{u} !�)!�eta!�y} u}u�m%�90� 2�2myBm^ynynxi!5mx\ nm2�I��2pyu � xy}) b�x�� �yu�x}��c+&=05�u�yu] DTu� E WuW * + 0"P~-&2 q Uxy}-2 ;y( �x%[y9Jf!�#EZaQ�d|2� �7y})%�*�d.i�9�x}+(2u} �xxE Wx ��x�}\\� 6�u1!�xu P!JQ� D%1@l�.X!r)�-#]:�)� � x}-3}2��|36�-&f1��.K�65<yA�9Ky� KyqX)[y V��Q�%2�2�%J%A�-!8 S �yAE\:�!Iy%"BH k%�A�3 4  ^JKh%�.�,e�T�F��63 Z, let u�� ?}!C \e z�$NS.S���{�x =0, "82�$\mbox{if }� � ( 9)J9��W�� *& $v$� $G�-=j :� >  (1). S"�� a��d (9, 10 D(11) ��(34��� e V/%�Q ce .\..d�/ng"X"�elE8M �6� �3ous mono��!��׊�..�"��Wng{�?�I�G�"� Y&�#�"�,{| r| l|�� M � &.��; !'$M��ZU�A�� _�(*�(�$&� _{.o+ <��`Ne�Ue3i�y>Wy2W2�>X�fK�gx>X�2]��-2�� � ���uFf�/$&$ Y% 3���B=�Z=�� > �B?���DdJ&"� LF'xEF�%H��Bj��@F]�.E2#�&Q� 6� {\it{T� 1: C&4(q� u���nd> F� ��J�$��A*%s :�'q��eI�yH1�A }Z&=&0;"o&$3cm}(15-1)J�jg�Wf2VfE|E��I��}- � "Q�Ar� 0Bg3Vg��a�R�42p��RH5:H) ) 1uVJ6:J!-uZ,7:, XZ-8:-Y� F�9:+XZ�10:-XZ�16��^-]si�y;$_A�9�� 12)�(�  (x);�'rm{3lw=l �=�@�$��\4QdeW�5: $��6=g )r0Z]%� u}+N $$\\�conven��}#c5� x(1-JA"���Y L}y .:Z)+�g}&:&%; m1:�[ 8 I>�+� u }])>�S�x eachpGI�m�=B+�nnt� $u=f�)$ (x/�e>v���u��J�u!�&=&f(x-�,y!�u_�Fx �:)5�\\5�-)06�x(5j}-1Z� y.�t2/fE#)|E">. �g� ��� � �}F�c�� ny,re��\�)�Qu�P"�a *�se����!�a�����: 9�c19�+ {|r|r|c|l"�$[�n ,v_{j}]$&�}1�v!� 3 v_{4 v_{f}� 20$-r/1g  D;~ >?2}$=0&� 227 ?yB? ~0��.��V�I'U1}�a D.�2� �.a� \psi�Xg!-�& � 6X  f)v_ E&0> e��1� 6�N�2�mEJm����.�si}� d g}$ >�M�$ �=-C x%��� yf� F�f.! ����it\(���7 ��mM� be a.�)!�Zdz if $i�u^�� t&� �b��$��^�3 к�$��6��6��6��6֤6�. {:�= of b�=��<&{�R�c,5i"ى �K�&*1�z3�p76A�re�9 6!%a \E�Q}s, �4��'+ "�-�61�6 �`p�/w�'&W�+ o�]�wm<y"p $g�A�Z y{ >` [ �]� 1�23q��. E v� O R!d,&O !����&� a nonzeros��*�&a�� +a��ō 3 3 4 4B$ >��aC �8J� . Our tas\toIZfy as m� �*Ts Us&b[47app*^�1�6S<L�vN)���%�6r<��use�ɡ���J%Ad( �o�� i}))��="� 2��h8� }{2} $ @]]-_�sɏ&� �"82�tŃ�2���a�� $Ad�LmA�6���Q*22E�&� � �(� !Z3}:ZJfZ5~ZTZv R[�E� �k4�e��J� ^� f\��"� � ���})2g"� 2}W �NJ}-1A� 3}$ 9�%r=Ie��� � 3: Aq]Eoj�>��whaf llow�6bSE�:4�0 \no�,nt{}\�6A�{�$bf{Case.1}%"� ݠ�:4}\ne 0$e��assum�at" =1$,"�.� �8t^�N���v�=%�)~y� Re�<�,ei�.h5fœ��n��a��bya���Ee a_{3��)v�f��N�)h&{e��pS� �)��8ed2B � �v=(�@M� xbL j%�a"� ) �\FJL$�"� yf[F/�8.�5Dsigma�  $\chi$ %,b!�ظby  gr&�!6�:���$(s\emph{ee"K6������"�s})�bich��E�F9^)dx}!�,�9"c3dy�� y}=5Q3A5A j�6��@�;y�o C���byJ�chiB�>�"@q*�e�.�va)� =u�+���x M Ej* EK"5�[ log(- x-- z\��]2>.VSrefore�1"T !�61� U �8V~C�,�)= -z%J�.�})J�-, �g} {)N��c6u>�A&.�$�bu$]'3erm� >imha��U��& �@>H5 _{���A�t%�!225%B�-m91K`t"&=, N"+)B�}�F�;}�+ �!cJ�e��� ��;11# 2�&(4��(4�&44�ltox>B� C ��U�!��! � B�����- �(chi�-� $�#$2}-� e�- )s!�2}9Z A6�!�5�=F�vFo�r�W C=E�ד]CKU�", &J� ?'� !�M�N� �b\ ��� �a�chij�c#=�#6�*# �x } Riccati2C9�bBran*�$"f@ v:J�y(w)=c ( e I �� F� aQply�byq�9uIpFuchs:�J��! y^{''}+e }+m JR*=�} $e�j�6M� $m :)�2~�8+��uX admi$��,e�@ i�>��5 he n��b�bga��, a�)?�:� h��J(y_{p})�(=\sum_{n=0}"g a_{nEF^{nF�� 0 �C n�; (-m)>$}{n!e(e+1)�(e+n-1Xn$n\ge 1p � � � < 0$Ain�,A!$U�82�!�4 \longmapsto - $, T�G�% �=5,ߤu��?ve{�c� r �7 �> fj e �( h�A $z.Pj %b^{'�^  }$, .$� 3r9�� U(46). Pu�[�� =z+w$,! be��s afgno�d61 :�Kc z��� zA�-2m�^zB� �9�l!�s a&��9� $zm1}�)F�f�2yf+ �B�Z"w of (51V�J�fM�g9�%��J�PUp}$ ia^�2Dk)�"�)�K}A��o� F�)� �G �})� J��]O$&) & 9�j.hdm\\H !����9F�Wi�s۵^� �( wށ l 6���F� -�=2U}x^�O�v �&\�M� bF26F*�t."�|� �3TF�v siti~ ��&� n:��f�=f`-�"� ^�it�W}} : If�1��2 �,*7�: v&=&d ��2 2}�3� "I�J�x 8^! 1,�'J=u&94B� a�.2re.��!� �2}Mhyl U� &=&u� y FC Nex��::y�g� \@ p& �1jfZ1 %�YRB �'�2� t����it�i�e>� ��13F� �I�} �:�!u5*Y � ( r  B� .Q"9�-J�b�&� %N� �#b� �� (61)�mM9�N��u'+(��)B� ���hheV� �5��.a}}: � $��!P6��4E)�$ ]�0�,a�n,6�� � �����$ �_{0}$� &V�%~.�4"�F� ��zBv�V?uE1�7by�e% n �v�Zble�=f+��ye�V��& ^� zYf�e-2%�e -�Ev!e)fB` 2Z1��$f&�h}$%�)a>� F� h' ?j���{Az 1} � �͞}h �9�i*=Iw&6 , �B � ���"zN=A��מz�"j�V)- V)�i�%�}�iq�:i>]� ��2��q�.S+F+�r� %1}{��6 M} ��Q) d�>}9 }�m +cte>.�@"�oFm5J = 1 ��A6� }{C}�C} )u�N�1�CҊ!yA%�2� $. F�N�(��� U& isJ�u �"> J�� �:&� )}=�:��"� !"6 �5�6Z*% .b�'If6&2m�)"M�^&�:�In}:� "� J'I��V2�I? �� L�i.0}� R��u�"~I�ed�p���5�G�#��m�JE�d �}{ ���� }=dxB�I.�ہ�mM��� , A_�V-z$,� AdRV�>�e�V���&S���"y9��j�)w+� A3V#Let! \Xi �z4>�-A{�k: N} �'\Xi >�L ,A�l o �2-of^&f� � M��}{2�}i~\Xi& q�B.1U�->*� t=�R\v7�6� �VO�Mc1�s#��}arctang���R�}{6)R�st�^������=%�x�B|` N����tg(F�P}6�Bf�"�.�oF6H�F|�WZ�R2JA jOM��6�r�JT1�M��1+j[rV."�3�1"��\"� m*B&� F����1}b�>�A� V�>,)v� �0}=��n��t:�2���2.#+ ,, � ��t �; ���}��*h���!i�s�R( $ `J�=E)JZ�"�1 &=&y2�Ku+&dQHe��2 �shp�"�Va�ݮFD E#1}}�6>-u�m�l +8&�a� \�y��s.��E͡:����:%���B�э6�"[ B� &SB� !4%gBw&-E� GM�2� �n ��B ��K�Fiu�5̍w2li, &p^� #B��qyiB��� 3m� i�-N>��D��a( The}m�m���'!� JvV_I�F� ��M/��a�;>��x-� u5TqN"�f����U-X�Lm*�:�r6!0J��'iz,^(>A�@&Ǒ�&B"� �K ti�� a`6(3t� e����W �Ex��4M��=a���I�?we}e�n�F�R<D-���BW*� x � = �X!���i('����1 B��n�A�+3�I��-K%�ر%(4�{35B ���m�is�iF����b�y&t1Yj��it{Case 3.1}} : $a_{1}a_{2} \ne 0$.\\ \noindent{The} vector field is of the form : \begin{equation} v=\frac{\partial}{\partial x}+a_{2}\frac{\p ! y}; \end{O and o�X invariants $\varsigma$ et $\chi$ are solutions of the following characteristics system J�\f�dx}{1}= y}{%)u}{0}.>�The� are `narray} �&=&x- \[ ;\\ � &=&u_:Dnext we have : $u=0$,!( refoVu u_{x}&=& 2_{�v u_{y �->#��Hj,S01�,By substitut!�4these express%� into Thomas Q (, we obtain9�".kuM�:��+(\beta-%�\alpha):(}+\gamma>@}^{2}=0�gput�$ $\theta =Bg$� �$Bernoulli r�P'R� � �1v� \newpage }�0}\underline{\�.a�If� 2} =m%4}{)0}$N*reduced9�takes-��. \>/ �'J�BewhichI��sm�R�% m�1}{)�!�+cte},>#�gi?,F�u>K}log( V(B�)+k_{0})lJ�ere $"\$, is arbitrary constant:^} \Z�b:�\ne�� We} adopt%KchangeQ��z�w.� ywA;ar9��Qyz'=Jlz-�B�)� admi �generalr�z=ke^{Jf!�}�b)�}I�.�R�bv=\int�$1}{�y}d� BM�nj�-U�E�1+ ��kJ V# J�}- Hn� $k=$��V�2.� 1} =B{,In} this sitIOA��Q$v$ asNqj}yb�2\z�>��H��Then >�-�BX5�S�~��,\\y0 �|0.>ySFW�Vt�+ �P� $correspond�դ����N��" �t = 0, \Longrightarrow u = cte �)�D} \section {Conclu@} \hspace{.1in} I��4is paper by us��cri� on�0 ce �åL2Xinfinitesimal prolonged6 �� tors��fi� xmost Lie point symmetries group�!Y:�. Look�adj=re ent�;/ed\yZn its|algebra� � prelimin�Ylassific_�-1&ts�f s. Wb see!na���B� in such c_ hcan be transformed on known9�5�4an appropriateъof !�� bles. ItAzinterE%0ng to extende# isI�ruICtoCsuper1�cFU m/ detailDžs quesA�L will be given elsew�4${\cite{13}}$.�t_ Y�$Appendix} Q�%�intro, A  methodQ %��he =�M�%��ted!E!&��2�Y� :Jy v=(� �� x)�GpB� x}+,2" yf,y_  x-� n.uR�u�t e found�!�grak �2� 6� � , VisF� �� 6 "� � � yu}M� yV�first-�se twou��� � J�*� $is} easilya�ved' )>���&i\log A 1}- " x)&* ' 'U, y)+cB�So, one-9�a�N�,  =Y1]�.iBgNotacat$6�for al*` ih^Iso���yUK{ wu x5 x1 kn��6� 2�Bt\}dx=d&F�� 2X has �Ls"_ � beg2� �-�5� � !71}+ � �)+�aU2� x)� %y.22- x)}=u+kBC A�$k$�[FZ FinallyA�0NT�  =uQ !��}x �� x) B �2�R�B�iYsecon� ,nt.���)�pthebibliography}{21} \bibitem~ $Olver P.J,�l*% � �ve�Differen� EMOd, Springer, New York 1986.d42} Stephani H,2Hu�$s: Their SMy U� S"V \, Cambridge University P;,s9s03} Bluman G.W� Kumei,P.�s�s^�.ct4} Ibragimov N.H, CRC Handbook�M!?G Analys> .s 9G= �$Boca Raton�.KD5}Rodr\'iguez M.A.�W�B�rnitz. P, J.PhysA:Maths.Gen 37(2004) �  re%�ces quoO therien=E6}�SbEngel F,!�o� der Tran� W gru� p Vol.39 (Leipzig Teubner) 189� Q|(7} Wong W.T �TFung P.C.W, Linuo cimeS,99B 1987.163� 8}Zheng K al., �(ica Scripta=40E#, 705=9}SakovZ4S.Yu, Journal Eacs A: )H!;Gen.21�8,L1123Y�410}Guang-Mei.W�(Gechoslovok\of _cs�(52 2002, 74.a 11} �ya Y,�H3H3, 298�12}� H.C�Ameri��pChemistry. Soc.66 1944, 16 64.H,3} A.OuhadanI8.H . El Kinani,C prepa� oAK�>�� docu!�} ��%�� e�on  ��RMP? Jun 12,� 5 \<� [12pt]{� \cle} \usepackage{amssymbBfontsB mathBthmBcd6epsfig6�nicx} %�([notref,notD $]{showkeys'input M %�$ .layout �� \textwidth 6in %%7in \oddsidemargin 0.25-  \even"61 Whe� 9in %9Xtop T -0.5 ��macros��4command{\Lap}{h,1}{2}\Delta}6&s�< L}{\Acal{L}R#H#H>#(grad}{\nabl>a ep}{iepsil:\ne�half}: �} \re."O}{\oper�name{OF$o>$oF$P>$PF$Re>%ReF&Im>&ImF&th�3!}RTT} { 5yT} :&T>iT>HJ>"J"0def\tinv{ {t^I )�U{ 9�UBt{� widetilde.+>,B.JBBbJB J % * $ from Yau'� �b" {{\bold�� ol \�  4/et"g{{�4k{{\kappfp{ �frak p(b)a bf kfq.,qr.ru.uw.w ({\left(} �[{ [  ){ \b) ]] ,hV{\hat{V}_0 bE kbf E}} %5t opp{ {p'�PP{ {Pbb{ {brr{ {r'E�Aqqq{{quu{{u<{\langŷ def\>{\ra bell9�{l�hj �j6� I-tsai �Stheorem�}�  [Ion].'4*{corollary}{C .#{lemma}[ Y]{L2#�osiF)Pro, \numberwith.Z{ �} .Q *{main}{M�T �Ce�def�io.qD %.  ��2 �9(6�r� k}{R 6claim}{C.{assump:�A6�.?66 \title!�" � Boltzmann"M �Low Den' LiWLof a Random Schr\"orer=8} \author{David� 4\thanks{Suppor, 8by MacCraken Fee"@ship. Courant Ins� e*&� P. 251 Mercer Street*, NY 100� eng@�i.,ford.edu} \;+HL\'aszl\'o Erd\H os�P � s.�NSF g�DMS-0x 35 � (EU-IHP Netw�``� jDQuantum'' HPRN-CT-;-0027. �!b. e cs, �unichF \resienstr. 39, D-80333 #D Germany, lerdos%XPk.uni-muenchen.de. On3ve�Schoolpat 4� GeorgiaTe� USA}af$date{June !p 2005b�i } \makeE| � abstT$$} We studyEvD time evogAx q)C bcl�teA�� a rI� poteiS A�U�(-Grad low dM�lA�.� prov�4ph�>-��� �BLrough C$Husimi funW�s!�$an environ� [ X impuritie�we=  xiaQ�$ne neglectiQEoxtw�eUf���blem ��$a one-bodyZ�,. With high!� cent�!��%NY� s localizqin ular noHdu%� occurs QdAi, AM, A, DK, FS, FMSS}.�eE�co� regak  Tis�ec��to c bu�re�,no rigorous �^�Wcofq%existenc���"pstateg ceptI%aBeATlattice �Kl, Kl2�"�wV3 y�in Va�R�0in a specifica+l�I�, calle�e B�-ory��K 1. Our me[Q�analogu1�NLoz gas. AI��$increases,�H6�Ysca� down�!F a wa� w tota��+Z�Ť!~�s �ins b?eaa typ%�configuI�. U �! our r�! far � ]>M}crequiriXc ��$e behaviorQY6z9� �&��K, �+U entl�J�,fixed (low) �y�jy��start�f��A+�)�A�Yn -.I Lk+ Lambda_L\�)et b{R}^d � a cubE,V$L� d l@V_0(x) )0smooth radial�c �p a suffici �str)decA o beQ�edaqer. � � by $\omeg�)(x_), D = 1, \ldots, N$, �2!?uni� ly dibu�QY`!4��1n$varrho := )N}{L^5label� :aC : b�2��u. �!�$��es�+YGVn (�p.��""T se2s�,2� �govy�!h&Wp} �is��Fi -E:shro} �i \APal_t \psi_t = H_{N,L}\, , \, {t=0} =  0\; >5 �!%�(Hamiltonian��h3��= H%�Lap + V_M�,\�qquad = \sum\�{s_{I�=1}^N%�9@ (x)geG-U� \; �UJ iGperiodic� $�%C sX$u�$�$usaU ower�#le� s, $(x,t)j.o�al!�a a�� &�# Q�mi� 4copic (atomic)�� � ,shall always�'�I� simultane�L$L\to \infty$, $N\to ���%it�H�aiity, 804rho= N/L^d$, b�any o� A.  Pe box.' A/,just a techn�Ndev�� to avoid �# sum� m"�  term���zethod z sP�d�, ,$d\geq 3$, �w�strict��selves ��!��%$d=3$�� As a-U(step toward�i� of�C , T �rs cerz/�a�I�. �ep��x#e ��\� amet�'� . and �Iv�1�%��al%� $\ep�� \AA / 1A��rm{cm�.( 10^{-8}$; ) we2R�idRzedQ \to0M6A�/� .�coordin� $(X,T��y>�*�$a�4(x\ep, t\ep)\;:�"*} �" t�veloc�is not�! , d"X}{T}w#x}{t}$."c&pa)�_ treB fo�!�O%� pr q#ve�{J�4 $\bf{G\,mG \, >4\,(L.D.L.):}$ Q ��= !� _0$E�soma��v��q�_0$n(ldl9gF'{�w ,t}^�= \Big[��Jr �s�xV�� }(x)@]ł:[ \,F�*An�G�!l6t+ p"b� a|��l�*ature is��(Weak\, coup!�\,)�\, (W.C9�FixE�1�1l!�)�!����istrength�a8� rnal ��bh sqrt{\ep}r�wc�� !x-� d��2�B�} aLa rel`)m ,� 4 � =$AWc ���&r'&d�,a Gaussian fL7$& �� a� ing�� ep$-*�  cova7ce��It tur���atAEbQ !�e�%�I �s� s'�es;"_ 1�� a��ul"$ a nontriv� $(non-free).,6�bASa�5�ƥu��fWigner "/,Aq�u$a�q0� � J& "U wigdef�0W_H (x,v���1_]� 3} \� �2{+A�(x A�f8z�)�  (x -� ( e^{ivz} dz��:�� eF��ly�no �ite sign� assoc.-dB� is nonne�ve at2^-!�_� >� at !$ $(\ell_1,2)~z��H%c^{:A}� )~ *_x G!/i�2*_v2\;,:� *� $G^\d��El tand�qj q7 $ 1^2y5 .e.,>�*� gm�Y@p(zE@(2\pi R )^{-�!�U^2}{2"}�F e>�9�)J=� _2��ell��l%co �0�:E $IPe> $$��.�, W}e(=} C_{a $ } (x, v):�� Q # \pi_{"�ll \�a,��  $>. 5� proj2on:$$L^2$ normb�e AEz�-zi� zv} $� (Clearly $ >� p"�� B �0B; !v)!#dx dv!| �(\|_2^2= 1\;!�l�cob#$"�  Thus $6_$i,be� � ed�a! babi ��o/� � !�i � .i�apacy� e4p�,e"ble"� :K�A }%�'r'E�$,)6Sd�' &I�|"� �. �is;pt�3un� (ty principl� Utu� �*can> keep���-�aR�proof �wR!` sm� extr �ing���2basic obA�5�� y��>�on�T %&_1A ep! +\mu`9 22 ^\mu$ - ($0<\mu < 1/��"9�&also A writte�J�ItE:h���H���, � �E6#�! \ast�� (� �� =]�b?z5\;>��% b1<N�9 y ^{-2}�j4\�!$. V!*re�� U:o%�.� baL�ngFFa�Hh:� \mu)}%B�  V� �3}::)�=<(X/FV) \ge 0� . :�2BF#(\ref�D), 5��* "2}) i�� $f��#+�i : �i.A�u�F$�M 6� No J�n $NQ$ :�. �e�T!"� (�) � �Z��~N���now2�eMDi�u�3�K._ �5#"� to resᑁ true"Umecha<2� . go��:��.�� |J_t$�B�� "�0  � a*&�as"5j*�Y, e�5� d*&/a_< s� �2"! ��r^C2B. 9!�re�%ef�A9a� dJ)A�2Q� $F_T(X,V)��B�($ \Sigma (Ua� &� alig*1 "�T & Ua� + V \cdot)_X F_T�J \notags2�s=&� :{ V U)-V, U)V� dU Rn`2�Z<- _ ��a���b�#��-� $ `: F?O �dU� e(�:��our sekC O (V,U%��9 �r��Y.8% . F�5ny}{f$..� 3$ w�!*�9t s < \| f� {M,N} <| \^{M} \< �*N} +2�   N, M!��bb{N}%P$$5/K: (1+x^` 1/2� S�#8EO���,"@� rZ�7E2c*��;a���-�!��la�0�|r�50, 5g$5�def 36��?2�c . �� �8� � Ha&�$H_1:= &�, �,aI_0 $ Ono � �  asympt��P completeness holds,  �Nincom�� outgo Hilbert�^�:A��"�� � (5�R}^3)�=R��w�o�,s  O��p'?  _{s &�}J \pm isH_0 mp1}  mXH%�J!� �i#of�s&S#� $ S^ �^� - _+ a Fourier �exist)ih be *� A�S(u$Z� (u-v) -2 iAf ^2-v^2) T!at��}} C.P�b62�����%&y A�Uąu&' \s�� �: = 4�,�Ebr: {  (�@}_{\hbox{ on-shel�* |Z�|^2 6R&�&s��iw6 data1���e�*��_0p%�! 3/2} hO  x!u_0ɏ x���PMdu_0\in*� �$�h�30,30} <���eD$h��a$-�<�&� mpl/A$�;X.�,�}�\|_]0} ] $ D!%�usu�( dropE�"hat"��a�i-;e�"m a�& ?bexa� in mo�%umI�� It should+��!]"�#!�!���s 6tisH Alyњ last� -id�'ficN&i%�B.  �"ly��� a�l � ��*��satisfy��|���$�>3a G$!Dz� O�A stra"3for�to checkX��>YsF� 1'�e*�( �ly !�*�  measu�#on2� {6}$,!va�2��0= L E�x 0}(X� dX dV8 |h(Xa��(V-u_0) "$$E҉��@�� F_0� :=ZB9#A'2��E;!�J�)aF��I 8A�. !Bc*�!.K&V : %_ 3�gm�.�$d = 3�l $\mu>0$aP J 9�}.�"�#�_&�# .�#Q"� !��#�Mrho_0` &l- ) _0>0�� �$V!b�$r�S  $�Z@ 50AJ� p _{ � �%0!"� �2�#"� u%7) ��.�61&:0$Ko&A��E� ��I�(x)��c�b.a<�Sb<��hA =1$.��n{ � $T>a���� f*continu#"t���$J- M��� �x \e�� im_{*b"}w |��ti� Je�\,�[ \bE[ .J"BF.T/A!H �7-i h Big] �= 0z,�-S"� $���]A0>&sP0� M$2C�- $�� Z�$ %�eyeff�v�6�- � =}� [ ss  $. H�+$2 S Ւ& �in�� )(.��E .Z" It lar!2��R�f�R�.�0�#ks��!�"�2Z��2F�^p�!�{+A���� .�es��venIH.~Spohn�,Sp}6� I+!@�P(6<acc�"g 3"Olaw%�.��%�� H, $T\leq T_0$. Hi�+Bwa1-�IoS.�EcnLl�u�s� Ho-L� u-Wilkins � HLW}h+� sameuf4s�+6*E�&� � �en globK !iime�Y3�Yau�- EY1} La�$!T�%:�`)l2��C~Mi1�Q �showed p2}'} �&�. exp�.BY�,F I��L^r�$rr&��?0�:%�imi�/�< spir&bM� *�-/� avu�ce &!D$I{!)rEs ) /� >�8!S�C$.cP !!uHol6'�'�u< ) Bor�?�ADof each individualu?*Q in!�tr� -o- ��J��o� �JiaM�1��0needed. Unlik26Oinq.� *&  o![hqu�5rz4n�>borhood;an�,4 %edei@ it m�yas a-vanis1 a� tu�5 MoreT!, if !�2w �7�M!^=% !HEc�#doubl �) pXn��is �!�ar� � s. O�"t"�)leveleis.�forced usJ-,ly reorganiz��diagrXticala�A.MPimporta�/D$�Gs> big�a�A�!�E�I;�}!�ir �Nmat!qq0d sev)Unew<a�)egc�Oca?al.�1[m�*p/L*�1 �2]6d�0G. Gallavotti � Ga}, H. 6}2}d Bold�<i&CBun5FuD� SinaGBBS.�2�.�*s"� �.R��*.�> ", . How!HAeOmr "�1�.A�J! a BrowI.mo insteaaN���m - \Q K�/JDPapolaou-RKP}%U  $( z�_1*9 ,�s A��*�& T_n7 g belie*>9�)W�Qinsic s �ty���/������. B�'�<oofn&� be m7Smolnŏd-� %A &�?  P"�S� F" �DI>{21} Z&F�,� F6 % 4�7{No 8} \�ni�,� fix a e#W )/�lem�Ifal`e $%Agri K"�5F�"3(38 $dx$_J3Lebes�6� >�3$ ] �؅�} $�%�%/$;)B,&.nVdx� )( 1}{(�)}@� 3} d^*x� �"�&�/erE�ev)�$6� a�,genuine $3$-"/0al�6�$is.�<app�;ny� o 8@$ $3$ es�($=^ not}%uone.�a;�So��7V� )Gr), � G-�Son �-��' , un ,B�!�!!��� �:d I�A���three �alFb (w}^%2be&qeb� hat)�-k9�_"c f}(pH\�cal{F}fmALf(x<-ipx} dx�Q�Xi��seB +]�KA�j~$}.� E�>���F.- *} W�ha�&�3b�� QY:W� psi(pO4h�)nm o�A!�� q�i8-_b)8>� ell_j�j "�1�A9`$j=Gbh�]4)D&0!��^{� �.� {)' �p_0� � 0+1} >f+\under� {p_b&?p_bDb +1})C��defpto� �x �v.8�$og=O�\x �!� *�!>1 &�� p\�e��\5>N�6F>e��fAend �V,2m%]x\ge 1.?$ $x^{\O(1)� bk$PBe�5H t�J$Z� ��Lm�; (-&a ep$)�� Fin*$, if $A, Bi%y�/��=un� v$<"ba�'] �M��* (e.g.�]up�a in$, etc.��40 $A\oplus B$ �j2 D aten No��$B�B.�i�A� % ; suXbedeU-B$.GS�im"�d $AB����$A \prec!<� ) �ie�&$Aut2�-� co1d� �N duhamelaA mulaZ� 2� D 8Fo8� ss:duh} "S)�; $n_0@e ?W wj bP (e^{-it H } �~`sum_{m=0}^{n_0 -1} (-i)^m��t+$@t*} \[ ds_j\]_0^mF^T s_0 N'V}  s_1 BC�+s�9]D Rm 9�B �&+ ��0^ ��  L0 H6� 1�B��^� ]= a1����!�2" |$H��(a�)2�)� �0E:.C�0�<bDM�|i.�- m^n �_0^t ɠ t5  Big(\prod�A }%�)\JVV 9t-L ;n A' Big).5�ex2�$m� ��q�^GU\�a�co�Na�  $�DA�|a�$YH5i*�+vai�)=-"F +$. Expa�i�&rB"s<eV\a?�N#� m� q�� g�mte �erm WeQ u m'1seque��8"�, say,t�U f a� \a_2��j a_n��� V with�<$etH�( �F '��, I�)� #.+0ed�A�y e%.ed}�/ / �7IK% trun�H d}. ~0��!e-413a"r ',.� 6�+�;:� ��oB�5" ��E � K�&Ri 0^n �U � p_0^2/TU�w�Y a_1} -p_1**-31 p_1 3 +2+1-p_2*) %�mn p_n:6�}�F!D. rmed�<-> a $pApElA� n-1}�aU)ut*$9�M4.I-Is% !NEI $�05 $ r�? �Ij s_0Hv�@Eh-�A'��H/2�%E ��F�� UM0u�A�b�%�,a�n)� a_6�repeaCG��be�m:ofiW�Lers� b�3�*�A:>%�m) , \dIx�C_jLinA' \�-� �} j:Z *}w���of6� �WBf9�(kA�kY�, k_m)�1� ��9b$k_j +1$� M e j�B $\a^)Zs�elf�secutiv�:(QPMA?W�V �Oe`�*�s)*#�� $A$ R1a��Rer�W� \neq!� {j+1�2In � E-V18 orig ; $`@iv�$�1y(\*���,,{1}_{k_� ��68228282*,^9m29m9m  oK"�9I�B�A��/Y%se] ��#toi1�}B c!� �.I��run�O.J# ��u�;�S kr �KNZ_��;y��n�q(reB#"Z loop"� )�' nce M�ed M�Y�oth�2�, �yz!2T;5 ���a�iD\�hy�8)9� 9refer7�:&b"�#a)�-�j�%alpea�f�ydA*�act�0r� � N< } vs.u  ex "eI#� uQ .})!Fr�E$� j� m(k_j+1):�)A�$m$h%M =k�v5zQ�Mi am�Qa�)��� �%� ���m{_j$> C� histSg9�c�S:GH!�aC$AA T�Sly !�:-e�6�Nca�K?A�AUCm = |A|K Next,(8,!��e�lexico�d���$&ce6*EB<B�m Jdef1��(J=J_{m,\bk}� Bigl( 11,�Z��1�p21, 2�� 2�����% mk_mErJ�ٌ\bk� VFi��R�� !q� Q&�k�}!�!��R�=&@? b\J(fq_J:=(q_{jv})_{j��  5% Sin $"�� 1:k= p JQ}5�$,52�\S&to�N ��0�8AJ�"i  hl !&a0�[,"�|termin��N. Coni�t5))3\F5+"�w?3:Tya,�p:X .< efch*Btn(A;zm}�F"yY4j i�� ${j-1}-p_j)B] �NBiTWi6m!)>c"�oJ%Bs3DbX&� defLyjL(�gq_{YU)i|t �uZ>\hVj%A�1}) 2*Em�*k_j)C>� \�� k_j= 1�}P*�S!KAP:GVp)�B jK�#�R� !e"}� BItloc��ao�.QxLA� #b"tai'�+.��chi�� G �bm�#fr�m!E"zpL*(Las:FZ9�K1rK(t;r�fr_m):��FL \[d�\]40}^m Q �1�s_j r_j�>�6�B�\�o�Bk��Q�-a �ide86�s}u u�KXpreviously established&S��qvP" y�^t"�L�I)���ce�� ]k]_k� "�(*O !� r�=&2�� , q_9n,iZ k_�H 1q_r��-%q_{m12>�<},p_mq���%mH �[.Z9s)bK5" Y� defs[K�|�N�+ K}(t=&):=� ��1k_<- �Dt d�e��%~W�m!-> -L)�A!HJ*> �%/�� wN��=[�:�;A{�eVy (�r� � I% *VO�agXl�v< psiA95�$ _A(tX0�:)�\i)�p_m \,9�)�.�) �X(A|,-�&�> �� m}2�&}I~[eB��6:�<>�%��6."/�n3Z�b�um,���HiN�B=�!R�0 QI� e2>u$ � "�&&��".CUmY � F�)6E�| U�s (�m is �Z coun2l5!58 s��*�,�A�^�JUi%�{H rm{no\, b` B� m(t) 7M�:=��}A:O = 6_ \,_ }}P si_AJ@I�ea[q"FgW "naIc''g�jw}� mind�?� r(sum o�w sets��%�cot*]�5�)� $\� i O ��-TK6 ����Error� s�-2o TG,>Div>}�am_0=m_0�A�Z�$ ^U$-&�par�a|'hosenN(era�XD*cK�Cof)f �A�� Z��#2x�)Ł*!e fQ�P4�/ 4k fX fu�'<�EBO%o��Ws.��:b&G_&inu��Hf for �w!N.�ec1� ]( an !�$%�s p:WA^a�?. 2%�A^�1���n�(�&="� U�z9aches �or�!�Q�uine�"� �f�i�Dl� !9decomP"on:�`f_1st /�{8  t���0 "��{m_0-1}^2�rec}}��+F;\Ps8eah}}1'0�y :jmp.:� r {< m > +z^J�Z:m�be �5�"&� G,%�eLc .I"5: �B ��Tdt)lsH%M _s \; ds &^2\�$tee|!_s\�Fd/*�U!�add�al $t$�BAVi�prZao� rude�?kBaP�j� =�Qa9 h�`talvy[0,t]$ i?$n$ piec�X|#�wr?G $n=n�+?5 c88ay����m�a�4he���rgu!1 :[a,"e�1a}Q r $n�%q+E :.]� k~n)�7,t}{n} H�ZmI��� *(n-k)/H} \(e\f�Zk %�0 \F. ��! divm�C< �!�/&$0EOkn$. B]c���8CY��Plenc^$ ��$��ucU6� JbA'| � erm�Re eᥒ. �$ �$-sR*D�0 �;o � �)$&Fthe�c�A�"�Ba�th���n�h��"� ),-Nphi�9��Dph��}_ks ::%�e�1�%�mJ6\()d �\2".rJPs>I mBKt�T�( �S78D%?F�!U�%J�]Z =�Z--/_k %  =&i �EGQ({k-�� u}� \3 mQJ�va!�_k9MEj 9!� #�-o3k�-6M EqZ�&.C 2��!Cq�),Ze��])�U#UFJL."�R�Jx1n1�JY� �total} 2T<cec -�N\=��|��(�h �C8C6th5N&�)� �=�#Z^��KqM .+]id�rj6deGoyitLQ"� �ie%�7KNt+u��q�� ] 'g$ � ��ng�:2�s as "#t_1� E�t_2 %��&�� ��*.b&k.l.ߏD:� L Z �2� r�uhow clos!�1 �p��yr . C"#?intuin, tell"'improb��� pa�oy'_f,very short �=e &L�@,que employed�huexploR6hiQ68� gendD ��52now�u��-S ed=es(�medskipQA��!�-f s�@&!p$tK"�K$�2�l0$ $t_1,t_ �H y $m�2+m_�\$$t=t_1+t_25-�-!�A&�', 2�pro�a&�to�a>u�J�(_1,m_2;A}&(� t_2���N"��3 <�&\Kj 1}O"D_.?1Ŏ� 32} (t_2��J�� %�2)meJmF� �u� norectdiv�"6�EF_^� "�c9N�6�%I�%F2�)>0,�#)#�def�K� �e2L��A��� �&���A�SZ�]�6O ^%F5 .>d.�\� G6F\�5�bv;qi�2�. 9< Umm0�$-7�3A_1�e�.�!o�p+�$ ele �u!^!C$A_2$��R$a�>*,�7!g2Q* ��B��"!F?Am�)RE�1-aZ0)2'*}� � A �Euwe:� s T"w��4:E;.E��<a&G  (2 ��&}.5�mCt2�n�,p �E+n>6�,)�D{A &R;\t(\� ,p)� � �4m=|A|��1�&� !�oA��Rm!�I�"">"l5[�' �2�9�=Y=o��aq:?�:���xa��36�J[t� ��^0��:5s; )sBZu�1�& m_1- { Z�:�&Lq��*Cg �,s� ) %�2R_.M�xe)>u$�& cirlCE��S�R!A4�[r,B @ -s)Hj�6�s,>Xt1"$;�CS��)= =0Yk s ${1�0 }� $y�R% �y�fm(set{(\sim)}N?!�i�� } ,m_��6 Z BsU��^�7"�+E:uAC6.� �  K*� ��7>G�er��\K��hBy5�* )VKy RW��B� A�lEvolAF� .q <#$KH:�DasMVv?#�HWe] d%"rL �wo do so."� " , u&�>&w�ta]eta(tYM8�$r�; &,B r�q 1v�;��.�;t >6b2$ � �t�ly7 $�_j�7 (t�%�$ eta'.'$#4 :=$�� 1les� [$\a$-RYE� ]1PL:K�Bty}!�"&�� !)�h >0$q��SES5">%� �vi�npi (� t�8{�H } d\a \, �� \ &e' k%j�1� -�@t% +i�R,a�� �5%�1F)E!-!ZN�M�)B��/|:�|IqC��2�B�� �= 0C&�|�~� i%F�|} F�*��I&��� ��o�Sgc' 3c���S#;��;� �a1|*cH75-6%�3C�� variA� p#�\a,a�tw6�J�$)�=y64C!�on me�a���59'o�|EO$b)fu9w�ED?�Wl�k��} �0Odo�f"t�$�s6t *XB//"l��R&re�@in�7w�!{"�� V6 q}>$��6�%� �mreq!�!�BvbI{; 6iyixaQ -8+ iLFCQ�1Y�B(!�p^*,�+{\2�M�} ]� E:KFa�&:AB_�2Ia��&�*}�&� �)U+ k}�)\([hB�+F��2�=:6\' s'%]Mh 1} -2���1}�~)3 J4�8m�2�+i��N�+jP"� defB �I/&�@,��he�a�6 ,%ca8a�,"m�)� i@reg�Fiz�i*O"$oft�5&pp�*89!ea_^2 2}� p,r):�OM\9j_0QE�*M�$�� 2� �Eoa�nd $M*.5�Z Ŧ �y���W,�sS&mar�d^\a�% =A�a��] 1""q�n�i`PU 0+0} ��!(�p2.MzA�40 j#��=>it}"c1*6�8t+i:� e��i�7�ŏ�J srN%:0 "�foE�&Ej$$T$-matrix6V't�] rd �ZsM[&�$ (seea�$orem XI.43��RS}).]!2�*� ���&8Hda�."oo3e�"A�e 1sectG*sGO assi}�@��{ s �H�Xt-hAR�/%Z��F�� )tsa}e calcu�FDweĐG�L"�*reader.Qt�$a��!P:�`ing!s}�l�a&ogq#A�sCt K?.)� � AF) ��:1s 8^"/ e�e�*�(N a,2�w�}{=oa\>�! a- pav Q leq& w �It*Se�inz &i� � j*\<irp \>^4t�6uJvF�� inta��}.h �p,\�d}�,{4}}B�| Crufty^vrv zdp󩵂�5hB�QzE�no^~.�1}{� Fb� � p Fl=^ftym,25}5C�i6j6$t� $$\;\;\Box$�3.LA� ng��(�b9 keyU�YN)*ra� so-:[Dq��3:<�� } UnoR6dpI 'm���>����6��� M�\a,\a'2 I A�4 \|:5<'\>}{|\a' -(p+q)qW:%� /C (i�$)^2}{|q| +}2�*b�J�G�S�$ch� � sp��M3.臡�3Z%�an ` onenP p$ a| st�+ez& vect�'q$.H |q|>,$r:=|p|t]v ��@.��)^�& �Ie���B��I=&�_0"� Ea�p?* \r r^2;d r �{\< 4IHr2 .Jj��^1-dz�� (X + q^�2rA(z)^u�� ��&� �!&' E� E�JK z )/XE��� Ka=��&� PCE�iG�a5}  rn+r����-%� -1 wRQ�+:d)zi 2� � aw- z�;moB�\� *C i|Z� �~�Z�Bw �B�2�*} Combi�B� "� tri���f��G1�A"Q ��.�:� s�l S")f����2��!�B=|� �C�� �@$q�v�c���-$ &��7�4a.B)�h, �5reee8enjoys a "semi-R�"��yIm eD �givp usB,2s�t ���&"�etC�R���;*/ ��}Ȏm.1�1 $I_1, I_2�4bwB\{ͶRA, mpZS 0 \cap4 omptysetO \cu{09L!T!=is,M82$z�4$9 �. jx�R%�5�n x7\�G� t"�GE?�� F� -ąint�P_0�O12 K(s_1E�_{I�$ $dX;,UG"� K=�� ���-PC= (r_j)Bin I_k� If�o�"�5,�Fy!Ch&v=!� � ? $B�:=��Z (s_2$\�0ase=�+� �0��Nw J� �S s di�%lyh��(, q�"�An im(Mc*�&s!)F9orN�\ES8ds d\tau \,K(s;"b:m)F� F(*;&�:mN�~& �:�&�FP-i�*�I�<����d:�< K��<:�A5*�<�I�0U� defF6� �N$~T^oL}�<�q!�aF�C$k_:�U=! =�; Ԋ%).�B&L�>�o��.nt�?�v�6-le$, ee �c��I$�q"�I$)��a�a#;� afte�+�V,t�$i>7� ��$a^erm�I����2�'f�[W�A�u>yy)k�c]�G2&s�|e�i uE)�ToK9vimWK}�u$(3\mu_1<2�m��W Pe�. ���-d�-\�v2F��p�uTM6i�� e^��!) �"��2*�"j i�a � .j�"B�"W�W%#  \Z{gN.�{j"*_1��YU�M)X�Y���­�1�š2/�i"�!  6�;B  "e"E�8 E�}:8gomp��Yj*aTtoB v&� � "�L:�/ est}��m_0 = m.4<<b&d"m0choice��Y $j�0(tJ�(e�q*]1�y2�e:�.�ww�w 0} 2�w \bE2xn�T�~-1-�8=0B�:40J�m"Z6��ompXp�m�;���5@�= "�L�;RH�>�Is, ?S���JD�0 "�!3Nk r&�>q9clu�/ �%�xb<�����A2 '9w& �a�vy�ps 0of.ck � ��wM��0b?ur :�* �9w�&�2� (�9U)� reby e��]�vhem)_s� �St �sC1"uH),Bc��q 0o A$��$m:"�0)v%�..p d�M, �KaL9-!n.6-M �>- �$>-~?-:6oeD6N- �OWp^\a_{k}&)l$k$-thj/ �$2\�\kыe�� �R�*�5� m�< �in $(0�']�1$)�$�0�-2]-c =��_\kUb:�0.=-,&�5�=,\kF�'B).F�N�/� dr�8�Z�jp,[�7,\k}5. -r_0�\�(H9.*+�Z2�6 &5V�|.�0�-f�EoI;Al� �3 ��ag�F"�*N}$� ���22).��`� $!�$ 1 a�2#L���.��c. kB�+� heM@2���1�� +!�%��]+ �!s^+B�gzL (��_2!�. %U"* .5 oneA�=%�} Sum&� �up$>�a�o�xDUs�ys �2�Gab��9��5J rme,y)I��KJ \k=2C �*x+|A|:w+v+FN1Qv��4�+"h+ U1mm64%4 Z div �4�� � .��G�_a'.`��, togeC�3u eE�&�6 44U�E n�%*P,u�:fv-%��&BL�V�ll2�&� dK�L"� �,&t `&�a�"�C�y �} !&�a>S �ddiv+expsn} G`(�A ! i�<�$1�W�^n$,)ge+8:=t/n�t_2� k-1)./T 6 y�"2�YJ� =:& b�,1g3)+B$^�,2 1*�?�E�,3"FR�M�-M� >J�(a)_+�-max(a,0 i.�Q� �Bsc%̬���� _m(0�A0�i$m>� �60mK&6WjId�6�,�l������`E�1Ii0)� k zero u�'n ���H�[�>RkG_1,� �mi!B ��b�( b�careful"' ��"�.�YC�\Z�� 2f.L q@zCGEJ;E Yk� a _B(t*!�Qu��hzLO�t�?�C�N}(2F"�.4*�/n?�dehe5!�)&DK�2!O _�0"]J5N� n7C~"�� M��skQ.@or�\$2�-O �Kpb]#B&h �\�8ompensa"uby6�)at each_�oC�paX.. Per!=O A�� Fm.�5�O!�2�.�:�ق�: Hq7PV ��.D�*��}�� B�+ݿS�+k2l�e����R*�  &ѡ_V=F<F�=y5 R=:k_n�� veri���m5)R\� krel%1*�} +�P9:�e�!&)&%p=2I=�$�@�Eend��* ec���3eVI�A�g���of�;�]�+ud.�$k�Ad1�*Z R- the z#a&�Kfy}�1-�CH�_W�+�he>� �a.F�.B �)km�M� j V]no2��("���_�-@a�*� 4�%A}���/sy�����_"�o�t|-�in&8��M� '��or���.J�er$@o2aĮ.?qi 6�QB�  �p5��y �� $ t0*st��'&P!9�s�e��@n}] $X��[s � A��M2�g�s�D�C��Mt_�2+t_1]$&��!I @% �n�� �Aݖ�D :� "U!��c% F}SP"_�yU,6�M+�,YF.�B�, allo�rar��/��sA&�2&I �a�'F�:$��"y l #`,�ch6�_$.a�v@IIi|��?ecI� val"��se2\s. "� �is unaC1k@!aL �FgH -JisM�%�rA�-$��$ 7E>$2.[;�,{Ex�6�)#%�} net �(ar1� .[�* to�xducـ��liو �j�)(so�-"*pai�]"� Reh"F " �N!G0t�P�u1�Evin6��-��7:��varrho_ �$mbda}^{(n)#cf &N(N-1)�" (N-n+1)�)L/ |^{n}} =&gm�m� rho`R(1� j}{N�P��� def:rh���3}OP�de���en$-gcQ��-lL�(���E�.le-�`F$ � ��"c}�>�BF�A�(= 0_&�E�M�Q&cP��xWb��2� ])y9�6$F-&��7>p72( 12p%�^lnS"^rh�6`3*�S(b)$%� perm�Dq3% �9b&�>�<[S�0 Set }�]L:bF�"6e�1e-Y�2TZoz�"�$G� L^2" �R}^{3(mA�;�1bb{C}�nnd�.�WxA�i*���e)� en2~ &D \bE%p\| �8n�G��9=J��2D#5�G�J�]b#Big\|_{�dp_0)}g+�%�PY "i bA3m# igma͛~'"n=�S}(b)� 4},'�OQd{(2m-b).�F,! ��#p_b '_b �^{�g_0}�b^�|b}K�A�]{% -'. {\fp'}2�� ll'_4J���_{\% }5\br '_b)*�0E���q % ?~#~��_ �1D&Ŕ�\ �:.�Zth ok."Y {F[~:q $S!��db5i_�dJ'm-�~}^�J- A�,~f)/�%�� 1}^bJ�W'[(|!-2< - (\py"%�(j)-1}-6})]UC�;ۃf�@}.6��9 ���H>�# "�W$:�k�M �$ aZ6Gt�to�/c�witu� �'Qx�nF��.��� �\w�[�F8 �:a�ns�i �Os*�}�r $A'$)&#%q stooj�)�u,(�:!)� AL"�\O&"�* &V�9 "��[ ���B�= *�x squa�u&�veQ.\Big|&�rA:db,A��N�I���!*�&=BSsA':@F'�2fdE�mJ���.)���O'�� '_m)J � �.@ a[9\4� -(�4�X $�&�;5�� �Npossibl�ga� E&,6I.�Q�%�p�`,[aS�Z�!�$� thenIg,W ܏�men5� Expl�A6�V. )�U .�=�u ��2�(_{B: |B| =bJ� 0�rI,J h�_{ NeA')6�)*e�_�!w찡� �A'.F"$�� $A$.A' = {�$B�A%� $ �(B)�Rec �pkz6� �* f�eµ � ��_b� $!�s:�p�8/ 0 = 7vLHa�<|'ap�W"k ni�#$}�| ��&�n�$`kK &�NjwTt"��$�"� $(k�r�"membe�A$#%K^in8  ? Bli�H���\a}e  $jSa$��n!}4#+^�"e�$(4s� 1}$�!9�F�..2�a�)��j,{υ�sun>'s��u� �� us6��$ *�� l�w2�!>ddP &$Pl%!��A�Ѫb� e�jR {b}&bm - b���i3�ls:�See Fig�1"xE:" Feyn��dn�e bullet�bfe�_rc�} gULmE!�*�sSry�1a^um.�fi�fA^Ohe �app6�any� el��%D"XE&W�!]Vb�� r&sam*Xe*WS;�B$ (un6�)/��K MzP��3>^W�-'Q��Xěs�e�A'�2"�,$�e"V* fig:�&W \��deus[Le=0.7]/1.eps.ca�:{BM�1�D)�� u���;��%eF�^���. �- &�;�D!?v�Hs $�s��i�.X� �x&~ bE_{�r_j�h�&n|p B&(7�<1�A��AJ�dWJU�= �S ( p) }{m:��JB� �2�2���3pA1m}) &J�- �1Nڏ =�^{- &6. � b �6_ �l�8 b'��4*? >})]ŵ#O:�0� � [%  �k= �+Q`b(�d �Mm -p_k)nA'(j B'C�fG  D k)�]*�" Z fu� s�&1 }�w�-Z��&�% iota!�D��{ } + j &&��:R F;'2<�def�9;2�=};\�myui=n&�ax�S�m^{�q =���Pi���P� �Ke"� �os�� �-SYs;"߫<w�U$� .8V�!T}��� b} $i� prim��n rpar O��� lefte��B� $qѐp< )E%� �l�� j=0,*P5b��29"2.� &���� Z)) �p �%) *� � �/*� :� bB:|B|� qi�b� U� 6(A,� Nz�&\��FF�s\�J� �zy�"�bN��7� <*�_bP  )J":�*� ��b�. *�:mm"�I�A~ )fs+{A�29� @�s $N$,��/�Nf [iI D�� E�� "� &�  �&� '� : A�e  @!$�obxo&�sa��!}{(N�s )!� �"x�9G~� lo���oa�is�,�/+8'm}eNsebK$%�%�a=�0(R�@Y�i 6((;:�n ��.%�&r&.�7K�-�1N)05C!��(n��A0)�&ies4a&E�:�mak&�l�*+z�U� ��8 To_ ����&�m(��!�.�a�"�&stuff."��be��(DE*,qY�$0�*' m�0�\�2!�v b(\b�`eq3 < +1)-��&x72��?I�c ��%�b� <\b1g p-m) &&��'�8 b(\b+1) -1 -m_1 �\label{E:defellbeta12}. \end{align} In particular $\ell_\*=  {\b1} + 2}$.58other words, $\2�$ is the number of $B$-elements before "Dtime division, and {o,.n4 describe how B= lin Kde ~8$(A\setminus B)� betweenE �-th ~(�+1)2�8 (see Figure 2;? dashed ve!;al �indicat �2� ). We def��,{\it primed}G! |s analogously. Recalling (\ref)�ptoell})�J� � b�� F():�~� 6:� 6�;.F�2�aKFM�%�} A���future�6 will omitsub�ypts on $�GI%� $, $]Q$ ��=( $ wh�tDy are obvious fromhcontext.e�,what follows� adop � �convena� . Wa�@ll use upper case��4ex variables � summC over $se�f�0form $$ ( 0�o \b-1AO, !y \b+1��,b).$$ MoreU,.��mo a i��$way. If $UG$ is a�J ;,�$correspond�Ja!i�m d by6�ynP_JE�D p_J \qquad \mbox{a�$$J \neq \b �$}JP�z =& 2} := p}Y��lower}2�}Us� this=�%��rwrite�m^r]� , ��= (-i)^{��ds�d@\[ d\sigma_{J} \]��PFm92*} \[:8a�4}^b \prod_{J=0e^{-i bJ!� ^2/2N^frac{(i+)^:J}} !} \;,2f wher ��a( impli� aiN�uct is^]�����G=& �( �%W+1 %/)�) _ 5/1 J6..2..2}18;!*n !}.�&\� s� -�j=0; jm$B�j p_j � ��j�j�j%�>  \��ubsec!�{Estima o�Beffve pot�al} T� ,ext result e7�� size�R J@ $�v8)$ obtained aft�+t ta�ouICinternal��- (&� F})).Q_lemma�L� Lfdecay}Let $0\leq b m$� $I%et \{.�b\}$ � $|I |=n 7b+1 9\xi�� (\xi� "S xi_n)a� Sp1, 2\}^n$ be a multi-index. ��s $ &s�� stat� !UL� �$L:bcd}. ��Gwic� ffer%�ble�%�reA(a universal�8stant $M$ such� 1O��.} (Big| D^{\xi fp_I}( B�\ j�G(B� ) H |M%�M�M��4mbda_0)^m} {\<  \>^{3��J� \su�0xi'%�6�} �'�~6� �u�1a� �<1}{\��.���<\grad_{% j}} .!j}}\>.�} Now l�f� &�S}(� 8bb{R}^{3(b+1)}; !bb{C})� E�e6~9P|\! f -��� \sum_��]:^!�F�.�@=I - \> f��; Jhtripnorm2! W � language:��!̙�J� !leq 6U!\!| f\!!p}.Ur�basic�W:�$e now moveaAto�Zve6��f ."pproof}Wc  k:= \bk_u J:= J_{m,}$ (r���%�}�� Jdef1�  {F}� %eLw�6#*�DE���!8( F&(=f� *�&�= e A[ k_1, k_m � �A�t d\fq� 5~K� ]>���a� L&C 6>, m).�)A� Big)B'(For a fixed%�$��J1jK�")ba�q {�����] ��A�\y�=&�stauV&� jk}\]_{jk� JF�� �\|A�\|}R5�0Ee�"�jk} qe}a BF� � ��% N�$ ��a�E�j� m k_j $e AW�TQ �2).`U8f$F 2,B�Q)&MK�U� 68A m|.��P & C^-� \|}0|\!7 >���F�FiF$_| ���q_JE�]�2X.pM�R��A�!� JJ\0� .�� � J2FV E!^Aw\bk\| } 2 � fMJ� >��)��2ve^)=1^Be:  � g &r s due�1�ple��g� on ��ed�qYsH ex})aw��s(ibniz rule Ytriangl� equality,^�%� �Y!Fm!(�xJ=e lU�iY{ �x�ayc \binom}'}�\!as� I��xi-6}�%Bw �&�. l5 ��J}j�not� � \xi$ &�Hcomponentwise order�P!� $B����_anxi'_1} sn)_n  �c f��)�UydefL}) a usA�� b�!^  &)F)�1���B.e�9�A & (M\l"�{m�4�;}���wB�����.�r� -�1��0J� .4 +222)��.9:�O}-xU ^{o\bigg|!4r  m} = J� 6� !!�+.b.�*���\i1[JrHm.HNY4NX.FY�`R7MN7^1:mS.� $k_j�u- at $Un( \ll1$, we��x�.1R��  D�639�J_1�(1��!1: m_12k}=�g2�J_2 Qm_1+1\,:;F, A +1} g1p � mk_m �$j 2�� first douZ���($J_2$ has $�$ a-$ /�$��$(second, etc� ���D$!)\oplus�6.. Expa� �9de��#)� F}) yield6�* ҁ=��-��2�k_m  J�ue{* } 6A&u b}"� &CA>G _1;��{J_1})�o_2:#Again 8degenerate term�W k_1=m�=� =0� iast��as��d)�_1�#.2)6�*}* A sAe�ollary��2*�~" � 6�y��պw:*x  (&9�&#2 �,J�^�%*h6�Fi�.E &���t(2{a�m_2} &"_1{� \< ����6�6�6 ��E.�.�~��%J�E� \varphi^{nLrm{error, 1}}(t)$ } B�Q3E@��,e,A�vK,�6��(ivFexpsn��"#$L\to2 $ li*#}A�res2� Q&s'st�a��is F9* aken�every� 6* anyt*xs. �(��� �*L:0,0} <)04 $t = T\ep^{-1�� %qrho�*p !3rho_0���Lm_0 = m_0(\ep) \gg 1�#n=n  (we:$��( choices la:��m0 ��n�s� $1eK�) m�&�m_0-1$ & $m=mY \geq"� no , $t_1+t_2=t$v$tN,t_��%��b�bE� 9*U%a�^{\kA*(t_2)\psi_0\�^:*c&�& C6Q m \ Big[FG� (-��)�h} 22} }{�!%P! }*� + m!Q (\log tA+ \O(1)6[ p-1}Nq��]&�A�.�}CMt��$k!�1$z��J>k(t) %�%^� C!,0}!d��2mB'�[��1}{n})v1!M0!$. (;)58!~18 +);J] \; J���]� �<ai�y�� By���U lnorec�y��scriptUQ�� e|;AM�-M� (p_0).�=&"� p_{m} �+��a,K}-0,m�Fl:�,.� m})\chi(A" m}�ed(p_m):* We a6��!�B-Y�m��q�a5y� �e� �Ii }�i�� bx m  %�oorname�bao 3w �( ell'�arho^{2m-�&*�p_0�p_b'_b�  _ �}!��p_b,\f'N�1pb) \over�0{'".(.R%9V.t/1K;/^�&0}�_bbb!���Y8I���JX'YFwX'_ ,%g )�%F�� =��+ �7)(Dial)�  Cros�)0!; ,�m"( i�}de�J� 209� as �_:I96lA?,'}>5"!� ]7a�B�|1�!���F)1�=�J�!�a���JN-�.Q6�F�-U=�!�1B2}J� J�\�3B+6-Id.�%���q�\����i�J�B�{b}��JP-�n�5�usdefdirca�6{, i�os�Hdepends[whe�5$���'�$(id�'ty) orj. W�.J,� �' paia"�" " def }) reduc"�rel�s�  ;b� p_j-\pp_j�L$h��\��/&D.� � twoB �right h- sid� "| c�   / tre� e ��U� 2"�c$Schwarz in ol3�S�-e"'}1 = 2} 1� �m}{��$ 2^m$blm� �)}1&u�0}�)}L >\��]{UjB |>� t���D^ � })|^2. *}m1zde2� X' 2,*9:�F�%2^m�)m_�/--B�J�J�4 !/.'�4'_1FX�/tP/2�4] Il/ds'_2�4 .�"m.� b} .���4z 5�&mK(�,�"� "<1�}N�{+"�f>Jr"n E' F'AJM� J�6I7$u�a�, kernel. �$� dex �*n3roduc6*�1I��3��K| e�Q�,Ksemigroup})��E�:9#�� qN\.�a�,&2b6� - B Q9Q��BA)�-�=�B{��BGa�F�6v ��� ��^�^_�>^F�m�BK\m��3G3J*|3� ''�3��.\"-$'�4 ]_{0�^1�:O�Q&�3v{\b�3s�v JaA=-F�@ *? - Vg33J -�!'_J) P_v(48�6O J}} ell_J!)�-!O;)�"* � �split� �m��&��,�0 veni /, assumZ(!3b���7$b=%.E ��e!�� same7B*-� ay&i� al w�= > ;m`7um spac4d1N�!�6W.2� !�/�� &>�>�f{9c�| FN�R: 2X6z> �>�\�,p��.3� ^2A%s�1p_�{J�UB չ^5F:rb0 }�1b8-6��mhB��'[1,i�1}-q9)JW+5c &2}}�)]b?etaC(B�1�2K6eta}^{%S ��j� '_j) &`6-��� b�C^b!�=��!'" >� ��)�F,�| \b2$,�p}8ly, Eper�$6%��08onl=$�]h"P;�! B�|&�,f�~w7EJ9��& ��ə�A~eBbn��u^A�l* 6 �� B��{s'}_1��0�F�#&�F1}N*r!�2s";1}�:c[2 [%� +_a�_bJH${ L2o; � /!R�\o � U7� �%&"Z� "'.� et� J/?�7m�J �JZ�' alsoi�A� u� $1/(�j�1$a��34k@ � s (s�|%<��_j �j}�j�&)� g�!}{(m)�$j+1)!} s^{�$$+%90�OyO �sAu��?T2} t^{�C^�v!N� ��^GF nC^F~!.�a�J�JK,:b*,d#P�)Q�keb�h�H��3)Arcon�F:��r= #�g"gb>��B>eIDC2I* m}{\}5let._1 \rO-^{#JJ .2:.Y#'_1" @"l#}�6� which�&2��WɁO�&>�J��F�}>Y�\�Jd>.cVC�2^C TgH �N�)�q��$�$=m=��2�� )�9�6>:�J?ů ��}{B" !^*s��-��2!�.�A�&J�! T�!F��*�!'!R%!O(:./ A�.� �#"�est1.5D �iX *Wuses $9Qt.[H6�7 prov0De ���>I��<. \medskip IyB main�.���X7�� .�)�(W$?c4=.Gspiric%e "�/rect" Lg�A\cite{EY�i�Gbased�0$\a$-represen0oH�?  (2'&K��BI.�? &�B| /�6o2K.yb�/�� :1 =& -Iwe4 ta_1$� ta_2C�34 \piBC\i Cd\?2 \H �(t_1-\ S )}}{ -� 2/2 + i \u1Fu,2,A�`70/2.� � �. �BE1KO�A,�}{��|EU ��-Zm�-}^�".]2J] �:]6UR*�-$�j�7eta(t�< To shorten our*�Ps"8J�$ =\{1??6� �� [\a_k, p]�2B�&%k6�k�V,� :"green�d{?.f@its absolute valu�Dd5@ d byGK|�,p|�| �p] | . An�Q m5* se�in"k!aD3R&2R"b)same )s,k$ regulariz�sZA%@'�A'RB,8K�'6�' �8!.!�NUA��6��is`A" liciEB�Punted%��. How?*,�-%�$s $[\alpha�$, $|\ |$ alway�T�+d in ax �M�N>$ ���Qo�6vaeM $ (a� 2, 1' 2'� !�0 3$ ��&MT -5/i%�$+6<( it rنr�)> ��!�J�!�I�@H#B�>&8 &8 �%\�!{(H#&� X%N��E_ �.�% �%�.U!=\��d\b%�� 'A�B��� ( $ - ')� �!�$��ͬ\b�0A �uQr� 0�R$'r'}R" 6 g 2,bV4a72� "d�r#LF\�!m_1,P_J&f }{�\1,�]�r+�JL o =m ^-0B]Fi{[��2 o :pf���'1F[ �]��!�\P�)��(6N� �4 /�'_-f�!'U 1F�2 � .�F�!�� b�e�U��e�4ed8$ ing}. ~5$m:=� )�g ' � _2')��2 �!ee�_{n,m�2GI)j=n+1�" %8a'j) &&��0$n�  m$NQD$defBvector2� �#i1pr� �LC+3.5��*d byţoiN���$ &�$.� �� each almo�4in���y=l��a*\   A technical �2L:B- (to�M� n&~0S�on .sec:estK;f" �4yZ�ol ��_j}E7 %����0�� ) �����!P4N�L*5�*�L &a;�?-� "�L�:a%6.PiP{6@ �<S:k_i);4NҋJ�8�getde�OJ4k_TJre �\$0e $b �$bO2sen at�&�e� &�Os hol E�rX+  :�Yg-73&�'strucWo quit�61S�d. "\ � ka� I�s 2.4E�2.8:� w [�\J�ad F-ar�>bin� M� non- � ones�4&} : $$�2�-�= =:��7�Lp�J- l_j&�F)) , 0�LuL �ss $l_j/M"�VweI c�E:�  $hb !Vbe�+ �[),�~V2 / Id}$e��:%Yt�T*W0 $0<\kappa \pma� _�\ 2L�X!�*�)�)4Yaat le�93s;H�!!�a<� choos�!�� 2� $\;k_2)~}�$\!� rN�)%�>!}3 v'ALet2E.�a(j) ��b�_"*�]>�o� ext�� /Tj <\b�X&5>�6;\b�j�"b$�{� �.�"*}!�!Q a'(j����4� $\b'�Apl�"� )=D�>�(%q!p)^c$ s�Oa�*$�T\ )�d*2 14 \E\ً2\}W IaO�wseMJ$\{T�� UD!&���OQ3� }s=)!�Similarl|4eda'(\k)}.�$� , {"y � \&C>@LB d(SQb5RZ�� & Br ��1� 60}|�3� |^2JQ� 0� �E ( p'�>C"L \2s | 'j� FC �� 1���1 |2w fDu �1}D2FDfC\'':�%�P'_�� fH\� >�'�FHb� ^ai!�6� F�EP��k' 4 b���C6� � � h4X8����/ \>^4["d \ starm'25F�A��kB= \N�? _�!��=�Va�� �`� ul "� _ ells�; mak� �tJU.�� \stackrelaց# a_2}�dp?6i% }} &$ [N� Ex\<6>� -��EVDqE - factorE�ab5S!euc�2W� n<:�.Yd� �. ]T!U�e�,)� k'_2!� )�6�\> A�0�) :��])E 2G )�Ap0 if� ?��0��rA "@ K< HBA.6 � whilW�[2Lno1NM�()�jd)��?�t_2$. A�^*VAm2,fRX�k�� >_�*)8C d& -�-HM.�mc�6��le�?t# +u8F(E)Q+5a��'�;m� j=1;n`k}y(FV� (E&#$6�xJ�I���l \>�4- �*�OJp6<2A��<�4NI298M{\< w| �M^:A {'3 A|N� F9�0� ae\k/� �M o� � )}{ | � �\k|�Be|s 1),��U( � 2}.� �!&� )\>&! 2)\>���;E\k�CB�� {� �h4�?3:u,V)^csZ!�p_{k_3F�S6�wimeNsM Em \�__1If� w��� �\�+�{u80�+\�c.t�p_�[ }_{=:(ia�F�.�^p��j=0�!j%:�[e�>��J� � i=4}6� A)�*K  7� &N 6� B�`BA} ��.z *}By�&���M�AA�X~ Nm_2�C�E2 can &� _3&������E�%-)^c�Ea|�Fappear�!ei� $(ig(ii�dr bothj��6�����tto�<�� �] V�af��(i) ("1�F �)�Nͱu�- by6����v�4i�F$��Ɓ 2G ��.}�u���FY.���i_1I� �rJi_1k�.1E>opEE6E|DQ6� 2]da=he� ES ��*� NextP V�U )/�R � $ excep�lr� $� us�oving�ir*�=���"��aWA+en �b���2���Ij�sH��'�p�o\,��rGI�d�� 8�9[ N .6�.�A�:��)�"��4eK>aB��}2 " �� � � w:�� d.)V�1,�'.f �[%G��{\b�Q�] A (ii'�X]�)\@M tripleintNGB� )$�Yi�$ $�36 \> /�� $ i�"at� was=#�B"�8����y� Lq�nm�o��"�$% 2���$ ��������k:p�Vq�,yBf ^aI�E�U Y����g = g( | " 1}|)wppneg�f���-��"�5�r=|p|$b�a�I�eeTE��<5 4} &�3�n��d } 6� 6� Ep� 2) i�| \; ��%(�� 9app�j|  �ZM�'H*Q"R}_0fb � drA�r }�r\>l)1O M� ), ryFg(r)}{| �6�} �.i3�P2&o6�* abus�hh=d�*�wro��A� , |p| | =�� , p|���P�g�sparama��%Z4el�pV[E=1�$ �y�aS>c)�`f:_6bq� exac('� � M of Pro"E6 P"�eTo2)%E)��"u_4s_1-1$i�GE:"�)�{�X|m�il�->e� 6>�)�&qFen%..G_'%&=F|!�o;$��aM�l � �� � .b �g_\k_4}=di 6 lost, but]'i� stor�c�ad�al�C�yp� 4 �4>} Our!Tic �k_4�Qllb �r�+f enough �( {(M � necessrV] : ��2�Et"  "��O �ݺF ���C o6v/ �.�� 6@ 2� ,M Mb +1�Fc��� ��‰�2�Eh�F<�$ݤ ��r ;1}|�9٘��FQ2�B��)��m1| |J�=� y>�.1��%�" � ��" 6�4 �'B&@ #�[:)aNtha} �A�/%�u� majorize��[�;k_4O-�. Z�=� ) t�rto���>$$5�S �} 4%m)[B�I�1, [ .�.$A�2_ %|\ n� C&�T2�.W'n/�@e $YQ�$t� � coord�#es�-�7�t�/�&�O�is�-ed�K2 O3.�*!"�!C�!��k_5Ş2��!�u �2�A� >^{-��1$%��e �ai���IMՖA�d� %97!�D d".��, �b��b65&�$p�_.;�� �46��is �Lled ��]int&��.lV(st�s\p�QblyS%:��t!� Y$qQ"q#��\�2�2)^JK 6y"I inta�ra-o �H !e�qiAt�/ p#Aā�M�26;|$�;hj�.�oi�a�6'��mr"\l�W?&�5x ng ��� `$EvA�le�A 6o2> 2}|$� yX%log$ ���%�e!��5� a>ES�0I�;�O~O $\e&a�e$Finally f+F eA�^:����h�|�< bR�abC1S�m$$ Coll�*ng!&se }m!Ai�!$of!!M.�\kI ��a 7-� s easier�� hand�hA6%Ha�3ova�C.{Y� �2�;{2b"^"��tF 5m.mZ1YB���i&\\N'$ ,���&&�y of�) � L�P.�e�,!2be%N�$A�d*%��^6r ��^2}}_k$�^��_ ampugz"�4 Ao]e6-m+ebrJ$ sete���]�*^JA[ �!f���._ZR}):f"�Z�!U1}�v, �>@D$ �ee$2 <*�AZ'"�]e��^t_d�] - �] :�^� $k\�]�E"�� �B�e�h!s E�t&Z ([t�8,=<(@*_2)F& Z.R~G& :"#[a-m t� t"xB1�<�$ �! mi![� 0�h��lat8b.�="�� ly ecn �a pY��́$����1E2D# �E`W�# e/�*$�� i9Q. As a*�2%{�e "-s���0�t!Z�aid�� N�>b}> requi*�SA6��". �W�0um"�] Usu R amQ:S V�$m_j > 0� j=1,���>�preƇE���}M voidP&/.=1%J*,H � ��W2�h . A��ingV-e}no;!���?>��2}(��$  Z�?� J 05� � .<0T; r�\ ��1 $ t�duc!<�=�AUo �6����� . O�sp!G}��>/ u%Ge�3way� 66�;Tz>�� �y�2%�d Z ufull}) ��bl�n&E+B8)&2Fh c~�_&Gd E:crude �yͩ�{�zI^F4!!e�E��L = t/n�8r = (k-1)�=�#M �m:h?��&Fi m_0^�B1�Rb�j"?�!�^� 3� QBss�f3:P#m*+�)*= A;third ����v2  �E0wE@umb, a�7uin� coll$�� @=argue�� �sLe ���2�T�5"K"J�j_QAg U M�}@, ,^2�en(�y ey "�Vs�jas�O!q��!K� x�i���_�wf�� (�:�1� ��%�b�"O(n^{-2}/��is smal7^+/# o%k� �defE�c��"�m2g15 t be>MOK[ sufficienu-2�%Kr�-rc�o�inu&$e Duhamel S9an�q ide����F� keep ,O untilF& �+ anٗgeE��U�oE$get a new ce�A0� � wS.�X X]7!~�m/d� !p�9aebq%pR�1!�  by ���e=sly larׂ:vanish qZl !��bof���92!shouldA^ECer{� a�imj��guarante$ � � �Ia � �6tuii ;�y�� r�.s, ob�2les&%6e��in �Dl� vic..� -�� D9!as6�s<�� hi�y!:� s��probabilh��con�%�s aq higha�rzs(=�w�:� C � � prox�py��L '[/ w%�97travelNGy fa%M-HdA�d aitclass�� �aivto �� ���ec!�%GJ�Z�`�r 2.V di� ultyD p�Ks\ elf �awVieXthings6�i�;��=�dwo=`�g $k $ di% a ��E�h�#E]u$ve�dI]!A(9�%��0M]aVsuc�(a� r mo� 7-)i�gh��*�aFB-goa�c-�S>4�.�mie�e;�2�!� $rho� O�q5� ��B�A ensat� loss�!4��"�!�B�E����sum up��f-1\ Born sea� yI��. gI ��BK?=(2t�fed��is manne.�rigG)�!h "��is%�a7 $(31 "!>a_m�nd�o"@NAM�#EYj\�Z�$�\f�YjP Q�.P2×�simmediatcbe:�A=�*e��.���� ;�> �$ec���A� �Zta�!q�p�E�>6in��v� N�!u�8a`t��hbAm 3_�,2w�PD������tq?avma�U� � .V.��2S,�R.�� ! 6�occurra�is>ɩ1��a0%ctwV.!@!>�<-�(they��nNL �e�����AreadylmUQJ�>cs� B��8�ώ"נ�fe[stopp�rC���5D�  �a5�Av�7Q�%8socA�!%���l�C!^��Mk�+Giv�LA$!�$� $m$,�m_A�!mo8 be 2 )�er+/1=mAL%c $n_1�2$ �frA}( np A��53(�Z ,\�,�?  1�p_{n_1V-.SE�� b)}��of� >CA-�Cy= ʚion�A pr1�1��E.�is-d Zn&��t;�T~}_{[n_1]�2v;A����t .�) &�!aj$( d\fu_{0 ,n�B�5��rn_!���r, R Q�E Q=�/*27$ � F{u�A}(A'\�A w fx)(r_m)�Q^"3!�recB�Q!�ڤA� A�ke� n.�� 'ofI6=�s.6fAQ�]0��]p��d �ef� * .w [K1) K��:`�5"ڢ �q�D%�)gZfa}�L.=t r/��;b!.b�3�� !FF�pq.O e}-�fig:2ob*�^9�68�5Z9�Re*�f{ ��^, zF*R� 3�� ��U�p� F .M��5�;p#!_s 2Yr��]! �q 0�oyB F�vB16{)-��2M�E! plus :\' ��=�+p �6n.��t_{1,�O�e5*):M�����\hat{A}�� |=m+@% �N�6c.b�.�- � &j�$ yEia_0cZJ�A� _ repem�^ es.6�& s"��, $>D� � � chronolog� "c �" typdR� �r#r�  "� #l�qk�2!e ݉�]i���%���.� !Ia��q��}e�U�m�e�U�u>� �@V�r N�F�1� A;J�~�\,6� an6HX^]!/��9&E�F 2F M�f'2/ }_{ g>'5�6� *�-�6�cNf�2"J *R 2{�3}b�:R W 3�* ���^w�*f &�o��iE� �hv��gFP�F�J�� M�_3� uCB�Y����V2�F�� ^�ingpong��.,5T $f }9�_{*1�NF�m+_1.s U^P 1�.^8�1Ok_3=1}133U"�}�[Z?"� J ����CY�,� R�>� ���Won31� surew��e� .[ is unre�� �* e�&a/ta əFNgis~W>;>T��>���o@=�n=�&+ & *��, �56~� 3�^�9���q�2',&'-s)H}7t�&���=UU6; IHfa�),{  rap�r ?me�a�%��i�}�5�i�. � exa�2,�s>�/i$Y� k*do� �@$�d� J) �*>��%>�� been�;ed f4 �^ a4]�j ���V�%#-below)�A � !4�[ex�^"W1?w�!@��J�Ae �} Y �Zi�&���J��� �B2 Dr8g�5eV6 a�U� ZAag��l���!yon�?23�!��>�^eQ�b� �J�9L�_{R��w/�um_{2_�? mR֎.�A�A^2&q BYg)�� 2�V�f�U%�?`-!��D/aa-' < =p�-l#-5�^.�.���'(a�=qQ (� =1$).� a�sh& �� .{a5~o;g�$DC< 2$ or\�3 �3�Z�6 �ZJG,75"�-G U#�C!U ev�j* a�9Y �F 2$). �!|�wapD$A�� :~&e*y�!� erm.d4�pC (i  aF nd�0 &e 6&W&i��ja2� at a( <3[�equ �u WI��c  c�/� ����y �;)a�(P�d6� �o^For1(�� !���2tb�2�+rm>�!e�n_1` �M��a��� }e�61�a�0}B���Z,R� +2� �L�C���Bx�q��j� ��� :D���&E�+�7*�} Fro�/&5+� ,%e�QD�!� j# vergei��b�$. %�*:�,3x7"�s."p,L �$}� �kn$�a+fPbE�~jV6 3>W6CP64�-&6&Noq6�7� ^{3}Ac:�JY6G6:6) �L�-*�}eN-�*�}~+1��F!' �X%O~1 N��b�"E#�0&+S�J�/2"j�n�/R��-�� e>u��#�/u qQi�a�.� m�1bEXnZ�B\J�29R�6xJ:`%oB��:2%^)]:OFCNh t *ղ"s�-ul��U�E� An�>�te�i E�g  5E� >�(> :~�0. Ht%w�uɎa|*r6la%g��Sjh�4�;L�"E "�d�# +&�T2�27 �#��"f� >M2���Vr=�(&�U)^!�+",<��X:��rh.x��.�;;˜�!F3m�2]��.� )Px�� �'by&1:*7at~%(E�v*�� � OI squ�}JI d�w5. "=1�'k &� �&sV#�%rval $[t�B$t_2+t_1)$,-1��?�+an extra�*��5Ihh E�2 $1/n�\ljj�/2�2s carr� ]V�4:��U�-1}��WQK�J��Z�>��:K���U�s���JA�&Z�vaA¡�?M�B�E�> �9E� ^�>]yj-a2�165 ]�BM[Cs4e g�!anin� ^B3�;F+*.M5�Qaco21�ion��:� L:nested2d0A��Y�*��fV�@>cIBig�2� ZYF9�`.��  2&�'DA.�9h.�gI:6;m.�@3� 2m-36�@ � j~ M�+5�we 15��5��:\!s�anZ��=�a��knoj�ve to�0qish��>6>E 2�Y I �* *����M��&�"Y`>>�*��1�_{ Fo.0�.�FF�$ !�V!�A: dH(à m2 Še��r,�&"�*eF1]p��n�e1�ed.Iw&�G�2�,@/" /hav> woN��, Each.IIFy>����8-�@ util�Sa &�n�qr��f ?�!discuG��b�m%LFG6_ss� }� E�`19�2�{��/J�/"�5q����u��R*\$ (2-m_1)_+o� FQM4��?>������)2V�9J esCx �� }�> @$�>��  [{\bf�WoUG2�<Q�w}]<�E�=QBr#epiA$t.��7) �i�E.�<��7� \Psi�-!���m6�esAk�n}�m(n-k)�H}}f�Q�.�&[��O�(H$,�N��JC��)f m"v�{�Ar�n k���U�50`m�kY�%>\,1� bB>+�@2@F?�~.����-�E�sQ�0,0� ƋL:0�L� �M�_6:*� ��tB���*֨�SV��[�> /2}+FJuL�/JL�!��d&+"�$n^{5/2}\ep*� �BY+M�:�;A#m_��ep}#Q &U�):J� �B$I < easy� ��f sO��\�5to2�f! W&%!$]��� |}{1�N og |�]"am0f}2NnN�� T1H0�e�E"#�}�}>F?$�9T/ѭi�to q{�S���X�r �"��C� s \�{Pr�� >.�sM�gB>o'�:f!�?m]!� ?eed/�� Eg�/gu�6� �h8Q g. A/� \q�� 8 in detail�O�= Ta�n"k\modifT8�/If�Whe � thre: .�CsR9al/?��C,r5 *�RE�' .� 2�E5�%5B�� 6 \gi-!�!�#t�cocRi ex�?�!և J]DE�v5�&��r~ Vl3�A:�.� no\t�cNl*1 l2�3�1J�' �o��= �&�% �>�'_>;zf�mV��S B: |B|=b}�I�zm}�g)B\ �\in6}S} �+Bh 9(A, A'���"�(��+p �nRnjN_/\J�!� a{FZ�u!B 2�;A'&~ ��f}\;:VwCA]um�& (A,A]�pt�e�A��E-ed�s $%*2< ų6�-e��l%�� $A� $cap A'= B7KB\prec�- �~(B)�mec*�o�r%�aa�^>� F4��� \|&�(�65q"�t6<;�%yA�&6�1���:�+\bE_{B�;}Ӿ E_{A"ޫ ,r-M�E�.-rN���+r�m':n2J�WiWiU}y��h!�F�b�F�����"�*{q� *� :E_�z,JV�>& %�B�B^{�f/1}�@2}�S��eqa>ɸN�9� ����e�.�1�!��BB>zV��7=��=e� m}H�{�2B� V\nX4e1�5�����Ŕ ��p � 122 �v$�m1'� N-m}��n m! (m-1)2)}{2} $)\"> �/H| (I�D&/*1b��+ $(\g�Xg_�+ L� w(_1 = b!*H�,22ʯ�C mean]'H�lada�(Hall�EN�$$\gamma_1$*�� ���/B ,:JDJ� > ��z�s] �9{�)�( TaX�.X P ey2� \ � D)�+6s �{q��w�{^>bI' \���5�UIiw��)&2< A�.b! ��J�WzE"� ; B, 2, 1��)� I�� 2�� 6!&QM�I. :���!=��2����r"Y�&|�W 7 :E*#;u'!c�:Ffd @b�7,NX\ے(6+4\2]":4b LV�;t^M�(r�Y*B e4\r9N�&ú,3"D�;�8b�9�}� .}B^%�kA.L�;{!`b}'>e� | Ͱ��MKeM��2elm-3��"�%f�� � _�-�&��1�=�~Ax [ -\��b{%^-1%%-j} (u��\uu��-(r_0-!�0) +(r_{����r �tN7QG��f{A-1�[ Ij�sr�d0a 0}) *}""�{M�VN6 �RV,Y �\W�gxE�)�r!)J�:=)�_1:�A�eli�, r_0,�0 � N�-Ge�_{v�(�,D_b!���5˭,"�#�IZ"�&�&e -os�6�5 se��]"�2�G�,� �1P�T�/?Qa)-ta1kh� � $2�$e1�)8$, h:*kb-1Śl��= �%&$.* >&�^�v$$D57+X�(,�($�q��sD2r�s�m'de�'��b^b�"��2 � �Vey�be omiDž��6. A�4 show�@e Feynman diagram^6* A�, �Jz\39�4 �2��1��!?piđ.?ate�0Sc"�0<t.�_C!�m�n;/p2c��. filll&� ($r$-my�a�ss>1y�?6;�"�8IM�fig���v\^�I48�I3Z�I>Se�7� Tj~K� �  qwd JVC� ���natXon��eM��� !�&,` ��n �{�,@ QAE2,�) $94$, $�&�$�8$1dsss:2,1�*n1}[��Q�*zڶ�Ly#g�E:K��]$�DAc-�a ded �Ls.\foot*d{e6A� m_2=�iw�i��b E �w� K!�&�b�"J%M��t@s)� Z�(�u�5as|�9�bs ime.� &g59*3� 68��0�^2ӑ�&� 2,1>kJ�=&6� aCt `�xH&ܜ��"��TZ� J����ݾX��ſZ X .� �4bNc2Dac [SV p_0]&v�K[�r1�n0]L "�\&��}B�zJKa\b1!�d�_1,R_J2�?�1, R_&� +1Nʦ L�V�R'X��}^ȬJa*�%]%+�R�:�\�� yo_2�2�![2��2R�}��c'_:���\aS�� 9�1� J��<` V�=*!U�E|!"aR-0�qI��[x H�!|8>� �aV[iV2�aO.����c c F� �6 �t% �Q� ] � � N�L>(=%} > , 0)NQ@ 1$ /i)1}A6_1,u_j].͏ =�EXA� e�!�]F���.&1 �7A� Notie�[b&��defʗ}�&���� ta3�6> ^,�0W�*)�Q�N�<$���C[a��E?�"� 5� � <M mab.��to \o�2gra� we j$���\|#�LC� 2�u�w���6:-y�j� ���>���.gs>�/r��"�e�Y�Ja�.�� � ?�,q�2��\f!F�j� �-���'J�u#|�|�yF�0"p��Xi�a�{ M ��:r� �u_j � �u'_j|M�֑��=�w.��w'�$��y*�:Y� �J�8{!��$�|a��"E��( p*&��� Np��J  P&�,�}p_0R\7� !1u_ F��[1& F%�6ku��!� pKb�Er E -r_6Ei�5 x�r��4J��%'1dF�6�:' �-E�� G -r'1^�F*'ƕ-, �<4\label{E:pairr�ecsmalln1} \end{align} where the last two lines wTobtained by estimating/H potential terms us8Lemma \ref{L:Bl} and (PE:getdecay}). As inP crosB h e of6N0,0},,�indices $k_i, k'_i$, for $1\leq i @5$ will be chosenmfollow� o0s. Let $k_1=S1 = 0$,42=k'_2 = \g_2$�$k_3 (\b$, !E�other $k$-values are arbitrary. We begin!R)21inftyno-e@summingells}) to9% \bO1� �&\prod_{J=0}^{\b1} \frac{1}{|\a_1, R_J|^{\ell_J } : |\a'('_.)} [ \b2}^b 2[2�[(B[!�0 t^{2m-2b} ,�\label{E)(ellN�4we also includI� factor $ � \<\a_2\>  ' ,}{\^4r }$ A�apply5�%�1�$twice if $%I{! >0$. EO \siga$in \{0,1\}A�th neqAA. Not�atE�anz$ropriatelyQ� $v$,�have $$ \Delta_1(\fu_{0,n_1-2}, \fu'_ r_0,�0, r_{A�} )A�dK<(u_0 - u'_0 \pm 4{ �(} + v) \; .{We us�e bound:A R� \sup_{v, I}E\} \int&Q@dwdv dr'_ q{ \FZ� }{u6� | \,F�|�n,2]1m�Du_0| } \notag \\K&e(,C (\log t)^2V` !` �dj �%U )/F��3aa�\> ��.|�J 7�j2d0pm v| + \eta}Fl �\\B�3Ax, ��;eR�$�A��$ee$\ba�0�� 6)(2(=e�Iɯsecond�,a�a0 Proposition�P�,} to perform��$A�v  ('$ integral�� This a���[>Ѫ?remain��6�1��u_{6 $Bpt�n. U��t��!�mak |�Z}Y!A1,pA��8j=2œ-�EaA* * r'_j| J��j=\b+1;!� 1}^{:EaZ�XFa�e(U1��casesFkt_1��Xb-3} &\text{$1<\b :2:wise ,}J�� � .� �}th�E ver4 variables $\f��2,b�[4hich gets rid A�@(trivial) pairingx $�;2��We now�s2�Y%yhandlIMyE�in $p_I� $r_j� all $j%�,\b, b$. The ]�QM(s depend ona�� I�Yb!�1��6�$alphaint})a get2�*9��~�ةq\b}.�� dE� \>�)'� B; H|N�:���)�:�, ,=�*}e�a�ue�Oy�taoo�}y� f�e�$��R $��\%E�Hleave�HbD �mo o.�f!�r_ eAX>\ �^ !� WA�e>, 9����=�as�� did �In�^c���� �7 get A9�\:2�$mathcal{W}�4X}(t_1,t_2; 2,1, b,\bellU b})e�<& (M\lambda_0)^�]+mS \varrho ( t_1))� b�$"� ${ b+ 2 n_1F$$+\O(1)} . � West6 e��@ is sufficient w!�$ 2��b $8$ since $= e� aLpower!�$log. Howe�fO n_1>8)pe needm�roducI]`two-obstacle Born series 5/assureAXat6u$� d$ does not grow too much. ��isI�edA�!� nextE. \subec��${Term (I), $(\g_1,  (2,1)��t4 !> 8$}-w$sss:2,1bigK.�expre�!=first�o reliinU��rec^ I}) as2�.�� _1 z� \ldots�F�int d\nu�  e^{i  ,[ -\Sigma_{j,- (-1I�$-j} (u_j -| j)FZ-(r_0-�z,0) +(r_{1} - {1}) ]E��|*}Def� b�scriptBe�,�}(�Q ,rf:=&F� ��a� � B ; p_0,u_0)F!� 'u&1)%)zu_0}}{~,-u_0^2/2 + i� _1F�2L uGu_2N- O1 Oi_1:Q � 2 times \c!� ~�-�)-$\exp{\big[79�2}I "8 %]} �� I�+� J�m%E:defR2�a�brackei���l.e}}) can�mOed as6".Ad2�*�\, q@B?m0 JFr AIE)� 1}{[A,u_j] \� line:e1]}}2�qquadM�;E�6�y 0) O-'_.� � 0)F�4!�=&mA�\,A�E�[.�a�1e�1)]N� >�}(�aV`6�60�p} ( iÉ+}.2 By 2DRest}�����kb,jr��(rr_1}\Big| 2�&����.�R} �9� I�(>��K.�*}-,a�light��~ &�, � > ; �$technique ��ena�a��  $Fkto plez �. Here%� no longer9�va*���e;} $ n���\� �x�1$ � �hem. O place.:Y) � sim"6� *� .��# conM�� {\� }men� t we6U � 5�i*3 toi3 eYr �1��H25���� X h sE�